Properties

Label 380.2.d.b.379.1
Level $380$
Weight $2$
Character 380.379
Analytic conductor $3.034$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $8$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.03431527681\)
Analytic rank: \(0\)
Dimension: \(40\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 379.1
Character \(\chi\) \(=\) 380.379
Dual form 380.2.d.b.379.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.39672 - 0.221721i) q^{2} -2.04365i q^{3} +(1.90168 + 0.619368i) q^{4} +(0.665544 - 2.13473i) q^{5} +(-0.453121 + 2.85442i) q^{6} +2.07881 q^{7} +(-2.51879 - 1.28673i) q^{8} -1.17650 q^{9} +O(q^{10})\) \(q+(-1.39672 - 0.221721i) q^{2} -2.04365i q^{3} +(1.90168 + 0.619368i) q^{4} +(0.665544 - 2.13473i) q^{5} +(-0.453121 + 2.85442i) q^{6} +2.07881 q^{7} +(-2.51879 - 1.28673i) q^{8} -1.17650 q^{9} +(-1.40290 + 2.83406i) q^{10} -4.08691i q^{11} +(1.26577 - 3.88637i) q^{12} +4.52166 q^{13} +(-2.90352 - 0.460916i) q^{14} +(-4.36263 - 1.36014i) q^{15} +(3.23277 + 2.35568i) q^{16} +6.58081i q^{17} +(1.64325 + 0.260856i) q^{18} +(4.31870 - 0.590625i) q^{19} +(2.58783 - 3.64735i) q^{20} -4.24835i q^{21} +(-0.906157 + 5.70829i) q^{22} -7.09670 q^{23} +(-2.62962 + 5.14753i) q^{24} +(-4.11410 - 2.84151i) q^{25} +(-6.31551 - 1.00255i) q^{26} -3.72659i q^{27} +(3.95323 + 1.28755i) q^{28} +5.90320i q^{29} +(5.79182 + 2.86703i) q^{30} -1.69936 q^{31} +(-3.99298 - 4.00701i) q^{32} -8.35222 q^{33} +(1.45911 - 9.19158i) q^{34} +(1.38354 - 4.43768i) q^{35} +(-2.23733 - 0.728688i) q^{36} -1.81756 q^{37} +(-6.16299 - 0.132608i) q^{38} -9.24068i q^{39} +(-4.42318 + 4.52056i) q^{40} -1.10137i q^{41} +(-0.941951 + 5.93378i) q^{42} -7.73444 q^{43} +(2.53130 - 7.77200i) q^{44} +(-0.783014 + 2.51151i) q^{45} +(9.91214 + 1.57349i) q^{46} +9.98526 q^{47} +(4.81418 - 6.60664i) q^{48} -2.67856 q^{49} +(5.11624 + 4.88099i) q^{50} +13.4489 q^{51} +(8.59874 + 2.80057i) q^{52} -2.18817 q^{53} +(-0.826265 + 5.20502i) q^{54} +(-8.72444 - 2.72002i) q^{55} +(-5.23609 - 2.67486i) q^{56} +(-1.20703 - 8.82591i) q^{57} +(1.30887 - 8.24514i) q^{58} -9.39966 q^{59} +(-7.45390 - 5.28862i) q^{60} +4.95794 q^{61} +(2.37353 + 0.376784i) q^{62} -2.44572 q^{63} +(4.68866 + 6.48201i) q^{64} +(3.00936 - 9.65250i) q^{65} +(11.6657 + 1.85187i) q^{66} +13.3041i q^{67} +(-4.07594 + 12.5146i) q^{68} +14.5032i q^{69} +(-2.91635 + 5.89146i) q^{70} +4.67605 q^{71} +(2.96337 + 1.51384i) q^{72} +6.18455i q^{73} +(2.53863 + 0.402992i) q^{74} +(-5.80704 + 8.40778i) q^{75} +(8.57859 + 1.55168i) q^{76} -8.49591i q^{77} +(-2.04886 + 12.9067i) q^{78} -4.04921 q^{79} +(7.18027 - 5.33326i) q^{80} -11.1453 q^{81} +(-0.244198 + 1.53831i) q^{82} +7.46362 q^{83} +(2.63129 - 8.07901i) q^{84} +(14.0482 + 4.37982i) q^{85} +(10.8029 + 1.71489i) q^{86} +12.0641 q^{87} +(-5.25875 + 10.2941i) q^{88} -0.553472i q^{89} +(1.65051 - 3.33428i) q^{90} +9.39966 q^{91} +(-13.4956 - 4.39547i) q^{92} +3.47289i q^{93} +(-13.9467 - 2.21395i) q^{94} +(1.61346 - 9.61232i) q^{95} +(-8.18892 + 8.16025i) q^{96} +12.4166 q^{97} +(3.74121 + 0.593894i) q^{98} +4.80826i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 4q^{5} + 8q^{6} - 8q^{9} + O(q^{10}) \) \( 40q - 4q^{5} + 8q^{6} - 8q^{9} - 8q^{16} - 20q^{20} - 40q^{24} - 84q^{25} - 24q^{26} + 24q^{30} + 24q^{36} - 40q^{44} - 12q^{45} + 128q^{49} - 120q^{54} + 24q^{61} + 72q^{64} + 112q^{66} + 32q^{74} + 56q^{76} + 96q^{80} - 72q^{81} + 44q^{85} - 40q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\) \(191\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.39672 0.221721i −0.987633 0.156781i
\(3\) 2.04365i 1.17990i −0.807439 0.589951i \(-0.799147\pi\)
0.807439 0.589951i \(-0.200853\pi\)
\(4\) 1.90168 + 0.619368i 0.950840 + 0.309684i
\(5\) 0.665544 2.13473i 0.297640 0.954678i
\(6\) −0.453121 + 2.85442i −0.184986 + 1.16531i
\(7\) 2.07881 0.785715 0.392858 0.919599i \(-0.371486\pi\)
0.392858 + 0.919599i \(0.371486\pi\)
\(8\) −2.51879 1.28673i −0.890528 0.454927i
\(9\) −1.17650 −0.392167
\(10\) −1.40290 + 2.83406i −0.443635 + 0.896208i
\(11\) 4.08691i 1.23225i −0.787648 0.616125i \(-0.788701\pi\)
0.787648 0.616125i \(-0.211299\pi\)
\(12\) 1.26577 3.88637i 0.365396 1.12190i
\(13\) 4.52166 1.25408 0.627041 0.778986i \(-0.284266\pi\)
0.627041 + 0.778986i \(0.284266\pi\)
\(14\) −2.90352 0.460916i −0.775999 0.123185i
\(15\) −4.36263 1.36014i −1.12643 0.351186i
\(16\) 3.23277 + 2.35568i 0.808192 + 0.588919i
\(17\) 6.58081i 1.59608i 0.602604 + 0.798041i \(0.294130\pi\)
−0.602604 + 0.798041i \(0.705870\pi\)
\(18\) 1.64325 + 0.260856i 0.387318 + 0.0614843i
\(19\) 4.31870 0.590625i 0.990778 0.135499i
\(20\) 2.58783 3.64735i 0.578657 0.815571i
\(21\) 4.24835i 0.927067i
\(22\) −0.906157 + 5.70829i −0.193193 + 1.21701i
\(23\) −7.09670 −1.47976 −0.739882 0.672736i \(-0.765119\pi\)
−0.739882 + 0.672736i \(0.765119\pi\)
\(24\) −2.62962 + 5.14753i −0.536770 + 1.05074i
\(25\) −4.11410 2.84151i −0.822820 0.568301i
\(26\) −6.31551 1.00255i −1.23857 0.196616i
\(27\) 3.72659i 0.717183i
\(28\) 3.95323 + 1.28755i 0.747089 + 0.243323i
\(29\) 5.90320i 1.09620i 0.836414 + 0.548098i \(0.184648\pi\)
−0.836414 + 0.548098i \(0.815352\pi\)
\(30\) 5.79182 + 2.86703i 1.05744 + 0.523445i
\(31\) −1.69936 −0.305214 −0.152607 0.988287i \(-0.548767\pi\)
−0.152607 + 0.988287i \(0.548767\pi\)
\(32\) −3.99298 4.00701i −0.705866 0.708345i
\(33\) −8.35222 −1.45393
\(34\) 1.45911 9.19158i 0.250235 1.57634i
\(35\) 1.38354 4.43768i 0.233861 0.750105i
\(36\) −2.23733 0.728688i −0.372888 0.121448i
\(37\) −1.81756 −0.298805 −0.149403 0.988776i \(-0.547735\pi\)
−0.149403 + 0.988776i \(0.547735\pi\)
\(38\) −6.16299 0.132608i −0.999769 0.0215119i
\(39\) 9.24068i 1.47969i
\(40\) −4.42318 + 4.52056i −0.699367 + 0.714763i
\(41\) 1.10137i 0.172005i −0.996295 0.0860027i \(-0.972591\pi\)
0.996295 0.0860027i \(-0.0274094\pi\)
\(42\) −0.941951 + 5.93378i −0.145346 + 0.915602i
\(43\) −7.73444 −1.17949 −0.589746 0.807589i \(-0.700772\pi\)
−0.589746 + 0.807589i \(0.700772\pi\)
\(44\) 2.53130 7.77200i 0.381608 1.17167i
\(45\) −0.783014 + 2.51151i −0.116725 + 0.374394i
\(46\) 9.91214 + 1.57349i 1.46146 + 0.231999i
\(47\) 9.98526 1.45650 0.728250 0.685312i \(-0.240334\pi\)
0.728250 + 0.685312i \(0.240334\pi\)
\(48\) 4.81418 6.60664i 0.694867 0.953587i
\(49\) −2.67856 −0.382651
\(50\) 5.11624 + 4.88099i 0.723546 + 0.690276i
\(51\) 13.4489 1.88322
\(52\) 8.59874 + 2.80057i 1.19243 + 0.388369i
\(53\) −2.18817 −0.300568 −0.150284 0.988643i \(-0.548019\pi\)
−0.150284 + 0.988643i \(0.548019\pi\)
\(54\) −0.826265 + 5.20502i −0.112440 + 0.708313i
\(55\) −8.72444 2.72002i −1.17640 0.366768i
\(56\) −5.23609 2.67486i −0.699702 0.357444i
\(57\) −1.20703 8.82591i −0.159875 1.16902i
\(58\) 1.30887 8.24514i 0.171863 1.08264i
\(59\) −9.39966 −1.22373 −0.611866 0.790962i \(-0.709581\pi\)
−0.611866 + 0.790962i \(0.709581\pi\)
\(60\) −7.45390 5.28862i −0.962294 0.682758i
\(61\) 4.95794 0.634800 0.317400 0.948292i \(-0.397190\pi\)
0.317400 + 0.948292i \(0.397190\pi\)
\(62\) 2.37353 + 0.376784i 0.301439 + 0.0478516i
\(63\) −2.44572 −0.308132
\(64\) 4.68866 + 6.48201i 0.586082 + 0.810252i
\(65\) 3.00936 9.65250i 0.373266 1.19724i
\(66\) 11.6657 + 1.85187i 1.43595 + 0.227949i
\(67\) 13.3041i 1.62536i 0.582713 + 0.812678i \(0.301991\pi\)
−0.582713 + 0.812678i \(0.698009\pi\)
\(68\) −4.07594 + 12.5146i −0.494281 + 1.51762i
\(69\) 14.5032i 1.74598i
\(70\) −2.91635 + 5.89146i −0.348571 + 0.704164i
\(71\) 4.67605 0.554945 0.277472 0.960734i \(-0.410503\pi\)
0.277472 + 0.960734i \(0.410503\pi\)
\(72\) 2.96337 + 1.51384i 0.349236 + 0.178408i
\(73\) 6.18455i 0.723846i 0.932208 + 0.361923i \(0.117880\pi\)
−0.932208 + 0.361923i \(0.882120\pi\)
\(74\) 2.53863 + 0.402992i 0.295110 + 0.0468469i
\(75\) −5.80704 + 8.40778i −0.670540 + 0.970847i
\(76\) 8.57859 + 1.55168i 0.984032 + 0.177990i
\(77\) 8.49591i 0.968199i
\(78\) −2.04886 + 12.9067i −0.231988 + 1.46139i
\(79\) −4.04921 −0.455572 −0.227786 0.973711i \(-0.573149\pi\)
−0.227786 + 0.973711i \(0.573149\pi\)
\(80\) 7.18027 5.33326i 0.802779 0.596277i
\(81\) −11.1453 −1.23837
\(82\) −0.244198 + 1.53831i −0.0269671 + 0.169878i
\(83\) 7.46362 0.819238 0.409619 0.912257i \(-0.365662\pi\)
0.409619 + 0.912257i \(0.365662\pi\)
\(84\) 2.63129 8.07901i 0.287098 0.881492i
\(85\) 14.0482 + 4.37982i 1.52374 + 0.475058i
\(86\) 10.8029 + 1.71489i 1.16491 + 0.184922i
\(87\) 12.0641 1.29340
\(88\) −5.25875 + 10.2941i −0.560585 + 1.09735i
\(89\) 0.553472i 0.0586680i −0.999570 0.0293340i \(-0.990661\pi\)
0.999570 0.0293340i \(-0.00933864\pi\)
\(90\) 1.65051 3.33428i 0.173979 0.351463i
\(91\) 9.39966 0.985352
\(92\) −13.4956 4.39547i −1.40702 0.458259i
\(93\) 3.47289i 0.360122i
\(94\) −13.9467 2.21395i −1.43849 0.228351i
\(95\) 1.61346 9.61232i 0.165538 0.986203i
\(96\) −8.18892 + 8.16025i −0.835778 + 0.832852i
\(97\) 12.4166 1.26071 0.630355 0.776307i \(-0.282909\pi\)
0.630355 + 0.776307i \(0.282909\pi\)
\(98\) 3.74121 + 0.593894i 0.377919 + 0.0599923i
\(99\) 4.80826i 0.483249i
\(100\) −6.06376 7.95178i −0.606376 0.795178i
\(101\) 9.53915 0.949181 0.474591 0.880207i \(-0.342596\pi\)
0.474591 + 0.880207i \(0.342596\pi\)
\(102\) −18.7844 2.98190i −1.85993 0.295252i
\(103\) 14.1699i 1.39620i 0.715998 + 0.698102i \(0.245972\pi\)
−0.715998 + 0.698102i \(0.754028\pi\)
\(104\) −11.3891 5.81815i −1.11680 0.570517i
\(105\) −9.06907 2.82747i −0.885050 0.275933i
\(106\) 3.05626 + 0.485163i 0.296851 + 0.0471232i
\(107\) 2.59574i 0.250940i 0.992097 + 0.125470i \(0.0400438\pi\)
−0.992097 + 0.125470i \(0.959956\pi\)
\(108\) 2.30813 7.08678i 0.222100 0.681926i
\(109\) 12.6595i 1.21256i −0.795251 0.606280i \(-0.792661\pi\)
0.795251 0.606280i \(-0.207339\pi\)
\(110\) 11.5825 + 5.73352i 1.10435 + 0.546669i
\(111\) 3.71446i 0.352561i
\(112\) 6.72030 + 4.89700i 0.635009 + 0.462723i
\(113\) 12.9394 1.21724 0.608620 0.793461i \(-0.291723\pi\)
0.608620 + 0.793461i \(0.291723\pi\)
\(114\) −0.271005 + 12.5950i −0.0253819 + 1.17963i
\(115\) −4.72317 + 15.1495i −0.440438 + 1.41270i
\(116\) −3.65625 + 11.2260i −0.339474 + 1.04231i
\(117\) −5.31974 −0.491810
\(118\) 13.1287 + 2.08411i 1.20860 + 0.191858i
\(119\) 13.6802i 1.25407i
\(120\) 9.23844 + 9.03943i 0.843350 + 0.825184i
\(121\) −5.70286 −0.518442
\(122\) −6.92488 1.09928i −0.626949 0.0995244i
\(123\) −2.25082 −0.202949
\(124\) −3.23163 1.05253i −0.290209 0.0945197i
\(125\) −8.80395 + 6.89133i −0.787449 + 0.616379i
\(126\) 3.41600 + 0.542269i 0.304322 + 0.0483092i
\(127\) 7.32119i 0.649651i −0.945774 0.324825i \(-0.894695\pi\)
0.945774 0.324825i \(-0.105305\pi\)
\(128\) −5.11156 10.0932i −0.451802 0.892118i
\(129\) 15.8065i 1.39168i
\(130\) −6.34342 + 12.8146i −0.556355 + 1.12392i
\(131\) 11.3901i 0.995160i 0.867418 + 0.497580i \(0.165778\pi\)
−0.867418 + 0.497580i \(0.834222\pi\)
\(132\) −15.8832 5.17309i −1.38246 0.450260i
\(133\) 8.97775 1.22780i 0.778469 0.106463i
\(134\) 2.94981 18.5822i 0.254825 1.60526i
\(135\) −7.95524 2.48021i −0.684678 0.213462i
\(136\) 8.46772 16.5757i 0.726101 1.42136i
\(137\) 7.24081i 0.618624i 0.950961 + 0.309312i \(0.100099\pi\)
−0.950961 + 0.309312i \(0.899901\pi\)
\(138\) 3.21566 20.2569i 0.273736 1.72438i
\(139\) 0.0394231i 0.00334382i −0.999999 0.00167191i \(-0.999468\pi\)
0.999999 0.00167191i \(-0.000532186\pi\)
\(140\) 5.37960 7.58213i 0.454659 0.640807i
\(141\) 20.4064i 1.71853i
\(142\) −6.53115 1.03678i −0.548082 0.0870047i
\(143\) 18.4796i 1.54534i
\(144\) −3.80336 2.77146i −0.316947 0.230955i
\(145\) 12.6017 + 3.92884i 1.04651 + 0.326272i
\(146\) 1.37125 8.63811i 0.113485 0.714895i
\(147\) 5.47403i 0.451491i
\(148\) −3.45642 1.12574i −0.284116 0.0925352i
\(149\) 7.71138 0.631741 0.315870 0.948802i \(-0.397704\pi\)
0.315870 + 0.948802i \(0.397704\pi\)
\(150\) 9.97503 10.4558i 0.814458 0.853713i
\(151\) −8.63740 −0.702902 −0.351451 0.936206i \(-0.614312\pi\)
−0.351451 + 0.936206i \(0.614312\pi\)
\(152\) −11.6379 4.06933i −0.943958 0.330067i
\(153\) 7.74234i 0.625931i
\(154\) −1.88373 + 11.8664i −0.151795 + 0.956225i
\(155\) −1.13100 + 3.62766i −0.0908439 + 0.291381i
\(156\) 5.72338 17.5728i 0.458237 1.40695i
\(157\) 17.2555i 1.37714i −0.725169 0.688571i \(-0.758238\pi\)
0.725169 0.688571i \(-0.241762\pi\)
\(158\) 5.65563 + 0.897797i 0.449938 + 0.0714249i
\(159\) 4.47184i 0.354640i
\(160\) −11.2114 + 5.85708i −0.886336 + 0.463043i
\(161\) −14.7527 −1.16267
\(162\) 15.5670 + 2.47116i 1.22306 + 0.194153i
\(163\) 5.21280 0.408298 0.204149 0.978940i \(-0.434557\pi\)
0.204149 + 0.978940i \(0.434557\pi\)
\(164\) 0.682154 2.09446i 0.0532673 0.163549i
\(165\) −5.55877 + 17.8297i −0.432750 + 1.38804i
\(166\) −10.4246 1.65484i −0.809107 0.128441i
\(167\) 14.1450i 1.09457i −0.836946 0.547285i \(-0.815661\pi\)
0.836946 0.547285i \(-0.184339\pi\)
\(168\) −5.46648 + 10.7007i −0.421748 + 0.825579i
\(169\) 7.44540 0.572723
\(170\) −18.6504 9.23220i −1.43042 0.708077i
\(171\) −5.08096 + 0.694871i −0.388551 + 0.0531381i
\(172\) −14.7084 4.79046i −1.12151 0.365269i
\(173\) −5.48227 −0.416809 −0.208405 0.978043i \(-0.566827\pi\)
−0.208405 + 0.978043i \(0.566827\pi\)
\(174\) −16.8502 2.67486i −1.27741 0.202781i
\(175\) −8.55243 5.90695i −0.646503 0.446523i
\(176\) 9.62745 13.2120i 0.725696 0.995895i
\(177\) 19.2096i 1.44388i
\(178\) −0.122717 + 0.773049i −0.00919801 + 0.0579424i
\(179\) −1.18947 −0.0889053 −0.0444527 0.999011i \(-0.514154\pi\)
−0.0444527 + 0.999011i \(0.514154\pi\)
\(180\) −3.04459 + 4.29111i −0.226930 + 0.319841i
\(181\) 5.10146i 0.379189i −0.981863 0.189594i \(-0.939283\pi\)
0.981863 0.189594i \(-0.0607173\pi\)
\(182\) −13.1287 2.08411i −0.973167 0.154484i
\(183\) 10.1323i 0.749001i
\(184\) 17.8751 + 9.13153i 1.31777 + 0.673186i
\(185\) −1.20967 + 3.87999i −0.0889365 + 0.285263i
\(186\) 0.770014 4.85067i 0.0564602 0.355668i
\(187\) 26.8952 1.96677
\(188\) 18.9888 + 6.18455i 1.38490 + 0.451054i
\(189\) 7.74686i 0.563501i
\(190\) −4.38482 + 13.0680i −0.318108 + 0.948054i
\(191\) 4.80768i 0.347872i 0.984757 + 0.173936i \(0.0556486\pi\)
−0.984757 + 0.173936i \(0.944351\pi\)
\(192\) 13.2470 9.58197i 0.956017 0.691519i
\(193\) −22.0347 −1.58609 −0.793045 0.609163i \(-0.791506\pi\)
−0.793045 + 0.609163i \(0.791506\pi\)
\(194\) −17.3425 2.75302i −1.24512 0.197655i
\(195\) −19.7263 6.15008i −1.41263 0.440417i
\(196\) −5.09376 1.65901i −0.363840 0.118501i
\(197\) 15.9745i 1.13814i −0.822290 0.569069i \(-0.807304\pi\)
0.822290 0.569069i \(-0.192696\pi\)
\(198\) 1.06610 6.71582i 0.0757641 0.477273i
\(199\) 12.4990i 0.886030i −0.896514 0.443015i \(-0.853909\pi\)
0.896514 0.443015i \(-0.146091\pi\)
\(200\) 6.70633 + 12.4509i 0.474209 + 0.880412i
\(201\) 27.1889 1.91776
\(202\) −13.3236 2.11504i −0.937443 0.148813i
\(203\) 12.2716i 0.861298i
\(204\) 25.5754 + 8.32980i 1.79064 + 0.583202i
\(205\) −2.35113 0.733011i −0.164210 0.0511957i
\(206\) 3.14178 19.7915i 0.218898 1.37894i
\(207\) 8.34929 0.580315
\(208\) 14.6175 + 10.6516i 1.01354 + 0.738553i
\(209\) −2.41383 17.6502i −0.166968 1.22089i
\(210\) 12.0401 + 5.96000i 0.830844 + 0.411279i
\(211\) 9.66236 0.665184 0.332592 0.943071i \(-0.392077\pi\)
0.332592 + 0.943071i \(0.392077\pi\)
\(212\) −4.16119 1.35528i −0.285792 0.0930810i
\(213\) 9.55620i 0.654780i
\(214\) 0.575531 3.62553i 0.0393425 0.247836i
\(215\) −5.14761 + 16.5109i −0.351064 + 1.12603i
\(216\) −4.79511 + 9.38651i −0.326266 + 0.638671i
\(217\) −3.53264 −0.239811
\(218\) −2.80688 + 17.6818i −0.190106 + 1.19757i
\(219\) 12.6390 0.854068
\(220\) −14.9064 10.5762i −1.00499 0.713050i
\(221\) 29.7562i 2.00162i
\(222\) 0.823575 5.18807i 0.0552747 0.348201i
\(223\) 8.38081i 0.561220i −0.959822 0.280610i \(-0.909463\pi\)
0.959822 0.280610i \(-0.0905368\pi\)
\(224\) −8.30064 8.32980i −0.554610 0.556558i
\(225\) 4.84025 + 3.34304i 0.322683 + 0.222869i
\(226\) −18.0728 2.86895i −1.20219 0.190840i
\(227\) 7.85463i 0.521330i 0.965429 + 0.260665i \(0.0839418\pi\)
−0.965429 + 0.260665i \(0.916058\pi\)
\(228\) 3.17110 17.5316i 0.210011 1.16106i
\(229\) −12.6232 −0.834162 −0.417081 0.908869i \(-0.636947\pi\)
−0.417081 + 0.908869i \(0.636947\pi\)
\(230\) 9.95594 20.1125i 0.656475 1.32618i
\(231\) −17.3627 −1.14238
\(232\) 7.59582 14.8689i 0.498690 0.976194i
\(233\) 7.08234i 0.463980i −0.972718 0.231990i \(-0.925476\pi\)
0.972718 0.231990i \(-0.0745236\pi\)
\(234\) 7.43021 + 1.17950i 0.485728 + 0.0771064i
\(235\) 6.64563 21.3158i 0.433513 1.39049i
\(236\) −17.8751 5.82185i −1.16357 0.378970i
\(237\) 8.27517i 0.537530i
\(238\) 3.03320 19.1075i 0.196613 1.23856i
\(239\) 17.5612i 1.13594i 0.823050 + 0.567969i \(0.192271\pi\)
−0.823050 + 0.567969i \(0.807729\pi\)
\(240\) −10.8993 14.6740i −0.703548 0.947200i
\(241\) 25.5078i 1.64310i 0.570134 + 0.821552i \(0.306891\pi\)
−0.570134 + 0.821552i \(0.693109\pi\)
\(242\) 7.96533 + 1.26445i 0.512031 + 0.0812818i
\(243\) 11.5974i 0.743975i
\(244\) 9.42842 + 3.07079i 0.603593 + 0.196587i
\(245\) −1.78270 + 5.71799i −0.113892 + 0.365309i
\(246\) 3.14377 + 0.499055i 0.200440 + 0.0318186i
\(247\) 19.5277 2.67060i 1.24252 0.169926i
\(248\) 4.28033 + 2.18661i 0.271801 + 0.138850i
\(249\) 15.2530i 0.966620i
\(250\) 13.8247 7.67326i 0.874348 0.485300i
\(251\) 17.7479i 1.12024i 0.828412 + 0.560120i \(0.189245\pi\)
−0.828412 + 0.560120i \(0.810755\pi\)
\(252\) −4.65098 1.51480i −0.292984 0.0954235i
\(253\) 29.0036i 1.82344i
\(254\) −1.62327 + 10.2257i −0.101853 + 0.641617i
\(255\) 8.95082 28.7096i 0.560522 1.79787i
\(256\) 4.90157 + 15.2307i 0.306348 + 0.951920i
\(257\) −11.6378 −0.725947 −0.362974 0.931799i \(-0.618238\pi\)
−0.362974 + 0.931799i \(0.618238\pi\)
\(258\) 3.50464 22.0773i 0.218189 1.37447i
\(259\) −3.77836 −0.234776
\(260\) 11.7013 16.4921i 0.725683 1.02279i
\(261\) 6.94513i 0.429893i
\(262\) 2.52544 15.9089i 0.156022 0.982854i
\(263\) 27.2166 1.67825 0.839123 0.543942i \(-0.183069\pi\)
0.839123 + 0.543942i \(0.183069\pi\)
\(264\) 21.0375 + 10.7470i 1.29477 + 0.661435i
\(265\) −1.45632 + 4.67113i −0.0894611 + 0.286945i
\(266\) −12.8117 0.275667i −0.785534 0.0169022i
\(267\) −1.13110 −0.0692224
\(268\) −8.24014 + 25.3002i −0.503347 + 1.54545i
\(269\) 20.4064i 1.24420i −0.782939 0.622099i \(-0.786280\pi\)
0.782939 0.622099i \(-0.213720\pi\)
\(270\) 10.5614 + 5.22802i 0.642744 + 0.318167i
\(271\) 2.86027i 0.173749i −0.996219 0.0868746i \(-0.972312\pi\)
0.996219 0.0868746i \(-0.0276879\pi\)
\(272\) −15.5023 + 21.2742i −0.939963 + 1.28994i
\(273\) 19.2096i 1.16262i
\(274\) 1.60544 10.1134i 0.0969883 0.610974i
\(275\) −11.6130 + 16.8140i −0.700290 + 1.01392i
\(276\) −8.98279 + 27.5804i −0.540701 + 1.66014i
\(277\) 0.796560i 0.0478606i 0.999714 + 0.0239303i \(0.00761799\pi\)
−0.999714 + 0.0239303i \(0.992382\pi\)
\(278\) −0.00874094 + 0.0550632i −0.000524247 + 0.00330247i
\(279\) 1.99930 0.119695
\(280\) −9.19495 + 9.39737i −0.549503 + 0.561601i
\(281\) 8.04650i 0.480014i 0.970771 + 0.240007i \(0.0771497\pi\)
−0.970771 + 0.240007i \(0.922850\pi\)
\(282\) −4.52453 + 28.5021i −0.269432 + 1.69727i
\(283\) −29.0701 −1.72804 −0.864019 0.503459i \(-0.832061\pi\)
−0.864019 + 0.503459i \(0.832061\pi\)
\(284\) 8.89234 + 2.89619i 0.527663 + 0.171857i
\(285\) −19.6442 3.29735i −1.16362 0.195318i
\(286\) −4.09733 + 25.8110i −0.242280 + 1.52623i
\(287\) 2.28954i 0.135147i
\(288\) 4.69775 + 4.71425i 0.276818 + 0.277790i
\(289\) −26.3071 −1.54748
\(290\) −16.7300 8.28157i −0.982420 0.486311i
\(291\) 25.3751i 1.48751i
\(292\) −3.83051 + 11.7610i −0.224164 + 0.688262i
\(293\) −0.297923 −0.0174048 −0.00870242 0.999962i \(-0.502770\pi\)
−0.00870242 + 0.999962i \(0.502770\pi\)
\(294\) 1.21371 7.64572i 0.0707851 0.445907i
\(295\) −6.25589 + 20.0657i −0.364232 + 1.16827i
\(296\) 4.57806 + 2.33871i 0.266095 + 0.135935i
\(297\) −15.2303 −0.883749
\(298\) −10.7707 1.70978i −0.623928 0.0990448i
\(299\) −32.0889 −1.85575
\(300\) −16.2506 + 12.3922i −0.938231 + 0.715464i
\(301\) −16.0784 −0.926745
\(302\) 12.0641 + 1.91510i 0.694209 + 0.110201i
\(303\) 19.4947i 1.11994i
\(304\) 15.3527 + 8.26411i 0.880536 + 0.473979i
\(305\) 3.29973 10.5838i 0.188942 0.606029i
\(306\) −1.71664 + 10.8139i −0.0981340 + 0.618190i
\(307\) 18.1387i 1.03523i 0.855613 + 0.517616i \(0.173181\pi\)
−0.855613 + 0.517616i \(0.826819\pi\)
\(308\) 5.26209 16.1565i 0.299835 0.920602i
\(309\) 28.9584 1.64738
\(310\) 2.38402 4.81608i 0.135403 0.273535i
\(311\) 3.19194i 0.180998i 0.995897 + 0.0904991i \(0.0288462\pi\)
−0.995897 + 0.0904991i \(0.971154\pi\)
\(312\) −11.8903 + 23.2754i −0.673153 + 1.31771i
\(313\) 5.38799i 0.304547i 0.988338 + 0.152274i \(0.0486595\pi\)
−0.988338 + 0.152274i \(0.951341\pi\)
\(314\) −3.82593 + 24.1012i −0.215909 + 1.36011i
\(315\) −1.62774 + 5.22094i −0.0917125 + 0.294167i
\(316\) −7.70030 2.50795i −0.433176 0.141083i
\(317\) 19.5632 1.09878 0.549389 0.835567i \(-0.314861\pi\)
0.549389 + 0.835567i \(0.314861\pi\)
\(318\) 0.991504 6.24593i 0.0556008 0.350255i
\(319\) 24.1259 1.35079
\(320\) 16.9578 5.69492i 0.947971 0.318356i
\(321\) 5.30478 0.296084
\(322\) 20.6054 + 3.27099i 1.14830 + 0.182285i
\(323\) 3.88679 + 28.4205i 0.216267 + 1.58136i
\(324\) −21.1949 6.90307i −1.17749 0.383504i
\(325\) −18.6026 12.8483i −1.03188 0.712697i
\(326\) −7.28084 1.15579i −0.403249 0.0640133i
\(327\) −25.8716 −1.43070
\(328\) −1.41717 + 2.77413i −0.0782500 + 0.153176i
\(329\) 20.7574 1.14439
\(330\) 11.7173 23.6707i 0.645016 1.30303i
\(331\) −4.81147 −0.264462 −0.132231 0.991219i \(-0.542214\pi\)
−0.132231 + 0.991219i \(0.542214\pi\)
\(332\) 14.1934 + 4.62272i 0.778964 + 0.253705i
\(333\) 2.13837 0.117182
\(334\) −3.13624 + 19.7566i −0.171608 + 1.08103i
\(335\) 28.4006 + 8.85448i 1.55169 + 0.483772i
\(336\) 10.0078 13.7339i 0.545968 0.749248i
\(337\) 2.60018 0.141641 0.0708205 0.997489i \(-0.477438\pi\)
0.0708205 + 0.997489i \(0.477438\pi\)
\(338\) −10.3992 1.65080i −0.565640 0.0897919i
\(339\) 26.4437i 1.43622i
\(340\) 24.0025 + 17.0300i 1.30172 + 0.923583i
\(341\) 6.94513i 0.376100i
\(342\) 7.25077 + 0.156014i 0.392077 + 0.00843627i
\(343\) −20.1199 −1.08637
\(344\) 19.4815 + 9.95213i 1.05037 + 0.536583i
\(345\) 30.9603 + 9.65250i 1.66685 + 0.519673i
\(346\) 7.65722 + 1.21554i 0.411655 + 0.0653476i
\(347\) −7.24605 −0.388988 −0.194494 0.980904i \(-0.562306\pi\)
−0.194494 + 0.980904i \(0.562306\pi\)
\(348\) 22.9420 + 7.47209i 1.22982 + 0.400546i
\(349\) 3.34575 0.179094 0.0895469 0.995983i \(-0.471458\pi\)
0.0895469 + 0.995983i \(0.471458\pi\)
\(350\) 10.6357 + 10.1466i 0.568501 + 0.542360i
\(351\) 16.8504i 0.899406i
\(352\) −16.3763 + 16.3190i −0.872859 + 0.869804i
\(353\) 12.2638i 0.652738i −0.945243 0.326369i \(-0.894175\pi\)
0.945243 0.326369i \(-0.105825\pi\)
\(354\) 4.25918 26.8305i 0.226373 1.42603i
\(355\) 3.11212 9.98207i 0.165174 0.529794i
\(356\) 0.342803 1.05253i 0.0181685 0.0557838i
\(357\) 27.9576 1.47967
\(358\) 1.66136 + 0.263732i 0.0878059 + 0.0139386i
\(359\) 4.98189i 0.262934i 0.991321 + 0.131467i \(0.0419688\pi\)
−0.991321 + 0.131467i \(0.958031\pi\)
\(360\) 5.20388 5.31845i 0.274269 0.280307i
\(361\) 18.3023 5.10146i 0.963280 0.268498i
\(362\) −1.13110 + 7.12534i −0.0594495 + 0.374499i
\(363\) 11.6547i 0.611711i
\(364\) 17.8751 + 5.82185i 0.936912 + 0.305148i
\(365\) 13.2023 + 4.11609i 0.691040 + 0.215446i
\(366\) −2.24655 + 14.1520i −0.117429 + 0.739739i
\(367\) −0.268098 −0.0139946 −0.00699731 0.999976i \(-0.502227\pi\)
−0.00699731 + 0.999976i \(0.502227\pi\)
\(368\) −22.9420 16.7175i −1.19593 0.871462i
\(369\) 1.29577i 0.0674549i
\(370\) 2.54985 5.15107i 0.132560 0.267792i
\(371\) −4.54878 −0.236161
\(372\) −2.15100 + 6.60432i −0.111524 + 0.342418i
\(373\) 37.5031 1.94183 0.970917 0.239415i \(-0.0769558\pi\)
0.970917 + 0.239415i \(0.0769558\pi\)
\(374\) −37.5652 5.96325i −1.94245 0.308352i
\(375\) 14.0835 + 17.9922i 0.727267 + 0.929113i
\(376\) −25.1508 12.8483i −1.29705 0.662602i
\(377\) 26.6922i 1.37472i
\(378\) −1.71765 + 10.8202i −0.0883462 + 0.556533i
\(379\) 13.5658 0.696829 0.348415 0.937340i \(-0.386720\pi\)
0.348415 + 0.937340i \(0.386720\pi\)
\(380\) 9.02185 17.2802i 0.462811 0.886457i
\(381\) −14.9619 −0.766524
\(382\) 1.06597 6.71501i 0.0545396 0.343570i
\(383\) 21.0817i 1.07722i −0.842554 0.538612i \(-0.818949\pi\)
0.842554 0.538612i \(-0.181051\pi\)
\(384\) −20.6269 + 10.4462i −1.05261 + 0.533082i
\(385\) −18.1364 5.65440i −0.924318 0.288175i
\(386\) 30.7764 + 4.88556i 1.56648 + 0.248669i
\(387\) 9.09959 0.462558
\(388\) 23.6123 + 7.69042i 1.19873 + 0.390422i
\(389\) −4.88919 −0.247892 −0.123946 0.992289i \(-0.539555\pi\)
−0.123946 + 0.992289i \(0.539555\pi\)
\(390\) 26.1886 + 12.9637i 1.32611 + 0.656443i
\(391\) 46.7021i 2.36182i
\(392\) 6.74674 + 3.44658i 0.340762 + 0.174079i
\(393\) 23.2774 1.17419
\(394\) −3.54189 + 22.3120i −0.178438 + 1.12406i
\(395\) −2.69493 + 8.64395i −0.135597 + 0.434925i
\(396\) −2.97808 + 9.14378i −0.149654 + 0.459492i
\(397\) 3.22742i 0.161980i −0.996715 0.0809899i \(-0.974192\pi\)
0.996715 0.0809899i \(-0.0258081\pi\)
\(398\) −2.77130 + 17.4577i −0.138912 + 0.875073i
\(399\) −2.50918 18.3474i −0.125616 0.918517i
\(400\) −6.60626 18.8774i −0.330313 0.943871i
\(401\) 22.8549i 1.14132i −0.821187 0.570659i \(-0.806688\pi\)
0.821187 0.570659i \(-0.193312\pi\)
\(402\) −37.9755 6.02837i −1.89404 0.300668i
\(403\) −7.68391 −0.382763
\(404\) 18.1404 + 5.90824i 0.902519 + 0.293946i
\(405\) −7.41772 + 23.7923i −0.368590 + 1.18225i
\(406\) 2.72088 17.1401i 0.135035 0.850647i
\(407\) 7.42822i 0.368203i
\(408\) −33.8749 17.3051i −1.67706 0.856728i
\(409\) 35.2947i 1.74521i −0.488425 0.872606i \(-0.662428\pi\)
0.488425 0.872606i \(-0.337572\pi\)
\(410\) 3.12135 + 1.54511i 0.154153 + 0.0763075i
\(411\) 14.7977 0.729915
\(412\) −8.77639 + 26.9466i −0.432382 + 1.32757i
\(413\) −19.5401 −0.961505
\(414\) −11.6617 1.85122i −0.573139 0.0909823i
\(415\) 4.96737 15.9328i 0.243838 0.782109i
\(416\) −18.0549 18.1183i −0.885214 0.888323i
\(417\) −0.0805669 −0.00394538
\(418\) −0.541959 + 25.1876i −0.0265081 + 1.23197i
\(419\) 0.942419i 0.0460402i −0.999735 0.0230201i \(-0.992672\pi\)
0.999735 0.0230201i \(-0.00732817\pi\)
\(420\) −15.4952 10.9940i −0.756089 0.536453i
\(421\) 6.45110i 0.314407i 0.987566 + 0.157204i \(0.0502479\pi\)
−0.987566 + 0.157204i \(0.949752\pi\)
\(422\) −13.4956 2.14235i −0.656958 0.104288i
\(423\) −11.7477 −0.571192
\(424\) 5.51154 + 2.81558i 0.267664 + 0.136737i
\(425\) 18.6994 27.0741i 0.907055 1.31329i
\(426\) −2.11881 + 13.3474i −0.102657 + 0.646683i
\(427\) 10.3066 0.498772
\(428\) −1.60772 + 4.93626i −0.0777120 + 0.238603i
\(429\) −37.7659 −1.82335
\(430\) 10.8506 21.9199i 0.523263 1.05707i
\(431\) −40.4739 −1.94956 −0.974779 0.223172i \(-0.928359\pi\)
−0.974779 + 0.223172i \(0.928359\pi\)
\(432\) 8.77864 12.0472i 0.422363 0.579621i
\(433\) −10.3942 −0.499516 −0.249758 0.968308i \(-0.580351\pi\)
−0.249758 + 0.968308i \(0.580351\pi\)
\(434\) 4.93412 + 0.783262i 0.236845 + 0.0375978i
\(435\) 8.02917 25.7535i 0.384969 1.23478i
\(436\) 7.84089 24.0743i 0.375510 1.15295i
\(437\) −30.6485 + 4.19149i −1.46612 + 0.200506i
\(438\) −17.6533 2.80235i −0.843506 0.133901i
\(439\) 13.7355 0.655558 0.327779 0.944754i \(-0.393700\pi\)
0.327779 + 0.944754i \(0.393700\pi\)
\(440\) 18.4751 + 18.0772i 0.880768 + 0.861795i
\(441\) 3.15133 0.150063
\(442\) 6.59759 41.5612i 0.313815 1.97686i
\(443\) 13.5116 0.641953 0.320977 0.947087i \(-0.395989\pi\)
0.320977 + 0.947087i \(0.395989\pi\)
\(444\) −2.30062 + 7.06371i −0.109182 + 0.335229i
\(445\) −1.18151 0.368360i −0.0560090 0.0174620i
\(446\) −1.85821 + 11.7057i −0.0879886 + 0.554280i
\(447\) 15.7594i 0.745392i
\(448\) 9.74681 + 13.4749i 0.460494 + 0.636627i
\(449\) 32.5385i 1.53559i 0.640697 + 0.767794i \(0.278645\pi\)
−0.640697 + 0.767794i \(0.721355\pi\)
\(450\) −6.01927 5.74249i −0.283751 0.270704i
\(451\) −4.50121 −0.211954
\(452\) 24.6067 + 8.01428i 1.15740 + 0.376960i
\(453\) 17.6518i 0.829355i
\(454\) 1.74154 10.9708i 0.0817346 0.514883i
\(455\) 6.25589 20.0657i 0.293281 0.940694i
\(456\) −8.31629 + 23.7838i −0.389446 + 1.11378i
\(457\) 4.01741i 0.187927i −0.995576 0.0939634i \(-0.970046\pi\)
0.995576 0.0939634i \(-0.0299537\pi\)
\(458\) 17.6311 + 2.79882i 0.823846 + 0.130780i
\(459\) 24.5240 1.14468
\(460\) −18.3651 + 25.8841i −0.856276 + 1.20685i
\(461\) −8.79412 −0.409583 −0.204792 0.978806i \(-0.565652\pi\)
−0.204792 + 0.978806i \(0.565652\pi\)
\(462\) 24.2508 + 3.84967i 1.12825 + 0.179103i
\(463\) −12.4815 −0.580065 −0.290032 0.957017i \(-0.593666\pi\)
−0.290032 + 0.957017i \(0.593666\pi\)
\(464\) −13.9060 + 19.0837i −0.645571 + 0.885937i
\(465\) 7.41367 + 2.31136i 0.343801 + 0.107187i
\(466\) −1.57031 + 9.89208i −0.0727431 + 0.458242i
\(467\) −6.35790 −0.294209 −0.147104 0.989121i \(-0.546995\pi\)
−0.147104 + 0.989121i \(0.546995\pi\)
\(468\) −10.1164 3.29488i −0.467633 0.152306i
\(469\) 27.6567i 1.27707i
\(470\) −14.0083 + 28.2988i −0.646154 + 1.30533i
\(471\) −35.2643 −1.62489
\(472\) 23.6758 + 12.0948i 1.08977 + 0.556709i
\(473\) 31.6100i 1.45343i
\(474\) 1.83478 11.5581i 0.0842744 0.530883i
\(475\) −19.4458 9.84172i −0.892236 0.451569i
\(476\) −8.47310 + 26.0154i −0.388364 + 1.19242i
\(477\) 2.57438 0.117873
\(478\) 3.89369 24.5281i 0.178093 1.12189i
\(479\) 26.0062i 1.18825i −0.804372 0.594127i \(-0.797498\pi\)
0.804372 0.594127i \(-0.202502\pi\)
\(480\) 11.9698 + 22.9121i 0.546345 + 1.04579i
\(481\) −8.21839 −0.374726
\(482\) 5.65563 35.6274i 0.257607 1.62278i
\(483\) 30.1493i 1.37184i
\(484\) −10.8450 3.53217i −0.492955 0.160553i
\(485\) 8.26377 26.5059i 0.375238 1.20357i
\(486\) 2.57140 16.1984i 0.116641 0.734774i
\(487\) 9.02248i 0.408848i 0.978882 + 0.204424i \(0.0655321\pi\)
−0.978882 + 0.204424i \(0.934468\pi\)
\(488\) −12.4880 6.37953i −0.565307 0.288788i
\(489\) 10.6531i 0.481751i
\(490\) 3.75774 7.59119i 0.169757 0.342935i
\(491\) 33.0190i 1.49013i 0.666994 + 0.745063i \(0.267581\pi\)
−0.666994 + 0.745063i \(0.732419\pi\)
\(492\) −4.28033 1.39408i −0.192972 0.0628501i
\(493\) −38.8478 −1.74962
\(494\) −27.8669 0.599610i −1.25379 0.0269777i
\(495\) 10.2643 + 3.20011i 0.461347 + 0.143834i
\(496\) −5.49363 4.00314i −0.246671 0.179746i
\(497\) 9.72060 0.436029
\(498\) −3.38192 + 21.3043i −0.151547 + 0.954667i
\(499\) 13.3058i 0.595649i −0.954621 0.297824i \(-0.903739\pi\)
0.954621 0.297824i \(-0.0962610\pi\)
\(500\) −21.0106 + 7.65221i −0.939621 + 0.342217i
\(501\) −28.9073 −1.29148
\(502\) 3.93510 24.7890i 0.175632 1.10639i
\(503\) 11.5983 0.517144 0.258572 0.965992i \(-0.416748\pi\)
0.258572 + 0.965992i \(0.416748\pi\)
\(504\) 6.16027 + 3.14698i 0.274400 + 0.140178i
\(505\) 6.34873 20.3635i 0.282515 0.906163i
\(506\) 6.43072 40.5101i 0.285881 1.80089i
\(507\) 15.2158i 0.675756i
\(508\) 4.53451 13.9226i 0.201186 0.617713i
\(509\) 15.7154i 0.696571i 0.937389 + 0.348285i \(0.113236\pi\)
−0.937389 + 0.348285i \(0.886764\pi\)
\(510\) −18.8674 + 38.1149i −0.835461 + 1.68775i
\(511\) 12.8565i 0.568737i
\(512\) −3.46916 22.3599i −0.153317 0.988177i
\(513\) −2.20102 16.0940i −0.0971772 0.710568i
\(514\) 16.2548 + 2.58035i 0.716970 + 0.113815i
\(515\) 30.2489 + 9.43071i 1.33293 + 0.415567i
\(516\) −9.79003 + 30.0589i −0.430982 + 1.32327i
\(517\) 40.8089i 1.79477i
\(518\) 5.27733 + 0.837744i 0.231873 + 0.0368083i
\(519\) 11.2038i 0.491794i
\(520\) −20.0001 + 20.4404i −0.877063 + 0.896372i
\(521\) 33.8676i 1.48377i 0.670529 + 0.741883i \(0.266067\pi\)
−0.670529 + 0.741883i \(0.733933\pi\)
\(522\) −1.53988 + 9.70043i −0.0673989 + 0.424576i
\(523\) 33.9095i 1.48276i −0.671086 0.741379i \(-0.734172\pi\)
0.671086 0.741379i \(-0.265828\pi\)
\(524\) −7.05468 + 21.6604i −0.308185 + 0.946238i
\(525\) −12.0717 + 17.4782i −0.526853 + 0.762810i
\(526\) −38.0140 6.03450i −1.65749 0.263117i
\(527\) 11.1831i 0.487146i
\(528\) −27.0008 19.6751i −1.17506 0.856250i
\(529\) 27.3632 1.18970
\(530\) 3.06977 6.20139i 0.133342 0.269371i
\(531\) 11.0587 0.479908
\(532\) 17.8332 + 3.22565i 0.773169 + 0.139850i
\(533\) 4.98003i 0.215709i
\(534\) 1.57984 + 0.250790i 0.0683664 + 0.0108527i
\(535\) 5.54119 + 1.72758i 0.239567 + 0.0746898i
\(536\) 17.1188 33.5103i 0.739419 1.44743i
\(537\) 2.43086i 0.104900i
\(538\) −4.52453 + 28.5021i −0.195066 + 1.22881i
\(539\) 10.9470i 0.471522i
\(540\) −13.5922 9.64378i −0.584913 0.415002i
\(541\) 12.8556 0.552705 0.276352 0.961056i \(-0.410874\pi\)
0.276352 + 0.961056i \(0.410874\pi\)
\(542\) −0.634184 + 3.99501i −0.0272405 + 0.171601i
\(543\) −10.4256 −0.447405
\(544\) 26.3694 26.2771i 1.13058 1.12662i
\(545\) −27.0246 8.42546i −1.15760 0.360907i
\(546\) −4.25918 + 26.8305i −0.182276 + 1.14824i
\(547\) 14.9025i 0.637187i 0.947892 + 0.318593i \(0.103210\pi\)
−0.947892 + 0.318593i \(0.896790\pi\)
\(548\) −4.48472 + 13.7697i −0.191578 + 0.588212i
\(549\) −5.83303 −0.248948
\(550\) 19.9482 20.9097i 0.850593 0.891590i
\(551\) 3.48657 + 25.4941i 0.148533 + 1.08609i
\(552\) 18.6617 36.5305i 0.794293 1.55484i
\(553\) −8.41753 −0.357950
\(554\) 0.176614 1.11257i 0.00750363 0.0472688i
\(555\) 7.92935 + 2.47214i 0.336582 + 0.104936i
\(556\) 0.0244174 0.0749700i 0.00103553 0.00317944i
\(557\) 10.7020i 0.453458i −0.973958 0.226729i \(-0.927197\pi\)
0.973958 0.226729i \(-0.0728032\pi\)
\(558\) −2.79247 0.443287i −0.118215 0.0187658i
\(559\) −34.9725 −1.47918
\(560\) 14.9264 11.0868i 0.630756 0.468504i
\(561\) 54.9644i 2.32060i
\(562\) 1.78408 11.2387i 0.0752569 0.474078i
\(563\) 27.6932i 1.16713i −0.812066 0.583565i \(-0.801657\pi\)
0.812066 0.583565i \(-0.198343\pi\)
\(564\) 12.6390 38.8064i 0.532200 1.63404i
\(565\) 8.61177 27.6222i 0.362300 1.16207i
\(566\) 40.6029 + 6.44547i 1.70667 + 0.270923i
\(567\) −23.1690 −0.973008
\(568\) −11.7780 6.01681i −0.494194 0.252460i
\(569\) 32.1609i 1.34825i 0.738616 + 0.674127i \(0.235480\pi\)
−0.738616 + 0.674127i \(0.764520\pi\)
\(570\) 26.7065 + 8.96104i 1.11861 + 0.375337i
\(571\) 44.0887i 1.84506i −0.385930 0.922528i \(-0.626119\pi\)
0.385930 0.922528i \(-0.373881\pi\)
\(572\) 11.4457 35.1423i 0.478568 1.46937i
\(573\) 9.82522 0.410455
\(574\) −0.507640 + 3.19786i −0.0211885 + 0.133476i
\(575\) 29.1966 + 20.1653i 1.21758 + 0.840952i
\(576\) −5.51621 7.62611i −0.229842 0.317754i
\(577\) 36.7343i 1.52927i 0.644465 + 0.764633i \(0.277080\pi\)
−0.644465 + 0.764633i \(0.722920\pi\)
\(578\) 36.7437 + 5.83285i 1.52834 + 0.242614i
\(579\) 45.0311i 1.87143i
\(580\) 21.5310 + 15.2765i 0.894026 + 0.634321i
\(581\) 15.5154 0.643688
\(582\) −5.62620 + 35.4420i −0.233214 + 1.46912i
\(583\) 8.94284i 0.370375i
\(584\) 7.95784 15.5776i 0.329298 0.644606i
\(585\) −3.54052 + 11.3562i −0.146383 + 0.469521i
\(586\) 0.416116 + 0.0660559i 0.0171896 + 0.00272874i
\(587\) −16.3518 −0.674912 −0.337456 0.941341i \(-0.609566\pi\)
−0.337456 + 0.941341i \(0.609566\pi\)
\(588\) −3.39044 + 10.4099i −0.139819 + 0.429295i
\(589\) −7.33901 + 1.00368i −0.302399 + 0.0413560i
\(590\) 13.1867 26.6392i 0.542890 1.09672i
\(591\) −32.6463 −1.34289
\(592\) −5.87575 4.28159i −0.241492 0.175972i
\(593\) 15.2822i 0.627565i 0.949495 + 0.313782i \(0.101596\pi\)
−0.949495 + 0.313782i \(0.898404\pi\)
\(594\) 21.2725 + 3.37687i 0.872820 + 0.138555i
\(595\) 29.2036 + 9.10480i 1.19723 + 0.373261i
\(596\) 14.6646 + 4.77618i 0.600684 + 0.195640i
\(597\) −25.5436 −1.04543
\(598\) 44.8193 + 7.11479i 1.83280 + 0.290945i
\(599\) −18.0855 −0.738954 −0.369477 0.929240i \(-0.620463\pi\)
−0.369477 + 0.929240i \(0.620463\pi\)
\(600\) 25.4453 13.7054i 1.03880 0.559520i
\(601\) 7.44723i 0.303779i −0.988397 0.151889i \(-0.951464\pi\)
0.988397 0.151889i \(-0.0485358\pi\)
\(602\) 22.4571 + 3.56493i 0.915284 + 0.145296i
\(603\) 15.6523i 0.637412i
\(604\) −16.4256 5.34973i −0.668347 0.217677i
\(605\) −3.79551 + 12.1740i −0.154309 + 0.494945i
\(606\) −4.32239 + 27.2287i −0.175585 + 1.10609i
\(607\) 14.8938i 0.604520i −0.953226 0.302260i \(-0.902259\pi\)
0.953226 0.302260i \(-0.0977410\pi\)
\(608\) −19.6111 14.9467i −0.795336 0.606169i
\(609\) 25.0789 1.01625
\(610\) −6.95548 + 14.0511i −0.281619 + 0.568912i
\(611\) 45.1499 1.82657
\(612\) 4.79536 14.7234i 0.193841 0.595160i
\(613\) 22.5813i 0.912048i −0.889967 0.456024i \(-0.849273\pi\)
0.889967 0.456024i \(-0.150727\pi\)
\(614\) 4.02175 25.3348i 0.162305 1.02243i
\(615\) −1.49802 + 4.80488i −0.0604059 + 0.193751i
\(616\) −10.9319 + 21.3995i −0.440460 + 0.862208i
\(617\) 22.8933i 0.921651i −0.887491 0.460826i \(-0.847553\pi\)
0.887491 0.460826i \(-0.152447\pi\)
\(618\) −40.4468 6.42069i −1.62701 0.258278i
\(619\) 20.8399i 0.837627i 0.908072 + 0.418813i \(0.137554\pi\)
−0.908072 + 0.418813i \(0.862446\pi\)
\(620\) −4.39765 + 6.19814i −0.176614 + 0.248923i
\(621\) 26.4465i 1.06126i
\(622\) 0.707721 4.45826i 0.0283770 0.178760i
\(623\) 1.15056i 0.0460963i
\(624\) 21.7681 29.8730i 0.871420 1.19588i
\(625\) 8.85167 + 23.3805i 0.354067 + 0.935220i
\(626\) 1.19463 7.52553i 0.0477471 0.300781i
\(627\) −36.0707 + 4.93303i −1.44053 + 0.197006i
\(628\) 10.6875 32.8145i 0.426479 1.30944i
\(629\) 11.9610i 0.476917i
\(630\) 3.43109 6.93132i 0.136698 0.276150i
\(631\) 39.1233i 1.55747i 0.627352 + 0.778736i \(0.284139\pi\)
−0.627352 + 0.778736i \(0.715861\pi\)
\(632\) 10.1991 + 5.21024i 0.405700 + 0.207252i
\(633\) 19.7465i 0.784852i
\(634\) −27.3244 4.33758i −1.08519 0.172267i
\(635\) −15.6287 4.87257i −0.620207 0.193362i
\(636\) −2.76972 + 8.50401i −0.109826 + 0.337206i
\(637\) −12.1115 −0.479876
\(638\) −33.6972 5.34922i −1.33408 0.211778i
\(639\) −5.50138 −0.217631
\(640\) −24.9481 + 4.19433i −0.986160 + 0.165795i
\(641\) 31.6593i 1.25047i −0.780438 0.625233i \(-0.785004\pi\)
0.780438 0.625233i \(-0.214996\pi\)
\(642\) −7.40932 1.17618i −0.292423 0.0464203i
\(643\) −41.4100 −1.63305 −0.816525 0.577310i \(-0.804102\pi\)
−0.816525 + 0.577310i \(0.804102\pi\)
\(644\) −28.0549 9.13733i −1.10552 0.360061i
\(645\) 33.7425 + 10.5199i 1.32861 + 0.414221i
\(646\) 0.872670 40.5575i 0.0343348 1.59571i
\(647\) −10.3940 −0.408632 −0.204316 0.978905i \(-0.565497\pi\)
−0.204316 + 0.978905i \(0.565497\pi\)
\(648\) 28.0728 + 14.3410i 1.10281 + 0.563370i
\(649\) 38.4156i 1.50794i
\(650\) 23.1339 + 22.0702i 0.907387 + 0.865663i
\(651\) 7.21947i 0.282953i
\(652\) 9.91307 + 3.22864i 0.388226 + 0.126443i
\(653\) 10.9657i 0.429122i 0.976711 + 0.214561i \(0.0688321\pi\)
−0.976711 + 0.214561i \(0.931168\pi\)
\(654\) 36.1355 + 5.73629i 1.41301 + 0.224307i
\(655\) 24.3148 + 7.58063i 0.950058 + 0.296200i
\(656\) 2.59448 3.56048i 0.101297 0.139013i
\(657\) 7.27613i 0.283869i
\(658\) −28.9924 4.60237i −1.13024 0.179419i
\(659\) 4.33670 0.168934 0.0844668 0.996426i \(-0.473081\pi\)
0.0844668 + 0.996426i \(0.473081\pi\)
\(660\) −21.6141 + 30.4634i −0.841329 + 1.18579i
\(661\) 37.7050i 1.46655i 0.679930 + 0.733277i \(0.262010\pi\)
−0.679930 + 0.733277i \(0.737990\pi\)
\(662\) 6.72030 + 1.06681i 0.261192 + 0.0414626i
\(663\) 60.8112 2.36171
\(664\) −18.7993 9.60365i −0.729555 0.372694i
\(665\) 3.35408 19.9822i 0.130066 0.774875i
\(666\) −2.98671 0.474122i −0.115733 0.0183718i
\(667\) 41.8932i 1.62211i
\(668\) 8.76093 26.8992i 0.338971 1.04076i
\(669\) −17.1274 −0.662185
\(670\) −37.7046 18.6643i −1.45666 0.721065i
\(671\) 20.2627i 0.782232i
\(672\) −17.0232 + 16.9636i −0.656684 + 0.654385i
\(673\) −6.00665 −0.231539 −0.115770 0.993276i \(-0.536933\pi\)
−0.115770 + 0.993276i \(0.536933\pi\)
\(674\) −3.63174 0.576517i −0.139889 0.0222066i
\(675\) −10.5891 + 15.3316i −0.407576 + 0.590112i
\(676\) 14.1588 + 4.61144i 0.544567 + 0.177363i
\(677\) −19.6709 −0.756013 −0.378007 0.925803i \(-0.623390\pi\)
−0.378007 + 0.925803i \(0.623390\pi\)
\(678\) −5.86314 + 36.9346i −0.225172 + 1.41846i
\(679\) 25.8116 0.990560
\(680\) −29.7490 29.1081i −1.14082 1.11625i
\(681\) 16.0521 0.615118
\(682\) 1.53988 9.70043i 0.0589652 0.371449i
\(683\) 38.4534i 1.47138i 0.677319 + 0.735690i \(0.263142\pi\)
−0.677319 + 0.735690i \(0.736858\pi\)
\(684\) −10.0927 1.82556i −0.385905 0.0698020i
\(685\) 15.4571 + 4.81908i 0.590587 + 0.184127i
\(686\) 28.1019 + 4.46101i 1.07294 + 0.170322i
\(687\) 25.7973i 0.984228i
\(688\) −25.0036 18.2198i −0.953255 0.694625i
\(689\) −9.89414 −0.376937
\(690\) −41.1028 20.3464i −1.56476 0.774576i
\(691\) 30.3813i 1.15576i 0.816121 + 0.577880i \(0.196120\pi\)
−0.816121 + 0.577880i \(0.803880\pi\)
\(692\) −10.4255 3.39554i −0.396319 0.129079i
\(693\) 9.99546i 0.379696i
\(694\) 10.1207 + 1.60660i 0.384178 + 0.0609859i
\(695\) −0.0841574 0.0262378i −0.00319227 0.000995256i
\(696\) −30.3869 15.5232i −1.15181 0.588405i
\(697\) 7.24792 0.274535
\(698\) −4.67309 0.741824i −0.176879 0.0280785i
\(699\) −14.4738 −0.547450
\(700\) −12.6054 16.5302i −0.476439 0.624783i
\(701\) 9.48317 0.358175 0.179087 0.983833i \(-0.442686\pi\)
0.179087 + 0.983833i \(0.442686\pi\)
\(702\) −3.73609 + 23.5353i −0.141010 + 0.888283i
\(703\) −7.84950 + 1.07350i −0.296050 + 0.0404877i
\(704\) 26.4914 19.1621i 0.998433 0.722200i
\(705\) −43.5620 13.5813i −1.64064 0.511503i
\(706\) −2.71915 + 17.1292i −0.102337 + 0.644665i
\(707\) 19.8301 0.745786
\(708\) −11.8978 + 36.5305i −0.447147 + 1.37290i
\(709\) 35.7244 1.34166 0.670829 0.741612i \(-0.265938\pi\)
0.670829 + 0.741612i \(0.265938\pi\)
\(710\) −6.56001 + 13.2522i −0.246193 + 0.497346i
\(711\) 4.76391 0.178660
\(712\) −0.712169 + 1.39408i −0.0266897 + 0.0522455i
\(713\) 12.0598 0.451644
\(714\) −39.0491 6.19880i −1.46138 0.231984i
\(715\) −39.4489 12.2990i −1.47531 0.459957i
\(716\) −2.26199 0.736721i −0.0845347 0.0275325i
\(717\) 35.8889 1.34030
\(718\) 1.10459 6.95833i 0.0412230 0.259683i
\(719\) 6.57919i 0.245362i −0.992446 0.122681i \(-0.960851\pi\)
0.992446 0.122681i \(-0.0391492\pi\)
\(720\) −8.44761 + 6.27460i −0.314824 + 0.233840i
\(721\) 29.4565i 1.09702i
\(722\) −26.6944 + 3.06732i −0.993463 + 0.114154i
\(723\) 52.1291 1.93870
\(724\) 3.15968 9.70134i 0.117429 0.360548i
\(725\) 16.7740 24.2864i 0.622970 0.901973i
\(726\) 2.58409 16.2783i 0.0959045 0.604146i
\(727\) −1.20206 −0.0445818 −0.0222909 0.999752i \(-0.507096\pi\)
−0.0222909 + 0.999752i \(0.507096\pi\)
\(728\) −23.6758 12.0948i −0.877484 0.448264i
\(729\) −9.73500 −0.360555
\(730\) −17.5274 8.67628i −0.648717 0.321123i
\(731\) 50.8989i 1.88256i
\(732\) 6.27562 19.2684i 0.231954 0.712180i
\(733\) 34.8374i 1.28675i 0.765551 + 0.643375i \(0.222466\pi\)
−0.765551 + 0.643375i \(0.777534\pi\)
\(734\) 0.374460 + 0.0594432i 0.0138216 + 0.00219409i
\(735\) 11.6856 + 3.64321i 0.431028 + 0.134382i
\(736\) 28.3370 + 28.4365i 1.04452 + 1.04818i
\(737\) 54.3728 2.00285
\(738\) 0.287299 1.80983i 0.0105756 0.0666207i
\(739\) 10.0566i 0.369939i −0.982744 0.184969i \(-0.940781\pi\)
0.982744 0.184969i \(-0.0592186\pi\)
\(740\) −4.70354 + 6.62927i −0.172906 + 0.243697i
\(741\) −5.45778 39.9077i −0.200496 1.46605i
\(742\) 6.35339 + 1.00856i 0.233240 + 0.0370255i
\(743\) 33.2676i 1.22047i 0.792220 + 0.610235i \(0.208925\pi\)
−0.792220 + 0.610235i \(0.791075\pi\)
\(744\) 4.46867 8.74750i 0.163829 0.320699i
\(745\) 5.13226 16.4617i 0.188032 0.603109i
\(746\) −52.3814 8.31523i −1.91782 0.304442i
\(747\) −8.78096 −0.321279
\(748\) 51.1461 + 16.6580i 1.87009 + 0.609078i
\(749\) 5.39604i 0.197167i
\(750\) −15.6815 28.2527i −0.572606 1.03164i
\(751\) −35.0253 −1.27809 −0.639045 0.769169i \(-0.720670\pi\)
−0.639045 + 0.769169i \(0.720670\pi\)
\(752\) 32.2800 + 23.5220i 1.17713 + 0.857761i
\(753\) 36.2705 1.32177
\(754\) 5.91824 37.2817i 0.215530 1.35772i
\(755\) −5.74857 + 18.4385i −0.209212 + 0.671045i
\(756\) 4.79816 14.7320i 0.174507 0.535799i
\(757\) 15.6212i 0.567764i −0.958859 0.283882i \(-0.908378\pi\)
0.958859 0.283882i \(-0.0916224\pi\)
\(758\) −18.9477 3.00783i −0.688212 0.109249i
\(759\) 59.2732 2.15148
\(760\) −16.4324 + 22.1354i −0.596067 + 0.802935i
\(761\) −39.5461 −1.43355 −0.716773 0.697307i \(-0.754381\pi\)
−0.716773 + 0.697307i \(0.754381\pi\)
\(762\) 20.8977 + 3.31738i 0.757044 + 0.120176i
\(763\) 26.3167i 0.952728i
\(764\) −2.97772 + 9.14267i −0.107730 + 0.330770i
\(765\) −16.5278 5.15287i −0.597563 0.186302i
\(766\) −4.67426 + 29.4453i −0.168888 + 1.06390i
\(767\) −42.5020 −1.53466
\(768\) 31.1262 10.0171i 1.12317 0.361460i
\(769\) −22.9425 −0.827327 −0.413664 0.910430i \(-0.635751\pi\)
−0.413664 + 0.910430i \(0.635751\pi\)
\(770\) 24.0779 + 11.9189i 0.867707 + 0.429527i
\(771\) 23.7836i 0.856546i
\(772\) −41.9029 13.6476i −1.50812 0.491187i
\(773\) −19.3863 −0.697276 −0.348638 0.937258i \(-0.613356\pi\)
−0.348638 + 0.937258i \(0.613356\pi\)
\(774\) −12.7096 2.01757i −0.456838 0.0725202i
\(775\) 6.99133 + 4.82874i 0.251136 + 0.173453i
\(776\) −31.2748 15.9767i −1.12270 0.573532i
\(777\) 7.72164i 0.277012i
\(778\) 6.82885 + 1.08404i 0.244826 + 0.0388647i
\(779\) −0.650497 4.75649i −0.0233065 0.170419i
\(780\) −33.7040 23.9133i −1.20680 0.856235i
\(781\) 19.1106i