# Properties

 Label 1152.2.k.f.289.2 Level $1152$ Weight $2$ Character 1152.289 Analytic conductor $9.199$ Analytic rank $0$ Dimension $8$ CM no Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1152,2,Mod(289,1152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1152, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("1152.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1152 = 2^{7} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1152.k (of order $$4$$, 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: $$9.19876631285$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(i)$$ Coefficient field: 8.0.18939904.2 comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2$$ x^8 - 4*x^7 + 14*x^6 - 28*x^5 + 43*x^4 - 44*x^3 + 30*x^2 - 12*x + 2 Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$2^{6}$$ Twist minimal: no (minimal twist has level 48) Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 289.2 Root $$0.500000 + 1.44392i$$ of defining polynomial Character $$\chi$$ $$=$$ 1152.289 Dual form 1152.2.k.f.865.2

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-0.334904 + 0.334904i) q^{5} +4.55765i q^{7} +O(q^{10})$$ $$q+(-0.334904 + 0.334904i) q^{5} +4.55765i q^{7} +(2.47363 - 2.47363i) q^{11} +(0.0594122 + 0.0594122i) q^{13} -3.61706 q^{17} +(2.55765 + 2.55765i) q^{19} +2.82843i q^{23} +4.77568i q^{25} +(-5.16333 - 5.16333i) q^{29} +0.557647 q^{31} +(-1.52637 - 1.52637i) q^{35} +(-4.38607 + 4.38607i) q^{37} +9.27391i q^{41} +(-1.61040 + 1.61040i) q^{43} +2.82843 q^{47} -13.7721 q^{49} +(-0.493523 + 0.493523i) q^{53} +1.65685i q^{55} +(-4.00000 + 4.00000i) q^{59} +(-2.72922 - 2.72922i) q^{61} -0.0397948 q^{65} +(3.77568 + 3.77568i) q^{67} +9.11529i q^{71} -0.541560i q^{73} +(11.2739 + 11.2739i) q^{77} +10.9937 q^{79} +(10.6417 + 10.6417i) q^{83} +(1.21137 - 1.21137i) q^{85} -14.6533i q^{89} +(-0.270780 + 0.270780i) q^{91} -1.71313 q^{95} +4.31724 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q+O(q^{10})$$ 8 * q $$8 q + 8 q^{11} - 8 q^{19} - 16 q^{29} - 24 q^{31} - 24 q^{35} + 16 q^{37} - 8 q^{43} - 8 q^{49} + 16 q^{53} - 32 q^{59} - 16 q^{61} + 16 q^{65} - 16 q^{67} + 16 q^{77} + 24 q^{79} + 40 q^{83} + 16 q^{85} - 8 q^{91} - 48 q^{95}+O(q^{100})$$ 8 * q + 8 * q^11 - 8 * q^19 - 16 * q^29 - 24 * q^31 - 24 * q^35 + 16 * q^37 - 8 * q^43 - 8 * q^49 + 16 * q^53 - 32 * q^59 - 16 * q^61 + 16 * q^65 - 16 * q^67 + 16 * q^77 + 24 * q^79 + 40 * q^83 + 16 * q^85 - 8 * q^91 - 48 * q^95

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$641$$ $$901$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{3}{4}\right)$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0 0
$$4$$ 0 0
$$5$$ −0.334904 + 0.334904i −0.149774 + 0.149774i −0.778017 0.628243i $$-0.783774\pi$$
0.628243 + 0.778017i $$0.283774\pi$$
$$6$$ 0 0
$$7$$ 4.55765i 1.72263i 0.508072 + 0.861314i $$0.330358\pi$$
−0.508072 + 0.861314i $$0.669642\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 2.47363 2.47363i 0.745826 0.745826i −0.227866 0.973692i $$-0.573175\pi$$
0.973692 + 0.227866i $$0.0731749\pi$$
$$12$$ 0 0
$$13$$ 0.0594122 + 0.0594122i 0.0164780 + 0.0164780i 0.715298 0.698820i $$-0.246291\pi$$
−0.698820 + 0.715298i $$0.746291\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −3.61706 −0.877266 −0.438633 0.898666i $$-0.644537\pi$$
−0.438633 + 0.898666i $$0.644537\pi$$
$$18$$ 0 0
$$19$$ 2.55765 + 2.55765i 0.586765 + 0.586765i 0.936754 0.349989i $$-0.113815\pi$$
−0.349989 + 0.936754i $$0.613815\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 2.82843i 0.589768i 0.955533 + 0.294884i $$0.0952810\pi$$
−0.955533 + 0.294884i $$0.904719\pi$$
$$24$$ 0 0
$$25$$ 4.77568i 0.955136i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −5.16333 5.16333i −0.958807 0.958807i 0.0403780 0.999184i $$-0.487144\pi$$
−0.999184 + 0.0403780i $$0.987144\pi$$
$$30$$ 0 0
$$31$$ 0.557647 0.100156 0.0500782 0.998745i $$-0.484053\pi$$
0.0500782 + 0.998745i $$0.484053\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −1.52637 1.52637i −0.258004 0.258004i
$$36$$ 0 0
$$37$$ −4.38607 + 4.38607i −0.721066 + 0.721066i −0.968822 0.247756i $$-0.920307\pi$$
0.247756 + 0.968822i $$0.420307\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 9.27391i 1.44834i 0.689620 + 0.724171i $$0.257777\pi$$
−0.689620 + 0.724171i $$0.742223\pi$$
$$42$$ 0 0
$$43$$ −1.61040 + 1.61040i −0.245583 + 0.245583i −0.819155 0.573572i $$-0.805557\pi$$
0.573572 + 0.819155i $$0.305557\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 2.82843 0.412568 0.206284 0.978492i $$-0.433863\pi$$
0.206284 + 0.978492i $$0.433863\pi$$
$$48$$ 0 0
$$49$$ −13.7721 −1.96745
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −0.493523 + 0.493523i −0.0677906 + 0.0677906i −0.740189 0.672399i $$-0.765264\pi$$
0.672399 + 0.740189i $$0.265264\pi$$
$$54$$ 0 0
$$55$$ 1.65685i 0.223410i
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −4.00000 + 4.00000i −0.520756 + 0.520756i −0.917800 0.397044i $$-0.870036\pi$$
0.397044 + 0.917800i $$0.370036\pi$$
$$60$$ 0 0
$$61$$ −2.72922 2.72922i −0.349441 0.349441i 0.510460 0.859901i $$-0.329475\pi$$
−0.859901 + 0.510460i $$0.829475\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −0.0397948 −0.00493593
$$66$$ 0 0
$$67$$ 3.77568 + 3.77568i 0.461273 + 0.461273i 0.899072 0.437800i $$-0.144242\pi$$
−0.437800 + 0.899072i $$0.644242\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 9.11529i 1.08179i 0.841091 + 0.540893i $$0.181914\pi$$
−0.841091 + 0.540893i $$0.818086\pi$$
$$72$$ 0 0
$$73$$ 0.541560i 0.0633848i −0.999498 0.0316924i $$-0.989910\pi$$
0.999498 0.0316924i $$-0.0100897\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 11.2739 + 11.2739i 1.28478 + 1.28478i
$$78$$ 0 0
$$79$$ 10.9937 1.23689 0.618445 0.785828i $$-0.287763\pi$$
0.618445 + 0.785828i $$0.287763\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 10.6417 + 10.6417i 1.16807 + 1.16807i 0.982660 + 0.185415i $$0.0593628\pi$$
0.185415 + 0.982660i $$0.440637\pi$$
$$84$$ 0 0
$$85$$ 1.21137 1.21137i 0.131391 0.131391i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 14.6533i 1.55325i −0.629964 0.776625i $$-0.716930\pi$$
0.629964 0.776625i $$-0.283070\pi$$
$$90$$ 0 0
$$91$$ −0.270780 + 0.270780i −0.0283854 + 0.0283854i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −1.71313 −0.175764
$$96$$ 0 0
$$97$$ 4.31724 0.438349 0.219175 0.975686i $$-0.429664\pi$$
0.219175 + 0.975686i $$0.429664\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −0.453728 + 0.453728i −0.0451477 + 0.0451477i −0.729320 0.684173i $$-0.760164\pi$$
0.684173 + 0.729320i $$0.260164\pi$$
$$102$$ 0 0
$$103$$ 1.33686i 0.131724i −0.997829 0.0658622i $$-0.979020\pi$$
0.997829 0.0658622i $$-0.0209798\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −6.06255 + 6.06255i −0.586088 + 0.586088i −0.936570 0.350481i $$-0.886018\pi$$
0.350481 + 0.936570i $$0.386018\pi$$
$$108$$ 0 0
$$109$$ −5.71627 5.71627i −0.547519 0.547519i 0.378203 0.925722i $$-0.376542\pi$$
−0.925722 + 0.378203i $$0.876542\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 9.55136 0.898516 0.449258 0.893402i $$-0.351688\pi$$
0.449258 + 0.893402i $$0.351688\pi$$
$$114$$ 0 0
$$115$$ −0.947252 0.947252i −0.0883317 0.0883317i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 16.4853i 1.51120i
$$120$$ 0 0
$$121$$ 1.23765i 0.112514i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −3.27391 3.27391i −0.292828 0.292828i
$$126$$ 0 0
$$127$$ −5.09921 −0.452481 −0.226241 0.974071i $$-0.572644\pi$$
−0.226241 + 0.974071i $$0.572644\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −2.11882 2.11882i −0.185123 0.185123i 0.608461 0.793584i $$-0.291787\pi$$
−0.793584 + 0.608461i $$0.791787\pi$$
$$132$$ 0 0
$$133$$ −11.6569 + 11.6569i −1.01078 + 1.01078i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 3.37941i 0.288723i 0.989525 + 0.144361i $$0.0461127\pi$$
−0.989525 + 0.144361i $$0.953887\pi$$
$$138$$ 0 0
$$139$$ 5.88118 5.88118i 0.498835 0.498835i −0.412240 0.911075i $$-0.635254\pi$$
0.911075 + 0.412240i $$0.135254\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0.293927 0.0245794
$$144$$ 0 0
$$145$$ 3.45844 0.287208
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −9.99176 + 9.99176i −0.818557 + 0.818557i −0.985899 0.167342i $$-0.946482\pi$$
0.167342 + 0.985899i $$0.446482\pi$$
$$150$$ 0 0
$$151$$ 9.97685i 0.811905i −0.913894 0.405952i $$-0.866940\pi$$
0.913894 0.405952i $$-0.133060\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −0.186758 + 0.186758i −0.0150008 + 0.0150008i
$$156$$ 0 0
$$157$$ 16.1618 + 16.1618i 1.28985 + 1.28985i 0.934877 + 0.354971i $$0.115509\pi$$
0.354971 + 0.934877i $$0.384491\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −12.8910 −1.01595
$$162$$ 0 0
$$163$$ −7.50490 7.50490i −0.587829 0.587829i 0.349214 0.937043i $$-0.386449\pi$$
−0.937043 + 0.349214i $$0.886449\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 5.83822i 0.451775i −0.974153 0.225888i $$-0.927472\pi$$
0.974153 0.225888i $$-0.0725282\pi$$
$$168$$ 0 0
$$169$$ 12.9929i 0.999457i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −3.62530 3.62530i −0.275627 0.275627i 0.555734 0.831360i $$-0.312437\pi$$
−0.831360 + 0.555734i $$0.812437\pi$$
$$174$$ 0 0
$$175$$ −21.7659 −1.64534
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −9.28334 9.28334i −0.693869 0.693869i 0.269212 0.963081i $$-0.413237\pi$$
−0.963081 + 0.269212i $$0.913237\pi$$
$$180$$ 0 0
$$181$$ 10.8316 10.8316i 0.805104 0.805104i −0.178785 0.983888i $$-0.557217\pi$$
0.983888 + 0.178785i $$0.0572165\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 2.93783i 0.215993i
$$186$$ 0 0
$$187$$ −8.94725 + 8.94725i −0.654288 + 0.654288i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −8.63001 −0.624446 −0.312223 0.950009i $$-0.601074\pi$$
−0.312223 + 0.950009i $$0.601074\pi$$
$$192$$ 0 0
$$193$$ 11.4514 0.824288 0.412144 0.911119i $$-0.364780\pi$$
0.412144 + 0.911119i $$0.364780\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 7.48999 7.48999i 0.533640 0.533640i −0.388014 0.921654i $$-0.626839\pi$$
0.921654 + 0.388014i $$0.126839\pi$$
$$198$$ 0 0
$$199$$ 3.68000i 0.260868i 0.991457 + 0.130434i $$0.0416371\pi$$
−0.991457 + 0.130434i $$0.958363\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 23.5326 23.5326i 1.65167 1.65167i
$$204$$ 0 0
$$205$$ −3.10587 3.10587i −0.216923 0.216923i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 12.6533 0.875249
$$210$$ 0 0
$$211$$ 10.1188 + 10.1188i 0.696609 + 0.696609i 0.963677 0.267069i $$-0.0860551\pi$$
−0.267069 + 0.963677i $$0.586055\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 1.07866i 0.0735637i
$$216$$ 0 0
$$217$$ 2.54156i 0.172532i
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −0.214897 0.214897i −0.0144556 0.0144556i
$$222$$ 0 0
$$223$$ 4.86156 0.325554 0.162777 0.986663i $$-0.447955\pi$$
0.162777 + 0.986663i $$0.447955\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −10.6417 10.6417i −0.706312 0.706312i 0.259445 0.965758i $$-0.416460\pi$$
−0.965758 + 0.259445i $$0.916460\pi$$
$$228$$ 0 0
$$229$$ 20.1712 20.1712i 1.33295 1.33295i 0.430229 0.902720i $$-0.358433\pi$$
0.902720 0.430229i $$-0.141567\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 13.5702i 0.889014i −0.895775 0.444507i $$-0.853379\pi$$
0.895775 0.444507i $$-0.146621\pi$$
$$234$$ 0 0
$$235$$ −0.947252 + 0.947252i −0.0617919 + 0.0617919i
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 29.3629 1.89933 0.949665 0.313267i $$-0.101424\pi$$
0.949665 + 0.313267i $$0.101424\pi$$
$$240$$ 0 0
$$241$$ 24.0063 1.54638 0.773190 0.634175i $$-0.218660\pi$$
0.773190 + 0.634175i $$0.218660\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 4.61235 4.61235i 0.294672 0.294672i
$$246$$ 0 0
$$247$$ 0.303911i 0.0193374i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −15.7570 + 15.7570i −0.994571 + 0.994571i −0.999985 0.00541463i $$-0.998276\pi$$
0.00541463 + 0.999985i $$0.498276\pi$$
$$252$$ 0 0
$$253$$ 6.99647 + 6.99647i 0.439864 + 0.439864i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −8.66038 −0.540220 −0.270110 0.962829i $$-0.587060\pi$$
−0.270110 + 0.962829i $$0.587060\pi$$
$$258$$ 0 0
$$259$$ −19.9902 19.9902i −1.24213 1.24213i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 13.3208i 0.821394i 0.911772 + 0.410697i $$0.134715\pi$$
−0.911772 + 0.410697i $$0.865285\pi$$
$$264$$ 0 0
$$265$$ 0.330566i 0.0203065i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −11.6714 11.6714i −0.711616 0.711616i 0.255257 0.966873i $$-0.417840\pi$$
−0.966873 + 0.255257i $$0.917840\pi$$
$$270$$ 0 0
$$271$$ 21.9769 1.33500 0.667499 0.744610i $$-0.267365\pi$$
0.667499 + 0.744610i $$0.267365\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 11.8132 + 11.8132i 0.712365 + 0.712365i
$$276$$ 0 0
$$277$$ 10.9504 10.9504i 0.657945 0.657945i −0.296949 0.954893i $$-0.595969\pi$$
0.954893 + 0.296949i $$0.0959690\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 22.8910i 1.36556i 0.730624 + 0.682780i $$0.239229\pi$$
−0.730624 + 0.682780i $$0.760771\pi$$
$$282$$ 0 0
$$283$$ 4.48528 4.48528i 0.266622 0.266622i −0.561115 0.827738i $$-0.689628\pi$$
0.827738 + 0.561115i $$0.189628\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −42.2672 −2.49496
$$288$$ 0 0
$$289$$ −3.91688 −0.230405
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 21.6221 21.6221i 1.26318 1.26318i 0.313636 0.949543i $$-0.398453\pi$$
0.949543 0.313636i $$-0.101547\pi$$
$$294$$ 0 0
$$295$$ 2.67923i 0.155991i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −0.168043 + 0.168043i −0.00971818 + 0.00971818i
$$300$$ 0 0
$$301$$ −7.33962 7.33962i −0.423048 0.423048i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 1.82805 0.104674
$$306$$ 0 0
$$307$$ −12.1118 12.1118i −0.691255 0.691255i 0.271253 0.962508i $$-0.412562\pi$$
−0.962508 + 0.271253i $$0.912562\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 26.8651i 1.52338i −0.647943 0.761689i $$-0.724370\pi$$
0.647943 0.761689i $$-0.275630\pi$$
$$312$$ 0 0
$$313$$ 19.6890i 1.11289i 0.830885 + 0.556445i $$0.187835\pi$$
−0.830885 + 0.556445i $$0.812165\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 21.3447 + 21.3447i 1.19884 + 1.19884i 0.974515 + 0.224323i $$0.0720171\pi$$
0.224323 + 0.974515i $$0.427983\pi$$
$$318$$ 0 0
$$319$$ −25.5443 −1.43021
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −9.25116 9.25116i −0.514748 0.514748i
$$324$$ 0 0
$$325$$ −0.283734 + 0.283734i −0.0157387 + 0.0157387i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 12.8910i 0.710702i
$$330$$ 0 0
$$331$$ 14.6926 14.6926i 0.807576 0.807576i −0.176690 0.984266i $$-0.556539\pi$$
0.984266 + 0.176690i $$0.0565391\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −2.52898 −0.138173
$$336$$ 0 0
$$337$$ −23.0098 −1.25342 −0.626712 0.779251i $$-0.715600\pi$$
−0.626712 + 0.779251i $$0.715600\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 1.37941 1.37941i 0.0746993 0.0746993i
$$342$$ 0 0
$$343$$ 30.8651i 1.66656i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 10.9026 10.9026i 0.585284 0.585284i −0.351067 0.936350i $$-0.614181\pi$$
0.936350 + 0.351067i $$0.114181\pi$$
$$348$$ 0 0
$$349$$ −20.0563 20.0563i −1.07359 1.07359i −0.997068 0.0765186i $$-0.975620\pi$$
−0.0765186 0.997068i $$-0.524380\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 12.2117 0.649965 0.324983 0.945720i $$-0.394642\pi$$
0.324983 + 0.945720i $$0.394642\pi$$
$$354$$ 0 0
$$355$$ −3.05275 3.05275i −0.162023 0.162023i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 33.4780i 1.76690i 0.468522 + 0.883452i $$0.344786\pi$$
−0.468522 + 0.883452i $$0.655214\pi$$
$$360$$ 0 0
$$361$$ 5.91688i 0.311415i
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 0.181370 + 0.181370i 0.00949337 + 0.00949337i
$$366$$ 0 0
$$367$$ 0.702379 0.0366639 0.0183319 0.999832i $$-0.494164\pi$$
0.0183319 + 0.999832i $$0.494164\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −2.24930 2.24930i −0.116778 0.116778i
$$372$$ 0 0
$$373$$ −18.9598 + 18.9598i −0.981702 + 0.981702i −0.999836 0.0181339i $$-0.994227\pi$$
0.0181339 + 0.999836i $$0.494227\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0.613530i 0.0315984i
$$378$$ 0 0
$$379$$ −1.77844 + 1.77844i −0.0913523 + 0.0913523i −0.751306 0.659954i $$-0.770576\pi$$
0.659954 + 0.751306i $$0.270576\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 25.4880 1.30238 0.651188 0.758916i $$-0.274271\pi$$
0.651188 + 0.758916i $$0.274271\pi$$
$$384$$ 0 0
$$385$$ −7.55136 −0.384853
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −11.7049 + 11.7049i −0.593462 + 0.593462i −0.938565 0.345103i $$-0.887844\pi$$
0.345103 + 0.938565i $$0.387844\pi$$
$$390$$ 0 0
$$391$$ 10.2306i 0.517383i
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −3.68184 + 3.68184i −0.185253 + 0.185253i
$$396$$ 0 0
$$397$$ 9.04646 + 9.04646i 0.454029 + 0.454029i 0.896689 0.442661i $$-0.145965\pi$$
−0.442661 + 0.896689i $$0.645965\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 18.0853 0.903137 0.451568 0.892237i $$-0.350865\pi$$
0.451568 + 0.892237i $$0.350865\pi$$
$$402$$ 0 0
$$403$$ 0.0331311 + 0.0331311i 0.00165038 + 0.00165038i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 21.6990i 1.07558i
$$408$$ 0 0
$$409$$ 25.2271i 1.24740i −0.781665 0.623699i $$-0.785629\pi$$
0.781665 0.623699i $$-0.214371\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −18.2306 18.2306i −0.897069 0.897069i
$$414$$ 0 0
$$415$$ −7.12787 −0.349894
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −7.25283 7.25283i −0.354324 0.354324i 0.507392 0.861716i $$-0.330610\pi$$
−0.861716 + 0.507392i $$0.830610\pi$$
$$420$$ 0 0
$$421$$ −2.39550 + 2.39550i −0.116749 + 0.116749i −0.763068 0.646318i $$-0.776308\pi$$
0.646318 + 0.763068i $$0.276308\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 17.2739i 0.837908i
$$426$$ 0 0
$$427$$ 12.4388 12.4388i 0.601957 0.601957i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −4.42454 −0.213123 −0.106561 0.994306i $$-0.533984\pi$$
−0.106561 + 0.994306i $$0.533984\pi$$
$$432$$ 0 0
$$433$$ 7.31371 0.351474 0.175737 0.984437i $$-0.443769\pi$$
0.175737 + 0.984437i $$0.443769\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −7.23412 + 7.23412i −0.346055 + 0.346055i
$$438$$ 0 0
$$439$$ 29.6533i 1.41527i 0.706576 + 0.707637i $$0.250239\pi$$
−0.706576 + 0.707637i $$0.749761\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −10.3056 + 10.3056i −0.489633 + 0.489633i −0.908190 0.418557i $$-0.862536\pi$$
0.418557 + 0.908190i $$0.362536\pi$$
$$444$$ 0 0
$$445$$ 4.90746 + 4.90746i 0.232636 + 0.232636i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 6.48844 0.306208 0.153104 0.988210i $$-0.451073\pi$$
0.153104 + 0.988210i $$0.451073\pi$$
$$450$$ 0 0
$$451$$ 22.9402 + 22.9402i 1.08021 + 1.08021i
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0.181370i 0.00850278i
$$456$$ 0 0
$$457$$ 9.00353i 0.421167i −0.977576 0.210584i $$-0.932464\pi$$
0.977576 0.210584i $$-0.0675364\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 14.6218 + 14.6218i 0.681004 + 0.681004i 0.960226 0.279223i $$-0.0900767\pi$$
−0.279223 + 0.960226i $$0.590077\pi$$
$$462$$ 0 0
$$463$$ 18.6435 0.866437 0.433219 0.901289i $$-0.357378\pi$$
0.433219 + 0.901289i $$0.357378\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 23.5138 + 23.5138i 1.08809 + 1.08809i 0.995725 + 0.0923633i $$0.0294421\pi$$
0.0923633 + 0.995725i $$0.470558\pi$$
$$468$$ 0 0
$$469$$ −17.2082 + 17.2082i −0.794601 + 0.794601i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 7.96703i 0.366325i
$$474$$ 0 0
$$475$$ −12.2145 + 12.2145i −0.560440 + 0.560440i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −1.08864 −0.0497412 −0.0248706 0.999691i $$-0.507917\pi$$
−0.0248706 + 0.999691i $$0.507917\pi$$
$$480$$ 0 0
$$481$$ −0.521173 −0.0237634
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −1.44586 + 1.44586i −0.0656531 + 0.0656531i
$$486$$ 0 0
$$487$$ 35.3298i 1.60095i 0.599369 + 0.800473i $$0.295418\pi$$
−0.599369 + 0.800473i $$0.704582\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 12.8910 12.8910i 0.581761 0.581761i −0.353626 0.935387i $$-0.615051\pi$$
0.935387 + 0.353626i $$0.115051\pi$$
$$492$$ 0 0
$$493$$ 18.6761 + 18.6761i 0.841128 + 0.841128i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −41.5443 −1.86352
$$498$$ 0 0
$$499$$ 14.3798 + 14.3798i 0.643728 + 0.643728i 0.951470 0.307742i $$-0.0995734\pi$$
−0.307742 + 0.951470i $$0.599573\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 30.2969i 1.35087i −0.737420 0.675435i $$-0.763956\pi$$
0.737420 0.675435i $$-0.236044\pi$$
$$504$$ 0 0
$$505$$ 0.303911i 0.0135239i
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 10.5825 + 10.5825i 0.469063 + 0.469063i 0.901611 0.432548i $$-0.142385\pi$$
−0.432548 + 0.901611i $$0.642385\pi$$
$$510$$ 0 0
$$511$$ 2.46824 0.109188
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 0.447718 + 0.447718i 0.0197288 + 0.0197288i
$$516$$ 0 0
$$517$$ 6.99647 6.99647i 0.307704 0.307704i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 24.9049i 1.09110i −0.838078 0.545551i $$-0.816320\pi$$
0.838078 0.545551i $$-0.183680\pi$$
$$522$$ 0 0
$$523$$ −12.9008 + 12.9008i −0.564112 + 0.564112i −0.930473 0.366361i $$-0.880604\pi$$
0.366361 + 0.930473i $$0.380604\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −2.01704 −0.0878638
$$528$$ 0 0
$$529$$ 15.0000 0.652174
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −0.550984 + 0.550984i −0.0238657 + 0.0238657i
$$534$$ 0 0
$$535$$ 4.06074i 0.175561i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −34.0671 + 34.0671i −1.46738 + 1.46738i
$$540$$ 0 0
$$541$$ −18.2767 18.2767i −0.785776 0.785776i 0.195023 0.980799i $$-0.437522\pi$$
−0.980799 + 0.195023i $$0.937522\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 3.82880 0.164008
$$546$$ 0 0
$$547$$ 13.7355 + 13.7355i 0.587287 + 0.587287i 0.936896 0.349609i $$-0.113685\pi$$
−0.349609 + 0.936896i $$0.613685\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 26.4120i 1.12519i
$$552$$ 0 0
$$553$$ 50.1055i 2.13070i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −27.5525 27.5525i −1.16744 1.16744i −0.982808 0.184631i $$-0.940891\pi$$
−0.184631 0.982808i $$-0.559109\pi$$
$$558$$ 0 0
$$559$$ −0.191354 −0.00809342
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 19.8928 + 19.8928i 0.838383 + 0.838383i 0.988646 0.150263i $$-0.0480121\pi$$
−0.150263 + 0.988646i $$0.548012\pi$$
$$564$$ 0 0
$$565$$ −3.19879 + 3.19879i −0.134574 + 0.134574i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 13.4849i 0.565317i −0.959221 0.282658i $$-0.908784\pi$$
0.959221 0.282658i $$-0.0912163\pi$$
$$570$$ 0 0
$$571$$ −14.8284 + 14.8284i −0.620550 + 0.620550i −0.945672 0.325122i $$-0.894595\pi$$
0.325122 + 0.945672i $$0.394595\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −13.5077 −0.563308
$$576$$ 0 0
$$577$$ −11.6176 −0.483648 −0.241824 0.970320i $$-0.577746\pi$$
−0.241824 + 0.970320i $$0.577746\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −48.5010 + 48.5010i −2.01216 + 2.01216i
$$582$$ 0 0
$$583$$ 2.44158i 0.101120i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 17.0268 17.0268i 0.702773 0.702773i −0.262232 0.965005i $$-0.584459\pi$$
0.965005 + 0.262232i $$0.0844585\pi$$
$$588$$ 0 0
$$589$$ 1.42627 + 1.42627i 0.0587682 + 0.0587682i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −41.5372 −1.70573 −0.852865 0.522132i $$-0.825137\pi$$
−0.852865 + 0.522132i $$0.825137\pi$$
$$594$$ 0 0
$$595$$ 5.52099 + 5.52099i 0.226338 + 0.226338i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 6.43160i 0.262788i −0.991330 0.131394i $$-0.958055\pi$$
0.991330 0.131394i $$-0.0419453\pi$$
$$600$$ 0 0
$$601$$ 3.45844i 0.141073i 0.997509 + 0.0705364i $$0.0224711\pi$$
−0.997509 + 0.0705364i $$0.977529\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 0.414494 + 0.414494i 0.0168516 + 0.0168516i
$$606$$ 0 0
$$607$$ 30.1019 1.22180 0.610900 0.791708i $$-0.290808\pi$$
0.610900 + 0.791708i $$0.290808\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0.168043 + 0.168043i 0.00679829 + 0.00679829i
$$612$$ 0 0
$$613$$ −2.50490 + 2.50490i −0.101172 + 0.101172i −0.755881 0.654709i $$-0.772791\pi$$
0.654709 + 0.755881i $$0.272791\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 22.9098i 0.922315i 0.887318 + 0.461157i $$0.152566\pi$$
−0.887318 + 0.461157i $$0.847434\pi$$
$$618$$ 0 0
$$619$$ −28.6104 + 28.6104i −1.14995 + 1.14995i −0.163386 + 0.986562i $$0.552242\pi$$
−0.986562 + 0.163386i $$0.947758\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 66.7847 2.67567
$$624$$ 0 0
$$625$$ −21.6855 −0.867420
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 15.8647 15.8647i 0.632567 0.632567i
$$630$$ 0 0
$$631$$ 11.1851i 0.445270i 0.974902 + 0.222635i $$0.0714659\pi$$
−0.974902 + 0.222635i $$0.928534\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 1.70774 1.70774i 0.0677698 0.0677698i
$$636$$ 0 0
$$637$$ −0.818234 0.818234i −0.0324196 0.0324196i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 6.69312 0.264362 0.132181 0.991226i $$-0.457802\pi$$
0.132181 + 0.991226i $$0.457802\pi$$
$$642$$ 0 0
$$643$$ −17.9410 17.9410i −0.707522 0.707522i 0.258491 0.966014i $$-0.416775\pi$$
−0.966014 + 0.258491i $$0.916775\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 6.72999i 0.264583i −0.991211 0.132292i $$-0.957766\pi$$
0.991211 0.132292i $$-0.0422335\pi$$
$$648$$ 0 0
$$649$$ 19.7890i 0.776786i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 26.1731 + 26.1731i 1.02423 + 1.02423i 0.999699 + 0.0245347i $$0.00781042\pi$$
0.0245347 + 0.999699i $$0.492190\pi$$
$$654$$ 0 0
$$655$$ 1.41921 0.0554529
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −13.9741 13.9741i −0.544353 0.544353i 0.380449 0.924802i $$-0.375770\pi$$
−0.924802 + 0.380449i $$0.875770\pi$$
$$660$$ 0 0
$$661$$ −11.9241 + 11.9241i −0.463794 + 0.463794i −0.899897 0.436103i $$-0.856358\pi$$
0.436103 + 0.899897i $$0.356358\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 7.80785i 0.302776i
$$666$$ 0 0
$$667$$ 14.6041 14.6041i 0.565473 0.565473i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −13.5021 −0.521244
$$672$$ 0 0
$$673$$ −37.3066 −1.43807 −0.719033 0.694976i $$-0.755415\pi$$
−0.719033 + 0.694976i $$0.755415\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 0.447461 0.447461i 0.0171973 0.0171973i −0.698456 0.715653i $$-0.746129\pi$$
0.715653 + 0.698456i $$0.246129\pi$$
$$678$$ 0 0
$$679$$ 19.6764i 0.755113i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 4.27521 4.27521i 0.163586 0.163586i −0.620567 0.784153i $$-0.713098\pi$$
0.784153 + 0.620567i $$0.213098\pi$$
$$684$$ 0 0
$$685$$ −1.13178 1.13178i −0.0432430 0.0432430i
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −0.0586426 −0.00223410
$$690$$ 0 0
$$691$$ 20.0786 + 20.0786i 0.763827 + 0.763827i 0.977012 0.213185i $$-0.0683836\pi$$
−0.213185 + 0.977012i $$0.568384\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 3.93926i 0.149425i
$$696$$ 0 0
$$697$$ 33.5443i 1.27058i
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −10.4467 10.4467i −0.394565 0.394565i 0.481746 0.876311i $$-0.340003\pi$$
−0.876311 + 0.481746i $$0.840003\pi$$
$$702$$ 0 0
$$703$$ −22.4361 −0.846192
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −2.06793 2.06793i −0.0777727 0.0777727i
$$708$$ 0 0
$$709$$ −16.0916 + 16.0916i −0.604332 + 0.604332i −0.941459 0.337127i $$-0.890545\pi$$
0.337127 + 0.941459i $$0.390545\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 1.57726i 0.0590690i
$$714$$ 0 0
$$715$$ −0.0984373 + 0.0984373i −0.00368135 + 0.00368135i
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −30.9957 −1.15594 −0.577972 0.816057i $$-0.696156\pi$$
−0.577972 + 0.816057i $$0.696156\pi$$
$$720$$ 0 0
$$721$$ 6.09292 0.226912
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 24.6584 24.6584i 0.915790 0.915790i
$$726$$ 0 0
$$727$$ 41.1117i 1.52475i −0.647135 0.762375i $$-0.724033\pi$$
0.647135 0.762375i $$-0.275967\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 5.82490 5.82490i 0.215442 0.215442i
$$732$$ 0 0
$$733$$ −0.146061 0.146061i −0.00539490 0.00539490i 0.704404 0.709799i $$-0.251214\pi$$
−0.709799 + 0.704404i $$0.751214\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 18.6792 0.688058
$$738$$ 0 0
$$739$$ −1.50766 1.50766i −0.0554601 0.0554601i 0.678833 0.734293i $$-0.262486\pi$$
−0.734293 + 0.678833i $$0.762486\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 40.5175i 1.48644i 0.669046 + 0.743221i $$0.266703\pi$$
−0.669046 + 0.743221i $$0.733297\pi$$
$$744$$ 0 0
$$745$$ 6.69256i 0.245196i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −27.6309 27.6309i −1.00961 1.00961i
$$750$$ 0 0
$$751$$ 12.5843 0.459208 0.229604 0.973284i $$-0.426257\pi$$
0.229604 + 0.973284i $$0.426257\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 3.34129 + 3.34129i 0.121602 + 0.121602i
$$756$$ 0 0
$$757$$ 7.49900 7.49900i 0.272556 0.272556i −0.557572 0.830128i $$-0.688267\pi$$
0.830128 + 0.557572i $$0.188267\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 42.8182i 1.55216i 0.630635 + 0.776079i $$0.282794\pi$$
−0.630635 + 0.776079i $$0.717206\pi$$
$$762$$ 0 0
$$763$$ 26.0527 26.0527i 0.943172 0.943172i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −0.475298 −0.0171620
$$768$$ 0 0
$$769$$ 12.7455 0.459614 0.229807 0.973236i $$-0.426190\pi$$
0.229807 + 0.973236i $$0.426190\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −22.8765 + 22.8765i −0.822809 + 0.822809i −0.986510 0.163701i $$-0.947657\pi$$
0.163701 + 0.986510i $$0.447657\pi$$
$$774$$ 0 0
$$775$$ 2.66314i 0.0956630i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −23.7194 + 23.7194i −0.849836 + 0.849836i
$$780$$ 0 0
$$781$$ 22.5478 + 22.5478i 0.806825 + 0.806825i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −10.8253 −0.386370
$$786$$ 0 0
$$787$$ 5.20470 + 5.20470i 0.185528 + 0.185528i 0.793759 0.608232i $$-0.208121\pi$$
−0.608232 + 0.793759i $$0.708121\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 43.5317i 1.54781i
$$792$$ 0 0
$$793$$ 0.324298i 0.0115162i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 17.0149 + 17.0149i 0.602698 + 0.602698i 0.941028 0.338330i $$-0.109862\pi$$
−0.338330 + 0.941028i $$0.609862\pi$$
$$798$$ 0 0