# Properties

 Label 360.2.s.b.17.1 Level $360$ Weight $2$ Character 360.17 Analytic conductor $2.875$ Analytic rank $0$ Dimension $8$ CM no Inner twists $4$

# Related objects

## Newspace parameters

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

## Newform invariants

 Self dual: no Analytic conductor: $$2.87461447277$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(i)$$ Coefficient field: 8.0.40960000.1 Defining polynomial: $$x^{8} + 7 x^{4} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$2^{6}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 17.1 Root $$1.14412 + 1.14412i$$ of defining polynomial Character $$\chi$$ $$=$$ 360.17 Dual form 360.2.s.b.233.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.58114 + 1.58114i) q^{5} +(-3.23607 - 3.23607i) q^{7} +O(q^{10})$$ $$q+(-1.58114 + 1.58114i) q^{5} +(-3.23607 - 3.23607i) q^{7} +4.57649i q^{11} +(-4.23607 + 4.23607i) q^{13} +(-1.74806 + 1.74806i) q^{17} -2.47214i q^{19} +(-2.82843 - 2.82843i) q^{23} -5.00000i q^{25} -5.99070 q^{29} +1.52786 q^{31} +10.2333 q^{35} +(2.23607 + 2.23607i) q^{37} +7.07107i q^{41} +(2.47214 - 2.47214i) q^{43} +(1.74806 - 1.74806i) q^{47} +13.9443i q^{49} +(-7.23607 - 7.23607i) q^{55} -1.08036 q^{59} +10.4721 q^{61} -13.3956i q^{65} +(-1.52786 - 1.52786i) q^{67} -12.6491i q^{71} +(-0.527864 + 0.527864i) q^{73} +(14.8098 - 14.8098i) q^{77} +14.4721i q^{79} +(-1.08036 - 1.08036i) q^{83} -5.52786i q^{85} -0.746512 q^{89} +27.4164 q^{91} +(3.90879 + 3.90879i) q^{95} +(1.00000 + 1.00000i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q - 8q^{7} + O(q^{10})$$ $$8q - 8q^{7} - 16q^{13} + 48q^{31} - 16q^{43} - 40q^{55} + 48q^{61} - 48q^{67} - 40q^{73} + 112q^{91} + 8q^{97} + O(q^{100})$$

## Character values

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

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

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0 0
$$4$$ 0 0
$$5$$ −1.58114 + 1.58114i −0.707107 + 0.707107i
$$6$$ 0 0
$$7$$ −3.23607 3.23607i −1.22312 1.22312i −0.966517 0.256601i $$-0.917397\pi$$
−0.256601 0.966517i $$-0.582603\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 4.57649i 1.37986i 0.723874 + 0.689932i $$0.242360\pi$$
−0.723874 + 0.689932i $$0.757640\pi$$
$$12$$ 0 0
$$13$$ −4.23607 + 4.23607i −1.17487 + 1.17487i −0.193841 + 0.981033i $$0.562095\pi$$
−0.981033 + 0.193841i $$0.937905\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −1.74806 + 1.74806i −0.423968 + 0.423968i −0.886567 0.462600i $$-0.846917\pi$$
0.462600 + 0.886567i $$0.346917\pi$$
$$18$$ 0 0
$$19$$ 2.47214i 0.567147i −0.958951 0.283573i $$-0.908480\pi$$
0.958951 0.283573i $$-0.0915200\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −2.82843 2.82843i −0.589768 0.589768i 0.347801 0.937568i $$-0.386929\pi$$
−0.937568 + 0.347801i $$0.886929\pi$$
$$24$$ 0 0
$$25$$ 5.00000i 1.00000i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −5.99070 −1.11245 −0.556223 0.831033i $$-0.687750\pi$$
−0.556223 + 0.831033i $$0.687750\pi$$
$$30$$ 0 0
$$31$$ 1.52786 0.274412 0.137206 0.990543i $$-0.456188\pi$$
0.137206 + 0.990543i $$0.456188\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 10.2333 1.72975
$$36$$ 0 0
$$37$$ 2.23607 + 2.23607i 0.367607 + 0.367607i 0.866604 0.498997i $$-0.166298\pi$$
−0.498997 + 0.866604i $$0.666298\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 7.07107i 1.10432i 0.833740 + 0.552158i $$0.186195\pi$$
−0.833740 + 0.552158i $$0.813805\pi$$
$$42$$ 0 0
$$43$$ 2.47214 2.47214i 0.376997 0.376997i −0.493020 0.870018i $$-0.664107\pi$$
0.870018 + 0.493020i $$0.164107\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 1.74806 1.74806i 0.254981 0.254981i −0.568028 0.823009i $$-0.692293\pi$$
0.823009 + 0.568028i $$0.192293\pi$$
$$48$$ 0 0
$$49$$ 13.9443i 1.99204i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$54$$ 0 0
$$55$$ −7.23607 7.23607i −0.975711 0.975711i
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −1.08036 −0.140651 −0.0703256 0.997524i $$-0.522404\pi$$
−0.0703256 + 0.997524i $$0.522404\pi$$
$$60$$ 0 0
$$61$$ 10.4721 1.34082 0.670410 0.741991i $$-0.266118\pi$$
0.670410 + 0.741991i $$0.266118\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 13.3956i 1.66152i
$$66$$ 0 0
$$67$$ −1.52786 1.52786i −0.186658 0.186658i 0.607591 0.794250i $$-0.292136\pi$$
−0.794250 + 0.607591i $$0.792136\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 12.6491i 1.50117i −0.660772 0.750587i $$-0.729771\pi$$
0.660772 0.750587i $$-0.270229\pi$$
$$72$$ 0 0
$$73$$ −0.527864 + 0.527864i −0.0617818 + 0.0617818i −0.737323 0.675541i $$-0.763910\pi$$
0.675541 + 0.737323i $$0.263910\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 14.8098 14.8098i 1.68774 1.68774i
$$78$$ 0 0
$$79$$ 14.4721i 1.62824i 0.580695 + 0.814121i $$0.302781\pi$$
−0.580695 + 0.814121i $$0.697219\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −1.08036 1.08036i −0.118585 0.118585i 0.645324 0.763909i $$-0.276722\pi$$
−0.763909 + 0.645324i $$0.776722\pi$$
$$84$$ 0 0
$$85$$ 5.52786i 0.599581i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −0.746512 −0.0791302 −0.0395651 0.999217i $$-0.512597\pi$$
−0.0395651 + 0.999217i $$0.512597\pi$$
$$90$$ 0 0
$$91$$ 27.4164 2.87402
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 3.90879 + 3.90879i 0.401033 + 0.401033i
$$96$$ 0 0
$$97$$ 1.00000 + 1.00000i 0.101535 + 0.101535i 0.756049 0.654515i $$-0.227127\pi$$
−0.654515 + 0.756049i $$0.727127\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 10.9799i 1.09254i 0.837610 + 0.546268i $$0.183952\pi$$
−0.837610 + 0.546268i $$0.816048\pi$$
$$102$$ 0 0
$$103$$ −12.1803 + 12.1803i −1.20016 + 1.20016i −0.226049 + 0.974116i $$0.572581\pi$$
−0.974116 + 0.226049i $$0.927419\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −10.2333 + 10.2333i −0.989295 + 0.989295i −0.999943 0.0106485i $$-0.996610\pi$$
0.0106485 + 0.999943i $$0.496610\pi$$
$$108$$ 0 0
$$109$$ 15.4164i 1.47662i −0.674459 0.738312i $$-0.735623\pi$$
0.674459 0.738312i $$-0.264377\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −3.16228 3.16228i −0.297482 0.297482i 0.542545 0.840027i $$-0.317461\pi$$
−0.840027 + 0.542545i $$0.817461\pi$$
$$114$$ 0 0
$$115$$ 8.94427 0.834058
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 11.3137 1.03713
$$120$$ 0 0
$$121$$ −9.94427 −0.904025
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 7.90569 + 7.90569i 0.707107 + 0.707107i
$$126$$ 0 0
$$127$$ −7.23607 7.23607i −0.642097 0.642097i 0.308973 0.951071i $$-0.400015\pi$$
−0.951071 + 0.308973i $$0.900015\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 2.41577i 0.211066i 0.994416 + 0.105533i $$0.0336549\pi$$
−0.994416 + 0.105533i $$0.966345\pi$$
$$132$$ 0 0
$$133$$ −8.00000 + 8.00000i −0.693688 + 0.693688i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 8.81913 8.81913i 0.753469 0.753469i −0.221656 0.975125i $$-0.571146\pi$$
0.975125 + 0.221656i $$0.0711461\pi$$
$$138$$ 0 0
$$139$$ 8.94427i 0.758643i 0.925265 + 0.379322i $$0.123843\pi$$
−0.925265 + 0.379322i $$0.876157\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −19.3863 19.3863i −1.62117 1.62117i
$$144$$ 0 0
$$145$$ 9.47214 9.47214i 0.786618 0.786618i
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −14.4760 −1.18592 −0.592959 0.805232i $$-0.702041\pi$$
−0.592959 + 0.805232i $$0.702041\pi$$
$$150$$ 0 0
$$151$$ −4.94427 −0.402359 −0.201180 0.979554i $$-0.564477\pi$$
−0.201180 + 0.979554i $$0.564477\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −2.41577 + 2.41577i −0.194039 + 0.194039i
$$156$$ 0 0
$$157$$ −0.708204 0.708204i −0.0565208 0.0565208i 0.678281 0.734802i $$-0.262725\pi$$
−0.734802 + 0.678281i $$0.762725\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 18.3060i 1.44271i
$$162$$ 0 0
$$163$$ 2.47214 2.47214i 0.193633 0.193633i −0.603631 0.797264i $$-0.706280\pi$$
0.797264 + 0.603631i $$0.206280\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −6.32456 + 6.32456i −0.489409 + 0.489409i −0.908120 0.418711i $$-0.862482\pi$$
0.418711 + 0.908120i $$0.362482\pi$$
$$168$$ 0 0
$$169$$ 22.8885i 1.76066i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 5.99070 + 5.99070i 0.455465 + 0.455465i 0.897163 0.441699i $$-0.145624\pi$$
−0.441699 + 0.897163i $$0.645624\pi$$
$$174$$ 0 0
$$175$$ −16.1803 + 16.1803i −1.22312 + 1.22312i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −13.7295 −1.02619 −0.513095 0.858332i $$-0.671501\pi$$
−0.513095 + 0.858332i $$0.671501\pi$$
$$180$$ 0 0
$$181$$ −10.4721 −0.778388 −0.389194 0.921156i $$-0.627246\pi$$
−0.389194 + 0.921156i $$0.627246\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −7.07107 −0.519875
$$186$$ 0 0
$$187$$ −8.00000 8.00000i −0.585018 0.585018i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 18.3060i 1.32457i 0.749251 + 0.662287i $$0.230414\pi$$
−0.749251 + 0.662287i $$0.769586\pi$$
$$192$$ 0 0
$$193$$ −1.47214 + 1.47214i −0.105967 + 0.105967i −0.758102 0.652136i $$-0.773873\pi$$
0.652136 + 0.758102i $$0.273873\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −3.82998 + 3.82998i −0.272875 + 0.272875i −0.830256 0.557382i $$-0.811806\pi$$
0.557382 + 0.830256i $$0.311806\pi$$
$$198$$ 0 0
$$199$$ 8.00000i 0.567105i 0.958957 + 0.283552i $$0.0915130\pi$$
−0.958957 + 0.283552i $$0.908487\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 19.3863 + 19.3863i 1.36065 + 1.36065i
$$204$$ 0 0
$$205$$ −11.1803 11.1803i −0.780869 0.780869i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 11.3137 0.782586
$$210$$ 0 0
$$211$$ 4.00000 0.275371 0.137686 0.990476i $$-0.456034\pi$$
0.137686 + 0.990476i $$0.456034\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 7.81758i 0.533155i
$$216$$ 0 0
$$217$$ −4.94427 4.94427i −0.335639 0.335639i
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 14.8098i 0.996217i
$$222$$ 0 0
$$223$$ 19.2361 19.2361i 1.28814 1.28814i 0.352228 0.935914i $$-0.385424\pi$$
0.935914 0.352228i $$-0.114576\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −20.4667 + 20.4667i −1.35842 + 1.35842i −0.482558 + 0.875864i $$0.660292\pi$$
−0.875864 + 0.482558i $$0.839708\pi$$
$$228$$ 0 0
$$229$$ 19.8885i 1.31427i 0.753772 + 0.657136i $$0.228232\pi$$
−0.753772 + 0.657136i $$0.771768\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 16.5579 + 16.5579i 1.08474 + 1.08474i 0.996060 + 0.0886844i $$0.0282662\pi$$
0.0886844 + 0.996060i $$0.471734\pi$$
$$234$$ 0 0
$$235$$ 5.52786i 0.360598i
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −12.6491 −0.818203 −0.409101 0.912489i $$-0.634158\pi$$
−0.409101 + 0.912489i $$0.634158\pi$$
$$240$$ 0 0
$$241$$ 2.94427 0.189657 0.0948286 0.995494i $$-0.469770\pi$$
0.0948286 + 0.995494i $$0.469770\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −22.0478 22.0478i −1.40858 1.40858i
$$246$$ 0 0
$$247$$ 10.4721 + 10.4721i 0.666326 + 0.666326i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 30.7000i 1.93777i −0.247513 0.968885i $$-0.579613\pi$$
0.247513 0.968885i $$-0.420387\pi$$
$$252$$ 0 0
$$253$$ 12.9443 12.9443i 0.813799 0.813799i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −3.16228 + 3.16228i −0.197257 + 0.197257i −0.798823 0.601566i $$-0.794544\pi$$
0.601566 + 0.798823i $$0.294544\pi$$
$$258$$ 0 0
$$259$$ 14.4721i 0.899255i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −14.1421 14.1421i −0.872041 0.872041i 0.120653 0.992695i $$-0.461501\pi$$
−0.992695 + 0.120653i $$0.961501\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 12.3153 0.750875 0.375437 0.926848i $$-0.377493\pi$$
0.375437 + 0.926848i $$0.377493\pi$$
$$270$$ 0 0
$$271$$ −28.9443 −1.75824 −0.879120 0.476601i $$-0.841869\pi$$
−0.879120 + 0.476601i $$0.841869\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 22.8825 1.37986
$$276$$ 0 0
$$277$$ 15.1803 + 15.1803i 0.912098 + 0.912098i 0.996437 0.0843389i $$-0.0268778\pi$$
−0.0843389 + 0.996437i $$0.526878\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 17.5595i 1.04751i −0.851869 0.523755i $$-0.824531\pi$$
0.851869 0.523755i $$-0.175469\pi$$
$$282$$ 0 0
$$283$$ −8.00000 + 8.00000i −0.475551 + 0.475551i −0.903705 0.428155i $$-0.859164\pi$$
0.428155 + 0.903705i $$0.359164\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 22.8825 22.8825i 1.35071 1.35071i
$$288$$ 0 0
$$289$$ 10.8885i 0.640503i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 8.15143 + 8.15143i 0.476212 + 0.476212i 0.903918 0.427706i $$-0.140678\pi$$
−0.427706 + 0.903918i $$0.640678\pi$$
$$294$$ 0 0
$$295$$ 1.70820 1.70820i 0.0994555 0.0994555i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 23.9628 1.38581
$$300$$ 0 0
$$301$$ −16.0000 −0.922225
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −16.5579 + 16.5579i −0.948103 + 0.948103i
$$306$$ 0 0
$$307$$ 10.4721 + 10.4721i 0.597676 + 0.597676i 0.939694 0.342017i $$-0.111110\pi$$
−0.342017 + 0.939694i $$0.611110\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 14.8098i 0.839789i −0.907573 0.419894i $$-0.862067\pi$$
0.907573 0.419894i $$-0.137933\pi$$
$$312$$ 0 0
$$313$$ −7.47214 + 7.47214i −0.422350 + 0.422350i −0.886012 0.463662i $$-0.846535\pi$$
0.463662 + 0.886012i $$0.346535\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −7.81758 + 7.81758i −0.439079 + 0.439079i −0.891702 0.452623i $$-0.850488\pi$$
0.452623 + 0.891702i $$0.350488\pi$$
$$318$$ 0 0
$$319$$ 27.4164i 1.53502i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 4.32145 + 4.32145i 0.240452 + 0.240452i
$$324$$ 0 0
$$325$$ 21.1803 + 21.1803i 1.17487 + 1.17487i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −11.3137 −0.623745
$$330$$ 0 0
$$331$$ −5.52786 −0.303839 −0.151919 0.988393i $$-0.548545\pi$$
−0.151919 + 0.988393i $$0.548545\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 4.83153 0.263975
$$336$$ 0 0
$$337$$ 14.4164 + 14.4164i 0.785312 + 0.785312i 0.980722 0.195410i $$-0.0626037\pi$$
−0.195410 + 0.980722i $$0.562604\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 6.99226i 0.378652i
$$342$$ 0 0
$$343$$ 22.4721 22.4721i 1.21338 1.21338i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 6.99226 6.99226i 0.375364 0.375364i −0.494062 0.869426i $$-0.664489\pi$$
0.869426 + 0.494062i $$0.164489\pi$$
$$348$$ 0 0
$$349$$ 5.52786i 0.295900i −0.988995 0.147950i $$-0.952733\pi$$
0.988995 0.147950i $$-0.0472674\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −20.0540 20.0540i −1.06737 1.06737i −0.997560 0.0698078i $$-0.977761\pi$$
−0.0698078 0.997560i $$-0.522239\pi$$
$$354$$ 0 0
$$355$$ 20.0000 + 20.0000i 1.06149 + 1.06149i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 33.1158 1.74779 0.873893 0.486119i $$-0.161588\pi$$
0.873893 + 0.486119i $$0.161588\pi$$
$$360$$ 0 0
$$361$$ 12.8885 0.678344
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 1.66925i 0.0873727i
$$366$$ 0 0
$$367$$ 2.29180 + 2.29180i 0.119631 + 0.119631i 0.764388 0.644757i $$-0.223041\pi$$
−0.644757 + 0.764388i $$0.723041\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 11.2918 11.2918i 0.584667 0.584667i −0.351515 0.936182i $$-0.614333\pi$$
0.936182 + 0.351515i $$0.114333\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 25.3770 25.3770i 1.30698 1.30698i
$$378$$ 0 0
$$379$$ 16.9443i 0.870369i −0.900341 0.435184i $$-0.856683\pi$$
0.900341 0.435184i $$-0.143317\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −3.90879 3.90879i −0.199730 0.199730i 0.600154 0.799884i $$-0.295106\pi$$
−0.799884 + 0.600154i $$0.795106\pi$$
$$384$$ 0 0
$$385$$ 46.8328i 2.38682i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 18.7974 0.953068 0.476534 0.879156i $$-0.341893\pi$$
0.476534 + 0.879156i $$0.341893\pi$$
$$390$$ 0 0
$$391$$ 9.88854 0.500085
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −22.8825 22.8825i −1.15134 1.15134i
$$396$$ 0 0
$$397$$ −6.23607 6.23607i −0.312979 0.312979i 0.533083 0.846063i $$-0.321033\pi$$
−0.846063 + 0.533083i $$0.821033\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 27.5378i 1.37517i −0.726104 0.687585i $$-0.758671\pi$$
0.726104 0.687585i $$-0.241329\pi$$
$$402$$ 0 0
$$403$$ −6.47214 + 6.47214i −0.322400 + 0.322400i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −10.2333 + 10.2333i −0.507248 + 0.507248i
$$408$$ 0 0
$$409$$ 25.8885i 1.28011i −0.768331 0.640053i $$-0.778912\pi$$
0.768331 0.640053i $$-0.221088\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 3.49613 + 3.49613i 0.172033 + 0.172033i
$$414$$ 0 0
$$415$$ 3.41641 0.167705
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −5.40182 −0.263896 −0.131948 0.991257i $$-0.542123\pi$$
−0.131948 + 0.991257i $$0.542123\pi$$
$$420$$ 0 0
$$421$$ −10.0000 −0.487370 −0.243685 0.969854i $$-0.578356\pi$$
−0.243685 + 0.969854i $$0.578356\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 8.74032 + 8.74032i 0.423968 + 0.423968i
$$426$$ 0 0
$$427$$ −33.8885 33.8885i −1.63998 1.63998i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 5.65685i 0.272481i 0.990676 + 0.136241i $$0.0435020\pi$$
−0.990676 + 0.136241i $$0.956498\pi$$
$$432$$ 0 0
$$433$$ −16.4164 + 16.4164i −0.788922 + 0.788922i −0.981318 0.192395i $$-0.938374\pi$$
0.192395 + 0.981318i $$0.438374\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −6.99226 + 6.99226i −0.334485 + 0.334485i
$$438$$ 0 0
$$439$$ 20.9443i 0.999616i 0.866136 + 0.499808i $$0.166596\pi$$
−0.866136 + 0.499808i $$0.833404\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 20.4667 + 20.4667i 0.972402 + 0.972402i 0.999629 0.0272274i $$-0.00866783\pi$$
−0.0272274 + 0.999629i $$0.508668\pi$$
$$444$$ 0 0
$$445$$ 1.18034 1.18034i 0.0559535 0.0559535i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −38.6938 −1.82608 −0.913038 0.407875i $$-0.866270\pi$$
−0.913038 + 0.407875i $$0.866270\pi$$
$$450$$ 0 0
$$451$$ −32.3607 −1.52380
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −43.3491 + 43.3491i −2.03224 + 2.03224i
$$456$$ 0 0
$$457$$ 13.0000 + 13.0000i 0.608114 + 0.608114i 0.942453 0.334339i $$-0.108513\pi$$
−0.334339 + 0.942453i $$0.608513\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 9.48683i 0.441846i 0.975291 + 0.220923i $$0.0709069\pi$$
−0.975291 + 0.220923i $$0.929093\pi$$
$$462$$ 0 0
$$463$$ 10.6525 10.6525i 0.495063 0.495063i −0.414834 0.909897i $$-0.636160\pi$$
0.909897 + 0.414834i $$0.136160\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 4.57649 4.57649i 0.211775 0.211775i −0.593246 0.805021i $$-0.702154\pi$$
0.805021 + 0.593246i $$0.202154\pi$$
$$468$$ 0 0
$$469$$ 9.88854i 0.456611i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 11.3137 + 11.3137i 0.520205 + 0.520205i
$$474$$ 0 0
$$475$$ −12.3607 −0.567147
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 39.5980 1.80928 0.904639 0.426179i $$-0.140141\pi$$
0.904639 + 0.426179i $$0.140141\pi$$
$$480$$ 0 0
$$481$$ −18.9443 −0.863784
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −3.16228 −0.143592
$$486$$ 0 0
$$487$$ 8.76393 + 8.76393i 0.397132 + 0.397132i 0.877220 0.480088i $$-0.159395\pi$$
−0.480088 + 0.877220i $$0.659395\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 30.7000i 1.38547i −0.721191 0.692737i $$-0.756405\pi$$
0.721191 0.692737i $$-0.243595\pi$$
$$492$$ 0 0
$$493$$ 10.4721 10.4721i 0.471641 0.471641i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −40.9334 + 40.9334i −1.83611 + 1.83611i
$$498$$ 0 0
$$499$$ 26.4721i 1.18506i −0.805550 0.592528i $$-0.798130\pi$$
0.805550 0.592528i $$-0.201870\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 29.2070 + 29.2070i 1.30228 + 1.30228i 0.926854 + 0.375422i $$0.122502\pi$$
0.375422 + 0.926854i $$0.377498\pi$$
$$504$$ 0 0
$$505$$ −17.3607 17.3607i −0.772540 0.772540i
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 12.9830 0.575460 0.287730 0.957712i $$-0.407099\pi$$
0.287730 + 0.957712i $$0.407099\pi$$
$$510$$ 0 0
$$511$$ 3.41641 0.151133
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 38.5176i 1.69729i
$$516$$ 0 0
$$517$$ 8.00000 + 8.00000i 0.351840 + 0.351840i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 6.24574i 0.273631i 0.990597 + 0.136816i $$0.0436867\pi$$
−0.990597 + 0.136816i $$0.956313\pi$$
$$522$$ 0 0
$$523$$ −9.88854 + 9.88854i −0.432396 + 0.432396i −0.889443 0.457047i $$-0.848907\pi$$
0.457047 + 0.889443i $$0.348907\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −2.67080 + 2.67080i −0.116342 + 0.116342i
$$528$$ 0 0
$$529$$ 7.00000i 0.304348i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −29.9535 29.9535i −1.29743 1.29743i
$$534$$ 0 0
$$535$$ 32.3607i 1.39907i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −63.8158 −2.74874
$$540$$ 0 0
$$541$$ −25.3050 −1.08794 −0.543972 0.839103i $$-0.683080\pi$$
−0.543972 + 0.839103i $$0.683080\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 24.3755 + 24.3755i 1.04413 + 1.04413i
$$546$$ 0 0
$$547$$ 12.0000 + 12.0000i 0.513083 + 0.513083i 0.915470 0.402387i $$-0.131819\pi$$
−0.402387 + 0.915470i $$0.631819\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 14.8098i 0.630920i
$$552$$ 0 0
$$553$$ 46.8328 46.8328i 1.99153 1.99153i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −26.1235 + 26.1235i −1.10689 + 1.10689i −0.113333 + 0.993557i $$0.536153\pi$$
−0.993557 + 0.113333i $$0.963847\pi$$
$$558$$ 0 0
$$559$$ 20.9443i 0.885848i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −1.33540 1.33540i −0.0562805 0.0562805i 0.678406 0.734687i $$-0.262671\pi$$
−0.734687 + 0.678406i $$0.762671\pi$$
$$564$$ 0 0
$$565$$ 10.0000 0.420703
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 30.3662 1.27302 0.636508 0.771270i $$-0.280378\pi$$
0.636508 + 0.771270i $$0.280378\pi$$
$$570$$ 0 0
$$571$$ −7.41641 −0.310367 −0.155184 0.987886i $$-0.549597\pi$$
−0.155184 + 0.987886i $$0.549597\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −14.1421 + 14.1421i −0.589768 + 0.589768i
$$576$$ 0 0
$$577$$ −12.0557 12.0557i −0.501887 0.501887i 0.410137 0.912024i $$-0.365481\pi$$
−0.912024 + 0.410137i $$0.865481\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 6.99226i 0.290088i
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −22.8825 + 22.8825i −0.944460 + 0.944460i −0.998537 0.0540767i $$-0.982778\pi$$
0.0540767 + 0.998537i $$0.482778\pi$$
$$588$$ 0 0
$$589$$ 3.77709i 0.155632i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 22.1359 + 22.1359i 0.909014 + 0.909014i 0.996193 0.0871785i $$-0.0277850\pi$$
−0.0871785 + 0.996193i $$0.527785\pi$$
$$594$$ 0 0
$$595$$ −17.8885 + 17.8885i −0.733359 + 0.733359i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −12.6491 −0.516829 −0.258414 0.966034i $$-0.583200\pi$$
−0.258414 + 0.966034i $$0.583200\pi$$
$$600$$ 0 0
$$601$$ −30.8328 −1.25770 −0.628848 0.777528i $$-0.716473\pi$$
−0.628848 + 0.777528i $$0.716473\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 15.7233 15.7233i 0.639242 0.639242i
$$606$$ 0 0
$$607$$ 30.6525 + 30.6525i 1.24415 + 1.24415i 0.958265 + 0.285880i $$0.0922860\pi$$
0.285880 + 0.958265i $$0.407714\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 14.8098i 0.599142i
$$612$$ 0 0
$$613$$ −26.7082 + 26.7082i −1.07873 + 1.07873i −0.0821110 + 0.996623i $$0.526166\pi$$
−0.996623 + 0.0821110i $$0.973834\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 16.5579 16.5579i 0.666596 0.666596i −0.290330 0.956926i $$-0.593765\pi$$
0.956926 + 0.290330i $$0.0937652\pi$$
$$618$$ 0 0
$$619$$ 5.88854i 0.236681i 0.992973 + 0.118340i $$0.0377574\pi$$
−0.992973 + 0.118340i $$0.962243\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 2.41577 + 2.41577i 0.0967856 + 0.0967856i
$$624$$ 0 0
$$625$$ −25.0000 −1.00000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −7.81758 −0.311707
$$630$$ 0 0
$$631$$ 8.36068 0.332833 0.166417 0.986056i $$-0.446780\pi$$
0.166417 + 0.986056i $$0.446780\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 22.8825 0.908063
$$636$$ 0 0
$$637$$ −59.0689 59.0689i −2.34039 2.34039i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 5.57804i 0.220319i −0.993914 0.110160i $$-0.964864\pi$$
0.993914 0.110160i $$-0.0351362\pi$$
$$642$$ 0 0
$$643$$ −20.0000 + 20.0000i −0.788723 + 0.788723i −0.981285 0.192562i $$-0.938320\pi$$
0.192562 + 0.981285i $$0.438320\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 24.3755 24.3755i 0.958299 0.958299i −0.0408656 0.999165i $$-0.513012\pi$$
0.999165 + 0.0408656i $$0.0130115\pi$$
$$648$$ 0 0
$$649$$ 4.94427i 0.194080i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −11.3137 11.3137i −0.442740 0.442740i 0.450192 0.892932i $$-0.351356\pi$$
−0.892932 + 0.450192i $$0.851356\pi$$
$$654$$ 0 0
$$655$$ −3.81966 3.81966i −0.149246 0.149246i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −35.5316 −1.38411 −0.692057 0.721843i $$-0.743295\pi$$
−0.692057 + 0.721843i $$0.743295\pi$$
$$660$$ 0 0
$$661$$ 41.3050 1.60658 0.803288 0.595591i $$-0.203082\pi$$
0.803288 + 0.595591i $$0.203082\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 25.2982i 0.981023i
$$666$$ 0 0
$$667$$ 16.9443 + 16.9443i 0.656085 + 0.656085i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 47.9256i 1.85015i
$$672$$ 0 0
$$673$$ 19.4721 19.4721i 0.750596 0.750596i −0.223995 0.974590i $$-0.571910\pi$$
0.974590 + 0.223995i $$0.0719098\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 18.3060 18.3060i 0.703555 0.703555i −0.261617 0.965172i $$-0.584256\pi$$
0.965172 + 0.261617i $$0.0842556\pi$$
$$678$$ 0 0
$$679$$ 6.47214i 0.248378i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −15.0649 15.0649i −0.576441 0.576441i 0.357480 0.933921i $$-0.383636\pi$$
−0.933921 + 0.357480i $$0.883636\pi$$
$$684$$ 0 0
$$685$$ 27.8885i 1.06557i
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ −20.3607 −0.774557 −0.387278 0.921963i $$-0.626585\pi$$
−0.387278 + 0.921963i $$0.626585\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −14.1421 14.1421i −0.536442 0.536442i
$$696$$ 0 0
$$697$$ −12.3607 12.3607i −0.468194 0.468194i
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 30.6212i 1.15655i −0.815843 0.578274i $$-0.803727\pi$$
0.815843 0.578274i $$-0.196273\pi$$
$$702$$ 0 0
$$703$$ 5.52786 5.52786i 0.208487 0.208487i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 35.5316 35.5316i 1.33630 1.33630i
$$708$$ 0 0
$$709$$ 15.8885i 0.596707i 0.954455 + 0.298353i $$0.0964374\pi$$
−0.954455 + 0.298353i $$0.903563\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −4.32145 4.32145i −0.161840 0.161840i
$$714$$ 0 0
$$715$$ 61.3050 2.29268
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −4.32145 −0.161163 −0.0805815 0.996748i $$-0.525678\pi$$
−0.0805815 + 0.996748i $$0.525678\pi$$
$$720$$ 0 0
$$721$$ 78.8328 2.93589
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 29.9535i 1.11245i
$$726$$ 0 0
$$727$$ 9.12461 + 9.12461i 0.338413 + 0.338413i 0.855770 0.517357i $$-0.173084\pi$$
−0.517357 + 0.855770i $$0.673084\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 8.64290i 0.319669i
$$732$$ 0 0
$$733$$ 11.1803 11.1803i 0.412955 0.412955i −0.469811 0.882767i $$-0.655678\pi$$
0.882767 + 0.469811i $$0.155678\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 6.99226 6.99226i 0.257563 0.257563i
$$738$$ 0 0
$$739$$ 12.3607i 0.454695i 0.973814 + 0.227347i $$0.0730053\pi$$
−0.973814 + 0.227347i $$0.926995\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −29.2070 29.2070i −1.07150 1.07150i −0.997239 0.0742626i $$-0.976340\pi$$
−0.0742626 0.997239i $$-0.523660\pi$$
$$744$$ 0 0
$$745$$ 22.8885 22.8885i 0.838571 0.838571i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 66.2316 2.42005
$$750$$ 0 0
$$751$$ 32.3607 1.18086 0.590429 0.807090i $$-0.298959\pi$$
0.590429 + 0.807090i $$0.298959\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 7.81758 7.81758i 0.284511 0.284511i
$$756$$ 0 0
$$757$$ 10.7082 + 10.7082i 0.389196 + 0.389196i 0.874401 0.485204i $$-0.161255\pi$$
−0.485204 + 0.874401i $$0.661255\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 26.0447i 0.944121i −0.881566 0.472060i $$-0.843510\pi$$
0.881566 0.472060i $$-0.156490\pi$$
$$762$$ 0 0
$$763$$ −49.8885 + 49.8885i −1.80609 + 1.80609i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 4.57649 4.57649i 0.165248 0.165248i
$$768$$ 0 0
$$769$$ 32.0000i 1.15395i 0.816762 + 0.576975i $$0.195767\pi$$
−0.816762 + 0.576975i $$0.804233\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 7.81758 + 7.81758i 0.281179 + 0.281179i 0.833579 0.552400i $$-0.186288\pi$$
−0.552400 + 0.833579i $$0.686288\pi$$
$$774$$ 0 0
$$775$$ 7.63932i 0.274412i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 17.4806 0.626309
$$780$$ 0 0
$$781$$ 57.8885 2.07141
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 2.23954 0.0799325
$$786$$ 0 0
$$787$$ −30.4721 30.4721i −1.08621 1.08621i −0.995915 0.0902997i $$-0.971218\pi$$
−0.0902997 0.995915i $$-0.528782\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 20.4667i 0.727712i
$$792$$ 0 0
$$793$$ −44.3607 + 44.3607i −1.57529 + 1.57529i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 1.66925 1.66925i 0.0591280 0.0591280i −0.676924 0.736052i $$-0.736688\pi$$
0.736052 + 0.676924i $$0.236688\pi$$
$$798$$ 0 0
$$799$$ 6.11146i 0.216208i
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ −2.41577 2.41577i −0.0852505 0.0852505i
$$804$$ 0 0
$$805$$ −28.9443 28.9443i −1.02015