Properties

Label 798.2.j.l.457.2
Level $798$
Weight $2$
Character 798.457
Analytic conductor $6.372$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 457.2
Root \(2.33086i\) of defining polynomial
Character \(\chi\) \(=\) 798.457
Dual form 798.2.j.l.571.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.05903 + 1.83430i) q^{5} +1.00000 q^{6} +(-1.11699 - 2.39840i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.05903 + 1.83430i) q^{5} +1.00000 q^{6} +(-1.11699 - 2.39840i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.05903 + 1.83430i) q^{10} +(-1.67602 - 2.90295i) q^{11} +(0.500000 - 0.866025i) q^{12} -4.23612 q^{13} +(-2.63557 - 0.231865i) q^{14} -2.11806 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.47814 - 6.02432i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-0.500000 + 0.866025i) q^{19} +2.11806 q^{20} +(1.51859 - 2.16654i) q^{21} -3.35203 q^{22} +(3.59035 - 6.21867i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(0.256906 + 0.444974i) q^{25} +(-2.11806 + 3.66859i) q^{26} -1.00000 q^{27} +(-1.51859 + 2.16654i) q^{28} +7.29877 q^{29} +(-1.05903 + 1.83430i) q^{30} +(-2.27442 - 3.93940i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.67602 - 2.90295i) q^{33} -6.95628 q^{34} +(5.58231 + 0.491104i) q^{35} +1.00000 q^{36} +(0.126109 - 0.218427i) q^{37} +(0.500000 + 0.866025i) q^{38} +(-2.11806 - 3.66859i) q^{39} +(1.05903 - 1.83430i) q^{40} -10.3359 q^{41} +(-1.11699 - 2.39840i) q^{42} +3.17133 q^{43} +(-1.67602 + 2.90295i) q^{44} +(-1.05903 - 1.83430i) q^{45} +(-3.59035 - 6.21867i) q^{46} +(-3.57762 + 6.19662i) q^{47} -1.00000 q^{48} +(-4.50469 + 5.35796i) q^{49} +0.513812 q^{50} +(3.47814 - 6.02432i) q^{51} +(2.11806 + 3.66859i) q^{52} +(-0.878666 - 1.52189i) q^{53} +(-0.500000 + 0.866025i) q^{54} +7.09982 q^{55} +(1.11699 + 2.39840i) q^{56} -1.00000 q^{57} +(3.64938 - 6.32092i) q^{58} +(-6.52327 - 11.2986i) q^{59} +(1.05903 + 1.83430i) q^{60} +(-3.45956 + 5.99213i) q^{61} -4.54883 q^{62} +(2.63557 + 0.231865i) q^{63} +1.00000 q^{64} +(4.48619 - 7.77031i) q^{65} +(-1.67602 - 2.90295i) q^{66} +(2.15308 + 3.72925i) q^{67} +(-3.47814 + 6.02432i) q^{68} +7.18070 q^{69} +(3.21646 - 4.58887i) q^{70} -10.4518 q^{71} +(0.500000 - 0.866025i) q^{72} +(6.38335 + 11.0563i) q^{73} +(-0.126109 - 0.218427i) q^{74} +(-0.256906 + 0.444974i) q^{75} +1.00000 q^{76} +(-5.09035 + 7.26231i) q^{77} -4.23612 q^{78} +(-1.13557 + 1.96687i) q^{79} +(-1.05903 - 1.83430i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-5.16797 + 8.95119i) q^{82} +16.5699 q^{83} +(-2.63557 - 0.231865i) q^{84} +14.7338 q^{85} +(1.58566 - 2.74645i) q^{86} +(3.64938 + 6.32092i) q^{87} +(1.67602 + 2.90295i) q^{88} +(-1.89683 + 3.28540i) q^{89} -2.11806 q^{90} +(4.73169 + 10.1599i) q^{91} -7.18070 q^{92} +(2.27442 - 3.93940i) q^{93} +(3.57762 + 6.19662i) q^{94} +(-1.05903 - 1.83430i) q^{95} +(-0.500000 + 0.866025i) q^{96} -6.18070 q^{97} +(2.38779 + 6.58016i) q^{98} +3.35203 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
\(5\) −1.05903 + 1.83430i −0.473613 + 0.820322i −0.999544 0.0302055i \(-0.990384\pi\)
0.525931 + 0.850528i \(0.323717\pi\)
\(6\) 1.00000 0.408248
\(7\) −1.11699 2.39840i −0.422181 0.906512i
\(8\) −1.00000 −0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 1.05903 + 1.83430i 0.334895 + 0.580055i
\(11\) −1.67602 2.90295i −0.505338 0.875271i −0.999981 0.00617477i \(-0.998034\pi\)
0.494643 0.869096i \(-0.335299\pi\)
\(12\) 0.500000 0.866025i 0.144338 0.250000i
\(13\) −4.23612 −1.17489 −0.587445 0.809264i \(-0.699866\pi\)
−0.587445 + 0.809264i \(0.699866\pi\)
\(14\) −2.63557 0.231865i −0.704386 0.0619684i
\(15\) −2.11806 −0.546881
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −3.47814 6.02432i −0.843573 1.46111i −0.886854 0.462049i \(-0.847114\pi\)
0.0432811 0.999063i \(-0.486219\pi\)
\(18\) 0.500000 + 0.866025i 0.117851 + 0.204124i
\(19\) −0.500000 + 0.866025i −0.114708 + 0.198680i
\(20\) 2.11806 0.473613
\(21\) 1.51859 2.16654i 0.331383 0.472778i
\(22\) −3.35203 −0.714656
\(23\) 3.59035 6.21867i 0.748640 1.29668i −0.199834 0.979830i \(-0.564040\pi\)
0.948475 0.316853i \(-0.102626\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) 0.256906 + 0.444974i 0.0513812 + 0.0889948i
\(26\) −2.11806 + 3.66859i −0.415386 + 0.719470i
\(27\) −1.00000 −0.192450
\(28\) −1.51859 + 2.16654i −0.286986 + 0.409438i
\(29\) 7.29877 1.35535 0.677673 0.735363i \(-0.262988\pi\)
0.677673 + 0.735363i \(0.262988\pi\)
\(30\) −1.05903 + 1.83430i −0.193352 + 0.334895i
\(31\) −2.27442 3.93940i −0.408497 0.707538i 0.586225 0.810149i \(-0.300614\pi\)
−0.994722 + 0.102611i \(0.967280\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 1.67602 2.90295i 0.291757 0.505338i
\(34\) −6.95628 −1.19299
\(35\) 5.58231 + 0.491104i 0.943582 + 0.0830117i
\(36\) 1.00000 0.166667
\(37\) 0.126109 0.218427i 0.0207322 0.0359092i −0.855473 0.517847i \(-0.826734\pi\)
0.876205 + 0.481938i \(0.160067\pi\)
\(38\) 0.500000 + 0.866025i 0.0811107 + 0.140488i
\(39\) −2.11806 3.66859i −0.339161 0.587445i
\(40\) 1.05903 1.83430i 0.167448 0.290028i
\(41\) −10.3359 −1.61420 −0.807101 0.590413i \(-0.798965\pi\)
−0.807101 + 0.590413i \(0.798965\pi\)
\(42\) −1.11699 2.39840i −0.172355 0.370082i
\(43\) 3.17133 0.483623 0.241812 0.970323i \(-0.422258\pi\)
0.241812 + 0.970323i \(0.422258\pi\)
\(44\) −1.67602 + 2.90295i −0.252669 + 0.437636i
\(45\) −1.05903 1.83430i −0.157871 0.273441i
\(46\) −3.59035 6.21867i −0.529369 0.916893i
\(47\) −3.57762 + 6.19662i −0.521849 + 0.903869i 0.477828 + 0.878454i \(0.341424\pi\)
−0.999677 + 0.0254158i \(0.991909\pi\)
\(48\) −1.00000 −0.144338
\(49\) −4.50469 + 5.35796i −0.643527 + 0.765424i
\(50\) 0.513812 0.0726639
\(51\) 3.47814 6.02432i 0.487037 0.843573i
\(52\) 2.11806 + 3.66859i 0.293722 + 0.508742i
\(53\) −0.878666 1.52189i −0.120694 0.209048i 0.799348 0.600869i \(-0.205179\pi\)
−0.920042 + 0.391821i \(0.871845\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) 7.09982 0.957339
\(56\) 1.11699 + 2.39840i 0.149263 + 0.320500i
\(57\) −1.00000 −0.132453
\(58\) 3.64938 6.32092i 0.479188 0.829977i
\(59\) −6.52327 11.2986i −0.849258 1.47096i −0.881871 0.471490i \(-0.843716\pi\)
0.0326134 0.999468i \(-0.489617\pi\)
\(60\) 1.05903 + 1.83430i 0.136720 + 0.236807i
\(61\) −3.45956 + 5.99213i −0.442951 + 0.767213i −0.997907 0.0646665i \(-0.979402\pi\)
0.554956 + 0.831880i \(0.312735\pi\)
\(62\) −4.54883 −0.577702
\(63\) 2.63557 + 0.231865i 0.332051 + 0.0292122i
\(64\) 1.00000 0.125000
\(65\) 4.48619 7.77031i 0.556443 0.963788i
\(66\) −1.67602 2.90295i −0.206303 0.357328i
\(67\) 2.15308 + 3.72925i 0.263041 + 0.455600i 0.967048 0.254592i \(-0.0819413\pi\)
−0.704008 + 0.710192i \(0.748608\pi\)
\(68\) −3.47814 + 6.02432i −0.421787 + 0.730556i
\(69\) 7.18070 0.864455
\(70\) 3.21646 4.58887i 0.384441 0.548474i
\(71\) −10.4518 −1.24041 −0.620203 0.784441i \(-0.712950\pi\)
−0.620203 + 0.784441i \(0.712950\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) 6.38335 + 11.0563i 0.747115 + 1.29404i 0.949200 + 0.314673i \(0.101895\pi\)
−0.202085 + 0.979368i \(0.564772\pi\)
\(74\) −0.126109 0.218427i −0.0146599 0.0253916i
\(75\) −0.256906 + 0.444974i −0.0296649 + 0.0513812i
\(76\) 1.00000 0.114708
\(77\) −5.09035 + 7.26231i −0.580099 + 0.827617i
\(78\) −4.23612 −0.479647
\(79\) −1.13557 + 1.96687i −0.127762 + 0.221290i −0.922809 0.385257i \(-0.874113\pi\)
0.795047 + 0.606547i \(0.207446\pi\)
\(80\) −1.05903 1.83430i −0.118403 0.205081i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −5.16797 + 8.95119i −0.570707 + 0.988493i
\(83\) 16.5699 1.81878 0.909392 0.415940i \(-0.136547\pi\)
0.909392 + 0.415940i \(0.136547\pi\)
\(84\) −2.63557 0.231865i −0.287564 0.0252985i
\(85\) 14.7338 1.59811
\(86\) 1.58566 2.74645i 0.170987 0.296157i
\(87\) 3.64938 + 6.32092i 0.391255 + 0.677673i
\(88\) 1.67602 + 2.90295i 0.178664 + 0.309455i
\(89\) −1.89683 + 3.28540i −0.201063 + 0.348252i −0.948871 0.315663i \(-0.897773\pi\)
0.747808 + 0.663915i \(0.231106\pi\)
\(90\) −2.11806 −0.223263
\(91\) 4.73169 + 10.1599i 0.496016 + 1.06505i
\(92\) −7.18070 −0.748640
\(93\) 2.27442 3.93940i 0.235846 0.408497i
\(94\) 3.57762 + 6.19662i 0.369003 + 0.639132i
\(95\) −1.05903 1.83430i −0.108654 0.188195i
\(96\) −0.500000 + 0.866025i −0.0510310 + 0.0883883i
\(97\) −6.18070 −0.627555 −0.313778 0.949496i \(-0.601595\pi\)
−0.313778 + 0.949496i \(0.601595\pi\)
\(98\) 2.38779 + 6.58016i 0.241203 + 0.664696i
\(99\) 3.35203 0.336892
\(100\) 0.256906 0.444974i 0.0256906 0.0444974i
\(101\) −6.61479 11.4572i −0.658196 1.14003i −0.981082 0.193592i \(-0.937986\pi\)
0.322886 0.946438i \(-0.395347\pi\)
\(102\) −3.47814 6.02432i −0.344387 0.596496i
\(103\) 3.72700 6.45536i 0.367232 0.636065i −0.621899 0.783097i \(-0.713639\pi\)
0.989132 + 0.147032i \(0.0469721\pi\)
\(104\) 4.23612 0.415386
\(105\) 2.36584 + 5.07997i 0.230883 + 0.495754i
\(106\) −1.75733 −0.170687
\(107\) −4.30354 + 7.45395i −0.416039 + 0.720601i −0.995537 0.0943730i \(-0.969915\pi\)
0.579498 + 0.814974i \(0.303249\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) −3.15373 5.46242i −0.302073 0.523205i 0.674533 0.738245i \(-0.264345\pi\)
−0.976605 + 0.215040i \(0.931012\pi\)
\(110\) 3.54991 6.14862i 0.338470 0.586248i
\(111\) 0.252218 0.0239395
\(112\) 2.63557 + 0.231865i 0.249038 + 0.0219091i
\(113\) 1.97453 0.185748 0.0928741 0.995678i \(-0.470395\pi\)
0.0928741 + 0.995678i \(0.470395\pi\)
\(114\) −0.500000 + 0.866025i −0.0468293 + 0.0811107i
\(115\) 7.60459 + 13.1715i 0.709132 + 1.22825i
\(116\) −3.64938 6.32092i −0.338837 0.586882i
\(117\) 2.11806 3.66859i 0.195815 0.339161i
\(118\) −13.0465 −1.20103
\(119\) −10.5637 + 15.0711i −0.968375 + 1.38156i
\(120\) 2.11806 0.193352
\(121\) −0.118062 + 0.204490i −0.0107329 + 0.0185900i
\(122\) 3.45956 + 5.99213i 0.313213 + 0.542502i
\(123\) −5.16797 8.95119i −0.465980 0.807101i
\(124\) −2.27442 + 3.93940i −0.204249 + 0.353769i
\(125\) −11.6786 −1.04457
\(126\) 1.51859 2.16654i 0.135286 0.193011i
\(127\) 12.2296 1.08520 0.542600 0.839991i \(-0.317440\pi\)
0.542600 + 0.839991i \(0.317440\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 1.58566 + 2.74645i 0.139610 + 0.241812i
\(130\) −4.48619 7.77031i −0.393465 0.681501i
\(131\) 0.510540 0.884281i 0.0446061 0.0772600i −0.842860 0.538132i \(-0.819130\pi\)
0.887466 + 0.460872i \(0.152463\pi\)
\(132\) −3.35203 −0.291757
\(133\) 2.63557 + 0.231865i 0.228533 + 0.0201052i
\(134\) 4.30616 0.371996
\(135\) 1.05903 1.83430i 0.0911469 0.157871i
\(136\) 3.47814 + 6.02432i 0.298248 + 0.516581i
\(137\) 3.06381 + 5.30667i 0.261759 + 0.453379i 0.966709 0.255877i \(-0.0823642\pi\)
−0.704951 + 0.709256i \(0.749031\pi\)
\(138\) 3.59035 6.21867i 0.305631 0.529369i
\(139\) 18.3476 1.55623 0.778113 0.628124i \(-0.216177\pi\)
0.778113 + 0.628124i \(0.216177\pi\)
\(140\) −2.36584 5.07997i −0.199950 0.429336i
\(141\) −7.15524 −0.602580
\(142\) −5.22592 + 9.05157i −0.438550 + 0.759591i
\(143\) 7.09982 + 12.2972i 0.593716 + 1.02835i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) −7.72962 + 13.3881i −0.641910 + 1.11182i
\(146\) 12.7667 1.05658
\(147\) −6.89248 1.22219i −0.568482 0.100805i
\(148\) −0.252218 −0.0207322
\(149\) 10.9551 18.9748i 0.897478 1.55448i 0.0667713 0.997768i \(-0.478730\pi\)
0.830707 0.556710i \(-0.187936\pi\)
\(150\) 0.256906 + 0.444974i 0.0209763 + 0.0363320i
\(151\) −0.174600 0.302416i −0.0142088 0.0246103i 0.858834 0.512255i \(-0.171190\pi\)
−0.873042 + 0.487644i \(0.837856\pi\)
\(152\) 0.500000 0.866025i 0.0405554 0.0702439i
\(153\) 6.95628 0.562382
\(154\) 3.74417 + 8.03953i 0.301714 + 0.647844i
\(155\) 9.63471 0.773878
\(156\) −2.11806 + 3.66859i −0.169581 + 0.293722i
\(157\) −6.52435 11.3005i −0.520700 0.901879i −0.999710 0.0240695i \(-0.992338\pi\)
0.479010 0.877809i \(-0.340996\pi\)
\(158\) 1.13557 + 1.96687i 0.0903412 + 0.156476i
\(159\) 0.878666 1.52189i 0.0696827 0.120694i
\(160\) −2.11806 −0.167448
\(161\) −18.9253 1.66495i −1.49152 0.131217i
\(162\) −1.00000 −0.0785674
\(163\) −7.73070 + 13.3900i −0.605515 + 1.04878i 0.386455 + 0.922308i \(0.373700\pi\)
−0.991970 + 0.126475i \(0.959634\pi\)
\(164\) 5.16797 + 8.95119i 0.403551 + 0.698970i
\(165\) 3.54991 + 6.14862i 0.276360 + 0.478669i
\(166\) 8.28496 14.3500i 0.643037 1.11377i
\(167\) −4.68797 −0.362766 −0.181383 0.983413i \(-0.558057\pi\)
−0.181383 + 0.983413i \(0.558057\pi\)
\(168\) −1.51859 + 2.16654i −0.117161 + 0.167152i
\(169\) 4.94475 0.380366
\(170\) 7.36692 12.7599i 0.565017 0.978638i
\(171\) −0.500000 0.866025i −0.0382360 0.0662266i
\(172\) −1.58566 2.74645i −0.120906 0.209415i
\(173\) 10.7642 18.6441i 0.818385 1.41748i −0.0884866 0.996077i \(-0.528203\pi\)
0.906872 0.421407i \(-0.138464\pi\)
\(174\) 7.29877 0.553318
\(175\) 0.780267 1.11319i 0.0589827 0.0841495i
\(176\) 3.35203 0.252669
\(177\) 6.52327 11.2986i 0.490319 0.849258i
\(178\) 1.89683 + 3.28540i 0.142173 + 0.246251i
\(179\) −0.919111 1.59195i −0.0686976 0.118988i 0.829631 0.558313i \(-0.188551\pi\)
−0.898328 + 0.439325i \(0.855218\pi\)
\(180\) −1.05903 + 1.83430i −0.0789355 + 0.136720i
\(181\) 20.3848 1.51519 0.757596 0.652724i \(-0.226374\pi\)
0.757596 + 0.652724i \(0.226374\pi\)
\(182\) 11.1646 + 0.982207i 0.827576 + 0.0728061i
\(183\) −6.91911 −0.511475
\(184\) −3.59035 + 6.21867i −0.264684 + 0.458447i
\(185\) 0.267107 + 0.462642i 0.0196381 + 0.0340141i
\(186\) −2.27442 3.93940i −0.166768 0.288851i
\(187\) −11.6588 + 20.1937i −0.852579 + 1.47671i
\(188\) 7.15524 0.521849
\(189\) 1.11699 + 2.39840i 0.0812487 + 0.174458i
\(190\) −2.11806 −0.153660
\(191\) 2.74895 4.76131i 0.198907 0.344517i −0.749267 0.662268i \(-0.769594\pi\)
0.948174 + 0.317751i \(0.102928\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) −3.94935 6.84048i −0.284281 0.492389i 0.688154 0.725565i \(-0.258421\pi\)
−0.972435 + 0.233176i \(0.925088\pi\)
\(194\) −3.09035 + 5.35265i −0.221874 + 0.384298i
\(195\) 8.97238 0.642525
\(196\) 6.89248 + 1.22219i 0.492320 + 0.0872994i
\(197\) −1.93736 −0.138031 −0.0690155 0.997616i \(-0.521986\pi\)
−0.0690155 + 0.997616i \(0.521986\pi\)
\(198\) 1.67602 2.90295i 0.119109 0.206303i
\(199\) −4.36912 7.56753i −0.309718 0.536448i 0.668582 0.743638i \(-0.266901\pi\)
−0.978301 + 0.207190i \(0.933568\pi\)
\(200\) −0.256906 0.444974i −0.0181660 0.0314644i
\(201\) −2.15308 + 3.72925i −0.151867 + 0.263041i
\(202\) −13.2296 −0.930830
\(203\) −8.15261 17.5054i −0.572201 1.22864i
\(204\) −6.95628 −0.487037
\(205\) 10.9461 18.9592i 0.764508 1.32417i
\(206\) −3.72700 6.45536i −0.259672 0.449766i
\(207\) 3.59035 + 6.21867i 0.249547 + 0.432228i
\(208\) 2.11806 3.66859i 0.146861 0.254371i
\(209\) 3.35203 0.231865
\(210\) 5.58231 + 0.491104i 0.385216 + 0.0338894i
\(211\) −23.3870 −1.61003 −0.805013 0.593257i \(-0.797842\pi\)
−0.805013 + 0.593257i \(0.797842\pi\)
\(212\) −0.878666 + 1.52189i −0.0603470 + 0.104524i
\(213\) −5.22592 9.05157i −0.358074 0.620203i
\(214\) 4.30354 + 7.45395i 0.294184 + 0.509542i
\(215\) −3.35854 + 5.81715i −0.229050 + 0.396727i
\(216\) 1.00000 0.0680414
\(217\) −6.90779 + 9.85522i −0.468932 + 0.669016i
\(218\) −6.30746 −0.427195
\(219\) −6.38335 + 11.0563i −0.431347 + 0.747115i
\(220\) −3.54991 6.14862i −0.239335 0.414540i
\(221\) 14.7338 + 25.5198i 0.991106 + 1.71665i
\(222\) 0.126109 0.218427i 0.00846388 0.0146599i
\(223\) 9.80320 0.656471 0.328236 0.944596i \(-0.393546\pi\)
0.328236 + 0.944596i \(0.393546\pi\)
\(224\) 1.51859 2.16654i 0.101465 0.144758i
\(225\) −0.513812 −0.0342541
\(226\) 0.987266 1.70999i 0.0656719 0.113747i
\(227\) 9.14176 + 15.8340i 0.606760 + 1.05094i 0.991771 + 0.128027i \(0.0408645\pi\)
−0.385011 + 0.922912i \(0.625802\pi\)
\(228\) 0.500000 + 0.866025i 0.0331133 + 0.0573539i
\(229\) 0.722313 1.25108i 0.0477318 0.0826739i −0.841172 0.540767i \(-0.818134\pi\)
0.888904 + 0.458093i \(0.151467\pi\)
\(230\) 15.2092 1.00286
\(231\) −8.83452 0.777218i −0.581269 0.0511372i
\(232\) −7.29877 −0.479188
\(233\) 7.84038 13.5799i 0.513640 0.889651i −0.486235 0.873828i \(-0.661630\pi\)
0.999875 0.0158225i \(-0.00503667\pi\)
\(234\) −2.11806 3.66859i −0.138462 0.239823i
\(235\) −7.57762 13.1248i −0.494309 0.856169i
\(236\) −6.52327 + 11.2986i −0.424629 + 0.735479i
\(237\) −2.27114 −0.147527
\(238\) 7.77007 + 16.6840i 0.503659 + 1.08146i
\(239\) 3.76818 0.243744 0.121872 0.992546i \(-0.461110\pi\)
0.121872 + 0.992546i \(0.461110\pi\)
\(240\) 1.05903 1.83430i 0.0683602 0.118403i
\(241\) −1.49781 2.59428i −0.0964821 0.167112i 0.813744 0.581223i \(-0.197426\pi\)
−0.910226 + 0.414111i \(0.864092\pi\)
\(242\) 0.118062 + 0.204490i 0.00758934 + 0.0131451i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 6.91911 0.442951
\(245\) −5.05749 13.9372i −0.323111 0.890414i
\(246\) −10.3359 −0.658995
\(247\) 2.11806 3.66859i 0.134769 0.233427i
\(248\) 2.27442 + 3.93940i 0.144426 + 0.250152i
\(249\) 8.28496 + 14.3500i 0.525038 + 0.909392i
\(250\) −5.83930 + 10.1140i −0.369310 + 0.639663i
\(251\) 26.2922 1.65955 0.829775 0.558098i \(-0.188469\pi\)
0.829775 + 0.558098i \(0.188469\pi\)
\(252\) −1.11699 2.39840i −0.0703635 0.151085i
\(253\) −24.0700 −1.51327
\(254\) 6.11479 10.5911i 0.383676 0.664547i
\(255\) 7.36692 + 12.7599i 0.461335 + 0.799055i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 9.86584 17.0881i 0.615414 1.06593i −0.374897 0.927066i \(-0.622322\pi\)
0.990312 0.138863i \(-0.0443447\pi\)
\(258\) 3.17133 0.197438
\(259\) −0.664738 0.0584804i −0.0413048 0.00363380i
\(260\) −8.97238 −0.556443
\(261\) −3.64938 + 6.32092i −0.225891 + 0.391255i
\(262\) −0.510540 0.884281i −0.0315413 0.0546311i
\(263\) 2.22124 + 3.84729i 0.136967 + 0.237234i 0.926347 0.376671i \(-0.122931\pi\)
−0.789380 + 0.613905i \(0.789598\pi\)
\(264\) −1.67602 + 2.90295i −0.103152 + 0.178664i
\(265\) 3.72214 0.228649
\(266\) 1.51859 2.16654i 0.0931105 0.132839i
\(267\) −3.79365 −0.232168
\(268\) 2.15308 3.72925i 0.131520 0.227800i
\(269\) −9.73982 16.8699i −0.593847 1.02857i −0.993708 0.111998i \(-0.964275\pi\)
0.399861 0.916576i \(-0.369058\pi\)
\(270\) −1.05903 1.83430i −0.0644506 0.111632i
\(271\) −0.787888 + 1.36466i −0.0478608 + 0.0828973i −0.888963 0.457978i \(-0.848574\pi\)
0.841103 + 0.540876i \(0.181907\pi\)
\(272\) 6.95628 0.421787
\(273\) −6.43292 + 9.17773i −0.389338 + 0.555462i
\(274\) 6.12761 0.370183
\(275\) 0.861157 1.49157i 0.0519297 0.0899449i
\(276\) −3.59035 6.21867i −0.216114 0.374320i
\(277\) −4.90306 8.49234i −0.294596 0.510256i 0.680295 0.732939i \(-0.261852\pi\)
−0.974891 + 0.222683i \(0.928518\pi\)
\(278\) 9.17382 15.8895i 0.550209 0.952990i
\(279\) 4.54883 0.272331
\(280\) −5.58231 0.491104i −0.333607 0.0293491i
\(281\) −3.60641 −0.215140 −0.107570 0.994198i \(-0.534307\pi\)
−0.107570 + 0.994198i \(0.534307\pi\)
\(282\) −3.57762 + 6.19662i −0.213044 + 0.369003i
\(283\) 10.7664 + 18.6479i 0.639994 + 1.10850i 0.985433 + 0.170061i \(0.0543966\pi\)
−0.345439 + 0.938441i \(0.612270\pi\)
\(284\) 5.22592 + 9.05157i 0.310102 + 0.537112i
\(285\) 1.05903 1.83430i 0.0627316 0.108654i
\(286\) 14.1996 0.839642
\(287\) 11.5451 + 24.7898i 0.681485 + 1.46329i
\(288\) −1.00000 −0.0589256
\(289\) −15.6949 + 27.1844i −0.923232 + 1.59908i
\(290\) 7.72962 + 13.3881i 0.453899 + 0.786176i
\(291\) −3.09035 5.35265i −0.181160 0.313778i
\(292\) 6.38335 11.0563i 0.373558 0.647021i
\(293\) −24.2946 −1.41930 −0.709651 0.704553i \(-0.751148\pi\)
−0.709651 + 0.704553i \(0.751148\pi\)
\(294\) −4.50469 + 5.35796i −0.262719 + 0.312483i
\(295\) 27.6334 1.60888
\(296\) −0.126109 + 0.218427i −0.00732993 + 0.0126958i
\(297\) 1.67602 + 2.90295i 0.0972523 + 0.168446i
\(298\) −10.9551 18.9748i −0.634613 1.09918i
\(299\) −15.2092 + 26.3431i −0.879570 + 1.52346i
\(300\) 0.513812 0.0296649
\(301\) −3.54233 7.60613i −0.204176 0.438410i
\(302\) −0.349200 −0.0200942
\(303\) 6.61479 11.4572i 0.380010 0.658196i
\(304\) −0.500000 0.866025i −0.0286770 0.0496700i
\(305\) −7.32755 12.6917i −0.419575 0.726724i
\(306\) 3.47814 6.02432i 0.198832 0.344387i
\(307\) 5.79365 0.330661 0.165331 0.986238i \(-0.447131\pi\)
0.165331 + 0.986238i \(0.447131\pi\)
\(308\) 8.83452 + 0.777218i 0.503394 + 0.0442861i
\(309\) 7.45400 0.424043
\(310\) 4.81735 8.34390i 0.273607 0.473902i
\(311\) −9.33930 16.1761i −0.529583 0.917265i −0.999405 0.0345033i \(-0.989015\pi\)
0.469822 0.882761i \(-0.344318\pi\)
\(312\) 2.11806 + 3.66859i 0.119912 + 0.207693i
\(313\) −12.8684 + 22.2888i −0.727366 + 1.25984i 0.230626 + 0.973042i \(0.425923\pi\)
−0.957993 + 0.286793i \(0.907411\pi\)
\(314\) −13.0487 −0.736381
\(315\) −3.21646 + 4.58887i −0.181227 + 0.258553i
\(316\) 2.27114 0.127762
\(317\) 10.3764 17.9724i 0.582796 1.00943i −0.412350 0.911025i \(-0.635292\pi\)
0.995146 0.0984067i \(-0.0313746\pi\)
\(318\) −0.878666 1.52189i −0.0492731 0.0853436i
\(319\) −12.2329 21.1879i −0.684908 1.18630i
\(320\) −1.05903 + 1.83430i −0.0592016 + 0.102540i
\(321\) −8.60708 −0.480401
\(322\) −10.9045 + 15.5573i −0.607685 + 0.866973i
\(323\) 6.95628 0.387058
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) −1.08828 1.88496i −0.0603672 0.104559i
\(326\) 7.73070 + 13.3900i 0.428164 + 0.741601i
\(327\) 3.15373 5.46242i 0.174402 0.302073i
\(328\) 10.3359 0.570707
\(329\) 18.8581 + 1.65905i 1.03968 + 0.0914662i
\(330\) 7.09982 0.390832
\(331\) 17.5018 30.3139i 0.961983 1.66620i 0.244474 0.969656i \(-0.421385\pi\)
0.717510 0.696548i \(-0.245282\pi\)
\(332\) −8.28496 14.3500i −0.454696 0.787557i
\(333\) 0.126109 + 0.218427i 0.00691073 + 0.0119697i
\(334\) −2.34399 + 4.05990i −0.128257 + 0.222148i
\(335\) −9.12072 −0.498318
\(336\) 1.11699 + 2.39840i 0.0609365 + 0.130844i
\(337\) −9.06565 −0.493837 −0.246919 0.969036i \(-0.579418\pi\)
−0.246919 + 0.969036i \(0.579418\pi\)
\(338\) 2.47238 4.28228i 0.134480 0.232925i
\(339\) 0.987266 + 1.70999i 0.0536209 + 0.0928741i
\(340\) −7.36692 12.7599i −0.399527 0.692002i
\(341\) −7.62391 + 13.2050i −0.412858 + 0.715091i
\(342\) −1.00000 −0.0540738
\(343\) 17.8822 + 4.81930i 0.965550 + 0.260218i
\(344\) −3.17133 −0.170987
\(345\) −7.60459 + 13.1715i −0.409417 + 0.709132i
\(346\) −10.7642 18.6441i −0.578686 1.00231i
\(347\) 8.82798 + 15.2905i 0.473911 + 0.820838i 0.999554 0.0298676i \(-0.00950857\pi\)
−0.525643 + 0.850705i \(0.676175\pi\)
\(348\) 3.64938 6.32092i 0.195627 0.338837i
\(349\) 19.9745 1.06921 0.534606 0.845101i \(-0.320460\pi\)
0.534606 + 0.845101i \(0.320460\pi\)
\(350\) −0.573920 1.23233i −0.0306773 0.0658707i
\(351\) 4.23612 0.226108
\(352\) 1.67602 2.90295i 0.0893320 0.154728i
\(353\) −11.2514 19.4880i −0.598851 1.03724i −0.992991 0.118190i \(-0.962291\pi\)
0.394140 0.919051i \(-0.371043\pi\)
\(354\) −6.52327 11.2986i −0.346708 0.600516i
\(355\) 11.0688 19.1718i 0.587473 1.01753i
\(356\) 3.79365 0.201063
\(357\) −18.3338 1.61292i −0.970327 0.0853646i
\(358\) −1.83822 −0.0971530
\(359\) 4.91795 8.51813i 0.259559 0.449570i −0.706565 0.707649i \(-0.749756\pi\)
0.966124 + 0.258079i \(0.0830894\pi\)
\(360\) 1.05903 + 1.83430i 0.0558158 + 0.0966759i
\(361\) −0.500000 0.866025i −0.0263158 0.0455803i
\(362\) 10.1924 17.6538i 0.535701 0.927862i
\(363\) −0.236125 −0.0123933
\(364\) 6.43292 9.17773i 0.337177 0.481044i
\(365\) −27.0407 −1.41537
\(366\) −3.45956 + 5.99213i −0.180834 + 0.313213i
\(367\) −17.6673 30.6006i −0.922224 1.59734i −0.795965 0.605342i \(-0.793036\pi\)
−0.126259 0.991997i \(-0.540297\pi\)
\(368\) 3.59035 + 6.21867i 0.187160 + 0.324171i
\(369\) 5.16797 8.95119i 0.269034 0.465980i
\(370\) 0.534213 0.0277724
\(371\) −2.66866 + 3.80733i −0.138550 + 0.197667i
\(372\) −4.54883 −0.235846
\(373\) −16.9147 + 29.2972i −0.875811 + 1.51695i −0.0199149 + 0.999802i \(0.506340\pi\)
−0.855896 + 0.517148i \(0.826994\pi\)
\(374\) 11.6588 + 20.1937i 0.602865 + 1.04419i
\(375\) −5.83930 10.1140i −0.301540 0.522283i
\(376\) 3.57762 6.19662i 0.184502 0.319566i
\(377\) −30.9185 −1.59238
\(378\) 2.63557 + 0.231865i 0.135559 + 0.0119258i
\(379\) 25.4999 1.30984 0.654920 0.755698i \(-0.272702\pi\)
0.654920 + 0.755698i \(0.272702\pi\)
\(380\) −1.05903 + 1.83430i −0.0543272 + 0.0940974i
\(381\) 6.11479 + 10.5911i 0.313270 + 0.542600i
\(382\) −2.74895 4.76131i −0.140648 0.243610i
\(383\) −17.8593 + 30.9332i −0.912568 + 1.58061i −0.102144 + 0.994770i \(0.532570\pi\)
−0.810424 + 0.585844i \(0.800763\pi\)
\(384\) 1.00000 0.0510310
\(385\) −7.93039 17.0282i −0.404170 0.867839i
\(386\) −7.89871 −0.402034
\(387\) −1.58566 + 2.74645i −0.0806038 + 0.139610i
\(388\) 3.09035 + 5.35265i 0.156889 + 0.271739i
\(389\) −11.0124 19.0740i −0.558350 0.967091i −0.997634 0.0687425i \(-0.978101\pi\)
0.439284 0.898348i \(-0.355232\pi\)
\(390\) 4.48619 7.77031i 0.227167 0.393465i
\(391\) −49.9510 −2.52613
\(392\) 4.50469 5.35796i 0.227521 0.270618i
\(393\) 1.02108 0.0515067
\(394\) −0.968679 + 1.67780i −0.0488013 + 0.0845264i
\(395\) −2.40521 4.16595i −0.121019 0.209612i
\(396\) −1.67602 2.90295i −0.0842230 0.145879i
\(397\) −9.86584 + 17.0881i −0.495153 + 0.857629i −0.999984 0.00558835i \(-0.998221\pi\)
0.504832 + 0.863218i \(0.331554\pi\)
\(398\) −8.73823 −0.438008
\(399\) 1.11699 + 2.39840i 0.0559192 + 0.120070i
\(400\) −0.513812 −0.0256906
\(401\) −7.42638 + 12.8629i −0.370856 + 0.642341i −0.989697 0.143175i \(-0.954269\pi\)
0.618842 + 0.785516i \(0.287602\pi\)
\(402\) 2.15308 + 3.72925i 0.107386 + 0.185998i
\(403\) 9.63471 + 16.6878i 0.479939 + 0.831279i
\(404\) −6.61479 + 11.4572i −0.329098 + 0.570015i
\(405\) 2.11806 0.105247
\(406\) −19.2364 1.69233i −0.954688 0.0839887i
\(407\) −0.845443 −0.0419070
\(408\) −3.47814 + 6.02432i −0.172194 + 0.298248i
\(409\) −3.01816 5.22761i −0.149238 0.258489i 0.781708 0.623645i \(-0.214349\pi\)
−0.930946 + 0.365156i \(0.881016\pi\)
\(410\) −10.9461 18.9592i −0.540589 0.936327i
\(411\) −3.06381 + 5.30667i −0.151126 + 0.261759i
\(412\) −7.45400 −0.367232
\(413\) −19.8123 + 28.2659i −0.974900 + 1.39087i
\(414\) 7.18070 0.352912
\(415\) −17.5481 + 30.3941i −0.861400 + 1.49199i
\(416\) −2.11806 3.66859i −0.103847 0.179868i
\(417\) 9.17382 + 15.8895i 0.449244 + 0.778113i
\(418\) 1.67602 2.90295i 0.0819766 0.141988i
\(419\) 14.1370 0.690637 0.345319 0.938486i \(-0.387771\pi\)
0.345319 + 0.938486i \(0.387771\pi\)
\(420\) 3.21646 4.58887i 0.156947 0.223914i
\(421\) −35.7565 −1.74266 −0.871331 0.490695i \(-0.836743\pi\)
−0.871331 + 0.490695i \(0.836743\pi\)
\(422\) −11.6935 + 20.2537i −0.569230 + 0.985935i
\(423\) −3.57762 6.19662i −0.173950 0.301290i
\(424\) 0.878666 + 1.52189i 0.0426718 + 0.0739097i
\(425\) 1.78711 3.09536i 0.0866875 0.150147i
\(426\) −10.4518 −0.506394
\(427\) 18.2358 + 1.60430i 0.882493 + 0.0776374i
\(428\) 8.60708 0.416039
\(429\) −7.09982 + 12.2972i −0.342782 + 0.593716i
\(430\) 3.35854 + 5.81715i 0.161963 + 0.280528i
\(431\) −8.71211 15.0898i −0.419648 0.726851i 0.576256 0.817269i \(-0.304513\pi\)
−0.995904 + 0.0904180i \(0.971180\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) −0.745628 −0.0358326 −0.0179163 0.999839i \(-0.505703\pi\)
−0.0179163 + 0.999839i \(0.505703\pi\)
\(434\) 5.08098 + 10.9099i 0.243895 + 0.523694i
\(435\) −15.4592 −0.741214
\(436\) −3.15373 + 5.46242i −0.151036 + 0.261603i
\(437\) 3.59035 + 6.21867i 0.171750 + 0.297479i
\(438\) 6.38335 + 11.0563i 0.305008 + 0.528290i
\(439\) −5.86443 + 10.1575i −0.279894 + 0.484790i −0.971358 0.237620i \(-0.923633\pi\)
0.691464 + 0.722411i \(0.256966\pi\)
\(440\) −7.09982 −0.338470
\(441\) −2.38779 6.58016i −0.113704 0.313341i
\(442\) 29.4677 1.40163
\(443\) −3.47805 + 6.02417i −0.165247 + 0.286217i −0.936743 0.350018i \(-0.886176\pi\)
0.771496 + 0.636234i \(0.219509\pi\)
\(444\) −0.126109 0.218427i −0.00598487 0.0103661i
\(445\) −4.01760 6.95868i −0.190452 0.329873i
\(446\) 4.90160 8.48982i 0.232098 0.402005i
\(447\) 21.9102 1.03632
\(448\) −1.11699 2.39840i −0.0527726 0.113314i
\(449\) −27.5823 −1.30169 −0.650844 0.759211i \(-0.725585\pi\)
−0.650844 + 0.759211i \(0.725585\pi\)
\(450\) −0.256906 + 0.444974i −0.0121107 + 0.0209763i
\(451\) 17.3232 + 30.0047i 0.815718 + 1.41286i
\(452\) −0.987266 1.70999i −0.0464371 0.0804314i
\(453\) 0.174600 0.302416i 0.00820343 0.0142088i
\(454\) 18.2835 0.858088
\(455\) −23.6473 2.08038i −1.10860 0.0975296i
\(456\) 1.00000 0.0468293
\(457\) −10.3866 + 17.9902i −0.485866 + 0.841544i −0.999868 0.0162445i \(-0.994829\pi\)
0.514002 + 0.857789i \(0.328162\pi\)
\(458\) −0.722313 1.25108i −0.0337515 0.0584593i
\(459\) 3.47814 + 6.02432i 0.162346 + 0.281191i
\(460\) 7.60459 13.1715i 0.354566 0.614126i
\(461\) 33.6610 1.56775 0.783875 0.620918i \(-0.213240\pi\)
0.783875 + 0.620918i \(0.213240\pi\)
\(462\) −5.09035 + 7.26231i −0.236825 + 0.337873i
\(463\) −18.4933 −0.859458 −0.429729 0.902958i \(-0.641391\pi\)
−0.429729 + 0.902958i \(0.641391\pi\)
\(464\) −3.64938 + 6.32092i −0.169418 + 0.293441i
\(465\) 4.81735 + 8.34390i 0.223399 + 0.386939i
\(466\) −7.84038 13.5799i −0.363198 0.629078i
\(467\) 6.71646 11.6333i 0.310801 0.538323i −0.667735 0.744399i \(-0.732736\pi\)
0.978536 + 0.206076i \(0.0660695\pi\)
\(468\) −4.23612 −0.195815
\(469\) 6.53928 9.32947i 0.301956 0.430795i
\(470\) −15.1552 −0.699059
\(471\) 6.52435 11.3005i 0.300626 0.520700i
\(472\) 6.52327 + 11.2986i 0.300258 + 0.520062i
\(473\) −5.31520 9.20619i −0.244393 0.423301i
\(474\) −1.13557 + 1.96687i −0.0521585 + 0.0903412i
\(475\) −0.513812 −0.0235753
\(476\) 18.3338 + 1.61292i 0.840328 + 0.0739279i
\(477\) 1.75733 0.0804627
\(478\) 1.88409 3.26334i 0.0861764 0.149262i
\(479\) 2.02947 + 3.51514i 0.0927287 + 0.160611i 0.908658 0.417540i \(-0.137108\pi\)
−0.815930 + 0.578151i \(0.803774\pi\)
\(480\) −1.05903 1.83430i −0.0483379 0.0837238i
\(481\) −0.534213 + 0.925285i −0.0243580 + 0.0421893i
\(482\) −2.99561 −0.136446
\(483\) −8.02074 17.2222i −0.364956 0.783639i
\(484\) 0.236125 0.0107329
\(485\) 6.54556 11.3372i 0.297219 0.514798i
\(486\) −0.500000 0.866025i −0.0226805 0.0392837i
\(487\) −18.7539 32.4827i −0.849820 1.47193i −0.881369 0.472429i \(-0.843377\pi\)
0.0315492 0.999502i \(-0.489956\pi\)
\(488\) 3.45956 5.99213i 0.156607 0.271251i
\(489\) −15.4614 −0.699189
\(490\) −14.5987 2.58868i −0.659502 0.116945i
\(491\) −27.2230 −1.22856 −0.614279 0.789089i \(-0.710553\pi\)
−0.614279 + 0.789089i \(0.710553\pi\)
\(492\) −5.16797 + 8.95119i −0.232990 + 0.403551i
\(493\) −25.3861 43.9701i −1.14333 1.98031i
\(494\) −2.11806 3.66859i −0.0952961 0.165058i
\(495\) −3.54991 + 6.14862i −0.159556 + 0.276360i
\(496\) 4.54883 0.204249
\(497\) 11.6746 + 25.0678i 0.523676 + 1.12444i
\(498\) 16.5699 0.742515
\(499\) −3.46825 + 6.00719i −0.155260 + 0.268919i −0.933154 0.359477i \(-0.882955\pi\)
0.777893 + 0.628396i \(0.216288\pi\)
\(500\) 5.83930 + 10.1140i 0.261141 + 0.452310i
\(501\) −2.34399 4.05990i −0.104722 0.181383i
\(502\) 13.1461 22.7697i 0.586740 1.01626i
\(503\) 24.0509 1.07237 0.536187 0.844099i \(-0.319864\pi\)
0.536187 + 0.844099i \(0.319864\pi\)
\(504\) −2.63557 0.231865i −0.117398 0.0103281i
\(505\) 28.0211 1.24692
\(506\) −12.0350 + 20.8452i −0.535020 + 0.926682i
\(507\) 2.47238 + 4.28228i 0.109802 + 0.190183i
\(508\) −6.11479 10.5911i −0.271300 0.469905i
\(509\) −16.1843 + 28.0320i −0.717355 + 1.24250i 0.244689 + 0.969602i \(0.421314\pi\)
−0.962044 + 0.272894i \(0.912019\pi\)
\(510\) 14.7338 0.652426
\(511\) 19.3874 27.6596i 0.857646 1.22359i
\(512\) −1.00000 −0.0441942
\(513\) 0.500000 0.866025i 0.0220755 0.0382360i
\(514\) −9.86584 17.0881i −0.435164 0.753726i
\(515\) 7.89402 + 13.6728i 0.347852 + 0.602498i
\(516\) 1.58566 2.74645i 0.0698050 0.120906i
\(517\) 23.9846 1.05484
\(518\) −0.383015 + 0.546440i −0.0168287 + 0.0240092i
\(519\) 21.5283 0.944990
\(520\) −4.48619 + 7.77031i −0.196732 + 0.340750i
\(521\) −6.25728 10.8379i −0.274137 0.474819i 0.695780 0.718255i \(-0.255059\pi\)
−0.969917 + 0.243436i \(0.921725\pi\)
\(522\) 3.64938 + 6.32092i 0.159729 + 0.276659i
\(523\) 7.98288 13.8267i 0.349067 0.604601i −0.637017 0.770850i \(-0.719832\pi\)
0.986084 + 0.166248i \(0.0531653\pi\)
\(524\) −1.02108 −0.0446061
\(525\) 1.35419 + 0.119135i 0.0591016 + 0.00519947i
\(526\) 4.44247 0.193701
\(527\) −15.8215 + 27.4036i −0.689194 + 1.19372i
\(528\) 1.67602 + 2.90295i 0.0729393 + 0.126334i
\(529\) −14.2813 24.7359i −0.620924 1.07547i
\(530\) 1.86107 3.22347i 0.0808397 0.140018i
\(531\) 13.0465 0.566172
\(532\) −1.11699 2.39840i −0.0484275 0.103984i
\(533\) 43.7843 1.89651
\(534\) −1.89683 + 3.28540i −0.0820837 + 0.142173i
\(535\) −9.11517 15.7879i −0.394083 0.682572i
\(536\) −2.15308 3.72925i −0.0929989 0.161079i
\(537\) 0.919111 1.59195i 0.0396626 0.0686976i
\(538\) −19.4796 −0.839827
\(539\) 23.1038 + 4.09683i 0.995152 + 0.176463i
\(540\) −2.11806 −0.0911469
\(541\) 20.1348 34.8745i 0.865662 1.49937i −0.000725557 1.00000i \(-0.500231\pi\)
0.866388 0.499372i \(-0.166436\pi\)
\(542\) 0.787888 + 1.36466i 0.0338427 + 0.0586172i
\(543\) 10.1924 + 17.6538i 0.437398 + 0.757596i
\(544\) 3.47814 6.02432i 0.149124 0.258291i
\(545\) 13.3596 0.572263
\(546\) 4.73169 + 10.1599i 0.202498 + 0.434805i
\(547\) 7.22088 0.308743 0.154371 0.988013i \(-0.450665\pi\)
0.154371 + 0.988013i \(0.450665\pi\)
\(548\) 3.06381 5.30667i 0.130879 0.226690i
\(549\) −3.45956 5.99213i −0.147650 0.255738i
\(550\) −0.861157 1.49157i −0.0367198 0.0636006i
\(551\) −3.64938 + 6.32092i −0.155469 + 0.269280i
\(552\) −7.18070 −0.305631
\(553\) 5.98576 + 0.526598i 0.254540 + 0.0223932i
\(554\) −9.80612 −0.416622
\(555\) −0.267107 + 0.462642i −0.0113380 + 0.0196381i
\(556\) −9.17382 15.8895i −0.389057 0.673866i
\(557\) −1.36266 2.36020i −0.0577378 0.100005i 0.835712 0.549168i \(-0.185055\pi\)
−0.893450 + 0.449164i \(0.851722\pi\)
\(558\) 2.27442 3.93940i 0.0962837 0.166768i
\(559\) −13.4341 −0.568204
\(560\) −3.21646 + 4.58887i −0.135920 + 0.193915i
\(561\) −23.3177 −0.984474
\(562\) −1.80320 + 3.12324i −0.0760635 + 0.131746i
\(563\) −9.17340 15.8888i −0.386613 0.669633i 0.605379 0.795937i \(-0.293022\pi\)
−0.991991 + 0.126305i \(0.959688\pi\)
\(564\) 3.57762 + 6.19662i 0.150645 + 0.260925i
\(565\) −2.09109 + 3.62187i −0.0879728 + 0.152373i
\(566\) 21.5327 0.905088
\(567\) −1.51859 + 2.16654i −0.0637746 + 0.0909861i
\(568\) 10.4518 0.438550
\(569\) −18.1465 + 31.4307i −0.760742 + 1.31764i 0.181726 + 0.983349i \(0.441832\pi\)
−0.942468 + 0.334295i \(0.891502\pi\)
\(570\) −1.05903 1.83430i −0.0443579 0.0768302i
\(571\) −22.9055 39.6735i −0.958566 1.66028i −0.725989 0.687707i \(-0.758617\pi\)
−0.232577 0.972578i \(-0.574716\pi\)
\(572\) 7.09982 12.2972i 0.296858 0.514173i
\(573\) 5.49789 0.229678
\(574\) 27.2411 + 2.39654i 1.13702 + 0.100030i
\(575\) 3.68953 0.153864
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 7.94463 + 13.7605i 0.330739 + 0.572857i 0.982657 0.185433i \(-0.0593686\pi\)
−0.651918 + 0.758290i \(0.726035\pi\)
\(578\) 15.6949 + 27.1844i 0.652824 + 1.13072i
\(579\) 3.94935 6.84048i 0.164130 0.284281i
\(580\) 15.4592 0.641910
\(581\) −18.5083 39.7413i −0.767856 1.64875i
\(582\) −6.18070 −0.256198
\(583\) −2.94532 + 5.10144i −0.121983 + 0.211280i
\(584\) −6.38335 11.0563i −0.264145 0.457513i
\(585\) 4.48619 + 7.77031i 0.185481 + 0.321263i
\(586\) −12.1473 + 21.0397i −0.501799 + 0.869142i
\(587\) −4.19680 −0.173220 −0.0866102 0.996242i \(-0.527603\pi\)
−0.0866102 + 0.996242i \(0.527603\pi\)
\(588\) 2.38779 + 6.58016i 0.0984708 + 0.271361i
\(589\) 4.54883 0.187431
\(590\) 13.8167 23.9312i 0.568825 0.985233i
\(591\) −0.968679 1.67780i −0.0398461 0.0690155i
\(592\) 0.126109 + 0.218427i 0.00518305 + 0.00897730i
\(593\) 12.3647 21.4163i 0.507758 0.879464i −0.492201 0.870481i \(-0.663808\pi\)
0.999960 0.00898203i \(-0.00285911\pi\)
\(594\) 3.35203 0.137536
\(595\) −16.4575 35.3377i −0.674691 1.44871i
\(596\) −21.9102 −0.897478
\(597\) 4.36912 7.56753i 0.178816 0.309718i
\(598\) 15.2092 + 26.3431i 0.621950 + 1.07725i
\(599\) 2.26964 + 3.93113i 0.0927350 + 0.160622i 0.908661 0.417535i \(-0.137106\pi\)
−0.815926 + 0.578156i \(0.803772\pi\)
\(600\) 0.256906 0.444974i 0.0104881 0.0181660i
\(601\) 9.37441 0.382390 0.191195 0.981552i \(-0.438764\pi\)
0.191195 + 0.981552i \(0.438764\pi\)
\(602\) −8.35826 0.735319i −0.340657 0.0299694i
\(603\) −4.30616 −0.175360
\(604\) −0.174600 + 0.302416i −0.00710438 + 0.0123051i
\(605\) −0.250064 0.433123i −0.0101665 0.0176089i
\(606\) −6.61479 11.4572i −0.268708 0.465415i
\(607\) −10.3804 + 17.9794i −0.421327 + 0.729760i −0.996070 0.0885743i \(-0.971769\pi\)
0.574742 + 0.818334i \(0.305102\pi\)
\(608\) −1.00000 −0.0405554
\(609\) 11.0838 15.8131i 0.449139 0.640778i
\(610\) −14.6551 −0.593368
\(611\) 15.1552 26.2496i 0.613115 1.06195i
\(612\) −3.47814 6.02432i −0.140596 0.243519i
\(613\) −1.62869 2.82097i −0.0657822 0.113938i 0.831259 0.555886i \(-0.187621\pi\)
−0.897041 + 0.441948i \(0.854288\pi\)
\(614\) 2.89683 5.01745i 0.116906 0.202488i
\(615\) 21.8922 0.882777
\(616\) 5.09035 7.26231i 0.205096 0.292607i
\(617\) −9.82446 −0.395518 −0.197759 0.980251i \(-0.563366\pi\)
−0.197759 + 0.980251i \(0.563366\pi\)
\(618\) 3.72700 6.45536i 0.149922 0.259672i
\(619\) 6.88508 + 11.9253i 0.276735 + 0.479319i 0.970571 0.240814i \(-0.0774143\pi\)
−0.693837 + 0.720133i \(0.744081\pi\)
\(620\) −4.81735 8.34390i −0.193470 0.335099i
\(621\) −3.59035 + 6.21867i −0.144076 + 0.249547i
\(622\) −18.6786 −0.748944
\(623\) 9.99844 + 0.879614i 0.400579 + 0.0352410i
\(624\) 4.23612 0.169581
\(625\) 11.0835 19.1971i 0.443339 0.767885i
\(626\) 12.8684 + 22.2888i 0.514326 + 0.890838i
\(627\) 1.67602 + 2.90295i 0.0669337 + 0.115932i
\(628\) −6.52435 + 11.3005i −0.260350 + 0.450939i
\(629\) −1.75450 −0.0699565
\(630\) 2.36584 + 5.07997i 0.0942575 + 0.202391i
\(631\) 45.3832 1.80668 0.903338 0.428930i \(-0.141109\pi\)
0.903338 + 0.428930i \(0.141109\pi\)
\(632\) 1.13557 1.96687i 0.0451706 0.0782378i
\(633\) −11.6935 20.2537i −0.464774 0.805013i
\(634\) −10.3764 17.9724i −0.412099 0.713776i
\(635\) −12.9515 + 22.4327i −0.513965 + 0.890213i
\(636\) −1.75733 −0.0696827
\(637\) 19.0824 22.6970i 0.756073 0.899288i
\(638\) −24.4657 −0.968607
\(639\) 5.22592 9.05157i 0.206734 0.358074i
\(640\) 1.05903 + 1.83430i 0.0418619 + 0.0725069i
\(641\) 10.5389 + 18.2540i 0.416263 + 0.720988i 0.995560 0.0941282i \(-0.0300064\pi\)
−0.579297 + 0.815116i \(0.696673\pi\)
\(642\) −4.30354 + 7.45395i −0.169847 + 0.294184i
\(643\) 28.6923 1.13151 0.565757 0.824572i \(-0.308584\pi\)
0.565757 + 0.824572i \(0.308584\pi\)
\(644\) 8.02074 + 17.2222i 0.316061 + 0.678651i
\(645\) −6.71707 −0.264484
\(646\) 3.47814 6.02432i 0.136846 0.237024i
\(647\) −0.425741 0.737405i −0.0167376 0.0289904i 0.857535 0.514425i \(-0.171995\pi\)
−0.874273 + 0.485435i \(0.838661\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) −21.8662 + 37.8734i −0.858325 + 1.48666i
\(650\) −2.17657 −0.0853721
\(651\) −11.9888 1.05471i −0.469877 0.0413375i
\(652\) 15.4614 0.605515
\(653\) 0.507356 0.878766i 0.0198544 0.0343888i −0.855928 0.517096i \(-0.827013\pi\)
0.875782 + 0.482707i \(0.160346\pi\)
\(654\) −3.15373 5.46242i −0.123321 0.213598i
\(655\) 1.08136 + 1.87296i 0.0422521 + 0.0731827i
\(656\) 5.16797 8.95119i 0.201775 0.349485i
\(657\) −12.7667 −0.498077
\(658\) 10.8658 15.5021i 0.423595 0.604335i
\(659\) 10.9687 0.427279 0.213639 0.976913i \(-0.431468\pi\)
0.213639 + 0.976913i \(0.431468\pi\)
\(660\) 3.54991 6.14862i 0.138180 0.239335i
\(661\) 10.1333 + 17.5514i 0.394141 + 0.682672i 0.992991 0.118189i \(-0.0377089\pi\)
−0.598850 + 0.800861i \(0.704376\pi\)
\(662\) −17.5018 30.3139i −0.680225 1.17818i
\(663\) −14.7338 + 25.5198i −0.572215 + 0.991106i
\(664\) −16.5699 −0.643037
\(665\) −3.21646 + 4.58887i −0.124729 + 0.177949i
\(666\) 0.252218 0.00977325
\(667\) 26.2051 45.3886i 1.01467 1.75746i
\(668\) 2.34399 + 4.05990i 0.0906916 + 0.157082i
\(669\) 4.90160 + 8.48982i 0.189507 + 0.328236i
\(670\) −4.56036 + 7.89878i −0.176182 + 0.305156i
\(671\) 23.1931 0.895359
\(672\) 2.63557 + 0.231865i 0.101669 + 0.00894437i
\(673\) 40.5792 1.56421 0.782107 0.623145i \(-0.214145\pi\)
0.782107 + 0.623145i \(0.214145\pi\)
\(674\) −4.53282 + 7.85108i −0.174598 + 0.302412i
\(675\) −0.256906 0.444974i −0.00988831 0.0171271i
\(676\) −2.47238 4.28228i −0.0950914 0.164703i
\(677\) 4.55641 7.89193i 0.175117 0.303312i −0.765085 0.643930i \(-0.777303\pi\)
0.940202 + 0.340618i \(0.110636\pi\)
\(678\) 1.97453 0.0758314
\(679\) 6.90376 + 14.8238i 0.264942 + 0.568886i
\(680\) −14.7338 −0.565017
\(681\) −9.14176 + 15.8340i −0.350313 + 0.606760i
\(682\) 7.62391 + 13.2050i 0.291935 + 0.505646i
\(683\) 2.03979 + 3.53303i 0.0780505 + 0.135188i 0.902409 0.430881i \(-0.141797\pi\)
−0.824358 + 0.566068i \(0.808464\pi\)
\(684\) −0.500000 + 0.866025i −0.0191180 + 0.0331133i
\(685\) −12.9787 −0.495889
\(686\) 13.1148 13.0768i 0.500724 0.499275i
\(687\) 1.44463 0.0551159
\(688\) −1.58566 + 2.74645i −0.0604529 + 0.104707i
\(689\) 3.72214 + 6.44693i 0.141802 + 0.245609i
\(690\) 7.60459 + 13.1715i 0.289502 + 0.501432i
\(691\) 0.733192 1.26993i 0.0278920 0.0483103i −0.851742 0.523961i \(-0.824454\pi\)
0.879634 + 0.475650i \(0.157787\pi\)
\(692\) −21.5283 −0.818385
\(693\) −3.74417 8.03953i −0.142229 0.305397i
\(694\) 17.6560 0.670211
\(695\) −19.4307 + 33.6550i −0.737050 + 1.27661i
\(696\) −3.64938 6.32092i −0.138330 0.239594i
\(697\) 35.9499 + 62.2670i 1.36170 + 2.35853i
\(698\) 9.98727 17.2985i 0.378024 0.654756i
\(699\) 15.6808 0.593100
\(700\) −1.35419 0.119135i −0.0511835 0.00450287i
\(701\) 18.9890 0.717204 0.358602 0.933491i \(-0.383254\pi\)
0.358602 + 0.933491i \(0.383254\pi\)
\(702\) 2.11806 3.66859i 0.0799411 0.138462i
\(703\) 0.126109 + 0.218427i 0.00475629 + 0.00823814i
\(704\) −1.67602 2.90295i −0.0631672 0.109409i
\(705\) 7.57762 13.1248i 0.285390 0.494309i
\(706\) −22.5028 −0.846904
\(707\) −20.0903 + 28.6624i −0.755572 + 1.07796i
\(708\) −13.0465 −0.490319
\(709\) 10.3040 17.8470i 0.386974 0.670258i −0.605067 0.796174i \(-0.706854\pi\)
0.992041 + 0.125916i \(0.0401871\pi\)
\(710\) −11.0688 19.1718i −0.415406 0.719504i
\(711\) −1.13557 1.96687i −0.0425873 0.0737633i
\(712\) 1.89683 3.28540i 0.0710866 0.123126i
\(713\) −32.6638 −1.22327
\(714\) −10.5637 + 15.0711i −0.395337 + 0.564020i
\(715\) −30.0757 −1.12477
\(716\) −0.919111 + 1.59195i −0.0343488 + 0.0594938i
\(717\) 1.88409 + 3.26334i 0.0703627 + 0.121872i
\(718\) −4.91795 8.51813i −0.183536 0.317894i
\(719\) −2.51399 + 4.35435i −0.0937559 + 0.162390i −0.909089 0.416603i \(-0.863221\pi\)
0.815333 + 0.578993i \(0.196554\pi\)
\(720\) 2.11806 0.0789355
\(721\) −19.6456 1.72832i −0.731639 0.0643660i
\(722\) −1.00000 −0.0372161
\(723\) 1.49781 2.59428i 0.0557040 0.0964821i
\(724\) −10.1924 17.6538i −0.378798 0.656097i
\(725\) 1.87510 + 3.24776i 0.0696393 + 0.120619i
\(726\) −0.118062 + 0.204490i −0.00438171 + 0.00758934i
\(727\) −12.6690 −0.469866 −0.234933 0.972012i \(-0.575487\pi\)
−0.234933 + 0.972012i \(0.575487\pi\)
\(728\) −4.73169 10.1599i −0.175368 0.376552i
\(729\) 1.00000 0.0370370
\(730\) −13.5203 + 23.4179i −0.500410 + 0.866736i
\(731\) −11.0303 19.1051i −0.407972 0.706627i
\(732\) 3.45956 + 5.99213i 0.127869 + 0.221475i
\(733\) −1.65416 + 2.86509i −0.0610977 + 0.105824i −0.894956 0.446154i \(-0.852793\pi\)
0.833859 + 0.551978i \(0.186127\pi\)
\(734\) −35.3346 −1.30422
\(735\) 9.54121 11.3485i 0.351933 0.418596i
\(736\) 7.18070 0.264684
\(737\) 7.21720 12.5006i 0.265849 0.460464i
\(738\) −5.16797 8.95119i −0.190236 0.329498i
\(739\) 10.2448 + 17.7446i 0.376863 + 0.652746i 0.990604 0.136762i \(-0.0436695\pi\)
−0.613741 + 0.789507i \(0.710336\pi\)
\(740\) 0.267107 0.462642i 0.00981904 0.0170071i
\(741\) 4.23612 0.155618
\(742\) 1.96291 + 4.21479i 0.0720608 + 0.154730i
\(743\) 13.7973 0.506172 0.253086 0.967444i \(-0.418554\pi\)
0.253086 + 0.967444i \(0.418554\pi\)
\(744\) −2.27442 + 3.93940i −0.0833841 + 0.144426i
\(745\) 23.2036 + 40.1899i 0.850115 + 1.47244i
\(746\) 16.9147 + 29.2972i 0.619292 + 1.07265i
\(747\) −8.28496 + 14.3500i −0.303131 + 0.525038i
\(748\) 23.3177 0.852579
\(749\) 22.6846 + 1.99568i 0.828877 + 0.0729205i
\(750\) −11.6786 −0.426442
\(751\) 4.40672 7.63266i 0.160803 0.278520i −0.774354 0.632753i \(-0.781925\pi\)
0.935157 + 0.354233i \(0.115258\pi\)
\(752\) −3.57762 6.19662i −0.130462 0.225967i
\(753\) 13.1461 + 22.7697i 0.479071 + 0.829775i
\(754\) −15.4592 + 26.7762i −0.562992 + 0.975132i
\(755\) 0.739628 0.0269178
\(756\) 1.51859 2.16654i 0.0552305 0.0787963i
\(757\) −16.4445 −0.597684 −0.298842 0.954303i \(-0.596600\pi\)
−0.298842 + 0.954303i \(0.596600\pi\)
\(758\) 12.7499 22.0835i 0.463099 0.802110i
\(759\) −12.0350 20.8452i −0.436842 0.756633i
\(760\) 1.05903 + 1.83430i 0.0384151 + 0.0665369i
\(761\) 13.8327 23.9589i 0.501434 0.868509i −0.498565 0.866852i \(-0.666139\pi\)
0.999999 0.00165644i \(-0.000527262\pi\)
\(762\) 12.2296 0.443031
\(763\) −9.57843 + 13.6654i −0.346762 + 0.494720i
\(764\) −5.49789 −0.198907
\(765\) −7.36692 + 12.7599i −0.266352 + 0.461335i
\(766\) 17.8593 + 30.9332i 0.645283 + 1.11766i
\(767\) 27.6334 + 47.8625i 0.997784 + 1.72821i
\(768\) 0.500000 0.866025i 0.0180422 0.0312500i
\(769\) −6.46278 −0.233054 −0.116527 0.993188i \(-0.537176\pi\)
−0.116527 + 0.993188i \(0.537176\pi\)
\(770\) −18.7121 1.64620i −0.674336 0.0593248i
\(771\) 19.7317 0.710619
\(772\) −3.94935 + 6.84048i −0.142140 + 0.246194i
\(773\) 12.2665 + 21.2461i 0.441194 + 0.764170i 0.997778 0.0666209i \(-0.0212218\pi\)
−0.556585 + 0.830791i \(0.687888\pi\)
\(774\) 1.58566 + 2.74645i 0.0569955 + 0.0987191i
\(775\) 1.16862 2.02411i 0.0419781 0.0727082i
\(776\) 6.18070 0.221874
\(777\) −0.281724 0.604921i −0.0101068