Properties

 Label 882.2.h.m.79.1 Level $882$ Weight $2$ Character 882.79 Analytic conductor $7.043$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$882 = 2 \cdot 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 882.h (of order $$3$$, degree $$2$$, not minimal)

Newform invariants

 Self dual: no Analytic conductor: $$7.04280545828$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\sqrt{-3}, \sqrt{-11})$$ Defining polynomial: $$x^{4} - x^{3} - 2 x^{2} - 3 x + 9$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 126) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

 Embedding label 79.1 Root $$1.68614 + 0.396143i$$ of defining polynomial Character $$\chi$$ $$=$$ 882.79 Dual form 882.2.h.m.67.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 + 0.866025i) q^{2} +(-1.68614 - 0.396143i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.37228 q^{5} +(-0.500000 - 1.65831i) q^{6} -1.00000 q^{8} +(2.68614 + 1.33591i) q^{9} +O(q^{10})$$ $$q+(0.500000 + 0.866025i) q^{2} +(-1.68614 - 0.396143i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.37228 q^{5} +(-0.500000 - 1.65831i) q^{6} -1.00000 q^{8} +(2.68614 + 1.33591i) q^{9} +(-0.686141 - 1.18843i) q^{10} +4.37228 q^{11} +(1.18614 - 1.26217i) q^{12} +(-1.00000 - 1.73205i) q^{13} +(2.31386 + 0.543620i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.18614 + 3.78651i) q^{17} +(0.186141 + 2.99422i) q^{18} +(-2.50000 + 4.33013i) q^{19} +(0.686141 - 1.18843i) q^{20} +(2.18614 + 3.78651i) q^{22} -7.37228 q^{23} +(1.68614 + 0.396143i) q^{24} -3.11684 q^{25} +(1.00000 - 1.73205i) q^{26} +(-4.00000 - 3.31662i) q^{27} +(-1.37228 + 2.37686i) q^{29} +(0.686141 + 2.27567i) q^{30} +(-1.00000 + 1.73205i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-7.37228 - 1.73205i) q^{33} +(-2.18614 + 3.78651i) q^{34} +(-2.50000 + 1.65831i) q^{36} +(-1.00000 + 1.73205i) q^{37} -5.00000 q^{38} +(1.00000 + 3.31662i) q^{39} +1.37228 q^{40} +(-5.18614 - 8.98266i) q^{41} +(-4.55842 + 7.89542i) q^{43} +(-2.18614 + 3.78651i) q^{44} +(-3.68614 - 1.83324i) q^{45} +(-3.68614 - 6.38458i) q^{46} +(0.500000 + 1.65831i) q^{48} +(-1.55842 - 2.69927i) q^{50} +(-2.18614 - 7.25061i) q^{51} +2.00000 q^{52} +(-1.37228 - 2.37686i) q^{53} +(0.872281 - 5.12241i) q^{54} -6.00000 q^{55} +(5.93070 - 6.31084i) q^{57} -2.74456 q^{58} +(-3.55842 + 6.16337i) q^{59} +(-1.62772 + 1.73205i) q^{60} +(7.05842 + 12.2255i) q^{61} -2.00000 q^{62} +1.00000 q^{64} +(1.37228 + 2.37686i) q^{65} +(-2.18614 - 7.25061i) q^{66} +(-7.55842 + 13.0916i) q^{67} -4.37228 q^{68} +(12.4307 + 2.92048i) q^{69} +10.1168 q^{71} +(-2.68614 - 1.33591i) q^{72} +(2.55842 + 4.43132i) q^{73} -2.00000 q^{74} +(5.25544 + 1.23472i) q^{75} +(-2.50000 - 4.33013i) q^{76} +(-2.37228 + 2.52434i) q^{78} +(-6.05842 - 10.4935i) q^{79} +(0.686141 + 1.18843i) q^{80} +(5.43070 + 7.17687i) q^{81} +(5.18614 - 8.98266i) q^{82} +(2.74456 - 4.75372i) q^{83} +(-3.00000 - 5.19615i) q^{85} -9.11684 q^{86} +(3.25544 - 3.46410i) q^{87} -4.37228 q^{88} +(-1.62772 + 2.81929i) q^{89} +(-0.255437 - 4.10891i) q^{90} +(3.68614 - 6.38458i) q^{92} +(2.37228 - 2.52434i) q^{93} +(3.43070 - 5.94215i) q^{95} +(-1.18614 + 1.26217i) q^{96} +(-4.55842 + 7.89542i) q^{97} +(11.7446 + 5.84096i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 2 q^{2} - q^{3} - 2 q^{4} + 6 q^{5} - 2 q^{6} - 4 q^{8} + 5 q^{9} + O(q^{10})$$ $$4 q + 2 q^{2} - q^{3} - 2 q^{4} + 6 q^{5} - 2 q^{6} - 4 q^{8} + 5 q^{9} + 3 q^{10} + 6 q^{11} - q^{12} - 4 q^{13} + 15 q^{15} - 2 q^{16} + 3 q^{17} - 5 q^{18} - 10 q^{19} - 3 q^{20} + 3 q^{22} - 18 q^{23} + q^{24} + 22 q^{25} + 4 q^{26} - 16 q^{27} + 6 q^{29} - 3 q^{30} - 4 q^{31} + 2 q^{32} - 18 q^{33} - 3 q^{34} - 10 q^{36} - 4 q^{37} - 20 q^{38} + 4 q^{39} - 6 q^{40} - 15 q^{41} - q^{43} - 3 q^{44} - 9 q^{45} - 9 q^{46} + 2 q^{48} + 11 q^{50} - 3 q^{51} + 8 q^{52} + 6 q^{53} - 8 q^{54} - 24 q^{55} - 5 q^{57} + 12 q^{58} + 3 q^{59} - 18 q^{60} + 11 q^{61} - 8 q^{62} + 4 q^{64} - 6 q^{65} - 3 q^{66} - 13 q^{67} - 6 q^{68} + 21 q^{69} + 6 q^{71} - 5 q^{72} - 7 q^{73} - 8 q^{74} + 44 q^{75} - 10 q^{76} + 2 q^{78} - 7 q^{79} - 3 q^{80} - 7 q^{81} + 15 q^{82} - 12 q^{83} - 12 q^{85} - 2 q^{86} + 36 q^{87} - 6 q^{88} - 18 q^{89} - 24 q^{90} + 9 q^{92} - 2 q^{93} - 15 q^{95} + q^{96} - q^{97} + 24 q^{99} + O(q^{100})$$

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$$.

 $$n$$ $$199$$ $$785$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$

Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.500000 + 0.866025i 0.353553 + 0.612372i
$$3$$ −1.68614 0.396143i −0.973494 0.228714i
$$4$$ −0.500000 + 0.866025i −0.250000 + 0.433013i
$$5$$ −1.37228 −0.613703 −0.306851 0.951757i $$-0.599275\pi$$
−0.306851 + 0.951757i $$0.599275\pi$$
$$6$$ −0.500000 1.65831i −0.204124 0.677003i
$$7$$ 0 0
$$8$$ −1.00000 −0.353553
$$9$$ 2.68614 + 1.33591i 0.895380 + 0.445302i
$$10$$ −0.686141 1.18843i −0.216977 0.375815i
$$11$$ 4.37228 1.31829 0.659146 0.752015i $$-0.270918\pi$$
0.659146 + 0.752015i $$0.270918\pi$$
$$12$$ 1.18614 1.26217i 0.342409 0.364357i
$$13$$ −1.00000 1.73205i −0.277350 0.480384i 0.693375 0.720577i $$-0.256123\pi$$
−0.970725 + 0.240192i $$0.922790\pi$$
$$14$$ 0 0
$$15$$ 2.31386 + 0.543620i 0.597436 + 0.140362i
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ 2.18614 + 3.78651i 0.530217 + 0.918363i 0.999379 + 0.0352504i $$0.0112229\pi$$
−0.469162 + 0.883112i $$0.655444\pi$$
$$18$$ 0.186141 + 2.99422i 0.0438738 + 0.705744i
$$19$$ −2.50000 + 4.33013i −0.573539 + 0.993399i 0.422659 + 0.906289i $$0.361097\pi$$
−0.996199 + 0.0871106i $$0.972237\pi$$
$$20$$ 0.686141 1.18843i 0.153426 0.265741i
$$21$$ 0 0
$$22$$ 2.18614 + 3.78651i 0.466087 + 0.807286i
$$23$$ −7.37228 −1.53723 −0.768613 0.639713i $$-0.779053\pi$$
−0.768613 + 0.639713i $$0.779053\pi$$
$$24$$ 1.68614 + 0.396143i 0.344182 + 0.0808625i
$$25$$ −3.11684 −0.623369
$$26$$ 1.00000 1.73205i 0.196116 0.339683i
$$27$$ −4.00000 3.31662i −0.769800 0.638285i
$$28$$ 0 0
$$29$$ −1.37228 + 2.37686i −0.254826 + 0.441372i −0.964848 0.262807i $$-0.915352\pi$$
0.710022 + 0.704179i $$0.248685\pi$$
$$30$$ 0.686141 + 2.27567i 0.125272 + 0.415479i
$$31$$ −1.00000 + 1.73205i −0.179605 + 0.311086i −0.941745 0.336327i $$-0.890815\pi$$
0.762140 + 0.647412i $$0.224149\pi$$
$$32$$ 0.500000 0.866025i 0.0883883 0.153093i
$$33$$ −7.37228 1.73205i −1.28335 0.301511i
$$34$$ −2.18614 + 3.78651i −0.374920 + 0.649381i
$$35$$ 0 0
$$36$$ −2.50000 + 1.65831i −0.416667 + 0.276385i
$$37$$ −1.00000 + 1.73205i −0.164399 + 0.284747i −0.936442 0.350823i $$-0.885902\pi$$
0.772043 + 0.635571i $$0.219235\pi$$
$$38$$ −5.00000 −0.811107
$$39$$ 1.00000 + 3.31662i 0.160128 + 0.531085i
$$40$$ 1.37228 0.216977
$$41$$ −5.18614 8.98266i −0.809939 1.40286i −0.912906 0.408171i $$-0.866167\pi$$
0.102966 0.994685i $$-0.467167\pi$$
$$42$$ 0 0
$$43$$ −4.55842 + 7.89542i −0.695153 + 1.20404i 0.274976 + 0.961451i $$0.411330\pi$$
−0.970129 + 0.242589i $$0.922003\pi$$
$$44$$ −2.18614 + 3.78651i −0.329573 + 0.570837i
$$45$$ −3.68614 1.83324i −0.549497 0.273283i
$$46$$ −3.68614 6.38458i −0.543492 0.941355i
$$47$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$48$$ 0.500000 + 1.65831i 0.0721688 + 0.239357i
$$49$$ 0 0
$$50$$ −1.55842 2.69927i −0.220394 0.381734i
$$51$$ −2.18614 7.25061i −0.306121 1.01529i
$$52$$ 2.00000 0.277350
$$53$$ −1.37228 2.37686i −0.188497 0.326487i 0.756252 0.654280i $$-0.227028\pi$$
−0.944749 + 0.327793i $$0.893695\pi$$
$$54$$ 0.872281 5.12241i 0.118702 0.697072i
$$55$$ −6.00000 −0.809040
$$56$$ 0 0
$$57$$ 5.93070 6.31084i 0.785541 0.835892i
$$58$$ −2.74456 −0.360379
$$59$$ −3.55842 + 6.16337i −0.463267 + 0.802402i −0.999121 0.0419083i $$-0.986656\pi$$
0.535854 + 0.844310i $$0.319990\pi$$
$$60$$ −1.62772 + 1.73205i −0.210138 + 0.223607i
$$61$$ 7.05842 + 12.2255i 0.903738 + 1.56532i 0.822602 + 0.568618i $$0.192522\pi$$
0.0811364 + 0.996703i $$0.474145\pi$$
$$62$$ −2.00000 −0.254000
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 1.37228 + 2.37686i 0.170211 + 0.294813i
$$66$$ −2.18614 7.25061i −0.269095 0.892488i
$$67$$ −7.55842 + 13.0916i −0.923408 + 1.59939i −0.129307 + 0.991605i $$0.541275\pi$$
−0.794101 + 0.607785i $$0.792058\pi$$
$$68$$ −4.37228 −0.530217
$$69$$ 12.4307 + 2.92048i 1.49648 + 0.351585i
$$70$$ 0 0
$$71$$ 10.1168 1.20065 0.600324 0.799757i $$-0.295038\pi$$
0.600324 + 0.799757i $$0.295038\pi$$
$$72$$ −2.68614 1.33591i −0.316565 0.157438i
$$73$$ 2.55842 + 4.43132i 0.299441 + 0.518646i 0.976008 0.217734i $$-0.0698666\pi$$
−0.676567 + 0.736381i $$0.736533\pi$$
$$74$$ −2.00000 −0.232495
$$75$$ 5.25544 + 1.23472i 0.606846 + 0.142573i
$$76$$ −2.50000 4.33013i −0.286770 0.496700i
$$77$$ 0 0
$$78$$ −2.37228 + 2.52434i −0.268608 + 0.285825i
$$79$$ −6.05842 10.4935i −0.681626 1.18061i −0.974485 0.224455i $$-0.927940\pi$$
0.292859 0.956156i $$-0.405393\pi$$
$$80$$ 0.686141 + 1.18843i 0.0767129 + 0.132871i
$$81$$ 5.43070 + 7.17687i 0.603411 + 0.797430i
$$82$$ 5.18614 8.98266i 0.572713 0.991969i
$$83$$ 2.74456 4.75372i 0.301255 0.521789i −0.675166 0.737666i $$-0.735928\pi$$
0.976420 + 0.215877i $$0.0692612\pi$$
$$84$$ 0 0
$$85$$ −3.00000 5.19615i −0.325396 0.563602i
$$86$$ −9.11684 −0.983095
$$87$$ 3.25544 3.46410i 0.349020 0.371391i
$$88$$ −4.37228 −0.466087
$$89$$ −1.62772 + 2.81929i −0.172538 + 0.298844i −0.939306 0.343079i $$-0.888530\pi$$
0.766769 + 0.641924i $$0.221863\pi$$
$$90$$ −0.255437 4.10891i −0.0269255 0.433117i
$$91$$ 0 0
$$92$$ 3.68614 6.38458i 0.384307 0.665639i
$$93$$ 2.37228 2.52434i 0.245994 0.261762i
$$94$$ 0 0
$$95$$ 3.43070 5.94215i 0.351983 0.609652i
$$96$$ −1.18614 + 1.26217i −0.121060 + 0.128820i
$$97$$ −4.55842 + 7.89542i −0.462838 + 0.801658i −0.999101 0.0423924i $$-0.986502\pi$$
0.536263 + 0.844051i $$0.319835\pi$$
$$98$$ 0 0
$$99$$ 11.7446 + 5.84096i 1.18037 + 0.587039i
$$100$$ 1.55842 2.69927i 0.155842 0.269927i
$$101$$ 7.37228 0.733569 0.366785 0.930306i $$-0.380459\pi$$
0.366785 + 0.930306i $$0.380459\pi$$
$$102$$ 5.18614 5.51856i 0.513504 0.546419i
$$103$$ −10.0000 −0.985329 −0.492665 0.870219i $$-0.663977\pi$$
−0.492665 + 0.870219i $$0.663977\pi$$
$$104$$ 1.00000 + 1.73205i 0.0980581 + 0.169842i
$$105$$ 0 0
$$106$$ 1.37228 2.37686i 0.133288 0.230861i
$$107$$ 0.813859 1.40965i 0.0786788 0.136276i −0.824001 0.566588i $$-0.808263\pi$$
0.902680 + 0.430312i $$0.141597\pi$$
$$108$$ 4.87228 1.80579i 0.468835 0.173762i
$$109$$ −7.00000 12.1244i −0.670478 1.16130i −0.977769 0.209687i $$-0.932756\pi$$
0.307290 0.951616i $$-0.400578\pi$$
$$110$$ −3.00000 5.19615i −0.286039 0.495434i
$$111$$ 2.37228 2.52434i 0.225167 0.239600i
$$112$$ 0 0
$$113$$ −0.686141 1.18843i −0.0645467 0.111798i 0.831946 0.554856i $$-0.187227\pi$$
−0.896493 + 0.443058i $$0.853893\pi$$
$$114$$ 8.43070 + 1.98072i 0.789608 + 0.185511i
$$115$$ 10.1168 0.943401
$$116$$ −1.37228 2.37686i −0.127413 0.220686i
$$117$$ −0.372281 5.98844i −0.0344174 0.553631i
$$118$$ −7.11684 −0.655159
$$119$$ 0 0
$$120$$ −2.31386 0.543620i −0.211225 0.0496255i
$$121$$ 8.11684 0.737895
$$122$$ −7.05842 + 12.2255i −0.639040 + 1.10685i
$$123$$ 5.18614 + 17.2005i 0.467619 + 1.55092i
$$124$$ −1.00000 1.73205i −0.0898027 0.155543i
$$125$$ 11.1386 0.996266
$$126$$ 0 0
$$127$$ −14.1168 −1.25267 −0.626334 0.779555i $$-0.715445\pi$$
−0.626334 + 0.779555i $$0.715445\pi$$
$$128$$ 0.500000 + 0.866025i 0.0441942 + 0.0765466i
$$129$$ 10.8139 11.5070i 0.952107 1.01313i
$$130$$ −1.37228 + 2.37686i −0.120357 + 0.208464i
$$131$$ −7.37228 −0.644119 −0.322060 0.946719i $$-0.604375\pi$$
−0.322060 + 0.946719i $$0.604375\pi$$
$$132$$ 5.18614 5.51856i 0.451396 0.480329i
$$133$$ 0 0
$$134$$ −15.1168 −1.30590
$$135$$ 5.48913 + 4.55134i 0.472429 + 0.391717i
$$136$$ −2.18614 3.78651i −0.187460 0.324690i
$$137$$ 16.3723 1.39878 0.699389 0.714741i $$-0.253455\pi$$
0.699389 + 0.714741i $$0.253455\pi$$
$$138$$ 3.68614 + 12.2255i 0.313785 + 1.04071i
$$139$$ 10.6168 + 18.3889i 0.900509 + 1.55973i 0.826835 + 0.562445i $$0.190139\pi$$
0.0736742 + 0.997282i $$0.476528\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 5.05842 + 8.76144i 0.424493 + 0.735244i
$$143$$ −4.37228 7.57301i −0.365629 0.633287i
$$144$$ −0.186141 2.99422i −0.0155117 0.249518i
$$145$$ 1.88316 3.26172i 0.156388 0.270871i
$$146$$ −2.55842 + 4.43132i −0.211737 + 0.366738i
$$147$$ 0 0
$$148$$ −1.00000 1.73205i −0.0821995 0.142374i
$$149$$ 14.7446 1.20792 0.603961 0.797014i $$-0.293588\pi$$
0.603961 + 0.797014i $$0.293588\pi$$
$$150$$ 1.55842 + 5.16870i 0.127245 + 0.422023i
$$151$$ −8.11684 −0.660539 −0.330270 0.943887i $$-0.607140\pi$$
−0.330270 + 0.943887i $$0.607140\pi$$
$$152$$ 2.50000 4.33013i 0.202777 0.351220i
$$153$$ 0.813859 + 13.0916i 0.0657966 + 1.05839i
$$154$$ 0 0
$$155$$ 1.37228 2.37686i 0.110224 0.190914i
$$156$$ −3.37228 0.792287i −0.269999 0.0634337i
$$157$$ 4.05842 7.02939i 0.323897 0.561007i −0.657391 0.753549i $$-0.728340\pi$$
0.981289 + 0.192543i $$0.0616734\pi$$
$$158$$ 6.05842 10.4935i 0.481982 0.834818i
$$159$$ 1.37228 + 4.55134i 0.108829 + 0.360945i
$$160$$ −0.686141 + 1.18843i −0.0542442 + 0.0939537i
$$161$$ 0 0
$$162$$ −3.50000 + 8.29156i −0.274986 + 0.651447i
$$163$$ −8.11684 + 14.0588i −0.635760 + 1.10117i 0.350593 + 0.936528i $$0.385980\pi$$
−0.986354 + 0.164641i $$0.947353\pi$$
$$164$$ 10.3723 0.809939
$$165$$ 10.1168 + 2.37686i 0.787595 + 0.185038i
$$166$$ 5.48913 0.426039
$$167$$ −8.74456 15.1460i −0.676675 1.17203i −0.975976 0.217876i $$-0.930087\pi$$
0.299302 0.954158i $$-0.403246\pi$$
$$168$$ 0 0
$$169$$ 4.50000 7.79423i 0.346154 0.599556i
$$170$$ 3.00000 5.19615i 0.230089 0.398527i
$$171$$ −12.5000 + 8.29156i −0.955899 + 0.634072i
$$172$$ −4.55842 7.89542i −0.347576 0.602020i
$$173$$ 3.00000 + 5.19615i 0.228086 + 0.395056i 0.957241 0.289292i $$-0.0934200\pi$$
−0.729155 + 0.684349i $$0.760087\pi$$
$$174$$ 4.62772 + 1.08724i 0.350826 + 0.0824235i
$$175$$ 0 0
$$176$$ −2.18614 3.78651i −0.164787 0.285419i
$$177$$ 8.44158 8.98266i 0.634508 0.675178i
$$178$$ −3.25544 −0.244005
$$179$$ −7.37228 12.7692i −0.551030 0.954412i −0.998201 0.0599635i $$-0.980902\pi$$
0.447170 0.894449i $$-0.352432\pi$$
$$180$$ 3.43070 2.27567i 0.255710 0.169619i
$$181$$ 18.1168 1.34661 0.673307 0.739363i $$-0.264873\pi$$
0.673307 + 0.739363i $$0.264873\pi$$
$$182$$ 0 0
$$183$$ −7.05842 23.4101i −0.521774 1.73053i
$$184$$ 7.37228 0.543492
$$185$$ 1.37228 2.37686i 0.100892 0.174750i
$$186$$ 3.37228 + 0.792287i 0.247268 + 0.0580933i
$$187$$ 9.55842 + 16.5557i 0.698981 + 1.21067i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 6.86141 0.497779
$$191$$ 0.941578 + 1.63086i 0.0681302 + 0.118005i 0.898078 0.439836i $$-0.144963\pi$$
−0.829948 + 0.557841i $$0.811630\pi$$
$$192$$ −1.68614 0.396143i −0.121687 0.0285892i
$$193$$ 3.50000 6.06218i 0.251936 0.436365i −0.712123 0.702055i $$-0.752266\pi$$
0.964059 + 0.265689i $$0.0855996\pi$$
$$194$$ −9.11684 −0.654551
$$195$$ −1.37228 4.55134i −0.0982711 0.325928i
$$196$$ 0 0
$$197$$ −6.00000 −0.427482 −0.213741 0.976890i $$-0.568565\pi$$
−0.213741 + 0.976890i $$0.568565\pi$$
$$198$$ 0.813859 + 13.0916i 0.0578385 + 0.930377i
$$199$$ 5.00000 + 8.66025i 0.354441 + 0.613909i 0.987022 0.160585i $$-0.0513380\pi$$
−0.632581 + 0.774494i $$0.718005\pi$$
$$200$$ 3.11684 0.220394
$$201$$ 17.9307 19.0800i 1.26473 1.34580i
$$202$$ 3.68614 + 6.38458i 0.259356 + 0.449218i
$$203$$ 0 0
$$204$$ 7.37228 + 1.73205i 0.516163 + 0.121268i
$$205$$ 7.11684 + 12.3267i 0.497062 + 0.860937i
$$206$$ −5.00000 8.66025i −0.348367 0.603388i
$$207$$ −19.8030 9.84868i −1.37640 0.684531i
$$208$$ −1.00000 + 1.73205i −0.0693375 + 0.120096i
$$209$$ −10.9307 + 18.9325i −0.756093 + 1.30959i
$$210$$ 0 0
$$211$$ 8.00000 + 13.8564i 0.550743 + 0.953914i 0.998221 + 0.0596196i $$0.0189888\pi$$
−0.447478 + 0.894295i $$0.647678\pi$$
$$212$$ 2.74456 0.188497
$$213$$ −17.0584 4.00772i −1.16882 0.274605i
$$214$$ 1.62772 0.111269
$$215$$ 6.25544 10.8347i 0.426617 0.738923i
$$216$$ 4.00000 + 3.31662i 0.272166 + 0.225668i
$$217$$ 0 0
$$218$$ 7.00000 12.1244i 0.474100 0.821165i
$$219$$ −2.55842 8.48533i −0.172882 0.573385i
$$220$$ 3.00000 5.19615i 0.202260 0.350325i
$$221$$ 4.37228 7.57301i 0.294111 0.509416i
$$222$$ 3.37228 + 0.792287i 0.226333 + 0.0531748i
$$223$$ 2.00000 3.46410i 0.133930 0.231973i −0.791258 0.611482i $$-0.790574\pi$$
0.925188 + 0.379509i $$0.123907\pi$$
$$224$$ 0 0
$$225$$ −8.37228 4.16381i −0.558152 0.277588i
$$226$$ 0.686141 1.18843i 0.0456414 0.0790532i
$$227$$ −23.7446 −1.57598 −0.787991 0.615687i $$-0.788879\pi$$
−0.787991 + 0.615687i $$0.788879\pi$$
$$228$$ 2.50000 + 8.29156i 0.165567 + 0.549122i
$$229$$ −20.1168 −1.32936 −0.664679 0.747129i $$-0.731432\pi$$
−0.664679 + 0.747129i $$0.731432\pi$$
$$230$$ 5.05842 + 8.76144i 0.333542 + 0.577713i
$$231$$ 0 0
$$232$$ 1.37228 2.37686i 0.0900947 0.156049i
$$233$$ 5.87228 10.1711i 0.384706 0.666330i −0.607022 0.794685i $$-0.707636\pi$$
0.991728 + 0.128354i $$0.0409695\pi$$
$$234$$ 5.00000 3.31662i 0.326860 0.216815i
$$235$$ 0 0
$$236$$ −3.55842 6.16337i −0.231634 0.401201i
$$237$$ 6.05842 + 20.0935i 0.393537 + 1.30521i
$$238$$ 0 0
$$239$$ 9.43070 + 16.3345i 0.610021 + 1.05659i 0.991236 + 0.132102i $$0.0421725\pi$$
−0.381215 + 0.924487i $$0.624494\pi$$
$$240$$ −0.686141 2.27567i −0.0442902 0.146894i
$$241$$ 0.883156 0.0568891 0.0284445 0.999595i $$-0.490945\pi$$
0.0284445 + 0.999595i $$0.490945\pi$$
$$242$$ 4.05842 + 7.02939i 0.260885 + 0.451867i
$$243$$ −6.31386 14.2525i −0.405034 0.914302i
$$244$$ −14.1168 −0.903738
$$245$$ 0 0
$$246$$ −12.3030 + 13.0916i −0.784410 + 0.834688i
$$247$$ 10.0000 0.636285
$$248$$ 1.00000 1.73205i 0.0635001 0.109985i
$$249$$ −6.51087 + 6.92820i −0.412610 + 0.439057i
$$250$$ 5.56930 + 9.64630i 0.352233 + 0.610086i
$$251$$ −9.00000 −0.568075 −0.284037 0.958813i $$-0.591674\pi$$
−0.284037 + 0.958813i $$0.591674\pi$$
$$252$$ 0 0
$$253$$ −32.2337 −2.02651
$$254$$ −7.05842 12.2255i −0.442885 0.767099i
$$255$$ 3.00000 + 9.94987i 0.187867 + 0.623085i
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ 21.8614 1.36368 0.681839 0.731503i $$-0.261181\pi$$
0.681839 + 0.731503i $$0.261181\pi$$
$$258$$ 15.3723 + 3.61158i 0.957036 + 0.224847i
$$259$$ 0 0
$$260$$ −2.74456 −0.170211
$$261$$ −6.86141 + 4.55134i −0.424710 + 0.281721i
$$262$$ −3.68614 6.38458i −0.227731 0.394441i
$$263$$ 13.3723 0.824570 0.412285 0.911055i $$-0.364731\pi$$
0.412285 + 0.911055i $$0.364731\pi$$
$$264$$ 7.37228 + 1.73205i 0.453733 + 0.106600i
$$265$$ 1.88316 + 3.26172i 0.115681 + 0.200366i
$$266$$ 0 0
$$267$$ 3.86141 4.10891i 0.236314 0.251461i
$$268$$ −7.55842 13.0916i −0.461704 0.799695i
$$269$$ 3.68614 + 6.38458i 0.224748 + 0.389275i 0.956244 0.292571i $$-0.0945108\pi$$
−0.731496 + 0.681846i $$0.761177\pi$$
$$270$$ −1.19702 + 7.02939i −0.0728480 + 0.427795i
$$271$$ 9.11684 15.7908i 0.553809 0.959225i −0.444186 0.895934i $$-0.646507\pi$$
0.997995 0.0632906i $$-0.0201595\pi$$
$$272$$ 2.18614 3.78651i 0.132554 0.229591i
$$273$$ 0 0
$$274$$ 8.18614 + 14.1788i 0.494543 + 0.856573i
$$275$$ −13.6277 −0.821782
$$276$$ −8.74456 + 9.30506i −0.526361 + 0.560099i
$$277$$ 22.2337 1.33589 0.667946 0.744209i $$-0.267174\pi$$
0.667946 + 0.744209i $$0.267174\pi$$
$$278$$ −10.6168 + 18.3889i −0.636756 + 1.10289i
$$279$$ −5.00000 + 3.31662i −0.299342 + 0.198561i
$$280$$ 0 0
$$281$$ −5.31386 + 9.20387i −0.316998 + 0.549057i −0.979860 0.199685i $$-0.936008\pi$$
0.662862 + 0.748742i $$0.269342\pi$$
$$282$$ 0 0
$$283$$ −4.94158 + 8.55906i −0.293746 + 0.508784i −0.974692 0.223550i $$-0.928235\pi$$
0.680946 + 0.732333i $$0.261569\pi$$
$$284$$ −5.05842 + 8.76144i −0.300162 + 0.519896i
$$285$$ −8.13859 + 8.66025i −0.482089 + 0.512989i
$$286$$ 4.37228 7.57301i 0.258538 0.447802i
$$287$$ 0 0
$$288$$ 2.50000 1.65831i 0.147314 0.0977170i
$$289$$ −1.05842 + 1.83324i −0.0622601 + 0.107838i
$$290$$ 3.76631 0.221165
$$291$$ 10.8139 11.5070i 0.633920 0.674552i
$$292$$ −5.11684 −0.299441
$$293$$ 2.31386 + 4.00772i 0.135177 + 0.234134i 0.925665 0.378344i $$-0.123506\pi$$
−0.790488 + 0.612478i $$0.790173\pi$$
$$294$$ 0 0
$$295$$ 4.88316 8.45787i 0.284308 0.492436i
$$296$$ 1.00000 1.73205i 0.0581238 0.100673i
$$297$$ −17.4891 14.5012i −1.01482 0.841446i
$$298$$ 7.37228 + 12.7692i 0.427065 + 0.739698i
$$299$$ 7.37228 + 12.7692i 0.426350 + 0.738460i
$$300$$ −3.69702 + 3.93398i −0.213447 + 0.227129i
$$301$$ 0 0
$$302$$ −4.05842 7.02939i −0.233536 0.404496i
$$303$$ −12.4307 2.92048i −0.714125 0.167777i
$$304$$ 5.00000 0.286770
$$305$$ −9.68614 16.7769i −0.554627 0.960642i
$$306$$ −10.9307 + 7.25061i −0.624867 + 0.414490i
$$307$$ −13.0000 −0.741949 −0.370975 0.928643i $$-0.620976\pi$$
−0.370975 + 0.928643i $$0.620976\pi$$
$$308$$ 0 0
$$309$$ 16.8614 + 3.96143i 0.959212 + 0.225358i
$$310$$ 2.74456 0.155881
$$311$$ 13.1168 22.7190i 0.743788 1.28828i −0.206971 0.978347i $$-0.566361\pi$$
0.950759 0.309931i $$-0.100306\pi$$
$$312$$ −1.00000 3.31662i −0.0566139 0.187767i
$$313$$ 1.44158 + 2.49689i 0.0814828 + 0.141132i 0.903887 0.427771i $$-0.140701\pi$$
−0.822404 + 0.568904i $$0.807368\pi$$
$$314$$ 8.11684 0.458060
$$315$$ 0 0
$$316$$ 12.1168 0.681626
$$317$$ 3.00000 + 5.19615i 0.168497 + 0.291845i 0.937892 0.346929i $$-0.112775\pi$$
−0.769395 + 0.638774i $$0.779442\pi$$
$$318$$ −3.25544 + 3.46410i −0.182556 + 0.194257i
$$319$$ −6.00000 + 10.3923i −0.335936 + 0.581857i
$$320$$ −1.37228 −0.0767129
$$321$$ −1.93070 + 2.05446i −0.107761 + 0.114669i
$$322$$ 0 0
$$323$$ −21.8614 −1.21640
$$324$$ −8.93070 + 1.11469i −0.496150 + 0.0619273i
$$325$$ 3.11684 + 5.39853i 0.172891 + 0.299457i
$$326$$ −16.2337 −0.899101
$$327$$ 7.00000 + 23.2164i 0.387101 + 1.28387i
$$328$$ 5.18614 + 8.98266i 0.286357 + 0.495984i
$$329$$ 0 0
$$330$$ 3.00000 + 9.94987i 0.165145 + 0.547723i
$$331$$ 6.11684 + 10.5947i 0.336212 + 0.582337i 0.983717 0.179725i $$-0.0575207\pi$$
−0.647505 + 0.762061i $$0.724187\pi$$
$$332$$ 2.74456 + 4.75372i 0.150627 + 0.260894i
$$333$$ −5.00000 + 3.31662i −0.273998 + 0.181750i
$$334$$ 8.74456 15.1460i 0.478481 0.828754i
$$335$$ 10.3723 17.9653i 0.566698 0.981550i
$$336$$ 0 0
$$337$$ −4.55842 7.89542i −0.248313 0.430091i 0.714745 0.699385i $$-0.246543\pi$$
−0.963058 + 0.269294i $$0.913210\pi$$
$$338$$ 9.00000 0.489535
$$339$$ 0.686141 + 2.27567i 0.0372660 + 0.123597i
$$340$$ 6.00000 0.325396
$$341$$ −4.37228 + 7.57301i −0.236772 + 0.410102i
$$342$$ −13.4307 6.67954i −0.726249 0.361188i
$$343$$ 0 0
$$344$$ 4.55842 7.89542i 0.245774 0.425692i
$$345$$ −17.0584 4.00772i −0.918395 0.215768i
$$346$$ −3.00000 + 5.19615i −0.161281 + 0.279347i
$$347$$ −3.55842 + 6.16337i −0.191026 + 0.330867i −0.945591 0.325359i $$-0.894515\pi$$
0.754564 + 0.656226i $$0.227848\pi$$
$$348$$ 1.37228 + 4.55134i 0.0735620 + 0.243978i
$$349$$ 11.0000 19.0526i 0.588817 1.01986i −0.405571 0.914063i $$-0.632927\pi$$
0.994388 0.105797i $$-0.0337393\pi$$
$$350$$ 0 0
$$351$$ −1.74456 + 10.2448i −0.0931179 + 0.546828i
$$352$$ 2.18614 3.78651i 0.116522 0.201821i
$$353$$ −7.62772 −0.405983 −0.202991 0.979181i $$-0.565066\pi$$
−0.202991 + 0.979181i $$0.565066\pi$$
$$354$$ 12.0000 + 2.81929i 0.637793 + 0.149844i
$$355$$ −13.8832 −0.736841
$$356$$ −1.62772 2.81929i −0.0862689 0.149422i
$$357$$ 0 0
$$358$$ 7.37228 12.7692i 0.389637 0.674871i
$$359$$ 3.43070 5.94215i 0.181066 0.313615i −0.761178 0.648543i $$-0.775379\pi$$
0.942244 + 0.334928i $$0.108712\pi$$
$$360$$ 3.68614 + 1.83324i 0.194277 + 0.0966203i
$$361$$ −3.00000 5.19615i −0.157895 0.273482i
$$362$$ 9.05842 + 15.6896i 0.476100 + 0.824630i
$$363$$ −13.6861 3.21543i −0.718336 0.168767i
$$364$$ 0 0
$$365$$ −3.51087 6.08101i −0.183768 0.318295i
$$366$$ 16.7446 17.8178i 0.875252 0.931353i
$$367$$ 22.2337 1.16059 0.580295 0.814407i $$-0.302937\pi$$
0.580295 + 0.814407i $$0.302937\pi$$
$$368$$ 3.68614 + 6.38458i 0.192153 + 0.332819i
$$369$$ −1.93070 31.0569i −0.100508 1.61676i
$$370$$ 2.74456 0.142683
$$371$$ 0 0
$$372$$ 1.00000 + 3.31662i 0.0518476 + 0.171959i
$$373$$ −10.0000 −0.517780 −0.258890 0.965907i $$-0.583357\pi$$
−0.258890 + 0.965907i $$0.583357\pi$$
$$374$$ −9.55842 + 16.5557i −0.494254 + 0.856073i
$$375$$ −18.7812 4.41248i −0.969859 0.227860i
$$376$$ 0 0
$$377$$ 5.48913 0.282704
$$378$$ 0 0
$$379$$ 9.11684 0.468301 0.234150 0.972200i $$-0.424769\pi$$
0.234150 + 0.972200i $$0.424769\pi$$
$$380$$ 3.43070 + 5.94215i 0.175991 + 0.304826i
$$381$$ 23.8030 + 5.59230i 1.21946 + 0.286502i
$$382$$ −0.941578 + 1.63086i −0.0481753 + 0.0834421i
$$383$$ −21.2554 −1.08610 −0.543051 0.839700i $$-0.682731\pi$$
−0.543051 + 0.839700i $$0.682731\pi$$
$$384$$ −0.500000 1.65831i −0.0255155 0.0846254i
$$385$$ 0 0
$$386$$ 7.00000 0.356291
$$387$$ −22.7921 + 15.1186i −1.15859 + 0.768520i
$$388$$ −4.55842 7.89542i −0.231419 0.400829i
$$389$$ −34.9783 −1.77347 −0.886734 0.462280i $$-0.847031\pi$$
−0.886734 + 0.462280i $$0.847031\pi$$
$$390$$ 3.25544 3.46410i 0.164845 0.175412i
$$391$$ −16.1168 27.9152i −0.815064 1.41173i
$$392$$ 0 0
$$393$$ 12.4307 + 2.92048i 0.627046 + 0.147319i
$$394$$ −3.00000 5.19615i −0.151138 0.261778i
$$395$$ 8.31386 + 14.4000i 0.418316 + 0.724544i
$$396$$ −10.9307 + 7.25061i −0.549289 + 0.364357i
$$397$$ 11.0000 19.0526i 0.552074 0.956221i −0.446051 0.895008i $$-0.647170\pi$$
0.998125 0.0612128i $$-0.0194968\pi$$
$$398$$ −5.00000 + 8.66025i −0.250627 + 0.434099i
$$399$$ 0 0
$$400$$ 1.55842 + 2.69927i 0.0779211 + 0.134963i
$$401$$ −0.255437 −0.0127559 −0.00637797 0.999980i $$-0.502030\pi$$
−0.00637797 + 0.999980i $$0.502030\pi$$
$$402$$ 25.4891 + 5.98844i 1.27128 + 0.298676i
$$403$$ 4.00000 0.199254
$$404$$ −3.68614 + 6.38458i −0.183392 + 0.317645i
$$405$$ −7.45245 9.84868i −0.370315 0.489385i
$$406$$ 0 0
$$407$$ −4.37228 + 7.57301i −0.216726 + 0.375380i
$$408$$ 2.18614 + 7.25061i 0.108230 + 0.358959i
$$409$$ −14.6753 + 25.4183i −0.725645 + 1.25685i 0.233063 + 0.972462i $$0.425125\pi$$
−0.958708 + 0.284393i $$0.908208\pi$$
$$410$$ −7.11684 + 12.3267i −0.351476 + 0.608774i
$$411$$ −27.6060 6.48577i −1.36170 0.319920i
$$412$$ 5.00000 8.66025i 0.246332 0.426660i
$$413$$ 0 0
$$414$$ −1.37228 22.0742i −0.0674439 1.08489i
$$415$$ −3.76631 + 6.52344i −0.184881 + 0.320223i
$$416$$ −2.00000 −0.0980581
$$417$$ −10.6168 35.2121i −0.519909 1.72434i
$$418$$ −21.8614 −1.06928
$$419$$ −13.8030 23.9075i −0.674320 1.16796i −0.976667 0.214759i $$-0.931104\pi$$
0.302347 0.953198i $$-0.402230\pi$$
$$420$$ 0 0
$$421$$ 0.116844 0.202380i 0.00569463 0.00986338i −0.863164 0.504924i $$-0.831521\pi$$
0.868859 + 0.495060i $$0.164854\pi$$
$$422$$ −8.00000 + 13.8564i −0.389434 + 0.674519i
$$423$$ 0 0
$$424$$ 1.37228 + 2.37686i 0.0666439 + 0.115431i
$$425$$ −6.81386 11.8020i −0.330521 0.572479i
$$426$$ −5.05842 16.7769i −0.245081 0.812843i
$$427$$ 0 0
$$428$$ 0.813859 + 1.40965i 0.0393394 + 0.0681378i
$$429$$ 4.37228 + 14.5012i 0.211096 + 0.700125i
$$430$$ 12.5109 0.603328
$$431$$ 14.7446 + 25.5383i 0.710221 + 1.23014i 0.964774 + 0.263079i $$0.0847381\pi$$
−0.254554 + 0.967059i $$0.581929\pi$$
$$432$$ −0.872281 + 5.12241i −0.0419677 + 0.246452i
$$433$$ −2.88316 −0.138556 −0.0692778 0.997597i $$-0.522069\pi$$
−0.0692778 + 0.997597i $$0.522069\pi$$
$$434$$ 0 0
$$435$$ −4.46738 + 4.75372i −0.214194 + 0.227924i
$$436$$ 14.0000 0.670478
$$437$$ 18.4307 31.9229i 0.881660 1.52708i
$$438$$ 6.06930 6.45832i 0.290002 0.308591i
$$439$$ −4.00000 6.92820i −0.190910 0.330665i 0.754642 0.656136i $$-0.227810\pi$$
−0.945552 + 0.325471i $$0.894477\pi$$
$$440$$ 6.00000 0.286039
$$441$$ 0 0
$$442$$ 8.74456 0.415936
$$443$$ 11.4416 + 19.8174i 0.543606 + 0.941553i 0.998693 + 0.0511061i $$0.0162747\pi$$
−0.455087 + 0.890447i $$0.650392\pi$$
$$444$$ 1.00000 + 3.31662i 0.0474579 + 0.157400i
$$445$$ 2.23369 3.86886i 0.105887 0.183402i
$$446$$ 4.00000 0.189405
$$447$$ −24.8614 5.84096i −1.17590 0.276268i
$$448$$ 0 0
$$449$$ 33.0000 1.55737 0.778683 0.627417i $$-0.215888\pi$$
0.778683 + 0.627417i $$0.215888\pi$$
$$450$$ −0.580171 9.33252i −0.0273495 0.439939i
$$451$$ −22.6753 39.2747i −1.06774 1.84937i
$$452$$ 1.37228 0.0645467
$$453$$ 13.6861 + 3.21543i 0.643031 + 0.151074i
$$454$$ −11.8723 20.5634i −0.557194 0.965088i
$$455$$ 0 0
$$456$$ −5.93070 + 6.31084i −0.277731 + 0.295532i
$$457$$ −16.7337 28.9836i −0.782769 1.35580i −0.930323 0.366742i $$-0.880473\pi$$
0.147554 0.989054i $$-0.452860\pi$$
$$458$$ −10.0584 17.4217i −0.469999 0.814062i
$$459$$ 3.81386 22.3966i 0.178016 1.04539i
$$460$$ −5.05842 + 8.76144i −0.235850 + 0.408504i
$$461$$ −15.4307 + 26.7268i −0.718680 + 1.24479i 0.242844 + 0.970065i $$0.421920\pi$$
−0.961523 + 0.274724i $$0.911414\pi$$
$$462$$ 0 0
$$463$$ 2.94158 + 5.09496i 0.136707 + 0.236783i 0.926248 0.376914i $$-0.123015\pi$$
−0.789541 + 0.613697i $$0.789682\pi$$
$$464$$ 2.74456 0.127413
$$465$$ −3.25544 + 3.46410i −0.150967 + 0.160644i
$$466$$ 11.7446 0.544056
$$467$$ 15.0475 26.0631i 0.696317 1.20606i −0.273417 0.961896i $$-0.588154\pi$$
0.969735 0.244162i $$-0.0785127\pi$$
$$468$$ 5.37228 + 2.67181i 0.248334 + 0.123505i
$$469$$ 0 0
$$470$$ 0 0
$$471$$ −9.62772 + 10.2448i −0.443622 + 0.472057i
$$472$$ 3.55842 6.16337i 0.163790 0.283692i
$$473$$ −19.9307 + 34.5210i −0.916415 + 1.58728i
$$474$$ −14.3723 + 15.2935i −0.660141 + 0.702454i
$$475$$ 7.79211 13.4963i 0.357527 0.619254i
$$476$$ 0 0
$$477$$ −0.510875 8.21782i −0.0233913 0.376268i
$$478$$ −9.43070 + 16.3345i −0.431350 + 0.747121i
$$479$$ 21.2554 0.971186 0.485593 0.874185i $$-0.338604\pi$$
0.485593 + 0.874185i $$0.338604\pi$$
$$480$$ 1.62772 1.73205i 0.0742949 0.0790569i
$$481$$ 4.00000 0.182384
$$482$$ 0.441578 + 0.764836i 0.0201133 + 0.0348373i
$$483$$ 0 0
$$484$$ −4.05842 + 7.02939i −0.184474 + 0.319518i
$$485$$ 6.25544 10.8347i 0.284045 0.491980i
$$486$$ 9.18614 12.5942i 0.416692 0.571286i
$$487$$ 8.17527 + 14.1600i 0.370457 + 0.641650i 0.989636 0.143600i $$-0.0458679\pi$$
−0.619179 + 0.785250i $$0.712535\pi$$
$$488$$ −7.05842 12.2255i −0.319520 0.553424i
$$489$$ 19.2554 20.4897i 0.870761 0.926574i
$$490$$ 0 0
$$491$$ 9.81386 + 16.9981i 0.442893 + 0.767114i 0.997903 0.0647303i $$-0.0206187\pi$$
−0.555010 + 0.831844i $$0.687285\pi$$
$$492$$ −17.4891 4.10891i −0.788471 0.185244i
$$493$$ −12.0000 −0.540453
$$494$$ 5.00000 + 8.66025i 0.224961 + 0.389643i
$$495$$ −16.1168 8.01544i −0.724398 0.360267i
$$496$$ 2.00000 0.0898027
$$497$$ 0 0
$$498$$ −9.25544 2.17448i −0.414746 0.0974408i
$$499$$ 0.883156 0.0395355 0.0197677 0.999805i $$-0.493707\pi$$
0.0197677 + 0.999805i $$0.493707\pi$$
$$500$$ −5.56930 + 9.64630i −0.249067 + 0.431396i
$$501$$ 8.74456 + 29.0024i 0.390678 + 1.29573i
$$502$$ −4.50000 7.79423i −0.200845 0.347873i
$$503$$ 2.23369 0.0995952 0.0497976 0.998759i $$-0.484142\pi$$
0.0497976 + 0.998759i $$0.484142\pi$$
$$504$$ 0 0
$$505$$ −10.1168 −0.450194
$$506$$ −16.1168 27.9152i −0.716481 1.24098i
$$507$$ −10.6753 + 11.3595i −0.474105 + 0.504494i
$$508$$ 7.05842 12.2255i 0.313167 0.542421i
$$509$$ 16.9783 0.752548 0.376274 0.926508i $$-0.377205\pi$$
0.376274 + 0.926508i $$0.377205\pi$$
$$510$$ −7.11684 + 7.57301i −0.315139 + 0.335339i
$$511$$ 0 0
$$512$$ −1.00000 −0.0441942
$$513$$ 24.3614 9.02895i 1.07558 0.398638i
$$514$$ 10.9307 + 18.9325i 0.482133 + 0.835078i
$$515$$ 13.7228 0.604699
$$516$$ 4.55842 + 15.1186i 0.200673 + 0.665558i
$$517$$ 0 0
$$518$$ 0 0
$$519$$ −3.00000 9.94987i −0.131685 0.436751i
$$520$$ −1.37228 2.37686i −0.0601785 0.104232i
$$521$$ −1.93070 3.34408i −0.0845856 0.146507i 0.820629 0.571461i $$-0.193623\pi$$
−0.905215 + 0.424955i $$0.860290\pi$$
$$522$$ −7.37228 3.66648i −0.322676 0.160478i
$$523$$ 8.94158 15.4873i 0.390988 0.677211i −0.601592 0.798803i $$-0.705467\pi$$
0.992580 + 0.121592i $$0.0388001\pi$$
$$524$$ 3.68614 6.38458i 0.161030 0.278912i
$$525$$ 0 0
$$526$$ 6.68614 + 11.5807i 0.291530 + 0.504944i
$$527$$ −8.74456 −0.380919
$$528$$ 2.18614 + 7.25061i 0.0951396 + 0.315542i
$$529$$ 31.3505 1.36307
$$530$$ −1.88316 + 3.26172i −0.0817991 + 0.141680i
$$531$$ −17.7921 + 11.8020i −0.772112 + 0.512161i
$$532$$ 0 0
$$533$$ −10.3723 + 17.9653i −0.449273 + 0.778164i
$$534$$ 5.48913 + 1.28962i 0.237538 + 0.0558073i
$$535$$ −1.11684 + 1.93443i −0.0482854 + 0.0836327i
$$536$$ 7.55842 13.0916i 0.326474 0.565470i
$$537$$ 7.37228 + 24.4511i 0.318137 + 1.05514i
$$538$$ −3.68614 + 6.38458i −0.158921 + 0.275259i
$$539$$ 0 0
$$540$$ −6.68614 + 2.47805i −0.287726 + 0.106638i
$$541$$ −14.1168 + 24.4511i −0.606931 + 1.05123i 0.384813 + 0.922995i $$0.374266\pi$$
−0.991743 + 0.128240i $$0.959067\pi$$
$$542$$ 18.2337 0.783204
$$543$$ −30.5475 7.17687i −1.31092 0.307989i
$$544$$ 4.37228 0.187460
$$545$$ 9.60597 + 16.6380i 0.411475 + 0.712695i
$$546$$ 0 0
$$547$$ −0.441578 + 0.764836i −0.0188805 + 0.0327020i −0.875311 0.483560i $$-0.839344\pi$$
0.856431 + 0.516262i $$0.172677\pi$$
$$548$$ −8.18614 + 14.1788i −0.349695 + 0.605689i
$$549$$ 2.62772 + 42.2689i 0.112148 + 1.80399i
$$550$$ −6.81386 11.8020i −0.290544 0.503237i
$$551$$ −6.86141 11.8843i −0.292306 0.506288i
$$552$$ −12.4307 2.92048i −0.529086 0.124304i
$$553$$ 0 0
$$554$$ 11.1168 + 19.2549i 0.472309 + 0.818064i
$$555$$ −3.25544 + 3.46410i −0.138186 + 0.147043i
$$556$$ −21.2337 −0.900509
$$557$$ −3.25544 5.63858i −0.137937 0.238914i 0.788778 0.614678i $$-0.210714\pi$$
−0.926716 + 0.375763i $$0.877381\pi$$
$$558$$ −5.37228 2.67181i −0.227427 0.113107i
$$559$$ 18.2337 0.771203
$$560$$ 0 0
$$561$$ −9.55842 31.7017i −0.403557 1.33845i
$$562$$ −10.6277 −0.448303
$$563$$ −1.50000 + 2.59808i −0.0632175 + 0.109496i −0.895902 0.444252i $$-0.853470\pi$$
0.832684 + 0.553748i $$0.186803\pi$$
$$564$$ 0 0
$$565$$ 0.941578 + 1.63086i 0.0396125 + 0.0686108i
$$566$$ −9.88316 −0.415420
$$567$$ 0 0
$$568$$ −10.1168 −0.424493
$$569$$ 0.558422 + 0.967215i 0.0234103 + 0.0405478i 0.877493 0.479589i $$-0.159214\pi$$
−0.854083 + 0.520137i $$0.825881\pi$$
$$570$$ −11.5693 2.71810i −0.484585 0.113849i
$$571$$ −14.6753 + 25.4183i −0.614141 + 1.06372i 0.376394 + 0.926460i $$0.377164\pi$$
−0.990535 + 0.137263i $$0.956169\pi$$
$$572$$ 8.74456 0.365629
$$573$$ −0.941578 3.12286i −0.0393350 0.130459i
$$574$$ 0 0
$$575$$ 22.9783 0.958259
$$576$$ 2.68614 + 1.33591i 0.111923 + 0.0556628i
$$577$$ −13.5584 23.4839i −0.564444 0.977647i −0.997101 0.0760878i $$-0.975757\pi$$
0.432657 0.901559i $$-0.357576\pi$$
$$578$$ −2.11684 −0.0880491
$$579$$ −8.30298 + 8.83518i −0.345060 + 0.367178i
$$580$$ 1.88316 + 3.26172i 0.0781938 + 0.135436i
$$581$$ 0 0
$$582$$ 15.3723 + 3.61158i 0.637202 + 0.149705i
$$583$$ −6.00000 10.3923i −0.248495 0.430405i
$$584$$ −2.55842 4.43132i −0.105868 0.183369i
$$585$$ 0.510875 + 8.21782i 0.0211221 + 0.339765i
$$586$$ −2.31386 + 4.00772i −0.0955846 + 0.165557i
$$587$$ 4.24456 7.35180i 0.175192 0.303441i −0.765036 0.643988i $$-0.777279\pi$$
0.940228 + 0.340547i $$0.110612\pi$$
$$588$$ 0 0
$$589$$ −5.00000 8.66025i −0.206021 0.356840i
$$590$$ 9.76631 0.402073
$$591$$ 10.1168 + 2.37686i 0.416151 + 0.0977710i
$$592$$ 2.00000 0.0821995
$$593$$ −1.62772 + 2.81929i −0.0668424 + 0.115774i −0.897510 0.440995i $$-0.854626\pi$$
0.830667 + 0.556769i $$0.187959\pi$$
$$594$$ 3.81386 22.3966i 0.156485 0.918945i
$$595$$ 0 0
$$596$$ −7.37228 + 12.7692i −0.301980 + 0.523045i
$$597$$ −5.00000 16.5831i −0.204636 0.678702i
$$598$$ −7.37228 + 12.7692i −0.301475 + 0.522170i
$$599$$ −12.0000 + 20.7846i −0.490307 + 0.849236i −0.999938 0.0111569i $$-0.996449\pi$$
0.509631 + 0.860393i $$0.329782\pi$$
$$600$$ −5.25544 1.23472i −0.214552 0.0504071i
$$601$$ −3.44158 + 5.96099i −0.140385 + 0.243154i −0.927642 0.373472i $$-0.878167\pi$$
0.787257 + 0.616625i $$0.211501\pi$$
$$602$$ 0 0
$$603$$ −37.7921 + 25.0684i −1.53901 + 1.02087i
$$604$$ 4.05842 7.02939i 0.165135 0.286022i
$$605$$ −11.1386 −0.452848
$$606$$ −3.68614 12.2255i −0.149739 0.496629i
$$607$$ −12.2337 −0.496550 −0.248275 0.968690i $$-0.579864\pi$$
−0.248275 + 0.968690i $$0.579864\pi$$
$$608$$ 2.50000 + 4.33013i 0.101388 + 0.175610i
$$609$$ 0 0
$$610$$ 9.68614 16.7769i 0.392180 0.679276i
$$611$$ 0 0
$$612$$ −11.7446 5.84096i −0.474746 0.236107i
$$613$$ 0.883156 + 1.52967i 0.0356703 + 0.0617828i 0.883309 0.468790i $$-0.155310\pi$$
−0.847639 + 0.530573i $$0.821977\pi$$
$$614$$ −6.50000 11.2583i −0.262319 0.454349i
$$615$$ −7.11684 23.6039i −0.286979 0.951801i
$$616$$ 0 0
$$617$$ 4.93070 + 8.54023i 0.198503 + 0.343817i 0.948043 0.318142i $$-0.103059\pi$$
−0.749540 + 0.661959i $$0.769725\pi$$
$$618$$ 5.00000 + 16.5831i 0.201129 + 0.667071i
$$619$$ −23.4674 −0.943233 −0.471617 0.881804i $$-0.656329\pi$$
−0.471617 + 0.881804i $$0.656329\pi$$
$$620$$ 1.37228 + 2.37686i 0.0551121 + 0.0954570i
$$621$$ 29.4891 + 24.4511i 1.18336 + 0.981188i
$$622$$ 26.2337 1.05188
$$623$$ 0 0
$$624$$ 2.37228 2.52434i 0.0949673 0.101054i
$$625$$ 0.298936 0.0119574
$$626$$ −1.44158 + 2.49689i −0.0576170 + 0.0997956i
$$627$$ 25.9307 27.5928i 1.03557 1.10195i
$$628$$ 4.05842 + 7.02939i 0.161949 + 0.280503i
$$629$$ −8.74456 −0.348669
$$630$$ 0 0
$$631$$ 14.3505 0.571286 0.285643 0.958336i $$-0.407793\pi$$
0.285643 + 0.958336i $$0.407793\pi$$
$$632$$ 6.05842 + 10.4935i 0.240991 + 0.417409i
$$633$$ −8.00000 26.5330i −0.317971 1.05459i
$$634$$ −3.00000 + 5.19615i −0.119145 + 0.206366i
$$635$$ 19.3723 0.768766
$$636$$ −4.62772 1.08724i −0.183501 0.0431119i
$$637$$ 0 0
$$638$$ −12.0000 −0.475085
$$639$$ 27.1753 + 13.5152i 1.07504 + 0.534652i
$$640$$ −0.686141 1.18843i −0.0271221 0.0469768i
$$641$$ −46.2119 −1.82526 −0.912631 0.408785i $$-0.865953\pi$$
−0.912631 + 0.408785i $$0.865953\pi$$
$$642$$ −2.74456 0.644810i −0.108319 0.0254486i
$$643$$ 12.6753 + 21.9542i 0.499864 + 0.865789i 1.00000 0.000157386i $$-5.00974e-5\pi$$
−0.500136 + 0.865947i $$0.666717\pi$$
$$644$$ 0 0
$$645$$ −14.8397 + 15.7908i −0.584311 + 0.621764i
$$646$$ −10.9307 18.9325i −0.430063 0.744891i
$$647$$ 8.74456 + 15.1460i 0.343784 + 0.595452i 0.985132 0.171798i $$-0.0549578\pi$$
−0.641348 + 0.767250i $$0.721624\pi$$
$$648$$ −5.43070 7.17687i −0.213338 0.281934i
$$649$$ −15.5584 + 26.9480i −0.610721 + 1.05780i
$$650$$ −3.11684 + 5.39853i −0.122253 + 0.211748i
$$651$$ 0 0
$$652$$ −8.11684 14.0588i −0.317880 0.550585i
$$653$$ −15.2554 −0.596991 −0.298496 0.954411i $$-0.596485\pi$$
−0.298496 + 0.954411i $$0.596485\pi$$
$$654$$ −16.6060 + 17.6704i −0.649345 + 0.690966i
$$655$$ 10.1168 0.395298
$$656$$ −5.18614 + 8.98266i −0.202485 + 0.350714i
$$657$$ 0.952453 + 15.3210i 0.0371587 + 0.597727i
$$658$$ 0 0
$$659$$ 4.62772 8.01544i 0.180270 0.312237i −0.761702 0.647927i $$-0.775636\pi$$
0.941973 + 0.335690i $$0.108969\pi$$
$$660$$ −7.11684 + 7.57301i −0.277023 + 0.294779i
$$661$$ −4.94158 + 8.55906i −0.192205 + 0.332909i −0.945981 0.324223i $$-0.894897\pi$$
0.753776 + 0.657132i $$0.228231\pi$$
$$662$$ −6.11684 + 10.5947i −0.237738 + 0.411774i
$$663$$ −10.3723 + 11.0371i −0.402826 + 0.428646i
$$664$$ −2.74456 + 4.75372i −0.106510 + 0.184480i
$$665$$ 0 0
$$666$$ −5.37228 2.67181i −0.208172 0.103531i
$$667$$ 10.1168 17.5229i 0.391726 0.678489i
$$668$$ 17.4891 0.676675
$$669$$ −4.74456 + 5.04868i −0.183435 + 0.195193i
$$670$$ 20.7446 0.801432
$$671$$ 30.8614 + 53.4535i 1.19139 + 2.06355i
$$672$$ 0 0
$$673$$ 10.0584 17.4217i 0.387724 0.671557i −0.604419 0.796666i $$-0.706595\pi$$
0.992143 + 0.125109i $$0.0399281\pi$$
$$674$$ 4.55842 7.89542i 0.175584 0.304120i
$$675$$ 12.4674 + 10.3374i 0.479870 + 0.397887i
$$676$$ 4.50000 + 7.79423i 0.173077 + 0.299778i
$$677$$ 17.2337 + 29.8496i 0.662344 + 1.14721i 0.979998 + 0.199007i $$0.0637718\pi$$
−0.317654 + 0.948207i $$0.602895\pi$$
$$678$$ −1.62772 + 1.73205i −0.0625122 + 0.0665190i
$$679$$ 0 0
$$680$$ 3.00000 + 5.19615i 0.115045 + 0.199263i
$$681$$ 40.0367 + 9.40625i 1.53421 + 0.360448i
$$682$$ −8.74456 −0.334847
$$683$$ 22.4198 + 38.8323i 0.857871 + 1.48588i 0.873956 + 0.486005i $$0.161546\pi$$
−0.0160849 + 0.999871i $$0.505120\pi$$
$$684$$ −0.930703 14.9711i −0.0355863 0.572434i
$$685$$ −22.4674 −0.858434
$$686$$ 0 0
$$687$$ 33.9198 + 7.96916i 1.29412 + 0.304042i
$$688$$ 9.11684 0.347576
$$689$$ −2.74456 + 4.75372i −0.104560 + 0.181102i
$$690$$ −5.05842 16.7769i −0.192571 0.638685i
$$691$$ 2.94158 + 5.09496i 0.111903 + 0.193822i 0.916537 0.399949i $$-0.130972\pi$$
−0.804635 + 0.593770i $$0.797639\pi$$
$$692$$ −6.00000 −0.228086
$$693$$ 0 0
$$694$$ −7.11684 −0.270152
$$695$$ −14.5693 25.2348i −0.552645 0.957209i
$$696$$ −3.25544 + 3.46410i −0.123397 + 0.131306i
$$697$$ 22.6753 39.2747i 0.858887 1.48764i
$$698$$ 22.0000 0.832712
$$699$$ −13.9307 + 14.8236i −0.526908 + 0.560681i
$$700$$ 0 0
$$701$$ −3.76631 −0.142252 −0.0711258 0.997467i $$-0.522659\pi$$
−0.0711258 + 0.997467i $$0.522659\pi$$
$$702$$ −9.74456 + 3.61158i −0.367785 + 0.136310i
$$703$$ −5.00000 8.66025i −0.188579 0.326628i
$$704$$ 4.37228 0.164787
$$705$$ 0 0
$$706$$ −3.81386 6.60580i −0.143536 0.248612i
$$707$$ 0 0
$$708$$ 3.55842 + 11.8020i 0.133734 + 0.443544i
$$709$$ −22.0000 38.1051i −0.826227 1.43107i −0.900978 0.433865i $$-0.857149\pi$$
0.0747503 0.997202i $$-0.476184\pi$$
$$710$$ −6.94158 12.0232i −0.260513 0.451221i
$$711$$ −2.25544 36.2805i −0.0845855 1.36062i
$$712$$ 1.62772 2.81929i 0.0610013 0.105657i
$$713$$ 7.37228 12.7692i 0.276094 0.478209i
$$714$$ 0 0
$$715$$ 6.00000 + 10.3923i 0.224387 + 0.388650i
$$716$$ 14.7446 0.551030
$$717$$ −9.43070 31.2781i −0.352196 1.16810i
$$718$$ 6.86141 0.256065
$$719$$ 4.37228 7.57301i 0.163059 0.282426i −0.772906 0.634521i $$-0.781197\pi$$
0.935964 + 0.352095i $$0.114531\pi$$
$$720$$ 0.255437 + 4.10891i 0.00951959 + 0.153130i
$$721$$ 0 0
$$722$$ 3.00000 5.19615i 0.111648 0.193381i
$$723$$ −1.48913 0.349857i −0.0553812 0.0130113i
$$724$$ −9.05842 + 15.6896i −0.336654 + 0.583101i
$$725$$ 4.27719 7.40830i 0.158851 0.275138i
$$726$$ −4.05842 13.4603i −0.150622 0.499557i
$$727$$ 0.883156 1.52967i 0.0327544 0.0567324i −0.849183 0.528098i $$-0.822905\pi$$
0.881938 + 0.471366i $$0.156239\pi$$
$$728$$ 0 0
$$729$$ 5.00000 + 26.5330i 0.185185 + 0.982704i
$$730$$ 3.51087 6.08101i 0.129943 0.225068i
$$731$$ −39.8614 −1.47433
$$732$$ 23.8030 + 5.59230i 0.879784 + 0.206697i
$$733$$ −23.8832 −0.882144 −0.441072 0.897472i $$-0.645402\pi$$
−0.441072 + 0.897472i $$0.645402\pi$$
$$734$$ 11.1168 + 19.2549i 0.410330 + 0.710713i
$$735$$ 0 0
$$736$$ −3.68614 + 6.38458i −0.135873 + 0.235339i
$$737$$ −33.0475 + 57.2400i −1.21732 + 2.10846i
$$738$$ 25.9307 17.2005i 0.954522 0.633159i
$$739$$ −4.55842 7.89542i −0.167684 0.290438i 0.769921 0.638139i $$-0.220296\pi$$
−0.937605 + 0.347702i $$0.886962\pi$$
$$740$$ 1.37228 + 2.37686i 0.0504461 + 0.0873751i
$$741$$ −16.8614 3.96143i −0.619419 0.145527i
$$742$$ 0 0
$$743$$ −21.8614 37.8651i −0.802017 1.38913i −0.918286 0.395917i $$-0.870427\pi$$
0.116269 0.993218i $$-0.462906\pi$$
$$744$$ −2.37228 + 2.52434i −0.0869721 + 0.0925467i
$$745$$ −20.2337 −0.741305
$$746$$ −5.00000 8.66025i −0.183063 0.317074i
$$747$$ 13.7228 9.10268i 0.502091 0.333050i
$$748$$ −19.1168 −0.698981
$$749$$ 0 0
$$750$$ −5.56930 18.4713i −0.203362 0.674475i
$$751$$ 0.116844 0.00426370 0.00213185 0.999998i $$-0.499321\pi$$
0.00213185 + 0.999998i $$0.499321\pi$$
$$752$$ 0 0
$$753$$ 15.1753 + 3.56529i 0.553017 + 0.129926i
$$754$$ 2.74456 + 4.75372i 0.0999511 + 0.173120i
$$755$$ 11.1386 0.405375
$$756$$ 0 0
$$757$$ 11.7663 0.427654 0.213827 0.976872i $$-0.431407\pi$$
0.213827 + 0.976872i $$0.431407\pi$$
$$758$$ 4.55842 + 7.89542i 0.165569 + 0.286775i
$$759$$ 54.3505 + 12.7692i 1.97280 + 0.463491i
$$760$$ −3.43070 + 5.94215i −0.124445 + 0.215545i
$$761$$ 12.5109 0.453519 0.226759 0.973951i $$-0.427187\pi$$
0.226759 + 0.973951i $$0.427187\pi$$
$$762$$ 7.05842 + 23.4101i 0.255700 + 0.848060i
$$763$$ 0 0
$$764$$ −1.88316 −0.0681302
$$765$$ −1.11684 17.9653i −0.0403796 0.649537i
$$766$$ −10.6277 18.4077i −0.383995 0.665099i
$$767$$ 14.2337 0.513949
$$768$$ 1.18614 1.26217i 0.0428012 0.0455446i
$$769$$ 5.00000 + 8.66025i 0.180305 + 0.312297i 0.941984 0.335657i $$-0.108958\pi$$
−0.761680 + 0.647954i $$0.775625\pi$$
$$770$$ 0 0
$$771$$ −36.8614 8.66025i −1.32753 0.311891i
$$772$$ 3.50000 + 6.06218i 0.125968 + 0.218183i
$$773$$ 5.56930 + 9.64630i 0.200314 + 0.346953i 0.948629 0.316389i $$-0.102471\pi$$
−0.748316 + 0.663343i $$0.769137\pi$$
$$774$$ −24.4891 12.1793i −0.880243 0.437774i
$$775$$ 3.11684 5.39853i 0.111960 0.193921i
$$776$$ 4.55842 7.89542i 0.163638 0.283429i
$$777$$ 0 0
$$778$$ −17.4891 30.2921i −0.627016 1.08602i
$$779$$ 51.8614 1.85813
$$780$$ 4.62772 + 1.08724i 0.165699 + 0.0389295i
$$781$$ 44.2337