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 $2$

Learn more

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})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$1272 q - 76 q^{2} - 395 q^{3} + 13542 q^{4} - 1610 q^{5} - 4334 q^{6} - 4827 q^{7} - 18627 q^{8} + 286810 q^{9}+O(q^{10})$$ 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 $$1272 q - 76 q^{2} - 395 q^{3} + 13542 q^{4} - 1610 q^{5} - 4334 q^{6} - 4827 q^{7} - 18627 q^{8} + 286810 q^{9} - 53448 q^{10} - 170685 q^{11} + 138323 q^{12} - 93291 q^{13} + 985964 q^{14} - 966194 q^{15} + 4755334 q^{16} + 2558412 q^{17} - 2619769 q^{18} - 172269 q^{19} + 738120 q^{20} + 1797929 q^{21} + 3015622 q^{22} + 6635088 q^{23} + 4803145 q^{24} - 115100016 q^{25} + 19254293 q^{26} - 17686931 q^{27} + 15761532 q^{28} - 10052927 q^{29} + 62637435 q^{30} - 23748991 q^{31} + 10388192 q^{32} - 15097203 q^{33} + 33217854 q^{34} - 24823174 q^{35} + 27856812 q^{36} - 27156308 q^{37} - 43400577 q^{38} + 251072838 q^{39} - 129856160 q^{40} + 62087988 q^{41} - 91873950 q^{42} - 167299067 q^{43} + 60914131 q^{44} - 31536191 q^{45} - 50201490 q^{46} - 23317743 q^{47} + 10641329 q^{48} + 338745866 q^{49} + 303770229 q^{50} + 448039613 q^{51} - 979580293 q^{52} + 12085215 q^{53} - 182583505 q^{54} - 243892552 q^{55} + 30440435 q^{56} + 714581966 q^{57} - 244549660 q^{58} - 859013315 q^{59} - 1894499000 q^{60} - 876373921 q^{61} + 186553636 q^{62} - 196611021 q^{63} + 5528242635 q^{64} + 867018244 q^{65} + 2727701199 q^{66} - 286780089 q^{67} - 1689988351 q^{68} - 3073308182 q^{69} - 41489396 q^{70} - 2538053548 q^{71} - 6821388000 q^{72} + 128479023 q^{73} + 3282772334 q^{74} + 3407782757 q^{75} + 7133788844 q^{76} + 1087098389 q^{77} + 2715049934 q^{78} + 144243625 q^{79} - 7443877603 q^{80} - 4083269278 q^{81} - 10375744380 q^{82} + 1543773955 q^{83} - 4117054288 q^{84} + 7843382686 q^{85} + 3545751759 q^{86} + 5261609811 q^{87} - 818728797 q^{88} - 1369081479 q^{89} + 10041256259 q^{90} - 7299574322 q^{91} + 602797624 q^{92} - 2146129677 q^{93} - 683447510 q^{94} - 7007204038 q^{95} + 6601829126 q^{96} - 10081488030 q^{97} - 5942379880 q^{98} - 4074592265 q^{99}+O(q^{100})$$ 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

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 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −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