# Properties

 Label 252.2.k.a.37.1 Level $252$ Weight $2$ Character 252.37 Analytic conductor $2.012$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$252 = 2^{2} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 252.k (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$2.01223013094$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 84) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 37.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 252.37 Dual form 252.2.k.a.109.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.00000 + 1.73205i) q^{5} +(0.500000 + 2.59808i) q^{7} +O(q^{10})$$ $$q+(-1.00000 + 1.73205i) q^{5} +(0.500000 + 2.59808i) q^{7} +(1.00000 + 1.73205i) q^{11} -3.00000 q^{13} +(4.00000 + 6.92820i) q^{17} +(0.500000 - 0.866025i) q^{19} +(4.00000 - 6.92820i) q^{23} +(0.500000 + 0.866025i) q^{25} -4.00000 q^{29} +(-1.50000 - 2.59808i) q^{31} +(-5.00000 - 1.73205i) q^{35} +(0.500000 - 0.866025i) q^{37} -6.00000 q^{41} +11.0000 q^{43} +(3.00000 - 5.19615i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(-6.00000 - 10.3923i) q^{53} -4.00000 q^{55} +(2.00000 + 3.46410i) q^{59} +(3.00000 - 5.19615i) q^{61} +(3.00000 - 5.19615i) q^{65} +(-6.50000 - 11.2583i) q^{67} +10.0000 q^{71} +(5.50000 + 9.52628i) q^{73} +(-4.00000 + 3.46410i) q^{77} +(1.50000 - 2.59808i) q^{79} -2.00000 q^{83} -16.0000 q^{85} +(-1.50000 - 7.79423i) q^{91} +(1.00000 + 1.73205i) q^{95} +10.0000 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - 2q^{5} + q^{7} + O(q^{10})$$ $$2q - 2q^{5} + q^{7} + 2q^{11} - 6q^{13} + 8q^{17} + q^{19} + 8q^{23} + q^{25} - 8q^{29} - 3q^{31} - 10q^{35} + q^{37} - 12q^{41} + 22q^{43} + 6q^{47} - 13q^{49} - 12q^{53} - 8q^{55} + 4q^{59} + 6q^{61} + 6q^{65} - 13q^{67} + 20q^{71} + 11q^{73} - 8q^{77} + 3q^{79} - 4q^{83} - 32q^{85} - 3q^{91} + 2q^{95} + 20q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$$.

 $$n$$ $$29$$ $$73$$ $$127$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$1$$

## 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 0
$$4$$ 0 0
$$5$$ −1.00000 + 1.73205i −0.447214 + 0.774597i −0.998203 0.0599153i $$-0.980917\pi$$
0.550990 + 0.834512i $$0.314250\pi$$
$$6$$ 0 0
$$7$$ 0.500000 + 2.59808i 0.188982 + 0.981981i
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 1.00000 + 1.73205i 0.301511 + 0.522233i 0.976478 0.215615i $$-0.0691756\pi$$
−0.674967 + 0.737848i $$0.735842\pi$$
$$12$$ 0 0
$$13$$ −3.00000 −0.832050 −0.416025 0.909353i $$-0.636577\pi$$
−0.416025 + 0.909353i $$0.636577\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 4.00000 + 6.92820i 0.970143 + 1.68034i 0.695113 + 0.718900i $$0.255354\pi$$
0.275029 + 0.961436i $$0.411312\pi$$
$$18$$ 0 0
$$19$$ 0.500000 0.866025i 0.114708 0.198680i −0.802955 0.596040i $$-0.796740\pi$$
0.917663 + 0.397360i $$0.130073\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 4.00000 6.92820i 0.834058 1.44463i −0.0607377 0.998154i $$-0.519345\pi$$
0.894795 0.446476i $$-0.147321\pi$$
$$24$$ 0 0
$$25$$ 0.500000 + 0.866025i 0.100000 + 0.173205i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 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 0.699301 0.714827i $$-0.253495\pi$$
−0.968709 + 0.248199i $$0.920161\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −5.00000 1.73205i −0.845154 0.292770i
$$36$$ 0 0
$$37$$ 0.500000 0.866025i 0.0821995 0.142374i −0.821995 0.569495i $$-0.807139\pi$$
0.904194 + 0.427121i $$0.140472\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −6.00000 −0.937043 −0.468521 0.883452i $$-0.655213\pi$$
−0.468521 + 0.883452i $$0.655213\pi$$
$$42$$ 0 0
$$43$$ 11.0000 1.67748 0.838742 0.544529i $$-0.183292\pi$$
0.838742 + 0.544529i $$0.183292\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 3.00000 5.19615i 0.437595 0.757937i −0.559908 0.828554i $$-0.689164\pi$$
0.997503 + 0.0706177i $$0.0224970\pi$$
$$48$$ 0 0
$$49$$ −6.50000 + 2.59808i −0.928571 + 0.371154i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −6.00000 10.3923i −0.824163 1.42749i −0.902557 0.430570i $$-0.858312\pi$$
0.0783936 0.996922i $$-0.475021\pi$$
$$54$$ 0 0
$$55$$ −4.00000 −0.539360
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 2.00000 + 3.46410i 0.260378 + 0.450988i 0.966342 0.257260i $$-0.0828195\pi$$
−0.705965 + 0.708247i $$0.749486\pi$$
$$60$$ 0 0
$$61$$ 3.00000 5.19615i 0.384111 0.665299i −0.607535 0.794293i $$-0.707841\pi$$
0.991645 + 0.128994i $$0.0411748\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 3.00000 5.19615i 0.372104 0.644503i
$$66$$ 0 0
$$67$$ −6.50000 11.2583i −0.794101 1.37542i −0.923408 0.383819i $$-0.874609\pi$$
0.129307 0.991605i $$-0.458725\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 10.0000 1.18678 0.593391 0.804914i $$-0.297789\pi$$
0.593391 + 0.804914i $$0.297789\pi$$
$$72$$ 0 0
$$73$$ 5.50000 + 9.52628i 0.643726 + 1.11497i 0.984594 + 0.174855i $$0.0559458\pi$$
−0.340868 + 0.940111i $$0.610721\pi$$
$$74$$ 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 −0.769222 0.638982i $$-0.779356\pi$$
0.937985 + 0.346675i $$0.112689\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −2.00000 −0.219529 −0.109764 0.993958i $$-0.535010\pi$$
−0.109764 + 0.993958i $$0.535010\pi$$
$$84$$ 0 0
$$85$$ −16.0000 −1.73544
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$90$$ 0 0
$$91$$ −1.50000 7.79423i −0.157243 0.817057i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 1.00000 + 1.73205i 0.102598 + 0.177705i
$$96$$ 0 0
$$97$$ 10.0000 1.01535 0.507673 0.861550i $$-0.330506\pi$$
0.507673 + 0.861550i $$0.330506\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 5.00000 + 8.66025i 0.497519 + 0.861727i 0.999996 0.00286291i $$-0.000911295\pi$$
−0.502477 + 0.864590i $$0.667578\pi$$
$$102$$ 0 0
$$103$$ −5.50000 + 9.52628i −0.541931 + 0.938652i 0.456862 + 0.889538i $$0.348973\pi$$
−0.998793 + 0.0491146i $$0.984360\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$108$$ 0 0
$$109$$ 5.50000 + 9.52628i 0.526804 + 0.912452i 0.999512 + 0.0312328i $$0.00994332\pi$$
−0.472708 + 0.881219i $$0.656723\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 14.0000 1.31701 0.658505 0.752577i $$-0.271189\pi$$
0.658505 + 0.752577i $$0.271189\pi$$
$$114$$ 0 0
$$115$$ 8.00000 + 13.8564i 0.746004 + 1.29212i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 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
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −12.0000 −1.07331
$$126$$ 0 0
$$127$$ 3.00000 0.266207 0.133103 0.991102i $$-0.457506\pi$$
0.133103 + 0.991102i $$0.457506\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −1.00000 + 1.73205i −0.0873704 + 0.151330i −0.906399 0.422423i $$-0.861180\pi$$
0.819028 + 0.573753i $$0.194513\pi$$
$$132$$ 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 0.938725 0.344668i $$-0.112008\pi$$
−0.767853 + 0.640626i $$0.778675\pi$$
$$138$$ 0 0
$$139$$ −5.00000 −0.424094 −0.212047 0.977259i $$-0.568013\pi$$
−0.212047 + 0.977259i $$0.568013\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −3.00000 5.19615i −0.250873 0.434524i
$$144$$ 0 0
$$145$$ 4.00000 6.92820i 0.332182 0.575356i
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −6.00000 + 10.3923i −0.491539 + 0.851371i −0.999953 0.00974235i $$-0.996899\pi$$
0.508413 + 0.861113i $$0.330232\pi$$
$$150$$ 0 0
$$151$$ 4.00000 + 6.92820i 0.325515 + 0.563809i 0.981617 0.190864i $$-0.0611289\pi$$
−0.656101 + 0.754673i $$0.727796\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 6.00000 0.481932
$$156$$ 0 0
$$157$$ −1.00000 1.73205i −0.0798087 0.138233i 0.823359 0.567521i $$-0.192098\pi$$
−0.903167 + 0.429289i $$0.858764\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 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 $$-0.783263\pi$$
0.933659 + 0.358162i $$0.116597\pi$$
$$164$$ 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 0
$$172$$ 0 0
$$173$$ 8.00000 13.8564i 0.608229 1.05348i −0.383304 0.923622i $$-0.625214\pi$$
0.991532 0.129861i $$-0.0414530\pi$$
$$174$$ 0 0
$$175$$ −2.00000 + 1.73205i −0.151186 + 0.130931i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 3.00000 + 5.19615i 0.224231 + 0.388379i 0.956088 0.293079i $$-0.0946798\pi$$
−0.731858 + 0.681457i $$0.761346\pi$$
$$180$$ 0 0
$$181$$ −15.0000 −1.11494 −0.557471 0.830197i $$-0.688228\pi$$
−0.557471 + 0.830197i $$0.688228\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 1.00000 + 1.73205i 0.0735215 + 0.127343i
$$186$$ 0 0
$$187$$ −8.00000 + 13.8564i −0.585018 + 1.01328i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 3.00000 5.19615i 0.217072 0.375980i −0.736839 0.676068i $$-0.763683\pi$$
0.953912 + 0.300088i $$0.0970159\pi$$
$$192$$ 0 0
$$193$$ −5.50000 9.52628i −0.395899 0.685717i 0.597317 0.802005i $$-0.296234\pi$$
−0.993215 + 0.116289i $$0.962900\pi$$
$$194$$ 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 0.688705 0.725042i $$-0.258180\pi$$
−0.972257 + 0.233915i $$0.924846\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −2.00000 10.3923i −0.140372 0.729397i
$$204$$ 0 0
$$205$$ 6.00000 10.3923i 0.419058 0.725830i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 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
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −11.0000 + 19.0526i −0.750194 + 1.29937i
$$216$$ 0 0
$$217$$ 6.00000 5.19615i 0.407307 0.352738i
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −12.0000 20.7846i −0.807207 1.39812i
$$222$$ 0 0
$$223$$ 8.00000 0.535720 0.267860 0.963458i $$-0.413684\pi$$
0.267860 + 0.963458i $$0.413684\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −9.00000 15.5885i −0.597351 1.03464i −0.993210 0.116331i $$-0.962887\pi$$
0.395860 0.918311i $$-0.370447\pi$$
$$228$$ 0 0
$$229$$ −0.500000 + 0.866025i −0.0330409 + 0.0572286i −0.882073 0.471113i $$-0.843853\pi$$
0.849032 + 0.528341i $$0.177186\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 7.00000 12.1244i 0.458585 0.794293i −0.540301 0.841472i $$-0.681690\pi$$
0.998886 + 0.0471787i $$0.0150230\pi$$
$$234$$ 0 0
$$235$$ 6.00000 + 10.3923i 0.391397 + 0.677919i
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 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 0.547533 0.836784i $$-0.315567\pi$$
−0.998443 + 0.0557856i $$0.982234\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 2.00000 13.8564i 0.127775 0.885253i
$$246$$ 0 0
$$247$$ −1.50000 + 2.59808i −0.0954427 + 0.165312i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 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 −0.435970 0.899961i $$-0.643595\pi$$
0.997374 0.0724199i $$-0.0230722\pi$$
$$258$$ 0 0
$$259$$ 2.50000 + 0.866025i 0.155342 + 0.0538122i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 6.00000 + 10.3923i 0.369976 + 0.640817i 0.989561 0.144112i $$-0.0460326\pi$$
−0.619586 + 0.784929i $$0.712699\pi$$
$$264$$ 0 0
$$265$$ 24.0000 1.47431
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −1.00000 1.73205i −0.0609711 0.105605i 0.833929 0.551872i $$-0.186086\pi$$
−0.894900 + 0.446267i $$0.852753\pi$$
$$270$$ 0 0
$$271$$ 12.0000 20.7846i 0.728948 1.26258i −0.228380 0.973572i $$-0.573343\pi$$
0.957328 0.289003i $$-0.0933238\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −1.00000 + 1.73205i −0.0603023 + 0.104447i
$$276$$ 0 0
$$277$$ −8.50000 14.7224i −0.510716 0.884585i −0.999923 0.0124177i $$-0.996047\pi$$
0.489207 0.872167i $$-0.337286\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −20.0000 −1.19310 −0.596550 0.802576i $$-0.703462\pi$$
−0.596550 + 0.802576i $$0.703462\pi$$
$$282$$ 0 0
$$283$$ −9.50000 16.4545i −0.564716 0.978117i −0.997076 0.0764162i $$-0.975652\pi$$
0.432360 0.901701i $$-0.357681\pi$$
$$284$$ 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
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 24.0000 1.40209 0.701047 0.713115i $$-0.252716\pi$$
0.701047 + 0.713115i $$0.252716\pi$$
$$294$$ 0 0
$$295$$ −8.00000 −0.465778
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 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
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 6.00000 + 10.3923i 0.343559 + 0.595062i
$$306$$ 0 0
$$307$$ −23.0000 −1.31268 −0.656340 0.754466i $$-0.727896\pi$$
−0.656340 + 0.754466i $$0.727896\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −1.00000 1.73205i −0.0567048 0.0982156i 0.836280 0.548303i $$-0.184726\pi$$
−0.892984 + 0.450088i $$0.851393\pi$$
$$312$$ 0 0
$$313$$ 8.50000 14.7224i 0.480448 0.832161i −0.519300 0.854592i $$-0.673807\pi$$
0.999748 + 0.0224310i $$0.00714060\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −12.0000 + 20.7846i −0.673987 + 1.16738i 0.302777 + 0.953062i $$0.402086\pi$$
−0.976764 + 0.214318i $$0.931247\pi$$
$$318$$ 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
$$325$$ −1.50000 2.59808i −0.0832050 0.144115i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 15.0000 + 5.19615i 0.826977 + 0.286473i
$$330$$ 0 0
$$331$$ −8.50000 + 14.7224i −0.467202 + 0.809218i −0.999298 0.0374662i $$-0.988071\pi$$
0.532096 + 0.846684i $$0.321405\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 26.0000 1.42053
$$336$$ 0 0
$$337$$ 21.0000 1.14394 0.571971 0.820274i $$-0.306179\pi$$
0.571971 + 0.820274i $$0.306179\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 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 0.984487 + 0.175457i $$0.0561403\pi$$
−0.340293 + 0.940319i $$0.610526\pi$$
$$348$$ 0 0
$$349$$ −14.0000 −0.749403 −0.374701 0.927146i $$-0.622255\pi$$
−0.374701 + 0.927146i $$0.622255\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −3.00000 5.19615i −0.159674 0.276563i 0.775077 0.631867i $$-0.217711\pi$$
−0.934751 + 0.355303i $$0.884378\pi$$
$$354$$ 0 0
$$355$$ −10.0000 + 17.3205i −0.530745 + 0.919277i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −10.0000 + 17.3205i −0.527780 + 0.914141i 0.471696 + 0.881761i $$0.343642\pi$$
−0.999476 + 0.0323801i $$0.989691\pi$$
$$360$$ 0 0
$$361$$ 9.00000 + 15.5885i 0.473684 + 0.820445i
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −22.0000 −1.15153
$$366$$ 0 0
$$367$$ −2.50000 4.33013i −0.130499 0.226031i 0.793370 0.608740i $$-0.208325\pi$$
−0.923869 + 0.382709i $$0.874991\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 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 $$-0.792014\pi$$
0.923462 + 0.383691i $$0.125347\pi$$
$$374$$ 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
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −14.0000 + 24.2487i −0.715367 + 1.23905i 0.247451 + 0.968900i $$0.420407\pi$$
−0.962818 + 0.270151i $$0.912926\pi$$
$$384$$ 0 0
$$385$$ −2.00000 10.3923i −0.101929 0.529641i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 5.00000 + 8.66025i 0.253510 + 0.439092i 0.964490 0.264120i $$-0.0850816\pi$$
−0.710980 + 0.703213i $$0.751748\pi$$
$$390$$ 0 0
$$391$$ 64.0000 3.23662
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 3.00000 + 5.19615i 0.150946 + 0.261447i
$$396$$ 0 0
$$397$$ −1.50000 + 2.59808i −0.0752828 + 0.130394i −0.901209 0.433384i $$-0.857319\pi$$
0.825926 + 0.563778i $$0.190653\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −6.00000 + 10.3923i −0.299626 + 0.518967i −0.976050 0.217545i $$-0.930195\pi$$
0.676425 + 0.736512i $$0.263528\pi$$
$$402$$ 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 0.999402 0.0345902i $$-0.0110126\pi$$
−0.529657 + 0.848212i $$0.677679\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −8.00000 + 6.92820i −0.393654 + 0.340915i
$$414$$ 0 0
$$415$$ 2.00000 3.46410i 0.0981761 0.170046i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 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
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −4.00000 + 6.92820i −0.194029 + 0.336067i
$$426$$ 0 0
$$427$$ 15.0000 + 5.19615i 0.725901 + 0.251459i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −15.0000 25.9808i −0.722525 1.25145i −0.959985 0.280052i $$-0.909648\pi$$
0.237460 0.971397i $$-0.423685\pi$$
$$432$$ 0 0
$$433$$ −25.0000 −1.20142 −0.600712 0.799466i $$-0.705116\pi$$
−0.600712 + 0.799466i $$0.705116\pi$$
$$434$$ 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 0.423556 + 0.905870i $$0.360782\pi$$
−0.996284 + 0.0861252i $$0.972552\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −2.00000 + 3.46410i −0.0950229 + 0.164584i −0.909618 0.415445i $$-0.863626\pi$$
0.814595 + 0.580030i $$0.196959\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 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
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 15.0000 + 5.19615i 0.703211 + 0.243599i
$$456$$ 0 0
$$457$$ −6.50000 + 11.2583i −0.304057 + 0.526642i −0.977051 0.213006i $$-0.931675\pi$$
0.672994 + 0.739648i $$0.265008\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −4.00000 −0.186299 −0.0931493 0.995652i $$-0.529693\pi$$
−0.0931493 + 0.995652i $$0.529693\pi$$
$$462$$ 0 0
$$463$$ −11.0000 −0.511213 −0.255607 0.966781i $$-0.582275\pi$$
−0.255607 + 0.966781i $$0.582275\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 17.0000 29.4449i 0.786666 1.36255i −0.141332 0.989962i $$-0.545139\pi$$
0.927999 0.372584i $$-0.121528\pi$$
$$468$$ 0 0
$$469$$ 26.0000 22.5167i 1.20057 1.03972i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 11.0000 + 19.0526i 0.505781 + 0.876038i
$$474$$ 0 0
$$475$$ 1.00000 0.0458831
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −14.0000 24.2487i −0.639676 1.10795i −0.985504 0.169654i $$-0.945735\pi$$
0.345827 0.938298i $$-0.387598\pi$$
$$480$$ 0 0
$$481$$ −1.50000 + 2.59808i −0.0683941 + 0.118462i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −10.0000 + 17.3205i −0.454077 + 0.786484i
$$486$$ 0 0
$$487$$ 9.50000 + 16.4545i 0.430486 + 0.745624i 0.996915 0.0784867i $$-0.0250088\pi$$
−0.566429 + 0.824110i $$0.691675\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 36.0000 1.62466 0.812329 0.583200i $$-0.198200\pi$$
0.812329 + 0.583200i $$0.198200\pi$$
$$492$$ 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 −0.334227 0.942493i $$-0.608475\pi$$
0.983336 0.181797i $$-0.0581915\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 30.0000 1.33763 0.668817 0.743427i $$-0.266801\pi$$
0.668817 + 0.743427i $$0.266801\pi$$
$$504$$ 0 0
$$505$$ −20.0000 −0.889988
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 9.00000 15.5885i 0.398918 0.690946i −0.594675 0.803966i $$-0.702719\pi$$
0.993593 + 0.113020i $$0.0360525\pi$$
$$510$$ 0 0
$$511$$ −22.0000 + 19.0526i −0.973223 + 0.842836i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −11.0000 19.0526i −0.484718 0.839556i
$$516$$ 0 0
$$517$$ 12.0000 0.527759
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −18.0000 31.1769i −0.788594 1.36589i −0.926828 0.375486i $$-0.877476\pi$$
0.138234 0.990400i $$-0.455857\pi$$
$$522$$ 0 0
$$523$$ 15.5000 26.8468i 0.677768 1.17393i −0.297884 0.954602i $$-0.596281\pi$$
0.975652 0.219326i $$-0.0703858\pi$$
$$524$$ 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
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 18.0000 0.779667
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −11.0000 8.66025i −0.473804 0.373024i
$$540$$ 0 0
$$541$$ 7.50000 12.9904i 0.322450 0.558500i −0.658543 0.752543i $$-0.728827\pi$$
0.980993 + 0.194043i $$0.0621602\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −22.0000 −0.942376
$$546$$ 0 0
$$547$$ −12.0000 −0.513083 −0.256541 0.966533i $$-0.582583\pi$$
−0.256541 + 0.966533i $$0.582583\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 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 0.999250 0.0387286i $$-0.0123308\pi$$
−0.533165 + 0.846011i $$0.678997\pi$$
$$558$$ 0 0
$$559$$ −33.0000 −1.39575
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −23.0000 39.8372i −0.969334 1.67894i −0.697489 0.716596i $$-0.745699\pi$$
−0.271846 0.962341i $$-0.587634\pi$$
$$564$$ 0 0
$$565$$ −14.0000 + 24.2487i −0.588984 + 1.02015i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 3.00000 5.19615i 0.125767 0.217834i −0.796266 0.604947i $$-0.793194\pi$$
0.922032 + 0.387113i $$0.126528\pi$$
$$570$$ 0 0
$$571$$ 10.5000 + 18.1865i 0.439411 + 0.761083i 0.997644 0.0686016i $$-0.0218537\pi$$
−0.558233 + 0.829684i $$0.688520\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 8.00000 0.333623
$$576$$ 0 0
$$577$$ 20.5000 + 35.5070i 0.853426 + 1.47818i 0.878097 + 0.478482i $$0.158813\pi$$
−0.0246713 + 0.999696i $$0.507854\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 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
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −3.00000 + 5.19615i −0.123195 + 0.213380i −0.921026 0.389501i $$-0.872647\pi$$
0.797831 + 0.602881i $$0.205981\pi$$
$$594$$ 0 0
$$595$$ −8.00000 41.5692i −0.327968 1.70417i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −6.00000 10.3923i −0.245153 0.424618i 0.717021 0.697051i $$-0.245505\pi$$
−0.962175 + 0.272433i $$0.912172\pi$$
$$600$$ 0 0
$$601$$ −1.00000 −0.0407909 −0.0203954 0.999792i $$-0.506493\pi$$
−0.0203954 + 0.999792i $$0.506493\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 7.00000 + 12.1244i 0.284590 + 0.492925i
$$606$$ 0 0
$$607$$ 1.50000 2.59808i 0.0608831 0.105453i −0.833977 0.551799i $$-0.813942\pi$$
0.894860 + 0.446346i $$0.147275\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −9.00000 + 15.5885i −0.364101 + 0.630641i
$$612$$ 0 0
$$613$$ 15.0000 + 25.9808i 0.605844 + 1.04935i 0.991917 + 0.126885i $$0.0404979\pi$$
−0.386073 + 0.922468i $$0.626169\pi$$
$$614$$ 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 0.955131 0.296183i $$-0.0957138\pi$$
−0.734068 + 0.679076i $$0.762380\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 9.50000 16.4545i 0.380000 0.658179i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 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
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −3.00000 + 5.19615i −0.119051 + 0.206203i
$$636$$ 0 0
$$637$$ 19.5000 7.79423i 0.772618 0.308819i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −20.0000 34.6410i −0.789953 1.36824i −0.925995 0.377535i $$-0.876772\pi$$
0.136043 0.990703i $$-0.456562\pi$$
$$642$$ 0 0
$$643$$ 35.0000 1.38027 0.690133 0.723683i $$-0.257552\pi$$
0.690133 + 0.723683i $$0.257552\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 3.00000 + 5.19615i 0.117942 + 0.204282i 0.918952 0.394369i $$-0.129037\pi$$
−0.801010 + 0.598651i $$0.795704\pi$$
$$648$$ 0 0
$$649$$ −4.00000 + 6.92820i −0.157014 + 0.271956i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −3.00000 + 5.19615i −0.117399 + 0.203341i −0.918736 0.394872i $$-0.870789\pi$$
0.801337 + 0.598213i $$0.204122\pi$$
$$654$$ 0 0
$$655$$ −2.00000 3.46410i −0.0781465 0.135354i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 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 0.997143 + 0.0755324i $$0.0240656\pi$$
−0.433159 + 0.901318i $$0.642601\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −4.00000 + 3.46410i −0.155113 + 0.134332i
$$666$$ 0 0
$$667$$ −16.0000 + 27.7128i −0.619522 + 1.07304i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 12.0000 0.463255
$$672$$ 0 0
$$673$$ −1.00000 −0.0385472 −0.0192736 0.999814i $$-0.506135\pi$$
−0.0192736 + 0.999814i $$0.506135\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 6.00000 10.3923i 0.230599 0.399409i −0.727386 0.686229i $$-0.759265\pi$$
0.957984 + 0.286820i $$0.0925982\pi$$
$$678$$ 0 0
$$679$$ 5.00000 + 25.9808i 0.191882 + 0.997050i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 18.0000 + 31.1769i 0.688751 + 1.19295i 0.972242 + 0.233977i $$0.0751739\pi$$
−0.283491 + 0.958975i $$0.591493\pi$$
$$684$$ 0 0
$$685$$ −8.00000 −0.305664
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 18.0000 + 31.1769i 0.685745 + 1.18775i
$$690$$ 0 0
$$691$$ 21.5000 37.2391i 0.817899 1.41664i −0.0893292 0.996002i $$-0.528472\pi$$
0.907228 0.420640i $$-0.138194\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 5.00000 8.66025i 0.189661 0.328502i
$$696$$ 0 0
$$697$$ −24.0000 41.5692i −0.909065 1.57455i
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 8.00000 0.302156 0.151078 0.988522i $$-0.451726\pi$$
0.151078 + 0.988522i $$0.451726\pi$$
$$702$$ 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 −0.967009 0.254743i $$-0.918009\pi$$
0.704118 + 0.710083i $$0.251342\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −24.0000 −0.898807
$$714$$ 0 0
$$715$$ 12.0000 0.448775
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −3.00000 + 5.19615i −0.111881 + 0.193784i −0.916529 0.399969i $$-0.869021\pi$$
0.804648 + 0.593753i $$0.202354\pi$$
$$720$$ 0 0
$$721$$ −27.5000 9.52628i −1.02415 0.354777i
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −2.00000 3.46410i −0.0742781 0.128654i
$$726$$ 0 0
$$727$$ −23.0000 −0.853023 −0.426511 0.904482i $$-0.640258\pi$$
−0.426511 + 0.904482i $$0.640258\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 44.0000 + 76.2102i 1.62740 + 2.81874i
$$732$$ 0 0
$$733$$ −22.5000 + 38.9711i −0.831056 + 1.43943i 0.0661448 + 0.997810i $$0.478930\pi$$
−0.897201 + 0.441622i $$0.854403\pi$$
$$734$$ 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 0.936845 0.349744i $$-0.113732\pi$$
−0.771310 + 0.636460i $$0.780398\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 18.0000 0.660356 0.330178 0.943919i $$-0.392891\pi$$
0.330178 + 0.943919i $$0.392891\pi$$
$$744$$ 0 0
$$745$$ −12.0000 20.7846i −0.439646 0.761489i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −7.50000 + 12.9904i −0.273679 + 0.474026i −0.969801 0.243898i $$-0.921574\pi$$
0.696122 + 0.717923i $$0.254907\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −16.0000 −0.582300
$$756$$ 0 0
$$757$$ 42.0000 1.52652 0.763258 0.646094i $$-0.223599\pi$$
0.763258 + 0.646094i $$0.223599\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 4.00000 6.92820i 0.145000 0.251147i −0.784373 0.620289i $$-0.787015\pi$$
0.929373 + 0.369142i $$0.120348\pi$$
$$762$$ 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
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 11.0000 + 19.0526i 0.395643 + 0.685273i 0.993183 0.116566i $$-0.0371886\pi$$
−0.597540 + 0.801839i $$0.703855\pi$$
$$774$$ 0 0
$$775$$ 1.50000 2.59808i 0.0538816 0.0933257i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 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
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 4.00000 0.142766
$$786$$ 0 0
$$787$$ −12.0000 20.7846i −0.427754 0.740891i 0.568919 0.822393i $$-0.307362\pi$$
−0.996673 + 0.0815020i $$0.974028\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 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
$$801$$ 0 0
$$802$$ 0 0
$$803$$ −11.0000 + 19.0526i −0.388182 +