# Properties

 Label 4.9.b.b.3.2 Level $4$ Weight $9$ Character 4.3 Analytic conductor $1.630$ Analytic rank $0$ Dimension $2$ Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4,9,Mod(3,4)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 9, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4.3");

S:= CuspForms(chi, 9);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$4 = 2^{2}$$ Weight: $$k$$ $$=$$ $$9$$ Character orbit: $$[\chi]$$ $$=$$ 4.b (of order $$2$$, degree $$1$$, 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: $$1.62951444024$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\sqrt{-39})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} - x + 10$$ x^2 - x + 10 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 3.2 Root $$0.500000 - 3.12250i$$ of defining polynomial Character $$\chi$$ $$=$$ 4.3 Dual form 4.9.b.b.3.1

## $q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-10.0000 + 12.4900i) q^{2} +99.9200i q^{3} +(-56.0000 - 249.800i) q^{4} +610.000 q^{5} +(-1248.00 - 999.200i) q^{6} +1398.88i q^{7} +(3680.00 + 1798.56i) q^{8} -3423.00 q^{9} +O(q^{10})$$ $$q+(-10.0000 + 12.4900i) q^{2} +99.9200i q^{3} +(-56.0000 - 249.800i) q^{4} +610.000 q^{5} +(-1248.00 - 999.200i) q^{6} +1398.88i q^{7} +(3680.00 + 1798.56i) q^{8} -3423.00 q^{9} +(-6100.00 + 7618.90i) q^{10} -18485.2i q^{11} +(24960.0 - 5595.52i) q^{12} -5470.00 q^{13} +(-17472.0 - 13988.8i) q^{14} +60951.2i q^{15} +(-59264.0 + 27977.6i) q^{16} +73090.0 q^{17} +(34230.0 - 42753.3i) q^{18} -19484.4i q^{19} +(-34160.0 - 152378. i) q^{20} -139776. q^{21} +(230880. + 184852. i) q^{22} -237210. i q^{23} +(-179712. + 367705. i) q^{24} -18525.0 q^{25} +(54700.0 - 68320.3i) q^{26} +313549. i q^{27} +(349440. - 78337.3i) q^{28} -128222. q^{29} +(-761280. - 609512. i) q^{30} -67945.6i q^{31} +(243200. - 1.01998e6i) q^{32} +1.84704e6 q^{33} +(-730900. + 912894. i) q^{34} +853317. i q^{35} +(191688. + 855065. i) q^{36} -3.47203e6 q^{37} +(243360. + 194844. i) q^{38} -546562. i q^{39} +(2.24480e6 + 1.09712e6i) q^{40} +2.14688e6 q^{41} +(1.39776e6 - 1.74580e6i) q^{42} -5.92815e6i q^{43} +(-4.61760e6 + 1.03517e6i) q^{44} -2.08803e6 q^{45} +(2.96275e6 + 2.37210e6i) q^{46} +7.62629e6i q^{47} +(-2.79552e6 - 5.92166e6i) q^{48} +3.80794e6 q^{49} +(185250. - 231377. i) q^{50} +7.30315e6i q^{51} +(306320. + 1.36641e6i) q^{52} +824290. q^{53} +(-3.91622e6 - 3.13549e6i) q^{54} -1.12760e7i q^{55} +(-2.51597e6 + 5.14788e6i) q^{56} +1.94688e6 q^{57} +(1.28222e6 - 1.60149e6i) q^{58} -3.72552e6i q^{59} +(1.52256e7 - 3.41327e6i) q^{60} -1.47461e7 q^{61} +(848640. + 679456. i) q^{62} -4.78836e6i q^{63} +(1.03076e7 + 1.32374e7i) q^{64} -3.33670e6 q^{65} +(-1.84704e7 + 2.30695e7i) q^{66} +1.52567e7i q^{67} +(-4.09304e6 - 1.82579e7i) q^{68} +2.37020e7 q^{69} +(-1.06579e7 - 8.53317e6i) q^{70} -1.19604e6i q^{71} +(-1.25966e7 - 6.15647e6i) q^{72} -5.72563e6 q^{73} +(3.47203e7 - 4.33656e7i) q^{74} -1.85102e6i q^{75} +(-4.86720e6 + 1.09113e6i) q^{76} +2.58586e7 q^{77} +(6.82656e6 + 5.46562e6i) q^{78} +3.59132e7i q^{79} +(-3.61510e7 + 1.70663e7i) q^{80} -5.37881e7 q^{81} +(-2.14688e7 + 2.68145e7i) q^{82} -5.19603e7i q^{83} +(7.82746e6 + 3.49160e7i) q^{84} +4.45849e7 q^{85} +(7.40426e7 + 5.92815e7i) q^{86} -1.28119e7i q^{87} +(3.32467e7 - 6.80255e7i) q^{88} -8.33242e7 q^{89} +(2.08803e7 - 2.60795e7i) q^{90} -7.65187e6i q^{91} +(-5.92550e7 + 1.32838e7i) q^{92} +6.78912e6 q^{93} +(-9.52524e7 - 7.62629e7i) q^{94} -1.18855e7i q^{95} +(1.01917e8 + 2.43005e7i) q^{96} +1.20619e8 q^{97} +(-3.80794e7 + 4.75611e7i) q^{98} +6.32748e7i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 20 q^{2} - 112 q^{4} + 1220 q^{5} - 2496 q^{6} + 7360 q^{8} - 6846 q^{9}+O(q^{10})$$ 2 * q - 20 * q^2 - 112 * q^4 + 1220 * q^5 - 2496 * q^6 + 7360 * q^8 - 6846 * q^9 $$2 q - 20 q^{2} - 112 q^{4} + 1220 q^{5} - 2496 q^{6} + 7360 q^{8} - 6846 q^{9} - 12200 q^{10} + 49920 q^{12} - 10940 q^{13} - 34944 q^{14} - 118528 q^{16} + 146180 q^{17} + 68460 q^{18} - 68320 q^{20} - 279552 q^{21} + 461760 q^{22} - 359424 q^{24} - 37050 q^{25} + 109400 q^{26} + 698880 q^{28} - 256444 q^{29} - 1522560 q^{30} + 486400 q^{32} + 3694080 q^{33} - 1461800 q^{34} + 383376 q^{36} - 6944060 q^{37} + 486720 q^{38} + 4489600 q^{40} + 4293764 q^{41} + 2795520 q^{42} - 9235200 q^{44} - 4176060 q^{45} + 5925504 q^{46} - 5591040 q^{48} + 7615874 q^{49} + 370500 q^{50} + 612640 q^{52} + 1648580 q^{53} - 7832448 q^{54} - 5031936 q^{56} + 3893760 q^{57} + 2564440 q^{58} + 30451200 q^{60} - 29492156 q^{61} + 1697280 q^{62} + 20615168 q^{64} - 6673400 q^{65} - 36940800 q^{66} - 8186080 q^{68} + 47404032 q^{69} - 21315840 q^{70} - 25193280 q^{72} - 11451260 q^{73} + 69440600 q^{74} - 9734400 q^{76} + 51717120 q^{77} + 13653120 q^{78} - 72302080 q^{80} - 107576190 q^{81} - 42937640 q^{82} + 15654912 q^{84} + 89169800 q^{85} + 148085184 q^{86} + 66493440 q^{88} - 166648444 q^{89} + 41760600 q^{90} - 118510080 q^{92} + 13578240 q^{93} - 190504704 q^{94} + 203833344 q^{96} + 241238020 q^{97} - 76158740 q^{98}+O(q^{100})$$ 2 * q - 20 * q^2 - 112 * q^4 + 1220 * q^5 - 2496 * q^6 + 7360 * q^8 - 6846 * q^9 - 12200 * q^10 + 49920 * q^12 - 10940 * q^13 - 34944 * q^14 - 118528 * q^16 + 146180 * q^17 + 68460 * q^18 - 68320 * q^20 - 279552 * q^21 + 461760 * q^22 - 359424 * q^24 - 37050 * q^25 + 109400 * q^26 + 698880 * q^28 - 256444 * q^29 - 1522560 * q^30 + 486400 * q^32 + 3694080 * q^33 - 1461800 * q^34 + 383376 * q^36 - 6944060 * q^37 + 486720 * q^38 + 4489600 * q^40 + 4293764 * q^41 + 2795520 * q^42 - 9235200 * q^44 - 4176060 * q^45 + 5925504 * q^46 - 5591040 * q^48 + 7615874 * q^49 + 370500 * q^50 + 612640 * q^52 + 1648580 * q^53 - 7832448 * q^54 - 5031936 * q^56 + 3893760 * q^57 + 2564440 * q^58 + 30451200 * q^60 - 29492156 * q^61 + 1697280 * q^62 + 20615168 * q^64 - 6673400 * q^65 - 36940800 * q^66 - 8186080 * q^68 + 47404032 * q^69 - 21315840 * q^70 - 25193280 * q^72 - 11451260 * q^73 + 69440600 * q^74 - 9734400 * q^76 + 51717120 * q^77 + 13653120 * q^78 - 72302080 * q^80 - 107576190 * q^81 - 42937640 * q^82 + 15654912 * q^84 + 89169800 * q^85 + 148085184 * q^86 + 66493440 * q^88 - 166648444 * q^89 + 41760600 * q^90 - 118510080 * q^92 + 13578240 * q^93 - 190504704 * q^94 + 203833344 * q^96 + 241238020 * q^97 - 76158740 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/4\mathbb{Z}\right)^\times$$.

 $$n$$ $$3$$ $$\chi(n)$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −10.0000 + 12.4900i −0.625000 + 0.780625i
$$3$$ 99.9200i 1.23358i 0.787128 + 0.616790i $$0.211567\pi$$
−0.787128 + 0.616790i $$0.788433\pi$$
$$4$$ −56.0000 249.800i −0.218750 0.975781i
$$5$$ 610.000 0.976000 0.488000 0.872844i $$-0.337727\pi$$
0.488000 + 0.872844i $$0.337727\pi$$
$$6$$ −1248.00 999.200i −0.962963 0.770987i
$$7$$ 1398.88i 0.582624i 0.956628 + 0.291312i $$0.0940917\pi$$
−0.956628 + 0.291312i $$0.905908\pi$$
$$8$$ 3680.00 + 1798.56i 0.898438 + 0.439101i
$$9$$ −3423.00 −0.521719
$$10$$ −6100.00 + 7618.90i −0.610000 + 0.761890i
$$11$$ 18485.2i 1.26256i −0.775554 0.631282i $$-0.782529\pi$$
0.775554 0.631282i $$-0.217471\pi$$
$$12$$ 24960.0 5595.52i 1.20370 0.269846i
$$13$$ −5470.00 −0.191520 −0.0957600 0.995404i $$-0.530528\pi$$
−0.0957600 + 0.995404i $$0.530528\pi$$
$$14$$ −17472.0 13988.8i −0.454810 0.364140i
$$15$$ 60951.2i 1.20397i
$$16$$ −59264.0 + 27977.6i −0.904297 + 0.426904i
$$17$$ 73090.0 0.875109 0.437555 0.899192i $$-0.355845\pi$$
0.437555 + 0.899192i $$0.355845\pi$$
$$18$$ 34230.0 42753.3i 0.326075 0.407267i
$$19$$ 19484.4i 0.149511i −0.997202 0.0747554i $$-0.976182\pi$$
0.997202 0.0747554i $$-0.0238176\pi$$
$$20$$ −34160.0 152378.i −0.213500 0.952362i
$$21$$ −139776. −0.718713
$$22$$ 230880. + 184852.i 0.985588 + 0.789102i
$$23$$ 237210.i 0.847660i −0.905742 0.423830i $$-0.860685\pi$$
0.905742 0.423830i $$-0.139315\pi$$
$$24$$ −179712. + 367705.i −0.541667 + 1.10829i
$$25$$ −18525.0 −0.0474240
$$26$$ 54700.0 68320.3i 0.119700 0.149505i
$$27$$ 313549.i 0.589997i
$$28$$ 349440. 78337.3i 0.568513 0.127449i
$$29$$ −128222. −0.181289 −0.0906443 0.995883i $$-0.528893\pi$$
−0.0906443 + 0.995883i $$0.528893\pi$$
$$30$$ −761280. 609512.i −0.939852 0.752484i
$$31$$ 67945.6i 0.0735723i −0.999323 0.0367862i $$-0.988288\pi$$
0.999323 0.0367862i $$-0.0117120\pi$$
$$32$$ 243200. 1.01998e6i 0.231934 0.972732i
$$33$$ 1.84704e6 1.55747
$$34$$ −730900. + 912894.i −0.546943 + 0.683132i
$$35$$ 853317.i 0.568641i
$$36$$ 191688. + 855065.i 0.114126 + 0.509084i
$$37$$ −3.47203e6 −1.85258 −0.926289 0.376813i $$-0.877020\pi$$
−0.926289 + 0.376813i $$0.877020\pi$$
$$38$$ 243360. + 194844.i 0.116712 + 0.0934442i
$$39$$ 546562.i 0.236255i
$$40$$ 2.24480e6 + 1.09712e6i 0.876875 + 0.428563i
$$41$$ 2.14688e6 0.759754 0.379877 0.925037i $$-0.375966\pi$$
0.379877 + 0.925037i $$0.375966\pi$$
$$42$$ 1.39776e6 1.74580e6i 0.449196 0.561045i
$$43$$ 5.92815e6i 1.73399i −0.498321 0.866993i $$-0.666050\pi$$
0.498321 0.866993i $$-0.333950\pi$$
$$44$$ −4.61760e6 + 1.03517e6i −1.23199 + 0.276186i
$$45$$ −2.08803e6 −0.509198
$$46$$ 2.96275e6 + 2.37210e6i 0.661704 + 0.529787i
$$47$$ 7.62629e6i 1.56287i 0.623989 + 0.781433i $$0.285511\pi$$
−0.623989 + 0.781433i $$0.714489\pi$$
$$48$$ −2.79552e6 5.92166e6i −0.526620 1.11552i
$$49$$ 3.80794e6 0.660550
$$50$$ 185250. 231377.i 0.0296400 0.0370203i
$$51$$ 7.30315e6i 1.07952i
$$52$$ 306320. + 1.36641e6i 0.0418950 + 0.186881i
$$53$$ 824290. 0.104466 0.0522332 0.998635i $$-0.483366\pi$$
0.0522332 + 0.998635i $$0.483366\pi$$
$$54$$ −3.91622e6 3.13549e6i −0.460567 0.368748i
$$55$$ 1.12760e7i 1.23226i
$$56$$ −2.51597e6 + 5.14788e6i −0.255831 + 0.523451i
$$57$$ 1.94688e6 0.184433
$$58$$ 1.28222e6 1.60149e6i 0.113305 0.141518i
$$59$$ 3.72552e6i 0.307453i −0.988113 0.153726i $$-0.950873\pi$$
0.988113 0.153726i $$-0.0491274\pi$$
$$60$$ 1.52256e7 3.41327e6i 1.17481 0.263369i
$$61$$ −1.47461e7 −1.06502 −0.532509 0.846424i $$-0.678751\pi$$
−0.532509 + 0.846424i $$0.678751\pi$$
$$62$$ 848640. + 679456.i 0.0574324 + 0.0459827i
$$63$$ 4.78836e6i 0.303966i
$$64$$ 1.03076e7 + 1.32374e7i 0.614380 + 0.789010i
$$65$$ −3.33670e6 −0.186923
$$66$$ −1.84704e7 + 2.30695e7i −0.973421 + 1.21580i
$$67$$ 1.52567e7i 0.757113i 0.925578 + 0.378557i $$0.123579\pi$$
−0.925578 + 0.378557i $$0.876421\pi$$
$$68$$ −4.09304e6 1.82579e7i −0.191430 0.853915i
$$69$$ 2.37020e7 1.04566
$$70$$ −1.06579e7 8.53317e6i −0.443895 0.355400i
$$71$$ 1.19604e6i 0.0470666i −0.999723 0.0235333i $$-0.992508\pi$$
0.999723 0.0235333i $$-0.00749158\pi$$
$$72$$ −1.25966e7 6.15647e6i −0.468732 0.229088i
$$73$$ −5.72563e6 −0.201619 −0.100810 0.994906i $$-0.532143\pi$$
−0.100810 + 0.994906i $$0.532143\pi$$
$$74$$ 3.47203e7 4.33656e7i 1.15786 1.44617i
$$75$$ 1.85102e6i 0.0585013i
$$76$$ −4.86720e6 + 1.09113e6i −0.145890 + 0.0327055i
$$77$$ 2.58586e7 0.735600
$$78$$ 6.82656e6 + 5.46562e6i 0.184427 + 0.147659i
$$79$$ 3.59132e7i 0.922032i 0.887392 + 0.461016i $$0.152515\pi$$
−0.887392 + 0.461016i $$0.847485\pi$$
$$80$$ −3.61510e7 + 1.70663e7i −0.882594 + 0.416658i
$$81$$ −5.37881e7 −1.24953
$$82$$ −2.14688e7 + 2.68145e7i −0.474846 + 0.593082i
$$83$$ 5.19603e7i 1.09486i −0.836851 0.547431i $$-0.815606\pi$$
0.836851 0.547431i $$-0.184394\pi$$
$$84$$ 7.82746e6 + 3.49160e7i 0.157218 + 0.701306i
$$85$$ 4.45849e7 0.854107
$$86$$ 7.40426e7 + 5.92815e7i 1.35359 + 1.08374i
$$87$$ 1.28119e7i 0.223634i
$$88$$ 3.32467e7 6.80255e7i 0.554393 1.13433i
$$89$$ −8.33242e7 −1.32804 −0.664020 0.747715i $$-0.731151\pi$$
−0.664020 + 0.747715i $$0.731151\pi$$
$$90$$ 2.08803e7 2.60795e7i 0.318249 0.397493i
$$91$$ 7.65187e6i 0.111584i
$$92$$ −5.92550e7 + 1.32838e7i −0.827130 + 0.185426i
$$93$$ 6.78912e6 0.0907573
$$94$$ −9.52524e7 7.62629e7i −1.22001 0.976792i
$$95$$ 1.18855e7i 0.145923i
$$96$$ 1.01917e8 + 2.43005e7i 1.19994 + 0.286109i
$$97$$ 1.20619e8 1.36248 0.681238 0.732062i $$-0.261442\pi$$
0.681238 + 0.732062i $$0.261442\pi$$
$$98$$ −3.80794e7 + 4.75611e7i −0.412844 + 0.515641i
$$99$$ 6.32748e7i 0.658704i
$$100$$ 1.03740e6 + 4.62754e6i 0.0103740 + 0.0462754i
$$101$$ 2.77246e7 0.266428 0.133214 0.991087i $$-0.457470\pi$$
0.133214 + 0.991087i $$0.457470\pi$$
$$102$$ −9.12163e7 7.30315e7i −0.842698 0.674698i
$$103$$ 1.04501e8i 0.928477i 0.885710 + 0.464238i $$0.153672\pi$$
−0.885710 + 0.464238i $$0.846328\pi$$
$$104$$ −2.01296e7 9.83812e6i −0.172069 0.0840967i
$$105$$ −8.52634e7 −0.701464
$$106$$ −8.24290e6 + 1.02954e7i −0.0652915 + 0.0815490i
$$107$$ 1.00328e8i 0.765394i 0.923874 + 0.382697i $$0.125005\pi$$
−0.923874 + 0.382697i $$0.874995\pi$$
$$108$$ 7.83245e7 1.75587e7i 0.575708 0.129062i
$$109$$ −5.90716e7 −0.418478 −0.209239 0.977865i $$-0.567099\pi$$
−0.209239 + 0.977865i $$0.567099\pi$$
$$110$$ 1.40837e8 + 1.12760e8i 0.961934 + 0.770164i
$$111$$ 3.46925e8i 2.28530i
$$112$$ −3.91373e7 8.29032e7i −0.248724 0.526865i
$$113$$ 5.50849e7 0.337846 0.168923 0.985629i $$-0.445971\pi$$
0.168923 + 0.985629i $$0.445971\pi$$
$$114$$ −1.94688e7 + 2.43165e7i −0.115271 + 0.143973i
$$115$$ 1.44698e8i 0.827316i
$$116$$ 7.18043e6 + 3.20298e7i 0.0396569 + 0.176898i
$$117$$ 1.87238e7 0.0999196
$$118$$ 4.65317e7 + 3.72552e7i 0.240005 + 0.192158i
$$119$$ 1.02244e8i 0.509859i
$$120$$ −1.09624e8 + 2.24300e8i −0.528667 + 1.08170i
$$121$$ −1.27344e8 −0.594067
$$122$$ 1.47461e8 1.84178e8i 0.665637 0.831380i
$$123$$ 2.14516e8i 0.937217i
$$124$$ −1.69728e7 + 3.80495e6i −0.0717905 + 0.0160939i
$$125$$ −2.49581e8 −1.02229
$$126$$ 5.98067e7 + 4.78836e7i 0.237283 + 0.189979i
$$127$$ 2.57160e8i 0.988529i 0.869312 + 0.494264i $$0.164562\pi$$
−0.869312 + 0.494264i $$0.835438\pi$$
$$128$$ −2.68411e8 3.63229e6i −0.999908 0.0135313i
$$129$$ 5.92341e8 2.13901
$$130$$ 3.33670e7 4.16754e7i 0.116827 0.145917i
$$131$$ 3.12175e8i 1.06002i −0.847992 0.530009i $$-0.822188\pi$$
0.847992 0.530009i $$-0.177812\pi$$
$$132$$ −1.03434e8 4.61390e8i −0.340697 1.51975i
$$133$$ 2.72563e7 0.0871085
$$134$$ −1.90556e8 1.52567e8i −0.591021 0.473196i
$$135$$ 1.91265e8i 0.575838i
$$136$$ 2.68971e8 + 1.31457e8i 0.786231 + 0.384262i
$$137$$ 2.21980e8 0.630132 0.315066 0.949070i $$-0.397973\pi$$
0.315066 + 0.949070i $$0.397973\pi$$
$$138$$ −2.37020e8 + 2.96038e8i −0.653535 + 0.816265i
$$139$$ 2.95030e8i 0.790328i −0.918611 0.395164i $$-0.870688\pi$$
0.918611 0.395164i $$-0.129312\pi$$
$$140$$ 2.13158e8 4.77857e7i 0.554869 0.124390i
$$141$$ −7.62019e8 −1.92792
$$142$$ 1.49386e7 + 1.19604e7i 0.0367414 + 0.0294166i
$$143$$ 1.01114e8i 0.241806i
$$144$$ 2.02861e8 9.57673e7i 0.471789 0.222724i
$$145$$ −7.82154e7 −0.176938
$$146$$ 5.72563e7 7.15131e7i 0.126012 0.157389i
$$147$$ 3.80489e8i 0.814841i
$$148$$ 1.94434e8 + 8.67313e8i 0.405252 + 1.80771i
$$149$$ 4.03603e8 0.818859 0.409429 0.912342i $$-0.365728\pi$$
0.409429 + 0.912342i $$0.365728\pi$$
$$150$$ 2.31192e7 + 1.85102e7i 0.0456676 + 0.0365633i
$$151$$ 8.36985e8i 1.60994i −0.593316 0.804970i $$-0.702181\pi$$
0.593316 0.804970i $$-0.297819\pi$$
$$152$$ 3.50438e7 7.17026e7i 0.0656504 0.134326i
$$153$$ −2.50187e8 −0.456561
$$154$$ −2.58586e8 + 3.22973e8i −0.459750 + 0.574227i
$$155$$ 4.14468e7i 0.0718066i
$$156$$ −1.36531e8 + 3.06075e7i −0.230533 + 0.0516808i
$$157$$ −2.71319e8 −0.446561 −0.223281 0.974754i $$-0.571677\pi$$
−0.223281 + 0.974754i $$0.571677\pi$$
$$158$$ −4.48556e8 3.59132e8i −0.719761 0.576270i
$$159$$ 8.23630e7i 0.128868i
$$160$$ 1.48352e8 6.22190e8i 0.226367 0.949386i
$$161$$ 3.31828e8 0.493867
$$162$$ 5.37881e8 6.71813e8i 0.780955 0.975413i
$$163$$ 5.78509e8i 0.819520i 0.912193 + 0.409760i $$0.134388\pi$$
−0.912193 + 0.409760i $$0.865612\pi$$
$$164$$ −1.20225e8 5.36291e8i −0.166196 0.741353i
$$165$$ 1.12669e9 1.52009
$$166$$ 6.48984e8 + 5.19603e8i 0.854676 + 0.684288i
$$167$$ 4.68118e8i 0.601852i 0.953647 + 0.300926i $$0.0972958\pi$$
−0.953647 + 0.300926i $$0.902704\pi$$
$$168$$ −5.14376e8 2.51395e8i −0.645719 0.315588i
$$169$$ −7.85810e8 −0.963320
$$170$$ −4.45849e8 + 5.56865e8i −0.533817 + 0.666737i
$$171$$ 6.66951e7i 0.0780026i
$$172$$ −1.48085e9 + 3.31976e8i −1.69199 + 0.379309i
$$173$$ −2.06197e8 −0.230196 −0.115098 0.993354i $$-0.536718\pi$$
−0.115098 + 0.993354i $$0.536718\pi$$
$$174$$ 1.60021e8 + 1.28119e8i 0.174574 + 0.139771i
$$175$$ 2.59142e7i 0.0276303i
$$176$$ 5.17171e8 + 1.09551e9i 0.538994 + 1.14173i
$$177$$ 3.72253e8 0.379268
$$178$$ 8.33242e8 1.04072e9i 0.830025 1.03670i
$$179$$ 1.41911e8i 0.138230i 0.997609 + 0.0691152i $$0.0220176\pi$$
−0.997609 + 0.0691152i $$0.977982\pi$$
$$180$$ 1.16930e8 + 5.21590e8i 0.111387 + 0.496866i
$$181$$ 4.82566e8 0.449616 0.224808 0.974403i $$-0.427824\pi$$
0.224808 + 0.974403i $$0.427824\pi$$
$$182$$ 9.55718e7 + 7.65187e7i 0.0871053 + 0.0697400i
$$183$$ 1.47343e9i 1.31379i
$$184$$ 4.26636e8 8.72933e8i 0.372209 0.761569i
$$185$$ −2.11794e9 −1.80812
$$186$$ −6.78912e7 + 8.47961e7i −0.0567233 + 0.0708474i
$$187$$ 1.35108e9i 1.10488i
$$188$$ 1.90505e9 4.27072e8i 1.52502 0.341877i
$$189$$ −4.38617e8 −0.343747
$$190$$ 1.48450e8 + 1.18855e8i 0.113911 + 0.0912016i
$$191$$ 9.92461e8i 0.745727i 0.927886 + 0.372864i $$0.121624\pi$$
−0.927886 + 0.372864i $$0.878376\pi$$
$$192$$ −1.32268e9 + 1.02993e9i −0.973307 + 0.757887i
$$193$$ 1.17593e9 0.847526 0.423763 0.905773i $$-0.360709\pi$$
0.423763 + 0.905773i $$0.360709\pi$$
$$194$$ −1.20619e9 + 1.50653e9i −0.851547 + 1.06358i
$$195$$ 3.33403e8i 0.230585i
$$196$$ −2.13244e8 9.51222e8i −0.144495 0.644552i
$$197$$ 1.70538e9 1.13229 0.566144 0.824306i $$-0.308435\pi$$
0.566144 + 0.824306i $$0.308435\pi$$
$$198$$ −7.90302e8 6.32748e8i −0.514200 0.411690i
$$199$$ 2.49036e9i 1.58800i 0.607919 + 0.793999i $$0.292004\pi$$
−0.607919 + 0.793999i $$0.707996\pi$$
$$200$$ −6.81720e7 3.33183e7i −0.0426075 0.0208239i
$$201$$ −1.52445e9 −0.933960
$$202$$ −2.77246e8 + 3.46281e8i −0.166518 + 0.207981i
$$203$$ 1.79367e8i 0.105623i
$$204$$ 1.82433e9 4.08976e8i 1.05337 0.236144i
$$205$$ 1.30960e9 0.741519
$$206$$ −1.30522e9 1.04501e9i −0.724792 0.580298i
$$207$$ 8.11970e8i 0.442241i
$$208$$ 3.24174e8 1.53037e8i 0.173191 0.0817606i
$$209$$ −3.60173e8 −0.188767
$$210$$ 8.52634e8 1.06494e9i 0.438415 0.547580i
$$211$$ 1.46774e9i 0.740491i 0.928934 + 0.370245i $$0.120726\pi$$
−0.928934 + 0.370245i $$0.879274\pi$$
$$212$$ −4.61602e7 2.05908e8i −0.0228520 0.101936i
$$213$$ 1.19508e8 0.0580604
$$214$$ −1.25309e9 1.00328e9i −0.597486 0.478371i
$$215$$ 3.61617e9i 1.69237i
$$216$$ −5.63936e8 + 1.15386e9i −0.259069 + 0.530076i
$$217$$ 9.50477e7 0.0428650
$$218$$ 5.90716e8 7.37804e8i 0.261549 0.326674i
$$219$$ 5.72105e8i 0.248713i
$$220$$ −2.81674e9 + 6.31454e8i −1.20242 + 0.269557i
$$221$$ −3.99802e8 −0.167601
$$222$$ 4.33309e9 + 3.46925e9i 1.78396 + 1.42831i
$$223$$ 1.47920e9i 0.598147i −0.954230 0.299073i $$-0.903322\pi$$
0.954230 0.299073i $$-0.0966776\pi$$
$$224$$ 1.42683e9 + 3.40208e8i 0.566737 + 0.135130i
$$225$$ 6.34111e7 0.0247420
$$226$$ −5.50849e8 + 6.88011e8i −0.211154 + 0.263731i
$$227$$ 7.50054e8i 0.282481i −0.989975 0.141241i $$-0.954891\pi$$
0.989975 0.141241i $$-0.0451091\pi$$
$$228$$ −1.09025e8 4.86330e8i −0.0403448 0.179967i
$$229$$ −2.84784e9 −1.03556 −0.517778 0.855515i $$-0.673241\pi$$
−0.517778 + 0.855515i $$0.673241\pi$$
$$230$$ 1.80728e9 + 1.44698e9i 0.645823 + 0.517073i
$$231$$ 2.58379e9i 0.907421i
$$232$$ −4.71857e8 2.30615e8i −0.162876 0.0796041i
$$233$$ 2.20621e8 0.0748553 0.0374276 0.999299i $$-0.488084\pi$$
0.0374276 + 0.999299i $$0.488084\pi$$
$$234$$ −1.87238e8 + 2.33860e8i −0.0624498 + 0.0779997i
$$235$$ 4.65204e9i 1.52536i
$$236$$ −9.30634e8 + 2.08629e8i −0.300007 + 0.0672553i
$$237$$ −3.58845e9 −1.13740
$$238$$ −1.27703e9 1.02244e9i −0.398009 0.318662i
$$239$$ 4.04493e9i 1.23971i −0.784717 0.619855i $$-0.787192\pi$$
0.784717 0.619855i $$-0.212808\pi$$
$$240$$ −1.70527e9 3.61221e9i −0.513981 1.08875i
$$241$$ 6.17983e9 1.83193 0.915964 0.401260i $$-0.131427\pi$$
0.915964 + 0.401260i $$0.131427\pi$$
$$242$$ 1.27344e9 1.59052e9i 0.371292 0.463743i
$$243$$ 3.31731e9i 0.951395i
$$244$$ 8.25780e8 + 3.68357e9i 0.232973 + 1.03922i
$$245$$ 2.32284e9 0.644696
$$246$$ −2.67931e9 2.14516e9i −0.731615 0.585760i
$$247$$ 1.06580e8i 0.0286343i
$$248$$ 1.22204e8 2.50040e8i 0.0323057 0.0661001i
$$249$$ 5.19187e9 1.35060
$$250$$ 2.49582e9 3.11727e9i 0.638929 0.798022i
$$251$$ 5.21367e9i 1.31356i 0.754084 + 0.656778i $$0.228081\pi$$
−0.754084 + 0.656778i $$0.771919\pi$$
$$252$$ −1.19613e9 + 2.68148e8i −0.296604 + 0.0664926i
$$253$$ −4.38487e9 −1.07022
$$254$$ −3.21193e9 2.57160e9i −0.771670 0.617830i
$$255$$ 4.45492e9i 1.05361i
$$256$$ 2.72948e9 3.31613e9i 0.635506 0.772096i
$$257$$ −6.13693e9 −1.40676 −0.703378 0.710816i $$-0.748326\pi$$
−0.703378 + 0.710816i $$0.748326\pi$$
$$258$$ −5.92341e9 + 7.39833e9i −1.33688 + 1.66976i
$$259$$ 4.85695e9i 1.07936i
$$260$$ 1.86855e8 + 8.33507e8i 0.0408895 + 0.182396i
$$261$$ 4.38904e8 0.0945818
$$262$$ 3.89907e9 + 3.12175e9i 0.827477 + 0.662512i
$$263$$ 6.96916e9i 1.45666i 0.685228 + 0.728329i $$0.259703\pi$$
−0.685228 + 0.728329i $$0.740297\pi$$
$$264$$ 6.79711e9 + 3.32201e9i 1.39929 + 0.683889i
$$265$$ 5.02817e8 0.101959
$$266$$ −2.72563e8 + 3.40431e8i −0.0544428 + 0.0679991i
$$267$$ 8.32575e9i 1.63824i
$$268$$ 3.81112e9 8.54374e8i 0.738777 0.165619i
$$269$$ 2.70720e9 0.517025 0.258513 0.966008i $$-0.416768\pi$$
0.258513 + 0.966008i $$0.416768\pi$$
$$270$$ −2.38890e9 1.91265e9i −0.449513 0.359898i
$$271$$ 7.99032e9i 1.48145i −0.671808 0.740725i $$-0.734482\pi$$
0.671808 0.740725i $$-0.265518\pi$$
$$272$$ −4.33161e9 + 2.04488e9i −0.791359 + 0.373588i
$$273$$ 7.64575e8 0.137648
$$274$$ −2.21980e9 + 2.77253e9i −0.393832 + 0.491897i
$$275$$ 3.42438e8i 0.0598758i
$$276$$ −1.32731e9 5.92076e9i −0.228737 1.02033i
$$277$$ −8.22965e9 −1.39786 −0.698928 0.715192i $$-0.746339\pi$$
−0.698928 + 0.715192i $$0.746339\pi$$
$$278$$ 3.68493e9 + 2.95030e9i 0.616949 + 0.493955i
$$279$$ 2.32578e8i 0.0383841i
$$280$$ −1.53474e9 + 3.14020e9i −0.249691 + 0.510888i
$$281$$ 3.08105e9 0.494167 0.247083 0.968994i $$-0.420528\pi$$
0.247083 + 0.968994i $$0.420528\pi$$
$$282$$ 7.62019e9 9.51761e9i 1.20495 1.50498i
$$283$$ 1.17112e9i 0.182582i 0.995824 + 0.0912908i $$0.0290993\pi$$
−0.995824 + 0.0912908i $$0.970901\pi$$
$$284$$ −2.98771e8 + 6.69784e7i −0.0459267 + 0.0102958i
$$285$$ 1.18760e9 0.180007
$$286$$ −1.26291e9 1.01114e9i −0.188760 0.151129i
$$287$$ 3.00323e9i 0.442650i
$$288$$ −8.32474e8 + 3.49140e9i −0.121004 + 0.507493i
$$289$$ −1.63361e9 −0.234184
$$290$$ 7.82154e8 9.76910e8i 0.110586 0.138122i
$$291$$ 1.20522e10i 1.68072i
$$292$$ 3.20635e8 + 1.43026e9i 0.0441042 + 0.196736i
$$293$$ 4.80980e9 0.652614 0.326307 0.945264i $$-0.394196\pi$$
0.326307 + 0.945264i $$0.394196\pi$$
$$294$$ −4.75231e9 3.80489e9i −0.636085 0.509275i
$$295$$ 2.27256e9i 0.300074i
$$296$$ −1.27771e10 6.24465e9i −1.66443 0.813470i
$$297$$ 5.79601e9 0.744909
$$298$$ −4.03603e9 + 5.04100e9i −0.511787 + 0.639221i
$$299$$ 1.29754e9i 0.162344i
$$300$$ −4.62384e8 + 1.03657e8i −0.0570844 + 0.0127972i
$$301$$ 8.29277e9 1.01026
$$302$$ 1.04539e10 + 8.36985e9i 1.25676 + 1.00621i
$$303$$ 2.77025e9i 0.328661i
$$304$$ 5.45126e8 + 1.15472e9i 0.0638268 + 0.135202i
$$305$$ −8.99511e9 −1.03946
$$306$$ 2.50187e9 3.12484e9i 0.285351 0.356403i
$$307$$ 3.49176e9i 0.393089i −0.980495 0.196545i $$-0.937028\pi$$
0.980495 0.196545i $$-0.0629721\pi$$
$$308$$ −1.44808e9 6.45947e9i −0.160912 0.717784i
$$309$$ −1.04417e10 −1.14535
$$310$$ 5.17670e8 + 4.14468e8i 0.0560540 + 0.0448791i
$$311$$ 1.29807e10i 1.38757i −0.720182 0.693785i $$-0.755942\pi$$
0.720182 0.693785i $$-0.244058\pi$$
$$312$$ 9.83025e8 2.01135e9i 0.103740 0.212260i
$$313$$ −6.31165e9 −0.657606 −0.328803 0.944399i $$-0.606645\pi$$
−0.328803 + 0.944399i $$0.606645\pi$$
$$314$$ 2.71319e9 3.38877e9i 0.279101 0.348597i
$$315$$ 2.92090e9i 0.296671i
$$316$$ 8.97112e9 2.01114e9i 0.899702 0.201695i
$$317$$ 1.65902e10 1.64291 0.821455 0.570273i $$-0.193163\pi$$
0.821455 + 0.570273i $$0.193163\pi$$
$$318$$ −1.02871e9 8.23630e8i −0.100597 0.0805423i
$$319$$ 2.37021e9i 0.228888i
$$320$$ 6.28763e9 + 8.07481e9i 0.599635 + 0.770074i
$$321$$ −1.00247e10 −0.944175
$$322$$ −3.31828e9 + 4.14453e9i −0.308667 + 0.385525i
$$323$$ 1.42411e9i 0.130838i
$$324$$ 3.01213e9 + 1.34363e10i 0.273334 + 1.21927i
$$325$$ 1.01332e8 0.00908264
$$326$$ −7.22557e9 5.78509e9i −0.639738 0.512200i
$$327$$ 5.90243e9i 0.516226i
$$328$$ 7.90053e9 + 3.86129e9i 0.682591 + 0.333609i
$$329$$ −1.06683e10 −0.910563
$$330$$ −1.12669e10 + 1.40724e10i −0.950059 + 1.18662i
$$331$$ 5.48640e9i 0.457062i 0.973537 + 0.228531i $$0.0733922\pi$$
−0.973537 + 0.228531i $$0.926608\pi$$
$$332$$ −1.29797e10 + 2.90978e9i −1.06834 + 0.239501i
$$333$$ 1.18848e10 0.966526
$$334$$ −5.84680e9 4.68118e9i −0.469821 0.376158i
$$335$$ 9.30657e9i 0.738942i
$$336$$ 8.28368e9 3.91060e9i 0.649930 0.306822i
$$337$$ −3.56226e8 −0.0276189 −0.0138095 0.999905i $$-0.504396\pi$$
−0.0138095 + 0.999905i $$0.504396\pi$$
$$338$$ 7.85810e9 9.81476e9i 0.602075 0.751992i
$$339$$ 5.50408e9i 0.416760i
$$340$$ −2.49675e9 1.11373e10i −0.186836 0.833421i
$$341$$ −1.25599e9 −0.0928897
$$342$$ −8.33021e8 6.66951e8i −0.0608908 0.0487517i
$$343$$ 1.33911e10i 0.967476i
$$344$$ 1.06621e10 2.18156e10i 0.761396 1.55788i
$$345$$ 1.44582e10 1.02056
$$346$$ 2.06197e9 2.57540e9i 0.143872 0.179697i
$$347$$ 1.59731e10i 1.10172i −0.834599 0.550859i $$-0.814300\pi$$
0.834599 0.550859i $$-0.185700\pi$$
$$348$$ −3.20042e9 + 7.17469e8i −0.218218 + 0.0489199i
$$349$$ 1.03634e10 0.698553 0.349277 0.937020i $$-0.386427\pi$$
0.349277 + 0.937020i $$0.386427\pi$$
$$350$$ 3.23669e8 + 2.59142e8i 0.0215689 + 0.0172690i
$$351$$ 1.71511e9i 0.112996i
$$352$$ −1.88546e10 4.49560e9i −1.22814 0.292831i
$$353$$ −1.30979e10 −0.843536 −0.421768 0.906704i $$-0.638590\pi$$
−0.421768 + 0.906704i $$0.638590\pi$$
$$354$$ −3.72253e9 + 4.64944e9i −0.237042 + 0.296066i
$$355$$ 7.29586e8i 0.0459370i
$$356$$ 4.66616e9 + 2.08144e10i 0.290509 + 1.29588i
$$357$$ −1.02162e10 −0.628952
$$358$$ −1.77247e9 1.41911e9i −0.107906 0.0863940i
$$359$$ 3.31454e9i 0.199547i 0.995010 + 0.0997737i $$0.0318119\pi$$
−0.995010 + 0.0997737i $$0.968188\pi$$
$$360$$ −7.68395e9 3.75545e9i −0.457483 0.223590i
$$361$$ 1.66039e10 0.977647
$$362$$ −4.82566e9 + 6.02724e9i −0.281010 + 0.350982i
$$363$$ 1.27242e10i 0.732829i
$$364$$ −1.91144e9 + 4.28505e8i −0.108882 + 0.0244090i
$$365$$ −3.49263e9 −0.196780
$$366$$ 1.84031e10 + 1.47343e10i 1.02557 + 0.821116i
$$367$$ 1.96628e10i 1.08388i 0.840418 + 0.541939i $$0.182309\pi$$
−0.840418 + 0.541939i $$0.817691\pi$$
$$368$$ 6.63656e9 + 1.40580e10i 0.361870 + 0.766536i
$$369$$ −7.34878e9 −0.396378
$$370$$ 2.11794e10 2.64530e10i 1.13007 1.41146i
$$371$$ 1.15308e9i 0.0608646i
$$372$$ −3.80191e8 1.69592e9i −0.0198532 0.0885593i
$$373$$ −2.10063e10 −1.08521 −0.542606 0.839987i $$-0.682562\pi$$
−0.542606 + 0.839987i $$0.682562\pi$$
$$374$$ 1.68750e10 + 1.35108e10i 0.862498 + 0.690551i
$$375$$ 2.49382e10i 1.26107i
$$376$$ −1.37163e10 + 2.80648e10i −0.686257 + 1.40414i
$$377$$ 7.01374e8 0.0347204
$$378$$ 4.38617e9 5.47833e9i 0.214842 0.268337i
$$379$$ 3.04816e9i 0.147734i 0.997268 + 0.0738670i $$0.0235340\pi$$
−0.997268 + 0.0738670i $$0.976466\pi$$
$$380$$ −2.96899e9 + 6.65587e8i −0.142388 + 0.0319206i
$$381$$ −2.56955e10 −1.21943
$$382$$ −1.23958e10 9.92461e9i −0.582133 0.466080i
$$383$$ 2.23357e10i 1.03802i −0.854770 0.519008i $$-0.826302\pi$$
0.854770 0.519008i $$-0.173698\pi$$
$$384$$ 3.62938e8 2.68196e10i 0.0166920 1.23347i
$$385$$ 1.57737e10 0.717945
$$386$$ −1.17593e10 + 1.46874e10i −0.529704 + 0.661599i
$$387$$ 2.02921e10i 0.904654i
$$388$$ −6.75466e9 3.01306e10i −0.298042 1.32948i
$$389$$ 3.13680e10 1.36990 0.684948 0.728592i $$-0.259825\pi$$
0.684948 + 0.728592i $$0.259825\pi$$
$$390$$ 4.16420e9 + 3.33403e9i 0.180000 + 0.144116i
$$391$$ 1.73377e10i 0.741795i
$$392$$ 1.40132e10 + 6.84880e9i 0.593463 + 0.290048i
$$393$$ 3.11926e10 1.30762
$$394$$ −1.70538e10 + 2.13002e10i −0.707680 + 0.883892i
$$395$$ 2.19071e10i 0.899904i
$$396$$ 1.58060e10 3.54339e9i 0.642751 0.144091i
$$397$$ 7.65788e9 0.308281 0.154140 0.988049i $$-0.450739\pi$$
0.154140 + 0.988049i $$0.450739\pi$$
$$398$$ −3.11046e10 2.49036e10i −1.23963 0.992499i
$$399$$ 2.72345e9i 0.107455i
$$400$$ 1.09787e9 5.18285e8i 0.0428854 0.0202455i
$$401$$ −3.26120e10 −1.26125 −0.630623 0.776089i $$-0.717201\pi$$
−0.630623 + 0.776089i $$0.717201\pi$$
$$402$$ 1.52445e10 1.90403e10i 0.583725 0.729072i
$$403$$ 3.71662e8i 0.0140906i
$$404$$ −1.55258e9 6.92561e9i −0.0582812 0.259976i
$$405$$ −3.28107e10 −1.21954
$$406$$ 2.24029e9 + 1.79367e9i 0.0824520 + 0.0660144i
$$407$$ 6.41811e10i 2.33900i
$$408$$ −1.31352e10 + 2.68756e10i −0.474018 + 0.969879i
$$409$$ 2.26168e10 0.808236 0.404118 0.914707i $$-0.367578\pi$$
0.404118 + 0.914707i $$0.367578\pi$$
$$410$$ −1.30960e10 + 1.63569e10i −0.463450 + 0.578848i
$$411$$ 2.21802e10i 0.777318i
$$412$$ 2.61043e10 5.85205e9i 0.905990 0.203104i
$$413$$ 5.21155e9 0.179129
$$414$$ −1.01415e10 8.11970e9i −0.345224 0.276400i
$$415$$ 3.16958e10i 1.06858i
$$416$$ −1.33030e9 + 5.57931e9i −0.0444199 + 0.186297i
$$417$$ 2.94794e10 0.974932
$$418$$ 3.60173e9 4.49856e9i 0.117979 0.147356i
$$419$$ 4.94503e10i 1.60440i −0.597054 0.802201i $$-0.703662\pi$$
0.597054 0.802201i $$-0.296338\pi$$
$$420$$ 4.77475e9 + 2.12988e10i 0.153445 + 0.684475i
$$421$$ −3.34077e10 −1.06345 −0.531726 0.846916i $$-0.678457\pi$$
−0.531726 + 0.846916i $$0.678457\pi$$
$$422$$ −1.83321e10 1.46774e10i −0.578045 0.462807i
$$423$$ 2.61048e10i 0.815378i
$$424$$ 3.03339e9 + 1.48253e9i 0.0938565 + 0.0458713i
$$425$$ −1.35399e9 −0.0415012
$$426$$ −1.19508e9 + 1.49266e9i −0.0362878 + 0.0453234i
$$427$$ 2.06280e10i 0.620505i
$$428$$ 2.50618e10 5.61834e9i 0.746857 0.167430i
$$429$$ −1.01033e10 −0.298287
$$430$$ 4.51660e10 + 3.61617e10i 1.32111 + 1.05773i
$$431$$ 3.06956e10i 0.889544i −0.895644 0.444772i $$-0.853285\pi$$
0.895644 0.444772i $$-0.146715\pi$$
$$432$$ −8.77234e9 1.85822e10i −0.251872 0.533533i
$$433$$ 2.88433e9 0.0820529 0.0410265 0.999158i $$-0.486937\pi$$
0.0410265 + 0.999158i $$0.486937\pi$$
$$434$$ −9.50477e8 + 1.18715e9i −0.0267906 + 0.0334615i
$$435$$ 7.81528e9i 0.218267i
$$436$$ 3.30801e9 + 1.47561e10i 0.0915421 + 0.408343i
$$437$$ −4.62189e9 −0.126734
$$438$$ 7.14559e9 + 5.72105e9i 0.194152 + 0.155446i
$$439$$ 6.92422e10i 1.86429i 0.362088 + 0.932144i $$0.382064\pi$$
−0.362088 + 0.932144i $$0.617936\pi$$
$$440$$ 2.02805e10 4.14956e10i 0.541088 1.10711i
$$441$$ −1.30346e10 −0.344621
$$442$$ 3.99802e9 4.99353e9i 0.104751 0.130833i
$$443$$ 2.06609e10i 0.536455i 0.963356 + 0.268228i $$0.0864379\pi$$
−0.963356 + 0.268228i $$0.913562\pi$$
$$444$$ −8.66619e10 + 1.94278e10i −2.22996 + 0.499910i
$$445$$ −5.08278e10 −1.29617
$$446$$ 1.84752e10 + 1.47920e10i 0.466928 + 0.373842i
$$447$$ 4.03280e10i 1.01013i
$$448$$ −1.85175e10 + 1.44191e10i −0.459696 + 0.357952i
$$449$$ 2.11092e10 0.519382 0.259691 0.965692i $$-0.416379\pi$$
0.259691 + 0.965692i $$0.416379\pi$$
$$450$$ −6.34111e8 + 7.92004e8i −0.0154638 + 0.0193142i
$$451$$ 3.96855e10i 0.959237i
$$452$$ −3.08476e9 1.37602e10i −0.0739039 0.329664i
$$453$$ 8.36315e10 1.98599
$$454$$ 9.36818e9 + 7.50054e9i 0.220512 + 0.176551i
$$455$$ 4.66764e9i 0.108906i
$$456$$ 7.16452e9 + 3.50158e9i 0.165702 + 0.0809850i
$$457$$ −2.06831e10 −0.474188 −0.237094 0.971487i $$-0.576195\pi$$
−0.237094 + 0.971487i $$0.576195\pi$$
$$458$$ 2.84784e10 3.55695e10i 0.647223 0.808381i
$$459$$ 2.29173e10i 0.516312i
$$460$$ −3.61456e10 + 8.10309e9i −0.807279 + 0.180975i
$$461$$ 7.65072e10 1.69394 0.846971 0.531640i $$-0.178424\pi$$
0.846971 + 0.531640i $$0.178424\pi$$
$$462$$ −3.22715e10 2.58379e10i −0.708355 0.567138i
$$463$$ 3.41303e9i 0.0742704i 0.999310 + 0.0371352i $$0.0118232\pi$$
−0.999310 + 0.0371352i $$0.988177\pi$$
$$464$$ 7.59895e9 3.58734e9i 0.163939 0.0773929i
$$465$$ 4.14136e9 0.0885791
$$466$$ −2.20621e9 + 2.75555e9i −0.0467845 + 0.0584339i
$$467$$ 1.92903e10i 0.405576i 0.979223 + 0.202788i $$0.0650002\pi$$
−0.979223 + 0.202788i $$0.935000\pi$$
$$468$$ −1.04853e9 4.67721e9i −0.0218574 0.0974997i
$$469$$ −2.13423e10 −0.441112
$$470$$ −5.81039e10 4.65204e10i −1.19073 0.953349i
$$471$$ 2.71102e10i 0.550869i
$$472$$ 6.70056e9 1.37099e10i 0.135003 0.276227i
$$473$$ −1.09583e11 −2.18927
$$474$$ 3.58845e10 4.48197e10i 0.710875 0.887883i
$$475$$ 3.60948e8i 0.00709040i
$$476$$ 2.55406e10 5.72567e9i 0.497511 0.111532i
$$477$$ −2.82154e9 −0.0545021
$$478$$ 5.05212e10 + 4.04493e10i 0.967748 + 0.774818i
$$479$$ 2.43887e10i 0.463282i −0.972801 0.231641i $$-0.925590\pi$$
0.972801 0.231641i $$-0.0744095\pi$$
$$480$$ 6.21692e10 + 1.48233e10i 1.17114 + 0.279242i
$$481$$ 1.89920e10 0.354806
$$482$$ −6.17983e10 + 7.71861e10i −1.14496 + 1.43005i
$$483$$ 3.31563e10i 0.609224i
$$484$$ 7.13124e9 + 3.18104e10i 0.129952 + 0.579679i
$$485$$ 7.35776e10 1.32978
$$486$$ 4.14332e10 + 3.31731e10i 0.742683 + 0.594622i
$$487$$ 9.30801e10i 1.65478i −0.561626 0.827391i $$-0.689824\pi$$
0.561626 0.827391i $$-0.310176\pi$$
$$488$$ −5.42656e10 2.65217e10i −0.956853 0.467651i
$$489$$ −5.78046e10 −1.01094
$$490$$ −2.32284e10 + 2.90123e10i −0.402935 + 0.503266i
$$491$$ 2.12850e9i 0.0366225i −0.999832 0.0183113i $$-0.994171\pi$$
0.999832 0.0183113i $$-0.00582898\pi$$
$$492$$ 5.35862e10 1.20129e10i 0.914518 0.205016i
$$493$$ −9.37175e9 −0.158647
$$494$$ −1.33118e9 1.06580e9i −0.0223526 0.0178964i
$$495$$ 3.85976e10i 0.642895i
$$496$$ 1.90095e9 + 4.02673e9i 0.0314083 + 0.0665312i
$$497$$ 1.67312e9 0.0274221
$$498$$ −5.19187e10 + 6.48464e10i −0.844124 + 1.05431i
$$499$$ 1.04101e10i 0.167901i 0.996470 + 0.0839503i $$0.0267537\pi$$
−0.996470 + 0.0839503i $$0.973246\pi$$
$$500$$ 1.39766e10 + 6.23454e10i 0.223625 + 0.997527i
$$501$$ −4.67744e10 −0.742433
$$502$$ −6.51187e10 5.21367e10i −1.02539 0.820973i
$$503$$ 3.93019e10i 0.613962i 0.951716 + 0.306981i $$0.0993188\pi$$
−0.951716 + 0.306981i $$0.900681\pi$$
$$504$$ 8.61216e9 1.76212e10i 0.133472 0.273094i
$$505$$ 1.69120e10 0.260034
$$506$$ 4.38487e10 5.47670e10i 0.668890 0.835444i
$$507$$ 7.85181e10i 1.18833i
$$508$$ 6.42387e10 1.44010e10i 0.964587 0.216241i
$$509$$ −3.25113e10 −0.484354 −0.242177 0.970232i $$-0.577861\pi$$
−0.242177 + 0.970232i $$0.577861\pi$$
$$510$$ −5.56420e10 4.45492e10i −0.822473 0.658505i
$$511$$ 8.00947e9i 0.117468i
$$512$$ 1.41237e10 + 6.72524e10i 0.205526 + 0.978652i
$$513$$ 6.10931e9 0.0882110
$$514$$ 6.13693e10 7.66503e10i 0.879223 1.09815i
$$515$$ 6.37455e10i 0.906194i
$$516$$ −3.31711e10 1.47967e11i −0.467908 2.08720i
$$517$$ 1.40973e11 1.97322
$$518$$ 6.06633e10 + 4.85695e10i 0.842572 + 0.674598i
$$519$$ 2.06032e10i 0.283965i
$$520$$ −1.22791e10 6.00125e9i −0.167939 0.0820783i
$$521$$ 1.84550e9 0.0250475 0.0125237 0.999922i $$-0.496013\pi$$
0.0125237 + 0.999922i $$0.496013\pi$$
$$522$$ −4.38904e9 + 5.48191e9i −0.0591136 + 0.0738329i
$$523$$ 6.23770e10i 0.833715i 0.908972 + 0.416858i $$0.136869\pi$$
−0.908972 + 0.416858i $$0.863131\pi$$
$$524$$ −7.79814e10 + 1.74818e10i −1.03435 + 0.231879i
$$525$$ 2.58935e9 0.0340842
$$526$$ −8.70448e10 6.96916e10i −1.13710 0.910411i
$$527$$ 4.96614e9i 0.0643838i
$$528$$ −1.09463e11 + 5.16757e10i −1.40842 + 0.664892i
$$529$$ 2.20424e10 0.281473
$$530$$ −5.02817e9 + 6.28018e9i −0.0637245 + 0.0795919i
$$531$$ 1.27524e10i 0.160404i
$$532$$ −1.52635e9 6.80863e9i −0.0190550 0.0849988i
$$533$$ −1.17434e10 −0.145508
$$534$$ 1.03989e11 + 8.32575e10i 1.27885 + 1.02390i
$$535$$ 6.11998e10i 0.747025i
$$536$$ −2.74400e10 + 5.61446e10i −0.332449 + 0.680219i
$$537$$ −1.41797e10 −0.170518
$$538$$ −2.70720e10 + 3.38130e10i −0.323141 + 0.403603i
$$539$$ 7.03905e10i 0.833986i
$$540$$ 4.77779e10 1.07108e10i 0.561891 0.125964i
$$541$$ −7.45917e10 −0.870766 −0.435383 0.900245i $$-0.643387\pi$$
−0.435383 + 0.900245i $$0.643387\pi$$
$$542$$ 9.97991e10 + 7.99032e10i 1.15646 + 0.925907i
$$543$$ 4.82179e10i 0.554638i
$$544$$ 1.77755e10 7.45506e10i 0.202967 0.851246i
$$545$$ −3.60337e10 −0.408435
$$546$$ −7.64575e9 + 9.54954e9i −0.0860299 + 0.107451i
$$547$$ 1.41531e9i 0.0158089i 0.999969 + 0.00790445i $$0.00251609\pi$$
−0.999969 + 0.00790445i $$0.997484\pi$$
$$548$$ −1.24309e10 5.54506e10i −0.137841 0.614871i
$$549$$ 5.04758e10 0.555641
$$550$$ −4.27705e9 3.42438e9i −0.0467405 0.0374224i
$$551$$ 2.49833e9i 0.0271046i
$$552$$ 8.72234e10 + 4.26295e10i 0.939457 + 0.459149i
$$553$$ −5.02383e10 −0.537198
$$554$$ 8.22965e10 1.02788e11i 0.873660 1.09120i
$$555$$ 2.11624e11i 2.23046i
$$556$$ −7.36985e10 + 1.65217e10i −0.771187 + 0.172884i
$$557$$ −1.37543e11 −1.42895 −0.714475 0.699661i $$-0.753334\pi$$
−0.714475 + 0.699661i $$0.753334\pi$$
$$558$$ −2.90489e9 2.32578e9i −0.0299636 0.0239901i
$$559$$ 3.24270e10i 0.332093i
$$560$$ −2.38737e10 5.05710e10i −0.242755 0.514220i
$$561$$ 1.35000e11 1.36296
$$562$$ −3.08105e10 + 3.84823e10i −0.308854 + 0.385759i
$$563$$ 1.06415e11i 1.05918i −0.848255 0.529589i $$-0.822346\pi$$
0.848255 0.529589i $$-0.177654\pi$$
$$564$$ 4.26731e10 + 1.90352e11i 0.421733 + 1.88123i
$$565$$ 3.36018e10 0.329738
$$566$$ −1.46273e10 1.17112e10i −0.142528 0.114113i
$$567$$ 7.52431e10i 0.728005i
$$568$$ 2.15115e9 4.40143e9i 0.0206670 0.0422864i
$$569$$ 4.02429e10 0.383919 0.191960 0.981403i $$-0.438516\pi$$
0.191960 + 0.981403i $$0.438516\pi$$
$$570$$ −1.18760e10 + 1.48331e10i −0.112504 + 0.140518i
$$571$$ 1.50341e11i 1.41427i 0.707077 + 0.707137i $$0.250014\pi$$
−0.707077 + 0.707137i $$0.749986\pi$$
$$572$$ 2.52583e10 5.66238e9i 0.235950 0.0528951i
$$573$$ −9.91667e10 −0.919914
$$574$$ −3.75103e10 3.00323e10i −0.345544 0.276657i
$$575$$ 4.39432e9i 0.0401994i
$$576$$ −3.52829e10 4.53116e10i −0.320534 0.411642i
$$577$$ 4.96477e9 0.0447915 0.0223958 0.999749i $$-0.492871\pi$$
0.0223958 + 0.999749i $$0.492871\pi$$
$$578$$ 1.63361e10 2.04038e10i 0.146365 0.182810i
$$579$$ 1.17499e11i 1.04549i
$$580$$ 4.38006e9 + 1.95382e10i 0.0387051 + 0.172652i
$$581$$ 7.26862e10 0.637892
$$582$$ −1.50533e11 1.20522e11i −1.31201 1.05045i
$$583$$ 1.52372e10i 0.131895i
$$584$$ −2.10703e10 1.02979e10i −0.181142 0.0885313i
$$585$$ 1.14215e10 0.0975216
$$586$$ −4.80980e10 + 6.00743e10i −0.407884 + 0.509446i
$$587$$ 1.53440e11i 1.29237i 0.763181 + 0.646185i $$0.223637\pi$$
−0.763181 + 0.646185i $$0.776363\pi$$
$$588$$ 9.50461e10 2.13074e10i 0.795106 0.178246i
$$589$$ −1.32388e9 −0.0109999
$$590$$ 2.83843e10 + 2.27256e10i 0.234245 + 0.187546i
$$591$$ 1.70402e11i 1.39677i
$$592$$ 2.05766e11 9.71390e10i 1.67528 0.790873i
$$593$$ 2.06036e11 1.66619 0.833094 0.553131i $$-0.186567\pi$$
0.833094 + 0.553131i $$0.186567\pi$$
$$594$$ −5.79601e10 + 7.23922e10i −0.465568 + 0.581495i
$$595$$ 6.23689e10i 0.497623i
$$596$$ −2.26017e10 1.00820e11i −0.179125 0.799027i
$$597$$ −2.48837e11 −1.95892
$$598$$ −1.62063e10 1.29754e10i −0.126730 0.101465i
$$599$$ 2.30634e11i 1.79150i −0.444558 0.895750i $$-0.646639\pi$$
0.444558 0.895750i $$-0.353361\pi$$
$$600$$ 3.32916e9 6.81174e9i 0.0256880 0.0525598i
$$601$$ 1.01422e11 0.777382 0.388691 0.921368i $$-0.372927\pi$$
0.388691 + 0.921368i $$0.372927\pi$$
$$602$$ −8.29277e10 + 1.03577e11i −0.631413 + 0.788635i
$$603$$ 5.22236e10i 0.395001i
$$604$$ −2.09079e11 + 4.68711e10i −1.57095 + 0.352174i
$$605$$ −7.76795e10 −0.579809
$$606$$ −3.46004e10 2.77025e10i −0.256561 0.205413i
$$607$$ 1.97883e11i 1.45765i −0.684700 0.728825i $$-0.740067\pi$$
0.684700 0.728825i $$-0.259933\pi$$
$$608$$ −1.98738e10 4.73860e9i −0.145434 0.0346766i
$$609$$ 1.79224e10 0.130294
$$610$$ 8.99511e10 1.12349e11i 0.649661 0.811427i
$$611$$ 4.17158e10i 0.299320i
$$612$$ 1.40105e10 + 6.24967e10i 0.0998728 + 0.445504i
$$613$$ 1.27158e11 0.900538 0.450269 0.892893i $$-0.351328\pi$$
0.450269 + 0.892893i $$0.351328\pi$$
$$614$$ 4.36121e10 + 3.49176e10i 0.306855 + 0.245681i
$$615$$ 1.30855e11i 0.914723i
$$616$$ 9.51595e10 + 4.65082e10i 0.660890 + 0.323003i
$$617$$ −5.06702e10 −0.349632 −0.174816 0.984601i $$-0.555933\pi$$
−0.174816 + 0.984601i $$0.555933\pi$$
$$618$$ 1.04417e11 1.30417e11i 0.715844 0.894089i
$$619$$ 7.06748e10i 0.481395i −0.970600 0.240698i $$-0.922624\pi$$
0.970600 0.240698i $$-0.0773762\pi$$
$$620$$ −1.03534e10 + 2.32102e9i −0.0700675 + 0.0157077i
$$621$$ 7.43769e10 0.500117
$$622$$ 1.62128e11 + 1.29807e11i 1.08317 + 0.867231i
$$623$$ 1.16561e11i 0.773748i
$$624$$ 1.52915e10 + 3.23915e10i 0.100858 + 0.213645i
$$625$$ −1.45008e11 −0.950327
$$626$$ 6.31165e10 7.88325e10i 0.411004 0.513343i
$$627$$ 3.59885e10i 0.232859i
$$628$$ 1.51938e10 + 6.77754e10i 0.0976853 + 0.435746i
$$629$$ −2.53771e11 −1.62121
$$630$$ 3.64821e10 + 2.92090e10i 0.231589 + 0.185419i
$$631$$ 1.65273e11i 1.04252i 0.853399 + 0.521259i $$0.174537\pi$$
−0.853399 + 0.521259i $$0.825463\pi$$
$$632$$ −6.45921e10 + 1.32161e11i −0.404866 + 0.828388i
$$633$$ −1.46657e11 −0.913454
$$634$$ −1.65902e11 + 2.07211e11i −1.02682 + 1.28250i
$$635$$ 1.56868e11i 0.964804i
$$636$$ 2.05743e10 4.61233e9i 0.125747 0.0281898i
$$637$$ −2.08294e10 −0.126508
$$638$$ −2.96039e10 2.37021e10i −0.178676 0.143055i
$$639$$ 4.09405e9i 0.0245556i
$$640$$ −1.63731e11 2.21570e9i −0.975911 0.0132066i
$$641$$ 1.12013e11 0.663490 0.331745 0.943369i $$-0.392363\pi$$
0.331745 + 0.943369i $$0.392363\pi$$
$$642$$ 1.00247e11 1.25209e11i 0.590109 0.737046i
$$643$$ 2.65913e11i 1.55559i −0.628518 0.777795i $$-0.716338\pi$$
0.628518 0.777795i $$-0.283662\pi$$
$$644$$ −1.85824e10 8.28907e10i −0.108033 0.481906i
$$645$$ 3.61328e11 2.08767
$$646$$ 1.77872e10 + 1.42411e10i 0.102136 + 0.0817739i
$$647$$ 2.71996e11i 1.55219i 0.630614 + 0.776097i $$0.282803\pi$$
−0.630614 + 0.776097i $$0.717197\pi$$
$$648$$ −1.97940e11 9.67411e10i −1.12262 0.548670i
$$649$$ −6.88669e10 −0.388179
$$650$$ −1.01332e9 + 1.26563e9i −0.00567665 + 0.00709013i
$$651$$ 9.49716e9i 0.0528774i
$$652$$ 1.44511e11 3.23965e10i 0.799672 0.179270i
$$653$$ 3.03789e11 1.67078 0.835391 0.549656i $$-0.185241\pi$$
0.835391 + 0.549656i $$0.185241\pi$$
$$654$$ 7.37213e10 + 5.90243e10i 0.402979 + 0.322641i
$$655$$ 1.90427e11i 1.03458i
$$656$$ −1.27233e11 + 6.00646e10i −0.687043 + 0.324342i
$$657$$ 1.95988e10 0.105189
$$658$$ 1.06683e11 1.33247e11i 0.569102 0.710808i
$$659$$ 4.18575e10i 0.221938i 0.993824 + 0.110969i $$0.0353954\pi$$
−0.993824 + 0.110969i $$0.964605\pi$$
$$660$$ −6.30949e10 2.81448e11i −0.332520 1.48328i
$$661$$ −2.46529e11 −1.29141 −0.645703 0.763589i $$-0.723435\pi$$
−0.645703 + 0.763589i $$0.723435\pi$$
$$662$$ −6.85251e10 5.48640e10i −0.356794 0.285664i
$$663$$ 3.99482e10i 0.206749i
$$664$$ 9.34537e10 1.91214e11i 0.480755 0.983665i
$$665$$ 1.66264e10 0.0850179
$$666$$ −1.18848e11 + 1.48441e11i −0.604079 + 0.754494i
$$667$$ 3.04155e10i 0.153671i
$$668$$ 1.16936e11 2.62146e10i 0.587276 0.131655i
$$669$$ 1.47802e11 0.737862
$$670$$ −1.16239e11 9.30657e10i −0.576837 0.461839i
$$671$$ 2.72584e11i 1.34465i
$$672$$ −3.39935e10 + 1.42569e11i −0.166694 + 0.699115i
$$673$$ −3.15336e11 −1.53714 −0.768569 0.639767i $$-0.779031\pi$$
−0.768569 + 0.639767i $$0.779031\pi$$
$$674$$ 3.56226e9 4.44927e9i 0.0172618 0.0215600i
$$675$$ 5.80849e9i 0.0279800i
$$676$$ 4.40053e10 + 1.96295e11i 0.210726 + 0.939989i
$$677$$ −2.47236e10 −0.117695 −0.0588475 0.998267i $$-0.518743\pi$$
−0.0588475 + 0.998267i $$0.518743\pi$$
$$678$$ −6.87460e10 5.50408e10i −0.325333 0.260475i
$$679$$ 1.68731e11i 0.793811i
$$680$$ 1.64072e11 + 8.01886e10i 0.767361 + 0.375039i
$$681$$ 7.49454e10 0.348463
$$682$$ 1.25599e10 1.56873e10i 0.0580561 0.0725120i
$$683$$ 7.20843e10i 0.331251i 0.986189 + 0.165626i $$0.0529644\pi$$
−0.986189 + 0.165626i $$0.947036\pi$$
$$684$$ 1.66604e10 3.73492e9i 0.0761135 0.0170631i
$$685$$ 1.35408e11 0.615009
$$686$$ −1.67255e11 1.33911e11i −0.755235 0.604672i
$$687$$ 2.84556e11i 1.27744i
$$688$$ 1.65855e11 + 3.51326e11i 0.740246 + 1.56804i
$$689$$ −4.50887e9 −0.0200074
$$690$$ −1.44582e11 + 1.80583e11i −0.637850 + 0.796675i
$$691$$ 2.95424e11i 1.29578i −0.761732 0.647892i $$-0.775651\pi$$
0.761732 0.647892i $$-0.224349\pi$$
$$692$$ 1.15470e10 + 5.15080e10i 0.0503554 + 0.224621i
$$693$$ −8.85139e10 −0.383776
$$694$$ 1.99503e11 + 1.59731e11i 0.860028 + 0.688573i
$$695$$ 1.79968e11i 0.771360i
$$696$$ 2.30430e10 4.71479e10i 0.0981980 0.200921i
$$697$$ 1.56916e11 0.664867
$$698$$ −1.03634e11 + 1.29438e11i −0.436596 + 0.545308i
$$699$$ 2.20444e10i 0.0923400i
$$700$$ −6.47338e9 + 1.45120e9i −0.0269612 + 0.00604414i
$$701$$ −2.87925e11 −1.19236 −0.596180 0.802851i $$-0.703315\pi$$
−0.596180 + 0.802851i $$0.703315\pi$$
$$702$$ 2.14217e10 + 1.71511e10i 0.0882077 + 0.0706227i
$$703$$ 6.76504e10i 0.276980i
$$704$$ 2.44696e11 1.90538e11i 0.996176 0.775694i
$$705$$ −4.64831e11 −1.88165
$$706$$ 1.30979e11 1.63593e11i 0.527210 0.658485i
$$707$$ 3.87834e10i 0.155227i
$$708$$ −2.08462e10 9.29889e10i −0.0829648 0.370082i
$$709$$ 2.51685e11 0.996030 0.498015 0.867168i $$-0.334062\pi$$
0.498015 + 0.867168i $$0.334062\pi$$
$$710$$ 9.11252e9 + 7.29586e9i 0.0358596 + 0.0287106i
$$711$$ 1.22931e11i 0.481042i
$$712$$ −3.06633e11 1.49864e11i −1.19316 0.583144i
$$713$$ −1.61174e10 −0.0623643
$$714$$ 1.02162e11 1.27601e11i 0.393095 0.490976i
$$715$$ 6.16795e10i 0.236003i
$$716$$ 3.54493e10 7.94701e9i 0.134883 0.0302379i
$$717$$ 4.04170e11 1.52928
$$718$$ −4.13986e10 3.31454e10i −0.155772 0.124717i
$$719$$ 1.38856e11i 0.519574i −0.965666 0.259787i $$-0.916348\pi$$
0.965666 0.259787i $$-0.0836524\pi$$
$$720$$ 1.23745e11 5.84180e10i 0.460466 0.217379i
$$721$$ −1.46184e11 −0.540953
$$722$$ −1.66039e11 + 2.07383e11i −0.611029 + 0.763175i
$$723$$ 6.17489e11i 2.25983i
$$724$$ −2.70237e10 1.20545e11i −0.0983536 0.438727i
$$725$$ 2.37531e9 0.00859743
$$726$$ 1.58925e11 + 1.27242e11i 0.572064 + 0.458018i
$$727$$ 1.79083e11i 0.641088i −0.947234 0.320544i $$-0.896134\pi$$
0.947234 0.320544i $$-0.103866\pi$$
$$728$$ 1.37623e10 2.81589e10i 0.0489967 0.100251i
$$729$$ −2.14381e10 −0.0759061
$$730$$ 3.49263e10 4.36230e10i 0.122988 0.153612i
$$731$$ 4.33289e11i 1.51743i
$$732$$ −3.68062e11 + 8.25119e10i −1.28197 + 0.287391i
$$733$$ 2.17618e11 0.753839 0.376920 0.926246i $$-0.376983\pi$$
0.376920 + 0.926246i $$0.376983\pi$$
$$734$$ −2.45588e11 1.96628e11i −0.846101 0.677423i
$$735$$ 2.32098e11i 0.795285i
$$736$$ −2.41950e11 5.76895e10i −0.824546 0.196601i
$$737$$ 2.82023e11 0.955904
$$738$$ 7.34878e10 9.17862e10i 0.247736 0.309423i
$$739$$ 4.84950e11i 1.62599i 0.582268 + 0.812997i $$0.302166\pi$$
−0.582268 + 0.812997i $$0.697834\pi$$
$$740$$ 1.18605e11 + 5.29061e11i 0.395525 + 1.76433i
$$741$$ −1.06494e10 −0.0353227
$$742$$ −1.44020e10 1.15308e10i −0.0475124 0.0380404i
$$743$$ 2.03509e11i 0.667771i 0.942614 + 0.333886i $$0.108360\pi$$
−0.942614 + 0.333886i $$0.891640\pi$$
$$744$$ 2.49840e10 + 1.22106e10i 0.0815398 + 0.0398517i
$$745$$ 2.46198e11 0.799206
$$746$$ 2.10063e11 2.62369e11i 0.678258 0.847144i
$$747$$ 1.77860e11i 0.571210i
$$748$$ −3.37500e11 + 7.56606e10i −1.07812 + 0.241693i
$$749$$ −1.40346e11 −0.445937
$$750$$ 3.11478e11 + 2.49382e11i 0.984423 + 0.788169i
$$751$$ 2.34693e11i 0.737804i 0.929468 + 0.368902i $$0.120266\pi$$
−0.929468 + 0.368902i $$0.879734\pi$$
$$752$$ −2.13365e11 4.51965e11i −0.667194 1.41330i
$$753$$ −5.20950e11 −1.62038
$$754$$ −7.01374e9 + 8.76016e9i −0.0217002 + 0.0271036i
$$755$$ 5.10561e11i 1.57130i
$$756$$ 2.45626e10 + 1.09567e11i 0.0751946 + 0.335421i
$$757$$ −3.84882e11 −1.17204 −0.586022 0.810295i $$-0.699307\pi$$
−0.586022 + 0.810295i $$0.699307\pi$$
$$758$$ −3.80715e10 3.04816e10i −0.115325 0.0923338i
$$759$$ 4.38136e11i 1.32021i