# Properties

 Label 1050.2.o.d.949.2 Level $1050$ Weight $2$ Character 1050.949 Analytic conductor $8.384$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1050.o (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$8.38429221223$$ 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: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 949.2 Root $$0.866025 + 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 1050.949 Dual form 1050.2.o.d.499.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-2.59808 + 0.500000i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$q+(0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-2.59808 + 0.500000i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.866025 + 0.500000i) q^{12} +5.00000i q^{13} +(-2.00000 + 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-5.19615 - 3.00000i) q^{17} +(0.866025 + 0.500000i) q^{18} +(-3.50000 - 6.06218i) q^{19} +(2.50000 + 0.866025i) q^{21} +(-5.19615 + 3.00000i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(2.50000 + 4.33013i) q^{26} -1.00000i q^{27} +(-0.866025 + 2.50000i) q^{28} +(-4.00000 + 6.92820i) q^{31} +(-0.866025 - 0.500000i) q^{32} -6.00000 q^{34} +1.00000 q^{36} +(0.866025 - 0.500000i) q^{37} +(-6.06218 - 3.50000i) q^{38} +(2.50000 - 4.33013i) q^{39} +(2.59808 - 0.500000i) q^{42} +8.00000i q^{43} +(-3.00000 + 5.19615i) q^{46} +(-5.19615 + 3.00000i) q^{47} +1.00000i q^{48} +(6.50000 - 2.59808i) q^{49} +(3.00000 + 5.19615i) q^{51} +(4.33013 + 2.50000i) q^{52} +(5.19615 + 3.00000i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(0.500000 + 2.59808i) q^{56} +7.00000i q^{57} +(-3.00000 + 5.19615i) q^{59} +(0.500000 + 0.866025i) q^{61} +8.00000i q^{62} +(-1.73205 - 2.00000i) q^{63} -1.00000 q^{64} +(-11.2583 - 6.50000i) q^{67} +(-5.19615 + 3.00000i) q^{68} +6.00000 q^{69} +12.0000 q^{71} +(0.866025 - 0.500000i) q^{72} +(-4.33013 - 2.50000i) q^{73} +(0.500000 - 0.866025i) q^{74} -7.00000 q^{76} -5.00000i q^{78} +(-3.50000 - 6.06218i) q^{79} +(-0.500000 + 0.866025i) q^{81} -18.0000i q^{83} +(2.00000 - 1.73205i) q^{84} +(4.00000 + 6.92820i) q^{86} +(-3.00000 - 5.19615i) q^{89} +(-2.50000 - 12.9904i) q^{91} +6.00000i q^{92} +(6.92820 - 4.00000i) q^{93} +(-3.00000 + 5.19615i) q^{94} +(0.500000 + 0.866025i) q^{96} +7.00000i q^{97} +(4.33013 - 5.50000i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q + 2q^{4} - 4q^{6} + 2q^{9} + O(q^{10})$$ $$4q + 2q^{4} - 4q^{6} + 2q^{9} - 8q^{14} - 2q^{16} - 14q^{19} + 10q^{21} - 2q^{24} + 10q^{26} - 16q^{31} - 24q^{34} + 4q^{36} + 10q^{39} - 12q^{46} + 26q^{49} + 12q^{51} - 2q^{54} + 2q^{56} - 12q^{59} + 2q^{61} - 4q^{64} + 24q^{69} + 48q^{71} + 2q^{74} - 28q^{76} - 14q^{79} - 2q^{81} + 8q^{84} + 16q^{86} - 12q^{89} - 10q^{91} - 12q^{94} + 2q^{96} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$451$$ $$701$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$1$$

## 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
$$3$$ −0.866025 0.500000i −0.500000 0.288675i
$$4$$ 0.500000 0.866025i 0.250000 0.433013i
$$5$$ 0 0
$$6$$ −1.00000 −0.408248
$$7$$ −2.59808 + 0.500000i −0.981981 + 0.188982i
$$8$$ 1.00000i 0.353553i
$$9$$ 0.500000 + 0.866025i 0.166667 + 0.288675i
$$10$$ 0 0
$$11$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$12$$ −0.866025 + 0.500000i −0.250000 + 0.144338i
$$13$$ 5.00000i 1.38675i 0.720577 + 0.693375i $$0.243877\pi$$
−0.720577 + 0.693375i $$0.756123\pi$$
$$14$$ −2.00000 + 1.73205i −0.534522 + 0.462910i
$$15$$ 0 0
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ −5.19615 3.00000i −1.26025 0.727607i −0.287129 0.957892i $$-0.592701\pi$$
−0.973123 + 0.230285i $$0.926034\pi$$
$$18$$ 0.866025 + 0.500000i 0.204124 + 0.117851i
$$19$$ −3.50000 6.06218i −0.802955 1.39076i −0.917663 0.397360i $$-0.869927\pi$$
0.114708 0.993399i $$-0.463407\pi$$
$$20$$ 0 0
$$21$$ 2.50000 + 0.866025i 0.545545 + 0.188982i
$$22$$ 0 0
$$23$$ −5.19615 + 3.00000i −1.08347 + 0.625543i −0.931831 0.362892i $$-0.881789\pi$$
−0.151642 + 0.988436i $$0.548456\pi$$
$$24$$ −0.500000 + 0.866025i −0.102062 + 0.176777i
$$25$$ 0 0
$$26$$ 2.50000 + 4.33013i 0.490290 + 0.849208i
$$27$$ 1.00000i 0.192450i
$$28$$ −0.866025 + 2.50000i −0.163663 + 0.472456i
$$29$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$30$$ 0 0
$$31$$ −4.00000 + 6.92820i −0.718421 + 1.24434i 0.243204 + 0.969975i $$0.421802\pi$$
−0.961625 + 0.274367i $$0.911532\pi$$
$$32$$ −0.866025 0.500000i −0.153093 0.0883883i
$$33$$ 0 0
$$34$$ −6.00000 −1.02899
$$35$$ 0 0
$$36$$ 1.00000 0.166667
$$37$$ 0.866025 0.500000i 0.142374 0.0821995i −0.427121 0.904194i $$-0.640472\pi$$
0.569495 + 0.821995i $$0.307139\pi$$
$$38$$ −6.06218 3.50000i −0.983415 0.567775i
$$39$$ 2.50000 4.33013i 0.400320 0.693375i
$$40$$ 0 0
$$41$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$42$$ 2.59808 0.500000i 0.400892 0.0771517i
$$43$$ 8.00000i 1.21999i 0.792406 + 0.609994i $$0.208828\pi$$
−0.792406 + 0.609994i $$0.791172\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ −3.00000 + 5.19615i −0.442326 + 0.766131i
$$47$$ −5.19615 + 3.00000i −0.757937 + 0.437595i −0.828554 0.559908i $$-0.810836\pi$$
0.0706177 + 0.997503i $$0.477503\pi$$
$$48$$ 1.00000i 0.144338i
$$49$$ 6.50000 2.59808i 0.928571 0.371154i
$$50$$ 0 0
$$51$$ 3.00000 + 5.19615i 0.420084 + 0.727607i
$$52$$ 4.33013 + 2.50000i 0.600481 + 0.346688i
$$53$$ 5.19615 + 3.00000i 0.713746 + 0.412082i 0.812447 0.583036i $$-0.198135\pi$$
−0.0987002 + 0.995117i $$0.531468\pi$$
$$54$$ −0.500000 0.866025i −0.0680414 0.117851i
$$55$$ 0 0
$$56$$ 0.500000 + 2.59808i 0.0668153 + 0.347183i
$$57$$ 7.00000i 0.927173i
$$58$$ 0 0
$$59$$ −3.00000 + 5.19615i −0.390567 + 0.676481i −0.992524 0.122047i $$-0.961054\pi$$
0.601958 + 0.798528i $$0.294388\pi$$
$$60$$ 0 0
$$61$$ 0.500000 + 0.866025i 0.0640184 + 0.110883i 0.896258 0.443533i $$-0.146275\pi$$
−0.832240 + 0.554416i $$0.812942\pi$$
$$62$$ 8.00000i 1.01600i
$$63$$ −1.73205 2.00000i −0.218218 0.251976i
$$64$$ −1.00000 −0.125000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −11.2583 6.50000i −1.37542 0.794101i −0.383819 0.923408i $$-0.625391\pi$$
−0.991605 + 0.129307i $$0.958725\pi$$
$$68$$ −5.19615 + 3.00000i −0.630126 + 0.363803i
$$69$$ 6.00000 0.722315
$$70$$ 0 0
$$71$$ 12.0000 1.42414 0.712069 0.702109i $$-0.247758\pi$$
0.712069 + 0.702109i $$0.247758\pi$$
$$72$$ 0.866025 0.500000i 0.102062 0.0589256i
$$73$$ −4.33013 2.50000i −0.506803 0.292603i 0.224716 0.974424i $$-0.427855\pi$$
−0.731519 + 0.681822i $$0.761188\pi$$
$$74$$ 0.500000 0.866025i 0.0581238 0.100673i
$$75$$ 0 0
$$76$$ −7.00000 −0.802955
$$77$$ 0 0
$$78$$ 5.00000i 0.566139i
$$79$$ −3.50000 6.06218i −0.393781 0.682048i 0.599164 0.800626i $$-0.295500\pi$$
−0.992945 + 0.118578i $$0.962166\pi$$
$$80$$ 0 0
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ 0 0
$$83$$ 18.0000i 1.97576i −0.155230 0.987878i $$-0.549612\pi$$
0.155230 0.987878i $$-0.450388\pi$$
$$84$$ 2.00000 1.73205i 0.218218 0.188982i
$$85$$ 0 0
$$86$$ 4.00000 + 6.92820i 0.431331 + 0.747087i
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −3.00000 5.19615i −0.317999 0.550791i 0.662071 0.749441i $$-0.269678\pi$$
−0.980071 + 0.198650i $$0.936344\pi$$
$$90$$ 0 0
$$91$$ −2.50000 12.9904i −0.262071 1.36176i
$$92$$ 6.00000i 0.625543i
$$93$$ 6.92820 4.00000i 0.718421 0.414781i
$$94$$ −3.00000 + 5.19615i −0.309426 + 0.535942i
$$95$$ 0 0
$$96$$ 0.500000 + 0.866025i 0.0510310 + 0.0883883i
$$97$$ 7.00000i 0.710742i 0.934725 + 0.355371i $$0.115646\pi$$
−0.934725 + 0.355371i $$0.884354\pi$$
$$98$$ 4.33013 5.50000i 0.437409 0.555584i
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$102$$ 5.19615 + 3.00000i 0.514496 + 0.297044i
$$103$$ −11.2583 + 6.50000i −1.10932 + 0.640464i −0.938652 0.344865i $$-0.887925\pi$$
−0.170664 + 0.985329i $$0.554591\pi$$
$$104$$ 5.00000 0.490290
$$105$$ 0 0
$$106$$ 6.00000 0.582772
$$107$$ 15.5885 9.00000i 1.50699 0.870063i 0.507026 0.861931i $$-0.330745\pi$$
0.999967 0.00813215i $$-0.00258857\pi$$
$$108$$ −0.866025 0.500000i −0.0833333 0.0481125i
$$109$$ −3.50000 + 6.06218i −0.335239 + 0.580651i −0.983531 0.180741i $$-0.942150\pi$$
0.648292 + 0.761392i $$0.275484\pi$$
$$110$$ 0 0
$$111$$ −1.00000 −0.0949158
$$112$$ 1.73205 + 2.00000i 0.163663 + 0.188982i
$$113$$ 6.00000i 0.564433i −0.959351 0.282216i $$-0.908930\pi$$
0.959351 0.282216i $$-0.0910696\pi$$
$$114$$ 3.50000 + 6.06218i 0.327805 + 0.567775i
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −4.33013 + 2.50000i −0.400320 + 0.231125i
$$118$$ 6.00000i 0.552345i
$$119$$ 15.0000 + 5.19615i 1.37505 + 0.476331i
$$120$$ 0 0
$$121$$ 5.50000 + 9.52628i 0.500000 + 0.866025i
$$122$$ 0.866025 + 0.500000i 0.0784063 + 0.0452679i
$$123$$ 0 0
$$124$$ 4.00000 + 6.92820i 0.359211 + 0.622171i
$$125$$ 0 0
$$126$$ −2.50000 0.866025i −0.222718 0.0771517i
$$127$$ 11.0000i 0.976092i −0.872818 0.488046i $$-0.837710\pi$$
0.872818 0.488046i $$-0.162290\pi$$
$$128$$ −0.866025 + 0.500000i −0.0765466 + 0.0441942i
$$129$$ 4.00000 6.92820i 0.352180 0.609994i
$$130$$ 0 0
$$131$$ −3.00000 5.19615i −0.262111 0.453990i 0.704692 0.709514i $$-0.251085\pi$$
−0.966803 + 0.255524i $$0.917752\pi$$
$$132$$ 0 0
$$133$$ 12.1244 + 14.0000i 1.05131 + 1.21395i
$$134$$ −13.0000 −1.12303
$$135$$ 0 0
$$136$$ −3.00000 + 5.19615i −0.257248 + 0.445566i
$$137$$ −15.5885 9.00000i −1.33181 0.768922i −0.346235 0.938148i $$-0.612540\pi$$
−0.985577 + 0.169226i $$0.945873\pi$$
$$138$$ 5.19615 3.00000i 0.442326 0.255377i
$$139$$ −11.0000 −0.933008 −0.466504 0.884519i $$-0.654487\pi$$
−0.466504 + 0.884519i $$0.654487\pi$$
$$140$$ 0 0
$$141$$ 6.00000 0.505291
$$142$$ 10.3923 6.00000i 0.872103 0.503509i
$$143$$ 0 0
$$144$$ 0.500000 0.866025i 0.0416667 0.0721688i
$$145$$ 0 0
$$146$$ −5.00000 −0.413803
$$147$$ −6.92820 1.00000i −0.571429 0.0824786i
$$148$$ 1.00000i 0.0821995i
$$149$$ 6.00000 + 10.3923i 0.491539 + 0.851371i 0.999953 0.00974235i $$-0.00310113\pi$$
−0.508413 + 0.861113i $$0.669768\pi$$
$$150$$ 0 0
$$151$$ 0.500000 0.866025i 0.0406894 0.0704761i −0.844963 0.534824i $$-0.820378\pi$$
0.885653 + 0.464348i $$0.153711\pi$$
$$152$$ −6.06218 + 3.50000i −0.491708 + 0.283887i
$$153$$ 6.00000i 0.485071i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ −2.50000 4.33013i −0.200160 0.346688i
$$157$$ −0.866025 0.500000i −0.0691164 0.0399043i 0.465044 0.885288i $$-0.346039\pi$$
−0.534160 + 0.845383i $$0.679372\pi$$
$$158$$ −6.06218 3.50000i −0.482281 0.278445i
$$159$$ −3.00000 5.19615i −0.237915 0.412082i
$$160$$ 0 0
$$161$$ 12.0000 10.3923i 0.945732 0.819028i
$$162$$ 1.00000i 0.0785674i
$$163$$ −0.866025 + 0.500000i −0.0678323 + 0.0391630i −0.533533 0.845780i $$-0.679136\pi$$
0.465700 + 0.884943i $$0.345802\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ −9.00000 15.5885i −0.698535 1.20990i
$$167$$ 6.00000i 0.464294i 0.972681 + 0.232147i $$0.0745750\pi$$
−0.972681 + 0.232147i $$0.925425\pi$$
$$168$$ 0.866025 2.50000i 0.0668153 0.192879i
$$169$$ −12.0000 −0.923077
$$170$$ 0 0
$$171$$ 3.50000 6.06218i 0.267652 0.463586i
$$172$$ 6.92820 + 4.00000i 0.528271 + 0.304997i
$$173$$ 15.5885 9.00000i 1.18517 0.684257i 0.227964 0.973670i $$-0.426793\pi$$
0.957205 + 0.289412i $$0.0934598\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 5.19615 3.00000i 0.390567 0.225494i
$$178$$ −5.19615 3.00000i −0.389468 0.224860i
$$179$$ 6.00000 10.3923i 0.448461 0.776757i −0.549825 0.835280i $$-0.685306\pi$$
0.998286 + 0.0585225i $$0.0186389\pi$$
$$180$$ 0 0
$$181$$ −10.0000 −0.743294 −0.371647 0.928374i $$-0.621207\pi$$
−0.371647 + 0.928374i $$0.621207\pi$$
$$182$$ −8.66025 10.0000i −0.641941 0.741249i
$$183$$ 1.00000i 0.0739221i
$$184$$ 3.00000 + 5.19615i 0.221163 + 0.383065i
$$185$$ 0 0
$$186$$ 4.00000 6.92820i 0.293294 0.508001i
$$187$$ 0 0
$$188$$ 6.00000i 0.437595i
$$189$$ 0.500000 + 2.59808i 0.0363696 + 0.188982i
$$190$$ 0 0
$$191$$ −12.0000 20.7846i −0.868290 1.50392i −0.863743 0.503932i $$-0.831886\pi$$
−0.00454614 0.999990i $$-0.501447\pi$$
$$192$$ 0.866025 + 0.500000i 0.0625000 + 0.0360844i
$$193$$ 8.66025 + 5.00000i 0.623379 + 0.359908i 0.778183 0.628037i $$-0.216141\pi$$
−0.154805 + 0.987945i $$0.549475\pi$$
$$194$$ 3.50000 + 6.06218i 0.251285 + 0.435239i
$$195$$ 0 0
$$196$$ 1.00000 6.92820i 0.0714286 0.494872i
$$197$$ 12.0000i 0.854965i 0.904024 + 0.427482i $$0.140599\pi$$
−0.904024 + 0.427482i $$0.859401\pi$$
$$198$$ 0 0
$$199$$ 5.50000 9.52628i 0.389885 0.675300i −0.602549 0.798082i $$-0.705848\pi$$
0.992434 + 0.122782i $$0.0391815\pi$$
$$200$$ 0 0
$$201$$ 6.50000 + 11.2583i 0.458475 + 0.794101i
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 6.00000 0.420084
$$205$$ 0 0
$$206$$ −6.50000 + 11.2583i −0.452876 + 0.784405i
$$207$$ −5.19615 3.00000i −0.361158 0.208514i
$$208$$ 4.33013 2.50000i 0.300240 0.173344i
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −13.0000 −0.894957 −0.447478 0.894295i $$-0.647678\pi$$
−0.447478 + 0.894295i $$0.647678\pi$$
$$212$$ 5.19615 3.00000i 0.356873 0.206041i
$$213$$ −10.3923 6.00000i −0.712069 0.411113i
$$214$$ 9.00000 15.5885i 0.615227 1.06561i
$$215$$ 0 0
$$216$$ −1.00000 −0.0680414
$$217$$ 6.92820 20.0000i 0.470317 1.35769i
$$218$$ 7.00000i 0.474100i
$$219$$ 2.50000 + 4.33013i 0.168934 + 0.292603i
$$220$$ 0 0
$$221$$ 15.0000 25.9808i 1.00901 1.74766i
$$222$$ −0.866025 + 0.500000i −0.0581238 + 0.0335578i
$$223$$ 17.0000i 1.13840i 0.822198 + 0.569202i $$0.192748\pi$$
−0.822198 + 0.569202i $$0.807252\pi$$
$$224$$ 2.50000 + 0.866025i 0.167038 + 0.0578638i
$$225$$ 0 0
$$226$$ −3.00000 5.19615i −0.199557 0.345643i
$$227$$ 10.3923 + 6.00000i 0.689761 + 0.398234i 0.803523 0.595274i $$-0.202957\pi$$
−0.113761 + 0.993508i $$0.536290\pi$$
$$228$$ 6.06218 + 3.50000i 0.401478 + 0.231793i
$$229$$ 2.50000 + 4.33013i 0.165205 + 0.286143i 0.936728 0.350058i $$-0.113838\pi$$
−0.771523 + 0.636201i $$0.780505\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 20.7846 12.0000i 1.36165 0.786146i 0.371802 0.928312i $$-0.378740\pi$$
0.989843 + 0.142166i $$0.0454066\pi$$
$$234$$ −2.50000 + 4.33013i −0.163430 + 0.283069i
$$235$$ 0 0
$$236$$ 3.00000 + 5.19615i 0.195283 + 0.338241i
$$237$$ 7.00000i 0.454699i
$$238$$ 15.5885 3.00000i 1.01045 0.194461i
$$239$$ 12.0000 0.776215 0.388108 0.921614i $$-0.373129\pi$$
0.388108 + 0.921614i $$0.373129\pi$$
$$240$$ 0 0
$$241$$ −2.50000 + 4.33013i −0.161039 + 0.278928i −0.935242 0.354010i $$-0.884818\pi$$
0.774202 + 0.632938i $$0.218151\pi$$
$$242$$ 9.52628 + 5.50000i 0.612372 + 0.353553i
$$243$$ 0.866025 0.500000i 0.0555556 0.0320750i
$$244$$ 1.00000 0.0640184
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 30.3109 17.5000i 1.92864 1.11350i
$$248$$ 6.92820 + 4.00000i 0.439941 + 0.254000i
$$249$$ −9.00000 + 15.5885i −0.570352 + 0.987878i
$$250$$ 0 0
$$251$$ −24.0000 −1.51487 −0.757433 0.652913i $$-0.773547\pi$$
−0.757433 + 0.652913i $$0.773547\pi$$
$$252$$ −2.59808 + 0.500000i −0.163663 + 0.0314970i
$$253$$ 0 0
$$254$$ −5.50000 9.52628i −0.345101 0.597732i
$$255$$ 0 0
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ 20.7846 12.0000i 1.29651 0.748539i 0.316709 0.948523i $$-0.397422\pi$$
0.979799 + 0.199983i $$0.0640888\pi$$
$$258$$ 8.00000i 0.498058i
$$259$$ −2.00000 + 1.73205i −0.124274 + 0.107624i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ −5.19615 3.00000i −0.321019 0.185341i
$$263$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 17.5000 + 6.06218i 1.07299 + 0.371696i
$$267$$ 6.00000i 0.367194i
$$268$$ −11.2583 + 6.50000i −0.687712 + 0.397051i
$$269$$ −12.0000 + 20.7846i −0.731653 + 1.26726i 0.224523 + 0.974469i $$0.427917\pi$$
−0.956176 + 0.292791i $$0.905416\pi$$
$$270$$ 0 0
$$271$$ −10.0000 17.3205i −0.607457 1.05215i −0.991658 0.128897i $$-0.958856\pi$$
0.384201 0.923249i $$-0.374477\pi$$
$$272$$ 6.00000i 0.363803i
$$273$$ −4.33013 + 12.5000i −0.262071 + 0.756534i
$$274$$ −18.0000 −1.08742
$$275$$ 0 0
$$276$$ 3.00000 5.19615i 0.180579 0.312772i
$$277$$ −16.4545 9.50000i −0.988654 0.570800i −0.0837823 0.996484i $$-0.526700\pi$$
−0.904872 + 0.425684i $$0.860033\pi$$
$$278$$ −9.52628 + 5.50000i −0.571348 + 0.329868i
$$279$$ −8.00000 −0.478947
$$280$$ 0 0
$$281$$ −18.0000 −1.07379 −0.536895 0.843649i $$-0.680403\pi$$
−0.536895 + 0.843649i $$0.680403\pi$$
$$282$$ 5.19615 3.00000i 0.309426 0.178647i
$$283$$ −4.33013 2.50000i −0.257399 0.148610i 0.365748 0.930714i $$-0.380813\pi$$
−0.623148 + 0.782104i $$0.714146\pi$$
$$284$$ 6.00000 10.3923i 0.356034 0.616670i
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 1.00000i 0.0589256i
$$289$$ 9.50000 + 16.4545i 0.558824 + 0.967911i
$$290$$ 0 0
$$291$$ 3.50000 6.06218i 0.205174 0.355371i
$$292$$ −4.33013 + 2.50000i −0.253402 + 0.146301i
$$293$$ 24.0000i 1.40209i −0.713115 0.701047i $$-0.752716\pi$$
0.713115 0.701047i $$-0.247284\pi$$
$$294$$ −6.50000 + 2.59808i −0.379088 + 0.151523i
$$295$$ 0 0
$$296$$ −0.500000 0.866025i −0.0290619 0.0503367i
$$297$$ 0 0
$$298$$ 10.3923 + 6.00000i 0.602010 + 0.347571i
$$299$$ −15.0000 25.9808i −0.867472 1.50251i
$$300$$ 0 0
$$301$$ −4.00000 20.7846i −0.230556 1.19800i
$$302$$ 1.00000i 0.0575435i
$$303$$ 0 0
$$304$$ −3.50000 + 6.06218i −0.200739 + 0.347690i
$$305$$ 0 0
$$306$$ −3.00000 5.19615i −0.171499 0.297044i
$$307$$ 28.0000i 1.59804i 0.601302 + 0.799022i $$0.294649\pi$$
−0.601302 + 0.799022i $$0.705351\pi$$
$$308$$ 0 0
$$309$$ 13.0000 0.739544
$$310$$ 0 0
$$311$$ −9.00000 + 15.5885i −0.510343 + 0.883940i 0.489585 + 0.871956i $$0.337148\pi$$
−0.999928 + 0.0119847i $$0.996185\pi$$
$$312$$ −4.33013 2.50000i −0.245145 0.141535i
$$313$$ 12.1244 7.00000i 0.685309 0.395663i −0.116543 0.993186i $$-0.537181\pi$$
0.801852 + 0.597522i $$0.203848\pi$$
$$314$$ −1.00000 −0.0564333
$$315$$ 0 0
$$316$$ −7.00000 −0.393781
$$317$$ 15.5885 9.00000i 0.875535 0.505490i 0.00635137 0.999980i $$-0.497978\pi$$
0.869184 + 0.494489i $$0.164645\pi$$
$$318$$ −5.19615 3.00000i −0.291386 0.168232i
$$319$$ 0 0
$$320$$ 0 0
$$321$$ −18.0000 −1.00466
$$322$$ 5.19615 15.0000i 0.289570 0.835917i
$$323$$ 42.0000i 2.33694i
$$324$$ 0.500000 + 0.866025i 0.0277778 + 0.0481125i
$$325$$ 0 0
$$326$$ −0.500000 + 0.866025i −0.0276924 + 0.0479647i
$$327$$ 6.06218 3.50000i 0.335239 0.193550i
$$328$$ 0 0
$$329$$ 12.0000 10.3923i 0.661581 0.572946i
$$330$$ 0 0
$$331$$ 9.50000 + 16.4545i 0.522167 + 0.904420i 0.999667 + 0.0257885i $$0.00820965\pi$$
−0.477500 + 0.878632i $$0.658457\pi$$
$$332$$ −15.5885 9.00000i −0.855528 0.493939i
$$333$$ 0.866025 + 0.500000i 0.0474579 + 0.0273998i
$$334$$ 3.00000 + 5.19615i 0.164153 + 0.284321i
$$335$$ 0 0
$$336$$ −0.500000 2.59808i −0.0272772 0.141737i
$$337$$ 34.0000i 1.85210i 0.377403 + 0.926049i $$0.376817\pi$$
−0.377403 + 0.926049i $$0.623183\pi$$
$$338$$ −10.3923 + 6.00000i −0.565267 + 0.326357i
$$339$$ −3.00000 + 5.19615i −0.162938 + 0.282216i
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 7.00000i 0.378517i
$$343$$ −15.5885 + 10.0000i −0.841698 + 0.539949i
$$344$$ 8.00000 0.431331
$$345$$ 0 0
$$346$$ 9.00000 15.5885i 0.483843 0.838041i
$$347$$ 15.5885 + 9.00000i 0.836832 + 0.483145i 0.856186 0.516667i $$-0.172828\pi$$
−0.0193540 + 0.999813i $$0.506161\pi$$
$$348$$ 0 0
$$349$$ −26.0000 −1.39175 −0.695874 0.718164i $$-0.744983\pi$$
−0.695874 + 0.718164i $$0.744983\pi$$
$$350$$ 0 0
$$351$$ 5.00000 0.266880
$$352$$ 0 0
$$353$$ 20.7846 + 12.0000i 1.10625 + 0.638696i 0.937856 0.347024i $$-0.112808\pi$$
0.168397 + 0.985719i $$0.446141\pi$$
$$354$$ 3.00000 5.19615i 0.159448 0.276172i
$$355$$ 0 0
$$356$$ −6.00000 −0.317999
$$357$$ −10.3923 12.0000i −0.550019 0.635107i
$$358$$ 12.0000i 0.634220i
$$359$$ 15.0000 + 25.9808i 0.791670 + 1.37121i 0.924932 + 0.380131i $$0.124121\pi$$
−0.133263 + 0.991081i $$0.542545\pi$$
$$360$$ 0 0
$$361$$ −15.0000 + 25.9808i −0.789474 + 1.36741i
$$362$$ −8.66025 + 5.00000i −0.455173 + 0.262794i
$$363$$ 11.0000i 0.577350i
$$364$$ −12.5000 4.33013i −0.655178 0.226960i
$$365$$ 0 0
$$366$$ −0.500000 0.866025i −0.0261354 0.0452679i
$$367$$ 6.92820 + 4.00000i 0.361649 + 0.208798i 0.669804 0.742538i $$-0.266378\pi$$
−0.308155 + 0.951336i $$0.599711\pi$$
$$368$$ 5.19615 + 3.00000i 0.270868 + 0.156386i
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −15.0000 5.19615i −0.778761 0.269771i
$$372$$ 8.00000i 0.414781i
$$373$$ −11.2583 + 6.50000i −0.582934 + 0.336557i −0.762299 0.647225i $$-0.775929\pi$$
0.179364 + 0.983783i $$0.442596\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 3.00000 + 5.19615i 0.154713 + 0.267971i
$$377$$ 0 0
$$378$$ 1.73205 + 2.00000i 0.0890871 + 0.102869i
$$379$$ −11.0000 −0.565032 −0.282516 0.959263i $$-0.591169\pi$$
−0.282516 + 0.959263i $$0.591169\pi$$
$$380$$ 0 0
$$381$$ −5.50000 + 9.52628i −0.281774 + 0.488046i
$$382$$ −20.7846 12.0000i −1.06343 0.613973i
$$383$$ −5.19615 + 3.00000i −0.265511 + 0.153293i −0.626846 0.779143i $$-0.715654\pi$$
0.361335 + 0.932436i $$0.382321\pi$$
$$384$$ 1.00000 0.0510310
$$385$$ 0 0
$$386$$ 10.0000 0.508987
$$387$$ −6.92820 + 4.00000i −0.352180 + 0.203331i
$$388$$ 6.06218 + 3.50000i 0.307760 + 0.177686i
$$389$$ −6.00000 + 10.3923i −0.304212 + 0.526911i −0.977086 0.212847i $$-0.931726\pi$$
0.672874 + 0.739758i $$0.265060\pi$$
$$390$$ 0 0
$$391$$ 36.0000 1.82060
$$392$$ −2.59808 6.50000i −0.131223 0.328300i
$$393$$ 6.00000i 0.302660i
$$394$$ 6.00000 + 10.3923i 0.302276 + 0.523557i
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −12.1244 + 7.00000i −0.608504 + 0.351320i −0.772380 0.635161i $$-0.780934\pi$$
0.163876 + 0.986481i $$0.447600\pi$$
$$398$$ 11.0000i 0.551380i
$$399$$ −3.50000 18.1865i −0.175219 0.910465i
$$400$$ 0 0
$$401$$ 18.0000 + 31.1769i 0.898877 + 1.55690i 0.828932 + 0.559350i $$0.188949\pi$$
0.0699455 + 0.997551i $$0.477717\pi$$
$$402$$ 11.2583 + 6.50000i 0.561514 + 0.324191i
$$403$$ −34.6410 20.0000i −1.72559 0.996271i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 5.19615 3.00000i 0.257248 0.148522i
$$409$$ 2.50000 4.33013i 0.123617 0.214111i −0.797574 0.603220i $$-0.793884\pi$$
0.921192 + 0.389109i $$0.127217\pi$$
$$410$$ 0 0
$$411$$ 9.00000 + 15.5885i 0.443937 + 0.768922i
$$412$$ 13.0000i 0.640464i
$$413$$ 5.19615 15.0000i 0.255686 0.738102i
$$414$$ −6.00000 −0.294884
$$415$$ 0 0
$$416$$ 2.50000 4.33013i 0.122573 0.212302i
$$417$$ 9.52628 + 5.50000i 0.466504 + 0.269336i
$$418$$ 0 0
$$419$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$420$$ 0 0
$$421$$ 5.00000 0.243685 0.121843 0.992549i $$-0.461120\pi$$
0.121843 + 0.992549i $$0.461120\pi$$
$$422$$ −11.2583 + 6.50000i −0.548047 + 0.316415i
$$423$$ −5.19615 3.00000i −0.252646 0.145865i
$$424$$ 3.00000 5.19615i 0.145693 0.252347i
$$425$$ 0 0
$$426$$ −12.0000 −0.581402
$$427$$ −1.73205 2.00000i −0.0838198 0.0967868i
$$428$$ 18.0000i 0.870063i
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 9.00000 15.5885i 0.433515 0.750870i −0.563658 0.826008i $$-0.690607\pi$$
0.997173 + 0.0751385i $$0.0239399\pi$$
$$432$$ −0.866025 + 0.500000i −0.0416667 + 0.0240563i
$$433$$ 34.0000i 1.63394i −0.576683 0.816968i $$-0.695653\pi$$
0.576683 0.816968i $$-0.304347\pi$$
$$434$$ −4.00000 20.7846i −0.192006 0.997693i
$$435$$ 0 0
$$436$$ 3.50000 + 6.06218i 0.167620 + 0.290326i
$$437$$ 36.3731 + 21.0000i 1.73996 + 1.00457i
$$438$$ 4.33013 + 2.50000i 0.206901 + 0.119455i
$$439$$ 2.50000 + 4.33013i 0.119318 + 0.206666i 0.919498 0.393095i $$-0.128596\pi$$
−0.800179 + 0.599761i $$0.795262\pi$$
$$440$$ 0 0
$$441$$ 5.50000 + 4.33013i 0.261905 + 0.206197i
$$442$$ 30.0000i 1.42695i
$$443$$ −36.3731 + 21.0000i −1.72814 + 0.997740i −0.830473 + 0.557059i $$0.811930\pi$$
−0.897664 + 0.440681i $$0.854737\pi$$
$$444$$ −0.500000 + 0.866025i −0.0237289 + 0.0410997i
$$445$$ 0 0
$$446$$ 8.50000 + 14.7224i 0.402487 + 0.697127i
$$447$$ 12.0000i 0.567581i
$$448$$ 2.59808 0.500000i 0.122748 0.0236228i
$$449$$ −6.00000 −0.283158 −0.141579 0.989927i $$-0.545218\pi$$
−0.141579 + 0.989927i $$0.545218\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ −5.19615 3.00000i −0.244406 0.141108i
$$453$$ −0.866025 + 0.500000i −0.0406894 + 0.0234920i
$$454$$ 12.0000 0.563188
$$455$$ 0 0
$$456$$ 7.00000 0.327805
$$457$$ −25.1147 + 14.5000i −1.17482 + 0.678281i −0.954810 0.297217i $$-0.903942\pi$$
−0.220008 + 0.975498i $$0.570608\pi$$
$$458$$ 4.33013 + 2.50000i 0.202334 + 0.116817i
$$459$$ −3.00000 + 5.19615i −0.140028 + 0.242536i
$$460$$ 0 0
$$461$$ 6.00000 0.279448 0.139724 0.990190i $$-0.455378\pi$$
0.139724 + 0.990190i $$0.455378\pi$$
$$462$$ 0 0
$$463$$ 31.0000i 1.44069i −0.693615 0.720346i $$-0.743983\pi$$
0.693615 0.720346i $$-0.256017\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 12.0000 20.7846i 0.555889 0.962828i
$$467$$ −25.9808 + 15.0000i −1.20225 + 0.694117i −0.961054 0.276360i $$-0.910872\pi$$
−0.241192 + 0.970477i $$0.577538\pi$$
$$468$$ 5.00000i 0.231125i
$$469$$ 32.5000 + 11.2583i 1.50071 + 0.519861i
$$470$$ 0 0
$$471$$ 0.500000 + 0.866025i 0.0230388 + 0.0399043i
$$472$$ 5.19615 + 3.00000i 0.239172 + 0.138086i
$$473$$ 0 0
$$474$$ 3.50000 + 6.06218i 0.160760 + 0.278445i
$$475$$ 0 0
$$476$$ 12.0000 10.3923i 0.550019 0.476331i
$$477$$ 6.00000i 0.274721i
$$478$$ 10.3923 6.00000i 0.475333 0.274434i
$$479$$ 9.00000 15.5885i 0.411220 0.712255i −0.583803 0.811895i $$-0.698436\pi$$
0.995023 + 0.0996406i $$0.0317693\pi$$
$$480$$ 0 0
$$481$$ 2.50000 + 4.33013i 0.113990 + 0.197437i
$$482$$ 5.00000i 0.227744i
$$483$$ −15.5885 + 3.00000i −0.709299 + 0.136505i
$$484$$ 11.0000 0.500000
$$485$$ 0 0
$$486$$ 0.500000 0.866025i 0.0226805 0.0392837i
$$487$$ −34.6410 20.0000i −1.56973 0.906287i −0.996199 0.0871056i $$-0.972238\pi$$
−0.573535 0.819181i $$-0.694428\pi$$
$$488$$ 0.866025 0.500000i 0.0392031 0.0226339i
$$489$$ 1.00000 0.0452216
$$490$$ 0 0
$$491$$ −6.00000 −0.270776 −0.135388 0.990793i $$-0.543228\pi$$
−0.135388 + 0.990793i $$0.543228\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 17.5000 30.3109i 0.787362 1.36375i
$$495$$ 0 0
$$496$$ 8.00000 0.359211
$$497$$ −31.1769 + 6.00000i −1.39848 + 0.269137i
$$498$$ 18.0000i 0.806599i
$$499$$ 2.50000 + 4.33013i 0.111915 + 0.193843i 0.916542 0.399937i $$-0.130968\pi$$
−0.804627 + 0.593780i $$0.797635\pi$$
$$500$$ 0 0
$$501$$ 3.00000 5.19615i 0.134030 0.232147i
$$502$$ −20.7846 + 12.0000i −0.927663 + 0.535586i
$$503$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$504$$ −2.00000 + 1.73205i −0.0890871 + 0.0771517i
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 10.3923 + 6.00000i 0.461538 + 0.266469i
$$508$$ −9.52628 5.50000i −0.422660 0.244023i
$$509$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$510$$ 0 0
$$511$$ 12.5000 + 4.33013i 0.552967 + 0.191554i
$$512$$ 1.00000i 0.0441942i
$$513$$ −6.06218 + 3.50000i −0.267652 + 0.154529i
$$514$$ 12.0000 20.7846i 0.529297 0.916770i
$$515$$ 0 0
$$516$$ −4.00000 6.92820i −0.176090 0.304997i
$$517$$ 0 0
$$518$$ −0.866025 + 2.50000i −0.0380510 + 0.109844i
$$519$$ −18.0000 −0.790112
$$520$$ 0 0
$$521$$ −21.0000 + 36.3731i −0.920027 + 1.59353i −0.120656 + 0.992694i $$0.538500\pi$$
−0.799370 + 0.600839i $$0.794833\pi$$
$$522$$ 0 0
$$523$$ 27.7128 16.0000i 1.21180 0.699631i 0.248646 0.968594i $$-0.420014\pi$$
0.963150 + 0.268963i $$0.0866810\pi$$
$$524$$ −6.00000 −0.262111
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 41.5692 24.0000i 1.81078 1.04546i
$$528$$ 0 0
$$529$$ 6.50000 11.2583i 0.282609 0.489493i
$$530$$ 0 0
$$531$$ −6.00000 −0.260378
$$532$$ 18.1865 3.50000i 0.788486 0.151744i
$$533$$ 0 0
$$534$$ 3.00000 + 5.19615i 0.129823 + 0.224860i
$$535$$ 0 0
$$536$$ −6.50000 + 11.2583i −0.280757 + 0.486286i
$$537$$ −10.3923 + 6.00000i −0.448461 + 0.258919i
$$538$$ 24.0000i 1.03471i
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 21.5000 + 37.2391i 0.924357 + 1.60103i 0.792592 + 0.609753i $$0.208731\pi$$
0.131765 + 0.991281i $$0.457935\pi$$
$$542$$ −17.3205 10.0000i −0.743980 0.429537i
$$543$$ 8.66025 + 5.00000i 0.371647 + 0.214571i
$$544$$ 3.00000 + 5.19615i 0.128624 + 0.222783i
$$545$$ 0 0
$$546$$ 2.50000 + 12.9904i 0.106990 + 0.555937i
$$547$$ 28.0000i 1.19719i 0.801050 + 0.598597i $$0.204275\pi$$
−0.801050 + 0.598597i $$0.795725\pi$$
$$548$$ −15.5885 + 9.00000i −0.665906 + 0.384461i
$$549$$ −0.500000 + 0.866025i −0.0213395 + 0.0369611i
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 6.00000i 0.255377i
$$553$$ 12.1244 + 14.0000i 0.515580 + 0.595341i
$$554$$ −19.0000 −0.807233
$$555$$ 0 0
$$556$$ −5.50000 + 9.52628i −0.233252 + 0.404004i
$$557$$ −10.3923 6.00000i −0.440336 0.254228i 0.263404 0.964686i $$-0.415155\pi$$
−0.703740 + 0.710457i $$0.748488\pi$$
$$558$$ −6.92820 + 4.00000i −0.293294 + 0.169334i
$$559$$ −40.0000 −1.69182
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −15.5885 + 9.00000i −0.657559 + 0.379642i
$$563$$ 10.3923 + 6.00000i 0.437983 + 0.252870i 0.702742 0.711445i $$-0.251959\pi$$
−0.264758 + 0.964315i $$0.585292\pi$$
$$564$$ 3.00000 5.19615i 0.126323 0.218797i
$$565$$ 0 0
$$566$$ −5.00000 −0.210166
$$567$$ 0.866025 2.50000i 0.0363696 0.104990i
$$568$$ 12.0000i 0.503509i
$$569$$ −18.0000 31.1769i −0.754599 1.30700i −0.945573 0.325409i $$-0.894498\pi$$
0.190974 0.981595i $$-0.438835\pi$$
$$570$$ 0 0
$$571$$ −2.50000 + 4.33013i −0.104622 + 0.181210i −0.913584 0.406651i $$-0.866697\pi$$
0.808962 + 0.587861i $$0.200030\pi$$
$$572$$ 0 0
$$573$$ 24.0000i 1.00261i
$$574$$ 0 0
$$575$$ 0 0
$$576$$ −0.500000 0.866025i −0.0208333 0.0360844i
$$577$$ 12.1244 + 7.00000i 0.504744 + 0.291414i 0.730670 0.682730i $$-0.239208\pi$$
−0.225927 + 0.974144i $$0.572541\pi$$
$$578$$ 16.4545 + 9.50000i 0.684416 + 0.395148i
$$579$$ −5.00000 8.66025i −0.207793 0.359908i
$$580$$ 0 0
$$581$$ 9.00000 + 46.7654i 0.373383 + 1.94015i
$$582$$ 7.00000i 0.290159i
$$583$$ 0 0
$$584$$ −2.50000 + 4.33013i −0.103451 + 0.179182i
$$585$$ 0 0
$$586$$ −12.0000 20.7846i −0.495715 0.858604i
$$587$$ 30.0000i 1.23823i 0.785299 + 0.619116i $$0.212509\pi$$
−0.785299 + 0.619116i $$0.787491\pi$$
$$588$$ −4.33013 + 5.50000i −0.178571 + 0.226816i
$$589$$ 56.0000 2.30744
$$590$$ 0 0
$$591$$ 6.00000 10.3923i 0.246807 0.427482i
$$592$$ −0.866025 0.500000i −0.0355934 0.0205499i
$$593$$ −5.19615 + 3.00000i −0.213380 + 0.123195i −0.602881 0.797831i $$-0.705981\pi$$
0.389501 + 0.921026i $$0.372647\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 12.0000 0.491539
$$597$$ −9.52628 + 5.50000i −0.389885 + 0.225100i
$$598$$ −25.9808 15.0000i −1.06243 0.613396i
$$599$$ −15.0000 + 25.9808i −0.612883 + 1.06155i 0.377869 + 0.925859i $$0.376657\pi$$
−0.990752 + 0.135686i $$0.956676\pi$$
$$600$$ 0 0
$$601$$ 35.0000 1.42768 0.713840 0.700309i $$-0.246954\pi$$
0.713840 + 0.700309i $$0.246954\pi$$
$$602$$ −13.8564 16.0000i −0.564745 0.652111i
$$603$$ 13.0000i 0.529401i
$$604$$ −0.500000 0.866025i −0.0203447 0.0352381i
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 37.2391 21.5000i 1.51149 0.872658i 0.511578 0.859237i $$-0.329061\pi$$
0.999910 0.0134214i $$-0.00427228\pi$$
$$608$$ 7.00000i 0.283887i
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −15.0000 25.9808i −0.606835 1.05107i
$$612$$ −5.19615 3.00000i −0.210042 0.121268i
$$613$$ −32.9090 19.0000i −1.32918 0.767403i −0.344008 0.938967i $$-0.611785\pi$$
−0.985173 + 0.171564i $$0.945118\pi$$
$$614$$ 14.0000 + 24.2487i 0.564994 + 0.978598i
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 48.0000i 1.93241i −0.257780 0.966204i $$-0.582991\pi$$
0.257780 0.966204i $$-0.417009\pi$$
$$618$$ 11.2583 6.50000i 0.452876 0.261468i
$$619$$ 10.0000 17.3205i 0.401934 0.696170i −0.592025 0.805919i $$-0.701671\pi$$
0.993959 + 0.109749i $$0.0350048\pi$$
$$620$$ 0 0
$$621$$ 3.00000 + 5.19615i 0.120386 + 0.208514i
$$622$$ 18.0000i 0.721734i
$$623$$ 10.3923 + 12.0000i 0.416359 + 0.480770i
$$624$$ −5.00000 −0.200160
$$625$$ 0 0
$$626$$ 7.00000 12.1244i 0.279776 0.484587i
$$627$$ 0 0
$$628$$ −0.866025 + 0.500000i −0.0345582 + 0.0199522i
$$629$$ −6.00000 −0.239236
$$630$$ 0 0
$$631$$ −19.0000 −0.756378 −0.378189 0.925728i $$-0.623453\pi$$
−0.378189 + 0.925728i $$0.623453\pi$$
$$632$$ −6.06218 + 3.50000i −0.241140 + 0.139223i
$$633$$ 11.2583 + 6.50000i 0.447478 + 0.258352i
$$634$$ 9.00000 15.5885i 0.357436 0.619097i
$$635$$ 0 0
$$636$$ −6.00000 −0.237915
$$637$$ 12.9904 + 32.5000i 0.514698 + 1.28770i
$$638$$ 0 0
$$639$$ 6.00000 + 10.3923i 0.237356 + 0.411113i
$$640$$ 0 0
$$641$$ 12.0000 20.7846i 0.473972 0.820943i −0.525584 0.850741i $$-0.676153\pi$$
0.999556 + 0.0297987i $$0.00948663\pi$$
$$642$$ −15.5885 + 9.00000i −0.615227 + 0.355202i
$$643$$ 11.0000i 0.433798i 0.976194 + 0.216899i $$0.0695942\pi$$
−0.976194 + 0.216899i $$0.930406\pi$$
$$644$$ −3.00000 15.5885i −0.118217 0.614271i
$$645$$ 0 0
$$646$$ 21.0000 + 36.3731i 0.826234 + 1.43108i
$$647$$ −10.3923 6.00000i −0.408564 0.235884i 0.281609 0.959529i $$-0.409132\pi$$
−0.690172 + 0.723645i $$0.742465\pi$$
$$648$$ 0.866025 + 0.500000i 0.0340207 + 0.0196419i
$$649$$ 0 0
$$650$$ 0 0
$$651$$ −16.0000 + 13.8564i −0.627089 + 0.543075i
$$652$$ 1.00000i 0.0391630i
$$653$$ −31.1769 + 18.0000i −1.22005 + 0.704394i −0.964928 0.262515i $$-0.915448\pi$$
−0.255119 + 0.966910i $$0.582115\pi$$
$$654$$ 3.50000 6.06218i 0.136861 0.237050i
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 5.00000i 0.195069i
$$658$$ 5.19615 15.0000i 0.202567 0.584761i
$$659$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$660$$ 0 0
$$661$$ −17.5000 + 30.3109i −0.680671 + 1.17896i 0.294105 + 0.955773i $$0.404978\pi$$
−0.974776 + 0.223184i $$0.928355\pi$$
$$662$$ 16.4545 + 9.50000i 0.639522 + 0.369228i
$$663$$ −25.9808 + 15.0000i −1.00901 + 0.582552i
$$664$$ −18.0000 −0.698535
$$665$$ 0 0
$$666$$ 1.00000 0.0387492
$$667$$ 0 0
$$668$$ 5.19615 + 3.00000i 0.201045 + 0.116073i
$$669$$ 8.50000 14.7224i 0.328629 0.569202i
$$670$$ 0 0
$$671$$ 0 0
$$672$$ −1.73205 2.00000i −0.0668153 0.0771517i
$$673$$ 1.00000i 0.0385472i −0.999814 0.0192736i $$-0.993865\pi$$
0.999814 0.0192736i $$-0.00613535\pi$$
$$674$$ 17.0000 + 29.4449i 0.654816 + 1.13417i
$$675$$ 0 0
$$676$$ −6.00000 + 10.3923i −0.230769 + 0.399704i
$$677$$ −36.3731 + 21.0000i −1.39793 + 0.807096i −0.994176 0.107772i $$-0.965628\pi$$
−0.403755 + 0.914867i $$0.632295\pi$$
$$678$$ 6.00000i 0.230429i
$$679$$ −3.50000 18.1865i −0.134318 0.697935i
$$680$$ 0 0
$$681$$ −6.00000 10.3923i −0.229920 0.398234i
$$682$$ 0 0
$$683$$ −20.7846 12.0000i −0.795301 0.459167i 0.0465244 0.998917i $$-0.485185\pi$$
−0.841825 + 0.539750i $$0.818519\pi$$
$$684$$ −3.50000 6.06218i −0.133826 0.231793i
$$685$$ 0 0
$$686$$ −8.50000 + 16.4545i −0.324532 + 0.628235i
$$687$$ 5.00000i 0.190762i
$$688$$ 6.92820 4.00000i 0.264135 0.152499i
$$689$$ −15.0000 + 25.9808i −0.571454 + 0.989788i
$$690$$ 0 0
$$691$$ 3.50000 + 6.06218i 0.133146 + 0.230616i 0.924888 0.380240i $$-0.124159\pi$$
−0.791742 + 0.610856i $$0.790825\pi$$
$$692$$ 18.0000i 0.684257i
$$693$$ 0 0
$$694$$ 18.0000 0.683271
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ −22.5167 + 13.0000i −0.852268 + 0.492057i
$$699$$ −24.0000 −0.907763
$$700$$ 0 0
$$701$$ −30.0000 −1.13308 −0.566542 0.824033i $$-0.691719\pi$$
−0.566542 + 0.824033i $$0.691719\pi$$
$$702$$ 4.33013 2.50000i 0.163430 0.0943564i
$$703$$ −6.06218 3.50000i −0.228639 0.132005i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 24.0000 0.903252
$$707$$ 0 0
$$708$$ 6.00000i 0.225494i
$$709$$ −3.50000 6.06218i −0.131445 0.227670i 0.792789 0.609497i $$-0.208628\pi$$
−0.924234 + 0.381827i $$0.875295\pi$$
$$710$$ 0 0
$$711$$ 3.50000 6.06218i 0.131260 0.227349i
$$712$$ −5.19615 + 3.00000i −0.194734 + 0.112430i
$$713$$ 48.0000i 1.79761i
$$714$$ −15.0000 5.19615i −0.561361 0.194461i
$$715$$ 0 0
$$716$$ −6.00000 10.3923i −0.224231 0.388379i
$$717$$ −10.3923 6.00000i −0.388108 0.224074i
$$718$$ 25.9808 + 15.0000i 0.969593 + 0.559795i
$$719$$ −18.0000 31.1769i −0.671287 1.16270i −0.977539 0.210752i $$-0.932409\pi$$
0.306253 0.951950i $$-0.400925\pi$$
$$720$$ 0 0
$$721$$ 26.0000 22.5167i 0.968291 0.838564i
$$722$$ 30.0000i 1.11648i
$$723$$ 4.33013 2.50000i 0.161039 0.0929760i
$$724$$ −5.00000 + 8.66025i −0.185824 + 0.321856i
$$725$$ 0 0
$$726$$ −5.50000 9.52628i −0.204124 0.353553i
$$727$$ 37.0000i 1.37225i 0.727482 + 0.686127i $$0.240691\pi$$
−0.727482 + 0.686127i $$0.759309\pi$$
$$728$$ −12.9904 + 2.50000i −0.481456 + 0.0926562i
$$729$$ −1.00000 −0.0370370
$$730$$ 0 0
$$731$$ 24.0000 41.5692i 0.887672 1.53749i
$$732$$ −0.866025 0.500000i −0.0320092 0.0184805i
$$733$$ 35.5070 20.5000i 1.31148 0.757185i 0.329141 0.944281i $$-0.393241\pi$$
0.982342 + 0.187096i $$0.0599076\pi$$
$$734$$ 8.00000 0.295285
$$735$$ 0 0
$$736$$ 6.00000 0.221163
$$737$$ 0 0
$$738$$ 0 0
$$739$$ −12.5000 + 21.6506i −0.459820 + 0.796431i −0.998951 0.0457903i $$-0.985419\pi$$
0.539131 + 0.842222i $$0.318753\pi$$
$$740$$ 0 0
$$741$$ −35.0000 −1.28576
$$742$$ −15.5885 + 3.00000i −0.572270 + 0.110133i
$$743$$ 30.0000i 1.10059i 0.834969 + 0.550297i $$0.185485\pi$$
−0.834969 + 0.550297i $$0.814515\pi$$
$$744$$ −4.00000 6.92820i −0.146647 0.254000i
$$745$$ 0 0
$$746$$ −6.50000 + 11.2583i −0.237982 + 0.412197i
$$747$$ 15.5885 9.00000i 0.570352 0.329293i
$$748$$ 0 0
$$749$$ −36.0000 + 31.1769i −1.31541 + 1.13918i
$$750$$ 0 0
$$751$$ 12.5000 + 21.6506i 0.456131 + 0.790043i 0.998752 0.0499348i $$-0.0159013\pi$$
−0.542621 + 0.839978i $$0.682568\pi$$
$$752$$ 5.19615 + 3.00000i 0.189484 + 0.109399i
$$753$$ 20.7846 + 12.0000i 0.757433 + 0.437304i
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 2.50000 + 0.866025i 0.0909241 + 0.0314970i
$$757$$ 29.0000i 1.05402i −0.849858 0.527011i $$-0.823312\pi$$
0.849858 0.527011i $$-0.176688\pi$$
$$758$$ −9.52628 + 5.50000i −0.346010 + 0.199769i
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −9.00000 15.5885i −0.326250 0.565081i 0.655515 0.755182i $$-0.272452\pi$$
−0.981764 + 0.190101i $$0.939118\pi$$
$$762$$ 11.0000i 0.398488i
$$763$$ 6.06218 17.5000i 0.219466 0.633543i
$$764$$ −24.0000 −0.868290
$$765$$ 0 0
$$766$$ −3.00000 + 5.19615i −0.108394 + 0.187745i
$$767$$ −25.9808 15.0000i −0.938111 0.541619i
$$768$$ 0.866025 0.500000i 0.0312500 0.0180422i
$$769$$ 10.0000 0.360609 0.180305 0.983611i $$-0.442292\pi$$
0.180305 + 0.983611i $$0.442292\pi$$
$$770$$ 0 0
$$771$$ −24.0000 −0.864339
$$772$$ 8.66025 5.00000i 0.311689 0.179954i
$$773$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$774$$ −4.00000 + 6.92820i −0.143777 + 0.249029i
$$775$$ 0 0
$$776$$ 7.00000 0.251285
$$777$$ 2.59808 0.500000i 0.0932055 0.0179374i
$$778$$ 12.0000i 0.430221i
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 31.1769 18.0000i 1.11488 0.643679i
$$783$$ 0 0
$$784$$ −5.50000 4.33013i −0.196429 0.154647i
$$785$$ 0 0
$$786$$ 3.00000 + 5.19615i 0.107006 + 0.185341i
$$787$$ 19.9186 + 11.5000i 0.710021 + 0.409931i 0.811069 0.584951i $$-0.198886\pi$$
−0.101048 + 0.994882i $$0.532220\pi$$
$$788$$ 10.3923 + 6.00000i 0.370211 + 0.213741i
$$789$$