# Properties

 Label 1078.2.e.k.67.1 Level $1078$ Weight $2$ Character 1078.67 Analytic conductor $8.608$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1078,2,Mod(67,1078)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1078, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1078.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1078 = 2 \cdot 7^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1078.e (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

 Self dual: no Analytic conductor: $$8.60787333789$$ 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: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 154) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 67.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 1078.67 Dual form 1078.2.e.k.177.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{6} -1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})$$ $$q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{6} -1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +(0.500000 - 0.866025i) q^{11} +(0.500000 + 0.866025i) q^{12} +1.00000 q^{13} +(-0.500000 - 0.866025i) q^{16} +(-3.00000 + 5.19615i) q^{17} +(-1.00000 + 1.73205i) q^{18} +(1.00000 + 1.73205i) q^{19} +1.00000 q^{22} +(3.00000 + 5.19615i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(2.50000 - 4.33013i) q^{25} +(0.500000 + 0.866025i) q^{26} +5.00000 q^{27} +9.00000 q^{29} +(-2.00000 + 3.46410i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.500000 - 0.866025i) q^{33} -6.00000 q^{34} -2.00000 q^{36} +(-1.00000 - 1.73205i) q^{37} +(-1.00000 + 1.73205i) q^{38} +(0.500000 - 0.866025i) q^{39} +6.00000 q^{41} -4.00000 q^{43} +(0.500000 + 0.866025i) q^{44} +(-3.00000 + 5.19615i) q^{46} +(-3.00000 - 5.19615i) q^{47} -1.00000 q^{48} +5.00000 q^{50} +(3.00000 + 5.19615i) q^{51} +(-0.500000 + 0.866025i) q^{52} +(2.50000 + 4.33013i) q^{54} +2.00000 q^{57} +(4.50000 + 7.79423i) q^{58} +(-1.50000 + 2.59808i) q^{59} +(5.50000 + 9.52628i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(0.500000 - 0.866025i) q^{66} +(-5.50000 + 9.52628i) q^{67} +(-3.00000 - 5.19615i) q^{68} +6.00000 q^{69} +(-1.00000 - 1.73205i) q^{72} +(1.00000 - 1.73205i) q^{73} +(1.00000 - 1.73205i) q^{74} +(-2.50000 - 4.33013i) q^{75} -2.00000 q^{76} +1.00000 q^{78} +(-2.50000 - 4.33013i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(3.00000 + 5.19615i) q^{82} +6.00000 q^{83} +(-2.00000 - 3.46410i) q^{86} +(4.50000 - 7.79423i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(-9.00000 - 15.5885i) q^{89} -6.00000 q^{92} +(2.00000 + 3.46410i) q^{93} +(3.00000 - 5.19615i) q^{94} +(-0.500000 - 0.866025i) q^{96} +13.0000 q^{97} +2.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + q^{2} + q^{3} - q^{4} + 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10})$$ 2 * q + q^2 + q^3 - q^4 + 2 * q^6 - 2 * q^8 + 2 * q^9 $$2 q + q^{2} + q^{3} - q^{4} + 2 q^{6} - 2 q^{8} + 2 q^{9} + q^{11} + q^{12} + 2 q^{13} - q^{16} - 6 q^{17} - 2 q^{18} + 2 q^{19} + 2 q^{22} + 6 q^{23} - q^{24} + 5 q^{25} + q^{26} + 10 q^{27} + 18 q^{29} - 4 q^{31} + q^{32} - q^{33} - 12 q^{34} - 4 q^{36} - 2 q^{37} - 2 q^{38} + q^{39} + 12 q^{41} - 8 q^{43} + q^{44} - 6 q^{46} - 6 q^{47} - 2 q^{48} + 10 q^{50} + 6 q^{51} - q^{52} + 5 q^{54} + 4 q^{57} + 9 q^{58} - 3 q^{59} + 11 q^{61} - 8 q^{62} + 2 q^{64} + q^{66} - 11 q^{67} - 6 q^{68} + 12 q^{69} - 2 q^{72} + 2 q^{73} + 2 q^{74} - 5 q^{75} - 4 q^{76} + 2 q^{78} - 5 q^{79} - q^{81} + 6 q^{82} + 12 q^{83} - 4 q^{86} + 9 q^{87} - q^{88} - 18 q^{89} - 12 q^{92} + 4 q^{93} + 6 q^{94} - q^{96} + 26 q^{97} + 4 q^{99}+O(q^{100})$$ 2 * q + q^2 + q^3 - q^4 + 2 * q^6 - 2 * q^8 + 2 * q^9 + q^11 + q^12 + 2 * q^13 - q^16 - 6 * q^17 - 2 * q^18 + 2 * q^19 + 2 * q^22 + 6 * q^23 - q^24 + 5 * q^25 + q^26 + 10 * q^27 + 18 * q^29 - 4 * q^31 + q^32 - q^33 - 12 * q^34 - 4 * q^36 - 2 * q^37 - 2 * q^38 + q^39 + 12 * q^41 - 8 * q^43 + q^44 - 6 * q^46 - 6 * q^47 - 2 * q^48 + 10 * q^50 + 6 * q^51 - q^52 + 5 * q^54 + 4 * q^57 + 9 * q^58 - 3 * q^59 + 11 * q^61 - 8 * q^62 + 2 * q^64 + q^66 - 11 * q^67 - 6 * q^68 + 12 * q^69 - 2 * q^72 + 2 * q^73 + 2 * q^74 - 5 * q^75 - 4 * q^76 + 2 * q^78 - 5 * q^79 - q^81 + 6 * q^82 + 12 * q^83 - 4 * q^86 + 9 * q^87 - q^88 - 18 * q^89 - 12 * q^92 + 4 * q^93 + 6 * q^94 - q^96 + 26 * q^97 + 4 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times$$.

 $$n$$ $$199$$ $$981$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.500000 + 0.866025i 0.353553 + 0.612372i
$$3$$ 0.500000 0.866025i 0.288675 0.500000i −0.684819 0.728714i $$-0.740119\pi$$
0.973494 + 0.228714i $$0.0734519\pi$$
$$4$$ −0.500000 + 0.866025i −0.250000 + 0.433013i
$$5$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$6$$ 1.00000 0.408248
$$7$$ 0 0
$$8$$ −1.00000 −0.353553
$$9$$ 1.00000 + 1.73205i 0.333333 + 0.577350i
$$10$$ 0 0
$$11$$ 0.500000 0.866025i 0.150756 0.261116i
$$12$$ 0.500000 + 0.866025i 0.144338 + 0.250000i
$$13$$ 1.00000 0.277350 0.138675 0.990338i $$-0.455716\pi$$
0.138675 + 0.990338i $$0.455716\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ −3.00000 + 5.19615i −0.727607 + 1.26025i 0.230285 + 0.973123i $$0.426034\pi$$
−0.957892 + 0.287129i $$0.907299\pi$$
$$18$$ −1.00000 + 1.73205i −0.235702 + 0.408248i
$$19$$ 1.00000 + 1.73205i 0.229416 + 0.397360i 0.957635 0.287984i $$-0.0929851\pi$$
−0.728219 + 0.685344i $$0.759652\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 1.00000 0.213201
$$23$$ 3.00000 + 5.19615i 0.625543 + 1.08347i 0.988436 + 0.151642i $$0.0484560\pi$$
−0.362892 + 0.931831i $$0.618211\pi$$
$$24$$ −0.500000 + 0.866025i −0.102062 + 0.176777i
$$25$$ 2.50000 4.33013i 0.500000 0.866025i
$$26$$ 0.500000 + 0.866025i 0.0980581 + 0.169842i
$$27$$ 5.00000 0.962250
$$28$$ 0 0
$$29$$ 9.00000 1.67126 0.835629 0.549294i $$-0.185103\pi$$
0.835629 + 0.549294i $$0.185103\pi$$
$$30$$ 0 0
$$31$$ −2.00000 + 3.46410i −0.359211 + 0.622171i −0.987829 0.155543i $$-0.950287\pi$$
0.628619 + 0.777714i $$0.283621\pi$$
$$32$$ 0.500000 0.866025i 0.0883883 0.153093i
$$33$$ −0.500000 0.866025i −0.0870388 0.150756i
$$34$$ −6.00000 −1.02899
$$35$$ 0 0
$$36$$ −2.00000 −0.333333
$$37$$ −1.00000 1.73205i −0.164399 0.284747i 0.772043 0.635571i $$-0.219235\pi$$
−0.936442 + 0.350823i $$0.885902\pi$$
$$38$$ −1.00000 + 1.73205i −0.162221 + 0.280976i
$$39$$ 0.500000 0.866025i 0.0800641 0.138675i
$$40$$ 0 0
$$41$$ 6.00000 0.937043 0.468521 0.883452i $$-0.344787\pi$$
0.468521 + 0.883452i $$0.344787\pi$$
$$42$$ 0 0
$$43$$ −4.00000 −0.609994 −0.304997 0.952353i $$-0.598656\pi$$
−0.304997 + 0.952353i $$0.598656\pi$$
$$44$$ 0.500000 + 0.866025i 0.0753778 + 0.130558i
$$45$$ 0 0
$$46$$ −3.00000 + 5.19615i −0.442326 + 0.766131i
$$47$$ −3.00000 5.19615i −0.437595 0.757937i 0.559908 0.828554i $$-0.310836\pi$$
−0.997503 + 0.0706177i $$0.977503\pi$$
$$48$$ −1.00000 −0.144338
$$49$$ 0 0
$$50$$ 5.00000 0.707107
$$51$$ 3.00000 + 5.19615i 0.420084 + 0.727607i
$$52$$ −0.500000 + 0.866025i −0.0693375 + 0.120096i
$$53$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$54$$ 2.50000 + 4.33013i 0.340207 + 0.589256i
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 2.00000 0.264906
$$58$$ 4.50000 + 7.79423i 0.590879 + 1.02343i
$$59$$ −1.50000 + 2.59808i −0.195283 + 0.338241i −0.946993 0.321253i $$-0.895896\pi$$
0.751710 + 0.659494i $$0.229229\pi$$
$$60$$ 0 0
$$61$$ 5.50000 + 9.52628i 0.704203 + 1.21972i 0.966978 + 0.254858i $$0.0820288\pi$$
−0.262776 + 0.964857i $$0.584638\pi$$
$$62$$ −4.00000 −0.508001
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 0.500000 0.866025i 0.0615457 0.106600i
$$67$$ −5.50000 + 9.52628i −0.671932 + 1.16382i 0.305424 + 0.952217i $$0.401202\pi$$
−0.977356 + 0.211604i $$0.932131\pi$$
$$68$$ −3.00000 5.19615i −0.363803 0.630126i
$$69$$ 6.00000 0.722315
$$70$$ 0 0
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ −1.00000 1.73205i −0.117851 0.204124i
$$73$$ 1.00000 1.73205i 0.117041 0.202721i −0.801553 0.597924i $$-0.795992\pi$$
0.918594 + 0.395203i $$0.129326\pi$$
$$74$$ 1.00000 1.73205i 0.116248 0.201347i
$$75$$ −2.50000 4.33013i −0.288675 0.500000i
$$76$$ −2.00000 −0.229416
$$77$$ 0 0
$$78$$ 1.00000 0.113228
$$79$$ −2.50000 4.33013i −0.281272 0.487177i 0.690426 0.723403i $$-0.257423\pi$$
−0.971698 + 0.236225i $$0.924090\pi$$
$$80$$ 0 0
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ 3.00000 + 5.19615i 0.331295 + 0.573819i
$$83$$ 6.00000 0.658586 0.329293 0.944228i $$-0.393190\pi$$
0.329293 + 0.944228i $$0.393190\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ −2.00000 3.46410i −0.215666 0.373544i
$$87$$ 4.50000 7.79423i 0.482451 0.835629i
$$88$$ −0.500000 + 0.866025i −0.0533002 + 0.0923186i
$$89$$ −9.00000 15.5885i −0.953998 1.65237i −0.736644 0.676280i $$-0.763591\pi$$
−0.217354 0.976093i $$-0.569742\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ −6.00000 −0.625543
$$93$$ 2.00000 + 3.46410i 0.207390 + 0.359211i
$$94$$ 3.00000 5.19615i 0.309426 0.535942i
$$95$$ 0 0
$$96$$ −0.500000 0.866025i −0.0510310 0.0883883i
$$97$$ 13.0000 1.31995 0.659975 0.751288i $$-0.270567\pi$$
0.659975 + 0.751288i $$0.270567\pi$$
$$98$$ 0 0
$$99$$ 2.00000 0.201008
$$100$$ 2.50000 + 4.33013i 0.250000 + 0.433013i
$$101$$ −7.50000 + 12.9904i −0.746278 + 1.29259i 0.203317 + 0.979113i $$0.434828\pi$$
−0.949595 + 0.313478i $$0.898506\pi$$
$$102$$ −3.00000 + 5.19615i −0.297044 + 0.514496i
$$103$$ −8.00000 13.8564i −0.788263 1.36531i −0.927030 0.374987i $$-0.877647\pi$$
0.138767 0.990325i $$-0.455686\pi$$
$$104$$ −1.00000 −0.0980581
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −6.00000 10.3923i −0.580042 1.00466i −0.995474 0.0950377i $$-0.969703\pi$$
0.415432 0.909624i $$-0.363630\pi$$
$$108$$ −2.50000 + 4.33013i −0.240563 + 0.416667i
$$109$$ −1.00000 + 1.73205i −0.0957826 + 0.165900i −0.909935 0.414751i $$-0.863869\pi$$
0.814152 + 0.580651i $$0.197202\pi$$
$$110$$ 0 0
$$111$$ −2.00000 −0.189832
$$112$$ 0 0
$$113$$ 9.00000 0.846649 0.423324 0.905978i $$-0.360863\pi$$
0.423324 + 0.905978i $$0.360863\pi$$
$$114$$ 1.00000 + 1.73205i 0.0936586 + 0.162221i
$$115$$ 0 0
$$116$$ −4.50000 + 7.79423i −0.417815 + 0.723676i
$$117$$ 1.00000 + 1.73205i 0.0924500 + 0.160128i
$$118$$ −3.00000 −0.276172
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −0.500000 0.866025i −0.0454545 0.0787296i
$$122$$ −5.50000 + 9.52628i −0.497947 + 0.862469i
$$123$$ 3.00000 5.19615i 0.270501 0.468521i
$$124$$ −2.00000 3.46410i −0.179605 0.311086i
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −7.00000 −0.621150 −0.310575 0.950549i $$-0.600522\pi$$
−0.310575 + 0.950549i $$0.600522\pi$$
$$128$$ 0.500000 + 0.866025i 0.0441942 + 0.0765466i
$$129$$ −2.00000 + 3.46410i −0.176090 + 0.304997i
$$130$$ 0 0
$$131$$ 9.00000 + 15.5885i 0.786334 + 1.36197i 0.928199 + 0.372084i $$0.121357\pi$$
−0.141865 + 0.989886i $$0.545310\pi$$
$$132$$ 1.00000 0.0870388
$$133$$ 0 0
$$134$$ −11.0000 −0.950255
$$135$$ 0 0
$$136$$ 3.00000 5.19615i 0.257248 0.445566i
$$137$$ 4.50000 7.79423i 0.384461 0.665906i −0.607233 0.794524i $$-0.707721\pi$$
0.991694 + 0.128618i $$0.0410540\pi$$
$$138$$ 3.00000 + 5.19615i 0.255377 + 0.442326i
$$139$$ −8.00000 −0.678551 −0.339276 0.940687i $$-0.610182\pi$$
−0.339276 + 0.940687i $$0.610182\pi$$
$$140$$ 0 0
$$141$$ −6.00000 −0.505291
$$142$$ 0 0
$$143$$ 0.500000 0.866025i 0.0418121 0.0724207i
$$144$$ 1.00000 1.73205i 0.0833333 0.144338i
$$145$$ 0 0
$$146$$ 2.00000 0.165521
$$147$$ 0 0
$$148$$ 2.00000 0.164399
$$149$$ −3.00000 5.19615i −0.245770 0.425685i 0.716578 0.697507i $$-0.245707\pi$$
−0.962348 + 0.271821i $$0.912374\pi$$
$$150$$ 2.50000 4.33013i 0.204124 0.353553i
$$151$$ 9.50000 16.4545i 0.773099 1.33905i −0.162758 0.986666i $$-0.552039\pi$$
0.935857 0.352381i $$-0.114628\pi$$
$$152$$ −1.00000 1.73205i −0.0811107 0.140488i
$$153$$ −12.0000 −0.970143
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0.500000 + 0.866025i 0.0400320 + 0.0693375i
$$157$$ −2.00000 + 3.46410i −0.159617 + 0.276465i −0.934731 0.355357i $$-0.884359\pi$$
0.775113 + 0.631822i $$0.217693\pi$$
$$158$$ 2.50000 4.33013i 0.198889 0.344486i
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ −1.00000 −0.0785674
$$163$$ −8.50000 14.7224i −0.665771 1.15315i −0.979076 0.203497i $$-0.934769\pi$$
0.313304 0.949653i $$-0.398564\pi$$
$$164$$ −3.00000 + 5.19615i −0.234261 + 0.405751i
$$165$$ 0 0
$$166$$ 3.00000 + 5.19615i 0.232845 + 0.403300i
$$167$$ −3.00000 −0.232147 −0.116073 0.993241i $$-0.537031\pi$$
−0.116073 + 0.993241i $$0.537031\pi$$
$$168$$ 0 0
$$169$$ −12.0000 −0.923077
$$170$$ 0 0
$$171$$ −2.00000 + 3.46410i −0.152944 + 0.264906i
$$172$$ 2.00000 3.46410i 0.152499 0.264135i
$$173$$ −10.5000 18.1865i −0.798300 1.38270i −0.920722 0.390218i $$-0.872399\pi$$
0.122422 0.992478i $$-0.460934\pi$$
$$174$$ 9.00000 0.682288
$$175$$ 0 0
$$176$$ −1.00000 −0.0753778
$$177$$ 1.50000 + 2.59808i 0.112747 + 0.195283i
$$178$$ 9.00000 15.5885i 0.674579 1.16840i
$$179$$ 7.50000 12.9904i 0.560576 0.970947i −0.436870 0.899525i $$-0.643913\pi$$
0.997446 0.0714220i $$-0.0227537\pi$$
$$180$$ 0 0
$$181$$ −2.00000 −0.148659 −0.0743294 0.997234i $$-0.523682\pi$$
−0.0743294 + 0.997234i $$0.523682\pi$$
$$182$$ 0 0
$$183$$ 11.0000 0.813143
$$184$$ −3.00000 5.19615i −0.221163 0.383065i
$$185$$ 0 0
$$186$$ −2.00000 + 3.46410i −0.146647 + 0.254000i
$$187$$ 3.00000 + 5.19615i 0.219382 + 0.379980i
$$188$$ 6.00000 0.437595
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −3.00000 5.19615i −0.217072 0.375980i 0.736839 0.676068i $$-0.236317\pi$$
−0.953912 + 0.300088i $$0.902984\pi$$
$$192$$ 0.500000 0.866025i 0.0360844 0.0625000i
$$193$$ −7.00000 + 12.1244i −0.503871 + 0.872730i 0.496119 + 0.868255i $$0.334758\pi$$
−0.999990 + 0.00447566i $$0.998575\pi$$
$$194$$ 6.50000 + 11.2583i 0.466673 + 0.808301i
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −3.00000 −0.213741 −0.106871 0.994273i $$-0.534083\pi$$
−0.106871 + 0.994273i $$0.534083\pi$$
$$198$$ 1.00000 + 1.73205i 0.0710669 + 0.123091i
$$199$$ 7.00000 12.1244i 0.496217 0.859473i −0.503774 0.863836i $$-0.668055\pi$$
0.999990 + 0.00436292i $$0.00138876\pi$$
$$200$$ −2.50000 + 4.33013i −0.176777 + 0.306186i
$$201$$ 5.50000 + 9.52628i 0.387940 + 0.671932i
$$202$$ −15.0000 −1.05540
$$203$$ 0 0
$$204$$ −6.00000 −0.420084
$$205$$ 0 0
$$206$$ 8.00000 13.8564i 0.557386 0.965422i
$$207$$ −6.00000 + 10.3923i −0.417029 + 0.722315i
$$208$$ −0.500000 0.866025i −0.0346688 0.0600481i
$$209$$ 2.00000 0.138343
$$210$$ 0 0
$$211$$ −10.0000 −0.688428 −0.344214 0.938891i $$-0.611855\pi$$
−0.344214 + 0.938891i $$0.611855\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 6.00000 10.3923i 0.410152 0.710403i
$$215$$ 0 0
$$216$$ −5.00000 −0.340207
$$217$$ 0 0
$$218$$ −2.00000 −0.135457
$$219$$ −1.00000 1.73205i −0.0675737 0.117041i
$$220$$ 0 0
$$221$$ −3.00000 + 5.19615i −0.201802 + 0.349531i
$$222$$ −1.00000 1.73205i −0.0671156 0.116248i
$$223$$ −26.0000 −1.74109 −0.870544 0.492090i $$-0.836233\pi$$
−0.870544 + 0.492090i $$0.836233\pi$$
$$224$$ 0 0
$$225$$ 10.0000 0.666667
$$226$$ 4.50000 + 7.79423i 0.299336 + 0.518464i
$$227$$ 9.00000 15.5885i 0.597351 1.03464i −0.395860 0.918311i $$-0.629553\pi$$
0.993210 0.116331i $$-0.0371134\pi$$
$$228$$ −1.00000 + 1.73205i −0.0662266 + 0.114708i
$$229$$ −8.00000 13.8564i −0.528655 0.915657i −0.999442 0.0334101i $$-0.989363\pi$$
0.470787 0.882247i $$-0.343970\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ −9.00000 −0.590879
$$233$$ 3.00000 + 5.19615i 0.196537 + 0.340411i 0.947403 0.320043i $$-0.103697\pi$$
−0.750867 + 0.660454i $$0.770364\pi$$
$$234$$ −1.00000 + 1.73205i −0.0653720 + 0.113228i
$$235$$ 0 0
$$236$$ −1.50000 2.59808i −0.0976417 0.169120i
$$237$$ −5.00000 −0.324785
$$238$$ 0 0
$$239$$ −9.00000 −0.582162 −0.291081 0.956698i $$-0.594015\pi$$
−0.291081 + 0.956698i $$0.594015\pi$$
$$240$$ 0 0
$$241$$ 13.0000 22.5167i 0.837404 1.45043i −0.0546547 0.998505i $$-0.517406\pi$$
0.892058 0.451920i $$-0.149261\pi$$
$$242$$ 0.500000 0.866025i 0.0321412 0.0556702i
$$243$$ 8.00000 + 13.8564i 0.513200 + 0.888889i
$$244$$ −11.0000 −0.704203
$$245$$ 0 0
$$246$$ 6.00000 0.382546
$$247$$ 1.00000 + 1.73205i 0.0636285 + 0.110208i
$$248$$ 2.00000 3.46410i 0.127000 0.219971i
$$249$$ 3.00000 5.19615i 0.190117 0.329293i
$$250$$ 0 0
$$251$$ 12.0000 0.757433 0.378717 0.925513i $$-0.376365\pi$$
0.378717 + 0.925513i $$0.376365\pi$$
$$252$$ 0 0
$$253$$ 6.00000 0.377217
$$254$$ −3.50000 6.06218i −0.219610 0.380375i
$$255$$ 0 0
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ 1.50000 + 2.59808i 0.0935674 + 0.162064i 0.909010 0.416775i $$-0.136840\pi$$
−0.815442 + 0.578838i $$0.803506\pi$$
$$258$$ −4.00000 −0.249029
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 9.00000 + 15.5885i 0.557086 + 0.964901i
$$262$$ −9.00000 + 15.5885i −0.556022 + 0.963058i
$$263$$ 4.50000 7.79423i 0.277482 0.480613i −0.693276 0.720672i $$-0.743833\pi$$
0.970758 + 0.240059i $$0.0771668\pi$$
$$264$$ 0.500000 + 0.866025i 0.0307729 + 0.0533002i
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −18.0000 −1.10158
$$268$$ −5.50000 9.52628i −0.335966 0.581910i
$$269$$ 6.00000 10.3923i 0.365826 0.633630i −0.623082 0.782157i $$-0.714120\pi$$
0.988908 + 0.148527i $$0.0474530\pi$$
$$270$$ 0 0
$$271$$ 14.5000 + 25.1147i 0.880812 + 1.52561i 0.850439 + 0.526073i $$0.176336\pi$$
0.0303728 + 0.999539i $$0.490331\pi$$
$$272$$ 6.00000 0.363803
$$273$$ 0 0
$$274$$ 9.00000 0.543710
$$275$$ −2.50000 4.33013i −0.150756 0.261116i
$$276$$ −3.00000 + 5.19615i −0.180579 + 0.312772i
$$277$$ −14.5000 + 25.1147i −0.871221 + 1.50900i −0.0104855 + 0.999945i $$0.503338\pi$$
−0.860735 + 0.509053i $$0.829996\pi$$
$$278$$ −4.00000 6.92820i −0.239904 0.415526i
$$279$$ −8.00000 −0.478947
$$280$$ 0 0
$$281$$ 18.0000 1.07379 0.536895 0.843649i $$-0.319597\pi$$
0.536895 + 0.843649i $$0.319597\pi$$
$$282$$ −3.00000 5.19615i −0.178647 0.309426i
$$283$$ −5.00000 + 8.66025i −0.297219 + 0.514799i −0.975499 0.220005i $$-0.929393\pi$$
0.678280 + 0.734804i $$0.262726\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 1.00000 0.0591312
$$287$$ 0 0
$$288$$ 2.00000 0.117851
$$289$$ −9.50000 16.4545i −0.558824 0.967911i
$$290$$ 0 0
$$291$$ 6.50000 11.2583i 0.381037 0.659975i
$$292$$ 1.00000 + 1.73205i 0.0585206 + 0.101361i
$$293$$ 30.0000 1.75262 0.876309 0.481749i $$-0.159998\pi$$
0.876309 + 0.481749i $$0.159998\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 1.00000 + 1.73205i 0.0581238 + 0.100673i
$$297$$ 2.50000 4.33013i 0.145065 0.251259i
$$298$$ 3.00000 5.19615i 0.173785 0.301005i
$$299$$ 3.00000 + 5.19615i 0.173494 + 0.300501i
$$300$$ 5.00000 0.288675
$$301$$ 0 0
$$302$$ 19.0000 1.09333
$$303$$ 7.50000 + 12.9904i 0.430864 + 0.746278i
$$304$$ 1.00000 1.73205i 0.0573539 0.0993399i
$$305$$ 0 0
$$306$$ −6.00000 10.3923i −0.342997 0.594089i
$$307$$ −20.0000 −1.14146 −0.570730 0.821138i $$-0.693340\pi$$
−0.570730 + 0.821138i $$0.693340\pi$$
$$308$$ 0 0
$$309$$ −16.0000 −0.910208
$$310$$ 0 0
$$311$$ 12.0000 20.7846i 0.680458 1.17859i −0.294384 0.955687i $$-0.595114\pi$$
0.974841 0.222900i $$-0.0715523\pi$$
$$312$$ −0.500000 + 0.866025i −0.0283069 + 0.0490290i
$$313$$ 8.50000 + 14.7224i 0.480448 + 0.832161i 0.999748 0.0224310i $$-0.00714060\pi$$
−0.519300 + 0.854592i $$0.673807\pi$$
$$314$$ −4.00000 −0.225733
$$315$$ 0 0
$$316$$ 5.00000 0.281272
$$317$$ −6.00000 10.3923i −0.336994 0.583690i 0.646872 0.762598i $$-0.276077\pi$$
−0.983866 + 0.178908i $$0.942743\pi$$
$$318$$ 0 0
$$319$$ 4.50000 7.79423i 0.251952 0.436393i
$$320$$ 0 0
$$321$$ −12.0000 −0.669775
$$322$$ 0 0
$$323$$ −12.0000 −0.667698
$$324$$ −0.500000 0.866025i −0.0277778 0.0481125i
$$325$$ 2.50000 4.33013i 0.138675 0.240192i
$$326$$ 8.50000 14.7224i 0.470771 0.815400i
$$327$$ 1.00000 + 1.73205i 0.0553001 + 0.0957826i
$$328$$ −6.00000 −0.331295
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −17.5000 30.3109i −0.961887 1.66604i −0.717756 0.696295i $$-0.754831\pi$$
−0.244131 0.969742i $$-0.578503\pi$$
$$332$$ −3.00000 + 5.19615i −0.164646 + 0.285176i
$$333$$ 2.00000 3.46410i 0.109599 0.189832i
$$334$$ −1.50000 2.59808i −0.0820763 0.142160i
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 14.0000 0.762629 0.381314 0.924445i $$-0.375472\pi$$
0.381314 + 0.924445i $$0.375472\pi$$
$$338$$ −6.00000 10.3923i −0.326357 0.565267i
$$339$$ 4.50000 7.79423i 0.244406 0.423324i
$$340$$ 0 0
$$341$$ 2.00000 + 3.46410i 0.108306 + 0.187592i
$$342$$ −4.00000 −0.216295
$$343$$ 0 0
$$344$$ 4.00000 0.215666
$$345$$ 0 0
$$346$$ 10.5000 18.1865i 0.564483 0.977714i
$$347$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$348$$ 4.50000 + 7.79423i 0.241225 + 0.417815i
$$349$$ −2.00000 −0.107058 −0.0535288 0.998566i $$-0.517047\pi$$
−0.0535288 + 0.998566i $$0.517047\pi$$
$$350$$ 0 0
$$351$$ 5.00000 0.266880
$$352$$ −0.500000 0.866025i −0.0266501 0.0461593i
$$353$$ −9.00000 + 15.5885i −0.479022 + 0.829690i −0.999711 0.0240566i $$-0.992342\pi$$
0.520689 + 0.853746i $$0.325675\pi$$
$$354$$ −1.50000 + 2.59808i −0.0797241 + 0.138086i
$$355$$ 0 0
$$356$$ 18.0000 0.953998
$$357$$ 0 0
$$358$$ 15.0000 0.792775
$$359$$ 1.50000 + 2.59808i 0.0791670 + 0.137121i 0.902891 0.429870i $$-0.141441\pi$$
−0.823724 + 0.566991i $$0.808107\pi$$
$$360$$ 0 0
$$361$$ 7.50000 12.9904i 0.394737 0.683704i
$$362$$ −1.00000 1.73205i −0.0525588 0.0910346i
$$363$$ −1.00000 −0.0524864
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 5.50000 + 9.52628i 0.287490 + 0.497947i
$$367$$ −5.00000 + 8.66025i −0.260998 + 0.452062i −0.966507 0.256639i $$-0.917385\pi$$
0.705509 + 0.708700i $$0.250718\pi$$
$$368$$ 3.00000 5.19615i 0.156386 0.270868i
$$369$$ 6.00000 + 10.3923i 0.312348 + 0.541002i
$$370$$ 0 0
$$371$$ 0 0
$$372$$ −4.00000 −0.207390
$$373$$ 15.5000 + 26.8468i 0.802560 + 1.39007i 0.917926 + 0.396751i $$0.129862\pi$$
−0.115367 + 0.993323i $$0.536804\pi$$
$$374$$ −3.00000 + 5.19615i −0.155126 + 0.268687i
$$375$$ 0 0
$$376$$ 3.00000 + 5.19615i 0.154713 + 0.267971i
$$377$$ 9.00000 0.463524
$$378$$ 0 0
$$379$$ 23.0000 1.18143 0.590715 0.806880i $$-0.298846\pi$$
0.590715 + 0.806880i $$0.298846\pi$$
$$380$$ 0 0
$$381$$ −3.50000 + 6.06218i −0.179310 + 0.310575i
$$382$$ 3.00000 5.19615i 0.153493 0.265858i
$$383$$ −18.0000 31.1769i −0.919757 1.59307i −0.799783 0.600289i $$-0.795052\pi$$
−0.119974 0.992777i $$-0.538281\pi$$
$$384$$ 1.00000 0.0510310
$$385$$ 0 0
$$386$$ −14.0000 −0.712581
$$387$$ −4.00000 6.92820i −0.203331 0.352180i
$$388$$ −6.50000 + 11.2583i −0.329988 + 0.571555i
$$389$$ −6.00000 + 10.3923i −0.304212 + 0.526911i −0.977086 0.212847i $$-0.931726\pi$$
0.672874 + 0.739758i $$0.265060\pi$$
$$390$$ 0 0
$$391$$ −36.0000 −1.82060
$$392$$ 0 0
$$393$$ 18.0000 0.907980
$$394$$ −1.50000 2.59808i −0.0755689 0.130889i
$$395$$ 0 0
$$396$$ −1.00000 + 1.73205i −0.0502519 + 0.0870388i
$$397$$ −11.0000 19.0526i −0.552074 0.956221i −0.998125 0.0612128i $$-0.980503\pi$$
0.446051 0.895008i $$-0.352830\pi$$
$$398$$ 14.0000 0.701757
$$399$$ 0 0
$$400$$ −5.00000 −0.250000
$$401$$ 16.5000 + 28.5788i 0.823971 + 1.42716i 0.902703 + 0.430263i $$0.141579\pi$$
−0.0787327 + 0.996896i $$0.525087\pi$$
$$402$$ −5.50000 + 9.52628i −0.274315 + 0.475128i
$$403$$ −2.00000 + 3.46410i −0.0996271 + 0.172559i
$$404$$ −7.50000 12.9904i −0.373139 0.646296i
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −2.00000 −0.0991363
$$408$$ −3.00000 5.19615i −0.148522 0.257248i
$$409$$ −2.00000 + 3.46410i −0.0988936 + 0.171289i −0.911227 0.411905i $$-0.864864\pi$$
0.812333 + 0.583193i $$0.198197\pi$$
$$410$$ 0 0
$$411$$ −4.50000 7.79423i −0.221969 0.384461i
$$412$$ 16.0000 0.788263
$$413$$ 0 0
$$414$$ −12.0000 −0.589768
$$415$$ 0 0
$$416$$ 0.500000 0.866025i 0.0245145 0.0424604i
$$417$$ −4.00000 + 6.92820i −0.195881 + 0.339276i
$$418$$ 1.00000 + 1.73205i 0.0489116 + 0.0847174i
$$419$$ 12.0000 0.586238 0.293119 0.956076i $$-0.405307\pi$$
0.293119 + 0.956076i $$0.405307\pi$$
$$420$$ 0 0
$$421$$ −28.0000 −1.36464 −0.682318 0.731055i $$-0.739028\pi$$
−0.682318 + 0.731055i $$0.739028\pi$$
$$422$$ −5.00000 8.66025i −0.243396 0.421575i
$$423$$ 6.00000 10.3923i 0.291730 0.505291i
$$424$$ 0 0
$$425$$ 15.0000 + 25.9808i 0.727607 + 1.26025i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 12.0000 0.580042
$$429$$ −0.500000 0.866025i −0.0241402 0.0418121i
$$430$$ 0 0
$$431$$ 1.50000 2.59808i 0.0722525 0.125145i −0.827636 0.561266i $$-0.810315\pi$$
0.899888 + 0.436121i $$0.143648\pi$$
$$432$$ −2.50000 4.33013i −0.120281 0.208333i
$$433$$ 34.0000 1.63394 0.816968 0.576683i $$-0.195653\pi$$
0.816968 + 0.576683i $$0.195653\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −1.00000 1.73205i −0.0478913 0.0829502i
$$437$$ −6.00000 + 10.3923i −0.287019 + 0.497131i
$$438$$ 1.00000 1.73205i 0.0477818 0.0827606i
$$439$$ −0.500000 0.866025i −0.0238637 0.0413331i 0.853847 0.520524i $$-0.174263\pi$$
−0.877711 + 0.479191i $$0.840930\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ −6.00000 −0.285391
$$443$$ −6.00000 10.3923i −0.285069 0.493753i 0.687557 0.726130i $$-0.258683\pi$$
−0.972626 + 0.232377i $$0.925350\pi$$
$$444$$ 1.00000 1.73205i 0.0474579 0.0821995i
$$445$$ 0 0
$$446$$ −13.0000 22.5167i −0.615568 1.06619i
$$447$$ −6.00000 −0.283790
$$448$$ 0 0
$$449$$ −18.0000 −0.849473 −0.424736 0.905317i $$-0.639633\pi$$
−0.424736 + 0.905317i $$0.639633\pi$$
$$450$$ 5.00000 + 8.66025i 0.235702 + 0.408248i
$$451$$ 3.00000 5.19615i 0.141264 0.244677i
$$452$$ −4.50000 + 7.79423i −0.211662 + 0.366610i
$$453$$ −9.50000 16.4545i −0.446349 0.773099i
$$454$$ 18.0000 0.844782
$$455$$ 0 0
$$456$$ −2.00000 −0.0936586
$$457$$ 11.0000 + 19.0526i 0.514558 + 0.891241i 0.999857 + 0.0168929i $$0.00537742\pi$$
−0.485299 + 0.874348i $$0.661289\pi$$
$$458$$ 8.00000 13.8564i 0.373815 0.647467i
$$459$$ −15.0000 + 25.9808i −0.700140 + 1.21268i
$$460$$ 0 0
$$461$$ −21.0000 −0.978068 −0.489034 0.872265i $$-0.662651\pi$$
−0.489034 + 0.872265i $$0.662651\pi$$
$$462$$ 0 0
$$463$$ −22.0000 −1.02243 −0.511213 0.859454i $$-0.670804\pi$$
−0.511213 + 0.859454i $$0.670804\pi$$
$$464$$ −4.50000 7.79423i −0.208907 0.361838i
$$465$$ 0 0
$$466$$ −3.00000 + 5.19615i −0.138972 + 0.240707i
$$467$$ 6.00000 + 10.3923i 0.277647 + 0.480899i 0.970799 0.239892i $$-0.0771121\pi$$
−0.693153 + 0.720791i $$0.743779\pi$$
$$468$$ −2.00000 −0.0924500
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 2.00000 + 3.46410i 0.0921551 + 0.159617i
$$472$$ 1.50000 2.59808i 0.0690431 0.119586i
$$473$$ −2.00000 + 3.46410i −0.0919601 + 0.159280i
$$474$$ −2.50000 4.33013i −0.114829 0.198889i
$$475$$ 10.0000 0.458831
$$476$$ 0 0
$$477$$ 0 0
$$478$$ −4.50000 7.79423i −0.205825 0.356500i
$$479$$ 7.50000 12.9904i 0.342684 0.593546i −0.642246 0.766498i $$-0.721997\pi$$
0.984930 + 0.172953i $$0.0553307\pi$$
$$480$$ 0 0
$$481$$ −1.00000 1.73205i −0.0455961 0.0789747i
$$482$$ 26.0000 1.18427
$$483$$ 0 0
$$484$$ 1.00000 0.0454545
$$485$$ 0 0
$$486$$ −8.00000 + 13.8564i −0.362887 + 0.628539i
$$487$$ −10.0000 + 17.3205i −0.453143 + 0.784867i −0.998579 0.0532853i $$-0.983031\pi$$
0.545436 + 0.838152i $$0.316364\pi$$
$$488$$ −5.50000 9.52628i −0.248973 0.431234i
$$489$$ −17.0000 −0.768767
$$490$$ 0 0
$$491$$ 42.0000 1.89543 0.947717 0.319113i $$-0.103385\pi$$
0.947717 + 0.319113i $$0.103385\pi$$
$$492$$ 3.00000 + 5.19615i 0.135250 + 0.234261i
$$493$$ −27.0000 + 46.7654i −1.21602 + 2.10621i
$$494$$ −1.00000 + 1.73205i −0.0449921 + 0.0779287i
$$495$$ 0 0
$$496$$ 4.00000 0.179605
$$497$$ 0 0
$$498$$ 6.00000 0.268866
$$499$$ 20.0000 + 34.6410i 0.895323 + 1.55074i 0.833404 + 0.552664i $$0.186389\pi$$
0.0619186 + 0.998081i $$0.480278\pi$$
$$500$$ 0 0
$$501$$ −1.50000 + 2.59808i −0.0670151 + 0.116073i
$$502$$ 6.00000 + 10.3923i 0.267793 + 0.463831i
$$503$$ 33.0000 1.47140 0.735699 0.677309i $$-0.236854\pi$$
0.735699 + 0.677309i $$0.236854\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 3.00000 + 5.19615i 0.133366 + 0.230997i
$$507$$ −6.00000 + 10.3923i −0.266469 + 0.461538i
$$508$$ 3.50000 6.06218i 0.155287 0.268966i
$$509$$ −3.00000 5.19615i −0.132973 0.230315i 0.791849 0.610718i $$-0.209119\pi$$
−0.924821 + 0.380402i $$0.875786\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −1.00000 −0.0441942
$$513$$ 5.00000 + 8.66025i 0.220755 + 0.382360i
$$514$$ −1.50000 + 2.59808i −0.0661622 + 0.114596i
$$515$$ 0 0
$$516$$ −2.00000 3.46410i −0.0880451 0.152499i
$$517$$ −6.00000 −0.263880
$$518$$ 0 0
$$519$$ −21.0000 −0.921798
$$520$$ 0 0
$$521$$ −21.0000 + 36.3731i −0.920027 + 1.59353i −0.120656 + 0.992694i $$0.538500\pi$$
−0.799370 + 0.600839i $$0.794833\pi$$
$$522$$ −9.00000 + 15.5885i −0.393919 + 0.682288i
$$523$$ −8.00000 13.8564i −0.349816 0.605898i 0.636401 0.771358i $$-0.280422\pi$$
−0.986216 + 0.165460i $$0.947089\pi$$
$$524$$ −18.0000 −0.786334
$$525$$ 0 0
$$526$$ 9.00000 0.392419
$$527$$ −12.0000 20.7846i −0.522728 0.905392i
$$528$$ −0.500000 + 0.866025i −0.0217597 + 0.0376889i
$$529$$ −6.50000 + 11.2583i −0.282609 + 0.489493i
$$530$$ 0 0
$$531$$ −6.00000 −0.260378
$$532$$ 0 0
$$533$$ 6.00000 0.259889
$$534$$ −9.00000 15.5885i −0.389468 0.674579i
$$535$$ 0 0
$$536$$ 5.50000 9.52628i 0.237564 0.411473i
$$537$$ −7.50000 12.9904i −0.323649 0.560576i
$$538$$ 12.0000 0.517357
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 12.5000 + 21.6506i 0.537417 + 0.930834i 0.999042 + 0.0437584i $$0.0139332\pi$$
−0.461625 + 0.887075i $$0.652733\pi$$
$$542$$ −14.5000 + 25.1147i −0.622828 + 1.07877i
$$543$$ −1.00000 + 1.73205i −0.0429141 + 0.0743294i
$$544$$ 3.00000 + 5.19615i 0.128624 + 0.222783i
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −28.0000 −1.19719 −0.598597 0.801050i $$-0.704275\pi$$
−0.598597 + 0.801050i $$0.704275\pi$$
$$548$$ 4.50000 + 7.79423i 0.192230 + 0.332953i
$$549$$ −11.0000 + 19.0526i −0.469469 + 0.813143i
$$550$$ 2.50000 4.33013i 0.106600 0.184637i
$$551$$ 9.00000 + 15.5885i 0.383413 + 0.664091i
$$552$$ −6.00000 −0.255377
$$553$$ 0 0
$$554$$ −29.0000 −1.23209
$$555$$ 0 0
$$556$$ 4.00000 6.92820i 0.169638 0.293821i
$$557$$ 9.00000 15.5885i 0.381342 0.660504i −0.609912 0.792469i $$-0.708795\pi$$
0.991254 + 0.131965i $$0.0421286\pi$$
$$558$$ −4.00000 6.92820i −0.169334 0.293294i
$$559$$ −4.00000 −0.169182
$$560$$ 0 0
$$561$$ 6.00000 0.253320
$$562$$ 9.00000 + 15.5885i 0.379642 + 0.657559i
$$563$$ −9.00000 + 15.5885i −0.379305 + 0.656975i −0.990961 0.134148i $$-0.957170\pi$$
0.611656 + 0.791123i $$0.290503\pi$$
$$564$$ 3.00000 5.19615i 0.126323 0.218797i
$$565$$ 0 0
$$566$$ −10.0000 −0.420331
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 18.0000 + 31.1769i 0.754599 + 1.30700i 0.945573 + 0.325409i $$0.105502\pi$$
−0.190974 + 0.981595i $$0.561165\pi$$
$$570$$ 0 0
$$571$$ −16.0000 + 27.7128i −0.669579 + 1.15975i 0.308443 + 0.951243i $$0.400192\pi$$
−0.978022 + 0.208502i $$0.933141\pi$$
$$572$$ 0.500000 + 0.866025i 0.0209061 + 0.0362103i
$$573$$ −6.00000 −0.250654
$$574$$ 0 0
$$575$$ 30.0000 1.25109
$$576$$ 1.00000 + 1.73205i 0.0416667 + 0.0721688i
$$577$$ −3.50000 + 6.06218i −0.145707 + 0.252372i −0.929636 0.368478i $$-0.879879\pi$$
0.783930 + 0.620850i $$0.213212\pi$$
$$578$$ 9.50000 16.4545i 0.395148 0.684416i
$$579$$ 7.00000 + 12.1244i 0.290910 + 0.503871i
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 13.0000 0.538867
$$583$$ 0 0
$$584$$ −1.00000 + 1.73205i −0.0413803 + 0.0716728i
$$585$$ 0 0
$$586$$ 15.0000 + 25.9808i 0.619644 + 1.07326i
$$587$$ −9.00000 −0.371470 −0.185735 0.982600i $$-0.559467\pi$$
−0.185735 + 0.982600i $$0.559467\pi$$
$$588$$ 0 0
$$589$$ −8.00000 −0.329634
$$590$$ 0 0
$$591$$ −1.50000 + 2.59808i −0.0617018 + 0.106871i
$$592$$ −1.00000 + 1.73205i −0.0410997 + 0.0711868i
$$593$$ 18.0000 + 31.1769i 0.739171 + 1.28028i 0.952869 + 0.303383i $$0.0981160\pi$$
−0.213697 + 0.976900i $$0.568551\pi$$
$$594$$ 5.00000 0.205152
$$595$$ 0 0
$$596$$ 6.00000 0.245770
$$597$$ −7.00000 12.1244i −0.286491 0.496217i
$$598$$ −3.00000 + 5.19615i −0.122679 + 0.212486i
$$599$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$600$$ 2.50000 + 4.33013i 0.102062 + 0.176777i
$$601$$ −2.00000 −0.0815817 −0.0407909 0.999168i $$-0.512988\pi$$
−0.0407909 + 0.999168i $$0.512988\pi$$
$$602$$ 0 0
$$603$$ −22.0000 −0.895909
$$604$$ 9.50000 + 16.4545i 0.386550 + 0.669523i
$$605$$ 0 0
$$606$$ −7.50000 + 12.9904i −0.304667 + 0.527698i
$$607$$ −20.0000 34.6410i −0.811775 1.40604i −0.911621 0.411033i $$-0.865168\pi$$
0.0998457 0.995003i $$-0.468165\pi$$
$$608$$ 2.00000 0.0811107
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −3.00000 5.19615i −0.121367 0.210214i
$$612$$ 6.00000 10.3923i 0.242536 0.420084i
$$613$$ 5.00000 8.66025i 0.201948 0.349784i −0.747208 0.664590i $$-0.768606\pi$$
0.949156 + 0.314806i $$0.101939\pi$$
$$614$$ −10.0000 17.3205i −0.403567 0.698999i
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 21.0000 0.845428 0.422714 0.906263i $$-0.361077\pi$$
0.422714 + 0.906263i $$0.361077\pi$$
$$618$$ −8.00000 13.8564i −0.321807 0.557386i
$$619$$ 10.0000 17.3205i 0.401934 0.696170i −0.592025 0.805919i $$-0.701671\pi$$
0.993959 + 0.109749i $$0.0350048\pi$$
$$620$$ 0 0
$$621$$ 15.0000 + 25.9808i 0.601929 + 1.04257i
$$622$$ 24.0000 0.962312
$$623$$ 0 0
$$624$$ −1.00000 −0.0400320
$$625$$ −12.5000 21.6506i −0.500000 0.866025i
$$626$$ −8.50000 + 14.7224i −0.339728 + 0.588427i
$$627$$ 1.00000 1.73205i 0.0399362 0.0691714i
$$628$$ −2.00000 3.46410i −0.0798087 0.138233i
$$629$$ 12.0000 0.478471
$$630$$ 0 0
$$631$$ 20.0000 0.796187 0.398094 0.917345i $$-0.369672\pi$$
0.398094 + 0.917345i $$0.369672\pi$$
$$632$$ 2.50000 + 4.33013i 0.0994447 + 0.172243i
$$633$$ −5.00000 + 8.66025i −0.198732 + 0.344214i
$$634$$ 6.00000 10.3923i 0.238290 0.412731i
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 9.00000 0.356313
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −4.50000 + 7.79423i −0.177739 + 0.307854i −0.941106 0.338112i $$-0.890212\pi$$
0.763367 + 0.645966i $$0.223545\pi$$
$$642$$ −6.00000 10.3923i −0.236801 0.410152i
$$643$$ −5.00000 −0.197181 −0.0985904 0.995128i $$-0.531433\pi$$
−0.0985904 + 0.995128i $$0.531433\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ −6.00000 10.3923i −0.236067 0.408880i
$$647$$ −6.00000 + 10.3923i −0.235884 + 0.408564i −0.959529 0.281609i $$-0.909132\pi$$
0.723645 + 0.690172i $$0.242465\pi$$
$$648$$ 0.500000 0.866025i 0.0196419 0.0340207i
$$649$$ 1.50000 + 2.59808i 0.0588802 + 0.101983i
$$650$$ 5.00000 0.196116
$$651$$ 0 0
$$652$$ 17.0000 0.665771
$$653$$ −9.00000 15.5885i −0.352197 0.610023i 0.634437 0.772975i $$-0.281232\pi$$
−0.986634 + 0.162951i $$0.947899\pi$$
$$654$$ −1.00000 + 1.73205i −0.0391031 + 0.0677285i
$$655$$ 0 0
$$656$$ −3.00000 5.19615i −0.117130 0.202876i
$$657$$ 4.00000 0.156055
$$658$$ 0 0
$$659$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$660$$ 0 0
$$661$$ 7.00000 12.1244i 0.272268 0.471583i −0.697174 0.716902i $$-0.745559\pi$$
0.969442 + 0.245319i $$0.0788928\pi$$
$$662$$ 17.5000 30.3109i 0.680157 1.17807i
$$663$$ 3.00000 + 5.19615i 0.116510 + 0.201802i
$$664$$ −6.00000 −0.232845
$$665$$ 0 0
$$666$$ 4.00000 0.154997
$$667$$ 27.0000 + 46.7654i 1.04544 + 1.81076i
$$668$$ 1.50000 2.59808i 0.0580367 0.100523i
$$669$$ −13.0000 + 22.5167i −0.502609 + 0.870544i
$$670$$ 0 0
$$671$$ 11.0000 0.424650
$$672$$ 0 0
$$673$$ −28.0000 −1.07932 −0.539660 0.841883i $$-0.681447\pi$$
−0.539660 + 0.841883i $$0.681447\pi$$
$$674$$ 7.00000 + 12.1244i 0.269630 + 0.467013i
$$675$$ 12.5000 21.6506i 0.481125 0.833333i
$$676$$ 6.00000 10.3923i 0.230769 0.399704i
$$677$$ 3.00000 + 5.19615i 0.115299 + 0.199704i 0.917899 0.396813i $$-0.129884\pi$$
−0.802600 + 0.596518i $$0.796551\pi$$
$$678$$ 9.00000 0.345643
$$679$$ 0 0
$$680$$ 0 0
$$681$$ −9.00000 15.5885i −0.344881 0.597351i
$$682$$ −2.00000 + 3.46410i −0.0765840 + 0.132647i
$$683$$ 10.5000 18.1865i 0.401771 0.695888i −0.592168 0.805814i $$-0.701728\pi$$
0.993940 + 0.109926i $$0.0350613\pi$$
$$684$$ −2.00000 3.46410i −0.0764719 0.132453i
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −16.0000 −0.610438
$$688$$ 2.00000 + 3.46410i 0.0762493 + 0.132068i
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 5.50000 + 9.52628i 0.209230 + 0.362397i 0.951472 0.307735i $$-0.0995710\pi$$
−0.742242 + 0.670132i $$0.766238\pi$$
$$692$$ 21.0000 0.798300
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ −4.50000 + 7.79423i −0.170572 + 0.295439i
$$697$$ −18.0000 + 31.1769i −0.681799 + 1.18091i
$$698$$ −1.00000 1.73205i −0.0378506 0.0655591i
$$699$$ 6.00000 0.226941
$$700$$ 0 0
$$701$$ 39.0000 1.47301 0.736505 0.676432i $$-0.236475\pi$$
0.736505 + 0.676432i $$0.236475\pi$$
$$702$$ 2.50000 + 4.33013i 0.0943564 + 0.163430i
$$703$$ 2.00000 3.46410i 0.0754314 0.130651i
$$704$$ 0.500000 0.866025i 0.0188445 0.0326396i
$$705$$ 0 0
$$706$$ −18.0000 −0.677439
$$707$$ 0 0
$$708$$ −3.00000 −0.112747
$$709$$ −13.0000 22.5167i −0.488225 0.845631i 0.511683 0.859174i $$-0.329022\pi$$
−0.999908 + 0.0135434i $$0.995689\pi$$
$$710$$ 0 0
$$711$$ 5.00000 8.66025i 0.187515 0.324785i
$$712$$ 9.00000 + 15.5885i 0.337289 + 0.584202i
$$713$$ −24.0000 −0.898807
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 7.50000 + 12.9904i 0.280288 + 0.485473i
$$717$$ −4.50000 + 7.79423i −0.168056 + 0.291081i
$$718$$ −1.50000 + 2.59808i −0.0559795 + 0.0969593i
$$719$$ −21.0000 36.3731i −0.783168 1.35649i −0.930087 0.367338i $$-0.880269\pi$$
0.146920 0.989148i $$-0.453064\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 15.0000 0.558242
$$723$$ −13.0000 22.5167i −0.483475 0.837404i
$$724$$ 1.00000 1.73205i 0.0371647 0.0643712i
$$725$$ 22.5000 38.9711i 0.835629 1.44735i
$$726$$ −0.500000 0.866025i −0.0185567 0.0321412i
$$727$$ −14.0000 −0.519231 −0.259616 0.965712i $$-0.583596\pi$$
−0.259616 + 0.965712i $$0.583596\pi$$
$$728$$ 0 0
$$729$$ 13.0000 0.481481
$$730$$ 0 0
$$731$$ 12.0000 20.7846i 0.443836 0.768747i
$$732$$ −5.50000 + 9.52628i −0.203286 + 0.352101i
$$733$$ −12.5000 21.6506i −0.461698 0.799684i 0.537348 0.843361i $$-0.319426\pi$$
−0.999046 + 0.0436764i $$0.986093\pi$$
$$734$$ −10.0000 −0.369107
$$735$$ 0 0
$$736$$ 6.00000 0.221163
$$737$$ 5.50000 + 9.52628i 0.202595 + 0.350905i
$$738$$ −6.00000 + 10.3923i −0.220863 + 0.382546i
$$739$$ −25.0000 + 43.3013i −0.919640 + 1.59286i −0.119677 + 0.992813i $$0.538186\pi$$
−0.799962 + 0.600050i $$0.795147\pi$$
$$740$$ 0 0
$$741$$ 2.00000 0.0734718
$$742$$ 0 0
$$743$$ −36.0000 −1.32071 −0.660356 0.750953i $$-0.729595\pi$$
−0.660356 + 0.750953i $$0.729595\pi$$
$$744$$ −2.00000 3.46410i −0.0733236 0.127000i
$$745$$ 0 0
$$746$$ −15.5000 + 26.8468i −0.567495 + 0.982931i
$$747$$ 6.00000 + 10.3923i 0.219529 + 0.380235i
$$748$$ −6.00000 −0.219382
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 2.00000 + 3.46410i 0.0729810 + 0.126407i 0.900207 0.435463i $$-0.143415\pi$$
−0.827225 + 0.561870i $$0.810082\pi$$
$$752$$ −3.00000 + 5.19615i −0.109399 + 0.189484i
$$753$$ 6.00000 10.3923i 0.218652 0.378717i
$$754$$ 4.50000 + 7.79423i 0.163880 + 0.283849i
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −46.0000 −1.67190 −0.835949 0.548807i $$-0.815082\pi$$
−0.835949 + 0.548807i $$0.815082\pi$$
$$758$$ 11.5000 + 19.9186i 0.417699 + 0.723476i
$$759$$ 3.00000 5.19615i 0.108893 0.188608i
$$760$$ 0 0
$$761$$ −9.00000 15.5885i −0.326250 0.565081i 0.655515 0.755182i $$-0.272452\pi$$
−0.981764 + 0.190101i $$0.939118\pi$$
$$762$$ −7.00000 −0.253583
$$763$$ 0 0
$$764$$ 6.00000 0.217072
$$765$$ 0 0
$$766$$ 18.0000 31.1769i 0.650366 1.12647i
$$767$$ −1.50000 + 2.59808i −0.0541619 + 0.0938111i
$$768$$ 0.500000 + 0.866025i 0.0180422 + 0.0312500i
$$769$$ 22.0000 0.793340 0.396670 0.917961i $$-0.370166\pi$$
0.396670 + 0.917961i $$0.370166\pi$$
$$770$$ 0 0
$$771$$ 3.00000 0.108042
$$772$$ −7.00000 12.1244i −0.251936 0.436365i
$$773$$ 12.0000 20.7846i 0.431610 0.747570i −0.565402 0.824815i $$-0.691279\pi$$
0.997012 + 0.0772449i $$0.0246123\pi$$
$$774$$ 4.00000 6.92820i 0.143777 0.249029i
$$775$$ 10.0000 + 17.3205i 0.359211 + 0.622171i
$$776$$ −13.0000 −0.466673
$$777$$ 0 0
$$778$$ −12.0000 −0.430221
$$779$$ 6.00000 + 10.3923i 0.214972 + 0.372343i
$$780$$ 0 0
$$781$$ 0 0
$$782$$ −18.0000 31.1769i −0.643679 1.11488i
$$783$$ 45.0000 1.60817