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Properties

Label 71.10.g.a.2.14
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 2.14
Character \(\chi\) \(=\) 71.2
Dual form 71.10.g.a.36.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.21648 + 27.0870i) q^{2} +(-47.8440 - 41.8000i) q^{3} +(-222.290 - 20.0064i) q^{4} +(598.391 + 1841.66i) q^{5} +(1190.44 - 1245.10i) q^{6} +(1606.04 + 443.240i) q^{7} +(-1051.17 + 7760.08i) q^{8} +(-2100.31 - 15505.1i) q^{9} +O(q^{10})\) \(q+(-1.21648 + 27.0870i) q^{2} +(-47.8440 - 41.8000i) q^{3} +(-222.290 - 20.0064i) q^{4} +(598.391 + 1841.66i) q^{5} +(1190.44 - 1245.10i) q^{6} +(1606.04 + 443.240i) q^{7} +(-1051.17 + 7760.08i) q^{8} +(-2100.31 - 15505.1i) q^{9} +(-50613.0 + 13968.3i) q^{10} +(-930.745 + 1729.61i) q^{11} +(9798.95 + 10248.9i) q^{12} +(56675.3 + 105320. i) q^{13} +(-13959.8 + 42963.8i) q^{14} +(48351.9 - 113125. i) q^{15} +(-321355. - 58317.3i) q^{16} +(462161. + 335780. i) q^{17} +(422543. - 38029.5i) q^{18} +(216695. + 506982. i) q^{19} +(-96171.1 - 421353. i) q^{20} +(-58312.0 - 88339.0i) q^{21} +(-45717.9 - 27315.2i) q^{22} +(-305530. - 383122. i) q^{23} +(374664. - 327334. i) q^{24} +(-1.45352e6 + 1.05604e6i) q^{25} +(-2.92176e6 + 1.40705e6i) q^{26} +(-1.23652e6 + 1.87325e6i) q^{27} +(-348139. - 130659. i) q^{28} +(-227822. + 136117. i) q^{29} +(3.00540e6 + 1.44733e6i) q^{30} +(-1.44977e6 + 263095. i) q^{31} +(1.07838e6 - 4.72469e6i) q^{32} +(116828. - 43846.5i) q^{33} +(-9.65749e6 + 1.21101e7i) q^{34} +(144746. + 3.22301e6i) q^{35} +(156675. + 3.48864e6i) q^{36} +(-3.32671e6 + 4.17157e6i) q^{37} +(-1.39963e7 + 5.25289e6i) q^{38} +(1.69082e6 - 7.40797e6i) q^{39} +(-1.49204e7 + 2.70766e6i) q^{40} +(-2.22245e7 - 1.07028e7i) q^{41} +(2.46378e6 - 1.47204e6i) q^{42} +(3.19526e6 + 1.19920e6i) q^{43} +(241498. - 365854. i) q^{44} +(2.72983e7 - 1.31462e7i) q^{45} +(1.07493e7 - 7.80984e6i) q^{46} +(3.90210e7 - 3.40916e7i) q^{47} +(1.29372e7 + 1.62228e7i) q^{48} +(-3.22586e7 - 1.92736e7i) q^{49} +(-2.68369e7 - 4.06562e7i) q^{50} +(-8.07602e6 - 3.53834e7i) q^{51} +(-1.04912e7 - 2.45455e7i) q^{52} +(-3.74665e7 + 3.37205e6i) q^{53} +(-4.92366e7 - 3.57725e7i) q^{54} +(-3.74231e6 - 679129. i) q^{55} +(-5.12780e6 + 1.19971e7i) q^{56} +(1.08243e7 - 3.33139e7i) q^{57} +(-3.40988e6 - 6.33661e6i) q^{58} +(-6.14182e7 - 6.42384e7i) q^{59} +(-1.30114e7 + 2.41792e7i) q^{60} +(1.57421e7 - 4.34453e6i) q^{61} +(-5.36285e6 - 3.95901e7i) q^{62} +(3.49929e6 - 2.58328e7i) q^{63} +(-3.45287e7 - 9.52931e6i) q^{64} +(-1.60050e8 + 1.67399e8i) q^{65} +(1.04555e6 + 3.21788e6i) q^{66} +(5.53291e6 + 497971. i) q^{67} +(-9.60159e7 - 8.38865e7i) q^{68} +(-1.39676e6 + 3.11012e7i) q^{69} -8.74779e7 q^{70} +(-2.17915e7 + 2.13011e8i) q^{71} +1.22529e8 q^{72} +(1.55936e6 - 3.47218e7i) q^{73} +(-1.08949e8 - 9.51855e7i) q^{74} +(1.13685e8 + 1.02318e7i) q^{75} +(-3.80261e7 - 1.17032e8i) q^{76} +(-2.26145e6 + 2.36529e6i) q^{77} +(1.98603e8 + 5.48110e7i) q^{78} +(-5.60365e7 + 4.13678e8i) q^{79} +(-8.48952e7 - 6.26722e8i) q^{80} +(-1.59414e8 + 4.39954e7i) q^{81} +(3.16942e8 - 5.88977e8i) q^{82} +(-6.87567e7 - 7.19138e7i) q^{83} +(1.11948e7 + 2.08034e7i) q^{84} +(-3.41838e8 + 1.05207e9i) q^{85} +(-3.63698e7 + 8.50914e7i) q^{86} +(1.65896e7 + 3.01057e6i) q^{87} +(-1.24436e7 - 9.04078e6i) q^{88} +(-5.69864e8 + 5.12887e7i) q^{89} +(3.22883e8 + 7.55422e8i) q^{90} +(4.43408e7 + 1.94270e8i) q^{91} +(6.02512e7 + 9.12767e7i) q^{92} +(8.03603e7 + 4.80130e7i) q^{93} +(8.75974e8 + 1.09844e9i) q^{94} +(-8.04020e8 + 7.02451e8i) q^{95} +(-2.49086e8 + 1.80972e8i) q^{96} +(6.30407e8 - 3.03588e8i) q^{97} +(5.61307e8 - 8.50344e8i) q^{98} +(2.87727e7 + 1.07986e7i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.21648 + 27.0870i −0.0537614 + 1.19709i 0.772951 + 0.634465i \(0.218780\pi\)
−0.826713 + 0.562624i \(0.809792\pi\)
\(3\) −47.8440 − 41.8000i −0.341021 − 0.297941i 0.470341 − 0.882485i \(-0.344131\pi\)
−0.811363 + 0.584543i \(0.801274\pi\)
\(4\) −222.290 − 20.0064i −0.434159 − 0.0390751i
\(5\) 598.391 + 1841.66i 0.428174 + 1.31778i 0.899923 + 0.436050i \(0.143623\pi\)
−0.471749 + 0.881733i \(0.656377\pi\)
\(6\) 1190.44 − 1245.10i 0.374996 − 0.392215i
\(7\) 1606.04 + 443.240i 0.252823 + 0.0697746i 0.390151 − 0.920751i \(-0.372423\pi\)
−0.137328 + 0.990526i \(0.543851\pi\)
\(8\) −1051.17 + 7760.08i −0.0907339 + 0.669824i
\(9\) −2100.31 − 15505.1i −0.106707 − 0.787741i
\(10\) −50613.0 + 13968.3i −1.60052 + 0.441716i
\(11\) −930.745 + 1729.61i −0.0191674 + 0.0356190i −0.889999 − 0.455962i \(-0.849295\pi\)
0.870832 + 0.491581i \(0.163581\pi\)
\(12\) 9798.95 + 10248.9i 0.136416 + 0.142679i
\(13\) 56675.3 + 105320.i 0.550362 + 1.02274i 0.992082 + 0.125592i \(0.0400829\pi\)
−0.441720 + 0.897153i \(0.645631\pi\)
\(14\) −13959.8 + 42963.8i −0.0971186 + 0.298900i
\(15\) 48351.9 − 113125.i 0.246606 − 0.576963i
\(16\) −321355. − 58317.3i −1.22587 − 0.222463i
\(17\) 462161. + 335780.i 1.34206 + 0.975067i 0.999365 + 0.0356211i \(0.0113410\pi\)
0.342699 + 0.939445i \(0.388659\pi\)
\(18\) 422543. − 38029.5i 0.948733 − 0.0853876i
\(19\) 216695. + 506982.i 0.381467 + 0.892487i 0.994723 + 0.102602i \(0.0327168\pi\)
−0.613255 + 0.789885i \(0.710140\pi\)
\(20\) −96171.1 − 421353.i −0.134403 − 0.588859i
\(21\) −58312.0 − 88339.0i −0.0654292 − 0.0991210i
\(22\) −45717.9 − 27315.2i −0.0416087 − 0.0248601i
\(23\) −305530. − 383122.i −0.227656 − 0.285471i 0.654864 − 0.755747i \(-0.272726\pi\)
−0.882520 + 0.470276i \(0.844154\pi\)
\(24\) 374664. − 327334.i 0.230511 − 0.201391i
\(25\) −1.45352e6 + 1.05604e6i −0.744202 + 0.540694i
\(26\) −2.92176e6 + 1.40705e6i −1.25391 + 0.603849i
\(27\) −1.23652e6 + 1.87325e6i −0.447780 + 0.678358i
\(28\) −348139. − 130659.i −0.107039 − 0.0401724i
\(29\) −227822. + 136117.i −0.0598143 + 0.0357374i −0.542495 − 0.840059i \(-0.682520\pi\)
0.482681 + 0.875796i \(0.339663\pi\)
\(30\) 3.00540e6 + 1.44733e6i 0.677418 + 0.326227i
\(31\) −1.44977e6 + 263095.i −0.281950 + 0.0511664i −0.317690 − 0.948195i \(-0.602907\pi\)
0.0357396 + 0.999361i \(0.488621\pi\)
\(32\) 1.07838e6 − 4.72469e6i 0.181801 − 0.796523i
\(33\) 116828. − 43846.5i 0.0171489 − 0.00643609i
\(34\) −9.65749e6 + 1.21101e7i −1.23939 + 1.55415i
\(35\) 144746. + 3.22301e6i 0.0163042 + 0.363041i
\(36\) 156675. + 3.48864e6i 0.0155467 + 0.346175i
\(37\) −3.32671e6 + 4.17157e6i −0.291815 + 0.365924i −0.906029 − 0.423215i \(-0.860902\pi\)
0.614214 + 0.789139i \(0.289473\pi\)
\(38\) −1.39963e7 + 5.25289e6i −1.08889 + 0.408669i
\(39\) 1.69082e6 − 7.40797e6i 0.117033 − 0.512754i
\(40\) −1.49204e7 + 2.70766e6i −0.921533 + 0.167234i
\(41\) −2.22245e7 − 1.07028e7i −1.22830 − 0.591519i −0.296690 − 0.954974i \(-0.595883\pi\)
−0.931612 + 0.363455i \(0.881597\pi\)
\(42\) 2.46378e6 − 1.47204e6i 0.122174 − 0.0729957i
\(43\) 3.19526e6 + 1.19920e6i 0.142527 + 0.0534914i 0.421619 − 0.906773i \(-0.361462\pi\)
−0.279092 + 0.960264i \(0.590033\pi\)
\(44\) 241498. − 365854.i 0.00971353 − 0.0147154i
\(45\) 2.72983e7 − 1.31462e7i 0.992383 − 0.477906i
\(46\) 1.07493e7 − 7.80984e6i 0.353974 − 0.257177i
\(47\) 3.90210e7 − 3.40916e7i 1.16643 − 1.01908i 0.166978 − 0.985961i \(-0.446599\pi\)
0.999451 − 0.0331177i \(-0.0105436\pi\)
\(48\) 1.29372e7 + 1.62228e7i 0.351767 + 0.441102i
\(49\) −3.22586e7 − 1.92736e7i −0.799398 − 0.477618i
\(50\) −2.68369e7 − 4.06562e7i −0.607250 − 0.919945i
\(51\) −8.07602e6 − 3.53834e7i −0.167160 − 0.732375i
\(52\) −1.04912e7 − 2.45455e7i −0.198981 − 0.465540i
\(53\) −3.74665e7 + 3.37205e6i −0.652232 + 0.0587019i −0.410814 − 0.911719i \(-0.634755\pi\)
−0.241418 + 0.970421i \(0.577612\pi\)
\(54\) −4.92366e7 − 3.57725e7i −0.787982 − 0.572502i
\(55\) −3.74231e6 − 679129.i −0.0551451 − 0.0100074i
\(56\) −5.12780e6 + 1.19971e7i −0.0696763 + 0.163016i
\(57\) 1.08243e7 − 3.33139e7i 0.135820 − 0.418012i
\(58\) −3.40988e6 − 6.33661e6i −0.0395651 − 0.0735243i
\(59\) −6.14182e7 − 6.42384e7i −0.659877 − 0.690177i 0.305157 − 0.952302i \(-0.401291\pi\)
−0.965034 + 0.262125i \(0.915577\pi\)
\(60\) −1.30114e7 + 2.41792e7i −0.129611 + 0.240858i
\(61\) 1.57421e7 − 4.34453e6i 0.145572 − 0.0401753i −0.192491 − 0.981299i \(-0.561657\pi\)
0.338063 + 0.941123i \(0.390228\pi\)
\(62\) −5.36285e6 − 3.95901e7i −0.0460928 − 0.340270i
\(63\) 3.49929e6 − 2.58328e7i 0.0279864 − 0.206604i
\(64\) −3.45287e7 − 9.52931e6i −0.257259 − 0.0709989i
\(65\) −1.60050e8 + 1.67399e8i −1.11210 + 1.16317i
\(66\) 1.04555e6 + 3.21788e6i 0.00678263 + 0.0208748i
\(67\) 5.53291e6 + 497971.i 0.0335442 + 0.00301903i 0.106399 − 0.994324i \(-0.466068\pi\)
−0.0728545 + 0.997343i \(0.523211\pi\)
\(68\) −9.60159e7 − 8.38865e7i −0.544569 − 0.475776i
\(69\) −1.39676e6 + 3.11012e7i −0.00741823 + 0.165180i
\(70\) −8.74779e7 −0.435469
\(71\) −2.17915e7 + 2.13011e8i −0.101771 + 0.994808i
\(72\) 1.22529e8 0.537330
\(73\) 1.55936e6 − 3.47218e7i 0.00642677 − 0.143103i −0.993214 − 0.116301i \(-0.962896\pi\)
0.999641 − 0.0268020i \(-0.00853236\pi\)
\(74\) −1.08949e8 − 9.51855e7i −0.422356 − 0.369001i
\(75\) 1.13685e8 + 1.02318e7i 0.414884 + 0.0373402i
\(76\) −3.80261e7 − 1.17032e8i −0.130744 − 0.402387i
\(77\) −2.26145e6 + 2.36529e6i −0.00733126 + 0.00766790i
\(78\) 1.98603e8 + 5.48110e7i 0.607520 + 0.167665i
\(79\) −5.60365e7 + 4.13678e8i −0.161864 + 1.19492i 0.709650 + 0.704554i \(0.248853\pi\)
−0.871514 + 0.490371i \(0.836861\pi\)
\(80\) −8.48952e7 − 6.26722e8i −0.231728 − 1.71068i
\(81\) −1.59414e8 + 4.39954e7i −0.411475 + 0.113560i
\(82\) 3.16942e8 − 5.88977e8i 0.774136 − 1.43859i
\(83\) −6.87567e7 − 7.19138e7i −0.159024 − 0.166326i 0.638483 − 0.769636i \(-0.279562\pi\)
−0.797507 + 0.603310i \(0.793848\pi\)
\(84\) 1.11948e7 + 2.08034e7i 0.0245335 + 0.0455909i
\(85\) −3.41838e8 + 1.05207e9i −0.710290 + 2.18605i
\(86\) −3.63698e7 + 8.50914e7i −0.0716965 + 0.167742i
\(87\) 1.65896e7 + 3.01057e6i 0.0310456 + 0.00563394i
\(88\) −1.24436e7 − 9.04078e6i −0.0221194 − 0.0160707i
\(89\) −5.69864e8 + 5.12887e7i −0.962756 + 0.0866496i −0.559852 − 0.828593i \(-0.689142\pi\)
−0.402904 + 0.915242i \(0.631999\pi\)
\(90\) 3.22883e8 + 7.55422e8i 0.518745 + 1.21366i
\(91\) 4.43408e7 + 1.94270e8i 0.0677824 + 0.296974i
\(92\) 6.02512e7 + 9.12767e7i 0.0876840 + 0.132836i
\(93\) 8.03603e7 + 4.80130e7i 0.111396 + 0.0665558i
\(94\) 8.75974e8 + 1.09844e9i 1.15722 + 1.45111i
\(95\) −8.04020e8 + 7.02451e8i −1.01277 + 0.884830i
\(96\) −2.49086e8 + 1.80972e8i −0.299315 + 0.217465i
\(97\) 6.30407e8 − 3.03588e8i 0.723017 − 0.348187i −0.0359165 − 0.999355i \(-0.511435\pi\)
0.758933 + 0.651168i \(0.225721\pi\)
\(98\) 5.61307e8 − 8.50344e8i 0.614728 − 0.931274i
\(99\) 2.87727e7 + 1.07986e7i 0.0301039 + 0.0112982i
\(100\) 3.44230e8 − 2.05668e8i 0.344230 − 0.205668i
\(101\) 1.03966e8 + 5.00672e7i 0.0994131 + 0.0478748i 0.482929 − 0.875659i \(-0.339573\pi\)
−0.383516 + 0.923534i \(0.625287\pi\)
\(102\) 9.68256e8 − 1.75712e8i 0.885705 − 0.160732i
\(103\) −5.39110e7 + 2.36199e8i −0.0471965 + 0.206781i −0.993028 − 0.117875i \(-0.962392\pi\)
0.945832 + 0.324657i \(0.105249\pi\)
\(104\) −8.76870e8 + 3.29095e8i −0.734996 + 0.275849i
\(105\) 1.27797e8 − 1.60252e8i 0.102605 − 0.128662i
\(106\) −4.57615e7 − 1.01896e9i −0.0352066 − 0.783936i
\(107\) −3.84344e7 − 8.55809e8i −0.0283461 − 0.631175i −0.962008 − 0.273020i \(-0.911977\pi\)
0.933662 − 0.358155i \(-0.116594\pi\)
\(108\) 3.12343e8 − 3.91666e8i 0.220915 − 0.277018i
\(109\) 1.62468e9 − 6.09751e8i 1.10242 − 0.413746i 0.267190 − 0.963644i \(-0.413905\pi\)
0.835232 + 0.549898i \(0.185333\pi\)
\(110\) 2.29480e7 − 1.00542e8i 0.0149444 − 0.0654757i
\(111\) 3.33535e8 − 6.05276e7i 0.208539 − 0.0378443i
\(112\) −4.90261e8 − 2.36097e8i −0.294406 − 0.141778i
\(113\) −9.17489e7 + 5.48174e7i −0.0529356 + 0.0316276i −0.539123 − 0.842227i \(-0.681244\pi\)
0.486188 + 0.873854i \(0.338387\pi\)
\(114\) 8.89208e8 + 3.33725e8i 0.493096 + 0.185062i
\(115\) 5.22754e8 − 7.91938e8i 0.278713 − 0.422232i
\(116\) 5.33657e7 − 2.56996e7i 0.0273654 − 0.0131785i
\(117\) 1.51397e9 − 1.09996e9i 0.746931 − 0.542677i
\(118\) 1.81474e9 − 1.58549e9i 0.861680 − 0.752827i
\(119\) 5.93420e8 + 7.44125e8i 0.271269 + 0.340161i
\(120\) 8.27032e8 + 4.94129e8i 0.364088 + 0.217533i
\(121\) 1.29686e9 + 1.96466e9i 0.549996 + 0.833208i
\(122\) 9.85307e7 + 4.31691e8i 0.0402673 + 0.176422i
\(123\) 6.15933e8 + 1.44105e9i 0.242639 + 0.567682i
\(124\) 3.27533e8 − 2.94785e7i 0.124411 − 0.0111972i
\(125\) 2.45137e8 + 1.78102e8i 0.0898077 + 0.0652491i
\(126\) 6.95478e8 + 1.26211e8i 0.245819 + 0.0446096i
\(127\) −7.62709e8 + 1.78445e9i −0.260161 + 0.608677i −0.997784 − 0.0665360i \(-0.978805\pi\)
0.737623 + 0.675213i \(0.235948\pi\)
\(128\) 1.06687e9 − 3.28350e9i 0.351292 − 1.08116i
\(129\) −1.02747e8 − 1.90937e8i −0.0326676 − 0.0607066i
\(130\) −4.33965e9 − 4.53892e9i −1.33263 − 1.39382i
\(131\) 1.60833e9 − 2.98878e9i 0.477150 − 0.886694i −0.522275 − 0.852777i \(-0.674916\pi\)
0.999425 − 0.0339162i \(-0.0107979\pi\)
\(132\) −2.68470e7 + 7.40929e6i −0.00769684 + 0.00212419i
\(133\) 1.23306e8 + 9.10283e8i 0.0341706 + 0.252257i
\(134\) −2.02192e7 + 1.49264e8i −0.00541743 + 0.0399931i
\(135\) −4.18981e9 − 1.15631e9i −1.08566 − 0.299622i
\(136\) −3.09149e9 + 3.23344e9i −0.774894 + 0.810476i
\(137\) 1.46747e9 + 4.51642e9i 0.355900 + 1.09535i 0.955486 + 0.295037i \(0.0953319\pi\)
−0.599586 + 0.800310i \(0.704668\pi\)
\(138\) −8.40742e8 − 7.56681e7i −0.197336 − 0.0177606i
\(139\) 4.67898e9 + 4.08790e9i 1.06313 + 0.928825i 0.997615 − 0.0690264i \(-0.0219893\pi\)
0.0655114 + 0.997852i \(0.479132\pi\)
\(140\) 3.23055e7 − 7.19338e8i 0.00710723 − 0.158255i
\(141\) −3.29195e9 −0.701403
\(142\) −5.74333e9 − 8.49392e8i −1.18540 − 0.175312i
\(143\) −2.34914e8 −0.0469782
\(144\) −2.29271e8 + 5.10512e9i −0.0444343 + 0.989407i
\(145\) −3.87008e8 − 3.38119e8i −0.0727050 − 0.0635204i
\(146\) 9.38614e8 + 8.44768e7i 0.170962 + 0.0153868i
\(147\) 7.37742e8 + 2.27054e9i 0.130310 + 0.401052i
\(148\) 8.22952e8 − 8.60740e8i 0.140993 − 0.147467i
\(149\) −5.46989e9 − 1.50959e9i −0.909161 − 0.250912i −0.219982 − 0.975504i \(-0.570600\pi\)
−0.689179 + 0.724591i \(0.742028\pi\)
\(150\) −4.15445e8 + 3.06694e9i −0.0670043 + 0.494646i
\(151\) 2.99821e8 + 2.21337e9i 0.0469316 + 0.346463i 0.999156 + 0.0410654i \(0.0130752\pi\)
−0.952225 + 0.305398i \(0.901211\pi\)
\(152\) −4.16201e9 + 1.14864e9i −0.632421 + 0.174537i
\(153\) 4.23562e9 − 7.87110e9i 0.624893 − 1.16124i
\(154\) −6.13178e7 − 6.41334e7i −0.00878503 − 0.00918842i
\(155\) −1.35206e9 − 2.51255e9i −0.188150 − 0.349641i
\(156\) −5.24059e8 + 1.61289e9i −0.0708467 + 0.218044i
\(157\) −4.42003e9 + 1.03412e10i −0.580600 + 1.35838i 0.329565 + 0.944133i \(0.393098\pi\)
−0.910164 + 0.414247i \(0.864045\pi\)
\(158\) −1.11371e10 − 2.02109e9i −1.42173 − 0.258006i
\(159\) 1.93350e9 + 1.40477e9i 0.239915 + 0.174308i
\(160\) 9.34655e9 − 8.41205e8i 1.12749 − 0.101476i
\(161\) −3.20879e8 − 7.50734e8i −0.0376379 − 0.0880581i
\(162\) −9.97782e8 − 4.37157e9i −0.113820 − 0.498677i
\(163\) −4.52063e8 − 6.84846e8i −0.0501596 − 0.0759886i 0.808628 − 0.588320i \(-0.200210\pi\)
−0.858788 + 0.512332i \(0.828782\pi\)
\(164\) 4.72615e9 + 2.82375e9i 0.510165 + 0.304809i
\(165\) 1.50659e8 + 1.88921e8i 0.0158241 + 0.0198427i
\(166\) 2.03157e9 − 1.77493e9i 0.207657 − 0.181424i
\(167\) 1.06621e10 − 7.74649e9i 1.06077 − 0.770692i 0.0865368 − 0.996249i \(-0.472420\pi\)
0.974230 + 0.225556i \(0.0724200\pi\)
\(168\) 7.46813e8 − 3.59646e8i 0.0723303 − 0.0348324i
\(169\) −2.03830e9 + 3.08789e9i −0.192211 + 0.291187i
\(170\) −2.80816e10 − 1.05392e10i −2.57871 − 0.967805i
\(171\) 7.40569e9 − 4.42469e9i 0.662343 − 0.395732i
\(172\) −6.86282e8 − 3.30496e8i −0.0597895 − 0.0287931i
\(173\) −5.23715e9 + 9.50402e8i −0.444516 + 0.0806677i −0.396200 − 0.918164i \(-0.629671\pi\)
−0.0483162 + 0.998832i \(0.515386\pi\)
\(174\) −1.01728e8 + 4.45701e8i −0.00841339 + 0.0368615i
\(175\) −2.80249e9 + 1.05179e9i −0.225878 + 0.0847734i
\(176\) 3.99966e8 − 5.01541e8i 0.0314207 − 0.0394003i
\(177\) 2.53324e8 + 5.64070e9i 0.0193998 + 0.431970i
\(178\) −6.96031e8 − 1.54983e10i −0.0519683 − 1.15716i
\(179\) 1.11043e10 − 1.39244e10i 0.808450 − 1.01376i −0.191032 − 0.981584i \(-0.561184\pi\)
0.999482 − 0.0321801i \(-0.0102450\pi\)
\(180\) −6.33113e9 + 2.37611e9i −0.449526 + 0.168710i
\(181\) −4.94509e9 + 2.16658e10i −0.342468 + 1.50045i 0.451378 + 0.892333i \(0.350933\pi\)
−0.793846 + 0.608119i \(0.791924\pi\)
\(182\) −5.31613e9 + 9.64736e8i −0.359149 + 0.0651759i
\(183\) −9.34764e8 − 4.50159e8i −0.0616130 − 0.0296713i
\(184\) 3.29422e9 − 1.96821e9i 0.211872 − 0.126587i
\(185\) −9.67327e9 − 3.63044e9i −0.607156 − 0.227870i
\(186\) −1.39829e9 + 2.11832e9i −0.0856620 + 0.129772i
\(187\) −1.01092e9 + 4.86835e8i −0.0604548 + 0.0291135i
\(188\) −9.35602e9 + 6.79755e9i −0.546237 + 0.396864i
\(189\) −2.81620e9 + 2.46044e9i −0.160541 + 0.140260i
\(190\) −1.80492e10 − 2.26330e10i −1.00477 − 1.25995i
\(191\) 1.68454e10 + 1.00647e10i 0.915865 + 0.547204i 0.891761 − 0.452506i \(-0.149470\pi\)
0.0241033 + 0.999709i \(0.492327\pi\)
\(192\) 1.25366e9 + 1.89922e9i 0.0665772 + 0.100860i
\(193\) 5.18334e9 + 2.27097e10i 0.268907 + 1.17816i 0.911287 + 0.411772i \(0.135090\pi\)
−0.642380 + 0.766386i \(0.722053\pi\)
\(194\) 7.45643e9 + 1.74452e10i 0.377940 + 0.884235i
\(195\) 1.46547e10 − 1.31895e9i 0.725808 − 0.0653239i
\(196\) 6.78515e9 + 4.92970e9i 0.328403 + 0.238599i
\(197\) −1.92936e10 − 3.50127e9i −0.912671 − 0.165625i −0.298144 − 0.954521i \(-0.596368\pi\)
−0.614527 + 0.788896i \(0.710653\pi\)
\(198\) −3.27503e8 + 7.66232e8i −0.0151434 + 0.0354296i
\(199\) 8.21945e9 − 2.52969e10i 0.371539 − 1.14348i −0.574246 − 0.818683i \(-0.694705\pi\)
0.945784 − 0.324795i \(-0.105295\pi\)
\(200\) −6.66708e9 − 1.23895e10i −0.294646 − 0.547544i
\(201\) −2.43901e8 − 2.55101e8i −0.0105398 − 0.0110237i
\(202\) −1.48264e9 + 2.75522e9i −0.0626550 + 0.116433i
\(203\) −4.26224e8 + 1.17630e8i −0.0176160 + 0.00486169i
\(204\) 1.08732e9 + 8.02693e9i 0.0439564 + 0.324499i
\(205\) 6.41188e9 − 4.73344e10i 0.253567 − 1.87191i
\(206\) −6.33236e9 − 1.74762e9i −0.244998 − 0.0676153i
\(207\) −5.29864e9 + 5.54195e9i −0.200585 + 0.209795i
\(208\) −1.20709e10 − 3.71503e10i −0.447151 − 1.37619i
\(209\) −1.07857e9 − 9.70732e7i −0.0391013 − 0.00351918i
\(210\) 4.18529e9 + 3.65658e9i 0.148504 + 0.129744i
\(211\) 2.23719e9 − 4.98149e10i 0.0777020 − 1.73017i −0.460765 − 0.887522i \(-0.652425\pi\)
0.538467 − 0.842647i \(-0.319004\pi\)
\(212\) 8.39588e9 0.285466
\(213\) 9.94645e9 − 9.28040e9i 0.331101 − 0.308929i
\(214\) 2.32281e10 0.757097
\(215\) −2.96504e8 + 6.60217e9i −0.00946362 + 0.210724i
\(216\) −1.32368e10 − 1.15646e10i −0.413752 − 0.361484i
\(217\) −2.44501e9 − 2.20055e8i −0.0748535 − 0.00673694i
\(218\) 1.45400e10 + 4.47495e10i 0.436023 + 1.34194i
\(219\) −1.52598e9 + 1.59605e9i −0.0448280 + 0.0468864i
\(220\) 8.18289e8 + 2.25833e8i 0.0235507 + 0.00649959i
\(221\) −9.17132e9 + 6.77054e10i −0.258623 + 1.90923i
\(222\) 1.23378e9 + 9.10810e9i 0.0340916 + 0.251675i
\(223\) 5.06935e10 − 1.39905e10i 1.37272 − 0.378845i 0.499556 − 0.866281i \(-0.333496\pi\)
0.873159 + 0.487436i \(0.162068\pi\)
\(224\) 3.82609e9 − 7.11007e9i 0.101541 − 0.188694i
\(225\) 1.94269e10 + 2.03190e10i 0.505338 + 0.528543i
\(226\) −1.37323e9 − 2.55189e9i −0.0350151 − 0.0650690i
\(227\) 1.96058e10 − 6.03404e10i 0.490081 − 1.50831i −0.334404 − 0.942430i \(-0.608535\pi\)
0.824485 − 0.565884i \(-0.191465\pi\)
\(228\) −3.07263e9 + 7.18878e9i −0.0753015 + 0.176177i
\(229\) 2.36018e10 + 4.28310e9i 0.567135 + 0.102920i 0.454548 − 0.890722i \(-0.349801\pi\)
0.112587 + 0.993642i \(0.464086\pi\)
\(230\) 2.08153e10 + 1.51232e10i 0.490465 + 0.356344i
\(231\) 2.07066e8 − 1.86363e7i 0.00478470 − 0.000430631i
\(232\) −8.16800e8 − 1.91100e9i −0.0185106 − 0.0433076i
\(233\) 1.66409e10 + 7.29088e10i 0.369893 + 1.62061i 0.727064 + 0.686569i \(0.240884\pi\)
−0.357171 + 0.934039i \(0.616259\pi\)
\(234\) 2.79530e10 + 4.23470e10i 0.609477 + 0.923318i
\(235\) 8.61350e10 + 5.14632e10i 1.84236 + 1.10076i
\(236\) 1.23674e10 + 1.55083e10i 0.259523 + 0.325432i
\(237\) 1.99728e10 − 1.74497e10i 0.411216 − 0.359269i
\(238\) −2.08780e10 + 1.51688e10i −0.421787 + 0.306446i
\(239\) −2.89029e10 + 1.39189e10i −0.572996 + 0.275940i −0.697861 − 0.716233i \(-0.745865\pi\)
0.124865 + 0.992174i \(0.460150\pi\)
\(240\) −2.21353e10 + 3.35335e10i −0.430660 + 0.652421i
\(241\) −5.88238e10 − 2.20770e10i −1.12325 − 0.421563i −0.280493 − 0.959856i \(-0.590498\pi\)
−0.842758 + 0.538293i \(0.819069\pi\)
\(242\) −5.47945e10 + 3.27382e10i −1.02699 + 0.613600i
\(243\) 4.92705e10 + 2.37274e10i 0.906481 + 0.436538i
\(244\) −3.58622e9 + 6.50802e8i −0.0647712 + 0.0117542i
\(245\) 1.61921e10 − 7.09424e10i 0.287116 − 1.25794i
\(246\) −3.97830e10 + 1.49308e10i −0.692611 + 0.259941i
\(247\) −4.11143e10 + 5.15557e10i −0.702841 + 0.881334i
\(248\) −5.17674e8 − 1.15269e10i −0.00869008 − 0.193500i
\(249\) 2.83592e8 + 6.31467e9i 0.00467517 + 0.104101i
\(250\) −5.12247e9 + 6.42338e9i −0.0829373 + 0.104000i
\(251\) −8.35214e10 + 3.13461e10i −1.32821 + 0.498485i −0.911778 − 0.410683i \(-0.865290\pi\)
−0.416430 + 0.909168i \(0.636719\pi\)
\(252\) −1.29468e9 + 5.67236e9i −0.0202236 + 0.0886056i
\(253\) 9.47024e8 − 1.71860e8i 0.0145318 − 0.00263713i
\(254\) −4.74076e10 − 2.28303e10i −0.714654 − 0.344159i
\(255\) 6.03314e10 − 3.60464e10i 0.893538 − 0.533864i
\(256\) 7.04723e10 + 2.64487e10i 1.02551 + 0.384879i
\(257\) 2.48815e10 − 3.76939e10i 0.355777 − 0.538979i −0.611977 − 0.790875i \(-0.709626\pi\)
0.967754 + 0.251896i \(0.0810542\pi\)
\(258\) 5.29690e9 − 2.55085e9i 0.0744275 − 0.0358424i
\(259\) −7.19185e9 + 5.22518e9i −0.0993096 + 0.0721527i
\(260\) 3.89265e10 − 3.40091e10i 0.528282 − 0.461546i
\(261\) 2.58901e9 + 3.24652e9i 0.0345344 + 0.0433047i
\(262\) 7.90008e10 + 4.72008e10i 1.03580 + 0.618861i
\(263\) 2.82042e10 + 4.27275e10i 0.363507 + 0.550689i 0.969597 − 0.244707i \(-0.0786917\pi\)
−0.606091 + 0.795396i \(0.707263\pi\)
\(264\) 2.17445e8 + 9.52688e8i 0.00275506 + 0.0120707i
\(265\) −2.86298e10 − 6.69827e10i −0.356625 − 0.834365i
\(266\) −2.48069e10 + 2.23266e9i −0.303812 + 0.0273436i
\(267\) 2.94084e10 + 2.13665e10i 0.354137 + 0.257295i
\(268\) −1.21995e9 − 2.21387e8i −0.0144455 − 0.00262148i
\(269\) 1.24971e10 − 2.92385e10i 0.145521 − 0.340463i −0.830872 − 0.556463i \(-0.812158\pi\)
0.976393 + 0.216000i \(0.0693010\pi\)
\(270\) 3.64179e10 − 1.12083e11i 0.417041 − 1.28352i
\(271\) 4.23916e10 + 7.87767e10i 0.477439 + 0.887230i 0.999413 + 0.0342683i \(0.0109101\pi\)
−0.521974 + 0.852961i \(0.674804\pi\)
\(272\) −1.28936e11 − 1.34856e11i −1.42828 − 1.49387i
\(273\) 5.99904e9 − 1.11481e10i 0.0653657 − 0.121470i
\(274\) −1.24122e11 + 3.42554e10i −1.33036 + 0.367157i
\(275\) −4.73692e8 − 3.49694e9i −0.00499458 − 0.0368715i
\(276\) 9.32710e8 − 6.88554e9i 0.00967510 − 0.0714245i
\(277\) 1.05882e11 + 2.92215e10i 1.08059 + 0.298225i 0.760617 − 0.649201i \(-0.224896\pi\)
0.319976 + 0.947426i \(0.396325\pi\)
\(278\) −1.16421e11 + 1.21767e11i −1.16904 + 1.22272i
\(279\) 7.12429e9 + 2.19263e10i 0.0703919 + 0.216644i
\(280\) −2.51630e10 − 2.26471e9i −0.244653 − 0.0220192i
\(281\) −6.93018e10 − 6.05472e10i −0.663081 − 0.579316i 0.259206 − 0.965822i \(-0.416539\pi\)
−0.922287 + 0.386506i \(0.873682\pi\)
\(282\) 4.00460e9 − 8.91693e10i 0.0377084 − 0.839642i
\(283\) 4.13812e8 0.00383498 0.00191749 − 0.999998i \(-0.499390\pi\)
0.00191749 + 0.999998i \(0.499390\pi\)
\(284\) 9.10562e9 − 4.69141e10i 0.0830571 − 0.427928i
\(285\) 6.78300e10 0.609003
\(286\) 2.85768e8 − 6.36312e9i 0.00252561 − 0.0562371i
\(287\) −3.09496e10 − 2.70399e10i −0.269269 − 0.235254i
\(288\) −7.55217e10 − 6.79708e9i −0.646853 − 0.0582179i
\(289\) 6.41992e10 + 1.97585e11i 0.541364 + 1.66615i
\(290\) 9.62943e9 − 1.00716e10i 0.0799483 − 0.0836194i
\(291\) −4.28512e10 − 1.18262e10i −0.350303 − 0.0966776i
\(292\) −1.04129e9 + 7.68710e9i −0.00838201 + 0.0618785i
\(293\) −2.11167e10 − 1.55890e11i −0.167387 − 1.23570i −0.858447 − 0.512902i \(-0.828570\pi\)
0.691060 − 0.722797i \(-0.257144\pi\)
\(294\) −6.23996e10 + 1.72212e10i −0.487101 + 0.134431i
\(295\) 8.15530e10 − 1.51551e11i 0.626962 − 1.16509i
\(296\) −2.88747e10 − 3.02006e10i −0.218628 − 0.228667i
\(297\) −2.08911e9 − 3.88222e9i −0.0155797 − 0.0289519i
\(298\) 4.75445e10 − 1.46327e11i 0.349242 − 1.07486i
\(299\) 2.30346e10 − 5.38921e10i 0.166671 − 0.389946i
\(300\) −2.50662e10 − 4.54885e9i −0.178667 − 0.0324232i
\(301\) 4.60019e9 + 3.34224e9i 0.0323018 + 0.0234686i
\(302\) −6.03183e10 + 5.42875e9i −0.417271 + 0.0375551i
\(303\) −2.88132e9 − 6.74118e9i −0.0196381 − 0.0459456i
\(304\) −4.00700e10 − 1.75558e11i −0.269084 − 1.17894i
\(305\) 1.74210e10 + 2.63918e10i 0.115272 + 0.174630i
\(306\) 2.08052e11 + 1.24305e11i 1.35652 + 0.810483i
\(307\) −4.01651e10 − 5.03655e10i −0.258063 − 0.323601i 0.635874 − 0.771793i \(-0.280640\pi\)
−0.893938 + 0.448191i \(0.852068\pi\)
\(308\) 5.50018e8 − 4.80536e8i 0.00348256 − 0.00304262i
\(309\) 1.24525e10 − 9.04724e9i 0.0777037 − 0.0564550i
\(310\) 6.97024e10 − 3.35669e10i 0.428667 − 0.206435i
\(311\) −1.51175e11 + 2.29021e11i −0.916344 + 1.38820i 0.00522413 + 0.999986i \(0.498337\pi\)
−0.921568 + 0.388216i \(0.873091\pi\)
\(312\) 5.57091e10 + 2.09080e10i 0.332836 + 0.124915i
\(313\) −9.11549e10 + 5.44625e10i −0.536822 + 0.320736i −0.755595 − 0.655040i \(-0.772652\pi\)
0.218772 + 0.975776i \(0.429795\pi\)
\(314\) −2.74735e11 − 1.32305e11i −1.59489 − 0.768058i
\(315\) 4.96691e10 − 9.01362e9i 0.284242 − 0.0515824i
\(316\) 2.07325e10 − 9.08352e10i 0.116966 − 0.512463i
\(317\) −1.19156e11 + 4.47201e10i −0.662751 + 0.248735i −0.660005 − 0.751261i \(-0.729446\pi\)
−0.00274665 + 0.999996i \(0.500874\pi\)
\(318\) −4.04031e10 + 5.06639e10i −0.221561 + 0.277828i
\(319\) −2.33862e7 − 5.20735e8i −0.000126445 − 0.00281552i
\(320\) −3.11192e9 − 6.92923e10i −0.0165903 − 0.369411i
\(321\) −3.39340e10 + 4.25519e10i −0.178387 + 0.223690i
\(322\) 2.07255e10 − 7.77841e9i 0.107437 − 0.0403218i
\(323\) −7.00865e10 + 3.07069e11i −0.358281 + 1.56973i
\(324\) 3.63162e10 − 6.59042e9i 0.183083 − 0.0332247i
\(325\) −1.93602e11 − 9.32336e10i −0.962573 − 0.463551i
\(326\) 1.91004e10 − 1.14119e10i 0.0936618 − 0.0559603i
\(327\) −1.03219e11 − 3.87386e10i −0.499221 − 0.187361i
\(328\) 1.06416e11 − 1.61213e11i 0.507662 − 0.769076i
\(329\) 7.77802e10 − 3.74570e10i 0.366005 − 0.176259i
\(330\) −5.30058e9 + 3.85110e9i −0.0246043 + 0.0178761i
\(331\) 5.23255e10 − 4.57154e10i 0.239601 − 0.209333i −0.529760 − 0.848148i \(-0.677718\pi\)
0.769360 + 0.638815i \(0.220575\pi\)
\(332\) 1.38452e10 + 1.73613e10i 0.0625427 + 0.0784260i
\(333\) 7.16677e10 + 4.28195e10i 0.319392 + 0.190828i
\(334\) 1.96859e11 + 2.98229e11i 0.865560 + 1.31127i
\(335\) 2.39375e9 + 1.04877e10i 0.0103843 + 0.0454966i
\(336\) 1.35872e10 + 3.17887e10i 0.0581570 + 0.136065i
\(337\) −3.80014e11 + 3.42019e10i −1.60496 + 0.144449i −0.855575 − 0.517680i \(-0.826796\pi\)
−0.749390 + 0.662129i \(0.769653\pi\)
\(338\) −8.11624e10 − 5.89679e10i −0.338244 − 0.245748i
\(339\) 6.68100e9 + 1.21242e9i 0.0274753 + 0.00498604i
\(340\) 9.70352e10 − 2.27025e11i 0.393799 − 0.921338i
\(341\) 8.94316e8 − 2.75242e9i 0.00358176 − 0.0110235i
\(342\) 1.10843e11 + 2.05981e11i 0.438118 + 0.814159i
\(343\) −8.97277e10 − 9.38478e10i −0.350028 − 0.366101i
\(344\) −1.26647e10 + 2.35349e10i −0.0487620 + 0.0906149i
\(345\) −5.81136e10 + 1.60383e10i −0.220847 + 0.0609500i
\(346\) −1.93727e10 − 1.43015e11i −0.0726688 − 0.536462i
\(347\) −3.90783e10 + 2.88487e11i −0.144695 + 1.06818i 0.762356 + 0.647158i \(0.224042\pi\)
−0.907051 + 0.421021i \(0.861672\pi\)
\(348\) −3.62747e9 − 1.00112e9i −0.0132586 − 0.00365914i
\(349\) 2.57540e11 − 2.69366e11i 0.929245 − 0.971914i −0.0704274 − 0.997517i \(-0.522436\pi\)
0.999672 + 0.0256031i \(0.00815060\pi\)
\(350\) −2.50808e10 − 7.71908e10i −0.0893378 − 0.274954i
\(351\) −2.67372e11 − 2.40639e10i −0.940228 − 0.0846220i
\(352\) 7.16820e9 + 6.26266e9i 0.0248867 + 0.0217429i
\(353\) −1.60127e10 + 3.56549e11i −0.0548880 + 1.22218i 0.762846 + 0.646580i \(0.223801\pi\)
−0.817734 + 0.575596i \(0.804770\pi\)
\(354\) −1.53098e11 −0.518150
\(355\) −4.05333e11 + 8.73312e10i −1.35452 + 0.291838i
\(356\) 1.27701e11 0.421375
\(357\) 2.71287e9 − 6.04068e10i 0.00883940 − 0.196824i
\(358\) 3.63662e11 + 3.17722e11i 1.17010 + 1.02229i
\(359\) 3.76198e11 + 3.38585e10i 1.19534 + 0.107583i 0.669376 − 0.742924i \(-0.266561\pi\)
0.525965 + 0.850506i \(0.323704\pi\)
\(360\) 7.33200e10 + 2.25656e11i 0.230071 + 0.708084i
\(361\) 1.29229e10 − 1.35162e10i 0.0400476 − 0.0418865i
\(362\) −5.80848e11 − 1.60304e11i −1.77776 − 0.490632i
\(363\) 2.00759e10 − 1.48206e11i 0.0606868 − 0.448008i
\(364\) −5.96986e9 − 4.40712e10i −0.0178241 − 0.131583i
\(365\) 6.48788e10 − 1.79054e10i 0.191331 − 0.0528039i
\(366\) 1.33306e10 − 2.47724e10i 0.0388315 − 0.0721611i
\(367\) 2.67898e11 + 2.80199e11i 0.770853 + 0.806249i 0.985362 − 0.170473i \(-0.0545296\pi\)
−0.214510 + 0.976722i \(0.568815\pi\)
\(368\) 7.58408e10 + 1.40936e11i 0.215570 + 0.400596i
\(369\) −1.19269e11 + 3.67073e11i −0.334896 + 1.03070i
\(370\) 1.10105e11 − 2.57604e11i 0.305422 − 0.714570i
\(371\) −6.16674e10 − 1.11910e10i −0.168995 − 0.0306680i
\(372\) −1.69027e10 − 1.22805e10i −0.0457628 − 0.0332486i
\(373\) 5.08512e11 − 4.57669e10i 1.36023 − 0.122423i 0.614628 − 0.788817i \(-0.289306\pi\)
0.745599 + 0.666394i \(0.232163\pi\)
\(374\) −1.19572e10 − 2.79752e10i −0.0316014 − 0.0739351i
\(375\) −4.28364e9 − 1.87679e10i −0.0111859 − 0.0490088i
\(376\) 2.23536e11 + 3.38642e11i 0.576769 + 0.873768i
\(377\) −2.72478e10 − 1.62798e10i −0.0694697 − 0.0415062i
\(378\) −6.32203e10 − 7.92757e10i −0.159273 − 0.199723i
\(379\) 1.10774e11 − 9.67799e10i 0.275778 − 0.240940i −0.508927 − 0.860810i \(-0.669958\pi\)
0.784705 + 0.619870i \(0.212815\pi\)
\(380\) 1.92779e11 − 1.40062e11i 0.474278 − 0.344583i
\(381\) 1.11081e11 − 5.34937e10i 0.270070 − 0.130059i
\(382\) −2.93114e11 + 4.44049e11i −0.704290 + 1.06695i
\(383\) 5.10093e11 + 1.91441e11i 1.21131 + 0.454612i 0.873603 − 0.486640i \(-0.161778\pi\)
0.337706 + 0.941252i \(0.390349\pi\)
\(384\) −1.88294e11 + 1.12500e11i −0.441922 + 0.264036i
\(385\) −5.70929e9 − 2.74945e9i −0.0132437 − 0.00637782i
\(386\) −6.21444e11 + 1.12776e11i −1.42482 + 0.258566i
\(387\) 1.18827e10 − 5.20616e10i 0.0269288 − 0.117983i
\(388\) −1.46207e11 + 5.48723e10i −0.327510 + 0.122917i
\(389\) 9.31874e10 − 1.16853e11i 0.206340 − 0.258743i −0.667883 − 0.744266i \(-0.732800\pi\)
0.874224 + 0.485523i \(0.161371\pi\)
\(390\) 1.78992e10 + 3.98558e11i 0.0391782 + 0.872369i
\(391\) −1.25593e10 − 2.79655e11i −0.0271751 − 0.605100i
\(392\) 1.83474e11 − 2.30069e11i 0.392453 − 0.492120i
\(393\) −2.01880e11 + 7.57669e10i −0.426901 + 0.160219i
\(394\) 1.18309e11 − 5.18346e11i 0.247335 − 1.08365i
\(395\) −7.95385e11 + 1.44341e11i −1.64396 + 0.298334i
\(396\) −6.17983e9 − 2.97605e9i −0.0126284 − 0.00608152i
\(397\) 4.03101e11 − 2.40842e11i 0.814436 − 0.486603i −0.0443020 − 0.999018i \(-0.514106\pi\)
0.858738 + 0.512416i \(0.171249\pi\)
\(398\) 6.75219e11 + 2.53414e11i 1.34887 + 0.506240i
\(399\) 3.21504e10 − 4.87058e10i 0.0635050 − 0.0962060i
\(400\) 5.28681e11 − 2.54599e11i 1.03258 − 0.497264i
\(401\) 5.42822e11 − 3.94383e11i 1.04835 − 0.761673i 0.0764548 − 0.997073i \(-0.475640\pi\)
0.971899 + 0.235400i \(0.0756399\pi\)
\(402\) 7.20662e9 − 6.29624e9i 0.0137630 − 0.0120244i
\(403\) −1.09876e11 − 1.37780e11i −0.207505 − 0.260203i
\(404\) −2.21088e10 − 1.32094e10i −0.0412904 − 0.0246699i
\(405\) −1.76416e11 − 2.67259e11i −0.325830 − 0.493611i
\(406\) −2.66777e9 − 1.16883e10i −0.00487283 − 0.0213493i
\(407\) −4.11888e9 − 9.63660e9i −0.00744054 − 0.0174080i
\(408\) 2.83067e11 − 2.54765e10i 0.505730 − 0.0455165i
\(409\) −3.40589e11 − 2.47452e11i −0.601832 − 0.437256i 0.244697 − 0.969600i \(-0.421312\pi\)
−0.846529 + 0.532343i \(0.821312\pi\)
\(410\) 1.27435e12 + 2.31260e11i 2.22721 + 0.404179i
\(411\) 1.18577e11 − 2.77424e11i 0.204980 − 0.479574i
\(412\) 1.67093e10 − 5.14261e10i 0.0285708 − 0.0879318i
\(413\) −7.01672e10 − 1.30393e11i −0.118675 − 0.220535i
\(414\) −1.43669e11 − 1.50266e11i −0.240360 − 0.251397i
\(415\) 9.12973e10 − 1.69659e11i 0.151092 − 0.280776i
\(416\) 5.58723e11 − 1.54198e11i 0.914696 − 0.252440i
\(417\) −5.29867e10 − 3.91163e11i −0.0858132 − 0.633499i
\(418\) 3.94149e9 − 2.90972e10i 0.00631491 − 0.0466185i
\(419\) 8.59518e11 + 2.37212e11i 1.36236 + 0.375988i 0.869419 − 0.494075i \(-0.164493\pi\)
0.492941 + 0.870063i \(0.335922\pi\)
\(420\) −3.16140e10 + 3.30656e10i −0.0495743 + 0.0518507i
\(421\) 3.02309e11 + 9.30412e11i 0.469010 + 1.44346i 0.853869 + 0.520488i \(0.174250\pi\)
−0.384859 + 0.922975i \(0.625750\pi\)
\(422\) 1.34662e12 + 1.21198e11i 2.06699 + 0.186032i
\(423\) −6.10551e11 − 5.33422e11i −0.927236 − 0.810101i
\(424\) 1.32165e10 − 2.94288e11i 0.0198595 − 0.442207i
\(425\) −1.02636e12 −1.52598
\(426\) 2.39279e11 + 2.80709e11i 0.352015 + 0.412966i
\(427\) 2.72081e10 0.0396071
\(428\) −8.57811e9 + 1.91006e11i −0.0123565 + 0.275138i
\(429\) 1.12392e10 + 9.81941e9i 0.0160206 + 0.0139968i
\(430\) −1.78473e11 − 1.60628e10i −0.251747 − 0.0226576i
\(431\) 4.04890e11 + 1.24612e12i 0.565184 + 1.73946i 0.667405 + 0.744695i \(0.267405\pi\)
−0.102221 + 0.994762i \(0.532595\pi\)
\(432\) 5.06605e11 − 5.29867e11i 0.699830 − 0.731965i
\(433\) −6.21746e11 − 1.71591e11i −0.849998 − 0.234584i −0.186214 − 0.982509i \(-0.559622\pi\)
−0.663784 + 0.747925i \(0.731050\pi\)
\(434\) 8.93495e9 − 6.59604e10i 0.0120889 − 0.0892442i
\(435\) 4.38263e9 + 3.23539e10i 0.00586858 + 0.0433236i
\(436\) −3.73348e11 + 1.03037e11i −0.494794 + 0.136554i
\(437\) 1.28030e11 − 2.37919e11i 0.167936 − 0.312077i
\(438\) −4.13759e10 − 4.32758e10i −0.0537173 − 0.0561839i
\(439\) −6.45799e11 − 1.20010e12i −0.829864 − 1.54215i −0.840249 − 0.542200i \(-0.817592\pi\)
0.0103853 − 0.999946i \(-0.496694\pi\)
\(440\) 9.20390e9 − 2.83267e10i 0.0117067 − 0.0360296i
\(441\) −2.31086e11 + 5.40653e11i −0.290938 + 0.680684i
\(442\) −1.82278e12 − 3.30786e11i −2.27161 − 0.412237i
\(443\) −4.68053e11 − 3.40060e11i −0.577402 − 0.419507i 0.260385 − 0.965505i \(-0.416151\pi\)
−0.837786 + 0.545998i \(0.816151\pi\)
\(444\) −7.53522e10 + 6.78182e9i −0.0920180 + 0.00828177i
\(445\) −4.35458e11 − 1.01880e12i −0.526412 − 1.23160i
\(446\) 3.17294e11 + 1.39016e12i 0.379713 + 1.66363i
\(447\) 1.98600e11 + 3.00867e11i 0.235286 + 0.356443i
\(448\) −5.12308e10 − 3.06090e10i −0.0600869 − 0.0359003i
\(449\) −8.45074e11 − 1.05969e12i −0.981265 − 1.23047i −0.973072 − 0.230501i \(-0.925964\pi\)
−0.00819281 − 0.999966i \(-0.502608\pi\)
\(450\) −5.74013e11 + 5.01500e11i −0.659881 + 0.576520i
\(451\) 3.91970e10 − 2.84783e10i 0.0446127 − 0.0324130i
\(452\) 2.14915e10 − 1.03498e10i 0.0242183 − 0.0116629i
\(453\) 7.81742e10 − 1.18429e11i 0.0872211 − 0.132134i
\(454\) 1.61059e12 + 6.04466e11i 1.77924 + 0.667760i
\(455\) −3.31245e11 + 1.97910e11i −0.362325 + 0.216479i
\(456\) 2.47140e11 + 1.19016e11i 0.267671 + 0.128904i
\(457\) −5.57094e11 + 1.01098e11i −0.597455 + 0.108422i −0.468856 − 0.883274i \(-0.655334\pi\)
−0.128599 + 0.991697i \(0.541048\pi\)
\(458\) −1.44728e11 + 6.34094e11i −0.153694 + 0.673378i
\(459\) −1.20047e12 + 4.50544e11i −1.26239 + 0.473784i
\(460\) −1.32047e11 + 1.65581e11i −0.137505 + 0.172425i
\(461\) 2.76669e10 + 6.16052e11i 0.0285303 + 0.635277i 0.961415 + 0.275102i \(0.0887116\pi\)
−0.932885 + 0.360175i \(0.882717\pi\)
\(462\) 2.52910e8 + 5.63148e9i 0.000258272 + 0.00575087i
\(463\) 2.90045e11 − 3.63705e11i 0.293326 − 0.367820i −0.613230 − 0.789904i \(-0.710130\pi\)
0.906556 + 0.422085i \(0.138702\pi\)
\(464\) 8.11497e10 − 3.04560e10i 0.0812748 − 0.0305029i
\(465\) −4.03367e10 + 1.76727e11i −0.0400094 + 0.175293i
\(466\) −1.99513e12 + 3.62062e11i −1.95990 + 0.355669i
\(467\) 1.44834e12 + 6.97485e11i 1.40911 + 0.678592i 0.974987 − 0.222261i \(-0.0713438\pi\)
0.434124 + 0.900853i \(0.357058\pi\)
\(468\) −3.58546e11 + 2.14221e11i −0.345492 + 0.206422i
\(469\) 8.66537e9 + 3.25217e9i 0.00827007 + 0.00310381i
\(470\) −1.49877e12 + 2.27054e12i −1.41675 + 2.14629i
\(471\) 6.43733e11 − 3.10006e11i 0.602715 − 0.290252i
\(472\) 5.63056e11 − 4.09084e11i 0.522171 − 0.379379i
\(473\) −5.04813e9 + 4.41042e9i −0.00463720 + 0.00405140i
\(474\) 4.48364e11 + 5.62230e11i 0.407970 + 0.511578i
\(475\) −8.50365e11 − 5.08070e11i −0.766451 − 0.457933i
\(476\) −1.17024e11 − 1.77283e11i −0.104482 − 0.158284i
\(477\) 1.30975e11 + 5.73840e11i 0.115839 + 0.507526i
\(478\) −3.41863e11 − 7.99828e11i −0.299520 − 0.700763i
\(479\) 1.58466e11 − 1.42622e10i 0.137539 − 0.0123787i −0.0206558 − 0.999787i \(-0.506575\pi\)
0.158195 + 0.987408i \(0.449433\pi\)
\(480\) −4.82339e11 − 3.50440e11i −0.414731 − 0.301320i
\(481\) −6.27893e11 − 1.13946e11i −0.534851 − 0.0970612i
\(482\) 6.69558e11 − 1.56651e12i 0.565036 − 1.32197i
\(483\) −1.60286e10 + 4.93308e10i −0.0134009 + 0.0412436i
\(484\) −2.48973e11 − 4.62669e11i −0.206228 − 0.383236i
\(485\) 9.36335e11 + 9.79330e11i 0.768411 + 0.803695i
\(486\) −7.02643e11 + 1.30573e12i −0.571309 + 1.06167i
\(487\) −7.16732e11 + 1.97805e11i −0.577399 + 0.159352i −0.542525 − 0.840040i \(-0.682532\pi\)
−0.0348743 + 0.999392i \(0.511103\pi\)
\(488\) 1.71663e10 + 1.26726e11i 0.0137021 + 0.101153i
\(489\) −6.99809e9 + 5.16620e10i −0.00553464 + 0.0408584i
\(490\) 1.90192e12 + 5.24898e11i 1.49043 + 0.411332i
\(491\) 1.07909e12 − 1.12864e12i 0.837898 − 0.876373i −0.155877 − 0.987776i \(-0.549820\pi\)
0.993775 + 0.111403i \(0.0355346\pi\)
\(492\) −1.08085e11 − 3.32653e11i −0.0831618 − 0.255946i
\(493\) −1.50996e11 − 1.35899e10i −0.115121 − 0.0103611i
\(494\) −1.34648e12 − 1.17638e12i −1.01725 − 0.888745i
\(495\) −2.66996e9 + 5.94512e10i −0.00199885 + 0.0445079i
\(496\) 4.81234e11 0.357017
\(497\) −1.29413e11 + 3.32446e11i −0.0951424 + 0.244409i
\(498\) −1.71391e11 −0.124869
\(499\) 7.00744e10 − 1.56033e12i 0.0505949 − 1.12658i −0.799741 − 0.600345i \(-0.795030\pi\)
0.850336 − 0.526239i \(-0.176398\pi\)
\(500\) −5.09282e10 − 4.44946e10i −0.0364413 − 0.0318378i
\(501\) −8.33922e11 − 7.50544e10i −0.591365 − 0.0532238i
\(502\) −7.47472e11 − 2.30048e12i −0.525325 − 1.61678i
\(503\) −1.79769e11 + 1.88024e11i −0.125216 + 0.130966i −0.782430 − 0.622738i \(-0.786020\pi\)
0.657215 + 0.753704i \(0.271735\pi\)
\(504\) 1.96786e11 + 5.43095e10i 0.135849 + 0.0374920i
\(505\) −2.99946e10 + 2.21429e11i −0.0205225 + 0.151504i
\(506\) 3.50313e9 + 2.58612e10i 0.00237563 + 0.0175376i
\(507\) 2.26594e11 − 6.25361e10i 0.152305 − 0.0420334i
\(508\) 2.05243e11 − 3.81405e11i 0.136735 − 0.254097i
\(509\) −9.16331e11 − 9.58407e11i −0.605093 − 0.632878i 0.347298 − 0.937755i \(-0.387099\pi\)
−0.952392 + 0.304877i \(0.901385\pi\)
\(510\) 9.02997e11 + 1.67805e12i 0.591045 + 1.09835i
\(511\) 1.78945e10 − 5.50735e10i 0.0116098 − 0.0357313i
\(512\) −1.07408e11 + 2.51293e11i −0.0690750 + 0.161609i
\(513\) −1.21765e12 − 2.20971e11i −0.776238 − 0.140866i
\(514\) 9.90749e11 + 7.19821e11i 0.626079 + 0.454873i
\(515\) −4.67258e11 + 4.20540e10i −0.292701 + 0.0263436i
\(516\) 1.90197e10 + 4.44988e10i 0.0118108 + 0.0276328i
\(517\) 2.26468e10 + 9.92220e10i 0.0139412 + 0.0610802i
\(518\) −1.32786e11 − 2.01162e11i −0.0810342 − 0.122762i
\(519\) 2.90293e11 + 1.73442e11i 0.175624 + 0.104930i
\(520\) −1.13079e12 − 1.41797e12i −0.678214 − 0.850454i
\(521\) −3.55108e11 + 3.10248e11i −0.211150 + 0.184476i −0.757016 − 0.653396i \(-0.773344\pi\)
0.545866 + 0.837872i \(0.316201\pi\)
\(522\) −9.10880e10 + 6.61793e10i −0.0536963 + 0.0390126i
\(523\) 8.91767e11 − 4.29452e11i 0.521187 − 0.250991i −0.154745 − 0.987954i \(-0.549456\pi\)
0.675932 + 0.736964i \(0.263741\pi\)
\(524\) −4.17311e11 + 6.32198e11i −0.241807 + 0.366322i
\(525\) 1.78047e11 + 6.68223e10i 0.102287 + 0.0383888i
\(526\) −1.19167e12 + 7.11990e11i −0.678767 + 0.405544i
\(527\) −7.58371e11 − 3.65212e11i −0.428286 − 0.206252i
\(528\) −4.01004e10 + 7.27715e9i −0.0224541 + 0.00407482i
\(529\) 3.47360e11 − 1.52188e12i 0.192854 − 0.844950i
\(530\) 1.84919e12 − 6.94013e11i 1.01798 − 0.382055i
\(531\) −8.67026e11 + 1.08722e12i −0.473268 + 0.593459i
\(532\) −9.19818e9 − 2.04813e11i −0.00497851 − 0.110855i
\(533\) −1.32362e11 − 2.94728e12i −0.0710382 − 1.58179i
\(534\) −6.14529e11 + 7.70596e11i −0.327045 + 0.410101i
\(535\) 1.55311e12 − 5.82891e11i 0.819615 − 0.307607i
\(536\) −9.68034e9 + 4.24123e10i −0.00506581 + 0.0221948i
\(537\) −1.11331e12 + 2.02037e11i −0.577741 + 0.104845i
\(538\) 7.76783e11 + 3.74079e11i 0.399742 + 0.192505i
\(539\) 6.33605e10 − 3.78561e10i 0.0323347 − 0.0193191i
\(540\) 9.08217e11 + 3.40859e11i 0.459640 + 0.172506i
\(541\) 1.27643e12 − 1.93370e12i 0.640631 − 0.970514i −0.358682 − 0.933460i \(-0.616774\pi\)
0.999313 − 0.0370547i \(-0.0117976\pi\)
\(542\) −2.18540e12 + 1.05243e12i −1.08776 + 0.523838i
\(543\) 1.14223e12 − 8.29875e11i 0.563836 − 0.409651i
\(544\) 2.08484e12 − 1.82147e12i 1.02065 − 0.891717i
\(545\) 2.09515e12 + 2.62723e12i 1.01726 + 1.27560i
\(546\) 2.94671e11 + 1.76058e11i 0.141896 + 0.0847790i
\(547\) 1.34931e11 + 2.04412e11i 0.0644421 + 0.0976256i 0.865366 − 0.501141i \(-0.167086\pi\)
−0.800924 + 0.598767i \(0.795658\pi\)
\(548\) −2.35847e11 − 1.03331e12i −0.111716 − 0.489462i
\(549\) −1.00426e11 − 2.34957e11i −0.0471812 − 0.110386i
\(550\) 9.52979e10 − 8.57697e9i 0.0444070 − 0.00399670i
\(551\) −1.18377e11 − 8.60058e10i −0.0547123 − 0.0397508i
\(552\) −2.39880e11 − 4.35318e10i −0.109968 − 0.0199563i
\(553\) −2.73355e11 + 6.39547e11i −0.124298 + 0.290810i
\(554\) −9.20328e11 + 2.83248e12i −0.415096 + 1.27753i
\(555\) 3.11055e11 + 5.78037e11i 0.139161 + 0.258605i
\(556\) −9.58305e11 − 1.00231e12i −0.425272 − 0.444800i
\(557\) 3.00617e11 − 5.58640e11i 0.132332 − 0.245914i −0.805803 − 0.592184i \(-0.798266\pi\)
0.938135 + 0.346269i \(0.112552\pi\)
\(558\) −6.02585e11 + 1.66303e11i −0.263127 + 0.0726183i
\(559\) 5.47921e10 + 4.04491e11i 0.0237337 + 0.175209i
\(560\) 1.41443e11 − 1.04417e12i 0.0607763 − 0.448668i
\(561\) 6.87163e10 + 1.89645e10i 0.0292905 + 0.00808367i
\(562\) 1.72435e12 − 1.80353e12i 0.729141 − 0.762622i
\(563\) 1.21795e12 + 3.74845e12i 0.510905 + 1.57240i 0.790611 + 0.612319i \(0.209763\pi\)
−0.279706 + 0.960086i \(0.590237\pi\)
\(564\) 7.31767e11 + 6.58602e10i 0.304521 + 0.0274074i
\(565\) −1.55857e11 − 1.36168e11i −0.0643439 − 0.0562156i
\(566\) −5.03394e8 + 1.12089e10i −0.000206174 + 0.00459082i
\(567\) −2.75526e11 −0.111954
\(568\) −1.63007e12 − 3.93015e11i −0.657113 − 0.158432i
\(569\) 1.68795e12 0.675077 0.337539 − 0.941312i \(-0.390406\pi\)
0.337539 + 0.941312i \(0.390406\pi\)
\(570\) −8.25139e10 + 1.83731e12i −0.0327409 + 0.729032i
\(571\) 1.12881e11 + 9.86209e10i 0.0444383 + 0.0388246i 0.679871 − 0.733331i \(-0.262036\pi\)
−0.635433 + 0.772156i \(0.719178\pi\)
\(572\) 5.22189e10 + 4.69979e9i 0.0203960 + 0.00183568i
\(573\) −3.85248e11 − 1.18567e12i −0.149295 − 0.459482i
\(574\) 7.70080e11 − 8.05441e11i 0.296096 − 0.309692i
\(575\) 8.48687e11 + 2.34223e11i 0.323774 + 0.0893560i
\(576\) −7.52321e10 + 5.55385e11i −0.0284775 + 0.210229i
\(577\) 1.90923e11 + 1.40945e12i 0.0717080 + 0.529370i 0.990801 + 0.135329i \(0.0432090\pi\)
−0.919093 + 0.394041i \(0.871077\pi\)
\(578\) −5.43009e12 + 1.49861e12i −2.02363 + 0.558487i
\(579\) 7.01274e11 − 1.30319e12i 0.259319 − 0.481896i
\(580\) 7.92633e10 + 8.29029e10i 0.0290835 + 0.0304189i
\(581\) −7.85511e10 − 1.45972e11i −0.0285996 − 0.0531469i
\(582\) 3.72464e11 − 1.14633e12i 0.134565 − 0.414147i
\(583\) 2.90394e10 − 6.79411e10i 0.0104107 − 0.0243570i
\(584\) 2.67805e11 + 4.85994e10i 0.0952709 + 0.0172891i
\(585\) 2.93170e12 + 2.13000e12i 1.03495 + 0.751932i
\(586\) 4.24828e12 − 3.82352e11i 1.48824 − 0.133944i
\(587\) −1.35286e12 − 3.16517e12i −0.470306 − 1.10034i −0.971934 − 0.235252i \(-0.924408\pi\)
0.501628 − 0.865083i \(-0.332734\pi\)
\(588\) −1.18567e11 − 5.19476e11i −0.0409040 − 0.179212i
\(589\) −4.47543e11 − 6.77998e11i −0.153220 − 0.232118i
\(590\) 4.00586e12 + 2.39339e12i 1.36101 + 0.813166i
\(591\) 7.76728e11 + 9.73986e11i 0.261894 + 0.328404i
\(592\) 1.31233e12 − 1.14655e12i 0.439132 − 0.383658i
\(593\) 1.90510e12 − 1.38414e12i 0.632662 − 0.459656i −0.224659 − 0.974437i \(-0.572127\pi\)
0.857321 + 0.514781i \(0.172127\pi\)
\(594\) 1.07699e11 − 5.18653e10i 0.0354956 − 0.0170938i
\(595\) −1.01533e12 + 1.53815e12i −0.332108 + 0.503122i
\(596\) 1.18570e12 + 4.45000e11i 0.384916 + 0.144461i
\(597\) −1.45066e12 + 8.66730e11i −0.467392 + 0.279254i
\(598\) 1.43176e12 + 6.89498e11i 0.457840 + 0.220484i
\(599\) 9.39968e11 − 1.70579e11i 0.298327 − 0.0541384i −0.0273296 − 0.999626i \(-0.508700\pi\)
0.325657 + 0.945488i \(0.394415\pi\)
\(600\) −1.98902e11 + 8.71447e11i −0.0626554 + 0.274511i
\(601\) 8.07334e11 − 3.02998e11i 0.252417 − 0.0947336i −0.221959 − 0.975056i \(-0.571245\pi\)
0.474376 + 0.880322i \(0.342674\pi\)
\(602\) −9.61274e10 + 1.20540e11i −0.0298307 + 0.0374065i
\(603\) −3.89973e9 − 8.68342e10i −0.00120118 − 0.0267463i
\(604\) −2.23655e10 − 4.98007e11i −0.00683774 − 0.152254i
\(605\) −2.84220e12 + 3.56401e12i −0.862493 + 1.08153i
\(606\) 1.86104e11 − 6.98459e10i 0.0560568 − 0.0210385i
\(607\) 2.43556e11 − 1.06709e12i 0.0728198 − 0.319045i −0.925379 − 0.379044i \(-0.876253\pi\)
0.998198 + 0.0599996i \(0.0191100\pi\)
\(608\) 2.62901e12 − 4.77096e11i 0.780237 − 0.141592i
\(609\) 2.53092e10 + 1.21883e10i 0.00745592 + 0.00359058i
\(610\) −7.36067e11 + 4.39780e11i −0.215245 + 0.128603i
\(611\) 5.80207e12 + 2.17755e12i 1.68422 + 0.632097i
\(612\) −1.09901e12 + 1.66492e12i −0.316679 + 0.479748i
\(613\) −1.61825e12 + 7.79309e11i −0.462886 + 0.222914i −0.650767 − 0.759278i \(-0.725552\pi\)
0.187881 + 0.982192i \(0.439838\pi\)
\(614\) 1.41311e12 − 1.02669e12i 0.401254 − 0.291528i
\(615\) −2.28535e12 + 1.99665e12i −0.644190 + 0.562812i
\(616\) −1.59777e10 − 2.00354e10i −0.00447095 − 0.00560640i
\(617\) −2.15434e12 − 1.28716e12i −0.598455 − 0.357560i 0.181504 − 0.983390i \(-0.441903\pi\)
−0.779960 + 0.625830i \(0.784761\pi\)
\(618\) 2.29915e11 + 3.48306e11i 0.0634043 + 0.0960534i
\(619\) 1.48776e12 + 6.51830e12i 0.407310 + 1.78454i 0.596515 + 0.802602i \(0.296552\pi\)
−0.189205 + 0.981938i \(0.560591\pi\)
\(620\) 2.50282e11 + 5.85564e11i 0.0680248 + 0.159152i
\(621\) 1.09548e12 − 9.85948e10i 0.295591 − 0.0266037i
\(622\) −6.01959e12 − 4.37349e12i −1.61254 − 1.17158i
\(623\) −9.37959e11 − 1.70214e11i −0.249452 − 0.0452689i
\(624\) −9.75366e11 + 2.28198e12i −0.257536 + 0.602534i
\(625\) −1.26568e12 + 3.89537e12i −0.331791 + 1.02115i
\(626\) −1.36434e12 − 2.53537e12i −0.355090 − 0.659867i
\(627\) 4.75455e10 + 4.97287e10i 0.0122859 + 0.0128500i
\(628\) 1.18942e12 − 2.21031e12i 0.305152 − 0.567067i
\(629\) −2.93820e12 + 8.10893e11i −0.748435 + 0.206555i
\(630\) 1.83731e11 + 1.35635e12i 0.0464675 + 0.343037i
\(631\) −4.21557e11 + 3.11206e12i −0.105858 + 0.781476i 0.857733 + 0.514095i \(0.171872\pi\)
−0.963591 + 0.267380i \(0.913842\pi\)
\(632\) −3.15127e12 − 8.69695e11i −0.785703 − 0.216840i
\(633\) −2.18930e12 + 2.28983e12i −0.541987 + 0.566874i
\(634\) −1.06639e12 − 3.28200e12i −0.262127 − 0.806745i
\(635\) −3.74274e12 − 3.36852e11i −0.913498 − 0.0822163i
\(636\) −4.01692e11 − 3.50948e11i −0.0973501 − 0.0850522i
\(637\) 2.01638e11 − 4.48982e12i 0.0485228 − 1.08044i
\(638\) 1.41336e10 0.00337723
\(639\) 3.34852e12 − 1.09509e11i 0.794511 − 0.0259833i
\(640\) 6.68549e12 1.57515
\(641\) −2.52065e11 + 5.61267e12i −0.0589728 + 1.31313i 0.723447 + 0.690380i \(0.242557\pi\)
−0.782420 + 0.622751i \(0.786015\pi\)
\(642\) −1.11132e12 − 9.70935e11i −0.258186 − 0.225571i
\(643\) 6.99115e10 + 6.29215e9i 0.0161287 + 0.00145161i 0.0977007 − 0.995216i \(-0.468851\pi\)
−0.0815720 + 0.996667i \(0.525994\pi\)
\(644\) 5.63086e10 + 1.73300e11i 0.0129000 + 0.0397020i
\(645\) 2.90157e11 − 3.03480e11i 0.0660107 − 0.0690417i
\(646\) −8.23234e12 − 2.27198e12i −1.85985 − 0.513285i
\(647\) −4.39002e11 + 3.24084e12i −0.0984912 + 0.727091i 0.872609 + 0.488419i \(0.162426\pi\)
−0.971100 + 0.238672i \(0.923288\pi\)
\(648\) −1.73836e11 − 1.28331e12i −0.0387304 − 0.285920i
\(649\) 1.68272e11 − 4.64402e10i 0.0372316 − 0.0102753i
\(650\) 2.76094e12 − 5.13068e12i 0.606661 − 1.12737i
\(651\) 1.07781e11 + 1.12730e11i 0.0235194 + 0.0245994i
\(652\) 8.67875e10 + 1.61278e11i 0.0188080 + 0.0349512i
\(653\) −4.84581e11 + 1.49139e12i −0.104293 + 0.320982i −0.989564 − 0.144094i \(-0.953973\pi\)
0.885271 + 0.465076i \(0.153973\pi\)
\(654\) 1.17488e12 − 2.74876e12i 0.251127 − 0.587540i
\(655\) 6.46673e12 + 1.17354e12i 1.37277 + 0.249122i
\(656\) 6.51780e12 + 4.73546e12i 1.37415 + 0.998377i
\(657\) −5.41640e11 + 4.87485e10i −0.113414 + 0.0102074i
\(658\) 9.19981e11 + 2.15240e12i 0.191321 + 0.447617i
\(659\) −8.65264e11 − 3.79097e12i −0.178716 − 0.783008i −0.982224 − 0.187713i \(-0.939892\pi\)
0.803507 − 0.595295i \(-0.202965\pi\)
\(660\) −2.97104e10 − 4.50093e10i −0.00609481 − 0.00923324i
\(661\) 1.54872e12 + 9.25319e11i 0.315549 + 0.188532i 0.661937 − 0.749560i \(-0.269735\pi\)
−0.346388 + 0.938091i \(0.612592\pi\)
\(662\) 1.17464e12 + 1.47296e12i 0.237709 + 0.298077i
\(663\) 3.26888e12 − 2.85593e12i 0.657034 − 0.574033i
\(664\) 6.30332e11 − 4.57963e11i 0.125838 − 0.0914269i
\(665\) −1.60264e12 + 7.71793e11i −0.317790 + 0.153039i
\(666\) −1.24704e12 + 1.88918e12i −0.245609 + 0.372082i
\(667\) 1.21756e11 + 4.56958e10i 0.0238190 + 0.00893943i
\(668\) −2.52506e12 + 1.50865e12i −0.490657 + 0.293154i
\(669\) −3.01018e12 − 1.44963e12i −0.580999 − 0.279794i
\(670\) −2.86993e11 + 5.20815e10i −0.0550218 + 0.00998498i
\(671\) −7.13748e9 + 3.12714e10i −0.00135923 + 0.00595519i
\(672\) −4.80257e11 + 1.80243e11i −0.0908472 + 0.0340955i
\(673\) 2.65941e12 − 3.33479e12i 0.499709 − 0.626615i −0.466455 − 0.884545i \(-0.654469\pi\)
0.966164 + 0.257930i \(0.0830404\pi\)
\(674\) −4.64149e11 − 1.03351e13i −0.0866338 − 1.92905i
\(675\) −1.80926e11 − 4.02862e12i −0.0335454 − 0.746947i
\(676\) 5.14871e11 − 6.45628e11i 0.0948284 − 0.118911i
\(677\) 5.73350e12 − 2.15182e12i 1.04899 − 0.393692i 0.233435 − 0.972373i \(-0.425004\pi\)
0.815554 + 0.578680i \(0.196432\pi\)
\(678\) −4.09683e10 + 1.79494e11i −0.00744585 + 0.0326224i
\(679\) 1.14702e12 − 2.08154e11i 0.207090 − 0.0375812i
\(680\) −7.80481e12 − 3.75860e12i −1.39982 − 0.674118i
\(681\) −3.46025e12 + 2.06740e12i −0.616517 + 0.368352i
\(682\) 7.34671e10 + 2.75727e10i 0.0130036 + 0.00488033i
\(683\) 5.80416e11 − 8.79293e11i 0.102058 − 0.154611i −0.779956 − 0.625834i \(-0.784759\pi\)
0.882014 + 0.471223i \(0.156187\pi\)
\(684\) −1.73473e12 + 8.35402e11i −0.303026 + 0.145929i
\(685\) −7.43957e12 + 5.40517e12i −1.29104 + 0.937997i
\(686\) 2.65121e12 − 2.31629e12i 0.457074 − 0.399333i
\(687\) −9.50172e11 − 1.19148e12i −0.162741 − 0.204071i
\(688\) −9.56879e11 − 5.71708e11i −0.162820 − 0.0972807i
\(689\) −2.47857e12 − 3.75487e12i −0.419001 − 0.634759i
\(690\) −3.63737e11 − 1.59364e12i −0.0610896 − 0.267651i
\(691\) 1.05874e12 + 2.47704e12i 0.176659 + 0.413315i 0.984334 − 0.176313i \(-0.0564172\pi\)
−0.807675 + 0.589628i \(0.799274\pi\)
\(692\) 1.18318e12 − 1.06488e11i 0.196143 − 0.0176532i
\(693\) 4.14238e10 + 3.00962e10i 0.00682261 + 0.00495692i
\(694\) −7.76673e12 − 1.40945e12i −1.27093 − 0.230639i
\(695\) −4.72866e12 + 1.10632e13i −0.768788 + 1.79867i
\(696\) −4.08008e10 + 1.25572e11i −0.00659064 + 0.0202839i
\(697\) −6.67754e12 − 1.24089e13i −1.07169 − 1.99153i
\(698\) 6.98303e12 + 7.30367e12i 1.11351 + 1.16464i
\(699\) 2.25142e12 − 4.18384e12i 0.356705 − 0.662869i
\(700\) 6.44008e11 − 1.77735e11i 0.101379 − 0.0279790i
\(701\) −6.91302e11 − 5.10340e12i −0.108128 − 0.798230i −0.961086 − 0.276251i \(-0.910908\pi\)
0.852958 − 0.521980i \(-0.174806\pi\)
\(702\) 9.77072e11 − 7.21303e12i 0.151848 − 1.12099i
\(703\) −2.83579e12 − 7.82629e11i −0.437900 − 0.120853i
\(704\) 4.86195e10 − 5.08520e10i 0.00745990 − 0.00780245i
\(705\) −1.96987e12 − 6.06265e12i −0.300322 − 0.924297i
\(706\) −9.63839e12 − 8.67471e11i −1.46010 − 0.131412i
\(707\) 1.44781e11 + 1.26492e11i 0.0217934 + 0.0190403i
\(708\) 5.65389e10 − 1.25894e12i 0.00845664 − 0.188302i
\(709\) 8.57399e12 1.27431 0.637155 − 0.770736i \(-0.280111\pi\)
0.637155 + 0.770736i \(0.280111\pi\)
\(710\) −1.87246e12 − 1.10855e13i −0.276536 − 1.63717i
\(711\) 6.53182e12 0.958563
\(712\) 2.01022e11 − 4.47610e12i 0.0293146 − 0.652740i
\(713\) 5.43746e11 + 4.75057e11i 0.0787941 + 0.0688403i
\(714\) 1.63294e12 + 1.46967e11i 0.235141 + 0.0211631i
\(715\) −1.40570e11 − 4.32631e11i −0.0201148 − 0.0619071i
\(716\) −2.74695e12 + 2.87308e12i −0.390609 + 0.408545i
\(717\) 1.96464e12 + 5.42207e11i 0.277618 + 0.0766177i
\(718\) −1.37476e12 + 1.01489e13i −0.193049 + 1.42515i
\(719\) 1.01161e11 + 7.46803e11i 0.0141167 + 0.104214i 0.996637 − 0.0819406i \(-0.0261118\pi\)
−0.982520 + 0.186155i \(0.940397\pi\)
\(720\) −9.53908e12 + 2.63262e12i −1.32285 + 0.365083i
\(721\) −1.91276e11 + 3.55451e11i −0.0263604 + 0.0489859i
\(722\) 3.50395e11 + 3.66484e11i 0.0479889 + 0.0501924i
\(723\) 1.89155e12 + 3.51509e12i 0.257451 + 0.478425i
\(724\) 1.53270e12 − 4.71716e12i 0.207316 − 0.638053i
\(725\) 1.87398e11 − 4.38439e11i 0.0251909 − 0.0589370i
\(726\) 3.99004e12 + 7.24086e11i 0.533043 + 0.0967331i
\(727\) 5.26428e11 + 3.82473e11i 0.0698931 + 0.0507803i 0.622183 − 0.782872i \(-0.286246\pi\)
−0.552290 + 0.833652i \(0.686246\pi\)
\(728\) −1.55416e12 + 1.39877e11i −0.205071 + 0.0184567i
\(729\) −8.61762e10 − 2.01619e11i −0.0113009 − 0.0264398i
\(730\) 4.06081e11 + 1.77916e12i 0.0529248 + 0.231879i
\(731\) 1.07406e12 + 1.62713e12i 0.139123 + 0.210763i
\(732\) 1.98782e11 + 1.18767e11i 0.0255905 + 0.0152896i
\(733\) 3.50477e12 + 4.39484e12i 0.448427 + 0.562310i 0.953742 − 0.300625i \(-0.0971953\pi\)
−0.505315 + 0.862935i \(0.668624\pi\)
\(734\) −7.91565e12 + 6.91570e12i −1.00659 + 0.879435i
\(735\) −3.74009e12 + 2.71734e12i −0.472704 + 0.343440i
\(736\) −2.13961e12 + 1.03038e12i −0.268772 + 0.129434i
\(737\) −6.01103e9 + 9.10632e9i −0.000750490 + 0.00113694i
\(738\) −9.79782e12 − 3.67719e12i −1.21584 − 0.456312i
\(739\) −5.39151e12 + 3.22128e12i −0.664983 + 0.397309i −0.805357 − 0.592790i \(-0.798026\pi\)
0.140375 + 0.990098i \(0.455169\pi\)
\(740\) 2.07764e12 + 1.00054e12i 0.254699 + 0.122656i
\(741\) 4.12210e12 − 7.48052e11i 0.502270 − 0.0911485i
\(742\) 3.78148e11 − 1.65678e12i 0.0457978 − 0.200653i
\(743\) −9.64167e12 + 3.61858e12i −1.16065 + 0.435601i −0.856057 − 0.516881i \(-0.827093\pi\)
−0.304597 + 0.952481i \(0.598522\pi\)
\(744\) −4.57057e11 + 5.73132e11i −0.0546881 + 0.0685767i
\(745\) −4.92978e11 − 1.09770e13i −0.0586305 − 1.30551i
\(746\) 6.21096e11 + 1.38298e13i 0.0734233 + 1.63490i
\(747\) −9.70621e11 + 1.21712e12i −0.114053 + 0.143018i
\(748\) 2.34458e11 − 8.79934e10i 0.0273847 − 0.0102776i
\(749\) 3.17601e11 − 1.39150e12i 0.0368735 − 0.161553i
\(750\) 5.13577e11 − 9.32004e10i 0.0592693 − 0.0107558i
\(751\) 1.45311e13 + 6.99779e12i 1.66693 + 0.802751i 0.998246 + 0.0592051i \(0.0188566\pi\)
0.668684 + 0.743546i \(0.266858\pi\)
\(752\) −1.45277e13 + 8.67991e12i