# Properties

 Label 325.2.e.e.276.6 Level $325$ Weight $2$ Character 325.276 Analytic conductor $2.595$ Analytic rank $0$ Dimension $12$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$325 = 5^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 325.e (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$2.59513806569$$ Analytic rank: $$0$$ Dimension: $$12$$ Relative dimension: $$6$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ Defining polynomial: $$x^{12} + 8 x^{10} + 54 x^{8} + 78 x^{6} + 92 x^{4} + 10 x^{2} + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 65) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 276.6 Root $$1.27287 - 2.20467i$$ of defining polynomial Character $$\chi$$ $$=$$ 325.276 Dual form 325.2.e.e.126.6

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.27287 + 2.20467i) q^{2} +(1.07646 + 1.86449i) q^{3} +(-2.24039 + 3.88048i) q^{4} +(-2.74039 + 4.74650i) q^{6} +(1.46928 - 2.54486i) q^{7} -6.31544 q^{8} +(-0.817544 + 1.41603i) q^{9} +O(q^{10})$$ $$q+(1.27287 + 2.20467i) q^{2} +(1.07646 + 1.86449i) q^{3} +(-2.24039 + 3.88048i) q^{4} +(-2.74039 + 4.74650i) q^{6} +(1.46928 - 2.54486i) q^{7} -6.31544 q^{8} +(-0.817544 + 1.41603i) q^{9} +(0.317544 + 0.550003i) q^{11} -9.64680 q^{12} +(0.0716710 - 3.60484i) q^{13} +7.48079 q^{14} +(-3.55794 - 6.16253i) q^{16} +(0.611979 - 1.05998i) q^{17} -4.16251 q^{18} +(-0.682456 + 1.18205i) q^{19} +6.32648 q^{21} +(-0.808385 + 1.40016i) q^{22} +(-1.07646 - 1.86449i) q^{23} +(-6.79833 - 11.7751i) q^{24} +(8.03872 - 4.43048i) q^{26} +2.93855 q^{27} +(6.58351 + 11.4030i) q^{28} +(-1.50000 - 2.59808i) q^{29} -8.96157 q^{31} +(2.74215 - 4.74954i) q^{32} +(-0.683650 + 1.18412i) q^{33} +3.11588 q^{34} +(-3.66324 - 6.34492i) q^{36} +(-0.611979 - 1.05998i) q^{37} -3.47471 q^{38} +(6.79833 - 3.74685i) q^{39} +(4.98079 + 8.62698i) q^{41} +(8.05279 + 13.9478i) q^{42} +(0.683650 - 1.18412i) q^{43} -2.84570 q^{44} +(2.74039 - 4.74650i) q^{46} -6.16379 q^{47} +(7.65998 - 13.2675i) q^{48} +(-0.817544 - 1.41603i) q^{49} +2.63509 q^{51} +(13.8279 + 8.35437i) q^{52} +0.642285 q^{53} +(3.74039 + 6.47855i) q^{54} +(-9.27912 + 16.0719i) q^{56} -2.93855 q^{57} +(3.81861 - 6.61402i) q^{58} +(-3.79833 + 6.57890i) q^{59} +(1.13509 - 1.96603i) q^{61} +(-11.4069 - 19.7574i) q^{62} +(2.40240 + 4.16107i) q^{63} -0.270178 q^{64} -3.48079 q^{66} +(-4.01502 - 6.95421i) q^{67} +(2.74215 + 4.74954i) q^{68} +(2.31754 - 4.01410i) q^{69} +(-1.31754 + 2.28205i) q^{71} +(5.16315 - 8.94284i) q^{72} -10.3263 q^{73} +(1.55794 - 2.69843i) q^{74} +(-3.05794 - 5.29650i) q^{76} +1.86624 q^{77} +(16.9140 + 10.2189i) q^{78} +1.03843 q^{79} +(5.61588 + 9.72698i) q^{81} +(-12.6798 + 21.9620i) q^{82} +11.8452 q^{83} +(-14.1738 + 24.5498i) q^{84} +3.48079 q^{86} +(3.22939 - 5.59346i) q^{87} +(-2.00543 - 3.47351i) q^{88} +(6.27912 + 10.8758i) q^{89} +(-9.06851 - 5.47890i) q^{91} +9.64680 q^{92} +(-9.64680 - 16.7087i) q^{93} +(-7.84570 - 13.5891i) q^{94} +11.8073 q^{96} +(7.39190 - 12.8031i) q^{97} +(2.08125 - 3.60484i) q^{98} -1.03843 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$12 q - 4 q^{4} - 10 q^{6} - 6 q^{9} + O(q^{10})$$ $$12 q - 4 q^{4} - 10 q^{6} - 6 q^{9} + 44 q^{14} - 16 q^{16} - 12 q^{19} - 8 q^{21} - 32 q^{24} + 24 q^{26} - 18 q^{29} - 16 q^{31} - 16 q^{34} - 2 q^{36} + 32 q^{39} + 14 q^{41} + 4 q^{44} + 10 q^{46} - 6 q^{49} + 24 q^{51} + 22 q^{54} - 16 q^{56} + 4 q^{59} + 6 q^{61} + 12 q^{64} + 4 q^{66} + 24 q^{69} - 12 q^{71} - 8 q^{74} - 10 q^{76} + 104 q^{79} + 14 q^{81} - 90 q^{84} - 4 q^{86} - 20 q^{89} - 44 q^{91} - 56 q^{94} + 12 q^{96} - 104 q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$$.

 $$n$$ $$27$$ $$301$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.27287 + 2.20467i 0.900055 + 1.55894i 0.827421 + 0.561582i $$0.189807\pi$$
0.0726333 + 0.997359i $$0.476860\pi$$
$$3$$ 1.07646 + 1.86449i 0.621496 + 1.07646i 0.989207 + 0.146523i $$0.0468082\pi$$
−0.367711 + 0.929940i $$0.619858\pi$$
$$4$$ −2.24039 + 3.88048i −1.12020 + 1.94024i
$$5$$ 0 0
$$6$$ −2.74039 + 4.74650i −1.11876 + 1.93775i
$$7$$ 1.46928 2.54486i 0.555334 0.961867i −0.442543 0.896747i $$-0.645924\pi$$
0.997877 0.0651198i $$-0.0207430\pi$$
$$8$$ −6.31544 −2.23284
$$9$$ −0.817544 + 1.41603i −0.272515 + 0.472010i
$$10$$ 0 0
$$11$$ 0.317544 + 0.550003i 0.0957433 + 0.165832i 0.909919 0.414787i $$-0.136144\pi$$
−0.814175 + 0.580619i $$0.802811\pi$$
$$12$$ −9.64680 −2.78479
$$13$$ 0.0716710 3.60484i 0.0198779 0.999802i
$$14$$ 7.48079 1.99932
$$15$$ 0 0
$$16$$ −3.55794 6.16253i −0.889484 1.54063i
$$17$$ 0.611979 1.05998i 0.148427 0.257082i −0.782220 0.623003i $$-0.785912\pi$$
0.930646 + 0.365920i $$0.119246\pi$$
$$18$$ −4.16251 −0.981113
$$19$$ −0.682456 + 1.18205i −0.156566 + 0.271180i −0.933628 0.358244i $$-0.883376\pi$$
0.777062 + 0.629424i $$0.216709\pi$$
$$20$$ 0 0
$$21$$ 6.32648 1.38055
$$22$$ −0.808385 + 1.40016i −0.172348 + 0.298516i
$$23$$ −1.07646 1.86449i −0.224458 0.388773i 0.731699 0.681628i $$-0.238728\pi$$
−0.956157 + 0.292856i $$0.905394\pi$$
$$24$$ −6.79833 11.7751i −1.38770 2.40357i
$$25$$ 0 0
$$26$$ 8.03872 4.43048i 1.57652 0.868888i
$$27$$ 2.93855 0.565525
$$28$$ 6.58351 + 11.4030i 1.24417 + 2.15496i
$$29$$ −1.50000 2.59808i −0.278543 0.482451i 0.692480 0.721437i $$-0.256518\pi$$
−0.971023 + 0.238987i $$0.923185\pi$$
$$30$$ 0 0
$$31$$ −8.96157 −1.60955 −0.804773 0.593583i $$-0.797713\pi$$
−0.804773 + 0.593583i $$0.797713\pi$$
$$32$$ 2.74215 4.74954i 0.484747 0.839607i
$$33$$ −0.683650 + 1.18412i −0.119008 + 0.206128i
$$34$$ 3.11588 0.534368
$$35$$ 0 0
$$36$$ −3.66324 6.34492i −0.610540 1.05749i
$$37$$ −0.611979 1.05998i −0.100609 0.174259i 0.811327 0.584593i $$-0.198746\pi$$
−0.911936 + 0.410333i $$0.865412\pi$$
$$38$$ −3.47471 −0.563672
$$39$$ 6.79833 3.74685i 1.08860 0.599975i
$$40$$ 0 0
$$41$$ 4.98079 + 8.62698i 0.777868 + 1.34731i 0.933168 + 0.359440i $$0.117032\pi$$
−0.155300 + 0.987867i $$0.549634\pi$$
$$42$$ 8.05279 + 13.9478i 1.24257 + 2.15220i
$$43$$ 0.683650 1.18412i 0.104256 0.180576i −0.809178 0.587563i $$-0.800087\pi$$
0.913434 + 0.406987i $$0.133421\pi$$
$$44$$ −2.84570 −0.429005
$$45$$ 0 0
$$46$$ 2.74039 4.74650i 0.404049 0.699833i
$$47$$ −6.16379 −0.899081 −0.449540 0.893260i $$-0.648412\pi$$
−0.449540 + 0.893260i $$0.648412\pi$$
$$48$$ 7.65998 13.2675i 1.10562 1.91499i
$$49$$ −0.817544 1.41603i −0.116792 0.202290i
$$50$$ 0 0
$$51$$ 2.63509 0.368986
$$52$$ 13.8279 + 8.35437i 1.91759 + 1.15854i
$$53$$ 0.642285 0.0882246 0.0441123 0.999027i $$-0.485954\pi$$
0.0441123 + 0.999027i $$0.485954\pi$$
$$54$$ 3.74039 + 6.47855i 0.509003 + 0.881619i
$$55$$ 0 0
$$56$$ −9.27912 + 16.0719i −1.23997 + 2.14770i
$$57$$ −2.93855 −0.389221
$$58$$ 3.81861 6.61402i 0.501408 0.868464i
$$59$$ −3.79833 + 6.57890i −0.494501 + 0.856500i −0.999980 0.00633858i $$-0.997982\pi$$
0.505479 + 0.862839i $$0.331316\pi$$
$$60$$ 0 0
$$61$$ 1.13509 1.96603i 0.145333 0.251725i −0.784164 0.620554i $$-0.786908\pi$$
0.929497 + 0.368829i $$0.120241\pi$$
$$62$$ −11.4069 19.7574i −1.44868 2.50919i
$$63$$ 2.40240 + 4.16107i 0.302674 + 0.524246i
$$64$$ −0.270178 −0.0337722
$$65$$ 0 0
$$66$$ −3.48079 −0.428455
$$67$$ −4.01502 6.95421i −0.490512 0.849592i 0.509428 0.860513i $$-0.329857\pi$$
−0.999940 + 0.0109212i $$0.996524\pi$$
$$68$$ 2.74215 + 4.74954i 0.332534 + 0.575966i
$$69$$ 2.31754 4.01410i 0.279000 0.483241i
$$70$$ 0 0
$$71$$ −1.31754 + 2.28205i −0.156364 + 0.270830i −0.933555 0.358435i $$-0.883311\pi$$
0.777191 + 0.629265i $$0.216644\pi$$
$$72$$ 5.16315 8.94284i 0.608483 1.05392i
$$73$$ −10.3263 −1.20860 −0.604301 0.796756i $$-0.706547\pi$$
−0.604301 + 0.796756i $$0.706547\pi$$
$$74$$ 1.55794 2.69843i 0.181107 0.313686i
$$75$$ 0 0
$$76$$ −3.05794 5.29650i −0.350770 0.607551i
$$77$$ 1.86624 0.212678
$$78$$ 16.9140 + 10.2189i 1.91513 + 1.15706i
$$79$$ 1.03843 0.116832 0.0584161 0.998292i $$-0.481395\pi$$
0.0584161 + 0.998292i $$0.481395\pi$$
$$80$$ 0 0
$$81$$ 5.61588 + 9.72698i 0.623986 + 1.08078i
$$82$$ −12.6798 + 21.9620i −1.40025 + 2.42530i
$$83$$ 11.8452 1.30018 0.650092 0.759855i $$-0.274730\pi$$
0.650092 + 0.759855i $$0.274730\pi$$
$$84$$ −14.1738 + 24.5498i −1.54649 + 2.67860i
$$85$$ 0 0
$$86$$ 3.48079 0.375343
$$87$$ 3.22939 5.59346i 0.346227 0.599682i
$$88$$ −2.00543 3.47351i −0.213780 0.370277i
$$89$$ 6.27912 + 10.8758i 0.665585 + 1.15283i 0.979126 + 0.203253i $$0.0651513\pi$$
−0.313541 + 0.949575i $$0.601515\pi$$
$$90$$ 0 0
$$91$$ −9.06851 5.47890i −0.950638 0.574344i
$$92$$ 9.64680 1.00575
$$93$$ −9.64680 16.7087i −1.00033 1.73262i
$$94$$ −7.84570 13.5891i −0.809222 1.40161i
$$95$$ 0 0
$$96$$ 11.8073 1.20507
$$97$$ 7.39190 12.8031i 0.750534 1.29996i −0.197031 0.980397i $$-0.563130\pi$$
0.947564 0.319565i $$-0.103537\pi$$
$$98$$ 2.08125 3.60484i 0.210238 0.364144i
$$99$$ −1.03843 −0.104366
$$100$$ 0 0
$$101$$ −6.61588 11.4590i −0.658304 1.14022i −0.981054 0.193732i $$-0.937941\pi$$
0.322750 0.946484i $$-0.395393\pi$$
$$102$$ 3.35412 + 5.80951i 0.332108 + 0.575228i
$$103$$ 10.9686 1.08077 0.540383 0.841419i $$-0.318279\pi$$
0.540383 + 0.841419i $$0.318279\pi$$
$$104$$ −0.452633 + 22.7661i −0.0443843 + 2.23240i
$$105$$ 0 0
$$106$$ 0.817544 + 1.41603i 0.0794069 + 0.137537i
$$107$$ 5.33680 + 9.24360i 0.515928 + 0.893613i 0.999829 + 0.0184903i $$0.00588599\pi$$
−0.483901 + 0.875123i $$0.660781\pi$$
$$108$$ −6.58351 + 11.4030i −0.633499 + 1.09725i
$$109$$ −3.27018 −0.313226 −0.156613 0.987660i $$-0.550058\pi$$
−0.156613 + 0.987660i $$0.550058\pi$$
$$110$$ 0 0
$$111$$ 1.31754 2.28205i 0.125056 0.216603i
$$112$$ −20.9104 −1.97584
$$113$$ 2.76490 4.78895i 0.260100 0.450507i −0.706168 0.708044i $$-0.749578\pi$$
0.966268 + 0.257537i $$0.0829110\pi$$
$$114$$ −3.74039 6.47855i −0.350320 0.606772i
$$115$$ 0 0
$$116$$ 13.4424 1.24809
$$117$$ 5.04596 + 3.04860i 0.466499 + 0.281844i
$$118$$ −19.3391 −1.78031
$$119$$ −1.79833 3.11480i −0.164853 0.285533i
$$120$$ 0 0
$$121$$ 5.29833 9.17698i 0.481666 0.834271i
$$122$$ 5.77928 0.523231
$$123$$ −10.7233 + 18.5732i −0.966884 + 1.67469i
$$124$$ 20.0774 34.7752i 1.80301 3.12290i
$$125$$ 0 0
$$126$$ −6.11588 + 10.5930i −0.544845 + 0.943700i
$$127$$ 8.61586 + 14.9231i 0.764534 + 1.32421i 0.940493 + 0.339813i $$0.110364\pi$$
−0.175959 + 0.984397i $$0.556303\pi$$
$$128$$ −5.82819 10.0947i −0.515144 0.892256i
$$129$$ 2.94369 0.259178
$$130$$ 0 0
$$131$$ 10.0000 0.873704 0.436852 0.899533i $$-0.356093\pi$$
0.436852 + 0.899533i $$0.356093\pi$$
$$132$$ −3.06329 5.30577i −0.266625 0.461808i
$$133$$ 2.00543 + 3.47351i 0.173893 + 0.301191i
$$134$$ 10.2212 17.7036i 0.882975 1.52936i
$$135$$ 0 0
$$136$$ −3.86491 + 6.69422i −0.331413 + 0.574025i
$$137$$ 4.33616 7.51044i 0.370463 0.641661i −0.619174 0.785254i $$-0.712532\pi$$
0.989637 + 0.143593i $$0.0458657\pi$$
$$138$$ 11.7997 1.00446
$$139$$ −7.16324 + 12.4071i −0.607578 + 1.05236i 0.384060 + 0.923308i $$0.374526\pi$$
−0.991638 + 0.129048i $$0.958808\pi$$
$$140$$ 0 0
$$141$$ −6.63509 11.4923i −0.558775 0.967827i
$$142$$ −6.70825 −0.562944
$$143$$ 2.00543 1.10528i 0.167703 0.0924279i
$$144$$ 11.6351 0.969591
$$145$$ 0 0
$$146$$ −13.1440 22.7661i −1.08781 1.88414i
$$147$$ 1.76011 3.04860i 0.145172 0.251445i
$$148$$ 5.48429 0.450806
$$149$$ 8.57745 14.8566i 0.702692 1.21710i −0.264826 0.964296i $$-0.585315\pi$$
0.967518 0.252802i $$-0.0813521\pi$$
$$150$$ 0 0
$$151$$ −21.3828 −1.74011 −0.870053 0.492957i $$-0.835916\pi$$
−0.870053 + 0.492957i $$0.835916\pi$$
$$152$$ 4.31000 7.46515i 0.349587 0.605503i
$$153$$ 1.00064 + 1.73316i 0.0808969 + 0.140118i
$$154$$ 2.37548 + 4.11446i 0.191422 + 0.331552i
$$155$$ 0 0
$$156$$ −0.691395 + 34.7752i −0.0553559 + 2.78424i
$$157$$ −18.3646 −1.46566 −0.732829 0.680413i $$-0.761800\pi$$
−0.732829 + 0.680413i $$0.761800\pi$$
$$158$$ 1.32178 + 2.28939i 0.105155 + 0.182134i
$$159$$ 0.691395 + 1.19753i 0.0548312 + 0.0949705i
$$160$$ 0 0
$$161$$ −6.32648 −0.498597
$$162$$ −14.2966 + 24.7624i −1.12324 + 1.94551i
$$163$$ 2.00543 3.47351i 0.157078 0.272066i −0.776736 0.629826i $$-0.783126\pi$$
0.933814 + 0.357760i $$0.116459\pi$$
$$164$$ −44.6357 −3.48546
$$165$$ 0 0
$$166$$ 15.0774 + 26.1149i 1.17024 + 2.02691i
$$167$$ −1.46928 2.54486i −0.113696 0.196927i 0.803562 0.595221i $$-0.202936\pi$$
−0.917258 + 0.398294i $$0.869602\pi$$
$$168$$ −39.9545 −3.08256
$$169$$ −12.9897 0.516725i −0.999210 0.0397480i
$$170$$ 0 0
$$171$$ −1.11588 1.93275i −0.0853331 0.147801i
$$172$$ 3.06329 + 5.30577i 0.233574 + 0.404561i
$$173$$ −0.683650 + 1.18412i −0.0519769 + 0.0900267i −0.890843 0.454311i $$-0.849886\pi$$
0.838866 + 0.544337i $$0.183219\pi$$
$$174$$ 16.4424 1.24649
$$175$$ 0 0
$$176$$ 2.25961 3.91375i 0.170324 0.295010i
$$177$$ −16.3550 −1.22932
$$178$$ −15.9850 + 27.6868i −1.19813 + 2.07522i
$$179$$ −3.89306 6.74299i −0.290981 0.503994i 0.683061 0.730362i $$-0.260648\pi$$
−0.974042 + 0.226367i $$0.927315\pi$$
$$180$$ 0 0
$$181$$ −3.86684 −0.287420 −0.143710 0.989620i $$-0.545903\pi$$
−0.143710 + 0.989620i $$0.545903\pi$$
$$182$$ 0.536155 26.9670i 0.0397425 1.99893i
$$183$$ 4.88752 0.361296
$$184$$ 6.79833 + 11.7751i 0.501180 + 0.868069i
$$185$$ 0 0
$$186$$ 24.5582 42.5361i 1.80070 3.11890i
$$187$$ 0.777322 0.0568434
$$188$$ 13.8093 23.9184i 1.00715 1.74443i
$$189$$ 4.31754 7.47821i 0.314055 0.543959i
$$190$$ 0 0
$$191$$ −2.47185 + 4.28136i −0.178857 + 0.309789i −0.941489 0.337043i $$-0.890573\pi$$
0.762633 + 0.646832i $$0.223906\pi$$
$$192$$ −0.290836 0.503743i −0.0209893 0.0363545i
$$193$$ −2.47822 4.29240i −0.178386 0.308974i 0.762942 0.646467i $$-0.223754\pi$$
−0.941328 + 0.337493i $$0.890421\pi$$
$$194$$ 37.6357 2.70208
$$195$$ 0 0
$$196$$ 7.32648 0.523320
$$197$$ −3.37273 5.84174i −0.240297 0.416207i 0.720502 0.693453i $$-0.243912\pi$$
−0.960799 + 0.277246i $$0.910578\pi$$
$$198$$ −1.32178 2.28939i −0.0939349 0.162700i
$$199$$ −2.58772 + 4.48207i −0.183439 + 0.317725i −0.943049 0.332653i $$-0.892056\pi$$
0.759611 + 0.650378i $$0.225390\pi$$
$$200$$ 0 0
$$201$$ 8.64403 14.9719i 0.609703 1.05604i
$$202$$ 16.8423 29.1717i 1.18502 2.05251i
$$203$$ −8.81566 −0.618738
$$204$$ −5.90364 + 10.2254i −0.413337 + 0.715921i
$$205$$ 0 0
$$206$$ 13.9616 + 24.1822i 0.972749 + 1.68485i
$$207$$ 3.52022 0.244673
$$208$$ −22.4699 + 12.3841i −1.55801 + 0.858684i
$$209$$ −0.866840 −0.0599606
$$210$$ 0 0
$$211$$ 7.00894 + 12.1398i 0.482515 + 0.835741i 0.999799 0.0200732i $$-0.00638994\pi$$
−0.517283 + 0.855814i $$0.673057\pi$$
$$212$$ −1.43897 + 2.49237i −0.0988289 + 0.171177i
$$213$$ −5.67315 −0.388718
$$214$$ −13.5861 + 23.5318i −0.928726 + 1.60860i
$$215$$ 0 0
$$216$$ −18.5582 −1.26273
$$217$$ −13.1670 + 22.8060i −0.893836 + 1.54817i
$$218$$ −4.16251 7.20968i −0.281921 0.488301i
$$219$$ −11.1159 19.2533i −0.751141 1.30101i
$$220$$ 0 0
$$221$$ −3.77719 2.28205i −0.254081 0.153508i
$$222$$ 6.70825 0.450228
$$223$$ 0.00415245 + 0.00719226i 0.000278069 + 0.000481629i 0.866164 0.499759i $$-0.166578\pi$$
−0.865886 + 0.500241i $$0.833245\pi$$
$$224$$ −8.05794 13.9568i −0.538394 0.932525i
$$225$$ 0 0
$$226$$ 14.0774 0.936418
$$227$$ −5.63179 + 9.75454i −0.373795 + 0.647431i −0.990146 0.140040i $$-0.955277\pi$$
0.616351 + 0.787471i $$0.288610\pi$$
$$228$$ 6.58351 11.4030i 0.436004 0.755181i
$$229$$ −16.5404 −1.09302 −0.546509 0.837453i $$-0.684043\pi$$
−0.546509 + 0.837453i $$0.684043\pi$$
$$230$$ 0 0
$$231$$ 2.00894 + 3.47959i 0.132179 + 0.228940i
$$232$$ 9.47315 + 16.4080i 0.621943 + 1.07724i
$$233$$ 6.94941 0.455271 0.227636 0.973746i $$-0.426900\pi$$
0.227636 + 0.973746i $$0.426900\pi$$
$$234$$ −0.298331 + 15.0052i −0.0195025 + 0.980919i
$$235$$ 0 0
$$236$$ −17.0195 29.4787i −1.10788 1.91890i
$$237$$ 1.11783 + 1.93613i 0.0726107 + 0.125765i
$$238$$ 4.57808 7.92947i 0.296753 0.513991i
$$239$$ 4.00000 0.258738 0.129369 0.991596i $$-0.458705\pi$$
0.129369 + 0.991596i $$0.458705\pi$$
$$240$$ 0 0
$$241$$ −9.88605 + 17.1231i −0.636817 + 1.10300i 0.349310 + 0.937007i $$0.386416\pi$$
−0.986127 + 0.165992i $$0.946917\pi$$
$$242$$ 26.9763 1.73410
$$243$$ −7.68273 + 13.3069i −0.492848 + 0.853637i
$$244$$ 5.08609 + 8.80937i 0.325604 + 0.563962i
$$245$$ 0 0
$$246$$ −54.5973 −3.48099
$$247$$ 4.21218 + 2.54486i 0.268015 + 0.161926i
$$248$$ 56.5962 3.59386
$$249$$ 12.7510 + 22.0853i 0.808060 + 1.39960i
$$250$$ 0 0
$$251$$ −1.83676 + 3.18136i −0.115935 + 0.200806i −0.918153 0.396226i $$-0.870320\pi$$
0.802218 + 0.597031i $$0.203653\pi$$
$$252$$ −21.5293 −1.35622
$$253$$ 0.683650 1.18412i 0.0429807 0.0744447i
$$254$$ −21.9337 + 37.9903i −1.37624 + 2.38372i
$$255$$ 0 0
$$256$$ 14.5669 25.2306i 0.910430 1.57691i
$$257$$ 6.63242 + 11.4877i 0.413719 + 0.716583i 0.995293 0.0969108i $$-0.0308962\pi$$
−0.581574 + 0.813494i $$0.697563\pi$$
$$258$$ 3.74694 + 6.48989i 0.233274 + 0.404043i
$$259$$ −3.59666 −0.223486
$$260$$ 0 0
$$261$$ 4.90527 0.303628
$$262$$ 12.7287 + 22.0467i 0.786381 + 1.36205i
$$263$$ 15.1352 + 26.2150i 0.933279 + 1.61649i 0.777674 + 0.628667i $$0.216399\pi$$
0.155605 + 0.987819i $$0.450267\pi$$
$$264$$ 4.31754 7.47821i 0.265726 0.460252i
$$265$$ 0 0
$$266$$ −5.10530 + 8.84265i −0.313026 + 0.542177i
$$267$$ −13.5185 + 23.4147i −0.827317 + 1.43296i
$$268$$ 35.9809 2.19788
$$269$$ 11.1248 19.2687i 0.678292 1.17484i −0.297203 0.954814i $$-0.596054\pi$$
0.975495 0.220022i $$-0.0706129\pi$$
$$270$$ 0 0
$$271$$ 5.91421 + 10.2437i 0.359262 + 0.622261i 0.987838 0.155488i $$-0.0496950\pi$$
−0.628575 + 0.777749i $$0.716362\pi$$
$$272$$ −8.70953 −0.528093
$$273$$ 0.453425 22.8060i 0.0274425 1.38028i
$$274$$ 22.0774 1.33375
$$275$$ 0 0
$$276$$ 10.3844 + 17.9863i 0.625069 + 1.08265i
$$277$$ 8.39254 14.5363i 0.504259 0.873402i −0.495729 0.868477i $$-0.665099\pi$$
0.999988 0.00492452i $$-0.00156753\pi$$
$$278$$ −36.4715 −2.18741
$$279$$ 7.32648 12.6898i 0.438625 0.759721i
$$280$$ 0 0
$$281$$ −10.5967 −0.632144 −0.316072 0.948735i $$-0.602364\pi$$
−0.316072 + 0.948735i $$0.602364\pi$$
$$282$$ 16.8912 29.2564i 1.00586 1.74219i
$$283$$ −4.40783 7.63458i −0.262018 0.453829i 0.704760 0.709446i $$-0.251055\pi$$
−0.966778 + 0.255617i $$0.917721\pi$$
$$284$$ −5.90364 10.2254i −0.350316 0.606766i
$$285$$ 0 0
$$286$$ 4.98943 + 3.01445i 0.295031 + 0.178248i
$$287$$ 29.2726 1.72791
$$288$$ 4.48365 + 7.76591i 0.264202 + 0.457611i
$$289$$ 7.75096 + 13.4251i 0.455939 + 0.789710i
$$290$$ 0 0
$$291$$ 31.8284 1.86581
$$292$$ 23.1350 40.0709i 1.35387 2.34497i
$$293$$ −14.1263 + 24.4675i −0.825267 + 1.42940i 0.0764476 + 0.997074i $$0.475642\pi$$
−0.901715 + 0.432331i $$0.857691\pi$$
$$294$$ 8.96157 0.522650
$$295$$ 0 0
$$296$$ 3.86491 + 6.69422i 0.224643 + 0.389094i
$$297$$ 0.933121 + 1.61621i 0.0541452 + 0.0937822i
$$298$$ 43.6719 2.52984
$$299$$ −6.79833 + 3.74685i −0.393158 + 0.216686i
$$300$$ 0 0
$$301$$ −2.00894 3.47959i −0.115793 0.200560i
$$302$$ −27.2175 47.1421i −1.56619 2.71272i
$$303$$ 14.2435 24.6704i 0.818267 1.41728i
$$304$$ 9.71254 0.557052
$$305$$ 0 0
$$306$$ −2.54737 + 4.41217i −0.145623 + 0.252227i
$$307$$ −12.7219 −0.726077 −0.363039 0.931774i $$-0.618261\pi$$
−0.363039 + 0.931774i $$0.618261\pi$$
$$308$$ −4.18112 + 7.24190i −0.238241 + 0.412646i
$$309$$ 11.8073 + 20.4508i 0.671692 + 1.16340i
$$310$$ 0 0
$$311$$ 27.9231 1.58338 0.791688 0.610925i $$-0.209202\pi$$
0.791688 + 0.610925i $$0.209202\pi$$
$$312$$ −42.9344 + 23.6630i −2.43068 + 1.33965i
$$313$$ −24.5807 −1.38938 −0.694692 0.719307i $$-0.744460\pi$$
−0.694692 + 0.719307i $$0.744460\pi$$
$$314$$ −23.3758 40.4880i −1.31917 2.28487i
$$315$$ 0 0
$$316$$ −2.32648 + 4.02959i −0.130875 + 0.226682i
$$317$$ 0.234377 0.0131639 0.00658196 0.999978i $$-0.497905\pi$$
0.00658196 + 0.999978i $$0.497905\pi$$
$$318$$ −1.76011 + 3.04860i −0.0987022 + 0.170957i
$$319$$ 0.952633 1.65001i 0.0533372 0.0923828i
$$320$$ 0 0
$$321$$ −11.4897 + 19.9008i −0.641294 + 1.11075i
$$322$$ −8.05279 13.9478i −0.448764 0.777283i
$$323$$ 0.835296 + 1.44678i 0.0464771 + 0.0805008i
$$324$$ −50.3271 −2.79595
$$325$$ 0 0
$$326$$ 10.2106 0.565513
$$327$$ −3.52022 6.09721i −0.194669 0.337176i
$$328$$ −31.4558 54.4831i −1.73686 3.00833i
$$329$$ −9.05631 + 15.6860i −0.499290 + 0.864796i
$$330$$ 0 0
$$331$$ 9.16324 15.8712i 0.503657 0.872360i −0.496334 0.868132i $$-0.665321\pi$$
0.999991 0.00422829i $$-0.00134591\pi$$
$$332$$ −26.5380 + 45.9652i −1.45646 + 2.52267i
$$333$$ 2.00128 0.109669
$$334$$ 3.74039 6.47855i 0.204665 0.354491i
$$335$$ 0 0
$$336$$ −22.5092 38.9871i −1.22798 2.12692i
$$337$$ 21.2949 1.16001 0.580003 0.814614i $$-0.303051\pi$$
0.580003 + 0.814614i $$0.303051\pi$$
$$338$$ −15.3950 29.2958i −0.837379 1.59348i
$$339$$ 11.9053 0.646605
$$340$$ 0 0
$$341$$ −2.84570 4.92889i −0.154103 0.266915i
$$342$$ 2.84073 4.92028i 0.153609 0.266059i
$$343$$ 15.7651 0.851234
$$344$$ −4.31754 + 7.47821i −0.232786 + 0.403198i
$$345$$ 0 0
$$346$$ −3.48079 −0.187128
$$347$$ −1.90761 + 3.30407i −0.102406 + 0.177372i −0.912675 0.408685i $$-0.865987\pi$$
0.810270 + 0.586057i $$0.199321\pi$$
$$348$$ 14.4702 + 25.0631i 0.775684 + 1.34352i
$$349$$ −12.1632 21.0674i −0.651083 1.12771i −0.982860 0.184352i $$-0.940981\pi$$
0.331777 0.943358i $$-0.392352\pi$$
$$350$$ 0 0
$$351$$ 0.210609 10.5930i 0.0112415 0.565413i
$$352$$ 3.48301 0.185645
$$353$$ −13.5295 23.4338i −0.720104 1.24726i −0.960958 0.276696i $$-0.910761\pi$$
0.240853 0.970562i $$-0.422573\pi$$
$$354$$ −20.8178 36.0576i −1.10646 1.91644i
$$355$$ 0 0
$$356$$ −56.2708 −2.98235
$$357$$ 3.87167 6.70593i 0.204911 0.354916i
$$358$$ 9.91073 17.1659i 0.523798 0.907245i
$$359$$ 27.0039 1.42521 0.712605 0.701566i $$-0.247515\pi$$
0.712605 + 0.701566i $$0.247515\pi$$
$$360$$ 0 0
$$361$$ 8.56851 + 14.8411i 0.450974 + 0.781110i
$$362$$ −4.92198 8.52512i −0.258694 0.448071i
$$363$$ 22.8138 1.19742
$$364$$ 41.5777 22.9152i 2.17927 1.20108i
$$365$$ 0 0
$$366$$ 6.22118 + 10.7754i 0.325186 + 0.563239i
$$367$$ −3.47055 6.01118i −0.181161 0.313781i 0.761115 0.648617i $$-0.224652\pi$$
−0.942276 + 0.334836i $$0.891319\pi$$
$$368$$ −7.65998 + 13.2675i −0.399304 + 0.691615i
$$369$$ −16.2881 −0.847922
$$370$$ 0 0
$$371$$ 0.943693 1.63452i 0.0489941 0.0848603i
$$372$$ 86.4505 4.48225
$$373$$ 1.15644 2.00301i 0.0598781 0.103712i −0.834532 0.550959i $$-0.814262\pi$$
0.894411 + 0.447247i $$0.147595\pi$$
$$374$$ 0.989429 + 1.71374i 0.0511622 + 0.0886154i
$$375$$ 0 0
$$376$$ 38.9270 2.00751
$$377$$ −9.47315 + 5.22105i −0.487892 + 0.268898i
$$378$$ 21.9827 1.13067
$$379$$ −2.58772 4.48207i −0.132922 0.230228i 0.791880 0.610677i $$-0.209103\pi$$
−0.924802 + 0.380449i $$0.875769\pi$$
$$380$$ 0 0
$$381$$ −18.5493 + 32.1283i −0.950309 + 1.64598i
$$382$$ −12.5854 −0.643923
$$383$$ −10.3305 + 17.8929i −0.527861 + 0.914283i 0.471611 + 0.881807i $$0.343673\pi$$
−0.999473 + 0.0324760i $$0.989661\pi$$
$$384$$ 12.5477 21.7332i 0.640320 1.10907i
$$385$$ 0 0
$$386$$ 6.30890 10.9273i 0.321115 0.556187i
$$387$$ 1.11783 + 1.93613i 0.0568224 + 0.0984193i
$$388$$ 33.1215 + 57.3682i 1.68149 + 2.91243i
$$389$$ 19.7477 1.00125 0.500624 0.865665i $$-0.333104\pi$$
0.500624 + 0.865665i $$0.333104\pi$$
$$390$$ 0 0
$$391$$ −2.63509 −0.133262
$$392$$ 5.16315 + 8.94284i 0.260778 + 0.451681i
$$393$$ 10.7646 + 18.6449i 0.543004 + 0.940510i
$$394$$ 8.58609 14.8715i 0.432561 0.749218i
$$395$$ 0 0
$$396$$ 2.32648 4.02959i 0.116910 0.202494i
$$397$$ −4.69451 + 8.13113i −0.235611 + 0.408090i −0.959450 0.281879i $$-0.909042\pi$$
0.723839 + 0.689969i $$0.242376\pi$$
$$398$$ −13.1753 −0.660420
$$399$$ −4.31754 + 7.47821i −0.216148 + 0.374379i
$$400$$ 0 0
$$401$$ −12.2510 21.2193i −0.611784 1.05964i −0.990940 0.134308i $$-0.957119\pi$$
0.379156 0.925333i $$-0.376214\pi$$
$$402$$ 44.0109 2.19506
$$403$$ −0.642285 + 32.3050i −0.0319945 + 1.60923i
$$404$$ 59.2887 2.94972
$$405$$ 0 0
$$406$$ −11.2212 19.4357i −0.556898 0.964575i
$$407$$ 0.388661 0.673180i 0.0192652 0.0333683i
$$408$$ −16.6417 −0.823889
$$409$$ −18.0582 + 31.2778i −0.892922 + 1.54659i −0.0565671 + 0.998399i $$0.518015\pi$$
−0.836355 + 0.548188i $$0.815318\pi$$
$$410$$ 0 0
$$411$$ 18.6708 0.920965
$$412$$ −24.5739 + 42.5633i −1.21067 + 2.09694i
$$413$$ 11.1616 + 19.3324i 0.549226 + 0.951288i
$$414$$ 4.48079 + 7.76095i 0.220219 + 0.381430i
$$415$$ 0 0
$$416$$ −16.9248 10.2254i −0.829805 0.501341i
$$417$$ −30.8439 −1.51043
$$418$$ −1.10337 1.91110i −0.0539678 0.0934749i
$$419$$ 3.43342 + 5.94686i 0.167734 + 0.290523i 0.937623 0.347655i $$-0.113022\pi$$
−0.769889 + 0.638178i $$0.779689\pi$$
$$420$$ 0 0
$$421$$ 33.9795 1.65606 0.828029 0.560686i $$-0.189462\pi$$
0.828029 + 0.560686i $$0.189462\pi$$
$$422$$ −17.8429 + 30.9049i −0.868580 + 1.50443i
$$423$$ 5.03917 8.72810i 0.245013 0.424375i
$$424$$ −4.05631 −0.196992
$$425$$ 0 0
$$426$$ −7.22118 12.5075i −0.349867 0.605988i
$$427$$ −3.33552 5.77729i −0.161417 0.279582i
$$428$$ −47.8261 −2.31176
$$429$$ 4.21955 + 2.54931i 0.203722 + 0.123082i
$$430$$ 0 0
$$431$$ 8.12482 + 14.0726i 0.391359 + 0.677853i 0.992629 0.121193i $$-0.0386719\pi$$
−0.601270 + 0.799046i $$0.705339\pi$$
$$432$$ −10.4552 18.1089i −0.503025 0.871265i
$$433$$ 0.128130 0.221929i 0.00615756 0.0106652i −0.862930 0.505323i $$-0.831373\pi$$
0.869088 + 0.494658i $$0.164707\pi$$
$$434$$ −67.0396 −3.21800
$$435$$ 0 0
$$436$$ 7.32648 12.6898i 0.350875 0.607733i
$$437$$ 2.93855 0.140570
$$438$$ 28.2981 49.0138i 1.35214 2.34197i
$$439$$ 3.79833 + 6.57890i 0.181284 + 0.313994i 0.942318 0.334718i $$-0.108641\pi$$
−0.761034 + 0.648712i $$0.775308\pi$$
$$440$$ 0 0
$$441$$ 2.67352 0.127310
$$442$$ 0.223318 11.2322i 0.0106221 0.534263i
$$443$$ −4.32246 −0.205366 −0.102683 0.994714i $$-0.532743\pi$$
−0.102683 + 0.994714i $$0.532743\pi$$
$$444$$ 5.90364 + 10.2254i 0.280174 + 0.485276i
$$445$$ 0 0
$$446$$ −0.0105711 + 0.0183096i −0.000500554 + 0.000866986i
$$447$$ 36.9332 1.74688
$$448$$ −0.396966 + 0.687565i −0.0187549 + 0.0324844i
$$449$$ −1.64403 + 2.84754i −0.0775865 + 0.134384i −0.902208 0.431301i $$-0.858055\pi$$
0.824622 + 0.565685i $$0.191388\pi$$
$$450$$ 0 0
$$451$$ −3.16324 + 5.47890i −0.148951 + 0.257991i
$$452$$ 12.3889 + 21.4583i 0.582727 + 1.00931i
$$453$$ −23.0178 39.8680i −1.08147 1.87316i
$$454$$ −28.6741 −1.34574
$$455$$ 0 0
$$456$$ 18.5582 0.869069
$$457$$ −7.71304 13.3594i −0.360801 0.624925i 0.627292 0.778784i $$-0.284163\pi$$
−0.988093 + 0.153859i $$0.950830\pi$$
$$458$$ −21.0537 36.4661i −0.983775 1.70395i
$$459$$ 1.79833 3.11480i 0.0839389 0.145386i
$$460$$ 0 0
$$461$$ −12.9424 + 22.4168i −0.602786 + 1.04406i 0.389611 + 0.920979i $$0.372609\pi$$
−0.992397 + 0.123076i $$0.960724\pi$$
$$462$$ −5.11424 + 8.85812i −0.237936 + 0.412117i
$$463$$ −7.04045 −0.327197 −0.163599 0.986527i $$-0.552310\pi$$
−0.163599 + 0.986527i $$0.552310\pi$$
$$464$$ −10.6738 + 18.4876i −0.495519 + 0.858265i
$$465$$ 0 0
$$466$$ 8.84570 + 15.3212i 0.409769 + 0.709741i
$$467$$ −18.8113 −0.870482 −0.435241 0.900314i $$-0.643337\pi$$
−0.435241 + 0.900314i $$0.643337\pi$$
$$468$$ −23.1350 + 12.7507i −1.06941 + 0.589399i
$$469$$ −23.5967 −1.08959
$$470$$ 0 0
$$471$$ −19.7688 34.2406i −0.910900 1.57773i
$$472$$ 23.9881 41.5486i 1.10414 1.91243i
$$473$$ 0.868356 0.0399271
$$474$$ −2.84570 + 4.92889i −0.130707 + 0.226392i
$$475$$ 0 0
$$476$$ 16.1159 0.738670
$$477$$ −0.525096 + 0.909493i −0.0240425 + 0.0416428i
$$478$$ 5.09148 + 8.81870i 0.232879 + 0.403358i
$$479$$ 9.73876 + 16.8680i 0.444975 + 0.770720i 0.998051 0.0624114i $$-0.0198791\pi$$
−0.553075 + 0.833131i $$0.686546\pi$$
$$480$$ 0 0
$$481$$ −3.86491 + 2.13011i −0.176225 + 0.0971249i
$$482$$ −50.3346 −2.29268
$$483$$ −6.81023 11.7957i −0.309876 0.536721i
$$484$$ 23.7407 + 41.1201i 1.07912 + 1.86909i
$$485$$ 0 0
$$486$$ −39.1165 −1.77436
$$487$$ −16.1620 + 27.9935i −0.732372 + 1.26851i 0.223495 + 0.974705i $$0.428253\pi$$
−0.955867 + 0.293800i $$0.905080\pi$$
$$488$$ −7.16858 + 12.4163i −0.324506 + 0.562062i
$$489$$ 8.63509 0.390492
$$490$$ 0 0
$$491$$ −14.3354 24.8297i −0.646949 1.12055i −0.983848 0.179007i $$-0.942711\pi$$
0.336899 0.941541i $$-0.390622\pi$$
$$492$$ −48.0487 83.2227i −2.16620 3.75197i
$$493$$ −3.67187 −0.165373
$$494$$ −0.249036 + 12.5258i −0.0112046 + 0.563561i
$$495$$ 0 0
$$496$$ 31.8847 + 55.2260i 1.43167 + 2.47972i
$$497$$ 3.87167 + 6.70593i 0.173668 + 0.300802i
$$498$$ −32.4606 + 56.2235i −1.45460 + 2.51943i
$$499$$ 28.9616 1.29650 0.648249 0.761428i $$-0.275502\pi$$
0.648249 + 0.761428i $$0.275502\pi$$
$$500$$ 0 0
$$501$$ 3.16324 5.47890i 0.141323 0.244779i
$$502$$ −9.35181 −0.417392
$$503$$ −14.0546 + 24.3433i −0.626665 + 1.08542i 0.361551 + 0.932352i $$0.382247\pi$$
−0.988216 + 0.153063i $$0.951086\pi$$
$$504$$ −15.1722 26.2790i −0.675823 1.17056i
$$505$$ 0 0
$$506$$ 3.48079 0.154740
$$507$$ −13.0195 24.7754i −0.578218 1.10032i
$$508$$ −77.2116 −3.42571
$$509$$ −10.5563 18.2841i −0.467900 0.810427i 0.531427 0.847104i $$-0.321656\pi$$
−0.999327 + 0.0366773i $$0.988323\pi$$
$$510$$ 0 0
$$511$$ −15.1722 + 26.2790i −0.671178 + 1.16251i
$$512$$ 50.8542 2.24746
$$513$$ −2.00543 + 3.47351i −0.0885420 + 0.153359i
$$514$$ −16.8844 + 29.2447i −0.744740 + 1.28993i
$$515$$ 0 0
$$516$$ −6.59503 + 11.4229i −0.290330 + 0.502866i
$$517$$ −1.95728 3.39010i −0.0860809 0.149097i
$$518$$ −4.57808 7.92947i −0.201149 0.348401i
$$519$$ −2.94369 −0.129214
$$520$$ 0 0
$$521$$ 0.673516 0.0295073 0.0147536 0.999891i $$-0.495304\pi$$
0.0147536 + 0.999891i $$0.495304\pi$$
$$522$$ 6.24376 + 10.8145i 0.273282 + 0.473339i
$$523$$ −14.9313 25.8618i −0.652900 1.13086i −0.982416 0.186706i $$-0.940219\pi$$
0.329516 0.944150i $$-0.393114\pi$$
$$524$$ −22.4039 + 38.8048i −0.978720 + 1.69519i
$$525$$ 0 0
$$526$$ −38.5304 + 66.7366i −1.68000 + 2.90985i
$$527$$ −5.48429 + 9.49907i −0.238899 + 0.413786i
$$528$$ 9.72953 0.423423
$$529$$ 9.18246 15.9045i 0.399237 0.691499i
$$530$$ 0 0
$$531$$ −6.21061 10.7571i −0.269517 0.466818i
$$532$$ −17.9718 −0.779177
$$533$$ 31.4558 17.3366i 1.36250 0.750933i
$$534$$ −68.8290 −2.97852
$$535$$ 0 0
$$536$$ 25.3566 + 43.9189i 1.09524 + 1.89701i
$$537$$ 8.38148 14.5171i 0.361687 0.626461i
$$538$$ 56.6418 2.44200
$$539$$ 0.519213 0.899304i 0.0223641 0.0387358i
$$540$$ 0 0
$$541$$ 6.28806 0.270345 0.135172 0.990822i $$-0.456841\pi$$
0.135172 + 0.990822i $$0.456841\pi$$
$$542$$ −15.0560 + 26.0778i −0.646712 + 1.12014i
$$543$$ −4.16251 7.20968i −0.178630 0.309397i
$$544$$ −3.35627 5.81323i −0.143899 0.249240i
$$545$$ 0 0
$$546$$ 50.8569 28.0294i 2.17647 1.19955i
$$547$$ 3.03789 0.129891 0.0649454 0.997889i $$-0.479313\pi$$
0.0649454 + 0.997889i $$0.479313\pi$$
$$548$$ 19.4294 + 33.6527i 0.829983 + 1.43757i
$$549$$ 1.85597 + 3.21464i 0.0792109 + 0.137197i
$$550$$ 0 0
$$551$$ 4.09473 0.174442
$$552$$ −14.6363 + 25.3508i −0.622962 + 1.07900i
$$553$$ 1.52574 2.64265i 0.0648809 0.112377i
$$554$$ 42.7304 1.81544
$$555$$ 0 0
$$556$$ −32.0970 55.5936i −1.36121 2.35769i
$$557$$ 10.3498 + 17.9264i 0.438536 + 0.759566i 0.997577 0.0695738i $$-0.0221639\pi$$
−0.559041 + 0.829140i $$0.688831\pi$$
$$558$$ 37.3026 1.57915
$$559$$ −4.21955 2.54931i −0.178468 0.107824i
$$560$$ 0 0
$$561$$ 0.836758 + 1.44931i 0.0353279 + 0.0611898i
$$562$$ −13.4882 23.3622i −0.568964 0.985475i
$$563$$ 5.48014 9.49188i 0.230960 0.400035i −0.727131 0.686499i $$-0.759147\pi$$
0.958091 + 0.286464i $$0.0924799\pi$$
$$564$$ 59.4608 2.50375
$$565$$ 0 0
$$566$$ 11.2212 19.4357i 0.471661 0.816941i
$$567$$ 33.0051 1.38608
$$568$$ 8.32087 14.4122i 0.349136 0.604721i
$$569$$ −21.3566 36.9907i −0.895314 1.55073i −0.833416 0.552647i $$-0.813618\pi$$
−0.0618981 0.998082i $$-0.519715\pi$$
$$570$$ 0 0
$$571$$ −23.6145 −0.988238 −0.494119 0.869394i $$-0.664509\pi$$
−0.494119 + 0.869394i $$0.664509\pi$$
$$572$$ −0.203954 + 10.2583i −0.00852774 + 0.428920i
$$573$$ −10.6434 −0.444635
$$574$$ 37.2602 + 64.5366i 1.55521 + 2.69370i
$$575$$ 0 0
$$576$$ 0.220882 0.382579i 0.00920343 0.0159408i
$$577$$ 18.3646 0.764530 0.382265 0.924053i $$-0.375144\pi$$
0.382265 + 0.924053i $$0.375144\pi$$
$$578$$ −19.7319 + 34.1767i −0.820740 + 1.42156i
$$579$$ 5.33542 9.24123i 0.221733 0.384052i
$$580$$ 0 0
$$581$$ 17.4039 30.1445i 0.722037 1.25060i
$$582$$ 40.5134 + 70.1713i 1.67934 + 2.90869i
$$583$$ 0.203954 + 0.353259i 0.00844691 + 0.0146305i
$$584$$ 65.2151 2.69862
$$585$$ 0 0
$$586$$ −71.9237 −2.97114
$$587$$ −0.351448 0.608726i −0.0145058 0.0251248i 0.858681 0.512510i $$-0.171284\pi$$
−0.873187 + 0.487385i $$0.837951\pi$$
$$588$$ 7.88669 + 13.6601i 0.325242 + 0.563335i
$$589$$ 6.11588 10.5930i 0.252000 0.436477i
$$590$$ 0 0
$$591$$ 7.26124 12.5768i 0.298687 0.517342i
$$592$$ −4.35476 + 7.54267i −0.178980 + 0.310002i
$$593$$ 37.1593 1.52595 0.762975 0.646428i $$-0.223738\pi$$
0.762975 + 0.646428i $$0.223738\pi$$
$$594$$ −2.37548 + 4.11446i −0.0974672 + 0.168818i
$$595$$ 0 0
$$596$$ 38.4337 + 66.5692i 1.57431 + 2.72678i
$$597$$ −11.1423 −0.456026
$$598$$ −16.9140 10.2189i −0.691663 0.417880i
$$599$$ −15.6914 −0.641133 −0.320567 0.947226i $$-0.603873\pi$$
−0.320567 + 0.947226i $$0.603873\pi$$
$$600$$ 0 0
$$601$$ −6.00193 10.3956i −0.244824 0.424047i 0.717258 0.696807i $$-0.245397\pi$$
−0.962082 + 0.272760i $$0.912063\pi$$
$$602$$ 5.11424 8.85812i 0.208441 0.361030i
$$603$$ 13.1298 0.534687
$$604$$ 47.9059 82.9754i 1.94926 3.37622i
$$605$$ 0 0
$$606$$ 72.5204 2.94594
$$607$$ 19.3433 33.5035i 0.785119 1.35987i −0.143809 0.989606i $$-0.545935\pi$$
0.928928 0.370261i $$-0.120732\pi$$
$$608$$ 3.74278 + 6.48269i 0.151790 + 0.262908i
$$609$$ −9.48973 16.4367i −0.384543 0.666048i
$$610$$ 0 0
$$611$$ −0.441765 + 22.2195i −0.0178719 + 0.898903i
$$612$$ −8.96730 −0.362482
$$613$$ −8.64201 14.9684i −0.349047 0.604568i 0.637033 0.770836i $$-0.280161\pi$$
−0.986081 + 0.166269i $$0.946828\pi$$
$$614$$ −16.1933 28.0477i −0.653509 1.13191i
$$615$$ 0 0
$$616$$ −11.7861 −0.474877
$$617$$ 13.2345 22.9229i 0.532803 0.922841i −0.466464 0.884540i $$-0.654472\pi$$
0.999266 0.0383009i $$-0.0121945\pi$$
$$618$$ −30.0582 + 52.0624i −1.20912 + 2.09426i
$$619$$ −31.0039 −1.24615 −0.623075 0.782162i $$-0.714117\pi$$
−0.623075 + 0.782162i $$0.714117\pi$$
$$620$$ 0 0
$$621$$ −3.16324 5.47890i −0.126937 0.219861i
$$622$$ 35.5425 + 61.5615i 1.42513 + 2.46839i
$$623$$ 36.9030 1.47849
$$624$$ −47.2781 28.5639i −1.89264 1.14347i
$$625$$ 0 0
$$626$$ −31.2881 54.1925i −1.25052 2.16597i
$$627$$ −0.933121 1.61621i −0.0372653 0.0645453i
$$628$$ 41.1440 71.2635i 1.64182 2.84372i
$$629$$ −1.49807 −0.0597320
$$630$$ 0 0
$$631$$ 10.3566 17.9381i 0.412288 0.714104i −0.582851 0.812579i $$-0.698063\pi$$
0.995140 + 0.0984745i $$0.0313963\pi$$
$$632$$ −6.55812 −0.260868
$$633$$ −15.0897 + 26.1362i −0.599763 + 1.03882i
$$634$$ 0.298331 + 0.516725i 0.0118482 + 0.0205218i
$$635$$ 0 0
$$636$$ −6.19599 −0.245687
$$637$$ −5.16315 + 2.84563i −0.204571 + 0.112748i
$$638$$ 4.85031 0.192026
$$639$$ −2.15430 3.73136i −0.0852229 0.147610i
$$640$$ 0 0
$$641$$ −10.5947 + 18.3506i −0.418467 + 0.724806i −0.995785 0.0917132i $$-0.970766\pi$$
0.577319 + 0.816519i $$0.304099\pi$$
$$642$$ −58.4997 −2.30880
$$643$$ −5.76682 + 9.98843i −0.227421 + 0.393905i −0.957043 0.289946i $$-0.906363\pi$$
0.729622 + 0.683851i $$0.239696\pi$$
$$644$$ 14.1738 24.5498i 0.558526 0.967396i
$$645$$ 0 0
$$646$$ −2.12645 + 3.68311i −0.0836639 + 0.144910i
$$647$$ −17.4232 30.1779i −0.684977 1.18641i −0.973444 0.228925i $$-0.926479\pi$$
0.288467 0.957490i $$-0.406854\pi$$
$$648$$ −35.4667 61.4301i −1.39326 2.41320i
$$649$$ −4.82456 −0.189380
$$650$$ 0 0
$$651$$ −56.6953 −2.22206
$$652$$ 8.98591 + 15.5641i 0.351915 + 0.609535i
$$653$$ 11.1616 + 19.3324i 0.436787 + 0.756537i 0.997440 0.0715139i $$-0.0227830\pi$$
−0.560653 + 0.828051i $$0.689450\pi$$
$$654$$ 8.96157 15.5219i 0.350425 0.606954i
$$655$$ 0 0
$$656$$ 35.4427 61.3885i 1.38380 2.39682i
$$657$$ 8.44221 14.6223i 0.329362 0.570471i
$$658$$ −46.1100 −1.79755
$$659$$ 0.433420 0.750705i 0.0168836 0.0292433i −0.857460 0.514550i $$-0.827959\pi$$
0.874344 + 0.485307i $$0.161292\pi$$
$$660$$ 0 0
$$661$$ −6.65430 11.5256i −0.258822 0.448293i 0.707104 0.707109i $$-0.250001\pi$$
−0.965927 + 0.258816i $$0.916668\pi$$
$$662$$ 46.6544 1.81328
$$663$$ 0.188859 9.49907i 0.00733469 0.368913i
$$664$$ −74.8079 −2.90311
$$665$$ 0 0
$$666$$ 2.54737 + 4.41217i 0.0987085 + 0.170968i
$$667$$ −3.22939 + 5.59346i −0.125042 + 0.216580i
$$668$$ 13.1670 0.509448
$$669$$ −0.00893993 + 0.0154844i −0.000345637 + 0.000598662i
$$670$$ 0 0
$$671$$ 1.44176 0.0556587
$$672$$ 17.3481 30.0479i 0.669219 1.15912i
$$673$$ −2.75660 4.77457i −0.106259 0.184046i 0.807993 0.589192i $$-0.200554\pi$$
−0.914252 + 0.405146i $$0.867221\pi$$
$$674$$ 27.1056 + 46.9483i 1.04407 + 1.80838i
$$675$$ 0 0
$$676$$ 31.1072 49.2486i 1.19643 1.89418i
$$677$$ 4.80479 0.184663 0.0923316 0.995728i $$-0.470568\pi$$
0.0923316 + 0.995728i $$0.470568\pi$$
$$678$$ 15.1539 + 26.2472i 0.581980 + 1.00802i
$$679$$ −21.7215 37.6227i −0.833594 1.44383i
$$680$$ 0 0
$$681$$ −24.2496 −0.929248
$$682$$ 7.24440 12.5477i 0.277403 0.480475i
$$683$$ 5.88126 10.1866i 0.225040 0.389781i −0.731291 0.682065i $$-0.761082\pi$$
0.956331 + 0.292284i $$0.0944154\pi$$
$$684$$ 10.0000 0.382360
$$685$$ 0 0
$$686$$ 20.0669 + 34.7569i 0.766157 + 1.32702i
$$687$$ −17.8051 30.8393i −0.679306 1.17659i
$$688$$ −9.72953 −0.370935
$$689$$ 0.0460332 2.31533i 0.00175372 0.0882071i
$$690$$ 0 0
$$691$$ −2.43342 4.21481i −0.0925717 0.160339i 0.816021 0.578022i $$-0.196175\pi$$
−0.908593 + 0.417684i $$0.862842\pi$$
$$692$$ −3.06329 5.30577i −0.116449 0.201695i
$$693$$ −1.52574 + 2.64265i −0.0579579 + 0.100386i
$$694$$ −9.71254 −0.368683
$$695$$ 0 0
$$696$$ −20.3950 + 35.3252i −0.773070 + 1.33900i
$$697$$ 12.1925 0.461825
$$698$$ 30.9644 53.6320i 1.17202 2.03000i
$$699$$ 7.48079 + 12.9571i 0.282949 + 0.490083i
$$700$$ 0 0
$$701$$ 21.3828 0.807617 0.403808 0.914844i $$-0.367686\pi$$
0.403808 + 0.914844i $$0.367686\pi$$
$$702$$ 23.6222 13.0192i 0.891563 0.491378i
$$703$$ 1.67059 0.0630076
$$704$$ −0.0857934 0.148599i −0.00323346 0.00560052i
$$705$$ 0 0
$$706$$ 34.4427 59.6564i 1.29627 2.24520i
$$707$$ −38.8822 −1.46232
$$708$$ 36.6417 63.4654i 1.37708 2.38517i
$$709$$ 13.0582 22.6175i 0.490412 0.849419i −0.509527 0.860455i $$-0.670180\pi$$
0.999939 + 0.0110357i $$0.00351286\pi$$
$$710$$ 0 0
$$711$$ −0.848960 + 1.47044i −0.0318385 + 0.0551459i
$$712$$ −39.6554 68.6851i −1.48615 2.57408i
$$713$$ 9.64680 + 16.7087i 0.361276 + 0.625748i
$$714$$ 19.7125 0.737723
$$715$$ 0 0
$$716$$ 34.8880 1.30383
$$717$$ 4.30585 + 7.45795i 0.160805 + 0.278522i
$$718$$ 34.3724 + 59.5347i 1.28277 + 2.22182i
$$719$$ −18.3387 + 31.7635i −0.683918 + 1.18458i 0.289858 + 0.957070i $$0.406392\pi$$
−0.973776 + 0.227510i $$0.926941\pi$$
$$720$$ 0 0
$$721$$ 16.1159 27.9135i 0.600187 1.03955i
$$722$$ −21.8132 + 37.7815i −0.811803 + 1.40608i
$$723$$ −42.5679 −1.58312
$$724$$ 8.66324 15.0052i 0.321967 0.557663i
$$725$$ 0 0
$$726$$ 29.0390 + 50.2971i 1.07774 + 1.86670i
$$727$$ 26.2596 0.973916 0.486958 0.873425i $$-0.338107\pi$$
0.486958 + 0.873425i $$0.338107\pi$$
$$728$$ 57.2716 + 34.6016i 2.12263 + 1.28242i
$$729$$ 0.614542 0.0227608
$$730$$ 0 0
$$731$$ −0.836758 1.44931i −0.0309486 0.0536046i
$$732$$ −10.9500 + 18.9659i −0.404723 + 0.701000i
$$733$$ −31.7811 −1.17386 −0.586931 0.809637i $$-0.699664\pi$$
−0.586931 + 0.809637i $$0.699664\pi$$
$$734$$ 8.83513 15.3029i 0.326110 0.564840i
$$735$$ 0 0
$$736$$ −11.8073 −0.435222
$$737$$ 2.54989 4.41654i 0.0939265 0.162685i
$$738$$ −20.7326 35.9099i −0.763176 1.32186i
$$739$$ 17.0685 + 29.5635i 0.627875 + 1.08751i 0.987977 + 0.154599i $$0.0494085\pi$$
−0.360102 + 0.932913i $$0.617258\pi$$
$$740$$ 0 0
$$741$$ −0.210609 + 10.5930i −0.00773691 + 0.389144i
$$742$$ 4.80479 0.176390
$$743$$ 1.56031 + 2.70254i 0.0572423 + 0.0991465i 0.893227 0.449607i $$-0.148436\pi$$
−0.835984 + 0.548753i $$0.815103\pi$$
$$744$$ 60.9237 + 105.523i 2.23357 + 3.86866i
$$745$$ 0 0
$$746$$ 5.88798 0.215574
$$747$$ −9.68401 + 16.7732i −0.354320 + 0.613699i
$$748$$ −1.74151 + 3.01638i −0.0636758 + 0.110290i
$$749$$ 31.3649 1.14605
$$750$$ 0 0
$$751$$ −0.742024 1.28522i −0.0270769 0.0468985i 0.852169 0.523266i $$-0.175287\pi$$
−0.879246 + 0.476367i $$0.841953\pi$$
$$752$$ 21.9304 + 37.9845i 0.799718 + 1.38515i
$$753$$ −7.90881 −0.288213
$$754$$ −23.5688 14.2395i −0.858325 0.518572i
$$755$$ 0 0
$$756$$ 19.3460 + 33.5082i 0.703607 + 1.21868i
$$757$$ 2.54989 + 4.41654i 0.0926774 + 0.160522i 0.908637 0.417587i $$-0.137124\pi$$
−0.815960 + 0.578109i $$0.803791\pi$$
$$758$$ 6.58767 11.4102i 0.239275 0.414436i
$$759$$ 2.94369 0.106849
$$760$$ 0 0
$$761$$ 14.8931 25.7955i 0.539873 0.935088i −0.459037 0.888417i $$-0.651806\pi$$
0.998910 0.0466707i $$-0.0148611\pi$$
$$762$$ −94.4433 −3.42132
$$763$$ −4.80479 + 8.32215i −0.173945 + 0.301282i
$$764$$ −11.0758 19.1839i −0.400709 0.694048i
$$765$$ 0 0
$$766$$ −52.5973 −1.90042
$$767$$ 23.4437 + 14.1639i 0.846501 + 0.511428i
$$768$$ 62.7228 2.26331
$$769$$ −9.54930 16.5399i −0.344356 0.596443i 0.640880 0.767641i $$-0.278570\pi$$
−0.985237 + 0.171198i $$0.945236\pi$$
$$770$$ 0 0
$$771$$ −14.2791 + 24.7322i −0.514250 + 0.890707i
$$772$$ 22.2088 0.799311
$$773$$ 24.6153 42.6350i 0.885351 1.53347i 0.0400400 0.999198i $$-0.487251\pi$$
0.845311 0.534275i $$-0.179415\pi$$
$$774$$ −2.84570 + 4.92889i −0.102286 + 0.177165i
$$775$$ 0 0
$$776$$ −46.6831 + 80.8574i −1.67582 + 2.90261i
$$777$$ −3.87167 6.70593i −0.138895 0.240574i
$$778$$ 25.1362 + 43.5373i 0.901178 + 1.56089i
$$779$$ −13.5967 −0.487151
$$780$$ 0 0
$$781$$ −1.67352 −0.0598831
$$782$$ −3.35412 5.80951i −0.119943 0.207748i
$$783$$ −4.40783 7.63458i −0.157523 0.272838i
$$784$$ −5.81754 + 10.0763i −0.207769 + 0.359867i
$$785$$ 0 0
$$786$$ −27.4039 +