# Properties

 Label 5520.2.be.a.1471.14 Level $5520$ Weight $2$ Character 5520.1471 Analytic conductor $44.077$ Analytic rank $0$ Dimension $16$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$5520 = 2^{4} \cdot 3 \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 5520.be (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$44.0774219157$$ Analytic rank: $$0$$ Dimension: $$16$$ Coefficient field: $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ Defining polynomial: $$x^{16} - 4 x^{15} + 8 x^{14} + 28 x^{13} + 373 x^{12} - 920 x^{11} + 1088 x^{10} - 168 x^{9} + 16460 x^{8} - 45408 x^{7} + 62624 x^{6} - 18048 x^{5} + 2160 x^{4} - 1664 x^{3} + 6272 x^{2} - 896 x + 64$$ Coefficient ring: $$\Z[a_1, \ldots, a_{19}]$$ Coefficient ring index: $$2^{8}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 1471.14 Root $$1.30491 + 1.30491i$$ of defining polynomial Character $$\chi$$ $$=$$ 5520.1471 Dual form 5520.2.be.a.1471.6

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000i q^{3} -1.00000i q^{5} +0.482745 q^{7} -1.00000 q^{9} +O(q^{10})$$ $$q+1.00000i q^{3} -1.00000i q^{5} +0.482745 q^{7} -1.00000 q^{9} +1.10189 q^{11} +2.25517 q^{13} +1.00000 q^{15} -6.03534i q^{17} -1.48254 q^{19} +0.482745i q^{21} +(-4.55260 + 1.50793i) q^{23} -1.00000 q^{25} -1.00000i q^{27} -7.68679 q^{29} -5.12465i q^{31} +1.10189i q^{33} -0.482745i q^{35} -5.83765i q^{37} +2.25517i q^{39} +1.27767 q^{41} -8.46629 q^{43} +1.00000i q^{45} +11.2632i q^{47} -6.76696 q^{49} +6.03534 q^{51} +8.81467i q^{53} -1.10189i q^{55} -1.48254i q^{57} +8.08002i q^{59} +0.0392191i q^{61} -0.482745 q^{63} -2.25517i q^{65} -8.39370 q^{67} +(-1.50793 - 4.55260i) q^{69} -1.25598i q^{71} -3.47480 q^{73} -1.00000i q^{75} +0.531931 q^{77} -3.61831 q^{79} +1.00000 q^{81} +9.12164 q^{83} -6.03534 q^{85} -7.68679i q^{87} +6.85106i q^{89} +1.08867 q^{91} +5.12465 q^{93} +1.48254i q^{95} +0.330286i q^{97} -1.10189 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$16q - 8q^{7} - 16q^{9} + O(q^{10})$$ $$16q - 8q^{7} - 16q^{9} + 8q^{11} + 8q^{13} + 16q^{15} + 12q^{23} - 16q^{25} - 4q^{29} + 4q^{41} + 20q^{49} - 4q^{51} + 8q^{63} - 16q^{67} + 40q^{73} + 24q^{77} + 32q^{79} + 16q^{81} + 4q^{85} - 48q^{91} - 8q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/5520\mathbb{Z}\right)^\times$$.

 $$n$$ $$1201$$ $$1381$$ $$1841$$ $$4417$$ $$4831$$ $$\chi(n)$$ $$-1$$ $$1$$ $$1$$ $$1$$ $$-1$$

## 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
$$3$$ 1.00000i 0.577350i
$$4$$ 0 0
$$5$$ 1.00000i 0.447214i
$$6$$ 0 0
$$7$$ 0.482745 0.182460 0.0912302 0.995830i $$-0.470920\pi$$
0.0912302 + 0.995830i $$0.470920\pi$$
$$8$$ 0 0
$$9$$ −1.00000 −0.333333
$$10$$ 0 0
$$11$$ 1.10189 0.332232 0.166116 0.986106i $$-0.446877\pi$$
0.166116 + 0.986106i $$0.446877\pi$$
$$12$$ 0 0
$$13$$ 2.25517 0.625471 0.312735 0.949840i $$-0.398755\pi$$
0.312735 + 0.949840i $$0.398755\pi$$
$$14$$ 0 0
$$15$$ 1.00000 0.258199
$$16$$ 0 0
$$17$$ 6.03534i 1.46379i −0.681420 0.731893i $$-0.738637\pi$$
0.681420 0.731893i $$-0.261363\pi$$
$$18$$ 0 0
$$19$$ −1.48254 −0.340118 −0.170059 0.985434i $$-0.554396\pi$$
−0.170059 + 0.985434i $$0.554396\pi$$
$$20$$ 0 0
$$21$$ 0.482745i 0.105344i
$$22$$ 0 0
$$23$$ −4.55260 + 1.50793i −0.949283 + 0.314424i
$$24$$ 0 0
$$25$$ −1.00000 −0.200000
$$26$$ 0 0
$$27$$ 1.00000i 0.192450i
$$28$$ 0 0
$$29$$ −7.68679 −1.42740 −0.713700 0.700451i $$-0.752982\pi$$
−0.713700 + 0.700451i $$0.752982\pi$$
$$30$$ 0 0
$$31$$ 5.12465i 0.920414i −0.887812 0.460207i $$-0.847775\pi$$
0.887812 0.460207i $$-0.152225\pi$$
$$32$$ 0 0
$$33$$ 1.10189i 0.191814i
$$34$$ 0 0
$$35$$ 0.482745i 0.0815987i
$$36$$ 0 0
$$37$$ 5.83765i 0.959705i −0.877349 0.479852i $$-0.840690\pi$$
0.877349 0.479852i $$-0.159310\pi$$
$$38$$ 0 0
$$39$$ 2.25517i 0.361116i
$$40$$ 0 0
$$41$$ 1.27767 0.199538 0.0997689 0.995011i $$-0.468190\pi$$
0.0997689 + 0.995011i $$0.468190\pi$$
$$42$$ 0 0
$$43$$ −8.46629 −1.29110 −0.645548 0.763720i $$-0.723371\pi$$
−0.645548 + 0.763720i $$0.723371\pi$$
$$44$$ 0 0
$$45$$ 1.00000i 0.149071i
$$46$$ 0 0
$$47$$ 11.2632i 1.64290i 0.570278 + 0.821452i $$0.306836\pi$$
−0.570278 + 0.821452i $$0.693164\pi$$
$$48$$ 0 0
$$49$$ −6.76696 −0.966708
$$50$$ 0 0
$$51$$ 6.03534 0.845117
$$52$$ 0 0
$$53$$ 8.81467i 1.21079i 0.795926 + 0.605394i $$0.206985\pi$$
−0.795926 + 0.605394i $$0.793015\pi$$
$$54$$ 0 0
$$55$$ 1.10189i 0.148579i
$$56$$ 0 0
$$57$$ 1.48254i 0.196367i
$$58$$ 0 0
$$59$$ 8.08002i 1.05193i 0.850507 + 0.525964i $$0.176295\pi$$
−0.850507 + 0.525964i $$0.823705\pi$$
$$60$$ 0 0
$$61$$ 0.0392191i 0.00502149i 0.999997 + 0.00251075i $$0.000799197\pi$$
−0.999997 + 0.00251075i $$0.999201\pi$$
$$62$$ 0 0
$$63$$ −0.482745 −0.0608201
$$64$$ 0 0
$$65$$ 2.25517i 0.279719i
$$66$$ 0 0
$$67$$ −8.39370 −1.02545 −0.512727 0.858552i $$-0.671365\pi$$
−0.512727 + 0.858552i $$0.671365\pi$$
$$68$$ 0 0
$$69$$ −1.50793 4.55260i −0.181533 0.548069i
$$70$$ 0 0
$$71$$ 1.25598i 0.149058i −0.997219 0.0745289i $$-0.976255\pi$$
0.997219 0.0745289i $$-0.0237453\pi$$
$$72$$ 0 0
$$73$$ −3.47480 −0.406694 −0.203347 0.979107i $$-0.565182\pi$$
−0.203347 + 0.979107i $$0.565182\pi$$
$$74$$ 0 0
$$75$$ 1.00000i 0.115470i
$$76$$ 0 0
$$77$$ 0.531931 0.0606192
$$78$$ 0 0
$$79$$ −3.61831 −0.407092 −0.203546 0.979065i $$-0.565247\pi$$
−0.203546 + 0.979065i $$0.565247\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 0 0
$$83$$ 9.12164 1.00123 0.500615 0.865670i $$-0.333107\pi$$
0.500615 + 0.865670i $$0.333107\pi$$
$$84$$ 0 0
$$85$$ −6.03534 −0.654625
$$86$$ 0 0
$$87$$ 7.68679i 0.824110i
$$88$$ 0 0
$$89$$ 6.85106i 0.726211i 0.931748 + 0.363105i $$0.118283\pi$$
−0.931748 + 0.363105i $$0.881717\pi$$
$$90$$ 0 0
$$91$$ 1.08867 0.114124
$$92$$ 0 0
$$93$$ 5.12465 0.531401
$$94$$ 0 0
$$95$$ 1.48254i 0.152105i
$$96$$ 0 0
$$97$$ 0.330286i 0.0335355i 0.999859 + 0.0167677i $$0.00533759\pi$$
−0.999859 + 0.0167677i $$0.994662\pi$$
$$98$$ 0 0
$$99$$ −1.10189 −0.110744
$$100$$ 0 0
$$101$$ −3.89119 −0.387188 −0.193594 0.981082i $$-0.562014\pi$$
−0.193594 + 0.981082i $$0.562014\pi$$
$$102$$ 0 0
$$103$$ 11.2588 1.10937 0.554683 0.832062i $$-0.312840\pi$$
0.554683 + 0.832062i $$0.312840\pi$$
$$104$$ 0 0
$$105$$ 0.482745 0.0471111
$$106$$ 0 0
$$107$$ −0.801493 −0.0774833 −0.0387416 0.999249i $$-0.512335\pi$$
−0.0387416 + 0.999249i $$0.512335\pi$$
$$108$$ 0 0
$$109$$ 1.25885i 0.120576i −0.998181 0.0602880i $$-0.980798\pi$$
0.998181 0.0602880i $$-0.0192019\pi$$
$$110$$ 0 0
$$111$$ 5.83765 0.554086
$$112$$ 0 0
$$113$$ 8.70667i 0.819054i −0.912298 0.409527i $$-0.865694\pi$$
0.912298 0.409527i $$-0.134306\pi$$
$$114$$ 0 0
$$115$$ 1.50793 + 4.55260i 0.140615 + 0.424532i
$$116$$ 0 0
$$117$$ −2.25517 −0.208490
$$118$$ 0 0
$$119$$ 2.91353i 0.267083i
$$120$$ 0 0
$$121$$ −9.78584 −0.889622
$$122$$ 0 0
$$123$$ 1.27767i 0.115203i
$$124$$ 0 0
$$125$$ 1.00000i 0.0894427i
$$126$$ 0 0
$$127$$ 5.51836i 0.489676i −0.969564 0.244838i $$-0.921265\pi$$
0.969564 0.244838i $$-0.0787347\pi$$
$$128$$ 0 0
$$129$$ 8.46629i 0.745415i
$$130$$ 0 0
$$131$$ 14.5197i 1.26859i 0.773089 + 0.634297i $$0.218711\pi$$
−0.773089 + 0.634297i $$0.781289\pi$$
$$132$$ 0 0
$$133$$ −0.715687 −0.0620580
$$134$$ 0 0
$$135$$ −1.00000 −0.0860663
$$136$$ 0 0
$$137$$ 4.50448i 0.384844i −0.981312 0.192422i $$-0.938366\pi$$
0.981312 0.192422i $$-0.0616342\pi$$
$$138$$ 0 0
$$139$$ 2.13377i 0.180984i 0.995897 + 0.0904921i $$0.0288440\pi$$
−0.995897 + 0.0904921i $$0.971156\pi$$
$$140$$ 0 0
$$141$$ −11.2632 −0.948531
$$142$$ 0 0
$$143$$ 2.48494 0.207801
$$144$$ 0 0
$$145$$ 7.68679i 0.638353i
$$146$$ 0 0
$$147$$ 6.76696i 0.558129i
$$148$$ 0 0
$$149$$ 11.9315i 0.977468i −0.872433 0.488734i $$-0.837459\pi$$
0.872433 0.488734i $$-0.162541\pi$$
$$150$$ 0 0
$$151$$ 9.63555i 0.784130i 0.919937 + 0.392065i $$0.128239\pi$$
−0.919937 + 0.392065i $$0.871761\pi$$
$$152$$ 0 0
$$153$$ 6.03534i 0.487929i
$$154$$ 0 0
$$155$$ −5.12465 −0.411622
$$156$$ 0 0
$$157$$ 0.935197i 0.0746368i 0.999303 + 0.0373184i $$0.0118816\pi$$
−0.999303 + 0.0373184i $$0.988118\pi$$
$$158$$ 0 0
$$159$$ −8.81467 −0.699049
$$160$$ 0 0
$$161$$ −2.19774 + 0.727943i −0.173206 + 0.0573700i
$$162$$ 0 0
$$163$$ 13.8165i 1.08220i 0.840960 + 0.541098i $$0.181991\pi$$
−0.840960 + 0.541098i $$0.818009\pi$$
$$164$$ 0 0
$$165$$ 1.10189 0.0857820
$$166$$ 0 0
$$167$$ 6.69307i 0.517925i 0.965887 + 0.258963i $$0.0833807\pi$$
−0.965887 + 0.258963i $$0.916619\pi$$
$$168$$ 0 0
$$169$$ −7.91423 −0.608787
$$170$$ 0 0
$$171$$ 1.48254 0.113373
$$172$$ 0 0
$$173$$ −24.6878 −1.87698 −0.938490 0.345305i $$-0.887775\pi$$
−0.938490 + 0.345305i $$0.887775\pi$$
$$174$$ 0 0
$$175$$ −0.482745 −0.0364921
$$176$$ 0 0
$$177$$ −8.08002 −0.607331
$$178$$ 0 0
$$179$$ 4.65679i 0.348065i −0.984740 0.174032i $$-0.944320\pi$$
0.984740 0.174032i $$-0.0556797\pi$$
$$180$$ 0 0
$$181$$ 10.4913i 0.779809i −0.920855 0.389905i $$-0.872508\pi$$
0.920855 0.389905i $$-0.127492\pi$$
$$182$$ 0 0
$$183$$ −0.0392191 −0.00289916
$$184$$ 0 0
$$185$$ −5.83765 −0.429193
$$186$$ 0 0
$$187$$ 6.65028i 0.486317i
$$188$$ 0 0
$$189$$ 0.482745i 0.0351145i
$$190$$ 0 0
$$191$$ −10.1702 −0.735886 −0.367943 0.929848i $$-0.619938\pi$$
−0.367943 + 0.929848i $$0.619938\pi$$
$$192$$ 0 0
$$193$$ −13.3593 −0.961626 −0.480813 0.876823i $$-0.659658\pi$$
−0.480813 + 0.876823i $$0.659658\pi$$
$$194$$ 0 0
$$195$$ 2.25517 0.161496
$$196$$ 0 0
$$197$$ −2.65615 −0.189243 −0.0946216 0.995513i $$-0.530164\pi$$
−0.0946216 + 0.995513i $$0.530164\pi$$
$$198$$ 0 0
$$199$$ 8.43038 0.597614 0.298807 0.954314i $$-0.403411\pi$$
0.298807 + 0.954314i $$0.403411\pi$$
$$200$$ 0 0
$$201$$ 8.39370i 0.592046i
$$202$$ 0 0
$$203$$ −3.71075 −0.260444
$$204$$ 0 0
$$205$$ 1.27767i 0.0892360i
$$206$$ 0 0
$$207$$ 4.55260 1.50793i 0.316428 0.104808i
$$208$$ 0 0
$$209$$ −1.63359 −0.112998
$$210$$ 0 0
$$211$$ 0.771524i 0.0531139i −0.999647 0.0265570i $$-0.991546\pi$$
0.999647 0.0265570i $$-0.00845434\pi$$
$$212$$ 0 0
$$213$$ 1.25598 0.0860586
$$214$$ 0 0
$$215$$ 8.46629i 0.577396i
$$216$$ 0 0
$$217$$ 2.47390i 0.167939i
$$218$$ 0 0
$$219$$ 3.47480i 0.234805i
$$220$$ 0 0
$$221$$ 13.6107i 0.915555i
$$222$$ 0 0
$$223$$ 19.0727i 1.27720i −0.769538 0.638601i $$-0.779513\pi$$
0.769538 0.638601i $$-0.220487\pi$$
$$224$$ 0 0
$$225$$ 1.00000 0.0666667
$$226$$ 0 0
$$227$$ −6.95607 −0.461691 −0.230845 0.972990i $$-0.574149\pi$$
−0.230845 + 0.972990i $$0.574149\pi$$
$$228$$ 0 0
$$229$$ 1.27163i 0.0840316i −0.999117 0.0420158i $$-0.986622\pi$$
0.999117 0.0420158i $$-0.0133780\pi$$
$$230$$ 0 0
$$231$$ 0.531931i 0.0349985i
$$232$$ 0 0
$$233$$ −9.90098 −0.648635 −0.324317 0.945948i $$-0.605135\pi$$
−0.324317 + 0.945948i $$0.605135\pi$$
$$234$$ 0 0
$$235$$ 11.2632 0.734729
$$236$$ 0 0
$$237$$ 3.61831i 0.235035i
$$238$$ 0 0
$$239$$ 10.3420i 0.668968i −0.942401 0.334484i $$-0.891438\pi$$
0.942401 0.334484i $$-0.108562\pi$$
$$240$$ 0 0
$$241$$ 10.9888i 0.707852i −0.935273 0.353926i $$-0.884847\pi$$
0.935273 0.353926i $$-0.115153\pi$$
$$242$$ 0 0
$$243$$ 1.00000i 0.0641500i
$$244$$ 0 0
$$245$$ 6.76696i 0.432325i
$$246$$ 0 0
$$247$$ −3.34337 −0.212734
$$248$$ 0 0
$$249$$ 9.12164i 0.578061i
$$250$$ 0 0
$$251$$ 8.22629 0.519239 0.259619 0.965711i $$-0.416403\pi$$
0.259619 + 0.965711i $$0.416403\pi$$
$$252$$ 0 0
$$253$$ −5.01646 + 1.66157i −0.315382 + 0.104462i
$$254$$ 0 0
$$255$$ 6.03534i 0.377948i
$$256$$ 0 0
$$257$$ −30.1958 −1.88357 −0.941783 0.336223i $$-0.890851\pi$$
−0.941783 + 0.336223i $$0.890851\pi$$
$$258$$ 0 0
$$259$$ 2.81810i 0.175108i
$$260$$ 0 0
$$261$$ 7.68679 0.475800
$$262$$ 0 0
$$263$$ −19.7029 −1.21493 −0.607466 0.794346i $$-0.707814\pi$$
−0.607466 + 0.794346i $$0.707814\pi$$
$$264$$ 0 0
$$265$$ 8.81467 0.541481
$$266$$ 0 0
$$267$$ −6.85106 −0.419278
$$268$$ 0 0
$$269$$ 12.1993 0.743805 0.371902 0.928272i $$-0.378706\pi$$
0.371902 + 0.928272i $$0.378706\pi$$
$$270$$ 0 0
$$271$$ 17.7526i 1.07840i −0.842179 0.539198i $$-0.818727\pi$$
0.842179 0.539198i $$-0.181273\pi$$
$$272$$ 0 0
$$273$$ 1.08867i 0.0658893i
$$274$$ 0 0
$$275$$ −1.10189 −0.0664465
$$276$$ 0 0
$$277$$ −17.0510 −1.02449 −0.512246 0.858839i $$-0.671187\pi$$
−0.512246 + 0.858839i $$0.671187\pi$$
$$278$$ 0 0
$$279$$ 5.12465i 0.306805i
$$280$$ 0 0
$$281$$ 19.4880i 1.16256i 0.813705 + 0.581278i $$0.197447\pi$$
−0.813705 + 0.581278i $$0.802553\pi$$
$$282$$ 0 0
$$283$$ 4.52826 0.269177 0.134589 0.990902i $$-0.457029\pi$$
0.134589 + 0.990902i $$0.457029\pi$$
$$284$$ 0 0
$$285$$ −1.48254 −0.0878180
$$286$$ 0 0
$$287$$ 0.616786 0.0364077
$$288$$ 0 0
$$289$$ −19.4254 −1.14267
$$290$$ 0 0
$$291$$ −0.330286 −0.0193617
$$292$$ 0 0
$$293$$ 14.3433i 0.837942i 0.908000 + 0.418971i $$0.137609\pi$$
−0.908000 + 0.418971i $$0.862391\pi$$
$$294$$ 0 0
$$295$$ 8.08002 0.470437
$$296$$ 0 0
$$297$$ 1.10189i 0.0639381i
$$298$$ 0 0
$$299$$ −10.2669 + 3.40062i −0.593748 + 0.196663i
$$300$$ 0 0
$$301$$ −4.08705 −0.235574
$$302$$ 0 0
$$303$$ 3.89119i 0.223543i
$$304$$ 0 0
$$305$$ 0.0392191 0.00224568
$$306$$ 0 0
$$307$$ 20.1488i 1.14995i −0.818170 0.574976i $$-0.805011\pi$$
0.818170 0.574976i $$-0.194989\pi$$
$$308$$ 0 0
$$309$$ 11.2588i 0.640493i
$$310$$ 0 0
$$311$$ 7.50388i 0.425506i −0.977106 0.212753i $$-0.931757\pi$$
0.977106 0.212753i $$-0.0682430\pi$$
$$312$$ 0 0
$$313$$ 27.7341i 1.56763i 0.620997 + 0.783813i $$0.286728\pi$$
−0.620997 + 0.783813i $$0.713272\pi$$
$$314$$ 0 0
$$315$$ 0.482745i 0.0271996i
$$316$$ 0 0
$$317$$ 23.7305 1.33284 0.666419 0.745577i $$-0.267826\pi$$
0.666419 + 0.745577i $$0.267826\pi$$
$$318$$ 0 0
$$319$$ −8.46999 −0.474228
$$320$$ 0 0
$$321$$ 0.801493i 0.0447350i
$$322$$ 0 0
$$323$$ 8.94763i 0.497859i
$$324$$ 0 0
$$325$$ −2.25517 −0.125094
$$326$$ 0 0
$$327$$ 1.25885 0.0696146
$$328$$ 0 0
$$329$$ 5.43724i 0.299765i
$$330$$ 0 0
$$331$$ 14.4675i 0.795205i −0.917558 0.397602i $$-0.869842\pi$$
0.917558 0.397602i $$-0.130158\pi$$
$$332$$ 0 0
$$333$$ 5.83765i 0.319902i
$$334$$ 0 0
$$335$$ 8.39370i 0.458597i
$$336$$ 0 0
$$337$$ 2.09258i 0.113990i −0.998374 0.0569950i $$-0.981848\pi$$
0.998374 0.0569950i $$-0.0181519\pi$$
$$338$$ 0 0
$$339$$ 8.70667 0.472881
$$340$$ 0 0
$$341$$ 5.64680i 0.305791i
$$342$$ 0 0
$$343$$ −6.64593 −0.358846
$$344$$ 0 0
$$345$$ −4.55260 + 1.50793i −0.245104 + 0.0811840i
$$346$$ 0 0
$$347$$ 35.3150i 1.89581i 0.318552 + 0.947905i $$0.396804\pi$$
−0.318552 + 0.947905i $$0.603196\pi$$
$$348$$ 0 0
$$349$$ 25.4994 1.36495 0.682477 0.730907i $$-0.260903\pi$$
0.682477 + 0.730907i $$0.260903\pi$$
$$350$$ 0 0
$$351$$ 2.25517i 0.120372i
$$352$$ 0 0
$$353$$ −22.8722 −1.21737 −0.608683 0.793414i $$-0.708302\pi$$
−0.608683 + 0.793414i $$0.708302\pi$$
$$354$$ 0 0
$$355$$ −1.25598 −0.0666607
$$356$$ 0 0
$$357$$ 2.91353 0.154200
$$358$$ 0 0
$$359$$ 29.5592 1.56008 0.780038 0.625732i $$-0.215200\pi$$
0.780038 + 0.625732i $$0.215200\pi$$
$$360$$ 0 0
$$361$$ −16.8021 −0.884320
$$362$$ 0 0
$$363$$ 9.78584i 0.513623i
$$364$$ 0 0
$$365$$ 3.47480i 0.181879i
$$366$$ 0 0
$$367$$ −13.9579 −0.728598 −0.364299 0.931282i $$-0.618691\pi$$
−0.364299 + 0.931282i $$0.618691\pi$$
$$368$$ 0 0
$$369$$ −1.27767 −0.0665126
$$370$$ 0 0
$$371$$ 4.25524i 0.220921i
$$372$$ 0 0
$$373$$ 18.8723i 0.977170i −0.872516 0.488585i $$-0.837513\pi$$
0.872516 0.488585i $$-0.162487\pi$$
$$374$$ 0 0
$$375$$ −1.00000 −0.0516398
$$376$$ 0 0
$$377$$ −17.3350 −0.892797
$$378$$ 0 0
$$379$$ 15.7908 0.811121 0.405560 0.914068i $$-0.367076\pi$$
0.405560 + 0.914068i $$0.367076\pi$$
$$380$$ 0 0
$$381$$ 5.51836 0.282714
$$382$$ 0 0
$$383$$ 12.4419 0.635749 0.317875 0.948133i $$-0.397031\pi$$
0.317875 + 0.948133i $$0.397031\pi$$
$$384$$ 0 0
$$385$$ 0.531931i 0.0271097i
$$386$$ 0 0
$$387$$ 8.46629 0.430365
$$388$$ 0 0
$$389$$ 13.3784i 0.678312i −0.940730 0.339156i $$-0.889858\pi$$
0.940730 0.339156i $$-0.110142\pi$$
$$390$$ 0 0
$$391$$ 9.10085 + 27.4765i 0.460250 + 1.38955i
$$392$$ 0 0
$$393$$ −14.5197 −0.732424
$$394$$ 0 0
$$395$$ 3.61831i 0.182057i
$$396$$ 0 0
$$397$$ 22.8329 1.14595 0.572976 0.819572i $$-0.305789\pi$$
0.572976 + 0.819572i $$0.305789\pi$$
$$398$$ 0 0
$$399$$ 0.715687i 0.0358292i
$$400$$ 0 0
$$401$$ 24.0495i 1.20098i −0.799634 0.600488i $$-0.794973\pi$$
0.799634 0.600488i $$-0.205027\pi$$
$$402$$ 0 0
$$403$$ 11.5569i 0.575692i
$$404$$ 0 0
$$405$$ 1.00000i 0.0496904i
$$406$$ 0 0
$$407$$ 6.43245i 0.318845i
$$408$$ 0 0
$$409$$ −19.5572 −0.967042 −0.483521 0.875333i $$-0.660642\pi$$
−0.483521 + 0.875333i $$0.660642\pi$$
$$410$$ 0 0
$$411$$ 4.50448 0.222190
$$412$$ 0 0
$$413$$ 3.90059i 0.191935i
$$414$$ 0 0
$$415$$ 9.12164i 0.447764i
$$416$$ 0 0
$$417$$ −2.13377 −0.104491
$$418$$ 0 0
$$419$$ −26.0411 −1.27219 −0.636095 0.771611i $$-0.719451\pi$$
−0.636095 + 0.771611i $$0.719451\pi$$
$$420$$ 0 0
$$421$$ 37.9967i 1.85185i −0.377711 0.925924i $$-0.623289\pi$$
0.377711 0.925924i $$-0.376711\pi$$
$$422$$ 0 0
$$423$$ 11.2632i 0.547635i
$$424$$ 0 0
$$425$$ 6.03534i 0.292757i
$$426$$ 0 0
$$427$$ 0.0189328i 0.000916224i
$$428$$ 0 0
$$429$$ 2.48494i 0.119974i
$$430$$ 0 0
$$431$$ 41.2449 1.98670 0.993348 0.115152i $$-0.0367354\pi$$
0.993348 + 0.115152i $$0.0367354\pi$$
$$432$$ 0 0
$$433$$ 2.54638i 0.122371i 0.998126 + 0.0611856i $$0.0194882\pi$$
−0.998126 + 0.0611856i $$0.980512\pi$$
$$434$$ 0 0
$$435$$ −7.68679 −0.368553
$$436$$ 0 0
$$437$$ 6.74940 2.23556i 0.322868 0.106941i
$$438$$ 0 0
$$439$$ 9.22800i 0.440428i 0.975452 + 0.220214i $$0.0706756\pi$$
−0.975452 + 0.220214i $$0.929324\pi$$
$$440$$ 0 0
$$441$$ 6.76696 0.322236
$$442$$ 0 0
$$443$$ 10.8713i 0.516511i 0.966077 + 0.258256i $$0.0831477\pi$$
−0.966077 + 0.258256i $$0.916852\pi$$
$$444$$ 0 0
$$445$$ 6.85106 0.324771
$$446$$ 0 0
$$447$$ 11.9315 0.564341
$$448$$ 0 0
$$449$$ −12.3548 −0.583061 −0.291530 0.956562i $$-0.594164\pi$$
−0.291530 + 0.956562i $$0.594164\pi$$
$$450$$ 0 0
$$451$$ 1.40785 0.0662929
$$452$$ 0 0
$$453$$ −9.63555 −0.452718
$$454$$ 0 0
$$455$$ 1.08867i 0.0510376i
$$456$$ 0 0
$$457$$ 36.0224i 1.68506i −0.538651 0.842529i $$-0.681066\pi$$
0.538651 0.842529i $$-0.318934\pi$$
$$458$$ 0 0
$$459$$ −6.03534 −0.281706
$$460$$ 0 0
$$461$$ −1.41328 −0.0658229 −0.0329115 0.999458i $$-0.510478\pi$$
−0.0329115 + 0.999458i $$0.510478\pi$$
$$462$$ 0 0
$$463$$ 22.3322i 1.03787i −0.854815 0.518934i $$-0.826329\pi$$
0.854815 0.518934i $$-0.173671\pi$$
$$464$$ 0 0
$$465$$ 5.12465i 0.237650i
$$466$$ 0 0
$$467$$ −13.6777 −0.632930 −0.316465 0.948604i $$-0.602496\pi$$
−0.316465 + 0.948604i $$0.602496\pi$$
$$468$$ 0 0
$$469$$ −4.05201 −0.187105
$$470$$ 0 0
$$471$$ −0.935197 −0.0430916
$$472$$ 0 0
$$473$$ −9.32891 −0.428944
$$474$$ 0 0
$$475$$ 1.48254 0.0680235
$$476$$ 0 0
$$477$$ 8.81467i 0.403596i
$$478$$ 0 0
$$479$$ −19.9153 −0.909954 −0.454977 0.890503i $$-0.650353\pi$$
−0.454977 + 0.890503i $$0.650353\pi$$
$$480$$ 0 0
$$481$$ 13.1649i 0.600267i
$$482$$ 0 0
$$483$$ −0.727943 2.19774i −0.0331226 0.100001i
$$484$$ 0 0
$$485$$ 0.330286 0.0149975
$$486$$ 0 0
$$487$$ 36.4307i 1.65083i −0.564524 0.825417i $$-0.690940\pi$$
0.564524 0.825417i $$-0.309060\pi$$
$$488$$ 0 0
$$489$$ −13.8165 −0.624806
$$490$$ 0 0
$$491$$ 18.4791i 0.833948i 0.908918 + 0.416974i $$0.136909\pi$$
−0.908918 + 0.416974i $$0.863091\pi$$
$$492$$ 0 0
$$493$$ 46.3924i 2.08941i
$$494$$ 0 0
$$495$$ 1.10189i 0.0495263i
$$496$$ 0 0
$$497$$ 0.606320i 0.0271971i
$$498$$ 0 0
$$499$$ 11.1690i 0.499993i −0.968247 0.249997i $$-0.919571\pi$$
0.968247 0.249997i $$-0.0804295\pi$$
$$500$$ 0 0
$$501$$ −6.69307 −0.299024
$$502$$ 0 0
$$503$$ −6.27100 −0.279610 −0.139805 0.990179i $$-0.544648\pi$$
−0.139805 + 0.990179i $$0.544648\pi$$
$$504$$ 0 0
$$505$$ 3.89119i 0.173156i
$$506$$ 0 0
$$507$$ 7.91423i 0.351483i
$$508$$ 0 0
$$509$$ 39.1536 1.73545 0.867726 0.497043i $$-0.165581\pi$$
0.867726 + 0.497043i $$0.165581\pi$$
$$510$$ 0 0
$$511$$ −1.67744 −0.0742056
$$512$$ 0 0
$$513$$ 1.48254i 0.0654557i
$$514$$ 0 0
$$515$$ 11.2588i 0.496124i
$$516$$ 0 0
$$517$$ 12.4108i 0.545826i
$$518$$ 0 0
$$519$$ 24.6878i 1.08368i
$$520$$ 0 0
$$521$$ 37.4123i 1.63906i −0.573035 0.819531i $$-0.694234\pi$$
0.573035 0.819531i $$-0.305766\pi$$
$$522$$ 0 0
$$523$$ −14.7986 −0.647098 −0.323549 0.946211i $$-0.604876\pi$$
−0.323549 + 0.946211i $$0.604876\pi$$
$$524$$ 0 0
$$525$$ 0.482745i 0.0210687i
$$526$$ 0 0
$$527$$ −30.9290 −1.34729
$$528$$ 0 0
$$529$$ 18.4523 13.7300i 0.802275 0.596955i
$$530$$ 0 0
$$531$$ 8.08002i 0.350643i
$$532$$ 0 0
$$533$$ 2.88135 0.124805
$$534$$ 0 0
$$535$$ 0.801493i 0.0346516i
$$536$$ 0 0
$$537$$ 4.65679 0.200955
$$538$$ 0 0
$$539$$ −7.45644 −0.321172
$$540$$ 0 0
$$541$$ 1.29246 0.0555670 0.0277835 0.999614i $$-0.491155\pi$$
0.0277835 + 0.999614i $$0.491155\pi$$
$$542$$ 0 0
$$543$$ 10.4913 0.450223
$$544$$ 0 0
$$545$$ −1.25885 −0.0539232
$$546$$ 0 0
$$547$$ 12.2259i 0.522741i 0.965239 + 0.261370i $$0.0841744\pi$$
−0.965239 + 0.261370i $$0.915826\pi$$
$$548$$ 0 0
$$549$$ 0.0392191i 0.00167383i
$$550$$ 0 0
$$551$$ 11.3960 0.485484
$$552$$ 0 0
$$553$$ −1.74672 −0.0742781
$$554$$ 0 0
$$555$$ 5.83765i 0.247795i
$$556$$ 0 0
$$557$$ 17.1020i 0.724637i 0.932054 + 0.362318i $$0.118015\pi$$
−0.932054 + 0.362318i $$0.881985\pi$$
$$558$$ 0 0
$$559$$ −19.0929 −0.807543
$$560$$ 0 0
$$561$$ 6.65028 0.280775
$$562$$ 0 0
$$563$$ 23.9801 1.01064 0.505321 0.862931i $$-0.331374\pi$$
0.505321 + 0.862931i $$0.331374\pi$$
$$564$$ 0 0
$$565$$ −8.70667 −0.366292
$$566$$ 0 0
$$567$$ 0.482745 0.0202734
$$568$$ 0 0
$$569$$ 2.83032i 0.118653i −0.998239 0.0593265i $$-0.981105\pi$$
0.998239 0.0593265i $$-0.0188953\pi$$
$$570$$ 0 0
$$571$$ −7.44436 −0.311537 −0.155768 0.987794i $$-0.549785\pi$$
−0.155768 + 0.987794i $$0.549785\pi$$
$$572$$ 0 0
$$573$$ 10.1702i 0.424864i
$$574$$ 0 0
$$575$$ 4.55260 1.50793i 0.189857 0.0628849i
$$576$$ 0 0
$$577$$ −10.4658 −0.435695 −0.217848 0.975983i $$-0.569904\pi$$
−0.217848 + 0.975983i $$0.569904\pi$$
$$578$$ 0 0
$$579$$ 13.3593i 0.555195i
$$580$$ 0 0
$$581$$ 4.40342 0.182685
$$582$$ 0 0
$$583$$ 9.71280i 0.402263i
$$584$$ 0 0
$$585$$ 2.25517i 0.0932396i
$$586$$ 0 0
$$587$$ 5.27783i 0.217839i 0.994051 + 0.108920i $$0.0347391\pi$$
−0.994051 + 0.108920i $$0.965261\pi$$
$$588$$ 0 0
$$589$$ 7.59749i 0.313049i
$$590$$ 0 0
$$591$$ 2.65615i 0.109260i
$$592$$ 0 0
$$593$$ 18.1506 0.745357 0.372679 0.927960i $$-0.378439\pi$$
0.372679 + 0.927960i $$0.378439\pi$$
$$594$$ 0 0
$$595$$ −2.91353 −0.119443
$$596$$ 0 0
$$597$$ 8.43038i 0.345033i
$$598$$ 0 0
$$599$$ 15.0499i 0.614921i 0.951561 + 0.307460i $$0.0994792\pi$$
−0.951561 + 0.307460i $$0.900521\pi$$
$$600$$ 0 0
$$601$$ 17.8769 0.729213 0.364607 0.931162i $$-0.381203\pi$$
0.364607 + 0.931162i $$0.381203\pi$$
$$602$$ 0 0
$$603$$ 8.39370 0.341818
$$604$$ 0 0
$$605$$ 9.78584i 0.397851i
$$606$$ 0 0
$$607$$ 16.8849i 0.685336i 0.939457 + 0.342668i $$0.111331\pi$$
−0.939457 + 0.342668i $$0.888669\pi$$
$$608$$ 0 0
$$609$$ 3.71075i 0.150367i
$$610$$ 0 0
$$611$$ 25.4003i 1.02759i
$$612$$ 0 0
$$613$$ 25.0275i 1.01085i 0.862871 + 0.505425i $$0.168664\pi$$
−0.862871 + 0.505425i $$0.831336\pi$$
$$614$$ 0 0
$$615$$ 1.27767 0.0515204
$$616$$ 0 0
$$617$$ 32.3884i 1.30391i −0.758259 0.651953i $$-0.773950\pi$$
0.758259 0.651953i $$-0.226050\pi$$
$$618$$ 0 0
$$619$$ 34.1700 1.37341 0.686703 0.726938i $$-0.259057\pi$$
0.686703 + 0.726938i $$0.259057\pi$$
$$620$$ 0 0
$$621$$ 1.50793 + 4.55260i 0.0605110 + 0.182690i
$$622$$ 0 0
$$623$$ 3.30731i 0.132505i
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ 0 0
$$627$$ 1.63359i 0.0652394i
$$628$$ 0 0
$$629$$ −35.2323 −1.40480
$$630$$ 0 0
$$631$$ 8.12167 0.323319 0.161659 0.986847i $$-0.448315\pi$$
0.161659 + 0.986847i $$0.448315\pi$$
$$632$$ 0 0
$$633$$ 0.771524 0.0306653
$$634$$ 0 0
$$635$$ −5.51836 −0.218990
$$636$$ 0 0
$$637$$ −15.2606 −0.604648
$$638$$ 0 0
$$639$$ 1.25598i 0.0496860i
$$640$$ 0 0
$$641$$ 32.8333i 1.29684i −0.761285 0.648418i $$-0.775431\pi$$
0.761285 0.648418i $$-0.224569\pi$$
$$642$$ 0 0
$$643$$ −11.4559 −0.451776 −0.225888 0.974153i $$-0.572528\pi$$
−0.225888 + 0.974153i $$0.572528\pi$$
$$644$$ 0 0
$$645$$ −8.46629 −0.333360
$$646$$ 0 0
$$647$$ 11.8499i 0.465867i 0.972493 + 0.232933i $$0.0748324\pi$$
−0.972493 + 0.232933i $$0.925168\pi$$
$$648$$ 0 0
$$649$$ 8.90329i 0.349485i
$$650$$ 0 0
$$651$$ 2.47390 0.0969597
$$652$$ 0 0
$$653$$ 19.4675 0.761821 0.380911 0.924612i $$-0.375611\pi$$
0.380911 + 0.924612i $$0.375611\pi$$
$$654$$ 0 0
$$655$$ 14.5197 0.567333
$$656$$ 0 0
$$657$$ 3.47480 0.135565
$$658$$ 0 0
$$659$$ −38.7108 −1.50796 −0.753980 0.656897i $$-0.771869\pi$$
−0.753980 + 0.656897i $$0.771869\pi$$
$$660$$ 0 0
$$661$$ 23.6248i 0.918900i 0.888204 + 0.459450i $$0.151953\pi$$
−0.888204 + 0.459450i $$0.848047\pi$$
$$662$$ 0 0
$$663$$ 13.6107 0.528596
$$664$$ 0 0
$$665$$ 0.715687i 0.0277532i
$$666$$ 0 0
$$667$$ 34.9949 11.5911i 1.35501 0.448809i
$$668$$ 0 0
$$669$$ 19.0727 0.737393
$$670$$ 0 0
$$671$$ 0.0432152i 0.00166830i
$$672$$ 0 0
$$673$$ −41.6743 −1.60643 −0.803213 0.595692i $$-0.796878\pi$$
−0.803213 + 0.595692i $$0.796878\pi$$
$$674$$ 0 0
$$675$$ 1.00000i 0.0384900i
$$676$$ 0 0
$$677$$ 2.61727i 0.100590i −0.998734 0.0502948i $$-0.983984\pi$$
0.998734 0.0502948i $$-0.0160161\pi$$
$$678$$ 0 0
$$679$$ 0.159444i 0.00611890i
$$680$$ 0 0
$$681$$ 6.95607i 0.266557i
$$682$$ 0 0
$$683$$ 17.4757i 0.668688i 0.942451 + 0.334344i $$0.108515\pi$$
−0.942451 + 0.334344i $$0.891485\pi$$
$$684$$ 0 0
$$685$$ −4.50448 −0.172107
$$686$$ 0 0
$$687$$ 1.27163 0.0485157
$$688$$ 0 0
$$689$$ 19.8786i 0.757313i
$$690$$ 0 0
$$691$$ 33.9569i 1.29178i −0.763430 0.645890i $$-0.776486\pi$$
0.763430 0.645890i $$-0.223514\pi$$
$$692$$ 0 0
$$693$$ −0.531931 −0.0202064
$$694$$ 0 0
$$695$$ 2.13377 0.0809386
$$696$$ 0 0
$$697$$ 7.71115i 0.292081i
$$698$$ 0 0
$$699$$ 9.90098i 0.374489i
$$700$$ 0 0
$$701$$ 17.9294i 0.677183i −0.940933 0.338592i $$-0.890049\pi$$
0.940933 0.338592i $$-0.109951\pi$$
$$702$$ 0 0
$$703$$ 8.65455i 0.326412i
$$704$$ 0 0
$$705$$ 11.2632i 0.424196i
$$706$$ 0 0
$$707$$ −1.87845 −0.0706464
$$708$$ 0 0
$$709$$ 23.2328i 0.872526i −0.899819 0.436263i $$-0.856302\pi$$
0.899819 0.436263i $$-0.143698\pi$$
$$710$$ 0 0
$$711$$ 3.61831 0.135697
$$712$$ 0 0
$$713$$ 7.72759 + 23.3305i 0.289401 + 0.873733i
$$714$$ 0 0
$$715$$ 2.48494i 0.0929317i
$$716$$ 0 0
$$717$$ 10.3420 0.386229
$$718$$ 0 0
$$719$$ 34.5036i 1.28677i 0.765544 + 0.643384i $$0.222470\pi$$
−0.765544 + 0.643384i $$0.777530\pi$$
$$720$$ 0 0
$$721$$ 5.43514 0.202415
$$722$$ 0 0
$$723$$ 10.9888 0.408678
$$724$$ 0 0
$$725$$ 7.68679 0.285480
$$726$$ 0 0
$$727$$ −45.7234 −1.69579 −0.847893 0.530168i $$-0.822129\pi$$
−0.847893 + 0.530168i $$0.822129\pi$$
$$728$$ 0 0
$$729$$ −1.00000 −0.0370370
$$730$$ 0 0
$$731$$ 51.0969i 1.88989i
$$732$$ 0 0
$$733$$ 4.56648i 0.168667i 0.996438 + 0.0843333i $$0.0268760\pi$$
−0.996438 + 0.0843333i $$0.973124\pi$$
$$734$$ 0 0
$$735$$ −6.76696 −0.249603
$$736$$ 0 0
$$737$$ −9.24893 −0.340689
$$738$$ 0 0
$$739$$ 8.71551i 0.320605i −0.987068 0.160303i $$-0.948753\pi$$
0.987068 0.160303i $$-0.0512470\pi$$
$$740$$ 0 0
$$741$$ 3.34337i 0.122822i
$$742$$ 0 0
$$743$$ −39.8622 −1.46240 −0.731202 0.682161i $$-0.761040\pi$$
−0.731202 + 0.682161i $$0.761040\pi$$
$$744$$ 0 0
$$745$$ −11.9315 −0.437137
$$746$$ 0 0
$$747$$ −9.12164 −0.333743
$$748$$ 0 0
$$749$$ −0.386917 −0.0141376
$$750$$ 0 0
$$751$$ −6.71643 −0.245086 −0.122543 0.992463i $$-0.539105\pi$$
−0.122543 + 0.992463i $$0.539105\pi$$
$$752$$ 0 0
$$753$$ 8.22629i 0.299783i
$$754$$ 0 0
$$755$$ 9.63555 0.350674
$$756$$ 0 0
$$757$$ 39.8926i 1.44992i 0.688790 + 0.724961i $$0.258142\pi$$
−0.688790 + 0.724961i $$0.741858\pi$$
$$758$$ 0 0
$$759$$ −1.66157 5.01646i −0.0603111 0.182086i
$$760$$ 0 0
$$761$$ 2.24308 0.0813116 0.0406558 0.999173i $$-0.487055\pi$$
0.0406558 + 0.999173i $$0.487055\pi$$
$$762$$ 0 0
$$763$$ 0.607703i 0.0220003i
$$764$$ 0 0
$$765$$ 6.03534 0.218208
$$766$$ 0 0
$$767$$ 18.2218i 0.657950i
$$768$$ 0 0
$$769$$ 26.5172i 0.956233i −0.878296 0.478117i $$-0.841320\pi$$
0.878296 0.478117i $$-0.158680\pi$$
$$770$$ 0 0
$$771$$ 30.1958i 1.08748i
$$772$$ 0 0
$$773$$ 49.8502i 1.79299i 0.443057 + 0.896493i $$0.353894\pi$$
−0.443057 + 0.896493i $$0.646106\pi$$
$$774$$ 0 0
$$775$$ 5.12465i 0.184083i
$$776$$ 0 0
$$777$$ 2.81810 0.101099
$$778$$ 0 0
$$779$$ −1.89419 −0.0678663
$$780$$ 0 0
$$781$$ 1.38396i 0.0495218i
$$782$$ 0 0
$$783$$ 7.68679i 0.274703i
$$784$$ 0 0
$$785$$ 0.935197 0.0333786
$$786$$ 0 0
$$787$$ 25.8578 0.921732 0.460866 0.887470i $$-0.347539\pi$$
0.460866 + 0.887470i $$0.347539\pi$$
$$788$$ 0 0
$$789$$ 19.7029i 0.701441i
$$790$$ 0 0
$$791$$ 4.20310i 0.149445i
$$792$$ 0 0
$$793$$ 0.0884456i 0.00314080i
$$794$$ 0 0
$$795$$ 8.81467i 0.312624i
$$796$$ 0 0
$$797$$ 5.23771i 0.185529i −0.995688 0.0927647i $$-0.970430\pi$$
0.995688 0.0927647i $$-0.0295704\pi$$
$$798$$ 0 0
$$799$$ 67.9772 2.40486
$$800$$ 0 0
$$801$$ 6.85106i 0.242070i
$$802$$ 0 0
$$803$$ −3.82884 −0.135117
$$804$$ 0 0