Properties

Label 17.10.d.a.8.7
Level $17$
Weight $10$
Character 17.8
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 8.7
Character \(\chi\) \(=\) 17.8
Dual form 17.10.d.a.15.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.763172 + 0.763172i) q^{2} +(-66.0099 + 159.362i) q^{3} +510.835i q^{4} +(-1926.04 - 797.791i) q^{5} +(-71.2437 - 171.997i) q^{6} +(7148.81 - 2961.13i) q^{7} +(-780.599 - 780.599i) q^{8} +(-7120.96 - 7120.96i) q^{9} +O(q^{10})\) \(q+(-0.763172 + 0.763172i) q^{2} +(-66.0099 + 159.362i) q^{3} +510.835i q^{4} +(-1926.04 - 797.791i) q^{5} +(-71.2437 - 171.997i) q^{6} +(7148.81 - 2961.13i) q^{7} +(-780.599 - 780.599i) q^{8} +(-7120.96 - 7120.96i) q^{9} +(2078.75 - 861.046i) q^{10} +(-33234.4 - 80234.8i) q^{11} +(-81407.7 - 33720.2i) q^{12} +121107. i q^{13} +(-3195.92 + 7715.62i) q^{14} +(254275. - 254275. i) q^{15} -260356. q^{16} +(-277938. - 203318. i) q^{17} +10869.0 q^{18} +(-66596.2 + 66596.2i) q^{19} +(407540. - 983888. i) q^{20} +1.33471e6i q^{21} +(86596.5 + 35869.4i) q^{22} +(283246. + 683817. i) q^{23} +(175925. - 72870.6i) q^{24} +(1.69208e6 + 1.69208e6i) q^{25} +(-92425.5 - 92425.5i) q^{26} +(-1.53186e6 + 634516. i) q^{27} +(1.51265e6 + 3.65186e6i) q^{28} +(-3.63139e6 - 1.50417e6i) q^{29} +388111. i q^{30} +(1.54840e6 - 3.73817e6i) q^{31} +(598363. - 598363. i) q^{32} +1.49802e7 q^{33} +(367281. - 56948.3i) q^{34} -1.61312e7 q^{35} +(3.63764e6 - 3.63764e6i) q^{36} +(-805034. + 1.94352e6i) q^{37} -101649. i q^{38} +(-1.92999e7 - 7.99427e6i) q^{39} +(880708. + 2.12622e6i) q^{40} +(-1.08648e7 + 4.50036e6i) q^{41} +(-1.01862e6 - 1.01862e6i) q^{42} +(-2.84382e7 - 2.84382e7i) q^{43} +(4.09868e7 - 1.69773e7i) q^{44} +(8.03421e6 + 1.93963e7i) q^{45} +(-738035. - 305704. i) q^{46} +4.45793e7i q^{47} +(1.71861e7 - 4.14909e7i) q^{48} +(1.38029e7 - 1.38029e7i) q^{49} -2.58270e6 q^{50} +(5.07478e7 - 3.08718e7i) q^{51} -6.18657e7 q^{52} +(-2.84995e7 + 2.84995e7i) q^{53} +(684826. - 1.65332e6i) q^{54} +1.81049e8i q^{55} +(-7.89181e6 - 3.26890e6i) q^{56} +(-6.21689e6 - 1.50089e7i) q^{57} +(3.91931e6 - 1.62343e6i) q^{58} +(2.86821e7 + 2.86821e7i) q^{59} +(1.29893e8 + 1.29893e8i) q^{60} +(1.51274e7 - 6.26597e6i) q^{61} +(1.67117e6 + 4.03456e6i) q^{62} +(-7.19925e7 - 2.98203e7i) q^{63} -1.32389e8i q^{64} +(9.66182e7 - 2.33257e8i) q^{65} +(-1.14325e7 + 1.14325e7i) q^{66} -1.48699e8 q^{67} +(1.03862e8 - 1.41981e8i) q^{68} -1.27672e8 q^{69} +(1.23109e7 - 1.23109e7i) q^{70} +(-8.18384e7 + 1.97575e8i) q^{71} +1.11172e7i q^{72} +(2.44520e8 + 1.01283e8i) q^{73} +(-868864. - 2.09762e6i) q^{74} +(-3.81348e8 + 1.57960e8i) q^{75} +(-3.40197e7 - 3.40197e7i) q^{76} +(-4.75172e8 - 4.75172e8i) q^{77} +(2.08301e7 - 8.62812e6i) q^{78} +(1.19634e7 + 2.88823e7i) q^{79} +(5.01456e8 + 2.07710e8i) q^{80} -4.84223e8i q^{81} +(4.85718e6 - 1.17263e7i) q^{82} +(2.43270e8 - 2.43270e8i) q^{83} -6.81818e8 q^{84} +(3.73115e8 + 6.13335e8i) q^{85} +4.34065e7 q^{86} +(4.79415e8 - 4.79415e8i) q^{87} +(-3.66885e7 + 8.85739e7i) q^{88} +3.04789e7i q^{89} +(-2.09342e7 - 8.67122e6i) q^{90} +(3.58614e8 + 8.65772e8i) q^{91} +(-3.49318e8 + 1.44692e8i) q^{92} +(4.93513e8 + 4.93513e8i) q^{93} +(-3.40216e7 - 3.40216e7i) q^{94} +(1.81397e8 - 7.51369e7i) q^{95} +(5.58585e7 + 1.34854e8i) q^{96} +(-4.54629e8 - 1.88314e8i) q^{97} +2.10679e7i q^{98} +(-3.34689e8 + 8.08010e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52 q - 4 q^{2} - 4 q^{3} - 1140 q^{5} + 12308 q^{6} - 4 q^{7} + 2044 q^{8} - 83224 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 52 q - 4 q^{2} - 4 q^{3} - 1140 q^{5} + 12308 q^{6} - 4 q^{7} + 2044 q^{8} - 83224 q^{9} - 117636 q^{10} - 115768 q^{11} - 145528 q^{12} + 463660 q^{14} + 288244 q^{15} - 3407880 q^{16} - 271932 q^{17} + 2193336 q^{18} - 406700 q^{19} + 493564 q^{20} + 800964 q^{22} - 4172180 q^{23} + 15078440 q^{24} + 11946576 q^{25} - 14209012 q^{26} - 7973656 q^{27} + 13540804 q^{28} + 7833752 q^{29} + 5936252 q^{31} - 26730116 q^{32} - 1635208 q^{33} - 53493988 q^{34} + 46992776 q^{35} - 12761764 q^{36} + 74606796 q^{37} + 74096776 q^{39} - 69317672 q^{40} - 71362288 q^{41} - 308117664 q^{42} - 3765712 q^{43} + 163659820 q^{44} + 14167408 q^{45} + 72135428 q^{46} + 164621412 q^{48} - 284548508 q^{49} + 226223888 q^{50} - 406733132 q^{51} + 103553016 q^{52} - 244724728 q^{53} + 971226260 q^{54} + 470691652 q^{56} - 440646580 q^{57} - 308561768 q^{58} - 481734984 q^{59} + 379626176 q^{60} + 507966228 q^{61} + 358867236 q^{62} + 1070586456 q^{63} + 366263684 q^{65} - 2244715148 q^{66} - 311910088 q^{67} - 1839196668 q^{68} + 533688136 q^{69} + 34867672 q^{70} + 186006812 q^{71} + 487115192 q^{73} - 214149412 q^{74} + 533015920 q^{75} + 1104236912 q^{76} - 237869092 q^{77} - 2081523384 q^{78} - 136338052 q^{79} - 922534152 q^{80} + 1951892384 q^{82} + 1843663888 q^{83} - 2630025952 q^{84} - 395061976 q^{85} + 1538547296 q^{86} - 369395636 q^{87} - 3388839640 q^{88} + 874363684 q^{90} + 2087197720 q^{91} + 1061427500 q^{92} + 576415420 q^{93} + 6899365112 q^{94} + 5031766876 q^{95} + 490811364 q^{96} - 3419996368 q^{97} - 5630536112 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{5}{8}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.763172 + 0.763172i −0.0337277 + 0.0337277i −0.723770 0.690042i \(-0.757592\pi\)
0.690042 + 0.723770i \(0.257592\pi\)
\(3\) −66.0099 + 159.362i −0.470504 + 1.13590i 0.493437 + 0.869782i \(0.335740\pi\)
−0.963941 + 0.266116i \(0.914260\pi\)
\(4\) 510.835i 0.997725i
\(5\) −1926.04 797.791i −1.37816 0.570853i −0.434172 0.900830i \(-0.642959\pi\)
−0.943989 + 0.329977i \(0.892959\pi\)
\(6\) −71.2437 171.997i −0.0224422 0.0541803i
\(7\) 7148.81 2961.13i 1.12536 0.466141i 0.259161 0.965834i \(-0.416554\pi\)
0.866202 + 0.499694i \(0.166554\pi\)
\(8\) −780.599 780.599i −0.0673788 0.0673788i
\(9\) −7120.96 7120.96i −0.361782 0.361782i
\(10\) 2078.75 861.046i 0.0657358 0.0272287i
\(11\) −33234.4 80234.8i −0.684416 1.65233i −0.755739 0.654873i \(-0.772722\pi\)
0.0713230 0.997453i \(-0.477278\pi\)
\(12\) −81407.7 33720.2i −1.13331 0.469434i
\(13\) 121107.i 1.17605i 0.808844 + 0.588023i \(0.200094\pi\)
−0.808844 + 0.588023i \(0.799906\pi\)
\(14\) −3195.92 + 7715.62i −0.0222341 + 0.0536778i
\(15\) 254275. 254275.i 1.29686 1.29686i
\(16\) −260356. −0.993180
\(17\) −277938. 203318.i −0.807102 0.590412i
\(18\) 10869.0 0.0244042
\(19\) −66596.2 + 66596.2i −0.117235 + 0.117235i −0.763291 0.646055i \(-0.776418\pi\)
0.646055 + 0.763291i \(0.276418\pi\)
\(20\) 407540. 983888.i 0.569554 1.37503i
\(21\) 1.33471e6i 1.49762i
\(22\) 86596.5 + 35869.4i 0.0788130 + 0.0326454i
\(23\) 283246. + 683817.i 0.211052 + 0.509524i 0.993585 0.113084i \(-0.0360730\pi\)
−0.782534 + 0.622608i \(0.786073\pi\)
\(24\) 175925. 72870.6i 0.108237 0.0448334i
\(25\) 1.69208e6 + 1.69208e6i 0.866347 + 0.866347i
\(26\) −92425.5 92425.5i −0.0396654 0.0396654i
\(27\) −1.53186e6 + 634516.i −0.554730 + 0.229777i
\(28\) 1.51265e6 + 3.65186e6i 0.465080 + 1.12280i
\(29\) −3.63139e6 1.50417e6i −0.953415 0.394917i −0.148901 0.988852i \(-0.547574\pi\)
−0.804513 + 0.593935i \(0.797574\pi\)
\(30\) 388111.i 0.0874804i
\(31\) 1.54840e6 3.73817e6i 0.301131 0.726995i −0.698801 0.715316i \(-0.746283\pi\)
0.999932 0.0116785i \(-0.00371746\pi\)
\(32\) 598363. 598363.i 0.100876 0.100876i
\(33\) 1.49802e7 2.19889
\(34\) 367281. 56948.3i 0.0471350 0.00730846i
\(35\) −1.61312e7 −1.81703
\(36\) 3.63764e6 3.63764e6i 0.360959 0.360959i
\(37\) −805034. + 1.94352e6i −0.0706166 + 0.170483i −0.955247 0.295809i \(-0.904411\pi\)
0.884630 + 0.466293i \(0.154411\pi\)
\(38\) 101649.i 0.00790816i
\(39\) −1.92999e7 7.99427e6i −1.33587 0.553335i
\(40\) 880708. + 2.12622e6i 0.0543954 + 0.131322i
\(41\) −1.08648e7 + 4.50036e6i −0.600476 + 0.248725i −0.662150 0.749371i \(-0.730356\pi\)
0.0616744 + 0.998096i \(0.480356\pi\)
\(42\) −1.01862e6 1.01862e6i −0.0505113 0.0505113i
\(43\) −2.84382e7 2.84382e7i −1.26851 1.26851i −0.946857 0.321655i \(-0.895761\pi\)
−0.321655 0.946857i \(-0.604239\pi\)
\(44\) 4.09868e7 1.69773e7i 1.64857 0.682859i
\(45\) 8.03421e6 + 1.93963e7i 0.292070 + 0.705119i
\(46\) −738035. 305704.i −0.0243034 0.0100668i
\(47\) 4.45793e7i 1.33258i 0.745694 + 0.666289i \(0.232118\pi\)
−0.745694 + 0.666289i \(0.767882\pi\)
\(48\) 1.71861e7 4.14909e7i 0.467295 1.12815i
\(49\) 1.38029e7 1.38029e7i 0.342048 0.342048i
\(50\) −2.58270e6 −0.0584399
\(51\) 5.07478e7 3.08718e7i 1.05039 0.638994i
\(52\) −6.18657e7 −1.17337
\(53\) −2.84995e7 + 2.84995e7i −0.496131 + 0.496131i −0.910231 0.414100i \(-0.864096\pi\)
0.414100 + 0.910231i \(0.364096\pi\)
\(54\) 684826. 1.65332e6i 0.0109599 0.0264596i
\(55\) 1.81049e8i 2.66787i
\(56\) −7.89181e6 3.26890e6i −0.107234 0.0444176i
\(57\) −6.21689e6 1.50089e7i −0.0780075 0.188327i
\(58\) 3.91931e6 1.62343e6i 0.0454762 0.0188369i
\(59\) 2.86821e7 + 2.86821e7i 0.308161 + 0.308161i 0.844196 0.536035i \(-0.180078\pi\)
−0.536035 + 0.844196i \(0.680078\pi\)
\(60\) 1.29893e8 + 1.29893e8i 1.29391 + 1.29391i
\(61\) 1.51274e7 6.26597e6i 0.139888 0.0579434i −0.311641 0.950200i \(-0.600879\pi\)
0.451529 + 0.892256i \(0.350879\pi\)
\(62\) 1.67117e6 + 4.03456e6i 0.0143634 + 0.0346764i
\(63\) −7.19925e7 2.98203e7i −0.575778 0.238495i
\(64\) 1.32389e8i 0.986375i
\(65\) 9.66182e7 2.33257e8i 0.671349 1.62078i
\(66\) −1.14325e7 + 1.14325e7i −0.0741637 + 0.0741637i
\(67\) −1.48699e8 −0.901511 −0.450755 0.892648i \(-0.648845\pi\)
−0.450755 + 0.892648i \(0.648845\pi\)
\(68\) 1.03862e8 1.41981e8i 0.589069 0.805266i
\(69\) −1.27672e8 −0.678068
\(70\) 1.23109e7 1.23109e7i 0.0612843 0.0612843i
\(71\) −8.18384e7 + 1.97575e8i −0.382204 + 0.922721i 0.609336 + 0.792912i \(0.291436\pi\)
−0.991539 + 0.129808i \(0.958564\pi\)
\(72\) 1.11172e7i 0.0487529i
\(73\) 2.44520e8 + 1.01283e8i 1.00777 + 0.417432i 0.824641 0.565657i \(-0.191377\pi\)
0.183129 + 0.983089i \(0.441377\pi\)
\(74\) −868864. 2.09762e6i −0.00336828 0.00813176i
\(75\) −3.81348e8 + 1.57960e8i −1.39170 + 0.576462i
\(76\) −3.40197e7 3.40197e7i −0.116968 0.116968i
\(77\) −4.75172e8 4.75172e8i −1.54043 1.54043i
\(78\) 2.08301e7 8.62812e6i 0.0637186 0.0263931i
\(79\) 1.19634e7 + 2.88823e7i 0.0345568 + 0.0834276i 0.940216 0.340579i \(-0.110623\pi\)
−0.905659 + 0.424007i \(0.860623\pi\)
\(80\) 5.01456e8 + 2.07710e8i 1.36876 + 0.566960i
\(81\) 4.84223e8i 1.24986i
\(82\) 4.85718e6 1.17263e7i 0.0118638 0.0286416i
\(83\) 2.43270e8 2.43270e8i 0.562649 0.562649i −0.367410 0.930059i \(-0.619756\pi\)
0.930059 + 0.367410i \(0.119756\pi\)
\(84\) −6.81818e8 −1.49421
\(85\) 3.73115e8 + 6.13335e8i 0.775278 + 1.27442i
\(86\) 4.34065e7 0.0855681
\(87\) 4.79415e8 4.79415e8i 0.897171 0.897171i
\(88\) −3.66885e7 + 8.85739e7i −0.0652166 + 0.157447i
\(89\) 3.04789e7i 0.0514926i 0.999669 + 0.0257463i \(0.00819621\pi\)
−0.999669 + 0.0257463i \(0.991804\pi\)
\(90\) −2.09342e7 8.67122e6i −0.0336329 0.0139312i
\(91\) 3.58614e8 + 8.65772e8i 0.548203 + 1.32348i
\(92\) −3.49318e8 + 1.44692e8i −0.508365 + 0.210572i
\(93\) 4.93513e8 + 4.93513e8i 0.684108 + 0.684108i
\(94\) −3.40216e7 3.40216e7i −0.0449448 0.0449448i
\(95\) 1.81397e8 7.51369e7i 0.228493 0.0946449i
\(96\) 5.58585e7 + 1.34854e8i 0.0671225 + 0.162048i
\(97\) −4.54629e8 1.88314e8i −0.521416 0.215978i 0.106423 0.994321i \(-0.466060\pi\)
−0.627839 + 0.778343i \(0.716060\pi\)
\(98\) 2.10679e7i 0.0230730i
\(99\) −3.34689e8 + 8.08010e8i −0.350173 + 0.845392i
\(100\) −8.64376e8 + 8.64376e8i −0.864376 + 0.864376i
\(101\) −4.15380e8 −0.397191 −0.198596 0.980082i \(-0.563638\pi\)
−0.198596 + 0.980082i \(0.563638\pi\)
\(102\) −1.51688e7 + 6.22898e7i −0.0138756 + 0.0569792i
\(103\) 1.47645e9 1.29256 0.646280 0.763100i \(-0.276324\pi\)
0.646280 + 0.763100i \(0.276324\pi\)
\(104\) 9.45360e7 9.45360e7i 0.0792405 0.0792405i
\(105\) 1.06482e9 2.57071e9i 0.854920 2.06396i
\(106\) 4.35001e7i 0.0334668i
\(107\) 8.55530e8 + 3.54372e8i 0.630970 + 0.261356i 0.675165 0.737667i \(-0.264072\pi\)
−0.0441954 + 0.999023i \(0.514072\pi\)
\(108\) −3.24133e8 7.82527e8i −0.229254 0.553468i
\(109\) −5.98247e8 + 2.47802e8i −0.405939 + 0.168146i −0.576304 0.817236i \(-0.695506\pi\)
0.170364 + 0.985381i \(0.445506\pi\)
\(110\) −1.38172e8 1.38172e8i −0.0899813 0.0899813i
\(111\) −2.56584e8 2.56584e8i −0.160426 0.160426i
\(112\) −1.86124e9 + 7.70949e8i −1.11769 + 0.462961i
\(113\) 2.73312e8 + 6.59833e8i 0.157690 + 0.380698i 0.982903 0.184124i \(-0.0589448\pi\)
−0.825213 + 0.564822i \(0.808945\pi\)
\(114\) 1.61989e7 + 6.70982e6i 0.00898286 + 0.00372082i
\(115\) 1.54303e9i 0.822685i
\(116\) 7.68383e8 1.85504e9i 0.394019 0.951245i
\(117\) 8.62399e8 8.62399e8i 0.425473 0.425473i
\(118\) −4.37788e7 −0.0207871
\(119\) −2.58898e9 6.30467e8i −1.18350 0.288205i
\(120\) −3.96974e8 −0.174762
\(121\) −3.66578e9 + 3.66578e9i −1.55465 + 1.55465i
\(122\) −6.76278e6 + 1.63268e7i −0.00276380 + 0.00667240i
\(123\) 2.02851e9i 0.799105i
\(124\) 1.90959e9 + 7.90977e8i 0.725341 + 0.300446i
\(125\) −3.50904e8 8.47157e8i −0.128556 0.310362i
\(126\) 7.77007e7 3.21847e7i 0.0274636 0.0113758i
\(127\) −8.46557e8 8.46557e8i −0.288762 0.288762i 0.547829 0.836590i \(-0.315455\pi\)
−0.836590 + 0.547829i \(0.815455\pi\)
\(128\) 4.07397e8 + 4.07397e8i 0.134145 + 0.134145i
\(129\) 6.40918e9 2.65477e9i 2.03774 0.844059i
\(130\) 1.04279e8 + 2.51751e8i 0.0320222 + 0.0773084i
\(131\) −5.41307e8 2.24217e8i −0.160592 0.0665192i 0.300940 0.953643i \(-0.402700\pi\)
−0.461531 + 0.887124i \(0.652700\pi\)
\(132\) 7.65240e9i 2.19389i
\(133\) −2.78883e8 + 6.73283e8i −0.0772840 + 0.186580i
\(134\) 1.13483e8 1.13483e8i 0.0304059 0.0304059i
\(135\) 3.45663e9 0.895675
\(136\) 5.82488e7 + 3.75668e8i 0.0146003 + 0.0941628i
\(137\) −3.05114e9 −0.739978 −0.369989 0.929036i \(-0.620639\pi\)
−0.369989 + 0.929036i \(0.620639\pi\)
\(138\) 9.74353e7 9.74353e7i 0.0228697 0.0228697i
\(139\) −2.95994e9 + 7.14593e9i −0.672537 + 1.62365i 0.104747 + 0.994499i \(0.466597\pi\)
−0.777284 + 0.629149i \(0.783403\pi\)
\(140\) 8.24041e9i 1.81289i
\(141\) −7.10424e9 2.94267e9i −1.51367 0.626983i
\(142\) −8.83272e7 2.13241e8i −0.0182304 0.0440122i
\(143\) 9.71700e9 4.02492e9i 1.94321 0.804905i
\(144\) 1.85399e9 + 1.85399e9i 0.359315 + 0.359315i
\(145\) 5.79418e9 + 5.79418e9i 1.08852 + 1.08852i
\(146\) −2.63907e8 + 1.09314e8i −0.0480688 + 0.0199108i
\(147\) 1.28853e9 + 3.11078e9i 0.227596 + 0.549466i
\(148\) −9.92820e8 4.11240e8i −0.170096 0.0704559i
\(149\) 3.24948e9i 0.540102i 0.962846 + 0.270051i \(0.0870405\pi\)
−0.962846 + 0.270051i \(0.912959\pi\)
\(150\) 1.70484e8 4.11585e8i 0.0274962 0.0663817i
\(151\) −5.53922e9 + 5.53922e9i −0.867067 + 0.867067i −0.992147 0.125080i \(-0.960081\pi\)
0.125080 + 0.992147i \(0.460081\pi\)
\(152\) 1.03970e8 0.0157983
\(153\) 5.31370e8 + 3.42701e9i 0.0783946 + 0.505596i
\(154\) 7.25276e8 0.103911
\(155\) −5.96456e9 + 5.96456e9i −0.830014 + 0.830014i
\(156\) 4.08375e9 9.85905e9i 0.552076 1.33283i
\(157\) 4.52103e9i 0.593867i −0.954898 0.296933i \(-0.904036\pi\)
0.954898 0.296933i \(-0.0959640\pi\)
\(158\) −3.11723e7 1.29120e7i −0.00397935 0.00164830i
\(159\) −2.66049e9 6.42300e9i −0.330122 0.796986i
\(160\) −1.62984e9 + 6.75101e8i −0.196610 + 0.0814384i
\(161\) 4.04975e9 + 4.04975e9i 0.475020 + 0.475020i
\(162\) 3.69545e8 + 3.69545e8i 0.0421551 + 0.0421551i
\(163\) 6.54828e9 2.71239e9i 0.726580 0.300959i 0.0114341 0.999935i \(-0.496360\pi\)
0.715146 + 0.698975i \(0.246360\pi\)
\(164\) −2.29894e9 5.55014e9i −0.248159 0.599110i
\(165\) −2.88524e10 1.19511e10i −3.03043 1.25525i
\(166\) 3.71314e8i 0.0379537i
\(167\) 3.82039e9 9.22324e9i 0.380087 0.917612i −0.611860 0.790966i \(-0.709579\pi\)
0.991948 0.126647i \(-0.0404214\pi\)
\(168\) 1.04188e9 1.04188e9i 0.100908 0.100908i
\(169\) −4.06242e9 −0.383085
\(170\) −7.52830e8 1.83329e8i −0.0691317 0.0168349i
\(171\) 9.48457e8 0.0848272
\(172\) 1.45272e10 1.45272e10i 1.26563 1.26563i
\(173\) −1.89068e9 + 4.56449e9i −0.160476 + 0.387423i −0.983581 0.180466i \(-0.942240\pi\)
0.823106 + 0.567888i \(0.192240\pi\)
\(174\) 7.31752e8i 0.0605191i
\(175\) 1.71069e10 + 7.08590e9i 1.37879 + 0.571116i
\(176\) 8.65277e9 + 2.08896e10i 0.679748 + 1.64106i
\(177\) −6.46415e9 + 2.67754e9i −0.495030 + 0.205048i
\(178\) −2.32607e7 2.32607e7i −0.00173673 0.00173673i
\(179\) 3.20249e9 + 3.20249e9i 0.233157 + 0.233157i 0.814009 0.580852i \(-0.197280\pi\)
−0.580852 + 0.814009i \(0.697280\pi\)
\(180\) −9.90831e9 + 4.10415e9i −0.703515 + 0.291405i
\(181\) −1.06968e10 2.58243e10i −0.740796 1.78844i −0.602613 0.798033i \(-0.705874\pi\)
−0.138183 0.990407i \(-0.544126\pi\)
\(182\) −9.34417e8 3.87048e8i −0.0631276 0.0261483i
\(183\) 2.82435e9i 0.186161i
\(184\) 3.12685e8 7.54888e8i 0.0201107 0.0485515i
\(185\) 3.10105e9 3.10105e9i 0.194642 0.194642i
\(186\) −7.53270e8 −0.0461469
\(187\) −7.07606e9 + 2.90575e10i −0.423160 + 1.73768i
\(188\) −2.27727e10 −1.32955
\(189\) −9.07207e9 + 9.07207e9i −0.517164 + 0.517164i
\(190\) −8.10944e7 + 1.95779e8i −0.00451439 + 0.0108987i
\(191\) 1.16299e10i 0.632303i −0.948709 0.316151i \(-0.897609\pi\)
0.948709 0.316151i \(-0.102391\pi\)
\(192\) 2.10978e10 + 8.73899e9i 1.12042 + 0.464094i
\(193\) −2.10829e9 5.08986e9i −0.109376 0.264057i 0.859709 0.510784i \(-0.170645\pi\)
−0.969085 + 0.246727i \(0.920645\pi\)
\(194\) 4.90676e8 2.03245e8i 0.0248706 0.0103018i
\(195\) 3.07945e10 + 3.07945e10i 1.52517 + 1.52517i
\(196\) 7.05099e9 + 7.05099e9i 0.341270 + 0.341270i
\(197\) 2.30545e10 9.54947e9i 1.09058 0.451733i 0.236370 0.971663i \(-0.424042\pi\)
0.854209 + 0.519930i \(0.174042\pi\)
\(198\) −3.61225e8 8.72075e8i −0.0167026 0.0403237i
\(199\) −1.46010e9 6.04792e8i −0.0659998 0.0273380i 0.349439 0.936959i \(-0.386372\pi\)
−0.415439 + 0.909621i \(0.636372\pi\)
\(200\) 2.64168e9i 0.116747i
\(201\) 9.81560e9 2.36969e10i 0.424165 1.02402i
\(202\) 3.17006e8 3.17006e8i 0.0133964 0.0133964i
\(203\) −3.04142e10 −1.25702
\(204\) 1.57704e10 + 2.59238e10i 0.637540 + 1.04800i
\(205\) 2.45164e10 0.969538
\(206\) −1.12678e9 + 1.12678e9i −0.0435951 + 0.0435951i
\(207\) 2.85245e9 6.88642e9i 0.107982 0.260692i
\(208\) 3.15310e10i 1.16803i
\(209\) 7.55661e9 + 3.13005e9i 0.273948 + 0.113473i
\(210\) 1.14925e9 + 2.77453e9i 0.0407782 + 0.0984472i
\(211\) −3.40724e10 + 1.41133e10i −1.18340 + 0.490181i −0.885601 0.464447i \(-0.846253\pi\)
−0.297801 + 0.954628i \(0.596253\pi\)
\(212\) −1.45586e10 1.45586e10i −0.495002 0.495002i
\(213\) −2.60839e10 2.60839e10i −0.868288 0.868288i
\(214\) −9.23364e8 + 3.82470e8i −0.0300961 + 0.0124662i
\(215\) 3.20853e10 + 7.74609e10i 1.02408 + 2.47235i
\(216\) 1.69107e9 + 7.00464e8i 0.0528591 + 0.0218949i
\(217\) 3.13085e10i 0.958503i
\(218\) 2.67450e8 6.45681e8i 0.00802025 0.0193626i
\(219\) −3.22815e10 + 3.22815e10i −0.948320 + 0.948320i
\(220\) −9.24864e10 −2.66180
\(221\) 2.46232e10 3.36603e10i 0.694352 0.949189i
\(222\) 3.91635e8 0.0108216
\(223\) −9.56028e8 + 9.56028e8i −0.0258880 + 0.0258880i −0.719932 0.694044i \(-0.755827\pi\)
0.694044 + 0.719932i \(0.255827\pi\)
\(224\) 2.50575e9 6.04942e9i 0.0665000 0.160545i
\(225\) 2.40985e10i 0.626858i
\(226\) −7.12150e8 2.94982e8i −0.0181586 0.00752155i
\(227\) −8.63112e9 2.08374e10i −0.215750 0.520866i 0.778538 0.627597i \(-0.215962\pi\)
−0.994288 + 0.106731i \(0.965962\pi\)
\(228\) 7.66708e9 3.17581e9i 0.187898 0.0778300i
\(229\) 2.12485e10 + 2.12485e10i 0.510586 + 0.510586i 0.914706 0.404120i \(-0.132422\pi\)
−0.404120 + 0.914706i \(0.632422\pi\)
\(230\) 1.17760e9 + 1.17760e9i 0.0277473 + 0.0277473i
\(231\) 1.07090e11 4.43583e10i 2.47455 1.02499i
\(232\) 1.66050e9 + 4.00881e9i 0.0376309 + 0.0908489i
\(233\) −3.63512e10 1.50572e10i −0.808011 0.334689i −0.0598507 0.998207i \(-0.519062\pi\)
−0.748160 + 0.663518i \(0.769062\pi\)
\(234\) 1.31632e9i 0.0287005i
\(235\) 3.55649e10 8.58614e10i 0.760706 1.83651i
\(236\) −1.46518e10 + 1.46518e10i −0.307460 + 0.307460i
\(237\) −5.39245e9 −0.111024
\(238\) 2.45699e9 1.49468e9i 0.0496372 0.0301962i
\(239\) −4.73381e10 −0.938469 −0.469235 0.883074i \(-0.655470\pi\)
−0.469235 + 0.883074i \(0.655470\pi\)
\(240\) −6.62021e10 + 6.62021e10i −1.28802 + 1.28802i
\(241\) 2.07552e10 5.01075e10i 0.396324 0.956811i −0.592206 0.805787i \(-0.701743\pi\)
0.988530 0.151024i \(-0.0482572\pi\)
\(242\) 5.59525e9i 0.104870i
\(243\) 4.70152e10 + 1.94743e10i 0.864988 + 0.358290i
\(244\) 3.20088e9 + 7.72760e9i 0.0578116 + 0.139569i
\(245\) −3.75967e10 + 1.55730e10i −0.666656 + 0.276138i
\(246\) 1.54810e9 + 1.54810e9i 0.0269520 + 0.0269520i
\(247\) −8.06526e9 8.06526e9i −0.137874 0.137874i
\(248\) −4.12669e9 + 1.70933e9i −0.0692739 + 0.0286942i
\(249\) 2.27098e10 + 5.48262e10i 0.374383 + 0.903840i
\(250\) 9.14326e8 + 3.78726e8i 0.0148037 + 0.00613190i
\(251\) 1.22308e11i 1.94501i 0.232885 + 0.972504i \(0.425183\pi\)
−0.232885 + 0.972504i \(0.574817\pi\)
\(252\) 1.52332e10 3.67763e10i 0.237952 0.574468i
\(253\) 4.54524e10 4.54524e10i 0.697453 0.697453i
\(254\) 1.29214e9 0.0194786
\(255\) −1.22372e11 + 1.89742e10i −1.81238 + 0.281017i
\(256\) 6.71614e10 0.977326
\(257\) −7.32687e10 + 7.32687e10i −1.04766 + 1.04766i −0.0488514 + 0.998806i \(0.515556\pi\)
−0.998806 + 0.0488514i \(0.984444\pi\)
\(258\) −2.86526e9 + 6.91735e9i −0.0402601 + 0.0971966i
\(259\) 1.62777e10i 0.224773i
\(260\) 1.19156e11 + 4.93559e10i 1.61709 + 0.669822i
\(261\) 1.51478e10 + 3.65701e10i 0.202054 + 0.487803i
\(262\) 5.84226e8 2.41994e8i 0.00765994 0.00317285i
\(263\) 3.38370e10 + 3.38370e10i 0.436105 + 0.436105i 0.890699 0.454594i \(-0.150216\pi\)
−0.454594 + 0.890699i \(0.650216\pi\)
\(264\) −1.16935e10 1.16935e10i −0.148159 0.148159i
\(265\) 7.76279e10 3.21545e10i 0.966966 0.400531i
\(266\) −3.00995e8 7.26667e8i −0.00368631 0.00889955i
\(267\) −4.85719e9 2.01191e9i −0.0584903 0.0242275i
\(268\) 7.59606e10i 0.899460i
\(269\) 5.11431e9 1.23470e10i 0.0595528 0.143773i −0.891302 0.453410i \(-0.850207\pi\)
0.950855 + 0.309637i \(0.100207\pi\)
\(270\) −2.63800e9 + 2.63800e9i −0.0302091 + 0.0302091i
\(271\) 4.73253e10 0.533006 0.266503 0.963834i \(-0.414132\pi\)
0.266503 + 0.963834i \(0.414132\pi\)
\(272\) 7.23630e10 + 5.29350e10i 0.801597 + 0.586385i
\(273\) −1.61643e11 −1.76127
\(274\) 2.32854e9 2.32854e9i 0.0249578 0.0249578i
\(275\) 7.95288e10 1.91999e11i 0.838547 2.02443i
\(276\) 6.52191e10i 0.676525i
\(277\) −1.22012e11 5.05391e10i −1.24521 0.515785i −0.339874 0.940471i \(-0.610384\pi\)
−0.905340 + 0.424687i \(0.860384\pi\)
\(278\) −3.19463e9 7.71251e9i −0.0320788 0.0774452i
\(279\) −3.76455e10 + 1.55933e10i −0.371958 + 0.154070i
\(280\) 1.25920e10 + 1.25920e10i 0.122429 + 0.122429i
\(281\) 2.87424e10 + 2.87424e10i 0.275008 + 0.275008i 0.831112 0.556104i \(-0.187705\pi\)
−0.556104 + 0.831112i \(0.687705\pi\)
\(282\) 7.66752e9 3.17599e9i 0.0721995 0.0299060i
\(283\) 4.11214e10 + 9.92759e10i 0.381092 + 0.920037i 0.991755 + 0.128146i \(0.0409028\pi\)
−0.610664 + 0.791890i \(0.709097\pi\)
\(284\) −1.00928e11 4.18059e10i −0.920622 0.381334i
\(285\) 3.38675e10i 0.304075i
\(286\) −4.34404e9 + 1.04874e10i −0.0383925 + 0.0926878i
\(287\) −6.43444e10 + 6.43444e10i −0.559812 + 0.559812i
\(288\) −8.52184e9 −0.0729907
\(289\) 3.59116e10 + 1.13020e11i 0.302827 + 0.953046i
\(290\) −8.84391e9 −0.0734266
\(291\) 6.00201e10 6.00201e10i 0.490657 0.490657i
\(292\) −5.17391e10 + 1.24909e11i −0.416482 + 1.00548i
\(293\) 2.08224e11i 1.65054i −0.564738 0.825270i \(-0.691023\pi\)
0.564738 0.825270i \(-0.308977\pi\)
\(294\) −3.35743e9 1.39069e9i −0.0262086 0.0108559i
\(295\) −3.23605e10 7.81253e10i −0.248781 0.600610i
\(296\) 2.14552e9 8.88704e8i 0.0162450 0.00672891i
\(297\) 1.01821e11 + 1.01821e11i 0.759332 + 0.759332i
\(298\) −2.47991e9 2.47991e9i −0.0182164 0.0182164i
\(299\) −8.28151e10 + 3.43031e10i −0.599224 + 0.248207i
\(300\) −8.06914e10 1.94806e11i −0.575150 1.38854i
\(301\) −2.87509e11 1.19090e11i −2.01884 0.836231i
\(302\) 8.45475e9i 0.0584884i
\(303\) 2.74192e10 6.61958e10i 0.186880 0.451169i
\(304\) 1.73387e10 1.73387e10i 0.116436 0.116436i
\(305\) −3.41349e10 −0.225865
\(306\) −3.02092e9 2.20987e9i −0.0196967 0.0144085i
\(307\) 1.25476e11 0.806189 0.403094 0.915158i \(-0.367935\pi\)
0.403094 + 0.915158i \(0.367935\pi\)
\(308\) 2.42735e11 2.42735e11i 1.53693 1.53693i
\(309\) −9.74602e10 + 2.35290e11i −0.608155 + 1.46822i
\(310\) 9.10396e9i 0.0559890i
\(311\) 5.67055e9 + 2.34882e9i 0.0343719 + 0.0142373i 0.399803 0.916601i \(-0.369078\pi\)
−0.365431 + 0.930838i \(0.619078\pi\)
\(312\) 8.82514e9 + 2.13058e10i 0.0527261 + 0.127292i
\(313\) 2.81655e11 1.16665e11i 1.65870 0.687057i 0.660725 0.750628i \(-0.270249\pi\)
0.997977 + 0.0635704i \(0.0202487\pi\)
\(314\) 3.45032e9 + 3.45032e9i 0.0200298 + 0.0200298i
\(315\) 1.14870e11 + 1.14870e11i 0.657369 + 0.657369i
\(316\) −1.47541e10 + 6.11135e9i −0.0832378 + 0.0344782i
\(317\) −1.31555e11 3.17601e11i −0.731711 1.76651i −0.636812 0.771020i \(-0.719747\pi\)
−0.0948994 0.995487i \(-0.530253\pi\)
\(318\) 6.93226e9 + 2.87144e9i 0.0380148 + 0.0157463i
\(319\) 3.41354e11i 1.84564i
\(320\) −1.05619e11 + 2.54986e11i −0.563075 + 1.35938i
\(321\) −1.12947e11 + 1.12947e11i −0.593748 + 0.593748i
\(322\) −6.18131e9 −0.0320427
\(323\) 3.20498e10 4.96944e9i 0.163838 0.0254037i
\(324\) 2.47358e11 1.24702
\(325\) −2.04923e11 + 2.04923e11i −1.01886 + 1.01886i
\(326\) −2.92745e9 + 7.06748e9i −0.0143552 + 0.0346566i
\(327\) 1.11695e11i 0.540219i
\(328\) 1.19941e10 + 4.96810e9i 0.0572181 + 0.0237005i
\(329\) 1.32005e11 + 3.18689e11i 0.621169 + 1.49963i
\(330\) 3.11400e10 1.28986e10i 0.144546 0.0598730i
\(331\) −1.76789e11 1.76789e11i −0.809524 0.809524i 0.175038 0.984562i \(-0.443995\pi\)
−0.984562 + 0.175038i \(0.943995\pi\)
\(332\) 1.24271e11 + 1.24271e11i 0.561368 + 0.561368i
\(333\) 1.95724e10 8.10715e9i 0.0872257 0.0361301i
\(334\) 4.12330e9 + 9.95453e9i 0.0181295 + 0.0437685i
\(335\) 2.86400e11 + 1.18631e11i 1.24243 + 0.514630i
\(336\) 3.47501e11i 1.48740i
\(337\) 7.31768e10 1.76664e11i 0.309057 0.746130i −0.690679 0.723161i \(-0.742688\pi\)
0.999736 0.0229686i \(-0.00731178\pi\)
\(338\) 3.10033e9 3.10033e9i 0.0129206 0.0129206i
\(339\) −1.23194e11 −0.506628
\(340\) −3.13313e11 + 1.90600e11i −1.27152 + 0.773514i
\(341\) −3.51391e11 −1.40733
\(342\) −7.23836e8 + 7.23836e8i −0.00286103 + 0.00286103i
\(343\) −6.16905e10 + 1.48934e11i −0.240655 + 0.580993i
\(344\) 4.43977e10i 0.170941i
\(345\) 2.45900e11 + 1.01855e11i 0.934486 + 0.387077i
\(346\) −2.04058e9 4.92640e9i −0.00765441 0.0184794i
\(347\) 1.10225e11 4.56568e10i 0.408130 0.169053i −0.169167 0.985587i \(-0.554108\pi\)
0.577297 + 0.816535i \(0.304108\pi\)
\(348\) 2.44902e11 + 2.44902e11i 0.895130 + 0.895130i
\(349\) 1.72144e11 + 1.72144e11i 0.621124 + 0.621124i 0.945819 0.324695i \(-0.105262\pi\)
−0.324695 + 0.945819i \(0.605262\pi\)
\(350\) −1.84633e10 + 7.64773e9i −0.0657661 + 0.0272412i
\(351\) −7.68444e10 1.85519e11i −0.270228 0.652388i
\(352\) −6.78958e10 2.81233e10i −0.235722 0.0976394i
\(353\) 9.89156e10i 0.339061i −0.985525 0.169531i \(-0.945775\pi\)
0.985525 0.169531i \(-0.0542252\pi\)
\(354\) 2.88983e9 6.97668e9i 0.00978044 0.0236121i
\(355\) 3.15248e11 3.15248e11i 1.05348 1.05348i
\(356\) −1.55697e10 −0.0513755
\(357\) 2.71371e11 3.70968e11i 0.884212 1.20873i
\(358\) −4.88810e9 −0.0157277
\(359\) −7.80803e10 + 7.80803e10i −0.248094 + 0.248094i −0.820188 0.572094i \(-0.806131\pi\)
0.572094 + 0.820188i \(0.306131\pi\)
\(360\) 8.86923e9 2.14122e10i 0.0278307 0.0671893i
\(361\) 3.13818e11i 0.972512i
\(362\) 2.78718e10 + 1.15449e10i 0.0853054 + 0.0353347i
\(363\) −3.42209e11 8.26165e11i −1.03445 2.49739i
\(364\) −4.42267e11 + 1.83193e11i −1.32047 + 0.546956i
\(365\) −3.90152e11 3.90152e11i −1.15058 1.15058i
\(366\) −2.15546e9 2.15546e9i −0.00627878 0.00627878i
\(367\) −3.11552e11 + 1.29049e11i −0.896466 + 0.371328i −0.782860 0.622198i \(-0.786240\pi\)
−0.113606 + 0.993526i \(0.536240\pi\)
\(368\) −7.37449e10 1.78036e11i −0.209612 0.506049i
\(369\) 1.09415e11 + 4.53212e10i 0.307226 + 0.127257i
\(370\) 4.73327e9i 0.0131297i
\(371\) −1.19347e11 + 2.88129e11i −0.327061 + 0.789594i
\(372\) −2.52104e11 + 2.52104e11i −0.682552 + 0.682552i
\(373\) 6.84960e11 1.83221 0.916106 0.400936i \(-0.131315\pi\)
0.916106 + 0.400936i \(0.131315\pi\)
\(374\) −1.67756e10 2.75761e10i −0.0443359 0.0728804i
\(375\) 1.58168e11 0.413026
\(376\) 3.47985e10 3.47985e10i 0.0897874 0.0897874i
\(377\) 1.82166e11 4.39787e11i 0.464441 1.12126i
\(378\) 1.38471e10i 0.0348856i
\(379\) −7.03308e11 2.91320e11i −1.75093 0.725259i −0.997721 0.0674797i \(-0.978504\pi\)
−0.753210 0.657780i \(-0.771496\pi\)
\(380\) 3.83826e10 + 9.26637e10i 0.0944296 + 0.227973i
\(381\) 1.90790e11 7.90279e10i 0.463867 0.192140i
\(382\) 8.87559e9 + 8.87559e9i 0.0213261 + 0.0213261i
\(383\) −3.33399e11 3.33399e11i −0.791716 0.791716i 0.190057 0.981773i \(-0.439133\pi\)
−0.981773 + 0.190057i \(0.939133\pi\)
\(384\) −9.18160e10 + 3.80314e10i −0.215490 + 0.0892590i
\(385\) 5.36112e11 + 1.29429e12i 1.24360 + 3.00232i
\(386\) 5.49343e9 + 2.27545e9i 0.0125951 + 0.00521705i
\(387\) 4.05015e11i 0.917850i
\(388\) 9.61972e10 2.32241e11i 0.215486 0.520230i
\(389\) 1.06272e11 1.06272e11i 0.235314 0.235314i −0.579593 0.814906i \(-0.696788\pi\)
0.814906 + 0.579593i \(0.196788\pi\)
\(390\) −4.70030e10 −0.102881
\(391\) 6.03071e10 2.47648e11i 0.130489 0.535845i
\(392\) −2.15490e10 −0.0460935
\(393\) 7.14632e10 7.14632e10i 0.151118 0.151118i
\(394\) −1.03066e10 + 2.48824e10i −0.0215468 + 0.0520187i
\(395\) 6.51727e10i 0.134704i
\(396\) −4.12760e11 1.70971e11i −0.843469 0.349376i
\(397\) 2.34830e11 + 5.66930e11i 0.474456 + 1.14544i 0.962174 + 0.272437i \(0.0878297\pi\)
−0.487717 + 0.873002i \(0.662170\pi\)
\(398\) 1.57586e9 6.52744e8i 0.00314807 0.00130397i
\(399\) −8.88868e10 8.88868e10i −0.175574 0.175574i
\(400\) −4.40545e11 4.40545e11i −0.860439 0.860439i
\(401\) 6.11517e11 2.53299e11i 1.18102 0.489196i 0.296202 0.955125i \(-0.404280\pi\)
0.884822 + 0.465929i \(0.154280\pi\)
\(402\) 1.05939e10 + 2.55758e10i 0.0202319 + 0.0488441i
\(403\) 4.52719e11 + 1.87522e11i 0.854980 + 0.354144i
\(404\) 2.12191e11i 0.396288i
\(405\) −3.86309e11 + 9.32632e11i −0.713489 + 1.72251i
\(406\) 2.32112e10 2.32112e10i 0.0423966 0.0423966i
\(407\) 1.82693e11 0.330025
\(408\) −6.37122e10 1.55152e10i −0.113829 0.0277195i
\(409\) 4.49654e11 0.794553 0.397277 0.917699i \(-0.369955\pi\)
0.397277 + 0.917699i \(0.369955\pi\)
\(410\) −1.87102e10 + 1.87102e10i −0.0327003 + 0.0327003i
\(411\) 2.01405e11 4.86235e11i 0.348163 0.840539i
\(412\) 7.54222e11i 1.28962i
\(413\) 2.89975e11 + 1.20112e11i 0.490439 + 0.203147i
\(414\) 3.07861e9 + 7.43243e9i 0.00515055 + 0.0124345i
\(415\) −6.62626e11 + 2.74469e11i −1.09661 + 0.454231i
\(416\) 7.24660e10 + 7.24660e10i 0.118635 + 0.118635i
\(417\) −9.43404e11 9.43404e11i −1.52787 1.52787i
\(418\) −8.15576e9 + 3.37823e9i −0.0130669 + 0.00541247i
\(419\) 2.74311e11 + 6.62246e11i 0.434791 + 1.04968i 0.977723 + 0.209901i \(0.0673143\pi\)
−0.542932 + 0.839777i \(0.682686\pi\)
\(420\) 1.31321e12 + 5.43949e11i 2.05926 + 0.852975i
\(421\) 3.92011e11i 0.608175i −0.952644 0.304088i \(-0.901648\pi\)
0.952644 0.304088i \(-0.0983515\pi\)
\(422\) 1.52323e10 3.67740e10i 0.0233808 0.0564462i
\(423\) 3.17447e11 3.17447e11i 0.482103 0.482103i
\(424\) 4.44934e10 0.0668574
\(425\) −1.26264e11 8.14326e11i −0.187729 1.21073i
\(426\) 3.98129e10 0.0585708
\(427\) 8.95884e10 8.95884e10i 0.130415 0.130415i
\(428\) −1.81026e11 + 4.37035e11i −0.260762 + 0.629534i
\(429\) 1.81421e12i 2.58600i
\(430\) −8.36026e10 3.46293e10i −0.117927 0.0488468i
\(431\) 3.99931e11 + 9.65518e11i 0.558260 + 1.34776i 0.911142 + 0.412092i \(0.135202\pi\)
−0.352882 + 0.935668i \(0.614798\pi\)
\(432\) 3.98829e11 1.65200e11i 0.550946 0.228209i
\(433\) −5.15211e11 5.15211e11i −0.704351 0.704351i 0.260990 0.965341i \(-0.415951\pi\)
−0.965341 + 0.260990i \(0.915951\pi\)
\(434\) 2.38938e10 + 2.38938e10i 0.0323281 + 0.0323281i
\(435\) −1.30585e12 + 5.40899e11i −1.74860 + 0.724293i
\(436\) −1.26586e11 3.05606e11i −0.167763 0.405016i
\(437\) −6.44027e10 2.66765e10i −0.0844768 0.0349914i
\(438\) 4.92726e10i 0.0639694i
\(439\) 4.99273e11 1.20535e12i 0.641576 1.54890i −0.182977 0.983117i \(-0.558573\pi\)
0.824553 0.565784i \(-0.191427\pi\)
\(440\) 1.41327e11 1.41327e11i 0.179758 0.179758i
\(441\) −1.96579e11 −0.247494
\(442\) 6.89685e9 + 4.44803e10i 0.00859509 + 0.0554329i
\(443\) −1.10948e12 −1.36869 −0.684343 0.729161i \(-0.739911\pi\)
−0.684343 + 0.729161i \(0.739911\pi\)
\(444\) 1.31072e11 1.31072e11i 0.160061 0.160061i
\(445\) 2.43158e10 5.87036e10i 0.0293947 0.0709651i
\(446\) 1.45923e9i 0.00174629i
\(447\) −5.17844e11 2.14498e11i −0.613500 0.254120i
\(448\) −3.92022e11 9.46424e11i −0.459789 1.11003i
\(449\) −1.27187e11 + 5.26826e10i −0.147684 + 0.0611729i −0.455301 0.890337i \(-0.650468\pi\)
0.307617 + 0.951510i \(0.400468\pi\)
\(450\) 1.83913e10 + 1.83913e10i 0.0211425 + 0.0211425i
\(451\) 7.22171e11 + 7.22171e11i 0.821951 + 0.821951i
\(452\) −3.37066e11 + 1.39617e11i −0.379832 + 0.157332i
\(453\) −5.17098e11 1.24838e12i −0.576940 1.39286i
\(454\) 2.24895e10 + 9.31546e9i 0.0248444 + 0.0102909i
\(455\) 1.95361e12i 2.13691i
\(456\) −6.86303e9 + 1.65688e10i −0.00743318 + 0.0179453i
\(457\) 9.68719e10 9.68719e10i 0.103890 0.103890i −0.653251 0.757141i \(-0.726595\pi\)
0.757141 + 0.653251i \(0.226595\pi\)
\(458\) −3.24325e10 −0.0344418
\(459\) 5.54770e11 + 1.35097e11i 0.583386 + 0.142066i
\(460\) 7.88233e11 0.820814
\(461\) 6.44026e11 6.44026e11i 0.664124 0.664124i −0.292225 0.956349i \(-0.594396\pi\)
0.956349 + 0.292225i \(0.0943957\pi\)
\(462\) −4.78754e10 + 1.15581e11i −0.0488904 + 0.118032i
\(463\) 2.81914e10i 0.0285103i −0.999898 0.0142552i \(-0.995462\pi\)
0.999898 0.0142552i \(-0.00453772\pi\)
\(464\) 9.45454e11 + 3.91620e11i 0.946912 + 0.392224i
\(465\) −5.56804e11 1.34424e12i −0.552286 1.33334i
\(466\) 3.92334e10 1.62510e10i 0.0385407 0.0159641i
\(467\) 2.03950e11 + 2.03950e11i 0.198426 + 0.198426i 0.799325 0.600899i \(-0.205191\pi\)
−0.600899 + 0.799325i \(0.705191\pi\)
\(468\) 4.40544e11 + 4.40544e11i 0.424505 + 0.424505i
\(469\) −1.06302e12 + 4.40317e11i −1.01453 + 0.420231i
\(470\) 3.83848e10 + 9.26691e10i 0.0362843 + 0.0875981i
\(471\) 7.20481e11 + 2.98433e11i 0.674572 + 0.279417i
\(472\) 4.47785e10i 0.0415270i
\(473\) −1.33661e12 + 3.22686e12i −1.22781 + 2.96418i
\(474\) 4.11536e9 4.11536e9i 0.00374460 0.00374460i
\(475\) −2.25373e11 −0.203133
\(476\) 3.22065e11 1.32254e12i 0.287549 1.18081i
\(477\) 4.05888e11 0.358983
\(478\) 3.61271e10 3.61271e10i 0.0316525 0.0316525i
\(479\) −7.52691e11 + 1.81716e12i −0.653291 + 1.57718i 0.154681 + 0.987964i \(0.450565\pi\)
−0.807972 + 0.589220i \(0.799435\pi\)
\(480\) 3.04298e11i 0.261645i
\(481\) −2.35375e11 9.74953e10i −0.200496 0.0830483i
\(482\) 2.24009e10 + 5.40804e10i 0.0189040 + 0.0456382i
\(483\) −9.12699e11 + 3.78052e11i −0.763072 + 0.316075i
\(484\) −1.87261e12 1.87261e12i −1.55111 1.55111i
\(485\) 7.25398e11 + 7.25398e11i 0.595304 + 0.595304i
\(486\) −5.07430e10 + 2.10184e10i −0.0412584 + 0.0170898i
\(487\) −6.05436e11 1.46165e12i −0.487739 1.17751i −0.955855 0.293840i \(-0.905067\pi\)
0.468115 0.883667i \(-0.344933\pi\)
\(488\) −1.66996e10 6.91721e9i −0.0133296 0.00552131i
\(489\) 1.22259e12i 0.966923i
\(490\) 1.68078e10 4.05776e10i 0.0131713 0.0317983i
\(491\) 2.60508e11 2.60508e11i 0.202281 0.202281i −0.598696 0.800977i \(-0.704314\pi\)
0.800977 + 0.598696i \(0.204314\pi\)
\(492\) 1.03623e12 0.797287
\(493\) 7.03478e11 + 1.15639e12i 0.536339 + 0.881646i
\(494\) 1.23104e10 0.00930036
\(495\) 1.28925e12 1.28925e12i 0.965189 0.965189i
\(496\) −4.03136e11 + 9.73255e11i −0.299077 + 0.722037i
\(497\) 1.65476e12i 1.21656i
\(498\) −5.91733e10 2.45104e10i −0.0431116 0.0178574i
\(499\) −1.46301e10 3.53202e10i −0.0105632 0.0255018i 0.918510 0.395398i \(-0.129393\pi\)
−0.929073 + 0.369896i \(0.879393\pi\)
\(500\) 4.32758e11 1.79254e11i 0.309656 0.128264i
\(501\) 1.21765e12 + 1.21765e12i 0.863481 + 0.863481i
\(502\) −9.33417e10 9.33417e10i −0.0656007 0.0656007i
\(503\) 5.80642e11 2.40510e11i 0.404438 0.167524i −0.171185 0.985239i \(-0.554760\pi\)
0.575623 + 0.817715i \(0.304760\pi\)
\(504\) 3.29196e10 + 7.94750e10i 0.0227257 + 0.0548647i
\(505\) 8.00038e11 + 3.31387e11i 0.547393 + 0.226738i
\(506\) 6.93760e10i 0.0470470i
\(507\) 2.68160e11 6.47396e11i 0.180243 0.435145i
\(508\) 4.32451e11 4.32451e11i 0.288105 0.288105i
\(509\) −4.42214e11 −0.292013 −0.146006 0.989284i \(-0.546642\pi\)
−0.146006 + 0.989284i \(0.546642\pi\)
\(510\) 7.89099e10 1.07871e11i 0.0516495 0.0706056i
\(511\) 2.04794e12 1.32869
\(512\) −2.59843e11 + 2.59843e11i −0.167108 + 0.167108i
\(513\) 5.97595e10 1.44272e11i 0.0380959 0.0919717i
\(514\) 1.11833e11i 0.0706702i
\(515\) −2.84370e12 1.17790e12i −1.78136 0.737862i
\(516\) 1.35615e12 + 3.27403e12i 0.842139 + 2.03310i
\(517\) 3.57681e12 1.48156e12i 2.20185 0.912038i
\(518\) −1.24227e10 1.24227e10i −0.00758109 0.00758109i
\(519\) −6.02604e11 6.02604e11i −0.364568 0.364568i
\(520\) −2.57500e11 + 1.06660e11i −0.154441 + 0.0639715i
\(521\) −8.15293e11 1.96829e12i −0.484779 1.17036i −0.957314 0.289049i \(-0.906661\pi\)
0.472535 0.881312i \(-0.343339\pi\)
\(522\) −3.94697e10 1.63489e10i −0.0232673 0.00963764i
\(523\) 5.32549e11i 0.311245i 0.987817 + 0.155622i \(0.0497383\pi\)
−0.987817 + 0.155622i \(0.950262\pi\)
\(524\) 1.14538e11 2.76519e11i 0.0663679 0.160226i
\(525\) −2.25845e12 + 2.25845e12i −1.29746 + 1.29746i
\(526\) −5.16469e10 −0.0294177
\(527\) −1.19040e12 + 7.24164e11i −0.672270 + 0.408968i
\(528\) −3.90018e12 −2.18390
\(529\) 8.86230e11 8.86230e11i 0.492035 0.492035i
\(530\) −3.47040e10 + 8.37828e10i −0.0191046 + 0.0461226i
\(531\) 4.08489e11i 0.222974i
\(532\) −3.43937e11 1.42463e11i −0.186156 0.0771082i
\(533\) −5.45025e11 1.31581e12i −0.292512 0.706187i
\(534\) 5.24230e9 2.17143e9i 0.00278989 0.00115561i
\(535\) −1.36507e12 1.36507e12i −0.720382 0.720382i
\(536\) 1.16074e11 + 1.16074e11i 0.0607427 + 0.0607427i
\(537\) −7.21751e11 + 2.98959e11i −0.374544 + 0.155141i
\(538\) 5.51982e9 + 1.33260e10i 0.00284056 + 0.00685773i
\(539\) −1.56620e12 6.48741e11i −0.799278 0.331072i
\(540\) 1.76577e12i 0.893638i
\(541\) −4.21323e11 + 1.01716e12i −0.211460 + 0.510509i −0.993648 0.112533i \(-0.964103\pi\)
0.782188 + 0.623042i \(0.214103\pi\)
\(542\) −3.61173e10 + 3.61173e10i −0.0179771 + 0.0179771i
\(543\) 4.82150e12 2.38003
\(544\) −2.87966e11 + 4.46502e10i −0.140976 + 0.0218589i
\(545\) 1.34994e12 0.655436
\(546\) 1.23362e11 1.23362e11i 0.0594036 0.0594036i
\(547\) −1.06061e11 + 2.56053e11i −0.0506537 + 0.122289i −0.947181 0.320700i \(-0.896082\pi\)
0.896527 + 0.442989i \(0.146082\pi\)
\(548\) 1.55863e12i 0.738295i
\(549\) −1.52341e11 6.31018e10i −0.0715718 0.0296460i
\(550\) 8.58344e10 + 2.07223e11i 0.0399972 + 0.0965618i
\(551\) 3.42008e11 1.41665e11i 0.158072 0.0654755i
\(552\) 9.96602e10 + 9.96602e10i 0.0456874 + 0.0456874i
\(553\) 1.71049e11 + 1.71049e11i 0.0777780 + 0.0777780i
\(554\) 1.31686e11 5.45462e10i 0.0593945 0.0246020i
\(555\) 2.89490e11 + 6.98890e11i 0.129513 + 0.312673i
\(556\) −3.65039e12 1.51204e12i −1.61995 0.671007i
\(557\) 1.24921e12i 0.549904i −0.961458 0.274952i \(-0.911338\pi\)
0.961458 0.274952i \(-0.0886620\pi\)
\(558\) 1.68296e10 4.06303e10i 0.00734887 0.0177417i
\(559\) 3.44407e12 3.44407e12i 1.49183 1.49183i
\(560\) 4.19987e12 1.80464
\(561\) −4.16357e12 3.04574e12i −1.77473 1.29825i
\(562\) −4.38708e10 −0.0185508
\(563\) −2.26646e12 + 2.26646e12i −0.950735 + 0.950735i −0.998842 0.0481072i \(-0.984681\pi\)
0.0481072 + 0.998842i \(0.484681\pi\)
\(564\) 1.50322e12 3.62910e12i 0.625557 1.51023i
\(565\) 1.48891e12i 0.614682i
\(566\) −1.07147e11 4.43819e10i −0.0438841 0.0181774i
\(567\) −1.43385e12 3.46162e12i −0.582613 1.40655i
\(568\) 2.18110e11 9.03442e10i 0.0879242 0.0364194i
\(569\) 2.02331e12 + 2.02331e12i 0.809204 + 0.809204i 0.984513 0.175309i \(-0.0560924\pi\)
−0.175309 + 0.984513i \(0.556092\pi\)
\(570\) −2.58467e10 2.58467e10i −0.0102558 0.0102558i
\(571\) −2.00853e12 + 8.31961e11i −0.790708 + 0.327522i −0.741228 0.671253i \(-0.765756\pi\)
−0.0494796 + 0.998775i \(0.515756\pi\)
\(572\) 2.05607e12 + 4.96379e12i 0.803074 + 1.93879i
\(573\) 1.85336e12 + 7.67687e11i 0.718231 + 0.297501i
\(574\) 9.82117e10i 0.0377624i
\(575\) −6.77800e11 + 1.63635e12i −0.258581 + 0.624269i
\(576\) −9.42737e11 + 9.42737e11i −0.356853 + 0.356853i
\(577\) −4.26119e12 −1.60044 −0.800221 0.599705i \(-0.795285\pi\)
−0.800221 + 0.599705i \(0.795285\pi\)
\(578\) −1.13660e11 5.88467e10i −0.0423578 0.0219304i
\(579\) 9.50299e11 0.351404
\(580\) −2.95987e12 + 2.95987e12i −1.08604 + 1.08604i
\(581\) 1.01874e12 2.45945e12i 0.370910 0.895457i
\(582\) 9.16112e10i 0.0330975i
\(583\) 3.23382e12 + 1.33949e12i 1.15933 + 0.480210i
\(584\) −1.11810e11 2.69934e11i −0.0397762 0.0960283i
\(585\) −2.34903e12 + 9.72999e11i −0.829252 + 0.343488i
\(586\) 1.58911e11 + 1.58911e11i 0.0556690 + 0.0556690i
\(587\) 2.37770e12 + 2.37770e12i 0.826581 + 0.826581i 0.987042 0.160461i \(-0.0512981\pi\)
−0.160461 + 0.987042i \(0.551298\pi\)
\(588\) −1.58909e12 + 6.58225e11i −0.548216 + 0.227079i
\(589\) 1.45830e11 + 3.52065e11i 0.0499262 + 0.120533i
\(590\) 8.43196e10 + 3.49263e10i 0.0286480 + 0.0118664i
\(591\) 4.30437e12i 1.45133i
\(592\) 2.09596e11 5.06008e11i 0.0701349 0.169321i
\(593\) −3.31328e11 + 3.31328e11i −0.110030 + 0.110030i −0.759978 0.649948i \(-0.774791\pi\)
0.649948 + 0.759978i \(0.274791\pi\)
\(594\) −1.55413e11 −0.0512211
\(595\) 4.48349e12 + 3.27977e12i 1.46653 + 1.07280i
\(596\) −1.65995e12 −0.538873
\(597\) 1.92762e11 1.92762e11i 0.0621064 0.0621064i
\(598\) 3.70229e10 8.93813e10i 0.0118390 0.0285819i
\(599\) 3.79639e10i 0.0120490i 0.999982 + 0.00602449i \(0.00191767\pi\)
−0.999982 + 0.00602449i \(0.998082\pi\)
\(600\) 4.20983e11 + 1.74377e11i 0.132612 + 0.0549299i
\(601\) 3.76533e11 + 9.09031e11i 0.117725 + 0.284213i 0.971747 0.236023i \(-0.0758441\pi\)
−0.854023 + 0.520236i \(0.825844\pi\)
\(602\) 3.10305e11 1.28532e11i 0.0962951 0.0398868i
\(603\) 1.05888e12 + 1.05888e12i 0.326151 + 0.326151i
\(604\) −2.82963e12 2.82963e12i −0.865094 0.865094i
\(605\) 9.98497e12 4.13591e12i 3.03003 1.25508i
\(606\) 2.95932e10 + 7.14444e10i 0.00891385 + 0.0215199i
\(607\) 1.27743e12 + 5.29128e11i 0.381933 + 0.158202i 0.565386 0.824827i \(-0.308727\pi\)
−0.183453 + 0.983029i \(0.558727\pi\)
\(608\) 7.96974e10i 0.0236525i
\(609\) 2.00764e12 4.84686e12i 0.591435 1.42785i
\(610\) 2.60508e10 2.60508e10i 0.00761792 0.00761792i
\(611\) −5.39886e12 −1.56717
\(612\) −1.75064e12 + 2.71443e11i −0.504446 + 0.0782162i
\(613\) 2.52907e12 0.723417 0.361708 0.932291i \(-0.382194\pi\)
0.361708 + 0.932291i \(0.382194\pi\)
\(614\) −9.57595e10 + 9.57595e10i −0.0271909 + 0.0271909i
\(615\) −1.61833e12 + 3.90699e12i −0.456172 + 1.10130i
\(616\) 7.41838e11i 0.207585i
\(617\) −1.77484e12 7.35161e11i −0.493032 0.204220i 0.122293 0.992494i \(-0.460975\pi\)
−0.615325 + 0.788274i \(0.710975\pi\)
\(618\) −1.05188e11 2.53945e11i −0.0290079 0.0700313i
\(619\) −3.07609e12 + 1.27416e12i −0.842153 + 0.348831i −0.761702 0.647927i \(-0.775636\pi\)
−0.0804512 + 0.996759i \(0.525636\pi\)
\(620\) −3.04691e12 3.04691e12i −0.828126 0.828126i
\(621\) −8.67786e11 8.67786e11i −0.234153 0.234153i
\(622\) −6.12016e9 + 2.53505e9i −0.00163948 + 0.000679094i
\(623\) 9.02522e10 + 2.17888e11i 0.0240028 + 0.0579479i
\(624\) 5.02484e12 + 2.08136e12i 1.32676 + 0.549561i
\(625\) 2.76216e12i 0.724085i
\(626\) −1.25916e11 + 3.03987e11i −0.0327714 + 0.0791172i
\(627\) −9.97622e11 + 9.97622e11i −0.257788 + 0.257788i
\(628\) 2.30950e12 0.592516
\(629\) 6.18903e11 3.76502e11i 0.157650 0.0959046i
\(630\) −1.75331e11 −0.0443431
\(631\) −3.38595e11 + 3.38595e11i −0.0850254 + 0.0850254i −0.748340 0.663315i \(-0.769149\pi\)
0.663315 + 0.748340i \(0.269149\pi\)
\(632\) 1.32068e10 3.18841e10i 0.00329285 0.00794965i
\(633\) 6.36147e12i 1.57486i
\(634\) 3.42783e11 + 1.41985e11i 0.0842592 + 0.0349013i
\(635\) 9.55125e11 + 2.30588e12i 0.233120 + 0.562800i
\(636\) 3.28109e12 1.35907e12i 0.795173 0.329371i
\(637\) 1.67162e12 + 1.67162e12i 0.402264 + 0.402264i
\(638\) −2.60512e11 2.60512e11i −0.0622493 0.0622493i
\(639\) 1.98970e12 8.24159e11i 0.472099 0.195550i
\(640\) −4.59645e11 1.10968e12i −0.108296 0.261450i
\(641\) −5.61573e12 2.32611e12i −1.31385 0.544214i −0.387844 0.921725i \(-0.626780\pi\)
−0.926005 + 0.377511i \(0.876780\pi\)
\(642\) 1.72396e11i 0.0400515i
\(643\) −1.98792e12 + 4.79926e12i −0.458616 + 1.10720i 0.510342 + 0.859972i \(0.329519\pi\)
−0.968958 + 0.247226i \(0.920481\pi\)
\(644\) −2.06875e12 + 2.06875e12i −0.473939 + 0.473939i
\(645\) −1.44623e13 −3.29017
\(646\) −2.06670e10 + 2.82520e10i −0.00466907 + 0.00638269i
\(647\) −4.64638e11 −0.104243 −0.0521213 0.998641i \(-0.516598\pi\)
−0.0521213 + 0.998641i \(0.516598\pi\)
\(648\) −3.77984e11 + 3.77984e11i −0.0842143 + 0.0842143i
\(649\) 1.34807e12 3.25454e12i 0.298272 0.720092i
\(650\) 3.12784e11i 0.0687280i
\(651\) 4.98938e12 + 2.06667e12i 1.08876 + 0.450980i
\(652\) 1.38558e12 + 3.34509e12i 0.300274 + 0.724927i
\(653\) −4.84356e12 + 2.00627e12i −1.04245 + 0.431797i −0.837191 0.546911i \(-0.815804\pi\)
−0.205259 + 0.978708i \(0.565804\pi\)
\(654\) 8.52426e10 + 8.52426e10i 0.0182204 + 0.0182204i
\(655\) 8.63700e11 + 8.63700e11i 0.183348 + 0.183348i
\(656\) 2.82873e12 1.17170e12i 0.596381 0.247029i
\(657\) −1.01998e12 2.46245e12i −0.213574 0.515613i
\(658\) −3.43957e11 1.42472e11i −0.0715299 0.0296286i
\(659\) 9.11236e12i 1.88212i −0.338245 0.941058i \(-0.609833\pi\)
0.338245 0.941058i \(-0.390167\pi\)
\(660\) 6.10502e12 1.47388e13i 1.25239 3.02353i
\(661\) −6.42026e12 + 6.42026e12i −1.30812 + 1.30812i −0.385342 + 0.922774i \(0.625917\pi\)
−0.922774 + 0.385342i \(0.874083\pi\)
\(662\) 2.69841e11 0.0546068
\(663\) 3.73880e12 + 6.14592e12i 0.751486 + 1.23531i
\(664\) −3.79793e11 −0.0758211
\(665\) 1.07428e12 1.07428e12i 0.213020 0.213020i
\(666\) −8.74994e9 + 2.11242e10i −0.00172334 + 0.00416051i
\(667\) 2.90926e12i 0.569135i
\(668\) 4.71155e12 + 1.95159e12i 0.915525 + 0.379223i
\(669\) −8.92472e10 2.15462e11i −0.0172257 0.0415866i
\(670\) −3.09108e11 + 1.28037e11i −0.0592616 + 0.0245469i
\(671\) −1.00550e12 1.00550e12i −0.191483 0.191483i
\(672\) 7.98643e11 + 7.98643e11i 0.151074 + 0.151074i
\(673\) −4.83853e12 + 2.00419e12i −0.909172 + 0.376591i −0.787740 0.616008i \(-0.788749\pi\)
−0.121432 + 0.992600i \(0.538749\pi\)
\(674\) 7.89788e10 + 1.90672e11i 0.0147415 + 0.0355891i
\(675\) −3.66569e12 1.51838e12i −0.679655 0.281522i
\(676\) 2.07523e12i 0.382213i
\(677\) 5.40939e11 1.30594e12i 0.0989691 0.238933i −0.866638 0.498937i \(-0.833724\pi\)
0.965607 + 0.260004i \(0.0837240\pi\)
\(678\) 9.40179e10 9.40179e10i 0.0170874 0.0170874i
\(679\) −3.80768e12 −0.687459
\(680\) 1.87515e11 7.70021e11i 0.0336315 0.138106i
\(681\) 3.89042e12 0.693162
\(682\) 2.68172e11 2.68172e11i 0.0474661 0.0474661i
\(683\) 4.82765e11 1.16550e12i 0.0848873 0.204936i −0.875736 0.482790i \(-0.839623\pi\)
0.960623 + 0.277854i \(0.0896233\pi\)
\(684\) 4.84505e11i 0.0846342i
\(685\) 5.87660e12 + 2.43417e12i 1.01981 + 0.422419i
\(686\) −6.65818e10 1.60743e11i −0.0114788 0.0277123i
\(687\) −4.78882e12 + 1.98359e12i −0.820207 + 0.339741i
\(688\) 7.40407e12 + 7.40407e12i 1.25986 + 1.25986i
\(689\) −3.45150e12 3.45150e12i −0.583473 0.583473i
\(690\) −2.65397e11 + 1.09931e11i −0.0445733 + 0.0184629i
\(691\) 3.26232e12 + 7.87593e12i 0.544346 + 1.31417i 0.921630 + 0.388069i \(0.126858\pi\)
−0.377285 + 0.926097i \(0.623142\pi\)
\(692\) −2.33170e12 9.65823e11i −0.386541 0.160111i
\(693\) 6.76737e12i 1.11460i
\(694\) −4.92768e10 + 1.18965e11i −0.00806353 + 0.0194671i
\(695\) 1.14019e13 1.14019e13i 1.85373 1.85373i
\(696\) −7.48462e11 −0.120901
\(697\) 3.93476e12 + 9.58191e11i 0.631496 + 0.153782i
\(698\) −2.62751e11 −0.0418982
\(699\) 4.79908e12 4.79908e12i 0.760345 0.760345i
\(700\) −3.61973e12 + 8.73880e12i −0.569816 + 1.37566i
\(701\) 8.13343e12i 1.27216i 0.771622 + 0.636082i \(0.219446\pi\)
−0.771622 + 0.636082i \(0.780554\pi\)
\(702\) 2.00228e11 + 8.29372e10i 0.0311177 + 0.0128894i
\(703\) −7.58191e10 1.83043e11i −0.0117079 0.0282654i
\(704\) −1.06222e13 + 4.39986e12i −1.62981 + 0.675091i
\(705\) 1.13354e13 + 1.13354e13i 1.72817 + 1.72817i
\(706\) 7.54896e10 + 7.54896e10i 0.0114358 + 0.0114358i
\(707\) −2.96947e12 + 1.23000e12i −0.446984 + 0.185147i
\(708\) −1.36778e12 3.30211e12i −0.204582 0.493904i
\(709\) −9.27753e12 3.84288e12i −1.37887 0.571148i −0.434693 0.900579i \(-0.643143\pi\)
−0.944180 + 0.329431i \(0.893143\pi\)
\(710\) 4.81177e11i 0.0710627i
\(711\) 1.20479e11 2.90861e11i 0.0176806 0.0426847i
\(712\) 2.37918e10 2.37918e10i 0.00346951 0.00346951i
\(713\) 2.99480e12 0.433976
\(714\) 7.60097e10 + 4.90215e11i 0.0109453 + 0.0705902i
\(715\) −2.19264e13 −3.13754
\(716\) −1.63594e12 + 1.63594e12i −0.232627 + 0.232627i
\(717\) 3.12478e12 7.54389e12i 0.441554 1.06600i
\(718\) 1.19177e11i 0.0167353i
\(719\) 3.15304e12 + 1.30603e12i 0.439997 + 0.182253i 0.591674 0.806177i \(-0.298467\pi\)
−0.151677 + 0.988430i \(0.548467\pi\)
\(720\) −2.09175e12 5.04994e12i −0.290078 0.700310i
\(721\) 1.05549e13 4.37196e12i 1.45460 0.602515i
\(722\) −2.39497e11 2.39497e11i −0.0328006 0.0328006i
\(723\) 6.61519e12 + 6.61519e12i 0.900367 + 0.900367i
\(724\) 1.31919e13 5.46428e12i 1.78437 0.739111i
\(725\) −3.59943e12 8.68980e12i −0.483853 1.16812i
\(726\) 8.91670e11 + 3.69342e11i 0.119121 + 0.0493416i
\(727\) 5.87052e12i 0.779421i 0.920937 + 0.389710i \(0.127425\pi\)
−0.920937 + 0.389710i \(0.872575\pi\)
\(728\) 3.95886e11 9.55754e11i 0.0522371 0.126112i
\(729\) 5.32468e11 5.32468e11i 0.0698264 0.0698264i
\(730\) 5.95505e11 0.0776127
\(731\) 2.12208e12 + 1.36861e13i 0.274874 + 1.77276i
\(732\) −1.44278e12 −0.185737
\(733\) −5.72149e12 + 5.72149e12i −0.732051 + 0.732051i −0.971026 0.238975i \(-0.923189\pi\)
0.238975 + 0.971026i \(0.423189\pi\)
\(734\) 1.39281e11 3.36255e11i 0.0177117 0.0427598i
\(735\) 7.01945e12i 0.887177i
\(736\) 5.78655e11 + 2.39687e11i 0.0726891 + 0.0301088i
\(737\) 4.94191e12 + 1.19308e13i 0.617008 + 1.48959i
\(738\) −1.18090e11 + 4.89146e10i −0.0146541 + 0.00606994i
\(739\) −2.86882e12 2.86882e12i −0.353838 0.353838i 0.507698 0.861535i \(-0.330497\pi\)
−0.861535 + 0.507698i \(0.830497\pi\)
\(740\) 1.58413e12 + 1.58413e12i 0.194199 + 0.194199i
\(741\) 1.81768e12 7.52910e11i 0.221481 0.0917404i
\(742\) −1.28810e11 3.10974e11i −0.0156002 0.0376623i
\(743\) −7.38771e12 3.06009e12i −0.889324 0.368370i −0.109218 0.994018i \(-0.534835\pi\)
−0.780106 + 0.625648i \(0.784835\pi\)
\(744\) 7.70471e11i 0.0921887i
\(745\) 2.59241e12 6.25862e12i 0.308319 0.744347i
\(746\) −5.22742e11 + 5.22742e11i −0.0617964 + 0.0617964i
\(747\) −3.46463e12 −0.407113
\(748\) −1.48436e13 3.61470e12i −1.73373 0.422197i
\(749\) 7.16537e12 0.831899
\(750\) −1.20709e11 + 1.20709e11i −0.0139304 + 0.0139304i
\(751\) 5.61852e12 1.35643e13i 0.644528 1.55603i −0.175980 0.984394i \(-0.556309\pi\)
0.820508 0.571635i \(-0.193691\pi\)
\(752\) 1.16065e13i 1.32349i
\(753\) −1.94912e13 8.07351e12i −2.20933 0.915135i
\(754\) 1.96609e11 + 4.74657e11i 0.0221530 + 0.0534821i
\(755\) 1.50879e13 6.24961e12i 1.68992 0.699990i
\(756\) −4.63433e12 4.63433e12i −0.515987 0.515987i
\(757\) −6.59455e12 6.59455e12i −0.729883 0.729883i 0.240713 0.970596i \(-0.422619\pi\)
−0.970596 + 0.240713i \(0.922619\pi\)
\(758\) 7.59072e11 3.14418e11i 0.0835163 0.0345936i
\(759\) 4.24308e12 + 1.02437e13i 0.464080 + 1.12039i