# Properties

 Label 60.3.f.a.19.4 Level $60$ Weight $3$ Character 60.19 Analytic conductor $1.635$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$60 = 2^{2} \cdot 3 \cdot 5$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 60.f (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$1.63488158616$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\zeta_{12})$$ Defining polynomial: $$x^{4} - x^{2} + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 19.4 Root $$0.866025 + 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 60.19 Dual form 60.3.f.a.19.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.73205 + 1.00000i) q^{2} +1.73205 q^{3} +(2.00000 + 3.46410i) q^{4} -5.00000i q^{5} +(3.00000 + 1.73205i) q^{6} -10.3923 q^{7} +8.00000i q^{8} +3.00000 q^{9} +O(q^{10})$$ $$q+(1.73205 + 1.00000i) q^{2} +1.73205 q^{3} +(2.00000 + 3.46410i) q^{4} -5.00000i q^{5} +(3.00000 + 1.73205i) q^{6} -10.3923 q^{7} +8.00000i q^{8} +3.00000 q^{9} +(5.00000 - 8.66025i) q^{10} +10.3923i q^{11} +(3.46410 + 6.00000i) q^{12} -18.0000i q^{13} +(-18.0000 - 10.3923i) q^{14} -8.66025i q^{15} +(-8.00000 + 13.8564i) q^{16} +10.0000i q^{17} +(5.19615 + 3.00000i) q^{18} -13.8564i q^{19} +(17.3205 - 10.0000i) q^{20} -18.0000 q^{21} +(-10.3923 + 18.0000i) q^{22} +6.92820 q^{23} +13.8564i q^{24} -25.0000 q^{25} +(18.0000 - 31.1769i) q^{26} +5.19615 q^{27} +(-20.7846 - 36.0000i) q^{28} +36.0000 q^{29} +(8.66025 - 15.0000i) q^{30} -6.92820i q^{31} +(-27.7128 + 16.0000i) q^{32} +18.0000i q^{33} +(-10.0000 + 17.3205i) q^{34} +51.9615i q^{35} +(6.00000 + 10.3923i) q^{36} +54.0000i q^{37} +(13.8564 - 24.0000i) q^{38} -31.1769i q^{39} +40.0000 q^{40} +18.0000 q^{41} +(-31.1769 - 18.0000i) q^{42} +20.7846 q^{43} +(-36.0000 + 20.7846i) q^{44} -15.0000i q^{45} +(12.0000 + 6.92820i) q^{46} +(-13.8564 + 24.0000i) q^{48} +59.0000 q^{49} +(-43.3013 - 25.0000i) q^{50} +17.3205i q^{51} +(62.3538 - 36.0000i) q^{52} +26.0000i q^{53} +(9.00000 + 5.19615i) q^{54} +51.9615 q^{55} -83.1384i q^{56} -24.0000i q^{57} +(62.3538 + 36.0000i) q^{58} +31.1769i q^{59} +(30.0000 - 17.3205i) q^{60} -74.0000 q^{61} +(6.92820 - 12.0000i) q^{62} -31.1769 q^{63} -64.0000 q^{64} -90.0000 q^{65} +(-18.0000 + 31.1769i) q^{66} -41.5692 q^{67} +(-34.6410 + 20.0000i) q^{68} +12.0000 q^{69} +(-51.9615 + 90.0000i) q^{70} -103.923i q^{71} +24.0000i q^{72} -36.0000i q^{73} +(-54.0000 + 93.5307i) q^{74} -43.3013 q^{75} +(48.0000 - 27.7128i) q^{76} -108.000i q^{77} +(31.1769 - 54.0000i) q^{78} -90.0666i q^{79} +(69.2820 + 40.0000i) q^{80} +9.00000 q^{81} +(31.1769 + 18.0000i) q^{82} -90.0666 q^{83} +(-36.0000 - 62.3538i) q^{84} +50.0000 q^{85} +(36.0000 + 20.7846i) q^{86} +62.3538 q^{87} -83.1384 q^{88} +18.0000 q^{89} +(15.0000 - 25.9808i) q^{90} +187.061i q^{91} +(13.8564 + 24.0000i) q^{92} -12.0000i q^{93} -69.2820 q^{95} +(-48.0000 + 27.7128i) q^{96} -72.0000i q^{97} +(102.191 + 59.0000i) q^{98} +31.1769i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q + 8q^{4} + 12q^{6} + 12q^{9} + O(q^{10})$$ $$4q + 8q^{4} + 12q^{6} + 12q^{9} + 20q^{10} - 72q^{14} - 32q^{16} - 72q^{21} - 100q^{25} + 72q^{26} + 144q^{29} - 40q^{34} + 24q^{36} + 160q^{40} + 72q^{41} - 144q^{44} + 48q^{46} + 236q^{49} + 36q^{54} + 120q^{60} - 296q^{61} - 256q^{64} - 360q^{65} - 72q^{66} + 48q^{69} - 216q^{74} + 192q^{76} + 36q^{81} - 144q^{84} + 200q^{85} + 144q^{86} + 72q^{89} + 60q^{90} - 192q^{96} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$$.

 $$n$$ $$31$$ $$37$$ $$41$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.73205 + 1.00000i 0.866025 + 0.500000i
$$3$$ 1.73205 0.577350
$$4$$ 2.00000 + 3.46410i 0.500000 + 0.866025i
$$5$$ 5.00000i 1.00000i
$$6$$ 3.00000 + 1.73205i 0.500000 + 0.288675i
$$7$$ −10.3923 −1.48461 −0.742307 0.670059i $$-0.766269\pi$$
−0.742307 + 0.670059i $$0.766269\pi$$
$$8$$ 8.00000i 1.00000i
$$9$$ 3.00000 0.333333
$$10$$ 5.00000 8.66025i 0.500000 0.866025i
$$11$$ 10.3923i 0.944755i 0.881396 + 0.472377i $$0.156604\pi$$
−0.881396 + 0.472377i $$0.843396\pi$$
$$12$$ 3.46410 + 6.00000i 0.288675 + 0.500000i
$$13$$ 18.0000i 1.38462i −0.721602 0.692308i $$-0.756594\pi$$
0.721602 0.692308i $$-0.243406\pi$$
$$14$$ −18.0000 10.3923i −1.28571 0.742307i
$$15$$ 8.66025i 0.577350i
$$16$$ −8.00000 + 13.8564i −0.500000 + 0.866025i
$$17$$ 10.0000i 0.588235i 0.955769 + 0.294118i $$0.0950258\pi$$
−0.955769 + 0.294118i $$0.904974\pi$$
$$18$$ 5.19615 + 3.00000i 0.288675 + 0.166667i
$$19$$ 13.8564i 0.729285i −0.931148 0.364642i $$-0.881191\pi$$
0.931148 0.364642i $$-0.118809\pi$$
$$20$$ 17.3205 10.0000i 0.866025 0.500000i
$$21$$ −18.0000 −0.857143
$$22$$ −10.3923 + 18.0000i −0.472377 + 0.818182i
$$23$$ 6.92820 0.301226 0.150613 0.988593i $$-0.451875\pi$$
0.150613 + 0.988593i $$0.451875\pi$$
$$24$$ 13.8564i 0.577350i
$$25$$ −25.0000 −1.00000
$$26$$ 18.0000 31.1769i 0.692308 1.19911i
$$27$$ 5.19615 0.192450
$$28$$ −20.7846 36.0000i −0.742307 1.28571i
$$29$$ 36.0000 1.24138 0.620690 0.784056i $$-0.286853\pi$$
0.620690 + 0.784056i $$0.286853\pi$$
$$30$$ 8.66025 15.0000i 0.288675 0.500000i
$$31$$ 6.92820i 0.223490i −0.993737 0.111745i $$-0.964356\pi$$
0.993737 0.111745i $$-0.0356441\pi$$
$$32$$ −27.7128 + 16.0000i −0.866025 + 0.500000i
$$33$$ 18.0000i 0.545455i
$$34$$ −10.0000 + 17.3205i −0.294118 + 0.509427i
$$35$$ 51.9615i 1.48461i
$$36$$ 6.00000 + 10.3923i 0.166667 + 0.288675i
$$37$$ 54.0000i 1.45946i 0.683736 + 0.729730i $$0.260354\pi$$
−0.683736 + 0.729730i $$0.739646\pi$$
$$38$$ 13.8564 24.0000i 0.364642 0.631579i
$$39$$ 31.1769i 0.799408i
$$40$$ 40.0000 1.00000
$$41$$ 18.0000 0.439024 0.219512 0.975610i $$-0.429553\pi$$
0.219512 + 0.975610i $$0.429553\pi$$
$$42$$ −31.1769 18.0000i −0.742307 0.428571i
$$43$$ 20.7846 0.483363 0.241682 0.970356i $$-0.422301\pi$$
0.241682 + 0.970356i $$0.422301\pi$$
$$44$$ −36.0000 + 20.7846i −0.818182 + 0.472377i
$$45$$ 15.0000i 0.333333i
$$46$$ 12.0000 + 6.92820i 0.260870 + 0.150613i
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ −13.8564 + 24.0000i −0.288675 + 0.500000i
$$49$$ 59.0000 1.20408
$$50$$ −43.3013 25.0000i −0.866025 0.500000i
$$51$$ 17.3205i 0.339618i
$$52$$ 62.3538 36.0000i 1.19911 0.692308i
$$53$$ 26.0000i 0.490566i 0.969452 + 0.245283i $$0.0788809\pi$$
−0.969452 + 0.245283i $$0.921119\pi$$
$$54$$ 9.00000 + 5.19615i 0.166667 + 0.0962250i
$$55$$ 51.9615 0.944755
$$56$$ 83.1384i 1.48461i
$$57$$ 24.0000i 0.421053i
$$58$$ 62.3538 + 36.0000i 1.07507 + 0.620690i
$$59$$ 31.1769i 0.528422i 0.964465 + 0.264211i $$0.0851116\pi$$
−0.964465 + 0.264211i $$0.914888\pi$$
$$60$$ 30.0000 17.3205i 0.500000 0.288675i
$$61$$ −74.0000 −1.21311 −0.606557 0.795040i $$-0.707450\pi$$
−0.606557 + 0.795040i $$0.707450\pi$$
$$62$$ 6.92820 12.0000i 0.111745 0.193548i
$$63$$ −31.1769 −0.494872
$$64$$ −64.0000 −1.00000
$$65$$ −90.0000 −1.38462
$$66$$ −18.0000 + 31.1769i −0.272727 + 0.472377i
$$67$$ −41.5692 −0.620436 −0.310218 0.950665i $$-0.600402\pi$$
−0.310218 + 0.950665i $$0.600402\pi$$
$$68$$ −34.6410 + 20.0000i −0.509427 + 0.294118i
$$69$$ 12.0000 0.173913
$$70$$ −51.9615 + 90.0000i −0.742307 + 1.28571i
$$71$$ 103.923i 1.46370i −0.681463 0.731852i $$-0.738656\pi$$
0.681463 0.731852i $$-0.261344\pi$$
$$72$$ 24.0000i 0.333333i
$$73$$ 36.0000i 0.493151i −0.969124 0.246575i $$-0.920695\pi$$
0.969124 0.246575i $$-0.0793053\pi$$
$$74$$ −54.0000 + 93.5307i −0.729730 + 1.26393i
$$75$$ −43.3013 −0.577350
$$76$$ 48.0000 27.7128i 0.631579 0.364642i
$$77$$ 108.000i 1.40260i
$$78$$ 31.1769 54.0000i 0.399704 0.692308i
$$79$$ 90.0666i 1.14008i −0.821616 0.570042i $$-0.806927\pi$$
0.821616 0.570042i $$-0.193073\pi$$
$$80$$ 69.2820 + 40.0000i 0.866025 + 0.500000i
$$81$$ 9.00000 0.111111
$$82$$ 31.1769 + 18.0000i 0.380206 + 0.219512i
$$83$$ −90.0666 −1.08514 −0.542570 0.840011i $$-0.682549\pi$$
−0.542570 + 0.840011i $$0.682549\pi$$
$$84$$ −36.0000 62.3538i −0.428571 0.742307i
$$85$$ 50.0000 0.588235
$$86$$ 36.0000 + 20.7846i 0.418605 + 0.241682i
$$87$$ 62.3538 0.716711
$$88$$ −83.1384 −0.944755
$$89$$ 18.0000 0.202247 0.101124 0.994874i $$-0.467756\pi$$
0.101124 + 0.994874i $$0.467756\pi$$
$$90$$ 15.0000 25.9808i 0.166667 0.288675i
$$91$$ 187.061i 2.05562i
$$92$$ 13.8564 + 24.0000i 0.150613 + 0.260870i
$$93$$ 12.0000i 0.129032i
$$94$$ 0 0
$$95$$ −69.2820 −0.729285
$$96$$ −48.0000 + 27.7128i −0.500000 + 0.288675i
$$97$$ 72.0000i 0.742268i −0.928579 0.371134i $$-0.878969\pi$$
0.928579 0.371134i $$-0.121031\pi$$
$$98$$ 102.191 + 59.0000i 1.04277 + 0.602041i
$$99$$ 31.1769i 0.314918i
$$100$$ −50.0000 86.6025i −0.500000 0.866025i
$$101$$ 36.0000 0.356436 0.178218 0.983991i $$-0.442967\pi$$
0.178218 + 0.983991i $$0.442967\pi$$
$$102$$ −17.3205 + 30.0000i −0.169809 + 0.294118i
$$103$$ 10.3923 0.100896 0.0504481 0.998727i $$-0.483935\pi$$
0.0504481 + 0.998727i $$0.483935\pi$$
$$104$$ 144.000 1.38462
$$105$$ 90.0000i 0.857143i
$$106$$ −26.0000 + 45.0333i −0.245283 + 0.424843i
$$107$$ 187.061 1.74824 0.874119 0.485712i $$-0.161439\pi$$
0.874119 + 0.485712i $$0.161439\pi$$
$$108$$ 10.3923 + 18.0000i 0.0962250 + 0.166667i
$$109$$ 26.0000 0.238532 0.119266 0.992862i $$-0.461946\pi$$
0.119266 + 0.992862i $$0.461946\pi$$
$$110$$ 90.0000 + 51.9615i 0.818182 + 0.472377i
$$111$$ 93.5307i 0.842619i
$$112$$ 83.1384 144.000i 0.742307 1.28571i
$$113$$ 10.0000i 0.0884956i 0.999021 + 0.0442478i $$0.0140891\pi$$
−0.999021 + 0.0442478i $$0.985911\pi$$
$$114$$ 24.0000 41.5692i 0.210526 0.364642i
$$115$$ 34.6410i 0.301226i
$$116$$ 72.0000 + 124.708i 0.620690 + 1.07507i
$$117$$ 54.0000i 0.461538i
$$118$$ −31.1769 + 54.0000i −0.264211 + 0.457627i
$$119$$ 103.923i 0.873303i
$$120$$ 69.2820 0.577350
$$121$$ 13.0000 0.107438
$$122$$ −128.172 74.0000i −1.05059 0.606557i
$$123$$ 31.1769 0.253471
$$124$$ 24.0000 13.8564i 0.193548 0.111745i
$$125$$ 125.000i 1.00000i
$$126$$ −54.0000 31.1769i −0.428571 0.247436i
$$127$$ −218.238 −1.71841 −0.859206 0.511629i $$-0.829042\pi$$
−0.859206 + 0.511629i $$0.829042\pi$$
$$128$$ −110.851 64.0000i −0.866025 0.500000i
$$129$$ 36.0000 0.279070
$$130$$ −155.885 90.0000i −1.19911 0.692308i
$$131$$ 135.100i 1.03130i −0.856800 0.515649i $$-0.827551\pi$$
0.856800 0.515649i $$-0.172449\pi$$
$$132$$ −62.3538 + 36.0000i −0.472377 + 0.272727i
$$133$$ 144.000i 1.08271i
$$134$$ −72.0000 41.5692i −0.537313 0.310218i
$$135$$ 25.9808i 0.192450i
$$136$$ −80.0000 −0.588235
$$137$$ 110.000i 0.802920i 0.915877 + 0.401460i $$0.131497\pi$$
−0.915877 + 0.401460i $$0.868503\pi$$
$$138$$ 20.7846 + 12.0000i 0.150613 + 0.0869565i
$$139$$ 187.061i 1.34577i 0.739749 + 0.672883i $$0.234944\pi$$
−0.739749 + 0.672883i $$0.765056\pi$$
$$140$$ −180.000 + 103.923i −1.28571 + 0.742307i
$$141$$ 0 0
$$142$$ 103.923 180.000i 0.731852 1.26761i
$$143$$ 187.061 1.30812
$$144$$ −24.0000 + 41.5692i −0.166667 + 0.288675i
$$145$$ 180.000i 1.24138i
$$146$$ 36.0000 62.3538i 0.246575 0.427081i
$$147$$ 102.191 0.695177
$$148$$ −187.061 + 108.000i −1.26393 + 0.729730i
$$149$$ −288.000 −1.93289 −0.966443 0.256881i $$-0.917305\pi$$
−0.966443 + 0.256881i $$0.917305\pi$$
$$150$$ −75.0000 43.3013i −0.500000 0.288675i
$$151$$ 187.061i 1.23882i −0.785069 0.619409i $$-0.787372\pi$$
0.785069 0.619409i $$-0.212628\pi$$
$$152$$ 110.851 0.729285
$$153$$ 30.0000i 0.196078i
$$154$$ 108.000 187.061i 0.701299 1.21468i
$$155$$ −34.6410 −0.223490
$$156$$ 108.000 62.3538i 0.692308 0.399704i
$$157$$ 234.000i 1.49045i 0.666815 + 0.745223i $$0.267657\pi$$
−0.666815 + 0.745223i $$0.732343\pi$$
$$158$$ 90.0666 156.000i 0.570042 0.987342i
$$159$$ 45.0333i 0.283228i
$$160$$ 80.0000 + 138.564i 0.500000 + 0.866025i
$$161$$ −72.0000 −0.447205
$$162$$ 15.5885 + 9.00000i 0.0962250 + 0.0555556i
$$163$$ 124.708 0.765078 0.382539 0.923939i $$-0.375050\pi$$
0.382539 + 0.923939i $$0.375050\pi$$
$$164$$ 36.0000 + 62.3538i 0.219512 + 0.380206i
$$165$$ 90.0000 0.545455
$$166$$ −156.000 90.0666i −0.939759 0.542570i
$$167$$ −131.636 −0.788239 −0.394119 0.919059i $$-0.628950\pi$$
−0.394119 + 0.919059i $$0.628950\pi$$
$$168$$ 144.000i 0.857143i
$$169$$ −155.000 −0.917160
$$170$$ 86.6025 + 50.0000i 0.509427 + 0.294118i
$$171$$ 41.5692i 0.243095i
$$172$$ 41.5692 + 72.0000i 0.241682 + 0.418605i
$$173$$ 146.000i 0.843931i −0.906612 0.421965i $$-0.861340\pi$$
0.906612 0.421965i $$-0.138660\pi$$
$$174$$ 108.000 + 62.3538i 0.620690 + 0.358355i
$$175$$ 259.808 1.48461
$$176$$ −144.000 83.1384i −0.818182 0.472377i
$$177$$ 54.0000i 0.305085i
$$178$$ 31.1769 + 18.0000i 0.175151 + 0.101124i
$$179$$ 72.7461i 0.406403i 0.979137 + 0.203201i $$0.0651346\pi$$
−0.979137 + 0.203201i $$0.934865\pi$$
$$180$$ 51.9615 30.0000i 0.288675 0.166667i
$$181$$ 262.000 1.44751 0.723757 0.690055i $$-0.242414\pi$$
0.723757 + 0.690055i $$0.242414\pi$$
$$182$$ −187.061 + 324.000i −1.02781 + 1.78022i
$$183$$ −128.172 −0.700392
$$184$$ 55.4256i 0.301226i
$$185$$ 270.000 1.45946
$$186$$ 12.0000 20.7846i 0.0645161 0.111745i
$$187$$ −103.923 −0.555738
$$188$$ 0 0
$$189$$ −54.0000 −0.285714
$$190$$ −120.000 69.2820i −0.631579 0.364642i
$$191$$ 187.061i 0.979380i 0.871897 + 0.489690i $$0.162890\pi$$
−0.871897 + 0.489690i $$0.837110\pi$$
$$192$$ −110.851 −0.577350
$$193$$ 180.000i 0.932642i −0.884615 0.466321i $$-0.845579\pi$$
0.884615 0.466321i $$-0.154421\pi$$
$$194$$ 72.0000 124.708i 0.371134 0.642823i
$$195$$ −155.885 −0.799408
$$196$$ 118.000 + 204.382i 0.602041 + 1.04277i
$$197$$ 154.000i 0.781726i −0.920449 0.390863i $$-0.872177\pi$$
0.920449 0.390863i $$-0.127823\pi$$
$$198$$ −31.1769 + 54.0000i −0.157459 + 0.272727i
$$199$$ 187.061i 0.940007i 0.882664 + 0.470004i $$0.155747\pi$$
−0.882664 + 0.470004i $$0.844253\pi$$
$$200$$ 200.000i 1.00000i
$$201$$ −72.0000 −0.358209
$$202$$ 62.3538 + 36.0000i 0.308682 + 0.178218i
$$203$$ −374.123 −1.84297
$$204$$ −60.0000 + 34.6410i −0.294118 + 0.169809i
$$205$$ 90.0000i 0.439024i
$$206$$ 18.0000 + 10.3923i 0.0873786 + 0.0504481i
$$207$$ 20.7846 0.100409
$$208$$ 249.415 + 144.000i 1.19911 + 0.692308i
$$209$$ 144.000 0.688995
$$210$$ −90.0000 + 155.885i −0.428571 + 0.742307i
$$211$$ 242.487i 1.14923i −0.818425 0.574614i $$-0.805152\pi$$
0.818425 0.574614i $$-0.194848\pi$$
$$212$$ −90.0666 + 52.0000i −0.424843 + 0.245283i
$$213$$ 180.000i 0.845070i
$$214$$ 324.000 + 187.061i 1.51402 + 0.874119i
$$215$$ 103.923i 0.483363i
$$216$$ 41.5692i 0.192450i
$$217$$ 72.0000i 0.331797i
$$218$$ 45.0333 + 26.0000i 0.206575 + 0.119266i
$$219$$ 62.3538i 0.284721i
$$220$$ 103.923 + 180.000i 0.472377 + 0.818182i
$$221$$ 180.000 0.814480
$$222$$ −93.5307 + 162.000i −0.421310 + 0.729730i
$$223$$ 93.5307 0.419420 0.209710 0.977764i $$-0.432748\pi$$
0.209710 + 0.977764i $$0.432748\pi$$
$$224$$ 288.000 166.277i 1.28571 0.742307i
$$225$$ −75.0000 −0.333333
$$226$$ −10.0000 + 17.3205i −0.0442478 + 0.0766394i
$$227$$ 214.774 0.946142 0.473071 0.881024i $$-0.343145\pi$$
0.473071 + 0.881024i $$0.343145\pi$$
$$228$$ 83.1384 48.0000i 0.364642 0.210526i
$$229$$ −338.000 −1.47598 −0.737991 0.674810i $$-0.764225\pi$$
−0.737991 + 0.674810i $$0.764225\pi$$
$$230$$ 34.6410 60.0000i 0.150613 0.260870i
$$231$$ 187.061i 0.809790i
$$232$$ 288.000i 1.24138i
$$233$$ 182.000i 0.781116i 0.920578 + 0.390558i $$0.127718\pi$$
−0.920578 + 0.390558i $$0.872282\pi$$
$$234$$ 54.0000 93.5307i 0.230769 0.399704i
$$235$$ 0 0
$$236$$ −108.000 + 62.3538i −0.457627 + 0.264211i
$$237$$ 156.000i 0.658228i
$$238$$ 103.923 180.000i 0.436651 0.756303i
$$239$$ 353.338i 1.47840i 0.673484 + 0.739202i $$0.264797\pi$$
−0.673484 + 0.739202i $$0.735203\pi$$
$$240$$ 120.000 + 69.2820i 0.500000 + 0.288675i
$$241$$ −106.000 −0.439834 −0.219917 0.975519i $$-0.570579\pi$$
−0.219917 + 0.975519i $$0.570579\pi$$
$$242$$ 22.5167 + 13.0000i 0.0930441 + 0.0537190i
$$243$$ 15.5885 0.0641500
$$244$$ −148.000 256.344i −0.606557 1.05059i
$$245$$ 295.000i 1.20408i
$$246$$ 54.0000 + 31.1769i 0.219512 + 0.126735i
$$247$$ −249.415 −1.00978
$$248$$ 55.4256 0.223490
$$249$$ −156.000 −0.626506
$$250$$ −125.000 + 216.506i −0.500000 + 0.866025i
$$251$$ 322.161i 1.28351i 0.766909 + 0.641756i $$0.221794\pi$$
−0.766909 + 0.641756i $$0.778206\pi$$
$$252$$ −62.3538 108.000i −0.247436 0.428571i
$$253$$ 72.0000i 0.284585i
$$254$$ −378.000 218.238i −1.48819 0.859206i
$$255$$ 86.6025 0.339618
$$256$$ −128.000 221.703i −0.500000 0.866025i
$$257$$ 14.0000i 0.0544747i 0.999629 + 0.0272374i $$0.00867099\pi$$
−0.999629 + 0.0272374i $$0.991329\pi$$
$$258$$ 62.3538 + 36.0000i 0.241682 + 0.139535i
$$259$$ 561.184i 2.16674i
$$260$$ −180.000 311.769i −0.692308 1.19911i
$$261$$ 108.000 0.413793
$$262$$ 135.100 234.000i 0.515649 0.893130i
$$263$$ 187.061 0.711260 0.355630 0.934627i $$-0.384266\pi$$
0.355630 + 0.934627i $$0.384266\pi$$
$$264$$ −144.000 −0.545455
$$265$$ 130.000 0.490566
$$266$$ −144.000 + 249.415i −0.541353 + 0.937652i
$$267$$ 31.1769 0.116767
$$268$$ −83.1384 144.000i −0.310218 0.537313i
$$269$$ 108.000 0.401487 0.200743 0.979644i $$-0.435664\pi$$
0.200743 + 0.979644i $$0.435664\pi$$
$$270$$ 25.9808 45.0000i 0.0962250 0.166667i
$$271$$ 325.626i 1.20157i 0.799411 + 0.600785i $$0.205145\pi$$
−0.799411 + 0.600785i $$0.794855\pi$$
$$272$$ −138.564 80.0000i −0.509427 0.294118i
$$273$$ 324.000i 1.18681i
$$274$$ −110.000 + 190.526i −0.401460 + 0.695349i
$$275$$ 259.808i 0.944755i
$$276$$ 24.0000 + 41.5692i 0.0869565 + 0.150613i
$$277$$ 270.000i 0.974729i 0.873199 + 0.487365i $$0.162042\pi$$
−0.873199 + 0.487365i $$0.837958\pi$$
$$278$$ −187.061 + 324.000i −0.672883 + 1.16547i
$$279$$ 20.7846i 0.0744968i
$$280$$ −415.692 −1.48461
$$281$$ −234.000 −0.832740 −0.416370 0.909195i $$-0.636698\pi$$
−0.416370 + 0.909195i $$0.636698\pi$$
$$282$$ 0 0
$$283$$ −83.1384 −0.293775 −0.146888 0.989153i $$-0.546926\pi$$
−0.146888 + 0.989153i $$0.546926\pi$$
$$284$$ 360.000 207.846i 1.26761 0.731852i
$$285$$ −120.000 −0.421053
$$286$$ 324.000 + 187.061i 1.13287 + 0.654061i
$$287$$ −187.061 −0.651782
$$288$$ −83.1384 + 48.0000i −0.288675 + 0.166667i
$$289$$ 189.000 0.653979
$$290$$ 180.000 311.769i 0.620690 1.07507i
$$291$$ 124.708i 0.428549i
$$292$$ 124.708 72.0000i 0.427081 0.246575i
$$293$$ 58.0000i 0.197952i 0.995090 + 0.0989761i $$0.0315567\pi$$
−0.995090 + 0.0989761i $$0.968443\pi$$
$$294$$ 177.000 + 102.191i 0.602041 + 0.347588i
$$295$$ 155.885 0.528422
$$296$$ −432.000 −1.45946
$$297$$ 54.0000i 0.181818i
$$298$$ −498.831 288.000i −1.67393 0.966443i
$$299$$ 124.708i 0.417082i
$$300$$ −86.6025 150.000i −0.288675 0.500000i
$$301$$ −216.000 −0.717608
$$302$$ 187.061 324.000i 0.619409 1.07285i
$$303$$ 62.3538 0.205788
$$304$$ 192.000 + 110.851i 0.631579 + 0.364642i
$$305$$ 370.000i 1.21311i
$$306$$ −30.0000 + 51.9615i −0.0980392 + 0.169809i
$$307$$ 270.200 0.880130 0.440065 0.897966i $$-0.354955\pi$$
0.440065 + 0.897966i $$0.354955\pi$$
$$308$$ 374.123 216.000i 1.21468 0.701299i
$$309$$ 18.0000 0.0582524
$$310$$ −60.0000 34.6410i −0.193548 0.111745i
$$311$$ 270.200i 0.868810i 0.900718 + 0.434405i $$0.143041\pi$$
−0.900718 + 0.434405i $$0.856959\pi$$
$$312$$ 249.415 0.799408
$$313$$ 468.000i 1.49521i −0.664145 0.747604i $$-0.731204\pi$$
0.664145 0.747604i $$-0.268796\pi$$
$$314$$ −234.000 + 405.300i −0.745223 + 1.29076i
$$315$$ 155.885i 0.494872i
$$316$$ 312.000 180.133i 0.987342 0.570042i
$$317$$ 250.000i 0.788644i 0.918972 + 0.394322i $$0.129020\pi$$
−0.918972 + 0.394322i $$0.870980\pi$$
$$318$$ −45.0333 + 78.0000i −0.141614 + 0.245283i
$$319$$ 374.123i 1.17280i
$$320$$ 320.000i 1.00000i
$$321$$ 324.000 1.00935
$$322$$ −124.708 72.0000i −0.387291 0.223602i
$$323$$ 138.564 0.428991
$$324$$ 18.0000 + 31.1769i 0.0555556 + 0.0962250i
$$325$$ 450.000i 1.38462i
$$326$$ 216.000 + 124.708i 0.662577 + 0.382539i
$$327$$ 45.0333 0.137717
$$328$$ 144.000i 0.439024i
$$329$$ 0 0
$$330$$ 155.885 + 90.0000i 0.472377 + 0.272727i
$$331$$ 374.123i 1.13028i −0.824995 0.565140i $$-0.808822\pi$$
0.824995 0.565140i $$-0.191178\pi$$
$$332$$ −180.133 312.000i −0.542570 0.939759i
$$333$$ 162.000i 0.486486i
$$334$$ −228.000 131.636i −0.682635 0.394119i
$$335$$ 207.846i 0.620436i
$$336$$ 144.000 249.415i 0.428571 0.742307i
$$337$$ 468.000i 1.38872i −0.719626 0.694362i $$-0.755687\pi$$
0.719626 0.694362i $$-0.244313\pi$$
$$338$$ −268.468 155.000i −0.794284 0.458580i
$$339$$ 17.3205i 0.0510929i
$$340$$ 100.000 + 173.205i 0.294118 + 0.509427i
$$341$$ 72.0000 0.211144
$$342$$ 41.5692 72.0000i 0.121547 0.210526i
$$343$$ −103.923 −0.302983
$$344$$ 166.277i 0.483363i
$$345$$ 60.0000i 0.173913i
$$346$$ 146.000 252.879i 0.421965 0.730865i
$$347$$ 561.184 1.61725 0.808623 0.588327i $$-0.200213\pi$$
0.808623 + 0.588327i $$0.200213\pi$$
$$348$$ 124.708 + 216.000i 0.358355 + 0.620690i
$$349$$ 434.000 1.24355 0.621777 0.783195i $$-0.286411\pi$$
0.621777 + 0.783195i $$0.286411\pi$$
$$350$$ 450.000 + 259.808i 1.28571 + 0.742307i
$$351$$ 93.5307i 0.266469i
$$352$$ −166.277 288.000i −0.472377 0.818182i
$$353$$ 158.000i 0.447592i 0.974636 + 0.223796i $$0.0718449\pi$$
−0.974636 + 0.223796i $$0.928155\pi$$
$$354$$ −54.0000 + 93.5307i −0.152542 + 0.264211i
$$355$$ −519.615 −1.46370
$$356$$ 36.0000 + 62.3538i 0.101124 + 0.175151i
$$357$$ 180.000i 0.504202i
$$358$$ −72.7461 + 126.000i −0.203201 + 0.351955i
$$359$$ 457.261i 1.27371i −0.770984 0.636854i $$-0.780235\pi$$
0.770984 0.636854i $$-0.219765\pi$$
$$360$$ 120.000 0.333333
$$361$$ 169.000 0.468144
$$362$$ 453.797 + 262.000i 1.25358 + 0.723757i
$$363$$ 22.5167 0.0620294
$$364$$ −648.000 + 374.123i −1.78022 + 1.02781i
$$365$$ −180.000 −0.493151
$$366$$ −222.000 128.172i −0.606557 0.350196i
$$367$$ −218.238 −0.594655 −0.297328 0.954776i $$-0.596095\pi$$
−0.297328 + 0.954776i $$0.596095\pi$$
$$368$$ −55.4256 + 96.0000i −0.150613 + 0.260870i
$$369$$ 54.0000 0.146341
$$370$$ 467.654 + 270.000i 1.26393 + 0.729730i
$$371$$ 270.200i 0.728302i
$$372$$ 41.5692 24.0000i 0.111745 0.0645161i
$$373$$ 270.000i 0.723861i 0.932205 + 0.361930i $$0.117882\pi$$
−0.932205 + 0.361930i $$0.882118\pi$$
$$374$$ −180.000 103.923i −0.481283 0.277869i
$$375$$ 216.506i 0.577350i
$$376$$ 0 0
$$377$$ 648.000i 1.71883i
$$378$$ −93.5307 54.0000i −0.247436 0.142857i
$$379$$ 325.626i 0.859170i 0.903026 + 0.429585i $$0.141340\pi$$
−0.903026 + 0.429585i $$0.858660\pi$$
$$380$$ −138.564 240.000i −0.364642 0.631579i
$$381$$ −378.000 −0.992126
$$382$$ −187.061 + 324.000i −0.489690 + 0.848168i
$$383$$ −55.4256 −0.144714 −0.0723572 0.997379i $$-0.523052\pi$$
−0.0723572 + 0.997379i $$0.523052\pi$$
$$384$$ −192.000 110.851i −0.500000 0.288675i
$$385$$ −540.000 −1.40260
$$386$$ 180.000 311.769i 0.466321 0.807692i
$$387$$ 62.3538 0.161121
$$388$$ 249.415 144.000i 0.642823 0.371134i
$$389$$ 288.000 0.740360 0.370180 0.928960i $$-0.379296\pi$$
0.370180 + 0.928960i $$0.379296\pi$$
$$390$$ −270.000 155.885i −0.692308 0.399704i
$$391$$ 69.2820i 0.177192i
$$392$$ 472.000i 1.20408i
$$393$$ 234.000i 0.595420i
$$394$$ 154.000 266.736i 0.390863 0.676994i
$$395$$ −450.333 −1.14008
$$396$$ −108.000 + 62.3538i −0.272727 + 0.157459i
$$397$$ 306.000i 0.770781i −0.922754 0.385390i $$-0.874067\pi$$
0.922754 0.385390i $$-0.125933\pi$$
$$398$$ −187.061 + 324.000i −0.470004 + 0.814070i
$$399$$ 249.415i 0.625101i
$$400$$ 200.000 346.410i 0.500000 0.866025i
$$401$$ −450.000 −1.12219 −0.561097 0.827750i $$-0.689621\pi$$
−0.561097 + 0.827750i $$0.689621\pi$$
$$402$$ −124.708 72.0000i −0.310218 0.179104i
$$403$$ −124.708 −0.309448
$$404$$ 72.0000 + 124.708i 0.178218 + 0.308682i
$$405$$ 45.0000i 0.111111i
$$406$$ −648.000 374.123i −1.59606 0.921485i
$$407$$ −561.184 −1.37883
$$408$$ −138.564 −0.339618
$$409$$ 50.0000 0.122249 0.0611247 0.998130i $$-0.480531\pi$$
0.0611247 + 0.998130i $$0.480531\pi$$
$$410$$ 90.0000 155.885i 0.219512 0.380206i
$$411$$ 190.526i 0.463566i
$$412$$ 20.7846 + 36.0000i 0.0504481 + 0.0873786i
$$413$$ 324.000i 0.784504i
$$414$$ 36.0000 + 20.7846i 0.0869565 + 0.0502044i
$$415$$ 450.333i 1.08514i
$$416$$ 288.000 + 498.831i 0.692308 + 1.19911i
$$417$$ 324.000i 0.776978i
$$418$$ 249.415 + 144.000i 0.596687 + 0.344498i
$$419$$ 737.854i 1.76099i −0.474058 0.880494i $$-0.657211\pi$$
0.474058 0.880494i $$-0.342789\pi$$
$$420$$ −311.769 + 180.000i −0.742307 + 0.428571i
$$421$$ −286.000 −0.679335 −0.339667 0.940546i $$-0.610315\pi$$
−0.339667 + 0.940546i $$0.610315\pi$$
$$422$$ 242.487 420.000i 0.574614 0.995261i
$$423$$ 0 0
$$424$$ −208.000 −0.490566
$$425$$ 250.000i 0.588235i
$$426$$ 180.000 311.769i 0.422535 0.731852i
$$427$$ 769.031 1.80101
$$428$$ 374.123 + 648.000i 0.874119 + 1.51402i
$$429$$ 324.000 0.755245
$$430$$ 103.923 180.000i 0.241682 0.418605i
$$431$$ 124.708i 0.289345i −0.989480 0.144672i $$-0.953787\pi$$
0.989480 0.144672i $$-0.0462128\pi$$
$$432$$ −41.5692 + 72.0000i −0.0962250 + 0.166667i
$$433$$ 36.0000i 0.0831409i 0.999136 + 0.0415704i $$0.0132361\pi$$
−0.999136 + 0.0415704i $$0.986764\pi$$
$$434$$ −72.0000 + 124.708i −0.165899 + 0.287345i
$$435$$ 311.769i 0.716711i
$$436$$ 52.0000 + 90.0666i 0.119266 + 0.206575i
$$437$$ 96.0000i 0.219680i
$$438$$ 62.3538 108.000i 0.142360 0.246575i
$$439$$ 782.887i 1.78334i −0.452684 0.891671i $$-0.649534\pi$$
0.452684 0.891671i $$-0.350466\pi$$
$$440$$ 415.692i 0.944755i
$$441$$ 177.000 0.401361
$$442$$ 311.769 + 180.000i 0.705360 + 0.407240i
$$443$$ −214.774 −0.484818 −0.242409 0.970174i $$-0.577938\pi$$
−0.242409 + 0.970174i $$0.577938\pi$$
$$444$$ −324.000 + 187.061i −0.729730 + 0.421310i
$$445$$ 90.0000i 0.202247i
$$446$$ 162.000 + 93.5307i 0.363229 + 0.209710i
$$447$$ −498.831 −1.11595
$$448$$ 665.108 1.48461
$$449$$ −54.0000 −0.120267 −0.0601336 0.998190i $$-0.519153\pi$$
−0.0601336 + 0.998190i $$0.519153\pi$$
$$450$$ −129.904 75.0000i −0.288675 0.166667i
$$451$$ 187.061i 0.414770i
$$452$$ −34.6410 + 20.0000i −0.0766394 + 0.0442478i
$$453$$ 324.000i 0.715232i
$$454$$ 372.000 + 214.774i 0.819383 + 0.473071i
$$455$$ 935.307 2.05562
$$456$$ 192.000 0.421053
$$457$$ 288.000i 0.630197i 0.949059 + 0.315098i $$0.102038\pi$$
−0.949059 + 0.315098i $$0.897962\pi$$
$$458$$ −585.433 338.000i −1.27824 0.737991i
$$459$$ 51.9615i 0.113206i
$$460$$ 120.000 69.2820i 0.260870 0.150613i
$$461$$ −288.000 −0.624729 −0.312364 0.949962i $$-0.601121\pi$$
−0.312364 + 0.949962i $$0.601121\pi$$
$$462$$ 187.061 324.000i 0.404895 0.701299i
$$463$$ 405.300 0.875378 0.437689 0.899126i $$-0.355797\pi$$
0.437689 + 0.899126i $$0.355797\pi$$
$$464$$ −288.000 + 498.831i −0.620690 + 1.07507i
$$465$$ −60.0000 −0.129032
$$466$$ −182.000 + 315.233i −0.390558 + 0.676466i
$$467$$ −575.041 −1.23135 −0.615675 0.788000i $$-0.711117\pi$$
−0.615675 + 0.788000i $$0.711117\pi$$
$$468$$ 187.061 108.000i 0.399704 0.230769i
$$469$$ 432.000 0.921109
$$470$$ 0 0
$$471$$ 405.300i 0.860509i
$$472$$ −249.415 −0.528422
$$473$$ 216.000i 0.456660i
$$474$$ 156.000 270.200i 0.329114 0.570042i
$$475$$ 346.410i 0.729285i
$$476$$ 360.000 207.846i 0.756303 0.436651i
$$477$$ 78.0000i 0.163522i
$$478$$ −353.338 + 612.000i −0.739202 + 1.28033i
$$479$$ 145.492i 0.303742i 0.988400 + 0.151871i $$0.0485298\pi$$
−0.988400 + 0.151871i $$0.951470\pi$$
$$480$$ 138.564 + 240.000i 0.288675 + 0.500000i
$$481$$ 972.000 2.02079
$$482$$ −183.597 106.000i −0.380907 0.219917i
$$483$$ −124.708 −0.258194
$$484$$ 26.0000 + 45.0333i 0.0537190 + 0.0930441i
$$485$$ −360.000 −0.742268
$$486$$ 27.0000 + 15.5885i 0.0555556 + 0.0320750i
$$487$$ 259.808 0.533486 0.266743 0.963768i $$-0.414053\pi$$
0.266743 + 0.963768i $$0.414053\pi$$
$$488$$ 592.000i 1.21311i
$$489$$ 216.000 0.441718
$$490$$ 295.000 510.955i 0.602041 1.04277i
$$491$$ 72.7461i 0.148159i 0.997252 + 0.0740796i $$0.0236019\pi$$
−0.997252 + 0.0740796i $$0.976398\pi$$
$$492$$ 62.3538 + 108.000i 0.126735 + 0.219512i
$$493$$ 360.000i 0.730223i
$$494$$ −432.000 249.415i −0.874494 0.504889i
$$495$$ 155.885 0.314918
$$496$$ 96.0000 + 55.4256i 0.193548 + 0.111745i
$$497$$ 1080.00i 2.17304i
$$498$$ −270.200 156.000i −0.542570 0.313253i
$$499$$ 443.405i 0.888587i 0.895881 + 0.444294i $$0.146545\pi$$
−0.895881 + 0.444294i $$0.853455\pi$$
$$500$$ −433.013 + 250.000i −0.866025 + 0.500000i
$$501$$ −228.000 −0.455090
$$502$$ −322.161 + 558.000i −0.641756 + 1.11155i
$$503$$ 110.851 0.220380 0.110190 0.993911i $$-0.464854\pi$$
0.110190 + 0.993911i $$0.464854\pi$$
$$504$$ 249.415i 0.494872i
$$505$$ 180.000i 0.356436i
$$506$$ −72.0000 + 124.708i −0.142292 + 0.246458i
$$507$$ −268.468 −0.529522
$$508$$ −436.477 756.000i −0.859206 1.48819i
$$509$$ 252.000 0.495088 0.247544 0.968877i $$-0.420376\pi$$
0.247544 + 0.968877i $$0.420376\pi$$
$$510$$ 150.000 + 86.6025i 0.294118 + 0.169809i
$$511$$ 374.123i 0.732139i
$$512$$ 512.000i 1.00000i
$$513$$ 72.0000i 0.140351i
$$514$$ −14.0000 + 24.2487i −0.0272374 + 0.0471765i
$$515$$ 51.9615i 0.100896i
$$516$$ 72.0000 + 124.708i 0.139535 + 0.241682i
$$517$$ 0 0
$$518$$ 561.184 972.000i 1.08337 1.87645i
$$519$$ 252.879i 0.487244i
$$520$$ 720.000i 1.38462i
$$521$$ 54.0000 0.103647 0.0518234 0.998656i $$-0.483497\pi$$
0.0518234 + 0.998656i $$0.483497\pi$$
$$522$$ 187.061 + 108.000i 0.358355 + 0.206897i
$$523$$ −623.538 −1.19223 −0.596117 0.802898i $$-0.703291\pi$$
−0.596117 + 0.802898i $$0.703291\pi$$
$$524$$ 468.000 270.200i 0.893130 0.515649i
$$525$$ 450.000 0.857143
$$526$$ 324.000 + 187.061i 0.615970 + 0.355630i
$$527$$ 69.2820 0.131465
$$528$$ −249.415 144.000i −0.472377 0.272727i
$$529$$ −481.000 −0.909263
$$530$$ 225.167 + 130.000i 0.424843 + 0.245283i
$$531$$ 93.5307i 0.176141i
$$532$$ −498.831 + 288.000i −0.937652 + 0.541353i
$$533$$ 324.000i 0.607880i
$$534$$ 54.0000 + 31.1769i 0.101124 + 0.0583837i
$$535$$ 935.307i 1.74824i
$$536$$ 332.554i 0.620436i
$$537$$ 126.000i 0.234637i
$$538$$ 187.061 + 108.000i 0.347698 + 0.200743i
$$539$$ 613.146i 1.13756i
$$540$$ 90.0000 51.9615i 0.166667 0.0962250i
$$541$$ −650.000 −1.20148 −0.600739 0.799445i $$-0.705127\pi$$
−0.600739 + 0.799445i $$0.705127\pi$$
$$542$$ −325.626 + 564.000i −0.600785 + 1.04059i
$$543$$ 453.797 0.835722
$$544$$ −160.000 277.128i −0.294118 0.509427i
$$545$$ 130.000i 0.238532i
$$546$$ −324.000 + 561.184i −0.593407 + 1.02781i
$$547$$ 685.892 1.25392 0.626958 0.779053i $$-0.284300\pi$$
0.626958 + 0.779053i $$0.284300\pi$$
$$548$$ −381.051 + 220.000i −0.695349 + 0.401460i
$$549$$ −222.000 −0.404372
$$550$$ 259.808 450.000i 0.472377 0.818182i
$$551$$ 498.831i 0.905319i
$$552$$ 96.0000i 0.173913i
$$553$$ 936.000i 1.69259i
$$554$$ −270.000 + 467.654i −0.487365 + 0.844140i
$$555$$ 467.654 0.842619
$$556$$ −648.000 + 374.123i −1.16547 + 0.672883i
$$557$$ 574.000i 1.03052i 0.857034 + 0.515260i $$0.172305\pi$$
−0.857034 + 0.515260i $$0.827695\pi$$
$$558$$ 20.7846 36.0000i 0.0372484 0.0645161i
$$559$$ 374.123i 0.669272i
$$560$$ −720.000 415.692i −1.28571 0.742307i
$$561$$ −180.000 −0.320856
$$562$$ −405.300 234.000i −0.721174 0.416370i
$$563$$ 561.184 0.996775 0.498388 0.866954i $$-0.333926\pi$$
0.498388 + 0.866954i $$0.333926\pi$$
$$564$$ 0 0
$$565$$ 50.0000 0.0884956
$$566$$ −144.000 83.1384i −0.254417 0.146888i
$$567$$ −93.5307 −0.164957
$$568$$ 831.384 1.46370
$$569$$ −198.000 −0.347979 −0.173989 0.984748i $$-0.555666\pi$$
−0.173989 + 0.984748i $$0.555666\pi$$
$$570$$ −207.846 120.000i −0.364642 0.210526i
$$571$$ 180.133i 0.315470i 0.987481 + 0.157735i $$0.0504192\pi$$
−0.987481 + 0.157735i $$0.949581\pi$$
$$572$$ 374.123 + 648.000i 0.654061 + 1.13287i
$$573$$ 324.000i 0.565445i
$$574$$ −324.000 187.061i −0.564460 0.325891i
$$575$$ −173.205 −0.301226
$$576$$ −192.000 −0.333333
$$577$$ 504.000i 0.873484i −0.899587 0.436742i $$-0.856132\pi$$
0.899587 0.436742i $$-0.143868\pi$$
$$578$$ 327.358 + 189.000i 0.566363 + 0.326990i
$$579$$ 311.769i 0.538461i
$$580$$ 623.538 360.000i 1.07507 0.620690i
$$581$$ 936.000 1.61102
$$582$$ 124.708 216.000i 0.214274 0.371134i
$$583$$ −270.200 −0.463465
$$584$$ 288.000 0.493151
$$585$$ −270.000 −0.461538
$$586$$ −58.0000 + 100.459i −0.0989761 + 0.171432i
$$587$$ 408.764 0.696361 0.348181 0.937427i $$-0.386800\pi$$
0.348181 + 0.937427i $$0.386800\pi$$
$$588$$ 204.382 + 354.000i 0.347588 + 0.602041i
$$589$$ −96.0000 −0.162988
$$590$$ 270.000 + 155.885i 0.457627 + 0.264211i
$$591$$ 266.736i 0.451330i
$$592$$ −748.246 432.000i −1.26393 0.729730i
$$593$$ 998.000i 1.68297i −0.540282 0.841484i $$-0.681682\pi$$
0.540282 0.841484i $$-0.318318\pi$$
$$594$$ −54.0000 + 93.5307i −0.0909091 + 0.157459i
$$595$$ −519.615 −0.873303
$$596$$ −576.000 997.661i −0.966443 1.67393i
$$597$$ 324.000i 0.542714i
$$598$$ 124.708 216.000i 0.208541 0.361204i
$$599$$ 540.400i 0.902170i 0.892481 + 0.451085i $$0.148963\pi$$
−0.892481 + 0.451085i $$0.851037\pi$$
$$600$$ 346.410i 0.577350i
$$601$$ −614.000 −1.02163 −0.510815 0.859690i $$-0.670656\pi$$
−0.510815 + 0.859690i $$0.670656\pi$$
$$602$$ −374.123 216.000i −0.621467 0.358804i
$$603$$ −124.708 −0.206812
$$604$$ 648.000 374.123i 1.07285 0.619409i
$$605$$ 65.0000i 0.107438i
$$606$$ 108.000 + 62.3538i 0.178218 + 0.102894i
$$607$$ −654.715 −1.07861 −0.539304 0.842111i $$-0.681313\pi$$
−0.539304 + 0.842111i $$0.681313\pi$$
$$608$$ 221.703 + 384.000i 0.364642 + 0.631579i
$$609$$ −648.000 −1.06404
$$610$$ −370.000 + 640.859i −0.606557 + 1.05059i
$$611$$ 0 0
$$612$$ −103.923 + 60.0000i −0.169809 + 0.0980392i
$$613$$ 414.000i 0.675367i −0.941260 0.337684i $$-0.890357\pi$$
0.941260 0.337684i $$-0.109643\pi$$
$$614$$ 468.000 + 270.200i 0.762215 + 0.440065i
$$615$$ 155.885i 0.253471i
$$616$$ 864.000 1.40260
$$617$$ 58.0000i 0.0940032i 0.998895 + 0.0470016i $$0.0149666\pi$$
−0.998895 + 0.0470016i $$0.985033\pi$$
$$618$$ 31.1769 + 18.0000i 0.0504481 + 0.0291262i
$$619$$ 187.061i 0.302199i −0.988519 0.151100i $$-0.951719\pi$$
0.988519 0.151100i $$-0.0482815\pi$$
$$620$$ −69.2820 120.000i −0.111745 0.193548i
$$621$$ 36.0000 0.0579710
$$622$$ −270.200 + 468.000i −0.434405 + 0.752412i
$$623$$ −187.061 −0.300259
$$624$$ 432.000 + 249.415i 0.692308 + 0.399704i
$$625$$ 625.000 1.00000
$$626$$ 468.000 810.600i 0.747604 1.29489i
$$627$$ 249.415 0.397792
$$628$$ −810.600 + 468.000i −1.29076 + 0.745223i
$$629$$ −540.000 −0.858506
$$630$$ −155.885 + 270.000i −0.247436 + 0.428571i
$$631$$ 824.456i 1.30659i −0.757105 0.653293i $$-0.773387\pi$$
0.757105 0.653293i $$-0.226613\pi$$
$$632$$ 720.533 1.14008
$$633$$ 420.000i 0.663507i
$$634$$ −250.000 + 433.013i −0.394322 + 0.682985i
$$635$$ 1091.19i 1.71841i
$$636$$ −156.000 + 90.0666i −0.245283 + 0.141614i
$$637$$ 1062.00i 1.66719i
$$638$$ −374.123 + 648.000i −0.586400 + 1.01567i
$$639$$ 311.769i 0.487902i
$$640$$ −320.000 + 554.256i −0.500000 + 0.866025i
$$641$$ 810.000 1.26365 0.631825 0.775111i $$-0.282306\pi$$
0.631825 + 0.775111i $$0.282306\pi$$
$$642$$ 561.184 + 324.000i 0.874119 + 0.504673i
$$643$$ −415.692 −0.646489 −0.323244 0.946316i $$-0.604774\pi$$
−0.323244 + 0.946316i $$0.604774\pi$$
$$644$$ −144.000 249.415i −0.223602 0.387291i
$$645$$ 180.000i 0.279070i
$$646$$ 240.000 + 138.564i 0.371517 + 0.214495i
$$647$$ −983.805 −1.52056 −0.760282 0.649593i $$-0.774939\pi$$
−0.760282 + 0.649593i $$0.774939\pi$$
$$648$$ 72.0000i 0.111111i
$$649$$ −324.000 −0.499230
$$650$$ −450.000 + 779.423i −0.692308 + 1.19911i
$$651$$ 124.708i 0.191563i
$$652$$ 249.415 + 432.000i 0.382539 + 0.662577i
$$653$$ 950.000i 1.45482i 0.686201 + 0.727412i $$0.259277\pi$$
−0.686201 + 0.727412i $$0.740723\pi$$
$$654$$ 78.0000 + 45.0333i 0.119266 + 0.0688583i
$$655$$ −675.500 −1.03130
$$656$$ −144.000 + 249.415i −0.219512 + 0.380206i
$$657$$ 108.000i 0.164384i
$$658$$ 0 0
$$659$$ 1132.76i 1.71891i 0.511212 + 0.859455i $$0.329197\pi$$
−0.511212 + 0.859455i $$0.670803\pi$$
$$660$$ 180.000 + 311.769i 0.272727 + 0.472377i
$$661$$ −242.000 −0.366112 −0.183056 0.983102i $$-0.558599\pi$$
−0.183056 + 0.983102i $$0.558599\pi$$
$$662$$ 374.123 648.000i 0.565140 0.978852i
$$663$$ 311.769 0.470240
$$664$$ 720.533i 1.08514i
$$665$$ 720.000 1.08271
$$666$$ −162.000 + 280.592i −0.243243 + 0.421310i
$$667$$ 249.415 0.373936
$$668$$ −263.272 456.000i −0.394119 0.682635i
$$669$$ 162.000 0.242152
$$670$$ −207.846 + 360.000i −0.310218 + 0.537313i
$$671$$ 769.031i 1.14610i
$$672$$ 498.831 288.000i 0.742307 0.428571i
$$673$$ 324.000i 0.481426i −0.970596 0.240713i $$-0.922619\pi$$
0.970596 0.240713i $$-0.0773813\pi$$
$$674$$ 468.000 810.600i 0.694362 1.20267i
$$675$$ −129.904 −0.192450
$$676$$ −310.000 536.936i −0.458580 0.794284i
$$677$$ 806.000i 1.19055i −0.803523 0.595273i $$-0.797044\pi$$
0.803523 0.595273i $$-0.202956\pi$$
$$678$$ −17.3205 + 30.0000i −0.0255465 + 0.0442478i
$$679$$ 748.246i 1.10198i
$$680$$ 400.000i 0.588235i
$$681$$ 372.000 0.546256
$$682$$ 124.708 + 72.0000i 0.182856 + 0.105572i
$$683$$ 575.041 0.841934 0.420967 0.907076i $$-0.361691\pi$$
0.420967 + 0.907076i $$0.361691\pi$$
$$684$$ 144.000 83.1384i 0.210526 0.121547i
$$685$$ 550.000 0.802920
$$686$$ −180.000 103.923i −0.262391 0.151491i
$$687$$ −585.433 −0.852159
$$688$$ −166.277 + 288.000i −0.241682 + 0.418605i
$$689$$ 468.000 0.679245
$$690$$ 60.0000 103.923i 0.0869565 0.150613i
$$691$$ 775.959i 1.12295i 0.827494 + 0.561475i $$0.189766\pi$$
−0.827494 + 0.561475i $$0.810234\pi$$
$$692$$ 505.759 292.000i 0.730865 0.421965i
$$693$$ 324.000i 0.467532i
$$694$$ 972.000 + 561.184i 1.40058 + 0.808623i
$$695$$ 935.307 1.34577
$$696$$ 498.831i 0.716711i
$$697$$ 180.000i 0.258250i
$$698$$ 751.710 + 434.000i 1.07695 + 0.621777i
$$699$$ 315.233i 0.450977i
$$700$$ 519.615 + 900.000i 0.742307 + 1.28571i
$$701$$ 756.000 1.07846 0.539230 0.842159i $$-0.318715\pi$$
0.539230 + 0.842159i $$0.318715\pi$$
$$702$$ 93.5307 162.000i 0.133235 0.230769i
$$703$$ 748.246 1.06436
$$704$$ 665.108i 0.944755i
$$705$$ 0 0
$$706$$ −158.000 + 273.664i −0.223796 + 0.387626i
$$707$$ −374.123 −0.529170
$$708$$ −187.061 + 108.000i −0.264211 + 0.152542i
$$709$$ 310.000 0.437236 0.218618 0.975811i $$-0.429845\pi$$
0.218618 + 0.975811i $$0.429845\pi$$
$$710$$ −900.000 519.615i −1.26761 0.731852i
$$711$$ 270.200i 0.380028i
$$712$$ 144.000i 0.202247i
$$713$$ 48.0000i 0.0673212i
$$714$$ 180.000 311.769i 0.252101 0.436651i
$$715$$ 935.307i 1.30812i
$$716$$ −252.000 + 145.492i −0.351955 + 0.203201i
$$717$$ 612.000i 0.853556i
$$718$$ 457.261 792.000i 0.636854 1.10306i
$$719$$ 83.1384i 0.115631i −0.998327 0.0578153i $$-0.981587\pi$$
0.998327 0.0578153i $$-0.0184135\pi$$
$$720$$ 207.846 + 120.000i 0.288675 + 0.166667i
$$721$$ −108.000 −0.149792
$$722$$ 292.717 + 169.000i 0.405425 + 0.234072i
$$723$$ −183.597 −0.253938
$$724$$ 524.000 + 907.595i 0.723757 + 1.25358i
$$725$$ −900.000 −1.24138
$$726$$ 39.0000 + 22.5167i 0.0537190 + 0.0310147i
$$727$$ 1091.19 1.50095 0.750476 0.660898i $$-0.229824\pi$$
0.750476 + 0.660898i $$0.229824\pi$$
$$728$$ −1496.49 −2.05562
$$729$$ 27.0000 0.0370370
$$730$$ −311.769 180.000i −0.427081 0.246575i
$$731$$ 207.846i 0.284331i
$$732$$ −256.344 444.000i −0.350196 0.606557i
$$733$$ 1206.00i 1.64529i −0.568553 0.822647i $$-0.692497\pi$$
0.568553 0.822647i $$-0.307503\pi$$
$$734$$ −378.000 218.238i −0.514986 0.297328i
$$735$$ 510.955i 0.695177i
$$736$$ −192.000 + 110.851i −0.260870 + 0.150613i
$$737$$ 432.000i 0.586160i
$$738$$ 93.5307 + 54.0000i 0.126735 + 0.0731707i
$$739$$ 484.974i 0.656257i −0.944633 0.328129i $$-0.893582\pi$$
0.944633 0.328129i $$-0.106418\pi$$
$$740$$ 540.000 + 935.307i 0.729730 + 1.26393i
$$741$$ −432.000 −0.582996
$$742$$ 270.200 468.000i 0.364151 0.630728i
$$743$$ −1122.37 −1.51059 −0.755295 0.655385i $$-0.772507\pi$$
−0.755295 + 0.655385i $$0.772507\pi$$
$$744$$ 96.0000 0.129032
$$745$$ 1440.00i 1.93289i
$$746$$ −270.000 + 467.654i −0.361930 + 0.626882i
$$747$$ −270.200 −0.361713
$$748$$ −207.846 360.000i −0.277869 0.481283i
$$749$$ −1944.00 −2.59546
$$750$$ −216.506 + 375.000i −0.288675 + 0.500000i
$$751$$ 242.487i 0.322886i −0.986882 0.161443i $$-0.948385\pi$$
0.986882 0.161443i $$-0.0516147\pi$$
$$752$$ 0 0
$$753$$ 558.000i 0.741036i
$$754$$ 648.000 1122.37i 0.859416 1.48855i
$$755$$ −935.307 −1.23882
$$756$$ −108.000 187.061i −0.142857 0.247436i
$$757$$ 846.000i 1.11757i 0.829313 + 0.558785i $$0.188732\pi$$
−0.829313 + 0.558785i $$0.811268\pi$$
$$758$$ −325.626 + 564.000i −0.429585 + 0.744063i
$$759$$ 124.708i 0.164305i
$$760$$ 554.256i 0.729285i
$$761$$ −1458.00 −1.91590 −0.957950 0.286935i $$-0.907364\pi$$
−0.957950 + 0.286935i $$0.907364\pi$$
$$762$$ −654.715 378.000i −0.859206 0.496063i
$$763$$ −270.200 −0.354128
$$764$$ −648.000 + 374.123i −0.848168 + 0.489690i
$$765$$ 150.000 0.196078
$$766$$ −96.0000 55.4256i −0.125326 0.0723572i
$$767$$ 561.184 0.731662
$$768$$ −221.703 384.000i −0.288675 0.500000i
$$769$$ −1282.00 −1.66710 −0.833550 0.552444i $$-0.813695\pi$$
−0.833550 + 0.552444i $$0.813695\pi$$
$$770$$ −935.307 540.000i −1.21468 0.701299i
$$771$$ 24.2487i 0.0314510i
$$772$$ 623.538 360.000i 0.807692 0.466321i
$$773$$ 422.000i 0.545925i 0.962025 + 0.272962i $$0.0880035\pi$$
−0.962025 + 0.272962i $$0.911997\pi$$
$$774$$ 108.000 + 62.3538i 0.139535 + 0.0805605i
$$775$$ 173.205i 0.223490i
$$776$$ 576.000 0.742268
$$777$$ 972.000i 1.25097i
$$778$$ 498.831 + 288.000i 0.641170 + 0.370180i
$$779$$ 249.415i 0.320174i
$$780$$ −311.769 540.000i −0.399704 0.692308i
$$781$$ 1080.00 1.38284