# Properties

 Label 2268.2.l.g.109.1 Level $2268$ Weight $2$ Character 2268.109 Analytic conductor $18.110$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2268 = 2^{2} \cdot 3^{4} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2268.l (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$18.1100711784$$ 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 109.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 2268.109 Dual form 2268.2.l.g.541.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+2.00000 q^{5} +(-2.50000 + 0.866025i) q^{7} +O(q^{10})$$ $$q+2.00000 q^{5} +(-2.50000 + 0.866025i) q^{7} -2.00000 q^{11} +(1.50000 - 2.59808i) q^{13} +(4.00000 - 6.92820i) q^{17} +(0.500000 + 0.866025i) q^{19} -8.00000 q^{23} -1.00000 q^{25} +(2.00000 + 3.46410i) q^{29} +(-1.50000 - 2.59808i) q^{31} +(-5.00000 + 1.73205i) q^{35} +(0.500000 + 0.866025i) q^{37} +(3.00000 - 5.19615i) q^{41} +(-5.50000 - 9.52628i) q^{43} +(3.00000 - 5.19615i) q^{47} +(5.50000 - 4.33013i) q^{49} +(-6.00000 + 10.3923i) q^{53} -4.00000 q^{55} +(2.00000 + 3.46410i) q^{59} +(3.00000 - 5.19615i) q^{61} +(3.00000 - 5.19615i) q^{65} +(-6.50000 - 11.2583i) q^{67} +10.0000 q^{71} +(5.50000 - 9.52628i) q^{73} +(5.00000 - 1.73205i) q^{77} +(1.50000 - 2.59808i) q^{79} +(1.00000 + 1.73205i) q^{83} +(8.00000 - 13.8564i) q^{85} +(-1.50000 + 7.79423i) q^{91} +(1.00000 + 1.73205i) q^{95} +(-5.00000 - 8.66025i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + 4q^{5} - 5q^{7} + O(q^{10})$$ $$2q + 4q^{5} - 5q^{7} - 4q^{11} + 3q^{13} + 8q^{17} + q^{19} - 16q^{23} - 2q^{25} + 4q^{29} - 3q^{31} - 10q^{35} + q^{37} + 6q^{41} - 11q^{43} + 6q^{47} + 11q^{49} - 12q^{53} - 8q^{55} + 4q^{59} + 6q^{61} + 6q^{65} - 13q^{67} + 20q^{71} + 11q^{73} + 10q^{77} + 3q^{79} + 2q^{83} + 16q^{85} - 3q^{91} + 2q^{95} - 10q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times$$.

 $$n$$ $$325$$ $$1135$$ $$1541$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$

## 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 0
$$4$$ 0 0
$$5$$ 2.00000 0.894427 0.447214 0.894427i $$-0.352416\pi$$
0.447214 + 0.894427i $$0.352416\pi$$
$$6$$ 0 0
$$7$$ −2.50000 + 0.866025i −0.944911 + 0.327327i
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −2.00000 −0.603023 −0.301511 0.953463i $$-0.597491\pi$$
−0.301511 + 0.953463i $$0.597491\pi$$
$$12$$ 0 0
$$13$$ 1.50000 2.59808i 0.416025 0.720577i −0.579510 0.814965i $$-0.696756\pi$$
0.995535 + 0.0943882i $$0.0300895\pi$$
$$14$$ 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
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −8.00000 −1.66812 −0.834058 0.551677i $$-0.813988\pi$$
−0.834058 + 0.551677i $$0.813988\pi$$
$$24$$ 0 0
$$25$$ −1.00000 −0.200000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 2.00000 + 3.46410i 0.371391 + 0.643268i 0.989780 0.142605i $$-0.0455477\pi$$
−0.618389 + 0.785872i $$0.712214\pi$$
$$30$$ 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 0.904194 0.427121i $$-0.140472\pi$$
−0.821995 + 0.569495i $$0.807139\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 3.00000 5.19615i 0.468521 0.811503i −0.530831 0.847477i $$-0.678120\pi$$
0.999353 + 0.0359748i $$0.0114536\pi$$
$$42$$ 0 0
$$43$$ −5.50000 9.52628i −0.838742 1.45274i −0.890947 0.454108i $$-0.849958\pi$$
0.0522047 0.998636i $$-0.483375\pi$$
$$44$$ 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
$$49$$ 5.50000 4.33013i 0.785714 0.618590i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 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
$$55$$ −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 −0.340868 0.940111i $$-0.610721\pi$$
0.984594 0.174855i $$-0.0559458\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 5.00000 1.73205i 0.569803 0.197386i
$$78$$ 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
$$83$$ 1.00000 + 1.73205i 0.109764 + 0.190117i 0.915675 0.401920i $$-0.131657\pi$$
−0.805910 + 0.592037i $$0.798324\pi$$
$$84$$ 0 0
$$85$$ 8.00000 13.8564i 0.867722 1.50294i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 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
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 1.00000 + 1.73205i 0.102598 + 0.177705i
$$96$$ 0 0
$$97$$ −5.00000 8.66025i −0.507673 0.879316i −0.999961 0.00888289i $$-0.997172\pi$$
0.492287 0.870433i $$-0.336161\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −10.0000 −0.995037 −0.497519 0.867453i $$-0.665755\pi$$
−0.497519 + 0.867453i $$0.665755\pi$$
$$102$$ 0 0
$$103$$ 11.0000 1.08386 0.541931 0.840423i $$-0.317693\pi$$
0.541931 + 0.840423i $$0.317693\pi$$
$$104$$ 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
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −7.00000 + 12.1244i −0.658505 + 1.14056i 0.322498 + 0.946570i $$0.395477\pi$$
−0.981003 + 0.193993i $$0.937856\pi$$
$$114$$ 0 0
$$115$$ −16.0000 −1.49201
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −4.00000 + 20.7846i −0.366679 + 1.90532i
$$120$$ 0 0
$$121$$ −7.00000 −0.636364
$$122$$ 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
$$131$$ 2.00000 0.174741 0.0873704 0.996176i $$-0.472154\pi$$
0.0873704 + 0.996176i $$0.472154\pi$$
$$132$$ 0 0
$$133$$ −2.00000 1.73205i −0.173422 0.150188i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −4.00000 −0.341743 −0.170872 0.985293i $$-0.554658\pi$$
−0.170872 + 0.985293i $$0.554658\pi$$
$$138$$ 0 0
$$139$$ 2.50000 4.33013i 0.212047 0.367277i −0.740308 0.672268i $$-0.765320\pi$$
0.952355 + 0.304991i $$0.0986536\pi$$
$$140$$ 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
$$149$$ 12.0000 0.983078 0.491539 0.870855i $$-0.336434\pi$$
0.491539 + 0.870855i $$0.336434\pi$$
$$150$$ 0 0
$$151$$ −8.00000 −0.651031 −0.325515 0.945537i $$-0.605538\pi$$
−0.325515 + 0.945537i $$0.605538\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −3.00000 5.19615i −0.240966 0.417365i
$$156$$ 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 0.933659 0.358162i $$-0.116597\pi$$
−0.777007 + 0.629492i $$0.783263\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −1.00000 + 1.73205i −0.0773823 + 0.134030i −0.902120 0.431486i $$-0.857990\pi$$
0.824737 + 0.565516i $$0.191323\pi$$
$$168$$ 0 0
$$169$$ 2.00000 + 3.46410i 0.153846 + 0.266469i
$$170$$ 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
$$175$$ 2.50000 0.866025i 0.188982 0.0654654i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 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
$$183$$ 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 −0.972257 0.233915i $$-0.924846\pi$$
0.688705 + 0.725042i $$0.258180\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −8.00000 6.92820i −0.561490 0.486265i
$$204$$ 0 0
$$205$$ 6.00000 10.3923i 0.419058 0.725830i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −1.00000 1.73205i −0.0691714 0.119808i
$$210$$ 0 0
$$211$$ 2.00000 3.46410i 0.137686 0.238479i −0.788935 0.614477i $$-0.789367\pi$$
0.926620 + 0.375999i $$0.122700\pi$$
$$212$$ 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
$$223$$ −4.00000 6.92820i −0.267860 0.463947i 0.700449 0.713702i $$-0.252983\pi$$
−0.968309 + 0.249756i $$0.919650\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 18.0000 1.19470 0.597351 0.801980i $$-0.296220\pi$$
0.597351 + 0.801980i $$0.296220\pi$$
$$228$$ 0 0
$$229$$ 1.00000 0.0660819 0.0330409 0.999454i $$-0.489481\pi$$
0.0330409 + 0.999454i $$0.489481\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 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
$$235$$ 6.00000 10.3923i 0.391397 0.677919i
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 9.00000 15.5885i 0.582162 1.00833i −0.413061 0.910703i $$-0.635540\pi$$
0.995223 0.0976302i $$-0.0311262\pi$$
$$240$$ 0 0
$$241$$ 14.0000 0.901819 0.450910 0.892570i $$-0.351100\pi$$
0.450910 + 0.892570i $$0.351100\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 11.0000 8.66025i 0.702764 0.553283i
$$246$$ 0 0
$$247$$ 3.00000 0.190885
$$248$$ 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
$$257$$ −18.0000 −1.12281 −0.561405 0.827541i $$-0.689739\pi$$
−0.561405 + 0.827541i $$0.689739\pi$$
$$258$$ 0 0
$$259$$ −2.00000 1.73205i −0.124274 0.107624i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −12.0000 −0.739952 −0.369976 0.929041i $$-0.620634\pi$$
−0.369976 + 0.929041i $$0.620634\pi$$
$$264$$ 0 0
$$265$$ −12.0000 + 20.7846i −0.737154 + 1.27679i
$$266$$ 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
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 2.00000 0.120605
$$276$$ 0 0
$$277$$ 17.0000 1.02143 0.510716 0.859750i $$-0.329381\pi$$
0.510716 + 0.859750i $$0.329381\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 10.0000 + 17.3205i 0.596550 + 1.03325i 0.993326 + 0.115339i $$0.0367956\pi$$
−0.396776 + 0.917915i $$0.629871\pi$$
$$282$$ 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
$$293$$ −12.0000 + 20.7846i −0.701047 + 1.21425i 0.267052 + 0.963682i $$0.413951\pi$$
−0.968099 + 0.250568i $$0.919383\pi$$
$$294$$ 0 0
$$295$$ 4.00000 + 6.92820i 0.232889 + 0.403376i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −12.0000 + 20.7846i −0.693978 + 1.20201i
$$300$$ 0 0
$$301$$ 22.0000 + 19.0526i 1.26806 + 1.09817i
$$302$$ 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
$$329$$ −3.00000 + 15.5885i −0.165395 + 0.859419i
$$330$$ 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
$$335$$ −13.0000 22.5167i −0.710266 1.23022i
$$336$$ 0 0
$$337$$ −10.5000 + 18.1865i −0.571971 + 0.990684i 0.424392 + 0.905479i $$0.360488\pi$$
−0.996363 + 0.0852050i $$0.972845\pi$$
$$338$$ 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
$$349$$ 7.00000 + 12.1244i 0.374701 + 0.649002i 0.990282 0.139072i $$-0.0444119\pi$$
−0.615581 + 0.788074i $$0.711079\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 6.00000 0.319348 0.159674 0.987170i $$-0.448956\pi$$
0.159674 + 0.987170i $$0.448956\pi$$
$$354$$ 0 0
$$355$$ 20.0000 1.06149
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 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
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 11.0000 19.0526i 0.575766 0.997257i
$$366$$ 0 0
$$367$$ 5.00000 0.260998 0.130499 0.991448i $$-0.458342\pi$$
0.130499 + 0.991448i $$0.458342\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 6.00000 31.1769i 0.311504 1.61862i
$$372$$ 0 0
$$373$$ −5.00000 −0.258890 −0.129445 0.991587i $$-0.541320\pi$$
−0.129445 + 0.991587i $$0.541320\pi$$
$$374$$ 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
$$383$$ 28.0000 1.43073 0.715367 0.698749i $$-0.246260\pi$$
0.715367 + 0.698749i $$0.246260\pi$$
$$384$$ 0 0
$$385$$ 10.0000 3.46410i 0.509647 0.176547i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −10.0000 −0.507020 −0.253510 0.967333i $$-0.581585\pi$$
−0.253510 + 0.967333i $$0.581585\pi$$
$$390$$ 0 0
$$391$$ −32.0000 + 55.4256i −1.61831 + 2.80299i
$$392$$ 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 0.825926 0.563778i $$-0.190653\pi$$
−0.901209 + 0.433384i $$0.857319\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 12.0000 0.599251 0.299626 0.954057i $$-0.403138\pi$$
0.299626 + 0.954057i $$0.403138\pi$$
$$402$$ 0 0
$$403$$ −9.00000 −0.448322
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −1.00000 1.73205i −0.0495682 0.0858546i
$$408$$ 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
$$419$$ 9.00000 15.5885i 0.439679 0.761546i −0.557986 0.829851i $$-0.688426\pi$$
0.997665 + 0.0683046i $$0.0217590\pi$$
$$420$$ 0 0
$$421$$ 13.5000 + 23.3827i 0.657950 + 1.13960i 0.981146 + 0.193270i $$0.0619094\pi$$
−0.323196 + 0.946332i $$0.604757\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −4.00000 + 6.92820i −0.194029 + 0.336067i
$$426$$ 0 0
$$427$$ −3.00000 + 15.5885i −0.145180 + 0.754378i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −15.0000 + 25.9808i −0.722525 + 1.25145i 0.237460 + 0.971397i $$0.423685\pi$$
−0.959985 + 0.280052i $$0.909648\pi$$
$$432$$ 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
$$455$$ −3.00000 + 15.5885i −0.140642 + 0.730798i
$$456$$ 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
$$461$$ 2.00000 + 3.46410i 0.0931493 + 0.161339i 0.908835 0.417156i $$-0.136973\pi$$
−0.815685 + 0.578496i $$0.803640\pi$$
$$462$$ 0 0
$$463$$ 5.50000 9.52628i 0.255607 0.442724i −0.709453 0.704752i $$-0.751058\pi$$
0.965060 + 0.262029i $$0.0843915\pi$$
$$464$$ 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
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 11.0000 + 19.0526i 0.505781 + 0.876038i
$$474$$ 0 0
$$475$$ −0.500000 0.866025i −0.0229416 0.0397360i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 28.0000 1.27935 0.639676 0.768644i $$-0.279068\pi$$
0.639676 + 0.768644i $$0.279068\pi$$
$$480$$ 0 0
$$481$$ 3.00000 0.136788
$$482$$ 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 −0.566429 0.824110i $$-0.691675\pi$$
0.996915 + 0.0784867i $$0.0250088\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −18.0000 + 31.1769i −0.812329 + 1.40699i 0.0989017 + 0.995097i $$0.468467\pi$$
−0.911230 + 0.411897i $$0.864866\pi$$
$$492$$ 0 0
$$493$$ 32.0000 1.44121
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −25.0000 + 8.66025i −1.12140 + 0.388465i
$$498$$ 0 0
$$499$$ −29.0000 −1.29822 −0.649109 0.760695i $$-0.724858\pi$$
−0.649109 + 0.760695i $$0.724858\pi$$
$$500$$ 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
$$509$$ −18.0000 −0.797836 −0.398918 0.916987i $$-0.630614\pi$$
−0.398918 + 0.916987i $$0.630614\pi$$
$$510$$ 0 0
$$511$$ −5.50000 + 28.5788i −0.243306 + 1.26425i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 22.0000 0.969436
$$516$$ 0 0
$$517$$ −6.00000 + 10.3923i −0.263880 + 0.457053i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −18.0000 + 31.1769i −0.788594 + 1.36589i 0.138234 + 0.990400i $$0.455857\pi$$
−0.926828 + 0.375486i $$0.877476\pi$$
$$522$$ 0 0
$$523$$ 15.5000 + 26.8468i 0.677768 + 1.17393i 0.975652 + 0.219326i $$0.0703858\pi$$
−0.297884 + 0.954602i $$0.596281\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −24.0000 −1.04546
$$528$$ 0 0
$$529$$ 41.0000 1.78261
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −9.00000 15.5885i −0.389833 0.675211i
$$534$$ 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 0.980993 0.194043i $$-0.0621602\pi$$
−0.658543 + 0.752543i $$0.728827\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 11.0000 19.0526i 0.471188 0.816122i
$$546$$ 0 0
$$547$$ 6.00000 + 10.3923i 0.256541 + 0.444343i 0.965313 0.261095i $$-0.0840836\pi$$
−0.708772 + 0.705438i $$0.750750\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −2.00000 + 3.46410i −0.0852029 + 0.147576i
$$552$$ 0 0
$$553$$ −1.50000 + 7.79423i −0.0637865 + 0.331444i
$$554$$ 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
$$561$$ 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 −0.0246713 0.999696i $$-0.507854\pi$$
0.878097 0.478482i $$-0.158813\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −4.00000 3.46410i −0.165948 0.143715i
$$582$$ 0 0
$$583$$ 12.0000 20.7846i 0.496989 0.860811i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 16.0000 + 27.7128i 0.660391 + 1.14383i 0.980513 + 0.196454i $$0.0629426\pi$$
−0.320122 + 0.947376i $$0.603724\pi$$
$$588$$ 0 0
$$589$$ 1.50000 2.59808i 0.0618064 0.107052i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 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
$$595$$ −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
$$601$$ 0.500000 + 0.866025i 0.0203954 + 0.0353259i 0.876043 0.482233i $$-0.160174\pi$$
−0.855648 + 0.517559i $$0.826841\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −14.0000 −0.569181
$$606$$ 0 0
$$607$$ −3.00000 −0.121766 −0.0608831 0.998145i $$-0.519392\pi$$
−0.0608831 + 0.998145i $$0.519392\pi$$
$$608$$ 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 −0.386073 0.922468i $$-0.626169\pi$$
0.991917 0.126885i $$-0.0404979\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 13.0000 22.5167i 0.523360 0.906487i −0.476270 0.879299i $$-0.658012\pi$$
0.999630 0.0271876i $$-0.00865514\pi$$
$$618$$ 0 0
$$619$$ −11.0000 −0.442127 −0.221064 0.975259i $$-0.570953\pi$$
−0.221064 + 0.975259i $$0.570953\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −19.0000 −0.760000
$$626$$ 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
$$635$$ 6.00000 0.238103
$$636$$ 0 0
$$637$$ −3.00000 20.7846i −0.118864 0.823516i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 40.0000 1.57991 0.789953 0.613168i $$-0.210105\pi$$
0.789953 + 0.613168i $$0.210105\pi$$
$$642$$ 0 0
$$643$$ −17.5000 + 30.3109i −0.690133 + 1.19534i 0.281661 + 0.959514i $$0.409114\pi$$
−0.971794 + 0.235831i $$0.924219\pi$$
$$644$$ 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
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 6.00000 0.234798 0.117399 0.993085i $$-0.462544\pi$$
0.117399 + 0.993085i $$0.462544\pi$$
$$654$$ 0 0
$$655$$ 4.00000 0.156293
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −14.0000 24.2487i −0.545363 0.944596i −0.998584 0.0531977i $$-0.983059\pi$$
0.453221 0.891398i $$-0.350275\pi$$
$$660$$ 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
$$671$$ −6.00000 + 10.3923i −0.231627 + 0.401190i
$$672$$ 0 0
$$673$$ 0.500000 + 0.866025i 0.0192736 + 0.0333828i 0.875501 0.483216i $$-0.160531\pi$$
−0.856228 + 0.516599i $$0.827198\pi$$
$$674$$ 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
$$679$$ 20.0000 + 17.3205i 0.767530 + 0.664700i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 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
$$685$$ −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
$$707$$ 25.0000 8.66025i 0.940222 0.325702i
$$708$$ 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
$$713$$ 12.0000 + 20.7846i 0.449404 + 0.778390i
$$714$$ 0 0
$$715$$ −6.00000 + 10.3923i −0.224387 + 0.388650i
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 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
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −2.00000 3.46410i −0.0742781 0.128654i
$$726$$ 0 0
$$727$$ 11.5000 + 19.9186i 0.426511 + 0.738739i 0.996560 0.0828714i $$-0.0264091\pi$$
−0.570049 + 0.821611i $$0.693076\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −88.0000 −3.25480
$$732$$ 0 0
$$733$$ 45.0000 1.66211 0.831056 0.556188i $$-0.187737\pi$$
0.831056 + 0.556188i $$0.187737\pi$$
$$734$$ 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
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −9.00000 + 15.5885i −0.330178 + 0.571885i −0.982547 0.186017i $$-0.940442\pi$$
0.652369 + 0.757902i $$0.273775\pi$$
$$744$$ 0 0
$$745$$ 24.0000 0.879292
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 15.0000 0.547358 0.273679 0.961821i $$-0.411759\pi$$
0.273679 + 0.961821i $$0.411759\pi$$
$$752$$ 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
$$761$$ −8.00000 −0.290000 −0.145000 0.989432i $$-0.546318\pi$$
−0.145000 + 0.989432i $$0.546318\pi$$
$$762$$ 0 0
$$763$$ −5.50000 + 28.5788i −0.199113 + 1.03462i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 12.0000 0.433295
$$768$$ 0 0
$$769$$ −15.5000 + 26.8468i −0.558944 + 0.968120i 0.438641 + 0.898663i $$0.355460\pi$$
−0.997585 + 0.0694574i $$0.977873\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 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
$$775$$ 1.50000 + 2.59808i 0.0538816 + 0.0933257i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 6.00000 0.214972
$$780$$ 0 0
$$781$$ −20.0000 −0.715656
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −2.00000 3.46410i −0.0713831 0.123639i
$$786$$ 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
$$797$$ −24.0000 + 41.5692i −0.850124 + 1.47246i 0.0309726 + 0.999520i $$0.490140\pi$$
−0.881096 + 0.472937i $$0.843194\pi$$
$$798$$ 0 0
$$799$$ −24.0000 41.5692i −0.849059 1.47061i
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ <