# Properties

 Label 1900.2.s.a.349.1 Level $1900$ Weight $2$ Character 1900.349 Analytic conductor $15.172$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$1900 = 2^{2} \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1900.s (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$15.1715763840$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\zeta_{12})$$ Defining polynomial: $$x^{4} - x^{2} + 1$$ x^4 - x^2 + 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: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 349.1 Root $$-0.866025 + 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 1900.349 Dual form 1900.2.s.a.49.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.866025 + 0.500000i) q^{3} +(-1.00000 + 1.73205i) q^{9} +O(q^{10})$$ $$q+(-0.866025 + 0.500000i) q^{3} +(-1.00000 + 1.73205i) q^{9} -4.00000 q^{11} +(0.866025 + 0.500000i) q^{13} +(-2.59808 + 1.50000i) q^{17} +(4.00000 + 1.73205i) q^{19} +(-4.33013 - 2.50000i) q^{23} -5.00000i q^{27} +(3.50000 - 6.06218i) q^{29} +4.00000 q^{31} +(3.46410 - 2.00000i) q^{33} -10.0000i q^{37} -1.00000 q^{39} +(2.50000 + 4.33013i) q^{41} +(-4.33013 + 2.50000i) q^{43} +(-6.06218 - 3.50000i) q^{47} +7.00000 q^{49} +(1.50000 - 2.59808i) q^{51} +(-9.52628 - 5.50000i) q^{53} +(-4.33013 + 0.500000i) q^{57} +(1.50000 + 2.59808i) q^{59} +(-5.50000 + 9.52628i) q^{61} +(-2.59808 - 1.50000i) q^{67} +5.00000 q^{69} +(-5.50000 - 9.52628i) q^{71} +(12.9904 - 7.50000i) q^{73} +(-6.50000 - 11.2583i) q^{79} +(-0.500000 - 0.866025i) q^{81} +7.00000i q^{87} +(1.50000 - 2.59808i) q^{89} +(-3.46410 + 2.00000i) q^{93} +(4.33013 - 2.50000i) q^{97} +(4.00000 - 6.92820i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 4 q^{9}+O(q^{10})$$ 4 * q - 4 * q^9 $$4 q - 4 q^{9} - 16 q^{11} + 16 q^{19} + 14 q^{29} + 16 q^{31} - 4 q^{39} + 10 q^{41} + 28 q^{49} + 6 q^{51} + 6 q^{59} - 22 q^{61} + 20 q^{69} - 22 q^{71} - 26 q^{79} - 2 q^{81} + 6 q^{89} + 16 q^{99}+O(q^{100})$$ 4 * q - 4 * q^9 - 16 * q^11 + 16 * q^19 + 14 * q^29 + 16 * q^31 - 4 * q^39 + 10 * q^41 + 28 * q^49 + 6 * q^51 + 6 * q^59 - 22 * q^61 + 20 * q^69 - 22 * q^71 - 26 * q^79 - 2 * q^81 + 6 * q^89 + 16 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times$$.

 $$n$$ $$77$$ $$401$$ $$951$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$1$$

## 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
$$3$$ −0.866025 + 0.500000i −0.500000 + 0.288675i −0.728714 0.684819i $$-0.759881\pi$$
0.228714 + 0.973494i $$0.426548\pi$$
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$8$$ 0 0
$$9$$ −1.00000 + 1.73205i −0.333333 + 0.577350i
$$10$$ 0 0
$$11$$ −4.00000 −1.20605 −0.603023 0.797724i $$-0.706037\pi$$
−0.603023 + 0.797724i $$0.706037\pi$$
$$12$$ 0 0
$$13$$ 0.866025 + 0.500000i 0.240192 + 0.138675i 0.615265 0.788320i $$-0.289049\pi$$
−0.375073 + 0.926995i $$0.622382\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −2.59808 + 1.50000i −0.630126 + 0.363803i −0.780801 0.624780i $$-0.785189\pi$$
0.150675 + 0.988583i $$0.451855\pi$$
$$18$$ 0 0
$$19$$ 4.00000 + 1.73205i 0.917663 + 0.397360i
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −4.33013 2.50000i −0.902894 0.521286i −0.0247559 0.999694i $$-0.507881\pi$$
−0.878138 + 0.478407i $$0.841214\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ 5.00000i 0.962250i
$$28$$ 0 0
$$29$$ 3.50000 6.06218i 0.649934 1.12572i −0.333205 0.942855i $$-0.608130\pi$$
0.983138 0.182864i $$-0.0585367\pi$$
$$30$$ 0 0
$$31$$ 4.00000 0.718421 0.359211 0.933257i $$-0.383046\pi$$
0.359211 + 0.933257i $$0.383046\pi$$
$$32$$ 0 0
$$33$$ 3.46410 2.00000i 0.603023 0.348155i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 10.0000i 1.64399i −0.569495 0.821995i $$-0.692861\pi$$
0.569495 0.821995i $$-0.307139\pi$$
$$38$$ 0 0
$$39$$ −1.00000 −0.160128
$$40$$ 0 0
$$41$$ 2.50000 + 4.33013i 0.390434 + 0.676252i 0.992507 0.122189i $$-0.0389915\pi$$
−0.602072 + 0.798441i $$0.705658\pi$$
$$42$$ 0 0
$$43$$ −4.33013 + 2.50000i −0.660338 + 0.381246i −0.792406 0.609994i $$-0.791172\pi$$
0.132068 + 0.991241i $$0.457838\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −6.06218 3.50000i −0.884260 0.510527i −0.0121990 0.999926i $$-0.503883\pi$$
−0.872060 + 0.489398i $$0.837217\pi$$
$$48$$ 0 0
$$49$$ 7.00000 1.00000
$$50$$ 0 0
$$51$$ 1.50000 2.59808i 0.210042 0.363803i
$$52$$ 0 0
$$53$$ −9.52628 5.50000i −1.30854 0.755483i −0.326683 0.945134i $$-0.605931\pi$$
−0.981852 + 0.189651i $$0.939264\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ −4.33013 + 0.500000i −0.573539 + 0.0662266i
$$58$$ 0 0
$$59$$ 1.50000 + 2.59808i 0.195283 + 0.338241i 0.946993 0.321253i $$-0.104104\pi$$
−0.751710 + 0.659494i $$0.770771\pi$$
$$60$$ 0 0
$$61$$ −5.50000 + 9.52628i −0.704203 + 1.21972i 0.262776 + 0.964857i $$0.415362\pi$$
−0.966978 + 0.254858i $$0.917971\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −2.59808 1.50000i −0.317406 0.183254i 0.332830 0.942987i $$-0.391996\pi$$
−0.650236 + 0.759733i $$0.725330\pi$$
$$68$$ 0 0
$$69$$ 5.00000 0.601929
$$70$$ 0 0
$$71$$ −5.50000 9.52628i −0.652730 1.13056i −0.982458 0.186485i $$-0.940290\pi$$
0.329728 0.944076i $$-0.393043\pi$$
$$72$$ 0 0
$$73$$ 12.9904 7.50000i 1.52041 0.877809i 0.520699 0.853740i $$-0.325671\pi$$
0.999710 0.0240681i $$-0.00766187\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −6.50000 11.2583i −0.731307 1.26666i −0.956325 0.292306i $$-0.905577\pi$$
0.225018 0.974355i $$-0.427756\pi$$
$$80$$ 0 0
$$81$$ −0.500000 0.866025i −0.0555556 0.0962250i
$$82$$ 0 0
$$83$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 7.00000i 0.750479i
$$88$$ 0 0
$$89$$ 1.50000 2.59808i 0.159000 0.275396i −0.775509 0.631337i $$-0.782506\pi$$
0.934508 + 0.355942i $$0.115840\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ −3.46410 + 2.00000i −0.359211 + 0.207390i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 4.33013 2.50000i 0.439658 0.253837i −0.263795 0.964579i $$-0.584974\pi$$
0.703452 + 0.710742i $$0.251641\pi$$
$$98$$ 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 $$-0.817490\pi$$
0.889829 + 0.456294i $$0.150824\pi$$
$$102$$ 0 0
$$103$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 20.0000i 1.93347i −0.255774 0.966736i $$-0.582330\pi$$
0.255774 0.966736i $$-0.417670\pi$$
$$108$$ 0 0
$$109$$ 1.50000 + 2.59808i 0.143674 + 0.248851i 0.928877 0.370387i $$-0.120775\pi$$
−0.785203 + 0.619238i $$0.787442\pi$$
$$110$$ 0 0
$$111$$ 5.00000 + 8.66025i 0.474579 + 0.821995i
$$112$$ 0 0
$$113$$ 14.0000i 1.31701i 0.752577 + 0.658505i $$0.228811\pi$$
−0.752577 + 0.658505i $$0.771189\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −1.73205 + 1.00000i −0.160128 + 0.0924500i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 5.00000 0.454545
$$122$$ 0 0
$$123$$ −4.33013 2.50000i −0.390434 0.225417i
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −2.59808 1.50000i −0.230542 0.133103i 0.380280 0.924871i $$-0.375828\pi$$
−0.610822 + 0.791768i $$0.709161\pi$$
$$128$$ 0 0
$$129$$ 2.50000 4.33013i 0.220113 0.381246i
$$130$$ 0 0
$$131$$ −7.50000 12.9904i −0.655278 1.13497i −0.981824 0.189794i $$-0.939218\pi$$
0.326546 0.945181i $$-0.394115\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −4.33013 2.50000i −0.369948 0.213589i 0.303488 0.952835i $$-0.401849\pi$$
−0.673436 + 0.739246i $$0.735182\pi$$
$$138$$ 0 0
$$139$$ 4.50000 7.79423i 0.381685 0.661098i −0.609618 0.792695i $$-0.708677\pi$$
0.991303 + 0.131597i $$0.0420106\pi$$
$$140$$ 0 0
$$141$$ 7.00000 0.589506
$$142$$ 0 0
$$143$$ −3.46410 2.00000i −0.289683 0.167248i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −6.06218 + 3.50000i −0.500000 + 0.288675i
$$148$$ 0 0
$$149$$ 1.50000 + 2.59808i 0.122885 + 0.212843i 0.920904 0.389789i $$-0.127452\pi$$
−0.798019 + 0.602632i $$0.794119\pi$$
$$150$$ 0 0
$$151$$ −16.0000 −1.30206 −0.651031 0.759051i $$-0.725663\pi$$
−0.651031 + 0.759051i $$0.725663\pi$$
$$152$$ 0 0
$$153$$ 6.00000i 0.485071i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −6.06218 + 3.50000i −0.483814 + 0.279330i −0.722005 0.691888i $$-0.756779\pi$$
0.238190 + 0.971219i $$0.423446\pi$$
$$158$$ 0 0
$$159$$ 11.0000 0.872357
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 4.00000i 0.313304i −0.987654 0.156652i $$-0.949930\pi$$
0.987654 0.156652i $$-0.0500701\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −12.9904 7.50000i −1.00523 0.580367i −0.0954356 0.995436i $$-0.530424\pi$$
−0.909790 + 0.415068i $$0.863758\pi$$
$$168$$ 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
$$173$$ 12.9904 7.50000i 0.987640 0.570214i 0.0830722 0.996544i $$-0.473527\pi$$
0.904568 + 0.426329i $$0.140193\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ −2.59808 1.50000i −0.195283 0.112747i
$$178$$ 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 $$-0.773838\pi$$
0.943854 + 0.330364i $$0.107171\pi$$
$$182$$ 0 0
$$183$$ 11.0000i 0.813143i
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 10.3923 6.00000i 0.759961 0.438763i
$$188$$ 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
$$193$$ 12.9904 7.50000i 0.935068 0.539862i 0.0466572 0.998911i $$-0.485143\pi$$
0.888411 + 0.459049i $$0.151810\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 2.00000i 0.142494i −0.997459 0.0712470i $$-0.977302\pi$$
0.997459 0.0712470i $$-0.0226979\pi$$
$$198$$ 0 0
$$199$$ −3.50000 + 6.06218i −0.248108 + 0.429736i −0.963001 0.269498i $$-0.913142\pi$$
0.714893 + 0.699234i $$0.246476\pi$$
$$200$$ 0 0
$$201$$ 3.00000 0.211604
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 8.66025 5.00000i 0.601929 0.347524i
$$208$$ 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 $$-0.0664070\pi$$
−0.668524 + 0.743690i $$0.733074\pi$$
$$212$$ 0 0
$$213$$ 9.52628 + 5.50000i 0.652730 + 0.376854i
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 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
$$223$$ −21.6506 + 12.5000i −1.44983 + 0.837062i −0.998471 0.0552786i $$-0.982395\pi$$
−0.451363 + 0.892341i $$0.649062\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 20.0000i 1.32745i 0.747978 + 0.663723i $$0.231025\pi$$
−0.747978 + 0.663723i $$0.768975\pi$$
$$228$$ 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
$$233$$ −18.1865 + 10.5000i −1.19144 + 0.687878i −0.958633 0.284645i $$-0.908124\pi$$
−0.232806 + 0.972523i $$0.574791\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 11.2583 + 6.50000i 0.731307 + 0.422220i
$$238$$ 0 0
$$239$$ −12.0000 −0.776215 −0.388108 0.921614i $$-0.626871\pi$$
−0.388108 + 0.921614i $$0.626871\pi$$
$$240$$ 0 0
$$241$$ −9.50000 + 16.4545i −0.611949 + 1.05993i 0.378963 + 0.925412i $$0.376281\pi$$
−0.990912 + 0.134515i $$0.957053\pi$$
$$242$$ 0 0
$$243$$ 13.8564 + 8.00000i 0.888889 + 0.513200i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 2.59808 + 3.50000i 0.165312 + 0.222700i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 15.5000 26.8468i 0.978351 1.69455i 0.309951 0.950753i $$-0.399687\pi$$
0.668400 0.743802i $$-0.266979\pi$$
$$252$$ 0 0
$$253$$ 17.3205 + 10.0000i 1.08893 + 0.628695i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 19.9186 + 11.5000i 1.24249 + 0.717350i 0.969600 0.244696i $$-0.0786881\pi$$
0.272887 + 0.962046i $$0.412021\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 7.00000 + 12.1244i 0.433289 + 0.750479i
$$262$$ 0 0
$$263$$ −7.79423 + 4.50000i −0.480613 + 0.277482i −0.720672 0.693276i $$-0.756167\pi$$
0.240059 + 0.970758i $$0.422833\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 3.00000i 0.183597i
$$268$$ 0 0
$$269$$ 13.5000 + 23.3827i 0.823110 + 1.42567i 0.903356 + 0.428892i $$0.141096\pi$$
−0.0802460 + 0.996775i $$0.525571\pi$$
$$270$$ 0 0
$$271$$ −15.5000 26.8468i −0.941558 1.63083i −0.762501 0.646988i $$-0.776029\pi$$
−0.179057 0.983839i $$-0.557305\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 10.0000i 0.600842i −0.953807 0.300421i $$-0.902873\pi$$
0.953807 0.300421i $$-0.0971271\pi$$
$$278$$ 0 0
$$279$$ −4.00000 + 6.92820i −0.239474 + 0.414781i
$$280$$ 0 0
$$281$$ −3.50000 + 6.06218i −0.208792 + 0.361639i −0.951334 0.308160i $$-0.900287\pi$$
0.742542 + 0.669800i $$0.233620\pi$$
$$282$$ 0 0
$$283$$ −7.79423 + 4.50000i −0.463319 + 0.267497i −0.713439 0.700718i $$-0.752863\pi$$
0.250120 + 0.968215i $$0.419530\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 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
$$293$$ 30.0000i 1.75262i −0.481749 0.876309i $$-0.659998\pi$$
0.481749 0.876309i $$-0.340002\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 20.0000i 1.16052i
$$298$$ 0 0
$$299$$ −2.50000 4.33013i −0.144579 0.250418i
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 1.00000i 0.0574485i
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −23.3827 + 13.5000i −1.33452 + 0.770486i −0.985989 0.166811i $$-0.946653\pi$$
−0.348532 + 0.937297i $$0.613320\pi$$
$$308$$ 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
$$313$$ −9.52628 5.50000i −0.538457 0.310878i 0.205996 0.978553i $$-0.433957\pi$$
−0.744453 + 0.667674i $$0.767290\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 12.9904 + 7.50000i 0.729612 + 0.421242i 0.818280 0.574819i $$-0.194928\pi$$
−0.0886679 + 0.996061i $$0.528261\pi$$
$$318$$ 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
$$323$$ −12.9904 + 1.50000i −0.722804 + 0.0834622i
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ −2.59808 1.50000i −0.143674 0.0829502i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 20.0000 1.09930 0.549650 0.835395i $$-0.314761\pi$$
0.549650 + 0.835395i $$0.314761\pi$$
$$332$$ 0 0
$$333$$ 17.3205 + 10.0000i 0.949158 + 0.547997i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 4.33013 2.50000i 0.235877 0.136184i −0.377403 0.926049i $$-0.623183\pi$$
0.613280 + 0.789865i $$0.289850\pi$$
$$338$$ 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
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 4.33013 2.50000i 0.232453 0.134207i −0.379250 0.925294i $$-0.623818\pi$$
0.611703 + 0.791087i $$0.290485\pi$$
$$348$$ 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
$$353$$ 30.0000i 1.59674i 0.602168 + 0.798369i $$0.294304\pi$$
−0.602168 + 0.798369i $$0.705696\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 7.50000 + 12.9904i 0.395835 + 0.685606i 0.993207 0.116358i $$-0.0371219\pi$$
−0.597372 + 0.801964i $$0.703789\pi$$
$$360$$ 0 0
$$361$$ 13.0000 + 13.8564i 0.684211 + 0.729285i
$$362$$ 0 0
$$363$$ −4.33013 + 2.50000i −0.227273 + 0.131216i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 21.6506 + 12.5000i 1.13015 + 0.652495i 0.943974 0.330021i $$-0.107056\pi$$
0.186180 + 0.982516i $$0.440389\pi$$
$$368$$ 0 0
$$369$$ −10.0000 −0.520579
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 10.0000i 0.517780i −0.965907 0.258890i $$-0.916643\pi$$
0.965907 0.258890i $$-0.0833568\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 6.06218 3.50000i 0.312218 0.180259i
$$378$$ 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
$$383$$ −25.1147 + 14.5000i −1.28330 + 0.740915i −0.977451 0.211164i $$-0.932275\pi$$
−0.305852 + 0.952079i $$0.598941\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 10.0000i 0.508329i
$$388$$ 0 0
$$389$$ 1.50000 2.59808i 0.0760530 0.131728i −0.825491 0.564416i $$-0.809102\pi$$
0.901544 + 0.432688i $$0.142435\pi$$
$$390$$ 0 0
$$391$$ 15.0000 0.758583
$$392$$ 0 0
$$393$$ 12.9904 + 7.50000i 0.655278 + 0.378325i
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 21.6506 12.5000i 1.08661 0.627357i 0.153941 0.988080i $$-0.450803\pi$$
0.932673 + 0.360723i $$0.117470\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −9.50000 16.4545i −0.474407 0.821698i 0.525163 0.851002i $$-0.324004\pi$$
−0.999571 + 0.0293039i $$0.990671\pi$$
$$402$$ 0 0
$$403$$ 3.46410 + 2.00000i 0.172559 + 0.0996271i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 40.0000i 1.98273i
$$408$$ 0 0
$$409$$ −8.50000 + 14.7224i −0.420298 + 0.727977i −0.995968 0.0897044i $$-0.971408\pi$$
0.575670 + 0.817682i $$0.304741\pi$$
$$410$$ 0 0
$$411$$ 5.00000 0.246632
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 9.00000i 0.440732i
$$418$$ 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 $$-0.158909\pi$$
−0.853584 + 0.520955i $$0.825576\pi$$
$$422$$ 0 0
$$423$$ 12.1244 7.00000i 0.589506 0.340352i
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 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 0.494211 + 0.869342i $$0.335457\pi$$
−0.999978 + 0.00667224i $$0.997876\pi$$
$$432$$ 0 0
$$433$$ 21.6506 + 12.5000i 1.04046 + 0.600712i 0.919964 0.392002i $$-0.128217\pi$$
0.120499 + 0.992713i $$0.461551\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −12.9904 17.5000i −0.621414 0.837139i
$$438$$ 0 0
$$439$$ −6.50000 11.2583i −0.310228 0.537331i 0.668184 0.743996i $$-0.267072\pi$$
−0.978412 + 0.206666i $$0.933739\pi$$
$$440$$ 0 0
$$441$$ −7.00000 + 12.1244i −0.333333 + 0.577350i
$$442$$ 0 0
$$443$$ −21.6506 12.5000i −1.02865 0.593893i −0.112054 0.993702i $$-0.535743\pi$$
−0.916598 + 0.399809i $$0.869076\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ −2.59808 1.50000i −0.122885 0.0709476i
$$448$$ 0 0
$$449$$ −22.0000 −1.03824 −0.519122 0.854700i $$-0.673741\pi$$
−0.519122 + 0.854700i $$0.673741\pi$$
$$450$$ 0 0
$$451$$ −10.0000 17.3205i −0.470882 0.815591i
$$452$$ 0 0
$$453$$ 13.8564 8.00000i 0.651031 0.375873i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 22.0000i 1.02912i 0.857455 + 0.514558i $$0.172044\pi$$
−0.857455 + 0.514558i $$0.827956\pi$$
$$458$$ 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 $$-0.249124\pi$$
−0.965210 + 0.261476i $$0.915791\pi$$
$$462$$ 0 0
$$463$$ 20.0000i 0.929479i −0.885448 0.464739i $$-0.846148\pi$$
0.885448 0.464739i $$-0.153852\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 20.0000i 0.925490i 0.886492 + 0.462745i $$0.153135\pi$$
−0.886492 + 0.462745i $$0.846865\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 3.50000 6.06218i 0.161271 0.279330i
$$472$$ 0 0
$$473$$ 17.3205 10.0000i 0.796398 0.459800i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 19.0526 11.0000i 0.872357 0.503655i
$$478$$ 0 0
$$479$$ −11.5000 + 19.9186i −0.525448 + 0.910103i 0.474112 + 0.880464i $$0.342769\pi$$
−0.999561 + 0.0296389i $$0.990564\pi$$
$$480$$ 0 0
$$481$$ 5.00000 8.66025i 0.227980 0.394874i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 8.00000i 0.362515i 0.983436 + 0.181257i $$0.0580167\pi$$
−0.983436 + 0.181257i $$0.941983\pi$$
$$488$$ 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 $$-0.159483\pi$$
−0.854523 + 0.519414i $$0.826150\pi$$
$$492$$ 0 0
$$493$$ 21.0000i 0.945792i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −2.50000 4.33013i −0.111915 0.193843i 0.804627 0.593780i $$-0.202365\pi$$
−0.916542 + 0.399937i $$0.869032\pi$$
$$500$$ 0 0
$$501$$ 15.0000 0.670151
$$502$$ 0 0
$$503$$ −18.1865 10.5000i −0.810897 0.468172i 0.0363700 0.999338i $$-0.488421\pi$$
−0.847267 + 0.531167i $$0.821754\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 10.3923 + 6.00000i 0.461538 + 0.266469i
$$508$$ 0 0
$$509$$ 7.50000 12.9904i 0.332432 0.575789i −0.650556 0.759458i $$-0.725464\pi$$
0.982988 + 0.183669i $$0.0587976\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 8.66025 20.0000i 0.382360 0.883022i
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 24.2487 + 14.0000i 1.06646 + 0.615719i
$$518$$ 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
$$523$$ 16.4545 + 9.50000i 0.719504 + 0.415406i 0.814570 0.580065i $$-0.196973\pi$$
−0.0950659 + 0.995471i $$0.530306\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −10.3923 + 6.00000i −0.452696 + 0.261364i
$$528$$ 0 0
$$529$$ 1.00000 + 1.73205i 0.0434783 + 0.0753066i
$$530$$ 0 0
$$531$$ −6.00000 −0.260378
$$532$$ 0 0
$$533$$ 5.00000i 0.216574i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ −10.3923 + 6.00000i −0.448461 + 0.258919i
$$538$$ 0 0
$$539$$ −28.0000 −1.20605
$$540$$ 0 0
$$541$$ 0.500000 0.866025i 0.0214967 0.0372333i −0.855077 0.518501i $$-0.826490\pi$$
0.876574 + 0.481268i $$0.159824\pi$$
$$542$$ 0 0
$$543$$ 5.00000i 0.214571i
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 21.6506 + 12.5000i 0.925714 + 0.534461i 0.885454 0.464728i $$-0.153848\pi$$
0.0402607 + 0.999189i $$0.487181\pi$$
$$548$$ 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
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −4.33013 2.50000i −0.183473 0.105928i 0.405450 0.914117i $$-0.367115\pi$$
−0.588924 + 0.808189i $$0.700448\pi$$
$$558$$ 0 0
$$559$$ −5.00000 −0.211477
$$560$$ 0 0
$$561$$ −6.00000 + 10.3923i −0.253320 + 0.438763i
$$562$$ 0 0
$$563$$ 36.0000i 1.51722i 0.651546 + 0.758610i $$0.274121\pi$$
−0.651546 + 0.758610i $$0.725879\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −22.0000 −0.922288 −0.461144 0.887325i $$-0.652561\pi$$
−0.461144 + 0.887325i $$0.652561\pi$$
$$570$$ 0 0
$$571$$ −4.00000 −0.167395 −0.0836974 0.996491i $$-0.526673\pi$$
−0.0836974 + 0.996491i $$0.526673\pi$$
$$572$$ 0 0
$$573$$ −13.8564 + 8.00000i −0.578860 + 0.334205i
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 10.0000i 0.416305i 0.978096 + 0.208153i $$0.0667451\pi$$
−0.978096 + 0.208153i $$0.933255\pi$$
$$578$$ 0 0
$$579$$ −7.50000 + 12.9904i −0.311689 + 0.539862i
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 38.1051 + 22.0000i 1.57815 + 0.911147i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −12.9904 + 7.50000i −0.536170 + 0.309558i −0.743525 0.668708i $$-0.766848\pi$$
0.207355 + 0.978266i $$0.433514\pi$$
$$588$$ 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
$$593$$ 4.33013 + 2.50000i 0.177817 + 0.102663i 0.586267 0.810118i $$-0.300597\pi$$
−0.408450 + 0.912781i $$0.633930\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 7.00000i 0.286491i
$$598$$ 0 0
$$599$$ 22.5000 38.9711i 0.919325 1.59232i 0.118882 0.992908i $$-0.462069\pi$$
0.800443 0.599409i $$-0.204598\pi$$
$$600$$ 0 0
$$601$$ −26.0000 −1.06056 −0.530281 0.847822i $$-0.677914\pi$$
−0.530281 + 0.847822i $$0.677914\pi$$
$$602$$ 0 0
$$603$$ 5.19615 3.00000i 0.211604 0.122169i
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 32.0000i 1.29884i −0.760430 0.649420i $$-0.775012\pi$$
0.760430 0.649420i $$-0.224988\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −3.50000 6.06218i −0.141595 0.245249i
$$612$$ 0 0
$$613$$ −25.1147 + 14.5000i −1.01437 + 0.585649i −0.912470 0.409145i $$-0.865827\pi$$
−0.101905 + 0.994794i $$0.532494\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −38.9711 22.5000i −1.56892 0.905816i −0.996295 0.0859976i $$-0.972592\pi$$
−0.572624 0.819818i $$-0.694074\pi$$
$$618$$ 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
$$625$$ 0 0
$$626$$ 0 0
$$627$$ 17.3205 2.00000i 0.691714 0.0798723i
$$628$$ 0 0
$$629$$ 15.0000 + 25.9808i 0.598089 + 1.03592i
$$630$$ 0 0
$$631$$ −20.5000 + 35.5070i −0.816092 + 1.41351i 0.0924489 + 0.995717i $$0.470531\pi$$
−0.908541 + 0.417796i $$0.862803\pi$$
$$632$$ 0 0
$$633$$ −7.79423 4.50000i −0.309793 0.178859i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 6.06218 + 3.50000i 0.240192 + 0.138675i
$$638$$ 0 0
$$639$$ 22.0000 0.870307
$$640$$ 0 0
$$641$$ −19.5000 33.7750i −0.770204 1.33403i −0.937451 0.348117i $$-0.886821\pi$$
0.167247 0.985915i $$-0.446512\pi$$
$$642$$ 0 0
$$643$$ 16.4545 9.50000i 0.648901 0.374643i −0.139134 0.990274i $$-0.544432\pi$$
0.788035 + 0.615630i $$0.211098\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 32.0000i 1.25805i −0.777385 0.629025i $$-0.783454\pi$$
0.777385 0.629025i $$-0.216546\pi$$
$$648$$ 0 0
$$649$$ −6.00000 10.3923i −0.235521 0.407934i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 30.0000i 1.17399i −0.809590 0.586995i $$-0.800311\pi$$
0.809590 0.586995i $$-0.199689\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 30.0000i 1.17041i
$$658$$ 0 0
$$659$$ 2.50000 4.33013i 0.0973862 0.168678i −0.813216 0.581962i $$-0.802285\pi$$
0.910602 + 0.413284i $$0.135618\pi$$
$$660$$ 0 0
$$661$$ −15.5000 + 26.8468i −0.602880 + 1.04422i 0.389503 + 0.921025i $$0.372647\pi$$
−0.992383 + 0.123194i $$0.960686\pi$$
$$662$$ 0 0
$$663$$ 2.59808 1.50000i 0.100901 0.0582552i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −30.3109 + 17.5000i −1.17364 + 0.677603i
$$668$$ 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
$$673$$ 10.0000i 0.385472i −0.981251 0.192736i $$-0.938264\pi$$
0.981251 0.192736i $$-0.0617360\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 10.0000i 0.384331i −0.981363 0.192166i $$-0.938449\pi$$
0.981363 0.192166i $$-0.0615511\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ −10.0000 17.3205i −0.383201 0.663723i
$$682$$ 0 0
$$683$$ 16.0000i 0.612223i 0.951996 + 0.306111i $$0.0990280\pi$$
−0.951996 + 0.306111i $$0.900972\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 1.73205 1.00000i 0.0660819 0.0381524i
$$688$$ 0 0
$$689$$ −5.50000 9.52628i −0.209533 0.362922i
$$690$$ 0 0
$$691$$ 36.0000 1.36950 0.684752 0.728776i $$-0.259910\pi$$
0.684752 + 0.728776i $$0.259910\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −12.9904 7.50000i −0.492046 0.284083i
$$698$$ 0 0
$$699$$ 10.5000 18.1865i 0.397146 0.687878i
$$700$$ 0 0
$$701$$ −17.5000 30.3109i −0.660966 1.14483i −0.980362 0.197205i $$-0.936813\pi$$
0.319396 0.947621i $$-0.396520\pi$$
$$702$$ 0 0
$$703$$ 17.3205 40.0000i 0.653255 1.50863i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 1.50000 2.59808i 0.0563337 0.0975728i −0.836483 0.547992i $$-0.815392\pi$$
0.892817 + 0.450420i $$0.148726\pi$$
$$710$$ 0 0
$$711$$ 26.0000 0.975076
$$712$$ 0 0
$$713$$ −17.3205 10.0000i −0.648658 0.374503i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 10.3923 6.00000i 0.388108 0.224074i
$$718$$ 0 0
$$719$$ 3.50000 + 6.06218i 0.130528 + 0.226081i 0.923880 0.382682i $$-0.124999\pi$$
−0.793352 + 0.608763i $$0.791666\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 19.0000i 0.706618i
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −6.06218 + 3.50000i −0.224834 + 0.129808i −0.608186 0.793794i $$-0.708103\pi$$
0.383353 + 0.923602i $$0.374769\pi$$
$$728$$ 0 0
$$729$$ −13.0000 −0.481481
$$730$$ 0 0
$$731$$ 7.50000 12.9904i 0.277398 0.480467i
$$732$$ 0 0
$$733$$ 30.0000i 1.10808i −0.832492 0.554038i $$-0.813086\pi$$
0.832492 0.554038i $$-0.186914\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 10.3923 + 6.00000i 0.382805 + 0.221013i
$$738$$ 0 0
$$739$$ −6.50000 11.2583i −0.239106 0.414144i 0.721352 0.692569i $$-0.243521\pi$$
−0.960458 + 0.278425i $$0.910188\pi$$
$$740$$ 0 0
$$741$$ −4.00000 1.73205i −0.146944 0.0636285i
$$742$$ 0 0
$$743$$ −21.6506 + 12.5000i −0.794285 + 0.458581i −0.841469 0.540306i $$-0.818309\pi$$
0.0471840 + 0.998886i $$0.484975\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −14.5000 + 25.1147i −0.529113 + 0.916450i 0.470311 + 0.882501i $$0.344142\pi$$
−0.999424 + 0.0339490i $$0.989192\pi$$
$$752$$ 0 0
$$753$$ 31.0000i 1.12970i
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 14.7224 8.50000i 0.535096 0.308938i −0.207993 0.978130i $$-0.566693\pi$$
0.743089 + 0.669193i $$0.233360\pi$$
$$758$$ 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
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 3.00000i 0.108324i
$$768$$ 0 0
$$769$$ 3.50000 6.06218i 0.126213 0.218608i −0.795993 0.605305i $$-0.793051\pi$$
0.922207 + 0.386698i $$0.126384\pi$$
$$770$$ 0 0
$$771$$ −23.0000 −0.828325
$$772$$ 0 0
$$773$$ 18.1865 + 10.5000i 0.654124 + 0.377659i 0.790034 0.613062i $$-0.210063\pi$$
−0.135910 + 0.990721i $$0.543396\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 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
$$783$$ −30.3109 17.5000i −1.08322 0.625399i
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 52.0000i 1.85360i −0.375555 0.926800i $$-0.622548\pi$$
0.375555 0.926800i $$-0.377452\pi$$
$$788$$ 0 0
$$789$$ 4.50000 7.79423i 0.160204 0.277482i
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ −9.52628 + 5.50000i −0.338288 + 0.195311i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 18.0000i 0.637593i −0.947823 0.318796i $$-0.896721\pi$$
0.947823 0.318796i $$-0.103279\pi$$
$$798$$ 0 0
$$799$$ 21.0000 0.742927
$$800$$ 0