# Properties

 Label 1296.2.i.n.865.1 Level $1296$ Weight $2$ Character 1296.865 Analytic conductor $10.349$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1296,2,Mod(433,1296)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1296, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("1296.433");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1296 = 2^{4} \cdot 3^{4}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1296.i (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: $$10.3486121020$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 162) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 865.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 1296.865 Dual form 1296.2.i.n.433.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(1.50000 + 2.59808i) q^{5} +(-2.00000 + 3.46410i) q^{7} +O(q^{10})$$ $$q+(1.50000 + 2.59808i) q^{5} +(-2.00000 + 3.46410i) q^{7} +(0.500000 + 0.866025i) q^{13} -3.00000 q^{17} +4.00000 q^{19} +(-2.00000 + 3.46410i) q^{25} +(-4.50000 + 7.79423i) q^{29} +(-2.00000 - 3.46410i) q^{31} -12.0000 q^{35} -1.00000 q^{37} +(-3.00000 - 5.19615i) q^{41} +(4.00000 - 6.92820i) q^{43} +(-6.00000 + 10.3923i) q^{47} +(-4.50000 - 7.79423i) q^{49} -6.00000 q^{53} +(0.500000 - 0.866025i) q^{61} +(-1.50000 + 2.59808i) q^{65} +(-2.00000 - 3.46410i) q^{67} +12.0000 q^{71} +11.0000 q^{73} +(-8.00000 + 13.8564i) q^{79} +(-6.00000 + 10.3923i) q^{83} +(-4.50000 - 7.79423i) q^{85} -3.00000 q^{89} -4.00000 q^{91} +(6.00000 + 10.3923i) q^{95} +(-1.00000 + 1.73205i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 3 q^{5} - 4 q^{7}+O(q^{10})$$ 2 * q + 3 * q^5 - 4 * q^7 $$2 q + 3 q^{5} - 4 q^{7} + q^{13} - 6 q^{17} + 8 q^{19} - 4 q^{25} - 9 q^{29} - 4 q^{31} - 24 q^{35} - 2 q^{37} - 6 q^{41} + 8 q^{43} - 12 q^{47} - 9 q^{49} - 12 q^{53} + q^{61} - 3 q^{65} - 4 q^{67} + 24 q^{71} + 22 q^{73} - 16 q^{79} - 12 q^{83} - 9 q^{85} - 6 q^{89} - 8 q^{91} + 12 q^{95} - 2 q^{97}+O(q^{100})$$ 2 * q + 3 * q^5 - 4 * q^7 + q^13 - 6 * q^17 + 8 * q^19 - 4 * q^25 - 9 * q^29 - 4 * q^31 - 24 * q^35 - 2 * q^37 - 6 * q^41 + 8 * q^43 - 12 * q^47 - 9 * q^49 - 12 * q^53 + q^61 - 3 * q^65 - 4 * q^67 + 24 * q^71 + 22 * q^73 - 16 * q^79 - 12 * q^83 - 9 * q^85 - 6 * q^89 - 8 * q^91 + 12 * q^95 - 2 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1296\mathbb{Z}\right)^\times$$.

 $$n$$ $$325$$ $$1135$$ $$1217$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## 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 0
$$3$$ 0 0
$$4$$ 0 0
$$5$$ 1.50000 + 2.59808i 0.670820 + 1.16190i 0.977672 + 0.210138i $$0.0673912\pi$$
−0.306851 + 0.951757i $$0.599275\pi$$
$$6$$ 0 0
$$7$$ −2.00000 + 3.46410i −0.755929 + 1.30931i 0.188982 + 0.981981i $$0.439481\pi$$
−0.944911 + 0.327327i $$0.893852\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$12$$ 0 0
$$13$$ 0.500000 + 0.866025i 0.138675 + 0.240192i 0.926995 0.375073i $$-0.122382\pi$$
−0.788320 + 0.615265i $$0.789049\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −3.00000 −0.727607 −0.363803 0.931476i $$-0.618522\pi$$
−0.363803 + 0.931476i $$0.618522\pi$$
$$18$$ 0 0
$$19$$ 4.00000 0.917663 0.458831 0.888523i $$-0.348268\pi$$
0.458831 + 0.888523i $$0.348268\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$24$$ 0 0
$$25$$ −2.00000 + 3.46410i −0.400000 + 0.692820i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −4.50000 + 7.79423i −0.835629 + 1.44735i 0.0578882 + 0.998323i $$0.481563\pi$$
−0.893517 + 0.449029i $$0.851770\pi$$
$$30$$ 0 0
$$31$$ −2.00000 3.46410i −0.359211 0.622171i 0.628619 0.777714i $$-0.283621\pi$$
−0.987829 + 0.155543i $$0.950287\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −12.0000 −2.02837
$$36$$ 0 0
$$37$$ −1.00000 −0.164399 −0.0821995 0.996616i $$-0.526194\pi$$
−0.0821995 + 0.996616i $$0.526194\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −3.00000 5.19615i −0.468521 0.811503i 0.530831 0.847477i $$-0.321880\pi$$
−0.999353 + 0.0359748i $$0.988546\pi$$
$$42$$ 0 0
$$43$$ 4.00000 6.92820i 0.609994 1.05654i −0.381246 0.924473i $$-0.624505\pi$$
0.991241 0.132068i $$-0.0421616\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −6.00000 + 10.3923i −0.875190 + 1.51587i −0.0186297 + 0.999826i $$0.505930\pi$$
−0.856560 + 0.516047i $$0.827403\pi$$
$$48$$ 0 0
$$49$$ −4.50000 7.79423i −0.642857 1.11346i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −6.00000 −0.824163 −0.412082 0.911147i $$-0.635198\pi$$
−0.412082 + 0.911147i $$0.635198\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$60$$ 0 0
$$61$$ 0.500000 0.866025i 0.0640184 0.110883i −0.832240 0.554416i $$-0.812942\pi$$
0.896258 + 0.443533i $$0.146275\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −1.50000 + 2.59808i −0.186052 + 0.322252i
$$66$$ 0 0
$$67$$ −2.00000 3.46410i −0.244339 0.423207i 0.717607 0.696449i $$-0.245238\pi$$
−0.961946 + 0.273241i $$0.911904\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 12.0000 1.42414 0.712069 0.702109i $$-0.247758\pi$$
0.712069 + 0.702109i $$0.247758\pi$$
$$72$$ 0 0
$$73$$ 11.0000 1.28745 0.643726 0.765256i $$-0.277388\pi$$
0.643726 + 0.765256i $$0.277388\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −8.00000 + 13.8564i −0.900070 + 1.55897i −0.0726692 + 0.997356i $$0.523152\pi$$
−0.827401 + 0.561611i $$0.810182\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −6.00000 + 10.3923i −0.658586 + 1.14070i 0.322396 + 0.946605i $$0.395512\pi$$
−0.980982 + 0.194099i $$0.937822\pi$$
$$84$$ 0 0
$$85$$ −4.50000 7.79423i −0.488094 0.845403i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −3.00000 −0.317999 −0.159000 0.987279i $$-0.550827\pi$$
−0.159000 + 0.987279i $$0.550827\pi$$
$$90$$ 0 0
$$91$$ −4.00000 −0.419314
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 6.00000 + 10.3923i 0.615587 + 1.06623i
$$96$$ 0 0
$$97$$ −1.00000 + 1.73205i −0.101535 + 0.175863i −0.912317 0.409484i $$-0.865709\pi$$
0.810782 + 0.585348i $$0.199042\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 3.00000 5.19615i 0.298511 0.517036i −0.677284 0.735721i $$-0.736843\pi$$
0.975796 + 0.218685i $$0.0701767\pi$$
$$102$$ 0 0
$$103$$ −2.00000 3.46410i −0.197066 0.341328i 0.750510 0.660859i $$-0.229808\pi$$
−0.947576 + 0.319531i $$0.896475\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −12.0000 −1.16008 −0.580042 0.814587i $$-0.696964\pi$$
−0.580042 + 0.814587i $$0.696964\pi$$
$$108$$ 0 0
$$109$$ 11.0000 1.05361 0.526804 0.849987i $$-0.323390\pi$$
0.526804 + 0.849987i $$0.323390\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 7.50000 + 12.9904i 0.705541 + 1.22203i 0.966496 + 0.256681i $$0.0826291\pi$$
−0.260955 + 0.965351i $$0.584038\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 6.00000 10.3923i 0.550019 0.952661i
$$120$$ 0 0
$$121$$ 5.50000 + 9.52628i 0.500000 + 0.866025i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 3.00000 0.268328
$$126$$ 0 0
$$127$$ 16.0000 1.41977 0.709885 0.704317i $$-0.248747\pi$$
0.709885 + 0.704317i $$0.248747\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −6.00000 10.3923i −0.524222 0.907980i −0.999602 0.0281993i $$-0.991023\pi$$
0.475380 0.879781i $$-0.342311\pi$$
$$132$$ 0 0
$$133$$ −8.00000 + 13.8564i −0.693688 + 1.20150i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −4.50000 + 7.79423i −0.384461 + 0.665906i −0.991694 0.128618i $$-0.958946\pi$$
0.607233 + 0.794524i $$0.292279\pi$$
$$138$$ 0 0
$$139$$ 10.0000 + 17.3205i 0.848189 + 1.46911i 0.882823 + 0.469706i $$0.155640\pi$$
−0.0346338 + 0.999400i $$0.511026\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ −27.0000 −2.24223
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −4.50000 7.79423i −0.368654 0.638528i 0.620701 0.784047i $$-0.286848\pi$$
−0.989355 + 0.145519i $$0.953515\pi$$
$$150$$ 0 0
$$151$$ 4.00000 6.92820i 0.325515 0.563809i −0.656101 0.754673i $$-0.727796\pi$$
0.981617 + 0.190864i $$0.0611289\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 6.00000 10.3923i 0.481932 0.834730i
$$156$$ 0 0
$$157$$ 6.50000 + 11.2583i 0.518756 + 0.898513i 0.999762 + 0.0217953i $$0.00693820\pi$$
−0.481006 + 0.876717i $$0.659728\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −8.00000 −0.626608 −0.313304 0.949653i $$-0.601436\pi$$
−0.313304 + 0.949653i $$0.601436\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 6.00000 + 10.3923i 0.464294 + 0.804181i 0.999169 0.0407502i $$-0.0129748\pi$$
−0.534875 + 0.844931i $$0.679641\pi$$
$$168$$ 0 0
$$169$$ 6.00000 10.3923i 0.461538 0.799408i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 1.50000 2.59808i 0.114043 0.197528i −0.803354 0.595502i $$-0.796953\pi$$
0.917397 + 0.397974i $$0.130287\pi$$
$$174$$ 0 0
$$175$$ −8.00000 13.8564i −0.604743 1.04745i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −12.0000 −0.896922 −0.448461 0.893802i $$-0.648028\pi$$
−0.448461 + 0.893802i $$0.648028\pi$$
$$180$$ 0 0
$$181$$ −10.0000 −0.743294 −0.371647 0.928374i $$-0.621207\pi$$
−0.371647 + 0.928374i $$0.621207\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −1.50000 2.59808i −0.110282 0.191014i
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 6.00000 10.3923i 0.434145 0.751961i −0.563081 0.826402i $$-0.690384\pi$$
0.997225 + 0.0744412i $$0.0237173\pi$$
$$192$$ 0 0
$$193$$ 6.50000 + 11.2583i 0.467880 + 0.810392i 0.999326 0.0366998i $$-0.0116845\pi$$
−0.531446 + 0.847092i $$0.678351\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −3.00000 −0.213741 −0.106871 0.994273i $$-0.534083\pi$$
−0.106871 + 0.994273i $$0.534083\pi$$
$$198$$ 0 0
$$199$$ 4.00000 0.283552 0.141776 0.989899i $$-0.454719\pi$$
0.141776 + 0.989899i $$0.454719\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −18.0000 31.1769i −1.26335 2.18819i
$$204$$ 0 0
$$205$$ 9.00000 15.5885i 0.628587 1.08875i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 4.00000 + 6.92820i 0.275371 + 0.476957i 0.970229 0.242190i $$-0.0778659\pi$$
−0.694857 + 0.719148i $$0.744533\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 24.0000 1.63679
$$216$$ 0 0
$$217$$ 16.0000 1.08615
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −1.50000 2.59808i −0.100901 0.174766i
$$222$$ 0 0
$$223$$ 4.00000 6.92820i 0.267860 0.463947i −0.700449 0.713702i $$-0.747017\pi$$
0.968309 + 0.249756i $$0.0803503\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −6.00000 + 10.3923i −0.398234 + 0.689761i −0.993508 0.113761i $$-0.963710\pi$$
0.595274 + 0.803523i $$0.297043\pi$$
$$228$$ 0 0
$$229$$ −11.5000 19.9186i −0.759941 1.31626i −0.942880 0.333133i $$-0.891894\pi$$
0.182939 0.983124i $$-0.441439\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 21.0000 1.37576 0.687878 0.725826i $$-0.258542\pi$$
0.687878 + 0.725826i $$0.258542\pi$$
$$234$$ 0 0
$$235$$ −36.0000 −2.34838
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 6.00000 + 10.3923i 0.388108 + 0.672222i 0.992195 0.124696i $$-0.0397955\pi$$
−0.604087 + 0.796918i $$0.706462\pi$$
$$240$$ 0 0
$$241$$ 6.50000 11.2583i 0.418702 0.725213i −0.577107 0.816668i $$-0.695819\pi$$
0.995809 + 0.0914555i $$0.0291519\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 13.5000 23.3827i 0.862483 1.49387i
$$246$$ 0 0
$$247$$ 2.00000 + 3.46410i 0.127257 + 0.220416i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 24.0000 1.51487 0.757433 0.652913i $$-0.226453\pi$$
0.757433 + 0.652913i $$0.226453\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 7.50000 + 12.9904i 0.467837 + 0.810318i 0.999325 0.0367485i $$-0.0117000\pi$$
−0.531487 + 0.847066i $$0.678367\pi$$
$$258$$ 0 0
$$259$$ 2.00000 3.46410i 0.124274 0.215249i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 6.00000 10.3923i 0.369976 0.640817i −0.619586 0.784929i $$-0.712699\pi$$
0.989561 + 0.144112i $$0.0460326\pi$$
$$264$$ 0 0
$$265$$ −9.00000 15.5885i −0.552866 0.957591i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 21.0000 1.28039 0.640196 0.768211i $$-0.278853\pi$$
0.640196 + 0.768211i $$0.278853\pi$$
$$270$$ 0 0
$$271$$ 16.0000 0.971931 0.485965 0.873978i $$-0.338468\pi$$
0.485965 + 0.873978i $$0.338468\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 5.00000 8.66025i 0.300421 0.520344i −0.675810 0.737075i $$-0.736206\pi$$
0.976231 + 0.216731i $$0.0695395\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 13.5000 23.3827i 0.805342 1.39489i −0.110717 0.993852i $$-0.535315\pi$$
0.916060 0.401042i $$-0.131352\pi$$
$$282$$ 0 0
$$283$$ −2.00000 3.46410i −0.118888 0.205919i 0.800439 0.599414i $$-0.204600\pi$$
−0.919327 + 0.393494i $$0.871266\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 24.0000 1.41668
$$288$$ 0 0
$$289$$ −8.00000 −0.470588
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −4.50000 7.79423i −0.262893 0.455344i 0.704117 0.710084i $$-0.251343\pi$$
−0.967009 + 0.254741i $$0.918010\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 16.0000 + 27.7128i 0.922225 + 1.59734i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 3.00000 0.171780
$$306$$ 0 0
$$307$$ −20.0000 −1.14146 −0.570730 0.821138i $$-0.693340\pi$$
−0.570730 + 0.821138i $$0.693340\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 12.0000 + 20.7846i 0.680458 + 1.17859i 0.974841 + 0.222900i $$0.0715523\pi$$
−0.294384 + 0.955687i $$0.595114\pi$$
$$312$$ 0 0
$$313$$ −11.5000 + 19.9186i −0.650018 + 1.12586i 0.333099 + 0.942892i $$0.391906\pi$$
−0.983118 + 0.182973i $$0.941428\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −10.5000 + 18.1865i −0.589739 + 1.02146i 0.404528 + 0.914526i $$0.367436\pi$$
−0.994266 + 0.106932i $$0.965897\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −12.0000 −0.667698
$$324$$ 0 0
$$325$$ −4.00000 −0.221880
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −24.0000 41.5692i −1.32316 2.29179i
$$330$$ 0 0
$$331$$ 10.0000 17.3205i 0.549650 0.952021i −0.448649 0.893708i $$-0.648095\pi$$
0.998298 0.0583130i $$-0.0185721\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 6.00000 10.3923i 0.327815 0.567792i
$$336$$ 0 0
$$337$$ −1.00000 1.73205i −0.0544735 0.0943508i 0.837503 0.546433i $$-0.184015\pi$$
−0.891976 + 0.452082i $$0.850681\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 8.00000 0.431959
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 6.00000 + 10.3923i 0.322097 + 0.557888i 0.980921 0.194409i $$-0.0622790\pi$$
−0.658824 + 0.752297i $$0.728946\pi$$
$$348$$ 0 0
$$349$$ −7.00000 + 12.1244i −0.374701 + 0.649002i −0.990282 0.139072i $$-0.955588\pi$$
0.615581 + 0.788074i $$0.288921\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 9.00000 15.5885i 0.479022 0.829690i −0.520689 0.853746i $$-0.674325\pi$$
0.999711 + 0.0240566i $$0.00765819\pi$$
$$354$$ 0 0
$$355$$ 18.0000 + 31.1769i 0.955341 + 1.65470i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$360$$ 0 0
$$361$$ −3.00000 −0.157895
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 16.5000 + 28.5788i 0.863649 + 1.49588i
$$366$$ 0 0
$$367$$ 4.00000 6.92820i 0.208798 0.361649i −0.742538 0.669804i $$-0.766378\pi$$
0.951336 + 0.308155i $$0.0997115\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 12.0000 20.7846i 0.623009 1.07908i
$$372$$ 0 0
$$373$$ 5.00000 + 8.66025i 0.258890 + 0.448411i 0.965945 0.258748i $$-0.0833099\pi$$
−0.707055 + 0.707159i $$0.749977\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −9.00000 −0.463524
$$378$$ 0 0
$$379$$ 28.0000 1.43826 0.719132 0.694874i $$-0.244540\pi$$
0.719132 + 0.694874i $$0.244540\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −6.00000 10.3923i −0.306586 0.531022i 0.671027 0.741433i $$-0.265853\pi$$
−0.977613 + 0.210411i $$0.932520\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 3.00000 5.19615i 0.152106 0.263455i −0.779895 0.625910i $$-0.784728\pi$$
0.932002 + 0.362454i $$0.118061\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −48.0000 −2.41514
$$396$$ 0 0
$$397$$ −25.0000 −1.25471 −0.627357 0.778732i $$-0.715863\pi$$
−0.627357 + 0.778732i $$0.715863\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 1.50000 + 2.59808i 0.0749064 + 0.129742i 0.901046 0.433724i $$-0.142801\pi$$
−0.826139 + 0.563466i $$0.809468\pi$$
$$402$$ 0 0
$$403$$ 2.00000 3.46410i 0.0996271 0.172559i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 12.5000 + 21.6506i 0.618085 + 1.07056i 0.989835 + 0.142222i $$0.0454247\pi$$
−0.371750 + 0.928333i $$0.621242\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ −36.0000 −1.76717
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −12.0000 20.7846i −0.586238 1.01539i −0.994720 0.102628i $$-0.967275\pi$$
0.408481 0.912767i $$-0.366058\pi$$
$$420$$ 0 0
$$421$$ 6.50000 11.2583i 0.316791 0.548697i −0.663026 0.748596i $$-0.730728\pi$$
0.979817 + 0.199899i $$0.0640614\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 6.00000 10.3923i 0.291043 0.504101i
$$426$$ 0 0
$$427$$ 2.00000 + 3.46410i 0.0967868 + 0.167640i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 12.0000 0.578020 0.289010 0.957326i $$-0.406674\pi$$
0.289010 + 0.957326i $$0.406674\pi$$
$$432$$ 0 0
$$433$$ 11.0000 0.528626 0.264313 0.964437i $$-0.414855\pi$$
0.264313 + 0.964437i $$0.414855\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ −14.0000 + 24.2487i −0.668184 + 1.15733i 0.310228 + 0.950662i $$0.399595\pi$$
−0.978412 + 0.206666i $$0.933739\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −6.00000 + 10.3923i −0.285069 + 0.493753i −0.972626 0.232377i $$-0.925350\pi$$
0.687557 + 0.726130i $$0.258683\pi$$
$$444$$ 0 0
$$445$$ −4.50000 7.79423i −0.213320 0.369482i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −18.0000 −0.849473 −0.424736 0.905317i $$-0.639633\pi$$
−0.424736 + 0.905317i $$0.639633\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −6.00000 10.3923i −0.281284 0.487199i
$$456$$ 0 0
$$457$$ 0.500000 0.866025i 0.0233890 0.0405110i −0.854094 0.520119i $$-0.825888\pi$$
0.877483 + 0.479608i $$0.159221\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −9.00000 + 15.5885i −0.419172 + 0.726027i −0.995856 0.0909401i $$-0.971013\pi$$
0.576685 + 0.816967i $$0.304346\pi$$
$$462$$ 0 0
$$463$$ 4.00000 + 6.92820i 0.185896 + 0.321981i 0.943878 0.330294i $$-0.107148\pi$$
−0.757982 + 0.652275i $$0.773815\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 24.0000 1.11059 0.555294 0.831654i $$-0.312606\pi$$
0.555294 + 0.831654i $$0.312606\pi$$
$$468$$ 0 0
$$469$$ 16.0000 0.738811
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ −8.00000 + 13.8564i −0.367065 + 0.635776i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −6.00000 + 10.3923i −0.274147 + 0.474837i −0.969920 0.243426i $$-0.921729\pi$$
0.695773 + 0.718262i $$0.255062\pi$$
$$480$$ 0 0
$$481$$ −0.500000 0.866025i −0.0227980 0.0394874i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −6.00000 −0.272446
$$486$$ 0 0
$$487$$ 4.00000 0.181257 0.0906287 0.995885i $$-0.471112\pi$$
0.0906287 + 0.995885i $$0.471112\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$492$$ 0 0
$$493$$ 13.5000 23.3827i 0.608009 1.05310i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −24.0000 + 41.5692i −1.07655 + 1.86463i
$$498$$ 0 0
$$499$$ −20.0000 34.6410i −0.895323 1.55074i −0.833404 0.552664i $$-0.813611\pi$$
−0.0619186 0.998081i $$-0.519722\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$504$$ 0 0
$$505$$ 18.0000 0.800989
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 15.0000 + 25.9808i 0.664863 + 1.15158i 0.979322 + 0.202306i $$0.0648436\pi$$
−0.314459 + 0.949271i $$0.601823\pi$$
$$510$$ 0 0
$$511$$ −22.0000 + 38.1051i −0.973223 + 1.68567i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 6.00000 10.3923i 0.264392 0.457940i
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 6.00000 0.262865 0.131432 0.991325i $$-0.458042\pi$$
0.131432 + 0.991325i $$0.458042\pi$$
$$522$$ 0 0
$$523$$ 16.0000 0.699631 0.349816 0.936819i $$-0.386244\pi$$
0.349816 + 0.936819i $$0.386244\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 6.00000 + 10.3923i 0.261364 + 0.452696i
$$528$$ 0 0
$$529$$ 11.5000 19.9186i 0.500000 0.866025i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 3.00000 5.19615i 0.129944 0.225070i
$$534$$ 0 0
$$535$$ −18.0000 31.1769i −0.778208 1.34790i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −1.00000 −0.0429934 −0.0214967 0.999769i $$-0.506843\pi$$
−0.0214967 + 0.999769i $$0.506843\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 16.5000 + 28.5788i 0.706782 + 1.22418i
$$546$$ 0 0
$$547$$ 22.0000 38.1051i 0.940652 1.62926i 0.176421 0.984315i $$-0.443548\pi$$
0.764231 0.644942i $$-0.223119\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −18.0000 + 31.1769i −0.766826 + 1.32818i
$$552$$ 0 0
$$553$$ −32.0000 55.4256i −1.36078 2.35694i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −3.00000 −0.127114 −0.0635570 0.997978i $$-0.520244\pi$$
−0.0635570 + 0.997978i $$0.520244\pi$$
$$558$$ 0 0
$$559$$ 8.00000 0.338364
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 6.00000 + 10.3923i 0.252870 + 0.437983i 0.964315 0.264758i $$-0.0852922\pi$$
−0.711445 + 0.702742i $$0.751959\pi$$
$$564$$ 0 0
$$565$$ −22.5000 + 38.9711i −0.946582 + 1.63953i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 7.50000 12.9904i 0.314416 0.544585i −0.664897 0.746935i $$-0.731525\pi$$
0.979313 + 0.202350i $$0.0648579\pi$$
$$570$$ 0 0
$$571$$ −8.00000 13.8564i −0.334790 0.579873i 0.648655 0.761083i $$-0.275332\pi$$
−0.983444 + 0.181210i $$0.941999\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −25.0000 −1.04076 −0.520382 0.853934i $$-0.674210\pi$$
−0.520382 + 0.853934i $$0.674210\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −24.0000 41.5692i −0.995688 1.72458i
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −12.0000 + 20.7846i −0.495293 + 0.857873i −0.999985 0.00542667i $$-0.998273\pi$$
0.504692 + 0.863299i $$0.331606\pi$$
$$588$$ 0 0
$$589$$ −8.00000 13.8564i −0.329634 0.570943i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 33.0000 1.35515 0.677574 0.735455i $$-0.263031\pi$$
0.677574 + 0.735455i $$0.263031\pi$$
$$594$$ 0 0
$$595$$ 36.0000 1.47586
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −18.0000 31.1769i −0.735460 1.27385i −0.954521 0.298143i $$-0.903633\pi$$
0.219061 0.975711i $$-0.429701\pi$$
$$600$$ 0 0
$$601$$ −17.5000 + 30.3109i −0.713840 + 1.23641i 0.249565 + 0.968358i $$0.419712\pi$$
−0.963405 + 0.268049i $$0.913621\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −16.5000 + 28.5788i −0.670820 + 1.16190i
$$606$$ 0 0
$$607$$ 10.0000 + 17.3205i 0.405887 + 0.703018i 0.994424 0.105453i $$-0.0336291\pi$$
−0.588537 + 0.808470i $$0.700296\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −12.0000 −0.485468
$$612$$ 0 0
$$613$$ 38.0000 1.53481 0.767403 0.641165i $$-0.221549\pi$$
0.767403 + 0.641165i $$0.221549\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 1.50000 + 2.59808i 0.0603877 + 0.104595i 0.894639 0.446790i $$-0.147433\pi$$
−0.834251 + 0.551385i $$0.814100\pi$$
$$618$$ 0 0
$$619$$ 4.00000 6.92820i 0.160774 0.278468i −0.774373 0.632730i $$-0.781934\pi$$
0.935146 + 0.354262i $$0.115268\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 6.00000 10.3923i 0.240385 0.416359i
$$624$$ 0 0
$$625$$ 14.5000 + 25.1147i 0.580000 + 1.00459i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 3.00000 0.119618
$$630$$ 0 0
$$631$$ −8.00000 −0.318475 −0.159237 0.987240i $$-0.550904\pi$$
−0.159237 + 0.987240i $$0.550904\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 24.0000 + 41.5692i 0.952411 + 1.64962i
$$636$$ 0 0
$$637$$ 4.50000 7.79423i 0.178296 0.308819i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −22.5000 + 38.9711i −0.888697 + 1.53927i −0.0472793 + 0.998882i $$0.515055\pi$$
−0.841417 + 0.540386i $$0.818278\pi$$
$$642$$ 0 0
$$643$$ −2.00000 3.46410i −0.0788723 0.136611i 0.823891 0.566748i $$-0.191799\pi$$
−0.902764 + 0.430137i $$0.858465\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −36.0000 −1.41531 −0.707653 0.706560i $$-0.750246\pi$$
−0.707653 + 0.706560i $$0.750246\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −9.00000 15.5885i −0.352197 0.610023i 0.634437 0.772975i $$-0.281232\pi$$
−0.986634 + 0.162951i $$0.947899\pi$$
$$654$$ 0 0
$$655$$ 18.0000 31.1769i 0.703318 1.21818i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 6.00000 10.3923i 0.233727 0.404827i −0.725175 0.688565i $$-0.758241\pi$$
0.958902 + 0.283738i $$0.0915745\pi$$
$$660$$ 0 0
$$661$$ −11.5000 19.9186i −0.447298 0.774743i 0.550911 0.834564i $$-0.314280\pi$$
−0.998209 + 0.0598209i $$0.980947\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −48.0000 −1.86136
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ −5.50000 + 9.52628i −0.212009 + 0.367211i −0.952343 0.305028i $$-0.901334\pi$$
0.740334 + 0.672239i $$0.234667\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 3.00000 5.19615i 0.115299 0.199704i −0.802600 0.596518i $$-0.796551\pi$$
0.917899 + 0.396813i $$0.129884\pi$$
$$678$$ 0 0
$$679$$ −4.00000 6.92820i −0.153506 0.265880i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −36.0000 −1.37750 −0.688751 0.724998i $$-0.741841\pi$$
−0.688751 + 0.724998i $$0.741841\pi$$
$$684$$ 0 0
$$685$$ −27.0000 −1.03162
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −3.00000 5.19615i −0.114291 0.197958i
$$690$$ 0 0
$$691$$ −14.0000 + 24.2487i −0.532585 + 0.922464i 0.466691 + 0.884420i $$0.345446\pi$$
−0.999276 + 0.0380440i $$0.987887\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −30.0000 + 51.9615i −1.13796 + 1.97101i
$$696$$ 0 0
$$697$$ 9.00000 + 15.5885i 0.340899 + 0.590455i
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −51.0000 −1.92624 −0.963122 0.269066i $$-0.913285\pi$$
−0.963122 + 0.269066i $$0.913285\pi$$
$$702$$ 0 0
$$703$$ −4.00000 −0.150863
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 12.0000 + 20.7846i 0.451306 + 0.781686i
$$708$$ 0 0
$$709$$ −23.5000 + 40.7032i −0.882561 + 1.52864i −0.0340772 + 0.999419i $$0.510849\pi$$
−0.848484 + 0.529221i $$0.822484\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$720$$ 0 0
$$721$$ 16.0000 0.595871
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −18.0000 31.1769i −0.668503 1.15788i
$$726$$ 0 0
$$727$$ −14.0000 + 24.2487i −0.519231 + 0.899335i 0.480519 + 0.876984i $$0.340448\pi$$
−0.999750 + 0.0223506i $$0.992885\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −12.0000 + 20.7846i −0.443836 + 0.768747i
$$732$$ 0 0
$$733$$ −7.00000 12.1244i −0.258551 0.447823i 0.707303 0.706910i $$-0.249912\pi$$
−0.965854 + 0.259087i $$0.916578\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ −20.0000 −0.735712 −0.367856 0.929883i $$-0.619908\pi$$
−0.367856 + 0.929883i $$0.619908\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 6.00000 + 10.3923i 0.220119 + 0.381257i 0.954844 0.297108i $$-0.0960222\pi$$
−0.734725 + 0.678365i $$0.762689\pi$$
$$744$$ 0 0
$$745$$ 13.5000 23.3827i 0.494602 0.856675i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 24.0000 41.5692i 0.876941 1.51891i
$$750$$ 0 0
$$751$$ 10.0000 + 17.3205i 0.364905 + 0.632034i 0.988761 0.149505i $$-0.0477681\pi$$
−0.623856 + 0.781540i $$0.714435\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 24.0000 0.873449
$$756$$ 0 0
$$757$$ 38.0000 1.38113 0.690567 0.723269i $$-0.257361\pi$$
0.690567 + 0.723269i $$0.257361\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 7.50000 + 12.9904i 0.271875 + 0.470901i 0.969342 0.245716i $$-0.0790230\pi$$
−0.697467 + 0.716617i $$0.745690\pi$$
$$762$$ 0 0
$$763$$ −22.0000 + 38.1051i −0.796453 + 1.37950i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 18.5000 + 32.0429i 0.667127 + 1.15550i 0.978704 + 0.205277i $$0.0658095\pi$$
−0.311577 + 0.950221i $$0.600857\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −27.0000 −0.971123 −0.485561 0.874203i $$-0.661385\pi$$
−0.485561 + 0.874203i $$0.661385\pi$$
$$774$$ 0 0
$$775$$ 16.0000 0.574737
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −12.0000 20.7846i −0.429945 0.744686i
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −19.5000 + 33.7750i −0.695985 + 1.20548i
$$786$$ 0 0
$$787$$ 16.0000 + 27.7128i 0.570338 + 0.987855i 0.996531 + 0.0832226i $$0.0265213\pi$$
−0.426193 + 0.904632i $$0.640145\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −60.0000 −2.13335
$$792$$ 0 0
$$793$$ 1.00000 0.0355110
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 25.5000 + 44.1673i 0.903256 + 1.56449i 0.823241 + 0.567692i $$0.192164\pi$$
0.0800155 + 0.996794i $$0.474503\pi$$
$$798$$ 0