# Properties

 Label 930.2.i.e.811.1 Level $930$ Weight $2$ Character 930.811 Analytic conductor $7.426$ 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] = [930,2,Mod(211,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("930.211");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$930 = 2 \cdot 3 \cdot 5 \cdot 31$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 930.i (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

comment: select newform

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

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

 Self dual: no Analytic conductor: $$7.42608738798$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 811.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 930.811 Dual form 930.2.i.e.211.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(3.00000 + 5.19615i) q^{13} +1.00000 q^{15} +1.00000 q^{16} +(0.500000 - 0.866025i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-2.00000 + 3.46410i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(0.500000 + 0.866025i) q^{22} +7.00000 q^{23} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(3.00000 + 5.19615i) q^{26} +1.00000 q^{27} +6.00000 q^{29} +1.00000 q^{30} +(2.00000 - 5.19615i) q^{31} +1.00000 q^{32} -1.00000 q^{33} +(0.500000 - 0.866025i) q^{34} +(-0.500000 - 0.866025i) q^{36} +(-3.50000 + 6.06218i) q^{37} +(-2.00000 + 3.46410i) q^{38} -6.00000 q^{39} +(-0.500000 - 0.866025i) q^{40} +(1.00000 + 1.73205i) q^{41} +(3.50000 - 6.06218i) q^{43} +(0.500000 + 0.866025i) q^{44} +(-0.500000 + 0.866025i) q^{45} +7.00000 q^{46} +3.00000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(3.50000 + 6.06218i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(0.500000 + 0.866025i) q^{51} +(3.00000 + 5.19615i) q^{52} +(2.00000 + 3.46410i) q^{53} +1.00000 q^{54} +(0.500000 - 0.866025i) q^{55} +(-2.00000 - 3.46410i) q^{57} +6.00000 q^{58} +(-6.00000 + 10.3923i) q^{59} +1.00000 q^{60} -14.0000 q^{61} +(2.00000 - 5.19615i) q^{62} +1.00000 q^{64} +(3.00000 - 5.19615i) q^{65} -1.00000 q^{66} +(-2.50000 - 4.33013i) q^{67} +(0.500000 - 0.866025i) q^{68} +(-3.50000 + 6.06218i) q^{69} +(-3.00000 - 5.19615i) q^{71} +(-0.500000 - 0.866025i) q^{72} +(-1.00000 - 1.73205i) q^{73} +(-3.50000 + 6.06218i) q^{74} +(-0.500000 - 0.866025i) q^{75} +(-2.00000 + 3.46410i) q^{76} -6.00000 q^{78} +(-1.50000 + 2.59808i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.00000 + 1.73205i) q^{82} +(-8.00000 - 13.8564i) q^{83} -1.00000 q^{85} +(3.50000 - 6.06218i) q^{86} +(-3.00000 + 5.19615i) q^{87} +(0.500000 + 0.866025i) q^{88} +4.00000 q^{89} +(-0.500000 + 0.866025i) q^{90} +7.00000 q^{92} +(3.50000 + 4.33013i) q^{93} +3.00000 q^{94} +4.00000 q^{95} +(-0.500000 + 0.866025i) q^{96} -6.00000 q^{97} +(3.50000 + 6.06218i) q^{98} +(0.500000 - 0.866025i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 2 q^{2} - q^{3} + 2 q^{4} - q^{5} - q^{6} + 2 q^{8} - q^{9}+O(q^{10})$$ 2 * q + 2 * q^2 - q^3 + 2 * q^4 - q^5 - q^6 + 2 * q^8 - q^9 $$2 q + 2 q^{2} - q^{3} + 2 q^{4} - q^{5} - q^{6} + 2 q^{8} - q^{9} - q^{10} + q^{11} - q^{12} + 6 q^{13} + 2 q^{15} + 2 q^{16} + q^{17} - q^{18} - 4 q^{19} - q^{20} + q^{22} + 14 q^{23} - q^{24} - q^{25} + 6 q^{26} + 2 q^{27} + 12 q^{29} + 2 q^{30} + 4 q^{31} + 2 q^{32} - 2 q^{33} + q^{34} - q^{36} - 7 q^{37} - 4 q^{38} - 12 q^{39} - q^{40} + 2 q^{41} + 7 q^{43} + q^{44} - q^{45} + 14 q^{46} + 6 q^{47} - q^{48} + 7 q^{49} - q^{50} + q^{51} + 6 q^{52} + 4 q^{53} + 2 q^{54} + q^{55} - 4 q^{57} + 12 q^{58} - 12 q^{59} + 2 q^{60} - 28 q^{61} + 4 q^{62} + 2 q^{64} + 6 q^{65} - 2 q^{66} - 5 q^{67} + q^{68} - 7 q^{69} - 6 q^{71} - q^{72} - 2 q^{73} - 7 q^{74} - q^{75} - 4 q^{76} - 12 q^{78} - 3 q^{79} - q^{80} - q^{81} + 2 q^{82} - 16 q^{83} - 2 q^{85} + 7 q^{86} - 6 q^{87} + q^{88} + 8 q^{89} - q^{90} + 14 q^{92} + 7 q^{93} + 6 q^{94} + 8 q^{95} - q^{96} - 12 q^{97} + 7 q^{98} + q^{99}+O(q^{100})$$ 2 * q + 2 * q^2 - q^3 + 2 * q^4 - q^5 - q^6 + 2 * q^8 - q^9 - q^10 + q^11 - q^12 + 6 * q^13 + 2 * q^15 + 2 * q^16 + q^17 - q^18 - 4 * q^19 - q^20 + q^22 + 14 * q^23 - q^24 - q^25 + 6 * q^26 + 2 * q^27 + 12 * q^29 + 2 * q^30 + 4 * q^31 + 2 * q^32 - 2 * q^33 + q^34 - q^36 - 7 * q^37 - 4 * q^38 - 12 * q^39 - q^40 + 2 * q^41 + 7 * q^43 + q^44 - q^45 + 14 * q^46 + 6 * q^47 - q^48 + 7 * q^49 - q^50 + q^51 + 6 * q^52 + 4 * q^53 + 2 * q^54 + q^55 - 4 * q^57 + 12 * q^58 - 12 * q^59 + 2 * q^60 - 28 * q^61 + 4 * q^62 + 2 * q^64 + 6 * q^65 - 2 * q^66 - 5 * q^67 + q^68 - 7 * q^69 - 6 * q^71 - q^72 - 2 * q^73 - 7 * q^74 - q^75 - 4 * q^76 - 12 * q^78 - 3 * q^79 - q^80 - q^81 + 2 * q^82 - 16 * q^83 - 2 * q^85 + 7 * q^86 - 6 * q^87 + q^88 + 8 * q^89 - q^90 + 14 * q^92 + 7 * q^93 + 6 * q^94 + 8 * q^95 - q^96 - 12 * q^97 + 7 * q^98 + q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$$.

 $$n$$ $$187$$ $$311$$ $$871$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000 0.707107
$$3$$ −0.500000 + 0.866025i −0.288675 + 0.500000i
$$4$$ 1.00000 0.500000
$$5$$ −0.500000 0.866025i −0.223607 0.387298i
$$6$$ −0.500000 + 0.866025i −0.204124 + 0.353553i
$$7$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$8$$ 1.00000 0.353553
$$9$$ −0.500000 0.866025i −0.166667 0.288675i
$$10$$ −0.500000 0.866025i −0.158114 0.273861i
$$11$$ 0.500000 + 0.866025i 0.150756 + 0.261116i 0.931505 0.363727i $$-0.118496\pi$$
−0.780750 + 0.624844i $$0.785163\pi$$
$$12$$ −0.500000 + 0.866025i −0.144338 + 0.250000i
$$13$$ 3.00000 + 5.19615i 0.832050 + 1.44115i 0.896410 + 0.443227i $$0.146166\pi$$
−0.0643593 + 0.997927i $$0.520500\pi$$
$$14$$ 0 0
$$15$$ 1.00000 0.258199
$$16$$ 1.00000 0.250000
$$17$$ 0.500000 0.866025i 0.121268 0.210042i −0.799000 0.601331i $$-0.794637\pi$$
0.920268 + 0.391289i $$0.127971\pi$$
$$18$$ −0.500000 0.866025i −0.117851 0.204124i
$$19$$ −2.00000 + 3.46410i −0.458831 + 0.794719i −0.998899 0.0469020i $$-0.985065\pi$$
0.540068 + 0.841621i $$0.318398\pi$$
$$20$$ −0.500000 0.866025i −0.111803 0.193649i
$$21$$ 0 0
$$22$$ 0.500000 + 0.866025i 0.106600 + 0.184637i
$$23$$ 7.00000 1.45960 0.729800 0.683660i $$-0.239613\pi$$
0.729800 + 0.683660i $$0.239613\pi$$
$$24$$ −0.500000 + 0.866025i −0.102062 + 0.176777i
$$25$$ −0.500000 + 0.866025i −0.100000 + 0.173205i
$$26$$ 3.00000 + 5.19615i 0.588348 + 1.01905i
$$27$$ 1.00000 0.192450
$$28$$ 0 0
$$29$$ 6.00000 1.11417 0.557086 0.830455i $$-0.311919\pi$$
0.557086 + 0.830455i $$0.311919\pi$$
$$30$$ 1.00000 0.182574
$$31$$ 2.00000 5.19615i 0.359211 0.933257i
$$32$$ 1.00000 0.176777
$$33$$ −1.00000 −0.174078
$$34$$ 0.500000 0.866025i 0.0857493 0.148522i
$$35$$ 0 0
$$36$$ −0.500000 0.866025i −0.0833333 0.144338i
$$37$$ −3.50000 + 6.06218i −0.575396 + 0.996616i 0.420602 + 0.907245i $$0.361819\pi$$
−0.995998 + 0.0893706i $$0.971514\pi$$
$$38$$ −2.00000 + 3.46410i −0.324443 + 0.561951i
$$39$$ −6.00000 −0.960769
$$40$$ −0.500000 0.866025i −0.0790569 0.136931i
$$41$$ 1.00000 + 1.73205i 0.156174 + 0.270501i 0.933486 0.358614i $$-0.116751\pi$$
−0.777312 + 0.629115i $$0.783417\pi$$
$$42$$ 0 0
$$43$$ 3.50000 6.06218i 0.533745 0.924473i −0.465478 0.885059i $$-0.654118\pi$$
0.999223 0.0394140i $$-0.0125491\pi$$
$$44$$ 0.500000 + 0.866025i 0.0753778 + 0.130558i
$$45$$ −0.500000 + 0.866025i −0.0745356 + 0.129099i
$$46$$ 7.00000 1.03209
$$47$$ 3.00000 0.437595 0.218797 0.975770i $$-0.429787\pi$$
0.218797 + 0.975770i $$0.429787\pi$$
$$48$$ −0.500000 + 0.866025i −0.0721688 + 0.125000i
$$49$$ 3.50000 + 6.06218i 0.500000 + 0.866025i
$$50$$ −0.500000 + 0.866025i −0.0707107 + 0.122474i
$$51$$ 0.500000 + 0.866025i 0.0700140 + 0.121268i
$$52$$ 3.00000 + 5.19615i 0.416025 + 0.720577i
$$53$$ 2.00000 + 3.46410i 0.274721 + 0.475831i 0.970065 0.242846i $$-0.0780811\pi$$
−0.695344 + 0.718677i $$0.744748\pi$$
$$54$$ 1.00000 0.136083
$$55$$ 0.500000 0.866025i 0.0674200 0.116775i
$$56$$ 0 0
$$57$$ −2.00000 3.46410i −0.264906 0.458831i
$$58$$ 6.00000 0.787839
$$59$$ −6.00000 + 10.3923i −0.781133 + 1.35296i 0.150148 + 0.988663i $$0.452025\pi$$
−0.931282 + 0.364299i $$0.881308\pi$$
$$60$$ 1.00000 0.129099
$$61$$ −14.0000 −1.79252 −0.896258 0.443533i $$-0.853725\pi$$
−0.896258 + 0.443533i $$0.853725\pi$$
$$62$$ 2.00000 5.19615i 0.254000 0.659912i
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 3.00000 5.19615i 0.372104 0.644503i
$$66$$ −1.00000 −0.123091
$$67$$ −2.50000 4.33013i −0.305424 0.529009i 0.671932 0.740613i $$-0.265465\pi$$
−0.977356 + 0.211604i $$0.932131\pi$$
$$68$$ 0.500000 0.866025i 0.0606339 0.105021i
$$69$$ −3.50000 + 6.06218i −0.421350 + 0.729800i
$$70$$ 0 0
$$71$$ −3.00000 5.19615i −0.356034 0.616670i 0.631260 0.775571i $$-0.282538\pi$$
−0.987294 + 0.158901i $$0.949205\pi$$
$$72$$ −0.500000 0.866025i −0.0589256 0.102062i
$$73$$ −1.00000 1.73205i −0.117041 0.202721i 0.801553 0.597924i $$-0.204008\pi$$
−0.918594 + 0.395203i $$0.870674\pi$$
$$74$$ −3.50000 + 6.06218i −0.406867 + 0.704714i
$$75$$ −0.500000 0.866025i −0.0577350 0.100000i
$$76$$ −2.00000 + 3.46410i −0.229416 + 0.397360i
$$77$$ 0 0
$$78$$ −6.00000 −0.679366
$$79$$ −1.50000 + 2.59808i −0.168763 + 0.292306i −0.937985 0.346675i $$-0.887311\pi$$
0.769222 + 0.638982i $$0.220644\pi$$
$$80$$ −0.500000 0.866025i −0.0559017 0.0968246i
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ 1.00000 + 1.73205i 0.110432 + 0.191273i
$$83$$ −8.00000 13.8564i −0.878114 1.52094i −0.853408 0.521243i $$-0.825468\pi$$
−0.0247060 0.999695i $$-0.507865\pi$$
$$84$$ 0 0
$$85$$ −1.00000 −0.108465
$$86$$ 3.50000 6.06218i 0.377415 0.653701i
$$87$$ −3.00000 + 5.19615i −0.321634 + 0.557086i
$$88$$ 0.500000 + 0.866025i 0.0533002 + 0.0923186i
$$89$$ 4.00000 0.423999 0.212000 0.977270i $$-0.432002\pi$$
0.212000 + 0.977270i $$0.432002\pi$$
$$90$$ −0.500000 + 0.866025i −0.0527046 + 0.0912871i
$$91$$ 0 0
$$92$$ 7.00000 0.729800
$$93$$ 3.50000 + 4.33013i 0.362933 + 0.449013i
$$94$$ 3.00000 0.309426
$$95$$ 4.00000 0.410391
$$96$$ −0.500000 + 0.866025i −0.0510310 + 0.0883883i
$$97$$ −6.00000 −0.609208 −0.304604 0.952479i $$-0.598524\pi$$
−0.304604 + 0.952479i $$0.598524\pi$$
$$98$$ 3.50000 + 6.06218i 0.353553 + 0.612372i
$$99$$ 0.500000 0.866025i 0.0502519 0.0870388i
$$100$$ −0.500000 + 0.866025i −0.0500000 + 0.0866025i
$$101$$ 15.0000 1.49256 0.746278 0.665635i $$-0.231839\pi$$
0.746278 + 0.665635i $$0.231839\pi$$
$$102$$ 0.500000 + 0.866025i 0.0495074 + 0.0857493i
$$103$$ 1.00000 + 1.73205i 0.0985329 + 0.170664i 0.911078 0.412235i $$-0.135252\pi$$
−0.812545 + 0.582899i $$0.801918\pi$$
$$104$$ 3.00000 + 5.19615i 0.294174 + 0.509525i
$$105$$ 0 0
$$106$$ 2.00000 + 3.46410i 0.194257 + 0.336463i
$$107$$ 2.00000 3.46410i 0.193347 0.334887i −0.753010 0.658009i $$-0.771399\pi$$
0.946357 + 0.323122i $$0.104732\pi$$
$$108$$ 1.00000 0.0962250
$$109$$ −12.0000 −1.14939 −0.574696 0.818367i $$-0.694880\pi$$
−0.574696 + 0.818367i $$0.694880\pi$$
$$110$$ 0.500000 0.866025i 0.0476731 0.0825723i
$$111$$ −3.50000 6.06218i −0.332205 0.575396i
$$112$$ 0 0
$$113$$ −9.50000 16.4545i −0.893685 1.54791i −0.835424 0.549606i $$-0.814778\pi$$
−0.0582609 0.998301i $$-0.518556\pi$$
$$114$$ −2.00000 3.46410i −0.187317 0.324443i
$$115$$ −3.50000 6.06218i −0.326377 0.565301i
$$116$$ 6.00000 0.557086
$$117$$ 3.00000 5.19615i 0.277350 0.480384i
$$118$$ −6.00000 + 10.3923i −0.552345 + 0.956689i
$$119$$ 0 0
$$120$$ 1.00000 0.0912871
$$121$$ 5.00000 8.66025i 0.454545 0.787296i
$$122$$ −14.0000 −1.26750
$$123$$ −2.00000 −0.180334
$$124$$ 2.00000 5.19615i 0.179605 0.466628i
$$125$$ 1.00000 0.0894427
$$126$$ 0 0
$$127$$ 9.00000 15.5885i 0.798621 1.38325i −0.121894 0.992543i $$-0.538897\pi$$
0.920514 0.390709i $$-0.127770\pi$$
$$128$$ 1.00000 0.0883883
$$129$$ 3.50000 + 6.06218i 0.308158 + 0.533745i
$$130$$ 3.00000 5.19615i 0.263117 0.455733i
$$131$$ 0.500000 0.866025i 0.0436852 0.0756650i −0.843356 0.537355i $$-0.819423\pi$$
0.887041 + 0.461690i $$0.152757\pi$$
$$132$$ −1.00000 −0.0870388
$$133$$ 0 0
$$134$$ −2.50000 4.33013i −0.215967 0.374066i
$$135$$ −0.500000 0.866025i −0.0430331 0.0745356i
$$136$$ 0.500000 0.866025i 0.0428746 0.0742611i
$$137$$ 3.50000 + 6.06218i 0.299025 + 0.517927i 0.975913 0.218159i $$-0.0700052\pi$$
−0.676888 + 0.736086i $$0.736672\pi$$
$$138$$ −3.50000 + 6.06218i −0.297940 + 0.516047i
$$139$$ −10.0000 −0.848189 −0.424094 0.905618i $$-0.639408\pi$$
−0.424094 + 0.905618i $$0.639408\pi$$
$$140$$ 0 0
$$141$$ −1.50000 + 2.59808i −0.126323 + 0.218797i
$$142$$ −3.00000 5.19615i −0.251754 0.436051i
$$143$$ −3.00000 + 5.19615i −0.250873 + 0.434524i
$$144$$ −0.500000 0.866025i −0.0416667 0.0721688i
$$145$$ −3.00000 5.19615i −0.249136 0.431517i
$$146$$ −1.00000 1.73205i −0.0827606 0.143346i
$$147$$ −7.00000 −0.577350
$$148$$ −3.50000 + 6.06218i −0.287698 + 0.498308i
$$149$$ −7.00000 + 12.1244i −0.573462 + 0.993266i 0.422744 + 0.906249i $$0.361067\pi$$
−0.996207 + 0.0870170i $$0.972267\pi$$
$$150$$ −0.500000 0.866025i −0.0408248 0.0707107i
$$151$$ −7.00000 −0.569652 −0.284826 0.958579i $$-0.591936\pi$$
−0.284826 + 0.958579i $$0.591936\pi$$
$$152$$ −2.00000 + 3.46410i −0.162221 + 0.280976i
$$153$$ −1.00000 −0.0808452
$$154$$ 0 0
$$155$$ −5.50000 + 0.866025i −0.441771 + 0.0695608i
$$156$$ −6.00000 −0.480384
$$157$$ 14.0000 1.11732 0.558661 0.829396i $$-0.311315\pi$$
0.558661 + 0.829396i $$0.311315\pi$$
$$158$$ −1.50000 + 2.59808i −0.119334 + 0.206692i
$$159$$ −4.00000 −0.317221
$$160$$ −0.500000 0.866025i −0.0395285 0.0684653i
$$161$$ 0 0
$$162$$ −0.500000 + 0.866025i −0.0392837 + 0.0680414i
$$163$$ 5.00000 0.391630 0.195815 0.980641i $$-0.437265\pi$$
0.195815 + 0.980641i $$0.437265\pi$$
$$164$$ 1.00000 + 1.73205i 0.0780869 + 0.135250i
$$165$$ 0.500000 + 0.866025i 0.0389249 + 0.0674200i
$$166$$ −8.00000 13.8564i −0.620920 1.07547i
$$167$$ 12.0000 20.7846i 0.928588 1.60836i 0.142901 0.989737i $$-0.454357\pi$$
0.785687 0.618624i $$-0.212310\pi$$
$$168$$ 0 0
$$169$$ −11.5000 + 19.9186i −0.884615 + 1.53220i
$$170$$ −1.00000 −0.0766965
$$171$$ 4.00000 0.305888
$$172$$ 3.50000 6.06218i 0.266872 0.462237i
$$173$$ −1.00000 1.73205i −0.0760286 0.131685i 0.825505 0.564396i $$-0.190891\pi$$
−0.901533 + 0.432710i $$0.857557\pi$$
$$174$$ −3.00000 + 5.19615i −0.227429 + 0.393919i
$$175$$ 0 0
$$176$$ 0.500000 + 0.866025i 0.0376889 + 0.0652791i
$$177$$ −6.00000 10.3923i −0.450988 0.781133i
$$178$$ 4.00000 0.299813
$$179$$ 5.50000 9.52628i 0.411089 0.712028i −0.583920 0.811811i $$-0.698482\pi$$
0.995009 + 0.0997838i $$0.0318151\pi$$
$$180$$ −0.500000 + 0.866025i −0.0372678 + 0.0645497i
$$181$$ −10.0000 17.3205i −0.743294 1.28742i −0.950988 0.309229i $$-0.899929\pi$$
0.207693 0.978194i $$-0.433404\pi$$
$$182$$ 0 0
$$183$$ 7.00000 12.1244i 0.517455 0.896258i
$$184$$ 7.00000 0.516047
$$185$$ 7.00000 0.514650
$$186$$ 3.50000 + 4.33013i 0.256632 + 0.317500i
$$187$$ 1.00000 0.0731272
$$188$$ 3.00000 0.218797
$$189$$ 0 0
$$190$$ 4.00000 0.290191
$$191$$ 3.00000 + 5.19615i 0.217072 + 0.375980i 0.953912 0.300088i $$-0.0970159\pi$$
−0.736839 + 0.676068i $$0.763683\pi$$
$$192$$ −0.500000 + 0.866025i −0.0360844 + 0.0625000i
$$193$$ −5.00000 + 8.66025i −0.359908 + 0.623379i −0.987945 0.154805i $$-0.950525\pi$$
0.628037 + 0.778183i $$0.283859\pi$$
$$194$$ −6.00000 −0.430775
$$195$$ 3.00000 + 5.19615i 0.214834 + 0.372104i
$$196$$ 3.50000 + 6.06218i 0.250000 + 0.433013i
$$197$$ −4.00000 6.92820i −0.284988 0.493614i 0.687618 0.726073i $$-0.258656\pi$$
−0.972606 + 0.232458i $$0.925323\pi$$
$$198$$ 0.500000 0.866025i 0.0355335 0.0615457i
$$199$$ −8.00000 13.8564i −0.567105 0.982255i −0.996850 0.0793045i $$-0.974730\pi$$
0.429745 0.902950i $$-0.358603\pi$$
$$200$$ −0.500000 + 0.866025i −0.0353553 + 0.0612372i
$$201$$ 5.00000 0.352673
$$202$$ 15.0000 1.05540
$$203$$ 0 0
$$204$$ 0.500000 + 0.866025i 0.0350070 + 0.0606339i
$$205$$ 1.00000 1.73205i 0.0698430 0.120972i
$$206$$ 1.00000 + 1.73205i 0.0696733 + 0.120678i
$$207$$ −3.50000 6.06218i −0.243267 0.421350i
$$208$$ 3.00000 + 5.19615i 0.208013 + 0.360288i
$$209$$ −4.00000 −0.276686
$$210$$ 0 0
$$211$$ 4.00000 6.92820i 0.275371 0.476957i −0.694857 0.719148i $$-0.744533\pi$$
0.970229 + 0.242190i $$0.0778659\pi$$
$$212$$ 2.00000 + 3.46410i 0.137361 + 0.237915i
$$213$$ 6.00000 0.411113
$$214$$ 2.00000 3.46410i 0.136717 0.236801i
$$215$$ −7.00000 −0.477396
$$216$$ 1.00000 0.0680414
$$217$$ 0 0
$$218$$ −12.0000 −0.812743
$$219$$ 2.00000 0.135147
$$220$$ 0.500000 0.866025i 0.0337100 0.0583874i
$$221$$ 6.00000 0.403604
$$222$$ −3.50000 6.06218i −0.234905 0.406867i
$$223$$ −7.00000 + 12.1244i −0.468755 + 0.811907i −0.999362 0.0357107i $$-0.988630\pi$$
0.530607 + 0.847618i $$0.321964\pi$$
$$224$$ 0 0
$$225$$ 1.00000 0.0666667
$$226$$ −9.50000 16.4545i −0.631931 1.09454i
$$227$$ 4.00000 + 6.92820i 0.265489 + 0.459841i 0.967692 0.252136i $$-0.0811332\pi$$
−0.702202 + 0.711977i $$0.747800\pi$$
$$228$$ −2.00000 3.46410i −0.132453 0.229416i
$$229$$ −10.0000 + 17.3205i −0.660819 + 1.14457i 0.319582 + 0.947559i $$0.396457\pi$$
−0.980401 + 0.197013i $$0.936876\pi$$
$$230$$ −3.50000 6.06218i −0.230783 0.399728i
$$231$$ 0 0
$$232$$ 6.00000 0.393919
$$233$$ 25.0000 1.63780 0.818902 0.573933i $$-0.194583\pi$$
0.818902 + 0.573933i $$0.194583\pi$$
$$234$$ 3.00000 5.19615i 0.196116 0.339683i
$$235$$ −1.50000 2.59808i −0.0978492 0.169480i
$$236$$ −6.00000 + 10.3923i −0.390567 + 0.676481i
$$237$$ −1.50000 2.59808i −0.0974355 0.168763i
$$238$$ 0 0
$$239$$ −9.00000 15.5885i −0.582162 1.00833i −0.995223 0.0976302i $$-0.968874\pi$$
0.413061 0.910703i $$-0.364460\pi$$
$$240$$ 1.00000 0.0645497
$$241$$ −9.00000 + 15.5885i −0.579741 + 1.00414i 0.415768 + 0.909471i $$0.363513\pi$$
−0.995509 + 0.0946700i $$0.969820\pi$$
$$242$$ 5.00000 8.66025i 0.321412 0.556702i
$$243$$ −0.500000 0.866025i −0.0320750 0.0555556i
$$244$$ −14.0000 −0.896258
$$245$$ 3.50000 6.06218i 0.223607 0.387298i
$$246$$ −2.00000 −0.127515
$$247$$ −24.0000 −1.52708
$$248$$ 2.00000 5.19615i 0.127000 0.329956i
$$249$$ 16.0000 1.01396
$$250$$ 1.00000 0.0632456
$$251$$ −1.50000 + 2.59808i −0.0946792 + 0.163989i −0.909475 0.415759i $$-0.863516\pi$$
0.814795 + 0.579748i $$0.196849\pi$$
$$252$$ 0 0
$$253$$ 3.50000 + 6.06218i 0.220043 + 0.381126i
$$254$$ 9.00000 15.5885i 0.564710 0.978107i
$$255$$ 0.500000 0.866025i 0.0313112 0.0542326i
$$256$$ 1.00000 0.0625000
$$257$$ −11.5000 19.9186i −0.717350 1.24249i −0.962046 0.272887i $$-0.912021\pi$$
0.244696 0.969600i $$-0.421312\pi$$
$$258$$ 3.50000 + 6.06218i 0.217900 + 0.377415i
$$259$$ 0 0
$$260$$ 3.00000 5.19615i 0.186052 0.322252i
$$261$$ −3.00000 5.19615i −0.185695 0.321634i
$$262$$ 0.500000 0.866025i 0.0308901 0.0535032i
$$263$$ −11.0000 −0.678289 −0.339145 0.940734i $$-0.610138\pi$$
−0.339145 + 0.940734i $$0.610138\pi$$
$$264$$ −1.00000 −0.0615457
$$265$$ 2.00000 3.46410i 0.122859 0.212798i
$$266$$ 0 0
$$267$$ −2.00000 + 3.46410i −0.122398 + 0.212000i
$$268$$ −2.50000 4.33013i −0.152712 0.264505i
$$269$$ 12.5000 + 21.6506i 0.762138 + 1.32006i 0.941746 + 0.336324i $$0.109184\pi$$
−0.179608 + 0.983738i $$0.557483\pi$$
$$270$$ −0.500000 0.866025i −0.0304290 0.0527046i
$$271$$ −28.0000 −1.70088 −0.850439 0.526073i $$-0.823664\pi$$
−0.850439 + 0.526073i $$0.823664\pi$$
$$272$$ 0.500000 0.866025i 0.0303170 0.0525105i
$$273$$ 0 0
$$274$$ 3.50000 + 6.06218i 0.211443 + 0.366230i
$$275$$ −1.00000 −0.0603023
$$276$$ −3.50000 + 6.06218i −0.210675 + 0.364900i
$$277$$ 13.0000 0.781094 0.390547 0.920583i $$-0.372286\pi$$
0.390547 + 0.920583i $$0.372286\pi$$
$$278$$ −10.0000 −0.599760
$$279$$ −5.50000 + 0.866025i −0.329276 + 0.0518476i
$$280$$ 0 0
$$281$$ 22.0000 1.31241 0.656205 0.754583i $$-0.272161\pi$$
0.656205 + 0.754583i $$0.272161\pi$$
$$282$$ −1.50000 + 2.59808i −0.0893237 + 0.154713i
$$283$$ −19.0000 −1.12943 −0.564716 0.825285i $$-0.691014\pi$$
−0.564716 + 0.825285i $$0.691014\pi$$
$$284$$ −3.00000 5.19615i −0.178017 0.308335i
$$285$$ −2.00000 + 3.46410i −0.118470 + 0.205196i
$$286$$ −3.00000 + 5.19615i −0.177394 + 0.307255i
$$287$$ 0 0
$$288$$ −0.500000 0.866025i −0.0294628 0.0510310i
$$289$$ 8.00000 + 13.8564i 0.470588 + 0.815083i
$$290$$ −3.00000 5.19615i −0.176166 0.305129i
$$291$$ 3.00000 5.19615i 0.175863 0.304604i
$$292$$ −1.00000 1.73205i −0.0585206 0.101361i
$$293$$ −8.00000 + 13.8564i −0.467365 + 0.809500i −0.999305 0.0372823i $$-0.988130\pi$$
0.531940 + 0.846782i $$0.321463\pi$$
$$294$$ −7.00000 −0.408248
$$295$$ 12.0000 0.698667
$$296$$ −3.50000 + 6.06218i −0.203433 + 0.352357i
$$297$$ 0.500000 + 0.866025i 0.0290129 + 0.0502519i
$$298$$ −7.00000 + 12.1244i −0.405499 + 0.702345i
$$299$$ 21.0000 + 36.3731i 1.21446 + 2.10351i
$$300$$ −0.500000 0.866025i −0.0288675 0.0500000i
$$301$$ 0 0
$$302$$ −7.00000 −0.402805
$$303$$ −7.50000 + 12.9904i −0.430864 + 0.746278i
$$304$$ −2.00000 + 3.46410i −0.114708 + 0.198680i
$$305$$ 7.00000 + 12.1244i 0.400819 + 0.694239i
$$306$$ −1.00000 −0.0571662
$$307$$ −8.00000 + 13.8564i −0.456584 + 0.790827i −0.998778 0.0494267i $$-0.984261\pi$$
0.542194 + 0.840254i $$0.317594\pi$$
$$308$$ 0 0
$$309$$ −2.00000 −0.113776
$$310$$ −5.50000 + 0.866025i −0.312379 + 0.0491869i
$$311$$ −6.00000 −0.340229 −0.170114 0.985424i $$-0.554414\pi$$
−0.170114 + 0.985424i $$0.554414\pi$$
$$312$$ −6.00000 −0.339683
$$313$$ −3.00000 + 5.19615i −0.169570 + 0.293704i −0.938269 0.345907i $$-0.887571\pi$$
0.768699 + 0.639611i $$0.220905\pi$$
$$314$$ 14.0000 0.790066
$$315$$ 0 0
$$316$$ −1.50000 + 2.59808i −0.0843816 + 0.146153i
$$317$$ 6.00000 10.3923i 0.336994 0.583690i −0.646872 0.762598i $$-0.723923\pi$$
0.983866 + 0.178908i $$0.0572566\pi$$
$$318$$ −4.00000 −0.224309
$$319$$ 3.00000 + 5.19615i 0.167968 + 0.290929i
$$320$$ −0.500000 0.866025i −0.0279508 0.0484123i
$$321$$ 2.00000 + 3.46410i 0.111629 + 0.193347i
$$322$$ 0 0
$$323$$ 2.00000 + 3.46410i 0.111283 + 0.192748i
$$324$$ −0.500000 + 0.866025i −0.0277778 + 0.0481125i
$$325$$ −6.00000 −0.332820
$$326$$ 5.00000 0.276924
$$327$$ 6.00000 10.3923i 0.331801 0.574696i
$$328$$ 1.00000 + 1.73205i 0.0552158 + 0.0956365i
$$329$$ 0 0
$$330$$ 0.500000 + 0.866025i 0.0275241 + 0.0476731i
$$331$$ −2.00000 3.46410i −0.109930 0.190404i 0.805812 0.592172i $$-0.201729\pi$$
−0.915742 + 0.401768i $$0.868396\pi$$
$$332$$ −8.00000 13.8564i −0.439057 0.760469i
$$333$$ 7.00000 0.383598
$$334$$ 12.0000 20.7846i 0.656611 1.13728i
$$335$$ −2.50000 + 4.33013i −0.136590 + 0.236580i
$$336$$ 0 0
$$337$$ 8.00000 0.435788 0.217894 0.975972i $$-0.430081\pi$$
0.217894 + 0.975972i $$0.430081\pi$$
$$338$$ −11.5000 + 19.9186i −0.625518 + 1.08343i
$$339$$ 19.0000 1.03194
$$340$$ −1.00000 −0.0542326
$$341$$ 5.50000 0.866025i 0.297842 0.0468979i
$$342$$ 4.00000 0.216295
$$343$$ 0 0
$$344$$ 3.50000 6.06218i 0.188707 0.326851i
$$345$$ 7.00000 0.376867
$$346$$ −1.00000 1.73205i −0.0537603 0.0931156i
$$347$$ 7.00000 12.1244i 0.375780 0.650870i −0.614664 0.788789i $$-0.710708\pi$$
0.990443 + 0.137920i $$0.0440416\pi$$
$$348$$ −3.00000 + 5.19615i −0.160817 + 0.278543i
$$349$$ 18.0000 0.963518 0.481759 0.876304i $$-0.339998\pi$$
0.481759 + 0.876304i $$0.339998\pi$$
$$350$$ 0 0
$$351$$ 3.00000 + 5.19615i 0.160128 + 0.277350i
$$352$$ 0.500000 + 0.866025i 0.0266501 + 0.0461593i
$$353$$ 5.50000 9.52628i 0.292735 0.507033i −0.681720 0.731613i $$-0.738768\pi$$
0.974456 + 0.224580i $$0.0721011\pi$$
$$354$$ −6.00000 10.3923i −0.318896 0.552345i
$$355$$ −3.00000 + 5.19615i −0.159223 + 0.275783i
$$356$$ 4.00000 0.212000
$$357$$ 0 0
$$358$$ 5.50000 9.52628i 0.290684 0.503480i
$$359$$ −10.0000 17.3205i −0.527780 0.914141i −0.999476 0.0323801i $$-0.989691\pi$$
0.471696 0.881761i $$-0.343642\pi$$
$$360$$ −0.500000 + 0.866025i −0.0263523 + 0.0456435i
$$361$$ 1.50000 + 2.59808i 0.0789474 + 0.136741i
$$362$$ −10.0000 17.3205i −0.525588 0.910346i
$$363$$ 5.00000 + 8.66025i 0.262432 + 0.454545i
$$364$$ 0 0
$$365$$ −1.00000 + 1.73205i −0.0523424 + 0.0906597i
$$366$$ 7.00000 12.1244i 0.365896 0.633750i
$$367$$ 2.00000 + 3.46410i 0.104399 + 0.180825i 0.913493 0.406855i $$-0.133375\pi$$
−0.809093 + 0.587680i $$0.800041\pi$$
$$368$$ 7.00000 0.364900
$$369$$ 1.00000 1.73205i 0.0520579 0.0901670i
$$370$$ 7.00000 0.363913
$$371$$ 0 0
$$372$$ 3.50000 + 4.33013i 0.181467 + 0.224507i
$$373$$ −19.0000 −0.983783 −0.491891 0.870657i $$-0.663694\pi$$
−0.491891 + 0.870657i $$0.663694\pi$$
$$374$$ 1.00000 0.0517088
$$375$$ −0.500000 + 0.866025i −0.0258199 + 0.0447214i
$$376$$ 3.00000 0.154713
$$377$$ 18.0000 + 31.1769i 0.927047 + 1.60569i
$$378$$ 0 0
$$379$$ −3.00000 + 5.19615i −0.154100 + 0.266908i −0.932731 0.360573i $$-0.882581\pi$$
0.778631 + 0.627482i $$0.215914\pi$$
$$380$$ 4.00000 0.205196
$$381$$ 9.00000 + 15.5885i 0.461084 + 0.798621i
$$382$$ 3.00000 + 5.19615i 0.153493 + 0.265858i
$$383$$ −9.50000 16.4545i −0.485427 0.840785i 0.514432 0.857531i $$-0.328003\pi$$
−0.999860 + 0.0167461i $$0.994669\pi$$
$$384$$ −0.500000 + 0.866025i −0.0255155 + 0.0441942i
$$385$$ 0 0
$$386$$ −5.00000 + 8.66025i −0.254493 + 0.440795i
$$387$$ −7.00000 −0.355830
$$388$$ −6.00000 −0.304604
$$389$$ −4.50000 + 7.79423i −0.228159 + 0.395183i −0.957263 0.289220i $$-0.906604\pi$$
0.729103 + 0.684403i $$0.239937\pi$$
$$390$$ 3.00000 + 5.19615i 0.151911 + 0.263117i
$$391$$ 3.50000 6.06218i 0.177003 0.306578i
$$392$$ 3.50000 + 6.06218i 0.176777 + 0.306186i
$$393$$ 0.500000 + 0.866025i 0.0252217 + 0.0436852i
$$394$$ −4.00000 6.92820i −0.201517 0.349038i
$$395$$ 3.00000 0.150946
$$396$$ 0.500000 0.866025i 0.0251259 0.0435194i
$$397$$ 10.5000 18.1865i 0.526980 0.912756i −0.472526 0.881317i $$-0.656658\pi$$
0.999506 0.0314391i $$-0.0100090\pi$$
$$398$$ −8.00000 13.8564i −0.401004 0.694559i
$$399$$ 0 0
$$400$$ −0.500000 + 0.866025i −0.0250000 + 0.0433013i
$$401$$ 2.00000 0.0998752 0.0499376 0.998752i $$-0.484098\pi$$
0.0499376 + 0.998752i $$0.484098\pi$$
$$402$$ 5.00000 0.249377
$$403$$ 33.0000 5.19615i 1.64385 0.258839i
$$404$$ 15.0000 0.746278
$$405$$ 1.00000 0.0496904
$$406$$ 0 0
$$407$$ −7.00000 −0.346977
$$408$$ 0.500000 + 0.866025i 0.0247537 + 0.0428746i
$$409$$ −9.50000 + 16.4545i −0.469745 + 0.813622i −0.999402 0.0345902i $$-0.988987\pi$$
0.529657 + 0.848212i $$0.322321\pi$$
$$410$$ 1.00000 1.73205i 0.0493865 0.0855399i
$$411$$ −7.00000 −0.345285
$$412$$ 1.00000 + 1.73205i 0.0492665 + 0.0853320i
$$413$$ 0 0
$$414$$ −3.50000 6.06218i −0.172016 0.297940i
$$415$$ −8.00000 + 13.8564i −0.392705 + 0.680184i
$$416$$ 3.00000 + 5.19615i 0.147087 + 0.254762i
$$417$$ 5.00000 8.66025i 0.244851 0.424094i
$$418$$ −4.00000 −0.195646
$$419$$ 7.00000 0.341972 0.170986 0.985273i $$-0.445305\pi$$
0.170986 + 0.985273i $$0.445305\pi$$
$$420$$ 0 0
$$421$$ −13.0000 22.5167i −0.633581 1.09739i −0.986814 0.161859i $$-0.948251\pi$$
0.353233 0.935536i $$-0.385082\pi$$
$$422$$ 4.00000 6.92820i 0.194717 0.337260i
$$423$$ −1.50000 2.59808i −0.0729325 0.126323i
$$424$$ 2.00000 + 3.46410i 0.0971286 + 0.168232i
$$425$$ 0.500000 + 0.866025i 0.0242536 + 0.0420084i
$$426$$ 6.00000 0.290701
$$427$$ 0 0
$$428$$ 2.00000 3.46410i 0.0966736 0.167444i
$$429$$ −3.00000 5.19615i −0.144841 0.250873i
$$430$$ −7.00000 −0.337570
$$431$$ −15.0000 + 25.9808i −0.722525 + 1.25145i 0.237460 + 0.971397i $$0.423685\pi$$
−0.959985 + 0.280052i $$0.909648\pi$$
$$432$$ 1.00000 0.0481125
$$433$$ 8.00000 0.384455 0.192228 0.981350i $$-0.438429\pi$$
0.192228 + 0.981350i $$0.438429\pi$$
$$434$$ 0 0
$$435$$ 6.00000 0.287678
$$436$$ −12.0000 −0.574696
$$437$$ −14.0000 + 24.2487i −0.669711 + 1.15997i
$$438$$ 2.00000 0.0955637
$$439$$ 17.5000 + 30.3109i 0.835229 + 1.44666i 0.893843 + 0.448379i $$0.147999\pi$$
−0.0586141 + 0.998281i $$0.518668\pi$$
$$440$$ 0.500000 0.866025i 0.0238366 0.0412861i
$$441$$ 3.50000 6.06218i 0.166667 0.288675i
$$442$$ 6.00000 0.285391
$$443$$ −17.0000 29.4449i −0.807694 1.39897i −0.914457 0.404683i $$-0.867382\pi$$
0.106763 0.994285i $$-0.465952\pi$$
$$444$$ −3.50000 6.06218i −0.166103 0.287698i
$$445$$ −2.00000 3.46410i −0.0948091 0.164214i
$$446$$ −7.00000 + 12.1244i −0.331460 + 0.574105i
$$447$$ −7.00000 12.1244i −0.331089 0.573462i
$$448$$ 0 0
$$449$$ −30.0000 −1.41579 −0.707894 0.706319i $$-0.750354\pi$$
−0.707894 + 0.706319i $$0.750354\pi$$
$$450$$ 1.00000 0.0471405
$$451$$ −1.00000 + 1.73205i −0.0470882 + 0.0815591i
$$452$$ −9.50000 16.4545i −0.446842 0.773954i
$$453$$ 3.50000 6.06218i 0.164444 0.284826i
$$454$$ 4.00000 + 6.92820i 0.187729 + 0.325157i
$$455$$ 0 0
$$456$$ −2.00000 3.46410i −0.0936586 0.162221i
$$457$$ 32.0000 1.49690 0.748448 0.663193i $$-0.230799\pi$$
0.748448 + 0.663193i $$0.230799\pi$$
$$458$$ −10.0000 + 17.3205i −0.467269 + 0.809334i
$$459$$ 0.500000 0.866025i 0.0233380 0.0404226i
$$460$$ −3.50000 6.06218i −0.163188 0.282650i
$$461$$ 33.0000 1.53696 0.768482 0.639872i $$-0.221013\pi$$
0.768482 + 0.639872i $$0.221013\pi$$
$$462$$ 0 0
$$463$$ 20.0000 0.929479 0.464739 0.885448i $$-0.346148\pi$$
0.464739 + 0.885448i $$0.346148\pi$$
$$464$$ 6.00000 0.278543
$$465$$ 2.00000 5.19615i 0.0927478 0.240966i
$$466$$ 25.0000 1.15810
$$467$$ 12.0000 0.555294 0.277647 0.960683i $$-0.410445\pi$$
0.277647 + 0.960683i $$0.410445\pi$$
$$468$$ 3.00000 5.19615i 0.138675 0.240192i
$$469$$ 0 0
$$470$$ −1.50000 2.59808i −0.0691898 0.119840i
$$471$$ −7.00000 + 12.1244i −0.322543 + 0.558661i
$$472$$ −6.00000 + 10.3923i −0.276172 + 0.478345i
$$473$$ 7.00000 0.321860
$$474$$ −1.50000 2.59808i −0.0688973 0.119334i
$$475$$ −2.00000 3.46410i −0.0917663 0.158944i
$$476$$ 0 0
$$477$$ 2.00000 3.46410i 0.0915737 0.158610i
$$478$$ −9.00000 15.5885i −0.411650 0.712999i
$$479$$ −9.00000 + 15.5885i −0.411220 + 0.712255i −0.995023 0.0996406i $$-0.968231\pi$$
0.583803 + 0.811895i $$0.301564\pi$$
$$480$$ 1.00000 0.0456435
$$481$$ −42.0000 −1.91504
$$482$$ −9.00000 + 15.5885i −0.409939 + 0.710035i
$$483$$ 0 0
$$484$$ 5.00000 8.66025i 0.227273 0.393648i
$$485$$ 3.00000 + 5.19615i 0.136223 + 0.235945i
$$486$$ −0.500000 0.866025i −0.0226805 0.0392837i
$$487$$ −16.0000 27.7128i −0.725029 1.25579i −0.958962 0.283535i $$-0.908493\pi$$
0.233933 0.972253i $$-0.424840\pi$$
$$488$$ −14.0000 −0.633750
$$489$$ −2.50000 + 4.33013i −0.113054 + 0.195815i
$$490$$ 3.50000 6.06218i 0.158114 0.273861i
$$491$$ 14.5000 + 25.1147i 0.654376 + 1.13341i 0.982050 + 0.188621i $$0.0604019\pi$$
−0.327674 + 0.944791i $$0.606265\pi$$
$$492$$ −2.00000 −0.0901670
$$493$$ 3.00000 5.19615i 0.135113 0.234023i
$$494$$ −24.0000 −1.07981
$$495$$ −1.00000 −0.0449467
$$496$$ 2.00000 5.19615i 0.0898027 0.233314i
$$497$$ 0 0
$$498$$ 16.0000 0.716977
$$499$$ 10.0000 17.3205i 0.447661 0.775372i −0.550572 0.834788i $$-0.685590\pi$$
0.998233 + 0.0594153i $$0.0189236\pi$$
$$500$$ 1.00000 0.0447214
$$501$$ 12.0000 + 20.7846i 0.536120 + 0.928588i
$$502$$ −1.50000 + 2.59808i −0.0669483 + 0.115958i
$$503$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$504$$ 0 0
$$505$$ −7.50000 12.9904i −0.333746 0.578064i
$$506$$ 3.50000 + 6.06218i 0.155594 + 0.269497i
$$507$$ −11.5000 19.9186i −0.510733 0.884615i
$$508$$ 9.00000 15.5885i 0.399310 0.691626i
$$509$$ −14.5000 25.1147i −0.642701 1.11319i −0.984827 0.173537i $$-0.944480\pi$$
0.342126 0.939654i $$-0.388853\pi$$
$$510$$ 0.500000 0.866025i 0.0221404 0.0383482i
$$511$$ 0 0
$$512$$ 1.00000 0.0441942
$$513$$ −2.00000 + 3.46410i −0.0883022 + 0.152944i
$$514$$ −11.5000 19.9186i −0.507243 0.878571i
$$515$$ 1.00000 1.73205i 0.0440653 0.0763233i
$$516$$ 3.50000 + 6.06218i 0.154079 + 0.266872i
$$517$$ 1.50000 + 2.59808i 0.0659699 + 0.114263i
$$518$$ 0 0
$$519$$ 2.00000 0.0877903
$$520$$ 3.00000 5.19615i 0.131559 0.227866i
$$521$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$522$$ −3.00000 5.19615i −0.131306 0.227429i
$$523$$ 29.0000 1.26808 0.634041 0.773300i $$-0.281395\pi$$
0.634041 + 0.773300i $$0.281395\pi$$
$$524$$ 0.500000 0.866025i 0.0218426 0.0378325i
$$525$$ 0 0
$$526$$ −11.0000 −0.479623
$$527$$ −3.50000 4.33013i −0.152462 0.188623i
$$528$$ −1.00000 −0.0435194
$$529$$ 26.0000 1.13043
$$530$$ 2.00000 3.46410i 0.0868744 0.150471i
$$531$$ 12.0000 0.520756
$$532$$ 0 0
$$533$$ −6.00000 + 10.3923i −0.259889 + 0.450141i
$$534$$ −2.00000 + 3.46410i −0.0865485 + 0.149906i
$$535$$ −4.00000 −0.172935
$$536$$ −2.50000 4.33013i −0.107984 0.187033i
$$537$$ 5.50000 + 9.52628i 0.237343 + 0.411089i
$$538$$ 12.5000 + 21.6506i 0.538913 + 0.933425i
$$539$$ −3.50000 + 6.06218i −0.150756 + 0.261116i
$$540$$ −0.500000 0.866025i −0.0215166 0.0372678i
$$541$$ 5.00000 8.66025i 0.214967 0.372333i −0.738296 0.674477i $$-0.764369\pi$$
0.953262 + 0.302144i $$0.0977023\pi$$
$$542$$ −28.0000 −1.20270
$$543$$ 20.0000 0.858282
$$544$$ 0.500000 0.866025i 0.0214373 0.0371305i
$$545$$ 6.00000 + 10.3923i 0.257012 + 0.445157i
$$546$$ 0 0
$$547$$ 8.50000 + 14.7224i 0.363434 + 0.629486i 0.988524 0.151067i $$-0.0482710\pi$$
−0.625090 + 0.780553i $$0.714938\pi$$
$$548$$ 3.50000 + 6.06218i 0.149513 + 0.258963i
$$549$$ 7.00000 + 12.1244i 0.298753 + 0.517455i
$$550$$ −1.00000 −0.0426401
$$551$$ −12.0000 + 20.7846i −0.511217 + 0.885454i
$$552$$ −3.50000 + 6.06218i −0.148970 + 0.258023i
$$553$$ 0 0
$$554$$ 13.0000 0.552317
$$555$$ −3.50000 + 6.06218i −0.148567 + 0.257325i
$$556$$ −10.0000 −0.424094
$$557$$ 12.0000 0.508456 0.254228 0.967144i $$-0.418179\pi$$
0.254228 + 0.967144i $$0.418179\pi$$
$$558$$ −5.50000 + 0.866025i −0.232834 + 0.0366618i
$$559$$ 42.0000 1.77641
$$560$$ 0 0
$$561$$ −0.500000 + 0.866025i −0.0211100 + 0.0365636i
$$562$$ 22.0000 0.928014
$$563$$ −9.00000 15.5885i −0.379305 0.656975i 0.611656 0.791123i $$-0.290503\pi$$
−0.990961 + 0.134148i $$0.957170\pi$$
$$564$$ −1.50000 + 2.59808i −0.0631614 + 0.109399i
$$565$$ −9.50000 + 16.4545i −0.399668 + 0.692245i
$$566$$ −19.0000 −0.798630
$$567$$ 0 0
$$568$$ −3.00000 5.19615i −0.125877 0.218026i
$$569$$ −17.0000 29.4449i −0.712677 1.23439i −0.963849 0.266450i $$-0.914149\pi$$
0.251172 0.967943i $$-0.419184\pi$$
$$570$$ −2.00000 + 3.46410i −0.0837708 + 0.145095i
$$571$$ 16.0000 + 27.7128i 0.669579 + 1.15975i 0.978022 + 0.208502i $$0.0668588\pi$$
−0.308443 + 0.951243i $$0.599808\pi$$
$$572$$ −3.00000 + 5.19615i −0.125436 + 0.217262i
$$573$$ −6.00000 −0.250654
$$574$$ 0 0
$$575$$ −3.50000 + 6.06218i −0.145960 + 0.252810i
$$576$$ −0.500000 0.866025i −0.0208333 0.0360844i
$$577$$ −16.0000 + 27.7128i −0.666089 + 1.15370i 0.312900 + 0.949786i $$0.398699\pi$$
−0.978989 + 0.203913i $$0.934634\pi$$
$$578$$ 8.00000 + 13.8564i 0.332756 + 0.576351i
$$579$$ −5.00000 8.66025i −0.207793 0.359908i
$$580$$ −3.00000 5.19615i −0.124568 0.215758i
$$581$$ 0 0
$$582$$ 3.00000 5.19615i 0.124354 0.215387i
$$583$$ −2.00000 + 3.46410i −0.0828315 + 0.143468i
$$584$$ −1.00000 1.73205i −0.0413803 0.0716728i
$$585$$ −6.00000 −0.248069
$$586$$ −8.00000 + 13.8564i −0.330477 + 0.572403i
$$587$$ 18.0000 0.742940 0.371470 0.928445i $$-0.378854\pi$$
0.371470 + 0.928445i $$0.378854\pi$$
$$588$$ −7.00000 −0.288675
$$589$$ 14.0000 + 17.3205i 0.576860 + 0.713679i
$$590$$ 12.0000 0.494032
$$591$$ 8.00000 0.329076
$$592$$ −3.50000 + 6.06218i −0.143849 + 0.249154i
$$593$$ 6.00000 0.246390 0.123195 0.992382i $$-0.460686\pi$$
0.123195 + 0.992382i $$0.460686\pi$$
$$594$$ 0.500000 + 0.866025i 0.0205152 + 0.0355335i
$$595$$ 0 0
$$596$$ −7.00000 + 12.1244i −0.286731 + 0.496633i
$$597$$ 16.0000 0.654836
$$598$$ 21.0000 + 36.3731i 0.858754 + 1.48741i
$$599$$ −17.0000 29.4449i −0.694601 1.20308i −0.970315 0.241845i $$-0.922248\pi$$
0.275714 0.961240i $$-0.411086\pi$$
$$600$$ −0.500000 0.866025i −0.0204124 0.0353553i
$$601$$ 21.5000 37.2391i 0.877003 1.51901i 0.0223900 0.999749i $$-0.492872\pi$$
0.854613 0.519265i $$-0.173794\pi$$
$$602$$ 0 0
$$603$$ −2.50000 + 4.33013i −0.101808 + 0.176336i
$$604$$ −7.00000 −0.284826
$$605$$ −10.0000 −0.406558
$$606$$ −7.50000 + 12.9904i −0.304667 + 0.527698i
$$607$$ −10.0000 17.3205i −0.405887 0.703018i 0.588537 0.808470i $$-0.299704\pi$$
−0.994424 + 0.105453i $$0.966371\pi$$
$$608$$ −2.00000 + 3.46410i −0.0811107 + 0.140488i
$$609$$ 0 0
$$610$$ 7.00000 + 12.1244i 0.283422 + 0.490901i
$$611$$ 9.00000 + 15.5885i 0.364101 + 0.630641i
$$612$$ −1.00000 −0.0404226
$$613$$ −1.00000 + 1.73205i −0.0403896 + 0.0699569i −0.885514 0.464614i $$-0.846193\pi$$
0.845124 + 0.534570i $$0.179527\pi$$
$$614$$ −8.00000 + 13.8564i −0.322854 + 0.559199i
$$615$$ 1.00000 + 1.73205i 0.0403239 + 0.0698430i
$$616$$ 0 0
$$617$$ 3.50000 6.06218i 0.140905 0.244054i −0.786933 0.617039i $$-0.788332\pi$$
0.927838 + 0.372985i $$0.121666\pi$$
$$618$$ −2.00000 −0.0804518
$$619$$ 36.0000 1.44696 0.723481 0.690344i $$-0.242541\pi$$
0.723481 + 0.690344i $$0.242541\pi$$
$$620$$ −5.50000 + 0.866025i −0.220885 + 0.0347804i
$$621$$ 7.00000 0.280900
$$622$$ −6.00000 −0.240578
$$623$$ 0 0
$$624$$ −6.00000 −0.240192
$$625$$ −0.500000 0.866025i −0.0200000 0.0346410i
$$626$$ −3.00000 + 5.19615i −0.119904 + 0.207680i
$$627$$ 2.00000 3.46410i 0.0798723 0.138343i
$$628$$ 14.0000 0.558661
$$629$$ 3.50000 + 6.06218i 0.139554 + 0.241715i
$$630$$ 0 0
$$631$$ −14.5000 25.1147i −0.577236 0.999802i −0.995795 0.0916122i $$-0.970798\pi$$
0.418559 0.908190i $$-0.362535\pi$$
$$632$$ −1.50000 + 2.59808i −0.0596668 + 0.103346i
$$633$$ 4.00000 + 6.92820i 0.158986 + 0.275371i
$$634$$ 6.00000 10.3923i 0.238290 0.412731i
$$635$$ −18.0000 −0.714308
$$636$$ −4.00000 −0.158610
$$637$$ −21.0000 + 36.3731i −0.832050 + 1.44115i
$$638$$ 3.00000 + 5.19615i 0.118771 + 0.205718i
$$639$$ −3.00000 + 5.19615i −0.118678 + 0.205557i
$$640$$ −0.500000 0.866025i −0.0197642 0.0342327i
$$641$$ −2.00000 3.46410i −0.0789953 0.136824i 0.823821 0.566849i $$-0.191838\pi$$
−0.902817 + 0.430026i $$0.858505\pi$$
$$642$$ 2.00000 + 3.46410i 0.0789337 + 0.136717i
$$643$$ −4.00000 −0.157745 −0.0788723 0.996885i $$-0.525132\pi$$
−0.0788723 + 0.996885i $$0.525132\pi$$
$$644$$ 0 0
$$645$$ 3.50000 6.06218i 0.137812 0.238698i
$$646$$ 2.00000 + 3.46410i 0.0786889 + 0.136293i
$$647$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$648$$ −0.500000 + 0.866025i −0.0196419 + 0.0340207i
$$649$$ −12.0000 −0.471041
$$650$$ −6.00000 −0.235339
$$651$$ 0 0
$$652$$ 5.00000 0.195815
$$653$$ −12.0000 −0.469596 −0.234798 0.972044i $$-0.575443\pi$$
−0.234798 + 0.972044i $$0.575443\pi$$
$$654$$ 6.00000 10.3923i 0.234619 0.406371i
$$655$$ −1.00000 −0.0390732
$$656$$ 1.00000 + 1.73205i 0.0390434 + 0.0676252i
$$657$$ −1.00000 + 1.73205i −0.0390137 + 0.0675737i
$$658$$ 0 0
$$659$$ −37.0000 −1.44132 −0.720658 0.693291i $$-0.756160\pi$$
−0.720658 + 0.693291i $$0.756160\pi$$
$$660$$ 0.500000 + 0.866025i 0.0194625 + 0.0337100i
$$661$$ 5.00000 + 8.66025i 0.194477 + 0.336845i 0.946729 0.322031i $$-0.104366\pi$$
−0.752252 + 0.658876i $$0.771032\pi$$
$$662$$ −2.00000 3.46410i −0.0777322 0.134636i
$$663$$ −3.00000 + 5.19615i −0.116510 + 0.201802i
$$664$$ −8.00000 13.8564i −0.310460 0.537733i
$$665$$ 0 0
$$666$$ 7.00000 0.271244
$$667$$ 42.0000 1.62625
$$668$$ 12.0000 20.7846i 0.464294 0.804181i
$$669$$ −7.00000 12.1244i −0.270636 0.468755i
$$670$$ −2.50000 + 4.33013i −0.0965834 + 0.167287i
$$671$$ −7.00000 12.1244i −0.270232 0.468056i
$$672$$ 0 0
$$673$$ −5.00000 8.66025i −0.192736 0.333828i 0.753420 0.657539i $$-0.228403\pi$$
−0.946156 + 0.323711i $$0.895069\pi$$
$$674$$ 8.00000 0.308148
$$675$$ −0.500000 + 0.866025i −0.0192450 + 0.0333333i
$$676$$ −11.5000 + 19.9186i −0.442308 + 0.766099i
$$677$$ 25.0000 + 43.3013i 0.960828 + 1.66420i 0.720429 + 0.693529i $$0.243945\pi$$
0.240399 + 0.970674i $$0.422722\pi$$
$$678$$ 19.0000 0.729691
$$679$$ 0 0
$$680$$ −1.00000 −0.0383482
$$681$$ −8.00000 −0.306561
$$682$$ 5.50000 0.866025i 0.210606 0.0331618i
$$683$$ −4.00000 −0.153056 −0.0765279 0.997067i $$-0.524383\pi$$
−0.0765279 + 0.997067i $$0.524383\pi$$
$$684$$ 4.00000 0.152944
$$685$$ 3.50000 6.06218i 0.133728 0.231624i
$$686$$ 0 0
$$687$$ −10.0000 17.3205i −0.381524 0.660819i
$$688$$ 3.50000 6.06218i 0.133436 0.231118i
$$689$$ −12.0000 + 20.7846i −0.457164 + 0.791831i
$$690$$ 7.00000 0.266485
$$691$$ 11.0000 + 19.0526i 0.418460 + 0.724793i 0.995785 0.0917209i $$-0.0292368\pi$$
−0.577325 + 0.816514i $$0.695903\pi$$
$$692$$ −1.00000 1.73205i −0.0380143 0.0658427i
$$693$$ 0 0
$$694$$ 7.00000 12.1244i 0.265716 0.460234i
$$695$$ 5.00000 + 8.66025i 0.189661 + 0.328502i
$$696$$ −3.00000 + 5.19615i −0.113715 + 0.196960i
$$697$$ 2.00000 0.0757554
$$698$$ 18.0000 0.681310
$$699$$ −12.5000 + 21.6506i −0.472793 + 0.818902i
$$700$$ 0 0
$$701$$ −12.5000 + 21.6506i −0.472118 + 0.817733i −0.999491 0.0319010i $$-0.989844\pi$$
0.527373 + 0.849634i $$0.323177\pi$$
$$702$$ 3.00000 + 5.19615i 0.113228 + 0.196116i
$$703$$ −14.0000 24.2487i −0.528020 0.914557i
$$704$$ 0.500000 + 0.866025i 0.0188445 + 0.0326396i
$$705$$ 3.00000 0.112987
$$706$$ 5.50000 9.52628i 0.206995 0.358526i
$$707$$ 0 0
$$708$$ −6.00000 10.3923i −0.225494 0.390567i
$$709$$ −10.0000 −0.375558 −0.187779 0.982211i $$-0.560129\pi$$
−0.187779 + 0.982211i $$0.560129\pi$$
$$710$$ −3.00000 + 5.19615i −0.112588 + 0.195008i
$$711$$ 3.00000 0.112509
$$712$$ 4.00000 0.149906
$$713$$ 14.0000 36.3731i 0.524304 1.36218i
$$714$$ 0 0
$$715$$ 6.00000 0.224387
$$716$$ 5.50000 9.52628i 0.205545 0.356014i
$$717$$ 18.0000 0.672222
$$718$$ −10.0000 17.3205i −0.373197 0.646396i
$$719$$ −2.00000 + 3.46410i −0.0745874 + 0.129189i −0.900907 0.434013i $$-0.857097\pi$$
0.826319 + 0.563202i $$0.190431\pi$$
$$720$$ −0.500000 + 0.866025i −0.0186339 + 0.0322749i
$$721$$ 0 0
$$722$$ 1.50000 + 2.59808i 0.0558242 + 0.0966904i
$$723$$ −9.00000 15.5885i −0.334714 0.579741i
$$724$$ −10.0000 17.3205i −0.371647 0.643712i
$$725$$ −3.00000 + 5.19615i −0.111417 + 0.192980i
$$726$$ 5.00000 + 8.66025i 0.185567 + 0.321412i
$$727$$ −12.0000 + 20.7846i −0.445055 + 0.770859i −0.998056 0.0623223i $$-0.980149\pi$$
0.553001 + 0.833181i $$0.313483\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ −1.00000 + 1.73205i −0.0370117 + 0.0641061i
$$731$$ −3.50000 6.06218i −0.129452 0.224218i
$$732$$ 7.00000 12.1244i 0.258727 0.448129i
$$733$$ 17.5000 + 30.3109i 0.646377 + 1.11956i 0.983982 + 0.178270i $$0.0570501\pi$$
−0.337604 + 0.941288i $$0.609617\pi$$
$$734$$ 2.00000 + 3.46410i 0.0738213 + 0.127862i
$$735$$ 3.50000 + 6.06218i 0.129099 + 0.223607i
$$736$$ 7.00000 0.258023
$$737$$ 2.50000 4.33013i 0.0920887 0.159502i
$$738$$ 1.00000 1.73205i 0.0368105 0.0637577i
$$739$$ 19.0000 + 32.9090i 0.698926 + 1.21058i 0.968839 + 0.247691i $$0.0796718\pi$$
−0.269913 + 0.962885i $$0.586995\pi$$
$$740$$ 7.00000 0.257325
$$741$$ 12.0000 20.7846i 0.440831 0.763542i
$$742$$ 0 0
$$743$$ −27.0000 −0.990534 −0.495267 0.868741i $$-0.664930\pi$$
−0.495267 + 0.868741i $$0.664930\pi$$
$$744$$ 3.50000 + 4.33013i 0.128316 + 0.158750i
$$745$$ 14.0000 0.512920
$$746$$ −19.0000 −0.695639
$$747$$ −8.00000 + 13.8564i −0.292705 + 0.506979i
$$748$$ 1.00000 0.0365636
$$749$$ 0 0
$$750$$ −0.500000 + 0.866025i −0.0182574 + 0.0316228i
$$751$$ 12.5000 21.6506i 0.456131 0.790043i −0.542621 0.839978i $$-0.682568\pi$$
0.998752 + 0.0499348i $$0.0159013\pi$$
$$752$$ 3.00000 0.109399
$$753$$ −1.50000 2.59808i −0.0546630 0.0946792i
$$754$$ 18.0000 + 31.1769i 0.655521 + 1.13540i
$$755$$ 3.50000 + 6.06218i 0.127378 + 0.220625i
$$756$$ 0 0
$$757$$ 9.50000 + 16.4545i 0.345283 + 0.598048i 0.985405 0.170225i $$-0.0544495\pi$$
−0.640122 + 0.768273i $$0.721116\pi$$
$$758$$ −3.00000 + 5.19615i −0.108965 + 0.188733i
$$759$$ −7.00000 −0.254084
$$760$$ 4.00000 0.145095
$$761$$ 8.00000 13.8564i 0.290000 0.502294i −0.683810 0.729661i $$-0.739678\pi$$
0.973809 + 0.227366i $$0.0730114\pi$$
$$762$$ 9.00000 + 15.5885i 0.326036 + 0.564710i
$$763$$ 0 0
$$764$$ 3.00000 + 5.19615i 0.108536 + 0.187990i
$$765$$ 0.500000 + 0.866025i 0.0180775 + 0.0313112i
$$766$$ −9.50000 16.4545i −0.343249 0.594525i
$$767$$ −72.0000 −2.59977
$$768$$ −0.500000 + 0.866025i −0.0180422 + 0.0312500i
$$769$$ 13.0000 22.5167i 0.468792 0.811972i −0.530572 0.847640i $$-0.678023\pi$$
0.999364 + 0.0356685i $$0.0113561\pi$$
$$770$$ 0 0
$$771$$ 23.0000 0.828325
$$772$$ −5.00000 + 8.66025i −0.179954 + 0.311689i
$$773$$ −30.0000 −1.07903 −0.539513 0.841978i $$-0.681391\pi$$
−0.539513 + 0.841978i $$0.681391\pi$$
$$774$$ −7.00000 −0.251610
$$775$$ 3.50000 + 4.33013i 0.125724 +