Properties

 Label 882.2.h.p.67.2 Level $882$ Weight $2$ Character 882.67 Analytic conductor $7.043$ Analytic rank $0$ Dimension $6$ CM no Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(67,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("882.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$882 = 2 \cdot 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 882.h (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: $$7.04280545828$$ Analytic rank: $$0$$ Dimension: $$6$$ Relative dimension: $$3$$ over $$\Q(\zeta_{3})$$ Coefficient field: 6.0.309123.1 comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3$$ x^6 - 3*x^5 + 10*x^4 - 15*x^3 + 19*x^2 - 12*x + 3 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 126) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

 Embedding label 67.2 Root $$0.500000 - 2.05195i$$ of defining polynomial Character $$\chi$$ $$=$$ 882.67 Dual form 882.2.h.p.79.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(0.500000 - 0.866025i) q^{2} +(-0.796790 + 1.53790i) q^{3} +(-0.500000 - 0.866025i) q^{4} -0.593579 q^{5} +(0.933463 + 1.45899i) q^{6} -1.00000 q^{8} +(-1.73025 - 2.45076i) q^{9} +O(q^{10})$$ $$q+(0.500000 - 0.866025i) q^{2} +(-0.796790 + 1.53790i) q^{3} +(-0.500000 - 0.866025i) q^{4} -0.593579 q^{5} +(0.933463 + 1.45899i) q^{6} -1.00000 q^{8} +(-1.73025 - 2.45076i) q^{9} +(-0.296790 + 0.514055i) q^{10} -0.593579 q^{11} +(1.73025 - 0.0789082i) q^{12} +(1.25729 - 2.17770i) q^{13} +(0.472958 - 0.912864i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.46050 + 2.52967i) q^{17} +(-2.98755 + 0.273062i) q^{18} +(-2.69076 - 4.66053i) q^{19} +(0.296790 + 0.514055i) q^{20} +(-0.296790 + 0.514055i) q^{22} +4.46050 q^{23} +(0.796790 - 1.53790i) q^{24} -4.64766 q^{25} +(-1.25729 - 2.17770i) q^{26} +(5.14766 - 0.708209i) q^{27} +(-3.09718 - 5.36447i) q^{29} +(-0.554084 - 0.866025i) q^{30} +(-3.93346 - 6.81296i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.472958 - 0.912864i) q^{33} +(1.46050 + 2.52967i) q^{34} +(-1.25729 + 2.72382i) q^{36} +(0.500000 + 0.866025i) q^{37} -5.38151 q^{38} +(2.34728 + 3.66876i) q^{39} +0.593579 q^{40} +(0.136673 - 0.236725i) q^{41} +(-5.58113 - 9.66679i) q^{43} +(0.296790 + 0.514055i) q^{44} +(1.02704 + 1.45472i) q^{45} +(2.23025 - 3.86291i) q^{46} +(6.08113 - 10.5328i) q^{47} +(-0.933463 - 1.45899i) q^{48} +(-2.32383 + 4.02499i) q^{50} +(-2.72665 - 4.26172i) q^{51} -2.51459 q^{52} +(4.02704 - 6.97504i) q^{53} +(1.96050 - 4.81211i) q^{54} +0.352336 q^{55} +(9.31138 - 0.424646i) q^{57} -6.19436 q^{58} +(4.32383 + 7.48910i) q^{59} +(-1.02704 + 0.0468383i) q^{60} +(-3.32383 + 5.75705i) q^{61} -7.86693 q^{62} +1.00000 q^{64} +(-0.746304 + 1.29264i) q^{65} +(-0.554084 - 0.866025i) q^{66} +(0.956906 + 1.65741i) q^{67} +2.92101 q^{68} +(-3.55408 + 6.85980i) q^{69} -14.4107 q^{71} +(1.73025 + 2.45076i) q^{72} +(-3.95691 + 6.85356i) q^{73} +1.00000 q^{74} +(3.70321 - 7.14763i) q^{75} +(-2.69076 + 4.66053i) q^{76} +(4.35087 - 0.198422i) q^{78} +(4.62422 - 8.00938i) q^{79} +(0.296790 - 0.514055i) q^{80} +(-3.01245 + 8.48087i) q^{81} +(-0.136673 - 0.236725i) q^{82} +(-3.85087 - 6.66991i) q^{83} +(0.866926 - 1.50156i) q^{85} -11.1623 q^{86} +(10.7178 - 0.488786i) q^{87} +0.593579 q^{88} +(6.21780 + 10.7695i) q^{89} +(1.77335 - 0.162084i) q^{90} +(-2.23025 - 3.86291i) q^{92} +(13.6118 - 0.620765i) q^{93} +(-6.08113 - 10.5328i) q^{94} +(1.59718 + 2.76639i) q^{95} +(-1.73025 + 0.0789082i) q^{96} +(-5.86693 - 10.1618i) q^{97} +(1.02704 + 1.45472i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$6 q + 3 q^{2} - 2 q^{3} - 3 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{8} - 4 q^{9}+O(q^{10})$$ 6 * q + 3 * q^2 - 2 * q^3 - 3 * q^4 + 2 * q^5 + 2 * q^6 - 6 * q^8 - 4 * q^9 $$6 q + 3 q^{2} - 2 q^{3} - 3 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{8} - 4 q^{9} + q^{10} + 2 q^{11} + 4 q^{12} - 8 q^{13} + 12 q^{15} - 3 q^{16} + 4 q^{17} + 4 q^{18} + 3 q^{19} - q^{20} + q^{22} + 14 q^{23} + 2 q^{24} - 4 q^{25} + 8 q^{26} + 7 q^{27} - 5 q^{29} + 15 q^{30} - 20 q^{31} + 3 q^{32} + 12 q^{33} - 4 q^{34} + 8 q^{36} + 3 q^{37} + 6 q^{38} + q^{39} - 2 q^{40} - 6 q^{43} - q^{44} - 3 q^{45} + 7 q^{46} + 9 q^{47} - 2 q^{48} - 2 q^{50} - 18 q^{51} + 16 q^{52} + 15 q^{53} - q^{54} + 26 q^{55} + 22 q^{57} - 10 q^{58} + 14 q^{59} + 3 q^{60} - 8 q^{61} - 40 q^{62} + 6 q^{64} - 12 q^{65} + 15 q^{66} + q^{67} - 8 q^{68} - 3 q^{69} + 14 q^{71} + 4 q^{72} - 19 q^{73} + 6 q^{74} + 25 q^{75} + 3 q^{76} + 5 q^{78} + 5 q^{79} - q^{80} - 40 q^{81} - 2 q^{83} - 2 q^{85} - 12 q^{86} + 36 q^{87} - 2 q^{88} + 9 q^{89} + 9 q^{90} - 7 q^{92} + 37 q^{93} - 9 q^{94} - 4 q^{95} - 4 q^{96} - 28 q^{97} - 3 q^{99}+O(q^{100})$$ 6 * q + 3 * q^2 - 2 * q^3 - 3 * q^4 + 2 * q^5 + 2 * q^6 - 6 * q^8 - 4 * q^9 + q^10 + 2 * q^11 + 4 * q^12 - 8 * q^13 + 12 * q^15 - 3 * q^16 + 4 * q^17 + 4 * q^18 + 3 * q^19 - q^20 + q^22 + 14 * q^23 + 2 * q^24 - 4 * q^25 + 8 * q^26 + 7 * q^27 - 5 * q^29 + 15 * q^30 - 20 * q^31 + 3 * q^32 + 12 * q^33 - 4 * q^34 + 8 * q^36 + 3 * q^37 + 6 * q^38 + q^39 - 2 * q^40 - 6 * q^43 - q^44 - 3 * q^45 + 7 * q^46 + 9 * q^47 - 2 * q^48 - 2 * q^50 - 18 * q^51 + 16 * q^52 + 15 * q^53 - q^54 + 26 * q^55 + 22 * q^57 - 10 * q^58 + 14 * q^59 + 3 * q^60 - 8 * q^61 - 40 * q^62 + 6 * q^64 - 12 * q^65 + 15 * q^66 + q^67 - 8 * q^68 - 3 * q^69 + 14 * q^71 + 4 * q^72 - 19 * q^73 + 6 * q^74 + 25 * q^75 + 3 * q^76 + 5 * q^78 + 5 * q^79 - q^80 - 40 * q^81 - 2 * q^83 - 2 * q^85 - 12 * q^86 + 36 * q^87 - 2 * q^88 + 9 * q^89 + 9 * q^90 - 7 * q^92 + 37 * q^93 - 9 * q^94 - 4 * q^95 - 4 * q^96 - 28 * q^97 - 3 * q^99

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$$.

 $$n$$ $$199$$ $$785$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$

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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.500000 0.866025i 0.353553 0.612372i
$$3$$ −0.796790 + 1.53790i −0.460027 + 0.887905i
$$4$$ −0.500000 0.866025i −0.250000 0.433013i
$$5$$ −0.593579 −0.265457 −0.132728 0.991152i $$-0.542374\pi$$
−0.132728 + 0.991152i $$0.542374\pi$$
$$6$$ 0.933463 + 1.45899i 0.381085 + 0.595630i
$$7$$ 0 0
$$8$$ −1.00000 −0.353553
$$9$$ −1.73025 2.45076i −0.576751 0.816920i
$$10$$ −0.296790 + 0.514055i −0.0938531 + 0.162558i
$$11$$ −0.593579 −0.178971 −0.0894855 0.995988i $$-0.528522\pi$$
−0.0894855 + 0.995988i $$0.528522\pi$$
$$12$$ 1.73025 0.0789082i 0.499481 0.0227788i
$$13$$ 1.25729 2.17770i 0.348711 0.603985i −0.637310 0.770608i $$-0.719953\pi$$
0.986021 + 0.166623i $$0.0532862\pi$$
$$14$$ 0 0
$$15$$ 0.472958 0.912864i 0.122117 0.235700i
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ −1.46050 + 2.52967i −0.354224 + 0.613535i −0.986985 0.160813i $$-0.948588\pi$$
0.632760 + 0.774348i $$0.281922\pi$$
$$18$$ −2.98755 + 0.273062i −0.704172 + 0.0643614i
$$19$$ −2.69076 4.66053i −0.617302 1.06920i −0.989976 0.141236i $$-0.954892\pi$$
0.372674 0.927962i $$-0.378441\pi$$
$$20$$ 0.296790 + 0.514055i 0.0663642 + 0.114946i
$$21$$ 0 0
$$22$$ −0.296790 + 0.514055i −0.0632758 + 0.109597i
$$23$$ 4.46050 0.930080 0.465040 0.885290i $$-0.346040\pi$$
0.465040 + 0.885290i $$0.346040\pi$$
$$24$$ 0.796790 1.53790i 0.162644 0.313922i
$$25$$ −4.64766 −0.929533
$$26$$ −1.25729 2.17770i −0.246576 0.427082i
$$27$$ 5.14766 0.708209i 0.990668 0.136295i
$$28$$ 0 0
$$29$$ −3.09718 5.36447i −0.575132 0.996157i −0.996027 0.0890480i $$-0.971618\pi$$
0.420896 0.907109i $$-0.361716\pi$$
$$30$$ −0.554084 0.866025i −0.101161 0.158114i
$$31$$ −3.93346 6.81296i −0.706471 1.22364i −0.966158 0.257951i $$-0.916953\pi$$
0.259687 0.965693i $$-0.416380\pi$$
$$32$$ 0.500000 + 0.866025i 0.0883883 + 0.153093i
$$33$$ 0.472958 0.912864i 0.0823314 0.158909i
$$34$$ 1.46050 + 2.52967i 0.250475 + 0.433835i
$$35$$ 0 0
$$36$$ −1.25729 + 2.72382i −0.209549 + 0.453970i
$$37$$ 0.500000 + 0.866025i 0.0821995 + 0.142374i 0.904194 0.427121i $$-0.140472\pi$$
−0.821995 + 0.569495i $$0.807139\pi$$
$$38$$ −5.38151 −0.872997
$$39$$ 2.34728 + 3.66876i 0.375865 + 0.587471i
$$40$$ 0.593579 0.0938531
$$41$$ 0.136673 0.236725i 0.0213448 0.0369702i −0.855156 0.518371i $$-0.826539\pi$$
0.876500 + 0.481401i $$0.159872\pi$$
$$42$$ 0 0
$$43$$ −5.58113 9.66679i −0.851114 1.47417i −0.880204 0.474596i $$-0.842594\pi$$
0.0290902 0.999577i $$-0.490739\pi$$
$$44$$ 0.296790 + 0.514055i 0.0447427 + 0.0774967i
$$45$$ 1.02704 + 1.45472i 0.153102 + 0.216857i
$$46$$ 2.23025 3.86291i 0.328833 0.569555i
$$47$$ 6.08113 10.5328i 0.887023 1.53637i 0.0436467 0.999047i $$-0.486102\pi$$
0.843377 0.537323i $$-0.180564\pi$$
$$48$$ −0.933463 1.45899i −0.134734 0.210587i
$$49$$ 0 0
$$50$$ −2.32383 + 4.02499i −0.328639 + 0.569220i
$$51$$ −2.72665 4.26172i −0.381808 0.596760i
$$52$$ −2.51459 −0.348711
$$53$$ 4.02704 6.97504i 0.553157 0.958096i −0.444888 0.895586i $$-0.646756\pi$$
0.998044 0.0625092i $$-0.0199103\pi$$
$$54$$ 1.96050 4.81211i 0.266791 0.654845i
$$55$$ 0.352336 0.0475090
$$56$$ 0 0
$$57$$ 9.31138 0.424646i 1.23332 0.0562457i
$$58$$ −6.19436 −0.813359
$$59$$ 4.32383 + 7.48910i 0.562915 + 0.974997i 0.997240 + 0.0742412i $$0.0236535\pi$$
−0.434325 + 0.900756i $$0.643013\pi$$
$$60$$ −1.02704 + 0.0468383i −0.132591 + 0.00604680i
$$61$$ −3.32383 + 5.75705i −0.425573 + 0.737114i −0.996474 0.0839050i $$-0.973261\pi$$
0.570901 + 0.821019i $$0.306594\pi$$
$$62$$ −7.86693 −0.999101
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ −0.746304 + 1.29264i −0.0925676 + 0.160332i
$$66$$ −0.554084 0.866025i −0.0682031 0.106600i
$$67$$ 0.956906 + 1.65741i 0.116905 + 0.202485i 0.918540 0.395329i $$-0.129369\pi$$
−0.801635 + 0.597814i $$0.796036\pi$$
$$68$$ 2.92101 0.354224
$$69$$ −3.55408 + 6.85980i −0.427861 + 0.825822i
$$70$$ 0 0
$$71$$ −14.4107 −1.71023 −0.855117 0.518435i $$-0.826515\pi$$
−0.855117 + 0.518435i $$0.826515\pi$$
$$72$$ 1.73025 + 2.45076i 0.203912 + 0.288825i
$$73$$ −3.95691 + 6.85356i −0.463121 + 0.802149i −0.999115 0.0420732i $$-0.986604\pi$$
0.535994 + 0.844222i $$0.319937\pi$$
$$74$$ 1.00000 0.116248
$$75$$ 3.70321 7.14763i 0.427610 0.825337i
$$76$$ −2.69076 + 4.66053i −0.308651 + 0.534599i
$$77$$ 0 0
$$78$$ 4.35087 0.198422i 0.492639 0.0224668i
$$79$$ 4.62422 8.00938i 0.520265 0.901126i −0.479457 0.877565i $$-0.659166\pi$$
0.999722 0.0235607i $$-0.00750031\pi$$
$$80$$ 0.296790 0.514055i 0.0331821 0.0574731i
$$81$$ −3.01245 + 8.48087i −0.334717 + 0.942319i
$$82$$ −0.136673 0.236725i −0.0150930 0.0261419i
$$83$$ −3.85087 6.66991i −0.422688 0.732118i 0.573513 0.819196i $$-0.305580\pi$$
−0.996201 + 0.0870787i $$0.972247\pi$$
$$84$$ 0 0
$$85$$ 0.866926 1.50156i 0.0940313 0.162867i
$$86$$ −11.1623 −1.20366
$$87$$ 10.7178 0.488786i 1.14907 0.0524033i
$$88$$ 0.593579 0.0632758
$$89$$ 6.21780 + 10.7695i 0.659085 + 1.14157i 0.980853 + 0.194751i $$0.0623898\pi$$
−0.321767 + 0.946819i $$0.604277\pi$$
$$90$$ 1.77335 0.162084i 0.186927 0.0170852i
$$91$$ 0 0
$$92$$ −2.23025 3.86291i −0.232520 0.402736i
$$93$$ 13.6118 0.620765i 1.41147 0.0643704i
$$94$$ −6.08113 10.5328i −0.627220 1.08638i
$$95$$ 1.59718 + 2.76639i 0.163867 + 0.283826i
$$96$$ −1.73025 + 0.0789082i −0.176593 + 0.00805354i
$$97$$ −5.86693 10.1618i −0.595696 1.03178i −0.993448 0.114283i $$-0.963543\pi$$
0.397752 0.917493i $$-0.369790\pi$$
$$98$$ 0 0
$$99$$ 1.02704 + 1.45472i 0.103222 + 0.146205i
$$100$$ 2.32383 + 4.02499i 0.232383 + 0.402499i
$$101$$ 1.62276 0.161470 0.0807352 0.996736i $$-0.474273\pi$$
0.0807352 + 0.996736i $$0.474273\pi$$
$$102$$ −5.05408 + 0.230492i −0.500429 + 0.0228221i
$$103$$ −6.38151 −0.628789 −0.314395 0.949292i $$-0.601802\pi$$
−0.314395 + 0.949292i $$0.601802\pi$$
$$104$$ −1.25729 + 2.17770i −0.123288 + 0.213541i
$$105$$ 0 0
$$106$$ −4.02704 6.97504i −0.391141 0.677476i
$$107$$ 9.35447 + 16.2024i 0.904331 + 1.56635i 0.821813 + 0.569758i $$0.192963\pi$$
0.0825182 + 0.996590i $$0.473704\pi$$
$$108$$ −3.18716 4.10390i −0.306684 0.394898i
$$109$$ −1.43346 + 2.48283i −0.137301 + 0.237812i −0.926474 0.376359i $$-0.877176\pi$$
0.789173 + 0.614171i $$0.210509\pi$$
$$110$$ 0.176168 0.305132i 0.0167970 0.0290932i
$$111$$ −1.73025 + 0.0789082i −0.164228 + 0.00748964i
$$112$$ 0 0
$$113$$ −6.16012 + 10.6696i −0.579495 + 1.00371i 0.416042 + 0.909345i $$0.363417\pi$$
−0.995537 + 0.0943695i $$0.969916\pi$$
$$114$$ 4.28794 8.27621i 0.401602 0.775138i
$$115$$ −2.64766 −0.246896
$$116$$ −3.09718 + 5.36447i −0.287566 + 0.498078i
$$117$$ −7.51245 + 0.686640i −0.694527 + 0.0634799i
$$118$$ 8.64766 0.796082
$$119$$ 0 0
$$120$$ −0.472958 + 0.912864i −0.0431750 + 0.0833327i
$$121$$ −10.6477 −0.967969
$$122$$ 3.32383 + 5.75705i 0.300926 + 0.521218i
$$123$$ 0.255158 + 0.398809i 0.0230069 + 0.0359594i
$$124$$ −3.93346 + 6.81296i −0.353235 + 0.611822i
$$125$$ 5.72665 0.512207
$$126$$ 0 0
$$127$$ 12.3346 1.09452 0.547261 0.836962i $$-0.315671\pi$$
0.547261 + 0.836962i $$0.315671\pi$$
$$128$$ 0.500000 0.866025i 0.0441942 0.0765466i
$$129$$ 19.3135 0.880794i 1.70046 0.0775496i
$$130$$ 0.746304 + 1.29264i 0.0654552 + 0.113372i
$$131$$ 1.18716 0.103723 0.0518613 0.998654i $$-0.483485\pi$$
0.0518613 + 0.998654i $$0.483485\pi$$
$$132$$ −1.02704 + 0.0468383i −0.0893925 + 0.00407675i
$$133$$ 0 0
$$134$$ 1.91381 0.165328
$$135$$ −3.05555 + 0.420378i −0.262980 + 0.0361804i
$$136$$ 1.46050 2.52967i 0.125237 0.216917i
$$137$$ 2.52179 0.215451 0.107725 0.994181i $$-0.465643\pi$$
0.107725 + 0.994181i $$0.465643\pi$$
$$138$$ 4.16372 + 6.50783i 0.354439 + 0.553983i
$$139$$ −2.45691 + 4.25549i −0.208392 + 0.360946i −0.951208 0.308550i $$-0.900156\pi$$
0.742816 + 0.669496i $$0.233490\pi$$
$$140$$ 0 0
$$141$$ 11.3530 + 17.7446i 0.956096 + 1.49436i
$$142$$ −7.20535 + 12.4800i −0.604659 + 1.04730i
$$143$$ −0.746304 + 1.29264i −0.0624091 + 0.108096i
$$144$$ 2.98755 0.273062i 0.248962 0.0227552i
$$145$$ 1.83842 + 3.18424i 0.152673 + 0.264437i
$$146$$ 3.95691 + 6.85356i 0.327476 + 0.567205i
$$147$$ 0 0
$$148$$ 0.500000 0.866025i 0.0410997 0.0711868i
$$149$$ 18.0512 1.47881 0.739404 0.673262i $$-0.235107\pi$$
0.739404 + 0.673262i $$0.235107\pi$$
$$150$$ −4.33842 6.78089i −0.354231 0.553657i
$$151$$ 1.64766 0.134085 0.0670425 0.997750i $$-0.478644\pi$$
0.0670425 + 0.997750i $$0.478644\pi$$
$$152$$ 2.69076 + 4.66053i 0.218249 + 0.378019i
$$153$$ 8.72665 0.797618i 0.705508 0.0644836i
$$154$$ 0 0
$$155$$ 2.33482 + 4.04403i 0.187537 + 0.324824i
$$156$$ 2.00360 3.86718i 0.160416 0.309622i
$$157$$ −3.30039 5.71644i −0.263400 0.456222i 0.703743 0.710454i $$-0.251510\pi$$
−0.967143 + 0.254233i $$0.918177\pi$$
$$158$$ −4.62422 8.00938i −0.367883 0.637192i
$$159$$ 7.51819 + 11.7508i 0.596231 + 0.931900i
$$160$$ −0.296790 0.514055i −0.0234633 0.0406396i
$$161$$ 0 0
$$162$$ 5.83842 + 6.84929i 0.458710 + 0.538131i
$$163$$ −2.99115 5.18082i −0.234285 0.405793i 0.724780 0.688980i $$-0.241941\pi$$
−0.959065 + 0.283188i $$0.908608\pi$$
$$164$$ −0.273346 −0.0213448
$$165$$ −0.280738 + 0.541857i −0.0218554 + 0.0421835i
$$166$$ −7.70175 −0.597772
$$167$$ −3.73025 + 6.46099i −0.288656 + 0.499966i −0.973489 0.228733i $$-0.926542\pi$$
0.684833 + 0.728700i $$0.259875\pi$$
$$168$$ 0 0
$$169$$ 3.33842 + 5.78231i 0.256802 + 0.444793i
$$170$$ −0.866926 1.50156i −0.0664902 0.115164i
$$171$$ −6.76615 + 14.6583i −0.517420 + 1.12095i
$$172$$ −5.58113 + 9.66679i −0.425557 + 0.737086i
$$173$$ −12.8296 + 22.2215i −0.975414 + 1.68947i −0.296851 + 0.954924i $$0.595937\pi$$
−0.678562 + 0.734543i $$0.737397\pi$$
$$174$$ 4.93560 9.52628i 0.374167 0.722185i
$$175$$ 0 0
$$176$$ 0.296790 0.514055i 0.0223714 0.0387483i
$$177$$ −14.9626 + 0.682372i −1.12466 + 0.0512902i
$$178$$ 12.4356 0.932088
$$179$$ 7.51819 13.0219i 0.561936 0.973301i −0.435392 0.900241i $$-0.643390\pi$$
0.997328 0.0730602i $$-0.0232765\pi$$
$$180$$ 0.746304 1.61680i 0.0556262 0.120510i
$$181$$ 0.0861875 0.00640627 0.00320313 0.999995i $$-0.498980\pi$$
0.00320313 + 0.999995i $$0.498980\pi$$
$$182$$ 0 0
$$183$$ −6.20535 9.69886i −0.458712 0.716961i
$$184$$ −4.46050 −0.328833
$$185$$ −0.296790 0.514055i −0.0218204 0.0377941i
$$186$$ 6.26829 12.0985i 0.459613 0.887106i
$$187$$ 0.866926 1.50156i 0.0633959 0.109805i
$$188$$ −12.1623 −0.887023
$$189$$ 0 0
$$190$$ 3.19436 0.231743
$$191$$ −1.99115 + 3.44877i −0.144074 + 0.249544i −0.929027 0.370011i $$-0.879354\pi$$
0.784953 + 0.619555i $$0.212687\pi$$
$$192$$ −0.796790 + 1.53790i −0.0575033 + 0.110988i
$$193$$ −3.39037 5.87229i −0.244044 0.422697i 0.717818 0.696230i $$-0.245141\pi$$
−0.961862 + 0.273534i $$0.911808\pi$$
$$194$$ −11.7339 −0.842441
$$195$$ −1.39329 2.17770i −0.0997759 0.155948i
$$196$$ 0 0
$$197$$ 11.0584 0.787875 0.393938 0.919137i $$-0.371113\pi$$
0.393938 + 0.919137i $$0.371113\pi$$
$$198$$ 1.77335 0.162084i 0.126026 0.0115188i
$$199$$ −2.80924 + 4.86575i −0.199142 + 0.344924i −0.948250 0.317523i $$-0.897149\pi$$
0.749109 + 0.662447i $$0.230482\pi$$
$$200$$ 4.64766 0.328639
$$201$$ −3.31138 + 0.151016i −0.233567 + 0.0106518i
$$202$$ 0.811379 1.40535i 0.0570884 0.0988800i
$$203$$ 0 0
$$204$$ −2.32743 + 4.49221i −0.162953 + 0.314518i
$$205$$ −0.0811263 + 0.140515i −0.00566611 + 0.00981399i
$$206$$ −3.19076 + 5.52655i −0.222311 + 0.385053i
$$207$$ −7.71780 10.9316i −0.536424 0.759801i
$$208$$ 1.25729 + 2.17770i 0.0871777 + 0.150996i
$$209$$ 1.59718 + 2.76639i 0.110479 + 0.191355i
$$210$$ 0 0
$$211$$ 9.66225 16.7355i 0.665177 1.15212i −0.314060 0.949403i $$-0.601689\pi$$
0.979237 0.202717i $$-0.0649772\pi$$
$$212$$ −8.05408 −0.553157
$$213$$ 11.4823 22.1622i 0.786754 1.51853i
$$214$$ 18.7089 1.27892
$$215$$ 3.31284 + 5.73801i 0.225934 + 0.391329i
$$216$$ −5.14766 + 0.708209i −0.350254 + 0.0481875i
$$217$$ 0 0
$$218$$ 1.43346 + 2.48283i 0.0970863 + 0.168158i
$$219$$ −7.38725 11.5462i −0.499184 0.780217i
$$220$$ −0.176168 0.305132i −0.0118773 0.0205720i
$$221$$ 3.67257 + 6.36108i 0.247044 + 0.427892i
$$222$$ −0.796790 + 1.53790i −0.0534770 + 0.103217i
$$223$$ −12.6623 21.9317i −0.847927 1.46865i −0.883055 0.469270i $$-0.844517\pi$$
0.0351275 0.999383i $$-0.488816\pi$$
$$224$$ 0 0
$$225$$ 8.04163 + 11.3903i 0.536109 + 0.759354i
$$226$$ 6.16012 + 10.6696i 0.409765 + 0.709734i
$$227$$ −4.81711 −0.319723 −0.159862 0.987139i $$-0.551105\pi$$
−0.159862 + 0.987139i $$0.551105\pi$$
$$228$$ −5.02344 7.85157i −0.332686 0.519983i
$$229$$ 9.29533 0.614253 0.307126 0.951669i $$-0.400633\pi$$
0.307126 + 0.951669i $$0.400633\pi$$
$$230$$ −1.32383 + 2.29294i −0.0872909 + 0.151192i
$$231$$ 0 0
$$232$$ 3.09718 + 5.36447i 0.203340 + 0.352195i
$$233$$ 0.0971780 + 0.168317i 0.00636634 + 0.0110268i 0.869191 0.494476i $$-0.164640\pi$$
−0.862825 + 0.505503i $$0.831307\pi$$
$$234$$ −3.16158 + 6.84929i −0.206679 + 0.447752i
$$235$$ −3.60963 + 6.25206i −0.235466 + 0.407840i
$$236$$ 4.32383 7.48910i 0.281457 0.487499i
$$237$$ 8.63307 + 13.4934i 0.560778 + 0.876488i
$$238$$ 0 0
$$239$$ −6.82743 + 11.8255i −0.441630 + 0.764925i −0.997811 0.0661361i $$-0.978933\pi$$
0.556181 + 0.831061i $$0.312266\pi$$
$$240$$ 0.554084 + 0.866025i 0.0357660 + 0.0559017i
$$241$$ 13.0000 0.837404 0.418702 0.908124i $$-0.362485\pi$$
0.418702 + 0.908124i $$0.362485\pi$$
$$242$$ −5.32383 + 9.22115i −0.342229 + 0.592758i
$$243$$ −10.6424 11.3903i −0.682711 0.730689i
$$244$$ 6.64766 0.425573
$$245$$ 0 0
$$246$$ 0.472958 0.0215693i 0.0301547 0.00137521i
$$247$$ −13.5323 −0.861039
$$248$$ 3.93346 + 6.81296i 0.249775 + 0.432623i
$$249$$ 13.3260 0.607731i 0.844499 0.0385134i
$$250$$ 2.86333 4.95943i 0.181093 0.313662i
$$251$$ 19.5438 1.23359 0.616796 0.787123i $$-0.288430\pi$$
0.616796 + 0.787123i $$0.288430\pi$$
$$252$$ 0 0
$$253$$ −2.64766 −0.166457
$$254$$ 6.16731 10.6821i 0.386972 0.670255i
$$255$$ 1.61849 + 2.52967i 0.101353 + 0.158414i
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ −8.32743 −0.519451 −0.259725 0.965683i $$-0.583632\pi$$
−0.259725 + 0.965683i $$0.583632\pi$$
$$258$$ 8.89397 17.1664i 0.553714 1.06873i
$$259$$ 0 0
$$260$$ 1.49261 0.0925676
$$261$$ −7.78813 + 16.8723i −0.482073 + 1.04437i
$$262$$ 0.593579 1.02811i 0.0366715 0.0635168i
$$263$$ −17.0905 −1.05384 −0.526921 0.849914i $$-0.676654\pi$$
−0.526921 + 0.849914i $$0.676654\pi$$
$$264$$ −0.472958 + 0.912864i −0.0291085 + 0.0561829i
$$265$$ −2.39037 + 4.14024i −0.146839 + 0.254333i
$$266$$ 0 0
$$267$$ −21.5167 + 0.981271i −1.31680 + 0.0600528i
$$268$$ 0.956906 1.65741i 0.0584524 0.101242i
$$269$$ 5.00720 8.67272i 0.305294 0.528785i −0.672033 0.740522i $$-0.734579\pi$$
0.977327 + 0.211737i $$0.0679119\pi$$
$$270$$ −1.16372 + 2.85637i −0.0708215 + 0.173833i
$$271$$ −5.10457 8.84137i −0.310081 0.537075i 0.668299 0.743893i $$-0.267023\pi$$
−0.978380 + 0.206818i $$0.933689\pi$$
$$272$$ −1.46050 2.52967i −0.0885561 0.153384i
$$273$$ 0 0
$$274$$ 1.26089 2.18393i 0.0761733 0.131936i
$$275$$ 2.75876 0.166359
$$276$$ 7.71780 0.351971i 0.464557 0.0211861i
$$277$$ 19.3422 1.16216 0.581081 0.813846i $$-0.302630\pi$$
0.581081 + 0.813846i $$0.302630\pi$$
$$278$$ 2.45691 + 4.25549i 0.147355 + 0.255227i
$$279$$ −9.89104 + 21.4281i −0.592161 + 1.28287i
$$280$$ 0 0
$$281$$ −6.40136 11.0875i −0.381873 0.661424i 0.609457 0.792819i $$-0.291388\pi$$
−0.991330 + 0.131396i $$0.958054\pi$$
$$282$$ 21.0438 0.959702i 1.25314 0.0571494i
$$283$$ −8.17617 14.1615i −0.486023 0.841816i 0.513848 0.857881i $$-0.328219\pi$$
−0.999871 + 0.0160650i $$0.994886\pi$$
$$284$$ 7.20535 + 12.4800i 0.427559 + 0.740553i
$$285$$ −5.52704 + 0.252061i −0.327394 + 0.0149308i
$$286$$ 0.746304 + 1.29264i 0.0441299 + 0.0764352i
$$287$$ 0 0
$$288$$ 1.25729 2.72382i 0.0740868 0.160503i
$$289$$ 4.23385 + 7.33325i 0.249050 + 0.431367i
$$290$$ 3.67684 0.215912
$$291$$ 20.3025 0.925898i 1.19016 0.0542771i
$$292$$ 7.91381 0.463121
$$293$$ 10.3889 17.9941i 0.606926 1.05123i −0.384817 0.922993i $$-0.625736\pi$$
0.991744 0.128235i $$-0.0409311\pi$$
$$294$$ 0 0
$$295$$ −2.56654 4.44537i −0.149430 0.258820i
$$296$$ −0.500000 0.866025i −0.0290619 0.0503367i
$$297$$ −3.05555 + 0.420378i −0.177301 + 0.0243928i
$$298$$ 9.02558 15.6328i 0.522838 0.905582i
$$299$$ 5.60817 9.71363i 0.324329 0.561754i
$$300$$ −8.04163 + 0.366739i −0.464284 + 0.0211737i
$$301$$ 0 0
$$302$$ 0.823832 1.42692i 0.0474062 0.0821099i
$$303$$ −1.29300 + 2.49563i −0.0742807 + 0.143370i
$$304$$ 5.38151 0.308651
$$305$$ 1.97296 3.41726i 0.112971 0.195672i
$$306$$ 3.67257 7.95631i 0.209947 0.454832i
$$307$$ 22.6768 1.29424 0.647118 0.762390i $$-0.275974\pi$$
0.647118 + 0.762390i $$0.275974\pi$$
$$308$$ 0 0
$$309$$ 5.08472 9.81411i 0.289260 0.558305i
$$310$$ 4.66964 0.265218
$$311$$ −3.25729 5.64180i −0.184704 0.319917i 0.758773 0.651356i $$-0.225799\pi$$
−0.943477 + 0.331439i $$0.892466\pi$$
$$312$$ −2.34728 3.66876i −0.132888 0.207702i
$$313$$ 0.133074 0.230492i 0.00752181 0.0130282i −0.862240 0.506500i $$-0.830939\pi$$
0.869762 + 0.493472i $$0.164272\pi$$
$$314$$ −6.60078 −0.372503
$$315$$ 0 0
$$316$$ −9.24844 −0.520265
$$317$$ −7.86186 + 13.6171i −0.441566 + 0.764815i −0.997806 0.0662067i $$-0.978910\pi$$
0.556240 + 0.831022i $$0.312244\pi$$
$$318$$ 13.9356 0.635534i 0.781470 0.0356390i
$$319$$ 1.83842 + 3.18424i 0.102932 + 0.178283i
$$320$$ −0.593579 −0.0331821
$$321$$ −32.3712 + 1.47629i −1.80678 + 0.0823985i
$$322$$ 0 0
$$323$$ 15.7195 0.874654
$$324$$ 8.85087 1.63157i 0.491715 0.0906430i
$$325$$ −5.84348 + 10.1212i −0.324138 + 0.561424i
$$326$$ −5.98229 −0.331328
$$327$$ −2.67617 4.18281i −0.147992 0.231310i
$$328$$ −0.136673 + 0.236725i −0.00754651 + 0.0130709i
$$329$$ 0 0
$$330$$ 0.328893 + 0.514055i 0.0181050 + 0.0282978i
$$331$$ 12.5811 21.7912i 0.691521 1.19775i −0.279818 0.960053i $$-0.590274\pi$$
0.971339 0.237697i $$-0.0763925\pi$$
$$332$$ −3.85087 + 6.66991i −0.211344 + 0.366059i
$$333$$ 1.25729 2.72382i 0.0688993 0.149265i
$$334$$ 3.73025 + 6.46099i 0.204110 + 0.353529i
$$335$$ −0.568000 0.983804i −0.0310331 0.0537510i
$$336$$ 0 0
$$337$$ −9.36693 + 16.2240i −0.510249 + 0.883777i 0.489681 + 0.871902i $$0.337113\pi$$
−0.999929 + 0.0118752i $$0.996220\pi$$
$$338$$ 6.67684 0.363172
$$339$$ −11.5005 17.9751i −0.624620 0.976272i
$$340$$ −1.73385 −0.0940313
$$341$$ 2.33482 + 4.04403i 0.126438 + 0.218997i
$$342$$ 9.31138 + 13.1888i 0.503502 + 0.713169i
$$343$$ 0 0
$$344$$ 5.58113 + 9.66679i 0.300914 + 0.521199i
$$345$$ 2.10963 4.07183i 0.113579 0.219220i
$$346$$ 12.8296 + 22.2215i 0.689722 + 1.19463i
$$347$$ −11.2719 19.5235i −0.605106 1.04808i −0.992035 0.125965i $$-0.959797\pi$$
0.386928 0.922110i $$-0.373536\pi$$
$$348$$ −5.78220 9.03749i −0.309958 0.484461i
$$349$$ −1.89543 3.28298i −0.101460 0.175734i 0.810826 0.585287i $$-0.199018\pi$$
−0.912286 + 0.409553i $$0.865685\pi$$
$$350$$ 0 0
$$351$$ 4.92986 12.1005i 0.263137 0.645876i
$$352$$ −0.296790 0.514055i −0.0158189 0.0273992i
$$353$$ −6.83482 −0.363781 −0.181890 0.983319i $$-0.558222\pi$$
−0.181890 + 0.983319i $$0.558222\pi$$
$$354$$ −6.89037 + 13.2992i −0.366219 + 0.706845i
$$355$$ 8.55389 0.453993
$$356$$ 6.21780 10.7695i 0.329543 0.570785i
$$357$$ 0 0
$$358$$ −7.51819 13.0219i −0.397349 0.688228i
$$359$$ −6.32237 10.9507i −0.333682 0.577954i 0.649549 0.760320i $$-0.274958\pi$$
−0.983231 + 0.182366i $$0.941624\pi$$
$$360$$ −1.02704 1.45472i −0.0541299 0.0766705i
$$361$$ −4.98035 + 8.62622i −0.262124 + 0.454012i
$$362$$ 0.0430937 0.0746406i 0.00226496 0.00392302i
$$363$$ 8.48395 16.3750i 0.445292 0.859465i
$$364$$ 0 0
$$365$$ 2.34874 4.06813i 0.122939 0.212936i
$$366$$ −11.5021 + 0.524555i −0.601226 + 0.0274190i
$$367$$ −6.54377 −0.341582 −0.170791 0.985307i $$-0.554632\pi$$
−0.170791 + 0.985307i $$0.554632\pi$$
$$368$$ −2.23025 + 3.86291i −0.116260 + 0.201368i
$$369$$ −0.816635 + 0.0746406i −0.0425123 + 0.00388563i
$$370$$ −0.593579 −0.0308587
$$371$$ 0 0
$$372$$ −7.34348 11.4778i −0.380742 0.595094i
$$373$$ 9.42840 0.488184 0.244092 0.969752i $$-0.421510\pi$$
0.244092 + 0.969752i $$0.421510\pi$$
$$374$$ −0.866926 1.50156i −0.0448277 0.0776438i
$$375$$ −4.56294 + 8.80700i −0.235629 + 0.454792i
$$376$$ −6.08113 + 10.5328i −0.313610 + 0.543189i
$$377$$ −15.5763 −0.802218
$$378$$ 0 0
$$379$$ −7.27762 −0.373826 −0.186913 0.982376i $$-0.559848\pi$$
−0.186913 + 0.982376i $$0.559848\pi$$
$$380$$ 1.59718 2.76639i 0.0819335 0.141913i
$$381$$ −9.82810 + 18.9694i −0.503509 + 0.971831i
$$382$$ 1.99115 + 3.44877i 0.101876 + 0.176454i
$$383$$ 24.0833 1.23060 0.615299 0.788294i $$-0.289035\pi$$
0.615299 + 0.788294i $$0.289035\pi$$
$$384$$ 0.933463 + 1.45899i 0.0476356 + 0.0744537i
$$385$$ 0 0
$$386$$ −6.78074 −0.345130
$$387$$ −14.0342 + 30.4040i −0.713400 + 1.54552i
$$388$$ −5.86693 + 10.1618i −0.297848 + 0.515888i
$$389$$ −16.2983 −0.826354 −0.413177 0.910651i $$-0.635581\pi$$
−0.413177 + 0.910651i $$0.635581\pi$$
$$390$$ −2.58259 + 0.117779i −0.130774 + 0.00596398i
$$391$$ −6.51459 + 11.2836i −0.329457 + 0.570636i
$$392$$ 0 0
$$393$$ −0.945916 + 1.82573i −0.0477151 + 0.0920958i
$$394$$ 5.52918 9.57682i 0.278556 0.482473i
$$395$$ −2.74484 + 4.75420i −0.138108 + 0.239210i
$$396$$ 0.746304 1.61680i 0.0375032 0.0812475i
$$397$$ 6.08619 + 10.5416i 0.305457 + 0.529067i 0.977363 0.211569i $$-0.0678574\pi$$
−0.671906 + 0.740636i $$0.734524\pi$$
$$398$$ 2.80924 + 4.86575i 0.140815 + 0.243898i
$$399$$ 0 0
$$400$$ 2.32383 4.02499i 0.116192 0.201250i
$$401$$ −33.3609 −1.66596 −0.832981 0.553301i $$-0.813368\pi$$
−0.832981 + 0.553301i $$0.813368\pi$$
$$402$$ −1.52491 + 2.94325i −0.0760554 + 0.146796i
$$403$$ −19.7821 −0.985416
$$404$$ −0.811379 1.40535i −0.0403676 0.0699187i
$$405$$ 1.78813 5.03407i 0.0888529 0.250145i
$$406$$ 0 0
$$407$$ −0.296790 0.514055i −0.0147113 0.0254808i
$$408$$ 2.72665 + 4.26172i 0.134989 + 0.210987i
$$409$$ −2.89037 5.00627i −0.142920 0.247544i 0.785675 0.618639i $$-0.212316\pi$$
−0.928595 + 0.371095i $$0.878982\pi$$
$$410$$ 0.0811263 + 0.140515i 0.00400654 + 0.00693954i
$$411$$ −2.00933 + 3.87825i −0.0991131 + 0.191300i
$$412$$ 3.19076 + 5.52655i 0.157197 + 0.272274i
$$413$$ 0 0
$$414$$ −13.3260 + 1.21800i −0.654936 + 0.0598612i
$$415$$ 2.28580 + 3.95912i 0.112205 + 0.194346i
$$416$$ 2.51459 0.123288
$$417$$ −4.58686 7.16920i −0.224620 0.351077i
$$418$$ 3.19436 0.156241
$$419$$ −15.4356 + 26.7352i −0.754078 + 1.30610i 0.191753 + 0.981443i $$0.438583\pi$$
−0.945831 + 0.324659i $$0.894751\pi$$
$$420$$ 0 0
$$421$$ −1.86693 3.23361i −0.0909884 0.157597i 0.816939 0.576724i $$-0.195669\pi$$
−0.907927 + 0.419128i $$0.862336\pi$$
$$422$$ −9.66225 16.7355i −0.470351 0.814672i
$$423$$ −36.3353 + 3.32105i −1.76668 + 0.161475i
$$424$$ −4.02704 + 6.97504i −0.195570 + 0.338738i
$$425$$ 6.78794 11.7570i 0.329263 0.570301i
$$426$$ −13.4518 21.0250i −0.651744 1.01867i
$$427$$ 0 0
$$428$$ 9.35447 16.2024i 0.452165 0.783174i
$$429$$ −1.39329 2.17770i −0.0672689 0.105140i
$$430$$ 6.62568 0.319519
$$431$$ −14.0979 + 24.4182i −0.679070 + 1.17618i 0.296192 + 0.955128i $$0.404283\pi$$
−0.975261 + 0.221055i $$0.929050\pi$$
$$432$$ −1.96050 + 4.81211i −0.0943248 + 0.231523i
$$433$$ −12.5438 −0.602815 −0.301407 0.953495i $$-0.597456\pi$$
−0.301407 + 0.953495i $$0.597456\pi$$
$$434$$ 0 0
$$435$$ −6.36186 + 0.290133i −0.305028 + 0.0139108i
$$436$$ 2.86693 0.137301
$$437$$ −12.0021 20.7883i −0.574140 0.994440i
$$438$$ −13.6929 + 0.624465i −0.654272 + 0.0298381i
$$439$$ 13.0203 22.5519i 0.621426 1.07634i −0.367794 0.929907i $$-0.619887\pi$$
0.989220 0.146434i $$-0.0467797\pi$$
$$440$$ −0.352336 −0.0167970
$$441$$ 0 0
$$442$$ 7.34514 0.349373
$$443$$ 11.7865 20.4148i 0.559992 0.969935i −0.437504 0.899216i $$-0.644137\pi$$
0.997496 0.0707186i $$-0.0225292\pi$$
$$444$$ 0.933463 + 1.45899i 0.0443002 + 0.0692405i
$$445$$ −3.69076 6.39258i −0.174959 0.303037i
$$446$$ −25.3245 −1.19915
$$447$$ −14.3830 + 27.7608i −0.680291 + 1.31304i
$$448$$ 0 0
$$449$$ 13.6870 0.645928 0.322964 0.946411i $$-0.395321\pi$$
0.322964 + 0.946411i $$0.395321\pi$$
$$450$$ 13.8851 1.26910i 0.654551 0.0598260i
$$451$$ −0.0811263 + 0.140515i −0.00382009 + 0.00661659i
$$452$$ 12.3202 0.579495
$$453$$ −1.31284 + 2.53394i −0.0616827 + 0.119055i
$$454$$ −2.40856 + 4.17174i −0.113039 + 0.195790i
$$455$$ 0 0
$$456$$ −9.31138 + 0.424646i −0.436045 + 0.0198859i
$$457$$ 11.1762 19.3577i 0.522799 0.905515i −0.476849 0.878985i $$-0.658221\pi$$
0.999648 0.0265293i $$-0.00844554\pi$$
$$458$$ 4.64766 8.04999i 0.217171 0.376151i
$$459$$ −5.72665 + 14.0562i −0.267297 + 0.656088i
$$460$$ 1.32383 + 2.29294i 0.0617240 + 0.106909i
$$461$$ 3.98755 + 6.90663i 0.185719 + 0.321674i 0.943818 0.330464i $$-0.107205\pi$$
−0.758100 + 0.652138i $$0.773872\pi$$
$$462$$ 0 0
$$463$$ −14.3676 + 24.8854i −0.667719 + 1.15652i 0.310821 + 0.950468i $$0.399396\pi$$
−0.978540 + 0.206055i $$0.933937\pi$$
$$464$$ 6.19436 0.287566
$$465$$ −8.07966 + 0.368473i −0.374685 + 0.0170875i
$$466$$ 0.194356 0.00900336
$$467$$ −16.7829 29.0688i −0.776619 1.34514i −0.933880 0.357586i $$-0.883600\pi$$
0.157261 0.987557i $$-0.449733\pi$$
$$468$$ 4.35087 + 6.16266i 0.201119 + 0.284869i
$$469$$ 0 0
$$470$$ 3.60963 + 6.25206i 0.166500 + 0.288386i
$$471$$ 11.4210 0.520856i 0.526252 0.0239998i
$$472$$ −4.32383 7.48910i −0.199020 0.344714i
$$473$$ 3.31284 + 5.73801i 0.152325 + 0.263834i
$$474$$ 16.0021 0.729778i 0.735002 0.0335198i
$$475$$ 12.5057 + 21.6606i 0.573802 + 0.993855i
$$476$$ 0 0
$$477$$ −24.0620 + 2.19927i −1.10172 + 0.100698i
$$478$$ 6.82743 + 11.8255i 0.312279 + 0.540884i
$$479$$ −0.367120 −0.0167741 −0.00838707 0.999965i $$-0.502670\pi$$
−0.00838707 + 0.999965i $$0.502670\pi$$
$$480$$ 1.02704 0.0468383i 0.0468778 0.00213787i
$$481$$ 2.51459 0.114655
$$482$$ 6.50000 11.2583i 0.296067 0.512803i
$$483$$ 0 0
$$484$$ 5.32383 + 9.22115i 0.241992 + 0.419143i
$$485$$ 3.48249 + 6.03184i 0.158132 + 0.273892i
$$486$$ −15.1855 + 3.52144i −0.688828 + 0.159736i
$$487$$ −14.9538 + 25.9007i −0.677621 + 1.17367i 0.298075 + 0.954543i $$0.403656\pi$$
−0.975695 + 0.219131i $$0.929678\pi$$
$$488$$ 3.32383 5.75705i 0.150463 0.260609i
$$489$$ 10.3509 0.472052i 0.468083 0.0213469i
$$490$$ 0 0
$$491$$ −0.255158 + 0.441947i −0.0115151 + 0.0199448i −0.871726 0.489994i $$-0.836999\pi$$
0.860210 + 0.509939i $$0.170332\pi$$
$$492$$ 0.217799 0.420378i 0.00981916 0.0189521i
$$493$$ 18.0938 0.814903
$$494$$ −6.76615 + 11.7193i −0.304423 + 0.527277i
$$495$$ −0.609631 0.863492i −0.0274009 0.0388111i
$$496$$ 7.86693 0.353235
$$497$$ 0 0
$$498$$ 6.13667 11.8445i 0.274991 0.530764i
$$499$$ −19.0191 −0.851410 −0.425705 0.904862i $$-0.639974\pi$$
−0.425705 + 0.904862i $$0.639974\pi$$
$$500$$ −2.86333 4.95943i −0.128052 0.221792i
$$501$$ −6.96410 10.8848i −0.311133 0.486297i
$$502$$ 9.77188 16.9254i 0.436141 0.755418i
$$503$$ 37.7807 1.68456 0.842280 0.539040i $$-0.181213\pi$$
0.842280 + 0.539040i $$0.181213\pi$$
$$504$$ 0 0
$$505$$ −0.963235 −0.0428634
$$506$$ −1.32383 + 2.29294i −0.0588515 + 0.101934i
$$507$$ −11.5526 + 0.526858i −0.513070 + 0.0233986i
$$508$$ −6.16731 10.6821i −0.273630 0.473942i
$$509$$ 11.2163 0.497155 0.248578 0.968612i $$-0.420037\pi$$
0.248578 + 0.968612i $$0.420037\pi$$
$$510$$ 3.00000 0.136815i 0.132842 0.00605828i
$$511$$ 0 0
$$512$$ −1.00000 −0.0441942
$$513$$ −17.1517 22.0852i −0.757268 0.975086i
$$514$$ −4.16372 + 7.21177i −0.183654 + 0.318097i
$$515$$ 3.78794 0.166916
$$516$$ −10.4195 16.2856i −0.458695 0.716933i
$$517$$ −3.60963 + 6.25206i −0.158751 + 0.274965i
$$518$$ 0 0
$$519$$ −23.9518 37.4364i −1.05137 1.64327i
$$520$$ 0.746304 1.29264i 0.0327276 0.0566859i
$$521$$ 13.7360 23.7914i 0.601785 1.04232i −0.390766 0.920490i $$-0.627790\pi$$
0.992551 0.121831i $$-0.0388767\pi$$
$$522$$ 10.7178 + 15.1809i 0.469105 + 0.664449i
$$523$$ −11.0919 19.2118i −0.485016 0.840072i 0.514836 0.857289i $$-0.327853\pi$$
−0.999852 + 0.0172166i $$0.994520\pi$$
$$524$$ −0.593579 1.02811i −0.0259306 0.0449132i
$$525$$ 0 0
$$526$$ −8.54523 + 14.8008i −0.372590 + 0.645344i
$$527$$ 22.9794 1.00100
$$528$$ 0.554084 + 0.866025i 0.0241134 + 0.0376889i
$$529$$ −3.10390 −0.134952
$$530$$ 2.39037 + 4.14024i 0.103831 + 0.179841i
$$531$$ 10.8727 23.5547i 0.471833 1.02219i
$$532$$ 0 0
$$533$$ −0.343677 0.595265i −0.0148863 0.0257838i
$$534$$ −9.90856 + 19.1247i −0.428785 + 0.827605i
$$535$$ −5.55262 9.61742i −0.240061 0.415797i
$$536$$ −0.956906 1.65741i −0.0413321 0.0715892i
$$537$$ 14.0359 + 21.9379i 0.605694 + 0.946690i
$$538$$ −5.00720 8.67272i −0.215876 0.373908i
$$539$$ 0 0
$$540$$ 1.89183 + 2.43599i 0.0814115 + 0.104828i
$$541$$ 14.9246 + 25.8502i 0.641659 + 1.11139i 0.985062 + 0.172198i $$0.0550869\pi$$
−0.343403 + 0.939188i $$0.611580\pi$$
$$542$$ −10.2091 −0.438520
$$543$$ −0.0686733 + 0.132547i −0.00294705 + 0.00568816i
$$544$$ −2.92101 −0.125237
$$545$$ 0.850874 1.47376i 0.0364474 0.0631288i
$$546$$ 0 0
$$547$$ 8.84348 + 15.3174i 0.378120 + 0.654923i 0.990789 0.135417i $$-0.0432373\pi$$
−0.612669 + 0.790340i $$0.709904\pi$$
$$548$$ −1.26089 2.18393i −0.0538627 0.0932929i
$$549$$ 19.8602 1.81523i 0.847613 0.0774720i
$$550$$ 1.37938 2.38915i 0.0588169 0.101874i
$$551$$ −16.6675 + 28.8690i −0.710060 + 1.22986i
$$552$$ 3.55408 6.85980i 0.151272 0.291972i
$$553$$ 0 0
$$554$$ 9.67111 16.7508i 0.410886 0.711675i
$$555$$ 1.02704 0.0468383i 0.0435955 0.00198818i
$$556$$ 4.91381 0.208392
$$557$$ 15.0651 26.0935i 0.638328 1.10562i −0.347472 0.937690i $$-0.612960\pi$$
0.985800 0.167926i $$-0.0537069\pi$$
$$558$$ 13.6118 + 19.2799i 0.576232 + 0.816185i
$$559$$ −28.0685 −1.18717
$$560$$ 0 0
$$561$$ 1.61849 + 2.52967i 0.0683325 + 0.106803i
$$562$$ −12.8027 −0.540050
$$563$$ 2.04883 + 3.54867i 0.0863478 + 0.149559i 0.905965 0.423353i $$-0.139147\pi$$
−0.819617 + 0.572912i $$0.805814\pi$$
$$564$$ 9.69076 18.7043i 0.408054 0.787593i
$$565$$ 3.65652 6.33327i 0.153831 0.266443i
$$566$$ −16.3523 −0.687340
$$567$$ 0 0
$$568$$ 14.4107 0.604659
$$569$$ −3.11849 + 5.40138i −0.130734 + 0.226437i −0.923960 0.382490i $$-0.875067\pi$$
0.793226 + 0.608927i $$0.208400\pi$$
$$570$$ −2.54523 + 4.91259i −0.106608 + 0.205766i
$$571$$ −17.8011 30.8323i −0.744951 1.29029i −0.950218 0.311587i $$-0.899139\pi$$
0.205266 0.978706i $$-0.434194\pi$$
$$572$$ 1.49261 0.0624091
$$573$$ −3.71732 5.81012i −0.155293 0.242721i
$$574$$ 0 0
$$575$$ −20.7309 −0.864539
$$576$$ −1.73025 2.45076i −0.0720939 0.102115i
$$577$$ −23.1388 + 40.0776i −0.963281 + 1.66845i −0.249118 + 0.968473i $$0.580141\pi$$
−0.714164 + 0.699979i $$0.753193\pi$$
$$578$$ 8.46770 0.352210
$$579$$ 11.7324 0.535056i 0.487581 0.0222362i
$$580$$ 1.83842 3.18424i 0.0763363 0.132218i
$$581$$ 0 0
$$582$$ 9.34941 18.0455i 0.387546 0.748008i
$$583$$ −2.39037 + 4.14024i −0.0989990 + 0.171471i
$$584$$ 3.95691 6.85356i 0.163738 0.283602i
$$585$$ 4.45924 0.407575i 0.184367 0.0168512i
$$586$$ −10.3889 17.9941i −0.429162 0.743330i
$$587$$ −1.13161 1.96001i −0.0467066 0.0808982i 0.841727 0.539903i $$-0.181539\pi$$
−0.888434 + 0.459005i $$0.848206\pi$$
$$588$$ 0 0
$$589$$ −21.1680 + 36.6640i −0.872212 + 1.51072i
$$590$$ −5.13307 −0.211325
$$591$$ −8.81118 + 17.0066i −0.362444 + 0.699558i
$$592$$ −1.00000 −0.0410997
$$593$$ −23.0979 40.0067i −0.948515 1.64288i −0.748555 0.663072i $$-0.769252\pi$$
−0.199960 0.979804i $$-0.564081\pi$$
$$594$$ −1.16372 + 2.85637i −0.0477478 + 0.117198i
$$595$$ 0 0
$$596$$ −9.02558 15.6328i −0.369702 0.640343i
$$597$$ −5.24465 8.19731i −0.214649 0.335493i
$$598$$ −5.60817 9.71363i −0.229335 0.397220i
$$599$$ 8.39037 + 14.5325i 0.342821 + 0.593784i 0.984955 0.172808i $$-0.0552842\pi$$
−0.642134 + 0.766592i $$0.721951\pi$$
$$600$$ −3.70321 + 7.14763i −0.151183 + 0.291801i
$$601$$ 5.69961 + 9.87202i 0.232492 + 0.402688i 0.958541 0.284955i $$-0.0919787\pi$$
−0.726049 + 0.687643i $$0.758645\pi$$
$$602$$ 0 0
$$603$$ 2.40623 5.21289i 0.0979891 0.212285i
$$604$$ −0.823832 1.42692i −0.0335212 0.0580605i
$$605$$ 6.32023 0.256954
$$606$$ 1.51478 + 2.36758i 0.0615339 + 0.0961765i
$$607$$ 14.4284 0.585631 0.292815 0.956169i $$-0.405408\pi$$
0.292815 + 0.956169i $$0.405408\pi$$
$$608$$ 2.69076 4.66053i 0.109125 0.189009i
$$609$$ 0 0
$$610$$ −1.97296 3.41726i −0.0798827 0.138361i
$$611$$ −15.2915 26.4857i −0.618629 1.07150i
$$612$$ −5.05408 7.15869i −0.204299 0.289373i
$$613$$ 12.2053 21.1403i 0.492969 0.853848i −0.506998 0.861947i $$-0.669245\pi$$
0.999967 + 0.00809942i $$0.00257815\pi$$
$$614$$ 11.3384 19.6387i 0.457581 0.792554i
$$615$$ −0.151457 0.236725i −0.00610733 0.00954566i
$$616$$ 0 0
$$617$$ 24.4698 42.3830i 0.985119 1.70628i 0.343710 0.939076i $$-0.388316\pi$$
0.641408 0.767200i $$-0.278350\pi$$
$$618$$ −5.95691 9.31056i −0.239622 0.374525i
$$619$$ 44.6591 1.79500 0.897501 0.441012i $$-0.145380\pi$$
0.897501 + 0.441012i $$0.145380\pi$$
$$620$$ 2.33482 4.04403i 0.0937687 0.162412i
$$621$$ 22.9612 3.15897i 0.921400 0.126765i
$$622$$ −6.51459 −0.261211
$$623$$ 0 0
$$624$$ −4.35087 + 0.198422i −0.174174 + 0.00794323i
$$625$$ 19.8391 0.793564
$$626$$ −0.133074 0.230492i −0.00531873 0.00921230i
$$627$$ −5.52704 + 0.252061i −0.220729 + 0.0100663i
$$628$$ −3.30039 + 5.71644i −0.131700 + 0.228111i
$$629$$ −2.92101 −0.116468
$$630$$ 0 0
$$631$$ 33.2852 1.32506 0.662532 0.749034i $$-0.269482\pi$$
0.662532 + 0.749034i $$0.269482\pi$$
$$632$$ −4.62422 + 8.00938i −0.183942 + 0.318596i
$$633$$ 18.0387 + 28.1942i 0.716974 + 1.12062i
$$634$$ 7.86186 + 13.6171i 0.312235 + 0.540806i
$$635$$ −7.32158 −0.290548
$$636$$ 6.41741 12.3863i 0.254467 0.491151i
$$637$$ 0 0
$$638$$ 3.67684 0.145568
$$639$$ 24.9341 + 35.3172i 0.986379 + 1.39713i
$$640$$ −0.296790 + 0.514055i −0.0117316 + 0.0203198i
$$641$$ 30.7879 1.21605 0.608025 0.793918i $$-0.291962\pi$$
0.608025 + 0.793918i $$0.291962\pi$$
$$642$$ −14.9071 + 28.7724i −0.588336 + 1.13556i
$$643$$ 13.7345 23.7889i 0.541637 0.938142i −0.457174 0.889378i $$-0.651138\pi$$
0.998810 0.0487649i $$-0.0155285\pi$$
$$644$$ 0 0
$$645$$ −11.4641 + 0.522821i −0.451399 + 0.0205861i
$$646$$ 7.85973 13.6134i 0.309237 0.535614i
$$647$$ 6.63521 11.4925i 0.260857 0.451818i −0.705613 0.708598i $$-0.749328\pi$$
0.966470 + 0.256780i $$0.0826615\pi$$
$$648$$ 3.01245 8.48087i 0.118340 0.333160i
$$649$$ −2.56654 4.44537i −0.100745 0.174496i
$$650$$ 5.84348 + 10.1212i 0.229200 + 0.396986i
$$651$$ 0 0
$$652$$ −2.99115 + 5.18082i −0.117142 + 0.202896i
$$653$$ −17.1416 −0.670803 −0.335402 0.942075i $$-0.608872\pi$$
−0.335402 + 0.942075i $$0.608872\pi$$
$$654$$ −4.96050 + 0.226224i −0.193971 + 0.00884606i
$$655$$ −0.704673 −0.0275338
$$656$$ 0.136673 + 0.236725i 0.00533619 + 0.00924255i
$$657$$ 23.6429 2.16096i 0.922397 0.0843072i
$$658$$ 0 0
$$659$$ 4.26089 + 7.38008i 0.165981 + 0.287487i 0.937003 0.349321i $$-0.113588\pi$$
−0.771022 + 0.636808i $$0.780254\pi$$
$$660$$ 0.609631 0.0278023i 0.0237299 0.00108220i
$$661$$ 17.1680 + 29.7358i 0.667757 + 1.15659i 0.978530 + 0.206105i $$0.0660789\pi$$
−0.310773 + 0.950484i $$0.600588\pi$$
$$662$$ −12.5811 21.7912i −0.488979 0.846937i
$$663$$ −12.7089 + 0.579592i −0.493575 + 0.0225095i
$$664$$ 3.85087 + 6.66991i 0.149443 + 0.258843i
$$665$$ 0 0
$$666$$ −1.73025 2.45076i −0.0670459 0.0949650i
$$667$$ −13.8150 23.9282i −0.534918 0.926505i
$$668$$ 7.46050 0.288656
$$669$$ 43.8178 1.99831i 1.69409 0.0772592i
$$670$$ −1.13600 −0.0438875
$$671$$ 1.97296 3.41726i 0.0761652 0.131922i
$$672$$ 0 0
$$673$$ −7.70155 13.3395i −0.296873 0.514199i 0.678546 0.734558i $$-0.262610\pi$$
−0.975419 + 0.220359i $$0.929277\pi$$
$$674$$ 9.36693 + 16.2240i 0.360800 + 0.624925i
$$675$$ −23.9246 + 3.29152i −0.920859 + 0.126691i
$$676$$ 3.33842 5.78231i 0.128401 0.222397i
$$677$$ −3.69076 + 6.39258i −0.141847 + 0.245687i −0.928192 0.372101i $$-0.878638\pi$$
0.786345 + 0.617788i $$0.211971\pi$$
$$678$$ −21.3171 + 0.972168i −0.818679 + 0.0373359i
$$679$$ 0 0
$$680$$ −0.866926 + 1.50156i −0.0332451 + 0.0575822i
$$681$$ 3.83823 7.40822i 0.147081 0.283884i
$$682$$ 4.66964 0.178810
$$683$$ 4.79893 8.31198i 0.183626 0.318049i −0.759487 0.650523i $$-0.774550\pi$$
0.943113 + 0.332474i $$0.107883\pi$$
$$684$$ 16.0775 1.46949i 0.614740 0.0561873i
$$685$$ −1.49688 −0.0571929
$$686$$ 0 0
$$687$$ −7.40642 + 14.2953i −0.282573 + 0.545398i
$$688$$ 11.1623 0.425557
$$689$$ −10.1264 17.5394i −0.385783 0.668197i
$$690$$ −2.47150 3.86291i −0.0940882 0.147058i
$$691$$ −7.07227 + 12.2495i −0.269042 + 0.465994i −0.968615 0.248567i $$-0.920040\pi$$
0.699573 + 0.714561i $$0.253374\pi$$
$$692$$ 25.6591 0.975414
$$693$$ 0 0
$$694$$ −22.5438 −0.855750
$$695$$ 1.45837 2.52597i 0.0553191 0.0958155i
$$696$$ −10.7178 + 0.488786i −0.406257 + 0.0185274i
$$697$$ 0.399223 + 0.691475i 0.0151217 + 0.0261915i
$$698$$ −3.79086 −0.143486
$$699$$ −0.336285 + 0.0153363i −0.0127195 + 0.000580072i
$$700$$ 0 0
$$701$$ 37.3753 1.41164 0.705822 0.708389i $$-0.250578\pi$$
0.705822 + 0.708389i $$0.250578\pi$$
$$702$$ −8.01439 10.3196i −0.302484 0.389489i
$$703$$ 2.69076 4.66053i 0.101484 0.175775i
$$704$$ −0.593579 −0.0223714
$$705$$ −6.73891 10.5328i −0.253802 0.396689i
$$706$$ −3.41741 + 5.91913i −0.128616 + 0.222769i
$$707$$ 0 0
$$708$$ 8.07227 + 12.6168i 0.303375 + 0.474170i
$$709$$ 5.24338 9.08180i 0.196919 0.341074i −0.750609 0.660747i $$-0.770240\pi$$
0.947528 + 0.319673i $$0.103573\pi$$
$$710$$ 4.27694 7.40789i 0.160511 0.278013i
$$711$$ −27.6301 + 2.52540i −1.03621 + 0.0947099i
$$712$$ −6.21780 10.7695i −0.233022 0.403606i
$$713$$ −17.5452 30.3892i −0.657074 1.13809i
$$714$$ 0 0
$$715$$ 0.442991 0.767282i 0.0165669 0.0286947i
$$716$$ −15.0364 −0.561936
$$717$$ −12.7463 19.9223i −0.476019 0.744011i
$$718$$ −12.6447 −0.471897
$$719$$ −1.11995 1.93981i −0.0417670 0.0723426i 0.844386 0.535735i $$-0.179965\pi$$
−0.886153 + 0.463392i $$0.846632\pi$$
$$720$$ −1.77335 + 0.162084i −0.0660887 + 0.00604052i
$$721$$ 0 0
$$722$$ 4.98035 + 8.62622i 0.185349 + 0.321035i
$$723$$ −10.3583 + 19.9927i −0.385228 + 0.743535i
$$724$$ −0.0430937 0.0746406i −0.00160157 0.00277399i
$$725$$ 14.3946 + 24.9322i 0.534604 + 0.925961i
$$726$$ −9.93920 15.5348i −0.368878 0.576551i
$$727$$ −0.185023 0.320469i −0.00686211 0.0118855i 0.862574 0.505931i $$-0.168851\pi$$
−0.869436 + 0.494045i $$0.835518\pi$$
$$728$$ 0 0
$$729$$ 25.9969 7.29124i 0.962847 0.270046i
$$730$$ −2.34874 4.06813i −0.0869307 0.150568i
$$731$$ 32.6050 1.20594
$$732$$ −5.29679 + 10.2234i −0.195775 + 0.377868i
$$733$$ −14.0191 −0.517806 −0.258903 0.965903i $$-0.583361\pi$$
−0.258903 + 0.965903i $$0.583361\pi$$
$$734$$ −3.27188 + 5.66707i −0.120767 + 0.209175i
$$735$$ 0 0
$$736$$ 2.23025 + 3.86291i 0.0822082 + 0.142389i
$$737$$ −0.568000 0.983804i −0.0209225 0.0362389i
$$738$$ −0.343677 + 0.744547i −0.0126509 + 0.0274071i
$$739$$ 13.3872 23.1874i 0.492458 0.852962i −0.507504 0.861649i $$-0.669432\pi$$
0.999962 + 0.00868705i $$0.00276521\pi$$
$$740$$ −0.296790 + 0.514055i −0.0109102 + 0.0188970i
$$741$$ 10.7824 20.8113i 0.396101 0.764521i
$$742$$ 0 0
$$743$$ −5.04669 + 8.74113i −0.185145 + 0.320681i −0.943625 0.331015i $$-0.892609\pi$$
0.758480 + 0.651696i $$0.225942\pi$$
$$744$$ −13.6118 + 0.620765i −0.499032 + 0.0227584i
$$745$$ −10.7148 −0.392560
$$746$$ 4.71420 8.16524i 0.172599 0.298951i
$$747$$ −9.68337 + 20.9782i −0.354296 + 0.767552i
$$748$$ −1.73385 −0.0633959
$$749$$ 0 0
$$750$$ 5.34562 + 8.35512i 0.195194 + 0.305086i
$$751$$ 11.5146 0.420173 0.210087 0.977683i $$-0.432625\pi$$
0.210087 + 0.977683i $$0.432625\pi$$
$$752$$ 6.08113 + 10.5328i 0.221756 + 0.384092i
$$753$$ −15.5723 + 30.0563i −0.567485 + 1.09531i
$$754$$ −7.78813 + 13.4894i −0.283627 + 0.491256i
$$755$$ −0.978019 −0.0355938
$$756$$ 0 0
$$757$$ −15.2484 −0.554214 −0.277107 0.960839i $$-0.589376\pi$$
−0.277107 + 0.960839i $$0.589376\pi$$
$$758$$ −3.63881 + 6.30260i −0.132168 + 0.228921i
$$759$$ 2.10963 4.07183i 0.0765748 0.147798i
$$760$$ −1.59718 2.76639i −0.0579357 0.100348i
$$761$$ 1.70175 0.0616883 0.0308442 0.999524i $$-0.490180\pi$$
0.0308442 + 0.999524i $$0.490180\pi$$
$$762$$ 11.5139 + 17.9961i 0.417105 + 0.651929i
$$763$$ 0 0
$$764$$ 3.98229 0.144074
$$765$$ −5.17996 + 0.473449i −0.187282 + 0.0171176i
$$766$$ 12.0416 20.8567i 0.435082 0.753584i
$$767$$ 21.7453 0.785178
$$768$$ 1.73025 0.0789082i 0.0624351 0.00284736i
$$769$$ −24.1211 + 41.7790i −0.869829 + 1.50659i −0.00765823 + 0.999971i $$0.502438\pi$$
−0.862171 + 0.506618i $$0.830896\pi$$
$$770$$ 0 0
$$771$$ 6.63521 12.8067i 0.238961 0.461223i
$$772$$ −3.39037 + 5.87229i −0.122022 + 0.211348i
$$773$$ −3.10243 + 5.37357i −0.111587 + 0.193274i −0.916410 0.400240i $$-0.868927\pi$$