# Properties

 Label 432.2.y.b.181.1 Level $432$ Weight $2$ Character 432.181 Analytic conductor $3.450$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$432 = 2^{4} \cdot 3^{3}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 432.y (of order $$12$$, degree $$4$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$3.44953736732$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\zeta_{12})$$ Defining polynomial: $$x^{4} - x^{2} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 144) Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

## Embedding invariants

 Embedding label 181.1 Root $$-0.866025 + 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 432.181 Dual form 432.2.y.b.253.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.36603 - 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} +(-1.00000 + 3.73205i) q^{5} +(0.633975 + 0.366025i) q^{7} +(2.00000 - 2.00000i) q^{8} +O(q^{10})$$ $$q+(1.36603 - 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} +(-1.00000 + 3.73205i) q^{5} +(0.633975 + 0.366025i) q^{7} +(2.00000 - 2.00000i) q^{8} +5.46410i q^{10} +(-2.86603 + 0.767949i) q^{11} +(6.09808 + 1.63397i) q^{13} +(1.00000 + 0.267949i) q^{14} +(2.00000 - 3.46410i) q^{16} +2.26795 q^{17} +(-0.633975 + 0.633975i) q^{19} +(2.00000 + 7.46410i) q^{20} +(-3.63397 + 2.09808i) q^{22} +(-1.09808 + 0.633975i) q^{23} +(-8.59808 - 4.96410i) q^{25} +8.92820 q^{26} +1.46410 q^{28} +(-0.633975 - 2.36603i) q^{29} +(-3.73205 - 6.46410i) q^{31} +(1.46410 - 5.46410i) q^{32} +(3.09808 - 0.830127i) q^{34} +(-2.00000 + 2.00000i) q^{35} +(1.26795 + 1.26795i) q^{37} +(-0.633975 + 1.09808i) q^{38} +(5.46410 + 9.46410i) q^{40} +(-2.59808 + 1.50000i) q^{41} +(-1.23205 + 0.330127i) q^{43} +(-4.19615 + 4.19615i) q^{44} +(-1.26795 + 1.26795i) q^{46} +(4.83013 - 8.36603i) q^{47} +(-3.23205 - 5.59808i) q^{49} +(-13.5622 - 3.63397i) q^{50} +(12.1962 - 3.26795i) q^{52} +(0.535898 + 0.535898i) q^{53} -11.4641i q^{55} +(2.00000 - 0.535898i) q^{56} +(-1.73205 - 3.00000i) q^{58} +(1.33013 - 4.96410i) q^{59} +(0.803848 + 3.00000i) q^{61} +(-7.46410 - 7.46410i) q^{62} -8.00000i q^{64} +(-12.1962 + 21.1244i) q^{65} +(-5.23205 - 1.40192i) q^{67} +(3.92820 - 2.26795i) q^{68} +(-2.00000 + 3.46410i) q^{70} -10.9282i q^{71} +9.73205i q^{73} +(2.19615 + 1.26795i) q^{74} +(-0.464102 + 1.73205i) q^{76} +(-2.09808 - 0.562178i) q^{77} +(-6.00000 + 10.3923i) q^{79} +(10.9282 + 10.9282i) q^{80} +(-3.00000 + 3.00000i) q^{82} +(-0.366025 - 1.36603i) q^{83} +(-2.26795 + 8.46410i) q^{85} +(-1.56218 + 0.901924i) q^{86} +(-4.19615 + 7.26795i) q^{88} -2.00000i q^{89} +(3.26795 + 3.26795i) q^{91} +(-1.26795 + 2.19615i) q^{92} +(3.53590 - 13.1962i) q^{94} +(-1.73205 - 3.00000i) q^{95} +(-4.13397 + 7.16025i) q^{97} +(-6.46410 - 6.46410i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q + 2q^{2} - 4q^{5} + 6q^{7} + 8q^{8} + O(q^{10})$$ $$4q + 2q^{2} - 4q^{5} + 6q^{7} + 8q^{8} - 8q^{11} + 14q^{13} + 4q^{14} + 8q^{16} + 16q^{17} - 6q^{19} + 8q^{20} - 18q^{22} + 6q^{23} - 24q^{25} + 8q^{26} - 8q^{28} - 6q^{29} - 8q^{31} - 8q^{32} + 2q^{34} - 8q^{35} + 12q^{37} - 6q^{38} + 8q^{40} + 2q^{43} + 4q^{44} - 12q^{46} + 2q^{47} - 6q^{49} - 30q^{50} + 28q^{52} + 16q^{53} + 8q^{56} - 12q^{59} + 24q^{61} - 16q^{62} - 28q^{65} - 14q^{67} - 12q^{68} - 8q^{70} - 12q^{74} + 12q^{76} + 2q^{77} - 24q^{79} + 16q^{80} - 12q^{82} + 2q^{83} - 16q^{85} + 18q^{86} + 4q^{88} + 20q^{91} - 12q^{92} + 28q^{94} - 20q^{97} - 12q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$$.

 $$n$$ $$271$$ $$325$$ $$353$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{4}\right)$$ $$e\left(\frac{2}{3}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.36603 0.366025i 0.965926 0.258819i
$$3$$ 0 0
$$4$$ 1.73205 1.00000i 0.866025 0.500000i
$$5$$ −1.00000 + 3.73205i −0.447214 + 1.66902i 0.262811 + 0.964847i $$0.415350\pi$$
−0.710025 + 0.704177i $$0.751316\pi$$
$$6$$ 0 0
$$7$$ 0.633975 + 0.366025i 0.239620 + 0.138345i 0.615002 0.788526i $$-0.289155\pi$$
−0.375382 + 0.926870i $$0.622489\pi$$
$$8$$ 2.00000 2.00000i 0.707107 0.707107i
$$9$$ 0 0
$$10$$ 5.46410i 1.72790i
$$11$$ −2.86603 + 0.767949i −0.864139 + 0.231545i −0.663552 0.748130i $$-0.730952\pi$$
−0.200587 + 0.979676i $$0.564285\pi$$
$$12$$ 0 0
$$13$$ 6.09808 + 1.63397i 1.69130 + 0.453183i 0.970725 0.240192i $$-0.0772105\pi$$
0.720577 + 0.693375i $$0.243877\pi$$
$$14$$ 1.00000 + 0.267949i 0.267261 + 0.0716124i
$$15$$ 0 0
$$16$$ 2.00000 3.46410i 0.500000 0.866025i
$$17$$ 2.26795 0.550058 0.275029 0.961436i $$-0.411312\pi$$
0.275029 + 0.961436i $$0.411312\pi$$
$$18$$ 0 0
$$19$$ −0.633975 + 0.633975i −0.145444 + 0.145444i −0.776079 0.630635i $$-0.782794\pi$$
0.630635 + 0.776079i $$0.282794\pi$$
$$20$$ 2.00000 + 7.46410i 0.447214 + 1.66902i
$$21$$ 0 0
$$22$$ −3.63397 + 2.09808i −0.774766 + 0.447311i
$$23$$ −1.09808 + 0.633975i −0.228965 + 0.132193i −0.610094 0.792329i $$-0.708868\pi$$
0.381130 + 0.924522i $$0.375535\pi$$
$$24$$ 0 0
$$25$$ −8.59808 4.96410i −1.71962 0.992820i
$$26$$ 8.92820 1.75096
$$27$$ 0 0
$$28$$ 1.46410 0.276689
$$29$$ −0.633975 2.36603i −0.117726 0.439360i 0.881750 0.471717i $$-0.156365\pi$$
−0.999476 + 0.0323566i $$0.989699\pi$$
$$30$$ 0 0
$$31$$ −3.73205 6.46410i −0.670296 1.16099i −0.977820 0.209447i $$-0.932834\pi$$
0.307524 0.951540i $$-0.400500\pi$$
$$32$$ 1.46410 5.46410i 0.258819 0.965926i
$$33$$ 0 0
$$34$$ 3.09808 0.830127i 0.531316 0.142366i
$$35$$ −2.00000 + 2.00000i −0.338062 + 0.338062i
$$36$$ 0 0
$$37$$ 1.26795 + 1.26795i 0.208450 + 0.208450i 0.803608 0.595159i $$-0.202911\pi$$
−0.595159 + 0.803608i $$0.702911\pi$$
$$38$$ −0.633975 + 1.09808i −0.102844 + 0.178131i
$$39$$ 0 0
$$40$$ 5.46410 + 9.46410i 0.863950 + 1.49641i
$$41$$ −2.59808 + 1.50000i −0.405751 + 0.234261i −0.688963 0.724797i $$-0.741934\pi$$
0.283211 + 0.959058i $$0.408600\pi$$
$$42$$ 0 0
$$43$$ −1.23205 + 0.330127i −0.187886 + 0.0503439i −0.351535 0.936175i $$-0.614340\pi$$
0.163649 + 0.986519i $$0.447674\pi$$
$$44$$ −4.19615 + 4.19615i −0.632594 + 0.632594i
$$45$$ 0 0
$$46$$ −1.26795 + 1.26795i −0.186949 + 0.186949i
$$47$$ 4.83013 8.36603i 0.704546 1.22031i −0.262309 0.964984i $$-0.584484\pi$$
0.966855 0.255326i $$-0.0821828\pi$$
$$48$$ 0 0
$$49$$ −3.23205 5.59808i −0.461722 0.799725i
$$50$$ −13.5622 3.63397i −1.91798 0.513922i
$$51$$ 0 0
$$52$$ 12.1962 3.26795i 1.69130 0.453183i
$$53$$ 0.535898 + 0.535898i 0.0736113 + 0.0736113i 0.742954 0.669343i $$-0.233424\pi$$
−0.669343 + 0.742954i $$0.733424\pi$$
$$54$$ 0 0
$$55$$ 11.4641i 1.54582i
$$56$$ 2.00000 0.535898i 0.267261 0.0716124i
$$57$$ 0 0
$$58$$ −1.73205 3.00000i −0.227429 0.393919i
$$59$$ 1.33013 4.96410i 0.173168 0.646271i −0.823689 0.567042i $$-0.808088\pi$$
0.996856 0.0792287i $$-0.0252457\pi$$
$$60$$ 0 0
$$61$$ 0.803848 + 3.00000i 0.102922 + 0.384111i 0.998101 0.0615961i $$-0.0196191\pi$$
−0.895179 + 0.445707i $$0.852952\pi$$
$$62$$ −7.46410 7.46410i −0.947942 0.947942i
$$63$$ 0 0
$$64$$ 8.00000i 1.00000i
$$65$$ −12.1962 + 21.1244i −1.51275 + 2.62015i
$$66$$ 0 0
$$67$$ −5.23205 1.40192i −0.639197 0.171272i −0.0753572 0.997157i $$-0.524010\pi$$
−0.563840 + 0.825884i $$0.690676\pi$$
$$68$$ 3.92820 2.26795i 0.476365 0.275029i
$$69$$ 0 0
$$70$$ −2.00000 + 3.46410i −0.239046 + 0.414039i
$$71$$ 10.9282i 1.29694i −0.761241 0.648470i $$-0.775409\pi$$
0.761241 0.648470i $$-0.224591\pi$$
$$72$$ 0 0
$$73$$ 9.73205i 1.13905i 0.821974 + 0.569525i $$0.192873\pi$$
−0.821974 + 0.569525i $$0.807127\pi$$
$$74$$ 2.19615 + 1.26795i 0.255298 + 0.147396i
$$75$$ 0 0
$$76$$ −0.464102 + 1.73205i −0.0532361 + 0.198680i
$$77$$ −2.09808 0.562178i −0.239098 0.0640661i
$$78$$ 0 0
$$79$$ −6.00000 + 10.3923i −0.675053 + 1.16923i 0.301401 + 0.953498i $$0.402546\pi$$
−0.976453 + 0.215728i $$0.930788\pi$$
$$80$$ 10.9282 + 10.9282i 1.22181 + 1.22181i
$$81$$ 0 0
$$82$$ −3.00000 + 3.00000i −0.331295 + 0.331295i
$$83$$ −0.366025 1.36603i −0.0401765 0.149941i 0.942924 0.333009i $$-0.108064\pi$$
−0.983100 + 0.183068i $$0.941397\pi$$
$$84$$ 0 0
$$85$$ −2.26795 + 8.46410i −0.245994 + 0.918061i
$$86$$ −1.56218 + 0.901924i −0.168454 + 0.0972569i
$$87$$ 0 0
$$88$$ −4.19615 + 7.26795i −0.447311 + 0.774766i
$$89$$ 2.00000i 0.212000i −0.994366 0.106000i $$-0.966196\pi$$
0.994366 0.106000i $$-0.0338043\pi$$
$$90$$ 0 0
$$91$$ 3.26795 + 3.26795i 0.342574 + 0.342574i
$$92$$ −1.26795 + 2.19615i −0.132193 + 0.228965i
$$93$$ 0 0
$$94$$ 3.53590 13.1962i 0.364700 1.36108i
$$95$$ −1.73205 3.00000i −0.177705 0.307794i
$$96$$ 0 0
$$97$$ −4.13397 + 7.16025i −0.419742 + 0.727014i −0.995913 0.0903150i $$-0.971213\pi$$
0.576172 + 0.817329i $$0.304546\pi$$
$$98$$ −6.46410 6.46410i −0.652973 0.652973i
$$99$$ 0 0
$$100$$ −19.8564 −1.98564
$$101$$ −7.46410 + 2.00000i −0.742706 + 0.199007i −0.610280 0.792186i $$-0.708943\pi$$
−0.132426 + 0.991193i $$0.542277\pi$$
$$102$$ 0 0
$$103$$ 7.90192 4.56218i 0.778600 0.449525i −0.0573341 0.998355i $$-0.518260\pi$$
0.835934 + 0.548830i $$0.184927\pi$$
$$104$$ 15.4641 8.92820i 1.51638 0.875482i
$$105$$ 0 0
$$106$$ 0.928203 + 0.535898i 0.0901551 + 0.0520511i
$$107$$ 13.4904 + 13.4904i 1.30416 + 1.30416i 0.925558 + 0.378607i $$0.123597\pi$$
0.378607 + 0.925558i $$0.376403\pi$$
$$108$$ 0 0
$$109$$ 7.26795 7.26795i 0.696143 0.696143i −0.267433 0.963576i $$-0.586175\pi$$
0.963576 + 0.267433i $$0.0861754\pi$$
$$110$$ −4.19615 15.6603i −0.400087 1.49315i
$$111$$ 0 0
$$112$$ 2.53590 1.46410i 0.239620 0.138345i
$$113$$ −6.92820 12.0000i −0.651751 1.12887i −0.982698 0.185216i $$-0.940702\pi$$
0.330947 0.943649i $$-0.392632\pi$$
$$114$$ 0 0
$$115$$ −1.26795 4.73205i −0.118237 0.441266i
$$116$$ −3.46410 3.46410i −0.321634 0.321634i
$$117$$ 0 0
$$118$$ 7.26795i 0.669069i
$$119$$ 1.43782 + 0.830127i 0.131805 + 0.0760976i
$$120$$ 0 0
$$121$$ −1.90192 + 1.09808i −0.172902 + 0.0998251i
$$122$$ 2.19615 + 3.80385i 0.198830 + 0.344384i
$$123$$ 0 0
$$124$$ −12.9282 7.46410i −1.16099 0.670296i
$$125$$ 13.4641 13.4641i 1.20427 1.20427i
$$126$$ 0 0
$$127$$ −6.19615 −0.549820 −0.274910 0.961470i $$-0.588648\pi$$
−0.274910 + 0.961470i $$0.588648\pi$$
$$128$$ −2.92820 10.9282i −0.258819 0.965926i
$$129$$ 0 0
$$130$$ −8.92820 + 33.3205i −0.783055 + 2.92240i
$$131$$ 3.09808 + 0.830127i 0.270680 + 0.0725285i 0.391606 0.920133i $$-0.371920\pi$$
−0.120926 + 0.992662i $$0.538586\pi$$
$$132$$ 0 0
$$133$$ −0.633975 + 0.169873i −0.0549726 + 0.0147299i
$$134$$ −7.66025 −0.661745
$$135$$ 0 0
$$136$$ 4.53590 4.53590i 0.388950 0.388950i
$$137$$ 14.2583 + 8.23205i 1.21817 + 0.703312i 0.964527 0.263986i $$-0.0850372\pi$$
0.253645 + 0.967297i $$0.418371\pi$$
$$138$$ 0 0
$$139$$ 2.42820 9.06218i 0.205958 0.768644i −0.783198 0.621772i $$-0.786413\pi$$
0.989156 0.146872i $$-0.0469204\pi$$
$$140$$ −1.46410 + 5.46410i −0.123739 + 0.461801i
$$141$$ 0 0
$$142$$ −4.00000 14.9282i −0.335673 1.25275i
$$143$$ −18.7321 −1.56645
$$144$$ 0 0
$$145$$ 9.46410 0.785951
$$146$$ 3.56218 + 13.2942i 0.294808 + 1.10024i
$$147$$ 0 0
$$148$$ 3.46410 + 0.928203i 0.284747 + 0.0762978i
$$149$$ 0.830127 3.09808i 0.0680067 0.253804i −0.923550 0.383478i $$-0.874726\pi$$
0.991557 + 0.129674i $$0.0413929\pi$$
$$150$$ 0 0
$$151$$ 2.36603 + 1.36603i 0.192544 + 0.111166i 0.593173 0.805075i $$-0.297875\pi$$
−0.400629 + 0.916240i $$0.631208\pi$$
$$152$$ 2.53590i 0.205689i
$$153$$ 0 0
$$154$$ −3.07180 −0.247532
$$155$$ 27.8564 7.46410i 2.23748 0.599531i
$$156$$ 0 0
$$157$$ 4.73205 + 1.26795i 0.377659 + 0.101193i 0.442655 0.896692i $$-0.354037\pi$$
−0.0649959 + 0.997886i $$0.520703\pi$$
$$158$$ −4.39230 + 16.3923i −0.349433 + 1.30410i
$$159$$ 0 0
$$160$$ 18.9282 + 10.9282i 1.49641 + 0.863950i
$$161$$ −0.928203 −0.0731527
$$162$$ 0 0
$$163$$ −7.00000 + 7.00000i −0.548282 + 0.548282i −0.925944 0.377661i $$-0.876728\pi$$
0.377661 + 0.925944i $$0.376728\pi$$
$$164$$ −3.00000 + 5.19615i −0.234261 + 0.405751i
$$165$$ 0 0
$$166$$ −1.00000 1.73205i −0.0776151 0.134433i
$$167$$ 0.464102 0.267949i 0.0359133 0.0207345i −0.481936 0.876206i $$-0.660066\pi$$
0.517849 + 0.855472i $$0.326733\pi$$
$$168$$ 0 0
$$169$$ 23.2583 + 13.4282i 1.78910 + 1.03294i
$$170$$ 12.3923i 0.950446i
$$171$$ 0 0
$$172$$ −1.80385 + 1.80385i −0.137542 + 0.137542i
$$173$$ −3.36603 12.5622i −0.255914 0.955085i −0.967580 0.252566i $$-0.918725\pi$$
0.711665 0.702519i $$-0.247941\pi$$
$$174$$ 0 0
$$175$$ −3.63397 6.29423i −0.274703 0.475799i
$$176$$ −3.07180 + 11.4641i −0.231545 + 0.864139i
$$177$$ 0 0
$$178$$ −0.732051 2.73205i −0.0548695 0.204776i
$$179$$ −11.9282 + 11.9282i −0.891556 + 0.891556i −0.994670 0.103114i $$-0.967119\pi$$
0.103114 + 0.994670i $$0.467119\pi$$
$$180$$ 0 0
$$181$$ 13.3923 + 13.3923i 0.995442 + 0.995442i 0.999990 0.00454748i $$-0.00144751\pi$$
−0.00454748 + 0.999990i $$0.501448\pi$$
$$182$$ 5.66025 + 3.26795i 0.419566 + 0.242237i
$$183$$ 0 0
$$184$$ −0.928203 + 3.46410i −0.0684280 + 0.255377i
$$185$$ −6.00000 + 3.46410i −0.441129 + 0.254686i
$$186$$ 0 0
$$187$$ −6.50000 + 1.74167i −0.475327 + 0.127364i
$$188$$ 19.3205i 1.40909i
$$189$$ 0 0
$$190$$ −3.46410 3.46410i −0.251312 0.251312i
$$191$$ −7.02628 + 12.1699i −0.508404 + 0.880581i 0.491549 + 0.870850i $$0.336431\pi$$
−0.999953 + 0.00973114i $$0.996902\pi$$
$$192$$ 0 0
$$193$$ −9.13397 15.8205i −0.657478 1.13879i −0.981266 0.192656i $$-0.938290\pi$$
0.323789 0.946129i $$-0.395043\pi$$
$$194$$ −3.02628 + 11.2942i −0.217274 + 0.810878i
$$195$$ 0 0
$$196$$ −11.1962 6.46410i −0.799725 0.461722i
$$197$$ 3.66025 + 3.66025i 0.260782 + 0.260782i 0.825372 0.564590i $$-0.190966\pi$$
−0.564590 + 0.825372i $$0.690966\pi$$
$$198$$ 0 0
$$199$$ 0.875644i 0.0620728i −0.999518 0.0310364i $$-0.990119\pi$$
0.999518 0.0310364i $$-0.00988078\pi$$
$$200$$ −27.1244 + 7.26795i −1.91798 + 0.513922i
$$201$$ 0 0
$$202$$ −9.46410 + 5.46410i −0.665892 + 0.384453i
$$203$$ 0.464102 1.73205i 0.0325735 0.121566i
$$204$$ 0 0
$$205$$ −3.00000 11.1962i −0.209529 0.781973i
$$206$$ 9.12436 9.12436i 0.635724 0.635724i
$$207$$ 0 0
$$208$$ 17.8564 17.8564i 1.23812 1.23812i
$$209$$ 1.33013 2.30385i 0.0920068 0.159360i
$$210$$ 0 0
$$211$$ 4.09808 + 1.09808i 0.282123 + 0.0755947i 0.397106 0.917773i $$-0.370015\pi$$
−0.114983 + 0.993367i $$0.536681\pi$$
$$212$$ 1.46410 + 0.392305i 0.100555 + 0.0269436i
$$213$$ 0 0
$$214$$ 23.3660 + 13.4904i 1.59727 + 0.922183i
$$215$$ 4.92820i 0.336101i
$$216$$ 0 0
$$217$$ 5.46410i 0.370927i
$$218$$ 7.26795 12.5885i 0.492248 0.852598i
$$219$$ 0 0
$$220$$ −11.4641 19.8564i −0.772910 1.33872i
$$221$$ 13.8301 + 3.70577i 0.930315 + 0.249277i
$$222$$ 0 0
$$223$$ 11.0263 19.0981i 0.738374 1.27890i −0.214853 0.976646i $$-0.568927\pi$$
0.953227 0.302255i $$-0.0977395\pi$$
$$224$$ 2.92820 2.92820i 0.195649 0.195649i
$$225$$ 0 0
$$226$$ −13.8564 13.8564i −0.921714 0.921714i
$$227$$ −3.86603 14.4282i −0.256597 0.957633i −0.967195 0.254035i $$-0.918242\pi$$
0.710598 0.703598i $$-0.248425\pi$$
$$228$$ 0 0
$$229$$ −1.83013 + 6.83013i −0.120938 + 0.451347i −0.999662 0.0259823i $$-0.991729\pi$$
0.878724 + 0.477330i $$0.158395\pi$$
$$230$$ −3.46410 6.00000i −0.228416 0.395628i
$$231$$ 0 0
$$232$$ −6.00000 3.46410i −0.393919 0.227429i
$$233$$ 7.19615i 0.471436i 0.971822 + 0.235718i $$0.0757441\pi$$
−0.971822 + 0.235718i $$0.924256\pi$$
$$234$$ 0 0
$$235$$ 26.3923 + 26.3923i 1.72164 + 1.72164i
$$236$$ −2.66025 9.92820i −0.173168 0.646271i
$$237$$ 0 0
$$238$$ 2.26795 + 0.607695i 0.147009 + 0.0393910i
$$239$$ 13.0981 + 22.6865i 0.847244 + 1.46747i 0.883658 + 0.468133i $$0.155073\pi$$
−0.0364139 + 0.999337i $$0.511593\pi$$
$$240$$ 0 0
$$241$$ −6.40192 + 11.0885i −0.412384 + 0.714270i −0.995150 0.0983699i $$-0.968637\pi$$
0.582766 + 0.812640i $$0.301971\pi$$
$$242$$ −2.19615 + 2.19615i −0.141174 + 0.141174i
$$243$$ 0 0
$$244$$ 4.39230 + 4.39230i 0.281189 + 0.281189i
$$245$$ 24.1244 6.46410i 1.54125 0.412976i
$$246$$ 0 0
$$247$$ −4.90192 + 2.83013i −0.311902 + 0.180077i
$$248$$ −20.3923 5.46410i −1.29491 0.346971i
$$249$$ 0 0
$$250$$ 13.4641 23.3205i 0.851545 1.47492i
$$251$$ −2.83013 2.83013i −0.178636 0.178636i 0.612125 0.790761i $$-0.290315\pi$$
−0.790761 + 0.612125i $$0.790315\pi$$
$$252$$ 0 0
$$253$$ 2.66025 2.66025i 0.167249 0.167249i
$$254$$ −8.46410 + 2.26795i −0.531085 + 0.142304i
$$255$$ 0 0
$$256$$ −8.00000 13.8564i −0.500000 0.866025i
$$257$$ 4.42820 + 7.66987i 0.276224 + 0.478434i 0.970443 0.241330i $$-0.0775836\pi$$
−0.694219 + 0.719763i $$0.744250\pi$$
$$258$$ 0 0
$$259$$ 0.339746 + 1.26795i 0.0211108 + 0.0787865i
$$260$$ 48.7846i 3.02549i
$$261$$ 0 0
$$262$$ 4.53590 0.280229
$$263$$ −23.4904 13.5622i −1.44848 0.836280i −0.450088 0.892984i $$-0.648607\pi$$
−0.998391 + 0.0567045i $$0.981941\pi$$
$$264$$ 0 0
$$265$$ −2.53590 + 1.46410i −0.155779 + 0.0899390i
$$266$$ −0.803848 + 0.464102i −0.0492871 + 0.0284559i
$$267$$ 0 0
$$268$$ −10.4641 + 2.80385i −0.639197 + 0.171272i
$$269$$ −4.73205 + 4.73205i −0.288518 + 0.288518i −0.836494 0.547976i $$-0.815399\pi$$
0.547976 + 0.836494i $$0.315399\pi$$
$$270$$ 0 0
$$271$$ 20.3923 1.23874 0.619372 0.785098i $$-0.287387\pi$$
0.619372 + 0.785098i $$0.287387\pi$$
$$272$$ 4.53590 7.85641i 0.275029 0.476365i
$$273$$ 0 0
$$274$$ 22.4904 + 6.02628i 1.35869 + 0.364061i
$$275$$ 28.4545 + 7.62436i 1.71587 + 0.459766i
$$276$$ 0 0
$$277$$ 15.7583 4.22243i 0.946826 0.253701i 0.247811 0.968808i $$-0.420289\pi$$
0.699015 + 0.715107i $$0.253622\pi$$
$$278$$ 13.2679i 0.795759i
$$279$$ 0 0
$$280$$ 8.00000i 0.478091i
$$281$$ −8.66025 5.00000i −0.516627 0.298275i 0.218926 0.975741i $$-0.429745\pi$$
−0.735554 + 0.677466i $$0.763078\pi$$
$$282$$ 0 0
$$283$$ −7.43782 + 27.7583i −0.442133 + 1.65006i 0.281265 + 0.959630i $$0.409246\pi$$
−0.723398 + 0.690431i $$0.757421\pi$$
$$284$$ −10.9282 18.9282i −0.648470 1.12318i
$$285$$ 0 0
$$286$$ −25.5885 + 6.85641i −1.51308 + 0.405428i
$$287$$ −2.19615 −0.129635
$$288$$ 0 0
$$289$$ −11.8564 −0.697436
$$290$$ 12.9282 3.46410i 0.759170 0.203419i
$$291$$ 0 0
$$292$$ 9.73205 + 16.8564i 0.569525 + 0.986447i
$$293$$ 3.63397 13.5622i 0.212299 0.792311i −0.774801 0.632205i $$-0.782150\pi$$
0.987100 0.160106i $$-0.0511834\pi$$
$$294$$ 0 0
$$295$$ 17.1962 + 9.92820i 1.00120 + 0.578042i
$$296$$ 5.07180 0.294792
$$297$$ 0 0
$$298$$ 4.53590i 0.262758i
$$299$$ −7.73205 + 2.07180i −0.447156 + 0.119815i
$$300$$ 0 0
$$301$$ −0.901924 0.241670i −0.0519860 0.0139296i
$$302$$ 3.73205 + 1.00000i 0.214755 + 0.0575435i
$$303$$ 0 0
$$304$$ 0.928203 + 3.46410i 0.0532361 + 0.198680i
$$305$$ −12.0000 −0.687118
$$306$$ 0 0
$$307$$ −16.0263 + 16.0263i −0.914668 + 0.914668i −0.996635 0.0819670i $$-0.973880\pi$$
0.0819670 + 0.996635i $$0.473880\pi$$
$$308$$ −4.19615 + 1.12436i −0.239098 + 0.0640661i
$$309$$ 0 0
$$310$$ 35.3205 20.3923i 2.00607 1.15821i
$$311$$ 13.9019 8.02628i 0.788306 0.455129i −0.0510600 0.998696i $$-0.516260\pi$$
0.839366 + 0.543567i $$0.182927\pi$$
$$312$$ 0 0
$$313$$ −24.6506 14.2321i −1.39334 0.804443i −0.399653 0.916666i $$-0.630869\pi$$
−0.993683 + 0.112223i $$0.964203\pi$$
$$314$$ 6.92820 0.390981
$$315$$ 0 0
$$316$$ 24.0000i 1.35011i
$$317$$ 8.43782 + 31.4904i 0.473915 + 1.76868i 0.625492 + 0.780231i $$0.284898\pi$$
−0.151577 + 0.988445i $$0.548435\pi$$
$$318$$ 0 0
$$319$$ 3.63397 + 6.29423i 0.203464 + 0.352409i
$$320$$ 29.8564 + 8.00000i 1.66902 + 0.447214i
$$321$$ 0 0
$$322$$ −1.26795 + 0.339746i −0.0706600 + 0.0189333i
$$323$$ −1.43782 + 1.43782i −0.0800026 + 0.0800026i
$$324$$ 0 0
$$325$$ −44.3205 44.3205i −2.45846 2.45846i
$$326$$ −7.00000 + 12.1244i −0.387694 + 0.671506i
$$327$$ 0 0
$$328$$ −2.19615 + 8.19615i −0.121262 + 0.452557i
$$329$$ 6.12436 3.53590i 0.337647 0.194940i
$$330$$ 0 0
$$331$$ −19.0263 + 5.09808i −1.04578 + 0.280216i −0.740506 0.672049i $$-0.765414\pi$$
−0.305273 + 0.952265i $$0.598748\pi$$
$$332$$ −2.00000 2.00000i −0.109764 0.109764i
$$333$$ 0 0
$$334$$ 0.535898 0.535898i 0.0293231 0.0293231i
$$335$$ 10.4641 18.1244i 0.571715 0.990239i
$$336$$ 0 0
$$337$$ −11.8923 20.5981i −0.647815 1.12205i −0.983644 0.180126i $$-0.942350\pi$$
0.335829 0.941923i $$-0.390984\pi$$
$$338$$ 36.6865 + 9.83013i 1.99548 + 0.534688i
$$339$$ 0 0
$$340$$ 4.53590 + 16.9282i 0.245994 + 0.918061i
$$341$$ 15.6603 + 15.6603i 0.848050 + 0.848050i
$$342$$ 0 0
$$343$$ 9.85641i 0.532196i
$$344$$ −1.80385 + 3.12436i −0.0972569 + 0.168454i
$$345$$ 0 0
$$346$$ −9.19615 15.9282i −0.494388 0.856306i
$$347$$ −6.62436 + 24.7224i −0.355614 + 1.32717i 0.524096 + 0.851659i $$0.324403\pi$$
−0.879710 + 0.475510i $$0.842263\pi$$
$$348$$ 0 0
$$349$$ 2.07180 + 7.73205i 0.110901 + 0.413887i 0.998948 0.0458657i $$-0.0146046\pi$$
−0.888047 + 0.459753i $$0.847938\pi$$
$$350$$ −7.26795 7.26795i −0.388488 0.388488i
$$351$$ 0 0
$$352$$ 16.7846i 0.894623i
$$353$$ 10.1603 17.5981i 0.540776 0.936651i −0.458084 0.888909i $$-0.651464\pi$$
0.998860 0.0477421i $$-0.0152026\pi$$
$$354$$ 0 0
$$355$$ 40.7846 + 10.9282i 2.16462 + 0.580009i
$$356$$ −2.00000 3.46410i −0.106000 0.183597i
$$357$$ 0 0
$$358$$ −11.9282 + 20.6603i −0.630425 + 1.09193i
$$359$$ 14.7321i 0.777528i 0.921337 + 0.388764i $$0.127098\pi$$
−0.921337 + 0.388764i $$0.872902\pi$$
$$360$$ 0 0
$$361$$ 18.1962i 0.957692i
$$362$$ 23.1962 + 13.3923i 1.21916 + 0.703884i
$$363$$ 0 0
$$364$$ 8.92820 + 2.39230i 0.467965 + 0.125391i
$$365$$ −36.3205 9.73205i −1.90110 0.509399i
$$366$$ 0 0
$$367$$ −10.1244 + 17.5359i −0.528487 + 0.915366i 0.470961 + 0.882154i $$0.343907\pi$$
−0.999448 + 0.0332125i $$0.989426\pi$$
$$368$$ 5.07180i 0.264386i
$$369$$ 0 0
$$370$$ −6.92820 + 6.92820i −0.360180 + 0.360180i
$$371$$ 0.143594 + 0.535898i 0.00745501 + 0.0278225i
$$372$$ 0 0
$$373$$ 1.50962 5.63397i 0.0781651 0.291716i −0.915767 0.401709i $$-0.868416\pi$$
0.993932 + 0.109993i $$0.0350829\pi$$
$$374$$ −8.24167 + 4.75833i −0.426167 + 0.246047i
$$375$$ 0 0
$$376$$ −7.07180 26.3923i −0.364700 1.36108i
$$377$$ 15.4641i 0.796442i
$$378$$ 0 0
$$379$$ −18.7583 18.7583i −0.963551 0.963551i 0.0358080 0.999359i $$-0.488600\pi$$
−0.999359 + 0.0358080i $$0.988600\pi$$
$$380$$ −6.00000 3.46410i −0.307794 0.177705i
$$381$$ 0 0
$$382$$ −5.14359 + 19.1962i −0.263169 + 0.982161i
$$383$$ 3.26795 + 5.66025i 0.166984 + 0.289225i 0.937358 0.348367i $$-0.113264\pi$$
−0.770374 + 0.637593i $$0.779930\pi$$
$$384$$ 0 0
$$385$$ 4.19615 7.26795i 0.213856 0.370409i
$$386$$ −18.2679 18.2679i −0.929814 0.929814i
$$387$$ 0 0
$$388$$ 16.5359i 0.839483i
$$389$$ −10.2942 + 2.75833i −0.521938 + 0.139853i −0.510163 0.860078i $$-0.670415\pi$$
−0.0117752 + 0.999931i $$0.503748\pi$$
$$390$$ 0 0
$$391$$ −2.49038 + 1.43782i −0.125944 + 0.0727138i
$$392$$ −17.6603 4.73205i −0.891978 0.239005i
$$393$$ 0 0
$$394$$ 6.33975 + 3.66025i 0.319392 + 0.184401i
$$395$$ −32.7846 32.7846i −1.64957 1.64957i
$$396$$ 0 0
$$397$$ −12.7321 + 12.7321i −0.639003 + 0.639003i −0.950310 0.311306i $$-0.899233\pi$$
0.311306 + 0.950310i $$0.399233\pi$$
$$398$$ −0.320508 1.19615i −0.0160656 0.0599577i
$$399$$ 0 0
$$400$$ −34.3923 + 19.8564i −1.71962 + 0.992820i
$$401$$ −13.7942 23.8923i −0.688851 1.19312i −0.972210 0.234111i $$-0.924782\pi$$
0.283359 0.959014i $$-0.408551\pi$$
$$402$$ 0 0
$$403$$ −12.1962 45.5167i −0.607534 2.26735i
$$404$$ −10.9282 + 10.9282i −0.543698 + 0.543698i
$$405$$ 0 0
$$406$$ 2.53590i 0.125855i
$$407$$ −4.60770 2.66025i −0.228395 0.131864i
$$408$$ 0 0
$$409$$ 26.1340 15.0885i 1.29224 0.746076i 0.313191 0.949690i $$-0.398602\pi$$
0.979051 + 0.203614i $$0.0652688\pi$$
$$410$$ −8.19615 14.1962i −0.404779 0.701098i
$$411$$ 0 0
$$412$$ 9.12436 15.8038i 0.449525 0.778600i
$$413$$ 2.66025 2.66025i 0.130903 0.130903i
$$414$$ 0 0
$$415$$ 5.46410 0.268222
$$416$$ 17.8564 30.9282i 0.875482 1.51638i
$$417$$ 0 0
$$418$$ 0.973721 3.63397i 0.0476262 0.177744i
$$419$$ −31.2224 8.36603i −1.52532 0.408707i −0.603828 0.797115i $$-0.706359\pi$$
−0.921488 + 0.388408i $$0.873025\pi$$
$$420$$ 0 0
$$421$$ −2.19615 + 0.588457i −0.107034 + 0.0286797i −0.311938 0.950102i $$-0.600978\pi$$
0.204905 + 0.978782i $$0.434312\pi$$
$$422$$ 6.00000 0.292075
$$423$$ 0 0
$$424$$ 2.14359 0.104102
$$425$$ −19.5000 11.2583i −0.945889 0.546109i
$$426$$ 0 0
$$427$$ −0.588457 + 2.19615i −0.0284774 + 0.106279i
$$428$$ 36.8564 + 9.87564i 1.78152 + 0.477357i
$$429$$ 0 0
$$430$$ −1.80385 6.73205i −0.0869893 0.324648i
$$431$$ 5.80385 0.279562 0.139781 0.990182i $$-0.455360\pi$$
0.139781 + 0.990182i $$0.455360\pi$$
$$432$$ 0 0
$$433$$ −2.26795 −0.108991 −0.0544953 0.998514i $$-0.517355\pi$$
−0.0544953 + 0.998514i $$0.517355\pi$$
$$434$$ −2.00000 7.46410i −0.0960031 0.358288i
$$435$$ 0 0
$$436$$ 5.32051 19.8564i 0.254806 0.950949i
$$437$$ 0.294229 1.09808i 0.0140749 0.0525281i
$$438$$ 0 0
$$439$$ 4.85641 + 2.80385i 0.231784 + 0.133820i 0.611395 0.791326i $$-0.290609\pi$$
−0.379611 + 0.925146i $$0.623942\pi$$
$$440$$ −22.9282 22.9282i −1.09306 1.09306i
$$441$$ 0 0
$$442$$ 20.2487 0.963133
$$443$$ −19.6244 + 5.25833i −0.932381 + 0.249831i −0.692870 0.721063i $$-0.743654\pi$$
−0.239511 + 0.970894i $$0.576987\pi$$
$$444$$ 0 0
$$445$$ 7.46410 + 2.00000i 0.353832 + 0.0948091i
$$446$$ 8.07180 30.1244i 0.382211 1.42643i
$$447$$ 0 0
$$448$$ 2.92820 5.07180i 0.138345 0.239620i
$$449$$ 20.6603 0.975018 0.487509 0.873118i $$-0.337906\pi$$
0.487509 + 0.873118i $$0.337906\pi$$
$$450$$ 0 0
$$451$$ 6.29423 6.29423i 0.296384 0.296384i
$$452$$ −24.0000 13.8564i −1.12887 0.651751i
$$453$$ 0 0
$$454$$ −10.5622 18.2942i −0.495708 0.858591i
$$455$$ −15.4641 + 8.92820i −0.724968 + 0.418561i
$$456$$ 0 0
$$457$$ −20.2583 11.6962i −0.947645 0.547123i −0.0552962 0.998470i $$-0.517610\pi$$
−0.892348 + 0.451347i $$0.850944\pi$$
$$458$$ 10.0000i 0.467269i
$$459$$ 0 0
$$460$$ −6.92820 6.92820i −0.323029 0.323029i
$$461$$ 0.686533 + 2.56218i 0.0319751 + 0.119333i 0.980069 0.198659i $$-0.0636585\pi$$
−0.948094 + 0.317991i $$0.896992\pi$$
$$462$$ 0 0
$$463$$ −9.19615 15.9282i −0.427381 0.740246i 0.569258 0.822159i $$-0.307231\pi$$
−0.996640 + 0.0819125i $$0.973897\pi$$
$$464$$ −9.46410 2.53590i −0.439360 0.117726i
$$465$$ 0 0
$$466$$ 2.63397 + 9.83013i 0.122017 + 0.455372i
$$467$$ −4.36603 + 4.36603i −0.202036 + 0.202036i −0.800872 0.598836i $$-0.795630\pi$$
0.598836 + 0.800872i $$0.295630\pi$$
$$468$$ 0 0
$$469$$ −2.80385 2.80385i −0.129470 0.129470i
$$470$$ 45.7128 + 26.3923i 2.10857 + 1.21739i
$$471$$ 0 0
$$472$$ −7.26795 12.5885i −0.334534 0.579431i
$$473$$ 3.27757 1.89230i 0.150703 0.0870083i
$$474$$ 0 0
$$475$$ 8.59808 2.30385i 0.394507 0.105708i
$$476$$ 3.32051 0.152195
$$477$$ 0 0
$$478$$ 26.1962 + 26.1962i 1.19818 + 1.19818i
$$479$$ −12.8301 + 22.2224i −0.586223 + 1.01537i 0.408498 + 0.912759i $$0.366053\pi$$
−0.994722 + 0.102610i $$0.967281\pi$$
$$480$$ 0 0
$$481$$ 5.66025 + 9.80385i 0.258085 + 0.447017i
$$482$$ −4.68653 + 17.4904i −0.213466 + 0.796665i
$$483$$ 0 0
$$484$$ −2.19615 + 3.80385i −0.0998251 + 0.172902i
$$485$$ −22.5885 22.5885i −1.02569 1.02569i
$$486$$ 0 0
$$487$$ 16.1962i 0.733918i −0.930237 0.366959i $$-0.880399\pi$$
0.930237 0.366959i $$-0.119601\pi$$
$$488$$ 7.60770 + 4.39230i 0.344384 + 0.198830i
$$489$$ 0 0
$$490$$ 30.5885 17.6603i 1.38185 0.797809i
$$491$$ −6.89230 + 25.7224i −0.311045 + 1.16084i 0.616570 + 0.787300i $$0.288522\pi$$
−0.927615 + 0.373537i $$0.878145\pi$$
$$492$$ 0 0
$$493$$ −1.43782 5.36603i −0.0647563 0.241674i
$$494$$ −5.66025 + 5.66025i −0.254667 + 0.254667i
$$495$$ 0 0
$$496$$ −29.8564 −1.34059
$$497$$ 4.00000 6.92820i 0.179425 0.310772i
$$498$$ 0 0
$$499$$ 6.33013 + 1.69615i 0.283375 + 0.0759302i 0.397707 0.917512i $$-0.369806\pi$$
−0.114332 + 0.993443i $$0.536473\pi$$
$$500$$ 9.85641 36.7846i 0.440792 1.64506i
$$501$$ 0 0
$$502$$ −4.90192 2.83013i −0.218784 0.126315i
$$503$$ 27.7128i 1.23565i 0.786314 + 0.617827i $$0.211987\pi$$
−0.786314 + 0.617827i $$0.788013\pi$$
$$504$$ 0 0
$$505$$ 29.8564i 1.32859i
$$506$$ 2.66025 4.60770i 0.118263 0.204837i
$$507$$ 0 0
$$508$$ −10.7321 + 6.19615i −0.476158 + 0.274910i
$$509$$ −16.9282 4.53590i −0.750329 0.201050i −0.136665 0.990617i $$-0.543638\pi$$
−0.613664 + 0.789567i $$0.710305\pi$$
$$510$$ 0 0
$$511$$ −3.56218 + 6.16987i −0.157581 + 0.272939i
$$512$$ −16.0000 16.0000i −0.707107 0.707107i
$$513$$ 0 0
$$514$$ 8.85641 + 8.85641i 0.390639 + 0.390639i
$$515$$ 9.12436 + 34.0526i 0.402067 + 1.50054i
$$516$$ 0 0
$$517$$ −7.41858 + 27.6865i −0.326269 + 1.21765i
$$518$$ 0.928203 + 1.60770i 0.0407829 + 0.0706381i
$$519$$ 0 0
$$520$$ 17.8564 + 66.6410i 0.783055 + 2.92240i
$$521$$ 13.0000i 0.569540i 0.958596 + 0.284770i $$0.0919173\pi$$
−0.958596 + 0.284770i $$0.908083\pi$$
$$522$$ 0 0
$$523$$ −14.4641 14.4641i −0.632471 0.632471i 0.316216 0.948687i $$-0.397588\pi$$
−0.948687 + 0.316216i $$0.897588\pi$$
$$524$$ 6.19615 1.66025i 0.270680 0.0725285i
$$525$$ 0 0
$$526$$ −37.0526 9.92820i −1.61557 0.432890i
$$527$$ −8.46410 14.6603i −0.368702 0.638611i
$$528$$ 0 0
$$529$$ −10.6962 + 18.5263i −0.465050 + 0.805490i
$$530$$ −2.92820 + 2.92820i −0.127193 + 0.127193i
$$531$$ 0 0
$$532$$ −0.928203 + 0.928203i −0.0402427 + 0.0402427i
$$533$$ −18.2942 + 4.90192i −0.792411 + 0.212326i
$$534$$ 0 0
$$535$$ −63.8372 + 36.8564i −2.75992 + 1.59344i
$$536$$ −13.2679 + 7.66025i −0.573088 + 0.330873i
$$537$$ 0 0
$$538$$ −4.73205 + 8.19615i −0.204013 + 0.353361i
$$539$$ 13.5622 + 13.5622i 0.584164 + 0.584164i
$$540$$ 0 0
$$541$$ −8.19615 + 8.19615i −0.352380 + 0.352380i −0.860994 0.508614i $$-0.830158\pi$$
0.508614 + 0.860994i $$0.330158\pi$$
$$542$$ 27.8564 7.46410i 1.19654 0.320611i
$$543$$ 0 0
$$544$$ 3.32051 12.3923i 0.142366 0.531316i
$$545$$ 19.8564 + 34.3923i 0.850555 + 1.47320i
$$546$$ 0 0
$$547$$ 8.37564 + 31.2583i 0.358117 + 1.33651i 0.876517 + 0.481371i $$0.159861\pi$$
−0.518400 + 0.855138i $$0.673472\pi$$
$$548$$ 32.9282 1.40662
$$549$$ 0 0
$$550$$ 41.6603 1.77640
$$551$$ 1.90192 + 1.09808i 0.0810247 + 0.0467796i
$$552$$ 0 0
$$553$$ −7.60770 + 4.39230i −0.323512 + 0.186780i
$$554$$ 19.9808 11.5359i 0.848901 0.490113i
$$555$$ 0 0
$$556$$ −4.85641 18.1244i −0.205958 0.768644i
$$557$$ 25.1962 25.1962i 1.06760 1.06760i 0.0700519 0.997543i $$-0.477684\pi$$
0.997543 0.0700519i $$-0.0223165\pi$$
$$558$$ 0 0
$$559$$ −8.05256 −0.340587
$$560$$ 2.92820 + 10.9282i 0.123739 + 0.461801i
$$561$$ 0 0
$$562$$ −13.6603 3.66025i −0.576223 0.154398i
$$563$$ 3.76795 + 1.00962i 0.158800 + 0.0425504i 0.337343 0.941382i $$-0.390472\pi$$
−0.178543 + 0.983932i $$0.557138\pi$$
$$564$$ 0 0
$$565$$ 51.7128 13.8564i 2.17557 0.582943i
$$566$$ 40.6410i 1.70827i
$$567$$ 0 0
$$568$$ −21.8564 21.8564i −0.917074 0.917074i
$$569$$ 23.5981 + 13.6244i 0.989283 + 0.571163i 0.905060 0.425284i $$-0.139826\pi$$
0.0842230 + 0.996447i $$0.473159\pi$$
$$570$$ 0 0
$$571$$ 5.33013 19.8923i 0.223059 0.832467i −0.760114 0.649790i $$-0.774857\pi$$
0.983173 0.182677i $$-0.0584764\pi$$
$$572$$ −32.4449 + 18.7321i −1.35659 + 0.783226i
$$573$$ 0 0
$$574$$ −3.00000 + 0.803848i −0.125218 + 0.0335519i
$$575$$ 12.5885 0.524975
$$576$$ 0 0
$$577$$ 35.7846 1.48973 0.744866 0.667214i $$-0.232513\pi$$
0.744866 + 0.667214i $$0.232513\pi$$
$$578$$ −16.1962 + 4.33975i −0.673671 + 0.180510i
$$579$$ 0 0
$$580$$ 16.3923 9.46410i 0.680653 0.392975i
$$581$$ 0.267949 1.00000i 0.0111164 0.0414870i
$$582$$ 0 0
$$583$$ −1.94744 1.12436i −0.0806548 0.0465661i
$$584$$ 19.4641 + 19.4641i 0.805430 + 0.805430i
$$585$$ 0 0
$$586$$ 19.8564i 0.820261i
$$587$$ −3.76795 + 1.00962i −0.155520 + 0.0416714i −0.335739 0.941955i $$-0.608986\pi$$
0.180219 + 0.983626i $$0.442319\pi$$
$$588$$ 0 0
$$589$$ 6.46410 + 1.73205i 0.266349 + 0.0713679i
$$590$$ 27.1244 + 7.26795i 1.11669 + 0.299217i
$$591$$ 0 0
$$592$$ 6.92820 1.85641i 0.284747 0.0762978i
$$593$$ −10.5359 −0.432657 −0.216329 0.976321i $$-0.569408\pi$$
−0.216329 + 0.976321i $$0.569408\pi$$
$$594$$ 0 0
$$595$$ −4.53590 + 4.53590i −0.185954 + 0.185954i
$$596$$ −1.66025 6.19615i −0.0680067 0.253804i
$$597$$ 0 0
$$598$$ −9.80385 + 5.66025i −0.400909 + 0.231465i
$$599$$ 23.3205 13.4641i 0.952850 0.550128i 0.0588850 0.998265i $$-0.481245\pi$$
0.893965 + 0.448136i $$0.147912\pi$$
$$600$$ 0 0
$$601$$ 17.5526 + 10.1340i 0.715984 + 0.413373i 0.813273 0.581883i $$-0.197684\pi$$
−0.0972889 + 0.995256i $$0.531017\pi$$
$$602$$ −1.32051 −0.0538199
$$603$$ 0 0
$$604$$ 5.46410 0.222331
$$605$$ −2.19615 8.19615i −0.0892863 0.333221i
$$606$$ 0 0
$$607$$ 22.5885 + 39.1244i 0.916837 + 1.58801i 0.804189 + 0.594374i $$0.202600\pi$$
0.112648 + 0.993635i $$0.464067\pi$$
$$608$$ 2.53590 + 4.39230i 0.102844 + 0.178131i
$$609$$ 0 0
$$610$$ −16.3923 + 4.39230i −0.663705 + 0.177839i
$$611$$ 43.1244 43.1244i 1.74462 1.74462i
$$612$$ 0 0
$$613$$ 1.66025 + 1.66025i 0.0670570 + 0.0670570i 0.739840 0.672783i $$-0.234901\pi$$
−0.672783 + 0.739840i $$0.734901\pi$$
$$614$$ −16.0263 + 27.7583i −0.646768 + 1.12024i
$$615$$ 0 0
$$616$$ −5.32051 + 3.07180i −0.214369 + 0.123766i
$$617$$ 3.91154 2.25833i 0.157473 0.0909170i −0.419193 0.907897i $$-0.637687\pi$$
0.576666 + 0.816980i $$0.304354\pi$$
$$618$$ 0 0
$$619$$ 38.8205 10.4019i 1.56033 0.418089i 0.627561 0.778568i $$-0.284053\pi$$
0.932767 + 0.360479i $$0.117387\pi$$
$$620$$ 40.7846 40.7846i 1.63795 1.63795i
$$621$$ 0 0
$$622$$ 16.0526 16.0526i 0.643649 0.643649i
$$623$$ 0.732051 1.26795i 0.0293290 0.0507993i
$$624$$ 0 0
$$625$$ 11.9641 + 20.7224i 0.478564 + 0.828897i
$$626$$ −38.8827 10.4186i −1.55406 0.416410i
$$627$$ 0 0
$$628$$ 9.46410 2.53590i 0.377659 0.101193i
$$629$$ 2.87564 + 2.87564i 0.114659 + 0.114659i
$$630$$ 0 0
$$631$$ 38.3923i 1.52837i −0.644995 0.764187i $$-0.723141\pi$$
0.644995 0.764187i $$-0.276859\pi$$
$$632$$ 8.78461 + 32.7846i 0.349433 + 1.30410i
$$633$$ 0 0
$$634$$ 23.0526 + 39.9282i 0.915534 + 1.58575i
$$635$$ 6.19615 23.1244i 0.245887 0.917662i
$$636$$ 0 0
$$637$$ −10.5622 39.4186i −0.418489 1.56182i
$$638$$ 7.26795 + 7.26795i 0.287741 + 0.287741i
$$639$$ 0 0
$$640$$ 43.7128 1.72790
$$641$$ 4.20577 7.28461i 0.166118 0.287725i −0.770934 0.636915i $$-0.780210\pi$$
0.937052 + 0.349191i $$0.113543\pi$$
$$642$$ 0 0
$$643$$ −45.6506 12.2321i −1.80029 0.482385i −0.806263 0.591558i $$-0.798513\pi$$
−0.994023 + 0.109173i $$0.965180\pi$$
$$644$$ −1.60770 + 0.928203i −0.0633521 + 0.0365763i
$$645$$ 0 0
$$646$$ −1.43782 + 2.49038i −0.0565704 + 0.0979827i
$$647$$ 13.2679i 0.521617i 0.965391 + 0.260808i $$0.0839891\pi$$
−0.965391 + 0.260808i $$0.916011\pi$$
$$648$$ 0 0
$$649$$ 15.2487i 0.598564i
$$650$$ −76.7654 44.3205i −3.01099 1.73839i
$$651$$ 0 0
$$652$$ −5.12436 + 19.1244i −0.200685 + 0.748968i
$$653$$ −5.63397 1.50962i −0.220474 0.0590760i 0.146891 0.989153i $$-0.453073\pi$$
−0.367365 + 0.930077i $$0.619740\pi$$
$$654$$ 0 0
$$655$$ −6.19615 + 10.7321i −0.242104 + 0.419336i
$$656$$ 12.0000i 0.468521i
$$657$$ 0 0
$$658$$ 7.07180 7.07180i 0.275687 0.275687i
$$659$$ −4.02628 15.0263i −0.156842 0.585341i −0.998941 0.0460178i $$-0.985347\pi$$
0.842099 0.539323i $$-0.181320\pi$$
$$660$$ 0 0
$$661$$ 2.19615 8.19615i 0.0854204 0.318793i −0.909973 0.414667i $$-0.863898\pi$$
0.995393 + 0.0958740i $$0.0305646\pi$$
$$662$$ −24.1244 + 13.9282i −0.937620 + 0.541335i
$$663$$ 0 0
$$664$$ −3.46410 2.00000i −0.134433 0.0776151i
$$665$$ 2.53590i 0.0983379i
$$666$$ 0 0
$$667$$ 2.19615 + 2.19615i 0.0850354 + 0.0850354i
$$668$$ 0.535898 0.928203i 0.0207345 0.0359133i
$$669$$ 0 0
$$670$$ 7.66025 28.5885i 0.295941 1.10447i
$$671$$ −4.60770 7.98076i −0.177878 0.308094i
$$672$$ 0 0
$$673$$ 8.80385 15.2487i 0.339363 0.587795i −0.644950 0.764225i $$-0.723122\pi$$
0.984313 + 0.176430i $$0.0564550\pi$$
$$674$$ −23.7846 23.7846i −0.916149 0.916149i
$$675$$ 0 0
$$676$$ 53.7128 2.06588
$$677$$ −4.73205 + 1.26795i −0.181867 + 0.0487312i −0.348603 0.937270i $$-0.613344\pi$$
0.166736 + 0.986002i $$0.446677\pi$$
$$678$$ 0 0
$$679$$ −5.24167 + 3.02628i −0.201157 + 0.116138i
$$680$$ 12.3923 + 21.4641i 0.475223 + 0.823111i
$$681$$ 0 0
$$682$$ 27.1244 + 15.6603i 1.03865 + 0.599662i
$$683$$ 4.70577 + 4.70577i 0.180061 + 0.180061i 0.791383 0.611321i $$-0.209362\pi$$
−0.611321 + 0.791383i $$0.709362\pi$$
$$684$$ 0 0
$$685$$ −44.9808 + 44.9808i −1.71863 + 1.71863i
$$686$$ −3.60770 13.4641i −0.137742 0.514062i
$$687$$ 0 0
$$688$$ −1.32051 + 4.92820i −0.0503439 + 0.187886i
$$689$$ 2.39230 + 4.14359i 0.0911396 + 0.157858i
$$690$$ 0 0
$$691$$ −6.29423 23.4904i −0.239444 0.893616i −0.976095 0.217344i $$-0.930261\pi$$
0.736651 0.676273i $$-0.236406\pi$$
$$692$$ −18.3923 18.3923i −0.699171 0.699171i
$$693$$ 0 0
$$694$$ 36.1962i 1.37399i
$$695$$ 31.3923 + 18.1244i 1.19078 + 0.687496i
$$696$$ 0 0
$$697$$ −5.89230 + 3.40192i −0.223187 + 0.128857i
$$698$$ 5.66025 + 9.80385i 0.214244 + 0.371081i
$$699$$ 0 0
$$700$$ −12.5885 7.26795i −0.475799 0.274703i
$$701$$ −10.6603 + 10.6603i −0.402632 + 0.402632i −0.879160 0.476527i $$-0.841895\pi$$
0.476527 + 0.879160i $$0.341895\pi$$
$$702$$ 0 0
$$703$$ −1.60770 −0.0606354
$$704$$ 6.14359 + 22.9282i 0.231545 + 0.864139i
$$705$$ 0 0
$$706$$ 7.43782 27.7583i 0.279926 1.04470i
$$707$$ −5.46410 1.46410i −0.205499 0.0550632i
$$708$$ 0 0
$$709$$ −20.1962 + 5.41154i −0.758482 + 0.203235i −0.617277 0.786746i $$-0.711764\pi$$
−0.141205 + 0.989980i $$0.545098\pi$$
$$710$$ 59.7128 2.24098
$$711$$ 0 0
$$712$$ −4.00000 4.00000i −0.149906 0.149906i
$$713$$ 8.19615 + 4.73205i 0.306948 + 0.177217i
$$714$$ 0 0
$$715$$ 18.7321 69.9090i 0.700539 2.61445i
$$716$$ −8.73205 + 32.5885i −0.326332 + 1.21789i
$$717$$ 0 0
$$718$$ 5.39230 + 20.1244i 0.201239 + 0.751034i
$$719$$ 16.3923 0.611330 0.305665 0.952139i $$-0.401121\pi$$
0.305665 + 0.952139i $$0.401121\pi$$
$$720$$ 0 0
$$721$$ 6.67949 0.248757
$$722$$ 6.66025 + 24.8564i 0.247869 + 0.925060i
$$723$$ 0 0
$$724$$ 36.5885 + 9.80385i 1.35980 + 0.364357i
$$725$$ −6.29423 + 23.4904i −0.233762 + 0.872411i
$$726$$ 0 0
$$727$$ 31.8109 + 18.3660i 1.17980 + 0.681158i 0.955968 0.293470i $$-0.0948099\pi$$
0.223832 + 0.974628i $$0.428143\pi$$
$$728$$ 13.0718 0.484473
$$729$$ 0 0
$$730$$ −53.1769 −1.96817
$$731$$ −2.79423 + 0.748711i −0.103348 + 0.0276921i
$$732$$ 0 0
$$733$$ −29.9545 8.02628i −1.10639 0.296457i −0.341028 0.940053i $$-0.610775\pi$$
−0.765366 + 0.643596i $$0.777442\pi$$
$$734$$ −7.41154 + 27.6603i −0.273565 + 1.02096i
$$735$$ 0 0
$$736$$ 1.85641 + 6.92820i 0.0684280 + 0.255377i
$$737$$ 16.0718 0.592012
$$738$$ 0 0
$$739$$ 21.2224 21.2224i 0.780680 0.780680i −0.199266 0.979945i $$-0.563856\pi$$
0.979945 + 0.199266i $$0.0638557\pi$$
$$740$$ −6.92820 + 12.0000i −0.254686 + 0.441129i
$$741$$ 0 0
$$742$$ 0.392305 + 0.679492i 0.0144020 + 0.0249449i
$$743$$ −2.24167 + 1.29423i −0.0822389 + 0.0474806i −0.540556 0.841308i $$-0.681786\pi$$
0.458317 + 0.888789i $$0.348453\pi$$
$$744$$ 0 0
$$745$$ 10.7321 + 6.19615i 0.393192 + 0.227009i
$$746$$ 8.24871i 0.302007i
$$747$$ 0 0
$$748$$ −9.51666 + 9.51666i −0.347964 + 0.347964i
$$749$$ 3.61474 + 13.4904i 0.132080 + 0.492928i
$$750$$ 0 0
$$751$$ 18.8564 + 32.6603i 0.688080 + 1.19179i 0.972458 + 0.233077i $$0.0748796\pi$$
−0.284378 + 0.958712i $$0.591787\pi$$
$$752$$ −19.3205 33.4641i −0.704546 1.22031i
$$753$$ 0 0
$$754$$ −5.66025 21.1244i −0.206134 0.769304i
$$755$$ −7.46410 + 7.46410i −0.271646 + 0.271646i
$$756$$ 0 0
$$757$$ −6.07180 6.07180i −0.220683 0.220683i 0.588103 0.808786i $$-0.299875\pi$$
−0.808786 + 0.588103i $$0.799875\pi$$
$$758$$ −32.4904 18.7583i −1.18010 0.681333i
$$759$$ 0 0
$$760$$ −9.46410 2.53590i −0.343299 0.0919867i
$$761$$ 27.3731 15.8038i 0.992273 0.572889i 0.0863200 0.996267i $$-0.472489\pi$$
0.905953 + 0.423378i $$0.139156\pi$$
$$762$$ 0 0
$$763$$ 7.26795 1.94744i 0.263117 0.0705021i
$$764$$ 28.1051i 1.01681i
$$765$$ 0 0
$$766$$ 6.53590 + 6.53590i 0.236152 + 0.236152i
$$767$$ 16.2224 28.0981i 0.585758 1.01456i
$$768$$ 0 0
$$769$$ 10.1244 + 17.5359i 0.365094 + 0.632361i 0.988791 0.149305i $$-0.0477036\pi$$
−0.623698 + 0.781666i $$0.714370\pi$$
$$770$$ 3.07180 11.4641i 0.110700 0.413138i
$$771$$ 0 0
$$772$$ −31.6410 18.2679i −1.13879 0.657478i
$$773$$ −4.41154 4.41154i −0.158672 0.158672i 0.623306 0.781978i $$-0.285789\pi$$
−0.781978 + 0.623306i $$0.785789\pi$$
$$774$$ 0 0
$$775$$ 74.1051i 2.66193i
$$776$$ 6.05256 + 22.5885i 0.217274 + 0.810878i
$$777$$ 0 0
$$778$$ −13.0526 + 7.53590i −0.467957 + 0.270175i
$$779$$ 0.696152 2.59808i 0.0249422 0.0930857i
$$780$$ 0 0
$$781$$ 8.39230 + 31.3205i 0.300300 + 1.12074i
$$782$$ −2.87564 + 2.87564i −0.102833 + 0.102833i
$$783$$ 0 0
$$784$$ −25.8564 −0.923443
$$785$$ −9.46410 + 16.3923i −0.337788 + 0.585066i
$$786$$ 0 0