# Properties

 Label 1620.2.i.m.1081.1 Level $1620$ Weight $2$ Character 1620.1081 Analytic conductor $12.936$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1620 = 2^{2} \cdot 3^{4} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1620.i (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$12.9357651274$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\zeta_{12})$$ Defining polynomial: $$x^{4} - x^{2} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$3$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 1081.1 Root $$0.866025 + 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 1620.1081 Dual form 1620.2.i.m.541.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 + 0.866025i) q^{5} +(-0.366025 - 0.633975i) q^{7} +O(q^{10})$$ $$q+(-0.500000 + 0.866025i) q^{5} +(-0.366025 - 0.633975i) q^{7} +(-0.866025 - 1.50000i) q^{11} +(0.732051 - 1.26795i) q^{13} +1.26795 q^{17} +2.46410 q^{19} +(-1.73205 + 3.00000i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-2.13397 - 3.69615i) q^{29} +(3.96410 - 6.86603i) q^{31} +0.732051 q^{35} +4.19615 q^{37} +(-0.401924 + 0.696152i) q^{41} +(-3.36603 - 5.83013i) q^{43} +(-2.36603 - 4.09808i) q^{47} +(3.23205 - 5.59808i) q^{49} +10.7321 q^{53} +1.73205 q^{55} +(-2.13397 + 3.69615i) q^{59} +(2.00000 + 3.46410i) q^{61} +(0.732051 + 1.26795i) q^{65} +(7.19615 - 12.4641i) q^{67} +0.803848 q^{71} +10.1962 q^{73} +(-0.633975 + 1.09808i) q^{77} +(-3.19615 - 5.53590i) q^{79} +(4.56218 + 7.90192i) q^{83} +(-0.633975 + 1.09808i) q^{85} +5.19615 q^{89} -1.07180 q^{91} +(-1.23205 + 2.13397i) q^{95} +(1.36603 + 2.36603i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q - 2q^{5} + 2q^{7} + O(q^{10})$$ $$4q - 2q^{5} + 2q^{7} - 4q^{13} + 12q^{17} - 4q^{19} - 2q^{25} - 12q^{29} + 2q^{31} - 4q^{35} - 4q^{37} - 12q^{41} - 10q^{43} - 6q^{47} + 6q^{49} + 36q^{53} - 12q^{59} + 8q^{61} - 4q^{65} + 8q^{67} + 24q^{71} + 20q^{73} - 6q^{77} + 8q^{79} - 6q^{83} - 6q^{85} - 32q^{91} + 2q^{95} + 2q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times$$.

 $$n$$ $$811$$ $$1297$$ $$1541$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$

## 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
$$5$$ −0.500000 + 0.866025i −0.223607 + 0.387298i
$$6$$ 0 0
$$7$$ −0.366025 0.633975i −0.138345 0.239620i 0.788526 0.615002i $$-0.210845\pi$$
−0.926870 + 0.375382i $$0.877511\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −0.866025 1.50000i −0.261116 0.452267i 0.705422 0.708787i $$-0.250757\pi$$
−0.966539 + 0.256520i $$0.917424\pi$$
$$12$$ 0 0
$$13$$ 0.732051 1.26795i 0.203034 0.351666i −0.746470 0.665419i $$-0.768253\pi$$
0.949505 + 0.313753i $$0.101586\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 1.26795 0.307523 0.153761 0.988108i $$-0.450861\pi$$
0.153761 + 0.988108i $$0.450861\pi$$
$$18$$ 0 0
$$19$$ 2.46410 0.565304 0.282652 0.959223i $$-0.408786\pi$$
0.282652 + 0.959223i $$0.408786\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −1.73205 + 3.00000i −0.361158 + 0.625543i −0.988152 0.153481i $$-0.950952\pi$$
0.626994 + 0.779024i $$0.284285\pi$$
$$24$$ 0 0
$$25$$ −0.500000 0.866025i −0.100000 0.173205i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −2.13397 3.69615i −0.396269 0.686358i 0.596993 0.802246i $$-0.296362\pi$$
−0.993262 + 0.115888i $$0.963029\pi$$
$$30$$ 0 0
$$31$$ 3.96410 6.86603i 0.711974 1.23317i −0.252142 0.967690i $$-0.581135\pi$$
0.964115 0.265484i $$-0.0855318\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0.732051 0.123739
$$36$$ 0 0
$$37$$ 4.19615 0.689843 0.344922 0.938631i $$-0.387905\pi$$
0.344922 + 0.938631i $$0.387905\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −0.401924 + 0.696152i −0.0627700 + 0.108721i −0.895703 0.444654i $$-0.853327\pi$$
0.832933 + 0.553374i $$0.186660\pi$$
$$42$$ 0 0
$$43$$ −3.36603 5.83013i −0.513314 0.889086i −0.999881 0.0154426i $$-0.995084\pi$$
0.486567 0.873643i $$-0.338249\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −2.36603 4.09808i −0.345120 0.597766i 0.640255 0.768162i $$-0.278829\pi$$
−0.985376 + 0.170396i $$0.945495\pi$$
$$48$$ 0 0
$$49$$ 3.23205 5.59808i 0.461722 0.799725i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 10.7321 1.47416 0.737080 0.675805i $$-0.236204\pi$$
0.737080 + 0.675805i $$0.236204\pi$$
$$54$$ 0 0
$$55$$ 1.73205 0.233550
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −2.13397 + 3.69615i −0.277820 + 0.481198i −0.970843 0.239718i $$-0.922945\pi$$
0.693023 + 0.720916i $$0.256278\pi$$
$$60$$ 0 0
$$61$$ 2.00000 + 3.46410i 0.256074 + 0.443533i 0.965187 0.261562i $$-0.0842377\pi$$
−0.709113 + 0.705095i $$0.750904\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 0.732051 + 1.26795i 0.0907997 + 0.157270i
$$66$$ 0 0
$$67$$ 7.19615 12.4641i 0.879150 1.52273i 0.0268747 0.999639i $$-0.491444\pi$$
0.852275 0.523094i $$-0.175222\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0.803848 0.0953992 0.0476996 0.998862i $$-0.484811\pi$$
0.0476996 + 0.998862i $$0.484811\pi$$
$$72$$ 0 0
$$73$$ 10.1962 1.19337 0.596685 0.802476i $$-0.296484\pi$$
0.596685 + 0.802476i $$0.296484\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −0.633975 + 1.09808i −0.0722481 + 0.125137i
$$78$$ 0 0
$$79$$ −3.19615 5.53590i −0.359595 0.622837i 0.628298 0.777973i $$-0.283752\pi$$
−0.987893 + 0.155136i $$0.950419\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 4.56218 + 7.90192i 0.500764 + 0.867349i 1.00000 0.000882500i $$0.000280909\pi$$
−0.499236 + 0.866466i $$0.666386\pi$$
$$84$$ 0 0
$$85$$ −0.633975 + 1.09808i −0.0687642 + 0.119103i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 5.19615 0.550791 0.275396 0.961331i $$-0.411191\pi$$
0.275396 + 0.961331i $$0.411191\pi$$
$$90$$ 0 0
$$91$$ −1.07180 −0.112355
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −1.23205 + 2.13397i −0.126406 + 0.218941i
$$96$$ 0 0
$$97$$ 1.36603 + 2.36603i 0.138699 + 0.240233i 0.927004 0.375051i $$-0.122375\pi$$
−0.788305 + 0.615284i $$0.789041\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −9.06218 15.6962i −0.901720 1.56183i −0.825260 0.564753i $$-0.808971\pi$$
−0.0764604 0.997073i $$-0.524362\pi$$
$$102$$ 0 0
$$103$$ 1.19615 2.07180i 0.117860 0.204140i −0.801059 0.598585i $$-0.795730\pi$$
0.918920 + 0.394445i $$0.129063\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 3.46410 0.334887 0.167444 0.985882i $$-0.446449\pi$$
0.167444 + 0.985882i $$0.446449\pi$$
$$108$$ 0 0
$$109$$ 5.92820 0.567819 0.283909 0.958851i $$-0.408368\pi$$
0.283909 + 0.958851i $$0.408368\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −8.83013 + 15.2942i −0.830668 + 1.43876i 0.0668404 + 0.997764i $$0.478708\pi$$
−0.897509 + 0.440996i $$0.854625\pi$$
$$114$$ 0 0
$$115$$ −1.73205 3.00000i −0.161515 0.279751i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −0.464102 0.803848i −0.0425441 0.0736886i
$$120$$ 0 0
$$121$$ 4.00000 6.92820i 0.363636 0.629837i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 1.00000 0.0894427
$$126$$ 0 0
$$127$$ −6.19615 −0.549820 −0.274910 0.961470i $$-0.588648\pi$$
−0.274910 + 0.961470i $$0.588648\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 6.86603 11.8923i 0.599887 1.03904i −0.392950 0.919560i $$-0.628545\pi$$
0.992837 0.119476i $$-0.0381213\pi$$
$$132$$ 0 0
$$133$$ −0.901924 1.56218i −0.0782067 0.135458i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −8.19615 14.1962i −0.700245 1.21286i −0.968380 0.249478i $$-0.919741\pi$$
0.268136 0.963381i $$-0.413592\pi$$
$$138$$ 0 0
$$139$$ 2.69615 4.66987i 0.228685 0.396093i −0.728734 0.684797i $$-0.759891\pi$$
0.957419 + 0.288704i $$0.0932242\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −2.53590 −0.212062
$$144$$ 0 0
$$145$$ 4.26795 0.354434
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$150$$ 0 0
$$151$$ −1.69615 2.93782i −0.138031 0.239077i 0.788720 0.614752i $$-0.210744\pi$$
−0.926751 + 0.375676i $$0.877411\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 3.96410 + 6.86603i 0.318404 + 0.551492i
$$156$$ 0 0
$$157$$ −3.36603 + 5.83013i −0.268638 + 0.465295i −0.968510 0.248973i $$-0.919907\pi$$
0.699872 + 0.714268i $$0.253240\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 2.53590 0.199857
$$162$$ 0 0
$$163$$ 15.2679 1.19588 0.597939 0.801542i $$-0.295986\pi$$
0.597939 + 0.801542i $$0.295986\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 1.56218 2.70577i 0.120885 0.209379i −0.799232 0.601023i $$-0.794760\pi$$
0.920117 + 0.391644i $$0.128093\pi$$
$$168$$ 0 0
$$169$$ 5.42820 + 9.40192i 0.417554 + 0.723225i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 12.1244 + 21.0000i 0.921798 + 1.59660i 0.796632 + 0.604465i $$0.206613\pi$$
0.125166 + 0.992136i $$0.460054\pi$$
$$174$$ 0 0
$$175$$ −0.366025 + 0.633975i −0.0276689 + 0.0479240i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −12.1244 −0.906217 −0.453108 0.891455i $$-0.649685\pi$$
−0.453108 + 0.891455i $$0.649685\pi$$
$$180$$ 0 0
$$181$$ −9.53590 −0.708798 −0.354399 0.935094i $$-0.615314\pi$$
−0.354399 + 0.935094i $$0.615314\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −2.09808 + 3.63397i −0.154254 + 0.267175i
$$186$$ 0 0
$$187$$ −1.09808 1.90192i −0.0802993 0.139082i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −9.52628 16.5000i −0.689297 1.19390i −0.972065 0.234710i $$-0.924586\pi$$
0.282768 0.959188i $$-0.408747\pi$$
$$192$$ 0 0
$$193$$ −10.2942 + 17.8301i −0.740995 + 1.28344i 0.211048 + 0.977476i $$0.432312\pi$$
−0.952043 + 0.305965i $$0.901021\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −13.8564 −0.987228 −0.493614 0.869681i $$-0.664324\pi$$
−0.493614 + 0.869681i $$0.664324\pi$$
$$198$$ 0 0
$$199$$ −11.8564 −0.840478 −0.420239 0.907413i $$-0.638054\pi$$
−0.420239 + 0.907413i $$0.638054\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −1.56218 + 2.70577i −0.109643 + 0.189908i
$$204$$ 0 0
$$205$$ −0.401924 0.696152i −0.0280716 0.0486214i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −2.13397 3.69615i −0.147610 0.255668i
$$210$$ 0 0
$$211$$ 3.03590 5.25833i 0.209000 0.361998i −0.742400 0.669957i $$-0.766313\pi$$
0.951400 + 0.307959i $$0.0996458\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 6.73205 0.459122
$$216$$ 0 0
$$217$$ −5.80385 −0.393991
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0.928203 1.60770i 0.0624377 0.108145i
$$222$$ 0 0
$$223$$ −10.9282 18.9282i −0.731807 1.26753i −0.956110 0.293007i $$-0.905344\pi$$
0.224304 0.974519i $$-0.427989\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 7.90192 + 13.6865i 0.524469 + 0.908407i 0.999594 + 0.0284888i $$0.00906950\pi$$
−0.475125 + 0.879918i $$0.657597\pi$$
$$228$$ 0 0
$$229$$ −4.92820 + 8.53590i −0.325665 + 0.564068i −0.981647 0.190709i $$-0.938921\pi$$
0.655982 + 0.754777i $$0.272255\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 6.58846 0.431624 0.215812 0.976435i $$-0.430760\pi$$
0.215812 + 0.976435i $$0.430760\pi$$
$$234$$ 0 0
$$235$$ 4.73205 0.308685
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 7.73205 13.3923i 0.500145 0.866276i −0.499855 0.866109i $$-0.666613\pi$$
1.00000 0.000167197i $$-5.32203e-5\pi$$
$$240$$ 0 0
$$241$$ 12.1603 + 21.0622i 0.783311 + 1.35673i 0.930003 + 0.367552i $$0.119804\pi$$
−0.146692 + 0.989182i $$0.546863\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 3.23205 + 5.59808i 0.206488 + 0.357648i
$$246$$ 0 0
$$247$$ 1.80385 3.12436i 0.114776 0.198798i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −27.4641 −1.73352 −0.866759 0.498727i $$-0.833801\pi$$
−0.866759 + 0.498727i $$0.833801\pi$$
$$252$$ 0 0
$$253$$ 6.00000 0.377217
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 4.26795 7.39230i 0.266227 0.461119i −0.701657 0.712515i $$-0.747556\pi$$
0.967884 + 0.251395i $$0.0808895\pi$$
$$258$$ 0 0
$$259$$ −1.53590 2.66025i −0.0954361 0.165300i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 12.1244 + 21.0000i 0.747620 + 1.29492i 0.948961 + 0.315394i $$0.102137\pi$$
−0.201341 + 0.979521i $$0.564530\pi$$
$$264$$ 0 0
$$265$$ −5.36603 + 9.29423i −0.329632 + 0.570940i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 19.7321 1.20308 0.601542 0.798841i $$-0.294553\pi$$
0.601542 + 0.798841i $$0.294553\pi$$
$$270$$ 0 0
$$271$$ −24.7846 −1.50556 −0.752779 0.658273i $$-0.771287\pi$$
−0.752779 + 0.658273i $$0.771287\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −0.866025 + 1.50000i −0.0522233 + 0.0904534i
$$276$$ 0 0
$$277$$ 9.56218 + 16.5622i 0.574536 + 0.995125i 0.996092 + 0.0883226i $$0.0281506\pi$$
−0.421556 + 0.906802i $$0.638516\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −2.66025 4.60770i −0.158697 0.274872i 0.775702 0.631100i $$-0.217396\pi$$
−0.934399 + 0.356228i $$0.884063\pi$$
$$282$$ 0 0
$$283$$ −11.7321 + 20.3205i −0.697398 + 1.20793i 0.271968 + 0.962306i $$0.412326\pi$$
−0.969366 + 0.245622i $$0.921008\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0.588457 0.0347355
$$288$$ 0 0
$$289$$ −15.3923 −0.905430
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −3.29423 + 5.70577i −0.192451 + 0.333335i −0.946062 0.323986i $$-0.894977\pi$$
0.753611 + 0.657321i $$0.228310\pi$$
$$294$$ 0 0
$$295$$ −2.13397 3.69615i −0.124245 0.215198i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 2.53590 + 4.39230i 0.146655 + 0.254014i
$$300$$ 0 0
$$301$$ −2.46410 + 4.26795i −0.142028 + 0.246001i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −4.00000 −0.229039
$$306$$ 0 0
$$307$$ −12.1962 −0.696071 −0.348036 0.937481i $$-0.613151\pi$$
−0.348036 + 0.937481i $$0.613151\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 14.2583 24.6962i 0.808516 1.40039i −0.105376 0.994432i $$-0.533605\pi$$
0.913892 0.405958i $$-0.133062\pi$$
$$312$$ 0 0
$$313$$ −0.535898 0.928203i −0.0302908 0.0524651i 0.850483 0.526003i $$-0.176310\pi$$
−0.880773 + 0.473538i $$0.842977\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −10.5622 18.2942i −0.593231 1.02751i −0.993794 0.111237i $$-0.964519\pi$$
0.400563 0.916269i $$-0.368815\pi$$
$$318$$ 0 0
$$319$$ −3.69615 + 6.40192i −0.206945 + 0.358439i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 3.12436 0.173844
$$324$$ 0 0
$$325$$ −1.46410 −0.0812137
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −1.73205 + 3.00000i −0.0954911 + 0.165395i
$$330$$ 0 0
$$331$$ 4.30385 + 7.45448i 0.236561 + 0.409735i 0.959725 0.280941i $$-0.0906464\pi$$
−0.723164 + 0.690676i $$0.757313\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 7.19615 + 12.4641i 0.393168 + 0.680987i
$$336$$ 0 0
$$337$$ −7.12436 + 12.3397i −0.388088 + 0.672189i −0.992192 0.124717i $$-0.960198\pi$$
0.604104 + 0.796905i $$0.293531\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −13.7321 −0.743632
$$342$$ 0 0
$$343$$ −9.85641 −0.532196
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 16.0981 27.8827i 0.864190 1.49682i −0.00365919 0.999993i $$-0.501165\pi$$
0.867849 0.496828i $$-0.165502\pi$$
$$348$$ 0 0
$$349$$ 12.5000 + 21.6506i 0.669110 + 1.15893i 0.978153 + 0.207884i $$0.0666577\pi$$
−0.309044 + 0.951048i $$0.600009\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 11.4904 + 19.9019i 0.611571 + 1.05927i 0.990976 + 0.134042i $$0.0427956\pi$$
−0.379404 + 0.925231i $$0.623871\pi$$
$$354$$ 0 0
$$355$$ −0.401924 + 0.696152i −0.0213319 + 0.0369479i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −26.6603 −1.40707 −0.703537 0.710658i $$-0.748397\pi$$
−0.703537 + 0.710658i $$0.748397\pi$$
$$360$$ 0 0
$$361$$ −12.9282 −0.680432
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −5.09808 + 8.83013i −0.266846 + 0.462190i
$$366$$ 0 0
$$367$$ 2.80385 + 4.85641i 0.146360 + 0.253502i 0.929879 0.367865i $$-0.119911\pi$$
−0.783520 + 0.621367i $$0.786578\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −3.92820 6.80385i −0.203942 0.353238i
$$372$$ 0 0
$$373$$ −12.0263 + 20.8301i −0.622697 + 1.07854i 0.366284 + 0.930503i $$0.380630\pi$$
−0.988981 + 0.148040i $$0.952704\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −6.24871 −0.321825
$$378$$ 0 0
$$379$$ 11.4641 0.588871 0.294436 0.955671i $$-0.404868\pi$$
0.294436 + 0.955671i $$0.404868\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −15.1244 + 26.1962i −0.772818 + 1.33856i 0.163194 + 0.986594i $$0.447820\pi$$
−0.936012 + 0.351967i $$0.885513\pi$$
$$384$$ 0 0
$$385$$ −0.633975 1.09808i −0.0323103 0.0559631i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 10.2679 + 17.7846i 0.520606 + 0.901716i 0.999713 + 0.0239591i $$0.00762716\pi$$
−0.479107 + 0.877756i $$0.659040\pi$$
$$390$$ 0 0
$$391$$ −2.19615 + 3.80385i −0.111064 + 0.192369i
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 6.39230 0.321632
$$396$$ 0 0
$$397$$ 2.67949 0.134480 0.0672399 0.997737i $$-0.478581\pi$$
0.0672399 + 0.997737i $$0.478581\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 13.3923 23.1962i 0.668780 1.15836i −0.309466 0.950911i $$-0.600150\pi$$
0.978246 0.207450i $$-0.0665164\pi$$
$$402$$ 0 0
$$403$$ −5.80385 10.0526i −0.289110 0.500754i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −3.63397 6.29423i −0.180129 0.311993i
$$408$$ 0 0
$$409$$ −4.92820 + 8.53590i −0.243684 + 0.422073i −0.961761 0.273891i $$-0.911689\pi$$
0.718077 + 0.695964i $$0.245023\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 3.12436 0.153739
$$414$$ 0 0
$$415$$ −9.12436 −0.447897
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 7.26795 12.5885i 0.355063 0.614986i −0.632066 0.774914i $$-0.717793\pi$$
0.987129 + 0.159928i $$0.0511262\pi$$
$$420$$ 0 0
$$421$$ 13.8923 + 24.0622i 0.677070 + 1.17272i 0.975859 + 0.218400i $$0.0700837\pi$$
−0.298790 + 0.954319i $$0.596583\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −0.633975 1.09808i −0.0307523 0.0532645i
$$426$$ 0 0
$$427$$ 1.46410 2.53590i 0.0708528 0.122721i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 2.41154 0.116160 0.0580800 0.998312i $$-0.481502\pi$$
0.0580800 + 0.998312i $$0.481502\pi$$
$$432$$ 0 0
$$433$$ 4.53590 0.217981 0.108991 0.994043i $$-0.465238\pi$$
0.108991 + 0.994043i $$0.465238\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −4.26795 + 7.39230i −0.204164 + 0.353622i
$$438$$ 0 0
$$439$$ −13.6962 23.7224i −0.653682 1.13221i −0.982223 0.187720i $$-0.939890\pi$$
0.328541 0.944490i $$-0.393443\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 20.3660 + 35.2750i 0.967619 + 1.67597i 0.702407 + 0.711775i $$0.252109\pi$$
0.265212 + 0.964190i $$0.414558\pi$$
$$444$$ 0 0
$$445$$ −2.59808 + 4.50000i −0.123161 + 0.213320i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 0.124356 0.00586871 0.00293435 0.999996i $$-0.499066\pi$$
0.00293435 + 0.999996i $$0.499066\pi$$
$$450$$ 0 0
$$451$$ 1.39230 0.0655611
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0.535898 0.928203i 0.0251233 0.0435148i
$$456$$ 0 0
$$457$$ −5.90192 10.2224i −0.276080 0.478185i 0.694327 0.719660i $$-0.255702\pi$$
−0.970407 + 0.241475i $$0.922369\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −10.7942 18.6962i −0.502737 0.870767i −0.999995 0.00316371i $$-0.998993\pi$$
0.497258 0.867603i $$-0.334340\pi$$
$$462$$ 0 0
$$463$$ −9.19615 + 15.9282i −0.427381 + 0.740246i −0.996640 0.0819125i $$-0.973897\pi$$
0.569258 + 0.822159i $$0.307231\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −15.8038 −0.731315 −0.365657 0.930750i $$-0.619156\pi$$
−0.365657 + 0.930750i $$0.619156\pi$$
$$468$$ 0 0
$$469$$ −10.5359 −0.486503
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −5.83013 + 10.0981i −0.268070 + 0.464310i
$$474$$ 0 0
$$475$$ −1.23205 2.13397i −0.0565304 0.0979135i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −10.3301 17.8923i −0.471996 0.817520i 0.527491 0.849561i $$-0.323133\pi$$
−0.999487 + 0.0320403i $$0.989800\pi$$
$$480$$ 0 0
$$481$$ 3.07180 5.32051i 0.140062 0.242594i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −2.73205 −0.124056
$$486$$ 0 0
$$487$$ −37.4641 −1.69766 −0.848830 0.528666i $$-0.822693\pi$$
−0.848830 + 0.528666i $$0.822693\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −3.86603 + 6.69615i −0.174471 + 0.302193i −0.939978 0.341235i $$-0.889155\pi$$
0.765507 + 0.643428i $$0.222488\pi$$
$$492$$ 0 0
$$493$$ −2.70577 4.68653i −0.121862 0.211071i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −0.294229 0.509619i −0.0131980 0.0228595i
$$498$$ 0 0
$$499$$ −3.30385 + 5.72243i −0.147901 + 0.256171i −0.930451 0.366416i $$-0.880585\pi$$
0.782551 + 0.622587i $$0.213918\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 0.679492 0.0302970 0.0151485 0.999885i $$-0.495178\pi$$
0.0151485 + 0.999885i $$0.495178\pi$$
$$504$$ 0 0
$$505$$ 18.1244 0.806523
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 7.39230 12.8038i 0.327658 0.567521i −0.654389 0.756158i $$-0.727074\pi$$
0.982047 + 0.188638i $$0.0604072\pi$$
$$510$$ 0 0
$$511$$ −3.73205 6.46410i −0.165096 0.285955i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 1.19615 + 2.07180i 0.0527088 + 0.0912943i
$$516$$ 0 0
$$517$$ −4.09808 + 7.09808i −0.180233 + 0.312173i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −10.3923 −0.455295 −0.227648 0.973744i $$-0.573103\pi$$
−0.227648 + 0.973744i $$0.573103\pi$$
$$522$$ 0 0
$$523$$ 24.3923 1.06660 0.533301 0.845926i $$-0.320952\pi$$
0.533301 + 0.845926i $$0.320952\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 5.02628 8.70577i 0.218948 0.379229i
$$528$$ 0 0
$$529$$ 5.50000 + 9.52628i 0.239130 + 0.414186i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0.588457 + 1.01924i 0.0254889 + 0.0441481i
$$534$$ 0 0
$$535$$ −1.73205 + 3.00000i −0.0748831 + 0.129701i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −11.1962 −0.482252
$$540$$ 0 0
$$541$$ −4.46410 −0.191927 −0.0959634 0.995385i $$-0.530593\pi$$
−0.0959634 + 0.995385i $$0.530593\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −2.96410 + 5.13397i −0.126968 + 0.219915i
$$546$$ 0 0
$$547$$ 18.3923 + 31.8564i 0.786398 + 1.36208i 0.928160 + 0.372181i $$0.121390\pi$$
−0.141762 + 0.989901i $$0.545277\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −5.25833 9.10770i −0.224012 0.388001i
$$552$$ 0 0
$$553$$ −2.33975 + 4.05256i −0.0994961 + 0.172332i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −16.3923 −0.694564 −0.347282 0.937761i $$-0.612895\pi$$
−0.347282 + 0.937761i $$0.612895\pi$$
$$558$$ 0 0
$$559$$ −9.85641 −0.416882
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 9.63397 16.6865i 0.406024 0.703254i −0.588416 0.808558i $$-0.700248\pi$$
0.994440 + 0.105305i $$0.0335817\pi$$
$$564$$ 0 0
$$565$$ −8.83013 15.2942i −0.371486 0.643433i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −2.47372 4.28461i −0.103704 0.179620i 0.809504 0.587114i $$-0.199736\pi$$
−0.913208 + 0.407494i $$0.866403\pi$$
$$570$$ 0 0
$$571$$ 13.4282 23.2583i 0.561953 0.973331i −0.435373 0.900250i $$-0.643384\pi$$
0.997326 0.0730808i $$-0.0232831\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 3.46410 0.144463
$$576$$ 0 0
$$577$$ 22.1962 0.924038 0.462019 0.886870i $$-0.347125\pi$$
0.462019 + 0.886870i $$0.347125\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 3.33975 5.78461i 0.138556 0.239986i
$$582$$ 0 0
$$583$$ −9.29423 16.0981i −0.384928 0.666714i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 7.09808 + 12.2942i 0.292969 + 0.507437i 0.974510 0.224342i $$-0.0720234\pi$$
−0.681541 + 0.731780i $$0.738690\pi$$
$$588$$ 0 0
$$589$$ 9.76795 16.9186i 0.402481 0.697118i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 36.9282 1.51646 0.758230 0.651987i $$-0.226065\pi$$
0.758230 + 0.651987i $$0.226065\pi$$
$$594$$ 0 0
$$595$$ 0.928203 0.0380526
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −22.7942 + 39.4808i −0.931347 + 1.61314i −0.150325 + 0.988637i $$0.548032\pi$$
−0.781022 + 0.624504i $$0.785301\pi$$
$$600$$ 0 0
$$601$$ −5.16025 8.93782i −0.210491 0.364581i 0.741377 0.671089i $$-0.234173\pi$$
−0.951868 + 0.306507i $$0.900840\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 4.00000 + 6.92820i 0.162623 + 0.281672i
$$606$$ 0 0
$$607$$ 14.2942 24.7583i 0.580185 1.00491i −0.415272 0.909697i $$-0.636314\pi$$
0.995457 0.0952124i $$-0.0303530\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −6.92820 −0.280285
$$612$$ 0 0
$$613$$ 3.60770 0.145713 0.0728567 0.997342i $$-0.476788\pi$$
0.0728567 + 0.997342i $$0.476788\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −6.00000 + 10.3923i −0.241551 + 0.418378i −0.961156 0.276005i $$-0.910989\pi$$
0.719605 + 0.694383i $$0.244323\pi$$
$$618$$ 0 0
$$619$$ 5.00000 + 8.66025i 0.200967 + 0.348085i 0.948840 0.315757i $$-0.102258\pi$$
−0.747873 + 0.663842i $$0.768925\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −1.90192 3.29423i −0.0761990 0.131980i
$$624$$ 0 0
$$625$$ −0.500000 + 0.866025i −0.0200000 + 0.0346410i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 5.32051 0.212143
$$630$$ 0 0
$$631$$ −13.9282 −0.554473 −0.277237 0.960802i $$-0.589419\pi$$
−0.277237 + 0.960802i $$0.589419\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 3.09808 5.36603i 0.122943 0.212944i
$$636$$ 0 0
$$637$$ −4.73205 8.19615i −0.187491 0.324743i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −11.5981 20.0885i −0.458096 0.793446i 0.540764 0.841174i $$-0.318135\pi$$
−0.998860 + 0.0477281i $$0.984802\pi$$
$$642$$ 0 0
$$643$$ 8.29423 14.3660i 0.327092 0.566541i −0.654841 0.755767i $$-0.727264\pi$$
0.981934 + 0.189226i $$0.0605978\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 48.2487 1.89685 0.948426 0.316998i $$-0.102675\pi$$
0.948426 + 0.316998i $$0.102675\pi$$
$$648$$ 0 0
$$649$$ 7.39230 0.290173
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −4.73205 + 8.19615i −0.185179 + 0.320740i −0.943637 0.330982i $$-0.892620\pi$$
0.758458 + 0.651722i $$0.225953\pi$$
$$654$$ 0 0
$$655$$ 6.86603 + 11.8923i 0.268278 + 0.464671i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −4.73205 8.19615i −0.184335 0.319277i 0.759018 0.651070i $$-0.225680\pi$$
−0.943352 + 0.331793i $$0.892346\pi$$
$$660$$ 0 0
$$661$$ 2.69615 4.66987i 0.104868 0.181637i −0.808816 0.588062i $$-0.799891\pi$$
0.913684 + 0.406425i $$0.133225\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 1.80385 0.0699502
$$666$$ 0 0
$$667$$ 14.7846 0.572462
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 3.46410 6.00000i 0.133730 0.231627i
$$672$$ 0 0
$$673$$ 8.80385 + 15.2487i 0.339363 + 0.587795i 0.984313 0.176430i $$-0.0564550\pi$$
−0.644950 + 0.764225i $$0.723122\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −14.3205 24.8038i −0.550382 0.953289i −0.998247 0.0591881i $$-0.981149\pi$$
0.447865 0.894101i $$-0.352185\pi$$
$$678$$ 0 0
$$679$$ 1.00000 1.73205i 0.0383765 0.0664700i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −14.5359 −0.556201 −0.278100 0.960552i $$-0.589705\pi$$
−0.278100 + 0.960552i $$0.589705\pi$$
$$684$$ 0 0
$$685$$ 16.3923 0.626318
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 7.85641 13.6077i 0.299305 0.518412i
$$690$$ 0 0
$$691$$ 5.00000 + 8.66025i 0.190209 + 0.329452i 0.945319 0.326146i $$-0.105750\pi$$
−0.755110 + 0.655598i $$0.772417\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 2.69615 + 4.66987i 0.102271 + 0.177138i
$$696$$ 0 0
$$697$$ −0.509619 + 0.882686i −0.0193032 + 0.0334341i
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 42.1244 1.59101 0.795507 0.605944i $$-0.207204\pi$$
0.795507 + 0.605944i $$0.207204\pi$$
$$702$$ 0 0
$$703$$ 10.3397 0.389971
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −6.63397 + 11.4904i −0.249496 + 0.432140i
$$708$$ 0 0
$$709$$ −8.73205 15.1244i −0.327939 0.568007i 0.654164 0.756353i $$-0.273021\pi$$
−0.982103 + 0.188346i $$0.939687\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 13.7321 + 23.7846i 0.514269 + 0.890741i
$$714$$ 0 0
$$715$$ 1.26795 2.19615i 0.0474186 0.0821314i
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 6.80385 0.253741 0.126870 0.991919i $$-0.459507\pi$$
0.126870 + 0.991919i $$0.459507\pi$$
$$720$$ 0 0
$$721$$ −1.75129 −0.0652214
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −2.13397 + 3.69615i −0.0792538 + 0.137272i
$$726$$ 0 0
$$727$$ −16.5885 28.7321i −0.615232 1.06561i −0.990344 0.138633i $$-0.955729\pi$$
0.375112 0.926980i $$-0.377604\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −4.26795 7.39230i −0.157856 0.273414i
$$732$$ 0 0
$$733$$ 19.7846 34.2679i 0.730761 1.26572i −0.225797 0.974174i $$-0.572499\pi$$
0.956558 0.291541i $$-0.0941680\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −24.9282 −0.918242
$$738$$ 0 0
$$739$$ 36.1769 1.33079 0.665395 0.746492i $$-0.268263\pi$$
0.665395 + 0.746492i $$0.268263\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −18.2942 + 31.6865i −0.671150 + 1.16247i 0.306428 + 0.951894i $$0.400866\pi$$
−0.977578 + 0.210572i $$0.932467\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −1.26795 2.19615i −0.0463299 0.0802457i
$$750$$ 0 0
$$751$$ 0.392305 0.679492i 0.0143154 0.0247950i −0.858779 0.512346i $$-0.828776\pi$$
0.873094 + 0.487551i $$0.162110\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 3.39230 0.123459
$$756$$ 0 0
$$757$$ 0.392305 0.0142586 0.00712928 0.999975i $$-0.497731\pi$$
0.00712928 + 0.999975i $$0.497731\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −2.93782 + 5.08846i −0.106496 + 0.184456i −0.914348 0.404928i $$-0.867296\pi$$
0.807852 + 0.589385i $$0.200630\pi$$
$$762$$ 0 0
$$763$$ −2.16987 3.75833i −0.0785547 0.136061i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 3.12436 + 5.41154i 0.112814 + 0.195399i
$$768$$ 0 0
$$769$$ 6.62436 11.4737i 0.238880 0.413753i −0.721513 0.692401i $$-0.756553\pi$$
0.960393 + 0.278648i $$0.0898863\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −0.339746 −0.0122198 −0.00610991 0.999981i $$-0.501945\pi$$
−0.00610991 + 0.999981i $$0.501945\pi$$
$$774$$ 0 0
$$775$$ −7.92820 −0.284789
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −0.990381 + 1.71539i −0.0354841 + 0.0614602i
$$780$$ 0 0
$$781$$ −0.696152 1.20577i −0.0249103 0.0431459i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −3.36603 5.83013i −0.120139 0.208086i
$$786$$ 0 0
$$787$$ 12.9019 22.3468i 0.459904 0.796577i −0.539051 0.842273i $$-0.681217\pi$$
0.998955 + 0.0456959i $$0.0145505\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 12.9282 0.459674
$$792$$ 0 0
$$793$$ 5.85641 0.207967
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −5.66025 + 9.80385i −0.200496 + 0.347270i −0.948688 0.316212i $$-0.897589\pi$$
0.748192 + 0.663482i $$0.230922\pi$$
$$798$$ 0 0
$$799$$ −3.00000 5.19615i −0.106132 0.183827i
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ −8.83013 15.2942i −0.311608 0.539722i
$$804$$