# Properties

 Label 637.2.f.g.295.3 Level $637$ Weight $2$ Character 637.295 Analytic conductor $5.086$ Analytic rank $0$ Dimension $8$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$637 = 7^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 637.f (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$5.08647060876$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(\zeta_{3})$$ Coefficient field: 8.0.1485512441856.7 Defining polynomial: $$x^{8} + 24 x^{6} + 455 x^{4} + 2904 x^{2} + 14641$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 295.3 Root $$-2.04914 - 3.54921i$$ of defining polynomial Character $$\chi$$ $$=$$ 637.295 Dual form 637.2.f.g.393.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 + 0.866025i) q^{2} +(0.707107 - 1.22474i) q^{3} +(0.500000 + 0.866025i) q^{4} -4.09827 q^{5} +(0.707107 + 1.22474i) q^{6} -3.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$q+(-0.500000 + 0.866025i) q^{2} +(0.707107 - 1.22474i) q^{3} +(0.500000 + 0.866025i) q^{4} -4.09827 q^{5} +(0.707107 + 1.22474i) q^{6} -3.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(2.04914 - 3.54921i) q^{10} +(1.89792 - 3.28729i) q^{11} +1.41421 q^{12} +(0.634922 - 3.54921i) q^{13} +(-2.89792 + 5.01934i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.634922 - 1.09972i) q^{17} -1.00000 q^{18} +(-1.41421 - 2.44949i) q^{19} +(-2.04914 - 3.54921i) q^{20} +(1.89792 + 3.28729i) q^{22} +(3.89792 - 6.75139i) q^{23} +(-2.12132 + 3.67423i) q^{24} +11.7958 q^{25} +(2.75624 + 2.32446i) q^{26} +5.65685 q^{27} +(-0.397916 + 0.689210i) q^{29} +(-2.89792 - 5.01934i) q^{30} +1.41421 q^{31} +(-2.50000 - 4.33013i) q^{32} +(-2.68406 - 4.64893i) q^{33} +1.26984 q^{34} +(-0.500000 + 0.866025i) q^{36} +(-1.39792 + 2.42126i) q^{37} +2.82843 q^{38} +(-3.89792 - 3.28729i) q^{39} +12.2948 q^{40} +(1.48640 - 2.57452i) q^{41} +(-3.89792 - 6.75139i) q^{43} +3.79583 q^{44} +(-2.04914 - 3.54921i) q^{45} +(3.89792 + 6.75139i) q^{46} -2.82843 q^{47} +(-0.707107 - 1.22474i) q^{48} +(-5.89792 + 10.2155i) q^{50} -1.79583 q^{51} +(3.39116 - 1.22474i) q^{52} -12.5917 q^{53} +(-2.82843 + 4.89898i) q^{54} +(-7.77817 + 13.4722i) q^{55} -4.00000 q^{57} +(-0.397916 - 0.689210i) q^{58} +(-6.21959 - 10.7726i) q^{59} -5.79583 q^{60} +(4.17046 + 7.22344i) q^{61} +(-0.707107 + 1.22474i) q^{62} +7.00000 q^{64} +(-2.60208 + 14.5456i) q^{65} +5.36812 q^{66} +(1.89792 - 3.28729i) q^{67} +(0.634922 - 1.09972i) q^{68} +(-5.51249 - 9.54790i) q^{69} +(-3.00000 - 5.19615i) q^{71} +(-1.50000 - 2.59808i) q^{72} +12.5836 q^{73} +(-1.39792 - 2.42126i) q^{74} +(8.34091 - 14.4469i) q^{75} +(1.41421 - 2.44949i) q^{76} +(4.79583 - 1.73205i) q^{78} -2.20417 q^{79} +(-2.04914 + 3.54921i) q^{80} +(2.50000 - 4.33013i) q^{81} +(1.48640 + 2.57452i) q^{82} +9.89949 q^{83} +(2.60208 + 4.50694i) q^{85} +7.79583 q^{86} +(0.562738 + 0.974691i) q^{87} +(-5.69375 + 9.86186i) q^{88} +(-7.48944 + 12.9721i) q^{89} +4.09827 q^{90} +7.79583 q^{92} +(1.00000 - 1.73205i) q^{93} +(1.41421 - 2.44949i) q^{94} +(5.79583 + 10.0387i) q^{95} -7.07107 q^{96} +(-2.12132 - 3.67423i) q^{97} +3.79583 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q - 4 q^{2} + 4 q^{4} - 24 q^{8} + 4 q^{9} + O(q^{10})$$ $$8 q - 4 q^{2} + 4 q^{4} - 24 q^{8} + 4 q^{9} - 4 q^{11} - 4 q^{15} + 4 q^{16} - 8 q^{18} - 4 q^{22} + 12 q^{23} + 56 q^{25} + 16 q^{29} - 4 q^{30} - 20 q^{32} - 4 q^{36} + 8 q^{37} - 12 q^{39} - 12 q^{43} - 8 q^{44} + 12 q^{46} - 28 q^{50} + 24 q^{51} - 24 q^{53} - 32 q^{57} + 16 q^{58} - 8 q^{60} + 56 q^{64} - 40 q^{65} - 4 q^{67} - 24 q^{71} - 12 q^{72} + 8 q^{74} - 56 q^{79} + 20 q^{81} + 40 q^{85} + 24 q^{86} + 12 q^{88} + 24 q^{92} + 8 q^{93} + 8 q^{95} - 8 q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$$.

 $$n$$ $$197$$ $$248$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.500000 + 0.866025i −0.353553 + 0.612372i −0.986869 0.161521i $$-0.948360\pi$$
0.633316 + 0.773893i $$0.281693\pi$$
$$3$$ 0.707107 1.22474i 0.408248 0.707107i −0.586445 0.809989i $$-0.699473\pi$$
0.994694 + 0.102882i $$0.0328064\pi$$
$$4$$ 0.500000 + 0.866025i 0.250000 + 0.433013i
$$5$$ −4.09827 −1.83280 −0.916401 0.400260i $$-0.868920\pi$$
−0.916401 + 0.400260i $$0.868920\pi$$
$$6$$ 0.707107 + 1.22474i 0.288675 + 0.500000i
$$7$$ 0 0
$$8$$ −3.00000 −1.06066
$$9$$ 0.500000 + 0.866025i 0.166667 + 0.288675i
$$10$$ 2.04914 3.54921i 0.647994 1.12236i
$$11$$ 1.89792 3.28729i 0.572243 0.991154i −0.424092 0.905619i $$-0.639407\pi$$
0.996335 0.0855351i $$-0.0272600\pi$$
$$12$$ 1.41421 0.408248
$$13$$ 0.634922 3.54921i 0.176096 0.984373i
$$14$$ 0 0
$$15$$ −2.89792 + 5.01934i −0.748239 + 1.29599i
$$16$$ 0.500000 0.866025i 0.125000 0.216506i
$$17$$ −0.634922 1.09972i −0.153991 0.266721i 0.778700 0.627396i $$-0.215879\pi$$
−0.932691 + 0.360676i $$0.882546\pi$$
$$18$$ −1.00000 −0.235702
$$19$$ −1.41421 2.44949i −0.324443 0.561951i 0.656957 0.753928i $$-0.271843\pi$$
−0.981399 + 0.191977i $$0.938510\pi$$
$$20$$ −2.04914 3.54921i −0.458201 0.793627i
$$21$$ 0 0
$$22$$ 1.89792 + 3.28729i 0.404637 + 0.700852i
$$23$$ 3.89792 6.75139i 0.812772 1.40776i −0.0981454 0.995172i $$-0.531291\pi$$
0.910917 0.412590i $$-0.135376\pi$$
$$24$$ −2.12132 + 3.67423i −0.433013 + 0.750000i
$$25$$ 11.7958 2.35917
$$26$$ 2.75624 + 2.32446i 0.540544 + 0.455865i
$$27$$ 5.65685 1.08866
$$28$$ 0 0
$$29$$ −0.397916 + 0.689210i −0.0738911 + 0.127983i −0.900604 0.434642i $$-0.856875\pi$$
0.826712 + 0.562625i $$0.190208\pi$$
$$30$$ −2.89792 5.01934i −0.529085 0.916401i
$$31$$ 1.41421 0.254000 0.127000 0.991903i $$-0.459465\pi$$
0.127000 + 0.991903i $$0.459465\pi$$
$$32$$ −2.50000 4.33013i −0.441942 0.765466i
$$33$$ −2.68406 4.64893i −0.467235 0.809274i
$$34$$ 1.26984 0.217777
$$35$$ 0 0
$$36$$ −0.500000 + 0.866025i −0.0833333 + 0.144338i
$$37$$ −1.39792 + 2.42126i −0.229816 + 0.398053i −0.957753 0.287591i $$-0.907146\pi$$
0.727937 + 0.685643i $$0.240479\pi$$
$$38$$ 2.82843 0.458831
$$39$$ −3.89792 3.28729i −0.624166 0.526387i
$$40$$ 12.2948 1.94398
$$41$$ 1.48640 2.57452i 0.232136 0.402072i −0.726300 0.687378i $$-0.758762\pi$$
0.958437 + 0.285306i $$0.0920951\pi$$
$$42$$ 0 0
$$43$$ −3.89792 6.75139i −0.594427 1.02958i −0.993628 0.112714i $$-0.964046\pi$$
0.399201 0.916863i $$-0.369288\pi$$
$$44$$ 3.79583 0.572243
$$45$$ −2.04914 3.54921i −0.305467 0.529085i
$$46$$ 3.89792 + 6.75139i 0.574716 + 0.995438i
$$47$$ −2.82843 −0.412568 −0.206284 0.978492i $$-0.566137\pi$$
−0.206284 + 0.978492i $$0.566137\pi$$
$$48$$ −0.707107 1.22474i −0.102062 0.176777i
$$49$$ 0 0
$$50$$ −5.89792 + 10.2155i −0.834091 + 1.44469i
$$51$$ −1.79583 −0.251467
$$52$$ 3.39116 1.22474i 0.470270 0.169842i
$$53$$ −12.5917 −1.72960 −0.864799 0.502118i $$-0.832554\pi$$
−0.864799 + 0.502118i $$0.832554\pi$$
$$54$$ −2.82843 + 4.89898i −0.384900 + 0.666667i
$$55$$ −7.77817 + 13.4722i −1.04881 + 1.81659i
$$56$$ 0 0
$$57$$ −4.00000 −0.529813
$$58$$ −0.397916 0.689210i −0.0522489 0.0904977i
$$59$$ −6.21959 10.7726i −0.809722 1.40248i −0.913057 0.407833i $$-0.866285\pi$$
0.103335 0.994647i $$-0.467049\pi$$
$$60$$ −5.79583 −0.748239
$$61$$ 4.17046 + 7.22344i 0.533972 + 0.924867i 0.999212 + 0.0396825i $$0.0126346\pi$$
−0.465240 + 0.885185i $$0.654032\pi$$
$$62$$ −0.707107 + 1.22474i −0.0898027 + 0.155543i
$$63$$ 0 0
$$64$$ 7.00000 0.875000
$$65$$ −2.60208 + 14.5456i −0.322749 + 1.80416i
$$66$$ 5.36812 0.660769
$$67$$ 1.89792 3.28729i 0.231867 0.401606i −0.726490 0.687177i $$-0.758850\pi$$
0.958358 + 0.285571i $$0.0921831\pi$$
$$68$$ 0.634922 1.09972i 0.0769956 0.133360i
$$69$$ −5.51249 9.54790i −0.663625 1.14943i
$$70$$ 0 0
$$71$$ −3.00000 5.19615i −0.356034 0.616670i 0.631260 0.775571i $$-0.282538\pi$$
−0.987294 + 0.158901i $$0.949205\pi$$
$$72$$ −1.50000 2.59808i −0.176777 0.306186i
$$73$$ 12.5836 1.47279 0.736397 0.676550i $$-0.236526\pi$$
0.736397 + 0.676550i $$0.236526\pi$$
$$74$$ −1.39792 2.42126i −0.162504 0.281466i
$$75$$ 8.34091 14.4469i 0.963126 1.66818i
$$76$$ 1.41421 2.44949i 0.162221 0.280976i
$$77$$ 0 0
$$78$$ 4.79583 1.73205i 0.543021 0.196116i
$$79$$ −2.20417 −0.247988 −0.123994 0.992283i $$-0.539570\pi$$
−0.123994 + 0.992283i $$0.539570\pi$$
$$80$$ −2.04914 + 3.54921i −0.229100 + 0.396813i
$$81$$ 2.50000 4.33013i 0.277778 0.481125i
$$82$$ 1.48640 + 2.57452i 0.164145 + 0.284308i
$$83$$ 9.89949 1.08661 0.543305 0.839535i $$-0.317173\pi$$
0.543305 + 0.839535i $$0.317173\pi$$
$$84$$ 0 0
$$85$$ 2.60208 + 4.50694i 0.282236 + 0.488847i
$$86$$ 7.79583 0.840646
$$87$$ 0.562738 + 0.974691i 0.0603318 + 0.104498i
$$88$$ −5.69375 + 9.86186i −0.606955 + 1.05128i
$$89$$ −7.48944 + 12.9721i −0.793879 + 1.37504i 0.129670 + 0.991557i $$0.458608\pi$$
−0.923549 + 0.383481i $$0.874725\pi$$
$$90$$ 4.09827 0.431996
$$91$$ 0 0
$$92$$ 7.79583 0.812772
$$93$$ 1.00000 1.73205i 0.103695 0.179605i
$$94$$ 1.41421 2.44949i 0.145865 0.252646i
$$95$$ 5.79583 + 10.0387i 0.594640 + 1.02995i
$$96$$ −7.07107 −0.721688
$$97$$ −2.12132 3.67423i −0.215387 0.373062i 0.738005 0.674795i $$-0.235768\pi$$
−0.953392 + 0.301733i $$0.902435\pi$$
$$98$$ 0 0
$$99$$ 3.79583 0.381495
$$100$$ 5.89792 + 10.2155i 0.589792 + 1.02155i
$$101$$ −4.87756 + 8.44819i −0.485336 + 0.840626i −0.999858 0.0168509i $$-0.994636\pi$$
0.514522 + 0.857477i $$0.327969\pi$$
$$102$$ 0.897916 1.55524i 0.0889069 0.153991i
$$103$$ −5.36812 −0.528936 −0.264468 0.964394i $$-0.585196\pi$$
−0.264468 + 0.964394i $$0.585196\pi$$
$$104$$ −1.90477 + 10.6476i −0.186778 + 1.04409i
$$105$$ 0 0
$$106$$ 6.29583 10.9047i 0.611505 1.05916i
$$107$$ 3.00000 5.19615i 0.290021 0.502331i −0.683793 0.729676i $$-0.739671\pi$$
0.973814 + 0.227345i $$0.0730044\pi$$
$$108$$ 2.82843 + 4.89898i 0.272166 + 0.471405i
$$109$$ 1.59166 0.152454 0.0762268 0.997091i $$-0.475713\pi$$
0.0762268 + 0.997091i $$0.475713\pi$$
$$110$$ −7.77817 13.4722i −0.741620 1.28452i
$$111$$ 1.97695 + 3.42418i 0.187644 + 0.325009i
$$112$$ 0 0
$$113$$ −1.29583 2.24445i −0.121902 0.211140i 0.798616 0.601841i $$-0.205566\pi$$
−0.920518 + 0.390701i $$0.872233\pi$$
$$114$$ 2.00000 3.46410i 0.187317 0.324443i
$$115$$ −15.9747 + 27.6690i −1.48965 + 2.58015i
$$116$$ −0.795832 −0.0738911
$$117$$ 3.39116 1.22474i 0.313513 0.113228i
$$118$$ 12.4392 1.14512
$$119$$ 0 0
$$120$$ 8.69375 15.0580i 0.793627 1.37460i
$$121$$ −1.70417 2.95171i −0.154924 0.268337i
$$122$$ −8.34091 −0.755151
$$123$$ −2.10208 3.64092i −0.189539 0.328290i
$$124$$ 0.707107 + 1.22474i 0.0635001 + 0.109985i
$$125$$ −27.8512 −2.49108
$$126$$ 0 0
$$127$$ 5.79583 10.0387i 0.514297 0.890788i −0.485566 0.874200i $$-0.661386\pi$$
0.999862 0.0165881i $$-0.00528038\pi$$
$$128$$ 1.50000 2.59808i 0.132583 0.229640i
$$129$$ −11.0250 −0.970695
$$130$$ −11.2958 9.52628i −0.990710 0.835510i
$$131$$ −5.36812 −0.469015 −0.234507 0.972114i $$-0.575348\pi$$
−0.234507 + 0.972114i $$0.575348\pi$$
$$132$$ 2.68406 4.64893i 0.233617 0.404637i
$$133$$ 0 0
$$134$$ 1.89792 + 3.28729i 0.163955 + 0.283978i
$$135$$ −23.1833 −1.99530
$$136$$ 1.90477 + 3.29915i 0.163332 + 0.282900i
$$137$$ 9.39792 + 16.2777i 0.802918 + 1.39069i 0.917688 + 0.397303i $$0.130054\pi$$
−0.114769 + 0.993392i $$0.536613\pi$$
$$138$$ 11.0250 0.938508
$$139$$ −0.851476 1.47480i −0.0722212 0.125091i 0.827653 0.561240i $$-0.189675\pi$$
−0.899875 + 0.436149i $$0.856342\pi$$
$$140$$ 0 0
$$141$$ −2.00000 + 3.46410i −0.168430 + 0.291730i
$$142$$ 6.00000 0.503509
$$143$$ −10.4622 8.82327i −0.874896 0.737839i
$$144$$ 1.00000 0.0833333
$$145$$ 1.63077 2.82457i 0.135428 0.234568i
$$146$$ −6.29178 + 10.8977i −0.520711 + 0.901898i
$$147$$ 0 0
$$148$$ −2.79583 −0.229816
$$149$$ 7.29583 + 12.6368i 0.597698 + 1.03524i 0.993160 + 0.116761i $$0.0372511\pi$$
−0.395462 + 0.918482i $$0.629416\pi$$
$$150$$ 8.34091 + 14.4469i 0.681033 + 1.17958i
$$151$$ 1.59166 0.129528 0.0647639 0.997901i $$-0.479371\pi$$
0.0647639 + 0.997901i $$0.479371\pi$$
$$152$$ 4.24264 + 7.34847i 0.344124 + 0.596040i
$$153$$ 0.634922 1.09972i 0.0513304 0.0889069i
$$154$$ 0 0
$$155$$ −5.79583 −0.465532
$$156$$ 0.897916 5.01934i 0.0718908 0.401869i
$$157$$ 0.144369 0.0115219 0.00576095 0.999983i $$-0.498166\pi$$
0.00576095 + 0.999983i $$0.498166\pi$$
$$158$$ 1.10208 1.90887i 0.0876771 0.151861i
$$159$$ −8.90365 + 15.4216i −0.706105 + 1.22301i
$$160$$ 10.2457 + 17.7460i 0.809992 + 1.40295i
$$161$$ 0 0
$$162$$ 2.50000 + 4.33013i 0.196419 + 0.340207i
$$163$$ −7.69375 13.3260i −0.602621 1.04377i −0.992423 0.122871i $$-0.960790\pi$$
0.389802 0.920899i $$-0.372543\pi$$
$$164$$ 2.97280 0.232136
$$165$$ 11.0000 + 19.0526i 0.856349 + 1.48324i
$$166$$ −4.94975 + 8.57321i −0.384175 + 0.665410i
$$167$$ 0.851476 1.47480i 0.0658892 0.114123i −0.831199 0.555975i $$-0.812345\pi$$
0.897088 + 0.441852i $$0.145678\pi$$
$$168$$ 0 0
$$169$$ −12.1937 4.50694i −0.937981 0.346688i
$$170$$ −5.20417 −0.399142
$$171$$ 1.41421 2.44949i 0.108148 0.187317i
$$172$$ 3.89792 6.75139i 0.297213 0.514789i
$$173$$ −8.90365 15.4216i −0.676932 1.17248i −0.975900 0.218218i $$-0.929976\pi$$
0.298968 0.954263i $$-0.403358\pi$$
$$174$$ −1.12548 −0.0853221
$$175$$ 0 0
$$176$$ −1.89792 3.28729i −0.143061 0.247789i
$$177$$ −17.5917 −1.32227
$$178$$ −7.48944 12.9721i −0.561357 0.972299i
$$179$$ 9.79583 16.9669i 0.732175 1.26816i −0.223777 0.974640i $$-0.571839\pi$$
0.955952 0.293524i $$-0.0948279\pi$$
$$180$$ 2.04914 3.54921i 0.152734 0.264542i
$$181$$ −3.80953 −0.283160 −0.141580 0.989927i $$-0.545218\pi$$
−0.141580 + 0.989927i $$0.545218\pi$$
$$182$$ 0 0
$$183$$ 11.7958 0.871973
$$184$$ −11.6937 + 20.2542i −0.862074 + 1.49316i
$$185$$ 5.72904 9.92299i 0.421207 0.729552i
$$186$$ 1.00000 + 1.73205i 0.0733236 + 0.127000i
$$187$$ −4.82012 −0.352482
$$188$$ −1.41421 2.44949i −0.103142 0.178647i
$$189$$ 0 0
$$190$$ −11.5917 −0.840948
$$191$$ 8.10208 + 14.0332i 0.586246 + 1.01541i 0.994719 + 0.102638i $$0.0327282\pi$$
−0.408473 + 0.912771i $$0.633938\pi$$
$$192$$ 4.94975 8.57321i 0.357217 0.618718i
$$193$$ −11.2958 + 19.5650i −0.813092 + 1.40832i 0.0975983 + 0.995226i $$0.468884\pi$$
−0.910690 + 0.413090i $$0.864449\pi$$
$$194$$ 4.24264 0.304604
$$195$$ 15.9747 + 13.4722i 1.14397 + 0.964764i
$$196$$ 0 0
$$197$$ 4.00000 6.92820i 0.284988 0.493614i −0.687618 0.726073i $$-0.741344\pi$$
0.972606 + 0.232458i $$0.0746770\pi$$
$$198$$ −1.89792 + 3.28729i −0.134879 + 0.233617i
$$199$$ 2.53969 + 4.39887i 0.180034 + 0.311828i 0.941892 0.335916i $$-0.109046\pi$$
−0.761858 + 0.647744i $$0.775713\pi$$
$$200$$ −35.3875 −2.50227
$$201$$ −2.68406 4.64893i −0.189319 0.327910i
$$202$$ −4.87756 8.44819i −0.343184 0.594412i
$$203$$ 0 0
$$204$$ −0.897916 1.55524i −0.0628667 0.108888i
$$205$$ −6.09166 + 10.5511i −0.425460 + 0.736919i
$$206$$ 2.68406 4.64893i 0.187007 0.323906i
$$207$$ 7.79583 0.541848
$$208$$ −2.75624 2.32446i −0.191111 0.161172i
$$209$$ −10.7362 −0.742641
$$210$$ 0 0
$$211$$ −3.89792 + 6.75139i −0.268344 + 0.464785i −0.968434 0.249269i $$-0.919810\pi$$
0.700091 + 0.714054i $$0.253143\pi$$
$$212$$ −6.29583 10.9047i −0.432399 0.748938i
$$213$$ −8.48528 −0.581402
$$214$$ 3.00000 + 5.19615i 0.205076 + 0.355202i
$$215$$ 15.9747 + 27.6690i 1.08947 + 1.88701i
$$216$$ −16.9706 −1.15470
$$217$$ 0 0
$$218$$ −0.795832 + 1.37842i −0.0539005 + 0.0933584i
$$219$$ 8.89792 15.4116i 0.601265 1.04142i
$$220$$ −15.5563 −1.04881
$$221$$ −4.30625 + 1.55524i −0.289670 + 0.104616i
$$222$$ −3.95390 −0.265369
$$223$$ −2.82843 + 4.89898i −0.189405 + 0.328060i −0.945052 0.326920i $$-0.893989\pi$$
0.755647 + 0.654979i $$0.227323\pi$$
$$224$$ 0 0
$$225$$ 5.89792 + 10.2155i 0.393194 + 0.681033i
$$226$$ 2.59166 0.172395
$$227$$ 3.67990 + 6.37378i 0.244244 + 0.423043i 0.961919 0.273336i $$-0.0881270\pi$$
−0.717675 + 0.696378i $$0.754794\pi$$
$$228$$ −2.00000 3.46410i −0.132453 0.229416i
$$229$$ −12.7279 −0.841085 −0.420542 0.907273i $$-0.638160\pi$$
−0.420542 + 0.907273i $$0.638160\pi$$
$$230$$ −15.9747 27.6690i −1.05334 1.82444i
$$231$$ 0 0
$$232$$ 1.19375 2.06763i 0.0783733 0.135747i
$$233$$ 17.1833 1.12572 0.562859 0.826553i $$-0.309702\pi$$
0.562859 + 0.826553i $$0.309702\pi$$
$$234$$ −0.634922 + 3.54921i −0.0415062 + 0.232019i
$$235$$ 11.5917 0.756157
$$236$$ 6.21959 10.7726i 0.404861 0.701240i
$$237$$ −1.55858 + 2.69954i −0.101241 + 0.175354i
$$238$$ 0 0
$$239$$ −10.2042 −0.660053 −0.330026 0.943972i $$-0.607058\pi$$
−0.330026 + 0.943972i $$0.607058\pi$$
$$240$$ 2.89792 + 5.01934i 0.187060 + 0.323997i
$$241$$ 5.58467 + 9.67293i 0.359740 + 0.623088i 0.987917 0.154982i $$-0.0495320\pi$$
−0.628177 + 0.778070i $$0.716199\pi$$
$$242$$ 3.40834 0.219096
$$243$$ 4.94975 + 8.57321i 0.317526 + 0.549972i
$$244$$ −4.17046 + 7.22344i −0.266986 + 0.462433i
$$245$$ 0 0
$$246$$ 4.20417 0.268048
$$247$$ −9.59166 + 3.46410i −0.610303 + 0.220416i
$$248$$ −4.24264 −0.269408
$$249$$ 7.00000 12.1244i 0.443607 0.768350i
$$250$$ 13.9256 24.1198i 0.880731 1.52547i
$$251$$ −8.34091 14.4469i −0.526474 0.911879i −0.999524 0.0308439i $$-0.990181\pi$$
0.473050 0.881035i $$-0.343153\pi$$
$$252$$ 0 0
$$253$$ −14.7958 25.6271i −0.930206 1.61116i
$$254$$ 5.79583 + 10.0387i 0.363663 + 0.629882i
$$255$$ 7.35981 0.460889
$$256$$ 8.50000 + 14.7224i 0.531250 + 0.920152i
$$257$$ 4.31483 7.47350i 0.269151 0.466184i −0.699492 0.714641i $$-0.746590\pi$$
0.968643 + 0.248457i $$0.0799235\pi$$
$$258$$ 5.51249 9.54790i 0.343192 0.594427i
$$259$$ 0 0
$$260$$ −13.8979 + 5.01934i −0.861912 + 0.311286i
$$261$$ −0.795832 −0.0492607
$$262$$ 2.68406 4.64893i 0.165822 0.287212i
$$263$$ −1.69375 + 2.93366i −0.104441 + 0.180897i −0.913510 0.406817i $$-0.866639\pi$$
0.809069 + 0.587714i $$0.199972\pi$$
$$264$$ 8.05217 + 13.9468i 0.495577 + 0.858365i
$$265$$ 51.6041 3.17001
$$266$$ 0 0
$$267$$ 10.5917 + 18.3453i 0.648199 + 1.12271i
$$268$$ 3.79583 0.231867
$$269$$ 6.21959 + 10.7726i 0.379215 + 0.656820i 0.990948 0.134244i $$-0.0428607\pi$$
−0.611733 + 0.791064i $$0.709527\pi$$
$$270$$ 11.5917 20.0773i 0.705446 1.22187i
$$271$$ 8.75928 15.1715i 0.532088 0.921604i −0.467210 0.884147i $$-0.654741\pi$$
0.999298 0.0374577i $$-0.0119260\pi$$
$$272$$ −1.26984 −0.0769956
$$273$$ 0 0
$$274$$ −18.7958 −1.13550
$$275$$ 22.3875 38.7763i 1.35002 2.33830i
$$276$$ 5.51249 9.54790i 0.331813 0.574716i
$$277$$ −16.0917 27.8716i −0.966854 1.67464i −0.704548 0.709656i $$-0.748850\pi$$
−0.262306 0.964985i $$-0.584483\pi$$
$$278$$ 1.70295 0.102136
$$279$$ 0.707107 + 1.22474i 0.0423334 + 0.0733236i
$$280$$ 0 0
$$281$$ 24.7958 1.47920 0.739598 0.673049i $$-0.235016\pi$$
0.739598 + 0.673049i $$0.235016\pi$$
$$282$$ −2.00000 3.46410i −0.119098 0.206284i
$$283$$ −7.92254 + 13.7222i −0.470946 + 0.815703i −0.999448 0.0332294i $$-0.989421\pi$$
0.528501 + 0.848932i $$0.322754\pi$$
$$284$$ 3.00000 5.19615i 0.178017 0.308335i
$$285$$ 16.3931 0.971043
$$286$$ 12.8723 4.64893i 0.761155 0.274897i
$$287$$ 0 0
$$288$$ 2.50000 4.33013i 0.147314 0.255155i
$$289$$ 7.69375 13.3260i 0.452573 0.783880i
$$290$$ 1.63077 + 2.82457i 0.0957619 + 0.165865i
$$291$$ −6.00000 −0.351726
$$292$$ 6.29178 + 10.8977i 0.368198 + 0.637738i
$$293$$ −1.48640 2.57452i −0.0868363 0.150405i 0.819336 0.573314i $$-0.194342\pi$$
−0.906172 + 0.422909i $$0.861009\pi$$
$$294$$ 0 0
$$295$$ 25.4896 + 44.1492i 1.48406 + 2.57047i
$$296$$ 4.19375 7.26378i 0.243757 0.422199i
$$297$$ 10.7362 18.5957i 0.622979 1.07903i
$$298$$ −14.5917 −0.845272
$$299$$ −21.4872 18.1211i −1.24264 1.04797i
$$300$$ 16.6818 0.963126
$$301$$ 0 0
$$302$$ −0.795832 + 1.37842i −0.0457950 + 0.0793192i
$$303$$ 6.89792 + 11.9475i 0.396275 + 0.686368i
$$304$$ −2.82843 −0.162221
$$305$$ −17.0917 29.6036i −0.978666 1.69510i
$$306$$ 0.634922 + 1.09972i 0.0362961 + 0.0628667i
$$307$$ 20.0583 1.14478 0.572392 0.819980i $$-0.306015\pi$$
0.572392 + 0.819980i $$0.306015\pi$$
$$308$$ 0 0
$$309$$ −3.79583 + 6.57457i −0.215937 + 0.374014i
$$310$$ 2.89792 5.01934i 0.164591 0.285079i
$$311$$ 28.8323 1.63493 0.817464 0.575980i $$-0.195379\pi$$
0.817464 + 0.575980i $$0.195379\pi$$
$$312$$ 11.6937 + 9.86186i 0.662028 + 0.558318i
$$313$$ −15.2676 −0.862976 −0.431488 0.902119i $$-0.642011\pi$$
−0.431488 + 0.902119i $$0.642011\pi$$
$$314$$ −0.0721845 + 0.125027i −0.00407360 + 0.00705569i
$$315$$ 0 0
$$316$$ −1.10208 1.90887i −0.0619971 0.107382i
$$317$$ 6.59166 0.370225 0.185112 0.982717i $$-0.440735\pi$$
0.185112 + 0.982717i $$0.440735\pi$$
$$318$$ −8.90365 15.4216i −0.499292 0.864799i
$$319$$ 1.51042 + 2.61613i 0.0845674 + 0.146475i
$$320$$ −28.6879 −1.60370
$$321$$ −4.24264 7.34847i −0.236801 0.410152i
$$322$$ 0 0
$$323$$ −1.79583 + 3.11047i −0.0999227 + 0.173071i
$$324$$ 5.00000 0.277778
$$325$$ 7.48944 41.8659i 0.415439 2.32230i
$$326$$ 15.3875 0.852235
$$327$$ 1.12548 1.94938i 0.0622390 0.107801i
$$328$$ −4.45919 + 7.72355i −0.246218 + 0.426462i
$$329$$ 0 0
$$330$$ −22.0000 −1.21106
$$331$$ −14.6937 25.4503i −0.807641 1.39888i −0.914493 0.404601i $$-0.867410\pi$$
0.106852 0.994275i $$-0.465923\pi$$
$$332$$ 4.94975 + 8.57321i 0.271653 + 0.470516i
$$333$$ −2.79583 −0.153211
$$334$$ 0.851476 + 1.47480i 0.0465907 + 0.0806974i
$$335$$ −7.77817 + 13.4722i −0.424967 + 0.736065i
$$336$$ 0 0
$$337$$ 17.9792 0.979387 0.489694 0.871895i $$-0.337109\pi$$
0.489694 + 0.871895i $$0.337109\pi$$
$$338$$ 10.0000 8.30662i 0.543928 0.451821i
$$339$$ −3.66517 −0.199064
$$340$$ −2.60208 + 4.50694i −0.141118 + 0.244423i
$$341$$ 2.68406 4.64893i 0.145350 0.251753i
$$342$$ 1.41421 + 2.44949i 0.0764719 + 0.132453i
$$343$$ 0 0
$$344$$ 11.6937 + 20.2542i 0.630485 + 1.09203i
$$345$$ 22.5917 + 39.1299i 1.21629 + 2.10668i
$$346$$ 17.8073 0.957326
$$347$$ 16.4896 + 28.5608i 0.885207 + 1.53322i 0.845476 + 0.534013i $$0.179317\pi$$
0.0397307 + 0.999210i $$0.487350\pi$$
$$348$$ −0.562738 + 0.974691i −0.0301659 + 0.0522489i
$$349$$ 13.2907 23.0201i 0.711433 1.23224i −0.252887 0.967496i $$-0.581380\pi$$
0.964319 0.264742i $$-0.0852867\pi$$
$$350$$ 0 0
$$351$$ 3.59166 20.0773i 0.191709 1.07165i
$$352$$ −18.9792 −1.01159
$$353$$ 2.61187 4.52390i 0.139016 0.240783i −0.788108 0.615536i $$-0.788939\pi$$
0.927124 + 0.374754i $$0.122273\pi$$
$$354$$ 8.79583 15.2348i 0.467493 0.809722i
$$355$$ 12.2948 + 21.2952i 0.652541 + 1.13023i
$$356$$ −14.9789 −0.793879
$$357$$ 0 0
$$358$$ 9.79583 + 16.9669i 0.517726 + 0.896727i
$$359$$ −4.00000 −0.211112 −0.105556 0.994413i $$-0.533662\pi$$
−0.105556 + 0.994413i $$0.533662\pi$$
$$360$$ 6.14741 + 10.6476i 0.323997 + 0.561179i
$$361$$ 5.50000 9.52628i 0.289474 0.501383i
$$362$$ 1.90477 3.29915i 0.100112 0.173400i
$$363$$ −4.82012 −0.252990
$$364$$ 0 0
$$365$$ −51.5708 −2.69934
$$366$$ −5.89792 + 10.2155i −0.308289 + 0.533972i
$$367$$ 10.6066 18.3712i 0.553660 0.958967i −0.444346 0.895855i $$-0.646564\pi$$
0.998006 0.0631123i $$-0.0201026\pi$$
$$368$$ −3.89792 6.75139i −0.203193 0.351940i
$$369$$ 2.97280 0.154758
$$370$$ 5.72904 + 9.92299i 0.297839 + 0.515871i
$$371$$ 0 0
$$372$$ 2.00000 0.103695
$$373$$ −3.29583 5.70855i −0.170652 0.295577i 0.767996 0.640454i $$-0.221254\pi$$
−0.938648 + 0.344877i $$0.887921\pi$$
$$374$$ 2.41006 4.17434i 0.124621 0.215850i
$$375$$ −19.6937 + 34.1106i −1.01698 + 1.76146i
$$376$$ 8.48528 0.437595
$$377$$ 2.19350 + 1.84988i 0.112971 + 0.0952737i
$$378$$ 0 0
$$379$$ −12.6937 + 21.9862i −0.652034 + 1.12936i 0.330595 + 0.943773i $$0.392751\pi$$
−0.982629 + 0.185583i $$0.940583\pi$$
$$380$$ −5.79583 + 10.0387i −0.297320 + 0.514973i
$$381$$ −8.19654 14.1968i −0.419922 0.727326i
$$382$$ −16.2042 −0.829077
$$383$$ 6.07522 + 10.5226i 0.310429 + 0.537680i 0.978455 0.206458i $$-0.0661938\pi$$
−0.668026 + 0.744138i $$0.732860\pi$$
$$384$$ −2.12132 3.67423i −0.108253 0.187500i
$$385$$ 0 0
$$386$$ −11.2958 19.5650i −0.574943 0.995830i
$$387$$ 3.89792 6.75139i 0.198142 0.343192i
$$388$$ 2.12132 3.67423i 0.107694 0.186531i
$$389$$ −0.387495 −0.0196468 −0.00982338 0.999952i $$-0.503127\pi$$
−0.00982338 + 0.999952i $$0.503127\pi$$
$$390$$ −19.6546 + 7.09841i −0.995250 + 0.359442i
$$391$$ −9.89949 −0.500639
$$392$$ 0 0
$$393$$ −3.79583 + 6.57457i −0.191474 + 0.331643i
$$394$$ 4.00000 + 6.92820i 0.201517 + 0.349038i
$$395$$ 9.03328 0.454514
$$396$$ 1.89792 + 3.28729i 0.0953739 + 0.165192i
$$397$$ 3.53553 + 6.12372i 0.177443 + 0.307341i 0.941004 0.338395i $$-0.109884\pi$$
−0.763561 + 0.645736i $$0.776551\pi$$
$$398$$ −5.07938 −0.254606
$$399$$ 0 0
$$400$$ 5.89792 10.2155i 0.294896 0.510774i
$$401$$ 2.19375 3.79968i 0.109551 0.189747i −0.806038 0.591864i $$-0.798392\pi$$
0.915588 + 0.402117i $$0.131726\pi$$
$$402$$ 5.36812 0.267737
$$403$$ 0.897916 5.01934i 0.0447284 0.250031i
$$404$$ −9.75513 −0.485336
$$405$$ −10.2457 + 17.7460i −0.509112 + 0.881808i
$$406$$ 0 0
$$407$$ 5.30625 + 9.19070i 0.263021 + 0.455566i
$$408$$ 5.38749 0.266721
$$409$$ 9.39420 + 16.2712i 0.464513 + 0.804561i 0.999179 0.0405026i $$-0.0128959\pi$$
−0.534666 + 0.845063i $$0.679563\pi$$
$$410$$ −6.09166 10.5511i −0.300846 0.521080i
$$411$$ 26.5813 1.31116
$$412$$ −2.68406 4.64893i −0.132234 0.229036i
$$413$$ 0 0
$$414$$ −3.89792 + 6.75139i −0.191572 + 0.331813i
$$415$$ −40.5708 −1.99154
$$416$$ −16.9558 + 6.12372i −0.831328 + 0.300240i
$$417$$ −2.40834 −0.117937
$$418$$ 5.36812 9.29785i 0.262563 0.454773i
$$419$$ −12.8576 + 22.2699i −0.628133 + 1.08796i 0.359794 + 0.933032i $$0.382847\pi$$
−0.987926 + 0.154926i $$0.950486\pi$$
$$420$$ 0 0
$$421$$ 12.5917 0.613680 0.306840 0.951761i $$-0.400728\pi$$
0.306840 + 0.951761i $$0.400728\pi$$
$$422$$ −3.89792 6.75139i −0.189748 0.328652i
$$423$$ −1.41421 2.44949i −0.0687614 0.119098i
$$424$$ 37.7750 1.83452
$$425$$ −7.48944 12.9721i −0.363291 0.629239i
$$426$$ 4.24264 7.34847i 0.205557 0.356034i
$$427$$ 0 0
$$428$$ 6.00000 0.290021
$$429$$ −18.2042 + 6.57457i −0.878906 + 0.317423i
$$430$$ −31.9494 −1.54074
$$431$$ −16.5917 + 28.7376i −0.799192 + 1.38424i 0.120950 + 0.992659i $$0.461406\pi$$
−0.920143 + 0.391583i $$0.871928\pi$$
$$432$$ 2.82843 4.89898i 0.136083 0.235702i
$$433$$ −10.2457 17.7460i −0.492376 0.852820i 0.507586 0.861601i $$-0.330538\pi$$
−0.999961 + 0.00878126i $$0.997205\pi$$
$$434$$ 0 0
$$435$$ −2.30625 3.99455i −0.110576 0.191524i
$$436$$ 0.795832 + 1.37842i 0.0381134 + 0.0660144i
$$437$$ −22.0499 −1.05479
$$438$$ 8.89792 + 15.4116i 0.425159 + 0.736397i
$$439$$ −10.0291 + 17.3710i −0.478664 + 0.829070i −0.999701 0.0244638i $$-0.992212\pi$$
0.521037 + 0.853534i $$0.325545\pi$$
$$440$$ 23.3345 40.4166i 1.11243 1.92678i
$$441$$ 0 0
$$442$$ 0.806253 4.50694i 0.0383495 0.214373i
$$443$$ 10.0000 0.475114 0.237557 0.971374i $$-0.423653\pi$$
0.237557 + 0.971374i $$0.423653\pi$$
$$444$$ −1.97695 + 3.42418i −0.0938220 + 0.162504i
$$445$$ 30.6937 53.1631i 1.45502 2.52017i
$$446$$ −2.82843 4.89898i −0.133930 0.231973i
$$447$$ 20.6357 0.976036
$$448$$ 0 0
$$449$$ −11.7958 20.4310i −0.556680 0.964198i −0.997771 0.0667352i $$-0.978742\pi$$
0.441091 0.897462i $$-0.354592\pi$$
$$450$$ −11.7958 −0.556061
$$451$$ −5.64212 9.77243i −0.265677 0.460166i
$$452$$ 1.29583 2.24445i 0.0609508 0.105570i
$$453$$ 1.12548 1.94938i 0.0528795 0.0915899i
$$454$$ −7.35981 −0.345413
$$455$$ 0 0
$$456$$ 12.0000 0.561951
$$457$$ −2.29583 + 3.97650i −0.107394 + 0.186013i −0.914714 0.404102i $$-0.867584\pi$$
0.807320 + 0.590115i $$0.200917\pi$$
$$458$$ 6.36396 11.0227i 0.297368 0.515057i
$$459$$ −3.59166 6.22094i −0.167644 0.290369i
$$460$$ −31.9494 −1.48965
$$461$$ 12.0930 + 20.9457i 0.563227 + 0.975538i 0.997212 + 0.0746180i $$0.0237737\pi$$
−0.433985 + 0.900920i $$0.642893\pi$$
$$462$$ 0 0
$$463$$ −17.3875 −0.808065 −0.404033 0.914745i $$-0.632392\pi$$
−0.404033 + 0.914745i $$0.632392\pi$$
$$464$$ 0.397916 + 0.689210i 0.0184728 + 0.0319958i
$$465$$ −4.09827 + 7.09841i −0.190053 + 0.329181i
$$466$$ −8.59166 + 14.8812i −0.398001 + 0.689358i
$$467$$ 31.9494 1.47844 0.739222 0.673462i $$-0.235194\pi$$
0.739222 + 0.673462i $$0.235194\pi$$
$$468$$ 2.75624 + 2.32446i 0.127407 + 0.107448i
$$469$$ 0 0
$$470$$ −5.79583 + 10.0387i −0.267342 + 0.463050i
$$471$$ 0.102084 0.176815i 0.00470379 0.00814721i
$$472$$ 18.6588 + 32.3179i 0.858840 + 1.48755i
$$473$$ −29.5917 −1.36063
$$474$$ −1.55858 2.69954i −0.0715881 0.123994i
$$475$$ −16.6818 28.8938i −0.765415 1.32574i
$$476$$ 0 0
$$477$$ −6.29583 10.9047i −0.288266 0.499292i
$$478$$ 5.10208 8.83707i 0.233364 0.404198i
$$479$$ −10.4622 + 18.1211i −0.478032 + 0.827975i −0.999683 0.0251838i $$-0.991983\pi$$
0.521651 + 0.853159i $$0.325316\pi$$
$$480$$ 28.9792 1.32271
$$481$$ 7.70599 + 6.49881i 0.351363 + 0.296320i
$$482$$ −11.1693 −0.508749
$$483$$ 0 0
$$484$$ 1.70417 2.95171i 0.0774622 0.134168i
$$485$$ 8.69375 + 15.0580i 0.394763 + 0.683749i
$$486$$ −9.89949 −0.449050
$$487$$ −0.204168 0.353630i −0.00925176 0.0160245i 0.861362 0.507991i $$-0.169612\pi$$
−0.870614 + 0.491966i $$0.836278\pi$$
$$488$$ −12.5114 21.6703i −0.566363 0.980970i
$$489$$ −21.7612 −0.984076
$$490$$ 0 0
$$491$$ −4.79583 + 8.30662i −0.216433 + 0.374873i −0.953715 0.300712i $$-0.902776\pi$$
0.737282 + 0.675585i $$0.236109\pi$$
$$492$$ 2.10208 3.64092i 0.0947693 0.164145i
$$493$$ 1.01058 0.0455143
$$494$$ 1.79583 10.0387i 0.0807983 0.451661i
$$495$$ −15.5563 −0.699206
$$496$$ 0.707107 1.22474i 0.0317500 0.0549927i
$$497$$ 0 0
$$498$$ 7.00000 + 12.1244i 0.313678 + 0.543305i
$$499$$ 25.7958 1.15478 0.577390 0.816468i $$-0.304071\pi$$
0.577390 + 0.816468i $$0.304071\pi$$
$$500$$ −13.9256 24.1198i −0.622771 1.07867i
$$501$$ −1.20417 2.08568i −0.0537983 0.0931814i
$$502$$ 16.6818 0.744546
$$503$$ 12.8576 + 22.2699i 0.573290 + 0.992967i 0.996225 + 0.0868074i $$0.0276665\pi$$
−0.422935 + 0.906160i $$0.639000\pi$$
$$504$$ 0 0
$$505$$ 19.9896 34.6230i 0.889525 1.54070i
$$506$$ 29.5917 1.31551
$$507$$ −14.1421 + 11.7473i −0.628074 + 0.521718i
$$508$$ 11.5917 0.514297
$$509$$ 3.04498 5.27406i 0.134966 0.233769i −0.790618 0.612309i $$-0.790241\pi$$
0.925585 + 0.378541i $$0.123574\pi$$
$$510$$ −3.67990 + 6.37378i −0.162949 + 0.282236i
$$511$$ 0 0
$$512$$ −11.0000 −0.486136
$$513$$ −8.00000 13.8564i −0.353209 0.611775i
$$514$$ 4.31483 + 7.47350i 0.190319 + 0.329642i
$$515$$ 22.0000 0.969436
$$516$$ −5.51249 9.54790i −0.242674 0.420323i
$$517$$ −5.36812 + 9.29785i −0.236089 + 0.408919i
$$518$$ 0 0
$$519$$ −25.1833 −1.10543
$$520$$ 7.80625 43.6369i 0.342327 1.91360i
$$521$$ −4.67575 −0.204848 −0.102424 0.994741i $$-0.532660\pi$$
−0.102424 + 0.994741i $$0.532660\pi$$
$$522$$ 0.397916 0.689210i 0.0174163 0.0301659i
$$523$$ 21.0688 36.4923i 0.921276 1.59570i 0.123832 0.992303i $$-0.460482\pi$$
0.797444 0.603393i $$-0.206185\pi$$
$$524$$ −2.68406 4.64893i −0.117254 0.203089i
$$525$$ 0 0
$$526$$ −1.69375 2.93366i −0.0738509 0.127913i
$$527$$ −0.897916 1.55524i −0.0391138 0.0677471i
$$528$$ −5.36812 −0.233617
$$529$$ −18.8875 32.7141i −0.821195 1.42235i
$$530$$ −25.8020 + 44.6904i −1.12077 + 1.94123i
$$531$$ 6.21959 10.7726i 0.269907 0.467493i
$$532$$ 0 0
$$533$$ −8.19375 6.91015i −0.354911 0.299312i
$$534$$ −21.1833 −0.916692
$$535$$ −12.2948 + 21.2952i −0.531551 + 0.920674i
$$536$$ −5.69375 + 9.86186i −0.245932 + 0.425967i
$$537$$ −13.8534 23.9948i −0.597818 1.03545i
$$538$$ −12.4392 −0.536291
$$539$$ 0 0
$$540$$ −11.5917 20.0773i −0.498826 0.863992i
$$541$$ 6.59166 0.283398 0.141699 0.989910i $$-0.454744\pi$$
0.141699 + 0.989910i $$0.454744\pi$$
$$542$$ 8.75928 + 15.1715i 0.376243 + 0.651673i
$$543$$ −2.69375 + 4.66571i −0.115600 + 0.200225i
$$544$$ −3.17461 + 5.49859i −0.136110 + 0.235750i
$$545$$ −6.52307 −0.279418
$$546$$ 0 0
$$547$$ 10.9792 0.469435 0.234717 0.972064i $$-0.424584\pi$$
0.234717 + 0.972064i $$0.424584\pi$$
$$548$$ −9.39792 + 16.2777i −0.401459 + 0.695347i
$$549$$ −4.17046 + 7.22344i −0.177991 + 0.308289i
$$550$$ 22.3875 + 38.7763i 0.954606 + 1.65343i
$$551$$ 2.25095 0.0958938
$$552$$ 16.5375 + 28.6437i 0.703881 + 1.21916i
$$553$$ 0 0
$$554$$ 32.1833 1.36734
$$555$$ −8.10208 14.0332i −0.343914 0.595677i
$$556$$ 0.851476 1.47480i 0.0361106 0.0625454i
$$557$$ −0.704168 + 1.21966i −0.0298366 + 0.0516785i −0.880558 0.473938i $$-0.842832\pi$$
0.850722 + 0.525617i $$0.176165\pi$$
$$558$$ −1.41421 −0.0598684
$$559$$ −26.4370 + 9.54790i −1.11816 + 0.403833i
$$560$$ 0 0
$$561$$ −3.40834 + 5.90341i −0.143900 + 0.249242i
$$562$$ −12.3979 + 21.4738i −0.522975 + 0.905818i
$$563$$ 6.21959 + 10.7726i 0.262125 + 0.454013i 0.966806 0.255511i $$-0.0822435\pi$$
−0.704682 + 0.709524i $$0.748910\pi$$
$$564$$ −4.00000 −0.168430
$$565$$ 5.31067 + 9.19835i 0.223422 + 0.386977i
$$566$$ −7.92254 13.7222i −0.333009 0.576789i
$$567$$ 0 0
$$568$$ 9.00000 + 15.5885i 0.377632 + 0.654077i
$$569$$ −12.7958 + 22.1630i −0.536429 + 0.929123i 0.462664 + 0.886534i $$0.346894\pi$$
−0.999093 + 0.0425886i $$0.986440\pi$$
$$570$$ −8.19654 + 14.1968i −0.343315 + 0.594640i
$$571$$ −23.1833 −0.970192 −0.485096 0.874461i $$-0.661215\pi$$
−0.485096 + 0.874461i $$0.661215\pi$$
$$572$$ 2.41006 13.4722i 0.100770 0.563301i
$$573$$ 22.9162 0.957336
$$574$$ 0 0
$$575$$ 45.9792 79.6382i 1.91746 3.32114i
$$576$$ 3.50000 + 6.06218i 0.145833 + 0.252591i
$$577$$ −24.7340 −1.02969 −0.514845 0.857283i $$-0.672151\pi$$
−0.514845 + 0.857283i $$0.672151\pi$$
$$578$$ 7.69375 + 13.3260i 0.320018 + 0.554287i
$$579$$ 15.9747 + 27.6690i 0.663887 + 1.14989i
$$580$$ 3.26153 0.135428
$$581$$ 0 0
$$582$$ 3.00000 5.19615i 0.124354 0.215387i
$$583$$ −23.8979 + 41.3924i −0.989751 + 1.71430i
$$584$$ −37.7507 −1.56213
$$585$$ −13.8979 + 5.01934i −0.574608 + 0.207524i
$$586$$ 2.97280 0.122805
$$587$$ 8.34091 14.4469i 0.344266 0.596287i −0.640954 0.767579i $$-0.721461\pi$$
0.985220 + 0.171293i $$0.0547944\pi$$
$$588$$ 0 0
$$589$$ −2.00000 3.46410i −0.0824086 0.142736i
$$590$$ −50.9792 −2.09878
$$591$$ −5.65685 9.79796i −0.232692 0.403034i
$$592$$ 1.39792 + 2.42126i 0.0574540 + 0.0995132i
$$593$$ 8.34091 0.342520 0.171260 0.985226i $$-0.445216\pi$$
0.171260 + 0.985226i $$0.445216\pi$$
$$594$$ 10.7362 + 18.5957i 0.440513 + 0.762991i
$$595$$ 0 0
$$596$$ −7.29583 + 12.6368i −0.298849 + 0.517621i
$$597$$ 7.18333 0.293994
$$598$$ 26.4370 9.54790i 1.08109 0.390443i
$$599$$ −33.5917 −1.37252 −0.686259 0.727357i $$-0.740748\pi$$
−0.686259 + 0.727357i $$0.740748\pi$$
$$600$$ −25.0227 + 43.3407i −1.02155 + 1.76937i
$$601$$ −12.0930 + 20.9457i −0.493284 + 0.854393i −0.999970 0.00773797i $$-0.997537\pi$$
0.506686 + 0.862130i $$0.330870\pi$$
$$602$$ 0 0
$$603$$ 3.79583 0.154578
$$604$$ 0.795832 + 1.37842i 0.0323819 + 0.0560871i
$$605$$ 6.98415 + 12.0969i 0.283946 + 0.491809i
$$606$$ −13.7958 −0.560417
$$607$$ 2.39532 + 4.14882i 0.0972231 + 0.168395i 0.910534 0.413434i $$-0.135671\pi$$
−0.813311 + 0.581829i $$0.802337\pi$$
$$608$$ −7.07107 + 12.2474i −0.286770 + 0.496700i
$$609$$ 0 0
$$610$$ 34.1833 1.38404
$$611$$ −1.79583 + 10.0387i −0.0726516 + 0.406121i
$$612$$ 1.26984 0.0513304
$$613$$ −20.9896 + 36.3550i −0.847761 + 1.46837i 0.0354405 + 0.999372i $$0.488717\pi$$
−0.883202 + 0.468994i $$0.844617\pi$$
$$614$$ −10.0291 + 17.3710i −0.404743 + 0.701035i
$$615$$ 8.61491 + 14.9215i 0.347387 + 0.601692i
$$616$$ 0 0
$$617$$ −2.19375 3.79968i −0.0883169 0.152969i 0.818483 0.574531i $$-0.194815\pi$$
−0.906800 + 0.421561i $$0.861482\pi$$
$$618$$ −3.79583 6.57457i −0.152691 0.264468i
$$619$$ 33.9116 1.36302 0.681512 0.731807i $$-0.261323\pi$$
0.681512 + 0.731807i $$0.261323\pi$$
$$620$$ −2.89792 5.01934i −0.116383 0.201581i
$$621$$ 22.0499 38.1916i 0.884834 1.53258i
$$622$$ −14.4161 + 24.9695i −0.578034 + 1.00118i
$$623$$ 0 0
$$624$$ −4.79583 + 1.73205i −0.191987 + 0.0693375i
$$625$$ 55.1625 2.20650
$$626$$ 7.63381 13.2221i 0.305108 0.528463i
$$627$$ −7.59166 + 13.1491i −0.303182 + 0.525126i
$$628$$ 0.0721845 + 0.125027i 0.00288047 + 0.00498913i
$$629$$ 3.55027 0.141559
$$630$$ 0 0
$$631$$ 19.7958 + 34.2874i 0.788060 + 1.36496i 0.927154 + 0.374680i $$0.122247\pi$$
−0.139095 + 0.990279i $$0.544419\pi$$
$$632$$ 6.61251 0.263031
$$633$$ 5.51249 + 9.54790i 0.219102 + 0.379495i
$$634$$ −3.29583 + 5.70855i −0.130894 + 0.226715i
$$635$$ −23.7529 + 41.1412i −0.942605 + 1.63264i
$$636$$ −17.8073 −0.706105
$$637$$ 0 0
$$638$$ −3.02084 −0.119596
$$639$$ 3.00000 5.19615i 0.118678 0.205557i
$$640$$ −6.14741 + 10.6476i −0.242998 + 0.420884i
$$641$$ 2.39792 + 4.15331i 0.0947120 + 0.164046i 0.909488 0.415729i $$-0.136474\pi$$
−0.814776 + 0.579775i $$0.803140\pi$$
$$642$$ 8.48528 0.334887
$$643$$ 2.82843 + 4.89898i 0.111542 + 0.193197i 0.916392 0.400281i $$-0.131088\pi$$
−0.804850 + 0.593478i $$0.797754\pi$$
$$644$$ 0 0
$$645$$ 45.1833 1.77909
$$646$$ −1.79583 3.11047i −0.0706560 0.122380i
$$647$$ 19.3659 33.5427i 0.761351 1.31870i −0.180803 0.983519i $$-0.557870\pi$$
0.942154 0.335180i $$-0.108797\pi$$
$$648$$ −7.50000 + 12.9904i −0.294628 + 0.510310i
$$649$$ −47.2170 −1.85343
$$650$$ 32.5122 + 27.4190i 1.27523 + 1.07546i
$$651$$ 0 0
$$652$$ 7.69375 13.3260i 0.301310 0.521885i
$$653$$ 6.59166 11.4171i 0.257952 0.446785i −0.707741 0.706472i $$-0.750286\pi$$
0.965693 + 0.259686i $$0.0836191\pi$$
$$654$$ 1.12548 + 1.94938i 0.0440096 + 0.0762268i
$$655$$ 22.0000 0.859611
$$656$$ −1.48640 2.57452i −0.0580341 0.100518i
$$657$$ 6.29178 + 10.8977i 0.245466 + 0.425159i
$$658$$ 0 0
$$659$$ 9.20417 + 15.9421i 0.358543 + 0.621016i 0.987718 0.156249i $$-0.0499401\pi$$
−0.629174 + 0.777264i $$0.716607\pi$$
$$660$$ −11.0000 + 19.0526i −0.428174 + 0.741620i
$$661$$ 3.75209 6.49881i 0.145939 0.252774i −0.783784 0.621034i $$-0.786713\pi$$
0.929723 + 0.368260i $$0.120046\pi$$
$$662$$ 29.3875 1.14218
$$663$$ −1.14021 + 6.37378i −0.0442822 + 0.247537i
$$664$$ −29.6985 −1.15252
$$665$$ 0 0
$$666$$ 1.39792 2.42126i 0.0541681 0.0938220i
$$667$$ 3.10208 + 5.37297i 0.120113 + 0.208042i
$$668$$ 1.70295 0.0658892
$$669$$ 4.00000 + 6.92820i 0.154649 + 0.267860i
$$670$$ −7.77817 13.4722i −0.300497 0.520476i
$$671$$ 31.6607 1.22225
$$672$$ 0 0
$$673$$ 11.9896 20.7666i 0.462164 0.800492i −0.536904 0.843643i $$-0.680406\pi$$
0.999069 + 0.0431511i $$0.0137397\pi$$
$$674$$ −8.98958 + 15.5704i −0.346266 + 0.599750i
$$675$$ 66.7273 2.56833
$$676$$ −2.19375 12.8136i −0.0843749 0.492829i
$$677$$ −7.64854 −0.293957 −0.146979 0.989140i $$-0.546955\pi$$
−0.146979 + 0.989140i $$0.546955\pi$$
$$678$$ 1.83258 3.17413i 0.0703799 0.121902i
$$679$$ 0 0
$$680$$ −7.80625 13.5208i −0.299356 0.518500i
$$681$$ 10.4083 0.398848
$$682$$ 2.68406 + 4.64893i 0.102778 + 0.178017i
$$683$$ 3.38749 + 5.86731i 0.129619 + 0.224506i 0.923529 0.383529i $$-0.125291\pi$$
−0.793910 + 0.608035i $$0.791958\pi$$
$$684$$ 2.82843 0.108148
$$685$$ −38.5152 66.7103i −1.47159 2.54887i
$$686$$ 0 0
$$687$$ −9.00000 + 15.5885i −0.343371 + 0.594737i
$$688$$ −7.79583 −0.297213
$$689$$ −7.99473 + 44.6904i −0.304575 + 1.70257i
$$690$$ −45.1833 −1.72010
$$691$$ −1.26984 + 2.19944i −0.0483072 + 0.0836705i −0.889168 0.457581i $$-0.848716\pi$$
0.840861 + 0.541251i $$0.182049\pi$$
$$692$$ 8.90365 15.4216i 0.338466 0.586240i
$$693$$ 0 0
$$694$$ −32.9792 −1.25187
$$695$$ 3.48958 + 6.04413i 0.132367 + 0.229267i
$$696$$ −1.68821 2.92407i −0.0639916 0.110837i
$$697$$ −3.77499 −0.142988
$$698$$ 13.2907 + 23.0201i 0.503059 + 0.871324i
$$699$$ 12.1504 21.0452i 0.459572 0.796002i
$$700$$ 0 0
$$701$$ −29.5917 −1.11766 −0.558831 0.829282i $$-0.688750\pi$$
−0.558831 + 0.829282i $$0.688750\pi$$
$$702$$ 15.5917 + 13.1491i 0.588469 + 0.496283i
$$703$$ 7.90781 0.298249
$$704$$ 13.2854 23.0110i 0.500713 0.867260i
$$705$$ 8.19654 14.1968i 0.308700 0.534684i
$$706$$ 2.61187 + 4.52390i 0.0982992 + 0.170259i
$$707$$ 0 0
$$708$$ −8.79583 15.2348i −0.330568 0.572560i
$$709$$ 4.60208 + 7.97104i 0.172835 + 0.299359i 0.939410 0.342796i $$-0.111374\pi$$
−0.766575 + 0.642155i $$0.778041\pi$$
$$710$$ −24.5896 −0.922832
$$711$$ −1.10208 1.90887i −0.0413314 0.0715881i
$$712$$ 22.4683 38.9163i 0.842036 1.45845i
$$713$$ 5.51249 9.54790i 0.206444 0.357572i
$$714$$ 0 0
$$715$$ 42.8771 + 36.1602i 1.60351 + 1.35231i
$$716$$ 19.5917 0.732175
$$717$$ −7.21544 + 12.4975i −0.269465 + 0.466728i
$$718$$ 2.00000 3.46410i 0.0746393 0.129279i
$$719$$ 0.995845 + 1.72485i 0.0371387 + 0.0643262i 0.883997 0.467492i $$-0.154842\pi$$
−0.846859 + 0.531818i $$0.821509\pi$$
$$720$$ −4.09827 −0.152734
$$721$$ 0 0
$$722$$ 5.50000 + 9.52628i 0.204689 + 0.354531i
$$723$$ 15.7958 0.587453
$$724$$ −1.90477 3.29915i −0.0707901 0.122612i
$$725$$ −4.69375 + 8.12981i −0.174321 + 0.301934i
$$726$$ 2.41006 4.17434i 0.0894456 0.154924i
$$727$$ −32.4974 −1.20526 −0.602632 0.798020i $$-0.705881\pi$$
−0.602632 + 0.798020i $$0.705881\pi$$
$$728$$ 0 0
$$729$$ 29.0000 1.07407
$$730$$ 25.7854 44.6616i 0.954361 1.65300i
$$731$$ −4.94975 + 8.57321i −0.183073 + 0.317092i
$$732$$ 5.89792 + 10.2155i 0.217993 + 0.377575i
$$733$$ 33.2193 1.22698 0.613491 0.789702i $$-0.289765\pi$$
0.613491 + 0.789702i $$0.289765\pi$$
$$734$$ 10.6066 + 18.3712i 0.391497 + 0.678092i
$$735$$ 0 0
$$736$$ −38.9792 −1.43679
$$737$$ −7.20417 12.4780i −0.265369 0.459633i
$$738$$ −1.48640 + 2.57452i −0.0547151 + 0.0947693i
$$739$$ 11.5917 20.0773i 0.426406 0.738557i −0.570144 0.821545i $$-0.693113\pi$$
0.996551 + 0.0829873i $$0.0264461\pi$$
$$740$$ 11.4581 0.421207
$$741$$ −2.53969 + 14.1968i −0.0932978 + 0.521534i
$$742$$ 0 0
$$743$$ 14.5917 25.2735i 0.535316 0.927195i −0.463832 0.885923i $$-0.653526\pi$$
0.999148 0.0412716i $$-0.0131409\pi$$
$$744$$ −3.00000 + 5.19615i −0.109985 + 0.190500i
$$745$$ −29.9003 51.7888i −1.09546 1.89740i
$$746$$ 6.59166 0.241338
$$747$$ 4.94975 + 8.57321i 0.181102 + 0.313678i
$$748$$ −2.41006 4.17434i −0.0881205 0.152629i
$$749$$ 0 0
$$750$$ −19.6937 34.1106i −0.719114 1.24554i
$$751$$ 3.89792 6.75139i 0.142237 0.246362i −0.786102 0.618097i $$-0.787904\pi$$
0.928339 + 0.371735i $$0.121237\pi$$
$$752$$ −1.41421 + 2.44949i −0.0515711 + 0.0893237i
$$753$$ −23.5917 −0.859728
$$754$$ −2.69880 + 0.974691i −0.0982844 + 0.0354961i
$$755$$ −6.52307 −0.237399
$$756$$ 0 0
$$757$$ −6.59166 + 11.4171i −0.239578 + 0.414961i −0.960593 0.277958i $$-0.910342\pi$$
0.721015 + 0.692919i $$0.243676\pi$$
$$758$$ −12.6937 21.9862i −0.461058 0.798575i
$$759$$ −41.8489 −1.51902
$$760$$ −17.3875 30.1160i −0.630711 1.09242i
$$761$$ −8.90365 15.4216i −0.322757 0.559032i 0.658299 0.752757i $$-0.271276\pi$$
−0.981056 + 0.193725i $$0.937943\pi$$
$$762$$ 16.3931 0.593859
$$763$$ 0 0
$$764$$ −8.10208 + 14.0332i −0.293123 + 0.507704i
$$765$$ −2.60208 + 4.50694i −0.0940786 + 0.162949i
$$766$$ −12.1504 −0.439013
$$767$$ −42.1833 + 15.2348i −1.52315 + 0.550098i
$$768$$ 24.0416 0.867528
$$769$$ 2.12132 3.67423i 0.0764968 0.132496i −0.825239 0.564783i $$-0.808960\pi$$
0.901736 + 0.432287i $$0.142293\pi$$
$$770$$ 0 0
$$771$$ −6.10208 10.5691i −0.219761 0.380638i
$$772$$ −22.5917 −0.813092
$$773$$ 17.3889 + 30.1185i 0.625436 + 1.08329i 0.988456 + 0.151506i $$0.0484124\pi$$
−0.363020 + 0.931781i $$0.618254\pi$$
$$774$$ 3.89792 + 6.75139i 0.140108 + 0.242674i
$$775$$ 16.6818 0.599229
$$776$$ 6.36396 + 11.0227i 0.228453 + 0.395692i
$$777$$ 0 0
$$778$$ 0.193747 0.335580i 0.00694618 0.0120311i
$$779$$ −8.40834 −0.301260
$$780$$ −3.67990 + 20.5706i −0.131762 + 0.736546i
$$781$$ −22.7750 −0.814953
$$782$$ 4.94975 8.57321i 0.177003 0.306578i
$$783$$ −2.25095 +