# Properties

 Label 3150.2.b.b.251.2 Level 3150 Weight 2 Character 3150.251 Analytic conductor 25.153 Analytic rank 0 Dimension 8 CM no Inner twists 8

# Learn more about

## Newspace parameters

 Level: $$N$$ = $$3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 3150.b (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$25.1528766367$$ Analytic rank: $$0$$ Dimension: $$8$$ Coefficient field: 8.0.40960000.1 Coefficient ring: $$\Z[a_1, \ldots, a_{17}]$$ Coefficient ring index: $$2^{6}$$ Twist minimal: no (minimal twist has level 630) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 251.2 Root $$-0.437016 + 0.437016i$$ Character $$\chi$$ = 3150.251 Dual form 3150.2.b.b.251.5

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000i q^{2} -1.00000 q^{4} +(-1.41421 + 2.23607i) q^{7} +1.00000i q^{8} +O(q^{10})$$ $$q-1.00000i q^{2} -1.00000 q^{4} +(-1.41421 + 2.23607i) q^{7} +1.00000i q^{8} -5.65685i q^{11} +4.47214i q^{13} +(2.23607 + 1.41421i) q^{14} +1.00000 q^{16} -3.16228 q^{17} +3.16228i q^{19} -5.65685 q^{22} -4.00000i q^{23} +4.47214 q^{26} +(1.41421 - 2.23607i) q^{28} +2.82843i q^{29} -6.32456i q^{31} -1.00000i q^{32} +3.16228i q^{34} +9.89949 q^{37} +3.16228 q^{38} -4.47214 q^{41} -1.41421 q^{43} +5.65685i q^{44} -4.00000 q^{46} +9.48683 q^{47} +(-3.00000 - 6.32456i) q^{49} -4.47214i q^{52} -4.00000i q^{53} +(-2.23607 - 1.41421i) q^{56} +2.82843 q^{58} +4.47214 q^{59} -9.48683i q^{61} -6.32456 q^{62} -1.00000 q^{64} +7.07107 q^{67} +3.16228 q^{68} -1.41421i q^{71} +13.4164i q^{73} -9.89949i q^{74} -3.16228i q^{76} +(12.6491 + 8.00000i) q^{77} -6.00000 q^{79} +4.47214i q^{82} +12.6491 q^{83} +1.41421i q^{86} +5.65685 q^{88} -4.47214 q^{89} +(-10.0000 - 6.32456i) q^{91} +4.00000i q^{92} -9.48683i q^{94} +(-6.32456 + 3.00000i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q - 8q^{4} + O(q^{10})$$ $$8q - 8q^{4} + 8q^{16} - 32q^{46} - 24q^{49} - 8q^{64} - 48q^{79} - 80q^{91} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$451$$ $$2801$$ $$\chi(n)$$ $$1$$ $$-1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000i 0.707107i
$$3$$ 0 0
$$4$$ −1.00000 −0.500000
$$5$$ 0 0
$$6$$ 0 0
$$7$$ −1.41421 + 2.23607i −0.534522 + 0.845154i
$$8$$ 1.00000i 0.353553i
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 5.65685i 1.70561i −0.522233 0.852803i $$-0.674901\pi$$
0.522233 0.852803i $$-0.325099\pi$$
$$12$$ 0 0
$$13$$ 4.47214i 1.24035i 0.784465 + 0.620174i $$0.212938\pi$$
−0.784465 + 0.620174i $$0.787062\pi$$
$$14$$ 2.23607 + 1.41421i 0.597614 + 0.377964i
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ −3.16228 −0.766965 −0.383482 0.923548i $$-0.625275\pi$$
−0.383482 + 0.923548i $$0.625275\pi$$
$$18$$ 0 0
$$19$$ 3.16228i 0.725476i 0.931891 + 0.362738i $$0.118158\pi$$
−0.931891 + 0.362738i $$0.881842\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ −5.65685 −1.20605
$$23$$ 4.00000i 0.834058i −0.908893 0.417029i $$-0.863071\pi$$
0.908893 0.417029i $$-0.136929\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 4.47214 0.877058
$$27$$ 0 0
$$28$$ 1.41421 2.23607i 0.267261 0.422577i
$$29$$ 2.82843i 0.525226i 0.964901 + 0.262613i $$0.0845842\pi$$
−0.964901 + 0.262613i $$0.915416\pi$$
$$30$$ 0 0
$$31$$ 6.32456i 1.13592i −0.823055 0.567962i $$-0.807732\pi$$
0.823055 0.567962i $$-0.192268\pi$$
$$32$$ 1.00000i 0.176777i
$$33$$ 0 0
$$34$$ 3.16228i 0.542326i
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 9.89949 1.62747 0.813733 0.581238i $$-0.197432\pi$$
0.813733 + 0.581238i $$0.197432\pi$$
$$38$$ 3.16228 0.512989
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −4.47214 −0.698430 −0.349215 0.937043i $$-0.613552\pi$$
−0.349215 + 0.937043i $$0.613552\pi$$
$$42$$ 0 0
$$43$$ −1.41421 −0.215666 −0.107833 0.994169i $$-0.534391\pi$$
−0.107833 + 0.994169i $$0.534391\pi$$
$$44$$ 5.65685i 0.852803i
$$45$$ 0 0
$$46$$ −4.00000 −0.589768
$$47$$ 9.48683 1.38380 0.691898 0.721995i $$-0.256775\pi$$
0.691898 + 0.721995i $$0.256775\pi$$
$$48$$ 0 0
$$49$$ −3.00000 6.32456i −0.428571 0.903508i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 4.47214i 0.620174i
$$53$$ 4.00000i 0.549442i −0.961524 0.274721i $$-0.911414\pi$$
0.961524 0.274721i $$-0.0885855\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ −2.23607 1.41421i −0.298807 0.188982i
$$57$$ 0 0
$$58$$ 2.82843 0.371391
$$59$$ 4.47214 0.582223 0.291111 0.956689i $$-0.405975\pi$$
0.291111 + 0.956689i $$0.405975\pi$$
$$60$$ 0 0
$$61$$ 9.48683i 1.21466i −0.794448 0.607332i $$-0.792240\pi$$
0.794448 0.607332i $$-0.207760\pi$$
$$62$$ −6.32456 −0.803219
$$63$$ 0 0
$$64$$ −1.00000 −0.125000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 7.07107 0.863868 0.431934 0.901905i $$-0.357831\pi$$
0.431934 + 0.901905i $$0.357831\pi$$
$$68$$ 3.16228 0.383482
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 1.41421i 0.167836i −0.996473 0.0839181i $$-0.973257\pi$$
0.996473 0.0839181i $$-0.0267434\pi$$
$$72$$ 0 0
$$73$$ 13.4164i 1.57027i 0.619324 + 0.785136i $$0.287407\pi$$
−0.619324 + 0.785136i $$0.712593\pi$$
$$74$$ 9.89949i 1.15079i
$$75$$ 0 0
$$76$$ 3.16228i 0.362738i
$$77$$ 12.6491 + 8.00000i 1.44150 + 0.911685i
$$78$$ 0 0
$$79$$ −6.00000 −0.675053 −0.337526 0.941316i $$-0.609590\pi$$
−0.337526 + 0.941316i $$0.609590\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 4.47214i 0.493865i
$$83$$ 12.6491 1.38842 0.694210 0.719772i $$-0.255754\pi$$
0.694210 + 0.719772i $$0.255754\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 1.41421i 0.152499i
$$87$$ 0 0
$$88$$ 5.65685 0.603023
$$89$$ −4.47214 −0.474045 −0.237023 0.971504i $$-0.576172\pi$$
−0.237023 + 0.971504i $$0.576172\pi$$
$$90$$ 0 0
$$91$$ −10.0000 6.32456i −1.04828 0.662994i
$$92$$ 4.00000i 0.417029i
$$93$$ 0 0
$$94$$ 9.48683i 0.978492i
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$98$$ −6.32456 + 3.00000i −0.638877 + 0.303046i
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 17.8885 1.77998 0.889988 0.455983i $$-0.150712\pi$$
0.889988 + 0.455983i $$0.150712\pi$$
$$102$$ 0 0
$$103$$ 8.94427i 0.881305i −0.897678 0.440653i $$-0.854747\pi$$
0.897678 0.440653i $$-0.145253\pi$$
$$104$$ −4.47214 −0.438529
$$105$$ 0 0
$$106$$ −4.00000 −0.388514
$$107$$ 18.0000i 1.74013i −0.492941 0.870063i $$-0.664078\pi$$
0.492941 0.870063i $$-0.335922\pi$$
$$108$$ 0 0
$$109$$ 10.0000 0.957826 0.478913 0.877862i $$-0.341031\pi$$
0.478913 + 0.877862i $$0.341031\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ −1.41421 + 2.23607i −0.133631 + 0.211289i
$$113$$ 6.00000i 0.564433i −0.959351 0.282216i $$-0.908930\pi$$
0.959351 0.282216i $$-0.0910696\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 2.82843i 0.262613i
$$117$$ 0 0
$$118$$ 4.47214i 0.411693i
$$119$$ 4.47214 7.07107i 0.409960 0.648204i
$$120$$ 0 0
$$121$$ −21.0000 −1.90909
$$122$$ −9.48683 −0.858898
$$123$$ 0 0
$$124$$ 6.32456i 0.567962i
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −14.1421 −1.25491 −0.627456 0.778652i $$-0.715904\pi$$
−0.627456 + 0.778652i $$0.715904\pi$$
$$128$$ 1.00000i 0.0883883i
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 17.8885 1.56293 0.781465 0.623949i $$-0.214473\pi$$
0.781465 + 0.623949i $$0.214473\pi$$
$$132$$ 0 0
$$133$$ −7.07107 4.47214i −0.613139 0.387783i
$$134$$ 7.07107i 0.610847i
$$135$$ 0 0
$$136$$ 3.16228i 0.271163i
$$137$$ 2.00000i 0.170872i −0.996344 0.0854358i $$-0.972772\pi$$
0.996344 0.0854358i $$-0.0272282\pi$$
$$138$$ 0 0
$$139$$ 15.8114i 1.34110i −0.741862 0.670552i $$-0.766057\pi$$
0.741862 0.670552i $$-0.233943\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ −1.41421 −0.118678
$$143$$ 25.2982 2.11554
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 13.4164 1.11035
$$147$$ 0 0
$$148$$ −9.89949 −0.813733
$$149$$ 16.9706i 1.39028i −0.718873 0.695141i $$-0.755342\pi$$
0.718873 0.695141i $$-0.244658\pi$$
$$150$$ 0 0
$$151$$ 10.0000 0.813788 0.406894 0.913475i $$-0.366612\pi$$
0.406894 + 0.913475i $$0.366612\pi$$
$$152$$ −3.16228 −0.256495
$$153$$ 0 0
$$154$$ 8.00000 12.6491i 0.644658 1.01929i
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 4.47214i 0.356915i −0.983948 0.178458i $$-0.942889\pi$$
0.983948 0.178458i $$-0.0571108\pi$$
$$158$$ 6.00000i 0.477334i
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 8.94427 + 5.65685i 0.704907 + 0.445823i
$$162$$ 0 0
$$163$$ 21.2132 1.66155 0.830773 0.556611i $$-0.187899\pi$$
0.830773 + 0.556611i $$0.187899\pi$$
$$164$$ 4.47214 0.349215
$$165$$ 0 0
$$166$$ 12.6491i 0.981761i
$$167$$ 9.48683 0.734113 0.367057 0.930199i $$-0.380366\pi$$
0.367057 + 0.930199i $$0.380366\pi$$
$$168$$ 0 0
$$169$$ −7.00000 −0.538462
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 1.41421 0.107833
$$173$$ −25.2982 −1.92339 −0.961694 0.274125i $$-0.911612\pi$$
−0.961694 + 0.274125i $$0.911612\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 5.65685i 0.426401i
$$177$$ 0 0
$$178$$ 4.47214i 0.335201i
$$179$$ 2.82843i 0.211407i 0.994398 + 0.105703i $$0.0337094\pi$$
−0.994398 + 0.105703i $$0.966291\pi$$
$$180$$ 0 0
$$181$$ 3.16228i 0.235050i 0.993070 + 0.117525i $$0.0374961\pi$$
−0.993070 + 0.117525i $$0.962504\pi$$
$$182$$ −6.32456 + 10.0000i −0.468807 + 0.741249i
$$183$$ 0 0
$$184$$ 4.00000 0.294884
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 17.8885i 1.30814i
$$188$$ −9.48683 −0.691898
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 1.41421i 0.102329i 0.998690 + 0.0511645i $$0.0162933\pi$$
−0.998690 + 0.0511645i $$0.983707\pi$$
$$192$$ 0 0
$$193$$ 8.48528 0.610784 0.305392 0.952227i $$-0.401213\pi$$
0.305392 + 0.952227i $$0.401213\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 3.00000 + 6.32456i 0.214286 + 0.451754i
$$197$$ 12.0000i 0.854965i −0.904024 0.427482i $$-0.859401\pi$$
0.904024 0.427482i $$-0.140599\pi$$
$$198$$ 0 0
$$199$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 17.8885i 1.25863i
$$203$$ −6.32456 4.00000i −0.443897 0.280745i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ −8.94427 −0.623177
$$207$$ 0 0
$$208$$ 4.47214i 0.310087i
$$209$$ 17.8885 1.23738
$$210$$ 0 0
$$211$$ −20.0000 −1.37686 −0.688428 0.725304i $$-0.741699\pi$$
−0.688428 + 0.725304i $$0.741699\pi$$
$$212$$ 4.00000i 0.274721i
$$213$$ 0 0
$$214$$ −18.0000 −1.23045
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 14.1421 + 8.94427i 0.960031 + 0.607177i
$$218$$ 10.0000i 0.677285i
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 14.1421i 0.951303i
$$222$$ 0 0
$$223$$ 8.94427i 0.598953i 0.954104 + 0.299476i $$0.0968120\pi$$
−0.954104 + 0.299476i $$0.903188\pi$$
$$224$$ 2.23607 + 1.41421i 0.149404 + 0.0944911i
$$225$$ 0 0
$$226$$ −6.00000 −0.399114
$$227$$ −18.9737 −1.25933 −0.629663 0.776868i $$-0.716807\pi$$
−0.629663 + 0.776868i $$0.716807\pi$$
$$228$$ 0 0
$$229$$ 15.8114i 1.04485i −0.852686 0.522423i $$-0.825028\pi$$
0.852686 0.522423i $$-0.174972\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ −2.82843 −0.185695
$$233$$ 14.0000i 0.917170i 0.888650 + 0.458585i $$0.151644\pi$$
−0.888650 + 0.458585i $$0.848356\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ −4.47214 −0.291111
$$237$$ 0 0
$$238$$ −7.07107 4.47214i −0.458349 0.289886i
$$239$$ 4.24264i 0.274434i 0.990541 + 0.137217i $$0.0438157\pi$$
−0.990541 + 0.137217i $$0.956184\pi$$
$$240$$ 0 0
$$241$$ 25.2982i 1.62960i −0.579741 0.814801i $$-0.696846\pi$$
0.579741 0.814801i $$-0.303154\pi$$
$$242$$ 21.0000i 1.34993i
$$243$$ 0 0
$$244$$ 9.48683i 0.607332i
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −14.1421 −0.899843
$$248$$ 6.32456 0.401610
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 0 0
$$253$$ −22.6274 −1.42257
$$254$$ 14.1421i 0.887357i
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 15.8114 0.986287 0.493144 0.869948i $$-0.335848\pi$$
0.493144 + 0.869948i $$0.335848\pi$$
$$258$$ 0 0
$$259$$ −14.0000 + 22.1359i −0.869918 + 1.37546i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 17.8885i 1.10516i
$$263$$ 16.0000i 0.986602i 0.869859 + 0.493301i $$0.164210\pi$$
−0.869859 + 0.493301i $$0.835790\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ −4.47214 + 7.07107i −0.274204 + 0.433555i
$$267$$ 0 0
$$268$$ −7.07107 −0.431934
$$269$$ −17.8885 −1.09068 −0.545342 0.838214i $$-0.683600\pi$$
−0.545342 + 0.838214i $$0.683600\pi$$
$$270$$ 0 0
$$271$$ 6.32456i 0.384189i −0.981376 0.192095i $$-0.938472\pi$$
0.981376 0.192095i $$-0.0615281\pi$$
$$272$$ −3.16228 −0.191741
$$273$$ 0 0
$$274$$ −2.00000 −0.120824
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 21.2132 1.27458 0.637289 0.770625i $$-0.280056\pi$$
0.637289 + 0.770625i $$0.280056\pi$$
$$278$$ −15.8114 −0.948304
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 12.7279i 0.759284i −0.925133 0.379642i $$-0.876047\pi$$
0.925133 0.379642i $$-0.123953\pi$$
$$282$$ 0 0
$$283$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$284$$ 1.41421i 0.0839181i
$$285$$ 0 0
$$286$$ 25.2982i 1.49592i
$$287$$ 6.32456 10.0000i 0.373327 0.590281i
$$288$$ 0 0
$$289$$ −7.00000 −0.411765
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 13.4164i 0.785136i
$$293$$ −6.32456 −0.369484 −0.184742 0.982787i $$-0.559145\pi$$
−0.184742 + 0.982787i $$0.559145\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 9.89949i 0.575396i
$$297$$ 0 0
$$298$$ −16.9706 −0.983078
$$299$$ 17.8885 1.03452
$$300$$ 0 0
$$301$$ 2.00000 3.16228i 0.115278 0.182271i
$$302$$ 10.0000i 0.575435i
$$303$$ 0 0
$$304$$ 3.16228i 0.181369i
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 26.8328i 1.53143i 0.643180 + 0.765715i $$0.277615\pi$$
−0.643180 + 0.765715i $$0.722385\pi$$
$$308$$ −12.6491 8.00000i −0.720750 0.455842i
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −8.94427 −0.507183 −0.253592 0.967311i $$-0.581612\pi$$
−0.253592 + 0.967311i $$0.581612\pi$$
$$312$$ 0 0
$$313$$ 13.4164i 0.758340i −0.925327 0.379170i $$-0.876210\pi$$
0.925327 0.379170i $$-0.123790\pi$$
$$314$$ −4.47214 −0.252377
$$315$$ 0 0
$$316$$ 6.00000 0.337526
$$317$$ 18.0000i 1.01098i 0.862832 + 0.505490i $$0.168688\pi$$
−0.862832 + 0.505490i $$0.831312\pi$$
$$318$$ 0 0
$$319$$ 16.0000 0.895828
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 5.65685 8.94427i 0.315244 0.498445i
$$323$$ 10.0000i 0.556415i
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 21.2132i 1.17489i
$$327$$ 0 0
$$328$$ 4.47214i 0.246932i
$$329$$ −13.4164 + 21.2132i −0.739671 + 1.16952i
$$330$$ 0 0
$$331$$ 20.0000 1.09930 0.549650 0.835395i $$-0.314761\pi$$
0.549650 + 0.835395i $$0.314761\pi$$
$$332$$ −12.6491 −0.694210
$$333$$ 0 0
$$334$$ 9.48683i 0.519096i
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −25.4558 −1.38667 −0.693334 0.720616i $$-0.743859\pi$$
−0.693334 + 0.720616i $$0.743859\pi$$
$$338$$ 7.00000i 0.380750i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −35.7771 −1.93744
$$342$$ 0 0
$$343$$ 18.3848 + 2.23607i 0.992685 + 0.120736i
$$344$$ 1.41421i 0.0762493i
$$345$$ 0 0
$$346$$ 25.2982i 1.36004i
$$347$$ 12.0000i 0.644194i 0.946707 + 0.322097i $$0.104388\pi$$
−0.946707 + 0.322097i $$0.895612\pi$$
$$348$$ 0 0
$$349$$ 15.8114i 0.846364i −0.906045 0.423182i $$-0.860913\pi$$
0.906045 0.423182i $$-0.139087\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ −5.65685 −0.301511
$$353$$ 3.16228 0.168311 0.0841555 0.996453i $$-0.473181\pi$$
0.0841555 + 0.996453i $$0.473181\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 4.47214 0.237023
$$357$$ 0 0
$$358$$ 2.82843 0.149487
$$359$$ 18.3848i 0.970311i 0.874428 + 0.485156i $$0.161237\pi$$
−0.874428 + 0.485156i $$0.838763\pi$$
$$360$$ 0 0
$$361$$ 9.00000 0.473684
$$362$$ 3.16228 0.166206
$$363$$ 0 0
$$364$$ 10.0000 + 6.32456i 0.524142 + 0.331497i
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 13.4164i 0.700331i −0.936688 0.350165i $$-0.886125\pi$$
0.936688 0.350165i $$-0.113875\pi$$
$$368$$ 4.00000i 0.208514i
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 8.94427 + 5.65685i 0.464363 + 0.293689i
$$372$$ 0 0
$$373$$ −21.2132 −1.09838 −0.549189 0.835698i $$-0.685063\pi$$
−0.549189 + 0.835698i $$0.685063\pi$$
$$374$$ 17.8885 0.924995
$$375$$ 0 0
$$376$$ 9.48683i 0.489246i
$$377$$ −12.6491 −0.651462
$$378$$ 0 0
$$379$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 1.41421 0.0723575
$$383$$ 9.48683 0.484755 0.242377 0.970182i $$-0.422073\pi$$
0.242377 + 0.970182i $$0.422073\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 8.48528i 0.431889i
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 16.9706i 0.860442i −0.902724 0.430221i $$-0.858436\pi$$
0.902724 0.430221i $$-0.141564\pi$$
$$390$$ 0 0
$$391$$ 12.6491i 0.639693i
$$392$$ 6.32456 3.00000i 0.319438 0.151523i
$$393$$ 0 0
$$394$$ −12.0000 −0.604551
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 4.47214i 0.224450i 0.993683 + 0.112225i $$0.0357978\pi$$
−0.993683 + 0.112225i $$0.964202\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 1.41421i 0.0706225i 0.999376 + 0.0353112i $$0.0112422\pi$$
−0.999376 + 0.0353112i $$0.988758\pi$$
$$402$$ 0 0
$$403$$ 28.2843 1.40894
$$404$$ −17.8885 −0.889988
$$405$$ 0 0
$$406$$ −4.00000 + 6.32456i −0.198517 + 0.313882i
$$407$$ 56.0000i 2.77582i
$$408$$ 0 0
$$409$$ 37.9473i 1.87637i 0.346128 + 0.938187i $$0.387496\pi$$
−0.346128 + 0.938187i $$0.612504\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 8.94427i 0.440653i
$$413$$ −6.32456 + 10.0000i −0.311211 + 0.492068i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 4.47214 0.219265
$$417$$ 0 0
$$418$$ 17.8885i 0.874957i
$$419$$ 13.4164 0.655434 0.327717 0.944776i $$-0.393721\pi$$
0.327717 + 0.944776i $$0.393721\pi$$
$$420$$ 0 0
$$421$$ 38.0000 1.85201 0.926003 0.377515i $$-0.123221\pi$$
0.926003 + 0.377515i $$0.123221\pi$$
$$422$$ 20.0000i 0.973585i
$$423$$ 0 0
$$424$$ 4.00000 0.194257
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 21.2132 + 13.4164i 1.02658 + 0.649265i
$$428$$ 18.0000i 0.870063i
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 15.5563i 0.749323i −0.927162 0.374661i $$-0.877759\pi$$
0.927162 0.374661i $$-0.122241\pi$$
$$432$$ 0 0
$$433$$ 26.8328i 1.28950i −0.764392 0.644751i $$-0.776961\pi$$
0.764392 0.644751i $$-0.223039\pi$$
$$434$$ 8.94427 14.1421i 0.429339 0.678844i
$$435$$ 0 0
$$436$$ −10.0000 −0.478913
$$437$$ 12.6491 0.605089
$$438$$ 0 0
$$439$$ 6.32456i 0.301855i 0.988545 + 0.150927i $$0.0482259\pi$$
−0.988545 + 0.150927i $$0.951774\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ −14.1421 −0.672673
$$443$$ 4.00000i 0.190046i 0.995475 + 0.0950229i $$0.0302924\pi$$
−0.995475 + 0.0950229i $$0.969708\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 8.94427 0.423524
$$447$$ 0 0
$$448$$ 1.41421 2.23607i 0.0668153 0.105644i
$$449$$ 9.89949i 0.467186i 0.972334 + 0.233593i $$0.0750483\pi$$
−0.972334 + 0.233593i $$0.924952\pi$$
$$450$$ 0 0
$$451$$ 25.2982i 1.19125i
$$452$$ 6.00000i 0.282216i
$$453$$ 0 0
$$454$$ 18.9737i 0.890478i
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −16.9706 −0.793849 −0.396925 0.917851i $$-0.629923\pi$$
−0.396925 + 0.917851i $$0.629923\pi$$
$$458$$ −15.8114 −0.738818
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 8.94427 0.416576 0.208288 0.978068i $$-0.433211\pi$$
0.208288 + 0.978068i $$0.433211\pi$$
$$462$$ 0 0
$$463$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$464$$ 2.82843i 0.131306i
$$465$$ 0 0
$$466$$ 14.0000 0.648537
$$467$$ 12.6491 0.585331 0.292666 0.956215i $$-0.405458\pi$$
0.292666 + 0.956215i $$0.405458\pi$$
$$468$$ 0 0
$$469$$ −10.0000 + 15.8114i −0.461757 + 0.730102i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 4.47214i 0.205847i
$$473$$ 8.00000i 0.367840i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ −4.47214 + 7.07107i −0.204980 + 0.324102i
$$477$$ 0 0
$$478$$ 4.24264 0.194054
$$479$$ −17.8885 −0.817348 −0.408674 0.912680i $$-0.634009\pi$$
−0.408674 + 0.912680i $$0.634009\pi$$
$$480$$ 0 0
$$481$$ 44.2719i 2.01862i
$$482$$ −25.2982 −1.15230
$$483$$ 0 0
$$484$$ 21.0000 0.954545
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 25.4558 1.15351 0.576757 0.816916i $$-0.304318\pi$$
0.576757 + 0.816916i $$0.304318\pi$$
$$488$$ 9.48683 0.429449
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 19.7990i 0.893516i 0.894655 + 0.446758i $$0.147421\pi$$
−0.894655 + 0.446758i $$0.852579\pi$$
$$492$$ 0 0
$$493$$ 8.94427i 0.402830i
$$494$$ 14.1421i 0.636285i
$$495$$ 0 0
$$496$$ 6.32456i 0.283981i
$$497$$ 3.16228 + 2.00000i 0.141848 + 0.0897123i
$$498$$ 0 0
$$499$$ 20.0000 0.895323 0.447661 0.894203i $$-0.352257\pi$$
0.447661 + 0.894203i $$0.352257\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 9.48683 0.422997 0.211498 0.977378i $$-0.432166\pi$$
0.211498 + 0.977378i $$0.432166\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 22.6274i 1.00591i
$$507$$ 0 0
$$508$$ 14.1421 0.627456
$$509$$ 13.4164 0.594672 0.297336 0.954773i $$-0.403902\pi$$
0.297336 + 0.954773i $$0.403902\pi$$
$$510$$ 0 0
$$511$$ −30.0000 18.9737i −1.32712 0.839346i
$$512$$ 1.00000i 0.0441942i
$$513$$ 0 0
$$514$$ 15.8114i 0.697410i
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 53.6656i 2.36021i
$$518$$ 22.1359 + 14.0000i 0.972598 + 0.615125i
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −13.4164 −0.587784 −0.293892 0.955839i $$-0.594951\pi$$
−0.293892 + 0.955839i $$0.594951\pi$$
$$522$$ 0 0
$$523$$ 17.8885i 0.782211i 0.920346 + 0.391106i $$0.127907\pi$$
−0.920346 + 0.391106i $$0.872093\pi$$
$$524$$ −17.8885 −0.781465
$$525$$ 0 0
$$526$$ 16.0000 0.697633
$$527$$ 20.0000i 0.871214i
$$528$$ 0 0
$$529$$ 7.00000 0.304348
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 7.07107 + 4.47214i 0.306570 + 0.193892i
$$533$$ 20.0000i 0.866296i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 7.07107i 0.305424i
$$537$$ 0 0
$$538$$ 17.8885i 0.771230i
$$539$$ −35.7771 + 16.9706i −1.54103 + 0.730974i
$$540$$ 0 0
$$541$$ −22.0000 −0.945854 −0.472927 0.881102i $$-0.656803\pi$$
−0.472927 + 0.881102i $$0.656803\pi$$
$$542$$ −6.32456 −0.271663
$$543$$ 0 0
$$544$$ 3.16228i 0.135582i
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −21.2132 −0.907011 −0.453506 0.891253i $$-0.649827\pi$$
−0.453506 + 0.891253i $$0.649827\pi$$
$$548$$ 2.00000i 0.0854358i
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −8.94427 −0.381039
$$552$$ 0 0
$$553$$ 8.48528 13.4164i 0.360831 0.570524i
$$554$$ 21.2132i 0.901263i
$$555$$ 0 0
$$556$$ 15.8114i 0.670552i
$$557$$ 38.0000i 1.61011i 0.593199 + 0.805056i $$0.297865\pi$$
−0.593199 + 0.805056i $$0.702135\pi$$
$$558$$ 0 0
$$559$$ 6.32456i 0.267500i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −12.7279 −0.536895
$$563$$ −18.9737 −0.799645 −0.399822 0.916593i $$-0.630928\pi$$
−0.399822 + 0.916593i $$0.630928\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 1.41421 0.0593391
$$569$$ 24.0416i 1.00788i −0.863739 0.503939i $$-0.831884\pi$$
0.863739 0.503939i $$-0.168116\pi$$
$$570$$ 0 0
$$571$$ 28.0000 1.17176 0.585882 0.810397i $$-0.300748\pi$$
0.585882 + 0.810397i $$0.300748\pi$$
$$572$$ −25.2982 −1.05777
$$573$$ 0 0
$$574$$ −10.0000 6.32456i −0.417392 0.263982i
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 22.3607i 0.930887i 0.885078 + 0.465444i $$0.154105\pi$$
−0.885078 + 0.465444i $$0.845895\pi$$
$$578$$ 7.00000i 0.291162i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −17.8885 + 28.2843i −0.742142 + 1.17343i
$$582$$ 0 0
$$583$$ −22.6274 −0.937132
$$584$$ −13.4164 −0.555175
$$585$$ 0 0
$$586$$ 6.32456i 0.261265i
$$587$$ 31.6228 1.30521 0.652606 0.757698i $$-0.273676\pi$$
0.652606 + 0.757698i $$0.273676\pi$$
$$588$$ 0 0
$$589$$ 20.0000 0.824086
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 9.89949 0.406867
$$593$$ 9.48683 0.389578 0.194789 0.980845i $$-0.437598\pi$$
0.194789 + 0.980845i $$0.437598\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 16.9706i 0.695141i
$$597$$ 0 0
$$598$$ 17.8885i 0.731517i
$$599$$ 32.5269i 1.32901i −0.747282 0.664507i $$-0.768642\pi$$
0.747282 0.664507i $$-0.231358\pi$$
$$600$$ 0 0
$$601$$ 25.2982i 1.03194i 0.856608 + 0.515968i $$0.172568\pi$$
−0.856608 + 0.515968i $$0.827432\pi$$
$$602$$ −3.16228 2.00000i −0.128885 0.0815139i
$$603$$ 0 0
$$604$$ −10.0000 −0.406894
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 8.94427i 0.363037i −0.983388 0.181518i $$-0.941899\pi$$
0.983388 0.181518i $$-0.0581012\pi$$
$$608$$ 3.16228 0.128247
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 42.4264i 1.71639i
$$612$$ 0 0
$$613$$ −35.3553 −1.42799 −0.713994 0.700151i $$-0.753116\pi$$
−0.713994 + 0.700151i $$0.753116\pi$$
$$614$$ 26.8328 1.08288
$$615$$ 0 0
$$616$$ −8.00000 + 12.6491i −0.322329 + 0.509647i
$$617$$ 38.0000i 1.52982i −0.644136 0.764911i $$-0.722783\pi$$
0.644136 0.764911i $$-0.277217\pi$$
$$618$$ 0 0
$$619$$ 28.4605i 1.14392i −0.820280 0.571962i $$-0.806182\pi$$
0.820280 0.571962i $$-0.193818\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 8.94427i 0.358633i
$$623$$ 6.32456 10.0000i 0.253388 0.400642i
$$624$$ 0 0
$$625$$ 0 0
$$626$$ −13.4164 −0.536228
$$627$$ 0 0
$$628$$ 4.47214i 0.178458i
$$629$$ −31.3050 −1.24821
$$630$$ 0 0
$$631$$ −8.00000 −0.318475 −0.159237 0.987240i $$-0.550904\pi$$
−0.159237 + 0.987240i $$0.550904\pi$$
$$632$$ 6.00000i 0.238667i
$$633$$ 0 0
$$634$$ 18.0000 0.714871
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 28.2843 13.4164i 1.12066 0.531577i
$$638$$ 16.0000i 0.633446i
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 1.41421i 0.0558581i −0.999610 0.0279290i $$-0.991109\pi$$
0.999610 0.0279290i $$-0.00889125\pi$$
$$642$$ 0 0
$$643$$ 44.7214i 1.76364i 0.471588 + 0.881819i $$0.343681\pi$$
−0.471588 + 0.881819i $$0.656319\pi$$
$$644$$ −8.94427 5.65685i −0.352454 0.222911i
$$645$$ 0 0
$$646$$ −10.0000 −0.393445
$$647$$ 34.7851 1.36754 0.683771 0.729697i $$-0.260339\pi$$
0.683771 + 0.729697i $$0.260339\pi$$
$$648$$ 0 0
$$649$$ 25.2982i 0.993042i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −21.2132 −0.830773
$$653$$ 14.0000i 0.547862i −0.961749 0.273931i $$-0.911676\pi$$
0.961749 0.273931i $$-0.0883240\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ −4.47214 −0.174608
$$657$$ 0 0
$$658$$ 21.2132 + 13.4164i 0.826977 + 0.523026i
$$659$$ 16.9706i 0.661079i −0.943792 0.330540i $$-0.892769\pi$$
0.943792 0.330540i $$-0.107231\pi$$
$$660$$ 0 0
$$661$$ 3.16228i 0.122998i −0.998107 0.0614992i $$-0.980412\pi$$
0.998107 0.0614992i $$-0.0195882\pi$$
$$662$$ 20.0000i 0.777322i
$$663$$ 0 0
$$664$$ 12.6491i 0.490881i
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 11.3137 0.438069
$$668$$ −9.48683 −0.367057
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −53.6656 −2.07174
$$672$$ 0 0
$$673$$ −19.7990 −0.763195 −0.381597 0.924329i $$-0.624626\pi$$
−0.381597 + 0.924329i $$0.624626\pi$$
$$674$$ 25.4558i 0.980522i
$$675$$ 0 0
$$676$$ 7.00000 0.269231
$$677$$ −37.9473 −1.45843 −0.729217 0.684282i $$-0.760116\pi$$
−0.729217 + 0.684282i $$0.760116\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 35.7771i 1.36998i
$$683$$ 14.0000i 0.535695i −0.963461 0.267848i $$-0.913688\pi$$
0.963461 0.267848i $$-0.0863124\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 2.23607 18.3848i 0.0853735 0.701934i
$$687$$ 0 0
$$688$$ −1.41421 −0.0539164
$$689$$ 17.8885 0.681499
$$690$$ 0 0
$$691$$ 28.4605i 1.08269i 0.840801 + 0.541344i $$0.182084\pi$$
−0.840801 + 0.541344i $$0.817916\pi$$
$$692$$ 25.2982 0.961694
$$693$$ 0 0
$$694$$ 12.0000 0.455514
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 14.1421 0.535672
$$698$$ −15.8114 −0.598470
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 19.7990i 0.747798i 0.927470 + 0.373899i $$0.121979\pi$$
−0.927470 + 0.373899i $$0.878021\pi$$
$$702$$ 0 0
$$703$$ 31.3050i 1.18069i
$$704$$ 5.65685i 0.213201i
$$705$$ 0 0
$$706$$ 3.16228i 0.119014i
$$707$$ −25.2982 + 40.0000i −0.951438 + 1.50435i
$$708$$ 0 0
$$709$$ 30.0000 1.12667 0.563337 0.826227i $$-0.309517\pi$$
0.563337 + 0.826227i $$0.309517\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 4.47214i 0.167600i
$$713$$ −25.2982 −0.947426
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 2.82843i 0.105703i
$$717$$ 0 0
$$718$$ 18.3848 0.686114
$$719$$ −44.7214 −1.66783 −0.833913 0.551896i $$-0.813904\pi$$
−0.833913 + 0.551896i $$0.813904\pi$$
$$720$$ 0 0
$$721$$ 20.0000 + 12.6491i 0.744839 + 0.471077i
$$722$$ 9.00000i 0.334945i
$$723$$ 0 0
$$724$$ 3.16228i 0.117525i
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 26.8328i 0.995174i 0.867414 + 0.497587i $$0.165780\pi$$
−0.867414 + 0.497587i $$0.834220\pi$$
$$728$$ 6.32456 10.0000i 0.234404 0.370625i
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 4.47214 0.165408
$$732$$ 0 0
$$733$$ 40.2492i 1.48664i 0.668937 + 0.743319i $$0.266750\pi$$
−0.668937 + 0.743319i $$0.733250\pi$$
$$734$$ −13.4164 −0.495209
$$735$$ 0 0
$$736$$ −4.00000 −0.147442
$$737$$ 40.0000i 1.47342i
$$738$$ 0 0
$$739$$ −16.0000 −0.588570 −0.294285 0.955718i $$-0.595081\pi$$
−0.294285 + 0.955718i $$0.595081\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 5.65685 8.94427i 0.207670 0.328355i
$$743$$ 36.0000i 1.32071i −0.750953 0.660356i $$-0.770405\pi$$
0.750953 0.660356i $$-0.229595\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 21.2132i 0.776671i
$$747$$ 0 0
$$748$$ 17.8885i 0.654070i
$$749$$ 40.2492 + 25.4558i 1.47067 + 0.930136i
$$750$$ 0 0
$$751$$ 40.0000 1.45962 0.729810 0.683650i $$-0.239608\pi$$
0.729810 + 0.683650i $$0.239608\pi$$
$$752$$ 9.48683 0.345949
$$753$$ 0 0
$$754$$ 12.6491i 0.460653i
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −32.5269 −1.18221 −0.591105 0.806594i $$-0.701308\pi$$
−0.591105 + 0.806594i $$0.701308\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 31.3050 1.13480 0.567402 0.823441i $$-0.307949\pi$$
0.567402 + 0.823441i $$0.307949\pi$$
$$762$$ 0 0
$$763$$ −14.1421 + 22.3607i −0.511980 + 0.809511i
$$764$$ 1.41421i 0.0511645i
$$765$$ 0 0
$$766$$ 9.48683i 0.342773i
$$767$$ 20.0000i 0.722158i
$$768$$ 0 0
$$769$$ 31.6228i 1.14035i 0.821524 + 0.570173i $$0.193124\pi$$
−0.821524 + 0.570173i $$0.806876\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −8.48528 −0.305392
$$773$$ −31.6228 −1.13739 −0.568696 0.822548i $$-0.692552\pi$$
−0.568696 + 0.822548i $$0.692552\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ −16.9706 −0.608424
$$779$$ 14.1421i 0.506695i
$$780$$ 0 0
$$781$$ −8.00000 −0.286263
$$782$$ 12.6491 0.452331
$$783$$ 0 0
$$784$$ −3.00000 6.32456i −0.107143 0.225877i
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 26.8328i 0.956487i 0.878227 + 0.478243i $$0.158726\pi$$
−0.878227 + 0.478243i $$0.841274\pi$$
$$788$$ 12.0000i 0.427482i
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 13.4164 + 8.48528i 0.477033 + 0.301702i
$$792$$ 0 0
$$793$$ 42.4264 1.50661
$$794$$ 4.47214 0.158710
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −25.2982 −0.896109 −0.448054 0.894006i $$-0.647883\pi$$
−0.448054 + 0.894006i $$0.647883\pi$$
$$798$$ 0 0
$$799$$ −30.0000 −1.06132
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 1.41421 0.0499376
$$803$$ 75.8947 2.67826
$$804$$ 0 0