Properties

Label 722.2.c.n.429.4
Level $722$
Weight $2$
Character 722.429
Analytic conductor $5.765$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 722 = 2 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 722.c (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.76519902594\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.324000000.2
Defining polynomial: \(x^{8} + 5 x^{6} + 20 x^{4} + 25 x^{2} + 25\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 429.4
Root \(-0.951057 + 1.64728i\) of defining polynomial
Character \(\chi\) \(=\) 722.429
Dual form 722.2.c.n.653.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(1.39680 - 2.41933i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.17229 - 2.03046i) q^{5} +(-1.39680 - 2.41933i) q^{6} -1.28408 q^{7} -1.00000 q^{8} +(-2.40211 - 4.16058i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(1.39680 - 2.41933i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.17229 - 2.03046i) q^{5} +(-1.39680 - 2.41933i) q^{6} -1.28408 q^{7} -1.00000 q^{8} +(-2.40211 - 4.16058i) q^{9} +(-1.17229 - 2.03046i) q^{10} +5.75621 q^{11} -2.79360 q^{12} +(0.152141 + 0.263516i) q^{13} +(-0.642040 + 1.11205i) q^{14} +(-3.27491 - 5.67231i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.09310 + 3.62535i) q^{17} -4.80423 q^{18} -2.34458 q^{20} +(-1.79360 + 3.10661i) q^{21} +(2.87811 - 4.98503i) q^{22} +(3.23842 + 5.60910i) q^{23} +(-1.39680 + 2.41933i) q^{24} +(-0.248520 - 0.430448i) q^{25} +0.304282 q^{26} -5.04029 q^{27} +(0.642040 + 1.11205i) q^{28} +(-1.56378 - 2.70855i) q^{29} -6.54982 q^{30} -6.44246 q^{31} +(0.500000 + 0.866025i) q^{32} +(8.04029 - 13.9262i) q^{33} +(2.09310 + 3.62535i) q^{34} +(-1.50531 + 2.60727i) q^{35} +(-2.40211 + 4.16058i) q^{36} +3.97980 q^{37} +0.850045 q^{39} +(-1.17229 + 2.03046i) q^{40} +(-2.50859 + 4.34501i) q^{41} +(1.79360 + 3.10661i) q^{42} +(0.494689 - 0.856827i) q^{43} +(-2.87811 - 4.98503i) q^{44} -11.2639 q^{45} +6.47684 q^{46} +(2.19723 + 3.80571i) q^{47} +(1.39680 + 2.41933i) q^{48} -5.35114 q^{49} -0.497039 q^{50} +(5.84728 + 10.1278i) q^{51} +(0.152141 - 0.263516i) q^{52} +(1.64532 + 2.84978i) q^{53} +(-2.52015 + 4.36502i) q^{54} +(6.74794 - 11.6878i) q^{55} +1.28408 q^{56} -3.12756 q^{58} +(1.65688 - 2.86979i) q^{59} +(-3.27491 + 5.67231i) q^{60} +(5.48073 + 9.49290i) q^{61} +(-3.22123 + 5.57934i) q^{62} +(3.08450 + 5.34252i) q^{63} +1.00000 q^{64} +0.713414 q^{65} +(-8.04029 - 13.9262i) q^{66} +(-2.19041 - 3.79390i) q^{67} +4.18619 q^{68} +18.0937 q^{69} +(1.50531 + 2.60727i) q^{70} +(-2.20785 + 3.82410i) q^{71} +(2.40211 + 4.16058i) q^{72} +(1.13345 - 1.96319i) q^{73} +(1.98990 - 3.44660i) q^{74} -1.38853 q^{75} -7.39144 q^{77} +(0.425022 - 0.736160i) q^{78} +(4.28829 - 7.42754i) q^{79} +(1.17229 + 2.03046i) q^{80} +(0.166045 - 0.287598i) q^{81} +(2.50859 + 4.34501i) q^{82} -9.76464 q^{83} +3.58721 q^{84} +(4.90742 + 8.49991i) q^{85} +(-0.494689 - 0.856827i) q^{86} -8.73716 q^{87} -5.75621 q^{88} +(-7.53827 - 13.0567i) q^{89} +(-5.63194 + 9.75480i) q^{90} +(-0.195361 - 0.338376i) q^{91} +(3.23842 - 5.60910i) q^{92} +(-8.99885 + 15.5865i) q^{93} +4.39445 q^{94} +2.79360 q^{96} +(8.67609 - 15.0274i) q^{97} +(-2.67557 + 4.63422i) q^{98} +(-13.8271 - 23.9492i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{2} + 2 q^{3} - 4 q^{4} + 2 q^{5} - 2 q^{6} - 4 q^{7} - 8 q^{8} - 4 q^{9} + O(q^{10}) \) \( 8 q + 4 q^{2} + 2 q^{3} - 4 q^{4} + 2 q^{5} - 2 q^{6} - 4 q^{7} - 8 q^{8} - 4 q^{9} - 2 q^{10} + 4 q^{11} - 4 q^{12} + 18 q^{13} - 2 q^{14} + 4 q^{15} - 4 q^{16} - 6 q^{17} - 8 q^{18} - 4 q^{20} + 4 q^{21} + 2 q^{22} + 10 q^{23} - 2 q^{24} - 6 q^{25} + 36 q^{26} + 8 q^{27} + 2 q^{28} - 2 q^{29} + 8 q^{30} - 52 q^{31} + 4 q^{32} + 16 q^{33} + 6 q^{34} - 6 q^{35} - 4 q^{36} - 8 q^{37} - 12 q^{39} - 2 q^{40} - 12 q^{41} - 4 q^{42} + 10 q^{43} - 2 q^{44} - 44 q^{45} + 20 q^{46} + 12 q^{47} + 2 q^{48} - 24 q^{49} - 12 q^{50} - 2 q^{51} + 18 q^{52} + 8 q^{53} + 4 q^{54} + 26 q^{55} + 4 q^{56} - 4 q^{58} - 8 q^{59} + 4 q^{60} - 26 q^{62} + 22 q^{63} + 8 q^{64} + 8 q^{65} - 16 q^{66} + 10 q^{67} + 12 q^{68} + 40 q^{69} + 6 q^{70} + 4 q^{72} + 14 q^{73} - 4 q^{74} - 16 q^{75} + 8 q^{77} - 6 q^{78} + 22 q^{79} + 2 q^{80} + 4 q^{81} + 12 q^{82} - 24 q^{83} - 8 q^{84} + 18 q^{85} - 10 q^{86} - 52 q^{87} - 4 q^{88} - 16 q^{89} - 22 q^{90} - 4 q^{91} + 10 q^{92} - 8 q^{93} + 24 q^{94} + 4 q^{96} + 28 q^{97} - 12 q^{98} - 22 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/722\mathbb{Z}\right)^\times\).

\(n\) \(363\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) 1.39680 2.41933i 0.806444 1.39680i −0.108868 0.994056i \(-0.534722\pi\)
0.915312 0.402746i \(-0.131944\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 1.17229 2.03046i 0.524263 0.908051i −0.475338 0.879803i \(-0.657674\pi\)
0.999601 0.0282472i \(-0.00899255\pi\)
\(6\) −1.39680 2.41933i −0.570242 0.987688i
\(7\) −1.28408 −0.485336 −0.242668 0.970109i \(-0.578023\pi\)
−0.242668 + 0.970109i \(0.578023\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.40211 4.16058i −0.800704 1.38686i
\(10\) −1.17229 2.03046i −0.370710 0.642089i
\(11\) 5.75621 1.73556 0.867782 0.496945i \(-0.165545\pi\)
0.867782 + 0.496945i \(0.165545\pi\)
\(12\) −2.79360 −0.806444
\(13\) 0.152141 + 0.263516i 0.0421964 + 0.0730863i 0.886352 0.463012i \(-0.153231\pi\)
−0.844156 + 0.536098i \(0.819898\pi\)
\(14\) −0.642040 + 1.11205i −0.171592 + 0.297207i
\(15\) −3.27491 5.67231i −0.845578 1.46458i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −2.09310 + 3.62535i −0.507650 + 0.879276i 0.492310 + 0.870420i \(0.336152\pi\)
−0.999961 + 0.00885651i \(0.997181\pi\)
\(18\) −4.80423 −1.13237
\(19\) 0 0
\(20\) −2.34458 −0.524263
\(21\) −1.79360 + 3.10661i −0.391397 + 0.677919i
\(22\) 2.87811 4.98503i 0.613615 1.06281i
\(23\) 3.23842 + 5.60910i 0.675257 + 1.16958i 0.976394 + 0.215998i \(0.0693005\pi\)
−0.301137 + 0.953581i \(0.597366\pi\)
\(24\) −1.39680 + 2.41933i −0.285121 + 0.493844i
\(25\) −0.248520 0.430448i −0.0497039 0.0860897i
\(26\) 0.304282 0.0596747
\(27\) −5.04029 −0.970005
\(28\) 0.642040 + 1.11205i 0.121334 + 0.210157i
\(29\) −1.56378 2.70855i −0.290387 0.502964i 0.683515 0.729937i \(-0.260451\pi\)
−0.973901 + 0.226973i \(0.927117\pi\)
\(30\) −6.54982 −1.19583
\(31\) −6.44246 −1.15710 −0.578550 0.815647i \(-0.696381\pi\)
−0.578550 + 0.815647i \(0.696381\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 8.04029 13.9262i 1.39964 2.42424i
\(34\) 2.09310 + 3.62535i 0.358963 + 0.621742i
\(35\) −1.50531 + 2.60727i −0.254444 + 0.440710i
\(36\) −2.40211 + 4.16058i −0.400352 + 0.693430i
\(37\) 3.97980 0.654275 0.327137 0.944977i \(-0.393916\pi\)
0.327137 + 0.944977i \(0.393916\pi\)
\(38\) 0 0
\(39\) 0.850045 0.136116
\(40\) −1.17229 + 2.03046i −0.185355 + 0.321044i
\(41\) −2.50859 + 4.34501i −0.391776 + 0.678577i −0.992684 0.120742i \(-0.961473\pi\)
0.600908 + 0.799319i \(0.294806\pi\)
\(42\) 1.79360 + 3.10661i 0.276759 + 0.479361i
\(43\) 0.494689 0.856827i 0.0754394 0.130665i −0.825838 0.563908i \(-0.809297\pi\)
0.901277 + 0.433243i \(0.142631\pi\)
\(44\) −2.87811 4.98503i −0.433891 0.751521i
\(45\) −11.2639 −1.67912
\(46\) 6.47684 0.954957
\(47\) 2.19723 + 3.80571i 0.320498 + 0.555119i 0.980591 0.196065i \(-0.0628163\pi\)
−0.660093 + 0.751184i \(0.729483\pi\)
\(48\) 1.39680 + 2.41933i 0.201611 + 0.349201i
\(49\) −5.35114 −0.764449
\(50\) −0.497039 −0.0702919
\(51\) 5.84728 + 10.1278i 0.818783 + 1.41817i
\(52\) 0.152141 0.263516i 0.0210982 0.0365431i
\(53\) 1.64532 + 2.84978i 0.226002 + 0.391448i 0.956620 0.291340i \(-0.0941010\pi\)
−0.730617 + 0.682787i \(0.760768\pi\)
\(54\) −2.52015 + 4.36502i −0.342949 + 0.594004i
\(55\) 6.74794 11.6878i 0.909892 1.57598i
\(56\) 1.28408 0.171592
\(57\) 0 0
\(58\) −3.12756 −0.410669
\(59\) 1.65688 2.86979i 0.215707 0.373615i −0.737784 0.675037i \(-0.764128\pi\)
0.953491 + 0.301421i \(0.0974611\pi\)
\(60\) −3.27491 + 5.67231i −0.422789 + 0.732292i
\(61\) 5.48073 + 9.49290i 0.701735 + 1.21544i 0.967857 + 0.251502i \(0.0809245\pi\)
−0.266121 + 0.963940i \(0.585742\pi\)
\(62\) −3.22123 + 5.57934i −0.409097 + 0.708577i
\(63\) 3.08450 + 5.34252i 0.388611 + 0.673094i
\(64\) 1.00000 0.125000
\(65\) 0.713414 0.0884881
\(66\) −8.04029 13.9262i −0.989692 1.71420i
\(67\) −2.19041 3.79390i −0.267601 0.463498i 0.700641 0.713514i \(-0.252897\pi\)
−0.968242 + 0.250016i \(0.919564\pi\)
\(68\) 4.18619 0.507650
\(69\) 18.0937 2.17823
\(70\) 1.50531 + 2.60727i 0.179919 + 0.311629i
\(71\) −2.20785 + 3.82410i −0.262023 + 0.453838i −0.966779 0.255612i \(-0.917723\pi\)
0.704756 + 0.709450i \(0.251056\pi\)
\(72\) 2.40211 + 4.16058i 0.283092 + 0.490329i
\(73\) 1.13345 1.96319i 0.132660 0.229774i −0.792041 0.610468i \(-0.790982\pi\)
0.924701 + 0.380694i \(0.124315\pi\)
\(74\) 1.98990 3.44660i 0.231321 0.400660i
\(75\) −1.38853 −0.160334
\(76\) 0 0
\(77\) −7.39144 −0.842332
\(78\) 0.425022 0.736160i 0.0481243 0.0833538i
\(79\) 4.28829 7.42754i 0.482471 0.835664i −0.517327 0.855788i \(-0.673073\pi\)
0.999797 + 0.0201241i \(0.00640614\pi\)
\(80\) 1.17229 + 2.03046i 0.131066 + 0.227013i
\(81\) 0.166045 0.287598i 0.0184495 0.0319554i
\(82\) 2.50859 + 4.34501i 0.277028 + 0.479826i
\(83\) −9.76464 −1.07181 −0.535904 0.844279i \(-0.680029\pi\)
−0.535904 + 0.844279i \(0.680029\pi\)
\(84\) 3.58721 0.391397
\(85\) 4.90742 + 8.49991i 0.532285 + 0.921944i
\(86\) −0.494689 0.856827i −0.0533437 0.0923940i
\(87\) −8.73716 −0.936722
\(88\) −5.75621 −0.613615
\(89\) −7.53827 13.0567i −0.799055 1.38400i −0.920232 0.391372i \(-0.872000\pi\)
0.121178 0.992631i \(-0.461333\pi\)
\(90\) −5.63194 + 9.75480i −0.593658 + 1.02825i
\(91\) −0.195361 0.338376i −0.0204794 0.0354714i
\(92\) 3.23842 5.60910i 0.337628 0.584790i
\(93\) −8.99885 + 15.5865i −0.933137 + 1.61624i
\(94\) 4.39445 0.453253
\(95\) 0 0
\(96\) 2.79360 0.285121
\(97\) 8.67609 15.0274i 0.880924 1.52580i 0.0306077 0.999531i \(-0.490256\pi\)
0.850316 0.526273i \(-0.176411\pi\)
\(98\) −2.67557 + 4.63422i −0.270273 + 0.468127i
\(99\) −13.8271 23.9492i −1.38967 2.40699i
\(100\) −0.248520 + 0.430448i −0.0248520 + 0.0430448i
\(101\) −1.83833 3.18409i −0.182921 0.316828i 0.759953 0.649978i \(-0.225222\pi\)
−0.942874 + 0.333150i \(0.891889\pi\)
\(102\) 11.6946 1.15793
\(103\) −19.0135 −1.87346 −0.936729 0.350055i \(-0.886163\pi\)
−0.936729 + 0.350055i \(0.886163\pi\)
\(104\) −0.152141 0.263516i −0.0149187 0.0258399i
\(105\) 4.20524 + 7.28369i 0.410390 + 0.710816i
\(106\) 3.29064 0.319616
\(107\) −10.0373 −0.970340 −0.485170 0.874420i \(-0.661242\pi\)
−0.485170 + 0.874420i \(0.661242\pi\)
\(108\) 2.52015 + 4.36502i 0.242501 + 0.420025i
\(109\) −4.42174 + 7.65868i −0.423526 + 0.733568i −0.996282 0.0861578i \(-0.972541\pi\)
0.572756 + 0.819726i \(0.305874\pi\)
\(110\) −6.74794 11.6878i −0.643391 1.11439i
\(111\) 5.55899 9.62845i 0.527636 0.913892i
\(112\) 0.642040 1.11205i 0.0606670 0.105078i
\(113\) 14.2502 1.34055 0.670275 0.742113i \(-0.266176\pi\)
0.670275 + 0.742113i \(0.266176\pi\)
\(114\) 0 0
\(115\) 15.1854 1.41605
\(116\) −1.56378 + 2.70855i −0.145193 + 0.251482i
\(117\) 0.730921 1.26599i 0.0675737 0.117041i
\(118\) −1.65688 2.86979i −0.152528 0.264186i
\(119\) 2.68770 4.65523i 0.246381 0.426745i
\(120\) 3.27491 + 5.67231i 0.298957 + 0.517809i
\(121\) 22.1340 2.01218
\(122\) 10.9615 0.992404
\(123\) 7.00802 + 12.1382i 0.631892 + 1.09447i
\(124\) 3.22123 + 5.57934i 0.289275 + 0.501039i
\(125\) 10.5575 0.944295
\(126\) 6.16901 0.549579
\(127\) 1.11507 + 1.93136i 0.0989467 + 0.171381i 0.911249 0.411856i \(-0.135119\pi\)
−0.812302 + 0.583237i \(0.801786\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) −1.38197 2.39364i −0.121675 0.210748i
\(130\) 0.356707 0.617834i 0.0312853 0.0541876i
\(131\) −0.761327 + 1.31866i −0.0665175 + 0.115212i −0.897366 0.441287i \(-0.854522\pi\)
0.830849 + 0.556498i \(0.187855\pi\)
\(132\) −16.0806 −1.39964
\(133\) 0 0
\(134\) −4.38081 −0.378445
\(135\) −5.90868 + 10.2341i −0.508538 + 0.880814i
\(136\) 2.09310 3.62535i 0.179482 0.310871i
\(137\) −5.35588 9.27665i −0.457583 0.792558i 0.541249 0.840862i \(-0.317952\pi\)
−0.998833 + 0.0483046i \(0.984618\pi\)
\(138\) 9.04686 15.6696i 0.770120 1.33389i
\(139\) 5.40717 + 9.36549i 0.458630 + 0.794371i 0.998889 0.0471283i \(-0.0150070\pi\)
−0.540259 + 0.841499i \(0.681674\pi\)
\(140\) 3.01062 0.254444
\(141\) 12.2764 1.03386
\(142\) 2.20785 + 3.82410i 0.185278 + 0.320912i
\(143\) 0.875758 + 1.51686i 0.0732345 + 0.126846i
\(144\) 4.80423 0.400352
\(145\) −7.33280 −0.608956
\(146\) −1.13345 1.96319i −0.0938047 0.162475i
\(147\) −7.47449 + 12.9462i −0.616485 + 1.06778i
\(148\) −1.98990 3.44660i −0.163569 0.283309i
\(149\) 4.66692 8.08334i 0.382329 0.662213i −0.609066 0.793120i \(-0.708455\pi\)
0.991395 + 0.130906i \(0.0417887\pi\)
\(150\) −0.694265 + 1.20250i −0.0566865 + 0.0981839i
\(151\) −19.8232 −1.61319 −0.806593 0.591107i \(-0.798691\pi\)
−0.806593 + 0.591107i \(0.798691\pi\)
\(152\) 0 0
\(153\) 20.1114 1.62591
\(154\) −3.69572 + 6.40117i −0.297809 + 0.515821i
\(155\) −7.55242 + 13.0812i −0.606625 + 1.05071i
\(156\) −0.425022 0.736160i −0.0340290 0.0589400i
\(157\) −6.93381 + 12.0097i −0.553379 + 0.958480i 0.444649 + 0.895705i \(0.353328\pi\)
−0.998028 + 0.0627750i \(0.980005\pi\)
\(158\) −4.28829 7.42754i −0.341158 0.590904i
\(159\) 9.19276 0.729033
\(160\) 2.34458 0.185355
\(161\) −4.15838 7.20253i −0.327727 0.567639i
\(162\) −0.166045 0.287598i −0.0130457 0.0225959i
\(163\) 14.2496 1.11611 0.558057 0.829803i \(-0.311547\pi\)
0.558057 + 0.829803i \(0.311547\pi\)
\(164\) 5.01719 0.391776
\(165\) −18.8511 32.6510i −1.46755 2.54188i
\(166\) −4.88232 + 8.45643i −0.378942 + 0.656346i
\(167\) 5.79506 + 10.0373i 0.448435 + 0.776712i 0.998284 0.0585517i \(-0.0186482\pi\)
−0.549849 + 0.835264i \(0.685315\pi\)
\(168\) 1.79360 3.10661i 0.138380 0.239680i
\(169\) 6.45371 11.1781i 0.496439 0.859857i
\(170\) 9.81485 0.752764
\(171\) 0 0
\(172\) −0.989378 −0.0754394
\(173\) 1.99176 3.44983i 0.151431 0.262286i −0.780323 0.625377i \(-0.784945\pi\)
0.931754 + 0.363091i \(0.118279\pi\)
\(174\) −4.36858 + 7.56661i −0.331181 + 0.573623i
\(175\) 0.319119 + 0.552730i 0.0241231 + 0.0417824i
\(176\) −2.87811 + 4.98503i −0.216946 + 0.375761i
\(177\) −4.62866 8.01707i −0.347911 0.602600i
\(178\) −15.0765 −1.13003
\(179\) 8.45089 0.631649 0.315825 0.948818i \(-0.397719\pi\)
0.315825 + 0.948818i \(0.397719\pi\)
\(180\) 5.63194 + 9.75480i 0.419780 + 0.727080i
\(181\) 4.24263 + 7.34845i 0.315352 + 0.546206i 0.979512 0.201384i \(-0.0645440\pi\)
−0.664160 + 0.747591i \(0.731211\pi\)
\(182\) −0.390723 −0.0289623
\(183\) 30.6220 2.26364
\(184\) −3.23842 5.60910i −0.238739 0.413509i
\(185\) 4.66547 8.08083i 0.343012 0.594114i
\(186\) 8.99885 + 15.5865i 0.659828 + 1.14285i
\(187\) −12.0483 + 20.8683i −0.881060 + 1.52604i
\(188\) 2.19723 3.80571i 0.160249 0.277560i
\(189\) 6.47214 0.470779
\(190\) 0 0
\(191\) −22.3790 −1.61929 −0.809644 0.586921i \(-0.800340\pi\)
−0.809644 + 0.586921i \(0.800340\pi\)
\(192\) 1.39680 2.41933i 0.100806 0.174600i
\(193\) 3.71406 6.43293i 0.267344 0.463053i −0.700831 0.713327i \(-0.747187\pi\)
0.968175 + 0.250274i \(0.0805208\pi\)
\(194\) −8.67609 15.0274i −0.622907 1.07891i
\(195\) 0.996498 1.72598i 0.0713607 0.123600i
\(196\) 2.67557 + 4.63422i 0.191112 + 0.331016i
\(197\) 8.53554 0.608132 0.304066 0.952651i \(-0.401656\pi\)
0.304066 + 0.952651i \(0.401656\pi\)
\(198\) −27.6542 −1.96530
\(199\) 3.17963 + 5.50728i 0.225398 + 0.390400i 0.956439 0.291933i \(-0.0942985\pi\)
−0.731041 + 0.682334i \(0.760965\pi\)
\(200\) 0.248520 + 0.430448i 0.0175730 + 0.0304373i
\(201\) −12.2383 −0.863220
\(202\) −3.67667 −0.258689
\(203\) 2.00802 + 3.47799i 0.140935 + 0.244107i
\(204\) 5.84728 10.1278i 0.409392 0.709087i
\(205\) 5.88159 + 10.1872i 0.410788 + 0.711506i
\(206\) −9.50676 + 16.4662i −0.662368 + 1.14725i
\(207\) 15.5581 26.9474i 1.08136 1.87297i
\(208\) −0.304282 −0.0210982
\(209\) 0 0
\(210\) 8.41049 0.580379
\(211\) −6.97890 + 12.0878i −0.480447 + 0.832159i −0.999748 0.0224323i \(-0.992859\pi\)
0.519301 + 0.854591i \(0.326192\pi\)
\(212\) 1.64532 2.84978i 0.113001 0.195724i
\(213\) 6.16785 + 10.6830i 0.422614 + 0.731990i
\(214\) −5.01864 + 8.69254i −0.343067 + 0.594210i
\(215\) −1.15984 2.00890i −0.0791002 0.137006i
\(216\) 5.04029 0.342949
\(217\) 8.27263 0.561583
\(218\) 4.42174 + 7.65868i 0.299478 + 0.518711i
\(219\) −3.16640 5.48437i −0.213966 0.370599i
\(220\) −13.4959 −0.909892
\(221\) −1.27378 −0.0856840
\(222\) −5.55899 9.62845i −0.373095 0.646219i
\(223\) 4.46200 7.72841i 0.298798 0.517533i −0.677064 0.735925i \(-0.736748\pi\)
0.975861 + 0.218392i \(0.0700811\pi\)
\(224\) −0.642040 1.11205i −0.0428981 0.0743016i
\(225\) −1.19394 + 2.06797i −0.0795963 + 0.137865i
\(226\) 7.12512 12.3411i 0.473956 0.820916i
\(227\) 0.659796 0.0437922 0.0218961 0.999760i \(-0.493030\pi\)
0.0218961 + 0.999760i \(0.493030\pi\)
\(228\) 0 0
\(229\) −6.97208 −0.460728 −0.230364 0.973105i \(-0.573992\pi\)
−0.230364 + 0.973105i \(0.573992\pi\)
\(230\) 7.59272 13.1510i 0.500649 0.867150i
\(231\) −10.3244 + 17.8823i −0.679294 + 1.17657i
\(232\) 1.56378 + 2.70855i 0.102667 + 0.177825i
\(233\) 14.8048 25.6427i 0.969898 1.67991i 0.274061 0.961712i \(-0.411633\pi\)
0.695837 0.718200i \(-0.255034\pi\)
\(234\) −0.730921 1.26599i −0.0477818 0.0827605i
\(235\) 10.3031 0.672102
\(236\) −3.31375 −0.215707
\(237\) −11.9798 20.7496i −0.778171 1.34783i
\(238\) −2.68770 4.65523i −0.174218 0.301754i
\(239\) −24.7034 −1.59793 −0.798965 0.601378i \(-0.794619\pi\)
−0.798965 + 0.601378i \(0.794619\pi\)
\(240\) 6.54982 0.422789
\(241\) 13.7793 + 23.8665i 0.887604 + 1.53738i 0.842699 + 0.538384i \(0.180965\pi\)
0.0449048 + 0.998991i \(0.485702\pi\)
\(242\) 11.0670 19.1686i 0.711414 1.23221i
\(243\) −8.02431 13.8985i −0.514759 0.891589i
\(244\) 5.48073 9.49290i 0.350868 0.607721i
\(245\) −6.27308 + 10.8653i −0.400772 + 0.694158i
\(246\) 14.0160 0.893630
\(247\) 0 0
\(248\) 6.44246 0.409097
\(249\) −13.6393 + 23.6239i −0.864354 + 1.49711i
\(250\) 5.27877 9.14309i 0.333859 0.578260i
\(251\) 1.49428 + 2.58816i 0.0943179 + 0.163363i 0.909324 0.416089i \(-0.136600\pi\)
−0.815006 + 0.579453i \(0.803266\pi\)
\(252\) 3.08450 5.34252i 0.194305 0.336547i
\(253\) 18.6410 + 32.2872i 1.17195 + 2.02988i
\(254\) 2.23015 0.139932
\(255\) 27.4188 1.71703
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 7.06613 + 12.2389i 0.440773 + 0.763441i 0.997747 0.0670886i \(-0.0213710\pi\)
−0.556974 + 0.830530i \(0.688038\pi\)
\(258\) −2.76393 −0.172075
\(259\) −5.11037 −0.317543
\(260\) −0.356707 0.617834i −0.0221220 0.0383165i
\(261\) −7.51275 + 13.0125i −0.465028 + 0.805451i
\(262\) 0.761327 + 1.31866i 0.0470350 + 0.0814669i
\(263\) −3.78444 + 6.55483i −0.233358 + 0.404188i −0.958794 0.284101i \(-0.908305\pi\)
0.725436 + 0.688290i \(0.241638\pi\)
\(264\) −8.04029 + 13.9262i −0.494846 + 0.857098i
\(265\) 7.71517 0.473939
\(266\) 0 0
\(267\) −42.1179 −2.57757
\(268\) −2.19041 + 3.79390i −0.133800 + 0.231749i
\(269\) −3.83537 + 6.64306i −0.233847 + 0.405035i −0.958937 0.283619i \(-0.908465\pi\)
0.725090 + 0.688654i \(0.241798\pi\)
\(270\) 5.90868 + 10.2341i 0.359591 + 0.622829i
\(271\) −5.83245 + 10.1021i −0.354296 + 0.613658i −0.986997 0.160737i \(-0.948613\pi\)
0.632701 + 0.774396i \(0.281946\pi\)
\(272\) −2.09310 3.62535i −0.126913 0.219819i
\(273\) −1.09152 −0.0660621
\(274\) −10.7118 −0.647121
\(275\) −1.43053 2.47775i −0.0862643 0.149414i
\(276\) −9.04686 15.6696i −0.544557 0.943200i
\(277\) 27.4405 1.64874 0.824370 0.566052i \(-0.191530\pi\)
0.824370 + 0.566052i \(0.191530\pi\)
\(278\) 10.8143 0.648601
\(279\) 15.4755 + 26.8044i 0.926495 + 1.60474i
\(280\) 1.50531 2.60727i 0.0899595 0.155814i
\(281\) 8.13574 + 14.0915i 0.485338 + 0.840629i 0.999858 0.0168488i \(-0.00536339\pi\)
−0.514520 + 0.857478i \(0.672030\pi\)
\(282\) 6.13818 10.6316i 0.365523 0.633105i
\(283\) −1.69687 + 2.93907i −0.100868 + 0.174709i −0.912043 0.410095i \(-0.865495\pi\)
0.811174 + 0.584805i \(0.198829\pi\)
\(284\) 4.41570 0.262023
\(285\) 0 0
\(286\) 1.75152 0.103569
\(287\) 3.22123 5.57934i 0.190143 0.329338i
\(288\) 2.40211 4.16058i 0.141546 0.245165i
\(289\) −0.262102 0.453974i −0.0154178 0.0267044i
\(290\) −3.66640 + 6.35039i −0.215298 + 0.372908i
\(291\) −24.2376 41.9807i −1.42083 2.46095i
\(292\) −2.26689 −0.132660
\(293\) −23.3783 −1.36578 −0.682888 0.730523i \(-0.739276\pi\)
−0.682888 + 0.730523i \(0.739276\pi\)
\(294\) 7.47449 + 12.9462i 0.435921 + 0.755037i
\(295\) −3.88467 6.72845i −0.226174 0.391745i
\(296\) −3.97980 −0.231321
\(297\) −29.0130 −1.68351
\(298\) −4.66692 8.08334i −0.270347 0.468256i
\(299\) −0.985394 + 1.70675i −0.0569868 + 0.0987040i
\(300\) 0.694265 + 1.20250i 0.0400834 + 0.0694265i
\(301\) −0.635220 + 1.10023i −0.0366135 + 0.0634164i
\(302\) −9.91158 + 17.1674i −0.570347 + 0.987871i
\(303\) −10.2712 −0.590062
\(304\) 0 0
\(305\) 25.7000 1.47158
\(306\) 10.0557 17.4170i 0.574846 0.995663i
\(307\) −0.694010 + 1.20206i −0.0396093 + 0.0686052i −0.885150 0.465305i \(-0.845945\pi\)
0.845541 + 0.533910i \(0.179278\pi\)
\(308\) 3.69572 + 6.40117i 0.210583 + 0.364741i
\(309\) −26.5581 + 46.0000i −1.51084 + 2.61685i
\(310\) 7.55242 + 13.0812i 0.428949 + 0.742961i
\(311\) −12.1902 −0.691246 −0.345623 0.938374i \(-0.612332\pi\)
−0.345623 + 0.938374i \(0.612332\pi\)
\(312\) −0.850045 −0.0481243
\(313\) −8.26571 14.3166i −0.467205 0.809223i 0.532093 0.846686i \(-0.321406\pi\)
−0.999298 + 0.0374628i \(0.988072\pi\)
\(314\) 6.93381 + 12.0097i 0.391298 + 0.677748i
\(315\) 14.4637 0.814938
\(316\) −8.57659 −0.482471
\(317\) 1.34406 + 2.32797i 0.0754897 + 0.130752i 0.901299 0.433197i \(-0.142615\pi\)
−0.825809 + 0.563949i \(0.809281\pi\)
\(318\) 4.59638 7.96116i 0.257752 0.446440i
\(319\) −9.00145 15.5910i −0.503985 0.872927i
\(320\) 1.17229 2.03046i 0.0655329 0.113506i
\(321\) −14.0201 + 24.2835i −0.782525 + 1.35537i
\(322\) −8.31677 −0.463475
\(323\) 0 0
\(324\) −0.332090 −0.0184495
\(325\) 0.0756201 0.130978i 0.00419465 0.00726535i
\(326\) 7.12480 12.3405i 0.394606 0.683478i
\(327\) 12.3526 + 21.3953i 0.683100 + 1.18316i
\(328\) 2.50859 4.34501i 0.138514 0.239913i
\(329\) −2.82141 4.88683i −0.155549 0.269420i
\(330\) −37.7022 −2.07544
\(331\) −5.21303 −0.286534 −0.143267 0.989684i \(-0.545761\pi\)
−0.143267 + 0.989684i \(0.545761\pi\)
\(332\) 4.88232 + 8.45643i 0.267952 + 0.464107i
\(333\) −9.55992 16.5583i −0.523880 0.907388i
\(334\) 11.5901 0.634183
\(335\) −10.2712 −0.561173
\(336\) −1.79360 3.10661i −0.0978491 0.169480i
\(337\) −13.3637 + 23.1467i −0.727969 + 1.26088i 0.229771 + 0.973245i \(0.426202\pi\)
−0.957740 + 0.287635i \(0.907131\pi\)
\(338\) −6.45371 11.1781i −0.351035 0.608011i
\(339\) 19.9048 34.4761i 1.08108 1.87248i
\(340\) 4.90742 8.49991i 0.266142 0.460972i
\(341\) −37.0842 −2.00822
\(342\) 0 0
\(343\) 15.8598 0.856351
\(344\) −0.494689 + 0.856827i −0.0266719 + 0.0461970i
\(345\) 21.2111 36.7386i 1.14196 1.97794i
\(346\) −1.99176 3.44983i −0.107078 0.185464i
\(347\) 16.3341 28.2915i 0.876860 1.51877i 0.0220925 0.999756i \(-0.492967\pi\)
0.854768 0.519011i \(-0.173699\pi\)
\(348\) 4.36858 + 7.56661i 0.234181 + 0.405613i
\(349\) −29.1058 −1.55800 −0.778998 0.627026i \(-0.784272\pi\)
−0.778998 + 0.627026i \(0.784272\pi\)
\(350\) 0.638237 0.0341152
\(351\) −0.766837 1.32820i −0.0409307 0.0708941i
\(352\) 2.87811 + 4.98503i 0.153404 + 0.265703i
\(353\) −14.3049 −0.761372 −0.380686 0.924704i \(-0.624312\pi\)
−0.380686 + 0.924704i \(0.624312\pi\)
\(354\) −9.25731 −0.492021
\(355\) 5.17647 + 8.96591i 0.274738 + 0.475861i
\(356\) −7.53827 + 13.0567i −0.399527 + 0.692002i
\(357\) −7.50837 13.0049i −0.397385 0.688291i
\(358\) 4.22545 7.31869i 0.223322 0.386805i
\(359\) −9.83535 + 17.0353i −0.519090 + 0.899090i 0.480664 + 0.876905i \(0.340396\pi\)
−0.999754 + 0.0221853i \(0.992938\pi\)
\(360\) 11.2639 0.593658
\(361\) 0 0
\(362\) 8.48526 0.445976
\(363\) 30.9168 53.5495i 1.62271 2.81062i
\(364\) −0.195361 + 0.338376i −0.0102397 + 0.0177357i
\(365\) −2.65745 4.60284i −0.139097 0.240924i
\(366\) 15.3110 26.5194i 0.800318 1.38619i
\(367\) −4.77527 8.27100i −0.249267 0.431743i 0.714056 0.700089i \(-0.246856\pi\)
−0.963323 + 0.268346i \(0.913523\pi\)
\(368\) −6.47684 −0.337628
\(369\) 24.1037 1.25479
\(370\) −4.66547 8.08083i −0.242546 0.420102i
\(371\) −2.11272 3.65934i −0.109687 0.189984i
\(372\) 17.9977 0.933137
\(373\) −3.64010 −0.188477 −0.0942387 0.995550i \(-0.530042\pi\)
−0.0942387 + 0.995550i \(0.530042\pi\)
\(374\) 12.0483 + 20.8683i 0.623003 + 1.07907i
\(375\) 14.7468 25.5422i 0.761521 1.31899i
\(376\) −2.19723 3.80571i −0.113313 0.196264i
\(377\) 0.475831 0.824163i 0.0245065 0.0424466i
\(378\) 3.23607 5.60503i 0.166445 0.288292i
\(379\) −8.34741 −0.428778 −0.214389 0.976748i \(-0.568776\pi\)
−0.214389 + 0.976748i \(0.568776\pi\)
\(380\) 0 0
\(381\) 6.23015 0.319180
\(382\) −11.1895 + 19.3808i −0.572505 + 0.991608i
\(383\) −4.74283 + 8.21482i −0.242347 + 0.419758i −0.961382 0.275216i \(-0.911251\pi\)
0.719035 + 0.694974i \(0.244584\pi\)
\(384\) −1.39680 2.41933i −0.0712803 0.123461i
\(385\) −8.66489 + 15.0080i −0.441604 + 0.764880i
\(386\) −3.71406 6.43293i −0.189040 0.327428i
\(387\) −4.75320 −0.241619
\(388\) −17.3522 −0.880924
\(389\) −18.0240 31.2185i −0.913852 1.58284i −0.808573 0.588396i \(-0.799760\pi\)
−0.105279 0.994443i \(-0.533574\pi\)
\(390\) −0.996498 1.72598i −0.0504596 0.0873986i
\(391\) −27.1133 −1.37118
\(392\) 5.35114 0.270273
\(393\) 2.12685 + 3.68381i 0.107285 + 0.185823i
\(394\) 4.26777 7.39199i 0.215007 0.372403i
\(395\) −10.0542 17.4144i −0.505883 0.876216i
\(396\) −13.8271 + 23.9492i −0.694837 + 1.20349i
\(397\) 3.20453 5.55041i 0.160831 0.278567i −0.774336 0.632775i \(-0.781916\pi\)
0.935167 + 0.354207i \(0.115249\pi\)
\(398\) 6.35926 0.318761
\(399\) 0 0
\(400\) 0.497039 0.0248520
\(401\) 0.0938299 0.162518i 0.00468564 0.00811577i −0.863673 0.504052i \(-0.831842\pi\)
0.868359 + 0.495937i \(0.165175\pi\)
\(402\) −6.11913 + 10.5986i −0.305194 + 0.528612i
\(403\) −0.980164 1.69769i −0.0488255 0.0845682i
\(404\) −1.83833 + 3.18409i −0.0914605 + 0.158414i
\(405\) −0.389305 0.674297i −0.0193447 0.0335061i
\(406\) 4.01603 0.199312
\(407\) 22.9086 1.13554
\(408\) −5.84728 10.1278i −0.289484 0.501400i
\(409\) 8.63314 + 14.9530i 0.426881 + 0.739380i 0.996594 0.0824641i \(-0.0262790\pi\)
−0.569713 + 0.821844i \(0.692946\pi\)
\(410\) 11.7632 0.580942
\(411\) −29.9244 −1.47606
\(412\) 9.50676 + 16.4662i 0.468365 + 0.811231i
\(413\) −2.12756 + 3.68504i −0.104690 + 0.181329i
\(414\) −15.5581 26.9474i −0.764638 1.32439i
\(415\) −11.4470 + 19.8267i −0.561910 + 0.973257i
\(416\) −0.152141 + 0.263516i −0.00745934 + 0.0129200i
\(417\) 30.2110 1.47944
\(418\) 0 0
\(419\) −1.72572 −0.0843068 −0.0421534 0.999111i \(-0.513422\pi\)
−0.0421534 + 0.999111i \(0.513422\pi\)
\(420\) 4.20524 7.28369i 0.205195 0.355408i
\(421\) 16.3773 28.3663i 0.798180 1.38249i −0.122621 0.992454i \(-0.539130\pi\)
0.920800 0.390034i \(-0.127537\pi\)
\(422\) 6.97890 + 12.0878i 0.339727 + 0.588425i
\(423\) 10.5560 18.2835i 0.513249 0.888973i
\(424\) −1.64532 2.84978i −0.0799039 0.138398i
\(425\) 2.08070 0.100929
\(426\) 12.3357 0.597667
\(427\) −7.03769 12.1896i −0.340578 0.589898i
\(428\) 5.01864 + 8.69254i 0.242585 + 0.420170i
\(429\) 4.89304 0.236238
\(430\) −2.31967 −0.111865
\(431\) −12.7560 22.0940i −0.614433 1.06423i −0.990484 0.137630i \(-0.956051\pi\)
0.376051 0.926599i \(-0.377282\pi\)
\(432\) 2.52015 4.36502i 0.121251 0.210012i
\(433\) 12.2417 + 21.2032i 0.588299 + 1.01896i 0.994455 + 0.105160i \(0.0335353\pi\)
−0.406157 + 0.913803i \(0.633131\pi\)
\(434\) 4.13632 7.16431i 0.198550 0.343898i
\(435\) −10.2425 + 17.7405i −0.491089 + 0.850591i
\(436\) 8.84348 0.423526
\(437\) 0 0
\(438\) −6.33280 −0.302593
\(439\) −15.4194 + 26.7072i −0.735928 + 1.27466i 0.218387 + 0.975862i \(0.429920\pi\)
−0.954315 + 0.298802i \(0.903413\pi\)
\(440\) −6.74794 + 11.6878i −0.321696 + 0.557193i
\(441\) 12.8540 + 22.2639i 0.612097 + 1.06018i
\(442\) −0.636892 + 1.10313i −0.0302939 + 0.0524705i
\(443\) −5.35234 9.27052i −0.254297 0.440456i 0.710407 0.703791i \(-0.248511\pi\)
−0.964704 + 0.263335i \(0.915177\pi\)
\(444\) −11.1180 −0.527636
\(445\) −35.3481 −1.67566
\(446\) −4.46200 7.72841i −0.211282 0.365951i
\(447\) −13.0375 22.5817i −0.616654 1.06808i
\(448\) −1.28408 −0.0606670
\(449\) −2.31562 −0.109281 −0.0546403 0.998506i \(-0.517401\pi\)
−0.0546403 + 0.998506i \(0.517401\pi\)
\(450\) 1.19394 + 2.06797i 0.0562831 + 0.0974851i
\(451\) −14.4400 + 25.0108i −0.679953 + 1.17771i
\(452\) −7.12512 12.3411i −0.335137 0.580475i
\(453\) −27.6890 + 47.9588i −1.30094 + 2.25330i
\(454\) 0.329898 0.571400i 0.0154829 0.0268171i
\(455\) −0.916079 −0.0429465
\(456\) 0 0
\(457\) −0.0521810 −0.00244092 −0.00122046 0.999999i \(-0.500388\pi\)
−0.00122046 + 0.999999i \(0.500388\pi\)
\(458\) −3.48604 + 6.03800i −0.162892 + 0.282137i
\(459\) 10.5498 18.2728i 0.492423 0.852902i
\(460\) −7.59272 13.1510i −0.354012 0.613167i
\(461\) −19.7360 + 34.1838i −0.919198 + 1.59210i −0.118561 + 0.992947i \(0.537828\pi\)
−0.800637 + 0.599150i \(0.795505\pi\)
\(462\) 10.3244 + 17.8823i 0.480333 + 0.831962i
\(463\) −6.19056 −0.287700 −0.143850 0.989600i \(-0.545948\pi\)
−0.143850 + 0.989600i \(0.545948\pi\)
\(464\) 3.12756 0.145193
\(465\) 21.0985 + 36.5437i 0.978419 + 1.69467i
\(466\) −14.8048 25.6427i −0.685821 1.18788i
\(467\) −20.9962 −0.971586 −0.485793 0.874074i \(-0.661469\pi\)
−0.485793 + 0.874074i \(0.661469\pi\)
\(468\) −1.46184 −0.0675737
\(469\) 2.81266 + 4.87166i 0.129876 + 0.224952i
\(470\) 5.15156 8.92277i 0.237624 0.411577i
\(471\) 19.3703 + 33.5504i 0.892538 + 1.54592i
\(472\) −1.65688 + 2.86979i −0.0762639 + 0.132093i
\(473\) 2.84754 4.93208i 0.130930 0.226777i
\(474\) −23.9596 −1.10050
\(475\) 0 0
\(476\) −5.37540 −0.246381
\(477\) 7.90450 13.6910i 0.361922 0.626867i
\(478\) −12.3517 + 21.3938i −0.564953 + 0.978528i
\(479\) −7.76147 13.4433i −0.354631 0.614238i 0.632424 0.774622i \(-0.282060\pi\)
−0.987055 + 0.160384i \(0.948727\pi\)
\(480\) 3.27491 5.67231i 0.149478 0.258904i
\(481\) 0.605491 + 1.04874i 0.0276080 + 0.0478185i
\(482\) 27.5586 1.25526
\(483\) −23.2338 −1.05717
\(484\) −11.0670 19.1686i −0.503046 0.871301i
\(485\) −20.3418 35.2330i −0.923672 1.59985i
\(486\) −16.0486 −0.727980
\(487\) 28.6065 1.29629 0.648143 0.761519i \(-0.275546\pi\)
0.648143 + 0.761519i \(0.275546\pi\)
\(488\) −5.48073 9.49290i −0.248101 0.429723i
\(489\) 19.9039 34.4745i 0.900084 1.55899i
\(490\) 6.27308 + 10.8653i 0.283389 + 0.490844i
\(491\) 15.1744 26.2829i 0.684812 1.18613i −0.288684 0.957424i \(-0.593218\pi\)
0.973496 0.228705i \(-0.0734490\pi\)
\(492\) 7.00802 12.1382i 0.315946 0.547234i
\(493\) 13.0926 0.589659
\(494\) 0 0
\(495\) −64.8373 −2.91422
\(496\) 3.22123 5.57934i 0.144638 0.250520i
\(497\) 2.83505 4.91045i 0.127169 0.220264i
\(498\) 13.6393 + 23.6239i 0.611191 + 1.05861i
\(499\) −4.38812 + 7.60044i −0.196439 + 0.340243i −0.947371 0.320137i \(-0.896271\pi\)
0.750932 + 0.660379i \(0.229604\pi\)
\(500\) −5.27877 9.14309i −0.236074 0.408892i
\(501\) 32.3782 1.44655
\(502\) 2.98855 0.133386
\(503\) 10.5522 + 18.2769i 0.470498 + 0.814926i 0.999431 0.0337373i \(-0.0107410\pi\)
−0.528933 + 0.848664i \(0.677408\pi\)
\(504\) −3.08450 5.34252i −0.137395 0.237975i
\(505\) −8.62023 −0.383595
\(506\) 37.2821 1.65739
\(507\) −18.0291 31.2273i −0.800701 1.38685i
\(508\) 1.11507 1.93136i 0.0494734 0.0856904i
\(509\) 11.1106 + 19.2441i 0.492468 + 0.852979i 0.999962 0.00867561i \(-0.00276157\pi\)
−0.507494 + 0.861655i \(0.669428\pi\)
\(510\) 13.7094 23.7454i 0.607062 1.05146i
\(511\) −1.45543 + 2.52089i −0.0643846 + 0.111517i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 14.1323 0.623347
\(515\) −22.2893 + 38.6063i −0.982185 + 1.70119i
\(516\) −1.38197 + 2.39364i −0.0608377 + 0.105374i
\(517\) 12.6477 + 21.9065i 0.556245 + 0.963445i
\(518\) −2.55519 + 4.42571i −0.112268 + 0.194455i
\(519\) −5.56420 9.63747i −0.244241 0.423038i
\(520\) −0.713414 −0.0312853
\(521\) −10.0332 −0.439563 −0.219782 0.975549i \(-0.570534\pi\)
−0.219782 + 0.975549i \(0.570534\pi\)
\(522\) 7.51275 + 13.0125i 0.328824 + 0.569540i
\(523\) 14.6411 + 25.3592i 0.640212 + 1.10888i 0.985385 + 0.170341i \(0.0544870\pi\)
−0.345173 + 0.938539i \(0.612180\pi\)
\(524\) 1.52265 0.0665175
\(525\) 1.78298 0.0778158
\(526\) 3.78444 + 6.55483i 0.165009 + 0.285804i
\(527\) 13.4847 23.3562i 0.587403 1.01741i
\(528\) 8.04029 + 13.9262i 0.349909 + 0.606060i
\(529\) −9.47470 + 16.4107i −0.411943 + 0.713507i
\(530\) 3.85758 6.68153i 0.167563 0.290227i
\(531\) −15.9200 −0.690870
\(532\) 0 0
\(533\) −1.52664 −0.0661262
\(534\) −21.0589 + 36.4751i −0.911309 + 1.57843i
\(535\) −11.7666 + 20.3803i −0.508714 + 0.881118i
\(536\) 2.19041 + 3.79390i 0.0946112 + 0.163871i
\(537\) 11.8042 20.4455i 0.509390 0.882289i
\(538\) 3.83537 + 6.64306i 0.165355 + 0.286403i
\(539\) −30.8023 −1.32675
\(540\) 11.8174 0.508538
\(541\) 18.9202 + 32.7707i 0.813442 + 1.40892i 0.910441 + 0.413638i \(0.135742\pi\)
−0.0969995 + 0.995284i \(0.530925\pi\)
\(542\) 5.83245 + 10.1021i 0.250525 + 0.433922i
\(543\) 23.7045 1.01726
\(544\) −4.18619 −0.179482
\(545\) 10.3671 + 17.9564i 0.444078 + 0.769166i
\(546\) −0.545762 + 0.945288i −0.0233565 + 0.0404546i
\(547\) −7.24878 12.5553i −0.309936 0.536824i 0.668412 0.743791i \(-0.266974\pi\)
−0.978348 + 0.206967i \(0.933641\pi\)
\(548\) −5.35588 + 9.27665i −0.228792 + 0.396279i
\(549\) 26.3307 45.6060i 1.12377 1.94642i
\(550\) −2.86106 −0.121996
\(551\) 0 0
\(552\) −18.0937 −0.770120
\(553\) −5.50651 + 9.53755i −0.234161 + 0.405578i
\(554\) 13.7202 23.7642i 0.582917 1.00964i
\(555\) −13.0335 22.5746i −0.553240 0.958240i
\(556\) 5.40717 9.36549i 0.229315 0.397185i
\(557\) 2.16901 + 3.75683i 0.0919037 + 0.159182i 0.908312 0.418293i \(-0.137371\pi\)
−0.816408 + 0.577475i \(0.804038\pi\)
\(558\) 30.9511 1.31026
\(559\) 0.301051 0.0127331
\(560\) −1.50531 2.60727i −0.0636110 0.110177i
\(561\) 33.6582 + 58.2977i 1.42105 + 2.46133i
\(562\) 16.2715 0.686371
\(563\) 27.2936 1.15029 0.575144 0.818052i \(-0.304946\pi\)
0.575144 + 0.818052i \(0.304946\pi\)
\(564\) −6.13818 10.6316i −0.258464 0.447673i
\(565\) 16.7054 28.9346i 0.702801 1.21729i
\(566\) 1.69687 + 2.93907i 0.0713248 + 0.123538i
\(567\) −0.213215 + 0.369299i −0.00895419 + 0.0155091i
\(568\) 2.20785 3.82410i 0.0926392 0.160456i
\(569\) 7.19043 0.301439 0.150719 0.988577i \(-0.451841\pi\)
0.150719 + 0.988577i \(0.451841\pi\)
\(570\) 0 0
\(571\) 42.0134 1.75821 0.879103 0.476631i \(-0.158142\pi\)
0.879103 + 0.476631i \(0.158142\pi\)
\(572\) 0.875758 1.51686i 0.0366173 0.0634230i
\(573\) −31.2591 + 54.1423i −1.30587 + 2.26183i
\(574\) −3.22123 5.57934i −0.134452 0.232877i
\(575\) 1.60962 2.78794i 0.0671258 0.116265i
\(576\) −2.40211 4.16058i −0.100088 0.173358i
\(577\) 21.6713 0.902190 0.451095 0.892476i \(-0.351034\pi\)
0.451095 + 0.892476i \(0.351034\pi\)
\(578\) −0.524204 −0.0218040
\(579\) −10.3756 17.9711i −0.431195 0.746852i
\(580\) 3.66640 + 6.35039i 0.152239 + 0.263686i
\(581\) 12.5386 0.520188
\(582\) −48.4751 −2.00936
\(583\) 9.47083 + 16.4040i 0.392242 + 0.679382i
\(584\) −1.13345 + 1.96319i −0.0469023 + 0.0812373i
\(585\) −1.71370 2.96822i −0.0708528 0.122721i
\(586\) −11.6892 + 20.2462i −0.482874 + 0.836363i
\(587\) 0.634322 1.09868i 0.0261813 0.0453473i −0.852638 0.522502i \(-0.824999\pi\)
0.878819 + 0.477155i \(0.158332\pi\)
\(588\) 14.9490 0.616485
\(589\) 0 0
\(590\) −7.76934 −0.319859
\(591\) 11.9225 20.6503i 0.490424 0.849440i
\(592\) −1.98990 + 3.44660i −0.0817843 + 0.141655i
\(593\) −10.7800 18.6715i −0.442682 0.766747i 0.555206 0.831713i \(-0.312639\pi\)
−0.997887 + 0.0649660i \(0.979306\pi\)
\(594\) −14.5065 + 25.1260i −0.595209 + 1.03093i
\(595\) −6.30152 10.9146i −0.258337 0.447453i
\(596\) −9.33384 −0.382329
\(597\) 17.7652 0.727083
\(598\) 0.985394 + 1.70675i 0.0402957 + 0.0697943i
\(599\) −14.3209 24.8045i −0.585135 1.01348i −0.994859 0.101274i \(-0.967708\pi\)
0.409724 0.912210i \(-0.365625\pi\)
\(600\) 1.38853 0.0566865
\(601\) −7.55865 −0.308324 −0.154162 0.988046i \(-0.549268\pi\)
−0.154162 + 0.988046i \(0.549268\pi\)
\(602\) 0.635220 + 1.10023i 0.0258896 + 0.0448422i
\(603\) −10.5232 + 18.2267i −0.428538 + 0.742250i
\(604\) 9.91158 + 17.1674i 0.403297 + 0.698530i
\(605\) 25.9474 44.9423i 1.05491 1.82716i
\(606\) −5.13558 + 8.89508i −0.208619 + 0.361338i
\(607\) −1.72737 −0.0701117 −0.0350558 0.999385i \(-0.511161\pi\)
−0.0350558 + 0.999385i \(0.511161\pi\)
\(608\) 0 0
\(609\) 11.2192 0.454625
\(610\) 12.8500 22.2568i 0.520281 0.901153i
\(611\) −0.668577 + 1.15801i −0.0270477 + 0.0468481i
\(612\) −10.0557 17.4170i −0.406478 0.704040i
\(613\) 13.7085 23.7438i 0.553680 0.959002i −0.444325 0.895866i \(-0.646556\pi\)
0.998005 0.0631360i \(-0.0201102\pi\)
\(614\) 0.694010 + 1.20206i 0.0280080 + 0.0485112i
\(615\) 32.8617 1.32511
\(616\) 7.39144 0.297809
\(617\) −5.31375 9.20369i −0.213924 0.370527i 0.739015 0.673688i \(-0.235291\pi\)
−0.952939 + 0.303162i \(0.901958\pi\)
\(618\) 26.5581 + 46.0000i 1.06832 + 1.85039i
\(619\) 8.36008 0.336020 0.168010 0.985785i \(-0.446266\pi\)
0.168010 + 0.985785i \(0.446266\pi\)
\(620\) 15.1048 0.606625
\(621\) −16.3226 28.2715i −0.655002 1.13450i
\(622\) −6.09512 + 10.5571i −0.244392 + 0.423300i
\(623\) 9.67973 + 16.7658i 0.387810 + 0.671707i
\(624\) −0.425022 + 0.736160i −0.0170145 + 0.0294700i
\(625\) 13.6191 23.5889i 0.544763 0.943557i
\(626\) −16.5314 −0.660728
\(627\) 0 0
\(628\) 13.8676 0.553379
\(629\) −8.33010 + 14.4282i −0.332143 + 0.575288i
\(630\) 7.23185 12.5259i 0.288124 0.499045i
\(631\) −12.2651 21.2437i −0.488265 0.845700i 0.511644 0.859198i \(-0.329037\pi\)
−0.999909 + 0.0134980i \(0.995703\pi\)
\(632\) −4.28829 + 7.42754i −0.170579 + 0.295452i
\(633\) 19.4963 + 33.7686i 0.774908 + 1.34218i
\(634\) 2.68811 0.106759
\(635\) 5.22875 0.207497
\(636\) −4.59638 7.96116i −0.182258 0.315681i
\(637\) −0.814129 1.41011i −0.0322570 0.0558707i
\(638\) −18.0029 −0.712742
\(639\) 21.2140 0.839213
\(640\) −1.17229 2.03046i −0.0463388 0.0802611i
\(641\) −3.48635 + 6.03854i −0.137703 + 0.238508i −0.926627 0.375983i \(-0.877305\pi\)
0.788924 + 0.614491i \(0.210638\pi\)
\(642\) 14.0201 + 24.2835i 0.553329 + 0.958394i
\(643\) 4.54512 7.87238i 0.179242 0.310456i −0.762379 0.647131i \(-0.775969\pi\)
0.941621 + 0.336674i \(0.109302\pi\)
\(644\) −4.15838 + 7.20253i −0.163863 + 0.283820i
\(645\) −6.48025 −0.255160
\(646\) 0 0
\(647\) 30.0074 1.17971 0.589856 0.807509i \(-0.299185\pi\)
0.589856 + 0.807509i \(0.299185\pi\)
\(648\) −0.166045 + 0.287598i −0.00652287 + 0.0112979i
\(649\) 9.53733 16.5191i 0.374373 0.648433i
\(650\) −0.0756201 0.130978i −0.00296607 0.00513738i
\(651\) 11.5552 20.0142i 0.452885 0.784420i
\(652\) −7.12480 12.3405i −0.279029 0.483292i
\(653\) 10.4191 0.407732 0.203866 0.978999i \(-0.434649\pi\)
0.203866 + 0.978999i \(0.434649\pi\)
\(654\) 24.7052 0.966049
\(655\) 1.78499 + 3.09169i 0.0697453 + 0.120802i
\(656\) −2.50859 4.34501i −0.0979441 0.169644i
\(657\) −10.8907 −0.424885
\(658\) −5.64282 −0.219980
\(659\) −13.1878 22.8419i −0.513724 0.889796i −0.999873 0.0159201i \(-0.994932\pi\)
0.486149 0.873876i \(-0.338401\pi\)
\(660\) −18.8511 + 32.6510i −0.733777 + 1.27094i
\(661\) −12.3470 21.3856i −0.480242 0.831803i 0.519502 0.854470i \(-0.326118\pi\)
−0.999743 + 0.0226668i \(0.992784\pi\)
\(662\) −2.60651 + 4.51462i −0.101305 + 0.175466i
\(663\) −1.77923 + 3.08171i −0.0690994 + 0.119684i
\(664\) 9.76464 0.378942
\(665\) 0 0
\(666\) −19.1198 −0.740879
\(667\) 10.1283 17.5428i 0.392171 0.679260i
\(668\) 5.79506 10.0373i 0.224217 0.388356i
\(669\) −12.4651 21.5901i −0.481927 0.834722i
\(670\) −5.13558 + 8.89508i −0.198405 + 0.343647i
\(671\) 31.5483 + 54.6432i 1.21791 + 2.10948i
\(672\) −3.58721 −0.138380
\(673\) 9.77380 0.376752 0.188376 0.982097i \(-0.439678\pi\)
0.188376 + 0.982097i \(0.439678\pi\)
\(674\) 13.3637 + 23.1467i 0.514752 + 0.891576i
\(675\) 1.25261 + 2.16959i 0.0482130 + 0.0835074i
\(676\) −12.9074 −0.496439
\(677\) 21.5747 0.829184 0.414592 0.910007i \(-0.363924\pi\)
0.414592 + 0.910007i \(0.363924\pi\)
\(678\) −19.9048 34.4761i −0.764438 1.32405i
\(679\) −11.1408 + 19.2964i −0.427544 + 0.740528i
\(680\) −4.90742 8.49991i −0.188191 0.325957i
\(681\) 0.921604 1.59627i 0.0353159 0.0611690i
\(682\) −18.5421 + 32.1159i −0.710014 + 1.22978i
\(683\) −33.2509 −1.27231 −0.636155 0.771561i \(-0.719476\pi\)
−0.636155 + 0.771561i \(0.719476\pi\)
\(684\) 0 0
\(685\) −25.1145 −0.959576
\(686\) 7.92992 13.7350i 0.302766 0.524406i
\(687\) −9.73862 + 16.8678i −0.371551 + 0.643546i
\(688\) 0.494689 + 0.856827i 0.0188598 + 0.0326662i
\(689\) −0.500643 + 0.867138i −0.0190730 + 0.0330353i
\(690\) −21.2111 36.7386i −0.807491 1.39862i
\(691\) 4.80932 0.182955 0.0914776 0.995807i \(-0.470841\pi\)
0.0914776 + 0.995807i \(0.470841\pi\)
\(692\) −3.98353 −0.151431
\(693\) 17.7551 + 30.7527i 0.674459 + 1.16820i
\(694\) −16.3341 28.2915i −0.620034 1.07393i
\(695\) 25.3550 0.961772
\(696\) 8.73716 0.331181
\(697\) −10.5015 18.1890i −0.397771 0.688959i
\(698\) −14.5529 + 25.2063i −0.550835 + 0.954074i
\(699\) −41.3589 71.6357i −1.56434 2.70951i
\(700\) 0.319119 0.552730i 0.0120616 0.0208912i
\(701\) −1.73233 + 3.00049i −0.0654293 + 0.113327i −0.896884 0.442265i \(-0.854175\pi\)
0.831455 + 0.555592i \(0.187508\pi\)
\(702\) −1.53367 −0.0578848
\(703\) 0 0
\(704\) 5.75621 0.216946
\(705\) 14.3914 24.9267i 0.542013 0.938794i
\(706\) −7.15244 + 12.3884i −0.269186 + 0.466243i
\(707\) 2.36057 + 4.08862i 0.0887782 + 0.153768i
\(708\) −4.62866 + 8.01707i −0.173956 + 0.301300i
\(709\) −10.2871 17.8179i −0.386342 0.669164i 0.605612 0.795760i \(-0.292928\pi\)
−0.991954 + 0.126596i \(0.959595\pi\)
\(710\) 10.3529 0.388539
\(711\) −41.2039 −1.54527
\(712\) 7.53827 + 13.0567i 0.282508 + 0.489319i
\(713\) −20.8634 36.1364i −0.781340 1.35332i
\(714\) −15.0167 −0.561988
\(715\) 4.10656 0.153577
\(716\) −4.22545 7.31869i −0.157912 0.273512i
\(717\) −34.5058 + 59.7657i −1.28864 + 2.23199i
\(718\) 9.83535 + 17.0353i 0.367052 + 0.635753i
\(719\) −12.0943 + 20.9479i −0.451040 + 0.781225i −0.998451 0.0556395i \(-0.982280\pi\)
0.547411 + 0.836864i \(0.315614\pi\)
\(720\) 5.63194 9.75480i 0.209890 0.363540i
\(721\) 24.4149 0.909257
\(722\) 0 0
\(723\) 76.9880 2.86321
\(724\) 4.24263 7.34845i 0.157676 0.273103i
\(725\) −0.777260 + 1.34625i −0.0288667 + 0.0499986i
\(726\) −30.9168 53.5495i −1.14743 1.98741i
\(727\) −9.06381 + 15.6990i −0.336158 + 0.582243i −0.983707 0.179781i \(-0.942461\pi\)
0.647548 + 0.762024i \(0.275794\pi\)
\(728\) 0.195361 + 0.338376i 0.00724057 + 0.0125410i
\(729\) −43.8372 −1.62360
\(730\) −5.31490 −0.196713
\(731\) 2.07086 + 3.58684i 0.0765937 + 0.132664i
\(732\) −15.3110 26.5194i −0.565910 0.980186i
\(733\) 22.7363 0.839785 0.419893 0.907574i \(-0.362068\pi\)
0.419893 + 0.907574i \(0.362068\pi\)
\(734\) −9.55053 −0.352517
\(735\) 17.5245 + 30.3533i 0.646401 + 1.11960i
\(736\) −3.23842 + 5.60910i −0.119370 + 0.206754i
\(737\) −12.6085 21.8385i −0.464438 0.804431i
\(738\) 12.0518 20.8744i 0.443635 0.768398i
\(739\) −7.58933 + 13.1451i −0.279178 + 0.483550i −0.971181 0.238344i \(-0.923395\pi\)
0.692003 + 0.721895i \(0.256729\pi\)
\(740\) −9.33094 −0.343012
\(741\) 0 0
\(742\) −4.22545 −0.155121
\(743\) −1.63812 + 2.83732i −0.0600970 + 0.104091i −0.894509 0.447051i \(-0.852474\pi\)
0.834412 + 0.551142i \(0.185808\pi\)
\(744\) 8.99885 15.5865i 0.329914 0.571427i
\(745\) −10.9420 18.9520i −0.400882 0.694348i
\(746\) −1.82005 + 3.15242i −0.0666368 + 0.115418i
\(747\) 23.4558 + 40.6266i 0.858202 + 1.48645i
\(748\) 24.0966 0.881060
\(749\) 12.8887 0.470941
\(750\) −14.7468 25.5422i −0.538477 0.932669i
\(751\) 26.1162 + 45.2345i 0.952992 + 1.65063i 0.738897 + 0.673818i \(0.235347\pi\)
0.214095 + 0.976813i \(0.431320\pi\)
\(752\) −4.39445 −0.160249
\(753\) 8.34884 0.304248
\(754\) −0.475831 0.824163i −0.0173287 0.0300142i
\(755\) −23.2385 + 40.2502i −0.845734 + 1.46485i
\(756\) −3.23607 5.60503i −0.117695 0.203853i
\(757\) 12.1171 20.9874i 0.440404 0.762801i −0.557316 0.830301i \(-0.688169\pi\)
0.997719 + 0.0674993i \(0.0215020\pi\)
\(758\) −4.17371 + 7.22907i −0.151596 + 0.262572i
\(759\) 104.151 3.78045
\(760\) 0 0
\(761\) −24.8054 −0.899195 −0.449597 0.893231i \(-0.648433\pi\)
−0.449597 + 0.893231i \(0.648433\pi\)
\(762\) 3.11507 5.39546i 0.112847 0.195457i
\(763\) 5.67786 9.83435i 0.205552 0.356027i
\(764\) 11.1895 + 19.3808i 0.404822 + 0.701173i
\(765\) 23.5764 40.8355i 0.852406 1.47641i
\(766\) 4.74283 + 8.21482i 0.171365 + 0.296814i
\(767\) 1.00832 0.0364082
\(768\) −2.79360 −0.100806
\(769\) −4.82145 8.35099i −0.173866 0.301144i 0.765902 0.642957i \(-0.222293\pi\)
−0.939768 + 0.341812i \(0.888959\pi\)
\(770\) 8.66489 + 15.0080i 0.312261 + 0.540852i
\(771\) 39.4799 1.42184
\(772\) −7.42811 −0.267344
\(773\) 0.643656 + 1.11484i 0.0231507 + 0.0400982i 0.877369 0.479817i \(-0.159297\pi\)
−0.854218 + 0.519915i \(0.825964\pi\)
\(774\) −2.37660 + 4.11639i −0.0854251 + 0.147961i
\(775\) 1.60108 + 2.77315i 0.0575124 + 0.0996144i
\(776\) −8.67609 + 15.0274i −0.311453 + 0.539453i
\(777\) −7.13818 + 12.3637i −0.256081 + 0.443545i
\(778\) −36.0480 −1.29238
\(779\) 0 0
\(780\) −1.99300 −0.0713607