# Properties

 Label 567.2.s.d.458.1 Level $567$ Weight $2$ Character 567.458 Analytic conductor $4.528$ Analytic rank $0$ Dimension $4$ Inner twists $4$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(26,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 5]))

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

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

chi := DirichletCharacter("567.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$567 = 3^{4} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 567.s (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: $$4.52751779461$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\sqrt{-2}, \sqrt{-3})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{4} - 2x^{2} + 4$$ x^4 - 2*x^2 + 4 Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 63) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 458.1 Root $$-1.22474 - 0.707107i$$ of defining polynomial Character $$\chi$$ $$=$$ 567.458 Dual form 567.2.s.d.26.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-1.22474 - 0.707107i) q^{2} +2.44949 q^{5} +(2.50000 - 0.866025i) q^{7} +2.82843i q^{8} +O(q^{10})$$ $$q+(-1.22474 - 0.707107i) q^{2} +2.44949 q^{5} +(2.50000 - 0.866025i) q^{7} +2.82843i q^{8} +(-3.00000 - 1.73205i) q^{10} +1.41421i q^{11} +(4.50000 + 2.59808i) q^{13} +(-3.67423 - 0.707107i) q^{14} +(2.00000 - 3.46410i) q^{16} +(-2.44949 + 4.24264i) q^{17} +(1.50000 - 0.866025i) q^{19} +(1.00000 - 1.73205i) q^{22} +5.65685i q^{23} +1.00000 q^{25} +(-3.67423 - 6.36396i) q^{26} +(-2.44949 + 1.41421i) q^{29} +(-1.50000 + 0.866025i) q^{31} +(6.00000 - 3.46410i) q^{34} +(6.12372 - 2.12132i) q^{35} +(0.500000 + 0.866025i) q^{37} -2.44949 q^{38} +6.92820i q^{40} +(3.67423 - 6.36396i) q^{41} +(0.500000 + 0.866025i) q^{43} +(4.00000 - 6.92820i) q^{46} +(6.12372 - 10.6066i) q^{47} +(5.50000 - 4.33013i) q^{49} +(-1.22474 - 0.707107i) q^{50} +(2.44949 + 1.41421i) q^{53} +3.46410i q^{55} +(2.44949 + 7.07107i) q^{56} +4.00000 q^{58} +(-2.44949 - 4.24264i) q^{59} +(3.00000 + 1.73205i) q^{61} +2.44949 q^{62} -8.00000 q^{64} +(11.0227 + 6.36396i) q^{65} +(-5.50000 - 9.52628i) q^{67} +(-9.00000 - 1.73205i) q^{70} -7.07107i q^{71} +(1.50000 + 0.866025i) q^{73} -1.41421i q^{74} +(1.22474 + 3.53553i) q^{77} +(-2.50000 + 4.33013i) q^{79} +(4.89898 - 8.48528i) q^{80} +(-9.00000 + 5.19615i) q^{82} +(-3.67423 - 6.36396i) q^{83} +(-6.00000 + 10.3923i) q^{85} -1.41421i q^{86} -4.00000 q^{88} +(2.44949 + 4.24264i) q^{89} +(13.5000 + 2.59808i) q^{91} +(-15.0000 + 8.66025i) q^{94} +(3.67423 - 2.12132i) q^{95} +(-9.00000 + 5.19615i) q^{97} +(-9.79796 + 1.41421i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 10 q^{7}+O(q^{10})$$ 4 * q + 10 * q^7 $$4 q + 10 q^{7} - 12 q^{10} + 18 q^{13} + 8 q^{16} + 6 q^{19} + 4 q^{22} + 4 q^{25} - 6 q^{31} + 24 q^{34} + 2 q^{37} + 2 q^{43} + 16 q^{46} + 22 q^{49} + 16 q^{58} + 12 q^{61} - 32 q^{64} - 22 q^{67} - 36 q^{70} + 6 q^{73} - 10 q^{79} - 36 q^{82} - 24 q^{85} - 16 q^{88} + 54 q^{91} - 60 q^{94} - 36 q^{97}+O(q^{100})$$ 4 * q + 10 * q^7 - 12 * q^10 + 18 * q^13 + 8 * q^16 + 6 * q^19 + 4 * q^22 + 4 * q^25 - 6 * q^31 + 24 * q^34 + 2 * q^37 + 2 * q^43 + 16 * q^46 + 22 * q^49 + 16 * q^58 + 12 * q^61 - 32 * q^64 - 22 * q^67 - 36 * q^70 + 6 * q^73 - 10 * q^79 - 36 * q^82 - 24 * q^85 - 16 * q^88 + 54 * q^91 - 60 * q^94 - 36 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$$.

 $$n$$ $$325$$ $$407$$ $$\chi(n)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.22474 0.707107i −0.866025 0.500000i 1.00000i $$-0.5\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$3$$ 0 0
$$4$$ 0 0
$$5$$ 2.44949 1.09545 0.547723 0.836660i $$-0.315495\pi$$
0.547723 + 0.836660i $$0.315495\pi$$
$$6$$ 0 0
$$7$$ 2.50000 0.866025i 0.944911 0.327327i
$$8$$ 2.82843i 1.00000i
$$9$$ 0 0
$$10$$ −3.00000 1.73205i −0.948683 0.547723i
$$11$$ 1.41421i 0.426401i 0.977008 + 0.213201i $$0.0683888\pi$$
−0.977008 + 0.213201i $$0.931611\pi$$
$$12$$ 0 0
$$13$$ 4.50000 + 2.59808i 1.24808 + 0.720577i 0.970725 0.240192i $$-0.0772105\pi$$
0.277350 + 0.960769i $$0.410544\pi$$
$$14$$ −3.67423 0.707107i −0.981981 0.188982i
$$15$$ 0 0
$$16$$ 2.00000 3.46410i 0.500000 0.866025i
$$17$$ −2.44949 + 4.24264i −0.594089 + 1.02899i 0.399586 + 0.916696i $$0.369154\pi$$
−0.993675 + 0.112296i $$0.964180\pi$$
$$18$$ 0 0
$$19$$ 1.50000 0.866025i 0.344124 0.198680i −0.317970 0.948101i $$-0.603001\pi$$
0.662094 + 0.749421i $$0.269668\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 1.00000 1.73205i 0.213201 0.369274i
$$23$$ 5.65685i 1.17954i 0.807573 + 0.589768i $$0.200781\pi$$
−0.807573 + 0.589768i $$0.799219\pi$$
$$24$$ 0 0
$$25$$ 1.00000 0.200000
$$26$$ −3.67423 6.36396i −0.720577 1.24808i
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −2.44949 + 1.41421i −0.454859 + 0.262613i −0.709880 0.704323i $$-0.751251\pi$$
0.255021 + 0.966935i $$0.417918\pi$$
$$30$$ 0 0
$$31$$ −1.50000 + 0.866025i −0.269408 + 0.155543i −0.628619 0.777714i $$-0.716379\pi$$
0.359211 + 0.933257i $$0.383046\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 6.00000 3.46410i 1.02899 0.594089i
$$35$$ 6.12372 2.12132i 1.03510 0.358569i
$$36$$ 0 0
$$37$$ 0.500000 + 0.866025i 0.0821995 + 0.142374i 0.904194 0.427121i $$-0.140472\pi$$
−0.821995 + 0.569495i $$0.807139\pi$$
$$38$$ −2.44949 −0.397360
$$39$$ 0 0
$$40$$ 6.92820i 1.09545i
$$41$$ 3.67423 6.36396i 0.573819 0.993884i −0.422350 0.906433i $$-0.638795\pi$$
0.996169 0.0874508i $$-0.0278721\pi$$
$$42$$ 0 0
$$43$$ 0.500000 + 0.866025i 0.0762493 + 0.132068i 0.901629 0.432511i $$-0.142372\pi$$
−0.825380 + 0.564578i $$0.809039\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 4.00000 6.92820i 0.589768 1.02151i
$$47$$ 6.12372 10.6066i 0.893237 1.54713i 0.0572655 0.998359i $$-0.481762\pi$$
0.835971 0.548773i $$-0.184905\pi$$
$$48$$ 0 0
$$49$$ 5.50000 4.33013i 0.785714 0.618590i
$$50$$ −1.22474 0.707107i −0.173205 0.100000i
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 2.44949 + 1.41421i 0.336463 + 0.194257i 0.658707 0.752400i $$-0.271104\pi$$
−0.322244 + 0.946657i $$0.604437\pi$$
$$54$$ 0 0
$$55$$ 3.46410i 0.467099i
$$56$$ 2.44949 + 7.07107i 0.327327 + 0.944911i
$$57$$ 0 0
$$58$$ 4.00000 0.525226
$$59$$ −2.44949 4.24264i −0.318896 0.552345i 0.661362 0.750067i $$-0.269979\pi$$
−0.980258 + 0.197722i $$0.936646\pi$$
$$60$$ 0 0
$$61$$ 3.00000 + 1.73205i 0.384111 + 0.221766i 0.679605 0.733578i $$-0.262151\pi$$
−0.295495 + 0.955344i $$0.595484\pi$$
$$62$$ 2.44949 0.311086
$$63$$ 0 0
$$64$$ −8.00000 −1.00000
$$65$$ 11.0227 + 6.36396i 1.36720 + 0.789352i
$$66$$ 0 0
$$67$$ −5.50000 9.52628i −0.671932 1.16382i −0.977356 0.211604i $$-0.932131\pi$$
0.305424 0.952217i $$-0.401202\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ −9.00000 1.73205i −1.07571 0.207020i
$$71$$ 7.07107i 0.839181i −0.907713 0.419591i $$-0.862174\pi$$
0.907713 0.419591i $$-0.137826\pi$$
$$72$$ 0 0
$$73$$ 1.50000 + 0.866025i 0.175562 + 0.101361i 0.585206 0.810885i $$-0.301014\pi$$
−0.409644 + 0.912245i $$0.634347\pi$$
$$74$$ 1.41421i 0.164399i
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 1.22474 + 3.53553i 0.139573 + 0.402911i
$$78$$ 0 0
$$79$$ −2.50000 + 4.33013i −0.281272 + 0.487177i −0.971698 0.236225i $$-0.924090\pi$$
0.690426 + 0.723403i $$0.257423\pi$$
$$80$$ 4.89898 8.48528i 0.547723 0.948683i
$$81$$ 0 0
$$82$$ −9.00000 + 5.19615i −0.993884 + 0.573819i
$$83$$ −3.67423 6.36396i −0.403300 0.698535i 0.590822 0.806802i $$-0.298803\pi$$
−0.994122 + 0.108266i $$0.965470\pi$$
$$84$$ 0 0
$$85$$ −6.00000 + 10.3923i −0.650791 + 1.12720i
$$86$$ 1.41421i 0.152499i
$$87$$ 0 0
$$88$$ −4.00000 −0.426401
$$89$$ 2.44949 + 4.24264i 0.259645 + 0.449719i 0.966147 0.257993i $$-0.0830610\pi$$
−0.706502 + 0.707712i $$0.749728\pi$$
$$90$$ 0 0
$$91$$ 13.5000 + 2.59808i 1.41518 + 0.272352i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ −15.0000 + 8.66025i −1.54713 + 0.893237i
$$95$$ 3.67423 2.12132i 0.376969 0.217643i
$$96$$ 0 0
$$97$$ −9.00000 + 5.19615i −0.913812 + 0.527589i −0.881656 0.471894i $$-0.843571\pi$$
−0.0321560 + 0.999483i $$0.510237\pi$$
$$98$$ −9.79796 + 1.41421i −0.989743 + 0.142857i
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −17.1464 −1.70613 −0.853067 0.521802i $$-0.825260\pi$$
−0.853067 + 0.521802i $$0.825260\pi$$
$$102$$ 0 0
$$103$$ 8.66025i 0.853320i −0.904412 0.426660i $$-0.859690\pi$$
0.904412 0.426660i $$-0.140310\pi$$
$$104$$ −7.34847 + 12.7279i −0.720577 + 1.24808i
$$105$$ 0 0
$$106$$ −2.00000 3.46410i −0.194257 0.336463i
$$107$$ −2.44949 + 1.41421i −0.236801 + 0.136717i −0.613706 0.789535i $$-0.710322\pi$$
0.376905 + 0.926252i $$0.376988\pi$$
$$108$$ 0 0
$$109$$ 0.500000 0.866025i 0.0478913 0.0829502i −0.841086 0.540901i $$-0.818083\pi$$
0.888977 + 0.457951i $$0.151417\pi$$
$$110$$ 2.44949 4.24264i 0.233550 0.404520i
$$111$$ 0 0
$$112$$ 2.00000 10.3923i 0.188982 0.981981i
$$113$$ −1.22474 0.707107i −0.115214 0.0665190i 0.441285 0.897367i $$-0.354523\pi$$
−0.556500 + 0.830848i $$0.687856\pi$$
$$114$$ 0 0
$$115$$ 13.8564i 1.29212i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 6.92820i 0.637793i
$$119$$ −2.44949 + 12.7279i −0.224544 + 1.16677i
$$120$$ 0 0
$$121$$ 9.00000 0.818182
$$122$$ −2.44949 4.24264i −0.221766 0.384111i
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −9.79796 −0.876356
$$126$$ 0 0
$$127$$ 11.0000 0.976092 0.488046 0.872818i $$-0.337710\pi$$
0.488046 + 0.872818i $$0.337710\pi$$
$$128$$ 9.79796 + 5.65685i 0.866025 + 0.500000i
$$129$$ 0 0
$$130$$ −9.00000 15.5885i −0.789352 1.36720i
$$131$$ 2.44949 0.214013 0.107006 0.994258i $$-0.465873\pi$$
0.107006 + 0.994258i $$0.465873\pi$$
$$132$$ 0 0
$$133$$ 3.00000 3.46410i 0.260133 0.300376i
$$134$$ 15.5563i 1.34386i
$$135$$ 0 0
$$136$$ −12.0000 6.92820i −1.02899 0.594089i
$$137$$ 11.3137i 0.966595i −0.875456 0.483298i $$-0.839439\pi$$
0.875456 0.483298i $$-0.160561\pi$$
$$138$$ 0 0
$$139$$ 4.50000 + 2.59808i 0.381685 + 0.220366i 0.678551 0.734553i $$-0.262608\pi$$
−0.296866 + 0.954919i $$0.595942\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ −5.00000 + 8.66025i −0.419591 + 0.726752i
$$143$$ −3.67423 + 6.36396i −0.307255 + 0.532181i
$$144$$ 0 0
$$145$$ −6.00000 + 3.46410i −0.498273 + 0.287678i
$$146$$ −1.22474 2.12132i −0.101361 0.175562i
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 5.65685i 0.463428i 0.972784 + 0.231714i $$0.0744333\pi$$
−0.972784 + 0.231714i $$0.925567\pi$$
$$150$$ 0 0
$$151$$ −22.0000 −1.79033 −0.895167 0.445730i $$-0.852944\pi$$
−0.895167 + 0.445730i $$0.852944\pi$$
$$152$$ 2.44949 + 4.24264i 0.198680 + 0.344124i
$$153$$ 0 0
$$154$$ 1.00000 5.19615i 0.0805823 0.418718i
$$155$$ −3.67423 + 2.12132i −0.295122 + 0.170389i
$$156$$ 0 0
$$157$$ −15.0000 + 8.66025i −1.19713 + 0.691164i −0.959914 0.280293i $$-0.909568\pi$$
−0.237216 + 0.971457i $$0.576235\pi$$
$$158$$ 6.12372 3.53553i 0.487177 0.281272i
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 4.89898 + 14.1421i 0.386094 + 1.11456i
$$162$$ 0 0
$$163$$ 5.00000 + 8.66025i 0.391630 + 0.678323i 0.992665 0.120900i $$-0.0385779\pi$$
−0.601035 + 0.799223i $$0.705245\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 10.3923i 0.806599i
$$167$$ 3.67423 6.36396i 0.284321 0.492458i −0.688123 0.725594i $$-0.741565\pi$$
0.972444 + 0.233136i $$0.0748986\pi$$
$$168$$ 0 0
$$169$$ 7.00000 + 12.1244i 0.538462 + 0.932643i
$$170$$ 14.6969 8.48528i 1.12720 0.650791i
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −4.89898 + 8.48528i −0.372463 + 0.645124i −0.989944 0.141462i $$-0.954820\pi$$
0.617481 + 0.786586i $$0.288153\pi$$
$$174$$ 0 0
$$175$$ 2.50000 0.866025i 0.188982 0.0654654i
$$176$$ 4.89898 + 2.82843i 0.369274 + 0.213201i
$$177$$ 0 0
$$178$$ 6.92820i 0.519291i
$$179$$ −8.57321 4.94975i −0.640792 0.369961i 0.144127 0.989559i $$-0.453962\pi$$
−0.784920 + 0.619598i $$0.787296\pi$$
$$180$$ 0 0
$$181$$ 15.5885i 1.15868i 0.815086 + 0.579340i $$0.196690\pi$$
−0.815086 + 0.579340i $$0.803310\pi$$
$$182$$ −14.6969 12.7279i −1.08941 0.943456i
$$183$$ 0 0
$$184$$ −16.0000 −1.17954
$$185$$ 1.22474 + 2.12132i 0.0900450 + 0.155963i
$$186$$ 0 0
$$187$$ −6.00000 3.46410i −0.438763 0.253320i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ −6.00000 −0.435286
$$191$$ −1.22474 0.707107i −0.0886194 0.0511645i 0.455035 0.890473i $$-0.349627\pi$$
−0.543655 + 0.839309i $$0.682960\pi$$
$$192$$ 0 0
$$193$$ −5.50000 9.52628i −0.395899 0.685717i 0.597317 0.802005i $$-0.296234\pi$$
−0.993215 + 0.116289i $$0.962900\pi$$
$$194$$ 14.6969 1.05518
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 19.7990i 1.41062i −0.708899 0.705310i $$-0.750808\pi$$
0.708899 0.705310i $$-0.249192\pi$$
$$198$$ 0 0
$$199$$ −12.0000 6.92820i −0.850657 0.491127i 0.0102152 0.999948i $$-0.496748\pi$$
−0.860873 + 0.508821i $$0.830082\pi$$
$$200$$ 2.82843i 0.200000i
$$201$$ 0 0
$$202$$ 21.0000 + 12.1244i 1.47755 + 0.853067i
$$203$$ −4.89898 + 5.65685i −0.343841 + 0.397033i
$$204$$ 0 0
$$205$$ 9.00000 15.5885i 0.628587 1.08875i
$$206$$ −6.12372 + 10.6066i −0.426660 + 0.738997i
$$207$$ 0 0
$$208$$ 18.0000 10.3923i 1.24808 0.720577i
$$209$$ 1.22474 + 2.12132i 0.0847174 + 0.146735i
$$210$$ 0 0
$$211$$ 11.0000 19.0526i 0.757271 1.31163i −0.186966 0.982366i $$-0.559865\pi$$
0.944237 0.329266i $$-0.106801\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 4.00000 0.273434
$$215$$ 1.22474 + 2.12132i 0.0835269 + 0.144673i
$$216$$ 0 0
$$217$$ −3.00000 + 3.46410i −0.203653 + 0.235159i
$$218$$ −1.22474 + 0.707107i −0.0829502 + 0.0478913i
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −22.0454 + 12.7279i −1.48293 + 0.856173i
$$222$$ 0 0
$$223$$ 18.0000 10.3923i 1.20537 0.695920i 0.243625 0.969870i $$-0.421663\pi$$
0.961744 + 0.273949i $$0.0883300\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 1.00000 + 1.73205i 0.0665190 + 0.115214i
$$227$$ 26.9444 1.78836 0.894181 0.447706i $$-0.147759\pi$$
0.894181 + 0.447706i $$0.147759\pi$$
$$228$$ 0 0
$$229$$ 22.5167i 1.48794i 0.668211 + 0.743971i $$0.267060\pi$$
−0.668211 + 0.743971i $$0.732940\pi$$
$$230$$ 9.79796 16.9706i 0.646058 1.11901i
$$231$$ 0 0
$$232$$ −4.00000 6.92820i −0.262613 0.454859i
$$233$$ 8.57321 4.94975i 0.561650 0.324269i −0.192158 0.981364i $$-0.561548\pi$$
0.753807 + 0.657095i $$0.228215\pi$$
$$234$$ 0 0
$$235$$ 15.0000 25.9808i 0.978492 1.69480i
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 12.0000 13.8564i 0.777844 0.898177i
$$239$$ −23.2702 13.4350i −1.50522 0.869040i −0.999982 0.00606055i $$-0.998071\pi$$
−0.505239 0.862979i $$-0.668596\pi$$
$$240$$ 0 0
$$241$$ 13.8564i 0.892570i 0.894891 + 0.446285i $$0.147253\pi$$
−0.894891 + 0.446285i $$0.852747\pi$$
$$242$$ −11.0227 6.36396i −0.708566 0.409091i
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 13.4722 10.6066i 0.860707 0.677631i
$$246$$ 0 0
$$247$$ 9.00000 0.572656
$$248$$ −2.44949 4.24264i −0.155543 0.269408i
$$249$$ 0 0
$$250$$ 12.0000 + 6.92820i 0.758947 + 0.438178i
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 0 0
$$253$$ −8.00000 −0.502956
$$254$$ −13.4722 7.77817i −0.845321 0.488046i
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 2.44949 0.152795 0.0763975 0.997077i $$-0.475658\pi$$
0.0763975 + 0.997077i $$0.475658\pi$$
$$258$$ 0 0
$$259$$ 2.00000 + 1.73205i 0.124274 + 0.107624i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ −3.00000 1.73205i −0.185341 0.107006i
$$263$$ 14.1421i 0.872041i 0.899937 + 0.436021i $$0.143613\pi$$
−0.899937 + 0.436021i $$0.856387\pi$$
$$264$$ 0 0
$$265$$ 6.00000 + 3.46410i 0.368577 + 0.212798i
$$266$$ −6.12372 + 2.12132i −0.375470 + 0.130066i
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 8.57321 14.8492i 0.522718 0.905374i −0.476932 0.878940i $$-0.658251\pi$$
0.999651 0.0264343i $$-0.00841529\pi$$
$$270$$ 0 0
$$271$$ −12.0000 + 6.92820i −0.728948 + 0.420858i −0.818037 0.575165i $$-0.804938\pi$$
0.0890891 + 0.996024i $$0.471604\pi$$
$$272$$ 9.79796 + 16.9706i 0.594089 + 1.02899i
$$273$$ 0 0
$$274$$ −8.00000 + 13.8564i −0.483298 + 0.837096i
$$275$$ 1.41421i 0.0852803i
$$276$$ 0 0
$$277$$ 23.0000 1.38194 0.690968 0.722885i $$-0.257185\pi$$
0.690968 + 0.722885i $$0.257185\pi$$
$$278$$ −3.67423 6.36396i −0.220366 0.381685i
$$279$$ 0 0
$$280$$ 6.00000 + 17.3205i 0.358569 + 1.03510i
$$281$$ 19.5959 11.3137i 1.16899 0.674919i 0.215551 0.976492i $$-0.430845\pi$$
0.953443 + 0.301573i $$0.0975118\pi$$
$$282$$ 0 0
$$283$$ −1.50000 + 0.866025i −0.0891657 + 0.0514799i −0.543920 0.839137i $$-0.683060\pi$$
0.454754 + 0.890617i $$0.349727\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 9.00000 5.19615i 0.532181 0.307255i
$$287$$ 3.67423 19.0919i 0.216883 1.12696i
$$288$$ 0 0
$$289$$ −3.50000 6.06218i −0.205882 0.356599i
$$290$$ 9.79796 0.575356
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −7.34847 + 12.7279i −0.429302 + 0.743573i −0.996811 0.0797939i $$-0.974574\pi$$
0.567509 + 0.823367i $$0.307907\pi$$
$$294$$ 0 0
$$295$$ −6.00000 10.3923i −0.349334 0.605063i
$$296$$ −2.44949 + 1.41421i −0.142374 + 0.0821995i
$$297$$ 0 0
$$298$$ 4.00000 6.92820i 0.231714 0.401340i
$$299$$ −14.6969 + 25.4558i −0.849946 + 1.47215i
$$300$$ 0 0
$$301$$ 2.00000 + 1.73205i 0.115278 + 0.0998337i
$$302$$ 26.9444 + 15.5563i 1.55048 + 0.895167i
$$303$$ 0 0
$$304$$ 6.92820i 0.397360i
$$305$$ 7.34847 + 4.24264i 0.420772 + 0.242933i
$$306$$ 0 0
$$307$$ 15.5885i 0.889680i −0.895610 0.444840i $$-0.853260\pi$$
0.895610 0.444840i $$-0.146740\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 6.00000 0.340777
$$311$$ 8.57321 + 14.8492i 0.486142 + 0.842023i 0.999873 0.0159282i $$-0.00507031\pi$$
−0.513731 + 0.857951i $$0.671737\pi$$
$$312$$ 0 0
$$313$$ −10.5000 6.06218i −0.593495 0.342655i 0.172983 0.984925i $$-0.444659\pi$$
−0.766478 + 0.642270i $$0.777993\pi$$
$$314$$ 24.4949 1.38233
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −12.2474 7.07107i −0.687885 0.397151i 0.114934 0.993373i $$-0.463334\pi$$
−0.802819 + 0.596222i $$0.796668\pi$$
$$318$$ 0 0
$$319$$ −2.00000 3.46410i −0.111979 0.193952i
$$320$$ −19.5959 −1.09545
$$321$$ 0 0
$$322$$ 4.00000 20.7846i 0.222911 1.15828i
$$323$$ 8.48528i 0.472134i
$$324$$ 0 0
$$325$$ 4.50000 + 2.59808i 0.249615 + 0.144115i
$$326$$ 14.1421i 0.783260i
$$327$$ 0 0
$$328$$ 18.0000 + 10.3923i 0.993884 + 0.573819i
$$329$$ 6.12372 31.8198i 0.337612 1.75428i
$$330$$ 0 0
$$331$$ 15.5000 26.8468i 0.851957 1.47563i −0.0274825 0.999622i $$-0.508749\pi$$
0.879440 0.476011i $$-0.157918\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ −9.00000 + 5.19615i −0.492458 + 0.284321i
$$335$$ −13.4722 23.3345i −0.736065 1.27490i
$$336$$ 0 0
$$337$$ −11.5000 + 19.9186i −0.626445 + 1.08503i 0.361815 + 0.932250i $$0.382157\pi$$
−0.988260 + 0.152784i $$0.951176\pi$$
$$338$$ 19.7990i 1.07692i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −1.22474 2.12132i −0.0663237 0.114876i
$$342$$ 0 0
$$343$$ 10.0000 15.5885i 0.539949 0.841698i
$$344$$ −2.44949 + 1.41421i −0.132068 + 0.0762493i
$$345$$ 0 0
$$346$$ 12.0000 6.92820i 0.645124 0.372463i
$$347$$ 26.9444 15.5563i 1.44645 0.835109i 0.448183 0.893942i $$-0.352071\pi$$
0.998268 + 0.0588334i $$0.0187381\pi$$
$$348$$ 0 0
$$349$$ −9.00000 + 5.19615i −0.481759 + 0.278144i −0.721149 0.692780i $$-0.756386\pi$$
0.239390 + 0.970923i $$0.423052\pi$$
$$350$$ −3.67423 0.707107i −0.196396 0.0377964i
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −17.1464 −0.912612 −0.456306 0.889823i $$-0.650828\pi$$
−0.456306 + 0.889823i $$0.650828\pi$$
$$354$$ 0 0
$$355$$ 17.3205i 0.919277i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 7.00000 + 12.1244i 0.369961 + 0.640792i
$$359$$ −24.4949 + 14.1421i −1.29279 + 0.746393i −0.979148 0.203148i $$-0.934883\pi$$
−0.313643 + 0.949541i $$0.601550\pi$$
$$360$$ 0 0
$$361$$ −8.00000 + 13.8564i −0.421053 + 0.729285i
$$362$$ 11.0227 19.0919i 0.579340 1.00345i
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 3.67423 + 2.12132i 0.192318 + 0.111035i
$$366$$ 0 0
$$367$$ 1.73205i 0.0904123i −0.998978 0.0452062i $$-0.985606\pi$$
0.998978 0.0452062i $$-0.0143945\pi$$
$$368$$ 19.5959 + 11.3137i 1.02151 + 0.589768i
$$369$$ 0 0
$$370$$ 3.46410i 0.180090i
$$371$$ 7.34847 + 1.41421i 0.381514 + 0.0734223i
$$372$$ 0 0
$$373$$ 29.0000 1.50156 0.750782 0.660551i $$-0.229677\pi$$
0.750782 + 0.660551i $$0.229677\pi$$
$$374$$ 4.89898 + 8.48528i 0.253320 + 0.438763i
$$375$$ 0 0
$$376$$ 30.0000 + 17.3205i 1.54713 + 0.893237i
$$377$$ −14.6969 −0.756931
$$378$$ 0 0
$$379$$ −7.00000 −0.359566 −0.179783 0.983706i $$-0.557540\pi$$
−0.179783 + 0.983706i $$0.557540\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 1.00000 + 1.73205i 0.0511645 + 0.0886194i
$$383$$ −19.5959 −1.00130 −0.500652 0.865648i $$-0.666906\pi$$
−0.500652 + 0.865648i $$0.666906\pi$$
$$384$$ 0 0
$$385$$ 3.00000 + 8.66025i 0.152894 + 0.441367i
$$386$$ 15.5563i 0.791797i
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 26.8701i 1.36237i 0.732113 + 0.681183i $$0.238534\pi$$
−0.732113 + 0.681183i $$0.761466\pi$$
$$390$$ 0 0
$$391$$ −24.0000 13.8564i −1.21373 0.700749i
$$392$$ 12.2474 + 15.5563i 0.618590 + 0.785714i
$$393$$ 0 0
$$394$$ −14.0000 + 24.2487i −0.705310 + 1.22163i
$$395$$ −6.12372 + 10.6066i −0.308118 + 0.533676i
$$396$$ 0 0
$$397$$ 1.50000 0.866025i 0.0752828 0.0434646i −0.461886 0.886939i $$-0.652827\pi$$
0.537169 + 0.843475i $$0.319494\pi$$
$$398$$ 9.79796 + 16.9706i 0.491127 + 0.850657i
$$399$$ 0 0
$$400$$ 2.00000 3.46410i 0.100000 0.173205i
$$401$$ 19.7990i 0.988714i −0.869259 0.494357i $$-0.835403\pi$$
0.869259 0.494357i $$-0.164597\pi$$
$$402$$ 0 0
$$403$$ −9.00000 −0.448322
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 10.0000 3.46410i 0.496292 0.171920i
$$407$$ −1.22474 + 0.707107i −0.0607083 + 0.0350500i
$$408$$ 0 0
$$409$$ −28.5000 + 16.4545i −1.40923 + 0.813622i −0.995314 0.0966915i $$-0.969174\pi$$
−0.413920 + 0.910313i $$0.635841\pi$$
$$410$$ −22.0454 + 12.7279i −1.08875 + 0.628587i
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −9.79796 8.48528i −0.482126 0.417533i
$$414$$ 0 0
$$415$$ −9.00000 15.5885i −0.441793 0.765207i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 3.46410i 0.169435i
$$419$$ −18.3712 + 31.8198i −0.897491 + 1.55450i −0.0667989 + 0.997766i $$0.521279\pi$$
−0.830692 + 0.556733i $$0.812055\pi$$
$$420$$ 0 0
$$421$$ 0.500000 + 0.866025i 0.0243685 + 0.0422075i 0.877952 0.478748i $$-0.158909\pi$$
−0.853584 + 0.520955i $$0.825576\pi$$
$$422$$ −26.9444 + 15.5563i −1.31163 + 0.757271i
$$423$$ 0 0
$$424$$ −4.00000 + 6.92820i −0.194257 + 0.336463i
$$425$$ −2.44949 + 4.24264i −0.118818 + 0.205798i
$$426$$ 0 0
$$427$$ 9.00000 + 1.73205i 0.435541 + 0.0838198i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 3.46410i 0.167054i
$$431$$ 13.4722 + 7.77817i 0.648933 + 0.374661i 0.788047 0.615615i $$-0.211092\pi$$
−0.139114 + 0.990276i $$0.544426\pi$$
$$432$$ 0 0
$$433$$ 15.5885i 0.749133i 0.927200 + 0.374567i $$0.122209\pi$$
−0.927200 + 0.374567i $$0.877791\pi$$
$$434$$ 6.12372 2.12132i 0.293948 0.101827i
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 4.89898 + 8.48528i 0.234350 + 0.405906i
$$438$$ 0 0
$$439$$ −24.0000 13.8564i −1.14546 0.661330i −0.197681 0.980266i $$-0.563341\pi$$
−0.947776 + 0.318936i $$0.896674\pi$$
$$440$$ −9.79796 −0.467099
$$441$$ 0 0
$$442$$ 36.0000 1.71235
$$443$$ −34.2929 19.7990i −1.62930 0.940678i −0.984301 0.176497i $$-0.943523\pi$$
−0.645002 0.764181i $$-0.723143\pi$$
$$444$$ 0 0
$$445$$ 6.00000 + 10.3923i 0.284427 + 0.492642i
$$446$$ −29.3939 −1.39184
$$447$$ 0 0
$$448$$ −20.0000 + 6.92820i −0.944911 + 0.327327i
$$449$$ 7.07107i 0.333704i −0.985982 0.166852i $$-0.946640\pi$$
0.985982 0.166852i $$-0.0533603\pi$$
$$450$$ 0 0
$$451$$ 9.00000 + 5.19615i 0.423793 + 0.244677i
$$452$$ 0 0
$$453$$ 0 0
$$454$$ −33.0000 19.0526i −1.54877 0.894181i
$$455$$ 33.0681 + 6.36396i 1.55026 + 0.298347i
$$456$$ 0 0
$$457$$ −2.50000 + 4.33013i −0.116945 + 0.202555i −0.918556 0.395292i $$-0.870643\pi$$
0.801611 + 0.597847i $$0.203977\pi$$
$$458$$ 15.9217 27.5772i 0.743971 1.28860i
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 7.34847 + 12.7279i 0.342252 + 0.592798i 0.984851 0.173405i $$-0.0554769\pi$$
−0.642598 + 0.766203i $$0.722144\pi$$
$$462$$ 0 0
$$463$$ 6.50000 11.2583i 0.302081 0.523219i −0.674526 0.738251i $$-0.735652\pi$$
0.976607 + 0.215032i $$0.0689855\pi$$
$$464$$ 11.3137i 0.525226i
$$465$$ 0 0
$$466$$ −14.0000 −0.648537
$$467$$ 13.4722 + 23.3345i 0.623419 + 1.07979i 0.988844 + 0.148952i $$0.0475901\pi$$
−0.365426 + 0.930841i $$0.619077\pi$$
$$468$$ 0 0
$$469$$ −22.0000 19.0526i −1.01587 0.879765i
$$470$$ −36.7423 + 21.2132i −1.69480 + 0.978492i
$$471$$ 0 0
$$472$$ 12.0000 6.92820i 0.552345 0.318896i
$$473$$ −1.22474 + 0.707107i −0.0563138 + 0.0325128i
$$474$$ 0 0
$$475$$ 1.50000 0.866025i 0.0688247 0.0397360i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 19.0000 + 32.9090i 0.869040 + 1.50522i
$$479$$ 4.89898 0.223840 0.111920 0.993717i $$-0.464300\pi$$
0.111920 + 0.993717i $$0.464300\pi$$
$$480$$ 0 0
$$481$$ 5.19615i 0.236924i
$$482$$ 9.79796 16.9706i 0.446285 0.772988i
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −22.0454 + 12.7279i −1.00103 + 0.577945i
$$486$$ 0 0
$$487$$ −8.50000 + 14.7224i −0.385172 + 0.667137i −0.991793 0.127854i $$-0.959191\pi$$
0.606621 + 0.794991i $$0.292524\pi$$
$$488$$ −4.89898 + 8.48528i −0.221766 + 0.384111i
$$489$$ 0 0
$$490$$ −24.0000 + 3.46410i −1.08421 + 0.156492i
$$491$$ 9.79796 + 5.65685i 0.442176 + 0.255290i 0.704520 0.709684i $$-0.251162\pi$$
−0.262344 + 0.964974i $$0.584496\pi$$
$$492$$ 0 0
$$493$$ 13.8564i 0.624061i
$$494$$ −11.0227 6.36396i −0.495935 0.286328i
$$495$$ 0 0
$$496$$ 6.92820i 0.311086i
$$497$$ −6.12372 17.6777i −0.274687 0.792952i
$$498$$ 0 0
$$499$$ −25.0000 −1.11915 −0.559577 0.828778i $$-0.689036\pi$$
−0.559577 + 0.828778i $$0.689036\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 22.0454 0.982956 0.491478 0.870890i $$-0.336457\pi$$
0.491478 + 0.870890i $$0.336457\pi$$
$$504$$ 0 0
$$505$$ −42.0000 −1.86898
$$506$$ 9.79796 + 5.65685i 0.435572 + 0.251478i
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 2.44949 0.108572 0.0542859 0.998525i $$-0.482712\pi$$
0.0542859 + 0.998525i $$0.482712\pi$$
$$510$$ 0 0
$$511$$ 4.50000 + 0.866025i 0.199068 + 0.0383107i
$$512$$ 22.6274i 1.00000i
$$513$$ 0 0
$$514$$ −3.00000 1.73205i −0.132324 0.0763975i
$$515$$ 21.2132i 0.934765i
$$516$$ 0 0
$$517$$ 15.0000 + 8.66025i 0.659699 + 0.380878i
$$518$$ −1.22474 3.53553i −0.0538122 0.155342i
$$519$$ 0 0
$$520$$ −18.0000 + 31.1769i −0.789352 + 1.36720i
$$521$$ −2.44949 + 4.24264i −0.107314 + 0.185873i −0.914681 0.404176i $$-0.867558\pi$$
0.807367 + 0.590049i $$0.200892\pi$$
$$522$$ 0 0
$$523$$ 1.50000 0.866025i 0.0655904 0.0378686i −0.466846 0.884339i $$-0.654610\pi$$
0.532437 + 0.846470i $$0.321276\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 10.0000 17.3205i 0.436021 0.755210i
$$527$$ 8.48528i 0.369625i
$$528$$ 0 0
$$529$$ −9.00000 −0.391304
$$530$$ −4.89898 8.48528i −0.212798 0.368577i
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 33.0681 19.0919i 1.43234 0.826961i
$$534$$ 0 0
$$535$$ −6.00000 + 3.46410i −0.259403 + 0.149766i
$$536$$ 26.9444 15.5563i 1.16382 0.671932i
$$537$$ 0 0
$$538$$ −21.0000 + 12.1244i −0.905374 + 0.522718i
$$539$$ 6.12372 + 7.77817i 0.263767 + 0.335030i
$$540$$ 0 0
$$541$$ −8.50000 14.7224i −0.365444 0.632967i 0.623404 0.781900i $$-0.285749\pi$$
−0.988847 + 0.148933i $$0.952416\pi$$
$$542$$ 19.5959 0.841717
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 1.22474 2.12132i 0.0524623 0.0908674i
$$546$$ 0 0
$$547$$ 5.00000 + 8.66025i 0.213785 + 0.370286i 0.952896 0.303298i $$-0.0980876\pi$$
−0.739111 + 0.673583i $$0.764754\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 1.00000 1.73205i 0.0426401 0.0738549i
$$551$$ −2.44949 + 4.24264i −0.104352 + 0.180743i
$$552$$ 0 0
$$553$$ −2.50000 + 12.9904i −0.106311 + 0.552407i
$$554$$ −28.1691 16.2635i −1.19679 0.690968i
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 13.4722 + 7.77817i 0.570835 + 0.329572i 0.757483 0.652855i $$-0.226429\pi$$
−0.186648 + 0.982427i $$0.559762\pi$$
$$558$$ 0 0
$$559$$ 5.19615i 0.219774i
$$560$$ 4.89898 25.4558i 0.207020 1.07571i
$$561$$ 0 0
$$562$$ −32.0000 −1.34984
$$563$$ −13.4722 23.3345i −0.567785 0.983433i −0.996785 0.0801281i $$-0.974467\pi$$
0.428999 0.903305i $$-0.358866\pi$$
$$564$$ 0 0
$$565$$ −3.00000 1.73205i −0.126211 0.0728679i
$$566$$ 2.44949 0.102960
$$567$$ 0 0
$$568$$ 20.0000 0.839181
$$569$$ −1.22474 0.707107i −0.0513440 0.0296435i 0.474108 0.880467i $$-0.342771\pi$$
−0.525452 + 0.850823i $$0.676104\pi$$
$$570$$ 0 0
$$571$$ −5.50000 9.52628i −0.230168 0.398662i 0.727690 0.685907i $$-0.240594\pi$$
−0.957857 + 0.287244i $$0.907261\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ −18.0000 + 20.7846i −0.751305 + 0.867533i
$$575$$ 5.65685i 0.235907i
$$576$$ 0 0
$$577$$ 1.50000 + 0.866025i 0.0624458 + 0.0360531i 0.530898 0.847436i $$-0.321855\pi$$
−0.468452 + 0.883489i $$0.655188\pi$$
$$578$$ 9.89949i 0.411765i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −14.6969 12.7279i −0.609732 0.528043i
$$582$$ 0 0
$$583$$ −2.00000 + 3.46410i −0.0828315 + 0.143468i
$$584$$ −2.44949 + 4.24264i −0.101361 + 0.175562i
$$585$$ 0 0
$$586$$ 18.0000 10.3923i 0.743573 0.429302i
$$587$$ 7.34847 + 12.7279i 0.303304 + 0.525338i 0.976882 0.213778i $$-0.0685770\pi$$
−0.673578 + 0.739116i $$0.735244\pi$$
$$588$$ 0 0
$$589$$ −1.50000 + 2.59808i −0.0618064 + 0.107052i
$$590$$ 16.9706i 0.698667i
$$591$$ 0 0
$$592$$ 4.00000 0.164399
$$593$$ −8.57321 14.8492i −0.352060 0.609785i 0.634550 0.772881i $$-0.281185\pi$$
−0.986610 + 0.163096i $$0.947852\pi$$
$$594$$ 0 0
$$595$$ −6.00000 + 31.1769i −0.245976 + 1.27813i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 36.0000 20.7846i 1.47215 0.849946i
$$599$$ 4.89898 2.82843i 0.200167 0.115566i −0.396566 0.918006i $$-0.629798\pi$$
0.596733 + 0.802440i $$0.296465\pi$$
$$600$$ 0 0
$$601$$ −22.5000 + 12.9904i −0.917794 + 0.529889i −0.882931 0.469503i $$-0.844433\pi$$
−0.0348635 + 0.999392i $$0.511100\pi$$
$$602$$ −1.22474 3.53553i −0.0499169 0.144098i
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 22.0454 0.896273
$$606$$ 0 0
$$607$$ 39.8372i 1.61694i −0.588537 0.808470i $$-0.700296\pi$$
0.588537 0.808470i $$-0.299704\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ −6.00000 10.3923i −0.242933 0.420772i
$$611$$ 55.1135 31.8198i 2.22965 1.28729i
$$612$$ 0 0
$$613$$ −4.00000 + 6.92820i −0.161558 + 0.279827i −0.935428 0.353518i $$-0.884985\pi$$
0.773869 + 0.633345i $$0.218319\pi$$
$$614$$ −11.0227 + 19.0919i −0.444840 + 0.770486i
$$615$$ 0 0
$$616$$ −10.0000 + 3.46410i −0.402911 + 0.139573i
$$617$$ 20.8207 + 12.0208i 0.838208 + 0.483940i 0.856655 0.515890i $$-0.172539\pi$$
−0.0184465 + 0.999830i $$0.505872\pi$$
$$618$$ 0 0
$$619$$ 29.4449i 1.18349i 0.806126 + 0.591744i $$0.201561\pi$$
−0.806126 + 0.591744i $$0.798439\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 24.2487i 0.972285i
$$623$$ 9.79796 + 8.48528i 0.392547 + 0.339956i
$$624$$ 0 0
$$625$$ −29.0000 −1.16000
$$626$$ 8.57321 + 14.8492i 0.342655 + 0.593495i
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −4.89898 −0.195335
$$630$$ 0 0
$$631$$ 38.0000 1.51276 0.756378 0.654135i $$-0.226967\pi$$
0.756378 + 0.654135i $$0.226967\pi$$
$$632$$ −12.2474 7.07107i −0.487177 0.281272i
$$633$$ 0 0
$$634$$ 10.0000 + 17.3205i 0.397151 + 0.687885i
$$635$$ 26.9444 1.06926
$$636$$ 0 0
$$637$$ 36.0000 5.19615i 1.42637 0.205879i
$$638$$ 5.65685i 0.223957i
$$639$$ 0 0
$$640$$ 24.0000 + 13.8564i 0.948683 + 0.547723i
$$641$$ 14.1421i 0.558581i 0.960207 + 0.279290i $$0.0900992\pi$$
−0.960207 + 0.279290i $$0.909901\pi$$
$$642$$ 0 0
$$643$$ −22.5000 12.9904i −0.887313 0.512291i −0.0142506 0.999898i $$-0.504536\pi$$
−0.873063 + 0.487608i $$0.837870\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 6.00000 10.3923i 0.236067 0.408880i
$$647$$ 8.57321 14.8492i 0.337048 0.583784i −0.646828 0.762636i $$-0.723905\pi$$
0.983876 + 0.178852i $$0.0572383\pi$$
$$648$$ 0 0
$$649$$ 6.00000 3.46410i 0.235521 0.135978i
$$650$$ −3.67423 6.36396i −0.144115 0.249615i
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 7.07107i 0.276712i −0.990383 0.138356i $$-0.955818\pi$$
0.990383 0.138356i $$-0.0441819\pi$$
$$654$$ 0 0
$$655$$ 6.00000 0.234439
$$656$$ −14.6969 25.4558i −0.573819 0.993884i
$$657$$ 0 0
$$658$$ −30.0000 + 34.6410i −1.16952 + 1.35045i
$$659$$ 19.5959 11.3137i 0.763349 0.440720i −0.0671481 0.997743i $$-0.521390\pi$$
0.830497 + 0.557024i $$0.188057\pi$$
$$660$$ 0 0
$$661$$ 25.5000 14.7224i 0.991835 0.572636i 0.0860127 0.996294i $$-0.472587\pi$$
0.905822 + 0.423658i $$0.139254\pi$$
$$662$$ −37.9671 + 21.9203i −1.47563 + 0.851957i
$$663$$ 0 0
$$664$$ 18.0000 10.3923i 0.698535 0.403300i
$$665$$ 7.34847 8.48528i 0.284961 0.329045i
$$666$$ 0 0
$$667$$ −8.00000 13.8564i −0.309761 0.536522i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 38.1051i 1.47213i
$$671$$ −2.44949 + 4.24264i −0.0945615 + 0.163785i
$$672$$ 0 0
$$673$$ −17.5000 30.3109i −0.674575 1.16840i −0.976593 0.215096i $$-0.930993\pi$$
0.302017 0.953302i $$-0.402340\pi$$
$$674$$ 28.1691 16.2635i 1.08503 0.626445i
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −4.89898 + 8.48528i −0.188283 + 0.326116i −0.944678 0.327999i $$-0.893626\pi$$
0.756395 + 0.654115i $$0.226959\pi$$
$$678$$ 0 0
$$679$$ −18.0000 + 20.7846i −0.690777 + 0.797640i
$$680$$ −29.3939 16.9706i −1.12720 0.650791i
$$681$$ 0 0
$$682$$ 3.46410i 0.132647i
$$683$$ −41.6413 24.0416i −1.59336 0.919927i −0.992725 0.120405i $$-0.961581\pi$$
−0.600636 0.799522i $$-0.705086\pi$$
$$684$$ 0 0
$$685$$ 27.7128i 1.05885i
$$686$$ −23.2702 + 12.0208i −0.888459 + 0.458957i
$$687$$ 0 0
$$688$$ 4.00000 0.152499
$$689$$ 7.34847 + 12.7279i 0.279954 + 0.484895i
$$690$$ 0 0
$$691$$ −37.5000 21.6506i −1.42657 0.823629i −0.429719 0.902963i $$-0.641387\pi$$
−0.996848 + 0.0793336i $$0.974721\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ −44.0000 −1.67022
$$695$$ 11.0227 + 6.36396i 0.418115 + 0.241399i
$$696$$ 0 0
$$697$$ 18.0000 + 31.1769i 0.681799 + 1.18091i
$$698$$ 14.6969 0.556287
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 5.65685i 0.213656i 0.994277 + 0.106828i $$0.0340695\pi$$
−0.994277 + 0.106828i $$0.965931\pi$$
$$702$$ 0 0
$$703$$ 1.50000 + 0.866025i 0.0565736 + 0.0326628i
$$704$$ 11.3137i 0.426401i
$$705$$ 0 0
$$706$$ 21.0000 + 12.1244i 0.790345 + 0.456306i
$$707$$ −42.8661 + 14.8492i −1.61214 + 0.558463i
$$708$$ 0 0
$$709$$ 20.0000 34.6410i 0.751116 1.30097i −0.196167 0.980571i $$-0.562849\pi$$
0.947282 0.320400i $$-0.103817\pi$$
$$710$$ −12.2474 + 21.2132i −0.459639 + 0.796117i
$$711$$ 0 0
$$712$$ −12.0000 + 6.92820i −0.449719 + 0.259645i
$$713$$ −4.89898 8.48528i −0.183468 0.317776i
$$714$$ 0 0
$$715$$ −9.00000 + 15.5885i −0.336581 + 0.582975i
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 40.0000 1.49279
$$719$$ 13.4722 + 23.3345i 0.502428 + 0.870231i 0.999996 + 0.00280593i $$0.000893157\pi$$
−0.497568 + 0.867425i $$0.665774\pi$$
$$720$$ 0 0
$$721$$ −7.50000 21.6506i −0.279315 0.806312i
$$722$$ 19.5959 11.3137i 0.729285 0.421053i
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −2.44949 + 1.41421i −0.0909718 + 0.0525226i
$$726$$ 0 0
$$727$$ −22.5000 + 12.9904i −0.834479 + 0.481787i −0.855384 0.517995i $$-0.826679\pi$$
0.0209049 + 0.999781i $$0.493345\pi$$
$$728$$ −7.34847 + 38.1838i −0.272352 + 1.41518i
$$729$$ 0 0
$$730$$ −3.00000 5.19615i −0.111035 0.192318i
$$731$$ −4.89898 −0.181195
$$732$$ 0 0
$$733$$ 39.8372i 1.47142i −0.677297 0.735710i $$-0.736849\pi$$
0.677297 0.735710i $$-0.263151\pi$$
$$734$$ −1.22474 + 2.12132i −0.0452062 + 0.0782994i
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 13.4722 7.77817i 0.496255 0.286513i
$$738$$ 0 0
$$739$$ 0.500000 0.866025i 0.0183928 0.0318573i −0.856683 0.515844i $$-0.827478\pi$$
0.875075 + 0.483987i $$0.160812\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ −8.00000 6.92820i −0.293689 0.254342i
$$743$$ 20.8207 + 12.0208i 0.763836 + 0.441001i 0.830671 0.556763i $$-0.187957\pi$$
−0.0668353 + 0.997764i $$0.521290\pi$$
$$744$$ 0 0
$$745$$ 13.8564i 0.507659i
$$746$$ −35.5176 20.5061i −1.30039 0.750782i
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −4.89898 + 5.65685i −0.179005 + 0.206697i
$$750$$ 0 0
$$751$$ 29.0000 1.05823 0.529113 0.848552i $$-0.322525\pi$$
0.529113 + 0.848552i $$0.322525\pi$$
$$752$$ −24.4949 42.4264i −0.893237 1.54713i
$$753$$ 0 0
$$754$$ 18.0000 + 10.3923i 0.655521 + 0.378465i
$$755$$ −53.8888 −1.96121
$$756$$ 0 0
$$757$$ 2.00000 0.0726912 0.0363456 0.999339i $$-0.488428\pi$$
0.0363456 + 0.999339i $$0.488428\pi$$
$$758$$ 8.57321 + 4.94975i 0.311393 + 0.179783i
$$759$$ 0 0
$$760$$ 6.00000 + 10.3923i 0.217643 + 0.376969i
$$761$$ 24.4949 0.887939 0.443970 0.896042i $$-0.353570\pi$$
0.443970 + 0.896042i $$0.353570\pi$$
$$762$$ 0 0
$$763$$ 0.500000 2.59808i 0.0181012 0.0940567i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 24.0000 + 13.8564i 0.867155 + 0.500652i
$$767$$ 25.4558i 0.919157i
$$768$$ 0 0
$$769$$ −22.5000 12.9904i −0.811371 0.468445i 0.0360609 0.999350i $$-0.488519\pi$$
−0.847432 + 0.530904i $$0.821852\pi$$
$$770$$ 2.44949 12.7279i 0.0882735 0.458682i
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −13.4722 + 23.3345i −0.484561 + 0.839284i −0.999843 0.0177365i $$-0.994354\pi$$
0.515282 + 0.857021i $$0.327687\pi$$
$$774$$ 0 0
$$775$$ −1.50000 + 0.866025i −0.0538816 + 0.0311086i
$$776$$ −14.6969 25.4558i −0.527589 0.913812i
$$777$$ 0 0
$$778$$ 19.0000 32.9090i 0.681183 1.17984i
$$779$$ 12.7279i 0.456025i
$$780$$ 0 0
$$781$$ 10.0000 0.357828
$$782$$ 19.5959 + 33.9411i 0.700749 + 1.21373i
$$783$$ 0 0
$$784$$ −4.00000 27.7128i −0.142857 0.989743i
$$785$$ −36.7423 + 21.2132i −1.31139 + 0.757132i
$$786$$ 0