# Properties

 Label 3240.2.q.p.2161.1 Level $3240$ Weight $2$ Character 3240.2161 Analytic conductor $25.872$ Analytic rank $1$ Dimension $2$ Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3240,2,Mod(1081,3240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3240, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("3240.1081");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$3240 = 2^{3} \cdot 3^{4} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3240.q (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: $$25.8715302549$$ Analytic rank: $$1$$ 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: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 1080) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 2161.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 3240.2161 Dual form 3240.2.q.p.1081.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(0.500000 + 0.866025i) q^{5} +(-1.00000 + 1.73205i) q^{7} +O(q^{10})$$ $$q+(0.500000 + 0.866025i) q^{5} +(-1.00000 + 1.73205i) q^{7} +(2.00000 - 3.46410i) q^{11} +(1.00000 + 1.73205i) q^{13} -5.00000 q^{17} -5.00000 q^{19} +(0.500000 + 0.866025i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-1.00000 + 1.73205i) q^{29} +(-3.50000 - 6.06218i) q^{31} -2.00000 q^{35} -6.00000 q^{37} +(-2.00000 + 3.46410i) q^{43} +(2.00000 - 3.46410i) q^{47} +(1.50000 + 2.59808i) q^{49} -9.00000 q^{53} +4.00000 q^{55} +(7.00000 + 12.1244i) q^{59} +(5.50000 - 9.52628i) q^{61} +(-1.00000 + 1.73205i) q^{65} +(-7.00000 - 12.1244i) q^{67} -12.0000 q^{73} +(4.00000 + 6.92820i) q^{77} +(1.50000 - 2.59808i) q^{79} +(-0.500000 + 0.866025i) q^{83} +(-2.50000 - 4.33013i) q^{85} -4.00000 q^{91} +(-2.50000 - 4.33013i) q^{95} +(-8.00000 + 13.8564i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + q^{5} - 2 q^{7}+O(q^{10})$$ 2 * q + q^5 - 2 * q^7 $$2 q + q^{5} - 2 q^{7} + 4 q^{11} + 2 q^{13} - 10 q^{17} - 10 q^{19} + q^{23} - q^{25} - 2 q^{29} - 7 q^{31} - 4 q^{35} - 12 q^{37} - 4 q^{43} + 4 q^{47} + 3 q^{49} - 18 q^{53} + 8 q^{55} + 14 q^{59} + 11 q^{61} - 2 q^{65} - 14 q^{67} - 24 q^{73} + 8 q^{77} + 3 q^{79} - q^{83} - 5 q^{85} - 8 q^{91} - 5 q^{95} - 16 q^{97}+O(q^{100})$$ 2 * q + q^5 - 2 * q^7 + 4 * q^11 + 2 * q^13 - 10 * q^17 - 10 * q^19 + q^23 - q^25 - 2 * q^29 - 7 * q^31 - 4 * q^35 - 12 * q^37 - 4 * q^43 + 4 * q^47 + 3 * q^49 - 18 * q^53 + 8 * q^55 + 14 * q^59 + 11 * q^61 - 2 * q^65 - 14 * q^67 - 24 * q^73 + 8 * q^77 + 3 * q^79 - q^83 - 5 * q^85 - 8 * q^91 - 5 * q^95 - 16 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/3240\mathbb{Z}\right)^\times$$.

 $$n$$ $$1297$$ $$1621$$ $$2431$$ $$3161$$ $$\chi(n)$$ $$1$$ $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## 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
$$5$$ 0.500000 + 0.866025i 0.223607 + 0.387298i
$$6$$ 0 0
$$7$$ −1.00000 + 1.73205i −0.377964 + 0.654654i −0.990766 0.135583i $$-0.956709\pi$$
0.612801 + 0.790237i $$0.290043\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 2.00000 3.46410i 0.603023 1.04447i −0.389338 0.921095i $$-0.627296\pi$$
0.992361 0.123371i $$-0.0393705\pi$$
$$12$$ 0 0
$$13$$ 1.00000 + 1.73205i 0.277350 + 0.480384i 0.970725 0.240192i $$-0.0772105\pi$$
−0.693375 + 0.720577i $$0.743877\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −5.00000 −1.21268 −0.606339 0.795206i $$-0.707363\pi$$
−0.606339 + 0.795206i $$0.707363\pi$$
$$18$$ 0 0
$$19$$ −5.00000 −1.14708 −0.573539 0.819178i $$-0.694430\pi$$
−0.573539 + 0.819178i $$0.694430\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 0.500000 + 0.866025i 0.104257 + 0.180579i 0.913434 0.406986i $$-0.133420\pi$$
−0.809177 + 0.587565i $$0.800087\pi$$
$$24$$ 0 0
$$25$$ −0.500000 + 0.866025i −0.100000 + 0.173205i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −1.00000 + 1.73205i −0.185695 + 0.321634i −0.943811 0.330487i $$-0.892787\pi$$
0.758115 + 0.652121i $$0.226120\pi$$
$$30$$ 0 0
$$31$$ −3.50000 6.06218i −0.628619 1.08880i −0.987829 0.155543i $$-0.950287\pi$$
0.359211 0.933257i $$-0.383046\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −2.00000 −0.338062
$$36$$ 0 0
$$37$$ −6.00000 −0.986394 −0.493197 0.869918i $$-0.664172\pi$$
−0.493197 + 0.869918i $$0.664172\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$42$$ 0 0
$$43$$ −2.00000 + 3.46410i −0.304997 + 0.528271i −0.977261 0.212041i $$-0.931989\pi$$
0.672264 + 0.740312i $$0.265322\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 2.00000 3.46410i 0.291730 0.505291i −0.682489 0.730896i $$-0.739102\pi$$
0.974219 + 0.225605i $$0.0724358\pi$$
$$48$$ 0 0
$$49$$ 1.50000 + 2.59808i 0.214286 + 0.371154i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −9.00000 −1.23625 −0.618123 0.786082i $$-0.712106\pi$$
−0.618123 + 0.786082i $$0.712106\pi$$
$$54$$ 0 0
$$55$$ 4.00000 0.539360
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 7.00000 + 12.1244i 0.911322 + 1.57846i 0.812198 + 0.583382i $$0.198271\pi$$
0.0991242 + 0.995075i $$0.468396\pi$$
$$60$$ 0 0
$$61$$ 5.50000 9.52628i 0.704203 1.21972i −0.262776 0.964857i $$-0.584638\pi$$
0.966978 0.254858i $$-0.0820288\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −1.00000 + 1.73205i −0.124035 + 0.214834i
$$66$$ 0 0
$$67$$ −7.00000 12.1244i −0.855186 1.48123i −0.876472 0.481452i $$-0.840109\pi$$
0.0212861 0.999773i $$-0.493224\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ 0 0
$$73$$ −12.0000 −1.40449 −0.702247 0.711934i $$-0.747820\pi$$
−0.702247 + 0.711934i $$0.747820\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 4.00000 + 6.92820i 0.455842 + 0.789542i
$$78$$ 0 0
$$79$$ 1.50000 2.59808i 0.168763 0.292306i −0.769222 0.638982i $$-0.779356\pi$$
0.937985 + 0.346675i $$0.112689\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −0.500000 + 0.866025i −0.0548821 + 0.0950586i −0.892161 0.451717i $$-0.850812\pi$$
0.837279 + 0.546776i $$0.184145\pi$$
$$84$$ 0 0
$$85$$ −2.50000 4.33013i −0.271163 0.469668i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$90$$ 0 0
$$91$$ −4.00000 −0.419314
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −2.50000 4.33013i −0.256495 0.444262i
$$96$$ 0 0
$$97$$ −8.00000 + 13.8564i −0.812277 + 1.40690i 0.0989899 + 0.995088i $$0.468439\pi$$
−0.911267 + 0.411816i $$0.864894\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 6.00000 10.3923i 0.597022 1.03407i −0.396236 0.918149i $$-0.629684\pi$$
0.993258 0.115924i $$-0.0369830\pi$$
$$102$$ 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 $$-0.303036\pi$$
0.580042 + 0.814587i $$0.303036\pi$$
$$108$$ 0 0
$$109$$ −19.0000 −1.81987 −0.909935 0.414751i $$-0.863869\pi$$
−0.909935 + 0.414751i $$0.863869\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 3.00000 + 5.19615i 0.282216 + 0.488813i 0.971930 0.235269i $$-0.0755971\pi$$
−0.689714 + 0.724082i $$0.742264\pi$$
$$114$$ 0 0
$$115$$ −0.500000 + 0.866025i −0.0466252 + 0.0807573i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 5.00000 8.66025i 0.458349 0.793884i
$$120$$ 0 0
$$121$$ −2.50000 4.33013i −0.227273 0.393648i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −1.00000 −0.0894427
$$126$$ 0 0
$$127$$ 6.00000 0.532414 0.266207 0.963916i $$-0.414230\pi$$
0.266207 + 0.963916i $$0.414230\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −9.00000 15.5885i −0.786334 1.36197i −0.928199 0.372084i $$-0.878643\pi$$
0.141865 0.989886i $$-0.454690\pi$$
$$132$$ 0 0
$$133$$ 5.00000 8.66025i 0.433555 0.750939i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −8.50000 + 14.7224i −0.726204 + 1.25782i 0.232273 + 0.972651i $$0.425384\pi$$
−0.958477 + 0.285171i $$0.907949\pi$$
$$138$$ 0 0
$$139$$ −6.00000 10.3923i −0.508913 0.881464i −0.999947 0.0103230i $$-0.996714\pi$$
0.491033 0.871141i $$-0.336619\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 8.00000 0.668994
$$144$$ 0 0
$$145$$ −2.00000 −0.166091
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −8.00000 13.8564i −0.655386 1.13516i −0.981797 0.189933i $$-0.939173\pi$$
0.326411 0.945228i $$-0.394160\pi$$
$$150$$ 0 0
$$151$$ −4.00000 + 6.92820i −0.325515 + 0.563809i −0.981617 0.190864i $$-0.938871\pi$$
0.656101 + 0.754673i $$0.272204\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 3.50000 6.06218i 0.281127 0.486926i
$$156$$ 0 0
$$157$$ −8.00000 13.8564i −0.638470 1.10586i −0.985769 0.168107i $$-0.946235\pi$$
0.347299 0.937754i $$-0.387099\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −2.00000 −0.157622
$$162$$ 0 0
$$163$$ −14.0000 −1.09656 −0.548282 0.836293i $$-0.684718\pi$$
−0.548282 + 0.836293i $$0.684718\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −1.50000 2.59808i −0.116073 0.201045i 0.802135 0.597143i $$-0.203697\pi$$
−0.918208 + 0.396098i $$0.870364\pi$$
$$168$$ 0 0
$$169$$ 4.50000 7.79423i 0.346154 0.599556i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −6.50000 + 11.2583i −0.494186 + 0.855955i −0.999978 0.00670064i $$-0.997867\pi$$
0.505792 + 0.862656i $$0.331200\pi$$
$$174$$ 0 0
$$175$$ −1.00000 1.73205i −0.0755929 0.130931i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 4.00000 0.298974 0.149487 0.988764i $$-0.452238\pi$$
0.149487 + 0.988764i $$0.452238\pi$$
$$180$$ 0 0
$$181$$ −19.0000 −1.41226 −0.706129 0.708083i $$-0.749560\pi$$
−0.706129 + 0.708083i $$0.749560\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −3.00000 5.19615i −0.220564 0.382029i
$$186$$ 0 0
$$187$$ −10.0000 + 17.3205i −0.731272 + 1.26660i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 7.00000 12.1244i 0.506502 0.877288i −0.493469 0.869763i $$-0.664272\pi$$
0.999972 0.00752447i $$-0.00239513\pi$$
$$192$$ 0 0
$$193$$ −5.00000 8.66025i −0.359908 0.623379i 0.628037 0.778183i $$-0.283859\pi$$
−0.987945 + 0.154805i $$0.950525\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 5.00000 0.356235 0.178118 0.984009i $$-0.442999\pi$$
0.178118 + 0.984009i $$0.442999\pi$$
$$198$$ 0 0
$$199$$ −16.0000 −1.13421 −0.567105 0.823646i $$-0.691937\pi$$
−0.567105 + 0.823646i $$0.691937\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −2.00000 3.46410i −0.140372 0.243132i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −10.0000 + 17.3205i −0.691714 + 1.19808i
$$210$$ 0 0
$$211$$ 9.50000 + 16.4545i 0.654007 + 1.13277i 0.982142 + 0.188142i $$0.0602466\pi$$
−0.328135 + 0.944631i $$0.606420\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −4.00000 −0.272798
$$216$$ 0 0
$$217$$ 14.0000 0.950382
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −5.00000 8.66025i −0.336336 0.582552i
$$222$$ 0 0
$$223$$ 5.00000 8.66025i 0.334825 0.579934i −0.648626 0.761107i $$-0.724656\pi$$
0.983451 + 0.181173i $$0.0579895\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 1.50000 2.59808i 0.0995585 0.172440i −0.811943 0.583736i $$-0.801590\pi$$
0.911502 + 0.411296i $$0.134924\pi$$
$$228$$ 0 0
$$229$$ 14.5000 + 25.1147i 0.958187 + 1.65963i 0.726900 + 0.686743i $$0.240960\pi$$
0.231287 + 0.972886i $$0.425707\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −6.00000 −0.393073 −0.196537 0.980497i $$-0.562969\pi$$
−0.196537 + 0.980497i $$0.562969\pi$$
$$234$$ 0 0
$$235$$ 4.00000 0.260931
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −3.00000 5.19615i −0.194054 0.336111i 0.752536 0.658551i $$-0.228830\pi$$
−0.946590 + 0.322440i $$0.895497\pi$$
$$240$$ 0 0
$$241$$ −5.50000 + 9.52628i −0.354286 + 0.613642i −0.986996 0.160748i $$-0.948609\pi$$
0.632709 + 0.774389i $$0.281943\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −1.50000 + 2.59808i −0.0958315 + 0.165985i
$$246$$ 0 0
$$247$$ −5.00000 8.66025i −0.318142 0.551039i
$$248$$ 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
$$253$$ 4.00000 0.251478
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 13.5000 + 23.3827i 0.842107 + 1.45857i 0.888110 + 0.459631i $$0.152018\pi$$
−0.0460033 + 0.998941i $$0.514648\pi$$
$$258$$ 0 0
$$259$$ 6.00000 10.3923i 0.372822 0.645746i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −12.0000 + 20.7846i −0.739952 + 1.28163i 0.212565 + 0.977147i $$0.431818\pi$$
−0.952517 + 0.304487i $$0.901515\pi$$
$$264$$ 0 0
$$265$$ −4.50000 7.79423i −0.276433 0.478796i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 10.0000 0.609711 0.304855 0.952399i $$-0.401392\pi$$
0.304855 + 0.952399i $$0.401392\pi$$
$$270$$ 0 0
$$271$$ −9.00000 −0.546711 −0.273356 0.961913i $$-0.588134\pi$$
−0.273356 + 0.961913i $$0.588134\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 2.00000 + 3.46410i 0.120605 + 0.208893i
$$276$$ 0 0
$$277$$ 2.00000 3.46410i 0.120168 0.208138i −0.799666 0.600446i $$-0.794990\pi$$
0.919834 + 0.392308i $$0.128323\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −7.00000 + 12.1244i −0.417585 + 0.723278i −0.995696 0.0926797i $$-0.970457\pi$$
0.578111 + 0.815958i $$0.303790\pi$$
$$282$$ 0 0
$$283$$ −4.00000 6.92820i −0.237775 0.411839i 0.722300 0.691580i $$-0.243085\pi$$
−0.960076 + 0.279741i $$0.909752\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 8.00000 0.470588
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 3.50000 + 6.06218i 0.204472 + 0.354156i 0.949964 0.312358i $$-0.101119\pi$$
−0.745492 + 0.666514i $$0.767786\pi$$
$$294$$ 0 0
$$295$$ −7.00000 + 12.1244i −0.407556 + 0.705907i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −1.00000 + 1.73205i −0.0578315 + 0.100167i
$$300$$ 0 0
$$301$$ −4.00000 6.92820i −0.230556 0.399335i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 11.0000 0.629858
$$306$$ 0 0
$$307$$ 22.0000 1.25561 0.627803 0.778372i $$-0.283954\pi$$
0.627803 + 0.778372i $$0.283954\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −11.0000 19.0526i −0.623753 1.08037i −0.988781 0.149375i $$-0.952274\pi$$
0.365028 0.930997i $$-0.381059\pi$$
$$312$$ 0 0
$$313$$ −4.00000 + 6.92820i −0.226093 + 0.391605i −0.956647 0.291250i $$-0.905929\pi$$
0.730554 + 0.682855i $$0.239262\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −13.5000 + 23.3827i −0.758236 + 1.31330i 0.185514 + 0.982642i $$0.440605\pi$$
−0.943750 + 0.330661i $$0.892728\pi$$
$$318$$ 0 0
$$319$$ 4.00000 + 6.92820i 0.223957 + 0.387905i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 25.0000 1.39104
$$324$$ 0 0
$$325$$ −2.00000 −0.110940
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 4.00000 + 6.92820i 0.220527 + 0.381964i
$$330$$ 0 0
$$331$$ −6.00000 + 10.3923i −0.329790 + 0.571213i −0.982470 0.186421i $$-0.940311\pi$$
0.652680 + 0.757634i $$0.273645\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 7.00000 12.1244i 0.382451 0.662424i
$$336$$ 0 0
$$337$$ −11.0000 19.0526i −0.599208 1.03786i −0.992938 0.118633i $$-0.962149\pi$$
0.393730 0.919226i $$-0.371184\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −28.0000 −1.51629
$$342$$ 0 0
$$343$$ −20.0000 −1.07990
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 10.0000 + 17.3205i 0.536828 + 0.929814i 0.999072 + 0.0430610i $$0.0137110\pi$$
−0.462244 + 0.886753i $$0.652956\pi$$
$$348$$ 0 0
$$349$$ 1.50000 2.59808i 0.0802932 0.139072i −0.823083 0.567922i $$-0.807748\pi$$
0.903376 + 0.428850i $$0.141081\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 13.0000 22.5167i 0.691920 1.19844i −0.279288 0.960207i $$-0.590098\pi$$
0.971208 0.238233i $$-0.0765683\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −18.0000 −0.950004 −0.475002 0.879985i $$-0.657553\pi$$
−0.475002 + 0.879985i $$0.657553\pi$$
$$360$$ 0 0
$$361$$ 6.00000 0.315789
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −6.00000 10.3923i −0.314054 0.543958i
$$366$$ 0 0
$$367$$ 11.0000 19.0526i 0.574195 0.994535i −0.421933 0.906627i $$-0.638648\pi$$
0.996129 0.0879086i $$-0.0280183\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 9.00000 15.5885i 0.467257 0.809312i
$$372$$ 0 0
$$373$$ 16.0000 + 27.7128i 0.828449 + 1.43492i 0.899255 + 0.437425i $$0.144109\pi$$
−0.0708063 + 0.997490i $$0.522557\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −4.00000 −0.206010
$$378$$ 0 0
$$379$$ −23.0000 −1.18143 −0.590715 0.806880i $$-0.701154\pi$$
−0.590715 + 0.806880i $$0.701154\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −13.5000 23.3827i −0.689818 1.19480i −0.971897 0.235408i $$-0.924357\pi$$
0.282079 0.959391i $$-0.408976\pi$$
$$384$$ 0 0
$$385$$ −4.00000 + 6.92820i −0.203859 + 0.353094i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −18.0000 + 31.1769i −0.912636 + 1.58073i −0.102311 + 0.994753i $$0.532624\pi$$
−0.810326 + 0.585980i $$0.800710\pi$$
$$390$$ 0 0
$$391$$ −2.50000 4.33013i −0.126430 0.218984i
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 3.00000 0.150946
$$396$$ 0 0
$$397$$ −14.0000 −0.702640 −0.351320 0.936255i $$-0.614267\pi$$
−0.351320 + 0.936255i $$0.614267\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −15.0000 25.9808i −0.749064 1.29742i −0.948272 0.317460i $$-0.897170\pi$$
0.199207 0.979957i $$-0.436163\pi$$
$$402$$ 0 0
$$403$$ 7.00000 12.1244i 0.348695 0.603957i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −12.0000 + 20.7846i −0.594818 + 1.03025i
$$408$$ 0 0
$$409$$ −12.5000 21.6506i −0.618085 1.07056i −0.989835 0.142222i $$-0.954575\pi$$
0.371750 0.928333i $$-0.378758\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −28.0000 −1.37779
$$414$$ 0 0
$$415$$ −1.00000 −0.0490881
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 18.0000 + 31.1769i 0.879358 + 1.52309i 0.852047 + 0.523465i $$0.175361\pi$$
0.0273103 + 0.999627i $$0.491306\pi$$
$$420$$ 0 0
$$421$$ −1.50000 + 2.59808i −0.0731055 + 0.126622i −0.900261 0.435351i $$-0.856624\pi$$
0.827155 + 0.561973i $$0.189958\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 2.50000 4.33013i 0.121268 0.210042i
$$426$$ 0 0
$$427$$ 11.0000 + 19.0526i 0.532327 + 0.922018i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −14.0000 −0.674356 −0.337178 0.941441i $$-0.609472\pi$$
−0.337178 + 0.941441i $$0.609472\pi$$
$$432$$ 0 0
$$433$$ 26.0000 1.24948 0.624740 0.780833i $$-0.285205\pi$$
0.624740 + 0.780833i $$0.285205\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −2.50000 4.33013i −0.119591 0.207138i
$$438$$ 0 0
$$439$$ 8.50000 14.7224i 0.405683 0.702663i −0.588718 0.808339i $$-0.700367\pi$$
0.994401 + 0.105675i $$0.0337004\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 19.5000 33.7750i 0.926473 1.60470i 0.137298 0.990530i $$-0.456158\pi$$
0.789175 0.614168i $$-0.210508\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −6.00000 −0.283158 −0.141579 0.989927i $$-0.545218\pi$$
−0.141579 + 0.989927i $$0.545218\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −2.00000 3.46410i −0.0937614 0.162400i
$$456$$ 0 0
$$457$$ −14.0000 + 24.2487i −0.654892 + 1.13431i 0.327028 + 0.945015i $$0.393953\pi$$
−0.981921 + 0.189292i $$0.939381\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 21.0000 36.3731i 0.978068 1.69406i 0.308651 0.951175i $$-0.400123\pi$$
0.669417 0.742887i $$-0.266544\pi$$
$$462$$ 0 0
$$463$$ 9.00000 + 15.5885i 0.418265 + 0.724457i 0.995765 0.0919339i $$-0.0293048\pi$$
−0.577500 + 0.816391i $$0.695972\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 13.0000 0.601568 0.300784 0.953692i $$-0.402752\pi$$
0.300784 + 0.953692i $$0.402752\pi$$
$$468$$ 0 0
$$469$$ 28.0000 1.29292
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 8.00000 + 13.8564i 0.367840 + 0.637118i
$$474$$ 0 0
$$475$$ 2.50000 4.33013i 0.114708 0.198680i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 14.0000 24.2487i 0.639676 1.10795i −0.345827 0.938298i $$-0.612402\pi$$
0.985504 0.169654i $$-0.0542649\pi$$
$$480$$ 0 0
$$481$$ −6.00000 10.3923i −0.273576 0.473848i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −16.0000 −0.726523
$$486$$ 0 0
$$487$$ 40.0000 1.81257 0.906287 0.422664i $$-0.138905\pi$$
0.906287 + 0.422664i $$0.138905\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −3.00000 5.19615i −0.135388 0.234499i 0.790358 0.612646i $$-0.209895\pi$$
−0.925746 + 0.378147i $$0.876561\pi$$
$$492$$ 0 0
$$493$$ 5.00000 8.66025i 0.225189 0.390038i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 12.5000 + 21.6506i 0.559577 + 0.969216i 0.997532 + 0.0702185i $$0.0223697\pi$$
−0.437955 + 0.898997i $$0.644297\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 15.0000 0.668817 0.334408 0.942428i $$-0.391463\pi$$
0.334408 + 0.942428i $$0.391463\pi$$
$$504$$ 0 0
$$505$$ 12.0000 0.533993
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 14.0000 + 24.2487i 0.620539 + 1.07481i 0.989385 + 0.145315i $$0.0464195\pi$$
−0.368846 + 0.929490i $$0.620247\pi$$
$$510$$ 0 0
$$511$$ 12.0000 20.7846i 0.530849 0.919457i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 2.00000 3.46410i 0.0881305 0.152647i
$$516$$ 0 0
$$517$$ −8.00000 13.8564i −0.351840 0.609404i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −40.0000 −1.75243 −0.876216 0.481919i $$-0.839940\pi$$
−0.876216 + 0.481919i $$0.839940\pi$$
$$522$$ 0 0
$$523$$ 10.0000 0.437269 0.218635 0.975807i $$-0.429840\pi$$
0.218635 + 0.975807i $$0.429840\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 17.5000 + 30.3109i 0.762312 + 1.32036i
$$528$$ 0 0
$$529$$ 11.0000 19.0526i 0.478261 0.828372i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 6.00000 + 10.3923i 0.259403 + 0.449299i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 12.0000 0.516877
$$540$$ 0 0
$$541$$ 22.0000 0.945854 0.472927 0.881102i $$-0.343197\pi$$
0.472927 + 0.881102i $$0.343197\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −9.50000 16.4545i −0.406935 0.704833i
$$546$$ 0 0
$$547$$ 14.0000 24.2487i 0.598597 1.03680i −0.394432 0.918925i $$-0.629059\pi$$
0.993028 0.117875i $$-0.0376081\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 5.00000 8.66025i 0.213007 0.368939i
$$552$$ 0 0
$$553$$ 3.00000 + 5.19615i 0.127573 + 0.220963i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 10.0000 0.423714 0.211857 0.977301i $$-0.432049\pi$$
0.211857 + 0.977301i $$0.432049\pi$$
$$558$$ 0 0
$$559$$ −8.00000 −0.338364
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 2.00000 + 3.46410i 0.0842900 + 0.145994i 0.905088 0.425223i $$-0.139804\pi$$
−0.820798 + 0.571218i $$0.806471\pi$$
$$564$$ 0 0
$$565$$ −3.00000 + 5.19615i −0.126211 + 0.218604i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −5.00000 + 8.66025i −0.209611 + 0.363057i −0.951592 0.307364i $$-0.900553\pi$$
0.741981 + 0.670421i $$0.233886\pi$$
$$570$$ 0 0
$$571$$ 2.50000 + 4.33013i 0.104622 + 0.181210i 0.913584 0.406651i $$-0.133303\pi$$
−0.808962 + 0.587861i $$0.799970\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −1.00000 −0.0417029
$$576$$ 0 0
$$577$$ −16.0000 −0.666089 −0.333044 0.942911i $$-0.608076\pi$$
−0.333044 + 0.942911i $$0.608076\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −1.00000 1.73205i −0.0414870 0.0718576i
$$582$$ 0 0
$$583$$ −18.0000 + 31.1769i −0.745484 + 1.29122i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −7.50000 + 12.9904i −0.309558 + 0.536170i −0.978266 0.207355i $$-0.933514\pi$$
0.668708 + 0.743525i $$0.266848\pi$$
$$588$$ 0 0
$$589$$ 17.5000 + 30.3109i 0.721075 + 1.24894i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 9.00000 0.369586 0.184793 0.982777i $$-0.440839\pi$$
0.184793 + 0.982777i $$0.440839\pi$$
$$594$$ 0 0
$$595$$ 10.0000 0.409960
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 9.00000 + 15.5885i 0.367730 + 0.636927i 0.989210 0.146503i $$-0.0468017\pi$$
−0.621480 + 0.783430i $$0.713468\pi$$
$$600$$ 0 0
$$601$$ 5.50000 9.52628i 0.224350 0.388585i −0.731774 0.681547i $$-0.761308\pi$$
0.956124 + 0.292962i $$0.0946409\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 2.50000 4.33013i 0.101639 0.176045i
$$606$$ 0 0
$$607$$ 18.0000 + 31.1769i 0.730597 + 1.26543i 0.956628 + 0.291312i $$0.0940917\pi$$
−0.226031 + 0.974120i $$0.572575\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 8.00000 0.323645
$$612$$ 0 0
$$613$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 16.5000 + 28.5788i 0.664265 + 1.15054i 0.979484 + 0.201522i $$0.0645887\pi$$
−0.315219 + 0.949019i $$0.602078\pi$$
$$618$$ 0 0
$$619$$ −16.0000 + 27.7128i −0.643094 + 1.11387i 0.341644 + 0.939829i $$0.389016\pi$$
−0.984738 + 0.174042i $$0.944317\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −0.500000 0.866025i −0.0200000 0.0346410i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 30.0000 1.19618
$$630$$ 0 0
$$631$$ 13.0000 0.517522 0.258761 0.965941i $$-0.416686\pi$$
0.258761 + 0.965941i $$0.416686\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 3.00000 + 5.19615i 0.119051 + 0.206203i
$$636$$ 0 0
$$637$$ −3.00000 + 5.19615i −0.118864 + 0.205879i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$642$$ 0 0
$$643$$ −3.00000 5.19615i −0.118308 0.204916i 0.800789 0.598947i $$-0.204414\pi$$
−0.919097 + 0.394030i $$0.871080\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −33.0000 −1.29736 −0.648682 0.761060i $$-0.724679\pi$$
−0.648682 + 0.761060i $$0.724679\pi$$
$$648$$ 0 0
$$649$$ 56.0000 2.19819
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 20.5000 + 35.5070i 0.802227 + 1.38950i 0.918147 + 0.396239i $$0.129685\pi$$
−0.115920 + 0.993259i $$0.536982\pi$$
$$654$$ 0 0
$$655$$ 9.00000 15.5885i 0.351659 0.609091i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 9.00000 15.5885i 0.350590 0.607240i −0.635763 0.771885i $$-0.719314\pi$$
0.986353 + 0.164644i $$0.0526477\pi$$
$$660$$ 0 0
$$661$$ 21.0000 + 36.3731i 0.816805 + 1.41475i 0.908024 + 0.418917i $$0.137590\pi$$
−0.0912190 + 0.995831i $$0.529076\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 10.0000 0.387783
$$666$$ 0 0
$$667$$ −2.00000 −0.0774403
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −22.0000 38.1051i −0.849301 1.47103i
$$672$$ 0 0
$$673$$ −15.0000 + 25.9808i −0.578208 + 1.00148i 0.417477 + 0.908687i $$0.362914\pi$$
−0.995685 + 0.0927975i $$0.970419\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −1.00000 + 1.73205i −0.0384331 + 0.0665681i −0.884602 0.466347i $$-0.845570\pi$$
0.846169 + 0.532915i $$0.178903\pi$$
$$678$$ 0 0
$$679$$ −16.0000 27.7128i −0.614024 1.06352i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 9.00000 0.344375 0.172188 0.985064i $$-0.444916\pi$$
0.172188 + 0.985064i $$0.444916\pi$$
$$684$$ 0 0
$$685$$ −17.0000 −0.649537
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −9.00000 15.5885i −0.342873 0.593873i
$$690$$ 0 0
$$691$$ 9.50000 16.4545i 0.361397 0.625958i −0.626794 0.779185i $$-0.715633\pi$$
0.988191 + 0.153227i $$0.0489666\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 6.00000 10.3923i 0.227593 0.394203i
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 10.0000 0.377695 0.188847 0.982006i $$-0.439525\pi$$
0.188847 + 0.982006i $$0.439525\pi$$
$$702$$ 0 0
$$703$$ 30.0000 1.13147
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 12.0000 + 20.7846i 0.451306 + 0.781686i
$$708$$ 0 0
$$709$$ −13.0000 + 22.5167i −0.488225 + 0.845631i −0.999908 0.0135434i $$-0.995689\pi$$
0.511683 + 0.859174i $$0.329022\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 3.50000 6.06218i 0.131076 0.227030i
$$714$$ 0 0
$$715$$ 4.00000 + 6.92820i 0.149592 + 0.259100i
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −46.0000 −1.71551 −0.857755 0.514058i $$-0.828142\pi$$
−0.857755 + 0.514058i $$0.828142\pi$$
$$720$$ 0 0
$$721$$ 8.00000 0.297936
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −1.00000 1.73205i −0.0371391 0.0643268i
$$726$$ 0 0
$$727$$ −16.0000 + 27.7128i −0.593407 + 1.02781i 0.400362 + 0.916357i $$0.368884\pi$$
−0.993770 + 0.111454i $$0.964449\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 10.0000 17.3205i 0.369863 0.640622i
$$732$$ 0 0
$$733$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −56.0000 −2.06279
$$738$$ 0 0
$$739$$ −15.0000 −0.551784 −0.275892 0.961189i $$-0.588973\pi$$
−0.275892 + 0.961189i $$0.588973\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$744$$ 0 0
$$745$$ 8.00000 13.8564i 0.293097 0.507659i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −12.0000 + 20.7846i −0.438470 + 0.759453i
$$750$$ 0 0
$$751$$ 1.50000 + 2.59808i 0.0547358 + 0.0948051i 0.892095 0.451848i $$-0.149235\pi$$
−0.837359 + 0.546653i $$0.815902\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −8.00000 −0.291150
$$756$$ 0 0
$$757$$ 2.00000 0.0726912 0.0363456 0.999339i $$-0.488428\pi$$
0.0363456 + 0.999339i $$0.488428\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −15.0000 25.9808i −0.543750 0.941802i −0.998684 0.0512772i $$-0.983671\pi$$
0.454935 0.890525i $$-0.349663\pi$$
$$762$$ 0 0
$$763$$ 19.0000 32.9090i 0.687846 1.19138i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −14.0000 + 24.2487i −0.505511 + 0.875570i
$$768$$ 0 0
$$769$$ 17.5000 + 30.3109i 0.631066 + 1.09304i 0.987334 + 0.158655i $$0.0507157\pi$$
−0.356268 + 0.934384i $$0.615951\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 15.0000 0.539513 0.269756 0.962929i $$-0.413057\pi$$
0.269756 + 0.962929i $$0.413057\pi$$
$$774$$ 0 0
$$775$$ 7.00000 0.251447
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 8.00000 13.8564i 0.285532 0.494556i
$$786$$ 0 0
$$787$$ 20.0000 + 34.6410i 0.712923 + 1.23482i 0.963755 + 0.266788i $$0.0859624\pi$$
−0.250832 + 0.968031i $$0.580704\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −12.0000 −0.426671
$$792$$ 0 0
$$793$$ 22.0000 0.781243
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 1.50000 + 2.59808i 0.0531327 + 0.0920286i 0.891368 0.453279i $$-0.149746\pi$$
−0.838236 + 0.545308i $$0.816413\pi$$