# Properties

 Label 1078.2.e.n.177.1 Level $1078$ Weight $2$ Character 1078.177 Analytic conductor $8.608$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1078,2,Mod(67,1078)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1078, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1078.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1078 = 2 \cdot 7^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1078.e (of order $$3$$, degree $$2$$, not 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: $$8.60787333789$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\sqrt{-3}, \sqrt{5})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{4} - x^{3} + 2x^{2} + x + 1$$ x^4 - x^3 + 2*x^2 + x + 1 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: no (minimal twist has level 154) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 177.1 Root $$0.809017 + 1.40126i$$ of defining polynomial Character $$\chi$$ $$=$$ 1078.177 Dual form 1078.2.e.n.67.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-0.500000 + 0.866025i) q^{2} +(-1.61803 - 2.80252i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.61803 - 2.80252i) q^{5} +3.23607 q^{6} +1.00000 q^{8} +(-3.73607 + 6.47106i) q^{9} +O(q^{10})$$ $$q+(-0.500000 + 0.866025i) q^{2} +(-1.61803 - 2.80252i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.61803 - 2.80252i) q^{5} +3.23607 q^{6} +1.00000 q^{8} +(-3.73607 + 6.47106i) q^{9} +(1.61803 + 2.80252i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(-1.61803 + 2.80252i) q^{12} -1.23607 q^{13} -10.4721 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.23607 - 5.60503i) q^{17} +(-3.73607 - 6.47106i) q^{18} +(-1.38197 + 2.39364i) q^{19} -3.23607 q^{20} +1.00000 q^{22} +(-2.00000 + 3.46410i) q^{23} +(-1.61803 - 2.80252i) q^{24} +(-2.73607 - 4.73901i) q^{25} +(0.618034 - 1.07047i) q^{26} +14.4721 q^{27} -4.47214 q^{29} +(5.23607 - 9.06914i) q^{30} +(1.00000 + 1.73205i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.61803 + 2.80252i) q^{33} +6.47214 q^{34} +7.47214 q^{36} +(5.47214 - 9.47802i) q^{37} +(-1.38197 - 2.39364i) q^{38} +(2.00000 + 3.46410i) q^{39} +(1.61803 - 2.80252i) q^{40} -6.47214 q^{41} -1.52786 q^{43} +(-0.500000 + 0.866025i) q^{44} +(12.0902 + 20.9408i) q^{45} +(-2.00000 - 3.46410i) q^{46} +(-1.00000 + 1.73205i) q^{47} +3.23607 q^{48} +5.47214 q^{50} +(-10.4721 + 18.1383i) q^{51} +(0.618034 + 1.07047i) q^{52} +(0.236068 + 0.408882i) q^{53} +(-7.23607 + 12.5332i) q^{54} -3.23607 q^{55} +8.94427 q^{57} +(2.23607 - 3.87298i) q^{58} +(3.61803 + 6.26662i) q^{59} +(5.23607 + 9.06914i) q^{60} +(-2.61803 + 4.53457i) q^{61} -2.00000 q^{62} +1.00000 q^{64} +(-2.00000 + 3.46410i) q^{65} +(-1.61803 - 2.80252i) q^{66} +(7.70820 + 13.3510i) q^{67} +(-3.23607 + 5.60503i) q^{68} +12.9443 q^{69} -2.47214 q^{71} +(-3.73607 + 6.47106i) q^{72} +(-2.47214 - 4.28187i) q^{73} +(5.47214 + 9.47802i) q^{74} +(-8.85410 + 15.3358i) q^{75} +2.76393 q^{76} -4.00000 q^{78} +(1.61803 + 2.80252i) q^{80} +(-12.2082 - 21.1452i) q^{81} +(3.23607 - 5.60503i) q^{82} -10.1803 q^{83} -20.9443 q^{85} +(0.763932 - 1.32317i) q^{86} +(7.23607 + 12.5332i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(5.00000 - 8.66025i) q^{89} -24.1803 q^{90} +4.00000 q^{92} +(3.23607 - 5.60503i) q^{93} +(-1.00000 - 1.73205i) q^{94} +(4.47214 + 7.74597i) q^{95} +(-1.61803 + 2.80252i) q^{96} -3.52786 q^{97} +7.47214 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} + 4 q^{6} + 4 q^{8} - 6 q^{9}+O(q^{10})$$ 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 + 4 * q^6 + 4 * q^8 - 6 * q^9 $$4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} + 4 q^{6} + 4 q^{8} - 6 q^{9} + 2 q^{10} - 2 q^{11} - 2 q^{12} + 4 q^{13} - 24 q^{15} - 2 q^{16} - 4 q^{17} - 6 q^{18} - 10 q^{19} - 4 q^{20} + 4 q^{22} - 8 q^{23} - 2 q^{24} - 2 q^{25} - 2 q^{26} + 40 q^{27} + 12 q^{30} + 4 q^{31} - 2 q^{32} - 2 q^{33} + 8 q^{34} + 12 q^{36} + 4 q^{37} - 10 q^{38} + 8 q^{39} + 2 q^{40} - 8 q^{41} - 24 q^{43} - 2 q^{44} + 26 q^{45} - 8 q^{46} - 4 q^{47} + 4 q^{48} + 4 q^{50} - 24 q^{51} - 2 q^{52} - 8 q^{53} - 20 q^{54} - 4 q^{55} + 10 q^{59} + 12 q^{60} - 6 q^{61} - 8 q^{62} + 4 q^{64} - 8 q^{65} - 2 q^{66} + 4 q^{67} - 4 q^{68} + 16 q^{69} + 8 q^{71} - 6 q^{72} + 8 q^{73} + 4 q^{74} - 22 q^{75} + 20 q^{76} - 16 q^{78} + 2 q^{80} - 22 q^{81} + 4 q^{82} + 4 q^{83} - 48 q^{85} + 12 q^{86} + 20 q^{87} - 2 q^{88} + 20 q^{89} - 52 q^{90} + 16 q^{92} + 4 q^{93} - 4 q^{94} - 2 q^{96} - 32 q^{97} + 12 q^{99}+O(q^{100})$$ 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 + 4 * q^6 + 4 * q^8 - 6 * q^9 + 2 * q^10 - 2 * q^11 - 2 * q^12 + 4 * q^13 - 24 * q^15 - 2 * q^16 - 4 * q^17 - 6 * q^18 - 10 * q^19 - 4 * q^20 + 4 * q^22 - 8 * q^23 - 2 * q^24 - 2 * q^25 - 2 * q^26 + 40 * q^27 + 12 * q^30 + 4 * q^31 - 2 * q^32 - 2 * q^33 + 8 * q^34 + 12 * q^36 + 4 * q^37 - 10 * q^38 + 8 * q^39 + 2 * q^40 - 8 * q^41 - 24 * q^43 - 2 * q^44 + 26 * q^45 - 8 * q^46 - 4 * q^47 + 4 * q^48 + 4 * q^50 - 24 * q^51 - 2 * q^52 - 8 * q^53 - 20 * q^54 - 4 * q^55 + 10 * q^59 + 12 * q^60 - 6 * q^61 - 8 * q^62 + 4 * q^64 - 8 * q^65 - 2 * q^66 + 4 * q^67 - 4 * q^68 + 16 * q^69 + 8 * q^71 - 6 * q^72 + 8 * q^73 + 4 * q^74 - 22 * q^75 + 20 * q^76 - 16 * q^78 + 2 * q^80 - 22 * q^81 + 4 * q^82 + 4 * q^83 - 48 * q^85 + 12 * q^86 + 20 * q^87 - 2 * q^88 + 20 * q^89 - 52 * q^90 + 16 * q^92 + 4 * q^93 - 4 * q^94 - 2 * q^96 - 32 * q^97 + 12 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times$$.

 $$n$$ $$199$$ $$981$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.500000 + 0.866025i −0.353553 + 0.612372i
$$3$$ −1.61803 2.80252i −0.934172 1.61803i −0.776103 0.630606i $$-0.782806\pi$$
−0.158069 0.987428i $$-0.550527\pi$$
$$4$$ −0.500000 0.866025i −0.250000 0.433013i
$$5$$ 1.61803 2.80252i 0.723607 1.25332i −0.235938 0.971768i $$-0.575816\pi$$
0.959545 0.281556i $$-0.0908504\pi$$
$$6$$ 3.23607 1.32112
$$7$$ 0 0
$$8$$ 1.00000 0.353553
$$9$$ −3.73607 + 6.47106i −1.24536 + 2.15702i
$$10$$ 1.61803 + 2.80252i 0.511667 + 0.886234i
$$11$$ −0.500000 0.866025i −0.150756 0.261116i
$$12$$ −1.61803 + 2.80252i −0.467086 + 0.809017i
$$13$$ −1.23607 −0.342824 −0.171412 0.985199i $$-0.554833\pi$$
−0.171412 + 0.985199i $$0.554833\pi$$
$$14$$ 0 0
$$15$$ −10.4721 −2.70389
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ −3.23607 5.60503i −0.784862 1.35942i −0.929082 0.369875i $$-0.879401\pi$$
0.144220 0.989546i $$-0.453933\pi$$
$$18$$ −3.73607 6.47106i −0.880600 1.52524i
$$19$$ −1.38197 + 2.39364i −0.317045 + 0.549138i −0.979870 0.199636i $$-0.936024\pi$$
0.662825 + 0.748774i $$0.269357\pi$$
$$20$$ −3.23607 −0.723607
$$21$$ 0 0
$$22$$ 1.00000 0.213201
$$23$$ −2.00000 + 3.46410i −0.417029 + 0.722315i −0.995639 0.0932891i $$-0.970262\pi$$
0.578610 + 0.815604i $$0.303595\pi$$
$$24$$ −1.61803 2.80252i −0.330280 0.572061i
$$25$$ −2.73607 4.73901i −0.547214 0.947802i
$$26$$ 0.618034 1.07047i 0.121206 0.209936i
$$27$$ 14.4721 2.78516
$$28$$ 0 0
$$29$$ −4.47214 −0.830455 −0.415227 0.909718i $$-0.636298\pi$$
−0.415227 + 0.909718i $$0.636298\pi$$
$$30$$ 5.23607 9.06914i 0.955971 1.65579i
$$31$$ 1.00000 + 1.73205i 0.179605 + 0.311086i 0.941745 0.336327i $$-0.109185\pi$$
−0.762140 + 0.647412i $$0.775851\pi$$
$$32$$ −0.500000 0.866025i −0.0883883 0.153093i
$$33$$ −1.61803 + 2.80252i −0.281664 + 0.487856i
$$34$$ 6.47214 1.10996
$$35$$ 0 0
$$36$$ 7.47214 1.24536
$$37$$ 5.47214 9.47802i 0.899614 1.55818i 0.0716249 0.997432i $$-0.477182\pi$$
0.827989 0.560745i $$-0.189485\pi$$
$$38$$ −1.38197 2.39364i −0.224184 0.388299i
$$39$$ 2.00000 + 3.46410i 0.320256 + 0.554700i
$$40$$ 1.61803 2.80252i 0.255834 0.443117i
$$41$$ −6.47214 −1.01078 −0.505389 0.862892i $$-0.668651\pi$$
−0.505389 + 0.862892i $$0.668651\pi$$
$$42$$ 0 0
$$43$$ −1.52786 −0.232997 −0.116499 0.993191i $$-0.537167\pi$$
−0.116499 + 0.993191i $$0.537167\pi$$
$$44$$ −0.500000 + 0.866025i −0.0753778 + 0.130558i
$$45$$ 12.0902 + 20.9408i 1.80230 + 3.12167i
$$46$$ −2.00000 3.46410i −0.294884 0.510754i
$$47$$ −1.00000 + 1.73205i −0.145865 + 0.252646i −0.929695 0.368329i $$-0.879930\pi$$
0.783830 + 0.620975i $$0.213263\pi$$
$$48$$ 3.23607 0.467086
$$49$$ 0 0
$$50$$ 5.47214 0.773877
$$51$$ −10.4721 + 18.1383i −1.46639 + 2.53987i
$$52$$ 0.618034 + 1.07047i 0.0857059 + 0.148447i
$$53$$ 0.236068 + 0.408882i 0.0324264 + 0.0561642i 0.881783 0.471655i $$-0.156343\pi$$
−0.849357 + 0.527819i $$0.823010\pi$$
$$54$$ −7.23607 + 12.5332i −0.984704 + 1.70556i
$$55$$ −3.23607 −0.436351
$$56$$ 0 0
$$57$$ 8.94427 1.18470
$$58$$ 2.23607 3.87298i 0.293610 0.508548i
$$59$$ 3.61803 + 6.26662i 0.471028 + 0.815844i 0.999451 0.0331370i $$-0.0105498\pi$$
−0.528423 + 0.848981i $$0.677216\pi$$
$$60$$ 5.23607 + 9.06914i 0.675973 + 1.17082i
$$61$$ −2.61803 + 4.53457i −0.335205 + 0.580592i −0.983524 0.180777i $$-0.942139\pi$$
0.648319 + 0.761369i $$0.275472\pi$$
$$62$$ −2.00000 −0.254000
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ −2.00000 + 3.46410i −0.248069 + 0.429669i
$$66$$ −1.61803 2.80252i −0.199166 0.344966i
$$67$$ 7.70820 + 13.3510i 0.941707 + 1.63108i 0.762214 + 0.647325i $$0.224112\pi$$
0.179493 + 0.983759i $$0.442554\pi$$
$$68$$ −3.23607 + 5.60503i −0.392431 + 0.679710i
$$69$$ 12.9443 1.55831
$$70$$ 0 0
$$71$$ −2.47214 −0.293389 −0.146694 0.989182i $$-0.546863\pi$$
−0.146694 + 0.989182i $$0.546863\pi$$
$$72$$ −3.73607 + 6.47106i −0.440300 + 0.762622i
$$73$$ −2.47214 4.28187i −0.289342 0.501154i 0.684311 0.729190i $$-0.260103\pi$$
−0.973653 + 0.228036i $$0.926770\pi$$
$$74$$ 5.47214 + 9.47802i 0.636123 + 1.10180i
$$75$$ −8.85410 + 15.3358i −1.02238 + 1.77082i
$$76$$ 2.76393 0.317045
$$77$$ 0 0
$$78$$ −4.00000 −0.452911
$$79$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$80$$ 1.61803 + 2.80252i 0.180902 + 0.313331i
$$81$$ −12.2082 21.1452i −1.35647 2.34947i
$$82$$ 3.23607 5.60503i 0.357364 0.618972i
$$83$$ −10.1803 −1.11744 −0.558719 0.829357i $$-0.688707\pi$$
−0.558719 + 0.829357i $$0.688707\pi$$
$$84$$ 0 0
$$85$$ −20.9443 −2.27173
$$86$$ 0.763932 1.32317i 0.0823769 0.142681i
$$87$$ 7.23607 + 12.5332i 0.775788 + 1.34370i
$$88$$ −0.500000 0.866025i −0.0533002 0.0923186i
$$89$$ 5.00000 8.66025i 0.529999 0.917985i −0.469389 0.882992i $$-0.655526\pi$$
0.999388 0.0349934i $$-0.0111410\pi$$
$$90$$ −24.1803 −2.54883
$$91$$ 0 0
$$92$$ 4.00000 0.417029
$$93$$ 3.23607 5.60503i 0.335565 0.581215i
$$94$$ −1.00000 1.73205i −0.103142 0.178647i
$$95$$ 4.47214 + 7.74597i 0.458831 + 0.794719i
$$96$$ −1.61803 + 2.80252i −0.165140 + 0.286031i
$$97$$ −3.52786 −0.358200 −0.179100 0.983831i $$-0.557319\pi$$
−0.179100 + 0.983831i $$0.557319\pi$$
$$98$$ 0 0
$$99$$ 7.47214 0.750978
$$100$$ −2.73607 + 4.73901i −0.273607 + 0.473901i
$$101$$ −7.09017 12.2805i −0.705498 1.22196i −0.966511 0.256624i $$-0.917390\pi$$
0.261013 0.965335i $$-0.415943\pi$$
$$102$$ −10.4721 18.1383i −1.03690 1.79596i
$$103$$ 1.47214 2.54981i 0.145054 0.251241i −0.784339 0.620332i $$-0.786998\pi$$
0.929393 + 0.369092i $$0.120331\pi$$
$$104$$ −1.23607 −0.121206
$$105$$ 0 0
$$106$$ −0.472136 −0.0458579
$$107$$ 3.23607 5.60503i 0.312842 0.541859i −0.666134 0.745832i $$-0.732052\pi$$
0.978977 + 0.203973i $$0.0653855\pi$$
$$108$$ −7.23607 12.5332i −0.696291 1.20601i
$$109$$ 5.00000 + 8.66025i 0.478913 + 0.829502i 0.999708 0.0241802i $$-0.00769755\pi$$
−0.520794 + 0.853682i $$0.674364\pi$$
$$110$$ 1.61803 2.80252i 0.154273 0.267210i
$$111$$ −35.4164 −3.36158
$$112$$ 0 0
$$113$$ 8.47214 0.796992 0.398496 0.917170i $$-0.369532\pi$$
0.398496 + 0.917170i $$0.369532\pi$$
$$114$$ −4.47214 + 7.74597i −0.418854 + 0.725476i
$$115$$ 6.47214 + 11.2101i 0.603530 + 1.04534i
$$116$$ 2.23607 + 3.87298i 0.207614 + 0.359597i
$$117$$ 4.61803 7.99867i 0.426937 0.739477i
$$118$$ −7.23607 −0.666134
$$119$$ 0 0
$$120$$ −10.4721 −0.955971
$$121$$ −0.500000 + 0.866025i −0.0454545 + 0.0787296i
$$122$$ −2.61803 4.53457i −0.237026 0.410540i
$$123$$ 10.4721 + 18.1383i 0.944241 + 1.63547i
$$124$$ 1.00000 1.73205i 0.0898027 0.155543i
$$125$$ −1.52786 −0.136656
$$126$$ 0 0
$$127$$ −12.0000 −1.06483 −0.532414 0.846484i $$-0.678715\pi$$
−0.532414 + 0.846484i $$0.678715\pi$$
$$128$$ −0.500000 + 0.866025i −0.0441942 + 0.0765466i
$$129$$ 2.47214 + 4.28187i 0.217659 + 0.376997i
$$130$$ −2.00000 3.46410i −0.175412 0.303822i
$$131$$ 4.61803 7.99867i 0.403480 0.698847i −0.590664 0.806918i $$-0.701134\pi$$
0.994143 + 0.108071i $$0.0344673\pi$$
$$132$$ 3.23607 0.281664
$$133$$ 0 0
$$134$$ −15.4164 −1.33177
$$135$$ 23.4164 40.5584i 2.01536 3.49071i
$$136$$ −3.23607 5.60503i −0.277491 0.480628i
$$137$$ −7.94427 13.7599i −0.678725 1.17559i −0.975365 0.220597i $$-0.929200\pi$$
0.296640 0.954989i $$-0.404134\pi$$
$$138$$ −6.47214 + 11.2101i −0.550945 + 0.954264i
$$139$$ 8.29180 0.703301 0.351650 0.936131i $$-0.385621\pi$$
0.351650 + 0.936131i $$0.385621\pi$$
$$140$$ 0 0
$$141$$ 6.47214 0.545052
$$142$$ 1.23607 2.14093i 0.103729 0.179663i
$$143$$ 0.618034 + 1.07047i 0.0516826 + 0.0895169i
$$144$$ −3.73607 6.47106i −0.311339 0.539255i
$$145$$ −7.23607 + 12.5332i −0.600923 + 1.04083i
$$146$$ 4.94427 0.409191
$$147$$ 0 0
$$148$$ −10.9443 −0.899614
$$149$$ −11.1803 + 19.3649i −0.915929 + 1.58644i −0.110394 + 0.993888i $$0.535211\pi$$
−0.805535 + 0.592548i $$0.798122\pi$$
$$150$$ −8.85410 15.3358i −0.722934 1.25216i
$$151$$ −6.00000 10.3923i −0.488273 0.845714i 0.511636 0.859202i $$-0.329040\pi$$
−0.999909 + 0.0134886i $$0.995706\pi$$
$$152$$ −1.38197 + 2.39364i −0.112092 + 0.194149i
$$153$$ 48.3607 3.90973
$$154$$ 0 0
$$155$$ 6.47214 0.519854
$$156$$ 2.00000 3.46410i 0.160128 0.277350i
$$157$$ 9.32624 + 16.1535i 0.744315 + 1.28919i 0.950514 + 0.310681i $$0.100557\pi$$
−0.206199 + 0.978510i $$0.566110\pi$$
$$158$$ 0 0
$$159$$ 0.763932 1.32317i 0.0605838 0.104934i
$$160$$ −3.23607 −0.255834
$$161$$ 0 0
$$162$$ 24.4164 1.91833
$$163$$ −3.70820 + 6.42280i −0.290449 + 0.503072i −0.973916 0.226909i $$-0.927138\pi$$
0.683467 + 0.729981i $$0.260471\pi$$
$$164$$ 3.23607 + 5.60503i 0.252694 + 0.437680i
$$165$$ 5.23607 + 9.06914i 0.407627 + 0.706031i
$$166$$ 5.09017 8.81643i 0.395074 0.684288i
$$167$$ 15.4164 1.19296 0.596479 0.802629i $$-0.296566\pi$$
0.596479 + 0.802629i $$0.296566\pi$$
$$168$$ 0 0
$$169$$ −11.4721 −0.882472
$$170$$ 10.4721 18.1383i 0.803176 1.39114i
$$171$$ −10.3262 17.8856i −0.789667 1.36774i
$$172$$ 0.763932 + 1.32317i 0.0582493 + 0.100891i
$$173$$ 0.618034 1.07047i 0.0469883 0.0813860i −0.841575 0.540141i $$-0.818371\pi$$
0.888563 + 0.458755i $$0.151704\pi$$
$$174$$ −14.4721 −1.09713
$$175$$ 0 0
$$176$$ 1.00000 0.0753778
$$177$$ 11.7082 20.2792i 0.880042 1.52428i
$$178$$ 5.00000 + 8.66025i 0.374766 + 0.649113i
$$179$$ −4.47214 7.74597i −0.334263 0.578961i 0.649080 0.760720i $$-0.275154\pi$$
−0.983343 + 0.181760i $$0.941821\pi$$
$$180$$ 12.0902 20.9408i 0.901148 1.56083i
$$181$$ −4.76393 −0.354100 −0.177050 0.984202i $$-0.556655\pi$$
−0.177050 + 0.984202i $$0.556655\pi$$
$$182$$ 0 0
$$183$$ 16.9443 1.25256
$$184$$ −2.00000 + 3.46410i −0.147442 + 0.255377i
$$185$$ −17.7082 30.6715i −1.30193 2.25501i
$$186$$ 3.23607 + 5.60503i 0.237280 + 0.410981i
$$187$$ −3.23607 + 5.60503i −0.236645 + 0.409881i
$$188$$ 2.00000 0.145865
$$189$$ 0 0
$$190$$ −8.94427 −0.648886
$$191$$ −3.23607 + 5.60503i −0.234154 + 0.405566i −0.959026 0.283317i $$-0.908565\pi$$
0.724873 + 0.688883i $$0.241899\pi$$
$$192$$ −1.61803 2.80252i −0.116772 0.202254i
$$193$$ −1.47214 2.54981i −0.105967 0.183540i 0.808166 0.588955i $$-0.200460\pi$$
−0.914133 + 0.405415i $$0.867127\pi$$
$$194$$ 1.76393 3.05522i 0.126643 0.219352i
$$195$$ 12.9443 0.926959
$$196$$ 0 0
$$197$$ 18.0000 1.28245 0.641223 0.767354i $$-0.278427\pi$$
0.641223 + 0.767354i $$0.278427\pi$$
$$198$$ −3.73607 + 6.47106i −0.265511 + 0.459878i
$$199$$ 0.527864 + 0.914287i 0.0374193 + 0.0648121i 0.884129 0.467244i $$-0.154753\pi$$
−0.846709 + 0.532056i $$0.821420\pi$$
$$200$$ −2.73607 4.73901i −0.193469 0.335099i
$$201$$ 24.9443 43.2047i 1.75943 3.04743i
$$202$$ 14.1803 0.997725
$$203$$ 0 0
$$204$$ 20.9443 1.46639
$$205$$ −10.4721 + 18.1383i −0.731406 + 1.26683i
$$206$$ 1.47214 + 2.54981i 0.102569 + 0.177654i
$$207$$ −14.9443 25.8842i −1.03870 1.79908i
$$208$$ 0.618034 1.07047i 0.0428529 0.0742235i
$$209$$ 2.76393 0.191185
$$210$$ 0 0
$$211$$ −22.4721 −1.54705 −0.773523 0.633768i $$-0.781507\pi$$
−0.773523 + 0.633768i $$0.781507\pi$$
$$212$$ 0.236068 0.408882i 0.0162132 0.0280821i
$$213$$ 4.00000 + 6.92820i 0.274075 + 0.474713i
$$214$$ 3.23607 + 5.60503i 0.221213 + 0.383152i
$$215$$ −2.47214 + 4.28187i −0.168598 + 0.292021i
$$216$$ 14.4721 0.984704
$$217$$ 0 0
$$218$$ −10.0000 −0.677285
$$219$$ −8.00000 + 13.8564i −0.540590 + 0.936329i
$$220$$ 1.61803 + 2.80252i 0.109088 + 0.188946i
$$221$$ 4.00000 + 6.92820i 0.269069 + 0.466041i
$$222$$ 17.7082 30.6715i 1.18850 2.05854i
$$223$$ −8.47214 −0.567336 −0.283668 0.958923i $$-0.591551\pi$$
−0.283668 + 0.958923i $$0.591551\pi$$
$$224$$ 0 0
$$225$$ 40.8885 2.72590
$$226$$ −4.23607 + 7.33708i −0.281779 + 0.488056i
$$227$$ −7.38197 12.7859i −0.489958 0.848633i 0.509975 0.860189i $$-0.329655\pi$$
−0.999933 + 0.0115566i $$0.996321\pi$$
$$228$$ −4.47214 7.74597i −0.296174 0.512989i
$$229$$ 6.38197 11.0539i 0.421732 0.730462i −0.574377 0.818591i $$-0.694756\pi$$
0.996109 + 0.0881294i $$0.0280889\pi$$
$$230$$ −12.9443 −0.853520
$$231$$ 0 0
$$232$$ −4.47214 −0.293610
$$233$$ −1.47214 + 2.54981i −0.0964428 + 0.167044i −0.910210 0.414147i $$-0.864080\pi$$
0.813767 + 0.581191i $$0.197413\pi$$
$$234$$ 4.61803 + 7.99867i 0.301890 + 0.522889i
$$235$$ 3.23607 + 5.60503i 0.211098 + 0.365632i
$$236$$ 3.61803 6.26662i 0.235514 0.407922i
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 20.0000 1.29369 0.646846 0.762620i $$-0.276088\pi$$
0.646846 + 0.762620i $$0.276088\pi$$
$$240$$ 5.23607 9.06914i 0.337987 0.585410i
$$241$$ −5.70820 9.88690i −0.367698 0.636871i 0.621507 0.783408i $$-0.286521\pi$$
−0.989205 + 0.146537i $$0.953187\pi$$
$$242$$ −0.500000 0.866025i −0.0321412 0.0556702i
$$243$$ −17.7984 + 30.8277i −1.14177 + 1.97760i
$$244$$ 5.23607 0.335205
$$245$$ 0 0
$$246$$ −20.9443 −1.33536
$$247$$ 1.70820 2.95870i 0.108690 0.188257i
$$248$$ 1.00000 + 1.73205i 0.0635001 + 0.109985i
$$249$$ 16.4721 + 28.5306i 1.04388 + 1.80805i
$$250$$ 0.763932 1.32317i 0.0483153 0.0836846i
$$251$$ −24.7639 −1.56309 −0.781543 0.623852i $$-0.785567\pi$$
−0.781543 + 0.623852i $$0.785567\pi$$
$$252$$ 0 0
$$253$$ 4.00000 0.251478
$$254$$ 6.00000 10.3923i 0.376473 0.652071i
$$255$$ 33.8885 + 58.6967i 2.12218 + 3.67573i
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ −5.47214 + 9.47802i −0.341342 + 0.591222i −0.984682 0.174358i $$-0.944215\pi$$
0.643340 + 0.765581i $$0.277548\pi$$
$$258$$ −4.94427 −0.307817
$$259$$ 0 0
$$260$$ 4.00000 0.248069
$$261$$ 16.7082 28.9395i 1.03421 1.79131i
$$262$$ 4.61803 + 7.99867i 0.285303 + 0.494159i
$$263$$ −6.47214 11.2101i −0.399089 0.691242i 0.594525 0.804077i $$-0.297340\pi$$
−0.993614 + 0.112835i $$0.964007\pi$$
$$264$$ −1.61803 + 2.80252i −0.0995831 + 0.172483i
$$265$$ 1.52786 0.0938559
$$266$$ 0 0
$$267$$ −32.3607 −1.98044
$$268$$ 7.70820 13.3510i 0.470853 0.815542i
$$269$$ −13.6180 23.5871i −0.830306 1.43813i −0.897796 0.440413i $$-0.854832\pi$$
0.0674893 0.997720i $$-0.478501\pi$$
$$270$$ 23.4164 + 40.5584i 1.42508 + 2.46831i
$$271$$ −8.47214 + 14.6742i −0.514646 + 0.891392i 0.485210 + 0.874398i $$0.338743\pi$$
−0.999856 + 0.0169947i $$0.994590\pi$$
$$272$$ 6.47214 0.392431
$$273$$ 0 0
$$274$$ 15.8885 0.959862
$$275$$ −2.73607 + 4.73901i −0.164991 + 0.285773i
$$276$$ −6.47214 11.2101i −0.389577 0.674767i
$$277$$ −6.23607 10.8012i −0.374689 0.648980i 0.615591 0.788065i $$-0.288917\pi$$
−0.990280 + 0.139085i $$0.955584\pi$$
$$278$$ −4.14590 + 7.18091i −0.248654 + 0.430682i
$$279$$ −14.9443 −0.894690
$$280$$ 0 0
$$281$$ −24.8328 −1.48140 −0.740701 0.671835i $$-0.765506\pi$$
−0.740701 + 0.671835i $$0.765506\pi$$
$$282$$ −3.23607 + 5.60503i −0.192705 + 0.333775i
$$283$$ −8.32624 14.4215i −0.494943 0.857267i 0.505040 0.863096i $$-0.331478\pi$$
−0.999983 + 0.00582897i $$0.998145\pi$$
$$284$$ 1.23607 + 2.14093i 0.0733471 + 0.127041i
$$285$$ 14.4721 25.0665i 0.857255 1.48481i
$$286$$ −1.23607 −0.0730902
$$287$$ 0 0
$$288$$ 7.47214 0.440300
$$289$$ −12.4443 + 21.5541i −0.732016 + 1.26789i
$$290$$ −7.23607 12.5332i −0.424917 0.735977i
$$291$$ 5.70820 + 9.88690i 0.334621 + 0.579580i
$$292$$ −2.47214 + 4.28187i −0.144671 + 0.250577i
$$293$$ −4.65248 −0.271801 −0.135900 0.990723i $$-0.543393\pi$$
−0.135900 + 0.990723i $$0.543393\pi$$
$$294$$ 0 0
$$295$$ 23.4164 1.36336
$$296$$ 5.47214 9.47802i 0.318061 0.550899i
$$297$$ −7.23607 12.5332i −0.419879 0.727252i
$$298$$ −11.1803 19.3649i −0.647660 1.12178i
$$299$$ 2.47214 4.28187i 0.142967 0.247627i
$$300$$ 17.7082 1.02238
$$301$$ 0 0
$$302$$ 12.0000 0.690522
$$303$$ −22.9443 + 39.7406i −1.31811 + 2.28304i
$$304$$ −1.38197 2.39364i −0.0792612 0.137284i
$$305$$ 8.47214 + 14.6742i 0.485113 + 0.840241i
$$306$$ −24.1803 + 41.8816i −1.38230 + 2.39421i
$$307$$ −32.0689 −1.83027 −0.915134 0.403150i $$-0.867915\pi$$
−0.915134 + 0.403150i $$0.867915\pi$$
$$308$$ 0 0
$$309$$ −9.52786 −0.542021
$$310$$ −3.23607 + 5.60503i −0.183796 + 0.318345i
$$311$$ 2.70820 + 4.69075i 0.153568 + 0.265988i 0.932537 0.361075i $$-0.117590\pi$$
−0.778969 + 0.627063i $$0.784257\pi$$
$$312$$ 2.00000 + 3.46410i 0.113228 + 0.196116i
$$313$$ 14.2361 24.6576i 0.804670 1.39373i −0.111843 0.993726i $$-0.535675\pi$$
0.916514 0.400004i $$-0.130991\pi$$
$$314$$ −18.6525 −1.05262
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 6.52786 11.3066i 0.366641 0.635041i −0.622397 0.782702i $$-0.713841\pi$$
0.989038 + 0.147660i $$0.0471743\pi$$
$$318$$ 0.763932 + 1.32317i 0.0428392 + 0.0741996i
$$319$$ 2.23607 + 3.87298i 0.125196 + 0.216845i
$$320$$ 1.61803 2.80252i 0.0904508 0.156665i
$$321$$ −20.9443 −1.16900
$$322$$ 0 0
$$323$$ 17.8885 0.995345
$$324$$ −12.2082 + 21.1452i −0.678234 + 1.17473i
$$325$$ 3.38197 + 5.85774i 0.187598 + 0.324929i
$$326$$ −3.70820 6.42280i −0.205378 0.355726i
$$327$$ 16.1803 28.0252i 0.894775 1.54980i
$$328$$ −6.47214 −0.357364
$$329$$ 0 0
$$330$$ −10.4721 −0.576472
$$331$$ −0.472136 + 0.817763i −0.0259509 + 0.0449483i −0.878709 0.477357i $$-0.841595\pi$$
0.852758 + 0.522306i $$0.174928\pi$$
$$332$$ 5.09017 + 8.81643i 0.279359 + 0.483865i
$$333$$ 40.8885 + 70.8210i 2.24068 + 3.88097i
$$334$$ −7.70820 + 13.3510i −0.421774 + 0.730534i
$$335$$ 49.8885 2.72570
$$336$$ 0 0
$$337$$ 18.0000 0.980522 0.490261 0.871576i $$-0.336901\pi$$
0.490261 + 0.871576i $$0.336901\pi$$
$$338$$ 5.73607 9.93516i 0.312001 0.540402i
$$339$$ −13.7082 23.7433i −0.744527 1.28956i
$$340$$ 10.4721 + 18.1383i 0.567931 + 0.983686i
$$341$$ 1.00000 1.73205i 0.0541530 0.0937958i
$$342$$ 20.6525 1.11676
$$343$$ 0 0
$$344$$ −1.52786 −0.0823769
$$345$$ 20.9443 36.2765i 1.12760 1.95306i
$$346$$ 0.618034 + 1.07047i 0.0332257 + 0.0575486i
$$347$$ 3.23607 + 5.60503i 0.173721 + 0.300894i 0.939718 0.341950i $$-0.111087\pi$$
−0.765997 + 0.642844i $$0.777754\pi$$
$$348$$ 7.23607 12.5332i 0.387894 0.671852i
$$349$$ −8.29180 −0.443850 −0.221925 0.975064i $$-0.571234\pi$$
−0.221925 + 0.975064i $$0.571234\pi$$
$$350$$ 0 0
$$351$$ −17.8885 −0.954820
$$352$$ −0.500000 + 0.866025i −0.0266501 + 0.0461593i
$$353$$ −17.4721 30.2626i −0.929948 1.61072i −0.783404 0.621513i $$-0.786518\pi$$
−0.146544 0.989204i $$-0.546815\pi$$
$$354$$ 11.7082 + 20.2792i 0.622284 + 1.07783i
$$355$$ −4.00000 + 6.92820i −0.212298 + 0.367711i
$$356$$ −10.0000 −0.529999
$$357$$ 0 0
$$358$$ 8.94427 0.472719
$$359$$ 13.4164 23.2379i 0.708091 1.22645i −0.257473 0.966285i $$-0.582890\pi$$
0.965564 0.260164i $$-0.0837767\pi$$
$$360$$ 12.0902 + 20.9408i 0.637208 + 1.10368i
$$361$$ 5.68034 + 9.83864i 0.298965 + 0.517823i
$$362$$ 2.38197 4.12569i 0.125193 0.216841i
$$363$$ 3.23607 0.169850
$$364$$ 0 0
$$365$$ −16.0000 −0.837478
$$366$$ −8.47214 + 14.6742i −0.442846 + 0.767031i
$$367$$ 10.7082 + 18.5472i 0.558964 + 0.968154i 0.997583 + 0.0694807i $$0.0221342\pi$$
−0.438620 + 0.898673i $$0.644532\pi$$
$$368$$ −2.00000 3.46410i −0.104257 0.180579i
$$369$$ 24.1803 41.8816i 1.25878 2.18027i
$$370$$ 35.4164 1.84121
$$371$$ 0 0
$$372$$ −6.47214 −0.335565
$$373$$ 3.00000 5.19615i 0.155334 0.269047i −0.777847 0.628454i $$-0.783688\pi$$
0.933181 + 0.359408i $$0.117021\pi$$
$$374$$ −3.23607 5.60503i −0.167333 0.289829i
$$375$$ 2.47214 + 4.28187i 0.127661 + 0.221115i
$$376$$ −1.00000 + 1.73205i −0.0515711 + 0.0893237i
$$377$$ 5.52786 0.284699
$$378$$ 0 0
$$379$$ 5.52786 0.283947 0.141974 0.989870i $$-0.454655\pi$$
0.141974 + 0.989870i $$0.454655\pi$$
$$380$$ 4.47214 7.74597i 0.229416 0.397360i
$$381$$ 19.4164 + 33.6302i 0.994733 + 1.72293i
$$382$$ −3.23607 5.60503i −0.165572 0.286778i
$$383$$ 5.94427 10.2958i 0.303738 0.526090i −0.673241 0.739423i $$-0.735099\pi$$
0.976980 + 0.213333i $$0.0684319\pi$$
$$384$$ 3.23607 0.165140
$$385$$ 0 0
$$386$$ 2.94427 0.149859
$$387$$ 5.70820 9.88690i 0.290164 0.502579i
$$388$$ 1.76393 + 3.05522i 0.0895501 + 0.155105i
$$389$$ −3.29180 5.70156i −0.166901 0.289080i 0.770428 0.637527i $$-0.220043\pi$$
−0.937329 + 0.348447i $$0.886709\pi$$
$$390$$ −6.47214 + 11.2101i −0.327729 + 0.567644i
$$391$$ 25.8885 1.30924
$$392$$ 0 0
$$393$$ −29.8885 −1.50768
$$394$$ −9.00000 + 15.5885i −0.453413 + 0.785335i
$$395$$ 0 0
$$396$$ −3.73607 6.47106i −0.187744 0.325183i
$$397$$ −5.14590 + 8.91296i −0.258265 + 0.447328i −0.965777 0.259373i $$-0.916484\pi$$
0.707512 + 0.706701i $$0.249818\pi$$
$$398$$ −1.05573 −0.0529189
$$399$$ 0 0
$$400$$ 5.47214 0.273607
$$401$$ 15.1803 26.2931i 0.758070 1.31302i −0.185764 0.982594i $$-0.559476\pi$$
0.943834 0.330421i $$-0.107191\pi$$
$$402$$ 24.9443 + 43.2047i 1.24411 + 2.15486i
$$403$$ −1.23607 2.14093i −0.0615729 0.106647i
$$404$$ −7.09017 + 12.2805i −0.352749 + 0.610979i
$$405$$ −79.0132 −3.92620
$$406$$ 0 0
$$407$$ −10.9443 −0.542487
$$408$$ −10.4721 + 18.1383i −0.518448 + 0.897978i
$$409$$ −11.7082 20.2792i −0.578933 1.00274i −0.995602 0.0936836i $$-0.970136\pi$$
0.416669 0.909058i $$-0.363198\pi$$
$$410$$ −10.4721 18.1383i −0.517182 0.895785i
$$411$$ −25.7082 + 44.5279i −1.26809 + 2.19640i
$$412$$ −2.94427 −0.145054
$$413$$ 0 0
$$414$$ 29.8885 1.46894
$$415$$ −16.4721 + 28.5306i −0.808585 + 1.40051i
$$416$$ 0.618034 + 1.07047i 0.0303016 + 0.0524839i
$$417$$ −13.4164 23.2379i −0.657004 1.13796i
$$418$$ −1.38197 + 2.39364i −0.0675942 + 0.117077i
$$419$$ −12.7639 −0.623559 −0.311779 0.950155i $$-0.600925\pi$$
−0.311779 + 0.950155i $$0.600925\pi$$
$$420$$ 0 0
$$421$$ 7.52786 0.366886 0.183443 0.983030i $$-0.441276\pi$$
0.183443 + 0.983030i $$0.441276\pi$$
$$422$$ 11.2361 19.4614i 0.546963 0.947368i
$$423$$ −7.47214 12.9421i −0.363308 0.629267i
$$424$$ 0.236068 + 0.408882i 0.0114645 + 0.0198571i
$$425$$ −17.7082 + 30.6715i −0.858974 + 1.48779i
$$426$$ −8.00000 −0.387601
$$427$$ 0 0
$$428$$ −6.47214 −0.312842
$$429$$ 2.00000 3.46410i 0.0965609 0.167248i
$$430$$ −2.47214 4.28187i −0.119217 0.206490i
$$431$$ −20.4721 35.4588i −0.986108 1.70799i −0.636905 0.770942i $$-0.719786\pi$$
−0.349203 0.937047i $$-0.613548\pi$$
$$432$$ −7.23607 + 12.5332i −0.348145 + 0.603006i
$$433$$ −19.5279 −0.938449 −0.469225 0.883079i $$-0.655467\pi$$
−0.469225 + 0.883079i $$0.655467\pi$$
$$434$$ 0 0
$$435$$ 46.8328 2.24546
$$436$$ 5.00000 8.66025i 0.239457 0.414751i
$$437$$ −5.52786 9.57454i −0.264434 0.458012i
$$438$$ −8.00000 13.8564i −0.382255 0.662085i
$$439$$ −4.47214 + 7.74597i −0.213443 + 0.369695i −0.952790 0.303630i $$-0.901801\pi$$
0.739347 + 0.673325i $$0.235135\pi$$
$$440$$ −3.23607 −0.154273
$$441$$ 0 0
$$442$$ −8.00000 −0.380521
$$443$$ 3.52786 6.11044i 0.167614 0.290316i −0.769967 0.638084i $$-0.779727\pi$$
0.937580 + 0.347768i $$0.113060\pi$$
$$444$$ 17.7082 + 30.6715i 0.840394 + 1.45561i
$$445$$ −16.1803 28.0252i −0.767022 1.32852i
$$446$$ 4.23607 7.33708i 0.200584 0.347421i
$$447$$ 72.3607 3.42254
$$448$$ 0 0
$$449$$ 1.05573 0.0498229 0.0249114 0.999690i $$-0.492070\pi$$
0.0249114 + 0.999690i $$0.492070\pi$$
$$450$$ −20.4443 + 35.4105i −0.963752 + 1.66927i
$$451$$ 3.23607 + 5.60503i 0.152380 + 0.263931i
$$452$$ −4.23607 7.33708i −0.199248 0.345107i
$$453$$ −19.4164 + 33.6302i −0.912262 + 1.58008i
$$454$$ 14.7639 0.692906
$$455$$ 0 0
$$456$$ 8.94427 0.418854
$$457$$ −4.52786 + 7.84249i −0.211805 + 0.366856i −0.952279 0.305228i $$-0.901267\pi$$
0.740475 + 0.672084i $$0.234601\pi$$
$$458$$ 6.38197 + 11.0539i 0.298210 + 0.516514i
$$459$$ −46.8328 81.1168i −2.18597 3.78621i
$$460$$ 6.47214 11.2101i 0.301765 0.522672i
$$461$$ −29.2361 −1.36166 −0.680830 0.732442i $$-0.738381\pi$$
−0.680830 + 0.732442i $$0.738381\pi$$
$$462$$ 0 0
$$463$$ −21.5279 −1.00048 −0.500242 0.865885i $$-0.666756\pi$$
−0.500242 + 0.865885i $$0.666756\pi$$
$$464$$ 2.23607 3.87298i 0.103807 0.179799i
$$465$$ −10.4721 18.1383i −0.485634 0.841142i
$$466$$ −1.47214 2.54981i −0.0681954 0.118118i
$$467$$ 6.56231 11.3662i 0.303667 0.525967i −0.673296 0.739373i $$-0.735122\pi$$
0.976964 + 0.213405i $$0.0684555\pi$$
$$468$$ −9.23607 −0.426937
$$469$$ 0 0
$$470$$ −6.47214 −0.298537
$$471$$ 30.1803 52.2739i 1.39064 2.40865i
$$472$$ 3.61803 + 6.26662i 0.166534 + 0.288445i
$$473$$ 0.763932 + 1.32317i 0.0351256 + 0.0608394i
$$474$$ 0 0
$$475$$ 15.1246 0.693965
$$476$$ 0 0
$$477$$ −3.52786 −0.161530
$$478$$ −10.0000 + 17.3205i −0.457389 + 0.792222i
$$479$$ −16.1803 28.0252i −0.739299 1.28050i −0.952812 0.303562i $$-0.901824\pi$$
0.213513 0.976940i $$-0.431509\pi$$
$$480$$ 5.23607 + 9.06914i 0.238993 + 0.413948i
$$481$$ −6.76393 + 11.7155i −0.308409 + 0.534180i
$$482$$ 11.4164 0.520003
$$483$$ 0 0
$$484$$ 1.00000 0.0454545
$$485$$ −5.70820 + 9.88690i −0.259196 + 0.448941i
$$486$$ −17.7984 30.8277i −0.807351 1.39837i
$$487$$ 0.472136 + 0.817763i 0.0213945 + 0.0370564i 0.876524 0.481357i $$-0.159856\pi$$
−0.855130 + 0.518414i $$0.826523\pi$$
$$488$$ −2.61803 + 4.53457i −0.118513 + 0.205270i
$$489$$ 24.0000 1.08532
$$490$$ 0 0
$$491$$ 0.944272 0.0426144 0.0213072 0.999773i $$-0.493217\pi$$
0.0213072 + 0.999773i $$0.493217\pi$$
$$492$$ 10.4721 18.1383i 0.472120 0.817736i
$$493$$ 14.4721 + 25.0665i 0.651792 + 1.12894i
$$494$$ 1.70820 + 2.95870i 0.0768557 + 0.133118i
$$495$$ 12.0902 20.9408i 0.543413 0.941218i
$$496$$ −2.00000 −0.0898027
$$497$$ 0 0
$$498$$ −32.9443 −1.47627
$$499$$ −6.18034 + 10.7047i −0.276670 + 0.479207i −0.970555 0.240879i $$-0.922564\pi$$
0.693885 + 0.720086i $$0.255898\pi$$
$$500$$ 0.763932 + 1.32317i 0.0341641 + 0.0591739i
$$501$$ −24.9443 43.2047i −1.11443 1.93025i
$$502$$ 12.3820 21.4462i 0.552634 0.957190i
$$503$$ −4.00000 −0.178351 −0.0891756 0.996016i $$-0.528423\pi$$
−0.0891756 + 0.996016i $$0.528423\pi$$
$$504$$ 0 0
$$505$$ −45.8885 −2.04201
$$506$$ −2.00000 + 3.46410i −0.0889108 + 0.153998i
$$507$$ 18.5623 + 32.1509i 0.824381 + 1.42787i
$$508$$ 6.00000 + 10.3923i 0.266207 + 0.461084i
$$509$$ −17.0344 + 29.5045i −0.755038 + 1.30776i 0.190317 + 0.981723i $$0.439048\pi$$
−0.945355 + 0.326042i $$0.894285\pi$$
$$510$$ −67.7771 −3.00122
$$511$$ 0 0
$$512$$ 1.00000 0.0441942
$$513$$ −20.0000 + 34.6410i −0.883022 + 1.52944i
$$514$$ −5.47214 9.47802i −0.241366 0.418057i
$$515$$ −4.76393 8.25137i −0.209924 0.363599i
$$516$$ 2.47214 4.28187i 0.108830 0.188499i
$$517$$ 2.00000 0.0879599
$$518$$ 0 0
$$519$$ −4.00000 −0.175581
$$520$$ −2.00000 + 3.46410i −0.0877058 + 0.151911i
$$521$$ 17.1803 + 29.7572i 0.752684 + 1.30369i 0.946517 + 0.322653i $$0.104575\pi$$
−0.193833 + 0.981035i $$0.562092\pi$$
$$522$$ 16.7082 + 28.9395i 0.731298 + 1.26665i
$$523$$ −13.8541 + 23.9960i −0.605798 + 1.04927i 0.386127 + 0.922446i $$0.373813\pi$$
−0.991925 + 0.126827i $$0.959521\pi$$
$$524$$ −9.23607 −0.403480
$$525$$ 0 0
$$526$$ 12.9443 0.564397
$$527$$ 6.47214 11.2101i 0.281931 0.488318i
$$528$$ −1.61803 2.80252i −0.0704159 0.121964i
$$529$$ 3.50000 + 6.06218i 0.152174 + 0.263573i
$$530$$ −0.763932 + 1.32317i −0.0331831 + 0.0574748i
$$531$$ −54.0689 −2.34639
$$532$$ 0 0
$$533$$ 8.00000 0.346518
$$534$$ 16.1803 28.0252i 0.700192 1.21277i
$$535$$ −10.4721 18.1383i −0.452750 0.784186i
$$536$$ 7.70820 + 13.3510i 0.332944 + 0.576675i
$$537$$ −14.4721 + 25.0665i −0.624519 + 1.08170i
$$538$$ 27.2361 1.17423
$$539$$ 0 0
$$540$$ −46.8328 −2.01536
$$541$$ 4.52786 7.84249i 0.194668 0.337175i −0.752124 0.659022i $$-0.770970\pi$$
0.946792 + 0.321847i $$0.104304\pi$$
$$542$$ −8.47214 14.6742i −0.363909 0.630310i
$$543$$ 7.70820 + 13.3510i 0.330791 + 0.572946i
$$544$$ −3.23607 + 5.60503i −0.138745 + 0.240314i
$$545$$ 32.3607 1.38618
$$546$$ 0 0
$$547$$ 16.9443 0.724485 0.362242 0.932084i $$-0.382011\pi$$
0.362242 + 0.932084i $$0.382011\pi$$
$$548$$ −7.94427 + 13.7599i −0.339362 + 0.587793i
$$549$$ −19.5623 33.8829i −0.834899 1.44609i
$$550$$ −2.73607 4.73901i −0.116666 0.202072i
$$551$$ 6.18034 10.7047i 0.263291 0.456034i
$$552$$ 12.9443 0.550945
$$553$$ 0 0
$$554$$ 12.4721 0.529890
$$555$$ −57.3050 + 99.2551i −2.43246 + 4.21314i
$$556$$ −4.14590 7.18091i −0.175825 0.304538i
$$557$$ 14.4164 + 24.9700i 0.610843 + 1.05801i 0.991099 + 0.133129i $$0.0425026\pi$$
−0.380256 + 0.924881i $$0.624164\pi$$
$$558$$ 7.47214 12.9421i 0.316321 0.547884i
$$559$$ 1.88854 0.0798769
$$560$$ 0 0
$$561$$ 20.9443 0.884268
$$562$$ 12.4164 21.5058i 0.523755 0.907169i
$$563$$ 13.3820 + 23.1782i 0.563983 + 0.976847i 0.997144 + 0.0755300i $$0.0240648\pi$$
−0.433161 + 0.901317i $$0.642602\pi$$
$$564$$ −3.23607 5.60503i −0.136263 0.236015i
$$565$$ 13.7082 23.7433i 0.576708 0.998888i
$$566$$ 16.6525 0.699956
$$567$$ 0 0
$$568$$ −2.47214 −0.103729
$$569$$ −8.41641 + 14.5776i −0.352834 + 0.611127i −0.986745 0.162280i $$-0.948115\pi$$
0.633911 + 0.773406i $$0.281449\pi$$
$$570$$ 14.4721 + 25.0665i 0.606171 + 1.04992i
$$571$$ 22.9443 + 39.7406i 0.960188 + 1.66309i 0.722022 + 0.691870i $$0.243213\pi$$
0.238165 + 0.971225i $$0.423454\pi$$
$$572$$ 0.618034 1.07047i 0.0258413 0.0447584i
$$573$$ 20.9443 0.874960
$$574$$ 0 0
$$575$$ 21.8885 0.912815
$$576$$ −3.73607 + 6.47106i −0.155669 + 0.269627i
$$577$$ 4.52786 + 7.84249i 0.188497 + 0.326487i 0.944749 0.327793i $$-0.106305\pi$$
−0.756252 + 0.654280i $$0.772972\pi$$
$$578$$ −12.4443 21.5541i −0.517613 0.896533i
$$579$$ −4.76393 + 8.25137i −0.197982 + 0.342915i
$$580$$ 14.4721 0.600923
$$581$$ 0 0
$$582$$ −11.4164 −0.473225
$$583$$ 0.236068 0.408882i 0.00977694 0.0169342i
$$584$$ −2.47214 4.28187i −0.102298 0.177185i
$$585$$ −14.9443 25.8842i −0.617870 1.07018i
$$586$$ 2.32624 4.02916i 0.0960960 0.166443i
$$587$$ 28.1803 1.16313 0.581564 0.813501i $$-0.302441\pi$$
0.581564 + 0.813501i $$0.302441\pi$$
$$588$$ 0 0
$$589$$ −5.52786 −0.227772
$$590$$ −11.7082 + 20.2792i −0.482019 + 0.834882i
$$591$$ −29.1246 50.4453i −1.19803 2.07504i
$$592$$ 5.47214 + 9.47802i 0.224903 + 0.389544i
$$593$$ 12.0000 20.7846i 0.492781 0.853522i −0.507184 0.861838i $$-0.669314\pi$$
0.999965 + 0.00831589i $$0.00264706\pi$$
$$594$$ 14.4721 0.593799
$$595$$ 0 0
$$596$$ 22.3607 0.915929
$$597$$ 1.70820 2.95870i 0.0699121 0.121091i
$$598$$ 2.47214 + 4.28187i 0.101093 + 0.175098i
$$599$$ −6.18034 10.7047i −0.252522 0.437381i 0.711698 0.702486i $$-0.247927\pi$$
−0.964219 + 0.265105i $$0.914593\pi$$
$$600$$ −8.85410 + 15.3358i −0.361467 + 0.626080i
$$601$$ −18.8328 −0.768207 −0.384103 0.923290i $$-0.625489\pi$$
−0.384103 + 0.923290i $$0.625489\pi$$
$$602$$ 0 0
$$603$$ −115.193 −4.69104
$$604$$ −6.00000 + 10.3923i −0.244137 + 0.422857i
$$605$$ 1.61803 + 2.80252i 0.0657824 + 0.113939i
$$606$$ −22.9443 39.7406i −0.932047 1.61435i
$$607$$ −16.0000 + 27.7128i −0.649420 + 1.12483i 0.333842 + 0.942629i $$0.391655\pi$$
−0.983262 + 0.182199i $$0.941678\pi$$
$$608$$ 2.76393 0.112092
$$609$$ 0 0
$$610$$ −16.9443 −0.686054
$$611$$ 1.23607 2.14093i 0.0500060 0.0866129i
$$612$$ −24.1803 41.8816i −0.977432 1.69296i
$$613$$ −9.76393 16.9116i −0.394362 0.683054i 0.598658 0.801005i $$-0.295701\pi$$
−0.993019 + 0.117951i $$0.962368\pi$$
$$614$$ 16.0344 27.7725i 0.647097 1.12081i
$$615$$ 67.7771 2.73304
$$616$$ 0 0
$$617$$ −5.41641 −0.218056 −0.109028 0.994039i $$-0.534774\pi$$
−0.109028 + 0.994039i $$0.534774\pi$$
$$618$$ 4.76393 8.25137i 0.191633 0.331919i
$$619$$ −24.2705 42.0378i −0.975514 1.68964i −0.678228 0.734852i $$-0.737252\pi$$
−0.297286 0.954788i $$-0.596082\pi$$
$$620$$ −3.23607 5.60503i −0.129964 0.225104i
$$621$$ −28.9443 + 50.1329i −1.16149 + 2.01177i
$$622$$ −5.41641 −0.217178
$$623$$ 0 0
$$624$$ −4.00000 −0.160128
$$625$$ 11.2082 19.4132i 0.448328 0.776527i
$$626$$ 14.2361 + 24.6576i 0.568988 + 0.985516i
$$627$$ −4.47214 7.74597i −0.178600 0.309344i
$$628$$ 9.32624 16.1535i 0.372157 0.644596i
$$629$$ −70.8328 −2.82429
$$630$$ 0 0
$$631$$ −4.58359 −0.182470 −0.0912350 0.995829i $$-0.529081\pi$$
−0.0912350 + 0.995829i $$0.529081\pi$$
$$632$$ 0 0
$$633$$ 36.3607 + 62.9785i 1.44521 + 2.50317i
$$634$$ 6.52786 + 11.3066i 0.259255 + 0.449042i
$$635$$ −19.4164 + 33.6302i −0.770517 + 1.33457i
$$636$$ −1.52786 −0.0605838
$$637$$ 0 0
$$638$$ −4.47214 −0.177054
$$639$$ 9.23607 15.9973i 0.365373 0.632845i
$$640$$ 1.61803 + 2.80252i 0.0639584 + 0.110779i
$$641$$ −18.2361 31.5858i −0.720281 1.24756i −0.960887 0.276941i $$-0.910679\pi$$
0.240606 0.970623i $$-0.422654\pi$$
$$642$$ 10.4721 18.1383i 0.413302 0.715860i
$$643$$ 23.2361 0.916341 0.458171 0.888864i $$-0.348505\pi$$
0.458171 + 0.888864i $$0.348505\pi$$
$$644$$ 0 0
$$645$$ 16.0000 0.629999
$$646$$ −8.94427 + 15.4919i −0.351908 + 0.609522i
$$647$$ 12.4164 + 21.5058i 0.488139 + 0.845482i 0.999907 0.0136418i $$-0.00434244\pi$$
−0.511768 + 0.859124i $$0.671009\pi$$
$$648$$ −12.2082 21.1452i −0.479584 0.830663i
$$649$$ 3.61803 6.26662i 0.142020 0.245986i
$$650$$ −6.76393 −0.265303
$$651$$ 0 0
$$652$$ 7.41641 0.290449
$$653$$ −0.819660 + 1.41969i −0.0320758 + 0.0555569i −0.881618 0.471964i $$-0.843545\pi$$
0.849542 + 0.527521i $$0.176878\pi$$
$$654$$ 16.1803 + 28.0252i 0.632701 + 1.09587i
$$655$$ −14.9443 25.8842i −0.583921 1.01138i
$$656$$ 3.23607 5.60503i 0.126347 0.218840i
$$657$$ 36.9443 1.44133
$$658$$ 0 0
$$659$$ 43.4164 1.69126 0.845632 0.533767i $$-0.179224\pi$$
0.845632 + 0.533767i $$0.179224\pi$$
$$660$$ 5.23607 9.06914i 0.203814 0.353016i
$$661$$ 18.5623 + 32.1509i 0.721990 + 1.25052i 0.960201 + 0.279310i $$0.0901057\pi$$
−0.238211 + 0.971213i $$0.576561\pi$$
$$662$$ −0.472136 0.817763i −0.0183501 0.0317833i
$$663$$ 12.9443 22.4201i 0.502714 0.870726i
$$664$$ −10.1803 −0.395074
$$665$$ 0 0
$$666$$ −81.7771 −3.16880
$$667$$ 8.94427 15.4919i 0.346324 0.599850i
$$668$$ −7.70820 13.3510i −0.298239 0.516566i
$$669$$ 13.7082 + 23.7433i 0.529990 + 0.917969i
$$670$$ −24.9443 + 43.2047i −0.963681 + 1.66914i
$$671$$ 5.23607 0.202136
$$672$$ 0 0
$$673$$ 31.8885 1.22921 0.614607 0.788834i $$-0.289315\pi$$
0.614607 + 0.788834i $$0.289315\pi$$
$$674$$ −9.00000 + 15.5885i −0.346667 + 0.600445i
$$675$$ −39.5967 68.5836i −1.52408 2.63978i
$$676$$ 5.73607 + 9.93516i 0.220618 + 0.382122i
$$677$$ 16.0344 27.7725i 0.616254 1.06738i −0.373910 0.927465i $$-0.621983\pi$$
0.990163 0.139917i $$-0.0446837\pi$$
$$678$$ 27.4164 1.05292
$$679$$ 0 0
$$680$$ −20.9443 −0.803176
$$681$$ −23.8885 + 41.3762i −0.915411 + 1.58554i
$$682$$ 1.00000 + 1.73205i 0.0382920 + 0.0663237i
$$683$$ −7.52786 13.0386i −0.288046 0.498910i 0.685297 0.728263i $$-0.259672\pi$$
−0.973343 + 0.229353i $$0.926339\pi$$
$$684$$ −10.3262 + 17.8856i −0.394834 + 0.683872i
$$685$$ −51.4164 −1.96452
$$686$$ 0 0
$$687$$ −41.3050 −1.57588
$$688$$ 0.763932 1.32317i 0.0291246 0.0504453i
$$689$$ −0.291796 0.505406i −0.0111165 0.0192544i
$$690$$ 20.9443 + 36.2765i 0.797335 + 1.38102i
$$691$$ −9.32624 + 16.1535i −0.354787 + 0.614509i −0.987081 0.160219i $$-0.948780\pi$$
0.632295 + 0.774728i $$0.282113\pi$$
$$692$$ −1.23607 −0.0469883
$$693$$ 0 0
$$694$$ −6.47214 −0.245679
$$695$$ 13.4164 23.2379i 0.508913 0.881464i
$$696$$ 7.23607 + 12.5332i 0.274282 + 0.475071i
$$697$$ 20.9443 + 36.2765i 0.793321 + 1.37407i
$$698$$ 4.14590 7.18091i 0.156925 0.271801i
$$699$$ 9.52786 0.360377
$$700$$ 0 0
$$701$$ 46.7214 1.76464 0.882321 0.470649i $$-0.155980\pi$$
0.882321 + 0.470649i $$0.155980\pi$$
$$702$$ 8.94427 15.4919i 0.337580 0.584705i
$$703$$ 15.1246 + 26.1966i 0.570436 + 0.988023i
$$704$$ −0.500000 0.866025i −0.0188445 0.0326396i
$$705$$ 10.4721 18.1383i 0.394403 0.683127i
$$706$$ 34.9443 1.31515
$$707$$ 0 0
$$708$$ −23.4164 −0.880042
$$709$$ 2.23607 3.87298i 0.0839773 0.145453i −0.820978 0.570960i $$-0.806571\pi$$
0.904955 + 0.425507i $$0.139904\pi$$
$$710$$ −4.00000 6.92820i −0.150117 0.260011i
$$711$$ 0 0
$$712$$ 5.00000 8.66025i 0.187383 0.324557i
$$713$$ −8.00000 −0.299602
$$714$$ 0 0
$$715$$ 4.00000 0.149592
$$716$$ −4.47214 + 7.74597i −0.167132 + 0.289480i
$$717$$ −32.3607 56.0503i −1.20853 2.09324i
$$718$$ 13.4164 + 23.2379i 0.500696 + 0.867231i
$$719$$ −18.4164 + 31.8982i −0.686816 + 1.18960i 0.286046 + 0.958216i $$0.407659\pi$$
−0.972862 + 0.231385i $$0.925674\pi$$
$$720$$ −24.1803 −0.901148
$$721$$ 0 0
$$722$$ −11.3607 −0.422801
$$723$$ −18.4721 + 31.9947i −0.686986 + 1.18989i
$$724$$ 2.38197 + 4.12569i 0.0885251 + 0.153330i
$$725$$ 12.2361 + 21.1935i 0.454436 + 0.787107i
$$726$$ −1.61803 + 2.80252i −0.0600509 + 0.104011i
$$727$$ −18.0000 −0.667583 −0.333792 0.942647i $$-0.608328\pi$$
−0.333792 + 0.942647i $$0.608328\pi$$
$$728$$ 0 0
$$729$$ 41.9443 1.55349
$$730$$ 8.00000 13.8564i 0.296093 0.512849i
$$731$$ 4.94427 + 8.56373i 0.182871 + 0.316741i
$$732$$ −8.47214 14.6742i −0.313139 0.542373i
$$733$$ 4.43769 7.68631i 0.163910 0.283900i −0.772358 0.635188i $$-0.780923\pi$$
0.936268 + 0.351287i $$0.114256\pi$$
$$734$$ −21.4164 −0.790494
$$735$$ 0 0
$$736$$ 4.00000 0.147442
$$737$$ 7.70820 13.3510i 0.283935 0.491790i
$$738$$ 24.1803 + 41.8816i 0.890091 + 1.54168i
$$739$$ −10.0000 17.3205i −0.367856 0.637145i 0.621374 0.783514i $$-0.286575\pi$$
−0.989230 + 0.146369i $$0.953241\pi$$
$$740$$ −17.7082 + 30.6715i −0.650967 + 1.12751i
$$741$$ −11.0557 −0.406142
$$742$$ 0 0
$$743$$ −13.8885 −0.509521 −0.254761 0.967004i $$-0.581997\pi$$
−0.254761 + 0.967004i $$0.581997\pi$$
$$744$$ 3.23607 5.60503i 0.118640 0.205491i
$$745$$ 36.1803 + 62.6662i 1.32555 + 2.29591i
$$746$$ 3.00000 + 5.19615i 0.109838 + 0.190245i
$$747$$ 38.0344 65.8776i 1.39161 2.41033i
$$748$$ 6.47214 0.236645
$$749$$ 0 0
$$750$$ −4.94427 −0.180539
$$751$$ −0.472136 + 0.817763i −0.0172285 + 0.0298406i −0.874511 0.485005i $$-0.838818\pi$$
0.857283 + 0.514846i $$0.172151\pi$$
$$752$$ −1.00000 1.73205i −0.0364662 0.0631614i
$$753$$ 40.0689 + 69.4013i 1.46019 + 2.52913i
$$754$$ −2.76393 + 4.78727i −0.100656 + 0.174342i
$$755$$ −38.8328 −1.41327
$$756$$ 0 0
$$757$$ 39.3050 1.42856 0.714281 0.699859i $$-0.246754\pi$$
0.714281 + 0.699859i $$0.246754\pi$$
$$758$$ −2.76393 + 4.78727i −0.100391 + 0.173882i
$$759$$ −6.47214 11.2101i −0.234924 0.406900i
$$760$$ 4.47214 + 7.74597i 0.162221 + 0.280976i
$$761$$ 7.70820 13.3510i 0.279422 0.483973i −0.691819 0.722071i $$-0.743190\pi$$
0.971241 + 0.238097i $$0.0765238\pi$$
$$762$$ −38.8328 −1.40676
$$763$$ 0 0
$$764$$ 6.47214 0.234154
$$765$$ 78.2492 135.532i 2.82911 4.90016i
$$766$$ 5.94427 + 10.2958i 0.214775 + 0.372002i
$$767$$ −4.47214 7.74597i −0.161479 0.279691i
$$768$$ −1.61803 + 2.80252i −0.0583858 + 0.101127i
$$769$$ 16.5836 0.598020 0.299010 0.954250i $$-0.403344\pi$$
0.299010 + 0.954250i $$0.403344\pi$$
$$770$$ 0 0
$$771$$ 35.4164 1.27549
$$772$$ −1.47214 + 2.54981i −0.0529833 + 0.0917698i
$$773$$ 1.14590 + 1.98475i 0.0412151 + 0.0713866i 0.885897 0.463882i $$-0.153544\pi$$
−0.844682 + 0.535268i $$0.820210\pi$$
$$774$$ 5.70820 + 9.88690i 0.205177 + 0.355377i
$$775$$ 5.47214 9.47802i 0.196565 0.340460i
$$776$$ −3.52786