# Properties

 Label 1680.2.bg.g.961.1 Level $1680$ Weight $2$ Character 1680.961 Analytic conductor $13.415$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1680.bg (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$13.4148675396$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 210) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 961.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 1680.961 Dual form 1680.2.bg.g.1201.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-2.00000 + 1.73205i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$q+(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-2.00000 + 1.73205i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{11} +1.00000 q^{13} -1.00000 q^{15} +(-1.50000 + 2.59808i) q^{19} +(2.50000 + 0.866025i) q^{21} +(3.50000 - 6.06218i) q^{23} +(-0.500000 - 0.866025i) q^{25} +1.00000 q^{27} -8.00000 q^{29} +(-1.00000 - 1.73205i) q^{31} +(-0.500000 + 0.866025i) q^{33} +(0.500000 + 2.59808i) q^{35} +(-5.50000 + 9.52628i) q^{37} +(-0.500000 - 0.866025i) q^{39} -11.0000 q^{41} -8.00000 q^{43} +(0.500000 + 0.866025i) q^{45} +(-2.50000 + 4.33013i) q^{47} +(1.00000 - 6.92820i) q^{49} +(5.50000 + 9.52628i) q^{53} -1.00000 q^{55} +3.00000 q^{57} +(2.00000 + 3.46410i) q^{59} +(-0.500000 - 2.59808i) q^{63} +(0.500000 - 0.866025i) q^{65} -7.00000 q^{69} +6.00000 q^{71} +(3.00000 + 5.19615i) q^{73} +(-0.500000 + 0.866025i) q^{75} +(2.50000 + 0.866025i) q^{77} +(-4.00000 + 6.92820i) q^{79} +(-0.500000 - 0.866025i) q^{81} -8.00000 q^{83} +(4.00000 + 6.92820i) q^{87} +(5.00000 - 8.66025i) q^{89} +(-2.00000 + 1.73205i) q^{91} +(-1.00000 + 1.73205i) q^{93} +(1.50000 + 2.59808i) q^{95} -16.0000 q^{97} +1.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - q^{3} + q^{5} - 4q^{7} - q^{9} + O(q^{10})$$ $$2q - q^{3} + q^{5} - 4q^{7} - q^{9} - q^{11} + 2q^{13} - 2q^{15} - 3q^{19} + 5q^{21} + 7q^{23} - q^{25} + 2q^{27} - 16q^{29} - 2q^{31} - q^{33} + q^{35} - 11q^{37} - q^{39} - 22q^{41} - 16q^{43} + q^{45} - 5q^{47} + 2q^{49} + 11q^{53} - 2q^{55} + 6q^{57} + 4q^{59} - q^{63} + q^{65} - 14q^{69} + 12q^{71} + 6q^{73} - q^{75} + 5q^{77} - 8q^{79} - q^{81} - 16q^{83} + 8q^{87} + 10q^{89} - 4q^{91} - 2q^{93} + 3q^{95} - 32q^{97} + 2q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times$$.

 $$n$$ $$241$$ $$337$$ $$421$$ $$1121$$ $$1471$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$1$$ $$1$$ $$1$$

## 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
$$4$$ 0 0
$$5$$ 0.500000 0.866025i 0.223607 0.387298i
$$6$$ 0 0
$$7$$ −2.00000 + 1.73205i −0.755929 + 0.654654i
$$8$$ 0 0
$$9$$ −0.500000 + 0.866025i −0.166667 + 0.288675i
$$10$$ 0 0
$$11$$ −0.500000 0.866025i −0.150756 0.261116i 0.780750 0.624844i $$-0.214837\pi$$
−0.931505 + 0.363727i $$0.881504\pi$$
$$12$$ 0 0
$$13$$ 1.00000 0.277350 0.138675 0.990338i $$-0.455716\pi$$
0.138675 + 0.990338i $$0.455716\pi$$
$$14$$ 0 0
$$15$$ −1.00000 −0.258199
$$16$$ 0 0
$$17$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$18$$ 0 0
$$19$$ −1.50000 + 2.59808i −0.344124 + 0.596040i −0.985194 0.171442i $$-0.945157\pi$$
0.641071 + 0.767482i $$0.278491\pi$$
$$20$$ 0 0
$$21$$ 2.50000 + 0.866025i 0.545545 + 0.188982i
$$22$$ 0 0
$$23$$ 3.50000 6.06218i 0.729800 1.26405i −0.227167 0.973856i $$-0.572946\pi$$
0.956967 0.290196i $$-0.0937204\pi$$
$$24$$ 0 0
$$25$$ −0.500000 0.866025i −0.100000 0.173205i
$$26$$ 0 0
$$27$$ 1.00000 0.192450
$$28$$ 0 0
$$29$$ −8.00000 −1.48556 −0.742781 0.669534i $$-0.766494\pi$$
−0.742781 + 0.669534i $$0.766494\pi$$
$$30$$ 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 0
$$33$$ −0.500000 + 0.866025i −0.0870388 + 0.150756i
$$34$$ 0 0
$$35$$ 0.500000 + 2.59808i 0.0845154 + 0.439155i
$$36$$ 0 0
$$37$$ −5.50000 + 9.52628i −0.904194 + 1.56611i −0.0821995 + 0.996616i $$0.526194\pi$$
−0.821995 + 0.569495i $$0.807139\pi$$
$$38$$ 0 0
$$39$$ −0.500000 0.866025i −0.0800641 0.138675i
$$40$$ 0 0
$$41$$ −11.0000 −1.71791 −0.858956 0.512050i $$-0.828886\pi$$
−0.858956 + 0.512050i $$0.828886\pi$$
$$42$$ 0 0
$$43$$ −8.00000 −1.21999 −0.609994 0.792406i $$-0.708828\pi$$
−0.609994 + 0.792406i $$0.708828\pi$$
$$44$$ 0 0
$$45$$ 0.500000 + 0.866025i 0.0745356 + 0.129099i
$$46$$ 0 0
$$47$$ −2.50000 + 4.33013i −0.364662 + 0.631614i −0.988722 0.149763i $$-0.952149\pi$$
0.624059 + 0.781377i $$0.285482\pi$$
$$48$$ 0 0
$$49$$ 1.00000 6.92820i 0.142857 0.989743i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 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
$$55$$ −1.00000 −0.134840
$$56$$ 0 0
$$57$$ 3.00000 0.397360
$$58$$ 0 0
$$59$$ 2.00000 + 3.46410i 0.260378 + 0.450988i 0.966342 0.257260i $$-0.0828195\pi$$
−0.705965 + 0.708247i $$0.749486\pi$$
$$60$$ 0 0
$$61$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$62$$ 0 0
$$63$$ −0.500000 2.59808i −0.0629941 0.327327i
$$64$$ 0 0
$$65$$ 0.500000 0.866025i 0.0620174 0.107417i
$$66$$ 0 0
$$67$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$68$$ 0 0
$$69$$ −7.00000 −0.842701
$$70$$ 0 0
$$71$$ 6.00000 0.712069 0.356034 0.934473i $$-0.384129\pi$$
0.356034 + 0.934473i $$0.384129\pi$$
$$72$$ 0 0
$$73$$ 3.00000 + 5.19615i 0.351123 + 0.608164i 0.986447 0.164083i $$-0.0524664\pi$$
−0.635323 + 0.772246i $$0.719133\pi$$
$$74$$ 0 0
$$75$$ −0.500000 + 0.866025i −0.0577350 + 0.100000i
$$76$$ 0 0
$$77$$ 2.50000 + 0.866025i 0.284901 + 0.0986928i
$$78$$ 0 0
$$79$$ −4.00000 + 6.92820i −0.450035 + 0.779484i −0.998388 0.0567635i $$-0.981922\pi$$
0.548352 + 0.836247i $$0.315255\pi$$
$$80$$ 0 0
$$81$$ −0.500000 0.866025i −0.0555556 0.0962250i
$$82$$ 0 0
$$83$$ −8.00000 −0.878114 −0.439057 0.898459i $$-0.644687\pi$$
−0.439057 + 0.898459i $$0.644687\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 4.00000 + 6.92820i 0.428845 + 0.742781i
$$88$$ 0 0
$$89$$ 5.00000 8.66025i 0.529999 0.917985i −0.469389 0.882992i $$-0.655526\pi$$
0.999388 0.0349934i $$-0.0111410\pi$$
$$90$$ 0 0
$$91$$ −2.00000 + 1.73205i −0.209657 + 0.181568i
$$92$$ 0 0
$$93$$ −1.00000 + 1.73205i −0.103695 + 0.179605i
$$94$$ 0 0
$$95$$ 1.50000 + 2.59808i 0.153897 + 0.266557i
$$96$$ 0 0
$$97$$ −16.0000 −1.62455 −0.812277 0.583272i $$-0.801772\pi$$
−0.812277 + 0.583272i $$0.801772\pi$$
$$98$$ 0 0
$$99$$ 1.00000 0.100504
$$100$$ 0 0
$$101$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$102$$ 0 0
$$103$$ −8.00000 + 13.8564i −0.788263 + 1.36531i 0.138767 + 0.990325i $$0.455686\pi$$
−0.927030 + 0.374987i $$0.877647\pi$$
$$104$$ 0 0
$$105$$ 2.00000 1.73205i 0.195180 0.169031i
$$106$$ 0 0
$$107$$ −5.00000 + 8.66025i −0.483368 + 0.837218i −0.999818 0.0190994i $$-0.993920\pi$$
0.516449 + 0.856318i $$0.327253\pi$$
$$108$$ 0 0
$$109$$ −3.00000 5.19615i −0.287348 0.497701i 0.685828 0.727764i $$-0.259440\pi$$
−0.973176 + 0.230063i $$0.926107\pi$$
$$110$$ 0 0
$$111$$ 11.0000 1.04407
$$112$$ 0 0
$$113$$ 6.00000 0.564433 0.282216 0.959351i $$-0.408930\pi$$
0.282216 + 0.959351i $$0.408930\pi$$
$$114$$ 0 0
$$115$$ −3.50000 6.06218i −0.326377 0.565301i
$$116$$ 0 0
$$117$$ −0.500000 + 0.866025i −0.0462250 + 0.0800641i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 5.00000 8.66025i 0.454545 0.787296i
$$122$$ 0 0
$$123$$ 5.50000 + 9.52628i 0.495918 + 0.858956i
$$124$$ 0 0
$$125$$ −1.00000 −0.0894427
$$126$$ 0 0
$$127$$ 17.0000 1.50851 0.754253 0.656584i $$-0.227999\pi$$
0.754253 + 0.656584i $$0.227999\pi$$
$$128$$ 0 0
$$129$$ 4.00000 + 6.92820i 0.352180 + 0.609994i
$$130$$ 0 0
$$131$$ −2.50000 + 4.33013i −0.218426 + 0.378325i −0.954327 0.298764i $$-0.903426\pi$$
0.735901 + 0.677089i $$0.236759\pi$$
$$132$$ 0 0
$$133$$ −1.50000 7.79423i −0.130066 0.675845i
$$134$$ 0 0
$$135$$ 0.500000 0.866025i 0.0430331 0.0745356i
$$136$$ 0 0
$$137$$ 9.00000 + 15.5885i 0.768922 + 1.33181i 0.938148 + 0.346235i $$0.112540\pi$$
−0.169226 + 0.985577i $$0.554127\pi$$
$$138$$ 0 0
$$139$$ −20.0000 −1.69638 −0.848189 0.529694i $$-0.822307\pi$$
−0.848189 + 0.529694i $$0.822307\pi$$
$$140$$ 0 0
$$141$$ 5.00000 0.421076
$$142$$ 0 0
$$143$$ −0.500000 0.866025i −0.0418121 0.0724207i
$$144$$ 0 0
$$145$$ −4.00000 + 6.92820i −0.332182 + 0.575356i
$$146$$ 0 0
$$147$$ −6.50000 + 2.59808i −0.536111 + 0.214286i
$$148$$ 0 0
$$149$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$150$$ 0 0
$$151$$ 3.00000 + 5.19615i 0.244137 + 0.422857i 0.961888 0.273442i $$-0.0881622\pi$$
−0.717752 + 0.696299i $$0.754829\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −2.00000 −0.160644
$$156$$ 0 0
$$157$$ 3.50000 + 6.06218i 0.279330 + 0.483814i 0.971219 0.238190i $$-0.0765542\pi$$
−0.691888 + 0.722005i $$0.743221\pi$$
$$158$$ 0 0
$$159$$ 5.50000 9.52628i 0.436178 0.755483i
$$160$$ 0 0
$$161$$ 3.50000 + 18.1865i 0.275839 + 1.43330i
$$162$$ 0 0
$$163$$ 8.00000 13.8564i 0.626608 1.08532i −0.361619 0.932326i $$-0.617776\pi$$
0.988227 0.152992i $$-0.0488907\pi$$
$$164$$ 0 0
$$165$$ 0.500000 + 0.866025i 0.0389249 + 0.0674200i
$$166$$ 0 0
$$167$$ 3.00000 0.232147 0.116073 0.993241i $$-0.462969\pi$$
0.116073 + 0.993241i $$0.462969\pi$$
$$168$$ 0 0
$$169$$ −12.0000 −0.923077
$$170$$ 0 0
$$171$$ −1.50000 2.59808i −0.114708 0.198680i
$$172$$ 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
$$175$$ 2.50000 + 0.866025i 0.188982 + 0.0654654i
$$176$$ 0 0
$$177$$ 2.00000 3.46410i 0.150329 0.260378i
$$178$$ 0 0
$$179$$ −9.50000 16.4545i −0.710063 1.22987i −0.964833 0.262864i $$-0.915333\pi$$
0.254770 0.967002i $$-0.418000\pi$$
$$180$$ 0 0
$$181$$ −24.0000 −1.78391 −0.891953 0.452128i $$-0.850665\pi$$
−0.891953 + 0.452128i $$0.850665\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 5.50000 + 9.52628i 0.404368 + 0.700386i
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ −2.00000 + 1.73205i −0.145479 + 0.125988i
$$190$$ 0 0
$$191$$ −3.00000 + 5.19615i −0.217072 + 0.375980i −0.953912 0.300088i $$-0.902984\pi$$
0.736839 + 0.676068i $$0.236317\pi$$
$$192$$ 0 0
$$193$$ −11.0000 19.0526i −0.791797 1.37143i −0.924853 0.380325i $$-0.875812\pi$$
0.133056 0.991109i $$-0.457521\pi$$
$$194$$ 0 0
$$195$$ −1.00000 −0.0716115
$$196$$ 0 0
$$197$$ −1.00000 −0.0712470 −0.0356235 0.999365i $$-0.511342\pi$$
−0.0356235 + 0.999365i $$0.511342\pi$$
$$198$$ 0 0
$$199$$ −12.0000 20.7846i −0.850657 1.47338i −0.880616 0.473831i $$-0.842871\pi$$
0.0299585 0.999551i $$-0.490462\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 16.0000 13.8564i 1.12298 0.972529i
$$204$$ 0 0
$$205$$ −5.50000 + 9.52628i −0.384137 + 0.665344i
$$206$$ 0 0
$$207$$ 3.50000 + 6.06218i 0.243267 + 0.421350i
$$208$$ 0 0
$$209$$ 3.00000 0.207514
$$210$$ 0 0
$$211$$ −5.00000 −0.344214 −0.172107 0.985078i $$-0.555058\pi$$
−0.172107 + 0.985078i $$0.555058\pi$$
$$212$$ 0 0
$$213$$ −3.00000 5.19615i −0.205557 0.356034i
$$214$$ 0 0
$$215$$ −4.00000 + 6.92820i −0.272798 + 0.472500i
$$216$$ 0 0
$$217$$ 5.00000 + 1.73205i 0.339422 + 0.117579i
$$218$$ 0 0
$$219$$ 3.00000 5.19615i 0.202721 0.351123i
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ −12.0000 −0.803579 −0.401790 0.915732i $$-0.631612\pi$$
−0.401790 + 0.915732i $$0.631612\pi$$
$$224$$ 0 0
$$225$$ 1.00000 0.0666667
$$226$$ 0 0
$$227$$ 4.00000 + 6.92820i 0.265489 + 0.459841i 0.967692 0.252136i $$-0.0811332\pi$$
−0.702202 + 0.711977i $$0.747800\pi$$
$$228$$ 0 0
$$229$$ −7.00000 + 12.1244i −0.462573 + 0.801200i −0.999088 0.0426906i $$-0.986407\pi$$
0.536515 + 0.843891i $$0.319740\pi$$
$$230$$ 0 0
$$231$$ −0.500000 2.59808i −0.0328976 0.170941i
$$232$$ 0 0
$$233$$ −9.00000 + 15.5885i −0.589610 + 1.02123i 0.404674 + 0.914461i $$0.367385\pi$$
−0.994283 + 0.106773i $$0.965948\pi$$
$$234$$ 0 0
$$235$$ 2.50000 + 4.33013i 0.163082 + 0.282466i
$$236$$ 0 0
$$237$$ 8.00000 0.519656
$$238$$ 0 0
$$239$$ 18.0000 1.16432 0.582162 0.813073i $$-0.302207\pi$$
0.582162 + 0.813073i $$0.302207\pi$$
$$240$$ 0 0
$$241$$ −3.50000 6.06218i −0.225455 0.390499i 0.731001 0.682376i $$-0.239053\pi$$
−0.956456 + 0.291877i $$0.905720\pi$$
$$242$$ 0 0
$$243$$ −0.500000 + 0.866025i −0.0320750 + 0.0555556i
$$244$$ 0 0
$$245$$ −5.50000 4.33013i −0.351382 0.276642i
$$246$$ 0 0
$$247$$ −1.50000 + 2.59808i −0.0954427 + 0.165312i
$$248$$ 0 0
$$249$$ 4.00000 + 6.92820i 0.253490 + 0.439057i
$$250$$ 0 0
$$251$$ −13.0000 −0.820553 −0.410276 0.911961i $$-0.634568\pi$$
−0.410276 + 0.911961i $$0.634568\pi$$
$$252$$ 0 0
$$253$$ −7.00000 −0.440086
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 10.0000 17.3205i 0.623783 1.08042i −0.364992 0.931011i $$-0.618928\pi$$
0.988775 0.149413i $$-0.0477384\pi$$
$$258$$ 0 0
$$259$$ −5.50000 28.5788i −0.341753 1.77580i
$$260$$ 0 0
$$261$$ 4.00000 6.92820i 0.247594 0.428845i
$$262$$ 0 0
$$263$$ 12.0000 + 20.7846i 0.739952 + 1.28163i 0.952517 + 0.304487i $$0.0984850\pi$$
−0.212565 + 0.977147i $$0.568182\pi$$
$$264$$ 0 0
$$265$$ 11.0000 0.675725
$$266$$ 0 0
$$267$$ −10.0000 −0.611990
$$268$$ 0 0
$$269$$ −10.0000 17.3205i −0.609711 1.05605i −0.991288 0.131713i $$-0.957952\pi$$
0.381577 0.924337i $$-0.375381\pi$$
$$270$$ 0 0
$$271$$ 16.0000 27.7128i 0.971931 1.68343i 0.282218 0.959350i $$-0.408930\pi$$
0.689713 0.724083i $$-0.257737\pi$$
$$272$$ 0 0
$$273$$ 2.50000 + 0.866025i 0.151307 + 0.0524142i
$$274$$ 0 0
$$275$$ −0.500000 + 0.866025i −0.0301511 + 0.0522233i
$$276$$ 0 0
$$277$$ 11.0000 + 19.0526i 0.660926 + 1.14476i 0.980373 + 0.197153i $$0.0631696\pi$$
−0.319447 + 0.947604i $$0.603497\pi$$
$$278$$ 0 0
$$279$$ 2.00000 0.119737
$$280$$ 0 0
$$281$$ −1.00000 −0.0596550 −0.0298275 0.999555i $$-0.509496\pi$$
−0.0298275 + 0.999555i $$0.509496\pi$$
$$282$$ 0 0
$$283$$ −7.00000 12.1244i −0.416107 0.720718i 0.579437 0.815017i $$-0.303272\pi$$
−0.995544 + 0.0942988i $$0.969939\pi$$
$$284$$ 0 0
$$285$$ 1.50000 2.59808i 0.0888523 0.153897i
$$286$$ 0 0
$$287$$ 22.0000 19.0526i 1.29862 1.12464i
$$288$$ 0 0
$$289$$ 8.50000 14.7224i 0.500000 0.866025i
$$290$$ 0 0
$$291$$ 8.00000 + 13.8564i 0.468968 + 0.812277i
$$292$$ 0 0
$$293$$ 27.0000 1.57736 0.788678 0.614806i $$-0.210766\pi$$
0.788678 + 0.614806i $$0.210766\pi$$
$$294$$ 0 0
$$295$$ 4.00000 0.232889
$$296$$ 0 0
$$297$$ −0.500000 0.866025i −0.0290129 0.0502519i
$$298$$ 0 0
$$299$$ 3.50000 6.06218i 0.202410 0.350585i
$$300$$ 0 0
$$301$$ 16.0000 13.8564i 0.922225 0.798670i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −20.0000 −1.14146 −0.570730 0.821138i $$-0.693340\pi$$
−0.570730 + 0.821138i $$0.693340\pi$$
$$308$$ 0 0
$$309$$ 16.0000 0.910208
$$310$$ 0 0
$$311$$ 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
$$313$$ 6.00000 10.3923i 0.339140 0.587408i −0.645131 0.764072i $$-0.723197\pi$$
0.984271 + 0.176664i $$0.0565306\pi$$
$$314$$ 0 0
$$315$$ −2.50000 0.866025i −0.140859 0.0487950i
$$316$$ 0 0
$$317$$ 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
$$319$$ 4.00000 + 6.92820i 0.223957 + 0.387905i
$$320$$ 0 0
$$321$$ 10.0000 0.558146
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ −0.500000 0.866025i −0.0277350 0.0480384i
$$326$$ 0 0
$$327$$ −3.00000 + 5.19615i −0.165900 + 0.287348i
$$328$$ 0 0
$$329$$ −2.50000 12.9904i −0.137829 0.716183i
$$330$$ 0 0
$$331$$ −6.50000 + 11.2583i −0.357272 + 0.618814i −0.987504 0.157593i $$-0.949627\pi$$
0.630232 + 0.776407i $$0.282960\pi$$
$$332$$ 0 0
$$333$$ −5.50000 9.52628i −0.301398 0.522037i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −12.0000 −0.653682 −0.326841 0.945079i $$-0.605984\pi$$
−0.326841 + 0.945079i $$0.605984\pi$$
$$338$$ 0 0
$$339$$ −3.00000 5.19615i −0.162938 0.282216i
$$340$$ 0 0
$$341$$ −1.00000 + 1.73205i −0.0541530 + 0.0937958i
$$342$$ 0 0
$$343$$ 10.0000 + 15.5885i 0.539949 + 0.841698i
$$344$$ 0 0
$$345$$ −3.50000 + 6.06218i −0.188434 + 0.326377i
$$346$$ 0 0
$$347$$ 7.00000 + 12.1244i 0.375780 + 0.650870i 0.990443 0.137920i $$-0.0440416\pi$$
−0.614664 + 0.788789i $$0.710708\pi$$
$$348$$ 0 0
$$349$$ 12.0000 0.642345 0.321173 0.947021i $$-0.395923\pi$$
0.321173 + 0.947021i $$0.395923\pi$$
$$350$$ 0 0
$$351$$ 1.00000 0.0533761
$$352$$ 0 0
$$353$$ −12.0000 20.7846i −0.638696 1.10625i −0.985719 0.168397i $$-0.946141\pi$$
0.347024 0.937856i $$-0.387192\pi$$
$$354$$ 0 0
$$355$$ 3.00000 5.19615i 0.159223 0.275783i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 2.00000 3.46410i 0.105556 0.182828i −0.808409 0.588621i $$-0.799671\pi$$
0.913965 + 0.405793i $$0.133004\pi$$
$$360$$ 0 0
$$361$$ 5.00000 + 8.66025i 0.263158 + 0.455803i
$$362$$ 0 0
$$363$$ −10.0000 −0.524864
$$364$$ 0 0
$$365$$ 6.00000 0.314054
$$366$$ 0 0
$$367$$ 12.5000 + 21.6506i 0.652495 + 1.13015i 0.982516 + 0.186180i $$0.0596109\pi$$
−0.330021 + 0.943974i $$0.607056\pi$$
$$368$$ 0 0
$$369$$ 5.50000 9.52628i 0.286319 0.495918i
$$370$$ 0 0
$$371$$ −27.5000 9.52628i −1.42773 0.494580i
$$372$$ 0 0
$$373$$ −3.00000 + 5.19615i −0.155334 + 0.269047i −0.933181 0.359408i $$-0.882979\pi$$
0.777847 + 0.628454i $$0.216312\pi$$
$$374$$ 0 0
$$375$$ 0.500000 + 0.866025i 0.0258199 + 0.0447214i
$$376$$ 0 0
$$377$$ −8.00000 −0.412021
$$378$$ 0 0
$$379$$ 19.0000 0.975964 0.487982 0.872854i $$-0.337733\pi$$
0.487982 + 0.872854i $$0.337733\pi$$
$$380$$ 0 0
$$381$$ −8.50000 14.7224i −0.435468 0.754253i
$$382$$ 0 0
$$383$$ 17.5000 30.3109i 0.894208 1.54881i 0.0594268 0.998233i $$-0.481073\pi$$
0.834781 0.550581i $$-0.185594\pi$$
$$384$$ 0 0
$$385$$ 2.00000 1.73205i 0.101929 0.0882735i
$$386$$ 0 0
$$387$$ 4.00000 6.92820i 0.203331 0.352180i
$$388$$ 0 0
$$389$$ −5.00000 8.66025i −0.253510 0.439092i 0.710980 0.703213i $$-0.248252\pi$$
−0.964490 + 0.264120i $$0.914918\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 5.00000 0.252217
$$394$$ 0 0
$$395$$ 4.00000 + 6.92820i 0.201262 + 0.348596i
$$396$$ 0 0
$$397$$ −7.00000 + 12.1244i −0.351320 + 0.608504i −0.986481 0.163876i $$-0.947600\pi$$
0.635161 + 0.772380i $$0.280934\pi$$
$$398$$ 0 0
$$399$$ −6.00000 + 5.19615i −0.300376 + 0.260133i
$$400$$ 0 0
$$401$$ 2.50000 4.33013i 0.124844 0.216236i −0.796828 0.604206i $$-0.793490\pi$$
0.921672 + 0.387970i $$0.126824\pi$$
$$402$$ 0 0
$$403$$ −1.00000 1.73205i −0.0498135 0.0862796i
$$404$$ 0 0
$$405$$ −1.00000 −0.0496904
$$406$$ 0 0
$$407$$ 11.0000 0.545250
$$408$$ 0 0
$$409$$ −1.00000 1.73205i −0.0494468 0.0856444i 0.840243 0.542211i $$-0.182412\pi$$
−0.889689 + 0.456566i $$0.849079\pi$$
$$410$$ 0 0
$$411$$ 9.00000 15.5885i 0.443937 0.768922i
$$412$$ 0 0
$$413$$ −10.0000 3.46410i −0.492068 0.170457i
$$414$$ 0 0
$$415$$ −4.00000 + 6.92820i −0.196352 + 0.340092i
$$416$$ 0 0
$$417$$ 10.0000 + 17.3205i 0.489702 + 0.848189i
$$418$$ 0 0
$$419$$ 5.00000 0.244266 0.122133 0.992514i $$-0.461027\pi$$
0.122133 + 0.992514i $$0.461027\pi$$
$$420$$ 0 0
$$421$$ 22.0000 1.07221 0.536107 0.844150i $$-0.319894\pi$$
0.536107 + 0.844150i $$0.319894\pi$$
$$422$$ 0 0
$$423$$ −2.50000 4.33013i −0.121554 0.210538i
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ −0.500000 + 0.866025i −0.0241402 + 0.0418121i
$$430$$ 0 0
$$431$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$432$$ 0 0
$$433$$ −32.0000 −1.53782 −0.768911 0.639356i $$-0.779201\pi$$
−0.768911 + 0.639356i $$0.779201\pi$$
$$434$$ 0 0
$$435$$ 8.00000 0.383571
$$436$$ 0 0
$$437$$ 10.5000 + 18.1865i 0.502283 + 0.869980i
$$438$$ 0 0
$$439$$ 16.0000 27.7128i 0.763638 1.32266i −0.177325 0.984152i $$-0.556744\pi$$
0.940963 0.338508i $$-0.109922\pi$$
$$440$$ 0 0
$$441$$ 5.50000 + 4.33013i 0.261905 + 0.206197i
$$442$$ 0 0
$$443$$ 8.00000 13.8564i 0.380091 0.658338i −0.610984 0.791643i $$-0.709226\pi$$
0.991075 + 0.133306i $$0.0425592\pi$$
$$444$$ 0 0
$$445$$ −5.00000 8.66025i −0.237023 0.410535i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 11.0000 0.519122 0.259561 0.965727i $$-0.416422\pi$$
0.259561 + 0.965727i $$0.416422\pi$$
$$450$$ 0 0
$$451$$ 5.50000 + 9.52628i 0.258985 + 0.448575i
$$452$$ 0 0
$$453$$ 3.00000 5.19615i 0.140952 0.244137i
$$454$$ 0 0
$$455$$ 0.500000 + 2.59808i 0.0234404 + 0.121800i
$$456$$ 0 0
$$457$$ 9.00000 15.5885i 0.421002 0.729197i −0.575036 0.818128i $$-0.695012\pi$$
0.996038 + 0.0889312i $$0.0283451\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −12.0000 −0.558896 −0.279448 0.960161i $$-0.590151\pi$$
−0.279448 + 0.960161i $$0.590151\pi$$
$$462$$ 0 0
$$463$$ 13.0000 0.604161 0.302081 0.953282i $$-0.402319\pi$$
0.302081 + 0.953282i $$0.402319\pi$$
$$464$$ 0 0
$$465$$ 1.00000 + 1.73205i 0.0463739 + 0.0803219i
$$466$$ 0 0
$$467$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 3.50000 6.06218i 0.161271 0.279330i
$$472$$ 0 0
$$473$$ 4.00000 + 6.92820i 0.183920 + 0.318559i
$$474$$ 0 0
$$475$$ 3.00000 0.137649
$$476$$ 0 0
$$477$$ −11.0000 −0.503655
$$478$$ 0 0
$$479$$ 11.0000 + 19.0526i 0.502603 + 0.870534i 0.999995 + 0.00300810i $$0.000957509\pi$$
−0.497393 + 0.867526i $$0.665709\pi$$
$$480$$ 0 0
$$481$$ −5.50000 + 9.52628i −0.250778 + 0.434361i
$$482$$ 0 0
$$483$$ 14.0000 12.1244i 0.637022 0.551677i
$$484$$ 0 0
$$485$$ −8.00000 + 13.8564i −0.363261 + 0.629187i
$$486$$ 0 0
$$487$$ −8.00000 13.8564i −0.362515 0.627894i 0.625859 0.779936i $$-0.284748\pi$$
−0.988374 + 0.152042i $$0.951415\pi$$
$$488$$ 0 0
$$489$$ −16.0000 −0.723545
$$490$$ 0 0
$$491$$ −20.0000 −0.902587 −0.451294 0.892375i $$-0.649037\pi$$
−0.451294 + 0.892375i $$0.649037\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0.500000 0.866025i 0.0224733 0.0389249i
$$496$$ 0 0
$$497$$ −12.0000 + 10.3923i −0.538274 + 0.466159i
$$498$$ 0 0
$$499$$ −16.0000 + 27.7128i −0.716258 + 1.24060i 0.246214 + 0.969216i $$0.420813\pi$$
−0.962472 + 0.271380i $$0.912520\pi$$
$$500$$ 0 0
$$501$$ −1.50000 2.59808i −0.0670151 0.116073i
$$502$$ 0 0
$$503$$ −36.0000 −1.60516 −0.802580 0.596544i $$-0.796540\pi$$
−0.802580 + 0.596544i $$0.796540\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 6.00000 + 10.3923i 0.266469 + 0.461538i
$$508$$ 0 0
$$509$$ 17.0000 29.4449i 0.753512 1.30512i −0.192599 0.981278i $$-0.561692\pi$$
0.946111 0.323843i $$-0.104975\pi$$
$$510$$ 0 0
$$511$$ −15.0000 5.19615i −0.663561 0.229864i
$$512$$ 0 0
$$513$$ −1.50000 + 2.59808i −0.0662266 + 0.114708i
$$514$$ 0 0
$$515$$ 8.00000 + 13.8564i 0.352522 + 0.610586i
$$516$$ 0 0
$$517$$ 5.00000 0.219900
$$518$$ 0 0
$$519$$ −15.0000 −0.658427
$$520$$ 0 0
$$521$$ 16.5000 + 28.5788i 0.722878 + 1.25206i 0.959841 + 0.280543i $$0.0905145\pi$$
−0.236963 + 0.971519i $$0.576152\pi$$
$$522$$ 0 0
$$523$$ 1.00000 1.73205i 0.0437269 0.0757373i −0.843334 0.537390i $$-0.819410\pi$$
0.887061 + 0.461653i $$0.152744\pi$$
$$524$$ 0 0
$$525$$ −0.500000 2.59808i −0.0218218 0.113389i
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −13.0000 22.5167i −0.565217 0.978985i
$$530$$ 0 0
$$531$$ −4.00000 −0.173585
$$532$$ 0 0
$$533$$ −11.0000 −0.476463
$$534$$ 0 0
$$535$$ 5.00000 + 8.66025i 0.216169 + 0.374415i
$$536$$ 0 0
$$537$$ −9.50000 + 16.4545i −0.409955 + 0.710063i
$$538$$ 0 0
$$539$$ −6.50000 + 2.59808i −0.279975 + 0.111907i
$$540$$ 0 0
$$541$$ 5.00000 8.66025i 0.214967 0.372333i −0.738296 0.674477i $$-0.764369\pi$$
0.953262 + 0.302144i $$0.0977023\pi$$
$$542$$ 0 0
$$543$$ 12.0000 + 20.7846i 0.514969 + 0.891953i
$$544$$ 0 0
$$545$$ −6.00000 −0.257012
$$546$$ 0 0
$$547$$ −16.0000 −0.684111 −0.342055 0.939680i $$-0.611123\pi$$
−0.342055 + 0.939680i $$0.611123\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 12.0000 20.7846i 0.511217 0.885454i
$$552$$ 0 0
$$553$$ −4.00000 20.7846i −0.170097 0.883852i
$$554$$ 0 0
$$555$$ 5.50000 9.52628i 0.233462 0.404368i
$$556$$ 0 0
$$557$$ 16.5000 + 28.5788i 0.699127 + 1.21092i 0.968769 + 0.247964i $$0.0797613\pi$$
−0.269642 + 0.962961i $$0.586905\pi$$
$$558$$ 0 0
$$559$$ −8.00000 −0.338364
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −19.0000 32.9090i −0.800755 1.38695i −0.919120 0.393977i $$-0.871099\pi$$
0.118366 0.992970i $$-0.462235\pi$$
$$564$$ 0 0
$$565$$ 3.00000 5.19615i 0.126211 0.218604i
$$566$$ 0 0
$$567$$ 2.50000 + 0.866025i 0.104990 + 0.0363696i
$$568$$ 0 0
$$569$$ 4.50000 7.79423i 0.188650 0.326751i −0.756151 0.654398i $$-0.772922\pi$$
0.944800 + 0.327647i $$0.106256\pi$$
$$570$$ 0 0
$$571$$ −16.0000 27.7128i −0.669579 1.15975i −0.978022 0.208502i $$-0.933141\pi$$
0.308443 0.951243i $$-0.400192\pi$$
$$572$$ 0 0
$$573$$ 6.00000 0.250654
$$574$$ 0 0
$$575$$ −7.00000 −0.291920
$$576$$ 0 0
$$577$$ 7.00000 + 12.1244i 0.291414 + 0.504744i 0.974144 0.225927i $$-0.0725410\pi$$
−0.682730 + 0.730670i $$0.739208\pi$$
$$578$$ 0 0
$$579$$ −11.0000 + 19.0526i −0.457144 + 0.791797i
$$580$$ 0 0
$$581$$ 16.0000 13.8564i 0.663792 0.574861i
$$582$$ 0 0
$$583$$ 5.50000 9.52628i 0.227787 0.394538i
$$584$$ 0 0
$$585$$ 0.500000 + 0.866025i 0.0206725 + 0.0358057i
$$586$$ 0 0
$$587$$ 18.0000 0.742940 0.371470 0.928445i $$-0.378854\pi$$
0.371470 + 0.928445i $$0.378854\pi$$
$$588$$ 0 0
$$589$$ 6.00000 0.247226
$$590$$ 0 0
$$591$$ 0.500000 + 0.866025i 0.0205673 + 0.0356235i
$$592$$ 0 0
$$593$$ −8.00000 + 13.8564i −0.328521 + 0.569014i −0.982219 0.187741i $$-0.939883\pi$$
0.653698 + 0.756756i $$0.273217\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ −12.0000 + 20.7846i −0.491127 + 0.850657i
$$598$$ 0 0
$$599$$ 1.00000 + 1.73205i 0.0408589 + 0.0707697i 0.885732 0.464198i $$-0.153657\pi$$
−0.844873 + 0.534967i $$0.820324\pi$$
$$600$$ 0 0
$$601$$ −26.0000 −1.06056 −0.530281 0.847822i $$-0.677914\pi$$
−0.530281 + 0.847822i $$0.677914\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −5.00000 8.66025i −0.203279 0.352089i
$$606$$ 0 0
$$607$$ −18.5000 + 32.0429i −0.750892 + 1.30058i 0.196499 + 0.980504i $$0.437043\pi$$
−0.947391 + 0.320079i $$0.896291\pi$$
$$608$$ 0 0
$$609$$ −20.0000 6.92820i −0.810441 0.280745i
$$610$$ 0 0
$$611$$ −2.50000 + 4.33013i −0.101139 + 0.175178i
$$612$$ 0 0
$$613$$ 20.5000 + 35.5070i 0.827987 + 1.43412i 0.899615 + 0.436684i $$0.143847\pi$$
−0.0716275 + 0.997431i $$0.522819\pi$$
$$614$$ 0 0
$$615$$ 11.0000 0.443563
$$616$$ 0 0
$$617$$ 28.0000 1.12724 0.563619 0.826035i $$-0.309409\pi$$
0.563619 + 0.826035i $$0.309409\pi$$
$$618$$ 0 0
$$619$$ 14.5000 + 25.1147i 0.582804 + 1.00945i 0.995145 + 0.0984169i $$0.0313779\pi$$
−0.412341 + 0.911030i $$0.635289\pi$$
$$620$$ 0 0
$$621$$ 3.50000 6.06218i 0.140450 0.243267i
$$622$$ 0 0
$$623$$ 5.00000 + 25.9808i 0.200321 + 1.04090i
$$624$$ 0 0
$$625$$ −0.500000 + 0.866025i −0.0200000 + 0.0346410i
$$626$$ 0 0
$$627$$ −1.50000 2.59808i −0.0599042 0.103757i
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 26.0000 1.03504 0.517522 0.855670i $$-0.326855\pi$$
0.517522 + 0.855670i $$0.326855\pi$$
$$632$$ 0 0
$$633$$ 2.50000 + 4.33013i 0.0993661 + 0.172107i
$$634$$ 0 0
$$635$$ 8.50000 14.7224i 0.337312 0.584242i
$$636$$ 0 0
$$637$$ 1.00000 6.92820i 0.0396214 0.274505i
$$638$$ 0 0
$$639$$ −3.00000 + 5.19615i −0.118678 + 0.205557i
$$640$$ 0 0
$$641$$ 1.50000 + 2.59808i 0.0592464 + 0.102618i 0.894127 0.447813i $$-0.147797\pi$$
−0.834881 + 0.550431i $$0.814464\pi$$
$$642$$ 0 0
$$643$$ 10.0000 0.394362 0.197181 0.980367i $$-0.436821\pi$$
0.197181 + 0.980367i $$0.436821\pi$$
$$644$$ 0 0
$$645$$ 8.00000 0.315000
$$646$$ 0 0
$$647$$ −8.50000 14.7224i −0.334169 0.578799i 0.649155 0.760656i $$-0.275122\pi$$
−0.983325 + 0.181857i $$0.941789\pi$$
$$648$$ 0 0
$$649$$ 2.00000 3.46410i 0.0785069 0.135978i
$$650$$ 0 0
$$651$$ −1.00000 5.19615i −0.0391931 0.203653i
$$652$$ 0 0
$$653$$ −3.50000 + 6.06218i −0.136966 + 0.237231i −0.926347 0.376672i $$-0.877068\pi$$
0.789381 + 0.613904i $$0.210402\pi$$
$$654$$ 0 0
$$655$$ 2.50000 + 4.33013i 0.0976831 + 0.169192i
$$656$$ 0 0
$$657$$ −6.00000 −0.234082
$$658$$ 0 0
$$659$$ −36.0000 −1.40236 −0.701180 0.712984i $$-0.747343\pi$$
−0.701180 + 0.712984i $$0.747343\pi$$
$$660$$ 0 0
$$661$$ 12.0000 + 20.7846i 0.466746 + 0.808428i 0.999278 0.0379819i $$-0.0120929\pi$$
−0.532533 + 0.846410i $$0.678760\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −7.50000 2.59808i −0.290838 0.100749i
$$666$$ 0 0
$$667$$ −28.0000 + 48.4974i −1.08416 + 1.87783i
$$668$$ 0 0
$$669$$ 6.00000 + 10.3923i 0.231973 + 0.401790i
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 28.0000 1.07932 0.539660 0.841883i $$-0.318553\pi$$
0.539660 + 0.841883i $$0.318553\pi$$
$$674$$ 0 0
$$675$$ −0.500000 0.866025i −0.0192450 0.0333333i
$$676$$ 0 0
$$677$$ 6.50000 11.2583i 0.249815 0.432693i −0.713659 0.700493i $$-0.752963\pi$$
0.963474 + 0.267800i $$0.0862968\pi$$
$$678$$ 0 0
$$679$$ 32.0000 27.7128i 1.22805 1.06352i
$$680$$ 0 0
$$681$$ 4.00000 6.92820i 0.153280 0.265489i
$$682$$ 0 0
$$683$$ 2.00000 + 3.46410i 0.0765279 + 0.132550i 0.901750 0.432259i $$-0.142283\pi$$
−0.825222 + 0.564809i $$0.808950\pi$$
$$684$$ 0 0
$$685$$ 18.0000 0.687745
$$686$$ 0 0
$$687$$ 14.0000 0.534133
$$688$$ 0 0
$$689$$ 5.50000 + 9.52628i 0.209533 + 0.362922i
$$690$$ 0 0
$$691$$ −6.00000 + 10.3923i −0.228251 + 0.395342i −0.957290 0.289130i $$-0.906634\pi$$
0.729039 + 0.684472i $$0.239967\pi$$
$$692$$ 0 0
$$693$$ −2.00000 + 1.73205i −0.0759737 + 0.0657952i
$$694$$ 0 0
$$695$$ −10.0000 + 17.3205i −0.379322 + 0.657004i
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 18.0000 0.680823
$$700$$ 0 0
$$701$$ −18.0000 −0.679851 −0.339925 0.940452i $$-0.610402\pi$$
−0.339925 + 0.940452i $$0.610402\pi$$
$$702$$ 0 0
$$703$$ −16.5000 28.5788i −0.622309 1.07787i
$$704$$ 0 0
$$705$$ 2.50000 4.33013i 0.0941554 0.163082i
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −22.0000 + 38.1051i −0.826227 + 1.43107i 0.0747503 + 0.997202i $$0.476184\pi$$
−0.900978 + 0.433865i $$0.857149\pi$$
$$710$$ 0 0
$$711$$ −4.00000 6.92820i −0.150012 0.259828i
$$712$$ 0 0
$$713$$ −14.0000 −0.524304
$$714$$ 0 0
$$715$$ −1.00000 −0.0373979
$$716$$ 0 0
$$717$$ −9.00000 15.5885i −0.336111 0.582162i
$$718$$ 0 0
$$719$$ 1.00000 1.73205i 0.0372937 0.0645946i −0.846776 0.531949i $$-0.821460\pi$$
0.884070 + 0.467355i $$0.154793\pi$$
$$720$$ 0 0
$$721$$ −8.00000 41.5692i −0.297936 1.54812i
$$722$$ 0 0
$$723$$ −3.50000 + 6.06218i −0.130166 + 0.225455i
$$724$$ 0 0
$$725$$ 4.00000 + 6.92820i 0.148556 + 0.257307i
$$726$$ 0 0
$$727$$ −11.0000 −0.407967 −0.203984 0.978974i $$-0.565389\pi$$
−0.203984 + 0.978974i $$0.565389\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ −5.50000 + 9.52628i −0.203147 + 0.351861i −0.949541 0.313644i $$-0.898450\pi$$
0.746394 + 0.665505i $$0.231784\pi$$
$$734$$ 0 0
$$735$$ −1.00000 + 6.92820i −0.0368856 + 0.255551i
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ −9.50000 16.4545i −0.349463 0.605288i 0.636691 0.771119i $$-0.280303\pi$$
−0.986154 + 0.165831i $$0.946969\pi$$
$$740$$ 0 0
$$741$$ 3.00000 0.110208
$$742$$ 0 0
$$743$$ −49.0000 −1.79764 −0.898818 0.438322i $$-0.855573\pi$$
−0.898818 + 0.438322i $$0.855573\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 4.00000 6.92820i 0.146352 0.253490i
$$748$$ 0 0
$$749$$ −5.00000 25.9808i −0.182696 0.949316i
$$750$$ 0 0
$$751$$ 13.0000 22.5167i 0.474377 0.821645i −0.525193 0.850983i $$-0.676007\pi$$
0.999570 + 0.0293387i $$0.00934013\pi$$
$$752$$ 0 0
$$753$$ 6.50000 + 11.2583i 0.236873 + 0.410276i
$$754$$ 0 0
$$755$$ 6.00000 0.218362
$$756$$ 0 0
$$757$$ 2.00000 0.0726912 0.0363456 0.999339i $$-0.488428\pi$$
0.0363456 + 0.999339i $$0.488428\pi$$
$$758$$ 0 0
$$759$$ 3.50000 + 6.06218i 0.127042 + 0.220043i
$$760$$ 0 0
$$761$$ −13.5000 + 23.3827i −0.489375 + 0.847622i −0.999925 0.0122260i $$-0.996108\pi$$
0.510551 + 0.859848i $$0.329442\pi$$
$$762$$ 0 0
$$763$$ 15.0000 + 5.19615i 0.543036 + 0.188113i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 2.00000 + 3.46410i 0.0722158 + 0.125081i
$$768$$ 0 0
$$769$$ −5.00000 −0.180305 −0.0901523 0.995928i $$-0.528735\pi$$
−0.0901523 + 0.995928i $$0.528735\pi$$
$$770$$ 0 0
$$771$$ −20.0000 −0.720282
$$772$$ 0 0
$$773$$ −16.5000 28.5788i −0.593464 1.02791i −0.993762 0.111524i $$-0.964427\pi$$
0.400298 0.916385i $$-0.368907\pi$$
$$774$$ 0 0
$$775$$ −1.00000 + 1.73205i −0.0359211 + 0.0622171i
$$776$$ 0 0
$$777$$ −22.0000 + 19.0526i −0.789246 + 0.683507i
$$778$$ 0 0
$$779$$ 16.5000 28.5788i 0.591174 1.02394i
$$780$$ 0 0
$$781$$ −3.00000 5.19615i −0.107348 0.185933i
$$782$$ 0 0
$$783$$ −8.00000 −0.285897
$$784$$ 0 0
$$785$$ 7.00000 0.249841
$$786$$ 0 0
$$787$$ 11.0000 + 19.0526i 0.392108 + 0.679150i 0.992727 0.120384i $$-0.0384127\pi$$
−0.600620 + 0.799535i $$0.705079\pi$$
$$788$$ 0 0
$$789$$ 12.0000 20.7846i 0.427211 0.739952i
$$790$$ 0 0
$$791$$ −12.0000 + 10.3923i −0.426671 + 0.369508i
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ −5.50000 9.52628i −0.195065 0.337862i
$$796$$ 0 0
$$797$$ −18.0000 −0.637593 −0.318796 0.947823i $$-0.603279\pi$$
−0.318796 + 0.947823i $$0.603279\pi$$
$$798$$