# Properties

 Label 1680.2.t.f.1009.1 Level $1680$ Weight $2$ Character 1680.1009 Analytic conductor $13.415$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1680.t (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$13.4148675396$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ Defining polynomial: $$x^{2} + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 105) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 1009.1 Root $$-1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 1680.1009 Dual form 1680.2.t.f.1009.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000i q^{3} +(1.00000 - 2.00000i) q^{5} -1.00000i q^{7} -1.00000 q^{9} +O(q^{10})$$ $$q-1.00000i q^{3} +(1.00000 - 2.00000i) q^{5} -1.00000i q^{7} -1.00000 q^{9} +6.00000 q^{11} -2.00000i q^{13} +(-2.00000 - 1.00000i) q^{15} -4.00000i q^{17} -6.00000 q^{19} -1.00000 q^{21} +(-3.00000 - 4.00000i) q^{25} +1.00000i q^{27} +2.00000 q^{29} +10.0000 q^{31} -6.00000i q^{33} +(-2.00000 - 1.00000i) q^{35} +4.00000i q^{37} -2.00000 q^{39} +2.00000 q^{41} +4.00000i q^{43} +(-1.00000 + 2.00000i) q^{45} -1.00000 q^{49} -4.00000 q^{51} +6.00000i q^{53} +(6.00000 - 12.0000i) q^{55} +6.00000i q^{57} -8.00000 q^{59} -2.00000 q^{61} +1.00000i q^{63} +(-4.00000 - 2.00000i) q^{65} -16.0000i q^{67} -10.0000 q^{71} -6.00000i q^{73} +(-4.00000 + 3.00000i) q^{75} -6.00000i q^{77} +4.00000 q^{79} +1.00000 q^{81} -8.00000i q^{83} +(-8.00000 - 4.00000i) q^{85} -2.00000i q^{87} -6.00000 q^{89} -2.00000 q^{91} -10.0000i q^{93} +(-6.00000 + 12.0000i) q^{95} +2.00000i q^{97} -6.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 2 q^{5} - 2 q^{9} + O(q^{10})$$ $$2 q + 2 q^{5} - 2 q^{9} + 12 q^{11} - 4 q^{15} - 12 q^{19} - 2 q^{21} - 6 q^{25} + 4 q^{29} + 20 q^{31} - 4 q^{35} - 4 q^{39} + 4 q^{41} - 2 q^{45} - 2 q^{49} - 8 q^{51} + 12 q^{55} - 16 q^{59} - 4 q^{61} - 8 q^{65} - 20 q^{71} - 8 q^{75} + 8 q^{79} + 2 q^{81} - 16 q^{85} - 12 q^{89} - 4 q^{91} - 12 q^{95} - 12 q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times$$.

 $$n$$ $$241$$ $$337$$ $$421$$ $$1121$$ $$1471$$ $$\chi(n)$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$1$$

## 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
$$5$$ 1.00000 2.00000i 0.447214 0.894427i
$$6$$ 0 0
$$7$$ 1.00000i 0.377964i
$$8$$ 0 0
$$9$$ −1.00000 −0.333333
$$10$$ 0 0
$$11$$ 6.00000 1.80907 0.904534 0.426401i $$-0.140219\pi$$
0.904534 + 0.426401i $$0.140219\pi$$
$$12$$ 0 0
$$13$$ 2.00000i 0.554700i −0.960769 0.277350i $$-0.910544\pi$$
0.960769 0.277350i $$-0.0894562\pi$$
$$14$$ 0 0
$$15$$ −2.00000 1.00000i −0.516398 0.258199i
$$16$$ 0 0
$$17$$ 4.00000i 0.970143i −0.874475 0.485071i $$-0.838794\pi$$
0.874475 0.485071i $$-0.161206\pi$$
$$18$$ 0 0
$$19$$ −6.00000 −1.37649 −0.688247 0.725476i $$-0.741620\pi$$
−0.688247 + 0.725476i $$0.741620\pi$$
$$20$$ 0 0
$$21$$ −1.00000 −0.218218
$$22$$ 0 0
$$23$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$24$$ 0 0
$$25$$ −3.00000 4.00000i −0.600000 0.800000i
$$26$$ 0 0
$$27$$ 1.00000i 0.192450i
$$28$$ 0 0
$$29$$ 2.00000 0.371391 0.185695 0.982607i $$-0.440546\pi$$
0.185695 + 0.982607i $$0.440546\pi$$
$$30$$ 0 0
$$31$$ 10.0000 1.79605 0.898027 0.439941i $$-0.145001\pi$$
0.898027 + 0.439941i $$0.145001\pi$$
$$32$$ 0 0
$$33$$ 6.00000i 1.04447i
$$34$$ 0 0
$$35$$ −2.00000 1.00000i −0.338062 0.169031i
$$36$$ 0 0
$$37$$ 4.00000i 0.657596i 0.944400 + 0.328798i $$0.106644\pi$$
−0.944400 + 0.328798i $$0.893356\pi$$
$$38$$ 0 0
$$39$$ −2.00000 −0.320256
$$40$$ 0 0
$$41$$ 2.00000 0.312348 0.156174 0.987730i $$-0.450084\pi$$
0.156174 + 0.987730i $$0.450084\pi$$
$$42$$ 0 0
$$43$$ 4.00000i 0.609994i 0.952353 + 0.304997i $$0.0986555\pi$$
−0.952353 + 0.304997i $$0.901344\pi$$
$$44$$ 0 0
$$45$$ −1.00000 + 2.00000i −0.149071 + 0.298142i
$$46$$ 0 0
$$47$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$48$$ 0 0
$$49$$ −1.00000 −0.142857
$$50$$ 0 0
$$51$$ −4.00000 −0.560112
$$52$$ 0 0
$$53$$ 6.00000i 0.824163i 0.911147 + 0.412082i $$0.135198\pi$$
−0.911147 + 0.412082i $$0.864802\pi$$
$$54$$ 0 0
$$55$$ 6.00000 12.0000i 0.809040 1.61808i
$$56$$ 0 0
$$57$$ 6.00000i 0.794719i
$$58$$ 0 0
$$59$$ −8.00000 −1.04151 −0.520756 0.853706i $$-0.674350\pi$$
−0.520756 + 0.853706i $$0.674350\pi$$
$$60$$ 0 0
$$61$$ −2.00000 −0.256074 −0.128037 0.991769i $$-0.540868\pi$$
−0.128037 + 0.991769i $$0.540868\pi$$
$$62$$ 0 0
$$63$$ 1.00000i 0.125988i
$$64$$ 0 0
$$65$$ −4.00000 2.00000i −0.496139 0.248069i
$$66$$ 0 0
$$67$$ 16.0000i 1.95471i −0.211604 0.977356i $$-0.567869\pi$$
0.211604 0.977356i $$-0.432131\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −10.0000 −1.18678 −0.593391 0.804914i $$-0.702211\pi$$
−0.593391 + 0.804914i $$0.702211\pi$$
$$72$$ 0 0
$$73$$ 6.00000i 0.702247i −0.936329 0.351123i $$-0.885800\pi$$
0.936329 0.351123i $$-0.114200\pi$$
$$74$$ 0 0
$$75$$ −4.00000 + 3.00000i −0.461880 + 0.346410i
$$76$$ 0 0
$$77$$ 6.00000i 0.683763i
$$78$$ 0 0
$$79$$ 4.00000 0.450035 0.225018 0.974355i $$-0.427756\pi$$
0.225018 + 0.974355i $$0.427756\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 0 0
$$83$$ 8.00000i 0.878114i −0.898459 0.439057i $$-0.855313\pi$$
0.898459 0.439057i $$-0.144687\pi$$
$$84$$ 0 0
$$85$$ −8.00000 4.00000i −0.867722 0.433861i
$$86$$ 0 0
$$87$$ 2.00000i 0.214423i
$$88$$ 0 0
$$89$$ −6.00000 −0.635999 −0.317999 0.948091i $$-0.603011\pi$$
−0.317999 + 0.948091i $$0.603011\pi$$
$$90$$ 0 0
$$91$$ −2.00000 −0.209657
$$92$$ 0 0
$$93$$ 10.0000i 1.03695i
$$94$$ 0 0
$$95$$ −6.00000 + 12.0000i −0.615587 + 1.23117i
$$96$$ 0 0
$$97$$ 2.00000i 0.203069i 0.994832 + 0.101535i $$0.0323753\pi$$
−0.994832 + 0.101535i $$0.967625\pi$$
$$98$$ 0 0
$$99$$ −6.00000 −0.603023
$$100$$ 0 0
$$101$$ −6.00000 −0.597022 −0.298511 0.954406i $$-0.596490\pi$$
−0.298511 + 0.954406i $$0.596490\pi$$
$$102$$ 0 0
$$103$$ 8.00000i 0.788263i −0.919054 0.394132i $$-0.871045\pi$$
0.919054 0.394132i $$-0.128955\pi$$
$$104$$ 0 0
$$105$$ −1.00000 + 2.00000i −0.0975900 + 0.195180i
$$106$$ 0 0
$$107$$ 4.00000i 0.386695i 0.981130 + 0.193347i $$0.0619344\pi$$
−0.981130 + 0.193347i $$0.938066\pi$$
$$108$$ 0 0
$$109$$ −2.00000 −0.191565 −0.0957826 0.995402i $$-0.530535\pi$$
−0.0957826 + 0.995402i $$0.530535\pi$$
$$110$$ 0 0
$$111$$ 4.00000 0.379663
$$112$$ 0 0
$$113$$ 6.00000i 0.564433i 0.959351 + 0.282216i $$0.0910696\pi$$
−0.959351 + 0.282216i $$0.908930\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 2.00000i 0.184900i
$$118$$ 0 0
$$119$$ −4.00000 −0.366679
$$120$$ 0 0
$$121$$ 25.0000 2.27273
$$122$$ 0 0
$$123$$ 2.00000i 0.180334i
$$124$$ 0 0
$$125$$ −11.0000 + 2.00000i −0.983870 + 0.178885i
$$126$$ 0 0
$$127$$ 20.0000i 1.77471i 0.461084 + 0.887357i $$0.347461\pi$$
−0.461084 + 0.887357i $$0.652539\pi$$
$$128$$ 0 0
$$129$$ 4.00000 0.352180
$$130$$ 0 0
$$131$$ −4.00000 −0.349482 −0.174741 0.984614i $$-0.555909\pi$$
−0.174741 + 0.984614i $$0.555909\pi$$
$$132$$ 0 0
$$133$$ 6.00000i 0.520266i
$$134$$ 0 0
$$135$$ 2.00000 + 1.00000i 0.172133 + 0.0860663i
$$136$$ 0 0
$$137$$ 6.00000i 0.512615i 0.966595 + 0.256307i $$0.0825059\pi$$
−0.966595 + 0.256307i $$0.917494\pi$$
$$138$$ 0 0
$$139$$ 2.00000 0.169638 0.0848189 0.996396i $$-0.472969\pi$$
0.0848189 + 0.996396i $$0.472969\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 12.0000i 1.00349i
$$144$$ 0 0
$$145$$ 2.00000 4.00000i 0.166091 0.332182i
$$146$$ 0 0
$$147$$ 1.00000i 0.0824786i
$$148$$ 0 0
$$149$$ 14.0000 1.14692 0.573462 0.819232i $$-0.305600\pi$$
0.573462 + 0.819232i $$0.305600\pi$$
$$150$$ 0 0
$$151$$ −8.00000 −0.651031 −0.325515 0.945537i $$-0.605538\pi$$
−0.325515 + 0.945537i $$0.605538\pi$$
$$152$$ 0 0
$$153$$ 4.00000i 0.323381i
$$154$$ 0 0
$$155$$ 10.0000 20.0000i 0.803219 1.60644i
$$156$$ 0 0
$$157$$ 18.0000i 1.43656i −0.695756 0.718278i $$-0.744931\pi$$
0.695756 0.718278i $$-0.255069\pi$$
$$158$$ 0 0
$$159$$ 6.00000 0.475831
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 4.00000i 0.313304i −0.987654 0.156652i $$-0.949930\pi$$
0.987654 0.156652i $$-0.0500701\pi$$
$$164$$ 0 0
$$165$$ −12.0000 6.00000i −0.934199 0.467099i
$$166$$ 0 0
$$167$$ 12.0000i 0.928588i 0.885681 + 0.464294i $$0.153692\pi$$
−0.885681 + 0.464294i $$0.846308\pi$$
$$168$$ 0 0
$$169$$ 9.00000 0.692308
$$170$$ 0 0
$$171$$ 6.00000 0.458831
$$172$$ 0 0
$$173$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$174$$ 0 0
$$175$$ −4.00000 + 3.00000i −0.302372 + 0.226779i
$$176$$ 0 0
$$177$$ 8.00000i 0.601317i
$$178$$ 0 0
$$179$$ −14.0000 −1.04641 −0.523205 0.852207i $$-0.675264\pi$$
−0.523205 + 0.852207i $$0.675264\pi$$
$$180$$ 0 0
$$181$$ −6.00000 −0.445976 −0.222988 0.974821i $$-0.571581\pi$$
−0.222988 + 0.974821i $$0.571581\pi$$
$$182$$ 0 0
$$183$$ 2.00000i 0.147844i
$$184$$ 0 0
$$185$$ 8.00000 + 4.00000i 0.588172 + 0.294086i
$$186$$ 0 0
$$187$$ 24.0000i 1.75505i
$$188$$ 0 0
$$189$$ 1.00000 0.0727393
$$190$$ 0 0
$$191$$ 18.0000 1.30243 0.651217 0.758891i $$-0.274259\pi$$
0.651217 + 0.758891i $$0.274259\pi$$
$$192$$ 0 0
$$193$$ 8.00000i 0.575853i −0.957653 0.287926i $$-0.907034\pi$$
0.957653 0.287926i $$-0.0929658\pi$$
$$194$$ 0 0
$$195$$ −2.00000 + 4.00000i −0.143223 + 0.286446i
$$196$$ 0 0
$$197$$ 2.00000i 0.142494i −0.997459 0.0712470i $$-0.977302\pi$$
0.997459 0.0712470i $$-0.0226979\pi$$
$$198$$ 0 0
$$199$$ 14.0000 0.992434 0.496217 0.868199i $$-0.334722\pi$$
0.496217 + 0.868199i $$0.334722\pi$$
$$200$$ 0 0
$$201$$ −16.0000 −1.12855
$$202$$ 0 0
$$203$$ 2.00000i 0.140372i
$$204$$ 0 0
$$205$$ 2.00000 4.00000i 0.139686 0.279372i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −36.0000 −2.49017
$$210$$ 0 0
$$211$$ 16.0000 1.10149 0.550743 0.834675i $$-0.314345\pi$$
0.550743 + 0.834675i $$0.314345\pi$$
$$212$$ 0 0
$$213$$ 10.0000i 0.685189i
$$214$$ 0 0
$$215$$ 8.00000 + 4.00000i 0.545595 + 0.272798i
$$216$$ 0 0
$$217$$ 10.0000i 0.678844i
$$218$$ 0 0
$$219$$ −6.00000 −0.405442
$$220$$ 0 0
$$221$$ −8.00000 −0.538138
$$222$$ 0 0
$$223$$ 24.0000i 1.60716i 0.595198 + 0.803579i $$0.297074\pi$$
−0.595198 + 0.803579i $$0.702926\pi$$
$$224$$ 0 0
$$225$$ 3.00000 + 4.00000i 0.200000 + 0.266667i
$$226$$ 0 0
$$227$$ 8.00000i 0.530979i 0.964114 + 0.265489i $$0.0855335\pi$$
−0.964114 + 0.265489i $$0.914466\pi$$
$$228$$ 0 0
$$229$$ 10.0000 0.660819 0.330409 0.943838i $$-0.392813\pi$$
0.330409 + 0.943838i $$0.392813\pi$$
$$230$$ 0 0
$$231$$ −6.00000 −0.394771
$$232$$ 0 0
$$233$$ 26.0000i 1.70332i −0.524097 0.851658i $$-0.675597\pi$$
0.524097 0.851658i $$-0.324403\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 4.00000i 0.259828i
$$238$$ 0 0
$$239$$ −6.00000 −0.388108 −0.194054 0.980991i $$-0.562164\pi$$
−0.194054 + 0.980991i $$0.562164\pi$$
$$240$$ 0 0
$$241$$ 22.0000 1.41714 0.708572 0.705638i $$-0.249340\pi$$
0.708572 + 0.705638i $$0.249340\pi$$
$$242$$ 0 0
$$243$$ 1.00000i 0.0641500i
$$244$$ 0 0
$$245$$ −1.00000 + 2.00000i −0.0638877 + 0.127775i
$$246$$ 0 0
$$247$$ 12.0000i 0.763542i
$$248$$ 0 0
$$249$$ −8.00000 −0.506979
$$250$$ 0 0
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ −4.00000 + 8.00000i −0.250490 + 0.500979i
$$256$$ 0 0
$$257$$ 16.0000i 0.998053i −0.866587 0.499026i $$-0.833691\pi$$
0.866587 0.499026i $$-0.166309\pi$$
$$258$$ 0 0
$$259$$ 4.00000 0.248548
$$260$$ 0 0
$$261$$ −2.00000 −0.123797
$$262$$ 0 0
$$263$$ 24.0000i 1.47990i 0.672660 + 0.739952i $$0.265152\pi$$
−0.672660 + 0.739952i $$0.734848\pi$$
$$264$$ 0 0
$$265$$ 12.0000 + 6.00000i 0.737154 + 0.368577i
$$266$$ 0 0
$$267$$ 6.00000i 0.367194i
$$268$$ 0 0
$$269$$ 14.0000 0.853595 0.426798 0.904347i $$-0.359642\pi$$
0.426798 + 0.904347i $$0.359642\pi$$
$$270$$ 0 0
$$271$$ 14.0000 0.850439 0.425220 0.905090i $$-0.360197\pi$$
0.425220 + 0.905090i $$0.360197\pi$$
$$272$$ 0 0
$$273$$ 2.00000i 0.121046i
$$274$$ 0 0
$$275$$ −18.0000 24.0000i −1.08544 1.44725i
$$276$$ 0 0
$$277$$ 28.0000i 1.68236i 0.540758 + 0.841178i $$0.318138\pi$$
−0.540758 + 0.841178i $$0.681862\pi$$
$$278$$ 0 0
$$279$$ −10.0000 −0.598684
$$280$$ 0 0
$$281$$ −2.00000 −0.119310 −0.0596550 0.998219i $$-0.519000\pi$$
−0.0596550 + 0.998219i $$0.519000\pi$$
$$282$$ 0 0
$$283$$ 20.0000i 1.18888i −0.804141 0.594438i $$-0.797374\pi$$
0.804141 0.594438i $$-0.202626\pi$$
$$284$$ 0 0
$$285$$ 12.0000 + 6.00000i 0.710819 + 0.355409i
$$286$$ 0 0
$$287$$ 2.00000i 0.118056i
$$288$$ 0 0
$$289$$ 1.00000 0.0588235
$$290$$ 0 0
$$291$$ 2.00000 0.117242
$$292$$ 0 0
$$293$$ 24.0000i 1.40209i 0.713115 + 0.701047i $$0.247284\pi$$
−0.713115 + 0.701047i $$0.752716\pi$$
$$294$$ 0 0
$$295$$ −8.00000 + 16.0000i −0.465778 + 0.931556i
$$296$$ 0 0
$$297$$ 6.00000i 0.348155i
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 4.00000 0.230556
$$302$$ 0 0
$$303$$ 6.00000i 0.344691i
$$304$$ 0 0
$$305$$ −2.00000 + 4.00000i −0.114520 + 0.229039i
$$306$$ 0 0
$$307$$ 4.00000i 0.228292i 0.993464 + 0.114146i $$0.0364132\pi$$
−0.993464 + 0.114146i $$0.963587\pi$$
$$308$$ 0 0
$$309$$ −8.00000 −0.455104
$$310$$ 0 0
$$311$$ 24.0000 1.36092 0.680458 0.732787i $$-0.261781\pi$$
0.680458 + 0.732787i $$0.261781\pi$$
$$312$$ 0 0
$$313$$ 6.00000i 0.339140i 0.985518 + 0.169570i $$0.0542379\pi$$
−0.985518 + 0.169570i $$0.945762\pi$$
$$314$$ 0 0
$$315$$ 2.00000 + 1.00000i 0.112687 + 0.0563436i
$$316$$ 0 0
$$317$$ 18.0000i 1.01098i 0.862832 + 0.505490i $$0.168688\pi$$
−0.862832 + 0.505490i $$0.831312\pi$$
$$318$$ 0 0
$$319$$ 12.0000 0.671871
$$320$$ 0 0
$$321$$ 4.00000 0.223258
$$322$$ 0 0
$$323$$ 24.0000i 1.33540i
$$324$$ 0 0
$$325$$ −8.00000 + 6.00000i −0.443760 + 0.332820i
$$326$$ 0 0
$$327$$ 2.00000i 0.110600i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 24.0000 1.31916 0.659580 0.751635i $$-0.270734\pi$$
0.659580 + 0.751635i $$0.270734\pi$$
$$332$$ 0 0
$$333$$ 4.00000i 0.219199i
$$334$$ 0 0
$$335$$ −32.0000 16.0000i −1.74835 0.874173i
$$336$$ 0 0
$$337$$ 24.0000i 1.30736i 0.756770 + 0.653682i $$0.226776\pi$$
−0.756770 + 0.653682i $$0.773224\pi$$
$$338$$ 0 0
$$339$$ 6.00000 0.325875
$$340$$ 0 0
$$341$$ 60.0000 3.24918
$$342$$ 0 0
$$343$$ 1.00000i 0.0539949i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 12.0000i 0.644194i 0.946707 + 0.322097i $$0.104388\pi$$
−0.946707 + 0.322097i $$0.895612\pi$$
$$348$$ 0 0
$$349$$ 2.00000 0.107058 0.0535288 0.998566i $$-0.482953\pi$$
0.0535288 + 0.998566i $$0.482953\pi$$
$$350$$ 0 0
$$351$$ 2.00000 0.106752
$$352$$ 0 0
$$353$$ 20.0000i 1.06449i 0.846590 + 0.532246i $$0.178652\pi$$
−0.846590 + 0.532246i $$0.821348\pi$$
$$354$$ 0 0
$$355$$ −10.0000 + 20.0000i −0.530745 + 1.06149i
$$356$$ 0 0
$$357$$ 4.00000i 0.211702i
$$358$$ 0 0
$$359$$ 22.0000 1.16112 0.580558 0.814219i $$-0.302835\pi$$
0.580558 + 0.814219i $$0.302835\pi$$
$$360$$ 0 0
$$361$$ 17.0000 0.894737
$$362$$ 0 0
$$363$$ 25.0000i 1.31216i
$$364$$ 0 0
$$365$$ −12.0000 6.00000i −0.628109 0.314054i
$$366$$ 0 0
$$367$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$368$$ 0 0
$$369$$ −2.00000 −0.104116
$$370$$ 0 0
$$371$$ 6.00000 0.311504
$$372$$ 0 0
$$373$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$374$$ 0 0
$$375$$ 2.00000 + 11.0000i 0.103280 + 0.568038i
$$376$$ 0 0
$$377$$ 4.00000i 0.206010i
$$378$$ 0 0
$$379$$ −28.0000 −1.43826 −0.719132 0.694874i $$-0.755460\pi$$
−0.719132 + 0.694874i $$0.755460\pi$$
$$380$$ 0 0
$$381$$ 20.0000 1.02463
$$382$$ 0 0
$$383$$ 20.0000i 1.02195i 0.859595 + 0.510976i $$0.170716\pi$$
−0.859595 + 0.510976i $$0.829284\pi$$
$$384$$ 0 0
$$385$$ −12.0000 6.00000i −0.611577 0.305788i
$$386$$ 0 0
$$387$$ 4.00000i 0.203331i
$$388$$ 0 0
$$389$$ −26.0000 −1.31825 −0.659126 0.752032i $$-0.729074\pi$$
−0.659126 + 0.752032i $$0.729074\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 4.00000i 0.201773i
$$394$$ 0 0
$$395$$ 4.00000 8.00000i 0.201262 0.402524i
$$396$$ 0 0
$$397$$ 22.0000i 1.10415i −0.833795 0.552074i $$-0.813837\pi$$
0.833795 0.552074i $$-0.186163\pi$$
$$398$$ 0 0
$$399$$ 6.00000 0.300376
$$400$$ 0 0
$$401$$ −30.0000 −1.49813 −0.749064 0.662497i $$-0.769497\pi$$
−0.749064 + 0.662497i $$0.769497\pi$$
$$402$$ 0 0
$$403$$ 20.0000i 0.996271i
$$404$$ 0 0
$$405$$ 1.00000 2.00000i 0.0496904 0.0993808i
$$406$$ 0 0
$$407$$ 24.0000i 1.18964i
$$408$$ 0 0
$$409$$ 22.0000 1.08783 0.543915 0.839140i $$-0.316941\pi$$
0.543915 + 0.839140i $$0.316941\pi$$
$$410$$ 0 0
$$411$$ 6.00000 0.295958
$$412$$ 0 0
$$413$$ 8.00000i 0.393654i
$$414$$ 0 0
$$415$$ −16.0000 8.00000i −0.785409 0.392705i
$$416$$ 0 0
$$417$$ 2.00000i 0.0979404i
$$418$$ 0 0
$$419$$ −12.0000 −0.586238 −0.293119 0.956076i $$-0.594693\pi$$
−0.293119 + 0.956076i $$0.594693\pi$$
$$420$$ 0 0
$$421$$ 18.0000 0.877266 0.438633 0.898666i $$-0.355463\pi$$
0.438633 + 0.898666i $$0.355463\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −16.0000 + 12.0000i −0.776114 + 0.582086i
$$426$$ 0 0
$$427$$ 2.00000i 0.0967868i
$$428$$ 0 0
$$429$$ −12.0000 −0.579365
$$430$$ 0 0
$$431$$ 14.0000 0.674356 0.337178 0.941441i $$-0.390528\pi$$
0.337178 + 0.941441i $$0.390528\pi$$
$$432$$ 0 0
$$433$$ 34.0000i 1.63394i −0.576683 0.816968i $$-0.695653\pi$$
0.576683 0.816968i $$-0.304347\pi$$
$$434$$ 0 0
$$435$$ −4.00000 2.00000i −0.191785 0.0958927i
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 6.00000 0.286364 0.143182 0.989696i $$-0.454267\pi$$
0.143182 + 0.989696i $$0.454267\pi$$
$$440$$ 0 0
$$441$$ 1.00000 0.0476190
$$442$$ 0 0
$$443$$ 4.00000i 0.190046i 0.995475 + 0.0950229i $$0.0302924\pi$$
−0.995475 + 0.0950229i $$0.969708\pi$$
$$444$$ 0 0
$$445$$ −6.00000 + 12.0000i −0.284427 + 0.568855i
$$446$$ 0 0
$$447$$ 14.0000i 0.662177i
$$448$$ 0 0
$$449$$ −10.0000 −0.471929 −0.235965 0.971762i $$-0.575825\pi$$
−0.235965 + 0.971762i $$0.575825\pi$$
$$450$$ 0 0
$$451$$ 12.0000 0.565058
$$452$$ 0 0
$$453$$ 8.00000i 0.375873i
$$454$$ 0 0
$$455$$ −2.00000 + 4.00000i −0.0937614 + 0.187523i
$$456$$ 0 0
$$457$$ 20.0000i 0.935561i 0.883845 + 0.467780i $$0.154946\pi$$
−0.883845 + 0.467780i $$0.845054\pi$$
$$458$$ 0 0
$$459$$ 4.00000 0.186704
$$460$$ 0 0
$$461$$ 30.0000 1.39724 0.698620 0.715493i $$-0.253798\pi$$
0.698620 + 0.715493i $$0.253798\pi$$
$$462$$ 0 0
$$463$$ 36.0000i 1.67306i −0.547920 0.836531i $$-0.684580\pi$$
0.547920 0.836531i $$-0.315420\pi$$
$$464$$ 0 0
$$465$$ −20.0000 10.0000i −0.927478 0.463739i
$$466$$ 0 0
$$467$$ 24.0000i 1.11059i −0.831654 0.555294i $$-0.812606\pi$$
0.831654 0.555294i $$-0.187394\pi$$
$$468$$ 0 0
$$469$$ −16.0000 −0.738811
$$470$$ 0 0
$$471$$ −18.0000 −0.829396
$$472$$ 0 0
$$473$$ 24.0000i 1.10352i
$$474$$ 0 0
$$475$$ 18.0000 + 24.0000i 0.825897 + 1.10120i
$$476$$ 0 0
$$477$$ 6.00000i 0.274721i
$$478$$ 0 0
$$479$$ 24.0000 1.09659 0.548294 0.836286i $$-0.315277\pi$$
0.548294 + 0.836286i $$0.315277\pi$$
$$480$$ 0 0
$$481$$ 8.00000 0.364769
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 4.00000 + 2.00000i 0.181631 + 0.0908153i
$$486$$ 0 0
$$487$$ 12.0000i 0.543772i 0.962329 + 0.271886i $$0.0876473\pi$$
−0.962329 + 0.271886i $$0.912353\pi$$
$$488$$ 0 0
$$489$$ −4.00000 −0.180886
$$490$$ 0 0
$$491$$ −10.0000 −0.451294 −0.225647 0.974209i $$-0.572450\pi$$
−0.225647 + 0.974209i $$0.572450\pi$$
$$492$$ 0 0
$$493$$ 8.00000i 0.360302i
$$494$$ 0 0
$$495$$ −6.00000 + 12.0000i −0.269680 + 0.539360i
$$496$$ 0 0
$$497$$ 10.0000i 0.448561i
$$498$$ 0 0
$$499$$ 4.00000 0.179065 0.0895323 0.995984i $$-0.471463\pi$$
0.0895323 + 0.995984i $$0.471463\pi$$
$$500$$ 0 0
$$501$$ 12.0000 0.536120
$$502$$ 0 0
$$503$$ 36.0000i 1.60516i 0.596544 + 0.802580i $$0.296540\pi$$
−0.596544 + 0.802580i $$0.703460\pi$$
$$504$$ 0 0
$$505$$ −6.00000 + 12.0000i −0.266996 + 0.533993i
$$506$$ 0 0
$$507$$ 9.00000i 0.399704i
$$508$$ 0 0
$$509$$ −30.0000 −1.32973 −0.664863 0.746965i $$-0.731510\pi$$
−0.664863 + 0.746965i $$0.731510\pi$$
$$510$$ 0 0
$$511$$ −6.00000 −0.265424
$$512$$ 0 0
$$513$$ 6.00000i 0.264906i
$$514$$ 0 0
$$515$$ −16.0000 8.00000i −0.705044 0.352522i
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 38.0000 1.66481 0.832405 0.554168i $$-0.186963\pi$$
0.832405 + 0.554168i $$0.186963\pi$$
$$522$$ 0 0
$$523$$ 20.0000i 0.874539i −0.899331 0.437269i $$-0.855946\pi$$
0.899331 0.437269i $$-0.144054\pi$$
$$524$$ 0 0
$$525$$ 3.00000 + 4.00000i 0.130931 + 0.174574i
$$526$$ 0 0
$$527$$ 40.0000i 1.74243i
$$528$$ 0 0
$$529$$ 23.0000 1.00000
$$530$$ 0 0
$$531$$ 8.00000 0.347170
$$532$$ 0 0
$$533$$ 4.00000i 0.173259i
$$534$$ 0 0
$$535$$ 8.00000 + 4.00000i 0.345870 + 0.172935i
$$536$$ 0 0
$$537$$ 14.0000i 0.604145i
$$538$$ 0 0
$$539$$ −6.00000 −0.258438
$$540$$ 0 0
$$541$$ 6.00000 0.257960 0.128980 0.991647i $$-0.458830\pi$$
0.128980 + 0.991647i $$0.458830\pi$$
$$542$$ 0 0
$$543$$ 6.00000i 0.257485i
$$544$$ 0 0
$$545$$ −2.00000 + 4.00000i −0.0856706 + 0.171341i
$$546$$ 0 0
$$547$$ 16.0000i 0.684111i −0.939680 0.342055i $$-0.888877\pi$$
0.939680 0.342055i $$-0.111123\pi$$
$$548$$ 0 0
$$549$$ 2.00000 0.0853579
$$550$$ 0 0
$$551$$ −12.0000 −0.511217
$$552$$ 0 0
$$553$$ 4.00000i 0.170097i
$$554$$ 0 0
$$555$$ 4.00000 8.00000i 0.169791 0.339581i
$$556$$ 0 0
$$557$$ 38.0000i 1.61011i −0.593199 0.805056i $$-0.702135\pi$$
0.593199 0.805056i $$-0.297865\pi$$
$$558$$ 0 0
$$559$$ 8.00000 0.338364
$$560$$ 0 0
$$561$$ −24.0000 −1.01328
$$562$$ 0 0
$$563$$ 36.0000i 1.51722i 0.651546 + 0.758610i $$0.274121\pi$$
−0.651546 + 0.758610i $$0.725879\pi$$
$$564$$ 0 0
$$565$$ 12.0000 + 6.00000i 0.504844 + 0.252422i
$$566$$ 0 0
$$567$$ 1.00000i 0.0419961i
$$568$$ 0 0
$$569$$ 30.0000 1.25767 0.628833 0.777541i $$-0.283533\pi$$
0.628833 + 0.777541i $$0.283533\pi$$
$$570$$ 0 0
$$571$$ −36.0000 −1.50655 −0.753277 0.657704i $$-0.771528\pi$$
−0.753277 + 0.657704i $$0.771528\pi$$
$$572$$ 0 0
$$573$$ 18.0000i 0.751961i
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 14.0000i 0.582828i −0.956597 0.291414i $$-0.905874\pi$$
0.956597 0.291414i $$-0.0941257\pi$$
$$578$$ 0 0
$$579$$ −8.00000 −0.332469
$$580$$ 0 0
$$581$$ −8.00000 −0.331896
$$582$$ 0 0
$$583$$ 36.0000i 1.49097i
$$584$$ 0 0
$$585$$ 4.00000 + 2.00000i 0.165380 + 0.0826898i
$$586$$ 0 0
$$587$$ 12.0000i 0.495293i −0.968850 0.247647i $$-0.920343\pi$$
0.968850 0.247647i $$-0.0796572\pi$$
$$588$$ 0 0
$$589$$ −60.0000 −2.47226
$$590$$ 0 0
$$591$$ −2.00000 −0.0822690
$$592$$ 0 0
$$593$$ 44.0000i 1.80686i 0.428732 + 0.903432i $$0.358960\pi$$
−0.428732 + 0.903432i $$0.641040\pi$$
$$594$$ 0 0
$$595$$ −4.00000 + 8.00000i −0.163984 + 0.327968i
$$596$$ 0 0
$$597$$ 14.0000i 0.572982i
$$598$$ 0 0
$$599$$ −2.00000 −0.0817178 −0.0408589 0.999165i $$-0.513009\pi$$
−0.0408589 + 0.999165i $$0.513009\pi$$
$$600$$ 0 0
$$601$$ −26.0000 −1.06056 −0.530281 0.847822i $$-0.677914\pi$$
−0.530281 + 0.847822i $$0.677914\pi$$
$$602$$ 0 0
$$603$$ 16.0000i 0.651570i
$$604$$ 0 0
$$605$$ 25.0000 50.0000i 1.01639 2.03279i
$$606$$ 0 0
$$607$$ 24.0000i 0.974130i 0.873366 + 0.487065i $$0.161933\pi$$
−0.873366 + 0.487065i $$0.838067\pi$$
$$608$$ 0 0
$$609$$ −2.00000 −0.0810441
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 4.00000i 0.161558i 0.996732 + 0.0807792i $$0.0257409\pi$$
−0.996732 + 0.0807792i $$0.974259\pi$$
$$614$$ 0 0
$$615$$ −4.00000 2.00000i −0.161296 0.0806478i
$$616$$ 0 0
$$617$$ 26.0000i 1.04672i 0.852111 + 0.523360i $$0.175322\pi$$
−0.852111 + 0.523360i $$0.824678\pi$$
$$618$$ 0 0
$$619$$ 10.0000 0.401934 0.200967 0.979598i $$-0.435592\pi$$
0.200967 + 0.979598i $$0.435592\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 6.00000i 0.240385i
$$624$$ 0 0
$$625$$ −7.00000 + 24.0000i −0.280000 + 0.960000i
$$626$$ 0 0
$$627$$ 36.0000i 1.43770i
$$628$$ 0 0
$$629$$ 16.0000 0.637962
$$630$$ 0 0
$$631$$ 20.0000 0.796187 0.398094 0.917345i $$-0.369672\pi$$
0.398094 + 0.917345i $$0.369672\pi$$
$$632$$ 0 0
$$633$$ 16.0000i 0.635943i
$$634$$ 0 0
$$635$$ 40.0000 + 20.0000i 1.58735 + 0.793676i
$$636$$ 0 0
$$637$$ 2.00000i 0.0792429i
$$638$$ 0 0
$$639$$ 10.0000 0.395594
$$640$$ 0 0
$$641$$ −2.00000 −0.0789953 −0.0394976 0.999220i $$-0.512576\pi$$
−0.0394976 + 0.999220i $$0.512576\pi$$
$$642$$ 0 0
$$643$$ 20.0000i 0.788723i 0.918955 + 0.394362i $$0.129034\pi$$
−0.918955 + 0.394362i $$0.870966\pi$$
$$644$$ 0 0
$$645$$ 4.00000 8.00000i 0.157500 0.315000i
$$646$$ 0 0
$$647$$ 20.0000i 0.786281i −0.919478 0.393141i $$-0.871389\pi$$
0.919478 0.393141i $$-0.128611\pi$$
$$648$$ 0 0
$$649$$ −48.0000 −1.88416
$$650$$ 0 0
$$651$$ −10.0000 −0.391931
$$652$$ 0 0
$$653$$ 2.00000i 0.0782660i 0.999234 + 0.0391330i $$0.0124596\pi$$
−0.999234 + 0.0391330i $$0.987540\pi$$
$$654$$ 0 0
$$655$$ −4.00000 + 8.00000i −0.156293 + 0.312586i
$$656$$ 0 0
$$657$$ 6.00000i 0.234082i
$$658$$ 0 0
$$659$$ −18.0000 −0.701180 −0.350590 0.936529i $$-0.614019\pi$$
−0.350590 + 0.936529i $$0.614019\pi$$
$$660$$ 0 0
$$661$$ −18.0000 −0.700119 −0.350059 0.936727i $$-0.613839\pi$$
−0.350059 + 0.936727i $$0.613839\pi$$
$$662$$ 0 0
$$663$$ 8.00000i 0.310694i
$$664$$ 0 0
$$665$$ 12.0000 + 6.00000i 0.465340 + 0.232670i
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 24.0000 0.927894
$$670$$ 0 0
$$671$$ −12.0000 −0.463255
$$672$$ 0 0
$$673$$ 36.0000i 1.38770i −0.720121 0.693849i $$-0.755914\pi$$
0.720121 0.693849i $$-0.244086\pi$$
$$674$$ 0 0
$$675$$ 4.00000 3.00000i 0.153960 0.115470i
$$676$$ 0 0
$$677$$ 32.0000i 1.22986i −0.788582 0.614930i $$-0.789184\pi$$
0.788582 0.614930i $$-0.210816\pi$$
$$678$$ 0 0
$$679$$ 2.00000 0.0767530
$$680$$ 0 0
$$681$$ 8.00000 0.306561
$$682$$ 0 0
$$683$$ 28.0000i 1.07139i −0.844411 0.535695i $$-0.820050\pi$$
0.844411 0.535695i $$-0.179950\pi$$
$$684$$ 0 0
$$685$$ 12.0000 + 6.00000i 0.458496 + 0.229248i
$$686$$ 0 0
$$687$$ 10.0000i 0.381524i
$$688$$ 0 0
$$689$$ 12.0000 0.457164
$$690$$ 0 0
$$691$$ 50.0000 1.90209 0.951045 0.309053i $$-0.100012\pi$$
0.951045 + 0.309053i $$0.100012\pi$$
$$692$$ 0 0
$$693$$ 6.00000i 0.227921i
$$694$$ 0 0
$$695$$ 2.00000 4.00000i 0.0758643 0.151729i
$$696$$ 0 0
$$697$$ 8.00000i 0.303022i
$$698$$ 0 0
$$699$$ −26.0000 −0.983410
$$700$$ 0 0
$$701$$ −10.0000 −0.377695 −0.188847 0.982006i $$-0.560475\pi$$
−0.188847 + 0.982006i $$0.560475\pi$$
$$702$$ 0 0
$$703$$ 24.0000i 0.905177i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 6.00000i 0.225653i
$$708$$ 0 0
$$709$$ −26.0000 −0.976450 −0.488225 0.872718i $$-0.662356\pi$$
−0.488225 + 0.872718i $$0.662356\pi$$
$$710$$ 0 0
$$711$$ −4.00000 −0.150012
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ −24.0000 12.0000i −0.897549 0.448775i
$$716$$ 0 0
$$717$$ 6.00000i 0.224074i
$$718$$ 0 0
$$719$$ 12.0000 0.447524 0.223762 0.974644i $$-0.428166\pi$$
0.223762 + 0.974644i $$0.428166\pi$$
$$720$$ 0 0
$$721$$ −8.00000 −0.297936
$$722$$ 0 0
$$723$$ 22.0000i 0.818189i
$$724$$ 0 0
$$725$$ −6.00000 8.00000i −0.222834 0.297113i
$$726$$ 0 0
$$727$$ 40.0000i 1.48352i −0.670667 0.741759i $$-0.733992\pi$$
0.670667 0.741759i $$-0.266008\pi$$
$$728$$ 0 0
$$729$$ −1.00000 −0.0370370
$$730$$ 0 0
$$731$$ 16.0000 0.591781
$$732$$ 0 0
$$733$$ 22.0000i 0.812589i 0.913742 + 0.406294i $$0.133179\pi$$
−0.913742 + 0.406294i $$0.866821\pi$$
$$734$$ 0 0
$$735$$ 2.00000 + 1.00000i 0.0737711 + 0.0368856i
$$736$$ 0 0
$$737$$ 96.0000i 3.53621i
$$738$$ 0 0
$$739$$ −44.0000 −1.61857 −0.809283 0.587419i $$-0.800144\pi$$
−0.809283 + 0.587419i $$0.800144\pi$$
$$740$$ 0 0
$$741$$ 12.0000 0.440831
$$742$$ 0 0
$$743$$ 40.0000i 1.46746i −0.679442 0.733729i $$-0.737778\pi$$
0.679442 0.733729i $$-0.262222\pi$$
$$744$$ 0 0
$$745$$ 14.0000 28.0000i 0.512920 1.02584i
$$746$$ 0 0
$$747$$ 8.00000i 0.292705i
$$748$$ 0 0
$$749$$ 4.00000 0.146157
$$750$$ 0 0
$$751$$ 12.0000 0.437886 0.218943 0.975738i $$-0.429739\pi$$
0.218943 + 0.975738i $$0.429739\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −8.00000 + 16.0000i −0.291150 + 0.582300i
$$756$$ 0 0
$$757$$ 40.0000i 1.45382i 0.686730 + 0.726912i $$0.259045\pi$$
−0.686730 + 0.726912i $$0.740955\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −22.0000 −0.797499 −0.398750 0.917060i $$-0.630556\pi$$
−0.398750 + 0.917060i $$0.630556\pi$$
$$762$$ 0 0
$$763$$ 2.00000i 0.0724049i
$$764$$ 0 0
$$765$$ 8.00000 + 4.00000i 0.289241 + 0.144620i
$$766$$ 0 0
$$767$$ 16.0000i 0.577727i
$$768$$ 0 0
$$769$$ 18.0000 0.649097 0.324548 0.945869i $$-0.394788\pi$$
0.324548 + 0.945869i $$0.394788\pi$$
$$770$$ 0 0
$$771$$ −16.0000 −0.576226
$$772$$ 0 0
$$773$$ 24.0000i 0.863220i 0.902060 + 0.431610i $$0.142054\pi$$
−0.902060 + 0.431610i $$0.857946\pi$$
$$774$$ 0 0
$$775$$ −30.0000 40.0000i −1.07763 1.43684i
$$776$$ 0 0
$$777$$ 4.00000i 0.143499i
$$778$$ 0 0
$$779$$ −12.0000 −0.429945
$$780$$ 0 0
$$781$$ −60.0000 −2.14697
$$782$$ 0 0
$$783$$ 2.00000i 0.0714742i
$$784$$ 0 0
$$785$$ −36.0000 18.0000i −1.28490 0.642448i
$$786$$ 0 0
$$787$$ 4.00000i 0.142585i −0.997455 0.0712923i $$-0.977288\pi$$
0.997455 0.0712923i $$-0.0227123\pi$$
$$788$$ 0 0
$$789$$ 24.0000 0.854423
$$790$$ 0 0
$$791$$ 6.00000 0.213335
$$792$$ 0 0
$$793$$ 4.00000i 0.142044i
$$794$$ 0 0
$$795$$ 6.00000 12.0000i 0.212798 0.425596i
$$796$$ 0 0
$$797$$ 16.0000i 0.566749i 0.959009 + 0.283375i $$0.0914540\pi$$
−0.959009 + 0.283375i $$0.908546\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 6.00000 0.212000
$$802$$ 0 0