# Properties

 Label 2100.2.q.b.1201.1 Level $2100$ Weight $2$ Character 2100.1201 Analytic conductor $16.769$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2100.q (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$16.7685844245$$ 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 84) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 1201.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 2100.1201 Dual form 2100.2.q.b.1801.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 2.59808i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 2.59808i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-1.00000 + 1.73205i) q^{11} +3.00000 q^{13} +(4.00000 - 6.92820i) q^{17} +(0.500000 + 0.866025i) q^{19} +(-2.00000 - 1.73205i) q^{21} +(4.00000 + 6.92820i) q^{23} +1.00000 q^{27} +4.00000 q^{29} +(-1.50000 + 2.59808i) q^{31} +(-1.00000 - 1.73205i) q^{33} +(-0.500000 - 0.866025i) q^{37} +(-1.50000 + 2.59808i) q^{39} +6.00000 q^{41} -11.0000 q^{43} +(3.00000 + 5.19615i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(4.00000 + 6.92820i) q^{51} +(-6.00000 + 10.3923i) q^{53} -1.00000 q^{57} +(-2.00000 + 3.46410i) q^{59} +(3.00000 + 5.19615i) q^{61} +(2.50000 - 0.866025i) q^{63} +(6.50000 - 11.2583i) q^{67} -8.00000 q^{69} -10.0000 q^{71} +(-5.50000 + 9.52628i) q^{73} +(-4.00000 - 3.46410i) q^{77} +(1.50000 + 2.59808i) q^{79} +(-0.500000 + 0.866025i) q^{81} -2.00000 q^{83} +(-2.00000 + 3.46410i) q^{87} +(-1.50000 + 7.79423i) q^{91} +(-1.50000 - 2.59808i) q^{93} -10.0000 q^{97} +2.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - q^{3} - q^{7} - q^{9} + O(q^{10})$$ $$2q - q^{3} - q^{7} - q^{9} - 2q^{11} + 6q^{13} + 8q^{17} + q^{19} - 4q^{21} + 8q^{23} + 2q^{27} + 8q^{29} - 3q^{31} - 2q^{33} - q^{37} - 3q^{39} + 12q^{41} - 22q^{43} + 6q^{47} - 13q^{49} + 8q^{51} - 12q^{53} - 2q^{57} - 4q^{59} + 6q^{61} + 5q^{63} + 13q^{67} - 16q^{69} - 20q^{71} - 11q^{73} - 8q^{77} + 3q^{79} - q^{81} - 4q^{83} - 4q^{87} - 3q^{91} - 3q^{93} - 20q^{97} + 4q^{99} + O(q^{100})$$

## 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
$$3$$ −0.500000 + 0.866025i −0.288675 + 0.500000i
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ −0.500000 + 2.59808i −0.188982 + 0.981981i
$$8$$ 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
$$13$$ 3.00000 0.832050 0.416025 0.909353i $$-0.363423\pi$$
0.416025 + 0.909353i $$0.363423\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 4.00000 6.92820i 0.970143 1.68034i 0.275029 0.961436i $$-0.411312\pi$$
0.695113 0.718900i $$-0.255354\pi$$
$$18$$ 0 0
$$19$$ 0.500000 + 0.866025i 0.114708 + 0.198680i 0.917663 0.397360i $$-0.130073\pi$$
−0.802955 + 0.596040i $$0.796740\pi$$
$$20$$ 0 0
$$21$$ −2.00000 1.73205i −0.436436 0.377964i
$$22$$ 0 0
$$23$$ 4.00000 + 6.92820i 0.834058 + 1.44463i 0.894795 + 0.446476i $$0.147321\pi$$
−0.0607377 + 0.998154i $$0.519345\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ 1.00000 0.192450
$$28$$ 0 0
$$29$$ 4.00000 0.742781 0.371391 0.928477i $$-0.378881\pi$$
0.371391 + 0.928477i $$0.378881\pi$$
$$30$$ 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
$$33$$ −1.00000 1.73205i −0.174078 0.301511i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −0.500000 0.866025i −0.0821995 0.142374i 0.821995 0.569495i $$-0.192861\pi$$
−0.904194 + 0.427121i $$0.859528\pi$$
$$38$$ 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
$$43$$ −11.0000 −1.67748 −0.838742 0.544529i $$-0.816708\pi$$
−0.838742 + 0.544529i $$0.816708\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 3.00000 + 5.19615i 0.437595 + 0.757937i 0.997503 0.0706177i $$-0.0224970\pi$$
−0.559908 + 0.828554i $$0.689164\pi$$
$$48$$ 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
$$53$$ −6.00000 + 10.3923i −0.824163 + 1.42749i 0.0783936 + 0.996922i $$0.475021\pi$$
−0.902557 + 0.430570i $$0.858312\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ −1.00000 −0.132453
$$58$$ 0 0
$$59$$ −2.00000 + 3.46410i −0.260378 + 0.450988i −0.966342 0.257260i $$-0.917180\pi$$
0.705965 + 0.708247i $$0.250514\pi$$
$$60$$ 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
$$63$$ 2.50000 0.866025i 0.314970 0.109109i
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 6.50000 11.2583i 0.794101 1.37542i −0.129307 0.991605i $$-0.541275\pi$$
0.923408 0.383819i $$-0.125391\pi$$
$$68$$ 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
$$73$$ −5.50000 + 9.52628i −0.643726 + 1.11497i 0.340868 + 0.940111i $$0.389279\pi$$
−0.984594 + 0.174855i $$0.944054\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −4.00000 3.46410i −0.455842 0.394771i
$$78$$ 0 0
$$79$$ 1.50000 + 2.59808i 0.168763 + 0.292306i 0.937985 0.346675i $$-0.112689\pi$$
−0.769222 + 0.638982i $$0.779356\pi$$
$$80$$ 0 0
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ 0 0
$$83$$ −2.00000 −0.219529 −0.109764 0.993958i $$-0.535010\pi$$
−0.109764 + 0.993958i $$0.535010\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ −2.00000 + 3.46410i −0.214423 + 0.371391i
$$88$$ 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
$$93$$ −1.50000 2.59808i −0.155543 0.269408i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −10.0000 −1.01535 −0.507673 0.861550i $$-0.669494\pi$$
−0.507673 + 0.861550i $$0.669494\pi$$
$$98$$ 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
$$103$$ 5.50000 + 9.52628i 0.541931 + 0.938652i 0.998793 + 0.0491146i $$0.0156400\pi$$
−0.456862 + 0.889538i $$0.651027\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$108$$ 0 0
$$109$$ 5.50000 9.52628i 0.526804 0.912452i −0.472708 0.881219i $$-0.656723\pi$$
0.999512 0.0312328i $$-0.00994332\pi$$
$$110$$ 0 0
$$111$$ 1.00000 0.0949158
$$112$$ 0 0
$$113$$ 14.0000 1.31701 0.658505 0.752577i $$-0.271189\pi$$
0.658505 + 0.752577i $$0.271189\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −1.50000 2.59808i −0.138675 0.240192i
$$118$$ 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
$$123$$ −3.00000 + 5.19615i −0.270501 + 0.468521i
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −3.00000 −0.266207 −0.133103 0.991102i $$-0.542494\pi$$
−0.133103 + 0.991102i $$0.542494\pi$$
$$128$$ 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
$$133$$ −2.50000 + 0.866025i −0.216777 + 0.0750939i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 2.00000 3.46410i 0.170872 0.295958i −0.767853 0.640626i $$-0.778675\pi$$
0.938725 + 0.344668i $$0.112008\pi$$
$$138$$ 0 0
$$139$$ −5.00000 −0.424094 −0.212047 0.977259i $$-0.568013\pi$$
−0.212047 + 0.977259i $$0.568013\pi$$
$$140$$ 0 0
$$141$$ −6.00000 −0.505291
$$142$$ 0 0
$$143$$ −3.00000 + 5.19615i −0.250873 + 0.434524i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 5.50000 4.33013i 0.453632 0.357143i
$$148$$ 0 0
$$149$$ 6.00000 + 10.3923i 0.491539 + 0.851371i 0.999953 0.00974235i $$-0.00310113\pi$$
−0.508413 + 0.861113i $$0.669768\pi$$
$$150$$ 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
$$153$$ −8.00000 −0.646762
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 1.00000 1.73205i 0.0798087 0.138233i −0.823359 0.567521i $$-0.807902\pi$$
0.903167 + 0.429289i $$0.141236\pi$$
$$158$$ 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
$$163$$ −2.00000 3.46410i −0.156652 0.271329i 0.777007 0.629492i $$-0.216737\pi$$
−0.933659 + 0.358162i $$0.883403\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 2.00000 0.154765 0.0773823 0.997001i $$-0.475344\pi$$
0.0773823 + 0.997001i $$0.475344\pi$$
$$168$$ 0 0
$$169$$ −4.00000 −0.307692
$$170$$ 0 0
$$171$$ 0.500000 0.866025i 0.0382360 0.0662266i
$$172$$ 0 0
$$173$$ 8.00000 + 13.8564i 0.608229 + 1.05348i 0.991532 + 0.129861i $$0.0414530\pi$$
−0.383304 + 0.923622i $$0.625214\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ −2.00000 3.46410i −0.150329 0.260378i
$$178$$ 0 0
$$179$$ −3.00000 + 5.19615i −0.224231 + 0.388379i −0.956088 0.293079i $$-0.905320\pi$$
0.731858 + 0.681457i $$0.238654\pi$$
$$180$$ 0 0
$$181$$ −15.0000 −1.11494 −0.557471 0.830197i $$-0.688228\pi$$
−0.557471 + 0.830197i $$0.688228\pi$$
$$182$$ 0 0
$$183$$ −6.00000 −0.443533
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 8.00000 + 13.8564i 0.585018 + 1.01328i
$$188$$ 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
$$193$$ 5.50000 9.52628i 0.395899 0.685717i −0.597317 0.802005i $$-0.703766\pi$$
0.993215 + 0.116289i $$0.0370998\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −8.00000 −0.569976 −0.284988 0.958531i $$-0.591990\pi$$
−0.284988 + 0.958531i $$0.591990\pi$$
$$198$$ 0 0
$$199$$ −4.00000 + 6.92820i −0.283552 + 0.491127i −0.972257 0.233915i $$-0.924846\pi$$
0.688705 + 0.725042i $$0.258180\pi$$
$$200$$ 0 0
$$201$$ 6.50000 + 11.2583i 0.458475 + 0.794101i
$$202$$ 0 0
$$203$$ −2.00000 + 10.3923i −0.140372 + 0.729397i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 4.00000 6.92820i 0.278019 0.481543i
$$208$$ 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
$$213$$ 5.00000 8.66025i 0.342594 0.593391i
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −6.00000 5.19615i −0.407307 0.352738i
$$218$$ 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
$$223$$ −8.00000 −0.535720 −0.267860 0.963458i $$-0.586316\pi$$
−0.267860 + 0.963458i $$0.586316\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −9.00000 + 15.5885i −0.597351 + 1.03464i 0.395860 + 0.918311i $$0.370447\pi$$
−0.993210 + 0.116331i $$0.962887\pi$$
$$228$$ 0 0
$$229$$ −0.500000 0.866025i −0.0330409 0.0572286i 0.849032 0.528341i $$-0.177186\pi$$
−0.882073 + 0.471113i $$0.843853\pi$$
$$230$$ 0 0
$$231$$ 5.00000 1.73205i 0.328976 0.113961i
$$232$$ 0 0
$$233$$ 7.00000 + 12.1244i 0.458585 + 0.794293i 0.998886 0.0471787i $$-0.0150230\pi$$
−0.540301 + 0.841472i $$0.681690\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ −3.00000 −0.194871
$$238$$ 0 0
$$239$$ 18.0000 1.16432 0.582162 0.813073i $$-0.302207\pi$$
0.582162 + 0.813073i $$0.302207\pi$$
$$240$$ 0 0
$$241$$ −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
$$243$$ −0.500000 0.866025i −0.0320750 0.0555556i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 1.50000 + 2.59808i 0.0954427 + 0.165312i
$$248$$ 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
$$253$$ −16.0000 −1.00591
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 9.00000 + 15.5885i 0.561405 + 0.972381i 0.997374 + 0.0724199i $$0.0230722\pi$$
−0.435970 + 0.899961i $$0.643595\pi$$
$$258$$ 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
$$263$$ 6.00000 10.3923i 0.369976 0.640817i −0.619586 0.784929i $$-0.712699\pi$$
0.989561 + 0.144112i $$0.0460326\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 1.00000 1.73205i 0.0609711 0.105605i −0.833929 0.551872i $$-0.813914\pi$$
0.894900 + 0.446267i $$0.147247\pi$$
$$270$$ 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
$$273$$ −6.00000 5.19615i −0.363137 0.314485i
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 8.50000 14.7224i 0.510716 0.884585i −0.489207 0.872167i $$-0.662714\pi$$
0.999923 0.0124177i $$-0.00395278\pi$$
$$278$$ 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
$$283$$ 9.50000 16.4545i 0.564716 0.978117i −0.432360 0.901701i $$-0.642319\pi$$
0.997076 0.0764162i $$-0.0243478\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −3.00000 + 15.5885i −0.177084 + 0.920158i
$$288$$ 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
$$293$$ 24.0000 1.40209 0.701047 0.713115i $$-0.252716\pi$$
0.701047 + 0.713115i $$0.252716\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ −1.00000 + 1.73205i −0.0580259 + 0.100504i
$$298$$ 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
$$303$$ −5.00000 8.66025i −0.287242 0.497519i
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 23.0000 1.31268 0.656340 0.754466i $$-0.272104\pi$$
0.656340 + 0.754466i $$0.272104\pi$$
$$308$$ 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
$$313$$ −8.50000 14.7224i −0.480448 0.832161i 0.519300 0.854592i $$-0.326193\pi$$
−0.999748 + 0.0224310i $$0.992859\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −12.0000 20.7846i −0.673987 1.16738i −0.976764 0.214318i $$-0.931247\pi$$
0.302777 0.953062i $$-0.402086\pi$$
$$318$$ 0 0
$$319$$ −4.00000 + 6.92820i −0.223957 + 0.387905i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 8.00000 0.445132
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 5.50000 + 9.52628i 0.304151 + 0.526804i
$$328$$ 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
$$333$$ −0.500000 + 0.866025i −0.0273998 + 0.0474579i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −21.0000 −1.14394 −0.571971 0.820274i $$-0.693821\pi$$
−0.571971 + 0.820274i $$0.693821\pi$$
$$338$$ 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
$$343$$ 10.0000 15.5885i 0.539949 0.841698i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 12.0000 20.7846i 0.644194 1.11578i −0.340293 0.940319i $$-0.610526\pi$$
0.984487 0.175457i $$-0.0561403\pi$$
$$348$$ 0 0
$$349$$ −14.0000 −0.749403 −0.374701 0.927146i $$-0.622255\pi$$
−0.374701 + 0.927146i $$0.622255\pi$$
$$350$$ 0 0
$$351$$ 3.00000 0.160128
$$352$$ 0 0
$$353$$ −3.00000 + 5.19615i −0.159674 + 0.276563i −0.934751 0.355303i $$-0.884378\pi$$
0.775077 + 0.631867i $$0.217711\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ −20.0000 + 6.92820i −1.05851 + 0.366679i
$$358$$ 0 0
$$359$$ 10.0000 + 17.3205i 0.527780 + 0.914141i 0.999476 + 0.0323801i $$0.0103087\pi$$
−0.471696 + 0.881761i $$0.656358\pi$$
$$360$$ 0 0
$$361$$ 9.00000 15.5885i 0.473684 0.820445i
$$362$$ 0 0
$$363$$ −7.00000 −0.367405
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 2.50000 4.33013i 0.130499 0.226031i −0.793370 0.608740i $$-0.791675\pi$$
0.923869 + 0.382709i $$0.125009\pi$$
$$368$$ 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
$$373$$ −2.50000 4.33013i −0.129445 0.224205i 0.794017 0.607896i $$-0.207986\pi$$
−0.923462 + 0.383691i $$0.874653\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 12.0000 0.618031
$$378$$ 0 0
$$379$$ 13.0000 0.667765 0.333883 0.942615i $$-0.391641\pi$$
0.333883 + 0.942615i $$0.391641\pi$$
$$380$$ 0 0
$$381$$ 1.50000 2.59808i 0.0768473 0.133103i
$$382$$ 0 0
$$383$$ −14.0000 24.2487i −0.715367 1.23905i −0.962818 0.270151i $$-0.912926\pi$$
0.247451 0.968900i $$-0.420407\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 5.50000 + 9.52628i 0.279581 + 0.484248i
$$388$$ 0 0
$$389$$ −5.00000 + 8.66025i −0.253510 + 0.439092i −0.964490 0.264120i $$-0.914918\pi$$
0.710980 + 0.703213i $$0.248252\pi$$
$$390$$ 0 0
$$391$$ 64.0000 3.23662
$$392$$ 0 0
$$393$$ −2.00000 −0.100887
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 1.50000 + 2.59808i 0.0752828 + 0.130394i 0.901209 0.433384i $$-0.142681\pi$$
−0.825926 + 0.563778i $$0.809347\pi$$
$$398$$ 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
$$403$$ −4.50000 + 7.79423i −0.224161 + 0.388258i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 2.00000 0.0991363
$$408$$ 0 0
$$409$$ 9.50000 16.4545i 0.469745 0.813622i −0.529657 0.848212i $$-0.677679\pi$$
0.999402 + 0.0345902i $$0.0110126\pi$$
$$410$$ 0 0
$$411$$ 2.00000 + 3.46410i 0.0986527 + 0.170872i
$$412$$ 0 0
$$413$$ −8.00000 6.92820i −0.393654 0.340915i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 2.50000 4.33013i 0.122426 0.212047i
$$418$$ 0 0
$$419$$ 18.0000 0.879358 0.439679 0.898155i $$-0.355092\pi$$
0.439679 + 0.898155i $$0.355092\pi$$
$$420$$ 0 0
$$421$$ −27.0000 −1.31590 −0.657950 0.753062i $$-0.728576\pi$$
−0.657950 + 0.753062i $$0.728576\pi$$
$$422$$ 0 0
$$423$$ 3.00000 5.19615i 0.145865 0.252646i
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −15.0000 + 5.19615i −0.725901 + 0.251459i
$$428$$ 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
$$433$$ 25.0000 1.20142 0.600712 0.799466i $$-0.294884\pi$$
0.600712 + 0.799466i $$0.294884\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −4.00000 + 6.92820i −0.191346 + 0.331421i
$$438$$ 0 0
$$439$$ −12.0000 20.7846i −0.572729 0.991995i −0.996284 0.0861252i $$-0.972552\pi$$
0.423556 0.905870i $$-0.360782\pi$$
$$440$$ 0 0
$$441$$ 1.00000 + 6.92820i 0.0476190 + 0.329914i
$$442$$ 0 0
$$443$$ −2.00000 3.46410i −0.0950229 0.164584i 0.814595 0.580030i $$-0.196959\pi$$
−0.909618 + 0.415445i $$0.863626\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ −12.0000 −0.567581
$$448$$ 0 0
$$449$$ 22.0000 1.03824 0.519122 0.854700i $$-0.326259\pi$$
0.519122 + 0.854700i $$0.326259\pi$$
$$450$$ 0 0
$$451$$ −6.00000 + 10.3923i −0.282529 + 0.489355i
$$452$$ 0 0
$$453$$ 4.00000 + 6.92820i 0.187936 + 0.325515i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 6.50000 + 11.2583i 0.304057 + 0.526642i 0.977051 0.213006i $$-0.0683253\pi$$
−0.672994 + 0.739648i $$0.734992\pi$$
$$458$$ 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
$$463$$ 11.0000 0.511213 0.255607 0.966781i $$-0.417725\pi$$
0.255607 + 0.966781i $$0.417725\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 17.0000 + 29.4449i 0.786666 + 1.36255i 0.927999 + 0.372584i $$0.121528\pi$$
−0.141332 + 0.989962i $$0.545139\pi$$
$$468$$ 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
$$473$$ 11.0000 19.0526i 0.505781 0.876038i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 12.0000 0.549442
$$478$$ 0 0
$$479$$ 14.0000 24.2487i 0.639676 1.10795i −0.345827 0.938298i $$-0.612402\pi$$
0.985504 0.169654i $$-0.0542649\pi$$
$$480$$ 0 0
$$481$$ −1.50000 2.59808i −0.0683941 0.118462i
$$482$$ 0 0
$$483$$ 4.00000 20.7846i 0.182006 0.945732i
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −9.50000 + 16.4545i −0.430486 + 0.745624i −0.996915 0.0784867i $$-0.974991\pi$$
0.566429 + 0.824110i $$0.308325\pi$$
$$488$$ 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
$$493$$ 16.0000 27.7128i 0.720604 1.24812i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 5.00000 25.9808i 0.224281 1.16540i
$$498$$ 0 0
$$499$$ 14.5000 + 25.1147i 0.649109 + 1.12429i 0.983336 + 0.181797i $$0.0581915\pi$$
−0.334227 + 0.942493i $$0.608475\pi$$
$$500$$ 0 0
$$501$$ −1.00000 + 1.73205i −0.0446767 + 0.0773823i
$$502$$ 0 0
$$503$$ 30.0000 1.33763 0.668817 0.743427i $$-0.266801\pi$$
0.668817 + 0.743427i $$0.266801\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 2.00000 3.46410i 0.0888231 0.153846i
$$508$$ 0 0
$$509$$ −9.00000 15.5885i −0.398918 0.690946i 0.594675 0.803966i $$-0.297281\pi$$
−0.993593 + 0.113020i $$0.963948\pi$$
$$510$$ 0 0
$$511$$ −22.0000 19.0526i −0.973223 0.842836i
$$512$$ 0 0
$$513$$ 0.500000 + 0.866025i 0.0220755 + 0.0382360i
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ −12.0000 −0.527759
$$518$$ 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
$$523$$ −15.5000 26.8468i −0.677768 1.17393i −0.975652 0.219326i $$-0.929614\pi$$
0.297884 0.954602i $$-0.403719\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 12.0000 + 20.7846i 0.522728 + 0.905392i
$$528$$ 0 0
$$529$$ −20.5000 + 35.5070i −0.891304 + 1.54378i
$$530$$ 0 0
$$531$$ 4.00000 0.173585
$$532$$ 0 0
$$533$$ 18.0000 0.779667
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ −3.00000 5.19615i −0.129460 0.224231i
$$538$$ 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
$$543$$ 7.50000 12.9904i 0.321856 0.557471i
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 12.0000 0.513083 0.256541 0.966533i $$-0.417417\pi$$
0.256541 + 0.966533i $$0.417417\pi$$
$$548$$ 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
$$553$$ −7.50000 + 2.59808i −0.318932 + 0.110481i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 11.0000 19.0526i 0.466085 0.807283i −0.533165 0.846011i $$-0.678997\pi$$
0.999250 + 0.0387286i $$0.0123308\pi$$
$$558$$ 0 0
$$559$$ −33.0000 −1.39575
$$560$$ 0 0
$$561$$ −16.0000 −0.675521
$$562$$ 0 0
$$563$$ −23.0000 + 39.8372i −0.969334 + 1.67894i −0.271846 + 0.962341i $$0.587634\pi$$
−0.697489 + 0.716596i $$0.745699\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ −2.00000 1.73205i −0.0839921 0.0727393i
$$568$$ 0 0
$$569$$ −3.00000 5.19615i −0.125767 0.217834i 0.796266 0.604947i $$-0.206806\pi$$
−0.922032 + 0.387113i $$0.873472\pi$$
$$570$$ 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
$$573$$ 6.00000 0.250654
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −20.5000 + 35.5070i −0.853426 + 1.47818i 0.0246713 + 0.999696i $$0.492146\pi$$
−0.878097 + 0.478482i $$0.841187\pi$$
$$578$$ 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
$$583$$ −12.0000 20.7846i −0.496989 0.860811i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −32.0000 −1.32078 −0.660391 0.750922i $$-0.729609\pi$$
−0.660391 + 0.750922i $$0.729609\pi$$
$$588$$ 0 0
$$589$$ −3.00000 −0.123613
$$590$$ 0 0
$$591$$ 4.00000 6.92820i 0.164538 0.284988i
$$592$$ 0 0
$$593$$ −3.00000 5.19615i −0.123195 0.213380i 0.797831 0.602881i $$-0.205981\pi$$
−0.921026 + 0.389501i $$0.872647\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ −4.00000 6.92820i −0.163709 0.283552i
$$598$$ 0 0
$$599$$ 6.00000 10.3923i 0.245153 0.424618i −0.717021 0.697051i $$-0.754495\pi$$
0.962175 + 0.272433i $$0.0878284\pi$$
$$600$$ 0 0
$$601$$ −1.00000 −0.0407909 −0.0203954 0.999792i $$-0.506493\pi$$
−0.0203954 + 0.999792i $$0.506493\pi$$
$$602$$ 0 0
$$603$$ −13.0000 −0.529401
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −1.50000 2.59808i −0.0608831 0.105453i 0.833977 0.551799i $$-0.186058\pi$$
−0.894860 + 0.446346i $$0.852725\pi$$
$$608$$ 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
$$613$$ −15.0000 + 25.9808i −0.605844 + 1.04935i 0.386073 + 0.922468i $$0.373831\pi$$
−0.991917 + 0.126885i $$0.959502\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −26.0000 −1.04672 −0.523360 0.852111i $$-0.675322\pi$$
−0.523360 + 0.852111i $$0.675322\pi$$
$$618$$ 0 0
$$619$$ 5.50000 9.52628i 0.221064 0.382893i −0.734068 0.679076i $$-0.762380\pi$$
0.955131 + 0.296183i $$0.0957138\pi$$
$$620$$ 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
$$627$$ 1.00000 1.73205i 0.0399362 0.0691714i
$$628$$ 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
$$633$$ 2.00000 3.46410i 0.0794929 0.137686i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −19.5000 7.79423i −0.772618 0.308819i
$$638$$ 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
$$643$$ −35.0000 −1.38027 −0.690133 0.723683i $$-0.742448\pi$$
−0.690133 + 0.723683i $$0.742448\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 3.00000 5.19615i 0.117942 0.204282i −0.801010 0.598651i $$-0.795704\pi$$
0.918952 + 0.394369i $$0.129037\pi$$
$$648$$ 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
$$653$$ −3.00000 5.19615i −0.117399 0.203341i 0.801337 0.598213i $$-0.204122\pi$$
−0.918736 + 0.394872i $$0.870789\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 11.0000 0.429151
$$658$$ 0 0
$$659$$ −28.0000 −1.09073 −0.545363 0.838200i $$-0.683608\pi$$
−0.545363 + 0.838200i $$0.683608\pi$$
$$660$$ 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
$$663$$ 12.0000 + 20.7846i 0.466041 + 0.807207i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 16.0000 + 27.7128i 0.619522 + 1.07304i
$$668$$ 0 0
$$669$$ 4.00000 6.92820i 0.154649 0.267860i
$$670$$ 0 0
$$671$$ −12.0000 −0.463255
$$672$$ 0 0
$$673$$ 1.00000 0.0385472 0.0192736 0.999814i $$-0.493865\pi$$
0.0192736 + 0.999814i $$0.493865\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 6.00000 + 10.3923i 0.230599 + 0.399409i 0.957984 0.286820i $$-0.0925982\pi$$
−0.727386 + 0.686229i $$0.759265\pi$$
$$678$$ 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
$$683$$ 18.0000 31.1769i 0.688751 1.19295i −0.283491 0.958975i $$-0.591493\pi$$
0.972242 0.233977i $$-0.0751739\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 1.00000 0.0381524
$$688$$ 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
$$693$$ −1.00000 + 5.19615i −0.0379869 + 0.197386i
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 24.0000 41.5692i 0.909065 1.57455i
$$698$$ 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
$$703$$ 0.500000 0.866025i 0.0188579 0.0326628i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −20.0000 17.3205i −0.752177 0.651405i
$$708$$ 0 0
$$709$$ −7.00000 12.1244i −0.262891 0.455340i 0.704118 0.710083i $$-0.251342\pi$$
−0.967009 + 0.254743i $$0.918009\pi$$
$$710$$ 0 0
$$711$$ 1.50000 2.59808i 0.0562544 0.0974355i
$$712$$ 0 0
$$713$$ −24.0000 −0.898807
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ −9.00000 + 15.5885i −0.336111 + 0.582162i
$$718$$ 0 0
$$719$$ 3.00000 + 5.19615i 0.111881 + 0.193784i 0.916529 0.399969i $$-0.130979\pi$$
−0.804648 + 0.593753i $$0.797646\pi$$
$$720$$ 0 0
$$721$$ −27.5000 + 9.52628i −1.02415 + 0.354777i
$$722$$ 0 0
$$723$$ −7.00000 12.1244i −0.260333 0.450910i
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 23.0000 0.853023 0.426511 0.904482i $$-0.359742\pi$$
0.426511 + 0.904482i $$0.359742\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ −44.0000 + 76.2102i −1.62740 + 2.81874i
$$732$$ 0 0
$$733$$ 22.5000 + 38.9711i 0.831056 + 1.43943i 0.897201 + 0.441622i $$0.145597\pi$$
−0.0661448 + 0.997810i $$0.521070\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 13.0000 + 22.5167i 0.478861 + 0.829412i
$$738$$ 0 0
$$739$$ 4.50000 7.79423i 0.165535 0.286715i −0.771310 0.636460i $$-0.780398\pi$$
0.936845 + 0.349744i $$0.113732\pi$$
$$740$$ 0 0
$$741$$ −3.00000 −0.110208
$$742$$ 0 0
$$743$$ 18.0000 0.660356 0.330178 0.943919i $$-0.392891\pi$$
0.330178 + 0.943919i $$0.392891\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 1.00000 + 1.73205i 0.0365881 + 0.0633724i
$$748$$ 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
$$757$$ −42.0000 −1.52652 −0.763258 0.646094i $$-0.776401\pi$$
−0.763258 + 0.646094i $$0.776401\pi$$
$$758$$ 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
$$763$$ 22.0000 + 19.0526i 0.796453 + 0.689749i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −6.00000 + 10.3923i −0.216647 + 0.375244i
$$768$$ 0 0
$$769$$ 31.0000 1.11789 0.558944 0.829205i $$-0.311207\pi$$
0.558944 + 0.829205i $$0.311207\pi$$
$$770$$ 0 0
$$771$$ −18.0000 −0.648254
$$772$$ 0 0
$$773$$ 11.0000 19.0526i 0.395643 0.685273i −0.597540 0.801839i $$-0.703855\pi$$
0.993183 + 0.116566i $$0.0371886\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ −0.500000 + 2.59808i −0.0179374 + 0.0932055i
$$778$$ 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
$$783$$ 4.00000 0.142948
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 12.0000 20.7846i 0.427754 0.740891i −0.568919 0.822393i $$-0.692638\pi$$
0.996673 + 0.0815020i $$0.0259717\pi$$
$$788$$ 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
$$793$$ 9.00000 + 15.5885i 0.319599 + 0.553562i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 48.0000 1.70025 0.850124 0.526583i $$-0.176527\pi$$
0.850124 + 0.526583i $$0.176527\pi$$
$$798$$ 0 0
$$799$$ 48.0000 1.69812
$$800$$ 0 0