Properties

Label 6.19.b.a.5.3
Level 6
Weight 19
Character 6.5
Analytic conductor 12.323
Analytic rank 0
Dimension 6
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 6 = 2 \cdot 3 \)
Weight: \( k \) = \( 19 \)
Character orbit: \([\chi]\) = 6.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(12.3231682626\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{31}\cdot 3^{14} \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 5.3
Root \(-112.126 - 31.1763i\)
Character \(\chi\) = 6.5
Dual form 6.19.b.a.5.6

$q$-expansion

\(f(q)\) \(=\) \(q-362.039i q^{2} +(19502.4 + 2660.56i) q^{3} -131072. q^{4} -1.30525e6i q^{5} +(963226. - 7.06061e6i) q^{6} +3.15845e7 q^{7} +4.74531e7i q^{8} +(3.73263e8 + 1.03774e8i) q^{9} +O(q^{10})\) \(q-362.039i q^{2} +(19502.4 + 2660.56i) q^{3} -131072. q^{4} -1.30525e6i q^{5} +(963226. - 7.06061e6i) q^{6} +3.15845e7 q^{7} +4.74531e7i q^{8} +(3.73263e8 + 1.03774e8i) q^{9} -4.72550e8 q^{10} -3.81148e9i q^{11} +(-2.55621e9 - 3.48725e8i) q^{12} -5.50456e9 q^{13} -1.14348e10i q^{14} +(3.47269e9 - 2.54554e10i) q^{15} +1.71799e10 q^{16} -1.95721e11i q^{17} +(3.75704e10 - 1.35136e11i) q^{18} -1.56485e11 q^{19} +1.71081e11i q^{20} +(6.15971e11 + 8.40324e10i) q^{21} -1.37990e12 q^{22} +1.49039e12i q^{23} +(-1.26252e11 + 9.25448e11i) q^{24} +2.11102e12 q^{25} +1.99286e12i q^{26} +(7.00342e12 + 3.01694e12i) q^{27} -4.13984e12 q^{28} +7.21871e12i q^{29} +(-9.21584e12 - 1.25725e12i) q^{30} +3.81624e12 q^{31} -6.21978e12i q^{32} +(1.01407e13 - 7.43328e13i) q^{33} -7.08587e13 q^{34} -4.12256e13i q^{35} +(-4.89244e13 - 1.36019e13i) q^{36} +2.50324e14 q^{37} +5.66536e13i q^{38} +(-1.07352e14 - 1.46452e13i) q^{39} +6.19381e13 q^{40} +4.39043e14i q^{41} +(3.04230e13 - 2.23005e14i) q^{42} -5.41174e14 q^{43} +4.99578e14i q^{44} +(1.35451e14 - 4.87201e14i) q^{45} +5.39578e14 q^{46} +1.94037e15i q^{47} +(3.35048e14 + 4.57081e13i) q^{48} -6.30835e14 q^{49} -7.64273e14i q^{50} +(5.20729e14 - 3.81703e15i) q^{51} +7.21494e14 q^{52} -1.53546e15i q^{53} +(1.09225e15 - 2.53551e15i) q^{54} -4.97492e15 q^{55} +1.49878e15i q^{56} +(-3.05182e15 - 4.16338e14i) q^{57} +2.61345e15 q^{58} +6.50072e15i q^{59} +(-4.55173e14 + 3.33649e15i) q^{60} +3.87413e15 q^{61} -1.38163e15i q^{62} +(1.17893e16 + 3.27766e15i) q^{63} -2.25180e15 q^{64} +7.18482e15i q^{65} +(-2.69113e16 - 3.67131e15i) q^{66} +3.71114e16 q^{67} +2.56536e16i q^{68} +(-3.96527e15 + 2.90661e16i) q^{69} -1.49252e16 q^{70} -6.33282e16i q^{71} +(-4.92442e15 + 1.77125e16i) q^{72} -5.51216e16 q^{73} -9.06269e16i q^{74} +(4.11700e16 + 5.61651e15i) q^{75} +2.05108e16 q^{76} -1.20383e17i q^{77} +(-5.30214e15 + 3.88655e16i) q^{78} -7.16429e16 q^{79} -2.24240e16i q^{80} +(1.28556e17 + 7.74704e16i) q^{81} +1.58951e17 q^{82} +1.18877e17i q^{83} +(-8.07366e16 - 1.10143e16i) q^{84} -2.55465e17 q^{85} +1.95926e17i q^{86} +(-1.92058e16 + 1.40782e17i) q^{87} +1.80867e17 q^{88} +9.49218e16i q^{89} +(-1.76386e17 - 4.90386e16i) q^{90} -1.73859e17 q^{91} -1.95348e17i q^{92} +(7.44258e16 + 1.01534e16i) q^{93} +7.02490e17 q^{94} +2.04252e17i q^{95} +(1.65481e16 - 1.21300e17i) q^{96} -3.38927e17 q^{97} +2.28387e17i q^{98} +(3.95534e17 - 1.42268e18i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 6258q^{3} - 786432q^{4} - 15753216q^{6} + 28233804q^{7} + 695971638q^{9} + O(q^{10}) \) \( 6q - 6258q^{3} - 786432q^{4} - 15753216q^{6} + 28233804q^{7} + 695971638q^{9} - 434257920q^{10} + 820248576q^{12} + 29566196220q^{13} + 119627095680q^{15} + 103079215104q^{16} + 315939373056q^{18} - 438814047012q^{19} + 2876527406172q^{21} - 2844452929536q^{22} + 2064805527552q^{24} - 25696048717290q^{25} + 11197265522814q^{27} - 3700661157888q^{28} + 13072787619840q^{30} + 21775814927148q^{31} - 962560003968q^{33} + 99067611119616q^{34} - 91222394535936q^{36} + 638446564817436q^{37} - 736541155104180q^{39} + 56919054090240q^{40} - 203954622480384q^{42} - 1688313718883652q^{43} + 390590504075520q^{45} + 1979247919104q^{46} - 107511621353472q^{48} - 895767896448270q^{49} + 9636273526722048q^{51} - 3875300470947840q^{52} + 2993011804200960q^{54} - 1259959207783680q^{55} + 4023767318253996q^{57} + 21251172660756480q^{58} - 15679762684968960q^{60} - 16279597277700036q^{61} - 32525159214131028q^{63} - 13510798882111488q^{64} - 60047751762690048q^{66} + 11153724314613276q^{67} + 3612037794746112q^{69} + 161904998736691200q^{70} - 41410805505196032q^{72} - 78910243347781140q^{73} + 348225828845090910q^{75} + 57516234769956864q^{76} - 168903906208235520q^{78} - 476518976428926228q^{79} + 630680446106425062q^{81} + 396536393269149696q^{82} - 377032200181776384q^{84} - 967978669078932480q^{85} + 419256510981966720q^{87} + 372828134380142592q^{88} - 2046848246643179520q^{90} - 1032060167365562760q^{91} + 764294136047005116q^{93} + 2566175766871080960q^{94} - 270638190107295744q^{96} + 834695417243310348q^{97} + 761688154713814272q^{99} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6\mathbb{Z}\right)^\times\).

\(n\) \(5\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 362.039i 0.707107i
\(3\) 19502.4 + 2660.56i 0.990822 + 0.135171i
\(4\) −131072. −0.500000
\(5\) 1.30525e6i 0.668287i −0.942522 0.334143i \(-0.891553\pi\)
0.942522 0.334143i \(-0.108447\pi\)
\(6\) 963226. 7.06061e6i 0.0955800 0.700617i
\(7\) 3.15845e7 0.782692 0.391346 0.920244i \(-0.372009\pi\)
0.391346 + 0.920244i \(0.372009\pi\)
\(8\) 4.74531e7i 0.353553i
\(9\) 3.73263e8 + 1.03774e8i 0.963458 + 0.267860i
\(10\) −4.72550e8 −0.472550
\(11\) 3.81148e9i 1.61644i −0.588882 0.808219i \(-0.700432\pi\)
0.588882 0.808219i \(-0.299568\pi\)
\(12\) −2.55621e9 3.48725e8i −0.495411 0.0675853i
\(13\) −5.50456e9 −0.519078 −0.259539 0.965733i \(-0.583571\pi\)
−0.259539 + 0.965733i \(0.583571\pi\)
\(14\) 1.14348e10i 0.553447i
\(15\) 3.47269e9 2.54554e10i 0.0903327 0.662154i
\(16\) 1.71799e10 0.250000
\(17\) 1.95721e11i 1.65043i −0.564816 0.825217i \(-0.691053\pi\)
0.564816 0.825217i \(-0.308947\pi\)
\(18\) 3.75704e10 1.35136e11i 0.189406 0.681268i
\(19\) −1.56485e11 −0.484942 −0.242471 0.970159i \(-0.577958\pi\)
−0.242471 + 0.970159i \(0.577958\pi\)
\(20\) 1.71081e11i 0.334143i
\(21\) 6.15971e11 + 8.40324e10i 0.775509 + 0.105797i
\(22\) −1.37990e12 −1.14299
\(23\) 1.49039e12i 0.827463i 0.910399 + 0.413732i \(0.135775\pi\)
−0.910399 + 0.413732i \(0.864225\pi\)
\(24\) −1.26252e11 + 9.25448e11i −0.0477900 + 0.350309i
\(25\) 2.11102e12 0.553392
\(26\) 1.99286e12i 0.367044i
\(27\) 7.00342e12 + 3.01694e12i 0.918409 + 0.395633i
\(28\) −4.13984e12 −0.391346
\(29\) 7.21871e12i 0.497597i 0.968555 + 0.248799i \(0.0800357\pi\)
−0.968555 + 0.248799i \(0.919964\pi\)
\(30\) −9.21584e12 1.25725e12i −0.468213 0.0638749i
\(31\) 3.81624e12 0.144338 0.0721690 0.997392i \(-0.477008\pi\)
0.0721690 + 0.997392i \(0.477008\pi\)
\(32\) 6.21978e12i 0.176777i
\(33\) 1.01407e13 7.43328e13i 0.218495 1.60160i
\(34\) −7.08587e13 −1.16703
\(35\) 4.12256e13i 0.523063i
\(36\) −4.89244e13 1.36019e13i −0.481729 0.133930i
\(37\) 2.50324e14 1.92614 0.963068 0.269260i \(-0.0867791\pi\)
0.963068 + 0.269260i \(0.0867791\pi\)
\(38\) 5.66536e13i 0.342906i
\(39\) −1.07352e14 1.46452e13i −0.514314 0.0701641i
\(40\) 6.19381e13 0.236275
\(41\) 4.39043e14i 1.34107i 0.741876 + 0.670537i \(0.233936\pi\)
−0.741876 + 0.670537i \(0.766064\pi\)
\(42\) 3.04230e13 2.23005e14i 0.0748098 0.548368i
\(43\) −5.41174e14 −1.07676 −0.538382 0.842701i \(-0.680964\pi\)
−0.538382 + 0.842701i \(0.680964\pi\)
\(44\) 4.99578e14i 0.808219i
\(45\) 1.35451e14 4.87201e14i 0.179007 0.643866i
\(46\) 5.39578e14 0.585105
\(47\) 1.94037e15i 1.73382i 0.498464 + 0.866911i \(0.333898\pi\)
−0.498464 + 0.866911i \(0.666102\pi\)
\(48\) 3.35048e14 + 4.57081e13i 0.247706 + 0.0337926i
\(49\) −6.30835e14 −0.387392
\(50\) 7.64273e14i 0.391308i
\(51\) 5.20729e14 3.81703e15i 0.223090 1.63529i
\(52\) 7.21494e14 0.259539
\(53\) 1.53546e15i 0.465325i −0.972558 0.232663i \(-0.925256\pi\)
0.972558 0.232663i \(-0.0747438\pi\)
\(54\) 1.09225e15 2.53551e15i 0.279755 0.649413i
\(55\) −4.97492e15 −1.08024
\(56\) 1.49878e15i 0.276724i
\(57\) −3.05182e15 4.16338e14i −0.480492 0.0655499i
\(58\) 2.61345e15 0.351854
\(59\) 6.50072e15i 0.750401i 0.926944 + 0.375201i \(0.122426\pi\)
−0.926944 + 0.375201i \(0.877574\pi\)
\(60\) −4.55173e14 + 3.33649e15i −0.0451664 + 0.331077i
\(61\) 3.87413e15 0.331288 0.165644 0.986186i \(-0.447030\pi\)
0.165644 + 0.986186i \(0.447030\pi\)
\(62\) 1.38163e15i 0.102062i
\(63\) 1.17893e16 + 3.27766e15i 0.754091 + 0.209652i
\(64\) −2.25180e15 −0.125000
\(65\) 7.18482e15i 0.346893i
\(66\) −2.69113e16 3.67131e15i −1.13250 0.154499i
\(67\) 3.71114e16 1.36406 0.682032 0.731322i \(-0.261097\pi\)
0.682032 + 0.731322i \(0.261097\pi\)
\(68\) 2.56536e16i 0.825217i
\(69\) −3.96527e15 + 2.90661e16i −0.111849 + 0.819869i
\(70\) −1.49252e16 −0.369862
\(71\) 6.33282e16i 1.38125i −0.723214 0.690624i \(-0.757336\pi\)
0.723214 0.690624i \(-0.242664\pi\)
\(72\) −4.92442e15 + 1.77125e16i −0.0947028 + 0.340634i
\(73\) −5.51216e16 −0.936302 −0.468151 0.883648i \(-0.655080\pi\)
−0.468151 + 0.883648i \(0.655080\pi\)
\(74\) 9.06269e16i 1.36198i
\(75\) 4.11700e16 + 5.61651e15i 0.548314 + 0.0748024i
\(76\) 2.05108e16 0.242471
\(77\) 1.20383e17i 1.26517i
\(78\) −5.30214e15 + 3.88655e16i −0.0496135 + 0.363675i
\(79\) −7.16429e16 −0.597763 −0.298882 0.954290i \(-0.596614\pi\)
−0.298882 + 0.954290i \(0.596614\pi\)
\(80\) 2.24240e16i 0.167072i
\(81\) 1.28556e17 + 7.74704e16i 0.856502 + 0.516144i
\(82\) 1.58951e17 0.948283
\(83\) 1.18877e17i 0.635911i 0.948106 + 0.317956i \(0.102996\pi\)
−0.948106 + 0.317956i \(0.897004\pi\)
\(84\) −8.07366e16 1.10143e16i −0.387755 0.0528985i
\(85\) −2.55465e17 −1.10296
\(86\) 1.95926e17i 0.761388i
\(87\) −1.92058e16 + 1.40782e17i −0.0672605 + 0.493030i
\(88\) 1.80867e17 0.571497
\(89\) 9.49218e16i 0.270929i 0.990782 + 0.135465i \(0.0432527\pi\)
−0.990782 + 0.135465i \(0.956747\pi\)
\(90\) −1.76386e17 4.90386e16i −0.455282 0.126577i
\(91\) −1.73859e17 −0.406278
\(92\) 1.95348e17i 0.413732i
\(93\) 7.44258e16 + 1.01534e16i 0.143013 + 0.0195103i
\(94\) 7.02490e17 1.22600
\(95\) 2.04252e17i 0.324081i
\(96\) 1.65481e16 1.21300e17i 0.0238950 0.175154i
\(97\) −3.38927e17 −0.445821 −0.222910 0.974839i \(-0.571556\pi\)
−0.222910 + 0.974839i \(0.571556\pi\)
\(98\) 2.28387e17i 0.273928i
\(99\) 3.95534e17 1.42268e18i 0.432979 1.55737i
\(100\) −2.76696e17 −0.276696
\(101\) 2.06526e17i 0.188835i −0.995533 0.0944176i \(-0.969901\pi\)
0.995533 0.0944176i \(-0.0300989\pi\)
\(102\) −1.38191e18 1.88524e17i −1.15632 0.157748i
\(103\) 1.06701e18 0.817772 0.408886 0.912585i \(-0.365917\pi\)
0.408886 + 0.912585i \(0.365917\pi\)
\(104\) 2.61209e17i 0.183522i
\(105\) 1.09683e17 8.03996e17i 0.0707027 0.518263i
\(106\) −5.55897e17 −0.329035
\(107\) 8.00886e17i 0.435629i 0.975990 + 0.217814i \(0.0698928\pi\)
−0.975990 + 0.217814i \(0.930107\pi\)
\(108\) −9.17952e17 3.95436e17i −0.459204 0.197816i
\(109\) −2.27655e18 −1.04819 −0.524094 0.851660i \(-0.675596\pi\)
−0.524094 + 0.851660i \(0.675596\pi\)
\(110\) 1.80111e18i 0.763848i
\(111\) 4.88191e18 + 6.66002e17i 1.90846 + 0.260357i
\(112\) 5.42617e17 0.195673
\(113\) 5.22481e18i 1.73926i 0.493703 + 0.869630i \(0.335643\pi\)
−0.493703 + 0.869630i \(0.664357\pi\)
\(114\) −1.50730e17 + 1.10488e18i −0.0463508 + 0.339759i
\(115\) 1.94533e18 0.552983
\(116\) 9.46171e17i 0.248799i
\(117\) −2.05465e18 5.71233e17i −0.500110 0.139040i
\(118\) 2.35351e18 0.530614
\(119\) 6.18176e18i 1.29178i
\(120\) 1.20794e18 + 1.64790e17i 0.234107 + 0.0319374i
\(121\) −8.96744e18 −1.61287
\(122\) 1.40258e18i 0.234256i
\(123\) −1.16810e18 + 8.56238e18i −0.181274 + 1.32877i
\(124\) −5.00203e17 −0.0721690
\(125\) 7.73454e18i 1.03811i
\(126\) 1.18664e18 4.26819e18i 0.148246 0.533223i
\(127\) 1.03674e19 1.20625 0.603123 0.797648i \(-0.293923\pi\)
0.603123 + 0.797648i \(0.293923\pi\)
\(128\) 8.15239e17i 0.0883883i
\(129\) −1.05542e19 1.43983e18i −1.06688 0.145547i
\(130\) 2.60118e18 0.245290
\(131\) 7.19901e18i 0.633623i −0.948488 0.316812i \(-0.897388\pi\)
0.948488 0.316812i \(-0.102612\pi\)
\(132\) −1.32916e18 + 9.74295e18i −0.109247 + 0.800802i
\(133\) −4.94249e18 −0.379561
\(134\) 1.34358e19i 0.964539i
\(135\) 3.93785e18 9.14119e18i 0.264396 0.613761i
\(136\) 9.28760e18 0.583516
\(137\) 3.99891e18i 0.235210i 0.993060 + 0.117605i \(0.0375217\pi\)
−0.993060 + 0.117605i \(0.962478\pi\)
\(138\) 1.05230e19 + 1.43558e18i 0.579735 + 0.0790889i
\(139\) 2.78138e18 0.143591 0.0717956 0.997419i \(-0.477127\pi\)
0.0717956 + 0.997419i \(0.477127\pi\)
\(140\) 5.40352e18i 0.261532i
\(141\) −5.16248e18 + 3.78418e19i −0.234362 + 1.71791i
\(142\) −2.29272e19 −0.976690
\(143\) 2.09805e19i 0.839057i
\(144\) 6.41261e18 + 1.78283e18i 0.240864 + 0.0669650i
\(145\) 9.42221e18 0.332538
\(146\) 1.99561e19i 0.662066i
\(147\) −1.23028e19 1.67838e18i −0.383837 0.0523641i
\(148\) −3.28104e19 −0.963068
\(149\) 1.35043e19i 0.373074i −0.982448 0.186537i \(-0.940274\pi\)
0.982448 0.186537i \(-0.0597264\pi\)
\(150\) 2.03339e18 1.49051e19i 0.0528933 0.387716i
\(151\) 6.29355e19 1.54207 0.771034 0.636794i \(-0.219740\pi\)
0.771034 + 0.636794i \(0.219740\pi\)
\(152\) 7.42570e18i 0.171453i
\(153\) 2.03109e19 7.30556e19i 0.442085 1.59012i
\(154\) −4.35835e19 −0.894613
\(155\) 4.98115e18i 0.0964593i
\(156\) 1.40708e19 + 1.91958e18i 0.257157 + 0.0350820i
\(157\) −1.52297e19 −0.262781 −0.131391 0.991331i \(-0.541944\pi\)
−0.131391 + 0.991331i \(0.541944\pi\)
\(158\) 2.59375e19i 0.422683i
\(159\) 4.08519e18 2.99451e19i 0.0628983 0.461055i
\(160\) −8.11835e18 −0.118138
\(161\) 4.70731e19i 0.647649i
\(162\) 2.80473e19 4.65424e19i 0.364969 0.605638i
\(163\) 2.05524e19 0.253032 0.126516 0.991965i \(-0.459621\pi\)
0.126516 + 0.991965i \(0.459621\pi\)
\(164\) 5.75463e19i 0.670537i
\(165\) −9.70227e19 1.32361e19i −1.07033 0.146017i
\(166\) 4.30382e19 0.449657
\(167\) 9.65270e18i 0.0955434i 0.998858 + 0.0477717i \(0.0152120\pi\)
−0.998858 + 0.0477717i \(0.984788\pi\)
\(168\) −3.98760e18 + 2.92298e19i −0.0374049 + 0.274184i
\(169\) −8.21552e19 −0.730558
\(170\) 9.24882e19i 0.779913i
\(171\) −5.84101e19 1.62391e19i −0.467221 0.129897i
\(172\) 7.09328e19 0.538382
\(173\) 8.60111e19i 0.619640i 0.950795 + 0.309820i \(0.100269\pi\)
−0.950795 + 0.309820i \(0.899731\pi\)
\(174\) 5.09685e19 + 6.95326e18i 0.348625 + 0.0475603i
\(175\) 6.66756e19 0.433136
\(176\) 6.54807e19i 0.404110i
\(177\) −1.72956e19 + 1.26779e20i −0.101432 + 0.743514i
\(178\) 3.43654e19 0.191576
\(179\) 1.49036e20i 0.789977i 0.918686 + 0.394988i \(0.129251\pi\)
−0.918686 + 0.394988i \(0.870749\pi\)
\(180\) −1.77539e19 + 6.38584e19i −0.0895037 + 0.321933i
\(181\) 2.50765e20 1.20271 0.601354 0.798983i \(-0.294628\pi\)
0.601354 + 0.798983i \(0.294628\pi\)
\(182\) 6.29436e19i 0.287282i
\(183\) 7.55547e19 + 1.03074e19i 0.328248 + 0.0447804i
\(184\) −7.07235e19 −0.292552
\(185\) 3.26735e20i 1.28721i
\(186\) 3.67591e18 2.69450e19i 0.0137958 0.101126i
\(187\) −7.45988e20 −2.66782
\(188\) 2.54328e20i 0.866911i
\(189\) 2.21199e20 + 9.52883e19i 0.718832 + 0.309659i
\(190\) 7.39470e19 0.229160
\(191\) 4.59540e20i 1.35839i −0.733959 0.679193i \(-0.762330\pi\)
0.733959 0.679193i \(-0.237670\pi\)
\(192\) −4.39154e19 5.99105e18i −0.123853 0.0168963i
\(193\) 7.00243e19 0.188466 0.0942330 0.995550i \(-0.469960\pi\)
0.0942330 + 0.995550i \(0.469960\pi\)
\(194\) 1.22705e20i 0.315243i
\(195\) −1.91157e19 + 1.40121e20i −0.0468897 + 0.343709i
\(196\) 8.26848e19 0.193696
\(197\) 3.14404e20i 0.703545i −0.936086 0.351772i \(-0.885579\pi\)
0.936086 0.351772i \(-0.114421\pi\)
\(198\) −5.15067e20 1.43199e20i −1.10123 0.306162i
\(199\) 1.46711e20 0.299768 0.149884 0.988704i \(-0.452110\pi\)
0.149884 + 0.988704i \(0.452110\pi\)
\(200\) 1.00175e20i 0.195654i
\(201\) 7.23761e20 + 9.87373e19i 1.35154 + 0.184381i
\(202\) −7.47705e19 −0.133527
\(203\) 2.27999e20i 0.389466i
\(204\) −6.82530e19 + 5.00306e20i −0.111545 + 0.817643i
\(205\) 5.73061e20 0.896222
\(206\) 3.86298e20i 0.578252i
\(207\) −1.54664e20 + 5.56307e20i −0.221644 + 0.797226i
\(208\) −9.45677e19 −0.129769
\(209\) 5.96438e20i 0.783879i
\(210\) −2.91077e20 3.97095e19i −0.366467 0.0499944i
\(211\) −5.46493e20 −0.659239 −0.329619 0.944114i \(-0.606920\pi\)
−0.329619 + 0.944114i \(0.606920\pi\)
\(212\) 2.01256e20i 0.232663i
\(213\) 1.68488e20 1.23505e21i 0.186704 1.36857i
\(214\) 2.89952e20 0.308036
\(215\) 7.06366e20i 0.719588i
\(216\) −1.43163e20 + 3.32334e20i −0.139877 + 0.324707i
\(217\) 1.20534e20 0.112972
\(218\) 8.24200e20i 0.741181i
\(219\) −1.07500e21 1.46654e20i −0.927709 0.126560i
\(220\) 6.52073e20 0.540122
\(221\) 1.07736e21i 0.856704i
\(222\) 2.41119e20 1.76744e21i 0.184100 1.34948i
\(223\) −1.21601e21 −0.891648 −0.445824 0.895121i \(-0.647089\pi\)
−0.445824 + 0.895121i \(0.647089\pi\)
\(224\) 1.96448e20i 0.138362i
\(225\) 7.87968e20 + 2.19070e20i 0.533170 + 0.148232i
\(226\) 1.89158e21 1.22984
\(227\) 1.82295e21i 1.13905i −0.821974 0.569524i \(-0.807127\pi\)
0.821974 0.569524i \(-0.192873\pi\)
\(228\) 4.00009e20 + 5.45702e19i 0.240246 + 0.0327749i
\(229\) −1.70915e21 −0.986872 −0.493436 0.869782i \(-0.664259\pi\)
−0.493436 + 0.869782i \(0.664259\pi\)
\(230\) 7.04283e20i 0.391018i
\(231\) 3.20288e20 2.34776e21i 0.171014 1.25356i
\(232\) −3.42551e20 −0.175927
\(233\) 7.67655e20i 0.379283i −0.981853 0.189641i \(-0.939267\pi\)
0.981853 0.189641i \(-0.0607325\pi\)
\(234\) −2.06808e20 + 7.43863e20i −0.0983163 + 0.353631i
\(235\) 2.53267e21 1.15869
\(236\) 8.52063e20i 0.375201i
\(237\) −1.39721e21 1.90610e20i −0.592277 0.0808000i
\(238\) −2.23804e21 −0.913428
\(239\) 2.79282e21i 1.09765i 0.835938 + 0.548823i \(0.184924\pi\)
−0.835938 + 0.548823i \(0.815076\pi\)
\(240\) 5.96604e19 4.37321e20i 0.0225832 0.165538i
\(241\) −2.42709e21 −0.884979 −0.442490 0.896774i \(-0.645905\pi\)
−0.442490 + 0.896774i \(0.645905\pi\)
\(242\) 3.24656e21i 1.14047i
\(243\) 2.30104e21 + 1.85289e21i 0.778874 + 0.627180i
\(244\) −5.07790e20 −0.165644
\(245\) 8.23396e20i 0.258889i
\(246\) 3.09991e21 + 4.22898e20i 0.939580 + 0.128180i
\(247\) 8.61381e20 0.251723
\(248\) 1.81093e20i 0.0510312i
\(249\) −3.16281e20 + 2.31839e21i −0.0859565 + 0.630075i
\(250\) −2.80020e21 −0.734056
\(251\) 6.90800e20i 0.174698i 0.996178 + 0.0873492i \(0.0278396\pi\)
−0.996178 + 0.0873492i \(0.972160\pi\)
\(252\) −1.54525e21 4.29610e20i −0.377046 0.104826i
\(253\) 5.68058e21 1.33754
\(254\) 3.75340e21i 0.852945i
\(255\) −4.98217e21 6.79680e20i −1.09284 0.149088i
\(256\) 2.95148e20 0.0625000
\(257\) 4.00679e21i 0.819216i −0.912262 0.409608i \(-0.865666\pi\)
0.912262 0.409608i \(-0.134334\pi\)
\(258\) −5.21273e20 + 3.82102e21i −0.102917 + 0.754400i
\(259\) 7.90635e21 1.50757
\(260\) 9.41729e20i 0.173447i
\(261\) −7.49118e20 + 2.69448e21i −0.133286 + 0.479414i
\(262\) −2.60632e21 −0.448039
\(263\) 3.40224e21i 0.565149i −0.959245 0.282575i \(-0.908812\pi\)
0.959245 0.282575i \(-0.0911885\pi\)
\(264\) 3.52732e21 + 4.81207e20i 0.566252 + 0.0772496i
\(265\) −2.00416e21 −0.310971
\(266\) 1.78937e21i 0.268390i
\(267\) −2.52545e20 + 1.85120e21i −0.0366217 + 0.268443i
\(268\) −4.86427e21 −0.682032
\(269\) 8.26566e21i 1.12075i −0.828241 0.560373i \(-0.810658\pi\)
0.828241 0.560373i \(-0.189342\pi\)
\(270\) −3.30947e21 1.42565e21i −0.433994 0.186956i
\(271\) −6.07257e20 −0.0770280 −0.0385140 0.999258i \(-0.512262\pi\)
−0.0385140 + 0.999258i \(0.512262\pi\)
\(272\) 3.36247e21i 0.412608i
\(273\) −3.39065e21 4.62562e20i −0.402550 0.0549169i
\(274\) 1.44776e21 0.166319
\(275\) 8.04612e21i 0.894525i
\(276\) 5.19736e20 3.80975e21i 0.0559243 0.409934i
\(277\) −7.76370e21 −0.808632 −0.404316 0.914619i \(-0.632490\pi\)
−0.404316 + 0.914619i \(0.632490\pi\)
\(278\) 1.00697e21i 0.101534i
\(279\) 1.42446e21 + 3.96029e20i 0.139064 + 0.0386624i
\(280\) 1.95628e21 0.184931
\(281\) 1.12811e22i 1.03274i 0.856364 + 0.516372i \(0.172718\pi\)
−0.856364 + 0.516372i \(0.827282\pi\)
\(282\) 1.37002e22 + 1.86902e21i 1.21474 + 0.165719i
\(283\) 1.16922e22 1.00419 0.502096 0.864812i \(-0.332562\pi\)
0.502096 + 0.864812i \(0.332562\pi\)
\(284\) 8.30055e21i 0.690624i
\(285\) −5.43424e20 + 3.98339e21i −0.0438061 + 0.321106i
\(286\) 7.59576e21 0.593303
\(287\) 1.38670e22i 1.04965i
\(288\) 6.45454e20 2.32161e21i 0.0473514 0.170317i
\(289\) −2.42438e22 −1.72393
\(290\) 3.41121e21i 0.235140i
\(291\) −6.60987e21 9.01735e20i −0.441729 0.0602618i
\(292\) 7.22490e21 0.468151
\(293\) 2.56349e22i 1.61073i 0.592777 + 0.805367i \(0.298032\pi\)
−0.592777 + 0.805367i \(0.701968\pi\)
\(294\) −6.07637e20 + 4.45408e21i −0.0370270 + 0.271414i
\(295\) 8.48505e21 0.501483
\(296\) 1.18787e22i 0.680992i
\(297\) 1.14990e22 2.66934e22i 0.639516 1.48455i
\(298\) −4.88907e21 −0.263803
\(299\) 8.20393e21i 0.429518i
\(300\) −5.39623e21 7.36167e20i −0.274157 0.0374012i
\(301\) −1.70927e22 −0.842776
\(302\) 2.27851e22i 1.09041i
\(303\) 5.49476e20 4.02775e21i 0.0255250 0.187102i
\(304\) −2.68839e21 −0.121236
\(305\) 5.05670e21i 0.221395i
\(306\) −2.64490e22 7.35333e21i −1.12439 0.312601i
\(307\) 1.11726e22 0.461221 0.230610 0.973046i \(-0.425928\pi\)
0.230610 + 0.973046i \(0.425928\pi\)
\(308\) 1.57789e22i 0.632587i
\(309\) 2.08092e22 + 2.83884e21i 0.810267 + 0.110539i
\(310\) −1.80337e21 −0.0682070
\(311\) 2.40165e21i 0.0882403i 0.999026 + 0.0441202i \(0.0140484\pi\)
−0.999026 + 0.0441202i \(0.985952\pi\)
\(312\) 6.94962e20 5.09419e21i 0.0248067 0.181837i
\(313\) 7.63802e21 0.264900 0.132450 0.991190i \(-0.457716\pi\)
0.132450 + 0.991190i \(0.457716\pi\)
\(314\) 5.51374e21i 0.185815i
\(315\) 4.27816e21 1.53880e22i 0.140108 0.503949i
\(316\) 9.39038e21 0.298882
\(317\) 5.61795e22i 1.73798i −0.494830 0.868990i \(-0.664770\pi\)
0.494830 0.868990i \(-0.335230\pi\)
\(318\) −1.08413e22 1.47900e21i −0.326015 0.0444758i
\(319\) 2.75140e22 0.804335
\(320\) 2.93916e21i 0.0835359i
\(321\) −2.13081e21 + 1.56192e22i −0.0588842 + 0.431631i
\(322\) 1.70423e22 0.457957
\(323\) 3.06274e22i 0.800365i
\(324\) −1.68501e22 1.01542e22i −0.428251 0.258072i
\(325\) −1.16203e22 −0.287254
\(326\) 7.44077e21i 0.178920i
\(327\) −4.43981e22 6.05691e21i −1.03857 0.141684i
\(328\) −2.08340e22 −0.474141
\(329\) 6.12856e22i 1.35705i
\(330\) −4.79198e21 + 3.51260e22i −0.103250 + 0.756838i
\(331\) −4.49114e22 −0.941684 −0.470842 0.882218i \(-0.656050\pi\)
−0.470842 + 0.882218i \(0.656050\pi\)
\(332\) 1.55815e22i 0.317956i
\(333\) 9.34367e22 + 2.59772e22i 1.85575 + 0.515935i
\(334\) 3.49465e21 0.0675594
\(335\) 4.84396e22i 0.911586i
\(336\) 1.05823e22 + 1.44367e21i 0.193877 + 0.0264492i
\(337\) 1.02040e22 0.182012 0.0910061 0.995850i \(-0.470992\pi\)
0.0910061 + 0.995850i \(0.470992\pi\)
\(338\) 2.97434e22i 0.516583i
\(339\) −1.39009e22 + 1.01896e23i −0.235097 + 1.72330i
\(340\) 3.34843e22 0.551482
\(341\) 1.45455e22i 0.233314i
\(342\) −5.87919e21 + 2.11467e22i −0.0918508 + 0.330375i
\(343\) −7.13572e22 −1.08590
\(344\) 2.56804e22i 0.380694i
\(345\) 3.79384e22 + 5.17566e21i 0.547908 + 0.0747470i
\(346\) 3.11394e22 0.438152
\(347\) 6.29266e22i 0.862718i −0.902180 0.431359i \(-0.858034\pi\)
0.902180 0.431359i \(-0.141966\pi\)
\(348\) 2.51735e21 1.84526e22i 0.0336302 0.246515i
\(349\) 4.44746e22 0.579006 0.289503 0.957177i \(-0.406510\pi\)
0.289503 + 0.957177i \(0.406510\pi\)
\(350\) 2.41391e22i 0.306274i
\(351\) −3.85507e22 1.66069e22i −0.476726 0.205364i
\(352\) −2.37065e22 −0.285749
\(353\) 1.05940e23i 1.24476i −0.782715 0.622380i \(-0.786166\pi\)
0.782715 0.622380i \(-0.213834\pi\)
\(354\) 4.58990e22 + 6.26167e21i 0.525744 + 0.0717233i
\(355\) −8.26590e22 −0.923070
\(356\) 1.24416e22i 0.135465i
\(357\) 1.64469e22 1.20559e23i 0.174611 1.27993i
\(358\) 5.39568e22 0.558598
\(359\) 1.13366e23i 1.14455i 0.820063 + 0.572273i \(0.193938\pi\)
−0.820063 + 0.572273i \(0.806062\pi\)
\(360\) 2.31192e22 + 6.42759e21i 0.227641 + 0.0632887i
\(361\) −7.96398e22 −0.764831
\(362\) 9.07867e22i 0.850443i
\(363\) −1.74886e23 2.38584e22i −1.59807 0.218013i
\(364\) 2.27880e22 0.203139
\(365\) 7.19474e22i 0.625719i
\(366\) 3.73166e21 2.73537e22i 0.0316645 0.232106i
\(367\) 1.89333e23 1.56759 0.783795 0.621019i \(-0.213281\pi\)
0.783795 + 0.621019i \(0.213281\pi\)
\(368\) 2.56047e22i 0.206866i
\(369\) −4.55615e22 + 1.63879e23i −0.359220 + 1.29207i
\(370\) −1.18291e23 −0.910196
\(371\) 4.84968e22i 0.364207i
\(372\) −9.75513e21 1.33082e21i −0.0715067 0.00975513i
\(373\) 9.21191e22 0.659128 0.329564 0.944133i \(-0.393098\pi\)
0.329564 + 0.944133i \(0.393098\pi\)
\(374\) 2.70076e23i 1.88644i
\(375\) 2.05782e22 1.50842e23i 0.140322 1.02858i
\(376\) −9.20767e22 −0.612998
\(377\) 3.97359e22i 0.258292i
\(378\) 3.44981e22 8.00826e22i 0.218962 0.508291i
\(379\) 2.72704e23 1.69020 0.845102 0.534605i \(-0.179540\pi\)
0.845102 + 0.534605i \(0.179540\pi\)
\(380\) 2.67717e22i 0.162040i
\(381\) 2.02189e23 + 2.75831e22i 1.19518 + 0.163049i
\(382\) −1.66371e23 −0.960524
\(383\) 3.04293e23i 1.71595i 0.513696 + 0.857973i \(0.328276\pi\)
−0.513696 + 0.857973i \(0.671724\pi\)
\(384\) −2.16899e21 + 1.58991e22i −0.0119475 + 0.0875772i
\(385\) −1.57130e23 −0.845499
\(386\) 2.53515e22i 0.133266i
\(387\) −2.02000e23 5.61600e22i −1.03742 0.288422i
\(388\) 4.44238e22 0.222910
\(389\) 5.34134e22i 0.261881i 0.991390 + 0.130940i \(0.0417997\pi\)
−0.991390 + 0.130940i \(0.958200\pi\)
\(390\) 5.07292e22 + 6.92061e21i 0.243039 + 0.0331560i
\(391\) 2.91701e23 1.36567
\(392\) 2.99351e22i 0.136964i
\(393\) 1.91534e22 1.40398e23i 0.0856472 0.627808i
\(394\) −1.13826e23 −0.497481
\(395\) 9.35117e22i 0.399477i
\(396\) −5.18434e22 + 1.86474e23i −0.216490 + 0.778685i
\(397\) −2.54444e23 −1.03867 −0.519334 0.854571i \(-0.673820\pi\)
−0.519334 + 0.854571i \(0.673820\pi\)
\(398\) 5.31151e22i 0.211968i
\(399\) −9.63902e22 1.31498e22i −0.376077 0.0513054i
\(400\) 3.62671e22 0.138348
\(401\) 1.36946e23i 0.510799i 0.966836 + 0.255400i \(0.0822071\pi\)
−0.966836 + 0.255400i \(0.917793\pi\)
\(402\) 3.57467e22 2.62029e23i 0.130377 0.955687i
\(403\) −2.10068e22 −0.0749227
\(404\) 2.70698e22i 0.0944176i
\(405\) 1.01118e23 1.67798e23i 0.344932 0.572389i
\(406\) 8.25445e22 0.275394
\(407\) 9.54104e23i 3.11348i
\(408\) 1.81130e23 + 2.47102e22i 0.578161 + 0.0788742i
\(409\) −3.94768e23 −1.23263 −0.616314 0.787501i \(-0.711375\pi\)
−0.616314 + 0.787501i \(0.711375\pi\)
\(410\) 2.07470e23i 0.633725i
\(411\) −1.06393e22 + 7.79881e22i −0.0317935 + 0.233052i
\(412\) −1.39855e23 −0.408886
\(413\) 2.05322e23i 0.587333i
\(414\) 2.01405e23 + 5.59944e22i 0.563724 + 0.156726i
\(415\) 1.55165e23 0.424971
\(416\) 3.42371e22i 0.0917609i
\(417\) 5.42435e22 + 7.40004e21i 0.142273 + 0.0194093i
\(418\) 2.15934e23 0.554286
\(419\) 3.47824e23i 0.873843i 0.899500 + 0.436922i \(0.143931\pi\)
−0.899500 + 0.436922i \(0.856069\pi\)
\(420\) −1.43764e22 + 1.05381e23i −0.0353514 + 0.259131i
\(421\) 2.83789e23 0.683056 0.341528 0.939872i \(-0.389056\pi\)
0.341528 + 0.939872i \(0.389056\pi\)
\(422\) 1.97852e23i 0.466152i
\(423\) −2.01361e23 + 7.24270e23i −0.464421 + 1.67046i
\(424\) 7.28625e22 0.164517
\(425\) 4.13173e23i 0.913338i
\(426\) −4.47135e23 6.09993e22i −0.967726 0.132020i
\(427\) 1.22362e23 0.259297
\(428\) 1.04974e23i 0.217814i
\(429\) −5.58199e22 + 4.09169e23i −0.113416 + 0.831357i
\(430\) 2.55732e23 0.508825
\(431\) 2.66986e23i 0.520228i 0.965578 + 0.260114i \(0.0837601\pi\)
−0.965578 + 0.260114i \(0.916240\pi\)
\(432\) 1.20318e23 + 5.18306e22i 0.229602 + 0.0989082i
\(433\) −9.50235e23 −1.77599 −0.887994 0.459856i \(-0.847901\pi\)
−0.887994 + 0.459856i \(0.847901\pi\)
\(434\) 4.36380e22i 0.0798835i
\(435\) 1.83755e23 + 2.50684e22i 0.329486 + 0.0449493i
\(436\) 2.98392e23 0.524094
\(437\) 2.33223e23i 0.401272i
\(438\) −5.30946e22 + 3.89192e23i −0.0894918 + 0.655989i
\(439\) −8.77998e22 −0.144982 −0.0724908 0.997369i \(-0.523095\pi\)
−0.0724908 + 0.997369i \(0.523095\pi\)
\(440\) 2.36076e23i 0.381924i
\(441\) −2.35468e23 6.54646e22i −0.373236 0.103767i
\(442\) 3.90046e23 0.605781
\(443\) 5.17374e23i 0.787356i −0.919248 0.393678i \(-0.871203\pi\)
0.919248 0.393678i \(-0.128797\pi\)
\(444\) −6.39881e23 8.72942e22i −0.954229 0.130178i
\(445\) 1.23897e23 0.181059
\(446\) 4.40243e23i 0.630490i
\(447\) 3.59290e22 2.63365e23i 0.0504286 0.369650i
\(448\) −7.11219e22 −0.0978366
\(449\) 6.77346e23i 0.913258i 0.889657 + 0.456629i \(0.150943\pi\)
−0.889657 + 0.456629i \(0.849057\pi\)
\(450\) 7.93120e22 2.85275e23i 0.104816 0.377008i
\(451\) 1.67340e24 2.16776
\(452\) 6.84827e23i 0.869630i
\(453\) 1.22739e24 + 1.67444e23i 1.52791 + 0.208442i
\(454\) −6.59979e23 −0.805429
\(455\) 2.26929e23i 0.271511i
\(456\) 1.97565e22 1.44819e23i 0.0231754 0.169879i
\(457\) −1.62058e24 −1.86391 −0.931956 0.362571i \(-0.881899\pi\)
−0.931956 + 0.362571i \(0.881899\pi\)
\(458\) 6.18778e23i 0.697824i
\(459\) 5.90479e23 1.37072e24i 0.652966 1.51577i
\(460\) −2.54978e23 −0.276491
\(461\) 1.38120e24i 1.46876i −0.678741 0.734378i \(-0.737474\pi\)
0.678741 0.734378i \(-0.262526\pi\)
\(462\) −8.49980e23 1.15957e23i −0.886403 0.120925i
\(463\) −6.56869e23 −0.671815 −0.335908 0.941895i \(-0.609043\pi\)
−0.335908 + 0.941895i \(0.609043\pi\)
\(464\) 1.24017e23i 0.124399i
\(465\) 1.32526e22 9.71441e22i 0.0130385 0.0955740i
\(466\) −2.77921e23 −0.268193
\(467\) 2.48434e23i 0.235158i −0.993064 0.117579i \(-0.962487\pi\)
0.993064 0.117579i \(-0.0375133\pi\)
\(468\) 2.69307e23 + 7.48726e22i 0.250055 + 0.0695201i
\(469\) 1.17215e24 1.06764
\(470\) 9.16923e23i 0.819318i
\(471\) −2.97015e23 4.05196e22i −0.260370 0.0355203i
\(472\) −3.08480e23 −0.265307
\(473\) 2.06267e24i 1.74052i
\(474\) −6.90083e22 + 5.05842e23i −0.0571342 + 0.418803i
\(475\) −3.30343e23 −0.268363
\(476\) 8.10255e23i 0.645891i
\(477\) 1.59342e23 5.73132e23i 0.124642 0.448321i
\(478\) 1.01111e24 0.776153
\(479\) 1.29607e24i 0.976359i 0.872743 + 0.488180i \(0.162339\pi\)
−0.872743 + 0.488180i \(0.837661\pi\)
\(480\) −1.58327e23 2.15994e22i −0.117053 0.0159687i
\(481\) −1.37792e24 −0.999814
\(482\) 8.78701e23i 0.625775i
\(483\) −1.25241e23 + 9.18036e23i −0.0875431 + 0.641705i
\(484\) 1.17538e24 0.806436
\(485\) 4.42383e23i 0.297936i
\(486\) 6.70817e23 8.33064e23i 0.443484 0.550747i
\(487\) 9.72420e22 0.0631093 0.0315547 0.999502i \(-0.489954\pi\)
0.0315547 + 0.999502i \(0.489954\pi\)
\(488\) 1.83840e23i 0.117128i
\(489\) 4.00821e23 + 5.46810e22i 0.250709 + 0.0342024i
\(490\) 2.98101e23 0.183062
\(491\) 1.80548e24i 1.08858i 0.838898 + 0.544289i \(0.183201\pi\)
−0.838898 + 0.544289i \(0.816799\pi\)
\(492\) 1.53105e23 1.12229e24i 0.0906369 0.664383i
\(493\) 1.41286e24 0.821251
\(494\) 3.11853e23i 0.177995i
\(495\) −1.85696e24 5.16270e23i −1.04077 0.289354i
\(496\) 6.55626e22 0.0360845
\(497\) 2.00019e24i 1.08109i
\(498\) 8.39347e23 + 1.14506e23i 0.445531 + 0.0607804i
\(499\) −6.98251e23 −0.364004 −0.182002 0.983298i \(-0.558258\pi\)
−0.182002 + 0.983298i \(0.558258\pi\)
\(500\) 1.01378e24i 0.519056i
\(501\) −2.56816e22 + 1.88250e23i −0.0129146 + 0.0946665i
\(502\) 2.50096e23 0.123530
\(503\) 2.15858e24i 1.04726i −0.851945 0.523632i \(-0.824577\pi\)
0.851945 0.523632i \(-0.175423\pi\)
\(504\) −1.55535e23 + 5.59440e23i −0.0741232 + 0.266612i
\(505\) −2.69568e23 −0.126196
\(506\) 2.05659e24i 0.945786i
\(507\) −1.60222e24 2.18579e23i −0.723853 0.0987499i
\(508\) −1.35887e24 −0.603123
\(509\) 2.38712e23i 0.104091i −0.998645 0.0520456i \(-0.983426\pi\)
0.998645 0.0520456i \(-0.0165741\pi\)
\(510\) −2.46071e23 + 1.80374e24i −0.105421 + 0.772755i
\(511\) −1.74099e24 −0.732837
\(512\) 1.06855e23i 0.0441942i
\(513\) −1.09593e24 4.72105e23i −0.445375 0.191859i
\(514\) −1.45061e24 −0.579273
\(515\) 1.39271e24i 0.546506i
\(516\) 1.38336e24 + 1.88721e23i 0.533441 + 0.0727734i
\(517\) 7.39568e24 2.80261
\(518\) 2.86240e24i 1.06601i
\(519\) −2.28838e23 + 1.67742e24i −0.0837571 + 0.613953i
\(520\) −3.40942e23 −0.122645
\(521\) 6.08131e23i 0.215010i −0.994205 0.107505i \(-0.965714\pi\)
0.994205 0.107505i \(-0.0342861\pi\)
\(522\) 9.75506e23 + 2.71210e23i 0.338997 + 0.0942477i
\(523\) −3.17661e24 −1.08505 −0.542523 0.840041i \(-0.682531\pi\)
−0.542523 + 0.840041i \(0.682531\pi\)
\(524\) 9.43589e23i 0.316812i
\(525\) 1.30033e24 + 1.77395e23i 0.429161 + 0.0585472i
\(526\) −1.23174e24 −0.399621
\(527\) 7.46921e23i 0.238220i
\(528\) 1.74215e23 1.27703e24i 0.0546237 0.400401i
\(529\) 1.02290e24 0.315305
\(530\) 7.25584e23i 0.219890i
\(531\) −6.74609e23 + 2.42648e24i −0.201002 + 0.722980i
\(532\) 6.47822e23 0.189780
\(533\) 2.41674e24i 0.696122i
\(534\) 6.70206e23 + 9.14312e22i 0.189818 + 0.0258954i
\(535\) 1.04535e24 0.291125
\(536\) 1.76105e24i 0.482269i
\(537\) −3.96520e23 + 2.90656e24i −0.106782 + 0.782726i
\(538\) −2.99249e24 −0.792487
\(539\) 2.40441e24i 0.626196i
\(540\) −5.16142e23 + 1.19815e24i −0.132198 + 0.306880i
\(541\) 9.87736e23 0.248809 0.124404 0.992232i \(-0.460298\pi\)
0.124404 + 0.992232i \(0.460298\pi\)
\(542\) 2.19850e23i 0.0544670i
\(543\) 4.89051e24 + 6.67176e23i 1.19167 + 0.162571i
\(544\) −1.21734e24 −0.291758
\(545\) 2.97147e24i 0.700490i
\(546\) −1.67465e23 + 1.22755e24i −0.0388321 + 0.284646i
\(547\) −6.90954e23 −0.157603 −0.0788013 0.996890i \(-0.525109\pi\)
−0.0788013 + 0.996890i \(0.525109\pi\)
\(548\) 5.24145e23i 0.117605i
\(549\) 1.44607e24 + 4.02036e23i 0.319182 + 0.0887388i
\(550\) −2.91301e24 −0.632525
\(551\) 1.12962e24i 0.241306i
\(552\) −1.37928e24 1.88164e23i −0.289867 0.0395445i
\(553\) −2.26280e24 −0.467865
\(554\) 2.81076e24i 0.571789i
\(555\) 8.69298e23 6.37210e24i 0.173993 1.27540i
\(556\) −3.64561e23 −0.0717956
\(557\) 5.42846e24i 1.05191i 0.850512 + 0.525956i \(0.176292\pi\)
−0.850512 + 0.525956i \(0.823708\pi\)
\(558\) 1.43378e23 5.15711e23i 0.0273384 0.0983329i
\(559\) 2.97893e24 0.558925
\(560\) 7.08250e23i 0.130766i
\(561\) −1.45485e25 1.98475e24i −2.64334 0.360611i
\(562\) 4.08418e24 0.730261
\(563\) 4.18442e24i 0.736308i −0.929765 0.368154i \(-0.879990\pi\)
0.929765 0.368154i \(-0.120010\pi\)
\(564\) 6.76657e23 4.96000e24i 0.117181 0.858954i
\(565\) 6.81968e24 1.16233
\(566\) 4.23301e24i 0.710071i
\(567\) 4.06038e24 + 2.44686e24i 0.670378 + 0.403982i
\(568\) 3.00512e24 0.488345
\(569\) 7.47092e24i 1.19499i −0.801873 0.597494i \(-0.796163\pi\)
0.801873 0.597494i \(-0.203837\pi\)
\(570\) 1.44214e24 + 1.96740e23i 0.227056 + 0.0309756i
\(571\) −3.78796e23 −0.0587057 −0.0293528 0.999569i \(-0.509345\pi\)
−0.0293528 + 0.999569i \(0.509345\pi\)
\(572\) 2.74996e24i 0.419529i
\(573\) 1.22264e24 8.96212e24i 0.183614 1.34592i
\(574\) 5.02037e24 0.742214
\(575\) 3.14624e24i 0.457912i
\(576\) −8.40514e23 2.33679e23i −0.120432 0.0334825i
\(577\) −1.36291e25 −1.92258 −0.961291 0.275534i \(-0.911145\pi\)
−0.961291 + 0.275534i \(0.911145\pi\)
\(578\) 8.77719e24i 1.21900i
\(579\) 1.36564e24 + 1.86304e23i 0.186736 + 0.0254750i
\(580\) −1.23499e24 −0.166269
\(581\) 3.75468e24i 0.497723i
\(582\) −3.26463e23 + 2.39303e24i −0.0426115 + 0.312350i
\(583\) −5.85238e24 −0.752169
\(584\) 2.61569e24i 0.331033i
\(585\) −7.45601e23 + 2.68183e24i −0.0929188 + 0.334217i
\(586\) 9.28084e24 1.13896
\(587\) 1.35788e25i 1.64104i 0.571617 + 0.820520i \(0.306316\pi\)
−0.571617 + 0.820520i \(0.693684\pi\)
\(588\) 1.61255e24 + 2.19988e23i 0.191919 + 0.0261820i
\(589\) −5.97184e23 −0.0699956
\(590\) 3.07192e24i 0.354602i
\(591\) 8.36491e23 6.13161e24i 0.0950985 0.697088i
\(592\) 4.30053e24 0.481534
\(593\) 6.16432e24i 0.679819i 0.940458 + 0.339909i \(0.110396\pi\)
−0.940458 + 0.339909i \(0.889604\pi\)
\(594\) −9.66403e24 4.16308e24i −1.04974 0.452206i
\(595\) −8.06873e24 −0.863281
\(596\) 1.77003e24i 0.186537i
\(597\) 2.86121e24 + 3.90334e23i 0.297017 + 0.0405198i
\(598\) −2.97014e24 −0.303715
\(599\) 8.55875e24i 0.862122i −0.902323 0.431061i \(-0.858139\pi\)
0.902323 0.431061i \(-0.141861\pi\)
\(600\) −2.66521e23 + 1.95364e24i −0.0264466 + 0.193858i
\(601\) 6.20429e24 0.606488 0.303244 0.952913i \(-0.401930\pi\)
0.303244 + 0.952913i \(0.401930\pi\)
\(602\) 6.18821e24i 0.595932i
\(603\) 1.38523e25 + 3.85122e24i 1.31422 + 0.365378i
\(604\) −8.24909e24 −0.771034
\(605\) 1.17047e25i 1.07786i
\(606\) −1.45820e24 1.98932e23i −0.132301 0.0180489i
\(607\) 7.07816e24 0.632735 0.316368 0.948637i \(-0.397537\pi\)
0.316368 + 0.948637i \(0.397537\pi\)
\(608\) 9.73301e23i 0.0857265i
\(609\) −6.06606e23 + 4.44652e24i −0.0526443 + 0.385891i
\(610\) −1.83072e24 −0.156550
\(611\) 1.06809e25i 0.899988i
\(612\) −2.66219e24 + 9.57555e24i −0.221043 + 0.795062i
\(613\) −4.11449e24 −0.336644 −0.168322 0.985732i \(-0.553835\pi\)
−0.168322 + 0.985732i \(0.553835\pi\)
\(614\) 4.04491e24i 0.326132i
\(615\) 1.11760e25 + 1.52466e24i 0.887997 + 0.121143i
\(616\) 5.71257e24 0.447307
\(617\) 9.81674e24i 0.757532i −0.925493 0.378766i \(-0.876349\pi\)
0.925493 0.378766i \(-0.123651\pi\)
\(618\) 1.02777e24 7.53372e24i 0.0781627 0.572945i
\(619\) 3.40269e24 0.255039 0.127519 0.991836i \(-0.459299\pi\)
0.127519 + 0.991836i \(0.459299\pi\)
\(620\) 6.52889e23i 0.0482296i
\(621\) −4.49640e24 + 1.04378e25i −0.327372 + 0.759949i
\(622\) 8.69492e23 0.0623953
\(623\) 2.99805e24i 0.212054i
\(624\) −1.84429e24 2.51603e23i −0.128579 0.0175410i
\(625\) −2.04257e24 −0.140364
\(626\) 2.76526e24i 0.187312i
\(627\) −1.58686e24 + 1.16320e25i −0.105957 + 0.776685i
\(628\) 1.99619e24 0.131391
\(629\) 4.89937e25i 3.17896i
\(630\) −5.57105e24 1.54886e24i −0.356346 0.0990711i
\(631\) −7.72031e24 −0.486822 −0.243411 0.969923i \(-0.578266\pi\)
−0.243411 + 0.969923i \(0.578266\pi\)
\(632\) 3.39968e24i 0.211341i
\(633\) −1.06579e25 1.45398e24i −0.653188 0.0891097i
\(634\) −2.03392e25 −1.22894
\(635\) 1.35320e25i 0.806119i
\(636\) −5.35455e23 + 3.92497e24i −0.0314491 + 0.230527i
\(637\) 3.47247e24 0.201087
\(638\) 9.96112e24i 0.568751i
\(639\) 6.57185e24 2.36381e25i 0.369981 1.33077i
\(640\) 1.06409e24 0.0590688
\(641\) 2.62444e25i 1.43653i 0.695770 + 0.718265i \(0.255063\pi\)
−0.695770 + 0.718265i \(0.744937\pi\)
\(642\) 5.65474e24 + 7.71434e23i 0.305209 + 0.0416374i
\(643\) 4.38088e23 0.0233164 0.0116582 0.999932i \(-0.496289\pi\)
0.0116582 + 0.999932i \(0.496289\pi\)
\(644\) 6.16996e24i 0.323825i
\(645\) −1.87933e24 + 1.37758e25i −0.0972671 + 0.712984i
\(646\) 1.10883e25 0.565943
\(647\) 3.47092e25i 1.74705i 0.486776 + 0.873527i \(0.338173\pi\)
−0.486776 + 0.873527i \(0.661827\pi\)
\(648\) −3.67621e24 + 6.10040e24i −0.182484 + 0.302819i
\(649\) 2.47773e25 1.21298
\(650\) 4.20699e24i 0.203119i
\(651\) 2.35070e24 + 3.20688e23i 0.111936 + 0.0152705i
\(652\) −2.69385e24 −0.126516
\(653\) 2.96983e24i 0.137567i −0.997632 0.0687833i \(-0.978088\pi\)
0.997632 0.0687833i \(-0.0219117\pi\)
\(654\) −2.19283e24 + 1.60738e25i −0.100186 + 0.734379i
\(655\) −9.39650e24 −0.423442
\(656\) 7.54271e24i 0.335269i
\(657\) −2.05749e25 5.72021e24i −0.902088 0.250798i
\(658\) 2.21878e25 0.959578
\(659\) 5.37440e24i 0.229277i −0.993407 0.114639i \(-0.963429\pi\)
0.993407 0.114639i \(-0.0365710\pi\)
\(660\) 1.27170e25 + 1.73488e24i 0.535165 + 0.0730086i
\(661\) 3.04882e25 1.26566 0.632831 0.774290i \(-0.281893\pi\)
0.632831 + 0.774290i \(0.281893\pi\)
\(662\) 1.62597e25i 0.665871i
\(663\) −2.86638e24 + 2.10111e25i −0.115801 + 0.848841i
\(664\) −5.64111e24 −0.224829
\(665\) 6.45118e24i 0.253655i
\(666\) 9.40476e24 3.38277e25i 0.364821 1.31221i
\(667\) −1.07587e25 −0.411743
\(668\) 1.26520e24i 0.0477717i
\(669\) −2.37151e25 3.23527e24i −0.883464 0.120525i
\(670\) −1.75370e25 −0.644589
\(671\) 1.47662e25i 0.535507i
\(672\) 5.22663e23 3.83121e24i 0.0187024 0.137092i
\(673\) −4.74754e25 −1.67623 −0.838114 0.545495i \(-0.816342\pi\)
−0.838114 + 0.545495i \(0.816342\pi\)
\(674\) 3.69423e24i 0.128702i
\(675\) 1.47844e25 + 6.36883e24i 0.508241 + 0.218940i
\(676\) 1.07682e25 0.365279
\(677\) 5.46641e25i 1.82980i 0.403678 + 0.914901i \(0.367732\pi\)
−0.403678 + 0.914901i \(0.632268\pi\)
\(678\) 3.68904e25 + 5.03268e24i 1.21856 + 0.166239i
\(679\) −1.07048e25 −0.348940
\(680\) 1.21226e25i 0.389956i
\(681\) 4.85007e24 3.55518e25i 0.153966 1.12859i
\(682\) −5.26604e24 −0.164978
\(683\) 1.33062e25i 0.411404i −0.978615 0.205702i \(-0.934052\pi\)
0.978615 0.205702i \(-0.0659478\pi\)
\(684\) 7.65592e24 + 2.12850e24i 0.233611 + 0.0649483i
\(685\) 5.21956e24 0.157188
\(686\) 2.58341e25i 0.767848i
\(687\) −3.33324e25 4.54730e24i −0.977814 0.133396i
\(688\) −9.29730e24 −0.269191
\(689\) 8.45205e24i 0.241540i
\(690\) 1.87379e24 1.37352e25i 0.0528541 0.387429i
\(691\) −2.30153e24 −0.0640787 −0.0320393 0.999487i \(-0.510200\pi\)
−0.0320393 + 0.999487i \(0.510200\pi\)
\(692\) 1.12736e25i 0.309820i
\(693\) 1.24927e25 4.49347e25i 0.338890 1.21894i
\(694\) −2.27818e25 −0.610034
\(695\) 3.63040e24i 0.0959601i
\(696\) −6.68054e24 9.11377e23i −0.174313 0.0237802i
\(697\) 8.59302e25 2.21335
\(698\) 1.61015e25i 0.409419i
\(699\) 2.04239e24 1.49711e25i 0.0512678 0.375802i
\(700\) −8.73930e24 −0.216568
\(701\) 4.35484e25i 1.06539i −0.846306 0.532697i \(-0.821178\pi\)
0.846306 0.532697i \(-0.178822\pi\)
\(702\) −6.01234e24 + 1.39569e25i −0.145214 + 0.337096i
\(703\) −3.91719e25 −0.934064
\(704\) 8.58268e24i 0.202055i
\(705\) 4.93930e25 + 6.73832e24i 1.14806 + 0.156621i
\(706\) −3.83542e25 −0.880179
\(707\) 6.52302e24i 0.147800i
\(708\) 2.26697e24 1.66172e25i 0.0507161 0.371757i
\(709\) 3.77583e25 0.834059 0.417030 0.908893i \(-0.363071\pi\)
0.417030 + 0.908893i \(0.363071\pi\)
\(710\) 2.99257e25i 0.652709i
\(711\) −2.67417e25 7.43470e24i −0.575920 0.160117i
\(712\) −4.50434e24 −0.0957880
\(713\) 5.68768e24i 0.119434i
\(714\) −4.36470e25 5.95443e24i −0.905045 0.123469i
\(715\) 2.73848e25 0.560731
\(716\) 1.95345e25i 0.394988i
\(717\) −7.43048e24 + 5.44666e25i −0.148369 + 1.08757i
\(718\) 4.10429e25 0.809316
\(719\) 5.42700e25i 1.05682i 0.848990 + 0.528408i \(0.177211\pi\)
−0.848990 + 0.528408i \(0.822789\pi\)
\(720\) 2.32704e24 8.37005e24i 0.0447518 0.160967i
\(721\) 3.37009e25 0.640064
\(722\) 2.88327e25i 0.540817i
\(723\) −4.73340e25 6.45743e24i −0.876857 0.119623i
\(724\) −3.28683e25 −0.601354
\(725\) 1.52389e25i 0.275367i
\(726\) −8.63767e24 + 6.33156e25i −0.154158 + 1.13001i
\(727\) −3.54138e25 −0.624257 −0.312128 0.950040i \(-0.601042\pi\)
−0.312128 + 0.950040i \(0.601042\pi\)
\(728\) 8.25014e24i 0.143641i
\(729\) 3.99459e25 + 4.22577e25i 0.686949 + 0.726705i
\(730\) 2.60477e25 0.442450
\(731\) 1.05919e26i 1.77713i
\(732\) −9.90310e24 1.35101e24i −0.164124 0.0223902i
\(733\) −7.56671e25 −1.23872 −0.619358 0.785109i \(-0.712607\pi\)
−0.619358 + 0.785109i \(0.712607\pi\)
\(734\) 6.85460e25i 1.10845i
\(735\) −2.19070e24 + 1.60582e25i −0.0349942 + 0.256513i
\(736\) 9.26988e24 0.146276
\(737\) 1.41449e26i 2.20492i
\(738\) 5.93305e25 + 1.64950e25i 0.913630 + 0.254007i
\(739\) 5.97970e25 0.909660 0.454830 0.890578i \(-0.349700\pi\)
0.454830 + 0.890578i \(0.349700\pi\)
\(740\) 4.28258e25i 0.643606i
\(741\) 1.67990e25 + 2.29176e24i 0.249413 + 0.0340255i
\(742\) −1.75577e25 −0.257533
\(743\) 1.08144e26i 1.56713i −0.621311 0.783564i \(-0.713399\pi\)
0.621311 0.783564i \(-0.286601\pi\)
\(744\) −4.81808e23 + 3.53174e24i −0.00689792 + 0.0505629i
\(745\) −1.76264e25 −0.249321
\(746\) 3.33507e25i 0.466074i
\(747\) −1.23364e25 + 4.43726e25i −0.170335 + 0.612674i
\(748\) 9.77781e25 1.33391
\(749\) 2.52956e25i 0.340963i
\(750\) −5.46105e25 7.45011e24i −0.727319 0.0992228i
\(751\) 1.63334e25 0.214940 0.107470 0.994208i \(-0.465725\pi\)
0.107470 + 0.994208i \(0.465725\pi\)
\(752\) 3.33353e25i 0.433455i
\(753\) −1.83792e24 + 1.34722e25i −0.0236141 + 0.173095i
\(754\) −1.43859e25 −0.182640
\(755\) 8.21465e25i 1.03054i
\(756\) −2.89930e25 1.24896e25i −0.359416 0.154829i
\(757\) −9.00151e25 −1.10269 −0.551344 0.834278i \(-0.685885\pi\)
−0.551344 + 0.834278i \(0.685885\pi\)
\(758\) 9.87295e25i 1.19515i
\(759\) 1.10785e26 + 1.51135e25i 1.32527 + 0.180796i
\(760\) −9.69238e24 −0.114580
\(761\) 1.56524e25i 0.182860i −0.995811 0.0914302i \(-0.970856\pi\)
0.995811 0.0914302i \(-0.0291438\pi\)
\(762\) 9.98614e24 7.32001e25i 0.115293 0.845117i
\(763\) −7.19037e25 −0.820409
\(764\) 6.02329e25i 0.679193i
\(765\) −9.53557e25 2.65107e25i −1.06266 0.295440i
\(766\) 1.10166e26 1.21336
\(767\) 3.57836e25i 0.389517i
\(768\) 5.75608e24 + 7.85259e23i 0.0619264 + 0.00844816i
\(769\) −4.92978e25 −0.524192 −0.262096 0.965042i \(-0.584414\pi\)
−0.262096 + 0.965042i \(0.584414\pi\)
\(770\) 5.68872e25i 0.597858i
\(771\) 1.06603e25 7.81418e25i 0.110734 0.811697i