# Properties

 Label 84.2.i.a.25.1 Level $84$ Weight $2$ Character 84.25 Analytic conductor $0.671$ Analytic rank $0$ Dimension $2$ Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [84,2,Mod(25,84)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(84, 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("84.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$84 = 2^{2} \cdot 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 84.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: $$0.670743376979$$ 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 25.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 84.25 Dual form 84.2.i.a.37.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(0.500000 - 0.866025i) q^{3} +(1.00000 + 1.73205i) q^{5} +(0.500000 - 2.59808i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+(0.500000 - 0.866025i) q^{3} +(1.00000 + 1.73205i) q^{5} +(0.500000 - 2.59808i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-1.00000 + 1.73205i) q^{11} -3.00000 q^{13} +2.00000 q^{15} +(-4.00000 + 6.92820i) q^{17} +(0.500000 + 0.866025i) q^{19} +(-2.00000 - 1.73205i) q^{21} +(-4.00000 - 6.92820i) q^{23} +(0.500000 - 0.866025i) q^{25} -1.00000 q^{27} +4.00000 q^{29} +(-1.50000 + 2.59808i) q^{31} +(1.00000 + 1.73205i) q^{33} +(5.00000 - 1.73205i) q^{35} +(0.500000 + 0.866025i) q^{37} +(-1.50000 + 2.59808i) q^{39} +6.00000 q^{41} +11.0000 q^{43} +(1.00000 - 1.73205i) q^{45} +(-3.00000 - 5.19615i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(4.00000 + 6.92820i) q^{51} +(6.00000 - 10.3923i) q^{53} -4.00000 q^{55} +1.00000 q^{57} +(-2.00000 + 3.46410i) q^{59} +(3.00000 + 5.19615i) q^{61} +(-2.50000 + 0.866025i) q^{63} +(-3.00000 - 5.19615i) q^{65} +(-6.50000 + 11.2583i) q^{67} -8.00000 q^{69} -10.0000 q^{71} +(5.50000 - 9.52628i) q^{73} +(-0.500000 - 0.866025i) q^{75} +(4.00000 + 3.46410i) q^{77} +(1.50000 + 2.59808i) q^{79} +(-0.500000 + 0.866025i) q^{81} +2.00000 q^{83} -16.0000 q^{85} +(2.00000 - 3.46410i) q^{87} +(-1.50000 + 7.79423i) q^{91} +(1.50000 + 2.59808i) q^{93} +(-1.00000 + 1.73205i) q^{95} +10.0000 q^{97} +2.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + q^{3} + 2 q^{5} + q^{7} - q^{9}+O(q^{10})$$ 2 * q + q^3 + 2 * q^5 + q^7 - q^9 $$2 q + q^{3} + 2 q^{5} + q^{7} - q^{9} - 2 q^{11} - 6 q^{13} + 4 q^{15} - 8 q^{17} + q^{19} - 4 q^{21} - 8 q^{23} + q^{25} - 2 q^{27} + 8 q^{29} - 3 q^{31} + 2 q^{33} + 10 q^{35} + q^{37} - 3 q^{39} + 12 q^{41} + 22 q^{43} + 2 q^{45} - 6 q^{47} - 13 q^{49} + 8 q^{51} + 12 q^{53} - 8 q^{55} + 2 q^{57} - 4 q^{59} + 6 q^{61} - 5 q^{63} - 6 q^{65} - 13 q^{67} - 16 q^{69} - 20 q^{71} + 11 q^{73} - q^{75} + 8 q^{77} + 3 q^{79} - q^{81} + 4 q^{83} - 32 q^{85} + 4 q^{87} - 3 q^{91} + 3 q^{93} - 2 q^{95} + 20 q^{97} + 4 q^{99}+O(q^{100})$$ 2 * q + q^3 + 2 * q^5 + q^7 - q^9 - 2 * q^11 - 6 * q^13 + 4 * q^15 - 8 * q^17 + q^19 - 4 * q^21 - 8 * q^23 + q^25 - 2 * q^27 + 8 * q^29 - 3 * q^31 + 2 * q^33 + 10 * q^35 + q^37 - 3 * q^39 + 12 * q^41 + 22 * q^43 + 2 * q^45 - 6 * q^47 - 13 * q^49 + 8 * q^51 + 12 * q^53 - 8 * q^55 + 2 * q^57 - 4 * q^59 + 6 * q^61 - 5 * q^63 - 6 * q^65 - 13 * q^67 - 16 * q^69 - 20 * q^71 + 11 * q^73 - q^75 + 8 * q^77 + 3 * q^79 - q^81 + 4 * q^83 - 32 * q^85 + 4 * q^87 - 3 * q^91 + 3 * q^93 - 2 * q^95 + 20 * q^97 + 4 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$$.

 $$n$$ $$29$$ $$43$$ $$73$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0.500000 0.866025i 0.288675 0.500000i
$$4$$ 0 0
$$5$$ 1.00000 + 1.73205i 0.447214 + 0.774597i 0.998203 0.0599153i $$-0.0190830\pi$$
−0.550990 + 0.834512i $$0.685750\pi$$
$$6$$ 0 0
$$7$$ 0.500000 2.59808i 0.188982 0.981981i
$$8$$ 0 0
$$9$$ −0.500000 0.866025i −0.166667 0.288675i
$$10$$ 0 0
$$11$$ −1.00000 + 1.73205i −0.301511 + 0.522233i −0.976478 0.215615i $$-0.930824\pi$$
0.674967 + 0.737848i $$0.264158\pi$$
$$12$$ 0 0
$$13$$ −3.00000 −0.832050 −0.416025 0.909353i $$-0.636577\pi$$
−0.416025 + 0.909353i $$0.636577\pi$$
$$14$$ 0 0
$$15$$ 2.00000 0.516398
$$16$$ 0 0
$$17$$ −4.00000 + 6.92820i −0.970143 + 1.68034i −0.275029 + 0.961436i $$0.588688\pi$$
−0.695113 + 0.718900i $$0.744646\pi$$
$$18$$ 0 0
$$19$$ 0.500000 + 0.866025i 0.114708 + 0.198680i 0.917663 0.397360i $$-0.130073\pi$$
−0.802955 + 0.596040i $$0.796740\pi$$
$$20$$ 0 0
$$21$$ −2.00000 1.73205i −0.436436 0.377964i
$$22$$ 0 0
$$23$$ −4.00000 6.92820i −0.834058 1.44463i −0.894795 0.446476i $$-0.852679\pi$$
0.0607377 0.998154i $$-0.480655\pi$$
$$24$$ 0 0
$$25$$ 0.500000 0.866025i 0.100000 0.173205i
$$26$$ 0 0
$$27$$ −1.00000 −0.192450
$$28$$ 0 0
$$29$$ 4.00000 0.742781 0.371391 0.928477i $$-0.378881\pi$$
0.371391 + 0.928477i $$0.378881\pi$$
$$30$$ 0 0
$$31$$ −1.50000 + 2.59808i −0.269408 + 0.466628i −0.968709 0.248199i $$-0.920161\pi$$
0.699301 + 0.714827i $$0.253495\pi$$
$$32$$ 0 0
$$33$$ 1.00000 + 1.73205i 0.174078 + 0.301511i
$$34$$ 0 0
$$35$$ 5.00000 1.73205i 0.845154 0.292770i
$$36$$ 0 0
$$37$$ 0.500000 + 0.866025i 0.0821995 + 0.142374i 0.904194 0.427121i $$-0.140472\pi$$
−0.821995 + 0.569495i $$0.807139\pi$$
$$38$$ 0 0
$$39$$ −1.50000 + 2.59808i −0.240192 + 0.416025i
$$40$$ 0 0
$$41$$ 6.00000 0.937043 0.468521 0.883452i $$-0.344787\pi$$
0.468521 + 0.883452i $$0.344787\pi$$
$$42$$ 0 0
$$43$$ 11.0000 1.67748 0.838742 0.544529i $$-0.183292\pi$$
0.838742 + 0.544529i $$0.183292\pi$$
$$44$$ 0 0
$$45$$ 1.00000 1.73205i 0.149071 0.258199i
$$46$$ 0 0
$$47$$ −3.00000 5.19615i −0.437595 0.757937i 0.559908 0.828554i $$-0.310836\pi$$
−0.997503 + 0.0706177i $$0.977503\pi$$
$$48$$ 0 0
$$49$$ −6.50000 2.59808i −0.928571 0.371154i
$$50$$ 0 0
$$51$$ 4.00000 + 6.92820i 0.560112 + 0.970143i
$$52$$ 0 0
$$53$$ 6.00000 10.3923i 0.824163 1.42749i −0.0783936 0.996922i $$-0.524979\pi$$
0.902557 0.430570i $$-0.141688\pi$$
$$54$$ 0 0
$$55$$ −4.00000 −0.539360
$$56$$ 0 0
$$57$$ 1.00000 0.132453
$$58$$ 0 0
$$59$$ −2.00000 + 3.46410i −0.260378 + 0.450988i −0.966342 0.257260i $$-0.917180\pi$$
0.705965 + 0.708247i $$0.250514\pi$$
$$60$$ 0 0
$$61$$ 3.00000 + 5.19615i 0.384111 + 0.665299i 0.991645 0.128994i $$-0.0411748\pi$$
−0.607535 + 0.794293i $$0.707841\pi$$
$$62$$ 0 0
$$63$$ −2.50000 + 0.866025i −0.314970 + 0.109109i
$$64$$ 0 0
$$65$$ −3.00000 5.19615i −0.372104 0.644503i
$$66$$ 0 0
$$67$$ −6.50000 + 11.2583i −0.794101 + 1.37542i 0.129307 + 0.991605i $$0.458725\pi$$
−0.923408 + 0.383819i $$0.874609\pi$$
$$68$$ 0 0
$$69$$ −8.00000 −0.963087
$$70$$ 0 0
$$71$$ −10.0000 −1.18678 −0.593391 0.804914i $$-0.702211\pi$$
−0.593391 + 0.804914i $$0.702211\pi$$
$$72$$ 0 0
$$73$$ 5.50000 9.52628i 0.643726 1.11497i −0.340868 0.940111i $$-0.610721\pi$$
0.984594 0.174855i $$-0.0559458\pi$$
$$74$$ 0 0
$$75$$ −0.500000 0.866025i −0.0577350 0.100000i
$$76$$ 0 0
$$77$$ 4.00000 + 3.46410i 0.455842 + 0.394771i
$$78$$ 0 0
$$79$$ 1.50000 + 2.59808i 0.168763 + 0.292306i 0.937985 0.346675i $$-0.112689\pi$$
−0.769222 + 0.638982i $$0.779356\pi$$
$$80$$ 0 0
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ 0 0
$$83$$ 2.00000 0.219529 0.109764 0.993958i $$-0.464990\pi$$
0.109764 + 0.993958i $$0.464990\pi$$
$$84$$ 0 0
$$85$$ −16.0000 −1.73544
$$86$$ 0 0
$$87$$ 2.00000 3.46410i 0.214423 0.371391i
$$88$$ 0 0
$$89$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$90$$ 0 0
$$91$$ −1.50000 + 7.79423i −0.157243 + 0.817057i
$$92$$ 0 0
$$93$$ 1.50000 + 2.59808i 0.155543 + 0.269408i
$$94$$ 0 0
$$95$$ −1.00000 + 1.73205i −0.102598 + 0.177705i
$$96$$ 0 0
$$97$$ 10.0000 1.01535 0.507673 0.861550i $$-0.330506\pi$$
0.507673 + 0.861550i $$0.330506\pi$$
$$98$$ 0 0
$$99$$ 2.00000 0.201008
$$100$$ 0 0
$$101$$ −5.00000 + 8.66025i −0.497519 + 0.861727i −0.999996 0.00286291i $$-0.999089\pi$$
0.502477 + 0.864590i $$0.332422\pi$$
$$102$$ 0 0
$$103$$ −5.50000 9.52628i −0.541931 0.938652i −0.998793 0.0491146i $$-0.984360\pi$$
0.456862 0.889538i $$-0.348973\pi$$
$$104$$ 0 0
$$105$$ 1.00000 5.19615i 0.0975900 0.507093i
$$106$$ 0 0
$$107$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$108$$ 0 0
$$109$$ 5.50000 9.52628i 0.526804 0.912452i −0.472708 0.881219i $$-0.656723\pi$$
0.999512 0.0312328i $$-0.00994332\pi$$
$$110$$ 0 0
$$111$$ 1.00000 0.0949158
$$112$$ 0 0
$$113$$ −14.0000 −1.31701 −0.658505 0.752577i $$-0.728811\pi$$
−0.658505 + 0.752577i $$0.728811\pi$$
$$114$$ 0 0
$$115$$ 8.00000 13.8564i 0.746004 1.29212i
$$116$$ 0 0
$$117$$ 1.50000 + 2.59808i 0.138675 + 0.240192i
$$118$$ 0 0
$$119$$ 16.0000 + 13.8564i 1.46672 + 1.27021i
$$120$$ 0 0
$$121$$ 3.50000 + 6.06218i 0.318182 + 0.551107i
$$122$$ 0 0
$$123$$ 3.00000 5.19615i 0.270501 0.468521i
$$124$$ 0 0
$$125$$ 12.0000 1.07331
$$126$$ 0 0
$$127$$ 3.00000 0.266207 0.133103 0.991102i $$-0.457506\pi$$
0.133103 + 0.991102i $$0.457506\pi$$
$$128$$ 0 0
$$129$$ 5.50000 9.52628i 0.484248 0.838742i
$$130$$ 0 0
$$131$$ 1.00000 + 1.73205i 0.0873704 + 0.151330i 0.906399 0.422423i $$-0.138820\pi$$
−0.819028 + 0.573753i $$0.805487\pi$$
$$132$$ 0 0
$$133$$ 2.50000 0.866025i 0.216777 0.0750939i
$$134$$ 0 0
$$135$$ −1.00000 1.73205i −0.0860663 0.149071i
$$136$$ 0 0
$$137$$ −2.00000 + 3.46410i −0.170872 + 0.295958i −0.938725 0.344668i $$-0.887992\pi$$
0.767853 + 0.640626i $$0.221325\pi$$
$$138$$ 0 0
$$139$$ −5.00000 −0.424094 −0.212047 0.977259i $$-0.568013\pi$$
−0.212047 + 0.977259i $$0.568013\pi$$
$$140$$ 0 0
$$141$$ −6.00000 −0.505291
$$142$$ 0 0
$$143$$ 3.00000 5.19615i 0.250873 0.434524i
$$144$$ 0 0
$$145$$ 4.00000 + 6.92820i 0.332182 + 0.575356i
$$146$$ 0 0
$$147$$ −5.50000 + 4.33013i −0.453632 + 0.357143i
$$148$$ 0 0
$$149$$ 6.00000 + 10.3923i 0.491539 + 0.851371i 0.999953 0.00974235i $$-0.00310113\pi$$
−0.508413 + 0.861113i $$0.669768\pi$$
$$150$$ 0 0
$$151$$ 4.00000 6.92820i 0.325515 0.563809i −0.656101 0.754673i $$-0.727796\pi$$
0.981617 + 0.190864i $$0.0611289\pi$$
$$152$$ 0 0
$$153$$ 8.00000 0.646762
$$154$$ 0 0
$$155$$ −6.00000 −0.481932
$$156$$ 0 0
$$157$$ −1.00000 + 1.73205i −0.0798087 + 0.138233i −0.903167 0.429289i $$-0.858764\pi$$
0.823359 + 0.567521i $$0.192098\pi$$
$$158$$ 0 0
$$159$$ −6.00000 10.3923i −0.475831 0.824163i
$$160$$ 0 0
$$161$$ −20.0000 + 6.92820i −1.57622 + 0.546019i
$$162$$ 0 0
$$163$$ 2.00000 + 3.46410i 0.156652 + 0.271329i 0.933659 0.358162i $$-0.116597\pi$$
−0.777007 + 0.629492i $$0.783263\pi$$
$$164$$ 0 0
$$165$$ −2.00000 + 3.46410i −0.155700 + 0.269680i
$$166$$ 0 0
$$167$$ −2.00000 −0.154765 −0.0773823 0.997001i $$-0.524656\pi$$
−0.0773823 + 0.997001i $$0.524656\pi$$
$$168$$ 0 0
$$169$$ −4.00000 −0.307692
$$170$$ 0 0
$$171$$ 0.500000 0.866025i 0.0382360 0.0662266i
$$172$$ 0 0
$$173$$ −8.00000 13.8564i −0.608229 1.05348i −0.991532 0.129861i $$-0.958547\pi$$
0.383304 0.923622i $$-0.374786\pi$$
$$174$$ 0 0
$$175$$ −2.00000 1.73205i −0.151186 0.130931i
$$176$$ 0 0
$$177$$ 2.00000 + 3.46410i 0.150329 + 0.260378i
$$178$$ 0 0
$$179$$ −3.00000 + 5.19615i −0.224231 + 0.388379i −0.956088 0.293079i $$-0.905320\pi$$
0.731858 + 0.681457i $$0.238654\pi$$
$$180$$ 0 0
$$181$$ −15.0000 −1.11494 −0.557471 0.830197i $$-0.688228\pi$$
−0.557471 + 0.830197i $$0.688228\pi$$
$$182$$ 0 0
$$183$$ 6.00000 0.443533
$$184$$ 0 0
$$185$$ −1.00000 + 1.73205i −0.0735215 + 0.127343i
$$186$$ 0 0
$$187$$ −8.00000 13.8564i −0.585018 1.01328i
$$188$$ 0 0
$$189$$ −0.500000 + 2.59808i −0.0363696 + 0.188982i
$$190$$ 0 0
$$191$$ −3.00000 5.19615i −0.217072 0.375980i 0.736839 0.676068i $$-0.236317\pi$$
−0.953912 + 0.300088i $$0.902984\pi$$
$$192$$ 0 0
$$193$$ −5.50000 + 9.52628i −0.395899 + 0.685717i −0.993215 0.116289i $$-0.962900\pi$$
0.597317 + 0.802005i $$0.296234\pi$$
$$194$$ 0 0
$$195$$ −6.00000 −0.429669
$$196$$ 0 0
$$197$$ 8.00000 0.569976 0.284988 0.958531i $$-0.408010\pi$$
0.284988 + 0.958531i $$0.408010\pi$$
$$198$$ 0 0
$$199$$ −4.00000 + 6.92820i −0.283552 + 0.491127i −0.972257 0.233915i $$-0.924846\pi$$
0.688705 + 0.725042i $$0.258180\pi$$
$$200$$ 0 0
$$201$$ 6.50000 + 11.2583i 0.458475 + 0.794101i
$$202$$ 0 0
$$203$$ 2.00000 10.3923i 0.140372 0.729397i
$$204$$ 0 0
$$205$$ 6.00000 + 10.3923i 0.419058 + 0.725830i
$$206$$ 0 0
$$207$$ −4.00000 + 6.92820i −0.278019 + 0.481543i
$$208$$ 0 0
$$209$$ −2.00000 −0.138343
$$210$$ 0 0
$$211$$ −4.00000 −0.275371 −0.137686 0.990476i $$-0.543966\pi$$
−0.137686 + 0.990476i $$0.543966\pi$$
$$212$$ 0 0
$$213$$ −5.00000 + 8.66025i −0.342594 + 0.593391i
$$214$$ 0 0
$$215$$ 11.0000 + 19.0526i 0.750194 + 1.29937i
$$216$$ 0 0
$$217$$ 6.00000 + 5.19615i 0.407307 + 0.352738i
$$218$$ 0 0
$$219$$ −5.50000 9.52628i −0.371656 0.643726i
$$220$$ 0 0
$$221$$ 12.0000 20.7846i 0.807207 1.39812i
$$222$$ 0 0
$$223$$ 8.00000 0.535720 0.267860 0.963458i $$-0.413684\pi$$
0.267860 + 0.963458i $$0.413684\pi$$
$$224$$ 0 0
$$225$$ −1.00000 −0.0666667
$$226$$ 0 0
$$227$$ 9.00000 15.5885i 0.597351 1.03464i −0.395860 0.918311i $$-0.629553\pi$$
0.993210 0.116331i $$-0.0371134\pi$$
$$228$$ 0 0
$$229$$ −0.500000 0.866025i −0.0330409 0.0572286i 0.849032 0.528341i $$-0.177186\pi$$
−0.882073 + 0.471113i $$0.843853\pi$$
$$230$$ 0 0
$$231$$ 5.00000 1.73205i 0.328976 0.113961i
$$232$$ 0 0
$$233$$ −7.00000 12.1244i −0.458585 0.794293i 0.540301 0.841472i $$-0.318310\pi$$
−0.998886 + 0.0471787i $$0.984977\pi$$
$$234$$ 0 0
$$235$$ 6.00000 10.3923i 0.391397 0.677919i
$$236$$ 0 0
$$237$$ 3.00000 0.194871
$$238$$ 0 0
$$239$$ 18.0000 1.16432 0.582162 0.813073i $$-0.302207\pi$$
0.582162 + 0.813073i $$0.302207\pi$$
$$240$$ 0 0
$$241$$ −7.00000 + 12.1244i −0.450910 + 0.780998i −0.998443 0.0557856i $$-0.982234\pi$$
0.547533 + 0.836784i $$0.315567\pi$$
$$242$$ 0 0
$$243$$ 0.500000 + 0.866025i 0.0320750 + 0.0555556i
$$244$$ 0 0
$$245$$ −2.00000 13.8564i −0.127775 0.885253i
$$246$$ 0 0
$$247$$ −1.50000 2.59808i −0.0954427 0.165312i
$$248$$ 0 0
$$249$$ 1.00000 1.73205i 0.0633724 0.109764i
$$250$$ 0 0
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 0 0
$$253$$ 16.0000 1.00591
$$254$$ 0 0
$$255$$ −8.00000 + 13.8564i −0.500979 + 0.867722i
$$256$$ 0 0
$$257$$ −9.00000 15.5885i −0.561405 0.972381i −0.997374 0.0724199i $$-0.976928\pi$$
0.435970 0.899961i $$-0.356405\pi$$
$$258$$ 0 0
$$259$$ 2.50000 0.866025i 0.155342 0.0538122i
$$260$$ 0 0
$$261$$ −2.00000 3.46410i −0.123797 0.214423i
$$262$$ 0 0
$$263$$ −6.00000 + 10.3923i −0.369976 + 0.640817i −0.989561 0.144112i $$-0.953967\pi$$
0.619586 + 0.784929i $$0.287301\pi$$
$$264$$ 0 0
$$265$$ 24.0000 1.47431
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 1.00000 1.73205i 0.0609711 0.105605i −0.833929 0.551872i $$-0.813914\pi$$
0.894900 + 0.446267i $$0.147247\pi$$
$$270$$ 0 0
$$271$$ 12.0000 + 20.7846i 0.728948 + 1.26258i 0.957328 + 0.289003i $$0.0933238\pi$$
−0.228380 + 0.973572i $$0.573343\pi$$
$$272$$ 0 0
$$273$$ 6.00000 + 5.19615i 0.363137 + 0.314485i
$$274$$ 0 0
$$275$$ 1.00000 + 1.73205i 0.0603023 + 0.104447i
$$276$$ 0 0
$$277$$ −8.50000 + 14.7224i −0.510716 + 0.884585i 0.489207 + 0.872167i $$0.337286\pi$$
−0.999923 + 0.0124177i $$0.996047\pi$$
$$278$$ 0 0
$$279$$ 3.00000 0.179605
$$280$$ 0 0
$$281$$ 20.0000 1.19310 0.596550 0.802576i $$-0.296538\pi$$
0.596550 + 0.802576i $$0.296538\pi$$
$$282$$ 0 0
$$283$$ −9.50000 + 16.4545i −0.564716 + 0.978117i 0.432360 + 0.901701i $$0.357681\pi$$
−0.997076 + 0.0764162i $$0.975652\pi$$
$$284$$ 0 0
$$285$$ 1.00000 + 1.73205i 0.0592349 + 0.102598i
$$286$$ 0 0
$$287$$ 3.00000 15.5885i 0.177084 0.920158i
$$288$$ 0 0
$$289$$ −23.5000 40.7032i −1.38235 2.39431i
$$290$$ 0 0
$$291$$ 5.00000 8.66025i 0.293105 0.507673i
$$292$$ 0 0
$$293$$ −24.0000 −1.40209 −0.701047 0.713115i $$-0.747284\pi$$
−0.701047 + 0.713115i $$0.747284\pi$$
$$294$$ 0 0
$$295$$ −8.00000 −0.465778
$$296$$ 0 0
$$297$$ 1.00000 1.73205i 0.0580259 0.100504i
$$298$$ 0 0
$$299$$ 12.0000 + 20.7846i 0.693978 + 1.20201i
$$300$$ 0 0
$$301$$ 5.50000 28.5788i 0.317015 1.64726i
$$302$$ 0 0
$$303$$ 5.00000 + 8.66025i 0.287242 + 0.497519i
$$304$$ 0 0
$$305$$ −6.00000 + 10.3923i −0.343559 + 0.595062i
$$306$$ 0 0
$$307$$ −23.0000 −1.31268 −0.656340 0.754466i $$-0.727896\pi$$
−0.656340 + 0.754466i $$0.727896\pi$$
$$308$$ 0 0
$$309$$ −11.0000 −0.625768
$$310$$ 0 0
$$311$$ 1.00000 1.73205i 0.0567048 0.0982156i −0.836280 0.548303i $$-0.815274\pi$$
0.892984 + 0.450088i $$0.148607\pi$$
$$312$$ 0 0
$$313$$ 8.50000 + 14.7224i 0.480448 + 0.832161i 0.999748 0.0224310i $$-0.00714060\pi$$
−0.519300 + 0.854592i $$0.673807\pi$$
$$314$$ 0 0
$$315$$ −4.00000 3.46410i −0.225374 0.195180i
$$316$$ 0 0
$$317$$ 12.0000 + 20.7846i 0.673987 + 1.16738i 0.976764 + 0.214318i $$0.0687530\pi$$
−0.302777 + 0.953062i $$0.597914\pi$$
$$318$$ 0 0
$$319$$ −4.00000 + 6.92820i −0.223957 + 0.387905i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −8.00000 −0.445132
$$324$$ 0 0
$$325$$ −1.50000 + 2.59808i −0.0832050 + 0.144115i
$$326$$ 0 0
$$327$$ −5.50000 9.52628i −0.304151 0.526804i
$$328$$ 0 0
$$329$$ −15.0000 + 5.19615i −0.826977 + 0.286473i
$$330$$ 0 0
$$331$$ −8.50000 14.7224i −0.467202 0.809218i 0.532096 0.846684i $$-0.321405\pi$$
−0.999298 + 0.0374662i $$0.988071\pi$$
$$332$$ 0 0
$$333$$ 0.500000 0.866025i 0.0273998 0.0474579i
$$334$$ 0 0
$$335$$ −26.0000 −1.42053
$$336$$ 0 0
$$337$$ 21.0000 1.14394 0.571971 0.820274i $$-0.306179\pi$$
0.571971 + 0.820274i $$0.306179\pi$$
$$338$$ 0 0
$$339$$ −7.00000 + 12.1244i −0.380188 + 0.658505i
$$340$$ 0 0
$$341$$ −3.00000 5.19615i −0.162459 0.281387i
$$342$$ 0 0
$$343$$ −10.0000 + 15.5885i −0.539949 + 0.841698i
$$344$$ 0 0
$$345$$ −8.00000 13.8564i −0.430706 0.746004i
$$346$$ 0 0
$$347$$ −12.0000 + 20.7846i −0.644194 + 1.11578i 0.340293 + 0.940319i $$0.389474\pi$$
−0.984487 + 0.175457i $$0.943860\pi$$
$$348$$ 0 0
$$349$$ −14.0000 −0.749403 −0.374701 0.927146i $$-0.622255\pi$$
−0.374701 + 0.927146i $$0.622255\pi$$
$$350$$ 0 0
$$351$$ 3.00000 0.160128
$$352$$ 0 0
$$353$$ 3.00000 5.19615i 0.159674 0.276563i −0.775077 0.631867i $$-0.782289\pi$$
0.934751 + 0.355303i $$0.115622\pi$$
$$354$$ 0 0
$$355$$ −10.0000 17.3205i −0.530745 0.919277i
$$356$$ 0 0
$$357$$ 20.0000 6.92820i 1.05851 0.366679i
$$358$$ 0 0
$$359$$ 10.0000 + 17.3205i 0.527780 + 0.914141i 0.999476 + 0.0323801i $$0.0103087\pi$$
−0.471696 + 0.881761i $$0.656358\pi$$
$$360$$ 0 0
$$361$$ 9.00000 15.5885i 0.473684 0.820445i
$$362$$ 0 0
$$363$$ 7.00000 0.367405
$$364$$ 0 0
$$365$$ 22.0000 1.15153
$$366$$ 0 0
$$367$$ −2.50000 + 4.33013i −0.130499 + 0.226031i −0.923869 0.382709i $$-0.874991\pi$$
0.793370 + 0.608740i $$0.208325\pi$$
$$368$$ 0 0
$$369$$ −3.00000 5.19615i −0.156174 0.270501i
$$370$$ 0 0
$$371$$ −24.0000 20.7846i −1.24602 1.07908i
$$372$$ 0 0
$$373$$ 2.50000 + 4.33013i 0.129445 + 0.224205i 0.923462 0.383691i $$-0.125347\pi$$
−0.794017 + 0.607896i $$0.792014\pi$$
$$374$$ 0 0
$$375$$ 6.00000 10.3923i 0.309839 0.536656i
$$376$$ 0 0
$$377$$ −12.0000 −0.618031
$$378$$ 0 0
$$379$$ 13.0000 0.667765 0.333883 0.942615i $$-0.391641\pi$$
0.333883 + 0.942615i $$0.391641\pi$$
$$380$$ 0 0
$$381$$ 1.50000 2.59808i 0.0768473 0.133103i
$$382$$ 0 0
$$383$$ 14.0000 + 24.2487i 0.715367 + 1.23905i 0.962818 + 0.270151i $$0.0870736\pi$$
−0.247451 + 0.968900i $$0.579593\pi$$
$$384$$ 0 0
$$385$$ −2.00000 + 10.3923i −0.101929 + 0.529641i
$$386$$ 0 0
$$387$$ −5.50000 9.52628i −0.279581 0.484248i
$$388$$ 0 0
$$389$$ −5.00000 + 8.66025i −0.253510 + 0.439092i −0.964490 0.264120i $$-0.914918\pi$$
0.710980 + 0.703213i $$0.248252\pi$$
$$390$$ 0 0
$$391$$ 64.0000 3.23662
$$392$$ 0 0
$$393$$ 2.00000 0.100887
$$394$$ 0 0
$$395$$ −3.00000 + 5.19615i −0.150946 + 0.261447i
$$396$$ 0 0
$$397$$ −1.50000 2.59808i −0.0752828 0.130394i 0.825926 0.563778i $$-0.190653\pi$$
−0.901209 + 0.433384i $$0.857319\pi$$
$$398$$ 0 0
$$399$$ 0.500000 2.59808i 0.0250313 0.130066i
$$400$$ 0 0
$$401$$ 6.00000 + 10.3923i 0.299626 + 0.518967i 0.976050 0.217545i $$-0.0698049\pi$$
−0.676425 + 0.736512i $$0.736472\pi$$
$$402$$ 0 0
$$403$$ 4.50000 7.79423i 0.224161 0.388258i
$$404$$ 0 0
$$405$$ −2.00000 −0.0993808
$$406$$ 0 0
$$407$$ −2.00000 −0.0991363
$$408$$ 0 0
$$409$$ 9.50000 16.4545i 0.469745 0.813622i −0.529657 0.848212i $$-0.677679\pi$$
0.999402 + 0.0345902i $$0.0110126\pi$$
$$410$$ 0 0
$$411$$ 2.00000 + 3.46410i 0.0986527 + 0.170872i
$$412$$ 0 0
$$413$$ 8.00000 + 6.92820i 0.393654 + 0.340915i
$$414$$ 0 0
$$415$$ 2.00000 + 3.46410i 0.0981761 + 0.170046i
$$416$$ 0 0
$$417$$ −2.50000 + 4.33013i −0.122426 + 0.212047i
$$418$$ 0 0
$$419$$ 18.0000 0.879358 0.439679 0.898155i $$-0.355092\pi$$
0.439679 + 0.898155i $$0.355092\pi$$
$$420$$ 0 0
$$421$$ −27.0000 −1.31590 −0.657950 0.753062i $$-0.728576\pi$$
−0.657950 + 0.753062i $$0.728576\pi$$
$$422$$ 0 0
$$423$$ −3.00000 + 5.19615i −0.145865 + 0.252646i
$$424$$ 0 0
$$425$$ 4.00000 + 6.92820i 0.194029 + 0.336067i
$$426$$ 0 0
$$427$$ 15.0000 5.19615i 0.725901 0.251459i
$$428$$ 0 0
$$429$$ −3.00000 5.19615i −0.144841 0.250873i
$$430$$ 0 0
$$431$$ 15.0000 25.9808i 0.722525 1.25145i −0.237460 0.971397i $$-0.576315\pi$$
0.959985 0.280052i $$-0.0903517\pi$$
$$432$$ 0 0
$$433$$ −25.0000 −1.20142 −0.600712 0.799466i $$-0.705116\pi$$
−0.600712 + 0.799466i $$0.705116\pi$$
$$434$$ 0 0
$$435$$ 8.00000 0.383571
$$436$$ 0 0
$$437$$ 4.00000 6.92820i 0.191346 0.331421i
$$438$$ 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
$$441$$ 1.00000 + 6.92820i 0.0476190 + 0.329914i
$$442$$ 0 0
$$443$$ 2.00000 + 3.46410i 0.0950229 + 0.164584i 0.909618 0.415445i $$-0.136374\pi$$
−0.814595 + 0.580030i $$0.803041\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 12.0000 0.567581
$$448$$ 0 0
$$449$$ 22.0000 1.03824 0.519122 0.854700i $$-0.326259\pi$$
0.519122 + 0.854700i $$0.326259\pi$$
$$450$$ 0 0
$$451$$ −6.00000 + 10.3923i −0.282529 + 0.489355i
$$452$$ 0 0
$$453$$ −4.00000 6.92820i −0.187936 0.325515i
$$454$$ 0 0
$$455$$ −15.0000 + 5.19615i −0.703211 + 0.243599i
$$456$$ 0 0
$$457$$ −6.50000 11.2583i −0.304057 0.526642i 0.672994 0.739648i $$-0.265008\pi$$
−0.977051 + 0.213006i $$0.931675\pi$$
$$458$$ 0 0
$$459$$ 4.00000 6.92820i 0.186704 0.323381i
$$460$$ 0 0
$$461$$ 4.00000 0.186299 0.0931493 0.995652i $$-0.470307\pi$$
0.0931493 + 0.995652i $$0.470307\pi$$
$$462$$ 0 0
$$463$$ −11.0000 −0.511213 −0.255607 0.966781i $$-0.582275\pi$$
−0.255607 + 0.966781i $$0.582275\pi$$
$$464$$ 0 0
$$465$$ −3.00000 + 5.19615i −0.139122 + 0.240966i
$$466$$ 0 0
$$467$$ −17.0000 29.4449i −0.786666 1.36255i −0.927999 0.372584i $$-0.878472\pi$$
0.141332 0.989962i $$-0.454861\pi$$
$$468$$ 0 0
$$469$$ 26.0000 + 22.5167i 1.20057 + 1.03972i
$$470$$ 0 0
$$471$$ 1.00000 + 1.73205i 0.0460776 + 0.0798087i
$$472$$ 0 0
$$473$$ −11.0000 + 19.0526i −0.505781 + 0.876038i
$$474$$ 0 0
$$475$$ 1.00000 0.0458831
$$476$$ 0 0
$$477$$ −12.0000 −0.549442
$$478$$ 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
$$481$$ −1.50000 2.59808i −0.0683941 0.118462i
$$482$$ 0 0
$$483$$ −4.00000 + 20.7846i −0.182006 + 0.945732i
$$484$$ 0 0
$$485$$ 10.0000 + 17.3205i 0.454077 + 0.786484i
$$486$$ 0 0
$$487$$ 9.50000 16.4545i 0.430486 0.745624i −0.566429 0.824110i $$-0.691675\pi$$
0.996915 + 0.0784867i $$0.0250088\pi$$
$$488$$ 0 0
$$489$$ 4.00000 0.180886
$$490$$ 0 0
$$491$$ −36.0000 −1.62466 −0.812329 0.583200i $$-0.801800\pi$$
−0.812329 + 0.583200i $$0.801800\pi$$
$$492$$ 0 0
$$493$$ −16.0000 + 27.7128i −0.720604 + 1.24812i
$$494$$ 0 0
$$495$$ 2.00000 + 3.46410i 0.0898933 + 0.155700i
$$496$$ 0 0
$$497$$ −5.00000 + 25.9808i −0.224281 + 1.16540i
$$498$$ 0 0
$$499$$ 14.5000 + 25.1147i 0.649109 + 1.12429i 0.983336 + 0.181797i $$0.0581915\pi$$
−0.334227 + 0.942493i $$0.608475\pi$$
$$500$$ 0 0
$$501$$ −1.00000 + 1.73205i −0.0446767 + 0.0773823i
$$502$$ 0 0
$$503$$ −30.0000 −1.33763 −0.668817 0.743427i $$-0.733199\pi$$
−0.668817 + 0.743427i $$0.733199\pi$$
$$504$$ 0 0
$$505$$ −20.0000 −0.889988
$$506$$ 0 0
$$507$$ −2.00000 + 3.46410i −0.0888231 + 0.153846i
$$508$$ 0 0
$$509$$ −9.00000 15.5885i −0.398918 0.690946i 0.594675 0.803966i $$-0.297281\pi$$
−0.993593 + 0.113020i $$0.963948\pi$$
$$510$$ 0 0
$$511$$ −22.0000 19.0526i −0.973223 0.842836i
$$512$$ 0 0
$$513$$ −0.500000 0.866025i −0.0220755 0.0382360i
$$514$$ 0 0
$$515$$ 11.0000 19.0526i 0.484718 0.839556i
$$516$$ 0 0
$$517$$ 12.0000 0.527759
$$518$$ 0 0
$$519$$ −16.0000 −0.702322
$$520$$ 0 0
$$521$$ 18.0000 31.1769i 0.788594 1.36589i −0.138234 0.990400i $$-0.544143\pi$$
0.926828 0.375486i $$-0.122524\pi$$
$$522$$ 0 0
$$523$$ 15.5000 + 26.8468i 0.677768 + 1.17393i 0.975652 + 0.219326i $$0.0703858\pi$$
−0.297884 + 0.954602i $$0.596281\pi$$
$$524$$ 0 0
$$525$$ −2.50000 + 0.866025i −0.109109 + 0.0377964i
$$526$$ 0 0
$$527$$ −12.0000 20.7846i −0.522728 0.905392i
$$528$$ 0 0
$$529$$ −20.5000 + 35.5070i −0.891304 + 1.54378i
$$530$$ 0 0
$$531$$ 4.00000 0.173585
$$532$$ 0 0
$$533$$ −18.0000 −0.779667
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 3.00000 + 5.19615i 0.129460 + 0.224231i
$$538$$ 0 0
$$539$$ 11.0000 8.66025i 0.473804 0.373024i
$$540$$ 0 0
$$541$$ 7.50000 + 12.9904i 0.322450 + 0.558500i 0.980993 0.194043i $$-0.0621602\pi$$
−0.658543 + 0.752543i $$0.728827\pi$$
$$542$$ 0 0
$$543$$ −7.50000 + 12.9904i −0.321856 + 0.557471i
$$544$$ 0 0
$$545$$ 22.0000 0.942376
$$546$$ 0 0
$$547$$ −12.0000 −0.513083 −0.256541 0.966533i $$-0.582583\pi$$
−0.256541 + 0.966533i $$0.582583\pi$$
$$548$$ 0 0
$$549$$ 3.00000 5.19615i 0.128037 0.221766i
$$550$$ 0 0
$$551$$ 2.00000 + 3.46410i 0.0852029 + 0.147576i
$$552$$ 0 0
$$553$$ 7.50000 2.59808i 0.318932 0.110481i
$$554$$ 0 0
$$555$$ 1.00000 + 1.73205i 0.0424476 + 0.0735215i
$$556$$ 0 0
$$557$$ −11.0000 + 19.0526i −0.466085 + 0.807283i −0.999250 0.0387286i $$-0.987669\pi$$
0.533165 + 0.846011i $$0.321003\pi$$
$$558$$ 0 0
$$559$$ −33.0000 −1.39575
$$560$$ 0 0
$$561$$ −16.0000 −0.675521
$$562$$ 0 0
$$563$$ 23.0000 39.8372i 0.969334 1.67894i 0.271846 0.962341i $$-0.412366\pi$$
0.697489 0.716596i $$-0.254301\pi$$
$$564$$ 0 0
$$565$$ −14.0000 24.2487i −0.588984 1.02015i
$$566$$ 0 0
$$567$$ 2.00000 + 1.73205i 0.0839921 + 0.0727393i
$$568$$ 0 0
$$569$$ −3.00000 5.19615i −0.125767 0.217834i 0.796266 0.604947i $$-0.206806\pi$$
−0.922032 + 0.387113i $$0.873472\pi$$
$$570$$ 0 0
$$571$$ 10.5000 18.1865i 0.439411 0.761083i −0.558233 0.829684i $$-0.688520\pi$$
0.997644 + 0.0686016i $$0.0218537\pi$$
$$572$$ 0 0
$$573$$ −6.00000 −0.250654
$$574$$ 0 0
$$575$$ −8.00000 −0.333623
$$576$$ 0 0
$$577$$ 20.5000 35.5070i 0.853426 1.47818i −0.0246713 0.999696i $$-0.507854\pi$$
0.878097 0.478482i $$-0.158813\pi$$
$$578$$ 0 0
$$579$$ 5.50000 + 9.52628i 0.228572 + 0.395899i
$$580$$ 0 0
$$581$$ 1.00000 5.19615i 0.0414870 0.215573i
$$582$$ 0 0
$$583$$ 12.0000 + 20.7846i 0.496989 + 0.860811i
$$584$$ 0 0
$$585$$ −3.00000 + 5.19615i −0.124035 + 0.214834i
$$586$$ 0 0
$$587$$ 32.0000 1.32078 0.660391 0.750922i $$-0.270391\pi$$
0.660391 + 0.750922i $$0.270391\pi$$
$$588$$ 0 0
$$589$$ −3.00000 −0.123613
$$590$$ 0 0
$$591$$ 4.00000 6.92820i 0.164538 0.284988i
$$592$$ 0 0
$$593$$ 3.00000 + 5.19615i 0.123195 + 0.213380i 0.921026 0.389501i $$-0.127353\pi$$
−0.797831 + 0.602881i $$0.794019\pi$$
$$594$$ 0 0
$$595$$ −8.00000 + 41.5692i −0.327968 + 1.70417i
$$596$$ 0 0
$$597$$ 4.00000 + 6.92820i 0.163709 + 0.283552i
$$598$$ 0 0
$$599$$ 6.00000 10.3923i 0.245153 0.424618i −0.717021 0.697051i $$-0.754495\pi$$
0.962175 + 0.272433i $$0.0878284\pi$$
$$600$$ 0 0
$$601$$ −1.00000 −0.0407909 −0.0203954 0.999792i $$-0.506493\pi$$
−0.0203954 + 0.999792i $$0.506493\pi$$
$$602$$ 0 0
$$603$$ 13.0000 0.529401
$$604$$ 0 0
$$605$$ −7.00000 + 12.1244i −0.284590 + 0.492925i
$$606$$ 0 0
$$607$$ 1.50000 + 2.59808i 0.0608831 + 0.105453i 0.894860 0.446346i $$-0.147275\pi$$
−0.833977 + 0.551799i $$0.813942\pi$$
$$608$$ 0 0
$$609$$ −8.00000 6.92820i −0.324176 0.280745i
$$610$$ 0 0
$$611$$ 9.00000 + 15.5885i 0.364101 + 0.630641i
$$612$$ 0 0
$$613$$ 15.0000 25.9808i 0.605844 1.04935i −0.386073 0.922468i $$-0.626169\pi$$
0.991917 0.126885i $$-0.0404979\pi$$
$$614$$ 0 0
$$615$$ 12.0000 0.483887
$$616$$ 0 0
$$617$$ 26.0000 1.04672 0.523360 0.852111i $$-0.324678\pi$$
0.523360 + 0.852111i $$0.324678\pi$$
$$618$$ 0 0
$$619$$ 5.50000 9.52628i 0.221064 0.382893i −0.734068 0.679076i $$-0.762380\pi$$
0.955131 + 0.296183i $$0.0957138\pi$$
$$620$$ 0 0
$$621$$ 4.00000 + 6.92820i 0.160514 + 0.278019i
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 9.50000 + 16.4545i 0.380000 + 0.658179i
$$626$$ 0 0
$$627$$ −1.00000 + 1.73205i −0.0399362 + 0.0691714i
$$628$$ 0 0
$$629$$ −8.00000 −0.318981
$$630$$ 0 0
$$631$$ −16.0000 −0.636950 −0.318475 0.947931i $$-0.603171\pi$$
−0.318475 + 0.947931i $$0.603171\pi$$
$$632$$ 0 0
$$633$$ −2.00000 + 3.46410i −0.0794929 + 0.137686i
$$634$$ 0 0
$$635$$ 3.00000 + 5.19615i 0.119051 + 0.206203i
$$636$$ 0 0
$$637$$ 19.5000 + 7.79423i 0.772618 + 0.308819i
$$638$$ 0 0
$$639$$ 5.00000 + 8.66025i 0.197797 + 0.342594i
$$640$$ 0 0
$$641$$ 20.0000 34.6410i 0.789953 1.36824i −0.136043 0.990703i $$-0.543438\pi$$
0.925995 0.377535i $$-0.123228\pi$$
$$642$$ 0 0
$$643$$ 35.0000 1.38027 0.690133 0.723683i $$-0.257552\pi$$
0.690133 + 0.723683i $$0.257552\pi$$
$$644$$ 0 0
$$645$$ 22.0000 0.866249
$$646$$ 0 0
$$647$$ −3.00000 + 5.19615i −0.117942 + 0.204282i −0.918952 0.394369i $$-0.870963\pi$$
0.801010 + 0.598651i $$0.204296\pi$$
$$648$$ 0 0
$$649$$ −4.00000 6.92820i −0.157014 0.271956i
$$650$$ 0 0
$$651$$ 7.50000 2.59808i 0.293948 0.101827i
$$652$$ 0 0
$$653$$ 3.00000 + 5.19615i 0.117399 + 0.203341i 0.918736 0.394872i $$-0.129211\pi$$
−0.801337 + 0.598213i $$0.795878\pi$$
$$654$$ 0 0
$$655$$ −2.00000 + 3.46410i −0.0781465 + 0.135354i
$$656$$ 0 0
$$657$$ −11.0000 −0.429151
$$658$$ 0 0
$$659$$ −28.0000 −1.09073 −0.545363 0.838200i $$-0.683608\pi$$
−0.545363 + 0.838200i $$0.683608\pi$$
$$660$$ 0 0
$$661$$ 14.5000 25.1147i 0.563985 0.976850i −0.433159 0.901318i $$-0.642601\pi$$
0.997143 0.0755324i $$-0.0240656\pi$$
$$662$$ 0 0
$$663$$ −12.0000 20.7846i −0.466041 0.807207i
$$664$$ 0 0
$$665$$ 4.00000 + 3.46410i 0.155113 + 0.134332i
$$666$$ 0 0
$$667$$ −16.0000 27.7128i −0.619522 1.07304i
$$668$$ 0 0
$$669$$ 4.00000 6.92820i 0.154649 0.267860i
$$670$$ 0 0
$$671$$ −12.0000 −0.463255
$$672$$ 0 0
$$673$$ −1.00000 −0.0385472 −0.0192736 0.999814i $$-0.506135\pi$$
−0.0192736 + 0.999814i $$0.506135\pi$$
$$674$$ 0 0
$$675$$ −0.500000 + 0.866025i −0.0192450 + 0.0333333i
$$676$$ 0 0
$$677$$ −6.00000 10.3923i −0.230599 0.399409i 0.727386 0.686229i $$-0.240735\pi$$
−0.957984 + 0.286820i $$0.907402\pi$$
$$678$$ 0 0
$$679$$ 5.00000 25.9808i 0.191882 0.997050i
$$680$$ 0 0
$$681$$ −9.00000 15.5885i −0.344881 0.597351i
$$682$$ 0 0
$$683$$ −18.0000 + 31.1769i −0.688751 + 1.19295i 0.283491 + 0.958975i $$0.408507\pi$$
−0.972242 + 0.233977i $$0.924826\pi$$
$$684$$ 0 0
$$685$$ −8.00000 −0.305664
$$686$$ 0 0
$$687$$ −1.00000 −0.0381524
$$688$$ 0 0
$$689$$ −18.0000 + 31.1769i −0.685745 + 1.18775i
$$690$$ 0 0
$$691$$ 21.5000 + 37.2391i 0.817899 + 1.41664i 0.907228 + 0.420640i $$0.138194\pi$$
−0.0893292 + 0.996002i $$0.528472\pi$$
$$692$$ 0 0
$$693$$ 1.00000 5.19615i 0.0379869 0.197386i
$$694$$ 0 0
$$695$$ −5.00000 8.66025i −0.189661 0.328502i
$$696$$ 0 0
$$697$$ −24.0000 + 41.5692i −0.909065 + 1.57455i
$$698$$ 0 0
$$699$$ −14.0000 −0.529529
$$700$$ 0 0
$$701$$ −8.00000 −0.302156 −0.151078 0.988522i $$-0.548274\pi$$
−0.151078 + 0.988522i $$0.548274\pi$$
$$702$$ 0 0
$$703$$ −0.500000 + 0.866025i −0.0188579 + 0.0326628i
$$704$$ 0 0
$$705$$ −6.00000 10.3923i −0.225973 0.391397i
$$706$$ 0 0
$$707$$ 20.0000 + 17.3205i 0.752177 + 0.651405i
$$708$$ 0 0
$$709$$ −7.00000 12.1244i −0.262891 0.455340i 0.704118 0.710083i $$-0.251342\pi$$
−0.967009 + 0.254743i $$0.918009\pi$$
$$710$$ 0 0
$$711$$ 1.50000 2.59808i 0.0562544 0.0974355i
$$712$$ 0 0
$$713$$ 24.0000 0.898807
$$714$$ 0 0
$$715$$ 12.0000 0.448775
$$716$$ 0 0
$$717$$ 9.00000 15.5885i 0.336111 0.582162i
$$718$$ 0 0
$$719$$ 3.00000 + 5.19615i 0.111881 + 0.193784i 0.916529 0.399969i $$-0.130979\pi$$
−0.804648 + 0.593753i $$0.797646\pi$$
$$720$$ 0 0
$$721$$ −27.5000 + 9.52628i −1.02415 + 0.354777i
$$722$$ 0 0
$$723$$ 7.00000 + 12.1244i 0.260333 + 0.450910i
$$724$$ 0 0
$$725$$ 2.00000 3.46410i 0.0742781 0.128654i
$$726$$ 0 0
$$727$$ −23.0000 −0.853023 −0.426511 0.904482i $$-0.640258\pi$$
−0.426511 + 0.904482i $$0.640258\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ −44.0000 + 76.2102i −1.62740 + 2.81874i
$$732$$ 0 0
$$733$$ −22.5000 38.9711i −0.831056 1.43943i −0.897201 0.441622i $$-0.854403\pi$$
0.0661448 0.997810i $$-0.478930\pi$$
$$734$$ 0 0
$$735$$ −13.0000 5.19615i −0.479512 0.191663i
$$736$$ 0 0
$$737$$ −13.0000 22.5167i −0.478861 0.829412i
$$738$$ 0 0
$$739$$ 4.50000 7.79423i 0.165535 0.286715i −0.771310 0.636460i $$-0.780398\pi$$
0.936845 + 0.349744i $$0.113732\pi$$
$$740$$ 0 0
$$741$$ −3.00000 −0.110208
$$742$$ 0 0
$$743$$ −18.0000 −0.660356 −0.330178 0.943919i $$-0.607109\pi$$
−0.330178 + 0.943919i $$0.607109\pi$$
$$744$$ 0 0
$$745$$ −12.0000 + 20.7846i −0.439646 + 0.761489i
$$746$$ 0 0
$$747$$ −1.00000 1.73205i −0.0365881 0.0633724i
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −7.50000 12.9904i −0.273679 0.474026i 0.696122 0.717923i $$-0.254907\pi$$
−0.969801 + 0.243898i $$0.921574\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 16.0000 0.582300
$$756$$ 0 0
$$757$$ 42.0000 1.52652 0.763258 0.646094i $$-0.223599\pi$$
0.763258 + 0.646094i $$0.223599\pi$$
$$758$$ 0 0
$$759$$ 8.00000 13.8564i 0.290382 0.502956i
$$760$$ 0 0
$$761$$ −4.00000 6.92820i −0.145000 0.251147i 0.784373 0.620289i $$-0.212985\pi$$
−0.929373 + 0.369142i $$0.879652\pi$$
$$762$$ 0 0
$$763$$ −22.0000 19.0526i −0.796453 0.689749i
$$764$$ 0 0
$$765$$ 8.00000 + 13.8564i 0.289241 + 0.500979i
$$766$$ 0 0
$$767$$ 6.00000 10.3923i 0.216647 0.375244i
$$768$$ 0 0
$$769$$ 31.0000 1.11789 0.558944 0.829205i $$-0.311207\pi$$
0.558944 + 0.829205i $$0.311207\pi$$
$$770$$ 0 0
$$771$$ −18.0000 −0.648254
$$772$$ 0 0
$$773$$ −11.0000 + 19.0526i −0.395643 + 0.685273i −0.993183 0.116566i $$-0.962811\pi$$
0.597540 + 0.801839i $$0.296145\pi$$
$$774$$ 0 0
$$775$$ 1.50000 + 2.59808i 0.0538816 + 0.0933257i
$$776$$ 0 0
$$777$$ 0.500000 2.59808i 0.0179374 0.0932055i
$$778$$ 0 0
$$779$$ 3.00000 + 5.19615i 0.107486 + 0.186171i
$$780$$ 0 0
$$781$$ 10.0000 17.3205i 0.357828 0.619777i
$$782$$ 0 0
$$783$$ −4.00000 −0.142948
$$784$$ 0 0
$$785$$ −4.00000 −0.142766
$$786$$ 0 0
$$787$$ −12.0000 + 20.7846i −0.427754 + 0.740891i −0.996673 0.0815020i $$-0.974028\pi$$
0.568919 + 0.822393i $$0.307362\pi$$
$$788$$ 0 0
$$789$$ 6.00000 + 10.3923i 0.213606 + 0.369976i
$$790$$ 0 0