# Properties

 Label 1183.2.e.i.508.6 Level $1183$ Weight $2$ Character 1183.508 Analytic conductor $9.446$ Analytic rank $0$ Dimension $16$ CM no Inner twists $4$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$1183 = 7 \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1183.e (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$9.44630255912$$ Analytic rank: $$0$$ Dimension: $$16$$ Relative dimension: $$8$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ Defining polynomial: $$x^{16} + 11 x^{14} + 85 x^{12} + 334 x^{10} + 952 x^{8} + 1050 x^{6} + 853 x^{4} + 93 x^{2} + 9$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 91) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 508.6 Root $$0.536527 - 0.929293i$$ of defining polynomial Character $$\chi$$ $$=$$ 1183.508 Dual form 1183.2.e.i.170.6

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.536527 + 0.929293i) q^{2} +(1.21570 - 2.10566i) q^{3} +(0.424277 - 0.734868i) q^{4} +(-0.312716 - 0.541640i) q^{5} +2.60903 q^{6} +(1.21561 + 2.34996i) q^{7} +3.05665 q^{8} +(-1.45586 - 2.52163i) q^{9} +O(q^{10})$$ $$q+(0.536527 + 0.929293i) q^{2} +(1.21570 - 2.10566i) q^{3} +(0.424277 - 0.734868i) q^{4} +(-0.312716 - 0.541640i) q^{5} +2.60903 q^{6} +(1.21561 + 2.34996i) q^{7} +3.05665 q^{8} +(-1.45586 - 2.52163i) q^{9} +(0.335561 - 0.581209i) q^{10} +(0.354260 - 0.613597i) q^{11} +(-1.03159 - 1.78676i) q^{12} +(-1.53159 + 2.39047i) q^{14} -1.52068 q^{15} +(0.791426 + 1.37079i) q^{16} +(1.67157 - 2.89524i) q^{17} +(1.56222 - 2.70585i) q^{18} +(2.60138 + 4.50573i) q^{19} -0.530712 q^{20} +(6.42602 + 0.297185i) q^{21} +0.760282 q^{22} +(2.21570 + 3.83771i) q^{23} +(3.71598 - 6.43627i) q^{24} +(2.30442 - 3.99137i) q^{25} +0.214623 q^{27} +(2.24266 + 0.103717i) q^{28} -6.59711 q^{29} +(-0.815886 - 1.41316i) q^{30} +(2.19530 - 3.80238i) q^{31} +(2.20741 - 3.82335i) q^{32} +(-0.861351 - 1.49190i) q^{33} +3.58737 q^{34} +(0.892689 - 1.39329i) q^{35} -2.47076 q^{36} +(-0.211704 - 0.366683i) q^{37} +(-2.79143 + 4.83489i) q^{38} +(-0.955864 - 1.65561i) q^{40} -5.01604 q^{41} +(3.17157 + 6.13111i) q^{42} -11.2059 q^{43} +(-0.300609 - 0.520670i) q^{44} +(-0.910544 + 1.57711i) q^{45} +(-2.37757 + 4.11807i) q^{46} +(-4.03635 - 6.99116i) q^{47} +3.84855 q^{48} +(-4.04458 + 5.71326i) q^{49} +4.94553 q^{50} +(-4.06426 - 7.03950i) q^{51} +(0.348553 - 0.603712i) q^{53} +(0.115151 + 0.199447i) q^{54} -0.443132 q^{55} +(3.71570 + 7.18300i) q^{56} +12.6500 q^{57} +(-3.53953 - 6.13065i) q^{58} +(-4.93159 + 8.54177i) q^{59} +(-0.645188 + 1.11750i) q^{60} +(-2.34855 - 4.06781i) q^{61} +4.71136 q^{62} +(4.15596 - 6.48654i) q^{63} +7.90305 q^{64} +(0.924277 - 1.60089i) q^{66} +(-5.21041 + 9.02470i) q^{67} +(-1.41841 - 2.45676i) q^{68} +10.7745 q^{69} +(1.77373 + 0.0820297i) q^{70} -14.0876 q^{71} +(-4.45007 - 7.70775i) q^{72} +(2.54191 - 4.40273i) q^{73} +(0.227170 - 0.393471i) q^{74} +(-5.60297 - 9.70463i) q^{75} +4.41482 q^{76} +(1.87257 + 0.0866008i) q^{77} +(1.95586 + 3.38766i) q^{79} +(0.494983 - 0.857336i) q^{80} +(4.62851 - 8.01682i) q^{81} +(-2.69124 - 4.66137i) q^{82} +10.2035 q^{83} +(2.94480 - 4.59619i) q^{84} -2.09090 q^{85} +(-6.01230 - 10.4136i) q^{86} +(-8.02012 + 13.8913i) q^{87} +(1.08285 - 1.87555i) q^{88} +(6.68955 + 11.5866i) q^{89} -1.95413 q^{90} +3.76028 q^{92} +(-5.33767 - 9.24512i) q^{93} +(4.33122 - 7.50190i) q^{94} +(1.62699 - 2.81802i) q^{95} +(-5.36711 - 9.29610i) q^{96} -0.202023 q^{97} +(-7.47932 - 0.693276i) q^{98} -2.06302 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$16q - 4q^{3} - 6q^{4} - 12q^{9} + O(q^{10})$$ $$16q - 4q^{3} - 6q^{4} - 12q^{9} + 6q^{10} - 18q^{12} - 26q^{14} + 2q^{16} - 8q^{17} - 36q^{22} + 12q^{23} + 32q^{27} - 16q^{29} - 38q^{30} + 56q^{36} - 34q^{38} - 4q^{40} + 16q^{42} - 16q^{43} + 36q^{48} - 40q^{49} - 16q^{51} - 20q^{53} + 24q^{55} + 36q^{56} - 12q^{61} - 44q^{62} - 88q^{64} + 2q^{66} - 2q^{68} + 56q^{69} + 42q^{74} - 8q^{75} + 76q^{77} + 20q^{79} - 24q^{81} + 16q^{82} - 68q^{87} - 4q^{88} + 216q^{90} + 12q^{92} - 26q^{94} + 16q^{95} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times$$.

 $$n$$ $$339$$ $$1016$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.536527 + 0.929293i 0.379382 + 0.657109i 0.990972 0.134065i $$-0.0428032\pi$$
−0.611590 + 0.791175i $$0.709470\pi$$
$$3$$ 1.21570 2.10566i 0.701886 1.21570i −0.265918 0.963996i $$-0.585675\pi$$
0.967804 0.251707i $$-0.0809918\pi$$
$$4$$ 0.424277 0.734868i 0.212138 0.367434i
$$5$$ −0.312716 0.541640i −0.139851 0.242229i 0.787589 0.616201i $$-0.211329\pi$$
−0.927440 + 0.373972i $$0.877996\pi$$
$$6$$ 2.60903 1.06513
$$7$$ 1.21561 + 2.34996i 0.459458 + 0.888200i
$$8$$ 3.05665 1.08069
$$9$$ −1.45586 2.52163i −0.485288 0.840544i
$$10$$ 0.335561 0.581209i 0.106114 0.183795i
$$11$$ 0.354260 0.613597i 0.106814 0.185006i −0.807664 0.589643i $$-0.799269\pi$$
0.914478 + 0.404636i $$0.132602\pi$$
$$12$$ −1.03159 1.78676i −0.297794 0.515794i
$$13$$ 0 0
$$14$$ −1.53159 + 2.39047i −0.409334 + 0.638881i
$$15$$ −1.52068 −0.392637
$$16$$ 0.791426 + 1.37079i 0.197856 + 0.342697i
$$17$$ 1.67157 2.89524i 0.405414 0.702199i −0.588955 0.808166i $$-0.700461\pi$$
0.994370 + 0.105967i $$0.0337939\pi$$
$$18$$ 1.56222 2.70585i 0.368219 0.637775i
$$19$$ 2.60138 + 4.50573i 0.596798 + 1.03368i 0.993290 + 0.115646i $$0.0368939\pi$$
−0.396492 + 0.918038i $$0.629773\pi$$
$$20$$ −0.530712 −0.118671
$$21$$ 6.42602 + 0.297185i 1.40227 + 0.0648510i
$$22$$ 0.760282 0.162093
$$23$$ 2.21570 + 3.83771i 0.462006 + 0.800218i 0.999061 0.0433296i $$-0.0137966\pi$$
−0.537055 + 0.843547i $$0.680463\pi$$
$$24$$ 3.71598 6.43627i 0.758522 1.31380i
$$25$$ 2.30442 3.99137i 0.460883 0.798274i
$$26$$ 0 0
$$27$$ 0.214623 0.0413042
$$28$$ 2.24266 + 0.103717i 0.423824 + 0.0196006i
$$29$$ −6.59711 −1.22505 −0.612526 0.790450i $$-0.709847\pi$$
−0.612526 + 0.790450i $$0.709847\pi$$
$$30$$ −0.815886 1.41316i −0.148960 0.258006i
$$31$$ 2.19530 3.80238i 0.394288 0.682927i −0.598722 0.800957i $$-0.704325\pi$$
0.993010 + 0.118030i $$0.0376579\pi$$
$$32$$ 2.20741 3.82335i 0.390219 0.675879i
$$33$$ −0.861351 1.49190i −0.149942 0.259707i
$$34$$ 3.58737 0.615228
$$35$$ 0.892689 1.39329i 0.150892 0.235509i
$$36$$ −2.47076 −0.411793
$$37$$ −0.211704 0.366683i −0.0348040 0.0602823i 0.848099 0.529838i $$-0.177747\pi$$
−0.882903 + 0.469556i $$0.844414\pi$$
$$38$$ −2.79143 + 4.83489i −0.452829 + 0.784323i
$$39$$ 0 0
$$40$$ −0.955864 1.65561i −0.151135 0.261774i
$$41$$ −5.01604 −0.783374 −0.391687 0.920099i $$-0.628108\pi$$
−0.391687 + 0.920099i $$0.628108\pi$$
$$42$$ 3.17157 + 6.13111i 0.489383 + 0.946050i
$$43$$ −11.2059 −1.70889 −0.854445 0.519542i $$-0.826103\pi$$
−0.854445 + 0.519542i $$0.826103\pi$$
$$44$$ −0.300609 0.520670i −0.0453185 0.0784939i
$$45$$ −0.910544 + 1.57711i −0.135736 + 0.235101i
$$46$$ −2.37757 + 4.11807i −0.350554 + 0.607177i
$$47$$ −4.03635 6.99116i −0.588762 1.01977i −0.994395 0.105729i $$-0.966282\pi$$
0.405633 0.914036i $$-0.367051\pi$$
$$48$$ 3.84855 0.555491
$$49$$ −4.04458 + 5.71326i −0.577797 + 0.816180i
$$50$$ 4.94553 0.699404
$$51$$ −4.06426 7.03950i −0.569110 0.985727i
$$52$$ 0 0
$$53$$ 0.348553 0.603712i 0.0478774 0.0829262i −0.841094 0.540890i $$-0.818088\pi$$
0.888971 + 0.457964i $$0.151421\pi$$
$$54$$ 0.115151 + 0.199447i 0.0156701 + 0.0271414i
$$55$$ −0.443132 −0.0597519
$$56$$ 3.71570 + 7.18300i 0.496532 + 0.959869i
$$57$$ 12.6500 1.67554
$$58$$ −3.53953 6.13065i −0.464763 0.804993i
$$59$$ −4.93159 + 8.54177i −0.642039 + 1.11204i 0.342938 + 0.939358i $$0.388578\pi$$
−0.984977 + 0.172686i $$0.944756\pi$$
$$60$$ −0.645188 + 1.11750i −0.0832934 + 0.144268i
$$61$$ −2.34855 4.06781i −0.300701 0.520830i 0.675594 0.737274i $$-0.263887\pi$$
−0.976295 + 0.216444i $$0.930554\pi$$
$$62$$ 4.71136 0.598344
$$63$$ 4.15596 6.48654i 0.523601 0.817227i
$$64$$ 7.90305 0.987881
$$65$$ 0 0
$$66$$ 0.924277 1.60089i 0.113771 0.197056i
$$67$$ −5.21041 + 9.02470i −0.636553 + 1.10254i 0.349631 + 0.936888i $$0.386307\pi$$
−0.986184 + 0.165655i $$0.947026\pi$$
$$68$$ −1.41841 2.45676i −0.172008 0.297926i
$$69$$ 10.7745 1.29710
$$70$$ 1.77373 + 0.0820297i 0.212001 + 0.00980443i
$$71$$ −14.0876 −1.67189 −0.835946 0.548812i $$-0.815080\pi$$
−0.835946 + 0.548812i $$0.815080\pi$$
$$72$$ −4.45007 7.70775i −0.524446 0.908368i
$$73$$ 2.54191 4.40273i 0.297509 0.515300i −0.678057 0.735010i $$-0.737178\pi$$
0.975565 + 0.219710i $$0.0705110\pi$$
$$74$$ 0.227170 0.393471i 0.0264080 0.0457400i
$$75$$ −5.60297 9.70463i −0.646975 1.12059i
$$76$$ 4.41482 0.506415
$$77$$ 1.87257 + 0.0866008i 0.213399 + 0.00986908i
$$78$$ 0 0
$$79$$ 1.95586 + 3.38766i 0.220052 + 0.381141i 0.954823 0.297174i $$-0.0960440\pi$$
−0.734772 + 0.678315i $$0.762711\pi$$
$$80$$ 0.494983 0.857336i 0.0553408 0.0958530i
$$81$$ 4.62851 8.01682i 0.514279 0.890757i
$$82$$ −2.69124 4.66137i −0.297198 0.514762i
$$83$$ 10.2035 1.11998 0.559990 0.828499i $$-0.310805\pi$$
0.559990 + 0.828499i $$0.310805\pi$$
$$84$$ 2.94480 4.59619i 0.321304 0.501486i
$$85$$ −2.09090 −0.226790
$$86$$ −6.01230 10.4136i −0.648323 1.12293i
$$87$$ −8.02012 + 13.8913i −0.859847 + 1.48930i
$$88$$ 1.08285 1.87555i 0.115432 0.199935i
$$89$$ 6.68955 + 11.5866i 0.709090 + 1.22818i 0.965195 + 0.261532i $$0.0842276\pi$$
−0.256104 + 0.966649i $$0.582439\pi$$
$$90$$ −1.95413 −0.205983
$$91$$ 0 0
$$92$$ 3.76028 0.392036
$$93$$ −5.33767 9.24512i −0.553491 0.958674i
$$94$$ 4.33122 7.50190i 0.446731 0.773761i
$$95$$ 1.62699 2.81802i 0.166925 0.289123i
$$96$$ −5.36711 9.29610i −0.547778 0.948780i
$$97$$ −0.202023 −0.0205123 −0.0102562 0.999947i $$-0.503265\pi$$
−0.0102562 + 0.999947i $$0.503265\pi$$
$$98$$ −7.47932 0.693276i −0.755526 0.0700315i
$$99$$ −2.06302 −0.207341
$$100$$ −1.95542 3.38689i −0.195542 0.338689i
$$101$$ 8.66723 15.0121i 0.862421 1.49376i −0.00716374 0.999974i $$-0.502280\pi$$
0.869585 0.493783i $$-0.164386\pi$$
$$102$$ 4.36117 7.55377i 0.431820 0.747934i
$$103$$ 5.40739 + 9.36587i 0.532806 + 0.922847i 0.999266 + 0.0383047i $$0.0121957\pi$$
−0.466460 + 0.884542i $$0.654471\pi$$
$$104$$ 0 0
$$105$$ −1.84855 3.57353i −0.180400 0.348740i
$$106$$ 0.748033 0.0726554
$$107$$ 3.05839 + 5.29729i 0.295666 + 0.512108i 0.975140 0.221592i $$-0.0711252\pi$$
−0.679474 + 0.733700i $$0.737792\pi$$
$$108$$ 0.0910594 0.157720i 0.00876220 0.0151766i
$$109$$ −5.69958 + 9.87196i −0.545921 + 0.945563i 0.452628 + 0.891700i $$0.350487\pi$$
−0.998548 + 0.0538629i $$0.982847\pi$$
$$110$$ −0.237752 0.411799i −0.0226688 0.0392635i
$$111$$ −1.02948 −0.0977137
$$112$$ −2.25923 + 3.52616i −0.213477 + 0.333191i
$$113$$ −0.923456 −0.0868714 −0.0434357 0.999056i $$-0.513830\pi$$
−0.0434357 + 0.999056i $$0.513830\pi$$
$$114$$ 6.78709 + 11.7556i 0.635669 + 1.10101i
$$115$$ 1.38577 2.40023i 0.129224 0.223822i
$$116$$ −2.79900 + 4.84801i −0.259880 + 0.450126i
$$117$$ 0 0
$$118$$ −10.5837 −0.974312
$$119$$ 8.83566 + 0.408623i 0.809963 + 0.0374584i
$$120$$ −4.64819 −0.424319
$$121$$ 5.24900 + 9.09153i 0.477182 + 0.826503i
$$122$$ 2.52013 4.36499i 0.228162 0.395187i
$$123$$ −6.09801 + 10.5621i −0.549839 + 0.952349i
$$124$$ −1.86283 3.22652i −0.167287 0.289750i
$$125$$ −6.00967 −0.537521
$$126$$ 8.25768 + 0.381893i 0.735652 + 0.0340218i
$$127$$ −8.50972 −0.755116 −0.377558 0.925986i $$-0.623236\pi$$
−0.377558 + 0.925986i $$0.623236\pi$$
$$128$$ −0.174618 0.302447i −0.0154342 0.0267328i
$$129$$ −13.6231 + 23.5959i −1.19945 + 2.07750i
$$130$$ 0 0
$$131$$ 3.50152 + 6.06482i 0.305930 + 0.529885i 0.977468 0.211084i $$-0.0676995\pi$$
−0.671538 + 0.740970i $$0.734366\pi$$
$$132$$ −1.46180 −0.127234
$$133$$ −7.42599 + 11.5903i −0.643915 + 1.00501i
$$134$$ −11.1821 −0.965988
$$135$$ −0.0671160 0.116248i −0.00577642 0.0100051i
$$136$$ 5.10940 8.84974i 0.438128 0.758859i
$$137$$ 3.10847 5.38403i 0.265575 0.459989i −0.702139 0.712040i $$-0.747772\pi$$
0.967714 + 0.252051i $$0.0811050\pi$$
$$138$$ 5.78084 + 10.0127i 0.492097 + 0.852338i
$$139$$ 6.53140 0.553986 0.276993 0.960872i $$-0.410662\pi$$
0.276993 + 0.960872i $$0.410662\pi$$
$$140$$ −0.645140 1.24715i −0.0545242 0.105403i
$$141$$ −19.6280 −1.65297
$$142$$ −7.55839 13.0915i −0.634286 1.09862i
$$143$$ 0 0
$$144$$ 2.30442 3.99137i 0.192035 0.332614i
$$145$$ 2.06302 + 3.57326i 0.171325 + 0.296743i
$$146$$ 5.45523 0.451478
$$147$$ 7.11317 + 15.4621i 0.586685 + 1.27529i
$$148$$ −0.359285 −0.0295330
$$149$$ 1.84869 + 3.20203i 0.151451 + 0.262320i 0.931761 0.363072i $$-0.118272\pi$$
−0.780310 + 0.625393i $$0.784939\pi$$
$$150$$ 6.01230 10.4136i 0.490902 0.850267i
$$151$$ 2.43887 4.22425i 0.198473 0.343764i −0.749561 0.661935i $$-0.769735\pi$$
0.948033 + 0.318171i $$0.103069\pi$$
$$152$$ 7.95152 + 13.7724i 0.644954 + 1.11709i
$$153$$ −9.73430 −0.786971
$$154$$ 0.924207 + 1.78663i 0.0744747 + 0.143971i
$$155$$ −2.74603 −0.220566
$$156$$ 0 0
$$157$$ 4.75984 8.24428i 0.379876 0.657965i −0.611168 0.791501i $$-0.709300\pi$$
0.991044 + 0.133536i $$0.0426332\pi$$
$$158$$ −2.09875 + 3.63514i −0.166968 + 0.289196i
$$159$$ −0.847473 1.46787i −0.0672090 0.116409i
$$160$$ −2.76117 −0.218290
$$161$$ −6.32501 + 9.87196i −0.498481 + 0.778020i
$$162$$ 9.93329 0.780433
$$163$$ 11.8544 + 20.5325i 0.928511 + 1.60823i 0.785815 + 0.618461i $$0.212244\pi$$
0.142696 + 0.989767i $$0.454423\pi$$
$$164$$ −2.12819 + 3.68613i −0.166184 + 0.287838i
$$165$$ −0.538716 + 0.933084i −0.0419390 + 0.0726405i
$$166$$ 5.47446 + 9.48204i 0.424901 + 0.735949i
$$167$$ 1.13193 0.0875914 0.0437957 0.999041i $$-0.486055\pi$$
0.0437957 + 0.999041i $$0.486055\pi$$
$$168$$ 19.6421 + 0.908391i 1.51542 + 0.0700839i
$$169$$ 0 0
$$170$$ −1.12183 1.94306i −0.0860402 0.149026i
$$171$$ 7.57452 13.1195i 0.579238 1.00327i
$$172$$ −4.75442 + 8.23489i −0.362521 + 0.627905i
$$173$$ −5.99458 10.3829i −0.455760 0.789399i 0.542972 0.839751i $$-0.317299\pi$$
−0.998732 + 0.0503522i $$0.983966\pi$$
$$174$$ −17.2121 −1.30484
$$175$$ 12.1808 + 0.563327i 0.920783 + 0.0425835i
$$176$$ 1.12148 0.0845350
$$177$$ 11.9907 + 20.7685i 0.901276 + 1.56106i
$$178$$ −7.17825 + 12.4331i −0.538033 + 0.931900i
$$179$$ −4.73538 + 8.20192i −0.353939 + 0.613040i −0.986936 0.161114i $$-0.948491\pi$$
0.632997 + 0.774154i $$0.281825\pi$$
$$180$$ 0.772645 + 1.33826i 0.0575896 + 0.0997480i
$$181$$ 11.4314 0.849690 0.424845 0.905266i $$-0.360329\pi$$
0.424845 + 0.905266i $$0.360329\pi$$
$$182$$ 0 0
$$183$$ −11.4206 −0.844233
$$184$$ 6.77264 + 11.7305i 0.499285 + 0.864788i
$$185$$ −0.132407 + 0.229335i −0.00973473 + 0.0168611i
$$186$$ 5.72761 9.92052i 0.419969 0.727408i
$$187$$ −1.18434 2.05134i −0.0866075 0.150009i
$$188$$ −6.85011 −0.499595
$$189$$ 0.260898 + 0.504354i 0.0189775 + 0.0366864i
$$190$$ 3.49169 0.253314
$$191$$ −7.84377 13.5858i −0.567555 0.983034i −0.996807 0.0798496i $$-0.974556\pi$$
0.429252 0.903185i $$-0.358777\pi$$
$$192$$ 9.60776 16.6411i 0.693380 1.20097i
$$193$$ −11.5036 + 19.9248i −0.828045 + 1.43422i 0.0715256 + 0.997439i $$0.477213\pi$$
−0.899570 + 0.436776i $$0.856120\pi$$
$$194$$ −0.108391 0.187739i −0.00778202 0.0134788i
$$195$$ 0 0
$$196$$ 2.48248 + 5.39624i 0.177320 + 0.385446i
$$197$$ −10.2035 −0.726970 −0.363485 0.931600i $$-0.618413\pi$$
−0.363485 + 0.931600i $$0.618413\pi$$
$$198$$ −1.10687 1.91715i −0.0786616 0.136246i
$$199$$ −5.96173 + 10.3260i −0.422616 + 0.731992i −0.996194 0.0871586i $$-0.972221\pi$$
0.573579 + 0.819150i $$0.305555\pi$$
$$200$$ 7.04381 12.2002i 0.498072 0.862687i
$$201$$ 12.6686 + 21.9427i 0.893576 + 1.54772i
$$202$$ 18.6008 1.30875
$$203$$ −8.01952 15.5029i −0.562860 1.08809i
$$204$$ −6.89747 −0.482920
$$205$$ 1.56860 + 2.71689i 0.109555 + 0.189756i
$$206$$ −5.80243 + 10.0501i −0.404274 + 0.700223i
$$207$$ 6.45152 11.1744i 0.448412 0.776672i
$$208$$ 0 0
$$209$$ 3.68627 0.254984
$$210$$ 2.32905 3.63514i 0.160720 0.250849i
$$211$$ −15.5893 −1.07321 −0.536606 0.843833i $$-0.680294\pi$$
−0.536606 + 0.843833i $$0.680294\pi$$
$$212$$ −0.295766 0.512281i −0.0203133 0.0351836i
$$213$$ −17.1263 + 29.6637i −1.17348 + 2.03252i
$$214$$ −3.28182 + 5.68428i −0.224341 + 0.388570i
$$215$$ 3.50428 + 6.06959i 0.238990 + 0.413942i
$$216$$ 0.656028 0.0446370
$$217$$ 11.6041 + 0.536653i 0.787734 + 0.0364304i
$$218$$ −12.2319 −0.828451
$$219$$ −6.18042 10.7048i −0.417634 0.723364i
$$220$$ −0.188010 + 0.325643i −0.0126757 + 0.0219549i
$$221$$ 0 0
$$222$$ −0.552343 0.956687i −0.0370709 0.0642086i
$$223$$ 6.76662 0.453126 0.226563 0.973996i $$-0.427251\pi$$
0.226563 + 0.973996i $$0.427251\pi$$
$$224$$ 11.6680 + 0.539613i 0.779604 + 0.0360544i
$$225$$ −13.4197 −0.894645
$$226$$ −0.495459 0.858161i −0.0329575 0.0570840i
$$227$$ 8.41225 14.5704i 0.558340 0.967074i −0.439295 0.898343i $$-0.644772\pi$$
0.997635 0.0687311i $$-0.0218950\pi$$
$$228$$ 5.36711 9.29610i 0.355445 0.615650i
$$229$$ 5.51286 + 9.54855i 0.364300 + 0.630986i 0.988664 0.150148i $$-0.0479750\pi$$
−0.624364 + 0.781134i $$0.714642\pi$$
$$230$$ 2.97402 0.196101
$$231$$ 2.45884 3.83771i 0.161780 0.252503i
$$232$$ −20.1651 −1.32390
$$233$$ −8.67743 15.0298i −0.568477 0.984632i −0.996717 0.0809664i $$-0.974199\pi$$
0.428239 0.903665i $$-0.359134\pi$$
$$234$$ 0 0
$$235$$ −2.52446 + 4.37249i −0.164678 + 0.285230i
$$236$$ 4.18472 + 7.24814i 0.272402 + 0.471814i
$$237$$ 9.51100 0.617806
$$238$$ 4.36084 + 8.43015i 0.282671 + 0.546445i
$$239$$ −19.7223 −1.27573 −0.637865 0.770148i $$-0.720182\pi$$
−0.637865 + 0.770148i $$0.720182\pi$$
$$240$$ −1.20350 2.08453i −0.0776858 0.134556i
$$241$$ 1.39206 2.41112i 0.0896706 0.155314i −0.817701 0.575643i $$-0.804752\pi$$
0.907372 + 0.420329i $$0.138085\pi$$
$$242$$ −5.63246 + 9.75571i −0.362069 + 0.627121i
$$243$$ −10.9318 18.9345i −0.701278 1.21465i
$$244$$ −3.98574 −0.255161
$$245$$ 4.35934 + 0.404077i 0.278508 + 0.0258155i
$$246$$ −13.0870 −0.834397
$$247$$ 0 0
$$248$$ 6.71028 11.6226i 0.426103 0.738033i
$$249$$ 12.4044 21.4851i 0.786098 1.36156i
$$250$$ −3.22435 5.58475i −0.203926 0.353210i
$$251$$ 23.5608 1.48714 0.743572 0.668655i $$-0.233130\pi$$
0.743572 + 0.668655i $$0.233130\pi$$
$$252$$ −3.00348 5.80617i −0.189201 0.365754i
$$253$$ 3.13974 0.197394
$$254$$ −4.56570 7.90803i −0.286478 0.496194i
$$255$$ −2.54191 + 4.40273i −0.159181 + 0.275709i
$$256$$ 8.09042 14.0130i 0.505651 0.875814i
$$257$$ 1.71615 + 2.97245i 0.107050 + 0.185417i 0.914574 0.404419i $$-0.132526\pi$$
−0.807524 + 0.589835i $$0.799193\pi$$
$$258$$ −29.2367 −1.82019
$$259$$ 0.604338 0.943239i 0.0375517 0.0586100i
$$260$$ 0 0
$$261$$ 9.60450 + 16.6355i 0.594503 + 1.02971i
$$262$$ −3.75733 + 6.50788i −0.232128 + 0.402058i
$$263$$ 10.7245 18.5754i 0.661303 1.14541i −0.318970 0.947765i $$-0.603337\pi$$
0.980273 0.197646i $$-0.0633298\pi$$
$$264$$ −2.63285 4.56023i −0.162041 0.280663i
$$265$$ −0.435992 −0.0267828
$$266$$ −14.7551 0.682378i −0.904691 0.0418393i
$$267$$ 32.5300 1.99080
$$268$$ 4.42131 + 7.65794i 0.270075 + 0.467783i
$$269$$ −7.32843 + 12.6932i −0.446822 + 0.773919i −0.998177 0.0603517i $$-0.980778\pi$$
0.551355 + 0.834271i $$0.314111\pi$$
$$270$$ 0.0720191 0.124741i 0.00438294 0.00759148i
$$271$$ −1.02183 1.76986i −0.0620717 0.107511i 0.833320 0.552792i $$-0.186437\pi$$
−0.895391 + 0.445280i $$0.853104\pi$$
$$272$$ 5.29168 0.320856
$$273$$ 0 0
$$274$$ 6.67112 0.403017
$$275$$ −1.63273 2.82797i −0.0984572 0.170533i
$$276$$ 4.57138 7.91787i 0.275165 0.476600i
$$277$$ 2.71678 4.70560i 0.163236 0.282732i −0.772792 0.634660i $$-0.781140\pi$$
0.936027 + 0.351927i $$0.114474\pi$$
$$278$$ 3.50428 + 6.06959i 0.210173 + 0.364030i
$$279$$ −12.7843 −0.765373
$$280$$ 2.72864 4.25881i 0.163067 0.254513i
$$281$$ −20.2356 −1.20715 −0.603577 0.797305i $$-0.706258\pi$$
−0.603577 + 0.797305i $$0.706258\pi$$
$$282$$ −10.5310 18.2401i −0.627109 1.08618i
$$283$$ −0.867593 + 1.50272i −0.0515731 + 0.0893272i −0.890659 0.454671i $$-0.849757\pi$$
0.839086 + 0.543998i $$0.183090\pi$$
$$284$$ −5.97704 + 10.3525i −0.354672 + 0.614310i
$$285$$ −3.95586 6.85176i −0.234325 0.405863i
$$286$$ 0 0
$$287$$ −6.09755 11.7875i −0.359927 0.695792i
$$288$$ −12.8548 −0.757474
$$289$$ 2.91173 + 5.04326i 0.171278 + 0.296662i
$$290$$ −2.21373 + 3.83430i −0.129995 + 0.225158i
$$291$$ −0.245600 + 0.425392i −0.0143973 + 0.0249369i
$$292$$ −2.15695 3.73595i −0.126226 0.218630i
$$293$$ −27.2441 −1.59162 −0.795810 0.605547i $$-0.792954\pi$$
−0.795810 + 0.605547i $$0.792954\pi$$
$$294$$ −10.5524 + 14.9061i −0.615430 + 0.869340i
$$295$$ 6.16875 0.359159
$$296$$ −0.647107 1.12082i −0.0376123 0.0651465i
$$297$$ 0.0760324 0.131692i 0.00441185 0.00764154i
$$298$$ −1.98375 + 3.43595i −0.114915 + 0.199039i
$$299$$ 0 0
$$300$$ −9.50884 −0.548993
$$301$$ −13.6221 26.3335i −0.785163 1.51784i
$$302$$ 5.23409 0.301188
$$303$$ −21.0735 36.5004i −1.21064 2.09690i
$$304$$ −4.11760 + 7.13190i −0.236161 + 0.409042i
$$305$$ −1.46886 + 2.54414i −0.0841067 + 0.145677i
$$306$$ −5.22272 9.04601i −0.298563 0.517126i
$$307$$ −12.7138 −0.725612 −0.362806 0.931865i $$-0.618181\pi$$
−0.362806 + 0.931865i $$0.618181\pi$$
$$308$$ 0.858127 1.33935i 0.0488963 0.0763165i
$$309$$ 26.2951 1.49588
$$310$$ −1.47332 2.55186i −0.0836788 0.144936i
$$311$$ −4.80939 + 8.33011i −0.272716 + 0.472357i −0.969556 0.244869i $$-0.921255\pi$$
0.696841 + 0.717226i $$0.254588\pi$$
$$312$$ 0 0
$$313$$ 4.51273 + 7.81628i 0.255075 + 0.441802i 0.964916 0.262559i $$-0.0845666\pi$$
−0.709841 + 0.704362i $$0.751233\pi$$
$$314$$ 10.2151 0.576473
$$315$$ −4.81300 0.222587i −0.271182 0.0125414i
$$316$$ 3.31931 0.186726
$$317$$ 12.3131 + 21.3269i 0.691572 + 1.19784i 0.971323 + 0.237766i $$0.0764150\pi$$
−0.279750 + 0.960073i $$0.590252\pi$$
$$318$$ 0.909386 1.57510i 0.0509958 0.0883273i
$$319$$ −2.33709 + 4.04797i −0.130852 + 0.226643i
$$320$$ −2.47141 4.28061i −0.138156 0.239293i
$$321$$ 14.8724 0.830095
$$322$$ −12.5675 0.581209i −0.700359 0.0323895i
$$323$$ 17.3935 0.967802
$$324$$ −3.92754 6.80269i −0.218196 0.377927i
$$325$$ 0 0
$$326$$ −12.7205 + 22.0325i −0.704521 + 1.22027i
$$327$$ 13.8580 + 24.0027i 0.766348 + 1.32735i
$$328$$ −15.3323 −0.846584
$$329$$ 11.5223 17.9838i 0.635244 0.991477i
$$330$$ −1.15614 −0.0636436
$$331$$ 6.58591 + 11.4071i 0.361994 + 0.626993i 0.988289 0.152594i $$-0.0487626\pi$$
−0.626295 + 0.779586i $$0.715429\pi$$
$$332$$ 4.32911 7.49823i 0.237591 0.411519i
$$333$$ −0.616426 + 1.06768i −0.0337799 + 0.0585085i
$$334$$ 0.607311 + 1.05189i 0.0332306 + 0.0575571i
$$335$$ 6.51752 0.356090
$$336$$ 4.67834 + 9.04393i 0.255225 + 0.493387i
$$337$$ −17.0307 −0.927720 −0.463860 0.885909i $$-0.653536\pi$$
−0.463860 + 0.885909i $$0.653536\pi$$
$$338$$ 0 0
$$339$$ −1.12265 + 1.94448i −0.0609738 + 0.105610i
$$340$$ −0.887121 + 1.53654i −0.0481109 + 0.0833305i
$$341$$ −1.55542 2.69406i −0.0842306 0.145892i
$$342$$ 16.2558 0.879010
$$343$$ −18.3425 2.55948i −0.990405 0.138199i
$$344$$ −34.2527 −1.84678
$$345$$ −3.36937 5.83592i −0.181401 0.314195i
$$346$$ 6.43251 11.1414i 0.345814 0.598968i
$$347$$ −0.229959 + 0.398300i −0.0123448 + 0.0213819i −0.872132 0.489271i $$-0.837263\pi$$
0.859787 + 0.510653i $$0.170596\pi$$
$$348$$ 6.80550 + 11.7875i 0.364813 + 0.631875i
$$349$$ 6.87822 0.368183 0.184091 0.982909i $$-0.441066\pi$$
0.184091 + 0.982909i $$0.441066\pi$$
$$350$$ 6.01184 + 11.6218i 0.321347 + 0.621210i
$$351$$ 0 0
$$352$$ −1.56400 2.70892i −0.0833613 0.144386i
$$353$$ 0.766631 1.32784i 0.0408036 0.0706740i −0.844902 0.534921i $$-0.820342\pi$$
0.885706 + 0.464247i $$0.153675\pi$$
$$354$$ −12.8667 + 22.2857i −0.683856 + 1.18447i
$$355$$ 4.40542 + 7.63041i 0.233815 + 0.404980i
$$356$$ 11.3529 0.601701
$$357$$ 11.6019 18.1081i 0.614040 0.958383i
$$358$$ −10.1626 −0.537112
$$359$$ −13.6034 23.5617i −0.717959 1.24354i −0.961807 0.273728i $$-0.911743\pi$$
0.243848 0.969813i $$-0.421590\pi$$
$$360$$ −2.78322 + 4.82068i −0.146688 + 0.254072i
$$361$$ −4.03438 + 6.98774i −0.212336 + 0.367776i
$$362$$ 6.13326 + 10.6231i 0.322357 + 0.558339i
$$363$$ 25.5249 1.33971
$$364$$ 0 0
$$365$$ −3.17959 −0.166427
$$366$$ −6.12745 10.6131i −0.320287 0.554753i
$$367$$ −13.4907 + 23.3666i −0.704208 + 1.21972i 0.262769 + 0.964859i $$0.415364\pi$$
−0.966977 + 0.254865i $$0.917969\pi$$
$$368$$ −3.50713 + 6.07452i −0.182822 + 0.316656i
$$369$$ 7.30267 + 12.6486i 0.380162 + 0.658460i
$$370$$ −0.284159 −0.0147727
$$371$$ 1.84240 + 0.0852056i 0.0956526 + 0.00442365i
$$372$$ −9.05859 −0.469666
$$373$$ −1.98619 3.44018i −0.102841 0.178126i 0.810013 0.586412i $$-0.199460\pi$$
−0.912854 + 0.408286i $$0.866127\pi$$
$$374$$ 1.27086 2.20120i 0.0657147 0.113821i
$$375$$ −7.30597 + 12.6543i −0.377279 + 0.653466i
$$376$$ −12.3377 21.3695i −0.636269 1.10205i
$$377$$ 0 0
$$378$$ −0.328714 + 0.513050i −0.0169072 + 0.0263885i
$$379$$ 11.4059 0.585884 0.292942 0.956130i $$-0.405366\pi$$
0.292942 + 0.956130i $$0.405366\pi$$
$$380$$ −1.38058 2.39124i −0.0708225 0.122668i
$$381$$ −10.3453 + 17.9186i −0.530005 + 0.917996i
$$382$$ 8.41680 14.5783i 0.430641 0.745892i
$$383$$ −11.8960 20.6044i −0.607856 1.05284i −0.991593 0.129395i $$-0.958696\pi$$
0.383737 0.923442i $$-0.374637\pi$$
$$384$$ −0.849134 −0.0433322
$$385$$ −0.538676 1.04134i −0.0274535 0.0530716i
$$386$$ −24.6879 −1.25658
$$387$$ 16.3143 + 28.2573i 0.829304 + 1.43640i
$$388$$ −0.0857137 + 0.148460i −0.00435145 + 0.00753694i
$$389$$ 14.2055 24.6046i 0.720247 1.24751i −0.240653 0.970611i $$-0.577362\pi$$
0.960901 0.276894i $$-0.0893051\pi$$
$$390$$ 0 0
$$391$$ 14.8148 0.749216
$$392$$ −12.3629 + 17.4635i −0.624420 + 0.882038i
$$393$$ 17.0272 0.858911
$$394$$ −5.47446 9.48204i −0.275799 0.477698i
$$395$$ 1.22326 2.11875i 0.0615489 0.106606i
$$396$$ −0.875291 + 1.51605i −0.0439850 + 0.0761843i
$$397$$ −4.92956 8.53825i −0.247408 0.428522i 0.715398 0.698717i $$-0.246245\pi$$
−0.962806 + 0.270195i $$0.912912\pi$$
$$398$$ −12.7945 −0.641332
$$399$$ 15.3775 + 29.7270i 0.769838 + 1.48821i
$$400$$ 7.29510 0.364755
$$401$$ 6.30971 + 10.9287i 0.315092 + 0.545756i 0.979457 0.201653i $$-0.0646313\pi$$
−0.664365 + 0.747408i $$0.731298\pi$$
$$402$$ −13.5941 + 23.5457i −0.678013 + 1.17435i
$$403$$ 0 0
$$404$$ −7.35460 12.7385i −0.365905 0.633766i
$$405$$ −5.78964 −0.287689
$$406$$ 10.1041 15.7702i 0.501456 0.782663i
$$407$$ −0.299994 −0.0148701
$$408$$ −12.4230 21.5173i −0.615031 1.06527i
$$409$$ −9.02867 + 15.6381i −0.446439 + 0.773255i −0.998151 0.0607793i $$-0.980641\pi$$
0.551712 + 0.834035i $$0.313975\pi$$
$$410$$ −1.68319 + 2.91537i −0.0831268 + 0.143980i
$$411$$ −7.55795 13.0908i −0.372806 0.645720i
$$412$$ 9.17691 0.452114
$$413$$ −26.0677 1.20555i −1.28271 0.0593214i
$$414$$ 13.8457 0.680478
$$415$$ −3.19080 5.52663i −0.156630 0.271291i
$$416$$ 0 0
$$417$$ 7.94024 13.7529i 0.388835 0.673483i
$$418$$ 1.97778 + 3.42562i 0.0967366 + 0.167553i
$$419$$ 14.2805 0.697647 0.348823 0.937188i $$-0.386581\pi$$
0.348823 + 0.937188i $$0.386581\pi$$
$$420$$ −3.41037 0.157720i −0.166409 0.00769593i
$$421$$ −4.27439 −0.208321 −0.104160 0.994561i $$-0.533216\pi$$
−0.104160 + 0.994561i $$0.533216\pi$$
$$422$$ −8.36410 14.4870i −0.407158 0.705218i
$$423$$ −11.7527 + 20.3564i −0.571438 + 0.989760i
$$424$$ 1.06541 1.84534i 0.0517407 0.0896175i
$$425$$ −7.70398 13.3437i −0.373698 0.647263i
$$426$$ −36.7550 −1.78079
$$427$$ 6.70425 10.4639i 0.324441 0.506382i
$$428$$ 5.19042 0.250888
$$429$$ 0 0
$$430$$ −3.76028 + 6.51300i −0.181337 + 0.314085i
$$431$$ 7.30335 12.6498i 0.351790 0.609318i −0.634773 0.772698i $$-0.718906\pi$$
0.986563 + 0.163381i $$0.0522398\pi$$
$$432$$ 0.169858 + 0.294203i 0.00817230 + 0.0141548i
$$433$$ −28.0099 −1.34607 −0.673035 0.739611i $$-0.735009\pi$$
−0.673035 + 0.739611i $$0.735009\pi$$
$$434$$ 5.72718 + 11.0715i 0.274914 + 0.531449i
$$435$$ 10.0321 0.481001
$$436$$ 4.83640 + 8.37688i 0.231621 + 0.401180i
$$437$$ −11.5278 + 19.9667i −0.551448 + 0.955137i
$$438$$ 6.63193 11.4868i 0.316886 0.548863i
$$439$$ −8.53872 14.7895i −0.407531 0.705864i 0.587082 0.809528i $$-0.300277\pi$$
−0.994612 + 0.103664i $$0.966943\pi$$
$$440$$ −1.35450 −0.0645733
$$441$$ 20.2951 + 1.88120i 0.966433 + 0.0895810i
$$442$$ 0 0
$$443$$ −6.90783 11.9647i −0.328201 0.568461i 0.653954 0.756534i $$-0.273109\pi$$
−0.982155 + 0.188073i $$0.939776\pi$$
$$444$$ −0.436783 + 0.756531i −0.0207288 + 0.0359034i
$$445$$ 4.18386 7.24665i 0.198334 0.343524i
$$446$$ 3.63048 + 6.28817i 0.171908 + 0.297754i
$$447$$ 8.98984 0.425205
$$448$$ 9.60703 + 18.5718i 0.453890 + 0.877436i
$$449$$ −32.6410 −1.54042 −0.770211 0.637789i $$-0.779849\pi$$
−0.770211 + 0.637789i $$0.779849\pi$$
$$450$$ −7.20003 12.4708i −0.339412 0.587880i
$$451$$ −1.77698 + 3.07783i −0.0836749 + 0.144929i
$$452$$ −0.391801 + 0.678619i −0.0184287 + 0.0319195i
$$453$$ −5.92988 10.2709i −0.278610 0.482567i
$$454$$ 18.0536 0.847298
$$455$$ 0 0
$$456$$ 38.6667 1.81074
$$457$$ −1.58517 2.74559i −0.0741511 0.128433i 0.826566 0.562840i $$-0.190291\pi$$
−0.900717 + 0.434407i $$0.856958\pi$$
$$458$$ −5.91560 + 10.2461i −0.276418 + 0.478769i
$$459$$ 0.358756 0.621384i 0.0167453 0.0290037i
$$460$$ −1.17590 2.03672i −0.0548266 0.0949625i
$$461$$ 0.202023 0.00940915 0.00470458 0.999989i $$-0.498502\pi$$
0.00470458 + 0.999989i $$0.498502\pi$$
$$462$$ 4.88559 + 0.225944i 0.227298 + 0.0105119i
$$463$$ 17.2121 0.799912 0.399956 0.916534i $$-0.369025\pi$$
0.399956 + 0.916534i $$0.369025\pi$$
$$464$$ −5.22112 9.04325i −0.242384 0.419822i
$$465$$ −3.33835 + 5.78219i −0.154812 + 0.268143i
$$466$$ 9.31136 16.1277i 0.431340 0.747103i
$$467$$ 0.0955845 + 0.165557i 0.00442312 + 0.00766108i 0.868228 0.496165i $$-0.165259\pi$$
−0.863805 + 0.503826i $$0.831925\pi$$
$$468$$ 0 0
$$469$$ −27.5415 1.27371i −1.27175 0.0588146i
$$470$$ −5.41777 −0.249903
$$471$$ −11.5731 20.0452i −0.533260 0.923633i
$$472$$ −15.0742 + 26.1092i −0.693845 + 1.20177i
$$473$$ −3.96982 + 6.87593i −0.182533 + 0.316156i
$$474$$ 5.10291 + 8.83850i 0.234384 + 0.405966i
$$475$$ 23.9787 1.10022
$$476$$ 4.04905 6.31968i 0.185588 0.289662i
$$477$$ −2.02978 −0.0929374
$$478$$ −10.5816 18.3278i −0.483989 0.838294i
$$479$$ 10.7392 18.6009i 0.490688 0.849897i −0.509254 0.860616i $$-0.670079\pi$$
0.999943 + 0.0107189i $$0.00341199\pi$$
$$480$$ −3.35676 + 5.81408i −0.153214 + 0.265375i
$$481$$ 0 0
$$482$$ 2.98752 0.136078
$$483$$ 13.0976 + 25.3197i 0.595964 + 1.15209i
$$484$$ 8.90811 0.404914
$$485$$ 0.0631758 + 0.109424i 0.00286867 + 0.00496868i
$$486$$ 11.7305 20.3178i 0.532105 0.921633i
$$487$$ 9.52422 16.4964i 0.431584 0.747525i −0.565426 0.824799i $$-0.691288\pi$$
0.997010 + 0.0772740i $$0.0246216\pi$$
$$488$$ −7.17871 12.4339i −0.324965 0.562856i
$$489$$ 57.6458 2.60684
$$490$$ 1.96340 + 4.26790i 0.0886973 + 0.192804i
$$491$$ 35.7559 1.61364 0.806821 0.590796i $$-0.201186\pi$$
0.806821 + 0.590796i $$0.201186\pi$$
$$492$$ 5.17448 + 8.96247i 0.233284 + 0.404059i
$$493$$ −11.0275 + 19.1002i −0.496654 + 0.860230i
$$494$$ 0 0
$$495$$ 0.645140 + 1.11741i 0.0289969 + 0.0502240i
$$496$$ 6.94968 0.312050
$$497$$ −17.1251 33.1053i −0.768164 1.48497i
$$498$$ 26.6213 1.19293
$$499$$ 8.84457 + 15.3192i 0.395937 + 0.685784i 0.993220 0.116247i $$-0.0370864\pi$$
−0.597283 + 0.802031i $$0.703753\pi$$
$$500$$ −2.54976 + 4.41632i −0.114029 + 0.197504i
$$501$$ 1.37609 2.38346i 0.0614792 0.106485i
$$502$$ 12.6410 + 21.8949i 0.564196 + 0.977217i
$$503$$ 11.3305 0.505203 0.252601 0.967570i $$-0.418714\pi$$
0.252601 + 0.967570i $$0.418714\pi$$
$$504$$ 12.7033 19.8271i 0.565851 0.883169i
$$505$$ −10.8415 −0.482441
$$506$$ 1.68456 + 2.91774i 0.0748878 + 0.129709i
$$507$$ 0 0
$$508$$ −3.61048 + 6.25353i −0.160189 + 0.277455i
$$509$$ −9.67569 16.7588i −0.428868 0.742821i 0.567905 0.823094i $$-0.307754\pi$$
−0.996773 + 0.0802734i $$0.974421\pi$$
$$510$$ −5.45523 −0.241562
$$511$$ 13.4362 + 0.621384i 0.594382 + 0.0274884i
$$512$$ 16.6645 0.736472
$$513$$ 0.558316 + 0.967032i 0.0246502 + 0.0426955i
$$514$$ −1.84152 + 3.18961i −0.0812259 + 0.140687i
$$515$$ 3.38195 5.85772i 0.149027 0.258122i
$$516$$ 11.5599 + 20.0224i 0.508897 + 0.881435i
$$517$$ −5.71967 −0.251551
$$518$$ 1.20079 + 0.0555330i 0.0527597 + 0.00243998i
$$519$$ −29.1505 −1.27957
$$520$$ 0 0
$$521$$ 3.85550 6.67791i 0.168912 0.292565i −0.769125 0.639098i $$-0.779308\pi$$
0.938038 + 0.346533i $$0.112641\pi$$
$$522$$ −10.3062 + 17.8508i −0.451088 + 0.781307i
$$523$$ 17.5251 + 30.3543i 0.766317 + 1.32730i 0.939547 + 0.342419i $$0.111246\pi$$
−0.173230 + 0.984881i $$0.555420\pi$$
$$524$$ 5.94246 0.259597
$$525$$ 15.9944 24.9638i 0.698054 1.08951i
$$526$$ 23.0160 1.00355
$$527$$ −7.33919 12.7119i −0.319700 0.553737i
$$528$$ 1.36339 2.36146i 0.0593339 0.102769i
$$529$$ 1.68133 2.91214i 0.0731011 0.126615i
$$530$$ −0.233922 0.405165i −0.0101609 0.0175992i
$$531$$ 28.7189 1.24630
$$532$$ 5.36671 + 10.3746i 0.232676 + 0.449797i
$$533$$ 0 0
$$534$$ 17.4532 + 30.2299i 0.755275 + 1.30818i
$$535$$ 1.91282 3.31309i 0.0826982 0.143238i
$$536$$ −15.9264 + 27.5854i −0.687917 + 1.19151i
$$537$$ 11.5136 + 19.9422i 0.496849 + 0.860568i
$$538$$ −15.7276 −0.678066
$$539$$ 2.07281 + 4.50573i 0.0892821 + 0.194075i
$$540$$ −0.113903 −0.00490160
$$541$$ 6.06674 + 10.5079i 0.260829 + 0.451770i 0.966463 0.256807i $$-0.0826706\pi$$
−0.705633 + 0.708577i $$0.749337\pi$$
$$542$$ 1.09648 1.89916i 0.0470978 0.0815758i
$$543$$ 13.8972 24.0706i 0.596385 1.03297i
$$544$$ −7.37967 12.7820i −0.316401 0.548022i
$$545$$ 7.12940 0.305390
$$546$$ 0 0
$$547$$ −5.12546 −0.219149 −0.109575 0.993979i $$-0.534949\pi$$
−0.109575 + 0.993979i $$0.534949\pi$$
$$548$$ −2.63770 4.56864i −0.112677 0.195162i
$$549$$ −6.83835 + 11.8444i −0.291854 + 0.505505i
$$550$$ 1.75201 3.03457i 0.0747058 0.129394i
$$551$$ −17.1616 29.7248i −0.731109 1.26632i
$$552$$ 32.9340 1.40177
$$553$$ −5.58327 + 8.71427i −0.237425 + 0.370568i
$$554$$ 5.83051 0.247715
$$555$$ 0.321934 + 0.557606i 0.0136653 + 0.0236691i
$$556$$ 2.77112 4.79972i 0.117522 0.203554i
$$557$$ 18.7793 32.5267i 0.795705 1.37820i −0.126686 0.991943i $$-0.540434\pi$$
0.922391 0.386258i $$-0.126233\pi$$
$$558$$ −6.85911 11.8803i −0.290369 0.502934i
$$559$$ 0 0
$$560$$ 2.61641 + 0.121001i 0.110563 + 0.00511323i
$$561$$ −5.75922 −0.243154
$$562$$ −10.8569 18.8048i −0.457973 0.793232i
$$563$$ −14.3504 + 24.8557i −0.604799 + 1.04754i 0.387284 + 0.921960i $$0.373413\pi$$
−0.992083 + 0.125583i $$0.959920\pi$$
$$564$$ −8.32769 + 14.4240i −0.350659 + 0.607359i
$$565$$ 0.288779 + 0.500180i 0.0121490 + 0.0210428i
$$566$$ −1.86195 −0.0782636
$$567$$ 24.4656 + 1.13146i 1.02746 + 0.0475170i
$$568$$ −43.0610 −1.80680
$$569$$ −8.97417 15.5437i −0.376217 0.651627i 0.614291 0.789079i $$-0.289442\pi$$
−0.990508 + 0.137452i $$0.956109\pi$$
$$570$$ 4.24486 7.35231i 0.177798 0.307955i
$$571$$ −8.91370 + 15.4390i −0.373027 + 0.646101i −0.990030 0.140860i $$-0.955013\pi$$
0.617003 + 0.786961i $$0.288347\pi$$
$$572$$ 0 0
$$573$$ −38.1428 −1.59344
$$574$$ 7.68250 11.9907i 0.320662 0.500483i
$$575$$ 20.4236 0.851724
$$576$$ −11.5058 19.9286i −0.479407 0.830357i
$$577$$ 16.5285 28.6282i 0.688091 1.19181i −0.284363 0.958717i $$-0.591782\pi$$
0.972455 0.233092i $$-0.0748844\pi$$
$$578$$ −3.12445 + 5.41170i −0.129960 + 0.225097i
$$579$$ 27.9698 + 48.4451i 1.16239 + 2.01331i
$$580$$ 3.50117 0.145378
$$581$$ 12.4035 + 23.9778i 0.514584 + 0.994766i
$$582$$ −0.527085 −0.0218484
$$583$$ −0.246957 0.427742i −0.0102279 0.0177153i
$$584$$ 7.76975 13.4576i 0.321515 0.556880i
$$585$$ 0 0
$$586$$ −14.6172 25.3178i −0.603832 1.04587i
$$587$$ −14.7295 −0.607953 −0.303976 0.952680i $$-0.598314\pi$$
−0.303976 + 0.952680i $$0.598314\pi$$
$$588$$ 14.3806 + 1.33297i 0.593045 + 0.0549708i
$$589$$ 22.8433 0.941241
$$590$$ 3.30970 + 5.73258i 0.136258 + 0.236006i
$$591$$ −12.4044 + 21.4851i −0.510250 + 0.883779i
$$592$$ 0.335097 0.580404i 0.0137724 0.0238545i
$$593$$ −4.60494 7.97598i −0.189102 0.327534i 0.755849 0.654746i $$-0.227224\pi$$
−0.944951 + 0.327212i $$0.893891\pi$$
$$594$$ 0.163174 0.00669510
$$595$$ −2.54172 4.91353i −0.104201 0.201435i
$$596$$ 3.13743 0.128514
$$597$$ 14.4954 + 25.1067i 0.593256 + 1.02755i
$$598$$ 0 0
$$599$$ 5.28727 9.15782i 0.216032 0.374178i −0.737559 0.675282i $$-0.764022\pi$$
0.953591 + 0.301104i $$0.0973551\pi$$
$$600$$ −17.1263 29.6637i −0.699180 1.21102i
$$601$$ 4.08916 0.166800 0.0834001 0.996516i $$-0.473422\pi$$
0.0834001 + 0.996516i $$0.473422\pi$$
$$602$$ 17.1629 26.7875i 0.699507 1.09178i
$$603$$ 30.3426 1.23565
$$604$$ −2.06951 3.58450i −0.0842072 0.145851i
$$605$$ 3.28289 5.68613i 0.133469 0.231174i
$$606$$ 22.6131 39.1670i 0.918593 1.59105i
$$607$$ −1.80353 3.12380i −0.0732030 0.126791i 0.827100 0.562054i $$-0.189989\pi$$
−0.900303 + 0.435263i $$0.856655\pi$$
$$608$$ 22.9693 0.931527
$$609$$ −42.3932 1.96056i −1.71786 0.0794459i
$$610$$ −3.15233 −0.127634
$$611$$ 0 0
$$612$$ −4.13003 + 7.15343i −0.166947 + 0.289160i
$$613$$ −19.2422 + 33.3285i −0.777186 + 1.34613i 0.156371 + 0.987698i $$0.450020\pi$$
−0.933557 + 0.358428i $$0.883313\pi$$
$$614$$ −6.82128 11.8148i −0.275284 0.476806i
$$615$$ 7.62778 0.307582
$$616$$ 5.72379 + 0.264709i 0.230618 + 0.0106654i
$$617$$ 3.09503 0.124601 0.0623007 0.998057i $$-0.480156\pi$$
0.0623007 + 0.998057i $$0.480156\pi$$
$$618$$ 14.1080 + 24.4359i 0.567509 + 0.982954i
$$619$$ 6.13462 10.6255i 0.246571 0.427074i −0.716001 0.698099i $$-0.754029\pi$$
0.962572 + 0.271025i $$0.0873627\pi$$
$$620$$ −1.16507 + 2.01797i −0.0467905 + 0.0810435i
$$621$$ 0.475540 + 0.823660i 0.0190828 + 0.0330523i
$$622$$ −10.3215 −0.413854
$$623$$ −19.0962 + 29.8050i −0.765073 + 1.19411i
$$624$$ 0 0
$$625$$ −9.64277 16.7018i −0.385711 0.668071i
$$626$$ −4.84241 + 8.38730i −0.193542 + 0.335224i
$$627$$ 4.48140 7.76202i 0.178970 0.309985i
$$628$$ −4.03897 6.99571i −0.161173 0.279159i
$$629$$ −1.41551 −0.0564402
$$630$$ −2.37546 4.59211i −0.0946406 0.182954i
$$631$$ 5.31780 0.211698 0.105849 0.994382i $$-0.466244\pi$$
0.105849 + 0.994382i $$0.466244\pi$$
$$632$$ 5.97840 + 10.3549i 0.237808 + 0.411896i
$$633$$ −18.9520 + 32.8258i −0.753273 + 1.30471i
$$634$$ −13.2126 + 22.8849i −0.524740 + 0.908877i
$$635$$ 2.66113 + 4.60921i 0.105604 + 0.182911i
$$636$$ −1.43825 −0.0570304
$$637$$ 0 0
$$638$$ −5.01566 −0.198572
$$639$$ 20.5097 + 35.5238i 0.811349 + 1.40530i
$$640$$ −0.109212 + 0.189160i −0.00431697 + 0.00747721i
$$641$$ −6.09521 + 10.5572i −0.240746 + 0.416985i −0.960927 0.276801i $$-0.910726\pi$$
0.720181 + 0.693787i $$0.244059\pi$$
$$642$$ 7.97944 + 13.8208i 0.314923 + 0.545463i
$$643$$ 18.9733 0.748235 0.374117 0.927381i $$-0.377946\pi$$
0.374117 + 0.927381i $$0.377946\pi$$
$$644$$ 4.57104 + 8.83649i 0.180124 + 0.348207i
$$645$$ 17.0406 0.670974
$$646$$ 9.33211 + 16.1637i 0.367167 + 0.635952i
$$647$$ −9.85587 + 17.0709i −0.387474 + 0.671125i −0.992109 0.125378i $$-0.959986\pi$$
0.604635 + 0.796503i $$0.293319\pi$$
$$648$$ 14.1478 24.5046i 0.555776 0.962633i
$$649$$ 3.49414 + 6.05202i 0.137157 + 0.237563i
$$650$$ 0 0
$$651$$ 15.2371 23.7818i 0.597188 0.932080i
$$652$$ 20.1182 0.787891
$$653$$ 10.1986 + 17.6645i 0.399103 + 0.691267i 0.993616 0.112819i $$-0.0359882\pi$$
−0.594512 + 0.804087i $$0.702655\pi$$
$$654$$ −14.8704 + 25.7563i −0.581478 + 1.00715i
$$655$$ 2.18996 3.79313i 0.0855690 0.148210i
$$656$$ −3.96982 6.87593i −0.154996 0.268460i
$$657$$ −14.8027 −0.577510
$$658$$ 22.8942 + 1.05879i 0.892509 + 0.0412759i
$$659$$ 32.6628 1.27236 0.636181 0.771540i $$-0.280513\pi$$
0.636181 + 0.771540i $$0.280513\pi$$
$$660$$ 0.457129 + 0.791771i 0.0177937 + 0.0308196i
$$661$$ −4.86846 + 8.43242i −0.189361 + 0.327983i −0.945037 0.326962i $$-0.893975\pi$$
0.755676 + 0.654945i $$0.227308\pi$$
$$662$$ −7.06704 + 12.2405i −0.274668 + 0.475740i
$$663$$ 0 0
$$664$$ 31.1886 1.21035
$$665$$ 8.60002 + 0.397725i 0.333494 + 0.0154231i
$$666$$ −1.32292 −0.0512620
$$667$$ −14.6172 25.3178i −0.565981 0.980308i
$$668$$ 0.480251 0.831819i 0.0185815 0.0321841i
$$669$$ 8.22620 14.2482i 0.318043 0.550867i
$$670$$ 3.49683 + 6.05668i 0.135094 + 0.233990i
$$671$$ −3.32800 −0.128476
$$672$$ 15.3211 23.9129i 0.591025 0.922461i
$$673$$ 39.4512 1.52073 0.760367 0.649494i $$-0.225019\pi$$
0.760367 + 0.649494i $$0.225019\pi$$
$$674$$ −9.13742 15.8265i −0.351960 0.609613i
$$675$$ 0.494581 0.856639i 0.0190364 0.0329720i
$$676$$ 0 0
$$677$$ 24.3169 + 42.1182i 0.934576 + 1.61873i 0.775389 + 0.631484i $$0.217554\pi$$
0.159187 + 0.987248i $$0.449113\pi$$
$$678$$ −2.40932 −0.0925296
$$679$$ −0.245582 0.474745i −0.00942455 0.0182191i
$$680$$ −6.39117 −0.245090
$$681$$ −20.4536 35.4266i −0.783783 1.35755i
$$682$$ 1.66905 2.89088i 0.0639112 0.110697i
$$683$$ 2.85387 4.94304i 0.109200 0.189140i −0.806246 0.591580i $$-0.798504\pi$$
0.915446 + 0.402440i $$0.131838\pi$$
$$684$$ −6.42738 11.1326i −0.245757 0.425664i
$$685$$ −3.88828 −0.148563
$$686$$ −7.46278 18.4188i −0.284930 0.703234i
$$687$$ 26.8080 1.02279
$$688$$ −8.86867 15.3610i −0.338115 0.585632i
$$689$$ 0 0
$$690$$ 3.61552 6.26226i 0.137640 0.238400i
$$691$$ −20.8866 36.1766i −0.794563 1.37622i −0.923116 0.384521i $$-0.874367\pi$$
0.128553 0.991703i $$-0.458967\pi$$
$$692$$ −10.1734 −0.386736
$$693$$ −2.50783 4.84801i −0.0952646 0.184161i
$$694$$ −0.493517 −0.0187336
$$695$$ −2.04247 3.53767i −0.0774754 0.134191i
$$696$$ −24.5147 + 42.4608i −0.929228 + 1.60947i
$$697$$ −8.38464 + 14.5226i −0.317591 + 0.550084i
$$698$$ 3.69035 + 6.39188i 0.139682 + 0.241936i
$$699$$ −42.1967 −1.59603
$$700$$ 5.58200 8.71229i 0.210980 0.329294i
$$701$$ −22.4361 −0.847399 −0.423700 0.905803i $$-0.639269\pi$$
−0.423700 + 0.905803i $$0.639269\pi$$
$$702$$ 0 0
$$703$$ 1.10145 1.90776i 0.0415419 0.0719527i
$$704$$ 2.79974 4.84929i 0.105519 0.182764i
$$705$$ 6.13798 + 10.6313i 0.231170 + 0.400398i
$$706$$ 1.64527 0.0619207
$$707$$ 45.8137 + 2.11875i 1.72300 + 0.0796837i
$$708$$ 20.3495 0.764780
$$709$$ −14.3734 24.8955i −0.539804 0.934969i −0.998914 0.0465891i $$-0.985165\pi$$
0.459110 0.888380i $$-0.348168\pi$$
$$710$$ −4.72726 + 8.18785i −0.177411 + 0.307285i
$$711$$ 5.69495 9.86394i 0.213577 0.369927i
$$712$$ 20.4476 + 35.4163i 0.766307 + 1.32728i
$$713$$ 19.4566 0.728654
$$714$$ 23.0525 + 1.06611i 0.862718 + 0.0398982i
$$715$$ 0 0
$$716$$ 4.01822 + 6.95976i 0.150168 + 0.260098i
$$717$$ −23.9765 + 41.5284i −0.895417 + 1.55091i
$$718$$ 14.5972 25.2830i 0.544762 0.943555i
$$719$$ 2.10450 + 3.64509i 0.0784844 + 0.135939i 0.902596 0.430488i $$-0.141659\pi$$
−0.824112 + 0.566427i $$0.808325\pi$$
$$720$$ −2.88251 −0.107425
$$721$$ −15.4361 + 24.0924i −0.574870 + 0.897247i
$$722$$ −8.65821 −0.322225
$$723$$ −3.38467 5.86242i −0.125877 0.218026i
$$724$$ 4.85008 8.40058i 0.180252 0.312205i
$$725$$ −15.2025 + 26.3315i −0.564606 + 0.977927i
$$726$$ 13.6948 + 23.7201i 0.508262 + 0.880335i
$$727$$ 43.4680 1.61214 0.806070 0.591820i $$-0.201591\pi$$
0.806070 + 0.591820i $$0.201591\pi$$
$$728$$ 0 0
$$729$$ −25.3884 −0.940312
$$730$$ −1.70594 2.95477i −0.0631396 0.109361i
$$731$$ −18.7315 + 32.4439i −0.692809 + 1.19998i
$$732$$ −4.84548 + 8.39261i −0.179094 + 0.310200i
$$733$$ −4.54710 7.87581i −0.167951 0.290900i 0.769748 0.638348i $$-0.220382\pi$$
−0.937699 + 0.347448i $$0.887048\pi$$
$$734$$ −28.9525 −1.06866
$$735$$ 6.15050 8.68803i 0.226865 0.320463i
$$736$$ 19.5639 0.721133
$$737$$ 3.69169 + 6.39419i 0.135985 + 0.235533i
$$738$$ −7.83617 + 13.5726i −0.288453 + 0.499616i
$$739$$ −4.80433 + 8.32135i −0.176730 + 0.306106i −0.940759 0.339077i $$-0.889885\pi$$
0.764028 + 0.645183i $$0.223219\pi$$
$$740$$ 0.112354 + 0.194603i 0.00413022 + 0.00715375i
$$741$$ 0 0
$$742$$ 0.909317 + 1.75784i 0.0333821 + 0.0645325i
$$743$$ 32.1771 1.18046 0.590231 0.807234i $$-0.299036\pi$$
0.590231 + 0.807234i $$0.299036\pi$$
$$744$$ −16.3154 28.2591i −0.598152 1.03603i
$$745$$ 1.15623 2.00265i 0.0423610 0.0733714i
$$746$$ 2.13129 3.69150i 0.0780320 0.135155i
$$747$$ −14.8549 25.7295i −0.543513 0.941392i
$$748$$ −2.00995 −0.0734911
$$749$$ −8.73058 + 13.6265i −0.319008 + 0.497903i
$$750$$ −15.6794 −0.572531
$$751$$ −3.89892 6.75313i −0.142274 0.246425i 0.786079 0.618126i $$-0.212108\pi$$
−0.928352 + 0.371701i $$0.878775\pi$$
$$752$$ 6.38894 11.0660i 0.232981 0.403534i
$$753$$ 28.6429 49.6110i 1.04381 1.80793i
$$754$$ 0 0
$$755$$ −3.05070 −0.111026
$$756$$ 0.481327 + 0.0222599i 0.0175057 + 0.000809586i
$$757$$ 17.9970 0.654110 0.327055 0.945005i $$-0.393944\pi$$
0.327055 + 0.945005i $$0.393944\pi$$
$$758$$ 6.11960 + 10.5995i 0.222274 + 0.384990i
$$759$$ 3.81699 6.61123i 0.138548 0.239972i
$$760$$ 4.97314 8.61373i 0.180395 0.312453i
$$761$$ −20.3395 35.2290i −0.737306 1.27705i −0.953704 0.300746i $$-0.902764\pi$$
0.216398 0.976305i $$-0.430569\pi$$
$$762$$ −22.2021 −0.804299
$$763$$ −30.1271 1.39329i −1.09068 0.0504406i
$$764$$ −13.3117 −0.481601
$$765$$ 3.04407 + 5.27248i 0.110059 + 0.190627i
$$766$$ 12.7650 22.1097i 0.461220 0.798856i
$$767$$ 0 0
$$768$$ −19.6711 34.0713i −0.709819 1.22944i
$$769$$ −39.3098 −1.41755 −0.708774 0.705435i $$-0.750752\pi$$
−0.708774 + 0.705435i $$0.750752\pi$$
$$770$$ 0.678695 1.05929i 0.0244585 0.0381743i
$$771$$ 8.34529 0.300548
$$772$$ 9.76138 + 16.9072i 0.351320 + 0.608504i
$$773$$ 6.73679 11.6685i 0.242306 0.419685i −0.719065 0.694943i $$-0.755430\pi$$
0.961371 + 0.275257i $$0.0887630\pi$$
$$774$$ −17.5062 + 30.3216i −0.629247 + 1.08989i
$$775$$ −10.1178 17.5245i −0.363442 0.629500i
$$776$$ −0.617515 −0.0221675
$$777$$ −1.25144 2.41923i −0.0448953 0.0867893i
$$778$$ 30.4866 1.09300
$$779$$ −13.0486 22.6009i −0.467516 0.809761i
$$780$$ 0 0