# Properties

 Label 60.2.e.a.11.1 Level $60$ Weight $2$ Character 60.11 Analytic conductor $0.479$ Analytic rank $0$ Dimension $8$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$60 = 2^{2} \cdot 3 \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 60.e (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.479102412128$$ Analytic rank: $$0$$ Dimension: $$8$$ Coefficient field: 8.0.342102016.5 Defining polynomial: $$x^{8} + x^{6} + 4 x^{4} + 4 x^{2} + 16$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 11.1 Root $$-1.17915 + 0.780776i$$ of defining polynomial Character $$\chi$$ $$=$$ 60.11 Dual form 60.2.e.a.11.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.17915 - 0.780776i) q^{2} +(1.51022 + 0.848071i) q^{3} +(0.780776 + 1.84130i) q^{4} +1.00000i q^{5} +(-1.11862 - 2.17915i) q^{6} -3.02045i q^{7} +(0.516994 - 2.78078i) q^{8} +(1.56155 + 2.56155i) q^{9} +O(q^{10})$$ $$q+(-1.17915 - 0.780776i) q^{2} +(1.51022 + 0.848071i) q^{3} +(0.780776 + 1.84130i) q^{4} +1.00000i q^{5} +(-1.11862 - 2.17915i) q^{6} -3.02045i q^{7} +(0.516994 - 2.78078i) q^{8} +(1.56155 + 2.56155i) q^{9} +(0.780776 - 1.17915i) q^{10} -1.32431 q^{11} +(-0.382406 + 3.44293i) q^{12} -5.12311 q^{13} +(-2.35829 + 3.56155i) q^{14} +(-0.848071 + 1.51022i) q^{15} +(-2.78078 + 2.87529i) q^{16} -2.00000i q^{17} +(0.158699 - 4.23967i) q^{18} +1.32431i q^{19} +(-1.84130 + 0.780776i) q^{20} +(2.56155 - 4.56155i) q^{21} +(1.56155 + 1.03399i) q^{22} -0.371834 q^{23} +(3.13907 - 3.76115i) q^{24} -1.00000 q^{25} +(6.04090 + 4.00000i) q^{26} +(0.185917 + 5.19283i) q^{27} +(5.56155 - 2.35829i) q^{28} -3.12311i q^{29} +(2.17915 - 1.11862i) q^{30} -4.71659i q^{31} +(5.52390 - 1.21922i) q^{32} +(-2.00000 - 1.12311i) q^{33} +(-1.56155 + 2.35829i) q^{34} +3.02045 q^{35} +(-3.49737 + 4.87529i) q^{36} +5.12311 q^{37} +(1.03399 - 1.56155i) q^{38} +(-7.73704 - 4.34475i) q^{39} +(2.78078 + 0.516994i) q^{40} +1.12311i q^{41} +(-6.58200 + 3.37874i) q^{42} +7.73704i q^{43} +(-1.03399 - 2.43845i) q^{44} +(-2.56155 + 1.56155i) q^{45} +(0.438447 + 0.290319i) q^{46} -3.02045 q^{47} +(-6.63804 + 1.98403i) q^{48} -2.12311 q^{49} +(1.17915 + 0.780776i) q^{50} +(1.69614 - 3.02045i) q^{51} +(-4.00000 - 9.43318i) q^{52} +12.2462i q^{53} +(3.83521 - 6.26827i) q^{54} -1.32431i q^{55} +(-8.39919 - 1.56155i) q^{56} +(-1.12311 + 2.00000i) q^{57} +(-2.43845 + 3.68260i) q^{58} +14.1498 q^{59} +(-3.44293 - 0.382406i) q^{60} +3.12311 q^{61} +(-3.68260 + 5.56155i) q^{62} +(7.73704 - 4.71659i) q^{63} +(-7.46543 - 2.87529i) q^{64} -5.12311i q^{65} +(1.48140 + 2.88586i) q^{66} -4.34475i q^{67} +(3.68260 - 1.56155i) q^{68} +(-0.561553 - 0.315342i) q^{69} +(-3.56155 - 2.35829i) q^{70} -3.39228 q^{71} +(7.93042 - 3.01802i) q^{72} +8.24621 q^{73} +(-6.04090 - 4.00000i) q^{74} +(-1.51022 - 0.848071i) q^{75} +(-2.43845 + 1.03399i) q^{76} +4.00000i q^{77} +(5.73082 + 11.1640i) q^{78} +8.10887i q^{79} +(-2.87529 - 2.78078i) q^{80} +(-4.12311 + 8.00000i) q^{81} +(0.876894 - 1.32431i) q^{82} -15.1022 q^{83} +(10.3992 + 1.15504i) q^{84} +2.00000 q^{85} +(6.04090 - 9.12311i) q^{86} +(2.64861 - 4.71659i) q^{87} +(-0.684658 + 3.68260i) q^{88} -10.2462i q^{89} +(4.23967 + 0.158699i) q^{90} +15.4741i q^{91} +(-0.290319 - 0.684658i) q^{92} +(4.00000 - 7.12311i) q^{93} +(3.56155 + 2.35829i) q^{94} -1.32431 q^{95} +(9.37632 + 2.84336i) q^{96} -6.00000 q^{97} +(2.50345 + 1.65767i) q^{98} +(-2.06798 - 3.39228i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q - 2q^{4} - 6q^{6} - 4q^{9} + O(q^{10})$$ $$8q - 2q^{4} - 6q^{6} - 4q^{9} - 2q^{10} + 4q^{12} - 8q^{13} - 14q^{16} + 16q^{18} + 4q^{21} - 4q^{22} - 2q^{24} - 8q^{25} + 28q^{28} + 8q^{30} - 16q^{33} + 4q^{34} + 18q^{36} + 8q^{37} + 14q^{40} - 12q^{42} - 4q^{45} + 20q^{46} - 36q^{48} + 16q^{49} - 32q^{52} - 10q^{54} + 24q^{57} - 36q^{58} - 14q^{60} - 8q^{61} - 2q^{64} - 40q^{66} + 12q^{69} - 12q^{70} + 24q^{72} - 36q^{76} + 40q^{78} + 40q^{82} + 16q^{84} + 16q^{85} + 44q^{88} + 18q^{90} + 32q^{93} + 12q^{94} + 42q^{96} - 48q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$$.

 $$n$$ $$31$$ $$37$$ $$41$$ $$\chi(n)$$ $$-1$$ $$1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.17915 0.780776i −0.833783 0.552092i
$$3$$ 1.51022 + 0.848071i 0.871928 + 0.489634i
$$4$$ 0.780776 + 1.84130i 0.390388 + 0.920650i
$$5$$ 1.00000i 0.447214i
$$6$$ −1.11862 2.17915i −0.456676 0.889633i
$$7$$ 3.02045i 1.14162i −0.821081 0.570811i $$-0.806629\pi$$
0.821081 0.570811i $$-0.193371\pi$$
$$8$$ 0.516994 2.78078i 0.182785 0.983153i
$$9$$ 1.56155 + 2.56155i 0.520518 + 0.853851i
$$10$$ 0.780776 1.17915i 0.246903 0.372879i
$$11$$ −1.32431 −0.399294 −0.199647 0.979868i $$-0.563979\pi$$
−0.199647 + 0.979868i $$0.563979\pi$$
$$12$$ −0.382406 + 3.44293i −0.110391 + 0.993888i
$$13$$ −5.12311 −1.42089 −0.710447 0.703751i $$-0.751507\pi$$
−0.710447 + 0.703751i $$0.751507\pi$$
$$14$$ −2.35829 + 3.56155i −0.630281 + 0.951865i
$$15$$ −0.848071 + 1.51022i −0.218971 + 0.389938i
$$16$$ −2.78078 + 2.87529i −0.695194 + 0.718822i
$$17$$ 2.00000i 0.485071i −0.970143 0.242536i $$-0.922021\pi$$
0.970143 0.242536i $$-0.0779791\pi$$
$$18$$ 0.158699 4.23967i 0.0374058 0.999300i
$$19$$ 1.32431i 0.303817i 0.988395 + 0.151908i $$0.0485419\pi$$
−0.988395 + 0.151908i $$0.951458\pi$$
$$20$$ −1.84130 + 0.780776i −0.411727 + 0.174587i
$$21$$ 2.56155 4.56155i 0.558977 0.995412i
$$22$$ 1.56155 + 1.03399i 0.332924 + 0.220447i
$$23$$ −0.371834 −0.0775328 −0.0387664 0.999248i $$-0.512343\pi$$
−0.0387664 + 0.999248i $$0.512343\pi$$
$$24$$ 3.13907 3.76115i 0.640760 0.767741i
$$25$$ −1.00000 −0.200000
$$26$$ 6.04090 + 4.00000i 1.18472 + 0.784465i
$$27$$ 0.185917 + 5.19283i 0.0357798 + 0.999360i
$$28$$ 5.56155 2.35829i 1.05103 0.445676i
$$29$$ 3.12311i 0.579946i −0.957035 0.289973i $$-0.906354\pi$$
0.957035 0.289973i $$-0.0936464\pi$$
$$30$$ 2.17915 1.11862i 0.397856 0.204232i
$$31$$ 4.71659i 0.847124i −0.905867 0.423562i $$-0.860780\pi$$
0.905867 0.423562i $$-0.139220\pi$$
$$32$$ 5.52390 1.21922i 0.976497 0.215530i
$$33$$ −2.00000 1.12311i −0.348155 0.195508i
$$34$$ −1.56155 + 2.35829i −0.267804 + 0.404444i
$$35$$ 3.02045 0.510549
$$36$$ −3.49737 + 4.87529i −0.582894 + 0.812548i
$$37$$ 5.12311 0.842233 0.421117 0.907006i $$-0.361638\pi$$
0.421117 + 0.907006i $$0.361638\pi$$
$$38$$ 1.03399 1.56155i 0.167735 0.253317i
$$39$$ −7.73704 4.34475i −1.23892 0.695718i
$$40$$ 2.78078 + 0.516994i 0.439679 + 0.0817439i
$$41$$ 1.12311i 0.175400i 0.996147 + 0.0876998i $$0.0279516\pi$$
−0.996147 + 0.0876998i $$0.972048\pi$$
$$42$$ −6.58200 + 3.37874i −1.01562 + 0.521351i
$$43$$ 7.73704i 1.17989i 0.807445 + 0.589944i $$0.200850\pi$$
−0.807445 + 0.589944i $$0.799150\pi$$
$$44$$ −1.03399 2.43845i −0.155879 0.367610i
$$45$$ −2.56155 + 1.56155i −0.381854 + 0.232783i
$$46$$ 0.438447 + 0.290319i 0.0646455 + 0.0428052i
$$47$$ −3.02045 −0.440578 −0.220289 0.975435i $$-0.570700\pi$$
−0.220289 + 0.975435i $$0.570700\pi$$
$$48$$ −6.63804 + 1.98403i −0.958119 + 0.286371i
$$49$$ −2.12311 −0.303301
$$50$$ 1.17915 + 0.780776i 0.166757 + 0.110418i
$$51$$ 1.69614 3.02045i 0.237507 0.422947i
$$52$$ −4.00000 9.43318i −0.554700 1.30815i
$$53$$ 12.2462i 1.68215i 0.540921 + 0.841073i $$0.318076\pi$$
−0.540921 + 0.841073i $$0.681924\pi$$
$$54$$ 3.83521 6.26827i 0.521906 0.853003i
$$55$$ 1.32431i 0.178570i
$$56$$ −8.39919 1.56155i −1.12239 0.208671i
$$57$$ −1.12311 + 2.00000i −0.148759 + 0.264906i
$$58$$ −2.43845 + 3.68260i −0.320184 + 0.483549i
$$59$$ 14.1498 1.84214 0.921071 0.389394i $$-0.127315\pi$$
0.921071 + 0.389394i $$0.127315\pi$$
$$60$$ −3.44293 0.382406i −0.444480 0.0493683i
$$61$$ 3.12311 0.399873 0.199936 0.979809i $$-0.435926\pi$$
0.199936 + 0.979809i $$0.435926\pi$$
$$62$$ −3.68260 + 5.56155i −0.467691 + 0.706318i
$$63$$ 7.73704 4.71659i 0.974775 0.594234i
$$64$$ −7.46543 2.87529i −0.933179 0.359411i
$$65$$ 5.12311i 0.635443i
$$66$$ 1.48140 + 2.88586i 0.182348 + 0.355225i
$$67$$ 4.34475i 0.530796i −0.964139 0.265398i $$-0.914497\pi$$
0.964139 0.265398i $$-0.0855034\pi$$
$$68$$ 3.68260 1.56155i 0.446581 0.189366i
$$69$$ −0.561553 0.315342i −0.0676030 0.0379627i
$$70$$ −3.56155 2.35829i −0.425687 0.281870i
$$71$$ −3.39228 −0.402590 −0.201295 0.979531i $$-0.564515\pi$$
−0.201295 + 0.979531i $$0.564515\pi$$
$$72$$ 7.93042 3.01802i 0.934609 0.355677i
$$73$$ 8.24621 0.965146 0.482573 0.875856i $$-0.339702\pi$$
0.482573 + 0.875856i $$0.339702\pi$$
$$74$$ −6.04090 4.00000i −0.702240 0.464991i
$$75$$ −1.51022 0.848071i −0.174386 0.0979267i
$$76$$ −2.43845 + 1.03399i −0.279709 + 0.118607i
$$77$$ 4.00000i 0.455842i
$$78$$ 5.73082 + 11.1640i 0.648888 + 1.26407i
$$79$$ 8.10887i 0.912319i 0.889898 + 0.456160i $$0.150775\pi$$
−0.889898 + 0.456160i $$0.849225\pi$$
$$80$$ −2.87529 2.78078i −0.321467 0.310900i
$$81$$ −4.12311 + 8.00000i −0.458123 + 0.888889i
$$82$$ 0.876894 1.32431i 0.0968368 0.146245i
$$83$$ −15.1022 −1.65769 −0.828843 0.559481i $$-0.811000\pi$$
−0.828843 + 0.559481i $$0.811000\pi$$
$$84$$ 10.3992 + 1.15504i 1.13464 + 0.126025i
$$85$$ 2.00000 0.216930
$$86$$ 6.04090 9.12311i 0.651407 0.983770i
$$87$$ 2.64861 4.71659i 0.283961 0.505671i
$$88$$ −0.684658 + 3.68260i −0.0729848 + 0.392567i
$$89$$ 10.2462i 1.08610i −0.839702 0.543048i $$-0.817270\pi$$
0.839702 0.543048i $$-0.182730\pi$$
$$90$$ 4.23967 + 0.158699i 0.446901 + 0.0167284i
$$91$$ 15.4741i 1.62212i
$$92$$ −0.290319 0.684658i −0.0302679 0.0713806i
$$93$$ 4.00000 7.12311i 0.414781 0.738632i
$$94$$ 3.56155 + 2.35829i 0.367346 + 0.243240i
$$95$$ −1.32431 −0.135871
$$96$$ 9.37632 + 2.84336i 0.956966 + 0.290199i
$$97$$ −6.00000 −0.609208 −0.304604 0.952479i $$-0.598524\pi$$
−0.304604 + 0.952479i $$0.598524\pi$$
$$98$$ 2.50345 + 1.65767i 0.252887 + 0.167450i
$$99$$ −2.06798 3.39228i −0.207839 0.340937i
$$100$$ −0.780776 1.84130i −0.0780776 0.184130i
$$101$$ 0.876894i 0.0872543i 0.999048 + 0.0436271i $$0.0138914\pi$$
−0.999048 + 0.0436271i $$0.986109\pi$$
$$102$$ −4.35829 + 2.23725i −0.431535 + 0.221520i
$$103$$ 9.80501i 0.966117i −0.875588 0.483058i $$-0.839526\pi$$
0.875588 0.483058i $$-0.160474\pi$$
$$104$$ −2.64861 + 14.2462i −0.259718 + 1.39696i
$$105$$ 4.56155 + 2.56155i 0.445162 + 0.249982i
$$106$$ 9.56155 14.4401i 0.928700 1.40255i
$$107$$ 3.02045 0.291998 0.145999 0.989285i $$-0.453360\pi$$
0.145999 + 0.989285i $$0.453360\pi$$
$$108$$ −9.41639 + 4.39676i −0.906093 + 0.423079i
$$109$$ −0.876894 −0.0839912 −0.0419956 0.999118i $$-0.513372\pi$$
−0.0419956 + 0.999118i $$0.513372\pi$$
$$110$$ −1.03399 + 1.56155i −0.0985868 + 0.148888i
$$111$$ 7.73704 + 4.34475i 0.734367 + 0.412386i
$$112$$ 8.68466 + 8.39919i 0.820623 + 0.793649i
$$113$$ 14.0000i 1.31701i −0.752577 0.658505i $$-0.771189\pi$$
0.752577 0.658505i $$-0.228811\pi$$
$$114$$ 2.88586 1.48140i 0.270286 0.138746i
$$115$$ 0.371834i 0.0346737i
$$116$$ 5.75058 2.43845i 0.533928 0.226404i
$$117$$ −8.00000 13.1231i −0.739600 1.21323i
$$118$$ −16.6847 11.0478i −1.53595 1.01703i
$$119$$ −6.04090 −0.553768
$$120$$ 3.76115 + 3.13907i 0.343344 + 0.286557i
$$121$$ −9.24621 −0.840565
$$122$$ −3.68260 2.43845i −0.333407 0.220767i
$$123$$ −0.952473 + 1.69614i −0.0858816 + 0.152936i
$$124$$ 8.68466 3.68260i 0.779905 0.330707i
$$125$$ 1.00000i 0.0894427i
$$126$$ −12.8057 0.479343i −1.14082 0.0427033i
$$127$$ 15.1022i 1.34011i 0.742313 + 0.670054i $$0.233729\pi$$
−0.742313 + 0.670054i $$0.766271\pi$$
$$128$$ 6.55789 + 9.21922i 0.579641 + 0.814872i
$$129$$ −6.56155 + 11.6847i −0.577713 + 1.02878i
$$130$$ −4.00000 + 6.04090i −0.350823 + 0.529822i
$$131$$ −5.46026 −0.477065 −0.238532 0.971135i $$-0.576666\pi$$
−0.238532 + 0.971135i $$0.576666\pi$$
$$132$$ 0.506422 4.55950i 0.0440784 0.396853i
$$133$$ 4.00000 0.346844
$$134$$ −3.39228 + 5.12311i −0.293049 + 0.442569i
$$135$$ −5.19283 + 0.185917i −0.446927 + 0.0160012i
$$136$$ −5.56155 1.03399i −0.476899 0.0886637i
$$137$$ 8.24621i 0.704521i 0.935902 + 0.352261i $$0.114587\pi$$
−0.935902 + 0.352261i $$0.885413\pi$$
$$138$$ 0.415942 + 0.810281i 0.0354074 + 0.0689757i
$$139$$ 17.5420i 1.48790i −0.668237 0.743949i $$-0.732951\pi$$
0.668237 0.743949i $$-0.267049\pi$$
$$140$$ 2.35829 + 5.56155i 0.199312 + 0.470037i
$$141$$ −4.56155 2.56155i −0.384152 0.215722i
$$142$$ 4.00000 + 2.64861i 0.335673 + 0.222267i
$$143$$ 6.78456 0.567354
$$144$$ −11.7075 2.63319i −0.975628 0.219433i
$$145$$ 3.12311 0.259360
$$146$$ −9.72350 6.43845i −0.804722 0.532850i
$$147$$ −3.20636 1.80054i −0.264457 0.148506i
$$148$$ 4.00000 + 9.43318i 0.328798 + 0.775402i
$$149$$ 14.0000i 1.14692i 0.819232 + 0.573462i $$0.194400\pi$$
−0.819232 + 0.573462i $$0.805600\pi$$
$$150$$ 1.11862 + 2.17915i 0.0913352 + 0.177927i
$$151$$ 7.36520i 0.599372i −0.954038 0.299686i $$-0.903118\pi$$
0.954038 0.299686i $$-0.0968819\pi$$
$$152$$ 3.68260 + 0.684658i 0.298698 + 0.0555331i
$$153$$ 5.12311 3.12311i 0.414179 0.252488i
$$154$$ 3.12311 4.71659i 0.251667 0.380074i
$$155$$ 4.71659 0.378846
$$156$$ 1.95910 17.6385i 0.156854 1.41221i
$$157$$ −3.36932 −0.268901 −0.134450 0.990920i $$-0.542927\pi$$
−0.134450 + 0.990920i $$0.542927\pi$$
$$158$$ 6.33122 9.56155i 0.503684 0.760676i
$$159$$ −10.3857 + 18.4945i −0.823636 + 1.46671i
$$160$$ 1.21922 + 5.52390i 0.0963881 + 0.436703i
$$161$$ 1.12311i 0.0885131i
$$162$$ 11.1080 6.21395i 0.872724 0.488214i
$$163$$ 15.6829i 1.22838i −0.789159 0.614189i $$-0.789483\pi$$
0.789159 0.614189i $$-0.210517\pi$$
$$164$$ −2.06798 + 0.876894i −0.161482 + 0.0684739i
$$165$$ 1.12311 2.00000i 0.0874337 0.155700i
$$166$$ 17.8078 + 11.7915i 1.38215 + 0.915196i
$$167$$ 9.06134 0.701188 0.350594 0.936528i $$-0.385980\pi$$
0.350594 + 0.936528i $$0.385980\pi$$
$$168$$ −11.3604 9.48140i −0.876470 0.731506i
$$169$$ 13.2462 1.01894
$$170$$ −2.35829 1.56155i −0.180873 0.119766i
$$171$$ −3.39228 + 2.06798i −0.259414 + 0.158142i
$$172$$ −14.2462 + 6.04090i −1.08626 + 0.460614i
$$173$$ 2.00000i 0.152057i −0.997106 0.0760286i $$-0.975776\pi$$
0.997106 0.0760286i $$-0.0242240\pi$$
$$174$$ −6.80571 + 3.49358i −0.515939 + 0.264847i
$$175$$ 3.02045i 0.228324i
$$176$$ 3.68260 3.80776i 0.277587 0.287021i
$$177$$ 21.3693 + 12.0000i 1.60622 + 0.901975i
$$178$$ −8.00000 + 12.0818i −0.599625 + 0.905569i
$$179$$ 10.0138 0.748468 0.374234 0.927334i $$-0.377906\pi$$
0.374234 + 0.927334i $$0.377906\pi$$
$$180$$ −4.87529 3.49737i −0.363383 0.260678i
$$181$$ −12.2462 −0.910254 −0.455127 0.890427i $$-0.650406\pi$$
−0.455127 + 0.890427i $$0.650406\pi$$
$$182$$ 12.0818 18.2462i 0.895562 1.35250i
$$183$$ 4.71659 + 2.64861i 0.348660 + 0.195791i
$$184$$ −0.192236 + 1.03399i −0.0141718 + 0.0762266i
$$185$$ 5.12311i 0.376658i
$$186$$ −10.2781 + 5.27608i −0.753630 + 0.386861i
$$187$$ 2.64861i 0.193686i
$$188$$ −2.35829 5.56155i −0.171996 0.405618i
$$189$$ 15.6847 0.561553i 1.14089 0.0408470i
$$190$$ 1.56155 + 1.03399i 0.113287 + 0.0750133i
$$191$$ 24.9073 1.80223 0.901113 0.433585i $$-0.142752\pi$$
0.901113 + 0.433585i $$0.142752\pi$$
$$192$$ −8.83603 10.6735i −0.637686 0.770297i
$$193$$ −0.246211 −0.0177227 −0.00886134 0.999961i $$-0.502821\pi$$
−0.00886134 + 0.999961i $$0.502821\pi$$
$$194$$ 7.07488 + 4.68466i 0.507947 + 0.336339i
$$195$$ 4.34475 7.73704i 0.311134 0.554061i
$$196$$ −1.65767 3.90928i −0.118405 0.279234i
$$197$$ 4.24621i 0.302530i −0.988493 0.151265i $$-0.951665\pi$$
0.988493 0.151265i $$-0.0483347\pi$$
$$198$$ −0.210167 + 5.61463i −0.0149359 + 0.399014i
$$199$$ 5.46026i 0.387067i 0.981094 + 0.193534i $$0.0619949\pi$$
−0.981094 + 0.193534i $$0.938005\pi$$
$$200$$ −0.516994 + 2.78078i −0.0365570 + 0.196631i
$$201$$ 3.68466 6.56155i 0.259896 0.462816i
$$202$$ 0.684658 1.03399i 0.0481724 0.0727511i
$$203$$ −9.43318 −0.662079
$$204$$ 6.88586 + 0.764811i 0.482107 + 0.0535475i
$$205$$ −1.12311 −0.0784411
$$206$$ −7.65552 + 11.5616i −0.533385 + 0.805532i
$$207$$ −0.580639 0.952473i −0.0403572 0.0662014i
$$208$$ 14.2462 14.7304i 0.987797 1.02137i
$$209$$ 1.75379i 0.121312i
$$210$$ −3.37874 6.58200i −0.233155 0.454201i
$$211$$ 16.7984i 1.15645i −0.815878 0.578224i $$-0.803746\pi$$
0.815878 0.578224i $$-0.196254\pi$$
$$212$$ −22.5490 + 9.56155i −1.54867 + 0.656690i
$$213$$ −5.12311 2.87689i −0.351029 0.197122i
$$214$$ −3.56155 2.35829i −0.243463 0.161210i
$$215$$ −7.73704 −0.527662
$$216$$ 14.5362 + 2.16766i 0.989063 + 0.147491i
$$217$$ −14.2462 −0.967096
$$218$$ 1.03399 + 0.684658i 0.0700305 + 0.0463709i
$$219$$ 12.4536 + 6.99337i 0.841538 + 0.472568i
$$220$$ 2.43845 1.03399i 0.164400 0.0697114i
$$221$$ 10.2462i 0.689235i
$$222$$ −5.73082 11.1640i −0.384628 0.749279i
$$223$$ 8.31768i 0.556993i 0.960437 + 0.278496i $$0.0898360\pi$$
−0.960437 + 0.278496i $$0.910164\pi$$
$$224$$ −3.68260 16.6847i −0.246054 1.11479i
$$225$$ −1.56155 2.56155i −0.104104 0.170770i
$$226$$ −10.9309 + 16.5081i −0.727111 + 1.09810i
$$227$$ −21.8868 −1.45268 −0.726339 0.687337i $$-0.758780\pi$$
−0.726339 + 0.687337i $$0.758780\pi$$
$$228$$ −4.55950 0.506422i −0.301960 0.0335386i
$$229$$ −16.2462 −1.07358 −0.536790 0.843716i $$-0.680363\pi$$
−0.536790 + 0.843716i $$0.680363\pi$$
$$230$$ −0.290319 + 0.438447i −0.0191431 + 0.0289104i
$$231$$ −3.39228 + 6.04090i −0.223196 + 0.397462i
$$232$$ −8.68466 1.61463i −0.570176 0.106005i
$$233$$ 10.0000i 0.655122i 0.944830 + 0.327561i $$0.106227\pi$$
−0.944830 + 0.327561i $$0.893773\pi$$
$$234$$ −0.813033 + 21.7203i −0.0531497 + 1.41990i
$$235$$ 3.02045i 0.197032i
$$236$$ 11.0478 + 26.0540i 0.719151 + 1.69597i
$$237$$ −6.87689 + 12.2462i −0.446702 + 0.795477i
$$238$$ 7.12311 + 4.71659i 0.461722 + 0.305731i
$$239$$ −17.3790 −1.12416 −0.562078 0.827084i $$-0.689998\pi$$
−0.562078 + 0.827084i $$0.689998\pi$$
$$240$$ −1.98403 6.63804i −0.128069 0.428484i
$$241$$ 13.3693 0.861193 0.430597 0.902544i $$-0.358303\pi$$
0.430597 + 0.902544i $$0.358303\pi$$
$$242$$ 10.9026 + 7.21922i 0.700849 + 0.464069i
$$243$$ −13.0114 + 8.58511i −0.834680 + 0.550735i
$$244$$ 2.43845 + 5.75058i 0.156106 + 0.368143i
$$245$$ 2.12311i 0.135640i
$$246$$ 2.44741 1.25633i 0.156041 0.0801008i
$$247$$ 6.78456i 0.431691i
$$248$$ −13.1158 2.43845i −0.832853 0.154842i
$$249$$ −22.8078 12.8078i −1.44538 0.811659i
$$250$$ −0.780776 + 1.17915i −0.0493806 + 0.0745758i
$$251$$ −18.7033 −1.18054 −0.590272 0.807205i $$-0.700979\pi$$
−0.590272 + 0.807205i $$0.700979\pi$$
$$252$$ 14.7256 + 10.5636i 0.927623 + 0.665445i
$$253$$ 0.492423 0.0309583
$$254$$ 11.7915 17.8078i 0.739863 1.11736i
$$255$$ 3.02045 + 1.69614i 0.189148 + 0.106216i
$$256$$ −0.534565 15.9911i −0.0334103 0.999442i
$$257$$ 30.4924i 1.90207i −0.309091 0.951033i $$-0.600025\pi$$
0.309091 0.951033i $$-0.399975\pi$$
$$258$$ 16.8601 8.65483i 1.04967 0.538826i
$$259$$ 15.4741i 0.961512i
$$260$$ 9.43318 4.00000i 0.585021 0.248069i
$$261$$ 8.00000 4.87689i 0.495188 0.301872i
$$262$$ 6.43845 + 4.26324i 0.397769 + 0.263384i
$$263$$ 23.7917 1.46706 0.733531 0.679656i $$-0.237871\pi$$
0.733531 + 0.679656i $$0.237871\pi$$
$$264$$ −4.15709 + 4.98091i −0.255851 + 0.306554i
$$265$$ −12.2462 −0.752279
$$266$$ −4.71659 3.12311i −0.289193 0.191490i
$$267$$ 8.68951 15.4741i 0.531789 0.946998i
$$268$$ 8.00000 3.39228i 0.488678 0.207217i
$$269$$ 14.0000i 0.853595i −0.904347 0.426798i $$-0.859642\pi$$
0.904347 0.426798i $$-0.140358\pi$$
$$270$$ 6.26827 + 3.83521i 0.381474 + 0.233404i
$$271$$ 15.3110i 0.930080i 0.885290 + 0.465040i $$0.153960\pi$$
−0.885290 + 0.465040i $$0.846040\pi$$
$$272$$ 5.75058 + 5.56155i 0.348680 + 0.337219i
$$273$$ −13.1231 + 23.3693i −0.794246 + 1.41438i
$$274$$ 6.43845 9.72350i 0.388961 0.587418i
$$275$$ 1.32431 0.0798587
$$276$$ 0.142191 1.28020i 0.00855892 0.0770589i
$$277$$ 23.3693 1.40413 0.702063 0.712115i $$-0.252262\pi$$
0.702063 + 0.712115i $$0.252262\pi$$
$$278$$ −13.6964 + 20.6847i −0.821457 + 1.24058i
$$279$$ 12.0818 7.36520i 0.723318 0.440943i
$$280$$ 1.56155 8.39919i 0.0933206 0.501948i
$$281$$ 13.6155i 0.812234i −0.913821 0.406117i $$-0.866882\pi$$
0.913821 0.406117i $$-0.133118\pi$$
$$282$$ 3.37874 + 6.58200i 0.201201 + 0.391952i
$$283$$ 23.2111i 1.37976i 0.723925 + 0.689879i $$0.242336\pi$$
−0.723925 + 0.689879i $$0.757664\pi$$
$$284$$ −2.64861 6.24621i −0.157166 0.370644i
$$285$$ −2.00000 1.12311i −0.118470 0.0665270i
$$286$$ −8.00000 5.29723i −0.473050 0.313232i
$$287$$ 3.39228 0.200240
$$288$$ 11.7490 + 12.2459i 0.692315 + 0.721596i
$$289$$ 13.0000 0.764706
$$290$$ −3.68260 2.43845i −0.216250 0.143191i
$$291$$ −9.06134 5.08842i −0.531185 0.298289i
$$292$$ 6.43845 + 15.1838i 0.376782 + 0.888562i
$$293$$ 2.49242i 0.145609i −0.997346 0.0728044i $$-0.976805\pi$$
0.997346 0.0728044i $$-0.0231949\pi$$
$$294$$ 2.37495 + 4.62656i 0.138510 + 0.269826i
$$295$$ 14.1498i 0.823831i
$$296$$ 2.64861 14.2462i 0.153948 0.828044i
$$297$$ −0.246211 6.87689i −0.0142866 0.399038i
$$298$$ 10.9309 16.5081i 0.633208 0.956286i
$$299$$ 1.90495 0.110166
$$300$$ 0.382406 3.44293i 0.0220782 0.198778i
$$301$$ 23.3693 1.34699
$$302$$ −5.75058 + 8.68466i −0.330908 + 0.499746i
$$303$$ −0.743668 + 1.32431i −0.0427226 + 0.0760794i
$$304$$ −3.80776 3.68260i −0.218390 0.211212i
$$305$$ 3.12311i 0.178829i
$$306$$ −8.47934 0.317399i −0.484732 0.0181445i
$$307$$ 11.1293i 0.635184i 0.948227 + 0.317592i $$0.102874\pi$$
−0.948227 + 0.317592i $$0.897126\pi$$
$$308$$ −7.36520 + 3.12311i −0.419671 + 0.177955i
$$309$$ 8.31534 14.8078i 0.473043 0.842384i
$$310$$ −5.56155 3.68260i −0.315875 0.209158i
$$311$$ −20.7713 −1.17783 −0.588916 0.808194i $$-0.700445\pi$$
−0.588916 + 0.808194i $$0.700445\pi$$
$$312$$ −16.0818 + 19.2688i −0.910452 + 1.09088i
$$313$$ −22.4924 −1.27135 −0.635673 0.771958i $$-0.719278\pi$$
−0.635673 + 0.771958i $$0.719278\pi$$
$$314$$ 3.97292 + 2.63068i 0.224205 + 0.148458i
$$315$$ 4.71659 + 7.73704i 0.265750 + 0.435933i
$$316$$ −14.9309 + 6.33122i −0.839927 + 0.356159i
$$317$$ 16.7386i 0.940135i 0.882630 + 0.470068i $$0.155770\pi$$
−0.882630 + 0.470068i $$0.844230\pi$$
$$318$$ 26.6863 13.6989i 1.49649 0.768196i
$$319$$ 4.13595i 0.231569i
$$320$$ 2.87529 7.46543i 0.160734 0.417330i
$$321$$ 4.56155 + 2.56155i 0.254601 + 0.142972i
$$322$$ 0.876894 1.32431i 0.0488674 0.0738007i
$$323$$ 2.64861 0.147373
$$324$$ −17.9496 1.34567i −0.997202 0.0747592i
$$325$$ 5.12311 0.284179
$$326$$ −12.2448 + 18.4924i −0.678178 + 1.02420i
$$327$$ −1.32431 0.743668i −0.0732343 0.0411249i
$$328$$ 3.12311 + 0.580639i 0.172445 + 0.0320604i
$$329$$ 9.12311i 0.502973i
$$330$$ −2.88586 + 1.48140i −0.158861 + 0.0815484i
$$331$$ 3.22925i 0.177496i −0.996054 0.0887479i $$-0.971713\pi$$
0.996054 0.0887479i $$-0.0282865\pi$$
$$332$$ −11.7915 27.8078i −0.647141 1.52615i
$$333$$ 8.00000 + 13.1231i 0.438397 + 0.719142i
$$334$$ −10.6847 7.07488i −0.584638 0.387120i
$$335$$ 4.34475 0.237379
$$336$$ 5.99267 + 20.0499i 0.326927 + 1.09381i
$$337$$ −1.50758 −0.0821230 −0.0410615 0.999157i $$-0.513074\pi$$
−0.0410615 + 0.999157i $$0.513074\pi$$
$$338$$ −15.6192 10.3423i −0.849574 0.562549i
$$339$$ 11.8730 21.1431i 0.644852 1.14834i
$$340$$ 1.56155 + 3.68260i 0.0846871 + 0.199717i
$$341$$ 6.24621i 0.338251i
$$342$$ 5.61463 + 0.210167i 0.303604 + 0.0113645i
$$343$$ 14.7304i 0.795367i
$$344$$ 21.5150 + 4.00000i 1.16001 + 0.215666i
$$345$$ 0.315342 0.561553i 0.0169774 0.0302330i
$$346$$ −1.56155 + 2.35829i −0.0839496 + 0.126783i
$$347$$ 22.6305 1.21487 0.607434 0.794370i $$-0.292199\pi$$
0.607434 + 0.794370i $$0.292199\pi$$
$$348$$ 10.7526 + 1.19429i 0.576402 + 0.0640208i
$$349$$ −14.0000 −0.749403 −0.374701 0.927146i $$-0.622255\pi$$
−0.374701 + 0.927146i $$0.622255\pi$$
$$350$$ 2.35829 3.56155i 0.126056 0.190373i
$$351$$ −0.952473 26.6034i −0.0508392 1.41998i
$$352$$ −7.31534 + 1.61463i −0.389909 + 0.0860599i
$$353$$ 20.2462i 1.07760i 0.842435 + 0.538799i $$0.181122\pi$$
−0.842435 + 0.538799i $$0.818878\pi$$
$$354$$ −15.8283 30.8344i −0.841262 1.63883i
$$355$$ 3.39228i 0.180044i
$$356$$ 18.8664 8.00000i 0.999915 0.423999i
$$357$$ −9.12311 5.12311i −0.482846 0.271144i
$$358$$ −11.8078 7.81855i −0.624060 0.413223i
$$359$$ −21.5150 −1.13552 −0.567758 0.823195i $$-0.692189\pi$$
−0.567758 + 0.823195i $$0.692189\pi$$
$$360$$ 3.01802 + 7.93042i 0.159064 + 0.417970i
$$361$$ 17.2462 0.907695
$$362$$ 14.4401 + 9.56155i 0.758954 + 0.502544i
$$363$$ −13.9638 7.84144i −0.732912 0.411569i
$$364$$ −28.4924 + 12.0818i −1.49341 + 0.633258i
$$365$$ 8.24621i 0.431626i
$$366$$ −3.49358 6.80571i −0.182612 0.355740i
$$367$$ 10.9663i 0.572436i −0.958165 0.286218i $$-0.907602\pi$$
0.958165 0.286218i $$-0.0923981\pi$$
$$368$$ 1.03399 1.06913i 0.0539003 0.0557323i
$$369$$ −2.87689 + 1.75379i −0.149765 + 0.0912986i
$$370$$ 4.00000 6.04090i 0.207950 0.314051i
$$371$$ 36.9890 1.92038
$$372$$ 16.2389 + 1.80365i 0.841947 + 0.0935149i
$$373$$ −9.12311 −0.472377 −0.236188 0.971707i $$-0.575898\pi$$
−0.236188 + 0.971707i $$0.575898\pi$$
$$374$$ 2.06798 3.12311i 0.106932 0.161492i
$$375$$ 0.848071 1.51022i 0.0437942 0.0779876i
$$376$$ −1.56155 + 8.39919i −0.0805309 + 0.433155i
$$377$$ 16.0000i 0.824042i
$$378$$ −18.9330 11.5841i −0.973807 0.595820i
$$379$$ 18.7033i 0.960725i 0.877070 + 0.480363i $$0.159495\pi$$
−0.877070 + 0.480363i $$0.840505\pi$$
$$380$$ −1.03399 2.43845i −0.0530424 0.125090i
$$381$$ −12.8078 + 22.8078i −0.656162 + 1.16848i
$$382$$ −29.3693 19.4470i −1.50266 0.994995i
$$383$$ 15.1022 0.771688 0.385844 0.922564i $$-0.373910\pi$$
0.385844 + 0.922564i $$0.373910\pi$$
$$384$$ 2.08533 + 19.4846i 0.106417 + 0.994322i
$$385$$ −4.00000 −0.203859
$$386$$ 0.290319 + 0.192236i 0.0147769 + 0.00978455i
$$387$$ −19.8188 + 12.0818i −1.00745 + 0.614152i
$$388$$ −4.68466 11.0478i −0.237827 0.560867i
$$389$$ 20.7386i 1.05149i 0.850642 + 0.525745i $$0.176213\pi$$
−0.850642 + 0.525745i $$0.823787\pi$$
$$390$$ −11.1640 + 5.73082i −0.565311 + 0.290192i
$$391$$ 0.743668i 0.0376089i
$$392$$ −1.09763 + 5.90388i −0.0554388 + 0.298191i
$$393$$ −8.24621 4.63068i −0.415966 0.233587i
$$394$$ −3.31534 + 5.00691i −0.167024 + 0.252244i
$$395$$ −8.10887 −0.408002
$$396$$ 4.63159 6.45638i 0.232746 0.324445i
$$397$$ 14.8769 0.746650 0.373325 0.927701i $$-0.378218\pi$$
0.373325 + 0.927701i $$0.378218\pi$$
$$398$$ 4.26324 6.43845i 0.213697 0.322730i
$$399$$ 6.04090 + 3.39228i 0.302423 + 0.169827i
$$400$$ 2.78078 2.87529i 0.139039 0.143764i
$$401$$ 24.0000i 1.19850i −0.800561 0.599251i $$-0.795465\pi$$
0.800561 0.599251i $$-0.204535\pi$$
$$402$$ −9.46786 + 4.86014i −0.472214 + 0.242402i
$$403$$ 24.1636i 1.20367i
$$404$$ −1.61463 + 0.684658i −0.0803307 + 0.0340630i
$$405$$ −8.00000 4.12311i −0.397523 0.204879i
$$406$$ 11.1231 + 7.36520i 0.552030 + 0.365529i
$$407$$ −6.78456 −0.336298
$$408$$ −7.52230 6.27814i −0.372409 0.310814i
$$409$$ 25.3693 1.25443 0.627216 0.778845i $$-0.284194\pi$$
0.627216 + 0.778845i $$0.284194\pi$$
$$410$$ 1.32431 + 0.876894i 0.0654029 + 0.0433067i
$$411$$ −6.99337 + 12.4536i −0.344957 + 0.614292i
$$412$$ 18.0540 7.65552i 0.889456 0.377161i
$$413$$ 42.7386i 2.10303i
$$414$$ −0.0590098 + 1.57645i −0.00290017 + 0.0774785i
$$415$$ 15.1022i 0.741340i
$$416$$ −28.2995 + 6.24621i −1.38750 + 0.306246i
$$417$$ 14.8769 26.4924i 0.728525 1.29734i
$$418$$ −1.36932 + 2.06798i −0.0669755 + 0.101148i
$$419$$ −7.36520 −0.359814 −0.179907 0.983684i $$-0.557580\pi$$
−0.179907 + 0.983684i $$0.557580\pi$$
$$420$$ −1.15504 + 10.3992i −0.0563600 + 0.507429i
$$421$$ −25.3693 −1.23642 −0.618212 0.786011i $$-0.712143\pi$$
−0.618212 + 0.786011i $$0.712143\pi$$
$$422$$ −13.1158 + 19.8078i −0.638466 + 0.964227i
$$423$$ −4.71659 7.73704i −0.229328 0.376188i
$$424$$ 34.0540 + 6.33122i 1.65381 + 0.307471i
$$425$$ 2.00000i 0.0970143i
$$426$$ 3.79468 + 7.39228i 0.183853 + 0.358157i
$$427$$ 9.43318i 0.456503i
$$428$$ 2.35829 + 5.56155i 0.113992 + 0.268828i
$$429$$ 10.2462 + 5.75379i 0.494692 + 0.277796i
$$430$$ 9.12311 + 6.04090i 0.439955 + 0.291318i
$$431$$ 16.6354 0.801297 0.400648 0.916232i $$-0.368785\pi$$
0.400648 + 0.916232i $$0.368785\pi$$
$$432$$ −15.4479 13.9055i −0.743236 0.669030i
$$433$$ 18.0000 0.865025 0.432512 0.901628i $$-0.357627\pi$$
0.432512 + 0.901628i $$0.357627\pi$$
$$434$$ 16.7984 + 11.1231i 0.806348 + 0.533926i
$$435$$ 4.71659 + 2.64861i 0.226143 + 0.126991i
$$436$$ −0.684658 1.61463i −0.0327892 0.0773266i
$$437$$ 0.492423i 0.0235558i
$$438$$ −9.22440 17.9697i −0.440759 0.858626i
$$439$$ 9.27015i 0.442440i 0.975224 + 0.221220i $$0.0710039\pi$$
−0.975224 + 0.221220i $$0.928996\pi$$
$$440$$ −3.68260 0.684658i −0.175561 0.0326398i
$$441$$ −3.31534 5.43845i −0.157873 0.258974i
$$442$$ 8.00000 12.0818i 0.380521 0.574672i
$$443$$ 16.5896 0.788195 0.394097 0.919069i $$-0.371057\pi$$
0.394097 + 0.919069i $$0.371057\pi$$
$$444$$ −1.95910 + 17.6385i −0.0929750 + 0.837086i
$$445$$ 10.2462 0.485717
$$446$$ 6.49424 9.80776i 0.307511 0.464411i
$$447$$ −11.8730 + 21.1431i −0.561573 + 1.00004i
$$448$$ −8.68466 + 22.5490i −0.410312 + 1.06534i
$$449$$ 27.3693i 1.29164i 0.763491 + 0.645819i $$0.223484\pi$$
−0.763491 + 0.645819i $$0.776516\pi$$
$$450$$ −0.158699 + 4.23967i −0.00748116 + 0.199860i
$$451$$ 1.48734i 0.0700359i
$$452$$ 25.7782 10.9309i 1.21250 0.514145i
$$453$$ 6.24621 11.1231i 0.293473 0.522609i
$$454$$ 25.8078 + 17.0887i 1.21122 + 0.802012i
$$455$$ −15.4741 −0.725436
$$456$$ 4.98091 + 4.15709i 0.233253 + 0.194674i
$$457$$ −10.0000 −0.467780 −0.233890 0.972263i $$-0.575146\pi$$
−0.233890 + 0.972263i $$0.575146\pi$$
$$458$$ 19.1567 + 12.6847i 0.895133 + 0.592715i
$$459$$ 10.3857 0.371834i 0.484761 0.0173557i
$$460$$ 0.684658 0.290319i 0.0319224 0.0135362i
$$461$$ 41.8617i 1.94970i −0.222872 0.974848i $$-0.571543\pi$$
0.222872 0.974848i $$-0.428457\pi$$
$$462$$ 8.71659 4.47449i 0.405532 0.208172i
$$463$$ 3.02045i 0.140372i 0.997534 + 0.0701861i $$0.0223593\pi$$
−0.997534 + 0.0701861i $$0.977641\pi$$
$$464$$ 8.97983 + 8.68466i 0.416878 + 0.403175i
$$465$$ 7.12311 + 4.00000i 0.330326 + 0.185496i
$$466$$ 7.80776 11.7915i 0.361688 0.546229i
$$467$$ −2.27678 −0.105357 −0.0526784 0.998612i $$-0.516776\pi$$
−0.0526784 + 0.998612i $$0.516776\pi$$
$$468$$ 17.9174 24.9766i 0.828231 1.15454i
$$469$$ −13.1231 −0.605969
$$470$$ −2.35829 + 3.56155i −0.108780 + 0.164282i
$$471$$ −5.08842 2.85742i −0.234462 0.131663i
$$472$$ 7.31534 39.3473i 0.336716 1.81111i
$$473$$ 10.2462i 0.471121i
$$474$$ 17.6704 9.07077i 0.811629 0.416634i
$$475$$ 1.32431i 0.0607634i
$$476$$ −4.71659 11.1231i −0.216184 0.509827i
$$477$$ −31.3693 + 19.1231i −1.43630 + 0.875587i
$$478$$ 20.4924 + 13.5691i 0.937302 + 0.620637i
$$479$$ −25.6509 −1.17202 −0.586010 0.810304i $$-0.699302\pi$$
−0.586010 + 0.810304i $$0.699302\pi$$
$$480$$ −2.84336 + 9.37632i −0.129781 + 0.427968i
$$481$$ −26.2462 −1.19672
$$482$$ −15.7644 10.4384i −0.718048 0.475458i
$$483$$ −0.952473 + 1.69614i −0.0433390 + 0.0771771i
$$484$$ −7.21922 17.0251i −0.328147 0.773866i
$$485$$ 6.00000i 0.272446i
$$486$$ 22.0454 + 0.0358705i 0.999999 + 0.00162712i
$$487$$ 25.2791i 1.14550i −0.819728 0.572752i $$-0.805876\pi$$
0.819728 0.572752i $$-0.194124\pi$$
$$488$$ 1.61463 8.68466i 0.0730907 0.393136i
$$489$$ 13.3002 23.6847i 0.601455 1.07106i
$$490$$ −1.65767 + 2.50345i −0.0748859 + 0.113095i
$$491$$ −26.9752 −1.21737 −0.608687 0.793410i $$-0.708304\pi$$
−0.608687 + 0.793410i $$0.708304\pi$$
$$492$$ −3.86677 0.429482i −0.174328 0.0193625i
$$493$$ −6.24621 −0.281315
$$494$$ −5.29723 + 8.00000i −0.238334 + 0.359937i
$$495$$ 3.39228 2.06798i 0.152472 0.0929486i
$$496$$ 13.5616 + 13.1158i 0.608932 + 0.588916i
$$497$$ 10.2462i 0.459605i
$$498$$ 16.8937 + 32.9100i 0.757025 + 1.47473i
$$499$$ 32.2725i 1.44471i 0.691521 + 0.722357i $$0.256941\pi$$
−0.691521 + 0.722357i $$0.743059\pi$$
$$500$$ 1.84130 0.780776i 0.0823455 0.0349174i
$$501$$ 13.6847 + 7.68466i 0.611385 + 0.343325i
$$502$$ 22.0540 + 14.6031i 0.984317 + 0.651769i
$$503$$ −14.3586 −0.640217 −0.320109 0.947381i $$-0.603719\pi$$
−0.320109 + 0.947381i $$0.603719\pi$$
$$504$$ −9.11578 23.9534i −0.406049 1.06697i
$$505$$ −0.876894 −0.0390213
$$506$$ −0.580639 0.384472i −0.0258125 0.0170919i
$$507$$ 20.0047 + 11.2337i 0.888442 + 0.498907i
$$508$$ −27.8078 + 11.7915i −1.23377 + 0.523162i
$$509$$ 11.1231i 0.493023i −0.969140 0.246511i $$-0.920716\pi$$
0.969140 0.246511i $$-0.0792843\pi$$
$$510$$ −2.23725 4.35829i −0.0990669 0.192989i
$$511$$ 24.9073i 1.10183i
$$512$$ −11.8551 + 19.2732i −0.523927 + 0.851763i
$$513$$ −6.87689 + 0.246211i −0.303622 + 0.0108705i
$$514$$ −23.8078 + 35.9551i −1.05012 + 1.58591i
$$515$$ 9.80501 0.432060
$$516$$ −26.6381 2.95869i −1.17268 0.130249i
$$517$$ 4.00000 0.175920
$$518$$ −12.0818 + 18.2462i −0.530843 + 0.801692i
$$519$$ 1.69614 3.02045i 0.0744523 0.132583i
$$520$$ −14.2462 2.64861i −0.624738 0.116149i
$$521$$ 38.2462i 1.67560i 0.545980 + 0.837798i $$0.316158\pi$$
−0.545980 + 0.837798i $$0.683842\pi$$
$$522$$ −13.2409 0.495635i −0.579540 0.0216933i
$$523$$ 35.2929i 1.54325i −0.636077 0.771625i $$-0.719444\pi$$
0.636077 0.771625i $$-0.280556\pi$$
$$524$$ −4.26324 10.0540i −0.186241 0.439210i
$$525$$ −2.56155 + 4.56155i −0.111795 + 0.199082i
$$526$$ −28.0540 18.5760i −1.22321 0.809954i
$$527$$ −9.43318 −0.410916
$$528$$ 8.79081 2.62747i 0.382571 0.114346i
$$529$$ −22.8617 −0.993989
$$530$$ 14.4401 + 9.56155i 0.627237 + 0.415327i
$$531$$ 22.0956 + 36.2454i 0.958868 + 1.57292i
$$532$$ 3.12311 + 7.36520i 0.135404 + 0.319322i
$$533$$ 5.75379i 0.249224i
$$534$$ −22.3280 + 11.4616i −0.966227 + 0.495994i
$$535$$ 3.02045i 0.130585i
$$536$$ −12.0818 2.24621i −0.521854 0.0970215i
$$537$$ 15.1231 + 8.49242i 0.652610 + 0.366475i
$$538$$ −10.9309 + 16.5081i −0.471263 + 0.711713i
$$539$$ 2.81164 0.121106
$$540$$ −4.39676 9.41639i −0.189207 0.405217i
$$541$$ −26.9848 −1.16017 −0.580085 0.814556i $$-0.696980\pi$$
−0.580085 + 0.814556i $$0.696980\pi$$
$$542$$ 11.9545 18.0540i 0.513490 0.775485i
$$543$$ −18.4945 10.3857i −0.793676 0.445691i
$$544$$ −2.43845 11.0478i −0.104548 0.473671i
$$545$$ 0.876894i 0.0375620i
$$546$$ 33.7203 17.3097i 1.44309 0.740785i
$$547$$ 5.83209i 0.249362i 0.992197 + 0.124681i $$0.0397908\pi$$
−0.992197 + 0.124681i $$0.960209\pi$$
$$548$$ −15.1838 + 6.43845i −0.648618 + 0.275037i
$$549$$ 4.87689 + 8.00000i 0.208141 + 0.341432i
$$550$$ −1.56155 1.03399i −0.0665848 0.0440894i
$$551$$ 4.13595 0.176197
$$552$$ −1.16721 + 1.39852i −0.0496799 + 0.0595251i
$$553$$ 24.4924 1.04152
$$554$$ −27.5559 18.2462i −1.17074 0.775207i
$$555$$ −4.34475 + 7.73704i −0.184425 + 0.328419i
$$556$$ 32.3002 13.6964i 1.36983 0.580858i
$$557$$ 36.2462i 1.53580i −0.640569 0.767901i $$-0.721301\pi$$
0.640569 0.767901i $$-0.278699\pi$$
$$558$$ −19.9968 0.748519i −0.846532 0.0316874i
$$559$$ 39.6377i 1.67649i
$$560$$ −8.39919 + 8.68466i −0.354931 + 0.366994i
$$561$$ −2.24621 + 4.00000i −0.0948351 + 0.168880i
$$562$$ −10.6307 + 16.0547i −0.448428 + 0.677227i
$$563$$ 7.90007 0.332948 0.166474 0.986046i $$-0.446762\pi$$
0.166474 + 0.986046i $$0.446762\pi$$
$$564$$ 1.15504 10.3992i 0.0486358 0.437885i
$$565$$ 14.0000 0.588984
$$566$$ 18.1227 27.3693i 0.761753 1.15042i
$$567$$ 24.1636 + 12.4536i 1.01478 + 0.523003i
$$568$$ −1.75379 + 9.43318i −0.0735873 + 0.395807i
$$569$$ 13.1231i 0.550149i 0.961423 + 0.275075i $$0.0887026\pi$$
−0.961423 + 0.275075i $$0.911297\pi$$
$$570$$ 1.48140 + 2.88586i 0.0620490 + 0.120875i
$$571$$ 33.0161i 1.38168i 0.723007 + 0.690841i $$0.242759\pi$$
−0.723007 + 0.690841i $$0.757241\pi$$
$$572$$ 5.29723 + 12.4924i 0.221488 + 0.522334i
$$573$$ 37.6155 + 21.1231i 1.57141 + 0.882430i
$$574$$ −4.00000 2.64861i −0.166957 0.110551i
$$575$$ 0.371834 0.0155066
$$576$$ −4.29247 23.6130i −0.178853 0.983876i
$$577$$ −32.2462 −1.34243 −0.671214 0.741264i $$-0.734227\pi$$
−0.671214 + 0.741264i $$0.734227\pi$$
$$578$$ −15.3289 10.1501i −0.637599 0.422188i
$$579$$ −0.371834 0.208805i −0.0154529 0.00867762i
$$580$$ 2.43845 + 5.75058i 0.101251 + 0.238780i
$$581$$ 45.6155i 1.89245i
$$582$$ 6.71174 + 13.0749i 0.278210 + 0.541971i
$$583$$ 16.2177i 0.671670i
$$584$$ 4.26324 22.9309i 0.176414 0.948886i
$$585$$ 13.1231 8.00000i 0.542574 0.330759i
$$586$$ −1.94602 + 2.93893i −0.0803895 + 0.121406i
$$587$$ −1.85917 −0.0767362 −0.0383681 0.999264i $$-0.512216\pi$$
−0.0383681 + 0.999264i $$0.512216\pi$$
$$588$$ 0.811887 7.30970i 0.0334817 0.301447i
$$589$$ 6.24621 0.257371
$$590$$ 11.0478 16.6847i 0.454831 0.686897i
$$591$$ 3.60109 6.41273i 0.148129 0.263784i
$$592$$ −14.2462 + 14.7304i −0.585516 + 0.605416i
$$593$$ 8.24621i 0.338631i −0.985562 0.169316i $$-0.945844\pi$$
0.985562 0.169316i $$-0.0541557\pi$$
$$594$$ −5.07900 + 8.30111i −0.208394 + 0.340599i
$$595$$ 6.04090i 0.247653i
$$596$$ −25.7782 + 10.9309i −1.05592 + 0.447746i
$$597$$ −4.63068 + 8.24621i −0.189521 + 0.337495i
$$598$$ −2.24621 1.48734i −0.0918544 0.0608217i
$$599$$ 44.1912 1.80560 0.902802 0.430056i $$-0.141506\pi$$
0.902802 + 0.430056i $$0.141506\pi$$
$$600$$ −3.13907 + 3.76115i −0.128152 + 0.153548i
$$601$$ 23.1231 0.943211 0.471606 0.881810i $$-0.343675\pi$$
0.471606 + 0.881810i $$0.343675\pi$$
$$602$$ −27.5559 18.2462i −1.12309 0.743660i
$$603$$ 11.1293 6.78456i 0.453221 0.276289i
$$604$$ 13.5616 5.75058i 0.551812 0.233988i
$$605$$ 9.24621i 0.375912i
$$606$$ 1.91088 0.980914i 0.0776243 0.0398469i
$$607$$ 4.50778i 0.182965i 0.995807 + 0.0914827i $$0.0291606\pi$$
−0.995807 + 0.0914827i $$0.970839\pi$$
$$608$$ 1.61463 + 7.31534i 0.0654817 + 0.296676i
$$609$$ −14.2462 8.00000i −0.577286 0.324176i
$$610$$ 2.43845 3.68260i 0.0987298 0.149104i
$$611$$ 15.4741 0.626014
$$612$$ 9.75058 + 6.99473i 0.394144 + 0.282745i
$$613$$ 9.12311 0.368479 0.184239 0.982881i $$-0.441018\pi$$
0.184239 + 0.982881i $$0.441018\pi$$
$$614$$ 8.68951 13.1231i 0.350680 0.529605i
$$615$$ −1.69614 0.952473i −0.0683950 0.0384074i
$$616$$ 11.1231 + 2.06798i 0.448163 + 0.0833211i
$$617$$ 14.0000i 0.563619i 0.959470 + 0.281809i $$0.0909346\pi$$
−0.959470 + 0.281809i $$0.909065\pi$$
$$618$$ −21.3666 + 10.9681i −0.859489 + 0.441202i
$$619$$ 28.1365i 1.13090i −0.824782 0.565451i $$-0.808702\pi$$
0.824782 0.565451i $$-0.191298\pi$$
$$620$$ 3.68260 + 8.68466i 0.147897 + 0.348784i
$$621$$ −0.0691303 1.93087i −0.00277410 0.0774831i
$$622$$ 24.4924 + 16.2177i 0.982057 + 0.650272i
$$623$$ −30.9481 −1.23991
$$624$$ 34.0074 10.1644i 1.36139 0.406902i
$$625$$ 1.00000 0.0400000
$$626$$ 26.5219 + 17.5616i 1.06003 + 0.701901i
$$627$$ 1.48734 2.64861i 0.0593985 0.105775i
$$628$$ −2.63068 6.20393i −0.104976 0.247564i
$$629$$ 10.2462i 0.408543i
$$630$$ 0.479343 12.8057i 0.0190975 0.510192i
$$631$$ 39.8007i 1.58444i 0.610235 + 0.792220i $$0.291075\pi$$
−0.610235 + 0.792220i $$0.708925\pi$$
$$632$$ 22.5490 + 4.19224i 0.896949 + 0.166758i
$$633$$ 14.2462 25.3693i 0.566236 1.00834i
$$634$$ 13.0691 19.7373i 0.519041 0.783869i
$$635$$ −15.1022 −0.599314
$$636$$ −42.1628 4.68302i −1.67187 0.185694i
$$637$$ 10.8769 0.430958
$$638$$ 3.22925 4.87689i 0.127847 0.193078i
$$639$$ −5.29723 8.68951i −0.209555 0.343752i
$$640$$ −9.21922 + 6.55789i −0.364422 + 0.259223i
$$641$$ 6.38447i 0.252171i 0.992019 + 0.126086i $$0.0402414\pi$$
−0.992019 + 0.126086i $$0.959759\pi$$
$$642$$ −3.37874 6.58200i −0.133348 0.259771i
$$643$$ 3.60109i 0.142013i 0.997476 + 0.0710065i $$0.0226211\pi$$
−0.997476 + 0.0710065i $$0.977379\pi$$
$$644$$ −2.06798 + 0.876894i −0.0814896 + 0.0345545i
$$645$$ −11.6847 6.56155i −0.460083 0.258361i
$$646$$ −3.12311 2.06798i −0.122877 0.0813634i
$$647$$ 36.6172 1.43957 0.719786 0.694197i $$-0.244240\pi$$
0.719786 + 0.694197i $$0.244240\pi$$
$$648$$ 20.1146 + 15.6014i 0.790176 + 0.612880i
$$649$$ −18.7386 −0.735556
$$650$$ −6.04090 4.00000i −0.236943 0.156893i
$$651$$ −21.5150 12.0818i −0.843238 0.473523i
$$652$$ 28.8769 12.2448i 1.13091 0.479544i
$$653$$ 38.9848i 1.52559i 0.646638 + 0.762797i $$0.276175\pi$$
−0.646638 + 0.762797i $$0.723825\pi$$
$$654$$ 0.980914 + 1.91088i 0.0383568 + 0.0747214i
$$655$$ 5.46026i 0.213350i
$$656$$ −3.22925 3.12311i −0.126081 0.121937i
$$657$$ 12.8769 + 21.1231i 0.502375 + 0.824091i
$$658$$ 7.12311 10.7575i 0.277688 0.419370i
$$659$$ −24.7442 −0.963898 −0.481949 0.876199i $$-0.660071\pi$$
−0.481949 + 0.876199i $$0.660071\pi$$
$$660$$ 4.55950 + 0.506422i 0.177478 + 0.0197125i
$$661$$ 28.1080 1.09327 0.546636 0.837370i $$-0.315908\pi$$
0.546636 + 0.837370i $$0.315908\pi$$
$$662$$ −2.52132 + 3.80776i −0.0979940 + 0.147993i
$$663$$ −8.68951 + 15.4741i −0.337473 + 0.600963i
$$664$$ −7.80776 + 41.9960i −0.303000 + 1.62976i
$$665$$ 4.00000i 0.155113i
$$666$$ 0.813033 21.7203i 0.0315044 0.841644i
$$667$$ 1.16128i 0.0449648i
$$668$$ 7.07488 + 16.6847i 0.273735 + 0.645549i
$$669$$ −7.05398 + 12.5616i −0.272722 + 0.485658i
$$670$$ −5.12311 3.39228i −0.197923 0.131055i
$$671$$ −4.13595 −0.159667
$$672$$ 8.58821 28.3207i 0.331298 1.09249i
$$673$$ 22.4924 0.867019 0.433510 0.901149i $$-0.357275\pi$$
0.433510 + 0.901149i $$0.357275\pi$$
$$674$$ 1.77766 + 1.17708i 0.0684727 + 0.0453395i
$$675$$ −0.185917 5.19283i −0.00715595 0.199872i
$$676$$ 10.3423 + 24.3903i 0.397782 + 0.938087i
$$677$$ 1.50758i 0.0579409i −0.999580 0.0289705i $$-0.990777\pi$$
0.999580 0.0289705i $$-0.00922287\pi$$
$$678$$ −30.5081 + 15.6607i −1.17166 + 0.601446i
$$679$$ 18.1227i 0.695485i
$$680$$ 1.03399 5.56155i 0.0396516 0.213276i
$$681$$ −33.0540 18.5616i −1.26663 0.711280i
$$682$$ 4.87689 7.36520i 0.186746 0.282028i
$$683$$ −7.90007 −0.302288 −0.151144 0.988512i $$-0.548296\pi$$
−0.151144 + 0.988512i $$0.548296\pi$$
$$684$$ −6.45638 4.63159i −0.246866 0.177093i
$$685$$ −8.24621 −0.315072
$$686$$ −11.5012 + 17.3693i −0.439116 + 0.663164i
$$687$$ −24.5354 13.7779i −0.936085 0.525661i
$$688$$ −22.2462 21.5150i −0.848129 0.820251i
$$689$$ 62.7386i 2.39015i
$$690$$ −0.810281 + 0.415942i −0.0308469 + 0.0158346i
$$691$$ 18.2857i 0.695621i −0.937565 0.347811i $$-0.886925\pi$$
0.937565 0.347811i $$-0.113075\pi$$
$$692$$ 3.68260 1.56155i 0.139991 0.0593613i
$$693$$ −10.2462 + 6.24621i −0.389221 + 0.237274i
$$694$$ −26.6847 17.6693i −1.01294 0.670719i
$$695$$ 17.5420 0.665408
$$696$$ −11.7465 9.80365i −0.445249 0.371606i
$$697$$ 2.24621 0.0850813
$$698$$ 16.5081 + 10.9309i 0.624839 + 0.413740i
$$699$$ −8.48071 + 15.1022i −0.320770 + 0.571219i
$$700$$ −5.56155 + 2.35829i −0.210207 + 0.0891352i
$$701$$ 17.5076i 0.661252i −0.943762 0.330626i $$-0.892740\pi$$
0.943762 0.330626i $$-0.107260\pi$$
$$702$$ −19.6482 + 32.1130i −0.741573 + 1.21203i
$$703$$ 6.78456i 0.255885i
$$704$$ 9.88653 + 3.80776i 0.372612 + 0.143511i
$$705$$ 2.56155 4.56155i 0.0964737 0.171798i
$$706$$ 15.8078 23.8733i 0.594933 0.898482i
$$707$$ 2.64861 0.0996114
$$708$$ −5.41095 + 48.7167i −0.203356 + 1.83088i
$$709$$ 6.49242 0.243828 0.121914 0.992541i $$-0.461097\pi$$
0.121914 + 0.992541i $$0.461097\pi$$
$$710$$ −2.64861 + 4.00000i −0.0994007 + 0.150117i
$$711$$ −20.7713 + 12.6624i −0.778985 + 0.474878i
$$712$$ −28.4924 5.29723i −1.06780 0.198522i
$$713$$ 1.75379i 0.0656799i
$$714$$ 6.75748 + 13.1640i 0.252893 + 0.492650i
$$715$$ 6.78456i 0.253728i
$$716$$ 7.81855 + 18.4384i 0.292193 + 0.689077i
$$717$$ −26.2462 14.7386i −0.980183 0.550424i
$$718$$ 25.3693 + 16.7984i 0.946774 + 0.626910i
$$719$$ 30.9481 1.15417 0.577086 0.816684i $$-0.304190\pi$$
0.577086 + 0.816684i $$0.304190\pi$$
$$720$$ 2.63319 11.7075i 0.0981332 0.436314i
$$721$$ −29.6155 −1.10294
$$722$$ −20.3358 13.4654i −0.756821 0.501132i
$$723$$ 20.1907 + 11.3381i 0.750899 + 0.421669i
$$724$$ −9.56155 22.5490i −0.355352 0.838025i
$$725$$ 3.12311i 0.115989i
$$726$$ 10.3430 + 20.1489i 0.383866 + 0.747794i
$$727$$ 10.9663i 0.406717i 0.979104 + 0.203359i $$0.0651857\pi$$
−0.979104 + 0.203359i $$0.934814\pi$$
$$728$$ 43.0299 + 8.00000i 1.59480 + 0.296500i
$$729$$ −26.9309 + 1.93087i −0.997440 + 0.0715137i
$$730$$ 6.43845 9.72350i 0.238298 0.359883i
$$731$$ 15.4741 0.572329
$$732$$ −1.19429 + 10.7526i −0.0441423 + 0.397429i
$$733$$ −26.8769 −0.992721 −0.496360 0.868117i $$-0.665331\pi$$
−0.496360 + 0.868117i $$0.665331\pi$$
$$734$$ −8.56222 + 12.9309i −0.316037 + 0.477287i
$$735$$ 1.80054 3.20636i 0.0664140 0.118269i
$$736$$ −2.05398 + 0.453349i −0.0757105 + 0.0167107i
$$737$$ 5.75379i 0.211944i
$$738$$ 4.76160 + 0.178236i 0.175277 + 0.00656096i
$$739$$ 26.9752i 0.992300i 0.868237 + 0.496150i $$0.165253\pi$$
−0.868237 + 0.496150i $$0.834747\pi$$
$$740$$ −9.43318 + 4.00000i −0.346771 + 0.147043i
$$741$$ 5.75379 10.2462i 0.211371 0.376404i
$$742$$ −43.6155 28.8802i −1.60118 1.06022i
$$743$$ 9.80501 0.359711 0.179856 0.983693i $$-0.442437\pi$$
0.179856 + 0.983693i $$0.442437\pi$$
$$744$$ −17.7398 14.8057i −0.650372 0.542804i
$$745$$ −14.0000 −0.512920
$$746$$ 10.7575 + 7.12311i 0.393860 + 0.260795i
$$747$$ −23.5829 38.6852i −0.862855 1.41542i
$$748$$ −4.87689 + 2.06798i −0.178317 + 0.0756127i
$$749$$ 9.12311i 0.333351i
$$750$$ −2.17915 + 1.11862i −0.0795712 + 0.0408463i
$$751$$ 11.5012i 0.419683i −0.977735 0.209842i $$-0.932705\pi$$
0.977735 0.209842i $$-0.0672948\pi$$
$$752$$ 8.39919 8.68466i 0.306287 0.316697i
$$753$$ −28.2462 15.8617i −1.02935 0.578034i
$$754$$ 12.4924 18.8664i 0.454947 0.687072i
$$755$$ 7.36520 0.268047
$$756$$ 13.2802 + 28.4417i 0.482996 + 1.03442i
$$757$$ 10.8769 0.395327 0.197664 0.980270i $$-0.436665\pi$$
0.197664 + 0.980270i $$0.436665\pi$$
$$758$$ 14.6031 22.0540i 0.530409 0.801036i
$$759$$ 0.743668 + 0.417609i 0.0269934 + 0.0151582i
$$760$$ −0.684658 + 3.68260i −0.0248352 + 0.133582i
$$761$$ 31.2311i 1.13212i 0.824362 + 0.566062i $$0.191534\pi$$
−0.824362 + 0.566062i $$0.808466\pi$$
$$762$$ 32.9100 16.8937i 1.19220 0.611995i
$$763$$ 2.64861i 0.0958863i
$$764$$ 19.4470 + 45.8617i 0.703568 + 1.65922i
$$765$$ 3.12311 + 5.12311i 0.112916 + 0.185226i
$$766$$ −17.8078 11.7915i −0.643421 0.426043i
$$767$$ −72.4908 −2.61749
$$768$$ 12.7542 24.6034i 0.460229 0.887800i
$$769$$ 38.9848 1.40583 0.702915 0.711274i $$-0.251882\pi$$
0.702915 + 0.711274i $$0.251882\pi$$
$$770$$ 4.71659 + 3.12311i 0.169974 + 0.112549i
$$771$$ 25.8597 46.0504i 0.931315 1.65846i
$$772$$ −0.192236 0.453349i −0.00691872 0.0163164i
$$773$$ 0.246211i 0.00885560i 0.999990 + 0.00442780i $$0.00140942\pi$$
−0.999990 + 0.00442780i $$0.998591\pi$$
$$774$$ 32.8025 + 1.22786i 1.17906 + 0.0441346i
$$775$$ 4.71659i 0.169425i
$$776$$ −3.10196 + 16.6847i −0.111354 + 0.598944i
$$777$$ 13.1231 23.3693i 0.470789 0.838370i
$$778$$