Properties

Label 1950.2.bc.j.751.3
Level $1950$
Weight $2$
Character 1950.751
Analytic conductor $15.571$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.bc (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.5708283941\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 2 x^{11} - 8 x^{10} + 34 x^{9} + 8 x^{8} - 134 x^{7} + 98 x^{6} + 154 x^{5} + 104 x^{4} + 190 x^{3} - 1196 x^{2} - 338 x + 2197\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 751.3
Root \(-0.330925 - 1.46916i\) of defining polynomial
Character \(\chi\) \(=\) 1950.751
Dual form 1950.2.bc.j.901.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(1.04466 + 0.603137i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(1.04466 + 0.603137i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(4.46182 - 2.57603i) q^{11} +1.00000 q^{12} +(2.82126 - 2.24511i) q^{13} -1.20627 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.36800 + 4.10150i) q^{17} -1.00000i q^{18} +(1.84474 + 1.06506i) q^{19} +1.20627i q^{21} +(-2.57603 + 4.46182i) q^{22} +(1.08711 + 1.88293i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(-1.32073 + 3.35495i) q^{26} -1.00000 q^{27} +(1.04466 - 0.603137i) q^{28} +(-2.38346 - 4.12828i) q^{29} -5.91046i q^{31} +(0.866025 + 0.500000i) q^{32} +(4.46182 + 2.57603i) q^{33} -4.73601i q^{34} +(0.500000 + 0.866025i) q^{36} +(3.81110 - 2.20034i) q^{37} -2.13012 q^{38} +(3.35495 + 1.32073i) q^{39} +(4.10150 - 2.36800i) q^{41} +(-0.603137 - 1.04466i) q^{42} +(0.986944 - 1.70944i) q^{43} -5.15206i q^{44} +(-1.88293 - 1.08711i) q^{46} +0.852296i q^{47} +(0.500000 - 0.866025i) q^{48} +(-2.77245 - 4.80203i) q^{49} -4.73601 q^{51} +(-0.533691 - 3.56583i) q^{52} +4.48042 q^{53} +(0.866025 - 0.500000i) q^{54} +(-0.603137 + 1.04466i) q^{56} +2.13012i q^{57} +(4.12828 + 2.38346i) q^{58} +(-1.68133 - 0.970715i) q^{59} +(-1.53795 + 2.66381i) q^{61} +(2.95523 + 5.11861i) q^{62} +(-1.04466 + 0.603137i) q^{63} -1.00000 q^{64} -5.15206 q^{66} +(12.1723 - 7.02765i) q^{67} +(2.36800 + 4.10150i) q^{68} +(-1.08711 + 1.88293i) q^{69} +(-0.298707 - 0.172459i) q^{71} +(-0.866025 - 0.500000i) q^{72} +15.7228i q^{73} +(-2.20034 + 3.81110i) q^{74} +(1.84474 - 1.06506i) q^{76} +6.21480 q^{77} +(-3.56583 + 0.533691i) q^{78} +13.5863 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-2.36800 + 4.10150i) q^{82} +10.2045i q^{83} +(1.04466 + 0.603137i) q^{84} +1.97389i q^{86} +(2.38346 - 4.12828i) q^{87} +(2.57603 + 4.46182i) q^{88} +(-14.1941 + 8.19497i) q^{89} +(4.30137 - 0.643777i) q^{91} +2.17422 q^{92} +(5.11861 - 2.95523i) q^{93} +(-0.426148 - 0.738110i) q^{94} +1.00000i q^{96} +(-7.34631 - 4.24139i) q^{97} +(4.80203 + 2.77245i) q^{98} +5.15206i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 6q^{3} + 6q^{4} - 12q^{7} - 6q^{9} + O(q^{10}) \) \( 12q + 6q^{3} + 6q^{4} - 12q^{7} - 6q^{9} + 6q^{11} + 12q^{12} + 4q^{13} - 4q^{14} - 6q^{16} + 8q^{17} + 6q^{19} - 6q^{22} + 16q^{23} - 2q^{26} - 12q^{27} - 12q^{28} - 14q^{29} + 6q^{33} + 6q^{36} - 6q^{37} - 8q^{38} + 2q^{39} - 18q^{41} - 2q^{42} + 10q^{43} - 6q^{46} + 6q^{48} - 8q^{49} + 16q^{51} + 2q^{52} - 2q^{56} + 6q^{58} + 36q^{59} + 10q^{61} + 16q^{62} + 12q^{63} - 12q^{64} - 12q^{66} + 24q^{67} - 8q^{68} - 16q^{69} - 12q^{71} + 12q^{74} + 6q^{76} + 24q^{77} - 10q^{78} - 4q^{79} - 6q^{81} + 8q^{82} - 12q^{84} + 14q^{87} + 6q^{88} - 18q^{89} + 2q^{91} + 32q^{92} - 6q^{93} + 8q^{94} - 24q^{97} + 24q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0 0
\(6\) −0.866025 0.500000i −0.353553 0.204124i
\(7\) 1.04466 + 0.603137i 0.394846 + 0.227964i 0.684258 0.729240i \(-0.260126\pi\)
−0.289412 + 0.957205i \(0.593460\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 4.46182 2.57603i 1.34529 0.776703i 0.357711 0.933832i \(-0.383557\pi\)
0.987578 + 0.157130i \(0.0502240\pi\)
\(12\) 1.00000 0.288675
\(13\) 2.82126 2.24511i 0.782476 0.622681i
\(14\) −1.20627 −0.322390
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −2.36800 + 4.10150i −0.574326 + 0.994761i 0.421789 + 0.906694i \(0.361402\pi\)
−0.996115 + 0.0880670i \(0.971931\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 1.84474 + 1.06506i 0.423212 + 0.244341i 0.696450 0.717605i \(-0.254762\pi\)
−0.273239 + 0.961946i \(0.588095\pi\)
\(20\) 0 0
\(21\) 1.20627i 0.263231i
\(22\) −2.57603 + 4.46182i −0.549212 + 0.951263i
\(23\) 1.08711 + 1.88293i 0.226678 + 0.392618i 0.956822 0.290676i \(-0.0938802\pi\)
−0.730144 + 0.683294i \(0.760547\pi\)
\(24\) −0.866025 + 0.500000i −0.176777 + 0.102062i
\(25\) 0 0
\(26\) −1.32073 + 3.35495i −0.259016 + 0.657960i
\(27\) −1.00000 −0.192450
\(28\) 1.04466 0.603137i 0.197423 0.113982i
\(29\) −2.38346 4.12828i −0.442598 0.766602i 0.555283 0.831661i \(-0.312610\pi\)
−0.997881 + 0.0650589i \(0.979276\pi\)
\(30\) 0 0
\(31\) 5.91046i 1.06155i −0.847513 0.530775i \(-0.821901\pi\)
0.847513 0.530775i \(-0.178099\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 4.46182 + 2.57603i 0.776703 + 0.448430i
\(34\) 4.73601i 0.812219i
\(35\) 0 0
\(36\) 0.500000 + 0.866025i 0.0833333 + 0.144338i
\(37\) 3.81110 2.20034i 0.626541 0.361734i −0.152870 0.988246i \(-0.548852\pi\)
0.779411 + 0.626513i \(0.215518\pi\)
\(38\) −2.13012 −0.345551
\(39\) 3.35495 + 1.32073i 0.537222 + 0.211486i
\(40\) 0 0
\(41\) 4.10150 2.36800i 0.640547 0.369820i −0.144278 0.989537i \(-0.546086\pi\)
0.784825 + 0.619717i \(0.212753\pi\)
\(42\) −0.603137 1.04466i −0.0930660 0.161195i
\(43\) 0.986944 1.70944i 0.150508 0.260687i −0.780907 0.624648i \(-0.785243\pi\)
0.931414 + 0.363961i \(0.118576\pi\)
\(44\) 5.15206i 0.776703i
\(45\) 0 0
\(46\) −1.88293 1.08711i −0.277623 0.160285i
\(47\) 0.852296i 0.124320i 0.998066 + 0.0621600i \(0.0197989\pi\)
−0.998066 + 0.0621600i \(0.980201\pi\)
\(48\) 0.500000 0.866025i 0.0721688 0.125000i
\(49\) −2.77245 4.80203i −0.396065 0.686004i
\(50\) 0 0
\(51\) −4.73601 −0.663174
\(52\) −0.533691 3.56583i −0.0740096 0.494492i
\(53\) 4.48042 0.615433 0.307716 0.951478i \(-0.400435\pi\)
0.307716 + 0.951478i \(0.400435\pi\)
\(54\) 0.866025 0.500000i 0.117851 0.0680414i
\(55\) 0 0
\(56\) −0.603137 + 1.04466i −0.0805976 + 0.139599i
\(57\) 2.13012i 0.282141i
\(58\) 4.12828 + 2.38346i 0.542070 + 0.312964i
\(59\) −1.68133 0.970715i −0.218890 0.126376i 0.386546 0.922270i \(-0.373668\pi\)
−0.605436 + 0.795894i \(0.707001\pi\)
\(60\) 0 0
\(61\) −1.53795 + 2.66381i −0.196915 + 0.341066i −0.947527 0.319677i \(-0.896426\pi\)
0.750612 + 0.660744i \(0.229759\pi\)
\(62\) 2.95523 + 5.11861i 0.375315 + 0.650064i
\(63\) −1.04466 + 0.603137i −0.131615 + 0.0759881i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) −5.15206 −0.634175
\(67\) 12.1723 7.02765i 1.48708 0.858564i 0.487186 0.873298i \(-0.338023\pi\)
0.999891 + 0.0147340i \(0.00469016\pi\)
\(68\) 2.36800 + 4.10150i 0.287163 + 0.497380i
\(69\) −1.08711 + 1.88293i −0.130873 + 0.226678i
\(70\) 0 0
\(71\) −0.298707 0.172459i −0.0354500 0.0204671i 0.482170 0.876078i \(-0.339849\pi\)
−0.517620 + 0.855610i \(0.673182\pi\)
\(72\) −0.866025 0.500000i −0.102062 0.0589256i
\(73\) 15.7228i 1.84022i 0.391662 + 0.920109i \(0.371900\pi\)
−0.391662 + 0.920109i \(0.628100\pi\)
\(74\) −2.20034 + 3.81110i −0.255784 + 0.443031i
\(75\) 0 0
\(76\) 1.84474 1.06506i 0.211606 0.122171i
\(77\) 6.21480 0.708242
\(78\) −3.56583 + 0.533691i −0.403751 + 0.0604286i
\(79\) 13.5863 1.52858 0.764290 0.644873i \(-0.223090\pi\)
0.764290 + 0.644873i \(0.223090\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −2.36800 + 4.10150i −0.261502 + 0.452935i
\(83\) 10.2045i 1.12009i 0.828462 + 0.560046i \(0.189216\pi\)
−0.828462 + 0.560046i \(0.810784\pi\)
\(84\) 1.04466 + 0.603137i 0.113982 + 0.0658076i
\(85\) 0 0
\(86\) 1.97389i 0.212850i
\(87\) 2.38346 4.12828i 0.255534 0.442598i
\(88\) 2.57603 + 4.46182i 0.274606 + 0.475631i
\(89\) −14.1941 + 8.19497i −1.50457 + 0.868665i −0.504586 + 0.863361i \(0.668355\pi\)
−0.999986 + 0.00530346i \(0.998312\pi\)
\(90\) 0 0
\(91\) 4.30137 0.643777i 0.450906 0.0674862i
\(92\) 2.17422 0.226678
\(93\) 5.11861 2.95523i 0.530775 0.306443i
\(94\) −0.426148 0.738110i −0.0439538 0.0761302i
\(95\) 0 0
\(96\) 1.00000i 0.102062i
\(97\) −7.34631 4.24139i −0.745904 0.430648i 0.0783078 0.996929i \(-0.475048\pi\)
−0.824212 + 0.566281i \(0.808382\pi\)
\(98\) 4.80203 + 2.77245i 0.485078 + 0.280060i
\(99\) 5.15206i 0.517802i
\(100\) 0 0
\(101\) 6.79121 + 11.7627i 0.675751 + 1.17044i 0.976249 + 0.216653i \(0.0695139\pi\)
−0.300498 + 0.953783i \(0.597153\pi\)
\(102\) 4.10150 2.36800i 0.406109 0.234467i
\(103\) 2.15696 0.212531 0.106266 0.994338i \(-0.466111\pi\)
0.106266 + 0.994338i \(0.466111\pi\)
\(104\) 2.24511 + 2.82126i 0.220151 + 0.276647i
\(105\) 0 0
\(106\) −3.88016 + 2.24021i −0.376874 + 0.217588i
\(107\) −4.04699 7.00959i −0.391237 0.677642i 0.601376 0.798966i \(-0.294619\pi\)
−0.992613 + 0.121324i \(0.961286\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) 16.8839i 1.61718i −0.588370 0.808592i \(-0.700230\pi\)
0.588370 0.808592i \(-0.299770\pi\)
\(110\) 0 0
\(111\) 3.81110 + 2.20034i 0.361734 + 0.208847i
\(112\) 1.20627i 0.113982i
\(113\) −2.47551 + 4.28771i −0.232876 + 0.403354i −0.958653 0.284576i \(-0.908147\pi\)
0.725777 + 0.687930i \(0.241480\pi\)
\(114\) −1.06506 1.84474i −0.0997519 0.172775i
\(115\) 0 0
\(116\) −4.76693 −0.442598
\(117\) 0.533691 + 3.56583i 0.0493397 + 0.329661i
\(118\) 1.94143 0.178723
\(119\) −4.94754 + 2.85646i −0.453540 + 0.261851i
\(120\) 0 0
\(121\) 7.77188 13.4613i 0.706535 1.22375i
\(122\) 3.07591i 0.278480i
\(123\) 4.10150 + 2.36800i 0.369820 + 0.213516i
\(124\) −5.11861 2.95523i −0.459665 0.265388i
\(125\) 0 0
\(126\) 0.603137 1.04466i 0.0537317 0.0930660i
\(127\) 0.600957 + 1.04089i 0.0533263 + 0.0923639i 0.891456 0.453107i \(-0.149684\pi\)
−0.838130 + 0.545471i \(0.816351\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 1.97389 0.173791
\(130\) 0 0
\(131\) −6.65149 −0.581143 −0.290572 0.956853i \(-0.593845\pi\)
−0.290572 + 0.956853i \(0.593845\pi\)
\(132\) 4.46182 2.57603i 0.388351 0.224215i
\(133\) 1.28475 + 2.22526i 0.111402 + 0.192954i
\(134\) −7.02765 + 12.1723i −0.607097 + 1.05152i
\(135\) 0 0
\(136\) −4.10150 2.36800i −0.351701 0.203055i
\(137\) 12.7435 + 7.35746i 1.08875 + 0.628590i 0.933243 0.359245i \(-0.116966\pi\)
0.155507 + 0.987835i \(0.450299\pi\)
\(138\) 2.17422i 0.185082i
\(139\) 7.82540 13.5540i 0.663742 1.14963i −0.315883 0.948798i \(-0.602301\pi\)
0.979625 0.200837i \(-0.0643660\pi\)
\(140\) 0 0
\(141\) −0.738110 + 0.426148i −0.0621600 + 0.0358881i
\(142\) 0.344918 0.0289448
\(143\) 6.80447 17.2849i 0.569018 1.44544i
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) −7.86142 13.6164i −0.650615 1.12690i
\(147\) 2.77245 4.80203i 0.228668 0.396065i
\(148\) 4.40068i 0.361734i
\(149\) 19.7555 + 11.4058i 1.61843 + 0.934401i 0.987327 + 0.158702i \(0.0507309\pi\)
0.631103 + 0.775699i \(0.282602\pi\)
\(150\) 0 0
\(151\) 19.8995i 1.61940i 0.586845 + 0.809699i \(0.300370\pi\)
−0.586845 + 0.809699i \(0.699630\pi\)
\(152\) −1.06506 + 1.84474i −0.0863877 + 0.149628i
\(153\) −2.36800 4.10150i −0.191442 0.331587i
\(154\) −5.38217 + 3.10740i −0.433708 + 0.250401i
\(155\) 0 0
\(156\) 2.82126 2.24511i 0.225881 0.179752i
\(157\) 4.74392 0.378606 0.189303 0.981919i \(-0.439377\pi\)
0.189303 + 0.981919i \(0.439377\pi\)
\(158\) −11.7661 + 6.79315i −0.936060 + 0.540434i
\(159\) 2.24021 + 3.88016i 0.177660 + 0.307716i
\(160\) 0 0
\(161\) 2.62270i 0.206698i
\(162\) 0.866025 + 0.500000i 0.0680414 + 0.0392837i
\(163\) 3.34855 + 1.93329i 0.262279 + 0.151427i 0.625374 0.780325i \(-0.284947\pi\)
−0.363095 + 0.931752i \(0.618280\pi\)
\(164\) 4.73601i 0.369820i
\(165\) 0 0
\(166\) −5.10226 8.83737i −0.396012 0.685913i
\(167\) −19.6785 + 11.3614i −1.52277 + 0.879173i −0.523134 + 0.852250i \(0.675237\pi\)
−0.999638 + 0.0269225i \(0.991429\pi\)
\(168\) −1.20627 −0.0930660
\(169\) 2.91899 12.6681i 0.224538 0.974465i
\(170\) 0 0
\(171\) −1.84474 + 1.06506i −0.141071 + 0.0814471i
\(172\) −0.986944 1.70944i −0.0752538 0.130343i
\(173\) 2.34900 4.06859i 0.178591 0.309329i −0.762807 0.646626i \(-0.776179\pi\)
0.941398 + 0.337297i \(0.109513\pi\)
\(174\) 4.76693i 0.361380i
\(175\) 0 0
\(176\) −4.46182 2.57603i −0.336322 0.194176i
\(177\) 1.94143i 0.145927i
\(178\) 8.19497 14.1941i 0.614239 1.06389i
\(179\) 4.34913 + 7.53292i 0.325069 + 0.563037i 0.981526 0.191327i \(-0.0612790\pi\)
−0.656457 + 0.754363i \(0.727946\pi\)
\(180\) 0 0
\(181\) 9.75480 0.725069 0.362534 0.931970i \(-0.381912\pi\)
0.362534 + 0.931970i \(0.381912\pi\)
\(182\) −3.40321 + 2.70821i −0.252263 + 0.200746i
\(183\) −3.07591 −0.227378
\(184\) −1.88293 + 1.08711i −0.138811 + 0.0801427i
\(185\) 0 0
\(186\) −2.95523 + 5.11861i −0.216688 + 0.375315i
\(187\) 24.4002i 1.78432i
\(188\) 0.738110 + 0.426148i 0.0538322 + 0.0310800i
\(189\) −1.04466 0.603137i −0.0759881 0.0438718i
\(190\) 0 0
\(191\) −5.77729 + 10.0066i −0.418030 + 0.724049i −0.995741 0.0921920i \(-0.970613\pi\)
0.577711 + 0.816241i \(0.303946\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) −9.06130 + 5.23154i −0.652247 + 0.376575i −0.789316 0.613987i \(-0.789565\pi\)
0.137070 + 0.990561i \(0.456232\pi\)
\(194\) 8.48278 0.609028
\(195\) 0 0
\(196\) −5.54490 −0.396065
\(197\) −15.2329 + 8.79472i −1.08530 + 0.626598i −0.932321 0.361632i \(-0.882220\pi\)
−0.152978 + 0.988230i \(0.548887\pi\)
\(198\) −2.57603 4.46182i −0.183071 0.317088i
\(199\) −12.7858 + 22.1457i −0.906362 + 1.56986i −0.0872828 + 0.996184i \(0.527818\pi\)
−0.819079 + 0.573681i \(0.805515\pi\)
\(200\) 0 0
\(201\) 12.1723 + 7.02765i 0.858564 + 0.495692i
\(202\) −11.7627 6.79121i −0.827623 0.477828i
\(203\) 5.75022i 0.403586i
\(204\) −2.36800 + 4.10150i −0.165793 + 0.287163i
\(205\) 0 0
\(206\) −1.86798 + 1.07848i −0.130148 + 0.0751412i
\(207\) −2.17422 −0.151119
\(208\) −3.35495 1.32073i −0.232624 0.0915760i
\(209\) 10.9745 0.759122
\(210\) 0 0
\(211\) −6.45984 11.1888i −0.444714 0.770267i 0.553318 0.832970i \(-0.313361\pi\)
−0.998032 + 0.0627029i \(0.980028\pi\)
\(212\) 2.24021 3.88016i 0.153858 0.266490i
\(213\) 0.344918i 0.0236334i
\(214\) 7.00959 + 4.04699i 0.479165 + 0.276646i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) 3.56482 6.17445i 0.241996 0.419149i
\(218\) 8.44195 + 14.6219i 0.571761 + 0.990319i
\(219\) −13.6164 + 7.86142i −0.920109 + 0.531225i
\(220\) 0 0
\(221\) 2.52757 + 16.8878i 0.170022 + 1.13600i
\(222\) −4.40068 −0.295354
\(223\) 6.19518 3.57679i 0.414860 0.239519i −0.278016 0.960576i \(-0.589677\pi\)
0.692876 + 0.721057i \(0.256343\pi\)
\(224\) 0.603137 + 1.04466i 0.0402988 + 0.0697995i
\(225\) 0 0
\(226\) 4.95102i 0.329337i
\(227\) −22.3768 12.9192i −1.48520 0.857480i −0.485340 0.874325i \(-0.661304\pi\)
−0.999858 + 0.0168460i \(0.994638\pi\)
\(228\) 1.84474 + 1.06506i 0.122171 + 0.0705353i
\(229\) 8.95153i 0.591533i −0.955260 0.295767i \(-0.904425\pi\)
0.955260 0.295767i \(-0.0955751\pi\)
\(230\) 0 0
\(231\) 3.10740 + 5.38217i 0.204452 + 0.354121i
\(232\) 4.12828 2.38346i 0.271035 0.156482i
\(233\) 3.86657 0.253308 0.126654 0.991947i \(-0.459576\pi\)
0.126654 + 0.991947i \(0.459576\pi\)
\(234\) −2.24511 2.82126i −0.146767 0.184431i
\(235\) 0 0
\(236\) −1.68133 + 0.970715i −0.109445 + 0.0631882i
\(237\) 6.79315 + 11.7661i 0.441263 + 0.764290i
\(238\) 2.85646 4.94754i 0.185157 0.320701i
\(239\) 15.4177i 0.997286i 0.866807 + 0.498643i \(0.166168\pi\)
−0.866807 + 0.498643i \(0.833832\pi\)
\(240\) 0 0
\(241\) 9.76603 + 5.63842i 0.629085 + 0.363203i 0.780398 0.625283i \(-0.215017\pi\)
−0.151312 + 0.988486i \(0.548350\pi\)
\(242\) 15.5438i 0.999191i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 1.53795 + 2.66381i 0.0984574 + 0.170533i
\(245\) 0 0
\(246\) −4.73601 −0.301957
\(247\) 7.59565 1.13682i 0.483299 0.0723344i
\(248\) 5.91046 0.375315
\(249\) −8.83737 + 5.10226i −0.560046 + 0.323342i
\(250\) 0 0
\(251\) 6.15329 10.6578i 0.388392 0.672715i −0.603841 0.797104i \(-0.706364\pi\)
0.992233 + 0.124390i \(0.0396973\pi\)
\(252\) 1.20627i 0.0759881i
\(253\) 9.70096 + 5.60085i 0.609894 + 0.352123i
\(254\) −1.04089 0.600957i −0.0653112 0.0377074i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 14.0434 + 24.3239i 0.876004 + 1.51728i 0.855689 + 0.517490i \(0.173134\pi\)
0.0203154 + 0.999794i \(0.493533\pi\)
\(258\) −1.70944 + 0.986944i −0.106425 + 0.0614444i
\(259\) 5.30842 0.329849
\(260\) 0 0
\(261\) 4.76693 0.295065
\(262\) 5.76036 3.32575i 0.355876 0.205465i
\(263\) −3.79178 6.56756i −0.233811 0.404973i 0.725115 0.688628i \(-0.241787\pi\)
−0.958927 + 0.283654i \(0.908453\pi\)
\(264\) −2.57603 + 4.46182i −0.158544 + 0.274606i
\(265\) 0 0
\(266\) −2.22526 1.28475i −0.136439 0.0787732i
\(267\) −14.1941 8.19497i −0.868665 0.501524i
\(268\) 14.0553i 0.858564i
\(269\) 12.2355 21.1924i 0.746010 1.29213i −0.203712 0.979031i \(-0.565301\pi\)
0.949722 0.313096i \(-0.101366\pi\)
\(270\) 0 0
\(271\) 10.0199 5.78497i 0.608664 0.351412i −0.163779 0.986497i \(-0.552368\pi\)
0.772442 + 0.635085i \(0.219035\pi\)
\(272\) 4.73601 0.287163
\(273\) 2.70821 + 3.40321i 0.163909 + 0.205972i
\(274\) −14.7149 −0.888961
\(275\) 0 0
\(276\) 1.08711 + 1.88293i 0.0654363 + 0.113339i
\(277\) 6.47271 11.2111i 0.388908 0.673608i −0.603395 0.797442i \(-0.706186\pi\)
0.992303 + 0.123835i \(0.0395192\pi\)
\(278\) 15.6508i 0.938673i
\(279\) 5.11861 + 2.95523i 0.306443 + 0.176925i
\(280\) 0 0
\(281\) 2.57187i 0.153425i −0.997053 0.0767124i \(-0.975558\pi\)
0.997053 0.0767124i \(-0.0244423\pi\)
\(282\) 0.426148 0.738110i 0.0253767 0.0439538i
\(283\) 2.77427 + 4.80517i 0.164913 + 0.285638i 0.936624 0.350335i \(-0.113932\pi\)
−0.771711 + 0.635973i \(0.780599\pi\)
\(284\) −0.298707 + 0.172459i −0.0177250 + 0.0102335i
\(285\) 0 0
\(286\) 2.74961 + 18.3714i 0.162588 + 1.08632i
\(287\) 5.71292 0.337223
\(288\) −0.866025 + 0.500000i −0.0510310 + 0.0294628i
\(289\) −2.71489 4.70233i −0.159700 0.276608i
\(290\) 0 0
\(291\) 8.48278i 0.497270i
\(292\) 13.6164 + 7.86142i 0.796838 + 0.460055i
\(293\) −20.8986 12.0658i −1.22091 0.704891i −0.255795 0.966731i \(-0.582337\pi\)
−0.965111 + 0.261840i \(0.915671\pi\)
\(294\) 5.54490i 0.323385i
\(295\) 0 0
\(296\) 2.20034 + 3.81110i 0.127892 + 0.221516i
\(297\) −4.46182 + 2.57603i −0.258901 + 0.149477i
\(298\) −22.8116 −1.32144
\(299\) 7.29439 + 2.87155i 0.421845 + 0.166066i
\(300\) 0 0
\(301\) 2.06205 1.19052i 0.118855 0.0686207i
\(302\) −9.94975 17.2335i −0.572544 0.991675i
\(303\) −6.79121 + 11.7627i −0.390145 + 0.675751i
\(304\) 2.13012i 0.122171i
\(305\) 0 0
\(306\) 4.10150 + 2.36800i 0.234467 + 0.135370i
\(307\) 30.3243i 1.73070i 0.501171 + 0.865348i \(0.332903\pi\)
−0.501171 + 0.865348i \(0.667097\pi\)
\(308\) 3.10740 5.38217i 0.177061 0.306678i
\(309\) 1.07848 + 1.86798i 0.0613525 + 0.106266i
\(310\) 0 0
\(311\) 8.76406 0.496964 0.248482 0.968636i \(-0.420068\pi\)
0.248482 + 0.968636i \(0.420068\pi\)
\(312\) −1.32073 + 3.35495i −0.0747715 + 0.189937i
\(313\) −29.0155 −1.64005 −0.820026 0.572326i \(-0.806041\pi\)
−0.820026 + 0.572326i \(0.806041\pi\)
\(314\) −4.10836 + 2.37196i −0.231848 + 0.133857i
\(315\) 0 0
\(316\) 6.79315 11.7661i 0.382145 0.661894i
\(317\) 25.9970i 1.46014i −0.683375 0.730068i \(-0.739489\pi\)
0.683375 0.730068i \(-0.260511\pi\)
\(318\) −3.88016 2.24021i −0.217588 0.125625i
\(319\) −21.2692 12.2798i −1.19084 0.687534i
\(320\) 0 0
\(321\) 4.04699 7.00959i 0.225881 0.391237i
\(322\) −1.31135 2.27133i −0.0730787 0.126576i
\(323\) −8.73669 + 5.04413i −0.486122 + 0.280663i
\(324\) −1.00000 −0.0555556
\(325\) 0 0
\(326\) −3.86657 −0.214150
\(327\) 14.6219 8.44195i 0.808592 0.466841i
\(328\) 2.36800 + 4.10150i 0.130751 + 0.226468i
\(329\) −0.514051 + 0.890362i −0.0283405 + 0.0490873i
\(330\) 0 0
\(331\) −9.56025 5.51961i −0.525479 0.303385i 0.213694 0.976901i \(-0.431450\pi\)
−0.739173 + 0.673515i \(0.764784\pi\)
\(332\) 8.83737 + 5.10226i 0.485014 + 0.280023i
\(333\) 4.40068i 0.241156i
\(334\) 11.3614 19.6785i 0.621669 1.07676i
\(335\) 0 0
\(336\) 1.04466 0.603137i 0.0569911 0.0329038i
\(337\) −17.7108 −0.964769 −0.482384 0.875960i \(-0.660229\pi\)
−0.482384 + 0.875960i \(0.660229\pi\)
\(338\) 3.80611 + 12.4303i 0.207025 + 0.676122i
\(339\) −4.95102 −0.268902
\(340\) 0 0
\(341\) −15.2255 26.3714i −0.824509 1.42809i
\(342\) 1.06506 1.84474i 0.0575918 0.0997519i
\(343\) 15.1326i 0.817083i
\(344\) 1.70944 + 0.986944i 0.0921667 + 0.0532124i
\(345\) 0 0
\(346\) 4.69800i 0.252566i
\(347\) 17.3509 30.0526i 0.931443 1.61331i 0.150587 0.988597i \(-0.451884\pi\)
0.780857 0.624710i \(-0.214783\pi\)
\(348\) −2.38346 4.12828i −0.127767 0.221299i
\(349\) 30.4563 17.5840i 1.63029 0.941249i 0.646288 0.763093i \(-0.276320\pi\)
0.984002 0.178156i \(-0.0570131\pi\)
\(350\) 0 0
\(351\) −2.82126 + 2.24511i −0.150588 + 0.119835i
\(352\) 5.15206 0.274606
\(353\) 9.60495 5.54542i 0.511220 0.295153i −0.222115 0.975020i \(-0.571296\pi\)
0.733335 + 0.679868i \(0.237963\pi\)
\(354\) 0.970715 + 1.68133i 0.0515929 + 0.0893616i
\(355\) 0 0
\(356\) 16.3899i 0.868665i
\(357\) −4.94754 2.85646i −0.261851 0.151180i
\(358\) −7.53292 4.34913i −0.398127 0.229859i
\(359\) 26.1575i 1.38054i 0.723552 + 0.690270i \(0.242508\pi\)
−0.723552 + 0.690270i \(0.757492\pi\)
\(360\) 0 0
\(361\) −7.23130 12.5250i −0.380595 0.659209i
\(362\) −8.44791 + 4.87740i −0.444012 + 0.256351i
\(363\) 15.5438 0.815836
\(364\) 1.59316 4.04699i 0.0835042 0.212120i
\(365\) 0 0
\(366\) 2.66381 1.53795i 0.139240 0.0803901i
\(367\) −7.79352 13.4988i −0.406818 0.704630i 0.587713 0.809070i \(-0.300028\pi\)
−0.994531 + 0.104440i \(0.966695\pi\)
\(368\) 1.08711 1.88293i 0.0566695 0.0981544i
\(369\) 4.73601i 0.246547i
\(370\) 0 0
\(371\) 4.68053 + 2.70231i 0.243001 + 0.140297i
\(372\) 5.91046i 0.306443i
\(373\) −0.496728 + 0.860358i −0.0257196 + 0.0445476i −0.878599 0.477561i \(-0.841521\pi\)
0.852879 + 0.522108i \(0.174854\pi\)
\(374\) −12.2001 21.1312i −0.630853 1.09267i
\(375\) 0 0
\(376\) −0.852296 −0.0439538
\(377\) −15.9928 6.29581i −0.823671 0.324251i
\(378\) 1.20627 0.0620440
\(379\) −23.7856 + 13.7326i −1.22178 + 0.705398i −0.965298 0.261150i \(-0.915898\pi\)
−0.256486 + 0.966548i \(0.582565\pi\)
\(380\) 0 0
\(381\) −0.600957 + 1.04089i −0.0307880 + 0.0533263i
\(382\) 11.5546i 0.591184i
\(383\) −28.2067 16.2851i −1.44130 0.832132i −0.443359 0.896344i \(-0.646213\pi\)
−0.997936 + 0.0642122i \(0.979547\pi\)
\(384\) 0.866025 + 0.500000i 0.0441942 + 0.0255155i
\(385\) 0 0
\(386\) 5.23154 9.06130i 0.266279 0.461208i
\(387\) 0.986944 + 1.70944i 0.0501692 + 0.0868956i
\(388\) −7.34631 + 4.24139i −0.372952 + 0.215324i
\(389\) 16.9110 0.857421 0.428710 0.903442i \(-0.358968\pi\)
0.428710 + 0.903442i \(0.358968\pi\)
\(390\) 0 0
\(391\) −10.2971 −0.520747
\(392\) 4.80203 2.77245i 0.242539 0.140030i
\(393\) −3.32575 5.76036i −0.167762 0.290572i
\(394\) 8.79472 15.2329i 0.443072 0.767423i
\(395\) 0 0
\(396\) 4.46182 + 2.57603i 0.224215 + 0.129450i
\(397\) −27.9204 16.1198i −1.40128 0.809031i −0.406759 0.913536i \(-0.633341\pi\)
−0.994524 + 0.104504i \(0.966674\pi\)
\(398\) 25.5716i 1.28179i
\(399\) −1.28475 + 2.22526i −0.0643181 + 0.111402i
\(400\) 0 0
\(401\) 28.0082 16.1705i 1.39866 0.807518i 0.404410 0.914578i \(-0.367477\pi\)
0.994253 + 0.107060i \(0.0341437\pi\)
\(402\) −14.0553 −0.701015
\(403\) −13.2696 16.6749i −0.661007 0.830638i
\(404\) 13.5824 0.675751
\(405\) 0 0
\(406\) 2.87511 + 4.97984i 0.142689 + 0.247145i
\(407\) 11.3363 19.6350i 0.561919 0.973272i
\(408\) 4.73601i 0.234467i
\(409\) −1.00971 0.582957i −0.0499270 0.0288254i 0.474829 0.880078i \(-0.342510\pi\)
−0.524756 + 0.851253i \(0.675843\pi\)
\(410\) 0 0
\(411\) 14.7149i 0.725833i
\(412\) 1.07848 1.86798i 0.0531328 0.0920288i
\(413\) −1.17095 2.02814i −0.0576186 0.0997984i
\(414\) 1.88293 1.08711i 0.0925408 0.0534285i
\(415\) 0 0
\(416\) 3.56583 0.533691i 0.174829 0.0261663i
\(417\) 15.6508 0.766423
\(418\) −9.50420 + 5.48725i −0.464866 + 0.268390i
\(419\) −5.91396 10.2433i −0.288916 0.500417i 0.684635 0.728886i \(-0.259961\pi\)
−0.973551 + 0.228469i \(0.926628\pi\)
\(420\) 0 0
\(421\) 23.9102i 1.16531i 0.812719 + 0.582655i \(0.197986\pi\)
−0.812719 + 0.582655i \(0.802014\pi\)
\(422\) 11.1888 + 6.45984i 0.544661 + 0.314460i
\(423\) −0.738110 0.426148i −0.0358881 0.0207200i
\(424\) 4.48042i 0.217588i
\(425\) 0 0
\(426\) 0.172459 + 0.298707i 0.00835566 + 0.0144724i
\(427\) −3.21329 + 1.85519i −0.155502 + 0.0897791i
\(428\) −8.09397 −0.391237
\(429\) 18.3714 2.74961i 0.886980 0.132752i
\(430\) 0 0
\(431\) −22.8082 + 13.1683i −1.09863 + 0.634294i −0.935861 0.352370i \(-0.885376\pi\)
−0.162769 + 0.986664i \(0.552043\pi\)
\(432\) 0.500000 + 0.866025i 0.0240563 + 0.0416667i
\(433\) −6.47972 + 11.2232i −0.311396 + 0.539353i −0.978665 0.205464i \(-0.934130\pi\)
0.667269 + 0.744817i \(0.267463\pi\)
\(434\) 7.12964i 0.342234i
\(435\) 0 0
\(436\) −14.6219 8.44195i −0.700261 0.404296i
\(437\) 4.63134i 0.221547i
\(438\) 7.86142 13.6164i 0.375633 0.650615i
\(439\) −11.6234 20.1324i −0.554756 0.960865i −0.997922 0.0644259i \(-0.979478\pi\)
0.443167 0.896439i \(-0.353855\pi\)
\(440\) 0 0
\(441\) 5.54490 0.264043
\(442\) −10.6328 13.3615i −0.505753 0.635542i
\(443\) −23.3728 −1.11047 −0.555237 0.831692i \(-0.687373\pi\)
−0.555237 + 0.831692i \(0.687373\pi\)
\(444\) 3.81110 2.20034i 0.180867 0.104423i
\(445\) 0 0
\(446\) −3.57679 + 6.19518i −0.169366 + 0.293350i
\(447\) 22.8116i 1.07895i
\(448\) −1.04466 0.603137i −0.0493557 0.0284955i
\(449\) −1.20931 0.698196i −0.0570709 0.0329499i 0.471193 0.882030i \(-0.343824\pi\)
−0.528264 + 0.849080i \(0.677157\pi\)
\(450\) 0 0
\(451\) 12.2001 21.1312i 0.574481 0.995030i
\(452\) 2.47551 + 4.28771i 0.116438 + 0.201677i
\(453\) −17.2335 + 9.94975i −0.809699 + 0.467480i
\(454\) 25.8385 1.21266
\(455\) 0 0
\(456\) −2.13012 −0.0997519
\(457\) 6.23699 3.60093i 0.291754 0.168444i −0.346979 0.937873i \(-0.612792\pi\)
0.638733 + 0.769429i \(0.279459\pi\)
\(458\) 4.47576 + 7.75225i 0.209139 + 0.362239i
\(459\) 2.36800 4.10150i 0.110529 0.191442i
\(460\) 0 0
\(461\) −4.10920 2.37245i −0.191384 0.110496i 0.401246 0.915970i \(-0.368577\pi\)
−0.592630 + 0.805474i \(0.701911\pi\)
\(462\) −5.38217 3.10740i −0.250401 0.144569i
\(463\) 15.7510i 0.732012i 0.930612 + 0.366006i \(0.119275\pi\)
−0.930612 + 0.366006i \(0.880725\pi\)
\(464\) −2.38346 + 4.12828i −0.110650 + 0.191651i
\(465\) 0 0
\(466\) −3.34855 + 1.93329i −0.155119 + 0.0895578i
\(467\) −17.9789 −0.831962 −0.415981 0.909373i \(-0.636562\pi\)
−0.415981 + 0.909373i \(0.636562\pi\)
\(468\) 3.35495 + 1.32073i 0.155083 + 0.0610506i
\(469\) 16.9545 0.782888
\(470\) 0 0
\(471\) 2.37196 + 4.10836i 0.109294 + 0.189303i
\(472\) 0.970715 1.68133i 0.0446808 0.0773894i
\(473\) 10.1696i 0.467598i
\(474\) −11.7661 6.79315i −0.540434 0.312020i
\(475\) 0 0
\(476\) 5.71292i 0.261851i
\(477\) −2.24021 + 3.88016i −0.102572 + 0.177660i
\(478\) −7.70884 13.3521i −0.352594 0.610711i
\(479\) −2.83964 + 1.63947i −0.129747 + 0.0749093i −0.563468 0.826138i \(-0.690533\pi\)
0.433722 + 0.901047i \(0.357200\pi\)
\(480\) 0 0
\(481\) 5.81210 14.7640i 0.265009 0.673183i
\(482\) −11.2768 −0.513646
\(483\) −2.27133 + 1.31135i −0.103349 + 0.0596685i
\(484\) −7.77188 13.4613i −0.353267 0.611877i
\(485\) 0 0
\(486\) 1.00000i 0.0453609i
\(487\) 8.64037 + 4.98852i 0.391533 + 0.226052i 0.682824 0.730583i \(-0.260752\pi\)
−0.291291 + 0.956634i \(0.594085\pi\)
\(488\) −2.66381 1.53795i −0.120585 0.0696199i
\(489\) 3.86657i 0.174852i
\(490\) 0 0
\(491\) 10.0376 + 17.3857i 0.452992 + 0.784605i 0.998570 0.0534548i \(-0.0170233\pi\)
−0.545578 + 0.838060i \(0.683690\pi\)
\(492\) 4.10150 2.36800i 0.184910 0.106758i
\(493\) 22.5762 1.01678
\(494\) −6.00961 + 4.78234i −0.270385 + 0.215168i
\(495\) 0 0
\(496\) −5.11861 + 2.95523i −0.229832 + 0.132694i
\(497\) −0.208033 0.360323i −0.00933153 0.0161627i
\(498\) 5.10226 8.83737i 0.228638 0.396012i
\(499\) 23.9474i 1.07203i 0.844208 + 0.536016i \(0.180071\pi\)
−0.844208 + 0.536016i \(0.819929\pi\)
\(500\) 0 0
\(501\) −19.6785 11.3614i −0.879173 0.507591i
\(502\) 12.3066i 0.549269i
\(503\) −6.08395 + 10.5377i −0.271270 + 0.469853i −0.969187 0.246325i \(-0.920777\pi\)
0.697917 + 0.716178i \(0.254110\pi\)
\(504\) −0.603137 1.04466i −0.0268659 0.0465330i
\(505\) 0 0
\(506\) −11.2017 −0.497977
\(507\) 12.4303 3.80611i 0.552051 0.169035i
\(508\) 1.20191 0.0533263
\(509\) −34.9666 + 20.1880i −1.54987 + 0.894817i −0.551717 + 0.834031i \(0.686027\pi\)
−0.998151 + 0.0607857i \(0.980639\pi\)
\(510\) 0 0
\(511\) −9.48302 + 16.4251i −0.419504 + 0.726602i
\(512\) 1.00000i 0.0441942i
\(513\) −1.84474 1.06506i −0.0814471 0.0470235i
\(514\) −24.3239 14.0434i −1.07288 0.619429i
\(515\) 0 0
\(516\) 0.986944 1.70944i 0.0434478 0.0752538i
\(517\) 2.19554 + 3.80279i 0.0965598 + 0.167246i
\(518\) −4.59723 + 2.65421i −0.201991 + 0.116619i
\(519\) 4.69800 0.206219
\(520\) 0 0
\(521\) −0.259356 −0.0113626 −0.00568129 0.999984i \(-0.501808\pi\)
−0.00568129 + 0.999984i \(0.501808\pi\)
\(522\) −4.12828 + 2.38346i −0.180690 + 0.104321i
\(523\) −19.3139 33.4527i −0.844539 1.46278i −0.886021 0.463645i \(-0.846541\pi\)
0.0414825 0.999139i \(-0.486792\pi\)
\(524\) −3.32575 + 5.76036i −0.145286 + 0.251642i
\(525\) 0 0
\(526\) 6.56756 + 3.79178i 0.286359 + 0.165330i
\(527\) 24.2418 + 13.9960i 1.05599 + 0.609676i
\(528\) 5.15206i 0.224215i
\(529\) 9.13639 15.8247i 0.397234 0.688030i
\(530\) 0 0
\(531\) 1.68133 0.970715i 0.0729634 0.0421255i
\(532\) 2.56951 0.111402
\(533\) 6.25498 15.8891i 0.270933 0.688232i
\(534\) 16.3899 0.709262
\(535\) 0 0
\(536\) 7.02765 + 12.1723i 0.303548 + 0.525761i
\(537\) −4.34913 + 7.53292i −0.187679 + 0.325069i
\(538\) 24.4709i 1.05502i
\(539\) −24.7403 14.2838i −1.06564 0.615249i
\(540\) 0 0
\(541\) 19.4443i 0.835975i −0.908453 0.417988i \(-0.862736\pi\)
0.908453 0.417988i \(-0.137264\pi\)
\(542\) −5.78497 + 10.0199i −0.248486 + 0.430390i
\(543\) 4.87740 + 8.44791i 0.209309 + 0.362534i
\(544\) −4.10150 + 2.36800i −0.175851 + 0.101527i
\(545\) 0 0
\(546\) −4.04699 1.59316i −0.173195 0.0681809i
\(547\) −25.2121 −1.07799 −0.538997 0.842308i \(-0.681197\pi\)
−0.538997 + 0.842308i \(0.681197\pi\)
\(548\) 12.7435 7.35746i 0.544375 0.314295i
\(549\) −1.53795 2.66381i −0.0656383 0.113689i
\(550\) 0 0
\(551\) 10.1541i 0.432580i
\(552\) −1.88293 1.08711i −0.0801427 0.0462704i
\(553\) 14.1931 + 8.19440i 0.603553 + 0.348462i
\(554\) 12.9454i 0.549998i
\(555\) 0 0
\(556\) −7.82540 13.5540i −0.331871 0.574817i
\(557\) 9.75916 5.63445i 0.413509 0.238739i −0.278787 0.960353i \(-0.589933\pi\)
0.692296 + 0.721613i \(0.256599\pi\)
\(558\) −5.91046 −0.250210
\(559\) −1.05345 7.03856i −0.0445560 0.297699i
\(560\) 0 0
\(561\) −21.1312 + 12.2001i −0.892160 + 0.515089i
\(562\) 1.28593 + 2.22730i 0.0542439 + 0.0939531i
\(563\) 8.22694 14.2495i 0.346724 0.600544i −0.638941 0.769256i \(-0.720627\pi\)
0.985665 + 0.168712i \(0.0539607\pi\)
\(564\) 0.852296i 0.0358881i
\(565\) 0 0
\(566\) −4.80517 2.77427i −0.201976 0.116611i
\(567\) 1.20627i 0.0506587i
\(568\) 0.172459 0.298707i 0.00723621 0.0125335i
\(569\) −15.2444 26.4040i −0.639077 1.10691i −0.985636 0.168886i \(-0.945983\pi\)
0.346558 0.938028i \(-0.387350\pi\)
\(570\) 0 0
\(571\) 13.0909 0.547836 0.273918 0.961753i \(-0.411680\pi\)
0.273918 + 0.961753i \(0.411680\pi\)
\(572\) −11.5669 14.5353i −0.483638 0.607751i
\(573\) −11.5546 −0.482699
\(574\) −4.94754 + 2.85646i −0.206506 + 0.119226i
\(575\) 0 0
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) 13.1315i 0.546670i −0.961919 0.273335i \(-0.911873\pi\)
0.961919 0.273335i \(-0.0881268\pi\)
\(578\) 4.70233 + 2.71489i 0.195591 + 0.112925i
\(579\) −9.06130 5.23154i −0.376575 0.217416i
\(580\) 0 0
\(581\) −6.15472 + 10.6603i −0.255341 + 0.442263i
\(582\) 4.24139 + 7.34631i 0.175811 + 0.304514i
\(583\) 19.9908 11.5417i 0.827935 0.478009i
\(584\) −15.7228 −0.650615
\(585\) 0 0
\(586\) 24.1316 0.996866
\(587\) −5.26171 + 3.03785i −0.217174 + 0.125386i −0.604641 0.796498i \(-0.706683\pi\)
0.387467 + 0.921884i \(0.373350\pi\)
\(588\) −2.77245 4.80203i −0.114334 0.198032i
\(589\) 6.29499 10.9032i 0.259381 0.449260i
\(590\) 0 0
\(591\) −15.2329 8.79472i −0.626598 0.361767i
\(592\) −3.81110 2.20034i −0.156635 0.0904334i
\(593\) 18.3609i 0.753990i −0.926215 0.376995i \(-0.876957\pi\)
0.926215 0.376995i \(-0.123043\pi\)
\(594\) 2.57603 4.46182i 0.105696 0.183071i
\(595\) 0 0
\(596\) 19.7555 11.4058i 0.809215 0.467200i
\(597\) −25.5716 −1.04658
\(598\) −7.75290 + 1.16036i −0.317040 + 0.0474507i
\(599\) −22.1098 −0.903382 −0.451691 0.892174i \(-0.649179\pi\)
−0.451691 + 0.892174i \(0.649179\pi\)
\(600\) 0 0
\(601\) −5.90349 10.2251i −0.240808 0.417092i 0.720136 0.693832i \(-0.244079\pi\)
−0.960945 + 0.276740i \(0.910746\pi\)
\(602\) −1.19052 + 2.06205i −0.0485222 + 0.0840428i
\(603\) 14.0553i 0.572376i
\(604\) 17.2335 + 9.94975i 0.701220 + 0.404850i
\(605\) 0 0
\(606\) 13.5824i 0.551748i
\(607\) −12.8818 + 22.3119i −0.522856 + 0.905612i 0.476791 + 0.879017i \(0.341800\pi\)
−0.999646 + 0.0265955i \(0.991533\pi\)
\(608\) 1.06506 + 1.84474i 0.0431938 + 0.0748139i
\(609\) 4.97984 2.87511i 0.201793 0.116505i
\(610\) 0 0
\(611\) 1.91349 + 2.40455i 0.0774117 + 0.0972775i
\(612\) −4.73601 −0.191442
\(613\) 11.3307 6.54178i 0.457642 0.264220i −0.253410 0.967359i \(-0.581552\pi\)
0.711052 + 0.703139i \(0.248219\pi\)
\(614\) −15.1621 26.2616i −0.611894 1.05983i
\(615\) 0 0
\(616\) 6.21480i 0.250401i
\(617\) −3.82634 2.20914i −0.154043 0.0889366i 0.420997 0.907062i \(-0.361680\pi\)
−0.575040 + 0.818125i \(0.695014\pi\)
\(618\) −1.86798 1.07848i −0.0751412 0.0433828i
\(619\) 1.12760i 0.0453220i −0.999743 0.0226610i \(-0.992786\pi\)
0.999743 0.0226610i \(-0.00721383\pi\)
\(620\) 0 0
\(621\) −1.08711 1.88293i −0.0436242 0.0755593i
\(622\) −7.58990 + 4.38203i −0.304327 + 0.175703i
\(623\) −19.7708 −0.792099
\(624\) −0.533691 3.56583i −0.0213647 0.142748i
\(625\) 0 0
\(626\) 25.1282 14.5077i 1.00432 0.579846i
\(627\) 5.48725 + 9.50420i 0.219140 + 0.379561i
\(628\) 2.37196 4.10836i 0.0946515 0.163941i
\(629\) 20.8417i 0.831011i
\(630\) 0 0
\(631\) −14.3916 8.30898i −0.572920 0.330775i 0.185395 0.982664i \(-0.440644\pi\)
−0.758315 + 0.651889i \(0.773977\pi\)
\(632\) 13.5863i 0.540434i
\(633\) 6.45984 11.1888i 0.256756 0.444714i
\(634\) 12.9985 + 22.5140i 0.516236 + 0.894147i
\(635\) 0 0
\(636\) 4.48042 0.177660
\(637\) −18.6029 7.32331i −0.737072 0.290160i
\(638\) 24.5595 0.972320
\(639\) 0.298707 0.172459i 0.0118167 0.00682236i
\(640\) 0 0
\(641\) 5.05184 8.75005i 0.199536 0.345606i −0.748842 0.662748i \(-0.769390\pi\)
0.948378 + 0.317142i \(0.102723\pi\)
\(642\) 8.09397i 0.319444i
\(643\) 30.3469 + 17.5208i 1.19676 + 0.690951i 0.959832 0.280575i \(-0.0905251\pi\)
0.236931 + 0.971526i \(0.423858\pi\)
\(644\) 2.27133 + 1.31135i 0.0895028 + 0.0516745i
\(645\) 0 0
\(646\) 5.04413 8.73669i 0.198459 0.343740i
\(647\) −9.98031 17.2864i −0.392366 0.679598i 0.600395 0.799704i \(-0.295010\pi\)
−0.992761 + 0.120105i \(0.961677\pi\)
\(648\) 0.866025 0.500000i 0.0340207 0.0196419i
\(649\) −10.0024 −0.392628
\(650\) 0 0
\(651\) 7.12964 0.279433
\(652\) 3.34855 1.93329i 0.131139 0.0757133i
\(653\) −2.60621 4.51410i −0.101989 0.176650i 0.810515 0.585718i \(-0.199187\pi\)
−0.912504 + 0.409068i \(0.865854\pi\)
\(654\) −8.44195 + 14.6219i −0.330106 + 0.571761i
\(655\) 0 0
\(656\) −4.10150 2.36800i −0.160137 0.0924551i
\(657\) −13.6164 7.86142i −0.531225 0.306703i
\(658\) 1.02810i 0.0400796i
\(659\) −3.66183 + 6.34248i −0.142645 + 0.247068i −0.928492 0.371353i \(-0.878894\pi\)
0.785847 + 0.618421i \(0.212227\pi\)
\(660\) 0 0
\(661\) −31.7189 + 18.3129i −1.23372 + 0.712289i −0.967803 0.251707i \(-0.919008\pi\)
−0.265917 + 0.963996i \(0.585675\pi\)
\(662\) 11.0392 0.429052
\(663\) −13.3615 + 10.6328i −0.518918 + 0.412946i
\(664\) −10.2045 −0.396012
\(665\) 0 0
\(666\) −2.20034 3.81110i −0.0852614 0.147677i
\(667\) 5.18217 8.97578i 0.200654 0.347543i
\(668\) 22.7228i 0.879173i
\(669\) 6.19518 + 3.57679i 0.239519 + 0.138287i
\(670\) 0 0
\(671\) 15.8473i 0.611777i
\(672\) −0.603137 + 1.04466i −0.0232665 + 0.0402988i
\(673\) −16.9909 29.4292i −0.654952 1.13441i −0.981906 0.189370i \(-0.939355\pi\)
0.326953 0.945041i \(-0.393978\pi\)
\(674\) 15.3380 8.85540i 0.590798 0.341097i
\(675\) 0 0
\(676\) −9.51136 8.86194i −0.365822 0.340844i
\(677\) 41.7902 1.60613 0.803063 0.595894i \(-0.203202\pi\)
0.803063 + 0.595894i \(0.203202\pi\)
\(678\) 4.28771 2.47551i 0.164668 0.0950713i
\(679\) −5.11628 8.86166i −0.196345 0.340079i
\(680\) 0 0
\(681\) 25.8385i 0.990132i
\(682\) 26.3714 + 15.2255i 1.00981 + 0.583016i
\(683\) −41.9280 24.2071i −1.60433 0.926260i −0.990607 0.136737i \(-0.956338\pi\)
−0.613721 0.789523i \(-0.710328\pi\)
\(684\) 2.13012i 0.0814471i
\(685\) 0 0
\(686\) 7.56629 + 13.1052i 0.288882 + 0.500359i
\(687\) 7.75225 4.47576i 0.295767 0.170761i
\(688\) −1.97389 −0.0752538
\(689\) 12.6404 10.0590i 0.481562 0.383218i
\(690\) 0 0
\(691\) −23.8905 + 13.7932i −0.908837 + 0.524717i −0.880057 0.474868i \(-0.842496\pi\)
−0.0287804 + 0.999586i \(0.509162\pi\)
\(692\) −2.34900 4.06859i −0.0892955 0.154664i
\(693\) −3.10740 + 5.38217i −0.118040 + 0.204452i
\(694\) 34.7017i 1.31726i
\(695\) 0 0
\(696\) 4.12828 + 2.38346i 0.156482 + 0.0903449i
\(697\) 22.4298i 0.849589i
\(698\) −17.5840 + 30.4563i −0.665563 + 1.15279i
\(699\) 1.93329 + 3.34855i 0.0731236 + 0.126654i
\(700\) 0 0
\(701\) −19.7883 −0.747392 −0.373696 0.927551i \(-0.621910\pi\)
−0.373696 + 0.927551i \(0.621910\pi\)
\(702\) 1.32073 3.35495i 0.0498476 0.126624i
\(703\) 9.37396 0.353546
\(704\) −4.46182 + 2.57603i −0.168161 + 0.0970879i
\(705\) 0 0
\(706\) −5.54542 + 9.60495i −0.208705 + 0.361487i
\(707\) 16.3841i 0.616189i
\(708\) −1.68133 0.970715i −0.0631882 0.0364817i
\(709\) 6.09389 + 3.51831i 0.228861 + 0.132133i 0.610046 0.792366i \(-0.291151\pi\)
−0.381186 + 0.924499i \(0.624484\pi\)
\(710\) 0 0
\(711\) −6.79315 + 11.7661i −0.254763 + 0.441263i
\(712\) −8.19497 14.1941i −0.307119 0.531946i
\(713\) 11.1290 6.42532i 0.416783 0.240630i
\(714\) 5.71292 0.213801
\(715\) 0 0
\(716\) 8.69827 0.325069
\(717\) −13.3521 + 7.70884i −0.498643 + 0.287892i
\(718\) −13.0788 22.6531i −0.488095 0.845405i
\(719\) 5.52118 9.56296i 0.205905 0.356638i −0.744516 0.667605i \(-0.767319\pi\)
0.950421 + 0.310967i \(0.100653\pi\)
\(720\) 0 0
\(721\) 2.25330 + 1.30094i 0.0839171 + 0.0484496i
\(722\) 12.5250 + 7.23130i 0.466131 + 0.269121i
\(723\) 11.2768i 0.419390i
\(724\) 4.87740 8.44791i 0.181267 0.313964i
\(725\) 0 0
\(726\) −13.4613 + 7.77188i −0.499595 + 0.288442i
\(727\) −14.1056 −0.523147 −0.261573 0.965184i \(-0.584241\pi\)
−0.261573 + 0.965184i \(0.584241\pi\)
\(728\) 0.643777 + 4.30137i 0.0238600 + 0.159419i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 4.67418 + 8.09591i 0.172881 + 0.299438i
\(732\) −1.53795 + 2.66381i −0.0568444 + 0.0984574i
\(733\) 11.3855i 0.420535i 0.977644 + 0.210267i \(0.0674334\pi\)
−0.977644 + 0.210267i \(0.932567\pi\)
\(734\) 13.4988 + 7.79352i 0.498249 + 0.287664i
\(735\) 0 0
\(736\) 2.17422i 0.0801427i
\(737\) 36.2069 62.7122i 1.33370 2.31003i
\(738\) −2.36800 4.10150i −0.0871675 0.150978i
\(739\) 7.93251 4.57983i 0.291802 0.168472i −0.346952 0.937883i \(-0.612783\pi\)
0.638754 + 0.769411i \(0.279450\pi\)
\(740\) 0 0
\(741\) 4.78234 + 6.00961i 0.175684 + 0.220769i
\(742\) −5.40461 −0.198410
\(743\) 34.5658 19.9566i 1.26809 0.732135i 0.293468 0.955969i \(-0.405191\pi\)
0.974627 + 0.223834i \(0.0718574\pi\)
\(744\) 2.95523 + 5.11861i 0.108344 + 0.187657i
\(745\) 0 0
\(746\) 0.993455i 0.0363730i
\(747\) −8.83737 5.10226i −0.323342 0.186682i
\(748\) 21.1312 + 12.2001i 0.772634 + 0.446080i
\(749\) 9.76355i 0.356752i
\(750\) 0 0
\(751\) 8.79993 + 15.2419i 0.321114 + 0.556186i 0.980718 0.195427i \(-0.0626094\pi\)
−0.659604 + 0.751613i \(0.729276\pi\)
\(752\) 0.738110 0.426148i 0.0269161 0.0155400i
\(753\) 12.3066 0.448476
\(754\) 16.9981 2.54407i 0.619033 0.0926494i
\(755\) 0 0
\(756\) −1.04466 + 0.603137i −0.0379941 + 0.0219359i
\(757\) 11.0331 + 19.1099i 0.401004 + 0.694560i 0.993847 0.110758i \(-0.0353280\pi\)
−0.592843 + 0.805318i \(0.701995\pi\)
\(758\) 13.7326 23.7856i 0.498791 0.863932i
\(759\) 11.2017i 0.406596i
\(760\) 0 0
\(761\) −17.4454 10.0721i −0.632394 0.365113i 0.149285 0.988794i \(-0.452303\pi\)
−0.781678 + 0.623682i \(0.785636\pi\)
\(762\) 1.20191i 0.0435408i
\(763\) 10.1833 17.6380i 0.368660 0.638538i
\(764\) 5.77729 + 10.0066i 0.209015 + 0.362025i
\(765\) 0 0
\(766\) 32.5703 1.17681
\(767\) −6.92282 + 1.03612i −0.249969 + 0.0374123i
\(768\) −1.00000 −0.0360844
\(769\) −26.9356 + 15.5513i −0.971323 + 0.560794i −0.899639 0.436634i \(-0.856171\pi\)
−0.0716840 + 0.997427i \(0.522837\pi\)
\(770\) 0 0
\(771\) −14.0434 + 24.3239i −0.505761 + 0.876004i
\(772\) 10.4631i 0.376575i
\(773\) −0.720739 0.416119i −0.0259232 0.0149668i 0.486982 0.873412i \(-0.338098\pi\)
−0.512906 + 0.858445i \(0.671431\pi\)
\(774\) −1.70944 0.986944i −0.0614444 0.0354750i
\(775\) 0 0
\(776\) 4.24139 7.34631i 0.152257 0.263717i
\(777\) 2.65421 + 4.59723i 0.0952193 + 0.164925i
\(778\) −14.6453 + 8.45549i −0.525061 + 0.303144i
\(779\) 10.0883 0.361449
\(780\) 0 0
\(781\) −1.77704 −0.0635874
\(782\) 8.91756 5.14856i 0.318891 0.184112i
\(783\) 2.38346 + 4.12828i 0.0851780 + 0.147533i
\(784\) −2.77245 + 4.80203i −0.0990161 + 0.171501i