Properties

Label 17.10.d.a.9.9
Level $17$
Weight $10$
Character 17.9
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 9.9
Character \(\chi\) \(=\) 17.9
Dual form 17.10.d.a.2.9

$q$-expansion

\(f(q)\) \(=\) \(q+(13.0593 - 13.0593i) q^{2} +(116.759 + 48.3631i) q^{3} +170.907i q^{4} +(663.047 - 1600.74i) q^{5} +(2156.38 - 893.204i) q^{6} +(2945.54 + 7111.17i) q^{7} +(8918.32 + 8918.32i) q^{8} +(-2624.32 - 2624.32i) q^{9} +O(q^{10})\) \(q+(13.0593 - 13.0593i) q^{2} +(116.759 + 48.3631i) q^{3} +170.907i q^{4} +(663.047 - 1600.74i) q^{5} +(2156.38 - 893.204i) q^{6} +(2945.54 + 7111.17i) q^{7} +(8918.32 + 8918.32i) q^{8} +(-2624.32 - 2624.32i) q^{9} +(-12245.6 - 29563.5i) q^{10} +(57318.2 - 23742.0i) q^{11} +(-8265.62 + 19955.0i) q^{12} -70477.0i q^{13} +(131334. + 54400.3i) q^{14} +(154833. - 154833. i) q^{15} +145430. q^{16} +(-312389. + 144917. i) q^{17} -68543.9 q^{18} +(216406. - 216406. i) q^{19} +(273578. + 113320. i) q^{20} +972749. i q^{21} +(438483. - 1.05859e6i) q^{22} +(-1.51666e6 + 628220. i) q^{23} +(609976. + 1.47261e6i) q^{24} +(-741661. - 741661. i) q^{25} +(-920383. - 920383. i) q^{26} +(-1.13142e6 - 2.73150e6i) q^{27} +(-1.21535e6 + 503416. i) q^{28} +(-2.59546e6 + 6.26599e6i) q^{29} -4.04404e6i q^{30} +(-5.82656e6 - 2.41344e6i) q^{31} +(-2.66696e6 + 2.66696e6i) q^{32} +7.84065e6 q^{33} +(-2.18708e6 + 5.97211e6i) q^{34} +1.33362e7 q^{35} +(448517. - 448517. i) q^{36} +(6.43151e6 + 2.66402e6i) q^{37} -5.65224e6i q^{38} +(3.40849e6 - 8.22882e6i) q^{39} +(2.01892e7 - 8.36262e6i) q^{40} +(-2.52267e6 - 6.09025e6i) q^{41} +(1.27035e7 + 1.27035e7i) q^{42} +(-1.82896e7 - 1.82896e7i) q^{43} +(4.05768e6 + 9.79611e6i) q^{44} +(-5.94090e6 + 2.46080e6i) q^{45} +(-1.16024e7 + 2.80107e7i) q^{46} -2.56808e7i q^{47} +(1.69803e7 + 7.03345e6i) q^{48} +(-1.33582e7 + 1.33582e7i) q^{49} -1.93712e7 q^{50} +(-4.34829e7 + 1.81219e6i) q^{51} +1.20450e7 q^{52} +(8.36088e6 - 8.36088e6i) q^{53} +(-5.04472e7 - 2.08959e7i) q^{54} -1.07494e8i q^{55} +(-3.71504e7 + 8.96890e7i) q^{56} +(3.57334e7 - 1.48013e7i) q^{57} +(4.79347e7 + 1.15725e8i) q^{58} +(6.76570e7 + 6.76570e7i) q^{59} +(2.64622e7 + 2.64622e7i) q^{60} +(-5.29976e7 - 1.27948e8i) q^{61} +(-1.07609e8 + 4.45731e7i) q^{62} +(1.09320e7 - 2.63921e7i) q^{63} +1.44118e8i q^{64} +(-1.12815e8 - 4.67296e7i) q^{65} +(1.02394e8 - 1.02394e8i) q^{66} -5.84650e7 q^{67} +(-2.47673e7 - 5.33897e7i) q^{68} -2.07466e8 q^{69} +(1.74161e8 - 1.74161e8i) q^{70} +(2.81761e8 + 1.16709e8i) q^{71} -4.68091e7i q^{72} +(-2.76741e7 + 6.68113e7i) q^{73} +(1.18782e8 - 4.92009e7i) q^{74} +(-5.07265e7 - 1.22465e8i) q^{75} +(3.69854e7 + 3.69854e7i) q^{76} +(3.37667e8 + 3.37667e8i) q^{77} +(-6.29503e7 - 1.51976e8i) q^{78} +(4.09770e8 - 1.69732e8i) q^{79} +(9.64270e7 - 2.32795e8i) q^{80} -3.00596e8i q^{81} +(-1.12479e8 - 4.65903e7i) q^{82} +(-2.13664e8 + 2.13664e8i) q^{83} -1.66250e8 q^{84} +(2.48447e7 + 5.96140e8i) q^{85} -4.77699e8 q^{86} +(-6.06086e8 + 6.06086e8i) q^{87} +(7.22921e8 + 2.99444e8i) q^{88} +3.42227e7i q^{89} +(-4.54478e7 + 1.09721e8i) q^{90} +(5.01174e8 - 2.07593e8i) q^{91} +(-1.07367e8 - 2.59208e8i) q^{92} +(-5.63581e8 - 5.63581e8i) q^{93} +(-3.35374e8 - 3.35374e8i) q^{94} +(-2.02922e8 - 4.89897e8i) q^{95} +(-4.40374e8 + 1.82409e8i) q^{96} +(-9.00866e7 + 2.17488e8i) q^{97} +3.48900e8i q^{98} +(-2.12728e8 - 8.81149e7i) 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 \(\left(\mathbb{Z}/17\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{1}{8}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 13.0593 13.0593i 0.577147 0.577147i −0.356969 0.934116i \(-0.616190\pi\)
0.934116 + 0.356969i \(0.116190\pi\)
\(3\) 116.759 + 48.3631i 0.832232 + 0.344722i 0.757786 0.652503i \(-0.226281\pi\)
0.0744462 + 0.997225i \(0.476281\pi\)
\(4\) 170.907i 0.333804i
\(5\) 663.047 1600.74i 0.474438 1.14539i −0.487744 0.872987i \(-0.662180\pi\)
0.962182 0.272408i \(-0.0878200\pi\)
\(6\) 2156.38 893.204i 0.679275 0.281365i
\(7\) 2945.54 + 7111.17i 0.463686 + 1.11944i 0.966872 + 0.255260i \(0.0821611\pi\)
−0.503186 + 0.864178i \(0.667839\pi\)
\(8\) 8918.32 + 8918.32i 0.769800 + 0.769800i
\(9\) −2624.32 2624.32i −0.133329 0.133329i
\(10\) −12245.6 29563.5i −0.387240 0.934881i
\(11\) 57318.2 23742.0i 1.18039 0.488934i 0.295776 0.955257i \(-0.404422\pi\)
0.884614 + 0.466323i \(0.154422\pi\)
\(12\) −8265.62 + 19955.0i −0.115069 + 0.277802i
\(13\) 70477.0i 0.684388i −0.939629 0.342194i \(-0.888830\pi\)
0.939629 0.342194i \(-0.111170\pi\)
\(14\) 131334. + 54400.3i 0.913695 + 0.378465i
\(15\) 154833. 154833.i 0.789685 0.789685i
\(16\) 145430. 0.554771
\(17\) −312389. + 144917.i −0.907143 + 0.420822i
\(18\) −68543.9 −0.153901
\(19\) 216406. 216406.i 0.380959 0.380959i −0.490488 0.871448i \(-0.663182\pi\)
0.871448 + 0.490488i \(0.163182\pi\)
\(20\) 273578. + 113320.i 0.382337 + 0.158369i
\(21\) 972749.i 1.09148i
\(22\) 438483. 1.05859e6i 0.399072 0.963445i
\(23\) −1.51666e6 + 628220.i −1.13009 + 0.468098i −0.867811 0.496895i \(-0.834473\pi\)
−0.262277 + 0.964993i \(0.584473\pi\)
\(24\) 609976. + 1.47261e6i 0.375286 + 0.906020i
\(25\) −741661. 741661.i −0.379730 0.379730i
\(26\) −920383. 920383.i −0.394992 0.394992i
\(27\) −1.13142e6 2.73150e6i −0.409721 0.989155i
\(28\) −1.21535e6 + 503416.i −0.373673 + 0.154780i
\(29\) −2.59546e6 + 6.26599e6i −0.681433 + 1.64512i 0.0799315 + 0.996800i \(0.474530\pi\)
−0.761364 + 0.648324i \(0.775470\pi\)
\(30\) 4.04404e6i 0.911528i
\(31\) −5.82656e6 2.41344e6i −1.13314 0.469363i −0.264295 0.964442i \(-0.585139\pi\)
−0.868848 + 0.495079i \(0.835139\pi\)
\(32\) −2.66696e6 + 2.66696e6i −0.449616 + 0.449616i
\(33\) 7.84065e6 1.15091
\(34\) −2.18708e6 + 5.97211e6i −0.280679 + 0.766431i
\(35\) 1.33362e7 1.50219
\(36\) 448517. 448517.i 0.0445059 0.0445059i
\(37\) 6.43151e6 + 2.66402e6i 0.564164 + 0.233684i 0.646492 0.762921i \(-0.276235\pi\)
−0.0823279 + 0.996605i \(0.526235\pi\)
\(38\) 5.65224e6i 0.439739i
\(39\) 3.40849e6 8.22882e6i 0.235924 0.569570i
\(40\) 2.01892e7 8.36262e6i 1.24695 0.516502i
\(41\) −2.52267e6 6.09025e6i −0.139422 0.336595i 0.838710 0.544578i \(-0.183310\pi\)
−0.978132 + 0.207983i \(0.933310\pi\)
\(42\) 1.27035e7 + 1.27035e7i 0.629941 + 0.629941i
\(43\) −1.82896e7 1.82896e7i −0.815821 0.815821i 0.169678 0.985500i \(-0.445727\pi\)
−0.985500 + 0.169678i \(0.945727\pi\)
\(44\) 4.05768e6 + 9.79611e6i 0.163208 + 0.394019i
\(45\) −5.94090e6 + 2.46080e6i −0.215971 + 0.0894583i
\(46\) −1.16024e7 + 2.80107e7i −0.382065 + 0.922387i
\(47\) 2.56808e7i 0.767658i −0.923404 0.383829i \(-0.874605\pi\)
0.923404 0.383829i \(-0.125395\pi\)
\(48\) 1.69803e7 + 7.03345e6i 0.461699 + 0.191242i
\(49\) −1.33582e7 + 1.33582e7i −0.331030 + 0.331030i
\(50\) −1.93712e7 −0.438320
\(51\) −4.34829e7 + 1.81219e6i −0.900020 + 0.0375093i
\(52\) 1.20450e7 0.228451
\(53\) 8.36088e6 8.36088e6i 0.145549 0.145549i −0.630577 0.776127i \(-0.717182\pi\)
0.776127 + 0.630577i \(0.217182\pi\)
\(54\) −5.04472e7 2.08959e7i −0.807357 0.334418i
\(55\) 1.07494e8i 1.58398i
\(56\) −3.71504e7 + 8.96890e7i −0.504798 + 1.21869i
\(57\) 3.57334e7 1.48013e7i 0.448372 0.185722i
\(58\) 4.79347e7 + 1.15725e8i 0.556191 + 1.34276i
\(59\) 6.76570e7 + 6.76570e7i 0.726907 + 0.726907i 0.970002 0.243096i \(-0.0781628\pi\)
−0.243096 + 0.970002i \(0.578163\pi\)
\(60\) 2.64622e7 + 2.64622e7i 0.263600 + 0.263600i
\(61\) −5.29976e7 1.27948e8i −0.490086 1.18317i −0.954676 0.297646i \(-0.903799\pi\)
0.464591 0.885526i \(-0.346201\pi\)
\(62\) −1.07609e8 + 4.45731e7i −0.924881 + 0.383098i
\(63\) 1.09320e7 2.63921e7i 0.0874310 0.211077i
\(64\) 1.44118e8i 1.07376i
\(65\) −1.12815e8 4.67296e7i −0.783894 0.324700i
\(66\) 1.02394e8 1.02394e8i 0.664241 0.664241i
\(67\) −5.84650e7 −0.354453 −0.177227 0.984170i \(-0.556713\pi\)
−0.177227 + 0.984170i \(0.556713\pi\)
\(68\) −2.47673e7 5.33897e7i −0.140472 0.302808i
\(69\) −2.07466e8 −1.10186
\(70\) 1.74161e8 1.74161e8i 0.866983 0.866983i
\(71\) 2.81761e8 + 1.16709e8i 1.31589 + 0.545058i 0.926597 0.376057i \(-0.122720\pi\)
0.389291 + 0.921115i \(0.372720\pi\)
\(72\) 4.68091e7i 0.205274i
\(73\) −2.76741e7 + 6.68113e7i −0.114057 + 0.275357i −0.970592 0.240732i \(-0.922613\pi\)
0.856535 + 0.516089i \(0.172613\pi\)
\(74\) 1.18782e8 4.92009e7i 0.460475 0.190735i
\(75\) −5.07265e7 1.22465e8i −0.185122 0.446925i
\(76\) 3.69854e7 + 3.69854e7i 0.127166 + 0.127166i
\(77\) 3.37667e8 + 3.37667e8i 1.09466 + 1.09466i
\(78\) −6.29503e7 1.51976e8i −0.192563 0.464888i
\(79\) 4.09770e8 1.69732e8i 1.18363 0.490278i 0.297958 0.954579i \(-0.403695\pi\)
0.885677 + 0.464301i \(0.153695\pi\)
\(80\) 9.64270e7 2.32795e8i 0.263205 0.635432i
\(81\) 3.00596e8i 0.775890i
\(82\) −1.12479e8 4.65903e7i −0.274732 0.113798i
\(83\) −2.13664e8 + 2.13664e8i −0.494174 + 0.494174i −0.909618 0.415445i \(-0.863626\pi\)
0.415445 + 0.909618i \(0.363626\pi\)
\(84\) −1.66250e8 −0.364338
\(85\) 2.48447e7 + 5.96140e8i 0.0516237 + 1.23869i
\(86\) −4.77699e8 −0.941697
\(87\) −6.06086e8 + 6.06086e8i −1.13422 + 1.13422i
\(88\) 7.22921e8 + 2.99444e8i 1.28505 + 0.532284i
\(89\) 3.42227e7i 0.0578175i 0.999582 + 0.0289087i \(0.00920322\pi\)
−0.999582 + 0.0289087i \(0.990797\pi\)
\(90\) −4.54478e7 + 1.09721e8i −0.0730166 + 0.176278i
\(91\) 5.01174e8 2.07593e8i 0.766130 0.317341i
\(92\) −1.07367e8 2.59208e8i −0.156253 0.377227i
\(93\) −5.63581e8 5.63581e8i −0.781238 0.781238i
\(94\) −3.35374e8 3.35374e8i −0.443051 0.443051i
\(95\) −2.02922e8 4.89897e8i −0.255607 0.617090i
\(96\) −4.40374e8 + 1.82409e8i −0.529177 + 0.219192i
\(97\) −9.00866e7 + 2.17488e8i −0.103321 + 0.249438i −0.967083 0.254461i \(-0.918102\pi\)
0.863762 + 0.503900i \(0.168102\pi\)
\(98\) 3.48900e8i 0.382105i
\(99\) −2.12728e8 8.81149e7i −0.222570 0.0921916i
\(100\) 1.26755e8 1.26755e8i 0.126755 0.126755i
\(101\) −1.87410e9 −1.79203 −0.896017 0.444019i \(-0.853552\pi\)
−0.896017 + 0.444019i \(0.853552\pi\)
\(102\) −5.44191e8 + 5.91523e8i −0.497795 + 0.541092i
\(103\) 5.10125e8 0.446590 0.223295 0.974751i \(-0.428319\pi\)
0.223295 + 0.974751i \(0.428319\pi\)
\(104\) 6.28536e8 6.28536e8i 0.526842 0.526842i
\(105\) 1.55712e9 + 6.44978e8i 1.25017 + 0.517837i
\(106\) 2.18375e8i 0.168007i
\(107\) 1.82989e8 4.41775e8i 0.134958 0.325817i −0.841924 0.539596i \(-0.818577\pi\)
0.976882 + 0.213779i \(0.0685771\pi\)
\(108\) 4.66834e8 1.93369e8i 0.330184 0.136766i
\(109\) 5.74088e8 + 1.38597e9i 0.389546 + 0.940448i 0.990036 + 0.140815i \(0.0449724\pi\)
−0.600490 + 0.799633i \(0.705028\pi\)
\(110\) −1.40379e9 1.40379e9i −0.914190 0.914190i
\(111\) 6.22096e8 + 6.22096e8i 0.388959 + 0.388959i
\(112\) 4.28371e8 + 1.03418e9i 0.257240 + 0.621032i
\(113\) 2.68086e9 1.11045e9i 1.54675 0.640686i 0.564027 0.825756i \(-0.309251\pi\)
0.982725 + 0.185071i \(0.0592514\pi\)
\(114\) 2.73360e8 6.59950e8i 0.151588 0.365965i
\(115\) 2.84431e9i 1.51648i
\(116\) −1.07090e9 4.43583e8i −0.549149 0.227465i
\(117\) −1.84954e8 + 1.84954e8i −0.0912491 + 0.0912491i
\(118\) 1.76711e9 0.839064
\(119\) −1.95068e9 1.79460e9i −0.891714 0.820361i
\(120\) 2.76171e9 1.21580
\(121\) 1.05438e9 1.05438e9i 0.447159 0.447159i
\(122\) −2.36302e9 9.78796e8i −0.965715 0.400012i
\(123\) 8.33095e8i 0.328187i
\(124\) 4.12475e8 9.95803e8i 0.156675 0.378247i
\(125\) 1.44748e9 5.99566e8i 0.530295 0.219655i
\(126\) −2.01899e8 4.87427e8i −0.0713619 0.172283i
\(127\) 2.12648e9 + 2.12648e9i 0.725345 + 0.725345i 0.969689 0.244344i \(-0.0785725\pi\)
−0.244344 + 0.969689i \(0.578573\pi\)
\(128\) 5.16597e8 + 5.16597e8i 0.170101 + 0.170101i
\(129\) −1.25093e9 3.02001e9i −0.397721 0.960184i
\(130\) −2.08355e9 + 8.63034e8i −0.639821 + 0.265023i
\(131\) −1.56102e9 + 3.76863e9i −0.463112 + 1.11805i 0.504000 + 0.863704i \(0.331861\pi\)
−0.967113 + 0.254349i \(0.918139\pi\)
\(132\) 1.34003e9i 0.384176i
\(133\) 2.17634e9 + 9.01468e8i 0.603106 + 0.249815i
\(134\) −7.63514e8 + 7.63514e8i −0.204572 + 0.204572i
\(135\) −5.12260e9 −1.32736
\(136\) −4.07840e9 1.49357e9i −1.02227 0.374370i
\(137\) −5.66047e8 −0.137281 −0.0686404 0.997641i \(-0.521866\pi\)
−0.0686404 + 0.997641i \(0.521866\pi\)
\(138\) −2.70937e9 + 2.70937e9i −0.635934 + 0.635934i
\(139\) −6.23541e9 2.58279e9i −1.41677 0.586844i −0.462721 0.886504i \(-0.653127\pi\)
−0.954046 + 0.299660i \(0.903127\pi\)
\(140\) 2.27925e9i 0.501436i
\(141\) 1.24200e9 2.99846e9i 0.264629 0.638870i
\(142\) 5.20376e9 2.15547e9i 1.07404 0.444881i
\(143\) −1.67326e9 4.03962e9i −0.334620 0.807845i
\(144\) −3.81655e8 3.81655e8i −0.0739674 0.0739674i
\(145\) 8.30930e9 + 8.30930e9i 1.56102 + 1.56102i
\(146\) 5.11105e8 + 1.23392e9i 0.0930941 + 0.224749i
\(147\) −2.20574e9 + 9.13648e8i −0.389607 + 0.161380i
\(148\) −4.55301e8 + 1.09919e9i −0.0780047 + 0.188320i
\(149\) 4.27398e8i 0.0710386i 0.999369 + 0.0355193i \(0.0113085\pi\)
−0.999369 + 0.0355193i \(0.988691\pi\)
\(150\) −2.26176e9 9.36852e8i −0.364784 0.151099i
\(151\) 6.19780e8 6.19780e8i 0.0970155 0.0970155i −0.656933 0.753949i \(-0.728147\pi\)
0.753949 + 0.656933i \(0.228147\pi\)
\(152\) 3.85996e9 0.586525
\(153\) 1.20012e9 + 4.39502e8i 0.177057 + 0.0648410i
\(154\) 8.81941e9 1.26356
\(155\) −7.72657e9 + 7.72657e9i −1.07521 + 1.07521i
\(156\) 1.40637e9 + 5.82536e8i 0.190124 + 0.0787521i
\(157\) 1.92550e9i 0.252927i −0.991971 0.126463i \(-0.959637\pi\)
0.991971 0.126463i \(-0.0403626\pi\)
\(158\) 3.13473e9 7.56791e9i 0.400169 0.966093i
\(159\) 1.38057e9 5.71849e8i 0.171305 0.0709569i
\(160\) 2.50078e9 + 6.03742e9i 0.301673 + 0.728302i
\(161\) −8.93476e9 8.93476e9i −1.04801 1.04801i
\(162\) −3.92558e9 3.92558e9i −0.447802 0.447802i
\(163\) −3.62088e9 8.74159e9i −0.401763 0.969943i −0.987238 0.159252i \(-0.949092\pi\)
0.585474 0.810691i \(-0.300908\pi\)
\(164\) 1.04087e9 4.31142e8i 0.112357 0.0465397i
\(165\) 5.19872e9 1.25508e10i 0.546033 1.31824i
\(166\) 5.58062e9i 0.570421i
\(167\) 7.26899e9 + 3.01091e9i 0.723186 + 0.299553i 0.713749 0.700402i \(-0.246996\pi\)
0.00943748 + 0.999955i \(0.496996\pi\)
\(168\) −8.67528e9 + 8.67528e9i −0.840218 + 0.840218i
\(169\) 5.63749e9 0.531613
\(170\) 8.10964e9 + 7.46073e9i 0.744701 + 0.685112i
\(171\) −1.13584e9 −0.101586
\(172\) 3.12582e9 3.12582e9i 0.272324 0.272324i
\(173\) −1.64966e10 6.83313e9i −1.40019 0.579979i −0.450392 0.892831i \(-0.648716\pi\)
−0.949802 + 0.312852i \(0.898716\pi\)
\(174\) 1.58302e10i 1.30922i
\(175\) 3.08948e9 7.45867e9i 0.249009 0.601160i
\(176\) 8.33579e9 3.45280e9i 0.654847 0.271246i
\(177\) 4.62746e9 + 1.11717e10i 0.354375 + 0.855536i
\(178\) 4.46926e8 + 4.46926e8i 0.0333692 + 0.0333692i
\(179\) 1.42417e10 + 1.42417e10i 1.03687 + 1.03687i 0.999294 + 0.0375747i \(0.0119632\pi\)
0.0375747 + 0.999294i \(0.488037\pi\)
\(180\) −4.20570e8 1.01534e9i −0.0298615 0.0720920i
\(181\) 1.23775e10 5.12694e9i 0.857196 0.355062i 0.0895858 0.995979i \(-0.471446\pi\)
0.767610 + 0.640917i \(0.221446\pi\)
\(182\) 3.83397e9 9.25603e9i 0.259017 0.625322i
\(183\) 1.75021e10i 1.15362i
\(184\) −1.91287e10 7.92336e9i −1.23028 0.509600i
\(185\) 8.52879e9 8.52879e9i 0.535321 0.535321i
\(186\) −1.47200e10 −0.901778
\(187\) −1.44650e10 + 1.57231e10i −0.865029 + 0.940267i
\(188\) 4.38904e9 0.256247
\(189\) 1.60915e10 1.60915e10i 0.917315 0.917315i
\(190\) −9.04776e9 3.74770e9i −0.503674 0.208629i
\(191\) 2.68090e10i 1.45757i 0.684742 + 0.728786i \(0.259915\pi\)
−0.684742 + 0.728786i \(0.740085\pi\)
\(192\) −6.96998e9 + 1.68270e10i −0.370149 + 0.893618i
\(193\) −1.89127e10 + 7.83390e9i −0.981173 + 0.406415i −0.814860 0.579658i \(-0.803186\pi\)
−0.166313 + 0.986073i \(0.553186\pi\)
\(194\) 1.66378e9 + 4.01672e9i 0.0843312 + 0.203594i
\(195\) −1.09122e10 1.09122e10i −0.540451 0.540451i
\(196\) −2.28302e9 2.28302e9i −0.110499 0.110499i
\(197\) 1.52286e10 + 3.67651e10i 0.720381 + 1.73915i 0.672263 + 0.740313i \(0.265322\pi\)
0.0481184 + 0.998842i \(0.484678\pi\)
\(198\) −3.92881e9 + 1.62737e9i −0.181664 + 0.0752475i
\(199\) 1.02987e10 2.48633e10i 0.465526 1.12388i −0.500571 0.865696i \(-0.666876\pi\)
0.966096 0.258182i \(-0.0831235\pi\)
\(200\) 1.32287e10i 0.584633i
\(201\) −6.82631e9 2.82755e9i −0.294988 0.122188i
\(202\) −2.44745e10 + 2.44745e10i −1.03427 + 1.03427i
\(203\) −5.22036e10 −2.15759
\(204\) −3.09717e8 7.43155e9i −0.0125207 0.300430i
\(205\) −1.14215e10 −0.451682
\(206\) 6.66189e9 6.66189e9i 0.257748 0.257748i
\(207\) 5.62885e9 + 2.33155e9i 0.213085 + 0.0882628i
\(208\) 1.02495e10i 0.379679i
\(209\) 7.26611e9 1.75419e10i 0.263417 0.635945i
\(210\) 2.87579e10 1.19119e10i 1.02040 0.422663i
\(211\) 8.85597e9 + 2.13802e10i 0.307585 + 0.742576i 0.999782 + 0.0208673i \(0.00664276\pi\)
−0.692197 + 0.721708i \(0.743357\pi\)
\(212\) 1.42894e9 + 1.42894e9i 0.0485849 + 0.0485849i
\(213\) 2.72537e10 + 2.72537e10i 0.907230 + 0.907230i
\(214\) −3.37957e9 8.15900e9i −0.110154 0.265935i
\(215\) −4.14036e10 + 1.71499e10i −1.32149 + 0.547381i
\(216\) 1.42700e10 3.44508e10i 0.446048 1.07686i
\(217\) 4.85426e10i 1.48612i
\(218\) 2.55971e10 + 1.06026e10i 0.767601 + 0.317951i
\(219\) −6.46241e9 + 6.46241e9i −0.189844 + 0.189844i
\(220\) 1.83714e10 0.528739
\(221\) 1.02133e10 + 2.20163e10i 0.288005 + 0.620838i
\(222\) 1.62483e10 0.448973
\(223\) 2.03075e10 2.03075e10i 0.549900 0.549900i −0.376512 0.926412i \(-0.622877\pi\)
0.926412 + 0.376512i \(0.122877\pi\)
\(224\) −2.68209e10 1.11096e10i −0.711798 0.294836i
\(225\) 3.89272e9i 0.101258i
\(226\) 2.05085e10 4.95119e10i 0.522933 1.26247i
\(227\) 3.82575e10 1.58468e10i 0.956313 0.396118i 0.150713 0.988578i \(-0.451843\pi\)
0.805600 + 0.592460i \(0.201843\pi\)
\(228\) 2.52965e9 + 6.10711e9i 0.0619945 + 0.149668i
\(229\) 4.58663e10 + 4.58663e10i 1.10213 + 1.10213i 0.994153 + 0.107981i \(0.0344385\pi\)
0.107981 + 0.994153i \(0.465562\pi\)
\(230\) 3.71448e10 + 3.71448e10i 0.875231 + 0.875231i
\(231\) 2.30950e10 + 5.57562e10i 0.533659 + 1.28837i
\(232\) −7.90292e10 + 3.27350e10i −1.79098 + 0.741850i
\(233\) 1.35883e10 3.28050e10i 0.302039 0.729187i −0.697877 0.716218i \(-0.745872\pi\)
0.999916 0.0129690i \(-0.00412828\pi\)
\(234\) 4.83077e9i 0.105328i
\(235\) −4.11082e10 1.70276e10i −0.879272 0.364206i
\(236\) −1.15631e10 + 1.15631e10i −0.242644 + 0.242644i
\(237\) 5.60530e10 1.15407
\(238\) −4.89109e10 + 2.03841e9i −0.988118 + 0.0411808i
\(239\) −8.00754e9 −0.158748 −0.0793741 0.996845i \(-0.525292\pi\)
−0.0793741 + 0.996845i \(0.525292\pi\)
\(240\) 2.25174e10 2.25174e10i 0.438095 0.438095i
\(241\) −3.87630e10 1.60562e10i −0.740186 0.306595i −0.0194560 0.999811i \(-0.506193\pi\)
−0.720730 + 0.693215i \(0.756193\pi\)
\(242\) 2.75389e10i 0.516152i
\(243\) −7.73207e9 + 1.86669e10i −0.142255 + 0.343434i
\(244\) 2.18672e10 9.05769e9i 0.394947 0.163592i
\(245\) 1.25259e10 + 3.02402e10i 0.222107 + 0.536213i
\(246\) −1.08797e10 1.08797e10i −0.189412 0.189412i
\(247\) −1.52517e10 1.52517e10i −0.260724 0.260724i
\(248\) −3.04393e10 7.34869e10i −0.510978 1.23361i
\(249\) −3.52806e10 + 1.46137e10i −0.581620 + 0.240915i
\(250\) 1.10732e10 2.67331e10i 0.179285 0.432831i
\(251\) 5.41320e10i 0.860839i −0.902629 0.430420i \(-0.858366\pi\)
0.902629 0.430420i \(-0.141634\pi\)
\(252\) 4.51060e9 + 1.86835e9i 0.0704583 + 0.0291848i
\(253\) −7.20169e10 + 7.20169e10i −1.10508 + 1.10508i
\(254\) 5.55408e10 0.837261
\(255\) −2.59303e10 + 7.08062e10i −0.384041 + 1.04867i
\(256\) −6.02954e10 −0.877413
\(257\) 8.20175e9 8.20175e9i 0.117276 0.117276i −0.646034 0.763309i \(-0.723573\pi\)
0.763309 + 0.646034i \(0.223573\pi\)
\(258\) −5.57756e10 2.31030e10i −0.783711 0.324624i
\(259\) 5.35826e10i 0.739903i
\(260\) 7.98643e9 1.92810e10i 0.108386 0.261667i
\(261\) 2.32553e10 9.63267e9i 0.310199 0.128489i
\(262\) 2.88299e10 + 6.96016e10i 0.377996 + 0.912564i
\(263\) −8.84129e10 8.84129e10i −1.13950 1.13950i −0.988540 0.150961i \(-0.951763\pi\)
−0.150961 0.988540i \(-0.548237\pi\)
\(264\) 6.99254e10 + 6.99254e10i 0.885967 + 0.885967i
\(265\) −7.83991e9 1.89272e10i −0.0976573 0.235766i
\(266\) 4.01941e10 1.66489e10i 0.492260 0.203901i
\(267\) −1.65512e9 + 3.99581e9i −0.0199309 + 0.0481176i
\(268\) 9.99210e9i 0.118318i
\(269\) 1.01000e11 + 4.18356e10i 1.17608 + 0.487148i 0.883198 0.469001i \(-0.155386\pi\)
0.292881 + 0.956149i \(0.405386\pi\)
\(270\) −6.68978e10 + 6.68978e10i −0.766081 + 0.766081i
\(271\) −1.02637e11 −1.15596 −0.577980 0.816051i \(-0.696159\pi\)
−0.577980 + 0.816051i \(0.696159\pi\)
\(272\) −4.54308e10 + 2.10752e10i −0.503257 + 0.233460i
\(273\) 6.85564e10 0.746993
\(274\) −7.39220e9 + 7.39220e9i −0.0792312 + 0.0792312i
\(275\) −6.01192e10 2.49022e10i −0.633893 0.262567i
\(276\) 3.54575e10i 0.367804i
\(277\) 5.46310e10 1.31891e11i 0.557545 1.34603i −0.354159 0.935185i \(-0.615233\pi\)
0.911704 0.410848i \(-0.134767\pi\)
\(278\) −1.15160e11 + 4.77008e10i −1.15638 + 0.478987i
\(279\) 8.95713e9 + 2.16244e10i 0.0885014 + 0.213661i
\(280\) 1.18936e11 + 1.18936e11i 1.15639 + 1.15639i
\(281\) 5.69143e10 + 5.69143e10i 0.544556 + 0.544556i 0.924861 0.380305i \(-0.124181\pi\)
−0.380305 + 0.924861i \(0.624181\pi\)
\(282\) −2.29382e10 5.53777e10i −0.215992 0.521451i
\(283\) 1.04597e11 4.33256e10i 0.969351 0.401518i 0.158881 0.987298i \(-0.449211\pi\)
0.810471 + 0.585779i \(0.199211\pi\)
\(284\) −1.99465e10 + 4.81551e10i −0.181943 + 0.439248i
\(285\) 6.70138e10i 0.601676i
\(286\) −7.46064e10 3.09030e10i −0.659370 0.273120i
\(287\) 3.58782e10 3.58782e10i 0.312149 0.312149i
\(288\) 1.39979e10 0.119894
\(289\) 7.65862e10 9.05408e10i 0.645818 0.763491i
\(290\) 2.17028e11 1.80187
\(291\) −2.10368e10 + 2.10368e10i −0.171974 + 0.171974i
\(292\) −1.14185e10 4.72972e9i −0.0919153 0.0380726i
\(293\) 4.40078e10i 0.348839i 0.984671 + 0.174420i \(0.0558049\pi\)
−0.984671 + 0.174420i \(0.944195\pi\)
\(294\) −1.68739e10 + 4.07371e10i −0.131720 + 0.318000i
\(295\) 1.53161e11 6.34413e10i 1.17747 0.487723i
\(296\) 3.35997e10 + 8.11168e10i 0.254403 + 0.614184i
\(297\) −1.29703e11 1.29703e11i −0.967262 0.967262i
\(298\) 5.58154e9 + 5.58154e9i 0.0409997 + 0.0409997i
\(299\) 4.42751e10 + 1.06889e11i 0.320360 + 0.773418i
\(300\) 2.09301e10 8.66954e9i 0.149185 0.0617946i
\(301\) 7.61875e10 1.83933e11i 0.534976 1.29155i
\(302\) 1.61878e10i 0.111984i
\(303\) −2.18818e11 9.06373e10i −1.49139 0.617753i
\(304\) 3.14720e10 3.14720e10i 0.211345 0.211345i
\(305\) −2.39950e11 −1.58771
\(306\) 2.14124e10 9.93315e9i 0.139611 0.0647650i
\(307\) −3.65313e10 −0.234716 −0.117358 0.993090i \(-0.537443\pi\)
−0.117358 + 0.993090i \(0.537443\pi\)
\(308\) −5.77098e10 + 5.77098e10i −0.365402 + 0.365402i
\(309\) 5.95617e10 + 2.46712e10i 0.371667 + 0.153949i
\(310\) 2.01808e11i 1.24111i
\(311\) 1.13609e10 2.74276e10i 0.0688638 0.166252i −0.885700 0.464257i \(-0.846321\pi\)
0.954564 + 0.298005i \(0.0963213\pi\)
\(312\) 1.03785e11 4.29893e10i 0.620069 0.256841i
\(313\) −3.77426e10 9.11188e10i −0.222271 0.536609i 0.772927 0.634495i \(-0.218792\pi\)
−0.995198 + 0.0978858i \(0.968792\pi\)
\(314\) −2.51457e10 2.51457e10i −0.145976 0.145976i
\(315\) −3.49984e10 3.49984e10i −0.200286 0.200286i
\(316\) 2.90085e10 + 7.00327e10i 0.163656 + 0.395102i
\(317\) 2.21068e10 9.15692e9i 0.122958 0.0509311i −0.320356 0.947297i \(-0.603803\pi\)
0.443314 + 0.896366i \(0.353803\pi\)
\(318\) 1.05613e10 2.54972e10i 0.0579156 0.139821i
\(319\) 4.20777e11i 2.27507i
\(320\) 2.30694e11 + 9.55568e10i 1.22988 + 0.509432i
\(321\) 4.27312e10 4.27312e10i 0.224633 0.224633i
\(322\) −2.33364e11 −1.20971
\(323\) −3.62421e10 + 9.89638e10i −0.185269 + 0.505901i
\(324\) 5.13741e10 0.258995
\(325\) −5.22700e10 + 5.22700e10i −0.259883 + 0.259883i
\(326\) −1.61446e11 6.68730e10i −0.791676 0.327923i
\(327\) 1.89589e11i 0.916956i
\(328\) 3.18169e10 7.68127e10i 0.151784 0.366438i
\(329\) 1.82621e11 7.56439e10i 0.859346 0.355953i
\(330\) −9.60136e10 2.31797e11i −0.445677 1.07596i
\(331\) −1.56900e11 1.56900e11i −0.718452 0.718452i 0.249836 0.968288i \(-0.419623\pi\)
−0.968288 + 0.249836i \(0.919623\pi\)
\(332\) −3.65167e10 3.65167e10i −0.164957 0.164957i
\(333\) −9.88712e9 2.38696e10i −0.0440627 0.106377i
\(334\) 1.34249e11 5.56077e10i 0.590271 0.244498i
\(335\) −3.87650e10 + 9.35871e10i −0.168166 + 0.405989i
\(336\) 1.41467e11i 0.605519i
\(337\) −1.97014e11 8.16059e10i −0.832075 0.344657i −0.0743512 0.997232i \(-0.523689\pi\)
−0.757724 + 0.652575i \(0.773689\pi\)
\(338\) 7.36219e10 7.36219e10i 0.306819 0.306819i
\(339\) 3.66719e11 1.50812
\(340\) −1.01885e11 + 4.24615e9i −0.413480 + 0.0172322i
\(341\) −3.91268e11 −1.56704
\(342\) −1.48333e10 + 1.48333e10i −0.0586301 + 0.0586301i
\(343\) 1.52621e11 + 6.32179e10i 0.595377 + 0.246613i
\(344\) 3.26224e11i 1.25604i
\(345\) −1.37560e11 + 3.32098e11i −0.522764 + 1.26206i
\(346\) −3.04671e11 + 1.26199e11i −1.14285 + 0.473384i
\(347\) −8.76554e10 2.11619e11i −0.324561 0.783559i −0.998978 0.0452081i \(-0.985605\pi\)
0.674417 0.738351i \(-0.264395\pi\)
\(348\) −1.03585e11 1.03585e11i −0.378607 0.378607i
\(349\) 3.34684e11 + 3.34684e11i 1.20759 + 1.20759i 0.971805 + 0.235786i \(0.0757665\pi\)
0.235786 + 0.971805i \(0.424233\pi\)
\(350\) −5.70587e10 1.37752e11i −0.203243 0.490672i
\(351\) −1.92508e11 + 7.97394e10i −0.676966 + 0.280408i
\(352\) −8.95465e10 + 2.16184e11i −0.310890 + 0.750555i
\(353\) 2.29372e11i 0.786238i 0.919488 + 0.393119i \(0.128604\pi\)
−0.919488 + 0.393119i \(0.871396\pi\)
\(354\) 2.06326e11 + 8.54631e10i 0.698296 + 0.289244i
\(355\) 3.73642e11 3.73642e11i 1.24861 1.24861i
\(356\) −5.84891e9 −0.0192997
\(357\) −1.40968e11 3.03876e11i −0.459317 0.990125i
\(358\) 3.71975e11 1.19685
\(359\) −9.69127e10 + 9.69127e10i −0.307933 + 0.307933i −0.844107 0.536174i \(-0.819869\pi\)
0.536174 + 0.844107i \(0.319869\pi\)
\(360\) −7.49291e10 3.10366e10i −0.235120 0.0973898i
\(361\) 2.29024e11i 0.709740i
\(362\) 9.46878e10 2.28597e11i 0.289805 0.699651i
\(363\) 1.74101e11 7.21150e10i 0.526285 0.217995i
\(364\) 3.54792e10 + 8.56544e10i 0.105930 + 0.255737i
\(365\) 8.85981e10 + 8.85981e10i 0.261280 + 0.261280i
\(366\) −2.28566e11 2.28566e11i −0.665806 0.665806i
\(367\) −1.04354e11 2.51932e11i −0.300269 0.724913i −0.999945 0.0104533i \(-0.996673\pi\)
0.699677 0.714460i \(-0.253327\pi\)
\(368\) −2.20567e11 + 9.13620e10i −0.626940 + 0.259687i
\(369\) −9.36250e9 + 2.26031e10i −0.0262890 + 0.0634672i
\(370\) 2.22761e11i 0.617918i
\(371\) 8.40830e10 + 3.48283e10i 0.230423 + 0.0954443i
\(372\) 9.63203e10 9.63203e10i 0.260780 0.260780i
\(373\) 1.61092e11 0.430907 0.215453 0.976514i \(-0.430877\pi\)
0.215453 + 0.976514i \(0.430877\pi\)
\(374\) 1.64302e10 + 3.94237e11i 0.0434231 + 1.04192i
\(375\) 1.98003e11 0.517049
\(376\) 2.29029e11 2.29029e11i 0.590944 0.590944i
\(377\) 4.41608e11 + 1.82920e11i 1.12590 + 0.466364i
\(378\) 4.20289e11i 1.05885i
\(379\) 2.39263e10 5.77632e10i 0.0595661 0.143805i −0.891294 0.453425i \(-0.850202\pi\)
0.950860 + 0.309620i \(0.100202\pi\)
\(380\) 8.37271e10 3.46809e10i 0.205987 0.0853226i
\(381\) 1.45442e11 + 3.51129e11i 0.353613 + 0.853698i
\(382\) 3.50107e11 + 3.50107e11i 0.841232 + 0.841232i
\(383\) −2.18701e11 2.18701e11i −0.519345 0.519345i 0.398028 0.917373i \(-0.369695\pi\)
−0.917373 + 0.398028i \(0.869695\pi\)
\(384\) 3.53331e10 + 8.53016e10i 0.0829260 + 0.200201i
\(385\) 7.64405e11 3.16627e11i 1.77317 0.734471i
\(386\) −1.44682e11 + 3.49293e11i −0.331719 + 0.800842i
\(387\) 9.59954e10i 0.217546i
\(388\) −3.71704e10 1.53965e10i −0.0832634 0.0344888i
\(389\) −4.53138e11 + 4.53138e11i −1.00336 + 1.00336i −0.00336677 + 0.999994i \(0.501072\pi\)
−0.999994 + 0.00336677i \(0.998928\pi\)
\(390\) −2.85012e11 −0.623839
\(391\) 3.82748e11 4.16038e11i 0.828166 0.900197i
\(392\) −2.38266e11 −0.509653
\(393\) −3.64525e11 + 3.64525e11i −0.770834 + 0.770834i
\(394\) 6.79004e11 + 2.81253e11i 1.41951 + 0.587981i
\(395\) 7.68474e11i 1.58834i
\(396\) 1.50595e10 3.63569e10i 0.0307739 0.0742947i
\(397\) −8.55615e11 + 3.54407e11i −1.72871 + 0.716053i −0.729210 + 0.684290i \(0.760112\pi\)
−0.999495 + 0.0317632i \(0.989888\pi\)
\(398\) −1.90203e11 4.59192e11i −0.379966 0.917319i
\(399\) 2.10509e11 + 2.10509e11i 0.415808 + 0.415808i
\(400\) −1.07860e11 1.07860e11i −0.210664 0.210664i
\(401\) −1.86404e11 4.50020e11i −0.360003 0.869124i −0.995298 0.0968552i \(-0.969122\pi\)
0.635295 0.772269i \(-0.280878\pi\)
\(402\) −1.26073e11 + 5.22211e10i −0.240771 + 0.0997308i
\(403\) −1.70092e11 + 4.10639e11i −0.321226 + 0.775509i
\(404\) 3.20298e11i 0.598188i
\(405\) −4.81175e11 1.99309e11i −0.888700 0.368112i
\(406\) −6.81744e11 + 6.81744e11i −1.24524 + 1.24524i
\(407\) 4.31892e11 0.780190
\(408\) −4.03956e11 3.71632e11i −0.721711 0.663961i
\(409\) −8.32274e11 −1.47066 −0.735329 0.677711i \(-0.762972\pi\)
−0.735329 + 0.677711i \(0.762972\pi\)
\(410\) −1.49158e11 + 1.49158e11i −0.260686 + 0.260686i
\(411\) −6.60911e10 2.73758e10i −0.114250 0.0473237i
\(412\) 8.71842e10i 0.149073i
\(413\) −2.81834e11 + 6.80407e11i −0.476670 + 1.15078i
\(414\) 1.03958e11 4.30606e10i 0.173922 0.0720408i
\(415\) 2.00351e11 + 4.83689e11i 0.331569 + 0.800479i
\(416\) 1.87959e11 + 1.87959e11i 0.307712 + 0.307712i
\(417\) −6.03128e11 6.03128e11i −0.976781 0.976781i
\(418\) −1.34196e11 3.23977e11i −0.215003 0.519063i
\(419\) 1.62012e11 6.71076e10i 0.256794 0.106367i −0.250573 0.968098i \(-0.580619\pi\)
0.507367 + 0.861730i \(0.330619\pi\)
\(420\) −1.10232e11 + 2.66123e11i −0.172856 + 0.417311i
\(421\) 2.27037e11i 0.352231i −0.984369 0.176116i \(-0.943647\pi\)
0.984369 0.176116i \(-0.0563533\pi\)
\(422\) 3.94864e11 + 1.63558e11i 0.606097 + 0.251053i
\(423\) −6.73947e10 + 6.73947e10i −0.102351 + 0.102351i
\(424\) 1.49130e11 0.224088
\(425\) 3.39166e11 + 1.24208e11i 0.504269 + 0.184671i
\(426\) 7.11831e11 1.04721
\(427\) 7.53750e11 7.53750e11i 1.09724 1.09724i
\(428\) 7.55026e10 + 3.12742e10i 0.108759 + 0.0450494i
\(429\) 5.52586e11i 0.787666i
\(430\) −3.16737e11 + 7.64671e11i −0.446777 + 1.07861i
\(431\) 6.04324e11 2.50319e11i 0.843571 0.349419i 0.0813107 0.996689i \(-0.474089\pi\)
0.762261 + 0.647270i \(0.224089\pi\)
\(432\) −1.64543e11 3.97242e11i −0.227302 0.548755i
\(433\) 1.18904e10 + 1.18904e10i 0.0162555 + 0.0162555i 0.715188 0.698932i \(-0.246341\pi\)
−0.698932 + 0.715188i \(0.746341\pi\)
\(434\) −6.33934e11 6.33934e11i −0.857709 0.857709i
\(435\) 5.68321e11 + 1.37205e12i 0.761013 + 1.83725i
\(436\) −2.36873e11 + 9.81159e10i −0.313925 + 0.130032i
\(437\) −1.92263e11 + 4.64165e11i −0.252191 + 0.608843i
\(438\) 1.68789e11i 0.219135i
\(439\) 6.56544e11 + 2.71949e11i 0.843672 + 0.349460i 0.762300 0.647224i \(-0.224070\pi\)
0.0813715 + 0.996684i \(0.474070\pi\)
\(440\) 9.58661e11 9.58661e11i 1.21935 1.21935i
\(441\) 7.01127e10 0.0882720
\(442\) 4.20897e11 + 1.54139e11i 0.524536 + 0.192093i
\(443\) −1.15788e12 −1.42838 −0.714192 0.699949i \(-0.753206\pi\)
−0.714192 + 0.699949i \(0.753206\pi\)
\(444\) −1.06321e11 + 1.06321e11i −0.129836 + 0.129836i
\(445\) 5.47815e10 + 2.26913e10i 0.0662238 + 0.0274308i
\(446\) 5.30404e11i 0.634746i
\(447\) −2.06703e10 + 4.99026e10i −0.0244886 + 0.0591206i
\(448\) −1.02485e12 + 4.24505e11i −1.20201 + 0.497888i
\(449\) 6.85694e10 + 1.65541e11i 0.0796200 + 0.192220i 0.958677 0.284497i \(-0.0918267\pi\)
−0.879057 + 0.476717i \(0.841827\pi\)
\(450\) 5.08363e10 + 5.08363e10i 0.0584410 + 0.0584410i
\(451\) −2.89189e11 2.89189e11i −0.329146 0.329146i
\(452\) 1.89784e11 + 4.58179e11i 0.213863 + 0.516312i
\(453\) 1.02339e11 4.23904e10i 0.114183 0.0472961i
\(454\) 2.92669e11 7.06566e11i 0.323315 0.780551i
\(455\) 9.39892e11i 1.02808i
\(456\) 4.50685e11 + 1.86680e11i 0.488125 + 0.202188i
\(457\) 1.04584e12 1.04584e12i 1.12161 1.12161i 0.130116 0.991499i \(-0.458465\pi\)
0.991499 0.130116i \(-0.0415349\pi\)
\(458\) 1.19797e12 1.27219
\(459\) 7.49285e11 + 6.89329e11i 0.787934 + 0.724886i
\(460\) −4.86114e11 −0.506206
\(461\) 3.08680e11 3.08680e11i 0.318313 0.318313i −0.529806 0.848119i \(-0.677735\pi\)
0.848119 + 0.529806i \(0.177735\pi\)
\(462\) 1.02974e12 + 4.26534e11i 1.05158 + 0.435577i
\(463\) 1.67288e11i 0.169180i 0.996416 + 0.0845902i \(0.0269581\pi\)
−0.996416 + 0.0845902i \(0.973042\pi\)
\(464\) −3.77458e11 + 9.11263e11i −0.378040 + 0.912668i
\(465\) −1.27583e12 + 5.28465e11i −1.26547 + 0.524177i
\(466\) −2.50958e11 6.05866e11i −0.246527 0.595168i
\(467\) −4.66902e9 4.66902e9i −0.00454255 0.00454255i 0.704832 0.709374i \(-0.251022\pi\)
−0.709374 + 0.704832i \(0.751022\pi\)
\(468\) −3.16101e10 3.16101e10i −0.0304593 0.0304593i
\(469\) −1.72211e11 4.15755e11i −0.164355 0.396789i
\(470\) −7.59215e11 + 3.14477e11i −0.717669 + 0.297268i
\(471\) 9.31232e10 2.24819e11i 0.0871894 0.210494i
\(472\) 1.20677e12i 1.11915i
\(473\) −1.48256e12 6.14095e11i −1.36187 0.564105i
\(474\) 7.32016e11 7.32016e11i 0.666067 0.666067i
\(475\) −3.21000e11 −0.289324
\(476\) 3.06710e11 3.33386e11i 0.273840 0.297657i
\(477\) −4.38833e10 −0.0388121
\(478\) −1.04573e11 + 1.04573e11i −0.0916209 + 0.0916209i
\(479\) 8.12327e11 + 3.36477e11i 0.705052 + 0.292042i 0.706255 0.707957i \(-0.250383\pi\)
−0.00120343 + 0.999999i \(0.500383\pi\)
\(480\) 8.25869e11i 0.710110i
\(481\) 1.87752e11 4.53274e11i 0.159931 0.386107i
\(482\) −7.15902e11 + 2.96537e11i −0.604146 + 0.250246i
\(483\) −6.11100e11 1.47533e12i −0.510917 1.23346i
\(484\) 1.80201e11 + 1.80201e11i 0.149263 + 0.149263i
\(485\) 2.88410e11 + 2.88410e11i 0.236686 + 0.236686i
\(486\) 1.42801e11 + 3.44753e11i 0.116110 + 0.280314i
\(487\) −1.31852e12 + 5.46147e11i −1.06220 + 0.439976i −0.844231 0.535980i \(-0.819942\pi\)
−0.217966 + 0.975956i \(0.569942\pi\)
\(488\) 6.68427e11 1.61373e12i 0.533538 1.28807i
\(489\) 1.19578e12i 0.945714i
\(490\) 5.58497e11 + 2.31337e11i 0.437661 + 0.181285i
\(491\) 2.15375e10 2.15375e10i 0.0167235 0.0167235i −0.698696 0.715419i \(-0.746236\pi\)
0.715419 + 0.698696i \(0.246236\pi\)
\(492\) 1.42382e11 0.109550
\(493\) −9.72532e10 2.33355e12i −0.0741468 1.77913i
\(494\) −3.98353e11 −0.300952
\(495\) −2.82098e11 + 2.82098e11i −0.211191 + 0.211191i
\(496\) −8.47357e11 3.50987e11i −0.628635 0.260389i
\(497\) 2.34743e12i 1.72579i
\(498\) −2.69896e11 + 6.51587e11i −0.196637 + 0.474723i
\(499\) −7.94958e11 + 3.29283e11i −0.573974 + 0.237748i −0.650739 0.759302i \(-0.725541\pi\)
0.0767653 + 0.997049i \(0.475541\pi\)
\(500\) 1.02470e11 + 2.47385e11i 0.0733218 + 0.177014i
\(501\) 7.03103e11 + 7.03103e11i 0.498596 + 0.498596i
\(502\) −7.06928e11 7.06928e11i −0.496830 0.496830i
\(503\) 4.01038e11 + 9.68190e11i 0.279337 + 0.674380i 0.999818 0.0190953i \(-0.00607858\pi\)
−0.720480 + 0.693475i \(0.756079\pi\)
\(504\) 3.32868e11 1.37878e11i 0.229792 0.0951828i
\(505\) −1.24262e12 + 2.99994e12i −0.850209 + 2.05259i
\(506\) 1.88099e12i 1.27558i
\(507\) 6.58228e11 + 2.72647e11i 0.442426 + 0.183259i
\(508\) −3.63431e11 + 3.63431e11i −0.242123 + 0.242123i
\(509\) 1.04811e12 0.692112 0.346056 0.938214i \(-0.387521\pi\)
0.346056 + 0.938214i \(0.387521\pi\)
\(510\) 5.86049e11 + 1.26332e12i 0.383591 + 0.826887i
\(511\) −5.56622e11 −0.361132
\(512\) −1.05192e12 + 1.05192e12i −0.676497 + 0.676497i
\(513\) −8.35961e11 3.46266e11i −0.532915 0.220741i
\(514\) 2.14219e11i 0.135370i
\(515\) 3.38237e11 8.16576e11i 0.211879 0.511522i
\(516\) 5.16142e11 2.13793e11i 0.320513 0.132761i
\(517\) −6.09713e11 1.47198e12i −0.375334 0.906137i
\(518\) 6.99753e11 + 6.99753e11i 0.427032 + 0.427032i
\(519\) −1.59566e12 1.59566e12i −0.965355 0.965355i
\(520\) −5.89372e11 1.42287e12i −0.353488 0.853396i
\(521\) 1.23424e12 5.11238e11i 0.733886 0.303986i 0.0157384 0.999876i \(-0.494990\pi\)
0.718148 + 0.695890i \(0.244990\pi\)
\(522\) 1.77903e11 4.29495e11i 0.104873 0.253187i
\(523\) 1.91916e12i 1.12164i −0.827938 0.560820i \(-0.810486\pi\)
0.827938 0.560820i \(-0.189514\pi\)
\(524\) −6.44086e11 2.66789e11i −0.373210 0.154589i
\(525\) 7.21450e11 7.21450e11i 0.414466 0.414466i
\(526\) −2.30923e12 −1.31532
\(527\) 2.16990e12 9.04329e10i 1.22544 0.0510715i
\(528\) 1.14027e12 0.638489
\(529\) 6.31980e11 6.31980e11i 0.350876 0.350876i
\(530\) −3.49561e11 1.44793e11i −0.192434 0.0797088i
\(531\) 3.55108e11i 0.193836i
\(532\) −1.54068e11 + 3.71952e11i −0.0833891 + 0.201319i
\(533\) −4.29223e11 + 1.77790e11i −0.230362 + 0.0954189i
\(534\) 3.05678e10 + 7.37973e10i 0.0162678 + 0.0392740i
\(535\) −5.85835e11 5.85835e11i −0.309160 0.309160i
\(536\) −5.21409e11 5.21409e11i −0.272858 0.272858i
\(537\) 9.74074e11 + 2.35162e12i 0.505484 + 1.22035i
\(538\) 1.86534e12 7.72649e11i 0.959926 0.397614i
\(539\) −4.48520e11 + 1.08282e12i −0.228893 + 0.552596i
\(540\) 8.75491e11i 0.443078i
\(541\) 1.15419e12 + 4.78082e11i 0.579282 + 0.239947i 0.653032 0.757330i \(-0.273497\pi\)
−0.0737498 + 0.997277i \(0.523497\pi\)
\(542\) −1.34037e12 + 1.34037e12i −0.667158 + 0.667158i
\(543\) 1.69314e12 0.835784
\(544\) 4.46643e11 1.21962e12i 0.218658 0.597074i
\(545\) 2.59922e12 1.26200
\(546\) 8.95301e11 8.95301e11i 0.431124 0.431124i
\(547\) −2.00507e12 8.30528e11i −0.957606 0.396653i −0.151522 0.988454i \(-0.548417\pi\)
−0.806084 + 0.591800i \(0.798417\pi\)
\(548\) 9.67417e10i 0.0458249i
\(549\) −1.96693e11 + 4.74859e11i −0.0924088 + 0.223094i
\(550\) −1.11032e12 + 4.59911e11i −0.517389 + 0.214310i
\(551\) 7.94326e11 + 1.91767e12i 0.367127 + 0.886324i
\(552\) −1.85025e12 1.85025e12i −0.848211 0.848211i
\(553\) 2.41399e12 + 2.41399e12i 1.09767 + 1.09767i
\(554\) −1.00896e12 2.43585e12i −0.455073 1.09864i
\(555\) 1.40829e12 5.83334e11i 0.630049 0.260975i
\(556\) 4.41418e11 1.06568e12i 0.195891 0.472922i
\(557\) 1.80971e12i 0.796637i 0.917247 + 0.398319i \(0.130406\pi\)
−0.917247 + 0.398319i \(0.869594\pi\)
\(558\) 3.99375e11 + 1.65427e11i 0.174392 + 0.0722356i
\(559\) −1.28899e12 + 1.28899e12i −0.558338 + 0.558338i
\(560\) 1.93948e12 0.833371
\(561\) −2.44934e12 + 1.13624e12i −1.04404 + 0.484326i
\(562\) 1.48653e12 0.628578
\(563\) −2.63350e12 + 2.63350e12i −1.10470 + 1.10470i −0.110869 + 0.993835i \(0.535363\pi\)
−0.993835 + 0.110869i \(0.964637\pi\)
\(564\) 5.12460e11 + 2.12268e11i 0.213257 + 0.0883340i
\(565\) 5.02763e12i 2.07561i
\(566\) 8.00167e11 1.93177e12i 0.327723 0.791193i
\(567\) 2.13759e12 8.85418e11i 0.868561 0.359770i
\(568\) 1.47199e12 + 3.55369e12i 0.593384 + 1.43256i
\(569\) −1.32815e11 1.32815e11i −0.0531180 0.0531180i 0.680049 0.733167i \(-0.261959\pi\)
−0.733167 + 0.680049i \(0.761959\pi\)
\(570\) −8.75156e11 8.75156e11i −0.347255 0.347255i
\(571\) 1.89861e11 + 4.58365e11i 0.0747434 + 0.180447i 0.956835 0.290631i \(-0.0938652\pi\)
−0.882092 + 0.471078i \(0.843865\pi\)
\(572\) 6.90401e11 2.85973e11i 0.269662 0.111698i
\(573\) −1.29657e12 + 3.13019e12i −0.502457 + 1.21304i
\(574\) 9.37091e11i 0.360312i
\(575\) 1.59077e12 + 6.58919e11i 0.606879 + 0.251378i
\(576\) 3.78211e11 3.78211e11i 0.143164 0.143164i
\(577\) 1.69341e12 0.636022 0.318011 0.948087i \(-0.396985\pi\)
0.318011 + 0.948087i \(0.396985\pi\)
\(578\) −1.82238e11 2.18257e12i −0.0679147 0.813378i
\(579\) −2.58710e12 −0.956664
\(580\) −1.42012e12 + 1.42012e12i −0.521074 + 0.521074i
\(581\) −2.14876e12 8.90044e11i −0.782338 0.324055i
\(582\) 5.49454e11i 0.198508i
\(583\) 2.80727e11 6.77735e11i 0.100641 0.242969i
\(584\) −8.42651e11 + 3.49037e11i −0.299771 + 0.124169i
\(585\) 1.73430e11 + 4.18697e11i 0.0612242 + 0.147808i
\(586\) 5.74712e11 + 5.74712e11i 0.201331 + 0.201331i
\(587\) −3.04236e11 3.04236e11i −0.105764 0.105764i 0.652245 0.758009i \(-0.273828\pi\)
−0.758009 + 0.652245i \(0.773828\pi\)
\(588\) −1.56149e11 3.76978e11i −0.0538694 0.130052i
\(589\) −1.78319e12 + 7.38620e11i −0.610489 + 0.252873i
\(590\) 1.17168e12 2.82868e12i 0.398084 0.961059i
\(591\) 5.02916e12i 1.69571i
\(592\) 9.35335e11 + 3.87428e11i 0.312982 + 0.129641i
\(593\) 5.84287e11 5.84287e11i 0.194035 0.194035i −0.603402 0.797437i \(-0.706189\pi\)
0.797437 + 0.603402i \(0.206189\pi\)
\(594\) −3.38766e12 −1.11650
\(595\) −4.16607e12 + 1.93263e12i −1.36270 + 0.632154i
\(596\) −7.30455e10 −0.0237129
\(597\) 2.40493e12 2.40493e12i 0.774851 0.774851i
\(598\) 1.97411e12 + 8.17702e11i 0.631271 + 0.261481i
\(599\) 7.63092e11i 0.242190i −0.992641 0.121095i \(-0.961359\pi\)
0.992641 0.121095i \(-0.0386406\pi\)
\(600\) 6.39783e11 1.54457e12i 0.201536 0.486550i
\(601\) 2.88546e12 1.19520e12i 0.902152 0.373684i 0.117105 0.993120i \(-0.462639\pi\)
0.785047 + 0.619436i \(0.212639\pi\)
\(602\) −1.40708e12 3.39700e12i −0.436652 1.05417i
\(603\) 1.53431e11 + 1.53431e11i 0.0472591 + 0.0472591i
\(604\) 1.05925e11 + 1.05925e11i 0.0323841 + 0.0323841i
\(605\) −9.88679e11 2.38688e12i −0.300024 0.724322i
\(606\) −4.04128e12 + 1.67395e12i −1.21728 + 0.504216i
\(607\) −8.81119e11 + 2.12721e12i −0.263442 + 0.636006i −0.999147 0.0412967i \(-0.986851\pi\)
0.735705 + 0.677302i \(0.236851\pi\)
\(608\) 1.15429e12i 0.342571i
\(609\) −6.09524e12 2.52473e12i −1.79561 0.743767i
\(610\) −3.13359e12 + 3.13359e12i −0.916343 + 0.916343i
\(611\) −1.80991e12 −0.525376
\(612\) −7.51142e10 + 2.05109e11i −0.0216442 + 0.0591022i
\(613\) 3.66201e12 1.04748 0.523742 0.851877i \(-0.324535\pi\)
0.523742 + 0.851877i \(0.324535\pi\)
\(614\) −4.77075e11 + 4.77075e11i −0.135466 + 0.135466i
\(615\) −1.33357e12 5.52382e11i −0.375904 0.155704i
\(616\) 6.02284e12i 1.68534i
\(617\) −7.03069e11 + 1.69736e12i −0.195306 + 0.471510i −0.990946 0.134259i \(-0.957134\pi\)
0.795640 + 0.605769i \(0.207134\pi\)
\(618\) 1.10003e12 4.55646e11i 0.303358 0.125655i
\(619\) −6.90852e11 1.66786e12i −0.189137 0.456618i 0.800657 0.599123i \(-0.204484\pi\)
−0.989794 + 0.142506i \(0.954484\pi\)
\(620\) −1.32053e12 1.32053e12i −0.358910 0.358910i
\(621\) 3.43197e12 + 3.43197e12i 0.926042 + 0.926042i
\(622\) −2.09821e11 5.06552e11i −0.0562072 0.135696i
\(623\) −2.43363e11 + 1.00804e11i −0.0647231 + 0.0268092i
\(624\) 4.95697e11 1.19672e12i 0.130884 0.315981i
\(625\) 4.76314e12i 1.24863i
\(626\) −1.68284e12 6.97057e11i −0.437985 0.181419i
\(627\) 1.69677e12 1.69677e12i 0.438448 0.438448i
\(628\) 3.29082e11 0.0844279
\(629\) −2.39520e12 + 9.98222e10i −0.610117 + 0.0254272i
\(630\) −9.14112e11 −0.231189
\(631\) 1.54677e12 1.54677e12i 0.388412 0.388412i −0.485709 0.874121i \(-0.661438\pi\)
0.874121 + 0.485709i \(0.161438\pi\)
\(632\) 5.16818e12 + 2.14073e12i 1.28858 + 0.533747i
\(633\) 2.92463e12i 0.724027i
\(634\) 1.69116e11 4.08283e11i 0.0415704 0.100360i
\(635\) 4.81389e12 1.99398e12i 1.17494 0.486675i
\(636\) 9.77333e10 + 2.35949e11i 0.0236857 + 0.0571822i
\(637\) 9.41449e11 + 9.41449e11i 0.226553 + 0.226553i
\(638\) 5.49507e12 + 5.49507e12i 1.31305 + 1.31305i
\(639\) −4.33150e11 1.04572e12i −0.102774 0.248119i
\(640\) 1.16946e12 4.84408e11i 0.275535 0.114130i
\(641\) 2.27266e12 5.48668e12i 0.531707 1.28365i −0.398685 0.917088i \(-0.630533\pi\)
0.930392 0.366567i \(-0.119467\pi\)
\(642\) 1.11608e12i 0.259292i
\(643\) 2.59103e12 + 1.07324e12i 0.597754 + 0.247598i 0.660983 0.750401i \(-0.270140\pi\)
−0.0632283 + 0.997999i \(0.520140\pi\)
\(644\) 1.52702e12 1.52702e12i 0.349830 0.349830i
\(645\) −5.66367e12 −1.28848
\(646\) 8.19104e11 + 1.76570e12i 0.185052 + 0.398906i
\(647\) −5.00047e12 −1.12187 −0.560934 0.827861i \(-0.689558\pi\)
−0.560934 + 0.827861i \(0.689558\pi\)
\(648\) 2.68081e12 2.68081e12i 0.597280 0.597280i
\(649\) 5.48429e12 + 2.27167e12i 1.21344 + 0.502625i
\(650\) 1.36522e12i 0.299981i
\(651\) 2.34767e12 5.66778e12i 0.512298 1.23680i
\(652\) 1.49400e12 6.18836e11i 0.323770 0.134110i
\(653\) −5.96112e11 1.43914e12i −0.128298 0.309738i 0.846658 0.532137i \(-0.178611\pi\)
−0.974956 + 0.222400i \(0.928611\pi\)
\(654\) 2.47591e12 + 2.47591e12i 0.529218 + 0.529218i
\(655\) 4.99755e12 + 4.99755e12i 1.06089 + 1.06089i
\(656\) −3.66871e11 8.85705e11i −0.0773475 0.186733i
\(657\) 2.47960e11 1.02709e11i 0.0519204 0.0215061i
\(658\) 1.39704e12 3.37276e12i 0.290532 0.701406i
\(659\) 5.07071e12i 1.04733i 0.851924 + 0.523666i \(0.175436\pi\)
−0.851924 + 0.523666i \(0.824564\pi\)
\(660\) 2.14503e12 + 8.88501e11i 0.440034 + 0.182268i
\(661\) −1.99187e12 + 1.99187e12i −0.405840 + 0.405840i −0.880285 0.474445i \(-0.842649\pi\)
0.474445 + 0.880285i \(0.342649\pi\)
\(662\) −4.09803e12 −0.829304
\(663\) 1.27718e11 + 3.06454e12i 0.0256709 + 0.615963i
\(664\) −3.81104e12 −0.760830
\(665\) 2.88603e12 2.88603e12i 0.572273 0.572273i
\(666\) −4.40841e11 1.82602e11i −0.0868256 0.0359643i
\(667\) 1.11339e13i 2.17811i
\(668\) −5.14588e11 + 1.24233e12i −0.0999921 + 0.241402i
\(669\) 3.35321e12 1.38894e12i 0.647207 0.268082i
\(670\) 7.15939e11 + 1.72843e12i 0.137259 + 0.331372i
\(671\) −6.07546e12 6.07546e12i −1.15698 1.15698i
\(672\) −2.59428e12 2.59428e12i −0.490745 0.490745i
\(673\) 1.95888e12 + 4.72917e12i 0.368079 + 0.888621i 0.994065 + 0.108787i \(0.0346967\pi\)
−0.625986 + 0.779834i \(0.715303\pi\)
\(674\) −3.63859e12 + 1.50715e12i −0.679147 + 0.281312i
\(675\) −1.18671e12 + 2.86498e12i −0.220028 + 0.531196i
\(676\) 9.63489e11i 0.177454i
\(677\) −7.30922e12 3.02758e12i −1.33728 0.553919i −0.404556 0.914513i \(-0.632574\pi\)
−0.932723 + 0.360594i \(0.882574\pi\)
\(678\) 4.78910e12 4.78910e12i 0.870404 0.870404i
\(679\) −1.81195e12 −0.327139
\(680\) −5.09499e12 + 5.53814e12i −0.913805 + 0.993284i
\(681\) 5.23330e12 0.932425
\(682\) −5.10970e12 + 5.10970e12i −0.904411 + 0.904411i
\(683\) −9.87608e12 4.09081e12i −1.73657 0.719309i −0.999032 0.0439999i \(-0.985990\pi\)
−0.737535 0.675309i \(-0.764010\pi\)
\(684\) 1.94124e11i 0.0339098i
\(685\) −3.75316e11 + 9.06093e11i −0.0651313 + 0.157241i
\(686\) 2.81872e12 1.16755e12i 0.485952 0.201288i
\(687\) 3.13706e12 + 7.57354e12i 0.537302 + 1.29716i
\(688\) −2.65985e12 2.65985e12i −0.452594 0.452594i
\(689\) −5.89250e11 5.89250e11i −0.0996123 0.0996123i
\(690\) 2.54055e12 + 6.13342e12i 0.426684 + 1.03011i
\(691\) 5.92270e12 2.45326e12i 0.988254 0.409348i 0.170777 0.985310i \(-0.445372\pi\)
0.817477 + 0.575961i \(0.195372\pi\)
\(692\) 1.16783e12 2.81940e12i 0.193599 0.467390i
\(693\) 1.77229e12i 0.291901i
\(694\) −3.90832e12 1.61888e12i −0.639547 0.264909i
\(695\) −8.26874e12 + 8.26874e12i −1.34434 + 1.34434i
\(696\) −1.08105e13 −1.74625
\(697\) 1.67063e12 + 1.53695e12i 0.268123 + 0.246668i
\(698\) 8.74149e12 1.39391
\(699\) 3.17311e12 3.17311e12i 0.502733 0.502733i
\(700\) 1.27474e12 + 5.28016e11i 0.200670 + 0.0831201i
\(701\) 8.91711e12i 1.39474i 0.716712 + 0.697369i \(0.245646\pi\)
−0.716712 + 0.697369i \(0.754354\pi\)
\(702\) −1.47268e12 + 3.55537e12i −0.228872 + 0.552545i
\(703\) 1.96833e12 8.15309e11i 0.303948 0.125899i
\(704\) 3.42164e12 + 8.26057e12i 0.524997 + 1.26746i
\(705\) −3.97624e12 3.97624e12i −0.606208 0.606208i
\(706\) 2.99544e12 + 2.99544e12i 0.453775 + 0.453775i
\(707\) −5.52024e12 1.33270e13i −0.830942 2.00607i
\(708\) −1.90932e12 + 7.90867e11i −0.285581 + 0.118292i
\(709\) 4.39729e12 1.06160e13i 0.653547 1.57780i −0.154046 0.988064i \(-0.549230\pi\)
0.807594 0.589739i \(-0.200770\pi\)
\(710\) 9.75903e12i 1.44127i
\(711\) −1.52080e12 6.29936e11i −0.223182 0.0924450i
\(712\) −3.05209e11 + 3.05209e11i −0.0445079 + 0.0445079i
\(713\) 1.03531e13 1.50026
\(714\) −5.80936e12 2.12748e12i −0.836540 0.306354i
\(715\) −7.57582e12 −1.08406
\(716\) −2.43402e12 + 2.43402e12i −0.346111 + 0.346111i
\(717\) −9.34952e11 3.87270e11i −0.132115 0.0547240i
\(718\) 2.53123e12i 0.355445i
\(719\) −1.86059e12 + 4.49186e12i −0.259639 + 0.626825i −0.998915 0.0465784i \(-0.985168\pi\)
0.739275 + 0.673403i \(0.235168\pi\)
\(720\) −8.63986e11 + 3.57875e11i −0.119815 + 0.0496289i
\(721\) 1.50260e12 + 3.62759e12i 0.207078 + 0.499930i
\(722\) 2.99091e12 + 2.99091e12i 0.409624 + 0.409624i
\(723\) −3.74940e12 3.74940e12i −0.510317 0.510317i
\(724\) 8.76232e11 + 2.11541e12i 0.118521 + 0.286135i
\(725\) 6.57219e12 2.72229e12i 0.883465 0.365943i
\(726\) 1.33187e12 3.21542e12i 0.177929 0.429559i
\(727\) 6.42996e12i 0.853697i 0.904323 + 0.426848i \(0.140376\pi\)
−0.904323 + 0.426848i \(0.859624\pi\)
\(728\) 6.32101e12 + 2.61825e12i 0.834056 + 0.345478i
\(729\) −5.98926e12 + 5.98926e12i −0.785416 + 0.785416i
\(730\) 2.31406e12 0.301594
\(731\) 8.36392e12 + 3.06300e12i 1.08338 + 0.396752i
\(732\) 2.99125e12 0.385081
\(733\) −2.61678e12 + 2.61678e12i −0.334811 + 0.334811i −0.854410 0.519599i \(-0.826081\pi\)
0.519599 + 0.854410i \(0.326081\pi\)
\(734\) −4.65285e12 1.92727e12i −0.591680 0.245082i
\(735\) 4.13660e12i 0.522818i
\(736\) 2.36943e12 5.72030e12i 0.297641 0.718569i
\(737\) −3.35111e12 + 1.38807e12i −0.418393 + 0.173304i
\(738\) 1.72913e11 + 4.17449e11i 0.0214573 + 0.0518024i
\(739\) 1.28421e12 + 1.28421e12i 0.158393 + 0.158393i 0.781854 0.623462i \(-0.214274\pi\)
−0.623462 + 0.781854i \(0.714274\pi\)
\(740\) 1.45763e12 + 1.45763e12i 0.178692 + 0.178692i
\(741\) −1.04315e12 2.51839e12i −0.127106 0.306860i
\(742\) 1.55290e12 6.43233e11i 0.188073 0.0779024i
\(743\) −3.91916e12 + 9.46169e12i −0.471784 + 1.13899i 0.491590 + 0.870827i \(0.336416\pi\)
−0.963374 + 0.268161i \(0.913584\pi\)
\(744\) 1.00524e13i 1.20279i
\(745\) 6.84152e11 + 2.83385e11i 0.0813672 + 0.0337034i
\(746\) 2.10375e12 2.10375e12i 0.248696 0.248696i
\(747\) 1.12145e12 0.131776
\(748\) −2.68720e12 2.47217e12i −0.313865 0.288750i
\(749\) 3.68054e12 0.427310
\(750\) 2.58579e12 2.58579e12i 0.298413 0.298413i
\(751\) −9.44291e12 3.91138e12i −1.08324 0.448694i −0.231597 0.972812i \(-0.574395\pi\)
−0.851646 + 0.524118i \(0.824395\pi\)
\(752\) 3.73476e12i 0.425875i
\(753\) 2.61799e12 6.32039e12i 0.296750 0.716418i
\(754\) 8.15593e12 3.37830e12i 0.918972 0.380651i
\(755\) −5.81162e11 1.40305e12i −0.0650932 0.157149i
\(756\) 2.75016e12 + 2.75016e12i 0.306203 + 0.306203i
\(757\) 6.50006e12 + 6.50006e12i 0.719426 + 0.719426i 0.968488 0.249062i \(-0.0801222\pi\)
−0.249062 + 0.968488i \(0.580122\pi\)
\(758\) −4.41887e11 1.06681e12i −0.0486183 0.117375i
\(759\) −1.18916e13 + 4.92565e12i −1.30062 + 0.538736i
\(760\)