# Properties

 Label 1152.2.i.d.769.1 Level $1152$ Weight $2$ Character 1152.769 Analytic conductor $9.199$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Learn more

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1152,2,Mod(385,1152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1152, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1152.385");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1152 = 2^{7} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1152.i (of order $$3$$, degree $$2$$, 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: $$2$$ 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: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 769.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 1152.769 Dual form 1152.2.i.d.385.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(1.50000 - 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{5} +(1.00000 + 1.73205i) q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$$ $$q+(1.50000 - 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{5} +(1.00000 + 1.73205i) q^{7} +(1.50000 - 2.59808i) q^{9} +(2.50000 + 4.33013i) q^{11} +(-2.00000 + 3.46410i) q^{13} -3.46410i q^{15} +1.00000 q^{17} +5.00000 q^{19} +(3.00000 + 1.73205i) q^{21} +(2.00000 - 3.46410i) q^{23} +(0.500000 + 0.866025i) q^{25} -5.19615i q^{27} +(3.00000 + 5.19615i) q^{29} +(7.50000 + 4.33013i) q^{33} +4.00000 q^{35} -10.0000 q^{37} +6.92820i q^{39} +(1.50000 - 2.59808i) q^{41} +(-4.50000 - 7.79423i) q^{43} +(-3.00000 - 5.19615i) q^{45} +(-4.00000 - 6.92820i) q^{47} +(1.50000 - 2.59808i) q^{49} +(1.50000 - 0.866025i) q^{51} -12.0000 q^{53} +10.0000 q^{55} +(7.50000 - 4.33013i) q^{57} +(3.50000 - 6.06218i) q^{59} +(-2.00000 - 3.46410i) q^{61} +6.00000 q^{63} +(4.00000 + 6.92820i) q^{65} +(-3.50000 + 6.06218i) q^{67} -6.92820i q^{69} +6.00000 q^{71} -13.0000 q^{73} +(1.50000 + 0.866025i) q^{75} +(-5.00000 + 8.66025i) q^{77} +(-1.00000 - 1.73205i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(6.00000 + 10.3923i) q^{83} +(1.00000 - 1.73205i) q^{85} +(9.00000 + 5.19615i) q^{87} +10.0000 q^{89} -8.00000 q^{91} +(5.00000 - 8.66025i) q^{95} +(-6.50000 - 11.2583i) q^{97} +15.0000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 3 q^{3} + 2 q^{5} + 2 q^{7} + 3 q^{9}+O(q^{10})$$ 2 * q + 3 * q^3 + 2 * q^5 + 2 * q^7 + 3 * q^9 $$2 q + 3 q^{3} + 2 q^{5} + 2 q^{7} + 3 q^{9} + 5 q^{11} - 4 q^{13} + 2 q^{17} + 10 q^{19} + 6 q^{21} + 4 q^{23} + q^{25} + 6 q^{29} + 15 q^{33} + 8 q^{35} - 20 q^{37} + 3 q^{41} - 9 q^{43} - 6 q^{45} - 8 q^{47} + 3 q^{49} + 3 q^{51} - 24 q^{53} + 20 q^{55} + 15 q^{57} + 7 q^{59} - 4 q^{61} + 12 q^{63} + 8 q^{65} - 7 q^{67} + 12 q^{71} - 26 q^{73} + 3 q^{75} - 10 q^{77} - 2 q^{79} - 9 q^{81} + 12 q^{83} + 2 q^{85} + 18 q^{87} + 20 q^{89} - 16 q^{91} + 10 q^{95} - 13 q^{97} + 30 q^{99}+O(q^{100})$$ 2 * q + 3 * q^3 + 2 * q^5 + 2 * q^7 + 3 * q^9 + 5 * q^11 - 4 * q^13 + 2 * q^17 + 10 * q^19 + 6 * q^21 + 4 * q^23 + q^25 + 6 * q^29 + 15 * q^33 + 8 * q^35 - 20 * q^37 + 3 * q^41 - 9 * q^43 - 6 * q^45 - 8 * q^47 + 3 * q^49 + 3 * q^51 - 24 * q^53 + 20 * q^55 + 15 * q^57 + 7 * q^59 - 4 * q^61 + 12 * q^63 + 8 * q^65 - 7 * q^67 + 12 * q^71 - 26 * q^73 + 3 * q^75 - 10 * q^77 - 2 * q^79 - 9 * q^81 + 12 * q^83 + 2 * q^85 + 18 * q^87 + 20 * q^89 - 16 * q^91 + 10 * q^95 - 13 * q^97 + 30 * q^99

## Character values

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

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

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 1.50000 0.866025i 0.866025 0.500000i
$$4$$ 0 0
$$5$$ 1.00000 1.73205i 0.447214 0.774597i −0.550990 0.834512i $$-0.685750\pi$$
0.998203 + 0.0599153i $$0.0190830\pi$$
$$6$$ 0 0
$$7$$ 1.00000 + 1.73205i 0.377964 + 0.654654i 0.990766 0.135583i $$-0.0432908\pi$$
−0.612801 + 0.790237i $$0.709957\pi$$
$$8$$ 0 0
$$9$$ 1.50000 2.59808i 0.500000 0.866025i
$$10$$ 0 0
$$11$$ 2.50000 + 4.33013i 0.753778 + 1.30558i 0.945979 + 0.324227i $$0.105104\pi$$
−0.192201 + 0.981356i $$0.561563\pi$$
$$12$$ 0 0
$$13$$ −2.00000 + 3.46410i −0.554700 + 0.960769i 0.443227 + 0.896410i $$0.353834\pi$$
−0.997927 + 0.0643593i $$0.979500\pi$$
$$14$$ 0 0
$$15$$ 3.46410i 0.894427i
$$16$$ 0 0
$$17$$ 1.00000 0.242536 0.121268 0.992620i $$-0.461304\pi$$
0.121268 + 0.992620i $$0.461304\pi$$
$$18$$ 0 0
$$19$$ 5.00000 1.14708 0.573539 0.819178i $$-0.305570\pi$$
0.573539 + 0.819178i $$0.305570\pi$$
$$20$$ 0 0
$$21$$ 3.00000 + 1.73205i 0.654654 + 0.377964i
$$22$$ 0 0
$$23$$ 2.00000 3.46410i 0.417029 0.722315i −0.578610 0.815604i $$-0.696405\pi$$
0.995639 + 0.0932891i $$0.0297381\pi$$
$$24$$ 0 0
$$25$$ 0.500000 + 0.866025i 0.100000 + 0.173205i
$$26$$ 0 0
$$27$$ 5.19615i 1.00000i
$$28$$ 0 0
$$29$$ 3.00000 + 5.19615i 0.557086 + 0.964901i 0.997738 + 0.0672232i $$0.0214140\pi$$
−0.440652 + 0.897678i $$0.645253\pi$$
$$30$$ 0 0
$$31$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$32$$ 0 0
$$33$$ 7.50000 + 4.33013i 1.30558 + 0.753778i
$$34$$ 0 0
$$35$$ 4.00000 0.676123
$$36$$ 0 0
$$37$$ −10.0000 −1.64399 −0.821995 0.569495i $$-0.807139\pi$$
−0.821995 + 0.569495i $$0.807139\pi$$
$$38$$ 0 0
$$39$$ 6.92820i 1.10940i
$$40$$ 0 0
$$41$$ 1.50000 2.59808i 0.234261 0.405751i −0.724797 0.688963i $$-0.758066\pi$$
0.959058 + 0.283211i $$0.0913998\pi$$
$$42$$ 0 0
$$43$$ −4.50000 7.79423i −0.686244 1.18861i −0.973044 0.230618i $$-0.925925\pi$$
0.286801 0.957990i $$-0.407408\pi$$
$$44$$ 0 0
$$45$$ −3.00000 5.19615i −0.447214 0.774597i
$$46$$ 0 0
$$47$$ −4.00000 6.92820i −0.583460 1.01058i −0.995066 0.0992202i $$-0.968365\pi$$
0.411606 0.911362i $$-0.364968\pi$$
$$48$$ 0 0
$$49$$ 1.50000 2.59808i 0.214286 0.371154i
$$50$$ 0 0
$$51$$ 1.50000 0.866025i 0.210042 0.121268i
$$52$$ 0 0
$$53$$ −12.0000 −1.64833 −0.824163 0.566352i $$-0.808354\pi$$
−0.824163 + 0.566352i $$0.808354\pi$$
$$54$$ 0 0
$$55$$ 10.0000 1.34840
$$56$$ 0 0
$$57$$ 7.50000 4.33013i 0.993399 0.573539i
$$58$$ 0 0
$$59$$ 3.50000 6.06218i 0.455661 0.789228i −0.543065 0.839691i $$-0.682736\pi$$
0.998726 + 0.0504625i $$0.0160695\pi$$
$$60$$ 0 0
$$61$$ −2.00000 3.46410i −0.256074 0.443533i 0.709113 0.705095i $$-0.249096\pi$$
−0.965187 + 0.261562i $$0.915762\pi$$
$$62$$ 0 0
$$63$$ 6.00000 0.755929
$$64$$ 0 0
$$65$$ 4.00000 + 6.92820i 0.496139 + 0.859338i
$$66$$ 0 0
$$67$$ −3.50000 + 6.06218i −0.427593 + 0.740613i −0.996659 0.0816792i $$-0.973972\pi$$
0.569066 + 0.822292i $$0.307305\pi$$
$$68$$ 0 0
$$69$$ 6.92820i 0.834058i
$$70$$ 0 0
$$71$$ 6.00000 0.712069 0.356034 0.934473i $$-0.384129\pi$$
0.356034 + 0.934473i $$0.384129\pi$$
$$72$$ 0 0
$$73$$ −13.0000 −1.52153 −0.760767 0.649025i $$-0.775177\pi$$
−0.760767 + 0.649025i $$0.775177\pi$$
$$74$$ 0 0
$$75$$ 1.50000 + 0.866025i 0.173205 + 0.100000i
$$76$$ 0 0
$$77$$ −5.00000 + 8.66025i −0.569803 + 0.986928i
$$78$$ 0 0
$$79$$ −1.00000 1.73205i −0.112509 0.194871i 0.804272 0.594261i $$-0.202555\pi$$
−0.916781 + 0.399390i $$0.869222\pi$$
$$80$$ 0 0
$$81$$ −4.50000 7.79423i −0.500000 0.866025i
$$82$$ 0 0
$$83$$ 6.00000 + 10.3923i 0.658586 + 1.14070i 0.980982 + 0.194099i $$0.0621783\pi$$
−0.322396 + 0.946605i $$0.604488\pi$$
$$84$$ 0 0
$$85$$ 1.00000 1.73205i 0.108465 0.187867i
$$86$$ 0 0
$$87$$ 9.00000 + 5.19615i 0.964901 + 0.557086i
$$88$$ 0 0
$$89$$ 10.0000 1.06000 0.529999 0.847998i $$-0.322192\pi$$
0.529999 + 0.847998i $$0.322192\pi$$
$$90$$ 0 0
$$91$$ −8.00000 −0.838628
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 5.00000 8.66025i 0.512989 0.888523i
$$96$$ 0 0
$$97$$ −6.50000 11.2583i −0.659975 1.14311i −0.980622 0.195911i $$-0.937234\pi$$
0.320647 0.947199i $$-0.396100\pi$$
$$98$$ 0 0
$$99$$ 15.0000 1.50756
$$100$$ 0 0
$$101$$ 3.00000 + 5.19615i 0.298511 + 0.517036i 0.975796 0.218685i $$-0.0701767\pi$$
−0.677284 + 0.735721i $$0.736843\pi$$
$$102$$ 0 0
$$103$$ 4.00000 6.92820i 0.394132 0.682656i −0.598858 0.800855i $$-0.704379\pi$$
0.992990 + 0.118199i $$0.0377120\pi$$
$$104$$ 0 0
$$105$$ 6.00000 3.46410i 0.585540 0.338062i
$$106$$ 0 0
$$107$$ −11.0000 −1.06341 −0.531705 0.846930i $$-0.678449\pi$$
−0.531705 + 0.846930i $$0.678449\pi$$
$$108$$ 0 0
$$109$$ −12.0000 −1.14939 −0.574696 0.818367i $$-0.694880\pi$$
−0.574696 + 0.818367i $$0.694880\pi$$
$$110$$ 0 0
$$111$$ −15.0000 + 8.66025i −1.42374 + 0.821995i
$$112$$ 0 0
$$113$$ −7.00000 + 12.1244i −0.658505 + 1.14056i 0.322498 + 0.946570i $$0.395477\pi$$
−0.981003 + 0.193993i $$0.937856\pi$$
$$114$$ 0 0
$$115$$ −4.00000 6.92820i −0.373002 0.646058i
$$116$$ 0 0
$$117$$ 6.00000 + 10.3923i 0.554700 + 0.960769i
$$118$$ 0 0
$$119$$ 1.00000 + 1.73205i 0.0916698 + 0.158777i
$$120$$ 0 0
$$121$$ −7.00000 + 12.1244i −0.636364 + 1.10221i
$$122$$ 0 0
$$123$$ 5.19615i 0.468521i
$$124$$ 0 0
$$125$$ 12.0000 1.07331
$$126$$ 0 0
$$127$$ 20.0000 1.77471 0.887357 0.461084i $$-0.152539\pi$$
0.887357 + 0.461084i $$0.152539\pi$$
$$128$$ 0 0
$$129$$ −13.5000 7.79423i −1.18861 0.686244i
$$130$$ 0 0
$$131$$ −6.00000 + 10.3923i −0.524222 + 0.907980i 0.475380 + 0.879781i $$0.342311\pi$$
−0.999602 + 0.0281993i $$0.991023\pi$$
$$132$$ 0 0
$$133$$ 5.00000 + 8.66025i 0.433555 + 0.750939i
$$134$$ 0 0
$$135$$ −9.00000 5.19615i −0.774597 0.447214i
$$136$$ 0 0
$$137$$ −0.500000 0.866025i −0.0427179 0.0739895i 0.843876 0.536538i $$-0.180268\pi$$
−0.886594 + 0.462549i $$0.846935\pi$$
$$138$$ 0 0
$$139$$ 0.500000 0.866025i 0.0424094 0.0734553i −0.844042 0.536278i $$-0.819830\pi$$
0.886451 + 0.462822i $$0.153163\pi$$
$$140$$ 0 0
$$141$$ −12.0000 6.92820i −1.01058 0.583460i
$$142$$ 0 0
$$143$$ −20.0000 −1.67248
$$144$$ 0 0
$$145$$ 12.0000 0.996546
$$146$$ 0 0
$$147$$ 5.19615i 0.428571i
$$148$$ 0 0
$$149$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$150$$ 0 0
$$151$$ 8.00000 + 13.8564i 0.651031 + 1.12762i 0.982873 + 0.184284i $$0.0589965\pi$$
−0.331842 + 0.943335i $$0.607670\pi$$
$$152$$ 0 0
$$153$$ 1.50000 2.59808i 0.121268 0.210042i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 12.0000 20.7846i 0.957704 1.65879i 0.229650 0.973273i $$-0.426242\pi$$
0.728055 0.685519i $$-0.240425\pi$$
$$158$$ 0 0
$$159$$ −18.0000 + 10.3923i −1.42749 + 0.824163i
$$160$$ 0 0
$$161$$ 8.00000 0.630488
$$162$$ 0 0
$$163$$ −4.00000 −0.313304 −0.156652 0.987654i $$-0.550070\pi$$
−0.156652 + 0.987654i $$0.550070\pi$$
$$164$$ 0 0
$$165$$ 15.0000 8.66025i 1.16775 0.674200i
$$166$$ 0 0
$$167$$ −1.00000 + 1.73205i −0.0773823 + 0.134030i −0.902120 0.431486i $$-0.857990\pi$$
0.824737 + 0.565516i $$0.191323\pi$$
$$168$$ 0 0
$$169$$ −1.50000 2.59808i −0.115385 0.199852i
$$170$$ 0 0
$$171$$ 7.50000 12.9904i 0.573539 0.993399i
$$172$$ 0 0
$$173$$ 9.00000 + 15.5885i 0.684257 + 1.18517i 0.973670 + 0.227964i $$0.0732068\pi$$
−0.289412 + 0.957205i $$0.593460\pi$$
$$174$$ 0 0
$$175$$ −1.00000 + 1.73205i −0.0755929 + 0.130931i
$$176$$ 0 0
$$177$$ 12.1244i 0.911322i
$$178$$ 0 0
$$179$$ 12.0000 0.896922 0.448461 0.893802i $$-0.351972\pi$$
0.448461 + 0.893802i $$0.351972\pi$$
$$180$$ 0 0
$$181$$ −20.0000 −1.48659 −0.743294 0.668965i $$-0.766738\pi$$
−0.743294 + 0.668965i $$0.766738\pi$$
$$182$$ 0 0
$$183$$ −6.00000 3.46410i −0.443533 0.256074i
$$184$$ 0 0
$$185$$ −10.0000 + 17.3205i −0.735215 + 1.27343i
$$186$$ 0 0
$$187$$ 2.50000 + 4.33013i 0.182818 + 0.316650i
$$188$$ 0 0
$$189$$ 9.00000 5.19615i 0.654654 0.377964i
$$190$$ 0 0
$$191$$ 1.00000 + 1.73205i 0.0723575 + 0.125327i 0.899934 0.436026i $$-0.143614\pi$$
−0.827577 + 0.561353i $$0.810281\pi$$
$$192$$ 0 0
$$193$$ −0.500000 + 0.866025i −0.0359908 + 0.0623379i −0.883460 0.468507i $$-0.844792\pi$$
0.847469 + 0.530845i $$0.178125\pi$$
$$194$$ 0 0
$$195$$ 12.0000 + 6.92820i 0.859338 + 0.496139i
$$196$$ 0 0
$$197$$ 20.0000 1.42494 0.712470 0.701702i $$-0.247576\pi$$
0.712470 + 0.701702i $$0.247576\pi$$
$$198$$ 0 0
$$199$$ −2.00000 −0.141776 −0.0708881 0.997484i $$-0.522583\pi$$
−0.0708881 + 0.997484i $$0.522583\pi$$
$$200$$ 0 0
$$201$$ 12.1244i 0.855186i
$$202$$ 0 0
$$203$$ −6.00000 + 10.3923i −0.421117 + 0.729397i
$$204$$ 0 0
$$205$$ −3.00000 5.19615i −0.209529 0.362915i
$$206$$ 0 0
$$207$$ −6.00000 10.3923i −0.417029 0.722315i
$$208$$ 0 0
$$209$$ 12.5000 + 21.6506i 0.864643 + 1.49761i
$$210$$ 0 0
$$211$$ −10.0000 + 17.3205i −0.688428 + 1.19239i 0.283918 + 0.958849i $$0.408366\pi$$
−0.972346 + 0.233544i $$0.924968\pi$$
$$212$$ 0 0
$$213$$ 9.00000 5.19615i 0.616670 0.356034i
$$214$$ 0 0
$$215$$ −18.0000 −1.22759
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ −19.5000 + 11.2583i −1.31769 + 0.760767i
$$220$$ 0 0
$$221$$ −2.00000 + 3.46410i −0.134535 + 0.233021i
$$222$$ 0 0
$$223$$ −12.0000 20.7846i −0.803579 1.39184i −0.917246 0.398321i $$-0.869593\pi$$
0.113666 0.993519i $$-0.463740\pi$$
$$224$$ 0 0
$$225$$ 3.00000 0.200000
$$226$$ 0 0
$$227$$ −1.50000 2.59808i −0.0995585 0.172440i 0.811943 0.583736i $$-0.198410\pi$$
−0.911502 + 0.411296i $$0.865076\pi$$
$$228$$ 0 0
$$229$$ −7.00000 + 12.1244i −0.462573 + 0.801200i −0.999088 0.0426906i $$-0.986407\pi$$
0.536515 + 0.843891i $$0.319740\pi$$
$$230$$ 0 0
$$231$$ 17.3205i 1.13961i
$$232$$ 0 0
$$233$$ −9.00000 −0.589610 −0.294805 0.955557i $$-0.595255\pi$$
−0.294805 + 0.955557i $$0.595255\pi$$
$$234$$ 0 0
$$235$$ −16.0000 −1.04372
$$236$$ 0 0
$$237$$ −3.00000 1.73205i −0.194871 0.112509i
$$238$$ 0 0
$$239$$ 6.00000 10.3923i 0.388108 0.672222i −0.604087 0.796918i $$-0.706462\pi$$
0.992195 + 0.124696i $$0.0397955\pi$$
$$240$$ 0 0
$$241$$ −12.5000 21.6506i −0.805196 1.39464i −0.916159 0.400815i $$-0.868727\pi$$
0.110963 0.993825i $$-0.464606\pi$$
$$242$$ 0 0
$$243$$ −13.5000 7.79423i −0.866025 0.500000i
$$244$$ 0 0
$$245$$ −3.00000 5.19615i −0.191663 0.331970i
$$246$$ 0 0
$$247$$ −10.0000 + 17.3205i −0.636285 + 1.10208i
$$248$$ 0 0
$$249$$ 18.0000 + 10.3923i 1.14070 + 0.658586i
$$250$$ 0 0
$$251$$ 3.00000 0.189358 0.0946792 0.995508i $$-0.469817\pi$$
0.0946792 + 0.995508i $$0.469817\pi$$
$$252$$ 0 0
$$253$$ 20.0000 1.25739
$$254$$ 0 0
$$255$$ 3.46410i 0.216930i
$$256$$ 0 0
$$257$$ −1.50000 + 2.59808i −0.0935674 + 0.162064i −0.909010 0.416775i $$-0.863160\pi$$
0.815442 + 0.578838i $$0.196494\pi$$
$$258$$ 0 0
$$259$$ −10.0000 17.3205i −0.621370 1.07624i
$$260$$ 0 0
$$261$$ 18.0000 1.11417
$$262$$ 0 0
$$263$$ −9.00000 15.5885i −0.554964 0.961225i −0.997906 0.0646755i $$-0.979399\pi$$
0.442943 0.896550i $$-0.353935\pi$$
$$264$$ 0 0
$$265$$ −12.0000 + 20.7846i −0.737154 + 1.27679i
$$266$$ 0 0
$$267$$ 15.0000 8.66025i 0.917985 0.529999i
$$268$$ 0 0
$$269$$ −4.00000 −0.243884 −0.121942 0.992537i $$-0.538912\pi$$
−0.121942 + 0.992537i $$0.538912\pi$$
$$270$$ 0 0
$$271$$ −8.00000 −0.485965 −0.242983 0.970031i $$-0.578126\pi$$
−0.242983 + 0.970031i $$0.578126\pi$$
$$272$$ 0 0
$$273$$ −12.0000 + 6.92820i −0.726273 + 0.419314i
$$274$$ 0 0
$$275$$ −2.50000 + 4.33013i −0.150756 + 0.261116i
$$276$$ 0 0
$$277$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −15.0000 25.9808i −0.894825 1.54988i −0.834021 0.551733i $$-0.813967\pi$$
−0.0608039 0.998150i $$-0.519366\pi$$
$$282$$ 0 0
$$283$$ −12.0000 + 20.7846i −0.713326 + 1.23552i 0.250276 + 0.968175i $$0.419479\pi$$
−0.963602 + 0.267342i $$0.913855\pi$$
$$284$$ 0 0
$$285$$ 17.3205i 1.02598i
$$286$$ 0 0
$$287$$ 6.00000 0.354169
$$288$$ 0 0
$$289$$ −16.0000 −0.941176
$$290$$ 0 0
$$291$$ −19.5000 11.2583i −1.14311 0.659975i
$$292$$ 0 0
$$293$$ 5.00000 8.66025i 0.292103 0.505937i −0.682204 0.731162i $$-0.738978\pi$$
0.974307 + 0.225225i $$0.0723116\pi$$
$$294$$ 0 0
$$295$$ −7.00000 12.1244i −0.407556 0.705907i
$$296$$ 0 0
$$297$$ 22.5000 12.9904i 1.30558 0.753778i
$$298$$ 0 0
$$299$$ 8.00000 + 13.8564i 0.462652 + 0.801337i
$$300$$ 0 0
$$301$$ 9.00000 15.5885i 0.518751 0.898504i
$$302$$ 0 0
$$303$$ 9.00000 + 5.19615i 0.517036 + 0.298511i
$$304$$ 0 0
$$305$$ −8.00000 −0.458079
$$306$$ 0 0
$$307$$ 3.00000 0.171219 0.0856095 0.996329i $$-0.472716\pi$$
0.0856095 + 0.996329i $$0.472716\pi$$
$$308$$ 0 0
$$309$$ 13.8564i 0.788263i
$$310$$ 0 0
$$311$$ −5.00000 + 8.66025i −0.283524 + 0.491078i −0.972250 0.233944i $$-0.924837\pi$$
0.688726 + 0.725022i $$0.258170\pi$$
$$312$$ 0 0
$$313$$ −12.5000 21.6506i −0.706542 1.22377i −0.966132 0.258047i $$-0.916921\pi$$
0.259590 0.965719i $$-0.416412\pi$$
$$314$$ 0 0
$$315$$ 6.00000 10.3923i 0.338062 0.585540i
$$316$$ 0 0
$$317$$ 6.00000 + 10.3923i 0.336994 + 0.583690i 0.983866 0.178908i $$-0.0572566\pi$$
−0.646872 + 0.762598i $$0.723923\pi$$
$$318$$ 0 0
$$319$$ −15.0000 + 25.9808i −0.839839 + 1.45464i
$$320$$ 0 0
$$321$$ −16.5000 + 9.52628i −0.920940 + 0.531705i
$$322$$ 0 0
$$323$$ 5.00000 0.278207
$$324$$ 0 0
$$325$$ −4.00000 −0.221880
$$326$$ 0 0
$$327$$ −18.0000 + 10.3923i −0.995402 + 0.574696i
$$328$$ 0 0
$$329$$ 8.00000 13.8564i 0.441054 0.763928i
$$330$$ 0 0
$$331$$ −10.0000 17.3205i −0.549650 0.952021i −0.998298 0.0583130i $$-0.981428\pi$$
0.448649 0.893708i $$-0.351905\pi$$
$$332$$ 0 0
$$333$$ −15.0000 + 25.9808i −0.821995 + 1.42374i
$$334$$ 0 0
$$335$$ 7.00000 + 12.1244i 0.382451 + 0.662424i
$$336$$ 0 0
$$337$$ −9.50000 + 16.4545i −0.517498 + 0.896333i 0.482295 + 0.876009i $$0.339803\pi$$
−0.999793 + 0.0203242i $$0.993530\pi$$
$$338$$ 0 0
$$339$$ 24.2487i 1.31701i
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 20.0000 1.07990
$$344$$ 0 0
$$345$$ −12.0000 6.92820i −0.646058 0.373002i
$$346$$ 0 0
$$347$$ −1.50000 + 2.59808i −0.0805242 + 0.139472i −0.903475 0.428640i $$-0.858993\pi$$
0.822951 + 0.568112i $$0.192326\pi$$
$$348$$ 0 0
$$349$$ 8.00000 + 13.8564i 0.428230 + 0.741716i 0.996716 0.0809766i $$-0.0258039\pi$$
−0.568486 + 0.822693i $$0.692471\pi$$
$$350$$ 0 0
$$351$$ 18.0000 + 10.3923i 0.960769 + 0.554700i
$$352$$ 0 0
$$353$$ 4.50000 + 7.79423i 0.239511 + 0.414845i 0.960574 0.278024i $$-0.0896796\pi$$
−0.721063 + 0.692869i $$0.756346\pi$$
$$354$$ 0 0
$$355$$ 6.00000 10.3923i 0.318447 0.551566i
$$356$$ 0 0
$$357$$ 3.00000 + 1.73205i 0.158777 + 0.0916698i
$$358$$ 0 0
$$359$$ 34.0000 1.79445 0.897226 0.441572i $$-0.145579\pi$$
0.897226 + 0.441572i $$0.145579\pi$$
$$360$$ 0 0
$$361$$ 6.00000 0.315789
$$362$$ 0 0
$$363$$ 24.2487i 1.27273i
$$364$$ 0 0
$$365$$ −13.0000 + 22.5167i −0.680451 + 1.17858i
$$366$$ 0 0
$$367$$ 11.0000 + 19.0526i 0.574195 + 0.994535i 0.996129 + 0.0879086i $$0.0280183\pi$$
−0.421933 + 0.906627i $$0.638648\pi$$
$$368$$ 0 0
$$369$$ −4.50000 7.79423i −0.234261 0.405751i
$$370$$ 0 0
$$371$$ −12.0000 20.7846i −0.623009 1.07908i
$$372$$ 0 0
$$373$$ −16.0000 + 27.7128i −0.828449 + 1.43492i 0.0708063 + 0.997490i $$0.477443\pi$$
−0.899255 + 0.437425i $$0.855891\pi$$
$$374$$ 0 0
$$375$$ 18.0000 10.3923i 0.929516 0.536656i
$$376$$ 0 0
$$377$$ −24.0000 −1.23606
$$378$$ 0 0
$$379$$ 25.0000 1.28416 0.642082 0.766636i $$-0.278071\pi$$
0.642082 + 0.766636i $$0.278071\pi$$
$$380$$ 0 0
$$381$$ 30.0000 17.3205i 1.53695 0.887357i
$$382$$ 0 0
$$383$$ −3.00000 + 5.19615i −0.153293 + 0.265511i −0.932436 0.361335i $$-0.882321\pi$$
0.779143 + 0.626846i $$0.215654\pi$$
$$384$$ 0 0
$$385$$ 10.0000 + 17.3205i 0.509647 + 0.882735i
$$386$$ 0 0
$$387$$ −27.0000 −1.37249
$$388$$ 0 0
$$389$$ −19.0000 32.9090i −0.963338 1.66855i −0.714015 0.700130i $$-0.753125\pi$$
−0.249323 0.968420i $$-0.580208\pi$$
$$390$$ 0 0
$$391$$ 2.00000 3.46410i 0.101144 0.175187i
$$392$$ 0 0
$$393$$ 20.7846i 1.04844i
$$394$$ 0 0
$$395$$ −4.00000 −0.201262
$$396$$ 0 0
$$397$$ −18.0000 −0.903394 −0.451697 0.892171i $$-0.649181\pi$$
−0.451697 + 0.892171i $$0.649181\pi$$
$$398$$ 0 0
$$399$$ 15.0000 + 8.66025i 0.750939 + 0.433555i
$$400$$ 0 0
$$401$$ 1.50000 2.59808i 0.0749064 0.129742i −0.826139 0.563466i $$-0.809468\pi$$
0.901046 + 0.433724i $$0.142801\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ −18.0000 −0.894427
$$406$$ 0 0
$$407$$ −25.0000 43.3013i −1.23920 2.14636i
$$408$$ 0 0
$$409$$ −12.5000 + 21.6506i −0.618085 + 1.07056i 0.371750 + 0.928333i $$0.378758\pi$$
−0.989835 + 0.142222i $$0.954575\pi$$
$$410$$ 0 0
$$411$$ −1.50000 0.866025i −0.0739895 0.0427179i
$$412$$ 0 0
$$413$$ 14.0000 0.688895
$$414$$ 0 0
$$415$$ 24.0000 1.17811
$$416$$ 0 0
$$417$$ 1.73205i 0.0848189i
$$418$$ 0 0
$$419$$ −10.0000 + 17.3205i −0.488532 + 0.846162i −0.999913 0.0131919i $$-0.995801\pi$$
0.511381 + 0.859354i $$0.329134\pi$$
$$420$$ 0 0
$$421$$ −1.00000 1.73205i −0.0487370 0.0844150i 0.840628 0.541613i $$-0.182186\pi$$
−0.889365 + 0.457198i $$0.848853\pi$$
$$422$$ 0 0
$$423$$ −24.0000 −1.16692
$$424$$ 0 0
$$425$$ 0.500000 + 0.866025i 0.0242536 + 0.0420084i
$$426$$ 0 0
$$427$$ 4.00000 6.92820i 0.193574 0.335279i
$$428$$ 0 0
$$429$$ −30.0000 + 17.3205i −1.44841 + 0.836242i
$$430$$ 0 0
$$431$$ −10.0000 −0.481683 −0.240842 0.970564i $$-0.577423\pi$$
−0.240842 + 0.970564i $$0.577423\pi$$
$$432$$ 0 0
$$433$$ 33.0000 1.58588 0.792939 0.609301i $$-0.208550\pi$$
0.792939 + 0.609301i $$0.208550\pi$$
$$434$$ 0 0
$$435$$ 18.0000 10.3923i 0.863034 0.498273i
$$436$$ 0 0
$$437$$ 10.0000 17.3205i 0.478365 0.828552i
$$438$$ 0 0
$$439$$ −12.0000 20.7846i −0.572729 0.991995i −0.996284 0.0861252i $$-0.972552\pi$$
0.423556 0.905870i $$-0.360782\pi$$
$$440$$ 0 0
$$441$$ −4.50000 7.79423i −0.214286 0.371154i
$$442$$ 0 0
$$443$$ 7.50000 + 12.9904i 0.356336 + 0.617192i 0.987346 0.158583i $$-0.0506926\pi$$
−0.631010 + 0.775775i $$0.717359\pi$$
$$444$$ 0 0
$$445$$ 10.0000 17.3205i 0.474045 0.821071i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 17.0000 0.802280 0.401140 0.916017i $$-0.368614\pi$$
0.401140 + 0.916017i $$0.368614\pi$$
$$450$$ 0 0
$$451$$ 15.0000 0.706322
$$452$$ 0 0
$$453$$ 24.0000 + 13.8564i 1.12762 + 0.651031i
$$454$$ 0 0
$$455$$ −8.00000 + 13.8564i −0.375046 + 0.649598i
$$456$$ 0 0
$$457$$ 1.50000 + 2.59808i 0.0701670 + 0.121533i 0.898974 0.438001i $$-0.144313\pi$$
−0.828807 + 0.559534i $$0.810980\pi$$
$$458$$ 0 0
$$459$$ 5.19615i 0.242536i
$$460$$ 0 0
$$461$$ −10.0000 17.3205i −0.465746 0.806696i 0.533488 0.845807i $$-0.320881\pi$$
−0.999235 + 0.0391109i $$0.987547\pi$$
$$462$$ 0 0
$$463$$ −1.00000 + 1.73205i −0.0464739 + 0.0804952i −0.888327 0.459212i $$-0.848132\pi$$
0.841853 + 0.539707i $$0.181465\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −29.0000 −1.34196 −0.670980 0.741475i $$-0.734126\pi$$
−0.670980 + 0.741475i $$0.734126\pi$$
$$468$$ 0 0
$$469$$ −14.0000 −0.646460
$$470$$ 0 0
$$471$$ 41.5692i 1.91541i
$$472$$ 0 0
$$473$$ 22.5000 38.9711i 1.03455 1.79190i
$$474$$ 0 0
$$475$$ 2.50000 + 4.33013i 0.114708 + 0.198680i
$$476$$ 0 0
$$477$$ −18.0000 + 31.1769i −0.824163 + 1.42749i
$$478$$ 0 0
$$479$$ 9.00000 + 15.5885i 0.411220 + 0.712255i 0.995023 0.0996406i $$-0.0317693\pi$$
−0.583803 + 0.811895i $$0.698436\pi$$
$$480$$ 0 0
$$481$$ 20.0000 34.6410i 0.911922 1.57949i
$$482$$ 0 0
$$483$$ 12.0000 6.92820i 0.546019 0.315244i
$$484$$ 0 0
$$485$$ −26.0000 −1.18060
$$486$$ 0 0
$$487$$ −10.0000 −0.453143 −0.226572 0.973995i $$-0.572752\pi$$
−0.226572 + 0.973995i $$0.572752\pi$$
$$488$$ 0 0
$$489$$ −6.00000 + 3.46410i −0.271329 + 0.156652i
$$490$$ 0 0
$$491$$ 12.5000 21.6506i 0.564117 0.977079i −0.433014 0.901387i $$-0.642550\pi$$
0.997131 0.0756923i $$-0.0241167\pi$$
$$492$$ 0 0
$$493$$ 3.00000 + 5.19615i 0.135113 + 0.234023i
$$494$$ 0 0
$$495$$ 15.0000 25.9808i 0.674200 1.16775i
$$496$$ 0 0
$$497$$ 6.00000 + 10.3923i 0.269137 + 0.466159i
$$498$$ 0 0
$$499$$ −2.50000 + 4.33013i −0.111915 + 0.193843i −0.916542 0.399937i $$-0.869032\pi$$
0.804627 + 0.593780i $$0.202365\pi$$
$$500$$ 0 0
$$501$$ 3.46410i 0.154765i
$$502$$ 0 0
$$503$$ 4.00000 0.178351 0.0891756 0.996016i $$-0.471577\pi$$
0.0891756 + 0.996016i $$0.471577\pi$$
$$504$$ 0 0
$$505$$ 12.0000 0.533993
$$506$$ 0 0
$$507$$ −4.50000 2.59808i −0.199852 0.115385i
$$508$$ 0 0
$$509$$ 14.0000 24.2487i 0.620539 1.07481i −0.368846 0.929490i $$-0.620247\pi$$
0.989385 0.145315i $$-0.0464195\pi$$
$$510$$ 0 0
$$511$$ −13.0000 22.5167i −0.575086 0.996078i
$$512$$ 0 0
$$513$$ 25.9808i 1.14708i
$$514$$ 0 0
$$515$$ −8.00000 13.8564i −0.352522 0.610586i
$$516$$ 0 0
$$517$$ 20.0000 34.6410i 0.879599 1.52351i
$$518$$ 0 0
$$519$$ 27.0000 + 15.5885i 1.18517 + 0.684257i
$$520$$ 0 0
$$521$$ −7.00000 −0.306676 −0.153338 0.988174i $$-0.549002\pi$$
−0.153338 + 0.988174i $$0.549002\pi$$
$$522$$ 0 0
$$523$$ 44.0000 1.92399 0.961993 0.273075i $$-0.0880406\pi$$
0.961993 + 0.273075i $$0.0880406\pi$$
$$524$$ 0 0
$$525$$ 3.46410i 0.151186i
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 3.50000 + 6.06218i 0.152174 + 0.263573i
$$530$$ 0 0
$$531$$ −10.5000 18.1865i −0.455661 0.789228i
$$532$$ 0 0
$$533$$ 6.00000 + 10.3923i 0.259889 + 0.450141i
$$534$$ 0 0
$$535$$ −11.0000 + 19.0526i −0.475571 + 0.823714i
$$536$$ 0 0
$$537$$ 18.0000 10.3923i 0.776757 0.448461i
$$538$$ 0 0
$$539$$ 15.0000 0.646096
$$540$$ 0 0
$$541$$ 2.00000 0.0859867 0.0429934 0.999075i $$-0.486311\pi$$
0.0429934 + 0.999075i $$0.486311\pi$$
$$542$$ 0 0
$$543$$ −30.0000 + 17.3205i −1.28742 + 0.743294i
$$544$$ 0 0
$$545$$ −12.0000 + 20.7846i −0.514024 + 0.890315i
$$546$$ 0 0
$$547$$ −0.500000 0.866025i −0.0213785 0.0370286i 0.855138 0.518400i $$-0.173472\pi$$
−0.876517 + 0.481371i $$0.840139\pi$$
$$548$$ 0 0
$$549$$ −12.0000 −0.512148
$$550$$ 0 0
$$551$$ 15.0000 + 25.9808i 0.639021 + 1.10682i
$$552$$ 0 0
$$553$$ 2.00000 3.46410i 0.0850487 0.147309i
$$554$$ 0 0
$$555$$ 34.6410i 1.47043i
$$556$$ 0 0
$$557$$ −26.0000 −1.10166 −0.550828 0.834619i $$-0.685688\pi$$
−0.550828 + 0.834619i $$0.685688\pi$$
$$558$$ 0 0
$$559$$ 36.0000 1.52264
$$560$$ 0 0
$$561$$ 7.50000 + 4.33013i 0.316650 + 0.182818i
$$562$$ 0 0
$$563$$ 16.5000 28.5788i 0.695392 1.20445i −0.274656 0.961542i $$-0.588564\pi$$
0.970048 0.242912i $$-0.0781026\pi$$
$$564$$ 0 0
$$565$$ 14.0000 + 24.2487i 0.588984 + 1.02015i
$$566$$ 0 0
$$567$$ 9.00000 15.5885i 0.377964 0.654654i
$$568$$ 0 0
$$569$$ 9.50000 + 16.4545i 0.398261 + 0.689808i 0.993511 0.113732i $$-0.0362806\pi$$
−0.595251 + 0.803540i $$0.702947\pi$$
$$570$$ 0 0
$$571$$ 9.50000 16.4545i 0.397563 0.688599i −0.595862 0.803087i $$-0.703189\pi$$
0.993425 + 0.114488i $$0.0365228\pi$$
$$572$$ 0 0
$$573$$ 3.00000 + 1.73205i 0.125327 + 0.0723575i
$$574$$ 0 0
$$575$$ 4.00000 0.166812
$$576$$ 0 0
$$577$$ 23.0000 0.957503 0.478751 0.877951i $$-0.341090\pi$$
0.478751 + 0.877951i $$0.341090\pi$$
$$578$$ 0 0
$$579$$ 1.73205i 0.0719816i
$$580$$ 0 0
$$581$$ −12.0000 + 20.7846i −0.497844 + 0.862291i
$$582$$ 0 0
$$583$$ −30.0000 51.9615i −1.24247 2.15203i
$$584$$ 0 0
$$585$$ 24.0000 0.992278
$$586$$ 0 0
$$587$$ −2.50000 4.33013i −0.103186 0.178723i 0.809810 0.586693i $$-0.199570\pi$$
−0.912996 + 0.407969i $$0.866237\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 30.0000 17.3205i 1.23404 0.712470i
$$592$$ 0 0
$$593$$ 6.00000 0.246390 0.123195 0.992382i $$-0.460686\pi$$
0.123195 + 0.992382i $$0.460686\pi$$
$$594$$ 0 0
$$595$$ 4.00000 0.163984
$$596$$ 0 0
$$597$$ −3.00000 + 1.73205i −0.122782 + 0.0708881i
$$598$$ 0 0
$$599$$ −21.0000 + 36.3731i −0.858037 + 1.48616i 0.0157622 + 0.999876i $$0.494983\pi$$
−0.873799 + 0.486287i $$0.838351\pi$$
$$600$$ 0 0
$$601$$ 4.50000 + 7.79423i 0.183559 + 0.317933i 0.943090 0.332538i $$-0.107905\pi$$
−0.759531 + 0.650471i $$0.774572\pi$$
$$602$$ 0 0
$$603$$ 10.5000 + 18.1865i 0.427593 + 0.740613i
$$604$$ 0 0
$$605$$ 14.0000 + 24.2487i 0.569181 + 0.985850i
$$606$$ 0 0
$$607$$ 4.00000 6.92820i 0.162355 0.281207i −0.773358 0.633970i $$-0.781424\pi$$
0.935713 + 0.352763i $$0.114758\pi$$
$$608$$ 0 0
$$609$$ 20.7846i 0.842235i
$$610$$ 0 0
$$611$$ 32.0000 1.29458
$$612$$ 0 0
$$613$$ 26.0000 1.05013 0.525065 0.851062i $$-0.324041\pi$$
0.525065 + 0.851062i $$0.324041\pi$$
$$614$$ 0 0
$$615$$ −9.00000 5.19615i −0.362915 0.209529i
$$616$$ 0 0
$$617$$ 8.50000 14.7224i 0.342197 0.592703i −0.642643 0.766165i $$-0.722162\pi$$
0.984840 + 0.173463i $$0.0554956\pi$$
$$618$$ 0 0
$$619$$ 17.5000 + 30.3109i 0.703384 + 1.21830i 0.967271 + 0.253744i $$0.0816620\pi$$
−0.263887 + 0.964554i $$0.585005\pi$$
$$620$$ 0 0
$$621$$ −18.0000 10.3923i −0.722315 0.417029i
$$622$$ 0 0
$$623$$ 10.0000 + 17.3205i 0.400642 + 0.693932i
$$624$$ 0 0
$$625$$ 9.50000 16.4545i 0.380000 0.658179i
$$626$$ 0 0
$$627$$ 37.5000 + 21.6506i 1.49761 + 0.864643i
$$628$$ 0 0
$$629$$ −10.0000 −0.398726
$$630$$ 0 0
$$631$$ −22.0000 −0.875806 −0.437903 0.899022i $$-0.644279\pi$$
−0.437903 + 0.899022i $$0.644279\pi$$
$$632$$ 0 0
$$633$$ 34.6410i 1.37686i
$$634$$ 0 0
$$635$$ 20.0000 34.6410i 0.793676 1.37469i
$$636$$ 0 0
$$637$$ 6.00000 + 10.3923i 0.237729 + 0.411758i
$$638$$ 0 0
$$639$$ 9.00000 15.5885i 0.356034 0.616670i
$$640$$ 0 0
$$641$$ −16.5000 28.5788i −0.651711 1.12880i −0.982708 0.185164i $$-0.940718\pi$$
0.330997 0.943632i $$-0.392615\pi$$
$$642$$ 0 0
$$643$$ −10.5000 + 18.1865i −0.414080 + 0.717207i −0.995331 0.0965169i $$-0.969230\pi$$
0.581252 + 0.813724i $$0.302563\pi$$
$$644$$ 0 0
$$645$$ −27.0000 + 15.5885i −1.06312 + 0.613795i
$$646$$ 0 0
$$647$$ 42.0000 1.65119 0.825595 0.564263i $$-0.190840\pi$$
0.825595 + 0.564263i $$0.190840\pi$$
$$648$$ 0 0
$$649$$ 35.0000 1.37387
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −9.00000 + 15.5885i −0.352197 + 0.610023i −0.986634 0.162951i $$-0.947899\pi$$
0.634437 + 0.772975i $$0.281232\pi$$
$$654$$ 0 0
$$655$$ 12.0000 + 20.7846i 0.468879 + 0.812122i
$$656$$ 0 0
$$657$$ −19.5000 + 33.7750i −0.760767 + 1.31769i
$$658$$ 0 0
$$659$$ −12.0000 20.7846i −0.467454 0.809653i 0.531855 0.846836i $$-0.321495\pi$$
−0.999309 + 0.0371821i $$0.988162\pi$$
$$660$$ 0 0
$$661$$ −1.00000 + 1.73205i −0.0388955 + 0.0673690i −0.884818 0.465937i $$-0.845717\pi$$
0.845922 + 0.533306i $$0.179051\pi$$
$$662$$ 0 0
$$663$$ 6.92820i 0.269069i
$$664$$ 0 0
$$665$$ 20.0000 0.775567
$$666$$ 0 0
$$667$$ 24.0000 0.929284
$$668$$ 0 0
$$669$$ −36.0000 20.7846i −1.39184 0.803579i
$$670$$ 0 0
$$671$$ 10.0000 17.3205i 0.386046 0.668651i
$$672$$ 0 0
$$673$$ −5.00000 8.66025i −0.192736 0.333828i 0.753420 0.657539i $$-0.228403\pi$$
−0.946156 + 0.323711i $$0.895069\pi$$
$$674$$ 0 0
$$675$$ 4.50000 2.59808i 0.173205 0.100000i
$$676$$ 0 0
$$677$$ −14.0000 24.2487i −0.538064 0.931954i −0.999008 0.0445248i $$-0.985823\pi$$
0.460945 0.887429i $$-0.347511\pi$$
$$678$$ 0 0
$$679$$ 13.0000 22.5167i 0.498894 0.864110i
$$680$$ 0 0
$$681$$ −4.50000 2.59808i −0.172440 0.0995585i
$$682$$ 0 0
$$683$$ −15.0000 −0.573959 −0.286980 0.957937i $$-0.592651\pi$$
−0.286980 + 0.957937i $$0.592651\pi$$
$$684$$ 0 0
$$685$$ −2.00000 −0.0764161
$$686$$ 0 0
$$687$$ 24.2487i 0.925146i
$$688$$ 0 0
$$689$$ 24.0000 41.5692i 0.914327 1.58366i
$$690$$ 0 0
$$691$$ −6.00000 10.3923i −0.228251 0.395342i 0.729039 0.684472i $$-0.239967\pi$$
−0.957290 + 0.289130i $$0.906634\pi$$
$$692$$ 0 0
$$693$$ 15.0000 + 25.9808i 0.569803 + 0.986928i
$$694$$ 0 0
$$695$$ −1.00000 1.73205i −0.0379322 0.0657004i
$$696$$ 0 0
$$697$$ 1.50000 2.59808i 0.0568166 0.0984092i
$$698$$ 0 0
$$699$$ −13.5000 + 7.79423i −0.510617 + 0.294805i
$$700$$ 0 0
$$701$$ 16.0000 0.604312 0.302156 0.953259i $$-0.402294\pi$$
0.302156 + 0.953259i $$0.402294\pi$$
$$702$$ 0 0
$$703$$ −50.0000 −1.88579
$$704$$ 0 0
$$705$$ −24.0000 + 13.8564i −0.903892 + 0.521862i
$$706$$ 0 0
$$707$$ −6.00000 + 10.3923i −0.225653 + 0.390843i
$$708$$ 0 0
$$709$$ 10.0000 + 17.3205i 0.375558 + 0.650485i 0.990410 0.138157i $$-0.0441178\pi$$
−0.614852 + 0.788642i $$0.710784\pi$$
$$710$$ 0 0
$$711$$ −6.00000 −0.225018
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ −20.0000 + 34.6410i −0.747958 + 1.29550i
$$716$$ 0 0
$$717$$ 20.7846i 0.776215i
$$718$$ 0 0
$$719$$ 30.0000 1.11881 0.559406 0.828894i $$-0.311029\pi$$
0.559406 + 0.828894i $$0.311029\pi$$
$$720$$ 0 0
$$721$$ 16.0000 0.595871
$$722$$ 0 0
$$723$$ −37.5000 21.6506i −1.39464 0.805196i
$$724$$ 0 0
$$725$$ −3.00000 + 5.19615i −0.111417 + 0.192980i
$$726$$ 0 0
$$727$$ 24.0000 + 41.5692i 0.890111 + 1.54172i 0.839742 + 0.542986i $$0.182706\pi$$
0.0503692 + 0.998731i $$0.483960\pi$$
$$728$$ 0 0
$$729$$ −27.0000 −1.00000
$$730$$ 0 0
$$731$$ −4.50000 7.79423i −0.166439 0.288280i
$$732$$ 0 0
$$733$$ 9.00000 15.5885i 0.332423 0.575773i −0.650564 0.759452i $$-0.725467\pi$$
0.982986 + 0.183679i $$0.0588007\pi$$
$$734$$ 0 0
$$735$$ −9.00000 5.19615i −0.331970 0.191663i
$$736$$ 0 0
$$737$$ −35.0000 −1.28924
$$738$$ 0 0
$$739$$ 21.0000 0.772497 0.386249 0.922395i $$-0.373771\pi$$
0.386249 + 0.922395i $$0.373771\pi$$
$$740$$ 0 0
$$741$$ 34.6410i 1.27257i
$$742$$ 0 0
$$743$$ 19.0000 32.9090i 0.697042 1.20731i −0.272445 0.962171i $$-0.587832\pi$$
0.969487 0.245141i $$-0.0788344\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 36.0000 1.31717
$$748$$ 0 0
$$749$$ −11.0000 19.0526i −0.401931 0.696165i
$$750$$ 0 0
$$751$$ 1.00000 1.73205i 0.0364905 0.0632034i −0.847203 0.531269i $$-0.821715\pi$$
0.883694 + 0.468065i $$0.155049\pi$$
$$752$$ 0 0
$$753$$ 4.50000 2.59808i 0.163989 0.0946792i
$$754$$ 0 0
$$755$$ 32.0000 1.16460
$$756$$ 0 0
$$757$$ −14.0000 −0.508839 −0.254419 0.967094i $$-0.581884\pi$$
−0.254419 + 0.967094i $$0.581884\pi$$
$$758$$ 0 0
$$759$$ 30.0000 17.3205i 1.08893 0.628695i
$$760$$ 0 0
$$761$$ −5.00000 + 8.66025i −0.181250 + 0.313934i −0.942306 0.334752i $$-0.891348\pi$$
0.761057 + 0.648686i $$0.224681\pi$$
$$762$$ 0 0
$$763$$ −12.0000 20.7846i −0.434429 0.752453i
$$764$$ 0 0
$$765$$ −3.00000 5.19615i −0.108465 0.187867i
$$766$$ 0 0
$$767$$ 14.0000 + 24.2487i 0.505511 + 0.875570i
$$768$$ 0 0
$$769$$ −1.00000 + 1.73205i −0.0360609 + 0.0624593i −0.883493 0.468445i $$-0.844814\pi$$
0.847432 + 0.530904i $$0.178148\pi$$
$$770$$ 0 0
$$771$$ 5.19615i 0.187135i
$$772$$ 0 0
$$773$$ 24.0000 0.863220 0.431610 0.902060i $$-0.357946\pi$$
0.431610 + 0.902060i $$0.357946\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ −30.0000 17.3205i −1.07624 0.621370i
$$778$$ 0 0
$$779$$ 7.50000 12.9904i 0.268715 0.465429i
$$780$$ 0 0
$$781$$ 15.0000 + 25.9808i 0.536742 + 0.929665i
$$782$$ 0 0
$$783$$ 27.0000 15.5885i 0.964901 0.557086i
$$784$$ 0 0
$$785$$ −24.0000 41.5692i −0.856597 1.48367i
$$786$$ 0 0
$$787$$ 14.0000 24.2487i 0.499046 0.864373i −0.500953 0.865474i $$-0.667017\pi$$
0.999999 + 0.00110111i $$0.000350496\pi$$
$$788$$ 0 0
$$789$$ −27.0000 15.5885i −0.961225 0.554964i
$$790$$ 0 0