# Properties

 Label 360.2.w.d.163.1 Level $360$ Weight $2$ Character 360.163 Analytic conductor $2.875$ Analytic rank $0$ Dimension $16$ CM no Inner twists $8$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$360 = 2^{3} \cdot 3^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 360.w (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$2.87461447277$$ Analytic rank: $$0$$ Dimension: $$16$$ Relative dimension: $$8$$ over $$\Q(i)$$ Coefficient field: $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ Defining polynomial: $$x^{16} + 5 x^{12} + 28 x^{8} + 80 x^{4} + 256$$ Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$2^{8}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 163.1 Root $$-0.512386 + 1.31813i$$ of defining polynomial Character $$\chi$$ $$=$$ 360.163 Dual form 360.2.w.d.307.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.31813 - 0.512386i) q^{2} +(1.47492 + 1.35078i) q^{4} +(1.83051 + 1.28422i) q^{5} +(2.94984 + 2.94984i) q^{7} +(-1.25201 - 2.53623i) q^{8} +O(q^{10})$$ $$q+(-1.31813 - 0.512386i) q^{2} +(1.47492 + 1.35078i) q^{4} +(1.83051 + 1.28422i) q^{5} +(2.94984 + 2.94984i) q^{7} +(-1.25201 - 2.53623i) q^{8} +(-1.75483 - 2.63069i) q^{10} -1.61148 q^{11} +(-2.50967 + 2.50967i) q^{13} +(-2.37681 - 5.39972i) q^{14} +(0.350781 + 3.98459i) q^{16} +(-4.59398 + 4.59398i) q^{17} -4.00000i q^{19} +(0.965164 + 4.36674i) q^{20} +(2.12414 + 0.825702i) q^{22} +(1.09259 - 1.09259i) q^{23} +(1.70156 + 4.70156i) q^{25} +(4.59398 - 2.02214i) q^{26} +(0.366192 + 8.33537i) q^{28} +4.75362 q^{29} -5.01934i q^{31} +(1.57927 - 5.43193i) q^{32} +(8.40935 - 3.70156i) q^{34} +(1.61148 + 9.18797i) q^{35} +(2.50967 + 2.50967i) q^{37} +(-2.04955 + 5.27251i) q^{38} +(0.965252 - 6.25046i) q^{40} +9.18797 q^{41} +(-7.40312 - 7.40312i) q^{43} +(-2.37681 - 2.17676i) q^{44} +(-2.00000 + 0.880344i) q^{46} +(7.32206 + 7.32206i) q^{47} +10.4031i q^{49} +(0.166140 - 7.06912i) q^{50} +(-7.09158 + 0.311549i) q^{52} +(-3.11473 + 3.11473i) q^{53} +(-2.94984 - 2.06950i) q^{55} +(3.78824 - 11.1747i) q^{56} +(-6.26587 - 2.43569i) q^{58} -1.61148i q^{59} -6.78003i q^{61} +(-2.57184 + 6.61613i) q^{62} +(-4.86493 + 6.35078i) q^{64} +(-7.81695 + 1.37102i) q^{65} +(7.40312 - 7.40312i) q^{67} +(-12.9812 + 0.570295i) q^{68} +(2.58365 - 12.9366i) q^{70} +(5.00000 + 5.00000i) q^{73} +(-2.02214 - 4.59398i) q^{74} +(5.40312 - 5.89968i) q^{76} +(-4.75362 - 4.75362i) q^{77} +5.01934 q^{79} +(-4.47498 + 7.74433i) q^{80} +(-12.1109 - 4.70779i) q^{82} +(-7.57648 - 7.57648i) q^{83} +(-14.3090 + 2.50967i) q^{85} +(5.96500 + 13.5515i) q^{86} +(2.01759 + 4.08709i) q^{88} -2.74204i q^{89} -14.8062 q^{91} +(3.08733 - 0.135633i) q^{92} +(-5.89968 - 13.4031i) q^{94} +(5.13688 - 7.32206i) q^{95} +(2.40312 - 2.40312i) q^{97} +(5.33042 - 13.7126i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$16 q + O(q^{10})$$ $$16 q - 8 q^{10} - 20 q^{16} + 36 q^{22} - 24 q^{25} + 44 q^{28} + 32 q^{40} - 16 q^{43} - 32 q^{46} - 8 q^{52} - 44 q^{58} + 16 q^{67} - 44 q^{70} + 80 q^{73} - 16 q^{76} - 8 q^{82} - 28 q^{88} - 32 q^{91} - 64 q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$$.

 $$n$$ $$181$$ $$217$$ $$271$$ $$281$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{3}{4}\right)$$ $$-1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.31813 0.512386i −0.932057 0.362312i
$$3$$ 0 0
$$4$$ 1.47492 + 1.35078i 0.737460 + 0.675391i
$$5$$ 1.83051 + 1.28422i 0.818631 + 0.574320i
$$6$$ 0 0
$$7$$ 2.94984 + 2.94984i 1.11494 + 1.11494i 0.992473 + 0.122462i $$0.0390789\pi$$
0.122462 + 0.992473i $$0.460921\pi$$
$$8$$ −1.25201 2.53623i −0.442653 0.896693i
$$9$$ 0 0
$$10$$ −1.75483 2.63069i −0.554927 0.831899i
$$11$$ −1.61148 −0.485880 −0.242940 0.970041i $$-0.578112\pi$$
−0.242940 + 0.970041i $$0.578112\pi$$
$$12$$ 0 0
$$13$$ −2.50967 + 2.50967i −0.696057 + 0.696057i −0.963558 0.267501i $$-0.913802\pi$$
0.267501 + 0.963558i $$0.413802\pi$$
$$14$$ −2.37681 5.39972i −0.635229 1.44314i
$$15$$ 0 0
$$16$$ 0.350781 + 3.98459i 0.0876953 + 0.996147i
$$17$$ −4.59398 + 4.59398i −1.11420 + 1.11420i −0.121629 + 0.992576i $$0.538812\pi$$
−0.992576 + 0.121629i $$0.961188\pi$$
$$18$$ 0 0
$$19$$ 4.00000i 0.917663i −0.888523 0.458831i $$-0.848268\pi$$
0.888523 0.458831i $$-0.151732\pi$$
$$20$$ 0.965164 + 4.36674i 0.215817 + 0.976434i
$$21$$ 0 0
$$22$$ 2.12414 + 0.825702i 0.452868 + 0.176040i
$$23$$ 1.09259 1.09259i 0.227821 0.227821i −0.583961 0.811782i $$-0.698498\pi$$
0.811782 + 0.583961i $$0.198498\pi$$
$$24$$ 0 0
$$25$$ 1.70156 + 4.70156i 0.340312 + 0.940312i
$$26$$ 4.59398 2.02214i 0.900954 0.396575i
$$27$$ 0 0
$$28$$ 0.366192 + 8.33537i 0.0692037 + 1.57524i
$$29$$ 4.75362 0.882725 0.441362 0.897329i $$-0.354495\pi$$
0.441362 + 0.897329i $$0.354495\pi$$
$$30$$ 0 0
$$31$$ 5.01934i 0.901500i −0.892650 0.450750i $$-0.851157\pi$$
0.892650 0.450750i $$-0.148843\pi$$
$$32$$ 1.57927 5.43193i 0.279179 0.960239i
$$33$$ 0 0
$$34$$ 8.40935 3.70156i 1.44219 0.634813i
$$35$$ 1.61148 + 9.18797i 0.272390 + 1.55305i
$$36$$ 0 0
$$37$$ 2.50967 + 2.50967i 0.412587 + 0.412587i 0.882639 0.470052i $$-0.155765\pi$$
−0.470052 + 0.882639i $$0.655765\pi$$
$$38$$ −2.04955 + 5.27251i −0.332480 + 0.855314i
$$39$$ 0 0
$$40$$ 0.965252 6.25046i 0.152620 0.988285i
$$41$$ 9.18797 1.43492 0.717460 0.696600i $$-0.245305\pi$$
0.717460 + 0.696600i $$0.245305\pi$$
$$42$$ 0 0
$$43$$ −7.40312 7.40312i −1.12897 1.12897i −0.990346 0.138620i $$-0.955733\pi$$
−0.138620 0.990346i $$-0.544267\pi$$
$$44$$ −2.37681 2.17676i −0.358317 0.328159i
$$45$$ 0 0
$$46$$ −2.00000 + 0.880344i −0.294884 + 0.129800i
$$47$$ 7.32206 + 7.32206i 1.06803 + 1.06803i 0.997510 + 0.0705213i $$0.0224663\pi$$
0.0705213 + 0.997510i $$0.477534\pi$$
$$48$$ 0 0
$$49$$ 10.4031i 1.48616i
$$50$$ 0.166140 7.06912i 0.0234958 0.999724i
$$51$$ 0 0
$$52$$ −7.09158 + 0.311549i −0.983425 + 0.0432041i
$$53$$ −3.11473 + 3.11473i −0.427841 + 0.427841i −0.887892 0.460051i $$-0.847831\pi$$
0.460051 + 0.887892i $$0.347831\pi$$
$$54$$ 0 0
$$55$$ −2.94984 2.06950i −0.397756 0.279051i
$$56$$ 3.78824 11.1747i 0.506225 1.49328i
$$57$$ 0 0
$$58$$ −6.26587 2.43569i −0.822750 0.319822i
$$59$$ 1.61148i 0.209797i −0.994483 0.104899i $$-0.966548\pi$$
0.994483 0.104899i $$-0.0334518\pi$$
$$60$$ 0 0
$$61$$ 6.78003i 0.868093i −0.900890 0.434047i $$-0.857085\pi$$
0.900890 0.434047i $$-0.142915\pi$$
$$62$$ −2.57184 + 6.61613i −0.326624 + 0.840249i
$$63$$ 0 0
$$64$$ −4.86493 + 6.35078i −0.608117 + 0.793848i
$$65$$ −7.81695 + 1.37102i −0.969573 + 0.170054i
$$66$$ 0 0
$$67$$ 7.40312 7.40312i 0.904436 0.904436i −0.0913805 0.995816i $$-0.529128\pi$$
0.995816 + 0.0913805i $$0.0291279\pi$$
$$68$$ −12.9812 + 0.570295i −1.57421 + 0.0691584i
$$69$$ 0 0
$$70$$ 2.58365 12.9366i 0.308805 1.54622i
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ 0 0
$$73$$ 5.00000 + 5.00000i 0.585206 + 0.585206i 0.936329 0.351123i $$-0.114200\pi$$
−0.351123 + 0.936329i $$0.614200\pi$$
$$74$$ −2.02214 4.59398i −0.235069 0.534040i
$$75$$ 0 0
$$76$$ 5.40312 5.89968i 0.619781 0.676740i
$$77$$ −4.75362 4.75362i −0.541725 0.541725i
$$78$$ 0 0
$$79$$ 5.01934 0.564720 0.282360 0.959309i $$-0.408883\pi$$
0.282360 + 0.959309i $$0.408883\pi$$
$$80$$ −4.47498 + 7.74433i −0.500318 + 0.865842i
$$81$$ 0 0
$$82$$ −12.1109 4.70779i −1.33743 0.519888i
$$83$$ −7.57648 7.57648i −0.831627 0.831627i 0.156112 0.987739i $$-0.450104\pi$$
−0.987739 + 0.156112i $$0.950104\pi$$
$$84$$ 0 0
$$85$$ −14.3090 + 2.50967i −1.55203 + 0.272212i
$$86$$ 5.96500 + 13.5515i 0.643223 + 1.46130i
$$87$$ 0 0
$$88$$ 2.01759 + 4.08709i 0.215076 + 0.435685i
$$89$$ 2.74204i 0.290655i −0.989384 0.145328i $$-0.953576\pi$$
0.989384 0.145328i $$-0.0464236\pi$$
$$90$$ 0 0
$$91$$ −14.8062 −1.55212
$$92$$ 3.08733 0.135633i 0.321877 0.0141408i
$$93$$ 0 0
$$94$$ −5.89968 13.4031i −0.608506 1.38243i
$$95$$ 5.13688 7.32206i 0.527032 0.751227i
$$96$$ 0 0
$$97$$ 2.40312 2.40312i 0.244000 0.244000i −0.574503 0.818503i $$-0.694804\pi$$
0.818503 + 0.574503i $$0.194804\pi$$
$$98$$ 5.33042 13.7126i 0.538454 1.38519i
$$99$$ 0 0
$$100$$ −3.84111 + 9.23287i −0.384111 + 0.923287i
$$101$$ 8.79790i 0.875424i −0.899115 0.437712i $$-0.855789\pi$$
0.899115 0.437712i $$-0.144211\pi$$
$$102$$ 0 0
$$103$$ 7.96918 7.96918i 0.785227 0.785227i −0.195481 0.980707i $$-0.562627\pi$$
0.980707 + 0.195481i $$0.0626268\pi$$
$$104$$ 9.50723 + 3.22296i 0.932261 + 0.316038i
$$105$$ 0 0
$$106$$ 5.70156 2.50967i 0.553785 0.243761i
$$107$$ −1.61148 + 1.61148i −0.155788 + 0.155788i −0.780697 0.624909i $$-0.785136\pi$$
0.624909 + 0.780697i $$0.285136\pi$$
$$108$$ 0 0
$$109$$ −11.7994 −1.13017 −0.565087 0.825031i $$-0.691157\pi$$
−0.565087 + 0.825031i $$0.691157\pi$$
$$110$$ 2.82788 + 4.23932i 0.269628 + 0.404203i
$$111$$ 0 0
$$112$$ −10.7192 + 12.7887i −1.01287 + 1.20841i
$$113$$ −4.59398 4.59398i −0.432166 0.432166i 0.457199 0.889364i $$-0.348853\pi$$
−0.889364 + 0.457199i $$0.848853\pi$$
$$114$$ 0 0
$$115$$ 3.40312 0.596876i 0.317343 0.0556590i
$$116$$ 7.01121 + 6.42110i 0.650974 + 0.596184i
$$117$$ 0 0
$$118$$ −0.825702 + 2.12414i −0.0760120 + 0.195543i
$$119$$ −27.1030 −2.48453
$$120$$ 0 0
$$121$$ −8.40312 −0.763920
$$122$$ −3.47399 + 8.93694i −0.314521 + 0.809112i
$$123$$ 0 0
$$124$$ 6.78003 7.40312i 0.608864 0.664820i
$$125$$ −2.92310 + 10.7915i −0.261450 + 0.965217i
$$126$$ 0 0
$$127$$ 3.83019 + 3.83019i 0.339874 + 0.339874i 0.856320 0.516446i $$-0.172745\pi$$
−0.516446 + 0.856320i $$0.672745\pi$$
$$128$$ 9.66666 5.87841i 0.854420 0.519583i
$$129$$ 0 0
$$130$$ 11.0062 + 2.19812i 0.965310 + 0.192788i
$$131$$ 13.5415 1.18313 0.591563 0.806259i $$-0.298511\pi$$
0.591563 + 0.806259i $$0.298511\pi$$
$$132$$ 0 0
$$133$$ 11.7994 11.7994i 1.02313 1.02313i
$$134$$ −13.5515 + 5.96500i −1.17067 + 0.515298i
$$135$$ 0 0
$$136$$ 17.4031 + 5.89968i 1.49231 + 0.505894i
$$137$$ 11.0399 11.0399i 0.943203 0.943203i −0.0552681 0.998472i $$-0.517601\pi$$
0.998472 + 0.0552681i $$0.0176013\pi$$
$$138$$ 0 0
$$139$$ 4.00000i 0.339276i 0.985506 + 0.169638i $$0.0542598\pi$$
−0.985506 + 0.169638i $$0.945740\pi$$
$$140$$ −10.0341 + 15.7283i −0.848038 + 1.32928i
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 4.04429 4.04429i 0.338200 0.338200i
$$144$$ 0 0
$$145$$ 8.70156 + 6.10469i 0.722625 + 0.506967i
$$146$$ −4.02871 9.15257i −0.333418 0.757472i
$$147$$ 0 0
$$148$$ 0.311549 + 7.09158i 0.0256092 + 0.582924i
$$149$$ 8.79790 0.720752 0.360376 0.932807i $$-0.382648\pi$$
0.360376 + 0.932807i $$0.382648\pi$$
$$150$$ 0 0
$$151$$ 0.880344i 0.0716414i −0.999358 0.0358207i $$-0.988595\pi$$
0.999358 0.0358207i $$-0.0114045\pi$$
$$152$$ −10.1449 + 5.00805i −0.822862 + 0.406206i
$$153$$ 0 0
$$154$$ 3.83019 + 8.70156i 0.308645 + 0.701192i
$$155$$ 6.44593 9.18797i 0.517750 0.737995i
$$156$$ 0 0
$$157$$ 9.28970 + 9.28970i 0.741398 + 0.741398i 0.972847 0.231449i $$-0.0743465\pi$$
−0.231449 + 0.972847i $$0.574347\pi$$
$$158$$ −6.61613 2.57184i −0.526351 0.204605i
$$159$$ 0 0
$$160$$ 9.86668 7.91509i 0.780029 0.625743i
$$161$$ 6.44593 0.508010
$$162$$ 0 0
$$163$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$164$$ 13.5515 + 12.4109i 1.05820 + 0.969131i
$$165$$ 0 0
$$166$$ 6.10469 + 13.8689i 0.473816 + 1.07643i
$$167$$ −7.32206 7.32206i −0.566598 0.566598i 0.364576 0.931174i $$-0.381214\pi$$
−0.931174 + 0.364576i $$0.881214\pi$$
$$168$$ 0 0
$$169$$ 0.403124i 0.0310096i
$$170$$ 20.1471 + 4.02369i 1.54521 + 0.308603i
$$171$$ 0 0
$$172$$ −0.919020 20.9190i −0.0700746 1.59506i
$$173$$ −7.86835 + 7.86835i −0.598220 + 0.598220i −0.939839 0.341619i $$-0.889025\pi$$
0.341619 + 0.939839i $$0.389025\pi$$
$$174$$ 0 0
$$175$$ −8.84952 + 18.8882i −0.668961 + 1.42781i
$$176$$ −0.565278 6.42110i −0.0426094 0.484008i
$$177$$ 0 0
$$178$$ −1.40498 + 3.61436i −0.105308 + 0.270907i
$$179$$ 26.4333i 1.97572i −0.155343 0.987861i $$-0.549648\pi$$
0.155343 0.987861i $$-0.450352\pi$$
$$180$$ 0 0
$$181$$ 11.7994i 0.877040i 0.898721 + 0.438520i $$0.144497\pi$$
−0.898721 + 0.438520i $$0.855503\pi$$
$$182$$ 19.5165 + 7.58652i 1.44666 + 0.562350i
$$183$$ 0 0
$$184$$ −4.13899 1.40312i −0.305131 0.103440i
$$185$$ 1.37102 + 7.81695i 0.100799 + 0.574713i
$$186$$ 0 0
$$187$$ 7.40312 7.40312i 0.541370 0.541370i
$$188$$ 0.908956 + 20.6899i 0.0662924 + 1.50897i
$$189$$ 0 0
$$190$$ −10.5228 + 7.01934i −0.763403 + 0.509236i
$$191$$ 19.0145i 1.37584i 0.725787 + 0.687919i $$0.241476\pi$$
−0.725787 + 0.687919i $$0.758524\pi$$
$$192$$ 0 0
$$193$$ −12.4031 12.4031i −0.892796 0.892796i 0.101989 0.994786i $$-0.467479\pi$$
−0.994786 + 0.101989i $$0.967479\pi$$
$$194$$ −4.39895 + 1.93630i −0.315826 + 0.139018i
$$195$$ 0 0
$$196$$ −14.0523 + 15.3438i −1.00374 + 1.09598i
$$197$$ −9.34420 9.34420i −0.665747 0.665747i 0.290982 0.956729i $$-0.406018\pi$$
−0.956729 + 0.290982i $$0.906018\pi$$
$$198$$ 0 0
$$199$$ −20.9577 −1.48565 −0.742826 0.669485i $$-0.766515\pi$$
−0.742826 + 0.669485i $$0.766515\pi$$
$$200$$ 9.79387 10.2020i 0.692531 0.721388i
$$201$$ 0 0
$$202$$ −4.50793 + 11.5968i −0.317177 + 0.815945i
$$203$$ 14.0224 + 14.0224i 0.984181 + 0.984181i
$$204$$ 0 0
$$205$$ 16.8187 + 11.7994i 1.17467 + 0.824103i
$$206$$ −14.5877 + 6.42110i −1.01637 + 0.447379i
$$207$$ 0 0
$$208$$ −10.8803 9.11966i −0.754416 0.632334i
$$209$$ 6.44593i 0.445874i
$$210$$ 0 0
$$211$$ 12.0000 0.826114 0.413057 0.910705i $$-0.364461\pi$$
0.413057 + 0.910705i $$0.364461\pi$$
$$212$$ −8.80131 + 0.386661i −0.604476 + 0.0265560i
$$213$$ 0 0
$$214$$ 2.94984 1.29844i 0.201647 0.0887594i
$$215$$ −4.04429 23.0588i −0.275818 1.57259i
$$216$$ 0 0
$$217$$ 14.8062 14.8062i 1.00511 1.00511i
$$218$$ 15.5531 + 6.04583i 1.05339 + 0.409475i
$$219$$ 0 0
$$220$$ −1.55534 7.03693i −0.104861 0.474430i
$$221$$ 23.0588i 1.55110i
$$222$$ 0 0
$$223$$ 3.83019 3.83019i 0.256488 0.256488i −0.567136 0.823624i $$-0.691949\pi$$
0.823624 + 0.567136i $$0.191949\pi$$
$$224$$ 20.6819 11.3647i 1.38187 0.759338i
$$225$$ 0 0
$$226$$ 3.70156 + 8.40935i 0.246224 + 0.559382i
$$227$$ −15.6339 + 15.6339i −1.03766 + 1.03766i −0.0383956 + 0.999263i $$0.512225\pi$$
−0.999263 + 0.0383956i $$0.987775\pi$$
$$228$$ 0 0
$$229$$ 6.78003 0.448037 0.224018 0.974585i $$-0.428082\pi$$
0.224018 + 0.974585i $$0.428082\pi$$
$$230$$ −4.79158 0.956956i −0.315948 0.0630998i
$$231$$ 0 0
$$232$$ −5.95158 12.0563i −0.390741 0.791533i
$$233$$ −11.0399 11.0399i −0.723249 0.723249i 0.246017 0.969266i $$-0.420878\pi$$
−0.969266 + 0.246017i $$0.920878\pi$$
$$234$$ 0 0
$$235$$ 4.00000 + 22.8062i 0.260931 + 1.48772i
$$236$$ 2.17676 2.37681i 0.141695 0.154717i
$$237$$ 0 0
$$238$$ 35.7253 + 13.8872i 2.31573 + 0.900175i
$$239$$ 8.08857 0.523206 0.261603 0.965176i $$-0.415749\pi$$
0.261603 + 0.965176i $$0.415749\pi$$
$$240$$ 0 0
$$241$$ −6.80625 −0.438429 −0.219215 0.975677i $$-0.570349\pi$$
−0.219215 + 0.975677i $$0.570349\pi$$
$$242$$ 11.0764 + 4.30565i 0.712017 + 0.276777i
$$243$$ 0 0
$$244$$ 9.15833 10.0000i 0.586302 0.640184i
$$245$$ −13.3599 + 19.0431i −0.853532 + 1.21662i
$$246$$ 0 0
$$247$$ 10.0387 + 10.0387i 0.638746 + 0.638746i
$$248$$ −12.7302 + 6.28427i −0.808368 + 0.399051i
$$249$$ 0 0
$$250$$ 9.38242 12.7268i 0.593396 0.804911i
$$251$$ −19.9874 −1.26159 −0.630797 0.775948i $$-0.717272\pi$$
−0.630797 + 0.775948i $$0.717272\pi$$
$$252$$ 0 0
$$253$$ −1.76069 + 1.76069i −0.110694 + 0.110694i
$$254$$ −3.08614 7.01121i −0.193642 0.439922i
$$255$$ 0 0
$$256$$ −15.7539 + 2.79544i −0.984619 + 0.174715i
$$257$$ 13.7820 13.7820i 0.859694 0.859694i −0.131607 0.991302i $$-0.542014\pi$$
0.991302 + 0.131607i $$0.0420138\pi$$
$$258$$ 0 0
$$259$$ 14.8062i 0.920016i
$$260$$ −13.3813 8.53684i −0.829874 0.529432i
$$261$$ 0 0
$$262$$ −17.8494 6.93847i −1.10274 0.428660i
$$263$$ −2.95170 + 2.95170i −0.182009 + 0.182009i −0.792231 0.610221i $$-0.791080\pi$$
0.610221 + 0.792231i $$0.291080\pi$$
$$264$$ 0 0
$$265$$ −9.70156 + 1.70156i −0.595962 + 0.104526i
$$266$$ −21.5989 + 9.50723i −1.32431 + 0.582926i
$$267$$ 0 0
$$268$$ 20.9190 0.919020i 1.27783 0.0561381i
$$269$$ 18.3051 1.11608 0.558042 0.829813i $$-0.311553\pi$$
0.558042 + 0.829813i $$0.311553\pi$$
$$270$$ 0 0
$$271$$ 12.6797i 0.770237i −0.922867 0.385119i $$-0.874160\pi$$
0.922867 0.385119i $$-0.125840\pi$$
$$272$$ −19.9166 16.6937i −1.20762 1.01220i
$$273$$ 0 0
$$274$$ −20.2087 + 8.89531i −1.22085 + 0.537386i
$$275$$ −2.74204 7.57648i −0.165351 0.456879i
$$276$$ 0 0
$$277$$ −7.52901 7.52901i −0.452374 0.452374i 0.443768 0.896142i $$-0.353642\pi$$
−0.896142 + 0.443768i $$0.853642\pi$$
$$278$$ 2.04955 5.27251i 0.122924 0.316224i
$$279$$ 0 0
$$280$$ 21.2852 15.5905i 1.27203 0.931713i
$$281$$ −27.5639 −1.64432 −0.822162 0.569253i $$-0.807232\pi$$
−0.822162 + 0.569253i $$0.807232\pi$$
$$282$$ 0 0
$$283$$ 7.40312 + 7.40312i 0.440070 + 0.440070i 0.892035 0.451965i $$-0.149277\pi$$
−0.451965 + 0.892035i $$0.649277\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ −7.40312 + 3.25865i −0.437756 + 0.192688i
$$287$$ 27.1030 + 27.1030i 1.59984 + 1.59984i
$$288$$ 0 0
$$289$$ 25.2094i 1.48290i
$$290$$ −8.34181 12.5053i −0.489848 0.734337i
$$291$$ 0 0
$$292$$ 0.620697 + 14.1285i 0.0363236 + 0.826808i
$$293$$ 3.11473 3.11473i 0.181965 0.181965i −0.610247 0.792211i $$-0.708930\pi$$
0.792211 + 0.610247i $$0.208930\pi$$
$$294$$ 0 0
$$295$$ 2.06950 2.94984i 0.120491 0.171746i
$$296$$ 3.22296 9.50723i 0.187331 0.552597i
$$297$$ 0 0
$$298$$ −11.5968 4.50793i −0.671782 0.261137i
$$299$$ 5.48408i 0.317152i
$$300$$ 0 0
$$301$$ 43.6761i 2.51745i
$$302$$ −0.451076 + 1.16041i −0.0259565 + 0.0667739i
$$303$$ 0 0
$$304$$ 15.9384 1.40312i 0.914128 0.0804747i
$$305$$ 8.70704 12.4109i 0.498564 0.710648i
$$306$$ 0 0
$$307$$ −20.0000 + 20.0000i −1.14146 + 1.14146i −0.153277 + 0.988183i $$0.548983\pi$$
−0.988183 + 0.153277i $$0.951017\pi$$
$$308$$ −0.590111 13.4323i −0.0336247 0.765377i
$$309$$ 0 0
$$310$$ −13.2043 + 8.80811i −0.749956 + 0.500267i
$$311$$ 8.08857i 0.458661i 0.973349 + 0.229330i $$0.0736537\pi$$
−0.973349 + 0.229330i $$0.926346\pi$$
$$312$$ 0 0
$$313$$ −19.8062 19.8062i −1.11952 1.11952i −0.991812 0.127703i $$-0.959240\pi$$
−0.127703 0.991812i $$-0.540760\pi$$
$$314$$ −7.48509 17.0049i −0.422408 0.959643i
$$315$$ 0 0
$$316$$ 7.40312 + 6.78003i 0.416458 + 0.381406i
$$317$$ −4.59058 4.59058i −0.257833 0.257833i 0.566339 0.824172i $$-0.308359\pi$$
−0.824172 + 0.566339i $$0.808359\pi$$
$$318$$ 0 0
$$319$$ −7.66037 −0.428898
$$320$$ −17.0611 + 5.37755i −0.953746 + 0.300614i
$$321$$ 0 0
$$322$$ −8.49656 3.30281i −0.473495 0.184058i
$$323$$ 18.3759 + 18.3759i 1.02246 + 1.02246i
$$324$$ 0 0
$$325$$ −16.0697 7.52901i −0.891388 0.417634i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ −11.5034 23.3028i −0.635171 1.28668i
$$329$$ 43.1978i 2.38157i
$$330$$ 0 0
$$331$$ 2.80625 0.154245 0.0771227 0.997022i $$-0.475427\pi$$
0.0771227 + 0.997022i $$0.475427\pi$$
$$332$$ −0.940541 21.4089i −0.0516189 1.17497i
$$333$$ 0 0
$$334$$ 5.89968 + 13.4031i 0.322816 + 0.733386i
$$335$$ 23.0588 4.04429i 1.25983 0.220963i
$$336$$ 0 0
$$337$$ −2.40312 + 2.40312i −0.130907 + 0.130907i −0.769524 0.638618i $$-0.779507\pi$$
0.638618 + 0.769524i $$0.279507\pi$$
$$338$$ 0.206555 0.531369i 0.0112351 0.0289027i
$$339$$ 0 0
$$340$$ −24.4947 15.6268i −1.32841 0.847483i
$$341$$ 8.08857i 0.438021i
$$342$$ 0 0
$$343$$ −10.0387 + 10.0387i −0.542038 + 0.542038i
$$344$$ −9.50723 + 28.0448i −0.512596 + 1.51208i
$$345$$ 0 0
$$346$$ 14.4031 6.33985i 0.774317 0.340833i
$$347$$ 2.74204 2.74204i 0.147200 0.147200i −0.629666 0.776866i $$-0.716808\pi$$
0.776866 + 0.629666i $$0.216808\pi$$
$$348$$ 0 0
$$349$$ −6.78003 −0.362926 −0.181463 0.983398i $$-0.558083\pi$$
−0.181463 + 0.983398i $$0.558083\pi$$
$$350$$ 21.3429 20.3627i 1.14082 1.08843i
$$351$$ 0 0
$$352$$ −2.54497 + 8.75346i −0.135648 + 0.466561i
$$353$$ 13.7820 + 13.7820i 0.733539 + 0.733539i 0.971319 0.237780i $$-0.0764197\pi$$
−0.237780 + 0.971319i $$0.576420\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 3.70389 4.04429i 0.196306 0.214347i
$$357$$ 0 0
$$358$$ −13.5441 + 34.8425i −0.715827 + 1.84148i
$$359$$ −35.1916 −1.85734 −0.928671 0.370904i $$-0.879048\pi$$
−0.928671 + 0.370904i $$0.879048\pi$$
$$360$$ 0 0
$$361$$ 3.00000 0.157895
$$362$$ 6.04583 15.5531i 0.317762 0.817451i
$$363$$ 0 0
$$364$$ −21.8380 20.0000i −1.14462 1.04828i
$$365$$ 2.73147 + 15.5737i 0.142972 + 0.815163i
$$366$$ 0 0
$$367$$ −14.7492 14.7492i −0.769902 0.769902i 0.208187 0.978089i $$-0.433244\pi$$
−0.978089 + 0.208187i $$0.933244\pi$$
$$368$$ 4.73678 + 3.97026i 0.246922 + 0.206964i
$$369$$ 0 0
$$370$$ 2.19812 11.0062i 0.114275 0.572186i
$$371$$ −18.3759 −0.954031
$$372$$ 0 0
$$373$$ 14.3090 14.3090i 0.740894 0.740894i −0.231856 0.972750i $$-0.574480\pi$$
0.972750 + 0.231856i $$0.0744799\pi$$
$$374$$ −13.5515 + 5.96500i −0.700733 + 0.308443i
$$375$$ 0 0
$$376$$ 9.40312 27.7377i 0.484929 1.43046i
$$377$$ −11.9300 + 11.9300i −0.614427 + 0.614427i
$$378$$ 0 0
$$379$$ 18.8062i 0.966012i 0.875617 + 0.483006i $$0.160455\pi$$
−0.875617 + 0.483006i $$0.839545\pi$$
$$380$$ 17.4670 3.86065i 0.896037 0.198047i
$$381$$ 0 0
$$382$$ 9.74275 25.0635i 0.498483 1.28236i
$$383$$ 26.0105 26.0105i 1.32907 1.32907i 0.422892 0.906180i $$-0.361015\pi$$
0.906180 0.422892i $$-0.138985\pi$$
$$384$$ 0 0
$$385$$ −2.59688 14.8062i −0.132349 0.754596i
$$386$$ 9.99371 + 22.7041i 0.508666 + 1.15561i
$$387$$ 0 0
$$388$$ 6.79051 0.298323i 0.344736 0.0151450i
$$389$$ 37.3196 1.89218 0.946090 0.323905i $$-0.104996\pi$$
0.946090 + 0.323905i $$0.104996\pi$$
$$390$$ 0 0
$$391$$ 10.0387i 0.507678i
$$392$$ 26.3847 13.0248i 1.33263 0.657853i
$$393$$ 0 0
$$394$$ 7.52901 + 17.1047i 0.379306 + 0.861722i
$$395$$ 9.18797 + 6.44593i 0.462297 + 0.324330i
$$396$$ 0 0
$$397$$ 19.3284 + 19.3284i 0.970063 + 0.970063i 0.999565 0.0295016i $$-0.00939202\pi$$
−0.0295016 + 0.999565i $$0.509392\pi$$
$$398$$ 27.6249 + 10.7384i 1.38471 + 0.538269i
$$399$$ 0 0
$$400$$ −18.1369 + 8.42925i −0.906846 + 0.421462i
$$401$$ 12.8919 0.643789 0.321894 0.946776i $$-0.395680\pi$$
0.321894 + 0.946776i $$0.395680\pi$$
$$402$$ 0 0
$$403$$ 12.5969 + 12.5969i 0.627495 + 0.627495i
$$404$$ 11.8840 12.9762i 0.591253 0.645591i
$$405$$ 0 0
$$406$$ −11.2984 25.6682i −0.560732 1.27389i
$$407$$ −4.04429 4.04429i −0.200468 0.200468i
$$408$$ 0 0
$$409$$ 3.40312i 0.168274i −0.996454 0.0841368i $$-0.973187\pi$$
0.996454 0.0841368i $$-0.0268133\pi$$
$$410$$ −16.1234 24.1707i −0.796276 1.19371i
$$411$$ 0 0
$$412$$ 22.5185 0.989290i 1.10941 0.0487388i
$$413$$ 4.75362 4.75362i 0.233910 0.233910i
$$414$$ 0 0
$$415$$ −4.13899 23.5987i −0.203175 1.15842i
$$416$$ 9.66889 + 17.5958i 0.474057 + 0.862706i
$$417$$ 0 0
$$418$$ 3.30281 8.49656i 0.161546 0.415580i
$$419$$ 31.9174i 1.55927i 0.626235 + 0.779634i $$0.284595\pi$$
−0.626235 + 0.779634i $$0.715405\pi$$
$$420$$ 0 0
$$421$$ 30.3788i 1.48057i 0.672293 + 0.740285i $$0.265309\pi$$
−0.672293 + 0.740285i $$0.734691\pi$$
$$422$$ −15.8175 6.14864i −0.769985 0.299311i
$$423$$ 0 0
$$424$$ 11.7994 + 4.00000i 0.573028 + 0.194257i
$$425$$ −29.4158 13.7820i −1.42688 0.668523i
$$426$$ 0 0
$$427$$ 20.0000 20.0000i 0.967868 0.967868i
$$428$$ −4.55357 + 0.200049i −0.220105 + 0.00966971i
$$429$$ 0 0
$$430$$ −6.48410 + 32.4666i −0.312691 + 1.56568i
$$431$$ 27.1030i 1.30551i 0.757570 + 0.652754i $$0.226386\pi$$
−0.757570 + 0.652754i $$0.773614\pi$$
$$432$$ 0 0
$$433$$ 12.4031 + 12.4031i 0.596056 + 0.596056i 0.939261 0.343205i $$-0.111512\pi$$
−0.343205 + 0.939261i $$0.611512\pi$$
$$434$$ −27.1030 + 11.9300i −1.30099 + 0.572659i
$$435$$ 0 0
$$436$$ −17.4031 15.9384i −0.833458 0.763309i
$$437$$ −4.37036 4.37036i −0.209063 0.209063i
$$438$$ 0 0
$$439$$ 10.9190 0.521136 0.260568 0.965455i $$-0.416090\pi$$
0.260568 + 0.965455i $$0.416090\pi$$
$$440$$ −1.55549 + 10.0725i −0.0741549 + 0.480188i
$$441$$ 0 0
$$442$$ −11.8150 + 30.3944i −0.561982 + 1.44571i
$$443$$ −15.6339 15.6339i −0.742789 0.742789i 0.230325 0.973114i $$-0.426021\pi$$
−0.973114 + 0.230325i $$0.926021\pi$$
$$444$$ 0 0
$$445$$ 3.52138 5.01934i 0.166929 0.237939i
$$446$$ −7.01121 + 3.08614i −0.331990 + 0.146133i
$$447$$ 0 0
$$448$$ −33.0846 + 4.38301i −1.56310 + 0.207078i
$$449$$ 6.44593i 0.304202i 0.988365 + 0.152101i $$0.0486039\pi$$
−0.988365 + 0.152101i $$0.951396\pi$$
$$450$$ 0 0
$$451$$ −14.8062 −0.697199
$$452$$ −0.570295 12.9812i −0.0268244 0.610586i
$$453$$ 0 0
$$454$$ 28.6181 12.5969i 1.34311 0.591201i
$$455$$ −27.1030 19.0145i −1.27061 0.891412i
$$456$$ 0 0
$$457$$ −9.80625 + 9.80625i −0.458717 + 0.458717i −0.898234 0.439517i $$-0.855150\pi$$
0.439517 + 0.898234i $$0.355150\pi$$
$$458$$ −8.93694 3.47399i −0.417596 0.162329i
$$459$$ 0 0
$$460$$ 5.82559 + 3.71653i 0.271619 + 0.173284i
$$461$$ 18.3051i 0.852555i 0.904592 + 0.426278i $$0.140175\pi$$
−0.904592 + 0.426278i $$0.859825\pi$$
$$462$$ 0 0
$$463$$ −14.7492 + 14.7492i −0.685454 + 0.685454i −0.961224 0.275770i $$-0.911067\pi$$
0.275770 + 0.961224i $$0.411067\pi$$
$$464$$ 1.66748 + 18.9412i 0.0774108 + 0.879324i
$$465$$ 0 0
$$466$$ 8.89531 + 20.2087i 0.412067 + 0.936151i
$$467$$ 10.7994 10.7994i 0.499739 0.499739i −0.411618 0.911357i $$-0.635036\pi$$
0.911357 + 0.411618i $$0.135036\pi$$
$$468$$ 0 0
$$469$$ 43.6761 2.01677
$$470$$ 6.41310 32.1111i 0.295814 1.48117i
$$471$$ 0 0
$$472$$ −4.08709 + 2.01759i −0.188124 + 0.0928673i
$$473$$ 11.9300 + 11.9300i 0.548542 + 0.548542i
$$474$$ 0 0
$$475$$ 18.8062 6.80625i 0.862890 0.312292i
$$476$$ −39.9748 36.6103i −1.83224 1.67803i
$$477$$ 0 0
$$478$$ −10.6618 4.14448i −0.487658 0.189564i
$$479$$ 8.08857 0.369576 0.184788 0.982778i $$-0.440840\pi$$
0.184788 + 0.982778i $$0.440840\pi$$
$$480$$ 0 0
$$481$$ −12.5969 −0.574368
$$482$$ 8.97150 + 3.48743i 0.408641 + 0.158848i
$$483$$ 0 0
$$484$$ −12.3939 11.3508i −0.563361 0.515945i
$$485$$ 7.48509 1.31281i 0.339880 0.0596118i
$$486$$ 0 0
$$487$$ −2.06950 2.06950i −0.0937778 0.0937778i 0.658662 0.752439i $$-0.271123\pi$$
−0.752439 + 0.658662i $$0.771123\pi$$
$$488$$ −17.1957 + 8.48867i −0.778413 + 0.384264i
$$489$$ 0 0
$$490$$ 27.3674 18.2558i 1.23634 0.824711i
$$491$$ −11.2804 −0.509076 −0.254538 0.967063i $$-0.581923\pi$$
−0.254538 + 0.967063i $$0.581923\pi$$
$$492$$ 0 0
$$493$$ −21.8380 + 21.8380i −0.983536 + 0.983536i
$$494$$ −8.08857 18.3759i −0.363922 0.826772i
$$495$$ 0 0
$$496$$ 20.0000 1.76069i 0.898027 0.0790573i
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 18.8062i 0.841883i −0.907088 0.420942i $$-0.861700\pi$$
0.907088 0.420942i $$-0.138300\pi$$
$$500$$ −18.8882 + 11.9681i −0.844708 + 0.535228i
$$501$$ 0 0
$$502$$ 26.3460 + 10.2413i 1.17588 + 0.457091i
$$503$$ −5.13688 + 5.13688i −0.229042 + 0.229042i −0.812292 0.583250i $$-0.801781\pi$$
0.583250 + 0.812292i $$0.301781\pi$$
$$504$$ 0 0
$$505$$ 11.2984 16.1047i 0.502774 0.716649i
$$506$$ 3.22296 1.41866i 0.143278 0.0630671i
$$507$$ 0 0
$$508$$ 0.475477 + 10.8230i 0.0210959 + 0.480191i
$$509$$ 12.8422 0.569220 0.284610 0.958643i $$-0.408136\pi$$
0.284610 + 0.958643i $$0.408136\pi$$
$$510$$ 0 0
$$511$$ 29.4984i 1.30493i
$$512$$ 22.1980 + 4.38734i 0.981022 + 0.193895i
$$513$$ 0 0
$$514$$ −25.2281 + 11.1047i −1.11276 + 0.489807i
$$515$$ 24.8219 4.35352i 1.09378 0.191839i
$$516$$ 0 0
$$517$$ −11.7994 11.7994i −0.518935 0.518935i
$$518$$ 7.58652 19.5165i 0.333333 0.857507i
$$519$$ 0 0
$$520$$ 13.2641 + 18.1091i 0.581671 + 0.794135i
$$521$$ 6.44593 0.282401 0.141201 0.989981i $$-0.454904\pi$$
0.141201 + 0.989981i $$0.454904\pi$$
$$522$$ 0 0
$$523$$ −5.19375 5.19375i −0.227107 0.227107i 0.584376 0.811483i $$-0.301339\pi$$
−0.811483 + 0.584376i $$0.801339\pi$$
$$524$$ 19.9726 + 18.2916i 0.872508 + 0.799072i
$$525$$ 0 0
$$526$$ 5.40312 2.37830i 0.235587 0.103699i
$$527$$ 23.0588 + 23.0588i 1.00446 + 1.00446i
$$528$$ 0 0
$$529$$ 20.6125i 0.896196i
$$530$$ 13.6598 + 2.72807i 0.593342 + 0.118500i
$$531$$ 0 0
$$532$$ 33.3415 1.46477i 1.44554 0.0635057i
$$533$$ −23.0588 + 23.0588i −0.998786 + 0.998786i
$$534$$ 0 0
$$535$$ −5.01934 + 0.880344i −0.217005 + 0.0380606i
$$536$$ −28.0448 9.50723i −1.21135 0.410650i
$$537$$ 0 0
$$538$$ −24.1285 9.37930i −1.04025 0.404370i
$$539$$ 16.7645i 0.722096i
$$540$$ 0 0
$$541$$ 8.27799i 0.355898i 0.984040 + 0.177949i $$0.0569463\pi$$
−0.984040 + 0.177949i $$0.943054\pi$$
$$542$$ −6.49691 + 16.7135i −0.279066 + 0.717905i
$$543$$ 0 0
$$544$$ 17.6990 + 32.2094i 0.758840 + 1.38097i
$$545$$ −21.5989 15.1530i −0.925195 0.649082i
$$546$$ 0 0
$$547$$ −22.2094 + 22.2094i −0.949604 + 0.949604i −0.998790 0.0491855i $$-0.984337\pi$$
0.0491855 + 0.998790i $$0.484337\pi$$
$$548$$ 31.1955 1.37049i 1.33261 0.0585444i
$$549$$ 0 0
$$550$$ −0.267732 + 11.3918i −0.0114161 + 0.485746i
$$551$$ 19.0145i 0.810044i
$$552$$ 0 0
$$553$$ 14.8062 + 14.8062i 0.629626 + 0.629626i
$$554$$ 6.06643 + 13.7820i 0.257738 + 0.585539i
$$555$$ 0 0
$$556$$ −5.40312 + 5.89968i −0.229144 + 0.250202i
$$557$$ −13.7146 13.7146i −0.581104 0.581104i 0.354102 0.935207i $$-0.384786\pi$$
−0.935207 + 0.354102i $$0.884786\pi$$
$$558$$ 0 0
$$559$$ 37.1588 1.57165
$$560$$ −36.0450 + 9.64406i −1.52318 + 0.407536i
$$561$$ 0 0
$$562$$ 36.3327 + 14.1234i 1.53260 + 0.595758i
$$563$$ −2.74204 2.74204i −0.115563 0.115563i 0.646960 0.762524i $$-0.276040\pi$$
−0.762524 + 0.646960i $$0.776040\pi$$
$$564$$ 0 0
$$565$$ −2.50967 14.3090i −0.105583 0.601986i
$$566$$ −5.96500 13.5515i −0.250728 0.569613i
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 36.7519i 1.54072i −0.637610 0.770359i $$-0.720077\pi$$
0.637610 0.770359i $$-0.279923\pi$$
$$570$$ 0 0
$$571$$ 17.6125 0.737060 0.368530 0.929616i $$-0.379861\pi$$
0.368530 + 0.929616i $$0.379861\pi$$
$$572$$ 11.4279 0.502056i 0.477827 0.0209920i
$$573$$ 0 0
$$574$$ −21.8380 49.6125i −0.911502 2.07079i
$$575$$ 6.99599 + 3.27777i 0.291753 + 0.136692i
$$576$$ 0 0
$$577$$ 12.4031 12.4031i 0.516349 0.516349i −0.400116 0.916465i $$-0.631030\pi$$
0.916465 + 0.400116i $$0.131030\pi$$
$$578$$ −12.9169 + 33.2292i −0.537274 + 1.38215i
$$579$$ 0 0
$$580$$ 4.58802 + 20.7578i 0.190507 + 0.861922i
$$581$$ 44.6989i 1.85442i
$$582$$ 0 0
$$583$$ 5.01934 5.01934i 0.207880 0.207880i
$$584$$ 6.42110 18.9412i 0.265707 0.783793i
$$585$$ 0 0
$$586$$ −5.70156 + 2.50967i −0.235529 + 0.103673i
$$587$$ 1.61148 1.61148i 0.0665130 0.0665130i −0.673068 0.739581i $$-0.735024\pi$$
0.739581 + 0.673068i $$0.235024\pi$$
$$588$$ 0 0
$$589$$ −20.0774 −0.827273
$$590$$ −4.23932 + 2.82788i −0.174530 + 0.116422i
$$591$$ 0 0
$$592$$ −9.11966 + 10.8803i −0.374816 + 0.447179i
$$593$$ 4.59398 + 4.59398i 0.188652 + 0.188652i 0.795113 0.606461i $$-0.207411\pi$$
−0.606461 + 0.795113i $$0.707411\pi$$
$$594$$ 0 0
$$595$$ −49.6125 34.8062i −2.03391 1.42692i
$$596$$ 12.9762 + 11.8840i 0.531526 + 0.486789i
$$597$$ 0 0
$$598$$ 2.80997 7.22871i 0.114908 0.295604i
$$599$$ −27.1030 −1.10740 −0.553700 0.832716i $$-0.686785\pi$$
−0.553700 + 0.832716i $$0.686785\pi$$
$$600$$ 0 0
$$601$$ 20.2094 0.824358 0.412179 0.911103i $$-0.364768\pi$$
0.412179 + 0.911103i $$0.364768\pi$$
$$602$$ −22.3790 + 57.5706i −0.912101 + 2.34640i
$$603$$ 0 0
$$604$$ 1.18915 1.29844i 0.0483859 0.0528327i
$$605$$ −15.3820 10.7915i −0.625369 0.438735i
$$606$$ 0 0
$$607$$ 18.8882 + 18.8882i 0.766648 + 0.766648i 0.977515 0.210867i $$-0.0676285\pi$$
−0.210867 + 0.977515i $$0.567629\pi$$
$$608$$ −21.7277 6.31710i −0.881176 0.256192i
$$609$$ 0 0
$$610$$ −17.8362 + 11.8978i −0.722166 + 0.481729i
$$611$$ −36.7519 −1.48682
$$612$$ 0 0
$$613$$ −19.3284 + 19.3284i −0.780666 + 0.780666i −0.979943 0.199278i $$-0.936140\pi$$
0.199278 + 0.979943i $$0.436140\pi$$
$$614$$ 36.6103 16.1148i 1.47747 0.650341i
$$615$$ 0 0
$$616$$ −6.10469 + 18.0079i −0.245965 + 0.725557i
$$617$$ 7.33602 7.33602i 0.295337 0.295337i −0.543847 0.839184i $$-0.683033\pi$$
0.839184 + 0.543847i $$0.183033\pi$$
$$618$$ 0 0
$$619$$ 10.8062i 0.434340i −0.976134 0.217170i $$-0.930317\pi$$
0.976134 0.217170i $$-0.0696826\pi$$
$$620$$ 21.9182 4.84448i 0.880255 0.194559i
$$621$$ 0 0
$$622$$ 4.14448 10.6618i 0.166178 0.427498i
$$623$$ 8.08857 8.08857i 0.324062 0.324062i
$$624$$ 0 0
$$625$$ −19.2094 + 16.0000i −0.768375 + 0.640000i
$$626$$ 15.9587 + 36.2556i 0.637838 + 1.44907i
$$627$$ 0 0
$$628$$ 1.15322 + 26.2499i 0.0460184 + 1.04749i
$$629$$ −23.0588 −0.919413
$$630$$ 0 0
$$631$$ 25.0967i 0.999083i −0.866290 0.499542i $$-0.833502\pi$$
0.866290 0.499542i $$-0.166498\pi$$
$$632$$ −6.28427 12.7302i −0.249975 0.506380i
$$633$$ 0 0
$$634$$ 3.69882 + 8.40312i 0.146899 + 0.333731i
$$635$$ 2.09241 + 11.9300i 0.0830348 + 0.473428i
$$636$$ 0 0
$$637$$ −26.1084 26.1084i −1.03445 1.03445i
$$638$$ 10.0973 + 3.92507i 0.399758 + 0.155395i
$$639$$ 0 0
$$640$$ 25.2441 + 1.65359i 0.997862 + 0.0653638i
$$641$$ 2.74204 0.108304 0.0541520 0.998533i $$-0.482754\pi$$
0.0541520 + 0.998533i $$0.482754\pi$$
$$642$$ 0 0
$$643$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$644$$ 9.50723 + 8.70704i 0.374638 + 0.343105i
$$645$$ 0 0
$$646$$ −14.8062 33.6374i −0.582544 1.32345i
$$647$$ −19.7810 19.7810i −0.777671 0.777671i 0.201763 0.979434i $$-0.435333\pi$$
−0.979434 + 0.201763i $$0.935333\pi$$
$$648$$ 0 0
$$649$$ 2.59688i 0.101936i
$$650$$ 17.3242 + 18.1581i 0.679510 + 0.712219i
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −15.1904 + 15.1904i −0.594447 + 0.594447i −0.938829 0.344383i $$-0.888088\pi$$
0.344383 + 0.938829i $$0.388088\pi$$
$$654$$ 0 0
$$655$$ 24.7879 + 17.3902i 0.968543 + 0.679493i
$$656$$ 3.22296 + 36.6103i 0.125836 + 1.42939i
$$657$$ 0 0
$$658$$ 22.1340 56.9402i 0.862872 2.21976i
$$659$$ 4.83445i 0.188323i −0.995557 0.0941617i $$-0.969983\pi$$
0.995557 0.0941617i $$-0.0300171\pi$$
$$660$$ 0 0
$$661$$ 26.8574i 1.04463i 0.852752 + 0.522315i $$0.174932\pi$$
−0.852752 + 0.522315i $$0.825068\pi$$
$$662$$ −3.69899 1.43788i −0.143765 0.0558849i
$$663$$ 0 0
$$664$$ −9.72987 + 28.7016i −0.377592 + 1.11384i
$$665$$ 36.7519 6.44593i 1.42518 0.249962i
$$666$$ 0 0
$$667$$ 5.19375 5.19375i 0.201103 0.201103i
$$668$$ −0.908956 20.6899i −0.0351686 0.800518i
$$669$$ 0 0
$$670$$ −32.4666 6.48410i −1.25429 0.250503i
$$671$$ 10.9259i 0.421789i
$$672$$ 0 0
$$673$$ 15.0000 + 15.0000i 0.578208 + 0.578208i 0.934409 0.356202i $$-0.115928\pi$$
−0.356202 + 0.934409i $$0.615928\pi$$
$$674$$ 4.39895 1.93630i 0.169441 0.0745833i
$$675$$ 0 0
$$676$$ −0.544533 + 0.594576i −0.0209436 + 0.0228683i
$$677$$ −18.1421 18.1421i −0.697258 0.697258i 0.266560 0.963818i $$-0.414113\pi$$
−0.963818 + 0.266560i $$0.914113\pi$$
$$678$$ 0 0
$$679$$ 14.1777 0.544089
$$680$$ 24.2802 + 33.1489i 0.931102 + 1.27120i
$$681$$ 0 0
$$682$$ 4.14448 10.6618i 0.158700 0.408260i
$$683$$ −1.13056 1.13056i −0.0432595 0.0432595i 0.685146 0.728406i $$-0.259738\pi$$
−0.728406 + 0.685146i $$0.759738\pi$$
$$684$$ 0 0
$$685$$ 34.3864 6.03105i 1.31384 0.230434i
$$686$$ 18.3759 8.08857i 0.701596 0.308823i
$$687$$ 0 0
$$688$$ 26.9015 32.0953i 1.02561 1.22362i
$$689$$ 15.6339i 0.595604i
$$690$$ 0 0
$$691$$ 28.0000 1.06517 0.532585 0.846376i $$-0.321221\pi$$
0.532585 + 0.846376i $$0.321221\pi$$
$$692$$ −22.2336 + 0.976773i −0.845195 + 0.0371313i
$$693$$ 0 0
$$694$$ −5.01934 + 2.20937i −0.190531 + 0.0838666i
$$695$$ −5.13688 + 7.32206i −0.194853 + 0.277741i
$$696$$ 0 0
$$697$$ −42.2094 + 42.2094i −1.59879 + 1.59879i
$$698$$ 8.93694 + 3.47399i 0.338268 + 0.131493i
$$699$$ 0 0
$$700$$ −38.5662 + 15.9048i −1.45766 + 0.601146i
$$701$$ 3.33496i 0.125960i −0.998015 0.0629798i $$-0.979940\pi$$
0.998015 0.0629798i $$-0.0200604\pi$$
$$702$$ 0 0
$$703$$ 10.0387 10.0387i 0.378616 0.378616i
$$704$$ 7.83976 10.2342i 0.295472 0.385715i
$$705$$ 0 0
$$706$$ −11.1047 25.2281i −0.417930 0.949470i
$$707$$ 25.9524 25.9524i 0.976041 0.976041i
$$708$$ 0 0
$$709$$ −26.8574 −1.00865 −0.504325 0.863514i $$-0.668259\pi$$
−0.504325 + 0.863514i $$0.668259\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ −6.95444 + 3.43306i −0.260629 + 0.128659i
$$713$$ −5.48408 5.48408i −0.205380 0.205380i
$$714$$ 0 0
$$715$$ 12.5969 2.20937i 0.471096 0.0826259i
$$716$$ 35.7057 38.9871i 1.33438 1.45702i
$$717$$ 0 0
$$718$$ 46.3870 + 18.0317i 1.73115 + 0.672937i
$$719$$ 8.08857 0.301653 0.150826 0.988560i $$-0.451807\pi$$
0.150826 + 0.988560i $$0.451807\pi$$
$$720$$ 0 0
$$721$$ 47.0156 1.75095
$$722$$ −3.95438 1.53716i −0.147167 0.0572071i
$$723$$ 0 0
$$724$$ −15.9384 + 17.4031i −0.592344 + 0.646782i
$$725$$ 8.08857 + 22.3494i 0.300402 + 0.830037i
$$726$$ 0 0
$$727$$ −35.7069 35.7069i −1.32430 1.32430i −0.910261 0.414034i $$-0.864119\pi$$
−0.414034 0.910261i $$-0.635881\pi$$
$$728$$ 18.5376 + 37.5521i 0.687049 + 1.39177i
$$729$$ 0 0
$$730$$ 4.37930 21.9276i 0.162085 0.811579i
$$731$$ 68.0197 2.51580
$$732$$ 0 0
$$733$$ −2.50967 + 2.50967i −0.0926967 + 0.0926967i −0.751935 0.659238i $$-0.770879\pi$$
0.659238 + 0.751935i $$0.270879\pi$$
$$734$$ 11.8840 + 26.9986i 0.438648 + 0.996537i
$$735$$ 0 0
$$736$$ −4.20937 7.66037i −0.155160 0.282365i
$$737$$ −11.9300 + 11.9300i −0.439447 + 0.439447i
$$738$$ 0 0
$$739$$ 48.4187i 1.78111i −0.454873 0.890556i $$-0.650315\pi$$
0.454873 0.890556i $$-0.349685\pi$$
$$740$$ −8.53684 + 13.3813i −0.313821 + 0.491907i
$$741$$ 0 0
$$742$$ 24.2218 + 9.41558i 0.889211 + 0.345657i
$$743$$ −9.18116 + 9.18116i −0.336824 + 0.336824i −0.855171 0.518346i $$-0.826548\pi$$
0.518346 + 0.855171i $$0.326548\pi$$
$$744$$ 0 0
$$745$$ 16.1047 + 11.2984i 0.590030 + 0.413943i
$$746$$ −26.1929 + 11.5294i −0.958990 + 0.422121i
$$747$$ 0 0
$$748$$ 20.9190 0.919020i 0.764875 0.0336027i
$$749$$ −9.50723 −0.347387
$$750$$ 0 0
$$751$$ 15.0580i 0.549475i −0.961519 0.274737i $$-0.911409\pi$$
0.961519 0.274737i $$-0.0885909\pi$$
$$752$$ −26.6069 + 31.7438i −0.970256 + 1.15758i
$$753$$ 0 0
$$754$$ 21.8380 9.61250i 0.795294 0.350066i
$$755$$ 1.13056 1.61148i 0.0411451 0.0586479i
$$756$$ 0 0
$$757$$ −11.0504 11.0504i −0.401633 0.401633i 0.477175 0.878808i $$-0.341661\pi$$
−0.878808 + 0.477175i $$0.841661\pi$$
$$758$$ 9.63606 24.7890i 0.349998 0.900378i
$$759$$ 0 0
$$760$$ −25.0019 3.86101i −0.906913 0.140053i
$$761$$ 43.1978 1.56592 0.782960 0.622073i $$-0.213709\pi$$
0.782960 + 0.622073i $$0.213709\pi$$
$$762$$ 0 0
$$763$$ −34.8062 34.8062i −1.26007 1.26007i
$$764$$ −25.6844 + 28.0448i −0.929228 + 1.01463i
$$765$$ 0 0
$$766$$ −47.6125 + 20.9577i −1.72031 + 0.757232i
$$767$$ 4.04429 + 4.04429i 0.146031 + 0.146031i
$$768$$ 0 0
$$769$$ 1.40312i 0.0505980i −0.999680 0.0252990i $$-0.991946\pi$$
0.999680 0.0252990i $$-0.00805377\pi$$
$$770$$ −4.16351 + 20.8471i −0.150042 + 0.751278i
$$771$$ 0 0
$$772$$ −1.53972 35.0475i −0.0554156 1.26139i
$$773$$ 25.4642 25.4642i 0.915882 0.915882i −0.0808446 0.996727i $$-0.525762\pi$$
0.996727 + 0.0808446i $$0.0257617\pi$$
$$774$$ 0 0
$$775$$ 23.5987 8.54071i 0.847691 0.306792i
$$776$$ −9.10362 3.08614i −0.326801 0.110786i
$$777$$ 0 0
$$778$$ −49.1920 19.1221i −1.76362 0.685559i
$$779$$ 36.7519i 1.31677i
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 5.14368 13.2323i 0.183938 0.473184i
$$783$$ 0 0
$$784$$ −41.4522 + 3.64922i −1.48043 + 0.130329i
$$785$$ 5.07491 + 28.9349i 0.181131 + 1.03273i
$$786$$ 0 0
$$787$$ −20.0000 + 20.0000i −0.712923 + 0.712923i −0.967146 0.254223i $$-0.918180\pi$$
0.254223 + 0.967146i $$0.418180\pi$$
$$788$$ −1.15998 26.4039i −0.0413227 0.940601i
$$789$$ 0 0