Properties

Label 17.10.d.a.8.4
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 8.4
Character \(\chi\) \(=\) 17.8
Dual form 17.10.d.a.15.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-14.5474 + 14.5474i) q^{2} +(32.3594 - 78.1225i) q^{3} +88.7454i q^{4} +(31.3399 + 12.9814i) q^{5} +(665.735 + 1607.23i) q^{6} +(-4774.06 + 1977.48i) q^{7} +(-8739.29 - 8739.29i) q^{8} +(8861.98 + 8861.98i) q^{9} +O(q^{10})\) \(q+(-14.5474 + 14.5474i) q^{2} +(32.3594 - 78.1225i) q^{3} +88.7454i q^{4} +(31.3399 + 12.9814i) q^{5} +(665.735 + 1607.23i) q^{6} +(-4774.06 + 1977.48i) q^{7} +(-8739.29 - 8739.29i) q^{8} +(8861.98 + 8861.98i) q^{9} +(-644.761 + 267.069i) q^{10} +(-25659.9 - 61948.5i) q^{11} +(6933.01 + 2871.75i) q^{12} -194911. i q^{13} +(40683.0 - 98217.5i) q^{14} +(2028.28 - 2028.28i) q^{15} +208831. q^{16} +(-320627. - 125643. i) q^{17} -257838. q^{18} +(-328794. + 328794. i) q^{19} +(-1152.04 + 2781.27i) q^{20} +436952. i q^{21} +(1.27448e6 + 527906. i) q^{22} +(144382. + 348570. i) q^{23} +(-965534. + 399937. i) q^{24} +(-1.38025e6 - 1.38025e6i) q^{25} +(2.83545e6 + 2.83545e6i) q^{26} +(2.51678e6 - 1.04248e6i) q^{27} +(-175492. - 423676. i) q^{28} +(-941296. - 389898. i) q^{29} +59012.5i q^{30} +(-2.32857e6 + 5.62167e6i) q^{31} +(1.43657e6 - 1.43657e6i) q^{32} -5.66992e6 q^{33} +(6.49208e6 - 2.83651e6i) q^{34} -175289. q^{35} +(-786460. + 786460. i) q^{36} +(-1.67838e6 + 4.05197e6i) q^{37} -9.56621e6i q^{38} +(-1.52270e7 - 6.30721e6i) q^{39} +(-160440. - 387337. i) q^{40} +(1.46439e7 - 6.06570e6i) q^{41} +(-6.35652e6 - 6.35652e6i) q^{42} +(-3.45275e6 - 3.45275e6i) q^{43} +(5.49765e6 - 2.27720e6i) q^{44} +(162693. + 392775. i) q^{45} +(-7.17118e6 - 2.97040e6i) q^{46} -1.42598e7i q^{47} +(6.75764e6 - 1.63144e7i) q^{48} +(-9.65308e6 + 9.65308e6i) q^{49} +4.01583e7 q^{50} +(-2.01909e7 + 2.09825e7i) q^{51} +1.72975e7 q^{52} +(-2.43777e7 + 2.43777e7i) q^{53} +(-2.14472e7 + 5.17780e7i) q^{54} -2.27456e6i q^{55} +(5.90037e7 + 2.44401e7i) q^{56} +(1.50466e7 + 3.63258e7i) q^{57} +(1.93654e7 - 8.02143e6i) q^{58} +(7.93497e7 + 7.93497e7i) q^{59} +(180001. + 180001. i) q^{60} +(-1.65528e8 + 6.85638e7i) q^{61} +(-4.79061e7 - 1.15655e8i) q^{62} +(-5.98321e7 - 2.47832e7i) q^{63} +1.48718e8i q^{64} +(2.53022e6 - 6.10850e6i) q^{65} +(8.24826e7 - 8.24826e7i) q^{66} +1.06450e8 q^{67} +(1.11502e7 - 2.84542e7i) q^{68} +3.19033e7 q^{69} +(2.55000e6 - 2.55000e6i) q^{70} +(1.47032e8 - 3.54968e8i) q^{71} -1.54895e8i q^{72} +(-3.98621e8 - 1.65114e8i) q^{73} +(-3.45296e7 - 8.33619e7i) q^{74} +(-1.52493e8 + 6.31647e7i) q^{75} +(-2.91789e7 - 2.91789e7i) q^{76} +(2.45004e8 + 2.45004e8i) q^{77} +(3.13266e8 - 1.29759e8i) q^{78} +(-8.17294e7 - 1.97312e8i) q^{79} +(6.54473e6 + 2.71092e6i) q^{80} +1.63309e7i q^{81} +(-1.24791e8 + 3.01271e8i) q^{82} +(-2.68120e8 + 2.68120e8i) q^{83} -3.87775e7 q^{84} +(-8.41740e6 - 8.09984e6i) q^{85} +1.00457e8 q^{86} +(-6.09196e7 + 6.09196e7i) q^{87} +(-3.17137e8 + 7.65636e8i) q^{88} -9.12630e8i q^{89} +(-8.08062e6 - 3.34710e6i) q^{90} +(3.85433e8 + 9.30518e8i) q^{91} +(-3.09340e7 + 1.28133e7i) q^{92} +(3.63828e8 + 3.63828e8i) q^{93} +(2.07443e8 + 2.07443e8i) q^{94} +(-1.45726e7 + 6.03616e6i) q^{95} +(-6.57420e7 - 1.58715e8i) q^{96} +(1.34720e8 + 5.58030e7i) q^{97} -2.80855e8i q^{98} +(3.21589e8 - 7.76385e8i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −14.5474 + 14.5474i −0.642911 + 0.642911i −0.951270 0.308359i \(-0.900220\pi\)
0.308359 + 0.951270i \(0.400220\pi\)
\(3\) 32.3594 78.1225i 0.230651 0.556840i −0.765603 0.643313i \(-0.777559\pi\)
0.996254 + 0.0864725i \(0.0275595\pi\)
\(4\) 88.7454i 0.173331i
\(5\) 31.3399 + 12.9814i 0.0224250 + 0.00928875i 0.393868 0.919167i \(-0.371137\pi\)
−0.371443 + 0.928456i \(0.621137\pi\)
\(6\) 665.735 + 1607.23i 0.209711 + 0.506287i
\(7\) −4774.06 + 1977.48i −0.751531 + 0.311294i −0.725366 0.688363i \(-0.758329\pi\)
−0.0261648 + 0.999658i \(0.508329\pi\)
\(8\) −8739.29 8739.29i −0.754347 0.754347i
\(9\) 8861.98 + 8861.98i 0.450235 + 0.450235i
\(10\) −644.761 + 267.069i −0.0203891 + 0.00844545i
\(11\) −25659.9 61948.5i −0.528431 1.27575i −0.932551 0.361039i \(-0.882422\pi\)
0.404120 0.914706i \(-0.367578\pi\)
\(12\) 6933.01 + 2871.75i 0.0965176 + 0.0399789i
\(13\) 194911.i 1.89274i −0.323081 0.946371i \(-0.604719\pi\)
0.323081 0.946371i \(-0.395281\pi\)
\(14\) 40683.0 98217.5i 0.283033 0.683302i
\(15\) 2028.28 2028.28i 0.0103447 0.0103447i
\(16\) 208831. 0.796626
\(17\) −320627. 125643.i −0.931065 0.364854i
\(18\) −257838. −0.578923
\(19\) −328794. + 328794.i −0.578806 + 0.578806i −0.934574 0.355769i \(-0.884219\pi\)
0.355769 + 0.934574i \(0.384219\pi\)
\(20\) −1152.04 + 2781.27i −0.00161003 + 0.00388695i
\(21\) 436952.i 0.490283i
\(22\) 1.27448e6 + 527906.i 1.15992 + 0.480457i
\(23\) 144382. + 348570.i 0.107582 + 0.259725i 0.968498 0.249021i \(-0.0801089\pi\)
−0.860916 + 0.508747i \(0.830109\pi\)
\(24\) −965534. + 399937.i −0.594042 + 0.246060i
\(25\) −1.38025e6 1.38025e6i −0.706690 0.706690i
\(26\) 2.83545e6 + 2.83545e6i 1.21687 + 1.21687i
\(27\) 2.51678e6 1.04248e6i 0.911397 0.377513i
\(28\) −175492. 423676.i −0.0539569 0.130263i
\(29\) −941296. 389898.i −0.247136 0.102367i 0.255677 0.966762i \(-0.417702\pi\)
−0.502813 + 0.864395i \(0.667702\pi\)
\(30\) 59012.5i 0.0133014i
\(31\) −2.32857e6 + 5.62167e6i −0.452858 + 1.09330i 0.518373 + 0.855155i \(0.326538\pi\)
−0.971231 + 0.238141i \(0.923462\pi\)
\(32\) 1.43657e6 1.43657e6i 0.242188 0.242188i
\(33\) −5.66992e6 −0.832269
\(34\) 6.49208e6 2.83651e6i 0.833160 0.364023i
\(35\) −175289. −0.0197446
\(36\) −786460. + 786460.i −0.0780397 + 0.0780397i
\(37\) −1.67838e6 + 4.05197e6i −0.147226 + 0.355434i −0.980238 0.197820i \(-0.936614\pi\)
0.833013 + 0.553254i \(0.186614\pi\)
\(38\) 9.56621e6i 0.744241i
\(39\) −1.52270e7 6.30721e6i −1.05396 0.436563i
\(40\) −160440. 387337.i −0.00990931 0.0239232i
\(41\) 1.46439e7 6.06570e6i 0.809336 0.335238i 0.0606471 0.998159i \(-0.480684\pi\)
0.748689 + 0.662921i \(0.230684\pi\)
\(42\) −6.35652e6 6.35652e6i −0.315208 0.315208i
\(43\) −3.45275e6 3.45275e6i −0.154013 0.154013i 0.625895 0.779908i \(-0.284734\pi\)
−0.779908 + 0.625895i \(0.784734\pi\)
\(44\) 5.49765e6 2.27720e6i 0.221126 0.0915934i
\(45\) 162693. + 392775.i 0.00591441 + 0.0142787i
\(46\) −7.17118e6 2.97040e6i −0.236146 0.0978148i
\(47\) 1.42598e7i 0.426258i −0.977024 0.213129i \(-0.931634\pi\)
0.977024 0.213129i \(-0.0683655\pi\)
\(48\) 6.75764e6 1.63144e7i 0.183742 0.443593i
\(49\) −9.65308e6 + 9.65308e6i −0.239212 + 0.239212i
\(50\) 4.01583e7 0.908678
\(51\) −2.01909e7 + 2.09825e7i −0.417916 + 0.434301i
\(52\) 1.72975e7 0.328071
\(53\) −2.43777e7 + 2.43777e7i −0.424376 + 0.424376i −0.886707 0.462331i \(-0.847013\pi\)
0.462331 + 0.886707i \(0.347013\pi\)
\(54\) −2.14472e7 + 5.17780e7i −0.343240 + 0.828654i
\(55\) 2.27456e6i 0.0335171i
\(56\) 5.90037e7 + 2.44401e7i 0.801739 + 0.332091i
\(57\) 1.50466e7 + 3.63258e7i 0.188800 + 0.455804i
\(58\) 1.93654e7 8.02143e6i 0.224699 0.0930734i
\(59\) 7.93497e7 + 7.93497e7i 0.852533 + 0.852533i 0.990445 0.137912i \(-0.0440390\pi\)
−0.137912 + 0.990445i \(0.544039\pi\)
\(60\) 180001. + 180001.i 0.00179305 + 0.00179305i
\(61\) −1.65528e8 + 6.85638e7i −1.53069 + 0.634031i −0.979697 0.200482i \(-0.935749\pi\)
−0.550988 + 0.834513i \(0.685749\pi\)
\(62\) −4.79061e7 1.15655e8i −0.411745 0.994039i
\(63\) −5.98321e7 2.47832e7i −0.478521 0.198210i
\(64\) 1.48718e8i 1.10804i
\(65\) 2.53022e6 6.10850e6i 0.0175812 0.0424448i
\(66\) 8.24826e7 8.24826e7i 0.535075 0.535075i
\(67\) 1.06450e8 0.645371 0.322686 0.946506i \(-0.395414\pi\)
0.322686 + 0.946506i \(0.395414\pi\)
\(68\) 1.11502e7 2.84542e7i 0.0632404 0.161382i
\(69\) 3.19033e7 0.169439
\(70\) 2.55000e6 2.55000e6i 0.0126940 0.0126940i
\(71\) 1.47032e8 3.54968e8i 0.686674 1.65778i −0.0647032 0.997905i \(-0.520610\pi\)
0.751377 0.659873i \(-0.229390\pi\)
\(72\) 1.54895e8i 0.679268i
\(73\) −3.98621e8 1.65114e8i −1.64289 0.680506i −0.646302 0.763082i \(-0.723685\pi\)
−0.996585 + 0.0825762i \(0.973685\pi\)
\(74\) −3.45296e7 8.33619e7i −0.133859 0.323165i
\(75\) −1.52493e8 + 6.31647e7i −0.556512 + 0.230515i
\(76\) −2.91789e7 2.91789e7i −0.100325 0.100325i
\(77\) 2.45004e8 + 2.45004e8i 0.794264 + 0.794264i
\(78\) 3.13266e8 1.29759e8i 0.958270 0.396929i
\(79\) −8.17294e7 1.97312e8i −0.236078 0.569944i 0.760792 0.648996i \(-0.224811\pi\)
−0.996871 + 0.0790519i \(0.974811\pi\)
\(80\) 6.54473e6 + 2.71092e6i 0.0178643 + 0.00739965i
\(81\) 1.63309e7i 0.0421529i
\(82\) −1.24791e8 + 3.01271e8i −0.304803 + 0.735859i
\(83\) −2.68120e8 + 2.68120e8i −0.620122 + 0.620122i −0.945563 0.325440i \(-0.894487\pi\)
0.325440 + 0.945563i \(0.394487\pi\)
\(84\) −3.87775e7 −0.0849811
\(85\) −8.41740e6 8.09984e6i −0.0174901 0.0168303i
\(86\) 1.00457e8 0.198033
\(87\) −6.09196e7 + 6.09196e7i −0.114004 + 0.114004i
\(88\) −3.17137e8 + 7.65636e8i −0.563734 + 1.36098i
\(89\) 9.12630e8i 1.54184i −0.636931 0.770921i \(-0.719796\pi\)
0.636931 0.770921i \(-0.280204\pi\)
\(90\) −8.08062e6 3.34710e6i −0.0129824 0.00537747i
\(91\) 3.85433e8 + 9.30518e8i 0.589200 + 1.42245i
\(92\) −3.09340e7 + 1.28133e7i −0.0450184 + 0.0186472i
\(93\) 3.63828e8 + 3.63828e8i 0.504339 + 0.504339i
\(94\) 2.07443e8 + 2.07443e8i 0.274046 + 0.274046i
\(95\) −1.45726e7 + 6.03616e6i −0.0183561 + 0.00760335i
\(96\) −6.57420e7 1.58715e8i −0.0789992 0.190721i
\(97\) 1.34720e8 + 5.58030e7i 0.154511 + 0.0640007i 0.458599 0.888643i \(-0.348352\pi\)
−0.304087 + 0.952644i \(0.598352\pi\)
\(98\) 2.80855e8i 0.307584i
\(99\) 3.21589e8 7.76385e8i 0.336467 0.812304i
\(100\) 1.22491e8 1.22491e8i 0.122491 0.122491i
\(101\) 8.74690e8 0.836389 0.418194 0.908358i \(-0.362663\pi\)
0.418194 + 0.908358i \(0.362663\pi\)
\(102\) −1.15156e7 5.98965e8i −0.0105338 0.547900i
\(103\) 8.45970e8 0.740606 0.370303 0.928911i \(-0.379254\pi\)
0.370303 + 0.928911i \(0.379254\pi\)
\(104\) −1.70339e9 + 1.70339e9i −1.42779 + 1.42779i
\(105\) −5.67226e6 + 1.36940e7i −0.00455411 + 0.0109946i
\(106\) 7.09264e8i 0.545672i
\(107\) −3.18712e8 1.32015e8i −0.235056 0.0973634i 0.262046 0.965055i \(-0.415603\pi\)
−0.497102 + 0.867692i \(0.665603\pi\)
\(108\) 9.25155e7 + 2.23352e8i 0.0654346 + 0.157973i
\(109\) −9.38620e8 + 3.88789e8i −0.636899 + 0.263812i −0.677681 0.735356i \(-0.737015\pi\)
0.0407822 + 0.999168i \(0.487015\pi\)
\(110\) 3.30890e7 + 3.30890e7i 0.0215485 + 0.0215485i
\(111\) 2.62239e8 + 2.62239e8i 0.163962 + 0.163962i
\(112\) −9.96970e8 + 4.12959e8i −0.598689 + 0.247985i
\(113\) −4.33607e8 1.04682e9i −0.250175 0.603975i 0.748043 0.663650i \(-0.230994\pi\)
−0.998218 + 0.0596752i \(0.980994\pi\)
\(114\) −7.47336e8 3.09557e8i −0.414423 0.171660i
\(115\) 1.27984e7i 0.00682365i
\(116\) 3.46016e7 8.35357e7i 0.0177433 0.0428362i
\(117\) 1.72730e9 1.72730e9i 0.852180 0.852180i
\(118\) −2.30867e9 −1.09621
\(119\) 1.77915e9 3.42057e7i 0.813301 0.0156364i
\(120\) −3.54515e7 −0.0156070
\(121\) −1.51187e9 + 1.51187e9i −0.641180 + 0.641180i
\(122\) 1.41057e9 3.40542e9i 0.576469 1.39172i
\(123\) 1.34030e9i 0.527994i
\(124\) −4.98897e8 2.06650e8i −0.189502 0.0784942i
\(125\) −5.06937e7 1.22385e8i −0.0185720 0.0448368i
\(126\) 1.23093e9 5.09870e8i 0.435078 0.180215i
\(127\) 3.19930e9 + 3.19930e9i 1.09129 + 1.09129i 0.995391 + 0.0958949i \(0.0305713\pi\)
0.0958949 + 0.995391i \(0.469429\pi\)
\(128\) −1.42794e9 1.42794e9i −0.470181 0.470181i
\(129\) −3.81466e8 + 1.58008e8i −0.121284 + 0.0502374i
\(130\) 5.20547e7 + 1.25671e8i 0.0159851 + 0.0385914i
\(131\) −1.32472e9 5.48715e8i −0.393008 0.162789i 0.177423 0.984135i \(-0.443224\pi\)
−0.570431 + 0.821345i \(0.693224\pi\)
\(132\) 5.03179e8i 0.144258i
\(133\) 9.19499e8 2.21987e9i 0.254811 0.615169i
\(134\) −1.54858e9 + 1.54858e9i −0.414916 + 0.414916i
\(135\) 9.24084e7 0.0239447
\(136\) 1.70402e9 + 3.90009e9i 0.427120 + 0.977573i
\(137\) 3.33397e9 0.808573 0.404286 0.914632i \(-0.367520\pi\)
0.404286 + 0.914632i \(0.367520\pi\)
\(138\) −4.64110e8 + 4.64110e8i −0.108935 + 0.108935i
\(139\) −7.70375e8 + 1.85985e9i −0.175039 + 0.422582i −0.986914 0.161250i \(-0.948447\pi\)
0.811874 + 0.583832i \(0.198447\pi\)
\(140\) 1.55561e7i 0.00342235i
\(141\) −1.11401e9 4.61439e8i −0.237358 0.0983168i
\(142\) 3.02492e9 + 7.30280e9i 0.624333 + 1.50727i
\(143\) −1.20745e10 + 5.00140e9i −2.41466 + 1.00018i
\(144\) 1.85065e9 + 1.85065e9i 0.358669 + 0.358669i
\(145\) −2.44387e7 2.44387e7i −0.00459116 0.00459116i
\(146\) 8.20090e9 3.39692e9i 1.49373 0.618725i
\(147\) 4.41755e8 + 1.06649e9i 0.0780285 + 0.188378i
\(148\) −3.59594e8 1.48949e8i −0.0616076 0.0255187i
\(149\) 1.72052e9i 0.285971i 0.989725 + 0.142985i \(0.0456702\pi\)
−0.989725 + 0.142985i \(0.954330\pi\)
\(150\) 1.29950e9 3.13727e9i 0.209587 0.505988i
\(151\) −3.60005e9 + 3.60005e9i −0.563524 + 0.563524i −0.930307 0.366783i \(-0.880459\pi\)
0.366783 + 0.930307i \(0.380459\pi\)
\(152\) 5.74685e9 0.873241
\(153\) −1.72794e9 3.95484e9i −0.254928 0.583468i
\(154\) −7.12835e9 −1.02128
\(155\) −1.45954e8 + 1.45954e8i −0.0203107 + 0.0203107i
\(156\) 5.59736e8 1.35132e9i 0.0756697 0.182683i
\(157\) 1.10391e10i 1.45006i −0.688718 0.725029i \(-0.741826\pi\)
0.688718 0.725029i \(-0.258174\pi\)
\(158\) 4.05933e9 + 1.68143e9i 0.518201 + 0.214646i
\(159\) 1.11560e9 + 2.69329e9i 0.138427 + 0.334192i
\(160\) 6.36708e7 2.63733e7i 0.00768069 0.00318145i
\(161\) −1.37858e9 1.37858e9i −0.161702 0.161702i
\(162\) −2.37572e8 2.37572e8i −0.0271005 0.0271005i
\(163\) 2.52429e9 1.04559e9i 0.280088 0.116016i −0.238217 0.971212i \(-0.576563\pi\)
0.518305 + 0.855196i \(0.326563\pi\)
\(164\) 5.38302e8 + 1.29958e9i 0.0581071 + 0.140283i
\(165\) −1.77695e8 7.36036e7i −0.0186637 0.00773074i
\(166\) 7.80090e9i 0.797367i
\(167\) 4.54146e9 1.09640e10i 0.451826 1.09080i −0.519802 0.854287i \(-0.673994\pi\)
0.971627 0.236517i \(-0.0760058\pi\)
\(168\) 3.81865e9 3.81865e9i 0.369844 0.369844i
\(169\) −2.73858e10 −2.58247
\(170\) 2.40283e8 4.61965e6i 0.0220650 0.000424218i
\(171\) −5.82753e9 −0.521198
\(172\) 3.06415e8 3.06415e8i 0.0266952 0.0266952i
\(173\) 1.79430e9 4.33183e9i 0.152296 0.367674i −0.829257 0.558868i \(-0.811236\pi\)
0.981552 + 0.191194i \(0.0612358\pi\)
\(174\) 1.77245e9i 0.146589i
\(175\) 9.31884e9 + 3.85999e9i 0.751088 + 0.311111i
\(176\) −5.35858e9 1.29368e10i −0.420962 1.01629i
\(177\) 8.76671e9 3.63129e9i 0.671362 0.278087i
\(178\) 1.32764e10 + 1.32764e10i 0.991267 + 0.991267i
\(179\) 1.12383e10 + 1.12383e10i 0.818203 + 0.818203i 0.985847 0.167645i \(-0.0536161\pi\)
−0.167645 + 0.985847i \(0.553616\pi\)
\(180\) −3.48570e7 + 1.44382e7i −0.00247493 + 0.00102515i
\(181\) 1.78454e8 + 4.30825e8i 0.0123587 + 0.0298365i 0.929938 0.367715i \(-0.119860\pi\)
−0.917580 + 0.397552i \(0.869860\pi\)
\(182\) −1.91437e10 7.92957e9i −1.29331 0.535708i
\(183\) 1.51501e10i 0.998587i
\(184\) 1.78445e9 4.30805e9i 0.114769 0.277077i
\(185\) −1.05201e8 + 1.05201e8i −0.00660307 + 0.00660307i
\(186\) −1.05855e10 −0.648490
\(187\) 4.43855e8 + 2.30864e10i 0.0265432 + 1.38060i
\(188\) 1.26549e9 0.0738837
\(189\) −9.95375e9 + 9.95375e9i −0.567425 + 0.567425i
\(190\) 1.24183e8 2.99804e8i 0.00691307 0.0166896i
\(191\) 6.43277e9i 0.349742i 0.984591 + 0.174871i \(0.0559509\pi\)
−0.984591 + 0.174871i \(0.944049\pi\)
\(192\) 1.16182e10 + 4.81243e9i 0.616999 + 0.255569i
\(193\) −3.61203e9 8.72022e9i −0.187389 0.452397i 0.802066 0.597235i \(-0.203734\pi\)
−0.989455 + 0.144838i \(0.953734\pi\)
\(194\) −2.77162e9 + 1.14804e9i −0.140484 + 0.0581903i
\(195\) −3.95335e8 3.95335e8i −0.0195798 0.0195798i
\(196\) −8.56666e8 8.56666e8i −0.0414629 0.0414629i
\(197\) 3.07447e10 1.27349e10i 1.45436 0.602416i 0.491129 0.871087i \(-0.336584\pi\)
0.963232 + 0.268671i \(0.0865845\pi\)
\(198\) 6.61610e9 + 1.59727e10i 0.305921 + 0.738558i
\(199\) −1.06281e10 4.40229e9i −0.480414 0.198994i 0.129315 0.991604i \(-0.458722\pi\)
−0.609730 + 0.792609i \(0.708722\pi\)
\(200\) 2.41249e10i 1.06618i
\(201\) 3.44467e9 8.31616e9i 0.148855 0.359369i
\(202\) −1.27245e10 + 1.27245e10i −0.537723 + 0.537723i
\(203\) 5.26482e9 0.217596
\(204\) −1.86210e9 1.79185e9i −0.0752777 0.0724377i
\(205\) 5.37680e8 0.0212633
\(206\) −1.23067e10 + 1.23067e10i −0.476144 + 0.476144i
\(207\) −1.80951e9 + 4.36853e9i −0.0685005 + 0.165375i
\(208\) 4.07034e10i 1.50781i
\(209\) 2.88051e10 + 1.19315e10i 1.04427 + 0.432550i
\(210\) −1.16696e8 2.81730e8i −0.00414066 0.00999644i
\(211\) 3.66767e10 1.51920e10i 1.27385 0.527647i 0.359720 0.933060i \(-0.382872\pi\)
0.914134 + 0.405413i \(0.132872\pi\)
\(212\) −2.16341e9 2.16341e9i −0.0735574 0.0735574i
\(213\) −2.29731e10 2.29731e10i −0.764736 0.764736i
\(214\) 6.55691e9 2.71596e9i 0.213716 0.0885241i
\(215\) −6.33872e7 1.53030e8i −0.00202315 0.00488432i
\(216\) −3.11054e10 1.28843e10i −0.972286 0.402734i
\(217\) 3.14429e10i 0.962618i
\(218\) 7.99862e9 1.93104e10i 0.239862 0.579077i
\(219\) −2.57983e10 + 2.57983e10i −0.757866 + 0.757866i
\(220\) 2.01857e8 0.00580954
\(221\) −2.44892e10 + 6.24938e10i −0.690574 + 1.76227i
\(222\) −7.62980e9 −0.210826
\(223\) 3.38158e10 3.38158e10i 0.915689 0.915689i −0.0810235 0.996712i \(-0.525819\pi\)
0.996712 + 0.0810235i \(0.0258189\pi\)
\(224\) −4.01749e9 + 9.69908e9i −0.106620 + 0.257403i
\(225\) 2.44636e10i 0.636354i
\(226\) 2.15364e10 + 8.92066e9i 0.549142 + 0.227462i
\(227\) −1.36115e9 3.28611e9i −0.0340244 0.0821421i 0.905954 0.423376i \(-0.139155\pi\)
−0.939978 + 0.341234i \(0.889155\pi\)
\(228\) −3.22375e9 + 1.33532e9i −0.0790049 + 0.0327249i
\(229\) −1.64854e10 1.64854e10i −0.396131 0.396131i 0.480735 0.876866i \(-0.340370\pi\)
−0.876866 + 0.480735i \(0.840370\pi\)
\(230\) −1.86184e8 1.86184e8i −0.00438700 0.00438700i
\(231\) 2.70685e10 1.12122e10i 0.625476 0.259081i
\(232\) 4.81883e9 + 1.16337e10i 0.109206 + 0.263646i
\(233\) −6.63179e10 2.74698e10i −1.47411 0.610595i −0.506315 0.862349i \(-0.668993\pi\)
−0.967791 + 0.251754i \(0.918993\pi\)
\(234\) 5.02555e10i 1.09575i
\(235\) 1.85112e8 4.46901e8i 0.00395941 0.00955885i
\(236\) −7.04192e9 + 7.04192e9i −0.147770 + 0.147770i
\(237\) −1.80592e10 −0.371819
\(238\) −2.53844e10 + 2.63796e10i −0.512827 + 0.532933i
\(239\) −5.19129e10 −1.02916 −0.514582 0.857441i \(-0.672053\pi\)
−0.514582 + 0.857441i \(0.672053\pi\)
\(240\) 4.23568e8 4.23568e8i 0.00824085 0.00824085i
\(241\) 3.85817e10 9.31444e10i 0.736723 1.77861i 0.117977 0.993016i \(-0.462359\pi\)
0.618746 0.785591i \(-0.287641\pi\)
\(242\) 4.39875e10i 0.824443i
\(243\) 5.08135e10 + 2.10476e10i 0.934869 + 0.387235i
\(244\) −6.08472e9 1.46898e10i −0.109897 0.265315i
\(245\) −4.27837e8 + 1.77216e8i −0.00758632 + 0.00314236i
\(246\) 1.94979e10 + 1.94979e10i 0.339453 + 0.339453i
\(247\) 6.40856e10 + 6.40856e10i 1.09553 + 1.09553i
\(248\) 6.94795e10 2.87793e10i 1.16634 0.483113i
\(249\) 1.22700e10 + 2.96224e10i 0.202277 + 0.488341i
\(250\) 2.51786e9 + 1.04293e9i 0.0407662 + 0.0168859i
\(251\) 3.87316e10i 0.615933i 0.951397 + 0.307967i \(0.0996485\pi\)
−0.951397 + 0.307967i \(0.900351\pi\)
\(252\) 2.19940e9 5.30982e9i 0.0343559 0.0829425i
\(253\) 1.78886e10 1.78886e10i 0.274494 0.274494i
\(254\) −9.30832e10 −1.40320
\(255\) −9.05162e8 + 3.95482e8i −0.0134059 + 0.00585728i
\(256\) −3.45980e10 −0.503467
\(257\) −1.47987e10 + 1.47987e10i −0.211604 + 0.211604i −0.804949 0.593345i \(-0.797807\pi\)
0.593345 + 0.804949i \(0.297807\pi\)
\(258\) 3.25073e9 7.84796e9i 0.0456765 0.110273i
\(259\) 2.26633e10i 0.312950i
\(260\) 5.42101e8 + 2.24546e8i 0.00735699 + 0.00304736i
\(261\) −4.88649e9 1.17970e10i −0.0651800 0.157358i
\(262\) 2.72536e10 1.12888e10i 0.357329 0.148010i
\(263\) 1.01653e11 + 1.01653e11i 1.31015 + 1.31015i 0.921301 + 0.388850i \(0.127128\pi\)
0.388850 + 0.921301i \(0.372872\pi\)
\(264\) 4.95511e10 + 4.95511e10i 0.627820 + 0.627820i
\(265\) −1.08045e9 + 4.47537e8i −0.0134586 + 0.00557472i
\(266\) 1.89170e10 + 4.56697e10i 0.231678 + 0.559320i
\(267\) −7.12970e10 2.95322e10i −0.858559 0.355627i
\(268\) 9.44696e9i 0.111863i
\(269\) −1.07352e10 + 2.59170e10i −0.125004 + 0.301787i −0.973976 0.226652i \(-0.927222\pi\)
0.848972 + 0.528438i \(0.177222\pi\)
\(270\) −1.34430e9 + 1.34430e9i −0.0153943 + 0.0153943i
\(271\) −6.71035e10 −0.755759 −0.377880 0.925855i \(-0.623347\pi\)
−0.377880 + 0.925855i \(0.623347\pi\)
\(272\) −6.69567e10 2.62381e10i −0.741710 0.290652i
\(273\) 8.51668e10 0.927979
\(274\) −4.85006e10 + 4.85006e10i −0.519840 + 0.519840i
\(275\) −5.00875e10 + 1.20922e11i −0.528120 + 1.27499i
\(276\) 2.83127e9i 0.0293691i
\(277\) 8.47374e10 + 3.50994e10i 0.864801 + 0.358212i 0.770583 0.637339i \(-0.219965\pi\)
0.0942177 + 0.995552i \(0.469965\pi\)
\(278\) −1.58490e10 3.82630e10i −0.159148 0.384218i
\(279\) −7.04549e10 + 2.91834e10i −0.696133 + 0.288348i
\(280\) 1.53190e9 + 1.53190e9i 0.0148943 + 0.0148943i
\(281\) −9.54766e10 9.54766e10i −0.913521 0.913521i 0.0830266 0.996547i \(-0.473541\pi\)
−0.996547 + 0.0830266i \(0.973541\pi\)
\(282\) 2.29187e10 9.49325e9i 0.215809 0.0893910i
\(283\) −3.28190e10 7.92320e10i −0.304149 0.734280i −0.999872 0.0159707i \(-0.994916\pi\)
0.695724 0.718310i \(-0.255084\pi\)
\(284\) 3.15017e10 + 1.30484e10i 0.287344 + 0.119022i
\(285\) 1.33377e9i 0.0119751i
\(286\) 1.02895e11 2.48410e11i 0.909381 2.19544i
\(287\) −5.79160e10 + 5.79160e10i −0.503883 + 0.503883i
\(288\) 2.54618e10 0.218083
\(289\) 8.70155e10 + 8.05692e10i 0.733764 + 0.679405i
\(290\) 7.11041e8 0.00590342
\(291\) 8.71895e9 8.71895e9i 0.0712764 0.0712764i
\(292\) 1.46531e10 3.53758e10i 0.117953 0.284763i
\(293\) 1.58105e11i 1.25326i −0.779315 0.626632i \(-0.784433\pi\)
0.779315 0.626632i \(-0.215567\pi\)
\(294\) −2.19411e10 9.08829e9i −0.171275 0.0709446i
\(295\) 1.45674e9 + 3.51688e9i 0.0111991 + 0.0270370i
\(296\) 5.00792e10 2.07435e10i 0.379180 0.157061i
\(297\) −1.29161e11 1.29161e11i −0.963221 0.963221i
\(298\) −2.50291e10 2.50291e10i −0.183854 0.183854i
\(299\) 6.79401e10 2.81417e10i 0.491593 0.203625i
\(300\) −5.60558e9 1.35331e10i −0.0399553 0.0964607i
\(301\) 2.33114e10 + 9.65588e9i 0.163689 + 0.0678021i
\(302\) 1.04743e11i 0.724591i
\(303\) 2.83045e10 6.83330e10i 0.192914 0.465735i
\(304\) −6.86623e10 + 6.86623e10i −0.461091 + 0.461091i
\(305\) −6.07767e9 −0.0402150
\(306\) 8.26698e10 + 3.23956e10i 0.539015 + 0.211222i
\(307\) −1.17486e11 −0.754857 −0.377428 0.926039i \(-0.623192\pi\)
−0.377428 + 0.926039i \(0.623192\pi\)
\(308\) −2.17430e10 + 2.17430e10i −0.137670 + 0.137670i
\(309\) 2.73751e10 6.60893e10i 0.170821 0.412399i
\(310\) 4.24652e9i 0.0261159i
\(311\) −1.62159e8 6.71686e7i −0.000982925 0.000407141i 0.382192 0.924083i \(-0.375169\pi\)
−0.383175 + 0.923676i \(0.625169\pi\)
\(312\) 7.79522e10 + 1.88193e11i 0.465729 + 1.12437i
\(313\) −1.58501e11 + 6.56533e10i −0.933432 + 0.386640i −0.796979 0.604006i \(-0.793570\pi\)
−0.136452 + 0.990647i \(0.543570\pi\)
\(314\) 1.60590e11 + 1.60590e11i 0.932258 + 0.932258i
\(315\) −1.55341e9 1.55341e9i −0.00888973 0.00888973i
\(316\) 1.75105e10 7.25311e9i 0.0987888 0.0409197i
\(317\) −1.31565e9 3.17626e9i −0.00731768 0.0176664i 0.920178 0.391499i \(-0.128043\pi\)
−0.927496 + 0.373833i \(0.878043\pi\)
\(318\) −5.54095e10 2.29514e10i −0.303852 0.125860i
\(319\) 6.83167e10i 0.369376i
\(320\) −1.93057e9 + 4.66081e9i −0.0102923 + 0.0248477i
\(321\) −2.06267e10 + 2.06267e10i −0.108432 + 0.108432i
\(322\) 4.01096e10 0.207920
\(323\) 1.46731e11 6.41095e10i 0.750085 0.327726i
\(324\) −1.44929e9 −0.00730639
\(325\) −2.69027e11 + 2.69027e11i −1.33758 + 1.33758i
\(326\) −2.15112e10 + 5.19326e10i −0.105484 + 0.254660i
\(327\) 8.59084e10i 0.415500i
\(328\) −1.80987e11 7.49673e10i −0.863407 0.357635i
\(329\) 2.81985e10 + 6.80771e10i 0.132692 + 0.320346i
\(330\) 3.65574e9 1.51426e9i 0.0169692 0.00702889i
\(331\) 1.26814e11 + 1.26814e11i 0.580688 + 0.580688i 0.935092 0.354404i \(-0.115316\pi\)
−0.354404 + 0.935092i \(0.615316\pi\)
\(332\) −2.37944e10 2.37944e10i −0.107486 0.107486i
\(333\) −5.07823e10 + 2.10347e10i −0.226315 + 0.0937428i
\(334\) 9.34321e10 + 2.25565e11i 0.410806 + 0.991773i
\(335\) 3.33614e9 + 1.38187e9i 0.0144725 + 0.00599469i
\(336\) 9.12489e10i 0.390572i
\(337\) −7.77279e10 + 1.87652e11i −0.328279 + 0.792535i 0.670442 + 0.741962i \(0.266105\pi\)
−0.998720 + 0.0505724i \(0.983895\pi\)
\(338\) 3.98393e11 3.98393e11i 1.66030 1.66030i
\(339\) −9.58114e10 −0.394020
\(340\) 7.18823e8 7.47005e8i 0.00291721 0.00303158i
\(341\) 4.08005e11 1.63407
\(342\) 8.47756e10 8.47756e10i 0.335084 0.335084i
\(343\) 1.06794e11 2.57824e11i 0.416604 1.00577i
\(344\) 6.03491e10i 0.232358i
\(345\) 9.99847e8 + 4.14150e8i 0.00379968 + 0.00157388i
\(346\) 3.69144e10 + 8.91193e10i 0.138469 + 0.334295i
\(347\) −3.70724e11 + 1.53559e11i −1.37267 + 0.568581i −0.942512 0.334171i \(-0.891544\pi\)
−0.430162 + 0.902752i \(0.641544\pi\)
\(348\) −5.40633e9 5.40633e9i −0.0197604 0.0197604i
\(349\) 1.85580e11 + 1.85580e11i 0.669604 + 0.669604i 0.957624 0.288021i \(-0.0929972\pi\)
−0.288021 + 0.957624i \(0.592997\pi\)
\(350\) −1.91718e11 + 7.94122e10i −0.682899 + 0.282866i
\(351\) −2.03191e11 4.90547e11i −0.714535 1.72504i
\(352\) −1.25856e11 5.21312e10i −0.436950 0.180990i
\(353\) 4.23719e11i 1.45242i −0.687473 0.726210i \(-0.741280\pi\)
0.687473 0.726210i \(-0.258720\pi\)
\(354\) −7.47071e10 + 1.80359e11i −0.252841 + 0.610411i
\(355\) 9.21597e9 9.21597e9i 0.0307974 0.0307974i
\(356\) 8.09917e10 0.267249
\(357\) 5.49000e10 1.40099e11i 0.178882 0.456485i
\(358\) −3.26976e11 −1.05206
\(359\) 1.92102e11 1.92102e11i 0.610391 0.610391i −0.332657 0.943048i \(-0.607945\pi\)
0.943048 + 0.332657i \(0.107945\pi\)
\(360\) 2.01076e9 4.85439e9i 0.00630955 0.0152326i
\(361\) 1.06477e11i 0.329968i
\(362\) −8.86343e9 3.67135e9i −0.0271277 0.0112367i
\(363\) 6.91878e10 + 1.67034e11i 0.209146 + 0.504923i
\(364\) −8.25791e10 + 3.42054e10i −0.246555 + 0.102126i
\(365\) −1.03493e10 1.03493e10i −0.0305207 0.0305207i
\(366\) −2.20395e11 2.20395e11i −0.642003 0.642003i
\(367\) 9.01459e10 3.73396e10i 0.259387 0.107442i −0.249200 0.968452i \(-0.580168\pi\)
0.508588 + 0.861010i \(0.330168\pi\)
\(368\) 3.01515e10 + 7.27921e10i 0.0857024 + 0.206904i
\(369\) 1.83528e11 + 7.60198e10i 0.515328 + 0.213456i
\(370\) 3.06080e9i 0.00849037i
\(371\) 6.81741e10 1.64587e11i 0.186826 0.451037i
\(372\) −3.22880e10 + 3.22880e10i −0.0874175 + 0.0874175i
\(373\) 3.61489e11 0.966952 0.483476 0.875358i \(-0.339374\pi\)
0.483476 + 0.875358i \(0.339374\pi\)
\(374\) −3.42304e11 3.29390e11i −0.904669 0.870539i
\(375\) −1.12015e10 −0.0292506
\(376\) −1.24621e11 + 1.24621e11i −0.321547 + 0.321547i
\(377\) −7.59954e10 + 1.83469e11i −0.193754 + 0.467764i
\(378\) 2.89603e11i 0.729608i
\(379\) −4.52550e11 1.87453e11i −1.12665 0.466675i −0.260012 0.965605i \(-0.583726\pi\)
−0.866642 + 0.498930i \(0.833726\pi\)
\(380\) −5.35682e8 1.29325e9i −0.00131789 0.00318168i
\(381\) 3.53465e11 1.46410e11i 0.859378 0.355966i
\(382\) −9.35802e10 9.35802e10i −0.224853 0.224853i
\(383\) 2.43997e11 + 2.43997e11i 0.579415 + 0.579415i 0.934742 0.355327i \(-0.115631\pi\)
−0.355327 + 0.934742i \(0.615631\pi\)
\(384\) −1.57762e11 + 6.53470e10i −0.370263 + 0.153368i
\(385\) 4.49791e9 + 1.08589e10i 0.0104337 + 0.0251891i
\(386\) 1.79402e11 + 7.43109e10i 0.411325 + 0.170377i
\(387\) 6.11964e10i 0.138684i
\(388\) −4.95226e9 + 1.19558e10i −0.0110933 + 0.0267816i
\(389\) −2.59147e11 + 2.59147e11i −0.573816 + 0.573816i −0.933193 0.359377i \(-0.882989\pi\)
0.359377 + 0.933193i \(0.382989\pi\)
\(390\) 1.15022e10 0.0251762
\(391\) −2.49747e9 1.29902e11i −0.00540387 0.281073i
\(392\) 1.68722e11 0.360898
\(393\) −8.57340e10 + 8.57340e10i −0.181295 + 0.181295i
\(394\) −2.61996e11 + 6.32515e11i −0.547725 + 1.32232i
\(395\) 7.24471e9i 0.0149739i
\(396\) 6.89005e10 + 2.85395e10i 0.140797 + 0.0583201i
\(397\) −6.53459e9 1.57759e10i −0.0132027 0.0318740i 0.917141 0.398564i \(-0.130491\pi\)
−0.930343 + 0.366689i \(0.880491\pi\)
\(398\) 2.18653e11 9.05691e10i 0.436799 0.180928i
\(399\) −1.43667e11 1.43667e11i −0.283779 0.283779i
\(400\) −2.88239e11 2.88239e11i −0.562968 0.562968i
\(401\) −4.00633e11 + 1.65947e11i −0.773743 + 0.320495i −0.734387 0.678731i \(-0.762530\pi\)
−0.0393553 + 0.999225i \(0.512530\pi\)
\(402\) 7.08676e10 + 1.71090e11i 0.135341 + 0.326743i
\(403\) 1.09573e12 + 4.53865e11i 2.06933 + 0.857143i
\(404\) 7.76247e10i 0.144972i
\(405\) −2.11998e8 + 5.11808e8i −0.000391547 + 0.000945279i
\(406\) −7.65896e10 + 7.65896e10i −0.139895 + 0.139895i
\(407\) 2.94081e11 0.531242
\(408\) 3.59826e11 6.91796e9i 0.642867 0.0123597i
\(409\) 4.20491e11 0.743022 0.371511 0.928429i \(-0.378840\pi\)
0.371511 + 0.928429i \(0.378840\pi\)
\(410\) −7.82185e9 + 7.82185e9i −0.0136704 + 0.0136704i
\(411\) 1.07885e11 2.60458e11i 0.186498 0.450246i
\(412\) 7.50759e10i 0.128370i
\(413\) −5.35733e11 2.21908e11i −0.906093 0.375316i
\(414\) −3.72273e10 8.98745e10i −0.0622816 0.150361i
\(415\) −1.18834e10 + 4.92227e9i −0.0196664 + 0.00814609i
\(416\) −2.80004e11 2.80004e11i −0.458399 0.458399i
\(417\) 1.20367e11 + 1.20367e11i 0.194938 + 0.194938i
\(418\) −5.92613e11 + 2.45468e11i −0.949462 + 0.393280i
\(419\) −2.94913e11 7.11982e11i −0.467445 1.12851i −0.965275 0.261237i \(-0.915870\pi\)
0.497830 0.867275i \(-0.334130\pi\)
\(420\) −1.21528e9 5.03386e8i −0.00190570 0.000789368i
\(421\) 1.09759e12i 1.70282i 0.524498 + 0.851412i \(0.324253\pi\)
−0.524498 + 0.851412i \(0.675747\pi\)
\(422\) −3.12547e11 + 7.54556e11i −0.479744 + 1.15820i
\(423\) 1.26370e11 1.26370e11i 0.191917 0.191917i
\(424\) 4.26087e11 0.640254
\(425\) 2.69127e11 + 6.15966e11i 0.400136 + 0.915813i
\(426\) 6.68398e11 0.983314
\(427\) 6.54655e11 6.54655e11i 0.952987 0.952987i
\(428\) 1.17157e10 2.82842e10i 0.0168761 0.0407425i
\(429\) 1.10513e12i 1.57527i
\(430\) 3.14832e9 + 1.30408e9i 0.00444089 + 0.00183948i
\(431\) −4.37957e11 1.05732e12i −0.611341 1.47591i −0.861528 0.507710i \(-0.830492\pi\)
0.250187 0.968198i \(-0.419508\pi\)
\(432\) 5.25580e11 2.17702e11i 0.726042 0.300736i
\(433\) −5.77891e11 5.77891e11i −0.790042 0.790042i 0.191459 0.981501i \(-0.438678\pi\)
−0.981501 + 0.191459i \(0.938678\pi\)
\(434\) 4.57413e11 + 4.57413e11i 0.618877 + 0.618877i
\(435\) −2.70004e9 + 1.11839e9i −0.00361550 + 0.00149759i
\(436\) −3.45032e10 8.32982e10i −0.0457268 0.110394i
\(437\) −1.62080e11 6.71356e10i −0.212600 0.0880616i
\(438\) 7.50597e11i 0.974481i
\(439\) −5.59701e11 + 1.35124e12i −0.719226 + 1.73637i −0.0436819 + 0.999045i \(0.513909\pi\)
−0.675544 + 0.737320i \(0.736091\pi\)
\(440\) −1.98781e10 + 1.98781e10i −0.0252835 + 0.0252835i
\(441\) −1.71091e11 −0.215404
\(442\) −5.52868e11 1.26538e12i −0.689003 1.57696i
\(443\) −7.93546e11 −0.978938 −0.489469 0.872021i \(-0.662809\pi\)
−0.489469 + 0.872021i \(0.662809\pi\)
\(444\) −2.32725e10 + 2.32725e10i −0.0284197 + 0.0284197i
\(445\) 1.18472e10 2.86017e10i 0.0143218 0.0345758i
\(446\) 9.83865e11i 1.17741i
\(447\) 1.34411e11 + 5.56751e10i 0.159240 + 0.0659594i
\(448\) −2.94087e11 7.09989e11i −0.344925 0.832723i
\(449\) −2.04276e11 + 8.46139e10i −0.237197 + 0.0982501i −0.498116 0.867111i \(-0.665975\pi\)
0.260919 + 0.965361i \(0.415975\pi\)
\(450\) 3.55882e11 + 3.55882e11i 0.409119 + 0.409119i
\(451\) −7.51522e11 7.51522e11i −0.855357 0.855357i
\(452\) 9.29004e10 3.84806e10i 0.104687 0.0433629i
\(453\) 1.64749e11 + 3.97740e11i 0.183816 + 0.443770i
\(454\) 6.76056e10 + 2.80032e10i 0.0746847 + 0.0309354i
\(455\) 3.41658e10i 0.0373715i
\(456\) 1.85965e11 4.48959e11i 0.201414 0.486256i
\(457\) 9.07989e11 9.07989e11i 0.973773 0.973773i −0.0258919 0.999665i \(-0.508243\pi\)
0.999665 + 0.0258919i \(0.00824258\pi\)
\(458\) 4.79639e11 0.509354
\(459\) −9.37927e11 + 1.80324e10i −0.986306 + 0.0189626i
\(460\) −1.13580e9 −0.00118275
\(461\) 5.67089e11 5.67089e11i 0.584787 0.584787i −0.351428 0.936215i \(-0.614304\pi\)
0.936215 + 0.351428i \(0.114304\pi\)
\(462\) −2.30669e11 + 5.56885e11i −0.235560 + 0.568691i
\(463\) 4.65197e11i 0.470460i 0.971940 + 0.235230i \(0.0755844\pi\)
−0.971940 + 0.235230i \(0.924416\pi\)
\(464\) −1.96572e11 8.14226e10i −0.196875 0.0815481i
\(465\) 6.67933e9 + 1.61253e10i 0.00662514 + 0.0159945i
\(466\) 1.36437e12 5.65140e11i 1.34028 0.555161i
\(467\) −1.20171e12 1.20171e12i −1.16916 1.16916i −0.982408 0.186749i \(-0.940205\pi\)
−0.186749 0.982408i \(-0.559795\pi\)
\(468\) 1.53290e11 + 1.53290e11i 0.147709 + 0.147709i
\(469\) −5.08200e11 + 2.10503e11i −0.485017 + 0.200900i
\(470\) 3.80835e9 + 9.19416e9i 0.00359995 + 0.00869104i
\(471\) −8.62403e11 3.57219e11i −0.807451 0.334457i
\(472\) 1.38692e12i 1.28621i
\(473\) −1.25295e11 + 3.02490e11i −0.115096 + 0.277866i
\(474\) 2.62715e11 2.62715e11i 0.239047 0.239047i
\(475\) 9.07639e11 0.818072
\(476\) 3.03560e9 + 1.57891e11i 0.00271027 + 0.140970i
\(477\) −4.32069e11 −0.382138
\(478\) 7.55199e11 7.55199e11i 0.661661 0.661661i
\(479\) 4.04081e11 9.75538e11i 0.350719 0.846710i −0.645813 0.763496i \(-0.723481\pi\)
0.996532 0.0832141i \(-0.0265185\pi\)
\(480\) 5.82755e9i 0.00501072i
\(481\) 7.89775e11 + 3.27135e11i 0.672745 + 0.278660i
\(482\) 7.93747e11 + 1.91627e12i 0.669839 + 1.61713i
\(483\) −1.52308e11 + 6.30882e10i −0.127339 + 0.0527455i
\(484\) −1.34171e11 1.34171e11i −0.111136 0.111136i
\(485\) 3.49772e9 + 3.49772e9i 0.00287043 + 0.00287043i
\(486\) −1.04539e12 + 4.33016e11i −0.849996 + 0.352080i
\(487\) 3.79720e11 + 9.16725e11i 0.305903 + 0.738514i 0.999829 + 0.0184687i \(0.00587912\pi\)
−0.693927 + 0.720046i \(0.744121\pi\)
\(488\) 2.04579e12 + 8.47395e11i 1.63295 + 0.676389i
\(489\) 2.31039e11i 0.182724i
\(490\) 3.64589e9 8.80196e9i 0.00285707 0.00689759i
\(491\) −1.03967e12 + 1.03967e12i −0.807288 + 0.807288i −0.984223 0.176934i \(-0.943382\pi\)
0.176934 + 0.984223i \(0.443382\pi\)
\(492\) 1.18945e11 0.0915176
\(493\) 2.52817e11 + 2.43279e11i 0.192750 + 0.185479i
\(494\) −1.86456e12 −1.40866
\(495\) 2.01571e10 2.01571e10i 0.0150906 0.0150906i
\(496\) −4.86277e11 + 1.17398e12i −0.360758 + 0.870947i
\(497\) 1.98539e12i 1.45963i
\(498\) −6.09426e11 2.52432e11i −0.444006 0.183913i
\(499\) −6.50804e10 1.57118e11i −0.0469892 0.113442i 0.898642 0.438682i \(-0.144555\pi\)
−0.945631 + 0.325241i \(0.894555\pi\)
\(500\) 1.08611e10 4.49883e9i 0.00777160 0.00321910i
\(501\) −7.09580e11 7.09580e11i −0.503190 0.503190i
\(502\) −5.63445e11 5.63445e11i −0.395990 0.395990i
\(503\) 7.34308e11 3.04160e11i 0.511473 0.211859i −0.111994 0.993709i \(-0.535724\pi\)
0.623467 + 0.781850i \(0.285724\pi\)
\(504\) 3.06302e11 + 7.39478e11i 0.211452 + 0.510491i
\(505\) 2.74127e10 + 1.13547e10i 0.0187560 + 0.00776900i
\(506\) 5.20464e11i 0.352950i
\(507\) −8.86190e11 + 2.13945e12i −0.595650 + 1.43803i
\(508\) −2.83923e11 + 2.83923e11i −0.189154 + 0.189154i
\(509\) 7.47208e11 0.493414 0.246707 0.969090i \(-0.420651\pi\)
0.246707 + 0.969090i \(0.420651\pi\)
\(510\) 7.41452e9 1.89210e10i 0.00485308 0.0123845i
\(511\) 2.22955e12 1.44652
\(512\) 1.23442e12 1.23442e12i 0.793866 0.793866i
\(513\) −4.84739e11 + 1.17026e12i −0.309015 + 0.746028i
\(514\) 4.30565e11i 0.272085i
\(515\) 2.65126e10 + 1.09819e10i 0.0166081 + 0.00687930i
\(516\) −1.40225e10 3.38534e10i −0.00870768 0.0210222i
\(517\) −8.83373e11 + 3.65905e11i −0.543797 + 0.225248i
\(518\) 3.29693e11 + 3.29693e11i 0.201199 + 0.201199i
\(519\) −2.80351e11 2.80351e11i −0.169609 0.169609i
\(520\) −7.54963e10 + 3.12716e10i −0.0452804 + 0.0187558i
\(521\) 1.84838e10 + 4.46238e10i 0.0109906 + 0.0265336i 0.929280 0.369377i \(-0.120429\pi\)
−0.918289 + 0.395911i \(0.870429\pi\)
\(522\) 2.42702e11 + 1.00530e11i 0.143072 + 0.0592625i
\(523\) 1.41680e11i 0.0828041i 0.999143 + 0.0414020i \(0.0131824\pi\)
−0.999143 + 0.0414020i \(0.986818\pi\)
\(524\) 4.86959e10 1.17562e11i 0.0282164 0.0681205i
\(525\) 6.03105e11 6.03105e11i 0.346478 0.346478i
\(526\) −2.95759e12 −1.68462
\(527\) 1.45293e12 1.50989e12i 0.820533 0.852702i
\(528\) −1.18405e12 −0.663007
\(529\) 1.17295e12 1.17295e12i 0.651223 0.651223i
\(530\) 9.20725e9 2.22283e10i 0.00506861 0.0122367i
\(531\) 1.40639e12i 0.767681i
\(532\) 1.97003e11 + 8.16013e10i 0.106628 + 0.0441667i
\(533\) −1.18227e12 2.85426e12i −0.634519 1.53187i
\(534\) 1.46680e12 6.07570e11i 0.780614 0.323341i
\(535\) −8.27467e9 8.27467e9i −0.00436675 0.00436675i
\(536\) −9.30299e11 9.30299e11i −0.486834 0.486834i
\(537\) 1.24163e12 5.14298e11i 0.644327 0.266889i
\(538\) −2.20857e11 5.33195e11i −0.113655 0.274388i
\(539\) 8.45691e11 + 3.50297e11i 0.431581 + 0.178767i
\(540\) 8.20082e9i 0.00415036i
\(541\) 9.54742e11 2.30495e12i 0.479179 1.15684i −0.480815 0.876822i \(-0.659659\pi\)
0.959994 0.280019i \(-0.0903409\pi\)
\(542\) 9.76183e11 9.76183e11i 0.485886 0.485886i
\(543\) 3.94318e10 0.0194647
\(544\) −6.41099e11 + 2.80108e11i −0.313856 + 0.137130i
\(545\) −3.44633e10 −0.0167330
\(546\) −1.23896e12 + 1.23896e12i −0.596608 + 0.596608i
\(547\) 5.84199e11 1.41038e12i 0.279009 0.673586i −0.720800 0.693143i \(-0.756225\pi\)
0.999809 + 0.0195567i \(0.00622547\pi\)
\(548\) 2.95874e11i 0.140151i
\(549\) −2.07451e12 8.59292e11i −0.974632 0.403706i
\(550\) −1.03046e12 2.48775e12i −0.480173 1.15924i
\(551\) 4.37689e11 1.81297e11i 0.202294 0.0837929i
\(552\) −2.78812e11 2.78812e11i −0.127816 0.127816i
\(553\) 7.80362e11 + 7.80362e11i 0.354841 + 0.354841i
\(554\) −1.74332e12 + 7.22105e11i −0.786289 + 0.325691i
\(555\) 4.81431e9 + 1.16228e10i 0.00215385 + 0.00519986i
\(556\) −1.65053e11 6.83672e10i −0.0732465 0.0303397i
\(557\) 1.83453e12i 0.807563i 0.914855 + 0.403782i \(0.132304\pi\)
−0.914855 + 0.403782i \(0.867696\pi\)
\(558\) 6.00394e11 1.44948e12i 0.262170 0.632934i
\(559\) −6.72979e11 + 6.72979e11i −0.291507 + 0.291507i
\(560\) −3.66058e10 −0.0157291
\(561\) 1.81793e12 + 7.12386e11i 0.774897 + 0.303657i
\(562\) 2.77788e12 1.17463
\(563\) −3.01559e12 + 3.01559e12i −1.26498 + 1.26498i −0.316333 + 0.948648i \(0.602452\pi\)
−0.948648 + 0.316333i \(0.897548\pi\)
\(564\) 4.09505e10 9.88634e10i 0.0170413 0.0411414i
\(565\) 3.84361e10i 0.0158680i
\(566\) 1.63005e12 + 6.75190e11i 0.667618 + 0.276536i
\(567\) −3.22940e10 7.79646e10i −0.0131219 0.0316792i
\(568\) −4.38713e12 + 1.81721e12i −1.76853 + 0.732549i
\(569\) 1.30192e11 + 1.30192e11i 0.0520691 + 0.0520691i 0.732662 0.680593i \(-0.238278\pi\)
−0.680593 + 0.732662i \(0.738278\pi\)
\(570\) −1.94030e10 1.94030e10i −0.00769895 0.00769895i
\(571\) 5.88635e11 2.43820e11i 0.231731 0.0959860i −0.263797 0.964578i \(-0.584975\pi\)
0.495527 + 0.868592i \(0.334975\pi\)
\(572\) −4.43851e11 1.07155e12i −0.173363 0.418534i
\(573\) 5.02545e11 + 2.08161e11i 0.194751 + 0.0806683i
\(574\) 1.68506e12i 0.647905i
\(575\) 2.81831e11 6.80399e11i 0.107518 0.259572i
\(576\) −1.31794e12 + 1.31794e12i −0.498877 + 0.498877i
\(577\) −1.01674e12 −0.381873 −0.190936 0.981602i \(-0.561152\pi\)
−0.190936 + 0.981602i \(0.561152\pi\)
\(578\) −2.43792e12 + 9.37770e10i −0.908542 + 0.0349479i
\(579\) −7.98129e11 −0.295134
\(580\) 2.16882e9 2.16882e9i 0.000795790 0.000795790i
\(581\) 7.49818e11 1.81022e12i 0.273000 0.659081i
\(582\) 2.53676e11i 0.0916487i
\(583\) 2.13569e12 + 8.84632e11i 0.765649 + 0.317142i
\(584\) 2.04069e12 + 4.92665e12i 0.725969 + 1.75264i
\(585\) 7.65562e10 3.17106e10i 0.0270258 0.0111945i
\(586\) 2.30003e12 + 2.30003e12i 0.805737 + 0.805737i
\(587\) 1.55336e12 + 1.55336e12i 0.540010 + 0.540010i 0.923532 0.383522i \(-0.125289\pi\)
−0.383522 + 0.923532i \(0.625289\pi\)
\(588\) −9.46461e10 + 3.92037e10i −0.0326516 + 0.0135248i
\(589\) −1.08275e12 2.61399e12i −0.370689 0.894922i
\(590\) −7.23534e10 2.99698e10i −0.0245824 0.0101824i
\(591\) 2.81395e12i 0.948794i
\(592\) −3.50498e11 + 8.46176e11i −0.117284 + 0.283148i
\(593\) 2.04798e11 2.04798e11i 0.0680111 0.0680111i −0.672283 0.740294i \(-0.734686\pi\)
0.740294 + 0.672283i \(0.234686\pi\)
\(594\) 3.75790e12 1.23853
\(595\) 5.62024e10 + 2.20239e10i 0.0183835 + 0.00720390i
\(596\) −1.52688e11 −0.0495676
\(597\) −6.87837e11 + 6.87837e11i −0.221616 + 0.221616i
\(598\) −5.78964e11 + 1.39774e12i −0.185138 + 0.446963i
\(599\) 3.94569e12i 1.25228i −0.779710 0.626141i \(-0.784633\pi\)
0.779710 0.626141i \(-0.215367\pi\)
\(600\) 1.88470e12 + 7.80667e11i 0.593692 + 0.245915i
\(601\) 1.67836e12 + 4.05192e12i 0.524747 + 1.26685i 0.934925 + 0.354845i \(0.115466\pi\)
−0.410178 + 0.912005i \(0.634534\pi\)
\(602\) −4.79588e11 + 1.98652e11i −0.148828 + 0.0616465i
\(603\) 9.43360e11 + 9.43360e11i 0.290569 + 0.290569i
\(604\) −3.19488e11 3.19488e11i −0.0976760 0.0976760i
\(605\) −6.70080e10 + 2.77556e10i −0.0203342 + 0.00842271i
\(606\) 5.82312e11 + 1.40583e12i 0.175400 + 0.423452i
\(607\) −1.14973e11 4.76235e10i −0.0343754 0.0142388i 0.365429 0.930839i \(-0.380922\pi\)
−0.399805 + 0.916600i \(0.630922\pi\)
\(608\) 9.44673e11i 0.280359i
\(609\) 1.70367e11 4.11301e11i 0.0501888 0.121166i
\(610\) 8.84145e10 8.84145e10i 0.0258547 0.0258547i
\(611\) −2.77939e12 −0.806797
\(612\) 3.50974e11 1.53347e11i 0.101133 0.0441869i
\(613\) −2.13411e12 −0.610442 −0.305221 0.952282i \(-0.598730\pi\)
−0.305221 + 0.952282i \(0.598730\pi\)
\(614\) 1.70912e12 1.70912e12i 0.485306 0.485306i
\(615\) 1.73990e10 4.20049e10i 0.00490440 0.0118403i
\(616\) 4.28232e12i 1.19830i
\(617\) −5.29169e12 2.19189e12i −1.46998 0.608885i −0.503124 0.864214i \(-0.667816\pi\)
−0.966854 + 0.255329i \(0.917816\pi\)
\(618\) 5.63192e11 + 1.35967e12i 0.155313 + 0.374959i
\(619\) 1.28946e12 5.34113e11i 0.353022 0.146226i −0.199123 0.979974i \(-0.563809\pi\)
0.552145 + 0.833748i \(0.313809\pi\)
\(620\) −1.29528e10 1.29528e10i −0.00352047 0.00352047i
\(621\) 7.26756e11 + 7.26756e11i 0.196099 + 0.196099i
\(622\) 3.33613e9 1.38187e9i 0.000893688 0.000370178i
\(623\) 1.80471e12 + 4.35695e12i 0.479966 + 1.15874i
\(624\) −3.17985e12 1.31714e12i −0.839608 0.347777i
\(625\) 3.80796e12i 0.998233i
\(626\) 1.35070e12 3.26087e12i 0.351538 0.848689i
\(627\) 1.86423e12 1.86423e12i 0.481722 0.481722i
\(628\) 9.79669e11 0.251340
\(629\) 1.04724e12 1.08829e12i 0.266758 0.277216i
\(630\) 4.51962e10 0.0114306
\(631\) −4.02283e12 + 4.02283e12i −1.01018 + 1.01018i −0.0102352 + 0.999948i \(0.503258\pi\)
−0.999948 + 0.0102352i \(0.996742\pi\)
\(632\) −1.01011e12 + 2.43863e12i −0.251850 + 0.608021i
\(633\) 3.35688e12i 0.831035i
\(634\) 6.53456e10 + 2.70670e10i 0.0160626 + 0.00665333i
\(635\) 5.87344e10 + 1.41797e11i 0.0143354 + 0.0346088i
\(636\) −2.39017e11 + 9.90042e10i −0.0579258 + 0.0239937i
\(637\) 1.88149e12 + 1.88149e12i 0.452767 + 0.452767i
\(638\) −9.93831e11 9.93831e11i −0.237476 0.237476i
\(639\) 4.44872e12 1.84272e12i 1.05556 0.437225i
\(640\) −2.62148e10 6.32882e10i −0.00617642 0.0149112i
\(641\) −6.48020e12 2.68419e12i −1.51610 0.627989i −0.539294 0.842118i \(-0.681309\pi\)
−0.976805 + 0.214129i \(0.931309\pi\)
\(642\) 6.00129e11i 0.139424i
\(643\) −2.22025e12 + 5.36016e12i −0.512215 + 1.23660i 0.430377 + 0.902649i \(0.358381\pi\)
−0.942592 + 0.333947i \(0.891619\pi\)
\(644\) 1.22343e11 1.22343e11i 0.0280280 0.0280280i
\(645\) −1.40063e10 −0.00318643
\(646\) −1.20193e12 + 3.06718e12i −0.271539 + 0.692937i
\(647\) 1.98910e12 0.446260 0.223130 0.974789i \(-0.428373\pi\)
0.223130 + 0.974789i \(0.428373\pi\)
\(648\) 1.42720e11 1.42720e11i 0.0317979 0.0317979i
\(649\) 2.87949e12 6.95170e12i 0.637110 1.53812i
\(650\) 7.82729e12i 1.71989i
\(651\) −2.45640e12 1.01747e12i −0.536024 0.222029i
\(652\) 9.27917e10 + 2.24019e11i 0.0201092 + 0.0485479i
\(653\) −2.99785e12 + 1.24175e12i −0.645209 + 0.267254i −0.681199 0.732098i \(-0.738541\pi\)
0.0359906 + 0.999352i \(0.488541\pi\)
\(654\) −1.24974e12 1.24974e12i −0.267129 0.267129i
\(655\) −3.43934e10 3.43934e10i −0.00730111 0.00730111i
\(656\) 3.05809e12 1.26670e12i 0.644738 0.267059i
\(657\) −2.06933e12 4.99581e12i −0.433298 1.04607i
\(658\) −1.40056e12 5.80132e11i −0.291263 0.120645i
\(659\) 1.05636e12i 0.218186i 0.994032 + 0.109093i \(0.0347946\pi\)
−0.994032 + 0.109093i \(0.965205\pi\)
\(660\) 6.53197e9 1.57696e10i 0.00133998 0.00323499i
\(661\) −2.16113e12 + 2.16113e12i −0.440325 + 0.440325i −0.892121 0.451796i \(-0.850783\pi\)
0.451796 + 0.892121i \(0.350783\pi\)
\(662\) −3.68964e12 −0.746661
\(663\) 4.08971e12 + 3.93542e12i 0.822019 + 0.791008i
\(664\) 4.68635e12 0.935575
\(665\) 5.76340e10 5.76340e10i 0.0114283 0.0114283i
\(666\) 4.32751e11 1.04475e12i 0.0852322 0.205769i
\(667\) 3.84402e11i 0.0752002i
\(668\) 9.73008e11 + 4.03033e11i 0.189070 + 0.0783153i
\(669\) −1.54752e12 3.73604e12i −0.298688 0.721097i
\(670\) −6.86349e10 + 2.84295e10i −0.0131586 + 0.00545046i
\(671\) 8.49485e12 + 8.49485e12i 1.61772 + 1.61772i
\(672\) 6.27713e11 + 6.27713e11i 0.118741 + 0.118741i
\(673\) 1.31466e12 5.44550e11i 0.247028 0.102322i −0.255734 0.966747i \(-0.582317\pi\)
0.502762 + 0.864425i \(0.332317\pi\)
\(674\) −1.59911e12 3.86059e12i −0.298475 0.720583i
\(675\) −4.91268e12 2.03490e12i −0.910860 0.377290i
\(676\) 2.43037e12i 0.447622i
\(677\) 1.46887e12 3.54617e12i 0.268741 0.648799i −0.730683 0.682717i \(-0.760798\pi\)
0.999425 + 0.0339175i \(0.0107984\pi\)
\(678\) 1.39381e12 1.39381e12i 0.253320 0.253320i
\(679\) −7.53513e11 −0.136043
\(680\) 2.77523e9 + 1.44349e11i 0.000497748 + 0.0258895i
\(681\) −3.00765e11 −0.0535878
\(682\) −5.93542e12 + 5.93542e12i −1.05056 + 1.05056i
\(683\) −3.64873e11 + 8.80882e11i −0.0641577 + 0.154890i −0.952707 0.303891i \(-0.901714\pi\)
0.888549 + 0.458782i \(0.151714\pi\)
\(684\) 5.17167e11i 0.0903396i
\(685\) 1.04486e11 + 4.32797e10i 0.0181323 + 0.00751063i
\(686\) 2.19709e12 + 5.30425e12i 0.378782 + 0.914461i
\(687\) −1.82133e12 + 7.54421e11i −0.311949 + 0.129214i
\(688\) −7.21039e11 7.21039e11i −0.122691 0.122691i
\(689\) 4.75148e12 + 4.75148e12i 0.803234 + 0.803234i
\(690\) −2.05700e10 + 8.52037e9i −0.00345472 + 0.00143099i
\(691\) −8.65703e10 2.08999e11i −0.0144450 0.0348733i 0.916492 0.400052i \(-0.131008\pi\)
−0.930937 + 0.365179i \(0.881008\pi\)
\(692\) 3.84429e11 + 1.59236e11i 0.0637293 + 0.0263975i
\(693\) 4.34244e12i 0.715212i
\(694\) 3.15919e12 7.62695e12i 0.516961 1.24805i
\(695\) −4.82870e10 + 4.82870e10i −0.00785052 + 0.00785052i
\(696\) 1.06479e12 0.171997
\(697\) −5.45734e12 + 1.04922e11i −0.875857 + 0.0168391i
\(698\) −5.39943e12 −0.860991
\(699\) −4.29201e12 + 4.29201e12i −0.680008 + 0.680008i
\(700\) −3.42556e11 + 8.27004e11i −0.0539251 + 0.130187i
\(701\) 5.32445e12i 0.832805i −0.909180 0.416403i \(-0.863291\pi\)
0.909180 0.416403i \(-0.136709\pi\)
\(702\) 1.00921e13 + 4.18029e12i 1.56843 + 0.649665i
\(703\) −7.80422e11 1.88411e12i −0.120512 0.290942i
\(704\) 9.21287e12 3.81609e12i 1.41357 0.585521i
\(705\) −2.89229e10 2.89229e10i −0.00440951 0.00440951i
\(706\) 6.16402e12 + 6.16402e12i 0.933777 + 0.933777i
\(707\) −4.17582e12 + 1.72968e12i −0.628572 + 0.260363i
\(708\) 3.22260e11 + 7.78005e11i 0.0482011 + 0.116368i
\(709\) 6.75466e12 + 2.79787e12i 1.00391 + 0.415834i 0.823230 0.567708i \(-0.192170\pi\)
0.180681 + 0.983542i \(0.442170\pi\)
\(710\) 2.68137e11i 0.0395999i
\(711\) 1.02429e12 2.47286e12i 0.150318 0.362900i
\(712\) −7.97574e12 + 7.97574e12i −1.16308 + 1.16308i
\(713\) −2.29575e12 −0.332676
\(714\) 1.23942e12 + 2.83673e12i 0.178475 + 0.408484i
\(715\) −4.43338e11 −0.0634392
\(716\) −9.97345e11 + 9.97345e11i −0.141820 + 0.141820i
\(717\) −1.67987e12 + 4.05557e12i −0.237378 + 0.573080i
\(718\) 5.58919e12i 0.784854i
\(719\) 4.97906e12 + 2.06240e12i 0.694813 + 0.287801i 0.702004 0.712173i \(-0.252289\pi\)
−0.00719096 + 0.999974i \(0.502289\pi\)
\(720\) 3.39752e10 + 8.20234e10i 0.00471157 + 0.0113747i
\(721\) −4.03871e12 + 1.67289e12i −0.556588 + 0.230546i
\(722\) −1.54896e12 1.54896e12i −0.212140 0.212140i
\(723\) −6.02820e12 6.02820e12i −0.820474 0.820474i
\(724\) −3.82337e10 + 1.58369e10i −0.00517158 + 0.00214214i
\(725\) 7.61070e11 + 1.83739e12i 0.102307 + 0.246990i
\(726\) −3.43642e12 1.42341e12i −0.459083 0.190158i
\(727\) 1.11382e13i 1.47880i 0.673265 + 0.739402i \(0.264892\pi\)
−0.673265 + 0.739402i \(0.735108\pi\)
\(728\) 4.76365e12 1.15005e13i 0.628563 1.51749i
\(729\) 3.06130e12 3.06130e12i 0.401450 0.401450i
\(730\) 3.01112e11 0.0392442
\(731\) 6.73230e11 + 1.54086e12i 0.0872038 + 0.199588i
\(732\) −1.34450e12 −0.173086
\(733\) 2.52060e12 2.52060e12i 0.322505 0.322505i −0.527222 0.849727i \(-0.676766\pi\)
0.849727 + 0.527222i \(0.176766\pi\)
\(734\) −7.68194e11 + 1.85458e12i −0.0976874 + 0.235838i
\(735\) 3.91583e10i 0.00494916i
\(736\) 7.08161e11 + 2.93330e11i 0.0889574 + 0.0368474i
\(737\) −2.73150e12 6.59443e12i −0.341034 0.823330i
\(738\) −3.77575e12 + 1.56397e12i −0.468543 + 0.194077i
\(739\) −1.69412e12 1.69412e12i −0.208951 0.208951i 0.594870 0.803822i \(-0.297203\pi\)
−0.803822 + 0.594870i \(0.797203\pi\)
\(740\) −9.33608e9 9.33608e9i −0.00114452 0.00114452i
\(741\) 7.08030e12 2.93276e12i 0.862720 0.357350i
\(742\) 1.40256e12 + 3.38607e12i 0.169865 + 0.410089i
\(743\) −7.71248e12 3.19461e12i −0.928420 0.384564i −0.133341 0.991070i \(-0.542571\pi\)
−0.795079 + 0.606506i \(0.792571\pi\)
\(744\) 6.35920e12i 0.760894i
\(745\) −2.23348e10 + 5.39210e10i −0.00265631 + 0.00641290i
\(746\) −5.25873e12 + 5.25873e12i −0.621664 + 0.621664i
\(747\) −4.75214e12 −0.558402
\(748\) −2.04881e12 + 3.93901e10i −0.239301 + 0.00460076i
\(749\) 1.78261e12 0.206961
\(750\) 1.62953e11 1.62953e11i 0.0188055 0.0188055i
\(751\) 3.76419e12 9.08756e12i 0.431809 1.04248i −0.546895 0.837201i \(-0.684190\pi\)
0.978704 0.205278i \(-0.0658098\pi\)
\(752\) 2.97788e12i 0.339568i
\(753\) 3.02581e12 + 1.25333e12i 0.342977 + 0.142066i
\(754\) −1.56346e12 3.77454e12i −0.176164 0.425297i
\(755\) −1.59559e11 + 6.60915e10i −0.0178715 + 0.00740260i
\(756\) −8.83349e11 8.83349e11i −0.0983523 0.0983523i
\(757\) −6.70583e12 6.70583e12i −0.742200 0.742200i 0.230801 0.973001i \(-0.425865\pi\)
−0.973001 + 0.230801i \(0.925865\pi\)
\(758\) 9.31039e12 3.85649e12i 1.02437 0.424308i
\(759\) −8.18636e11 1.97636e12i −0.0895371 0.216162i