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Properties

Label 71.10.g.a.2.18
Level $71$
Weight $10$
Character 71.2
Analytic conductor $36.568$
Analytic rank $0$
Dimension $1272$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [71,10,Mod(2,71)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(71, base_ring=CyclotomicField(70))
 
chi = DirichletCharacter(H, H._module([6]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("71.2");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 71 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 71.g (of order \(35\), degree \(24\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(36.5675443676\)
Analytic rank: \(0\)
Dimension: \(1272\)
Relative dimension: \(53\) over \(\Q(\zeta_{35})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{35}]$

Embedding invariants

Embedding label 2.18
Character \(\chi\) \(=\) 71.2
Dual form 71.10.g.a.36.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.686555 + 15.2873i) q^{2} +(30.1497 + 26.3410i) q^{3} +(276.707 + 24.9041i) q^{4} +(-137.078 - 421.881i) q^{5} +(-423.383 + 442.824i) q^{6} +(-9439.10 - 2605.03i) q^{7} +(-1622.41 + 11977.1i) q^{8} +(-2426.96 - 17916.5i) q^{9} +O(q^{10})\) \(q+(-0.686555 + 15.2873i) q^{2} +(30.1497 + 26.3410i) q^{3} +(276.707 + 24.9041i) q^{4} +(-137.078 - 421.881i) q^{5} +(-423.383 + 442.824i) q^{6} +(-9439.10 - 2605.03i) q^{7} +(-1622.41 + 11977.1i) q^{8} +(-2426.96 - 17916.5i) q^{9} +(6543.55 - 1805.91i) q^{10} +(6700.68 - 12451.9i) q^{11} +(7686.65 + 8039.60i) q^{12} +(53880.8 + 100127. i) q^{13} +(46304.4 - 142510. i) q^{14} +(6979.93 - 16330.4i) q^{15} +(-42023.6 - 7626.16i) q^{16} +(543046. + 394546. i) q^{17} +(275562. - 24801.0i) q^{18} +(-281573. - 658774. i) q^{19} +(-27423.8 - 120151. i) q^{20} +(-215967. - 327176. i) q^{21} +(185757. + 110984. i) q^{22} +(-761886. - 955375. i) q^{23} +(-364405. + 318371. i) q^{24} +(1.42092e6 - 1.03236e6i) q^{25} +(-1.56767e6 + 754952. i) q^{26} +(832886. - 1.26177e6i) q^{27} +(-2.54699e6 - 955902. i) q^{28} +(3.26271e6 - 1.94938e6i) q^{29} +(244856. + 117916. i) q^{30} +(5.74810e6 - 1.04313e6i) q^{31} +(-1.23159e6 + 5.39594e6i) q^{32} +(530020. - 198920. i) q^{33} +(-6.40439e6 + 8.03086e6i) q^{34} +(194877. + 4.33927e6i) q^{35} +(-225362. - 5.01807e6i) q^{36} +(1.20760e7 - 1.51429e7i) q^{37} +(1.02642e7 - 3.85223e6i) q^{38} +(-1.01296e6 + 4.43809e6i) q^{39} +(5.27532e6 - 957329. i) q^{40} +(1.14003e7 + 5.49010e6i) q^{41} +(5.14993e6 - 3.07694e6i) q^{42} +(-6.34065e6 - 2.37969e6i) q^{43} +(2.16423e6 - 3.27867e6i) q^{44} +(-7.22596e6 + 3.47984e6i) q^{45} +(1.51282e7 - 1.09913e7i) q^{46} +(-3.83382e7 + 3.34951e7i) q^{47} +(-1.06612e6 - 1.33687e6i) q^{48} +(4.76689e7 + 2.84809e7i) q^{49} +(1.48065e7 + 2.24308e7i) q^{50} +(5.97994e6 + 2.61998e7i) q^{51} +(1.24156e7 + 2.90478e7i) q^{52} +(6.97130e7 - 6.27428e6i) q^{53} +(1.87173e7 + 1.35989e7i) q^{54} +(-6.17175e6 - 1.12001e6i) q^{55} +(4.65148e7 - 1.08827e8i) q^{56} +(8.86341e6 - 2.72788e7i) q^{57} +(2.75608e7 + 5.12165e7i) q^{58} +(-9.49813e6 - 9.93427e6i) q^{59} +(2.33809e6 - 4.34490e6i) q^{60} +(9.73154e7 - 2.68573e7i) q^{61} +(1.20002e7 + 8.85894e7i) q^{62} +(-2.37647e7 + 1.75438e8i) q^{63} +(-1.02724e8 - 2.83499e7i) q^{64} +(3.48560e7 - 3.64565e7i) q^{65} +(2.67707e6 + 8.23917e6i) q^{66} +(-1.09171e8 - 9.82561e6i) q^{67} +(1.40439e8 + 1.22698e8i) q^{68} +(2.19489e6 - 4.88731e7i) q^{69} -6.64697e7 q^{70} +(5.23322e7 - 2.07629e8i) q^{71} +2.18526e8 q^{72} +(-2.47309e6 + 5.50677e7i) q^{73} +(2.23203e8 + 1.95007e8i) q^{74} +(7.00336e7 + 6.30314e6i) q^{75} +(-6.15073e7 - 1.89300e8i) q^{76} +(-9.56860e7 + 1.00080e8i) q^{77} +(-6.71511e7 - 1.85325e7i) q^{78} +(4.98521e7 - 3.68023e8i) q^{79} +(2.54316e6 + 1.87743e7i) q^{80} +(-2.84699e8 + 7.85721e7i) q^{81} +(-9.17560e7 + 1.70511e8i) q^{82} +(2.16705e8 + 2.26655e8i) q^{83} +(-5.16117e7 - 9.59105e7i) q^{84} +(9.20122e7 - 2.83184e8i) q^{85} +(4.07323e7 - 9.52980e7i) q^{86} +(1.49718e8 + 2.71698e7i) q^{87} +(1.38267e8 + 1.00457e8i) q^{88} +(7.24922e8 - 6.52441e7i) q^{89} +(-4.82365e7 - 1.12855e8i) q^{90} +(-2.47752e8 - 1.08547e9i) q^{91} +(-1.87027e8 - 2.83333e8i) q^{92} +(2.00781e8 + 1.19961e8i) q^{93} +(-4.85730e8 - 6.09086e8i) q^{94} +(-2.39327e8 + 2.09094e8i) q^{95} +(-1.79267e8 + 1.30245e8i) q^{96} +(-1.18783e9 + 5.72028e8i) q^{97} +(-4.68124e8 + 7.09178e8i) q^{98} +(-2.39358e8 - 8.98325e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1272 q - 76 q^{2} - 395 q^{3} + 13542 q^{4} - 1610 q^{5} - 4334 q^{6} - 4827 q^{7} - 18627 q^{8} + 286810 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 1272 q - 76 q^{2} - 395 q^{3} + 13542 q^{4} - 1610 q^{5} - 4334 q^{6} - 4827 q^{7} - 18627 q^{8} + 286810 q^{9} - 53448 q^{10} - 170685 q^{11} + 138323 q^{12} - 93291 q^{13} + 985964 q^{14} - 966194 q^{15} + 4755334 q^{16} + 2558412 q^{17} - 2619769 q^{18} - 172269 q^{19} + 738120 q^{20} + 1797929 q^{21} + 3015622 q^{22} + 6635088 q^{23} + 4803145 q^{24} - 115100016 q^{25} + 19254293 q^{26} - 17686931 q^{27} + 15761532 q^{28} - 10052927 q^{29} + 62637435 q^{30} - 23748991 q^{31} + 10388192 q^{32} - 15097203 q^{33} + 33217854 q^{34} - 24823174 q^{35} + 27856812 q^{36} - 27156308 q^{37} - 43400577 q^{38} + 251072838 q^{39} - 129856160 q^{40} + 62087988 q^{41} - 91873950 q^{42} - 167299067 q^{43} + 60914131 q^{44} - 31536191 q^{45} - 50201490 q^{46} - 23317743 q^{47} + 10641329 q^{48} + 338745866 q^{49} + 303770229 q^{50} + 448039613 q^{51} - 979580293 q^{52} + 12085215 q^{53} - 182583505 q^{54} - 243892552 q^{55} + 30440435 q^{56} + 714581966 q^{57} - 244549660 q^{58} - 859013315 q^{59} - 1894499000 q^{60} - 876373921 q^{61} + 186553636 q^{62} - 196611021 q^{63} + 5528242635 q^{64} + 867018244 q^{65} + 2727701199 q^{66} - 286780089 q^{67} - 1689988351 q^{68} - 3073308182 q^{69} - 41489396 q^{70} - 2538053548 q^{71} - 6821388000 q^{72} + 128479023 q^{73} + 3282772334 q^{74} + 3407782757 q^{75} + 7133788844 q^{76} + 1087098389 q^{77} + 2715049934 q^{78} + 144243625 q^{79} - 7443877603 q^{80} - 4083269278 q^{81} - 10375744380 q^{82} + 1543773955 q^{83} - 4117054288 q^{84} + 7843382686 q^{85} + 3545751759 q^{86} + 5261609811 q^{87} - 818728797 q^{88} - 1369081479 q^{89} + 10041256259 q^{90} - 7299574322 q^{91} + 602797624 q^{92} - 2146129677 q^{93} - 683447510 q^{94} - 7007204038 q^{95} + 6601829126 q^{96} - 10081488030 q^{97} - 5942379880 q^{98} - 4074592265 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/71\mathbb{Z}\right)^\times\).

\(n\) \(7\)
\(\chi(n)\) \(e\left(\frac{3}{35}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.686555 + 15.2873i −0.0303417 + 0.675611i 0.924975 + 0.380028i \(0.124086\pi\)
−0.955317 + 0.295584i \(0.904486\pi\)
\(3\) 30.1497 + 26.3410i 0.214901 + 0.187753i 0.758657 − 0.651490i \(-0.225856\pi\)
−0.543757 + 0.839243i \(0.682999\pi\)
\(4\) 276.707 + 24.9041i 0.540444 + 0.0486409i
\(5\) −137.078 − 421.881i −0.0980847 − 0.301874i 0.889961 − 0.456037i \(-0.150732\pi\)
−0.988045 + 0.154164i \(0.950732\pi\)
\(6\) −423.383 + 442.824i −0.133368 + 0.139492i
\(7\) −9439.10 − 2605.03i −1.48590 − 0.410082i −0.573439 − 0.819248i \(-0.694391\pi\)
−0.912460 + 0.409166i \(0.865820\pi\)
\(8\) −1622.41 + 11977.1i −0.140041 + 1.03383i
\(9\) −2426.96 − 17916.5i −0.123302 − 0.910253i
\(10\) 6543.55 − 1805.91i 0.206925 − 0.0571078i
\(11\) 6700.68 − 12451.9i 0.137991 − 0.256431i −0.802216 − 0.597034i \(-0.796346\pi\)
0.940207 + 0.340603i \(0.110631\pi\)
\(12\) 7686.65 + 8039.60i 0.107009 + 0.111923i
\(13\) 53880.8 + 100127.i 0.523226 + 0.972317i 0.995846 + 0.0910506i \(0.0290225\pi\)
−0.472620 + 0.881266i \(0.656692\pi\)
\(14\) 46304.4 − 142510.i 0.322141 − 0.991448i
\(15\) 6979.93 − 16330.4i 0.0355992 − 0.0832885i
\(16\) −42023.6 − 7626.16i −0.160307 − 0.0290915i
\(17\) 543046. + 394546.i 1.57695 + 1.14572i 0.920094 + 0.391699i \(0.128112\pi\)
0.656852 + 0.754020i \(0.271888\pi\)
\(18\) 275562. − 24801.0i 0.618719 − 0.0556857i
\(19\) −281573. − 658774.i −0.495679 − 1.15970i −0.961496 − 0.274818i \(-0.911382\pi\)
0.465817 − 0.884881i \(-0.345760\pi\)
\(20\) −27423.8 − 120151.i −0.0383259 − 0.167917i
\(21\) −215967. − 327176.i −0.242326 − 0.367109i
\(22\) 185757. + 110984.i 0.169061 + 0.101009i
\(23\) −761886. − 955375.i −0.567695 − 0.711867i 0.412265 − 0.911064i \(-0.364738\pi\)
−0.979959 + 0.199197i \(0.936166\pi\)
\(24\) −364405. + 318371.i −0.224199 + 0.195877i
\(25\) 1.42092e6 − 1.03236e6i 0.727510 − 0.528567i
\(26\) −1.56767e6 + 754952.i −0.672784 + 0.323996i
\(27\) 832886. − 1.26177e6i 0.301612 − 0.456923i
\(28\) −2.54699e6 − 955902.i −0.783099 − 0.293902i
\(29\) 3.26271e6 − 1.94938e6i 0.856618 − 0.511805i −0.0161904 − 0.999869i \(-0.505154\pi\)
0.872808 + 0.488064i \(0.162297\pi\)
\(30\) 244856. + 117916.i 0.0551905 + 0.0265783i
\(31\) 5.74810e6 − 1.04313e6i 1.11788 − 0.202866i 0.411994 − 0.911187i \(-0.364833\pi\)
0.705891 + 0.708321i \(0.250547\pi\)
\(32\) −1.23159e6 + 5.39594e6i −0.207630 + 0.909688i
\(33\) 530020. − 198920.i 0.0778000 − 0.0291988i
\(34\) −6.40439e6 + 8.03086e6i −0.821907 + 1.03064i
\(35\) 194877. + 4.33927e6i 0.0219510 + 0.488777i
\(36\) −225362. − 5.01807e6i −0.0223624 − 0.497939i
\(37\) 1.20760e7 − 1.51429e7i 1.05929 − 1.32831i 0.117147 − 0.993115i \(-0.462625\pi\)
0.942148 − 0.335198i \(-0.108803\pi\)
\(38\) 1.02642e7 − 3.85223e6i 0.798545 − 0.299699i
\(39\) −1.01296e6 + 4.43809e6i −0.0701138 + 0.307189i
\(40\) 5.27532e6 − 957329.i 0.325821 − 0.0591277i
\(41\) 1.14003e7 + 5.49010e6i 0.630071 + 0.303426i 0.721531 − 0.692383i \(-0.243439\pi\)
−0.0914595 + 0.995809i \(0.529153\pi\)
\(42\) 5.14993e6 − 3.07694e6i 0.255376 − 0.152580i
\(43\) −6.34065e6 − 2.37969e6i −0.282830 − 0.106148i 0.205928 − 0.978567i \(-0.433979\pi\)
−0.488759 + 0.872419i \(0.662550\pi\)
\(44\) 2.16423e6 − 3.27867e6i 0.0870496 − 0.131874i
\(45\) −7.22596e6 + 3.47984e6i −0.262687 + 0.126504i
\(46\) 1.51282e7 − 1.09913e7i 0.498170 − 0.361942i
\(47\) −3.83382e7 + 3.34951e7i −1.14602 + 1.00125i −0.146091 + 0.989271i \(0.546669\pi\)
−0.999928 + 0.0119754i \(0.996188\pi\)
\(48\) −1.06612e6 − 1.33687e6i −0.0289881 − 0.0363499i
\(49\) 4.76689e7 + 2.84809e7i 1.18128 + 0.705783i
\(50\) 1.48065e7 + 2.24308e7i 0.335032 + 0.507552i
\(51\) 5.97994e6 + 2.61998e7i 0.123775 + 0.542292i
\(52\) 1.24156e7 + 2.90478e7i 0.235480 + 0.550933i
\(53\) 6.97130e7 − 6.27428e6i 1.21359 − 0.109225i 0.535713 − 0.844400i \(-0.320043\pi\)
0.677878 + 0.735175i \(0.262900\pi\)
\(54\) 1.87173e7 + 1.35989e7i 0.299551 + 0.217636i
\(55\) −6.17175e6 − 1.12001e6i −0.0909445 − 0.0165040i
\(56\) 4.65148e7 − 1.08827e8i 0.632041 − 1.47873i
\(57\) 8.86341e6 − 2.72788e7i 0.111215 − 0.342285i
\(58\) 2.75608e7 + 5.12165e7i 0.319790 + 0.594270i
\(59\) −9.49813e6 − 9.93427e6i −0.102048 − 0.106734i 0.669798 − 0.742543i \(-0.266381\pi\)
−0.771846 + 0.635810i \(0.780666\pi\)
\(60\) 2.33809e6 − 4.34490e6i 0.0232906 − 0.0432812i
\(61\) 9.73154e7 − 2.68573e7i 0.899906 − 0.248358i 0.214676 − 0.976685i \(-0.431130\pi\)
0.685230 + 0.728327i \(0.259702\pi\)
\(62\) 1.20002e7 + 8.85894e7i 0.103140 + 0.761411i
\(63\) −2.37647e7 + 1.75438e8i −0.190064 + 1.40311i
\(64\) −1.02724e8 − 2.83499e7i −0.765350 − 0.211223i
\(65\) 3.48560e7 − 3.64565e7i 0.242196 − 0.253317i
\(66\) 2.67707e6 + 8.23917e6i 0.0173665 + 0.0534485i
\(67\) −1.09171e8 − 9.82561e6i −0.661870 − 0.0595694i −0.246389 − 0.969171i \(-0.579244\pi\)
−0.415481 + 0.909602i \(0.636387\pi\)
\(68\) 1.40439e8 + 1.22698e8i 0.796522 + 0.695901i
\(69\) 2.19489e6 − 4.88731e7i 0.0116572 − 0.259567i
\(70\) −6.64697e7 −0.330889
\(71\) 5.23322e7 − 2.07629e8i 0.244403 − 0.969674i
\(72\) 2.18526e8 0.958311
\(73\) −2.47309e6 + 5.50677e7i −0.0101927 + 0.226957i 0.987431 + 0.158053i \(0.0505217\pi\)
−0.997623 + 0.0689042i \(0.978050\pi\)
\(74\) 2.23203e8 + 1.95007e8i 0.865283 + 0.755975i
\(75\) 7.00336e7 + 6.30314e6i 0.255582 + 0.0230028i
\(76\) −6.15073e7 − 1.89300e8i −0.211478 − 0.650863i
\(77\) −9.56860e7 + 1.00080e8i −0.310199 + 0.324443i
\(78\) −6.71511e7 − 1.85325e7i −0.205413 − 0.0566903i
\(79\) 4.98521e7 − 3.68023e8i 0.144000 − 1.06305i −0.764340 − 0.644814i \(-0.776935\pi\)
0.908339 − 0.418234i \(-0.137351\pi\)
\(80\) 2.54316e6 + 1.87743e7i 0.00694174 + 0.0512460i
\(81\) −2.84699e8 + 7.85721e7i −0.734859 + 0.202808i
\(82\) −9.17560e7 + 1.70511e8i −0.224116 + 0.416477i
\(83\) 2.16705e8 + 2.26655e8i 0.501207 + 0.524221i 0.924199 − 0.381912i \(-0.124734\pi\)
−0.422992 + 0.906134i \(0.639020\pi\)
\(84\) −5.16117e7 − 9.59105e7i −0.113107 − 0.210189i
\(85\) 9.20122e7 − 2.83184e8i 0.191188 − 0.588416i
\(86\) 4.07323e7 − 9.52980e7i 0.0802964 − 0.187863i
\(87\) 1.49718e8 + 2.71698e7i 0.280180 + 0.0508453i
\(88\) 1.38267e8 + 1.00457e8i 0.245780 + 0.178570i
\(89\) 7.24922e8 − 6.52441e7i 1.22472 − 0.110227i 0.541664 − 0.840595i \(-0.317794\pi\)
0.683053 + 0.730368i \(0.260652\pi\)
\(90\) −4.82365e7 − 1.12855e8i −0.0774969 − 0.181313i
\(91\) −2.47752e8 − 1.08547e9i −0.378731 − 1.65933i
\(92\) −1.87027e8 − 2.83333e8i −0.272181 − 0.412337i
\(93\) 2.00781e8 + 1.19961e8i 0.278323 + 0.166290i
\(94\) −4.85730e8 − 6.09086e8i −0.641681 − 0.804643i
\(95\) −2.39327e8 + 2.09094e8i −0.301464 + 0.263381i
\(96\) −1.79267e8 + 1.30245e8i −0.215417 + 0.156509i
\(97\) −1.18783e9 + 5.72028e8i −1.36232 + 0.656061i −0.965154 − 0.261683i \(-0.915722\pi\)
−0.397171 + 0.917745i \(0.630008\pi\)
\(98\) −4.68124e8 + 7.09178e8i −0.512677 + 0.776672i
\(99\) −2.39358e8 − 8.98325e7i −0.250432 − 0.0939885i
\(100\) 4.18888e8 − 2.50274e8i 0.418888 − 0.250274i
\(101\) −1.06621e9 − 5.13461e8i −1.01952 − 0.490977i −0.152004 − 0.988380i \(-0.548573\pi\)
−0.867520 + 0.497403i \(0.834287\pi\)
\(102\) −4.04631e8 + 7.34298e7i −0.370134 + 0.0671694i
\(103\) −2.98043e8 + 1.30581e9i −0.260923 + 1.14318i 0.659330 + 0.751853i \(0.270840\pi\)
−0.920253 + 0.391324i \(0.872017\pi\)
\(104\) −1.28665e9 + 4.82890e8i −1.07848 + 0.404760i
\(105\) −1.08425e8 + 1.35961e8i −0.0870520 + 0.109160i
\(106\) 4.80553e7 + 1.07003e9i 0.0369713 + 0.823230i
\(107\) −4.90218e7 − 1.09156e9i −0.0361545 − 0.805043i −0.932388 − 0.361460i \(-0.882279\pi\)
0.896233 − 0.443583i \(-0.146293\pi\)
\(108\) 2.61889e8 − 3.28398e8i 0.185230 − 0.232270i
\(109\) 9.28080e8 − 3.48314e8i 0.629747 − 0.236348i −0.0160329 − 0.999871i \(-0.505104\pi\)
0.645780 + 0.763523i \(0.276532\pi\)
\(110\) 2.13592e7 − 9.35808e7i 0.0139097 − 0.0609424i
\(111\) 7.62967e8 − 1.38458e8i 0.477038 − 0.0865696i
\(112\) 3.76799e8 + 1.81457e8i 0.226271 + 0.108966i
\(113\) −2.11674e9 + 1.26470e9i −1.22128 + 0.729681i −0.971136 − 0.238528i \(-0.923335\pi\)
−0.250144 + 0.968209i \(0.580478\pi\)
\(114\) 4.10935e8 + 1.54226e8i 0.227877 + 0.0855237i
\(115\) −2.98617e8 + 4.52386e8i −0.159212 + 0.241195i
\(116\) 9.51362e8 − 4.58152e8i 0.487849 − 0.234935i
\(117\) 1.66317e9 − 1.20836e9i 0.820540 − 0.596157i
\(118\) 1.58390e8 − 1.38381e8i 0.0752069 − 0.0657063i
\(119\) −4.09807e9 − 5.13881e9i −1.87334 − 2.34910i
\(120\) 1.84266e8 + 1.10094e8i 0.0811204 + 0.0484672i
\(121\) 1.18883e9 + 1.80101e9i 0.504182 + 0.763803i
\(122\) 3.43765e8 + 1.50613e9i 0.140489 + 0.615523i
\(123\) 1.99101e8 + 4.65821e8i 0.0784334 + 0.183504i
\(124\) 1.61652e9 − 1.45489e8i 0.614022 − 0.0552629i
\(125\) −1.33123e9 − 9.67197e8i −0.487707 − 0.354340i
\(126\) −2.66567e9 − 4.83747e8i −0.942190 − 0.170982i
\(127\) −3.45746e8 + 8.08913e8i −0.117934 + 0.275921i −0.968087 − 0.250616i \(-0.919367\pi\)
0.850152 + 0.526537i \(0.176510\pi\)
\(128\) −3.71764e8 + 1.14417e9i −0.122412 + 0.376744i
\(129\) −1.28486e8 − 2.38766e8i −0.0408508 − 0.0759135i
\(130\) 5.33393e8 + 5.57885e8i 0.163796 + 0.171317i
\(131\) 9.52776e7 − 1.77055e8i 0.0282664 − 0.0525277i −0.866071 − 0.499922i \(-0.833362\pi\)
0.894337 + 0.447394i \(0.147648\pi\)
\(132\) 1.51614e8 − 4.18429e7i 0.0434668 − 0.0119961i
\(133\) 9.41677e8 + 6.95174e9i 0.260957 + 1.92646i
\(134\) 2.25160e8 − 1.66220e9i 0.0603280 − 0.445359i
\(135\) −6.46486e8 − 1.78419e8i −0.167516 − 0.0462316i
\(136\) −5.60657e9 + 5.86402e9i −1.40531 + 1.46984i
\(137\) −1.37056e9 − 4.21816e9i −0.332397 − 1.02301i −0.967990 − 0.250988i \(-0.919245\pi\)
0.635594 − 0.772024i \(-0.280755\pi\)
\(138\) 7.45633e8 + 6.71082e7i 0.175013 + 0.0157514i
\(139\) −2.65484e9 − 2.31947e9i −0.603215 − 0.527013i 0.301259 − 0.953542i \(-0.402593\pi\)
−0.904474 + 0.426529i \(0.859736\pi\)
\(140\) −5.41418e7 + 1.20556e9i −0.0119112 + 0.265224i
\(141\) −2.03818e9 −0.434267
\(142\) 3.13817e9 + 9.42569e8i 0.647707 + 0.194543i
\(143\) 1.60782e9 0.321533
\(144\) −3.46447e7 + 7.71425e8i −0.00671438 + 0.149507i
\(145\) −1.26965e9 − 1.10926e9i −0.238522 − 0.208390i
\(146\) −8.40141e8 − 7.56140e7i −0.153026 − 0.0137726i
\(147\) 6.86990e8 + 2.11434e9i 0.121345 + 0.373462i
\(148\) 3.71865e9 − 3.88940e9i 0.637100 − 0.666354i
\(149\) 3.28096e9 + 9.05487e8i 0.545334 + 0.150503i 0.527839 − 0.849344i \(-0.323002\pi\)
0.0174948 + 0.999847i \(0.494431\pi\)
\(150\) −1.44440e8 + 1.06630e9i −0.0232958 + 0.171976i
\(151\) −9.04700e8 − 6.67877e9i −0.141615 − 1.04544i −0.912677 − 0.408682i \(-0.865988\pi\)
0.771062 − 0.636760i \(-0.219726\pi\)
\(152\) 8.34704e9 − 2.30364e9i 1.26834 − 0.350040i
\(153\) 5.75094e9 − 1.06870e10i 0.848453 − 1.57669i
\(154\) −1.46426e9 − 1.53149e9i −0.209785 − 0.219418i
\(155\) −1.22801e9 − 2.28203e9i −0.170887 − 0.317562i
\(156\) −3.90821e8 + 1.20282e9i −0.0528345 + 0.162608i
\(157\) 2.86225e9 − 6.69657e9i 0.375975 − 0.879638i −0.619534 − 0.784970i \(-0.712678\pi\)
0.995509 − 0.0946679i \(-0.0301789\pi\)
\(158\) 5.59186e9 + 1.01477e9i 0.713838 + 0.129543i
\(159\) 2.26710e9 + 1.64714e9i 0.281309 + 0.204383i
\(160\) 2.44527e9 − 2.20078e8i 0.294976 − 0.0265483i
\(161\) 4.70274e9 + 1.10026e10i 0.551613 + 1.29056i
\(162\) −1.00570e9 − 4.40624e9i −0.114723 − 0.502633i
\(163\) 2.88849e9 + 4.37588e9i 0.320499 + 0.485536i 0.958733 − 0.284307i \(-0.0917633\pi\)
−0.638234 + 0.769842i \(0.720335\pi\)
\(164\) 3.01783e9 + 1.80307e9i 0.325759 + 0.194632i
\(165\) −1.56574e8 − 1.96338e8i −0.0164453 − 0.0206218i
\(166\) −3.61374e9 + 3.15723e9i −0.369377 + 0.322715i
\(167\) 9.17275e8 − 6.66439e8i 0.0912589 − 0.0663035i −0.541220 − 0.840881i \(-0.682037\pi\)
0.632479 + 0.774577i \(0.282037\pi\)
\(168\) 4.26902e9 − 2.05585e9i 0.413462 − 0.199113i
\(169\) −1.28036e9 + 1.93966e9i −0.120738 + 0.182910i
\(170\) 4.26597e9 + 1.60104e9i 0.391739 + 0.147022i
\(171\) −1.11196e10 + 6.64363e9i −0.994501 + 0.594187i
\(172\) −1.69524e9 − 8.16386e8i −0.147691 − 0.0711242i
\(173\) 1.67018e10 − 3.03092e9i 1.41760 − 0.257257i 0.584959 − 0.811063i \(-0.301111\pi\)
0.832646 + 0.553806i \(0.186825\pi\)
\(174\) −5.18144e8 + 2.27014e9i −0.0428528 + 0.187750i
\(175\) −1.61015e10 + 6.04300e9i −1.29776 + 0.487058i
\(176\) −3.76547e8 + 4.72175e8i −0.0295810 + 0.0370934i
\(177\) −2.46873e7 − 5.49706e8i −0.00189058 − 0.0420969i
\(178\) 4.99710e8 + 1.11269e10i 0.0373103 + 0.830778i
\(179\) 1.11645e10 − 1.39999e10i 0.812834 − 1.01926i −0.186488 − 0.982457i \(-0.559711\pi\)
0.999322 − 0.0368044i \(-0.0117179\pi\)
\(180\) −2.08614e9 + 7.82941e8i −0.148121 + 0.0555908i
\(181\) −1.58849e9 + 6.95964e9i −0.110010 + 0.481984i 0.889668 + 0.456608i \(0.150936\pi\)
−0.999678 + 0.0253768i \(0.991921\pi\)
\(182\) 1.67641e10 − 3.04224e9i 1.13255 − 0.205528i
\(183\) 3.64148e9 + 1.75364e9i 0.240020 + 0.115588i
\(184\) 1.26787e10 − 7.57519e9i 0.815447 − 0.487207i
\(185\) −8.04384e9 − 3.01891e9i −0.504883 − 0.189486i
\(186\) −1.97173e9 + 2.98704e9i −0.120792 + 0.182992i
\(187\) 8.55165e9 − 4.11826e9i 0.511402 − 0.246278i
\(188\) −1.14426e10 + 8.31356e9i −0.668061 + 0.485374i
\(189\) −1.11486e10 + 9.74027e9i −0.635541 + 0.555255i
\(190\) −3.03217e9 − 3.80223e9i −0.168796 − 0.211664i
\(191\) 1.85727e10 + 1.10967e10i 1.00978 + 0.603314i 0.919700 − 0.392621i \(-0.128431\pi\)
0.0900772 + 0.995935i \(0.471289\pi\)
\(192\) −2.35032e9 − 3.56058e9i −0.124816 − 0.189089i
\(193\) 6.43302e8 + 2.81849e9i 0.0333739 + 0.146221i 0.988870 − 0.148784i \(-0.0475359\pi\)
−0.955496 + 0.295005i \(0.904679\pi\)
\(194\) −7.92927e9 − 1.85515e10i −0.401907 − 0.940308i
\(195\) 2.01120e9 − 1.81011e8i 0.0996092 − 0.00896499i
\(196\) 1.24811e10 + 9.06802e9i 0.604087 + 0.438895i
\(197\) −1.65067e9 − 2.99553e8i −0.0780841 − 0.0141702i 0.139374 − 0.990240i \(-0.455491\pi\)
−0.217458 + 0.976070i \(0.569777\pi\)
\(198\) 1.53763e9 − 3.59747e9i 0.0710983 − 0.166343i
\(199\) −5.54363e9 + 1.70615e10i −0.250585 + 0.771222i 0.744082 + 0.668088i \(0.232887\pi\)
−0.994667 + 0.103134i \(0.967113\pi\)
\(200\) 1.00594e10 + 1.86934e10i 0.444565 + 0.826140i
\(201\) −3.03267e9 − 3.17193e9i −0.131052 − 0.137069i
\(202\) 8.58146e9 − 1.59470e10i 0.362644 − 0.673905i
\(203\) −3.58752e10 + 9.90092e9i −1.48273 + 0.409207i
\(204\) 1.00221e9 + 7.39861e9i 0.0405157 + 0.299099i
\(205\) 7.53444e8 − 5.56215e9i 0.0297961 − 0.219963i
\(206\) −1.97578e10 − 5.45280e9i −0.764427 − 0.210968i
\(207\) −1.52679e10 + 1.59690e10i −0.577981 + 0.604521i
\(208\) −1.50068e9 − 4.61862e9i −0.0555908 − 0.171091i
\(209\) −1.00897e10 − 9.08094e8i −0.365782 − 0.0329210i
\(210\) −2.00404e9 − 1.75088e9i −0.0711082 − 0.0621254i
\(211\) 1.68601e9 − 3.75420e10i 0.0585585 − 1.30391i −0.727652 − 0.685947i \(-0.759388\pi\)
0.786210 − 0.617959i \(-0.212040\pi\)
\(212\) 1.94464e10 0.661191
\(213\) 7.04696e9 − 4.88147e9i 0.234581 − 0.162496i
\(214\) 1.67206e10 0.544993
\(215\) −1.34784e8 + 3.00120e9i −0.00430196 + 0.0957905i
\(216\) 1.37611e10 + 1.20227e10i 0.430140 + 0.375802i
\(217\) −5.69743e10 − 5.12778e9i −1.74426 − 0.156986i
\(218\) 4.68762e9 + 1.44270e10i 0.140572 + 0.432636i
\(219\) −1.52510e9 + 1.59513e9i −0.0448023 + 0.0468595i
\(220\) −1.67988e9 − 4.63617e8i −0.0483477 − 0.0133431i
\(221\) −1.02451e10 + 7.56323e10i −0.288902 + 2.13276i
\(222\) 1.59284e9 + 1.17588e10i 0.0440132 + 0.324919i
\(223\) −5.86834e10 + 1.61956e10i −1.58907 + 0.438556i −0.945177 − 0.326559i \(-0.894111\pi\)
−0.643894 + 0.765114i \(0.722682\pi\)
\(224\) 2.56817e10 − 4.77245e10i 0.681565 − 1.26656i
\(225\) −2.19448e10 − 2.29524e10i −0.570833 − 0.597045i
\(226\) −1.78806e10 − 3.32277e10i −0.455925 − 0.847251i
\(227\) 1.01360e10 − 3.11954e10i 0.253367 − 0.779783i −0.740780 − 0.671747i \(-0.765544\pi\)
0.994147 − 0.108035i \(-0.0344559\pi\)
\(228\) 3.13192e9 − 7.32750e9i 0.0767546 − 0.179576i
\(229\) −5.47250e10 − 9.93113e9i −1.31500 − 0.238638i −0.524664 − 0.851309i \(-0.675809\pi\)
−0.790338 + 0.612672i \(0.790095\pi\)
\(230\) −6.71076e9 − 4.87565e9i −0.158124 − 0.114883i
\(231\) −5.52111e9 + 4.96909e8i −0.127577 + 0.0114821i
\(232\) 1.80545e10 + 4.22405e10i 0.409156 + 0.957268i
\(233\) −9.54747e9 − 4.18302e10i −0.212220 − 0.929798i −0.963054 − 0.269307i \(-0.913205\pi\)
0.750834 − 0.660491i \(-0.229652\pi\)
\(234\) 1.73308e10 + 2.62550e10i 0.377874 + 0.572454i
\(235\) 1.93863e10 + 1.15828e10i 0.414657 + 0.247746i
\(236\) −2.38080e9 − 2.98543e9i −0.0499596 − 0.0626473i
\(237\) 1.11971e10 − 9.78263e9i 0.230536 − 0.201413i
\(238\) 8.13723e10 − 5.91204e10i 1.64392 − 1.19438i
\(239\) 5.91563e10 − 2.84882e10i 1.17276 − 0.564773i 0.256969 − 0.966420i \(-0.417276\pi\)
0.915795 + 0.401646i \(0.131562\pi\)
\(240\) −4.17860e8 + 6.33030e8i −0.00812980 + 0.0123161i
\(241\) −8.81313e10 − 3.30762e10i −1.68288 − 0.631596i −0.687376 − 0.726301i \(-0.741238\pi\)
−0.995505 + 0.0947052i \(0.969809\pi\)
\(242\) −2.83488e10 + 1.69376e10i −0.531332 + 0.317456i
\(243\) −3.74645e10 − 1.80419e10i −0.689273 − 0.331936i
\(244\) 2.75967e10 − 5.00807e9i 0.498429 − 0.0904516i
\(245\) 5.48120e9 − 2.40147e10i 0.0971915 − 0.425824i
\(246\) −7.25786e9 + 2.72392e9i −0.126357 + 0.0474227i
\(247\) 5.07899e10 − 6.36885e10i 0.868242 − 1.08874i
\(248\) 3.16787e9 + 7.05381e10i 0.0531783 + 1.18411i
\(249\) 5.63254e8 + 1.25418e10i 0.00928554 + 0.206759i
\(250\) 1.56998e10 − 1.96870e10i 0.254194 − 0.318749i
\(251\) 4.13943e10 − 1.55356e10i 0.658278 − 0.247056i 0.000193379 − 1.00000i \(-0.499938\pi\)
0.658084 + 0.752944i \(0.271367\pi\)
\(252\) −1.09450e10 + 4.79532e10i −0.170967 + 0.749057i
\(253\) −1.70014e10 + 3.08531e9i −0.260881 + 0.0473430i
\(254\) −1.21288e10 − 5.84090e9i −0.182837 − 0.0880498i
\(255\) 1.02335e10 − 6.11423e9i 0.151563 − 0.0905547i
\(256\) −6.83177e10 − 2.56401e10i −0.994153 − 0.373112i
\(257\) −2.20292e10 + 3.33728e10i −0.314992 + 0.477193i −0.957236 − 0.289308i \(-0.906575\pi\)
0.642244 + 0.766500i \(0.278004\pi\)
\(258\) 3.73831e9 − 1.80028e9i 0.0525275 − 0.0252959i
\(259\) −1.53434e11 + 1.11477e11i −2.11872 + 1.53934i
\(260\) 1.05528e10 − 9.21973e9i 0.143215 − 0.125123i
\(261\) −4.28445e10 − 5.37253e10i −0.571495 − 0.716632i
\(262\) 2.64129e9 + 1.57810e9i 0.0346307 + 0.0206909i
\(263\) 5.69589e10 + 8.62891e10i 0.734110 + 1.11213i 0.989393 + 0.145262i \(0.0464026\pi\)
−0.255284 + 0.966866i \(0.582169\pi\)
\(264\) 1.52258e9 + 6.67085e9i 0.0192913 + 0.0845207i
\(265\) −1.22031e10 − 2.85505e10i −0.152007 − 0.355638i
\(266\) −1.06920e11 + 9.62298e9i −1.30946 + 0.117853i
\(267\) 2.35748e10 + 1.71281e10i 0.283888 + 0.206257i
\(268\) −2.99639e10 − 5.43764e9i −0.354806 − 0.0643878i
\(269\) 5.21144e9 − 1.21928e10i 0.0606838 − 0.141977i −0.886442 − 0.462840i \(-0.846830\pi\)
0.947125 + 0.320864i \(0.103973\pi\)
\(270\) 3.17140e9 − 9.76056e9i 0.0363173 − 0.111773i
\(271\) 4.99431e10 + 9.28099e10i 0.562489 + 1.04528i 0.989973 + 0.141257i \(0.0451143\pi\)
−0.427484 + 0.904023i \(0.640600\pi\)
\(272\) −1.98119e10 − 2.07216e10i −0.219465 − 0.229543i
\(273\) 2.11228e10 − 3.92527e10i 0.230155 − 0.427699i
\(274\) 6.54254e10 − 1.80563e10i 0.701244 − 0.193531i
\(275\) −3.33374e9 − 2.46107e10i −0.0351508 − 0.259494i
\(276\) 1.82449e9 − 1.34689e10i 0.0189256 − 0.139714i
\(277\) −1.18371e10 − 3.26684e9i −0.120806 − 0.0333403i 0.205111 − 0.978739i \(-0.434244\pi\)
−0.325917 + 0.945398i \(0.605673\pi\)
\(278\) 3.72812e10 − 3.89931e10i 0.374359 − 0.391549i
\(279\) −3.26396e10 − 1.00454e11i −0.322497 − 0.992544i
\(280\) −5.22881e10 − 4.70602e9i −0.508384 − 0.0457554i
\(281\) −6.03541e9 − 5.27298e9i −0.0577469 − 0.0504519i 0.628582 − 0.777744i \(-0.283636\pi\)
−0.686328 + 0.727292i \(0.740779\pi\)
\(282\) 1.39932e9 − 3.11584e10i 0.0131764 − 0.293396i
\(283\) 1.18062e11 1.09414 0.547070 − 0.837087i \(-0.315743\pi\)
0.547070 + 0.837087i \(0.315743\pi\)
\(284\) 1.96515e10 − 5.61492e10i 0.179252 − 0.512167i
\(285\) −1.27234e10 −0.114235
\(286\) −1.10386e9 + 2.45793e10i −0.00975586 + 0.217231i
\(287\) −9.33069e10 − 8.15198e10i −0.811793 − 0.709242i
\(288\) 9.96656e10 + 8.97006e9i 0.853648 + 0.0768297i
\(289\) 1.02587e11 + 3.15730e11i 0.865071 + 2.66241i
\(290\) 1.78293e10 − 1.86480e10i 0.148028 − 0.154825i
\(291\) −5.08804e10 − 1.40421e10i −0.415942 − 0.114793i
\(292\) −2.05574e9 + 1.51760e10i −0.0165480 + 0.122162i
\(293\) 1.44607e10 + 1.06753e11i 0.114626 + 0.846205i 0.953397 + 0.301720i \(0.0975606\pi\)
−0.838771 + 0.544485i \(0.816725\pi\)
\(294\) −3.27943e10 + 9.05064e9i −0.255997 + 0.0706507i
\(295\) −2.88910e9 + 5.36885e9i −0.0222108 + 0.0412745i
\(296\) 1.61776e11 + 1.69204e11i 1.22490 + 1.28114i
\(297\) −1.01306e10 − 1.88257e10i −0.0755492 − 0.140394i
\(298\) −1.60950e10 + 4.95355e10i −0.118228 + 0.363867i
\(299\) 5.46081e10 − 1.27762e11i 0.395127 − 0.924446i
\(300\) 1.92218e10 + 3.48825e9i 0.137009 + 0.0248635i
\(301\) 5.36509e10 + 3.89797e10i 0.376728 + 0.273709i
\(302\) 1.02722e11 − 9.24512e9i 0.710609 − 0.0639560i
\(303\) −1.86209e10 − 4.35658e10i −0.126914 − 0.296930i
\(304\) 6.80882e9 + 2.98314e10i 0.0457236 + 0.200328i
\(305\) −2.46704e10 − 3.73740e10i −0.163240 − 0.247298i
\(306\) 1.59428e11 + 9.52539e10i 1.03949 + 0.621064i
\(307\) 1.28192e11 + 1.60748e11i 0.823642 + 1.03281i 0.998834 + 0.0482803i \(0.0153741\pi\)
−0.175192 + 0.984534i \(0.556055\pi\)
\(308\) −2.89694e10 + 2.53098e10i −0.183426 + 0.160255i
\(309\) −4.33824e10 + 3.15191e10i −0.270707 + 0.196680i
\(310\) 3.57292e10 − 1.72063e10i 0.219733 − 0.105818i
\(311\) −3.69217e10 + 5.59340e10i −0.223800 + 0.339043i −0.929075 − 0.369891i \(-0.879395\pi\)
0.705275 + 0.708934i \(0.250824\pi\)
\(312\) −5.15121e10 − 1.93328e10i −0.307761 − 0.115505i
\(313\) 1.50432e11 − 8.98787e10i 0.885910 − 0.529306i 0.00360948 − 0.999993i \(-0.498851\pi\)
0.882300 + 0.470687i \(0.155994\pi\)
\(314\) 1.00408e11 + 4.83538e10i 0.582886 + 0.280703i
\(315\) 7.72716e10 − 1.40227e10i 0.442204 − 0.0802482i
\(316\) 2.29597e10 − 1.00593e11i 0.129531 − 0.567514i
\(317\) −2.22427e11 + 8.34783e10i −1.23715 + 0.464309i −0.882332 − 0.470628i \(-0.844028\pi\)
−0.354815 + 0.934937i \(0.615456\pi\)
\(318\) −2.67369e10 + 3.35270e10i −0.146619 + 0.183854i
\(319\) −2.41118e9 − 5.36892e10i −0.0130368 − 0.290288i
\(320\) 2.12080e9 + 4.72233e10i 0.0113064 + 0.251757i
\(321\) 2.72747e10 − 3.42014e10i 0.143379 − 0.179792i
\(322\) −1.71429e11 + 6.43385e10i −0.888657 + 0.333518i
\(323\) 1.07009e11 − 4.68838e11i 0.547029 − 2.39669i
\(324\) −8.07352e10 + 1.46513e10i −0.407015 + 0.0738623i
\(325\) 1.79927e11 + 8.66485e10i 0.894587 + 0.430810i
\(326\) −6.88787e10 + 4.11531e10i −0.337758 + 0.201801i
\(327\) 3.71563e10 + 1.39450e10i 0.179708 + 0.0674456i
\(328\) −8.42516e10 + 1.27636e11i −0.401926 + 0.608892i
\(329\) 4.49134e11 − 2.16292e11i 2.11346 − 1.01779i
\(330\) 3.10898e9 − 2.25881e9i 0.0144313 − 0.0104850i
\(331\) −7.03276e10 + 6.14433e10i −0.322032 + 0.281351i −0.803740 − 0.594981i \(-0.797160\pi\)
0.481707 + 0.876332i \(0.340017\pi\)
\(332\) 5.43192e10 + 6.81141e10i 0.245376 + 0.307692i
\(333\) −3.00616e11 − 1.79609e11i −1.33971 − 0.800442i
\(334\) 9.55833e9 + 1.44802e10i 0.0420265 + 0.0636674i
\(335\) 1.08197e10 + 4.74043e10i 0.0469369 + 0.205644i
\(336\) 6.58062e9 + 1.53961e10i 0.0281670 + 0.0658999i
\(337\) 8.27031e10 − 7.44342e9i 0.349291 − 0.0314368i 0.0863950 − 0.996261i \(-0.472465\pi\)
0.262896 + 0.964824i \(0.415322\pi\)
\(338\) −2.87733e10 − 2.09050e10i −0.119912 − 0.0871215i
\(339\) −9.71325e10 − 1.76270e10i −0.399453 − 0.0724901i
\(340\) 3.25129e10 − 7.60677e10i 0.131947 − 0.308706i
\(341\) 2.55272e10 − 7.85647e10i 0.102237 − 0.314654i
\(342\) −9.39293e10 − 1.74550e11i −0.371265 − 0.689925i
\(343\) −1.02691e11 − 1.07406e11i −0.400598 − 0.418993i
\(344\) 3.87890e10 − 7.20820e10i 0.149347 − 0.277532i
\(345\) −2.09195e10 + 5.77342e9i −0.0794998 + 0.0219405i
\(346\) 3.48681e10 + 2.57407e11i 0.130793 + 0.965555i
\(347\) −1.47637e10 + 1.08990e11i −0.0546655 + 0.403557i 0.942856 + 0.333199i \(0.108128\pi\)
−0.997522 + 0.0703572i \(0.977586\pi\)
\(348\) 4.07515e10 + 1.12467e10i 0.148949 + 0.0411072i
\(349\) −3.20975e11 + 3.35714e11i −1.15813 + 1.21131i −0.184583 + 0.982817i \(0.559093\pi\)
−0.973546 + 0.228491i \(0.926621\pi\)
\(350\) −8.13268e10 − 2.50298e11i −0.289686 − 0.891561i
\(351\) 1.71214e11 + 1.54096e10i 0.602085 + 0.0541886i
\(352\) 5.89375e10 + 5.14922e10i 0.204621 + 0.178772i
\(353\) 7.35961e9 − 1.63875e11i 0.0252272 − 0.561727i −0.946085 − 0.323919i \(-0.895000\pi\)
0.971312 − 0.237808i \(-0.0764290\pi\)
\(354\) 8.42049e9 0.0284985
\(355\) −9.47684e10 + 6.38331e9i −0.316691 + 0.0213314i
\(356\) 2.02216e11 0.667253
\(357\) 1.18060e10 − 2.62881e11i 0.0384676 − 0.856548i
\(358\) 2.06356e11 + 1.80288e11i 0.663962 + 0.580086i
\(359\) 2.83742e11 + 2.55373e10i 0.901569 + 0.0811427i 0.530717 − 0.847549i \(-0.321923\pi\)
0.370852 + 0.928692i \(0.379066\pi\)
\(360\) −2.99550e10 − 9.21919e10i −0.0939956 − 0.289289i
\(361\) −1.31702e11 + 1.37749e11i −0.408141 + 0.426882i
\(362\) −1.05304e11 − 2.90620e10i −0.322296 − 0.0889481i
\(363\) −1.15973e10 + 8.56149e10i −0.0350573 + 0.258803i
\(364\) −4.15221e10 − 3.06529e11i −0.123972 − 0.915197i
\(365\) 2.35710e10 − 6.50519e9i 0.0695121 − 0.0191841i
\(366\) −2.93086e10 + 5.44646e10i −0.0853750 + 0.158653i
\(367\) 2.02197e11 + 2.11481e11i 0.581804 + 0.608519i 0.946538 − 0.322593i \(-0.104554\pi\)
−0.364734 + 0.931112i \(0.618840\pi\)
\(368\) 2.47314e10 + 4.59586e10i 0.0702964 + 0.130633i
\(369\) 7.06954e10 − 2.17578e11i 0.198506 − 0.610937i
\(370\) 5.16736e10 − 1.20896e11i 0.143338 − 0.335356i
\(371\) −6.74373e11 − 1.22381e11i −1.84807 − 0.335374i
\(372\) 5.25700e10 + 3.81943e10i 0.142329 + 0.103408i
\(373\) −2.47552e11 + 2.22801e10i −0.662180 + 0.0595973i −0.415631 − 0.909533i \(-0.636439\pi\)
−0.246549 + 0.969130i \(0.579297\pi\)
\(374\) 5.70860e10 + 1.33559e11i 0.150872 + 0.352982i
\(375\) −1.46593e10 − 6.42267e10i −0.0382801 − 0.167716i
\(376\) −3.38975e11 − 5.13525e11i −0.874625 − 1.32500i
\(377\) 3.70983e11 + 2.21652e11i 0.945841 + 0.565114i
\(378\) −1.41249e11 − 1.77120e11i −0.355853 − 0.446226i
\(379\) −4.55286e11 + 3.97771e11i −1.13346 + 0.990278i −1.00000 0.000775494i \(-0.999753\pi\)
−0.133465 + 0.991054i \(0.542610\pi\)
\(380\) −7.14308e10 + 5.18975e10i −0.175735 + 0.127679i
\(381\) −3.17317e10 + 1.52812e10i −0.0771492 + 0.0371531i
\(382\) −1.82390e11 + 2.76309e11i −0.438244 + 0.663912i
\(383\) 1.41675e11 + 5.31716e10i 0.336433 + 0.126266i 0.513873 − 0.857866i \(-0.328210\pi\)
−0.177440 + 0.984132i \(0.556782\pi\)
\(384\) −4.13472e10 + 2.47038e10i −0.0970411 + 0.0579793i
\(385\) 5.53382e10 + 2.66494e10i 0.128366 + 0.0618180i
\(386\) −4.35289e10 + 7.89933e9i −0.0998010 + 0.0181112i
\(387\) −2.72472e10 + 1.19378e11i −0.0617480 + 0.270536i
\(388\) −3.42927e11 + 1.28703e11i −0.768172 + 0.288300i
\(389\) −1.64724e11 + 2.06558e11i −0.364741 + 0.457371i −0.930009 − 0.367536i \(-0.880201\pi\)
0.565268 + 0.824907i \(0.308773\pi\)
\(390\) 1.38638e9 + 3.08702e10i 0.00303453 + 0.0675691i
\(391\) −3.67998e10 − 8.19412e11i −0.0796252 − 1.77299i
\(392\) −4.18457e11 + 5.24729e11i −0.895085 + 1.12240i
\(393\) 7.53641e9 − 2.82846e9i 0.0159367 − 0.00598114i
\(394\) 5.71264e9 − 2.50287e10i 0.0119427 − 0.0523245i
\(395\) −1.62095e11 + 2.94160e10i −0.335030 + 0.0607990i
\(396\) −6.39949e10 − 3.08183e10i −0.130773 − 0.0629768i
\(397\) 6.13547e11 − 3.66577e11i 1.23963 − 0.740642i 0.264949 − 0.964262i \(-0.414645\pi\)
0.974676 + 0.223621i \(0.0717877\pi\)
\(398\) −2.57019e11 − 9.64610e10i −0.513443 − 0.192698i
\(399\) −1.54725e11 + 2.34398e11i −0.305620 + 0.462994i
\(400\) −6.75850e10 + 3.25472e10i −0.132002 + 0.0635688i
\(401\) 5.09924e11 − 3.70481e11i 0.984817 − 0.715511i 0.0260368 − 0.999661i \(-0.491711\pi\)
0.958780 + 0.284150i \(0.0917113\pi\)
\(402\) 5.05724e10 − 4.41838e10i 0.0965821 − 0.0843812i
\(403\) 4.14158e11 + 5.19338e11i 0.782156 + 0.980793i
\(404\) −2.82242e11 − 1.68631e11i −0.527114 − 0.314936i
\(405\) 7.21740e10 + 1.09339e11i 0.133301 + 0.201942i
\(406\) −1.26728e11 − 5.55234e11i −0.231477 − 1.01417i
\(407\) −1.07641e11 − 2.51838e11i −0.194447 − 0.454931i
\(408\) −3.23501e11 + 2.91156e10i −0.577969 + 0.0520181i
\(409\) 1.00644e11 + 7.31221e10i 0.177841 + 0.129209i 0.673145 − 0.739511i \(-0.264943\pi\)
−0.495303 + 0.868720i \(0.664943\pi\)
\(410\) 8.45132e10 + 1.53369e10i 0.147706 + 0.0268046i
\(411\) 6.97885e10 − 1.63278e11i 0.120641 − 0.282254i
\(412\) −1.14991e11 + 3.53906e11i −0.196619 + 0.605132i
\(413\) 6.37748e10 + 1.18513e11i 0.107863 + 0.200444i
\(414\) −2.33641e11 − 2.44370e11i −0.390884 − 0.408833i
\(415\) 6.59163e10 − 1.22493e11i 0.109088 − 0.202719i
\(416\) −6.06641e11 + 1.67422e11i −0.993143 + 0.274090i
\(417\) −1.89457e10 − 1.39862e11i −0.0306830 − 0.226511i
\(418\) 2.08095e10 − 1.53622e11i 0.0333402 − 0.246127i
\(419\) −8.85612e11 − 2.44413e11i −1.40372 − 0.387402i −0.519499 − 0.854471i \(-0.673881\pi\)
−0.884221 + 0.467069i \(0.845310\pi\)
\(420\) −3.33881e10 + 3.49212e10i −0.0523563 + 0.0547604i
\(421\) 2.98358e11 + 9.18250e11i 0.462879 + 1.42460i 0.861630 + 0.507536i \(0.169444\pi\)
−0.398751 + 0.917059i \(0.630556\pi\)
\(422\) 5.72760e11 + 5.15493e10i 0.879157 + 0.0791256i
\(423\) 6.93161e11 + 6.05596e11i 1.05269 + 0.919712i
\(424\) −3.79553e10 + 8.45141e11i −0.0570330 + 1.26994i
\(425\) 1.17894e12 1.75283
\(426\) 6.97866e10 + 1.11081e11i 0.102667 + 0.163416i
\(427\) −9.88534e11 −1.43902
\(428\) 1.36195e10 − 3.03262e11i 0.0196185 − 0.436839i
\(429\) 4.84753e10 + 4.23516e10i 0.0690975 + 0.0603687i
\(430\) −4.57879e10 − 4.12099e9i −0.0645866 − 0.00581290i
\(431\) 8.45447e10 + 2.60202e11i 0.118015 + 0.363214i 0.992564 − 0.121724i \(-0.0388422\pi\)
−0.874549 + 0.484938i \(0.838842\pi\)
\(432\) −4.46233e10 + 4.66723e10i −0.0616432 + 0.0644737i
\(433\) −1.57139e11 − 4.33675e10i −0.214826 − 0.0592883i 0.156967 − 0.987604i \(-0.449828\pi\)
−0.371793 + 0.928316i \(0.621257\pi\)
\(434\) 1.17506e11 − 8.67465e11i 0.158985 − 1.17368i
\(435\) −9.06055e9 − 6.68877e10i −0.0121326 − 0.0895662i
\(436\) 2.65481e11 − 7.32681e10i 0.351839 − 0.0971015i
\(437\) −4.14849e11 + 7.70919e11i −0.544156 + 1.01121i
\(438\) −2.33382e10 − 2.44099e10i −0.0302994 − 0.0316907i
\(439\) 5.34651e11 + 9.93548e11i 0.687037 + 1.27673i 0.950099 + 0.311949i \(0.100982\pi\)
−0.263062 + 0.964779i \(0.584732\pi\)
\(440\) 2.34276e10 − 7.21027e10i 0.0297982 − 0.0917096i
\(441\) 3.94588e11 − 9.23183e11i 0.496786 − 1.16229i
\(442\) −1.14918e12 − 2.08546e11i −1.43215 − 0.259897i
\(443\) −1.06493e12 − 7.73717e11i −1.31373 − 0.954477i −0.999988 − 0.00496772i \(-0.998419\pi\)
−0.313738 − 0.949510i \(-0.601581\pi\)
\(444\) 2.14567e11 − 1.93114e10i 0.262023 − 0.0235825i
\(445\) −1.26896e11 − 2.96887e11i −0.153401 − 0.358898i
\(446\) −2.07298e11 − 9.08232e11i −0.248078 − 1.08690i
\(447\) 7.50685e10 + 1.13724e11i 0.0889352 + 0.134731i
\(448\) 8.95766e11 + 5.35195e11i 1.05061 + 0.627713i
\(449\) −5.78689e11 − 7.25652e11i −0.671949 − 0.842597i 0.322636 − 0.946523i \(-0.395431\pi\)
−0.994585 + 0.103926i \(0.966860\pi\)
\(450\) 3.65948e11 − 3.19719e11i 0.420690 − 0.367546i
\(451\) 1.44752e11 − 1.05169e11i 0.164752 − 0.119699i
\(452\) −6.17215e11 + 2.97235e11i −0.695526 + 0.334948i
\(453\) 1.48649e11 − 2.25194e11i 0.165852 − 0.251255i
\(454\) 4.69935e11 + 1.76370e11i 0.519142 + 0.194837i
\(455\) −4.23980e11 + 2.53316e11i −0.463760 + 0.277084i
\(456\) 3.12341e11 + 1.50416e11i 0.338289 + 0.162911i
\(457\) −9.04608e11 + 1.64162e11i −0.970147 + 0.176056i −0.640424 − 0.768022i \(-0.721241\pi\)
−0.329724 + 0.944078i \(0.606956\pi\)
\(458\) 1.89392e11 − 8.29782e11i 0.201126 − 0.881189i
\(459\) 9.50121e11 − 3.56587e11i 0.999130 − 0.374980i
\(460\) −9.38959e10 + 1.17742e11i −0.0977769 + 0.122608i
\(461\) 3.48891e10 + 7.76866e11i 0.0359779 + 0.801110i 0.933163 + 0.359454i \(0.117037\pi\)
−0.897185 + 0.441655i \(0.854391\pi\)
\(462\) −3.80587e9 − 8.47442e10i −0.00388655 − 0.0865408i
\(463\) −1.06915e12 + 1.34068e12i −1.08125 + 1.35584i −0.151159 + 0.988509i \(0.548300\pi\)
−0.930090 + 0.367333i \(0.880271\pi\)
\(464\) −1.51977e11 + 5.70379e10i −0.152211 + 0.0571258i
\(465\) 2.30867e10 − 1.01150e11i 0.0228994 − 0.100329i
\(466\) 6.46028e11 − 1.17237e11i 0.634621 − 0.115167i
\(467\) 1.31671e12 + 6.34094e11i 1.28104 + 0.616918i 0.945658 − 0.325162i \(-0.105419\pi\)
0.335386 + 0.942081i \(0.391133\pi\)
\(468\) 4.90304e11 − 2.92943e11i 0.472453 − 0.282278i
\(469\) 1.00488e12 + 3.77140e11i 0.959044 + 0.359935i
\(470\) −1.90379e11 + 2.88412e11i −0.179961 + 0.272630i
\(471\) 2.62690e11 − 1.26505e11i 0.245952 − 0.118444i
\(472\) 1.34394e11 − 9.76428e10i 0.124635 − 0.0905527i
\(473\) −7.21184e10 + 6.30080e10i −0.0662477 + 0.0578789i
\(474\) 1.41863e11 + 1.77890e11i 0.129082 + 0.161864i
\(475\) −1.08018e12 − 6.45379e11i −0.973590 − 0.581693i
\(476\) −1.00599e12 − 1.52401e12i −0.898176 − 1.36068i
\(477\) −2.81604e11 − 1.23379e12i −0.249061 − 1.09121i
\(478\) 3.94894e11 + 9.23902e11i 0.345984 + 0.809469i
\(479\) 6.06763e11 − 5.46096e10i 0.526634 − 0.0473979i 0.176867 − 0.984235i \(-0.443404\pi\)
0.349767 + 0.936837i \(0.386261\pi\)
\(480\) 7.95213e10 + 5.77756e10i 0.0683751 + 0.0496774i
\(481\) 2.16688e12 + 3.93231e11i 1.84579 + 0.334962i
\(482\) 5.66155e11 − 1.32458e12i 0.477775 − 1.11781i
\(483\) −1.48034e11 + 4.55601e11i −0.123765 + 0.380910i
\(484\) 2.84107e11 + 5.27959e11i 0.235330 + 0.437317i
\(485\) 4.04152e11 + 4.22710e11i 0.331671 + 0.346900i
\(486\) 3.01535e11 − 5.60345e11i 0.245174 − 0.455609i
\(487\) 1.47592e12 − 4.07329e11i 1.18900 − 0.328144i 0.385084 − 0.922882i \(-0.374173\pi\)
0.803920 + 0.594738i \(0.202744\pi\)
\(488\) 1.63788e11 + 1.20913e12i 0.130735 + 0.965127i
\(489\) −2.81779e10 + 2.08017e11i −0.0222853 + 0.164517i
\(490\) 3.63358e11 + 1.00280e11i 0.284743 + 0.0785840i
\(491\) −2.29814e11 + 2.40366e11i −0.178447 + 0.186641i −0.805969 − 0.591958i \(-0.798355\pi\)
0.627522 + 0.778599i \(0.284069\pi\)
\(492\) 4.34920e10 + 1.33854e11i 0.0334631 + 0.102989i
\(493\) 2.54092e12 + 2.28687e11i 1.93722 + 0.174353i
\(494\) 9.38758e11 + 8.20168e11i 0.709222 + 0.619629i
\(495\) −5.08806e9 + 1.13295e11i −0.00380916 + 0.0848175i
\(496\) −2.49511e11 −0.185107
\(497\) −1.03485e12 + 1.82351e12i −0.760804 + 1.34061i
\(498\) −1.92118e11 −0.139970
\(499\) 5.11769e10 − 1.13954e12i 0.0369506 − 0.822768i −0.891882 − 0.452268i \(-0.850615\pi\)
0.928832 − 0.370500i \(-0.120814\pi\)
\(500\) −3.44275e11 − 3.00784e11i −0.246343 − 0.215223i
\(501\) 4.52103e10 + 4.06900e9i 0.0320603 + 0.00288548i
\(502\) 2.09078e11 + 6.43475e11i 0.146940 + 0.452236i
\(503\) 1.77192e12 − 1.85329e12i 1.23421 − 1.29088i 0.291778 − 0.956486i \(-0.405753\pi\)
0.942433 − 0.334396i \(-0.108532\pi\)
\(504\) −2.06269e12 − 5.69265e11i −1.42395 − 0.392986i
\(505\) −7.04657e10 + 5.20199e11i −0.0482133 + 0.355925i
\(506\) −3.54937e10 − 2.62025e11i −0.0240699 − 0.177691i
\(507\) −8.96952e10 + 2.47543e10i −0.0602884 + 0.0166385i
\(508\) −1.15816e11 + 2.15222e11i −0.0771580 + 0.143384i
\(509\) −1.23047e12 − 1.28697e12i −0.812533 − 0.849843i 0.178433 − 0.983952i \(-0.442897\pi\)
−0.990967 + 0.134109i \(0.957183\pi\)
\(510\) 8.64445e10 + 1.60641e11i 0.0565811 + 0.105145i
\(511\) 1.66797e11 − 5.13347e11i 0.108216 − 0.333056i
\(512\) 1.96783e11 − 4.60398e11i 0.126553 − 0.296086i
\(513\) −1.06574e12 − 1.93403e11i −0.679395 − 0.123292i
\(514\) −4.95057e11 − 3.59680e11i −0.312839 − 0.227291i
\(515\) 5.91753e11 − 5.32587e10i 0.370688 − 0.0333625i
\(516\) −2.96066e10 − 6.92682e10i −0.0183851 − 0.0430140i
\(517\) 1.60187e11 + 7.01826e11i 0.0986098 + 0.432038i
\(518\) −1.59884e12 − 2.42214e12i −0.975711 − 1.47814i
\(519\) 5.83391e11 + 3.48560e11i 0.352945 + 0.210875i
\(520\) 3.80093e11 + 4.76622e11i 0.227969 + 0.285864i
\(521\) −1.25761e12 + 1.09874e12i −0.747786 + 0.653321i −0.945012 − 0.327037i \(-0.893950\pi\)
0.197225 + 0.980358i \(0.436807\pi\)
\(522\) 8.50732e11 − 6.18093e11i 0.501505 − 0.364365i
\(523\) −3.00250e11 + 1.44593e11i −0.175479 + 0.0845062i −0.519561 − 0.854433i \(-0.673904\pi\)
0.344082 + 0.938940i \(0.388190\pi\)
\(524\) 3.07734e10 − 4.66197e10i 0.0178314 − 0.0270134i
\(525\) −6.44634e11 − 2.41935e11i −0.370336 − 0.138990i
\(526\) −1.35824e12 + 8.11508e11i −0.773641 + 0.462229i
\(527\) 3.53305e12 + 1.70143e12i 1.99527 + 0.960872i
\(528\) −2.37904e10 + 4.31731e9i −0.0133214 + 0.00241747i
\(529\) 6.85232e10 − 3.00220e11i 0.0380441 − 0.166682i
\(530\) 4.44840e11 − 1.66951e11i 0.244885 − 0.0919069i
\(531\) −1.54936e11 + 1.94284e11i −0.0845720 + 0.106050i
\(532\) 8.74421e10 + 1.94705e12i 0.0473280 + 1.05384i
\(533\) 6.45490e10 + 1.43730e12i 0.0346431 + 0.771389i
\(534\) −2.78028e11 + 3.48636e11i −0.147963 + 0.185540i
\(535\) −4.53787e11 + 1.70309e11i −0.239475 + 0.0898764i
\(536\) 2.94804e11 − 1.29162e12i 0.154273 − 0.675916i
\(537\) 7.05378e11 − 1.28007e11i 0.366048 − 0.0664279i
\(538\) 1.82817e11 + 8.80401e10i 0.0940799 + 0.0453065i
\(539\) 6.74056e11 − 4.02730e11i 0.343991 − 0.205525i
\(540\) −1.74444e11 − 6.54700e10i −0.0882845 − 0.0331337i
\(541\) −1.87912e12 + 2.84675e12i −0.943120 + 1.42877i −0.0400860 + 0.999196i \(0.512763\pi\)
−0.903034 + 0.429569i \(0.858665\pi\)
\(542\) −1.45311e12 + 6.99779e11i −0.723270 + 0.348308i
\(543\) −2.31216e11 + 1.67989e11i −0.114135 + 0.0829240i
\(544\) −2.79776e12 + 2.44433e12i −1.36967 + 1.19664i
\(545\) −2.74166e11 − 3.43794e11i −0.133116 − 0.166922i
\(546\) 5.85568e11 + 3.49861e11i 0.281975 + 0.168472i
\(547\) −6.60076e11 − 9.99972e11i −0.315247 − 0.477579i 0.642059 − 0.766655i \(-0.278080\pi\)
−0.957306 + 0.289077i \(0.906652\pi\)
\(548\) −2.74195e11 − 1.20133e12i −0.129882 − 0.569049i
\(549\) −7.17370e11 − 1.67837e12i −0.337029 − 0.788520i
\(550\) 3.78521e11 − 3.40675e10i 0.176383 − 0.0158748i
\(551\) −2.20289e12 − 1.60049e12i −1.01815 − 0.739727i
\(552\) 5.81798e11 + 1.05581e11i 0.266715 + 0.0484015i
\(553\) −1.42927e12 + 3.34394e12i −0.649906 + 1.52053i
\(554\) 5.80682e10 − 1.78716e11i 0.0261905 − 0.0806062i
\(555\) −1.62999e11 − 3.02902e11i −0.0729231 − 0.135514i
\(556\) −6.76851e11 − 7.07930e11i −0.300370 − 0.314162i
\(557\) 1.42845e12 − 2.65450e12i 0.628805 − 1.16852i −0.344454 − 0.938803i \(-0.611936\pi\)
0.973259 − 0.229712i \(-0.0737784\pi\)
\(558\) 1.55809e12 − 4.30005e11i 0.680359 − 0.187767i
\(559\) −1.03368e11 − 7.63093e11i −0.0447747 − 0.330540i
\(560\) 2.49025e10 − 1.83838e11i 0.0107003 − 0.0789931i
\(561\) 3.66309e11 + 1.01095e11i 0.156140 + 0.0430919i
\(562\) 8.47535e10 − 8.86452e10i 0.0358380 − 0.0374837i
\(563\) 5.96146e11 + 1.83475e12i 0.250072 + 0.769642i 0.994761 + 0.102230i \(0.0325978\pi\)
−0.744689 + 0.667412i \(0.767402\pi\)
\(564\) −5.63980e11 − 5.07591e10i −0.234697 − 0.0211231i
\(565\) 8.23709e11 + 7.19653e11i 0.340060 + 0.297102i
\(566\) −8.10564e10 + 1.80486e12i −0.0331981 + 0.739213i
\(567\) 2.89199e12 1.17509
\(568\) 2.40189e12 + 9.63649e11i 0.968248 + 0.388464i
\(569\) 3.95185e12 1.58050 0.790251 − 0.612783i \(-0.209950\pi\)
0.790251 + 0.612783i \(0.209950\pi\)
\(570\) 8.73530e9 − 1.94507e11i 0.00346610 − 0.0771787i
\(571\) −1.23421e12 − 1.07830e12i −0.485878 − 0.424499i 0.379824 − 0.925059i \(-0.375985\pi\)
−0.865702 + 0.500560i \(0.833127\pi\)
\(572\) 4.44895e11 + 4.00413e10i 0.173770 + 0.0156396i
\(573\) 2.67665e11 + 8.23787e11i 0.103728 + 0.319241i
\(574\) 1.31028e12 − 1.37045e12i 0.503803 − 0.526937i
\(575\) −2.06887e12 − 5.70971e11i −0.789273 − 0.217825i
\(576\) −2.58626e11 + 1.90925e12i −0.0978973 + 0.722707i
\(577\) −1.88849e11 − 1.39414e12i −0.0709288 − 0.523617i −0.991204 − 0.132345i \(-0.957749\pi\)
0.920275 − 0.391272i \(-0.127965\pi\)
\(578\) −4.89710e12 + 1.35151e12i −1.82500 + 0.503669i
\(579\) −5.48465e10 + 1.01922e11i −0.0202813 + 0.0376890i
\(580\) −3.23696e11 − 3.38560e11i −0.118771 − 0.124225i
\(581\) −1.45506e12 − 2.70395e12i −0.529769 − 0.984476i
\(582\) 2.49599e11 − 7.68186e11i 0.0901756 − 0.277532i
\(583\) 3.88997e11 − 9.10104e11i 0.139456 − 0.326274i
\(584\) −6.55540e11 − 1.18963e11i −0.233207 − 0.0423208i
\(585\) −7.37768e11 − 5.36020e11i −0.260446 − 0.189225i
\(586\) −1.64190e12 + 1.47773e11i −0.575183 + 0.0517675i
\(587\) −1.36113e12 − 3.18451e12i −0.473181 − 1.10706i −0.970849 − 0.239694i \(-0.922953\pi\)
0.497668 − 0.867368i \(-0.334190\pi\)
\(588\) 1.37440e11 + 6.02162e11i 0.0474148 + 0.207738i
\(589\) −2.30570e12 − 3.49298e12i −0.789375 − 1.19585i
\(590\) −8.00919e10 − 4.78527e10i −0.0272116 − 0.0162582i
\(591\) −4.18767e10 − 5.25118e10i −0.0141198 − 0.0177057i
\(592\) −6.22961e11 + 5.44264e11i −0.208455 + 0.182122i
\(593\) −3.72759e12 + 2.70826e12i −1.23789 + 0.899381i −0.997456 − 0.0712844i \(-0.977290\pi\)
−0.240435 + 0.970665i \(0.577290\pi\)
\(594\) 2.94751e11 − 1.41945e11i 0.0971440 − 0.0467821i
\(595\) −1.60622e12 + 2.43331e12i −0.525385 + 0.795924i
\(596\) 8.85315e11 + 3.32264e11i 0.287402 + 0.107864i
\(597\) −6.16557e11 + 3.68376e11i −0.198650 + 0.118688i
\(598\) 1.91565e12 + 9.22529e11i 0.612578 + 0.295002i
\(599\) −2.09342e12 + 3.79899e11i −0.664409 + 0.120572i −0.500276 − 0.865866i \(-0.666768\pi\)
−0.164133 + 0.986438i \(0.552482\pi\)
\(600\) −1.89117e11 + 8.28574e11i −0.0595730 + 0.261006i
\(601\) −4.22049e12 + 1.58398e12i −1.31956 + 0.495238i −0.909076 − 0.416631i \(-0.863211\pi\)
−0.410481 + 0.911869i \(0.634639\pi\)
\(602\) −6.32730e11 + 7.93418e11i −0.196352 + 0.246217i
\(603\) 8.89138e10 + 1.97982e12i 0.0273868 + 0.609814i
\(604\) −8.40085e10 − 1.87059e12i −0.0256837 − 0.571891i
\(605\) 5.96849e11 − 7.48424e11i 0.181119 − 0.227117i
\(606\) 6.78789e11 − 2.54754e11i 0.204460 − 0.0767351i
\(607\) 6.85109e11 − 3.00166e12i 0.204838 − 0.897453i −0.763103 − 0.646276i \(-0.776325\pi\)
0.967941 − 0.251177i \(-0.0808176\pi\)
\(608\) 3.90149e12 − 7.08016e11i 1.15788 − 0.210125i
\(609\) −1.34243e12 − 6.46479e11i −0.395469 − 0.190448i
\(610\) 5.88287e11 − 3.51485e11i 0.172030 − 0.102783i
\(611\) −5.41947e12 − 2.03396e12i −1.57316 − 0.590415i
\(612\) 1.85748e12 − 2.81396e12i 0.535233 − 0.810843i
\(613\) 6.00043e12 − 2.88965e12i 1.71637 − 0.826559i 0.726066 − 0.687625i \(-0.241347\pi\)
0.990302 − 0.138934i \(-0.0443674\pi\)
\(614\) −2.54542e12 + 1.84935e12i −0.722772 + 0.525125i
\(615\) 1.69229e11 − 1.47851e11i 0.0477019 − 0.0416759i
\(616\) −1.04342e12 − 1.30841e12i −0.291977 − 0.366127i
\(617\) −1.60698e12 − 9.60128e11i −0.446404 − 0.266714i 0.272057 − 0.962281i \(-0.412296\pi\)
−0.718461 + 0.695567i \(0.755153\pi\)
\(618\) −4.52059e11 − 6.84840e11i −0.124666 − 0.188861i
\(619\) 5.98737e11 + 2.62324e12i 0.163919 + 0.718175i 0.988348 + 0.152210i \(0.0486390\pi\)
−0.824429 + 0.565965i \(0.808504\pi\)
\(620\) −2.82968e11 − 6.62036e11i −0.0769085 − 0.179936i
\(621\) −1.84003e12 + 1.65605e11i −0.496491 + 0.0446850i
\(622\) −8.29734e11 − 6.02837e11i −0.222271 − 0.161489i
\(623\) −7.01257e12 − 1.27259e12i −1.86501 − 0.338449i
\(624\) 7.64140e10 − 1.78779e11i 0.0201763 − 0.0472049i
\(625\) 8.34483e11 − 2.56828e12i 0.218755 − 0.673258i
\(626\) 1.27073e12 + 2.36141e12i 0.330725 + 0.614591i
\(627\) −2.80283e11 − 2.93153e11i −0.0724257 − 0.0757513i
\(628\) 9.58778e11 − 1.78171e12i 0.245980 − 0.457107i
\(629\) 1.25324e13 − 3.45873e12i 3.19232 − 0.881025i
\(630\) 1.61319e11 + 1.19091e12i 0.0407994 + 0.301193i
\(631\) −3.59536e11 + 2.65420e12i −0.0902839 + 0.666502i 0.888092 + 0.459666i \(0.152031\pi\)
−0.978376 + 0.206836i \(0.933683\pi\)
\(632\) 4.32697e12 + 1.19417e12i 1.07884 + 0.297741i
\(633\) 1.03973e12 − 1.08747e12i 0.257396 − 0.269216i
\(634\) −1.12345e12 − 3.45763e12i −0.276155 − 0.849919i
\(635\) 3.88659e11 + 3.49800e10i 0.0948609 + 0.00853764i
\(636\) 5.86302e11 + 5.12237e11i 0.142090 + 0.124141i
\(637\) −2.83272e11 + 6.30754e12i −0.0681673 + 1.51786i
\(638\) 8.22420e11 0.196517
\(639\) −3.84700e12 − 4.33704e11i −0.912784 − 0.102906i
\(640\) 5.33665e11 0.125736
\(641\) −1.40617e10 + 3.13109e11i −0.00328986 + 0.0732544i −0.999966 − 0.00820745i \(-0.997387\pi\)
0.996676 + 0.0814619i \(0.0259589\pi\)
\(642\) 5.04122e11 + 4.40438e11i 0.117119 + 0.102324i
\(643\) −6.21271e12 − 5.59154e11i −1.43328 − 0.128998i −0.654391 − 0.756156i \(-0.727075\pi\)
−0.778892 + 0.627158i \(0.784218\pi\)
\(644\) 1.02727e12 + 3.16162e12i 0.235342 + 0.724309i
\(645\) −8.31185e10 + 8.69351e10i −0.0189094 + 0.0197777i
\(646\) 7.09383e12 + 1.95777e12i 1.60263 + 0.442299i
\(647\) −3.18784e11 + 2.35336e12i −0.0715199 + 0.527981i 0.919379 + 0.393373i \(0.128692\pi\)
−0.990899 + 0.134608i \(0.957022\pi\)
\(648\) −4.79167e11 − 3.53736e12i −0.106758 − 0.788118i
\(649\) −1.87345e11 + 5.17039e10i −0.0414515 + 0.0114399i
\(650\) −1.44816e12 + 2.69112e12i −0.318204 + 0.591321i
\(651\) −1.58269e12 − 1.65536e12i −0.345367 − 0.361225i
\(652\) 6.90290e11 + 1.28277e12i 0.149595 + 0.277994i
\(653\) 8.51945e11 − 2.62202e12i 0.183359 − 0.564321i −0.816557 − 0.577264i \(-0.804120\pi\)
0.999916 + 0.0129436i \(0.00412019\pi\)
\(654\) −2.38692e11 + 5.58447e11i −0.0510197 + 0.119366i
\(655\) −8.77568e10 − 1.59255e10i −0.0186292 − 0.00338071i
\(656\) −4.37214e11 − 3.17655e11i −0.0921779 − 0.0669712i
\(657\) 9.92623e11 − 8.93377e10i 0.207845 − 0.0187064i
\(658\) 2.99817e12 + 7.01456e12i 0.623504 + 1.45876i
\(659\) −5.54991e11 − 2.43158e12i −0.114631 − 0.502231i −0.999348 − 0.0361027i \(-0.988506\pi\)
0.884717 − 0.466128i \(-0.154351\pi\)
\(660\) −3.84357e10 − 5.82276e10i −0.00788473 − 0.0119449i
\(661\) 4.77437e12 + 2.85255e12i 0.972768 + 0.581202i 0.909015 − 0.416764i \(-0.136836\pi\)
0.0637535 + 0.997966i \(0.479693\pi\)
\(662\) −8.91022e11 − 1.11731e12i −0.180313 − 0.226105i
\(663\) −2.30112e12 + 2.01043e12i −0.462517 + 0.404089i
\(664\) −3.06626e12 + 2.22777e12i −0.612143 + 0.444748i
\(665\) 2.80373e12 − 1.35020e12i 0.555953 − 0.267733i
\(666\) 2.95214e12 − 4.47230e12i 0.581437 − 0.880840i
\(667\) −4.34820e12 − 1.63191e12i −0.850634 − 0.319248i
\(668\) 2.70414e11 − 1.61565e11i 0.0525454 − 0.0313944i
\(669\) −2.19590e12 − 1.05749e12i −0.423832 − 0.204107i
\(670\) −7.32114e11 + 1.32859e11i −0.140360 + 0.0254715i
\(671\) 3.17653e11 − 1.39173e12i 0.0604925 − 0.265035i
\(672\) 2.03141e12 − 7.62400e11i 0.384269 − 0.144219i
\(673\) −3.86350e12 + 4.84468e12i −0.725961 + 0.910327i −0.998659 − 0.0517730i \(-0.983513\pi\)
0.272697 + 0.962100i \(0.412084\pi\)
\(674\) 5.70098e10 + 1.26942e12i 0.0106409 + 0.236939i
\(675\) −1.19133e11 − 2.65270e12i −0.0220885 − 0.491838i
\(676\) −4.02591e11 + 5.04833e11i −0.0741488 + 0.0929796i
\(677\) 3.03678e12 − 1.13972e12i 0.555603 − 0.208521i −0.0577486 − 0.998331i \(-0.518392\pi\)
0.613352 + 0.789810i \(0.289821\pi\)
\(678\) 3.36156e11 − 1.47280e12i 0.0610953 − 0.267676i
\(679\) 1.27022e13 − 2.30510e12i 2.29332 − 0.416176i
\(680\) 3.24245e12 + 1.56148e12i 0.581545 + 0.280057i
\(681\) 1.12731e12 − 6.73539e11i 0.200855 − 0.120005i
\(682\) 1.18352e12 + 4.44182e11i 0.209482 + 0.0786198i
\(683\) −3.46901e11 + 5.25532e11i −0.0609975 + 0.0924072i −0.863792 − 0.503848i \(-0.831917\pi\)
0.802795 + 0.596256i \(0.203346\pi\)
\(684\) −3.24232e12 + 1.56142e12i −0.566374 + 0.272751i
\(685\) −1.59169e12 + 1.15643e12i −0.276217 + 0.200684i
\(686\) 1.71246e12 − 1.49613e12i 0.295231 − 0.257936i
\(687\) −1.38835e12 − 1.74093e12i −0.237790 − 0.298179i
\(688\) 2.48309e11 + 1.48358e11i 0.0422518 + 0.0252443i
\(689\) 4.38442e12 + 6.64212e12i 0.741184 + 1.12285i
\(690\) −7.38979e10 − 3.23768e11i −0.0124111 − 0.0543767i
\(691\) 3.40604e11 + 7.96882e11i 0.0568327 + 0.132967i 0.945538 − 0.325513i \(-0.105537\pi\)
−0.888705 + 0.458480i \(0.848394\pi\)
\(692\) 4.69699e12 − 4.22736e11i 0.778649 − 0.0700797i
\(693\) 2.02531e12 + 1.47147e12i 0.333573 + 0.242355i
\(694\) −1.65603e12 − 3.00526e11i −0.270989 − 0.0491772i
\(695\) −6.14620e11 + 1.43798e12i −0.0999252 + 0.233787i
\(696\) −5.68321e11 + 1.74911e12i −0.0918020 + 0.282537i
\(697\) 4.02480e12 + 7.47933e12i 0.645947 + 1.20037i
\(698\) −4.91180e12 − 5.13734e12i −0.783234 − 0.819198i
\(699\) 8.13996e11 − 1.51266e12i 0.128966 − 0.239659i
\(700\) −4.60590e12 + 1.27115e12i −0.725059 + 0.200104i
\(701\) −8.40463e10 − 6.20455e11i −0.0131458 − 0.0970463i 0.983188 − 0.182595i \(-0.0584498\pi\)
−0.996334 + 0.0855491i \(0.972736\pi\)
\(702\) −3.53119e11 + 2.60683e12i −0.0548787 + 0.405131i
\(703\) −1.33760e13 − 3.69155e12i −2.06551 − 0.570045i
\(704\) −1.04133e12 + 1.08914e12i −0.159776 + 0.167112i
\(705\) 2.79389e11 + 8.59870e11i 0.0425949 + 0.131094i
\(706\) 2.50015e12 + 2.25018e11i 0.378744 + 0.0340875i
\(707\) 8.72651e12 + 7.62412e12i 1.31357 + 1.14763i
\(708\) 6.85877e9 − 1.52722e11i 0.00102588 − 0.0228430i
\(709\) 6.62763e12 0.985032 0.492516 − 0.870303i \(-0.336077\pi\)
0.492516 + 0.870303i \(0.336077\pi\)
\(710\) −3.25201e10 − 1.45314e12i −0.00480275 − 0.214607i
\(711\) −6.71468e12 −0.985398
\(712\) −3.94684e11 + 8.78833e12i −0.0575559 + 1.28158i
\(713\) −5.37598e12 − 4.69685e12i −0.779031 − 0.680619i
\(714\) 4.01064e12 + 3.60964e11i 0.577527 + 0.0519783i
\(715\) −2.20396e11 − 6.78309e11i −0.0315374 − 0.0970622i
\(716\) 3.43796e12 − 3.59583e12i 0.488869 − 0.511317i
\(717\) 2.53395e12 + 6.99327e11i 0.358065 + 0.0988198i
\(718\) −5.85202e11 + 4.32013e12i −0.0821761 + 0.606649i
\(719\) 1.76276e12 + 1.30132e13i 0.245988 + 1.81595i 0.519930 + 0.854209i \(0.325958\pi\)
−0.273943 + 0.961746i \(0.588328\pi\)
\(720\) 3.30199e11 − 9.11291e10i 0.0457909 − 0.0126375i
\(721\) 6.21494e12 − 1.15493e13i 0.856502 − 1.59165i
\(722\) −2.01540e12 − 2.10795e12i −0.276022 − 0.288697i
\(723\) −1.78587e12 − 3.31871e12i −0.243068 − 0.451696i
\(724\) −6.12871e11 + 1.88622e12i −0.0828983 + 0.255135i
\(725\) 2.62358e12 − 6.13818e12i 0.352675 − 0.825123i
\(726\) −1.30086e12 − 2.36072e11i −0.173787 − 0.0315376i
\(727\) 1.49324e12 + 1.08490e12i 0.198256 + 0.144041i 0.682484 − 0.730900i \(-0.260900\pi\)
−0.484228 + 0.874942i \(0.660900\pi\)
\(728\) 1.34028e13 − 1.20627e12i 1.76850 − 0.159168i
\(729\) 1.63045e12 + 3.81462e12i 0.213812 + 0.500238i
\(730\) 8.32642e10 + 3.64804e11i 0.0108519 + 0.0475453i
\(731\) −2.50437e12 − 3.79396e12i −0.324392 − 0.491434i
\(732\) 9.63952e11 + 5.75934e11i 0.124095 + 0.0741435i
\(733\) −5.30988e11 − 6.65837e11i −0.0679386 − 0.0851923i 0.746701 − 0.665160i \(-0.231637\pi\)
−0.814640 + 0.579968i \(0.803065\pi\)
\(734\) −3.37180e12 + 2.94586e12i −0.428775 + 0.374610i
\(735\) 7.97829e11 − 5.79656e11i 0.100836 − 0.0732618i
\(736\) 6.09348e12 − 2.93447e12i 0.765447 − 0.368620i
\(737\) −8.53871e11 + 1.29356e12i −0.106608 + 0.161504i
\(738\) 3.27766e12 + 1.23012e12i 0.406733 + 0.152650i
\(739\) −4.78376e12 + 2.85817e12i −0.590024 + 0.352523i −0.776673 − 0.629904i \(-0.783094\pi\)
0.186649 + 0.982427i \(0.440237\pi\)
\(740\) −2.15061e12 − 1.03568e12i −0.263644 − 0.126964i
\(741\) 3.20892e12 − 5.82333e11i 0.391000 − 0.0709561i
\(742\) 2.33387e12 − 1.02253e13i 0.282656 − 1.23840i
\(743\) −3.15578e12 + 1.18439e12i −0.379890 + 0.142575i −0.534012 − 0.845477i \(-0.679316\pi\)
0.154123 + 0.988052i \(0.450745\pi\)
\(744\) −1.76253e12 + 2.21015e12i −0.210892 + 0.264450i
\(745\) −6.77377e10 − 1.50830e12i −0.00805614 − 0.179384i
\(746\) −1.70645e11 − 3.79970e12i −0.0201729 − 0.449185i
\(747\) 3.53494e12 − 4.43268e12i 0.415374 − 0.520863i
\(748\) 2.46887e12 − 9.26581e11i 0.288363 − 0.108225i
\(749\) −2.38081e12 + 1.04310e13i −0.276412 + 1.21104i
\(750\) 9.91920e11 − 1.80007e11i 0.114472 − 0.0207737i
\(751\) −8.36686e10 − 4.02927e10i −0.00959804 − 0.00462217i 0.429079 − 0.903267i \(-0.358838\pi\)
−0.438677 + 0.898645i \(0.644553\pi\)
\(752\) 1.86655e12 − 1.11521e12i