# Properties

 Label 1950.2.bc.b.901.1 Level $1950$ Weight $2$ Character 1950.901 Analytic conductor $15.571$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1950.bc (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$15.5708283941$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\zeta_{12})$$ Defining polynomial: $$x^{4} - x^{2} + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 390) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 901.1 Root $$-0.866025 + 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 1950.901 Dual form 1950.2.bc.b.751.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(-1.73205 + 1.00000i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(-1.73205 + 1.00000i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.401924 + 0.232051i) q^{11} -1.00000 q^{12} +(-1.00000 + 3.46410i) q^{13} +2.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.00000 - 3.46410i) q^{17} +1.00000i q^{18} +(-0.464102 + 0.267949i) q^{19} -2.00000i q^{21} +(-0.232051 - 0.401924i) q^{22} +(0.133975 - 0.232051i) q^{23} +(0.866025 + 0.500000i) q^{24} +(2.59808 - 2.50000i) q^{26} +1.00000 q^{27} +(-1.73205 - 1.00000i) q^{28} +(-1.86603 + 3.23205i) q^{29} -1.73205i q^{31} +(0.866025 - 0.500000i) q^{32} +(-0.401924 + 0.232051i) q^{33} +4.00000i q^{34} +(0.500000 - 0.866025i) q^{36} +(-1.03590 - 0.598076i) q^{37} +0.535898 q^{38} +(-2.50000 - 2.59808i) q^{39} +(-1.73205 - 1.00000i) q^{41} +(-1.00000 + 1.73205i) q^{42} +(-0.964102 - 1.66987i) q^{43} +0.464102i q^{44} +(-0.232051 + 0.133975i) q^{46} -10.4641i q^{47} +(-0.500000 - 0.866025i) q^{48} +(-1.50000 + 2.59808i) q^{49} +4.00000 q^{51} +(-3.50000 + 0.866025i) q^{52} +12.9282 q^{53} +(-0.866025 - 0.500000i) q^{54} +(1.00000 + 1.73205i) q^{56} -0.535898i q^{57} +(3.23205 - 1.86603i) q^{58} +(-1.33013 + 0.767949i) q^{59} +(-5.19615 - 9.00000i) q^{61} +(-0.866025 + 1.50000i) q^{62} +(1.73205 + 1.00000i) q^{63} -1.00000 q^{64} +0.464102 q^{66} +(-3.92820 - 2.26795i) q^{67} +(2.00000 - 3.46410i) q^{68} +(0.133975 + 0.232051i) q^{69} +(-7.26795 + 4.19615i) q^{71} +(-0.866025 + 0.500000i) q^{72} +2.00000i q^{73} +(0.598076 + 1.03590i) q^{74} +(-0.464102 - 0.267949i) q^{76} -0.928203 q^{77} +(0.866025 + 3.50000i) q^{78} -0.0717968 q^{79} +(-0.500000 + 0.866025i) q^{81} +(1.00000 + 1.73205i) q^{82} -4.92820i q^{83} +(1.73205 - 1.00000i) q^{84} +1.92820i q^{86} +(-1.86603 - 3.23205i) q^{87} +(0.232051 - 0.401924i) q^{88} +(6.46410 + 3.73205i) q^{89} +(-1.73205 - 7.00000i) q^{91} +0.267949 q^{92} +(1.50000 + 0.866025i) q^{93} +(-5.23205 + 9.06218i) q^{94} +1.00000i q^{96} +(6.46410 - 3.73205i) q^{97} +(2.59808 - 1.50000i) q^{98} -0.464102i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q - 2q^{3} + 2q^{4} - 2q^{9} + O(q^{10})$$ $$4q - 2q^{3} + 2q^{4} - 2q^{9} + 12q^{11} - 4q^{12} - 4q^{13} + 8q^{14} - 2q^{16} - 8q^{17} + 12q^{19} + 6q^{22} + 4q^{23} + 4q^{27} - 4q^{29} - 12q^{33} + 2q^{36} - 18q^{37} + 16q^{38} - 10q^{39} - 4q^{42} + 10q^{43} + 6q^{46} - 2q^{48} - 6q^{49} + 16q^{51} - 14q^{52} + 24q^{53} + 4q^{56} + 6q^{58} + 12q^{59} - 4q^{64} - 12q^{66} + 12q^{67} + 8q^{68} + 4q^{69} - 36q^{71} - 8q^{74} + 12q^{76} + 24q^{77} - 28q^{79} - 2q^{81} + 4q^{82} - 4q^{87} - 6q^{88} + 12q^{89} + 8q^{92} + 6q^{93} - 14q^{94} + 12q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$$.

 $$n$$ $$301$$ $$1301$$ $$1327$$ $$\chi(n)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.866025 0.500000i −0.612372 0.353553i
$$3$$ −0.500000 + 0.866025i −0.288675 + 0.500000i
$$4$$ 0.500000 + 0.866025i 0.250000 + 0.433013i
$$5$$ 0 0
$$6$$ 0.866025 0.500000i 0.353553 0.204124i
$$7$$ −1.73205 + 1.00000i −0.654654 + 0.377964i −0.790237 0.612801i $$-0.790043\pi$$
0.135583 + 0.990766i $$0.456709\pi$$
$$8$$ 1.00000i 0.353553i
$$9$$ −0.500000 0.866025i −0.166667 0.288675i
$$10$$ 0 0
$$11$$ 0.401924 + 0.232051i 0.121185 + 0.0699660i 0.559367 0.828920i $$-0.311044\pi$$
−0.438182 + 0.898886i $$0.644378\pi$$
$$12$$ −1.00000 −0.288675
$$13$$ −1.00000 + 3.46410i −0.277350 + 0.960769i
$$14$$ 2.00000 0.534522
$$15$$ 0 0
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ −2.00000 3.46410i −0.485071 0.840168i 0.514782 0.857321i $$-0.327873\pi$$
−0.999853 + 0.0171533i $$0.994540\pi$$
$$18$$ 1.00000i 0.235702i
$$19$$ −0.464102 + 0.267949i −0.106472 + 0.0614718i −0.552291 0.833652i $$-0.686246\pi$$
0.445818 + 0.895123i $$0.352913\pi$$
$$20$$ 0 0
$$21$$ 2.00000i 0.436436i
$$22$$ −0.232051 0.401924i −0.0494734 0.0856904i
$$23$$ 0.133975 0.232051i 0.0279356 0.0483859i −0.851720 0.523998i $$-0.824440\pi$$
0.879655 + 0.475612i $$0.157773\pi$$
$$24$$ 0.866025 + 0.500000i 0.176777 + 0.102062i
$$25$$ 0 0
$$26$$ 2.59808 2.50000i 0.509525 0.490290i
$$27$$ 1.00000 0.192450
$$28$$ −1.73205 1.00000i −0.327327 0.188982i
$$29$$ −1.86603 + 3.23205i −0.346512 + 0.600177i −0.985627 0.168934i $$-0.945967\pi$$
0.639115 + 0.769111i $$0.279301\pi$$
$$30$$ 0 0
$$31$$ 1.73205i 0.311086i −0.987829 0.155543i $$-0.950287\pi$$
0.987829 0.155543i $$-0.0497126\pi$$
$$32$$ 0.866025 0.500000i 0.153093 0.0883883i
$$33$$ −0.401924 + 0.232051i −0.0699660 + 0.0403949i
$$34$$ 4.00000i 0.685994i
$$35$$ 0 0
$$36$$ 0.500000 0.866025i 0.0833333 0.144338i
$$37$$ −1.03590 0.598076i −0.170301 0.0983231i 0.412427 0.910991i $$-0.364681\pi$$
−0.582728 + 0.812668i $$0.698015\pi$$
$$38$$ 0.535898 0.0869342
$$39$$ −2.50000 2.59808i −0.400320 0.416025i
$$40$$ 0 0
$$41$$ −1.73205 1.00000i −0.270501 0.156174i 0.358614 0.933486i $$-0.383249\pi$$
−0.629115 + 0.777312i $$0.716583\pi$$
$$42$$ −1.00000 + 1.73205i −0.154303 + 0.267261i
$$43$$ −0.964102 1.66987i −0.147024 0.254653i 0.783102 0.621893i $$-0.213636\pi$$
−0.930126 + 0.367240i $$0.880303\pi$$
$$44$$ 0.464102i 0.0699660i
$$45$$ 0 0
$$46$$ −0.232051 + 0.133975i −0.0342140 + 0.0197535i
$$47$$ 10.4641i 1.52635i −0.646194 0.763173i $$-0.723640\pi$$
0.646194 0.763173i $$-0.276360\pi$$
$$48$$ −0.500000 0.866025i −0.0721688 0.125000i
$$49$$ −1.50000 + 2.59808i −0.214286 + 0.371154i
$$50$$ 0 0
$$51$$ 4.00000 0.560112
$$52$$ −3.50000 + 0.866025i −0.485363 + 0.120096i
$$53$$ 12.9282 1.77583 0.887913 0.460012i $$-0.152155\pi$$
0.887913 + 0.460012i $$0.152155\pi$$
$$54$$ −0.866025 0.500000i −0.117851 0.0680414i
$$55$$ 0 0
$$56$$ 1.00000 + 1.73205i 0.133631 + 0.231455i
$$57$$ 0.535898i 0.0709815i
$$58$$ 3.23205 1.86603i 0.424389 0.245021i
$$59$$ −1.33013 + 0.767949i −0.173168 + 0.0999785i −0.584079 0.811697i $$-0.698544\pi$$
0.410911 + 0.911676i $$0.365211\pi$$
$$60$$ 0 0
$$61$$ −5.19615 9.00000i −0.665299 1.15233i −0.979204 0.202878i $$-0.934971\pi$$
0.313905 0.949454i $$-0.398363\pi$$
$$62$$ −0.866025 + 1.50000i −0.109985 + 0.190500i
$$63$$ 1.73205 + 1.00000i 0.218218 + 0.125988i
$$64$$ −1.00000 −0.125000
$$65$$ 0 0
$$66$$ 0.464102 0.0571270
$$67$$ −3.92820 2.26795i −0.479906 0.277074i 0.240471 0.970656i $$-0.422698\pi$$
−0.720377 + 0.693582i $$0.756031\pi$$
$$68$$ 2.00000 3.46410i 0.242536 0.420084i
$$69$$ 0.133975 + 0.232051i 0.0161286 + 0.0279356i
$$70$$ 0 0
$$71$$ −7.26795 + 4.19615i −0.862547 + 0.497992i −0.864864 0.502006i $$-0.832596\pi$$
0.00231747 + 0.999997i $$0.499262\pi$$
$$72$$ −0.866025 + 0.500000i −0.102062 + 0.0589256i
$$73$$ 2.00000i 0.234082i 0.993127 + 0.117041i $$0.0373409\pi$$
−0.993127 + 0.117041i $$0.962659\pi$$
$$74$$ 0.598076 + 1.03590i 0.0695249 + 0.120421i
$$75$$ 0 0
$$76$$ −0.464102 0.267949i −0.0532361 0.0307359i
$$77$$ −0.928203 −0.105779
$$78$$ 0.866025 + 3.50000i 0.0980581 + 0.396297i
$$79$$ −0.0717968 −0.00807777 −0.00403888 0.999992i $$-0.501286\pi$$
−0.00403888 + 0.999992i $$0.501286\pi$$
$$80$$ 0 0
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ 1.00000 + 1.73205i 0.110432 + 0.191273i
$$83$$ 4.92820i 0.540941i −0.962728 0.270470i $$-0.912821\pi$$
0.962728 0.270470i $$-0.0871792\pi$$
$$84$$ 1.73205 1.00000i 0.188982 0.109109i
$$85$$ 0 0
$$86$$ 1.92820i 0.207924i
$$87$$ −1.86603 3.23205i −0.200059 0.346512i
$$88$$ 0.232051 0.401924i 0.0247367 0.0428452i
$$89$$ 6.46410 + 3.73205i 0.685193 + 0.395597i 0.801809 0.597581i $$-0.203871\pi$$
−0.116615 + 0.993177i $$0.537205\pi$$
$$90$$ 0 0
$$91$$ −1.73205 7.00000i −0.181568 0.733799i
$$92$$ 0.267949 0.0279356
$$93$$ 1.50000 + 0.866025i 0.155543 + 0.0898027i
$$94$$ −5.23205 + 9.06218i −0.539645 + 0.934692i
$$95$$ 0 0
$$96$$ 1.00000i 0.102062i
$$97$$ 6.46410 3.73205i 0.656330 0.378932i −0.134547 0.990907i $$-0.542958\pi$$
0.790877 + 0.611975i $$0.209625\pi$$
$$98$$ 2.59808 1.50000i 0.262445 0.151523i
$$99$$ 0.464102i 0.0466440i
$$100$$ 0 0
$$101$$ 5.46410 9.46410i 0.543698 0.941713i −0.454989 0.890497i $$-0.650357\pi$$
0.998688 0.0512163i $$-0.0163098\pi$$
$$102$$ −3.46410 2.00000i −0.342997 0.198030i
$$103$$ −15.8564 −1.56238 −0.781189 0.624295i $$-0.785387\pi$$
−0.781189 + 0.624295i $$0.785387\pi$$
$$104$$ 3.46410 + 1.00000i 0.339683 + 0.0980581i
$$105$$ 0 0
$$106$$ −11.1962 6.46410i −1.08747 0.627849i
$$107$$ 9.92820 17.1962i 0.959796 1.66241i 0.236805 0.971557i $$-0.423900\pi$$
0.722991 0.690858i $$-0.242767\pi$$
$$108$$ 0.500000 + 0.866025i 0.0481125 + 0.0833333i
$$109$$ 11.8564i 1.13564i −0.823154 0.567819i $$-0.807787\pi$$
0.823154 0.567819i $$-0.192213\pi$$
$$110$$ 0 0
$$111$$ 1.03590 0.598076i 0.0983231 0.0567669i
$$112$$ 2.00000i 0.188982i
$$113$$ 5.59808 + 9.69615i 0.526623 + 0.912137i 0.999519 + 0.0310191i $$0.00987527\pi$$
−0.472896 + 0.881118i $$0.656791\pi$$
$$114$$ −0.267949 + 0.464102i −0.0250957 + 0.0434671i
$$115$$ 0 0
$$116$$ −3.73205 −0.346512
$$117$$ 3.50000 0.866025i 0.323575 0.0800641i
$$118$$ 1.53590 0.141391
$$119$$ 6.92820 + 4.00000i 0.635107 + 0.366679i
$$120$$ 0 0
$$121$$ −5.39230 9.33975i −0.490210 0.849068i
$$122$$ 10.3923i 0.940875i
$$123$$ 1.73205 1.00000i 0.156174 0.0901670i
$$124$$ 1.50000 0.866025i 0.134704 0.0777714i
$$125$$ 0 0
$$126$$ −1.00000 1.73205i −0.0890871 0.154303i
$$127$$ 4.46410 7.73205i 0.396125 0.686109i −0.597119 0.802153i $$-0.703688\pi$$
0.993244 + 0.116044i $$0.0370214\pi$$
$$128$$ 0.866025 + 0.500000i 0.0765466 + 0.0441942i
$$129$$ 1.92820 0.169769
$$130$$ 0 0
$$131$$ −1.33975 −0.117054 −0.0585271 0.998286i $$-0.518640\pi$$
−0.0585271 + 0.998286i $$0.518640\pi$$
$$132$$ −0.401924 0.232051i −0.0349830 0.0201974i
$$133$$ 0.535898 0.928203i 0.0464683 0.0804854i
$$134$$ 2.26795 + 3.92820i 0.195921 + 0.339345i
$$135$$ 0 0
$$136$$ −3.46410 + 2.00000i −0.297044 + 0.171499i
$$137$$ 3.86603 2.23205i 0.330297 0.190697i −0.325676 0.945481i $$-0.605592\pi$$
0.655973 + 0.754784i $$0.272259\pi$$
$$138$$ 0.267949i 0.0228093i
$$139$$ −0.464102 0.803848i −0.0393646 0.0681815i 0.845672 0.533703i $$-0.179200\pi$$
−0.885036 + 0.465522i $$0.845867\pi$$
$$140$$ 0 0
$$141$$ 9.06218 + 5.23205i 0.763173 + 0.440618i
$$142$$ 8.39230 0.704267
$$143$$ −1.20577 + 1.16025i −0.100832 + 0.0970253i
$$144$$ 1.00000 0.0833333
$$145$$ 0 0
$$146$$ 1.00000 1.73205i 0.0827606 0.143346i
$$147$$ −1.50000 2.59808i −0.123718 0.214286i
$$148$$ 1.19615i 0.0983231i
$$149$$ 17.7224 10.2321i 1.45188 0.838242i 0.453290 0.891363i $$-0.350250\pi$$
0.998588 + 0.0531208i $$0.0169168\pi$$
$$150$$ 0 0
$$151$$ 10.3923i 0.845714i −0.906196 0.422857i $$-0.861027\pi$$
0.906196 0.422857i $$-0.138973\pi$$
$$152$$ 0.267949 + 0.464102i 0.0217335 + 0.0376436i
$$153$$ −2.00000 + 3.46410i −0.161690 + 0.280056i
$$154$$ 0.803848 + 0.464102i 0.0647759 + 0.0373984i
$$155$$ 0 0
$$156$$ 1.00000 3.46410i 0.0800641 0.277350i
$$157$$ 5.00000 0.399043 0.199522 0.979893i $$-0.436061\pi$$
0.199522 + 0.979893i $$0.436061\pi$$
$$158$$ 0.0621778 + 0.0358984i 0.00494660 + 0.00285592i
$$159$$ −6.46410 + 11.1962i −0.512637 + 0.887913i
$$160$$ 0 0
$$161$$ 0.535898i 0.0422347i
$$162$$ 0.866025 0.500000i 0.0680414 0.0392837i
$$163$$ −19.9641 + 11.5263i −1.56371 + 0.902808i −0.566833 + 0.823833i $$0.691831\pi$$
−0.996877 + 0.0789748i $$0.974835\pi$$
$$164$$ 2.00000i 0.156174i
$$165$$ 0 0
$$166$$ −2.46410 + 4.26795i −0.191251 + 0.331257i
$$167$$ −15.8660 9.16025i −1.22775 0.708842i −0.261191 0.965287i $$-0.584115\pi$$
−0.966559 + 0.256445i $$0.917449\pi$$
$$168$$ −2.00000 −0.154303
$$169$$ −11.0000 6.92820i −0.846154 0.532939i
$$170$$ 0 0
$$171$$ 0.464102 + 0.267949i 0.0354907 + 0.0204906i
$$172$$ 0.964102 1.66987i 0.0735121 0.127327i
$$173$$ −1.46410 2.53590i −0.111314 0.192801i 0.804987 0.593293i $$-0.202172\pi$$
−0.916300 + 0.400492i $$0.868839\pi$$
$$174$$ 3.73205i 0.282926i
$$175$$ 0 0
$$176$$ −0.401924 + 0.232051i −0.0302961 + 0.0174915i
$$177$$ 1.53590i 0.115445i
$$178$$ −3.73205 6.46410i −0.279729 0.484505i
$$179$$ 8.13397 14.0885i 0.607962 1.05302i −0.383614 0.923494i $$-0.625321\pi$$
0.991576 0.129527i $$-0.0413460\pi$$
$$180$$ 0 0
$$181$$ 10.9282 0.812287 0.406143 0.913809i $$-0.366873\pi$$
0.406143 + 0.913809i $$0.366873\pi$$
$$182$$ −2.00000 + 6.92820i −0.148250 + 0.513553i
$$183$$ 10.3923 0.768221
$$184$$ −0.232051 0.133975i −0.0171070 0.00987674i
$$185$$ 0 0
$$186$$ −0.866025 1.50000i −0.0635001 0.109985i
$$187$$ 1.85641i 0.135754i
$$188$$ 9.06218 5.23205i 0.660927 0.381587i
$$189$$ −1.73205 + 1.00000i −0.125988 + 0.0727393i
$$190$$ 0 0
$$191$$ −7.26795 12.5885i −0.525890 0.910869i −0.999545 0.0301582i $$-0.990399\pi$$
0.473655 0.880711i $$-0.342934\pi$$
$$192$$ 0.500000 0.866025i 0.0360844 0.0625000i
$$193$$ −20.1962 11.6603i −1.45375 0.839323i −0.455059 0.890461i $$-0.650382\pi$$
−0.998692 + 0.0511377i $$0.983715\pi$$
$$194$$ −7.46410 −0.535891
$$195$$ 0 0
$$196$$ −3.00000 −0.214286
$$197$$ −14.1962 8.19615i −1.01143 0.583952i −0.0998228 0.995005i $$-0.531828\pi$$
−0.911611 + 0.411054i $$0.865161\pi$$
$$198$$ −0.232051 + 0.401924i −0.0164911 + 0.0285635i
$$199$$ 9.46410 + 16.3923i 0.670892 + 1.16202i 0.977651 + 0.210232i $$0.0674221\pi$$
−0.306759 + 0.951787i $$0.599245\pi$$
$$200$$ 0 0
$$201$$ 3.92820 2.26795i 0.277074 0.159969i
$$202$$ −9.46410 + 5.46410i −0.665892 + 0.384453i
$$203$$ 7.46410i 0.523877i
$$204$$ 2.00000 + 3.46410i 0.140028 + 0.242536i
$$205$$ 0 0
$$206$$ 13.7321 + 7.92820i 0.956757 + 0.552384i
$$207$$ −0.267949 −0.0186238
$$208$$ −2.50000 2.59808i −0.173344 0.180144i
$$209$$ −0.248711 −0.0172037
$$210$$ 0 0
$$211$$ −11.6603 + 20.1962i −0.802725 + 1.39036i 0.115091 + 0.993355i $$0.463284\pi$$
−0.917816 + 0.397006i $$0.870049\pi$$
$$212$$ 6.46410 + 11.1962i 0.443956 + 0.768955i
$$213$$ 8.39230i 0.575031i
$$214$$ −17.1962 + 9.92820i −1.17550 + 0.678678i
$$215$$ 0 0
$$216$$ 1.00000i 0.0680414i
$$217$$ 1.73205 + 3.00000i 0.117579 + 0.203653i
$$218$$ −5.92820 + 10.2679i −0.401509 + 0.695433i
$$219$$ −1.73205 1.00000i −0.117041 0.0675737i
$$220$$ 0 0
$$221$$ 14.0000 3.46410i 0.941742 0.233021i
$$222$$ −1.19615 −0.0802805
$$223$$ −23.7846 13.7321i −1.59274 0.919566i −0.992835 0.119491i $$-0.961874\pi$$
−0.599900 0.800075i $$-0.704793\pi$$
$$224$$ −1.00000 + 1.73205i −0.0668153 + 0.115728i
$$225$$ 0 0
$$226$$ 11.1962i 0.744757i
$$227$$ 3.80385 2.19615i 0.252470 0.145764i −0.368425 0.929658i $$-0.620103\pi$$
0.620895 + 0.783894i $$0.286769\pi$$
$$228$$ 0.464102 0.267949i 0.0307359 0.0177454i
$$229$$ 19.8564i 1.31215i −0.754696 0.656074i $$-0.772216\pi$$
0.754696 0.656074i $$-0.227784\pi$$
$$230$$ 0 0
$$231$$ 0.464102 0.803848i 0.0305356 0.0528893i
$$232$$ 3.23205 + 1.86603i 0.212195 + 0.122511i
$$233$$ 18.1244 1.18737 0.593683 0.804699i $$-0.297673\pi$$
0.593683 + 0.804699i $$0.297673\pi$$
$$234$$ −3.46410 1.00000i −0.226455 0.0653720i
$$235$$ 0 0
$$236$$ −1.33013 0.767949i −0.0865839 0.0499892i
$$237$$ 0.0358984 0.0621778i 0.00233185 0.00403888i
$$238$$ −4.00000 6.92820i −0.259281 0.449089i
$$239$$ 4.39230i 0.284115i −0.989858 0.142057i $$-0.954628\pi$$
0.989858 0.142057i $$-0.0453717\pi$$
$$240$$ 0 0
$$241$$ −12.3564 + 7.13397i −0.795946 + 0.459540i −0.842052 0.539397i $$-0.818652\pi$$
0.0461056 + 0.998937i $$0.485319\pi$$
$$242$$ 10.7846i 0.693261i
$$243$$ −0.500000 0.866025i −0.0320750 0.0555556i
$$244$$ 5.19615 9.00000i 0.332650 0.576166i
$$245$$ 0 0
$$246$$ −2.00000 −0.127515
$$247$$ −0.464102 1.87564i −0.0295301 0.119344i
$$248$$ −1.73205 −0.109985
$$249$$ 4.26795 + 2.46410i 0.270470 + 0.156156i
$$250$$ 0 0
$$251$$ −6.13397 10.6244i −0.387173 0.670603i 0.604895 0.796305i $$-0.293215\pi$$
−0.992068 + 0.125702i $$0.959882\pi$$
$$252$$ 2.00000i 0.125988i
$$253$$ 0.107695 0.0621778i 0.00677074 0.00390909i
$$254$$ −7.73205 + 4.46410i −0.485152 + 0.280103i
$$255$$ 0 0
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ −11.3301 + 19.6244i −0.706754 + 1.22413i 0.259301 + 0.965797i $$0.416508\pi$$
−0.966055 + 0.258337i $$0.916825\pi$$
$$258$$ −1.66987 0.964102i −0.103962 0.0600223i
$$259$$ 2.39230 0.148651
$$260$$ 0 0
$$261$$ 3.73205 0.231008
$$262$$ 1.16025 + 0.669873i 0.0716807 + 0.0413849i
$$263$$ −9.06218 + 15.6962i −0.558798 + 0.967866i 0.438799 + 0.898585i $$0.355404\pi$$
−0.997597 + 0.0692812i $$0.977929\pi$$
$$264$$ 0.232051 + 0.401924i 0.0142817 + 0.0247367i
$$265$$ 0 0
$$266$$ −0.928203 + 0.535898i −0.0569118 + 0.0328580i
$$267$$ −6.46410 + 3.73205i −0.395597 + 0.228398i
$$268$$ 4.53590i 0.277074i
$$269$$ −6.00000 10.3923i −0.365826 0.633630i 0.623082 0.782157i $$-0.285880\pi$$
−0.988908 + 0.148527i $$0.952547\pi$$
$$270$$ 0 0
$$271$$ 7.96410 + 4.59808i 0.483785 + 0.279313i 0.721992 0.691901i $$-0.243227\pi$$
−0.238208 + 0.971214i $$0.576560\pi$$
$$272$$ 4.00000 0.242536
$$273$$ 6.92820 + 2.00000i 0.419314 + 0.121046i
$$274$$ −4.46410 −0.269686
$$275$$ 0 0
$$276$$ −0.133975 + 0.232051i −0.00806432 + 0.0139678i
$$277$$ 4.96410 + 8.59808i 0.298264 + 0.516608i 0.975739 0.218938i $$-0.0702591\pi$$
−0.677475 + 0.735546i $$0.736926\pi$$
$$278$$ 0.928203i 0.0556699i
$$279$$ −1.50000 + 0.866025i −0.0898027 + 0.0518476i
$$280$$ 0 0
$$281$$ 4.92820i 0.293992i −0.989137 0.146996i $$-0.953040\pi$$
0.989137 0.146996i $$-0.0469604\pi$$
$$282$$ −5.23205 9.06218i −0.311564 0.539645i
$$283$$ 1.96410 3.40192i 0.116754 0.202223i −0.801726 0.597692i $$-0.796085\pi$$
0.918479 + 0.395469i $$0.129418\pi$$
$$284$$ −7.26795 4.19615i −0.431273 0.248996i
$$285$$ 0 0
$$286$$ 1.62436 0.401924i 0.0960502 0.0237663i
$$287$$ 4.00000 0.236113
$$288$$ −0.866025 0.500000i −0.0510310 0.0294628i
$$289$$ 0.500000 0.866025i 0.0294118 0.0509427i
$$290$$ 0 0
$$291$$ 7.46410i 0.437553i
$$292$$ −1.73205 + 1.00000i −0.101361 + 0.0585206i
$$293$$ −3.58846 + 2.07180i −0.209640 + 0.121036i −0.601144 0.799141i $$-0.705288\pi$$
0.391504 + 0.920176i $$0.371955\pi$$
$$294$$ 3.00000i 0.174964i
$$295$$ 0 0
$$296$$ −0.598076 + 1.03590i −0.0347625 + 0.0602104i
$$297$$ 0.401924 + 0.232051i 0.0233220 + 0.0134650i
$$298$$ −20.4641 −1.18545
$$299$$ 0.669873 + 0.696152i 0.0387398 + 0.0402595i
$$300$$ 0 0
$$301$$ 3.33975 + 1.92820i 0.192500 + 0.111140i
$$302$$ −5.19615 + 9.00000i −0.299005 + 0.517892i
$$303$$ 5.46410 + 9.46410i 0.313904 + 0.543698i
$$304$$ 0.535898i 0.0307359i
$$305$$ 0 0
$$306$$ 3.46410 2.00000i 0.198030 0.114332i
$$307$$ 12.5359i 0.715462i 0.933825 + 0.357731i $$0.116449\pi$$
−0.933825 + 0.357731i $$0.883551\pi$$
$$308$$ −0.464102 0.803848i −0.0264446 0.0458035i
$$309$$ 7.92820 13.7321i 0.451020 0.781189i
$$310$$ 0 0
$$311$$ −7.60770 −0.431393 −0.215696 0.976460i $$-0.569202\pi$$
−0.215696 + 0.976460i $$0.569202\pi$$
$$312$$ −2.59808 + 2.50000i −0.147087 + 0.141535i
$$313$$ 28.0000 1.58265 0.791327 0.611393i $$-0.209391\pi$$
0.791327 + 0.611393i $$0.209391\pi$$
$$314$$ −4.33013 2.50000i −0.244363 0.141083i
$$315$$ 0 0
$$316$$ −0.0358984 0.0621778i −0.00201944 0.00349778i
$$317$$ 21.4641i 1.20554i 0.797913 + 0.602772i $$0.205937\pi$$
−0.797913 + 0.602772i $$0.794063\pi$$
$$318$$ 11.1962 6.46410i 0.627849 0.362489i
$$319$$ −1.50000 + 0.866025i −0.0839839 + 0.0484881i
$$320$$ 0 0
$$321$$ 9.92820 + 17.1962i 0.554138 + 0.959796i
$$322$$ 0.267949 0.464102i 0.0149322 0.0258634i
$$323$$ 1.85641 + 1.07180i 0.103293 + 0.0596364i
$$324$$ −1.00000 −0.0555556
$$325$$ 0 0
$$326$$ 23.0526 1.27676
$$327$$ 10.2679 + 5.92820i 0.567819 + 0.327830i
$$328$$ −1.00000 + 1.73205i −0.0552158 + 0.0956365i
$$329$$ 10.4641 + 18.1244i 0.576905 + 0.999228i
$$330$$ 0 0
$$331$$ −21.4641 + 12.3923i −1.17977 + 0.681143i −0.955962 0.293490i $$-0.905183\pi$$
−0.223812 + 0.974632i $$0.571850\pi$$
$$332$$ 4.26795 2.46410i 0.234234 0.135235i
$$333$$ 1.19615i 0.0655487i
$$334$$ 9.16025 + 15.8660i 0.501227 + 0.868150i
$$335$$ 0 0
$$336$$ 1.73205 + 1.00000i 0.0944911 + 0.0545545i
$$337$$ 25.3205 1.37930 0.689648 0.724145i $$-0.257765\pi$$
0.689648 + 0.724145i $$0.257765\pi$$
$$338$$ 6.06218 + 11.5000i 0.329739 + 0.625518i
$$339$$ −11.1962 −0.608092
$$340$$ 0 0
$$341$$ 0.401924 0.696152i 0.0217654 0.0376988i
$$342$$ −0.267949 0.464102i −0.0144890 0.0250957i
$$343$$ 20.0000i 1.07990i
$$344$$ −1.66987 + 0.964102i −0.0900335 + 0.0519809i
$$345$$ 0 0
$$346$$ 2.92820i 0.157421i
$$347$$ 11.1962 + 19.3923i 0.601041 + 1.04103i 0.992664 + 0.120908i $$0.0385805\pi$$
−0.391623 + 0.920126i $$0.628086\pi$$
$$348$$ 1.86603 3.23205i 0.100029 0.173256i
$$349$$ −12.5885 7.26795i −0.673845 0.389044i 0.123687 0.992321i $$-0.460528\pi$$
−0.797532 + 0.603277i $$0.793861\pi$$
$$350$$ 0 0
$$351$$ −1.00000 + 3.46410i −0.0533761 + 0.184900i
$$352$$ 0.464102 0.0247367
$$353$$ 1.73205 + 1.00000i 0.0921878 + 0.0532246i 0.545385 0.838186i $$-0.316383\pi$$
−0.453197 + 0.891410i $$0.649717\pi$$
$$354$$ −0.767949 + 1.33013i −0.0408160 + 0.0706955i
$$355$$ 0 0
$$356$$ 7.46410i 0.395597i
$$357$$ −6.92820 + 4.00000i −0.366679 + 0.211702i
$$358$$ −14.0885 + 8.13397i −0.744598 + 0.429894i
$$359$$ 18.9282i 0.998992i −0.866316 0.499496i $$-0.833518\pi$$
0.866316 0.499496i $$-0.166482\pi$$
$$360$$ 0 0
$$361$$ −9.35641 + 16.2058i −0.492442 + 0.852935i
$$362$$ −9.46410 5.46410i −0.497422 0.287187i
$$363$$ 10.7846 0.566045
$$364$$ 5.19615 5.00000i 0.272352 0.262071i
$$365$$ 0 0
$$366$$ −9.00000 5.19615i −0.470438 0.271607i
$$367$$ 18.1962 31.5167i 0.949831 1.64516i 0.204056 0.978959i $$-0.434588\pi$$
0.745776 0.666197i $$-0.232079\pi$$
$$368$$ 0.133975 + 0.232051i 0.00698391 + 0.0120965i
$$369$$ 2.00000i 0.104116i
$$370$$ 0 0
$$371$$ −22.3923 + 12.9282i −1.16255 + 0.671199i
$$372$$ 1.73205i 0.0898027i
$$373$$ 12.8923 + 22.3301i 0.667538 + 1.15621i 0.978590 + 0.205817i $$0.0659853\pi$$
−0.311052 + 0.950393i $$0.600681\pi$$
$$374$$ −0.928203 + 1.60770i −0.0479962 + 0.0831319i
$$375$$ 0 0
$$376$$ −10.4641 −0.539645
$$377$$ −9.33013 9.69615i −0.480526 0.499377i
$$378$$ 2.00000 0.102869
$$379$$ −0.124356 0.0717968i −0.00638772 0.00368795i 0.496803 0.867863i $$-0.334507\pi$$
−0.503190 + 0.864176i $$0.667841\pi$$
$$380$$ 0 0
$$381$$ 4.46410 + 7.73205i 0.228703 + 0.396125i
$$382$$ 14.5359i 0.743721i
$$383$$ 3.99038 2.30385i 0.203899 0.117721i −0.394574 0.918864i $$-0.629108\pi$$
0.598473 + 0.801143i $$0.295774\pi$$
$$384$$ −0.866025 + 0.500000i −0.0441942 + 0.0255155i
$$385$$ 0 0
$$386$$ 11.6603 + 20.1962i 0.593491 + 1.02796i
$$387$$ −0.964102 + 1.66987i −0.0490080 + 0.0848844i
$$388$$ 6.46410 + 3.73205i 0.328165 + 0.189466i
$$389$$ −20.2679 −1.02763 −0.513813 0.857902i $$-0.671767\pi$$
−0.513813 + 0.857902i $$0.671767\pi$$
$$390$$ 0 0
$$391$$ −1.07180 −0.0542031
$$392$$ 2.59808 + 1.50000i 0.131223 + 0.0757614i
$$393$$ 0.669873 1.16025i 0.0337906 0.0585271i
$$394$$ 8.19615 + 14.1962i 0.412916 + 0.715192i
$$395$$ 0 0
$$396$$ 0.401924 0.232051i 0.0201974 0.0116610i
$$397$$ −10.5000 + 6.06218i −0.526980 + 0.304252i −0.739786 0.672843i $$-0.765073\pi$$
0.212806 + 0.977095i $$0.431740\pi$$
$$398$$ 18.9282i 0.948785i
$$399$$ 0.535898 + 0.928203i 0.0268285 + 0.0464683i
$$400$$ 0 0
$$401$$ 27.7128 + 16.0000i 1.38391 + 0.799002i 0.992620 0.121265i $$-0.0386950\pi$$
0.391292 + 0.920267i $$0.372028\pi$$
$$402$$ −4.53590 −0.226230
$$403$$ 6.00000 + 1.73205i 0.298881 + 0.0862796i
$$404$$ 10.9282 0.543698
$$405$$ 0 0
$$406$$ −3.73205 + 6.46410i −0.185219 + 0.320808i
$$407$$ −0.277568 0.480762i −0.0137585 0.0238305i
$$408$$ 4.00000i 0.198030i
$$409$$ −3.46410 + 2.00000i −0.171289 + 0.0988936i −0.583193 0.812333i $$-0.698197\pi$$
0.411905 + 0.911227i $$0.364864\pi$$
$$410$$ 0 0
$$411$$ 4.46410i 0.220198i
$$412$$ −7.92820 13.7321i −0.390595 0.676530i
$$413$$ 1.53590 2.66025i 0.0755766 0.130903i
$$414$$ 0.232051 + 0.133975i 0.0114047 + 0.00658449i
$$415$$ 0 0
$$416$$ 0.866025 + 3.50000i 0.0424604 + 0.171602i
$$417$$ 0.928203 0.0454543
$$418$$ 0.215390 + 0.124356i 0.0105351 + 0.00608243i
$$419$$ −0.803848 + 1.39230i −0.0392705 + 0.0680185i −0.884993 0.465605i $$-0.845837\pi$$
0.845722 + 0.533624i $$0.179170\pi$$
$$420$$ 0 0
$$421$$ 16.3923i 0.798912i 0.916752 + 0.399456i $$0.130801\pi$$
−0.916752 + 0.399456i $$0.869199\pi$$
$$422$$ 20.1962 11.6603i 0.983133 0.567612i
$$423$$ −9.06218 + 5.23205i −0.440618 + 0.254391i
$$424$$ 12.9282i 0.627849i
$$425$$ 0 0
$$426$$ −4.19615 + 7.26795i −0.203304 + 0.352133i
$$427$$ 18.0000 + 10.3923i 0.871081 + 0.502919i
$$428$$ 19.8564 0.959796
$$429$$ −0.401924 1.62436i −0.0194051 0.0784246i
$$430$$ 0 0
$$431$$ −6.58846 3.80385i −0.317355 0.183225i 0.332858 0.942977i $$-0.391987\pi$$
−0.650213 + 0.759752i $$0.725320\pi$$
$$432$$ −0.500000 + 0.866025i −0.0240563 + 0.0416667i
$$433$$ −7.66025 13.2679i −0.368128 0.637617i 0.621145 0.783696i $$-0.286668\pi$$
−0.989273 + 0.146079i $$0.953335\pi$$
$$434$$ 3.46410i 0.166282i
$$435$$ 0 0
$$436$$ 10.2679 5.92820i 0.491746 0.283909i
$$437$$ 0.143594i 0.00686901i
$$438$$ 1.00000 + 1.73205i 0.0477818 + 0.0827606i
$$439$$ −4.92820 + 8.53590i −0.235210 + 0.407396i −0.959334 0.282274i $$-0.908911\pi$$
0.724123 + 0.689670i $$0.242245\pi$$
$$440$$ 0 0
$$441$$ 3.00000 0.142857
$$442$$ −13.8564 4.00000i −0.659082 0.190261i
$$443$$ 4.39230 0.208685 0.104342 0.994541i $$-0.466726\pi$$
0.104342 + 0.994541i $$0.466726\pi$$
$$444$$ 1.03590 + 0.598076i 0.0491616 + 0.0283834i
$$445$$ 0 0
$$446$$ 13.7321 + 23.7846i 0.650231 + 1.12623i
$$447$$ 20.4641i 0.967919i
$$448$$ 1.73205 1.00000i 0.0818317 0.0472456i
$$449$$ −34.3923 + 19.8564i −1.62307 + 0.937082i −0.636982 + 0.770879i $$0.719817\pi$$
−0.986092 + 0.166203i $$0.946849\pi$$
$$450$$ 0 0
$$451$$ −0.464102 0.803848i −0.0218537 0.0378517i
$$452$$ −5.59808 + 9.69615i −0.263311 + 0.456069i
$$453$$ 9.00000 + 5.19615i 0.422857 + 0.244137i
$$454$$ −4.39230 −0.206141
$$455$$ 0 0
$$456$$ −0.535898 −0.0250957
$$457$$ 27.2487 + 15.7321i 1.27464 + 0.735914i 0.975858 0.218407i $$-0.0700859\pi$$
0.298783 + 0.954321i $$0.403419\pi$$
$$458$$ −9.92820 + 17.1962i −0.463914 + 0.803523i
$$459$$ −2.00000 3.46410i −0.0933520 0.161690i
$$460$$ 0 0
$$461$$ 5.59808 3.23205i 0.260728 0.150532i −0.363938 0.931423i $$-0.618568\pi$$
0.624667 + 0.780891i $$0.285235\pi$$
$$462$$ −0.803848 + 0.464102i −0.0373984 + 0.0215920i
$$463$$ 20.9282i 0.972616i 0.873787 + 0.486308i $$0.161657\pi$$
−0.873787 + 0.486308i $$0.838343\pi$$
$$464$$ −1.86603 3.23205i −0.0866281 0.150044i
$$465$$ 0 0
$$466$$ −15.6962 9.06218i −0.727110 0.419797i
$$467$$ −11.8564 −0.548649 −0.274325 0.961637i $$-0.588454\pi$$
−0.274325 + 0.961637i $$0.588454\pi$$
$$468$$ 2.50000 + 2.59808i 0.115563 + 0.120096i
$$469$$ 9.07180 0.418897
$$470$$ 0 0
$$471$$ −2.50000 + 4.33013i −0.115194 + 0.199522i
$$472$$ 0.767949 + 1.33013i 0.0353477 + 0.0612241i
$$473$$ 0.894882i 0.0411467i
$$474$$ −0.0621778 + 0.0358984i −0.00285592 + 0.00164887i
$$475$$ 0 0
$$476$$ 8.00000i 0.366679i
$$477$$ −6.46410 11.1962i −0.295971 0.512637i
$$478$$ −2.19615 + 3.80385i −0.100450 + 0.173984i
$$479$$ 1.26795 + 0.732051i 0.0579341 + 0.0334483i 0.528687 0.848817i $$-0.322684\pi$$
−0.470753 + 0.882265i $$0.656018\pi$$
$$480$$ 0 0
$$481$$ 3.10770 2.99038i 0.141699 0.136350i
$$482$$ 14.2679 0.649887
$$483$$ −0.464102 0.267949i −0.0211174 0.0121921i
$$484$$ 5.39230 9.33975i 0.245105 0.424534i
$$485$$ 0 0
$$486$$ 1.00000i 0.0453609i
$$487$$ −33.9282 + 19.5885i −1.53743 + 0.887638i −0.538446 + 0.842660i $$0.680988\pi$$
−0.998988 + 0.0449775i $$0.985678\pi$$
$$488$$ −9.00000 + 5.19615i −0.407411 + 0.235219i
$$489$$ 23.0526i 1.04247i
$$490$$ 0 0
$$491$$ −8.66025 + 15.0000i −0.390832 + 0.676941i −0.992559 0.121761i $$-0.961146\pi$$
0.601728 + 0.798701i $$0.294479\pi$$
$$492$$ 1.73205 + 1.00000i 0.0780869 + 0.0450835i
$$493$$ 14.9282 0.672332
$$494$$ −0.535898 + 1.85641i −0.0241112 + 0.0835237i
$$495$$ 0 0
$$496$$ 1.50000 + 0.866025i 0.0673520 + 0.0388857i
$$497$$ 8.39230 14.5359i 0.376446 0.652024i
$$498$$ −2.46410 4.26795i −0.110419 0.191251i
$$499$$ 13.4641i 0.602736i −0.953508 0.301368i $$-0.902557\pi$$
0.953508 0.301368i $$-0.0974433\pi$$
$$500$$ 0 0
$$501$$ 15.8660 9.16025i 0.708842 0.409250i
$$502$$ 12.2679i 0.547545i
$$503$$ 15.5885 + 27.0000i 0.695055 + 1.20387i 0.970162 + 0.242457i $$0.0779533\pi$$
−0.275107 + 0.961414i $$0.588713\pi$$
$$504$$ 1.00000 1.73205i 0.0445435 0.0771517i
$$505$$ 0 0
$$506$$ −0.124356 −0.00552828
$$507$$ 11.5000 6.06218i 0.510733 0.269231i
$$508$$ 8.92820 0.396125
$$509$$ 16.7942 + 9.69615i 0.744391 + 0.429774i 0.823664 0.567079i $$-0.191926\pi$$
−0.0792726 + 0.996853i $$0.525260\pi$$
$$510$$ 0 0
$$511$$ −2.00000 3.46410i −0.0884748 0.153243i
$$512$$ 1.00000i 0.0441942i
$$513$$ −0.464102 + 0.267949i −0.0204906 + 0.0118302i
$$514$$ 19.6244 11.3301i 0.865593 0.499750i
$$515$$ 0 0
$$516$$ 0.964102 + 1.66987i 0.0424422 + 0.0735121i
$$517$$ 2.42820 4.20577i 0.106792 0.184970i
$$518$$ −2.07180 1.19615i −0.0910295 0.0525559i
$$519$$ 2.92820 0.128534
$$520$$ 0 0
$$521$$ 17.3205 0.758825 0.379413 0.925228i $$-0.376126\pi$$
0.379413 + 0.925228i $$0.376126\pi$$
$$522$$ −3.23205 1.86603i −0.141463 0.0816737i
$$523$$ −14.8923 + 25.7942i −0.651195 + 1.12790i 0.331638 + 0.943407i $$0.392399\pi$$
−0.982833 + 0.184496i $$0.940935\pi$$
$$524$$ −0.669873 1.16025i −0.0292635 0.0506859i
$$525$$ 0 0
$$526$$ 15.6962 9.06218i 0.684385 0.395130i
$$527$$ −6.00000 + 3.46410i −0.261364 + 0.150899i
$$528$$ 0.464102i 0.0201974i
$$529$$ 11.4641 + 19.8564i 0.498439 + 0.863322i
$$530$$ 0 0
$$531$$ 1.33013 + 0.767949i 0.0577226 + 0.0333262i
$$532$$ 1.07180 0.0464683
$$533$$ 5.19615 5.00000i 0.225070 0.216574i
$$534$$ 7.46410 0.323003
$$535$$ 0 0
$$536$$ −2.26795 + 3.92820i −0.0979605 + 0.169673i
$$537$$ 8.13397 + 14.0885i 0.351007 + 0.607962i
$$538$$ 12.0000i 0.517357i
$$539$$ −1.20577 + 0.696152i −0.0519362 + 0.0299854i
$$540$$ 0 0
$$541$$ 13.0718i 0.562000i −0.959708 0.281000i $$-0.909334\pi$$
0.959708 0.281000i $$-0.0906662\pi$$
$$542$$ −4.59808 7.96410i −0.197504 0.342087i
$$543$$ −5.46410 + 9.46410i −0.234487 + 0.406143i
$$544$$ −3.46410 2.00000i −0.148522 0.0857493i
$$545$$ 0 0
$$546$$ −5.00000 5.19615i −0.213980 0.222375i
$$547$$ −9.07180 −0.387882 −0.193941 0.981013i $$-0.562127\pi$$
−0.193941 + 0.981013i $$0.562127\pi$$
$$548$$ 3.86603 + 2.23205i 0.165148 + 0.0953485i
$$549$$ −5.19615 + 9.00000i −0.221766 + 0.384111i
$$550$$ 0 0
$$551$$ 2.00000i 0.0852029i
$$552$$ 0.232051 0.133975i 0.00987674 0.00570234i
$$553$$ 0.124356 0.0717968i 0.00528814 0.00305311i
$$554$$ 9.92820i 0.421809i
$$555$$ 0 0
$$556$$ 0.464102 0.803848i 0.0196823 0.0340907i
$$557$$ −32.6603 18.8564i −1.38386 0.798972i −0.391245 0.920286i $$-0.627956\pi$$
−0.992614 + 0.121315i $$0.961289\pi$$
$$558$$ 1.73205 0.0733236
$$559$$ 6.74871 1.66987i 0.285440 0.0706281i
$$560$$ 0 0
$$561$$ 1.60770 + 0.928203i 0.0678769 + 0.0391888i
$$562$$ −2.46410 + 4.26795i −0.103942 + 0.180033i
$$563$$ −19.6603 34.0526i −0.828581 1.43514i −0.899152 0.437637i $$-0.855815\pi$$
0.0705706 0.997507i $$-0.477518\pi$$
$$564$$ 10.4641i 0.440618i
$$565$$ 0 0
$$566$$ −3.40192 + 1.96410i −0.142994 + 0.0825573i
$$567$$ 2.00000i 0.0839921i
$$568$$ 4.19615 + 7.26795i 0.176067 + 0.304956i
$$569$$ 2.66025 4.60770i 0.111524 0.193165i −0.804861 0.593463i $$-0.797760\pi$$
0.916385 + 0.400299i $$0.131094\pi$$
$$570$$ 0 0
$$571$$ 45.1769 1.89060 0.945298 0.326209i $$-0.105771\pi$$
0.945298 + 0.326209i $$0.105771\pi$$
$$572$$ −1.60770 0.464102i −0.0672211 0.0194051i
$$573$$ 14.5359 0.607246
$$574$$ −3.46410 2.00000i −0.144589 0.0834784i
$$575$$ 0 0
$$576$$ 0.500000 + 0.866025i 0.0208333 + 0.0360844i
$$577$$ 10.0000i 0.416305i −0.978096 0.208153i $$-0.933255\pi$$
0.978096 0.208153i $$-0.0667451\pi$$
$$578$$ −0.866025 + 0.500000i −0.0360219 + 0.0207973i
$$579$$ 20.1962 11.6603i 0.839323 0.484584i
$$580$$ 0 0
$$581$$ 4.92820 + 8.53590i 0.204456 + 0.354129i
$$582$$ 3.73205 6.46410i 0.154698 0.267946i
$$583$$ 5.19615 + 3.00000i 0.215203 + 0.124247i
$$584$$ 2.00000 0.0827606
$$585$$ 0 0
$$586$$ 4.14359 0.171170
$$587$$ 15.9282 + 9.19615i 0.657427 + 0.379566i 0.791296 0.611433i $$-0.209407\pi$$
−0.133869 + 0.990999i $$0.542740\pi$$
$$588$$ 1.50000 2.59808i 0.0618590 0.107143i
$$589$$ 0.464102 + 0.803848i 0.0191230 + 0.0331220i
$$590$$ 0 0
$$591$$ 14.1962 8.19615i 0.583952 0.337145i
$$592$$ 1.03590 0.598076i 0.0425752 0.0245808i
$$593$$ 31.1051i 1.27733i −0.769483 0.638667i $$-0.779486\pi$$
0.769483 0.638667i $$-0.220514\pi$$
$$594$$ −0.232051 0.401924i −0.00952116 0.0164911i
$$595$$ 0 0
$$596$$ 17.7224 + 10.2321i 0.725939 + 0.419121i
$$597$$ −18.9282 −0.774680
$$598$$ −0.232051 0.937822i −0.00948926 0.0383504i
$$599$$ 10.3923 0.424618 0.212309 0.977203i $$-0.431902\pi$$
0.212309 + 0.977203i $$0.431902\pi$$
$$600$$ 0 0
$$601$$ −10.8923 + 18.8660i −0.444306 + 0.769561i −0.998004 0.0631568i $$-0.979883\pi$$
0.553697 + 0.832718i $$0.313216\pi$$
$$602$$ −1.92820 3.33975i −0.0785877 0.136118i
$$603$$ 4.53590i 0.184716i
$$604$$ 9.00000 5.19615i 0.366205 0.211428i
$$605$$ 0 0
$$606$$ 10.9282i 0.443928i
$$607$$ 21.5885 + 37.3923i 0.876248 + 1.51771i 0.855427 + 0.517924i $$0.173295\pi$$
0.0208216 + 0.999783i $$0.493372\pi$$
$$608$$ −0.267949 + 0.464102i −0.0108668 + 0.0188218i
$$609$$ 6.46410 + 3.73205i 0.261939 + 0.151230i
$$610$$ 0 0
$$611$$ 36.2487 + 10.4641i 1.46647 + 0.423332i
$$612$$ −4.00000 −0.161690
$$613$$ −0.820508 0.473721i −0.0331400 0.0191334i 0.483338 0.875434i $$-0.339424\pi$$
−0.516478 + 0.856300i $$0.672757\pi$$
$$614$$ 6.26795 10.8564i 0.252954 0.438129i
$$615$$ 0 0
$$616$$ 0.928203i 0.0373984i
$$617$$ −13.4545 + 7.76795i −0.541657 + 0.312726i −0.745750 0.666226i $$-0.767909\pi$$
0.204093 + 0.978951i $$0.434575\pi$$
$$618$$ −13.7321 + 7.92820i −0.552384 + 0.318919i
$$619$$ 24.2487i 0.974638i −0.873224 0.487319i $$-0.837975\pi$$
0.873224 0.487319i $$-0.162025\pi$$
$$620$$ 0 0
$$621$$ 0.133975 0.232051i 0.00537622 0.00931188i
$$622$$ 6.58846 + 3.80385i 0.264173 + 0.152520i
$$623$$ −14.9282 −0.598086
$$624$$ 3.50000 0.866025i 0.140112 0.0346688i
$$625$$ 0 0
$$626$$ −24.2487 14.0000i −0.969173 0.559553i
$$627$$ 0.124356 0.215390i 0.00496629 0.00860186i
$$628$$ 2.50000 + 4.33013i 0.0997609 + 0.172791i
$$629$$ 4.78461i 0.190775i
$$630$$ 0 0
$$631$$ −21.2487 + 12.2679i −0.845898 + 0.488379i −0.859265 0.511531i $$-0.829078\pi$$
0.0133668 + 0.999911i $$0.495745\pi$$
$$632$$ 0.0717968i 0.00285592i
$$633$$ −11.6603 20.1962i −0.463453 0.802725i
$$634$$ 10.7321 18.5885i 0.426224 0.738242i
$$635$$ 0 0
$$636$$ −12.9282 −0.512637
$$637$$ −7.50000 7.79423i −0.297161 0.308819i
$$638$$ 1.73205 0.0685725
$$639$$ 7.26795 + 4.19615i 0.287516 + 0.165997i
$$640$$ 0 0
$$641$$ −13.9282 24.1244i −0.550131 0.952855i −0.998265 0.0588882i $$-0.981244\pi$$
0.448134 0.893967i $$-0.352089\pi$$
$$642$$ 19.8564i 0.783670i
$$643$$ −23.7846 + 13.7321i −0.937973 + 0.541539i −0.889324 0.457277i $$-0.848825\pi$$
−0.0486490 + 0.998816i $$0.515492\pi$$
$$644$$ −0.464102 + 0.267949i −0.0182882 + 0.0105587i
$$645$$ 0 0
$$646$$ −1.07180 1.85641i −0.0421693 0.0730393i
$$647$$ 10.6603 18.4641i 0.419098 0.725899i −0.576751 0.816920i $$-0.695680\pi$$
0.995849 + 0.0910212i $$0.0290131\pi$$
$$648$$ 0.866025 + 0.500000i 0.0340207 + 0.0196419i
$$649$$ −0.712813 −0.0279804
$$650$$ 0 0
$$651$$ −3.46410 −0.135769
$$652$$ −19.9641 11.5263i −0.781855 0.451404i
$$653$$ −22.1244 + 38.3205i −0.865793 + 1.49960i 0.000464739 1.00000i $$0.499852\pi$$
−0.866258 + 0.499597i $$0.833481\pi$$
$$654$$ −5.92820 10.2679i −0.231811 0.401509i
$$655$$ 0 0
$$656$$ 1.73205 1.00000i 0.0676252 0.0390434i
$$657$$ 1.73205 1.00000i 0.0675737 0.0390137i
$$658$$ 20.9282i 0.815866i
$$659$$ 1.86603 + 3.23205i 0.0726900 + 0.125903i 0.900079 0.435726i $$-0.143508\pi$$
−0.827389 + 0.561629i $$0.810175\pi$$
$$660$$ 0 0
$$661$$ 37.5167 + 21.6603i 1.45923 + 0.842486i 0.998973 0.0453002i $$-0.0144244\pi$$
0.460256 + 0.887786i $$0.347758\pi$$
$$662$$ 24.7846 0.963281
$$663$$ −4.00000 + 13.8564i −0.155347 + 0.538138i
$$664$$ −4.92820 −0.191251
$$665$$ 0 0
$$666$$ 0.598076 1.03590i 0.0231750 0.0401402i
$$667$$ 0.500000 + 0.866025i 0.0193601 + 0.0335326i
$$668$$ 18.3205i 0.708842i
$$669$$ 23.7846 13.7321i 0.919566 0.530912i
$$670$$ 0 0
$$671$$ 4.82309i 0.186193i
$$672$$ −1.00000 1.73205i −0.0385758 0.0668153i
$$673$$ 16.0000 27.7128i 0.616755 1.06825i −0.373319 0.927703i $$-0.621780\pi$$
0.990074 0.140548i $$-0.0448863\pi$$
$$674$$ −21.9282 12.6603i −0.844643 0.487655i
$$675$$ 0 0
$$676$$ 0.500000 12.9904i 0.0192308 0.499630i
$$677$$ −11.6077 −0.446120 −0.223060 0.974805i $$-0.571605\pi$$
−0.223060 + 0.974805i $$0.571605\pi$$
$$678$$ 9.69615 + 5.59808i 0.372378 + 0.214993i
$$679$$ −7.46410 + 12.9282i −0.286446 + 0.496139i
$$680$$ 0 0
$$681$$ 4.39230i 0.168313i
$$682$$ −0.696152 + 0.401924i −0.0266571 + 0.0153905i
$$683$$ 0.679492 0.392305i 0.0260000 0.0150111i −0.486944 0.873433i $$-0.661888\pi$$
0.512944 + 0.858422i $$0.328555\pi$$
$$684$$ 0.535898i 0.0204906i
$$685$$ 0 0
$$686$$ −10.0000 + 17.3205i −0.381802 + 0.661300i
$$687$$ 17.1962 + 9.92820i 0.656074 + 0.378785i
$$688$$ 1.92820 0.0735121
$$689$$ −12.9282 + 44.7846i −0.492525 + 1.70616i
$$690$$ 0 0
$$691$$ −30.4641 17.5885i −1.15891 0.669096i −0.207867 0.978157i $$-0.566652\pi$$
−0.951042 + 0.309061i $$0.899985\pi$$
$$692$$ 1.46410 2.53590i 0.0556568 0.0964004i
$$693$$ 0.464102 + 0.803848i 0.0176298 + 0.0305356i
$$694$$ 22.3923i 0.850000i
$$695$$ 0 0
$$696$$ −3.23205 + 1.86603i −0.122511 + 0.0707315i
$$697$$ 8.00000i 0.303022i
$$698$$ 7.26795 + 12.5885i 0.275096 + 0.476480i
$$699$$ −9.06218 + 15.6962i −0.342763 + 0.593683i
$$700$$ 0 0
$$701$$ −3.73205 −0.140958 −0.0704788 0.997513i $$-0.522453\pi$$
−0.0704788 + 0.997513i $$0.522453\pi$$
$$702$$ 2.59808 2.50000i 0.0980581 0.0943564i
$$703$$ 0.641016 0.0241764
$$704$$ −0.401924 0.232051i −0.0151481 0.00874574i
$$705$$ 0 0
$$706$$ −1.00000 1.73205i −0.0376355 0.0651866i
$$707$$ 21.8564i 0.821995i
$$708$$ 1.33013 0.767949i 0.0499892 0.0288613i
$$709$$ 7.85641 4.53590i 0.295054 0.170349i −0.345165 0.938542i $$-0.612177\pi$$
0.640219 + 0.768193i $$0.278844\pi$$
$$710$$ 0 0
$$711$$ 0.0358984 + 0.0621778i 0.00134629 + 0.00233185i
$$712$$ 3.73205 6.46410i 0.139865 0.242252i
$$713$$ −0.401924 0.232051i −0.0150522 0.00869037i
$$714$$ 8.00000 0.299392
$$715$$ 0 0
$$716$$ 16.2679 0.607962
$$717$$ 3.80385 + 2.19615i 0.142057 + 0.0820168i
$$718$$ −9.46410 + 16.3923i −0.353197 + 0.611755i
$$719$$ −17.3205 30.0000i −0.645946 1.11881i −0.984082 0.177714i $$-0.943130\pi$$
0.338136 0.941097i $$-0.390204\pi$$
$$720$$ 0 0
$$721$$ 27.4641 15.8564i 1.02282 0.590523i
$$722$$ 16.2058 9.35641i 0.603116 0.348209i
$$723$$ 14.2679i 0.530631i
$$724$$ 5.46410 + 9.46410i 0.203072 + 0.351731i
$$725$$ 0 0
$$726$$ −9.33975 5.39230i −0.346630 0.200127i
$$727$$ −23.7128 −0.879460 −0.439730 0.898130i $$-0.644926\pi$$
−0.439730 + 0.898130i $$0.644926\pi$$
$$728$$ −7.00000 + 1.73205i −0.259437 + 0.0641941i
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ −3.85641 + 6.67949i −0.142634 + 0.247050i
$$732$$ 5.19615 + 9.00000i 0.192055 + 0.332650i
$$733$$ 37.0718i 1.36928i −0.728882 0.684639i $$-0.759960\pi$$
0.728882 0.684639i $$-0.240040\pi$$
$$734$$ −31.5167 + 18.1962i −1.16330 + 0.671632i
$$735$$ 0 0
$$736$$ 0.267949i 0.00987674i
$$737$$ −1.05256 1.82309i −0.0387715 0.0671542i
$$738$$ 1.00000 1.73205i 0.0368105 0.0637577i
$$739$$ −13.2679 7.66025i −0.488069 0.281787i 0.235704 0.971825i $$-0.424260\pi$$
−0.723773 + 0.690038i $$0.757594\pi$$
$$740$$ 0 0
$$741$$ 1.85641 + 0.535898i 0.0681968 + 0.0196867i
$$742$$ 25.8564 0.949219
$$743$$ −29.0429 16.7679i −1.06548 0.615156i −0.138539 0.990357i $$-0.544240\pi$$
−0.926944 + 0.375201i $$0.877574\pi$$
$$744$$ 0.866025 1.50000i 0.0317500 0.0549927i
$$745$$ 0 0
$$746$$ 25.7846i 0.944042i
$$747$$ −4.26795 + 2.46410i −0.156156 + 0.0901568i
$$748$$ 1.60770 0.928203i 0.0587832 0.0339385i
$$749$$ 39.7128i 1.45107i
$$750$$ 0 0
$$751$$ −13.9641 + 24.1865i −0.509557 + 0.882579i 0.490381 + 0.871508i $$0.336857\pi$$
−0.999939 + 0.0110712i $$0.996476\pi$$
$$752$$ 9.06218 + 5.23205i 0.330464 + 0.190793i
$$753$$ 12.2679 0.447069
$$754$$ 3.23205 + 13.0622i 0.117704 + 0.475696i
$$755$$ 0 0
$$756$$ −1.73205 1.00000i −0.0629941 0.0363696i
$$757$$ −9.00000 + 15.5885i −0.327111 + 0.566572i −0.981937 0.189207i $$-0.939408\pi$$
0.654827 + 0.755779i $$0.272742\pi$$
$$758$$ 0.0717968 + 0.124356i 0.00260778 + 0.00451680i
$$759$$ 0.124356i 0.00451382i
$$760$$ 0 0
$$761$$ −16.3923 + 9.46410i −0.594221 + 0.343073i −0.766765 0.641928i $$-0.778135\pi$$
0.172544 + 0.985002i $$0.444801\pi$$
$$762$$ 8.92820i 0.323435i
$$763$$ 11.8564 + 20.5359i 0.429231 + 0.743449i
$$764$$ 7.26795 12.5885i 0.262945 0.455434i
$$765$$ 0 0
$$766$$ −4.60770 −0.166483
$$767$$ −1.33013 5.37564i −0.0480281 0.194103i
$$768$$ 1.00000 0.0360844
$$769$$ −16.9641 9.79423i −0.611741 0.353189i 0.161905 0.986806i $$-0.448236\pi$$
−0.773647 + 0.633617i $$0.781569\pi$$
$$770$$ 0 0
$$771$$ −11.3301 19.6244i −0.408045 0.706754i
$$772$$ 23.3205i 0.839323i
$$773$$ −24.0000 + 13.8564i −0.863220 + 0.498380i −0.865089 0.501618i $$-0.832738\pi$$
0.00186926 + 0.999998i $$0.499405\pi$$
$$774$$ 1.66987 0.964102i 0.0600223 0.0346539i
$$775$$ 0 0
$$776$$ −3.73205 6.46410i −0.133973 0.232048i
$$777$$ −1.19615 + 2.07180i −0.0429117 + 0.0743253i
$$778$$ 17.5526 + 10.1340i 0.629290 + 0.363321i
$$779$$ 1.07180 0.0384011
$$780$$ 0 0
$$781$$ −3.89488 −0.139370
$$782$$ 0.928203 + 0.535898i 0.0331925 + 0.0191637i
$$783$$ −1.86603