# Properties

 Label 1008.2.cs.n.271.1 Level $1008$ Weight $2$ Character 1008.271 Analytic conductor $8.049$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1008 = 2^{4} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1008.cs (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$8.04892052375$$ 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 336) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 271.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 1008.271 Dual form 1008.2.cs.n.703.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(3.00000 + 1.73205i) q^{5} +(0.500000 + 2.59808i) q^{7} +O(q^{10})$$ $$q+(3.00000 + 1.73205i) q^{5} +(0.500000 + 2.59808i) q^{7} +(3.00000 - 1.73205i) q^{11} -5.19615i q^{13} +(6.00000 - 3.46410i) q^{17} +(-3.50000 + 6.06218i) q^{19} +(3.50000 + 6.06218i) q^{25} +(-2.50000 - 4.33013i) q^{31} +(-3.00000 + 8.66025i) q^{35} +(-0.500000 + 0.866025i) q^{37} +10.3923i q^{41} -1.73205i q^{43} +(-3.00000 + 5.19615i) q^{47} +(-6.50000 + 2.59808i) q^{49} +12.0000 q^{55} +(9.00000 - 15.5885i) q^{65} +(1.50000 - 0.866025i) q^{67} -3.46410i q^{71} +(7.50000 - 4.33013i) q^{73} +(6.00000 + 6.92820i) q^{77} +(-13.5000 - 7.79423i) q^{79} +6.00000 q^{83} +24.0000 q^{85} +(-6.00000 - 3.46410i) q^{89} +(13.5000 - 2.59808i) q^{91} +(-21.0000 + 12.1244i) q^{95} +6.92820i q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + 6q^{5} + q^{7} + O(q^{10})$$ $$2q + 6q^{5} + q^{7} + 6q^{11} + 12q^{17} - 7q^{19} + 7q^{25} - 5q^{31} - 6q^{35} - q^{37} - 6q^{47} - 13q^{49} + 24q^{55} + 18q^{65} + 3q^{67} + 15q^{73} + 12q^{77} - 27q^{79} + 12q^{83} + 48q^{85} - 12q^{89} + 27q^{91} - 42q^{95} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$577$$ $$757$$ $$785$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$1$$

## 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
$$5$$ 3.00000 + 1.73205i 1.34164 + 0.774597i 0.987048 0.160424i $$-0.0512862\pi$$
0.354593 + 0.935021i $$0.384620\pi$$
$$6$$ 0 0
$$7$$ 0.500000 + 2.59808i 0.188982 + 0.981981i
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 3.00000 1.73205i 0.904534 0.522233i 0.0258656 0.999665i $$-0.491766\pi$$
0.878668 + 0.477432i $$0.158432\pi$$
$$12$$ 0 0
$$13$$ 5.19615i 1.44115i −0.693375 0.720577i $$-0.743877\pi$$
0.693375 0.720577i $$-0.256123\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 6.00000 3.46410i 1.45521 0.840168i 0.456444 0.889752i $$-0.349123\pi$$
0.998770 + 0.0495842i $$0.0157896\pi$$
$$18$$ 0 0
$$19$$ −3.50000 + 6.06218i −0.802955 + 1.39076i 0.114708 + 0.993399i $$0.463407\pi$$
−0.917663 + 0.397360i $$0.869927\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$24$$ 0 0
$$25$$ 3.50000 + 6.06218i 0.700000 + 1.21244i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$30$$ 0 0
$$31$$ −2.50000 4.33013i −0.449013 0.777714i 0.549309 0.835619i $$-0.314891\pi$$
−0.998322 + 0.0579057i $$0.981558\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −3.00000 + 8.66025i −0.507093 + 1.46385i
$$36$$ 0 0
$$37$$ −0.500000 + 0.866025i −0.0821995 + 0.142374i −0.904194 0.427121i $$-0.859528\pi$$
0.821995 + 0.569495i $$0.192861\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 10.3923i 1.62301i 0.584349 + 0.811503i $$0.301350\pi$$
−0.584349 + 0.811503i $$0.698650\pi$$
$$42$$ 0 0
$$43$$ 1.73205i 0.264135i −0.991241 0.132068i $$-0.957838\pi$$
0.991241 0.132068i $$-0.0421616\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −3.00000 + 5.19615i −0.437595 + 0.757937i −0.997503 0.0706177i $$-0.977503\pi$$
0.559908 + 0.828554i $$0.310836\pi$$
$$48$$ 0 0
$$49$$ −6.50000 + 2.59808i −0.928571 + 0.371154i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$54$$ 0 0
$$55$$ 12.0000 1.61808
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$60$$ 0 0
$$61$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 9.00000 15.5885i 1.11631 1.93351i
$$66$$ 0 0
$$67$$ 1.50000 0.866025i 0.183254 0.105802i −0.405567 0.914066i $$-0.632926\pi$$
0.588821 + 0.808264i $$0.299592\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 3.46410i 0.411113i −0.978645 0.205557i $$-0.934100\pi$$
0.978645 0.205557i $$-0.0659005\pi$$
$$72$$ 0 0
$$73$$ 7.50000 4.33013i 0.877809 0.506803i 0.00787336 0.999969i $$-0.497494\pi$$
0.869935 + 0.493166i $$0.164160\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 6.00000 + 6.92820i 0.683763 + 0.789542i
$$78$$ 0 0
$$79$$ −13.5000 7.79423i −1.51887 0.876919i −0.999753 0.0222151i $$-0.992928\pi$$
−0.519115 0.854704i $$1.32626\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 6.00000 0.658586 0.329293 0.944228i $$-0.393190\pi$$
0.329293 + 0.944228i $$0.393190\pi$$
$$84$$ 0 0
$$85$$ 24.0000 2.60317
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −6.00000 3.46410i −0.635999 0.367194i 0.147073 0.989126i $$-0.453015\pi$$
−0.783072 + 0.621932i $$0.786348\pi$$
$$90$$ 0 0
$$91$$ 13.5000 2.59808i 1.41518 0.272352i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −21.0000 + 12.1244i −2.15455 + 1.24393i
$$96$$ 0 0
$$97$$ 6.92820i 0.703452i 0.936103 + 0.351726i $$0.114405\pi$$
−0.936103 + 0.351726i $$0.885595\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 3.00000 1.73205i 0.298511 0.172345i −0.343263 0.939239i $$-0.611532\pi$$
0.641774 + 0.766894i $$0.278199\pi$$
$$102$$ 0 0
$$103$$ −2.50000 + 4.33013i −0.246332 + 0.426660i −0.962505 0.271263i $$-0.912559\pi$$
0.716173 + 0.697923i $$0.245892\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 6.00000 + 3.46410i 0.580042 + 0.334887i 0.761150 0.648576i $$-0.224635\pi$$
−0.181108 + 0.983463i $$0.557968\pi$$
$$108$$ 0 0
$$109$$ −2.50000 4.33013i −0.239457 0.414751i 0.721102 0.692829i $$-0.243636\pi$$
−0.960558 + 0.278078i $$0.910303\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −6.00000 −0.564433 −0.282216 0.959351i $$-0.591070\pi$$
−0.282216 + 0.959351i $$0.591070\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 12.0000 + 13.8564i 1.10004 + 1.27021i
$$120$$ 0 0
$$121$$ 0.500000 0.866025i 0.0454545 0.0787296i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 6.92820i 0.619677i
$$126$$ 0 0
$$127$$ 15.5885i 1.38325i 0.722256 + 0.691626i $$0.243105\pi$$
−0.722256 + 0.691626i $$0.756895\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 9.00000 15.5885i 0.786334 1.36197i −0.141865 0.989886i $$-0.545310\pi$$
0.928199 0.372084i $$-0.121357\pi$$
$$132$$ 0 0
$$133$$ −17.5000 6.06218i −1.51744 0.525657i
$$134$$ 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
$$143$$ −9.00000 15.5885i −0.752618 1.30357i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 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
$$151$$ −9.00000 + 5.19615i −0.732410 + 0.422857i −0.819303 0.573361i $$-0.805639\pi$$
0.0868934 + 0.996218i $$0.472306\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 17.3205i 1.39122i
$$156$$ 0 0
$$157$$ −12.0000 + 6.92820i −0.957704 + 0.552931i −0.895466 0.445130i $$-0.853157\pi$$
−0.0622385 + 0.998061i $$0.519824\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −3.00000 1.73205i −0.234978 0.135665i 0.377888 0.925851i $$-0.376650\pi$$
−0.612866 + 0.790186i $$0.709984\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −6.00000 −0.464294 −0.232147 0.972681i $$-0.574575\pi$$
−0.232147 + 0.972681i $$0.574575\pi$$
$$168$$ 0 0
$$169$$ −14.0000 −1.07692
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$174$$ 0 0
$$175$$ −14.0000 + 12.1244i −1.05830 + 0.916515i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 15.0000 8.66025i 1.12115 0.647298i 0.179458 0.983766i $$-0.442566\pi$$
0.941695 + 0.336468i $$0.109232\pi$$
$$180$$ 0 0
$$181$$ 15.5885i 1.15868i −0.815086 0.579340i $$-0.803310\pi$$
0.815086 0.579340i $$-0.196690\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −3.00000 + 1.73205i −0.220564 + 0.127343i
$$186$$ 0 0
$$187$$ 12.0000 20.7846i 0.877527 1.51992i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 3.00000 + 1.73205i 0.217072 + 0.125327i 0.604594 0.796534i $$-0.293335\pi$$
−0.387522 + 0.921861i $$0.626669\pi$$
$$192$$ 0 0
$$193$$ −6.50000 11.2583i −0.467880 0.810392i 0.531446 0.847092i $$-0.321649\pi$$
−0.999326 + 0.0366998i $$0.988315\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −12.0000 −0.854965 −0.427482 0.904024i $$-0.640599\pi$$
−0.427482 + 0.904024i $$0.640599\pi$$
$$198$$ 0 0
$$199$$ −8.00000 13.8564i −0.567105 0.982255i −0.996850 0.0793045i $$-0.974730\pi$$
0.429745 0.902950i $$1.64140\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ −18.0000 + 31.1769i −1.25717 + 2.17749i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 24.2487i 1.67732i
$$210$$ 0 0
$$211$$ 17.3205i 1.19239i −0.802839 0.596196i $$-0.796678\pi$$
0.802839 0.596196i $$-0.203322\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 3.00000 5.19615i 0.204598 0.354375i
$$216$$ 0 0
$$217$$ 10.0000 8.66025i 0.678844 0.587896i
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −18.0000 31.1769i −1.21081 2.09719i
$$222$$ 0 0
$$223$$ −8.00000 −0.535720 −0.267860 0.963458i $$-0.586316\pi$$
−0.267860 + 0.963458i $$0.586316\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −15.0000 25.9808i −0.995585 1.72440i −0.579082 0.815270i $$-0.696589\pi$$
−0.416503 0.909134i $$1.36326\pi$$
$$228$$ 0 0
$$229$$ 1.50000 + 0.866025i 0.0991228 + 0.0572286i 0.548742 0.835992i $$-0.315107\pi$$
−0.449619 + 0.893220i $$0.648440\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −9.00000 + 15.5885i −0.589610 + 1.02123i 0.404674 + 0.914461i $$0.367385\pi$$
−0.994283 + 0.106773i $$0.965948\pi$$
$$234$$ 0 0
$$235$$ −18.0000 + 10.3923i −1.17419 + 0.677919i
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 17.3205i 1.12037i −0.828367 0.560185i $$-0.810730\pi$$
0.828367 0.560185i $$-0.189270\pi$$
$$240$$ 0 0
$$241$$ −12.0000 + 6.92820i −0.772988 + 0.446285i −0.833939 0.551856i $$-0.813920\pi$$
0.0609515 + 0.998141i $$0.480586\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −24.0000 3.46410i −1.53330 0.221313i
$$246$$ 0 0
$$247$$ 31.5000 + 18.1865i 2.00430 + 1.15718i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 24.0000 1.51487 0.757433 0.652913i $$-0.226453\pi$$
0.757433 + 0.652913i $$0.226453\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 9.00000 + 5.19615i 0.561405 + 0.324127i 0.753709 0.657208i $$-0.228263\pi$$
−0.192304 + 0.981335i $$0.561596\pi$$
$$258$$ 0 0
$$259$$ −2.50000 0.866025i −0.155342 0.0538122i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −24.0000 + 13.8564i −1.47990 + 0.854423i −0.999741 0.0227570i $$-0.992756\pi$$
−0.480162 + 0.877180i $$0.659422\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 27.0000 15.5885i 1.64622 0.950445i 0.667663 0.744463i $$-0.267295\pi$$
0.978556 0.205982i $$-0.0660387\pi$$
$$270$$ 0 0
$$271$$ 8.00000 13.8564i 0.485965 0.841717i −0.513905 0.857847i $$-0.671801\pi$$
0.999870 + 0.0161307i $$0.00513477\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 21.0000 + 12.1244i 1.26635 + 0.731126i
$$276$$ 0 0
$$277$$ 8.50000 + 14.7224i 0.510716 + 0.884585i 0.999923 + 0.0124177i $$0.00395278\pi$$
−0.489207 + 0.872167i $$0.662714\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −12.0000 −0.715860 −0.357930 0.933748i $$-0.616517\pi$$
−0.357930 + 0.933748i $$0.616517\pi$$
$$282$$ 0 0
$$283$$ 2.50000 + 4.33013i 0.148610 + 0.257399i 0.930714 0.365748i $$-0.119187\pi$$
−0.782104 + 0.623148i $$0.785854\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −27.0000 + 5.19615i −1.59376 + 0.306719i
$$288$$ 0 0
$$289$$ 15.5000 26.8468i 0.911765 1.57922i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 20.7846i 1.21425i −0.794606 0.607125i $$-0.792323\pi$$
0.794606 0.607125i $$-0.207677\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 4.50000 0.866025i 0.259376 0.0499169i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 25.0000 1.42683 0.713413 0.700744i $$-0.247149\pi$$
0.713413 + 0.700744i $$0.247149\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 9.00000 + 15.5885i 0.510343 + 0.883940i 0.999928 + 0.0119847i $$0.00381495\pi$$
−0.489585 + 0.871956i $$0.662852\pi$$
$$312$$ 0 0
$$313$$ 13.5000 + 7.79423i 0.763065 + 0.440556i 0.830395 0.557175i $$-0.188115\pi$$
−0.0673300 + 0.997731i $$0.521448\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −6.00000 + 10.3923i −0.336994 + 0.583690i −0.983866 0.178908i $$-0.942743\pi$$
0.646872 + 0.762598i $$0.276077\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 48.4974i 2.69847i
$$324$$ 0 0
$$325$$ 31.5000 18.1865i 1.74731 1.00881i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −15.0000 5.19615i −0.826977 0.286473i
$$330$$ 0 0
$$331$$ 7.50000 + 4.33013i 0.412237 + 0.238005i 0.691751 0.722137i $$-0.256840\pi$$
−0.279513 + 0.960142i $$0.590173\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 6.00000 0.327815
$$336$$ 0 0
$$337$$ −19.0000 −1.03500 −0.517498 0.855684i $$-0.673136\pi$$
−0.517498 + 0.855684i $$0.673136\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −15.0000 8.66025i −0.812296 0.468979i
$$342$$ 0 0
$$343$$ −10.0000 15.5885i −0.539949 0.841698i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −30.0000 + 17.3205i −1.61048 + 0.929814i −0.621227 + 0.783631i $$0.713365\pi$$
−0.989258 + 0.146183i $$0.953301\pi$$
$$348$$ 0 0
$$349$$ 13.8564i 0.741716i 0.928689 + 0.370858i $$0.120936\pi$$
−0.928689 + 0.370858i $$0.879064\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −15.0000 + 8.66025i −0.798369 + 0.460939i −0.842901 0.538069i $$-0.819154\pi$$
0.0445312 + 0.999008i $$0.485821\pi$$
$$354$$ 0 0
$$355$$ 6.00000 10.3923i 0.318447 0.551566i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −6.00000 3.46410i −0.316668 0.182828i 0.333238 0.942843i $$-0.391859\pi$$
−0.649906 + 0.760014i $$0.725192\pi$$
$$360$$ 0 0
$$361$$ −15.0000 25.9808i −0.789474 1.36741i
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 30.0000 1.57027
$$366$$ 0 0
$$367$$ −18.5000 32.0429i −0.965692 1.67263i −0.707744 0.706469i $$-0.750287\pi$$
−0.257948 0.966159i $$1.41695\pi$$
$$368$$ 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
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 12.1244i 0.622786i 0.950281 + 0.311393i $$0.100796\pi$$
−0.950281 + 0.311393i $$0.899204\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 18.0000 31.1769i 0.919757 1.59307i 0.119974 0.992777i $$-0.461719\pi$$
0.799783 0.600289i $$-0.204948\pi$$
$$384$$ 0 0
$$385$$ 6.00000 + 31.1769i 0.305788 + 1.58892i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 15.0000 + 25.9808i 0.760530 + 1.31728i 0.942578 + 0.333987i $$0.108394\pi$$
−0.182047 + 0.983290i $$0.558272\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −27.0000 46.7654i −1.35852 2.35302i
$$396$$ 0 0
$$397$$ 4.50000 + 2.59808i 0.225849 + 0.130394i 0.608655 0.793435i $$-0.291709\pi$$
−0.382807 + 0.923828i $$0.625043\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 12.0000 20.7846i 0.599251 1.03793i −0.393680 0.919247i $$-0.628798\pi$$
0.992932 0.118686i $$-0.0378683\pi$$
$$402$$ 0 0
$$403$$ −22.5000 + 12.9904i −1.12080 + 0.647097i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 3.46410i 0.171709i
$$408$$ 0 0
$$409$$ 16.5000 9.52628i 0.815872 0.471044i −0.0331186 0.999451i $$-0.510544\pi$$
0.848991 + 0.528407i $$0.177211\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 18.0000 + 10.3923i 0.883585 + 0.510138i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 30.0000 1.46560 0.732798 0.680446i $$-0.238214\pi$$
0.732798 + 0.680446i $$0.238214\pi$$
$$420$$ 0 0
$$421$$ −29.0000 −1.41337 −0.706687 0.707527i $$-0.749811\pi$$
−0.706687 + 0.707527i $$0.749811\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 42.0000 + 24.2487i 2.03730 + 1.17624i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −15.0000 + 8.66025i −0.722525 + 0.417150i −0.815681 0.578502i $$-0.803638\pi$$
0.0931566 + 0.995651i $$0.470304\pi$$
$$432$$ 0 0
$$433$$ 29.4449i 1.41503i 0.706698 + 0.707515i $$0.250184\pi$$
−0.706698 + 0.707515i $$0.749816\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ −8.00000 + 13.8564i −0.381819 + 0.661330i −0.991322 0.131453i $$-0.958036\pi$$
0.609503 + 0.792784i $$0.291369\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −6.00000 3.46410i −0.285069 0.164584i 0.350647 0.936508i $$-0.385962\pi$$
−0.635716 + 0.771923i $$0.719295\pi$$
$$444$$ 0 0
$$445$$ −12.0000 20.7846i −0.568855 0.985285i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 6.00000 0.283158 0.141579 0.989927i $$-0.454782\pi$$
0.141579 + 0.989927i $$0.454782\pi$$
$$450$$ 0 0
$$451$$ 18.0000 + 31.1769i 0.847587 + 1.46806i
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 45.0000 + 15.5885i 2.10963 + 0.730798i
$$456$$ 0 0
$$457$$ −2.50000 + 4.33013i −0.116945 + 0.202555i −0.918556 0.395292i $$-0.870643\pi$$
0.801611 + 0.597847i $$0.203977\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 13.8564i 0.645357i −0.946509 0.322679i $$-0.895417\pi$$
0.946509 0.322679i $$-0.104583\pi$$
$$462$$ 0 0
$$463$$ 12.1244i 0.563467i −0.959493 0.281733i $$-0.909091\pi$$
0.959493 0.281733i $$-0.0909093\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −3.00000 + 5.19615i −0.138823 + 0.240449i −0.927052 0.374934i $$-0.877665\pi$$
0.788228 + 0.615383i $$0.210999\pi$$
$$468$$ 0 0
$$469$$ 3.00000 + 3.46410i 0.138527 + 0.159957i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −3.00000 5.19615i −0.137940 0.238919i
$$474$$ 0 0
$$475$$ −49.0000 −2.24827
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 12.0000 + 20.7846i 0.548294 + 0.949673i 0.998392 + 0.0566937i $$0.0180558\pi$$
−0.450098 + 0.892979i $$0.648611\pi$$
$$480$$ 0 0
$$481$$ 4.50000 + 2.59808i 0.205182 + 0.118462i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −12.0000 + 20.7846i −0.544892 + 0.943781i
$$486$$ 0 0
$$487$$ 10.5000 6.06218i 0.475800 0.274703i −0.242864 0.970060i $$-0.578087\pi$$
0.718665 + 0.695357i $$0.244754\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 20.7846i 0.937996i −0.883199 0.468998i $$-0.844615\pi$$
0.883199 0.468998i $$-0.155385\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 9.00000 1.73205i 0.403705 0.0776931i
$$498$$ 0 0
$$499$$ −10.5000 6.06218i −0.470045 0.271380i 0.246214 0.969216i $$-0.420813\pi$$
−0.716258 + 0.697835i $$0.754147\pi$$
$$500$$ 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
$$505$$ 12.0000 0.533993
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 3.00000 + 1.73205i 0.132973 + 0.0767718i 0.565011 0.825084i $$-0.308872\pi$$
−0.432038 + 0.901855i $$0.642205\pi$$
$$510$$ 0 0
$$511$$ 15.0000 + 17.3205i 0.663561 + 0.766214i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −15.0000 + 8.66025i −0.660979 + 0.381616i
$$516$$ 0 0
$$517$$ 20.7846i 0.914106i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 12.0000 6.92820i 0.525730 0.303530i −0.213546 0.976933i $$-0.568501\pi$$
0.739276 + 0.673403i $$0.235168\pi$$
$$522$$ 0 0
$$523$$ 0.500000 0.866025i 0.0218635 0.0378686i −0.854887 0.518815i $$-0.826373\pi$$
0.876750 + 0.480946i $$0.159707\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −30.0000 17.3205i −1.30682 0.754493i
$$528$$ 0 0
$$529$$ −11.5000 19.9186i −0.500000 0.866025i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 54.0000 2.33900
$$534$$ 0 0
$$535$$ 12.0000 + 20.7846i 0.518805 + 0.898597i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −15.0000 + 19.0526i −0.646096 + 0.820652i
$$540$$ 0 0
$$541$$ 20.5000 35.5070i 0.881364 1.52657i 0.0315385 0.999503i $$-0.489959\pi$$
0.849825 0.527064i $$-0.176707\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 17.3205i 0.741929i
$$546$$ 0 0
$$547$$ 10.3923i 0.444343i −0.975008 0.222171i $$-0.928686\pi$$
0.975008 0.222171i $$-0.0713145\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 13.5000 38.9711i 0.574078 1.65722i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 9.00000 + 15.5885i 0.381342 + 0.660504i 0.991254 0.131965i $$-0.0421286\pi$$
−0.609912 + 0.792469i $$0.708795\pi$$
$$558$$ 0 0
$$559$$ −9.00000 −0.380659
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 9.00000 + 15.5885i 0.379305 + 0.656975i 0.990961 0.134148i $$-0.0428299\pi$$
−0.611656 + 0.791123i $$0.709497\pi$$
$$564$$ 0 0
$$565$$ −18.0000 10.3923i −0.757266 0.437208i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −3.00000 + 5.19615i −0.125767 + 0.217834i −0.922032 0.387113i $$-0.873472\pi$$
0.796266 + 0.604947i $$0.206806\pi$$
$$570$$ 0 0
$$571$$ −22.5000 + 12.9904i −0.941596 + 0.543631i −0.890460 0.455061i $$-0.849617\pi$$
−0.0511355 + 0.998692i $$0.516284\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −1.50000 + 0.866025i −0.0624458 + 0.0360531i −0.530898 0.847436i $$-0.678145\pi$$
0.468452 + 0.883489i $$0.344812\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 3.00000 + 15.5885i 0.124461 + 0.646718i
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −12.0000 −0.495293 −0.247647 0.968850i $$-0.579657\pi$$
−0.247647 + 0.968850i $$0.579657\pi$$
$$588$$ 0 0
$$589$$ 35.0000 1.44215
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 33.0000 + 19.0526i 1.35515 + 0.782395i 0.988965 0.148148i $$-0.0473313\pi$$
0.366182 + 0.930543i $$0.380665\pi$$
$$594$$ 0 0
$$595$$ 12.0000 + 62.3538i 0.491952 + 2.55626i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −6.00000 + 3.46410i −0.245153 + 0.141539i −0.617543 0.786537i $$-0.711872\pi$$
0.372390 + 0.928076i $$0.378539\pi$$
$$600$$ 0 0
$$601$$ 25.9808i 1.05978i 0.848067 + 0.529889i $$0.177766\pi$$
−0.848067 + 0.529889i $$0.822234\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 3.00000 1.73205i 0.121967 0.0704179i
$$606$$ 0 0
$$607$$ −18.5000 + 32.0429i −0.750892 + 1.30058i 0.196499 + 0.980504i $$0.437043\pi$$
−0.947391 + 0.320079i $$0.896291\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 27.0000 + 15.5885i 1.09230 + 0.630641i
$$612$$ 0 0
$$613$$ 11.0000 + 19.0526i 0.444286 + 0.769526i 0.998002 0.0631797i $$-0.0201241\pi$$
−0.553716 + 0.832705i $$0.686791\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 42.0000 1.69086 0.845428 0.534089i $$-0.179345\pi$$
0.845428 + 0.534089i $$0.179345\pi$$
$$618$$ 0 0
$$619$$ −17.5000 30.3109i −0.703384 1.21830i −0.967271 0.253744i $$-0.918338\pi$$
0.263887 0.964554i $$1.58500\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 6.00000 17.3205i 0.240385 0.693932i
$$624$$ 0 0
$$625$$ 5.50000 9.52628i 0.220000 0.381051i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 6.92820i 0.276246i
$$630$$ 0 0
$$631$$ 3.46410i 0.137904i −0.997620 0.0689519i $$-0.978035\pi$$
0.997620 0.0689519i $$-0.0219655\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −27.0000 + 46.7654i −1.07146 + 1.85583i
$$636$$ 0 0
$$637$$ 13.5000 + 33.7750i 0.534889 + 1.33821i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −18.0000 31.1769i −0.710957 1.23141i −0.964498 0.264089i $$-0.914929\pi$$
0.253541 0.967325i $$-0.418405\pi$$
$$642$$ 0 0
$$643$$ 43.0000 1.69575 0.847877 0.530193i $$-0.177880\pi$$
0.847877 + 0.530193i $$0.177880\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −9.00000 15.5885i −0.353827 0.612845i 0.633090 0.774078i $$-0.281786\pi$$
−0.986916 + 0.161233i $$0.948453\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −9.00000 + 15.5885i −0.352197 + 0.610023i −0.986634 0.162951i $$-0.947899\pi$$
0.634437 + 0.772975i $$0.281232\pi$$
$$654$$ 0 0
$$655$$ 54.0000 31.1769i 2.10995 1.21818i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 20.7846i 0.809653i 0.914393 + 0.404827i $$0.132668\pi$$
−0.914393 + 0.404827i $$0.867332\pi$$
$$660$$ 0 0
$$661$$ 16.5000 9.52628i 0.641776 0.370529i −0.143523 0.989647i $$-0.545843\pi$$
0.785298 + 0.619118i $$0.212510\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −42.0000 48.4974i −1.62869 1.88065i
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 1.00000 0.0385472 0.0192736 0.999814i $$-0.493865\pi$$
0.0192736 + 0.999814i $$0.493865\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −30.0000 17.3205i −1.15299 0.665681i −0.203379 0.979100i $$-0.565192\pi$$
−0.949615 + 0.313419i $$0.898526\pi$$
$$678$$ 0 0
$$679$$ −18.0000 + 3.46410i −0.690777 + 0.132940i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 36.0000 20.7846i 1.37750 0.795301i 0.385643 0.922648i $$-0.373979\pi$$
0.991858 + 0.127347i $$0.0406461\pi$$
$$684$$ 0 0
$$685$$ 41.5692i 1.58828i
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 6.50000 11.2583i 0.247272 0.428287i −0.715496 0.698617i $$-0.753799\pi$$
0.962768 + 0.270330i $$0.0871327\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 15.0000 + 8.66025i 0.568982 + 0.328502i
$$696$$ 0 0
$$697$$ 36.0000 + 62.3538i 1.36360 + 2.36182i
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$702$$ 0 0
$$703$$ −3.50000 6.06218i −0.132005 0.228639i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 6.00000 + 6.92820i 0.225653 + 0.260562i
$$708$$ 0 0
$$709$$ 5.00000 8.66025i 0.187779 0.325243i −0.756730 0.653727i $$-0.773204\pi$$
0.944509 + 0.328484i $$0.106538\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 62.3538i 2.33190i
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −9.00000 + 15.5885i −0.335643 + 0.581351i −0.983608 0.180319i $$-0.942287\pi$$
0.647965 + 0.761670i $$0.275620\pi$$
$$720$$ 0 0
$$721$$ −12.5000 4.33013i −0.465524 0.161262i
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −1.00000 −0.0370879 −0.0185440 0.999828i $$-0.505903\pi$$
−0.0185440 + 0.999828i $$0.505903\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −6.00000 10.3923i −0.221918 0.384373i
$$732$$ 0 0
$$733$$ −31.5000 18.1865i −1.16348 0.671735i −0.211344 0.977412i $$-0.567784\pi$$
−0.952135 + 0.305677i $$0.901117\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 3.00000 5.19615i 0.110506 0.191403i
$$738$$ 0 0
$$739$$ 31.5000 18.1865i 1.15875 0.669002i 0.207743 0.978183i $$-0.433388\pi$$
0.951003 + 0.309181i $$0.100055\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 3.46410i 0.127086i 0.997979 + 0.0635428i $$0.0202399\pi$$
−0.997979 + 0.0635428i $$0.979760\pi$$
$$744$$ 0 0
$$745$$ −36.0000 + 20.7846i −1.31894 + 0.761489i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −6.00000 + 17.3205i −0.219235 + 0.632878i
$$750$$ 0 0
$$751$$ −40.5000 23.3827i −1.47787 0.853246i −0.478179 0.878262i $$-0.658703\pi$$
−0.999687 + 0.0250161i $$0.992036\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −36.0000 −1.31017
$$756$$ 0 0
$$757$$ −22.0000 −0.799604 −0.399802 0.916602i $$-0.630921\pi$$
−0.399802 + 0.916602i $$0.630921\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −30.0000 17.3205i −1.08750 0.627868i −0.154590 0.987979i $$-0.549406\pi$$
−0.932910 + 0.360111i $$0.882739\pi$$
$$762$$ 0 0
$$763$$ 10.0000 8.66025i 0.362024 0.313522i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 29.4449i 1.06181i 0.847432 + 0.530904i $$0.178148\pi$$
−0.847432 + 0.530904i $$0.821852\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 27.0000 15.5885i 0.971123 0.560678i 0.0715442 0.997437i $$-0.477207\pi$$
0.899578 + 0.436760i $$0.143874\pi$$
$$774$$ 0 0
$$775$$ 17.5000 30.3109i 0.628619 1.08880i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −63.0000 36.3731i −2.25721 1.30320i
$$780$$ 0 0
$$781$$ −6.00000 10.3923i −0.214697 0.371866i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −48.0000 −1.71319
$$786$$ 0 0
$$787$$ −4.00000 6.92820i −0.142585 0.246964i 0.785885 0.618373i $$-0.212208\pi$$
−0.928469 + 0.371409i $$0.878875\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −3.00000 15.5885i −0.106668 0.554262i
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 41.5692i 1.47246i 0.676733 + 0.736229i $$0.263395\pi$$
−0.676733 + 0.736229i $$0.736605\pi$$
$$798$$ 0 0
$$799$$ 41.5692i 1.47061i
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 15.0000 25.9808i 0.529339 0.916841i
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 27.0000 + 46.7654i 0.949269 + 1.64418i 0.746968 + 0.664860i $$0.231509\pi$$
0.202301 + 0.979323i $$0.435158\pi$$
$$810$$ 0 0
$$811$$ −16.0000 −0.561836 −0.280918 0.959732i $$-0.590639\pi$$
−0.280918 + 0.959732i $$0.590639\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ −6.00000 10.3923i −0.210171 0.364027i
$$816$$ 0 0