Properties

Label 17.10.d.a.15.12
Level $17$
Weight $10$
Character 17.15
Analytic conductor $8.756$
Analytic rank $0$
Dimension $52$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 17 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 17.d (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.75560921479\)
Analytic rank: \(0\)
Dimension: \(52\)
Relative dimension: \(13\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 15.12
Character \(\chi\) \(=\) 17.15
Dual form 17.10.d.a.8.12

$q$-expansion

\(f(q)\) \(=\) \(q+(26.4264 + 26.4264i) q^{2} +(-94.0407 - 227.034i) q^{3} +884.705i q^{4} +(-1431.34 + 592.881i) q^{5} +(3514.54 - 8484.85i) q^{6} +(-8665.10 - 3589.20i) q^{7} +(-9849.24 + 9849.24i) q^{8} +(-28783.0 + 28783.0i) q^{9} +O(q^{10})\) \(q+(26.4264 + 26.4264i) q^{2} +(-94.0407 - 227.034i) q^{3} +884.705i q^{4} +(-1431.34 + 592.881i) q^{5} +(3514.54 - 8484.85i) q^{6} +(-8665.10 - 3589.20i) q^{7} +(-9849.24 + 9849.24i) q^{8} +(-28783.0 + 28783.0i) q^{9} +(-53492.8 - 22157.4i) q^{10} +(12187.7 - 29423.6i) q^{11} +(200859. - 83198.3i) q^{12} +3836.87i q^{13} +(-134137. - 323837. i) q^{14} +(269209. + 269209. i) q^{15} -67590.2 q^{16} +(271096. + 212355. i) q^{17} -1.52126e6 q^{18} +(-498424. - 498424. i) q^{19} +(-524525. - 1.26631e6i) q^{20} +2.30481e6i q^{21} +(1.09964e6 - 455484. i) q^{22} +(-54124.7 + 130669. i) q^{23} +(3.16235e6 + 1.30989e6i) q^{24} +(316161. - 316161. i) q^{25} +(-101394. + 101394. i) q^{26} +(4.77279e6 + 1.97695e6i) q^{27} +(3.17538e6 - 7.66606e6i) q^{28} +(-4.99241e6 + 2.06793e6i) q^{29} +1.42284e7i q^{30} +(-3.36298e6 - 8.11894e6i) q^{31} +(3.25665e6 + 3.25665e6i) q^{32} -7.82631e6 q^{33} +(1.55231e6 + 1.27759e7i) q^{34} +1.45307e7 q^{35} +(-2.54645e7 - 2.54645e7i) q^{36} +(-112891. - 272543. i) q^{37} -2.63431e7i q^{38} +(871101. - 360822. i) q^{39} +(8.25820e6 - 1.99370e7i) q^{40} +(1.30639e7 + 5.41125e6i) q^{41} +(-6.09077e7 + 6.09077e7i) q^{42} +(-1.32798e7 + 1.32798e7i) q^{43} +(2.60312e7 + 1.07825e7i) q^{44} +(2.41334e7 - 5.82631e7i) q^{45} +(-4.88341e6 + 2.02278e6i) q^{46} -2.19574e7i q^{47} +(6.35624e6 + 1.53453e7i) q^{48} +(3.36672e7 + 3.36672e7i) q^{49} +1.67099e7 q^{50} +(2.27179e7 - 8.15182e7i) q^{51} -3.39450e6 q^{52} +(-5.89440e7 - 5.89440e7i) q^{53} +(7.38837e7 + 1.78371e8i) q^{54} +4.93411e7i q^{55} +(1.20696e8 - 4.99937e7i) q^{56} +(-6.62872e7 + 1.60032e8i) q^{57} +(-1.86579e8 - 7.72836e7i) q^{58} +(7.42776e7 - 7.42776e7i) q^{59} +(-2.38170e8 + 2.38170e8i) q^{60} +(-9.05193e6 - 3.74943e6i) q^{61} +(1.25683e8 - 3.03425e8i) q^{62} +(3.52715e8 - 1.46099e8i) q^{63} +2.06729e8i q^{64} +(-2.27480e6 - 5.49186e6i) q^{65} +(-2.06821e8 - 2.06821e8i) q^{66} -1.49532e8 q^{67} +(-1.87872e8 + 2.39840e8i) q^{68} +3.47562e7 q^{69} +(3.83993e8 + 3.83993e8i) q^{70} +(-2.68600e6 - 6.48457e6i) q^{71} -5.66981e8i q^{72} +(-8.42466e7 + 3.48961e7i) q^{73} +(4.21901e6 - 1.01856e7i) q^{74} +(-1.01511e8 - 4.20474e7i) q^{75} +(4.40958e8 - 4.40958e8i) q^{76} +(-2.11215e8 + 2.11215e8i) q^{77} +(3.25552e7 + 1.34848e7i) q^{78} +(3.15962e7 - 7.62799e7i) q^{79} +(9.67446e7 - 4.00729e7i) q^{80} -4.68298e8i q^{81} +(2.02232e8 + 4.88231e8i) q^{82} +(-4.05665e7 - 4.05665e7i) q^{83} -2.03907e9 q^{84} +(-5.13932e8 - 1.43225e8i) q^{85} -7.01872e8 q^{86} +(9.38981e8 + 9.38981e8i) q^{87} +(1.69761e8 + 4.09840e8i) q^{88} -6.66119e7i q^{89} +(2.17744e9 - 9.01925e8i) q^{90} +(1.37713e7 - 3.32468e7i) q^{91} +(-1.15603e8 - 4.78844e7i) q^{92} +(-1.52702e9 + 1.52702e9i) q^{93} +(5.80254e8 - 5.80254e8i) q^{94} +(1.00892e9 + 4.17908e8i) q^{95} +(4.33114e8 - 1.04563e9i) q^{96} +(5.30835e8 - 2.19879e8i) q^{97} +1.77941e9i q^{98} +(4.96103e8 + 1.19770e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52q - 4q^{2} - 4q^{3} - 1140q^{5} + 12308q^{6} - 4q^{7} + 2044q^{8} - 83224q^{9} + O(q^{10}) \) \( 52q - 4q^{2} - 4q^{3} - 1140q^{5} + 12308q^{6} - 4q^{7} + 2044q^{8} - 83224q^{9} - 117636q^{10} - 115768q^{11} - 145528q^{12} + 463660q^{14} + 288244q^{15} - 3407880q^{16} - 271932q^{17} + 2193336q^{18} - 406700q^{19} + 493564q^{20} + 800964q^{22} - 4172180q^{23} + 15078440q^{24} + 11946576q^{25} - 14209012q^{26} - 7973656q^{27} + 13540804q^{28} + 7833752q^{29} + 5936252q^{31} - 26730116q^{32} - 1635208q^{33} - 53493988q^{34} + 46992776q^{35} - 12761764q^{36} + 74606796q^{37} + 74096776q^{39} - 69317672q^{40} - 71362288q^{41} - 308117664q^{42} - 3765712q^{43} + 163659820q^{44} + 14167408q^{45} + 72135428q^{46} + 164621412q^{48} - 284548508q^{49} + 226223888q^{50} - 406733132q^{51} + 103553016q^{52} - 244724728q^{53} + 971226260q^{54} + 470691652q^{56} - 440646580q^{57} - 308561768q^{58} - 481734984q^{59} + 379626176q^{60} + 507966228q^{61} + 358867236q^{62} + 1070586456q^{63} + 366263684q^{65} - 2244715148q^{66} - 311910088q^{67} - 1839196668q^{68} + 533688136q^{69} + 34867672q^{70} + 186006812q^{71} + 487115192q^{73} - 214149412q^{74} + 533015920q^{75} + 1104236912q^{76} - 237869092q^{77} - 2081523384q^{78} - 136338052q^{79} - 922534152q^{80} + 1951892384q^{82} + 1843663888q^{83} - 2630025952q^{84} - 395061976q^{85} + 1538547296q^{86} - 369395636q^{87} - 3388839640q^{88} + 874363684q^{90} + 2087197720q^{91} + 1061427500q^{92} + 576415420q^{93} + 6899365112q^{94} + 5031766876q^{95} + 490811364q^{96} - 3419996368q^{97} - 5630536112q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/17\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{3}{8}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 26.4264 + 26.4264i 1.16789 + 1.16789i 0.982703 + 0.185188i \(0.0592895\pi\)
0.185188 + 0.982703i \(0.440711\pi\)
\(3\) −94.0407 227.034i −0.670302 1.61825i −0.781098 0.624409i \(-0.785340\pi\)
0.110796 0.993843i \(-0.464660\pi\)
\(4\) 884.705i 1.72794i
\(5\) −1431.34 + 592.881i −1.02418 + 0.424231i −0.830610 0.556855i \(-0.812008\pi\)
−0.193574 + 0.981086i \(0.562008\pi\)
\(6\) 3514.54 8484.85i 1.10710 2.67278i
\(7\) −8665.10 3589.20i −1.36406 0.565011i −0.423886 0.905716i \(-0.639334\pi\)
−0.940170 + 0.340705i \(0.889334\pi\)
\(8\) −9849.24 + 9849.24i −0.850155 + 0.850155i
\(9\) −28783.0 + 28783.0i −1.46233 + 1.46233i
\(10\) −53492.8 22157.4i −1.69159 0.700680i
\(11\) 12187.7 29423.6i 0.250988 0.605939i −0.747296 0.664491i \(-0.768648\pi\)
0.998284 + 0.0585519i \(0.0186483\pi\)
\(12\) 200859. 83198.3i 2.79624 1.15824i
\(13\) 3836.87i 0.0372590i 0.999826 + 0.0186295i \(0.00593030\pi\)
−0.999826 + 0.0186295i \(0.994070\pi\)
\(14\) −134137. 323837.i −0.933198 2.25294i
\(15\) 269209. + 269209.i 1.37302 + 1.37302i
\(16\) −67590.2 −0.257836
\(17\) 271096. + 212355.i 0.787233 + 0.616656i
\(18\) −1.52126e6 −3.41568
\(19\) −498424. 498424.i −0.877420 0.877420i 0.115847 0.993267i \(-0.463042\pi\)
−0.993267 + 0.115847i \(0.963042\pi\)
\(20\) −524525. 1.26631e6i −0.733045 1.76973i
\(21\) 2.30481e6i 2.58611i
\(22\) 1.09964e6 455484.i 1.00080 0.414544i
\(23\) −54124.7 + 130669.i −0.0403293 + 0.0973634i −0.942761 0.333470i \(-0.891780\pi\)
0.902431 + 0.430834i \(0.141780\pi\)
\(24\) 3.16235e6 + 1.30989e6i 1.94562 + 0.805904i
\(25\) 316161. 316161.i 0.161874 0.161874i
\(26\) −101394. + 101394.i −0.0435145 + 0.0435145i
\(27\) 4.77279e6 + 1.97695e6i 1.72836 + 0.715911i
\(28\) 3.17538e6 7.66606e6i 0.976304 2.35701i
\(29\) −4.99241e6 + 2.06793e6i −1.31075 + 0.542930i −0.925103 0.379717i \(-0.876022\pi\)
−0.385646 + 0.922647i \(0.626022\pi\)
\(30\) 1.42284e7i 3.20709i
\(31\) −3.36298e6 8.11894e6i −0.654028 1.57896i −0.806881 0.590713i \(-0.798846\pi\)
0.152854 0.988249i \(-0.451154\pi\)
\(32\) 3.25665e6 + 3.25665e6i 0.549030 + 0.549030i
\(33\) −7.82631e6 −1.14880
\(34\) 1.55231e6 + 1.27759e7i 0.199215 + 1.63959i
\(35\) 1.45307e7 1.63674
\(36\) −2.54645e7 2.54645e7i −2.52681 2.52681i
\(37\) −112891. 272543.i −0.00990264 0.0239071i 0.918851 0.394605i \(-0.129119\pi\)
−0.928754 + 0.370698i \(0.879119\pi\)
\(38\) 2.63431e7i 2.04946i
\(39\) 871101. 360822.i 0.0602945 0.0249748i
\(40\) 8.25820e6 1.99370e7i 0.510053 1.23138i
\(41\) 1.30639e7 + 5.41125e6i 0.722015 + 0.299068i 0.713266 0.700893i \(-0.247215\pi\)
0.00874870 + 0.999962i \(0.497215\pi\)
\(42\) −6.09077e7 + 6.09077e7i −3.02030 + 3.02030i
\(43\) −1.32798e7 + 1.32798e7i −0.592355 + 0.592355i −0.938267 0.345912i \(-0.887570\pi\)
0.345912 + 0.938267i \(0.387570\pi\)
\(44\) 2.60312e7 + 1.07825e7i 1.04703 + 0.433693i
\(45\) 2.41334e7 5.82631e7i 0.877328 2.11806i
\(46\) −4.88341e6 + 2.02278e6i −0.160810 + 0.0666097i
\(47\) 2.19574e7i 0.656357i −0.944616 0.328179i \(-0.893565\pi\)
0.944616 0.328179i \(-0.106435\pi\)
\(48\) 6.35624e6 + 1.53453e7i 0.172828 + 0.417244i
\(49\) 3.36672e7 + 3.36672e7i 0.834306 + 0.834306i
\(50\) 1.67099e7 0.378103
\(51\) 2.27179e7 8.15182e7i 0.470221 1.68729i
\(52\) −3.39450e6 −0.0643814
\(53\) −5.89440e7 5.89440e7i −1.02612 1.02612i −0.999650 0.0264711i \(-0.991573\pi\)
−0.0264711 0.999650i \(-0.508427\pi\)
\(54\) 7.38837e7 + 1.78371e8i 1.18243 + 2.85465i
\(55\) 4.93411e7i 0.727070i
\(56\) 1.20696e8 4.99937e7i 1.64000 0.679312i
\(57\) −6.62872e7 + 1.60032e8i −0.831750 + 2.00802i
\(58\) −1.86579e8 7.72836e7i −2.16490 0.896729i
\(59\) 7.42776e7 7.42776e7i 0.798039 0.798039i −0.184748 0.982786i \(-0.559147\pi\)
0.982786 + 0.184748i \(0.0591467\pi\)
\(60\) −2.38170e8 + 2.38170e8i −2.37250 + 2.37250i
\(61\) −9.05193e6 3.74943e6i −0.0837061 0.0346722i 0.340438 0.940267i \(-0.389425\pi\)
−0.424144 + 0.905595i \(0.639425\pi\)
\(62\) 1.25683e8 3.03425e8i 1.08022 2.60789i
\(63\) 3.52715e8 1.46099e8i 2.82093 1.16847i
\(64\) 2.06729e8i 1.54025i
\(65\) −2.27480e6 5.49186e6i −0.0158064 0.0381601i
\(66\) −2.06821e8 2.06821e8i −1.34167 1.34167i
\(67\) −1.49532e8 −0.906560 −0.453280 0.891368i \(-0.649746\pi\)
−0.453280 + 0.891368i \(0.649746\pi\)
\(68\) −1.87872e8 + 2.39840e8i −1.06554 + 1.36029i
\(69\) 3.47562e7 0.184591
\(70\) 3.83993e8 + 3.83993e8i 1.91153 + 1.91153i
\(71\) −2.68600e6 6.48457e6i −0.0125442 0.0302844i 0.917483 0.397774i \(-0.130217\pi\)
−0.930028 + 0.367490i \(0.880217\pi\)
\(72\) 5.66981e8i 2.48641i
\(73\) −8.42466e7 + 3.48961e7i −0.347216 + 0.143821i −0.549474 0.835511i \(-0.685172\pi\)
0.202258 + 0.979332i \(0.435172\pi\)
\(74\) 4.21901e6 1.01856e7i 0.0163557 0.0394861i
\(75\) −1.01511e8 4.20474e7i −0.370458 0.153449i
\(76\) 4.40958e8 4.40958e8i 1.51613 1.51613i
\(77\) −2.11215e8 + 2.11215e8i −0.684724 + 0.684724i
\(78\) 3.25552e7 + 1.34848e7i 0.0995853 + 0.0412496i
\(79\) 3.15962e7 7.62799e7i 0.0912668 0.220337i −0.871654 0.490122i \(-0.836952\pi\)
0.962921 + 0.269784i \(0.0869524\pi\)
\(80\) 9.67446e7 4.00729e7i 0.264072 0.109382i
\(81\) 4.68298e8i 1.20876i
\(82\) 2.02232e8 + 4.88231e8i 0.493955 + 1.19251i
\(83\) −4.05665e7 4.05665e7i −0.0938244 0.0938244i 0.658637 0.752461i \(-0.271133\pi\)
−0.752461 + 0.658637i \(0.771133\pi\)
\(84\) −2.03907e9 −4.46865
\(85\) −5.13932e8 1.43225e8i −1.06788 0.297601i
\(86\) −7.01872e8 −1.38361
\(87\) 9.38981e8 + 9.38981e8i 1.75720 + 1.75720i
\(88\) 1.69761e8 + 4.09840e8i 0.301763 + 0.728521i
\(89\) 6.66119e7i 0.112537i −0.998416 0.0562687i \(-0.982080\pi\)
0.998416 0.0562687i \(-0.0179204\pi\)
\(90\) 2.17744e9 9.01925e8i 3.49828 1.44904i
\(91\) 1.37713e7 3.32468e7i 0.0210517 0.0508234i
\(92\) −1.15603e8 4.78844e7i −0.168238 0.0696865i
\(93\) −1.52702e9 + 1.52702e9i −2.11676 + 2.11676i
\(94\) 5.80254e8 5.80254e8i 0.766554 0.766554i
\(95\) 1.00892e9 + 4.17908e8i 1.27087 + 0.526411i
\(96\) 4.33114e8 1.04563e9i 0.520453 1.25648i
\(97\) 5.30835e8 2.19879e8i 0.608817 0.252180i −0.0569059 0.998380i \(-0.518124\pi\)
0.665722 + 0.746199i \(0.268124\pi\)
\(98\) 1.77941e9i 1.94876i
\(99\) 4.96103e8 + 1.19770e9i 0.519055 + 1.25311i
\(100\) 2.79709e8 + 2.79709e8i 0.279709 + 0.279709i
\(101\) 4.50136e8 0.430425 0.215213 0.976567i \(-0.430956\pi\)
0.215213 + 0.976567i \(0.430956\pi\)
\(102\) 2.75458e9 1.55388e9i 2.51973 1.42140i
\(103\) −7.34932e8 −0.643398 −0.321699 0.946842i \(-0.604254\pi\)
−0.321699 + 0.946842i \(0.604254\pi\)
\(104\) −3.77902e7 3.77902e7i −0.0316759 0.0316759i
\(105\) −1.36648e9 3.29896e9i −1.09711 2.64866i
\(106\) 3.11535e9i 2.39679i
\(107\) −1.14140e9 + 4.72783e8i −0.841803 + 0.348686i −0.761564 0.648090i \(-0.775568\pi\)
−0.0802385 + 0.996776i \(0.525568\pi\)
\(108\) −1.74902e9 + 4.22251e9i −1.23705 + 2.98651i
\(109\) 3.28499e8 + 1.36069e8i 0.222902 + 0.0923292i 0.491340 0.870968i \(-0.336507\pi\)
−0.268437 + 0.963297i \(0.586507\pi\)
\(110\) −1.30390e9 + 1.30390e9i −0.849139 + 0.849139i
\(111\) −5.12602e7 + 5.12602e7i −0.0320499 + 0.0320499i
\(112\) 5.85676e8 + 2.42595e8i 0.351703 + 0.145680i
\(113\) −2.73372e8 + 6.59979e8i −0.157725 + 0.380783i −0.982912 0.184078i \(-0.941070\pi\)
0.825186 + 0.564861i \(0.191070\pi\)
\(114\) −5.98078e9 + 2.47732e9i −3.31655 + 1.37376i
\(115\) 2.19121e8i 0.116827i
\(116\) −1.82950e9 4.41681e9i −0.938151 2.26490i
\(117\) −1.10436e8 1.10436e8i −0.0544849 0.0544849i
\(118\) 3.92577e9 1.86404
\(119\) −1.58689e9 2.81310e9i −0.725413 1.28595i
\(120\) −5.30300e9 −2.33457
\(121\) 9.50110e8 + 9.50110e8i 0.402939 + 0.402939i
\(122\) −1.40126e8 3.38293e8i −0.0572662 0.138253i
\(123\) 3.47484e9i 1.36887i
\(124\) 7.18287e9 2.97524e9i 2.72835 1.13012i
\(125\) 8.92882e8 2.15561e9i 0.327114 0.789723i
\(126\) 1.31819e10 + 5.46011e9i 4.65918 + 1.92989i
\(127\) 7.29299e8 7.29299e8i 0.248765 0.248765i −0.571699 0.820464i \(-0.693715\pi\)
0.820464 + 0.571699i \(0.193715\pi\)
\(128\) −3.79569e9 + 3.79569e9i −1.24982 + 1.24982i
\(129\) 4.26380e9 + 1.76612e9i 1.35564 + 0.561523i
\(130\) 8.50152e7 2.05245e8i 0.0261067 0.0630270i
\(131\) −5.00330e9 + 2.07244e9i −1.48435 + 0.614837i −0.970079 0.242791i \(-0.921937\pi\)
−0.514270 + 0.857628i \(0.671937\pi\)
\(132\) 6.92398e9i 1.98506i
\(133\) 2.52995e9 + 6.10783e9i 0.701099 + 1.69260i
\(134\) −3.95158e9 3.95158e9i −1.05876 1.05876i
\(135\) −8.00358e9 −2.07387
\(136\) −4.76163e9 + 5.78553e8i −1.19352 + 0.145017i
\(137\) 3.16964e9 0.768718 0.384359 0.923184i \(-0.374423\pi\)
0.384359 + 0.923184i \(0.374423\pi\)
\(138\) 9.18480e8 + 9.18480e8i 0.215583 + 0.215583i
\(139\) 2.74708e9 + 6.63205e9i 0.624174 + 1.50689i 0.846760 + 0.531975i \(0.178550\pi\)
−0.222586 + 0.974913i \(0.571450\pi\)
\(140\) 1.28554e10i 2.82819i
\(141\) −4.98508e9 + 2.06489e9i −1.06215 + 0.439958i
\(142\) 1.00383e8 2.42345e8i 0.0207186 0.0500191i
\(143\) 1.12895e8 + 4.67624e7i 0.0225767 + 0.00935158i
\(144\) 1.94545e9 1.94545e9i 0.377041 0.377041i
\(145\) 5.91981e9 5.91981e9i 1.11212 1.11212i
\(146\) −3.14851e9 1.30415e9i −0.573478 0.237542i
\(147\) 4.47753e9 1.08097e10i 0.790880 1.90935i
\(148\) 2.41120e8 9.98751e7i 0.0413100 0.0171112i
\(149\) 9.84251e9i 1.63594i −0.575260 0.817971i \(-0.695099\pi\)
0.575260 0.817971i \(-0.304901\pi\)
\(150\) −1.57142e9 3.79373e9i −0.253443 0.611866i
\(151\) 6.99899e9 + 6.99899e9i 1.09557 + 1.09557i 0.994922 + 0.100645i \(0.0320906\pi\)
0.100645 + 0.994922i \(0.467909\pi\)
\(152\) 9.81819e9 1.49189
\(153\) −1.39152e10 + 1.69074e9i −2.05295 + 0.249439i
\(154\) −1.11633e10 −1.59937
\(155\) 9.62713e9 + 9.62713e9i 1.33969 + 1.33969i
\(156\) 3.19221e8 + 7.70667e8i 0.0431550 + 0.104185i
\(157\) 1.10838e9i 0.145593i −0.997347 0.0727964i \(-0.976808\pi\)
0.997347 0.0727964i \(-0.0231923\pi\)
\(158\) 2.85077e9 1.18083e9i 0.363920 0.150741i
\(159\) −7.83918e9 + 1.89255e10i −0.972711 + 2.34833i
\(160\) −6.59218e9 2.73057e9i −0.795223 0.329392i
\(161\) 9.37992e8 9.37992e8i 0.110023 0.110023i
\(162\) 1.23754e10 1.23754e10i 1.41170 1.41170i
\(163\) −9.29176e9 3.84877e9i −1.03099 0.427049i −0.197919 0.980218i \(-0.563418\pi\)
−0.833069 + 0.553169i \(0.813418\pi\)
\(164\) −4.78736e9 + 1.15577e10i −0.516772 + 1.24760i
\(165\) 1.12021e10 4.64007e9i 1.17658 0.487357i
\(166\) 2.14405e9i 0.219153i
\(167\) 1.84264e6 + 4.44852e6i 0.000183322 + 0.000442579i 0.923971 0.382462i \(-0.124924\pi\)
−0.923788 + 0.382905i \(0.874924\pi\)
\(168\) −2.27006e10 2.27006e10i −2.19860 2.19860i
\(169\) 1.05898e10 0.998612
\(170\) −9.79644e9 1.73663e10i −0.899597 1.59473i
\(171\) 2.86923e10 2.56615
\(172\) −1.17487e10 1.17487e10i −1.02355 1.02355i
\(173\) −2.79005e9 6.73578e9i −0.236813 0.571716i 0.760137 0.649763i \(-0.225132\pi\)
−0.996950 + 0.0780466i \(0.975132\pi\)
\(174\) 4.96277e10i 4.10443i
\(175\) −3.87433e9 + 1.60480e9i −0.312266 + 0.129345i
\(176\) −8.23767e8 + 1.98875e9i −0.0647139 + 0.156233i
\(177\) −2.38487e10 9.87845e9i −1.82635 0.756501i
\(178\) 1.76031e9 1.76031e9i 0.131431 0.131431i
\(179\) 3.10178e9 3.10178e9i 0.225825 0.225825i −0.585121 0.810946i \(-0.698953\pi\)
0.810946 + 0.585121i \(0.198953\pi\)
\(180\) 5.15457e10 + 2.13509e10i 3.65987 + 1.51597i
\(181\) 3.80901e9 9.19577e9i 0.263790 0.636846i −0.735377 0.677659i \(-0.762995\pi\)
0.999167 + 0.0408127i \(0.0129947\pi\)
\(182\) 1.24252e9 5.14668e8i 0.0839424 0.0347701i
\(183\) 2.40770e9i 0.158698i
\(184\) −7.53899e8 1.82007e9i −0.0484879 0.117060i
\(185\) 3.23170e8 + 3.23170e8i 0.0202842 + 0.0202842i
\(186\) −8.07073e10 −4.94430
\(187\) 9.55229e9 5.38852e9i 0.571242 0.322242i
\(188\) 1.94258e10 1.13415
\(189\) −3.42610e10 3.42610e10i −1.95309 1.95309i
\(190\) 1.56183e10 + 3.77059e10i 0.869445 + 2.09903i
\(191\) 3.59313e9i 0.195354i −0.995218 0.0976771i \(-0.968859\pi\)
0.995218 0.0976771i \(-0.0311412\pi\)
\(192\) 4.69346e10 1.94409e10i 2.49251 1.03243i
\(193\) 7.09815e9 1.71365e10i 0.368246 0.889024i −0.625792 0.779990i \(-0.715224\pi\)
0.994038 0.109034i \(-0.0347757\pi\)
\(194\) 1.98386e10 + 8.21743e9i 1.00555 + 0.416513i
\(195\) −1.03292e9 + 1.03292e9i −0.0511576 + 0.0511576i
\(196\) −2.97856e10 + 2.97856e10i −1.44163 + 1.44163i
\(197\) −2.14241e10 8.87414e9i −1.01345 0.419786i −0.186740 0.982409i \(-0.559792\pi\)
−0.826713 + 0.562623i \(0.809792\pi\)
\(198\) −1.85406e10 + 4.47610e10i −0.857295 + 2.06969i
\(199\) −2.17177e10 + 8.99576e9i −0.981691 + 0.406630i −0.815052 0.579388i \(-0.803291\pi\)
−0.166639 + 0.986018i \(0.553291\pi\)
\(200\) 6.22788e9i 0.275236i
\(201\) 1.40621e10 + 3.39488e10i 0.607669 + 1.46704i
\(202\) 1.18955e10 + 1.18955e10i 0.502690 + 0.502690i
\(203\) 5.06820e10 2.09470
\(204\) 7.21196e10 + 2.00986e10i 2.91553 + 0.812514i
\(205\) −2.19071e10 −0.866350
\(206\) −1.94216e10 1.94216e10i −0.751419 0.751419i
\(207\) −2.20316e9 5.31890e9i −0.0834026 0.201352i
\(208\) 2.59335e8i 0.00960673i
\(209\) −2.07401e10 + 8.59081e9i −0.751886 + 0.311441i
\(210\) 5.10686e10 1.23291e11i 1.81204 4.37465i
\(211\) 2.31549e10 + 9.59106e9i 0.804213 + 0.333116i 0.746642 0.665226i \(-0.231665\pi\)
0.0575705 + 0.998341i \(0.481665\pi\)
\(212\) 5.21481e10 5.21481e10i 1.77307 1.77307i
\(213\) −1.21963e9 + 1.21963e9i −0.0405994 + 0.0405994i
\(214\) −4.26569e10 1.76691e10i −1.39036 0.575906i
\(215\) 1.11345e10 2.68812e10i 0.355385 0.857976i
\(216\) −6.64798e10 + 2.75368e10i −2.07801 + 0.860740i
\(217\) 8.24218e10i 2.52333i
\(218\) 5.08523e9 + 1.22768e10i 0.152495 + 0.368156i
\(219\) 1.58452e10 + 1.58452e10i 0.465479 + 0.465479i
\(220\) −4.36523e10 −1.25633
\(221\) −8.14779e8 + 1.04016e9i −0.0229760 + 0.0293315i
\(222\) −2.70924e9 −0.0748616
\(223\) −2.13526e10 2.13526e10i −0.578201 0.578201i 0.356207 0.934407i \(-0.384070\pi\)
−0.934407 + 0.356207i \(0.884070\pi\)
\(224\) −1.65304e10 3.99079e10i −0.438700 1.05912i
\(225\) 1.82001e10i 0.473426i
\(226\) −2.46651e10 + 1.02166e10i −0.628919 + 0.260507i
\(227\) −2.27430e10 + 5.49065e10i −0.568502 + 1.37248i 0.334316 + 0.942461i \(0.391495\pi\)
−0.902818 + 0.430023i \(0.858505\pi\)
\(228\) −1.41581e11 5.86447e10i −3.46974 1.43721i
\(229\) 2.24166e10 2.24166e10i 0.538654 0.538654i −0.384479 0.923134i \(-0.625619\pi\)
0.923134 + 0.384479i \(0.125619\pi\)
\(230\) 5.79056e9 5.79056e9i 0.136441 0.136441i
\(231\) 6.78158e10 + 2.80902e10i 1.56703 + 0.649084i
\(232\) 2.88040e10 6.95390e10i 0.652765 1.57591i
\(233\) −6.85760e10 + 2.84051e10i −1.52430 + 0.631386i −0.978448 0.206495i \(-0.933794\pi\)
−0.545853 + 0.837881i \(0.683794\pi\)
\(234\) 5.83687e9i 0.127265i
\(235\) 1.30181e10 + 3.14285e10i 0.278447 + 0.672231i
\(236\) 6.57138e10 + 6.57138e10i 1.37896 + 1.37896i
\(237\) −2.02895e10 −0.417738
\(238\) 3.24042e10 1.16276e11i 0.654645 2.34905i
\(239\) −5.76902e10 −1.14370 −0.571850 0.820358i \(-0.693774\pi\)
−0.571850 + 0.820358i \(0.693774\pi\)
\(240\) −1.81959e10 1.81959e10i −0.354016 0.354016i
\(241\) −1.17403e10 2.83437e10i −0.224183 0.541227i 0.771266 0.636512i \(-0.219624\pi\)
−0.995450 + 0.0952856i \(0.969624\pi\)
\(242\) 5.02159e10i 0.941179i
\(243\) −1.23771e10 + 5.12677e9i −0.227715 + 0.0943225i
\(244\) 3.31714e9 8.00829e9i 0.0599115 0.144639i
\(245\) −6.81500e10 2.82286e10i −1.20842 0.500544i
\(246\) 9.18273e10 9.18273e10i 1.59869 1.59869i
\(247\) 1.91239e9 1.91239e9i 0.0326918 0.0326918i
\(248\) 1.13088e11 + 4.68427e10i 1.89839 + 0.786337i
\(249\) −5.39508e9 + 1.30249e10i −0.0889408 + 0.214722i
\(250\) 8.05605e10 3.33693e10i 1.30434 0.540277i
\(251\) 6.41373e10i 1.01995i −0.860189 0.509975i \(-0.829655\pi\)
0.860189 0.509975i \(-0.170345\pi\)
\(252\) 1.29255e11 + 3.12049e11i 2.01904 + 4.87439i
\(253\) 3.18509e9 + 3.18509e9i 0.0488742 + 0.0488742i
\(254\) 3.85454e10 0.581060
\(255\) 1.58135e10 + 1.30149e11i 0.234206 + 1.92757i
\(256\) −9.47673e10 −1.37905
\(257\) −6.50297e9 6.50297e9i −0.0929850 0.0929850i 0.659084 0.752069i \(-0.270944\pi\)
−0.752069 + 0.659084i \(0.770944\pi\)
\(258\) 6.60045e10 + 1.59349e11i 0.927438 + 2.23903i
\(259\) 2.76680e9i 0.0382057i
\(260\) 4.85868e9 2.01253e9i 0.0659384 0.0273126i
\(261\) 8.41755e10 2.03218e11i 1.12280 2.71069i
\(262\) −1.86986e11 7.74521e10i −2.45162 1.01549i
\(263\) 4.80044e10 4.80044e10i 0.618701 0.618701i −0.326497 0.945198i \(-0.605868\pi\)
0.945198 + 0.326497i \(0.105868\pi\)
\(264\) 7.70833e10 7.70833e10i 0.976658 0.976658i
\(265\) 1.19316e11 + 4.94222e10i 1.48625 + 0.615624i
\(266\) −9.45505e10 + 2.28265e11i −1.15797 + 2.79558i
\(267\) −1.51232e10 + 6.26424e9i −0.182114 + 0.0754341i
\(268\) 1.32291e11i 1.56648i
\(269\) −5.21892e10 1.25996e11i −0.607708 1.46714i −0.865486 0.500933i \(-0.832990\pi\)
0.257778 0.966204i \(-0.417010\pi\)
\(270\) −2.11505e11 2.11505e11i −2.42206 2.42206i
\(271\) −2.89117e10 −0.325621 −0.162810 0.986657i \(-0.552056\pi\)
−0.162810 + 0.986657i \(0.552056\pi\)
\(272\) −1.83234e10 1.43531e10i −0.202977 0.158996i
\(273\) −8.84324e9 −0.0963561
\(274\) 8.37620e10 + 8.37620e10i 0.897779 + 0.897779i
\(275\) −5.44933e9 1.31558e10i −0.0574574 0.138714i
\(276\) 3.07490e10i 0.318963i
\(277\) −1.57641e11 + 6.52971e10i −1.60883 + 0.666400i −0.992630 0.121187i \(-0.961330\pi\)
−0.616203 + 0.787587i \(0.711330\pi\)
\(278\) −1.02665e11 + 2.47856e11i −1.03091 + 2.48885i
\(279\) 3.30484e11 + 1.36891e11i 3.26536 + 1.35256i
\(280\) −1.43116e11 + 1.43116e11i −1.39148 + 1.39148i
\(281\) −5.39003e10 + 5.39003e10i −0.515719 + 0.515719i −0.916273 0.400554i \(-0.868818\pi\)
0.400554 + 0.916273i \(0.368818\pi\)
\(282\) −1.86305e11 7.71701e10i −1.75430 0.726655i
\(283\) 2.99939e10 7.24117e10i 0.277968 0.671073i −0.721811 0.692090i \(-0.756690\pi\)
0.999779 + 0.0210164i \(0.00669024\pi\)
\(284\) 5.73694e9 2.37632e9i 0.0523296 0.0216756i
\(285\) 2.68360e11i 2.40944i
\(286\) 1.74763e9 + 4.21915e9i 0.0154455 + 0.0372888i
\(287\) −9.37780e10 9.37780e10i −0.815892 0.815892i
\(288\) −1.87472e11 −1.60572
\(289\) 2.83983e10 + 1.15137e11i 0.239471 + 0.970904i
\(290\) 3.12878e11 2.59767
\(291\) −9.98402e10 9.98402e10i −0.816182 0.816182i
\(292\) −3.08727e10 7.45334e10i −0.248515 0.599968i
\(293\) 4.34293e10i 0.344253i 0.985075 + 0.172127i \(0.0550639\pi\)
−0.985075 + 0.172127i \(0.944936\pi\)
\(294\) 4.03986e11 1.67337e11i 3.15358 1.30626i
\(295\) −6.22788e10 + 1.50354e11i −0.478786 + 1.15589i
\(296\) 3.79623e9 + 1.57245e9i 0.0287435 + 0.0119059i
\(297\) 1.16338e11 1.16338e11i 0.867598 0.867598i
\(298\) 2.60102e11 2.60102e11i 1.91060 1.91060i
\(299\) −5.01358e8 2.07669e8i −0.00362767 0.00150263i
\(300\) 3.71995e10 8.98076e10i 0.265150 0.640129i
\(301\) 1.62734e11 6.74067e10i 1.14269 0.473319i
\(302\) 3.69916e11i 2.55901i
\(303\) −4.23311e10 1.02196e11i −0.288515 0.696536i
\(304\) 3.36886e10 + 3.36886e10i 0.226231 + 0.226231i
\(305\) 1.51794e10 0.100439
\(306\) −4.12408e11 3.23048e11i −2.68893 2.10630i
\(307\) −2.26738e11 −1.45681 −0.728404 0.685148i \(-0.759738\pi\)
−0.728404 + 0.685148i \(0.759738\pi\)
\(308\) −1.86863e11 1.86863e11i −1.18316 1.18316i
\(309\) 6.91136e10 + 1.66855e11i 0.431271 + 1.04118i
\(310\) 5.08820e11i 3.12922i
\(311\) 2.31370e11 9.58366e10i 1.40244 0.580911i 0.452059 0.891988i \(-0.350690\pi\)
0.950385 + 0.311077i \(0.100690\pi\)
\(312\) −5.02586e9 + 1.21335e10i −0.0300272 + 0.0724921i
\(313\) 1.67983e11 + 6.95808e10i 0.989272 + 0.409770i 0.817852 0.575428i \(-0.195165\pi\)
0.171420 + 0.985198i \(0.445165\pi\)
\(314\) 2.92904e10 2.92904e10i 0.170037 0.170037i
\(315\) −4.18236e11 + 4.18236e11i −2.39345 + 2.39345i
\(316\) 6.74852e10 + 2.79533e10i 0.380730 + 0.157703i
\(317\) 1.18135e11 2.85204e11i 0.657073 1.58631i −0.145231 0.989398i \(-0.546393\pi\)
0.802304 0.596916i \(-0.203607\pi\)
\(318\) −7.07292e11 + 2.92970e11i −3.87862 + 1.60658i
\(319\) 1.72098e11i 0.930504i
\(320\) −1.22566e11 2.95900e11i −0.653422 1.57750i
\(321\) 2.14676e11 + 2.14676e11i 1.12852 + 1.12852i
\(322\) 4.95754e10 0.256989
\(323\) −2.92778e10 2.40964e11i −0.149668 1.23180i
\(324\) 4.14306e11 2.08866
\(325\) 1.21307e9 + 1.21307e9i 0.00603128 + 0.00603128i
\(326\) −1.43838e11 3.47256e11i −0.705335 1.70283i
\(327\) 8.73766e10i 0.422601i
\(328\) −1.81966e11 + 7.53730e10i −0.868078 + 0.359570i
\(329\) −7.88095e10 + 1.90263e11i −0.370849 + 0.895308i
\(330\) 4.18651e11 + 1.73411e11i 1.94330 + 0.804941i
\(331\) −1.71743e11 + 1.71743e11i −0.786419 + 0.786419i −0.980905 0.194487i \(-0.937696\pi\)
0.194487 + 0.980905i \(0.437696\pi\)
\(332\) 3.58894e10 3.58894e10i 0.162123 0.162123i
\(333\) 1.10939e10 + 4.59525e9i 0.0494409 + 0.0204791i
\(334\) −6.88640e7 + 1.66252e8i −0.000302784 + 0.000730985i
\(335\) 2.14031e11 8.86544e10i 0.928484 0.384591i
\(336\) 1.55782e11i 0.666794i
\(337\) −4.49530e10 1.08526e11i −0.189856 0.458352i 0.800076 0.599899i \(-0.204793\pi\)
−0.989932 + 0.141546i \(0.954793\pi\)
\(338\) 2.79849e11 + 2.79849e11i 1.16627 + 1.16627i
\(339\) 1.75546e11 0.721926
\(340\) 1.26712e11 4.54679e11i 0.514236 1.84522i
\(341\) −2.79876e11 −1.12091
\(342\) 7.58232e11 + 7.58232e11i 2.99699 + 2.99699i
\(343\) −2.60543e10 6.29005e10i −0.101638 0.245375i
\(344\) 2.61591e11i 1.00719i
\(345\) −4.97480e10 + 2.06063e10i −0.189055 + 0.0783093i
\(346\) 1.04271e11 2.51733e11i 0.391131 0.944273i
\(347\) 2.40585e11 + 9.96537e10i 0.890812 + 0.368987i 0.780681 0.624930i \(-0.214873\pi\)
0.110132 + 0.993917i \(0.464873\pi\)
\(348\) −8.30721e11 + 8.30721e11i −3.03633 + 3.03633i
\(349\) 3.40320e11 3.40320e11i 1.22793 1.22793i 0.263182 0.964746i \(-0.415228\pi\)
0.964746 0.263182i \(-0.0847719\pi\)
\(350\) −1.44793e11 5.99754e10i −0.515754 0.213632i
\(351\) −7.58530e9 + 1.83125e10i −0.0266742 + 0.0643971i
\(352\) 1.35513e11 5.61315e10i 0.470479 0.194879i
\(353\) 1.13877e11i 0.390347i −0.980769 0.195173i \(-0.937473\pi\)
0.980769 0.195173i \(-0.0625270\pi\)
\(354\) −3.69183e11 8.91286e11i −1.24947 3.01649i
\(355\) 7.68916e9 + 7.68916e9i 0.0256951 + 0.0256951i
\(356\) 5.89319e10 0.194458
\(357\) −4.89438e11 + 6.24824e11i −1.59474 + 2.03587i
\(358\) 1.63937e11 0.527478
\(359\) −3.38214e11 3.38214e11i −1.07465 1.07465i −0.996979 0.0776691i \(-0.975252\pi\)
−0.0776691 0.996979i \(-0.524748\pi\)
\(360\) 3.36152e11 + 8.11543e11i 1.05481 + 2.54654i
\(361\) 1.74165e11i 0.539732i
\(362\) 3.43669e11 1.42352e11i 1.05185 0.435689i
\(363\) 1.26359e11 3.05057e11i 0.381966 0.922148i
\(364\) 2.94136e10 + 1.21835e10i 0.0878198 + 0.0363762i
\(365\) 9.98963e10 9.98963e10i 0.294599 0.294599i
\(366\) −6.36267e10 + 6.36267e10i −0.185342 + 0.185342i
\(367\) −3.49206e11 1.44646e11i −1.00481 0.416206i −0.181252 0.983437i \(-0.558015\pi\)
−0.823559 + 0.567230i \(0.808015\pi\)
\(368\) 3.65830e9 8.83192e9i 0.0103983 0.0251038i
\(369\) −5.31771e11 + 2.20267e11i −1.49316 + 0.618486i
\(370\) 1.70804e10i 0.0473796i
\(371\) 2.99194e11 + 7.22318e11i 0.819917 + 1.97946i
\(372\) −1.35096e12 1.35096e12i −3.65764 3.65764i
\(373\) −6.03744e10 −0.161496 −0.0807482 0.996735i \(-0.525731\pi\)
−0.0807482 + 0.996735i \(0.525731\pi\)
\(374\) 3.94831e11 + 1.10033e11i 1.04349 + 0.290805i
\(375\) −5.73365e11 −1.49724
\(376\) 2.16264e11 + 2.16264e11i 0.558005 + 0.558005i
\(377\) −7.93435e9 1.91552e10i −0.0202291 0.0488372i
\(378\) 1.81079e12i 4.56199i
\(379\) 4.95094e11 2.05075e11i 1.23257 0.510547i 0.331184 0.943566i \(-0.392552\pi\)
0.901385 + 0.433019i \(0.142552\pi\)
\(380\) −3.69726e11 + 8.92597e11i −0.909606 + 2.19598i
\(381\) −2.34160e11 9.69921e10i −0.569311 0.235816i
\(382\) 9.49533e10 9.49533e10i 0.228152 0.228152i
\(383\) −4.38024e11 + 4.38024e11i −1.04017 + 1.04017i −0.0410087 + 0.999159i \(0.513057\pi\)
−0.999159 + 0.0410087i \(0.986943\pi\)
\(384\) 1.21870e12 + 5.04803e11i 2.86027 + 1.18476i
\(385\) 1.77095e11 4.27545e11i 0.410802 0.991765i
\(386\) 6.40433e11 2.65276e11i 1.46835 0.608212i
\(387\) 7.64462e11i 1.73243i
\(388\) 1.94528e11 + 4.69632e11i 0.435752 + 1.05200i
\(389\) 9.86519e9 + 9.86519e9i 0.0218440 + 0.0218440i 0.717944 0.696100i \(-0.245083\pi\)
−0.696100 + 0.717944i \(0.745083\pi\)
\(390\) −5.45925e10 −0.119493
\(391\) −4.24212e10 + 2.39301e10i −0.0917883 + 0.0517784i
\(392\) −6.63194e11 −1.41858
\(393\) 9.41028e11 + 9.41028e11i 1.98992 + 1.98992i
\(394\) −3.31649e11 8.00671e11i −0.693339 1.67387i
\(395\) 1.27915e11i 0.264384i
\(396\) −1.05961e12 + 4.38905e11i −2.16530 + 0.896895i
\(397\) −3.10626e11 + 7.49918e11i −0.627597 + 1.51515i 0.215004 + 0.976613i \(0.431024\pi\)
−0.842600 + 0.538539i \(0.818976\pi\)
\(398\) −8.11644e11 3.36194e11i −1.62141 0.671609i
\(399\) 1.14877e12 1.14877e12i 2.26911 2.26911i
\(400\) −2.13694e10 + 2.13694e10i −0.0417370 + 0.0417370i
\(401\) −6.27171e10 2.59783e10i −0.121126 0.0501719i 0.321297 0.946978i \(-0.395881\pi\)
−0.442423 + 0.896806i \(0.645881\pi\)
\(402\) −5.25535e11 + 1.26875e12i −1.00365 + 2.42304i
\(403\) 3.11513e10 1.29033e10i 0.0588306 0.0243684i
\(404\) 3.98238e11i 0.743749i
\(405\) 2.77645e11 + 6.70294e11i 0.512793 + 1.23799i
\(406\) 1.33934e12 + 1.33934e12i 2.44638 + 2.44638i
\(407\) −9.39507e9 −0.0169717
\(408\) 5.79139e11 + 1.02665e12i 1.03469 + 1.83421i
\(409\) −3.62017e11 −0.639697 −0.319848 0.947469i \(-0.603632\pi\)
−0.319848 + 0.947469i \(0.603632\pi\)
\(410\) −5.78926e11 5.78926e11i −1.01180 1.01180i
\(411\) −2.98075e11 7.19617e11i −0.515273 1.24398i
\(412\) 6.50198e11i 1.11175i
\(413\) −9.10220e11 + 3.77025e11i −1.53947 + 0.637669i
\(414\) 8.23377e10 1.98781e11i 0.137752 0.332562i
\(415\) 8.21155e10 + 3.40133e10i 0.135897 + 0.0562902i
\(416\) −1.24953e10 + 1.24953e10i −0.0204563 + 0.0204563i
\(417\) 1.24737e12 1.24737e12i 2.02014 2.02014i
\(418\) −7.75108e11 3.21060e11i −1.24185 0.514391i
\(419\) 2.00338e11 4.83660e11i 0.317542 0.766614i −0.681841 0.731500i \(-0.738821\pi\)
0.999383 0.0351140i \(-0.0111794\pi\)
\(420\) 2.91861e12 1.20893e12i 4.57672 1.89574i
\(421\) 3.45685e11i 0.536303i 0.963377 + 0.268152i \(0.0864128\pi\)
−0.963377 + 0.268152i \(0.913587\pi\)
\(422\) 3.58442e11 + 8.65355e11i 0.550190 + 1.32828i
\(423\) 6.31999e11 + 6.31999e11i 0.959809 + 0.959809i
\(424\) 1.16111e12 1.74472
\(425\) 1.52848e11 1.85715e10i 0.227253 0.0276120i
\(426\) −6.44607e10 −0.0948313
\(427\) 6.49784e10 + 6.49784e10i 0.0945896 + 0.0945896i
\(428\) −4.18273e11 1.00980e12i −0.602509 1.45458i
\(429\) 3.00285e10i 0.0428032i
\(430\) 1.00462e12 4.16126e11i 1.41707 0.586971i
\(431\) −1.38358e11 + 3.34025e11i −0.193133 + 0.466264i −0.990548 0.137167i \(-0.956200\pi\)
0.797415 + 0.603431i \(0.206200\pi\)
\(432\) −3.22594e11 1.33623e11i −0.445635 0.184588i
\(433\) −9.83339e11 + 9.83339e11i −1.34434 + 1.34434i −0.452643 + 0.891692i \(0.649519\pi\)
−0.891692 + 0.452643i \(0.850481\pi\)
\(434\) −2.17811e12 + 2.17811e12i −2.94697 + 2.94697i
\(435\) −1.90070e12 7.87298e11i −2.54515 1.05423i
\(436\) −1.20381e11 + 2.90625e11i −0.159539 + 0.385162i
\(437\) 9.21054e10 3.81513e10i 0.120814 0.0500429i
\(438\) 8.37463e11i 1.08726i
\(439\) −2.13618e11 5.15720e11i −0.274504 0.662711i 0.725162 0.688579i \(-0.241765\pi\)
−0.999665 + 0.0258681i \(0.991765\pi\)
\(440\) −4.85972e11 4.85972e11i −0.618122 0.618122i
\(441\) −1.93809e12 −2.44006
\(442\) −4.90193e10 + 5.95599e9i −0.0610895 + 0.00742256i
\(443\) 1.13238e12 1.39693 0.698463 0.715646i \(-0.253868\pi\)
0.698463 + 0.715646i \(0.253868\pi\)
\(444\) −4.53502e10 4.53502e10i −0.0553803 0.0553803i
\(445\) 3.94929e10 + 9.53444e10i 0.0477419 + 0.115259i
\(446\) 1.12854e12i 1.35055i
\(447\) −2.23459e12 + 9.25597e11i −2.64737 + 1.09657i
\(448\) 7.41992e11 1.79133e12i 0.870258 2.10099i
\(449\) 7.64244e11 + 3.16560e11i 0.887409 + 0.367577i 0.779366 0.626570i \(-0.215542\pi\)
0.108043 + 0.994146i \(0.465542\pi\)
\(450\) −4.80962e11 + 4.80962e11i −0.552910 + 0.552910i
\(451\) 3.18437e11 3.18437e11i 0.362434 0.362434i
\(452\) −5.83887e11 2.41854e11i −0.657969 0.272540i
\(453\) 9.30821e11 2.24720e12i 1.03854 2.50726i
\(454\) −2.05199e12 + 8.49964e11i −2.26686 + 0.938964i
\(455\) 5.57523e10i 0.0609833i
\(456\) −9.23310e11 2.22907e12i −1.00001 2.41425i
\(457\) 8.33417e11 + 8.33417e11i 0.893798 + 0.893798i 0.994878 0.101080i \(-0.0322299\pi\)
−0.101080 + 0.994878i \(0.532230\pi\)
\(458\) 1.18478e12 1.25818
\(459\) 8.74067e11 + 1.54947e12i 0.919153 + 1.62939i
\(460\) 1.93857e11 0.201870
\(461\) 1.77042e11 + 1.77042e11i 0.182566 + 0.182566i 0.792473 0.609907i \(-0.208793\pi\)
−0.609907 + 0.792473i \(0.708793\pi\)
\(462\) 1.04980e12 + 2.53445e12i 1.07206 + 2.58818i
\(463\) 8.92342e10i 0.0902437i 0.998981 + 0.0451218i \(0.0143676\pi\)
−0.998981 + 0.0451218i \(0.985632\pi\)
\(464\) 3.37438e11 1.39772e11i 0.337959 0.139987i
\(465\) 1.28035e12 3.09103e12i 1.26996 3.06595i
\(466\) −2.56286e12 1.06157e12i −2.51761 1.04283i
\(467\) 5.62308e11 5.62308e11i 0.547077 0.547077i −0.378517 0.925594i \(-0.623566\pi\)
0.925594 + 0.378517i \(0.123566\pi\)
\(468\) 9.77037e10 9.77037e10i 0.0941466 0.0941466i
\(469\) 1.29571e12 + 5.36699e11i 1.23660 + 0.512216i
\(470\) −4.86520e11 + 1.17456e12i −0.459896 + 1.11029i
\(471\) −2.51640e11 + 1.04233e11i −0.235606 + 0.0975911i
\(472\) 1.46316e12i 1.35691i
\(473\) 2.28889e11 + 5.52588e11i 0.210257 + 0.507606i
\(474\) −5.36178e11 5.36178e11i −0.487872 0.487872i
\(475\) −3.15164e11 −0.284063
\(476\) 2.48876e12 1.40393e12i 2.22204 1.25347i
\(477\) 3.39317e12 3.00105
\(478\) −1.52454e12 1.52454e12i −1.33572 1.33572i
\(479\) 2.57741e11 + 6.22243e11i 0.223704 + 0.540070i 0.995387 0.0959372i \(-0.0305848\pi\)
−0.771683 + 0.636007i \(0.780585\pi\)
\(480\) 1.75344e12i 1.50766i
\(481\) 1.04571e9 4.33147e8i 0.000890755 0.000368963i
\(482\) 4.38766e11 1.05927e12i 0.370272 0.893916i
\(483\) −3.01166e11 1.24747e11i −0.251793 0.104296i
\(484\) −8.40567e11 + 8.40567e11i −0.696255 + 0.696255i
\(485\) −6.29443e11 + 6.29443e11i −0.516558 + 0.516558i
\(486\) −4.62564e11 1.91600e11i −0.376105 0.155788i
\(487\) −4.97706e11 + 1.20157e12i −0.400952 + 0.967984i 0.586483 + 0.809961i \(0.300512\pi\)
−0.987435 + 0.158023i \(0.949488\pi\)
\(488\) 1.26084e11 5.22256e10i 0.100640 0.0416864i
\(489\) 2.47149e12i 1.95465i
\(490\) −1.05498e12 2.54694e12i −0.826723 1.99589i
\(491\) 9.01806e10 + 9.01806e10i 0.0700239 + 0.0700239i 0.741251 0.671227i \(-0.234233\pi\)
−0.671227 + 0.741251i \(0.734233\pi\)
\(492\) 3.07421e12 2.36532
\(493\) −1.79256e12 4.99559e11i −1.36667 0.380869i
\(494\) 1.01075e11 0.0763610
\(495\) −1.42018e12 1.42018e12i −1.06321 1.06321i
\(496\) 2.27304e11 + 5.48761e11i 0.168632 + 0.407114i
\(497\) 6.58300e10i 0.0483972i
\(498\) −4.86773e11 + 2.01628e11i −0.354645 + 0.146899i
\(499\) −1.70208e11 + 4.10917e11i −0.122893 + 0.296689i −0.973339 0.229373i \(-0.926332\pi\)
0.850446 + 0.526063i \(0.176332\pi\)
\(500\) 1.90708e12 + 7.89938e11i 1.36459 + 0.565233i
\(501\) 8.36684e8 8.36684e8i 0.000593324 0.000593324i
\(502\) 1.69491e12 1.69491e12i 1.19119 1.19119i
\(503\) −1.17715e12 4.87591e11i −0.819927 0.339625i −0.0670198 0.997752i \(-0.521349\pi\)
−0.752907 + 0.658127i \(0.771349\pi\)
\(504\) −2.03501e12 + 4.91295e12i −1.40485 + 3.39160i
\(505\) −6.44298e11 + 2.66877e11i −0.440834 + 0.182600i
\(506\) 1.68341e11i 0.114159i
\(507\) −9.95871e11 2.40424e12i −0.669371 1.61601i
\(508\) 6.45214e11 + 6.45214e11i 0.429850 + 0.429850i
\(509\) 1.02878e12 0.679348 0.339674 0.940543i \(-0.389683\pi\)
0.339674 + 0.940543i \(0.389683\pi\)
\(510\) −3.02148e12 + 3.85727e12i −1.97767 + 2.52472i
\(511\) 8.55254e11 0.554882
\(512\) −5.60962e11 5.60962e11i −0.360760 0.360760i
\(513\) −1.39351e12 3.36423e12i −0.888345 2.14466i
\(514\) 3.43700e11i 0.217193i
\(515\) 1.05194e12 4.35727e11i 0.658958 0.272949i
\(516\) −1.56250e12 + 3.77221e12i −0.970278 + 2.34246i
\(517\) −6.46066e11 2.67609e11i −0.397713 0.164738i
\(518\) −7.31163e10 + 7.31163e10i −0.0446201 + 0.0446201i
\(519\) −1.26688e12 + 1.26688e12i −0.766445 + 0.766445i
\(520\) 7.64958e10 + 3.16856e10i 0.0458799 + 0.0190041i
\(521\) 6.15281e10 1.48542e11i 0.0365851 0.0883241i −0.904531 0.426408i \(-0.859779\pi\)
0.941116 + 0.338084i \(0.109779\pi\)
\(522\) 7.59476e12 3.14585e12i 4.47710 1.85447i
\(523\) 5.92253e11i 0.346138i −0.984910 0.173069i \(-0.944632\pi\)
0.984910 0.173069i \(-0.0553684\pi\)
\(524\) −1.83349e12 4.42645e12i −1.06240 2.56486i
\(525\) 7.28689e11 + 7.28689e11i 0.418625 + 0.418625i
\(526\) 2.53717e12 1.44515
\(527\) 8.12410e11 2.91516e12i 0.458805 1.64632i
\(528\) 5.28982e11 0.296202
\(529\) 1.25946e12 + 1.25946e12i 0.699254 + 0.699254i
\(530\) 1.84703e12 + 4.45913e12i 1.01679 + 2.45476i
\(531\) 4.27586e12i 2.33399i
\(532\) −5.40363e12 + 2.23826e12i −2.92471 + 1.21146i
\(533\) −2.07622e10 + 5.01245e10i −0.0111430 + 0.0269016i
\(534\) −5.65192e11 2.34110e11i −0.300788 0.124590i
\(535\) 1.35343e12 1.35343e12i 0.714237 0.714237i
\(536\) 1.47277e12 1.47277e12i 0.770716 0.770716i
\(537\) −9.95904e11 4.12517e11i −0.516813 0.214071i
\(538\) 1.95044e12 4.70878e12i 1.00372 2.42319i
\(539\) 1.40094e12 5.80287e11i 0.714940 0.296138i
\(540\) 7.08081e12i 3.58353i
\(541\) 1.21404e12 + 2.93094e12i 0.609318 + 1.47102i 0.863744 + 0.503931i \(0.168113\pi\)
−0.254426 + 0.967092i \(0.581887\pi\)
\(542\) −7.64031e11 7.64031e11i −0.380289 0.380289i
\(543\) −2.44596e12 −1.20740
\(544\) 1.91298e11 + 1.57443e12i 0.0936517 + 0.770777i
\(545\) −5.50867e11 −0.267462
\(546\) −2.33695e11 2.33695e11i −0.112533 0.112533i
\(547\) −1.33959e12 3.23405e12i −0.639776 1.54456i −0.826978 0.562235i \(-0.809942\pi\)
0.187202 0.982322i \(-0.440058\pi\)
\(548\) 2.80419e12i 1.32830i
\(549\) 3.68462e11 1.52622e11i 0.173108 0.0717036i
\(550\) 2.03655e11 4.91667e11i 0.0948994 0.229107i
\(551\) 3.51904e12 + 1.45763e12i 1.62646 + 0.673700i
\(552\) −3.42322e11 + 3.42322e11i −0.156931 + 0.156931i
\(553\) −5.47568e11 + 5.47568e11i −0.248986 + 0.248986i
\(554\) −5.89145e12 2.44032e12i −2.65722 1.10066i
\(555\) 4.29796e10 1.03762e11i 0.0192284 0.0464216i
\(556\) −5.86741e12 + 2.43036e12i −2.60381 + 1.07853i
\(557\) 1.35176e12i 0.595045i −0.954715 0.297522i \(-0.903840\pi\)
0.954715 0.297522i \(-0.0961603\pi\)
\(558\) 5.11596e12 + 1.23510e13i 2.23395 + 5.39323i
\(559\) −5.09527e10 5.09527e10i −0.0220706 0.0220706i
\(560\) −9.82132e11 −0.422011
\(561\) −2.12168e12 1.66196e12i −0.904373 0.708415i
\(562\) −2.84878e12 −1.20461
\(563\) −9.61325e11 9.61325e11i −0.403258 0.403258i 0.476122 0.879379i \(-0.342042\pi\)
−0.879379 + 0.476122i \(0.842042\pi\)
\(564\) −1.82682e12 4.41033e12i −0.760220 1.83533i
\(565\) 1.10673e12i 0.456903i
\(566\) 2.70621e12 1.12095e12i 1.10838 0.459105i
\(567\) −1.68082e12 + 4.05785e12i −0.682962 + 1.64882i
\(568\) 9.03232e10 + 3.74131e10i 0.0364109 + 0.0150819i
\(569\) 1.04097e12 1.04097e12i 0.416326 0.416326i −0.467609 0.883935i \(-0.654885\pi\)
0.883935 + 0.467609i \(0.154885\pi\)
\(570\) 7.09178e12 7.09178e12i 2.81396 2.81396i
\(571\) 1.92135e12 + 7.95848e11i 0.756386 + 0.313305i 0.727344 0.686273i \(-0.240754\pi\)
0.0290418 + 0.999578i \(0.490754\pi\)
\(572\) −4.13710e10 + 9.98784e10i −0.0161590 + 0.0390112i
\(573\) −8.15764e11 + 3.37901e11i −0.316132 + 0.130946i
\(574\) 4.95642e12i 1.90575i
\(575\) 2.42002e10 + 5.84243e10i 0.00923236 + 0.0222889i
\(576\) −5.95028e12 5.95028e12i −2.25235 2.25235i
\(577\) −4.38287e12 −1.64614 −0.823072 0.567938i \(-0.807741\pi\)
−0.823072 + 0.567938i \(0.807741\pi\)
\(578\) −2.29220e12 + 3.79313e12i −0.854234 + 1.41359i
\(579\) −4.55808e12 −1.68550
\(580\) 5.23729e12 + 5.23729e12i 1.92168 + 1.92168i
\(581\) 2.05911e11 + 4.97113e11i 0.0749699 + 0.180993i
\(582\) 5.27682e12i 1.90642i
\(583\) −2.45274e12 + 1.01596e12i −0.879311 + 0.364223i
\(584\) 4.86065e11 1.17346e12i 0.172917 0.417457i
\(585\) 2.23548e11 + 9.25966e10i 0.0789168 + 0.0326884i
\(586\) −1.14768e12 + 1.14768e12i −0.402051 + 0.402051i
\(587\) −1.05748e12 + 1.05748e12i −0.367622 + 0.367622i −0.866609 0.498987i \(-0.833706\pi\)
0.498987 + 0.866609i \(0.333706\pi\)
\(588\) 9.56341e12 + 3.96130e12i 3.29925 + 1.36659i
\(589\) −2.37049e12 + 5.72286e12i −0.811556 + 1.95927i
\(590\) −5.61912e12 + 2.32752e12i −1.90912 + 0.790785i
\(591\) 5.69853e12i 1.92141i
\(592\) 7.63032e9 + 1.84212e10i 0.00255326 + 0.00616411i
\(593\) 2.49943e12 + 2.49943e12i 0.830032 + 0.830032i 0.987521 0.157489i \(-0.0503398\pi\)
−0.157489 + 0.987521i \(0.550340\pi\)
\(594\) 6.14879e12 2.02652
\(595\) 3.93921e12 + 3.08567e12i 1.28849 + 1.00931i
\(596\) 8.70772e12 2.82681
\(597\) 4.08469e12 + 4.08469e12i 1.31606 + 1.31606i
\(598\) −7.76112e9 1.87370e10i −0.00248181 0.00599163i
\(599\) 1.01514e12i 0.322186i −0.986939 0.161093i \(-0.948498\pi\)
0.986939 0.161093i \(-0.0515019\pi\)
\(600\) 1.41394e12 5.85675e11i 0.445401 0.184491i
\(601\) 1.57746e12 3.80834e12i 0.493202 1.19069i −0.459880 0.887981i \(-0.652108\pi\)
0.953082 0.302713i \(-0.0978924\pi\)
\(602\) 6.08179e12 + 2.51916e12i 1.88733 + 0.781756i
\(603\) 4.30397e12 4.30397e12i 1.32569 1.32569i
\(604\) −6.19204e12 + 6.19204e12i −1.89307 + 1.89307i
\(605\) −1.92323e12 7.96629e11i −0.583623 0.241745i
\(606\) 1.58202e12 3.81934e12i 0.476525 1.15043i
\(607\) 1.24089e12 5.13994e11i 0.371009 0.153677i −0.189386 0.981903i \(-0.560650\pi\)
0.560394 + 0.828226i \(0.310650\pi\)
\(608\) 3.24638e12i 0.963460i
\(609\) −4.76617e12 1.15065e13i −1.40408 3.38975i
\(610\) 4.01135e11 + 4.01135e11i 0.117302 + 0.117302i
\(611\) 8.42476e10 0.0244552
\(612\) −1.49580e12 1.23108e13i −0.431016 3.54737i
\(613\) −2.53955e11 −0.0726413 −0.0363207 0.999340i \(-0.511564\pi\)
−0.0363207 + 0.999340i \(0.511564\pi\)
\(614\) −5.99187e12 5.99187e12i −1.70139 1.70139i
\(615\) 2.06016e12 + 4.97368e12i 0.580716 + 1.40197i
\(616\) 4.16061e12i 1.16424i
\(617\) −7.84990e11 + 3.25153e11i −0.218062 + 0.0903244i −0.489040 0.872261i \(-0.662653\pi\)
0.270978 + 0.962586i \(0.412653\pi\)
\(618\) −2.58295e12 + 6.23579e12i −0.712308 + 1.71966i
\(619\) 2.60447e12 + 1.07881e12i 0.713036 + 0.295349i 0.709560 0.704645i \(-0.248894\pi\)
0.00347556 + 0.999994i \(0.498894\pi\)
\(620\) −8.51717e12 + 8.51717e12i −2.31490 + 2.31490i
\(621\) −5.16651e11 + 5.16651e11i −0.139407 + 0.139407i
\(622\) 8.64688e12 + 3.58166e12i 2.31634 + 0.959461i
\(623\) −2.39084e11 + 5.77199e11i −0.0635848 + 0.153507i
\(624\) −5.88779e10 + 2.43880e10i −0.0155461 + 0.00643941i
\(625\) 4.48806e12i 1.17652i
\(626\) 2.60041e12 + 6.27795e12i 0.676796 + 1.63393i
\(627\) 3.90082e12 + 3.90082e12i 1.00798 + 1.00798i
\(628\) 9.80589e11 0.251576
\(629\) 2.72716e10 9.78582e10i 0.00694676 0.0249270i
\(630\) −2.21049e13 −5.59058
\(631\) 3.76881e12 + 3.76881e12i 0.946395 + 0.946395i 0.998635 0.0522391i \(-0.0166358\pi\)
−0.0522391 + 0.998635i \(0.516636\pi\)
\(632\) 4.40101e11 + 1.06250e12i 0.109730 + 0.264912i
\(633\) 6.15890e12i 1.52471i
\(634\) 1.06588e13 4.41502e12i 2.62003 1.08525i
\(635\) −6.11488e11 + 1.47626e12i −0.149247 + 0.360314i
\(636\) −1.67435e13 6.93537e12i −4.05778 1.68079i
\(637\) −1.29177e11 + 1.29177e11i −0.0310854 + 0.0310854i
\(638\) −4.54793e12 + 4.54793e12i −1.08673 + 1.08673i
\(639\) 2.63956e11 + 1.09334e11i 0.0626294 + 0.0259420i
\(640\) 3.18253e12 7.68332e12i 0.749831 1.81025i
\(641\) −7.24300e12 + 3.00015e12i −1.69456 + 0.701911i −0.999849 0.0173765i \(-0.994469\pi\)
−0.694713 + 0.719287i \(0.744469\pi\)
\(642\) 1.13462e13i 2.63599i
\(643\) −3.04664e12 7.35523e12i −0.702864 1.69686i −0.717105 0.696965i \(-0.754533\pi\)
0.0142414 0.999899i \(-0.495467\pi\)
\(644\) 8.29846e11 + 8.29846e11i 0.190113 + 0.190113i
\(645\) −7.15005e12 −1.62664
\(646\) 5.59409e12 7.14150e12i 1.26381 1.61340i
\(647\) −6.01408e12 −1.34927 −0.674636 0.738150i \(-0.735700\pi\)
−0.674636 + 0.738150i \(0.735700\pi\)
\(648\) 4.61238e12 + 4.61238e12i 1.02763 + 1.02763i
\(649\) −1.28025e12 3.09079e12i −0.283265 0.683861i
\(650\) 6.41138e10i 0.0140877i
\(651\) 1.87126e13 7.75101e12i 4.08338 1.69139i
\(652\) 3.40503e12 8.22047e12i 0.737916 1.78149i
\(653\) 3.68774e12 + 1.52751e12i 0.793689 + 0.328757i 0.742426 0.669928i \(-0.233675\pi\)
0.0512635 + 0.998685i \(0.483675\pi\)
\(654\) 2.30905e12 2.30905e12i 0.493552 0.493552i
\(655\) 5.93272e12 5.93272e12i 1.25941 1.25941i
\(656\) −8.82993e11 3.65748e11i −0.186162 0.0771106i
\(657\) 1.42045e12 3.42928e12i 0.297429 0.718057i
\(658\) −7.11061e12 + 2.94531e12i −1.47873 + 0.612512i
\(659\) 5.58329e12i 1.15320i −0.817026 0.576601i \(-0.804379\pi\)
0.817026 0.576601i \(-0.195621\pi\)
\(660\) 4.10509e12 + 9.91057e12i 0.842123 + 2.03306i
\(661\) −5.13568e12 5.13568e12i −1.04638 1.04638i −0.998871 0.0475142i \(-0.984870\pi\)
−0.0475142 0.998871i \(-0.515130\pi\)
\(662\) −9.07710e12 −1.83690
\(663\) 3.12774e11 + 8.71655e10i 0.0628667 + 0.0175200i
\(664\) 7.99098e11 0.159530
\(665\) −7.24243e12 7.24243e12i −1.43611 1.43611i
\(666\) 1.71736e11 + 4.14608e11i 0.0338242 + 0.0816589i
\(667\) 7.64277e11i 0.149515i
\(668\) −3.93563e9 + 1.63019e9i −0.000764751 + 0.000316770i
\(669\) −2.83976e12 + 6.85579e12i −0.548105 + 1.32324i
\(670\) 7.99887e12 + 3.31324e12i 1.53353 + 0.635208i
\(671\) −2.20644e11 + 2.20644e11i −0.0420185 + 0.0420185i
\(672\) −7.50594e12 + 7.50594e12i −1.41985 + 1.41985i
\(673\) 2.05388e12 + 8.50745e11i 0.385929 + 0.159857i 0.567208 0.823575i \(-0.308024\pi\)
−0.181279 + 0.983432i \(0.558024\pi\)
\(674\) 1.68001e12 4.05589e12i 0.313575 0.757037i
\(675\) 2.13400e12 8.83932e11i 0.395665 0.163890i
\(676\) 9.36883e12i 1.72554i
\(677\) 3.66512e11 + 8.84838e11i 0.0670562 + 0.161888i 0.953855 0.300268i \(-0.0970760\pi\)
−0.886799 + 0.462156i \(0.847076\pi\)
\(678\) 4.63904e12 + 4.63904e12i 0.843131 + 0.843131i
\(679\) −5.38892e12 −0.972944
\(680\) 6.47250e12 3.65118e12i 1.16087 0.654853i
\(681\) 1.46044e13 2.60209
\(682\) −7.39609e12 7.39609e12i −1.30910 1.30910i
\(683\) 1.91863e12 + 4.63199e12i 0.337364 + 0.814468i 0.997967 + 0.0637328i \(0.0203005\pi\)
−0.660603 + 0.750735i \(0.729699\pi\)
\(684\) 2.53842e13i 4.43415i
\(685\) −4.53683e12 + 1.87922e12i −0.787308 + 0.326114i
\(686\) 9.73713e11 2.35075e12i 0.167870 0.405273i
\(687\) −7.19742e12 2.98127e12i −1.23274 0.510617i
\(688\) 8.97582e11 8.97582e11i 0.152731 0.152731i
\(689\) 2.26160e11 2.26160e11i 0.0382323 0.0382323i
\(690\) −1.85921e12 7.70108e11i −0.312253 0.129339i
\(691\) −1.06373e12 + 2.56806e12i −0.177492 + 0.428504i −0.987439 0.157999i \(-0.949496\pi\)
0.809947 + 0.586503i \(0.199496\pi\)
\(692\) 5.95918e12 2.46837e12i 0.987891 0.409198i
\(693\) 1.21588e13i 2.00258i
\(694\) 3.72431e12 + 8.99128e12i 0.609436 + 1.47131i
\(695\) −7.86403e12 7.86403e12i −1.27854 1.27854i
\(696\) −1.84965e13 −2.98777
\(697\) 2.39247e12 + 4.24116e12i 0.383971 + 0.680671i
\(698\) 1.79868e13 2.86817
\(699\) 1.28979e13 + 1.28979e13i 2.04348 + 2.04348i
\(700\) −1.41977e12 3.42764e12i −0.223500 0.539577i
\(701\) 2.98928e12i 0.467558i −0.972290 0.233779i \(-0.924891\pi\)
0.972290 0.233779i \(-0.0751092\pi\)
\(702\) −6.84386e11 + 2.83482e11i −0.106361 + 0.0440563i
\(703\) −7.95742e10 + 1.92109e11i −0.0122878 + 0.0296653i
\(704\) 6.08272e12 + 2.51954e12i 0.933298 + 0.386585i
\(705\) 5.91112e12 5.91112e12i 0.901195 0.901195i
\(706\) 3.00936e12 3.00936e12i 0.455883 0.455883i
\(707\) −3.90047e12 1.61563e12i −0.587124 0.243195i
\(708\) 8.73952e12 2.10991e13i 1.30719 3.15583i
\(709\) 1.50245e12 6.22333e11i 0.223301 0.0924943i −0.268228 0.963355i \(-0.586438\pi\)
0.491529 + 0.870861i \(0.336438\pi\)
\(710\) 4.06393e11i 0.0600183i
\(711\) 1.28613e12 + 3.10500e12i 0.188744 + 0.455667i
\(712\) 6.56077e11 + 6.56077e11i 0.0956742 + 0.0956742i
\(713\) 1.24291e12 0.180110
\(714\) −2.94459e13 + 3.57777e12i −4.24017 + 0.515193i
\(715\) −1.89315e11 −0.0270899
\(716\) 2.74416e12 + 2.74416e12i 0.390212 + 0.390212i
\(717\) 5.42523e12 + 1.30977e13i 0.766624 + 1.85079i
\(718\) 1.78755e13i 2.51014i
\(719\) −2.95985e12 + 1.22601e12i −0.413038 + 0.171086i −0.579519 0.814959i \(-0.696760\pi\)
0.166481 + 0.986045i \(0.446760\pi\)
\(720\) −1.63118e12 + 3.93802e12i −0.226207 + 0.546112i
\(721\) 6.36826e12 + 2.63782e12i 0.877631 + 0.363527i
\(722\) −4.60255e12 + 4.60255e12i −0.630349 + 0.630349i
\(723\) −5.33092e12 + 5.33092e12i −0.725571 + 0.725571i
\(724\) 8.13554e12 + 3.36985e12i 1.10043 + 0.455814i
\(725\) −9.24608e11 + 2.23220e12i −0.124290 + 0.300063i
\(726\) 1.14007e13 4.72234e12i 1.52306 0.630874i
\(727\) 1.01002e13i 1.34099i 0.741914 + 0.670495i \(0.233918\pi\)
−0.741914 + 0.670495i \(0.766082\pi\)
\(728\) 1.91819e11 + 4.63093e11i 0.0253105 + 0.0611050i
\(729\) −4.18986e12 4.18986e12i −0.549447 0.549447i
\(730\) 5.27979e12 0.688120
\(731\) −6.42012e12 + 7.80064e11i −0.831601 + 0.101042i
\(732\) −2.13010e12 −0.274221
\(733\) −1.06619e13 1.06619e13i −1.36417 1.36417i −0.868527 0.495643i \(-0.834933\pi\)
−0.495643 0.868527i \(-0.665067\pi\)
\(734\) −5.40578e12 1.30507e13i −0.687426 1.65959i
\(735\) 1.81270e13i 2.29104i
\(736\) −6.01807e11 + 2.49276e11i −0.0755974 + 0.0313135i
\(737\) −1.82244e12 + 4.39976e12i −0.227536 + 0.549320i
\(738\) −1.98736e13 8.23192e12i −2.46617 1.02152i
\(739\) −3.16247e12 + 3.16247e12i −0.390056 + 0.390056i −0.874707 0.484652i \(-0.838946\pi\)
0.484652 + 0.874707i \(0.338946\pi\)
\(740\) −2.85911e11 + 2.85911e11i −0.0350500 + 0.0350500i
\(741\) −6.14020e11 2.54335e11i −0.0748170 0.0309902i
\(742\) −1.11816e13 + 2.69948e13i −1.35421 + 3.26936i
\(743\) 1.22180e13 5.06085e12i 1.47079 0.609220i 0.503748 0.863851i \(-0.331954\pi\)
0.967038 + 0.254631i \(0.0819541\pi\)
\(744\) 3.00800e13i 3.59915i
\(745\) 5.83544e12 + 1.40880e13i 0.694017 + 1.67551i
\(746\) −1.59548e12 1.59548e12i −0.188610 0.188610i
\(747\) 2.33525e12 0.274404
\(748\) 4.76725e12 + 8.45096e12i 0.556815 + 0.987072i
\(749\) 1.15872e13 1.34528
\(750\) −1.51519e13 1.51519e13i −1.74861 1.74861i
\(751\) 1.78450e10 + 4.30817e10i 0.00204709 + 0.00494212i 0.924900 0.380211i \(-0.124149\pi\)
−0.922853 + 0.385153i \(0.874149\pi\)
\(752\) 1.48411e12i 0.169233i
\(753\) −1.45614e13 + 6.03152e12i −1.65054 + 0.683674i
\(754\) 2.96527e11 7.15879e11i 0.0334113 0.0806619i
\(755\) −1.41675e13 5.86837e12i −1.58684 0.657289i
\(756\) 3.03109e13 3.03109e13i 3.37482 3.37482i
\(757\) 6.01218e12 6.01218e12i 0.665427 0.665427i −0.291227 0.956654i \(-0.594064\pi\)
0.956654 + 0.291227i \(0.0940635\pi\)
\(758\) 1.85029e13 + 7.66416e12i 2.03577 + 0.843243i
\(759\) 4.23597e11 1.02265e12i 0.0463303 0.111851i
\(760\) −1.40532e13 + 5.82102e12i −1.52797 + 0.632904i
\(761\) 1.78762e12i 0.193217i 0.995322 + 0.0966083i \(0.0307994\pi\)
−0.995322 + 0.0966083i \(0.969201\pi\)
\(762\)