# Properties

 Label 637.2.u.b.30.1 Level $637$ Weight $2$ Character 637.30 Analytic conductor $5.086$ 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] = [637,2,Mod(30,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("637.30");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$637 = 7^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 637.u (of order $$6$$, 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: $$5.08647060876$$ 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 13) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 30.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 637.30 Dual form 637.2.u.b.361.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(1.50000 - 0.866025i) q^{2} -2.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.50000 - 0.866025i) q^{5} +(-3.00000 + 1.73205i) q^{6} +1.73205i q^{8} +1.00000 q^{9} +O(q^{10})$$ $$q+(1.50000 - 0.866025i) q^{2} -2.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.50000 - 0.866025i) q^{5} +(-3.00000 + 1.73205i) q^{6} +1.73205i q^{8} +1.00000 q^{9} -3.00000 q^{10} +(-1.00000 + 1.73205i) q^{12} +(2.50000 + 2.59808i) q^{13} +(3.00000 + 1.73205i) q^{15} +(2.50000 + 4.33013i) q^{16} +(-1.50000 + 2.59808i) q^{17} +(1.50000 - 0.866025i) q^{18} +3.46410i q^{19} +(-1.50000 + 0.866025i) q^{20} +(3.00000 + 5.19615i) q^{23} -3.46410i q^{24} +(-1.00000 - 1.73205i) q^{25} +(6.00000 + 1.73205i) q^{26} +4.00000 q^{27} +(-1.50000 + 2.59808i) q^{29} +6.00000 q^{30} +(-3.00000 + 1.73205i) q^{31} +(4.50000 + 2.59808i) q^{32} +5.19615i q^{34} +(0.500000 - 0.866025i) q^{36} +(-7.50000 + 4.33013i) q^{37} +(3.00000 + 5.19615i) q^{38} +(-5.00000 - 5.19615i) q^{39} +(1.50000 - 2.59808i) q^{40} +(4.50000 + 2.59808i) q^{41} +(-4.00000 - 6.92820i) q^{43} +(-1.50000 - 0.866025i) q^{45} +(9.00000 + 5.19615i) q^{46} +(-3.00000 - 1.73205i) q^{47} +(-5.00000 - 8.66025i) q^{48} +(-3.00000 - 1.73205i) q^{50} +(3.00000 - 5.19615i) q^{51} +(3.50000 - 0.866025i) q^{52} +(1.50000 + 2.59808i) q^{53} +(6.00000 - 3.46410i) q^{54} -6.92820i q^{57} +5.19615i q^{58} +(6.00000 + 3.46410i) q^{59} +(3.00000 - 1.73205i) q^{60} -1.00000 q^{61} +(-3.00000 + 5.19615i) q^{62} -1.00000 q^{64} +(-1.50000 - 6.06218i) q^{65} -3.46410i q^{67} +(1.50000 + 2.59808i) q^{68} +(-6.00000 - 10.3923i) q^{69} +(3.00000 - 1.73205i) q^{71} +1.73205i q^{72} +(-1.50000 + 0.866025i) q^{73} +(-7.50000 + 12.9904i) q^{74} +(2.00000 + 3.46410i) q^{75} +(3.00000 + 1.73205i) q^{76} +(-12.0000 - 3.46410i) q^{78} +(-2.00000 + 3.46410i) q^{79} -8.66025i q^{80} -11.0000 q^{81} +9.00000 q^{82} -13.8564i q^{83} +(4.50000 - 2.59808i) q^{85} +(-12.0000 - 6.92820i) q^{86} +(3.00000 - 5.19615i) q^{87} +(-6.00000 + 3.46410i) q^{89} -3.00000 q^{90} +6.00000 q^{92} +(6.00000 - 3.46410i) q^{93} -6.00000 q^{94} +(3.00000 - 5.19615i) q^{95} +(-9.00000 - 5.19615i) q^{96} +(-6.00000 + 3.46410i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 3 q^{2} - 4 q^{3} + q^{4} - 3 q^{5} - 6 q^{6} + 2 q^{9}+O(q^{10})$$ 2 * q + 3 * q^2 - 4 * q^3 + q^4 - 3 * q^5 - 6 * q^6 + 2 * q^9 $$2 q + 3 q^{2} - 4 q^{3} + q^{4} - 3 q^{5} - 6 q^{6} + 2 q^{9} - 6 q^{10} - 2 q^{12} + 5 q^{13} + 6 q^{15} + 5 q^{16} - 3 q^{17} + 3 q^{18} - 3 q^{20} + 6 q^{23} - 2 q^{25} + 12 q^{26} + 8 q^{27} - 3 q^{29} + 12 q^{30} - 6 q^{31} + 9 q^{32} + q^{36} - 15 q^{37} + 6 q^{38} - 10 q^{39} + 3 q^{40} + 9 q^{41} - 8 q^{43} - 3 q^{45} + 18 q^{46} - 6 q^{47} - 10 q^{48} - 6 q^{50} + 6 q^{51} + 7 q^{52} + 3 q^{53} + 12 q^{54} + 12 q^{59} + 6 q^{60} - 2 q^{61} - 6 q^{62} - 2 q^{64} - 3 q^{65} + 3 q^{68} - 12 q^{69} + 6 q^{71} - 3 q^{73} - 15 q^{74} + 4 q^{75} + 6 q^{76} - 24 q^{78} - 4 q^{79} - 22 q^{81} + 18 q^{82} + 9 q^{85} - 24 q^{86} + 6 q^{87} - 12 q^{89} - 6 q^{90} + 12 q^{92} + 12 q^{93} - 12 q^{94} + 6 q^{95} - 18 q^{96} - 12 q^{97}+O(q^{100})$$ 2 * q + 3 * q^2 - 4 * q^3 + q^4 - 3 * q^5 - 6 * q^6 + 2 * q^9 - 6 * q^10 - 2 * q^12 + 5 * q^13 + 6 * q^15 + 5 * q^16 - 3 * q^17 + 3 * q^18 - 3 * q^20 + 6 * q^23 - 2 * q^25 + 12 * q^26 + 8 * q^27 - 3 * q^29 + 12 * q^30 - 6 * q^31 + 9 * q^32 + q^36 - 15 * q^37 + 6 * q^38 - 10 * q^39 + 3 * q^40 + 9 * q^41 - 8 * q^43 - 3 * q^45 + 18 * q^46 - 6 * q^47 - 10 * q^48 - 6 * q^50 + 6 * q^51 + 7 * q^52 + 3 * q^53 + 12 * q^54 + 12 * q^59 + 6 * q^60 - 2 * q^61 - 6 * q^62 - 2 * q^64 - 3 * q^65 + 3 * q^68 - 12 * q^69 + 6 * q^71 - 3 * q^73 - 15 * q^74 + 4 * q^75 + 6 * q^76 - 24 * q^78 - 4 * q^79 - 22 * q^81 + 18 * q^82 + 9 * q^85 - 24 * q^86 + 6 * q^87 - 12 * q^89 - 6 * q^90 + 12 * q^92 + 12 * q^93 - 12 * q^94 + 6 * q^95 - 18 * q^96 - 12 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$$.

 $$n$$ $$197$$ $$248$$ $$\chi(n)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.50000 0.866025i 1.06066 0.612372i 0.135045 0.990839i $$-0.456882\pi$$
0.925615 + 0.378467i $$0.123549\pi$$
$$3$$ −2.00000 −1.15470 −0.577350 0.816497i $$-0.695913\pi$$
−0.577350 + 0.816497i $$0.695913\pi$$
$$4$$ 0.500000 0.866025i 0.250000 0.433013i
$$5$$ −1.50000 0.866025i −0.670820 0.387298i 0.125567 0.992085i $$-0.459925\pi$$
−0.796387 + 0.604787i $$0.793258\pi$$
$$6$$ −3.00000 + 1.73205i −1.22474 + 0.707107i
$$7$$ 0 0
$$8$$ 1.73205i 0.612372i
$$9$$ 1.00000 0.333333
$$10$$ −3.00000 −0.948683
$$11$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$12$$ −1.00000 + 1.73205i −0.288675 + 0.500000i
$$13$$ 2.50000 + 2.59808i 0.693375 + 0.720577i
$$14$$ 0 0
$$15$$ 3.00000 + 1.73205i 0.774597 + 0.447214i
$$16$$ 2.50000 + 4.33013i 0.625000 + 1.08253i
$$17$$ −1.50000 + 2.59808i −0.363803 + 0.630126i −0.988583 0.150675i $$-0.951855\pi$$
0.624780 + 0.780801i $$0.285189\pi$$
$$18$$ 1.50000 0.866025i 0.353553 0.204124i
$$19$$ 3.46410i 0.794719i 0.917663 + 0.397360i $$0.130073\pi$$
−0.917663 + 0.397360i $$0.869927\pi$$
$$20$$ −1.50000 + 0.866025i −0.335410 + 0.193649i
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 3.00000 + 5.19615i 0.625543 + 1.08347i 0.988436 + 0.151642i $$0.0484560\pi$$
−0.362892 + 0.931831i $$0.618211\pi$$
$$24$$ 3.46410i 0.707107i
$$25$$ −1.00000 1.73205i −0.200000 0.346410i
$$26$$ 6.00000 + 1.73205i 1.17670 + 0.339683i
$$27$$ 4.00000 0.769800
$$28$$ 0 0
$$29$$ −1.50000 + 2.59808i −0.278543 + 0.482451i −0.971023 0.238987i $$-0.923185\pi$$
0.692480 + 0.721437i $$0.256518\pi$$
$$30$$ 6.00000 1.09545
$$31$$ −3.00000 + 1.73205i −0.538816 + 0.311086i −0.744599 0.667512i $$-0.767359\pi$$
0.205783 + 0.978598i $$0.434026\pi$$
$$32$$ 4.50000 + 2.59808i 0.795495 + 0.459279i
$$33$$ 0 0
$$34$$ 5.19615i 0.891133i
$$35$$ 0 0
$$36$$ 0.500000 0.866025i 0.0833333 0.144338i
$$37$$ −7.50000 + 4.33013i −1.23299 + 0.711868i −0.967653 0.252286i $$-0.918817\pi$$
−0.265340 + 0.964155i $$0.585484\pi$$
$$38$$ 3.00000 + 5.19615i 0.486664 + 0.842927i
$$39$$ −5.00000 5.19615i −0.800641 0.832050i
$$40$$ 1.50000 2.59808i 0.237171 0.410792i
$$41$$ 4.50000 + 2.59808i 0.702782 + 0.405751i 0.808383 0.588657i $$-0.200343\pi$$
−0.105601 + 0.994409i $$0.533677\pi$$
$$42$$ 0 0
$$43$$ −4.00000 6.92820i −0.609994 1.05654i −0.991241 0.132068i $$-0.957838\pi$$
0.381246 0.924473i $$-0.375495\pi$$
$$44$$ 0 0
$$45$$ −1.50000 0.866025i −0.223607 0.129099i
$$46$$ 9.00000 + 5.19615i 1.32698 + 0.766131i
$$47$$ −3.00000 1.73205i −0.437595 0.252646i 0.264982 0.964253i $$-0.414634\pi$$
−0.702577 + 0.711608i $$0.747967\pi$$
$$48$$ −5.00000 8.66025i −0.721688 1.25000i
$$49$$ 0 0
$$50$$ −3.00000 1.73205i −0.424264 0.244949i
$$51$$ 3.00000 5.19615i 0.420084 0.727607i
$$52$$ 3.50000 0.866025i 0.485363 0.120096i
$$53$$ 1.50000 + 2.59808i 0.206041 + 0.356873i 0.950464 0.310835i $$-0.100609\pi$$
−0.744423 + 0.667708i $$0.767275\pi$$
$$54$$ 6.00000 3.46410i 0.816497 0.471405i
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 6.92820i 0.917663i
$$58$$ 5.19615i 0.682288i
$$59$$ 6.00000 + 3.46410i 0.781133 + 0.450988i 0.836832 0.547460i $$-0.184405\pi$$
−0.0556984 + 0.998448i $$0.517739\pi$$
$$60$$ 3.00000 1.73205i 0.387298 0.223607i
$$61$$ −1.00000 −0.128037 −0.0640184 0.997949i $$-0.520392\pi$$
−0.0640184 + 0.997949i $$0.520392\pi$$
$$62$$ −3.00000 + 5.19615i −0.381000 + 0.659912i
$$63$$ 0 0
$$64$$ −1.00000 −0.125000
$$65$$ −1.50000 6.06218i −0.186052 0.751921i
$$66$$ 0 0
$$67$$ 3.46410i 0.423207i −0.977356 0.211604i $$-0.932131\pi$$
0.977356 0.211604i $$-0.0678686\pi$$
$$68$$ 1.50000 + 2.59808i 0.181902 + 0.315063i
$$69$$ −6.00000 10.3923i −0.722315 1.25109i
$$70$$ 0 0
$$71$$ 3.00000 1.73205i 0.356034 0.205557i −0.311305 0.950310i $$-0.600766\pi$$
0.667340 + 0.744753i $$0.267433\pi$$
$$72$$ 1.73205i 0.204124i
$$73$$ −1.50000 + 0.866025i −0.175562 + 0.101361i −0.585206 0.810885i $$-0.698986\pi$$
0.409644 + 0.912245i $$0.365653\pi$$
$$74$$ −7.50000 + 12.9904i −0.871857 + 1.51010i
$$75$$ 2.00000 + 3.46410i 0.230940 + 0.400000i
$$76$$ 3.00000 + 1.73205i 0.344124 + 0.198680i
$$77$$ 0 0
$$78$$ −12.0000 3.46410i −1.35873 0.392232i
$$79$$ −2.00000 + 3.46410i −0.225018 + 0.389742i −0.956325 0.292306i $$-0.905577\pi$$
0.731307 + 0.682048i $$0.238911\pi$$
$$80$$ 8.66025i 0.968246i
$$81$$ −11.0000 −1.22222
$$82$$ 9.00000 0.993884
$$83$$ 13.8564i 1.52094i −0.649374 0.760469i $$-0.724969\pi$$
0.649374 0.760469i $$-0.275031\pi$$
$$84$$ 0 0
$$85$$ 4.50000 2.59808i 0.488094 0.281801i
$$86$$ −12.0000 6.92820i −1.29399 0.747087i
$$87$$ 3.00000 5.19615i 0.321634 0.557086i
$$88$$ 0 0
$$89$$ −6.00000 + 3.46410i −0.635999 + 0.367194i −0.783072 0.621932i $$-0.786348\pi$$
0.147073 + 0.989126i $$0.453015\pi$$
$$90$$ −3.00000 −0.316228
$$91$$ 0 0
$$92$$ 6.00000 0.625543
$$93$$ 6.00000 3.46410i 0.622171 0.359211i
$$94$$ −6.00000 −0.618853
$$95$$ 3.00000 5.19615i 0.307794 0.533114i
$$96$$ −9.00000 5.19615i −0.918559 0.530330i
$$97$$ −6.00000 + 3.46410i −0.609208 + 0.351726i −0.772655 0.634826i $$-0.781072\pi$$
0.163448 + 0.986552i $$0.447739\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ −2.00000 −0.200000
$$101$$ 3.00000 0.298511 0.149256 0.988799i $$-0.452312\pi$$
0.149256 + 0.988799i $$0.452312\pi$$
$$102$$ 10.3923i 1.02899i
$$103$$ −5.00000 + 8.66025i −0.492665 + 0.853320i −0.999964 0.00844953i $$-0.997310\pi$$
0.507300 + 0.861770i $$0.330644\pi$$
$$104$$ −4.50000 + 4.33013i −0.441261 + 0.424604i
$$105$$ 0 0
$$106$$ 4.50000 + 2.59808i 0.437079 + 0.252347i
$$107$$ −3.00000 5.19615i −0.290021 0.502331i 0.683793 0.729676i $$-0.260329\pi$$
−0.973814 + 0.227345i $$0.926996\pi$$
$$108$$ 2.00000 3.46410i 0.192450 0.333333i
$$109$$ −12.0000 + 6.92820i −1.14939 + 0.663602i −0.948739 0.316061i $$-0.897640\pi$$
−0.200653 + 0.979662i $$0.564306\pi$$
$$110$$ 0 0
$$111$$ 15.0000 8.66025i 1.42374 0.821995i
$$112$$ 0 0
$$113$$ 7.50000 + 12.9904i 0.705541 + 1.22203i 0.966496 + 0.256681i $$0.0826291\pi$$
−0.260955 + 0.965351i $$0.584038\pi$$
$$114$$ −6.00000 10.3923i −0.561951 0.973329i
$$115$$ 10.3923i 0.969087i
$$116$$ 1.50000 + 2.59808i 0.139272 + 0.241225i
$$117$$ 2.50000 + 2.59808i 0.231125 + 0.240192i
$$118$$ 12.0000 1.10469
$$119$$ 0 0
$$120$$ −3.00000 + 5.19615i −0.273861 + 0.474342i
$$121$$ 11.0000 1.00000
$$122$$ −1.50000 + 0.866025i −0.135804 + 0.0784063i
$$123$$ −9.00000 5.19615i −0.811503 0.468521i
$$124$$ 3.46410i 0.311086i
$$125$$ 12.1244i 1.08444i
$$126$$ 0 0
$$127$$ 1.00000 1.73205i 0.0887357 0.153695i −0.818241 0.574875i $$-0.805051\pi$$
0.906977 + 0.421180i $$0.138384\pi$$
$$128$$ −10.5000 + 6.06218i −0.928078 + 0.535826i
$$129$$ 8.00000 + 13.8564i 0.704361 + 1.21999i
$$130$$ −7.50000 7.79423i −0.657794 0.683599i
$$131$$ 9.00000 15.5885i 0.786334 1.36197i −0.141865 0.989886i $$-0.545310\pi$$
0.928199 0.372084i $$-0.121357\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ −3.00000 5.19615i −0.259161 0.448879i
$$135$$ −6.00000 3.46410i −0.516398 0.298142i
$$136$$ −4.50000 2.59808i −0.385872 0.222783i
$$137$$ 13.5000 + 7.79423i 1.15338 + 0.665906i 0.949709 0.313133i $$-0.101379\pi$$
0.203674 + 0.979039i $$0.434712\pi$$
$$138$$ −18.0000 10.3923i −1.53226 0.884652i
$$139$$ −2.00000 3.46410i −0.169638 0.293821i 0.768655 0.639664i $$-0.220926\pi$$
−0.938293 + 0.345843i $$0.887593\pi$$
$$140$$ 0 0
$$141$$ 6.00000 + 3.46410i 0.505291 + 0.291730i
$$142$$ 3.00000 5.19615i 0.251754 0.436051i
$$143$$ 0 0
$$144$$ 2.50000 + 4.33013i 0.208333 + 0.360844i
$$145$$ 4.50000 2.59808i 0.373705 0.215758i
$$146$$ −1.50000 + 2.59808i −0.124141 + 0.215018i
$$147$$ 0 0
$$148$$ 8.66025i 0.711868i
$$149$$ 19.0526i 1.56085i −0.625252 0.780423i $$-0.715004\pi$$
0.625252 0.780423i $$-0.284996\pi$$
$$150$$ 6.00000 + 3.46410i 0.489898 + 0.282843i
$$151$$ 15.0000 8.66025i 1.22068 0.704761i 0.255619 0.966778i $$-0.417721\pi$$
0.965064 + 0.262016i $$0.0843873\pi$$
$$152$$ −6.00000 −0.486664
$$153$$ −1.50000 + 2.59808i −0.121268 + 0.210042i
$$154$$ 0 0
$$155$$ 6.00000 0.481932
$$156$$ −7.00000 + 1.73205i −0.560449 + 0.138675i
$$157$$ −6.50000 11.2583i −0.518756 0.898513i −0.999762 0.0217953i $$-0.993062\pi$$
0.481006 0.876717i $$-0.340272\pi$$
$$158$$ 6.92820i 0.551178i
$$159$$ −3.00000 5.19615i −0.237915 0.412082i
$$160$$ −4.50000 7.79423i −0.355756 0.616188i
$$161$$ 0 0
$$162$$ −16.5000 + 9.52628i −1.29636 + 0.748455i
$$163$$ 20.7846i 1.62798i 0.580881 + 0.813988i $$0.302708\pi$$
−0.580881 + 0.813988i $$0.697292\pi$$
$$164$$ 4.50000 2.59808i 0.351391 0.202876i
$$165$$ 0 0
$$166$$ −12.0000 20.7846i −0.931381 1.61320i
$$167$$ 12.0000 + 6.92820i 0.928588 + 0.536120i 0.886365 0.462988i $$-0.153223\pi$$
0.0422232 + 0.999108i $$0.486556\pi$$
$$168$$ 0 0
$$169$$ −0.500000 + 12.9904i −0.0384615 + 0.999260i
$$170$$ 4.50000 7.79423i 0.345134 0.597790i
$$171$$ 3.46410i 0.264906i
$$172$$ −8.00000 −0.609994
$$173$$ −6.00000 −0.456172 −0.228086 0.973641i $$-0.573247\pi$$
−0.228086 + 0.973641i $$0.573247\pi$$
$$174$$ 10.3923i 0.787839i
$$175$$ 0 0
$$176$$ 0 0
$$177$$ −12.0000 6.92820i −0.901975 0.520756i
$$178$$ −6.00000 + 10.3923i −0.449719 + 0.778936i
$$179$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$180$$ −1.50000 + 0.866025i −0.111803 + 0.0645497i
$$181$$ −11.0000 −0.817624 −0.408812 0.912619i $$-0.634057\pi$$
−0.408812 + 0.912619i $$0.634057\pi$$
$$182$$ 0 0
$$183$$ 2.00000 0.147844
$$184$$ −9.00000 + 5.19615i −0.663489 + 0.383065i
$$185$$ 15.0000 1.10282
$$186$$ 6.00000 10.3923i 0.439941 0.762001i
$$187$$ 0 0
$$188$$ −3.00000 + 1.73205i −0.218797 + 0.126323i
$$189$$ 0 0
$$190$$ 10.3923i 0.753937i
$$191$$ 18.0000 1.30243 0.651217 0.758891i $$-0.274259\pi$$
0.651217 + 0.758891i $$0.274259\pi$$
$$192$$ 2.00000 0.144338
$$193$$ 5.19615i 0.374027i 0.982357 + 0.187014i $$0.0598809\pi$$
−0.982357 + 0.187014i $$0.940119\pi$$
$$194$$ −6.00000 + 10.3923i −0.430775 + 0.746124i
$$195$$ 3.00000 + 12.1244i 0.214834 + 0.868243i
$$196$$ 0 0
$$197$$ 12.0000 + 6.92820i 0.854965 + 0.493614i 0.862323 0.506359i $$-0.169009\pi$$
−0.00735824 + 0.999973i $$0.502342\pi$$
$$198$$ 0 0
$$199$$ −1.00000 + 1.73205i −0.0708881 + 0.122782i −0.899291 0.437351i $$-0.855917\pi$$
0.828403 + 0.560133i $$0.189250\pi$$
$$200$$ 3.00000 1.73205i 0.212132 0.122474i
$$201$$ 6.92820i 0.488678i
$$202$$ 4.50000 2.59808i 0.316619 0.182800i
$$203$$ 0 0
$$204$$ −3.00000 5.19615i −0.210042 0.363803i
$$205$$ −4.50000 7.79423i −0.314294 0.544373i
$$206$$ 17.3205i 1.20678i
$$207$$ 3.00000 + 5.19615i 0.208514 + 0.361158i
$$208$$ −5.00000 + 17.3205i −0.346688 + 1.20096i
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −5.00000 + 8.66025i −0.344214 + 0.596196i −0.985211 0.171347i $$-0.945188\pi$$
0.640996 + 0.767544i $$0.278521\pi$$
$$212$$ 3.00000 0.206041
$$213$$ −6.00000 + 3.46410i −0.411113 + 0.237356i
$$214$$ −9.00000 5.19615i −0.615227 0.355202i
$$215$$ 13.8564i 0.944999i
$$216$$ 6.92820i 0.471405i
$$217$$ 0 0
$$218$$ −12.0000 + 20.7846i −0.812743 + 1.40771i
$$219$$ 3.00000 1.73205i 0.202721 0.117041i
$$220$$ 0 0
$$221$$ −10.5000 + 2.59808i −0.706306 + 0.174766i
$$222$$ 15.0000 25.9808i 1.00673 1.74371i
$$223$$ 9.00000 + 5.19615i 0.602685 + 0.347960i 0.770097 0.637927i $$-0.220208\pi$$
−0.167412 + 0.985887i $$0.553541\pi$$
$$224$$ 0 0
$$225$$ −1.00000 1.73205i −0.0666667 0.115470i
$$226$$ 22.5000 + 12.9904i 1.49668 + 0.864107i
$$227$$ 21.0000 + 12.1244i 1.39382 + 0.804722i 0.993736 0.111757i $$-0.0356478\pi$$
0.400083 + 0.916479i $$0.368981\pi$$
$$228$$ −6.00000 3.46410i −0.397360 0.229416i
$$229$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$230$$ −9.00000 15.5885i −0.593442 1.02787i
$$231$$ 0 0
$$232$$ −4.50000 2.59808i −0.295439 0.170572i
$$233$$ −3.00000 + 5.19615i −0.196537 + 0.340411i −0.947403 0.320043i $$-0.896303\pi$$
0.750867 + 0.660454i $$0.229636\pi$$
$$234$$ 6.00000 + 1.73205i 0.392232 + 0.113228i
$$235$$ 3.00000 + 5.19615i 0.195698 + 0.338960i
$$236$$ 6.00000 3.46410i 0.390567 0.225494i
$$237$$ 4.00000 6.92820i 0.259828 0.450035i
$$238$$ 0 0
$$239$$ 20.7846i 1.34444i −0.740349 0.672222i $$-0.765340\pi$$
0.740349 0.672222i $$-0.234660\pi$$
$$240$$ 17.3205i 1.11803i
$$241$$ −1.50000 0.866025i −0.0966235 0.0557856i 0.450910 0.892570i $$-0.351100\pi$$
−0.547533 + 0.836784i $$0.684433\pi$$
$$242$$ 16.5000 9.52628i 1.06066 0.612372i
$$243$$ 10.0000 0.641500
$$244$$ −0.500000 + 0.866025i −0.0320092 + 0.0554416i
$$245$$ 0 0
$$246$$ −18.0000 −1.14764
$$247$$ −9.00000 + 8.66025i −0.572656 + 0.551039i
$$248$$ −3.00000 5.19615i −0.190500 0.329956i
$$249$$ 27.7128i 1.75623i
$$250$$ 10.5000 + 18.1865i 0.664078 + 1.15022i
$$251$$ −9.00000 15.5885i −0.568075 0.983935i −0.996756 0.0804789i $$-0.974355\pi$$
0.428681 0.903456i $$-0.358978\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 3.46410i 0.217357i
$$255$$ −9.00000 + 5.19615i −0.563602 + 0.325396i
$$256$$ −9.50000 + 16.4545i −0.593750 + 1.02841i
$$257$$ 1.50000 + 2.59808i 0.0935674 + 0.162064i 0.909010 0.416775i $$-0.136840\pi$$
−0.815442 + 0.578838i $$0.803506\pi$$
$$258$$ 24.0000 + 13.8564i 1.49417 + 0.862662i
$$259$$ 0 0
$$260$$ −6.00000 1.73205i −0.372104 0.107417i
$$261$$ −1.50000 + 2.59808i −0.0928477 + 0.160817i
$$262$$ 31.1769i 1.92612i
$$263$$ 12.0000 0.739952 0.369976 0.929041i $$-0.379366\pi$$
0.369976 + 0.929041i $$0.379366\pi$$
$$264$$ 0 0
$$265$$ 5.19615i 0.319197i
$$266$$ 0 0
$$267$$ 12.0000 6.92820i 0.734388 0.423999i
$$268$$ −3.00000 1.73205i −0.183254 0.105802i
$$269$$ −3.00000 + 5.19615i −0.182913 + 0.316815i −0.942871 0.333157i $$-0.891886\pi$$
0.759958 + 0.649972i $$0.225219\pi$$
$$270$$ −12.0000 −0.730297
$$271$$ 18.0000 10.3923i 1.09342 0.631288i 0.158937 0.987289i $$-0.449193\pi$$
0.934485 + 0.356001i $$0.115860\pi$$
$$272$$ −15.0000 −0.909509
$$273$$ 0 0
$$274$$ 27.0000 1.63113
$$275$$ 0 0
$$276$$ −12.0000 −0.722315
$$277$$ 3.50000 6.06218i 0.210295 0.364241i −0.741512 0.670940i $$-0.765891\pi$$
0.951807 + 0.306699i $$0.0992243\pi$$
$$278$$ −6.00000 3.46410i −0.359856 0.207763i
$$279$$ −3.00000 + 1.73205i −0.179605 + 0.103695i
$$280$$ 0 0
$$281$$ 22.5167i 1.34323i −0.740900 0.671616i $$-0.765601\pi$$
0.740900 0.671616i $$-0.234399\pi$$
$$282$$ 12.0000 0.714590
$$283$$ −4.00000 −0.237775 −0.118888 0.992908i $$-0.537933\pi$$
−0.118888 + 0.992908i $$0.537933\pi$$
$$284$$ 3.46410i 0.205557i
$$285$$ −6.00000 + 10.3923i −0.355409 + 0.615587i
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 4.50000 + 2.59808i 0.265165 + 0.153093i
$$289$$ 4.00000 + 6.92820i 0.235294 + 0.407541i
$$290$$ 4.50000 7.79423i 0.264249 0.457693i
$$291$$ 12.0000 6.92820i 0.703452 0.406138i
$$292$$ 1.73205i 0.101361i
$$293$$ −4.50000 + 2.59808i −0.262893 + 0.151781i −0.625653 0.780101i $$-0.715168\pi$$
0.362761 + 0.931882i $$0.381834\pi$$
$$294$$ 0 0
$$295$$ −6.00000 10.3923i −0.349334 0.605063i
$$296$$ −7.50000 12.9904i −0.435929 0.755051i
$$297$$ 0 0
$$298$$ −16.5000 28.5788i −0.955819 1.65553i
$$299$$ −6.00000 + 20.7846i −0.346989 + 1.20201i
$$300$$ 4.00000 0.230940
$$301$$ 0 0
$$302$$ 15.0000 25.9808i 0.863153 1.49502i
$$303$$ −6.00000 −0.344691
$$304$$ −15.0000 + 8.66025i −0.860309 + 0.496700i
$$305$$ 1.50000 + 0.866025i 0.0858898 + 0.0495885i
$$306$$ 5.19615i 0.297044i
$$307$$ 17.3205i 0.988534i 0.869310 + 0.494267i $$0.164563\pi$$
−0.869310 + 0.494267i $$0.835437\pi$$
$$308$$ 0 0
$$309$$ 10.0000 17.3205i 0.568880 0.985329i
$$310$$ 9.00000 5.19615i 0.511166 0.295122i
$$311$$ −15.0000 25.9808i −0.850572 1.47323i −0.880693 0.473688i $$-0.842923\pi$$
0.0301210 0.999546i $$-0.490411\pi$$
$$312$$ 9.00000 8.66025i 0.509525 0.490290i
$$313$$ 5.00000 8.66025i 0.282617 0.489506i −0.689412 0.724370i $$-0.742131\pi$$
0.972028 + 0.234863i $$0.0754642\pi$$
$$314$$ −19.5000 11.2583i −1.10045 0.635344i
$$315$$ 0 0
$$316$$ 2.00000 + 3.46410i 0.112509 + 0.194871i
$$317$$ 4.50000 + 2.59808i 0.252745 + 0.145922i 0.621021 0.783794i $$-0.286718\pi$$
−0.368275 + 0.929717i $$0.620052\pi$$
$$318$$ −9.00000 5.19615i −0.504695 0.291386i
$$319$$ 0 0
$$320$$ 1.50000 + 0.866025i 0.0838525 + 0.0484123i
$$321$$ 6.00000 + 10.3923i 0.334887 + 0.580042i
$$322$$ 0 0
$$323$$ −9.00000 5.19615i −0.500773 0.289122i
$$324$$ −5.50000 + 9.52628i −0.305556 + 0.529238i
$$325$$ 2.00000 6.92820i 0.110940 0.384308i
$$326$$ 18.0000 + 31.1769i 0.996928 + 1.72673i
$$327$$ 24.0000 13.8564i 1.32720 0.766261i
$$328$$ −4.50000 + 7.79423i −0.248471 + 0.430364i
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 27.7128i 1.52323i −0.648027 0.761617i $$-0.724406\pi$$
0.648027 0.761617i $$-0.275594\pi$$
$$332$$ −12.0000 6.92820i −0.658586 0.380235i
$$333$$ −7.50000 + 4.33013i −0.410997 + 0.237289i
$$334$$ 24.0000 1.31322
$$335$$ −3.00000 + 5.19615i −0.163908 + 0.283896i
$$336$$ 0 0
$$337$$ −23.0000 −1.25289 −0.626445 0.779466i $$-0.715491\pi$$
−0.626445 + 0.779466i $$0.715491\pi$$
$$338$$ 10.5000 + 19.9186i 0.571125 + 1.08343i
$$339$$ −15.0000 25.9808i −0.814688 1.41108i
$$340$$ 5.19615i 0.281801i
$$341$$ 0 0
$$342$$ 3.00000 + 5.19615i 0.162221 + 0.280976i
$$343$$ 0 0
$$344$$ 12.0000 6.92820i 0.646997 0.373544i
$$345$$ 20.7846i 1.11901i
$$346$$ −9.00000 + 5.19615i −0.483843 + 0.279347i
$$347$$ 15.0000 25.9808i 0.805242 1.39472i −0.110885 0.993833i $$-0.535369\pi$$
0.916127 0.400887i $$-0.131298\pi$$
$$348$$ −3.00000 5.19615i −0.160817 0.278543i
$$349$$ −12.0000 6.92820i −0.642345 0.370858i 0.143172 0.989698i $$-0.454270\pi$$
−0.785517 + 0.618840i $$0.787603\pi$$
$$350$$ 0 0
$$351$$ 10.0000 + 10.3923i 0.533761 + 0.554700i
$$352$$ 0 0
$$353$$ 32.9090i 1.75157i 0.482704 + 0.875784i $$0.339655\pi$$
−0.482704 + 0.875784i $$0.660345\pi$$
$$354$$ −24.0000 −1.27559
$$355$$ −6.00000 −0.318447
$$356$$ 6.92820i 0.367194i
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 6.00000 + 3.46410i 0.316668 + 0.182828i 0.649906 0.760014i $$-0.274808\pi$$
−0.333238 + 0.942843i $$0.608141\pi$$
$$360$$ 1.50000 2.59808i 0.0790569 0.136931i
$$361$$ 7.00000 0.368421
$$362$$ −16.5000 + 9.52628i −0.867221 + 0.500690i
$$363$$ −22.0000 −1.15470
$$364$$ 0 0
$$365$$ 3.00000 0.157027
$$366$$ 3.00000 1.73205i 0.156813 0.0905357i
$$367$$ 22.0000 1.14839 0.574195 0.818718i $$-0.305315\pi$$
0.574195 + 0.818718i $$0.305315\pi$$
$$368$$ −15.0000 + 25.9808i −0.781929 + 1.35434i
$$369$$ 4.50000 + 2.59808i 0.234261 + 0.135250i
$$370$$ 22.5000 12.9904i 1.16972 0.675338i
$$371$$ 0 0
$$372$$ 6.92820i 0.359211i
$$373$$ 19.0000 0.983783 0.491891 0.870657i $$-0.336306\pi$$
0.491891 + 0.870657i $$0.336306\pi$$
$$374$$ 0 0
$$375$$ 24.2487i 1.25220i
$$376$$ 3.00000 5.19615i 0.154713 0.267971i
$$377$$ −10.5000 + 2.59808i −0.540778 + 0.133808i
$$378$$ 0 0
$$379$$ −21.0000 12.1244i −1.07870 0.622786i −0.148153 0.988964i $$-0.547333\pi$$
−0.930545 + 0.366178i $$0.880666\pi$$
$$380$$ −3.00000 5.19615i −0.153897 0.266557i
$$381$$ −2.00000 + 3.46410i −0.102463 + 0.177471i
$$382$$ 27.0000 15.5885i 1.38144 0.797575i
$$383$$ 20.7846i 1.06204i 0.847358 + 0.531022i $$0.178192\pi$$
−0.847358 + 0.531022i $$0.821808\pi$$
$$384$$ 21.0000 12.1244i 1.07165 0.618718i
$$385$$ 0 0
$$386$$ 4.50000 + 7.79423i 0.229044 + 0.396716i
$$387$$ −4.00000 6.92820i −0.203331 0.352180i
$$388$$ 6.92820i 0.351726i
$$389$$ 4.50000 + 7.79423i 0.228159 + 0.395183i 0.957263 0.289220i $$-0.0933960\pi$$
−0.729103 + 0.684403i $$0.760063\pi$$
$$390$$ 15.0000 + 15.5885i 0.759555 + 0.789352i
$$391$$ −18.0000 −0.910299
$$392$$ 0 0
$$393$$ −18.0000 + 31.1769i −0.907980 + 1.57267i
$$394$$ 24.0000 1.20910
$$395$$ 6.00000 3.46410i 0.301893 0.174298i
$$396$$ 0 0
$$397$$ 13.8564i 0.695433i 0.937600 + 0.347717i $$0.113043\pi$$
−0.937600 + 0.347717i $$0.886957\pi$$
$$398$$ 3.46410i 0.173640i
$$399$$ 0 0
$$400$$ 5.00000 8.66025i 0.250000 0.433013i
$$401$$ 1.50000 0.866025i 0.0749064 0.0432472i −0.462079 0.886839i $$-0.652896\pi$$
0.536985 + 0.843592i $$0.319563\pi$$
$$402$$ 6.00000 + 10.3923i 0.299253 + 0.518321i
$$403$$ −12.0000 3.46410i −0.597763 0.172559i
$$404$$ 1.50000 2.59808i 0.0746278 0.129259i
$$405$$ 16.5000 + 9.52628i 0.819892 + 0.473365i
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 9.00000 + 5.19615i 0.445566 + 0.257248i
$$409$$ 13.5000 + 7.79423i 0.667532 + 0.385400i 0.795141 0.606425i $$-0.207397\pi$$
−0.127609 + 0.991825i $$0.540730\pi$$
$$410$$ −13.5000 7.79423i −0.666717 0.384930i
$$411$$ −27.0000 15.5885i −1.33181 0.768922i
$$412$$ 5.00000 + 8.66025i 0.246332 + 0.426660i
$$413$$ 0 0
$$414$$ 9.00000 + 5.19615i 0.442326 + 0.255377i
$$415$$ −12.0000 + 20.7846i −0.589057 + 1.02028i
$$416$$ 4.50000 + 18.1865i 0.220631 + 0.891668i
$$417$$ 4.00000 + 6.92820i 0.195881 + 0.339276i
$$418$$ 0 0
$$419$$ 9.00000 15.5885i 0.439679 0.761546i −0.557986 0.829851i $$-0.688426\pi$$
0.997665 + 0.0683046i $$0.0217590\pi$$
$$420$$ 0 0
$$421$$ 15.5885i 0.759735i 0.925041 + 0.379867i $$0.124030\pi$$
−0.925041 + 0.379867i $$0.875970\pi$$
$$422$$ 17.3205i 0.843149i
$$423$$ −3.00000 1.73205i −0.145865 0.0842152i
$$424$$ −4.50000 + 2.59808i −0.218539 + 0.126174i
$$425$$ 6.00000 0.291043
$$426$$ −6.00000 + 10.3923i −0.290701 + 0.503509i
$$427$$ 0 0
$$428$$ −6.00000 −0.290021
$$429$$ 0 0
$$430$$ 12.0000 + 20.7846i 0.578691 + 1.00232i
$$431$$ 6.92820i 0.333720i 0.985981 + 0.166860i $$0.0533628\pi$$
−0.985981 + 0.166860i $$0.946637\pi$$
$$432$$ 10.0000 + 17.3205i 0.481125 + 0.833333i
$$433$$ −8.50000 14.7224i −0.408484 0.707515i 0.586236 0.810140i $$-0.300609\pi$$
−0.994720 + 0.102625i $$0.967276\pi$$
$$434$$ 0 0
$$435$$ −9.00000 + 5.19615i −0.431517 + 0.249136i
$$436$$ 13.8564i 0.663602i
$$437$$ −18.0000 + 10.3923i −0.861057 + 0.497131i
$$438$$ 3.00000 5.19615i 0.143346 0.248282i
$$439$$ −14.0000 24.2487i −0.668184 1.15733i −0.978412 0.206666i $$-0.933739\pi$$
0.310228 0.950662i $$-0.399595\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ −13.5000 + 12.9904i −0.642130 + 0.617889i
$$443$$ 6.00000 10.3923i 0.285069 0.493753i −0.687557 0.726130i $$-0.741317\pi$$
0.972626 + 0.232377i $$0.0746503\pi$$
$$444$$ 17.3205i 0.821995i
$$445$$ 12.0000 0.568855
$$446$$ 18.0000 0.852325
$$447$$ 38.1051i 1.80231i
$$448$$ 0 0
$$449$$ −6.00000 + 3.46410i −0.283158 + 0.163481i −0.634852 0.772634i $$-0.718939\pi$$
0.351694 + 0.936115i $$0.385606\pi$$
$$450$$ −3.00000 1.73205i −0.141421 0.0816497i
$$451$$ 0 0
$$452$$ 15.0000 0.705541
$$453$$ −30.0000 + 17.3205i −1.40952 + 0.813788i
$$454$$ 42.0000 1.97116
$$455$$ 0 0
$$456$$ 12.0000 0.561951
$$457$$ −1.50000 + 0.866025i −0.0701670 + 0.0405110i −0.534673 0.845059i $$-0.679565\pi$$
0.464506 + 0.885570i $$0.346232\pi$$
$$458$$ 0 0
$$459$$ −6.00000 + 10.3923i −0.280056 + 0.485071i
$$460$$ −9.00000 5.19615i −0.419627 0.242272i
$$461$$ −19.5000 + 11.2583i −0.908206 + 0.524353i −0.879853 0.475245i $$-0.842359\pi$$
−0.0283522 + 0.999598i $$0.509026\pi$$
$$462$$ 0 0
$$463$$ 13.8564i 0.643962i 0.946746 + 0.321981i $$0.104349\pi$$
−0.946746 + 0.321981i $$0.895651\pi$$
$$464$$ −15.0000 −0.696358
$$465$$ −12.0000 −0.556487
$$466$$ 10.3923i 0.481414i
$$467$$ 6.00000 10.3923i 0.277647 0.480899i −0.693153 0.720791i $$-0.743779\pi$$
0.970799 + 0.239892i $$0.0771121\pi$$
$$468$$ 3.50000 0.866025i 0.161788 0.0400320i
$$469$$ 0 0
$$470$$ 9.00000 + 5.19615i 0.415139 + 0.239681i
$$471$$ 13.0000 + 22.5167i 0.599008 + 1.03751i
$$472$$ −6.00000 + 10.3923i −0.276172 + 0.478345i
$$473$$ 0 0
$$474$$ 13.8564i 0.636446i
$$475$$ 6.00000 3.46410i 0.275299 0.158944i
$$476$$ 0 0
$$477$$ 1.50000 + 2.59808i 0.0686803 + 0.118958i
$$478$$ −18.0000 31.1769i −0.823301 1.42600i
$$479$$ 24.2487i 1.10795i 0.832533 + 0.553976i $$0.186890\pi$$
−0.832533 + 0.553976i $$0.813110\pi$$
$$480$$ 9.00000 + 15.5885i 0.410792 + 0.711512i
$$481$$ −30.0000 8.66025i −1.36788 0.394874i
$$482$$ −3.00000 −0.136646
$$483$$ 0 0
$$484$$ 5.50000 9.52628i 0.250000 0.433013i
$$485$$ 12.0000 0.544892
$$486$$ 15.0000 8.66025i 0.680414 0.392837i
$$487$$ 6.00000 + 3.46410i 0.271886 + 0.156973i 0.629744 0.776802i $$-0.283160\pi$$
−0.357858 + 0.933776i $$0.616493\pi$$
$$488$$ 1.73205i 0.0784063i
$$489$$ 41.5692i 1.87983i
$$490$$ 0 0
$$491$$ −6.00000 + 10.3923i −0.270776 + 0.468998i −0.969061 0.246822i $$-0.920614\pi$$
0.698285 + 0.715820i $$0.253947\pi$$
$$492$$ −9.00000 + 5.19615i −0.405751 + 0.234261i
$$493$$ −4.50000 7.79423i −0.202670 0.351034i
$$494$$ −6.00000 + 20.7846i −0.269953 + 0.935144i
$$495$$ 0 0
$$496$$ −15.0000 8.66025i −0.673520 0.388857i
$$497$$ 0 0
$$498$$ 24.0000 + 41.5692i 1.07547 + 1.86276i
$$499$$ −27.0000 15.5885i −1.20869 0.697835i −0.246214 0.969216i $$-0.579187\pi$$
−0.962472 + 0.271380i $$0.912520\pi$$
$$500$$ 10.5000 + 6.06218i 0.469574 + 0.271109i
$$501$$ −24.0000 13.8564i −1.07224 0.619059i
$$502$$ −27.0000 15.5885i −1.20507 0.695747i
$$503$$ 18.0000 + 31.1769i 0.802580 + 1.39011i 0.917912 + 0.396783i $$0.129873\pi$$
−0.115332 + 0.993327i $$0.536793\pi$$
$$504$$ 0 0
$$505$$ −4.50000 2.59808i −0.200247 0.115613i
$$506$$ 0 0
$$507$$ 1.00000 25.9808i 0.0444116 1.15385i
$$508$$ −1.00000 1.73205i −0.0443678 0.0768473i
$$509$$ 16.5000 9.52628i 0.731350 0.422245i −0.0875661 0.996159i $$-0.527909\pi$$
0.818916 + 0.573914i $$0.194576\pi$$
$$510$$ −9.00000 + 15.5885i −0.398527 + 0.690268i
$$511$$ 0 0
$$512$$ 8.66025i 0.382733i
$$513$$ 13.8564i 0.611775i
$$514$$ 4.50000 + 2.59808i 0.198486 + 0.114596i
$$515$$ 15.0000 8.66025i 0.660979 0.381616i
$$516$$ 16.0000 0.704361
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 12.0000 0.526742
$$520$$ 10.5000 2.59808i 0.460455 0.113933i
$$521$$ 4.50000 + 7.79423i 0.197149 + 0.341471i 0.947603 0.319451i $$-0.103499\pi$$
−0.750454 + 0.660922i $$0.770165\pi$$
$$522$$ 5.19615i 0.227429i
$$523$$ −8.00000 13.8564i −0.349816 0.605898i 0.636401 0.771358i $$-0.280422\pi$$
−0.986216 + 0.165460i $$0.947089\pi$$
$$524$$ −9.00000 15.5885i −0.393167 0.680985i
$$525$$ 0 0
$$526$$ 18.0000 10.3923i 0.784837 0.453126i
$$527$$ 10.3923i 0.452696i
$$528$$ 0 0
$$529$$ −6.50000 + 11.2583i −0.282609 + 0.489493i
$$530$$ −4.50000 7.79423i −0.195468 0.338560i
$$531$$ 6.00000 + 3.46410i 0.260378 + 0.150329i
$$532$$ 0 0
$$533$$ 4.50000 + 18.1865i 0.194917 + 0.787746i
$$534$$ 12.0000 20.7846i 0.519291 0.899438i
$$535$$ 10.3923i 0.449299i
$$536$$ 6.00000 0.259161
$$537$$ 0 0
$$538$$ 10.3923i 0.448044i
$$539$$ 0 0
$$540$$ −6.00000 + 3.46410i −0.258199 + 0.149071i
$$541$$ −25.5000 14.7224i −1.09633 0.632967i −0.161076 0.986942i $$-0.551496\pi$$
−0.935255 + 0.353975i $$0.884830\pi$$
$$542$$ 18.0000 31.1769i 0.773166 1.33916i
$$543$$ 22.0000 0.944110
$$544$$ −13.5000 + 7.79423i −0.578808 + 0.334175i
$$545$$ 24.0000 1.02805
$$546$$ 0 0
$$547$$ −22.0000 −0.940652 −0.470326 0.882493i $$-0.655864\pi$$
−0.470326 + 0.882493i $$0.655864\pi$$
$$548$$ 13.5000 7.79423i 0.576691 0.332953i
$$549$$ −1.00000 −0.0426790
$$550$$ 0 0
$$551$$ −9.00000 5.19615i −0.383413 0.221364i
$$552$$ 18.0000 10.3923i 0.766131 0.442326i
$$553$$ 0 0
$$554$$ 12.1244i 0.515115i
$$555$$ −30.0000 −1.27343
$$556$$ −4.00000 −0.169638
$$557$$ 15.5885i 0.660504i 0.943893 + 0.330252i $$0.107134\pi$$
−0.943893 + 0.330252i $$0.892866\pi$$
$$558$$ −3.00000 + 5.19615i −0.127000 + 0.219971i
$$559$$ 8.00000 27.7128i 0.338364 1.17213i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −19.5000 33.7750i −0.822558 1.42471i
$$563$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$564$$ 6.00000 3.46410i 0.252646 0.145865i
$$565$$ 25.9808i 1.09302i
$$566$$ −6.00000 + 3.46410i −0.252199 + 0.145607i
$$567$$ 0 0
$$568$$ 3.00000 + 5.19615i 0.125877 + 0.218026i
$$569$$ 21.0000 + 36.3731i 0.880366 + 1.52484i 0.850935 + 0.525271i $$0.176036\pi$$
0.0294311 + 0.999567i $$0.490630\pi$$
$$570$$ 20.7846i 0.870572i
$$571$$ −20.0000 34.6410i −0.836974 1.44968i −0.892413 0.451219i $$-0.850989\pi$$
0.0554391 0.998462i $$-0.482344\pi$$
$$572$$ 0 0
$$573$$ −36.0000 −1.50392
$$574$$ 0 0
$$575$$ 6.00000 10.3923i 0.250217 0.433389i
$$576$$ −1.00000 −0.0416667
$$577$$ 16.5000 9.52628i 0.686904 0.396584i −0.115547 0.993302i $$-0.536862\pi$$
0.802451 + 0.596718i $$0.203529\pi$$
$$578$$ 12.0000 + 6.92820i 0.499134 + 0.288175i
$$579$$ 10.3923i 0.431889i
$$580$$ 5.19615i 0.215758i
$$581$$ 0 0
$$582$$ 12.0000 20.7846i 0.497416 0.861550i
$$583$$ 0 0
$$584$$ −1.50000 2.59808i −0.0620704 0.107509i
$$585$$ −1.50000 6.06218i −0.0620174 0.250640i
$$586$$ −4.50000 + 7.79423i −0.185893 + 0.321977i
$$587$$ 18.0000 + 10.3923i 0.742940 + 0.428936i 0.823137 0.567843i $$-0.192222\pi$$
−0.0801976 + 0.996779i $$0.525555\pi$$
$$588$$ 0 0
$$589$$ −6.00000 10.3923i −0.247226 0.428207i
$$590$$ −18.0000 10.3923i −0.741048 0.427844i
$$591$$ −24.0000 13.8564i −0.987228 0.569976i
$$592$$ −37.5000 21.6506i −1.54124 0.889836i
$$593$$ −22.5000 12.9904i −0.923964 0.533451i −0.0390666 0.999237i $$-0.512438\pi$$
−0.884898 + 0.465786i $$0.845772\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −16.5000 9.52628i −0.675866 0.390212i
$$597$$ 2.00000 3.46410i 0.0818546 0.141776i
$$598$$ 9.00000 + 36.3731i 0.368037 + 1.48741i
$$599$$ −15.0000 25.9808i −0.612883 1.06155i −0.990752 0.135686i $$-0.956676\pi$$
0.377869 0.925859i $$-0.376657\pi$$
$$600$$ −6.00000 + 3.46410i −0.244949 + 0.141421i
$$601$$ 12.5000 21.6506i 0.509886 0.883148i −0.490049 0.871695i $$-0.663021\pi$$
0.999934 0.0114528i $$-0.00364562\pi$$
$$602$$ 0 0
$$603$$ 3.46410i 0.141069i
$$604$$ 17.3205i 0.704761i
$$605$$ −16.5000 9.52628i −0.670820 0.387298i
$$606$$ −9.00000 + 5.19615i −0.365600 + 0.211079i
$$607$$ 34.0000 1.38002 0.690009 0.723801i $$-0.257607\pi$$
0.690009 + 0.723801i $$0.257607\pi$$
$$608$$ −9.00000 + 15.5885i −0.364998 + 0.632195i
$$609$$ 0 0
$$610$$ 3.00000 0.121466
$$611$$ −3.00000 12.1244i −0.121367 0.490499i
$$612$$ 1.50000 + 2.59808i 0.0606339 + 0.105021i
$$613$$ 12.1244i 0.489698i 0.969561 + 0.244849i $$0.0787384\pi$$
−0.969561 + 0.244849i $$0.921262\pi$$
$$614$$ 15.0000 + 25.9808i 0.605351 + 1.04850i
$$615$$ 9.00000 + 15.5885i 0.362915 + 0.628587i
$$616$$ 0 0
$$617$$ −19.5000 + 11.2583i −0.785040 + 0.453243i −0.838214 0.545342i $$-0.816400\pi$$
0.0531732 + 0.998585i $$0.483066\pi$$
$$618$$ 34.6410i 1.39347i
$$619$$ 18.0000 10.3923i 0.723481 0.417702i −0.0925515 0.995708i $$-0.529502\pi$$
0.816033 + 0.578006i $$0.196169\pi$$
$$620$$ 3.00000 5.19615i 0.120483 0.208683i
$$621$$ 12.0000 + 20.7846i 0.481543 + 0.834058i
$$622$$ −45.0000 25.9808i −1.80434 1.04173i
$$623$$ 0 0
$$624$$ 10.0000 34.6410i 0.400320 1.38675i
$$625$$ 5.50000 9.52628i 0.220000 0.381051i
$$626$$ 17.3205i 0.692267i
$$627$$ 0 0
$$628$$ −13.0000 −0.518756
$$629$$ 25.9808i 1.03592i
$$630$$ 0 0
$$631$$ −42.0000 + 24.2487i −1.67199 + 0.965326i −0.705473 + 0.708737i $$0.749265\pi$$
−0.966521 + 0.256589i $$0.917401\pi$$
$$632$$ −6.00000 3.46410i −0.238667 0.137795i
$$633$$ 10.0000 17.3205i 0.397464 0.688428i
$$634$$ 9.00000 0.357436
$$635$$ −3.00000 + 1.73205i −0.119051 + 0.0687343i
$$636$$ −6.00000 −0.237915
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 3.00000 1.73205i 0.118678 0.0685189i
$$640$$ 21.0000 0.830098
$$641$$ −16.5000 + 28.5788i −0.651711 + 1.12880i 0.330997 + 0.943632i $$0.392615\pi$$
−0.982708 + 0.185164i $$0.940718\pi$$
$$642$$ 18.0000 + 10.3923i 0.710403 + 0.410152i
$$643$$ −12.0000 + 6.92820i −0.473234 + 0.273222i −0.717592 0.696463i $$-0.754756\pi$$
0.244359 + 0.969685i $$0.421423\pi$$
$$644$$ 0 0
$$645$$ 27.7128i 1.09119i
$$646$$ −18.0000 −0.708201
$$647$$ −18.0000 −0.707653 −0.353827 0.935311i $$-0.615120\pi$$
−0.353827 + 0.935311i $$0.615120\pi$$
$$648$$ 19.0526i 0.748455i
$$649$$ 0 0
$$650$$ −3.00000 12.1244i −0.117670 0.475556i
$$651$$ 0 0
$$652$$ 18.0000 + 10.3923i 0.704934 + 0.406994i
$$653$$ 15.0000 + 25.9808i 0.586995 + 1.01671i 0.994623 + 0.103558i $$0.0330227\pi$$
−0.407628 + 0.913148i $$0.633644\pi$$
$$654$$ 24.0000 41.5692i 0.938474 1.62549i
$$655$$ −27.0000 + 15.5885i −1.05498 + 0.609091i
$$656$$ 25.9808i 1.01438i
$$657$$ −1.50000 + 0.866025i −0.0585206 + 0.0337869i
$$658$$ 0 0
$$659$$ 6.00000 + 10.3923i 0.233727 + 0.404827i 0.958902 0.283738i $$-0.0915745\pi$$
−0.725175 + 0.688565i $$0.758241\pi$$
$$660$$ 0 0
$$661$$ 46.7654i 1.81896i −0.415745 0.909481i $$-0.636479\pi$$
0.415745 0.909481i $$-0.363521\pi$$
$$662$$ −24.0000 41.5692i −0.932786 1.61563i
$$663$$ 21.0000 5.19615i 0.815572 0.201802i
$$664$$ 24.0000 0.931381
$$665$$ 0 0
$$666$$ −7.50000 + 12.9904i −0.290619 + 0.503367i
$$667$$ −18.0000 −0.696963
$$668$$ 12.0000 6.92820i 0.464294 0.268060i
$$669$$ −18.0000 10.3923i −0.695920 0.401790i
$$670$$ 10.3923i 0.401490i
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 9.50000 16.4545i 0.366198 0.634274i −0.622770 0.782405i $$-0.713993\pi$$
0.988968 + 0.148132i $$0.0473259\pi$$
$$674$$ −34.5000 + 19.9186i −1.32889 + 0.767235i
$$675$$ −4.00000 6.92820i −0.153960 0.266667i
$$676$$ 11.0000 + 6.92820i 0.423077 + 0.266469i
$$677$$ −3.00000 + 5.19615i −0.115299 + 0.199704i −0.917899 0.396813i $$-0.870116\pi$$
0.802600 + 0.596518i $$0.203449\pi$$
$$678$$ −45.0000 25.9808i −1.72821 0.997785i
$$679$$ 0 0
$$680$$ 4.50000 + 7.79423i 0.172567 + 0.298895i
$$681$$ −42.0000 24.2487i −1.60944 0.929213i
$$682$$ 0 0
$$683$$ −21.0000 12.1244i −0.803543 0.463926i 0.0411658 0.999152i $$-0.486893\pi$$
−0.844708 + 0.535227i $$0.820226\pi$$
$$684$$ 3.00000 + 1.73205i 0.114708 + 0.0662266i
$$685$$ −13.5000 23.3827i −0.515808 0.893407i
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 20.0000 34.6410i 0.762493 1.32068i
$$689$$ −3.00000 + 10.3923i −0.114291 + 0.395915i
$$690$$ 18.0000 + 31.1769i 0.685248 + 1.18688i
$$691$$ 12.0000 6.92820i 0.456502 0.263561i −0.254071 0.967186i $$-0.581770\pi$$
0.710572 + 0.703624i $$0.248436\pi$$
$$692$$ −3.00000 + 5.19615i −0.114043 + 0.197528i
$$693$$ 0 0
$$694$$ 51.9615i 1.97243i
$$695$$ 6.92820i 0.262802i
$$696$$ 9.00000 + 5.19615i 0.341144 + 0.196960i
$$697$$ −13.5000 + 7.79423i −0.511349 + 0.295227i
$$698$$ −24.0000 −0.908413
$$699$$ 6.00000 10.3923i 0.226941 0.393073i
$$700$$ 0 0
$$701$$ 18.0000 0.679851 0.339925 0.940452i $$-0.389598\pi$$
0.339925 + 0.940452i $$0.389598\pi$$
$$702$$ 24.0000 + 6.92820i 0.905822 + 0.261488i
$$703$$ −15.0000 25.9808i −0.565736 0.979883i
$$704$$ 0 0
$$705$$ −6.00000 10.3923i −0.225973 0.391397i
$$706$$ 28.5000 + 49.3634i 1.07261 + 1.85782i
$$707$$ 0 0
$$708$$ −12.0000 + 6.92820i −0.450988 + 0.260378i
$$709$$ 5.19615i 0.195146i −0.995228 0.0975728i $$-0.968892\pi$$
0.995228 0.0975728i $$-0.0311079\pi$$
$$710$$ −9.00000 + 5.19615i −0.337764 + 0.195008i
$$711$$ −2.00000 + 3.46410i −0.0750059 + 0.129914i
$$712$$ −6.00000 10.3923i −0.224860 0.389468i
$$713$$ −18.0000 10.3923i −0.674105 0.389195i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 41.5692i 1.55243i
$$718$$ 12.0000 0.447836
$$719$$ 48.0000 1.79010 0.895049 0.445968i $$-0.147140\pi$$
0.895049 + 0.445968i $$0.147140\pi$$
$$720$$ 8.66025i 0.322749i
$$721$$ 0 0
$$722$$ 10.5000 6.06218i 0.390770 0.225611i
$$723$$ 3.00000 + 1.73205i 0.111571 + 0.0644157i
$$724$$ −5.50000 + 9.52628i −0.204406 + 0.354041i
$$725$$ 6.00000 0.222834
$$726$$ −33.0000 + 19.0526i −1.22474 + 0.707107i
$$727$$ 32.0000 1.18681 0.593407 0.804902i $$-0.297782\pi$$
0.593407 + 0.804902i $$0.297782\pi$$
$$728$$ 0 0
$$729$$ 13.0000 0.481481
$$730$$ 4.50000 2.59808i 0.166552 0.0961591i
$$731$$ 24.0000 0.887672
$$732$$ 1.00000 1.73205i 0.0369611 0.0640184i
$$733$$ 10.5000 + 6.06218i 0.387826 + 0.223912i 0.681218 0.732081i $$-0.261451\pi$$
−0.293392 + 0.955992i $$0.594784\pi$$
$$734$$ 33.0000 19.0526i 1.21805 0.703243i
$$735$$ 0 0
$$736$$ 31.1769i 1.14920i
$$737$$ 0 0
$$738$$ 9.00000 0.331295
$$739$$ 20.7846i 0.764574i 0.924044 + 0.382287i $$0.124863\pi$$
−0.924044 + 0.382287i $$0.875137\pi$$
$$740$$ 7.50000 12.9904i 0.275705 0.477536i
$$741$$ 18.0000 17.3205i 0.661247 0.636285i
$$742$$ 0 0
$$743$$ −30.0000 17.3205i −1.10059 0.635428i −0.164216 0.986424i $$-0.552510\pi$$
−0.936377 + 0.350997i $$0.885843\pi$$
$$744$$ 6.00000 + 10.3923i 0.219971 + 0.381000i
$$745$$ −16.5000 + 28.5788i −0.604513 + 1.04705i
$$746$$ 28.5000 16.4545i 1.04346 0.602441i
$$747$$ 13.8564i 0.506979i
$$748$$ 0 0
$$749$$ 0 0
$$750$$ −21.0000 36.3731i −0.766812 1.32816i
$$751$$ 8.00000 + 13.8564i 0.291924 + 0.505627i 0.974265 0.225407i $$-0.0723712\pi$$
−0.682341 + 0.731034i $$0.739038\pi$$
$$752$$ 17.3205i 0.631614i
$$753$$ 18.0000 + 31.1769i 0.655956 + 1.13615i
$$754$$ −13.5000 + 12.9904i −0.491641 + 0.473082i
$$755$$ −30.0000 −1.09181
$$756$$ 0 0
$$757$$ 13.0000 22.5167i 0.472493 0.818382i −0.527011 0.849858i $$-0.676688\pi$$
0.999505 + 0.0314762i $$0.0100208\pi$$
$$758$$ −42.0000 −1.52551
$$759$$ 0 0
$$760$$ 9.00000 + 5.19615i 0.326464 + 0.188484i
$$761$$ 34.6410i 1.25574i −0.778320 0.627868i $$-0.783928\pi$$
0.778320 0.627868i $$-0.216072\pi$$
$$762$$ 6.92820i 0.250982i
$$763$$ 0 0
$$764$$ 9.00000 15.5885i 0.325609 0.563971i
$$765$$ 4.50000 2.59808i 0.162698 0.0939336i
$$766$$ 18.0000 + 31.1769i 0.650366 + 1.12647i
$$767$$ 6.00000 + 24.2487i 0.216647 + 0.875570i
$$768$$ 19.0000 32.9090i 0.685603 1.18750i
$$769$$ −6.00000 3.46410i −0.216366 0.124919i 0.387901 0.921701i $$-0.373200\pi$$
−0.604266 + 0.796782i $$0.706534\pi$$
$$770$$ 0 0
$$771$$ −3.00000 5.19615i −0.108042 0.187135i
$$772$$ 4.50000 + 2.59808i 0.161959 + 0.0935068i
$$773$$ −30.0000 17.3205i −1.07903 0.622975i −0.148392 0.988929i $$-0.547410\pi$$
−0.930633 + 0.365953i $$0.880743\pi$$
$$774$$ −12.0000 6.92820i −0.431331 0.249029i
$$775$$ 6.00000 + 3.46410i 0.215526 + 0.124434i
$$776$$