Properties

 Label 165.3.l.a.32.2 Level $165$ Weight $3$ Character 165.32 Analytic conductor $4.496$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,3,Mod(32,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("165.32");

S:= CuspForms(chi, 3);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$165 = 3 \cdot 5 \cdot 11$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 165.l (of order $$4$$, degree $$2$$, 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: $$4.49592436194$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(i)$$ Coefficient field: $$\Q(i, \sqrt{10})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{4} + 25$$ x^4 + 25 Coefficient ring: $$\Z[a_1, \ldots, a_{4}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

 Embedding label 32.2 Root $$1.58114 + 1.58114i$$ of defining polynomial Character $$\chi$$ $$=$$ 165.32 Dual form 165.3.l.a.98.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(1.58114 + 1.58114i) q^{2} -3.00000 q^{3} +1.00000i q^{4} +(-4.00000 - 3.00000i) q^{5} +(-4.74342 - 4.74342i) q^{6} +(3.16228 - 3.16228i) q^{7} +(4.74342 - 4.74342i) q^{8} +9.00000 q^{9} +O(q^{10})$$ $$q+(1.58114 + 1.58114i) q^{2} -3.00000 q^{3} +1.00000i q^{4} +(-4.00000 - 3.00000i) q^{5} +(-4.74342 - 4.74342i) q^{6} +(3.16228 - 3.16228i) q^{7} +(4.74342 - 4.74342i) q^{8} +9.00000 q^{9} +(-1.58114 - 11.0680i) q^{10} +(6.32456 - 9.00000i) q^{11} -3.00000i q^{12} +(3.16228 + 3.16228i) q^{13} +10.0000 q^{14} +(12.0000 + 9.00000i) q^{15} +19.0000 q^{16} +(-22.1359 - 22.1359i) q^{17} +(14.2302 + 14.2302i) q^{18} -12.6491 q^{19} +(3.00000 - 4.00000i) q^{20} +(-9.48683 + 9.48683i) q^{21} +(24.2302 - 4.23025i) q^{22} +(-7.00000 - 7.00000i) q^{23} +(-14.2302 + 14.2302i) q^{24} +(7.00000 + 24.0000i) q^{25} +10.0000i q^{26} -27.0000 q^{27} +(3.16228 + 3.16228i) q^{28} -18.9737i q^{29} +(4.74342 + 33.2039i) q^{30} +20.0000 q^{31} +(11.0680 + 11.0680i) q^{32} +(-18.9737 + 27.0000i) q^{33} -70.0000i q^{34} +(-22.1359 + 3.16228i) q^{35} +9.00000i q^{36} +(7.00000 + 7.00000i) q^{37} +(-20.0000 - 20.0000i) q^{38} +(-9.48683 - 9.48683i) q^{39} +(-33.2039 + 4.74342i) q^{40} +69.5701 q^{41} -30.0000 q^{42} +(22.1359 + 22.1359i) q^{43} +(9.00000 + 6.32456i) q^{44} +(-36.0000 - 27.0000i) q^{45} -22.1359i q^{46} +(-43.0000 + 43.0000i) q^{47} -57.0000 q^{48} +29.0000i q^{49} +(-26.8794 + 49.0153i) q^{50} +(66.4078 + 66.4078i) q^{51} +(-3.16228 + 3.16228i) q^{52} +(17.0000 + 17.0000i) q^{53} +(-42.6907 - 42.6907i) q^{54} +(-52.2982 + 17.0263i) q^{55} -30.0000i q^{56} +37.9473 q^{57} +(30.0000 - 30.0000i) q^{58} +22.0000 q^{59} +(-9.00000 + 12.0000i) q^{60} -94.8683i q^{61} +(31.6228 + 31.6228i) q^{62} +(28.4605 - 28.4605i) q^{63} -41.0000i q^{64} +(-3.16228 - 22.1359i) q^{65} +(-72.6907 + 12.6907i) q^{66} +(-47.0000 - 47.0000i) q^{67} +(22.1359 - 22.1359i) q^{68} +(21.0000 + 21.0000i) q^{69} +(-40.0000 - 30.0000i) q^{70} +120.000i q^{71} +(42.6907 - 42.6907i) q^{72} +(22.1359 + 22.1359i) q^{73} +22.1359i q^{74} +(-21.0000 - 72.0000i) q^{75} -12.6491i q^{76} +(-8.46050 - 48.4605i) q^{77} -30.0000i q^{78} +6.32456 q^{79} +(-76.0000 - 57.0000i) q^{80} +81.0000 q^{81} +(110.000 + 110.000i) q^{82} +(-60.0833 + 60.0833i) q^{83} +(-9.48683 - 9.48683i) q^{84} +(22.1359 + 154.952i) q^{85} +70.0000i q^{86} +56.9210i q^{87} +(-12.6907 - 72.6907i) q^{88} +100.000 q^{89} +(-14.2302 - 99.6117i) q^{90} +20.0000 q^{91} +(7.00000 - 7.00000i) q^{92} -60.0000 q^{93} -135.978 q^{94} +(50.5964 + 37.9473i) q^{95} +(-33.2039 - 33.2039i) q^{96} +(43.0000 + 43.0000i) q^{97} +(-45.8530 + 45.8530i) q^{98} +(56.9210 - 81.0000i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 12 q^{3} - 16 q^{5} + 36 q^{9}+O(q^{10})$$ 4 * q - 12 * q^3 - 16 * q^5 + 36 * q^9 $$4 q - 12 q^{3} - 16 q^{5} + 36 q^{9} + 40 q^{14} + 48 q^{15} + 76 q^{16} + 12 q^{20} + 40 q^{22} - 28 q^{23} + 28 q^{25} - 108 q^{27} + 80 q^{31} + 28 q^{37} - 80 q^{38} - 120 q^{42} + 36 q^{44} - 144 q^{45} - 172 q^{47} - 228 q^{48} + 68 q^{53} - 108 q^{55} + 120 q^{58} + 88 q^{59} - 36 q^{60} - 120 q^{66} - 188 q^{67} + 84 q^{69} - 160 q^{70} - 84 q^{75} + 80 q^{77} - 304 q^{80} + 324 q^{81} + 440 q^{82} + 120 q^{88} + 400 q^{89} + 80 q^{91} + 28 q^{92} - 240 q^{93} + 172 q^{97}+O(q^{100})$$ 4 * q - 12 * q^3 - 16 * q^5 + 36 * q^9 + 40 * q^14 + 48 * q^15 + 76 * q^16 + 12 * q^20 + 40 * q^22 - 28 * q^23 + 28 * q^25 - 108 * q^27 + 80 * q^31 + 28 * q^37 - 80 * q^38 - 120 * q^42 + 36 * q^44 - 144 * q^45 - 172 * q^47 - 228 * q^48 + 68 * q^53 - 108 * q^55 + 120 * q^58 + 88 * q^59 - 36 * q^60 - 120 * q^66 - 188 * q^67 + 84 * q^69 - 160 * q^70 - 84 * q^75 + 80 * q^77 - 304 * q^80 + 324 * q^81 + 440 * q^82 + 120 * q^88 + 400 * q^89 + 80 * q^91 + 28 * q^92 - 240 * q^93 + 172 * q^97

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$$.

 $$n$$ $$46$$ $$56$$ $$67$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$e\left(\frac{1}{4}\right)$$

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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.58114 + 1.58114i 0.790569 + 0.790569i 0.981587 0.191017i $$-0.0611786\pi$$
−0.191017 + 0.981587i $$0.561179\pi$$
$$3$$ −3.00000 −1.00000
$$4$$ 1.00000i 0.250000i
$$5$$ −4.00000 3.00000i −0.800000 0.600000i
$$6$$ −4.74342 4.74342i −0.790569 0.790569i
$$7$$ 3.16228 3.16228i 0.451754 0.451754i −0.444182 0.895936i $$-0.646506\pi$$
0.895936 + 0.444182i $$0.146506\pi$$
$$8$$ 4.74342 4.74342i 0.592927 0.592927i
$$9$$ 9.00000 1.00000
$$10$$ −1.58114 11.0680i −0.158114 1.10680i
$$11$$ 6.32456 9.00000i 0.574960 0.818182i
$$12$$ 3.00000i 0.250000i
$$13$$ 3.16228 + 3.16228i 0.243252 + 0.243252i 0.818194 0.574942i $$-0.194975\pi$$
−0.574942 + 0.818194i $$0.694975\pi$$
$$14$$ 10.0000 0.714286
$$15$$ 12.0000 + 9.00000i 0.800000 + 0.600000i
$$16$$ 19.0000 1.18750
$$17$$ −22.1359 22.1359i −1.30211 1.30211i −0.926964 0.375150i $$-0.877591\pi$$
−0.375150 0.926964i $$-0.622409\pi$$
$$18$$ 14.2302 + 14.2302i 0.790569 + 0.790569i
$$19$$ −12.6491 −0.665743 −0.332871 0.942972i $$-0.608017\pi$$
−0.332871 + 0.942972i $$0.608017\pi$$
$$20$$ 3.00000 4.00000i 0.150000 0.200000i
$$21$$ −9.48683 + 9.48683i −0.451754 + 0.451754i
$$22$$ 24.2302 4.23025i 1.10137 0.192284i
$$23$$ −7.00000 7.00000i −0.304348 0.304348i 0.538364 0.842712i $$-0.319042\pi$$
−0.842712 + 0.538364i $$0.819042\pi$$
$$24$$ −14.2302 + 14.2302i −0.592927 + 0.592927i
$$25$$ 7.00000 + 24.0000i 0.280000 + 0.960000i
$$26$$ 10.0000i 0.384615i
$$27$$ −27.0000 −1.00000
$$28$$ 3.16228 + 3.16228i 0.112938 + 0.112938i
$$29$$ 18.9737i 0.654264i −0.944979 0.327132i $$-0.893918\pi$$
0.944979 0.327132i $$-0.106082\pi$$
$$30$$ 4.74342 + 33.2039i 0.158114 + 1.10680i
$$31$$ 20.0000 0.645161 0.322581 0.946542i $$-0.395450\pi$$
0.322581 + 0.946542i $$0.395450\pi$$
$$32$$ 11.0680 + 11.0680i 0.345874 + 0.345874i
$$33$$ −18.9737 + 27.0000i −0.574960 + 0.818182i
$$34$$ 70.0000i 2.05882i
$$35$$ −22.1359 + 3.16228i −0.632456 + 0.0903508i
$$36$$ 9.00000i 0.250000i
$$37$$ 7.00000 + 7.00000i 0.189189 + 0.189189i 0.795346 0.606156i $$-0.207289\pi$$
−0.606156 + 0.795346i $$0.707289\pi$$
$$38$$ −20.0000 20.0000i −0.526316 0.526316i
$$39$$ −9.48683 9.48683i −0.243252 0.243252i
$$40$$ −33.2039 + 4.74342i −0.830098 + 0.118585i
$$41$$ 69.5701 1.69683 0.848416 0.529330i $$-0.177557\pi$$
0.848416 + 0.529330i $$0.177557\pi$$
$$42$$ −30.0000 −0.714286
$$43$$ 22.1359 + 22.1359i 0.514789 + 0.514789i 0.915990 0.401201i $$-0.131407\pi$$
−0.401201 + 0.915990i $$0.631407\pi$$
$$44$$ 9.00000 + 6.32456i 0.204545 + 0.143740i
$$45$$ −36.0000 27.0000i −0.800000 0.600000i
$$46$$ 22.1359i 0.481216i
$$47$$ −43.0000 + 43.0000i −0.914894 + 0.914894i −0.996652 0.0817585i $$-0.973946\pi$$
0.0817585 + 0.996652i $$0.473946\pi$$
$$48$$ −57.0000 −1.18750
$$49$$ 29.0000i 0.591837i
$$50$$ −26.8794 + 49.0153i −0.537587 + 0.980306i
$$51$$ 66.4078 + 66.4078i 1.30211 + 1.30211i
$$52$$ −3.16228 + 3.16228i −0.0608130 + 0.0608130i
$$53$$ 17.0000 + 17.0000i 0.320755 + 0.320755i 0.849057 0.528302i $$-0.177171\pi$$
−0.528302 + 0.849057i $$0.677171\pi$$
$$54$$ −42.6907 42.6907i −0.790569 0.790569i
$$55$$ −52.2982 + 17.0263i −0.950877 + 0.309570i
$$56$$ 30.0000i 0.535714i
$$57$$ 37.9473 0.665743
$$58$$ 30.0000 30.0000i 0.517241 0.517241i
$$59$$ 22.0000 0.372881 0.186441 0.982466i $$-0.440305\pi$$
0.186441 + 0.982466i $$0.440305\pi$$
$$60$$ −9.00000 + 12.0000i −0.150000 + 0.200000i
$$61$$ 94.8683i 1.55522i −0.628748 0.777609i $$-0.716432\pi$$
0.628748 0.777609i $$-0.283568\pi$$
$$62$$ 31.6228 + 31.6228i 0.510045 + 0.510045i
$$63$$ 28.4605 28.4605i 0.451754 0.451754i
$$64$$ 41.0000i 0.640625i
$$65$$ −3.16228 22.1359i −0.0486504 0.340553i
$$66$$ −72.6907 + 12.6907i −1.10137 + 0.192284i
$$67$$ −47.0000 47.0000i −0.701493 0.701493i 0.263238 0.964731i $$-0.415209\pi$$
−0.964731 + 0.263238i $$0.915209\pi$$
$$68$$ 22.1359 22.1359i 0.325529 0.325529i
$$69$$ 21.0000 + 21.0000i 0.304348 + 0.304348i
$$70$$ −40.0000 30.0000i −0.571429 0.428571i
$$71$$ 120.000i 1.69014i 0.534655 + 0.845070i $$0.320442\pi$$
−0.534655 + 0.845070i $$0.679558\pi$$
$$72$$ 42.6907 42.6907i 0.592927 0.592927i
$$73$$ 22.1359 + 22.1359i 0.303232 + 0.303232i 0.842277 0.539045i $$-0.181215\pi$$
−0.539045 + 0.842277i $$0.681215\pi$$
$$74$$ 22.1359i 0.299134i
$$75$$ −21.0000 72.0000i −0.280000 0.960000i
$$76$$ 12.6491i 0.166436i
$$77$$ −8.46050 48.4605i −0.109877 0.629357i
$$78$$ 30.0000i 0.384615i
$$79$$ 6.32456 0.0800577 0.0400288 0.999199i $$-0.487255\pi$$
0.0400288 + 0.999199i $$0.487255\pi$$
$$80$$ −76.0000 57.0000i −0.950000 0.712500i
$$81$$ 81.0000 1.00000
$$82$$ 110.000 + 110.000i 1.34146 + 1.34146i
$$83$$ −60.0833 + 60.0833i −0.723895 + 0.723895i −0.969396 0.245501i $$-0.921047\pi$$
0.245501 + 0.969396i $$0.421047\pi$$
$$84$$ −9.48683 9.48683i −0.112938 0.112938i
$$85$$ 22.1359 + 154.952i 0.260423 + 1.82296i
$$86$$ 70.0000i 0.813953i
$$87$$ 56.9210i 0.654264i
$$88$$ −12.6907 72.6907i −0.144213 0.826031i
$$89$$ 100.000 1.12360 0.561798 0.827275i $$-0.310110\pi$$
0.561798 + 0.827275i $$0.310110\pi$$
$$90$$ −14.2302 99.6117i −0.158114 1.10680i
$$91$$ 20.0000 0.219780
$$92$$ 7.00000 7.00000i 0.0760870 0.0760870i
$$93$$ −60.0000 −0.645161
$$94$$ −135.978 −1.44657
$$95$$ 50.5964 + 37.9473i 0.532594 + 0.399446i
$$96$$ −33.2039 33.2039i −0.345874 0.345874i
$$97$$ 43.0000 + 43.0000i 0.443299 + 0.443299i 0.893119 0.449820i $$-0.148512\pi$$
−0.449820 + 0.893119i $$0.648512\pi$$
$$98$$ −45.8530 + 45.8530i −0.467888 + 0.467888i
$$99$$ 56.9210 81.0000i 0.574960 0.818182i
$$100$$ −24.0000 + 7.00000i −0.240000 + 0.0700000i
$$101$$ −139.140 −1.37763 −0.688813 0.724939i $$-0.741868\pi$$
−0.688813 + 0.724939i $$0.741868\pi$$
$$102$$ 210.000i 2.05882i
$$103$$ 7.00000 7.00000i 0.0679612 0.0679612i −0.672309 0.740270i $$-0.734697\pi$$
0.740270 + 0.672309i $$0.234697\pi$$
$$104$$ 30.0000 0.288462
$$105$$ 66.4078 9.48683i 0.632456 0.0903508i
$$106$$ 53.7587i 0.507158i
$$107$$ −41.1096 41.1096i −0.384202 0.384202i 0.488411 0.872613i $$-0.337577\pi$$
−0.872613 + 0.488411i $$0.837577\pi$$
$$108$$ 27.0000i 0.250000i
$$109$$ 215.035 1.97280 0.986399 0.164371i $$-0.0525595\pi$$
0.986399 + 0.164371i $$0.0525595\pi$$
$$110$$ −109.612 55.7698i −0.996470 0.506998i
$$111$$ −21.0000 21.0000i −0.189189 0.189189i
$$112$$ 60.0833 60.0833i 0.536458 0.536458i
$$113$$ 53.0000 + 53.0000i 0.469027 + 0.469027i 0.901599 0.432573i $$-0.142394\pi$$
−0.432573 + 0.901599i $$0.642394\pi$$
$$114$$ 60.0000 + 60.0000i 0.526316 + 0.526316i
$$115$$ 7.00000 + 49.0000i 0.0608696 + 0.426087i
$$116$$ 18.9737 0.163566
$$117$$ 28.4605 + 28.4605i 0.243252 + 0.243252i
$$118$$ 34.7851 + 34.7851i 0.294789 + 0.294789i
$$119$$ −140.000 −1.17647
$$120$$ 99.6117 14.2302i 0.830098 0.118585i
$$121$$ −41.0000 113.842i −0.338843 0.940843i
$$122$$ 150.000 150.000i 1.22951 1.22951i
$$123$$ −208.710 −1.69683
$$124$$ 20.0000i 0.161290i
$$125$$ 44.0000 117.000i 0.352000 0.936000i
$$126$$ 90.0000 0.714286
$$127$$ 41.1096 41.1096i 0.323698 0.323698i −0.526486 0.850184i $$-0.676491\pi$$
0.850184 + 0.526486i $$0.176491\pi$$
$$128$$ 109.099 109.099i 0.852333 0.852333i
$$129$$ −66.4078 66.4078i −0.514789 0.514789i
$$130$$ 30.0000 40.0000i 0.230769 0.307692i
$$131$$ 126.491 0.965581 0.482790 0.875736i $$-0.339623\pi$$
0.482790 + 0.875736i $$0.339623\pi$$
$$132$$ −27.0000 18.9737i −0.204545 0.143740i
$$133$$ −40.0000 + 40.0000i −0.300752 + 0.300752i
$$134$$ 148.627i 1.10916i
$$135$$ 108.000 + 81.0000i 0.800000 + 0.600000i
$$136$$ −210.000 −1.54412
$$137$$ 83.0000 83.0000i 0.605839 0.605839i −0.336017 0.941856i $$-0.609080\pi$$
0.941856 + 0.336017i $$0.109080\pi$$
$$138$$ 66.4078i 0.481216i
$$139$$ −12.6491 −0.0910008 −0.0455004 0.998964i $$-0.514488\pi$$
−0.0455004 + 0.998964i $$0.514488\pi$$
$$140$$ −3.16228 22.1359i −0.0225877 0.158114i
$$141$$ 129.000 129.000i 0.914894 0.914894i
$$142$$ −189.737 + 189.737i −1.33617 + 1.33617i
$$143$$ 48.4605 8.46050i 0.338885 0.0591643i
$$144$$ 171.000 1.18750
$$145$$ −56.9210 + 75.8947i −0.392559 + 0.523411i
$$146$$ 70.0000i 0.479452i
$$147$$ 87.0000i 0.591837i
$$148$$ −7.00000 + 7.00000i −0.0472973 + 0.0472973i
$$149$$ 94.8683i 0.636700i −0.947973 0.318350i $$-0.896871\pi$$
0.947973 0.318350i $$-0.103129\pi$$
$$150$$ 80.6381 147.046i 0.537587 0.980306i
$$151$$ 113.842i 0.753921i −0.926229 0.376960i $$-0.876969\pi$$
0.926229 0.376960i $$-0.123031\pi$$
$$152$$ −60.0000 + 60.0000i −0.394737 + 0.394737i
$$153$$ −199.223 199.223i −1.30211 1.30211i
$$154$$ 63.2456 90.0000i 0.410685 0.584416i
$$155$$ −80.0000 60.0000i −0.516129 0.387097i
$$156$$ 9.48683 9.48683i 0.0608130 0.0608130i
$$157$$ 67.0000 + 67.0000i 0.426752 + 0.426752i 0.887520 0.460769i $$-0.152426\pi$$
−0.460769 + 0.887520i $$0.652426\pi$$
$$158$$ 10.0000 + 10.0000i 0.0632911 + 0.0632911i
$$159$$ −51.0000 51.0000i −0.320755 0.320755i
$$160$$ −11.0680 77.4758i −0.0691748 0.484224i
$$161$$ −44.2719 −0.274981
$$162$$ 128.072 + 128.072i 0.790569 + 0.790569i
$$163$$ −137.000 + 137.000i −0.840491 + 0.840491i −0.988923 0.148432i $$-0.952577\pi$$
0.148432 + 0.988923i $$0.452577\pi$$
$$164$$ 69.5701i 0.424208i
$$165$$ 156.895 51.0790i 0.950877 0.309570i
$$166$$ −190.000 −1.14458
$$167$$ 205.548 + 205.548i 1.23083 + 1.23083i 0.963647 + 0.267180i $$0.0860918\pi$$
0.267180 + 0.963647i $$0.413908\pi$$
$$168$$ 90.0000i 0.535714i
$$169$$ 149.000i 0.881657i
$$170$$ −210.000 + 280.000i −1.23529 + 1.64706i
$$171$$ −113.842 −0.665743
$$172$$ −22.1359 + 22.1359i −0.128697 + 0.128697i
$$173$$ 34.7851 34.7851i 0.201070 0.201070i −0.599389 0.800458i $$-0.704590\pi$$
0.800458 + 0.599389i $$0.204590\pi$$
$$174$$ −90.0000 + 90.0000i −0.517241 + 0.517241i
$$175$$ 98.0306 + 53.7587i 0.560175 + 0.307193i
$$176$$ 120.167 171.000i 0.682764 0.971591i
$$177$$ −66.0000 −0.372881
$$178$$ 158.114 + 158.114i 0.888280 + 0.888280i
$$179$$ −320.000 −1.78771 −0.893855 0.448357i $$-0.852009\pi$$
−0.893855 + 0.448357i $$0.852009\pi$$
$$180$$ 27.0000 36.0000i 0.150000 0.200000i
$$181$$ 80.0000 0.441989 0.220994 0.975275i $$-0.429070\pi$$
0.220994 + 0.975275i $$0.429070\pi$$
$$182$$ 31.6228 + 31.6228i 0.173752 + 0.173752i
$$183$$ 284.605i 1.55522i
$$184$$ −66.4078 −0.360912
$$185$$ −7.00000 49.0000i −0.0378378 0.264865i
$$186$$ −94.8683 94.8683i −0.510045 0.510045i
$$187$$ −339.223 + 59.2235i −1.81403 + 0.316703i
$$188$$ −43.0000 43.0000i −0.228723 0.228723i
$$189$$ −85.3815 + 85.3815i −0.451754 + 0.451754i
$$190$$ 20.0000 + 140.000i 0.105263 + 0.736842i
$$191$$ 258.000i 1.35079i 0.737458 + 0.675393i $$0.236026\pi$$
−0.737458 + 0.675393i $$0.763974\pi$$
$$192$$ 123.000i 0.640625i
$$193$$ 79.0569 + 79.0569i 0.409621 + 0.409621i 0.881607 0.471985i $$-0.156462\pi$$
−0.471985 + 0.881607i $$0.656462\pi$$
$$194$$ 135.978i 0.700917i
$$195$$ 9.48683 + 66.4078i 0.0486504 + 0.340553i
$$196$$ −29.0000 −0.147959
$$197$$ −230.846 230.846i −1.17181 1.17181i −0.981778 0.190030i $$-0.939141\pi$$
−0.190030 0.981778i $$-0.560859\pi$$
$$198$$ 218.072 38.0722i 1.10137 0.192284i
$$199$$ 120.000i 0.603015i 0.953464 + 0.301508i $$0.0974898\pi$$
−0.953464 + 0.301508i $$0.902510\pi$$
$$200$$ 147.046 + 80.6381i 0.735230 + 0.403190i
$$201$$ 141.000 + 141.000i 0.701493 + 0.701493i
$$202$$ −220.000 220.000i −1.08911 1.08911i
$$203$$ −60.0000 60.0000i −0.295567 0.295567i
$$204$$ −66.4078 + 66.4078i −0.325529 + 0.325529i
$$205$$ −278.280 208.710i −1.35747 1.01810i
$$206$$ 22.1359 0.107456
$$207$$ −63.0000 63.0000i −0.304348 0.304348i
$$208$$ 60.0833 + 60.0833i 0.288862 + 0.288862i
$$209$$ −80.0000 + 113.842i −0.382775 + 0.544699i
$$210$$ 120.000 + 90.0000i 0.571429 + 0.428571i
$$211$$ 246.658i 1.16899i 0.811396 + 0.584497i $$0.198708\pi$$
−0.811396 + 0.584497i $$0.801292\pi$$
$$212$$ −17.0000 + 17.0000i −0.0801887 + 0.0801887i
$$213$$ 360.000i 1.69014i
$$214$$ 130.000i 0.607477i
$$215$$ −22.1359 154.952i −0.102958 0.720705i
$$216$$ −128.072 + 128.072i −0.592927 + 0.592927i
$$217$$ 63.2456 63.2456i 0.291454 0.291454i
$$218$$ 340.000 + 340.000i 1.55963 + 1.55963i
$$219$$ −66.4078 66.4078i −0.303232 0.303232i
$$220$$ −17.0263 52.2982i −0.0773924 0.237719i
$$221$$ 140.000i 0.633484i
$$222$$ 66.4078i 0.299134i
$$223$$ 73.0000 73.0000i 0.327354 0.327354i −0.524225 0.851580i $$-0.675645\pi$$
0.851580 + 0.524225i $$0.175645\pi$$
$$224$$ 70.0000 0.312500
$$225$$ 63.0000 + 216.000i 0.280000 + 0.960000i
$$226$$ 167.601i 0.741596i
$$227$$ −154.952 154.952i −0.682606 0.682606i 0.277981 0.960587i $$-0.410335\pi$$
−0.960587 + 0.277981i $$0.910335\pi$$
$$228$$ 37.9473i 0.166436i
$$229$$ 180.000i 0.786026i 0.919533 + 0.393013i $$0.128567\pi$$
−0.919533 + 0.393013i $$0.871433\pi$$
$$230$$ −66.4078 + 88.5438i −0.288730 + 0.384973i
$$231$$ 25.3815 + 145.381i 0.109877 + 0.629357i
$$232$$ −90.0000 90.0000i −0.387931 0.387931i
$$233$$ −3.16228 + 3.16228i −0.0135720 + 0.0135720i −0.713860 0.700288i $$-0.753055\pi$$
0.700288 + 0.713860i $$0.253055\pi$$
$$234$$ 90.0000i 0.384615i
$$235$$ 301.000 43.0000i 1.28085 0.182979i
$$236$$ 22.0000i 0.0932203i
$$237$$ −18.9737 −0.0800577
$$238$$ −221.359 221.359i −0.930082 0.930082i
$$239$$ 379.473i 1.58775i 0.608078 + 0.793877i $$0.291941\pi$$
−0.608078 + 0.793877i $$0.708059\pi$$
$$240$$ 228.000 + 171.000i 0.950000 + 0.712500i
$$241$$ 151.789i 0.629831i 0.949120 + 0.314916i $$0.101976\pi$$
−0.949120 + 0.314916i $$0.898024\pi$$
$$242$$ 115.173 244.827i 0.475923 1.01168i
$$243$$ −243.000 −1.00000
$$244$$ 94.8683 0.388805
$$245$$ 87.0000 116.000i 0.355102 0.473469i
$$246$$ −330.000 330.000i −1.34146 1.34146i
$$247$$ −40.0000 40.0000i −0.161943 0.161943i
$$248$$ 94.8683 94.8683i 0.382534 0.382534i
$$249$$ 180.250 180.250i 0.723895 0.723895i
$$250$$ 254.563 115.423i 1.01825 0.461693i
$$251$$ 60.0000i 0.239044i 0.992832 + 0.119522i $$0.0381362\pi$$
−0.992832 + 0.119522i $$0.961864\pi$$
$$252$$ 28.4605 + 28.4605i 0.112938 + 0.112938i
$$253$$ −107.272 + 18.7281i −0.424000 + 0.0740242i
$$254$$ 130.000 0.511811
$$255$$ −66.4078 464.855i −0.260423 1.82296i
$$256$$ 181.000 0.707031
$$257$$ 23.0000 23.0000i 0.0894942 0.0894942i −0.660942 0.750437i $$-0.729843\pi$$
0.750437 + 0.660942i $$0.229843\pi$$
$$258$$ 210.000i 0.813953i
$$259$$ 44.2719 0.170934
$$260$$ 22.1359 3.16228i 0.0851382 0.0121626i
$$261$$ 170.763i 0.654264i
$$262$$ 200.000 + 200.000i 0.763359 + 0.763359i
$$263$$ 167.601 167.601i 0.637265 0.637265i −0.312615 0.949880i $$-0.601205\pi$$
0.949880 + 0.312615i $$0.101205\pi$$
$$264$$ 38.0722 + 218.072i 0.144213 + 0.826031i
$$265$$ −17.0000 119.000i −0.0641509 0.449057i
$$266$$ −126.491 −0.475530
$$267$$ −300.000 −1.12360
$$268$$ 47.0000 47.0000i 0.175373 0.175373i
$$269$$ −182.000 −0.676580 −0.338290 0.941042i $$-0.609848\pi$$
−0.338290 + 0.941042i $$0.609848\pi$$
$$270$$ 42.6907 + 298.835i 0.158114 + 1.10680i
$$271$$ 265.631i 0.980189i −0.871669 0.490095i $$-0.836962\pi$$
0.871669 0.490095i $$-0.163038\pi$$
$$272$$ −420.583 420.583i −1.54626 1.54626i
$$273$$ −60.0000 −0.219780
$$274$$ 262.469 0.957916
$$275$$ 260.272 + 88.7893i 0.946443 + 0.322870i
$$276$$ −21.0000 + 21.0000i −0.0760870 + 0.0760870i
$$277$$ 154.952 154.952i 0.559392 0.559392i −0.369742 0.929134i $$-0.620554\pi$$
0.929134 + 0.369742i $$0.120554\pi$$
$$278$$ −20.0000 20.0000i −0.0719424 0.0719424i
$$279$$ 180.000 0.645161
$$280$$ −90.0000 + 120.000i −0.321429 + 0.428571i
$$281$$ 335.201 1.19289 0.596444 0.802655i $$-0.296580\pi$$
0.596444 + 0.802655i $$0.296580\pi$$
$$282$$ 407.934 1.44657
$$283$$ −281.443 281.443i −0.994497 0.994497i 0.00548773 0.999985i $$-0.498253\pi$$
−0.999985 + 0.00548773i $$0.998253\pi$$
$$284$$ −120.000 −0.422535
$$285$$ −151.789 113.842i −0.532594 0.399446i
$$286$$ 90.0000 + 63.2456i 0.314685 + 0.221138i
$$287$$ 220.000 220.000i 0.766551 0.766551i
$$288$$ 99.6117 + 99.6117i 0.345874 + 0.345874i
$$289$$ 691.000i 2.39100i
$$290$$ −210.000 + 30.0000i −0.724138 + 0.103448i
$$291$$ −129.000 129.000i −0.443299 0.443299i
$$292$$ −22.1359 + 22.1359i −0.0758080 + 0.0758080i
$$293$$ −230.846 + 230.846i −0.787871 + 0.787871i −0.981145 0.193274i $$-0.938089\pi$$
0.193274 + 0.981145i $$0.438089\pi$$
$$294$$ 137.559 137.559i 0.467888 0.467888i
$$295$$ −88.0000 66.0000i −0.298305 0.223729i
$$296$$ 66.4078 0.224351
$$297$$ −170.763 + 243.000i −0.574960 + 0.818182i
$$298$$ 150.000 150.000i 0.503356 0.503356i
$$299$$ 44.2719i 0.148067i
$$300$$ 72.0000 21.0000i 0.240000 0.0700000i
$$301$$ 140.000 0.465116
$$302$$ 180.000 180.000i 0.596026 0.596026i
$$303$$ 417.421 1.37763
$$304$$ −240.333 −0.790569
$$305$$ −284.605 + 379.473i −0.933131 + 1.24417i
$$306$$ 630.000i 2.05882i
$$307$$ 154.952 154.952i 0.504728 0.504728i −0.408175 0.912904i $$-0.633835\pi$$
0.912904 + 0.408175i $$0.133835\pi$$
$$308$$ 48.4605 8.46050i 0.157339 0.0274692i
$$309$$ −21.0000 + 21.0000i −0.0679612 + 0.0679612i
$$310$$ −31.6228 221.359i −0.102009 0.714063i
$$311$$ 240.000i 0.771704i −0.922561 0.385852i $$-0.873908\pi$$
0.922561 0.385852i $$-0.126092\pi$$
$$312$$ −90.0000 −0.288462
$$313$$ 127.000 127.000i 0.405751 0.405751i −0.474503 0.880254i $$-0.657372\pi$$
0.880254 + 0.474503i $$0.157372\pi$$
$$314$$ 211.873i 0.674754i
$$315$$ −199.223 + 28.4605i −0.632456 + 0.0903508i
$$316$$ 6.32456i 0.0200144i
$$317$$ −127.000 + 127.000i −0.400631 + 0.400631i −0.878455 0.477824i $$-0.841426\pi$$
0.477824 + 0.878455i $$0.341426\pi$$
$$318$$ 161.276i 0.507158i
$$319$$ −170.763 120.000i −0.535307 0.376176i
$$320$$ −123.000 + 164.000i −0.384375 + 0.512500i
$$321$$ 123.329 + 123.329i 0.384202 + 0.384202i
$$322$$ −70.0000 70.0000i −0.217391 0.217391i
$$323$$ 280.000 + 280.000i 0.866873 + 0.866873i
$$324$$ 81.0000i 0.250000i
$$325$$ −53.7587 + 98.0306i −0.165411 + 0.301633i
$$326$$ −433.232 −1.32893
$$327$$ −645.105 −1.97280
$$328$$ 330.000 330.000i 1.00610 1.00610i
$$329$$ 271.956i 0.826614i
$$330$$ 328.835 + 167.309i 0.996470 + 0.506998i
$$331$$ 200.000 0.604230 0.302115 0.953272i $$-0.402307\pi$$
0.302115 + 0.953272i $$0.402307\pi$$
$$332$$ −60.0833 60.0833i −0.180974 0.180974i
$$333$$ 63.0000 + 63.0000i 0.189189 + 0.189189i
$$334$$ 650.000i 1.94611i
$$335$$ 47.0000 + 329.000i 0.140299 + 0.982090i
$$336$$ −180.250 + 180.250i −0.536458 + 0.536458i
$$337$$ 363.662 363.662i 1.07912 1.07912i 0.0825267 0.996589i $$-0.473701\pi$$
0.996589 0.0825267i $$-0.0262990\pi$$
$$338$$ 235.590 235.590i 0.697011 0.697011i
$$339$$ −159.000 159.000i −0.469027 0.469027i
$$340$$ −154.952 + 22.1359i −0.455740 + 0.0651057i
$$341$$ 126.491 180.000i 0.370942 0.527859i
$$342$$ −180.000 180.000i −0.526316 0.526316i
$$343$$ 246.658 + 246.658i 0.719119 + 0.719119i
$$344$$ 210.000 0.610465
$$345$$ −21.0000 147.000i −0.0608696 0.426087i
$$346$$ 110.000 0.317919
$$347$$ 91.7061 + 91.7061i 0.264283 + 0.264283i 0.826791 0.562509i $$-0.190164\pi$$
−0.562509 + 0.826791i $$0.690164\pi$$
$$348$$ −56.9210 −0.163566
$$349$$ 252.982 0.724877 0.362439 0.932008i $$-0.381944\pi$$
0.362439 + 0.932008i $$0.381944\pi$$
$$350$$ 70.0000 + 240.000i 0.200000 + 0.685714i
$$351$$ −85.3815 85.3815i −0.243252 0.243252i
$$352$$ 169.612 29.6117i 0.481852 0.0841243i
$$353$$ −313.000 313.000i −0.886686 0.886686i 0.107518 0.994203i $$-0.465710\pi$$
−0.994203 + 0.107518i $$0.965710\pi$$
$$354$$ −104.355 104.355i −0.294789 0.294789i
$$355$$ 360.000 480.000i 1.01408 1.35211i
$$356$$ 100.000i 0.280899i
$$357$$ 420.000 1.17647
$$358$$ −505.964 505.964i −1.41331 1.41331i
$$359$$ 75.8947i 0.211406i −0.994398 0.105703i $$-0.966291\pi$$
0.994398 0.105703i $$-0.0337092\pi$$
$$360$$ −298.835 + 42.6907i −0.830098 + 0.118585i
$$361$$ −201.000 −0.556787
$$362$$ 126.491 + 126.491i 0.349423 + 0.349423i
$$363$$ 123.000 + 341.526i 0.338843 + 0.940843i
$$364$$ 20.0000i 0.0549451i
$$365$$ −22.1359 154.952i −0.0606464 0.424525i
$$366$$ −450.000 + 450.000i −1.22951 + 1.22951i
$$367$$ 97.0000 + 97.0000i 0.264305 + 0.264305i 0.826800 0.562495i $$-0.190159\pi$$
−0.562495 + 0.826800i $$0.690159\pi$$
$$368$$ −133.000 133.000i −0.361413 0.361413i
$$369$$ 626.131 1.69683
$$370$$ 66.4078 88.5438i 0.179481 0.239307i
$$371$$ 107.517 0.289804
$$372$$ 60.0000i 0.161290i
$$373$$ 230.846 + 230.846i 0.618891 + 0.618891i 0.945247 0.326356i $$-0.105821\pi$$
−0.326356 + 0.945247i $$0.605821\pi$$
$$374$$ −630.000 442.719i −1.68449 1.18374i
$$375$$ −132.000 + 351.000i −0.352000 + 0.936000i
$$376$$ 407.934i 1.08493i
$$377$$ 60.0000 60.0000i 0.159151 0.159151i
$$378$$ −270.000 −0.714286
$$379$$ 60.0000i 0.158311i −0.996862 0.0791557i $$-0.974778\pi$$
0.996862 0.0791557i $$-0.0252224\pi$$
$$380$$ −37.9473 + 50.5964i −0.0998614 + 0.133149i
$$381$$ −123.329 + 123.329i −0.323698 + 0.323698i
$$382$$ −407.934 + 407.934i −1.06789 + 1.06789i
$$383$$ 413.000 + 413.000i 1.07833 + 1.07833i 0.996659 + 0.0816695i $$0.0260252\pi$$
0.0816695 + 0.996659i $$0.473975\pi$$
$$384$$ −327.296 + 327.296i −0.852333 + 0.852333i
$$385$$ −111.540 + 219.223i −0.289713 + 0.569412i
$$386$$ 250.000i 0.647668i
$$387$$ 199.223 + 199.223i 0.514789 + 0.514789i
$$388$$ −43.0000 + 43.0000i −0.110825 + 0.110825i
$$389$$ 298.000 0.766067 0.383033 0.923734i $$-0.374879\pi$$
0.383033 + 0.923734i $$0.374879\pi$$
$$390$$ −90.0000 + 120.000i −0.230769 + 0.307692i
$$391$$ 309.903i 0.792591i
$$392$$ 137.559 + 137.559i 0.350916 + 0.350916i
$$393$$ −379.473 −0.965581
$$394$$ 730.000i 1.85279i
$$395$$ −25.2982 18.9737i −0.0640461 0.0480346i
$$396$$ 81.0000 + 56.9210i 0.204545 + 0.143740i
$$397$$ 73.0000 + 73.0000i 0.183879 + 0.183879i 0.793044 0.609165i $$-0.208495\pi$$
−0.609165 + 0.793044i $$0.708495\pi$$
$$398$$ −189.737 + 189.737i −0.476725 + 0.476725i
$$399$$ 120.000 120.000i 0.300752 0.300752i
$$400$$ 133.000 + 456.000i 0.332500 + 1.14000i
$$401$$ 258.000i 0.643392i 0.946843 + 0.321696i $$0.104253\pi$$
−0.946843 + 0.321696i $$0.895747\pi$$
$$402$$ 445.881i 1.10916i
$$403$$ 63.2456 + 63.2456i 0.156937 + 0.156937i
$$404$$ 139.140i 0.344406i
$$405$$ −324.000 243.000i −0.800000 0.600000i
$$406$$ 189.737i 0.467332i
$$407$$ 107.272 18.7281i 0.263567 0.0460150i
$$408$$ 630.000 1.54412
$$409$$ −638.780 −1.56181 −0.780905 0.624650i $$-0.785242\pi$$
−0.780905 + 0.624650i $$0.785242\pi$$
$$410$$ −110.000 770.000i −0.268293 1.87805i
$$411$$ −249.000 + 249.000i −0.605839 + 0.605839i
$$412$$ 7.00000 + 7.00000i 0.0169903 + 0.0169903i
$$413$$ 69.5701 69.5701i 0.168451 0.168451i
$$414$$ 199.223i 0.481216i
$$415$$ 420.583 60.0833i 1.01345 0.144779i
$$416$$ 70.0000i 0.168269i
$$417$$ 37.9473 0.0910008
$$418$$ −306.491 + 53.5089i −0.733232 + 0.128012i
$$419$$ −200.000 −0.477327 −0.238663 0.971102i $$-0.576709\pi$$
−0.238663 + 0.971102i $$0.576709\pi$$
$$420$$ 9.48683 + 66.4078i 0.0225877 + 0.158114i
$$421$$ −400.000 −0.950119 −0.475059 0.879954i $$-0.657573\pi$$
−0.475059 + 0.879954i $$0.657573\pi$$
$$422$$ −390.000 + 390.000i −0.924171 + 0.924171i
$$423$$ −387.000 + 387.000i −0.914894 + 0.914894i
$$424$$ 161.276 0.380368
$$425$$ 376.311 686.214i 0.885438 1.61462i
$$426$$ 569.210 569.210i 1.33617 1.33617i
$$427$$ −300.000 300.000i −0.702576 0.702576i
$$428$$ 41.1096 41.1096i 0.0960505 0.0960505i
$$429$$ −145.381 + 25.3815i −0.338885 + 0.0591643i
$$430$$ 210.000 280.000i 0.488372 0.651163i
$$431$$ −158.114 −0.366854 −0.183427 0.983033i $$-0.558719\pi$$
−0.183427 + 0.983033i $$0.558719\pi$$
$$432$$ −513.000 −1.18750
$$433$$ 193.000 193.000i 0.445727 0.445727i −0.448204 0.893931i $$-0.647936\pi$$
0.893931 + 0.448204i $$0.147936\pi$$
$$434$$ 200.000 0.460829
$$435$$ 170.763 227.684i 0.392559 0.523411i
$$436$$ 215.035i 0.493199i
$$437$$ 88.5438 + 88.5438i 0.202617 + 0.202617i
$$438$$ 210.000i 0.479452i
$$439$$ −373.149 −0.849997 −0.424999 0.905194i $$-0.639725\pi$$
−0.424999 + 0.905194i $$0.639725\pi$$
$$440$$ −167.309 + 328.835i −0.380248 + 0.747353i
$$441$$ 261.000i 0.591837i
$$442$$ 221.359 221.359i 0.500813 0.500813i
$$443$$ −463.000 463.000i −1.04515 1.04515i −0.998932 0.0462152i $$-0.985284\pi$$
−0.0462152 0.998932i $$-0.514716\pi$$
$$444$$ 21.0000 21.0000i 0.0472973 0.0472973i
$$445$$ −400.000 300.000i −0.898876 0.674157i
$$446$$ 230.846 0.517593
$$447$$ 284.605i 0.636700i
$$448$$ −129.653 129.653i −0.289405 0.289405i
$$449$$ −260.000 −0.579065 −0.289532 0.957168i $$-0.593500\pi$$
−0.289532 + 0.957168i $$0.593500\pi$$
$$450$$ −241.914 + 441.138i −0.537587 + 0.980306i
$$451$$ 440.000 626.131i 0.975610 1.38832i
$$452$$ −53.0000 + 53.0000i −0.117257 + 0.117257i
$$453$$ 341.526i 0.753921i
$$454$$ 490.000i 1.07930i
$$455$$ −80.0000 60.0000i −0.175824 0.131868i
$$456$$ 180.000 180.000i 0.394737 0.394737i
$$457$$ −91.7061 + 91.7061i −0.200670 + 0.200670i −0.800287 0.599617i $$-0.795320\pi$$
0.599617 + 0.800287i $$0.295320\pi$$
$$458$$ −284.605 + 284.605i −0.621408 + 0.621408i
$$459$$ 597.670 + 597.670i 1.30211 + 1.30211i
$$460$$ −49.0000 + 7.00000i −0.106522 + 0.0152174i
$$461$$ 202.386 0.439015 0.219507 0.975611i $$-0.429555\pi$$
0.219507 + 0.975611i $$0.429555\pi$$
$$462$$ −189.737 + 270.000i −0.410685 + 0.584416i
$$463$$ −527.000 + 527.000i −1.13823 + 1.13823i −0.149461 + 0.988768i $$0.547754\pi$$
−0.988768 + 0.149461i $$0.952246\pi$$
$$464$$ 360.500i 0.776939i
$$465$$ 240.000 + 180.000i 0.516129 + 0.387097i
$$466$$ −10.0000 −0.0214592
$$467$$ 347.000 347.000i 0.743041 0.743041i −0.230121 0.973162i $$-0.573912\pi$$
0.973162 + 0.230121i $$0.0739123\pi$$
$$468$$ −28.4605 + 28.4605i −0.0608130 + 0.0608130i
$$469$$ −297.254 −0.633804
$$470$$ 543.912 + 407.934i 1.15726 + 0.867944i
$$471$$ −201.000 201.000i −0.426752 0.426752i
$$472$$ 104.355 104.355i 0.221091 0.221091i
$$473$$ 339.223 59.2235i 0.717174 0.125208i
$$474$$ −30.0000 30.0000i −0.0632911 0.0632911i
$$475$$ −88.5438 303.579i −0.186408 0.639113i
$$476$$ 140.000i 0.294118i
$$477$$ 153.000 + 153.000i 0.320755 + 0.320755i
$$478$$ −600.000 + 600.000i −1.25523 + 1.25523i
$$479$$ 37.9473i 0.0792220i −0.999215 0.0396110i $$-0.987388\pi$$
0.999215 0.0396110i $$-0.0126119\pi$$
$$480$$ 33.2039 + 232.427i 0.0691748 + 0.484224i
$$481$$ 44.2719i 0.0920413i
$$482$$ −240.000 + 240.000i −0.497925 + 0.497925i
$$483$$ 132.816 0.274981
$$484$$ 113.842 41.0000i 0.235211 0.0847107i
$$485$$ −43.0000 301.000i −0.0886598 0.620619i
$$486$$ −384.217 384.217i −0.790569 0.790569i
$$487$$ −257.000 257.000i −0.527721 0.527721i 0.392171 0.919892i $$-0.371724\pi$$
−0.919892 + 0.392171i $$0.871724\pi$$
$$488$$ −450.000 450.000i −0.922131 0.922131i
$$489$$ 411.000 411.000i 0.840491 0.840491i
$$490$$ 320.971 45.8530i 0.655043 0.0935776i
$$491$$ −101.193 −0.206095 −0.103048 0.994676i $$-0.532859\pi$$
−0.103048 + 0.994676i $$0.532859\pi$$
$$492$$ 208.710i 0.424208i
$$493$$ −420.000 + 420.000i −0.851927 + 0.851927i
$$494$$ 126.491i 0.256055i
$$495$$ −470.684 + 153.237i −0.950877 + 0.309570i
$$496$$ 380.000 0.766129
$$497$$ 379.473 + 379.473i 0.763528 + 0.763528i
$$498$$ 570.000 1.14458
$$499$$ 540.000i 1.08216i 0.840970 + 0.541082i $$0.181985\pi$$
−0.840970 + 0.541082i $$0.818015\pi$$
$$500$$ 117.000 + 44.0000i 0.234000 + 0.0880000i
$$501$$ −616.644 616.644i −1.23083 1.23083i
$$502$$ −94.8683 + 94.8683i −0.188981 + 0.188981i
$$503$$ 338.364 338.364i 0.672691 0.672691i −0.285644 0.958336i $$-0.592208\pi$$
0.958336 + 0.285644i $$0.0922076\pi$$
$$504$$ 270.000i 0.535714i
$$505$$ 556.561 + 417.421i 1.10210 + 0.826576i
$$506$$ −199.223 140.000i −0.393722 0.276680i
$$507$$ 447.000i 0.881657i
$$508$$ 41.1096 + 41.1096i 0.0809244 + 0.0809244i
$$509$$ 742.000 1.45776 0.728880 0.684641i $$-0.240041\pi$$
0.728880 + 0.684641i $$0.240041\pi$$
$$510$$ 630.000 840.000i 1.23529 1.64706i
$$511$$ 140.000 0.273973
$$512$$ −150.208 150.208i −0.293375 0.293375i
$$513$$ 341.526 0.665743
$$514$$ 72.7324 0.141503
$$515$$ −49.0000 + 7.00000i −0.0951456 + 0.0135922i
$$516$$ 66.4078 66.4078i 0.128697 0.128697i
$$517$$ 115.044 + 658.956i 0.222522 + 1.27458i
$$518$$ 70.0000 + 70.0000i 0.135135 + 0.135135i
$$519$$ −104.355 + 104.355i −0.201070 + 0.201070i
$$520$$ −120.000 90.0000i −0.230769 0.173077i
$$521$$ 942.000i 1.80806i 0.427468 + 0.904031i $$0.359406\pi$$
−0.427468 + 0.904031i $$0.640594\pi$$
$$522$$ 270.000 270.000i 0.517241 0.517241i
$$523$$ 79.0569 + 79.0569i 0.151161 + 0.151161i 0.778636 0.627476i $$-0.215912\pi$$
−0.627476 + 0.778636i $$0.715912\pi$$
$$524$$ 126.491i 0.241395i
$$525$$ −294.092 161.276i −0.560175 0.307193i
$$526$$ 530.000 1.00760
$$527$$ −442.719 442.719i −0.840074 0.840074i
$$528$$ −360.500 + 513.000i −0.682764 + 0.971591i
$$529$$ 431.000i 0.814745i
$$530$$ 161.276 215.035i 0.304295 0.405726i
$$531$$ 198.000 0.372881
$$532$$ −40.0000 40.0000i −0.0751880 0.0751880i
$$533$$ 220.000 + 220.000i 0.412758 + 0.412758i
$$534$$ −474.342 474.342i −0.888280 0.888280i
$$535$$ 41.1096 + 287.767i 0.0768404 + 0.537883i
$$536$$ −445.881 −0.831868
$$537$$ 960.000 1.78771
$$538$$ −287.767 287.767i −0.534883 0.534883i
$$539$$ 261.000 + 183.412i 0.484230 + 0.340282i
$$540$$ −81.0000 + 108.000i −0.150000 + 0.200000i
$$541$$ 436.394i 0.806644i 0.915058 + 0.403322i $$0.132145\pi$$
−0.915058 + 0.403322i $$0.867855\pi$$
$$542$$ 420.000 420.000i 0.774908 0.774908i
$$543$$ −240.000 −0.441989
$$544$$ 490.000i 0.900735i
$$545$$ −860.140 645.105i −1.57824 1.18368i
$$546$$ −94.8683 94.8683i −0.173752 0.173752i
$$547$$ −528.100 + 528.100i −0.965449 + 0.965449i −0.999423 0.0339741i $$-0.989184\pi$$
0.0339741 + 0.999423i $$0.489184\pi$$
$$548$$ 83.0000 + 83.0000i 0.151460 + 0.151460i
$$549$$ 853.815i 1.55522i
$$550$$ 271.138 + 551.914i 0.492978 + 1.00348i
$$551$$ 240.000i 0.435572i
$$552$$ 199.223 0.360912
$$553$$ 20.0000 20.0000i 0.0361664 0.0361664i
$$554$$ 490.000 0.884477
$$555$$ 21.0000 + 147.000i 0.0378378 + 0.264865i
$$556$$ 12.6491i 0.0227502i
$$557$$ 641.942 + 641.942i 1.15250 + 1.15250i 0.986050 + 0.166450i $$0.0532304\pi$$
0.166450 + 0.986050i $$0.446770\pi$$
$$558$$ 284.605 + 284.605i 0.510045 + 0.510045i
$$559$$ 140.000i 0.250447i
$$560$$ −420.583 + 60.0833i −0.751041 + 0.107292i
$$561$$ 1017.67 177.670i 1.81403 0.316703i
$$562$$ 530.000 + 530.000i 0.943060 + 0.943060i
$$563$$ −117.004 + 117.004i −0.207823 + 0.207823i −0.803341 0.595519i $$-0.796947\pi$$
0.595519 + 0.803341i $$0.296947\pi$$
$$564$$ 129.000 + 129.000i 0.228723 + 0.228723i
$$565$$ −53.0000 371.000i −0.0938053 0.656637i
$$566$$ 890.000i 1.57244i
$$567$$ 256.144 256.144i 0.451754 0.451754i
$$568$$ 569.210 + 569.210i 1.00213 + 1.00213i
$$569$$ 607.157i 1.06706i −0.845781 0.533530i $$-0.820865\pi$$
0.845781 0.533530i $$-0.179135\pi$$
$$570$$ −60.0000 420.000i −0.105263 0.736842i
$$571$$ 512.289i 0.897179i −0.893738 0.448589i $$-0.851927\pi$$
0.893738 0.448589i $$-0.148073\pi$$
$$572$$ 8.46050 + 48.4605i 0.0147911 + 0.0847212i
$$573$$ 774.000i 1.35079i
$$574$$ 695.701 1.21202
$$575$$ 119.000 217.000i 0.206957 0.377391i
$$576$$ 369.000i 0.640625i
$$577$$ 43.0000 + 43.0000i 0.0745234 + 0.0745234i 0.743386 0.668863i $$-0.233219\pi$$
−0.668863 + 0.743386i $$0.733219\pi$$
$$578$$ −1092.57 + 1092.57i −1.89025 + 1.89025i
$$579$$ −237.171 237.171i −0.409621 0.409621i
$$580$$ −75.8947 56.9210i −0.130853 0.0981397i
$$581$$ 380.000i 0.654045i
$$582$$ 407.934i 0.700917i
$$583$$ 260.517 45.4826i 0.446857 0.0780147i
$$584$$ 210.000 0.359589
$$585$$ −28.4605 199.223i −0.0486504 0.340553i
$$586$$ −730.000 −1.24573
$$587$$ −553.000 + 553.000i −0.942078 + 0.942078i −0.998412 0.0563336i $$-0.982059\pi$$
0.0563336 + 0.998412i $$0.482059\pi$$
$$588$$ 87.0000 0.147959
$$589$$ −252.982 −0.429511
$$590$$ −34.7851 243.495i −0.0589577 0.412704i
$$591$$ 692.539 + 692.539i 1.17181 + 1.17181i
$$592$$ 133.000 + 133.000i 0.224662 + 0.224662i
$$593$$ −363.662 + 363.662i −0.613258 + 0.613258i −0.943794 0.330536i $$-0.892771\pi$$
0.330536 + 0.943794i $$0.392771\pi$$
$$594$$ −654.217 + 114.217i −1.10137 + 0.192284i
$$595$$ 560.000 + 420.000i 0.941176 + 0.705882i
$$596$$ 94.8683 0.159175
$$597$$ 360.000i 0.603015i
$$598$$ 70.0000 70.0000i 0.117057 0.117057i
$$599$$ −860.000 −1.43573 −0.717863 0.696184i $$-0.754880\pi$$
−0.717863 + 0.696184i $$0.754880\pi$$
$$600$$ −441.138 241.914i −0.735230 0.403190i
$$601$$ 75.8947i 0.126281i −0.998005 0.0631403i $$-0.979888\pi$$
0.998005 0.0631403i $$-0.0201116\pi$$
$$602$$ 221.359 + 221.359i 0.367707 + 0.367707i
$$603$$ −423.000 423.000i −0.701493 0.701493i
$$604$$ 113.842 0.188480
$$605$$ −177.526 + 578.368i −0.293431 + 0.955980i
$$606$$ 660.000 + 660.000i 1.08911 + 1.08911i
$$607$$ 325.715 325.715i 0.536597 0.536597i −0.385930 0.922528i $$-0.626120\pi$$
0.922528 + 0.385930i $$0.126120\pi$$
$$608$$ −140.000 140.000i −0.230263 0.230263i
$$609$$ 180.000 + 180.000i 0.295567 + 0.295567i
$$610$$ −1050.00 + 150.000i −1.72131 + 0.245902i
$$611$$ −271.956 −0.445100
$$612$$ 199.223 199.223i 0.325529 0.325529i
$$613$$ −110.680 110.680i −0.180554 0.180554i 0.611043 0.791597i $$-0.290750\pi$$
−0.791597 + 0.611043i $$0.790750\pi$$
$$614$$ 490.000 0.798046
$$615$$ 834.841 + 626.131i 1.35747 + 1.01810i
$$616$$ −270.000 189.737i −0.438312 0.308014i
$$617$$ −757.000 + 757.000i −1.22690 + 1.22690i −0.261776 + 0.965129i $$0.584308\pi$$
−0.965129 + 0.261776i $$0.915692\pi$$
$$618$$ −66.4078 −0.107456
$$619$$ 162.000i 0.261712i −0.991401 0.130856i $$-0.958227\pi$$
0.991401 0.130856i $$-0.0417726\pi$$
$$620$$ 60.0000 80.0000i 0.0967742 0.129032i
$$621$$ 189.000 + 189.000i 0.304348 + 0.304348i
$$622$$ 379.473 379.473i 0.610086 0.610086i
$$623$$ 316.228 316.228i 0.507589 0.507589i
$$624$$ −180.250 180.250i −0.288862 0.288862i
$$625$$ −527.000 + 336.000i −0.843200 + 0.537600i
$$626$$ 401.609 0.641548
$$627$$ 240.000 341.526i 0.382775 0.544699i
$$628$$ −67.0000 + 67.0000i −0.106688 + 0.106688i
$$629$$ 309.903i 0.492692i
$$630$$ −360.000 270.000i −0.571429 0.428571i
$$631$$ 158.000 0.250396 0.125198 0.992132i $$-0.460043\pi$$
0.125198 + 0.992132i $$0.460043\pi$$
$$632$$ 30.0000 30.0000i 0.0474684 0.0474684i
$$633$$ 739.973i 1.16899i
$$634$$ −401.609 −0.633453
$$635$$ −287.767 + 41.1096i −0.453177 + 0.0647395i
$$636$$ 51.0000 51.0000i 0.0801887 0.0801887i
$$637$$ −91.7061 + 91.7061i −0.143966 + 0.143966i
$$638$$ −80.2633 459.737i −0.125805 0.720590i
$$639$$ 1080.00i 1.69014i
$$640$$ −763.690 + 109.099i −1.19327 + 0.170467i
$$641$$ 942.000i 1.46958i −0.678295 0.734789i $$-0.737281\pi$$
0.678295 0.734789i $$-0.262719\pi$$
$$642$$ 390.000i 0.607477i
$$643$$ 757.000 757.000i 1.17729 1.17729i 0.196863 0.980431i $$-0.436925\pi$$
0.980431 0.196863i $$-0.0630754\pi$$
$$644$$ 44.2719i 0.0687452i
$$645$$ 66.4078 + 464.855i 0.102958 + 0.720705i
$$646$$ 885.438i 1.37065i
$$647$$ 257.000 257.000i 0.397218 0.397218i −0.480033 0.877251i $$-0.659375\pi$$
0.877251 + 0.480033i $$0.159375\pi$$
$$648$$ 384.217 384.217i 0.592927 0.592927i
$$649$$ 139.140 198.000i 0.214392 0.305085i
$$650$$ −240.000 + 70.0000i −0.369231 + 0.107692i
$$651$$ −189.737 + 189.737i −0.291454 + 0.291454i
$$652$$ −137.000 137.000i −0.210123 0.210123i
$$653$$ 263.000 + 263.000i 0.402757 + 0.402757i 0.879203 0.476447i $$-0.158076\pi$$
−0.476447 + 0.879203i $$0.658076\pi$$
$$654$$ −1020.00 1020.00i −1.55963 1.55963i
$$655$$ −505.964 379.473i −0.772465 0.579349i
$$656$$ 1321.83 2.01499
$$657$$ 199.223 + 199.223i 0.303232 + 0.303232i
$$658$$ −430.000 + 430.000i −0.653495 + 0.653495i
$$659$$ 398.447i 0.604624i 0.953209 + 0.302312i $$0.0977584\pi$$
−0.953209 + 0.302312i $$0.902242\pi$$
$$660$$ 51.0790 + 156.895i 0.0773924 + 0.237719i
$$661$$ −1078.00 −1.63086 −0.815431 0.578854i $$-0.803500\pi$$
−0.815431 + 0.578854i $$0.803500\pi$$
$$662$$ 316.228 + 316.228i 0.477685 + 0.477685i
$$663$$ 420.000i 0.633484i
$$664$$ 570.000i 0.858434i
$$665$$ 280.000 40.0000i 0.421053 0.0601504i
$$666$$ 199.223i 0.299134i
$$667$$ −132.816 + 132.816i −0.199124 + 0.199124i
$$668$$ −205.548 + 205.548i −0.307707 + 0.307707i
$$669$$ −219.000 + 219.000i −0.327354 + 0.327354i
$$670$$ −445.881 + 594.508i −0.665494 + 0.887326i
$$671$$ −853.815 600.000i −1.27245 0.894188i
$$672$$ −210.000 −0.312500
$$673$$ −357.337 357.337i −0.530962 0.530962i 0.389897 0.920859i $$-0.372511\pi$$
−0.920859 + 0.389897i $$0.872511\pi$$
$$674$$ 1150.00 1.70623
$$675$$ −189.000 648.000i −0.280000 0.960000i
$$676$$ 149.000 0.220414
$$677$$ 110.680 + 110.680i 0.163486 + 0.163486i 0.784109 0.620623i $$-0.213120\pi$$
−0.620623 + 0.784109i $$0.713120\pi$$
$$678$$ 502.802i 0.741596i
$$679$$ 271.956 0.400524
$$680$$ 840.000 + 630.000i 1.23529 + 0.926471i
$$681$$ 464.855 + 464.855i 0.682606 + 0.682606i
$$682$$ 484.605 84.6050i 0.710565 0.124054i
$$683$$ −397.000 397.000i −0.581259 0.581259i 0.353990 0.935249i $$-0.384825\pi$$
−0.935249 + 0.353990i $$0.884825\pi$$
$$684$$ 113.842i 0.166436i
$$685$$ −581.000 + 83.0000i −0.848175 + 0.121168i
$$686$$ 780.000i 1.13703i
$$687$$ 540.000i 0.786026i
$$688$$ 420.583 + 420.583i 0.611312 + 0.611312i
$$689$$ 107.517i 0.156049i
$$690$$ 199.223 265.631i 0.288730 0.384973i
$$691$$ 362.000 0.523878 0.261939 0.965084i $$-0.415638\pi$$
0.261939 + 0.965084i $$0.415638\pi$$
$$692$$ 34.7851 + 34.7851i 0.0502674 + 0.0502674i
$$693$$ −76.1445 436.144i −0.109877 0.629357i
$$694$$ 290.000i 0.417867i
$$695$$ 50.5964 + 37.9473i 0.0728006 + 0.0546005i
$$696$$ 270.000 + 270.000i 0.387931 + 0.387931i
$$697$$ −1540.00 1540.00i −2.20947 2.20947i
$$698$$ 400.000 + 400.000i 0.573066 + 0.573066i
$$699$$ 9.48683 9.48683i 0.0135720 0.0135720i
$$700$$ −53.7587 + 98.0306i −0.0767982 + 0.140044i
$$701$$ −25.2982 −0.0360888 −0.0180444 0.999837i $$-0.505744\pi$$
−0.0180444 + 0.999837i $$0.505744\pi$$
$$702$$ 270.000i 0.384615i
$$703$$ −88.5438 88.5438i −0.125951 0.125951i
$$704$$ −369.000 259.307i −0.524148 0.368333i
$$705$$ −903.000 + 129.000i −1.28085 + 0.182979i
$$706$$ 989.793i 1.40197i
$$707$$ −440.000 + 440.000i −0.622348 + 0.622348i
$$708$$ 66.0000i 0.0932203i
$$709$$ 1038.00i 1.46403i −0.681286 0.732017i $$-0.738579\pi$$
0.681286 0.732017i $$-0.261421\pi$$
$$710$$ 1328.16 189.737i 1.87064 0.267235i
$$711$$ 56.9210 0.0800577
$$712$$ 474.342 474.342i 0.666210 0.666210i
$$713$$ −140.000 140.000i −0.196353 0.196353i
$$714$$ 664.078 + 664.078i 0.930082 + 0.930082i
$$715$$ −219.223 111.540i −0.306606 0.155999i
$$716$$ 320.000i 0.446927i
$$717$$ 1138.42i 1.58775i
$$718$$ 120.000 120.000i 0.167131 0.167131i
$$719$$ 940.000 1.30737 0.653686 0.756766i $$-0.273222\pi$$
0.653686 + 0.756766i $$0.273222\pi$$
$$720$$ −684.000 513.000i −0.950000 0.712500i
$$721$$ 44.2719i 0.0614034i
$$722$$ −317.809 317.809i −0.440179 0.440179i
$$723$$ 455.368i 0.629831i
$$724$$ 80.0000i 0.110497i
$$725$$ 455.368 132.816i 0.628094 0.183194i
$$726$$ −345.520 + 734.480i −0.475923 + 1.01168i
$$727$$ 517.000 + 517.000i 0.711142 + 0.711142i 0.966774 0.255632i $$-0.0822837\pi$$
−0.255632 + 0.966774i $$0.582284\pi$$
$$728$$ 94.8683 94.8683i 0.130314 0.130314i
$$729$$ 729.000 1.00000
$$730$$ 210.000 280.000i 0.287671 0.383562i
$$731$$ 980.000i 1.34063i
$$732$$ −284.605 −0.388805
$$733$$ 629.293 + 629.293i 0.858517 + 0.858517i 0.991163 0.132646i $$-0.0423474\pi$$
−0.132646 + 0.991163i $$0.542347\pi$$
$$734$$ 306.741i 0.417903i
$$735$$ −261.000 + 348.000i −0.355102 + 0.473469i
$$736$$ 154.952i 0.210532i
$$737$$ −720.254 + 125.746i −0.977278 + 0.170619i
$$738$$ 990.000 + 990.000i 1.34146 + 1.34146i
$$739$$ −885.438 −1.19816 −0.599078 0.800690i $$-0.704466\pi$$
−0.599078 + 0.800690i $$0.704466\pi$$
$$740$$ 49.0000 7.00000i 0.0662162 0.00945946i
$$741$$ 120.000 + 120.000i 0.161943 + 0.161943i
$$742$$ 170.000 + 170.000i 0.229111 + 0.229111i
$$743$$ −41.1096 + 41.1096i −0.0553292 + 0.0553292i −0.734230 0.678901i $$-0.762457\pi$$
0.678901 + 0.734230i $$0.262457\pi$$
$$744$$ −284.605 + 284.605i −0.382534 + 0.382534i
$$745$$ −284.605 + 379.473i −0.382020 + 0.509360i
$$746$$ 730.000i 0.978552i
$$747$$ −540.749 + 540.749i −0.723895 + 0.723895i
$$748$$ −59.2235 339.223i −0.0791758 0.453507i
$$749$$ −260.000 −0.347130
$$750$$ −763.690 + 346.269i −1.01825 + 0.461693i
$$751$$ −922.000 −1.22770 −0.613848 0.789424i $$-0.710379\pi$$
−0.613848 + 0.789424i $$0.710379\pi$$
$$752$$ −817.000 + 817.000i −1.08644 + 1.08644i
$$753$$ 180.000i 0.239044i
$$754$$ 189.737 0.251640
$$755$$ −341.526 + 455.368i −0.452352 + 0.603136i
$$756$$ −85.3815 85.3815i −0.112938 0.112938i
$$757$$ 607.000 + 607.000i 0.801849 + 0.801849i 0.983384 0.181535i $$-0.0581066\pi$$
−0.181535 + 0.983384i $$0.558107\pi$$
$$758$$ 94.8683 94.8683i 0.125156 0.125156i
$$759$$ 321.816 56.1843i 0.424000 0.0740242i
$$760$$ 420.000 60.0000i 0.552632 0.0789474i
$$761$$ −1144.74 −1.50426 −0.752132 0.659013i $$-0.770974\pi$$
−0.752132 + 0.659013i $$0.770974\pi$$
$$762$$ −390.000 −0.511811
$$763$$ 680.000 680.000i 0.891219 0.891219i
$$764$$ −258.000 −0.337696
$$765$$ 199.223 + 1394.56i 0.260423 + 1.82296i
$$766$$ 1306.02i 1.70499i
$$767$$ 69.5701 + 69.5701i 0.0907042 + 0.0907042i
$$768$$ −543.000 −0.707031