# Properties

 Label 2016.2.s.a.289.1 Level $2016$ Weight $2$ Character 2016.289 Analytic conductor $16.098$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2016 = 2^{5} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2016.s (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$16.0978410475$$ 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 672) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 289.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 2016.289 Dual form 2016.2.s.a.865.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-2.00000 + 3.46410i) q^{5} +(-2.50000 + 0.866025i) q^{7} +O(q^{10})$$ $$q+(-2.00000 + 3.46410i) q^{5} +(-2.50000 + 0.866025i) q^{7} +(3.00000 + 5.19615i) q^{11} +5.00000 q^{13} +(1.00000 + 1.73205i) q^{17} +(-0.500000 + 0.866025i) q^{19} +(-3.00000 + 5.19615i) q^{23} +(-5.50000 - 9.52628i) q^{25} +(1.50000 + 2.59808i) q^{31} +(2.00000 - 10.3923i) q^{35} +(-1.50000 + 2.59808i) q^{37} +6.00000 q^{41} +5.00000 q^{43} +(-2.00000 + 3.46410i) q^{47} +(5.50000 - 4.33013i) q^{49} +(-3.00000 - 5.19615i) q^{53} -24.0000 q^{55} +(-3.00000 - 5.19615i) q^{59} +(1.00000 - 1.73205i) q^{61} +(-10.0000 + 17.3205i) q^{65} +(-3.50000 - 6.06218i) q^{67} -16.0000 q^{71} +(1.50000 + 2.59808i) q^{73} +(-12.0000 - 10.3923i) q^{77} +(-5.50000 + 9.52628i) q^{79} -12.0000 q^{83} -8.00000 q^{85} +(2.00000 - 3.46410i) q^{89} +(-12.5000 + 4.33013i) q^{91} +(-2.00000 - 3.46410i) q^{95} -6.00000 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - 4q^{5} - 5q^{7} + O(q^{10})$$ $$2q - 4q^{5} - 5q^{7} + 6q^{11} + 10q^{13} + 2q^{17} - q^{19} - 6q^{23} - 11q^{25} + 3q^{31} + 4q^{35} - 3q^{37} + 12q^{41} + 10q^{43} - 4q^{47} + 11q^{49} - 6q^{53} - 48q^{55} - 6q^{59} + 2q^{61} - 20q^{65} - 7q^{67} - 32q^{71} + 3q^{73} - 24q^{77} - 11q^{79} - 24q^{83} - 16q^{85} + 4q^{89} - 25q^{91} - 4q^{95} - 12q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/2016\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$577$$ $$1765$$ $$1793$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$1$$

## 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
$$5$$ −2.00000 + 3.46410i −0.894427 + 1.54919i −0.0599153 + 0.998203i $$0.519083\pi$$
−0.834512 + 0.550990i $$0.814250\pi$$
$$6$$ 0 0
$$7$$ −2.50000 + 0.866025i −0.944911 + 0.327327i
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 3.00000 + 5.19615i 0.904534 + 1.56670i 0.821541 + 0.570149i $$0.193114\pi$$
0.0829925 + 0.996550i $$0.473552\pi$$
$$12$$ 0 0
$$13$$ 5.00000 1.38675 0.693375 0.720577i $$-0.256123\pi$$
0.693375 + 0.720577i $$0.256123\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 1.00000 + 1.73205i 0.242536 + 0.420084i 0.961436 0.275029i $$-0.0886875\pi$$
−0.718900 + 0.695113i $$0.755354\pi$$
$$18$$ 0 0
$$19$$ −0.500000 + 0.866025i −0.114708 + 0.198680i −0.917663 0.397360i $$-0.869927\pi$$
0.802955 + 0.596040i $$0.203260\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −3.00000 + 5.19615i −0.625543 + 1.08347i 0.362892 + 0.931831i $$0.381789\pi$$
−0.988436 + 0.151642i $$0.951544\pi$$
$$24$$ 0 0
$$25$$ −5.50000 9.52628i −1.10000 1.90526i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$30$$ 0 0
$$31$$ 1.50000 + 2.59808i 0.269408 + 0.466628i 0.968709 0.248199i $$-0.0798387\pi$$
−0.699301 + 0.714827i $$0.746505\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 2.00000 10.3923i 0.338062 1.75662i
$$36$$ 0 0
$$37$$ −1.50000 + 2.59808i −0.246598 + 0.427121i −0.962580 0.270998i $$-0.912646\pi$$
0.715981 + 0.698119i $$0.245980\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 6.00000 0.937043 0.468521 0.883452i $$-0.344787\pi$$
0.468521 + 0.883452i $$0.344787\pi$$
$$42$$ 0 0
$$43$$ 5.00000 0.762493 0.381246 0.924473i $$-0.375495\pi$$
0.381246 + 0.924473i $$0.375495\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −2.00000 + 3.46410i −0.291730 + 0.505291i −0.974219 0.225605i $$-0.927564\pi$$
0.682489 + 0.730896i $$0.260898\pi$$
$$48$$ 0 0
$$49$$ 5.50000 4.33013i 0.785714 0.618590i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −3.00000 5.19615i −0.412082 0.713746i 0.583036 0.812447i $$-0.301865\pi$$
−0.995117 + 0.0987002i $$0.968532\pi$$
$$54$$ 0 0
$$55$$ −24.0000 −3.23616
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −3.00000 5.19615i −0.390567 0.676481i 0.601958 0.798528i $$-0.294388\pi$$
−0.992524 + 0.122047i $$0.961054\pi$$
$$60$$ 0 0
$$61$$ 1.00000 1.73205i 0.128037 0.221766i −0.794879 0.606768i $$-0.792466\pi$$
0.922916 + 0.385002i $$0.125799\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −10.0000 + 17.3205i −1.24035 + 2.14834i
$$66$$ 0 0
$$67$$ −3.50000 6.06218i −0.427593 0.740613i 0.569066 0.822292i $$-0.307305\pi$$
−0.996659 + 0.0816792i $$0.973972\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −16.0000 −1.89885 −0.949425 0.313993i $$-0.898333\pi$$
−0.949425 + 0.313993i $$0.898333\pi$$
$$72$$ 0 0
$$73$$ 1.50000 + 2.59808i 0.175562 + 0.304082i 0.940356 0.340193i $$-0.110493\pi$$
−0.764794 + 0.644275i $$0.777159\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −12.0000 10.3923i −1.36753 1.18431i
$$78$$ 0 0
$$79$$ −5.50000 + 9.52628i −0.618798 + 1.07179i 0.370907 + 0.928670i $$0.379047\pi$$
−0.989705 + 0.143120i $$0.954286\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −12.0000 −1.31717 −0.658586 0.752506i $$-0.728845\pi$$
−0.658586 + 0.752506i $$0.728845\pi$$
$$84$$ 0 0
$$85$$ −8.00000 −0.867722
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 2.00000 3.46410i 0.212000 0.367194i −0.740341 0.672232i $$-0.765336\pi$$
0.952340 + 0.305038i $$0.0986691\pi$$
$$90$$ 0 0
$$91$$ −12.5000 + 4.33013i −1.31036 + 0.453921i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −2.00000 3.46410i −0.205196 0.355409i
$$96$$ 0 0
$$97$$ −6.00000 −0.609208 −0.304604 0.952479i $$-0.598524\pi$$
−0.304604 + 0.952479i $$0.598524\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 1.00000 + 1.73205i 0.0995037 + 0.172345i 0.911479 0.411346i $$-0.134941\pi$$
−0.811976 + 0.583691i $$0.801608\pi$$
$$102$$ 0 0
$$103$$ 5.50000 9.52628i 0.541931 0.938652i −0.456862 0.889538i $$-0.651027\pi$$
0.998793 0.0491146i $$-0.0156400\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 5.00000 8.66025i 0.483368 0.837218i −0.516449 0.856318i $$-0.672747\pi$$
0.999818 + 0.0190994i $$0.00607989\pi$$
$$108$$ 0 0
$$109$$ 7.50000 + 12.9904i 0.718370 + 1.24425i 0.961645 + 0.274296i $$0.0884447\pi$$
−0.243276 + 0.969957i $$0.578222\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 16.0000 1.50515 0.752577 0.658505i $$-0.228811\pi$$
0.752577 + 0.658505i $$0.228811\pi$$
$$114$$ 0 0
$$115$$ −12.0000 20.7846i −1.11901 1.93817i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −4.00000 3.46410i −0.366679 0.317554i
$$120$$ 0 0
$$121$$ −12.5000 + 21.6506i −1.13636 + 1.96824i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 24.0000 2.14663
$$126$$ 0 0
$$127$$ −7.00000 −0.621150 −0.310575 0.950549i $$-0.600522\pi$$
−0.310575 + 0.950549i $$0.600522\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 3.00000 5.19615i 0.262111 0.453990i −0.704692 0.709514i $$-0.748915\pi$$
0.966803 + 0.255524i $$0.0822479\pi$$
$$132$$ 0 0
$$133$$ 0.500000 2.59808i 0.0433555 0.225282i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −6.00000 10.3923i −0.512615 0.887875i −0.999893 0.0146279i $$-0.995344\pi$$
0.487278 0.873247i $$-0.337990\pi$$
$$138$$ 0 0
$$139$$ 5.00000 0.424094 0.212047 0.977259i $$-0.431987\pi$$
0.212047 + 0.977259i $$0.431987\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 15.0000 + 25.9808i 1.25436 + 2.17262i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −2.00000 + 3.46410i −0.163846 + 0.283790i −0.936245 0.351348i $$-0.885723\pi$$
0.772399 + 0.635138i $$0.219057\pi$$
$$150$$ 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
$$155$$ −12.0000 −0.963863
$$156$$ 0 0
$$157$$ −5.00000 8.66025i −0.399043 0.691164i 0.594565 0.804048i $$-0.297324\pi$$
−0.993608 + 0.112884i $$0.963991\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 3.00000 15.5885i 0.236433 1.22854i
$$162$$ 0 0
$$163$$ −10.0000 + 17.3205i −0.783260 + 1.35665i 0.146772 + 0.989170i $$0.453112\pi$$
−0.930033 + 0.367477i $$0.880222\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 8.00000 0.619059 0.309529 0.950890i $$-0.399829\pi$$
0.309529 + 0.950890i $$0.399829\pi$$
$$168$$ 0 0
$$169$$ 12.0000 0.923077
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 11.0000 19.0526i 0.836315 1.44854i −0.0566411 0.998395i $$-0.518039\pi$$
0.892956 0.450145i $$-0.148628\pi$$
$$174$$ 0 0
$$175$$ 22.0000 + 19.0526i 1.66304 + 1.44024i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$180$$ 0 0
$$181$$ 25.0000 1.85824 0.929118 0.369784i $$-0.120568\pi$$
0.929118 + 0.369784i $$0.120568\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −6.00000 10.3923i −0.441129 0.764057i
$$186$$ 0 0
$$187$$ −6.00000 + 10.3923i −0.438763 + 0.759961i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$192$$ 0 0
$$193$$ 0.500000 + 0.866025i 0.0359908 + 0.0623379i 0.883460 0.468507i $$-0.155208\pi$$
−0.847469 + 0.530845i $$0.821875\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −18.0000 −1.28245 −0.641223 0.767354i $$-0.721573\pi$$
−0.641223 + 0.767354i $$0.721573\pi$$
$$198$$ 0 0
$$199$$ −10.0000 17.3205i −0.708881 1.22782i −0.965272 0.261245i $$-0.915867\pi$$
0.256391 0.966573i $$-0.417466\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ −12.0000 + 20.7846i −0.838116 + 1.45166i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −6.00000 −0.415029
$$210$$ 0 0
$$211$$ 12.0000 0.826114 0.413057 0.910705i $$-0.364461\pi$$
0.413057 + 0.910705i $$0.364461\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −10.0000 + 17.3205i −0.681994 + 1.18125i
$$216$$ 0 0
$$217$$ −6.00000 5.19615i −0.407307 0.352738i
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 5.00000 + 8.66025i 0.336336 + 0.582552i
$$222$$ 0 0
$$223$$ 16.0000 1.07144 0.535720 0.844396i $$-0.320040\pi$$
0.535720 + 0.844396i $$0.320040\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 11.0000 + 19.0526i 0.730096 + 1.26456i 0.956842 + 0.290609i $$0.0938578\pi$$
−0.226746 + 0.973954i $$0.572809\pi$$
$$228$$ 0 0
$$229$$ 5.50000 9.52628i 0.363450 0.629514i −0.625076 0.780564i $$-0.714932\pi$$
0.988526 + 0.151050i $$0.0482653\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −4.00000 + 6.92820i −0.262049 + 0.453882i −0.966786 0.255586i $$-0.917731\pi$$
0.704737 + 0.709468i $$0.251065\pi$$
$$234$$ 0 0
$$235$$ −8.00000 13.8564i −0.521862 0.903892i
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −2.00000 −0.129369 −0.0646846 0.997906i $$-0.520604\pi$$
−0.0646846 + 0.997906i $$0.520604\pi$$
$$240$$ 0 0
$$241$$ −5.00000 8.66025i −0.322078 0.557856i 0.658838 0.752285i $$-0.271048\pi$$
−0.980917 + 0.194429i $$0.937715\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 4.00000 + 27.7128i 0.255551 + 1.77051i
$$246$$ 0 0
$$247$$ −2.50000 + 4.33013i −0.159071 + 0.275519i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 14.0000 0.883672 0.441836 0.897096i $$-0.354327\pi$$
0.441836 + 0.897096i $$0.354327\pi$$
$$252$$ 0 0
$$253$$ −36.0000 −2.26330
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −6.00000 + 10.3923i −0.374270 + 0.648254i −0.990217 0.139533i $$-0.955440\pi$$
0.615948 + 0.787787i $$0.288773\pi$$
$$258$$ 0 0
$$259$$ 1.50000 7.79423i 0.0932055 0.484310i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$264$$ 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
$$271$$ −8.00000 + 13.8564i −0.485965 + 0.841717i −0.999870 0.0161307i $$-0.994865\pi$$
0.513905 + 0.857847i $$0.328199\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 33.0000 57.1577i 1.98997 3.44674i
$$276$$ 0 0
$$277$$ −0.500000 0.866025i −0.0300421 0.0520344i 0.850613 0.525792i $$-0.176231\pi$$
−0.880656 + 0.473757i $$0.842897\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −6.00000 −0.357930 −0.178965 0.983855i $$-0.557275\pi$$
−0.178965 + 0.983855i $$0.557275\pi$$
$$282$$ 0 0
$$283$$ 5.50000 + 9.52628i 0.326941 + 0.566279i 0.981903 0.189383i $$-0.0606488\pi$$
−0.654962 + 0.755662i $$0.727315\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −15.0000 + 5.19615i −0.885422 + 0.306719i
$$288$$ 0 0
$$289$$ 6.50000 11.2583i 0.382353 0.662255i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 12.0000 0.701047 0.350524 0.936554i $$-0.386004\pi$$
0.350524 + 0.936554i $$0.386004\pi$$
$$294$$ 0 0
$$295$$ 24.0000 1.39733
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −15.0000 + 25.9808i −0.867472 + 1.50251i
$$300$$ 0 0
$$301$$ −12.5000 + 4.33013i −0.720488 + 0.249584i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 4.00000 + 6.92820i 0.229039 + 0.396708i
$$306$$ 0 0
$$307$$ 11.0000 0.627803 0.313902 0.949456i $$-0.398364\pi$$
0.313902 + 0.949456i $$0.398364\pi$$
$$308$$ 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
$$313$$ −15.5000 + 26.8468i −0.876112 + 1.51747i −0.0205381 + 0.999789i $$0.506538\pi$$
−0.855574 + 0.517681i $$0.826795\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −10.0000 + 17.3205i −0.561656 + 0.972817i 0.435696 + 0.900094i $$0.356502\pi$$
−0.997352 + 0.0727229i $$0.976831\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −2.00000 −0.111283
$$324$$ 0 0
$$325$$ −27.5000 47.6314i −1.52543 2.64211i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 2.00000 10.3923i 0.110264 0.572946i
$$330$$ 0 0
$$331$$ 2.50000 4.33013i 0.137412 0.238005i −0.789104 0.614260i $$-0.789455\pi$$
0.926516 + 0.376254i $$0.122788\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 28.0000 1.52980
$$336$$ 0 0
$$337$$ 1.00000 0.0544735 0.0272367 0.999629i $$-0.491329\pi$$
0.0272367 + 0.999629i $$0.491329\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −9.00000 + 15.5885i −0.487377 + 0.844162i
$$342$$ 0 0
$$343$$ −10.0000 + 15.5885i −0.539949 + 0.841698i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −11.0000 19.0526i −0.590511 1.02279i −0.994164 0.107883i $$-0.965593\pi$$
0.403653 0.914912i $$-0.367740\pi$$
$$348$$ 0 0
$$349$$ 26.0000 1.39175 0.695874 0.718164i $$-0.255017\pi$$
0.695874 + 0.718164i $$0.255017\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −2.00000 3.46410i −0.106449 0.184376i 0.807880 0.589347i $$-0.200615\pi$$
−0.914329 + 0.404971i $$0.867282\pi$$
$$354$$ 0 0
$$355$$ 32.0000 55.4256i 1.69838 2.94169i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −12.0000 + 20.7846i −0.633336 + 1.09697i 0.353529 + 0.935423i $$0.384981\pi$$
−0.986865 + 0.161546i $$0.948352\pi$$
$$360$$ 0 0
$$361$$ 9.00000 + 15.5885i 0.473684 + 0.820445i
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −12.0000 −0.628109
$$366$$ 0 0
$$367$$ −13.5000 23.3827i −0.704694 1.22057i −0.966802 0.255528i $$-0.917751\pi$$
0.262108 0.965039i $$-0.415582\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 12.0000 + 10.3923i 0.623009 + 0.539542i
$$372$$ 0 0
$$373$$ 14.5000 25.1147i 0.750782 1.30039i −0.196663 0.980471i $$-0.563010\pi$$
0.947444 0.319921i $$-0.103656\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 27.0000 1.38690 0.693448 0.720506i $$-0.256091\pi$$
0.693448 + 0.720506i $$0.256091\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 13.0000 22.5167i 0.664269 1.15055i −0.315214 0.949021i $$-0.602076\pi$$
0.979483 0.201527i $$-0.0645904\pi$$
$$384$$ 0 0
$$385$$ 60.0000 20.7846i 3.05788 1.05928i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −2.00000 3.46410i −0.101404 0.175637i 0.810859 0.585241i $$-0.199000\pi$$
−0.912263 + 0.409604i $$0.865667\pi$$
$$390$$ 0 0
$$391$$ −12.0000 −0.606866
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −22.0000 38.1051i −1.10694 1.91728i
$$396$$ 0 0
$$397$$ 10.5000 18.1865i 0.526980 0.912756i −0.472526 0.881317i $$-0.656658\pi$$
0.999506 0.0314391i $$-0.0100090\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −1.00000 + 1.73205i −0.0499376 + 0.0864945i −0.889914 0.456129i $$-0.849236\pi$$
0.839976 + 0.542623i $$0.182569\pi$$
$$402$$ 0 0
$$403$$ 7.50000 + 12.9904i 0.373602 + 0.647097i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −18.0000 −0.892227
$$408$$ 0 0
$$409$$ −6.50000 11.2583i −0.321404 0.556689i 0.659374 0.751815i $$-0.270822\pi$$
−0.980778 + 0.195127i $$0.937488\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 12.0000 + 10.3923i 0.590481 + 0.511372i
$$414$$ 0 0
$$415$$ 24.0000 41.5692i 1.17811 2.04055i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 26.0000 1.27018 0.635092 0.772437i $$-0.280962\pi$$
0.635092 + 0.772437i $$0.280962\pi$$
$$420$$ 0 0
$$421$$ 17.0000 0.828529 0.414265 0.910156i $$-0.364039\pi$$
0.414265 + 0.910156i $$0.364039\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 11.0000 19.0526i 0.533578 0.924185i
$$426$$ 0 0
$$427$$ −1.00000 + 5.19615i −0.0483934 + 0.251459i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$432$$ 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
$$437$$ −3.00000 5.19615i −0.143509 0.248566i
$$438$$ 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
$$443$$ −13.0000 + 22.5167i −0.617649 + 1.06980i 0.372265 + 0.928126i $$0.378581\pi$$
−0.989914 + 0.141672i $$0.954752\pi$$
$$444$$ 0 0
$$445$$ 8.00000 + 13.8564i 0.379236 + 0.656857i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −36.0000 −1.69895 −0.849473 0.527633i $$-0.823080\pi$$
−0.849473 + 0.527633i $$0.823080\pi$$
$$450$$ 0 0
$$451$$ 18.0000 + 31.1769i 0.847587 + 1.46806i
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 10.0000 51.9615i 0.468807 2.43599i
$$456$$ 0 0
$$457$$ −12.5000 + 21.6506i −0.584725 + 1.01277i 0.410184 + 0.912003i $$0.365464\pi$$
−0.994910 + 0.100771i $$0.967869\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 4.00000 0.186299 0.0931493 0.995652i $$-0.470307\pi$$
0.0931493 + 0.995652i $$0.470307\pi$$
$$462$$ 0 0
$$463$$ −5.00000 −0.232370 −0.116185 0.993228i $$-0.537067\pi$$
−0.116185 + 0.993228i $$0.537067\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 4.00000 6.92820i 0.185098 0.320599i −0.758512 0.651660i $$-0.774073\pi$$
0.943610 + 0.331061i $$0.107406\pi$$
$$468$$ 0 0
$$469$$ 14.0000 + 12.1244i 0.646460 + 0.559851i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 15.0000 + 25.9808i 0.689701 + 1.19460i
$$474$$ 0 0
$$475$$ 11.0000 0.504715
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 1.00000 + 1.73205i 0.0456912 + 0.0791394i 0.887967 0.459908i $$-0.152118\pi$$
−0.842275 + 0.539048i $$0.818784\pi$$
$$480$$ 0 0
$$481$$ −7.50000 + 12.9904i −0.341971 + 0.592310i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 12.0000 20.7846i 0.544892 0.943781i
$$486$$ 0 0
$$487$$ 0.500000 + 0.866025i 0.0226572 + 0.0392434i 0.877132 0.480250i $$-0.159454\pi$$
−0.854475 + 0.519493i $$0.826121\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −8.00000 −0.361035 −0.180517 0.983572i $$-0.557777\pi$$
−0.180517 + 0.983572i $$0.557777\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 40.0000 13.8564i 1.79425 0.621545i
$$498$$ 0 0
$$499$$ −14.5000 + 25.1147i −0.649109 + 1.12429i 0.334227 + 0.942493i $$0.391525\pi$$
−0.983336 + 0.181797i $$0.941809\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −18.0000 −0.802580 −0.401290 0.915951i $$-0.631438\pi$$
−0.401290 + 0.915951i $$0.631438\pi$$
$$504$$ 0 0
$$505$$ −8.00000 −0.355995
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −12.0000 + 20.7846i −0.531891 + 0.921262i 0.467416 + 0.884037i $$0.345185\pi$$
−0.999307 + 0.0372243i $$0.988148\pi$$
$$510$$ 0 0
$$511$$ −6.00000 5.19615i −0.265424 0.229864i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 22.0000 + 38.1051i 0.969436 + 1.67911i
$$516$$ 0 0
$$517$$ −24.0000 −1.05552
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 12.0000 + 20.7846i 0.525730 + 0.910590i 0.999551 + 0.0299693i $$0.00954094\pi$$
−0.473821 + 0.880621i $$0.657126\pi$$
$$522$$ 0 0
$$523$$ 8.50000 14.7224i 0.371679 0.643767i −0.618145 0.786064i $$-0.712116\pi$$
0.989824 + 0.142297i $$0.0454489\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −3.00000 + 5.19615i −0.130682 + 0.226348i
$$528$$ 0 0
$$529$$ −6.50000 11.2583i −0.282609 0.489493i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 30.0000 1.29944
$$534$$ 0 0
$$535$$ 20.0000 + 34.6410i 0.864675 + 1.49766i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 39.0000 + 15.5885i 1.67985 + 0.671442i
$$540$$ 0 0
$$541$$ −18.5000 + 32.0429i −0.795377 + 1.37763i 0.127222 + 0.991874i $$0.459394\pi$$
−0.922599 + 0.385759i $$0.873939\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −60.0000 −2.57012
$$546$$ 0 0
$$547$$ 28.0000 1.19719 0.598597 0.801050i $$-0.295725\pi$$
0.598597 + 0.801050i $$0.295725\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 5.50000 28.5788i 0.233884 1.21530i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −3.00000 5.19615i −0.127114 0.220168i 0.795443 0.606028i $$-0.207238\pi$$
−0.922557 + 0.385860i $$0.873905\pi$$
$$558$$ 0 0
$$559$$ 25.0000 1.05739
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 12.0000 + 20.7846i 0.505740 + 0.875967i 0.999978 + 0.00664037i $$0.00211371\pi$$
−0.494238 + 0.869326i $$0.664553\pi$$
$$564$$ 0 0
$$565$$ −32.0000 + 55.4256i −1.34625 + 2.33177i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 9.00000 15.5885i 0.377300 0.653502i −0.613369 0.789797i $$-0.710186\pi$$
0.990668 + 0.136295i $$0.0435194\pi$$
$$570$$ 0 0
$$571$$ −14.5000 25.1147i −0.606806 1.05102i −0.991763 0.128085i $$-0.959117\pi$$
0.384957 0.922934i $$-0.374216\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 66.0000 2.75239
$$576$$ 0 0
$$577$$ −11.5000 19.9186i −0.478751 0.829222i 0.520952 0.853586i $$-0.325577\pi$$
−0.999703 + 0.0243645i $$0.992244\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 30.0000 10.3923i 1.24461 0.431145i
$$582$$ 0 0
$$583$$ 18.0000 31.1769i 0.745484 1.29122i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −40.0000 −1.65098 −0.825488 0.564419i $$-0.809100\pi$$
−0.825488 + 0.564419i $$0.809100\pi$$
$$588$$ 0 0
$$589$$ −3.00000 −0.123613
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −13.0000 + 22.5167i −0.533846 + 0.924648i 0.465372 + 0.885115i $$0.345920\pi$$
−0.999218 + 0.0395334i $$0.987413\pi$$
$$594$$ 0 0
$$595$$ 20.0000 6.92820i 0.819920 0.284029i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 10.0000 + 17.3205i 0.408589 + 0.707697i 0.994732 0.102511i $$-0.0326876\pi$$
−0.586143 + 0.810208i $$0.699354\pi$$
$$600$$ 0 0
$$601$$ −21.0000 −0.856608 −0.428304 0.903635i $$-0.640889\pi$$
−0.428304 + 0.903635i $$0.640889\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −50.0000 86.6025i −2.03279 3.52089i
$$606$$ 0 0
$$607$$ 2.50000 4.33013i 0.101472 0.175754i −0.810819 0.585296i $$-0.800978\pi$$
0.912291 + 0.409542i $$0.134311\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −10.0000 + 17.3205i −0.404557 + 0.700713i
$$612$$ 0 0
$$613$$ 23.0000 + 39.8372i 0.928961 + 1.60901i 0.785063 + 0.619416i $$0.212630\pi$$
0.143898 + 0.989593i $$0.454036\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 14.0000 0.563619 0.281809 0.959470i $$-0.409065\pi$$
0.281809 + 0.959470i $$0.409065\pi$$
$$618$$ 0 0
$$619$$ 12.5000 + 21.6506i 0.502417 + 0.870212i 0.999996 + 0.00279365i $$0.000889247\pi$$
−0.497579 + 0.867419i $$0.665777\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −2.00000 + 10.3923i −0.0801283 + 0.416359i
$$624$$ 0 0
$$625$$ −20.5000 + 35.5070i −0.820000 + 1.42028i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −6.00000 −0.239236
$$630$$ 0 0
$$631$$ 28.0000 1.11466 0.557331 0.830290i $$-0.311825\pi$$
0.557331 + 0.830290i $$0.311825\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 14.0000 24.2487i 0.555573 0.962281i
$$636$$ 0 0
$$637$$ 27.5000 21.6506i 1.08959 0.857829i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 19.0000 + 32.9090i 0.750455 + 1.29983i 0.947602 + 0.319452i $$0.103499\pi$$
−0.197148 + 0.980374i $$0.563168\pi$$
$$642$$ 0 0
$$643$$ −23.0000 −0.907031 −0.453516 0.891248i $$-0.649830\pi$$
−0.453516 + 0.891248i $$0.649830\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 5.00000 + 8.66025i 0.196570 + 0.340470i 0.947414 0.320010i $$-0.103686\pi$$
−0.750844 + 0.660480i $$0.770353\pi$$
$$648$$ 0 0
$$649$$ 18.0000 31.1769i 0.706562 1.22380i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 17.0000 29.4449i 0.665261 1.15227i −0.313953 0.949439i $$-0.601653\pi$$
0.979214 0.202828i $$-0.0650132\pi$$
$$654$$ 0 0
$$655$$ 12.0000 + 20.7846i 0.468879 + 0.812122i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −6.00000 −0.233727 −0.116863 0.993148i $$-0.537284\pi$$
−0.116863 + 0.993148i $$0.537284\pi$$
$$660$$ 0 0
$$661$$ −1.50000 2.59808i −0.0583432 0.101053i 0.835379 0.549675i $$-0.185248\pi$$
−0.893722 + 0.448622i $$0.851915\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 8.00000 + 6.92820i 0.310227 + 0.268664i
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 12.0000 0.463255
$$672$$ 0 0
$$673$$ −29.0000 −1.11787 −0.558934 0.829212i $$-0.688789\pi$$
−0.558934 + 0.829212i $$0.688789\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −6.00000 + 10.3923i −0.230599 + 0.399409i −0.957984 0.286820i $$-0.907402\pi$$
0.727386 + 0.686229i $$0.240735\pi$$
$$678$$ 0 0
$$679$$ 15.0000 5.19615i 0.575647 0.199410i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 9.00000 + 15.5885i 0.344375 + 0.596476i 0.985240 0.171178i $$-0.0547574\pi$$
−0.640865 + 0.767654i $$0.721424\pi$$
$$684$$ 0 0
$$685$$ 48.0000 1.83399
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −15.0000 25.9808i −0.571454 0.989788i
$$690$$ 0 0
$$691$$ −11.5000 + 19.9186i −0.437481 + 0.757739i −0.997494 0.0707446i $$-0.977462\pi$$
0.560014 + 0.828483i $$0.310796\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −10.0000 + 17.3205i −0.379322 + 0.657004i
$$696$$ 0 0
$$697$$ 6.00000 + 10.3923i 0.227266 + 0.393637i
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −22.0000 −0.830929 −0.415464 0.909610i $$-0.636381\pi$$
−0.415464 + 0.909610i $$0.636381\pi$$
$$702$$ 0 0
$$703$$ −1.50000 2.59808i −0.0565736 0.0979883i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −4.00000 3.46410i −0.150435 0.130281i
$$708$$ 0 0
$$709$$ 3.00000 5.19615i 0.112667 0.195146i −0.804178 0.594389i $$-0.797394\pi$$
0.916845 + 0.399244i $$0.130727\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −18.0000 −0.674105
$$714$$ 0 0
$$715$$ −120.000 −4.48775
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 15.0000 25.9808i 0.559406 0.968919i −0.438141 0.898906i $$-0.644363\pi$$
0.997546 0.0700124i $$-0.0223039\pi$$
$$720$$ 0 0
$$721$$ −5.50000 + 28.5788i −0.204831 + 1.06433i
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −41.0000 −1.52061 −0.760303 0.649569i $$-0.774949\pi$$
−0.760303 + 0.649569i $$0.774949\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 5.00000 + 8.66025i 0.184932 + 0.320311i
$$732$$ 0 0
$$733$$ −10.5000 + 18.1865i −0.387826 + 0.671735i −0.992157 0.124999i $$-0.960107\pi$$
0.604331 + 0.796734i $$0.293441\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 21.0000 36.3731i 0.773545 1.33982i
$$738$$ 0 0
$$739$$ 25.5000 + 44.1673i 0.938033 + 1.62472i 0.769135 + 0.639087i $$0.220687\pi$$
0.168898 + 0.985634i $$0.445979\pi$$
$$740$$ 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
$$745$$ −8.00000 13.8564i −0.293097 0.507659i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −5.00000 + 25.9808i −0.182696 + 0.949316i
$$750$$ 0 0
$$751$$ 3.50000 6.06218i 0.127717 0.221212i −0.795075 0.606511i $$-0.792568\pi$$
0.922792 + 0.385299i $$0.125902\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −32.0000 −1.16460
$$756$$ 0 0
$$757$$ −26.0000 −0.944986 −0.472493 0.881334i $$-0.656646\pi$$
−0.472493 + 0.881334i $$0.656646\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 25.0000 43.3013i 0.906249 1.56967i 0.0870179 0.996207i $$-0.472266\pi$$
0.819231 0.573463i $$-0.194400\pi$$
$$762$$ 0 0
$$763$$ −30.0000 25.9808i −1.08607 0.940567i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −15.0000 25.9808i −0.541619 0.938111i
$$768$$ 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 0.597540 0.801839i $$-0.296145\pi$$
−0.993183 + 0.116566i $$0.962811\pi$$
$$774$$ 0 0
$$775$$ 16.5000 28.5788i 0.592697 1.02658i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −3.00000 + 5.19615i −0.107486 + 0.186171i
$$780$$ 0 0
$$781$$ −48.0000 83.1384i −1.71758 2.97493i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 40.0000 1.42766
$$786$$ 0 0
$$787$$ −16.0000 27.7128i −0.570338 0.987855i −0.996531 0.0832226i $$-0.973479\pi$$
0.426193 0.904632i $$-0.359855\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −40.0000 + 13.8564i −1.42224 + 0.492677i
$$792$$ 0 0
$$793$$ 5.00000 8.66025i 0.177555 0.307535i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 46.0000 1.62940 0.814702 0.579880i $$-0.196901\pi$$
0.814702 + 0.579880i $$0.196901\pi$$
$$798$$ 0 0
$$799$$ −8.00000 −0.283020
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ −9.00000 +