# Properties

 Label 1216.2.i.c.961.1 Level $1216$ Weight $2$ Character 1216.961 Analytic conductor $9.710$ Analytic rank $0$ Dimension $2$ Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1216,2,Mod(577,1216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1216, 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("1216.577");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1216 = 2^{6} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1216.i (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: $$9.70980888579$$ 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: no (minimal twist has level 76) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 961.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 1216.961 Dual form 1216.2.i.c.577.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(1.00000 + 1.73205i) q^{9} +O(q^{10})$$ $$q+(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(1.00000 + 1.73205i) q^{9} +4.00000 q^{11} +(-0.500000 - 0.866025i) q^{13} +(-0.500000 - 0.866025i) q^{15} +(-1.50000 + 2.59808i) q^{17} +(4.00000 - 1.73205i) q^{19} +(-2.50000 - 4.33013i) q^{23} +(2.00000 + 3.46410i) q^{25} -5.00000 q^{27} +(3.50000 + 6.06218i) q^{29} +4.00000 q^{31} +(-2.00000 + 3.46410i) q^{33} -10.0000 q^{37} +1.00000 q^{39} +(2.50000 - 4.33013i) q^{41} +(-2.50000 + 4.33013i) q^{43} -2.00000 q^{45} +(3.50000 + 6.06218i) q^{47} -7.00000 q^{49} +(-1.50000 - 2.59808i) q^{51} +(5.50000 + 9.52628i) q^{53} +(-2.00000 + 3.46410i) q^{55} +(-0.500000 + 4.33013i) q^{57} +(1.50000 - 2.59808i) q^{59} +(5.50000 + 9.52628i) q^{61} +1.00000 q^{65} +(-1.50000 - 2.59808i) q^{67} +5.00000 q^{69} +(-5.50000 + 9.52628i) q^{71} +(-7.50000 + 12.9904i) q^{73} -4.00000 q^{75} +(6.50000 - 11.2583i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-1.50000 - 2.59808i) q^{85} -7.00000 q^{87} +(-1.50000 - 2.59808i) q^{89} +(-2.00000 + 3.46410i) q^{93} +(-0.500000 + 4.33013i) q^{95} +(2.50000 - 4.33013i) q^{97} +(4.00000 + 6.92820i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - q^{3} - q^{5} + 2 q^{9}+O(q^{10})$$ 2 * q - q^3 - q^5 + 2 * q^9 $$2 q - q^{3} - q^{5} + 2 q^{9} + 8 q^{11} - q^{13} - q^{15} - 3 q^{17} + 8 q^{19} - 5 q^{23} + 4 q^{25} - 10 q^{27} + 7 q^{29} + 8 q^{31} - 4 q^{33} - 20 q^{37} + 2 q^{39} + 5 q^{41} - 5 q^{43} - 4 q^{45} + 7 q^{47} - 14 q^{49} - 3 q^{51} + 11 q^{53} - 4 q^{55} - q^{57} + 3 q^{59} + 11 q^{61} + 2 q^{65} - 3 q^{67} + 10 q^{69} - 11 q^{71} - 15 q^{73} - 8 q^{75} + 13 q^{79} - q^{81} - 3 q^{85} - 14 q^{87} - 3 q^{89} - 4 q^{93} - q^{95} + 5 q^{97} + 8 q^{99}+O(q^{100})$$ 2 * q - q^3 - q^5 + 2 * q^9 + 8 * q^11 - q^13 - q^15 - 3 * q^17 + 8 * q^19 - 5 * q^23 + 4 * q^25 - 10 * q^27 + 7 * q^29 + 8 * q^31 - 4 * q^33 - 20 * q^37 + 2 * q^39 + 5 * q^41 - 5 * q^43 - 4 * q^45 + 7 * q^47 - 14 * q^49 - 3 * q^51 + 11 * q^53 - 4 * q^55 - q^57 + 3 * q^59 + 11 * q^61 + 2 * q^65 - 3 * q^67 + 10 * q^69 - 11 * q^71 - 15 * q^73 - 8 * q^75 + 13 * q^79 - q^81 - 3 * q^85 - 14 * q^87 - 3 * q^89 - 4 * q^93 - q^95 + 5 * q^97 + 8 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times$$.

 $$n$$ $$191$$ $$705$$ $$837$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$1$$

## 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 0
$$3$$ −0.500000 + 0.866025i −0.288675 + 0.500000i −0.973494 0.228714i $$-0.926548\pi$$
0.684819 + 0.728714i $$0.259881\pi$$
$$4$$ 0 0
$$5$$ −0.500000 + 0.866025i −0.223607 + 0.387298i −0.955901 0.293691i $$-0.905116\pi$$
0.732294 + 0.680989i $$0.238450\pi$$
$$6$$ 0 0
$$7$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$8$$ 0 0
$$9$$ 1.00000 + 1.73205i 0.333333 + 0.577350i
$$10$$ 0 0
$$11$$ 4.00000 1.20605 0.603023 0.797724i $$-0.293963\pi$$
0.603023 + 0.797724i $$0.293963\pi$$
$$12$$ 0 0
$$13$$ −0.500000 0.866025i −0.138675 0.240192i 0.788320 0.615265i $$-0.210951\pi$$
−0.926995 + 0.375073i $$0.877618\pi$$
$$14$$ 0 0
$$15$$ −0.500000 0.866025i −0.129099 0.223607i
$$16$$ 0 0
$$17$$ −1.50000 + 2.59808i −0.363803 + 0.630126i −0.988583 0.150675i $$-0.951855\pi$$
0.624780 + 0.780801i $$0.285189\pi$$
$$18$$ 0 0
$$19$$ 4.00000 1.73205i 0.917663 0.397360i
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −2.50000 4.33013i −0.521286 0.902894i −0.999694 0.0247559i $$-0.992119\pi$$
0.478407 0.878138i $$-0.341214\pi$$
$$24$$ 0 0
$$25$$ 2.00000 + 3.46410i 0.400000 + 0.692820i
$$26$$ 0 0
$$27$$ −5.00000 −0.962250
$$28$$ 0 0
$$29$$ 3.50000 + 6.06218i 0.649934 + 1.12572i 0.983138 + 0.182864i $$0.0585367\pi$$
−0.333205 + 0.942855i $$0.608130\pi$$
$$30$$ 0 0
$$31$$ 4.00000 0.718421 0.359211 0.933257i $$-0.383046\pi$$
0.359211 + 0.933257i $$0.383046\pi$$
$$32$$ 0 0
$$33$$ −2.00000 + 3.46410i −0.348155 + 0.603023i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −10.0000 −1.64399 −0.821995 0.569495i $$-0.807139\pi$$
−0.821995 + 0.569495i $$0.807139\pi$$
$$38$$ 0 0
$$39$$ 1.00000 0.160128
$$40$$ 0 0
$$41$$ 2.50000 4.33013i 0.390434 0.676252i −0.602072 0.798441i $$-0.705658\pi$$
0.992507 + 0.122189i $$0.0389915\pi$$
$$42$$ 0 0
$$43$$ −2.50000 + 4.33013i −0.381246 + 0.660338i −0.991241 0.132068i $$-0.957838\pi$$
0.609994 + 0.792406i $$0.291172\pi$$
$$44$$ 0 0
$$45$$ −2.00000 −0.298142
$$46$$ 0 0
$$47$$ 3.50000 + 6.06218i 0.510527 + 0.884260i 0.999926 + 0.0121990i $$0.00388317\pi$$
−0.489398 + 0.872060i $$0.662783\pi$$
$$48$$ 0 0
$$49$$ −7.00000 −1.00000
$$50$$ 0 0
$$51$$ −1.50000 2.59808i −0.210042 0.363803i
$$52$$ 0 0
$$53$$ 5.50000 + 9.52628i 0.755483 + 1.30854i 0.945134 + 0.326683i $$0.105931\pi$$
−0.189651 + 0.981852i $$0.560736\pi$$
$$54$$ 0 0
$$55$$ −2.00000 + 3.46410i −0.269680 + 0.467099i
$$56$$ 0 0
$$57$$ −0.500000 + 4.33013i −0.0662266 + 0.573539i
$$58$$ 0 0
$$59$$ 1.50000 2.59808i 0.195283 0.338241i −0.751710 0.659494i $$-0.770771\pi$$
0.946993 + 0.321253i $$0.104104\pi$$
$$60$$ 0 0
$$61$$ 5.50000 + 9.52628i 0.704203 + 1.21972i 0.966978 + 0.254858i $$0.0820288\pi$$
−0.262776 + 0.964857i $$0.584638\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 1.00000 0.124035
$$66$$ 0 0
$$67$$ −1.50000 2.59808i −0.183254 0.317406i 0.759733 0.650236i $$-0.225330\pi$$
−0.942987 + 0.332830i $$0.891996\pi$$
$$68$$ 0 0
$$69$$ 5.00000 0.601929
$$70$$ 0 0
$$71$$ −5.50000 + 9.52628i −0.652730 + 1.13056i 0.329728 + 0.944076i $$0.393043\pi$$
−0.982458 + 0.186485i $$0.940290\pi$$
$$72$$ 0 0
$$73$$ −7.50000 + 12.9904i −0.877809 + 1.52041i −0.0240681 + 0.999710i $$0.507662\pi$$
−0.853740 + 0.520699i $$0.825671\pi$$
$$74$$ 0 0
$$75$$ −4.00000 −0.461880
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 6.50000 11.2583i 0.731307 1.26666i −0.225018 0.974355i $$-0.572244\pi$$
0.956325 0.292306i $$-0.0944227\pi$$
$$80$$ 0 0
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ 0 0
$$83$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$84$$ 0 0
$$85$$ −1.50000 2.59808i −0.162698 0.281801i
$$86$$ 0 0
$$87$$ −7.00000 −0.750479
$$88$$ 0 0
$$89$$ −1.50000 2.59808i −0.159000 0.275396i 0.775509 0.631337i $$-0.217494\pi$$
−0.934508 + 0.355942i $$0.884160\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ −2.00000 + 3.46410i −0.207390 + 0.359211i
$$94$$ 0 0
$$95$$ −0.500000 + 4.33013i −0.0512989 + 0.444262i
$$96$$ 0 0
$$97$$ 2.50000 4.33013i 0.253837 0.439658i −0.710742 0.703452i $$-0.751641\pi$$
0.964579 + 0.263795i $$0.0849741\pi$$
$$98$$ 0 0
$$99$$ 4.00000 + 6.92820i 0.402015 + 0.696311i
$$100$$ 0 0
$$101$$ −0.500000 0.866025i −0.0497519 0.0861727i 0.840077 0.542467i $$-0.182510\pi$$
−0.889829 + 0.456294i $$0.849176\pi$$
$$102$$ 0 0
$$103$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −20.0000 −1.93347 −0.966736 0.255774i $$-0.917670\pi$$
−0.966736 + 0.255774i $$0.917670\pi$$
$$108$$ 0 0
$$109$$ 1.50000 2.59808i 0.143674 0.248851i −0.785203 0.619238i $$-0.787442\pi$$
0.928877 + 0.370387i $$0.120775\pi$$
$$110$$ 0 0
$$111$$ 5.00000 8.66025i 0.474579 0.821995i
$$112$$ 0 0
$$113$$ 14.0000 1.31701 0.658505 0.752577i $$-0.271189\pi$$
0.658505 + 0.752577i $$0.271189\pi$$
$$114$$ 0 0
$$115$$ 5.00000 0.466252
$$116$$ 0 0
$$117$$ 1.00000 1.73205i 0.0924500 0.160128i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 5.00000 0.454545
$$122$$ 0 0
$$123$$ 2.50000 + 4.33013i 0.225417 + 0.390434i
$$124$$ 0 0
$$125$$ −9.00000 −0.804984
$$126$$ 0 0
$$127$$ 1.50000 + 2.59808i 0.133103 + 0.230542i 0.924871 0.380280i $$-0.124172\pi$$
−0.791768 + 0.610822i $$0.790839\pi$$
$$128$$ 0 0
$$129$$ −2.50000 4.33013i −0.220113 0.381246i
$$130$$ 0 0
$$131$$ 7.50000 12.9904i 0.655278 1.13497i −0.326546 0.945181i $$-0.605885\pi$$
0.981824 0.189794i $$-0.0607819\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 2.50000 4.33013i 0.215166 0.372678i
$$136$$ 0 0
$$137$$ 2.50000 + 4.33013i 0.213589 + 0.369948i 0.952835 0.303488i $$-0.0981512\pi$$
−0.739246 + 0.673436i $$0.764818\pi$$
$$138$$ 0 0
$$139$$ 4.50000 + 7.79423i 0.381685 + 0.661098i 0.991303 0.131597i $$-0.0420106\pi$$
−0.609618 + 0.792695i $$0.708677\pi$$
$$140$$ 0 0
$$141$$ −7.00000 −0.589506
$$142$$ 0 0
$$143$$ −2.00000 3.46410i −0.167248 0.289683i
$$144$$ 0 0
$$145$$ −7.00000 −0.581318
$$146$$ 0 0
$$147$$ 3.50000 6.06218i 0.288675 0.500000i
$$148$$ 0 0
$$149$$ 1.50000 2.59808i 0.122885 0.212843i −0.798019 0.602632i $$-0.794119\pi$$
0.920904 + 0.389789i $$0.127452\pi$$
$$150$$ 0 0
$$151$$ −16.0000 −1.30206 −0.651031 0.759051i $$-0.725663\pi$$
−0.651031 + 0.759051i $$0.725663\pi$$
$$152$$ 0 0
$$153$$ −6.00000 −0.485071
$$154$$ 0 0
$$155$$ −2.00000 + 3.46410i −0.160644 + 0.278243i
$$156$$ 0 0
$$157$$ 3.50000 6.06218i 0.279330 0.483814i −0.691888 0.722005i $$-0.743221\pi$$
0.971219 + 0.238190i $$0.0765542\pi$$
$$158$$ 0 0
$$159$$ −11.0000 −0.872357
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 4.00000 0.313304 0.156652 0.987654i $$-0.449930\pi$$
0.156652 + 0.987654i $$0.449930\pi$$
$$164$$ 0 0
$$165$$ −2.00000 3.46410i −0.155700 0.269680i
$$166$$ 0 0
$$167$$ 7.50000 + 12.9904i 0.580367 + 1.00523i 0.995436 + 0.0954356i $$0.0304244\pi$$
−0.415068 + 0.909790i $$0.636242\pi$$
$$168$$ 0 0
$$169$$ 6.00000 10.3923i 0.461538 0.799408i
$$170$$ 0 0
$$171$$ 7.00000 + 5.19615i 0.535303 + 0.397360i
$$172$$ 0 0
$$173$$ 7.50000 12.9904i 0.570214 0.987640i −0.426329 0.904568i $$-0.640193\pi$$
0.996544 0.0830722i $$-0.0264732\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 1.50000 + 2.59808i 0.112747 + 0.195283i
$$178$$ 0 0
$$179$$ 12.0000 0.896922 0.448461 0.893802i $$-0.351972\pi$$
0.448461 + 0.893802i $$0.351972\pi$$
$$180$$ 0 0
$$181$$ −2.50000 4.33013i −0.185824 0.321856i 0.758030 0.652219i $$-0.226162\pi$$
−0.943854 + 0.330364i $$0.892829\pi$$
$$182$$ 0 0
$$183$$ −11.0000 −0.813143
$$184$$ 0 0
$$185$$ 5.00000 8.66025i 0.367607 0.636715i
$$186$$ 0 0
$$187$$ −6.00000 + 10.3923i −0.438763 + 0.759961i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 16.0000 1.15772 0.578860 0.815427i $$-0.303498\pi$$
0.578860 + 0.815427i $$0.303498\pi$$
$$192$$ 0 0
$$193$$ −7.50000 + 12.9904i −0.539862 + 0.935068i 0.459049 + 0.888411i $$0.348190\pi$$
−0.998911 + 0.0466572i $$0.985143\pi$$
$$194$$ 0 0
$$195$$ −0.500000 + 0.866025i −0.0358057 + 0.0620174i
$$196$$ 0 0
$$197$$ −2.00000 −0.142494 −0.0712470 0.997459i $$-0.522698\pi$$
−0.0712470 + 0.997459i $$0.522698\pi$$
$$198$$ 0 0
$$199$$ 3.50000 + 6.06218i 0.248108 + 0.429736i 0.963001 0.269498i $$-0.0868577\pi$$
−0.714893 + 0.699234i $$0.753524\pi$$
$$200$$ 0 0
$$201$$ 3.00000 0.211604
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 2.50000 + 4.33013i 0.174608 + 0.302429i
$$206$$ 0 0
$$207$$ 5.00000 8.66025i 0.347524 0.601929i
$$208$$ 0 0
$$209$$ 16.0000 6.92820i 1.10674 0.479234i
$$210$$ 0 0
$$211$$ −4.50000 + 7.79423i −0.309793 + 0.536577i −0.978317 0.207114i $$-0.933593\pi$$
0.668524 + 0.743690i $$0.266926\pi$$
$$212$$ 0 0
$$213$$ −5.50000 9.52628i −0.376854 0.652730i
$$214$$ 0 0
$$215$$ −2.50000 4.33013i −0.170499 0.295312i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ −7.50000 12.9904i −0.506803 0.877809i
$$220$$ 0 0
$$221$$ 3.00000 0.201802
$$222$$ 0 0
$$223$$ 12.5000 21.6506i 0.837062 1.44983i −0.0552786 0.998471i $$-0.517605\pi$$
0.892341 0.451363i $$-0.149062\pi$$
$$224$$ 0 0
$$225$$ −4.00000 + 6.92820i −0.266667 + 0.461880i
$$226$$ 0 0
$$227$$ 20.0000 1.32745 0.663723 0.747978i $$-0.268975\pi$$
0.663723 + 0.747978i $$0.268975\pi$$
$$228$$ 0 0
$$229$$ −2.00000 −0.132164 −0.0660819 0.997814i $$-0.521050\pi$$
−0.0660819 + 0.997814i $$0.521050\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 10.5000 18.1865i 0.687878 1.19144i −0.284645 0.958633i $$-0.591876\pi$$
0.972523 0.232806i $$-0.0747909\pi$$
$$234$$ 0 0
$$235$$ −7.00000 −0.456630
$$236$$ 0 0
$$237$$ 6.50000 + 11.2583i 0.422220 + 0.731307i
$$238$$ 0 0
$$239$$ 12.0000 0.776215 0.388108 0.921614i $$-0.373129\pi$$
0.388108 + 0.921614i $$0.373129\pi$$
$$240$$ 0 0
$$241$$ −9.50000 16.4545i −0.611949 1.05993i −0.990912 0.134515i $$-0.957053\pi$$
0.378963 0.925412i $$-0.376281\pi$$
$$242$$ 0 0
$$243$$ −8.00000 13.8564i −0.513200 0.888889i
$$244$$ 0 0
$$245$$ 3.50000 6.06218i 0.223607 0.387298i
$$246$$ 0 0
$$247$$ −3.50000 2.59808i −0.222700 0.165312i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −15.5000 26.8468i −0.978351 1.69455i −0.668400 0.743802i $$-0.733021\pi$$
−0.309951 0.950753i $$-0.600313\pi$$
$$252$$ 0 0
$$253$$ −10.0000 17.3205i −0.628695 1.08893i
$$254$$ 0 0
$$255$$ 3.00000 0.187867
$$256$$ 0 0
$$257$$ −11.5000 19.9186i −0.717350 1.24249i −0.962046 0.272887i $$-0.912021\pi$$
0.244696 0.969600i $$-0.421312\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ −7.00000 + 12.1244i −0.433289 + 0.750479i
$$262$$ 0 0
$$263$$ 4.50000 7.79423i 0.277482 0.480613i −0.693276 0.720672i $$-0.743833\pi$$
0.970758 + 0.240059i $$0.0771668\pi$$
$$264$$ 0 0
$$265$$ −11.0000 −0.675725
$$266$$ 0 0
$$267$$ 3.00000 0.183597
$$268$$ 0 0
$$269$$ 13.5000 23.3827i 0.823110 1.42567i −0.0802460 0.996775i $$-0.525571\pi$$
0.903356 0.428892i $$-0.141096\pi$$
$$270$$ 0 0
$$271$$ −15.5000 + 26.8468i −0.941558 + 1.63083i −0.179057 + 0.983839i $$0.557305\pi$$
−0.762501 + 0.646988i $$0.776029\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 8.00000 + 13.8564i 0.482418 + 0.835573i
$$276$$ 0 0
$$277$$ −10.0000 −0.600842 −0.300421 0.953807i $$-0.597127\pi$$
−0.300421 + 0.953807i $$0.597127\pi$$
$$278$$ 0 0
$$279$$ 4.00000 + 6.92820i 0.239474 + 0.414781i
$$280$$ 0 0
$$281$$ −3.50000 6.06218i −0.208792 0.361639i 0.742542 0.669800i $$-0.233620\pi$$
−0.951334 + 0.308160i $$0.900287\pi$$
$$282$$ 0 0
$$283$$ −4.50000 + 7.79423i −0.267497 + 0.463319i −0.968215 0.250120i $$-0.919530\pi$$
0.700718 + 0.713439i $$0.252863\pi$$
$$284$$ 0 0
$$285$$ −3.50000 2.59808i −0.207322 0.153897i
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 4.00000 + 6.92820i 0.235294 + 0.407541i
$$290$$ 0 0
$$291$$ 2.50000 + 4.33013i 0.146553 + 0.253837i
$$292$$ 0 0
$$293$$ 30.0000 1.75262 0.876309 0.481749i $$-0.159998\pi$$
0.876309 + 0.481749i $$0.159998\pi$$
$$294$$ 0 0
$$295$$ 1.50000 + 2.59808i 0.0873334 + 0.151266i
$$296$$ 0 0
$$297$$ −20.0000 −1.16052
$$298$$ 0 0
$$299$$ −2.50000 + 4.33013i −0.144579 + 0.250418i
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 1.00000 0.0574485
$$304$$ 0 0
$$305$$ −11.0000 −0.629858
$$306$$ 0 0
$$307$$ 13.5000 23.3827i 0.770486 1.33452i −0.166811 0.985989i $$-0.553347\pi$$
0.937297 0.348532i $$-0.113320\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −20.0000 −1.13410 −0.567048 0.823685i $$-0.691915\pi$$
−0.567048 + 0.823685i $$0.691915\pi$$
$$312$$ 0 0
$$313$$ −5.50000 9.52628i −0.310878 0.538457i 0.667674 0.744453i $$-0.267290\pi$$
−0.978553 + 0.205996i $$0.933957\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 7.50000 + 12.9904i 0.421242 + 0.729612i 0.996061 0.0886679i $$-0.0282610\pi$$
−0.574819 + 0.818280i $$0.694928\pi$$
$$318$$ 0 0
$$319$$ 14.0000 + 24.2487i 0.783850 + 1.35767i
$$320$$ 0 0
$$321$$ 10.0000 17.3205i 0.558146 0.966736i
$$322$$ 0 0
$$323$$ −1.50000 + 12.9904i −0.0834622 + 0.722804i
$$324$$ 0 0
$$325$$ 2.00000 3.46410i 0.110940 0.192154i
$$326$$ 0 0
$$327$$ 1.50000 + 2.59808i 0.0829502 + 0.143674i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −20.0000 −1.09930 −0.549650 0.835395i $$-0.685239\pi$$
−0.549650 + 0.835395i $$0.685239\pi$$
$$332$$ 0 0
$$333$$ −10.0000 17.3205i −0.547997 0.949158i
$$334$$ 0 0
$$335$$ 3.00000 0.163908
$$336$$ 0 0
$$337$$ 2.50000 4.33013i 0.136184 0.235877i −0.789865 0.613280i $$-0.789850\pi$$
0.926049 + 0.377403i $$0.123183\pi$$
$$338$$ 0 0
$$339$$ −7.00000 + 12.1244i −0.380188 + 0.658505i
$$340$$ 0 0
$$341$$ 16.0000 0.866449
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ −2.50000 + 4.33013i −0.134595 + 0.233126i
$$346$$ 0 0
$$347$$ −2.50000 + 4.33013i −0.134207 + 0.232453i −0.925294 0.379250i $$-0.876182\pi$$
0.791087 + 0.611703i $$0.209515\pi$$
$$348$$ 0 0
$$349$$ −10.0000 −0.535288 −0.267644 0.963518i $$-0.586245\pi$$
−0.267644 + 0.963518i $$0.586245\pi$$
$$350$$ 0 0
$$351$$ 2.50000 + 4.33013i 0.133440 + 0.231125i
$$352$$ 0 0
$$353$$ 30.0000 1.59674 0.798369 0.602168i $$-0.205696\pi$$
0.798369 + 0.602168i $$0.205696\pi$$
$$354$$ 0 0
$$355$$ −5.50000 9.52628i −0.291910 0.505602i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −7.50000 + 12.9904i −0.395835 + 0.685606i −0.993207 0.116358i $$-0.962878\pi$$
0.597372 + 0.801964i $$0.296211\pi$$
$$360$$ 0 0
$$361$$ 13.0000 13.8564i 0.684211 0.729285i
$$362$$ 0 0
$$363$$ −2.50000 + 4.33013i −0.131216 + 0.227273i
$$364$$ 0 0
$$365$$ −7.50000 12.9904i −0.392568 0.679948i
$$366$$ 0 0
$$367$$ −12.5000 21.6506i −0.652495 1.13015i −0.982516 0.186180i $$-0.940389\pi$$
0.330021 0.943974i $$-0.392944\pi$$
$$368$$ 0 0
$$369$$ 10.0000 0.520579
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 10.0000 0.517780 0.258890 0.965907i $$-0.416643\pi$$
0.258890 + 0.965907i $$0.416643\pi$$
$$374$$ 0 0
$$375$$ 4.50000 7.79423i 0.232379 0.402492i
$$376$$ 0 0
$$377$$ 3.50000 6.06218i 0.180259 0.312218i
$$378$$ 0 0
$$379$$ 12.0000 0.616399 0.308199 0.951322i $$-0.400274\pi$$
0.308199 + 0.951322i $$0.400274\pi$$
$$380$$ 0 0
$$381$$ −3.00000 −0.153695
$$382$$ 0 0
$$383$$ 14.5000 25.1147i 0.740915 1.28330i −0.211164 0.977451i $$-0.567725\pi$$
0.952079 0.305852i $$-0.0989414\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −10.0000 −0.508329
$$388$$ 0 0
$$389$$ 1.50000 + 2.59808i 0.0760530 + 0.131728i 0.901544 0.432688i $$-0.142435\pi$$
−0.825491 + 0.564416i $$0.809102\pi$$
$$390$$ 0 0
$$391$$ 15.0000 0.758583
$$392$$ 0 0
$$393$$ 7.50000 + 12.9904i 0.378325 + 0.655278i
$$394$$ 0 0
$$395$$ 6.50000 + 11.2583i 0.327050 + 0.566468i
$$396$$ 0 0
$$397$$ −12.5000 + 21.6506i −0.627357 + 1.08661i 0.360723 + 0.932673i $$0.382530\pi$$
−0.988080 + 0.153941i $$0.950803\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −9.50000 + 16.4545i −0.474407 + 0.821698i −0.999571 0.0293039i $$-0.990671\pi$$
0.525163 + 0.851002i $$0.324004\pi$$
$$402$$ 0 0
$$403$$ −2.00000 3.46410i −0.0996271 0.172559i
$$404$$ 0 0
$$405$$ −0.500000 0.866025i −0.0248452 0.0430331i
$$406$$ 0 0
$$407$$ −40.0000 −1.98273
$$408$$ 0 0
$$409$$ 8.50000 + 14.7224i 0.420298 + 0.727977i 0.995968 0.0897044i $$-0.0285922\pi$$
−0.575670 + 0.817682i $$0.695259\pi$$
$$410$$ 0 0
$$411$$ −5.00000 −0.246632
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ −9.00000 −0.440732
$$418$$ 0 0
$$419$$ −12.0000 −0.586238 −0.293119 0.956076i $$-0.594693\pi$$
−0.293119 + 0.956076i $$0.594693\pi$$
$$420$$ 0 0
$$421$$ −0.500000 + 0.866025i −0.0243685 + 0.0422075i −0.877952 0.478748i $$-0.841091\pi$$
0.853584 + 0.520955i $$0.174424\pi$$
$$422$$ 0 0
$$423$$ −7.00000 + 12.1244i −0.340352 + 0.589506i
$$424$$ 0 0
$$425$$ −12.0000 −0.582086
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 4.00000 0.193122
$$430$$ 0 0
$$431$$ −10.5000 18.1865i −0.505767 0.876014i −0.999978 0.00667224i $$-0.997876\pi$$
0.494211 0.869342i $$-0.335457\pi$$
$$432$$ 0 0
$$433$$ 12.5000 + 21.6506i 0.600712 + 1.04046i 0.992713 + 0.120499i $$0.0384494\pi$$
−0.392002 + 0.919964i $$0.628217\pi$$
$$434$$ 0 0
$$435$$ 3.50000 6.06218i 0.167812 0.290659i
$$436$$ 0 0
$$437$$ −17.5000 12.9904i −0.837139 0.621414i
$$438$$ 0 0
$$439$$ 6.50000 11.2583i 0.310228 0.537331i −0.668184 0.743996i $$-0.732928\pi$$
0.978412 + 0.206666i $$0.0662612\pi$$
$$440$$ 0 0
$$441$$ −7.00000 12.1244i −0.333333 0.577350i
$$442$$ 0 0
$$443$$ 12.5000 + 21.6506i 0.593893 + 1.02865i 0.993702 + 0.112054i $$0.0357431\pi$$
−0.399809 + 0.916598i $$0.630924\pi$$
$$444$$ 0 0
$$445$$ 3.00000 0.142214
$$446$$ 0 0
$$447$$ 1.50000 + 2.59808i 0.0709476 + 0.122885i
$$448$$ 0 0
$$449$$ 22.0000 1.03824 0.519122 0.854700i $$-0.326259\pi$$
0.519122 + 0.854700i $$0.326259\pi$$
$$450$$ 0 0
$$451$$ 10.0000 17.3205i 0.470882 0.815591i
$$452$$ 0 0
$$453$$ 8.00000 13.8564i 0.375873 0.651031i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −22.0000 −1.02912 −0.514558 0.857455i $$-0.672044\pi$$
−0.514558 + 0.857455i $$0.672044\pi$$
$$458$$ 0 0
$$459$$ 7.50000 12.9904i 0.350070 0.606339i
$$460$$ 0 0
$$461$$ 5.50000 9.52628i 0.256161 0.443683i −0.709050 0.705159i $$-0.750876\pi$$
0.965210 + 0.261476i $$0.0842091\pi$$
$$462$$ 0 0
$$463$$ −20.0000 −0.929479 −0.464739 0.885448i $$-0.653852\pi$$
−0.464739 + 0.885448i $$0.653852\pi$$
$$464$$ 0 0
$$465$$ −2.00000 3.46410i −0.0927478 0.160644i
$$466$$ 0 0
$$467$$ 20.0000 0.925490 0.462745 0.886492i $$-0.346865\pi$$
0.462745 + 0.886492i $$0.346865\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 3.50000 + 6.06218i 0.161271 + 0.279330i
$$472$$ 0 0
$$473$$ −10.0000 + 17.3205i −0.459800 + 0.796398i
$$474$$ 0 0
$$475$$ 14.0000 + 10.3923i 0.642364 + 0.476832i
$$476$$ 0 0
$$477$$ −11.0000 + 19.0526i −0.503655 + 0.872357i
$$478$$ 0 0
$$479$$ 11.5000 + 19.9186i 0.525448 + 0.910103i 0.999561 + 0.0296389i $$0.00943575\pi$$
−0.474112 + 0.880464i $$0.657231\pi$$
$$480$$ 0 0
$$481$$ 5.00000 + 8.66025i 0.227980 + 0.394874i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 2.50000 + 4.33013i 0.113519 + 0.196621i
$$486$$ 0 0
$$487$$ −8.00000 −0.362515 −0.181257 0.983436i $$-0.558017\pi$$
−0.181257 + 0.983436i $$0.558017\pi$$
$$488$$ 0 0
$$489$$ −2.00000 + 3.46410i −0.0904431 + 0.156652i
$$490$$ 0 0
$$491$$ −0.500000 + 0.866025i −0.0225647 + 0.0390832i −0.877087 0.480331i $$-0.840517\pi$$
0.854523 + 0.519414i $$0.173850\pi$$
$$492$$ 0 0
$$493$$ −21.0000 −0.945792
$$494$$ 0 0
$$495$$ −8.00000 −0.359573
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −2.50000 + 4.33013i −0.111915 + 0.193843i −0.916542 0.399937i $$-0.869032\pi$$
0.804627 + 0.593780i $$0.202365\pi$$
$$500$$ 0 0
$$501$$ −15.0000 −0.670151
$$502$$ 0 0
$$503$$ −10.5000 18.1865i −0.468172 0.810897i 0.531167 0.847267i $$-0.321754\pi$$
−0.999338 + 0.0363700i $$0.988421\pi$$
$$504$$ 0 0
$$505$$ 1.00000 0.0444994
$$506$$ 0 0
$$507$$ 6.00000 + 10.3923i 0.266469 + 0.461538i
$$508$$ 0 0
$$509$$ 7.50000 + 12.9904i 0.332432 + 0.575789i 0.982988 0.183669i $$-0.0587976\pi$$
−0.650556 + 0.759458i $$0.725464\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ −20.0000 + 8.66025i −0.883022 + 0.382360i
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 14.0000 + 24.2487i 0.615719 + 1.06646i
$$518$$ 0 0
$$519$$ 7.50000 + 12.9904i 0.329213 + 0.570214i
$$520$$ 0 0
$$521$$ 26.0000 1.13908 0.569540 0.821963i $$-0.307121\pi$$
0.569540 + 0.821963i $$0.307121\pi$$
$$522$$ 0 0
$$523$$ −9.50000 16.4545i −0.415406 0.719504i 0.580065 0.814570i $$-0.303027\pi$$
−0.995471 + 0.0950659i $$0.969694\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −6.00000 + 10.3923i −0.261364 + 0.452696i
$$528$$ 0 0
$$529$$ −1.00000 + 1.73205i −0.0434783 + 0.0753066i
$$530$$ 0 0
$$531$$ 6.00000 0.260378
$$532$$ 0 0
$$533$$ −5.00000 −0.216574
$$534$$ 0 0
$$535$$ 10.0000 17.3205i 0.432338 0.748831i
$$536$$ 0 0
$$537$$ −6.00000 + 10.3923i −0.258919 + 0.448461i
$$538$$ 0 0
$$539$$ −28.0000 −1.20605
$$540$$ 0 0
$$541$$ −0.500000 0.866025i −0.0214967 0.0372333i 0.855077 0.518501i $$-0.173510\pi$$
−0.876574 + 0.481268i $$0.840176\pi$$
$$542$$ 0 0
$$543$$ 5.00000 0.214571
$$544$$ 0 0
$$545$$ 1.50000 + 2.59808i 0.0642529 + 0.111289i
$$546$$ 0 0
$$547$$ 12.5000 + 21.6506i 0.534461 + 0.925714i 0.999189 + 0.0402607i $$0.0128188\pi$$
−0.464728 + 0.885454i $$0.653848\pi$$
$$548$$ 0 0
$$549$$ −11.0000 + 19.0526i −0.469469 + 0.813143i
$$550$$ 0 0
$$551$$ 24.5000 + 18.1865i 1.04374 + 0.774772i
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 5.00000 + 8.66025i 0.212238 + 0.367607i
$$556$$ 0 0
$$557$$ −2.50000 4.33013i −0.105928 0.183473i 0.808189 0.588924i $$-0.200448\pi$$
−0.914117 + 0.405450i $$0.867115\pi$$
$$558$$ 0 0
$$559$$ 5.00000 0.211477
$$560$$ 0 0
$$561$$ −6.00000 10.3923i −0.253320 0.438763i
$$562$$ 0 0
$$563$$ −36.0000 −1.51722 −0.758610 0.651546i $$-0.774121\pi$$
−0.758610 + 0.651546i $$0.774121\pi$$
$$564$$ 0 0
$$565$$ −7.00000 + 12.1244i −0.294492 + 0.510075i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 22.0000 0.922288 0.461144 0.887325i $$-0.347439\pi$$
0.461144 + 0.887325i $$0.347439\pi$$
$$570$$ 0 0
$$571$$ 4.00000 0.167395 0.0836974 0.996491i $$-0.473327\pi$$
0.0836974 + 0.996491i $$0.473327\pi$$
$$572$$ 0 0
$$573$$ −8.00000 + 13.8564i −0.334205 + 0.578860i
$$574$$ 0 0
$$575$$ 10.0000 17.3205i 0.417029 0.722315i
$$576$$ 0 0
$$577$$ −10.0000 −0.416305 −0.208153 0.978096i $$-0.566745\pi$$
−0.208153 + 0.978096i $$0.566745\pi$$
$$578$$ 0 0
$$579$$ −7.50000 12.9904i −0.311689 0.539862i
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 22.0000 + 38.1051i 0.911147 + 1.57815i
$$584$$ 0 0
$$585$$ 1.00000 + 1.73205i 0.0413449 + 0.0716115i
$$586$$ 0 0
$$587$$ 7.50000 12.9904i 0.309558 0.536170i −0.668708 0.743525i $$-0.733152\pi$$
0.978266 + 0.207355i $$0.0664855\pi$$
$$588$$ 0 0
$$589$$ 16.0000 6.92820i 0.659269 0.285472i
$$590$$ 0 0
$$591$$ 1.00000 1.73205i 0.0411345 0.0712470i
$$592$$ 0 0
$$593$$ 2.50000 + 4.33013i 0.102663 + 0.177817i 0.912781 0.408450i $$-0.133930\pi$$
−0.810118 + 0.586267i $$0.800597\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ −7.00000 −0.286491
$$598$$ 0 0
$$599$$ −22.5000 38.9711i −0.919325 1.59232i −0.800443 0.599409i $$-0.795402\pi$$
−0.118882 0.992908i $$-0.537931\pi$$
$$600$$ 0 0
$$601$$ −26.0000 −1.06056 −0.530281 0.847822i $$-0.677914\pi$$
−0.530281 + 0.847822i $$0.677914\pi$$
$$602$$ 0 0
$$603$$ 3.00000 5.19615i 0.122169 0.211604i
$$604$$ 0 0
$$605$$ −2.50000 + 4.33013i −0.101639 + 0.176045i
$$606$$ 0 0
$$607$$ 32.0000 1.29884 0.649420 0.760430i $$-0.275012\pi$$
0.649420 + 0.760430i $$0.275012\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 3.50000 6.06218i 0.141595 0.245249i
$$612$$ 0 0
$$613$$ −14.5000 + 25.1147i −0.585649 + 1.01437i 0.409145 + 0.912470i $$0.365827\pi$$
−0.994794 + 0.101905i $$0.967506\pi$$
$$614$$ 0 0
$$615$$ −5.00000 −0.201619
$$616$$ 0 0
$$617$$ 22.5000 + 38.9711i 0.905816 + 1.56892i 0.819818 + 0.572624i $$0.194074\pi$$
0.0859976 + 0.996295i $$0.472592\pi$$
$$618$$ 0 0
$$619$$ 20.0000 0.803868 0.401934 0.915669i $$-0.368338\pi$$
0.401934 + 0.915669i $$0.368338\pi$$
$$620$$ 0 0
$$621$$ 12.5000 + 21.6506i 0.501608 + 0.868810i
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −5.50000 + 9.52628i −0.220000 + 0.381051i
$$626$$ 0 0
$$627$$ −2.00000 + 17.3205i −0.0798723 + 0.691714i
$$628$$ 0 0
$$629$$ 15.0000 25.9808i 0.598089 1.03592i
$$630$$ 0 0
$$631$$ −20.5000 35.5070i −0.816092 1.41351i −0.908541 0.417796i $$-0.862803\pi$$
0.0924489 0.995717i $$-0.470531\pi$$
$$632$$ 0 0
$$633$$ −4.50000 7.79423i −0.178859 0.309793i
$$634$$ 0 0
$$635$$ −3.00000 −0.119051
$$636$$ 0 0
$$637$$ 3.50000 + 6.06218i 0.138675 + 0.240192i
$$638$$ 0 0
$$639$$ −22.0000 −0.870307
$$640$$ 0 0
$$641$$ −19.5000 + 33.7750i −0.770204 + 1.33403i 0.167247 + 0.985915i $$0.446512\pi$$
−0.937451 + 0.348117i $$0.886821\pi$$
$$642$$ 0 0
$$643$$ 9.50000 16.4545i 0.374643 0.648901i −0.615630 0.788035i $$-0.711098\pi$$
0.990274 + 0.139134i $$0.0444318\pi$$
$$644$$ 0 0
$$645$$ 5.00000 0.196875
$$646$$ 0 0
$$647$$ 32.0000 1.25805 0.629025 0.777385i $$-0.283454\pi$$
0.629025 + 0.777385i $$0.283454\pi$$
$$648$$ 0 0
$$649$$ 6.00000 10.3923i 0.235521 0.407934i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 30.0000 1.17399 0.586995 0.809590i $$-0.300311\pi$$
0.586995 + 0.809590i $$0.300311\pi$$
$$654$$ 0 0
$$655$$ 7.50000 + 12.9904i 0.293049 + 0.507576i
$$656$$ 0 0
$$657$$ −30.0000 −1.17041
$$658$$ 0 0
$$659$$ 2.50000 + 4.33013i 0.0973862 + 0.168678i 0.910602 0.413284i $$-0.135618\pi$$
−0.813216 + 0.581962i $$0.802285\pi$$
$$660$$ 0 0
$$661$$ 15.5000 + 26.8468i 0.602880 + 1.04422i 0.992383 + 0.123194i $$0.0393136\pi$$
−0.389503 + 0.921025i $$0.627353\pi$$
$$662$$ 0 0
$$663$$ −1.50000 + 2.59808i −0.0582552 + 0.100901i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 17.5000 30.3109i 0.677603 1.17364i
$$668$$ 0 0
$$669$$ 12.5000 + 21.6506i 0.483278 + 0.837062i
$$670$$ 0 0
$$671$$ 22.0000 + 38.1051i 0.849301 + 1.47103i
$$672$$ 0 0
$$673$$ −10.0000 −0.385472 −0.192736 0.981251i $$-0.561736\pi$$
−0.192736 + 0.981251i $$0.561736\pi$$
$$674$$ 0 0
$$675$$ −10.0000 17.3205i −0.384900 0.666667i
$$676$$ 0 0
$$677$$ −10.0000 −0.384331 −0.192166 0.981363i $$-0.561551\pi$$
−0.192166 + 0.981363i $$0.561551\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ −10.0000 + 17.3205i −0.383201 + 0.663723i
$$682$$ 0 0
$$683$$ −16.0000 −0.612223 −0.306111 0.951996i $$-0.599028\pi$$
−0.306111 + 0.951996i $$0.599028\pi$$
$$684$$ 0 0
$$685$$ −5.00000 −0.191040
$$686$$ 0 0
$$687$$ 1.00000 1.73205i 0.0381524 0.0660819i
$$688$$ 0 0
$$689$$ 5.50000 9.52628i 0.209533 0.362922i
$$690$$ 0 0
$$691$$ −36.0000 −1.36950 −0.684752 0.728776i $$-0.740090\pi$$
−0.684752 + 0.728776i $$0.740090\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −9.00000 −0.341389
$$696$$ 0 0
$$697$$ 7.50000 + 12.9904i 0.284083 + 0.492046i
$$698$$ 0 0
$$699$$ 10.5000 + 18.1865i 0.397146 + 0.687878i
$$700$$ 0 0
$$701$$ 17.5000 30.3109i 0.660966 1.14483i −0.319396 0.947621i $$-0.603480\pi$$
0.980362 0.197205i $$-0.0631865\pi$$
$$702$$ 0 0
$$703$$ −40.0000 + 17.3205i −1.50863 + 0.653255i
$$704$$ 0 0
$$705$$ 3.50000 6.06218i 0.131818 0.228315i
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 1.50000 + 2.59808i 0.0563337 + 0.0975728i 0.892817 0.450420i $$-0.148726\pi$$
−0.836483 + 0.547992i $$0.815392\pi$$
$$710$$ 0 0
$$711$$ 26.0000 0.975076
$$712$$ 0 0
$$713$$ −10.0000 17.3205i −0.374503 0.648658i
$$714$$ 0 0
$$715$$ 4.00000 0.149592
$$716$$ 0 0
$$717$$ −6.00000 + 10.3923i −0.224074 + 0.388108i
$$718$$ 0 0
$$719$$ −3.50000 + 6.06218i −0.130528 + 0.226081i −0.923880 0.382682i $$-0.875001\pi$$
0.793352 + 0.608763i $$0.208334\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 19.0000 0.706618
$$724$$ 0 0
$$725$$ −14.0000 + 24.2487i −0.519947 + 0.900575i
$$726$$ 0 0
$$727$$ −3.50000 + 6.06218i −0.129808 + 0.224834i −0.923602 0.383353i $$-0.874769\pi$$
0.793794 + 0.608186i $$0.208103\pi$$
$$728$$ 0 0
$$729$$ 13.0000 0.481481
$$730$$ 0 0
$$731$$ −7.50000 12.9904i −0.277398 0.480467i
$$732$$ 0 0
$$733$$ 30.0000 1.10808 0.554038 0.832492i $$-0.313086\pi$$
0.554038 + 0.832492i $$0.313086\pi$$
$$734$$ 0 0
$$735$$ 3.50000 + 6.06218i 0.129099 + 0.223607i
$$736$$ 0 0
$$737$$ −6.00000 10.3923i −0.221013 0.382805i
$$738$$ 0 0
$$739$$ −6.50000 + 11.2583i −0.239106 + 0.414144i −0.960458 0.278425i $$-0.910188\pi$$
0.721352 + 0.692569i $$0.243521\pi$$
$$740$$ 0 0
$$741$$ 4.00000 1.73205i 0.146944 0.0636285i
$$742$$ 0 0
$$743$$ 12.5000 21.6506i 0.458581 0.794285i −0.540306 0.841469i $$-0.681691\pi$$
0.998886 + 0.0471840i $$0.0150247\pi$$
$$744$$ 0 0
$$745$$ 1.50000 + 2.59808i 0.0549557 + 0.0951861i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −14.5000 25.1147i −0.529113 0.916450i −0.999424 0.0339490i $$-0.989192\pi$$
0.470311 0.882501i $$-0.344142\pi$$
$$752$$ 0 0
$$753$$ 31.0000 1.12970
$$754$$ 0 0
$$755$$ 8.00000 13.8564i 0.291150 0.504286i
$$756$$ 0 0
$$757$$ −8.50000 + 14.7224i −0.308938 + 0.535096i −0.978130 0.207993i $$-0.933307\pi$$
0.669193 + 0.743089i $$0.266640\pi$$
$$758$$ 0 0
$$759$$ 20.0000 0.725954
$$760$$ 0 0
$$761$$ 30.0000 1.08750 0.543750 0.839248i $$-0.317004\pi$$
0.543750 + 0.839248i $$0.317004\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 3.00000 5.19615i 0.108465 0.187867i
$$766$$ 0 0
$$767$$ −3.00000 −0.108324
$$768$$ 0 0
$$769$$ −3.50000 6.06218i −0.126213 0.218608i 0.795993 0.605305i $$-0.206949\pi$$
−0.922207 + 0.386698i $$0.873616\pi$$
$$770$$ 0 0
$$771$$ 23.0000 0.828325
$$772$$ 0 0
$$773$$ −10.5000 18.1865i −0.377659 0.654124i 0.613062 0.790034i $$-0.289937\pi$$
−0.990721 + 0.135910i $$0.956604\pi$$
$$774$$ 0 0
$$775$$ 8.00000 + 13.8564i 0.287368 + 0.497737i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 2.50000 21.6506i 0.0895718 0.775715i
$$780$$ 0 0
$$781$$ −22.0000 + 38.1051i −0.787222 + 1.36351i
$$782$$ 0 0
$$783$$ −17.5000 30.3109i −0.625399 1.08322i
$$784$$ 0 0
$$785$$ 3.50000 + 6.06218i 0.124920 + 0.216368i
$$786$$ 0 0
$$787$$ −52.0000 −1.85360 −0.926800 0.375555i $$-0.877452\pi$$
−0.926800 + 0.375555i $$0.877452\pi$$
$$788$$ 0 0
$$789$$ 4.50000 + 7.79423i 0.160204 + 0.277482i
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0