Properties

Label 403.2.h.b.118.13
Level 403
Weight 2
Character 403.118
Analytic conductor 3.218
Analytic rank 0
Dimension 34
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 403 = 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 403.h (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.21797120146\)
Analytic rank: \(0\)
Dimension: \(34\)
Relative dimension: \(17\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 118.13
Character \(\chi\) \(=\) 403.118
Dual form 403.2.h.b.222.13

$q$-expansion

\(f(q)\) \(=\) \(q+1.55799 q^{2} +(-1.19850 - 2.07586i) q^{3} +0.427341 q^{4} +(-0.908804 + 1.57410i) q^{5} +(-1.86725 - 3.23417i) q^{6} +(-1.80502 - 3.12639i) q^{7} -2.45019 q^{8} +(-1.37279 + 2.37775i) q^{9} +O(q^{10})\) \(q+1.55799 q^{2} +(-1.19850 - 2.07586i) q^{3} +0.427341 q^{4} +(-0.908804 + 1.57410i) q^{5} +(-1.86725 - 3.23417i) q^{6} +(-1.80502 - 3.12639i) q^{7} -2.45019 q^{8} +(-1.37279 + 2.37775i) q^{9} +(-1.41591 + 2.45243i) q^{10} +(-0.657884 + 1.13949i) q^{11} +(-0.512167 - 0.887099i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(-2.81221 - 4.87090i) q^{14} +4.35680 q^{15} -4.67206 q^{16} +(-0.822939 - 1.42537i) q^{17} +(-2.13880 + 3.70451i) q^{18} +(-3.67118 - 6.35867i) q^{19} +(-0.388369 + 0.672675i) q^{20} +(-4.32663 + 7.49395i) q^{21} +(-1.02498 + 1.77532i) q^{22} +2.76670 q^{23} +(2.93655 + 5.08625i) q^{24} +(0.848150 + 1.46904i) q^{25} +(-0.778996 + 1.34926i) q^{26} -0.609825 q^{27} +(-0.771360 - 1.33603i) q^{28} +0.753167 q^{29} +6.78786 q^{30} +(3.74350 - 4.12143i) q^{31} -2.37865 q^{32} +3.15389 q^{33} +(-1.28213 - 2.22072i) q^{34} +6.56165 q^{35} +(-0.586650 + 1.01611i) q^{36} +(0.869574 + 1.50615i) q^{37} +(-5.71967 - 9.90677i) q^{38} +2.39700 q^{39} +(2.22674 - 3.85683i) q^{40} +(1.45616 - 2.52214i) q^{41} +(-6.74086 + 11.6755i) q^{42} +(-4.15151 - 7.19062i) q^{43} +(-0.281141 + 0.486950i) q^{44} +(-2.49520 - 4.32182i) q^{45} +4.31049 q^{46} +4.25594 q^{47} +(5.59945 + 9.69854i) q^{48} +(-3.01622 + 5.22425i) q^{49} +(1.32141 + 2.28875i) q^{50} +(-1.97258 + 3.41661i) q^{51} +(-0.213670 + 0.370088i) q^{52} +(4.95058 - 8.57466i) q^{53} -0.950103 q^{54} +(-1.19578 - 2.07114i) q^{55} +(4.42265 + 7.66026i) q^{56} +(-8.79981 + 15.2417i) q^{57} +1.17343 q^{58} +(2.40825 + 4.17121i) q^{59} +1.86184 q^{60} -10.1129 q^{61} +(5.83235 - 6.42116i) q^{62} +9.91170 q^{63} +5.63820 q^{64} +(-0.908804 - 1.57410i) q^{65} +4.91374 q^{66} +(-0.609051 + 1.05491i) q^{67} +(-0.351675 - 0.609119i) q^{68} +(-3.31588 - 5.74328i) q^{69} +10.2230 q^{70} +(-2.33787 + 4.04931i) q^{71} +(3.36361 - 5.82594i) q^{72} +(1.17426 - 2.03388i) q^{73} +(1.35479 + 2.34656i) q^{74} +(2.03301 - 3.52128i) q^{75} +(-1.56885 - 2.71732i) q^{76} +4.74999 q^{77} +3.73450 q^{78} +(-5.15237 - 8.92417i) q^{79} +(4.24599 - 7.35427i) q^{80} +(4.84926 + 8.39916i) q^{81} +(2.26868 - 3.92947i) q^{82} +(1.38928 - 2.40631i) q^{83} +(-1.84895 + 3.20247i) q^{84} +2.99156 q^{85} +(-6.46802 - 11.2029i) q^{86} +(-0.902669 - 1.56347i) q^{87} +(1.61194 - 2.79197i) q^{88} -15.2748 q^{89} +(-3.88751 - 6.73336i) q^{90} +3.61005 q^{91} +1.18232 q^{92} +(-13.0421 - 2.83145i) q^{93} +6.63073 q^{94} +13.3455 q^{95} +(2.85081 + 4.93775i) q^{96} +14.0402 q^{97} +(-4.69925 + 8.13934i) q^{98} +(-1.80628 - 3.12857i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34q + 6q^{2} - 2q^{3} + 34q^{4} - 5q^{5} - 2q^{7} + 36q^{8} - 23q^{9} + O(q^{10}) \) \( 34q + 6q^{2} - 2q^{3} + 34q^{4} - 5q^{5} - 2q^{7} + 36q^{8} - 23q^{9} - 7q^{10} - 5q^{11} - 28q^{12} - 17q^{13} - 7q^{14} + 8q^{15} + 18q^{16} - 8q^{17} + 6q^{18} + 3q^{19} - 8q^{20} + 13q^{21} + 12q^{22} - 14q^{23} - 6q^{24} - 26q^{25} - 3q^{26} + 28q^{27} - 7q^{28} - 18q^{29} - 60q^{30} - 9q^{31} + 58q^{32} - 14q^{33} - 15q^{34} + 50q^{35} - 49q^{36} - 6q^{37} + 2q^{38} + 4q^{39} - 29q^{40} - 5q^{41} + 8q^{42} - q^{43} - 22q^{44} + 13q^{45} + 34q^{46} + 16q^{47} - 49q^{48} + 3q^{49} - 35q^{51} - 17q^{52} + 30q^{53} - 2q^{54} + 21q^{55} - 7q^{56} + 34q^{58} - 9q^{59} - 38q^{60} - 28q^{61} - 62q^{62} + 88q^{63} + 56q^{64} - 5q^{65} + 140q^{66} - 31q^{67} - 39q^{68} + 5q^{69} + 56q^{70} + q^{71} - 32q^{72} - 10q^{73} - 39q^{74} - 2q^{75} - 16q^{76} + 76q^{77} - 23q^{79} - 22q^{80} - 29q^{81} - 10q^{82} + 3q^{83} + 52q^{84} - 32q^{85} + 4q^{86} + 18q^{87} - 10q^{88} + 26q^{89} + 35q^{90} + 4q^{91} - 94q^{92} - 41q^{93} + 70q^{94} + 28q^{95} - 23q^{96} + 32q^{97} - 38q^{98} - 70q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).

\(n\) \(249\) \(313\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.55799 1.10167 0.550834 0.834615i \(-0.314310\pi\)
0.550834 + 0.834615i \(0.314310\pi\)
\(3\) −1.19850 2.07586i −0.691953 1.19850i −0.971197 0.238278i \(-0.923417\pi\)
0.279244 0.960220i \(-0.409916\pi\)
\(4\) 0.427341 0.213670
\(5\) −0.908804 + 1.57410i −0.406430 + 0.703957i −0.994487 0.104863i \(-0.966560\pi\)
0.588057 + 0.808819i \(0.299893\pi\)
\(6\) −1.86725 3.23417i −0.762302 1.32035i
\(7\) −1.80502 3.12639i −0.682235 1.18167i −0.974297 0.225266i \(-0.927675\pi\)
0.292063 0.956399i \(-0.405658\pi\)
\(8\) −2.45019 −0.866274
\(9\) −1.37279 + 2.37775i −0.457598 + 0.792583i
\(10\) −1.41591 + 2.45243i −0.447750 + 0.775526i
\(11\) −0.657884 + 1.13949i −0.198360 + 0.343569i −0.947997 0.318280i \(-0.896895\pi\)
0.749637 + 0.661849i \(0.230228\pi\)
\(12\) −0.512167 0.887099i −0.147850 0.256083i
\(13\) −0.500000 + 0.866025i −0.138675 + 0.240192i
\(14\) −2.81221 4.87090i −0.751596 1.30180i
\(15\) 4.35680 1.12492
\(16\) −4.67206 −1.16802
\(17\) −0.822939 1.42537i −0.199592 0.345704i 0.748804 0.662791i \(-0.230628\pi\)
−0.948396 + 0.317088i \(0.897295\pi\)
\(18\) −2.13880 + 3.70451i −0.504121 + 0.873162i
\(19\) −3.67118 6.35867i −0.842227 1.45878i −0.888008 0.459828i \(-0.847911\pi\)
0.0457808 0.998952i \(-0.485422\pi\)
\(20\) −0.388369 + 0.672675i −0.0868419 + 0.150415i
\(21\) −4.32663 + 7.49395i −0.944149 + 1.63531i
\(22\) −1.02498 + 1.77532i −0.218526 + 0.378498i
\(23\) 2.76670 0.576896 0.288448 0.957495i \(-0.406861\pi\)
0.288448 + 0.957495i \(0.406861\pi\)
\(24\) 2.93655 + 5.08625i 0.599421 + 1.03823i
\(25\) 0.848150 + 1.46904i 0.169630 + 0.293808i
\(26\) −0.778996 + 1.34926i −0.152774 + 0.264612i
\(27\) −0.609825 −0.117361
\(28\) −0.771360 1.33603i −0.145773 0.252487i
\(29\) 0.753167 0.139860 0.0699298 0.997552i \(-0.477722\pi\)
0.0699298 + 0.997552i \(0.477722\pi\)
\(30\) 6.78786 1.23929
\(31\) 3.74350 4.12143i 0.672353 0.740231i
\(32\) −2.37865 −0.420490
\(33\) 3.15389 0.549022
\(34\) −1.28213 2.22072i −0.219884 0.380850i
\(35\) 6.56165 1.10912
\(36\) −0.586650 + 1.01611i −0.0977751 + 0.169351i
\(37\) 0.869574 + 1.50615i 0.142957 + 0.247609i 0.928609 0.371060i \(-0.121006\pi\)
−0.785652 + 0.618669i \(0.787672\pi\)
\(38\) −5.71967 9.90677i −0.927854 1.60709i
\(39\) 2.39700 0.383826
\(40\) 2.22674 3.85683i 0.352079 0.609819i
\(41\) 1.45616 2.52214i 0.227413 0.393891i −0.729627 0.683845i \(-0.760307\pi\)
0.957041 + 0.289954i \(0.0936398\pi\)
\(42\) −6.74086 + 11.6755i −1.04014 + 1.80157i
\(43\) −4.15151 7.19062i −0.633099 1.09656i −0.986914 0.161245i \(-0.948449\pi\)
0.353815 0.935315i \(-0.384884\pi\)
\(44\) −0.281141 + 0.486950i −0.0423835 + 0.0734104i
\(45\) −2.49520 4.32182i −0.371963 0.644258i
\(46\) 4.31049 0.635548
\(47\) 4.25594 0.620793 0.310396 0.950607i \(-0.399538\pi\)
0.310396 + 0.950607i \(0.399538\pi\)
\(48\) 5.59945 + 9.69854i 0.808212 + 1.39986i
\(49\) −3.01622 + 5.22425i −0.430889 + 0.746321i
\(50\) 1.32141 + 2.28875i 0.186876 + 0.323678i
\(51\) −1.97258 + 3.41661i −0.276217 + 0.478421i
\(52\) −0.213670 + 0.370088i −0.0296307 + 0.0513219i
\(53\) 4.95058 8.57466i 0.680015 1.17782i −0.294961 0.955509i \(-0.595307\pi\)
0.974976 0.222311i \(-0.0713600\pi\)
\(54\) −0.950103 −0.129293
\(55\) −1.19578 2.07114i −0.161238 0.279273i
\(56\) 4.42265 + 7.66026i 0.591002 + 1.02365i
\(57\) −8.79981 + 15.2417i −1.16556 + 2.01881i
\(58\) 1.17343 0.154079
\(59\) 2.40825 + 4.17121i 0.313528 + 0.543046i 0.979123 0.203267i \(-0.0651558\pi\)
−0.665596 + 0.746312i \(0.731823\pi\)
\(60\) 1.86184 0.240362
\(61\) −10.1129 −1.29483 −0.647415 0.762138i \(-0.724150\pi\)
−0.647415 + 0.762138i \(0.724150\pi\)
\(62\) 5.83235 6.42116i 0.740709 0.815488i
\(63\) 9.91170 1.24876
\(64\) 5.63820 0.704775
\(65\) −0.908804 1.57410i −0.112723 0.195242i
\(66\) 4.91374 0.604839
\(67\) −0.609051 + 1.05491i −0.0744074 + 0.128877i −0.900828 0.434175i \(-0.857040\pi\)
0.826421 + 0.563053i \(0.190373\pi\)
\(68\) −0.351675 0.609119i −0.0426469 0.0738666i
\(69\) −3.31588 5.74328i −0.399185 0.691409i
\(70\) 10.2230 1.22188
\(71\) −2.33787 + 4.04931i −0.277454 + 0.480565i −0.970751 0.240087i \(-0.922824\pi\)
0.693297 + 0.720652i \(0.256157\pi\)
\(72\) 3.36361 5.82594i 0.396405 0.686594i
\(73\) 1.17426 2.03388i 0.137437 0.238048i −0.789089 0.614279i \(-0.789447\pi\)
0.926526 + 0.376231i \(0.122780\pi\)
\(74\) 1.35479 + 2.34656i 0.157491 + 0.272783i
\(75\) 2.03301 3.52128i 0.234752 0.406602i
\(76\) −1.56885 2.71732i −0.179959 0.311698i
\(77\) 4.74999 0.541311
\(78\) 3.73450 0.422849
\(79\) −5.15237 8.92417i −0.579687 1.00405i −0.995515 0.0946040i \(-0.969842\pi\)
0.415828 0.909443i \(-0.363492\pi\)
\(80\) 4.24599 7.35427i 0.474716 0.822232i
\(81\) 4.84926 + 8.39916i 0.538806 + 0.933240i
\(82\) 2.26868 3.92947i 0.250534 0.433937i
\(83\) 1.38928 2.40631i 0.152494 0.264127i −0.779650 0.626216i \(-0.784603\pi\)
0.932144 + 0.362089i \(0.117936\pi\)
\(84\) −1.84895 + 3.20247i −0.201737 + 0.349418i
\(85\) 2.99156 0.324481
\(86\) −6.46802 11.2029i −0.697464 1.20804i
\(87\) −0.902669 1.56347i −0.0967763 0.167622i
\(88\) 1.61194 2.79197i 0.171834 0.297625i
\(89\) −15.2748 −1.61913 −0.809563 0.587033i \(-0.800296\pi\)
−0.809563 + 0.587033i \(0.800296\pi\)
\(90\) −3.88751 6.73336i −0.409779 0.709758i
\(91\) 3.61005 0.378436
\(92\) 1.18232 0.123266
\(93\) −13.0421 2.83145i −1.35240 0.293608i
\(94\) 6.63073 0.683907
\(95\) 13.3455 1.36922
\(96\) 2.85081 + 4.93775i 0.290960 + 0.503957i
\(97\) 14.0402 1.42557 0.712785 0.701382i \(-0.247433\pi\)
0.712785 + 0.701382i \(0.247433\pi\)
\(98\) −4.69925 + 8.13934i −0.474696 + 0.822197i
\(99\) −1.80628 3.12857i −0.181538 0.314433i
\(100\) 0.362449 + 0.627780i 0.0362449 + 0.0627780i
\(101\) 9.11956 0.907430 0.453715 0.891147i \(-0.350098\pi\)
0.453715 + 0.891147i \(0.350098\pi\)
\(102\) −3.07327 + 5.32306i −0.304299 + 0.527061i
\(103\) 1.77800 3.07958i 0.175191 0.303440i −0.765036 0.643987i \(-0.777279\pi\)
0.940227 + 0.340547i \(0.110612\pi\)
\(104\) 1.22510 2.12193i 0.120131 0.208072i
\(105\) −7.86413 13.6211i −0.767460 1.32928i
\(106\) 7.71297 13.3593i 0.749150 1.29757i
\(107\) 5.51002 + 9.54364i 0.532674 + 0.922618i 0.999272 + 0.0381489i \(0.0121461\pi\)
−0.466598 + 0.884469i \(0.654521\pi\)
\(108\) −0.260603 −0.0250765
\(109\) −17.6509 −1.69065 −0.845326 0.534250i \(-0.820594\pi\)
−0.845326 + 0.534250i \(0.820594\pi\)
\(110\) −1.86301 3.22683i −0.177631 0.307666i
\(111\) 2.08437 3.61023i 0.197839 0.342668i
\(112\) 8.43318 + 14.6067i 0.796861 + 1.38020i
\(113\) −2.95440 + 5.11717i −0.277926 + 0.481383i −0.970869 0.239610i \(-0.922980\pi\)
0.692943 + 0.720993i \(0.256314\pi\)
\(114\) −13.7100 + 23.7465i −1.28406 + 2.22406i
\(115\) −2.51439 + 4.35505i −0.234468 + 0.406110i
\(116\) 0.321859 0.0298839
\(117\) −1.37279 2.37775i −0.126915 0.219823i
\(118\) 3.75204 + 6.49872i 0.345403 + 0.598256i
\(119\) −2.97085 + 5.14566i −0.272337 + 0.471702i
\(120\) −10.6750 −0.974489
\(121\) 4.63438 + 8.02698i 0.421307 + 0.729725i
\(122\) −15.7559 −1.42647
\(123\) −6.98080 −0.629437
\(124\) 1.59975 1.76125i 0.143662 0.158165i
\(125\) −12.1713 −1.08863
\(126\) 15.4424 1.37571
\(127\) 7.95139 + 13.7722i 0.705572 + 1.22209i 0.966485 + 0.256724i \(0.0826431\pi\)
−0.260913 + 0.965362i \(0.584024\pi\)
\(128\) 13.5416 1.19692
\(129\) −9.95115 + 17.2359i −0.876150 + 1.51754i
\(130\) −1.41591 2.45243i −0.124184 0.215092i
\(131\) −8.44698 14.6306i −0.738016 1.27828i −0.953387 0.301749i \(-0.902429\pi\)
0.215371 0.976532i \(-0.430904\pi\)
\(132\) 1.34779 0.117310
\(133\) −13.2531 + 22.9551i −1.14919 + 1.99046i
\(134\) −0.948897 + 1.64354i −0.0819722 + 0.141980i
\(135\) 0.554212 0.959923i 0.0476989 0.0826170i
\(136\) 2.01636 + 3.49244i 0.172901 + 0.299474i
\(137\) −4.65469 + 8.06215i −0.397677 + 0.688796i −0.993439 0.114365i \(-0.963517\pi\)
0.595762 + 0.803161i \(0.296850\pi\)
\(138\) −5.16612 8.94798i −0.439769 0.761703i
\(139\) −10.8658 −0.921623 −0.460811 0.887498i \(-0.652442\pi\)
−0.460811 + 0.887498i \(0.652442\pi\)
\(140\) 2.80406 0.236986
\(141\) −5.10074 8.83474i −0.429560 0.744019i
\(142\) −3.64239 + 6.30880i −0.305662 + 0.529423i
\(143\) −0.657884 1.13949i −0.0550150 0.0952888i
\(144\) 6.41378 11.1090i 0.534481 0.925749i
\(145\) −0.684482 + 1.18556i −0.0568431 + 0.0984552i
\(146\) 1.82949 3.16877i 0.151410 0.262250i
\(147\) 14.4597 1.19262
\(148\) 0.371604 + 0.643637i 0.0305457 + 0.0529067i
\(149\) −6.60854 11.4463i −0.541392 0.937719i −0.998824 0.0484746i \(-0.984564\pi\)
0.457432 0.889245i \(-0.348769\pi\)
\(150\) 3.16742 5.48613i 0.258618 0.447940i
\(151\) −5.14020 −0.418304 −0.209152 0.977883i \(-0.567070\pi\)
−0.209152 + 0.977883i \(0.567070\pi\)
\(152\) 8.99510 + 15.5800i 0.729599 + 1.26370i
\(153\) 4.51890 0.365332
\(154\) 7.40044 0.596345
\(155\) 3.08542 + 9.63820i 0.247827 + 0.774159i
\(156\) 1.02433 0.0820123
\(157\) 18.3368 1.46344 0.731720 0.681606i \(-0.238718\pi\)
0.731720 + 0.681606i \(0.238718\pi\)
\(158\) −8.02735 13.9038i −0.638622 1.10613i
\(159\) −23.7330 −1.88215
\(160\) 2.16173 3.74423i 0.170900 0.296007i
\(161\) −4.99396 8.64978i −0.393579 0.681698i
\(162\) 7.55510 + 13.0858i 0.593585 + 1.02812i
\(163\) −7.63039 −0.597658 −0.298829 0.954307i \(-0.596596\pi\)
−0.298829 + 0.954307i \(0.596596\pi\)
\(164\) 0.622274 1.07781i 0.0485915 0.0841629i
\(165\) −2.86627 + 4.96452i −0.223139 + 0.386488i
\(166\) 2.16449 3.74901i 0.167997 0.290980i
\(167\) −6.39847 11.0825i −0.495128 0.857587i 0.504856 0.863204i \(-0.331546\pi\)
−0.999984 + 0.00561623i \(0.998212\pi\)
\(168\) 10.6011 18.3616i 0.817891 1.41663i
\(169\) −0.500000 0.866025i −0.0384615 0.0666173i
\(170\) 4.66083 0.357469
\(171\) 20.1591 1.54161
\(172\) −1.77411 3.07285i −0.135274 0.234302i
\(173\) 7.90130 13.6855i 0.600725 1.04049i −0.391987 0.919971i \(-0.628212\pi\)
0.992712 0.120515i \(-0.0384546\pi\)
\(174\) −1.40635 2.43587i −0.106615 0.184663i
\(175\) 3.06186 5.30330i 0.231455 0.400892i
\(176\) 3.07368 5.32376i 0.231687 0.401294i
\(177\) 5.77257 9.99838i 0.433893 0.751524i
\(178\) −23.7980 −1.78374
\(179\) −4.39967 7.62046i −0.328847 0.569580i 0.653436 0.756981i \(-0.273327\pi\)
−0.982283 + 0.187402i \(0.939993\pi\)
\(180\) −1.06630 1.84689i −0.0794774 0.137659i
\(181\) −8.00823 + 13.8707i −0.595247 + 1.03100i 0.398265 + 0.917270i \(0.369612\pi\)
−0.993512 + 0.113728i \(0.963721\pi\)
\(182\) 5.62443 0.416910
\(183\) 12.1203 + 20.9930i 0.895961 + 1.55185i
\(184\) −6.77894 −0.499750
\(185\) −3.16109 −0.232408
\(186\) −20.3195 4.41138i −1.48990 0.323458i
\(187\) 2.16559 0.158364
\(188\) 1.81874 0.132645
\(189\) 1.10075 + 1.90655i 0.0800677 + 0.138681i
\(190\) 20.7923 1.50843
\(191\) −8.40550 + 14.5587i −0.608200 + 1.05343i 0.383337 + 0.923609i \(0.374775\pi\)
−0.991537 + 0.129825i \(0.958558\pi\)
\(192\) −6.75737 11.7041i −0.487671 0.844671i
\(193\) −10.9057 18.8892i −0.785009 1.35967i −0.928994 0.370095i \(-0.879325\pi\)
0.143985 0.989580i \(-0.454008\pi\)
\(194\) 21.8746 1.57050
\(195\) −2.17840 + 3.77310i −0.155998 + 0.270197i
\(196\) −1.28895 + 2.23253i −0.0920681 + 0.159467i
\(197\) −0.395261 + 0.684613i −0.0281612 + 0.0487766i −0.879763 0.475413i \(-0.842299\pi\)
0.851601 + 0.524190i \(0.175632\pi\)
\(198\) −2.81417 4.87428i −0.199994 0.346400i
\(199\) 9.59845 16.6250i 0.680416 1.17852i −0.294438 0.955671i \(-0.595132\pi\)
0.974854 0.222845i \(-0.0715343\pi\)
\(200\) −2.07813 3.59943i −0.146946 0.254518i
\(201\) 2.91978 0.205946
\(202\) 14.2082 0.999686
\(203\) −1.35948 2.35470i −0.0954171 0.165267i
\(204\) −0.842964 + 1.46006i −0.0590193 + 0.102224i
\(205\) 2.64672 + 4.58425i 0.184855 + 0.320178i
\(206\) 2.77011 4.79797i 0.193002 0.334290i
\(207\) −3.79811 + 6.57851i −0.263987 + 0.457238i
\(208\) 2.33603 4.04612i 0.161975 0.280548i
\(209\) 9.66085 0.668255
\(210\) −12.2522 21.2215i −0.845485 1.46442i
\(211\) 9.22963 + 15.9862i 0.635394 + 1.10053i 0.986432 + 0.164173i \(0.0524955\pi\)
−0.351038 + 0.936361i \(0.614171\pi\)
\(212\) 2.11558 3.66430i 0.145299 0.251665i
\(213\) 11.2077 0.767942
\(214\) 8.58457 + 14.8689i 0.586829 + 1.01642i
\(215\) 15.0916 1.02924
\(216\) 1.49419 0.101667
\(217\) −19.6423 4.26437i −1.33341 0.289484i
\(218\) −27.5000 −1.86254
\(219\) −5.62941 −0.380400
\(220\) −0.511004 0.885084i −0.0344518 0.0596724i
\(221\) 1.64588 0.110714
\(222\) 3.24743 5.62471i 0.217953 0.377506i
\(223\) 6.02421 + 10.4342i 0.403411 + 0.698728i 0.994135 0.108145i \(-0.0344911\pi\)
−0.590724 + 0.806874i \(0.701158\pi\)
\(224\) 4.29352 + 7.43660i 0.286873 + 0.496879i
\(225\) −4.65734 −0.310489
\(226\) −4.60293 + 7.97251i −0.306182 + 0.530323i
\(227\) 4.79198 8.29995i 0.318055 0.550887i −0.662027 0.749480i \(-0.730304\pi\)
0.980082 + 0.198593i \(0.0636370\pi\)
\(228\) −3.76051 + 6.51340i −0.249046 + 0.431361i
\(229\) −1.50303 2.60333i −0.0993231 0.172033i 0.812082 0.583544i \(-0.198334\pi\)
−0.911405 + 0.411511i \(0.865001\pi\)
\(230\) −3.91740 + 6.78513i −0.258305 + 0.447398i
\(231\) −5.69285 9.86030i −0.374562 0.648760i
\(232\) −1.84540 −0.121157
\(233\) 23.6608 1.55007 0.775034 0.631920i \(-0.217733\pi\)
0.775034 + 0.631920i \(0.217733\pi\)
\(234\) −2.13880 3.70451i −0.139818 0.242172i
\(235\) −3.86782 + 6.69926i −0.252309 + 0.437011i
\(236\) 1.02914 + 1.78253i 0.0669915 + 0.116033i
\(237\) −12.3502 + 21.3912i −0.802232 + 1.38951i
\(238\) −4.62856 + 8.01690i −0.300025 + 0.519659i
\(239\) 0.991011 1.71648i 0.0641032 0.111030i −0.832193 0.554487i \(-0.812915\pi\)
0.896296 + 0.443457i \(0.146248\pi\)
\(240\) −20.3552 −1.31392
\(241\) −12.3362 21.3669i −0.794643 1.37636i −0.923066 0.384643i \(-0.874325\pi\)
0.128422 0.991720i \(-0.459009\pi\)
\(242\) 7.22032 + 12.5060i 0.464140 + 0.803914i
\(243\) 10.7089 18.5484i 0.686977 1.18988i
\(244\) −4.32167 −0.276667
\(245\) −5.48231 9.49563i −0.350252 0.606654i
\(246\) −10.8760 −0.693430
\(247\) 7.34236 0.467183
\(248\) −9.17229 + 10.0983i −0.582441 + 0.641243i
\(249\) −6.66021 −0.422074
\(250\) −18.9627 −1.19931
\(251\) 9.59668 + 16.6219i 0.605737 + 1.04917i 0.991935 + 0.126751i \(0.0404550\pi\)
−0.386197 + 0.922416i \(0.626212\pi\)
\(252\) 4.23567 0.266822
\(253\) −1.82017 + 3.15262i −0.114433 + 0.198204i
\(254\) 12.3882 + 21.4570i 0.777305 + 1.34633i
\(255\) −3.58538 6.21006i −0.224525 0.388889i
\(256\) 9.82128 0.613830
\(257\) 13.9975 24.2444i 0.873141 1.51232i 0.0144108 0.999896i \(-0.495413\pi\)
0.858730 0.512428i \(-0.171254\pi\)
\(258\) −15.5038 + 26.8534i −0.965225 + 1.67182i
\(259\) 3.13920 5.43726i 0.195061 0.337855i
\(260\) −0.388369 0.672675i −0.0240856 0.0417175i
\(261\) −1.03394 + 1.79084i −0.0639995 + 0.110850i
\(262\) −13.1603 22.7944i −0.813048 1.40824i
\(263\) 2.79753 0.172503 0.0862514 0.996273i \(-0.472511\pi\)
0.0862514 + 0.996273i \(0.472511\pi\)
\(264\) −7.72764 −0.475603
\(265\) 8.99822 + 15.5854i 0.552756 + 0.957402i
\(266\) −20.6483 + 35.7639i −1.26603 + 2.19282i
\(267\) 18.3068 + 31.7083i 1.12036 + 1.94052i
\(268\) −0.260272 + 0.450805i −0.0158987 + 0.0275373i
\(269\) 12.4313 21.5316i 0.757948 1.31280i −0.185947 0.982560i \(-0.559535\pi\)
0.943895 0.330245i \(-0.107131\pi\)
\(270\) 0.863457 1.49555i 0.0525483 0.0910164i
\(271\) −20.9959 −1.27541 −0.637704 0.770281i \(-0.720116\pi\)
−0.637704 + 0.770281i \(0.720116\pi\)
\(272\) 3.84482 + 6.65943i 0.233127 + 0.403787i
\(273\) −4.32663 7.49395i −0.261860 0.453554i
\(274\) −7.25197 + 12.5608i −0.438107 + 0.758824i
\(275\) −2.23194 −0.134591
\(276\) −1.41701 2.45433i −0.0852940 0.147734i
\(277\) 5.93564 0.356638 0.178319 0.983973i \(-0.442934\pi\)
0.178319 + 0.983973i \(0.442934\pi\)
\(278\) −16.9288 −1.01532
\(279\) 4.66067 + 14.5590i 0.279027 + 0.871623i
\(280\) −16.0773 −0.960803
\(281\) 6.61510 0.394624 0.197312 0.980341i \(-0.436779\pi\)
0.197312 + 0.980341i \(0.436779\pi\)
\(282\) −7.94691 13.7645i −0.473232 0.819661i
\(283\) 6.44100 0.382878 0.191439 0.981505i \(-0.438685\pi\)
0.191439 + 0.981505i \(0.438685\pi\)
\(284\) −0.999068 + 1.73044i −0.0592838 + 0.102682i
\(285\) −15.9946 27.7035i −0.947439 1.64101i
\(286\) −1.02498 1.77532i −0.0606083 0.104977i
\(287\) −10.5136 −0.620597
\(288\) 3.26540 5.65584i 0.192416 0.333274i
\(289\) 7.14554 12.3764i 0.420326 0.728026i
\(290\) −1.06642 + 1.84709i −0.0626222 + 0.108465i
\(291\) −16.8272 29.1456i −0.986428 1.70854i
\(292\) 0.501810 0.869161i 0.0293662 0.0508638i
\(293\) −13.4604 23.3142i −0.786367 1.36203i −0.928179 0.372135i \(-0.878626\pi\)
0.141811 0.989894i \(-0.454707\pi\)
\(294\) 22.5282 1.31387
\(295\) −8.75451 −0.509708
\(296\) −2.13062 3.69035i −0.123840 0.214497i
\(297\) 0.401194 0.694889i 0.0232797 0.0403215i
\(298\) −10.2961 17.8333i −0.596434 1.03305i
\(299\) −1.38335 + 2.39603i −0.0800011 + 0.138566i
\(300\) 0.868788 1.50479i 0.0501595 0.0868788i
\(301\) −14.9871 + 25.9585i −0.863845 + 1.49622i
\(302\) −8.00839 −0.460831
\(303\) −10.9298 18.9309i −0.627899 1.08755i
\(304\) 17.1520 + 29.7081i 0.983734 + 1.70388i
\(305\) 9.19068 15.9187i 0.526257 0.911504i
\(306\) 7.04042 0.402474
\(307\) 4.92019 + 8.52203i 0.280810 + 0.486378i 0.971585 0.236693i \(-0.0760635\pi\)
−0.690774 + 0.723071i \(0.742730\pi\)
\(308\) 2.02986 0.115662
\(309\) −8.52371 −0.484897
\(310\) 4.80705 + 15.0162i 0.273022 + 0.852865i
\(311\) 25.0139 1.41841 0.709205 0.705002i \(-0.249054\pi\)
0.709205 + 0.705002i \(0.249054\pi\)
\(312\) −5.87310 −0.332499
\(313\) −4.59944 7.96647i −0.259976 0.450291i 0.706259 0.707953i \(-0.250381\pi\)
−0.966235 + 0.257662i \(0.917048\pi\)
\(314\) 28.5687 1.61222
\(315\) −9.00780 + 15.6020i −0.507532 + 0.879071i
\(316\) −2.20182 3.81366i −0.123862 0.214535i
\(317\) 13.6909 + 23.7134i 0.768958 + 1.33187i 0.938128 + 0.346288i \(0.112558\pi\)
−0.169170 + 0.985587i \(0.554109\pi\)
\(318\) −36.9759 −2.07351
\(319\) −0.495497 + 0.858226i −0.0277425 + 0.0480514i
\(320\) −5.12402 + 8.87506i −0.286441 + 0.496131i
\(321\) 13.2075 22.8761i 0.737171 1.27682i
\(322\) −7.78054 13.4763i −0.433593 0.751005i
\(323\) −6.04232 + 10.4656i −0.336204 + 0.582322i
\(324\) 2.07228 + 3.58930i 0.115127 + 0.199406i
\(325\) −1.69630 −0.0940938
\(326\) −11.8881 −0.658421
\(327\) 21.1546 + 36.6409i 1.16985 + 2.02624i
\(328\) −3.56786 + 6.17971i −0.197002 + 0.341218i
\(329\) −7.68208 13.3057i −0.423527 0.733570i
\(330\) −4.46563 + 7.73469i −0.245825 + 0.425781i
\(331\) −8.55812 + 14.8231i −0.470397 + 0.814751i −0.999427 0.0338522i \(-0.989222\pi\)
0.529030 + 0.848603i \(0.322556\pi\)
\(332\) 0.593697 1.02831i 0.0325834 0.0564360i
\(333\) −4.77498 −0.261667
\(334\) −9.96876 17.2664i −0.545467 0.944776i
\(335\) −1.10702 1.91741i −0.0604828 0.104759i
\(336\) 20.2143 35.0122i 1.10278 1.91007i
\(337\) 9.62912 0.524531 0.262266 0.964996i \(-0.415530\pi\)
0.262266 + 0.964996i \(0.415530\pi\)
\(338\) −0.778996 1.34926i −0.0423718 0.0733901i
\(339\) 14.1634 0.769248
\(340\) 1.27842 0.0693318
\(341\) 2.23354 + 6.97710i 0.120953 + 0.377831i
\(342\) 31.4077 1.69834
\(343\) −3.49294 −0.188601
\(344\) 10.1720 + 17.6184i 0.548437 + 0.949921i
\(345\) 12.0539 0.648963
\(346\) 12.3102 21.3218i 0.661799 1.14627i
\(347\) −5.38246 9.32270i −0.288946 0.500469i 0.684613 0.728907i \(-0.259971\pi\)
−0.973558 + 0.228438i \(0.926638\pi\)
\(348\) −0.385747 0.668134i −0.0206782 0.0358157i
\(349\) −6.64494 −0.355695 −0.177848 0.984058i \(-0.556913\pi\)
−0.177848 + 0.984058i \(0.556913\pi\)
\(350\) 4.77036 8.26250i 0.254986 0.441649i
\(351\) 0.304913 0.528124i 0.0162750 0.0281892i
\(352\) 1.56488 2.71045i 0.0834083 0.144467i
\(353\) 15.3324 + 26.5564i 0.816059 + 1.41346i 0.908565 + 0.417744i \(0.137179\pi\)
−0.0925054 + 0.995712i \(0.529488\pi\)
\(354\) 8.99362 15.5774i 0.478005 0.827929i
\(355\) −4.24934 7.36007i −0.225531 0.390632i
\(356\) −6.52754 −0.345959
\(357\) 14.2422 0.753778
\(358\) −6.85466 11.8726i −0.362280 0.627487i
\(359\) 9.03091 15.6420i 0.476633 0.825553i −0.523008 0.852328i \(-0.675190\pi\)
0.999641 + 0.0267748i \(0.00852369\pi\)
\(360\) 6.11372 + 10.5893i 0.322221 + 0.558104i
\(361\) −17.4552 + 30.2332i −0.918693 + 1.59122i
\(362\) −12.4768 + 21.6104i −0.655764 + 1.13582i
\(363\) 11.1086 19.2406i 0.583049 1.00987i
\(364\) 1.54272 0.0808605
\(365\) 2.13435 + 3.69680i 0.111717 + 0.193499i
\(366\) 18.8834 + 32.7070i 0.987051 + 1.70962i
\(367\) 7.52229 13.0290i 0.392660 0.680108i −0.600139 0.799896i \(-0.704888\pi\)
0.992799 + 0.119788i \(0.0382215\pi\)
\(368\) −12.9262 −0.673824
\(369\) 3.99800 + 6.92474i 0.208128 + 0.360488i
\(370\) −4.92495 −0.256036
\(371\) −35.7437 −1.85572
\(372\) −5.57341 1.20999i −0.288968 0.0627353i
\(373\) 18.4221 0.953861 0.476930 0.878941i \(-0.341749\pi\)
0.476930 + 0.878941i \(0.341749\pi\)
\(374\) 3.37398 0.174464
\(375\) 14.5872 + 25.2658i 0.753281 + 1.30472i
\(376\) −10.4279 −0.537777
\(377\) −0.376584 + 0.652262i −0.0193950 + 0.0335932i
\(378\) 1.71496 + 2.97039i 0.0882079 + 0.152781i
\(379\) 11.8445 + 20.5153i 0.608411 + 1.05380i 0.991502 + 0.130089i \(0.0415262\pi\)
−0.383091 + 0.923711i \(0.625141\pi\)
\(380\) 5.70309 0.292562
\(381\) 19.0594 33.0119i 0.976445 1.69125i
\(382\) −13.0957 + 22.6824i −0.670034 + 1.16053i
\(383\) 17.4730 30.2641i 0.892829 1.54642i 0.0563600 0.998411i \(-0.482051\pi\)
0.836469 0.548014i \(-0.184616\pi\)
\(384\) −16.2296 28.1104i −0.828211 1.43450i
\(385\) −4.31681 + 7.47693i −0.220005 + 0.381060i
\(386\) −16.9910 29.4292i −0.864818 1.49791i
\(387\) 22.7967 1.15882
\(388\) 5.99996 0.304602
\(389\) −5.56378 9.63675i −0.282095 0.488603i 0.689806 0.723995i \(-0.257696\pi\)
−0.971901 + 0.235392i \(0.924363\pi\)
\(390\) −3.39393 + 5.87846i −0.171858 + 0.297667i
\(391\) −2.27682 3.94358i −0.115144 0.199435i
\(392\) 7.39032 12.8004i 0.373267 0.646518i
\(393\) −20.2474 + 35.0695i −1.02135 + 1.76902i
\(394\) −0.615814 + 1.06662i −0.0310243 + 0.0537356i
\(395\) 18.7300 0.942408
\(396\) −0.771896 1.33696i −0.0387892 0.0671849i
\(397\) −15.3987 26.6714i −0.772840 1.33860i −0.936000 0.351999i \(-0.885502\pi\)
0.163160 0.986600i \(-0.447831\pi\)
\(398\) 14.9543 25.9016i 0.749592 1.29833i
\(399\) 63.5354 3.18075
\(400\) −3.96261 6.86344i −0.198130 0.343172i
\(401\) 27.2777 1.36218 0.681091 0.732199i \(-0.261506\pi\)
0.681091 + 0.732199i \(0.261506\pi\)
\(402\) 4.54900 0.226884
\(403\) 1.69751 + 5.30268i 0.0845592 + 0.264145i
\(404\) 3.89716 0.193891
\(405\) −17.6281 −0.875947
\(406\) −2.11807 3.66860i −0.105118 0.182070i
\(407\) −2.28832 −0.113428
\(408\) 4.83320 8.37135i 0.239279 0.414444i
\(409\) 15.1406 + 26.2242i 0.748652 + 1.29670i 0.948469 + 0.316870i \(0.102632\pi\)
−0.199817 + 0.979833i \(0.564035\pi\)
\(410\) 4.12357 + 7.14223i 0.203649 + 0.352730i
\(411\) 22.3145 1.10069
\(412\) 0.759811 1.31603i 0.0374332 0.0648362i
\(413\) 8.69390 15.0583i 0.427799 0.740969i
\(414\) −5.91742 + 10.2493i −0.290825 + 0.503724i
\(415\) 2.52517 + 4.37373i 0.123956 + 0.214698i
\(416\) 1.18933 2.05997i 0.0583115 0.100999i
\(417\) 13.0226 + 22.5558i 0.637720 + 1.10456i
\(418\) 15.0515 0.736195
\(419\) 34.1128 1.66652 0.833261 0.552881i \(-0.186471\pi\)
0.833261 + 0.552881i \(0.186471\pi\)
\(420\) −3.36066 5.82083i −0.163983 0.284028i
\(421\) −10.9407 + 18.9498i −0.533216 + 0.923557i 0.466032 + 0.884768i \(0.345683\pi\)
−0.999247 + 0.0387886i \(0.987650\pi\)
\(422\) 14.3797 + 24.9064i 0.699992 + 1.21242i
\(423\) −5.84253 + 10.1196i −0.284074 + 0.492030i
\(424\) −12.1299 + 21.0096i −0.589079 + 1.02031i
\(425\) 1.39595 2.41786i 0.0677136 0.117283i
\(426\) 17.4616 0.846016
\(427\) 18.2541 + 31.6170i 0.883378 + 1.53006i
\(428\) 2.35466 + 4.07838i 0.113817 + 0.197136i
\(429\) −1.57695 + 2.73135i −0.0761356 + 0.131871i
\(430\) 23.5127 1.13388
\(431\) −13.7622 23.8368i −0.662902 1.14818i −0.979850 0.199737i \(-0.935991\pi\)
0.316948 0.948443i \(-0.397342\pi\)
\(432\) 2.84914 0.137079
\(433\) 3.53679 0.169967 0.0849835 0.996382i \(-0.472916\pi\)
0.0849835 + 0.996382i \(0.472916\pi\)
\(434\) −30.6026 6.64386i −1.46897 0.318915i
\(435\) 3.28140 0.157331
\(436\) −7.54296 −0.361242
\(437\) −10.1571 17.5925i −0.485878 0.841565i
\(438\) −8.77057 −0.419074
\(439\) −10.5977 + 18.3557i −0.505799 + 0.876070i 0.494178 + 0.869361i \(0.335469\pi\)
−0.999977 + 0.00670944i \(0.997864\pi\)
\(440\) 2.92988 + 5.07470i 0.139677 + 0.241927i
\(441\) −8.28130 14.3436i −0.394347 0.683030i
\(442\) 2.56427 0.121970
\(443\) −2.70926 + 4.69257i −0.128721 + 0.222951i −0.923181 0.384365i \(-0.874420\pi\)
0.794461 + 0.607316i \(0.207754\pi\)
\(444\) 0.890734 1.54280i 0.0422724 0.0732179i
\(445\) 13.8818 24.0440i 0.658061 1.13979i
\(446\) 9.38568 + 16.2565i 0.444425 + 0.769766i
\(447\) −15.8406 + 27.4368i −0.749236 + 1.29772i
\(448\) −10.1771 17.6272i −0.480822 0.832808i
\(449\) −9.81440 −0.463170 −0.231585 0.972815i \(-0.574391\pi\)
−0.231585 + 0.972815i \(0.574391\pi\)
\(450\) −7.25610 −0.342056
\(451\) 1.91596 + 3.31855i 0.0902192 + 0.156264i
\(452\) −1.26253 + 2.18677i −0.0593846 + 0.102857i
\(453\) 6.16052 + 10.6703i 0.289446 + 0.501336i
\(454\) 7.46587 12.9313i 0.350391 0.606894i
\(455\) −3.28083 + 5.68256i −0.153807 + 0.266402i
\(456\) 21.5612 37.3451i 1.00970 1.74885i
\(457\) 3.45047 0.161406 0.0807031 0.996738i \(-0.474283\pi\)
0.0807031 + 0.996738i \(0.474283\pi\)
\(458\) −2.34171 4.05596i −0.109421 0.189523i
\(459\) 0.501849 + 0.869228i 0.0234243 + 0.0405721i
\(460\) −1.07450 + 1.86109i −0.0500988 + 0.0867737i
\(461\) −28.8701 −1.34462 −0.672308 0.740272i \(-0.734697\pi\)
−0.672308 + 0.740272i \(0.734697\pi\)
\(462\) −8.86941 15.3623i −0.412642 0.714718i
\(463\) 3.37024 0.156628 0.0783141 0.996929i \(-0.475046\pi\)
0.0783141 + 0.996929i \(0.475046\pi\)
\(464\) −3.51884 −0.163358
\(465\) 16.3097 17.9563i 0.756343 0.832701i
\(466\) 36.8633 1.70766
\(467\) −4.74977 −0.219793 −0.109897 0.993943i \(-0.535052\pi\)
−0.109897 + 0.993943i \(0.535052\pi\)
\(468\) −0.586650 1.01611i −0.0271179 0.0469696i
\(469\) 4.39741 0.203053
\(470\) −6.02603 + 10.4374i −0.277960 + 0.481441i
\(471\) −21.9767 38.0647i −1.01263 1.75393i
\(472\) −5.90068 10.2203i −0.271601 0.470426i
\(473\) 10.9248 0.502325
\(474\) −19.2415 + 33.3273i −0.883793 + 1.53077i
\(475\) 6.22743 10.7862i 0.285734 0.494906i
\(476\) −1.26956 + 2.19895i −0.0581904 + 0.100789i
\(477\) 13.5923 + 23.5425i 0.622347 + 1.07794i
\(478\) 1.54399 2.67426i 0.0706203 0.122318i
\(479\) −3.43966 5.95766i −0.157162 0.272212i 0.776682 0.629893i \(-0.216901\pi\)
−0.933844 + 0.357680i \(0.883568\pi\)
\(480\) −10.3633 −0.473018
\(481\) −1.73915 −0.0792983
\(482\) −19.2197 33.2894i −0.875432 1.51629i
\(483\) −11.9705 + 20.7335i −0.544676 + 0.943407i
\(484\) 1.98046 + 3.43025i 0.0900208 + 0.155921i
\(485\) −12.7598 + 22.1007i −0.579394 + 1.00354i
\(486\) 16.6844 28.8982i 0.756820 1.31085i
\(487\) 10.7364 18.5961i 0.486515 0.842668i −0.513365 0.858170i \(-0.671601\pi\)
0.999880 + 0.0155020i \(0.00493463\pi\)
\(488\) 24.7786 1.12168
\(489\) 9.14501 + 15.8396i 0.413552 + 0.716292i
\(490\) −8.54139 14.7941i −0.385861 0.668330i
\(491\) 2.75897 4.77868i 0.124511 0.215659i −0.797031 0.603938i \(-0.793597\pi\)
0.921542 + 0.388280i \(0.126931\pi\)
\(492\) −2.98318 −0.134492
\(493\) −0.619811 1.07354i −0.0279149 0.0483500i
\(494\) 11.4393 0.514681
\(495\) 6.56621 0.295129
\(496\) −17.4899 + 19.2556i −0.785318 + 0.864601i
\(497\) 16.8797 0.757156
\(498\) −10.3766 −0.464985
\(499\) −11.7781 20.4003i −0.527261 0.913243i −0.999495 0.0317696i \(-0.989886\pi\)
0.472234 0.881473i \(-0.343448\pi\)
\(500\) −5.20127 −0.232608
\(501\) −15.3371 + 26.5646i −0.685211 + 1.18682i
\(502\) 14.9516 + 25.8969i 0.667321 + 1.15583i
\(503\) −0.951184 1.64750i −0.0424112 0.0734584i 0.844041 0.536279i \(-0.180171\pi\)
−0.886452 + 0.462821i \(0.846837\pi\)
\(504\) −24.2856 −1.08177
\(505\) −8.28789 + 14.3551i −0.368806 + 0.638791i
\(506\) −2.83581 + 4.91176i −0.126067 + 0.218354i
\(507\) −1.19850 + 2.07586i −0.0532272 + 0.0921921i
\(508\) 3.39795 + 5.88542i 0.150760 + 0.261123i
\(509\) 3.94397 6.83116i 0.174814 0.302786i −0.765283 0.643694i \(-0.777401\pi\)
0.940097 + 0.340908i \(0.110734\pi\)
\(510\) −5.58600 9.67523i −0.247352 0.428426i
\(511\) −8.47829 −0.375057
\(512\) −11.7817 −0.520682
\(513\) 2.23878 + 3.87768i 0.0988445 + 0.171204i
\(514\) 21.8080 37.7726i 0.961911 1.66608i
\(515\) 3.23170 + 5.59747i 0.142406 + 0.246654i
\(516\) −4.25253 + 7.36560i −0.187207 + 0.324252i
\(517\) −2.79992 + 4.84960i −0.123140 + 0.213285i
\(518\) 4.89086 8.47121i 0.214892 0.372204i
\(519\) −37.8788 −1.66269
\(520\) 2.22674 + 3.85683i 0.0976492 + 0.169133i
\(521\) −0.441868 0.765338i −0.0193586 0.0335301i 0.856184 0.516671i \(-0.172829\pi\)
−0.875542 + 0.483141i \(0.839496\pi\)
\(522\) −1.61088 + 2.79012i −0.0705061 + 0.122120i
\(523\) −31.5128 −1.37796 −0.688980 0.724780i \(-0.741941\pi\)
−0.688980 + 0.724780i \(0.741941\pi\)
\(524\) −3.60974 6.25225i −0.157692 0.273131i
\(525\) −14.6785 −0.640624
\(526\) 4.35852 0.190041
\(527\) −8.95525 1.94420i −0.390097 0.0846905i
\(528\) −14.7352 −0.641266
\(529\) −15.3454 −0.667190
\(530\) 14.0192 + 24.2819i 0.608953 + 1.05474i
\(531\) −13.2241 −0.573878
\(532\) −5.66360 + 9.80965i −0.245548 + 0.425302i
\(533\) 1.45616 + 2.52214i 0.0630731 + 0.109246i
\(534\) 28.5219 + 49.4014i 1.23426 + 2.13781i
\(535\) −20.0301 −0.865978
\(536\) 1.49229 2.58472i 0.0644572 0.111643i
\(537\) −10.5460 + 18.2662i −0.455093 + 0.788245i
\(538\) 19.3678 33.5461i 0.835007 1.44627i
\(539\) −3.96865 6.87390i −0.170942 0.296080i
\(540\) 0.236837 0.410214i 0.0101918 0.0176528i
\(541\) −2.46123 4.26298i −0.105817 0.183280i 0.808255 0.588833i \(-0.200412\pi\)
−0.914072 + 0.405553i \(0.867079\pi\)
\(542\) −32.7114 −1.40508
\(543\) 38.3914 1.64753
\(544\) 1.95749 + 3.39047i 0.0839266 + 0.145365i
\(545\) 16.0412 27.7842i 0.687131 1.19015i
\(546\) −6.74086 11.6755i −0.288482 0.499666i
\(547\) −10.7523 + 18.6235i −0.459735 + 0.796284i −0.998947 0.0458861i \(-0.985389\pi\)
0.539212 + 0.842170i \(0.318722\pi\)
\(548\) −1.98914 + 3.44529i −0.0849717 + 0.147175i
\(549\) 13.8830 24.0460i 0.592511 1.02626i
\(550\) −3.47734 −0.148274
\(551\) −2.76501 4.78915i −0.117794 0.204024i
\(552\) 8.12455 + 14.0721i 0.345804 + 0.598949i
\(553\) −18.6003 + 32.2167i −0.790965 + 1.36999i
\(554\) 9.24768 0.392896
\(555\) 3.78856 + 6.56198i 0.160815 + 0.278540i
\(556\) −4.64339 −0.196923
\(557\) −28.9206 −1.22541 −0.612703 0.790313i \(-0.709918\pi\)
−0.612703 + 0.790313i \(0.709918\pi\)
\(558\) 7.26130 + 22.6828i 0.307395 + 0.960239i
\(559\) 8.30302 0.351180
\(560\) −30.6564 −1.29547
\(561\) −2.59546 4.49547i −0.109580 0.189799i
\(562\) 10.3063 0.434744
\(563\) −6.39717 + 11.0802i −0.269609 + 0.466976i −0.968761 0.247997i \(-0.920228\pi\)
0.699152 + 0.714973i \(0.253561\pi\)
\(564\) −2.17975 3.77544i −0.0917841 0.158975i
\(565\) −5.36994 9.30101i −0.225915 0.391296i
\(566\) 10.0350 0.421804
\(567\) 17.5060 30.3214i 0.735185 1.27338i
\(568\) 5.72823 9.92159i 0.240351 0.416301i
\(569\) −19.8445 + 34.3716i −0.831923 + 1.44093i 0.0645884 + 0.997912i \(0.479427\pi\)
−0.896511 + 0.443021i \(0.853907\pi\)
\(570\) −24.9195 43.1618i −1.04376 1.80785i
\(571\) −4.43236 + 7.67707i −0.185488 + 0.321275i −0.943741 0.330686i \(-0.892720\pi\)
0.758253 + 0.651961i \(0.226053\pi\)
\(572\) −0.281141 0.486950i −0.0117551 0.0203604i
\(573\) 40.2959 1.68338
\(574\) −16.3801 −0.683691
\(575\) 2.34657 + 4.06439i 0.0978589 + 0.169497i
\(576\) −7.74008 + 13.4062i −0.322504 + 0.558593i
\(577\) 14.0345 + 24.3084i 0.584263 + 1.01197i 0.994967 + 0.100205i \(0.0319498\pi\)
−0.410704 + 0.911769i \(0.634717\pi\)
\(578\) 11.1327 19.2824i 0.463059 0.802042i
\(579\) −26.1409 + 45.2773i −1.08638 + 1.88166i
\(580\) −0.292507 + 0.506637i −0.0121457 + 0.0210369i
\(581\) −10.0308 −0.416146
\(582\) −26.2166 45.4086i −1.08672 1.88225i
\(583\) 6.51382 + 11.2823i 0.269775 + 0.467264i
\(584\) −2.87717 + 4.98340i −0.119058 + 0.206215i
\(585\) 4.99040 0.206328
\(586\) −20.9713 36.3233i −0.866315 1.50050i
\(587\) −17.8159 −0.735341 −0.367670 0.929956i \(-0.619845\pi\)
−0.367670 + 0.929956i \(0.619845\pi\)
\(588\) 6.17923 0.254827
\(589\) −39.9499 8.67318i −1.64611 0.357372i
\(590\) −13.6395 −0.561528
\(591\) 1.89488 0.0779449
\(592\) −4.06270 7.03681i −0.166976 0.289211i
\(593\) 15.9926 0.656738 0.328369 0.944550i \(-0.393501\pi\)
0.328369 + 0.944550i \(0.393501\pi\)
\(594\) 0.625058 1.08263i 0.0256464 0.0444209i
\(595\) −5.39984 9.35280i −0.221372 0.383427i
\(596\) −2.82410 4.89148i −0.115679 0.200363i
\(597\) −46.0149 −1.88326
\(598\) −2.15525 + 3.73300i −0.0881346 + 0.152654i
\(599\) −2.70591 + 4.68678i −0.110561 + 0.191497i −0.915996 0.401186i \(-0.868598\pi\)
0.805436 + 0.592683i \(0.201931\pi\)
\(600\) −4.98127 + 8.62781i −0.203359 + 0.352229i
\(601\) 4.85581 + 8.41051i 0.198073 + 0.343072i 0.947903 0.318558i \(-0.103198\pi\)
−0.749831 + 0.661630i \(0.769865\pi\)
\(602\) −23.3499 + 40.4431i −0.951669 + 1.64834i
\(603\) −1.67220 2.89634i −0.0680974 0.117948i
\(604\) −2.19662 −0.0893790
\(605\) −16.8470 −0.684927
\(606\) −17.0285 29.4942i −0.691735 1.19812i
\(607\) 10.4110 18.0323i 0.422568 0.731909i −0.573622 0.819120i \(-0.694462\pi\)
0.996190 + 0.0872109i \(0.0277954\pi\)
\(608\) 8.73247 + 15.1251i 0.354148 + 0.613403i
\(609\) −3.25868 + 5.64420i −0.132048 + 0.228714i
\(610\) 14.3190 24.8013i 0.579760 1.00417i
\(611\) −2.12797 + 3.68575i −0.0860885 + 0.149110i
\(612\) 1.93111 0.0780605
\(613\) 2.22287 + 3.85012i 0.0897807 + 0.155505i 0.907418 0.420228i \(-0.138050\pi\)
−0.817638 + 0.575733i \(0.804717\pi\)
\(614\) 7.66563 + 13.2773i 0.309359 + 0.535826i
\(615\) 6.34418 10.9884i 0.255822 0.443097i
\(616\) −11.6384 −0.468924
\(617\) 3.30069 + 5.71696i 0.132881 + 0.230156i 0.924786 0.380488i \(-0.124244\pi\)
−0.791905 + 0.610644i \(0.790911\pi\)
\(618\) −13.2799 −0.534195
\(619\) −25.5318 −1.02621 −0.513105 0.858326i \(-0.671505\pi\)
−0.513105 + 0.858326i \(0.671505\pi\)
\(620\) 1.31852 + 4.11879i 0.0529532 + 0.165415i
\(621\) −1.68720 −0.0677051
\(622\) 38.9715 1.56262
\(623\) 27.5714 + 47.7550i 1.10462 + 1.91327i
\(624\) −11.1989 −0.448315
\(625\) 6.82053 11.8135i 0.272821 0.472540i
\(626\) −7.16590 12.4117i −0.286407 0.496071i
\(627\) −11.5785 20.0546i −0.462401 0.800902i
\(628\) 7.83608 0.312694
\(629\) 1.43121 2.47893i 0.0570662 0.0988416i
\(630\) −14.0341 + 24.3077i −0.559131 + 0.968443i
\(631\) 18.1864 31.4998i 0.723989 1.25399i −0.235399 0.971899i \(-0.575640\pi\)
0.959389 0.282088i \(-0.0910269\pi\)
\(632\) 12.6243 + 21.8659i 0.502167 + 0.869780i
\(633\) 22.1234 38.3188i 0.879325 1.52304i
\(634\) 21.3303 + 36.9452i 0.847136 + 1.46728i
\(635\) −28.9050 −1.14706
\(636\) −10.1421 −0.402160
\(637\) −3.01622 5.22425i −0.119507 0.206992i
\(638\) −0.771980 + 1.33711i −0.0305630 + 0.0529367i
\(639\) −6.41883 11.1177i −0.253925 0.439811i
\(640\) −12.3066 + 21.3157i −0.486463 + 0.842578i
\(641\) 21.2262 36.7649i 0.838386 1.45213i −0.0528584 0.998602i \(-0.516833\pi\)
0.891244 0.453524i \(-0.149833\pi\)
\(642\) 20.5772 35.6407i 0.812117 1.40663i
\(643\) −23.5031 −0.926871 −0.463435 0.886131i \(-0.653383\pi\)
−0.463435 + 0.886131i \(0.653383\pi\)
\(644\) −2.13412 3.69640i −0.0840961 0.145659i
\(645\) −18.0873 31.3281i −0.712186 1.23354i
\(646\) −9.41389 + 16.3053i −0.370384 + 0.641525i
\(647\) −14.2007 −0.558289 −0.279144 0.960249i \(-0.590051\pi\)
−0.279144 + 0.960249i \(0.590051\pi\)
\(648\) −11.8816 20.5795i −0.466754 0.808441i
\(649\) −6.33740 −0.248765
\(650\) −2.64282 −0.103660
\(651\) 14.6890 + 45.8855i 0.575709 + 1.79840i
\(652\) −3.26078 −0.127702
\(653\) 17.7704 0.695411 0.347706 0.937604i \(-0.386961\pi\)
0.347706 + 0.937604i \(0.386961\pi\)
\(654\) 32.9587 + 57.0862i 1.28879 + 2.23225i
\(655\) 30.7066 1.19981
\(656\) −6.80325 + 11.7836i −0.265622 + 0.460071i
\(657\) 3.22404 + 5.58420i 0.125782 + 0.217861i
\(658\) −11.9686 20.7303i −0.466585 0.808149i
\(659\) 20.4374 0.796128 0.398064 0.917358i \(-0.369682\pi\)
0.398064 + 0.917358i \(0.369682\pi\)
\(660\) −1.22487 + 2.12154i −0.0476781 + 0.0825809i
\(661\) 13.3303 23.0888i 0.518489 0.898049i −0.481280 0.876567i \(-0.659828\pi\)
0.999769 0.0214823i \(-0.00683856\pi\)
\(662\) −13.3335 + 23.0943i −0.518220 + 0.897584i
\(663\) −1.97258 3.41661i −0.0766087 0.132690i
\(664\) −3.40401 + 5.89592i −0.132101 + 0.228806i
\(665\) −24.0890 41.7234i −0.934132 1.61796i
\(666\) −7.43939 −0.288270
\(667\) 2.08379 0.0806845
\(668\) −2.73432 4.73599i −0.105794 0.183241i
\(669\) 14.4400 25.0108i 0.558283 0.966975i
\(670\) −1.72472 2.98731i −0.0666319 0.115410i
\(671\) 6.65314 11.5236i 0.256842 0.444863i
\(672\) 10.2916 17.8255i 0.397006 0.687634i
\(673\) 20.6041 35.6874i 0.794230 1.37565i −0.129097 0.991632i \(-0.541208\pi\)
0.923327 0.384015i \(-0.125459\pi\)
\(674\) 15.0021 0.577859
\(675\) −0.517223 0.895857i −0.0199079 0.0344815i
\(676\) −0.213670 0.370088i −0.00821809 0.0142341i
\(677\) −11.4837 + 19.8903i −0.441354 + 0.764448i −0.997790 0.0664425i \(-0.978835\pi\)
0.556436 + 0.830890i \(0.312168\pi\)
\(678\) 22.0664 0.847455
\(679\) −25.3430 43.8953i −0.972574 1.68455i
\(680\) −7.32990 −0.281089
\(681\) −22.9727 −0.880316
\(682\) 3.47983 + 10.8703i 0.133250 + 0.416244i
\(683\) −1.53543 −0.0587514 −0.0293757 0.999568i \(-0.509352\pi\)
−0.0293757 + 0.999568i \(0.509352\pi\)
\(684\) 8.61480 0.329395
\(685\) −8.46040 14.6538i −0.323255 0.559894i
\(686\) −5.44197 −0.207775
\(687\) −3.60276 + 6.24016i −0.137454 + 0.238077i
\(688\) 19.3961 + 33.5950i 0.739469 + 1.28080i
\(689\) 4.95058 + 8.57466i 0.188602 + 0.326669i
\(690\) 18.7800 0.714941
\(691\) 11.5992 20.0904i 0.441255 0.764277i −0.556528 0.830829i \(-0.687867\pi\)
0.997783 + 0.0665525i \(0.0212000\pi\)
\(692\) 3.37655 5.84835i 0.128357 0.222321i
\(693\) −6.52075 + 11.2943i −0.247703 + 0.429034i
\(694\) −8.38583 14.5247i −0.318322 0.551350i
\(695\) 9.87486 17.1038i 0.374575 0.648783i
\(696\) 2.21171 + 3.83080i 0.0838348 + 0.145206i
\(697\) −4.79331 −0.181560
\(698\) −10.3528 −0.391858
\(699\) −28.3574 49.1164i −1.07257 1.85775i
\(700\) 1.30846 2.26631i 0.0494550 0.0856586i
\(701\) −3.24748 5.62480i −0.122656 0.212446i 0.798159 0.602447i \(-0.205808\pi\)
−0.920814 + 0.390002i \(0.872474\pi\)
\(702\) 0.475051 0.822813i 0.0179297 0.0310551i
\(703\) 6.38473 11.0587i 0.240805 0.417086i
\(704\) −3.70928 + 6.42466i −0.139799 + 0.242139i
\(705\) 18.5423 0.698343
\(706\) 23.8877 + 41.3747i 0.899026 + 1.55716i
\(707\) −16.4610 28.5113i −0.619080 1.07228i
\(708\) 2.46685 4.27271i 0.0927100 0.160578i
\(709\) 28.3668 1.06534 0.532670 0.846323i \(-0.321189\pi\)
0.532670 + 0.846323i \(0.321189\pi\)
\(710\) −6.62043 11.4669i −0.248460 0.430346i
\(711\) 28.2926 1.06105
\(712\) 37.4262 1.40261
\(713\) 10.3571 11.4028i 0.387878 0.427037i
\(714\) 22.1893 0.830413
\(715\) 2.39155 0.0894390
\(716\) −1.88016 3.25653i −0.0702648 0.121702i
\(717\) −4.75090 −0.177425
\(718\) 14.0701 24.3701i 0.525091 0.909484i
\(719\) −12.0513 20.8734i −0.449437 0.778448i 0.548912 0.835880i \(-0.315042\pi\)
−0.998349 + 0.0574321i \(0.981709\pi\)
\(720\) 11.6577 + 20.1918i 0.434458 + 0.752504i
\(721\) −12.8373 −0.478086
\(722\) −27.1950 + 47.1031i −1.01209 + 1.75300i
\(723\) −29.5698 + 51.2163i −1.09971 + 1.90476i
\(724\) −3.42224 + 5.92749i −0.127187 + 0.220294i
\(725\) 0.638799 + 1.10643i 0.0237244 + 0.0410919i
\(726\) 17.3071 29.9768i 0.642326 1.11254i
\(727\) 15.1624 + 26.2621i 0.562343 + 0.974006i 0.997291 + 0.0735510i \(0.0234332\pi\)
−0.434949 + 0.900455i \(0.643233\pi\)
\(728\) −8.84531 −0.327829
\(729\) −22.2429 −0.823810
\(730\) 3.32530 + 5.75959i 0.123075 + 0.213172i
\(731\) −6.83288 + 11.8349i −0.252723 + 0.437729i
\(732\) 5.17951 + 8.97118i 0.191440 + 0.331584i
\(733\) −21.7834 + 37.7299i −0.804587 + 1.39358i 0.111983 + 0.993710i \(0.464280\pi\)
−0.916570 + 0.399875i \(0.869054\pi\)
\(734\) 11.7197 20.2991i 0.432581 0.749252i
\(735\) −13.1411 + 22.7610i −0.484715 + 0.839552i
\(736\) −6.58101 −0.242579
\(737\) −0.801370 1.38801i −0.0295188 0.0511281i
\(738\) 6.22886 + 10.7887i 0.229287 + 0.397137i
\(739\) −10.5002 + 18.1868i −0.386255 + 0.669014i −0.991942 0.126689i \(-0.959565\pi\)
0.605687 + 0.795703i \(0.292898\pi\)
\(740\) −1.35086 −0.0496587
\(741\) −8.79981 15.2417i −0.323269 0.559918i
\(742\) −55.6884 −2.04438
\(743\) −49.1844 −1.80440 −0.902201 0.431316i \(-0.858049\pi\)
−0.902201 + 0.431316i \(0.858049\pi\)
\(744\) 31.9556 + 6.93760i 1.17155 + 0.254345i
\(745\) 24.0235 0.880152
\(746\) 28.7015 1.05084
\(747\) 3.81440 + 6.60673i 0.139562 + 0.241728i
\(748\) 0.925446 0.0338377
\(749\) 19.8914 34.4530i 0.726817 1.25888i
\(750\) 22.7268 + 39.3639i 0.829864 + 1.43737i
\(751\) 15.8023 + 27.3704i 0.576634 + 0.998760i 0.995862 + 0.0908789i \(0.0289676\pi\)
−0.419228 + 0.907881i \(0.637699\pi\)
\(752\) −19.8840 −0.725096
\(753\) 23.0032 39.8427i 0.838283 1.45195i
\(754\) −0.586715 + 1.01622i −0.0213669 + 0.0370085i
\(755\) 4.67144 8.09116i 0.170011 0.294468i
\(756\) 0.470394 + 0.814747i 0.0171081 + 0.0296321i
\(757\) 24.9598 43.2317i 0.907181 1.57128i 0.0892186 0.996012i \(-0.471563\pi\)
0.817962 0.575272i \(-0.195104\pi\)
\(758\) 18.4536 + 31.9626i 0.670267 + 1.16094i
\(759\) 8.72586 0.316729
\(760\) −32.6991 −1.18612
\(761\) 25.1475 + 43.5567i 0.911594 + 1.57893i 0.811812 + 0.583918i \(0.198481\pi\)
0.0997821 + 0.995009i \(0.468185\pi\)
\(762\) 29.6945 51.4323i 1.07572 1.86320i
\(763\) 31.8604 + 55.1837i 1.15342 + 1.99779i
\(764\) −3.59201 + 6.22154i −0.129954 + 0.225087i
\(765\) −4.10680 + 7.11318i −0.148482 + 0.257178i
\(766\) 27.2228 47.1513i 0.983600 1.70365i
\(767\) −4.81650 −0.173914
\(768\) −11.7708 20.3876i −0.424741 0.735674i
\(769\) 10.5401 + 18.2559i 0.380085 + 0.658326i 0.991074 0.133313i \(-0.0425615\pi\)
−0.610989 + 0.791639i \(0.709228\pi\)
\(770\) −6.72555 + 11.6490i −0.242372 + 0.419801i
\(771\) −67.1040 −2.41669