# Properties

 Label 1805.2.b.i.1084.4 Level $1805$ Weight $2$ Character 1805.1084 Analytic conductor $14.413$ Analytic rank $0$ Dimension $16$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1805 = 5 \cdot 19^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1805.b (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$14.4129975648$$ Analytic rank: $$0$$ Dimension: $$16$$ Coefficient field: $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ Defining polynomial: $$x^{16} + 22x^{14} + 190x^{12} + 820x^{10} + 1862x^{8} + 2154x^{6} + 1163x^{4} + 256x^{2} + 16$$ x^16 + 22*x^14 + 190*x^12 + 820*x^10 + 1862*x^8 + 2154*x^6 + 1163*x^4 + 256*x^2 + 16 Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 1084.4 Root $$-1.85244i$$ of defining polynomial Character $$\chi$$ $$=$$ 1805.1084 Dual form 1805.2.b.i.1084.13

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.85244i q^{2} -1.45440i q^{3} -1.43152 q^{4} +(-0.323421 + 2.21255i) q^{5} -2.69418 q^{6} +0.477604i q^{7} -1.05306i q^{8} +0.884731 q^{9} +O(q^{10})$$ $$q-1.85244i q^{2} -1.45440i q^{3} -1.43152 q^{4} +(-0.323421 + 2.21255i) q^{5} -2.69418 q^{6} +0.477604i q^{7} -1.05306i q^{8} +0.884731 q^{9} +(4.09862 + 0.599118i) q^{10} +1.95728 q^{11} +2.08200i q^{12} +3.06043i q^{13} +0.884731 q^{14} +(3.21793 + 0.470383i) q^{15} -4.81379 q^{16} +0.973502i q^{17} -1.63891i q^{18} +(0.462986 - 3.16733i) q^{20} +0.694625 q^{21} -3.62574i q^{22} +5.59328i q^{23} -1.53157 q^{24} +(-4.79080 - 1.43117i) q^{25} +5.66926 q^{26} -5.64994i q^{27} -0.683702i q^{28} +10.1756 q^{29} +(0.871355 - 5.96102i) q^{30} +5.60367 q^{31} +6.81111i q^{32} -2.84666i q^{33} +1.80335 q^{34} +(-1.05672 - 0.154467i) q^{35} -1.26651 q^{36} +5.65754i q^{37} +4.45108 q^{39} +(2.32996 + 0.340584i) q^{40} +10.4679 q^{41} -1.28675i q^{42} -6.20983i q^{43} -2.80189 q^{44} +(-0.286141 + 1.95752i) q^{45} +10.3612 q^{46} +2.47845i q^{47} +7.00115i q^{48} +6.77189 q^{49} +(-2.65116 + 8.87465i) q^{50} +1.41586 q^{51} -4.38109i q^{52} -10.7711i q^{53} -10.4662 q^{54} +(-0.633026 + 4.33059i) q^{55} +0.502948 q^{56} -18.8496i q^{58} -7.32031 q^{59} +(-4.60655 - 0.673365i) q^{60} +8.76766 q^{61} -10.3805i q^{62} +0.422551i q^{63} +2.98958 q^{64} +(-6.77138 - 0.989809i) q^{65} -5.27326 q^{66} -8.82042i q^{67} -1.39359i q^{68} +8.13485 q^{69} +(-0.286141 + 1.95752i) q^{70} -13.1846 q^{71} -0.931679i q^{72} -4.97121i q^{73} +10.4802 q^{74} +(-2.08150 + 6.96772i) q^{75} +0.934804i q^{77} -8.24535i q^{78} +0.707984 q^{79} +(1.55688 - 10.6508i) q^{80} -5.56306 q^{81} -19.3911i q^{82} +11.8783i q^{83} -0.994373 q^{84} +(-2.15393 - 0.314851i) q^{85} -11.5033 q^{86} -14.7993i q^{87} -2.06114i q^{88} -2.14855 q^{89} +(3.62618 + 0.530058i) q^{90} -1.46167 q^{91} -8.00692i q^{92} -8.14996i q^{93} +4.59117 q^{94} +9.90605 q^{96} -5.89541i q^{97} -12.5445i q^{98} +1.73167 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$16 q - 12 q^{4} + 4 q^{5} - 10 q^{6} - 6 q^{9}+O(q^{10})$$ 16 * q - 12 * q^4 + 4 * q^5 - 10 * q^6 - 6 * q^9 $$16 q - 12 q^{4} + 4 q^{5} - 10 q^{6} - 6 q^{9} - 16 q^{10} - 22 q^{11} - 6 q^{14} + 10 q^{15} + 8 q^{16} - 14 q^{20} - 20 q^{21} + 14 q^{24} + 4 q^{25} - 16 q^{26} - 2 q^{29} - 12 q^{30} + 16 q^{31} + 8 q^{34} - 10 q^{35} + 18 q^{36} + 36 q^{39} + 38 q^{40} + 26 q^{41} + 64 q^{44} - 2 q^{45} + 2 q^{46} + 20 q^{49} - 48 q^{50} - 38 q^{51} + 12 q^{54} - 10 q^{55} + 6 q^{56} - 10 q^{59} - 10 q^{60} - 30 q^{61} + 16 q^{64} - 36 q^{65} + 4 q^{66} - 68 q^{69} - 2 q^{70} - 20 q^{71} + 40 q^{74} - 32 q^{75} - 12 q^{79} + 40 q^{80} - 48 q^{81} + 2 q^{84} - 2 q^{85} - 20 q^{86} + 30 q^{90} - 86 q^{91} + 38 q^{94} + 22 q^{96} + 32 q^{99}+O(q^{100})$$ 16 * q - 12 * q^4 + 4 * q^5 - 10 * q^6 - 6 * q^9 - 16 * q^10 - 22 * q^11 - 6 * q^14 + 10 * q^15 + 8 * q^16 - 14 * q^20 - 20 * q^21 + 14 * q^24 + 4 * q^25 - 16 * q^26 - 2 * q^29 - 12 * q^30 + 16 * q^31 + 8 * q^34 - 10 * q^35 + 18 * q^36 + 36 * q^39 + 38 * q^40 + 26 * q^41 + 64 * q^44 - 2 * q^45 + 2 * q^46 + 20 * q^49 - 48 * q^50 - 38 * q^51 + 12 * q^54 - 10 * q^55 + 6 * q^56 - 10 * q^59 - 10 * q^60 - 30 * q^61 + 16 * q^64 - 36 * q^65 + 4 * q^66 - 68 * q^69 - 2 * q^70 - 20 * q^71 + 40 * q^74 - 32 * q^75 - 12 * q^79 + 40 * q^80 - 48 * q^81 + 2 * q^84 - 2 * q^85 - 20 * q^86 + 30 * q^90 - 86 * q^91 + 38 * q^94 + 22 * q^96 + 32 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1805\mathbb{Z}\right)^\times$$.

 $$n$$ $$362$$ $$1446$$ $$\chi(n)$$ $$-1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.85244i 1.30987i −0.755685 0.654936i $$-0.772696\pi$$
0.755685 0.654936i $$-0.227304\pi$$
$$3$$ 1.45440i 0.839696i −0.907594 0.419848i $$-0.862083\pi$$
0.907594 0.419848i $$-0.137917\pi$$
$$4$$ −1.43152 −0.715762
$$5$$ −0.323421 + 2.21255i −0.144638 + 0.989485i
$$6$$ −2.69418 −1.09989
$$7$$ 0.477604i 0.180517i 0.995918 + 0.0902586i $$0.0287694\pi$$
−0.995918 + 0.0902586i $$0.971231\pi$$
$$8$$ 1.05306i 0.372315i
$$9$$ 0.884731 0.294910
$$10$$ 4.09862 + 0.599118i 1.29610 + 0.189458i
$$11$$ 1.95728 0.590142 0.295071 0.955475i $$-0.404657\pi$$
0.295071 + 0.955475i $$0.404657\pi$$
$$12$$ 2.08200i 0.601023i
$$13$$ 3.06043i 0.848812i 0.905472 + 0.424406i $$0.139517\pi$$
−0.905472 + 0.424406i $$0.860483\pi$$
$$14$$ 0.884731 0.236454
$$15$$ 3.21793 + 0.470383i 0.830866 + 0.121452i
$$16$$ −4.81379 −1.20345
$$17$$ 0.973502i 0.236109i 0.993007 + 0.118054i $$0.0376657\pi$$
−0.993007 + 0.118054i $$0.962334\pi$$
$$18$$ 1.63891i 0.386295i
$$19$$ 0 0
$$20$$ 0.462986 3.16733i 0.103527 0.708236i
$$21$$ 0.694625 0.151580
$$22$$ 3.62574i 0.773010i
$$23$$ 5.59328i 1.16628i 0.812372 + 0.583140i $$0.198176\pi$$
−0.812372 + 0.583140i $$0.801824\pi$$
$$24$$ −1.53157 −0.312631
$$25$$ −4.79080 1.43117i −0.958159 0.286235i
$$26$$ 5.66926 1.11183
$$27$$ 5.64994i 1.08733i
$$28$$ 0.683702i 0.129207i
$$29$$ 10.1756 1.88955 0.944777 0.327714i $$-0.106278\pi$$
0.944777 + 0.327714i $$0.106278\pi$$
$$30$$ 0.871355 5.96102i 0.159087 1.08833i
$$31$$ 5.60367 1.00645 0.503225 0.864156i $$-0.332147\pi$$
0.503225 + 0.864156i $$0.332147\pi$$
$$32$$ 6.81111i 1.20405i
$$33$$ 2.84666i 0.495540i
$$34$$ 1.80335 0.309272
$$35$$ −1.05672 0.154467i −0.178619 0.0261097i
$$36$$ −1.26651 −0.211086
$$37$$ 5.65754i 0.930094i 0.885286 + 0.465047i $$0.153963\pi$$
−0.885286 + 0.465047i $$0.846037\pi$$
$$38$$ 0 0
$$39$$ 4.45108 0.712744
$$40$$ 2.32996 + 0.340584i 0.368400 + 0.0538510i
$$41$$ 10.4679 1.63481 0.817404 0.576065i $$-0.195413\pi$$
0.817404 + 0.576065i $$0.195413\pi$$
$$42$$ 1.28675i 0.198550i
$$43$$ 6.20983i 0.946990i −0.880796 0.473495i $$-0.842992\pi$$
0.880796 0.473495i $$-0.157008\pi$$
$$44$$ −2.80189 −0.422401
$$45$$ −0.286141 + 1.95752i −0.0426554 + 0.291809i
$$46$$ 10.3612 1.52768
$$47$$ 2.47845i 0.361519i 0.983527 + 0.180759i $$0.0578555\pi$$
−0.983527 + 0.180759i $$0.942144\pi$$
$$48$$ 7.00115i 1.01053i
$$49$$ 6.77189 0.967414
$$50$$ −2.65116 + 8.87465i −0.374931 + 1.25507i
$$51$$ 1.41586 0.198260
$$52$$ 4.38109i 0.607547i
$$53$$ 10.7711i 1.47953i −0.672866 0.739764i $$-0.734937\pi$$
0.672866 0.739764i $$-0.265063\pi$$
$$54$$ −10.4662 −1.42426
$$55$$ −0.633026 + 4.33059i −0.0853572 + 0.583936i
$$56$$ 0.502948 0.0672092
$$57$$ 0 0
$$58$$ 18.8496i 2.47507i
$$59$$ −7.32031 −0.953024 −0.476512 0.879168i $$-0.658099\pi$$
−0.476512 + 0.879168i $$0.658099\pi$$
$$60$$ −4.60655 0.673365i −0.594703 0.0869310i
$$61$$ 8.76766 1.12258 0.561292 0.827618i $$-0.310305\pi$$
0.561292 + 0.827618i $$0.310305\pi$$
$$62$$ 10.3805i 1.31832i
$$63$$ 0.422551i 0.0532364i
$$64$$ 2.98958 0.373698
$$65$$ −6.77138 0.989809i −0.839886 0.122771i
$$66$$ −5.27326 −0.649093
$$67$$ 8.82042i 1.07759i −0.842438 0.538793i $$-0.818880\pi$$
0.842438 0.538793i $$-0.181120\pi$$
$$68$$ 1.39359i 0.168998i
$$69$$ 8.13485 0.979321
$$70$$ −0.286141 + 1.95752i −0.0342004 + 0.233968i
$$71$$ −13.1846 −1.56472 −0.782362 0.622825i $$-0.785985\pi$$
−0.782362 + 0.622825i $$0.785985\pi$$
$$72$$ 0.931679i 0.109799i
$$73$$ 4.97121i 0.581836i −0.956748 0.290918i $$-0.906039\pi$$
0.956748 0.290918i $$-0.0939606\pi$$
$$74$$ 10.4802 1.21830
$$75$$ −2.08150 + 6.96772i −0.240350 + 0.804563i
$$76$$ 0 0
$$77$$ 0.934804i 0.106531i
$$78$$ 8.24535i 0.933603i
$$79$$ 0.707984 0.0796544 0.0398272 0.999207i $$-0.487319\pi$$
0.0398272 + 0.999207i $$0.487319\pi$$
$$80$$ 1.55688 10.6508i 0.174065 1.19079i
$$81$$ −5.56306 −0.618118
$$82$$ 19.3911i 2.14139i
$$83$$ 11.8783i 1.30382i 0.758297 + 0.651909i $$0.226032\pi$$
−0.758297 + 0.651909i $$0.773968\pi$$
$$84$$ −0.994373 −0.108495
$$85$$ −2.15393 0.314851i −0.233626 0.0341504i
$$86$$ −11.5033 −1.24043
$$87$$ 14.7993i 1.58665i
$$88$$ 2.06114i 0.219718i
$$89$$ −2.14855 −0.227746 −0.113873 0.993495i $$-0.536326\pi$$
−0.113873 + 0.993495i $$0.536326\pi$$
$$90$$ 3.62618 + 0.530058i 0.382232 + 0.0558730i
$$91$$ −1.46167 −0.153225
$$92$$ 8.00692i 0.834779i
$$93$$ 8.14996i 0.845112i
$$94$$ 4.59117 0.473543
$$95$$ 0 0
$$96$$ 9.90605 1.01103
$$97$$ 5.89541i 0.598588i −0.954161 0.299294i $$-0.903249\pi$$
0.954161 0.299294i $$-0.0967512\pi$$
$$98$$ 12.5445i 1.26719i
$$99$$ 1.73167 0.174039
$$100$$ 6.85815 + 2.04876i 0.685815 + 0.204876i
$$101$$ 0.258211 0.0256930 0.0128465 0.999917i $$-0.495911\pi$$
0.0128465 + 0.999917i $$0.495911\pi$$
$$102$$ 2.62279i 0.259695i
$$103$$ 14.3714i 1.41605i 0.706186 + 0.708026i $$0.250414\pi$$
−0.706186 + 0.708026i $$0.749586\pi$$
$$104$$ 3.22283 0.316025
$$105$$ −0.224657 + 1.53690i −0.0219242 + 0.149986i
$$106$$ −19.9529 −1.93799
$$107$$ 5.73115i 0.554051i 0.960863 + 0.277026i $$0.0893487\pi$$
−0.960863 + 0.277026i $$0.910651\pi$$
$$108$$ 8.08803i 0.778271i
$$109$$ 5.77812 0.553444 0.276722 0.960950i $$-0.410752\pi$$
0.276722 + 0.960950i $$0.410752\pi$$
$$110$$ 8.02214 + 1.17264i 0.764881 + 0.111807i
$$111$$ 8.22830 0.780996
$$112$$ 2.29908i 0.217243i
$$113$$ 13.9762i 1.31477i −0.753554 0.657386i $$-0.771662\pi$$
0.753554 0.657386i $$-0.228338\pi$$
$$114$$ 0 0
$$115$$ −12.3754 1.80899i −1.15402 0.168689i
$$116$$ −14.5666 −1.35247
$$117$$ 2.70766i 0.250323i
$$118$$ 13.5604i 1.24834i
$$119$$ −0.464948 −0.0426217
$$120$$ 0.495344 3.38869i 0.0452185 0.309344i
$$121$$ −7.16906 −0.651733
$$122$$ 16.2415i 1.47044i
$$123$$ 15.2244i 1.37274i
$$124$$ −8.02180 −0.720379
$$125$$ 4.71600 10.1370i 0.421812 0.906683i
$$126$$ 0.782749 0.0697328
$$127$$ 9.23319i 0.819313i 0.912240 + 0.409657i $$0.134351\pi$$
−0.912240 + 0.409657i $$0.865649\pi$$
$$128$$ 8.08421i 0.714550i
$$129$$ −9.03155 −0.795184
$$130$$ −1.83356 + 12.5436i −0.160814 + 1.10014i
$$131$$ −13.9316 −1.21721 −0.608603 0.793475i $$-0.708270\pi$$
−0.608603 + 0.793475i $$0.708270\pi$$
$$132$$ 4.07506i 0.354689i
$$133$$ 0 0
$$134$$ −16.3393 −1.41150
$$135$$ 12.5008 + 1.82731i 1.07590 + 0.157270i
$$136$$ 1.02516 0.0879068
$$137$$ 3.84336i 0.328360i 0.986430 + 0.164180i $$0.0524978\pi$$
−0.986430 + 0.164180i $$0.947502\pi$$
$$138$$ 15.0693i 1.28278i
$$139$$ 18.8730 1.60079 0.800395 0.599473i $$-0.204623\pi$$
0.800395 + 0.599473i $$0.204623\pi$$
$$140$$ 1.51273 + 0.221124i 0.127849 + 0.0186884i
$$141$$ 3.60464 0.303566
$$142$$ 24.4236i 2.04959i
$$143$$ 5.99012i 0.500919i
$$144$$ −4.25891 −0.354909
$$145$$ −3.29099 + 22.5140i −0.273302 + 1.86968i
$$146$$ −9.20885 −0.762130
$$147$$ 9.84902i 0.812333i
$$148$$ 8.09891i 0.665726i
$$149$$ 23.9268 1.96016 0.980082 0.198594i $$-0.0636375\pi$$
0.980082 + 0.198594i $$0.0636375\pi$$
$$150$$ 12.9073 + 3.85584i 1.05387 + 0.314828i
$$151$$ −5.90301 −0.480380 −0.240190 0.970726i $$-0.577210\pi$$
−0.240190 + 0.970726i $$0.577210\pi$$
$$152$$ 0 0
$$153$$ 0.861288i 0.0696310i
$$154$$ 1.73167 0.139542
$$155$$ −1.81235 + 12.3984i −0.145571 + 0.995866i
$$156$$ −6.37184 −0.510155
$$157$$ 10.5707i 0.843631i 0.906682 + 0.421815i $$0.138607\pi$$
−0.906682 + 0.421815i $$0.861393\pi$$
$$158$$ 1.31150i 0.104337i
$$159$$ −15.6655 −1.24235
$$160$$ −15.0700 2.20286i −1.19138 0.174151i
$$161$$ −2.67137 −0.210534
$$162$$ 10.3052i 0.809654i
$$163$$ 18.6090i 1.45757i 0.684743 + 0.728785i $$0.259915\pi$$
−0.684743 + 0.728785i $$0.740085\pi$$
$$164$$ −14.9850 −1.17013
$$165$$ 6.29839 + 0.920670i 0.490329 + 0.0716741i
$$166$$ 22.0039 1.70783
$$167$$ 2.77731i 0.214914i −0.994210 0.107457i $$-0.965729\pi$$
0.994210 0.107457i $$-0.0342708\pi$$
$$168$$ 0.731485i 0.0564353i
$$169$$ 3.63375 0.279519
$$170$$ −0.583242 + 3.99001i −0.0447327 + 0.306020i
$$171$$ 0 0
$$172$$ 8.88952i 0.677820i
$$173$$ 8.92075i 0.678232i −0.940745 0.339116i $$-0.889872\pi$$
0.940745 0.339116i $$-0.110128\pi$$
$$174$$ −27.4148 −2.07831
$$175$$ 0.683534 2.28810i 0.0516703 0.172964i
$$176$$ −9.42192 −0.710204
$$177$$ 10.6466i 0.800250i
$$178$$ 3.98006i 0.298318i
$$179$$ −15.2646 −1.14093 −0.570467 0.821321i $$-0.693238\pi$$
−0.570467 + 0.821321i $$0.693238\pi$$
$$180$$ 0.409618 2.80223i 0.0305311 0.208866i
$$181$$ −8.54101 −0.634848 −0.317424 0.948284i $$-0.602818\pi$$
−0.317424 + 0.948284i $$0.602818\pi$$
$$182$$ 2.70766i 0.200705i
$$183$$ 12.7516i 0.942629i
$$184$$ 5.89009 0.434223
$$185$$ −12.5176 1.82977i −0.920313 0.134527i
$$186$$ −15.0973 −1.10699
$$187$$ 1.90542i 0.139338i
$$188$$ 3.54796i 0.258761i
$$189$$ 2.69843 0.196282
$$190$$ 0 0
$$191$$ −16.2967 −1.17919 −0.589594 0.807700i $$-0.700712\pi$$
−0.589594 + 0.807700i $$0.700712\pi$$
$$192$$ 4.34804i 0.313792i
$$193$$ 16.4692i 1.18548i −0.805394 0.592739i $$-0.798046\pi$$
0.805394 0.592739i $$-0.201954\pi$$
$$194$$ −10.9209 −0.784074
$$195$$ −1.43958 + 9.84827i −0.103090 + 0.705249i
$$196$$ −9.69414 −0.692438
$$197$$ 10.0229i 0.714102i −0.934085 0.357051i $$-0.883782\pi$$
0.934085 0.357051i $$-0.116218\pi$$
$$198$$ 3.20780i 0.227969i
$$199$$ 12.6643 0.897748 0.448874 0.893595i $$-0.351825\pi$$
0.448874 + 0.893595i $$0.351825\pi$$
$$200$$ −1.50712 + 5.04502i −0.106569 + 0.356737i
$$201$$ −12.8284 −0.904845
$$202$$ 0.478321i 0.0336545i
$$203$$ 4.85988i 0.341097i
$$204$$ −2.02684 −0.141907
$$205$$ −3.38553 + 23.1607i −0.236456 + 1.61762i
$$206$$ 26.6221 1.85485
$$207$$ 4.94855i 0.343948i
$$208$$ 14.7323i 1.02150i
$$209$$ 0 0
$$210$$ 2.84700 + 0.416162i 0.196462 + 0.0287179i
$$211$$ 5.73609 0.394888 0.197444 0.980314i $$-0.436736\pi$$
0.197444 + 0.980314i $$0.436736\pi$$
$$212$$ 15.4191i 1.05899i
$$213$$ 19.1756i 1.31389i
$$214$$ 10.6166 0.725736
$$215$$ 13.7396 + 2.00839i 0.937032 + 0.136971i
$$216$$ −5.94975 −0.404829
$$217$$ 2.67634i 0.181682i
$$218$$ 10.7036i 0.724940i
$$219$$ −7.23010 −0.488565
$$220$$ 0.906192 6.19934i 0.0610955 0.417960i
$$221$$ −2.97934 −0.200412
$$222$$ 15.2424i 1.02300i
$$223$$ 12.8478i 0.860353i −0.902745 0.430176i $$-0.858451\pi$$
0.902745 0.430176i $$-0.141549\pi$$
$$224$$ −3.25301 −0.217351
$$225$$ −4.23857 1.26620i −0.282571 0.0844136i
$$226$$ −25.8901 −1.72218
$$227$$ 15.5808i 1.03413i 0.855945 + 0.517067i $$0.172976\pi$$
−0.855945 + 0.517067i $$0.827024\pi$$
$$228$$ 0 0
$$229$$ 3.77930 0.249743 0.124871 0.992173i $$-0.460148\pi$$
0.124871 + 0.992173i $$0.460148\pi$$
$$230$$ −3.35103 + 22.9247i −0.220961 + 1.51161i
$$231$$ 1.35958 0.0894535
$$232$$ 10.7155i 0.703508i
$$233$$ 11.0745i 0.725512i 0.931884 + 0.362756i $$0.118164\pi$$
−0.931884 + 0.362756i $$0.881836\pi$$
$$234$$ 5.01577 0.327891
$$235$$ −5.48370 0.801583i −0.357717 0.0522895i
$$236$$ 10.4792 0.682139
$$237$$ 1.02969i 0.0668855i
$$238$$ 0.861288i 0.0558290i
$$239$$ 10.6496 0.688865 0.344433 0.938811i $$-0.388071\pi$$
0.344433 + 0.938811i $$0.388071\pi$$
$$240$$ −15.4904 2.26432i −0.999903 0.146161i
$$241$$ 5.01271 0.322897 0.161448 0.986881i $$-0.448383\pi$$
0.161448 + 0.986881i $$0.448383\pi$$
$$242$$ 13.2802i 0.853686i
$$243$$ 8.85892i 0.568300i
$$244$$ −12.5511 −0.803503
$$245$$ −2.19018 + 14.9832i −0.139925 + 0.957241i
$$246$$ −28.2023 −1.79811
$$247$$ 0 0
$$248$$ 5.90103i 0.374716i
$$249$$ 17.2758 1.09481
$$250$$ −18.7782 8.73609i −1.18764 0.552519i
$$251$$ −26.1721 −1.65197 −0.825986 0.563691i $$-0.809381\pi$$
−0.825986 + 0.563691i $$0.809381\pi$$
$$252$$ 0.604892i 0.0381046i
$$253$$ 10.9476i 0.688271i
$$254$$ 17.1039 1.07319
$$255$$ −0.457919 + 3.13266i −0.0286760 + 0.196175i
$$256$$ 20.9546 1.30967
$$257$$ 22.4024i 1.39742i −0.715403 0.698712i $$-0.753757\pi$$
0.715403 0.698712i $$-0.246243\pi$$
$$258$$ 16.7304i 1.04159i
$$259$$ −2.70206 −0.167898
$$260$$ 9.69339 + 1.41694i 0.601159 + 0.0878747i
$$261$$ 9.00263 0.557249
$$262$$ 25.8074i 1.59438i
$$263$$ 25.9338i 1.59915i −0.600569 0.799573i $$-0.705059\pi$$
0.600569 0.799573i $$-0.294941\pi$$
$$264$$ −2.99772 −0.184497
$$265$$ 23.8317 + 3.48361i 1.46397 + 0.213997i
$$266$$ 0 0
$$267$$ 3.12485i 0.191238i
$$268$$ 12.6267i 0.771296i
$$269$$ 9.24978 0.563969 0.281985 0.959419i $$-0.409007\pi$$
0.281985 + 0.959419i $$0.409007\pi$$
$$270$$ 3.38498 23.1569i 0.206003 1.40929i
$$271$$ −22.4688 −1.36488 −0.682441 0.730941i $$-0.739082\pi$$
−0.682441 + 0.730941i $$0.739082\pi$$
$$272$$ 4.68623i 0.284145i
$$273$$ 2.12585i 0.128663i
$$274$$ 7.11958 0.430110
$$275$$ −9.37693 2.80121i −0.565450 0.168919i
$$276$$ −11.6452 −0.700961
$$277$$ 9.16598i 0.550730i 0.961340 + 0.275365i $$0.0887987\pi$$
−0.961340 + 0.275365i $$0.911201\pi$$
$$278$$ 34.9611i 2.09683i
$$279$$ 4.95774 0.296812
$$280$$ −0.162664 + 1.11280i −0.00972103 + 0.0665025i
$$281$$ −19.3577 −1.15479 −0.577393 0.816467i $$-0.695930\pi$$
−0.577393 + 0.816467i $$0.695930\pi$$
$$282$$ 6.67738i 0.397632i
$$283$$ 8.72514i 0.518656i −0.965789 0.259328i $$-0.916499\pi$$
0.965789 0.259328i $$-0.0835010\pi$$
$$284$$ 18.8741 1.11997
$$285$$ 0 0
$$286$$ 11.0963 0.656140
$$287$$ 4.99950i 0.295111i
$$288$$ 6.02600i 0.355085i
$$289$$ 16.0523 0.944253
$$290$$ 41.7057 + 6.09636i 2.44905 + 0.357990i
$$291$$ −8.57427 −0.502632
$$292$$ 7.11641i 0.416456i
$$293$$ 16.7749i 0.980002i 0.871722 + 0.490001i $$0.163004\pi$$
−0.871722 + 0.490001i $$0.836996\pi$$
$$294$$ −18.2447 −1.06405
$$295$$ 2.36755 16.1966i 0.137844 0.943002i
$$296$$ 5.95776 0.346287
$$297$$ 11.0585i 0.641680i
$$298$$ 44.3230i 2.56756i
$$299$$ −17.1179 −0.989952
$$300$$ 2.97971 9.97446i 0.172034 0.575876i
$$301$$ 2.96584 0.170948
$$302$$ 10.9350i 0.629236i
$$303$$ 0.375542i 0.0215743i
$$304$$ 0 0
$$305$$ −2.83565 + 19.3989i −0.162369 + 1.11078i
$$306$$ 1.59548 0.0912076
$$307$$ 6.40893i 0.365777i −0.983134 0.182889i $$-0.941455\pi$$
0.983134 0.182889i $$-0.0585448\pi$$
$$308$$ 1.33819i 0.0762507i
$$309$$ 20.9017 1.18905
$$310$$ 22.9673 + 3.35726i 1.30446 + 0.190680i
$$311$$ 10.6248 0.602477 0.301238 0.953549i $$-0.402600\pi$$
0.301238 + 0.953549i $$0.402600\pi$$
$$312$$ 4.68728i 0.265365i
$$313$$ 4.75656i 0.268857i 0.990923 + 0.134428i $$0.0429198\pi$$
−0.990923 + 0.134428i $$0.957080\pi$$
$$314$$ 19.5815 1.10505
$$315$$ −0.934917 0.136662i −0.0526766 0.00770003i
$$316$$ −1.01350 −0.0570136
$$317$$ 0.0612218i 0.00343856i −0.999999 0.00171928i $$-0.999453\pi$$
0.999999 0.00171928i $$-0.000547264\pi$$
$$318$$ 29.0194i 1.62732i
$$319$$ 19.9164 1.11510
$$320$$ −0.966894 + 6.61461i −0.0540510 + 0.369768i
$$321$$ 8.33536 0.465235
$$322$$ 4.94855i 0.275772i
$$323$$ 0 0
$$324$$ 7.96366 0.442425
$$325$$ 4.38002 14.6619i 0.242960 0.813297i
$$326$$ 34.4720 1.90923
$$327$$ 8.40368i 0.464724i
$$328$$ 11.0234i 0.608663i
$$329$$ −1.18372 −0.0652603
$$330$$ 1.70548 11.6674i 0.0938838 0.642268i
$$331$$ 17.6067 0.967752 0.483876 0.875137i $$-0.339229\pi$$
0.483876 + 0.875137i $$0.339229\pi$$
$$332$$ 17.0041i 0.933224i
$$333$$ 5.00540i 0.274294i
$$334$$ −5.14478 −0.281510
$$335$$ 19.5157 + 2.85271i 1.06625 + 0.155860i
$$336$$ −3.34378 −0.182418
$$337$$ 6.90874i 0.376343i −0.982136 0.188171i $$-0.939744\pi$$
0.982136 0.188171i $$-0.0602560\pi$$
$$338$$ 6.73129i 0.366134i
$$339$$ −20.3270 −1.10401
$$340$$ 3.08340 + 0.450718i 0.167221 + 0.0244436i
$$341$$ 10.9680 0.593948
$$342$$ 0 0
$$343$$ 6.57751i 0.355152i
$$344$$ −6.53935 −0.352578
$$345$$ −2.63098 + 17.9988i −0.141647 + 0.969023i
$$346$$ −16.5251 −0.888396
$$347$$ 7.32576i 0.393267i 0.980477 + 0.196634i $$0.0630010\pi$$
−0.980477 + 0.196634i $$0.936999\pi$$
$$348$$ 21.1856i 1.13567i
$$349$$ 2.16127 0.115690 0.0578452 0.998326i $$-0.481577\pi$$
0.0578452 + 0.998326i $$0.481577\pi$$
$$350$$ −4.23857 1.26620i −0.226561 0.0676815i
$$351$$ 17.2913 0.922939
$$352$$ 13.3312i 0.710557i
$$353$$ 16.6022i 0.883644i 0.897103 + 0.441822i $$0.145668\pi$$
−0.897103 + 0.441822i $$0.854332\pi$$
$$354$$ 19.7222 1.04822
$$355$$ 4.26418 29.1716i 0.226319 1.54827i
$$356$$ 3.07571 0.163012
$$357$$ 0.676219i 0.0357893i
$$358$$ 28.2768i 1.49448i
$$359$$ −17.0830 −0.901608 −0.450804 0.892623i $$-0.648863\pi$$
−0.450804 + 0.892623i $$0.648863\pi$$
$$360$$ 2.06139 + 0.301325i 0.108645 + 0.0158812i
$$361$$ 0 0
$$362$$ 15.8217i 0.831569i
$$363$$ 10.4267i 0.547257i
$$364$$ 2.09242 0.109673
$$365$$ 10.9991 + 1.60779i 0.575717 + 0.0841558i
$$366$$ −23.6216 −1.23472
$$367$$ 19.5631i 1.02119i 0.859822 + 0.510594i $$0.170574\pi$$
−0.859822 + 0.510594i $$0.829426\pi$$
$$368$$ 26.9249i 1.40356i
$$369$$ 9.26125 0.482122
$$370$$ −3.38953 + 23.1881i −0.176213 + 1.20549i
$$371$$ 5.14433 0.267080
$$372$$ 11.6669i 0.604899i
$$373$$ 6.59700i 0.341580i 0.985307 + 0.170790i $$0.0546320\pi$$
−0.985307 + 0.170790i $$0.945368\pi$$
$$374$$ 3.52966 0.182515
$$375$$ −14.7433 6.85893i −0.761339 0.354194i
$$376$$ 2.60997 0.134599
$$377$$ 31.1416i 1.60387i
$$378$$ 4.99868i 0.257104i
$$379$$ −21.6574 −1.11246 −0.556232 0.831027i $$-0.687753\pi$$
−0.556232 + 0.831027i $$0.687753\pi$$
$$380$$ 0 0
$$381$$ 13.4287 0.687974
$$382$$ 30.1886i 1.54458i
$$383$$ 24.3214i 1.24277i 0.783507 + 0.621383i $$0.213429\pi$$
−0.783507 + 0.621383i $$0.786571\pi$$
$$384$$ 11.7576 0.600005
$$385$$ −2.06830 0.302335i −0.105411 0.0154084i
$$386$$ −30.5082 −1.55282
$$387$$ 5.49403i 0.279277i
$$388$$ 8.43943i 0.428447i
$$389$$ −15.8227 −0.802241 −0.401120 0.916025i $$-0.631379\pi$$
−0.401120 + 0.916025i $$0.631379\pi$$
$$390$$ 18.2433 + 2.66672i 0.923785 + 0.135035i
$$391$$ −5.44507 −0.275369
$$392$$ 7.13124i 0.360182i
$$393$$ 20.2620i 1.02208i
$$394$$ −18.5668 −0.935381
$$395$$ −0.228977 + 1.56645i −0.0115211 + 0.0788168i
$$396$$ −2.47892 −0.124571
$$397$$ 35.4753i 1.78046i −0.455515 0.890228i $$-0.650545\pi$$
0.455515 0.890228i $$-0.349455\pi$$
$$398$$ 23.4598i 1.17593i
$$399$$ 0 0
$$400$$ 23.0619 + 6.88937i 1.15309 + 0.344468i
$$401$$ −11.2107 −0.559837 −0.279919 0.960024i $$-0.590307\pi$$
−0.279919 + 0.960024i $$0.590307\pi$$
$$402$$ 23.7638i 1.18523i
$$403$$ 17.1497i 0.854286i
$$404$$ −0.369636 −0.0183901
$$405$$ 1.79921 12.3086i 0.0894035 0.611618i
$$406$$ 9.00263 0.446793
$$407$$ 11.0734i 0.548887i
$$408$$ 1.49099i 0.0738150i
$$409$$ −1.91450 −0.0946660 −0.0473330 0.998879i $$-0.515072\pi$$
−0.0473330 + 0.998879i $$0.515072\pi$$
$$410$$ 42.9038 + 6.27149i 2.11887 + 0.309727i
$$411$$ 5.58977 0.275723
$$412$$ 20.5730i 1.01356i
$$413$$ 3.49621i 0.172037i
$$414$$ 9.16688 0.450528
$$415$$ −26.2815 3.84171i −1.29011 0.188582i
$$416$$ −20.8449 −1.02201
$$417$$ 27.4489i 1.34418i
$$418$$ 0 0
$$419$$ 22.1856 1.08384 0.541918 0.840431i $$-0.317698\pi$$
0.541918 + 0.840431i $$0.317698\pi$$
$$420$$ 0.321601 2.20010i 0.0156925 0.107354i
$$421$$ 13.3793 0.652069 0.326034 0.945358i $$-0.394287\pi$$
0.326034 + 0.945358i $$0.394287\pi$$
$$422$$ 10.6257i 0.517253i
$$423$$ 2.19276i 0.106616i
$$424$$ −11.3427 −0.550850
$$425$$ 1.39325 4.66385i 0.0675826 0.226230i
$$426$$ 35.5216 1.72103
$$427$$ 4.18747i 0.202646i
$$428$$ 8.20428i 0.396569i
$$429$$ 8.71201 0.420620
$$430$$ 3.72042 25.4517i 0.179415 1.22739i
$$431$$ −37.1687 −1.79035 −0.895177 0.445711i $$-0.852951\pi$$
−0.895177 + 0.445711i $$0.852951\pi$$
$$432$$ 27.1976i 1.30855i
$$433$$ 8.32630i 0.400137i 0.979782 + 0.200068i $$0.0641164\pi$$
−0.979782 + 0.200068i $$0.935884\pi$$
$$434$$ 4.95774 0.237979
$$435$$ 32.7443 + 4.78641i 1.56997 + 0.229491i
$$436$$ −8.27152 −0.396134
$$437$$ 0 0
$$438$$ 13.3933i 0.639957i
$$439$$ 17.0746 0.814928 0.407464 0.913221i $$-0.366413\pi$$
0.407464 + 0.913221i $$0.366413\pi$$
$$440$$ 4.56039 + 0.666617i 0.217408 + 0.0317797i
$$441$$ 5.99131 0.285300
$$442$$ 5.51904i 0.262514i
$$443$$ 7.18135i 0.341196i 0.985341 + 0.170598i $$0.0545700\pi$$
−0.985341 + 0.170598i $$0.945430\pi$$
$$444$$ −11.7790 −0.559008
$$445$$ 0.694888 4.75379i 0.0329409 0.225351i
$$446$$ −23.7998 −1.12695
$$447$$ 34.7991i 1.64594i
$$448$$ 1.42784i 0.0674589i
$$449$$ −23.1024 −1.09027 −0.545134 0.838349i $$-0.683521\pi$$
−0.545134 + 0.838349i $$0.683521\pi$$
$$450$$ −2.34557 + 7.85168i −0.110571 + 0.370132i
$$451$$ 20.4886 0.964768
$$452$$ 20.0073i 0.941065i
$$453$$ 8.58532i 0.403373i
$$454$$ 28.8625 1.35458
$$455$$ 0.472737 3.23403i 0.0221622 0.151614i
$$456$$ 0 0
$$457$$ 13.7430i 0.642872i 0.946931 + 0.321436i $$0.104166\pi$$
−0.946931 + 0.321436i $$0.895834\pi$$
$$458$$ 7.00091i 0.327131i
$$459$$ 5.50023 0.256729
$$460$$ 17.7158 + 2.58961i 0.826001 + 0.120741i
$$461$$ −26.0522 −1.21337 −0.606686 0.794942i $$-0.707501\pi$$
−0.606686 + 0.794942i $$0.707501\pi$$
$$462$$ 2.51853i 0.117173i
$$463$$ 4.24698i 0.197374i 0.995119 + 0.0986869i $$0.0314642\pi$$
−0.995119 + 0.0986869i $$0.968536\pi$$
$$464$$ −48.9830 −2.27398
$$465$$ 18.0322 + 2.63587i 0.836225 + 0.122236i
$$466$$ 20.5147 0.950327
$$467$$ 27.7571i 1.28444i −0.766519 0.642222i $$-0.778013\pi$$
0.766519 0.642222i $$-0.221987\pi$$
$$468$$ 3.87608i 0.179172i
$$469$$ 4.21267 0.194523
$$470$$ −1.48488 + 10.1582i −0.0684925 + 0.468563i
$$471$$ 15.3739 0.708394
$$472$$ 7.70877i 0.354825i
$$473$$ 12.1544i 0.558858i
$$474$$ −1.90744 −0.0876114
$$475$$ 0 0
$$476$$ 0.665585 0.0305070
$$477$$ 9.52956i 0.436328i
$$478$$ 19.7277i 0.902325i
$$479$$ 7.11883 0.325268 0.162634 0.986686i $$-0.448001\pi$$
0.162634 + 0.986686i $$0.448001\pi$$
$$480$$ −3.20383 + 21.9177i −0.146234 + 1.00040i
$$481$$ −17.3145 −0.789474
$$482$$ 9.28573i 0.422953i
$$483$$ 3.88523i 0.176784i
$$484$$ 10.2627 0.466486
$$485$$ 13.0439 + 1.90670i 0.592294 + 0.0865789i
$$486$$ −16.4106 −0.744400
$$487$$ 3.54621i 0.160694i 0.996767 + 0.0803470i $$0.0256028\pi$$
−0.996767 + 0.0803470i $$0.974397\pi$$
$$488$$ 9.23291i 0.417954i
$$489$$ 27.0649 1.22392
$$490$$ 27.7554 + 4.05716i 1.25386 + 0.183284i
$$491$$ −32.1308 −1.45004 −0.725020 0.688727i $$-0.758170\pi$$
−0.725020 + 0.688727i $$0.758170\pi$$
$$492$$ 21.7942i 0.982557i
$$493$$ 9.90593i 0.446141i
$$494$$ 0 0
$$495$$ −0.560057 + 3.83140i −0.0251727 + 0.172209i
$$496$$ −26.9749 −1.21121
$$497$$ 6.29701i 0.282459i
$$498$$ 32.0024i 1.43406i
$$499$$ 11.9147 0.533376 0.266688 0.963783i $$-0.414071\pi$$
0.266688 + 0.963783i $$0.414071\pi$$
$$500$$ −6.75107 + 14.5114i −0.301917 + 0.648970i
$$501$$ −4.03930 −0.180463
$$502$$ 48.4823i 2.16387i
$$503$$ 0.239744i 0.0106896i −0.999986 0.00534482i $$-0.998299\pi$$
0.999986 0.00534482i $$-0.00170132\pi$$
$$504$$ 0.444973 0.0198207
$$505$$ −0.0835111 + 0.571307i −0.00371620 + 0.0254228i
$$506$$ 20.2798 0.901546
$$507$$ 5.28491i 0.234711i
$$508$$ 13.2175i 0.586434i
$$509$$ 29.3663 1.30164 0.650819 0.759233i $$-0.274426\pi$$
0.650819 + 0.759233i $$0.274426\pi$$
$$510$$ 5.80306 + 0.848266i 0.256964 + 0.0375618i
$$511$$ 2.37427 0.105031
$$512$$ 22.6488i 1.00094i
$$513$$ 0 0
$$514$$ −41.4991 −1.83045
$$515$$ −31.7974 4.64801i −1.40116 0.204816i
$$516$$ 12.9289 0.569163
$$517$$ 4.85101i 0.213347i
$$518$$ 5.00540i 0.219925i
$$519$$ −12.9743 −0.569509
$$520$$ −1.04233 + 7.13070i −0.0457093 + 0.312702i
$$521$$ 12.1069 0.530414 0.265207 0.964191i $$-0.414560\pi$$
0.265207 + 0.964191i $$0.414560\pi$$
$$522$$ 16.6768i 0.729924i
$$523$$ 6.43779i 0.281505i −0.990045 0.140752i $$-0.955048\pi$$
0.990045 0.140752i $$-0.0449522\pi$$
$$524$$ 19.9434 0.871231
$$525$$ −3.32781 0.994130i −0.145237 0.0433874i
$$526$$ −48.0407 −2.09467
$$527$$ 5.45519i 0.237632i
$$528$$ 13.7032i 0.596356i
$$529$$ −8.28480 −0.360209
$$530$$ 6.45318 44.1468i 0.280308 1.91761i
$$531$$ −6.47651 −0.281057
$$532$$ 0 0
$$533$$ 32.0362i 1.38764i
$$534$$ 5.78859 0.250497
$$535$$ −12.6805 1.85358i −0.548225 0.0801371i
$$536$$ −9.28848 −0.401201
$$537$$ 22.2008i 0.958037i
$$538$$ 17.1346i 0.738727i
$$539$$ 13.2545 0.570911
$$540$$ −17.8952 2.61584i −0.770087 0.112568i
$$541$$ −15.1179 −0.649969 −0.324985 0.945719i $$-0.605359\pi$$
−0.324985 + 0.945719i $$0.605359\pi$$
$$542$$ 41.6220i 1.78782i
$$543$$ 12.4220i 0.533079i
$$544$$ −6.63063 −0.284286
$$545$$ −1.86877 + 12.7844i −0.0800492 + 0.547624i
$$546$$ 3.93801 0.168531
$$547$$ 36.1694i 1.54649i −0.634106 0.773246i $$-0.718632\pi$$
0.634106 0.773246i $$-0.281368\pi$$
$$548$$ 5.50186i 0.235028i
$$549$$ 7.75702 0.331061
$$550$$ −5.18906 + 17.3702i −0.221262 + 0.740667i
$$551$$ 0 0
$$552$$ 8.56652i 0.364615i
$$553$$ 0.338136i 0.0143790i
$$554$$ 16.9794 0.721386
$$555$$ −2.66121 + 18.2056i −0.112962 + 0.772784i
$$556$$ −27.0172 −1.14579
$$557$$ 37.0585i 1.57022i 0.619358 + 0.785109i $$0.287393\pi$$
−0.619358 + 0.785109i $$0.712607\pi$$
$$558$$ 9.18391i 0.388786i
$$559$$ 19.0048 0.803816
$$560$$ 5.08685 + 0.743572i 0.214958 + 0.0314217i
$$561$$ 2.77123 0.117001
$$562$$ 35.8590i 1.51262i
$$563$$ 12.9283i 0.544863i −0.962175 0.272432i $$-0.912172\pi$$
0.962175 0.272432i $$-0.0878279\pi$$
$$564$$ −5.16014 −0.217281
$$565$$ 30.9232 + 4.52021i 1.30095 + 0.190167i
$$566$$ −16.1628 −0.679372
$$567$$ 2.65694i 0.111581i
$$568$$ 13.8842i 0.582569i
$$569$$ −18.5114 −0.776038 −0.388019 0.921651i $$-0.626841\pi$$
−0.388019 + 0.921651i $$0.626841\pi$$
$$570$$ 0 0
$$571$$ 16.2207 0.678816 0.339408 0.940639i $$-0.389773\pi$$
0.339408 + 0.940639i $$0.389773\pi$$
$$572$$ 8.57501i 0.358539i
$$573$$ 23.7019i 0.990160i
$$574$$ 9.26125 0.386557
$$575$$ 8.00496 26.7963i 0.333830 1.11748i
$$576$$ 2.64498 0.110207
$$577$$ 17.7980i 0.740939i 0.928845 + 0.370470i $$0.120803\pi$$
−0.928845 + 0.370470i $$0.879197\pi$$
$$578$$ 29.7359i 1.23685i
$$579$$ −23.9527 −0.995442
$$580$$ 4.71114 32.2293i 0.195619 1.33825i
$$581$$ −5.67314 −0.235362
$$582$$ 15.8833i 0.658384i
$$583$$ 21.0821i 0.873132i
$$584$$ −5.23500 −0.216626
$$585$$ −5.99085 0.875715i −0.247691 0.0362064i
$$586$$ 31.0745 1.28368
$$587$$ 35.8593i 1.48007i 0.672567 + 0.740036i $$0.265191\pi$$
−0.672567 + 0.740036i $$0.734809\pi$$
$$588$$ 14.0991i 0.581438i
$$589$$ 0 0
$$590$$ −30.0032 4.38573i −1.23521 0.180558i
$$591$$ −14.5773 −0.599628
$$592$$ 27.2342i 1.11932i
$$593$$ 18.2848i 0.750868i −0.926849 0.375434i $$-0.877494\pi$$
0.926849 0.375434i $$-0.122506\pi$$
$$594$$ −20.4852 −0.840518
$$595$$ 0.150374 1.02872i 0.00616474 0.0421735i
$$596$$ −34.2519 −1.40301
$$597$$ 18.4189i 0.753836i
$$598$$ 31.7098i 1.29671i
$$599$$ 7.85141 0.320800 0.160400 0.987052i $$-0.448722\pi$$
0.160400 + 0.987052i $$0.448722\pi$$
$$600$$ 7.33746 + 2.19195i 0.299551 + 0.0894860i
$$601$$ 17.3527 0.707833 0.353917 0.935277i $$-0.384850\pi$$
0.353917 + 0.935277i $$0.384850\pi$$
$$602$$ 5.49403i 0.223920i
$$603$$ 7.80370i 0.317791i
$$604$$ 8.45030 0.343838
$$605$$ 2.31863 15.8619i 0.0942656 0.644879i
$$606$$ −0.695668 −0.0282596
$$607$$ 40.7364i 1.65344i 0.562614 + 0.826720i $$0.309796\pi$$
−0.562614 + 0.826720i $$0.690204\pi$$
$$608$$ 0 0
$$609$$ 7.06820 0.286418
$$610$$ 35.9353 + 5.25286i 1.45498 + 0.212682i
$$611$$ −7.58512 −0.306861
$$612$$ 1.23295i 0.0498392i
$$613$$ 27.0535i 1.09268i 0.837564 + 0.546340i $$0.183979\pi$$
−0.837564 + 0.546340i $$0.816021\pi$$
$$614$$ −11.8721 −0.479121
$$615$$ 33.6849 + 4.92391i 1.35831 + 0.198551i
$$616$$ 0.984409 0.0396630
$$617$$ 19.8932i 0.800871i −0.916325 0.400436i $$-0.868859\pi$$
0.916325 0.400436i $$-0.131141\pi$$
$$618$$ 38.7190i 1.55751i
$$619$$ −16.8447 −0.677044 −0.338522 0.940958i $$-0.609927\pi$$
−0.338522 + 0.940958i $$0.609927\pi$$
$$620$$ 2.59442 17.7487i 0.104194 0.712804i
$$621$$ 31.6017 1.26813
$$622$$ 19.6818i 0.789167i
$$623$$ 1.02616i 0.0411121i
$$624$$ −21.4266 −0.857749
$$625$$ 20.9035 + 13.7129i 0.836139 + 0.548517i
$$626$$ 8.81123 0.352168
$$627$$ 0 0
$$628$$ 15.1322i 0.603839i
$$629$$ −5.50763 −0.219603
$$630$$ −0.253158 + 1.73187i −0.0100860 + 0.0689995i
$$631$$ 27.2013 1.08287 0.541433 0.840744i $$-0.317882\pi$$
0.541433 + 0.840744i $$0.317882\pi$$
$$632$$ 0.745553i 0.0296565i
$$633$$ 8.34254i 0.331586i
$$634$$ −0.113410 −0.00450407
$$635$$ −20.4289 2.98621i −0.810698 0.118504i
$$636$$ 22.4255 0.889231
$$637$$ 20.7249i 0.821152i
$$638$$ 36.8939i 1.46064i
$$639$$ −11.6648 −0.461453
$$640$$ −17.8867 2.61460i −0.707036 0.103351i
$$641$$ −17.6090 −0.695514 −0.347757 0.937585i $$-0.613057\pi$$
−0.347757 + 0.937585i $$0.613057\pi$$
$$642$$ 15.4407i 0.609398i
$$643$$ 8.95765i 0.353255i −0.984278 0.176628i $$-0.943481\pi$$
0.984278 0.176628i $$-0.0565188\pi$$
$$644$$ 3.82414 0.150692
$$645$$ 2.92100 19.9828i 0.115014 0.786822i
$$646$$ 0 0
$$647$$ 49.1850i 1.93366i −0.255416 0.966831i $$-0.582212\pi$$
0.255416 0.966831i $$-0.417788\pi$$
$$648$$ 5.85826i 0.230134i
$$649$$ −14.3279 −0.562419
$$650$$ −27.1603 8.11371i −1.06531 0.318246i
$$651$$ 3.89245 0.152557
$$652$$ 26.6393i 1.04327i
$$653$$ 11.7035i 0.457993i 0.973427 + 0.228997i $$0.0735445\pi$$
−0.973427 + 0.228997i $$0.926456\pi$$
$$654$$ −15.5673 −0.608729
$$655$$ 4.50576 30.8243i 0.176055 1.20441i
$$656$$ −50.3901 −1.96740
$$657$$ 4.39818i 0.171589i
$$658$$ 2.19276i 0.0854826i
$$659$$ −34.7573 −1.35395 −0.676976 0.736005i $$-0.736710\pi$$
−0.676976 + 0.736005i $$0.736710\pi$$
$$660$$ −9.01630 1.31796i −0.350959 0.0513016i
$$661$$ −17.9064 −0.696477 −0.348239 0.937406i $$-0.613220\pi$$
−0.348239 + 0.937406i $$0.613220\pi$$
$$662$$ 32.6153i 1.26763i
$$663$$ 4.33314i 0.168285i
$$664$$ 12.5087 0.485431
$$665$$ 0 0
$$666$$ 9.27219 0.359290
$$667$$ 56.9148i 2.20375i
$$668$$ 3.97578i 0.153828i
$$669$$ −18.6858 −0.722435
$$670$$ 5.28447 36.1516i 0.204157 1.39666i
$$671$$ 17.1607 0.662483
$$672$$ 4.73117i 0.182509i
$$673$$ 10.9828i 0.423355i −0.977340 0.211677i $$-0.932107\pi$$
0.977340 0.211677i $$-0.0678926\pi$$
$$674$$ −12.7980 −0.492961
$$675$$ −8.08605 + 27.0677i −0.311232 + 1.04184i
$$676$$ −5.20180 −0.200069
$$677$$ 4.77520i 0.183526i 0.995781 + 0.0917630i $$0.0292502\pi$$
−0.995781 + 0.0917630i $$0.970750\pi$$
$$678$$ 37.6544i 1.44611i
$$679$$ 2.81567 0.108056
$$680$$ −0.331559 + 2.26822i −0.0127147 + 0.0869824i
$$681$$ 22.6607 0.868359
$$682$$ 20.3175i 0.777995i
$$683$$ 46.0853i 1.76341i 0.471805 + 0.881703i $$0.343603\pi$$
−0.471805 + 0.881703i $$0.656397\pi$$
$$684$$ 0 0
$$685$$ −8.50364 1.24302i −0.324907 0.0474935i
$$686$$ 12.1844 0.465203
$$687$$ 5.49660i 0.209708i
$$688$$ 29.8928i 1.13965i
$$689$$ 32.9643 1.25584
$$690$$ 33.3417 + 4.87373i 1.26930 + 0.185540i
$$691$$ 15.2699 0.580893 0.290447 0.956891i $$-0.406196\pi$$
0.290447 + 0.956891i $$0.406196\pi$$
$$692$$ 12.7703i 0.485453i
$$693$$ 0.827050i 0.0314170i
$$694$$ 13.5705 0.515130
$$695$$ −6.10394 + 41.7576i −0.231536 + 1.58396i
$$696$$ −15.5846 −0.590733
$$697$$ 10.1905i 0.385993i
$$698$$ 4.00362i 0.151539i
$$699$$ 16.1067 0.609210
$$700$$ −0.978496 + 3.27548i −0.0369837 + 0.123801i
$$701$$ −16.6852 −0.630191 −0.315096 0.949060i $$-0.602037\pi$$
−0.315096 + 0.949060i $$0.602037\pi$$
$$702$$ 32.0310i 1.20893i
$$703$$ 0 0
$$704$$ 5.85144 0.220535
$$705$$ −1.16582 + 7.97547i −0.0439073 + 0.300374i
$$706$$ 30.7545 1.15746
$$707$$ 0.123323i 0.00463803i
$$708$$ 15.2409i 0.572789i
$$709$$ −1.95870 −0.0735604 −0.0367802 0.999323i $$-0.511710\pi$$
−0.0367802 + 0.999323i $$0.511710\pi$$
$$710$$ −54.0386 7.89912i −2.02803 0.296449i
$$711$$ 0.626375 0.0234909
$$712$$ 2.26257i 0.0847933i
$$713$$ 31.3429i 1.17380i
$$714$$ 1.25265 0.0468794
$$715$$ −13.2535 1.93733i −0.495652 0.0724522i
$$716$$ 21.8517 0.816637
$$717$$ 15.4887i 0.578438i
$$718$$ 31.6452i 1.18099i
$$719$$ 23.0165 0.858370 0.429185 0.903217i $$-0.358801\pi$$
0.429185 + 0.903217i $$0.358801\pi$$
$$720$$ 1.37742 9.42306i 0.0513334 0.351177i
$$721$$ −6.86382 −0.255622
$$722$$ 0 0
$$723$$ 7.29046i 0.271135i
$$724$$ 12.2267 0.454400
$$725$$ −48.7490 14.5630i −1.81049 0.540856i
$$726$$ 19.3147 0.716837
$$727$$ 10.3883i 0.385279i −0.981270 0.192640i $$-0.938295\pi$$
0.981270 0.192640i $$-0.0617048\pi$$
$$728$$ 1.53924i 0.0570479i
$$729$$ −29.5736 −1.09532
$$730$$ 2.97834 20.3751i 0.110233 0.754116i
$$731$$ 6.04528 0.223593
$$732$$ 18.2543i 0.674698i
$$733$$ 40.7900i 1.50661i −0.657670 0.753306i $$-0.728458\pi$$
0.657670 0.753306i $$-0.271542\pi$$
$$734$$ 36.2395 1.33762
$$735$$ 21.7915 + 3.18538i 0.803791 + 0.117495i
$$736$$ −38.0965 −1.40425
$$737$$ 17.2640i 0.635929i
$$738$$ 17.1559i 0.631517i
$$739$$ 7.92965 0.291697 0.145848 0.989307i $$-0.453409\pi$$
0.145848 + 0.989307i $$0.453409\pi$$
$$740$$ 17.9193 + 2.61936i 0.658726 + 0.0962896i
$$741$$ 0 0
$$742$$ 9.52956i 0.349841i
$$743$$ 7.27911i 0.267045i 0.991046 + 0.133522i $$0.0426288\pi$$
−0.991046 + 0.133522i $$0.957371\pi$$
$$744$$ −8.58244 −0.314648
$$745$$ −7.73845 + 52.9395i −0.283515 + 1.93955i
$$746$$ 12.2205 0.447426
$$747$$ 10.5091i 0.384509i
$$748$$ 2.72765i 0.0997327i
$$749$$ −2.73722 −0.100016
$$750$$ −12.7057 + 27.3110i −0.463948 + 0.997255i
$$751$$ −37.8815 −1.38232 −0.691158 0.722704i $$-0.742899\pi$$
−0.691158 + 0.722704i $$0.742899\pi$$
$$752$$ 11.9307i 0.435068i
$$753$$ 38.0647i 1.38715i
$$754$$ 57.6879 2.10087
$$755$$ 1.90916 13.0607i 0.0694814 0.475329i
$$756$$ −3.86287 −0.140491
$$757$$ 51.1527i 1.85917i 0.368602 + 0.929587i $$0.379837\pi$$
−0.368602 + 0.929587i $$0.620163\pi$$
$$758$$ 40.1189i 1.45718i
$$759$$ 15.9222 0.577938
$$760$$ 0 0
$$761$$ −10.8749 −0.394213 −0.197107 0.980382i $$-0.563155\pi$$
−0.197107 + 0.980382i $$0.563155\pi$$
$$762$$ 24.8759i 0.901158i
$$763$$ 2.75965i 0.0999061i
$$764$$ 23.3291 0.844019
$$765$$ −1.90565 0.278559i −0.0688988 0.0100713i
$$766$$ 45.0539 1.62786
$$767$$ 22.4033i 0.808938i
$$768$$ 30.4764i 1.09972i
$$769$$ 18.8020 0.678016 0.339008 0.940783i $$-0.389909\pi$$
0.339008 + 0.940783i $$0.389909\pi$$
$$770$$ −0.560057 + 3.83140i −0.0201831 + 0.138074i
$$771$$ −32.5820 −1.17341
$$772$$ 23.5761i 0.848521i
$$773$$ 24.3856i 0.877090i 0.898709 + 0.438545i $$0.144506\pi$$
−0.898709 + 0.438545i $$0.855494\pi$$
$$774$$ −10.1773 −0.365817
$$775$$ −26.8461 8.01984i −0.964339 0.288081i
$$776$$ −6.20825 −0.222863
$$777$$ 3.92987i 0.140983i
$$778$$ 29.3105i 1.05083i
$$779$$ 0 0
$$780$$ 2.06079 14.0980i 0.0737880 0.504791i
$$781$$ −25.8059 −0.923408
$$782$$ 10.0867i 0.360698i
$$783$$ 57.4913i 2.05457i
$$784$$ −32.5985 −1.16423
$$785$$ −23.3882 3.41878i −0.834760 0.122021i
$$786$$ 37.5341 1.33880
$$787$$ 9.17617i 0.327095i 0.986535 + 0.163547i $$0.0522937\pi$$
−0.986535