# Properties

 Label 648.4.i.p.217.1 Level $648$ Weight $4$ Character 648.217 Analytic conductor $38.233$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$648 = 2^{3} \cdot 3^{4}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 648.i (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$38.2332376837$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\sqrt{-3}, \sqrt{-43})$$ Defining polynomial: $$x^{4} - x^{3} - 10 x^{2} - 11 x + 121$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{2}\cdot 3$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 217.1 Root $$-2.58945 - 2.07237i$$ of defining polynomial Character $$\chi$$ $$=$$ 648.217 Dual form 648.4.i.p.433.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-6.67891 - 11.5682i) q^{5} +(7.17891 - 12.4342i) q^{7} +O(q^{10})$$ $$q+(-6.67891 - 11.5682i) q^{5} +(7.17891 - 12.4342i) q^{7} +(-19.5367 + 33.8386i) q^{11} +(38.3945 + 66.5013i) q^{13} -62.4313 q^{17} -39.7891 q^{19} +(64.2524 + 111.288i) q^{23} +(-26.7156 + 46.2728i) q^{25} +(-32.4680 + 56.2362i) q^{29} +(4.56873 + 7.91328i) q^{31} -191.789 q^{35} +319.505 q^{37} +(-8.78908 - 15.2231i) q^{41} +(225.473 - 390.530i) q^{43} +(290.799 - 503.678i) q^{47} +(68.4265 + 118.518i) q^{49} +329.450 q^{53} +521.936 q^{55} +(120.927 + 209.451i) q^{59} +(-248.762 + 430.868i) q^{61} +(512.867 - 888.312i) q^{65} +(289.032 + 500.618i) q^{67} -660.927 q^{71} +696.559 q^{73} +(280.505 + 485.848i) q^{77} +(-365.134 + 632.430i) q^{79} +(-545.239 + 944.382i) q^{83} +(416.973 + 722.218i) q^{85} -317.588 q^{89} +1102.52 q^{91} +(265.748 + 460.288i) q^{95} +(742.827 - 1286.61i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q - 4q^{5} + 6q^{7} + O(q^{10})$$ $$4q - 4q^{5} + 6q^{7} - 10q^{11} + 40q^{13} - 68q^{17} + 68q^{19} + 98q^{23} - 16q^{25} + 120q^{29} + 200q^{31} - 540q^{35} + 960q^{37} + 192q^{41} + 334q^{43} + 300q^{47} + 410q^{49} - 136q^{53} + 1588q^{55} + 620q^{59} - 200q^{61} + 1370q^{65} + 1406q^{67} - 2780q^{71} + 3604q^{73} + 804q^{77} + 334q^{79} - 500q^{83} + 1100q^{85} - 180q^{89} + 2820q^{91} + 1222q^{95} + 200q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$$.

 $$n$$ $$325$$ $$487$$ $$569$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0 0
$$4$$ 0 0
$$5$$ −6.67891 11.5682i −0.597380 1.03469i −0.993206 0.116367i $$-0.962875\pi$$
0.395827 0.918325i $$-0.370458\pi$$
$$6$$ 0 0
$$7$$ 7.17891 12.4342i 0.387625 0.671386i −0.604505 0.796601i $$-0.706629\pi$$
0.992130 + 0.125216i $$0.0399624\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −19.5367 + 33.8386i −0.535504 + 0.927520i 0.463635 + 0.886026i $$0.346545\pi$$
−0.999139 + 0.0414937i $$0.986788\pi$$
$$12$$ 0 0
$$13$$ 38.3945 + 66.5013i 0.819133 + 1.41878i 0.906322 + 0.422588i $$0.138878\pi$$
−0.0871887 + 0.996192i $$0.527788\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −62.4313 −0.890694 −0.445347 0.895358i $$-0.646920\pi$$
−0.445347 + 0.895358i $$0.646920\pi$$
$$18$$ 0 0
$$19$$ −39.7891 −0.480434 −0.240217 0.970719i $$-0.577219\pi$$
−0.240217 + 0.970719i $$0.577219\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 64.2524 + 111.288i 0.582502 + 1.00892i 0.995182 + 0.0980467i $$0.0312595\pi$$
−0.412680 + 0.910876i $$0.635407\pi$$
$$24$$ 0 0
$$25$$ −26.7156 + 46.2728i −0.213725 + 0.370183i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −32.4680 + 56.2362i −0.207902 + 0.360097i −0.951053 0.309027i $$-0.899997\pi$$
0.743152 + 0.669123i $$0.233330\pi$$
$$30$$ 0 0
$$31$$ 4.56873 + 7.91328i 0.0264700 + 0.0458473i 0.878957 0.476901i $$-0.158240\pi$$
−0.852487 + 0.522748i $$0.824907\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −191.789 −0.926236
$$36$$ 0 0
$$37$$ 319.505 1.41963 0.709814 0.704389i $$-0.248779\pi$$
0.709814 + 0.704389i $$0.248779\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −8.78908 15.2231i −0.0334786 0.0579867i 0.848801 0.528713i $$-0.177325\pi$$
−0.882279 + 0.470726i $$0.843992\pi$$
$$42$$ 0 0
$$43$$ 225.473 390.530i 0.799634 1.38501i −0.120220 0.992747i $$-0.538360\pi$$
0.919855 0.392260i $$-0.128307\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 290.799 503.678i 0.902496 1.56317i 0.0782529 0.996934i $$-0.475066\pi$$
0.824243 0.566236i $$-0.191601\pi$$
$$48$$ 0 0
$$49$$ 68.4265 + 118.518i 0.199494 + 0.345534i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 329.450 0.853839 0.426919 0.904290i $$-0.359599\pi$$
0.426919 + 0.904290i $$0.359599\pi$$
$$54$$ 0 0
$$55$$ 521.936 1.27960
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 120.927 + 209.451i 0.266836 + 0.462173i 0.968043 0.250785i $$-0.0806886\pi$$
−0.701207 + 0.712957i $$0.747355\pi$$
$$60$$ 0 0
$$61$$ −248.762 + 430.868i −0.522142 + 0.904377i 0.477526 + 0.878618i $$0.341534\pi$$
−0.999668 + 0.0257594i $$0.991800\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 512.867 888.312i 0.978667 1.69510i
$$66$$ 0 0
$$67$$ 289.032 + 500.618i 0.527028 + 0.912839i 0.999504 + 0.0314957i $$0.0100271\pi$$
−0.472476 + 0.881344i $$0.656640\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −660.927 −1.10475 −0.552377 0.833594i $$-0.686279\pi$$
−0.552377 + 0.833594i $$0.686279\pi$$
$$72$$ 0 0
$$73$$ 696.559 1.11680 0.558398 0.829573i $$-0.311416\pi$$
0.558398 + 0.829573i $$0.311416\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 280.505 + 485.848i 0.415149 + 0.719059i
$$78$$ 0 0
$$79$$ −365.134 + 632.430i −0.520010 + 0.900683i 0.479720 + 0.877422i $$0.340738\pi$$
−0.999729 + 0.0232613i $$0.992595\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −545.239 + 944.382i −0.721058 + 1.24891i 0.239519 + 0.970892i $$0.423010\pi$$
−0.960576 + 0.278017i $$0.910323\pi$$
$$84$$ 0 0
$$85$$ 416.973 + 722.218i 0.532083 + 0.921594i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −317.588 −0.378250 −0.189125 0.981953i $$-0.560565\pi$$
−0.189125 + 0.981953i $$0.560565\pi$$
$$90$$ 0 0
$$91$$ 1102.52 1.27006
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 265.748 + 460.288i 0.287001 + 0.497101i
$$96$$ 0 0
$$97$$ 742.827 1286.61i 0.777553 1.34676i −0.155795 0.987789i $$-0.549794\pi$$
0.933348 0.358972i $$-0.116873\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 501.633 868.853i 0.494201 0.855982i −0.505776 0.862665i $$-0.668794\pi$$
0.999978 + 0.00668295i $$0.00212727\pi$$
$$102$$ 0 0
$$103$$ 858.799 + 1487.48i 0.821553 + 1.42297i 0.904526 + 0.426419i $$0.140225\pi$$
−0.0829729 + 0.996552i $$0.526441\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −1006.27 −0.909161 −0.454581 0.890706i $$-0.650211\pi$$
−0.454581 + 0.890706i $$0.650211\pi$$
$$108$$ 0 0
$$109$$ 1724.94 1.51577 0.757885 0.652388i $$-0.226233\pi$$
0.757885 + 0.652388i $$0.226233\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 313.509 + 543.014i 0.260995 + 0.452057i 0.966507 0.256641i $$-0.0826159\pi$$
−0.705511 + 0.708699i $$0.749283\pi$$
$$114$$ 0 0
$$115$$ 858.271 1486.57i 0.695950 1.20542i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −448.188 + 776.285i −0.345255 + 0.597999i
$$120$$ 0 0
$$121$$ −97.8673 169.511i −0.0735291 0.127356i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −956.002 −0.684059
$$126$$ 0 0
$$127$$ −1990.05 −1.39046 −0.695230 0.718788i $$-0.744697\pi$$
−0.695230 + 0.718788i $$0.744697\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −78.2072 135.459i −0.0521603 0.0903442i 0.838766 0.544491i $$-0.183277\pi$$
−0.890927 + 0.454147i $$0.849944\pi$$
$$132$$ 0 0
$$133$$ −285.642 + 494.747i −0.186228 + 0.322556i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 1059.66 1835.38i 0.660822 1.14458i −0.319579 0.947560i $$-0.603541\pi$$
0.980400 0.197017i $$-0.0631253\pi$$
$$138$$ 0 0
$$139$$ 1343.39 + 2326.81i 0.819745 + 1.41984i 0.905870 + 0.423555i $$0.139218\pi$$
−0.0861255 + 0.996284i $$0.527449\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −3000.41 −1.75460
$$144$$ 0 0
$$145$$ 867.403 0.496785
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 775.781 + 1343.69i 0.426540 + 0.738789i 0.996563 0.0828401i $$-0.0263991\pi$$
−0.570023 + 0.821629i $$0.693066\pi$$
$$150$$ 0 0
$$151$$ 9.05458 15.6830i 0.00487981 0.00845208i −0.863575 0.504220i $$-0.831780\pi$$
0.868455 + 0.495768i $$0.165113\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 61.0283 105.704i 0.0316252 0.0547765i
$$156$$ 0 0
$$157$$ −1870.75 3240.24i −0.950971 1.64713i −0.743330 0.668925i $$-0.766755\pi$$
−0.207641 0.978205i $$-0.566579\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 1845.05 0.903168
$$162$$ 0 0
$$163$$ 2608.90 1.25365 0.626826 0.779160i $$-0.284354\pi$$
0.626826 + 0.779160i $$0.284354\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 781.446 + 1353.50i 0.362097 + 0.627170i 0.988306 0.152485i $$-0.0487277\pi$$
−0.626209 + 0.779655i $$0.715394\pi$$
$$168$$ 0 0
$$169$$ −1849.78 + 3203.92i −0.841958 + 1.45831i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 751.385 1301.44i 0.330212 0.571945i −0.652341 0.757926i $$-0.726213\pi$$
0.982553 + 0.185981i $$0.0595463\pi$$
$$174$$ 0 0
$$175$$ 383.578 + 664.377i 0.165690 + 0.286984i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 4126.50 1.72307 0.861534 0.507700i $$-0.169504\pi$$
0.861534 + 0.507700i $$0.169504\pi$$
$$180$$ 0 0
$$181$$ 1582.33 0.649800 0.324900 0.945748i $$-0.394669\pi$$
0.324900 + 0.945748i $$0.394669\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −2133.94 3696.10i −0.848057 1.46888i
$$186$$ 0 0
$$187$$ 1219.70 2112.59i 0.476970 0.826137i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −1287.94 + 2230.78i −0.487916 + 0.845096i −0.999903 0.0138971i $$-0.995576\pi$$
0.511987 + 0.858993i $$0.328910\pi$$
$$192$$ 0 0
$$193$$ 697.649 + 1208.36i 0.260196 + 0.450673i 0.966294 0.257441i $$-0.0828794\pi$$
−0.706098 + 0.708114i $$0.749546\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 5047.62 1.82552 0.912761 0.408494i $$-0.133946\pi$$
0.912761 + 0.408494i $$0.133946\pi$$
$$198$$ 0 0
$$199$$ −2441.47 −0.869704 −0.434852 0.900502i $$-0.643199\pi$$
−0.434852 + 0.900502i $$0.643199\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 466.169 + 807.429i 0.161176 + 0.279165i
$$204$$ 0 0
$$205$$ −117.403 + 203.348i −0.0399989 + 0.0692802i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 777.348 1346.41i 0.257274 0.445612i
$$210$$ 0 0
$$211$$ −2133.08 3694.61i −0.695959 1.20544i −0.969856 0.243678i $$-0.921646\pi$$
0.273897 0.961759i $$-0.411687\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −6023.65 −1.91074
$$216$$ 0 0
$$217$$ 131.194 0.0410416
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −2397.02 4151.76i −0.729597 1.26370i
$$222$$ 0 0
$$223$$ −875.574 + 1516.54i −0.262927 + 0.455404i −0.967019 0.254706i $$-0.918021\pi$$
0.704091 + 0.710110i $$0.251355\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −1100.02 + 1905.29i −0.321635 + 0.557088i −0.980825 0.194888i $$-0.937566\pi$$
0.659191 + 0.751976i $$0.270899\pi$$
$$228$$ 0 0
$$229$$ 595.645 + 1031.69i 0.171884 + 0.297711i 0.939078 0.343703i $$-0.111681\pi$$
−0.767195 + 0.641414i $$0.778348\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 2644.52 0.743555 0.371778 0.928322i $$-0.378748\pi$$
0.371778 + 0.928322i $$0.378748\pi$$
$$234$$ 0 0
$$235$$ −7768.87 −2.15653
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −718.761 1244.93i −0.194530 0.336937i 0.752216 0.658917i $$-0.228985\pi$$
−0.946746 + 0.321980i $$0.895652\pi$$
$$240$$ 0 0
$$241$$ −1633.54 + 2829.37i −0.436620 + 0.756248i −0.997426 0.0716990i $$-0.977158\pi$$
0.560806 + 0.827947i $$0.310491\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 914.029 1583.15i 0.238348 0.412830i
$$246$$ 0 0
$$247$$ −1527.68 2646.03i −0.393539 0.681630i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −1871.89 −0.470727 −0.235364 0.971907i $$-0.575628\pi$$
−0.235364 + 0.971907i $$0.575628\pi$$
$$252$$ 0 0
$$253$$ −5021.12 −1.24773
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 2345.41 + 4062.37i 0.569271 + 0.986007i 0.996638 + 0.0819287i $$0.0261080\pi$$
−0.427367 + 0.904078i $$0.640559\pi$$
$$258$$ 0 0
$$259$$ 2293.70 3972.80i 0.550283 0.953118i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −2296.69 + 3977.98i −0.538479 + 0.932673i 0.460507 + 0.887656i $$0.347667\pi$$
−0.998986 + 0.0450168i $$0.985666\pi$$
$$264$$ 0 0
$$265$$ −2200.37 3811.15i −0.510066 0.883460i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 83.0074 0.0188143 0.00940716 0.999956i $$-0.497006\pi$$
0.00940716 + 0.999956i $$0.497006\pi$$
$$270$$ 0 0
$$271$$ −3464.08 −0.776487 −0.388244 0.921557i $$-0.626918\pi$$
−0.388244 + 0.921557i $$0.626918\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −1043.87 1808.04i −0.228901 0.396469i
$$276$$ 0 0
$$277$$ 635.350 1100.46i 0.137814 0.238701i −0.788855 0.614580i $$-0.789326\pi$$
0.926669 + 0.375879i $$0.122659\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −3825.90 + 6626.65i −0.812221 + 1.40681i 0.0990857 + 0.995079i $$0.468408\pi$$
−0.911306 + 0.411729i $$0.864925\pi$$
$$282$$ 0 0
$$283$$ 3.72507 + 6.45201i 0.000782446 + 0.00135524i 0.866416 0.499322i $$-0.166418\pi$$
−0.865634 + 0.500677i $$0.833084\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −252.384 −0.0519086
$$288$$ 0 0
$$289$$ −1015.34 −0.206663
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 1407.01 + 2437.02i 0.280541 + 0.485911i 0.971518 0.236965i $$-0.0761528\pi$$
−0.690977 + 0.722877i $$0.742819\pi$$
$$294$$ 0 0
$$295$$ 1615.31 2797.81i 0.318804 0.552185i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −4933.88 + 8545.73i −0.954293 + 1.65288i
$$300$$ 0 0
$$301$$ −3237.30 5607.16i −0.619916 1.07373i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 6645.83 1.24767
$$306$$ 0 0
$$307$$ −5096.55 −0.947477 −0.473739 0.880666i $$-0.657096\pi$$
−0.473739 + 0.880666i $$0.657096\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −3892.41 6741.85i −0.709705 1.22924i −0.964967 0.262373i $$-0.915495\pi$$
0.255262 0.966872i $$-0.417838\pi$$
$$312$$ 0 0
$$313$$ 123.235 213.448i 0.0222544 0.0385457i −0.854684 0.519149i $$-0.826249\pi$$
0.876938 + 0.480603i $$0.159582\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 29.6600 51.3727i 0.00525512 0.00910214i −0.863386 0.504544i $$-0.831661\pi$$
0.868641 + 0.495442i $$0.164994\pi$$
$$318$$ 0 0
$$319$$ −1268.64 2197.34i −0.222665 0.385666i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 2484.08 0.427920
$$324$$ 0 0
$$325$$ −4102.94 −0.700277
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −4175.23 7231.71i −0.699660 1.21185i
$$330$$ 0 0
$$331$$ −2204.55 + 3818.39i −0.366082 + 0.634072i −0.988949 0.148255i $$-0.952634\pi$$
0.622867 + 0.782327i $$0.285968\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 3860.84 6687.17i 0.629672 1.09062i
$$336$$ 0 0
$$337$$ −3016.15 5224.12i −0.487537 0.844440i 0.512360 0.858771i $$-0.328771\pi$$
−0.999897 + 0.0143313i $$0.995438\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −357.032 −0.0566991
$$342$$ 0 0
$$343$$ 6889.64 1.08456
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 3120.39 + 5404.68i 0.482742 + 0.836133i 0.999804 0.0198147i $$-0.00630762\pi$$
−0.517062 + 0.855948i $$0.672974\pi$$
$$348$$ 0 0
$$349$$ −2817.31 + 4879.72i −0.432111 + 0.748439i −0.997055 0.0766906i $$-0.975565\pi$$
0.564943 + 0.825130i $$0.308898\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 1720.66 2980.27i 0.259437 0.449359i −0.706654 0.707559i $$-0.749796\pi$$
0.966091 + 0.258201i $$0.0831296\pi$$
$$354$$ 0 0
$$355$$ 4414.27 + 7645.74i 0.659958 + 1.14308i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 7808.79 1.14800 0.574000 0.818855i $$-0.305391\pi$$
0.574000 + 0.818855i $$0.305391\pi$$
$$360$$ 0 0
$$361$$ −5275.83 −0.769183
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −4652.26 8057.94i −0.667151 1.15554i
$$366$$ 0 0
$$367$$ −6804.06 + 11785.0i −0.967763 + 1.67621i −0.265763 + 0.964038i $$0.585624\pi$$
−0.702001 + 0.712176i $$0.747710\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 2365.09 4096.46i 0.330969 0.573255i
$$372$$ 0 0
$$373$$ 1874.08 + 3246.01i 0.260151 + 0.450595i 0.966282 0.257486i $$-0.0828942\pi$$
−0.706131 + 0.708082i $$0.749561\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −4986.37 −0.681197
$$378$$ 0 0
$$379$$ −10210.3 −1.38382 −0.691909 0.721985i $$-0.743230\pi$$
−0.691909 + 0.721985i $$0.743230\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −3064.75 5308.30i −0.408880 0.708202i 0.585884 0.810395i $$-0.300747\pi$$
−0.994765 + 0.102193i $$0.967414\pi$$
$$384$$ 0 0
$$385$$ 3746.93 6489.87i 0.496003 0.859103i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 2432.99 4214.05i 0.317114 0.549257i −0.662771 0.748822i $$-0.730620\pi$$
0.979885 + 0.199565i $$0.0639530\pi$$
$$390$$ 0 0
$$391$$ −4011.36 6947.87i −0.518831 0.898642i
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 9754.78 1.24257
$$396$$ 0 0
$$397$$ −438.311 −0.0554110 −0.0277055 0.999616i $$-0.508820\pi$$
−0.0277055 + 0.999616i $$0.508820\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 5876.83 + 10179.0i 0.731857 + 1.26761i 0.956089 + 0.293078i $$0.0946796\pi$$
−0.224231 + 0.974536i $$0.571987\pi$$
$$402$$ 0 0
$$403$$ −350.829 + 607.653i −0.0433648 + 0.0751101i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −6242.08 + 10811.6i −0.760217 + 1.31673i
$$408$$ 0 0
$$409$$ −5623.24 9739.75i −0.679833 1.17750i −0.975031 0.222069i $$-0.928719\pi$$
0.295198 0.955436i $$-0.404614\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 3472.48 0.413728
$$414$$ 0 0
$$415$$ 14566.4 1.72298
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 6158.18 + 10666.3i 0.718012 + 1.24363i 0.961786 + 0.273801i $$0.0882810\pi$$
−0.243774 + 0.969832i $$0.578386\pi$$
$$420$$ 0 0
$$421$$ 2351.30 4072.57i 0.272198 0.471461i −0.697226 0.716851i $$-0.745583\pi$$
0.969424 + 0.245390i $$0.0789160\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 1667.89 2888.87i 0.190364 0.329720i
$$426$$ 0 0
$$427$$ 3571.68 + 6186.32i 0.404790 + 0.701118i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −2204.89 −0.246417 −0.123208 0.992381i $$-0.539318\pi$$
−0.123208 + 0.992381i $$0.539318\pi$$
$$432$$ 0 0
$$433$$ 9426.46 1.04620 0.523102 0.852270i $$-0.324775\pi$$
0.523102 + 0.852270i $$0.324775\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −2556.54 4428.06i −0.279854 0.484721i
$$438$$ 0 0
$$439$$ 3842.29 6655.05i 0.417728 0.723527i −0.577982 0.816049i $$-0.696160\pi$$
0.995711 + 0.0925227i $$0.0294931\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 6197.15 10733.8i 0.664640 1.15119i −0.314743 0.949177i $$-0.601918\pi$$
0.979383 0.202013i $$-0.0647483\pi$$
$$444$$ 0 0
$$445$$ 2121.14 + 3673.92i 0.225959 + 0.391372i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −14568.7 −1.53127 −0.765635 0.643275i $$-0.777575\pi$$
−0.765635 + 0.643275i $$0.777575\pi$$
$$450$$ 0 0
$$451$$ 686.840 0.0717118
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −7363.65 12754.2i −0.758711 1.31413i
$$456$$ 0 0
$$457$$ 323.024 559.493i 0.0330643 0.0572691i −0.849020 0.528361i $$-0.822807\pi$$
0.882084 + 0.471092i $$0.156140\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −9500.49 + 16455.3i −0.959831 + 1.66248i −0.236927 + 0.971528i $$0.576140\pi$$
−0.722904 + 0.690948i $$0.757193\pi$$
$$462$$ 0 0
$$463$$ −6832.86 11834.9i −0.685853 1.18793i −0.973168 0.230096i $$-0.926096\pi$$
0.287315 0.957836i $$-0.407237\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 3762.83 0.372855 0.186427 0.982469i $$-0.440309\pi$$
0.186427 + 0.982469i $$0.440309\pi$$
$$468$$ 0 0
$$469$$ 8299.74 0.817156
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 8810.00 + 15259.4i 0.856415 + 1.48335i
$$474$$ 0 0
$$475$$ 1062.99 1841.15i 0.102681 0.177848i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 3381.94 5857.68i 0.322598 0.558757i −0.658425 0.752646i $$-0.728777\pi$$
0.981023 + 0.193890i $$0.0621104\pi$$
$$480$$ 0 0
$$481$$ 12267.2 + 21247.5i 1.16286 + 2.01414i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −19845.1 −1.85798
$$486$$ 0 0
$$487$$ −1447.72 −0.134708 −0.0673538 0.997729i $$-0.521456\pi$$
−0.0673538 + 0.997729i $$0.521456\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 3919.14 + 6788.15i 0.360220 + 0.623920i 0.987997 0.154474i $$-0.0493682\pi$$
−0.627777 + 0.778394i $$0.716035\pi$$
$$492$$ 0 0
$$493$$ 2027.02 3510.90i 0.185177 0.320736i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −4744.73 + 8218.12i −0.428230 + 0.741716i
$$498$$ 0 0
$$499$$ 2122.67 + 3676.57i 0.190428 + 0.329832i 0.945392 0.325935i $$-0.105679\pi$$
−0.754964 + 0.655766i $$0.772346\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −17914.9 −1.58804 −0.794021 0.607891i $$-0.792016\pi$$
−0.794021 + 0.607891i $$0.792016\pi$$
$$504$$ 0 0
$$505$$ −13401.4 −1.18090
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 7260.14 + 12574.9i 0.632220 + 1.09504i 0.987097 + 0.160124i $$0.0511896\pi$$
−0.354877 + 0.934913i $$0.615477\pi$$
$$510$$ 0 0
$$511$$ 5000.54 8661.18i 0.432898 0.749801i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 11471.7 19869.5i 0.981558 1.70011i
$$516$$ 0 0
$$517$$ 11362.5 + 19680.4i 0.966581 + 1.67417i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 3372.49 0.283592 0.141796 0.989896i $$-0.454712\pi$$
0.141796 + 0.989896i $$0.454712\pi$$
$$522$$ 0 0
$$523$$ 4339.40 0.362808 0.181404 0.983409i $$-0.441936\pi$$
0.181404 + 0.983409i $$0.441936\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −285.232 494.036i −0.0235766 0.0408359i
$$528$$ 0 0
$$529$$ −2173.23 + 3764.15i −0.178617 + 0.309373i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 674.906 1168.97i 0.0548469 0.0949977i
$$534$$ 0 0
$$535$$ 6720.82 + 11640.8i 0.543115 + 0.940702i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −5347.32 −0.427320
$$540$$ 0 0
$$541$$ −3831.98 −0.304528 −0.152264 0.988340i $$-0.548656\pi$$
−0.152264 + 0.988340i $$0.548656\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −11520.7 19954.4i −0.905490 1.56835i
$$546$$ 0 0
$$547$$ −6701.34 + 11607.1i −0.523818 + 0.907280i 0.475797 + 0.879555i $$0.342160\pi$$
−0.999616 + 0.0277247i $$0.991174\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 1291.87 2237.59i 0.0998831 0.173003i
$$552$$ 0 0
$$553$$ 5242.52 + 9080.32i 0.403137 + 0.698254i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 14810.0 1.12661 0.563304 0.826249i $$-0.309530\pi$$
0.563304 + 0.826249i $$0.309530\pi$$
$$558$$ 0 0
$$559$$ 34627.7 2.62003
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 6116.61 + 10594.3i 0.457877 + 0.793066i 0.998849 0.0479751i $$-0.0152768\pi$$
−0.540972 + 0.841041i $$0.681943\pi$$
$$564$$ 0 0
$$565$$ 4187.80 7253.49i 0.311827 0.540100i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −4855.84 + 8410.56i −0.357763 + 0.619664i −0.987587 0.157074i $$-0.949794\pi$$
0.629823 + 0.776738i $$0.283127\pi$$
$$570$$ 0 0
$$571$$ −4264.81 7386.86i −0.312568 0.541384i 0.666349 0.745640i $$-0.267856\pi$$
−0.978918 + 0.204255i $$0.934523\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −6866.17 −0.497981
$$576$$ 0 0
$$577$$ 15314.0 1.10491 0.552453 0.833544i $$-0.313692\pi$$
0.552453 + 0.833544i $$0.313692\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 7828.44 + 13559.3i 0.558999 + 0.968215i
$$582$$ 0 0
$$583$$ −6436.38 + 11148.1i −0.457234 + 0.791953i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 9837.53 17039.1i 0.691717 1.19809i −0.279557 0.960129i $$-0.590188\pi$$
0.971275 0.237961i $$-0.0764790\pi$$
$$588$$ 0 0
$$589$$ −181.786 314.862i −0.0127171 0.0220266i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −15635.9 −1.08278 −0.541391 0.840771i $$-0.682102\pi$$
−0.541391 + 0.840771i $$0.682102\pi$$
$$594$$ 0 0
$$595$$ 11973.6 0.824994
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −242.594 420.186i −0.0165478 0.0286616i 0.857633 0.514262i $$-0.171934\pi$$
−0.874181 + 0.485601i $$0.838601\pi$$
$$600$$ 0 0
$$601$$ 7398.12 12813.9i 0.502123 0.869702i −0.497874 0.867249i $$-0.665886\pi$$
0.999997 0.00245282i $$-0.000780759\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −1307.29 + 2264.30i −0.0878496 + 0.152160i
$$606$$ 0 0
$$607$$ −1773.99 3072.64i −0.118623 0.205461i 0.800599 0.599200i $$-0.204515\pi$$
−0.919222 + 0.393739i $$0.871181\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 44660.3 2.95706
$$612$$ 0 0
$$613$$ 20450.9 1.34748 0.673740 0.738968i $$-0.264687\pi$$
0.673740 + 0.738968i $$0.264687\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −7652.60 13254.7i −0.499323 0.864853i 0.500677 0.865634i $$-0.333085\pi$$
−1.00000 0.000781625i $$0.999751\pi$$
$$618$$ 0 0
$$619$$ 2075.59 3595.03i 0.134774 0.233435i −0.790737 0.612156i $$-0.790302\pi$$
0.925511 + 0.378720i $$0.123636\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −2279.93 + 3948.96i −0.146619 + 0.253951i
$$624$$ 0 0
$$625$$ 9724.50 + 16843.3i 0.622368 + 1.07797i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −19947.1 −1.26446
$$630$$ 0 0
$$631$$ 25954.4 1.63745 0.818724 0.574187i $$-0.194682\pi$$
0.818724 + 0.574187i $$0.194682\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 13291.4 + 23021.3i 0.830632 + 1.43870i
$$636$$ 0 0
$$637$$ −5254.41 + 9100.91i −0.326825 + 0.566077i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 8630.66 14948.7i 0.531811 0.921123i −0.467500 0.883993i $$-0.654845\pi$$
0.999310 0.0371297i $$-0.0118215\pi$$
$$642$$ 0 0
$$643$$ −1430.18 2477.15i −0.0877152 0.151927i 0.818830 0.574036i $$-0.194623\pi$$
−0.906545 + 0.422109i $$0.861290\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −28384.9 −1.72477 −0.862384 0.506255i $$-0.831029\pi$$
−0.862384 + 0.506255i $$0.831029\pi$$
$$648$$ 0 0
$$649$$ −9450.04 −0.571566
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 5518.22 + 9557.84i 0.330696 + 0.572783i 0.982649 0.185477i $$-0.0593831\pi$$
−0.651952 + 0.758260i $$0.726050\pi$$
$$654$$ 0 0
$$655$$ −1044.68 + 1809.43i −0.0623190 + 0.107940i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 10647.5 18441.9i 0.629387 1.09013i −0.358288 0.933611i $$-0.616639\pi$$
0.987675 0.156519i $$-0.0500273\pi$$
$$660$$ 0 0
$$661$$ −6162.37 10673.5i −0.362615 0.628067i 0.625776 0.780003i $$-0.284783\pi$$
−0.988390 + 0.151936i $$0.951449\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 7631.11 0.444995
$$666$$ 0 0
$$667$$ −8344.58 −0.484413
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −9719.98 16835.5i −0.559219 0.968595i
$$672$$ 0 0
$$673$$ −1525.47 + 2642.19i −0.0873738 + 0.151336i −0.906400 0.422420i $$-0.861181\pi$$
0.819027 + 0.573756i $$0.194514\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 842.733 1459.66i 0.0478418 0.0828643i −0.841113 0.540860i $$-0.818099\pi$$
0.888955 + 0.457995i $$0.151432\pi$$
$$678$$ 0 0
$$679$$ −10665.4 18473.0i −0.602797 1.04408i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 34715.5 1.94488 0.972440 0.233155i $$-0.0749050\pi$$
0.972440 + 0.233155i $$0.0749050\pi$$
$$684$$ 0 0
$$685$$ −28309.4 −1.57905
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 12649.1 + 21908.9i 0.699408 + 1.21141i
$$690$$ 0 0
$$691$$ 4147.68 7184.00i 0.228343 0.395502i −0.728974 0.684542i $$-0.760002\pi$$
0.957317 + 0.289039i $$0.0933358\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 17944.7 31081.1i 0.979398 1.69637i
$$696$$ 0 0
$$697$$ 548.714 + 950.400i 0.0298192 + 0.0516484i
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −23420.5 −1.26188 −0.630942 0.775830i $$-0.717331\pi$$
−0.630942 + 0.775830i $$0.717331\pi$$
$$702$$ 0 0
$$703$$ −12712.8 −0.682037
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −7202.35 12474.8i −0.383129 0.663599i
$$708$$ 0 0
$$709$$ 2641.33 4574.92i 0.139912 0.242334i −0.787551 0.616249i $$-0.788651\pi$$
0.927463 + 0.373915i $$0.121985\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −587.104 + 1016.89i −0.0308376 + 0.0534123i
$$714$$ 0 0
$$715$$ 20039.5 + 34709.4i 1.04816 + 1.81547i
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −714.975 −0.0370849 −0.0185425 0.999828i $$-0.505903\pi$$
−0.0185425 + 0.999828i $$0.505903\pi$$
$$720$$ 0 0
$$721$$ 24660.9 1.27382
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −1734.81 3004.77i −0.0888677 0.153923i
$$726$$ 0 0
$$727$$ −12897.7 + 22339.5i −0.657979 + 1.13965i 0.323159 + 0.946345i $$0.395255\pi$$
−0.981138 + 0.193308i $$0.938078\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −14076.5 + 24381.3i −0.712230 + 1.23362i
$$732$$ 0 0
$$733$$ −1815.78 3145.02i −0.0914969 0.158477i 0.816644 0.577141i $$-0.195832\pi$$
−0.908141 + 0.418664i $$0.862498\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −22587.0 −1.12890
$$738$$ 0 0
$$739$$ −24758.3 −1.23241 −0.616203 0.787588i $$-0.711330\pi$$
−0.616203 + 0.787588i $$0.711330\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −4422.66 7660.28i −0.218374 0.378235i 0.735937 0.677050i $$-0.236742\pi$$
−0.954311 + 0.298815i $$0.903409\pi$$
$$744$$ 0 0
$$745$$ 10362.7 17948.8i 0.509612 0.882675i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −7223.96 + 12512.3i −0.352413 + 0.610398i
$$750$$ 0 0
$$751$$ −830.199 1437.95i −0.0403387 0.0698688i 0.845151 0.534527i $$-0.179510\pi$$
−0.885490 + 0.464659i $$0.846177\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −241.899 −0.0116604
$$756$$ 0 0
$$757$$ 19937.2 0.957239 0.478619 0.878022i $$-0.341137\pi$$
0.478619 + 0.878022i $$0.341137\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −4221.87 7312.50i −0.201107 0.348328i 0.747778 0.663949i $$-0.231121\pi$$
−0.948886 + 0.315620i $$0.897787\pi$$
$$762$$ 0 0
$$763$$ 12383.2 21448.3i 0.587550 1.01767i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −9285.84 + 16083.5i −0.437148 + 0.757162i
$$768$$ 0 0
$$769$$ −8553.93 14815.8i −0.401122 0.694763i 0.592740 0.805394i $$-0.298046\pi$$
−0.993862 + 0.110631i $$0.964713\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −9821.05 −0.456971 −0.228486 0.973547i $$-0.573377\pi$$
−0.228486 + 0.973547i $$0.573377\pi$$
$$774$$ 0 0
$$775$$ −488.226 −0.0226292
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 349.710 + 605.715i 0.0160843 + 0.0278588i
$$780$$ 0 0
$$781$$ 12912.3 22364.8i 0.591600 1.02468i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −24989.2 + 43282.6i −1.13618 + 1.96792i
$$786$$ 0 0
$$787$$ 2622.78 + 4542.80i 0.118796 + 0.205760i 0.919291 0.393579i $$-0.128763\pi$$
−0.800495 + 0.599339i $$0.795430\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 9002.62 0.404673
$$792$$ 0 0
$$793$$ −38204.4 −1.71082
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 4609.26 + 7983.47i 0.204854 + 0.354817i 0.950086 0.311988i $$-0.100995\pi$$
−0.745232 + 0.666805i $$0.767661\pi$$
$$798$$ 0 0
$$799$$ −18154.9 + 31445.2i −0.803848 + 1.39231i
$$800$$ 0 0
$$801$$ 0 0