# Properties

 Label 252.2.w.a.5.7 Level $252$ Weight $2$ Character 252.5 Analytic conductor $2.012$ Analytic rank $0$ Dimension $16$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$252 = 2^{2} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 252.w (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$2.01223013094$$ Analytic rank: $$0$$ Dimension: $$16$$ Relative dimension: $$8$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ Defining polynomial: $$x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} - 156 x^{7} + 558 x^{6} - 837 x^{5} + 1782 x^{4} - 4131 x^{3} + 3645 x^{2} - 4374 x + 6561$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$3^{4}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 5.7 Root $$-0.811340 + 1.53027i$$ of defining polynomial Character $$\chi$$ $$=$$ 252.5 Dual form 252.2.w.a.101.7

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.68085 + 0.418028i) q^{3} +(1.37166 + 2.37578i) q^{5} +(-2.60476 + 0.463945i) q^{7} +(2.65051 + 1.40528i) q^{9} +O(q^{10})$$ $$q+(1.68085 + 0.418028i) q^{3} +(1.37166 + 2.37578i) q^{5} +(-2.60476 + 0.463945i) q^{7} +(2.65051 + 1.40528i) q^{9} +(-0.362306 - 0.209178i) q^{11} +(1.32512 + 0.765056i) q^{13} +(1.31241 + 4.56672i) q^{15} +(-1.95291 - 3.38253i) q^{17} +(-5.11994 - 2.95600i) q^{19} +(-4.57214 - 0.309039i) q^{21} +(7.72884 - 4.46225i) q^{23} +(-1.26290 + 2.18740i) q^{25} +(3.86765 + 3.47005i) q^{27} +(6.00378 - 3.46629i) q^{29} +3.52907i q^{31} +(-0.521540 - 0.503050i) q^{33} +(-4.67507 - 5.55196i) q^{35} +(-4.54861 + 7.87842i) q^{37} +(1.90751 + 1.83988i) q^{39} +(1.06236 - 1.84006i) q^{41} +(-5.77846 - 10.0086i) q^{43} +(0.296944 + 8.22460i) q^{45} -1.77075 q^{47} +(6.56951 - 2.41692i) q^{49} +(-1.86855 - 6.50189i) q^{51} +(-3.39526 + 1.96025i) q^{53} -1.14768i q^{55} +(-7.37015 - 7.10886i) q^{57} -4.05456 q^{59} -1.86437i q^{61} +(-7.55590 - 2.43073i) q^{63} +4.19758i q^{65} -12.7688 q^{67} +(14.8564 - 4.26950i) q^{69} -8.51021i q^{71} +(1.65059 - 0.952971i) q^{73} +(-3.03713 + 3.14877i) q^{75} +(1.04077 + 0.376767i) q^{77} -0.867266 q^{79} +(5.05036 + 7.44942i) q^{81} +(3.45880 + 5.99082i) q^{83} +(5.35744 - 9.27936i) q^{85} +(11.5405 - 3.31656i) q^{87} +(-4.88864 + 8.46738i) q^{89} +(-3.80655 - 1.37800i) q^{91} +(-1.47525 + 5.93183i) q^{93} -16.2185i q^{95} +(0.200411 - 0.115707i) q^{97} +(-0.666342 - 1.06357i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$16 q - q^{7} + 6 q^{9} + O(q^{10})$$ $$16 q - q^{7} + 6 q^{9} - 6 q^{11} - 3 q^{13} - 3 q^{15} + 9 q^{17} + 6 q^{21} + 21 q^{23} - 8 q^{25} + 9 q^{27} + 6 q^{29} - 15 q^{35} + q^{37} - 3 q^{39} - 6 q^{41} - 2 q^{43} - 30 q^{45} - 36 q^{47} - 5 q^{49} - 33 q^{51} + 15 q^{57} - 30 q^{59} - 15 q^{63} + 14 q^{67} + 21 q^{69} - 57 q^{75} + 3 q^{77} + 2 q^{79} + 18 q^{81} + 6 q^{85} + 48 q^{87} + 21 q^{89} + 9 q^{91} + 21 q^{93} - 3 q^{97} - 9 q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$$.

 $$n$$ $$29$$ $$73$$ $$127$$ $$\chi(n)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$

## 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 0
$$3$$ 1.68085 + 0.418028i 0.970439 + 0.241348i
$$4$$ 0 0
$$5$$ 1.37166 + 2.37578i 0.613425 + 1.06248i 0.990659 + 0.136365i $$0.0435419\pi$$
−0.377234 + 0.926118i $$0.623125\pi$$
$$6$$ 0 0
$$7$$ −2.60476 + 0.463945i −0.984505 + 0.175355i
$$8$$ 0 0
$$9$$ 2.65051 + 1.40528i 0.883502 + 0.468427i
$$10$$ 0 0
$$11$$ −0.362306 0.209178i −0.109240 0.0630695i 0.444385 0.895836i $$-0.353422\pi$$
−0.553624 + 0.832767i $$0.686756\pi$$
$$12$$ 0 0
$$13$$ 1.32512 + 0.765056i 0.367521 + 0.212188i 0.672375 0.740211i $$-0.265274\pi$$
−0.304854 + 0.952399i $$0.598608\pi$$
$$14$$ 0 0
$$15$$ 1.31241 + 4.56672i 0.338862 + 1.17912i
$$16$$ 0 0
$$17$$ −1.95291 3.38253i −0.473649 0.820385i 0.525896 0.850549i $$-0.323730\pi$$
−0.999545 + 0.0301645i $$0.990397\pi$$
$$18$$ 0 0
$$19$$ −5.11994 2.95600i −1.17459 0.678152i −0.219836 0.975537i $$-0.570552\pi$$
−0.954758 + 0.297385i $$0.903886\pi$$
$$20$$ 0 0
$$21$$ −4.57214 0.309039i −0.997723 0.0674379i
$$22$$ 0 0
$$23$$ 7.72884 4.46225i 1.61157 0.930443i 0.622569 0.782565i $$-0.286089\pi$$
0.989006 0.147878i $$-0.0472444\pi$$
$$24$$ 0 0
$$25$$ −1.26290 + 2.18740i −0.252579 + 0.437480i
$$26$$ 0 0
$$27$$ 3.86765 + 3.47005i 0.744330 + 0.667812i
$$28$$ 0 0
$$29$$ 6.00378 3.46629i 1.11487 0.643673i 0.174787 0.984606i $$-0.444076\pi$$
0.940088 + 0.340933i $$0.110743\pi$$
$$30$$ 0 0
$$31$$ 3.52907i 0.633839i 0.948452 + 0.316920i $$0.102649\pi$$
−0.948452 + 0.316920i $$0.897351\pi$$
$$32$$ 0 0
$$33$$ −0.521540 0.503050i −0.0907885 0.0875698i
$$34$$ 0 0
$$35$$ −4.67507 5.55196i −0.790231 0.938453i
$$36$$ 0 0
$$37$$ −4.54861 + 7.87842i −0.747787 + 1.29520i 0.201095 + 0.979572i $$0.435550\pi$$
−0.948881 + 0.315633i $$0.897783\pi$$
$$38$$ 0 0
$$39$$ 1.90751 + 1.83988i 0.305445 + 0.294616i
$$40$$ 0 0
$$41$$ 1.06236 1.84006i 0.165913 0.287370i −0.771066 0.636755i $$-0.780276\pi$$
0.936979 + 0.349385i $$0.113610\pi$$
$$42$$ 0 0
$$43$$ −5.77846 10.0086i −0.881208 1.52630i −0.850000 0.526783i $$-0.823398\pi$$
−0.0312079 0.999513i $$-0.509935\pi$$
$$44$$ 0 0
$$45$$ 0.296944 + 8.22460i 0.0442659 + 1.22605i
$$46$$ 0 0
$$47$$ −1.77075 −0.258290 −0.129145 0.991626i $$-0.541223\pi$$
−0.129145 + 0.991626i $$0.541223\pi$$
$$48$$ 0 0
$$49$$ 6.56951 2.41692i 0.938502 0.345275i
$$50$$ 0 0
$$51$$ −1.86855 6.50189i −0.261649 0.910447i
$$52$$ 0 0
$$53$$ −3.39526 + 1.96025i −0.466374 + 0.269261i −0.714721 0.699410i $$-0.753446\pi$$
0.248346 + 0.968671i $$0.420113\pi$$
$$54$$ 0 0
$$55$$ 1.14768i 0.154753i
$$56$$ 0 0
$$57$$ −7.37015 7.10886i −0.976200 0.941591i
$$58$$ 0 0
$$59$$ −4.05456 −0.527859 −0.263929 0.964542i $$-0.585019\pi$$
−0.263929 + 0.964542i $$0.585019\pi$$
$$60$$ 0 0
$$61$$ 1.86437i 0.238708i −0.992852 0.119354i $$-0.961918\pi$$
0.992852 0.119354i $$-0.0380823\pi$$
$$62$$ 0 0
$$63$$ −7.55590 2.43073i −0.951953 0.306243i
$$64$$ 0 0
$$65$$ 4.19758i 0.520646i
$$66$$ 0 0
$$67$$ −12.7688 −1.55996 −0.779979 0.625805i $$-0.784770\pi$$
−0.779979 + 0.625805i $$0.784770\pi$$
$$68$$ 0 0
$$69$$ 14.8564 4.26950i 1.78850 0.513987i
$$70$$ 0 0
$$71$$ 8.51021i 1.00998i −0.863126 0.504988i $$-0.831497\pi$$
0.863126 0.504988i $$-0.168503\pi$$
$$72$$ 0 0
$$73$$ 1.65059 0.952971i 0.193187 0.111537i −0.400286 0.916390i $$-0.631089\pi$$
0.593474 + 0.804853i $$0.297756\pi$$
$$74$$ 0 0
$$75$$ −3.03713 + 3.14877i −0.350698 + 0.363588i
$$76$$ 0 0
$$77$$ 1.04077 + 0.376767i 0.118606 + 0.0429366i
$$78$$ 0 0
$$79$$ −0.867266 −0.0975750 −0.0487875 0.998809i $$-0.515536\pi$$
−0.0487875 + 0.998809i $$0.515536\pi$$
$$80$$ 0 0
$$81$$ 5.05036 + 7.44942i 0.561151 + 0.827713i
$$82$$ 0 0
$$83$$ 3.45880 + 5.99082i 0.379653 + 0.657578i 0.991012 0.133775i $$-0.0427100\pi$$
−0.611359 + 0.791354i $$0.709377\pi$$
$$84$$ 0 0
$$85$$ 5.35744 9.27936i 0.581096 1.00649i
$$86$$ 0 0
$$87$$ 11.5405 3.31656i 1.23727 0.355572i
$$88$$ 0 0
$$89$$ −4.88864 + 8.46738i −0.518195 + 0.897540i 0.481581 + 0.876401i $$0.340063\pi$$
−0.999777 + 0.0211389i $$0.993271\pi$$
$$90$$ 0 0
$$91$$ −3.80655 1.37800i −0.399035 0.144454i
$$92$$ 0 0
$$93$$ −1.47525 + 5.93183i −0.152976 + 0.615102i
$$94$$ 0 0
$$95$$ 16.2185i 1.66398i
$$96$$ 0 0
$$97$$ 0.200411 0.115707i 0.0203486 0.0117483i −0.489791 0.871840i $$-0.662927\pi$$
0.510140 + 0.860091i $$0.329594\pi$$
$$98$$ 0 0
$$99$$ −0.666342 1.06357i −0.0669699 0.106893i
$$100$$ 0 0
$$101$$ −7.14031 + 12.3674i −0.710487 + 1.23060i 0.254187 + 0.967155i $$0.418192\pi$$
−0.964674 + 0.263445i $$0.915141\pi$$
$$102$$ 0 0
$$103$$ −9.30617 + 5.37292i −0.916964 + 0.529410i −0.882665 0.470002i $$-0.844253\pi$$
−0.0342991 + 0.999412i $$0.510920\pi$$
$$104$$ 0 0
$$105$$ −5.53721 11.2863i −0.540376 1.10143i
$$106$$ 0 0
$$107$$ −5.50534 3.17851i −0.532221 0.307278i 0.209699 0.977766i $$-0.432751\pi$$
−0.741920 + 0.670488i $$0.766085\pi$$
$$108$$ 0 0
$$109$$ 2.58036 + 4.46932i 0.247154 + 0.428083i 0.962735 0.270447i $$-0.0871714\pi$$
−0.715581 + 0.698530i $$0.753838\pi$$
$$110$$ 0 0
$$111$$ −10.9389 + 11.3410i −1.03828 + 1.07644i
$$112$$ 0 0
$$113$$ 9.19186 + 5.30692i 0.864697 + 0.499233i 0.865582 0.500766i $$-0.166948\pi$$
−0.000885276 1.00000i $$0.500282\pi$$
$$114$$ 0 0
$$115$$ 21.2027 + 12.2414i 1.97716 + 1.14151i
$$116$$ 0 0
$$117$$ 2.43711 + 3.88995i 0.225311 + 0.359626i
$$118$$ 0 0
$$119$$ 6.65615 + 7.90463i 0.610168 + 0.724616i
$$120$$ 0 0
$$121$$ −5.41249 9.37471i −0.492044 0.852246i
$$122$$ 0 0
$$123$$ 2.55487 2.64877i 0.230365 0.238832i
$$124$$ 0 0
$$125$$ 6.78753 0.607096
$$126$$ 0 0
$$127$$ 10.2909 0.913169 0.456584 0.889680i $$-0.349073\pi$$
0.456584 + 0.889680i $$0.349073\pi$$
$$128$$ 0 0
$$129$$ −5.52886 19.2385i −0.486789 1.69385i
$$130$$ 0 0
$$131$$ 9.83048 + 17.0269i 0.858893 + 1.48765i 0.872986 + 0.487746i $$0.162181\pi$$
−0.0140928 + 0.999901i $$0.504486\pi$$
$$132$$ 0 0
$$133$$ 14.7076 + 5.32428i 1.27531 + 0.461674i
$$134$$ 0 0
$$135$$ −2.93899 + 13.9484i −0.252948 + 1.20049i
$$136$$ 0 0
$$137$$ −4.66411 2.69282i −0.398481 0.230063i 0.287347 0.957827i $$-0.407227\pi$$
−0.685829 + 0.727763i $$0.740560\pi$$
$$138$$ 0 0
$$139$$ 14.7839 + 8.53549i 1.25395 + 0.723971i 0.971892 0.235425i $$-0.0756484\pi$$
0.282062 + 0.959396i $$0.408982\pi$$
$$140$$ 0 0
$$141$$ −2.97636 0.740221i −0.250655 0.0623379i
$$142$$ 0 0
$$143$$ −0.320065 0.554369i −0.0267652 0.0463587i
$$144$$ 0 0
$$145$$ 16.4703 + 9.50912i 1.36778 + 0.789690i
$$146$$ 0 0
$$147$$ 12.0527 1.31625i 0.994090 0.108562i
$$148$$ 0 0
$$149$$ 9.31162 5.37607i 0.762838 0.440425i −0.0674758 0.997721i $$-0.521495\pi$$
0.830314 + 0.557296i $$0.188161\pi$$
$$150$$ 0 0
$$151$$ −3.78223 + 6.55102i −0.307794 + 0.533115i −0.977879 0.209169i $$-0.932924\pi$$
0.670086 + 0.742284i $$0.266257\pi$$
$$152$$ 0 0
$$153$$ −0.422776 11.7098i −0.0341794 0.946682i
$$154$$ 0 0
$$155$$ −8.38430 + 4.84068i −0.673443 + 0.388812i
$$156$$ 0 0
$$157$$ 12.2764i 0.979763i 0.871789 + 0.489882i $$0.162960\pi$$
−0.871789 + 0.489882i $$0.837040\pi$$
$$158$$ 0 0
$$159$$ −6.52635 + 1.87558i −0.517573 + 0.148743i
$$160$$ 0 0
$$161$$ −18.0615 + 15.2088i −1.42345 + 1.19862i
$$162$$ 0 0
$$163$$ 5.91745 10.2493i 0.463490 0.802789i −0.535642 0.844445i $$-0.679930\pi$$
0.999132 + 0.0416566i $$0.0132635\pi$$
$$164$$ 0 0
$$165$$ 0.479763 1.92908i 0.0373495 0.150179i
$$166$$ 0 0
$$167$$ 6.78854 11.7581i 0.525313 0.909869i −0.474252 0.880389i $$-0.657282\pi$$
0.999565 0.0294798i $$-0.00938508\pi$$
$$168$$ 0 0
$$169$$ −5.32938 9.23075i −0.409952 0.710058i
$$170$$ 0 0
$$171$$ −9.41641 15.0298i −0.720091 1.14936i
$$172$$ 0 0
$$173$$ −16.6217 −1.26372 −0.631862 0.775081i $$-0.717709\pi$$
−0.631862 + 0.775081i $$0.717709\pi$$
$$174$$ 0 0
$$175$$ 2.27471 6.28356i 0.171952 0.474993i
$$176$$ 0 0
$$177$$ −6.81510 1.69492i −0.512254 0.127398i
$$178$$ 0 0
$$179$$ 14.8080 8.54942i 1.10680 0.639014i 0.168805 0.985650i $$-0.446009\pi$$
0.938000 + 0.346636i $$0.112676\pi$$
$$180$$ 0 0
$$181$$ 18.2171i 1.35407i −0.735952 0.677034i $$-0.763265\pi$$
0.735952 0.677034i $$-0.236735\pi$$
$$182$$ 0 0
$$183$$ 0.779357 3.13372i 0.0576117 0.231651i
$$184$$ 0 0
$$185$$ −24.9566 −1.83484
$$186$$ 0 0
$$187$$ 1.63402i 0.119491i
$$188$$ 0 0
$$189$$ −11.6842 7.24426i −0.849901 0.526943i
$$190$$ 0 0
$$191$$ 20.9994i 1.51946i 0.650239 + 0.759730i $$0.274669\pi$$
−0.650239 + 0.759730i $$0.725331\pi$$
$$192$$ 0 0
$$193$$ −6.97483 −0.502059 −0.251030 0.967979i $$-0.580769\pi$$
−0.251030 + 0.967979i $$0.580769\pi$$
$$194$$ 0 0
$$195$$ −1.75471 + 7.05550i −0.125657 + 0.505255i
$$196$$ 0 0
$$197$$ 16.0756i 1.14534i 0.819786 + 0.572670i $$0.194092\pi$$
−0.819786 + 0.572670i $$0.805908\pi$$
$$198$$ 0 0
$$199$$ −5.44956 + 3.14630i −0.386309 + 0.223036i −0.680560 0.732693i $$-0.738263\pi$$
0.294251 + 0.955728i $$0.404930\pi$$
$$200$$ 0 0
$$201$$ −21.4624 5.33772i −1.51384 0.376493i
$$202$$ 0 0
$$203$$ −14.0302 + 11.8143i −0.984729 + 0.829198i
$$204$$ 0 0
$$205$$ 5.82879 0.407100
$$206$$ 0 0
$$207$$ 26.7561 0.966012i 1.85967 0.0671425i
$$208$$ 0 0
$$209$$ 1.23666 + 2.14195i 0.0855414 + 0.148162i
$$210$$ 0 0
$$211$$ −1.29814 + 2.24844i −0.0893674 + 0.154789i −0.907244 0.420605i $$-0.861818\pi$$
0.817876 + 0.575394i $$0.195151\pi$$
$$212$$ 0 0
$$213$$ 3.55750 14.3044i 0.243756 0.980120i
$$214$$ 0 0
$$215$$ 15.8522 27.4568i 1.08111 1.87254i
$$216$$ 0 0
$$217$$ −1.63729 9.19236i −0.111147 0.624018i
$$218$$ 0 0
$$219$$ 3.17277 0.911807i 0.214396 0.0616142i
$$220$$ 0 0
$$221$$ 5.97633i 0.402011i
$$222$$ 0 0
$$223$$ −20.7215 + 11.9636i −1.38762 + 0.801141i −0.993046 0.117725i $$-0.962440\pi$$
−0.394571 + 0.918866i $$0.629107\pi$$
$$224$$ 0 0
$$225$$ −6.42123 + 4.02299i −0.428082 + 0.268200i
$$226$$ 0 0
$$227$$ −1.86609 + 3.23216i −0.123857 + 0.214526i −0.921285 0.388887i $$-0.872860\pi$$
0.797429 + 0.603413i $$0.206193\pi$$
$$228$$ 0 0
$$229$$ 18.2455 10.5341i 1.20570 0.696111i 0.243882 0.969805i $$-0.421579\pi$$
0.961817 + 0.273694i $$0.0882457\pi$$
$$230$$ 0 0
$$231$$ 1.59187 + 1.06836i 0.104738 + 0.0702928i
$$232$$ 0 0
$$233$$ −11.0542 6.38215i −0.724186 0.418109i 0.0921057 0.995749i $$-0.470640\pi$$
−0.816291 + 0.577640i $$0.803974\pi$$
$$234$$ 0 0
$$235$$ −2.42886 4.20691i −0.158441 0.274429i
$$236$$ 0 0
$$237$$ −1.45774 0.362541i −0.0946905 0.0235496i
$$238$$ 0 0
$$239$$ 11.0521 + 6.38091i 0.714899 + 0.412747i 0.812872 0.582442i $$-0.197903\pi$$
−0.0979736 + 0.995189i $$0.531236\pi$$
$$240$$ 0 0
$$241$$ −2.63438 1.52096i −0.169695 0.0979737i 0.412747 0.910846i $$-0.364569\pi$$
−0.582442 + 0.812872i $$0.697903\pi$$
$$242$$ 0 0
$$243$$ 5.37484 + 14.6325i 0.344796 + 0.938678i
$$244$$ 0 0
$$245$$ 14.7532 + 12.2925i 0.942549 + 0.785341i
$$246$$ 0 0
$$247$$ −4.52301 7.83408i −0.287792 0.498470i
$$248$$ 0 0
$$249$$ 3.30940 + 11.5155i 0.209725 + 0.729768i
$$250$$ 0 0
$$251$$ −6.32067 −0.398957 −0.199478 0.979902i $$-0.563925\pi$$
−0.199478 + 0.979902i $$0.563925\pi$$
$$252$$ 0 0
$$253$$ −3.73361 −0.234730
$$254$$ 0 0
$$255$$ 12.8841 13.3576i 0.806832 0.836488i
$$256$$ 0 0
$$257$$ −12.2538 21.2242i −0.764372 1.32393i −0.940578 0.339577i $$-0.889716\pi$$
0.176206 0.984353i $$-0.443617\pi$$
$$258$$ 0 0
$$259$$ 8.19287 22.6317i 0.509080 1.40626i
$$260$$ 0 0
$$261$$ 20.7842 0.750401i 1.28651 0.0464486i
$$262$$ 0 0
$$263$$ −21.1163 12.1915i −1.30208 0.751759i −0.321323 0.946970i $$-0.604128\pi$$
−0.980761 + 0.195211i $$0.937461\pi$$
$$264$$ 0 0
$$265$$ −9.31427 5.37760i −0.572171 0.330343i
$$266$$ 0 0
$$267$$ −11.7567 + 12.1888i −0.719496 + 0.745942i
$$268$$ 0 0
$$269$$ 4.94525 + 8.56542i 0.301517 + 0.522243i 0.976480 0.215609i $$-0.0691737\pi$$
−0.674963 + 0.737852i $$0.735840\pi$$
$$270$$ 0 0
$$271$$ −5.10505 2.94740i −0.310110 0.179042i 0.336866 0.941553i $$-0.390633\pi$$
−0.646976 + 0.762511i $$0.723966\pi$$
$$272$$ 0 0
$$273$$ −5.82219 3.90746i −0.352375 0.236490i
$$274$$ 0 0
$$275$$ 0.915111 0.528340i 0.0551833 0.0318601i
$$276$$ 0 0
$$277$$ −11.6469 + 20.1731i −0.699796 + 1.21208i 0.268741 + 0.963213i $$0.413392\pi$$
−0.968537 + 0.248870i $$0.919941\pi$$
$$278$$ 0 0
$$279$$ −4.95933 + 9.35381i −0.296908 + 0.559998i
$$280$$ 0 0
$$281$$ 21.7962 12.5840i 1.30025 0.750700i 0.319803 0.947484i $$-0.396383\pi$$
0.980447 + 0.196784i $$0.0630499\pi$$
$$282$$ 0 0
$$283$$ 9.96439i 0.592322i 0.955138 + 0.296161i $$0.0957064\pi$$
−0.955138 + 0.296161i $$0.904294\pi$$
$$284$$ 0 0
$$285$$ 6.77977 27.2608i 0.401599 1.61479i
$$286$$ 0 0
$$287$$ −1.91350 + 5.28579i −0.112951 + 0.312011i
$$288$$ 0 0
$$289$$ 0.872317 1.51090i 0.0513128 0.0888764i
$$290$$ 0 0
$$291$$ 0.385229 0.110709i 0.0225825 0.00648989i
$$292$$ 0 0
$$293$$ −6.79065 + 11.7618i −0.396714 + 0.687129i −0.993318 0.115406i $$-0.963183\pi$$
0.596604 + 0.802536i $$0.296516\pi$$
$$294$$ 0 0
$$295$$ −5.56147 9.63275i −0.323801 0.560841i
$$296$$ 0 0
$$297$$ −0.675418 2.06625i −0.0391917 0.119896i
$$298$$ 0 0
$$299$$ 13.6555 0.789717
$$300$$ 0 0
$$301$$ 19.6949 + 23.3891i 1.13520 + 1.34812i
$$302$$ 0 0
$$303$$ −17.1717 + 17.8028i −0.986487 + 1.02275i
$$304$$ 0 0
$$305$$ 4.42933 2.55728i 0.253623 0.146429i
$$306$$ 0 0
$$307$$ 16.9849i 0.969381i 0.874686 + 0.484691i $$0.161068\pi$$
−0.874686 + 0.484691i $$0.838932\pi$$
$$308$$ 0 0
$$309$$ −17.8883 + 5.14083i −1.01763 + 0.292452i
$$310$$ 0 0
$$311$$ 0.00297881 0.000168913 8.44563e−5 1.00000i $$-0.499973\pi$$
8.44563e−5 1.00000i $$0.499973\pi$$
$$312$$ 0 0
$$313$$ 12.2576i 0.692838i −0.938080 0.346419i $$-0.887398\pi$$
0.938080 0.346419i $$-0.112602\pi$$
$$314$$ 0 0
$$315$$ −4.58922 21.2853i −0.258573 1.19929i
$$316$$ 0 0
$$317$$ 23.0950i 1.29714i −0.761154 0.648571i $$-0.775367\pi$$
0.761154 0.648571i $$-0.224633\pi$$
$$318$$ 0 0
$$319$$ −2.90028 −0.162384
$$320$$ 0 0
$$321$$ −7.92494 7.64397i −0.442327 0.426645i
$$322$$ 0 0
$$323$$ 23.0911i 1.28482i
$$324$$ 0 0
$$325$$ −3.34697 + 1.93237i −0.185656 + 0.107189i
$$326$$ 0 0
$$327$$ 2.46890 + 8.59091i 0.136530 + 0.475078i
$$328$$ 0 0
$$329$$ 4.61236 0.821528i 0.254288 0.0452923i
$$330$$ 0 0
$$331$$ −3.46213 −0.190296 −0.0951479 0.995463i $$-0.530332\pi$$
−0.0951479 + 0.995463i $$0.530332\pi$$
$$332$$ 0 0
$$333$$ −23.1275 + 14.4897i −1.26738 + 0.794032i
$$334$$ 0 0
$$335$$ −17.5145 30.3359i −0.956917 1.65743i
$$336$$ 0 0
$$337$$ −9.13018 + 15.8139i −0.497352 + 0.861440i −0.999995 0.00305455i $$-0.999028\pi$$
0.502643 + 0.864494i $$0.332361\pi$$
$$338$$ 0 0
$$339$$ 13.2317 + 12.7626i 0.718646 + 0.693168i
$$340$$ 0 0
$$341$$ 0.738202 1.27860i 0.0399759 0.0692403i
$$342$$ 0 0
$$343$$ −15.9907 + 9.34339i −0.863414 + 0.504496i
$$344$$ 0 0
$$345$$ 30.5213 + 29.4392i 1.64321 + 1.58495i
$$346$$ 0 0
$$347$$ 5.33917i 0.286622i −0.989678 0.143311i $$-0.954225\pi$$
0.989678 0.143311i $$-0.0457749\pi$$
$$348$$ 0 0
$$349$$ −0.0136817 + 0.00789914i −0.000732365 + 0.000422831i −0.500366 0.865814i $$-0.666801\pi$$
0.499634 + 0.866237i $$0.333468\pi$$
$$350$$ 0 0
$$351$$ 2.47030 + 7.55719i 0.131855 + 0.403373i
$$352$$ 0 0
$$353$$ 17.1543 29.7121i 0.913029 1.58141i 0.103268 0.994654i $$-0.467070\pi$$
0.809761 0.586760i $$-0.199597\pi$$
$$354$$ 0 0
$$355$$ 20.2184 11.6731i 1.07308 0.619544i
$$356$$ 0 0
$$357$$ 7.88363 + 16.0689i 0.417246 + 0.850459i
$$358$$ 0 0
$$359$$ −5.42754 3.13359i −0.286454 0.165385i 0.349887 0.936792i $$-0.386220\pi$$
−0.636342 + 0.771407i $$0.719553\pi$$
$$360$$ 0 0
$$361$$ 7.97583 + 13.8145i 0.419781 + 0.727081i
$$362$$ 0 0
$$363$$ −5.17869 18.0200i −0.271811 0.945807i
$$364$$ 0 0
$$365$$ 4.52811 + 2.61430i 0.237012 + 0.136839i
$$366$$ 0 0
$$367$$ 16.4888 + 9.51984i 0.860711 + 0.496931i 0.864250 0.503062i $$-0.167793\pi$$
−0.00353959 + 0.999994i $$0.501127\pi$$
$$368$$ 0 0
$$369$$ 5.40160 3.38418i 0.281196 0.176174i
$$370$$ 0 0
$$371$$ 7.93437 6.68119i 0.411932 0.346870i
$$372$$ 0 0
$$373$$ −5.41901 9.38600i −0.280586 0.485989i 0.690943 0.722909i $$-0.257195\pi$$
−0.971529 + 0.236920i $$0.923862\pi$$
$$374$$ 0 0
$$375$$ 11.4088 + 2.83738i 0.589149 + 0.146521i
$$376$$ 0 0
$$377$$ 10.6076 0.546320
$$378$$ 0 0
$$379$$ 0.700312 0.0359726 0.0179863 0.999838i $$-0.494274\pi$$
0.0179863 + 0.999838i $$0.494274\pi$$
$$380$$ 0 0
$$381$$ 17.2974 + 4.30188i 0.886174 + 0.220392i
$$382$$ 0 0
$$383$$ 19.0235 + 32.9497i 0.972056 + 1.68365i 0.689327 + 0.724451i $$0.257906\pi$$
0.282729 + 0.959200i $$0.408760\pi$$
$$384$$ 0 0
$$385$$ 0.532461 + 2.98943i 0.0271367 + 0.152356i
$$386$$ 0 0
$$387$$ −1.25095 34.6482i −0.0635896 1.76127i
$$388$$ 0 0
$$389$$ 16.6958 + 9.63934i 0.846512 + 0.488734i 0.859473 0.511182i $$-0.170792\pi$$
−0.0129603 + 0.999916i $$0.504125\pi$$
$$390$$ 0 0
$$391$$ −30.1874 17.4287i −1.52664 0.881407i
$$392$$ 0 0
$$393$$ 9.40584 + 32.7290i 0.474462 + 1.65096i
$$394$$ 0 0
$$395$$ −1.18959 2.06044i −0.0598549 0.103672i
$$396$$ 0 0
$$397$$ −17.3610 10.0234i −0.871325 0.503059i −0.00353639 0.999994i $$-0.501126\pi$$
−0.867788 + 0.496934i $$0.834459\pi$$
$$398$$ 0 0
$$399$$ 22.4956 + 15.0975i 1.12619 + 0.755820i
$$400$$ 0 0
$$401$$ 26.4232 15.2554i 1.31951 0.761820i 0.335861 0.941912i $$-0.390973\pi$$
0.983650 + 0.180092i $$0.0576395\pi$$
$$402$$ 0 0
$$403$$ −2.69993 + 4.67642i −0.134493 + 0.232949i
$$404$$ 0 0
$$405$$ −10.7708 + 22.2166i −0.535207 + 1.10395i
$$406$$ 0 0
$$407$$ 3.29598 1.90294i 0.163376 0.0943250i
$$408$$ 0 0
$$409$$ 0.173933i 0.00860045i 0.999991 + 0.00430023i $$0.00136881\pi$$
−0.999991 + 0.00430023i $$0.998631\pi$$
$$410$$ 0 0
$$411$$ −6.71398 6.47595i −0.331176 0.319435i
$$412$$ 0 0
$$413$$ 10.5611 1.88109i 0.519680 0.0925624i
$$414$$ 0 0
$$415$$ −9.48860 + 16.4347i −0.465777 + 0.806749i
$$416$$ 0 0
$$417$$ 21.2814 + 20.5269i 1.04216 + 1.00521i
$$418$$ 0 0
$$419$$ −14.0690 + 24.3682i −0.687316 + 1.19047i 0.285387 + 0.958412i $$0.407878\pi$$
−0.972703 + 0.232054i $$0.925455\pi$$
$$420$$ 0 0
$$421$$ −1.56130 2.70424i −0.0760929 0.131797i 0.825468 0.564449i $$-0.190911\pi$$
−0.901561 + 0.432652i $$0.857578\pi$$
$$422$$ 0 0
$$423$$ −4.69337 2.48840i −0.228200 0.120990i
$$424$$ 0 0
$$425$$ 9.86527 0.478536
$$426$$ 0 0
$$427$$ 0.864963 + 4.85622i 0.0418585 + 0.235009i
$$428$$ 0 0
$$429$$ −0.306240 1.06561i −0.0147854 0.0514480i
$$430$$ 0 0
$$431$$ 8.58876 4.95872i 0.413706 0.238853i −0.278675 0.960385i $$-0.589895\pi$$
0.692381 + 0.721532i $$0.256562\pi$$
$$432$$ 0 0
$$433$$ 17.1274i 0.823092i 0.911389 + 0.411546i $$0.135011\pi$$
−0.911389 + 0.411546i $$0.864989\pi$$
$$434$$ 0 0
$$435$$ 23.7090 + 22.8684i 1.13676 + 1.09646i
$$436$$ 0 0
$$437$$ −52.7616 −2.52393
$$438$$ 0 0
$$439$$ 21.4537i 1.02393i −0.859006 0.511965i $$-0.828918\pi$$
0.859006 0.511965i $$-0.171082\pi$$
$$440$$ 0 0
$$441$$ 20.8090 + 2.82594i 0.990904 + 0.134569i
$$442$$ 0 0
$$443$$ 6.74738i 0.320578i 0.987070 + 0.160289i $$0.0512425\pi$$
−0.987070 + 0.160289i $$0.948757\pi$$
$$444$$ 0 0
$$445$$ −26.8222 −1.27149
$$446$$ 0 0
$$447$$ 17.8988 5.14384i 0.846583 0.243295i
$$448$$ 0 0
$$449$$ 5.81624i 0.274485i 0.990537 + 0.137243i $$0.0438240\pi$$
−0.990537 + 0.137243i $$0.956176\pi$$
$$450$$ 0 0
$$451$$ −0.769801 + 0.444445i −0.0362485 + 0.0209281i
$$452$$ 0 0
$$453$$ −9.09587 + 9.43020i −0.427361 + 0.443069i
$$454$$ 0 0
$$455$$ −1.94745 10.9337i −0.0912977 0.512579i
$$456$$ 0 0
$$457$$ −33.3898 −1.56191 −0.780954 0.624588i $$-0.785267\pi$$
−0.780954 + 0.624588i $$0.785267\pi$$
$$458$$ 0 0
$$459$$ 4.18440 19.8591i 0.195311 0.926946i
$$460$$ 0 0
$$461$$ −18.5154 32.0696i −0.862347 1.49363i −0.869657 0.493656i $$-0.835660\pi$$
0.00730959 0.999973i $$-0.497673\pi$$
$$462$$ 0 0
$$463$$ 10.5618 18.2935i 0.490848 0.850173i −0.509097 0.860709i $$-0.670020\pi$$
0.999944 + 0.0105362i $$0.00335383\pi$$
$$464$$ 0 0
$$465$$ −16.1163 + 4.63158i −0.747374 + 0.214784i
$$466$$ 0 0
$$467$$ 9.30470 16.1162i 0.430570 0.745770i −0.566352 0.824163i $$-0.691646\pi$$
0.996922 + 0.0783937i $$0.0249791\pi$$
$$468$$ 0 0
$$469$$ 33.2596 5.92402i 1.53579 0.273546i
$$470$$ 0 0
$$471$$ −5.13187 + 20.6348i −0.236464 + 0.950800i
$$472$$ 0 0
$$473$$ 4.83490i 0.222309i
$$474$$ 0 0
$$475$$ 12.9319 7.46624i 0.593356 0.342574i
$$476$$ 0 0
$$477$$ −11.7539 + 0.424366i −0.538172 + 0.0194304i
$$478$$ 0 0
$$479$$ 7.16703 12.4137i 0.327470 0.567194i −0.654539 0.756028i $$-0.727137\pi$$
0.982009 + 0.188834i $$0.0604707\pi$$
$$480$$ 0 0
$$481$$ −12.0549 + 6.95988i −0.549655 + 0.317343i
$$482$$ 0 0
$$483$$ −36.7164 + 18.0135i −1.67065 + 0.819644i
$$484$$ 0 0
$$485$$ 0.549791 + 0.317422i 0.0249647 + 0.0144134i
$$486$$ 0 0
$$487$$ −5.64829 9.78313i −0.255949 0.443316i 0.709204 0.705003i $$-0.249054\pi$$
−0.965153 + 0.261687i $$0.915721\pi$$
$$488$$ 0 0
$$489$$ 14.2308 14.7539i 0.643541 0.667195i
$$490$$ 0 0
$$491$$ −8.84097 5.10434i −0.398988 0.230356i 0.287059 0.957913i $$-0.407322\pi$$
−0.686047 + 0.727557i $$0.740656\pi$$
$$492$$ 0 0
$$493$$ −23.4496 13.5387i −1.05612 0.609751i
$$494$$ 0 0
$$495$$ 1.61282 3.04194i 0.0724907 0.136725i
$$496$$ 0 0
$$497$$ 3.94827 + 22.1670i 0.177104 + 0.994327i
$$498$$ 0 0
$$499$$ 9.56672 + 16.5701i 0.428265 + 0.741777i 0.996719 0.0809379i $$-0.0257915\pi$$
−0.568454 + 0.822715i $$0.692458\pi$$
$$500$$ 0 0
$$501$$ 16.3257 16.9258i 0.729379 0.756188i
$$502$$ 0 0
$$503$$ 0.268917 0.0119904 0.00599520 0.999982i $$-0.498092\pi$$
0.00599520 + 0.999982i $$0.498092\pi$$
$$504$$ 0 0
$$505$$ −39.1763 −1.74332
$$506$$ 0 0
$$507$$ −5.09917 17.7433i −0.226462 0.788009i
$$508$$ 0 0
$$509$$ 10.9439 + 18.9553i 0.485079 + 0.840181i 0.999853 0.0171449i $$-0.00545767\pi$$
−0.514774 + 0.857326i $$0.672124\pi$$
$$510$$ 0 0
$$511$$ −3.85727 + 3.24804i −0.170636 + 0.143685i
$$512$$ 0 0
$$513$$ −9.54468 29.1992i −0.421408 1.28918i
$$514$$ 0 0
$$515$$ −25.5298 14.7396i −1.12498 0.649506i
$$516$$ 0 0
$$517$$ 0.641553 + 0.370401i 0.0282155 + 0.0162902i
$$518$$ 0 0
$$519$$ −27.9386 6.94833i −1.22637 0.304998i
$$520$$ 0 0
$$521$$ 0.856074 + 1.48276i 0.0375053 + 0.0649610i 0.884169 0.467168i $$-0.154726\pi$$
−0.846663 + 0.532129i $$0.821392\pi$$
$$522$$ 0 0
$$523$$ 7.16320 + 4.13568i 0.313225 + 0.180841i 0.648369 0.761326i $$-0.275452\pi$$
−0.335144 + 0.942167i $$0.608785\pi$$
$$524$$ 0 0
$$525$$ 6.45014 9.61083i 0.281507 0.419451i
$$526$$ 0 0
$$527$$ 11.9372 6.89193i 0.519992 0.300217i
$$528$$ 0 0
$$529$$ 28.3233 49.0574i 1.23145 2.13293i
$$530$$ 0 0
$$531$$ −10.7466 5.69780i −0.466364 0.247263i
$$532$$ 0 0
$$533$$ 2.81550 1.62553i 0.121953 0.0704096i
$$534$$ 0 0
$$535$$ 17.4393i 0.753967i
$$536$$ 0 0
$$537$$ 28.4640 8.18012i 1.22831 0.352998i
$$538$$ 0 0
$$539$$ −2.88574 0.498528i −0.124298 0.0214731i
$$540$$ 0 0
$$541$$ −10.1997 + 17.6664i −0.438518 + 0.759536i −0.997575 0.0695932i $$-0.977830\pi$$
0.559057 + 0.829129i $$0.311163\pi$$
$$542$$ 0 0
$$543$$ 7.61526 30.6202i 0.326802 1.31404i
$$544$$ 0 0
$$545$$ −7.07875 + 12.2608i −0.303220 + 0.525193i
$$546$$ 0 0
$$547$$ 18.9630 + 32.8449i 0.810801 + 1.40435i 0.912304 + 0.409513i $$0.134301\pi$$
−0.101503 + 0.994835i $$0.532365\pi$$
$$548$$ 0 0
$$549$$ 2.61996 4.94152i 0.111817 0.210899i
$$550$$ 0 0
$$551$$ −40.9853 −1.74603
$$552$$ 0 0
$$553$$ 2.25902 0.402363i 0.0960631 0.0171102i
$$554$$ 0 0
$$555$$ −41.9482 10.4325i −1.78060 0.442836i
$$556$$ 0 0
$$557$$ 14.5919 8.42463i 0.618278 0.356963i −0.157920 0.987452i $$-0.550479\pi$$
0.776198 + 0.630489i $$0.217146\pi$$
$$558$$ 0 0
$$559$$ 17.6834i 0.747928i
$$560$$ 0 0
$$561$$ −0.683064 + 2.74654i −0.0288390 + 0.115959i
$$562$$ 0 0
$$563$$ −16.5607 −0.697950 −0.348975 0.937132i $$-0.613470\pi$$
−0.348975 + 0.937132i $$0.613470\pi$$
$$564$$ 0 0
$$565$$ 29.1171i 1.22497i
$$566$$ 0 0
$$567$$ −16.6111 17.0608i −0.697600 0.716488i
$$568$$ 0 0
$$569$$ 6.34919i 0.266172i 0.991104 + 0.133086i $$0.0424886\pi$$
−0.991104 + 0.133086i $$0.957511\pi$$
$$570$$ 0 0
$$571$$ 45.7406 1.91418 0.957092 0.289785i $$-0.0935838\pi$$
0.957092 + 0.289785i $$0.0935838\pi$$
$$572$$ 0 0
$$573$$ −8.77831 + 35.2967i −0.366719 + 1.47454i
$$574$$ 0 0
$$575$$ 22.5414i 0.940043i
$$576$$ 0 0
$$577$$ 15.3719 8.87497i 0.639940 0.369470i −0.144651 0.989483i $$-0.546206\pi$$
0.784592 + 0.620013i $$0.212873\pi$$
$$578$$ 0 0
$$579$$ −11.7236 2.91567i −0.487218 0.121171i
$$580$$ 0 0
$$581$$ −11.7888 13.9999i −0.489080 0.580815i
$$582$$ 0 0
$$583$$ 1.64016 0.0679287
$$584$$ 0 0
$$585$$ −5.89879 + 11.1257i −0.243885 + 0.459992i
$$586$$ 0 0
$$587$$ 4.41148 + 7.64091i 0.182081 + 0.315374i 0.942589 0.333955i $$-0.108383\pi$$
−0.760508 + 0.649329i $$0.775050\pi$$
$$588$$ 0 0
$$589$$ 10.4319 18.0686i 0.429839 0.744503i
$$590$$ 0 0
$$591$$ −6.72005 + 27.0207i −0.276426 + 1.11148i
$$592$$ 0 0
$$593$$ 4.24849 7.35860i 0.174465 0.302181i −0.765511 0.643422i $$-0.777514\pi$$
0.939976 + 0.341241i $$0.110847\pi$$
$$594$$ 0 0
$$595$$ −9.64972 + 26.6560i −0.395600 + 1.09279i
$$596$$ 0 0
$$597$$ −10.4751 + 3.01040i −0.428718 + 0.123207i
$$598$$ 0 0
$$599$$ 3.70842i 0.151522i −0.997126 0.0757609i $$-0.975861\pi$$
0.997126 0.0757609i $$-0.0241386\pi$$
$$600$$ 0 0
$$601$$ 6.14043 3.54518i 0.250473 0.144611i −0.369508 0.929228i $$-0.620474\pi$$
0.619981 + 0.784617i $$0.287140\pi$$
$$602$$ 0 0
$$603$$ −33.8438 17.9438i −1.37823 0.730727i
$$604$$ 0 0
$$605$$ 14.8482 25.7178i 0.603664 1.04558i
$$606$$ 0 0
$$607$$ −29.4396 + 16.9970i −1.19492 + 0.689886i −0.959418 0.281988i $$-0.909006\pi$$
−0.235500 + 0.971874i $$0.575673\pi$$
$$608$$ 0 0
$$609$$ −28.5214 + 13.9930i −1.15574 + 0.567023i
$$610$$ 0 0
$$611$$ −2.34644 1.35472i −0.0949270 0.0548061i
$$612$$ 0 0
$$613$$ −11.6761 20.2237i −0.471595 0.816827i 0.527877 0.849321i $$-0.322988\pi$$
−0.999472 + 0.0324944i $$0.989655\pi$$
$$614$$ 0 0
$$615$$ 9.79732 + 2.43659i 0.395066 + 0.0982530i
$$616$$ 0 0
$$617$$ −39.0817 22.5638i −1.57337 0.908386i −0.995752 0.0920787i $$-0.970649\pi$$
−0.577618 0.816307i $$-0.696018\pi$$
$$618$$ 0 0
$$619$$ −7.97914 4.60676i −0.320709 0.185161i 0.331000 0.943631i $$-0.392614\pi$$
−0.651708 + 0.758470i $$0.725947\pi$$
$$620$$ 0 0
$$621$$ 45.3767 + 9.56105i 1.82090 + 0.383672i
$$622$$ 0 0
$$623$$ 8.80533 24.3235i 0.352778 0.974501i
$$624$$ 0 0
$$625$$ 15.6247 + 27.0627i 0.624987 + 1.08251i
$$626$$ 0 0
$$627$$ 1.18324 + 4.11726i 0.0472540 + 0.164427i
$$628$$ 0 0
$$629$$ 35.5320 1.41675
$$630$$ 0 0
$$631$$ 17.6136 0.701188 0.350594 0.936528i $$-0.385980\pi$$
0.350594 + 0.936528i $$0.385980\pi$$
$$632$$ 0 0
$$633$$ −3.12188 + 3.23663i −0.124084 + 0.128644i
$$634$$ 0 0
$$635$$ 14.1156 + 24.4489i 0.560160 + 0.970226i
$$636$$ 0 0
$$637$$ 10.5544 + 1.82334i 0.418182 + 0.0722433i
$$638$$ 0 0
$$639$$ 11.9593 22.5564i 0.473101 0.892316i
$$640$$ 0 0
$$641$$ 16.5759 + 9.57009i 0.654708 + 0.377996i 0.790258 0.612775i $$-0.209947\pi$$
−0.135550 + 0.990771i $$0.543280\pi$$
$$642$$ 0 0
$$643$$ −2.01129 1.16122i −0.0793177 0.0457941i 0.459817 0.888014i $$-0.347915\pi$$
−0.539134 + 0.842220i $$0.681248\pi$$
$$644$$ 0 0
$$645$$ 38.1228 39.5240i 1.50108 1.55626i
$$646$$ 0 0
$$647$$ 12.9310 + 22.3971i 0.508370 + 0.880522i 0.999953 + 0.00969167i $$0.00308500\pi$$
−0.491583 + 0.870831i $$0.663582\pi$$
$$648$$ 0 0
$$649$$ 1.46899 + 0.848123i 0.0576630 + 0.0332918i
$$650$$ 0 0
$$651$$ 1.09062 16.1354i 0.0427448 0.632396i
$$652$$ 0 0
$$653$$ −20.1140 + 11.6128i −0.787123 + 0.454446i −0.838949 0.544211i $$-0.816829\pi$$
0.0518258 + 0.998656i $$0.483496\pi$$
$$654$$ 0 0
$$655$$ −26.9681 + 46.7102i −1.05373 + 1.82512i
$$656$$ 0 0
$$657$$ 5.71410 0.206305i 0.222928 0.00804871i
$$658$$ 0 0
$$659$$ 13.7002 7.90981i 0.533684 0.308122i −0.208832 0.977952i $$-0.566966\pi$$
0.742515 + 0.669829i $$0.233633\pi$$
$$660$$ 0 0
$$661$$ 18.2450i 0.709647i 0.934933 + 0.354823i $$0.115459\pi$$
−0.934933 + 0.354823i $$0.884541\pi$$
$$662$$ 0 0
$$663$$ 2.49827 10.0453i 0.0970248 0.390127i
$$664$$ 0 0
$$665$$ 7.52447 + 42.2452i 0.291787 + 1.63820i
$$666$$ 0 0
$$667$$ 30.9349 53.5807i 1.19780 2.07465i
$$668$$ 0 0
$$669$$ −39.8309 + 11.4468i −1.53995 + 0.442559i
$$670$$ 0 0
$$671$$ −0.389984 + 0.675472i −0.0150552 + 0.0260763i
$$672$$ 0 0
$$673$$ 14.4184 + 24.9733i 0.555787 + 0.962651i 0.997842 + 0.0656633i $$0.0209163\pi$$
−0.442055 + 0.896988i $$0.645750\pi$$
$$674$$ 0 0
$$675$$ −12.4748 + 4.07779i −0.480157 + 0.156954i
$$676$$ 0 0
$$677$$ −33.5336 −1.28880 −0.644400 0.764689i $$-0.722893\pi$$
−0.644400 + 0.764689i $$0.722893\pi$$
$$678$$ 0 0
$$679$$ −0.468340 + 0.394369i −0.0179732 + 0.0151345i
$$680$$ 0 0
$$681$$ −4.48775 + 4.65270i −0.171971 + 0.178292i
$$682$$ 0 0
$$683$$ −19.0943 + 11.0241i −0.730621 + 0.421824i −0.818649 0.574294i $$-0.805277\pi$$
0.0880282 + 0.996118i $$0.471943\pi$$
$$684$$ 0 0
$$685$$ 14.7745i 0.564506i
$$686$$ 0 0
$$687$$ 35.0715 10.0790i 1.33806 0.384539i
$$688$$ 0 0
$$689$$ −5.99881 −0.228537
$$690$$ 0 0
$$691$$ 26.4036i 1.00444i −0.864740 0.502219i $$-0.832517\pi$$
0.864740 0.502219i $$-0.167483\pi$$
$$692$$ 0 0
$$693$$ 2.22910 + 2.46119i 0.0846763 + 0.0934930i
$$694$$ 0 0
$$695$$ 46.8311i 1.77641i
$$696$$ 0 0
$$697$$ −8.29877 −0.314338
$$698$$ 0 0
$$699$$ −15.9125 15.3484i −0.601868 0.580530i
$$700$$ 0 0
$$701$$ 20.5140i 0.774804i −0.921911 0.387402i $$-0.873373\pi$$
0.921911 0.387402i $$-0.126627\pi$$
$$702$$ 0 0
$$703$$ 46.5772 26.8913i 1.75669 1.01423i
$$704$$ 0 0
$$705$$ −2.32394 8.08651i −0.0875248 0.304556i
$$706$$ 0 0
$$707$$ 12.8610 35.5267i 0.483687 1.33612i
$$708$$ 0 0
$$709$$ −6.26109 −0.235140 −0.117570 0.993065i $$-0.537510\pi$$
−0.117570 + 0.993065i $$0.537510\pi$$
$$710$$ 0 0
$$711$$ −2.29869 1.21875i −0.0862077 0.0457068i
$$712$$ 0 0
$$713$$ 15.7476 + 27.2756i 0.589751 + 1.02148i
$$714$$ 0 0
$$715$$ 0.878041 1.52081i 0.0328369 0.0568751i
$$716$$ 0 0
$$717$$ 15.9095 + 15.3454i 0.594149 + 0.573085i
$$718$$ 0 0
$$719$$ −11.6111 + 20.1111i −0.433023 + 0.750017i −0.997132 0.0756828i $$-0.975886\pi$$
0.564109 + 0.825700i $$0.309220\pi$$
$$720$$ 0 0
$$721$$ 21.7476 18.3127i 0.809922 0.682001i
$$722$$ 0 0
$$723$$ −3.79220 3.65775i −0.141033 0.136033i
$$724$$ 0 0
$$725$$ 17.5102i 0.650314i
$$726$$ 0 0
$$727$$ 2.50999 1.44914i 0.0930903 0.0537457i −0.452732 0.891647i $$-0.649551\pi$$
0.545822 + 0.837901i $$0.316217\pi$$
$$728$$ 0 0
$$729$$ 2.91748 + 26.8419i 0.108055 + 0.994145i
$$730$$ 0 0
$$731$$ −22.5696 + 39.0917i −0.834767 + 1.44586i
$$732$$ 0 0
$$733$$ 10.2963 5.94457i 0.380302 0.219568i −0.297647 0.954676i $$-0.596202\pi$$
0.677950 + 0.735108i $$0.262869\pi$$
$$734$$ 0 0
$$735$$ 19.6593 + 26.8291i 0.725145 + 0.989608i
$$736$$ 0 0
$$737$$ 4.62622 + 2.67095i 0.170409 + 0.0983858i
$$738$$ 0 0
$$739$$ 17.2254 + 29.8354i 0.633648 + 1.09751i 0.986800 + 0.161945i $$0.0517767\pi$$
−0.353151 + 0.935566i $$0.614890\pi$$
$$740$$ 0 0
$$741$$ −4.32763 15.0586i −0.158979 0.553193i
$$742$$ 0 0
$$743$$ −2.44069 1.40913i −0.0895401 0.0516960i 0.454561 0.890715i $$-0.349796\pi$$
−0.544101 + 0.839019i $$0.683129\pi$$
$$744$$ 0 0
$$745$$ 25.5447 + 14.7483i 0.935887 + 0.540335i
$$746$$ 0 0
$$747$$ 0.748781 + 20.7393i 0.0273965 + 0.758812i
$$748$$ 0 0
$$749$$ 15.8147 + 5.72507i 0.577857 + 0.209189i
$$750$$ 0 0
$$751$$ −3.86045 6.68649i −0.140870 0.243993i 0.786955 0.617011i $$-0.211657\pi$$
−0.927824 + 0.373017i $$0.878323\pi$$
$$752$$ 0 0
$$753$$ −10.6241 2.64221i −0.387163 0.0962876i
$$754$$ 0 0
$$755$$ −20.7517 −0.755233
$$756$$ 0 0
$$757$$ 1.17924 0.0428603 0.0214302 0.999770i $$-0.493178\pi$$
0.0214302 + 0.999770i $$0.493178\pi$$
$$758$$ 0 0
$$759$$ −6.27564 1.56075i −0.227791 0.0566517i
$$760$$ 0 0
$$761$$ −1.56644 2.71316i −0.0567835 0.0983520i 0.836236 0.548369i $$-0.184751\pi$$
−0.893020 + 0.450017i $$0.851418\pi$$
$$762$$ 0 0
$$763$$ −8.79473 10.4443i −0.318391 0.378110i
$$764$$ 0 0
$$765$$ 27.2401 17.0663i 0.984866 0.617033i
$$766$$ 0 0
$$767$$ −5.37276 3.10196i −0.193999 0.112005i
$$768$$ 0 0
$$769$$ 5.53497 + 3.19562i 0.199596 + 0.115237i 0.596467 0.802637i $$-0.296571\pi$$
−0.396871 + 0.917874i $$0.629904\pi$$
$$770$$ 0 0
$$771$$ −11.7245 40.7971i −0.422247 1.46927i
$$772$$ 0 0
$$773$$ 23.9779 + 41.5309i 0.862425 + 1.49376i 0.869581 + 0.493790i $$0.164389\pi$$
−0.00715621 + 0.999974i $$0.502278\pi$$
$$774$$ 0 0
$$775$$ −7.71948 4.45685i −0.277292 0.160095i
$$776$$ 0 0
$$777$$ 23.2316 34.6156i 0.833430 1.24183i
$$778$$ 0 0
$$779$$ −10.8784 + 6.28067i −0.389761 + 0.225028i
$$780$$ 0 0
$$781$$ −1.78015 + 3.08331i −0.0636987 + 0.110329i
$$782$$ 0 0
$$783$$ 35.2487 + 7.42705i 1.25969 + 0.265421i
$$784$$ 0 0
$$785$$ −29.1661 + 16.8390i −1.04098 + 0.601011i
$$786$$ 0 0
$$787$$ 6.04066i 0.215326i −0.994187 0.107663i $$-0.965663\pi$$
0.994187 0.107663i $$-0.0343368\pi$$
$$788$$ 0 0
$$789$$ −30.3969 29.3192i −1.08216 1.04379i
$$790$$ 0 0
$$791$$ −26.4047 9.55872i −0.938842 0.339869i
$$792$$ 0 0
$$793$$ 1.42635 2.47050i 0.0506510 0.0877301i
$$794$$ 0 0
$$795$$ −13.4079 12.9325i −0.475529 0.458670i