# Properties

 Label 1520.2.d.i.609.2 Level $1520$ Weight $2$ Character 1520.609 Analytic conductor $12.137$ Analytic rank $0$ Dimension $6$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1520 = 2^{4} \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1520.d (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$12.1372611072$$ Analytic rank: $$0$$ Dimension: $$6$$ Coefficient field: 6.0.14077504.2 Defining polynomial: $$x^{6} + 9x^{4} + 14x^{2} + 4$$ x^6 + 9*x^4 + 14*x^2 + 4 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: no (minimal twist has level 380) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 609.2 Root $$-1.23277i$$ of defining polynomial Character $$\chi$$ $$=$$ 1520.609 Dual form 1520.2.d.i.609.5

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.62236i q^{3} +(-1.92411 - 1.13921i) q^{5} +4.74397i q^{7} +0.367938 q^{9} +O(q^{10})$$ $$q-1.62236i q^{3} +(-1.92411 - 1.13921i) q^{5} +4.74397i q^{7} +0.367938 q^{9} -4.48028 q^{11} +0.843176i q^{13} +(-1.84822 + 3.12160i) q^{15} -5.52315i q^{17} +1.00000 q^{19} +7.69643 q^{21} +0.779187i q^{23} +(2.40439 + 4.38394i) q^{25} -5.46402i q^{27} +10.6570 q^{29} +8.65699 q^{31} +7.26864i q^{33} +(5.40439 - 9.12790i) q^{35} -1.62236i q^{37} +1.36794 q^{39} +4.73588 q^{41} +9.67504i q^{43} +(-0.707953 - 0.419160i) q^{45} +3.18559i q^{47} -15.5052 q^{49} -8.96056 q^{51} -6.17922i q^{53} +(8.62054 + 5.10399i) q^{55} -1.62236i q^{57} +11.6964 q^{59} +6.48028 q^{61} +1.74549i q^{63} +(0.960558 - 1.62236i) q^{65} -14.8880i q^{67} +1.26412 q^{69} -0.303566 q^{71} +10.0800i q^{73} +(7.11234 - 3.90079i) q^{75} -21.2543i q^{77} +4.00000 q^{79} -7.76081 q^{81} -0.779187i q^{83} +(-6.29205 + 10.6271i) q^{85} -17.2895i q^{87} +5.69643 q^{89} -4.00000 q^{91} -14.0448i q^{93} +(-1.92411 - 1.13921i) q^{95} +6.17922i q^{97} -1.64847 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$6 q - q^{5} - 10 q^{9}+O(q^{10})$$ 6 * q - q^5 - 10 * q^9 $$6 q - q^{5} - 10 q^{9} - 18 q^{11} + 10 q^{15} + 6 q^{19} + 4 q^{21} - 5 q^{25} + 4 q^{29} - 8 q^{31} + 13 q^{35} - 4 q^{39} + 4 q^{41} - 27 q^{45} - 12 q^{49} - 36 q^{51} - q^{55} + 28 q^{59} + 30 q^{61} - 12 q^{65} + 32 q^{69} - 44 q^{71} + 46 q^{75} + 24 q^{79} + 50 q^{81} - 15 q^{85} - 8 q^{89} - 24 q^{91} - q^{95} + 90 q^{99}+O(q^{100})$$ 6 * q - q^5 - 10 * q^9 - 18 * q^11 + 10 * q^15 + 6 * q^19 + 4 * q^21 - 5 * q^25 + 4 * q^29 - 8 * q^31 + 13 * q^35 - 4 * q^39 + 4 * q^41 - 27 * q^45 - 12 * q^49 - 36 * q^51 - q^55 + 28 * q^59 + 30 * q^61 - 12 * q^65 + 32 * q^69 - 44 * q^71 + 46 * q^75 + 24 * q^79 + 50 * q^81 - 15 * q^85 - 8 * q^89 - 24 * q^91 - q^95 + 90 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times$$.

 $$n$$ $$191$$ $$401$$ $$1141$$ $$1217$$ $$\chi(n)$$ $$1$$ $$1$$ $$1$$ $$-1$$

## 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
$$3$$ 1.62236i 0.936672i −0.883551 0.468336i $$-0.844854\pi$$
0.883551 0.468336i $$-0.155146\pi$$
$$4$$ 0 0
$$5$$ −1.92411 1.13921i −0.860487 0.509472i
$$6$$ 0 0
$$7$$ 4.74397i 1.79305i 0.442993 + 0.896525i $$0.353917\pi$$
−0.442993 + 0.896525i $$0.646083\pi$$
$$8$$ 0 0
$$9$$ 0.367938 0.122646
$$10$$ 0 0
$$11$$ −4.48028 −1.35085 −0.675427 0.737426i $$-0.736041\pi$$
−0.675427 + 0.737426i $$0.736041\pi$$
$$12$$ 0 0
$$13$$ 0.843176i 0.233855i 0.993140 + 0.116928i $$0.0373045\pi$$
−0.993140 + 0.116928i $$0.962695\pi$$
$$14$$ 0 0
$$15$$ −1.84822 + 3.12160i −0.477208 + 0.805994i
$$16$$ 0 0
$$17$$ 5.52315i 1.33956i −0.742559 0.669781i $$-0.766388\pi$$
0.742559 0.669781i $$-0.233612\pi$$
$$18$$ 0 0
$$19$$ 1.00000 0.229416
$$20$$ 0 0
$$21$$ 7.69643 1.67950
$$22$$ 0 0
$$23$$ 0.779187i 0.162472i 0.996695 + 0.0812358i $$0.0258867\pi$$
−0.996695 + 0.0812358i $$0.974113\pi$$
$$24$$ 0 0
$$25$$ 2.40439 + 4.38394i 0.480877 + 0.876788i
$$26$$ 0 0
$$27$$ 5.46402i 1.05155i
$$28$$ 0 0
$$29$$ 10.6570 1.97895 0.989477 0.144691i $$-0.0462189\pi$$
0.989477 + 0.144691i $$0.0462189\pi$$
$$30$$ 0 0
$$31$$ 8.65699 1.55484 0.777421 0.628981i $$-0.216528\pi$$
0.777421 + 0.628981i $$0.216528\pi$$
$$32$$ 0 0
$$33$$ 7.26864i 1.26531i
$$34$$ 0 0
$$35$$ 5.40439 9.12790i 0.913508 1.54290i
$$36$$ 0 0
$$37$$ 1.62236i 0.266715i −0.991068 0.133357i $$-0.957424\pi$$
0.991068 0.133357i $$-0.0425758\pi$$
$$38$$ 0 0
$$39$$ 1.36794 0.219045
$$40$$ 0 0
$$41$$ 4.73588 0.739620 0.369810 0.929107i $$-0.379423\pi$$
0.369810 + 0.929107i $$0.379423\pi$$
$$42$$ 0 0
$$43$$ 9.67504i 1.47543i 0.675112 + 0.737715i $$0.264095\pi$$
−0.675112 + 0.737715i $$0.735905\pi$$
$$44$$ 0 0
$$45$$ −0.707953 0.419160i −0.105535 0.0624847i
$$46$$ 0 0
$$47$$ 3.18559i 0.464666i 0.972636 + 0.232333i $$0.0746360\pi$$
−0.972636 + 0.232333i $$0.925364\pi$$
$$48$$ 0 0
$$49$$ −15.5052 −2.21503
$$50$$ 0 0
$$51$$ −8.96056 −1.25473
$$52$$ 0 0
$$53$$ 6.17922i 0.848780i −0.905479 0.424390i $$-0.860488\pi$$
0.905479 0.424390i $$-0.139512\pi$$
$$54$$ 0 0
$$55$$ 8.62054 + 5.10399i 1.16239 + 0.688222i
$$56$$ 0 0
$$57$$ 1.62236i 0.214887i
$$58$$ 0 0
$$59$$ 11.6964 1.52275 0.761373 0.648314i $$-0.224526\pi$$
0.761373 + 0.648314i $$0.224526\pi$$
$$60$$ 0 0
$$61$$ 6.48028 0.829715 0.414857 0.909886i $$-0.363831\pi$$
0.414857 + 0.909886i $$0.363831\pi$$
$$62$$ 0 0
$$63$$ 1.74549i 0.219911i
$$64$$ 0 0
$$65$$ 0.960558 1.62236i 0.119143 0.201229i
$$66$$ 0 0
$$67$$ 14.8880i 1.81885i −0.415864 0.909427i $$-0.636521\pi$$
0.415864 0.909427i $$-0.363479\pi$$
$$68$$ 0 0
$$69$$ 1.26412 0.152183
$$70$$ 0 0
$$71$$ −0.303566 −0.0360266 −0.0180133 0.999838i $$-0.505734\pi$$
−0.0180133 + 0.999838i $$0.505734\pi$$
$$72$$ 0 0
$$73$$ 10.0800i 1.17978i 0.807485 + 0.589888i $$0.200828\pi$$
−0.807485 + 0.589888i $$0.799172\pi$$
$$74$$ 0 0
$$75$$ 7.11234 3.90079i 0.821262 0.450424i
$$76$$ 0 0
$$77$$ 21.2543i 2.42215i
$$78$$ 0 0
$$79$$ 4.00000 0.450035 0.225018 0.974355i $$-0.427756\pi$$
0.225018 + 0.974355i $$0.427756\pi$$
$$80$$ 0 0
$$81$$ −7.76081 −0.862312
$$82$$ 0 0
$$83$$ 0.779187i 0.0855268i −0.999085 0.0427634i $$-0.986384\pi$$
0.999085 0.0427634i $$-0.0136162\pi$$
$$84$$ 0 0
$$85$$ −6.29205 + 10.6271i −0.682468 + 1.15268i
$$86$$ 0 0
$$87$$ 17.2895i 1.85363i
$$88$$ 0 0
$$89$$ 5.69643 0.603821 0.301910 0.953336i $$-0.402376\pi$$
0.301910 + 0.953336i $$0.402376\pi$$
$$90$$ 0 0
$$91$$ −4.00000 −0.419314
$$92$$ 0 0
$$93$$ 14.0448i 1.45638i
$$94$$ 0 0
$$95$$ −1.92411 1.13921i −0.197409 0.116881i
$$96$$ 0 0
$$97$$ 6.17922i 0.627404i 0.949521 + 0.313702i $$0.101569\pi$$
−0.949521 + 0.313702i $$0.898431\pi$$
$$98$$ 0 0
$$99$$ −1.64847 −0.165677
$$100$$ 0 0
$$101$$ 3.36794 0.335122 0.167561 0.985862i $$-0.446411\pi$$
0.167561 + 0.985862i $$0.446411\pi$$
$$102$$ 0 0
$$103$$ 3.71368i 0.365919i −0.983120 0.182960i $$-0.941432\pi$$
0.983120 0.182960i $$-0.0585678\pi$$
$$104$$ 0 0
$$105$$ −14.8088 8.76788i −1.44519 0.855657i
$$106$$ 0 0
$$107$$ 10.2031i 0.986374i −0.869923 0.493187i $$-0.835832\pi$$
0.869923 0.493187i $$-0.164168\pi$$
$$108$$ 0 0
$$109$$ −2.96056 −0.283570 −0.141785 0.989897i $$-0.545284\pi$$
−0.141785 + 0.989897i $$0.545284\pi$$
$$110$$ 0 0
$$111$$ −2.63206 −0.249824
$$112$$ 0 0
$$113$$ 7.08638i 0.666631i 0.942815 + 0.333315i $$0.108167\pi$$
−0.942815 + 0.333315i $$0.891833\pi$$
$$114$$ 0 0
$$115$$ 0.887659 1.49924i 0.0827747 0.139805i
$$116$$ 0 0
$$117$$ 0.310237i 0.0286814i
$$118$$ 0 0
$$119$$ 26.2016 2.40190
$$120$$ 0 0
$$121$$ 9.07290 0.824809
$$122$$ 0 0
$$123$$ 7.68331i 0.692781i
$$124$$ 0 0
$$125$$ 0.367938 11.1743i 0.0329094 0.999458i
$$126$$ 0 0
$$127$$ 9.79817i 0.869447i −0.900564 0.434723i $$-0.856846\pi$$
0.900564 0.434723i $$-0.143154\pi$$
$$128$$ 0 0
$$129$$ 15.6964 1.38199
$$130$$ 0 0
$$131$$ −12.5841 −1.09948 −0.549739 0.835337i $$-0.685273\pi$$
−0.549739 + 0.835337i $$0.685273\pi$$
$$132$$ 0 0
$$133$$ 4.74397i 0.411354i
$$134$$ 0 0
$$135$$ −6.22468 + 10.5134i −0.535735 + 0.904846i
$$136$$ 0 0
$$137$$ 8.89586i 0.760024i 0.924981 + 0.380012i $$0.124080\pi$$
−0.924981 + 0.380012i $$0.875920\pi$$
$$138$$ 0 0
$$139$$ 6.25560 0.530593 0.265296 0.964167i $$-0.414530\pi$$
0.265296 + 0.964167i $$0.414530\pi$$
$$140$$ 0 0
$$141$$ 5.16819 0.435240
$$142$$ 0 0
$$143$$ 3.77767i 0.315904i
$$144$$ 0 0
$$145$$ −20.5052 12.1406i −1.70286 1.00822i
$$146$$ 0 0
$$147$$ 25.1551i 2.07476i
$$148$$ 0 0
$$149$$ −2.48028 −0.203192 −0.101596 0.994826i $$-0.532395\pi$$
−0.101596 + 0.994826i $$0.532395\pi$$
$$150$$ 0 0
$$151$$ −3.69643 −0.300812 −0.150406 0.988624i $$-0.548058\pi$$
−0.150406 + 0.988624i $$0.548058\pi$$
$$152$$ 0 0
$$153$$ 2.03218i 0.164292i
$$154$$ 0 0
$$155$$ −16.6570 9.86216i −1.33792 0.792148i
$$156$$ 0 0
$$157$$ 18.8479i 1.50422i 0.659035 + 0.752112i $$0.270965\pi$$
−0.659035 + 0.752112i $$0.729035\pi$$
$$158$$ 0 0
$$159$$ −10.0249 −0.795029
$$160$$ 0 0
$$161$$ −3.69643 −0.291320
$$162$$ 0 0
$$163$$ 2.46554i 0.193116i 0.995327 + 0.0965580i $$0.0307833\pi$$
−0.995327 + 0.0965580i $$0.969217\pi$$
$$164$$ 0 0
$$165$$ 8.28053 13.9856i 0.644638 1.08878i
$$166$$ 0 0
$$167$$ 7.49134i 0.579697i 0.957072 + 0.289849i $$0.0936050\pi$$
−0.957072 + 0.289849i $$0.906395\pi$$
$$168$$ 0 0
$$169$$ 12.2891 0.945312
$$170$$ 0 0
$$171$$ 0.367938 0.0281369
$$172$$ 0 0
$$173$$ 20.0653i 1.52554i 0.646673 + 0.762768i $$0.276160\pi$$
−0.646673 + 0.762768i $$0.723840\pi$$
$$174$$ 0 0
$$175$$ −20.7973 + 11.4063i −1.57212 + 0.862238i
$$176$$ 0 0
$$177$$ 18.9759i 1.42631i
$$178$$ 0 0
$$179$$ −3.69643 −0.276284 −0.138142 0.990412i $$-0.544113\pi$$
−0.138142 + 0.990412i $$0.544113\pi$$
$$180$$ 0 0
$$181$$ −2.00000 −0.148659 −0.0743294 0.997234i $$-0.523682\pi$$
−0.0743294 + 0.997234i $$0.523682\pi$$
$$182$$ 0 0
$$183$$ 10.5134i 0.777170i
$$184$$ 0 0
$$185$$ −1.84822 + 3.12160i −0.135884 + 0.229505i
$$186$$ 0 0
$$187$$ 24.7453i 1.80955i
$$188$$ 0 0
$$189$$ 25.9211 1.88548
$$190$$ 0 0
$$191$$ −0.887659 −0.0642288 −0.0321144 0.999484i $$-0.510224\pi$$
−0.0321144 + 0.999484i $$0.510224\pi$$
$$192$$ 0 0
$$193$$ 19.1581i 1.37903i −0.724271 0.689516i $$-0.757823\pi$$
0.724271 0.689516i $$-0.242177\pi$$
$$194$$ 0 0
$$195$$ −2.63206 1.55837i −0.188486 0.111597i
$$196$$ 0 0
$$197$$ 3.37271i 0.240295i 0.992756 + 0.120148i $$0.0383368\pi$$
−0.992756 + 0.120148i $$0.961663\pi$$
$$198$$ 0 0
$$199$$ 4.58409 0.324958 0.162479 0.986712i $$-0.448051\pi$$
0.162479 + 0.986712i $$0.448051\pi$$
$$200$$ 0 0
$$201$$ −24.1537 −1.70367
$$202$$ 0 0
$$203$$ 50.5564i 3.54836i
$$204$$ 0 0
$$205$$ −9.11234 5.39517i −0.636433 0.376815i
$$206$$ 0 0
$$207$$ 0.286693i 0.0199265i
$$208$$ 0 0
$$209$$ −4.48028 −0.309907
$$210$$ 0 0
$$211$$ 14.8817 1.02450 0.512248 0.858837i $$-0.328813\pi$$
0.512248 + 0.858837i $$0.328813\pi$$
$$212$$ 0 0
$$213$$ 0.492494i 0.0337451i
$$214$$ 0 0
$$215$$ 11.0219 18.6158i 0.751690 1.26959i
$$216$$ 0 0
$$217$$ 41.0685i 2.78791i
$$218$$ 0 0
$$219$$ 16.3534 1.10506
$$220$$ 0 0
$$221$$ 4.65699 0.313263
$$222$$ 0 0
$$223$$ 18.7839i 1.25786i 0.777461 + 0.628931i $$0.216507\pi$$
−0.777461 + 0.628931i $$0.783493\pi$$
$$224$$ 0 0
$$225$$ 0.884666 + 1.61302i 0.0589777 + 0.107535i
$$226$$ 0 0
$$227$$ 0.843176i 0.0559636i 0.999608 + 0.0279818i $$0.00890804\pi$$
−0.999608 + 0.0279818i $$0.991092\pi$$
$$228$$ 0 0
$$229$$ 4.86273 0.321338 0.160669 0.987008i $$-0.448635\pi$$
0.160669 + 0.987008i $$0.448635\pi$$
$$230$$ 0 0
$$231$$ −34.4822 −2.26876
$$232$$ 0 0
$$233$$ 4.90268i 0.321185i 0.987021 + 0.160593i $$0.0513405\pi$$
−0.987021 + 0.160593i $$0.948659\pi$$
$$234$$ 0 0
$$235$$ 3.62907 6.12943i 0.236734 0.399840i
$$236$$ 0 0
$$237$$ 6.48945i 0.421535i
$$238$$ 0 0
$$239$$ −6.20164 −0.401151 −0.200575 0.979678i $$-0.564281\pi$$
−0.200575 + 0.979678i $$0.564281\pi$$
$$240$$ 0 0
$$241$$ −3.26412 −0.210261 −0.105130 0.994458i $$-0.533526\pi$$
−0.105130 + 0.994458i $$0.533526\pi$$
$$242$$ 0 0
$$243$$ 3.80121i 0.243848i
$$244$$ 0 0
$$245$$ 29.8337 + 17.6637i 1.90601 + 1.12849i
$$246$$ 0 0
$$247$$ 0.843176i 0.0536500i
$$248$$ 0 0
$$249$$ −1.26412 −0.0801106
$$250$$ 0 0
$$251$$ −28.4263 −1.79425 −0.897127 0.441773i $$-0.854350\pi$$
−0.897127 + 0.441773i $$0.854350\pi$$
$$252$$ 0 0
$$253$$ 3.49097i 0.219476i
$$254$$ 0 0
$$255$$ 17.2411 + 10.2080i 1.07968 + 0.639249i
$$256$$ 0 0
$$257$$ 9.55192i 0.595832i −0.954592 0.297916i $$-0.903708\pi$$
0.954592 0.297916i $$-0.0962916\pi$$
$$258$$ 0 0
$$259$$ 7.69643 0.478233
$$260$$ 0 0
$$261$$ 3.92112 0.242711
$$262$$ 0 0
$$263$$ 9.54706i 0.588697i −0.955698 0.294349i $$-0.904897\pi$$
0.955698 0.294349i $$-0.0951027\pi$$
$$264$$ 0 0
$$265$$ −7.03944 + 11.8895i −0.432430 + 0.730365i
$$266$$ 0 0
$$267$$ 9.24168i 0.565582i
$$268$$ 0 0
$$269$$ 14.3534 0.875144 0.437572 0.899183i $$-0.355839\pi$$
0.437572 + 0.899183i $$0.355839\pi$$
$$270$$ 0 0
$$271$$ 12.1038 0.735254 0.367627 0.929973i $$-0.380170\pi$$
0.367627 + 0.929973i $$0.380170\pi$$
$$272$$ 0 0
$$273$$ 6.48945i 0.392760i
$$274$$ 0 0
$$275$$ −10.7723 19.6413i −0.649596 1.18441i
$$276$$ 0 0
$$277$$ 3.59055i 0.215735i 0.994165 + 0.107868i $$0.0344023\pi$$
−0.994165 + 0.107868i $$0.965598\pi$$
$$278$$ 0 0
$$279$$ 3.18524 0.190695
$$280$$ 0 0
$$281$$ 26.7069 1.59320 0.796599 0.604509i $$-0.206631\pi$$
0.796599 + 0.604509i $$0.206631\pi$$
$$282$$ 0 0
$$283$$ 20.4751i 1.21712i −0.793508 0.608559i $$-0.791748\pi$$
0.793508 0.608559i $$-0.208252\pi$$
$$284$$ 0 0
$$285$$ −1.84822 + 3.12160i −0.109479 + 0.184908i
$$286$$ 0 0
$$287$$ 22.4668i 1.32618i
$$288$$ 0 0
$$289$$ −13.5052 −0.794424
$$290$$ 0 0
$$291$$ 10.0249 0.587672
$$292$$ 0 0
$$293$$ 19.1581i 1.11923i −0.828753 0.559615i $$-0.810949\pi$$
0.828753 0.559615i $$-0.189051\pi$$
$$294$$ 0 0
$$295$$ −22.5052 13.3247i −1.31030 0.775796i
$$296$$ 0 0
$$297$$ 24.4803i 1.42049i
$$298$$ 0 0
$$299$$ −0.656992 −0.0379948
$$300$$ 0 0
$$301$$ −45.8981 −2.64552
$$302$$ 0 0
$$303$$ 5.46402i 0.313900i
$$304$$ 0 0
$$305$$ −12.4688 7.38242i −0.713959 0.422716i
$$306$$ 0 0
$$307$$ 32.0495i 1.82916i 0.404404 + 0.914580i $$0.367479\pi$$
−0.404404 + 0.914580i $$0.632521\pi$$
$$308$$ 0 0
$$309$$ −6.02493 −0.342746
$$310$$ 0 0
$$311$$ 20.5301 1.16416 0.582079 0.813132i $$-0.302240\pi$$
0.582079 + 0.813132i $$0.302240\pi$$
$$312$$ 0 0
$$313$$ 14.7932i 0.836163i −0.908409 0.418082i $$-0.862703\pi$$
0.908409 0.418082i $$-0.137297\pi$$
$$314$$ 0 0
$$315$$ 1.98848 3.35851i 0.112038 0.189230i
$$316$$ 0 0
$$317$$ 16.9485i 0.951925i 0.879466 + 0.475962i $$0.157900\pi$$
−0.879466 + 0.475962i $$0.842100\pi$$
$$318$$ 0 0
$$319$$ −47.7463 −2.67328
$$320$$ 0 0
$$321$$ −16.5532 −0.923908
$$322$$ 0 0
$$323$$ 5.52315i 0.307316i
$$324$$ 0 0
$$325$$ −3.69643 + 2.02732i −0.205041 + 0.112456i
$$326$$ 0 0
$$327$$ 4.80310i 0.265612i
$$328$$ 0 0
$$329$$ −15.1123 −0.833170
$$330$$ 0 0
$$331$$ 22.1287 1.21631 0.608153 0.793820i $$-0.291911\pi$$
0.608153 + 0.793820i $$0.291911\pi$$
$$332$$ 0 0
$$333$$ 0.596929i 0.0327115i
$$334$$ 0 0
$$335$$ −16.9606 + 28.6461i −0.926654 + 1.56510i
$$336$$ 0 0
$$337$$ 27.9948i 1.52498i −0.647002 0.762488i $$-0.723978\pi$$
0.647002 0.762488i $$-0.276022\pi$$
$$338$$ 0 0
$$339$$ 11.4967 0.624414
$$340$$ 0 0
$$341$$ −38.7857 −2.10037
$$342$$ 0 0
$$343$$ 40.3484i 2.17861i
$$344$$ 0 0
$$345$$ −2.43231 1.44011i −0.130951 0.0775327i
$$346$$ 0 0
$$347$$ 17.1024i 0.918105i −0.888409 0.459052i $$-0.848189\pi$$
0.888409 0.459052i $$-0.151811\pi$$
$$348$$ 0 0
$$349$$ 19.2411 1.02995 0.514976 0.857205i $$-0.327801\pi$$
0.514976 + 0.857205i $$0.327801\pi$$
$$350$$ 0 0
$$351$$ 4.60713 0.245910
$$352$$ 0 0
$$353$$ 7.42735i 0.395318i 0.980271 + 0.197659i $$0.0633339\pi$$
−0.980271 + 0.197659i $$0.936666\pi$$
$$354$$ 0 0
$$355$$ 0.584094 + 0.345826i 0.0310005 + 0.0183545i
$$356$$ 0 0
$$357$$ 42.5086i 2.24979i
$$358$$ 0 0
$$359$$ 28.1767 1.48711 0.743555 0.668675i $$-0.233138\pi$$
0.743555 + 0.668675i $$0.233138\pi$$
$$360$$ 0 0
$$361$$ 1.00000 0.0526316
$$362$$ 0 0
$$363$$ 14.7195i 0.772575i
$$364$$ 0 0
$$365$$ 11.4833 19.3950i 0.601062 1.01518i
$$366$$ 0 0
$$367$$ 26.1165i 1.36327i −0.731692 0.681636i $$-0.761269\pi$$
0.731692 0.681636i $$-0.238731\pi$$
$$368$$ 0 0
$$369$$ 1.74251 0.0907115
$$370$$ 0 0
$$371$$ 29.3140 1.52191
$$372$$ 0 0
$$373$$ 0.438217i 0.0226900i −0.999936 0.0113450i $$-0.996389\pi$$
0.999936 0.0113450i $$-0.00361130\pi$$
$$374$$ 0 0
$$375$$ −18.1287 0.596929i −0.936164 0.0308253i
$$376$$ 0 0
$$377$$ 8.98572i 0.462788i
$$378$$ 0 0
$$379$$ −13.7753 −0.707591 −0.353795 0.935323i $$-0.615109\pi$$
−0.353795 + 0.935323i $$0.615109\pi$$
$$380$$ 0 0
$$381$$ −15.8962 −0.814386
$$382$$ 0 0
$$383$$ 22.3153i 1.14026i 0.821555 + 0.570130i $$0.193107\pi$$
−0.821555 + 0.570130i $$0.806893\pi$$
$$384$$ 0 0
$$385$$ −24.2132 + 40.8956i −1.23402 + 2.08423i
$$386$$ 0 0
$$387$$ 3.55982i 0.180956i
$$388$$ 0 0
$$389$$ −14.4263 −0.731444 −0.365722 0.930724i $$-0.619178\pi$$
−0.365722 + 0.930724i $$0.619178\pi$$
$$390$$ 0 0
$$391$$ 4.30357 0.217641
$$392$$ 0 0
$$393$$ 20.4160i 1.02985i
$$394$$ 0 0
$$395$$ −7.69643 4.55685i −0.387250 0.229280i
$$396$$ 0 0
$$397$$ 16.4512i 0.825662i 0.910808 + 0.412831i $$0.135460\pi$$
−0.910808 + 0.412831i $$0.864540\pi$$
$$398$$ 0 0
$$399$$ 7.69643 0.385304
$$400$$ 0 0
$$401$$ 2.96056 0.147843 0.0739216 0.997264i $$-0.476449\pi$$
0.0739216 + 0.997264i $$0.476449\pi$$
$$402$$ 0 0
$$403$$ 7.29937i 0.363608i
$$404$$ 0 0
$$405$$ 14.9326 + 8.84121i 0.742009 + 0.439323i
$$406$$ 0 0
$$407$$ 7.26864i 0.360293i
$$408$$ 0 0
$$409$$ −17.0893 −0.845012 −0.422506 0.906360i $$-0.638849\pi$$
−0.422506 + 0.906360i $$0.638849\pi$$
$$410$$ 0 0
$$411$$ 14.4323 0.711893
$$412$$ 0 0
$$413$$ 55.4875i 2.73036i
$$414$$ 0 0
$$415$$ −0.887659 + 1.49924i −0.0435735 + 0.0735948i
$$416$$ 0 0
$$417$$ 10.1489i 0.496991i
$$418$$ 0 0
$$419$$ −15.3929 −0.751991 −0.375995 0.926622i $$-0.622699\pi$$
−0.375995 + 0.926622i $$0.622699\pi$$
$$420$$ 0 0
$$421$$ −16.4323 −0.800862 −0.400431 0.916327i $$-0.631140\pi$$
−0.400431 + 0.916327i $$0.631140\pi$$
$$422$$ 0 0
$$423$$ 1.17210i 0.0569895i
$$424$$ 0 0
$$425$$ 24.2132 13.2798i 1.17451 0.644165i
$$426$$ 0 0
$$427$$ 30.7422i 1.48772i
$$428$$ 0 0
$$429$$ −6.12874 −0.295899
$$430$$ 0 0
$$431$$ −15.1852 −0.731447 −0.365724 0.930724i $$-0.619178\pi$$
−0.365724 + 0.930724i $$0.619178\pi$$
$$432$$ 0 0
$$433$$ 23.4380i 1.12636i 0.826335 + 0.563179i $$0.190422\pi$$
−0.826335 + 0.563179i $$0.809578\pi$$
$$434$$ 0 0
$$435$$ −19.6964 + 33.2669i −0.944372 + 1.59503i
$$436$$ 0 0
$$437$$ 0.779187i 0.0372735i
$$438$$ 0 0
$$439$$ 0.511196 0.0243980 0.0121990 0.999926i $$-0.496117\pi$$
0.0121990 + 0.999926i $$0.496117\pi$$
$$440$$ 0 0
$$441$$ −5.70496 −0.271665
$$442$$ 0 0
$$443$$ 19.7834i 0.939940i 0.882682 + 0.469970i $$0.155735\pi$$
−0.882682 + 0.469970i $$0.844265\pi$$
$$444$$ 0 0
$$445$$ −10.9606 6.48945i −0.519580 0.307630i
$$446$$ 0 0
$$447$$ 4.02391i 0.190325i
$$448$$ 0 0
$$449$$ −31.1682 −1.47092 −0.735459 0.677569i $$-0.763033\pi$$
−0.735459 + 0.677569i $$0.763033\pi$$
$$450$$ 0 0
$$451$$ −21.2180 −0.999119
$$452$$ 0 0
$$453$$ 5.99696i 0.281762i
$$454$$ 0 0
$$455$$ 7.69643 + 4.55685i 0.360814 + 0.213629i
$$456$$ 0 0
$$457$$ 7.20950i 0.337246i 0.985681 + 0.168623i $$0.0539321\pi$$
−0.985681 + 0.168623i $$0.946068\pi$$
$$458$$ 0 0
$$459$$ −30.1786 −1.40862
$$460$$ 0 0
$$461$$ −5.41591 −0.252244 −0.126122 0.992015i $$-0.540253\pi$$
−0.126122 + 0.992015i $$0.540253\pi$$
$$462$$ 0 0
$$463$$ 8.73715i 0.406050i −0.979174 0.203025i $$-0.934923\pi$$
0.979174 0.203025i $$-0.0650772\pi$$
$$464$$ 0 0
$$465$$ −16.0000 + 27.0237i −0.741982 + 1.25319i
$$466$$ 0 0
$$467$$ 17.3584i 0.803249i −0.915804 0.401624i $$-0.868446\pi$$
0.915804 0.401624i $$-0.131554\pi$$
$$468$$ 0 0
$$469$$ 70.6280 3.26130
$$470$$ 0 0
$$471$$ 30.5781 1.40896
$$472$$ 0 0
$$473$$ 43.3469i 1.99309i
$$474$$ 0 0
$$475$$ 2.40439 + 4.38394i 0.110321 + 0.201149i
$$476$$ 0 0
$$477$$ 2.27357i 0.104100i
$$478$$ 0 0
$$479$$ 7.44682 0.340254 0.170127 0.985422i $$-0.445582\pi$$
0.170127 + 0.985422i $$0.445582\pi$$
$$480$$ 0 0
$$481$$ 1.36794 0.0623726
$$482$$ 0 0
$$483$$ 5.99696i 0.272871i
$$484$$ 0 0
$$485$$ 7.03944 11.8895i 0.319645 0.539874i
$$486$$ 0 0
$$487$$ 2.15530i 0.0976661i 0.998807 + 0.0488330i $$0.0155502\pi$$
−0.998807 + 0.0488330i $$0.984450\pi$$
$$488$$ 0 0
$$489$$ 4.00000 0.180886
$$490$$ 0 0
$$491$$ −29.3140 −1.32292 −0.661461 0.749980i $$-0.730063\pi$$
−0.661461 + 0.749980i $$0.730063\pi$$
$$492$$ 0 0
$$493$$ 58.8602i 2.65093i
$$494$$ 0 0
$$495$$ 3.17183 + 1.87795i 0.142563 + 0.0844078i
$$496$$ 0 0
$$497$$ 1.44011i 0.0645976i
$$498$$ 0 0
$$499$$ −23.5696 −1.05512 −0.527560 0.849518i $$-0.676893\pi$$
−0.527560 + 0.849518i $$0.676893\pi$$
$$500$$ 0 0
$$501$$ 12.1537 0.542986
$$502$$ 0 0
$$503$$ 9.08297i 0.404990i 0.979283 + 0.202495i $$0.0649049\pi$$
−0.979283 + 0.202495i $$0.935095\pi$$
$$504$$ 0 0
$$505$$ −6.48028 3.83680i −0.288369 0.170735i
$$506$$ 0 0
$$507$$ 19.9373i 0.885447i
$$508$$ 0 0
$$509$$ 18.5112 0.820494 0.410247 0.911974i $$-0.365442\pi$$
0.410247 + 0.911974i $$0.365442\pi$$
$$510$$ 0 0
$$511$$ −47.8192 −2.11540
$$512$$ 0 0
$$513$$ 5.46402i 0.241242i
$$514$$ 0 0
$$515$$ −4.23067 + 7.14552i −0.186425 + 0.314869i
$$516$$ 0 0
$$517$$ 14.2723i 0.627697i
$$518$$ 0 0
$$519$$ 32.5532 1.42893
$$520$$ 0 0
$$521$$ −25.0893 −1.09918 −0.549591 0.835434i $$-0.685216\pi$$
−0.549591 + 0.835434i $$0.685216\pi$$
$$522$$ 0 0
$$523$$ 28.5181i 1.24701i −0.781820 0.623504i $$-0.785708\pi$$
0.781820 0.623504i $$-0.214292\pi$$
$$524$$ 0 0
$$525$$ 18.5052 + 33.7407i 0.807634 + 1.47256i
$$526$$ 0 0
$$527$$ 47.8139i 2.08281i
$$528$$ 0 0
$$529$$ 22.3929 0.973603
$$530$$ 0 0
$$531$$ 4.30357 0.186759
$$532$$ 0 0
$$533$$ 3.99318i 0.172964i
$$534$$ 0 0
$$535$$ −11.6235 + 19.6319i −0.502529 + 0.848762i
$$536$$ 0 0
$$537$$ 5.99696i 0.258788i
$$538$$ 0 0
$$539$$ 69.4677 2.99218
$$540$$ 0 0
$$541$$ −15.6485 −0.672780 −0.336390 0.941723i $$-0.609206\pi$$
−0.336390 + 0.941723i $$0.609206\pi$$
$$542$$ 0 0
$$543$$ 3.24473i 0.139245i
$$544$$ 0 0
$$545$$ 5.69643 + 3.37271i 0.244008 + 0.144471i
$$546$$ 0 0
$$547$$ 10.8543i 0.464098i 0.972704 + 0.232049i $$0.0745429\pi$$
−0.972704 + 0.232049i $$0.925457\pi$$
$$548$$ 0 0
$$549$$ 2.38434 0.101761
$$550$$ 0 0
$$551$$ 10.6570 0.454003
$$552$$ 0 0
$$553$$ 18.9759i 0.806936i
$$554$$ 0 0
$$555$$ 5.06437 + 2.99848i 0.214971 + 0.127278i
$$556$$ 0 0
$$557$$ 18.8763i 0.799814i 0.916556 + 0.399907i $$0.130958\pi$$
−0.916556 + 0.399907i $$0.869042\pi$$
$$558$$ 0 0
$$559$$ −8.15777 −0.345037
$$560$$ 0 0
$$561$$ 40.1458 1.69496
$$562$$ 0 0
$$563$$ 22.2846i 0.939183i −0.882884 0.469591i $$-0.844401\pi$$
0.882884 0.469591i $$-0.155599\pi$$
$$564$$ 0 0
$$565$$ 8.07290 13.6350i 0.339629 0.573627i
$$566$$ 0 0
$$567$$ 36.8170i 1.54617i
$$568$$ 0 0
$$569$$ 7.11833 0.298416 0.149208 0.988806i $$-0.452328\pi$$
0.149208 + 0.988806i $$0.452328\pi$$
$$570$$ 0 0
$$571$$ −1.21017 −0.0506440 −0.0253220 0.999679i $$-0.508061\pi$$
−0.0253220 + 0.999679i $$0.508061\pi$$
$$572$$ 0 0
$$573$$ 1.44011i 0.0601613i
$$574$$ 0 0
$$575$$ −3.41591 + 1.87347i −0.142453 + 0.0781289i
$$576$$ 0 0
$$577$$ 41.4143i 1.72410i −0.506823 0.862050i $$-0.669180\pi$$
0.506823 0.862050i $$-0.330820\pi$$
$$578$$ 0 0
$$579$$ −31.0814 −1.29170
$$580$$ 0 0
$$581$$ 3.69643 0.153354
$$582$$ 0 0
$$583$$ 27.6846i 1.14658i
$$584$$ 0 0
$$585$$ 0.353426 0.596929i 0.0146124 0.0246800i
$$586$$ 0 0
$$587$$ 0.0591336i 0.00244071i 0.999999 + 0.00122035i $$0.000388450\pi$$
−0.999999 + 0.00122035i $$0.999612\pi$$
$$588$$ 0 0
$$589$$ 8.65699 0.356705
$$590$$ 0 0
$$591$$ 5.47175 0.225078
$$592$$ 0 0
$$593$$ 42.8828i 1.76099i −0.474059 0.880493i $$-0.657212\pi$$
0.474059 0.880493i $$-0.342788\pi$$
$$594$$ 0 0
$$595$$ −50.4148 29.8493i −2.06681 1.22370i
$$596$$ 0 0
$$597$$ 7.43706i 0.304379i
$$598$$ 0 0
$$599$$ 15.3430 0.626898 0.313449 0.949605i $$-0.398515\pi$$
0.313449 + 0.949605i $$0.398515\pi$$
$$600$$ 0 0
$$601$$ −12.5781 −0.513072 −0.256536 0.966535i $$-0.582581\pi$$
−0.256536 + 0.966535i $$0.582581\pi$$
$$602$$ 0 0
$$603$$ 5.47785i 0.223075i
$$604$$ 0 0
$$605$$ −17.4572 10.3360i −0.709738 0.420217i
$$606$$ 0 0
$$607$$ 2.65751i 0.107865i −0.998545 0.0539325i $$-0.982824\pi$$
0.998545 0.0539325i $$-0.0171756\pi$$
$$608$$ 0 0
$$609$$ 82.0208 3.32365
$$610$$ 0 0
$$611$$ −2.68602 −0.108665
$$612$$ 0 0
$$613$$ 34.1052i 1.37750i −0.725001 0.688748i $$-0.758161\pi$$
0.725001 0.688748i $$-0.241839\pi$$
$$614$$ 0 0
$$615$$ −8.75293 + 14.7835i −0.352952 + 0.596129i
$$616$$ 0 0
$$617$$ 29.9226i 1.20464i 0.798255 + 0.602319i $$0.205756\pi$$
−0.798255 + 0.602319i $$0.794244\pi$$
$$618$$ 0 0
$$619$$ 17.2102 0.691735 0.345868 0.938283i $$-0.387585\pi$$
0.345868 + 0.938283i $$0.387585\pi$$
$$620$$ 0 0
$$621$$ 4.25749 0.170847
$$622$$ 0 0
$$623$$ 27.0237i 1.08268i
$$624$$ 0 0
$$625$$ −13.4378 + 21.0814i −0.537514 + 0.843255i
$$626$$ 0 0
$$627$$ 7.26864i 0.290281i
$$628$$ 0 0
$$629$$ −8.96056 −0.357281
$$630$$ 0 0
$$631$$ 3.36195 0.133837 0.0669186 0.997758i $$-0.478683\pi$$
0.0669186 + 0.997758i $$0.478683\pi$$
$$632$$ 0 0
$$633$$ 24.1435i 0.959617i
$$634$$ 0 0
$$635$$ −11.1622 + 18.8527i −0.442958 + 0.748148i
$$636$$ 0 0
$$637$$ 13.0736i 0.517996i
$$638$$ 0 0
$$639$$ −0.111693 −0.00441853
$$640$$ 0 0
$$641$$ −16.2745 −0.642806 −0.321403 0.946943i $$-0.604154\pi$$
−0.321403 + 0.946943i $$0.604154\pi$$
$$642$$ 0 0
$$643$$ 35.7040i 1.40803i 0.710185 + 0.704015i $$0.248611\pi$$
−0.710185 + 0.704015i $$0.751389\pi$$
$$644$$ 0 0
$$645$$ −30.2016 17.8816i −1.18919 0.704087i
$$646$$ 0 0
$$647$$ 15.2881i 0.601036i −0.953776 0.300518i $$-0.902840\pi$$
0.953776 0.300518i $$-0.0971595\pi$$
$$648$$ 0 0
$$649$$ −52.4033 −2.05701
$$650$$ 0 0
$$651$$ 66.6280 2.61136
$$652$$ 0 0
$$653$$ 16.4512i 0.643785i −0.946776 0.321892i $$-0.895681\pi$$
0.946776 0.321892i $$-0.104319\pi$$
$$654$$ 0 0
$$655$$ 24.2132 + 14.3360i 0.946087 + 0.560152i
$$656$$ 0 0
$$657$$ 3.70882i 0.144695i
$$658$$ 0 0
$$659$$ 7.03944 0.274218 0.137109 0.990556i $$-0.456219\pi$$
0.137109 + 0.990556i $$0.456219\pi$$
$$660$$ 0 0
$$661$$ 6.35343 0.247120 0.123560 0.992337i $$-0.460569\pi$$
0.123560 + 0.992337i $$0.460569\pi$$
$$662$$ 0 0
$$663$$ 7.55533i 0.293425i
$$664$$ 0 0
$$665$$ 5.40439 9.12790i 0.209573 0.353965i
$$666$$ 0 0
$$667$$ 8.30378i 0.321524i
$$668$$ 0 0
$$669$$ 30.4743 1.17820
$$670$$ 0 0
$$671$$ −29.0335 −1.12082
$$672$$ 0 0
$$673$$ 7.08638i 0.273160i −0.990629 0.136580i $$-0.956389\pi$$
0.990629 0.136580i $$-0.0436111\pi$$
$$674$$ 0 0
$$675$$ 23.9539 13.1376i 0.921987 0.505667i
$$676$$ 0 0
$$677$$ 17.6095i 0.676786i −0.941005 0.338393i $$-0.890117\pi$$
0.941005 0.338393i $$-0.109883\pi$$
$$678$$ 0 0
$$679$$ −29.3140 −1.12497
$$680$$ 0 0
$$681$$ 1.36794 0.0524195
$$682$$ 0 0
$$683$$ 26.5855i 1.01726i −0.860984 0.508632i $$-0.830151\pi$$
0.860984 0.508632i $$-0.169849\pi$$
$$684$$ 0 0
$$685$$ 10.1343 17.1166i 0.387211 0.653992i
$$686$$ 0 0
$$687$$ 7.88911i 0.300988i
$$688$$ 0 0
$$689$$ 5.21017 0.198492
$$690$$ 0 0
$$691$$ −49.4907 −1.88271 −0.941357 0.337411i $$-0.890449\pi$$
−0.941357 + 0.337411i $$0.890449\pi$$
$$692$$ 0 0
$$693$$ 7.82027i 0.297067i
$$694$$ 0 0
$$695$$ −12.0364 7.12646i −0.456569 0.270322i
$$696$$ 0 0
$$697$$ 26.1570i 0.990766i
$$698$$ 0 0
$$699$$ 7.95392 0.300845
$$700$$ 0 0
$$701$$ 29.3389 1.10812 0.554058 0.832478i $$-0.313079\pi$$
0.554058 + 0.832478i $$0.313079\pi$$
$$702$$ 0 0
$$703$$ 1.62236i 0.0611886i
$$704$$ 0 0
$$705$$ −9.94415 5.88767i −0.374518 0.221742i
$$706$$ 0 0
$$707$$ 15.9774i 0.600891i
$$708$$ 0 0
$$709$$ −24.7359 −0.928975 −0.464488 0.885580i $$-0.653762\pi$$
−0.464488 + 0.885580i $$0.653762\pi$$
$$710$$ 0 0
$$711$$ 1.47175 0.0551951
$$712$$ 0 0
$$713$$ 6.74541i 0.252618i
$$714$$ 0 0
$$715$$ −4.30357 + 7.26864i −0.160944 + 0.271832i
$$716$$ 0 0
$$717$$ 10.0613i 0.375747i
$$718$$ 0 0
$$719$$ 26.7548 0.997786 0.498893 0.866663i $$-0.333740\pi$$
0.498893 + 0.866663i $$0.333740\pi$$
$$720$$ 0 0
$$721$$ 17.6175 0.656112
$$722$$ 0 0
$$723$$ 5.29559i 0.196945i
$$724$$ 0 0
$$725$$ 25.6235 + 46.7196i 0.951634 + 1.73512i
$$726$$ 0 0
$$727$$ 27.2108i 1.00919i −0.863355 0.504596i $$-0.831641\pi$$
0.863355 0.504596i $$-0.168359\pi$$
$$728$$ 0 0
$$729$$ −29.4494 −1.09072
$$730$$ 0 0
$$731$$ 53.4367 1.97643
$$732$$ 0 0
$$733$$ 40.0026i 1.47753i 0.673963 + 0.738765i $$0.264591\pi$$
−0.673963 + 0.738765i $$0.735409\pi$$
$$734$$ 0 0
$$735$$ 28.6570 48.4011i 1.05703 1.78530i
$$736$$ 0 0
$$737$$ 66.7022i 2.45701i
$$738$$ 0 0
$$739$$ 35.1123 1.29163 0.645814 0.763495i $$-0.276518\pi$$
0.645814 + 0.763495i $$0.276518\pi$$
$$740$$ 0 0
$$741$$ 1.36794 0.0502525
$$742$$ 0 0
$$743$$ 25.6476i 0.940918i −0.882422 0.470459i $$-0.844088\pi$$
0.882422 0.470459i $$-0.155912\pi$$
$$744$$ 0 0
$$745$$ 4.77233 + 2.82557i 0.174844 + 0.103521i
$$746$$ 0 0
$$747$$ 0.286693i 0.0104895i
$$748$$ 0 0
$$749$$ 48.4033 1.76862
$$750$$ 0 0
$$751$$ 13.2641 0.484015 0.242007 0.970274i $$-0.422194\pi$$
0.242007 + 0.970274i $$0.422194\pi$$
$$752$$ 0 0
$$753$$ 46.1178i 1.68063i
$$754$$ 0 0
$$755$$ 7.11234 + 4.21103i 0.258845 + 0.153255i
$$756$$ 0 0
$$757$$ 2.77092i 0.100711i −0.998731 0.0503554i $$-0.983965\pi$$
0.998731 0.0503554i $$-0.0160354\pi$$
$$758$$ 0 0
$$759$$ −5.66363 −0.205577
$$760$$ 0 0
$$761$$ 10.7838 0.390914 0.195457 0.980712i $$-0.437381\pi$$
0.195457 + 0.980712i $$0.437381\pi$$
$$762$$ 0 0
$$763$$ 14.0448i 0.508455i
$$764$$ 0 0
$$765$$ −2.31508 + 3.91013i −0.0837021 + 0.141371i
$$766$$ 0 0
$$767$$ 9.86216i 0.356102i
$$768$$ 0 0
$$769$$ 40.6090 1.46440 0.732199 0.681090i $$-0.238494\pi$$
0.732199 + 0.681090i $$0.238494\pi$$
$$770$$ 0 0
$$771$$ −15.4967 −0.558099
$$772$$ 0 0
$$773$$ 17.4410i 0.627310i −0.949537 0.313655i $$-0.898446\pi$$
0.949537 0.313655i $$-0.101554\pi$$
$$774$$ 0 0
$$775$$ 20.8148 + 37.9517i 0.747688 + 1.36327i
$$776$$ 0 0
$$777$$ 12.4864i 0.447947i
$$778$$ 0 0
$$779$$ 4.73588 0.169680
$$780$$ 0 0
$$781$$ 1.36006 0.0486668
$$782$$ 0 0
$$783$$ 58.2300i 2.08097i
$$784$$ 0 0
$$785$$ 21.4718 36.2654i 0.766360 1.29437i
$$786$$ 0 0
$$787$$ 30.8346i 1.09914i 0.835449 + 0.549568i $$0.185208\pi$$
−0.835449 + 0.549568i $$0.814792\pi$$
$$788$$ 0 0
$$789$$ −15.4888 −0.551416
$$790$$ 0 0
$$791$$ −33.6175 −1.19530
$$792$$ 0 0
$$793$$ 5.46402i 0.194033i
$$794$$ 0 0
$$795$$ 19.2891 + 11.4205i 0.684112 + 0.405044i
$$796$$ 0 0
$$797$$ 38.1340i 1.35077i 0.737463 + 0.675387i $$0.236024\pi$$
−0.737463 + 0.675387i $$0.763976\pi$$
$$798$$ 0 0
$$799$$ 17.5945 0.622449
$$800$$ 0 0