Properties

Label 16.12.e.a.5.4
Level 16
Weight 12
Character 16.5
Analytic conductor 12.293
Analytic rank 0
Dimension 42
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 12 \)
Character orbit: \([\chi]\) = 16.e (of order \(4\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(12.293490889\)
Analytic rank: \(0\)
Dimension: \(42\)
Relative dimension: \(21\) over \(\Q(i)\)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 5.4
Character \(\chi\) = 16.5
Dual form 16.12.e.a.13.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-36.4599 - 26.8082i) q^{2} +(-475.976 + 475.976i) q^{3} +(610.643 + 1954.84i) q^{4} +(2805.14 + 2805.14i) q^{5} +(30114.1 - 4593.97i) q^{6} +76033.6i q^{7} +(30141.9 - 87643.6i) q^{8} -275960. i q^{9} +O(q^{10})\) \(q+(-36.4599 - 26.8082i) q^{2} +(-475.976 + 475.976i) q^{3} +(610.643 + 1954.84i) q^{4} +(2805.14 + 2805.14i) q^{5} +(30114.1 - 4593.97i) q^{6} +76033.6i q^{7} +(30141.9 - 87643.6i) q^{8} -275960. i q^{9} +(-27074.3 - 177476. i) q^{10} +(409752. + 409752. i) q^{11} +(-1.22111e6 - 639808. i) q^{12} +(-1.80631e6 + 1.80631e6i) q^{13} +(2.03832e6 - 2.77217e6i) q^{14} -2.67036e6 q^{15} +(-3.44853e6 + 2.38743e6i) q^{16} -1.50853e6 q^{17} +(-7.39798e6 + 1.00615e7i) q^{18} +(5.45825e6 - 5.45825e6i) q^{19} +(-3.77067e6 + 7.19655e6i) q^{20} +(-3.61902e7 - 3.61902e7i) q^{21} +(-3.95480e6 - 2.59242e7i) q^{22} +2.28696e6i q^{23} +(2.73695e7 + 5.60631e7i) q^{24} -3.30905e7i q^{25} +(1.14282e8 - 1.74340e7i) q^{26} +(4.70326e7 + 4.70326e7i) q^{27} +(-1.48634e8 + 4.64294e7i) q^{28} +(4.38084e7 - 4.38084e7i) q^{29} +(9.73609e7 + 7.15874e7i) q^{30} +2.76655e7 q^{31} +(1.89736e8 + 5.40367e6i) q^{32} -3.90064e8 q^{33} +(5.50009e7 + 4.04410e7i) q^{34} +(-2.13285e8 + 2.13285e8i) q^{35} +(5.39459e8 - 1.68513e8i) q^{36} +(2.40566e8 + 2.40566e8i) q^{37} +(-3.45333e8 + 5.26813e7i) q^{38} -1.71953e9i q^{39} +(3.30404e8 - 1.61300e8i) q^{40} -1.08336e8i q^{41} +(3.49296e8 + 2.28968e9i) q^{42} +(1.91015e8 + 1.91015e8i) q^{43} +(-5.50789e8 + 1.05121e9i) q^{44} +(7.74106e8 - 7.74106e8i) q^{45} +(6.13092e7 - 8.33822e7i) q^{46} -1.72497e9 q^{47} +(5.05062e8 - 2.77778e9i) q^{48} -3.80378e9 q^{49} +(-8.87097e8 + 1.20648e9i) q^{50} +(7.18026e8 - 7.18026e8i) q^{51} +(-4.63408e9 - 2.42805e9i) q^{52} +(-8.00868e7 - 8.00868e7i) q^{53} +(-4.53944e8 - 2.97566e9i) q^{54} +2.29882e9i q^{55} +(6.66386e9 + 2.29179e9i) q^{56} +5.19599e9i q^{57} +(-2.77167e9 + 4.22825e8i) q^{58} +(6.70345e9 + 6.70345e9i) q^{59} +(-1.63064e9 - 5.22014e9i) q^{60} +(9.82284e7 - 9.82284e7i) q^{61} +(-1.00868e9 - 7.41661e8i) q^{62} +2.09822e10 q^{63} +(-6.77287e9 - 5.28348e9i) q^{64} -1.01339e10 q^{65} +(1.42217e10 + 1.04569e10i) q^{66} +(6.92288e9 - 6.92288e9i) q^{67} +(-9.21176e8 - 2.94895e9i) q^{68} +(-1.08854e9 - 1.08854e9i) q^{69} +(1.34941e10 - 2.05856e9i) q^{70} +1.20473e9i q^{71} +(-2.41861e10 - 8.31795e9i) q^{72} -2.00681e10i q^{73} +(-2.32186e9 - 1.52201e10i) q^{74} +(1.57503e10 + 1.57503e10i) q^{75} +(1.40031e10 + 7.33699e9i) q^{76} +(-3.11549e10 + 3.11549e10i) q^{77} +(-4.60973e10 + 6.26936e10i) q^{78} -1.65053e10 q^{79} +(-1.63707e10 - 2.97655e9i) q^{80} +4.11263e9 q^{81} +(-2.90430e9 + 3.94992e9i) q^{82} +(2.19541e10 - 2.19541e10i) q^{83} +(4.86469e10 - 9.28455e10i) q^{84} +(-4.23165e9 - 4.23165e9i) q^{85} +(-1.84362e9 - 1.20852e10i) q^{86} +4.17036e10i q^{87} +(4.82628e10 - 2.35614e10i) q^{88} +3.11065e10i q^{89} +(-4.89762e10 + 7.47143e9i) q^{90} +(-1.37341e11 - 1.37341e11i) q^{91} +(-4.47065e9 + 1.39652e9i) q^{92} +(-1.31681e10 + 1.31681e10i) q^{93} +(6.28922e10 + 4.62433e10i) q^{94} +3.06223e10 q^{95} +(-9.28817e10 + 8.77376e10i) q^{96} -1.12128e9 q^{97} +(1.38685e11 + 1.01972e11i) q^{98} +(1.13075e11 - 1.13075e11i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 42q - 2q^{2} - 2q^{3} + 3080q^{4} - 2q^{5} + 30352q^{6} + 74836q^{8} + O(q^{10}) \) \( 42q - 2q^{2} - 2q^{3} + 3080q^{4} - 2q^{5} + 30352q^{6} + 74836q^{8} - 988948q^{10} - 540846q^{11} + 2300260q^{12} - 2q^{13} - 1829956q^{14} - 6075004q^{15} - 3721448q^{16} - 4q^{17} - 32219106q^{18} - 11291290q^{19} + 68655164q^{20} + 354292q^{21} - 85011388q^{22} - 66180944q^{24} + 305685384q^{26} - 66463304q^{27} - 322075880q^{28} + 77673206q^{29} + 290643636q^{30} + 343549808q^{31} + 404698568q^{32} - 4q^{33} - 882461836q^{34} - 434731684q^{35} + 1854387628q^{36} - 522762058q^{37} - 1276252832q^{38} - 483241016q^{40} + 2372079160q^{42} + 3824193658q^{43} - 2657283740q^{44} + 97301954q^{45} - 1032658964q^{46} - 4586900144q^{47} - 1058870552q^{48} - 8474257474q^{49} + 6515930886q^{50} + 7074245796q^{51} - 13915491564q^{52} - 2100608058q^{53} + 4385621536q^{54} + 12910845976q^{56} - 21491153128q^{58} + 955824746q^{59} + 25615752768q^{60} + 2150827022q^{61} - 15814519760q^{62} + 27758037828q^{63} + 9674332160q^{64} - 1884965292q^{65} + 10932459412q^{66} - 3186519018q^{67} + 13817664656q^{68} - 16193060732q^{69} - 27206453120q^{70} - 20773133628q^{72} + 14141420908q^{74} + 28890034486q^{75} - 11786004940q^{76} - 22711870540q^{77} + 37031200508q^{78} + 48011833792q^{79} - 8952586328q^{80} - 90656394430q^{81} - 81555388352q^{82} + 55713221118q^{83} + 61178517160q^{84} - 84575506252q^{85} + 10047297860q^{86} - 162855622152q^{88} + 160133627736q^{90} - 147369662716q^{91} - 169766721928q^{92} - 69689773328q^{93} + 160320530128q^{94} + 375702304500q^{95} + 230764310192q^{96} - 4q^{97} - 108887063494q^{98} - 286271331106q^{99} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(15\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −36.4599 26.8082i −0.805657 0.592383i
\(3\) −475.976 + 475.976i −1.13089 + 1.13089i −0.140855 + 0.990030i \(0.544985\pi\)
−0.990030 + 0.140855i \(0.955015\pi\)
\(4\) 610.643 + 1954.84i 0.298166 + 0.954514i
\(5\) 2805.14 + 2805.14i 0.401439 + 0.401439i 0.878740 0.477301i \(-0.158385\pi\)
−0.477301 + 0.878740i \(0.658385\pi\)
\(6\) 30114.1 4593.97i 1.58102 0.241189i
\(7\) 76033.6i 1.70988i 0.518725 + 0.854941i \(0.326407\pi\)
−0.518725 + 0.854941i \(0.673593\pi\)
\(8\) 30141.9 87643.6i 0.325218 0.945639i
\(9\) 275960.i 1.55780i
\(10\) −27074.3 177476.i −0.0856165 0.561227i
\(11\) 409752. + 409752.i 0.767116 + 0.767116i 0.977598 0.210482i \(-0.0675032\pi\)
−0.210482 + 0.977598i \(0.567503\pi\)
\(12\) −1.22111e6 639808.i −1.41664 0.742255i
\(13\) −1.80631e6 + 1.80631e6i −1.34929 + 1.34929i −0.462853 + 0.886435i \(0.653174\pi\)
−0.886435 + 0.462853i \(0.846826\pi\)
\(14\) 2.03832e6 2.77217e6i 1.01290 1.37758i
\(15\) −2.67036e6 −0.907962
\(16\) −3.44853e6 + 2.38743e6i −0.822194 + 0.569207i
\(17\) −1.50853e6 −0.257683 −0.128842 0.991665i \(-0.541126\pi\)
−0.128842 + 0.991665i \(0.541126\pi\)
\(18\) −7.39798e6 + 1.00615e7i −0.922815 + 1.25505i
\(19\) 5.45825e6 5.45825e6i 0.505718 0.505718i −0.407491 0.913209i \(-0.633596\pi\)
0.913209 + 0.407491i \(0.133596\pi\)
\(20\) −3.77067e6 + 7.19655e6i −0.263484 + 0.502874i
\(21\) −3.61902e7 3.61902e7i −1.93368 1.93368i
\(22\) −3.95480e6 2.59242e7i −0.163606 1.07246i
\(23\) 2.28696e6i 0.0740893i 0.999314 + 0.0370446i \(0.0117944\pi\)
−0.999314 + 0.0370446i \(0.988206\pi\)
\(24\) 2.73695e7 + 5.60631e7i 0.701624 + 1.43719i
\(25\) 3.30905e7i 0.677694i
\(26\) 1.14282e8 1.74340e7i 1.88636 0.287768i
\(27\) 4.70326e7 + 4.70326e7i 0.630810 + 0.630810i
\(28\) −1.48634e8 + 4.64294e7i −1.63211 + 0.509828i
\(29\) 4.38084e7 4.38084e7i 0.396615 0.396615i −0.480422 0.877037i \(-0.659517\pi\)
0.877037 + 0.480422i \(0.159517\pi\)
\(30\) 9.73609e7 + 7.15874e7i 0.731506 + 0.537861i
\(31\) 2.76655e7 0.173560 0.0867798 0.996228i \(-0.472342\pi\)
0.0867798 + 0.996228i \(0.472342\pi\)
\(32\) 1.89736e8 + 5.40367e6i 0.999595 + 0.0284685i
\(33\) −3.90064e8 −1.73504
\(34\) 5.50009e7 + 4.04410e7i 0.207604 + 0.152647i
\(35\) −2.13285e8 + 2.13285e8i −0.686413 + 0.686413i
\(36\) 5.39459e8 1.68513e8i 1.48694 0.464483i
\(37\) 2.40566e8 + 2.40566e8i 0.570327 + 0.570327i 0.932220 0.361893i \(-0.117869\pi\)
−0.361893 + 0.932220i \(0.617869\pi\)
\(38\) −3.45333e8 + 5.26813e7i −0.707014 + 0.107857i
\(39\) 1.71953e9i 3.05178i
\(40\) 3.30404e8 1.61300e8i 0.510171 0.249061i
\(41\) 1.08336e8i 0.146037i −0.997331 0.0730184i \(-0.976737\pi\)
0.997331 0.0730184i \(-0.0232632\pi\)
\(42\) 3.49296e8 + 2.28968e9i 0.412404 + 2.70336i
\(43\) 1.91015e8 + 1.91015e8i 0.198149 + 0.198149i 0.799206 0.601057i \(-0.205254\pi\)
−0.601057 + 0.799206i \(0.705254\pi\)
\(44\) −5.50789e8 + 1.05121e9i −0.503495 + 0.960951i
\(45\) 7.74106e8 7.74106e8i 0.625362 0.625362i
\(46\) 6.13092e7 8.33822e7i 0.0438892 0.0596905i
\(47\) −1.72497e9 −1.09709 −0.548547 0.836120i \(-0.684819\pi\)
−0.548547 + 0.836120i \(0.684819\pi\)
\(48\) 5.05062e8 2.77778e9i 0.286100 1.57351i
\(49\) −3.80378e9 −1.92370
\(50\) −8.87097e8 + 1.20648e9i −0.401454 + 0.545989i
\(51\) 7.18026e8 7.18026e8i 0.291410 0.291410i
\(52\) −4.63408e9 2.42805e9i −1.69023 0.885603i
\(53\) −8.00868e7 8.00868e7i −0.0263053 0.0263053i 0.693832 0.720137i \(-0.255921\pi\)
−0.720137 + 0.693832i \(0.755921\pi\)
\(54\) −4.53944e8 2.97566e9i −0.134536 0.881898i
\(55\) 2.29882e9i 0.615900i
\(56\) 6.66386e9 + 2.29179e9i 1.61693 + 0.556085i
\(57\) 5.19599e9i 1.14382i
\(58\) −2.77167e9 + 4.22825e8i −0.554483 + 0.0845877i
\(59\) 6.70345e9 + 6.70345e9i 1.22071 + 1.22071i 0.967380 + 0.253328i \(0.0815253\pi\)
0.253328 + 0.967380i \(0.418475\pi\)
\(60\) −1.63064e9 5.22014e9i −0.270723 0.866663i
\(61\) 9.82284e7 9.82284e7i 0.0148910 0.0148910i −0.699622 0.714513i \(-0.746648\pi\)
0.714513 + 0.699622i \(0.246648\pi\)
\(62\) −1.00868e9 7.41661e8i −0.139829 0.102814i
\(63\) 2.09822e10 2.66366
\(64\) −6.77287e9 5.28348e9i −0.788466 0.615078i
\(65\) −1.01339e10 −1.08331
\(66\) 1.42217e10 + 1.04569e10i 1.39785 + 1.02781i
\(67\) 6.92288e9 6.92288e9i 0.626434 0.626434i −0.320735 0.947169i \(-0.603930\pi\)
0.947169 + 0.320735i \(0.103930\pi\)
\(68\) −9.21176e8 2.94895e9i −0.0768323 0.245962i
\(69\) −1.08854e9 1.08854e9i −0.0837865 0.0837865i
\(70\) 1.34941e10 2.05856e9i 0.959632 0.146394i
\(71\) 1.20473e9i 0.0792443i 0.999215 + 0.0396221i \(0.0126154\pi\)
−0.999215 + 0.0396221i \(0.987385\pi\)
\(72\) −2.41861e10 8.31795e9i −1.47312 0.506626i
\(73\) 2.00681e10i 1.13300i −0.824061 0.566501i \(-0.808297\pi\)
0.824061 0.566501i \(-0.191703\pi\)
\(74\) −2.32186e9 1.52201e10i −0.121636 0.797340i
\(75\) 1.57503e10 + 1.57503e10i 0.766394 + 0.766394i
\(76\) 1.40031e10 + 7.33699e9i 0.633503 + 0.331927i
\(77\) −3.11549e10 + 3.11549e10i −1.31168 + 1.31168i
\(78\) −4.60973e10 + 6.26936e10i −1.80782 + 2.45869i
\(79\) −1.65053e10 −0.603497 −0.301748 0.953388i \(-0.597570\pi\)
−0.301748 + 0.953388i \(0.597570\pi\)
\(80\) −1.63707e10 2.97655e9i −0.558562 0.101559i
\(81\) 4.11263e9 0.131054
\(82\) −2.90430e9 + 3.94992e9i −0.0865097 + 0.117656i
\(83\) 2.19541e10 2.19541e10i 0.611768 0.611768i −0.331638 0.943407i \(-0.607601\pi\)
0.943407 + 0.331638i \(0.107601\pi\)
\(84\) 4.86469e10 9.28455e10i 1.26917 2.42228i
\(85\) −4.23165e9 4.23165e9i −0.103444 0.103444i
\(86\) −1.84362e9 1.20852e10i −0.0422600 0.277020i
\(87\) 4.17036e10i 0.897051i
\(88\) 4.82628e10 2.35614e10i 0.974895 0.475935i
\(89\) 3.11065e10i 0.590482i 0.955423 + 0.295241i \(0.0953999\pi\)
−0.955423 + 0.295241i \(0.904600\pi\)
\(90\) −4.89762e10 + 7.47143e9i −0.874281 + 0.133374i
\(91\) −1.37341e11 1.37341e11i −2.30712 2.30712i
\(92\) −4.47065e9 + 1.39652e9i −0.0707193 + 0.0220909i
\(93\) −1.31681e10 + 1.31681e10i −0.196276 + 0.196276i
\(94\) 6.28922e10 + 4.62433e10i 0.883880 + 0.649899i
\(95\) 3.06223e10 0.406030
\(96\) −9.28817e10 + 8.77376e10i −1.16262 + 1.09823i
\(97\) −1.12128e9 −0.0132577 −0.00662884 0.999978i \(-0.502110\pi\)
−0.00662884 + 0.999978i \(0.502110\pi\)
\(98\) 1.38685e11 + 1.01972e11i 1.54984 + 1.13957i
\(99\) 1.13075e11 1.13075e11i 1.19502 1.19502i
\(100\) 6.46869e10 2.02065e10i 0.646869 0.202065i
\(101\) −6.44136e10 6.44136e10i −0.609831 0.609831i 0.333071 0.942902i \(-0.391915\pi\)
−0.942902 + 0.333071i \(0.891915\pi\)
\(102\) −4.54281e10 + 6.93017e9i −0.407403 + 0.0621502i
\(103\) 1.57692e11i 1.34031i 0.742220 + 0.670156i \(0.233773\pi\)
−0.742220 + 0.670156i \(0.766227\pi\)
\(104\) 1.03866e11 + 2.12757e11i 0.837126 + 1.71475i
\(105\) 2.03037e11i 1.55251i
\(106\) 7.72973e8 + 5.06693e9i 0.00561024 + 0.0367759i
\(107\) 1.50680e11 + 1.50680e11i 1.03859 + 1.03859i 0.999225 + 0.0393645i \(0.0125334\pi\)
0.0393645 + 0.999225i \(0.487467\pi\)
\(108\) −6.32214e10 + 1.20662e11i −0.414031 + 0.790203i
\(109\) 1.00044e11 1.00044e11i 0.622793 0.622793i −0.323452 0.946245i \(-0.604843\pi\)
0.946245 + 0.323452i \(0.104843\pi\)
\(110\) 6.16272e10 8.38147e10i 0.364849 0.496204i
\(111\) −2.29007e11 −1.28995
\(112\) −1.81525e11 2.62204e11i −0.973277 1.40586i
\(113\) −3.10659e11 −1.58618 −0.793090 0.609105i \(-0.791529\pi\)
−0.793090 + 0.609105i \(0.791529\pi\)
\(114\) 1.39295e11 1.89445e11i 0.677578 0.921525i
\(115\) −6.41524e9 + 6.41524e9i −0.0297423 + 0.0297423i
\(116\) 1.12390e11 + 5.88874e10i 0.496831 + 0.260317i
\(117\) 4.98470e11 + 4.98470e11i 2.10192 + 2.10192i
\(118\) −6.46996e10 4.24114e11i −0.260346 1.70660i
\(119\) 1.14699e11i 0.440608i
\(120\) −8.04896e10 + 2.34040e11i −0.295286 + 0.858604i
\(121\) 5.04814e10i 0.176934i
\(122\) −6.21472e9 + 9.48070e8i −0.0208182 + 0.00317586i
\(123\) 5.15655e10 + 5.15655e10i 0.165151 + 0.165151i
\(124\) 1.68937e10 + 5.40817e10i 0.0517495 + 0.165665i
\(125\) 2.29793e11 2.29793e11i 0.673491 0.673491i
\(126\) −7.65009e11 5.62495e11i −2.14600 1.57791i
\(127\) −1.13068e11 −0.303683 −0.151842 0.988405i \(-0.548520\pi\)
−0.151842 + 0.988405i \(0.548520\pi\)
\(128\) 1.05297e11 + 3.74203e11i 0.270871 + 0.962616i
\(129\) −1.81837e11 −0.448167
\(130\) 3.69481e11 + 2.71672e11i 0.872778 + 0.641736i
\(131\) −4.98223e11 + 4.98223e11i −1.12832 + 1.12832i −0.137868 + 0.990451i \(0.544025\pi\)
−0.990451 + 0.137868i \(0.955975\pi\)
\(132\) −2.38190e11 7.62515e11i −0.517329 1.65612i
\(133\) 4.15010e11 + 4.15010e11i 0.864718 + 0.864718i
\(134\) −4.37997e11 + 6.68175e10i −0.875780 + 0.133602i
\(135\) 2.63866e11i 0.506463i
\(136\) −4.54700e10 + 1.32213e11i −0.0838033 + 0.243675i
\(137\) 1.09163e11i 0.193246i −0.995321 0.0966231i \(-0.969196\pi\)
0.995321 0.0966231i \(-0.0308041\pi\)
\(138\) 1.05062e10 + 6.88697e10i 0.0178695 + 0.117137i
\(139\) −3.81502e11 3.81502e11i −0.623614 0.623614i 0.322840 0.946454i \(-0.395362\pi\)
−0.946454 + 0.322840i \(0.895362\pi\)
\(140\) −5.47179e11 2.86698e11i −0.859856 0.450526i
\(141\) 8.21045e11 8.21045e11i 1.24069 1.24069i
\(142\) 3.22966e10 4.39242e10i 0.0469429 0.0638437i
\(143\) −1.48028e12 −2.07012
\(144\) 6.58834e11 + 9.51657e11i 0.886711 + 1.28082i
\(145\) 2.45777e11 0.318433
\(146\) −5.37989e11 + 7.31680e11i −0.671170 + 0.912810i
\(147\) 1.81051e12 1.81051e12i 2.17548 2.17548i
\(148\) −3.23369e11 + 6.17168e11i −0.374333 + 0.714437i
\(149\) 9.96155e11 + 9.96155e11i 1.11123 + 1.11123i 0.992985 + 0.118241i \(0.0377256\pi\)
0.118241 + 0.992985i \(0.462274\pi\)
\(150\) −1.52017e11 9.96491e11i −0.163452 1.07145i
\(151\) 7.33435e11i 0.760306i 0.924924 + 0.380153i \(0.124129\pi\)
−0.924924 + 0.380153i \(0.875871\pi\)
\(152\) −3.13859e11 6.42902e11i −0.313758 0.642695i
\(153\) 4.16295e11i 0.401419i
\(154\) 1.97111e12 3.00697e11i 1.83378 0.279747i
\(155\) 7.76054e10 + 7.76054e10i 0.0696735 + 0.0696735i
\(156\) 3.36140e12 1.05002e12i 2.91297 0.909936i
\(157\) −1.44765e12 + 1.44765e12i −1.21120 + 1.21120i −0.240569 + 0.970632i \(0.577334\pi\)
−0.970632 + 0.240569i \(0.922666\pi\)
\(158\) 6.01782e11 + 4.42477e11i 0.486211 + 0.357501i
\(159\) 7.62388e10 0.0594966
\(160\) 5.17076e11 + 5.47393e11i 0.389848 + 0.412704i
\(161\) −1.73886e11 −0.126684
\(162\) −1.49946e11 1.10252e11i −0.105585 0.0776344i
\(163\) −3.22436e11 + 3.22436e11i −0.219488 + 0.219488i −0.808283 0.588795i \(-0.799603\pi\)
0.588795 + 0.808283i \(0.299603\pi\)
\(164\) 2.11780e11 6.61548e10i 0.139394 0.0435432i
\(165\) −1.09418e12 1.09418e12i −0.696512 0.696512i
\(166\) −1.38900e12 + 2.11895e11i −0.855276 + 0.130474i
\(167\) 2.78508e12i 1.65920i 0.558361 + 0.829598i \(0.311430\pi\)
−0.558361 + 0.829598i \(0.688570\pi\)
\(168\) −4.26268e12 + 2.08100e12i −2.45743 + 1.19970i
\(169\) 4.73338e12i 2.64116i
\(170\) 4.08425e10 + 2.67728e11i 0.0220619 + 0.144619i
\(171\) −1.50626e12 1.50626e12i −0.787809 0.787809i
\(172\) −2.56763e11 + 4.90047e11i −0.130055 + 0.248217i
\(173\) 1.03081e12 1.03081e12i 0.505740 0.505740i −0.407476 0.913216i \(-0.633591\pi\)
0.913216 + 0.407476i \(0.133591\pi\)
\(174\) 1.11800e12 1.52051e12i 0.531398 0.722715i
\(175\) 2.51599e12 1.15878
\(176\) −2.39129e12 4.34791e11i −1.06737 0.194071i
\(177\) −6.38136e12 −2.76096
\(178\) 8.33909e11 1.13414e12i 0.349791 0.475726i
\(179\) 1.53907e12 1.53907e12i 0.625990 0.625990i −0.321066 0.947057i \(-0.604041\pi\)
0.947057 + 0.321066i \(0.104041\pi\)
\(180\) 1.98596e12 + 1.04055e12i 0.783378 + 0.410455i
\(181\) −1.04299e12 1.04299e12i −0.399070 0.399070i 0.478835 0.877905i \(-0.341059\pi\)
−0.877905 + 0.478835i \(0.841059\pi\)
\(182\) 1.32557e12 + 8.68927e12i 0.492050 + 3.22545i
\(183\) 9.35088e10i 0.0336799i
\(184\) 2.00437e11 + 6.89332e10i 0.0700617 + 0.0240952i
\(185\) 1.34964e12i 0.457903i
\(186\) 8.33120e11 1.27094e11i 0.274401 0.0418606i
\(187\) −6.18124e11 6.18124e11i −0.197673 0.197673i
\(188\) −1.05334e12 3.37205e12i −0.327115 1.04719i
\(189\) −3.57606e12 + 3.57606e12i −1.07861 + 1.07861i
\(190\) −1.11648e12 8.20927e11i −0.327120 0.240525i
\(191\) −5.44868e11 −0.155099 −0.0775494 0.996989i \(-0.524710\pi\)
−0.0775494 + 0.996989i \(0.524710\pi\)
\(192\) 5.73854e12 7.08914e11i 1.58725 0.196082i
\(193\) 4.82936e12 1.29815 0.649074 0.760725i \(-0.275157\pi\)
0.649074 + 0.760725i \(0.275157\pi\)
\(194\) 4.08815e10 + 3.00593e10i 0.0106811 + 0.00785362i
\(195\) 4.82350e12 4.82350e12i 1.22510 1.22510i
\(196\) −2.32275e12 7.43580e12i −0.573581 1.83620i
\(197\) 1.97463e12 + 1.97463e12i 0.474156 + 0.474156i 0.903257 0.429101i \(-0.141169\pi\)
−0.429101 + 0.903257i \(0.641169\pi\)
\(198\) −7.15404e12 + 1.09137e12i −1.67068 + 0.254866i
\(199\) 8.29074e11i 0.188322i −0.995557 0.0941610i \(-0.969983\pi\)
0.995557 0.0941610i \(-0.0300169\pi\)
\(200\) −2.90017e12 9.97410e11i −0.640854 0.220399i
\(201\) 6.59026e12i 1.41685i
\(202\) 6.21700e11 + 4.07532e12i 0.130061 + 0.852568i
\(203\) 3.33091e12 + 3.33091e12i 0.678165 + 0.678165i
\(204\) 1.84209e12 + 9.65172e11i 0.365043 + 0.191267i
\(205\) 3.03898e11 3.03898e11i 0.0586248 0.0586248i
\(206\) 4.22744e12 5.74944e12i 0.793977 1.07983i
\(207\) 6.31109e11 0.115416
\(208\) 1.91669e12 1.05416e13i 0.341353 1.87740i
\(209\) 4.47305e12 0.775889
\(210\) −5.44305e12 + 7.40270e12i −0.919679 + 1.25079i
\(211\) −6.62494e12 + 6.62494e12i −1.09051 + 1.09051i −0.0950325 + 0.995474i \(0.530296\pi\)
−0.995474 + 0.0950325i \(0.969704\pi\)
\(212\) 1.07653e11 2.05462e11i 0.0172655 0.0329521i
\(213\) −5.73422e11 5.73422e11i −0.0896162 0.0896162i
\(214\) −1.45431e12 9.53321e12i −0.221504 1.45199i
\(215\) 1.07165e12i 0.159089i
\(216\) 5.53976e12 2.70446e12i 0.801670 0.391368i
\(217\) 2.10350e12i 0.296767i
\(218\) −6.32957e12 + 9.65590e11i −0.870689 + 0.132826i
\(219\) 9.55194e12 + 9.55194e12i 1.28129 + 1.28129i
\(220\) −4.49384e12 + 1.40376e12i −0.587885 + 0.183640i
\(221\) 2.72488e12 2.72488e12i 0.347689 0.347689i
\(222\) 8.34957e12 + 6.13926e12i 1.03926 + 0.764143i
\(223\) 4.00358e12 0.486152 0.243076 0.970007i \(-0.421844\pi\)
0.243076 + 0.970007i \(0.421844\pi\)
\(224\) −4.10861e11 + 1.44263e13i −0.0486777 + 1.70919i
\(225\) −9.13166e12 −1.05571
\(226\) 1.13266e13 + 8.32820e12i 1.27792 + 0.939625i
\(227\) −3.84203e12 + 3.84203e12i −0.423076 + 0.423076i −0.886261 0.463185i \(-0.846706\pi\)
0.463185 + 0.886261i \(0.346706\pi\)
\(228\) −1.01574e13 + 3.17290e12i −1.09179 + 0.341047i
\(229\) 2.03856e12 + 2.03856e12i 0.213909 + 0.213909i 0.805926 0.592017i \(-0.201668\pi\)
−0.592017 + 0.805926i \(0.701668\pi\)
\(230\) 4.05880e11 6.19179e10i 0.0415809 0.00634327i
\(231\) 2.96580e13i 2.96672i
\(232\) −2.51906e12 5.16000e12i −0.246068 0.504041i
\(233\) 1.18553e13i 1.13098i −0.824754 0.565491i \(-0.808687\pi\)
0.824754 0.565491i \(-0.191313\pi\)
\(234\) −4.81108e12 3.15372e13i −0.448286 2.93857i
\(235\) −4.83878e12 4.83878e12i −0.440416 0.440416i
\(236\) −9.01078e12 + 1.71976e13i −0.801210 + 1.52916i
\(237\) 7.85614e12 7.85614e12i 0.682485 0.682485i
\(238\) −3.07488e12 + 4.18192e12i −0.261008 + 0.354979i
\(239\) −4.13763e11 −0.0343213 −0.0171606 0.999853i \(-0.505463\pi\)
−0.0171606 + 0.999853i \(0.505463\pi\)
\(240\) 9.20882e12 6.37528e12i 0.746521 0.516818i
\(241\) −6.66336e12 −0.527958 −0.263979 0.964528i \(-0.585035\pi\)
−0.263979 + 0.964528i \(0.585035\pi\)
\(242\) 1.35332e12 1.84055e12i 0.104813 0.142548i
\(243\) −1.02892e13 + 1.02892e13i −0.779018 + 0.779018i
\(244\) 2.52004e11 + 1.32039e11i 0.0186536 + 0.00977366i
\(245\) −1.06701e13 1.06701e13i −0.772247 0.772247i
\(246\) −4.97694e11 3.26245e12i −0.0352224 0.230887i
\(247\) 1.97186e13i 1.36472i
\(248\) 8.33888e11 2.42470e12i 0.0564448 0.164125i
\(249\) 2.08993e13i 1.38368i
\(250\) −1.45386e13 + 2.21789e12i −0.941567 + 0.143638i
\(251\) −4.35293e12 4.35293e12i −0.275788 0.275788i 0.555637 0.831425i \(-0.312475\pi\)
−0.831425 + 0.555637i \(0.812475\pi\)
\(252\) 1.28127e13 + 4.10170e13i 0.794212 + 2.54250i
\(253\) −9.37086e11 + 9.37086e11i −0.0568351 + 0.0568351i
\(254\) 4.12246e12 + 3.03116e12i 0.244664 + 0.179897i
\(255\) 4.02833e12 0.233966
\(256\) 6.19258e12 1.64662e13i 0.352007 0.935997i
\(257\) 8.08461e12 0.449808 0.224904 0.974381i \(-0.427793\pi\)
0.224904 + 0.974381i \(0.427793\pi\)
\(258\) 6.62977e12 + 4.87473e12i 0.361069 + 0.265486i
\(259\) −1.82911e13 + 1.82911e13i −0.975193 + 0.975193i
\(260\) −6.18821e12 1.98102e13i −0.323007 1.03404i
\(261\) −1.20894e13 1.20894e13i −0.617847 0.617847i
\(262\) 3.15216e13 4.80869e12i 1.57743 0.240641i
\(263\) 1.83271e13i 0.898127i −0.893500 0.449064i \(-0.851758\pi\)
0.893500 0.449064i \(-0.148242\pi\)
\(264\) −1.17573e13 + 3.41866e13i −0.564267 + 1.64072i
\(265\) 4.49309e11i 0.0211199i
\(266\) −4.00555e12 2.62569e13i −0.184422 1.20891i
\(267\) −1.48060e13 1.48060e13i −0.667767 0.667767i
\(268\) 1.77606e13 + 9.30575e12i 0.784722 + 0.411159i
\(269\) −8.88707e12 + 8.88707e12i −0.384699 + 0.384699i −0.872792 0.488093i \(-0.837693\pi\)
0.488093 + 0.872792i \(0.337693\pi\)
\(270\) 7.07377e12 9.62052e12i 0.300020 0.408036i
\(271\) −3.04500e13 −1.26548 −0.632742 0.774363i \(-0.718071\pi\)
−0.632742 + 0.774363i \(0.718071\pi\)
\(272\) 5.20223e12 3.60151e12i 0.211866 0.146675i
\(273\) 1.30742e14 5.21819
\(274\) −2.92645e12 + 3.98005e12i −0.114476 + 0.155690i
\(275\) 1.35589e13 1.35589e13i 0.519870 0.519870i
\(276\) 1.46322e12 2.79263e12i 0.0549931 0.104958i
\(277\) −1.57011e13 1.57011e13i −0.578486 0.578486i 0.356000 0.934486i \(-0.384140\pi\)
−0.934486 + 0.356000i \(0.884140\pi\)
\(278\) 3.68214e12 + 2.41369e13i 0.133001 + 0.871836i
\(279\) 7.63456e12i 0.270371i
\(280\) 1.22642e13 + 2.51218e13i 0.425865 + 0.872333i
\(281\) 2.15542e13i 0.733919i −0.930237 0.366959i \(-0.880399\pi\)
0.930237 0.366959i \(-0.119601\pi\)
\(282\) −5.19459e13 + 7.92447e12i −1.73453 + 0.264606i
\(283\) −9.93257e12 9.93257e12i −0.325264 0.325264i 0.525518 0.850782i \(-0.323871\pi\)
−0.850782 + 0.525518i \(0.823871\pi\)
\(284\) −2.35506e12 + 7.35659e11i −0.0756398 + 0.0236279i
\(285\) −1.45755e13 + 1.45755e13i −0.459173 + 0.459173i
\(286\) 5.39708e13 + 3.96836e13i 1.66781 + 1.22630i
\(287\) 8.23719e12 0.249706
\(288\) 1.49120e12 5.23594e13i 0.0443482 1.55717i
\(289\) −3.19962e13 −0.933599
\(290\) −8.96101e12 6.58884e12i −0.256548 0.188634i
\(291\) 5.33701e11 5.33701e11i 0.0149929 0.0149929i
\(292\) 3.92300e13 1.22545e13i 1.08147 0.337822i
\(293\) 3.63841e13 + 3.63841e13i 0.984327 + 0.984327i 0.999879 0.0155521i \(-0.00495060\pi\)
−0.0155521 + 0.999879i \(0.504951\pi\)
\(294\) −1.14547e14 + 1.74745e13i −3.04141 + 0.463974i
\(295\) 3.76082e13i 0.980079i
\(296\) 2.83351e13 1.38329e13i 0.724805 0.353843i
\(297\) 3.85434e13i 0.967809i
\(298\) −9.61458e12 6.30248e13i −0.236996 1.55354i
\(299\) −4.13097e12 4.13097e12i −0.0999678 0.0999678i
\(300\) −2.11716e13 + 4.04072e13i −0.503022 + 0.960046i
\(301\) −1.45236e13 + 1.45236e13i −0.338811 + 0.338811i
\(302\) 1.96620e13 2.67409e13i 0.450392 0.612545i
\(303\) 6.13187e13 1.37930
\(304\) −5.79179e12 + 3.18541e13i −0.127940 + 0.703657i
\(305\) 5.51088e11 0.0119556
\(306\) 1.11601e13 1.51781e13i 0.237794 0.323406i
\(307\) −4.26294e13 + 4.26294e13i −0.892171 + 0.892171i −0.994727 0.102556i \(-0.967298\pi\)
0.102556 + 0.994727i \(0.467298\pi\)
\(308\) −7.99275e13 4.18785e13i −1.64311 0.860918i
\(309\) −7.50578e13 7.50578e13i −1.51574 1.51574i
\(310\) −7.49023e11 4.90994e12i −0.0148596 0.0974063i
\(311\) 5.98356e13i 1.16621i −0.812396 0.583106i \(-0.801837\pi\)
0.812396 0.583106i \(-0.198163\pi\)
\(312\) −1.50705e14 5.18297e13i −2.88588 0.992495i
\(313\) 6.26571e13i 1.17890i 0.807805 + 0.589449i \(0.200655\pi\)
−0.807805 + 0.589449i \(0.799345\pi\)
\(314\) 9.15901e13 1.39723e13i 1.69331 0.258318i
\(315\) 5.88581e13 + 5.88581e13i 1.06930 + 1.06930i
\(316\) −1.00789e13 3.22653e13i −0.179942 0.576046i
\(317\) 8.32656e12 8.32656e12i 0.146096 0.146096i −0.630275 0.776372i \(-0.717058\pi\)
0.776372 + 0.630275i \(0.217058\pi\)
\(318\) −2.77966e12 2.04382e12i −0.0479338 0.0352447i
\(319\) 3.59012e13 0.608499
\(320\) −4.17794e12 3.38197e13i −0.0696045 0.563437i
\(321\) −1.43440e14 −2.34905
\(322\) 6.33985e12 + 4.66156e12i 0.102064 + 0.0750454i
\(323\) −8.23395e12 + 8.23395e12i −0.130315 + 0.130315i
\(324\) 2.51135e12 + 8.03955e12i 0.0390759 + 0.125093i
\(325\) 5.97719e13 + 5.97719e13i 0.914404 + 0.914404i
\(326\) 2.03999e13 3.11205e12i 0.306853 0.0468112i
\(327\) 9.52368e13i 1.40862i
\(328\) −9.49497e12 3.26545e12i −0.138098 0.0474939i
\(329\) 1.31156e14i 1.87590i
\(330\) 1.05607e13 + 6.92269e13i 0.148548 + 0.973752i
\(331\) 8.11137e13 + 8.11137e13i 1.12212 + 1.12212i 0.991422 + 0.130701i \(0.0417227\pi\)
0.130701 + 0.991422i \(0.458277\pi\)
\(332\) 5.63231e13 + 2.95108e13i 0.766350 + 0.401533i
\(333\) 6.63865e13 6.63865e13i 0.888457 0.888457i
\(334\) 7.46630e13 1.01544e14i 0.982879 1.33674i
\(335\) 3.88393e13 0.502950
\(336\) 2.11205e14 + 3.84017e13i 2.69053 + 0.489198i
\(337\) −5.00143e13 −0.626801 −0.313401 0.949621i \(-0.601468\pi\)
−0.313401 + 0.949621i \(0.601468\pi\)
\(338\) −1.26893e14 + 1.72578e14i −1.56458 + 2.12787i
\(339\) 1.47866e14 1.47866e14i 1.79379 1.79379i
\(340\) 5.68818e12 1.08562e13i 0.0678953 0.129582i
\(341\) 1.13360e13 + 1.13360e13i 0.133140 + 0.133140i
\(342\) 1.45379e13 + 9.52980e13i 0.168019 + 1.10139i
\(343\) 1.38872e14i 1.57942i
\(344\) 2.24988e13 1.09837e13i 0.251819 0.122936i
\(345\) 6.10700e12i 0.0672703i
\(346\) −6.52176e13 + 9.94910e12i −0.707044 + 0.107861i
\(347\) −7.02184e13 7.02184e13i −0.749271 0.749271i 0.225072 0.974342i \(-0.427738\pi\)
−0.974342 + 0.225072i \(0.927738\pi\)
\(348\) −8.15240e13 + 2.54660e13i −0.856248 + 0.267470i
\(349\) −8.07392e13 + 8.07392e13i −0.834728 + 0.834728i −0.988159 0.153432i \(-0.950968\pi\)
0.153432 + 0.988159i \(0.450968\pi\)
\(350\) −9.17327e13 6.74492e13i −0.933577 0.686440i
\(351\) −1.69911e14 −1.70229
\(352\) 7.55303e13 + 7.99587e13i 0.744967 + 0.788644i
\(353\) −5.65562e13 −0.549186 −0.274593 0.961561i \(-0.588543\pi\)
−0.274593 + 0.961561i \(0.588543\pi\)
\(354\) 2.32664e14 + 1.71073e14i 2.22439 + 1.63555i
\(355\) −3.37943e12 + 3.37943e12i −0.0318117 + 0.0318117i
\(356\) −6.08084e13 + 1.89950e13i −0.563623 + 0.176061i
\(357\) 5.45941e13 + 5.45941e13i 0.498277 + 0.498277i
\(358\) −9.73742e13 + 1.48547e13i −0.875159 + 0.133508i
\(359\) 1.91411e13i 0.169413i −0.996406 0.0847065i \(-0.973005\pi\)
0.996406 0.0847065i \(-0.0269953\pi\)
\(360\) −4.45124e13 9.11784e13i −0.387987 0.794746i
\(361\) 5.69053e13i 0.488499i
\(362\) 1.00666e13 + 6.59881e13i 0.0851113 + 0.557916i
\(363\) −2.40280e13 2.40280e13i −0.200092 0.200092i
\(364\) 1.84613e14 3.52345e14i 1.51428 2.89009i
\(365\) 5.62938e13 5.62938e13i 0.454831 0.454831i
\(366\) 2.50680e12 3.40932e12i 0.0199514 0.0271345i
\(367\) −1.09458e14 −0.858189 −0.429095 0.903260i \(-0.641167\pi\)
−0.429095 + 0.903260i \(0.641167\pi\)
\(368\) −5.45995e12 7.88666e12i −0.0421721 0.0609158i
\(369\) −2.98965e13 −0.227496
\(370\) 3.61814e13 4.92077e13i 0.271254 0.368913i
\(371\) 6.08929e12 6.08929e12i 0.0449790 0.0449790i
\(372\) −3.37826e13 1.77006e13i −0.245871 0.128825i
\(373\) −8.82988e13 8.82988e13i −0.633222 0.633222i 0.315652 0.948875i \(-0.397777\pi\)
−0.948875 + 0.315652i \(0.897777\pi\)
\(374\) 5.96594e12 + 3.91075e13i 0.0421585 + 0.276354i
\(375\) 2.18752e14i 1.52328i
\(376\) −5.19938e13 + 1.51183e14i −0.356795 + 1.03745i
\(377\) 1.58264e14i 1.07029i
\(378\) 2.26250e14 3.45150e13i 1.50794 0.230040i
\(379\) −8.73807e13 8.73807e13i −0.573984 0.573984i 0.359255 0.933239i \(-0.383031\pi\)
−0.933239 + 0.359255i \(0.883031\pi\)
\(380\) 1.86993e13 + 5.98618e13i 0.121064 + 0.387561i
\(381\) 5.38179e13 5.38179e13i 0.343431 0.343431i
\(382\) 1.98658e13 + 1.46069e13i 0.124956 + 0.0918778i
\(383\) 2.54041e14 1.57511 0.787555 0.616245i \(-0.211347\pi\)
0.787555 + 0.616245i \(0.211347\pi\)
\(384\) −2.28231e14 1.27993e14i −1.39493 0.782283i
\(385\) −1.74788e14 −1.05312
\(386\) −1.76078e14 1.29466e14i −1.04586 0.769000i
\(387\) 5.27126e13 5.27126e13i 0.308677 0.308677i
\(388\) −6.84699e11 2.19192e12i −0.00395299 0.0126546i
\(389\) 2.20478e14 + 2.20478e14i 1.25499 + 1.25499i 0.953453 + 0.301540i \(0.0975008\pi\)
0.301540 + 0.953453i \(0.402499\pi\)
\(390\) −3.05174e14 + 4.65550e13i −1.71274 + 0.261283i
\(391\) 3.44996e12i 0.0190916i
\(392\) −1.14653e14 + 3.33377e14i −0.625622 + 1.81912i
\(393\) 4.74285e14i 2.55200i
\(394\) −1.90585e13 1.24931e14i −0.101125 0.662889i
\(395\) −4.62997e13 4.62997e13i −0.242267 0.242267i
\(396\) 2.90093e14 + 1.51996e14i 1.49697 + 0.784346i
\(397\) 3.45645e13 3.45645e13i 0.175907 0.175907i −0.613662 0.789569i \(-0.710304\pi\)
0.789569 + 0.613662i \(0.210304\pi\)
\(398\) −2.22260e13 + 3.02279e13i −0.111559 + 0.151723i
\(399\) −3.95070e14 −1.95579
\(400\) 7.90012e13 + 1.14114e14i 0.385748 + 0.557196i
\(401\) 1.54405e14 0.743646 0.371823 0.928304i \(-0.378733\pi\)
0.371823 + 0.928304i \(0.378733\pi\)
\(402\) 1.76673e14 2.40280e14i 0.839318 1.14150i
\(403\) −4.99725e13 + 4.99725e13i −0.234182 + 0.234182i
\(404\) 8.65848e13 1.65252e14i 0.400262 0.763923i
\(405\) 1.15365e13 + 1.15365e13i 0.0526103 + 0.0526103i
\(406\) −3.21489e13 2.10740e14i −0.144635 0.948101i
\(407\) 1.97144e14i 0.875014i
\(408\) −4.12878e13 8.45731e13i −0.180797 0.370341i
\(409\) 2.08138e14i 0.899236i −0.893221 0.449618i \(-0.851560\pi\)
0.893221 0.449618i \(-0.148440\pi\)
\(410\) −1.92270e13 + 2.93313e12i −0.0819598 + 0.0125032i
\(411\) 5.19588e13 + 5.19588e13i 0.218539 + 0.218539i
\(412\) −3.08264e14 + 9.62938e13i −1.27935 + 0.399635i
\(413\) −5.09687e14 + 5.09687e14i −2.08727 + 2.08727i
\(414\) −2.30102e13 1.69189e13i −0.0929861 0.0683707i
\(415\) 1.23169e14 0.491175
\(416\) −3.52483e14 + 3.32961e14i −1.38715 + 1.31033i
\(417\) 3.63172e14 1.41047
\(418\) −1.63087e14 1.19914e14i −0.625100 0.459623i
\(419\) 2.92778e14 2.92778e14i 1.10755 1.10755i 0.114073 0.993472i \(-0.463610\pi\)
0.993472 0.114073i \(-0.0363899\pi\)
\(420\) 3.96906e14 1.23983e14i 1.48189 0.462905i
\(421\) 1.64588e14 + 1.64588e14i 0.606521 + 0.606521i 0.942035 0.335515i \(-0.108910\pi\)
−0.335515 + 0.942035i \(0.608910\pi\)
\(422\) 4.19147e14 6.39418e13i 1.52457 0.232577i
\(423\) 4.76023e14i 1.70905i
\(424\) −9.43306e12 + 4.60513e12i −0.0334303 + 0.0163204i
\(425\) 4.99182e13i 0.174630i
\(426\) 5.53449e12 + 3.62793e13i 0.0191128 + 0.125287i
\(427\) 7.46866e12 + 7.46866e12i 0.0254618 + 0.0254618i
\(428\) −2.02544e14 + 3.86567e14i −0.681677 + 1.30102i
\(429\) 7.04578e14 7.04578e14i 2.34107 2.34107i
\(430\) 2.87289e13 3.90722e13i 0.0942417 0.128171i
\(431\) 2.93359e14 0.950113 0.475056 0.879955i \(-0.342428\pi\)
0.475056 + 0.879955i \(0.342428\pi\)
\(432\) −2.74481e14 4.99067e13i −0.877710 0.159587i
\(433\) 2.65581e14 0.838519 0.419260 0.907866i \(-0.362290\pi\)
0.419260 + 0.907866i \(0.362290\pi\)
\(434\) 5.63911e13 7.66935e13i 0.175799 0.239092i
\(435\) −1.16984e14 + 1.16984e14i −0.360111 + 0.360111i
\(436\) 2.56661e14 + 1.34479e14i 0.780160 + 0.408769i
\(437\) 1.24828e13 + 1.24828e13i 0.0374683 + 0.0374683i
\(438\) −9.21923e13 6.04333e14i −0.273267 1.79130i
\(439\) 4.88728e14i 1.43058i 0.698828 + 0.715290i \(0.253705\pi\)
−0.698828 + 0.715290i \(0.746295\pi\)
\(440\) 2.01477e14 + 6.92907e13i 0.582419 + 0.200302i
\(441\) 1.04969e15i 2.99674i
\(442\) −1.72398e14 + 2.62997e13i −0.486083 + 0.0741530i
\(443\) −2.17621e14 2.17621e14i −0.606010 0.606010i 0.335891 0.941901i \(-0.390963\pi\)
−0.941901 + 0.335891i \(0.890963\pi\)
\(444\) −1.39842e14 4.47673e14i −0.384619 1.23127i
\(445\) −8.72581e13 + 8.72581e13i −0.237042 + 0.237042i
\(446\) −1.45970e14 1.07329e14i −0.391671 0.287988i
\(447\) −9.48293e14 −2.51334
\(448\) 4.01722e14 5.14966e14i 1.05171 1.34818i
\(449\) −2.88213e14 −0.745346 −0.372673 0.927963i \(-0.621559\pi\)
−0.372673 + 0.927963i \(0.621559\pi\)
\(450\) 3.32939e14 + 2.44803e14i 0.850543 + 0.625386i
\(451\) 4.43909e13 4.43909e13i 0.112027 0.112027i
\(452\) −1.89702e14 6.07290e14i −0.472944 1.51403i
\(453\) −3.49098e14 3.49098e14i −0.859818 0.859818i
\(454\) 2.43078e14 3.70821e13i 0.591477 0.0902312i
\(455\) 7.70518e14i 1.85234i
\(456\) 4.55396e14 + 1.56617e14i 1.08164 + 0.371991i
\(457\) 7.33246e14i 1.72072i −0.509685 0.860361i \(-0.670238\pi\)
0.509685 0.860361i \(-0.329762\pi\)
\(458\) −1.96755e13 1.28976e14i −0.0456212 0.299053i
\(459\) −7.09503e13 7.09503e13i −0.162549 0.162549i
\(460\) −1.64582e13 8.62337e12i −0.0372576 0.0195213i
\(461\) 1.64165e13 1.64165e13i 0.0367220 0.0367220i −0.688507 0.725229i \(-0.741734\pi\)
0.725229 + 0.688507i \(0.241734\pi\)
\(462\) −7.95077e14 + 1.08133e15i −1.75743 + 2.39015i
\(463\) 5.07863e14 1.10931 0.554653 0.832082i \(-0.312851\pi\)
0.554653 + 0.832082i \(0.312851\pi\)
\(464\) −4.64855e13 + 2.55664e14i −0.100339 + 0.551850i
\(465\) −7.38767e13 −0.157585
\(466\) −3.17820e14 + 4.32244e14i −0.669975 + 0.911184i
\(467\) −5.51057e14 + 5.51057e14i −1.14803 + 1.14803i −0.161093 + 0.986939i \(0.551502\pi\)
−0.986939 + 0.161093i \(0.948498\pi\)
\(468\) −6.70045e14 + 1.27882e15i −1.37959 + 2.63304i
\(469\) 5.26372e14 + 5.26372e14i 1.07113 + 1.07113i
\(470\) 4.67024e13 + 3.06140e14i 0.0939293 + 0.615718i
\(471\) 1.37810e15i 2.73946i
\(472\) 7.89568e14 3.85460e14i 1.55135 0.757353i
\(473\) 1.56538e14i 0.304006i
\(474\) −4.97043e14 + 7.58250e13i −0.954141 + 0.145557i
\(475\) −1.80616e14 1.80616e14i −0.342722 0.342722i
\(476\) 2.24219e14 7.00403e13i 0.420566 0.131374i
\(477\) −2.21007e13 + 2.21007e13i −0.0409785 + 0.0409785i
\(478\) 1.50857e13 + 1.10922e13i 0.0276512 + 0.0203313i
\(479\) −3.92439e14 −0.711094 −0.355547 0.934658i \(-0.615705\pi\)
−0.355547 + 0.934658i \(0.615705\pi\)
\(480\) −5.06662e14 1.44297e13i −0.907594 0.0258483i
\(481\) −8.69074e14 −1.53907
\(482\) 2.42945e14 + 1.78632e14i 0.425353 + 0.312753i
\(483\) 8.27655e13 8.27655e13i 0.143265 0.143265i
\(484\) −9.86834e13 + 3.08261e13i −0.168886 + 0.0527557i
\(485\) −3.14533e12 3.14533e12i −0.00532215 0.00532215i
\(486\) 6.50978e14 9.93082e13i 1.08910 0.166144i
\(487\) 3.30426e14i 0.546594i −0.961930 0.273297i \(-0.911886\pi\)
0.961930 0.273297i \(-0.0881141\pi\)
\(488\) −5.64830e12 1.15699e13i −0.00923866 0.0189243i
\(489\) 3.06944e14i 0.496432i
\(490\) 1.02985e14 + 6.75078e14i 0.164700 + 1.07963i
\(491\) 4.42264e14 + 4.42264e14i 0.699412 + 0.699412i 0.964284 0.264871i \(-0.0853295\pi\)
−0.264871 + 0.964284i \(0.585330\pi\)
\(492\) −6.93144e13 + 1.32291e14i −0.108396 + 0.206881i
\(493\) −6.60865e13 + 6.60865e13i −0.102201 + 0.102201i
\(494\) 5.28620e14 7.18938e14i 0.808436 1.09949i
\(495\) 6.34383e14 0.959451
\(496\) −9.54053e13 + 6.60492e13i −0.142700 + 0.0987913i
\(497\) −9.15998e13 −0.135498
\(498\) 5.60272e14 7.61986e14i 0.819668 1.11477i
\(499\) −5.81971e14 + 5.81971e14i −0.842071 + 0.842071i −0.989128 0.147057i \(-0.953020\pi\)
0.147057 + 0.989128i \(0.453020\pi\)
\(500\) 5.89532e14 + 3.08888e14i 0.843669 + 0.442045i
\(501\) −1.32563e15 1.32563e15i −1.87636 1.87636i
\(502\) 4.20131e13 + 2.75401e14i 0.0588185 + 0.385563i
\(503\) 5.90788e14i 0.818102i −0.912512 0.409051i \(-0.865860\pi\)
0.912512 0.409051i \(-0.134140\pi\)
\(504\) 6.32443e14 1.83896e15i 0.866271 2.51886i
\(505\) 3.61378e14i 0.489620i
\(506\) 5.92876e13 9.04446e12i 0.0794577 0.0121215i
\(507\) 2.25298e15 + 2.25298e15i 2.98684 + 2.98684i
\(508\) −6.90445e13 2.21031e14i −0.0905479 0.289870i
\(509\) 1.70291e14 1.70291e14i 0.220924 0.220924i −0.587963 0.808887i \(-0.700070\pi\)
0.808887 + 0.587963i \(0.200070\pi\)
\(510\) −1.46872e14 1.07992e14i −0.188497 0.138598i
\(511\) 1.52585e15 1.93730
\(512\) −6.67210e14 + 4.34345e14i −0.838066 + 0.545569i
\(513\) 5.13432e14 0.638024
\(514\) −2.94764e14 2.16734e14i −0.362391 0.266458i
\(515\) −4.42349e14 + 4.42349e14i −0.538053 + 0.538053i
\(516\) −1.11038e14 3.55464e14i −0.133628 0.427782i
\(517\) −7.06810e14 7.06810e14i −0.841598 0.841598i
\(518\) 1.15724e15 1.76540e14i 1.36336 0.207983i
\(519\) 9.81287e14i 1.14387i
\(520\) −3.05455e14 + 8.88173e14i −0.352313 + 1.02442i
\(521\) 1.56998e15i 1.79179i 0.444266 + 0.895895i \(0.353465\pi\)
−0.444266 + 0.895895i \(0.646535\pi\)
\(522\) 1.16683e14 + 7.64871e14i 0.131771 + 0.863775i
\(523\) −8.14707e14 8.14707e14i −0.910421 0.910421i 0.0858840 0.996305i \(-0.472629\pi\)
−0.996305 + 0.0858840i \(0.972629\pi\)
\(524\) −1.27819e15 6.69712e14i −1.41342 0.740570i
\(525\) −1.19755e15 + 1.19755e15i −1.31044 + 1.31044i
\(526\) −4.91317e14 + 6.68205e14i −0.532035 + 0.723582i
\(527\) −4.17343e13 −0.0447234
\(528\) 1.34515e15 9.31250e14i 1.42654 0.987597i
\(529\) 9.47580e14 0.994511
\(530\) −1.20452e13 + 1.63817e13i −0.0125111 + 0.0170154i
\(531\) 1.84988e15 1.84988e15i 1.90162 1.90162i
\(532\) −5.57857e14 + 1.06470e15i −0.567557 + 1.08322i
\(533\) 1.95689e14 + 1.95689e14i 0.197046 + 0.197046i
\(534\) 1.42903e14 + 9.36745e14i 0.142417 + 0.933564i
\(535\) 8.45355e14i 0.833860i
\(536\) −3.98078e14 8.15415e14i −0.388653 0.796109i
\(537\) 1.46513e15i 1.41585i
\(538\) 5.62268e14 8.57752e13i 0.537824 0.0820464i
\(539\) −1.55861e15 1.55861e15i −1.47570 1.47570i
\(540\) −5.15817e14 + 1.61128e14i −0.483426 + 0.151010i
\(541\) −1.62507e14 + 1.62507e14i −0.150760 + 0.150760i −0.778458 0.627697i \(-0.783998\pi\)
0.627697 + 0.778458i \(0.283998\pi\)
\(542\) 1.11020e15 + 8.16310e14i 1.01955 + 0.749650i
\(543\) 9.92880e14 0.902605
\(544\) −2.86223e14 8.15162e12i −0.257579 0.00733584i
\(545\) 5.61273e14 0.500026
\(546\) −4.76682e15 3.50495e15i −4.20407 3.09116i
\(547\) −3.52073e14 + 3.52073e14i −0.307399 + 0.307399i −0.843900 0.536501i \(-0.819746\pi\)
0.536501 + 0.843900i \(0.319746\pi\)
\(548\) 2.13396e14 6.66594e13i 0.184456 0.0576194i
\(549\) −2.71071e13 2.71071e13i −0.0231972 0.0231972i
\(550\) −8.57845e14 + 1.30866e14i −0.726799 + 0.110875i
\(551\) 4.78235e14i 0.401150i
\(552\) −1.28214e14 + 6.25929e13i −0.106481 + 0.0519829i
\(553\) 1.25496e15i 1.03191i
\(554\) 1.51543e14 + 9.93381e14i 0.123376 + 0.808746i
\(555\) −6.42397e14 6.42397e14i −0.517835 0.517835i
\(556\) 5.12816e14 9.78739e14i 0.409308 0.781188i
\(557\) −8.52294e13 + 8.52294e13i −0.0673575 + 0.0673575i −0.739983 0.672626i \(-0.765166\pi\)
0.672626 + 0.739983i \(0.265166\pi\)
\(558\) −2.04669e14 + 2.78355e14i −0.160163 + 0.217827i
\(559\) −6.90067e14 −0.534720
\(560\) 2.26318e14 1.24472e15i 0.173654 0.955076i
\(561\) 5.88425e14 0.447091
\(562\) −5.77830e14 + 7.85865e14i −0.434761 + 0.591287i
\(563\) −6.50742e14 + 6.50742e14i −0.484856 + 0.484856i −0.906678 0.421823i \(-0.861390\pi\)
0.421823 + 0.906678i \(0.361390\pi\)
\(564\) 2.10638e15 + 1.10365e15i 1.55418 + 0.814322i
\(565\) −8.71441e14 8.71441e14i −0.636754 0.636754i
\(566\) 9.58660e13 + 6.28414e14i 0.0693704 + 0.454732i
\(567\) 3.12698e14i 0.224088i
\(568\) 1.05587e14 + 3.63127e13i 0.0749365 + 0.0257717i
\(569\) 1.48183e15i 1.04155i −0.853693 0.520777i \(-0.825642\pi\)
0.853693 0.520777i \(-0.174358\pi\)
\(570\) 9.22162e14 1.40678e14i 0.641942 0.0979297i
\(571\) 8.55470e14 + 8.55470e14i 0.589802 + 0.589802i 0.937578 0.347776i \(-0.113063\pi\)
−0.347776 + 0.937578i \(0.613063\pi\)
\(572\) −9.03923e14 2.89372e15i −0.617239 1.97596i
\(573\) 2.59345e14 2.59345e14i 0.175399 0.175399i
\(574\) −3.00327e14 2.20824e14i −0.201177 0.147921i
\(575\) 7.56767e13 0.0502099
\(576\) −1.45803e15 + 1.86904e15i −0.958170 + 1.22827i
\(577\) 2.53819e15 1.65218 0.826089 0.563539i \(-0.190561\pi\)
0.826089 + 0.563539i \(0.190561\pi\)
\(578\) 1.16658e15 + 8.57760e14i 0.752161 + 0.553048i
\(579\) −2.29866e15 + 2.29866e15i −1.46806 + 1.46806i
\(580\) 1.50082e14 + 4.80457e14i 0.0949458 + 0.303949i
\(581\) 1.66925e15 + 1.66925e15i 1.04605 + 1.04605i
\(582\) −3.37662e13 + 5.15111e12i −0.0209607 + 0.00319760i
\(583\) 6.56314e13i 0.0403585i
\(584\) −1.75884e15 6.04890e14i −1.07141 0.368473i
\(585\) 2.79656e15i 1.68759i
\(586\) −3.51168e14 2.30195e15i −0.209931 1.37613i
\(587\) 1.49682e14 + 1.49682e14i 0.0886464 + 0.0886464i 0.750039 0.661393i \(-0.230034\pi\)
−0.661393 + 0.750039i \(0.730034\pi\)
\(588\) 4.64484e15 + 2.43369e15i 2.72518 + 1.42787i
\(589\) 1.51005e14 1.51005e14i 0.0877722 0.0877722i
\(590\) 1.00821e15 1.37119e15i 0.580582 0.789607i
\(591\) −1.87975e15 −1.07243
\(592\) −1.40393e15 2.55266e14i −0.793554 0.144286i
\(593\) −2.51255e14 −0.140706 −0.0703532 0.997522i \(-0.522413\pi\)
−0.0703532 + 0.997522i \(0.522413\pi\)
\(594\) 1.03328e15 1.40529e15i 0.573313 0.779722i
\(595\) 3.21747e14 3.21747e14i 0.176877 0.176877i
\(596\) −1.33903e15 + 2.55562e15i −0.729352 + 1.39201i
\(597\) 3.94619e14 + 3.94619e14i 0.212971 + 0.212971i
\(598\) 3.98708e13 + 2.61358e14i 0.0213205 + 0.139759i
\(599\) 1.70110e15i 0.901329i −0.892693 0.450665i \(-0.851187\pi\)
0.892693 0.450665i \(-0.148813\pi\)
\(600\) 1.85516e15 9.05670e14i 0.973978 0.475487i
\(601\) 2.33302e15i 1.21369i −0.794819 0.606847i \(-0.792434\pi\)
0.794819 0.606847i \(-0.207566\pi\)
\(602\) 9.18878e14 1.40177e14i 0.473672 0.0722597i
\(603\) −1.91044e15 1.91044e15i −0.975861 0.975861i
\(604\) −1.43375e15 + 4.47867e14i −0.725723 + 0.226697i
\(605\) −1.41607e14 + 1.41607e14i −0.0710283 + 0.0710283i
\(606\) −2.23567e15 1.64384e15i −1.11124 0.817072i
\(607\) 1.91749e14 0.0944486 0.0472243 0.998884i \(-0.484962\pi\)
0.0472243 + 0.998884i \(0.484962\pi\)
\(608\) 1.06512e15 1.00613e15i 0.519910 0.491116i
\(609\) −3.17087e15 −1.53385
\(610\) −2.00926e13 1.47737e13i −0.00963213 0.00708230i
\(611\) 3.11584e15 3.11584e15i 1.48029 1.48029i
\(612\) −8.13792e14 + 2.54208e14i −0.383160 + 0.119689i
\(613\) −1.21713e14 1.21713e14i −0.0567944 0.0567944i 0.678139 0.734934i \(-0.262787\pi\)
−0.734934 + 0.678139i \(0.762787\pi\)
\(614\) 2.69708e15 4.11445e14i 1.24729 0.190277i
\(615\) 2.89296e14i 0.132596i
\(616\) 1.79146e15 + 3.66960e15i 0.813792 + 1.66696i
\(617\) 5.95192e14i 0.267972i 0.990983 + 0.133986i \(0.0427777\pi\)
−0.990983 + 0.133986i \(0.957222\pi\)
\(618\) 7.24434e14 + 4.74876e15i 0.323268 + 2.11906i
\(619\) 2.40823e15 + 2.40823e15i 1.06512 + 1.06512i 0.997726 + 0.0673975i \(0.0214696\pi\)
0.0673975 + 0.997726i \(0.478530\pi\)
\(620\) −1.04317e14 + 1.99096e14i −0.0457301 + 0.0872786i
\(621\) −1.07562e14 + 1.07562e14i −0.0467363 + 0.0467363i
\(622\) −1.60408e15 + 2.18160e15i −0.690844 + 0.939567i
\(623\) −2.36514e15 −1.00965
\(624\) 4.10524e15 + 5.92984e15i 1.73709 + 2.50916i
\(625\) −3.26546e14 −0.136963
\(626\) 1.67972e15 2.28447e15i 0.698359 0.949788i
\(627\) −2.12907e15 + 2.12907e15i −0.877441 + 0.877441i
\(628\) −3.71394e15 1.94594e15i −1.51725 0.794970i
\(629\) −3.62901e14 3.62901e14i −0.146964 0.146964i
\(630\) −5.68079e14 3.72383e15i −0.228053 1.49492i
\(631\) 4.59339e14i 0.182798i −0.995814 0.0913991i \(-0.970866\pi\)
0.995814 0.0913991i \(-0.0291339\pi\)
\(632\) −4.97501e14 + 1.44659e15i −0.196268 + 0.570690i
\(633\) 6.30663e15i 2.46648i
\(634\) −5.26805e14 + 8.03653e13i −0.204249 + 0.0311586i
\(635\) −3.17172e14 3.17172e14i −0.121910 0.121910i
\(636\) 4.65547e13 + 1.49035e14i 0.0177398 + 0.0567903i
\(637\) 6.87082e15 6.87082e15i 2.59562 2.59562i
\(638\) −1.30895e15 9.62445e14i −0.490241 0.360464i
\(639\) 3.32457e14 0.123447
\(640\) −7.54318e14 + 1.34507e15i −0.277693 + 0.495169i
\(641\) −1.14966e14 −0.0419613 −0.0209807 0.999780i \(-0.506679\pi\)
−0.0209807 + 0.999780i \(0.506679\pi\)
\(642\) 5.22980e15 + 3.84536e15i 1.89253 + 1.39154i
\(643\) 1.76444e14 1.76444e14i 0.0633061 0.0633061i −0.674745 0.738051i \(-0.735746\pi\)
0.738051 + 0.674745i \(0.235746\pi\)
\(644\) −1.06182e14 3.39920e14i −0.0377728 0.120922i
\(645\) −5.10079e14 5.10079e14i −0.179912 0.179912i
\(646\) 5.20946e14 7.94715e13i 0.182185 0.0277928i
\(647\) 2.12407e15i 0.736540i 0.929719 + 0.368270i \(0.120050\pi\)
−0.929719 + 0.368270i \(0.879950\pi\)
\(648\) 1.23962e14 3.60446e14i 0.0426213 0.123930i
\(649\) 5.49350e15i 1.87285i
\(650\) −5.76899e14 3.78165e15i −0.195019 1.27837i
\(651\) −1.00122e15 1.00122e15i −0.335609 0.335609i
\(652\) −8.27205e14 4.33419e14i −0.274948 0.144061i
\(653\) −2.15088e15 + 2.15088e15i −0.708913 + 0.708913i −0.966307 0.257393i \(-0.917136\pi\)
0.257393 + 0.966307i \(0.417136\pi\)
\(654\) 2.55313e15 3.47232e15i 0.834439 1.13486i
\(655\) −2.79517e15 −0.905901
\(656\) 2.58645e14 + 3.73601e14i 0.0831251 + 0.120071i
\(657\) −5.53799e15 −1.76499
\(658\) −3.51605e15 + 4.78192e15i −1.11125 + 1.51133i
\(659\) 3.09422e14 3.09422e14i 0.0969797 0.0969797i −0.656952 0.753932i \(-0.728155\pi\)
0.753932 + 0.656952i \(0.228155\pi\)
\(660\) 1.47080e15 2.80712e15i 0.457155 0.872507i
\(661\) 3.62461e15 + 3.62461e15i 1.11726 + 1.11726i 0.992142 + 0.125115i \(0.0399301\pi\)
0.125115 + 0.992142i \(0.460070\pi\)
\(662\) −7.82884e14 5.13191e15i −0.239320 1.56877i
\(663\) 2.59396e15i 0.786392i
\(664\) −1.26240e15 2.58588e15i −0.379554 0.777470i
\(665\) 2.32832e15i 0.694263i
\(666\) −4.20014e15 + 6.40742e14i −1.24210 + 0.189485i
\(667\) 1.00188e14 + 1.00188e14i 0.0293849 + 0.0293849i
\(668\) −5.44441e15 + 1.70069e15i −1.58373 + 0.494715i
\(669\) −1.90561e15 + 1.90561e15i −0.549782 + 0.549782i
\(670\) −1.41608e15 1.04121e15i −0.405205 0.297939i
\(671\) 8.04985e13 0.0228462
\(672\) −6.67101e15 7.06213e15i −1.87785 1.98795i
\(673\) −3.77117e14 −0.105291 −0.0526457 0.998613i \(-0.516765\pi\)
−0.0526457 + 0.998613i \(0.516765\pi\)
\(674\) 1.82352e15 + 1.34079e15i 0.504987 + 0.371306i
\(675\) 1.55634e15 1.55634e15i 0.427496 0.427496i
\(676\) 9.25302e15 2.89040e15i 2.52102 0.787502i
\(677\) 2.32594e15 + 2.32594e15i 0.628581 + 0.628581i 0.947711 0.319130i \(-0.103391\pi\)
−0.319130 + 0.947711i \(0.603391\pi\)
\(678\) −9.35521e15 + 1.42716e15i −2.50778 + 0.382568i
\(679\) 8.52546e13i 0.0226691i
\(680\) −4.98426e14 + 2.43327e14i −0.131463 + 0.0641788i
\(681\) 3.65743e15i 0.956901i
\(682\) −1.09411e14 7.17205e14i −0.0283954 0.186135i
\(683\) −1.34268e15 1.34268e15i −0.345669 0.345669i 0.512825 0.858493i \(-0.328599\pi\)
−0.858493 + 0.512825i \(0.828599\pi\)
\(684\) 2.02471e15 3.86429e15i 0.517077 0.986872i
\(685\) 3.06216e14 3.06216e14i 0.0775765 0.0775765i
\(686\) −3.72290e15 + 5.06325e15i −0.935619 + 1.27247i
\(687\) −1.94061e15 −0.483812
\(688\) −1.11476e15 2.02688e14i −0.275705 0.0501292i
\(689\) 2.89324e14 0.0709869
\(690\) −1.63718e14 + 2.22660e14i −0.0398497 + 0.0541967i
\(691\) 1.81110e15 1.81110e15i 0.437333 0.437333i −0.453781 0.891113i \(-0.649925\pi\)
0.891113 + 0.453781i \(0.149925\pi\)
\(692\) 2.64454e15 + 1.38562e15i 0.633530 + 0.331941i
\(693\) 8.59751e15 + 8.59751e15i 2.04334 + 2.04334i
\(694\) 6.77726e14 + 4.44258e15i 0.159800 + 1.04751i
\(695\) 2.14033e15i 0.500685i
\(696\) 3.65505e15 + 1.25702e15i 0.848287 + 0.291738i
\(697\) 1.63429e14i 0.0376312i
\(698\) 5.10821e15 7.79270e14i 1.16698 0.178026i
\(699\) 5.64286e15 + 5.64286e15i 1.27901 + 1.27901i
\(700\) 1.53637e15 + 4.91837e15i 0.345508 + 1.10607i
\(701\) −3.18446e15 + 3.18446e15i −0.710537 + 0.710537i −0.966648 0.256110i \(-0.917559\pi\)
0.256110 + 0.966648i \(0.417559\pi\)
\(702\) 6.19495e15 + 4.55502e15i 1.37146 + 1.00841i
\(703\) 2.62613e15 0.576850
\(704\) −6.10280e14 4.94011e15i −0.133008 1.07668i
\(705\) 4.60629e15 0.996119
\(706\) 2.06203e15 + 1.51617e15i 0.442455 + 0.325328i
\(707\) 4.89760e15 4.89760e15i 1.04274 1.04274i
\(708\) −3.89674e15 1.24746e16i −0.823224 2.63538i
\(709\) −6.07734e15 6.07734e15i −1.27397 1.27397i −0.943987 0.329982i \(-0.892957\pi\)
−0.329982 0.943987i \(-0.607043\pi\)
\(710\) 2.13810e14 3.26172e13i 0.0444740 0.00678462i
\(711\) 4.55481e15i 0.940128i
\(712\) 2.72629e15 + 9.37608e14i 0.558382 + 0.192035i
\(713\) 6.32698e13i 0.0128589i
\(714\) −5.26925e14 3.45406e15i −0.106270 0.696611i
\(715\) −4.15239e15 4.15239e15i −0.831027 0.831027i
\(716\) 3.94847e15 + 2.06882e15i 0.784166 + 0.410868i
\(717\) 1.96941e14 1.96941e14i 0.0388134 0.0388134i
\(718\) −5.13137e14 + 6.97881e14i −0.100357 + 0.136489i
\(719\) 6.62588e15 1.28598 0.642990 0.765874i \(-0.277694\pi\)
0.642990 + 0.765874i \(0.277694\pi\)
\(720\) −8.21410e14 + 4.51765e15i −0.158209 + 0.870129i
\(721\) −1.19899e16 −2.29178
\(722\) 1.52553e15 2.07476e15i 0.289378 0.393562i
\(723\) 3.17160e15 3.17160e15i 0.597060 0.597060i
\(724\) 1.40199e15 2.67579e15i 0.261929 0.499907i
\(725\) −1.44964e15 1.44964e15i −0.268783 0.268783i
\(726\) 2.31910e14 + 1.52020e15i 0.0426745 + 0.279737i
\(727\) 9.23539e15i 1.68662i 0.537431 + 0.843308i \(0.319395\pi\)
−0.537431 + 0.843308i \(0.680605\pi\)
\(728\) −1.61767e16 + 7.89732e15i −2.93203 + 1.43139i
\(729\) 9.06630e15i 1.63090i
\(730\) −3.56160e15 + 5.43330e14i −0.635871 + 0.0970036i
\(731\) −2.88153e14 2.88153e14i −0.0510596 0.0510596i
\(732\) −1.82795e14 + 5.71005e13i −0.0321480 + 0.0100422i
\(733\) 3.31578e15 3.31578e15i 0.578781 0.578781i −0.355787 0.934567i \(-0.615787\pi\)
0.934567 + 0.355787i \(0.115787\pi\)
\(734\) 3.99081e15 + 2.93436e15i 0.691406 + 0.508376i
\(735\) 1.01575e16 1.74665
\(736\) −1.23580e13 + 4.33918e14i −0.00210921 + 0.0740593i
\(737\) 5.67333e15 0.961096
\(738\) 1.09002e15 + 8.01469e14i 0.183284 + 0.134765i
\(739\) −3.68264e14 + 3.68264e14i −0.0614632 + 0.0614632i −0.737170 0.675707i \(-0.763838\pi\)
0.675707 + 0.737170i \(0.263838\pi\)
\(740\) −2.63834e15 + 8.24148e14i −0.437075 + 0.136531i
\(741\) −9.38559e15 9.38559e15i −1.54334 1.54334i
\(742\) −3.85257e14 + 5.87719e13i −0.0628824 + 0.00959286i
\(743\) 1.47188e15i 0.238469i 0.992866 + 0.119235i \(0.0380441\pi\)
−0.992866 + 0.119235i \(0.961956\pi\)
\(744\) 7.57189e14 + 1.55101e15i 0.121774 + 0.249439i
\(745\) 5.58870e15i 0.892178i
\(746\) 8.52232e14 + 5.58649e15i 0.135050 + 0.885270i
\(747\) −6.05847e15 6.05847e15i −0.953014 0.953014i
\(748\) 8.30884e14 1.58579e15i 0.129742 0.247621i
\(749\) −1.14567e16 + 1.14567e16i −1.77587 + 1.77587i
\(750\) 5.86435e15 7.97567e15i 0.902366 1.22724i
\(751\) 3.16182e14 0.0482966 0.0241483 0.999708i \(-0.492313\pi\)
0.0241483 + 0.999708i \(0.492313\pi\)
\(752\) 5.94862e15 4.11824e15i 0.902024 0.624473i
\(753\) 4.14378e15 0.623770
\(754\) 4.24276e15 5.77027e15i 0.634024 0.862290i
\(755\) −2.05739e15 + 2.05739e15i −0.305216 + 0.305216i
\(756\) −9.17434e15 4.80695e15i −1.35115 0.707945i
\(757\) −6.85861e15 6.85861e15i −1.00279 1.00279i −0.999996 0.00279044i \(-0.999112\pi\)
−0.00279044 0.999996i \(-0.500888\pi\)
\(758\) 8.43371e14 + 5.52841e15i 0.122416 + 0.802453i
\(759\) 8.92062e14i 0.128548i
\(760\) 9.23012e14 2.68385e15i 0.132048 0.383957i
\(761\) 1.01455e16i 1.44098i 0.693465 +