# Properties

 Label 1170.2.i.g.451.1 Level $1170$ Weight $2$ Character 1170.451 Analytic conductor $9.342$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1170.i (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$9.34249703649$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 390) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 451.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 1170.451 Dual form 1170.2.i.g.991.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(2.50000 + 4.33013i) q^{7} +1.00000 q^{8} +O(q^{10})$$ $$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(2.50000 + 4.33013i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} +(-1.50000 + 2.59808i) q^{11} +(-2.50000 + 2.59808i) q^{13} -5.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-4.00000 - 6.92820i) q^{17} +(2.50000 + 4.33013i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-1.50000 - 2.59808i) q^{22} +(-2.00000 + 3.46410i) q^{23} +1.00000 q^{25} +(-1.00000 - 3.46410i) q^{26} +(2.50000 - 4.33013i) q^{28} +(-2.00000 + 3.46410i) q^{29} -2.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +8.00000 q^{34} +(2.50000 + 4.33013i) q^{35} +(3.50000 - 6.06218i) q^{37} -5.00000 q^{38} +1.00000 q^{40} +(3.00000 - 5.19615i) q^{41} +(-3.00000 - 5.19615i) q^{43} +3.00000 q^{44} +(-2.00000 - 3.46410i) q^{46} +3.00000 q^{47} +(-9.00000 + 15.5885i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(3.50000 + 0.866025i) q^{52} -1.00000 q^{53} +(-1.50000 + 2.59808i) q^{55} +(2.50000 + 4.33013i) q^{56} +(-2.00000 - 3.46410i) q^{58} +(6.00000 + 10.3923i) q^{59} +(-1.00000 - 1.73205i) q^{61} +(1.00000 - 1.73205i) q^{62} +1.00000 q^{64} +(-2.50000 + 2.59808i) q^{65} +(-4.00000 + 6.92820i) q^{67} +(-4.00000 + 6.92820i) q^{68} -5.00000 q^{70} +(1.00000 + 1.73205i) q^{71} +(3.50000 + 6.06218i) q^{74} +(2.50000 - 4.33013i) q^{76} -15.0000 q^{77} -2.00000 q^{79} +(-0.500000 + 0.866025i) q^{80} +(3.00000 + 5.19615i) q^{82} -8.00000 q^{83} +(-4.00000 - 6.92820i) q^{85} +6.00000 q^{86} +(-1.50000 + 2.59808i) q^{88} +(-5.50000 + 9.52628i) q^{89} +(-17.5000 - 4.33013i) q^{91} +4.00000 q^{92} +(-1.50000 + 2.59808i) q^{94} +(2.50000 + 4.33013i) q^{95} +(-9.00000 - 15.5885i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - q^{2} - q^{4} + 2q^{5} + 5q^{7} + 2q^{8} + O(q^{10})$$ $$2q - q^{2} - q^{4} + 2q^{5} + 5q^{7} + 2q^{8} - q^{10} - 3q^{11} - 5q^{13} - 10q^{14} - q^{16} - 8q^{17} + 5q^{19} - q^{20} - 3q^{22} - 4q^{23} + 2q^{25} - 2q^{26} + 5q^{28} - 4q^{29} - 4q^{31} - q^{32} + 16q^{34} + 5q^{35} + 7q^{37} - 10q^{38} + 2q^{40} + 6q^{41} - 6q^{43} + 6q^{44} - 4q^{46} + 6q^{47} - 18q^{49} - q^{50} + 7q^{52} - 2q^{53} - 3q^{55} + 5q^{56} - 4q^{58} + 12q^{59} - 2q^{61} + 2q^{62} + 2q^{64} - 5q^{65} - 8q^{67} - 8q^{68} - 10q^{70} + 2q^{71} + 7q^{74} + 5q^{76} - 30q^{77} - 4q^{79} - q^{80} + 6q^{82} - 16q^{83} - 8q^{85} + 12q^{86} - 3q^{88} - 11q^{89} - 35q^{91} + 8q^{92} - 3q^{94} + 5q^{95} - 18q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$$.

 $$n$$ $$911$$ $$937$$ $$1081$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.500000 + 0.866025i −0.353553 + 0.612372i
$$3$$ 0 0
$$4$$ −0.500000 0.866025i −0.250000 0.433013i
$$5$$ 1.00000 0.447214
$$6$$ 0 0
$$7$$ 2.50000 + 4.33013i 0.944911 + 1.63663i 0.755929 + 0.654654i $$0.227186\pi$$
0.188982 + 0.981981i $$0.439481\pi$$
$$8$$ 1.00000 0.353553
$$9$$ 0 0
$$10$$ −0.500000 + 0.866025i −0.158114 + 0.273861i
$$11$$ −1.50000 + 2.59808i −0.452267 + 0.783349i −0.998526 0.0542666i $$-0.982718\pi$$
0.546259 + 0.837616i $$0.316051\pi$$
$$12$$ 0 0
$$13$$ −2.50000 + 2.59808i −0.693375 + 0.720577i
$$14$$ −5.00000 −1.33631
$$15$$ 0 0
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ −4.00000 6.92820i −0.970143 1.68034i −0.695113 0.718900i $$-0.744646\pi$$
−0.275029 0.961436i $$-0.588688\pi$$
$$18$$ 0 0
$$19$$ 2.50000 + 4.33013i 0.573539 + 0.993399i 0.996199 + 0.0871106i $$0.0277634\pi$$
−0.422659 + 0.906289i $$0.638903\pi$$
$$20$$ −0.500000 0.866025i −0.111803 0.193649i
$$21$$ 0 0
$$22$$ −1.50000 2.59808i −0.319801 0.553912i
$$23$$ −2.00000 + 3.46410i −0.417029 + 0.722315i −0.995639 0.0932891i $$-0.970262\pi$$
0.578610 + 0.815604i $$0.303595\pi$$
$$24$$ 0 0
$$25$$ 1.00000 0.200000
$$26$$ −1.00000 3.46410i −0.196116 0.679366i
$$27$$ 0 0
$$28$$ 2.50000 4.33013i 0.472456 0.818317i
$$29$$ −2.00000 + 3.46410i −0.371391 + 0.643268i −0.989780 0.142605i $$-0.954452\pi$$
0.618389 + 0.785872i $$0.287786\pi$$
$$30$$ 0 0
$$31$$ −2.00000 −0.359211 −0.179605 0.983739i $$-0.557482\pi$$
−0.179605 + 0.983739i $$0.557482\pi$$
$$32$$ −0.500000 0.866025i −0.0883883 0.153093i
$$33$$ 0 0
$$34$$ 8.00000 1.37199
$$35$$ 2.50000 + 4.33013i 0.422577 + 0.731925i
$$36$$ 0 0
$$37$$ 3.50000 6.06218i 0.575396 0.996616i −0.420602 0.907245i $$-0.638181\pi$$
0.995998 0.0893706i $$-0.0284856\pi$$
$$38$$ −5.00000 −0.811107
$$39$$ 0 0
$$40$$ 1.00000 0.158114
$$41$$ 3.00000 5.19615i 0.468521 0.811503i −0.530831 0.847477i $$-0.678120\pi$$
0.999353 + 0.0359748i $$0.0114536\pi$$
$$42$$ 0 0
$$43$$ −3.00000 5.19615i −0.457496 0.792406i 0.541332 0.840809i $$-0.317920\pi$$
−0.998828 + 0.0484030i $$0.984587\pi$$
$$44$$ 3.00000 0.452267
$$45$$ 0 0
$$46$$ −2.00000 3.46410i −0.294884 0.510754i
$$47$$ 3.00000 0.437595 0.218797 0.975770i $$-0.429787\pi$$
0.218797 + 0.975770i $$0.429787\pi$$
$$48$$ 0 0
$$49$$ −9.00000 + 15.5885i −1.28571 + 2.22692i
$$50$$ −0.500000 + 0.866025i −0.0707107 + 0.122474i
$$51$$ 0 0
$$52$$ 3.50000 + 0.866025i 0.485363 + 0.120096i
$$53$$ −1.00000 −0.137361 −0.0686803 0.997639i $$-0.521879\pi$$
−0.0686803 + 0.997639i $$0.521879\pi$$
$$54$$ 0 0
$$55$$ −1.50000 + 2.59808i −0.202260 + 0.350325i
$$56$$ 2.50000 + 4.33013i 0.334077 + 0.578638i
$$57$$ 0 0
$$58$$ −2.00000 3.46410i −0.262613 0.454859i
$$59$$ 6.00000 + 10.3923i 0.781133 + 1.35296i 0.931282 + 0.364299i $$0.118692\pi$$
−0.150148 + 0.988663i $$0.547975\pi$$
$$60$$ 0 0
$$61$$ −1.00000 1.73205i −0.128037 0.221766i 0.794879 0.606768i $$-0.207534\pi$$
−0.922916 + 0.385002i $$0.874201\pi$$
$$62$$ 1.00000 1.73205i 0.127000 0.219971i
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ −2.50000 + 2.59808i −0.310087 + 0.322252i
$$66$$ 0 0
$$67$$ −4.00000 + 6.92820i −0.488678 + 0.846415i −0.999915 0.0130248i $$-0.995854\pi$$
0.511237 + 0.859440i $$0.329187\pi$$
$$68$$ −4.00000 + 6.92820i −0.485071 + 0.840168i
$$69$$ 0 0
$$70$$ −5.00000 −0.597614
$$71$$ 1.00000 + 1.73205i 0.118678 + 0.205557i 0.919244 0.393688i $$-0.128801\pi$$
−0.800566 + 0.599245i $$0.795468\pi$$
$$72$$ 0 0
$$73$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$74$$ 3.50000 + 6.06218i 0.406867 + 0.704714i
$$75$$ 0 0
$$76$$ 2.50000 4.33013i 0.286770 0.496700i
$$77$$ −15.0000 −1.70941
$$78$$ 0 0
$$79$$ −2.00000 −0.225018 −0.112509 0.993651i $$-0.535889\pi$$
−0.112509 + 0.993651i $$0.535889\pi$$
$$80$$ −0.500000 + 0.866025i −0.0559017 + 0.0968246i
$$81$$ 0 0
$$82$$ 3.00000 + 5.19615i 0.331295 + 0.573819i
$$83$$ −8.00000 −0.878114 −0.439057 0.898459i $$-0.644687\pi$$
−0.439057 + 0.898459i $$0.644687\pi$$
$$84$$ 0 0
$$85$$ −4.00000 6.92820i −0.433861 0.751469i
$$86$$ 6.00000 0.646997
$$87$$ 0 0
$$88$$ −1.50000 + 2.59808i −0.159901 + 0.276956i
$$89$$ −5.50000 + 9.52628i −0.582999 + 1.00978i 0.412123 + 0.911128i $$0.364787\pi$$
−0.995122 + 0.0986553i $$0.968546\pi$$
$$90$$ 0 0
$$91$$ −17.5000 4.33013i −1.83450 0.453921i
$$92$$ 4.00000 0.417029
$$93$$ 0 0
$$94$$ −1.50000 + 2.59808i −0.154713 + 0.267971i
$$95$$ 2.50000 + 4.33013i 0.256495 + 0.444262i
$$96$$ 0 0
$$97$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$98$$ −9.00000 15.5885i −0.909137 1.57467i
$$99$$ 0 0
$$100$$ −0.500000 0.866025i −0.0500000 0.0866025i
$$101$$ −4.00000 + 6.92820i −0.398015 + 0.689382i −0.993481 0.113998i $$-0.963634\pi$$
0.595466 + 0.803380i $$0.296967\pi$$
$$102$$ 0 0
$$103$$ −7.00000 −0.689730 −0.344865 0.938652i $$-0.612075\pi$$
−0.344865 + 0.938652i $$0.612075\pi$$
$$104$$ −2.50000 + 2.59808i −0.245145 + 0.254762i
$$105$$ 0 0
$$106$$ 0.500000 0.866025i 0.0485643 0.0841158i
$$107$$ −3.00000 + 5.19615i −0.290021 + 0.502331i −0.973814 0.227345i $$-0.926996\pi$$
0.683793 + 0.729676i $$0.260329\pi$$
$$108$$ 0 0
$$109$$ 14.0000 1.34096 0.670478 0.741929i $$-0.266089\pi$$
0.670478 + 0.741929i $$0.266089\pi$$
$$110$$ −1.50000 2.59808i −0.143019 0.247717i
$$111$$ 0 0
$$112$$ −5.00000 −0.472456
$$113$$ 4.00000 + 6.92820i 0.376288 + 0.651751i 0.990519 0.137376i $$-0.0438669\pi$$
−0.614231 + 0.789127i $$0.710534\pi$$
$$114$$ 0 0
$$115$$ −2.00000 + 3.46410i −0.186501 + 0.323029i
$$116$$ 4.00000 0.371391
$$117$$ 0 0
$$118$$ −12.0000 −1.10469
$$119$$ 20.0000 34.6410i 1.83340 3.17554i
$$120$$ 0 0
$$121$$ 1.00000 + 1.73205i 0.0909091 + 0.157459i
$$122$$ 2.00000 0.181071
$$123$$ 0 0
$$124$$ 1.00000 + 1.73205i 0.0898027 + 0.155543i
$$125$$ 1.00000 0.0894427
$$126$$ 0 0
$$127$$ 10.5000 18.1865i 0.931724 1.61379i 0.151351 0.988480i $$-0.451638\pi$$
0.780373 0.625314i $$-0.215029\pi$$
$$128$$ −0.500000 + 0.866025i −0.0441942 + 0.0765466i
$$129$$ 0 0
$$130$$ −1.00000 3.46410i −0.0877058 0.303822i
$$131$$ 19.0000 1.66004 0.830019 0.557735i $$-0.188330\pi$$
0.830019 + 0.557735i $$0.188330\pi$$
$$132$$ 0 0
$$133$$ −12.5000 + 21.6506i −1.08389 + 1.87735i
$$134$$ −4.00000 6.92820i −0.345547 0.598506i
$$135$$ 0 0
$$136$$ −4.00000 6.92820i −0.342997 0.594089i
$$137$$ −6.00000 10.3923i −0.512615 0.887875i −0.999893 0.0146279i $$-0.995344\pi$$
0.487278 0.873247i $$-0.337990\pi$$
$$138$$ 0 0
$$139$$ −3.50000 6.06218i −0.296866 0.514187i 0.678551 0.734553i $$-0.262608\pi$$
−0.975417 + 0.220366i $$0.929275\pi$$
$$140$$ 2.50000 4.33013i 0.211289 0.365963i
$$141$$ 0 0
$$142$$ −2.00000 −0.167836
$$143$$ −3.00000 10.3923i −0.250873 0.869048i
$$144$$ 0 0
$$145$$ −2.00000 + 3.46410i −0.166091 + 0.287678i
$$146$$ 0 0
$$147$$ 0 0
$$148$$ −7.00000 −0.575396
$$149$$ −1.00000 1.73205i −0.0819232 0.141895i 0.822153 0.569267i $$-0.192773\pi$$
−0.904076 + 0.427372i $$0.859440\pi$$
$$150$$ 0 0
$$151$$ 22.0000 1.79033 0.895167 0.445730i $$-0.147056\pi$$
0.895167 + 0.445730i $$0.147056\pi$$
$$152$$ 2.50000 + 4.33013i 0.202777 + 0.351220i
$$153$$ 0 0
$$154$$ 7.50000 12.9904i 0.604367 1.04679i
$$155$$ −2.00000 −0.160644
$$156$$ 0 0
$$157$$ 15.0000 1.19713 0.598565 0.801074i $$-0.295738\pi$$
0.598565 + 0.801074i $$0.295738\pi$$
$$158$$ 1.00000 1.73205i 0.0795557 0.137795i
$$159$$ 0 0
$$160$$ −0.500000 0.866025i −0.0395285 0.0684653i
$$161$$ −20.0000 −1.57622
$$162$$ 0 0
$$163$$ 10.0000 + 17.3205i 0.783260 + 1.35665i 0.930033 + 0.367477i $$0.119778\pi$$
−0.146772 + 0.989170i $$0.546888\pi$$
$$164$$ −6.00000 −0.468521
$$165$$ 0 0
$$166$$ 4.00000 6.92820i 0.310460 0.537733i
$$167$$ −11.5000 + 19.9186i −0.889897 + 1.54135i −0.0499004 + 0.998754i $$0.515890\pi$$
−0.839996 + 0.542592i $$0.817443\pi$$
$$168$$ 0 0
$$169$$ −0.500000 12.9904i −0.0384615 0.999260i
$$170$$ 8.00000 0.613572
$$171$$ 0 0
$$172$$ −3.00000 + 5.19615i −0.228748 + 0.396203i
$$173$$ 2.50000 + 4.33013i 0.190071 + 0.329213i 0.945274 0.326278i $$-0.105795\pi$$
−0.755202 + 0.655492i $$0.772461\pi$$
$$174$$ 0 0
$$175$$ 2.50000 + 4.33013i 0.188982 + 0.327327i
$$176$$ −1.50000 2.59808i −0.113067 0.195837i
$$177$$ 0 0
$$178$$ −5.50000 9.52628i −0.412242 0.714025i
$$179$$ 2.00000 3.46410i 0.149487 0.258919i −0.781551 0.623841i $$-0.785571\pi$$
0.931038 + 0.364922i $$0.118904\pi$$
$$180$$ 0 0
$$181$$ −2.00000 −0.148659 −0.0743294 0.997234i $$-0.523682\pi$$
−0.0743294 + 0.997234i $$0.523682\pi$$
$$182$$ 12.5000 12.9904i 0.926562 0.962911i
$$183$$ 0 0
$$184$$ −2.00000 + 3.46410i −0.147442 + 0.255377i
$$185$$ 3.50000 6.06218i 0.257325 0.445700i
$$186$$ 0 0
$$187$$ 24.0000 1.75505
$$188$$ −1.50000 2.59808i −0.109399 0.189484i
$$189$$ 0 0
$$190$$ −5.00000 −0.362738
$$191$$ 1.00000 + 1.73205i 0.0723575 + 0.125327i 0.899934 0.436026i $$-0.143614\pi$$
−0.827577 + 0.561353i $$0.810281\pi$$
$$192$$ 0 0
$$193$$ −12.0000 + 20.7846i −0.863779 + 1.49611i 0.00447566 + 0.999990i $$0.498575\pi$$
−0.868255 + 0.496119i $$0.834758\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 18.0000 1.28571
$$197$$ 1.50000 2.59808i 0.106871 0.185105i −0.807630 0.589689i $$-0.799250\pi$$
0.914501 + 0.404584i $$0.132584\pi$$
$$198$$ 0 0
$$199$$ −11.0000 19.0526i −0.779769 1.35060i −0.932075 0.362267i $$-0.882003\pi$$
0.152305 0.988334i $$-0.451330\pi$$
$$200$$ 1.00000 0.0707107
$$201$$ 0 0
$$202$$ −4.00000 6.92820i −0.281439 0.487467i
$$203$$ −20.0000 −1.40372
$$204$$ 0 0
$$205$$ 3.00000 5.19615i 0.209529 0.362915i
$$206$$ 3.50000 6.06218i 0.243857 0.422372i
$$207$$ 0 0
$$208$$ −1.00000 3.46410i −0.0693375 0.240192i
$$209$$ −15.0000 −1.03757
$$210$$ 0 0
$$211$$ 7.50000 12.9904i 0.516321 0.894295i −0.483499 0.875345i $$-0.660634\pi$$
0.999820 0.0189499i $$-0.00603229\pi$$
$$212$$ 0.500000 + 0.866025i 0.0343401 + 0.0594789i
$$213$$ 0 0
$$214$$ −3.00000 5.19615i −0.205076 0.355202i
$$215$$ −3.00000 5.19615i −0.204598 0.354375i
$$216$$ 0 0
$$217$$ −5.00000 8.66025i −0.339422 0.587896i
$$218$$ −7.00000 + 12.1244i −0.474100 + 0.821165i
$$219$$ 0 0
$$220$$ 3.00000 0.202260
$$221$$ 28.0000 + 6.92820i 1.88348 + 0.466041i
$$222$$ 0 0
$$223$$ 1.50000 2.59808i 0.100447 0.173980i −0.811422 0.584461i $$-0.801306\pi$$
0.911869 + 0.410481i $$0.134639\pi$$
$$224$$ 2.50000 4.33013i 0.167038 0.289319i
$$225$$ 0 0
$$226$$ −8.00000 −0.532152
$$227$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$228$$ 0 0
$$229$$ 14.0000 0.925146 0.462573 0.886581i $$-0.346926\pi$$
0.462573 + 0.886581i $$0.346926\pi$$
$$230$$ −2.00000 3.46410i −0.131876 0.228416i
$$231$$ 0 0
$$232$$ −2.00000 + 3.46410i −0.131306 + 0.227429i
$$233$$ 14.0000 0.917170 0.458585 0.888650i $$-0.348356\pi$$
0.458585 + 0.888650i $$0.348356\pi$$
$$234$$ 0 0
$$235$$ 3.00000 0.195698
$$236$$ 6.00000 10.3923i 0.390567 0.676481i
$$237$$ 0 0
$$238$$ 20.0000 + 34.6410i 1.29641 + 2.24544i
$$239$$ 18.0000 1.16432 0.582162 0.813073i $$-0.302207\pi$$
0.582162 + 0.813073i $$0.302207\pi$$
$$240$$ 0 0
$$241$$ 12.5000 + 21.6506i 0.805196 + 1.39464i 0.916159 + 0.400815i $$0.131273\pi$$
−0.110963 + 0.993825i $$0.535394\pi$$
$$242$$ −2.00000 −0.128565
$$243$$ 0 0
$$244$$ −1.00000 + 1.73205i −0.0640184 + 0.110883i
$$245$$ −9.00000 + 15.5885i −0.574989 + 0.995910i
$$246$$ 0 0
$$247$$ −17.5000 4.33013i −1.11350 0.275519i
$$248$$ −2.00000 −0.127000
$$249$$ 0 0
$$250$$ −0.500000 + 0.866025i −0.0316228 + 0.0547723i
$$251$$ 7.50000 + 12.9904i 0.473396 + 0.819946i 0.999536 0.0304521i $$-0.00969471\pi$$
−0.526140 + 0.850398i $$0.676361\pi$$
$$252$$ 0 0
$$253$$ −6.00000 10.3923i −0.377217 0.653359i
$$254$$ 10.5000 + 18.1865i 0.658829 + 1.14112i
$$255$$ 0 0
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ 14.0000 24.2487i 0.873296 1.51259i 0.0147291 0.999892i $$-0.495311\pi$$
0.858567 0.512702i $$-0.171355\pi$$
$$258$$ 0 0
$$259$$ 35.0000 2.17479
$$260$$ 3.50000 + 0.866025i 0.217061 + 0.0537086i
$$261$$ 0 0
$$262$$ −9.50000 + 16.4545i −0.586912 + 1.01656i
$$263$$ −7.50000 + 12.9904i −0.462470 + 0.801021i −0.999083 0.0428069i $$-0.986370\pi$$
0.536614 + 0.843828i $$0.319703\pi$$
$$264$$ 0 0
$$265$$ −1.00000 −0.0614295
$$266$$ −12.5000 21.6506i −0.766424 1.32749i
$$267$$ 0 0
$$268$$ 8.00000 0.488678
$$269$$ 2.00000 + 3.46410i 0.121942 + 0.211210i 0.920534 0.390664i $$-0.127754\pi$$
−0.798591 + 0.601874i $$0.794421\pi$$
$$270$$ 0 0
$$271$$ −2.00000 + 3.46410i −0.121491 + 0.210429i −0.920356 0.391082i $$-0.872101\pi$$
0.798865 + 0.601511i $$0.205434\pi$$
$$272$$ 8.00000 0.485071
$$273$$ 0 0
$$274$$ 12.0000 0.724947
$$275$$ −1.50000 + 2.59808i −0.0904534 + 0.156670i
$$276$$ 0 0
$$277$$ 7.50000 + 12.9904i 0.450631 + 0.780516i 0.998425 0.0560969i $$-0.0178656\pi$$
−0.547794 + 0.836613i $$0.684532\pi$$
$$278$$ 7.00000 0.419832
$$279$$ 0 0
$$280$$ 2.50000 + 4.33013i 0.149404 + 0.258775i
$$281$$ −18.0000 −1.07379 −0.536895 0.843649i $$-0.680403\pi$$
−0.536895 + 0.843649i $$0.680403\pi$$
$$282$$ 0 0
$$283$$ 5.00000 8.66025i 0.297219 0.514799i −0.678280 0.734804i $$-0.737274\pi$$
0.975499 + 0.220005i $$0.0706075\pi$$
$$284$$ 1.00000 1.73205i 0.0593391 0.102778i
$$285$$ 0 0
$$286$$ 10.5000 + 2.59808i 0.620878 + 0.153627i
$$287$$ 30.0000 1.77084
$$288$$ 0 0
$$289$$ −23.5000 + 40.7032i −1.38235 + 2.39431i
$$290$$ −2.00000 3.46410i −0.117444 0.203419i
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −4.50000 7.79423i −0.262893 0.455344i 0.704117 0.710084i $$-0.251343\pi$$
−0.967009 + 0.254741i $$0.918010\pi$$
$$294$$ 0 0
$$295$$ 6.00000 + 10.3923i 0.349334 + 0.605063i
$$296$$ 3.50000 6.06218i 0.203433 0.352357i
$$297$$ 0 0
$$298$$ 2.00000 0.115857
$$299$$ −4.00000 13.8564i −0.231326 0.801337i
$$300$$ 0 0
$$301$$ 15.0000 25.9808i 0.864586 1.49751i
$$302$$ −11.0000 + 19.0526i −0.632979 + 1.09635i
$$303$$ 0 0
$$304$$ −5.00000 −0.286770
$$305$$ −1.00000 1.73205i −0.0572598 0.0991769i
$$306$$ 0 0
$$307$$ −6.00000 −0.342438 −0.171219 0.985233i $$-0.554771\pi$$
−0.171219 + 0.985233i $$0.554771\pi$$
$$308$$ 7.50000 + 12.9904i 0.427352 + 0.740196i
$$309$$ 0 0
$$310$$ 1.00000 1.73205i 0.0567962 0.0983739i
$$311$$ 12.0000 0.680458 0.340229 0.940343i $$-0.389495\pi$$
0.340229 + 0.940343i $$0.389495\pi$$
$$312$$ 0 0
$$313$$ −6.00000 −0.339140 −0.169570 0.985518i $$-0.554238\pi$$
−0.169570 + 0.985518i $$0.554238\pi$$
$$314$$ −7.50000 + 12.9904i −0.423249 + 0.733090i
$$315$$ 0 0
$$316$$ 1.00000 + 1.73205i 0.0562544 + 0.0974355i
$$317$$ 23.0000 1.29181 0.645904 0.763418i $$-0.276480\pi$$
0.645904 + 0.763418i $$0.276480\pi$$
$$318$$ 0 0
$$319$$ −6.00000 10.3923i −0.335936 0.581857i
$$320$$ 1.00000 0.0559017
$$321$$ 0 0
$$322$$ 10.0000 17.3205i 0.557278 0.965234i
$$323$$ 20.0000 34.6410i 1.11283 1.92748i
$$324$$ 0 0
$$325$$ −2.50000 + 2.59808i −0.138675 + 0.144115i
$$326$$ −20.0000 −1.10770
$$327$$ 0 0
$$328$$ 3.00000 5.19615i 0.165647 0.286910i
$$329$$ 7.50000 + 12.9904i 0.413488 + 0.716183i
$$330$$ 0 0
$$331$$ −2.00000 3.46410i −0.109930 0.190404i 0.805812 0.592172i $$-0.201729\pi$$
−0.915742 + 0.401768i $$0.868396\pi$$
$$332$$ 4.00000 + 6.92820i 0.219529 + 0.380235i
$$333$$ 0 0
$$334$$ −11.5000 19.9186i −0.629252 1.08990i
$$335$$ −4.00000 + 6.92820i −0.218543 + 0.378528i
$$336$$ 0 0
$$337$$ 14.0000 0.762629 0.381314 0.924445i $$-0.375472\pi$$
0.381314 + 0.924445i $$0.375472\pi$$
$$338$$ 11.5000 + 6.06218i 0.625518 + 0.329739i
$$339$$ 0 0
$$340$$ −4.00000 + 6.92820i −0.216930 + 0.375735i
$$341$$ 3.00000 5.19615i 0.162459 0.281387i
$$342$$ 0 0
$$343$$ −55.0000 −2.96972
$$344$$ −3.00000 5.19615i −0.161749 0.280158i
$$345$$ 0 0
$$346$$ −5.00000 −0.268802
$$347$$ −8.00000 13.8564i −0.429463 0.743851i 0.567363 0.823468i $$-0.307964\pi$$
−0.996826 + 0.0796169i $$0.974630\pi$$
$$348$$ 0 0
$$349$$ −4.00000 + 6.92820i −0.214115 + 0.370858i −0.952998 0.302975i $$-0.902020\pi$$
0.738883 + 0.673833i $$0.235353\pi$$
$$350$$ −5.00000 −0.267261
$$351$$ 0 0
$$352$$ 3.00000 0.159901
$$353$$ 8.00000 13.8564i 0.425797 0.737502i −0.570697 0.821160i $$-0.693327\pi$$
0.996495 + 0.0836583i $$0.0266604\pi$$
$$354$$ 0 0
$$355$$ 1.00000 + 1.73205i 0.0530745 + 0.0919277i
$$356$$ 11.0000 0.582999
$$357$$ 0 0
$$358$$ 2.00000 + 3.46410i 0.105703 + 0.183083i
$$359$$ 18.0000 0.950004 0.475002 0.879985i $$-0.342447\pi$$
0.475002 + 0.879985i $$0.342447\pi$$
$$360$$ 0 0
$$361$$ −3.00000 + 5.19615i −0.157895 + 0.273482i
$$362$$ 1.00000 1.73205i 0.0525588 0.0910346i
$$363$$ 0 0
$$364$$ 5.00000 + 17.3205i 0.262071 + 0.907841i
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 4.00000 6.92820i 0.208798 0.361649i −0.742538 0.669804i $$-0.766378\pi$$
0.951336 + 0.308155i $$0.0997115\pi$$
$$368$$ −2.00000 3.46410i −0.104257 0.180579i
$$369$$ 0 0
$$370$$ 3.50000 + 6.06218i 0.181956 + 0.315158i
$$371$$ −2.50000 4.33013i −0.129794 0.224809i
$$372$$ 0 0
$$373$$ −19.0000 32.9090i −0.983783 1.70396i −0.647225 0.762299i $$-0.724071\pi$$
−0.336557 0.941663i $$-0.609263\pi$$
$$374$$ −12.0000 + 20.7846i −0.620505 + 1.07475i
$$375$$ 0 0
$$376$$ 3.00000 0.154713
$$377$$ −4.00000 13.8564i −0.206010 0.713641i
$$378$$ 0 0
$$379$$ 12.5000 21.6506i 0.642082 1.11212i −0.342885 0.939377i $$-0.611404\pi$$
0.984967 0.172741i $$-0.0552624\pi$$
$$380$$ 2.50000 4.33013i 0.128247 0.222131i
$$381$$ 0 0
$$382$$ −2.00000 −0.102329
$$383$$ −14.0000 24.2487i −0.715367 1.23905i −0.962818 0.270151i $$-0.912926\pi$$
0.247451 0.968900i $$-0.420407\pi$$
$$384$$ 0 0
$$385$$ −15.0000 −0.764471
$$386$$ −12.0000 20.7846i −0.610784 1.05791i
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 32.0000 1.62246 0.811232 0.584724i $$-0.198797\pi$$
0.811232 + 0.584724i $$0.198797\pi$$
$$390$$ 0 0
$$391$$ 32.0000 1.61831
$$392$$ −9.00000 + 15.5885i −0.454569 + 0.787336i
$$393$$ 0 0
$$394$$ 1.50000 + 2.59808i 0.0755689 + 0.130889i
$$395$$ −2.00000 −0.100631
$$396$$ 0 0
$$397$$ −12.5000 21.6506i −0.627357 1.08661i −0.988080 0.153941i $$-0.950803\pi$$
0.360723 0.932673i $$-0.382530\pi$$
$$398$$ 22.0000 1.10276
$$399$$ 0 0
$$400$$ −0.500000 + 0.866025i −0.0250000 + 0.0433013i
$$401$$ −9.50000 + 16.4545i −0.474407 + 0.821698i −0.999571 0.0293039i $$-0.990671\pi$$
0.525163 + 0.851002i $$0.324004\pi$$
$$402$$ 0 0
$$403$$ 5.00000 5.19615i 0.249068 0.258839i
$$404$$ 8.00000 0.398015
$$405$$ 0 0
$$406$$ 10.0000 17.3205i 0.496292 0.859602i
$$407$$ 10.5000 + 18.1865i 0.520466 + 0.901473i
$$408$$ 0 0
$$409$$ −12.5000 21.6506i −0.618085 1.07056i −0.989835 0.142222i $$-0.954575\pi$$
0.371750 0.928333i $$-0.378758\pi$$
$$410$$ 3.00000 + 5.19615i 0.148159 + 0.256620i
$$411$$ 0 0
$$412$$ 3.50000 + 6.06218i 0.172433 + 0.298662i
$$413$$ −30.0000 + 51.9615i −1.47620 + 2.55686i
$$414$$ 0 0
$$415$$ −8.00000 −0.392705
$$416$$ 3.50000 + 0.866025i 0.171602 + 0.0424604i
$$417$$ 0 0
$$418$$ 7.50000 12.9904i 0.366837 0.635380i
$$419$$ −6.00000 + 10.3923i −0.293119 + 0.507697i −0.974546 0.224189i $$-0.928027\pi$$
0.681426 + 0.731887i $$0.261360\pi$$
$$420$$ 0 0
$$421$$ 12.0000 0.584844 0.292422 0.956289i $$-0.405539\pi$$
0.292422 + 0.956289i $$0.405539\pi$$
$$422$$ 7.50000 + 12.9904i 0.365094 + 0.632362i
$$423$$ 0 0
$$424$$ −1.00000 −0.0485643
$$425$$ −4.00000 6.92820i −0.194029 0.336067i
$$426$$ 0 0
$$427$$ 5.00000 8.66025i 0.241967 0.419099i
$$428$$ 6.00000 0.290021
$$429$$ 0 0
$$430$$ 6.00000 0.289346
$$431$$ 6.00000 10.3923i 0.289010 0.500580i −0.684564 0.728953i $$-0.740007\pi$$
0.973574 + 0.228373i $$0.0733406\pi$$
$$432$$ 0 0
$$433$$ −8.00000 13.8564i −0.384455 0.665896i 0.607238 0.794520i $$-0.292277\pi$$
−0.991693 + 0.128624i $$0.958944\pi$$
$$434$$ 10.0000 0.480015
$$435$$ 0 0
$$436$$ −7.00000 12.1244i −0.335239 0.580651i
$$437$$ −20.0000 −0.956730
$$438$$ 0 0
$$439$$ −5.00000 + 8.66025i −0.238637 + 0.413331i −0.960323 0.278889i $$-0.910034\pi$$
0.721686 + 0.692220i $$0.243367\pi$$
$$440$$ −1.50000 + 2.59808i −0.0715097 + 0.123858i
$$441$$ 0 0
$$442$$ −20.0000 + 20.7846i −0.951303 + 0.988623i
$$443$$ −6.00000 −0.285069 −0.142534 0.989790i $$-0.545525\pi$$
−0.142534 + 0.989790i $$0.545525\pi$$
$$444$$ 0 0
$$445$$ −5.50000 + 9.52628i −0.260725 + 0.451589i
$$446$$ 1.50000 + 2.59808i 0.0710271 + 0.123022i
$$447$$ 0 0
$$448$$ 2.50000 + 4.33013i 0.118114 + 0.204579i
$$449$$ −13.5000 23.3827i −0.637104 1.10350i −0.986065 0.166360i $$-0.946799\pi$$
0.348961 0.937137i $$-0.386535\pi$$
$$450$$ 0 0
$$451$$ 9.00000 + 15.5885i 0.423793 + 0.734032i
$$452$$ 4.00000 6.92820i 0.188144 0.325875i
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −17.5000 4.33013i −0.820413 0.202999i
$$456$$ 0 0
$$457$$ −15.0000 + 25.9808i −0.701670 + 1.21533i 0.266209 + 0.963915i $$0.414229\pi$$
−0.967880 + 0.251414i $$0.919105\pi$$
$$458$$ −7.00000 + 12.1244i −0.327089 + 0.566534i
$$459$$ 0 0
$$460$$ 4.00000 0.186501
$$461$$ 4.00000 + 6.92820i 0.186299 + 0.322679i 0.944013 0.329907i $$-0.107017\pi$$
−0.757715 + 0.652586i $$0.773684\pi$$
$$462$$ 0 0
$$463$$ 8.00000 0.371792 0.185896 0.982569i $$-0.440481\pi$$
0.185896 + 0.982569i $$0.440481\pi$$
$$464$$ −2.00000 3.46410i −0.0928477 0.160817i
$$465$$ 0 0
$$466$$ −7.00000 + 12.1244i −0.324269 + 0.561650i
$$467$$ 24.0000 1.11059 0.555294 0.831654i $$-0.312606\pi$$
0.555294 + 0.831654i $$0.312606\pi$$
$$468$$ 0 0
$$469$$ −40.0000 −1.84703
$$470$$ −1.50000 + 2.59808i −0.0691898 + 0.119840i
$$471$$ 0 0
$$472$$ 6.00000 + 10.3923i 0.276172 + 0.478345i
$$473$$ 18.0000 0.827641
$$474$$ 0 0
$$475$$ 2.50000 + 4.33013i 0.114708 + 0.198680i
$$476$$ −40.0000 −1.83340
$$477$$ 0 0
$$478$$ −9.00000 + 15.5885i −0.411650 + 0.712999i
$$479$$ −14.0000 + 24.2487i −0.639676 + 1.10795i 0.345827 + 0.938298i $$0.387598\pi$$
−0.985504 + 0.169654i $$0.945735\pi$$
$$480$$ 0 0
$$481$$ 7.00000 + 24.2487i 0.319173 + 1.10565i
$$482$$ −25.0000 −1.13872
$$483$$ 0 0
$$484$$ 1.00000 1.73205i 0.0454545 0.0787296i
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −18.5000 32.0429i −0.838315 1.45200i −0.891303 0.453409i $$-0.850208\pi$$
0.0529875 0.998595i $$-0.483126\pi$$
$$488$$ −1.00000 1.73205i −0.0452679 0.0784063i
$$489$$ 0 0
$$490$$ −9.00000 15.5885i −0.406579 0.704215i
$$491$$ 10.5000 18.1865i 0.473858 0.820747i −0.525694 0.850674i $$-0.676194\pi$$
0.999552 + 0.0299272i $$0.00952753\pi$$
$$492$$ 0 0
$$493$$ 32.0000 1.44121
$$494$$ 12.5000 12.9904i 0.562402 0.584465i
$$495$$ 0 0
$$496$$ 1.00000 1.73205i 0.0449013 0.0777714i
$$497$$ −5.00000 + 8.66025i −0.224281 + 0.388465i
$$498$$ 0 0
$$499$$ 4.00000 0.179065 0.0895323 0.995984i $$-0.471463\pi$$
0.0895323 + 0.995984i $$0.471463\pi$$
$$500$$ −0.500000 0.866025i −0.0223607 0.0387298i
$$501$$ 0 0
$$502$$ −15.0000 −0.669483
$$503$$ −5.50000 9.52628i −0.245233 0.424756i 0.716964 0.697110i $$-0.245531\pi$$
−0.962197 + 0.272354i $$0.912198\pi$$
$$504$$ 0 0
$$505$$ −4.00000 + 6.92820i −0.177998 + 0.308301i
$$506$$ 12.0000 0.533465
$$507$$ 0 0
$$508$$ −21.0000 −0.931724
$$509$$ 5.00000 8.66025i 0.221621 0.383859i −0.733679 0.679496i $$-0.762199\pi$$
0.955300 + 0.295637i $$0.0955319\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 1.00000 0.0441942
$$513$$ 0 0
$$514$$ 14.0000 + 24.2487i 0.617514 + 1.06956i
$$515$$ −7.00000 −0.308457
$$516$$ 0 0
$$517$$ −4.50000 + 7.79423i −0.197910 + 0.342790i
$$518$$ −17.5000 + 30.3109i −0.768906 + 1.33178i
$$519$$ 0 0
$$520$$ −2.50000 + 2.59808i −0.109632 + 0.113933i
$$521$$ −5.00000 −0.219054 −0.109527 0.993984i $$-0.534934\pi$$
−0.109527 + 0.993984i $$0.534934\pi$$
$$522$$ 0 0
$$523$$ 5.00000 8.66025i 0.218635 0.378686i −0.735756 0.677247i $$-0.763173\pi$$
0.954391 + 0.298560i $$0.0965063\pi$$
$$524$$ −9.50000 16.4545i −0.415009 0.718817i
$$525$$ 0 0
$$526$$ −7.50000 12.9904i −0.327016 0.566408i
$$527$$ 8.00000 + 13.8564i 0.348485 + 0.603595i
$$528$$ 0 0
$$529$$ 3.50000 + 6.06218i 0.152174 + 0.263573i
$$530$$ 0.500000 0.866025i 0.0217186 0.0376177i
$$531$$ 0 0
$$532$$ 25.0000 1.08389
$$533$$ 6.00000 + 20.7846i 0.259889 + 0.900281i
$$534$$ 0 0
$$535$$ −3.00000 + 5.19615i −0.129701 + 0.224649i
$$536$$ −4.00000 + 6.92820i −0.172774 + 0.299253i
$$537$$ 0 0
$$538$$ −4.00000 −0.172452
$$539$$ −27.0000 46.7654i −1.16297 2.01433i
$$540$$ 0 0
$$541$$ 34.0000 1.46177 0.730887 0.682498i $$-0.239107\pi$$
0.730887 + 0.682498i $$0.239107\pi$$
$$542$$ −2.00000 3.46410i −0.0859074 0.148796i
$$543$$ 0 0
$$544$$ −4.00000 + 6.92820i −0.171499 + 0.297044i
$$545$$ 14.0000 0.599694
$$546$$ 0 0
$$547$$ 6.00000 0.256541 0.128271 0.991739i $$-0.459057\pi$$
0.128271 + 0.991739i $$0.459057\pi$$
$$548$$ −6.00000 + 10.3923i −0.256307 + 0.443937i
$$549$$ 0 0
$$550$$ −1.50000 2.59808i −0.0639602 0.110782i
$$551$$ −20.0000 −0.852029
$$552$$ 0 0
$$553$$ −5.00000 8.66025i −0.212622 0.368271i
$$554$$ −15.0000 −0.637289
$$555$$ 0 0
$$556$$ −3.50000 + 6.06218i −0.148433 + 0.257094i
$$557$$ 7.50000 12.9904i 0.317785 0.550420i −0.662240 0.749291i $$-0.730394\pi$$
0.980026 + 0.198871i $$0.0637276\pi$$
$$558$$ 0 0
$$559$$ 21.0000 + 5.19615i 0.888205 + 0.219774i
$$560$$ −5.00000 −0.211289
$$561$$ 0 0
$$562$$ 9.00000 15.5885i 0.379642 0.657559i
$$563$$ 18.0000 + 31.1769i 0.758610 + 1.31395i 0.943560 + 0.331202i $$0.107454\pi$$
−0.184950 + 0.982748i $$0.559212\pi$$
$$564$$ 0 0
$$565$$ 4.00000 + 6.92820i 0.168281 + 0.291472i
$$566$$ 5.00000 + 8.66025i 0.210166 + 0.364018i
$$567$$ 0 0
$$568$$ 1.00000 + 1.73205i 0.0419591 + 0.0726752i
$$569$$ −7.50000 + 12.9904i −0.314416 + 0.544585i −0.979313 0.202350i $$-0.935142\pi$$
0.664897 + 0.746935i $$0.268475\pi$$
$$570$$ 0 0
$$571$$ −33.0000 −1.38101 −0.690504 0.723329i $$-0.742611\pi$$
−0.690504 + 0.723329i $$0.742611\pi$$
$$572$$ −7.50000 + 7.79423i −0.313591 + 0.325893i
$$573$$ 0 0
$$574$$ −15.0000 + 25.9808i −0.626088 + 1.08442i
$$575$$ −2.00000 + 3.46410i −0.0834058 + 0.144463i
$$576$$ 0 0
$$577$$ 2.00000 0.0832611 0.0416305 0.999133i $$-0.486745\pi$$
0.0416305 + 0.999133i $$0.486745\pi$$
$$578$$ −23.5000 40.7032i −0.977471 1.69303i
$$579$$ 0 0
$$580$$ 4.00000 0.166091
$$581$$ −20.0000 34.6410i −0.829740 1.43715i
$$582$$ 0 0
$$583$$ 1.50000 2.59808i 0.0621237 0.107601i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 9.00000 0.371787
$$587$$ 9.00000 15.5885i 0.371470 0.643404i −0.618322 0.785925i $$-0.712187\pi$$
0.989792 + 0.142520i $$0.0455206\pi$$
$$588$$ 0 0
$$589$$ −5.00000 8.66025i −0.206021 0.356840i
$$590$$ −12.0000 −0.494032
$$591$$ 0 0
$$592$$ 3.50000 + 6.06218i 0.143849 + 0.249154i
$$593$$ −20.0000 −0.821302 −0.410651 0.911793i $$-0.634698\pi$$
−0.410651 + 0.911793i $$0.634698\pi$$
$$594$$ 0 0
$$595$$ 20.0000 34.6410i 0.819920 1.42014i
$$596$$ −1.00000 + 1.73205i −0.0409616 + 0.0709476i
$$597$$ 0 0
$$598$$ 14.0000 + 3.46410i 0.572503 + 0.141658i
$$599$$ −34.0000 −1.38920 −0.694601 0.719395i $$-0.744419\pi$$
−0.694601 + 0.719395i $$0.744419\pi$$
$$600$$ 0 0
$$601$$ −18.5000 + 32.0429i −0.754631 + 1.30706i 0.190927 + 0.981604i $$0.438851\pi$$
−0.945558 + 0.325455i $$0.894483\pi$$
$$602$$ 15.0000 + 25.9808i 0.611354 + 1.05890i
$$603$$ 0 0
$$604$$ −11.0000 19.0526i −0.447584 0.775238i
$$605$$ 1.00000 + 1.73205i 0.0406558 + 0.0704179i
$$606$$ 0 0
$$607$$ 14.5000 + 25.1147i 0.588537 + 1.01938i 0.994424 + 0.105453i $$0.0336291\pi$$
−0.405887 + 0.913923i $$0.633038\pi$$
$$608$$ 2.50000 4.33013i 0.101388 0.175610i
$$609$$ 0 0
$$610$$ 2.00000 0.0809776
$$611$$ −7.50000 + 7.79423i −0.303418 + 0.315321i
$$612$$ 0 0
$$613$$ −12.5000 + 21.6506i −0.504870 + 0.874461i 0.495114 + 0.868828i $$0.335126\pi$$
−0.999984 + 0.00563283i $$0.998207\pi$$
$$614$$ 3.00000 5.19615i 0.121070 0.209700i
$$615$$ 0 0
$$616$$ −15.0000 −0.604367
$$617$$ −7.00000 12.1244i −0.281809 0.488108i 0.690021 0.723789i $$-0.257601\pi$$
−0.971830 + 0.235681i $$0.924268\pi$$
$$618$$ 0 0
$$619$$ 17.0000 0.683288 0.341644 0.939829i $$-0.389016\pi$$
0.341644 + 0.939829i $$0.389016\pi$$
$$620$$ 1.00000 + 1.73205i 0.0401610 + 0.0695608i
$$621$$ 0 0
$$622$$ −6.00000 + 10.3923i −0.240578 + 0.416693i
$$623$$ −55.0000 −2.20353
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ 3.00000 5.19615i 0.119904 0.207680i
$$627$$ 0 0
$$628$$ −7.50000 12.9904i −0.299283 0.518373i
$$629$$ −56.0000 −2.23287
$$630$$ 0 0
$$631$$ −6.00000 10.3923i −0.238856 0.413711i 0.721530 0.692383i $$-0.243439\pi$$
−0.960386 + 0.278672i $$0.910106\pi$$
$$632$$ −2.00000 −0.0795557
$$633$$ 0 0
$$634$$ −11.5000 + 19.9186i −0.456723 + 0.791068i
$$635$$ 10.5000 18.1865i 0.416680 0.721711i
$$636$$ 0 0
$$637$$ −18.0000 62.3538i −0.713186 2.47055i
$$638$$ 12.0000 0.475085
$$639$$ 0 0
$$640$$ −0.500000 + 0.866025i −0.0197642 + 0.0342327i
$$641$$ 13.5000 + 23.3827i 0.533218 + 0.923561i 0.999247 + 0.0387913i $$0.0123508\pi$$
−0.466029 + 0.884769i $$0.654316\pi$$
$$642$$ 0 0
$$643$$ 22.0000 + 38.1051i 0.867595 + 1.50272i 0.864447 + 0.502724i $$0.167669\pi$$
0.00314839 + 0.999995i $$0.498998\pi$$
$$644$$ 10.0000 + 17.3205i 0.394055 + 0.682524i
$$645$$ 0 0
$$646$$ 20.0000 + 34.6410i 0.786889 + 1.36293i
$$647$$ 1.50000 2.59808i 0.0589711 0.102141i −0.835033 0.550200i $$-0.814551\pi$$
0.894004 + 0.448059i $$0.147885\pi$$
$$648$$ 0 0
$$649$$ −36.0000 −1.41312
$$650$$ −1.00000 3.46410i −0.0392232 0.135873i
$$651$$ 0 0
$$652$$ 10.0000 17.3205i 0.391630 0.678323i
$$653$$ 13.5000 23.3827i 0.528296 0.915035i −0.471160 0.882048i $$-0.656165\pi$$
0.999456 0.0329874i $$-0.0105021\pi$$
$$654$$ 0 0
$$655$$ 19.0000 0.742391
$$656$$ 3.00000 + 5.19615i 0.117130 + 0.202876i
$$657$$ 0 0
$$658$$ −15.0000 −0.584761
$$659$$ 18.0000 + 31.1769i 0.701180 + 1.21448i 0.968052 + 0.250748i $$0.0806766\pi$$
−0.266872 + 0.963732i $$0.585990\pi$$
$$660$$ 0 0
$$661$$ 5.00000 8.66025i 0.194477 0.336845i −0.752252 0.658876i $$-0.771032\pi$$
0.946729 + 0.322031i $$0.104366\pi$$
$$662$$ 4.00000 0.155464
$$663$$ 0 0
$$664$$ −8.00000 −0.310460
$$665$$ −12.5000 + 21.6506i −0.484729 + 0.839576i
$$666$$ 0 0
$$667$$ −8.00000 13.8564i −0.309761 0.536522i
$$668$$ 23.0000 0.889897
$$669$$ 0 0
$$670$$ −4.00000 6.92820i −0.154533 0.267660i
$$671$$ 6.00000 0.231627
$$672$$ 0 0
$$673$$ 16.0000 27.7128i 0.616755 1.06825i −0.373319 0.927703i $$-0.621780\pi$$
0.990074 0.140548i $$-0.0448863\pi$$
$$674$$ −7.00000 + 12.1244i −0.269630 + 0.467013i
$$675$$ 0 0
$$676$$ −11.0000 + 6.92820i −0.423077 + 0.266469i
$$677$$ 22.0000 0.845529 0.422764 0.906240i $$-0.361060\pi$$
0.422764 + 0.906240i $$0.361060\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ −4.00000 6.92820i −0.153393 0.265684i
$$681$$ 0 0
$$682$$ 3.00000 + 5.19615i 0.114876 + 0.198971i
$$683$$ 15.0000 + 25.9808i 0.573959 + 0.994126i 0.996154 + 0.0876211i $$0.0279265\pi$$
−0.422195 + 0.906505i $$0.638740\pi$$
$$684$$ 0 0
$$685$$ −6.00000 10.3923i −0.229248 0.397070i
$$686$$ 27.5000 47.6314i 1.04995 1.81858i
$$687$$ 0 0
$$688$$ 6.00000 0.228748
$$689$$ 2.50000 2.59808i 0.0952424 0.0989788i
$$690$$ 0 0
$$691$$ −8.50000 + 14.7224i −0.323355 + 0.560068i −0.981178 0.193105i $$-0.938144\pi$$
0.657823 + 0.753173i $$0.271478\pi$$
$$692$$ 2.50000 4.33013i 0.0950357 0.164607i
$$693$$ 0 0
$$694$$ 16.0000 0.607352
$$695$$ −3.50000 6.06218i −0.132763 0.229952i
$$696$$ 0 0
$$697$$ −48.0000 −1.81813
$$698$$ −4.00000 6.92820i −0.151402 0.262236i
$$699$$ 0 0
$$700$$ 2.50000 4.33013i 0.0944911 0.163663i
$$701$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$702$$ 0 0
$$703$$ 35.0000 1.32005
$$704$$ −1.50000 + 2.59808i −0.0565334 + 0.0979187i
$$705$$ 0 0
$$706$$ 8.00000 + 13.8564i 0.301084 + 0.521493i
$$707$$ −40.0000 −1.50435
$$708$$ 0 0
$$709$$ −16.0000 27.7128i −0.600893 1.04078i −0.992686 0.120723i $$-0.961479\pi$$
0.391794 0.920053i $$-0.371855\pi$$
$$710$$ −2.00000 −0.0750587
$$711$$ 0 0
$$712$$ −5.50000 + 9.52628i −0.206121 + 0.357012i
$$713$$ 4.00000 6.92820i 0.149801 0.259463i
$$714$$ 0 0
$$715$$ −3.00000 10.3923i −0.112194 0.388650i
$$716$$ −4.00000 −0.149487
$$717$$ 0 0
$$718$$ −9.00000 + 15.5885i −0.335877 + 0.581756i
$$719$$ −10.0000 17.3205i −0.372937 0.645946i 0.617079 0.786901i $$-0.288316\pi$$
−0.990016 + 0.140955i $$0.954983\pi$$
$$720$$ 0 0
$$721$$ −17.5000 30.3109i −0.651734 1.12884i
$$722$$ −3.00000 5.19615i −0.111648 0.193381i
$$723$$ 0 0
$$724$$ 1.00000 + 1.73205i 0.0371647 + 0.0643712i
$$725$$ −2.00000 + 3.46410i −0.0742781 + 0.128654i
$$726$$ 0 0
$$727$$ −11.0000 −0.407967 −0.203984 0.978974i $$-0.565389\pi$$
−0.203984 + 0.978974i $$0.565389\pi$$
$$728$$ −17.5000 4.33013i −0.648593 0.160485i
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −24.0000 + 41.5692i −0.887672 + 1.53749i
$$732$$ 0 0
$$733$$ −43.0000 −1.58824 −0.794121 0.607760i $$-0.792068\pi$$
−0.794121 + 0.607760i $$0.792068\pi$$
$$734$$ 4.00000 + 6.92820i 0.147643 + 0.255725i
$$735$$ 0 0
$$736$$ 4.00000 0.147442
$$737$$ −12.0000 20.7846i −0.442026 0.765611i
$$738$$ 0 0
$$739$$ −9.50000 + 16.4545i −0.349463 + 0.605288i −0.986154 0.165831i $$-0.946969\pi$$
0.636691 + 0.771119i $$0.280303\pi$$
$$740$$ −7.00000 −0.257325
$$741$$ 0 0
$$742$$ 5.00000 0.183556
$$743$$ −8.00000 + 13.8564i −0.293492 + 0.508342i −0.974633 0.223810i $$-0.928151\pi$$
0.681141 + 0.732152i $$0.261484\pi$$
$$744$$ 0 0
$$745$$ −1.00000 1.73205i −0.0366372 0.0634574i
$$746$$ 38.0000 1.39128
$$747$$ 0 0
$$748$$ −12.0000 20.7846i −0.438763 0.759961i
$$749$$ −30.0000 −1.09618
$$750$$ 0 0
$$751$$ 4.00000 6.92820i 0.145962 0.252814i −0.783769 0.621052i $$-0.786706\pi$$
0.929731 + 0.368238i $$0.120039\pi$$
$$752$$ −1.50000 + 2.59808i −0.0546994 + 0.0947421i
$$753$$ 0 0
$$754$$ 14.0000 + 3.46410i 0.509850 + 0.126155i
$$755$$ 22.0000 0.800662
$$756$$ 0 0
$$757$$ −8.50000 + 14.7224i −0.308938 + 0.535096i −0.978130 0.207993i $$-0.933307\pi$$
0.669193 + 0.743089i $$0.266640\pi$$
$$758$$ 12.5000 + 21.6506i 0.454020 + 0.786386i
$$759$$ 0 0
$$760$$ 2.50000 + 4.33013i 0.0906845 + 0.157070i
$$761$$ 4.50000 + 7.79423i 0.163125 + 0.282541i 0.935988 0.352032i $$-0.114509\pi$$
−0.772863 + 0.634573i $$0.781176\pi$$
$$762$$ 0 0
$$763$$ 35.0000 + 60.6218i 1.26709 + 2.19466i
$$764$$ 1.00000 1.73205i 0.0361787 0.0626634i
$$765$$ 0 0
$$766$$ 28.0000 1.01168
$$767$$ −42.0000 10.3923i −1.51653 0.375244i
$$768$$ 0 0
$$769$$ 17.0000 29.4449i 0.613036 1.06181i −0.377690 0.925932i $$-0.623282\pi$$
0.990726 0.135877i $$-0.0433852\pi$$
$$770$$ 7.50000 12.9904i 0.270281 0.468141i
$$771$$ 0 0
$$772$$ 24.0000 0.863779
$$773$$ 0.500000 + 0.866025i 0.0179838 + 0.0311488i 0.874877 0.484345i $$-0.160942\pi$$
−0.856893 + 0.515494i $$0.827609\pi$$
$$774$$ 0 0
$$775$$ −2.00000 −0.0718421
$$776$$ 0 0
$$777$$ 0 0
$$778$$ −16.0000 + 27.7128i −0.573628 + 0.993552i
$$779$$ 30.0000 1.07486
$$780$$ 0 0
$$781$$ −6.00000 −0.214697
$$782$$ −16.0000 + 27.7128i −0.572159 + 0.991008i
$$783$$ 0 0
$$784$$ −9.00000 15.5885i −0.321429 0.556731i
$$785$$ 15.0000 0.535373
$$786$$ 0 0
$$787$$ 14.0000 + 24.2487i 0.499046 + 0.864373i 0.999999 0.00110111i $$-0.000350496\pi$$
−0.500953 + 0.865474i $$0.667017\pi$$
$$788$$ −3.00000 −0.106871
$$789$$ 0 0
$$790$$ 1.00000 1.73205i 0.0355784 0.0616236i