# Properties

 Label 570.2.c.c.569.6 Level $570$ Weight $2$ Character 570.569 Analytic conductor $4.551$ Analytic rank $0$ Dimension $8$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$570 = 2 \cdot 3 \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 570.c (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$4.55147291521$$ Analytic rank: $$0$$ Dimension: $$8$$ Coefficient field: 8.0.1499238400.2 Defining polynomial: $$x^{8} - 4 x^{7} + 16 x^{6} - 34 x^{5} + 59 x^{4} - 66 x^{3} + 54 x^{2} - 26 x + 5$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 569.6 Root $$0.500000 - 1.41267i$$ of defining polynomial Character $$\chi$$ $$=$$ 570.569 Dual form 570.2.c.c.569.4

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000i q^{2} +(-0.500000 - 1.65831i) q^{3} -1.00000 q^{4} +(1.91267 - 1.15831i) q^{5} +(1.65831 - 0.500000i) q^{6} +3.21974i q^{7} -1.00000i q^{8} +(-2.50000 + 1.65831i) q^{9} +O(q^{10})$$ $$q+1.00000i q^{2} +(-0.500000 - 1.65831i) q^{3} -1.00000 q^{4} +(1.91267 - 1.15831i) q^{5} +(1.65831 - 0.500000i) q^{6} +3.21974i q^{7} -1.00000i q^{8} +(-2.50000 + 1.65831i) q^{9} +(1.15831 + 1.91267i) q^{10} +4.31662i q^{11} +(0.500000 + 1.65831i) q^{12} +3.31662 q^{13} -3.21974 q^{14} +(-2.87718 - 2.59265i) q^{15} +1.00000 q^{16} +3.21974 q^{17} +(-1.65831 - 2.50000i) q^{18} +(-4.31662 - 0.605599i) q^{19} +(-1.91267 + 1.15831i) q^{20} +(5.33934 - 1.60987i) q^{21} -4.31662 q^{22} +7.04509 q^{23} +(-1.65831 + 0.500000i) q^{24} +(2.31662 - 4.43094i) q^{25} +3.31662i q^{26} +(4.00000 + 3.31662i) q^{27} -3.21974i q^{28} +8.25629 q^{29} +(2.59265 - 2.87718i) q^{30} -2.61414i q^{31} +1.00000i q^{32} +(7.15831 - 2.15831i) q^{33} +3.21974i q^{34} +(3.72947 + 6.15831i) q^{35} +(2.50000 - 1.65831i) q^{36} -2.00000 q^{37} +(0.605599 - 4.31662i) q^{38} +(-1.65831 - 5.50000i) q^{39} +(-1.15831 - 1.91267i) q^{40} -11.4760 q^{41} +(1.60987 + 5.33934i) q^{42} +3.82534i q^{43} -4.31662i q^{44} +(-2.86084 + 6.06759i) q^{45} +7.04509i q^{46} +8.86188 q^{47} +(-0.500000 - 1.65831i) q^{48} -3.36675 q^{49} +(4.43094 + 2.31662i) q^{50} +(-1.60987 - 5.33934i) q^{51} -3.31662 q^{52} +1.00000i q^{53} +(-3.31662 + 4.00000i) q^{54} +(5.00000 + 8.25629i) q^{55} +3.21974 q^{56} +(1.15404 + 7.46111i) q^{57} +8.25629i q^{58} -5.64214 q^{59} +(2.87718 + 2.59265i) q^{60} -2.31662 q^{61} +2.61414 q^{62} +(-5.33934 - 8.04936i) q^{63} -1.00000 q^{64} +(6.34361 - 3.84169i) q^{65} +(2.15831 + 7.15831i) q^{66} -7.00000 q^{67} -3.21974 q^{68} +(-3.52254 - 11.6830i) q^{69} +(-6.15831 + 3.72947i) q^{70} +10.2648 q^{71} +(1.65831 + 2.50000i) q^{72} -1.81680i q^{73} -2.00000i q^{74} +(-8.50620 - 1.62622i) q^{75} +(4.31662 + 0.605599i) q^{76} -13.8984 q^{77} +(5.50000 - 1.65831i) q^{78} +15.3014i q^{79} +(1.91267 - 1.15831i) q^{80} +(3.50000 - 8.29156i) q^{81} -11.4760i q^{82} -6.43949 q^{83} +(-5.33934 + 1.60987i) q^{84} +(6.15831 - 3.72947i) q^{85} -3.82534 q^{86} +(-4.12814 - 13.6915i) q^{87} +4.31662 q^{88} +2.61414 q^{89} +(-6.06759 - 2.86084i) q^{90} +10.6787i q^{91} -7.04509 q^{92} +(-4.33507 + 1.30707i) q^{93} +8.86188i q^{94} +(-8.95776 + 3.84169i) q^{95} +(1.65831 - 0.500000i) q^{96} -3.36675 q^{97} -3.36675i q^{98} +(-7.15831 - 10.7916i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q - 4q^{3} - 8q^{4} - 20q^{9} + O(q^{10})$$ $$8q - 4q^{3} - 8q^{4} - 20q^{9} - 4q^{10} + 4q^{12} - 22q^{15} + 8q^{16} - 8q^{19} - 8q^{22} - 8q^{25} + 32q^{27} + 2q^{30} + 44q^{33} + 20q^{36} - 16q^{37} + 4q^{40} + 22q^{45} - 4q^{48} - 80q^{49} + 40q^{55} + 4q^{57} + 22q^{60} + 8q^{61} - 8q^{64} + 4q^{66} - 56q^{67} - 36q^{70} + 4q^{75} + 8q^{76} + 44q^{78} + 28q^{81} + 36q^{85} + 8q^{88} + 10q^{90} - 80q^{97} - 44q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$$.

 $$n$$ $$191$$ $$211$$ $$457$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$-1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000i 0.707107i
$$3$$ −0.500000 1.65831i −0.288675 0.957427i
$$4$$ −1.00000 −0.500000
$$5$$ 1.91267 1.15831i 0.855373 0.518013i
$$6$$ 1.65831 0.500000i 0.677003 0.204124i
$$7$$ 3.21974i 1.21695i 0.793574 + 0.608474i $$0.208218\pi$$
−0.793574 + 0.608474i $$0.791782\pi$$
$$8$$ 1.00000i 0.353553i
$$9$$ −2.50000 + 1.65831i −0.833333 + 0.552771i
$$10$$ 1.15831 + 1.91267i 0.366291 + 0.604840i
$$11$$ 4.31662i 1.30151i 0.759287 + 0.650756i $$0.225548\pi$$
−0.759287 + 0.650756i $$0.774452\pi$$
$$12$$ 0.500000 + 1.65831i 0.144338 + 0.478714i
$$13$$ 3.31662 0.919866 0.459933 0.887954i $$-0.347873\pi$$
0.459933 + 0.887954i $$0.347873\pi$$
$$14$$ −3.21974 −0.860513
$$15$$ −2.87718 2.59265i −0.742885 0.669420i
$$16$$ 1.00000 0.250000
$$17$$ 3.21974 0.780903 0.390451 0.920624i $$-0.372319\pi$$
0.390451 + 0.920624i $$0.372319\pi$$
$$18$$ −1.65831 2.50000i −0.390868 0.589256i
$$19$$ −4.31662 0.605599i −0.990302 0.138934i
$$20$$ −1.91267 + 1.15831i −0.427686 + 0.259007i
$$21$$ 5.33934 1.60987i 1.16514 0.351303i
$$22$$ −4.31662 −0.920307
$$23$$ 7.04509 1.46900 0.734501 0.678608i $$-0.237416\pi$$
0.734501 + 0.678608i $$0.237416\pi$$
$$24$$ −1.65831 + 0.500000i −0.338502 + 0.102062i
$$25$$ 2.31662 4.43094i 0.463325 0.886188i
$$26$$ 3.31662i 0.650444i
$$27$$ 4.00000 + 3.31662i 0.769800 + 0.638285i
$$28$$ 3.21974i 0.608474i
$$29$$ 8.25629 1.53315 0.766577 0.642153i $$-0.221958\pi$$
0.766577 + 0.642153i $$0.221958\pi$$
$$30$$ 2.59265 2.87718i 0.473351 0.525299i
$$31$$ 2.61414i 0.469514i −0.972054 0.234757i $$-0.924571\pi$$
0.972054 0.234757i $$-0.0754295\pi$$
$$32$$ 1.00000i 0.176777i
$$33$$ 7.15831 2.15831i 1.24610 0.375714i
$$34$$ 3.21974i 0.552182i
$$35$$ 3.72947 + 6.15831i 0.630395 + 1.04094i
$$36$$ 2.50000 1.65831i 0.416667 0.276385i
$$37$$ −2.00000 −0.328798 −0.164399 0.986394i $$-0.552568\pi$$
−0.164399 + 0.986394i $$0.552568\pi$$
$$38$$ 0.605599 4.31662i 0.0982412 0.700249i
$$39$$ −1.65831 5.50000i −0.265543 0.880705i
$$40$$ −1.15831 1.91267i −0.183145 0.302420i
$$41$$ −11.4760 −1.79225 −0.896127 0.443797i $$-0.853631\pi$$
−0.896127 + 0.443797i $$0.853631\pi$$
$$42$$ 1.60987 + 5.33934i 0.248409 + 0.823878i
$$43$$ 3.82534i 0.583359i 0.956516 + 0.291680i $$0.0942141\pi$$
−0.956516 + 0.291680i $$0.905786\pi$$
$$44$$ 4.31662i 0.650756i
$$45$$ −2.86084 + 6.06759i −0.426468 + 0.904503i
$$46$$ 7.04509i 1.03874i
$$47$$ 8.86188 1.29264 0.646319 0.763067i $$-0.276307\pi$$
0.646319 + 0.763067i $$0.276307\pi$$
$$48$$ −0.500000 1.65831i −0.0721688 0.239357i
$$49$$ −3.36675 −0.480964
$$50$$ 4.43094 + 2.31662i 0.626630 + 0.327620i
$$51$$ −1.60987 5.33934i −0.225427 0.747657i
$$52$$ −3.31662 −0.459933
$$53$$ 1.00000i 0.137361i 0.997639 + 0.0686803i $$0.0218788\pi$$
−0.997639 + 0.0686803i $$0.978121\pi$$
$$54$$ −3.31662 + 4.00000i −0.451335 + 0.544331i
$$55$$ 5.00000 + 8.25629i 0.674200 + 1.11328i
$$56$$ 3.21974 0.430256
$$57$$ 1.15404 + 7.46111i 0.152856 + 0.988248i
$$58$$ 8.25629i 1.08410i
$$59$$ −5.64214 −0.734544 −0.367272 0.930114i $$-0.619708\pi$$
−0.367272 + 0.930114i $$0.619708\pi$$
$$60$$ 2.87718 + 2.59265i 0.371442 + 0.334710i
$$61$$ −2.31662 −0.296613 −0.148307 0.988941i $$-0.547382\pi$$
−0.148307 + 0.988941i $$0.547382\pi$$
$$62$$ 2.61414 0.331997
$$63$$ −5.33934 8.04936i −0.672694 1.01412i
$$64$$ −1.00000 −0.125000
$$65$$ 6.34361 3.84169i 0.786828 0.476503i
$$66$$ 2.15831 + 7.15831i 0.265670 + 0.881127i
$$67$$ −7.00000 −0.855186 −0.427593 0.903971i $$-0.640638\pi$$
−0.427593 + 0.903971i $$0.640638\pi$$
$$68$$ −3.21974 −0.390451
$$69$$ −3.52254 11.6830i −0.424064 1.40646i
$$70$$ −6.15831 + 3.72947i −0.736059 + 0.445757i
$$71$$ 10.2648 1.21821 0.609106 0.793089i $$-0.291529\pi$$
0.609106 + 0.793089i $$0.291529\pi$$
$$72$$ 1.65831 + 2.50000i 0.195434 + 0.294628i
$$73$$ 1.81680i 0.212640i −0.994332 0.106320i $$-0.966093\pi$$
0.994332 0.106320i $$-0.0339068\pi$$
$$74$$ 2.00000i 0.232495i
$$75$$ −8.50620 1.62622i −0.982211 0.187779i
$$76$$ 4.31662 + 0.605599i 0.495151 + 0.0694670i
$$77$$ −13.8984 −1.58387
$$78$$ 5.50000 1.65831i 0.622752 0.187767i
$$79$$ 15.3014i 1.72154i 0.508995 + 0.860769i $$0.330017\pi$$
−0.508995 + 0.860769i $$0.669983\pi$$
$$80$$ 1.91267 1.15831i 0.213843 0.129503i
$$81$$ 3.50000 8.29156i 0.388889 0.921285i
$$82$$ 11.4760i 1.26732i
$$83$$ −6.43949 −0.706826 −0.353413 0.935467i $$-0.614979\pi$$
−0.353413 + 0.935467i $$0.614979\pi$$
$$84$$ −5.33934 + 1.60987i −0.582570 + 0.175651i
$$85$$ 6.15831 3.72947i 0.667963 0.404518i
$$86$$ −3.82534 −0.412497
$$87$$ −4.12814 13.6915i −0.442583 1.46788i
$$88$$ 4.31662 0.460154
$$89$$ 2.61414 0.277099 0.138549 0.990356i $$-0.455756\pi$$
0.138549 + 0.990356i $$0.455756\pi$$
$$90$$ −6.06759 2.86084i −0.639580 0.301558i
$$91$$ 10.6787i 1.11943i
$$92$$ −7.04509 −0.734501
$$93$$ −4.33507 + 1.30707i −0.449526 + 0.135537i
$$94$$ 8.86188i 0.914034i
$$95$$ −8.95776 + 3.84169i −0.919047 + 0.394149i
$$96$$ 1.65831 0.500000i 0.169251 0.0510310i
$$97$$ −3.36675 −0.341842 −0.170921 0.985285i $$-0.554674\pi$$
−0.170921 + 0.985285i $$0.554674\pi$$
$$98$$ 3.36675i 0.340093i
$$99$$ −7.15831 10.7916i −0.719437 1.08459i
$$100$$ −2.31662 + 4.43094i −0.231662 + 0.443094i
$$101$$ 14.3166i 1.42456i −0.701897 0.712279i $$-0.747663\pi$$
0.701897 0.712279i $$-0.252337\pi$$
$$102$$ 5.33934 1.60987i 0.528674 0.159401i
$$103$$ −17.5831 −1.73252 −0.866258 0.499596i $$-0.833482\pi$$
−0.866258 + 0.499596i $$0.833482\pi$$
$$104$$ 3.31662i 0.325222i
$$105$$ 8.34767 9.26378i 0.814649 0.904052i
$$106$$ −1.00000 −0.0971286
$$107$$ 0.0501256i 0.00484583i 0.999997 + 0.00242291i $$0.000771238\pi$$
−0.999997 + 0.00242291i $$0.999229\pi$$
$$108$$ −4.00000 3.31662i −0.384900 0.319142i
$$109$$ 6.85334i 0.656431i −0.944603 0.328215i $$-0.893553\pi$$
0.944603 0.328215i $$-0.106447\pi$$
$$110$$ −8.25629 + 5.00000i −0.787206 + 0.476731i
$$111$$ 1.00000 + 3.31662i 0.0949158 + 0.314800i
$$112$$ 3.21974i 0.304237i
$$113$$ 1.68338i 0.158359i 0.996860 + 0.0791793i $$0.0252300\pi$$
−0.996860 + 0.0791793i $$0.974770\pi$$
$$114$$ −7.46111 + 1.15404i −0.698797 + 0.108086i
$$115$$ 13.4749 8.16041i 1.25654 0.760962i
$$116$$ −8.25629 −0.766577
$$117$$ −8.29156 + 5.50000i −0.766555 + 0.508475i
$$118$$ 5.64214i 0.519401i
$$119$$ 10.3668i 0.950318i
$$120$$ −2.59265 + 2.87718i −0.236676 + 0.262649i
$$121$$ −7.63325 −0.693932
$$122$$ 2.31662i 0.209737i
$$123$$ 5.73801 + 19.0308i 0.517379 + 1.71595i
$$124$$ 2.61414i 0.234757i
$$125$$ −0.701473 11.1583i −0.0627417 0.998030i
$$126$$ 8.04936 5.33934i 0.717094 0.475666i
$$127$$ 16.6332 1.47596 0.737981 0.674821i $$-0.235779\pi$$
0.737981 + 0.674821i $$0.235779\pi$$
$$128$$ 1.00000i 0.0883883i
$$129$$ 6.34361 1.91267i 0.558524 0.168401i
$$130$$ 3.84169 + 6.34361i 0.336938 + 0.556372i
$$131$$ 10.0000i 0.873704i −0.899533 0.436852i $$-0.856093\pi$$
0.899533 0.436852i $$-0.143907\pi$$
$$132$$ −7.15831 + 2.15831i −0.623051 + 0.187857i
$$133$$ 1.94987 13.8984i 0.169076 1.20515i
$$134$$ 7.00000i 0.604708i
$$135$$ 11.4924 + 1.71036i 0.989106 + 0.147205i
$$136$$ 3.21974i 0.276091i
$$137$$ 3.21974 0.275081 0.137541 0.990496i $$-0.456080\pi$$
0.137541 + 0.990496i $$0.456080\pi$$
$$138$$ 11.6830 3.52254i 0.994519 0.299859i
$$139$$ −10.0000 −0.848189 −0.424094 0.905618i $$-0.639408\pi$$
−0.424094 + 0.905618i $$0.639408\pi$$
$$140$$ −3.72947 6.15831i −0.315198 0.520472i
$$141$$ −4.43094 14.6958i −0.373153 1.23761i
$$142$$ 10.2648i 0.861405i
$$143$$ 14.3166i 1.19722i
$$144$$ −2.50000 + 1.65831i −0.208333 + 0.138193i
$$145$$ 15.7916 9.56336i 1.31142 0.794194i
$$146$$ 1.81680 0.150359
$$147$$ 1.68338 + 5.58312i 0.138842 + 0.460488i
$$148$$ 2.00000 0.164399
$$149$$ 4.00000i 0.327693i 0.986486 + 0.163846i $$0.0523901\pi$$
−0.986486 + 0.163846i $$0.947610\pi$$
$$150$$ 1.62622 8.50620i 0.132780 0.694528i
$$151$$ 16.5126i 1.34377i 0.740654 + 0.671887i $$0.234516\pi$$
−0.740654 + 0.671887i $$0.765484\pi$$
$$152$$ −0.605599 + 4.31662i −0.0491206 + 0.350125i
$$153$$ −8.04936 + 5.33934i −0.650752 + 0.431660i
$$154$$ 13.8984i 1.11997i
$$155$$ −3.02800 5.00000i −0.243215 0.401610i
$$156$$ 1.65831 + 5.50000i 0.132771 + 0.440352i
$$157$$ 7.65069i 0.610591i −0.952258 0.305296i $$-0.901245\pi$$
0.952258 0.305296i $$-0.0987553\pi$$
$$158$$ −15.3014 −1.21731
$$159$$ 1.65831 0.500000i 0.131513 0.0396526i
$$160$$ 1.15831 + 1.91267i 0.0915726 + 0.151210i
$$161$$ 22.6834i 1.78770i
$$162$$ 8.29156 + 3.50000i 0.651447 + 0.274986i
$$163$$ 1.40295i 0.109887i −0.998489 0.0549436i $$-0.982502\pi$$
0.998489 0.0549436i $$-0.0174979\pi$$
$$164$$ 11.4760 0.896127
$$165$$ 11.1915 12.4197i 0.871257 0.966873i
$$166$$ 6.43949i 0.499801i
$$167$$ 24.9499i 1.93068i −0.260997 0.965340i $$-0.584051\pi$$
0.260997 0.965340i $$-0.415949\pi$$
$$168$$ −1.60987 5.33934i −0.124204 0.411939i
$$169$$ −2.00000 −0.153846
$$170$$ 3.72947 + 6.15831i 0.286037 + 0.472321i
$$171$$ 11.7958 5.64431i 0.902050 0.431632i
$$172$$ 3.82534i 0.291680i
$$173$$ 13.2665i 1.00863i 0.863519 + 0.504317i $$0.168256\pi$$
−0.863519 + 0.504317i $$0.831744\pi$$
$$174$$ 13.6915 4.12814i 1.03795 0.312954i
$$175$$ 14.2665 + 7.45894i 1.07845 + 0.563843i
$$176$$ 4.31662i 0.325378i
$$177$$ 2.82107 + 9.35643i 0.212045 + 0.703272i
$$178$$ 2.61414i 0.195938i
$$179$$ −16.5126 −1.23421 −0.617104 0.786882i $$-0.711694\pi$$
−0.617104 + 0.786882i $$0.711694\pi$$
$$180$$ 2.86084 6.06759i 0.213234 0.452251i
$$181$$ 16.5126i 1.22737i −0.789551 0.613685i $$-0.789687\pi$$
0.789551 0.613685i $$-0.210313\pi$$
$$182$$ −10.6787 −0.791557
$$183$$ 1.15831 + 3.84169i 0.0856249 + 0.283986i
$$184$$ 7.04509i 0.519371i
$$185$$ −3.82534 + 2.31662i −0.281245 + 0.170322i
$$186$$ −1.30707 4.33507i −0.0958392 0.317863i
$$187$$ 13.8984i 1.01635i
$$188$$ −8.86188 −0.646319
$$189$$ −10.6787 + 12.8790i −0.776760 + 0.936808i
$$190$$ −3.84169 8.95776i −0.278705 0.649864i
$$191$$ 5.00000i 0.361787i −0.983503 0.180894i $$-0.942101\pi$$
0.983503 0.180894i $$-0.0578990\pi$$
$$192$$ 0.500000 + 1.65831i 0.0360844 + 0.119678i
$$193$$ −6.00000 −0.431889 −0.215945 0.976406i $$-0.569283\pi$$
−0.215945 + 0.976406i $$0.569283\pi$$
$$194$$ 3.36675i 0.241719i
$$195$$ −9.54253 8.59885i −0.683354 0.615776i
$$196$$ 3.36675 0.240482
$$197$$ −5.03654 −0.358839 −0.179419 0.983773i $$-0.557422\pi$$
−0.179419 + 0.983773i $$0.557422\pi$$
$$198$$ 10.7916 7.15831i 0.766923 0.508719i
$$199$$ −25.2164 −1.78754 −0.893771 0.448524i $$-0.851950\pi$$
−0.893771 + 0.448524i $$0.851950\pi$$
$$200$$ −4.43094 2.31662i −0.313315 0.163810i
$$201$$ 3.50000 + 11.6082i 0.246871 + 0.818778i
$$202$$ 14.3166 1.00731
$$203$$ 26.5831i 1.86577i
$$204$$ 1.60987 + 5.33934i 0.112714 + 0.373829i
$$205$$ −21.9499 + 13.2928i −1.53305 + 0.928411i
$$206$$ 17.5831i 1.22507i
$$207$$ −17.6127 + 11.6830i −1.22417 + 0.812022i
$$208$$ 3.31662 0.229967
$$209$$ 2.61414 18.6332i 0.180824 1.28889i
$$210$$ 9.26378 + 8.34767i 0.639262 + 0.576044i
$$211$$ 3.02800i 0.208456i −0.994553 0.104228i $$-0.966763\pi$$
0.994553 0.104228i $$-0.0332371\pi$$
$$212$$ 1.00000i 0.0686803i
$$213$$ −5.13242 17.0223i −0.351667 1.16635i
$$214$$ −0.0501256 −0.00342652
$$215$$ 4.43094 + 7.31662i 0.302188 + 0.498990i
$$216$$ 3.31662 4.00000i 0.225668 0.272166i
$$217$$ 8.41688 0.571375
$$218$$ 6.85334 0.464167
$$219$$ −3.01282 + 0.908399i −0.203587 + 0.0613839i
$$220$$ −5.00000 8.25629i −0.337100 0.556639i
$$221$$ 10.6787 0.718326
$$222$$ −3.31662 + 1.00000i −0.222597 + 0.0671156i
$$223$$ −3.26650 −0.218741 −0.109370 0.994001i $$-0.534883\pi$$
−0.109370 + 0.994001i $$0.534883\pi$$
$$224$$ −3.21974 −0.215128
$$225$$ 1.55632 + 14.9190i 0.103755 + 0.994603i
$$226$$ −1.68338 −0.111976
$$227$$ 19.9499i 1.32412i −0.749451 0.662060i $$-0.769682\pi$$
0.749451 0.662060i $$-0.230318\pi$$
$$228$$ −1.15404 7.46111i −0.0764281 0.494124i
$$229$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$230$$ 8.16041 + 13.4749i 0.538082 + 0.888511i
$$231$$ 6.94921 + 23.0479i 0.457225 + 1.51644i
$$232$$ 8.25629i 0.542052i
$$233$$ 26.5857 1.74168 0.870842 0.491563i $$-0.163574\pi$$
0.870842 + 0.491563i $$0.163574\pi$$
$$234$$ −5.50000 8.29156i −0.359546 0.542036i
$$235$$ 16.9499 10.2648i 1.10569 0.669604i
$$236$$ 5.64214 0.367272
$$237$$ 25.3745 7.65069i 1.64825 0.496965i
$$238$$ −10.3668 −0.671977
$$239$$ 19.6332i 1.26997i −0.772525 0.634985i $$-0.781006\pi$$
0.772525 0.634985i $$-0.218994\pi$$
$$240$$ −2.87718 2.59265i −0.185721 0.167355i
$$241$$ 5.22829i 0.336784i −0.985720 0.168392i $$-0.946143\pi$$
0.985720 0.168392i $$-0.0538574\pi$$
$$242$$ 7.63325i 0.490684i
$$243$$ −15.5000 1.65831i −0.994325 0.106381i
$$244$$ 2.31662 0.148307
$$245$$ −6.43949 + 3.89975i −0.411404 + 0.249146i
$$246$$ −19.0308 + 5.73801i −1.21336 + 0.365842i
$$247$$ −14.3166 2.00855i −0.910945 0.127801i
$$248$$ −2.61414 −0.165998
$$249$$ 3.21974 + 10.6787i 0.204043 + 0.676734i
$$250$$ 11.1583 0.701473i 0.705714 0.0443651i
$$251$$ 31.5831i 1.99351i 0.0805007 + 0.996755i $$0.474348\pi$$
−0.0805007 + 0.996755i $$0.525652\pi$$
$$252$$ 5.33934 + 8.04936i 0.336347 + 0.507062i
$$253$$ 30.4110i 1.91192i
$$254$$ 16.6332i 1.04366i
$$255$$ −9.26378 8.34767i −0.580120 0.522751i
$$256$$ 1.00000 0.0625000
$$257$$ 4.94987i 0.308765i −0.988011 0.154382i $$-0.950661\pi$$
0.988011 0.154382i $$-0.0493388\pi$$
$$258$$ 1.91267 + 6.34361i 0.119078 + 0.394936i
$$259$$ 6.43949i 0.400130i
$$260$$ −6.34361 + 3.84169i −0.393414 + 0.238251i
$$261$$ −20.6407 + 13.6915i −1.27763 + 0.847483i
$$262$$ 10.0000 0.617802
$$263$$ 20.5297 1.26591 0.632957 0.774187i $$-0.281841\pi$$
0.632957 + 0.774187i $$0.281841\pi$$
$$264$$ −2.15831 7.15831i −0.132835 0.440564i
$$265$$ 1.15831 + 1.91267i 0.0711546 + 0.117494i
$$266$$ 13.8984 + 1.94987i 0.852167 + 0.119554i
$$267$$ −1.30707 4.33507i −0.0799915 0.265302i
$$268$$ 7.00000 0.427593
$$269$$ −21.7409 −1.32556 −0.662782 0.748813i $$-0.730624\pi$$
−0.662782 + 0.748813i $$0.730624\pi$$
$$270$$ −1.71036 + 11.4924i −0.104089 + 0.699404i
$$271$$ 2.68338 0.163003 0.0815017 0.996673i $$-0.474028\pi$$
0.0815017 + 0.996673i $$0.474028\pi$$
$$272$$ 3.21974 0.195226
$$273$$ 17.7086 5.33934i 1.07177 0.323152i
$$274$$ 3.21974i 0.194512i
$$275$$ 19.1267 + 10.0000i 1.15338 + 0.603023i
$$276$$ 3.52254 + 11.6830i 0.212032 + 0.703231i
$$277$$ 14.0902i 0.846596i 0.905990 + 0.423298i $$0.139128\pi$$
−0.905990 + 0.423298i $$0.860872\pi$$
$$278$$ 10.0000i 0.599760i
$$279$$ 4.33507 + 6.53536i 0.259534 + 0.391262i
$$280$$ 6.15831 3.72947i 0.368030 0.222878i
$$281$$ −6.24774 −0.372709 −0.186354 0.982483i $$-0.559667\pi$$
−0.186354 + 0.982483i $$0.559667\pi$$
$$282$$ 14.6958 4.43094i 0.875121 0.263859i
$$283$$ 26.5857i 1.58035i −0.612879 0.790177i $$-0.709989\pi$$
0.612879 0.790177i $$-0.290011\pi$$
$$284$$ −10.2648 −0.609106
$$285$$ 10.8496 + 12.9339i 0.642675 + 0.766139i
$$286$$ −14.3166 −0.846560
$$287$$ 36.9499i 2.18108i
$$288$$ −1.65831 2.50000i −0.0977170 0.147314i
$$289$$ −6.63325 −0.390191
$$290$$ 9.56336 + 15.7916i 0.561580 + 0.927312i
$$291$$ 1.68338 + 5.58312i 0.0986812 + 0.327289i
$$292$$ 1.81680i 0.106320i
$$293$$ 18.2665i 1.06714i 0.845756 + 0.533570i $$0.179150\pi$$
−0.845756 + 0.533570i $$0.820850\pi$$
$$294$$ −5.58312 + 1.68338i −0.325614 + 0.0981764i
$$295$$ −10.7916 + 6.53536i −0.628309 + 0.380503i
$$296$$ 2.00000i 0.116248i
$$297$$ −14.3166 + 17.2665i −0.830735 + 1.00190i
$$298$$ −4.00000 −0.231714
$$299$$ 23.3659 1.35129
$$300$$ 8.50620 + 1.62622i 0.491106 + 0.0938897i
$$301$$ −12.3166 −0.709918
$$302$$ −16.5126 −0.950192
$$303$$ −23.7414 + 7.15831i −1.36391 + 0.411234i
$$304$$ −4.31662 0.605599i −0.247575 0.0347335i
$$305$$ −4.43094 + 2.68338i −0.253715 + 0.153650i
$$306$$ −5.33934 8.04936i −0.305230 0.460151i
$$307$$ −2.00000 −0.114146 −0.0570730 0.998370i $$-0.518177\pi$$
−0.0570730 + 0.998370i $$0.518177\pi$$
$$308$$ 13.8984 0.791936
$$309$$ 8.79156 + 29.1583i 0.500134 + 1.65876i
$$310$$ 5.00000 3.02800i 0.283981 0.171979i
$$311$$ 20.8997i 1.18512i −0.805528 0.592558i $$-0.798118\pi$$
0.805528 0.592558i $$-0.201882\pi$$
$$312$$ −5.50000 + 1.65831i −0.311376 + 0.0938835i
$$313$$ 20.7518i 1.17296i 0.809964 + 0.586480i $$0.199487\pi$$
−0.809964 + 0.586480i $$0.800513\pi$$
$$314$$ 7.65069 0.431753
$$315$$ −19.5361 9.21116i −1.10073 0.518990i
$$316$$ 15.3014i 0.860769i
$$317$$ 17.0000i 0.954815i −0.878682 0.477408i $$-0.841577\pi$$
0.878682 0.477408i $$-0.158423\pi$$
$$318$$ 0.500000 + 1.65831i 0.0280386 + 0.0929935i
$$319$$ 35.6393i 1.99542i
$$320$$ −1.91267 + 1.15831i −0.106922 + 0.0647516i
$$321$$ 0.0831240 0.0250628i 0.00463953 0.00139887i
$$322$$ −22.6834 −1.26410
$$323$$ −13.8984 1.94987i −0.773329 0.108494i
$$324$$ −3.50000 + 8.29156i −0.194444 + 0.460642i
$$325$$ 7.68338 14.6958i 0.426197 0.815175i
$$326$$ 1.40295 0.0777020
$$327$$ −11.3650 + 3.42667i −0.628485 + 0.189495i
$$328$$ 11.4760i 0.633658i
$$329$$ 28.5330i 1.57308i
$$330$$ 12.4197 + 11.1915i 0.683682 + 0.616072i
$$331$$ 13.4846i 0.741179i 0.928797 + 0.370590i $$0.120844\pi$$
−0.928797 + 0.370590i $$0.879156\pi$$
$$332$$ 6.43949 0.353413
$$333$$ 5.00000 3.31662i 0.273998 0.181750i
$$334$$ 24.9499 1.36520
$$335$$ −13.3887 + 8.10819i −0.731503 + 0.442998i
$$336$$ 5.33934 1.60987i 0.291285 0.0878257i
$$337$$ 28.2164 1.53704 0.768522 0.639823i $$-0.220993\pi$$
0.768522 + 0.639823i $$0.220993\pi$$
$$338$$ 2.00000i 0.108786i
$$339$$ 2.79156 0.841688i 0.151617 0.0457142i
$$340$$ −6.15831 + 3.72947i −0.333981 + 0.202259i
$$341$$ 11.2843 0.611078
$$342$$ 5.64431 + 11.7958i 0.305210 + 0.637846i
$$343$$ 11.6981i 0.631640i
$$344$$ 3.82534 0.206249
$$345$$ −20.2700 18.2654i −1.09130 0.983379i
$$346$$ −13.2665 −0.713211
$$347$$ 20.1462 1.08150 0.540751 0.841182i $$-0.318140\pi$$
0.540751 + 0.841182i $$0.318140\pi$$
$$348$$ 4.12814 + 13.6915i 0.221292 + 0.733941i
$$349$$ 8.63325 0.462127 0.231064 0.972939i $$-0.425779\pi$$
0.231064 + 0.972939i $$0.425779\pi$$
$$350$$ −7.45894 + 14.2665i −0.398697 + 0.762576i
$$351$$ 13.2665 + 11.0000i 0.708113 + 0.587137i
$$352$$ −4.31662 −0.230077
$$353$$ −23.3659 −1.24364 −0.621821 0.783159i $$-0.713607\pi$$
−0.621821 + 0.783159i $$0.713607\pi$$
$$354$$ −9.35643 + 2.82107i −0.497289 + 0.149938i
$$355$$ 19.6332 11.8899i 1.04202 0.631049i
$$356$$ −2.61414 −0.138549
$$357$$ 17.1913 5.18338i 0.909861 0.274333i
$$358$$ 16.5126i 0.872716i
$$359$$ 4.89975i 0.258599i 0.991606 + 0.129299i $$0.0412728\pi$$
−0.991606 + 0.129299i $$0.958727\pi$$
$$360$$ 6.06759 + 2.86084i 0.319790 + 0.150779i
$$361$$ 18.2665 + 5.22829i 0.961395 + 0.275173i
$$362$$ 16.5126 0.867881
$$363$$ 3.81662 + 12.6583i 0.200321 + 0.664389i
$$364$$ 10.6787i 0.559715i
$$365$$ −2.10442 3.47494i −0.110150 0.181887i
$$366$$ −3.84169 + 1.15831i −0.200808 + 0.0605460i
$$367$$ 7.65069i 0.399363i −0.979861 0.199681i $$-0.936009\pi$$
0.979861 0.199681i $$-0.0639907\pi$$
$$368$$ 7.04509 0.367251
$$369$$ 28.6901 19.0308i 1.49355 0.990706i
$$370$$ −2.31662 3.82534i −0.120436 0.198870i
$$371$$ −3.21974 −0.167161
$$372$$ 4.33507 1.30707i 0.224763 0.0677685i
$$373$$ 23.3166 1.20729 0.603645 0.797254i $$-0.293715\pi$$
0.603645 + 0.797254i $$0.293715\pi$$
$$374$$ −13.8984 −0.718671
$$375$$ −18.1532 + 6.74242i −0.937429 + 0.348177i
$$376$$ 8.86188i 0.457017i
$$377$$ 27.3830 1.41030
$$378$$ −12.8790 10.6787i −0.662423 0.549252i
$$379$$ 36.4366i 1.87162i −0.352499 0.935812i $$-0.614668\pi$$
0.352499 0.935812i $$-0.385332\pi$$
$$380$$ 8.95776 3.84169i 0.459523 0.197074i
$$381$$ −8.31662 27.5831i −0.426074 1.41313i
$$382$$ 5.00000 0.255822
$$383$$ 7.58312i 0.387480i 0.981053 + 0.193740i $$0.0620617\pi$$
−0.981053 + 0.193740i $$0.937938\pi$$
$$384$$ −1.65831 + 0.500000i −0.0846254 + 0.0255155i
$$385$$ −26.5831 + 16.0987i −1.35480 + 0.820467i
$$386$$ 6.00000i 0.305392i
$$387$$ −6.34361 9.56336i −0.322464 0.486133i
$$388$$ 3.36675 0.170921
$$389$$ 16.2164i 0.822203i −0.911590 0.411101i $$-0.865144\pi$$
0.911590 0.411101i $$-0.134856\pi$$
$$390$$ 8.59885 9.54253i 0.435420 0.483205i
$$391$$ 22.6834 1.14715
$$392$$ 3.36675i 0.170047i
$$393$$ −16.5831 + 5.00000i −0.836508 + 0.252217i
$$394$$ 5.03654i 0.253737i
$$395$$ 17.7238 + 29.2665i 0.891780 + 1.47256i
$$396$$ 7.15831 + 10.7916i 0.359719 + 0.542296i
$$397$$ 29.3915i 1.47512i −0.675282 0.737560i $$-0.735978\pi$$
0.675282 0.737560i $$-0.264022\pi$$
$$398$$ 25.2164i 1.26398i
$$399$$ −24.0229 + 3.71571i −1.20265 + 0.186018i
$$400$$ 2.31662 4.43094i 0.115831 0.221547i
$$401$$ 21.5491 1.07611 0.538056 0.842909i $$-0.319159\pi$$
0.538056 + 0.842909i $$0.319159\pi$$
$$402$$ −11.6082 + 3.50000i −0.578964 + 0.174564i
$$403$$ 8.67014i 0.431890i
$$404$$ 14.3166i 0.712279i
$$405$$ −2.90987 19.9131i −0.144593 0.989491i
$$406$$ −26.5831 −1.31930
$$407$$ 8.63325i 0.427934i
$$408$$ −5.33934 + 1.60987i −0.264337 + 0.0797005i
$$409$$ 3.82534i 0.189151i −0.995518 0.0945755i $$-0.969851\pi$$
0.995518 0.0945755i $$-0.0301494\pi$$
$$410$$ −13.2928 21.9499i −0.656486 1.08403i
$$411$$ −1.60987 5.33934i −0.0794091 0.263370i
$$412$$ 17.5831 0.866258
$$413$$ 18.1662i 0.893903i
$$414$$ −11.6830 17.6127i −0.574186 0.865618i
$$415$$ −12.3166 + 7.45894i −0.604599 + 0.366145i
$$416$$ 3.31662i 0.162611i
$$417$$ 5.00000 + 16.5831i 0.244851 + 0.812079i
$$418$$ 18.6332 + 2.61414i 0.911382 + 0.127862i
$$419$$ 3.05013i 0.149008i −0.997221 0.0745042i $$-0.976263\pi$$
0.997221 0.0745042i $$-0.0237374\pi$$
$$420$$ −8.34767 + 9.26378i −0.407325 + 0.452026i
$$421$$ 16.0987i 0.784604i −0.919837 0.392302i $$-0.871679\pi$$
0.919837 0.392302i $$-0.128321\pi$$
$$422$$ 3.02800 0.147401
$$423$$ −22.1547 + 14.6958i −1.07720 + 0.714533i
$$424$$ 1.00000 0.0485643
$$425$$ 7.45894 14.2665i 0.361812 0.692027i
$$426$$ 17.0223 5.13242i 0.824733 0.248666i
$$427$$ 7.45894i 0.360963i
$$428$$ 0.0501256i 0.00242291i
$$429$$ 23.7414 7.15831i 1.14625 0.345607i
$$430$$ −7.31662 + 4.43094i −0.352839 + 0.213679i
$$431$$ −17.5320 −0.844488 −0.422244 0.906482i $$-0.638757\pi$$
−0.422244 + 0.906482i $$0.638757\pi$$
$$432$$ 4.00000 + 3.31662i 0.192450 + 0.159571i
$$433$$ −1.68338 −0.0808978 −0.0404489 0.999182i $$-0.512879\pi$$
−0.0404489 + 0.999182i $$0.512879\pi$$
$$434$$ 8.41688i 0.404023i
$$435$$ −23.7548 21.4057i −1.13896 1.02632i
$$436$$ 6.85334i 0.328215i
$$437$$ −30.4110 4.26650i −1.45476 0.204094i
$$438$$ −0.908399 3.01282i −0.0434050 0.143958i
$$439$$ 3.82534i 0.182574i −0.995825 0.0912868i $$-0.970902\pi$$
0.995825 0.0912868i $$-0.0290980\pi$$
$$440$$ 8.25629 5.00000i 0.393603 0.238366i
$$441$$ 8.41688 5.58312i 0.400804 0.265863i
$$442$$ 10.6787i 0.507933i
$$443$$ 12.6872 0.602788 0.301394 0.953500i $$-0.402548\pi$$
0.301394 + 0.953500i $$0.402548\pi$$
$$444$$ −1.00000 3.31662i −0.0474579 0.157400i
$$445$$ 5.00000 3.02800i 0.237023 0.143541i
$$446$$ 3.26650i 0.154673i
$$447$$ 6.63325 2.00000i 0.313742 0.0945968i
$$448$$ 3.21974i 0.152119i
$$449$$ 26.9691 1.27275 0.636376 0.771379i $$-0.280433\pi$$
0.636376 + 0.771379i $$0.280433\pi$$
$$450$$ −14.9190 + 1.55632i −0.703290 + 0.0733658i
$$451$$ 49.5377i 2.33264i
$$452$$ 1.68338i 0.0791793i
$$453$$ 27.3830 8.25629i 1.28657 0.387914i
$$454$$ 19.9499 0.936294
$$455$$ 12.3693 + 20.4248i 0.579879 + 0.957530i
$$456$$ 7.46111 1.15404i 0.349399 0.0540429i
$$457$$ 27.1913i 1.27195i −0.771708 0.635977i $$-0.780597\pi$$
0.771708 0.635977i $$-0.219403\pi$$
$$458$$ 0 0
$$459$$ 12.8790 + 10.6787i 0.601139 + 0.498438i
$$460$$ −13.4749 + 8.16041i −0.628272 + 0.380481i
$$461$$ 21.5831i 1.00523i 0.864511 + 0.502613i $$0.167628\pi$$
−0.864511 + 0.502613i $$0.832372\pi$$
$$462$$ −23.0479 + 6.94921i −1.07229 + 0.323307i
$$463$$ 15.3014i 0.711115i −0.934654 0.355558i $$-0.884291\pi$$
0.934654 0.355558i $$-0.115709\pi$$
$$464$$ 8.25629 0.383288
$$465$$ −6.77756 + 7.52136i −0.314302 + 0.348795i
$$466$$ 26.5857i 1.23156i
$$467$$ −26.7774 −1.23911 −0.619555 0.784953i $$-0.712687\pi$$
−0.619555 + 0.784953i $$0.712687\pi$$
$$468$$ 8.29156 5.50000i 0.383278 0.254238i
$$469$$ 22.5382i 1.04072i
$$470$$ 10.2648 + 16.9499i 0.473481 + 0.781839i
$$471$$ −12.6872 + 3.82534i −0.584597 + 0.176263i
$$472$$ 5.64214i 0.259701i
$$473$$ −16.5126 −0.759249
$$474$$ 7.65069 + 25.3745i 0.351408 + 1.16549i
$$475$$ −12.6834 + 17.7238i −0.581953 + 0.813222i
$$476$$ 10.3668i 0.475159i
$$477$$ −1.65831 2.50000i −0.0759289 0.114467i
$$478$$ 19.6332 0.898004
$$479$$ 14.0000i 0.639676i 0.947472 + 0.319838i $$0.103629\pi$$
−0.947472 + 0.319838i $$0.896371\pi$$
$$480$$ 2.59265 2.87718i 0.118338 0.131325i
$$481$$ −6.63325 −0.302450
$$482$$ 5.22829 0.238142
$$483$$ 37.6161 11.3417i 1.71159 0.516065i
$$484$$ 7.63325 0.346966
$$485$$ −6.43949 + 3.89975i −0.292402 + 0.177078i
$$486$$ 1.65831 15.5000i 0.0752226 0.703094i
$$487$$ −36.5330 −1.65547 −0.827734 0.561121i $$-0.810370\pi$$
−0.827734 + 0.561121i $$0.810370\pi$$
$$488$$ 2.31662i 0.104869i
$$489$$ −2.32652 + 0.701473i −0.105209 + 0.0317217i
$$490$$ −3.89975 6.43949i −0.176173 0.290906i
$$491$$ 8.41688i 0.379848i 0.981799 + 0.189924i $$0.0608242\pi$$
−0.981799 + 0.189924i $$0.939176\pi$$
$$492$$ −5.73801 19.0308i −0.258690 0.857977i
$$493$$ 26.5831 1.19724
$$494$$ 2.00855 14.3166i 0.0903687 0.644135i
$$495$$ −26.1915 12.3492i −1.17722 0.555053i
$$496$$ 2.61414i 0.117379i
$$497$$ 33.0501i 1.48250i
$$498$$ −10.6787 + 3.21974i −0.478523 + 0.144280i
$$499$$ 8.41688 0.376791 0.188396 0.982093i $$-0.439671\pi$$
0.188396 + 0.982093i $$0.439671\pi$$
$$500$$ 0.701473 + 11.1583i 0.0313708 + 0.499015i
$$501$$ −41.3747 + 12.4749i −1.84848 + 0.557339i
$$502$$ −31.5831 −1.40962
$$503$$ 18.3294 0.817266 0.408633 0.912699i $$-0.366006\pi$$
0.408633 + 0.912699i $$0.366006\pi$$
$$504$$ −8.04936 + 5.33934i −0.358547 + 0.237833i
$$505$$ −16.5831 27.3830i −0.737939 1.21853i
$$506$$ −30.4110 −1.35193
$$507$$ 1.00000 + 3.31662i 0.0444116 + 0.147296i
$$508$$ −16.6332 −0.737981
$$509$$ −5.22829 −0.231740 −0.115870 0.993264i $$-0.536966\pi$$
−0.115870 + 0.993264i $$0.536966\pi$$
$$510$$ 8.34767 9.26378i 0.369641 0.410207i
$$511$$ 5.84962 0.258772
$$512$$ 1.00000i 0.0441942i
$$513$$ −15.2580 16.7390i −0.673655 0.739046i
$$514$$ 4.94987 0.218330
$$515$$ −33.6307 + 20.3668i −1.48195 + 0.897466i
$$516$$ −6.34361 + 1.91267i −0.279262 + 0.0842007i
$$517$$ 38.2534i 1.68238i
$$518$$ 6.43949 0.282935
$$519$$ 22.0000 6.63325i 0.965693 0.291167i
$$520$$ −3.84169 6.34361i −0.168469 0.278186i
$$521$$ −14.9179 −0.653564 −0.326782 0.945100i $$-0.605964\pi$$
−0.326782 + 0.945100i $$0.605964\pi$$
$$522$$ −13.6915 20.6407i −0.599261 0.903419i
$$523$$ 29.0000 1.26808 0.634041 0.773300i $$-0.281395\pi$$
0.634041 + 0.773300i $$0.281395\pi$$
$$524$$ 10.0000i 0.436852i
$$525$$ 5.23600 27.3878i 0.228518 1.19530i
$$526$$ 20.5297i 0.895136i
$$527$$ 8.41688i 0.366645i
$$528$$ 7.15831 2.15831i 0.311526 0.0939285i
$$529$$ 26.6332 1.15797
$$530$$ −1.91267 + 1.15831i −0.0830811 + 0.0503139i
$$531$$ 14.1054 9.35643i 0.612120 0.406035i
$$532$$ −1.94987 + 13.8984i −0.0845378 + 0.602573i
$$533$$ −38.0617 −1.64863
$$534$$ 4.33507 1.30707i 0.187597 0.0565626i
$$535$$ 0.0580611 + 0.0958739i 0.00251020 + 0.00414499i
$$536$$ 7.00000i 0.302354i
$$537$$ 8.25629 + 27.3830i 0.356285 + 1.18166i
$$538$$ 21.7409i 0.937315i
$$539$$ 14.5330i 0.625981i
$$540$$ −11.4924 1.71036i −0.494553 0.0736024i
$$541$$ 30.8496 1.32633 0.663164 0.748474i $$-0.269213\pi$$
0.663164 + 0.748474i $$0.269213\pi$$
$$542$$ 2.68338i 0.115261i
$$543$$ −27.3830 + 8.25629i −1.17512 + 0.354311i
$$544$$ 3.21974i 0.138045i
$$545$$ −7.93831 13.1082i −0.340040 0.561493i
$$546$$ 5.33934 + 17.7086i 0.228503 + 0.757858i
$$547$$ −12.0000 −0.513083 −0.256541 0.966533i $$-0.582583\pi$$
−0.256541 + 0.966533i $$0.582583\pi$$
$$548$$ −3.21974 −0.137541
$$549$$ 5.79156 3.84169i 0.247178 0.163959i
$$550$$ −10.0000 + 19.1267i −0.426401 + 0.815566i
$$551$$ −35.6393 5.00000i −1.51828 0.213007i
$$552$$ −11.6830 + 3.52254i −0.497260 + 0.149929i
$$553$$ −49.2665 −2.09502
$$554$$ −14.0902 −0.598634
$$555$$ 5.75436 + 5.18530i 0.244259 + 0.220104i
$$556$$ 10.0000 0.424094
$$557$$ −13.7067 −0.580771 −0.290385 0.956910i $$-0.593783\pi$$
−0.290385 + 0.956910i $$0.593783\pi$$
$$558$$ −6.53536 + 4.33507i −0.276664 + 0.183518i
$$559$$ 12.6872i 0.536613i
$$560$$ 3.72947 + 6.15831i 0.157599 + 0.260236i
$$561$$ 23.0479 6.94921i 0.973084 0.293396i
$$562$$ 6.24774i 0.263545i
$$563$$ 29.8997i 1.26012i −0.776545 0.630062i $$-0.783029\pi$$
0.776545 0.630062i $$-0.216971\pi$$
$$564$$ 4.43094 + 14.6958i 0.186576 + 0.618804i
$$565$$ 1.94987 + 3.21974i 0.0820318 + 0.135456i
$$566$$ 26.5857 1.11748
$$567$$ 26.6967 + 11.2691i 1.12116 + 0.473258i
$$568$$ 10.2648i 0.430703i
$$569$$ −5.22829 −0.219181 −0.109591 0.993977i $$-0.534954\pi$$
−0.109591 + 0.993977i $$0.534954\pi$$
$$570$$ −12.9339 + 10.8496i −0.541742 + 0.454440i
$$571$$ −32.3166 −1.35241 −0.676204 0.736714i $$-0.736376\pi$$
−0.676204 + 0.736714i $$0.736376\pi$$
$$572$$ 14.3166i 0.598608i
$$573$$ −8.29156 + 2.50000i −0.346385 + 0.104439i
$$574$$ 36.9499 1.54226
$$575$$ 16.3208 31.2164i 0.680625 1.30181i
$$576$$ 2.50000 1.65831i 0.104167 0.0690963i
$$577$$ 17.1182i 0.712639i 0.934364 + 0.356319i $$0.115968\pi$$
−0.934364 + 0.356319i $$0.884032\pi$$
$$578$$ 6.63325i 0.275907i
$$579$$ 3.00000 + 9.94987i 0.124676 + 0.413503i
$$580$$ −15.7916 + 9.56336i −0.655709 + 0.397097i
$$581$$ 20.7335i 0.860171i
$$582$$ −5.58312 + 1.68338i −0.231428 + 0.0697781i
$$583$$ −4.31662 −0.178776
$$584$$ −1.81680 −0.0751796
$$585$$ −9.48832 + 20.1239i −0.392294 + 0.832021i
$$586$$ −18.2665 −0.754582
$$587$$ −16.3208 −0.673632 −0.336816 0.941570i $$-0.609350\pi$$
−0.336816 + 0.941570i $$0.609350\pi$$
$$588$$ −1.68338 5.58312i −0.0694212 0.230244i
$$589$$ −1.58312 + 11.2843i −0.0652315 + 0.464961i
$$590$$ −6.53536 10.7916i −0.269057 0.444282i
$$591$$ 2.51827 + 8.35216i 0.103588 + 0.343562i
$$592$$ −2.00000 −0.0821995
$$593$$ 20.5297 0.843052 0.421526 0.906816i $$-0.361495\pi$$
0.421526 + 0.906816i $$0.361495\pi$$
$$594$$ −17.2665 14.3166i −0.708453 0.587418i
$$595$$ 12.0079 + 19.8282i 0.492277 + 0.812876i
$$596$$ 4.00000i 0.163846i
$$597$$ 12.6082 + 41.8166i 0.516019 + 1.71144i
$$598$$ 23.3659i 0.955503i
$$599$$ −19.9544 −0.815315 −0.407658 0.913135i $$-0.633654\pi$$
−0.407658 + 0.913135i $$0.633654\pi$$
$$600$$ −1.62622 + 8.50620i −0.0663900 + 0.347264i
$$601$$ 24.3550i 0.993461i 0.867905 + 0.496731i $$0.165466\pi$$
−0.867905 + 0.496731i $$0.834534\pi$$
$$602$$ 12.3166i 0.501988i
$$603$$ 17.5000 11.6082i 0.712655 0.472722i
$$604$$ 16.5126i 0.671887i
$$605$$ −14.5999 + 8.84169i −0.593570 + 0.359466i
$$606$$ −7.15831 23.7414i −0.290787 0.964430i
$$607$$ 36.6332 1.48690 0.743449 0.668793i $$-0.233189\pi$$
0.743449 + 0.668793i $$0.233189\pi$$
$$608$$ 0.605599 4.31662i 0.0245603 0.175062i
$$609$$ 44.0831 13.2916i 1.78634 0.538601i
$$610$$ −2.68338 4.43094i −0.108647 0.179404i
$$611$$ 29.3915 1.18905
$$612$$ 8.04936 5.33934i 0.325376 0.215830i
$$613$$ 17.9155i 0.723601i −0.932256 0.361800i $$-0.882162\pi$$
0.932256 0.361800i $$-0.117838\pi$$
$$614$$ 2.00000i 0.0807134i
$$615$$ 33.0186 + 29.7533i 1.33144 + 1.19977i
$$616$$ 13.8984i 0.559984i
$$617$$ −18.9350 −0.762293 −0.381147 0.924515i $$-0.624471\pi$$
−0.381147 + 0.924515i $$0.624471\pi$$
$$618$$ −29.1583 + 8.79156i −1.17292 + 0.353648i
$$619$$ 1.58312 0.0636311 0.0318156 0.999494i $$-0.489871\pi$$
0.0318156 + 0.999494i $$0.489871\pi$$
$$620$$ 3.02800 + 5.00000i 0.121607 + 0.200805i
$$621$$ 28.1803 + 23.3659i 1.13084 + 0.937642i
$$622$$ 20.8997 0.838004
$$623$$ 8.41688i 0.337215i
$$624$$ −1.65831 5.50000i −0.0663856 0.220176i
$$625$$ −14.2665 20.5297i −0.570660 0.821186i
$$626$$ −20.7518 −0.829407
$$627$$ −32.2068 + 4.98156i −1.28622 + 0.198944i
$$628$$ 7.65069i 0.305296i
$$629$$ −6.43949 −0.256759
$$630$$ 9.21116 19.5361i 0.366981 0.778336i
$$631$$ −23.8997 −0.951434 −0.475717 0.879598i $$-0.657811\pi$$
−0.475717 + 0.879598i $$0.657811\pi$$
$$632$$ 15.3014 0.608656
$$633$$ −5.02136 + 1.51400i −0.199581 + 0.0601760i
$$634$$ 17.0000 0.675156
$$635$$ 31.8139 19.2665i 1.26250 0.764568i
$$636$$ −1.65831 + 0.500000i −0.0657564 + 0.0198263i
$$637$$ −11.1662 −0.442423
$$638$$ −35.6393 −1.41097
$$639$$ −25.6621 + 17.0223i −1.01518 + 0.673392i
$$640$$ −1.15831 1.91267i −0.0457863 0.0756050i
$$641$$ −0.191748 −0.00757358 −0.00378679 0.999993i $$-0.501205\pi$$
−0.00378679 + 0.999993i $$0.501205\pi$$
$$642$$ 0.0250628 + 0.0831240i 0.000989150 + 0.00328064i
$$643$$ 0.383495i 0.0151236i 0.999971 + 0.00756179i $$0.00240702\pi$$
−0.999971 + 0.00756179i $$0.997593\pi$$
$$644$$ 22.6834i 0.893850i
$$645$$ 9.91778 11.0062i 0.390512 0.433369i
$$646$$ 1.94987 13.8984i 0.0767168 0.546826i
$$647$$ 0.605599 0.0238086 0.0119043 0.999929i $$-0.496211\pi$$
0.0119043 + 0.999929i $$0.496211\pi$$
$$648$$ −8.29156 3.50000i −0.325723 0.137493i
$$649$$ 24.3550i 0.956018i
$$650$$ 14.6958 + 7.68338i 0.576416 + 0.301367i
$$651$$ −4.20844 13.9578i −0.164942 0.547050i
$$652$$ 1.40295i 0.0549436i
$$653$$ −11.6678 −0.456595 −0.228298 0.973591i $$-0.573316\pi$$
−0.228298 + 0.973591i $$0.573316\pi$$
$$654$$ −3.42667 11.3650i −0.133993 0.444406i
$$655$$ −11.5831 19.1267i −0.452590 0.747343i
$$656$$ −11.4760 −0.448064
$$657$$ 3.01282 + 4.54199i 0.117541 + 0.177200i
$$658$$ −28.5330 −1.11233
$$659$$ 22.1547 0.863025 0.431513 0.902107i $$-0.357980\pi$$
0.431513 + 0.902107i $$0.357980\pi$$
$$660$$ −11.1915 + 12.4197i −0.435629 + 0.483436i
$$661$$ 32.6113i 1.26843i 0.773156 + 0.634216i $$0.218677\pi$$
−0.773156 + 0.634216i $$0.781323\pi$$
$$662$$ −13.4846 −0.524093
$$663$$ −5.33934 17.7086i −0.207363 0.687745i
$$664$$ 6.43949i 0.249901i
$$665$$ −12.3693 28.8417i −0.479659 1.11843i
$$666$$ 3.31662 + 5.00000i 0.128517 + 0.193746i
$$667$$ 58.1662 2.25221
$$668$$ 24.9499i 0.965340i
$$669$$ 1.63325 + 5.41688i 0.0631451 + 0.209429i
$$670$$ −8.10819 13.3887i −0.313247 0.517251i
$$671$$ 10.0000i 0.386046i
$$672$$ 1.60987 + 5.33934i 0.0621022 + 0.205970i
$$673$$ −13.2665 −0.511386 −0.255693 0.966758i $$-0.582304\pi$$
−0.255693 + 0.966758i $$0.582304\pi$$
$$674$$ 28.2164i 1.08685i
$$675$$ 23.9623 10.0404i 0.922308 0.386455i
$$676$$ 2.00000 0.0769231
$$677$$ 46.1662i 1.77431i 0.461469 + 0.887157i $$0.347323\pi$$
−0.461469 + 0.887157i $$0.652677\pi$$
$$678$$ 0.841688 + 2.79156i 0.0323248 + 0.107209i
$$679$$ 10.8401i 0.416004i
$$680$$ −3.72947 6.15831i −0.143019 0.236160i
$$681$$ −33.0831 + 9.97494i −1.26775 + 0.382240i
$$682$$ 11.2843i 0.432097i
$$683$$ 24.0000i 0.918334i −0.888350 0.459167i $$-0.848148\pi$$
0.888350 0.459167i $$-0.151852\pi$$
$$684$$ −11.7958 + 5.64431i −0.451025 + 0.215816i
$$685$$ 6.15831 3.72947i 0.235297 0.142496i
$$686$$ −11.6981 −0.446637
$$687$$ 0 0
$$688$$ 3.82534i 0.145840i
$$689$$ 3.31662i 0.126353i
$$690$$ 18.2654 20.2700i 0.695354 0.771665i
$$691$$ −13.8997 −0.528771 −0.264386 0.964417i $$-0.585169\pi$$
−0.264386 + 0.964417i $$0.585169\pi$$
$$692$$ 13.2665i 0.504317i
$$693$$ 34.7461 23.0479i 1.31989 0.875519i
$$694$$ 20.1462i 0.764738i
$$695$$ −19.1267 + 11.5831i −0.725518 + 0.439373i
$$696$$ −13.6915 + 4.12814i −0.518975 + 0.156477i
$$697$$ −36.9499 −1.39958
$$698$$ 8.63325i 0.326773i
$$699$$ −13.2928 44.0873i −0.502781 1.66754i
$$700$$ −14.2665 7.45894i −0.539223 0.281921i
$$701$$ 37.2665i 1.40754i −0.710430 0.703768i $$-0.751499\pi$$
0.710430 0.703768i $$-0.248501\pi$$
$$702$$ −11.0000 + 13.2665i −0.415168 + 0.500712i
$$703$$ 8.63325 + 1.21120i 0.325609 + 0.0456812i
$$704$$ 4.31662i 0.162689i
$$705$$ −25.4972 22.9758i −0.960281 0.865318i
$$706$$ 23.3659i 0.879388i
$$707$$ 46.0959 1.73361
$$708$$ −2.82107 9.35643i −0.106022 0.351636i
$$709$$ 28.6332 1.07534 0.537672 0.843154i $$-0.319304\pi$$
0.537672 + 0.843154i $$0.319304\pi$$
$$710$$ 11.8899 + 19.6332i 0.446219 + 0.736823i
$$711$$ −25.3745 38.2534i −0.951616 1.43462i
$$712$$ 2.61414i 0.0979692i
$$713$$ 18.4169i 0.689717i
$$714$$ 5.18338 + 17.1913i 0.193983 + 0.643369i
$$715$$ 16.5831 + 27.3830i 0.620174 + 1.02407i
$$716$$ 16.5126 0.617104
$$717$$ −32.5581 + 9.81662i −1.21590 + 0.366609i
$$718$$ −4.89975 −0.182857
$$719$$ 34.8997i 1.30154i 0.759274 + 0.650771i $$0.225554\pi$$
−0.759274 + 0.650771i $$0.774446\pi$$
$$720$$ −2.86084 + 6.06759i −0.106617 + 0.226126i
$$721$$ 56.6132i 2.10838i
$$722$$ −5.22829 + 18.2665i −0.194577 + 0.679809i
$$723$$ −8.67014 + 2.61414i −0.322446 + 0.0972211i
$$724$$ 16.5126i 0.613685i
$$725$$ 19.1267 36.5831i 0.710348 1.35866i
$$726$$ −12.6583 + 3.81662i −0.469794 + 0.141648i
$$727$$ 13.2928i 0.493004i −0.969142 0.246502i $$-0.920719\pi$$
0.969142 0.246502i $$-0.0792811\pi$$
$$728$$ 10.6787 0.395778
$$729$$ 5.00000 + 26.5330i 0.185185 + 0.982704i
$$730$$ 3.47494 2.10442i 0.128613 0.0778881i
$$731$$ 12.3166i 0.455547i
$$732$$ −1.15831 3.84169i −0.0428125 0.141993i
$$733$$ 6.43949i 0.237848i 0.992903 + 0.118924i $$0.0379445\pi$$
−0.992903 + 0.118924i $$0.962056\pi$$
$$734$$ 7.65069 0.282392
$$735$$ 9.68675 + 8.72881i 0.357301 + 0.321967i
$$736$$ 7.04509i 0.259685i
$$737$$ 30.2164i 1.11303i
$$738$$ 19.0308 + 28.6901i 0.700535 + 1.05610i
$$739$$ −10.2164 −0.375815 −0.187908 0.982187i $$-0.560171\pi$$
−0.187908 + 0.982187i $$0.560171\pi$$
$$740$$ 3.82534 2.31662i 0.140622 0.0851608i
$$741$$ 3.82752 + 24.7457i 0.140607 + 0.909056i
$$742$$ 3.21974i 0.118201i
$$743$$ 44.8496i 1.64537i 0.568495 + 0.822687i $$0.307526\pi$$
−0.568495 + 0.822687i $$0.692474\pi$$
$$744$$ 1.30707 + 4.33507i 0.0479196 + 0.158931i
$$745$$ 4.63325 + 7.65069i 0.169749 + 0.280299i
$$746$$ 23.3166i 0.853682i
$$747$$ 16.0987 10.6787i 0.589021 0.390713i
$$748$$ 13.8984i 0.508177i
$$749$$ −0.161392 −0.00589712
$$750$$ −6.74242 18.1532i −0.246198 0.662862i
$$751$$ 24.3550i 0.888727i 0.895847 + 0.444363i $$0.146570\pi$$
−0.895847 + 0.444363i $$0.853430\pi$$
$$752$$ 8.86188 0.323160
$$753$$ 52.3747 15.7916i 1.90864 0.575477i
$$754$$ 27.3830i 0.997230i
$$755$$ 19.1267 + 31.5831i 0.696092 + 1.14943i
$$756$$ 10.6787 12.8790i 0.388380 0.468404i
$$757$$ 12.8790i 0.468094i −0.972225 0.234047i $$-0.924803\pi$$
0.972225 0.234047i $$-0.0751970\pi$$
$$758$$ 36.4366 1.32344
$$759$$ 50.4309 15.2055i 1.83053 0.551925i
$$760$$ 3.84169 + 8.95776i 0.139353 + 0.324932i
$$761$$ 10.6834i 0.387272i −0.981073 0.193636i $$-0.937972\pi$$
0.981073 0.193636i $$-0.0620281\pi$$
$$762$$ 27.5831 8.31662i 0.999231 0.301280i
$$763$$ 22.0660 0.798843
$$764$$ 5.00000i 0.180894i
$$765$$ −9.21116 + 19.5361i −0.333030 + 0.706328i
$$766$$ −7.58312 −0.273989
$$767$$ −18.7129 −0.675682
$$768$$ −0.500000 1.65831i −0.0180422 0.0598392i
$$769$$ −48.1662 −1.73692 −0.868460 0.495760i $$-0.834890\pi$$
−0.868460 + 0.495760i $$0.834890\pi$$
$$770$$ −16.0987 26.5831i −0.580158 0.957989i
$$771$$ −8.20844 + 2.47494i −0.295620 + 0.0891327i
$$772$$ 6.00000 0.215945
$$773$$ 24.1662i 0.869200i 0.900624 + 0.434600i $$0.143110\pi$$
−0.900624 + 0.434600i $$0.856890\pi$$
$$774$$ 9.56336 6.34361i 0.343748 0.228016i
$$775$$ −11.5831 6.05599i −0.416078 0.217538i
$$776$$ 3.36675i 0.120859i
$$777$$ −10.6787 + 3.21974i −0.383096 + 0.115508i
$$778$$ 16.2164 0.581385
$$779$$ 49.5377 + 6.94987i 1.77487 + 0.249005i
$$780$$ 9.54253 + 8.59885i 0.341677 + 0.307888i
$$781$$ 44.3094i