# Properties

 Label 1280.3.e.f.639.4 Level $1280$ Weight $3$ Character 1280.639 Analytic conductor $34.877$ Analytic rank $0$ Dimension $6$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1280 = 2^{8} \cdot 5$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 1280.e (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$34.8774738381$$ Analytic rank: $$0$$ Dimension: $$6$$ Coefficient field: 6.0.1827904.1 Defining polynomial: $$x^{6} + 9 x^{4} + 14 x^{2} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{6}$$ Twist minimal: no (minimal twist has level 160) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 639.4 Root $$0.273891i$$ of defining polynomial Character $$\chi$$ $$=$$ 1280.639 Dual form 1280.3.e.f.639.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+0.547781i q^{3} +(3.30219 - 3.75441i) q^{5} -10.0566 q^{7} +8.69994 q^{9} +O(q^{10})$$ $$q+0.547781i q^{3} +(3.30219 - 3.75441i) q^{5} -10.0566 q^{7} +8.69994 q^{9} +17.2087 q^{11} -4.41325 q^{13} +(2.05659 + 1.80888i) q^{15} -27.0176i q^{17} -4.82650 q^{19} -5.50881i q^{21} -15.2653 q^{23} +(-3.19112 - 24.7955i) q^{25} +9.69569i q^{27} +2.38225i q^{29} +38.0352i q^{31} +9.42663i q^{33} +(-33.2087 + 37.7565i) q^{35} +16.5691 q^{37} -2.41749i q^{39} +13.3177 q^{41} -59.7918i q^{43} +(28.7288 - 32.6631i) q^{45} +62.4388 q^{47} +52.1351 q^{49} +14.7997 q^{51} -71.5952 q^{53} +(56.8265 - 64.6086i) q^{55} -2.64386i q^{57} -68.8265 q^{59} -40.9439i q^{61} -87.4917 q^{63} +(-14.5734 + 16.5691i) q^{65} -51.0080i q^{67} -8.36206i q^{69} +40.4527i q^{71} -35.8441i q^{73} +(13.5825 - 1.74804i) q^{75} -173.061 q^{77} -126.800i q^{79} +72.9883 q^{81} -75.1490i q^{83} +(-101.435 - 89.2172i) q^{85} -1.30495 q^{87} +106.523 q^{89} +44.3822 q^{91} -20.8350 q^{93} +(-15.9380 + 18.1206i) q^{95} -85.4351i q^{97} +149.715 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$6 q - 8 q^{5} - 12 q^{7} - 18 q^{9} + O(q^{10})$$ $$6 q - 8 q^{5} - 12 q^{7} - 18 q^{9} - 8 q^{11} - 36 q^{15} + 24 q^{19} + 68 q^{23} + 10 q^{25} - 88 q^{35} + 208 q^{37} + 68 q^{41} + 232 q^{45} + 268 q^{47} - 62 q^{49} - 192 q^{51} - 64 q^{53} + 288 q^{55} - 360 q^{59} - 172 q^{63} + 304 q^{75} - 400 q^{77} + 238 q^{81} - 304 q^{85} - 584 q^{87} - 76 q^{89} + 208 q^{91} + 320 q^{93} - 32 q^{95} + 856 q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times$$.

 $$n$$ $$257$$ $$261$$ $$511$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0.547781i 0.182594i 0.995824 + 0.0912969i $$0.0291012\pi$$
−0.995824 + 0.0912969i $$0.970899\pi$$
$$4$$ 0 0
$$5$$ 3.30219 3.75441i 0.660437 0.750881i
$$6$$ 0 0
$$7$$ −10.0566 −1.43666 −0.718328 0.695705i $$-0.755092\pi$$
−0.718328 + 0.695705i $$0.755092\pi$$
$$8$$ 0 0
$$9$$ 8.69994 0.966660
$$10$$ 0 0
$$11$$ 17.2087 1.56443 0.782216 0.623008i $$-0.214089\pi$$
0.782216 + 0.623008i $$0.214089\pi$$
$$12$$ 0 0
$$13$$ −4.41325 −0.339481 −0.169740 0.985489i $$-0.554293\pi$$
−0.169740 + 0.985489i $$0.554293\pi$$
$$14$$ 0 0
$$15$$ 2.05659 + 1.80888i 0.137106 + 0.120592i
$$16$$ 0 0
$$17$$ 27.0176i 1.58927i −0.607086 0.794636i $$-0.707662\pi$$
0.607086 0.794636i $$-0.292338\pi$$
$$18$$ 0 0
$$19$$ −4.82650 −0.254026 −0.127013 0.991901i $$-0.540539\pi$$
−0.127013 + 0.991901i $$0.540539\pi$$
$$20$$ 0 0
$$21$$ 5.50881i 0.262324i
$$22$$ 0 0
$$23$$ −15.2653 −0.663710 −0.331855 0.943330i $$-0.607675\pi$$
−0.331855 + 0.943330i $$0.607675\pi$$
$$24$$ 0 0
$$25$$ −3.19112 24.7955i −0.127645 0.991820i
$$26$$ 0 0
$$27$$ 9.69569i 0.359100i
$$28$$ 0 0
$$29$$ 2.38225i 0.0821465i 0.999156 + 0.0410733i $$0.0130777\pi$$
−0.999156 + 0.0410733i $$0.986922\pi$$
$$30$$ 0 0
$$31$$ 38.0352i 1.22694i 0.789717 + 0.613472i $$0.210228\pi$$
−0.789717 + 0.613472i $$0.789772\pi$$
$$32$$ 0 0
$$33$$ 9.42663i 0.285655i
$$34$$ 0 0
$$35$$ −33.2087 + 37.7565i −0.948821 + 1.07876i
$$36$$ 0 0
$$37$$ 16.5691 0.447814 0.223907 0.974610i $$-0.428119\pi$$
0.223907 + 0.974610i $$0.428119\pi$$
$$38$$ 0 0
$$39$$ 2.41749i 0.0619870i
$$40$$ 0 0
$$41$$ 13.3177 0.324822 0.162411 0.986723i $$-0.448073\pi$$
0.162411 + 0.986723i $$0.448073\pi$$
$$42$$ 0 0
$$43$$ 59.7918i 1.39051i −0.718765 0.695253i $$-0.755292\pi$$
0.718765 0.695253i $$-0.244708\pi$$
$$44$$ 0 0
$$45$$ 28.7288 32.6631i 0.638418 0.725846i
$$46$$ 0 0
$$47$$ 62.4388 1.32849 0.664243 0.747517i $$-0.268754\pi$$
0.664243 + 0.747517i $$0.268754\pi$$
$$48$$ 0 0
$$49$$ 52.1351 1.06398
$$50$$ 0 0
$$51$$ 14.7997 0.290191
$$52$$ 0 0
$$53$$ −71.5952 −1.35085 −0.675427 0.737427i $$-0.736041\pi$$
−0.675427 + 0.737427i $$0.736041\pi$$
$$54$$ 0 0
$$55$$ 56.8265 64.6086i 1.03321 1.17470i
$$56$$ 0 0
$$57$$ 2.64386i 0.0463836i
$$58$$ 0 0
$$59$$ −68.8265 −1.16655 −0.583275 0.812274i $$-0.698229\pi$$
−0.583275 + 0.812274i $$0.698229\pi$$
$$60$$ 0 0
$$61$$ 40.9439i 0.671212i −0.942002 0.335606i $$-0.891059\pi$$
0.942002 0.335606i $$-0.108941\pi$$
$$62$$ 0 0
$$63$$ −87.4917 −1.38876
$$64$$ 0 0
$$65$$ −14.5734 + 16.5691i −0.224206 + 0.254910i
$$66$$ 0 0
$$67$$ 51.0080i 0.761313i −0.924717 0.380656i $$-0.875698\pi$$
0.924717 0.380656i $$-0.124302\pi$$
$$68$$ 0 0
$$69$$ 8.36206i 0.121189i
$$70$$ 0 0
$$71$$ 40.4527i 0.569757i 0.958564 + 0.284878i $$0.0919532\pi$$
−0.958564 + 0.284878i $$0.908047\pi$$
$$72$$ 0 0
$$73$$ 35.8441i 0.491015i −0.969395 0.245508i $$-0.921045\pi$$
0.969395 0.245508i $$-0.0789547\pi$$
$$74$$ 0 0
$$75$$ 13.5825 1.74804i 0.181100 0.0233072i
$$76$$ 0 0
$$77$$ −173.061 −2.24755
$$78$$ 0 0
$$79$$ 126.800i 1.60506i −0.596612 0.802530i $$-0.703487\pi$$
0.596612 0.802530i $$-0.296513\pi$$
$$80$$ 0 0
$$81$$ 72.9883 0.901090
$$82$$ 0 0
$$83$$ 75.1490i 0.905409i −0.891661 0.452705i $$-0.850459\pi$$
0.891661 0.452705i $$-0.149541\pi$$
$$84$$ 0 0
$$85$$ −101.435 89.2172i −1.19335 1.04961i
$$86$$ 0 0
$$87$$ −1.30495 −0.0149994
$$88$$ 0 0
$$89$$ 106.523 1.19689 0.598445 0.801164i $$-0.295785\pi$$
0.598445 + 0.801164i $$0.295785\pi$$
$$90$$ 0 0
$$91$$ 44.3822 0.487717
$$92$$ 0 0
$$93$$ −20.8350 −0.224032
$$94$$ 0 0
$$95$$ −15.9380 + 18.1206i −0.167768 + 0.190744i
$$96$$ 0 0
$$97$$ 85.4351i 0.880774i −0.897808 0.440387i $$-0.854841\pi$$
0.897808 0.440387i $$-0.145159\pi$$
$$98$$ 0 0
$$99$$ 149.715 1.51227
$$100$$ 0 0
$$101$$ 83.2877i 0.824631i −0.911041 0.412315i $$-0.864720\pi$$
0.911041 0.412315i $$-0.135280\pi$$
$$102$$ 0 0
$$103$$ −47.2653 −0.458887 −0.229443 0.973322i $$-0.573691\pi$$
−0.229443 + 0.973322i $$0.573691\pi$$
$$104$$ 0 0
$$105$$ −20.6823 18.1911i −0.196974 0.173249i
$$106$$ 0 0
$$107$$ 189.628i 1.77223i 0.463467 + 0.886114i $$0.346605\pi$$
−0.463467 + 0.886114i $$0.653395\pi$$
$$108$$ 0 0
$$109$$ 84.5617i 0.775795i −0.921702 0.387898i $$-0.873201\pi$$
0.921702 0.387898i $$-0.126799\pi$$
$$110$$ 0 0
$$111$$ 9.07626i 0.0817681i
$$112$$ 0 0
$$113$$ 114.558i 1.01379i −0.862007 0.506896i $$-0.830793\pi$$
0.862007 0.506896i $$-0.169207\pi$$
$$114$$ 0 0
$$115$$ −50.4090 + 57.3123i −0.438339 + 0.498368i
$$116$$ 0 0
$$117$$ −38.3950 −0.328162
$$118$$ 0 0
$$119$$ 271.705i 2.28324i
$$120$$ 0 0
$$121$$ 175.141 1.44745
$$122$$ 0 0
$$123$$ 7.29518i 0.0593104i
$$124$$ 0 0
$$125$$ −103.630 69.8986i −0.829040 0.559189i
$$126$$ 0 0
$$127$$ 44.4121 0.349701 0.174851 0.984595i $$-0.444056\pi$$
0.174851 + 0.984595i $$0.444056\pi$$
$$128$$ 0 0
$$129$$ 32.7528 0.253898
$$130$$ 0 0
$$131$$ −47.1200 −0.359695 −0.179847 0.983695i $$-0.557560\pi$$
−0.179847 + 0.983695i $$0.557560\pi$$
$$132$$ 0 0
$$133$$ 48.5381 0.364948
$$134$$ 0 0
$$135$$ 36.4016 + 32.0170i 0.269641 + 0.237163i
$$136$$ 0 0
$$137$$ 62.8617i 0.458845i 0.973327 + 0.229422i $$0.0736837\pi$$
−0.973327 + 0.229422i $$0.926316\pi$$
$$138$$ 0 0
$$139$$ −128.320 −0.923167 −0.461584 0.887097i $$-0.652719\pi$$
−0.461584 + 0.887097i $$0.652719\pi$$
$$140$$ 0 0
$$141$$ 34.2028i 0.242573i
$$142$$ 0 0
$$143$$ −75.9465 −0.531094
$$144$$ 0 0
$$145$$ 8.94393 + 7.86663i 0.0616823 + 0.0542526i
$$146$$ 0 0
$$147$$ 28.5586i 0.194276i
$$148$$ 0 0
$$149$$ 165.561i 1.11115i −0.831467 0.555574i $$-0.812499\pi$$
0.831467 0.555574i $$-0.187501\pi$$
$$150$$ 0 0
$$151$$ 218.558i 1.44741i −0.690111 0.723704i $$-0.742438\pi$$
0.690111 0.723704i $$-0.257562\pi$$
$$152$$ 0 0
$$153$$ 235.052i 1.53628i
$$154$$ 0 0
$$155$$ 142.800 + 125.599i 0.921289 + 0.810319i
$$156$$ 0 0
$$157$$ 174.293 1.11014 0.555072 0.831802i $$-0.312691\pi$$
0.555072 + 0.831802i $$0.312691\pi$$
$$158$$ 0 0
$$159$$ 39.2185i 0.246657i
$$160$$ 0 0
$$161$$ 153.517 0.953524
$$162$$ 0 0
$$163$$ 52.6353i 0.322916i 0.986880 + 0.161458i $$0.0516196\pi$$
−0.986880 + 0.161458i $$0.948380\pi$$
$$164$$ 0 0
$$165$$ 35.3914 + 31.1285i 0.214493 + 0.188657i
$$166$$ 0 0
$$167$$ 76.6812 0.459169 0.229584 0.973289i $$-0.426263\pi$$
0.229584 + 0.973289i $$0.426263\pi$$
$$168$$ 0 0
$$169$$ −149.523 −0.884753
$$170$$ 0 0
$$171$$ −41.9902 −0.245557
$$172$$ 0 0
$$173$$ −9.72437 −0.0562102 −0.0281051 0.999605i $$-0.508947\pi$$
−0.0281051 + 0.999605i $$0.508947\pi$$
$$174$$ 0 0
$$175$$ 32.0918 + 249.358i 0.183382 + 1.42490i
$$176$$ 0 0
$$177$$ 37.7019i 0.213005i
$$178$$ 0 0
$$179$$ 155.502 0.868728 0.434364 0.900738i $$-0.356973\pi$$
0.434364 + 0.900738i $$0.356973\pi$$
$$180$$ 0 0
$$181$$ 250.346i 1.38313i 0.722316 + 0.691563i $$0.243077\pi$$
−0.722316 + 0.691563i $$0.756923\pi$$
$$182$$ 0 0
$$183$$ 22.4283 0.122559
$$184$$ 0 0
$$185$$ 54.7144 62.2072i 0.295753 0.336255i
$$186$$ 0 0
$$187$$ 464.939i 2.48631i
$$188$$ 0 0
$$189$$ 97.5056i 0.515903i
$$190$$ 0 0
$$191$$ 111.128i 0.581825i −0.956750 0.290912i $$-0.906041\pi$$
0.956750 0.290912i $$-0.0939588\pi$$
$$192$$ 0 0
$$193$$ 10.2701i 0.0532130i 0.999646 + 0.0266065i $$0.00847011\pi$$
−0.999646 + 0.0266065i $$0.991530\pi$$
$$194$$ 0 0
$$195$$ −9.07626 7.98302i −0.0465449 0.0409386i
$$196$$ 0 0
$$197$$ −163.213 −0.828492 −0.414246 0.910165i $$-0.635955\pi$$
−0.414246 + 0.910165i $$0.635955\pi$$
$$198$$ 0 0
$$199$$ 195.028i 0.980041i −0.871711 0.490021i $$-0.836989\pi$$
0.871711 0.490021i $$-0.163011\pi$$
$$200$$ 0 0
$$201$$ 27.9412 0.139011
$$202$$ 0 0
$$203$$ 23.9573i 0.118016i
$$204$$ 0 0
$$205$$ 43.9775 50.0000i 0.214524 0.243902i
$$206$$ 0 0
$$207$$ −132.807 −0.641582
$$208$$ 0 0
$$209$$ −83.0580 −0.397407
$$210$$ 0 0
$$211$$ −297.038 −1.40776 −0.703881 0.710317i $$-0.748551\pi$$
−0.703881 + 0.710317i $$0.748551\pi$$
$$212$$ 0 0
$$213$$ −22.1592 −0.104034
$$214$$ 0 0
$$215$$ −224.483 197.444i −1.04411 0.918342i
$$216$$ 0 0
$$217$$ 382.505i 1.76270i
$$218$$ 0 0
$$219$$ 19.6347 0.0896563
$$220$$ 0 0
$$221$$ 119.236i 0.539527i
$$222$$ 0 0
$$223$$ 405.335 1.81764 0.908822 0.417184i $$-0.136983\pi$$
0.908822 + 0.417184i $$0.136983\pi$$
$$224$$ 0 0
$$225$$ −27.7626 215.719i −0.123389 0.958752i
$$226$$ 0 0
$$227$$ 36.6013i 0.161239i 0.996745 + 0.0806196i $$0.0256899\pi$$
−0.996745 + 0.0806196i $$0.974310\pi$$
$$228$$ 0 0
$$229$$ 91.1467i 0.398021i −0.979997 0.199010i $$-0.936227\pi$$
0.979997 0.199010i $$-0.0637727\pi$$
$$230$$ 0 0
$$231$$ 94.7997i 0.410388i
$$232$$ 0 0
$$233$$ 338.802i 1.45409i 0.686592 + 0.727043i $$0.259106\pi$$
−0.686592 + 0.727043i $$0.740894\pi$$
$$234$$ 0 0
$$235$$ 206.185 234.421i 0.877382 0.997535i
$$236$$ 0 0
$$237$$ 69.4585 0.293074
$$238$$ 0 0
$$239$$ 30.7997i 0.128869i −0.997922 0.0644346i $$-0.979476\pi$$
0.997922 0.0644346i $$-0.0205244\pi$$
$$240$$ 0 0
$$241$$ 240.282 0.997020 0.498510 0.866884i $$-0.333881\pi$$
0.498510 + 0.866884i $$0.333881\pi$$
$$242$$ 0 0
$$243$$ 127.243i 0.523633i
$$244$$ 0 0
$$245$$ 172.160 195.736i 0.702693 0.798923i
$$246$$ 0 0
$$247$$ 21.3005 0.0862370
$$248$$ 0 0
$$249$$ 41.1652 0.165322
$$250$$ 0 0
$$251$$ −86.0268 −0.342736 −0.171368 0.985207i $$-0.554819\pi$$
−0.171368 + 0.985207i $$0.554819\pi$$
$$252$$ 0 0
$$253$$ −262.697 −1.03833
$$254$$ 0 0
$$255$$ 48.8715 55.5642i 0.191653 0.217899i
$$256$$ 0 0
$$257$$ 355.963i 1.38507i 0.721383 + 0.692536i $$0.243507\pi$$
−0.721383 + 0.692536i $$0.756493\pi$$
$$258$$ 0 0
$$259$$ −166.629 −0.643355
$$260$$ 0 0
$$261$$ 20.7254i 0.0794077i
$$262$$ 0 0
$$263$$ 73.1254 0.278043 0.139022 0.990289i $$-0.455604\pi$$
0.139022 + 0.990289i $$0.455604\pi$$
$$264$$ 0 0
$$265$$ −236.421 + 268.798i −0.892154 + 1.01433i
$$266$$ 0 0
$$267$$ 58.3514i 0.218545i
$$268$$ 0 0
$$269$$ 268.002i 0.996290i −0.867094 0.498145i $$-0.834015\pi$$
0.867094 0.498145i $$-0.165985\pi$$
$$270$$ 0 0
$$271$$ 229.412i 0.846538i 0.906004 + 0.423269i $$0.139117\pi$$
−0.906004 + 0.423269i $$0.860883\pi$$
$$272$$ 0 0
$$273$$ 24.3118i 0.0890541i
$$274$$ 0 0
$$275$$ −54.9153 426.699i −0.199692 1.55163i
$$276$$ 0 0
$$277$$ 126.327 0.456053 0.228026 0.973655i $$-0.426773\pi$$
0.228026 + 0.973655i $$0.426773\pi$$
$$278$$ 0 0
$$279$$ 330.904i 1.18604i
$$280$$ 0 0
$$281$$ 458.746 1.63255 0.816275 0.577664i $$-0.196036\pi$$
0.816275 + 0.577664i $$0.196036\pi$$
$$282$$ 0 0
$$283$$ 465.558i 1.64508i 0.568706 + 0.822541i $$0.307444\pi$$
−0.568706 + 0.822541i $$0.692556\pi$$
$$284$$ 0 0
$$285$$ −9.92614 8.73053i −0.0348286 0.0306335i
$$286$$ 0 0
$$287$$ −133.931 −0.466657
$$288$$ 0 0
$$289$$ −440.952 −1.52579
$$290$$ 0 0
$$291$$ 46.7997 0.160824
$$292$$ 0 0
$$293$$ −165.218 −0.563884 −0.281942 0.959431i $$-0.590979\pi$$
−0.281942 + 0.959431i $$0.590979\pi$$
$$294$$ 0 0
$$295$$ −227.278 + 258.403i −0.770434 + 0.875941i
$$296$$ 0 0
$$297$$ 166.851i 0.561787i
$$298$$ 0 0
$$299$$ 67.3697 0.225317
$$300$$ 0 0
$$301$$ 601.302i 1.99768i
$$302$$ 0 0
$$303$$ 45.6234 0.150572
$$304$$ 0 0
$$305$$ −153.720 135.205i −0.504000 0.443293i
$$306$$ 0 0
$$307$$ 235.339i 0.766577i 0.923629 + 0.383288i $$0.125208\pi$$
−0.923629 + 0.383288i $$0.874792\pi$$
$$308$$ 0 0
$$309$$ 25.8911i 0.0837898i
$$310$$ 0 0
$$311$$ 210.665i 0.677381i 0.940898 + 0.338691i $$0.109984\pi$$
−0.940898 + 0.338691i $$0.890016\pi$$
$$312$$ 0 0
$$313$$ 318.738i 1.01833i 0.860668 + 0.509166i $$0.170046\pi$$
−0.860668 + 0.509166i $$0.829954\pi$$
$$314$$ 0 0
$$315$$ −288.914 + 328.479i −0.917187 + 1.04279i
$$316$$ 0 0
$$317$$ −70.3950 −0.222066 −0.111033 0.993817i $$-0.535416\pi$$
−0.111033 + 0.993817i $$0.535416\pi$$
$$318$$ 0 0
$$319$$ 40.9955i 0.128513i
$$320$$ 0 0
$$321$$ −103.875 −0.323598
$$322$$ 0 0
$$323$$ 130.401i 0.403717i
$$324$$ 0 0
$$325$$ 14.0832 + 109.429i 0.0433330 + 0.336704i
$$326$$ 0 0
$$327$$ 46.3213 0.141655
$$328$$ 0 0
$$329$$ −627.922 −1.90858
$$330$$ 0 0
$$331$$ 280.807 0.848359 0.424180 0.905578i $$-0.360562\pi$$
0.424180 + 0.905578i $$0.360562\pi$$
$$332$$ 0 0
$$333$$ 144.150 0.432884
$$334$$ 0 0
$$335$$ −191.505 168.438i −0.571656 0.502800i
$$336$$ 0 0
$$337$$ 120.969i 0.358959i 0.983762 + 0.179480i $$0.0574414\pi$$
−0.983762 + 0.179480i $$0.942559\pi$$
$$338$$ 0 0
$$339$$ 62.7530 0.185112
$$340$$ 0 0
$$341$$ 654.539i 1.91947i
$$342$$ 0 0
$$343$$ −31.5280 −0.0919182
$$344$$ 0 0
$$345$$ −31.3946 27.6131i −0.0909988 0.0800380i
$$346$$ 0 0
$$347$$ 214.333i 0.617675i −0.951115 0.308838i $$-0.900060\pi$$
0.951115 0.308838i $$-0.0999399\pi$$
$$348$$ 0 0
$$349$$ 418.041i 1.19782i 0.800815 + 0.598912i $$0.204400\pi$$
−0.800815 + 0.598912i $$0.795600\pi$$
$$350$$ 0 0
$$351$$ 42.7895i 0.121907i
$$352$$ 0 0
$$353$$ 364.929i 1.03379i 0.856048 + 0.516897i $$0.172913\pi$$
−0.856048 + 0.516897i $$0.827087\pi$$
$$354$$ 0 0
$$355$$ 151.876 + 133.583i 0.427820 + 0.376289i
$$356$$ 0 0
$$357$$ −148.835 −0.416905
$$358$$ 0 0
$$359$$ 242.169i 0.674567i −0.941403 0.337283i $$-0.890492\pi$$
0.941403 0.337283i $$-0.109508\pi$$
$$360$$ 0 0
$$361$$ −337.705 −0.935471
$$362$$ 0 0
$$363$$ 95.9389i 0.264295i
$$364$$ 0 0
$$365$$ −134.573 118.364i −0.368694 0.324285i
$$366$$ 0 0
$$367$$ −224.564 −0.611891 −0.305945 0.952049i $$-0.598972\pi$$
−0.305945 + 0.952049i $$0.598972\pi$$
$$368$$ 0 0
$$369$$ 115.863 0.313992
$$370$$ 0 0
$$371$$ 720.004 1.94071
$$372$$ 0 0
$$373$$ 572.174 1.53398 0.766989 0.641660i $$-0.221754\pi$$
0.766989 + 0.641660i $$0.221754\pi$$
$$374$$ 0 0
$$375$$ 38.2891 56.7666i 0.102104 0.151378i
$$376$$ 0 0
$$377$$ 10.5135i 0.0278872i
$$378$$ 0 0
$$379$$ −122.896 −0.324263 −0.162132 0.986769i $$-0.551837\pi$$
−0.162132 + 0.986769i $$0.551837\pi$$
$$380$$ 0 0
$$381$$ 24.3281i 0.0638533i
$$382$$ 0 0
$$383$$ −289.717 −0.756442 −0.378221 0.925715i $$-0.623464\pi$$
−0.378221 + 0.925715i $$0.623464\pi$$
$$384$$ 0 0
$$385$$ −571.481 + 649.743i −1.48437 + 1.68764i
$$386$$ 0 0
$$387$$ 520.185i 1.34415i
$$388$$ 0 0
$$389$$ 111.590i 0.286863i 0.989660 + 0.143432i $$0.0458137\pi$$
−0.989660 + 0.143432i $$0.954186\pi$$
$$390$$ 0 0
$$391$$ 412.433i 1.05482i
$$392$$ 0 0
$$393$$ 25.8114i 0.0656780i
$$394$$ 0 0
$$395$$ −476.058 418.716i −1.20521 1.06004i
$$396$$ 0 0
$$397$$ 705.314 1.77661 0.888305 0.459253i $$-0.151883\pi$$
0.888305 + 0.459253i $$0.151883\pi$$
$$398$$ 0 0
$$399$$ 26.5883i 0.0666373i
$$400$$ 0 0
$$401$$ 432.052 1.07744 0.538718 0.842486i $$-0.318909\pi$$
0.538718 + 0.842486i $$0.318909\pi$$
$$402$$ 0 0
$$403$$ 167.859i 0.416524i
$$404$$ 0 0
$$405$$ 241.021 274.028i 0.595114 0.676612i
$$406$$ 0 0
$$407$$ 285.134 0.700575
$$408$$ 0 0
$$409$$ 98.8102 0.241590 0.120795 0.992677i $$-0.461456\pi$$
0.120795 + 0.992677i $$0.461456\pi$$
$$410$$ 0 0
$$411$$ −34.4345 −0.0837822
$$412$$ 0 0
$$413$$ 692.160 1.67593
$$414$$ 0 0
$$415$$ −282.140 248.156i −0.679855 0.597966i
$$416$$ 0 0
$$417$$ 70.2914i 0.168565i
$$418$$ 0 0
$$419$$ −204.980 −0.489213 −0.244607 0.969622i $$-0.578659\pi$$
−0.244607 + 0.969622i $$0.578659\pi$$
$$420$$ 0 0
$$421$$ 449.956i 1.06878i 0.845238 + 0.534390i $$0.179459\pi$$
−0.845238 + 0.534390i $$0.820541\pi$$
$$422$$ 0 0
$$423$$ 543.214 1.28419
$$424$$ 0 0
$$425$$ −669.915 + 86.2166i −1.57627 + 0.202863i
$$426$$ 0 0
$$427$$ 411.756i 0.964301i
$$428$$ 0 0
$$429$$ 41.6021i 0.0969745i
$$430$$ 0 0
$$431$$ 314.588i 0.729903i −0.931026 0.364952i $$-0.881086\pi$$
0.931026 0.364952i $$-0.118914\pi$$
$$432$$ 0 0
$$433$$ 330.441i 0.763143i −0.924339 0.381571i $$-0.875383\pi$$
0.924339 0.381571i $$-0.124617\pi$$
$$434$$ 0 0
$$435$$ −4.30919 + 4.89932i −0.00990619 + 0.0112628i
$$436$$ 0 0
$$437$$ 73.6781 0.168600
$$438$$ 0 0
$$439$$ 664.815i 1.51439i −0.653191 0.757193i $$-0.726570\pi$$
0.653191 0.757193i $$-0.273430\pi$$
$$440$$ 0 0
$$441$$ 453.572 1.02851
$$442$$ 0 0
$$443$$ 312.860i 0.706229i −0.935580 0.353115i $$-0.885123\pi$$
0.935580 0.353115i $$-0.114877\pi$$
$$444$$ 0 0
$$445$$ 351.760 399.931i 0.790471 0.898722i
$$446$$ 0 0
$$447$$ 90.6912 0.202889
$$448$$ 0 0
$$449$$ −246.330 −0.548620 −0.274310 0.961641i $$-0.588449\pi$$
−0.274310 + 0.961641i $$0.588449\pi$$
$$450$$ 0 0
$$451$$ 229.181 0.508161
$$452$$ 0 0
$$453$$ 119.722 0.264287
$$454$$ 0 0
$$455$$ 146.558 166.629i 0.322107 0.366218i
$$456$$ 0 0
$$457$$ 707.094i 1.54725i 0.633642 + 0.773626i $$0.281559\pi$$
−0.633642 + 0.773626i $$0.718441\pi$$
$$458$$ 0 0
$$459$$ 261.955 0.570707
$$460$$ 0 0
$$461$$ 611.288i 1.32600i 0.748618 + 0.663002i $$0.230718\pi$$
−0.748618 + 0.663002i $$0.769282\pi$$
$$462$$ 0 0
$$463$$ 334.063 0.721519 0.360760 0.932659i $$-0.382518\pi$$
0.360760 + 0.932659i $$0.382518\pi$$
$$464$$ 0 0
$$465$$ −68.8010 + 78.2230i −0.147959 + 0.168222i
$$466$$ 0 0
$$467$$ 128.864i 0.275939i 0.990436 + 0.137970i $$0.0440577\pi$$
−0.990436 + 0.137970i $$0.955942\pi$$
$$468$$ 0 0
$$469$$ 512.966i 1.09374i
$$470$$ 0 0
$$471$$ 95.4742i 0.202705i
$$472$$ 0 0
$$473$$ 1028.94i 2.17535i
$$474$$ 0 0
$$475$$ 15.4020 + 119.675i 0.0324252 + 0.251948i
$$476$$ 0 0
$$477$$ −622.874 −1.30582
$$478$$ 0 0
$$479$$ 510.257i 1.06525i 0.846350 + 0.532627i $$0.178795\pi$$
−0.846350 + 0.532627i $$0.821205\pi$$
$$480$$ 0 0
$$481$$ −73.1237 −0.152024
$$482$$ 0 0
$$483$$ 84.0939i 0.174107i
$$484$$ 0 0
$$485$$ −320.758 282.123i −0.661357 0.581696i
$$486$$ 0 0
$$487$$ −616.472 −1.26586 −0.632928 0.774211i $$-0.718147\pi$$
−0.632928 + 0.774211i $$0.718147\pi$$
$$488$$ 0 0
$$489$$ −28.8326 −0.0589624
$$490$$ 0 0
$$491$$ −603.190 −1.22849 −0.614247 0.789114i $$-0.710540\pi$$
−0.614247 + 0.789114i $$0.710540\pi$$
$$492$$ 0 0
$$493$$ 64.3627 0.130553
$$494$$ 0 0
$$495$$ 494.387 562.091i 0.998761 1.13554i
$$496$$ 0 0
$$497$$ 406.817i 0.818545i
$$498$$ 0 0
$$499$$ −867.976 −1.73943 −0.869716 0.493553i $$-0.835698\pi$$
−0.869716 + 0.493553i $$0.835698\pi$$
$$500$$ 0 0
$$501$$ 42.0045i 0.0838413i
$$502$$ 0 0
$$503$$ −57.8408 −0.114992 −0.0574958 0.998346i $$-0.518312\pi$$
−0.0574958 + 0.998346i $$0.518312\pi$$
$$504$$ 0 0
$$505$$ −312.696 275.032i −0.619200 0.544617i
$$506$$ 0 0
$$507$$ 81.9060i 0.161550i
$$508$$ 0 0
$$509$$ 168.498i 0.331038i 0.986207 + 0.165519i $$0.0529299\pi$$
−0.986207 + 0.165519i $$0.947070\pi$$
$$510$$ 0 0
$$511$$ 360.470i 0.705420i
$$512$$ 0 0
$$513$$ 46.7962i 0.0912207i
$$514$$ 0 0
$$515$$ −156.079 + 177.453i −0.303066 + 0.344569i
$$516$$ 0 0
$$517$$ 1074.49 2.07833
$$518$$ 0 0
$$519$$ 5.32682i 0.0102636i
$$520$$ 0 0
$$521$$ 87.1060 0.167190 0.0835951 0.996500i $$-0.473360\pi$$
0.0835951 + 0.996500i $$0.473360\pi$$
$$522$$ 0 0
$$523$$ 243.469i 0.465524i −0.972534 0.232762i $$-0.925224\pi$$
0.972534 0.232762i $$-0.0747763\pi$$
$$524$$ 0 0
$$525$$ −136.594 + 17.5793i −0.260179 + 0.0334844i
$$526$$ 0 0
$$527$$ 1027.62 1.94995
$$528$$ 0 0
$$529$$ −295.969 −0.559488
$$530$$ 0 0
$$531$$ −598.786 −1.12766
$$532$$ 0 0
$$533$$ −58.7743 −0.110271
$$534$$ 0 0
$$535$$ 711.942 + 626.189i 1.33073 + 1.17045i
$$536$$ 0 0
$$537$$ 85.1812i 0.158624i
$$538$$ 0 0
$$539$$ 897.179 1.66452
$$540$$ 0 0
$$541$$ 812.616i 1.50206i 0.660266 + 0.751032i $$0.270443\pi$$
−0.660266 + 0.751032i $$0.729557\pi$$
$$542$$ 0 0
$$543$$ −137.135 −0.252550
$$544$$ 0 0
$$545$$ −317.479 279.238i −0.582530 0.512364i
$$546$$ 0 0
$$547$$ 104.713i 0.191431i −0.995409 0.0957155i $$-0.969486\pi$$
0.995409 0.0957155i $$-0.0305139\pi$$
$$548$$ 0 0
$$549$$ 356.210i 0.648833i
$$550$$ 0 0
$$551$$ 11.4979i 0.0208674i
$$552$$ 0 0
$$553$$ 1275.17i 2.30592i
$$554$$ 0 0
$$555$$ 34.0759 + 29.9715i 0.0613981 + 0.0540027i
$$556$$ 0 0
$$557$$ −260.018 −0.466818 −0.233409 0.972379i $$-0.574988\pi$$
−0.233409 + 0.972379i $$0.574988\pi$$
$$558$$ 0 0
$$559$$ 263.876i 0.472050i
$$560$$ 0 0
$$561$$ 254.685 0.453984
$$562$$ 0 0
$$563$$ 39.9073i 0.0708833i 0.999372 + 0.0354416i $$0.0112838\pi$$
−0.999372 + 0.0354416i $$0.988716\pi$$
$$564$$ 0 0
$$565$$ −430.099 378.293i −0.761237 0.669546i
$$566$$ 0 0
$$567$$ −734.014 −1.29456
$$568$$ 0 0
$$569$$ 211.588 0.371860 0.185930 0.982563i $$-0.440470\pi$$
0.185930 + 0.982563i $$0.440470\pi$$
$$570$$ 0 0
$$571$$ 556.938 0.975372 0.487686 0.873019i $$-0.337841\pi$$
0.487686 + 0.873019i $$0.337841\pi$$
$$572$$ 0 0
$$573$$ 60.8741 0.106237
$$574$$ 0 0
$$575$$ 48.7136 + 378.512i 0.0847193 + 0.658281i
$$576$$ 0 0
$$577$$ 516.233i 0.894684i 0.894363 + 0.447342i $$0.147629\pi$$
−0.894363 + 0.447342i $$0.852371\pi$$
$$578$$ 0 0
$$579$$ −5.62577 −0.00971636
$$580$$ 0 0
$$581$$ 755.742i 1.30076i
$$582$$ 0 0
$$583$$ −1232.06 −2.11332
$$584$$ 0 0
$$585$$ −126.787 + 144.150i −0.216731 + 0.246411i
$$586$$ 0 0
$$587$$ 934.677i 1.59229i 0.605103 + 0.796147i $$0.293132\pi$$
−0.605103 + 0.796147i $$0.706868\pi$$
$$588$$ 0 0
$$589$$ 183.577i 0.311676i
$$590$$ 0 0
$$591$$ 89.4050i 0.151277i
$$592$$ 0 0
$$593$$ 634.665i 1.07026i 0.844769 + 0.535131i $$0.179738\pi$$
−0.844769 + 0.535131i $$0.820262\pi$$
$$594$$ 0 0
$$595$$ 1020.09 + 897.221i 1.71444 + 1.50794i
$$596$$ 0 0
$$597$$ 106.833 0.178949
$$598$$ 0 0
$$599$$ 914.029i 1.52593i −0.646443 0.762963i $$-0.723744\pi$$
0.646443 0.762963i $$-0.276256\pi$$
$$600$$ 0 0
$$601$$ 598.569 0.995955 0.497977 0.867190i $$-0.334076\pi$$
0.497977 + 0.867190i $$0.334076\pi$$
$$602$$ 0 0
$$603$$ 443.766i 0.735930i
$$604$$ 0 0
$$605$$ 578.348 657.550i 0.955948 1.08686i
$$606$$ 0 0
$$607$$ −201.830 −0.332504 −0.166252 0.986083i $$-0.553166\pi$$
−0.166252 + 0.986083i $$0.553166\pi$$
$$608$$ 0 0
$$609$$ 13.1234 0.0215490
$$610$$ 0 0
$$611$$ −275.558 −0.450995
$$612$$ 0 0
$$613$$ −71.9205 −0.117325 −0.0586627 0.998278i $$-0.518684\pi$$
−0.0586627 + 0.998278i $$0.518684\pi$$
$$614$$ 0 0
$$615$$ 27.3891 + 24.0900i 0.0445350 + 0.0391708i
$$616$$ 0 0
$$617$$ 204.485i 0.331418i 0.986175 + 0.165709i $$0.0529912\pi$$
−0.986175 + 0.165709i $$0.947009\pi$$
$$618$$ 0 0
$$619$$ 287.512 0.464479 0.232239 0.972659i $$-0.425395\pi$$
0.232239 + 0.972659i $$0.425395\pi$$
$$620$$ 0 0
$$621$$ 148.008i 0.238338i
$$622$$ 0 0
$$623$$ −1071.26 −1.71952
$$624$$ 0 0
$$625$$ −604.633 + 158.251i −0.967414 + 0.253202i
$$626$$ 0 0
$$627$$ 45.4976i 0.0725640i
$$628$$ 0 0
$$629$$ 447.658i 0.711699i
$$630$$ 0 0
$$631$$ 274.203i 0.434554i −0.976110 0.217277i $$-0.930283\pi$$
0.976110 0.217277i $$-0.0697175\pi$$
$$632$$ 0 0
$$633$$ 162.712i 0.257049i
$$634$$ 0 0
$$635$$ 146.657 166.741i 0.230956 0.262584i
$$636$$ 0 0
$$637$$ −230.085 −0.361201
$$638$$ 0 0
$$639$$ 351.936i 0.550761i
$$640$$ 0 0
$$641$$ 681.328 1.06291 0.531457 0.847085i $$-0.321645\pi$$
0.531457 + 0.847085i $$0.321645\pi$$
$$642$$ 0 0
$$643$$ 527.270i 0.820016i −0.912082 0.410008i $$-0.865526\pi$$
0.912082 0.410008i $$-0.134474\pi$$
$$644$$ 0 0
$$645$$ 108.156 122.967i 0.167684 0.190647i
$$646$$ 0 0
$$647$$ 551.627 0.852592 0.426296 0.904584i $$-0.359818\pi$$
0.426296 + 0.904584i $$0.359818\pi$$
$$648$$ 0 0
$$649$$ −1184.42 −1.82499
$$650$$ 0 0
$$651$$ 209.529 0.321857
$$652$$ 0 0
$$653$$ −699.422 −1.07109 −0.535545 0.844507i $$-0.679894\pi$$
−0.535545 + 0.844507i $$0.679894\pi$$
$$654$$ 0 0
$$655$$ −155.599 + 176.908i −0.237556 + 0.270088i
$$656$$ 0 0
$$657$$ 311.842i 0.474645i
$$658$$ 0 0
$$659$$ 38.3257 0.0581574 0.0290787 0.999577i $$-0.490743\pi$$
0.0290787 + 0.999577i $$0.490743\pi$$
$$660$$ 0 0
$$661$$ 392.364i 0.593591i 0.954941 + 0.296796i $$0.0959180\pi$$
−0.954941 + 0.296796i $$0.904082\pi$$
$$662$$ 0 0
$$663$$ −65.3150 −0.0985143
$$664$$ 0 0
$$665$$ 160.282 182.232i 0.241026 0.274033i
$$666$$ 0 0
$$667$$ 36.3658i 0.0545215i
$$668$$ 0 0
$$669$$ 222.035i 0.331890i
$$670$$ 0 0
$$671$$ 704.594i 1.05007i
$$672$$ 0 0
$$673$$ 427.290i 0.634904i 0.948274 + 0.317452i $$0.102827\pi$$
−0.948274 + 0.317452i $$0.897173\pi$$
$$674$$ 0 0
$$675$$ 240.409 30.9402i 0.356162 0.0458373i
$$676$$ 0 0
$$677$$ −131.234 −0.193847 −0.0969233 0.995292i $$-0.530900\pi$$
−0.0969233 + 0.995292i $$0.530900\pi$$
$$678$$ 0 0
$$679$$ 859.186i 1.26537i
$$680$$ 0 0
$$681$$ −20.0495 −0.0294413
$$682$$ 0 0
$$683$$ 896.229i 1.31219i −0.754676 0.656097i $$-0.772206\pi$$
0.754676 0.656097i $$-0.227794\pi$$
$$684$$ 0 0
$$685$$ 236.008 + 207.581i 0.344538 + 0.303038i
$$686$$ 0 0
$$687$$ 49.9285 0.0726761
$$688$$ 0 0
$$689$$ 315.968 0.458589
$$690$$ 0 0
$$691$$ 520.465 0.753206 0.376603 0.926375i $$-0.377092\pi$$
0.376603 + 0.926375i $$0.377092\pi$$
$$692$$ 0 0
$$693$$ −1505.62 −2.17262
$$694$$ 0 0
$$695$$ −423.737 + 481.766i −0.609694 + 0.693189i
$$696$$ 0 0
$$697$$ 359.812i 0.516230i
$$698$$ 0 0
$$699$$ −185.589 −0.265507
$$700$$ 0 0
$$701$$ 80.7527i 0.115196i −0.998340 0.0575982i $$-0.981656\pi$$
0.998340 0.0575982i $$-0.0183442\pi$$
$$702$$ 0 0
$$703$$ −79.9709 −0.113757
$$704$$ 0 0
$$705$$ 128.411 + 112.944i 0.182144 + 0.160204i
$$706$$ 0 0
$$707$$ 837.591i 1.18471i
$$708$$ 0 0
$$709$$ 174.828i 0.246584i −0.992370 0.123292i $$-0.960655\pi$$
0.992370 0.123292i $$-0.0393452\pi$$
$$710$$ 0 0
$$711$$ 1103.15i 1.55155i
$$712$$ 0 0
$$713$$ 580.621i 0.814335i
$$714$$ 0 0
$$715$$ −250.789 + 285.134i −0.350755 + 0.398789i
$$716$$ 0 0
$$717$$ 16.8715 0.0235307
$$718$$ 0 0
$$719$$ 889.905i 1.23770i 0.785510 + 0.618849i $$0.212401\pi$$
−0.785510 + 0.618849i $$0.787599\pi$$
$$720$$ 0 0
$$721$$ 475.328 0.659263
$$722$$ 0 0
$$723$$ 131.622i 0.182050i
$$724$$ 0 0
$$725$$ 59.0690 7.60205i 0.0814745 0.0104856i
$$726$$ 0 0
$$727$$ 408.818 0.562335 0.281168 0.959659i $$-0.409278\pi$$
0.281168 + 0.959659i $$0.409278\pi$$
$$728$$ 0 0
$$729$$ 587.194 0.805478
$$730$$ 0 0
$$731$$ −1615.43 −2.20989
$$732$$ 0 0
$$733$$ −388.369 −0.529835 −0.264917 0.964271i $$-0.585345\pi$$
−0.264917 + 0.964271i $$0.585345\pi$$
$$734$$ 0 0
$$735$$ 107.221 + 94.3058i 0.145878 + 0.128307i
$$736$$ 0 0
$$737$$ 877.783i 1.19102i
$$738$$ 0 0
$$739$$ 109.561 0.148256 0.0741280 0.997249i $$-0.476383\pi$$
0.0741280 + 0.997249i $$0.476383\pi$$
$$740$$ 0 0
$$741$$ 11.6680i 0.0157463i
$$742$$ 0 0
$$743$$ 732.717 0.986160 0.493080 0.869984i $$-0.335871\pi$$
0.493080 + 0.869984i $$0.335871\pi$$
$$744$$ 0 0
$$745$$ −621.583 546.713i −0.834340 0.733844i
$$746$$ 0 0
$$747$$ 653.791i 0.875222i
$$748$$ 0 0
$$749$$ 1907.02i 2.54608i
$$750$$ 0 0
$$751$$ 420.809i 0.560332i −0.959952 0.280166i $$-0.909610\pi$$
0.959952 0.280166i $$-0.0903895\pi$$
$$752$$ 0 0
$$753$$ 47.1238i 0.0625814i
$$754$$ 0 0
$$755$$ −820.557 721.721i −1.08683 0.955922i
$$756$$ 0 0
$$757$$ −1306.99 −1.72654 −0.863269 0.504744i $$-0.831587\pi$$
−0.863269 + 0.504744i $$0.831587\pi$$
$$758$$ 0 0
$$759$$ 143.901i 0.189592i
$$760$$ 0 0
$$761$$ 1402.25 1.84264 0.921320 0.388804i $$-0.127112\pi$$
0.921320 + 0.388804i $$0.127112\pi$$
$$762$$ 0 0
$$763$$ 850.402i 1.11455i
$$764$$ 0 0
$$765$$ −882.479 776.184i −1.15357 1.01462i
$$766$$ 0 0
$$767$$ 303.748 0.396021
$$768$$ 0 0
$$769$$ −359.952 −0.468078 −0.234039 0.972227i $$-0.575194\pi$$
−0.234039 + 0.972227i $$0.575194\pi$$
$$770$$ 0 0
$$771$$ −194.990 −0.252905
$$772$$ 0 0
$$773$$ 437.539 0.566027 0.283013 0.959116i $$-0.408666\pi$$
0.283013 + 0.959116i $$0.408666\pi$$
$$774$$ 0 0
$$775$$ 943.103 121.375i 1.21691 0.156613i
$$776$$ 0 0
$$777$$ 91.2762i 0.117473i
$$778$$ 0 0
$$779$$ −64.2778 −0.0825132
$$780$$ 0 0
$$781$$ 696.141i 0.891346i
$$782$$ 0 0
$$783$$ −23.0975 −0.0294988
$$784$$ 0 0
$$785$$ 575.547 654.365i 0.733181 0.833586i
$$786$$ 0 0
$$787$$ 438.946i 0.557746i −0.960328 0.278873i $$-0.910039\pi$$
0.960328 0.278873i $$-0.0899608\pi$$
$$788$$ 0 0
$$789$$ 40.0567i 0.0507690i
$$790$$ 0 0
$$791$$ 1152.07i 1.45647i
$$792$$ 0 0
$$793$$ 180.696i 0.227864i
$$794$$ 0 0
$$795$$ −147.242 129.507i −0.185210 0.162902i
$$796$$ 0 0
$$797$$ 982.414 1.23264 0.616320 0.787496i $$-0.288623\pi$$
0.616320 + 0.787496i $$0.288623\pi$$
$$798$$ 0 0
$$799$$ 1686.95i 2.11133i
$$800$$ 0 0