# Properties

 Label 1078.2.e.p.67.1 Level $1078$ Weight $2$ Character 1078.67 Analytic conductor $8.608$ Analytic rank $0$ Dimension $4$ Inner twists $4$

# 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: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\sqrt{2}, \sqrt{-3})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{4} + 2x^{2} + 4$$ x^4 + 2*x^2 + 4 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 67.1 Root $$-0.707107 + 1.22474i$$ of defining polynomial Character $$\chi$$ $$=$$ 1078.67 Dual form 1078.2.e.p.177.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-0.500000 - 0.866025i) q^{2} +(-0.707107 + 1.22474i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.12132 - 3.67423i) q^{5} +1.41421 q^{6} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$q+(-0.500000 - 0.866025i) q^{2} +(-0.707107 + 1.22474i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.12132 - 3.67423i) q^{5} +1.41421 q^{6} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.12132 + 3.67423i) q^{10} +(0.500000 - 0.866025i) q^{11} +(-0.707107 - 1.22474i) q^{12} +6.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.82843 - 4.89898i) q^{17} +(0.500000 - 0.866025i) q^{18} +4.24264 q^{20} -1.00000 q^{22} +(-3.00000 - 5.19615i) q^{23} +(-0.707107 + 1.22474i) q^{24} +(-6.50000 + 11.2583i) q^{25} -5.65685 q^{27} +2.00000 q^{29} +(-3.00000 - 5.19615i) q^{30} +(0.707107 - 1.22474i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.707107 + 1.22474i) q^{33} -5.65685 q^{34} -1.00000 q^{36} +(5.00000 + 8.66025i) q^{37} +(-2.12132 - 3.67423i) q^{40} -11.3137 q^{41} -8.00000 q^{43} +(0.500000 + 0.866025i) q^{44} +(2.12132 - 3.67423i) q^{45} +(-3.00000 + 5.19615i) q^{46} +(-2.12132 - 3.67423i) q^{47} +1.41421 q^{48} +13.0000 q^{50} +(4.00000 + 6.92820i) q^{51} +(-4.00000 + 6.92820i) q^{53} +(2.82843 + 4.89898i) q^{54} -4.24264 q^{55} +(-1.00000 - 1.73205i) q^{58} +(-0.707107 + 1.22474i) q^{59} +(-3.00000 + 5.19615i) q^{60} +(1.41421 + 2.44949i) q^{61} -1.41421 q^{62} +1.00000 q^{64} +(0.707107 - 1.22474i) q^{66} +(-1.00000 + 1.73205i) q^{67} +(2.82843 + 4.89898i) q^{68} +8.48528 q^{69} -2.00000 q^{71} +(0.500000 + 0.866025i) q^{72} +(-4.24264 + 7.34847i) q^{73} +(5.00000 - 8.66025i) q^{74} +(-9.19239 - 15.9217i) q^{75} +(-8.00000 - 13.8564i) q^{79} +(-2.12132 + 3.67423i) q^{80} +(2.50000 - 4.33013i) q^{81} +(5.65685 + 9.79796i) q^{82} -16.9706 q^{83} -24.0000 q^{85} +(4.00000 + 6.92820i) q^{86} +(-1.41421 + 2.44949i) q^{87} +(0.500000 - 0.866025i) q^{88} +(3.53553 + 6.12372i) q^{89} -4.24264 q^{90} +6.00000 q^{92} +(1.00000 + 1.73205i) q^{93} +(-2.12132 + 3.67423i) q^{94} +(-0.707107 - 1.22474i) q^{96} -9.89949 q^{97} +1.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 2 q^{2} - 2 q^{4} + 4 q^{8} + 2 q^{9}+O(q^{10})$$ 4 * q - 2 * q^2 - 2 * q^4 + 4 * q^8 + 2 * q^9 $$4 q - 2 q^{2} - 2 q^{4} + 4 q^{8} + 2 q^{9} + 2 q^{11} + 24 q^{15} - 2 q^{16} + 2 q^{18} - 4 q^{22} - 12 q^{23} - 26 q^{25} + 8 q^{29} - 12 q^{30} - 2 q^{32} - 4 q^{36} + 20 q^{37} - 32 q^{43} + 2 q^{44} - 12 q^{46} + 52 q^{50} + 16 q^{51} - 16 q^{53} - 4 q^{58} - 12 q^{60} + 4 q^{64} - 4 q^{67} - 8 q^{71} + 2 q^{72} + 20 q^{74} - 32 q^{79} + 10 q^{81} - 96 q^{85} + 16 q^{86} + 2 q^{88} + 24 q^{92} + 4 q^{93} + 4 q^{99}+O(q^{100})$$ 4 * q - 2 * q^2 - 2 * q^4 + 4 * q^8 + 2 * q^9 + 2 * q^11 + 24 * q^15 - 2 * q^16 + 2 * q^18 - 4 * q^22 - 12 * q^23 - 26 * q^25 + 8 * q^29 - 12 * q^30 - 2 * q^32 - 4 * q^36 + 20 * q^37 - 32 * q^43 + 2 * q^44 - 12 * q^46 + 52 * q^50 + 16 * q^51 - 16 * q^53 - 4 * q^58 - 12 * q^60 + 4 * q^64 - 4 * q^67 - 8 * q^71 + 2 * q^72 + 20 * q^74 - 32 * q^79 + 10 * q^81 - 96 * q^85 + 16 * q^86 + 2 * q^88 + 24 * q^92 + 4 * q^93 + 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
$$3$$ −0.707107 + 1.22474i −0.408248 + 0.707107i −0.994694 0.102882i $$-0.967194\pi$$
0.586445 + 0.809989i $$0.300527\pi$$
$$4$$ −0.500000 + 0.866025i −0.250000 + 0.433013i
$$5$$ −2.12132 3.67423i −0.948683 1.64317i −0.748203 0.663470i $$-0.769083\pi$$
−0.200480 0.979698i $$-0.564250\pi$$
$$6$$ 1.41421 0.577350
$$7$$ 0 0
$$8$$ 1.00000 0.353553
$$9$$ 0.500000 + 0.866025i 0.166667 + 0.288675i
$$10$$ −2.12132 + 3.67423i −0.670820 + 1.16190i
$$11$$ 0.500000 0.866025i 0.150756 0.261116i
$$12$$ −0.707107 1.22474i −0.204124 0.353553i
$$13$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$14$$ 0 0
$$15$$ 6.00000 1.54919
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ 2.82843 4.89898i 0.685994 1.18818i −0.287129 0.957892i $$-0.592701\pi$$
0.973123 0.230285i $$-0.0739659\pi$$
$$18$$ 0.500000 0.866025i 0.117851 0.204124i
$$19$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$20$$ 4.24264 0.948683
$$21$$ 0 0
$$22$$ −1.00000 −0.213201
$$23$$ −3.00000 5.19615i −0.625543 1.08347i −0.988436 0.151642i $$-0.951544\pi$$
0.362892 0.931831i $$-0.381789\pi$$
$$24$$ −0.707107 + 1.22474i −0.144338 + 0.250000i
$$25$$ −6.50000 + 11.2583i −1.30000 + 2.25167i
$$26$$ 0 0
$$27$$ −5.65685 −1.08866
$$28$$ 0 0
$$29$$ 2.00000 0.371391 0.185695 0.982607i $$-0.440546\pi$$
0.185695 + 0.982607i $$0.440546\pi$$
$$30$$ −3.00000 5.19615i −0.547723 0.948683i
$$31$$ 0.707107 1.22474i 0.127000 0.219971i −0.795513 0.605937i $$-0.792798\pi$$
0.922513 + 0.385966i $$0.126132\pi$$
$$32$$ −0.500000 + 0.866025i −0.0883883 + 0.153093i
$$33$$ 0.707107 + 1.22474i 0.123091 + 0.213201i
$$34$$ −5.65685 −0.970143
$$35$$ 0 0
$$36$$ −1.00000 −0.166667
$$37$$ 5.00000 + 8.66025i 0.821995 + 1.42374i 0.904194 + 0.427121i $$0.140472\pi$$
−0.0821995 + 0.996616i $$0.526194\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ −2.12132 3.67423i −0.335410 0.580948i
$$41$$ −11.3137 −1.76690 −0.883452 0.468521i $$-0.844787\pi$$
−0.883452 + 0.468521i $$0.844787\pi$$
$$42$$ 0 0
$$43$$ −8.00000 −1.21999 −0.609994 0.792406i $$-0.708828\pi$$
−0.609994 + 0.792406i $$0.708828\pi$$
$$44$$ 0.500000 + 0.866025i 0.0753778 + 0.130558i
$$45$$ 2.12132 3.67423i 0.316228 0.547723i
$$46$$ −3.00000 + 5.19615i −0.442326 + 0.766131i
$$47$$ −2.12132 3.67423i −0.309426 0.535942i 0.668811 0.743433i $$-0.266804\pi$$
−0.978237 + 0.207491i $$0.933470\pi$$
$$48$$ 1.41421 0.204124
$$49$$ 0 0
$$50$$ 13.0000 1.83848
$$51$$ 4.00000 + 6.92820i 0.560112 + 0.970143i
$$52$$ 0 0
$$53$$ −4.00000 + 6.92820i −0.549442 + 0.951662i 0.448871 + 0.893597i $$0.351826\pi$$
−0.998313 + 0.0580651i $$0.981507\pi$$
$$54$$ 2.82843 + 4.89898i 0.384900 + 0.666667i
$$55$$ −4.24264 −0.572078
$$56$$ 0 0
$$57$$ 0 0
$$58$$ −1.00000 1.73205i −0.131306 0.227429i
$$59$$ −0.707107 + 1.22474i −0.0920575 + 0.159448i −0.908377 0.418153i $$-0.862678\pi$$
0.816319 + 0.577601i $$0.196011\pi$$
$$60$$ −3.00000 + 5.19615i −0.387298 + 0.670820i
$$61$$ 1.41421 + 2.44949i 0.181071 + 0.313625i 0.942246 0.334922i $$-0.108710\pi$$
−0.761174 + 0.648547i $$0.775377\pi$$
$$62$$ −1.41421 −0.179605
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 0.707107 1.22474i 0.0870388 0.150756i
$$67$$ −1.00000 + 1.73205i −0.122169 + 0.211604i −0.920623 0.390453i $$-0.872318\pi$$
0.798454 + 0.602056i $$0.205652\pi$$
$$68$$ 2.82843 + 4.89898i 0.342997 + 0.594089i
$$69$$ 8.48528 1.02151
$$70$$ 0 0
$$71$$ −2.00000 −0.237356 −0.118678 0.992933i $$-0.537866\pi$$
−0.118678 + 0.992933i $$0.537866\pi$$
$$72$$ 0.500000 + 0.866025i 0.0589256 + 0.102062i
$$73$$ −4.24264 + 7.34847i −0.496564 + 0.860073i −0.999992 0.00396356i $$-0.998738\pi$$
0.503429 + 0.864037i $$0.332072\pi$$
$$74$$ 5.00000 8.66025i 0.581238 1.00673i
$$75$$ −9.19239 15.9217i −1.06145 1.83848i
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −8.00000 13.8564i −0.900070 1.55897i −0.827401 0.561611i $$-0.810182\pi$$
−0.0726692 0.997356i $$-0.523152\pi$$
$$80$$ −2.12132 + 3.67423i −0.237171 + 0.410792i
$$81$$ 2.50000 4.33013i 0.277778 0.481125i
$$82$$ 5.65685 + 9.79796i 0.624695 + 1.08200i
$$83$$ −16.9706 −1.86276 −0.931381 0.364047i $$-0.881395\pi$$
−0.931381 + 0.364047i $$0.881395\pi$$
$$84$$ 0 0
$$85$$ −24.0000 −2.60317
$$86$$ 4.00000 + 6.92820i 0.431331 + 0.747087i
$$87$$ −1.41421 + 2.44949i −0.151620 + 0.262613i
$$88$$ 0.500000 0.866025i 0.0533002 0.0923186i
$$89$$ 3.53553 + 6.12372i 0.374766 + 0.649113i 0.990292 0.139003i $$-0.0443898\pi$$
−0.615526 + 0.788116i $$0.711056\pi$$
$$90$$ −4.24264 −0.447214
$$91$$ 0 0
$$92$$ 6.00000 0.625543
$$93$$ 1.00000 + 1.73205i 0.103695 + 0.179605i
$$94$$ −2.12132 + 3.67423i −0.218797 + 0.378968i
$$95$$ 0 0
$$96$$ −0.707107 1.22474i −0.0721688 0.125000i
$$97$$ −9.89949 −1.00514 −0.502571 0.864536i $$-0.667612\pi$$
−0.502571 + 0.864536i $$0.667612\pi$$
$$98$$ 0 0
$$99$$ 1.00000 0.100504
$$100$$ −6.50000 11.2583i −0.650000 1.12583i
$$101$$ −2.82843 + 4.89898i −0.281439 + 0.487467i −0.971739 0.236056i $$-0.924145\pi$$
0.690300 + 0.723523i $$0.257478\pi$$
$$102$$ 4.00000 6.92820i 0.396059 0.685994i
$$103$$ −9.19239 15.9217i −0.905753 1.56881i −0.819903 0.572502i $$-0.805973\pi$$
−0.0858496 0.996308i $$-0.527360\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 8.00000 0.777029
$$107$$ −8.00000 13.8564i −0.773389 1.33955i −0.935695 0.352809i $$-0.885227\pi$$
0.162306 0.986740i $$-0.448107\pi$$
$$108$$ 2.82843 4.89898i 0.272166 0.471405i
$$109$$ 1.00000 1.73205i 0.0957826 0.165900i −0.814152 0.580651i $$-0.802798\pi$$
0.909935 + 0.414751i $$0.136131\pi$$
$$110$$ 2.12132 + 3.67423i 0.202260 + 0.350325i
$$111$$ −14.1421 −1.34231
$$112$$ 0 0
$$113$$ −2.00000 −0.188144 −0.0940721 0.995565i $$-0.529988\pi$$
−0.0940721 + 0.995565i $$0.529988\pi$$
$$114$$ 0 0
$$115$$ −12.7279 + 22.0454i −1.18688 + 2.05574i
$$116$$ −1.00000 + 1.73205i −0.0928477 + 0.160817i
$$117$$ 0 0
$$118$$ 1.41421 0.130189
$$119$$ 0 0
$$120$$ 6.00000 0.547723
$$121$$ −0.500000 0.866025i −0.0454545 0.0787296i
$$122$$ 1.41421 2.44949i 0.128037 0.221766i
$$123$$ 8.00000 13.8564i 0.721336 1.24939i
$$124$$ 0.707107 + 1.22474i 0.0635001 + 0.109985i
$$125$$ 33.9411 3.03579
$$126$$ 0 0
$$127$$ 16.0000 1.41977 0.709885 0.704317i $$-0.248747\pi$$
0.709885 + 0.704317i $$0.248747\pi$$
$$128$$ −0.500000 0.866025i −0.0441942 0.0765466i
$$129$$ 5.65685 9.79796i 0.498058 0.862662i
$$130$$ 0 0
$$131$$ 9.89949 + 17.1464i 0.864923 + 1.49809i 0.867124 + 0.498093i $$0.165966\pi$$
−0.00220084 + 0.999998i $$0.500701\pi$$
$$132$$ −1.41421 −0.123091
$$133$$ 0 0
$$134$$ 2.00000 0.172774
$$135$$ 12.0000 + 20.7846i 1.03280 + 1.78885i
$$136$$ 2.82843 4.89898i 0.242536 0.420084i
$$137$$ 9.00000 15.5885i 0.768922 1.33181i −0.169226 0.985577i $$-0.554127\pi$$
0.938148 0.346235i $$-0.112540\pi$$
$$138$$ −4.24264 7.34847i −0.361158 0.625543i
$$139$$ 11.3137 0.959616 0.479808 0.877373i $$-0.340706\pi$$
0.479808 + 0.877373i $$0.340706\pi$$
$$140$$ 0 0
$$141$$ 6.00000 0.505291
$$142$$ 1.00000 + 1.73205i 0.0839181 + 0.145350i
$$143$$ 0 0
$$144$$ 0.500000 0.866025i 0.0416667 0.0721688i
$$145$$ −4.24264 7.34847i −0.352332 0.610257i
$$146$$ 8.48528 0.702247
$$147$$ 0 0
$$148$$ −10.0000 −0.821995
$$149$$ 5.00000 + 8.66025i 0.409616 + 0.709476i 0.994847 0.101391i $$-0.0323294\pi$$
−0.585231 + 0.810867i $$0.698996\pi$$
$$150$$ −9.19239 + 15.9217i −0.750555 + 1.30000i
$$151$$ −2.00000 + 3.46410i −0.162758 + 0.281905i −0.935857 0.352381i $$-0.885372\pi$$
0.773099 + 0.634285i $$0.218706\pi$$
$$152$$ 0 0
$$153$$ 5.65685 0.457330
$$154$$ 0 0
$$155$$ −6.00000 −0.481932
$$156$$ 0 0
$$157$$ −2.12132 + 3.67423i −0.169300 + 0.293236i −0.938174 0.346164i $$-0.887484\pi$$
0.768874 + 0.639400i $$0.220817\pi$$
$$158$$ −8.00000 + 13.8564i −0.636446 + 1.10236i
$$159$$ −5.65685 9.79796i −0.448618 0.777029i
$$160$$ 4.24264 0.335410
$$161$$ 0 0
$$162$$ −5.00000 −0.392837
$$163$$ 5.00000 + 8.66025i 0.391630 + 0.678323i 0.992665 0.120900i $$-0.0385779\pi$$
−0.601035 + 0.799223i $$0.705245\pi$$
$$164$$ 5.65685 9.79796i 0.441726 0.765092i
$$165$$ 3.00000 5.19615i 0.233550 0.404520i
$$166$$ 8.48528 + 14.6969i 0.658586 + 1.14070i
$$167$$ 5.65685 0.437741 0.218870 0.975754i $$-0.429763\pi$$
0.218870 + 0.975754i $$0.429763\pi$$
$$168$$ 0 0
$$169$$ −13.0000 −1.00000
$$170$$ 12.0000 + 20.7846i 0.920358 + 1.59411i
$$171$$ 0 0
$$172$$ 4.00000 6.92820i 0.304997 0.528271i
$$173$$ 5.65685 + 9.79796i 0.430083 + 0.744925i 0.996880 0.0789322i $$-0.0251511\pi$$
−0.566797 + 0.823857i $$0.691818\pi$$
$$174$$ 2.82843 0.214423
$$175$$ 0 0
$$176$$ −1.00000 −0.0753778
$$177$$ −1.00000 1.73205i −0.0751646 0.130189i
$$178$$ 3.53553 6.12372i 0.264999 0.458993i
$$179$$ −6.00000 + 10.3923i −0.448461 + 0.776757i −0.998286 0.0585225i $$-0.981361\pi$$
0.549825 + 0.835280i $$0.314694\pi$$
$$180$$ 2.12132 + 3.67423i 0.158114 + 0.273861i
$$181$$ −7.07107 −0.525588 −0.262794 0.964852i $$-0.584644\pi$$
−0.262794 + 0.964852i $$0.584644\pi$$
$$182$$ 0 0
$$183$$ −4.00000 −0.295689
$$184$$ −3.00000 5.19615i −0.221163 0.383065i
$$185$$ 21.2132 36.7423i 1.55963 2.70135i
$$186$$ 1.00000 1.73205i 0.0733236 0.127000i
$$187$$ −2.82843 4.89898i −0.206835 0.358249i
$$188$$ 4.24264 0.309426
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −8.00000 13.8564i −0.578860 1.00261i −0.995610 0.0935936i $$-0.970165\pi$$
0.416751 0.909021i $$-0.363169\pi$$
$$192$$ −0.707107 + 1.22474i −0.0510310 + 0.0883883i
$$193$$ 3.00000 5.19615i 0.215945 0.374027i −0.737620 0.675216i $$-0.764050\pi$$
0.953564 + 0.301189i $$0.0973836\pi$$
$$194$$ 4.94975 + 8.57321i 0.355371 + 0.615521i
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 22.0000 1.56744 0.783718 0.621117i $$-0.213321\pi$$
0.783718 + 0.621117i $$0.213321\pi$$
$$198$$ −0.500000 0.866025i −0.0355335 0.0615457i
$$199$$ 0.707107 1.22474i 0.0501255 0.0868199i −0.839874 0.542781i $$-0.817371\pi$$
0.889999 + 0.455962i $$0.150705\pi$$
$$200$$ −6.50000 + 11.2583i −0.459619 + 0.796084i
$$201$$ −1.41421 2.44949i −0.0997509 0.172774i
$$202$$ 5.65685 0.398015
$$203$$ 0 0
$$204$$ −8.00000 −0.560112
$$205$$ 24.0000 + 41.5692i 1.67623 + 2.90332i
$$206$$ −9.19239 + 15.9217i −0.640464 + 1.10932i
$$207$$ 3.00000 5.19615i 0.208514 0.361158i
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 8.00000 0.550743 0.275371 0.961338i $$-0.411199\pi$$
0.275371 + 0.961338i $$0.411199\pi$$
$$212$$ −4.00000 6.92820i −0.274721 0.475831i
$$213$$ 1.41421 2.44949i 0.0969003 0.167836i
$$214$$ −8.00000 + 13.8564i −0.546869 + 0.947204i
$$215$$ 16.9706 + 29.3939i 1.15738 + 2.00465i
$$216$$ −5.65685 −0.384900
$$217$$ 0 0
$$218$$ −2.00000 −0.135457
$$219$$ −6.00000 10.3923i −0.405442 0.702247i
$$220$$ 2.12132 3.67423i 0.143019 0.247717i
$$221$$ 0 0
$$222$$ 7.07107 + 12.2474i 0.474579 + 0.821995i
$$223$$ −21.2132 −1.42054 −0.710271 0.703929i $$-0.751427\pi$$
−0.710271 + 0.703929i $$0.751427\pi$$
$$224$$ 0 0
$$225$$ −13.0000 −0.866667
$$226$$ 1.00000 + 1.73205i 0.0665190 + 0.115214i
$$227$$ 7.07107 12.2474i 0.469323 0.812892i −0.530062 0.847959i $$-0.677831\pi$$
0.999385 + 0.0350674i $$0.0111646\pi$$
$$228$$ 0 0
$$229$$ −4.94975 8.57321i −0.327089 0.566534i 0.654844 0.755764i $$-0.272734\pi$$
−0.981933 + 0.189230i $$0.939401\pi$$
$$230$$ 25.4558 1.67851
$$231$$ 0 0
$$232$$ 2.00000 0.131306
$$233$$ −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
$$235$$ −9.00000 + 15.5885i −0.587095 + 1.01688i
$$236$$ −0.707107 1.22474i −0.0460287 0.0797241i
$$237$$ 22.6274 1.46981
$$238$$ 0 0
$$239$$ −12.0000 −0.776215 −0.388108 0.921614i $$-0.626871\pi$$
−0.388108 + 0.921614i $$0.626871\pi$$
$$240$$ −3.00000 5.19615i −0.193649 0.335410i
$$241$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$242$$ −0.500000 + 0.866025i −0.0321412 + 0.0556702i
$$243$$ −4.94975 8.57321i −0.317526 0.549972i
$$244$$ −2.82843 −0.181071
$$245$$ 0 0
$$246$$ −16.0000 −1.02012
$$247$$ 0 0
$$248$$ 0.707107 1.22474i 0.0449013 0.0777714i
$$249$$ 12.0000 20.7846i 0.760469 1.31717i
$$250$$ −16.9706 29.3939i −1.07331 1.85903i
$$251$$ 18.3848 1.16044 0.580218 0.814461i $$-0.302967\pi$$
0.580218 + 0.814461i $$0.302967\pi$$
$$252$$ 0 0
$$253$$ −6.00000 −0.377217
$$254$$ −8.00000 13.8564i −0.501965 0.869428i
$$255$$ 16.9706 29.3939i 1.06274 1.84072i
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ −0.707107 1.22474i −0.0441081 0.0763975i 0.843129 0.537712i $$-0.180711\pi$$
−0.887237 + 0.461315i $$0.847378\pi$$
$$258$$ −11.3137 −0.704361
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 1.00000 + 1.73205i 0.0618984 + 0.107211i
$$262$$ 9.89949 17.1464i 0.611593 1.05931i
$$263$$ 4.00000 6.92820i 0.246651 0.427211i −0.715944 0.698158i $$-0.754003\pi$$
0.962594 + 0.270947i $$0.0873367\pi$$
$$264$$ 0.707107 + 1.22474i 0.0435194 + 0.0753778i
$$265$$ 33.9411 2.08499
$$266$$ 0 0
$$267$$ −10.0000 −0.611990
$$268$$ −1.00000 1.73205i −0.0610847 0.105802i
$$269$$ −9.19239 + 15.9217i −0.560470 + 0.970762i 0.436986 + 0.899469i $$0.356046\pi$$
−0.997455 + 0.0712937i $$0.977287\pi$$
$$270$$ 12.0000 20.7846i 0.730297 1.26491i
$$271$$ 4.24264 + 7.34847i 0.257722 + 0.446388i 0.965631 0.259916i $$-0.0836948\pi$$
−0.707909 + 0.706303i $$0.750361\pi$$
$$272$$ −5.65685 −0.342997
$$273$$ 0 0
$$274$$ −18.0000 −1.08742
$$275$$ 6.50000 + 11.2583i 0.391965 + 0.678903i
$$276$$ −4.24264 + 7.34847i −0.255377 + 0.442326i
$$277$$ 1.00000 1.73205i 0.0600842 0.104069i −0.834419 0.551131i $$-0.814196\pi$$
0.894503 + 0.447062i $$0.147530\pi$$
$$278$$ −5.65685 9.79796i −0.339276 0.587643i
$$279$$ 1.41421 0.0846668
$$280$$ 0 0
$$281$$ −14.0000 −0.835170 −0.417585 0.908638i $$-0.637123\pi$$
−0.417585 + 0.908638i $$0.637123\pi$$
$$282$$ −3.00000 5.19615i −0.178647 0.309426i
$$283$$ 9.89949 17.1464i 0.588464 1.01925i −0.405970 0.913886i $$-0.633066\pi$$
0.994434 0.105363i $$-0.0336004\pi$$
$$284$$ 1.00000 1.73205i 0.0593391 0.102778i
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ −1.00000 −0.0589256
$$289$$ −7.50000 12.9904i −0.441176 0.764140i
$$290$$ −4.24264 + 7.34847i −0.249136 + 0.431517i
$$291$$ 7.00000 12.1244i 0.410347 0.710742i
$$292$$ −4.24264 7.34847i −0.248282 0.430037i
$$293$$ −8.48528 −0.495715 −0.247858 0.968796i $$-0.579727\pi$$
−0.247858 + 0.968796i $$0.579727\pi$$
$$294$$ 0 0
$$295$$ 6.00000 0.349334
$$296$$ 5.00000 + 8.66025i 0.290619 + 0.503367i
$$297$$ −2.82843 + 4.89898i −0.164122 + 0.284268i
$$298$$ 5.00000 8.66025i 0.289642 0.501675i
$$299$$ 0 0
$$300$$ 18.3848 1.06145
$$301$$ 0 0
$$302$$ 4.00000 0.230174
$$303$$ −4.00000 6.92820i −0.229794 0.398015i
$$304$$ 0 0
$$305$$ 6.00000 10.3923i 0.343559 0.595062i
$$306$$ −2.82843 4.89898i −0.161690 0.280056i
$$307$$ −25.4558 −1.45284 −0.726421 0.687250i $$-0.758818\pi$$
−0.726421 + 0.687250i $$0.758818\pi$$
$$308$$ 0 0
$$309$$ 26.0000 1.47909
$$310$$ 3.00000 + 5.19615i 0.170389 + 0.295122i
$$311$$ −9.19239 + 15.9217i −0.521253 + 0.902836i 0.478442 + 0.878119i $$0.341202\pi$$
−0.999694 + 0.0247167i $$0.992132\pi$$
$$312$$ 0 0
$$313$$ 6.36396 + 11.0227i 0.359712 + 0.623040i 0.987913 0.155012i $$-0.0495415\pi$$
−0.628200 + 0.778052i $$0.716208\pi$$
$$314$$ 4.24264 0.239426
$$315$$ 0 0
$$316$$ 16.0000 0.900070
$$317$$ −15.0000 25.9808i −0.842484 1.45922i −0.887788 0.460252i $$-0.847759\pi$$
0.0453045 0.998973i $$-0.485574\pi$$
$$318$$ −5.65685 + 9.79796i −0.317221 + 0.549442i
$$319$$ 1.00000 1.73205i 0.0559893 0.0969762i
$$320$$ −2.12132 3.67423i −0.118585 0.205396i
$$321$$ 22.6274 1.26294
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 2.50000 + 4.33013i 0.138889 + 0.240563i
$$325$$ 0 0
$$326$$ 5.00000 8.66025i 0.276924 0.479647i
$$327$$ 1.41421 + 2.44949i 0.0782062 + 0.135457i
$$328$$ −11.3137 −0.624695
$$329$$ 0 0
$$330$$ −6.00000 −0.330289
$$331$$ −10.0000 17.3205i −0.549650 0.952021i −0.998298 0.0583130i $$-0.981428\pi$$
0.448649 0.893708i $$-0.351905\pi$$
$$332$$ 8.48528 14.6969i 0.465690 0.806599i
$$333$$ −5.00000 + 8.66025i −0.273998 + 0.474579i
$$334$$ −2.82843 4.89898i −0.154765 0.268060i
$$335$$ 8.48528 0.463600
$$336$$ 0 0
$$337$$ 2.00000 0.108947 0.0544735 0.998515i $$-0.482652\pi$$
0.0544735 + 0.998515i $$0.482652\pi$$
$$338$$ 6.50000 + 11.2583i 0.353553 + 0.612372i
$$339$$ 1.41421 2.44949i 0.0768095 0.133038i
$$340$$ 12.0000 20.7846i 0.650791 1.12720i
$$341$$ −0.707107 1.22474i −0.0382920 0.0663237i
$$342$$ 0 0
$$343$$ 0 0
$$344$$ −8.00000 −0.431331
$$345$$ −18.0000 31.1769i −0.969087 1.67851i
$$346$$ 5.65685 9.79796i 0.304114 0.526742i
$$347$$ −10.0000 + 17.3205i −0.536828 + 0.929814i 0.462244 + 0.886753i $$0.347044\pi$$
−0.999072 + 0.0430610i $$0.986289\pi$$
$$348$$ −1.41421 2.44949i −0.0758098 0.131306i
$$349$$ 14.1421 0.757011 0.378506 0.925599i $$-0.376438\pi$$
0.378506 + 0.925599i $$0.376438\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0.500000 + 0.866025i 0.0266501 + 0.0461593i
$$353$$ −0.707107 + 1.22474i −0.0376355 + 0.0651866i −0.884230 0.467052i $$-0.845316\pi$$
0.846594 + 0.532239i $$0.178649\pi$$
$$354$$ −1.00000 + 1.73205i −0.0531494 + 0.0920575i
$$355$$ 4.24264 + 7.34847i 0.225176 + 0.390016i
$$356$$ −7.07107 −0.374766
$$357$$ 0 0
$$358$$ 12.0000 0.634220
$$359$$ 6.00000 + 10.3923i 0.316668 + 0.548485i 0.979791 0.200026i $$-0.0641026\pi$$
−0.663123 + 0.748511i $$0.730769\pi$$
$$360$$ 2.12132 3.67423i 0.111803 0.193649i
$$361$$ 9.50000 16.4545i 0.500000 0.866025i
$$362$$ 3.53553 + 6.12372i 0.185824 + 0.321856i
$$363$$ 1.41421 0.0742270
$$364$$ 0 0
$$365$$ 36.0000 1.88433
$$366$$ 2.00000 + 3.46410i 0.104542 + 0.181071i
$$367$$ 10.6066 18.3712i 0.553660 0.958967i −0.444346 0.895855i $$-0.646564\pi$$
0.998006 0.0631123i $$-0.0201026\pi$$
$$368$$ −3.00000 + 5.19615i −0.156386 + 0.270868i
$$369$$ −5.65685 9.79796i −0.294484 0.510061i
$$370$$ −42.4264 −2.20564
$$371$$ 0 0
$$372$$ −2.00000 −0.103695
$$373$$ 5.00000 + 8.66025i 0.258890 + 0.448411i 0.965945 0.258748i $$-0.0833099\pi$$
−0.707055 + 0.707159i $$0.749977\pi$$
$$374$$ −2.82843 + 4.89898i −0.146254 + 0.253320i
$$375$$ −24.0000 + 41.5692i −1.23935 + 2.14663i
$$376$$ −2.12132 3.67423i −0.109399 0.189484i
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −6.00000 −0.308199 −0.154100 0.988055i $$-0.549248\pi$$
−0.154100 + 0.988055i $$0.549248\pi$$
$$380$$ 0 0
$$381$$ −11.3137 + 19.5959i −0.579619 + 1.00393i
$$382$$ −8.00000 + 13.8564i −0.409316 + 0.708955i
$$383$$ −7.77817 13.4722i −0.397446 0.688397i 0.595964 0.803011i $$-0.296770\pi$$
−0.993410 + 0.114614i $$0.963437\pi$$
$$384$$ 1.41421 0.0721688
$$385$$ 0 0
$$386$$ −6.00000 −0.305392
$$387$$ −4.00000 6.92820i −0.203331 0.352180i
$$388$$ 4.94975 8.57321i 0.251285 0.435239i
$$389$$ 12.0000 20.7846i 0.608424 1.05382i −0.383076 0.923717i $$-0.625135\pi$$
0.991500 0.130105i $$-0.0415314\pi$$
$$390$$ 0 0
$$391$$ −33.9411 −1.71648
$$392$$ 0 0
$$393$$ −28.0000 −1.41241
$$394$$ −11.0000 19.0526i −0.554172 0.959854i
$$395$$ −33.9411 + 58.7878i −1.70776 + 2.95793i
$$396$$ −0.500000 + 0.866025i −0.0251259 + 0.0435194i
$$397$$ −6.36396 11.0227i −0.319398 0.553214i 0.660965 0.750417i $$-0.270147\pi$$
−0.980363 + 0.197203i $$0.936814\pi$$
$$398$$ −1.41421 −0.0708881
$$399$$ 0 0
$$400$$ 13.0000 0.650000
$$401$$ −6.00000 10.3923i −0.299626 0.518967i 0.676425 0.736512i $$-0.263528\pi$$
−0.976050 + 0.217545i $$0.930195\pi$$
$$402$$ −1.41421 + 2.44949i −0.0705346 + 0.122169i
$$403$$ 0 0
$$404$$ −2.82843 4.89898i −0.140720 0.243733i
$$405$$ −21.2132 −1.05409
$$406$$ 0 0
$$407$$ 10.0000 0.495682
$$408$$ 4.00000 + 6.92820i 0.198030 + 0.342997i
$$409$$ 1.41421 2.44949i 0.0699284 0.121119i −0.828941 0.559336i $$-0.811056\pi$$
0.898870 + 0.438216i $$0.144390\pi$$
$$410$$ 24.0000 41.5692i 1.18528 2.05296i
$$411$$ 12.7279 + 22.0454i 0.627822 + 1.08742i
$$412$$ 18.3848 0.905753
$$413$$ 0 0
$$414$$ −6.00000 −0.294884
$$415$$ 36.0000 + 62.3538i 1.76717 + 3.06083i
$$416$$ 0 0
$$417$$ −8.00000 + 13.8564i −0.391762 + 0.678551i
$$418$$ 0 0
$$419$$ 24.0416 1.17451 0.587255 0.809402i $$-0.300208\pi$$
0.587255 + 0.809402i $$0.300208\pi$$
$$420$$ 0 0
$$421$$ −20.0000 −0.974740 −0.487370 0.873195i $$-0.662044\pi$$
−0.487370 + 0.873195i $$0.662044\pi$$
$$422$$ −4.00000 6.92820i −0.194717 0.337260i
$$423$$ 2.12132 3.67423i 0.103142 0.178647i
$$424$$ −4.00000 + 6.92820i −0.194257 + 0.336463i
$$425$$ 36.7696 + 63.6867i 1.78359 + 3.08926i
$$426$$ −2.82843 −0.137038
$$427$$ 0 0
$$428$$ 16.0000 0.773389
$$429$$ 0 0
$$430$$ 16.9706 29.3939i 0.818393 1.41750i
$$431$$ −16.0000 + 27.7128i −0.770693 + 1.33488i 0.166491 + 0.986043i $$0.446756\pi$$
−0.937184 + 0.348836i $$0.886577\pi$$
$$432$$ 2.82843 + 4.89898i 0.136083 + 0.235702i
$$433$$ −12.7279 −0.611665 −0.305832 0.952085i $$-0.598935\pi$$
−0.305832 + 0.952085i $$0.598935\pi$$
$$434$$ 0 0
$$435$$ 12.0000 0.575356
$$436$$ 1.00000 + 1.73205i 0.0478913 + 0.0829502i
$$437$$ 0 0
$$438$$ −6.00000 + 10.3923i −0.286691 + 0.496564i
$$439$$ 12.7279 + 22.0454i 0.607471 + 1.05217i 0.991656 + 0.128914i $$0.0411491\pi$$
−0.384185 + 0.923256i $$0.625518\pi$$
$$440$$ −4.24264 −0.202260
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −18.0000 31.1769i −0.855206 1.48126i −0.876454 0.481486i $$-0.840097\pi$$
0.0212481 0.999774i $$-0.493236\pi$$
$$444$$ 7.07107 12.2474i 0.335578 0.581238i
$$445$$ 15.0000 25.9808i 0.711068 1.23161i
$$446$$ 10.6066 + 18.3712i 0.502237 + 0.869900i
$$447$$ −14.1421 −0.668900
$$448$$ 0 0
$$449$$ −20.0000 −0.943858 −0.471929 0.881636i $$-0.656442\pi$$
−0.471929 + 0.881636i $$0.656442\pi$$
$$450$$ 6.50000 + 11.2583i 0.306413 + 0.530723i
$$451$$ −5.65685 + 9.79796i −0.266371 + 0.461368i
$$452$$ 1.00000 1.73205i 0.0470360 0.0814688i
$$453$$ −2.82843 4.89898i −0.132891 0.230174i
$$454$$ −14.1421 −0.663723
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −7.00000 12.1244i −0.327446 0.567153i 0.654558 0.756012i $$-0.272855\pi$$
−0.982004 + 0.188858i $$0.939521\pi$$
$$458$$ −4.94975 + 8.57321i −0.231287 + 0.400600i
$$459$$ −16.0000 + 27.7128i −0.746816 + 1.29352i
$$460$$ −12.7279 22.0454i −0.593442 1.02787i
$$461$$ 2.82843 0.131733 0.0658665 0.997828i $$-0.479019\pi$$
0.0658665 + 0.997828i $$0.479019\pi$$
$$462$$ 0 0
$$463$$ 26.0000 1.20832 0.604161 0.796862i $$-0.293508\pi$$
0.604161 + 0.796862i $$0.293508\pi$$
$$464$$ −1.00000 1.73205i −0.0464238 0.0804084i
$$465$$ 4.24264 7.34847i 0.196748 0.340777i
$$466$$ −7.00000 + 12.1244i −0.324269 + 0.561650i
$$467$$ 2.12132 + 3.67423i 0.0981630 + 0.170023i 0.910924 0.412574i $$-0.135370\pi$$
−0.812761 + 0.582597i $$0.802037\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 18.0000 0.830278
$$471$$ −3.00000 5.19615i −0.138233 0.239426i
$$472$$ −0.707107 + 1.22474i −0.0325472 + 0.0563735i
$$473$$ −4.00000 + 6.92820i −0.183920 + 0.318559i
$$474$$ −11.3137 19.5959i −0.519656 0.900070i
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −8.00000 −0.366295
$$478$$ 6.00000 + 10.3923i 0.274434 + 0.475333i
$$479$$ −1.41421 + 2.44949i −0.0646171 + 0.111920i −0.896524 0.442995i $$-0.853916\pi$$
0.831907 + 0.554915i $$0.187249\pi$$
$$480$$ −3.00000 + 5.19615i −0.136931 + 0.237171i
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 1.00000 0.0454545
$$485$$ 21.0000 + 36.3731i 0.953561 + 1.65162i
$$486$$ −4.94975 + 8.57321i −0.224525 + 0.388889i
$$487$$ −1.00000 + 1.73205i −0.0453143 + 0.0784867i −0.887793 0.460243i $$-0.847762\pi$$
0.842479 + 0.538730i $$0.181096\pi$$
$$488$$ 1.41421 + 2.44949i 0.0640184 + 0.110883i
$$489$$ −14.1421 −0.639529
$$490$$ 0 0
$$491$$ −12.0000 −0.541552 −0.270776 0.962642i $$-0.587280\pi$$
−0.270776 + 0.962642i $$0.587280\pi$$
$$492$$ 8.00000 + 13.8564i 0.360668 + 0.624695i
$$493$$ 5.65685 9.79796i 0.254772 0.441278i
$$494$$ 0 0
$$495$$ −2.12132 3.67423i −0.0953463 0.165145i
$$496$$ −1.41421 −0.0635001
$$497$$ 0 0
$$498$$ −24.0000 −1.07547
$$499$$ −3.00000 5.19615i −0.134298 0.232612i 0.791031 0.611776i $$-0.209545\pi$$
−0.925329 + 0.379165i $$0.876211\pi$$
$$500$$ −16.9706 + 29.3939i −0.758947 + 1.31453i
$$501$$ −4.00000 + 6.92820i −0.178707 + 0.309529i
$$502$$ −9.19239 15.9217i −0.410276 0.710620i
$$503$$ 31.1127 1.38725 0.693623 0.720338i $$-0.256013\pi$$
0.693623 + 0.720338i $$0.256013\pi$$
$$504$$ 0 0
$$505$$ 24.0000 1.06799
$$506$$ 3.00000 + 5.19615i 0.133366 + 0.230997i
$$507$$ 9.19239 15.9217i 0.408248 0.707107i
$$508$$ −8.00000 + 13.8564i −0.354943 + 0.614779i
$$509$$ −6.36396 11.0227i −0.282078 0.488573i 0.689819 0.723982i $$-0.257690\pi$$
−0.971896 + 0.235409i $$0.924357\pi$$
$$510$$ −33.9411 −1.50294
$$511$$ 0 0
$$512$$ 1.00000 0.0441942
$$513$$ 0 0
$$514$$ −0.707107 + 1.22474i −0.0311891 + 0.0540212i
$$515$$ −39.0000 + 67.5500i −1.71855 + 2.97661i
$$516$$ 5.65685 + 9.79796i 0.249029 + 0.431331i
$$517$$ −4.24264 −0.186591
$$518$$ 0 0
$$519$$ −16.0000 −0.702322
$$520$$ 0 0
$$521$$ −0.707107 + 1.22474i −0.0309789 + 0.0536570i −0.881099 0.472931i $$-0.843196\pi$$
0.850120 + 0.526589i $$0.176529\pi$$
$$522$$ 1.00000 1.73205i 0.0437688 0.0758098i
$$523$$ −4.24264 7.34847i −0.185518 0.321326i 0.758233 0.651984i $$-0.226063\pi$$
−0.943751 + 0.330657i $$0.892730\pi$$
$$524$$ −19.7990 −0.864923
$$525$$ 0 0
$$526$$ −8.00000 −0.348817
$$527$$ −4.00000 6.92820i −0.174243 0.301797i
$$528$$ 0.707107 1.22474i 0.0307729 0.0533002i
$$529$$ −6.50000 + 11.2583i −0.282609 + 0.489493i
$$530$$ −16.9706 29.3939i −0.737154 1.27679i
$$531$$ −1.41421 −0.0613716
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 5.00000 + 8.66025i 0.216371 + 0.374766i
$$535$$ −33.9411 + 58.7878i −1.46740 + 2.54162i
$$536$$ −1.00000 + 1.73205i −0.0431934 + 0.0748132i
$$537$$ −8.48528 14.6969i −0.366167 0.634220i
$$538$$ 18.3848 0.792624
$$539$$ 0 0
$$540$$ −24.0000 −1.03280
$$541$$ 15.0000 + 25.9808i 0.644900 + 1.11700i 0.984325 + 0.176367i $$0.0564345\pi$$
−0.339424 + 0.940633i $$0.610232\pi$$
$$542$$ 4.24264 7.34847i 0.182237 0.315644i
$$543$$ 5.00000 8.66025i 0.214571 0.371647i
$$544$$ 2.82843 + 4.89898i 0.121268 + 0.210042i
$$545$$ −8.48528 −0.363470
$$546$$ 0 0
$$547$$ 44.0000 1.88130 0.940652 0.339372i $$-0.110215\pi$$
0.940652 + 0.339372i $$0.110215\pi$$
$$548$$ 9.00000 + 15.5885i 0.384461 + 0.665906i
$$549$$ −1.41421 + 2.44949i −0.0603572 + 0.104542i
$$550$$ 6.50000 11.2583i 0.277161 0.480057i
$$551$$ 0 0
$$552$$ 8.48528 0.361158
$$553$$ 0 0
$$554$$ −2.00000 −0.0849719
$$555$$ 30.0000 + 51.9615i 1.27343 + 2.20564i
$$556$$ −5.65685 + 9.79796i −0.239904 + 0.415526i
$$557$$ 15.0000 25.9808i 0.635570 1.10084i −0.350824 0.936442i $$-0.614098\pi$$
0.986394 0.164399i $$-0.0525683\pi$$
$$558$$ −0.707107 1.22474i −0.0299342 0.0518476i
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 8.00000 0.337760
$$562$$ 7.00000 + 12.1244i 0.295277 + 0.511435i
$$563$$ −11.3137 + 19.5959i −0.476816 + 0.825869i −0.999647 0.0265668i $$-0.991543\pi$$
0.522831 + 0.852436i $$0.324876\pi$$
$$564$$ −3.00000 + 5.19615i −0.126323 + 0.218797i
$$565$$ 4.24264 + 7.34847i 0.178489 + 0.309152i
$$566$$ −19.7990 −0.832214
$$567$$ 0 0
$$568$$ −2.00000 −0.0839181
$$569$$ −15.0000 25.9808i −0.628833 1.08917i −0.987786 0.155815i $$-0.950200\pi$$
0.358954 0.933355i $$-0.383134\pi$$
$$570$$ 0 0
$$571$$ −4.00000 + 6.92820i −0.167395 + 0.289936i −0.937503 0.347977i $$-0.886869\pi$$
0.770108 + 0.637913i $$0.220202\pi$$
$$572$$ 0 0
$$573$$ 22.6274 0.945274
$$574$$ 0 0
$$575$$ 78.0000 3.25282
$$576$$ 0.500000 + 0.866025i 0.0208333 + 0.0360844i
$$577$$ 3.53553 6.12372i 0.147186 0.254934i −0.783000 0.622021i $$-0.786312\pi$$
0.930186 + 0.367087i $$0.119645\pi$$
$$578$$ −7.50000 + 12.9904i −0.311959 + 0.540329i
$$579$$ 4.24264 + 7.34847i 0.176318 + 0.305392i
$$580$$ 8.48528 0.352332
$$581$$ 0 0
$$582$$ −14.0000 −0.580319
$$583$$ 4.00000 + 6.92820i 0.165663 + 0.286937i
$$584$$ −4.24264 + 7.34847i −0.175562 + 0.304082i
$$585$$ 0 0
$$586$$ 4.24264 + 7.34847i 0.175262 + 0.303562i
$$587$$ −26.8701 −1.10905 −0.554523 0.832168i $$-0.687099\pi$$
−0.554523 + 0.832168i $$0.687099\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ −3.00000 5.19615i −0.123508 0.213922i
$$591$$ −15.5563 + 26.9444i −0.639903 + 1.10834i
$$592$$ 5.00000 8.66025i 0.205499 0.355934i
$$593$$ −21.2132 36.7423i −0.871122 1.50883i −0.860837 0.508880i $$-0.830060\pi$$
−0.0102845 0.999947i $$-0.503274\pi$$
$$594$$ 5.65685 0.232104
$$595$$ 0 0
$$596$$ −10.0000 −0.409616
$$597$$ 1.00000 + 1.73205i 0.0409273 + 0.0708881i
$$598$$ 0 0
$$599$$ 3.00000 5.19615i 0.122577 0.212309i −0.798206 0.602384i $$-0.794218\pi$$
0.920783 + 0.390075i $$0.127551\pi$$
$$600$$ −9.19239 15.9217i −0.375278 0.650000i
$$601$$ 5.65685 0.230748 0.115374 0.993322i $$-0.463193\pi$$
0.115374 + 0.993322i $$0.463193\pi$$
$$602$$ 0 0
$$603$$ −2.00000 −0.0814463
$$604$$ −2.00000 3.46410i −0.0813788 0.140952i
$$605$$ −2.12132 + 3.67423i −0.0862439 + 0.149379i
$$606$$ −4.00000 + 6.92820i −0.162489 + 0.281439i
$$607$$ −8.48528 14.6969i −0.344407 0.596530i 0.640839 0.767675i $$-0.278587\pi$$
−0.985246 + 0.171145i $$0.945253\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ −12.0000 −0.485866
$$611$$ 0 0
$$612$$ −2.82843 + 4.89898i −0.114332 + 0.198030i
$$613$$ 5.00000 8.66025i 0.201948 0.349784i −0.747208 0.664590i $$-0.768606\pi$$
0.949156 + 0.314806i $$0.101939\pi$$
$$614$$ 12.7279 + 22.0454i 0.513657 + 0.889680i
$$615$$ −67.8823 −2.73728
$$616$$ 0 0
$$617$$ 34.0000 1.36879 0.684394 0.729112i $$-0.260067\pi$$
0.684394 + 0.729112i $$0.260067\pi$$
$$618$$ −13.0000 22.5167i −0.522937 0.905753i
$$619$$ −4.94975 + 8.57321i −0.198947 + 0.344587i −0.948187 0.317712i $$-0.897086\pi$$
0.749240 + 0.662298i $$0.230419\pi$$
$$620$$ 3.00000 5.19615i 0.120483 0.208683i
$$621$$ 16.9706 + 29.3939i 0.681005 + 1.17954i
$$622$$ 18.3848 0.737162
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −39.5000 68.4160i −1.58000 2.73664i
$$626$$ 6.36396 11.0227i 0.254355 0.440556i
$$627$$ 0 0
$$628$$ −2.12132 3.67423i −0.0846499 0.146618i
$$629$$ 56.5685 2.25554
$$630$$ 0 0
$$631$$ 24.0000 0.955425 0.477712 0.878516i $$-0.341466\pi$$
0.477712 + 0.878516i $$0.341466\pi$$
$$632$$ −8.00000 13.8564i −0.318223 0.551178i
$$633$$ −5.65685 + 9.79796i −0.224840 + 0.389434i
$$634$$ −15.0000 + 25.9808i −0.595726 + 1.03183i
$$635$$ −33.9411 58.7878i −1.34691 2.33292i
$$636$$ 11.3137 0.448618
$$637$$ 0 0
$$638$$ −2.00000 −0.0791808
$$639$$ −1.00000 1.73205i −0.0395594 0.0685189i
$$640$$ −2.12132 + 3.67423i −0.0838525 + 0.145237i
$$641$$ 17.0000 29.4449i 0.671460 1.16300i −0.306031 0.952022i $$-0.599001\pi$$
0.977490 0.210981i $$-0.0676657\pi$$
$$642$$ −11.3137 19.5959i −0.446516 0.773389i
$$643$$ −38.1838 −1.50582 −0.752910 0.658123i $$-0.771351\pi$$
−0.752910 + 0.658123i $$0.771351\pi$$
$$644$$ 0 0
$$645$$ −48.0000 −1.89000
$$646$$ 0 0
$$647$$ 7.77817 13.4722i 0.305792 0.529647i −0.671646 0.740873i $$-0.734412\pi$$
0.977437 + 0.211226i $$0.0677456\pi$$
$$648$$ 2.50000 4.33013i 0.0982093 0.170103i
$$649$$ 0.707107 + 1.22474i 0.0277564 + 0.0480754i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −10.0000 −0.391630
$$653$$ −6.00000 10.3923i −0.234798 0.406682i 0.724416 0.689363i $$-0.242110\pi$$
−0.959214 + 0.282681i $$0.908776\pi$$
$$654$$ 1.41421 2.44949i 0.0553001 0.0957826i
$$655$$ 42.0000 72.7461i 1.64108 2.84243i
$$656$$ 5.65685 + 9.79796i 0.220863 + 0.382546i
$$657$$ −8.48528 −0.331042
$$658$$ 0 0
$$659$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$660$$ 3.00000 + 5.19615i 0.116775 + 0.202260i
$$661$$ −6.36396 + 11.0227i −0.247529 + 0.428733i −0.962840 0.270073i $$-0.912952\pi$$
0.715310 + 0.698807i $$0.246285\pi$$
$$662$$ −10.0000 + 17.3205i −0.388661 + 0.673181i
$$663$$ 0 0
$$664$$ −16.9706 −0.658586
$$665$$ 0 0
$$666$$ 10.0000 0.387492
$$667$$ −6.00000 10.3923i −0.232321 0.402392i
$$668$$ −2.82843 + 4.89898i −0.109435 + 0.189547i
$$669$$ 15.0000 25.9808i 0.579934 1.00447i
$$670$$ −4.24264 7.34847i −0.163908 0.283896i
$$671$$ 2.82843 0.109190
$$672$$ 0 0
$$673$$ −22.0000 −0.848038 −0.424019 0.905653i $$-0.639381\pi$$
−0.424019 + 0.905653i $$0.639381\pi$$
$$674$$ −1.00000 1.73205i −0.0385186 0.0667161i
$$675$$ 36.7696 63.6867i 1.41526 2.45130i
$$676$$ 6.50000 11.2583i 0.250000 0.433013i
$$677$$ 19.7990 + 34.2929i 0.760937 + 1.31798i 0.942368 + 0.334578i $$0.108594\pi$$
−0.181431 + 0.983404i $$0.558073\pi$$
$$678$$ −2.82843 −0.108625
$$679$$ 0 0
$$680$$ −24.0000 −0.920358
$$681$$ 10.0000 + 17.3205i 0.383201 + 0.663723i
$$682$$ −0.707107 + 1.22474i −0.0270765 + 0.0468979i
$$683$$ 14.0000 24.2487i 0.535695 0.927851i −0.463434 0.886131i $$-0.653383\pi$$
0.999129 0.0417198i $$-0.0132837\pi$$
$$684$$ 0 0
$$685$$ −76.3675 −2.91785
$$686$$ 0 0
$$687$$ 14.0000 0.534133
$$688$$ 4.00000 + 6.92820i 0.152499 + 0.264135i
$$689$$ 0 0
$$690$$ −18.0000 + 31.1769i −0.685248 + 1.18688i
$$691$$ −7.77817 13.4722i −0.295896 0.512506i 0.679297 0.733863i $$-0.262285\pi$$
−0.975193 + 0.221357i $$0.928951\pi$$
$$692$$ −11.3137 −0.430083
$$693$$ 0 0
$$694$$ 20.0000 0.759190
$$695$$ −24.0000 41.5692i −0.910372 1.57681i
$$696$$ −1.41421 + 2.44949i −0.0536056 + 0.0928477i
$$697$$ −32.0000 + 55.4256i −1.21209 + 2.09940i
$$698$$ −7.07107 12.2474i −0.267644 0.463573i
$$699$$ 19.7990 0.748867
$$700$$ 0 0
$$701$$ 50.0000 1.88847 0.944237 0.329267i $$-0.106802\pi$$
0.944237 + 0.329267i $$0.106802\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0.500000 0.866025i 0.0188445 0.0326396i
$$705$$ −12.7279 22.0454i −0.479361 0.830278i
$$706$$ 1.41421 0.0532246
$$707$$ 0 0
$$708$$ 2.00000 0.0751646
$$709$$ 10.0000 + 17.3205i 0.375558 + 0.650485i 0.990410 0.138157i $$-0.0441178\pi$$
−0.614852 + 0.788642i $$0.710784\pi$$
$$710$$ 4.24264 7.34847i 0.159223 0.275783i
$$711$$ 8.00000 13.8564i 0.300023 0.519656i
$$712$$ 3.53553 + 6.12372i 0.132500 + 0.229496i
$$713$$ −8.48528 −0.317776
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −6.00000 10.3923i −0.224231 0.388379i
$$717$$ 8.48528 14.6969i 0.316889 0.548867i
$$718$$ 6.00000 10.3923i 0.223918 0.387837i
$$719$$ −9.19239 15.9217i −0.342818 0.593779i 0.642137 0.766590i $$-0.278048\pi$$
−0.984955 + 0.172812i $$0.944715\pi$$
$$720$$ −4.24264 −0.158114
$$721$$ 0 0
$$722$$ −19.0000 −0.707107
$$723$$ 0 0
$$724$$ 3.53553 6.12372i 0.131397 0.227586i
$$725$$ −13.0000 + 22.5167i −0.482808 + 0.836248i
$$726$$ −0.707107 1.22474i −0.0262432 0.0454545i
$$727$$ 12.7279 0.472052 0.236026 0.971747i $$-0.424155\pi$$
0.236026 + 0.971747i $$0.424155\pi$$
$$728$$ 0 0
$$729$$ 29.0000 1.07407
$$730$$ −18.0000 31.1769i −0.666210 1.15391i
$$731$$ −22.6274 + 39.1918i −0.836905 + 1.44956i
$$732$$ 2.00000 3.46410i 0.0739221 0.128037i
$$733$$ −7.07107 12.2474i −0.261176 0.452370i 0.705379 0.708831i $$-0.250777\pi$$
−0.966555 + 0.256461i $$0.917444\pi$$
$$734$$ −21.2132 −0.782994
$$735$$ 0 0
$$736$$ 6.00000 0.221163
$$737$$ 1.00000 + 1.73205i 0.0368355 + 0.0638009i
$$738$$ −5.65685 + 9.79796i −0.208232 + 0.360668i
$$739$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$740$$ 21.2132 + 36.7423i 0.779813 + 1.35068i
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −44.0000 −1.61420 −0.807102 0.590412i $$-0.798965\pi$$
−0.807102 + 0.590412i $$0.798965\pi$$
$$744$$ 1.00000 + 1.73205i 0.0366618 + 0.0635001i
$$745$$ 21.2132 36.7423i 0.777192 1.34614i
$$746$$ 5.00000 8.66025i 0.183063 0.317074i
$$747$$ −8.48528 14.6969i −0.310460 0.537733i
$$748$$ 5.65685 0.206835
$$749$$ 0 0
$$750$$ 48.0000 1.75271
$$751$$ 7.00000 + 12.1244i 0.255434 + 0.442424i 0.965013 0.262201i $$-0.0844484\pi$$
−0.709580 + 0.704625i $$0.751115\pi$$
$$752$$ −2.12132 + 3.67423i −0.0773566 + 0.133986i
$$753$$ −13.0000 + 22.5167i −0.473746 + 0.820553i
$$754$$ 0 0
$$755$$ 16.9706 0.617622
$$756$$ 0 0
$$757$$ −8.00000 −0.290765 −0.145382 0.989376i $$-0.546441\pi$$
−0.145382 + 0.989376i $$0.546441\pi$$
$$758$$ 3.00000 + 5.19615i 0.108965 + 0.188733i
$$759$$ 4.24264 7.34847i 0.153998 0.266733i
$$760$$ 0 0
$$761$$ 21.2132 + 36.7423i 0.768978 + 1.33191i 0.938118 + 0.346317i $$0.112568\pi$$
−0.169140 + 0.985592i $$0.554099\pi$$
$$762$$ 22.6274 0.819705
$$763$$ 0 0
$$764$$ 16.0000 0.578860
$$765$$ −12.0000 20.7846i −0.433861 0.751469i
$$766$$ −7.77817 + 13.4722i −0.281037 + 0.486770i
$$767$$ 0 0
$$768$$ −0.707107 1.22474i −0.0255155 0.0441942i
$$769$$ 19.7990 0.713970 0.356985 0.934110i $$-0.383805\pi$$
0.356985 + 0.934110i $$0.383805\pi$$
$$770$$ 0 0
$$771$$ 2.00000 0.0720282
$$772$$ 3.00000 + 5.19615i 0.107972 + 0.187014i
$$773$$ −0.707107 + 1.22474i −0.0254329 + 0.0440510i −0.878462 0.477813i $$-0.841430\pi$$
0.853029 + 0.521864i $$0.174763\pi$$
$$774$$ −4.00000 + 6.92820i −0.143777 + 0.249029i
$$775$$ 9.19239 + 15.9217i 0.330200 + 0.571924i
$$776$$ −9.89949 −0.355371
$$777$$ 0 0
$$778$$ −24.0000 −0.860442
$$779$$ 0 0
$$780$$ 0 0
$$781$$ −1.00000