Properties

Label 950.2.e.n.201.1
Level $950$
Weight $2$
Character 950.201
Analytic conductor $7.586$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
Defining polynomial: \(x^{10} + 10 x^{8} - 12 x^{7} + 85 x^{6} - 70 x^{5} + 186 x^{4} - 110 x^{3} + 285 x^{2} - 150 x + 100\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 190)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 201.1
Root \(-1.58826 + 2.75095i\) of defining polynomial
Character \(\chi\) \(=\) 950.201
Dual form 950.2.e.n.501.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-1.58826 + 2.75095i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.58826 - 2.75095i) q^{6} -4.17652 q^{7} +1.00000 q^{8} +(-3.54514 - 6.14037i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-1.58826 + 2.75095i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.58826 - 2.75095i) q^{6} -4.17652 q^{7} +1.00000 q^{8} +(-3.54514 - 6.14037i) q^{9} -3.90260 q^{11} +3.17652 q^{12} +(-0.239434 - 0.414711i) q^{13} +(2.08826 - 3.61697i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.245018 - 0.424383i) q^{17} +7.09029 q^{18} +(2.74077 + 3.38942i) q^{19} +(6.63340 - 11.4894i) q^{21} +(1.95130 - 3.37975i) q^{22} +(2.84883 + 4.93431i) q^{23} +(-1.58826 + 2.75095i) q^{24} +0.478867 q^{26} +12.9929 q^{27} +(2.08826 + 3.61697i) q^{28} +(-1.21745 - 2.10868i) q^{29} +2.42373 q^{31} +(-0.500000 - 0.866025i) q^{32} +(6.19834 - 10.7358i) q^{33} +(0.245018 + 0.424383i) q^{34} +(-3.54514 + 6.14037i) q^{36} -8.47175 q^{37} +(-4.30571 + 0.678866i) q^{38} +1.52113 q^{39} +(0.254982 - 0.441643i) q^{41} +(6.63340 + 11.4894i) q^{42} +(2.91377 - 5.04679i) q^{43} +(1.95130 + 3.37975i) q^{44} -5.69765 q^{46} +(0.485788 + 0.841410i) q^{47} +(-1.58826 - 2.75095i) q^{48} +10.4433 q^{49} +(0.778304 + 1.34806i) q^{51} +(-0.239434 + 0.414711i) q^{52} +(-2.77899 - 4.81336i) q^{53} +(-6.49644 + 11.2522i) q^{54} -4.17652 q^{56} +(-13.6772 + 2.15643i) q^{57} +2.43490 q^{58} +(3.82769 - 6.62976i) q^{59} +(4.65673 + 8.06569i) q^{61} +(-1.21187 + 2.09901i) q^{62} +(14.8064 + 25.6454i) q^{63} +1.00000 q^{64} +(6.19834 + 10.7358i) q^{66} +(-0.809957 - 1.40289i) q^{67} -0.490035 q^{68} -18.0987 q^{69} +(0.937088 - 1.62308i) q^{71} +(-3.54514 - 6.14037i) q^{72} +(2.35307 - 4.07564i) q^{73} +(4.23588 - 7.33675i) q^{74} +(1.56494 - 4.06829i) q^{76} +16.2993 q^{77} +(-0.760566 + 1.31734i) q^{78} +(-3.19984 + 5.54229i) q^{79} +(-10.0007 + 17.3216i) q^{81} +(0.254982 + 0.441643i) q^{82} -7.96179 q^{83} -13.2668 q^{84} +(2.91377 + 5.04679i) q^{86} +7.73451 q^{87} -3.90260 q^{88} +(2.76126 + 4.78264i) q^{89} +(1.00000 + 1.73205i) q^{91} +(2.84883 - 4.93431i) q^{92} +(-3.84952 + 6.66756i) q^{93} -0.971577 q^{94} +3.17652 q^{96} +(7.24499 - 12.5487i) q^{97} +(-5.22167 + 9.04419i) q^{98} +(13.8353 + 23.9634i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 5q^{2} - 5q^{4} - 10q^{7} + 10q^{8} - 5q^{9} + O(q^{10}) \) \( 10q - 5q^{2} - 5q^{4} - 10q^{7} + 10q^{8} - 5q^{9} - 6q^{11} - 2q^{13} + 5q^{14} - 5q^{16} + 4q^{17} + 10q^{18} + 11q^{19} + 20q^{21} + 3q^{22} + 13q^{23} + 4q^{26} + 36q^{27} + 5q^{28} + 2q^{29} - 8q^{31} - 5q^{32} + 2q^{33} + 4q^{34} - 5q^{36} + 10q^{37} - 13q^{38} + 16q^{39} + q^{41} + 20q^{42} + 3q^{44} - 26q^{46} - 10q^{47} - 20q^{49} + 4q^{51} - 2q^{52} + 5q^{53} - 18q^{54} - 10q^{56} - 10q^{57} - 4q^{58} + 22q^{59} - 2q^{61} + 4q^{62} + 23q^{63} + 10q^{64} + 2q^{66} + 4q^{67} - 8q^{68} - 24q^{69} - 22q^{71} - 5q^{72} + 26q^{73} - 5q^{74} + 2q^{76} + 10q^{77} - 8q^{78} + 2q^{79} - 5q^{81} + q^{82} + 12q^{83} - 40q^{84} - 20q^{87} - 6q^{88} - q^{89} + 10q^{91} + 13q^{92} + 6q^{93} + 20q^{94} + 8q^{97} + 10q^{98} + 13q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) −1.58826 + 2.75095i −0.916983 + 1.58826i −0.113011 + 0.993594i \(0.536049\pi\)
−0.803972 + 0.594667i \(0.797284\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) −1.58826 2.75095i −0.648405 1.12307i
\(7\) −4.17652 −1.57858 −0.789288 0.614023i \(-0.789550\pi\)
−0.789288 + 0.614023i \(0.789550\pi\)
\(8\) 1.00000 0.353553
\(9\) −3.54514 6.14037i −1.18171 2.04679i
\(10\) 0 0
\(11\) −3.90260 −1.17668 −0.588339 0.808614i \(-0.700218\pi\)
−0.588339 + 0.808614i \(0.700218\pi\)
\(12\) 3.17652 0.916983
\(13\) −0.239434 0.414711i −0.0664070 0.115020i 0.830910 0.556406i \(-0.187820\pi\)
−0.897317 + 0.441386i \(0.854487\pi\)
\(14\) 2.08826 3.61697i 0.558111 0.966677i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0.245018 0.424383i 0.0594255 0.102928i −0.834782 0.550580i \(-0.814406\pi\)
0.894208 + 0.447652i \(0.147740\pi\)
\(18\) 7.09029 1.67120
\(19\) 2.74077 + 3.38942i 0.628776 + 0.777587i
\(20\) 0 0
\(21\) 6.63340 11.4894i 1.44753 2.50719i
\(22\) 1.95130 3.37975i 0.416018 0.720565i
\(23\) 2.84883 + 4.93431i 0.594021 + 1.02888i 0.993684 + 0.112213i \(0.0357939\pi\)
−0.399663 + 0.916662i \(0.630873\pi\)
\(24\) −1.58826 + 2.75095i −0.324202 + 0.561535i
\(25\) 0 0
\(26\) 0.478867 0.0939136
\(27\) 12.9929 2.50048
\(28\) 2.08826 + 3.61697i 0.394644 + 0.683544i
\(29\) −1.21745 2.10868i −0.226075 0.391573i 0.730567 0.682841i \(-0.239256\pi\)
−0.956641 + 0.291269i \(0.905923\pi\)
\(30\) 0 0
\(31\) 2.42373 0.435315 0.217657 0.976025i \(-0.430158\pi\)
0.217657 + 0.976025i \(0.430158\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 6.19834 10.7358i 1.07899 1.86887i
\(34\) 0.245018 + 0.424383i 0.0420202 + 0.0727811i
\(35\) 0 0
\(36\) −3.54514 + 6.14037i −0.590857 + 1.02339i
\(37\) −8.47175 −1.39275 −0.696374 0.717679i \(-0.745204\pi\)
−0.696374 + 0.717679i \(0.745204\pi\)
\(38\) −4.30571 + 0.678866i −0.698478 + 0.110127i
\(39\) 1.52113 0.243576
\(40\) 0 0
\(41\) 0.254982 0.441643i 0.0398216 0.0689730i −0.845428 0.534090i \(-0.820654\pi\)
0.885249 + 0.465117i \(0.153988\pi\)
\(42\) 6.63340 + 11.4894i 1.02356 + 1.77285i
\(43\) 2.91377 5.04679i 0.444345 0.769629i −0.553661 0.832742i \(-0.686770\pi\)
0.998006 + 0.0631136i \(0.0201030\pi\)
\(44\) 1.95130 + 3.37975i 0.294169 + 0.509516i
\(45\) 0 0
\(46\) −5.69765 −0.840073
\(47\) 0.485788 + 0.841410i 0.0708595 + 0.122732i 0.899278 0.437377i \(-0.144092\pi\)
−0.828419 + 0.560109i \(0.810759\pi\)
\(48\) −1.58826 2.75095i −0.229246 0.397065i
\(49\) 10.4433 1.49190
\(50\) 0 0
\(51\) 0.778304 + 1.34806i 0.108984 + 0.188766i
\(52\) −0.239434 + 0.414711i −0.0332035 + 0.0575101i
\(53\) −2.77899 4.81336i −0.381724 0.661166i 0.609585 0.792721i \(-0.291336\pi\)
−0.991309 + 0.131555i \(0.958003\pi\)
\(54\) −6.49644 + 11.2522i −0.884054 + 1.53123i
\(55\) 0 0
\(56\) −4.17652 −0.558111
\(57\) −13.6772 + 2.15643i −1.81159 + 0.285627i
\(58\) 2.43490 0.319718
\(59\) 3.82769 6.62976i 0.498323 0.863121i −0.501675 0.865056i \(-0.667283\pi\)
0.999998 + 0.00193493i \(0.000615909\pi\)
\(60\) 0 0
\(61\) 4.65673 + 8.06569i 0.596233 + 1.03271i 0.993372 + 0.114947i \(0.0366697\pi\)
−0.397139 + 0.917758i \(0.629997\pi\)
\(62\) −1.21187 + 2.09901i −0.153907 + 0.266575i
\(63\) 14.8064 + 25.6454i 1.86543 + 3.23101i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 6.19834 + 10.7358i 0.762963 + 1.32149i
\(67\) −0.809957 1.40289i −0.0989520 0.171390i 0.812299 0.583241i \(-0.198216\pi\)
−0.911251 + 0.411851i \(0.864882\pi\)
\(68\) −0.490035 −0.0594255
\(69\) −18.0987 −2.17883
\(70\) 0 0
\(71\) 0.937088 1.62308i 0.111212 0.192625i −0.805047 0.593211i \(-0.797860\pi\)
0.916259 + 0.400586i \(0.131193\pi\)
\(72\) −3.54514 6.14037i −0.417799 0.723649i
\(73\) 2.35307 4.07564i 0.275406 0.477018i −0.694831 0.719173i \(-0.744521\pi\)
0.970238 + 0.242155i \(0.0778542\pi\)
\(74\) 4.23588 7.33675i 0.492411 0.852880i
\(75\) 0 0
\(76\) 1.56494 4.06829i 0.179511 0.466665i
\(77\) 16.2993 1.85748
\(78\) −0.760566 + 1.31734i −0.0861172 + 0.149159i
\(79\) −3.19984 + 5.54229i −0.360010 + 0.623556i −0.987962 0.154696i \(-0.950560\pi\)
0.627952 + 0.778252i \(0.283894\pi\)
\(80\) 0 0
\(81\) −10.0007 + 17.3216i −1.11118 + 1.92463i
\(82\) 0.254982 + 0.441643i 0.0281581 + 0.0487713i
\(83\) −7.96179 −0.873920 −0.436960 0.899481i \(-0.643945\pi\)
−0.436960 + 0.899481i \(0.643945\pi\)
\(84\) −13.2668 −1.44753
\(85\) 0 0
\(86\) 2.91377 + 5.04679i 0.314200 + 0.544210i
\(87\) 7.73451 0.829226
\(88\) −3.90260 −0.416018
\(89\) 2.76126 + 4.78264i 0.292693 + 0.506958i 0.974445 0.224624i \(-0.0721154\pi\)
−0.681753 + 0.731583i \(0.738782\pi\)
\(90\) 0 0
\(91\) 1.00000 + 1.73205i 0.104828 + 0.181568i
\(92\) 2.84883 4.93431i 0.297011 0.514438i
\(93\) −3.84952 + 6.66756i −0.399176 + 0.691394i
\(94\) −0.971577 −0.100210
\(95\) 0 0
\(96\) 3.17652 0.324202
\(97\) 7.24499 12.5487i 0.735617 1.27413i −0.218835 0.975762i \(-0.570226\pi\)
0.954452 0.298364i \(-0.0964409\pi\)
\(98\) −5.22167 + 9.04419i −0.527468 + 0.913601i
\(99\) 13.8353 + 23.9634i 1.39050 + 2.40841i
\(100\) 0 0
\(101\) 0.280362 + 0.485601i 0.0278971 + 0.0483191i 0.879637 0.475646i \(-0.157786\pi\)
−0.851740 + 0.523965i \(0.824452\pi\)
\(102\) −1.55661 −0.154127
\(103\) 12.9533 1.27633 0.638163 0.769901i \(-0.279695\pi\)
0.638163 + 0.769901i \(0.279695\pi\)
\(104\) −0.239434 0.414711i −0.0234784 0.0406658i
\(105\) 0 0
\(106\) 5.55799 0.539839
\(107\) −10.0000 −0.966736 −0.483368 0.875417i \(-0.660587\pi\)
−0.483368 + 0.875417i \(0.660587\pi\)
\(108\) −6.49644 11.2522i −0.625121 1.08274i
\(109\) 4.83191 8.36911i 0.462813 0.801616i −0.536287 0.844036i \(-0.680173\pi\)
0.999100 + 0.0424201i \(0.0135068\pi\)
\(110\) 0 0
\(111\) 13.4554 23.3054i 1.27713 2.21205i
\(112\) 2.08826 3.61697i 0.197322 0.341772i
\(113\) −5.17920 −0.487218 −0.243609 0.969874i \(-0.578331\pi\)
−0.243609 + 0.969874i \(0.578331\pi\)
\(114\) 4.97106 12.9230i 0.465583 1.21035i
\(115\) 0 0
\(116\) −1.21745 + 2.10868i −0.113037 + 0.195786i
\(117\) −1.69765 + 2.94042i −0.156948 + 0.271842i
\(118\) 3.82769 + 6.62976i 0.352368 + 0.610319i
\(119\) −1.02332 + 1.77244i −0.0938077 + 0.162480i
\(120\) 0 0
\(121\) 4.23028 0.384571
\(122\) −9.31345 −0.843200
\(123\) 0.809957 + 1.40289i 0.0730314 + 0.126494i
\(124\) −1.21187 2.09901i −0.108829 0.188497i
\(125\) 0 0
\(126\) −29.6127 −2.63811
\(127\) 2.35526 + 4.07943i 0.208996 + 0.361991i 0.951398 0.307963i \(-0.0996472\pi\)
−0.742403 + 0.669954i \(0.766314\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 9.25564 + 16.0312i 0.814914 + 1.41147i
\(130\) 0 0
\(131\) −6.65454 + 11.5260i −0.581410 + 1.00703i 0.413903 + 0.910321i \(0.364165\pi\)
−0.995313 + 0.0967100i \(0.969168\pi\)
\(132\) −12.3967 −1.07899
\(133\) −11.4469 14.1560i −0.992571 1.22748i
\(134\) 1.61991 0.139939
\(135\) 0 0
\(136\) 0.245018 0.424383i 0.0210101 0.0363905i
\(137\) 0.194290 + 0.336520i 0.0165993 + 0.0287508i 0.874206 0.485556i \(-0.161383\pi\)
−0.857606 + 0.514307i \(0.828049\pi\)
\(138\) 9.04936 15.6740i 0.770333 1.33426i
\(139\) −8.82058 15.2777i −0.748152 1.29584i −0.948708 0.316155i \(-0.897608\pi\)
0.200556 0.979682i \(-0.435725\pi\)
\(140\) 0 0
\(141\) −3.08623 −0.259908
\(142\) 0.937088 + 1.62308i 0.0786386 + 0.136206i
\(143\) 0.934414 + 1.61845i 0.0781396 + 0.135342i
\(144\) 7.09029 0.590857
\(145\) 0 0
\(146\) 2.35307 + 4.07564i 0.194742 + 0.337303i
\(147\) −16.5867 + 28.7291i −1.36805 + 2.36953i
\(148\) 4.23588 + 7.33675i 0.348187 + 0.603077i
\(149\) 7.64556 13.2425i 0.626349 1.08487i −0.361930 0.932205i \(-0.617882\pi\)
0.988278 0.152662i \(-0.0487846\pi\)
\(150\) 0 0
\(151\) 16.6266 1.35306 0.676528 0.736416i \(-0.263484\pi\)
0.676528 + 0.736416i \(0.263484\pi\)
\(152\) 2.74077 + 3.38942i 0.222306 + 0.274918i
\(153\) −3.47449 −0.280896
\(154\) −8.14964 + 14.1156i −0.656717 + 1.13747i
\(155\) 0 0
\(156\) −0.760566 1.31734i −0.0608940 0.105472i
\(157\) 6.08401 10.5378i 0.485557 0.841010i −0.514305 0.857607i \(-0.671950\pi\)
0.999862 + 0.0165976i \(0.00528343\pi\)
\(158\) −3.19984 5.54229i −0.254566 0.440921i
\(159\) 17.6551 1.40014
\(160\) 0 0
\(161\) −11.8982 20.6083i −0.937708 1.62416i
\(162\) −10.0007 17.3216i −0.785726 1.36092i
\(163\) −14.4674 −1.13317 −0.566586 0.824002i \(-0.691736\pi\)
−0.566586 + 0.824002i \(0.691736\pi\)
\(164\) −0.509965 −0.0398216
\(165\) 0 0
\(166\) 3.98089 6.89511i 0.308977 0.535164i
\(167\) −1.64911 2.85635i −0.127612 0.221031i 0.795139 0.606428i \(-0.207398\pi\)
−0.922751 + 0.385397i \(0.874065\pi\)
\(168\) 6.63340 11.4894i 0.511778 0.886426i
\(169\) 6.38534 11.0597i 0.491180 0.850749i
\(170\) 0 0
\(171\) 11.0959 28.8453i 0.848523 2.20586i
\(172\) −5.82753 −0.444345
\(173\) 4.96668 8.60255i 0.377610 0.654040i −0.613104 0.790002i \(-0.710079\pi\)
0.990714 + 0.135963i \(0.0434127\pi\)
\(174\) −3.86725 + 6.69828i −0.293176 + 0.507795i
\(175\) 0 0
\(176\) 1.95130 3.37975i 0.147085 0.254758i
\(177\) 12.1588 + 21.0596i 0.913908 + 1.58293i
\(178\) −5.52251 −0.413930
\(179\) −10.7923 −0.806656 −0.403328 0.915056i \(-0.632147\pi\)
−0.403328 + 0.915056i \(0.632147\pi\)
\(180\) 0 0
\(181\) −5.95907 10.3214i −0.442934 0.767185i 0.554971 0.831869i \(-0.312729\pi\)
−0.997906 + 0.0646847i \(0.979396\pi\)
\(182\) −2.00000 −0.148250
\(183\) −29.5844 −2.18694
\(184\) 2.84883 + 4.93431i 0.210018 + 0.363762i
\(185\) 0 0
\(186\) −3.84952 6.66756i −0.282260 0.488889i
\(187\) −0.956205 + 1.65620i −0.0699247 + 0.121113i
\(188\) 0.485788 0.841410i 0.0354297 0.0613661i
\(189\) −54.2651 −3.94720
\(190\) 0 0
\(191\) −4.86980 −0.352366 −0.176183 0.984357i \(-0.556375\pi\)
−0.176183 + 0.984357i \(0.556375\pi\)
\(192\) −1.58826 + 2.75095i −0.114623 + 0.198533i
\(193\) 10.8919 18.8653i 0.784017 1.35796i −0.145568 0.989348i \(-0.546501\pi\)
0.929585 0.368609i \(-0.120166\pi\)
\(194\) 7.24499 + 12.5487i 0.520160 + 0.900943i
\(195\) 0 0
\(196\) −5.22167 9.04419i −0.372976 0.646014i
\(197\) 13.7359 0.978642 0.489321 0.872104i \(-0.337245\pi\)
0.489321 + 0.872104i \(0.337245\pi\)
\(198\) −27.6705 −1.96646
\(199\) −10.4433 18.0884i −0.740308 1.28225i −0.952355 0.304992i \(-0.901346\pi\)
0.212047 0.977259i \(-0.431987\pi\)
\(200\) 0 0
\(201\) 5.14569 0.362949
\(202\) −0.560724 −0.0394524
\(203\) 5.08470 + 8.80697i 0.356876 + 0.618128i
\(204\) 0.778304 1.34806i 0.0544921 0.0943832i
\(205\) 0 0
\(206\) −6.47665 + 11.2179i −0.451249 + 0.781587i
\(207\) 20.1990 34.9857i 1.40393 2.43167i
\(208\) 0.478867 0.0332035
\(209\) −10.6961 13.2276i −0.739867 0.914969i
\(210\) 0 0
\(211\) 8.30571 14.3859i 0.571789 0.990367i −0.424594 0.905384i \(-0.639583\pi\)
0.996382 0.0849830i \(-0.0270836\pi\)
\(212\) −2.77899 + 4.81336i −0.190862 + 0.330583i
\(213\) 2.97668 + 5.15576i 0.203959 + 0.353267i
\(214\) 5.00000 8.66025i 0.341793 0.592003i
\(215\) 0 0
\(216\) 12.9929 0.884054
\(217\) −10.1228 −0.687178
\(218\) 4.83191 + 8.36911i 0.327258 + 0.566828i
\(219\) 7.47459 + 12.9464i 0.505086 + 0.874835i
\(220\) 0 0
\(221\) −0.234662 −0.0157851
\(222\) 13.4554 + 23.3054i 0.903064 + 1.56415i
\(223\) −5.08826 + 8.81313i −0.340735 + 0.590171i −0.984569 0.174994i \(-0.944009\pi\)
0.643834 + 0.765165i \(0.277343\pi\)
\(224\) 2.08826 + 3.61697i 0.139528 + 0.241669i
\(225\) 0 0
\(226\) 2.58960 4.48531i 0.172257 0.298359i
\(227\) −8.50963 −0.564804 −0.282402 0.959296i \(-0.591131\pi\)
−0.282402 + 0.959296i \(0.591131\pi\)
\(228\) 8.70612 + 10.7666i 0.576577 + 0.713033i
\(229\) −6.80760 −0.449859 −0.224930 0.974375i \(-0.572215\pi\)
−0.224930 + 0.974375i \(0.572215\pi\)
\(230\) 0 0
\(231\) −25.8875 + 44.8385i −1.70327 + 2.95016i
\(232\) −1.21745 2.10868i −0.0799295 0.138442i
\(233\) −12.5225 + 21.6896i −0.820375 + 1.42093i 0.0850282 + 0.996379i \(0.472902\pi\)
−0.905403 + 0.424553i \(0.860431\pi\)
\(234\) −1.69765 2.94042i −0.110979 0.192221i
\(235\) 0 0
\(236\) −7.65539 −0.498323
\(237\) −10.1644 17.6052i −0.660247 1.14358i
\(238\) −1.02332 1.77244i −0.0663321 0.114890i
\(239\) 21.4122 1.38504 0.692519 0.721400i \(-0.256501\pi\)
0.692519 + 0.721400i \(0.256501\pi\)
\(240\) 0 0
\(241\) −5.64540 9.77811i −0.363652 0.629864i 0.624907 0.780699i \(-0.285137\pi\)
−0.988559 + 0.150836i \(0.951804\pi\)
\(242\) −2.11514 + 3.66353i −0.135966 + 0.235500i
\(243\) −12.2780 21.2661i −0.787633 1.36422i
\(244\) 4.65673 8.06569i 0.298116 0.516353i
\(245\) 0 0
\(246\) −1.61991 −0.103282
\(247\) 0.749399 1.94817i 0.0476831 0.123959i
\(248\) 2.42373 0.153907
\(249\) 12.6454 21.9025i 0.801369 1.38801i
\(250\) 0 0
\(251\) 8.08892 + 14.0104i 0.510568 + 0.884330i 0.999925 + 0.0122463i \(0.00389820\pi\)
−0.489357 + 0.872084i \(0.662768\pi\)
\(252\) 14.8064 25.6454i 0.932714 1.61551i
\(253\) −11.1178 19.2566i −0.698972 1.21065i
\(254\) −4.71052 −0.295565
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 4.92085 + 8.52316i 0.306954 + 0.531660i 0.977694 0.210032i \(-0.0673569\pi\)
−0.670740 + 0.741692i \(0.734024\pi\)
\(258\) −18.5113 −1.15246
\(259\) 35.3825 2.19856
\(260\) 0 0
\(261\) −8.63207 + 14.9512i −0.534312 + 0.925455i
\(262\) −6.65454 11.5260i −0.411119 0.712078i
\(263\) 14.1329 24.4789i 0.871471 1.50943i 0.0109968 0.999940i \(-0.496500\pi\)
0.860475 0.509493i \(-0.170167\pi\)
\(264\) 6.19834 10.7358i 0.381482 0.660746i
\(265\) 0 0
\(266\) 17.9829 2.83530i 1.10260 0.173843i
\(267\) −17.5424 −1.07358
\(268\) −0.809957 + 1.40289i −0.0494760 + 0.0856950i
\(269\) −16.1099 + 27.9031i −0.982237 + 1.70128i −0.328614 + 0.944464i \(0.606582\pi\)
−0.653623 + 0.756820i \(0.726752\pi\)
\(270\) 0 0
\(271\) 5.35390 9.27322i 0.325226 0.563308i −0.656332 0.754472i \(-0.727893\pi\)
0.981558 + 0.191164i \(0.0612262\pi\)
\(272\) 0.245018 + 0.424383i 0.0148564 + 0.0257320i
\(273\) −6.35304 −0.384504
\(274\) −0.388580 −0.0234750
\(275\) 0 0
\(276\) 9.04936 + 15.6740i 0.544707 + 0.943461i
\(277\) 0.293522 0.0176360 0.00881801 0.999961i \(-0.497193\pi\)
0.00881801 + 0.999961i \(0.497193\pi\)
\(278\) 17.6412 1.05805
\(279\) −8.59248 14.8826i −0.514418 0.890998i
\(280\) 0 0
\(281\) 8.30301 + 14.3812i 0.495316 + 0.857912i 0.999985 0.00540048i \(-0.00171903\pi\)
−0.504670 + 0.863313i \(0.668386\pi\)
\(282\) 1.54312 2.67276i 0.0918913 0.159160i
\(283\) −5.07118 + 8.78355i −0.301451 + 0.522128i −0.976465 0.215677i \(-0.930804\pi\)
0.675014 + 0.737805i \(0.264137\pi\)
\(284\) −1.87418 −0.111212
\(285\) 0 0
\(286\) −1.86883 −0.110506
\(287\) −1.06494 + 1.84453i −0.0628614 + 0.108879i
\(288\) −3.54514 + 6.14037i −0.208900 + 0.361825i
\(289\) 8.37993 + 14.5145i 0.492937 + 0.853792i
\(290\) 0 0
\(291\) 23.0139 + 39.8612i 1.34910 + 2.33670i
\(292\) −4.70615 −0.275406
\(293\) −5.09200 −0.297478 −0.148739 0.988877i \(-0.547521\pi\)
−0.148739 + 0.988877i \(0.547521\pi\)
\(294\) −16.5867 28.7291i −0.967358 1.67551i
\(295\) 0 0
\(296\) −8.47175 −0.492411
\(297\) −50.7060 −2.94226
\(298\) 7.64556 + 13.2425i 0.442895 + 0.767117i
\(299\) 1.36421 2.36288i 0.0788943 0.136649i
\(300\) 0 0
\(301\) −12.1694 + 21.0780i −0.701433 + 1.21492i
\(302\) −8.31332 + 14.3991i −0.478378 + 0.828575i
\(303\) −1.78115 −0.102324
\(304\) −4.30571 + 0.678866i −0.246949 + 0.0389357i
\(305\) 0 0
\(306\) 1.73725 3.00900i 0.0993117 0.172013i
\(307\) 9.46802 16.3991i 0.540368 0.935946i −0.458514 0.888687i \(-0.651618\pi\)
0.998883 0.0472585i \(-0.0150485\pi\)
\(308\) −8.14964 14.1156i −0.464369 0.804311i
\(309\) −20.5732 + 35.6338i −1.17037 + 2.02714i
\(310\) 0 0
\(311\) −8.61109 −0.488290 −0.244145 0.969739i \(-0.578507\pi\)
−0.244145 + 0.969739i \(0.578507\pi\)
\(312\) 1.52113 0.0861172
\(313\) −0.410884 0.711672i −0.0232245 0.0402261i 0.854180 0.519978i \(-0.174060\pi\)
−0.877404 + 0.479752i \(0.840727\pi\)
\(314\) 6.08401 + 10.5378i 0.343341 + 0.594684i
\(315\) 0 0
\(316\) 6.39968 0.360010
\(317\) −3.46887 6.00826i −0.194831 0.337458i 0.752014 0.659147i \(-0.229083\pi\)
−0.946845 + 0.321690i \(0.895749\pi\)
\(318\) −8.82753 + 15.2897i −0.495023 + 0.857406i
\(319\) 4.75122 + 8.22935i 0.266017 + 0.460755i
\(320\) 0 0
\(321\) 15.8826 27.5095i 0.886481 1.53543i
\(322\) 23.7964 1.32612
\(323\) 2.10995 0.332668i 0.117401 0.0185102i
\(324\) 20.0013 1.11118
\(325\) 0 0
\(326\) 7.23369 12.5291i 0.400637 0.693924i
\(327\) 15.3487 + 26.5847i 0.848783 + 1.47014i
\(328\) 0.254982 0.441643i 0.0140790 0.0243856i
\(329\) −2.02891 3.51417i −0.111857 0.193742i
\(330\) 0 0
\(331\) −35.4051 −1.94604 −0.973021 0.230718i \(-0.925893\pi\)
−0.973021 + 0.230718i \(0.925893\pi\)
\(332\) 3.98089 + 6.89511i 0.218480 + 0.378418i
\(333\) 30.0336 + 52.0197i 1.64583 + 2.85066i
\(334\) 3.29823 0.180471
\(335\) 0 0
\(336\) 6.63340 + 11.4894i 0.361882 + 0.626798i
\(337\) 1.27608 2.21024i 0.0695127 0.120400i −0.829174 0.558990i \(-0.811189\pi\)
0.898687 + 0.438591i \(0.144522\pi\)
\(338\) 6.38534 + 11.0597i 0.347317 + 0.601570i
\(339\) 8.22591 14.2477i 0.446770 0.773829i
\(340\) 0 0
\(341\) −9.45885 −0.512225
\(342\) 19.4329 + 24.0320i 1.05081 + 1.29950i
\(343\) −14.3811 −0.776509
\(344\) 2.91377 5.04679i 0.157100 0.272105i
\(345\) 0 0
\(346\) 4.96668 + 8.60255i 0.267011 + 0.462476i
\(347\) −14.1149 + 24.4477i −0.757728 + 1.31242i 0.186278 + 0.982497i \(0.440357\pi\)
−0.944006 + 0.329927i \(0.892976\pi\)
\(348\) −3.86725 6.69828i −0.207307 0.359066i
\(349\) 18.2442 0.976590 0.488295 0.872679i \(-0.337619\pi\)
0.488295 + 0.872679i \(0.337619\pi\)
\(350\) 0 0
\(351\) −3.11094 5.38830i −0.166049 0.287606i
\(352\) 1.95130 + 3.37975i 0.104005 + 0.180141i
\(353\) 35.7778 1.90426 0.952129 0.305696i \(-0.0988890\pi\)
0.952129 + 0.305696i \(0.0988890\pi\)
\(354\) −24.3175 −1.29246
\(355\) 0 0
\(356\) 2.76126 4.78264i 0.146346 0.253479i
\(357\) −3.25060 5.63021i −0.172040 0.297982i
\(358\) 5.39616 9.34642i 0.285196 0.493974i
\(359\) −15.9454 + 27.6182i −0.841565 + 1.45763i 0.0470054 + 0.998895i \(0.485032\pi\)
−0.888571 + 0.458739i \(0.848301\pi\)
\(360\) 0 0
\(361\) −3.97635 + 18.5793i −0.209282 + 0.977855i
\(362\) 11.9181 0.626404
\(363\) −6.71878 + 11.6373i −0.352645 + 0.610798i
\(364\) 1.00000 1.73205i 0.0524142 0.0907841i
\(365\) 0 0
\(366\) 14.7922 25.6208i 0.773200 1.33922i
\(367\) −16.4554 28.5015i −0.858962 1.48777i −0.872920 0.487864i \(-0.837776\pi\)
0.0139572 0.999903i \(-0.495557\pi\)
\(368\) −5.69765 −0.297011
\(369\) −3.61580 −0.188231
\(370\) 0 0
\(371\) 11.6065 + 20.1031i 0.602581 + 1.04370i
\(372\) 7.69903 0.399176
\(373\) 14.9290 0.772994 0.386497 0.922291i \(-0.373685\pi\)
0.386497 + 0.922291i \(0.373685\pi\)
\(374\) −0.956205 1.65620i −0.0494442 0.0856399i
\(375\) 0 0
\(376\) 0.485788 + 0.841410i 0.0250526 + 0.0433924i
\(377\) −0.582997 + 1.00978i −0.0300259 + 0.0520063i
\(378\) 27.1325 46.9949i 1.39555 2.41716i
\(379\) −26.5535 −1.36396 −0.681982 0.731369i \(-0.738882\pi\)
−0.681982 + 0.731369i \(0.738882\pi\)
\(380\) 0 0
\(381\) −14.9631 −0.766582
\(382\) 2.43490 4.21737i 0.124580 0.215779i
\(383\) 18.5490 32.1279i 0.947811 1.64166i 0.197789 0.980245i \(-0.436624\pi\)
0.750022 0.661413i \(-0.230043\pi\)
\(384\) −1.58826 2.75095i −0.0810506 0.140384i
\(385\) 0 0
\(386\) 10.8919 + 18.8653i 0.554384 + 0.960221i
\(387\) −41.3189 −2.10036
\(388\) −14.4900 −0.735617
\(389\) 3.91887 + 6.78768i 0.198695 + 0.344149i 0.948105 0.317956i \(-0.102997\pi\)
−0.749411 + 0.662105i \(0.769663\pi\)
\(390\) 0 0
\(391\) 2.79205 0.141200
\(392\) 10.4433 0.527468
\(393\) −21.1383 36.6126i −1.06629 1.84686i
\(394\) −6.86794 + 11.8956i −0.346002 + 0.599293i
\(395\) 0 0
\(396\) 13.8353 23.9634i 0.695249 1.20421i
\(397\) 11.5460 19.9983i 0.579477 1.00368i −0.416062 0.909336i \(-0.636590\pi\)
0.995539 0.0943476i \(-0.0300765\pi\)
\(398\) 20.8867 1.04695
\(399\) 57.1230 9.00639i 2.85973 0.450884i
\(400\) 0 0
\(401\) −1.94555 + 3.36979i −0.0971561 + 0.168279i −0.910506 0.413495i \(-0.864308\pi\)
0.813350 + 0.581774i \(0.197641\pi\)
\(402\) −2.57285 + 4.45630i −0.128322 + 0.222260i
\(403\) −0.580323 1.00515i −0.0289079 0.0500700i
\(404\) 0.280362 0.485601i 0.0139485 0.0241596i
\(405\) 0 0
\(406\) −10.1694 −0.504699
\(407\) 33.0619 1.63882
\(408\) 0.778304 + 1.34806i 0.0385318 + 0.0667390i
\(409\) −11.6831 20.2357i −0.577692 1.00059i −0.995743 0.0921681i \(-0.970620\pi\)
0.418052 0.908423i \(-0.362713\pi\)
\(410\) 0 0
\(411\) −1.23433 −0.0608851
\(412\) −6.47665 11.2179i −0.319082 0.552665i
\(413\) −15.9864 + 27.6893i −0.786642 + 1.36250i
\(414\) 20.1990 + 34.9857i 0.992727 + 1.71945i
\(415\) 0 0
\(416\) −0.239434 + 0.414711i −0.0117392 + 0.0203329i
\(417\) 56.0375 2.74417
\(418\) 16.8035 2.64934i 0.821884 0.129584i
\(419\) −3.10343 −0.151612 −0.0758062 0.997123i \(-0.524153\pi\)
−0.0758062 + 0.997123i \(0.524153\pi\)
\(420\) 0 0
\(421\) 12.3730 21.4307i 0.603024 1.04447i −0.389337 0.921096i \(-0.627296\pi\)
0.992360 0.123372i \(-0.0393710\pi\)
\(422\) 8.30571 + 14.3859i 0.404316 + 0.700295i
\(423\) 3.44438 5.96584i 0.167471 0.290069i
\(424\) −2.77899 4.81336i −0.134960 0.233757i
\(425\) 0 0
\(426\) −5.95336 −0.288441
\(427\) −19.4489 33.6865i −0.941199 1.63020i
\(428\) 5.00000 + 8.66025i 0.241684 + 0.418609i
\(429\) −5.93637 −0.286611
\(430\) 0 0
\(431\) −18.1220 31.3883i −0.872908 1.51192i −0.858975 0.512018i \(-0.828898\pi\)
−0.0139333 0.999903i \(-0.504435\pi\)
\(432\) −6.49644 + 11.2522i −0.312560 + 0.541370i
\(433\) 3.41037 + 5.90694i 0.163892 + 0.283869i 0.936261 0.351305i \(-0.114262\pi\)
−0.772369 + 0.635174i \(0.780928\pi\)
\(434\) 5.06138 8.76657i 0.242954 0.420809i
\(435\) 0 0
\(436\) −9.66382 −0.462813
\(437\) −8.91648 + 23.1797i −0.426533 + 1.10884i
\(438\) −14.9492 −0.714299
\(439\) −17.4391 + 30.2054i −0.832322 + 1.44162i 0.0638702 + 0.997958i \(0.479656\pi\)
−0.896192 + 0.443666i \(0.853678\pi\)
\(440\) 0 0
\(441\) −37.0231 64.1259i −1.76301 3.05361i
\(442\) 0.117331 0.203223i 0.00558086 0.00966634i
\(443\) −11.6008 20.0932i −0.551171 0.954656i −0.998190 0.0601320i \(-0.980848\pi\)
0.447019 0.894524i \(-0.352485\pi\)
\(444\) −26.9107 −1.27713
\(445\) 0 0
\(446\) −5.08826 8.81313i −0.240936 0.417314i
\(447\) 24.2863 + 42.0651i 1.14870 + 1.98961i
\(448\) −4.17652 −0.197322
\(449\) −38.9584 −1.83856 −0.919280 0.393603i \(-0.871228\pi\)
−0.919280 + 0.393603i \(0.871228\pi\)
\(450\) 0 0
\(451\) −0.995094 + 1.72355i −0.0468572 + 0.0811590i
\(452\) 2.58960 + 4.48531i 0.121804 + 0.210971i
\(453\) −26.4074 + 45.7390i −1.24073 + 2.14901i
\(454\) 4.25482 7.36956i 0.199688 0.345871i
\(455\) 0 0
\(456\) −13.6772 + 2.15643i −0.640493 + 0.100984i
\(457\) 10.0845 0.471732 0.235866 0.971786i \(-0.424207\pi\)
0.235866 + 0.971786i \(0.424207\pi\)
\(458\) 3.40380 5.89556i 0.159049 0.275481i
\(459\) 3.18349 5.51396i 0.148592 0.257370i
\(460\) 0 0
\(461\) 1.74501 3.02245i 0.0812734 0.140770i −0.822524 0.568731i \(-0.807435\pi\)
0.903797 + 0.427961i \(0.140768\pi\)
\(462\) −25.8875 44.8385i −1.20440 2.08608i
\(463\) 6.70988 0.311835 0.155917 0.987770i \(-0.450167\pi\)
0.155917 + 0.987770i \(0.450167\pi\)
\(464\) 2.43490 0.113037
\(465\) 0 0
\(466\) −12.5225 21.6896i −0.580093 1.00475i
\(467\) −32.1400 −1.48726 −0.743630 0.668592i \(-0.766897\pi\)
−0.743630 + 0.668592i \(0.766897\pi\)
\(468\) 3.39531 0.156948
\(469\) 3.38280 + 5.85919i 0.156203 + 0.270552i
\(470\) 0 0
\(471\) 19.3260 + 33.4736i 0.890495 + 1.54238i
\(472\) 3.82769 6.62976i 0.176184 0.305159i
\(473\) −11.3713 + 19.6956i −0.522851 + 0.905605i
\(474\) 20.3287 0.933730
\(475\) 0 0
\(476\) 2.04664 0.0938077
\(477\) −19.7039 + 34.1281i −0.902178 + 1.56262i
\(478\) −10.7061 + 18.5435i −0.489685 + 0.848159i
\(479\) −5.69498 9.86399i −0.260210 0.450697i 0.706087 0.708125i \(-0.250459\pi\)
−0.966298 + 0.257427i \(0.917125\pi\)
\(480\) 0 0
\(481\) 2.02842 + 3.51333i 0.0924882 + 0.160194i
\(482\) 11.2908 0.514282
\(483\) 75.5897 3.43945
\(484\) −2.11514 3.66353i −0.0961427 0.166524i
\(485\) 0 0
\(486\) 24.5560 1.11388
\(487\) 28.3103 1.28286 0.641432 0.767180i \(-0.278341\pi\)
0.641432 + 0.767180i \(0.278341\pi\)
\(488\) 4.65673 + 8.06569i 0.210800 + 0.365116i
\(489\) 22.9780 39.7990i 1.03910 1.79977i
\(490\) 0 0
\(491\) 7.91187 13.7038i 0.357058 0.618442i −0.630410 0.776262i \(-0.717113\pi\)
0.987468 + 0.157820i \(0.0504466\pi\)
\(492\) 0.809957 1.40289i 0.0365157 0.0632470i
\(493\) −1.19319 −0.0537384
\(494\) 1.31247 + 1.62308i 0.0590506 + 0.0730260i
\(495\) 0 0
\(496\) −1.21187 + 2.09901i −0.0544144 + 0.0942485i
\(497\) −3.91377 + 6.77884i −0.175556 + 0.304073i
\(498\) 12.6454 + 21.9025i 0.566654 + 0.981473i
\(499\) −0.827004 + 1.43241i −0.0370218 + 0.0641236i −0.883943 0.467595i \(-0.845120\pi\)
0.846921 + 0.531719i \(0.178454\pi\)
\(500\) 0 0
\(501\) 10.4769 0.468073
\(502\) −16.1778 −0.722052
\(503\) −8.21135 14.2225i −0.366126 0.634149i 0.622830 0.782357i \(-0.285983\pi\)
−0.988956 + 0.148208i \(0.952649\pi\)
\(504\) 14.8064 + 25.6454i 0.659528 + 1.14234i
\(505\) 0 0
\(506\) 22.2357 0.988496
\(507\) 20.2832 + 35.1315i 0.900808 + 1.56024i
\(508\) 2.35526 4.07943i 0.104498 0.180996i
\(509\) 3.12210 + 5.40764i 0.138385 + 0.239689i 0.926885 0.375345i \(-0.122476\pi\)
−0.788501 + 0.615034i \(0.789142\pi\)
\(510\) 0 0
\(511\) −9.82766 + 17.0220i −0.434750 + 0.753009i
\(512\) 1.00000 0.0441942
\(513\) 35.6105 + 44.0384i 1.57224 + 1.94434i
\(514\) −9.84170 −0.434099
\(515\) 0 0
\(516\) 9.25564 16.0312i 0.407457 0.705736i
\(517\) −1.89584 3.28369i −0.0833788 0.144416i
\(518\) −17.6912 + 30.6421i −0.777308 + 1.34634i
\(519\) 15.7768 + 27.3262i 0.692524 + 1.19949i
\(520\) 0 0
\(521\) −7.60025 −0.332973 −0.166487 0.986044i \(-0.553242\pi\)
−0.166487 + 0.986044i \(0.553242\pi\)
\(522\) −8.63207 14.9512i −0.377815 0.654395i
\(523\) −13.3321 23.0919i −0.582971 1.00974i −0.995125 0.0986218i \(-0.968557\pi\)
0.412153 0.911114i \(-0.364777\pi\)
\(524\) 13.3091 0.581410
\(525\) 0 0
\(526\) 14.1329 + 24.4789i 0.616223 + 1.06733i
\(527\) 0.593857 1.02859i 0.0258688 0.0448061i
\(528\) 6.19834 + 10.7358i 0.269748 + 0.467218i
\(529\) −4.73163 + 8.19542i −0.205723 + 0.356323i
\(530\) 0 0
\(531\) −54.2789 −2.35550
\(532\) −6.53600 + 16.9913i −0.283372 + 0.736666i
\(533\) −0.244206 −0.0105777
\(534\) 8.77119 15.1921i 0.379567 0.657428i
\(535\) 0 0
\(536\) −0.809957 1.40289i −0.0349848 0.0605955i
\(537\) 17.1410 29.6891i 0.739689 1.28118i
\(538\) −16.1099 27.9031i −0.694547 1.20299i
\(539\) −40.7561 −1.75549
\(540\) 0 0
\(541\) 7.84818 + 13.5934i 0.337420 + 0.584428i 0.983947 0.178463i \(-0.0571125\pi\)
−0.646527 + 0.762891i \(0.723779\pi\)
\(542\) 5.35390 + 9.27322i 0.229970 + 0.398319i
\(543\) 37.8582 1.62465
\(544\) −0.490035 −0.0210101
\(545\) 0 0
\(546\) 3.17652 5.50190i 0.135943 0.235459i
\(547\) 8.69054 + 15.0525i 0.371581 + 0.643597i 0.989809 0.142402i \(-0.0454826\pi\)
−0.618228 + 0.785999i \(0.712149\pi\)
\(548\) 0.194290 0.336520i 0.00829965 0.0143754i
\(549\) 33.0175 57.1880i 1.40915 2.44073i
\(550\) 0 0
\(551\) 3.81047 9.90587i 0.162331 0.422004i
\(552\) −18.0987 −0.770333
\(553\) 13.3642 23.1475i 0.568304 0.984331i
\(554\) −0.146761 + 0.254197i −0.00623527 + 0.0107998i
\(555\) 0 0
\(556\) −8.82058 + 15.2777i −0.374076 + 0.647919i
\(557\) 1.07696 + 1.86535i 0.0456324 + 0.0790376i 0.887939 0.459960i \(-0.152136\pi\)
−0.842307 + 0.538998i \(0.818803\pi\)
\(558\) 17.1850 0.727497
\(559\) −2.79062 −0.118030
\(560\) 0 0
\(561\) −3.03741 5.26094i −0.128239 0.222117i
\(562\) −16.6060 −0.700482
\(563\) −12.2897 −0.517951 −0.258975 0.965884i \(-0.583385\pi\)
−0.258975 + 0.965884i \(0.583385\pi\)
\(564\) 1.54312 + 2.67276i 0.0649769 + 0.112543i
\(565\) 0 0
\(566\) −5.07118 8.78355i −0.213158 0.369200i
\(567\) 41.7680 72.3442i 1.75409 3.03817i
\(568\) 0.937088 1.62308i 0.0393193 0.0681031i
\(569\) −14.8699 −0.623377 −0.311688 0.950184i \(-0.600894\pi\)
−0.311688 + 0.950184i \(0.600894\pi\)
\(570\) 0 0
\(571\) 44.1772 1.84876 0.924379 0.381475i \(-0.124584\pi\)
0.924379 + 0.381475i \(0.124584\pi\)
\(572\) 0.934414 1.61845i 0.0390698 0.0676709i
\(573\) 7.73451 13.3966i 0.323114 0.559649i
\(574\) −1.06494 1.84453i −0.0444497 0.0769892i
\(575\) 0 0
\(576\) −3.54514 6.14037i −0.147714 0.255849i
\(577\) −28.4224 −1.18324 −0.591621 0.806216i \(-0.701512\pi\)
−0.591621 + 0.806216i \(0.701512\pi\)
\(578\) −16.7599 −0.697119
\(579\) 34.5984 + 59.9262i 1.43786 + 2.49045i
\(580\) 0 0
\(581\) 33.2526 1.37955
\(582\) −46.0277 −1.90791
\(583\) 10.8453 + 18.7846i 0.449166 + 0.777979i
\(584\) 2.35307 4.07564i 0.0973709 0.168651i
\(585\) 0 0
\(586\) 2.54600 4.40980i 0.105174 0.182167i
\(587\) −9.18228 + 15.9042i −0.378993 + 0.656435i −0.990916 0.134482i \(-0.957063\pi\)
0.611923 + 0.790917i \(0.290396\pi\)
\(588\) 33.1735 1.36805
\(589\) 6.64289 + 8.21505i 0.273716 + 0.338495i
\(590\) 0 0
\(591\) −21.8162 + 37.7867i −0.897397 + 1.55434i
\(592\) 4.23588 7.33675i 0.174093 0.301539i
\(593\) 1.90092 + 3.29249i 0.0780614 + 0.135206i 0.902413 0.430871i \(-0.141794\pi\)
−0.824352 + 0.566077i \(0.808460\pi\)
\(594\) 25.3530 43.9127i 1.04025 1.80176i
\(595\) 0 0
\(596\) −15.2911 −0.626349
\(597\) 66.3469 2.71540
\(598\) 1.36421 + 2.36288i 0.0557867 + 0.0966254i
\(599\) −17.1530 29.7099i −0.700853 1.21391i −0.968167 0.250303i \(-0.919470\pi\)
0.267315 0.963609i \(-0.413864\pi\)
\(600\) 0 0
\(601\) −18.1820 −0.741660 −0.370830 0.928701i \(-0.620927\pi\)
−0.370830 + 0.928701i \(0.620927\pi\)
\(602\) −12.1694 21.0780i −0.495988 0.859076i
\(603\) −5.74283 + 9.94687i −0.233866 + 0.405068i
\(604\) −8.31332 14.3991i −0.338264 0.585891i
\(605\) 0 0
\(606\) 0.890576 1.54252i 0.0361772 0.0626607i
\(607\) −2.01961 −0.0819733 −0.0409867 0.999160i \(-0.513050\pi\)
−0.0409867 + 0.999160i \(0.513050\pi\)
\(608\) 1.56494 4.06829i 0.0634667 0.164991i
\(609\) −32.3033 −1.30900
\(610\) 0 0
\(611\) 0.232628 0.402924i 0.00941113 0.0163006i
\(612\) 1.73725 + 3.00900i 0.0702240 + 0.121631i
\(613\) −3.11850 + 5.40141i −0.125955 + 0.218161i −0.922106 0.386938i \(-0.873533\pi\)
0.796151 + 0.605098i \(0.206866\pi\)
\(614\) 9.46802 + 16.3991i 0.382098 + 0.661813i
\(615\) 0 0
\(616\) 16.2993 0.656717
\(617\) −3.84830 6.66545i −0.154927 0.268341i 0.778106 0.628133i \(-0.216181\pi\)
−0.933032 + 0.359793i \(0.882847\pi\)
\(618\) −20.5732 35.6338i −0.827576 1.43340i
\(619\) 41.1392 1.65352 0.826762 0.562551i \(-0.190180\pi\)
0.826762 + 0.562551i \(0.190180\pi\)
\(620\) 0 0
\(621\) 37.0145 + 64.1110i 1.48534 + 2.57268i
\(622\) 4.30554 7.45742i 0.172637 0.299015i
\(623\) −11.5324 19.9748i −0.462038 0.800273i
\(624\) −0.760566 + 1.31734i −0.0304470 + 0.0527358i
\(625\) 0 0
\(626\) 0.821768 0.0328444
\(627\) 53.3765 8.41570i 2.13165 0.336091i
\(628\) −12.1680 −0.485557
\(629\) −2.07573 + 3.59527i −0.0827647 + 0.143353i
\(630\) 0 0
\(631\) 7.59739 + 13.1591i 0.302447 + 0.523854i 0.976690 0.214656i \(-0.0688631\pi\)
−0.674243 + 0.738510i \(0.735530\pi\)
\(632\) −3.19984 + 5.54229i −0.127283 + 0.220460i
\(633\) 26.3833 + 45.6972i 1.04864 + 1.81630i
\(634\) 6.93774 0.275533
\(635\) 0 0
\(636\) −8.82753 15.2897i −0.350034 0.606277i
\(637\) −2.50049 4.33097i −0.0990728 0.171599i
\(638\) −9.50243 −0.376205
\(639\) −13.2884 −0.525683
\(640\) 0 0
\(641\) −18.0506 + 31.2645i −0.712955 + 1.23487i 0.250788 + 0.968042i \(0.419310\pi\)
−0.963743 + 0.266832i \(0.914023\pi\)
\(642\) 15.8826 + 27.5095i 0.626836 + 1.08571i
\(643\) −2.05734 + 3.56342i −0.0811336 + 0.140528i −0.903737 0.428088i \(-0.859187\pi\)
0.822604 + 0.568615i \(0.192521\pi\)
\(644\) −11.8982 + 20.6083i −0.468854 + 0.812079i
\(645\) 0 0
\(646\) −0.766875 + 1.99360i −0.0301723 + 0.0784373i
\(647\) 10.0471 0.394991 0.197495 0.980304i \(-0.436719\pi\)
0.197495 + 0.980304i \(0.436719\pi\)
\(648\) −10.0007 + 17.3216i −0.392863 + 0.680459i
\(649\) −14.9380 + 25.8733i −0.586366 + 1.01562i
\(650\) 0 0
\(651\) 16.0776 27.8472i 0.630130 1.09142i
\(652\) 7.23369 + 12.5291i 0.283293 + 0.490678i
\(653\) 41.5606 1.62639 0.813196 0.581989i \(-0.197725\pi\)
0.813196 + 0.581989i \(0.197725\pi\)
\(654\) −30.6973 −1.20036
\(655\) 0 0
\(656\) 0.254982 + 0.441643i 0.00995539 + 0.0172432i
\(657\) −33.3679 −1.30181
\(658\) 4.05781 0.158190
\(659\) −6.16587 10.6796i −0.240188 0.416018i 0.720580 0.693372i \(-0.243876\pi\)
−0.960768 + 0.277354i \(0.910542\pi\)
\(660\) 0 0
\(661\) 9.49203 + 16.4407i 0.369197 + 0.639469i 0.989440 0.144941i \(-0.0462993\pi\)
−0.620243 + 0.784410i \(0.712966\pi\)
\(662\) 17.7026 30.6617i 0.688030 1.19170i
\(663\) 0.372704 0.645543i 0.0144746 0.0250708i
\(664\) −7.96179 −0.308977
\(665\) 0 0
\(666\) −60.0672 −2.32756
\(667\) 6.93661 12.0146i 0.268586 0.465205i
\(668\) −1.64911 + 2.85635i −0.0638062 + 0.110516i
\(669\) −16.1630 27.9951i −0.624896 1.08235i
\(670\) 0 0
\(671\) −18.1733 31.4771i −0.701574 1.21516i
\(672\) −13.2668 −0.511778
\(673\) 7.23063 0.278720 0.139360 0.990242i \(-0.455495\pi\)
0.139360 + 0.990242i \(0.455495\pi\)
\(674\) 1.27608 + 2.21024i 0.0491529 + 0.0851353i
\(675\) 0 0
\(676\) −12.7707 −0.491180
\(677\) −13.0555 −0.501762 −0.250881 0.968018i \(-0.580720\pi\)
−0.250881 + 0.968018i \(0.580720\pi\)
\(678\) 8.22591 + 14.2477i 0.315914 + 0.547180i
\(679\) −30.2588 + 52.4098i −1.16123 + 2.01131i
\(680\) 0 0
\(681\) 13.5155 23.4096i 0.517916 0.897056i
\(682\) 4.72943 8.19161i 0.181099 0.313673i
\(683\) −4.98007 −0.190557 −0.0952785 0.995451i \(-0.530374\pi\)
−0.0952785 + 0.995451i \(0.530374\pi\)
\(684\) −30.5287 + 4.81336i −1.16729 + 0.184043i
\(685\) 0 0
\(686\) 7.19057 12.4544i 0.274537 0.475513i
\(687\) 10.8122 18.7274i 0.412513 0.714493i
\(688\) 2.91377 + 5.04679i 0.111086 + 0.192407i
\(689\) −1.33077 + 2.30496i −0.0506983 + 0.0878120i
\(690\) 0 0
\(691\) 20.2330 0.769699 0.384849 0.922979i \(-0.374253\pi\)
0.384849 + 0.922979i \(0.374253\pi\)
\(692\) −9.93337 −0.377610
\(693\) −57.7833 100.084i −2.19501 3.80186i
\(694\) −14.1149 24.4477i −0.535795 0.928024i
\(695\) 0 0
\(696\) 7.73451 0.293176
\(697\) −0.124950 0.216420i −0.00473283 0.00819751i
\(698\) −9.12210 + 15.7999i −0.345277 + 0.598037i
\(699\) −39.7779 68.8974i −1.50454 2.60594i
\(700\) 0 0
\(701\) −5.51907 + 9.55931i −0.208452 + 0.361050i −0.951227 0.308491i \(-0.900176\pi\)
0.742775 + 0.669541i \(0.233509\pi\)
\(702\) 6.22187 0.234829
\(703\) −23.2191 28.7143i −0.875726 1.08298i
\(704\) −3.90260 −0.147085
\(705\) 0 0
\(706\) −17.8889 + 30.9845i −0.673257 + 1.16612i
\(707\) −1.17094 2.02812i −0.0440376 0.0762754i
\(708\) 12.1588 21.0596i 0.456954 0.791467i
\(709\) 17.6384 + 30.5507i 0.662426 + 1.14735i 0.979976 + 0.199114i \(0.0638063\pi\)
−0.317551 + 0.948241i \(0.602860\pi\)
\(710\) 0 0
\(711\) 45.3756 1.70172
\(712\) 2.76126 + 4.78264i 0.103482 + 0.179237i
\(713\) 6.90479 + 11.9594i 0.258586 + 0.447885i
\(714\) 6.50120 0.243301
\(715\) 0 0
\(716\) 5.39616 + 9.34642i 0.201664 + 0.349292i
\(717\) −34.0081 + 58.9038i −1.27006 + 2.19980i
\(718\) −15.9454 27.6182i −0.595077 1.03070i
\(719\) 17.9276 31.0515i 0.668587 1.15803i −0.309712 0.950830i \(-0.600233\pi\)
0.978299 0.207196i \(-0.0664339\pi\)
\(720\) 0 0
\(721\) −54.0997 −2.01478
\(722\) −14.1019 12.7332i −0.524819 0.473882i
\(723\) 35.8654 1.33385
\(724\) −5.95907 + 10.3214i −0.221467 + 0.383592i
\(725\) 0 0
\(726\) −6.71878 11.6373i −0.249357 0.431900i
\(727\) −17.7426 + 30.7311i −0.658037 + 1.13975i 0.323086 + 0.946370i \(0.395280\pi\)
−0.981123 + 0.193384i \(0.938054\pi\)
\(728\) 1.00000 + 1.73205i 0.0370625 + 0.0641941i
\(729\) 17.9986 0.666613
\(730\) 0 0
\(731\) −1.42785 2.47311i −0.0528109 0.0914711i
\(732\) 14.7922 + 25.6208i 0.546735 + 0.946973i
\(733\) −8.13294 −0.300397 −0.150198 0.988656i \(-0.547991\pi\)
−0.150198 + 0.988656i \(0.547991\pi\)
\(734\) 32.9107 1.21476
\(735\) 0 0
\(736\) 2.84883 4.93431i 0.105009 0.181881i
\(737\) 3.16094 + 5.47490i 0.116435 + 0.201671i
\(738\) 1.80790 3.13137i 0.0665497 0.115267i
\(739\) −3.35916 + 5.81823i −0.123569 + 0.214027i −0.921172 0.389155i \(-0.872767\pi\)
0.797604 + 0.603182i \(0.206101\pi\)
\(740\) 0 0
\(741\) 4.16908 + 5.15576i 0.153155 + 0.189402i
\(742\) −23.2131 −0.852178
\(743\) −17.5641 + 30.4219i −0.644363 + 1.11607i 0.340085 + 0.940395i \(0.389544\pi\)
−0.984448 + 0.175675i \(0.943789\pi\)
\(744\) −3.84952 + 6.66756i −0.141130 + 0.244445i
\(745\) 0 0
\(746\) −7.46449 + 12.9289i −0.273295 + 0.473360i
\(747\) 28.2257 + 48.8883i 1.03272 + 1.78873i
\(748\) 1.91241 0.0699247
\(749\) 41.7652 1.52607
\(750\) 0 0
\(751\) −11.2029 19.4040i −0.408800 0.708062i 0.585956 0.810343i \(-0.300719\pi\)
−0.994756 + 0.102281i \(0.967386\pi\)
\(752\) −0.971577 −0.0354297
\(753\) −51.3893 −1.87273
\(754\) −0.582997 1.00978i −0.0212315 0.0367740i
\(755\) 0 0
\(756\) 27.1325 + 46.9949i 0.986801 + 1.70919i
\(757\) 2.64407 4.57967i 0.0961005 0.166451i −0.813967 0.580911i \(-0.802696\pi\)
0.910067 + 0.414460i \(0.136030\pi\)
\(758\) 13.2768 22.9960i 0.482234 0.835254i
\(759\) 70.6320 2.56378
\(760\) 0 0
\(761\) −25.9435 −0.940451 −0.470226 0.882546i \(-0.655827\pi\)
−0.470226 + 0.882546i \(0.655827\pi\)
\(762\) 7.48154 12.9584i 0.271028 0.469434i
\(763\) −20.1806 + 34.9538i −0.730586 + 1.26541i
\(764\) 2.43490 + 4.21737i 0.0880916 + 0.152579i
\(765\) 0 0
\(766\) 18.5490 + 32.1279i 0.670204 + 1.16083i
\(767\) −3.66592 −0.132369
\(768\) 3.17652 0.114623
\(769\) −16.4046 28.4137i −0.591566 1.02462i −0.994022 0.109183i \(-0.965176\pi\)
0.402455 0.915440i \(-0.368157\pi\)
\(770\) 0 0
\(771\) −31.2624 −1.12589
\(772\) −21.7838 −0.784017
\(773\) −0.437731 0.758172i −0.0157441 0.0272695i 0.858046 0.513573i \(-0.171678\pi\)
−0.873790 + 0.486303i \(0.838345\pi\)
\(774\) 20.6594 35.7832i 0.742588 1.28620i
\(775\) 0 0
\(776\) 7.24499 12.5487i 0.260080 0.450472i
\(777\) −56.1966 + 97.3353i −2.01604 + 3.49189i
\(778\) −7.83774 −0.280997
\(779\) 2.19576 0.346198i 0.0786713 0.0124038i
\(780\) 0 0
\(781\) −3.65708 + 6.33424i −0.130861 + 0.226657i
\(782\) −1.39603 + 2.41799i −0.0499218 + 0.0864670i
\(783\) −15.8182 27.3979i −0.565296 0.979121i
\(784\) −5.22167 + 9.04419i −0.186488 + 0.323007i
\(785\) 0 0
\(786\) 42.2766