# Properties

 Label 378.2.f.a.127.1 Level $378$ Weight $2$ Character 378.127 Analytic conductor $3.018$ Analytic rank $1$ Dimension $2$ CM no Inner twists $2$

# Learn more

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(127,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, 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("378.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$378 = 2 \cdot 3^{3} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 378.f (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: $$3.01834519640$$ Analytic rank: $$1$$ 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 126) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 127.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 378.127 Dual form 378.2.f.a.253.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})$$ $$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +3.00000 q^{10} +(-3.00000 + 5.19615i) q^{11} +(-1.00000 - 1.73205i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} -6.00000 q^{17} -7.00000 q^{19} +(-1.50000 + 2.59808i) q^{20} +(-3.00000 - 5.19615i) q^{22} +(1.50000 + 2.59808i) q^{23} +(-2.00000 + 3.46410i) q^{25} +2.00000 q^{26} +1.00000 q^{28} +(3.00000 - 5.19615i) q^{29} +(-1.00000 - 1.73205i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.00000 - 5.19615i) q^{34} +3.00000 q^{35} +2.00000 q^{37} +(3.50000 - 6.06218i) q^{38} +(-1.50000 - 2.59808i) q^{40} +(-1.00000 + 1.73205i) q^{43} +6.00000 q^{44} -3.00000 q^{46} +(-0.500000 - 0.866025i) q^{49} +(-2.00000 - 3.46410i) q^{50} +(-1.00000 + 1.73205i) q^{52} -6.00000 q^{53} +18.0000 q^{55} +(-0.500000 + 0.866025i) q^{56} +(3.00000 + 5.19615i) q^{58} +(-2.50000 + 4.33013i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(-3.00000 + 5.19615i) q^{65} +(-4.00000 - 6.92820i) q^{67} +(3.00000 + 5.19615i) q^{68} +(-1.50000 + 2.59808i) q^{70} -3.00000 q^{71} +2.00000 q^{73} +(-1.00000 + 1.73205i) q^{74} +(3.50000 + 6.06218i) q^{76} +(-3.00000 - 5.19615i) q^{77} +(-2.50000 + 4.33013i) q^{79} +3.00000 q^{80} +(6.00000 - 10.3923i) q^{83} +(9.00000 + 15.5885i) q^{85} +(-1.00000 - 1.73205i) q^{86} +(-3.00000 + 5.19615i) q^{88} +2.00000 q^{91} +(1.50000 - 2.59808i) q^{92} +(10.5000 + 18.1865i) q^{95} +(-1.00000 + 1.73205i) q^{97} +1.00000 q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - q^{2} - q^{4} - 3 q^{5} - q^{7} + 2 q^{8}+O(q^{10})$$ 2 * q - q^2 - q^4 - 3 * q^5 - q^7 + 2 * q^8 $$2 q - q^{2} - q^{4} - 3 q^{5} - q^{7} + 2 q^{8} + 6 q^{10} - 6 q^{11} - 2 q^{13} - q^{14} - q^{16} - 12 q^{17} - 14 q^{19} - 3 q^{20} - 6 q^{22} + 3 q^{23} - 4 q^{25} + 4 q^{26} + 2 q^{28} + 6 q^{29} - 2 q^{31} - q^{32} + 6 q^{34} + 6 q^{35} + 4 q^{37} + 7 q^{38} - 3 q^{40} - 2 q^{43} + 12 q^{44} - 6 q^{46} - q^{49} - 4 q^{50} - 2 q^{52} - 12 q^{53} + 36 q^{55} - q^{56} + 6 q^{58} - 5 q^{61} + 4 q^{62} + 2 q^{64} - 6 q^{65} - 8 q^{67} + 6 q^{68} - 3 q^{70} - 6 q^{71} + 4 q^{73} - 2 q^{74} + 7 q^{76} - 6 q^{77} - 5 q^{79} + 6 q^{80} + 12 q^{83} + 18 q^{85} - 2 q^{86} - 6 q^{88} + 4 q^{91} + 3 q^{92} + 21 q^{95} - 2 q^{97} + 2 q^{98}+O(q^{100})$$ 2 * q - q^2 - q^4 - 3 * q^5 - q^7 + 2 * q^8 + 6 * q^10 - 6 * q^11 - 2 * q^13 - q^14 - q^16 - 12 * q^17 - 14 * q^19 - 3 * q^20 - 6 * q^22 + 3 * q^23 - 4 * q^25 + 4 * q^26 + 2 * q^28 + 6 * q^29 - 2 * q^31 - q^32 + 6 * q^34 + 6 * q^35 + 4 * q^37 + 7 * q^38 - 3 * q^40 - 2 * q^43 + 12 * q^44 - 6 * q^46 - q^49 - 4 * q^50 - 2 * q^52 - 12 * q^53 + 36 * q^55 - q^56 + 6 * q^58 - 5 * q^61 + 4 * q^62 + 2 * q^64 - 6 * q^65 - 8 * q^67 + 6 * q^68 - 3 * q^70 - 6 * q^71 + 4 * q^73 - 2 * q^74 + 7 * q^76 - 6 * q^77 - 5 * q^79 + 6 * q^80 + 12 * q^83 + 18 * q^85 - 2 * q^86 - 6 * q^88 + 4 * q^91 + 3 * q^92 + 21 * q^95 - 2 * q^97 + 2 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$$.

 $$n$$ $$29$$ $$325$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$

## 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 0
$$4$$ −0.500000 0.866025i −0.250000 0.433013i
$$5$$ −1.50000 2.59808i −0.670820 1.16190i −0.977672 0.210138i $$-0.932609\pi$$
0.306851 0.951757i $$-0.400725\pi$$
$$6$$ 0 0
$$7$$ −0.500000 + 0.866025i −0.188982 + 0.327327i
$$8$$ 1.00000 0.353553
$$9$$ 0 0
$$10$$ 3.00000 0.948683
$$11$$ −3.00000 + 5.19615i −0.904534 + 1.56670i −0.0829925 + 0.996550i $$0.526448\pi$$
−0.821541 + 0.570149i $$0.806886\pi$$
$$12$$ 0 0
$$13$$ −1.00000 1.73205i −0.277350 0.480384i 0.693375 0.720577i $$-0.256123\pi$$
−0.970725 + 0.240192i $$0.922790\pi$$
$$14$$ −0.500000 0.866025i −0.133631 0.231455i
$$15$$ 0 0
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ −6.00000 −1.45521 −0.727607 0.685994i $$-0.759367\pi$$
−0.727607 + 0.685994i $$0.759367\pi$$
$$18$$ 0 0
$$19$$ −7.00000 −1.60591 −0.802955 0.596040i $$-0.796740\pi$$
−0.802955 + 0.596040i $$0.796740\pi$$
$$20$$ −1.50000 + 2.59808i −0.335410 + 0.580948i
$$21$$ 0 0
$$22$$ −3.00000 5.19615i −0.639602 1.10782i
$$23$$ 1.50000 + 2.59808i 0.312772 + 0.541736i 0.978961 0.204046i $$-0.0654092\pi$$
−0.666190 + 0.745782i $$0.732076\pi$$
$$24$$ 0 0
$$25$$ −2.00000 + 3.46410i −0.400000 + 0.692820i
$$26$$ 2.00000 0.392232
$$27$$ 0 0
$$28$$ 1.00000 0.188982
$$29$$ 3.00000 5.19615i 0.557086 0.964901i −0.440652 0.897678i $$-0.645253\pi$$
0.997738 0.0672232i $$-0.0214140\pi$$
$$30$$ 0 0
$$31$$ −1.00000 1.73205i −0.179605 0.311086i 0.762140 0.647412i $$-0.224149\pi$$
−0.941745 + 0.336327i $$0.890815\pi$$
$$32$$ −0.500000 0.866025i −0.0883883 0.153093i
$$33$$ 0 0
$$34$$ 3.00000 5.19615i 0.514496 0.891133i
$$35$$ 3.00000 0.507093
$$36$$ 0 0
$$37$$ 2.00000 0.328798 0.164399 0.986394i $$-0.447432\pi$$
0.164399 + 0.986394i $$0.447432\pi$$
$$38$$ 3.50000 6.06218i 0.567775 0.983415i
$$39$$ 0 0
$$40$$ −1.50000 2.59808i −0.237171 0.410792i
$$41$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$42$$ 0 0
$$43$$ −1.00000 + 1.73205i −0.152499 + 0.264135i −0.932145 0.362084i $$-0.882065\pi$$
0.779647 + 0.626219i $$0.215399\pi$$
$$44$$ 6.00000 0.904534
$$45$$ 0 0
$$46$$ −3.00000 −0.442326
$$47$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$48$$ 0 0
$$49$$ −0.500000 0.866025i −0.0714286 0.123718i
$$50$$ −2.00000 3.46410i −0.282843 0.489898i
$$51$$ 0 0
$$52$$ −1.00000 + 1.73205i −0.138675 + 0.240192i
$$53$$ −6.00000 −0.824163 −0.412082 0.911147i $$-0.635198\pi$$
−0.412082 + 0.911147i $$0.635198\pi$$
$$54$$ 0 0
$$55$$ 18.0000 2.42712
$$56$$ −0.500000 + 0.866025i −0.0668153 + 0.115728i
$$57$$ 0 0
$$58$$ 3.00000 + 5.19615i 0.393919 + 0.682288i
$$59$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$60$$ 0 0
$$61$$ −2.50000 + 4.33013i −0.320092 + 0.554416i −0.980507 0.196485i $$-0.937047\pi$$
0.660415 + 0.750901i $$0.270381\pi$$
$$62$$ 2.00000 0.254000
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ −3.00000 + 5.19615i −0.372104 + 0.644503i
$$66$$ 0 0
$$67$$ −4.00000 6.92820i −0.488678 0.846415i 0.511237 0.859440i $$-0.329187\pi$$
−0.999915 + 0.0130248i $$0.995854\pi$$
$$68$$ 3.00000 + 5.19615i 0.363803 + 0.630126i
$$69$$ 0 0
$$70$$ −1.50000 + 2.59808i −0.179284 + 0.310530i
$$71$$ −3.00000 −0.356034 −0.178017 0.984027i $$-0.556968\pi$$
−0.178017 + 0.984027i $$0.556968\pi$$
$$72$$ 0 0
$$73$$ 2.00000 0.234082 0.117041 0.993127i $$-0.462659\pi$$
0.117041 + 0.993127i $$0.462659\pi$$
$$74$$ −1.00000 + 1.73205i −0.116248 + 0.201347i
$$75$$ 0 0
$$76$$ 3.50000 + 6.06218i 0.401478 + 0.695379i
$$77$$ −3.00000 5.19615i −0.341882 0.592157i
$$78$$ 0 0
$$79$$ −2.50000 + 4.33013i −0.281272 + 0.487177i −0.971698 0.236225i $$-0.924090\pi$$
0.690426 + 0.723403i $$0.257423\pi$$
$$80$$ 3.00000 0.335410
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 6.00000 10.3923i 0.658586 1.14070i −0.322396 0.946605i $$-0.604488\pi$$
0.980982 0.194099i $$-0.0621783\pi$$
$$84$$ 0 0
$$85$$ 9.00000 + 15.5885i 0.976187 + 1.69081i
$$86$$ −1.00000 1.73205i −0.107833 0.186772i
$$87$$ 0 0
$$88$$ −3.00000 + 5.19615i −0.319801 + 0.553912i
$$89$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$90$$ 0 0
$$91$$ 2.00000 0.209657
$$92$$ 1.50000 2.59808i 0.156386 0.270868i
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 10.5000 + 18.1865i 1.07728 + 1.86590i
$$96$$ 0 0
$$97$$ −1.00000 + 1.73205i −0.101535 + 0.175863i −0.912317 0.409484i $$-0.865709\pi$$
0.810782 + 0.585348i $$0.199042\pi$$
$$98$$ 1.00000 0.101015
$$99$$ 0 0
$$100$$ 4.00000 0.400000
$$101$$ 4.50000 7.79423i 0.447767 0.775555i −0.550474 0.834853i $$-0.685553\pi$$
0.998240 + 0.0592978i $$0.0188862\pi$$
$$102$$ 0 0
$$103$$ 5.00000 + 8.66025i 0.492665 + 0.853320i 0.999964 0.00844953i $$-0.00268960\pi$$
−0.507300 + 0.861770i $$0.669356\pi$$
$$104$$ −1.00000 1.73205i −0.0980581 0.169842i
$$105$$ 0 0
$$106$$ 3.00000 5.19615i 0.291386 0.504695i
$$107$$ 12.0000 1.16008 0.580042 0.814587i $$-0.303036\pi$$
0.580042 + 0.814587i $$0.303036\pi$$
$$108$$ 0 0
$$109$$ −10.0000 −0.957826 −0.478913 0.877862i $$-0.658969\pi$$
−0.478913 + 0.877862i $$0.658969\pi$$
$$110$$ −9.00000 + 15.5885i −0.858116 + 1.48630i
$$111$$ 0 0
$$112$$ −0.500000 0.866025i −0.0472456 0.0818317i
$$113$$ 7.50000 + 12.9904i 0.705541 + 1.22203i 0.966496 + 0.256681i $$0.0826291\pi$$
−0.260955 + 0.965351i $$0.584038\pi$$
$$114$$ 0 0
$$115$$ 4.50000 7.79423i 0.419627 0.726816i
$$116$$ −6.00000 −0.557086
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 3.00000 5.19615i 0.275010 0.476331i
$$120$$ 0 0
$$121$$ −12.5000 21.6506i −1.13636 1.96824i
$$122$$ −2.50000 4.33013i −0.226339 0.392031i
$$123$$ 0 0
$$124$$ −1.00000 + 1.73205i −0.0898027 + 0.155543i
$$125$$ −3.00000 −0.268328
$$126$$ 0 0
$$127$$ 17.0000 1.50851 0.754253 0.656584i $$-0.227999\pi$$
0.754253 + 0.656584i $$0.227999\pi$$
$$128$$ −0.500000 + 0.866025i −0.0441942 + 0.0765466i
$$129$$ 0 0
$$130$$ −3.00000 5.19615i −0.263117 0.455733i
$$131$$ −4.50000 7.79423i −0.393167 0.680985i 0.599699 0.800226i $$-0.295287\pi$$
−0.992865 + 0.119241i $$0.961954\pi$$
$$132$$ 0 0
$$133$$ 3.50000 6.06218i 0.303488 0.525657i
$$134$$ 8.00000 0.691095
$$135$$ 0 0
$$136$$ −6.00000 −0.514496
$$137$$ 3.00000 5.19615i 0.256307 0.443937i −0.708942 0.705266i $$-0.750827\pi$$
0.965250 + 0.261329i $$0.0841608\pi$$
$$138$$ 0 0
$$139$$ −2.50000 4.33013i −0.212047 0.367277i 0.740308 0.672268i $$-0.234680\pi$$
−0.952355 + 0.304991i $$0.901346\pi$$
$$140$$ −1.50000 2.59808i −0.126773 0.219578i
$$141$$ 0 0
$$142$$ 1.50000 2.59808i 0.125877 0.218026i
$$143$$ 12.0000 1.00349
$$144$$ 0 0
$$145$$ −18.0000 −1.49482
$$146$$ −1.00000 + 1.73205i −0.0827606 + 0.143346i
$$147$$ 0 0
$$148$$ −1.00000 1.73205i −0.0821995 0.142374i
$$149$$ −3.00000 5.19615i −0.245770 0.425685i 0.716578 0.697507i $$-0.245707\pi$$
−0.962348 + 0.271821i $$0.912374\pi$$
$$150$$ 0 0
$$151$$ −11.5000 + 19.9186i −0.935857 + 1.62095i −0.162758 + 0.986666i $$0.552039\pi$$
−0.773099 + 0.634285i $$0.781294\pi$$
$$152$$ −7.00000 −0.567775
$$153$$ 0 0
$$154$$ 6.00000 0.483494
$$155$$ −3.00000 + 5.19615i −0.240966 + 0.417365i
$$156$$ 0 0
$$157$$ 6.50000 + 11.2583i 0.518756 + 0.898513i 0.999762 + 0.0217953i $$0.00693820\pi$$
−0.481006 + 0.876717i $$0.659728\pi$$
$$158$$ −2.50000 4.33013i −0.198889 0.344486i
$$159$$ 0 0
$$160$$ −1.50000 + 2.59808i −0.118585 + 0.205396i
$$161$$ −3.00000 −0.236433
$$162$$ 0 0
$$163$$ 2.00000 0.156652 0.0783260 0.996928i $$-0.475042\pi$$
0.0783260 + 0.996928i $$0.475042\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 6.00000 + 10.3923i 0.465690 + 0.806599i
$$167$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$168$$ 0 0
$$169$$ 4.50000 7.79423i 0.346154 0.599556i
$$170$$ −18.0000 −1.38054
$$171$$ 0 0
$$172$$ 2.00000 0.152499
$$173$$ −3.00000 + 5.19615i −0.228086 + 0.395056i −0.957241 0.289292i $$-0.906580\pi$$
0.729155 + 0.684349i $$0.239913\pi$$
$$174$$ 0 0
$$175$$ −2.00000 3.46410i −0.151186 0.261861i
$$176$$ −3.00000 5.19615i −0.226134 0.391675i
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −18.0000 −1.34538 −0.672692 0.739923i $$-0.734862\pi$$
−0.672692 + 0.739923i $$0.734862\pi$$
$$180$$ 0 0
$$181$$ −25.0000 −1.85824 −0.929118 0.369784i $$-0.879432\pi$$
−0.929118 + 0.369784i $$0.879432\pi$$
$$182$$ −1.00000 + 1.73205i −0.0741249 + 0.128388i
$$183$$ 0 0
$$184$$ 1.50000 + 2.59808i 0.110581 + 0.191533i
$$185$$ −3.00000 5.19615i −0.220564 0.382029i
$$186$$ 0 0
$$187$$ 18.0000 31.1769i 1.31629 2.27988i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ −21.0000 −1.52350
$$191$$ −4.50000 + 7.79423i −0.325609 + 0.563971i −0.981635 0.190767i $$-0.938902\pi$$
0.656027 + 0.754738i $$0.272236\pi$$
$$192$$ 0 0
$$193$$ −8.50000 14.7224i −0.611843 1.05974i −0.990930 0.134382i $$-0.957095\pi$$
0.379086 0.925361i $$-0.376238\pi$$
$$194$$ −1.00000 1.73205i −0.0717958 0.124354i
$$195$$ 0 0
$$196$$ −0.500000 + 0.866025i −0.0357143 + 0.0618590i
$$197$$ −18.0000 −1.28245 −0.641223 0.767354i $$-0.721573\pi$$
−0.641223 + 0.767354i $$0.721573\pi$$
$$198$$ 0 0
$$199$$ 14.0000 0.992434 0.496217 0.868199i $$-0.334722\pi$$
0.496217 + 0.868199i $$0.334722\pi$$
$$200$$ −2.00000 + 3.46410i −0.141421 + 0.244949i
$$201$$ 0 0
$$202$$ 4.50000 + 7.79423i 0.316619 + 0.548400i
$$203$$ 3.00000 + 5.19615i 0.210559 + 0.364698i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ −10.0000 −0.696733
$$207$$ 0 0
$$208$$ 2.00000 0.138675
$$209$$ 21.0000 36.3731i 1.45260 2.51598i
$$210$$ 0 0
$$211$$ −4.00000 6.92820i −0.275371 0.476957i 0.694857 0.719148i $$-0.255467\pi$$
−0.970229 + 0.242190i $$0.922134\pi$$
$$212$$ 3.00000 + 5.19615i 0.206041 + 0.356873i
$$213$$ 0 0
$$214$$ −6.00000 + 10.3923i −0.410152 + 0.710403i
$$215$$ 6.00000 0.409197
$$216$$ 0 0
$$217$$ 2.00000 0.135769
$$218$$ 5.00000 8.66025i 0.338643 0.586546i
$$219$$ 0 0
$$220$$ −9.00000 15.5885i −0.606780 1.05097i
$$221$$ 6.00000 + 10.3923i 0.403604 + 0.699062i
$$222$$ 0 0
$$223$$ 14.0000 24.2487i 0.937509 1.62381i 0.167412 0.985887i $$-0.446459\pi$$
0.770097 0.637927i $$-0.220208\pi$$
$$224$$ 1.00000 0.0668153
$$225$$ 0 0
$$226$$ −15.0000 −0.997785
$$227$$ −7.50000 + 12.9904i −0.497792 + 0.862202i −0.999997 0.00254715i $$-0.999189\pi$$
0.502204 + 0.864749i $$0.332523\pi$$
$$228$$ 0 0
$$229$$ 0.500000 + 0.866025i 0.0330409 + 0.0572286i 0.882073 0.471113i $$-0.156147\pi$$
−0.849032 + 0.528341i $$0.822814\pi$$
$$230$$ 4.50000 + 7.79423i 0.296721 + 0.513936i
$$231$$ 0 0
$$232$$ 3.00000 5.19615i 0.196960 0.341144i
$$233$$ −9.00000 −0.589610 −0.294805 0.955557i $$-0.595255\pi$$
−0.294805 + 0.955557i $$0.595255\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 3.00000 + 5.19615i 0.194461 + 0.336817i
$$239$$ −7.50000 12.9904i −0.485135 0.840278i 0.514719 0.857359i $$-0.327896\pi$$
−0.999854 + 0.0170808i $$0.994563\pi$$
$$240$$ 0 0
$$241$$ −4.00000 + 6.92820i −0.257663 + 0.446285i −0.965615 0.259975i $$-0.916286\pi$$
0.707953 + 0.706260i $$0.249619\pi$$
$$242$$ 25.0000 1.60706
$$243$$ 0 0
$$244$$ 5.00000 0.320092
$$245$$ −1.50000 + 2.59808i −0.0958315 + 0.165985i
$$246$$ 0 0
$$247$$ 7.00000 + 12.1244i 0.445399 + 0.771454i
$$248$$ −1.00000 1.73205i −0.0635001 0.109985i
$$249$$ 0 0
$$250$$ 1.50000 2.59808i 0.0948683 0.164317i
$$251$$ −3.00000 −0.189358 −0.0946792 0.995508i $$-0.530183\pi$$
−0.0946792 + 0.995508i $$0.530183\pi$$
$$252$$ 0 0
$$253$$ −18.0000 −1.13165
$$254$$ −8.50000 + 14.7224i −0.533337 + 0.923768i
$$255$$ 0 0
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ 9.00000 + 15.5885i 0.561405 + 0.972381i 0.997374 + 0.0724199i $$0.0230722\pi$$
−0.435970 + 0.899961i $$0.643595\pi$$
$$258$$ 0 0
$$259$$ −1.00000 + 1.73205i −0.0621370 + 0.107624i
$$260$$ 6.00000 0.372104
$$261$$ 0 0
$$262$$ 9.00000 0.556022
$$263$$ −10.5000 + 18.1865i −0.647458 + 1.12143i 0.336270 + 0.941766i $$0.390834\pi$$
−0.983728 + 0.179664i $$0.942499\pi$$
$$264$$ 0 0
$$265$$ 9.00000 + 15.5885i 0.552866 + 0.957591i
$$266$$ 3.50000 + 6.06218i 0.214599 + 0.371696i
$$267$$ 0 0
$$268$$ −4.00000 + 6.92820i −0.244339 + 0.423207i
$$269$$ 9.00000 0.548740 0.274370 0.961624i $$-0.411531\pi$$
0.274370 + 0.961624i $$0.411531\pi$$
$$270$$ 0 0
$$271$$ −28.0000 −1.70088 −0.850439 0.526073i $$-0.823664\pi$$
−0.850439 + 0.526073i $$0.823664\pi$$
$$272$$ 3.00000 5.19615i 0.181902 0.315063i
$$273$$ 0 0
$$274$$ 3.00000 + 5.19615i 0.181237 + 0.313911i
$$275$$ −12.0000 20.7846i −0.723627 1.25336i
$$276$$ 0 0
$$277$$ 8.00000 13.8564i 0.480673 0.832551i −0.519081 0.854725i $$-0.673726\pi$$
0.999754 + 0.0221745i $$0.00705893\pi$$
$$278$$ 5.00000 0.299880
$$279$$ 0 0
$$280$$ 3.00000 0.179284
$$281$$ −13.5000 + 23.3827i −0.805342 + 1.39489i 0.110717 + 0.993852i $$0.464685\pi$$
−0.916060 + 0.401042i $$0.868648\pi$$
$$282$$ 0 0
$$283$$ 9.50000 + 16.4545i 0.564716 + 0.978117i 0.997076 + 0.0764162i $$0.0243478\pi$$
−0.432360 + 0.901701i $$0.642319\pi$$
$$284$$ 1.50000 + 2.59808i 0.0890086 + 0.154167i
$$285$$ 0 0
$$286$$ −6.00000 + 10.3923i −0.354787 + 0.614510i
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 19.0000 1.11765
$$290$$ 9.00000 15.5885i 0.528498 0.915386i
$$291$$ 0 0
$$292$$ −1.00000 1.73205i −0.0585206 0.101361i
$$293$$ −1.50000 2.59808i −0.0876309 0.151781i 0.818878 0.573967i $$-0.194596\pi$$
−0.906509 + 0.422186i $$0.861263\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 2.00000 0.116248
$$297$$ 0 0
$$298$$ 6.00000 0.347571
$$299$$ 3.00000 5.19615i 0.173494 0.300501i
$$300$$ 0 0
$$301$$ −1.00000 1.73205i −0.0576390 0.0998337i
$$302$$ −11.5000 19.9186i −0.661751 1.14619i
$$303$$ 0 0
$$304$$ 3.50000 6.06218i 0.200739 0.347690i
$$305$$ 15.0000 0.858898
$$306$$ 0 0
$$307$$ −25.0000 −1.42683 −0.713413 0.700744i $$-0.752851\pi$$
−0.713413 + 0.700744i $$0.752851\pi$$
$$308$$ −3.00000 + 5.19615i −0.170941 + 0.296078i
$$309$$ 0 0
$$310$$ −3.00000 5.19615i −0.170389 0.295122i
$$311$$ 6.00000 + 10.3923i 0.340229 + 0.589294i 0.984475 0.175525i $$-0.0561621\pi$$
−0.644246 + 0.764818i $$0.722829\pi$$
$$312$$ 0 0
$$313$$ 5.00000 8.66025i 0.282617 0.489506i −0.689412 0.724370i $$-0.742131\pi$$
0.972028 + 0.234863i $$0.0754642\pi$$
$$314$$ −13.0000 −0.733632
$$315$$ 0 0
$$316$$ 5.00000 0.281272
$$317$$ 9.00000 15.5885i 0.505490 0.875535i −0.494489 0.869184i $$-0.664645\pi$$
0.999980 0.00635137i $$-0.00202172\pi$$
$$318$$ 0 0
$$319$$ 18.0000 + 31.1769i 1.00781 + 1.74557i
$$320$$ −1.50000 2.59808i −0.0838525 0.145237i
$$321$$ 0 0
$$322$$ 1.50000 2.59808i 0.0835917 0.144785i
$$323$$ 42.0000 2.33694
$$324$$ 0 0
$$325$$ 8.00000 0.443760
$$326$$ −1.00000 + 1.73205i −0.0553849 + 0.0959294i
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −13.0000 + 22.5167i −0.714545 + 1.23763i 0.248590 + 0.968609i $$0.420033\pi$$
−0.963135 + 0.269019i $$0.913301\pi$$
$$332$$ −12.0000 −0.658586
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −12.0000 + 20.7846i −0.655630 + 1.13558i
$$336$$ 0 0
$$337$$ 11.0000 + 19.0526i 0.599208 + 1.03786i 0.992938 + 0.118633i $$0.0378512\pi$$
−0.393730 + 0.919226i $$0.628816\pi$$
$$338$$ 4.50000 + 7.79423i 0.244768 + 0.423950i
$$339$$ 0 0
$$340$$ 9.00000 15.5885i 0.488094 0.845403i
$$341$$ 12.0000 0.649836
$$342$$ 0 0
$$343$$ 1.00000 0.0539949
$$344$$ −1.00000 + 1.73205i −0.0539164 + 0.0933859i
$$345$$ 0 0
$$346$$ −3.00000 5.19615i −0.161281 0.279347i
$$347$$ −12.0000 20.7846i −0.644194 1.11578i −0.984487 0.175457i $$-0.943860\pi$$
0.340293 0.940319i $$-0.389474\pi$$
$$348$$ 0 0
$$349$$ −13.0000 + 22.5167i −0.695874 + 1.20529i 0.274011 + 0.961727i $$0.411649\pi$$
−0.969885 + 0.243563i $$0.921684\pi$$
$$350$$ 4.00000 0.213809
$$351$$ 0 0
$$352$$ 6.00000 0.319801
$$353$$ −9.00000 + 15.5885i −0.479022 + 0.829690i −0.999711 0.0240566i $$-0.992342\pi$$
0.520689 + 0.853746i $$0.325675\pi$$
$$354$$ 0 0
$$355$$ 4.50000 + 7.79423i 0.238835 + 0.413675i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 9.00000 15.5885i 0.475665 0.823876i
$$359$$ 3.00000 0.158334 0.0791670 0.996861i $$-0.474774\pi$$
0.0791670 + 0.996861i $$0.474774\pi$$
$$360$$ 0 0
$$361$$ 30.0000 1.57895
$$362$$ 12.5000 21.6506i 0.656985 1.13793i
$$363$$ 0 0
$$364$$ −1.00000 1.73205i −0.0524142 0.0907841i
$$365$$ −3.00000 5.19615i −0.157027 0.271979i
$$366$$ 0 0
$$367$$ −4.00000 + 6.92820i −0.208798 + 0.361649i −0.951336 0.308155i $$-0.900289\pi$$
0.742538 + 0.669804i $$0.233622\pi$$
$$368$$ −3.00000 −0.156386
$$369$$ 0 0
$$370$$ 6.00000 0.311925
$$371$$ 3.00000 5.19615i 0.155752 0.269771i
$$372$$ 0 0
$$373$$ −7.00000 12.1244i −0.362446 0.627775i 0.625917 0.779890i $$-0.284725\pi$$
−0.988363 + 0.152115i $$0.951392\pi$$
$$374$$ 18.0000 + 31.1769i 0.930758 + 1.61212i
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −12.0000 −0.618031
$$378$$ 0 0
$$379$$ 2.00000 0.102733 0.0513665 0.998680i $$-0.483642\pi$$
0.0513665 + 0.998680i $$0.483642\pi$$
$$380$$ 10.5000 18.1865i 0.538639 0.932949i
$$381$$ 0 0
$$382$$ −4.50000 7.79423i −0.230240 0.398787i
$$383$$ −9.00000 15.5885i −0.459879 0.796533i 0.539076 0.842257i $$-0.318774\pi$$
−0.998954 + 0.0457244i $$0.985440\pi$$
$$384$$ 0 0
$$385$$ −9.00000 + 15.5885i −0.458682 + 0.794461i
$$386$$ 17.0000 0.865277
$$387$$ 0 0
$$388$$ 2.00000 0.101535
$$389$$ 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
$$391$$ −9.00000 15.5885i −0.455150 0.788342i
$$392$$ −0.500000 0.866025i −0.0252538 0.0437409i
$$393$$ 0 0
$$394$$ 9.00000 15.5885i 0.453413 0.785335i
$$395$$ 15.0000 0.754732
$$396$$ 0 0
$$397$$ 26.0000 1.30490 0.652451 0.757831i $$-0.273741\pi$$
0.652451 + 0.757831i $$0.273741\pi$$
$$398$$ −7.00000 + 12.1244i −0.350878 + 0.607739i
$$399$$ 0 0
$$400$$ −2.00000 3.46410i −0.100000 0.173205i
$$401$$ 1.50000 + 2.59808i 0.0749064 + 0.129742i 0.901046 0.433724i $$-0.142801\pi$$
−0.826139 + 0.563466i $$0.809468\pi$$
$$402$$ 0 0
$$403$$ −2.00000 + 3.46410i −0.0996271 + 0.172559i
$$404$$ −9.00000 −0.447767
$$405$$ 0 0
$$406$$ −6.00000 −0.297775
$$407$$ −6.00000 + 10.3923i −0.297409 + 0.515127i
$$408$$ 0 0
$$409$$ −16.0000 27.7128i −0.791149 1.37031i −0.925256 0.379344i $$-0.876150\pi$$
0.134107 0.990967i $$-0.457183\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 5.00000 8.66025i 0.246332 0.426660i
$$413$$ 0 0
$$414$$ 0 0
$$415$$ −36.0000 −1.76717
$$416$$ −1.00000 + 1.73205i −0.0490290 + 0.0849208i
$$417$$ 0 0
$$418$$ 21.0000 + 36.3731i 1.02714 + 1.77906i
$$419$$ 7.50000 + 12.9904i 0.366399 + 0.634622i 0.989000 0.147918i $$-0.0472572\pi$$
−0.622601 + 0.782540i $$0.713924\pi$$
$$420$$ 0 0
$$421$$ 5.00000 8.66025i 0.243685 0.422075i −0.718076 0.695965i $$-0.754977\pi$$
0.961761 + 0.273890i $$0.0883103\pi$$
$$422$$ 8.00000 0.389434
$$423$$ 0 0
$$424$$ −6.00000 −0.291386
$$425$$ 12.0000 20.7846i 0.582086 1.00820i
$$426$$ 0 0
$$427$$ −2.50000 4.33013i −0.120983 0.209550i
$$428$$ −6.00000 10.3923i −0.290021 0.502331i
$$429$$ 0 0
$$430$$ −3.00000 + 5.19615i −0.144673 + 0.250581i
$$431$$ −12.0000 −0.578020 −0.289010 0.957326i $$-0.593326\pi$$
−0.289010 + 0.957326i $$0.593326\pi$$
$$432$$ 0 0
$$433$$ 14.0000 0.672797 0.336399 0.941720i $$-0.390791\pi$$
0.336399 + 0.941720i $$0.390791\pi$$
$$434$$ −1.00000 + 1.73205i −0.0480015 + 0.0831411i
$$435$$ 0 0
$$436$$ 5.00000 + 8.66025i 0.239457 + 0.414751i
$$437$$ −10.5000 18.1865i −0.502283 0.869980i
$$438$$ 0 0
$$439$$ −4.00000 + 6.92820i −0.190910 + 0.330665i −0.945552 0.325471i $$-0.894477\pi$$
0.754642 + 0.656136i $$0.227810\pi$$
$$440$$ 18.0000 0.858116
$$441$$ 0 0
$$442$$ −12.0000 −0.570782
$$443$$ 9.00000 15.5885i 0.427603 0.740630i −0.569057 0.822298i $$-0.692691\pi$$
0.996660 + 0.0816684i $$0.0260248\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 14.0000 + 24.2487i 0.662919 + 1.14821i
$$447$$ 0 0
$$448$$ −0.500000 + 0.866025i −0.0236228 + 0.0409159i
$$449$$ −33.0000 −1.55737 −0.778683 0.627417i $$-0.784112\pi$$
−0.778683 + 0.627417i $$0.784112\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 7.50000 12.9904i 0.352770 0.611016i
$$453$$ 0 0
$$454$$ −7.50000 12.9904i −0.351992 0.609669i
$$455$$ −3.00000 5.19615i −0.140642 0.243599i
$$456$$ 0 0
$$457$$ −14.5000 + 25.1147i −0.678281 + 1.17482i 0.297217 + 0.954810i $$0.403942\pi$$
−0.975498 + 0.220008i $$0.929392\pi$$
$$458$$ −1.00000 −0.0467269
$$459$$ 0 0
$$460$$ −9.00000 −0.419627
$$461$$ −16.5000 + 28.5788i −0.768482 + 1.33105i 0.169904 + 0.985461i $$0.445654\pi$$
−0.938386 + 0.345589i $$0.887679\pi$$
$$462$$ 0 0
$$463$$ 6.50000 + 11.2583i 0.302081 + 0.523219i 0.976607 0.215032i $$-0.0689855\pi$$
−0.674526 + 0.738251i $$0.735652\pi$$
$$464$$ 3.00000 + 5.19615i 0.139272 + 0.241225i
$$465$$ 0 0
$$466$$ 4.50000 7.79423i 0.208458 0.361061i
$$467$$ −12.0000 −0.555294 −0.277647 0.960683i $$-0.589555\pi$$
−0.277647 + 0.960683i $$0.589555\pi$$
$$468$$ 0 0
$$469$$ 8.00000 0.369406
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −6.00000 10.3923i −0.275880 0.477839i
$$474$$ 0 0
$$475$$ 14.0000 24.2487i 0.642364 1.11261i
$$476$$ −6.00000 −0.275010
$$477$$ 0 0
$$478$$ 15.0000 0.686084
$$479$$ −3.00000 + 5.19615i −0.137073 + 0.237418i −0.926388 0.376571i $$-0.877103\pi$$
0.789314 + 0.613990i $$0.210436\pi$$
$$480$$ 0 0
$$481$$ −2.00000 3.46410i −0.0911922 0.157949i
$$482$$ −4.00000 6.92820i −0.182195 0.315571i
$$483$$ 0 0
$$484$$ −12.5000 + 21.6506i −0.568182 + 0.984120i
$$485$$ 6.00000 0.272446
$$486$$ 0 0
$$487$$ 29.0000 1.31412 0.657058 0.753840i $$-0.271801\pi$$
0.657058 + 0.753840i $$0.271801\pi$$
$$488$$ −2.50000 + 4.33013i −0.113170 + 0.196016i
$$489$$ 0 0
$$490$$ −1.50000 2.59808i −0.0677631 0.117369i
$$491$$ 9.00000 + 15.5885i 0.406164 + 0.703497i 0.994456 0.105151i $$-0.0335327\pi$$
−0.588292 + 0.808649i $$0.700199\pi$$
$$492$$ 0 0
$$493$$ −18.0000 + 31.1769i −0.810679 + 1.40414i
$$494$$ −14.0000 −0.629890
$$495$$ 0 0
$$496$$ 2.00000 0.0898027
$$497$$ 1.50000 2.59808i 0.0672842 0.116540i
$$498$$ 0 0
$$499$$ −16.0000 27.7128i −0.716258 1.24060i −0.962472 0.271380i $$-0.912520\pi$$
0.246214 0.969216i $$-0.420813\pi$$
$$500$$ 1.50000 + 2.59808i 0.0670820 + 0.116190i
$$501$$ 0 0
$$502$$ 1.50000 2.59808i 0.0669483 0.115958i
$$503$$ −12.0000 −0.535054 −0.267527 0.963550i $$-0.586206\pi$$
−0.267527 + 0.963550i $$0.586206\pi$$
$$504$$ 0 0
$$505$$ −27.0000 −1.20148
$$506$$ 9.00000 15.5885i 0.400099 0.692991i
$$507$$ 0 0
$$508$$ −8.50000 14.7224i −0.377127 0.653202i
$$509$$ 15.0000 + 25.9808i 0.664863 + 1.15158i 0.979322 + 0.202306i $$0.0648436\pi$$
−0.314459 + 0.949271i $$0.601823\pi$$
$$510$$ 0 0
$$511$$ −1.00000 + 1.73205i −0.0442374 + 0.0766214i
$$512$$ 1.00000 0.0441942
$$513$$ 0 0
$$514$$ −18.0000 −0.793946
$$515$$ 15.0000 25.9808i 0.660979 1.14485i
$$516$$ 0 0
$$517$$ 0 0
$$518$$ −1.00000 1.73205i −0.0439375 0.0761019i
$$519$$ 0 0
$$520$$ −3.00000 + 5.19615i −0.131559 + 0.227866i
$$521$$ −24.0000 −1.05146 −0.525730 0.850652i $$-0.676208\pi$$
−0.525730 + 0.850652i $$0.676208\pi$$
$$522$$ 0 0
$$523$$ −13.0000 −0.568450 −0.284225 0.958758i $$-0.591736\pi$$
−0.284225 + 0.958758i $$0.591736\pi$$
$$524$$ −4.50000 + 7.79423i −0.196583 + 0.340492i
$$525$$ 0 0
$$526$$ −10.5000 18.1865i −0.457822 0.792971i
$$527$$ 6.00000 + 10.3923i 0.261364 + 0.452696i
$$528$$ 0 0
$$529$$ 7.00000 12.1244i 0.304348 0.527146i
$$530$$ −18.0000 −0.781870
$$531$$ 0 0
$$532$$ −7.00000 −0.303488
$$533$$ 0 0
$$534$$ 0 0
$$535$$ −18.0000 31.1769i −0.778208 1.34790i
$$536$$ −4.00000 6.92820i −0.172774 0.299253i
$$537$$ 0 0
$$538$$ −4.50000 + 7.79423i −0.194009 + 0.336033i
$$539$$ 6.00000 0.258438
$$540$$ 0 0
$$541$$ 38.0000 1.63375 0.816874 0.576816i $$-0.195705\pi$$
0.816874 + 0.576816i $$0.195705\pi$$
$$542$$ 14.0000 24.2487i 0.601351 1.04157i
$$543$$ 0 0
$$544$$ 3.00000 + 5.19615i 0.128624 + 0.222783i
$$545$$ 15.0000 + 25.9808i 0.642529 + 1.11289i
$$546$$ 0 0
$$547$$ −16.0000 + 27.7128i −0.684111 + 1.18491i 0.289605 + 0.957146i $$0.406476\pi$$
−0.973715 + 0.227768i $$0.926857\pi$$
$$548$$ −6.00000 −0.256307
$$549$$ 0 0
$$550$$ 24.0000 1.02336
$$551$$ −21.0000 + 36.3731i −0.894630 + 1.54954i
$$552$$ 0 0
$$553$$ −2.50000 4.33013i −0.106311 0.184136i
$$554$$ 8.00000 + 13.8564i 0.339887 + 0.588702i
$$555$$ 0 0
$$556$$ −2.50000 + 4.33013i −0.106024 + 0.183638i
$$557$$ 24.0000 1.01691 0.508456 0.861088i $$-0.330216\pi$$
0.508456 + 0.861088i $$0.330216\pi$$
$$558$$ 0 0
$$559$$ 4.00000 0.169182
$$560$$ −1.50000 + 2.59808i −0.0633866 + 0.109789i
$$561$$ 0 0
$$562$$ −13.5000 23.3827i −0.569463 0.986339i
$$563$$ −16.5000 28.5788i −0.695392 1.20445i −0.970048 0.242912i $$-0.921897\pi$$
0.274656 0.961542i $$-0.411436\pi$$
$$564$$ 0 0
$$565$$ 22.5000 38.9711i 0.946582 1.63953i
$$566$$ −19.0000 −0.798630
$$567$$ 0 0
$$568$$ −3.00000 −0.125877
$$569$$ −9.00000 + 15.5885i −0.377300 + 0.653502i −0.990668 0.136295i $$-0.956481\pi$$
0.613369 + 0.789797i $$0.289814\pi$$
$$570$$ 0 0
$$571$$ −16.0000 27.7128i −0.669579 1.15975i −0.978022 0.208502i $$-0.933141\pi$$
0.308443 0.951243i $$-0.400192\pi$$
$$572$$ −6.00000 10.3923i −0.250873 0.434524i
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −12.0000 −0.500435
$$576$$ 0 0
$$577$$ −4.00000 −0.166522 −0.0832611 0.996528i $$-0.526534\pi$$
−0.0832611 + 0.996528i $$0.526534\pi$$
$$578$$ −9.50000 + 16.4545i −0.395148 + 0.684416i
$$579$$ 0 0
$$580$$ 9.00000 + 15.5885i 0.373705 + 0.647275i
$$581$$ 6.00000 + 10.3923i 0.248922 + 0.431145i
$$582$$ 0 0
$$583$$ 18.0000 31.1769i 0.745484 1.29122i
$$584$$ 2.00000 0.0827606
$$585$$ 0 0
$$586$$ 3.00000 0.123929
$$587$$ −1.50000 + 2.59808i −0.0619116 + 0.107234i −0.895320 0.445424i $$-0.853053\pi$$
0.833408 + 0.552658i $$0.186386\pi$$
$$588$$ 0 0
$$589$$ 7.00000 + 12.1244i 0.288430 + 0.499575i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −1.00000 + 1.73205i −0.0410997 + 0.0711868i
$$593$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$594$$ 0 0
$$595$$ −18.0000 −0.737928
$$596$$ −3.00000 + 5.19615i −0.122885 + 0.212843i
$$597$$ 0 0
$$598$$ 3.00000 + 5.19615i 0.122679 + 0.212486i
$$599$$ −12.0000 20.7846i −0.490307 0.849236i 0.509631 0.860393i $$-0.329782\pi$$
−0.999938 + 0.0111569i $$0.996449\pi$$
$$600$$ 0 0
$$601$$ −7.00000 + 12.1244i −0.285536 + 0.494563i −0.972739 0.231903i $$-0.925505\pi$$
0.687203 + 0.726465i $$0.258838\pi$$
$$602$$ 2.00000 0.0815139
$$603$$ 0 0
$$604$$ 23.0000 0.935857
$$605$$ −37.5000 + 64.9519i −1.52459 + 2.64067i
$$606$$ 0 0
$$607$$ 11.0000 + 19.0526i 0.446476 + 0.773320i 0.998154 0.0607380i $$-0.0193454\pi$$
−0.551678 + 0.834058i $$0.686012\pi$$
$$608$$ 3.50000 + 6.06218i 0.141944 + 0.245854i
$$609$$ 0 0
$$610$$ −7.50000 + 12.9904i −0.303666 + 0.525965i
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 8.00000 0.323117 0.161558 0.986863i $$-0.448348\pi$$
0.161558 + 0.986863i $$0.448348\pi$$
$$614$$ 12.5000 21.6506i 0.504459 0.873749i
$$615$$ 0 0
$$616$$ −3.00000 5.19615i −0.120873 0.209359i
$$617$$ 21.0000 + 36.3731i 0.845428 + 1.46432i 0.885249 + 0.465118i $$0.153988\pi$$
−0.0398207 + 0.999207i $$0.512679\pi$$
$$618$$ 0 0
$$619$$ 3.50000 6.06218i 0.140677 0.243659i −0.787075 0.616858i $$-0.788405\pi$$
0.927752 + 0.373198i $$0.121739\pi$$
$$620$$ 6.00000 0.240966
$$621$$ 0 0
$$622$$ −12.0000 −0.481156
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 14.5000 + 25.1147i 0.580000 + 1.00459i
$$626$$ 5.00000 + 8.66025i 0.199840 + 0.346133i
$$627$$ 0 0
$$628$$ 6.50000 11.2583i 0.259378 0.449256i
$$629$$ −12.0000 −0.478471
$$630$$ 0 0
$$631$$ −7.00000 −0.278666 −0.139333 0.990246i $$-0.544496\pi$$
−0.139333 + 0.990246i $$0.544496\pi$$
$$632$$ −2.50000 + 4.33013i −0.0994447 + 0.172243i
$$633$$ 0 0
$$634$$ 9.00000 + 15.5885i 0.357436 + 0.619097i
$$635$$ −25.5000 44.1673i −1.01194 1.75273i
$$636$$ 0 0
$$637$$ −1.00000 + 1.73205i −0.0396214 + 0.0686264i
$$638$$ −36.0000 −1.42525
$$639$$ 0 0
$$640$$ 3.00000 0.118585
$$641$$ 13.5000 23.3827i 0.533218 0.923561i −0.466029 0.884769i $$-0.654316\pi$$
0.999247 0.0387913i $$-0.0123508\pi$$
$$642$$ 0 0
$$643$$ 2.00000 + 3.46410i 0.0788723 + 0.136611i 0.902764 0.430137i $$-0.141535\pi$$
−0.823891 + 0.566748i $$0.808201\pi$$
$$644$$ 1.50000 + 2.59808i 0.0591083 + 0.102379i
$$645$$ 0 0
$$646$$ −21.0000 + 36.3731i −0.826234 + 1.43108i
$$647$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ −4.00000 + 6.92820i −0.156893 + 0.271746i
$$651$$ 0 0
$$652$$ −1.00000 1.73205i −0.0391630 0.0678323i
$$653$$ −18.0000 31.1769i −0.704394 1.22005i −0.966910 0.255119i $$-0.917885\pi$$
0.262515 0.964928i $$-0.415448\pi$$
$$654$$ 0 0
$$655$$ −13.5000 + 23.3827i −0.527489 + 0.913637i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 21.0000 36.3731i 0.818044 1.41689i −0.0890776 0.996025i $$-0.528392\pi$$
0.907122 0.420869i $$-0.138275\pi$$
$$660$$ 0 0
$$661$$ −2.50000 4.33013i −0.0972387 0.168422i 0.813302 0.581842i $$-0.197668\pi$$
−0.910541 + 0.413419i $$0.864334\pi$$
$$662$$ −13.0000 22.5167i −0.505259 0.875135i
$$663$$ 0 0
$$664$$ 6.00000 10.3923i 0.232845 0.403300i
$$665$$ −21.0000 −0.814345
$$666$$ 0 0
$$667$$ 18.0000 0.696963
$$668$$ 0 0
$$669$$ 0 0
$$670$$ −12.0000 20.7846i −0.463600 0.802980i
$$671$$ −15.0000 25.9808i −0.579069 1.00298i
$$672$$ 0 0
$$673$$ 18.5000 32.0429i 0.713123 1.23516i −0.250557 0.968102i $$-0.580614\pi$$
0.963679 0.267063i $$-0.0860531\pi$$
$$674$$ −22.0000 −0.847408
$$675$$ 0 0
$$676$$ −9.00000 −0.346154
$$677$$ 21.0000 36.3731i 0.807096 1.39793i −0.107772 0.994176i $$-0.534372\pi$$
0.914867 0.403755i $$-0.132295\pi$$
$$678$$ 0 0
$$679$$ −1.00000 1.73205i −0.0383765 0.0664700i
$$680$$ 9.00000 + 15.5885i 0.345134 + 0.597790i
$$681$$ 0 0
$$682$$ −6.00000 + 10.3923i −0.229752 + 0.397942i
$$683$$ 6.00000 0.229584 0.114792 0.993390i $$-0.463380\pi$$
0.114792 + 0.993390i $$0.463380\pi$$
$$684$$ 0 0
$$685$$ −18.0000 −0.687745
$$686$$ −0.500000 + 0.866025i −0.0190901 + 0.0330650i
$$687$$ 0 0
$$688$$ −1.00000 1.73205i −0.0381246 0.0660338i
$$689$$ 6.00000 + 10.3923i 0.228582 + 0.395915i
$$690$$ 0 0
$$691$$ −23.5000 + 40.7032i −0.893982 + 1.54842i −0.0589228 + 0.998263i $$0.518767\pi$$
−0.835059 + 0.550160i $$0.814567\pi$$
$$692$$ 6.00000 0.228086
$$693$$ 0 0
$$694$$ 24.0000 0.911028
$$695$$ −7.50000 + 12.9904i −0.284491 + 0.492753i
$$696$$ 0 0
$$697$$ 0 0
$$698$$ −13.0000 22.5167i −0.492057 0.852268i
$$699$$ 0 0
$$700$$ −2.00000 + 3.46410i −0.0755929 + 0.130931i
$$701$$ 18.0000 0.679851 0.339925 0.940452i $$-0.389598\pi$$
0.339925 + 0.940452i $$0.389598\pi$$
$$702$$ 0 0
$$703$$ −14.0000 −0.528020
$$704$$ −3.00000 + 5.19615i −0.113067 + 0.195837i
$$705$$ 0 0
$$706$$ −9.00000 15.5885i −0.338719 0.586679i
$$707$$ 4.50000 + 7.79423i 0.169240 + 0.293132i
$$708$$ 0 0
$$709$$ 26.0000 45.0333i 0.976450 1.69126i 0.301388 0.953502i $$-0.402550\pi$$
0.675063 0.737760i $$-0.264116\pi$$
$$710$$ −9.00000 −0.337764
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 3.00000 5.19615i 0.112351 0.194597i
$$714$$ 0 0
$$715$$ −18.0000 31.1769i −0.673162 1.16595i
$$716$$ 9.00000 + 15.5885i 0.336346 + 0.582568i
$$717$$ 0 0
$$718$$ −1.50000 + 2.59808i −0.0559795 + 0.0969593i
$$719$$ 36.0000 1.34257 0.671287 0.741198i $$-0.265742\pi$$
0.671287 + 0.741198i $$0.265742\pi$$
$$720$$ 0 0
$$721$$ −10.0000 −0.372419
$$722$$ −15.0000 + 25.9808i −0.558242 + 0.966904i
$$723$$ 0 0
$$724$$ 12.5000 + 21.6506i 0.464559 + 0.804640i
$$725$$ 12.0000 + 20.7846i 0.445669 + 0.771921i
$$726$$ 0 0
$$727$$ −4.00000 + 6.92820i −0.148352 + 0.256953i −0.930618 0.365991i $$-0.880730\pi$$
0.782267 + 0.622944i $$0.214063\pi$$
$$728$$ 2.00000 0.0741249
$$729$$ 0 0
$$730$$ 6.00000 0.222070
$$731$$ 6.00000 10.3923i 0.221918 0.384373i
$$732$$ 0 0
$$733$$ −14.5000 25.1147i −0.535570 0.927634i −0.999136 0.0415715i $$-0.986764\pi$$
0.463566 0.886062i $$-0.346570\pi$$
$$734$$ −4.00000 6.92820i −0.147643 0.255725i
$$735$$ 0 0
$$736$$ 1.50000 2.59808i 0.0552907 0.0957664i
$$737$$ 48.0000 1.76810
$$738$$ 0 0
$$739$$ 26.0000 0.956425 0.478213 0.878244i $$-0.341285\pi$$
0.478213 + 0.878244i $$0.341285\pi$$
$$740$$ −3.00000 + 5.19615i −0.110282 + 0.191014i
$$741$$ 0 0
$$742$$ 3.00000 + 5.19615i 0.110133 + 0.190757i
$$743$$ 18.0000 + 31.1769i 0.660356 + 1.14377i 0.980522 + 0.196409i $$0.0629279\pi$$
−0.320166 + 0.947361i $$0.603739\pi$$
$$744$$ 0 0
$$745$$ −9.00000 + 15.5885i −0.329734 + 0.571117i
$$746$$ 14.0000 0.512576
$$747$$ 0 0
$$748$$ −36.0000 −1.31629
$$749$$ −6.00000 + 10.3923i −0.219235 + 0.379727i
$$750$$ 0 0
$$751$$ 15.5000 + 26.8468i 0.565603 + 0.979653i 0.996993 + 0.0774878i $$0.0246899\pi$$
−0.431390 + 0.902165i $$0.641977\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 6.00000 10.3923i 0.218507 0.378465i
$$755$$ 69.0000 2.51117
$$756$$ 0 0
$$757$$ 26.0000 0.944986 0.472493 0.881334i $$-0.343354\pi$$
0.472493 + 0.881334i $$0.343354\pi$$
$$758$$ −1.00000 + 1.73205i −0.0363216 + 0.0629109i
$$759$$ 0 0
$$760$$ 10.5000 + 18.1865i 0.380875 + 0.659695i
$$761$$ −21.0000 36.3731i −0.761249 1.31852i −0.942207 0.335032i $$-0.891253\pi$$
0.180957 0.983491i $$-0.442080\pi$$
$$762$$ 0 0
$$763$$ 5.00000 8.66025i 0.181012 0.313522i
$$764$$ 9.00000 0.325609
$$765$$ 0 0
$$766$$ 18.0000 0.650366
$$767$$ 0 0
$$768$$ 0 0
$$769$$ −7.00000 12.1244i −0.252426 0.437215i 0.711767 0.702416i $$-0.247895\pi$$
−0.964193 + 0.265200i $$0.914562\pi$$
$$770$$ −9.00000 15.5885i −0.324337 0.561769i
$$771$$ 0 0
$$772$$ −8.50000 + 14.7224i −0.305922 + 0.529872i
$$773$$ 51.0000 1.83434 0.917171 0.398493i $$-0.130467\pi$$
0.917171 + 0.398493i $$0.130467\pi$$
$$774$$ 0 0
$$775$$ 8.00000 0.287368
$$776$$ −1.00000 + 1.73205i −0.0358979 + 0.0621770i
$$777$$ 0 0
$$778$$ 12.0000 + 20.7846i 0.430221 + 0.745164i
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 9.00000 15.5885i 0.322045 0.557799i
$$782$$ 18.0000 0.643679
$$783$$ 0 0
$$784$$ 1.00000 0.0357143
$$785$$ 19.5000 33.7750i 0.695985 1.20548i
$$786$$ 0 0
$$787$$ −10.0000 17.3205i −0.356462