# Properties

 Label 2268.2.x.j.377.1 Level $2268$ Weight $2$ Character 2268.377 Analytic conductor $18.110$ Analytic rank $0$ Dimension $8$ CM no Inner twists $8$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2268 = 2^{2} \cdot 3^{4} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2268.x (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$18.1100711784$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\zeta_{24})$$ Defining polynomial: $$x^{8} - x^{4} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$2^{2}\cdot 3^{4}$$ Twist minimal: no (minimal twist has level 756) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 377.1 Root $$-0.258819 + 0.965926i$$ of defining polynomial Character $$\chi$$ $$=$$ 2268.377 Dual form 2268.2.x.j.1889.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.866025 + 1.50000i) q^{5} +(-1.62132 + 2.09077i) q^{7} +O(q^{10})$$ $$q+(-0.866025 + 1.50000i) q^{5} +(-1.62132 + 2.09077i) q^{7} +(-3.67423 + 2.12132i) q^{11} +(-2.12132 - 1.22474i) q^{13} +1.73205 q^{17} -2.44949i q^{19} +(7.34847 + 4.24264i) q^{23} +(1.00000 + 1.73205i) q^{25} +(-3.67423 + 2.12132i) q^{29} +(-6.36396 - 3.67423i) q^{31} +(-1.73205 - 4.24264i) q^{35} +1.00000 q^{37} +(0.866025 - 1.50000i) q^{41} +(-3.50000 - 6.06218i) q^{43} +(-6.06218 - 10.5000i) q^{47} +(-1.74264 - 6.77962i) q^{49} -7.34847i q^{55} +(-4.33013 + 7.50000i) q^{59} +(-2.12132 + 1.22474i) q^{61} +(3.67423 - 2.12132i) q^{65} +(5.00000 - 8.66025i) q^{67} -8.48528i q^{71} -9.79796i q^{73} +(1.52192 - 11.1213i) q^{77} +(-2.50000 - 4.33013i) q^{79} +(6.06218 + 10.5000i) q^{83} +(-1.50000 + 2.59808i) q^{85} +10.3923 q^{89} +(6.00000 - 2.44949i) q^{91} +(3.67423 + 2.12132i) q^{95} +(2.12132 - 1.22474i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q + 4q^{7} + O(q^{10})$$ $$8q + 4q^{7} + 8q^{25} + 8q^{37} - 28q^{43} + 20q^{49} + 40q^{67} - 20q^{79} - 12q^{85} + 48q^{91} + O(q^{100})$$

## Character values

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

 $$n$$ $$325$$ $$1135$$ $$1541$$ $$\chi(n)$$ $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$

## 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
$$5$$ −0.866025 + 1.50000i −0.387298 + 0.670820i −0.992085 0.125567i $$-0.959925\pi$$
0.604787 + 0.796387i $$0.293258\pi$$
$$6$$ 0 0
$$7$$ −1.62132 + 2.09077i −0.612801 + 0.790237i
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −3.67423 + 2.12132i −1.10782 + 0.639602i −0.938265 0.345918i $$-0.887568\pi$$
−0.169559 + 0.985520i $$0.554234\pi$$
$$12$$ 0 0
$$13$$ −2.12132 1.22474i −0.588348 0.339683i 0.176096 0.984373i $$-0.443653\pi$$
−0.764444 + 0.644690i $$0.776986\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 1.73205 0.420084 0.210042 0.977692i $$-0.432640\pi$$
0.210042 + 0.977692i $$0.432640\pi$$
$$18$$ 0 0
$$19$$ 2.44949i 0.561951i −0.959715 0.280976i $$-0.909342\pi$$
0.959715 0.280976i $$-0.0906580\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 7.34847 + 4.24264i 1.53226 + 0.884652i 0.999257 + 0.0385394i $$0.0122705\pi$$
0.533005 + 0.846112i $$0.321063\pi$$
$$24$$ 0 0
$$25$$ 1.00000 + 1.73205i 0.200000 + 0.346410i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −3.67423 + 2.12132i −0.682288 + 0.393919i −0.800717 0.599043i $$-0.795548\pi$$
0.118428 + 0.992963i $$0.462214\pi$$
$$30$$ 0 0
$$31$$ −6.36396 3.67423i −1.14300 0.659912i −0.195829 0.980638i $$-0.562740\pi$$
−0.947172 + 0.320726i $$0.896073\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −1.73205 4.24264i −0.292770 0.717137i
$$36$$ 0 0
$$37$$ 1.00000 0.164399 0.0821995 0.996616i $$-0.473806\pi$$
0.0821995 + 0.996616i $$0.473806\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 0.866025 1.50000i 0.135250 0.234261i −0.790443 0.612536i $$-0.790149\pi$$
0.925693 + 0.378275i $$0.123483\pi$$
$$42$$ 0 0
$$43$$ −3.50000 6.06218i −0.533745 0.924473i −0.999223 0.0394140i $$-0.987451\pi$$
0.465478 0.885059i $$-0.345882\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −6.06218 10.5000i −0.884260 1.53158i −0.846560 0.532293i $$-0.821330\pi$$
−0.0376995 0.999289i $$-0.512003\pi$$
$$48$$ 0 0
$$49$$ −1.74264 6.77962i −0.248949 0.968517i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$54$$ 0 0
$$55$$ 7.34847i 0.990867i
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −4.33013 + 7.50000i −0.563735 + 0.976417i 0.433432 + 0.901186i $$0.357303\pi$$
−0.997166 + 0.0752304i $$0.976031\pi$$
$$60$$ 0 0
$$61$$ −2.12132 + 1.22474i −0.271607 + 0.156813i −0.629618 0.776905i $$-0.716789\pi$$
0.358011 + 0.933718i $$0.383455\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 3.67423 2.12132i 0.455733 0.263117i
$$66$$ 0 0
$$67$$ 5.00000 8.66025i 0.610847 1.05802i −0.380251 0.924883i $$-0.624162\pi$$
0.991098 0.133135i $$-0.0425044\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 8.48528i 1.00702i −0.863990 0.503509i $$-0.832042\pi$$
0.863990 0.503509i $$-0.167958\pi$$
$$72$$ 0 0
$$73$$ 9.79796i 1.14676i −0.819288 0.573382i $$-0.805631\pi$$
0.819288 0.573382i $$-0.194369\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 1.52192 11.1213i 0.173439 1.26739i
$$78$$ 0 0
$$79$$ −2.50000 4.33013i −0.281272 0.487177i 0.690426 0.723403i $$-0.257423\pi$$
−0.971698 + 0.236225i $$0.924090\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 6.06218 + 10.5000i 0.665410 + 1.15252i 0.979174 + 0.203024i $$0.0650768\pi$$
−0.313763 + 0.949501i $$0.601590\pi$$
$$84$$ 0 0
$$85$$ −1.50000 + 2.59808i −0.162698 + 0.281801i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 10.3923 1.10158 0.550791 0.834643i $$-0.314326\pi$$
0.550791 + 0.834643i $$0.314326\pi$$
$$90$$ 0 0
$$91$$ 6.00000 2.44949i 0.628971 0.256776i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 3.67423 + 2.12132i 0.376969 + 0.217643i
$$96$$ 0 0
$$97$$ 2.12132 1.22474i 0.215387 0.124354i −0.388425 0.921480i $$-0.626981\pi$$
0.603813 + 0.797126i $$0.293647\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 5.19615 + 9.00000i 0.517036 + 0.895533i 0.999804 + 0.0197851i $$0.00629819\pi$$
−0.482768 + 0.875748i $$0.660368\pi$$
$$102$$ 0 0
$$103$$ −16.9706 9.79796i −1.67216 0.965422i −0.966426 0.256943i $$-0.917285\pi$$
−0.705733 0.708478i $$-0.749382\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 8.48528i 0.820303i 0.912017 + 0.410152i $$0.134524\pi$$
−0.912017 + 0.410152i $$0.865476\pi$$
$$108$$ 0 0
$$109$$ 13.0000 1.24517 0.622587 0.782551i $$-0.286082\pi$$
0.622587 + 0.782551i $$0.286082\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −11.0227 6.36396i −1.03693 0.598671i −0.117967 0.993018i $$-0.537638\pi$$
−0.918962 + 0.394346i $$0.870971\pi$$
$$114$$ 0 0
$$115$$ −12.7279 + 7.34847i −1.18688 + 0.685248i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −2.80821 + 3.62132i −0.257428 + 0.331966i
$$120$$ 0 0
$$121$$ 3.50000 6.06218i 0.318182 0.551107i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −12.1244 −1.08444
$$126$$ 0 0
$$127$$ −13.0000 −1.15356 −0.576782 0.816898i $$-0.695692\pi$$
−0.576782 + 0.816898i $$0.695692\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −5.19615 + 9.00000i −0.453990 + 0.786334i −0.998630 0.0523366i $$-0.983333\pi$$
0.544640 + 0.838670i $$0.316666\pi$$
$$132$$ 0 0
$$133$$ 5.12132 + 3.97141i 0.444075 + 0.344365i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 18.3712 10.6066i 1.56956 0.906183i 0.573335 0.819321i $$-0.305649\pi$$
0.996220 0.0868620i $$-0.0276839\pi$$
$$138$$ 0 0
$$139$$ −10.6066 6.12372i −0.899640 0.519408i −0.0225568 0.999746i $$-0.507181\pi$$
−0.877083 + 0.480338i $$0.840514\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 10.3923 0.869048
$$144$$ 0 0
$$145$$ 7.34847i 0.610257i
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −11.0227 6.36396i −0.903015 0.521356i −0.0248379 0.999691i $$-0.507907\pi$$
−0.878177 + 0.478335i $$0.841240\pi$$
$$150$$ 0 0
$$151$$ 2.50000 + 4.33013i 0.203447 + 0.352381i 0.949637 0.313353i $$-0.101452\pi$$
−0.746190 + 0.665733i $$0.768119\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 11.0227 6.36396i 0.885365 0.511166i
$$156$$ 0 0
$$157$$ −6.36396 3.67423i −0.507899 0.293236i 0.224070 0.974573i $$-0.428065\pi$$
−0.731970 + 0.681337i $$0.761399\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −20.7846 + 8.48528i −1.63806 + 0.668734i
$$162$$ 0 0
$$163$$ −1.00000 −0.0783260 −0.0391630 0.999233i $$-0.512469\pi$$
−0.0391630 + 0.999233i $$0.512469\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 9.52628 16.5000i 0.737166 1.27681i −0.216601 0.976260i $$-0.569497\pi$$
0.953767 0.300548i $$-0.0971696\pi$$
$$168$$ 0 0
$$169$$ −3.50000 6.06218i −0.269231 0.466321i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −10.3923 18.0000i −0.790112 1.36851i −0.925897 0.377776i $$-0.876689\pi$$
0.135785 0.990738i $$-0.456644\pi$$
$$174$$ 0 0
$$175$$ −5.24264 0.717439i −0.396306 0.0542333i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 4.24264i 0.317110i 0.987350 + 0.158555i $$0.0506835\pi$$
−0.987350 + 0.158555i $$0.949317\pi$$
$$180$$ 0 0
$$181$$ 4.89898i 0.364138i −0.983286 0.182069i $$-0.941721\pi$$
0.983286 0.182069i $$-0.0582795\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −0.866025 + 1.50000i −0.0636715 + 0.110282i
$$186$$ 0 0
$$187$$ −6.36396 + 3.67423i −0.465379 + 0.268687i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −7.34847 + 4.24264i −0.531717 + 0.306987i −0.741715 0.670715i $$-0.765987\pi$$
0.209999 + 0.977702i $$0.432654\pi$$
$$192$$ 0 0
$$193$$ −3.50000 + 6.06218i −0.251936 + 0.436365i −0.964059 0.265689i $$-0.914400\pi$$
0.712123 + 0.702055i $$0.247734\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 21.2132i 1.51138i 0.654931 + 0.755689i $$0.272698\pi$$
−0.654931 + 0.755689i $$0.727302\pi$$
$$198$$ 0 0
$$199$$ 9.79796i 0.694559i 0.937762 + 0.347279i $$0.112894\pi$$
−0.937762 + 0.347279i $$0.887106\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 1.52192 11.1213i 0.106818 0.780564i
$$204$$ 0 0
$$205$$ 1.50000 + 2.59808i 0.104765 + 0.181458i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 5.19615 + 9.00000i 0.359425 + 0.622543i
$$210$$ 0 0
$$211$$ 4.00000 6.92820i 0.275371 0.476957i −0.694857 0.719148i $$-0.744533\pi$$
0.970229 + 0.242190i $$0.0778659\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 12.1244 0.826874
$$216$$ 0 0
$$217$$ 18.0000 7.34847i 1.22192 0.498847i
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −3.67423 2.12132i −0.247156 0.142695i
$$222$$ 0 0
$$223$$ −19.0919 + 11.0227i −1.27849 + 0.738135i −0.976570 0.215199i $$-0.930960\pi$$
−0.301917 + 0.953334i $$0.597627\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$228$$ 0 0
$$229$$ 12.7279 + 7.34847i 0.841085 + 0.485601i 0.857633 0.514263i $$-0.171934\pi$$
−0.0165480 + 0.999863i $$0.505268\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 4.24264i 0.277945i −0.990296 0.138972i $$-0.955620\pi$$
0.990296 0.138972i $$-0.0443799\pi$$
$$234$$ 0 0
$$235$$ 21.0000 1.36989
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 18.3712 + 10.6066i 1.18833 + 0.686084i 0.957927 0.287011i $$-0.0926616\pi$$
0.230405 + 0.973095i $$0.425995\pi$$
$$240$$ 0 0
$$241$$ 23.3345 13.4722i 1.50311 0.867820i 0.503115 0.864219i $$-0.332187\pi$$
0.999994 0.00360098i $$-0.00114623\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 11.6786 + 3.25736i 0.746118 + 0.208105i
$$246$$ 0 0
$$247$$ −3.00000 + 5.19615i −0.190885 + 0.330623i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −19.0526 −1.20259 −0.601293 0.799028i $$-0.705348\pi$$
−0.601293 + 0.799028i $$0.705348\pi$$
$$252$$ 0 0
$$253$$ −36.0000 −2.26330
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −5.19615 + 9.00000i −0.324127 + 0.561405i −0.981335 0.192304i $$-0.938404\pi$$
0.657208 + 0.753709i $$0.271737\pi$$
$$258$$ 0 0
$$259$$ −1.62132 + 2.09077i −0.100744 + 0.129914i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −18.3712 + 10.6066i −1.13282 + 0.654031i −0.944641 0.328105i $$-0.893590\pi$$
−0.188174 + 0.982136i $$0.560257\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −1.73205 −0.105605 −0.0528025 0.998605i $$-0.516815\pi$$
−0.0528025 + 0.998605i $$0.516815\pi$$
$$270$$ 0 0
$$271$$ 4.89898i 0.297592i −0.988868 0.148796i $$-0.952460\pi$$
0.988868 0.148796i $$-0.0475397\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −7.34847 4.24264i −0.443129 0.255841i
$$276$$ 0 0
$$277$$ 3.50000 + 6.06218i 0.210295 + 0.364241i 0.951807 0.306699i $$-0.0992243\pi$$
−0.741512 + 0.670940i $$0.765891\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −7.34847 + 4.24264i −0.438373 + 0.253095i −0.702907 0.711282i $$-0.748115\pi$$
0.264534 + 0.964376i $$0.414782\pi$$
$$282$$ 0 0
$$283$$ 6.36396 + 3.67423i 0.378298 + 0.218411i 0.677078 0.735912i $$-0.263246\pi$$
−0.298779 + 0.954322i $$0.596579\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 1.73205 + 4.24264i 0.102240 + 0.250435i
$$288$$ 0 0
$$289$$ −14.0000 −0.823529
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −4.33013 + 7.50000i −0.252969 + 0.438155i −0.964342 0.264660i $$-0.914740\pi$$
0.711373 + 0.702815i $$0.248074\pi$$
$$294$$ 0 0
$$295$$ −7.50000 12.9904i −0.436667 0.756329i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −10.3923 18.0000i −0.601003 1.04097i
$$300$$ 0 0
$$301$$ 18.3492 + 2.51104i 1.05763 + 0.144734i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 4.24264i 0.242933i
$$306$$ 0 0
$$307$$ 29.3939i 1.67760i 0.544442 + 0.838799i $$0.316741\pi$$
−0.544442 + 0.838799i $$0.683259\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −11.2583 + 19.5000i −0.638401 + 1.10574i 0.347382 + 0.937724i $$0.387071\pi$$
−0.985784 + 0.168020i $$0.946263\pi$$
$$312$$ 0 0
$$313$$ 21.2132 12.2474i 1.19904 0.692267i 0.238700 0.971093i $$-0.423279\pi$$
0.960341 + 0.278827i $$0.0899455\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$318$$ 0 0
$$319$$ 9.00000 15.5885i 0.503903 0.872786i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 4.24264i 0.236067i
$$324$$ 0 0
$$325$$ 4.89898i 0.271746i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 31.7818 + 4.34924i 1.75219 + 0.239781i
$$330$$ 0 0
$$331$$ −6.50000 11.2583i −0.357272 0.618814i 0.630232 0.776407i $$-0.282960\pi$$
−0.987504 + 0.157593i $$0.949627\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 8.66025 + 15.0000i 0.473160 + 0.819538i
$$336$$ 0 0
$$337$$ −12.5000 + 21.6506i −0.680918 + 1.17939i 0.293783 + 0.955872i $$0.405086\pi$$
−0.974701 + 0.223513i $$0.928247\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 31.1769 1.68832
$$342$$ 0 0
$$343$$ 17.0000 + 7.34847i 0.917914 + 0.396780i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −18.3712 10.6066i −0.986216 0.569392i −0.0820751 0.996626i $$-0.526155\pi$$
−0.904141 + 0.427234i $$0.859488\pi$$
$$348$$ 0 0
$$349$$ 16.9706 9.79796i 0.908413 0.524473i 0.0284931 0.999594i $$-0.490929\pi$$
0.879920 + 0.475121i $$0.157596\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −0.866025 1.50000i −0.0460939 0.0798369i 0.842058 0.539387i $$-0.181344\pi$$
−0.888152 + 0.459550i $$0.848011\pi$$
$$354$$ 0 0
$$355$$ 12.7279 + 7.34847i 0.675528 + 0.390016i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 33.9411i 1.79134i −0.444715 0.895672i $$-0.646695\pi$$
0.444715 0.895672i $$-0.353305\pi$$
$$360$$ 0 0
$$361$$ 13.0000 0.684211
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 14.6969 + 8.48528i 0.769273 + 0.444140i
$$366$$ 0 0
$$367$$ −4.24264 + 2.44949i −0.221464 + 0.127862i −0.606628 0.794986i $$-0.707478\pi$$
0.385164 + 0.922848i $$0.374145\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −5.50000 + 9.52628i −0.284779 + 0.493252i −0.972556 0.232671i $$-0.925254\pi$$
0.687776 + 0.725923i $$0.258587\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 10.3923 0.535231
$$378$$ 0 0
$$379$$ −35.0000 −1.79783 −0.898915 0.438124i $$-0.855643\pi$$
−0.898915 + 0.438124i $$0.855643\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −9.52628 + 16.5000i −0.486770 + 0.843111i −0.999884 0.0152097i $$-0.995158\pi$$
0.513114 + 0.858320i $$0.328492\pi$$
$$384$$ 0 0
$$385$$ 15.3640 + 11.9142i 0.783020 + 0.607205i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −25.7196 + 14.8492i −1.30404 + 0.752886i −0.981094 0.193532i $$-0.938006\pi$$
−0.322944 + 0.946418i $$0.604672\pi$$
$$390$$ 0 0
$$391$$ 12.7279 + 7.34847i 0.643679 + 0.371628i
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 8.66025 0.435745
$$396$$ 0 0
$$397$$ 29.3939i 1.47524i 0.675218 + 0.737618i $$0.264050\pi$$
−0.675218 + 0.737618i $$0.735950\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 7.34847 + 4.24264i 0.366965 + 0.211867i 0.672132 0.740432i $$-0.265379\pi$$
−0.305167 + 0.952299i $$0.598712\pi$$
$$402$$ 0 0
$$403$$ 9.00000 + 15.5885i 0.448322 + 0.776516i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −3.67423 + 2.12132i −0.182125 + 0.105150i
$$408$$ 0 0
$$409$$ 33.9411 + 19.5959i 1.67828 + 0.968956i 0.962757 + 0.270367i $$0.0871450\pi$$
0.715523 + 0.698589i $$0.246188\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −8.66025 21.2132i −0.426143 1.04383i
$$414$$ 0 0
$$415$$ −21.0000 −1.03085
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 14.7224 25.5000i 0.719238 1.24576i −0.242064 0.970260i $$-0.577824\pi$$
0.961302 0.275496i $$-0.0888422\pi$$
$$420$$ 0 0
$$421$$ −10.0000 17.3205i −0.487370 0.844150i 0.512524 0.858673i $$-0.328710\pi$$
−0.999895 + 0.0145228i $$0.995377\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 1.73205 + 3.00000i 0.0840168 + 0.145521i
$$426$$ 0 0
$$427$$ 0.878680 6.42090i 0.0425223 0.310729i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 16.9706i 0.817443i −0.912659 0.408722i $$-0.865975\pi$$
0.912659 0.408722i $$-0.134025\pi$$
$$432$$ 0 0
$$433$$ 22.0454i 1.05943i −0.848174 0.529717i $$-0.822298\pi$$
0.848174 0.529717i $$-0.177702\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 10.3923 18.0000i 0.497131 0.861057i
$$438$$ 0 0
$$439$$ −25.4558 + 14.6969i −1.21494 + 0.701447i −0.963832 0.266512i $$-0.914129\pi$$
−0.251110 + 0.967959i $$0.580795\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 11.0227 6.36396i 0.523704 0.302361i −0.214745 0.976670i $$-0.568892\pi$$
0.738449 + 0.674309i $$0.235559\pi$$
$$444$$ 0 0
$$445$$ −9.00000 + 15.5885i −0.426641 + 0.738964i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 21.2132i 1.00111i −0.865704 0.500556i $$-0.833129\pi$$
0.865704 0.500556i $$-0.166871\pi$$
$$450$$ 0 0
$$451$$ 7.34847i 0.346026i
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −1.52192 + 11.1213i −0.0713486 + 0.521376i
$$456$$ 0 0
$$457$$ 4.00000 + 6.92820i 0.187112 + 0.324088i 0.944286 0.329125i $$-0.106754\pi$$
−0.757174 + 0.653213i $$0.773421\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −14.7224 25.5000i −0.685692 1.18765i −0.973219 0.229881i $$-0.926166\pi$$
0.287527 0.957773i $$-0.407167\pi$$
$$462$$ 0 0
$$463$$ −14.5000 + 25.1147i −0.673872 + 1.16718i 0.302925 + 0.953014i $$0.402037\pi$$
−0.976797 + 0.214166i $$0.931297\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −20.7846 −0.961797 −0.480899 0.876776i $$-0.659689\pi$$
−0.480899 + 0.876776i $$0.659689\pi$$
$$468$$ 0 0
$$469$$ 10.0000 + 24.4949i 0.461757 + 1.13107i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 25.7196 + 14.8492i 1.18259 + 0.682769i
$$474$$ 0 0
$$475$$ 4.24264 2.44949i 0.194666 0.112390i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −19.9186 34.5000i −0.910103 1.57635i −0.813916 0.580982i $$-0.802669\pi$$
−0.0961869 0.995363i $$-0.530665\pi$$
$$480$$ 0 0
$$481$$ −2.12132 1.22474i −0.0967239 0.0558436i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 4.24264i 0.192648i
$$486$$ 0 0
$$487$$ 22.0000 0.996915 0.498458 0.866914i $$-0.333900\pi$$
0.498458 + 0.866914i $$0.333900\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −11.0227 6.36396i −0.497448 0.287202i 0.230211 0.973141i $$-0.426058\pi$$
−0.727659 + 0.685939i $$0.759392\pi$$
$$492$$ 0 0
$$493$$ −6.36396 + 3.67423i −0.286618 + 0.165479i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 17.7408 + 13.7574i 0.795782 + 0.617102i
$$498$$ 0 0
$$499$$ −9.50000 + 16.4545i −0.425278 + 0.736604i −0.996446 0.0842294i $$-0.973157\pi$$
0.571168 + 0.820833i $$0.306490\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −1.73205 −0.0772283 −0.0386142 0.999254i $$-0.512294\pi$$
−0.0386142 + 0.999254i $$0.512294\pi$$
$$504$$ 0 0
$$505$$ −18.0000 −0.800989
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −9.52628 + 16.5000i −0.422245 + 0.731350i −0.996159 0.0875661i $$-0.972091\pi$$
0.573914 + 0.818916i $$0.305424\pi$$
$$510$$ 0 0
$$511$$ 20.4853 + 15.8856i 0.906215 + 0.702739i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 29.3939 16.9706i 1.29525 0.747812i
$$516$$ 0 0
$$517$$ 44.5477 + 25.7196i 1.95921 + 1.13115i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −1.73205 −0.0758825 −0.0379413 0.999280i $$-0.512080\pi$$
−0.0379413 + 0.999280i $$0.512080\pi$$
$$522$$ 0 0
$$523$$ 31.8434i 1.39241i 0.717841 + 0.696207i $$0.245130\pi$$
−0.717841 + 0.696207i $$0.754870\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −11.0227 6.36396i −0.480157 0.277218i
$$528$$ 0 0
$$529$$ 24.5000 + 42.4352i 1.06522 + 1.84501i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −3.67423 + 2.12132i −0.159149 + 0.0918846i
$$534$$ 0 0
$$535$$ −12.7279 7.34847i −0.550276 0.317702i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 20.7846 + 21.2132i 0.895257 + 0.913717i
$$540$$ 0 0
$$541$$ 17.0000 0.730887 0.365444 0.930834i $$-0.380917\pi$$
0.365444 + 0.930834i $$0.380917\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −11.2583 + 19.5000i −0.482254 + 0.835288i
$$546$$ 0 0
$$547$$ −20.5000 35.5070i −0.876517 1.51817i −0.855138 0.518400i $$-0.826528\pi$$
−0.0213785 0.999771i $$-0.506805\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 5.19615 + 9.00000i 0.221364 + 0.383413i
$$552$$ 0 0
$$553$$ 13.1066 + 1.79360i 0.557349 + 0.0762715i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 8.48528i 0.359533i 0.983709 + 0.179766i $$0.0575342\pi$$
−0.983709 + 0.179766i $$0.942466\pi$$
$$558$$ 0 0
$$559$$ 17.1464i 0.725217i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 10.3923 18.0000i 0.437983 0.758610i −0.559550 0.828796i $$-0.689026\pi$$
0.997534 + 0.0701867i $$0.0223595\pi$$
$$564$$ 0 0
$$565$$ 19.0919 11.0227i 0.803202 0.463729i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −29.3939 + 16.9706i −1.23226 + 0.711443i −0.967500 0.252872i $$-0.918625\pi$$
−0.264756 + 0.964315i $$0.585291\pi$$
$$570$$ 0 0
$$571$$ 12.5000 21.6506i 0.523109 0.906051i −0.476530 0.879158i $$-0.658105\pi$$
0.999638 0.0268925i $$-0.00856117\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 16.9706i 0.707721i
$$576$$ 0 0
$$577$$ 19.5959i 0.815789i 0.913029 + 0.407894i $$0.133737\pi$$
−0.913029 + 0.407894i $$0.866263\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −31.7818 4.34924i −1.31853 0.180437i
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 20.7846 + 36.0000i 0.857873 + 1.48588i 0.873954 + 0.486008i $$0.161548\pi$$
−0.0160815 + 0.999871i $$0.505119\pi$$
$$588$$ 0 0
$$589$$ −9.00000 + 15.5885i −0.370839 + 0.642311i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 8.66025 0.355634 0.177817 0.984064i $$-0.443096\pi$$
0.177817 + 0.984064i $$0.443096\pi$$
$$594$$ 0 0
$$595$$ −3.00000 7.34847i −0.122988 0.301258i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 3.67423 + 2.12132i 0.150125 + 0.0866748i 0.573181 0.819429i $$-0.305709\pi$$
−0.423056 + 0.906104i $$0.639043\pi$$
$$600$$ 0 0
$$601$$ 19.0919 11.0227i 0.778774 0.449625i −0.0572215 0.998362i $$-0.518224\pi$$
0.835996 + 0.548736i $$0.184891\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 6.06218 + 10.5000i 0.246463 + 0.426886i
$$606$$ 0 0
$$607$$ 23.3345 + 13.4722i 0.947119 + 0.546819i 0.892185 0.451671i $$-0.149172\pi$$
0.0549343 + 0.998490i $$0.482505\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 29.6985i 1.20147i
$$612$$ 0 0
$$613$$ −4.00000 −0.161558 −0.0807792 0.996732i $$-0.525741\pi$$
−0.0807792 + 0.996732i $$0.525741\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −22.0454 12.7279i −0.887515 0.512407i −0.0143859 0.999897i $$-0.504579\pi$$
−0.873129 + 0.487490i $$0.837913\pi$$
$$618$$ 0 0
$$619$$ 2.12132 1.22474i 0.0852631 0.0492267i −0.456762 0.889589i $$-0.650991\pi$$
0.542025 + 0.840362i $$0.317658\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −16.8493 + 21.7279i −0.675051 + 0.870511i
$$624$$ 0 0
$$625$$ 5.50000 9.52628i 0.220000 0.381051i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 1.73205 0.0690614
$$630$$ 0 0
$$631$$ −37.0000 −1.47295 −0.736473 0.676467i $$-0.763510\pi$$
−0.736473 + 0.676467i $$0.763510\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 11.2583 19.5000i 0.446773 0.773834i
$$636$$ 0 0
$$637$$ −4.60660 + 16.5160i −0.182520 + 0.654389i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 18.3712 10.6066i 0.725618 0.418936i −0.0911991 0.995833i $$-0.529070\pi$$
0.816817 + 0.576897i $$0.195737\pi$$
$$642$$ 0 0
$$643$$ −12.7279 7.34847i −0.501940 0.289795i 0.227574 0.973761i $$-0.426921\pi$$
−0.729514 + 0.683965i $$0.760254\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −20.7846 −0.817127 −0.408564 0.912730i $$-0.633970\pi$$
−0.408564 + 0.912730i $$0.633970\pi$$
$$648$$ 0 0
$$649$$ 36.7423i 1.44226i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 25.7196 + 14.8492i 1.00649 + 0.581096i 0.910161 0.414254i $$-0.135958\pi$$
0.0963261 + 0.995350i $$0.469291\pi$$
$$654$$ 0 0
$$655$$ −9.00000 15.5885i −0.351659 0.609091i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 14.6969 8.48528i 0.572511 0.330540i −0.185640 0.982618i $$-0.559436\pi$$
0.758152 + 0.652078i $$0.226103\pi$$
$$660$$ 0 0
$$661$$ 10.6066 + 6.12372i 0.412549 + 0.238185i 0.691884 0.722008i $$-0.256781\pi$$
−0.279335 + 0.960194i $$0.590114\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −10.3923 + 4.24264i −0.402996 + 0.164523i
$$666$$ 0 0
$$667$$ −36.0000 −1.39393
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 5.19615 9.00000i 0.200595 0.347441i
$$672$$ 0 0
$$673$$ −8.00000 13.8564i −0.308377 0.534125i 0.669630 0.742695i $$-0.266453\pi$$
−0.978008 + 0.208569i $$0.933119\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 15.5885 + 27.0000i 0.599113 + 1.03769i 0.992952 + 0.118515i $$0.0378134\pi$$
−0.393839 + 0.919179i $$0.628853\pi$$
$$678$$ 0 0
$$679$$ −0.878680 + 6.42090i −0.0337206 + 0.246411i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 38.1838i 1.46106i 0.682880 + 0.730531i $$0.260727\pi$$
−0.682880 + 0.730531i $$0.739273\pi$$
$$684$$ 0 0
$$685$$ 36.7423i 1.40385i
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 19.0919 11.0227i 0.726289 0.419323i −0.0907737 0.995872i $$-0.528934\pi$$
0.817063 + 0.576548i $$0.195601\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 18.3712 10.6066i 0.696858 0.402331i
$$696$$ 0 0
$$697$$ 1.50000 2.59808i 0.0568166 0.0984092i
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 12.7279i 0.480727i −0.970683 0.240363i $$-0.922733\pi$$
0.970683 0.240363i $$-0.0772666\pi$$
$$702$$ 0 0
$$703$$ 2.44949i 0.0923843i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −27.2416 3.72792i −1.02452 0.140203i
$$708$$ 0 0
$$709$$ −24.5000 42.4352i −0.920117 1.59369i −0.799232 0.601023i $$-0.794760\pi$$
−0.120885 0.992667i $$-0.538573\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −31.1769 54.0000i −1.16758 2.02232i
$$714$$ 0 0
$$715$$ −9.00000 + 15.5885i −0.336581 + 0.582975i
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −32.9090 −1.22730 −0.613649 0.789579i $$-0.710299\pi$$
−0.613649 + 0.789579i $$0.710299\pi$$
$$720$$ 0 0
$$721$$ 48.0000 19.5959i 1.78761 0.729790i
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −7.34847 4.24264i −0.272915 0.157568i
$$726$$ 0 0
$$727$$ 6.36396 3.67423i 0.236026 0.136270i −0.377323 0.926082i $$-0.623155\pi$$
0.613349 + 0.789812i $$0.289822\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −6.06218 10.5000i −0.224218 0.388357i
$$732$$ 0 0
$$733$$ 25.4558 + 14.6969i 0.940233 + 0.542844i 0.890033 0.455895i $$-0.150681\pi$$
0.0501997 + 0.998739i $$0.484014\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 42.4264i 1.56280i
$$738$$ 0 0
$$739$$ 38.0000 1.39785 0.698926 0.715194i $$-0.253662\pi$$
0.698926 + 0.715194i $$0.253662\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −18.3712 10.6066i −0.673973 0.389118i 0.123607 0.992331i $$-0.460554\pi$$
−0.797580 + 0.603213i $$0.793887\pi$$
$$744$$ 0 0
$$745$$ 19.0919 11.0227i 0.699472 0.403841i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −17.7408 13.7574i −0.648234 0.502683i
$$750$$ 0 0
$$751$$ −5.00000 + 8.66025i −0.182453 + 0.316017i −0.942715 0.333599i $$-0.891737\pi$$
0.760263 + 0.649616i $$0.225070\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −8.66025 −0.315179
$$756$$ 0 0
$$757$$ −53.0000 −1.92632 −0.963159 0.268933i $$-0.913329\pi$$
−0.963159 + 0.268933i $$0.913329\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 11.2583 19.5000i 0.408114 0.706874i −0.586564 0.809903i $$-0.699520\pi$$
0.994678 + 0.103028i $$0.0328532\pi$$
$$762$$ 0 0
$$763$$ −21.0772 + 27.1800i −0.763045 + 0.983983i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 18.3712 10.6066i 0.663345 0.382982i
$$768$$ 0 0
$$769$$ −4.24264 2.44949i −0.152994 0.0883309i 0.421549 0.906806i $$-0.361487\pi$$
−0.574542 + 0.818475i $$0.694820\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −39.8372 −1.43284 −0.716422 0.697668i $$-0.754221\pi$$
−0.716422 + 0.697668i $$0.754221\pi$$
$$774$$ 0 0
$$775$$ 14.6969i 0.527930i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −3.67423 2.12132i −0.131643 0.0760042i
$$780$$ 0 0
$$781$$ 18.0000 + 31.1769i 0.644091 + 1.11560i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 11.0227 6.36396i 0.393417 0.227140i
$$786$$ 0 0
$$787$$ 4.24264 + 2.44949i 0.151234 + 0.0873149i 0.573707 0.819060i $$-0.305505\pi$$
−0.422473 + 0.906375i $$0.638838\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 31.1769 12.7279i 1.10852 0.452553i
$$792$$ 0 0
$$793$$ 6.00000 0.213066
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −5.19615 + 9.00000i −0.184057 + 0.318796i −0.943258 0.332060i $$-0.892256\pi$$
0.759201 + 0.650856i $$0.225590\pi$$
$$798$$ 0 0
$$799$$ −10.5000 18.1865i −0.371463 0.643393i
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 20.7846 + 36.0000i 0.733473 + 1.27041i
$$804$$ 0 0
$$805$$ 5.27208 38.5254i