# Properties

 Label 2100.2.bc.a.949.1 Level $2100$ Weight $2$ Character 2100.949 Analytic conductor $16.769$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2100.bc (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$16.7685844245$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\zeta_{12})$$ Defining polynomial: $$x^{4} - x^{2} + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 84) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 949.1 Root $$-0.866025 - 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 2100.949 Dual form 2100.2.bc.a.1549.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.866025 - 0.500000i) q^{3} +(2.59808 + 0.500000i) q^{7} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$q+(-0.866025 - 0.500000i) q^{3} +(2.59808 + 0.500000i) q^{7} +(0.500000 + 0.866025i) q^{9} +(-1.00000 + 1.73205i) q^{11} +3.00000i q^{13} +(-6.92820 - 4.00000i) q^{17} +(-0.500000 - 0.866025i) q^{19} +(-2.00000 - 1.73205i) q^{21} +(-6.92820 + 4.00000i) q^{23} -1.00000i q^{27} -4.00000 q^{29} +(-1.50000 + 2.59808i) q^{31} +(1.73205 - 1.00000i) q^{33} +(-0.866025 + 0.500000i) q^{37} +(1.50000 - 2.59808i) q^{39} +6.00000 q^{41} -11.0000i q^{43} +(5.19615 - 3.00000i) q^{47} +(6.50000 + 2.59808i) q^{49} +(4.00000 + 6.92820i) q^{51} +(-10.3923 - 6.00000i) q^{53} +1.00000i q^{57} +(2.00000 - 3.46410i) q^{59} +(3.00000 + 5.19615i) q^{61} +(0.866025 + 2.50000i) q^{63} +(-11.2583 - 6.50000i) q^{67} +8.00000 q^{69} -10.0000 q^{71} +(-9.52628 - 5.50000i) q^{73} +(-3.46410 + 4.00000i) q^{77} +(-1.50000 - 2.59808i) q^{79} +(-0.500000 + 0.866025i) q^{81} -2.00000i q^{83} +(3.46410 + 2.00000i) q^{87} +(-1.50000 + 7.79423i) q^{91} +(2.59808 - 1.50000i) q^{93} +10.0000i q^{97} -2.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q + 2q^{9} + O(q^{10})$$ $$4q + 2q^{9} - 4q^{11} - 2q^{19} - 8q^{21} - 16q^{29} - 6q^{31} + 6q^{39} + 24q^{41} + 26q^{49} + 16q^{51} + 8q^{59} + 12q^{61} + 32q^{69} - 40q^{71} - 6q^{79} - 2q^{81} - 6q^{91} - 8q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$$.

 $$n$$ $$701$$ $$1051$$ $$1177$$ $$1501$$ $$\chi(n)$$ $$1$$ $$1$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −0.866025 0.500000i −0.500000 0.288675i
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 2.59808 + 0.500000i 0.981981 + 0.188982i
$$8$$ 0 0
$$9$$ 0.500000 + 0.866025i 0.166667 + 0.288675i
$$10$$ 0 0
$$11$$ −1.00000 + 1.73205i −0.301511 + 0.522233i −0.976478 0.215615i $$-0.930824\pi$$
0.674967 + 0.737848i $$0.264158\pi$$
$$12$$ 0 0
$$13$$ 3.00000i 0.832050i 0.909353 + 0.416025i $$0.136577\pi$$
−0.909353 + 0.416025i $$0.863423\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −6.92820 4.00000i −1.68034 0.970143i −0.961436 0.275029i $$-0.911312\pi$$
−0.718900 0.695113i $$-0.755354\pi$$
$$18$$ 0 0
$$19$$ −0.500000 0.866025i −0.114708 0.198680i 0.802955 0.596040i $$-0.203260\pi$$
−0.917663 + 0.397360i $$0.869927\pi$$
$$20$$ 0 0
$$21$$ −2.00000 1.73205i −0.436436 0.377964i
$$22$$ 0 0
$$23$$ −6.92820 + 4.00000i −1.44463 + 0.834058i −0.998154 0.0607377i $$-0.980655\pi$$
−0.446476 + 0.894795i $$0.647321\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ 1.00000i 0.192450i
$$28$$ 0 0
$$29$$ −4.00000 −0.742781 −0.371391 0.928477i $$-0.621119\pi$$
−0.371391 + 0.928477i $$0.621119\pi$$
$$30$$ 0 0
$$31$$ −1.50000 + 2.59808i −0.269408 + 0.466628i −0.968709 0.248199i $$-0.920161\pi$$
0.699301 + 0.714827i $$0.253495\pi$$
$$32$$ 0 0
$$33$$ 1.73205 1.00000i 0.301511 0.174078i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −0.866025 + 0.500000i −0.142374 + 0.0821995i −0.569495 0.821995i $$-0.692861\pi$$
0.427121 + 0.904194i $$0.359528\pi$$
$$38$$ 0 0
$$39$$ 1.50000 2.59808i 0.240192 0.416025i
$$40$$ 0 0
$$41$$ 6.00000 0.937043 0.468521 0.883452i $$-0.344787\pi$$
0.468521 + 0.883452i $$0.344787\pi$$
$$42$$ 0 0
$$43$$ 11.0000i 1.67748i −0.544529 0.838742i $$-0.683292\pi$$
0.544529 0.838742i $$-0.316708\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 5.19615 3.00000i 0.757937 0.437595i −0.0706177 0.997503i $$-0.522497\pi$$
0.828554 + 0.559908i $$0.189164\pi$$
$$48$$ 0 0
$$49$$ 6.50000 + 2.59808i 0.928571 + 0.371154i
$$50$$ 0 0
$$51$$ 4.00000 + 6.92820i 0.560112 + 0.970143i
$$52$$ 0 0
$$53$$ −10.3923 6.00000i −1.42749 0.824163i −0.430570 0.902557i $$-0.641688\pi$$
−0.996922 + 0.0783936i $$0.975021\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 1.00000i 0.132453i
$$58$$ 0 0
$$59$$ 2.00000 3.46410i 0.260378 0.450988i −0.705965 0.708247i $$-0.749486\pi$$
0.966342 + 0.257260i $$0.0828195\pi$$
$$60$$ 0 0
$$61$$ 3.00000 + 5.19615i 0.384111 + 0.665299i 0.991645 0.128994i $$-0.0411748\pi$$
−0.607535 + 0.794293i $$0.707841\pi$$
$$62$$ 0 0
$$63$$ 0.866025 + 2.50000i 0.109109 + 0.314970i
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −11.2583 6.50000i −1.37542 0.794101i −0.383819 0.923408i $$-0.625391\pi$$
−0.991605 + 0.129307i $$0.958725\pi$$
$$68$$ 0 0
$$69$$ 8.00000 0.963087
$$70$$ 0 0
$$71$$ −10.0000 −1.18678 −0.593391 0.804914i $$-0.702211\pi$$
−0.593391 + 0.804914i $$0.702211\pi$$
$$72$$ 0 0
$$73$$ −9.52628 5.50000i −1.11497 0.643726i −0.174855 0.984594i $$-0.555946\pi$$
−0.940111 + 0.340868i $$0.889279\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −3.46410 + 4.00000i −0.394771 + 0.455842i
$$78$$ 0 0
$$79$$ −1.50000 2.59808i −0.168763 0.292306i 0.769222 0.638982i $$-0.220644\pi$$
−0.937985 + 0.346675i $$0.887311\pi$$
$$80$$ 0 0
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ 0 0
$$83$$ 2.00000i 0.219529i −0.993958 0.109764i $$-0.964990\pi$$
0.993958 0.109764i $$-0.0350096\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 3.46410 + 2.00000i 0.371391 + 0.214423i
$$88$$ 0 0
$$89$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$90$$ 0 0
$$91$$ −1.50000 + 7.79423i −0.157243 + 0.817057i
$$92$$ 0 0
$$93$$ 2.59808 1.50000i 0.269408 0.155543i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 10.0000i 1.01535i 0.861550 + 0.507673i $$0.169494\pi$$
−0.861550 + 0.507673i $$0.830506\pi$$
$$98$$ 0 0
$$99$$ −2.00000 −0.201008
$$100$$ 0 0
$$101$$ −5.00000 + 8.66025i −0.497519 + 0.861727i −0.999996 0.00286291i $$-0.999089\pi$$
0.502477 + 0.864590i $$0.332422\pi$$
$$102$$ 0 0
$$103$$ −9.52628 + 5.50000i −0.938652 + 0.541931i −0.889538 0.456862i $$-0.848973\pi$$
−0.0491146 + 0.998793i $$0.515640\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$108$$ 0 0
$$109$$ −5.50000 + 9.52628i −0.526804 + 0.912452i 0.472708 + 0.881219i $$0.343277\pi$$
−0.999512 + 0.0312328i $$0.990057\pi$$
$$110$$ 0 0
$$111$$ 1.00000 0.0949158
$$112$$ 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
$$117$$ −2.59808 + 1.50000i −0.240192 + 0.138675i
$$118$$ 0 0
$$119$$ −16.0000 13.8564i −1.46672 1.27021i
$$120$$ 0 0
$$121$$ 3.50000 + 6.06218i 0.318182 + 0.551107i
$$122$$ 0 0
$$123$$ −5.19615 3.00000i −0.468521 0.270501i
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 3.00000i 0.266207i 0.991102 + 0.133103i $$0.0424943\pi$$
−0.991102 + 0.133103i $$0.957506\pi$$
$$128$$ 0 0
$$129$$ −5.50000 + 9.52628i −0.484248 + 0.838742i
$$130$$ 0 0
$$131$$ 1.00000 + 1.73205i 0.0873704 + 0.151330i 0.906399 0.422423i $$-0.138820\pi$$
−0.819028 + 0.573753i $$0.805487\pi$$
$$132$$ 0 0
$$133$$ −0.866025 2.50000i −0.0750939 0.216777i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −3.46410 2.00000i −0.295958 0.170872i 0.344668 0.938725i $$-0.387992\pi$$
−0.640626 + 0.767853i $$0.721325\pi$$
$$138$$ 0 0
$$139$$ 5.00000 0.424094 0.212047 0.977259i $$-0.431987\pi$$
0.212047 + 0.977259i $$0.431987\pi$$
$$140$$ 0 0
$$141$$ −6.00000 −0.505291
$$142$$ 0 0
$$143$$ −5.19615 3.00000i −0.434524 0.250873i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −4.33013 5.50000i −0.357143 0.453632i
$$148$$ 0 0
$$149$$ −6.00000 10.3923i −0.491539 0.851371i 0.508413 0.861113i $$-0.330232\pi$$
−0.999953 + 0.00974235i $$0.996899\pi$$
$$150$$ 0 0
$$151$$ 4.00000 6.92820i 0.325515 0.563809i −0.656101 0.754673i $$-0.727796\pi$$
0.981617 + 0.190864i $$0.0611289\pi$$
$$152$$ 0 0
$$153$$ 8.00000i 0.646762i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −1.73205 1.00000i −0.138233 0.0798087i 0.429289 0.903167i $$-0.358764\pi$$
−0.567521 + 0.823359i $$0.692098\pi$$
$$158$$ 0 0
$$159$$ 6.00000 + 10.3923i 0.475831 + 0.824163i
$$160$$ 0 0
$$161$$ −20.0000 + 6.92820i −1.57622 + 0.546019i
$$162$$ 0 0
$$163$$ 3.46410 2.00000i 0.271329 0.156652i −0.358162 0.933659i $$-0.616597\pi$$
0.629492 + 0.777007i $$0.283263\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 2.00000i 0.154765i −0.997001 0.0773823i $$-0.975344\pi$$
0.997001 0.0773823i $$-0.0246562\pi$$
$$168$$ 0 0
$$169$$ 4.00000 0.307692
$$170$$ 0 0
$$171$$ 0.500000 0.866025i 0.0382360 0.0662266i
$$172$$ 0 0
$$173$$ −13.8564 + 8.00000i −1.05348 + 0.608229i −0.923622 0.383304i $$-0.874786\pi$$
−0.129861 + 0.991532i $$0.541453\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ −3.46410 + 2.00000i −0.260378 + 0.150329i
$$178$$ 0 0
$$179$$ 3.00000 5.19615i 0.224231 0.388379i −0.731858 0.681457i $$-0.761346\pi$$
0.956088 + 0.293079i $$0.0946798\pi$$
$$180$$ 0 0
$$181$$ −15.0000 −1.11494 −0.557471 0.830197i $$-0.688228\pi$$
−0.557471 + 0.830197i $$0.688228\pi$$
$$182$$ 0 0
$$183$$ 6.00000i 0.443533i
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 13.8564 8.00000i 1.01328 0.585018i
$$188$$ 0 0
$$189$$ 0.500000 2.59808i 0.0363696 0.188982i
$$190$$ 0 0
$$191$$ −3.00000 5.19615i −0.217072 0.375980i 0.736839 0.676068i $$-0.236317\pi$$
−0.953912 + 0.300088i $$0.902984\pi$$
$$192$$ 0 0
$$193$$ 9.52628 + 5.50000i 0.685717 + 0.395899i 0.802005 0.597317i $$-0.203766\pi$$
−0.116289 + 0.993215i $$0.537100\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 8.00000i 0.569976i 0.958531 + 0.284988i $$0.0919897\pi$$
−0.958531 + 0.284988i $$0.908010\pi$$
$$198$$ 0 0
$$199$$ 4.00000 6.92820i 0.283552 0.491127i −0.688705 0.725042i $$-0.741820\pi$$
0.972257 + 0.233915i $$0.0751537\pi$$
$$200$$ 0 0
$$201$$ 6.50000 + 11.2583i 0.458475 + 0.794101i
$$202$$ 0 0
$$203$$ −10.3923 2.00000i −0.729397 0.140372i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ −6.92820 4.00000i −0.481543 0.278019i
$$208$$ 0 0
$$209$$ 2.00000 0.138343
$$210$$ 0 0
$$211$$ −4.00000 −0.275371 −0.137686 0.990476i $$-0.543966\pi$$
−0.137686 + 0.990476i $$0.543966\pi$$
$$212$$ 0 0
$$213$$ 8.66025 + 5.00000i 0.593391 + 0.342594i
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −5.19615 + 6.00000i −0.352738 + 0.407307i
$$218$$ 0 0
$$219$$ 5.50000 + 9.52628i 0.371656 + 0.643726i
$$220$$ 0 0
$$221$$ 12.0000 20.7846i 0.807207 1.39812i
$$222$$ 0 0
$$223$$ 8.00000i 0.535720i −0.963458 0.267860i $$-0.913684\pi$$
0.963458 0.267860i $$-0.0863164\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 15.5885 + 9.00000i 1.03464 + 0.597351i 0.918311 0.395860i $$-0.129553\pi$$
0.116331 + 0.993210i $$0.462887\pi$$
$$228$$ 0 0
$$229$$ 0.500000 + 0.866025i 0.0330409 + 0.0572286i 0.882073 0.471113i $$-0.156147\pi$$
−0.849032 + 0.528341i $$0.822814\pi$$
$$230$$ 0 0
$$231$$ 5.00000 1.73205i 0.328976 0.113961i
$$232$$ 0 0
$$233$$ −12.1244 + 7.00000i −0.794293 + 0.458585i −0.841472 0.540301i $$-0.818310\pi$$
0.0471787 + 0.998886i $$0.484977\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 3.00000i 0.194871i
$$238$$ 0 0
$$239$$ −18.0000 −1.16432 −0.582162 0.813073i $$-0.697793\pi$$
−0.582162 + 0.813073i $$0.697793\pi$$
$$240$$ 0 0
$$241$$ −7.00000 + 12.1244i −0.450910 + 0.780998i −0.998443 0.0557856i $$-0.982234\pi$$
0.547533 + 0.836784i $$0.315567\pi$$
$$242$$ 0 0
$$243$$ 0.866025 0.500000i 0.0555556 0.0320750i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 2.59808 1.50000i 0.165312 0.0954427i
$$248$$ 0 0
$$249$$ −1.00000 + 1.73205i −0.0633724 + 0.109764i
$$250$$ 0 0
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 0 0
$$253$$ 16.0000i 1.00591i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 15.5885 9.00000i 0.972381 0.561405i 0.0724199 0.997374i $$-0.476928\pi$$
0.899961 + 0.435970i $$0.143595\pi$$
$$258$$ 0 0
$$259$$ −2.50000 + 0.866025i −0.155342 + 0.0538122i
$$260$$ 0 0
$$261$$ −2.00000 3.46410i −0.123797 0.214423i
$$262$$ 0 0
$$263$$ 10.3923 + 6.00000i 0.640817 + 0.369976i 0.784929 0.619586i $$-0.212699\pi$$
−0.144112 + 0.989561i $$0.546033\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −1.00000 + 1.73205i −0.0609711 + 0.105605i −0.894900 0.446267i $$-0.852753\pi$$
0.833929 + 0.551872i $$0.186086\pi$$
$$270$$ 0 0
$$271$$ 12.0000 + 20.7846i 0.728948 + 1.26258i 0.957328 + 0.289003i $$0.0933238\pi$$
−0.228380 + 0.973572i $$0.573343\pi$$
$$272$$ 0 0
$$273$$ 5.19615 6.00000i 0.314485 0.363137i
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −14.7224 8.50000i −0.884585 0.510716i −0.0124177 0.999923i $$-0.503953\pi$$
−0.872167 + 0.489207i $$0.837286\pi$$
$$278$$ 0 0
$$279$$ −3.00000 −0.179605
$$280$$ 0 0
$$281$$ 20.0000 1.19310 0.596550 0.802576i $$-0.296538\pi$$
0.596550 + 0.802576i $$0.296538\pi$$
$$282$$ 0 0
$$283$$ 16.4545 + 9.50000i 0.978117 + 0.564716i 0.901701 0.432360i $$-0.142319\pi$$
0.0764162 + 0.997076i $$0.475652\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 15.5885 + 3.00000i 0.920158 + 0.177084i
$$288$$ 0 0
$$289$$ 23.5000 + 40.7032i 1.38235 + 2.39431i
$$290$$ 0 0
$$291$$ 5.00000 8.66025i 0.293105 0.507673i
$$292$$ 0 0
$$293$$ 24.0000i 1.40209i 0.713115 + 0.701047i $$0.247284\pi$$
−0.713115 + 0.701047i $$0.752716\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 1.73205 + 1.00000i 0.100504 + 0.0580259i
$$298$$ 0 0
$$299$$ −12.0000 20.7846i −0.693978 1.20201i
$$300$$ 0 0
$$301$$ 5.50000 28.5788i 0.317015 1.64726i
$$302$$ 0 0
$$303$$ 8.66025 5.00000i 0.497519 0.287242i
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 23.0000i 1.31268i −0.754466 0.656340i $$-0.772104\pi$$
0.754466 0.656340i $$-0.227896\pi$$
$$308$$ 0 0
$$309$$ 11.0000 0.625768
$$310$$ 0 0
$$311$$ 1.00000 1.73205i 0.0567048 0.0982156i −0.836280 0.548303i $$-0.815274\pi$$
0.892984 + 0.450088i $$0.148607\pi$$
$$312$$ 0 0
$$313$$ 14.7224 8.50000i 0.832161 0.480448i −0.0224310 0.999748i $$-0.507141\pi$$
0.854592 + 0.519300i $$0.173807\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −20.7846 + 12.0000i −1.16738 + 0.673987i −0.953062 0.302777i $$-0.902086\pi$$
−0.214318 + 0.976764i $$0.568753\pi$$
$$318$$ 0 0
$$319$$ 4.00000 6.92820i 0.223957 0.387905i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 8.00000i 0.445132i
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 9.52628 5.50000i 0.526804 0.304151i
$$328$$ 0 0
$$329$$ 15.0000 5.19615i 0.826977 0.286473i
$$330$$ 0 0
$$331$$ −8.50000 14.7224i −0.467202 0.809218i 0.532096 0.846684i $$-0.321405\pi$$
−0.999298 + 0.0374662i $$0.988071\pi$$
$$332$$ 0 0
$$333$$ −0.866025 0.500000i −0.0474579 0.0273998i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 21.0000i 1.14394i 0.820274 + 0.571971i $$0.193821\pi$$
−0.820274 + 0.571971i $$0.806179\pi$$
$$338$$ 0 0
$$339$$ 7.00000 12.1244i 0.380188 0.658505i
$$340$$ 0 0
$$341$$ −3.00000 5.19615i −0.162459 0.281387i
$$342$$ 0 0
$$343$$ 15.5885 + 10.0000i 0.841698 + 0.539949i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −20.7846 12.0000i −1.11578 0.644194i −0.175457 0.984487i $$-0.556140\pi$$
−0.940319 + 0.340293i $$0.889474\pi$$
$$348$$ 0 0
$$349$$ 14.0000 0.749403 0.374701 0.927146i $$-0.377745\pi$$
0.374701 + 0.927146i $$0.377745\pi$$
$$350$$ 0 0
$$351$$ 3.00000 0.160128
$$352$$ 0 0
$$353$$ −5.19615 3.00000i −0.276563 0.159674i 0.355303 0.934751i $$-0.384378\pi$$
−0.631867 + 0.775077i $$0.717711\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 6.92820 + 20.0000i 0.366679 + 1.05851i
$$358$$ 0 0
$$359$$ −10.0000 17.3205i −0.527780 0.914141i −0.999476 0.0323801i $$-0.989691\pi$$
0.471696 0.881761i $$-0.343642\pi$$
$$360$$ 0 0
$$361$$ 9.00000 15.5885i 0.473684 0.820445i
$$362$$ 0 0
$$363$$ 7.00000i 0.367405i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −4.33013 2.50000i −0.226031 0.130499i 0.382709 0.923869i $$-0.374991\pi$$
−0.608740 + 0.793370i $$0.708325\pi$$
$$368$$ 0 0
$$369$$ 3.00000 + 5.19615i 0.156174 + 0.270501i
$$370$$ 0 0
$$371$$ −24.0000 20.7846i −1.24602 1.07908i
$$372$$ 0 0
$$373$$ 4.33013 2.50000i 0.224205 0.129445i −0.383691 0.923462i $$-0.625347\pi$$
0.607896 + 0.794017i $$0.292014\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 12.0000i 0.618031i
$$378$$ 0 0
$$379$$ −13.0000 −0.667765 −0.333883 0.942615i $$-0.608359\pi$$
−0.333883 + 0.942615i $$0.608359\pi$$
$$380$$ 0 0
$$381$$ 1.50000 2.59808i 0.0768473 0.133103i
$$382$$ 0 0
$$383$$ 24.2487 14.0000i 1.23905 0.715367i 0.270151 0.962818i $$-0.412926\pi$$
0.968900 + 0.247451i $$0.0795931\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 9.52628 5.50000i 0.484248 0.279581i
$$388$$ 0 0
$$389$$ 5.00000 8.66025i 0.253510 0.439092i −0.710980 0.703213i $$-0.751748\pi$$
0.964490 + 0.264120i $$0.0850816\pi$$
$$390$$ 0 0
$$391$$ 64.0000 3.23662
$$392$$ 0 0
$$393$$ 2.00000i 0.100887i
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 2.59808 1.50000i 0.130394 0.0752828i −0.433384 0.901209i $$-0.642681\pi$$
0.563778 + 0.825926i $$0.309347\pi$$
$$398$$ 0 0
$$399$$ −0.500000 + 2.59808i −0.0250313 + 0.130066i
$$400$$ 0 0
$$401$$ 6.00000 + 10.3923i 0.299626 + 0.518967i 0.976050 0.217545i $$-0.0698049\pi$$
−0.676425 + 0.736512i $$0.736472\pi$$
$$402$$ 0 0
$$403$$ −7.79423 4.50000i −0.388258 0.224161i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 2.00000i 0.0991363i
$$408$$ 0 0
$$409$$ −9.50000 + 16.4545i −0.469745 + 0.813622i −0.999402 0.0345902i $$-0.988987\pi$$
0.529657 + 0.848212i $$0.322321\pi$$
$$410$$ 0 0
$$411$$ 2.00000 + 3.46410i 0.0986527 + 0.170872i
$$412$$ 0 0
$$413$$ 6.92820 8.00000i 0.340915 0.393654i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ −4.33013 2.50000i −0.212047 0.122426i
$$418$$ 0 0
$$419$$ −18.0000 −0.879358 −0.439679 0.898155i $$-0.644908\pi$$
−0.439679 + 0.898155i $$0.644908\pi$$
$$420$$ 0 0
$$421$$ −27.0000 −1.31590 −0.657950 0.753062i $$-0.728576\pi$$
−0.657950 + 0.753062i $$0.728576\pi$$
$$422$$ 0 0
$$423$$ 5.19615 + 3.00000i 0.252646 + 0.145865i
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 5.19615 + 15.0000i 0.251459 + 0.725901i
$$428$$ 0 0
$$429$$ 3.00000 + 5.19615i 0.144841 + 0.250873i
$$430$$ 0 0
$$431$$ 15.0000 25.9808i 0.722525 1.25145i −0.237460 0.971397i $$-0.576315\pi$$
0.959985 0.280052i $$-0.0903517\pi$$
$$432$$ 0 0
$$433$$ 25.0000i 1.20142i 0.799466 + 0.600712i $$0.205116\pi$$
−0.799466 + 0.600712i $$0.794884\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 6.92820 + 4.00000i 0.331421 + 0.191346i
$$438$$ 0 0
$$439$$ 12.0000 + 20.7846i 0.572729 + 0.991995i 0.996284 + 0.0861252i $$0.0274485\pi$$
−0.423556 + 0.905870i $$0.639218\pi$$
$$440$$ 0 0
$$441$$ 1.00000 + 6.92820i 0.0476190 + 0.329914i
$$442$$ 0 0
$$443$$ 3.46410 2.00000i 0.164584 0.0950229i −0.415445 0.909618i $$-0.636374\pi$$
0.580030 + 0.814595i $$0.303041\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 12.0000i 0.567581i
$$448$$ 0 0
$$449$$ −22.0000 −1.03824 −0.519122 0.854700i $$-0.673741\pi$$
−0.519122 + 0.854700i $$0.673741\pi$$
$$450$$ 0 0
$$451$$ −6.00000 + 10.3923i −0.282529 + 0.489355i
$$452$$ 0 0
$$453$$ −6.92820 + 4.00000i −0.325515 + 0.187936i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 11.2583 6.50000i 0.526642 0.304057i −0.213006 0.977051i $$-0.568325\pi$$
0.739648 + 0.672994i $$0.234992\pi$$
$$458$$ 0 0
$$459$$ −4.00000 + 6.92820i −0.186704 + 0.323381i
$$460$$ 0 0
$$461$$ 4.00000 0.186299 0.0931493 0.995652i $$-0.470307\pi$$
0.0931493 + 0.995652i $$0.470307\pi$$
$$462$$ 0 0
$$463$$ 11.0000i 0.511213i 0.966781 + 0.255607i $$0.0822752\pi$$
−0.966781 + 0.255607i $$0.917725\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 29.4449 17.0000i 1.36255 0.786666i 0.372584 0.927999i $$-0.378472\pi$$
0.989962 + 0.141332i $$0.0451386\pi$$
$$468$$ 0 0
$$469$$ −26.0000 22.5167i −1.20057 1.03972i
$$470$$ 0 0
$$471$$ 1.00000 + 1.73205i 0.0460776 + 0.0798087i
$$472$$ 0 0
$$473$$ 19.0526 + 11.0000i 0.876038 + 0.505781i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 12.0000i 0.549442i
$$478$$ 0 0
$$479$$ −14.0000 + 24.2487i −0.639676 + 1.10795i 0.345827 + 0.938298i $$0.387598\pi$$
−0.985504 + 0.169654i $$0.945735\pi$$
$$480$$ 0 0
$$481$$ −1.50000 2.59808i −0.0683941 0.118462i
$$482$$ 0 0
$$483$$ 20.7846 + 4.00000i 0.945732 + 0.182006i
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 16.4545 + 9.50000i 0.745624 + 0.430486i 0.824110 0.566429i $$-0.191675\pi$$
−0.0784867 + 0.996915i $$0.525009\pi$$
$$488$$ 0 0
$$489$$ −4.00000 −0.180886
$$490$$ 0 0
$$491$$ −36.0000 −1.62466 −0.812329 0.583200i $$-0.801800\pi$$
−0.812329 + 0.583200i $$0.801800\pi$$
$$492$$ 0 0
$$493$$ 27.7128 + 16.0000i 1.24812 + 0.720604i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −25.9808 5.00000i −1.16540 0.224281i
$$498$$ 0 0
$$499$$ −14.5000 25.1147i −0.649109 1.12429i −0.983336 0.181797i $$-0.941809\pi$$
0.334227 0.942493i $$-0.391525\pi$$
$$500$$ 0 0
$$501$$ −1.00000 + 1.73205i −0.0446767 + 0.0773823i
$$502$$ 0 0
$$503$$ 30.0000i 1.33763i 0.743427 + 0.668817i $$0.233199\pi$$
−0.743427 + 0.668817i $$0.766801\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −3.46410 2.00000i −0.153846 0.0888231i
$$508$$ 0 0
$$509$$ 9.00000 + 15.5885i 0.398918 + 0.690946i 0.993593 0.113020i $$-0.0360525\pi$$
−0.594675 + 0.803966i $$0.702719\pi$$
$$510$$ 0 0
$$511$$ −22.0000 19.0526i −0.973223 0.842836i
$$512$$ 0 0
$$513$$ −0.866025 + 0.500000i −0.0382360 + 0.0220755i
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 12.0000i 0.527759i
$$518$$ 0 0
$$519$$ 16.0000 0.702322
$$520$$ 0 0
$$521$$ 18.0000 31.1769i 0.788594 1.36589i −0.138234 0.990400i $$-0.544143\pi$$
0.926828 0.375486i $$-0.122524\pi$$
$$522$$ 0 0
$$523$$ 26.8468 15.5000i 1.17393 0.677768i 0.219326 0.975652i $$-0.429614\pi$$
0.954602 + 0.297884i $$0.0962809\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 20.7846 12.0000i 0.905392 0.522728i
$$528$$ 0 0
$$529$$ 20.5000 35.5070i 0.891304 1.54378i
$$530$$ 0 0
$$531$$ 4.00000 0.173585
$$532$$ 0 0
$$533$$ 18.0000i 0.779667i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ −5.19615 + 3.00000i −0.224231 + 0.129460i
$$538$$ 0 0
$$539$$ −11.0000 + 8.66025i −0.473804 + 0.373024i
$$540$$ 0 0
$$541$$ 7.50000 + 12.9904i 0.322450 + 0.558500i 0.980993 0.194043i $$-0.0621602\pi$$
−0.658543 + 0.752543i $$0.728827\pi$$
$$542$$ 0 0
$$543$$ 12.9904 + 7.50000i 0.557471 + 0.321856i
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 12.0000i 0.513083i −0.966533 0.256541i $$-0.917417\pi$$
0.966533 0.256541i $$-0.0825830\pi$$
$$548$$ 0 0
$$549$$ −3.00000 + 5.19615i −0.128037 + 0.221766i
$$550$$ 0 0
$$551$$ 2.00000 + 3.46410i 0.0852029 + 0.147576i
$$552$$ 0 0
$$553$$ −2.59808 7.50000i −0.110481 0.318932i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −19.0526 11.0000i −0.807283 0.466085i 0.0387286 0.999250i $$-0.487669\pi$$
−0.846011 + 0.533165i $$0.821003\pi$$
$$558$$ 0 0
$$559$$ 33.0000 1.39575
$$560$$ 0 0
$$561$$ −16.0000 −0.675521
$$562$$ 0 0
$$563$$ −39.8372 23.0000i −1.67894 0.969334i −0.962341 0.271846i $$-0.912366\pi$$
−0.716596 0.697489i $$-0.754301\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ −1.73205 + 2.00000i −0.0727393 + 0.0839921i
$$568$$ 0 0
$$569$$ 3.00000 + 5.19615i 0.125767 + 0.217834i 0.922032 0.387113i $$-0.126528\pi$$
−0.796266 + 0.604947i $$0.793194\pi$$
$$570$$ 0 0
$$571$$ 10.5000 18.1865i 0.439411 0.761083i −0.558233 0.829684i $$-0.688520\pi$$
0.997644 + 0.0686016i $$0.0218537\pi$$
$$572$$ 0 0
$$573$$ 6.00000i 0.250654i
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 35.5070 + 20.5000i 1.47818 + 0.853426i 0.999696 0.0246713i $$-0.00785391\pi$$
0.478482 + 0.878097i $$0.341187\pi$$
$$578$$ 0 0
$$579$$ −5.50000 9.52628i −0.228572 0.395899i
$$580$$ 0 0
$$581$$ 1.00000 5.19615i 0.0414870 0.215573i
$$582$$ 0 0
$$583$$ 20.7846 12.0000i 0.860811 0.496989i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 32.0000i 1.32078i 0.750922 + 0.660391i $$0.229609\pi$$
−0.750922 + 0.660391i $$0.770391\pi$$
$$588$$ 0 0
$$589$$ 3.00000 0.123613
$$590$$ 0 0
$$591$$ 4.00000 6.92820i 0.164538 0.284988i
$$592$$ 0 0
$$593$$ 5.19615 3.00000i 0.213380 0.123195i −0.389501 0.921026i $$-0.627353\pi$$
0.602881 + 0.797831i $$0.294019\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ −6.92820 + 4.00000i −0.283552 + 0.163709i
$$598$$ 0 0
$$599$$ −6.00000 + 10.3923i −0.245153 + 0.424618i −0.962175 0.272433i $$-0.912172\pi$$
0.717021 + 0.697051i $$0.245505\pi$$
$$600$$ 0 0
$$601$$ −1.00000 −0.0407909 −0.0203954 0.999792i $$-0.506493\pi$$
−0.0203954 + 0.999792i $$0.506493\pi$$
$$602$$ 0 0
$$603$$ 13.0000i 0.529401i
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −2.59808 + 1.50000i −0.105453 + 0.0608831i −0.551799 0.833977i $$-0.686058\pi$$
0.446346 + 0.894860i $$0.352725\pi$$
$$608$$ 0 0
$$609$$ 8.00000 + 6.92820i 0.324176 + 0.280745i
$$610$$ 0 0
$$611$$ 9.00000 + 15.5885i 0.364101 + 0.630641i
$$612$$ 0 0
$$613$$ −25.9808 15.0000i −1.04935 0.605844i −0.126885 0.991917i $$-0.540498\pi$$
−0.922468 + 0.386073i $$0.873831\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 26.0000i 1.04672i 0.852111 + 0.523360i $$0.175322\pi$$
−0.852111 + 0.523360i $$0.824678\pi$$
$$618$$ 0 0
$$619$$ −5.50000 + 9.52628i −0.221064 + 0.382893i −0.955131 0.296183i $$-0.904286\pi$$
0.734068 + 0.679076i $$0.237620\pi$$
$$620$$ 0 0
$$621$$ 4.00000 + 6.92820i 0.160514 + 0.278019i
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ −1.73205 1.00000i −0.0691714 0.0399362i
$$628$$ 0 0
$$629$$ 8.00000 0.318981
$$630$$ 0 0
$$631$$ −16.0000 −0.636950 −0.318475 0.947931i $$-0.603171\pi$$
−0.318475 + 0.947931i $$0.603171\pi$$
$$632$$ 0 0
$$633$$ 3.46410 + 2.00000i 0.137686 + 0.0794929i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −7.79423 + 19.5000i −0.308819 + 0.772618i
$$638$$ 0 0
$$639$$ −5.00000 8.66025i −0.197797 0.342594i
$$640$$ 0 0
$$641$$ 20.0000 34.6410i 0.789953 1.36824i −0.136043 0.990703i $$-0.543438\pi$$
0.925995 0.377535i $$-0.123228\pi$$
$$642$$ 0 0
$$643$$ 35.0000i 1.38027i −0.723683 0.690133i $$-0.757552\pi$$
0.723683 0.690133i $$-0.242448\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −5.19615 3.00000i −0.204282 0.117942i 0.394369 0.918952i $$-0.370963\pi$$
−0.598651 + 0.801010i $$0.704296\pi$$
$$648$$ 0 0
$$649$$ 4.00000 + 6.92820i 0.157014 + 0.271956i
$$650$$ 0 0
$$651$$ 7.50000 2.59808i 0.293948 0.101827i
$$652$$ 0 0
$$653$$ 5.19615 3.00000i 0.203341 0.117399i −0.394872 0.918736i $$-0.629211\pi$$
0.598213 + 0.801337i $$0.295878\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 11.0000i 0.429151i
$$658$$ 0 0
$$659$$ 28.0000 1.09073 0.545363 0.838200i $$-0.316392\pi$$
0.545363 + 0.838200i $$0.316392\pi$$
$$660$$ 0 0
$$661$$ 14.5000 25.1147i 0.563985 0.976850i −0.433159 0.901318i $$-0.642601\pi$$
0.997143 0.0755324i $$-0.0240656\pi$$
$$662$$ 0 0
$$663$$ −20.7846 + 12.0000i −0.807207 + 0.466041i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 27.7128 16.0000i 1.07304 0.619522i
$$668$$ 0 0
$$669$$ −4.00000 + 6.92820i −0.154649 + 0.267860i
$$670$$ 0 0
$$671$$ −12.0000 −0.463255
$$672$$ 0 0
$$673$$ 1.00000i 0.0385472i 0.999814 + 0.0192736i $$0.00613535\pi$$
−0.999814 + 0.0192736i $$0.993865\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 10.3923 6.00000i 0.399409 0.230599i −0.286820 0.957984i $$-0.592598\pi$$
0.686229 + 0.727386i $$0.259265\pi$$
$$678$$ 0 0
$$679$$ −5.00000 + 25.9808i −0.191882 + 0.997050i
$$680$$ 0 0
$$681$$ −9.00000 15.5885i −0.344881 0.597351i
$$682$$ 0 0
$$683$$ 31.1769 + 18.0000i 1.19295 + 0.688751i 0.958975 0.283491i $$-0.0914927\pi$$
0.233977 + 0.972242i $$0.424826\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 1.00000i 0.0381524i
$$688$$ 0 0
$$689$$ 18.0000 31.1769i 0.685745 1.18775i
$$690$$ 0 0
$$691$$ 21.5000 + 37.2391i 0.817899 + 1.41664i 0.907228 + 0.420640i $$0.138194\pi$$
−0.0893292 + 0.996002i $$0.528472\pi$$
$$692$$ 0 0
$$693$$ −5.19615 1.00000i −0.197386 0.0379869i
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −41.5692 24.0000i −1.57455 0.909065i
$$698$$ 0 0
$$699$$ 14.0000 0.529529
$$700$$ 0 0
$$701$$ −8.00000 −0.302156 −0.151078 0.988522i $$-0.548274\pi$$
−0.151078 + 0.988522i $$0.548274\pi$$
$$702$$ 0 0
$$703$$ 0.866025 + 0.500000i 0.0326628 + 0.0188579i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −17.3205 + 20.0000i −0.651405 + 0.752177i
$$708$$ 0 0
$$709$$ 7.00000 + 12.1244i 0.262891 + 0.455340i 0.967009 0.254743i $$-0.0819909\pi$$
−0.704118 + 0.710083i $$0.748658\pi$$
$$710$$ 0 0
$$711$$ 1.50000 2.59808i 0.0562544 0.0974355i
$$712$$ 0 0
$$713$$ 24.0000i 0.898807i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 15.5885 + 9.00000i 0.582162 + 0.336111i
$$718$$ 0 0
$$719$$ −3.00000 5.19615i −0.111881 0.193784i 0.804648 0.593753i $$-0.202354\pi$$
−0.916529 + 0.399969i $$0.869021\pi$$
$$720$$ 0 0
$$721$$ −27.5000 + 9.52628i −1.02415 + 0.354777i
$$722$$ 0 0
$$723$$ 12.1244 7.00000i 0.450910 0.260333i
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 23.0000i 0.853023i −0.904482 0.426511i $$-0.859742\pi$$
0.904482 0.426511i $$-0.140258\pi$$
$$728$$ 0 0
$$729$$ −1.00000 −0.0370370
$$730$$ 0 0
$$731$$ −44.0000 + 76.2102i −1.62740 + 2.81874i
$$732$$ 0 0
$$733$$ −38.9711 + 22.5000i −1.43943 + 0.831056i −0.997810 0.0661448i $$-0.978930\pi$$
−0.441622 + 0.897201i $$0.645597\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 22.5167 13.0000i 0.829412 0.478861i
$$738$$ 0 0
$$739$$ −4.50000 + 7.79423i −0.165535 + 0.286715i −0.936845 0.349744i $$-0.886268\pi$$
0.771310 + 0.636460i $$0.219602\pi$$
$$740$$ 0 0
$$741$$ −3.00000 −0.110208
$$742$$ 0 0
$$743$$ 18.0000i 0.660356i 0.943919 + 0.330178i $$0.107109\pi$$
−0.943919 + 0.330178i $$0.892891\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 1.73205 1.00000i 0.0633724 0.0365881i
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −7.50000 12.9904i −0.273679 0.474026i 0.696122 0.717923i $$-0.254907\pi$$
−0.969801 + 0.243898i $$0.921574\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 42.0000i 1.52652i 0.646094 + 0.763258i $$0.276401\pi$$
−0.646094 + 0.763258i $$0.723599\pi$$
$$758$$ 0 0
$$759$$ −8.00000 + 13.8564i −0.290382 + 0.502956i
$$760$$ 0 0
$$761$$ −4.00000 6.92820i −0.145000 0.251147i 0.784373 0.620289i $$-0.212985\pi$$
−0.929373 + 0.369142i $$0.879652\pi$$
$$762$$ 0 0
$$763$$ −19.0526 + 22.0000i −0.689749 + 0.796453i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 10.3923 + 6.00000i 0.375244 + 0.216647i
$$768$$ 0 0
$$769$$ −31.0000 −1.11789 −0.558944 0.829205i $$-0.688793\pi$$
−0.558944 + 0.829205i $$0.688793\pi$$
$$770$$ 0 0
$$771$$ −18.0000 −0.648254
$$772$$ 0 0
$$773$$ 19.0526 + 11.0000i 0.685273 + 0.395643i 0.801839 0.597540i $$-0.203855\pi$$
−0.116566 + 0.993183i $$0.537189\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 2.59808 + 0.500000i 0.0932055 + 0.0179374i
$$778$$ 0 0
$$779$$ −3.00000 5.19615i −0.107486 0.186171i
$$780$$ 0 0
$$781$$ 10.0000 17.3205i 0.357828 0.619777i
$$782$$ 0 0
$$783$$ 4.00000i 0.142948i
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −20.7846 12.0000i −0.740891 0.427754i 0.0815020 0.996673i $$-0.474028\pi$$
−0.822393 + 0.568919i $$0.807362\pi$$
$$788$$ 0 0
$$789$$ −6.00000 10.3923i −0.213606 0.369976i
$$790$$ 0 0
$$791$$ −7.00000 + 36.3731i −0.248891 + 1.29328i
$$792$$ 0 0
$$793$$ −15.5885 + 9.00000i −0.553562 + 0.319599i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 48.0000i 1.70025i −0.526583 0.850124i $$-0.676527\pi$$
0.526583 0.850124i $$-0.323473\pi$$
$$798$$ 0 0
$$799$$ −48.0000 −1.69812
$$800$$ 0 0
$$801$$ 0