Properties

Label 14.14.c.b.11.2
Level $14$
Weight $14$
Character 14.11
Analytic conductor $15.012$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 14 = 2 \cdot 7 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 14.c (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.0123300533\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
Defining polynomial: \(x^{8} + 209077 x^{6} - 47718852 x^{5} + 40973427094 x^{4} - 4988457209802 x^{3} + 1142094021456771 x^{2} + 65369216338084710 x + 7506311351102577225\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{14}\cdot 3\cdot 7^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 11.2
Root \(-248.013 + 429.572i\) of defining polynomial
Character \(\chi\) \(=\) 14.11
Dual form 14.14.c.b.9.2

$q$-expansion

\(f(q)\) \(=\) \(q+(32.0000 + 55.4256i) q^{2} +(-244.702 + 423.837i) q^{3} +(-2048.00 + 3547.24i) q^{4} +(34096.3 + 59056.5i) q^{5} -31321.9 q^{6} +(100530. - 294589. i) q^{7} -262144. q^{8} +(677403. + 1.17330e6i) q^{9} +O(q^{10})\) \(q+(32.0000 + 55.4256i) q^{2} +(-244.702 + 423.837i) q^{3} +(-2048.00 + 3547.24i) q^{4} +(34096.3 + 59056.5i) q^{5} -31321.9 q^{6} +(100530. - 294589. i) q^{7} -262144. q^{8} +(677403. + 1.17330e6i) q^{9} +(-2.18216e6 + 3.77962e6i) q^{10} +(-1.01364e6 + 1.75568e6i) q^{11} +(-1.00230e6 - 1.73604e6i) q^{12} -1.22100e7 q^{13} +(1.95447e7 - 3.85491e6i) q^{14} -3.33738e7 q^{15} +(-8.38861e6 - 1.45295e7i) q^{16} +(-4.76426e7 + 8.25194e7i) q^{17} +(-4.33538e7 + 7.50910e7i) q^{18} +(-1.03590e8 - 1.79423e8i) q^{19} -2.79317e8 q^{20} +(1.00258e8 + 1.14695e8i) q^{21} -1.29746e8 q^{22} +(-1.66859e8 - 2.89008e8i) q^{23} +(6.41473e7 - 1.11106e8i) q^{24} +(-1.71476e9 + 2.97005e9i) q^{25} +(-3.90720e8 - 6.76747e8i) q^{26} -1.44332e9 q^{27} +(8.39093e8 + 9.59922e8i) q^{28} +4.91794e9 q^{29} +(-1.06796e9 - 1.84976e9i) q^{30} +(2.19527e9 - 3.80232e9i) q^{31} +(5.36871e8 - 9.29888e8i) q^{32} +(-4.96081e8 - 8.59238e8i) q^{33} -6.09825e9 q^{34} +(2.08251e10 - 4.10745e9i) q^{35} -5.54929e9 q^{36} +(4.86831e9 + 8.43216e9i) q^{37} +(6.62975e9 - 1.14831e10i) q^{38} +(2.98782e9 - 5.17505e9i) q^{39} +(-8.93813e9 - 1.54813e10i) q^{40} +2.57081e10 q^{41} +(-3.14879e9 + 9.22709e9i) q^{42} +2.25490e9 q^{43} +(-4.15188e9 - 7.19127e9i) q^{44} +(-4.61938e10 + 8.00101e10i) q^{45} +(1.06790e10 - 1.84965e10i) q^{46} +(6.30189e10 + 1.09152e11i) q^{47} +8.21085e9 q^{48} +(-7.66765e10 - 5.92301e10i) q^{49} -2.19489e11 q^{50} +(-2.33165e10 - 4.03854e10i) q^{51} +(2.50061e10 - 4.33118e10i) q^{52} +(8.56595e10 - 1.48367e11i) q^{53} +(-4.61862e10 - 7.99968e10i) q^{54} -1.38246e11 q^{55} +(-2.63533e10 + 7.72248e10i) q^{56} +1.01395e11 q^{57} +(1.57374e11 + 2.72580e11i) q^{58} +(-2.75382e11 + 4.76975e11i) q^{59} +(6.83495e10 - 1.18385e11i) q^{60} +(-2.20984e10 - 3.82756e10i) q^{61} +2.80995e11 q^{62} +(4.13740e11 - 8.16041e10i) q^{63} +6.87195e10 q^{64} +(-4.16316e11 - 7.21080e11i) q^{65} +(3.17492e10 - 5.49913e10i) q^{66} +(6.07062e10 - 1.05146e11i) q^{67} +(-1.95144e11 - 3.37999e11i) q^{68} +1.63323e11 q^{69} +(8.94061e11 + 1.02281e12i) q^{70} +1.25945e12 q^{71} +(-1.77577e11 - 3.07573e11i) q^{72} +(-7.26655e10 + 1.25860e11i) q^{73} +(-3.11572e11 + 5.39658e11i) q^{74} +(-8.39212e11 - 1.45356e12i) q^{75} +8.48608e11 q^{76} +(4.15303e11 + 4.75107e11i) q^{77} +3.82441e11 q^{78} +(-1.26635e12 - 2.19338e12i) q^{79} +(5.72041e11 - 9.90803e11i) q^{80} +(-7.26816e11 + 1.25888e12i) q^{81} +(8.22660e11 + 1.42489e12i) q^{82} -1.98753e11 q^{83} +(-6.12179e11 + 1.20743e11i) q^{84} -6.49774e12 q^{85} +(7.21568e10 + 1.24979e11i) q^{86} +(-1.20343e12 + 2.08440e12i) q^{87} +(2.65720e11 - 4.60241e11i) q^{88} +(2.74228e12 + 4.74977e12i) q^{89} -5.91281e12 q^{90} +(-1.22747e12 + 3.59693e12i) q^{91} +1.36691e12 q^{92} +(1.07438e12 + 1.86088e12i) q^{93} +(-4.03321e12 + 6.98572e12i) q^{94} +(7.06406e12 - 1.22353e13i) q^{95} +(2.62747e11 + 4.55091e11i) q^{96} +3.38474e12 q^{97} +(8.29217e11 - 6.14520e12i) q^{98} -2.74658e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 256q^{2} + 182q^{3} - 16384q^{4} + 1792q^{5} + 23296q^{6} - 268352q^{7} - 2097152q^{8} + 599840q^{9} + O(q^{10}) \) \( 8q + 256q^{2} + 182q^{3} - 16384q^{4} + 1792q^{5} + 23296q^{6} - 268352q^{7} - 2097152q^{8} + 599840q^{9} - 114688q^{10} - 8726914q^{11} + 745472q^{12} + 1438416q^{13} + 27004544q^{14} - 136873212q^{15} - 67108864q^{16} - 7943068q^{17} - 38389760q^{18} - 215706806q^{19} - 14680064q^{20} - 414124312q^{21} - 1117044992q^{22} - 61927978q^{23} - 47710208q^{24} - 1327844792q^{25} + 46029312q^{26} - 3268643812q^{27} + 2827460608q^{28} - 6325846064q^{29} - 4379942784q^{30} + 6113775570q^{31} + 4294967296q^{32} + 25235960652q^{33} - 1016712704q^{34} + 41542225382q^{35} - 4913889280q^{36} - 3945652880q^{37} + 13805235584q^{38} - 23545599116q^{39} - 469762048q^{40} + 86378579952q^{41} + 16061065216q^{42} - 109074124256q^{43} - 35745439744q^{44} - 104964468168q^{45} + 3963390592q^{46} - 3141202722q^{47} - 6106906624q^{48} + 151080461672q^{49} - 169964133376q^{50} - 241278267462q^{51} - 2945875968q^{52} + 149625680376q^{53} - 104596601984q^{54} + 174912009748q^{55} + 70346866688q^{56} - 128207489960q^{57} - 202427074048q^{58} - 866297313938q^{59} + 280316338176q^{60} - 477908594184q^{61} + 782563272960q^{62} + 953051390564q^{63} + 549755813888q^{64} - 1099748343120q^{65} - 1615101481728q^{66} + 1895501016278q^{67} - 32534806528q^{68} + 3503301895632q^{69} + 1443396653440q^{70} + 638832672128q^{71} - 157244456960q^{72} - 2966596192756q^{73} + 252521784320q^{74} - 1331079867376q^{75} + 1767070154752q^{76} + 6943031627392q^{77} - 3013836686848q^{78} - 6505959677634q^{79} + 30064771072q^{80} + 2449216493684q^{81} + 2764114558464q^{82} - 3379817135968q^{83} + 2724161355776q^{84} - 16684556982464q^{85} - 3490371976192q^{86} - 5273311164492q^{87} + 2287708143616q^{88} + 9586601667468q^{89} - 13435451925504q^{90} + 16069253407200q^{91} + 507313995776q^{92} - 14195747226896q^{93} + 201036974208q^{94} + 14384410136978q^{95} - 195421011968q^{96} - 44560735311568q^{97} - 2146516623104q^{98} + 24706419985464q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/14\mathbb{Z}\right)^\times\).

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 32.0000 + 55.4256i 0.353553 + 0.612372i
\(3\) −244.702 + 423.837i −0.193798 + 0.335669i −0.946506 0.322686i \(-0.895414\pi\)
0.752708 + 0.658355i \(0.228747\pi\)
\(4\) −2048.00 + 3547.24i −0.250000 + 0.433013i
\(5\) 34096.3 + 59056.5i 0.975892 + 1.69030i 0.676958 + 0.736022i \(0.263298\pi\)
0.298934 + 0.954274i \(0.403369\pi\)
\(6\) −31321.9 −0.274072
\(7\) 100530. 294589.i 0.322967 0.946410i
\(8\) −262144. −0.353553
\(9\) 677403. + 1.17330e6i 0.424884 + 0.735921i
\(10\) −2.18216e6 + 3.77962e6i −0.690060 + 1.19522i
\(11\) −1.01364e6 + 1.75568e6i −0.172517 + 0.298809i −0.939299 0.343099i \(-0.888523\pi\)
0.766782 + 0.641908i \(0.221857\pi\)
\(12\) −1.00230e6 1.73604e6i −0.0968992 0.167834i
\(13\) −1.22100e7 −0.701591 −0.350796 0.936452i \(-0.614089\pi\)
−0.350796 + 0.936452i \(0.614089\pi\)
\(14\) 1.95447e7 3.85491e6i 0.693742 0.136830i
\(15\) −3.33738e7 −0.756505
\(16\) −8.38861e6 1.45295e7i −0.125000 0.216506i
\(17\) −4.76426e7 + 8.25194e7i −0.478715 + 0.829159i −0.999702 0.0244054i \(-0.992231\pi\)
0.520987 + 0.853565i \(0.325564\pi\)
\(18\) −4.33538e7 + 7.50910e7i −0.300439 + 0.520375i
\(19\) −1.03590e8 1.79423e8i −0.505148 0.874942i −0.999982 0.00595495i \(-0.998104\pi\)
0.494834 0.868988i \(-0.335229\pi\)
\(20\) −2.79317e8 −0.975892
\(21\) 1.00258e8 + 1.14695e8i 0.255090 + 0.291823i
\(22\) −1.29746e8 −0.243976
\(23\) −1.66859e8 2.89008e8i −0.235027 0.407079i 0.724253 0.689534i \(-0.242185\pi\)
−0.959281 + 0.282455i \(0.908851\pi\)
\(24\) 6.41473e7 1.11106e8i 0.0685181 0.118677i
\(25\) −1.71476e9 + 2.97005e9i −1.40473 + 2.43307i
\(26\) −3.90720e8 6.76747e8i −0.248050 0.429635i
\(27\) −1.44332e9 −0.716964
\(28\) 8.39093e8 + 9.59922e8i 0.329066 + 0.376451i
\(29\) 4.91794e9 1.53531 0.767655 0.640864i \(-0.221424\pi\)
0.767655 + 0.640864i \(0.221424\pi\)
\(30\) −1.06796e9 1.84976e9i −0.267465 0.463263i
\(31\) 2.19527e9 3.80232e9i 0.444260 0.769481i −0.553740 0.832690i \(-0.686800\pi\)
0.998000 + 0.0632083i \(0.0201332\pi\)
\(32\) 5.36871e8 9.29888e8i 0.0883883 0.153093i
\(33\) −4.96081e8 8.59238e8i −0.0668671 0.115817i
\(34\) −6.09825e9 −0.677006
\(35\) 2.08251e10 4.10745e9i 1.91489 0.377685i
\(36\) −5.54929e9 −0.424884
\(37\) 4.86831e9 + 8.43216e9i 0.311937 + 0.540291i 0.978782 0.204906i \(-0.0656889\pi\)
−0.666845 + 0.745197i \(0.732356\pi\)
\(38\) 6.62975e9 1.14831e10i 0.357194 0.618678i
\(39\) 2.98782e9 5.17505e9i 0.135967 0.235502i
\(40\) −8.93813e9 1.54813e10i −0.345030 0.597610i
\(41\) 2.57081e10 0.845230 0.422615 0.906309i \(-0.361112\pi\)
0.422615 + 0.906309i \(0.361112\pi\)
\(42\) −3.14879e9 + 9.22709e9i −0.0885163 + 0.259385i
\(43\) 2.25490e9 0.0543980 0.0271990 0.999630i \(-0.491341\pi\)
0.0271990 + 0.999630i \(0.491341\pi\)
\(44\) −4.15188e9 7.19127e9i −0.0862586 0.149404i
\(45\) −4.61938e10 + 8.00101e10i −0.829283 + 1.43636i
\(46\) 1.06790e10 1.84965e10i 0.166189 0.287848i
\(47\) 6.30189e10 + 1.09152e11i 0.852775 + 1.47705i 0.878694 + 0.477385i \(0.158415\pi\)
−0.0259191 + 0.999664i \(0.508251\pi\)
\(48\) 8.21085e9 0.0968992
\(49\) −7.66765e10 5.92301e10i −0.791384 0.611319i
\(50\) −2.19489e11 −1.98659
\(51\) −2.33165e10 4.03854e10i −0.185548 0.321379i
\(52\) 2.50061e10 4.33118e10i 0.175398 0.303798i
\(53\) 8.56595e10 1.48367e11i 0.530863 0.919482i −0.468488 0.883470i \(-0.655201\pi\)
0.999351 0.0360120i \(-0.0114655\pi\)
\(54\) −4.61862e10 7.99968e10i −0.253485 0.439049i
\(55\) −1.38246e11 −0.673433
\(56\) −2.63533e10 + 7.72248e10i −0.114186 + 0.334607i
\(57\) 1.01395e11 0.391588
\(58\) 1.57374e11 + 2.72580e11i 0.542814 + 0.940181i
\(59\) −2.75382e11 + 4.76975e11i −0.849957 + 1.47217i 0.0312897 + 0.999510i \(0.490039\pi\)
−0.881246 + 0.472658i \(0.843295\pi\)
\(60\) 6.83495e10 1.18385e11i 0.189126 0.327576i
\(61\) −2.20984e10 3.82756e10i −0.0549184 0.0951214i 0.837259 0.546806i \(-0.184157\pi\)
−0.892178 + 0.451685i \(0.850823\pi\)
\(62\) 2.80995e11 0.628279
\(63\) 4.13740e11 8.16041e10i 0.833707 0.164437i
\(64\) 6.87195e10 0.125000
\(65\) −4.16316e11 7.21080e11i −0.684677 1.18590i
\(66\) 3.17492e10 5.49913e10i 0.0472822 0.0818951i
\(67\) 6.07062e10 1.05146e11i 0.0819874 0.142006i −0.822116 0.569320i \(-0.807207\pi\)
0.904104 + 0.427314i \(0.140540\pi\)
\(68\) −1.95144e11 3.37999e11i −0.239358 0.414580i
\(69\) 1.63323e11 0.182191
\(70\) 8.94061e11 + 1.02281e12i 0.908301 + 1.03910i
\(71\) 1.25945e12 1.16682 0.583408 0.812179i \(-0.301719\pi\)
0.583408 + 0.812179i \(0.301719\pi\)
\(72\) −1.77577e11 3.07573e11i −0.150219 0.260188i
\(73\) −7.26655e10 + 1.25860e11i −0.0561992 + 0.0973398i −0.892756 0.450540i \(-0.851232\pi\)
0.836557 + 0.547880i \(0.184565\pi\)
\(74\) −3.11572e11 + 5.39658e11i −0.220573 + 0.382043i
\(75\) −8.39212e11 1.45356e12i −0.544470 0.943049i
\(76\) 8.48608e11 0.505148
\(77\) 4.15303e11 + 4.75107e11i 0.227078 + 0.259777i
\(78\) 3.82441e11 0.192287
\(79\) −1.26635e12 2.19338e12i −0.586108 1.01517i −0.994736 0.102468i \(-0.967326\pi\)
0.408628 0.912701i \(-0.366007\pi\)
\(80\) 5.72041e11 9.90803e11i 0.243973 0.422574i
\(81\) −7.26816e11 + 1.25888e12i −0.285938 + 0.495259i
\(82\) 8.22660e11 + 1.42489e12i 0.298834 + 0.517596i
\(83\) −1.98753e11 −0.0667276 −0.0333638 0.999443i \(-0.510622\pi\)
−0.0333638 + 0.999443i \(0.510622\pi\)
\(84\) −6.12179e11 + 1.20743e11i −0.190135 + 0.0375014i
\(85\) −6.49774e12 −1.86870
\(86\) 7.21568e10 + 1.24979e11i 0.0192326 + 0.0333118i
\(87\) −1.20343e12 + 2.08440e12i −0.297540 + 0.515355i
\(88\) 2.65720e11 4.60241e11i 0.0609940 0.105645i
\(89\) 2.74228e12 + 4.74977e12i 0.584894 + 1.01307i 0.994889 + 0.100978i \(0.0321971\pi\)
−0.409995 + 0.912088i \(0.634470\pi\)
\(90\) −5.91281e12 −1.17278
\(91\) −1.22747e12 + 3.59693e12i −0.226591 + 0.663993i
\(92\) 1.36691e12 0.235027
\(93\) 1.07438e12 + 1.86088e12i 0.172194 + 0.298248i
\(94\) −4.03321e12 + 6.98572e12i −0.603003 + 1.04443i
\(95\) 7.06406e12 1.22353e13i 0.985941 1.70770i
\(96\) 2.62747e11 + 4.55091e11i 0.0342590 + 0.0593384i
\(97\) 3.38474e12 0.412581 0.206290 0.978491i \(-0.433861\pi\)
0.206290 + 0.978491i \(0.433861\pi\)
\(98\) 8.29217e11 6.14520e12i 0.0945581 0.700756i
\(99\) −2.74658e12 −0.293199
\(100\) −7.02366e12 1.21653e13i −0.702366 1.21653i
\(101\) 4.71449e12 8.16574e12i 0.441922 0.765432i −0.555910 0.831243i \(-0.687630\pi\)
0.997832 + 0.0658107i \(0.0209634\pi\)
\(102\) 1.49226e12 2.58466e12i 0.131203 0.227250i
\(103\) 9.52601e12 + 1.64995e13i 0.786084 + 1.36154i 0.928349 + 0.371709i \(0.121228\pi\)
−0.142265 + 0.989829i \(0.545438\pi\)
\(104\) 3.20078e12 0.248050
\(105\) −3.35506e12 + 9.83155e12i −0.244326 + 0.715964i
\(106\) 1.09644e13 0.750754
\(107\) 1.88106e12 + 3.25809e12i 0.121173 + 0.209879i 0.920231 0.391376i \(-0.128001\pi\)
−0.799057 + 0.601255i \(0.794668\pi\)
\(108\) 2.95591e12 5.11979e12i 0.179241 0.310455i
\(109\) 7.35138e12 1.27330e13i 0.419852 0.727206i −0.576072 0.817399i \(-0.695415\pi\)
0.995924 + 0.0901934i \(0.0287485\pi\)
\(110\) −4.42386e12 7.66236e12i −0.238094 0.412392i
\(111\) −4.76515e12 −0.241811
\(112\) −5.12354e12 + 1.01054e12i −0.245275 + 0.0483768i
\(113\) 1.91564e13 0.865572 0.432786 0.901497i \(-0.357531\pi\)
0.432786 + 0.901497i \(0.357531\pi\)
\(114\) 3.24463e12 + 5.61987e12i 0.138447 + 0.239797i
\(115\) 1.13785e13 1.97082e13i 0.458722 0.794530i
\(116\) −1.00719e13 + 1.74451e13i −0.383827 + 0.664809i
\(117\) −8.27109e12 1.43260e13i −0.298095 0.516316i
\(118\) −3.52488e13 −1.20202
\(119\) 1.95198e13 + 2.23307e13i 0.630116 + 0.720852i
\(120\) 8.74873e12 0.267465
\(121\) 1.52064e13 + 2.63383e13i 0.440476 + 0.762926i
\(122\) 1.41430e12 2.44964e12i 0.0388332 0.0672610i
\(123\) −6.29084e12 + 1.08960e13i −0.163804 + 0.283717i
\(124\) 8.99184e12 + 1.55743e13i 0.222130 + 0.384741i
\(125\) −1.50625e14 −3.53169
\(126\) 1.77626e13 + 2.03204e13i 0.395456 + 0.452402i
\(127\) 4.62943e13 0.979046 0.489523 0.871990i \(-0.337171\pi\)
0.489523 + 0.871990i \(0.337171\pi\)
\(128\) 2.19902e12 + 3.80882e12i 0.0441942 + 0.0765466i
\(129\) −5.51780e11 + 9.55711e11i −0.0105422 + 0.0182597i
\(130\) 2.66442e13 4.61491e13i 0.484140 0.838555i
\(131\) −1.05855e13 1.83346e13i −0.182999 0.316963i 0.759902 0.650038i \(-0.225247\pi\)
−0.942900 + 0.333075i \(0.891914\pi\)
\(132\) 4.06390e12 0.0668671
\(133\) −6.32699e13 + 1.24791e13i −0.991201 + 0.195500i
\(134\) 7.77040e12 0.115948
\(135\) −4.92118e13 8.52373e13i −0.699680 1.21188i
\(136\) 1.24892e13 2.16320e13i 0.169251 0.293152i
\(137\) 1.97958e13 3.42873e13i 0.255793 0.443046i −0.709318 0.704889i \(-0.750997\pi\)
0.965111 + 0.261843i \(0.0843301\pi\)
\(138\) 5.22633e12 + 9.05227e12i 0.0644144 + 0.111569i
\(139\) 9.29027e11 0.0109253 0.00546264 0.999985i \(-0.498261\pi\)
0.00546264 + 0.999985i \(0.498261\pi\)
\(140\) −2.80797e13 + 8.22837e13i −0.315181 + 0.923595i
\(141\) −6.16835e13 −0.661065
\(142\) 4.03025e13 + 6.98059e13i 0.412532 + 0.714526i
\(143\) 1.23766e13 2.14369e13i 0.121037 0.209641i
\(144\) 1.13649e13 1.96846e13i 0.106221 0.183980i
\(145\) 1.67683e14 + 2.90436e14i 1.49830 + 2.59513i
\(146\) −9.30119e12 −0.0794776
\(147\) 4.38668e13 1.80046e13i 0.358569 0.147170i
\(148\) −3.98812e13 −0.311937
\(149\) −8.78519e13 1.52164e14i −0.657719 1.13920i −0.981205 0.192970i \(-0.938188\pi\)
0.323486 0.946233i \(-0.395145\pi\)
\(150\) 5.37096e13 9.30277e13i 0.384998 0.666836i
\(151\) 1.22477e14 2.12136e14i 0.840823 1.45635i −0.0483769 0.998829i \(-0.515405\pi\)
0.889200 0.457519i \(-0.151262\pi\)
\(152\) 2.71555e13 + 4.70346e13i 0.178597 + 0.309339i
\(153\) −1.29093e14 −0.813595
\(154\) −1.30434e13 + 3.82218e13i −0.0787963 + 0.230902i
\(155\) 2.99402e14 1.73420
\(156\) 1.22381e13 + 2.11970e13i 0.0679836 + 0.117751i
\(157\) −1.76805e13 + 3.06236e13i −0.0942210 + 0.163196i −0.909283 0.416178i \(-0.863369\pi\)
0.815062 + 0.579373i \(0.196703\pi\)
\(158\) 8.10464e13 1.40376e14i 0.414441 0.717833i
\(159\) 4.19222e13 + 7.26113e13i 0.205761 + 0.356388i
\(160\) 7.32212e13 0.345030
\(161\) −1.01913e14 + 2.01008e13i −0.461170 + 0.0909590i
\(162\) −9.30324e13 −0.404377
\(163\) 3.33119e13 + 5.76980e13i 0.139117 + 0.240958i 0.927163 0.374659i \(-0.122240\pi\)
−0.788046 + 0.615617i \(0.788907\pi\)
\(164\) −5.26502e13 + 9.11928e13i −0.211308 + 0.365995i
\(165\) 3.38291e13 5.85937e13i 0.130510 0.226050i
\(166\) −6.36009e12 1.10160e13i −0.0235918 0.0408622i
\(167\) −3.09178e14 −1.10294 −0.551469 0.834195i \(-0.685933\pi\)
−0.551469 + 0.834195i \(0.685933\pi\)
\(168\) −2.62820e13 3.00666e13i −0.0901878 0.103175i
\(169\) −1.53791e14 −0.507770
\(170\) −2.07928e14 3.60141e14i −0.660685 1.14434i
\(171\) 1.40344e14 2.43083e14i 0.429259 0.743499i
\(172\) −4.61804e12 + 7.99868e12i −0.0135995 + 0.0235550i
\(173\) −5.20918e12 9.02256e12i −0.0147730 0.0255876i 0.858544 0.512739i \(-0.171369\pi\)
−0.873317 + 0.487152i \(0.838036\pi\)
\(174\) −1.54039e14 −0.420786
\(175\) 7.02560e14 + 8.03729e14i 1.84900 + 2.11525i
\(176\) 3.40122e13 0.0862586
\(177\) −1.34773e14 2.33434e14i −0.329440 0.570607i
\(178\) −1.75506e14 + 3.03985e14i −0.413582 + 0.716346i
\(179\) −2.19409e14 + 3.80028e14i −0.498552 + 0.863517i −0.999999 0.00167147i \(-0.999468\pi\)
0.501447 + 0.865188i \(0.332801\pi\)
\(180\) −1.89210e14 3.27721e14i −0.414641 0.718180i
\(181\) −1.08144e13 −0.0228607 −0.0114304 0.999935i \(-0.503638\pi\)
−0.0114304 + 0.999935i \(0.503638\pi\)
\(182\) −2.38641e14 + 4.70685e13i −0.486723 + 0.0959990i
\(183\) 2.16302e13 0.0425724
\(184\) 4.37410e13 + 7.57617e13i 0.0830946 + 0.143924i
\(185\) −3.31982e14 + 5.75010e14i −0.608834 + 1.05453i
\(186\) −6.87601e13 + 1.19096e14i −0.121759 + 0.210893i
\(187\) −9.65851e13 1.67290e14i −0.165173 0.286088i
\(188\) −5.16250e14 −0.852775
\(189\) −1.45097e14 + 4.25186e14i −0.231556 + 0.678542i
\(190\) 9.04199e14 1.39433
\(191\) −2.98828e14 5.17585e14i −0.445353 0.771374i 0.552724 0.833365i \(-0.313589\pi\)
−0.998077 + 0.0619904i \(0.980255\pi\)
\(192\) −1.68158e13 + 2.91259e13i −0.0242248 + 0.0419586i
\(193\) 2.27823e14 3.94600e14i 0.317303 0.549585i −0.662621 0.748955i \(-0.730556\pi\)
0.979924 + 0.199370i \(0.0638894\pi\)
\(194\) 1.08312e14 + 1.87601e14i 0.145869 + 0.252653i
\(195\) 4.07494e14 0.530757
\(196\) 3.67137e14 1.50687e14i 0.462555 0.189850i
\(197\) −8.49836e14 −1.03587 −0.517934 0.855421i \(-0.673299\pi\)
−0.517934 + 0.855421i \(0.673299\pi\)
\(198\) −8.78905e13 1.52231e14i −0.103662 0.179547i
\(199\) 7.26924e14 1.25907e15i 0.829743 1.43716i −0.0684964 0.997651i \(-0.521820\pi\)
0.898240 0.439506i \(-0.144847\pi\)
\(200\) 4.49514e14 7.78582e14i 0.496648 0.860219i
\(201\) 2.97099e13 + 5.14591e13i 0.0317780 + 0.0550412i
\(202\) 6.03455e14 0.624972
\(203\) 4.94400e14 1.44877e15i 0.495854 1.45303i
\(204\) 1.91009e14 0.185548
\(205\) 8.76551e14 + 1.51823e15i 0.824854 + 1.42869i
\(206\) −6.09665e14 + 1.05597e15i −0.555846 + 0.962753i
\(207\) 2.26061e14 3.91549e14i 0.199719 0.345923i
\(208\) 1.02425e14 + 1.77405e14i 0.0876989 + 0.151899i
\(209\) 4.20012e14 0.348587
\(210\) −6.52282e14 + 1.28653e14i −0.524819 + 0.103513i
\(211\) −1.00855e14 −0.0786797 −0.0393399 0.999226i \(-0.512526\pi\)
−0.0393399 + 0.999226i \(0.512526\pi\)
\(212\) 3.50861e14 + 6.07710e14i 0.265431 + 0.459741i
\(213\) −3.08191e14 + 5.33802e14i −0.226127 + 0.391663i
\(214\) −1.20388e14 + 2.08518e14i −0.0856826 + 0.148407i
\(215\) 7.68837e13 + 1.33167e14i 0.0530866 + 0.0919486i
\(216\) 3.78357e14 0.253485
\(217\) −8.99432e14 1.02895e15i −0.584763 0.668969i
\(218\) 9.40977e14 0.593761
\(219\) −3.55629e13 6.15967e13i −0.0217826 0.0377286i
\(220\) 2.83127e14 4.90391e14i 0.168358 0.291605i
\(221\) 5.81716e14 1.00756e15i 0.335862 0.581731i
\(222\) −1.52485e14 2.64111e14i −0.0854933 0.148079i
\(223\) −7.82121e14 −0.425885 −0.212942 0.977065i \(-0.568305\pi\)
−0.212942 + 0.977065i \(0.568305\pi\)
\(224\) −2.19963e14 2.51638e14i −0.116342 0.133096i
\(225\) −4.64634e15 −2.38740
\(226\) 6.13003e14 + 1.06175e15i 0.306026 + 0.530052i
\(227\) −1.40236e14 + 2.42895e14i −0.0680284 + 0.117829i −0.898033 0.439927i \(-0.855004\pi\)
0.830005 + 0.557756i \(0.188338\pi\)
\(228\) −2.07656e14 + 3.59672e14i −0.0978969 + 0.169562i
\(229\) 1.53748e15 + 2.66299e15i 0.704496 + 1.22022i 0.966873 + 0.255257i \(0.0821600\pi\)
−0.262378 + 0.964965i \(0.584507\pi\)
\(230\) 1.45645e15 0.648731
\(231\) −3.02993e14 + 5.97610e13i −0.131206 + 0.0258785i
\(232\) −1.28921e15 −0.542814
\(233\) −1.55317e15 2.69017e15i −0.635925 1.10145i −0.986318 0.164851i \(-0.947286\pi\)
0.350394 0.936603i \(-0.386048\pi\)
\(234\) 5.29350e14 9.16861e14i 0.210785 0.365090i
\(235\) −4.29742e15 + 7.44334e15i −1.66443 + 2.88288i
\(236\) −1.12796e15 1.95369e15i −0.424978 0.736084i
\(237\) 1.23952e15 0.454347
\(238\) −6.13057e14 + 1.79648e15i −0.218651 + 0.640725i
\(239\) 5.08395e15 1.76447 0.882237 0.470805i \(-0.156037\pi\)
0.882237 + 0.470805i \(0.156037\pi\)
\(240\) 2.79959e14 + 4.84904e14i 0.0945632 + 0.163788i
\(241\) 1.06886e15 1.85132e15i 0.351407 0.608655i −0.635089 0.772439i \(-0.719037\pi\)
0.986496 + 0.163784i \(0.0523699\pi\)
\(242\) −9.73210e14 + 1.68565e15i −0.311463 + 0.539470i
\(243\) −1.50626e15 2.60893e15i −0.469311 0.812870i
\(244\) 1.81030e14 0.0549184
\(245\) 8.83538e14 6.54777e15i 0.261003 1.93425i
\(246\) −8.05227e14 −0.231654
\(247\) 1.26483e15 + 2.19075e15i 0.354408 + 0.613852i
\(248\) −5.75477e14 + 9.96756e14i −0.157070 + 0.272053i
\(249\) 4.86353e13 8.42388e13i 0.0129317 0.0223984i
\(250\) −4.82000e15 8.34848e15i −1.24864 2.16271i
\(251\) −1.27798e15 −0.322585 −0.161293 0.986907i \(-0.551566\pi\)
−0.161293 + 0.986907i \(0.551566\pi\)
\(252\) −5.57869e14 + 1.63476e15i −0.137224 + 0.402115i
\(253\) 6.76540e14 0.162185
\(254\) 1.48142e15 + 2.56589e15i 0.346145 + 0.599541i
\(255\) 1.59001e15 2.75398e15i 0.362151 0.627264i
\(256\) −1.40737e14 + 2.43764e14i −0.0312500 + 0.0541266i
\(257\) 2.34815e15 + 4.06711e15i 0.508346 + 0.880482i 0.999953 + 0.00966455i \(0.00307637\pi\)
−0.491607 + 0.870817i \(0.663590\pi\)
\(258\) −7.06278e13 −0.0149090
\(259\) 2.97343e15 5.86466e14i 0.612082 0.120724i
\(260\) 3.41046e15 0.684677
\(261\) 3.33142e15 + 5.77020e15i 0.652329 + 1.12987i
\(262\) 6.77472e14 1.17342e15i 0.129400 0.224127i
\(263\) −4.72518e15 + 8.18424e15i −0.880452 + 1.52499i −0.0296123 + 0.999561i \(0.509427\pi\)
−0.850839 + 0.525426i \(0.823906\pi\)
\(264\) 1.30045e14 + 2.25244e14i 0.0236411 + 0.0409476i
\(265\) 1.16827e16 2.07226
\(266\) −2.71630e15 3.10744e15i −0.470161 0.537864i
\(267\) −2.68417e15 −0.453406
\(268\) 2.48653e14 + 4.30679e14i 0.0409937 + 0.0710032i
\(269\) −1.73652e15 + 3.00774e15i −0.279441 + 0.484005i −0.971246 0.238079i \(-0.923482\pi\)
0.691805 + 0.722084i \(0.256816\pi\)
\(270\) 3.14955e15 5.45519e15i 0.494748 0.856929i
\(271\) −2.33839e15 4.05021e15i −0.358605 0.621122i 0.629123 0.777306i \(-0.283414\pi\)
−0.987728 + 0.156184i \(0.950081\pi\)
\(272\) 1.59862e15 0.239358
\(273\) −1.22415e15 1.40043e15i −0.178969 0.204740i
\(274\) 2.53386e15 0.361746
\(275\) −3.47631e15 6.02114e15i −0.484681 0.839492i
\(276\) −3.34485e14 + 5.79346e14i −0.0455479 + 0.0788912i
\(277\) 3.58150e15 6.20334e15i 0.476372 0.825101i −0.523261 0.852172i \(-0.675285\pi\)
0.999634 + 0.0270712i \(0.00861810\pi\)
\(278\) 2.97289e13 + 5.14919e13i 0.00386267 + 0.00669034i
\(279\) 5.94834e15 0.755037
\(280\) −5.45917e15 + 1.07674e15i −0.677017 + 0.133532i
\(281\) −3.65564e15 −0.442968 −0.221484 0.975164i \(-0.571090\pi\)
−0.221484 + 0.975164i \(0.571090\pi\)
\(282\) −1.97387e15 3.41884e15i −0.233722 0.404818i
\(283\) −2.03067e14 + 3.51722e14i −0.0234978 + 0.0406993i −0.877535 0.479512i \(-0.840814\pi\)
0.854037 + 0.520212i \(0.174147\pi\)
\(284\) −2.57936e15 + 4.46758e15i −0.291704 + 0.505246i
\(285\) 3.45718e15 + 5.98802e15i 0.382147 + 0.661899i
\(286\) 1.58420e15 0.171171
\(287\) 2.58444e15 7.57333e15i 0.272982 0.799935i
\(288\) 1.45471e15 0.150219
\(289\) 4.12656e14 + 7.14740e14i 0.0416631 + 0.0721626i
\(290\) −1.07317e16 + 1.85879e16i −1.05946 + 1.83503i
\(291\) −8.28254e14 + 1.43458e15i −0.0799575 + 0.138490i
\(292\) −2.97638e14 5.15524e14i −0.0280996 0.0486699i
\(293\) −1.50550e15 −0.139008 −0.0695041 0.997582i \(-0.522142\pi\)
−0.0695041 + 0.997582i \(0.522142\pi\)
\(294\) 2.40165e15 + 1.85520e15i 0.216897 + 0.167545i
\(295\) −3.75579e16 −3.31786
\(296\) −1.27620e15 2.21044e15i −0.110286 0.191022i
\(297\) 1.46301e15 2.53400e15i 0.123689 0.214235i
\(298\) 5.62252e15 9.73849e15i 0.465078 0.805538i
\(299\) 2.03735e15 + 3.52879e15i 0.164893 + 0.285603i
\(300\) 6.87483e15 0.544470
\(301\) 2.26685e14 6.64269e14i 0.0175688 0.0514828i
\(302\) 1.56771e16 1.18910
\(303\) 2.30729e15 + 3.99635e15i 0.171288 + 0.296679i
\(304\) −1.73795e15 + 3.01022e15i −0.126287 + 0.218736i
\(305\) 1.50695e15 2.61011e15i 0.107189 0.185657i
\(306\) −4.13097e15 7.15506e15i −0.287649 0.498223i
\(307\) −1.99255e16 −1.35835 −0.679173 0.733978i \(-0.737661\pi\)
−0.679173 + 0.733978i \(0.737661\pi\)
\(308\) −2.53586e15 + 5.00161e14i −0.169256 + 0.0333833i
\(309\) −9.32415e15 −0.609367
\(310\) 9.58088e15 + 1.65946e16i 0.613133 + 1.06198i
\(311\) 2.21010e13 3.82801e13i 0.00138506 0.00239900i −0.865332 0.501199i \(-0.832892\pi\)
0.866717 + 0.498800i \(0.166226\pi\)
\(312\) −7.83238e14 + 1.35661e15i −0.0480717 + 0.0832626i
\(313\) −2.12499e15 3.68058e15i −0.127737 0.221248i 0.795062 0.606528i \(-0.207438\pi\)
−0.922800 + 0.385280i \(0.874105\pi\)
\(314\) −2.26311e15 −0.133249
\(315\) 1.89262e16 + 2.16516e16i 1.09155 + 1.24874i
\(316\) 1.03739e16 0.586108
\(317\) −5.50321e15 9.53184e15i −0.304601 0.527584i 0.672572 0.740032i \(-0.265190\pi\)
−0.977172 + 0.212448i \(0.931856\pi\)
\(318\) −2.68302e15 + 4.64713e15i −0.145495 + 0.252004i
\(319\) −4.98503e15 + 8.63432e15i −0.264867 + 0.458764i
\(320\) 2.34308e15 + 4.05833e15i 0.121987 + 0.211287i
\(321\) −1.84120e15 −0.0939329
\(322\) −4.37531e15 5.00536e15i −0.218749 0.250249i
\(323\) 1.97412e16 0.967289
\(324\) −2.97704e15 5.15638e15i −0.142969 0.247630i
\(325\) 2.09372e16 3.62644e16i 0.985548 1.70702i
\(326\) −2.13196e15 + 3.69267e15i −0.0983706 + 0.170383i
\(327\) 3.59780e15 + 6.23157e15i 0.162733 + 0.281862i
\(328\) −6.73923e15 −0.298834
\(329\) 3.84902e16 7.59163e15i 1.67331 0.330036i
\(330\) 4.33012e15 0.184569
\(331\) −2.11676e16 3.66633e16i −0.884687 1.53232i −0.846072 0.533068i \(-0.821039\pi\)
−0.0386146 0.999254i \(-0.512294\pi\)
\(332\) 4.07046e14 7.05024e14i 0.0166819 0.0288939i
\(333\) −6.59561e15 + 1.14239e16i −0.265074 + 0.459122i
\(334\) −9.89369e15 1.71364e16i −0.389948 0.675409i
\(335\) 8.27943e15 0.320043
\(336\) 8.25436e14 2.41883e15i 0.0312952 0.0917064i
\(337\) 2.81461e16 1.04670 0.523352 0.852117i \(-0.324681\pi\)
0.523352 + 0.852117i \(0.324681\pi\)
\(338\) −4.92131e15 8.52395e15i −0.179524 0.310944i
\(339\) −4.68761e15 + 8.11917e15i −0.167746 + 0.290545i
\(340\) 1.33074e16 2.30490e16i 0.467175 0.809170i
\(341\) 4.45044e15 + 7.70839e15i 0.153285 + 0.265497i
\(342\) 1.79641e16 0.607064
\(343\) −2.51568e16 + 1.66337e16i −0.834149 + 0.551539i
\(344\) −5.91109e14 −0.0192326
\(345\) 5.56870e15 + 9.64528e15i 0.177799 + 0.307957i
\(346\) 3.33387e14 5.77444e14i 0.0104461 0.0180932i
\(347\) 1.37022e16 2.37330e16i 0.421357 0.729811i −0.574716 0.818353i \(-0.694887\pi\)
0.996072 + 0.0885421i \(0.0282208\pi\)
\(348\) −4.92925e15 8.53772e15i −0.148770 0.257678i
\(349\) −5.20113e16 −1.54075 −0.770375 0.637591i \(-0.779931\pi\)
−0.770375 + 0.637591i \(0.779931\pi\)
\(350\) −2.20653e16 + 6.46592e16i −0.641604 + 1.88013i
\(351\) 1.76229e16 0.503016
\(352\) 1.08839e15 + 1.88515e15i 0.0304970 + 0.0528224i
\(353\) −1.02686e16 + 1.77857e16i −0.282471 + 0.489254i −0.971993 0.235011i \(-0.924487\pi\)
0.689522 + 0.724265i \(0.257821\pi\)
\(354\) 8.62547e15 1.49398e16i 0.232949 0.403480i
\(355\) 4.29426e16 + 7.43788e16i 1.13869 + 1.97226i
\(356\) −2.24648e16 −0.584894
\(357\) −1.42411e16 + 2.80885e15i −0.364083 + 0.0718100i
\(358\) −2.80844e16 −0.705059
\(359\) −2.44701e15 4.23835e15i −0.0603285 0.104492i 0.834284 0.551335i \(-0.185881\pi\)
−0.894612 + 0.446843i \(0.852548\pi\)
\(360\) 1.21094e16 2.09742e16i 0.293196 0.507830i
\(361\) −4.35230e14 + 7.53840e14i −0.0103496 + 0.0179259i
\(362\) −3.46059e14 5.99392e14i −0.00808248 0.0139993i
\(363\) −1.48842e16 −0.341454
\(364\) −1.02453e16 1.17207e16i −0.230870 0.264115i
\(365\) −9.91050e15 −0.219377
\(366\) 6.92165e14 + 1.19887e15i 0.0150516 + 0.0260701i
\(367\) −6.03722e13 + 1.04568e14i −0.00128976 + 0.00223392i −0.866670 0.498883i \(-0.833744\pi\)
0.865380 + 0.501117i \(0.167077\pi\)
\(368\) −2.79942e15 + 4.84875e15i −0.0587568 + 0.101770i
\(369\) 1.74148e16 + 3.01632e16i 0.359125 + 0.622023i
\(370\) −4.24937e16 −0.861021
\(371\) −3.50958e16 4.01497e16i −0.698756 0.799376i
\(372\) −8.80129e15 −0.172194
\(373\) 7.37286e15 + 1.27702e16i 0.141752 + 0.245521i 0.928156 0.372190i \(-0.121393\pi\)
−0.786405 + 0.617712i \(0.788060\pi\)
\(374\) 6.18145e15 1.07066e16i 0.116795 0.202295i
\(375\) 3.68583e16 6.38404e16i 0.684435 1.18548i
\(376\) −1.65200e16 2.86135e16i −0.301501 0.522216i
\(377\) −6.00480e16 −1.07716
\(378\) −2.82093e16 + 5.56387e15i −0.497388 + 0.0981025i
\(379\) 2.32876e15 0.0403617 0.0201809 0.999796i \(-0.493576\pi\)
0.0201809 + 0.999796i \(0.493576\pi\)
\(380\) 2.89344e16 + 5.01158e16i 0.492970 + 0.853850i
\(381\) −1.13283e16 + 1.96212e16i −0.189737 + 0.328635i
\(382\) 1.91250e16 3.31255e16i 0.314912 0.545444i
\(383\) 1.86847e16 + 3.23629e16i 0.302479 + 0.523909i 0.976697 0.214624i \(-0.0688525\pi\)
−0.674218 + 0.738532i \(0.735519\pi\)
\(384\) −2.15242e15 −0.0342590
\(385\) −1.38978e16 + 4.07257e16i −0.217497 + 0.637344i
\(386\) 2.91613e16 0.448734
\(387\) 1.52748e15 + 2.64567e15i 0.0231128 + 0.0400326i
\(388\) −6.93195e15 + 1.20065e16i −0.103145 + 0.178653i
\(389\) −2.40310e15 + 4.16229e15i −0.0351641 + 0.0609060i −0.883072 0.469238i \(-0.844529\pi\)
0.847908 + 0.530144i \(0.177862\pi\)
\(390\) 1.30398e16 + 2.25856e16i 0.187651 + 0.325021i
\(391\) 3.17983e16 0.450044
\(392\) 2.01003e16 + 1.55268e16i 0.279797 + 0.216134i
\(393\) 1.03612e16 0.141859
\(394\) −2.71947e16 4.71027e16i −0.366235 0.634337i
\(395\) 8.63556e16 1.49572e17i 1.14396 1.98139i
\(396\) 5.62499e15 9.74277e15i 0.0732999 0.126959i
\(397\) −1.18316e16 2.04930e16i −0.151672 0.262704i 0.780170 0.625568i \(-0.215133\pi\)
−0.931842 + 0.362863i \(0.881799\pi\)
\(398\) 9.30462e16 1.17343
\(399\) 1.01932e16 2.98698e16i 0.126470 0.370602i
\(400\) 5.75378e16 0.702366
\(401\) −2.64431e16 4.58009e16i −0.317596 0.550092i 0.662390 0.749159i \(-0.269542\pi\)
−0.979986 + 0.199067i \(0.936209\pi\)
\(402\) −1.90143e15 + 3.29338e15i −0.0224705 + 0.0389200i
\(403\) −2.68043e16 + 4.64264e16i −0.311689 + 0.539861i
\(404\) 1.93106e16 + 3.34469e16i 0.220961 + 0.382716i
\(405\) −9.91269e16 −1.11618
\(406\) 9.61198e16 1.89582e16i 1.06511 0.210077i
\(407\) −1.97389e16 −0.215258
\(408\) 6.11228e15 + 1.05868e16i 0.0656013 + 0.113625i
\(409\) 2.17697e16 3.77062e16i 0.229959 0.398301i −0.727837 0.685751i \(-0.759474\pi\)
0.957796 + 0.287450i \(0.0928074\pi\)
\(410\) −5.60993e16 + 9.71668e16i −0.583260 + 1.01024i
\(411\) 9.68814e15 + 1.67804e16i 0.0991445 + 0.171723i
\(412\) −7.80371e16 −0.786084
\(413\) 1.12827e17 + 1.29075e17i 1.11877 + 1.27987i
\(414\) 2.89358e16 0.282445
\(415\) −6.77673e15 1.17376e16i −0.0651190 0.112789i
\(416\) −6.55520e15 + 1.13539e16i −0.0620125 + 0.107409i
\(417\) −2.27335e14 + 3.93756e14i −0.00211730 + 0.00366727i
\(418\) 1.34404e16 + 2.32794e16i 0.123244 + 0.213465i
\(419\) 5.69881e16 0.514509 0.257255 0.966344i \(-0.417182\pi\)
0.257255 + 0.966344i \(0.417182\pi\)
\(420\) −2.80037e16 3.20362e16i −0.248940 0.284787i
\(421\) 6.97807e16 0.610803 0.305402 0.952224i \(-0.401209\pi\)
0.305402 + 0.952224i \(0.401209\pi\)
\(422\) −3.22737e15 5.58997e15i −0.0278175 0.0481813i
\(423\) −8.53783e16 + 1.47880e17i −0.724662 + 1.25515i
\(424\) −2.24551e16 + 3.88934e16i −0.187688 + 0.325086i
\(425\) −1.63391e17 2.83002e17i −1.34493 2.32949i
\(426\) −3.94484e16 −0.319792
\(427\) −1.34971e16 + 2.66211e15i −0.107761 + 0.0212542i
\(428\) −1.54096e16 −0.121173
\(429\) 6.05716e15 + 1.04913e16i 0.0469134 + 0.0812563i
\(430\) −4.92056e15 + 8.52266e15i −0.0375379 + 0.0650175i
\(431\) 1.26096e17 2.18405e17i 0.947545 1.64120i 0.196972 0.980409i \(-0.436889\pi\)
0.750573 0.660787i \(-0.229777\pi\)
\(432\) 1.21074e16 + 2.09707e16i 0.0896205 + 0.155227i
\(433\) −1.42066e16 −0.103590 −0.0517952 0.998658i \(-0.516494\pi\)
−0.0517952 + 0.998658i \(0.516494\pi\)
\(434\) 2.82484e16 8.27780e16i 0.202913 0.594609i
\(435\) −1.64130e17 −1.16147
\(436\) 3.01112e16 + 5.21542e16i 0.209926 + 0.363603i
\(437\) −3.45697e16 + 5.98766e16i −0.237447 + 0.411270i
\(438\) 2.27602e15 3.94219e15i 0.0154026 0.0266781i
\(439\) 2.71324e16 + 4.69947e16i 0.180912 + 0.313350i 0.942192 0.335075i \(-0.108762\pi\)
−0.761279 + 0.648424i \(0.775428\pi\)
\(440\) 3.62403e16 0.238094
\(441\) 1.75536e16 1.30087e17i 0.113636 0.842137i
\(442\) 7.44597e16 0.474981
\(443\) 1.22671e17 + 2.12472e17i 0.771110 + 1.33560i 0.936955 + 0.349450i \(0.113631\pi\)
−0.165845 + 0.986152i \(0.553035\pi\)
\(444\) 9.75902e15 1.69031e16i 0.0604529 0.104707i
\(445\) −1.87003e17 + 3.23899e17i −1.14159 + 1.97729i
\(446\) −2.50279e16 4.33495e16i −0.150573 0.260800i
\(447\) 8.59903e16 0.509859
\(448\) 6.90837e15 2.02440e16i 0.0403709 0.118301i
\(449\) −3.17982e17 −1.83148 −0.915739 0.401773i \(-0.868394\pi\)
−0.915739 + 0.401773i \(0.868394\pi\)
\(450\) −1.48683e17 2.57526e17i −0.844072 1.46197i
\(451\) −2.60588e16 + 4.51352e16i −0.145817 + 0.252562i
\(452\) −3.92322e16 + 6.79522e16i −0.216393 + 0.374804i
\(453\) 5.99409e16 + 1.03821e17i 0.325900 + 0.564476i
\(454\) −1.79502e16 −0.0962066
\(455\) −2.54275e17 + 5.01519e16i −1.34347 + 0.264980i
\(456\) −2.65800e16 −0.138447
\(457\) −2.38520e16 4.13129e16i −0.122481 0.212144i 0.798264 0.602307i \(-0.205752\pi\)
−0.920746 + 0.390163i \(0.872419\pi\)
\(458\) −9.83986e16 + 1.70431e17i −0.498154 + 0.862827i
\(459\) 6.87634e16 1.19102e17i 0.343222 0.594478i
\(460\) 4.66064e16 + 8.07247e16i 0.229361 + 0.397265i
\(461\) 3.80845e17 1.84796 0.923979 0.382444i \(-0.124917\pi\)
0.923979 + 0.382444i \(0.124917\pi\)
\(462\) −1.30081e16 1.48812e16i −0.0622358 0.0711978i
\(463\) 3.17540e17 1.49803 0.749017 0.662550i \(-0.230526\pi\)
0.749017 + 0.662550i \(0.230526\pi\)
\(464\) −4.12546e16 7.14551e16i −0.191914 0.332404i
\(465\) −7.32645e16 + 1.26898e17i −0.336085 + 0.582117i
\(466\) 9.94029e16 1.72171e17i 0.449667 0.778846i
\(467\) −1.35003e17 2.33833e17i −0.602261 1.04315i −0.992478 0.122424i \(-0.960933\pi\)
0.390217 0.920723i \(-0.372400\pi\)
\(468\) 6.77568e16 0.298095
\(469\) −2.48721e16 2.84537e16i −0.107917 0.123457i
\(470\) −5.50069e17 −2.35386
\(471\) −8.65294e15 1.49873e16i −0.0365197 0.0632540i
\(472\) 7.21896e16 1.25036e17i 0.300505 0.520490i
\(473\) −2.28566e15 + 3.95889e15i −0.00938458 + 0.0162546i
\(474\) 3.96645e16 + 6.87009e16i 0.160636 + 0.278230i
\(475\) 7.10527e17 2.83839
\(476\) −1.19189e17 + 2.35082e16i −0.469667 + 0.0926350i
\(477\) 2.32104e17 0.902222
\(478\) 1.62687e17 + 2.81781e17i 0.623836 + 1.08052i
\(479\) −2.00045e16 + 3.46489e16i −0.0756742 + 0.131072i −0.901379 0.433031i \(-0.857444\pi\)
0.825705 + 0.564102i \(0.190778\pi\)
\(480\) −1.79174e16 + 3.10339e16i −0.0668663 + 0.115816i
\(481\) −5.94421e16 1.02957e17i −0.218852 0.379063i
\(482\) 1.36814e17 0.496965
\(483\) 1.64188e16 4.81131e16i 0.0588418 0.172428i
\(484\) −1.24571e17 −0.440476
\(485\) 1.15407e17 + 1.99891e17i 0.402635 + 0.697384i
\(486\) 9.64009e16 1.66971e17i 0.331853 0.574786i
\(487\) −5.31091e16 + 9.19877e16i −0.180398 + 0.312458i −0.942016 0.335568i \(-0.891072\pi\)
0.761618 + 0.648026i \(0.224405\pi\)
\(488\) 5.79298e15 + 1.00337e16i 0.0194166 + 0.0336305i
\(489\) −3.26060e16 −0.107843
\(490\) 3.91187e17 1.60558e17i 1.27676 0.524031i
\(491\) 2.75703e16 0.0887998 0.0443999 0.999014i \(-0.485862\pi\)
0.0443999 + 0.999014i \(0.485862\pi\)
\(492\) −2.57673e16 4.46302e16i −0.0819021 0.141859i
\(493\) −2.34303e17 + 4.05825e17i −0.734976 + 1.27302i
\(494\) −8.09493e16 + 1.40208e17i −0.250604 + 0.434059i
\(495\) −9.36481e16 1.62203e17i −0.286131 0.495594i
\(496\) −7.36611e16 −0.222130
\(497\) 1.26613e17 3.71021e17i 0.376843 1.10429i
\(498\) 6.22532e15 0.0182882
\(499\) −2.30486e17 3.99213e17i −0.668329 1.15758i −0.978371 0.206857i \(-0.933677\pi\)
0.310042 0.950723i \(-0.399657\pi\)
\(500\) 3.08480e17 5.34303e17i 0.882921 1.52926i
\(501\) 7.56566e16 1.31041e17i 0.213748 0.370222i
\(502\) −4.08953e16 7.08328e16i −0.114051 0.197542i
\(503\) −5.56693e17 −1.53258 −0.766291 0.642494i \(-0.777900\pi\)
−0.766291 + 0.642494i \(0.777900\pi\)
\(504\) −1.08459e17 + 2.13920e16i −0.294760 + 0.0581371i
\(505\) 6.42986e17 1.72507
\(506\) 2.16493e16 + 3.74977e16i 0.0573410 + 0.0993175i
\(507\) 3.76330e16 6.51823e16i 0.0984050 0.170442i
\(508\) −9.48107e16 + 1.64217e17i −0.244762 + 0.423939i
\(509\) −2.46492e17 4.26937e17i −0.628257 1.08817i −0.987901 0.155084i \(-0.950435\pi\)
0.359644 0.933090i \(-0.382898\pi\)
\(510\) 2.03522e17 0.512159
\(511\) 2.97720e16 + 3.40592e16i 0.0739729 + 0.0846250i
\(512\) −1.80144e16 −0.0441942
\(513\) 1.49513e17 + 2.58964e17i 0.362173 + 0.627302i
\(514\) −1.50281e17 + 2.60295e17i −0.359455 + 0.622595i
\(515\) −6.49603e17 + 1.12515e18i −1.53427 + 2.65743i
\(516\) −2.26009e15 3.91459e15i −0.00527112 0.00912984i
\(517\) −2.55514e17 −0.588473
\(518\) 1.27655e17 + 1.46037e17i 0.290332 + 0.332140i
\(519\) 5.09879e15 0.0114520
\(520\) 1.09135e17 + 1.89027e17i 0.242070 + 0.419278i
\(521\) 2.89798e17 5.01944e17i 0.634819 1.09954i −0.351735 0.936100i \(-0.614408\pi\)
0.986553 0.163439i \(-0.0522586\pi\)
\(522\) −2.13211e17 + 3.69293e17i −0.461266 + 0.798937i
\(523\) 6.21615e16 + 1.07667e17i 0.132819 + 0.230049i 0.924762 0.380546i \(-0.124264\pi\)
−0.791943 + 0.610595i \(0.790930\pi\)
\(524\) 8.67164e16 0.182999
\(525\) −5.12568e17 + 1.01097e17i −1.06836 + 0.210718i
\(526\) −6.04822e17 −1.24515
\(527\) 2.09177e17 + 3.62305e17i 0.425348 + 0.736725i
\(528\) −8.32287e15 + 1.44156e16i −0.0167168 + 0.0289543i
\(529\) 1.96335e17 3.40061e17i 0.389525 0.674676i
\(530\) 3.73846e17 + 6.47520e17i 0.732655 + 1.26900i
\(531\) −7.46177e17 −1.44453
\(532\) 8.53106e16 2.49991e17i 0.163146 0.478077i
\(533\) −3.13896e17 −0.593006
\(534\) −8.58935e16 1.48772e17i −0.160303 0.277653i
\(535\) −1.28274e17 + 2.22177e17i −0.236505 + 0.409638i
\(536\) −1.59138e16 + 2.75635e16i −0.0289869 + 0.0502068i
\(537\) −1.07380e17 1.85988e17i −0.193237 0.334696i
\(538\) −2.22274e17 −0.395189
\(539\) 1.81712e17 7.45812e16i 0.319195 0.131009i
\(540\) 4.03143e17 0.699680
\(541\) −4.09563e16 7.09384e16i −0.0702325 0.121646i 0.828771 0.559588i \(-0.189041\pi\)
−0.899003 + 0.437942i \(0.855707\pi\)
\(542\) 1.49657e17 2.59213e17i 0.253572 0.439200i
\(543\) 2.64630e15 4.58352e15i 0.00443037 0.00767362i
\(544\) 5.11558e16 + 8.86045e16i 0.0846257 + 0.146576i
\(545\) 1.00262e18 1.63892
\(546\) 3.84467e16 1.12663e17i 0.0621023 0.181982i
\(547\) −3.99955e17 −0.638402 −0.319201 0.947687i \(-0.603414\pi\)
−0.319201 + 0.947687i \(0.603414\pi\)
\(548\) 8.10835e16 + 1.40441e17i 0.127897 + 0.221523i
\(549\) 2.99391e16 5.18561e16i 0.0466679 0.0808312i
\(550\) 2.22484e17 3.85353e17i 0.342721 0.593610i
\(551\) −5.09448e17 8.82391e17i −0.775559 1.34331i
\(552\) −4.28141e16 −0.0644144
\(553\) −7.73453e17 + 1.52552e17i −1.15006 + 0.226832i
\(554\) 4.58432e17 0.673692
\(555\) −1.62474e17 2.81413e17i −0.235982 0.408733i
\(556\) −1.90265e15 + 3.29548e15i −0.00273132 + 0.00473078i
\(557\) 5.23201e17 9.06211e17i 0.742352 1.28579i −0.209069 0.977901i \(-0.567043\pi\)
0.951422 0.307891i \(-0.0996232\pi\)
\(558\) 1.90347e17 + 3.29690e17i 0.266946 + 0.462364i
\(559\) −2.75324e16 −0.0381651
\(560\) −2.34373e17 2.68122e17i −0.321133 0.367376i
\(561\) 9.45384e16 0.128041
\(562\) −1.16981e17 2.02616e17i −0.156613 0.271261i
\(563\) −3.38309e17 + 5.85968e17i −0.447722 + 0.775478i −0.998237 0.0593473i \(-0.981098\pi\)
0.550515 + 0.834825i \(0.314431\pi\)
\(564\) 1.26328e17 2.18806e17i 0.165266 0.286250i
\(565\) 6.53160e17 + 1.13131e18i 0.844705 + 1.46307i
\(566\) −2.59925e16 −0.0332309
\(567\) 2.97786e17 + 3.40667e17i 0.376370 + 0.430567i
\(568\) −3.30158e17 −0.412532
\(569\) 5.76178e17 + 9.97969e17i 0.711749 + 1.23279i 0.964200 + 0.265176i \(0.0854300\pi\)
−0.252451 + 0.967610i \(0.581237\pi\)
\(570\) −2.21260e17 + 3.83233e17i −0.270219 + 0.468033i
\(571\) 6.95800e17 1.20516e18i 0.840137 1.45516i −0.0496423 0.998767i \(-0.515808\pi\)
0.889779 0.456392i \(-0.150859\pi\)
\(572\) 5.06945e16 + 8.78054e16i 0.0605183 + 0.104821i
\(573\) 2.92496e17 0.345235
\(574\) 5.02458e17 9.91026e16i 0.586372 0.115653i
\(575\) 1.14449e18 1.32060
\(576\) 4.65508e16 + 8.06283e16i 0.0531106 + 0.0919902i
\(577\) 6.39661e17 1.10793e18i 0.721618 1.24988i −0.238733 0.971085i \(-0.576732\pi\)
0.960351 0.278794i \(-0.0899346\pi\)
\(578\) −2.64100e16 + 4.57434e16i −0.0294603 + 0.0510267i
\(579\) 1.11497e17 + 1.93119e17i 0.122986 + 0.213017i
\(580\) −1.37366e18 −1.49830
\(581\) −1.99806e16 + 5.85504e16i −0.0215508 + 0.0631517i
\(582\) −1.06017e17 −0.113077
\(583\) 1.73656e17 + 3.00781e17i 0.183166 + 0.317253i
\(584\) 1.90488e16 3.29935e16i 0.0198694 0.0344148i
\(585\) 5.64027e17 9.76924e17i 0.581818 1.00774i
\(586\) −4.81759e16 8.34431e16i −0.0491468 0.0851248i
\(587\) −5.72711e17 −0.577813 −0.288907 0.957357i \(-0.593292\pi\)
−0.288907 + 0.957357i \(0.593292\pi\)
\(588\) −2.59726e16 + 1.92479e17i −0.0259157 + 0.192058i
\(589\) −9.09632e17 −0.897669
\(590\) −1.20185e18 2.08167e18i −1.17304 2.03177i
\(591\) 2.07957e17 3.60192e17i 0.200750 0.347708i
\(592\) 8.16767e16 1.41468e17i 0.0779842 0.135073i
\(593\) 5.24473e17 + 9.08413e17i 0.495299 + 0.857883i 0.999985 0.00541985i \(-0.00172520\pi\)
−0.504686 + 0.863303i \(0.668392\pi\)
\(594\) 1.87265e17 0.174922
\(595\) −6.53218e17 + 1.91416e18i −0.603528 + 1.76856i
\(596\) 7.19683e17 0.657719
\(597\) 3.55760e17 + 6.16194e17i 0.321606 + 0.557037i
\(598\) −1.30390e17 + 2.25842e17i −0.116597 + 0.201952i
\(599\) −3.84295e17 + 6.65618e17i −0.339931 + 0.588777i −0.984419 0.175837i \(-0.943737\pi\)
0.644489 + 0.764614i \(0.277070\pi\)
\(600\) 2.19994e17 + 3.81042e17i 0.192499 + 0.333418i
\(601\) −9.28666e16 −0.0803851 −0.0401926 0.999192i \(-0.512797\pi\)
−0.0401926 + 0.999192i \(0.512797\pi\)
\(602\) 4.40715e16 8.69245e15i 0.0377381 0.00744329i
\(603\) 1.64490e17 0.139341
\(604\) 5.01666e17 + 8.68911e17i 0.420411 + 0.728174i
\(605\) −1.03696e18 + 1.79607e18i −0.859714 + 1.48907i
\(606\) −1.47667e17 + 2.55766e17i −0.121119 + 0.209784i
\(607\) −7.85335e17 1.36024e18i −0.637278 1.10380i −0.986028 0.166581i \(-0.946727\pi\)
0.348750 0.937216i \(-0.386606\pi\)
\(608\) −2.22458e17 −0.178597
\(609\) 4.93062e17 + 5.64063e17i 0.391642 + 0.448038i
\(610\) 1.92890e17 0.151588
\(611\) −7.69461e17 1.33274e18i −0.598299 1.03628i
\(612\) 2.64382e17 4.57924e17i 0.203399 0.352297i
\(613\) −6.44651e17 + 1.11657e18i −0.490718 + 0.849948i −0.999943 0.0106854i \(-0.996599\pi\)
0.509225 + 0.860633i \(0.329932\pi\)
\(614\) −6.37617e17 1.10438e18i −0.480248 0.831813i
\(615\) −8.57976e17 −0.639421
\(616\) −1.08869e17 1.24546e17i −0.0802842 0.0918452i
\(617\) 8.41398e17 0.613971 0.306985 0.951714i \(-0.400680\pi\)
0.306985 + 0.951714i \(0.400680\pi\)
\(618\) −2.98373e17 5.16797e17i −0.215444 0.373160i
\(619\) 5.89250e17 1.02061e18i 0.421028 0.729241i −0.575013 0.818144i \(-0.695003\pi\)
0.996040 + 0.0889034i \(0.0283362\pi\)
\(620\) −6.13176e17 + 1.06205e18i −0.433550 + 0.750931i
\(621\) 2.40830e17 + 4.17130e17i 0.168506 + 0.291861i
\(622\) 2.82893e15 0.00195878
\(623\) 1.67491e18 3.30352e17i 1.14768 0.226362i
\(624\) −1.00255e17 −0.0679836
\(625\) −3.04254e18 5.26983e18i −2.04181 3.53652i
\(626\) 1.35999e17 2.35557e17i 0.0903240 0.156446i
\(627\) −1.02778e17 + 1.78017e17i −0.0675556 + 0.117010i
\(628\) −7.24195e16 1.25434e17i −0.0471105 0.0815978i
\(629\) −9.27755e17 −0.597316
\(630\) −5.94415e17 + 1.74185e18i −0.378770 + 1.10993i
\(631\) −1.91515e17 −0.120785 −0.0603923 0.998175i \(-0.519235\pi\)
−0.0603923 + 0.998175i \(0.519235\pi\)
\(632\) 3.31966e17 + 5.74982e17i 0.207220 + 0.358916i
\(633\) 2.46795e16 4.27462e16i 0.0152480 0.0264103i
\(634\) 3.52205e17 6.10038e17i 0.215385 0.373058i
\(635\) 1.57846e18 + 2.73398e18i 0.955444 + 1.65488i
\(636\) −3.43426e17 −0.205761
\(637\) 9.36220e17 + 7.23199e17i 0.555228 + 0.428896i
\(638\) −6.38084e17 −0.374579
\(639\) 8.53156e17 + 1.47771e18i 0.495762 + 0.858685i
\(640\) −1.49957e17 + 2.59733e17i −0.0862575 + 0.149402i
\(641\) 7.31765e17 1.26745e18i 0.416672 0.721697i −0.578930 0.815377i \(-0.696530\pi\)
0.995602 + 0.0936800i \(0.0298631\pi\)
\(642\) −5.89183e16 1.02050e17i −0.0332103 0.0575219i
\(643\) −1.79993e18 −1.00435 −0.502173 0.864767i \(-0.667466\pi\)
−0.502173 + 0.864767i \(0.667466\pi\)
\(644\) 1.37415e17 4.02676e17i 0.0759060 0.222432i
\(645\) −7.52545e16 −0.0411523
\(646\) 6.31717e17 + 1.09417e18i 0.341988 + 0.592341i
\(647\) −1.13239e18 + 1.96136e18i −0.606902 + 1.05119i 0.384846 + 0.922981i \(0.374255\pi\)
−0.991748 + 0.128204i \(0.959079\pi\)
\(648\) 1.90530e17 3.30008e17i 0.101094 0.175101i
\(649\) −5.58277e17 9.66964e17i −0.293264 0.507949i
\(650\) 2.67997e18 1.39377
\(651\) 6.56201e17 1.29426e17i 0.337878 0.0666415i
\(652\) −2.72891e17 −0.139117
\(653\) 9.13054e17 + 1.58146e18i 0.460851 + 0.798218i 0.999004 0.0446297i \(-0.0142108\pi\)
−0.538152 + 0.842848i \(0.680877\pi\)
\(654\) −2.30259e17 + 3.98821e17i −0.115070 + 0.199307i
\(655\) 7.21852e17 1.25029e18i 0.357174 0.618644i
\(656\) −2.15655e17 3.73526e17i −0.105654 0.182998i
\(657\) −1.96895e17 −0.0955126
\(658\) 1.65246e18 + 1.89041e18i 0.793711 + 0.908005i
\(659\) 1.72001e18 0.818044 0.409022 0.912525i \(-0.365870\pi\)
0.409022 + 0.912525i \(0.365870\pi\)
\(660\) 1.38564e17 + 2.40000e17i 0.0652551 + 0.113025i
\(661\) −7.91910e16 + 1.37163e17i −0.0369289 + 0.0639627i −0.883899 0.467678i \(-0.845091\pi\)
0.846970 + 0.531640i \(0.178424\pi\)
\(662\) 1.35473e18 2.34645e18i 0.625568 1.08352i
\(663\) 2.84695e17 + 4.93106e17i 0.130179 + 0.225477i
\(664\) 5.21019e16 0.0235918
\(665\) −2.89424e18 3.31101e18i −1.29776 1.48464i
\(666\) −8.44238e17 −0.374872
\(667\) −8.20601e17 1.42132e18i −0.360839 0.624992i
\(668\) 6.33196e17 1.09673e18i 0.275735 0.477587i
\(669\) 1.91387e17 3.31492e17i 0.0825358 0.142956i
\(670\) 2.64942e17 + 4.58892e17i 0.113152 + 0.195986i
\(671\) 8.95997e16 0.0378975
\(672\) 1.60479e17 3.16521e16i 0.0672230 0.0132587i
\(673\) −2.70067e18 −1.12040 −0.560201 0.828356i \(-0.689276\pi\)
−0.560201 + 0.828356i \(0.689276\pi\)
\(674\) 9.00675e17 + 1.56002e18i 0.370066 + 0.640973i
\(675\) 2.47494e18 4.28673e18i 1.00714 1.74442i
\(676\) 3.14964e17 5.45533e17i 0.126942 0.219871i
\(677\) 1.21728e18 + 2.10839e18i 0.485919 + 0.841637i 0.999869 0.0161835i \(-0.00515159\pi\)
−0.513950 + 0.857820i \(0.671818\pi\)
\(678\) −6.00014e17 −0.237229
\(679\) 3.40268e17 9.97108e17i 0.133250 0.390471i
\(680\) 1.70334e18 0.660685
\(681\) −6.86319e16 1.18874e17i −0.0263676 0.0456700i
\(682\) −2.84828e17 + 4.93337e17i −0.108389 + 0.187735i
\(683\) −7.37572e16 + 1.27751e17i −0.0278016 + 0.0481538i −0.879591 0.475730i \(-0.842184\pi\)
0.851790 + 0.523884i \(0.175517\pi\)
\(684\) 5.74850e17 + 9.95669e17i 0.214630 + 0.371749i
\(685\) 2.69985e18 0.998506
\(686\) −1.72695e18 8.62055e17i −0.632663 0.315812i
\(687\) −1.50490e18 −0.546120
\(688\) −1.89155e16 3.27626e16i −0.00679974 0.0117775i
\(689\) −1.04590e18 + 1.81156e18i −0.372449 + 0.645100i
\(690\) −3.56397e17 + 6.17298e17i −0.125723 + 0.217759i
\(691\) 1.28877e18 + 2.23222e18i 0.450369 + 0.780062i 0.998409 0.0563901i \(-0.0179591\pi\)
−0.548040 + 0.836452i \(0.684626\pi\)
\(692\) 4.26736e16 0.0147730
\(693\) −2.76113e17 + 8.09112e17i −0.0946938 + 0.277487i
\(694\) 1.75389e18 0.595888
\(695\) 3.16764e16 + 5.48651e16i 0.0106619 + 0.0184669i
\(696\) 3.15472e17 5.46414e17i 0.105196 0.182206i
\(697\) −1.22480e18 + 2.12142e18i −0.404625 + 0.700831i
\(698\) −1.66436e18 2.88276e18i −0.544737 0.943513i
\(699\) 1.52026e18 0.492965
\(700\) −4.28986e18 + 8.46113e17i −1.37818 + 0.271826i
\(701\) −1.66664e18 −0.530486 −0.265243 0.964182i \(-0.585452\pi\)
−0.265243 + 0.964182i \(0.585452\pi\)
\(702\) 5.63933e17 + 9.76761e17i 0.177843 + 0.308033i
\(703\) 1.00861e18 1.74697e18i 0.315149 0.545854i
\(704\) −6.96570e16 + 1.20649e17i −0.0215646 + 0.0373511i
\(705\) −2.10318e18 3.64281e18i −0.645129 1.11740i
\(706\) −1.31438e18 −0.399475
\(707\) −1.93159e18 2.20974e18i −0.581686 0.665449i
\(708\) 1.10406e18 0.329440
\(709\) 2.58063e18 + 4.46978e18i 0.763000 + 1.32156i 0.941297 + 0.337578i \(0.109608\pi\)
−0.178297 + 0.983977i \(0.557059\pi\)
\(710\) −2.74833e18 + 4.76024e18i −0.805173 + 1.39460i
\(711\) 1.71566e18 2.97161e18i 0.498056 0.862659i
\(712\) −7.18873e17 1.24512e18i −0.206791 0.358173i
\(713\) −1.46520e18 −0.417653
\(714\) −6.11397e17 6.99439e17i −0.172697 0.197566i
\(715\) 1.68798e18 0.472475
\(716\) −8.98700e17 1.55659e18i −0.249276 0.431758i
\(717\) −1.24406e18 + 2.15477e18i −0.341952 + 0.592279i
\(718\) 1.56609e17 2.71254e17i 0.0426587 0.0738870i
\(719\) −1.80992e18 3.13488e18i −0.488565 0.846220i 0.511348 0.859374i \(-0.329146\pi\)
−0.999913 + 0.0131535i \(0.995813\pi\)
\(720\) 1.55001e18 0.414641
\(721\) 5.81823e18 1.14756e18i 1.54245 0.304226i
\(722\) −5.57094e16 −0.0146365
\(723\) 5.23106e17 + 9.06047e17i 0.136204 + 0.235913i
\(724\) 2.21478e16 3.83611e16i 0.00571518 0.00989898i
\(725\) −8.43309e18 + 1.46065e19i −2.15670 + 3.73551i
\(726\) −4.76294e17 8.24965e17i −0.120722 0.209097i
\(727\) −4.45477e18 −1.11906 −0.559528 0.828811i \(-0.689018\pi\)
−0.559528 + 0.828811i \(0.689018\pi\)
\(728\) 3.21774e17 9.42915e17i 0.0801120 0.234757i
\(729\) −8.43212e17 −0.208069
\(730\) −3.17136e17 5.49295e17i −0.0775616 0.134341i
\(731\) −1.07429e17 + 1.86073e17i −0.0260411 + 0.0451046i
\(732\) −4.42986e16 + 7.67274e16i −0.0106431 + 0.0184344i
\(733\) 7.49497e17 + 1.29817e18i 0.178482 + 0.309139i 0.941361 0.337402i \(-0.109548\pi\)
−0.762879 + 0.646541i \(0.776215\pi\)
\(734\) −7.72764e15 −0.00182399
\(735\) 2.55898e18 + 1.97673e18i 0.598687 + 0.462466i
\(736\) −3.58326e17 −0.0830946
\(737\) 1.23069e17 + 2.13161e17i 0.0282885 + 0.0489971i
\(738\) −1.11454e18 + 1.93045e18i −0.253940 + 0.439837i
\(739\) −9.95675e17 + 1.72456e18i −0.224869 + 0.389484i −0.956280 0.292453i \(-0.905529\pi\)
0.731411 + 0.681936i \(0.238862\pi\)
\(740\) −1.35980e18 2.35524e18i −0.304417 0.527266i
\(741\) −1.23803e18 −0.274734
\(742\) 1.10225e18 3.23000e18i 0.242469 0.710521i
\(743\) −3.75670e18 −0.819179 −0.409590 0.912270i \(-0.634328\pi\)
−0.409590 + 0.912270i \(0.634328\pi\)
\(744\) −2.81641e17 4.87817e17i −0.0608797 0.105447i
\(745\) 5.99085e18 1.03764e19i 1.28373 2.22348i
\(746\) −4.71863e17 + 8.17291e17i −0.100234 + 0.173610i
\(747\) −1.34636e17 2.33196e17i −0.0283515 0.0491063i
\(748\) 7.91225e17 0.165173
\(749\) 1.14890e18 2.26604e17i 0.237766 0.0468959i
\(750\) 4.71786e18 0.967937
\(751\) 4.62860e18 + 8.01697e18i 0.941435 + 1.63061i 0.762737 + 0.646708i \(0.223855\pi\)
0.178697 + 0.983904i \(0.442812\pi\)
\(752\) 1.05728e18 1.83126e18i 0.213194 0.369262i
\(753\) 3.12725e17 5.41655e17i 0.0625165 0.108282i
\(754\) −1.92154e18 3.32820e18i −0.380833 0.659623i
\(755\) 1.67040e19 3.28221
\(756\) −1.21108e18 1.38547e18i −0.235928 0.269902i
\(757\) 9.65926e17 0.186561 0.0932805 0.995640i \(-0.470265\pi\)
0.0932805 + 0.995640i \(0.470265\pi\)