# Properties

 Label 980.2.c.e.979.22 Level $980$ Weight $2$ Character 980.979 Analytic conductor $7.825$ Analytic rank $0$ Dimension $48$ CM no Inner twists $8$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$980 = 2^{2} \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 980.c (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$7.82533939809$$ Analytic rank: $$0$$ Dimension: $$48$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 979.22 Character $$\chi$$ $$=$$ 980.979 Dual form 980.2.c.e.979.23

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.255919 - 1.39086i) q^{2} +3.18626i q^{3} +(-1.86901 + 0.711898i) q^{4} +(1.80715 + 1.31689i) q^{5} +(4.43165 - 0.815425i) q^{6} +(1.46847 + 2.41735i) q^{8} -7.15223 q^{9} +O(q^{10})$$ $$q+(-0.255919 - 1.39086i) q^{2} +3.18626i q^{3} +(-1.86901 + 0.711898i) q^{4} +(1.80715 + 1.31689i) q^{5} +(4.43165 - 0.815425i) q^{6} +(1.46847 + 2.41735i) q^{8} -7.15223 q^{9} +(1.36913 - 2.85052i) q^{10} +4.51680i q^{11} +(-2.26829 - 5.95515i) q^{12} -2.22528 q^{13} +(-4.19595 + 5.75805i) q^{15} +(2.98640 - 2.66109i) q^{16} -2.52865 q^{17} +(1.83040 + 9.94779i) q^{18} +5.21241 q^{19} +(-4.31508 - 1.17477i) q^{20} +(6.28226 - 1.15594i) q^{22} -1.71481 q^{23} +(-7.70231 + 4.67892i) q^{24} +(1.53160 + 4.75964i) q^{25} +(0.569493 + 3.09507i) q^{26} -13.2301i q^{27} -2.31039 q^{29} +(9.08250 + 4.36240i) q^{30} +4.62540 q^{31} +(-4.46550 - 3.47266i) q^{32} -14.3917 q^{33} +(0.647131 + 3.51701i) q^{34} +(13.3676 - 5.09167i) q^{36} -0.336766i q^{37} +(-1.33396 - 7.24976i) q^{38} -7.09032i q^{39} +(-0.529635 + 6.30234i) q^{40} -3.28064i q^{41} -6.66354 q^{43} +(-3.21551 - 8.44195i) q^{44} +(-12.9252 - 9.41870i) q^{45} +(0.438852 + 2.38506i) q^{46} +1.44644i q^{47} +(8.47892 + 9.51544i) q^{48} +(6.22805 - 3.34834i) q^{50} -8.05693i q^{51} +(4.15908 - 1.58418i) q^{52} -10.0769i q^{53} +(-18.4013 + 3.38584i) q^{54} +(-5.94813 + 8.16255i) q^{55} +16.6081i q^{57} +(0.591274 + 3.21344i) q^{58} +3.20322 q^{59} +(3.74312 - 13.7490i) q^{60} -6.05175i q^{61} +(-1.18373 - 6.43331i) q^{62} +(-3.68719 + 7.09962i) q^{64} +(-4.02143 - 2.93045i) q^{65} +(3.68311 + 20.0169i) q^{66} -11.1495 q^{67} +(4.72608 - 1.80014i) q^{68} -5.46381i q^{69} +9.15549i q^{71} +(-10.5028 - 17.2895i) q^{72} +3.24011 q^{73} +(-0.468396 + 0.0861849i) q^{74} +(-15.1654 + 4.88008i) q^{75} +(-9.74205 + 3.71071i) q^{76} +(-9.86168 + 1.81455i) q^{78} +14.2700i q^{79} +(8.90125 - 0.876239i) q^{80} +20.6978 q^{81} +(-4.56292 + 0.839579i) q^{82} +11.3059i q^{83} +(-4.56966 - 3.32995i) q^{85} +(1.70533 + 9.26808i) q^{86} -7.36150i q^{87} +(-10.9187 + 6.63279i) q^{88} +15.2152i q^{89} +(-9.79234 + 20.3876i) q^{90} +(3.20499 - 1.22077i) q^{92} +14.7377i q^{93} +(2.01181 - 0.370173i) q^{94} +(9.41962 + 6.86417i) q^{95} +(11.0648 - 14.2282i) q^{96} -4.49303 q^{97} -32.3052i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$48 q + 16 q^{4} - 64 q^{9} + O(q^{10})$$ $$48 q + 16 q^{4} - 64 q^{9} + 16 q^{16} - 16 q^{25} - 48 q^{29} - 8 q^{30} + 176 q^{36} - 48 q^{44} - 32 q^{46} + 32 q^{50} + 24 q^{60} - 80 q^{64} - 16 q^{65} - 112 q^{74} - 48 q^{81} - 64 q^{85} - 112 q^{86} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$$.

 $$n$$ $$101$$ $$197$$ $$491$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.255919 1.39086i −0.180962 0.983490i
$$3$$ 3.18626i 1.83959i 0.392403 + 0.919793i $$0.371644\pi$$
−0.392403 + 0.919793i $$0.628356\pi$$
$$4$$ −1.86901 + 0.711898i −0.934505 + 0.355949i
$$5$$ 1.80715 + 1.31689i 0.808183 + 0.588931i
$$6$$ 4.43165 0.815425i 1.80921 0.332896i
$$7$$ 0 0
$$8$$ 1.46847 + 2.41735i 0.519183 + 0.854663i
$$9$$ −7.15223 −2.38408
$$10$$ 1.36913 2.85052i 0.432957 0.901415i
$$11$$ 4.51680i 1.36187i 0.732345 + 0.680934i $$0.238426\pi$$
−0.732345 + 0.680934i $$0.761574\pi$$
$$12$$ −2.26829 5.95515i −0.654799 1.71910i
$$13$$ −2.22528 −0.617182 −0.308591 0.951195i $$-0.599858\pi$$
−0.308591 + 0.951195i $$0.599858\pi$$
$$14$$ 0 0
$$15$$ −4.19595 + 5.75805i −1.08339 + 1.48672i
$$16$$ 2.98640 2.66109i 0.746600 0.665273i
$$17$$ −2.52865 −0.613288 −0.306644 0.951824i $$-0.599206\pi$$
−0.306644 + 0.951824i $$0.599206\pi$$
$$18$$ 1.83040 + 9.94779i 0.431428 + 2.34472i
$$19$$ 5.21241 1.19581 0.597904 0.801568i $$-0.296000\pi$$
0.597904 + 0.801568i $$0.296000\pi$$
$$20$$ −4.31508 1.17477i −0.964881 0.262687i
$$21$$ 0 0
$$22$$ 6.28226 1.15594i 1.33938 0.246447i
$$23$$ −1.71481 −0.357562 −0.178781 0.983889i $$-0.557215\pi$$
−0.178781 + 0.983889i $$0.557215\pi$$
$$24$$ −7.70231 + 4.67892i −1.57223 + 0.955082i
$$25$$ 1.53160 + 4.75964i 0.306321 + 0.951928i
$$26$$ 0.569493 + 3.09507i 0.111687 + 0.606993i
$$27$$ 13.2301i 2.54613i
$$28$$ 0 0
$$29$$ −2.31039 −0.429029 −0.214514 0.976721i $$-0.568817\pi$$
−0.214514 + 0.976721i $$0.568817\pi$$
$$30$$ 9.08250 + 4.36240i 1.65823 + 0.796462i
$$31$$ 4.62540 0.830747 0.415373 0.909651i $$-0.363651\pi$$
0.415373 + 0.909651i $$0.363651\pi$$
$$32$$ −4.46550 3.47266i −0.789396 0.613885i
$$33$$ −14.3917 −2.50527
$$34$$ 0.647131 + 3.51701i 0.110982 + 0.603163i
$$35$$ 0 0
$$36$$ 13.3676 5.09167i 2.22793 0.848611i
$$37$$ 0.336766i 0.0553640i −0.999617 0.0276820i $$-0.991187\pi$$
0.999617 0.0276820i $$-0.00881258\pi$$
$$38$$ −1.33396 7.24976i −0.216396 1.17607i
$$39$$ 7.09032i 1.13536i
$$40$$ −0.529635 + 6.30234i −0.0837427 + 0.996487i
$$41$$ 3.28064i 0.512350i −0.966630 0.256175i $$-0.917538\pi$$
0.966630 0.256175i $$-0.0824623\pi$$
$$42$$ 0 0
$$43$$ −6.66354 −1.01618 −0.508090 0.861304i $$-0.669648\pi$$
−0.508090 + 0.861304i $$0.669648\pi$$
$$44$$ −3.21551 8.44195i −0.484756 1.27267i
$$45$$ −12.9252 9.41870i −1.92677 1.40406i
$$46$$ 0.438852 + 2.38506i 0.0647052 + 0.351659i
$$47$$ 1.44644i 0.210985i 0.994420 + 0.105493i $$0.0336420\pi$$
−0.994420 + 0.105493i $$0.966358\pi$$
$$48$$ 8.47892 + 9.51544i 1.22383 + 1.37344i
$$49$$ 0 0
$$50$$ 6.22805 3.34834i 0.880780 0.473527i
$$51$$ 8.05693i 1.12820i
$$52$$ 4.15908 1.58418i 0.576760 0.219686i
$$53$$ 10.0769i 1.38416i −0.721819 0.692082i $$-0.756694\pi$$
0.721819 0.692082i $$-0.243306\pi$$
$$54$$ −18.4013 + 3.38584i −2.50410 + 0.460754i
$$55$$ −5.94813 + 8.16255i −0.802046 + 1.10064i
$$56$$ 0 0
$$57$$ 16.6081i 2.19979i
$$58$$ 0.591274 + 3.21344i 0.0776380 + 0.421945i
$$59$$ 3.20322 0.417023 0.208512 0.978020i $$-0.433138\pi$$
0.208512 + 0.978020i $$0.433138\pi$$
$$60$$ 3.74312 13.7490i 0.483235 1.77498i
$$61$$ 6.05175i 0.774847i −0.921902 0.387424i $$-0.873365\pi$$
0.921902 0.387424i $$-0.126635\pi$$
$$62$$ −1.18373 6.43331i −0.150334 0.817031i
$$63$$ 0 0
$$64$$ −3.68719 + 7.09962i −0.460899 + 0.887453i
$$65$$ −4.02143 2.93045i −0.498797 0.363478i
$$66$$ 3.68311 + 20.0169i 0.453360 + 2.46391i
$$67$$ −11.1495 −1.36213 −0.681067 0.732221i $$-0.738484\pi$$
−0.681067 + 0.732221i $$0.738484\pi$$
$$68$$ 4.72608 1.80014i 0.573121 0.218299i
$$69$$ 5.46381i 0.657766i
$$70$$ 0 0
$$71$$ 9.15549i 1.08656i 0.839553 + 0.543278i $$0.182817\pi$$
−0.839553 + 0.543278i $$0.817183\pi$$
$$72$$ −10.5028 17.2895i −1.23777 2.03758i
$$73$$ 3.24011 0.379226 0.189613 0.981859i $$-0.439277\pi$$
0.189613 + 0.981859i $$0.439277\pi$$
$$74$$ −0.468396 + 0.0861849i −0.0544499 + 0.0100188i
$$75$$ −15.1654 + 4.88008i −1.75115 + 0.563504i
$$76$$ −9.74205 + 3.71071i −1.11749 + 0.425647i
$$77$$ 0 0
$$78$$ −9.86168 + 1.81455i −1.11662 + 0.205457i
$$79$$ 14.2700i 1.60550i 0.596318 + 0.802748i $$0.296630\pi$$
−0.596318 + 0.802748i $$0.703370\pi$$
$$80$$ 8.90125 0.876239i 0.995190 0.0979666i
$$81$$ 20.6978 2.29975
$$82$$ −4.56292 + 0.839579i −0.503891 + 0.0927160i
$$83$$ 11.3059i 1.24099i 0.784212 + 0.620493i $$0.213067\pi$$
−0.784212 + 0.620493i $$0.786933\pi$$
$$84$$ 0 0
$$85$$ −4.56966 3.32995i −0.495649 0.361184i
$$86$$ 1.70533 + 9.26808i 0.183890 + 0.999403i
$$87$$ 7.36150i 0.789235i
$$88$$ −10.9187 + 6.63279i −1.16394 + 0.707058i
$$89$$ 15.2152i 1.61281i 0.591364 + 0.806405i $$0.298590\pi$$
−0.591364 + 0.806405i $$0.701410\pi$$
$$90$$ −9.79234 + 20.3876i −1.03220 + 2.14904i
$$91$$ 0 0
$$92$$ 3.20499 1.22077i 0.334143 0.127274i
$$93$$ 14.7377i 1.52823i
$$94$$ 2.01181 0.370173i 0.207502 0.0381804i
$$95$$ 9.41962 + 6.86417i 0.966433 + 0.704249i
$$96$$ 11.0648 14.2282i 1.12929 1.45216i
$$97$$ −4.49303 −0.456198 −0.228099 0.973638i $$-0.573251\pi$$
−0.228099 + 0.973638i $$0.573251\pi$$
$$98$$ 0 0
$$99$$ 32.3052i 3.24680i
$$100$$ −6.25097 7.80547i −0.625097 0.780547i
$$101$$ 0.734445i 0.0730800i −0.999332 0.0365400i $$-0.988366\pi$$
0.999332 0.0365400i $$-0.0116336\pi$$
$$102$$ −11.2061 + 2.06193i −1.10957 + 0.204161i
$$103$$ 11.8422i 1.16685i −0.812167 0.583424i $$-0.801712\pi$$
0.812167 0.583424i $$-0.198288\pi$$
$$104$$ −3.26776 5.37929i −0.320430 0.527483i
$$105$$ 0 0
$$106$$ −14.0155 + 2.57886i −1.36131 + 0.250481i
$$107$$ −4.98954 −0.482357 −0.241179 0.970481i $$-0.577534\pi$$
−0.241179 + 0.970481i $$0.577534\pi$$
$$108$$ 9.41848 + 24.7272i 0.906294 + 2.37937i
$$109$$ 11.3159 1.08386 0.541931 0.840423i $$-0.317693\pi$$
0.541931 + 0.840423i $$0.317693\pi$$
$$110$$ 12.8753 + 6.18409i 1.22761 + 0.589630i
$$111$$ 1.07302 0.101847
$$112$$ 0 0
$$113$$ 1.57514i 0.148177i −0.997252 0.0740883i $$-0.976395\pi$$
0.997252 0.0740883i $$-0.0236047\pi$$
$$114$$ 23.0996 4.25033i 2.16347 0.398080i
$$115$$ −3.09892 2.25821i −0.288976 0.210579i
$$116$$ 4.31814 1.64476i 0.400930 0.152712i
$$117$$ 15.9157 1.47141
$$118$$ −0.819765 4.45524i −0.0754655 0.410138i
$$119$$ 0 0
$$120$$ −20.0809 1.68755i −1.83312 0.154052i
$$121$$ −9.40151 −0.854683
$$122$$ −8.41717 + 1.54876i −0.762054 + 0.140218i
$$123$$ 10.4530 0.942511
$$124$$ −8.64493 + 3.29282i −0.776337 + 0.295704i
$$125$$ −3.50008 + 10.6184i −0.313057 + 0.949734i
$$126$$ 0 0
$$127$$ 17.0124 1.50960 0.754801 0.655954i $$-0.227733\pi$$
0.754801 + 0.655954i $$0.227733\pi$$
$$128$$ 10.8182 + 3.31145i 0.956206 + 0.292694i
$$129$$ 21.2317i 1.86935i
$$130$$ −3.04670 + 6.34322i −0.267213 + 0.556337i
$$131$$ −8.95868 −0.782723 −0.391362 0.920237i $$-0.627996\pi$$
−0.391362 + 0.920237i $$0.627996\pi$$
$$132$$ 26.8982 10.2454i 2.34119 0.891750i
$$133$$ 0 0
$$134$$ 2.85339 + 15.5075i 0.246495 + 1.33965i
$$135$$ 17.4226 23.9088i 1.49950 2.05774i
$$136$$ −3.71325 6.11264i −0.318409 0.524155i
$$137$$ 8.32232i 0.711023i −0.934672 0.355512i $$-0.884307\pi$$
0.934672 0.355512i $$-0.115693\pi$$
$$138$$ −7.59943 + 1.39830i −0.646906 + 0.119031i
$$139$$ 15.5985 1.32305 0.661524 0.749924i $$-0.269910\pi$$
0.661524 + 0.749924i $$0.269910\pi$$
$$140$$ 0 0
$$141$$ −4.60874 −0.388126
$$142$$ 12.7341 2.34307i 1.06862 0.196626i
$$143$$ 10.0512i 0.840521i
$$144$$ −21.3594 + 19.0328i −1.77995 + 1.58606i
$$145$$ −4.17523 3.04253i −0.346734 0.252668i
$$146$$ −0.829206 4.50655i −0.0686256 0.372965i
$$147$$ 0 0
$$148$$ 0.239743 + 0.629419i 0.0197068 + 0.0517379i
$$149$$ 2.51385 0.205943 0.102971 0.994684i $$-0.467165\pi$$
0.102971 + 0.994684i $$0.467165\pi$$
$$150$$ 10.6687 + 19.8442i 0.871093 + 1.62027i
$$151$$ 12.7350i 1.03636i 0.855271 + 0.518181i $$0.173391\pi$$
−0.855271 + 0.518181i $$0.826609\pi$$
$$152$$ 7.65427 + 12.6002i 0.620843 + 1.02201i
$$153$$ 18.0855 1.46213
$$154$$ 0 0
$$155$$ 8.35881 + 6.09114i 0.671396 + 0.489253i
$$156$$ 5.04759 + 13.2519i 0.404131 + 1.06100i
$$157$$ 8.64749 0.690145 0.345073 0.938576i $$-0.387854\pi$$
0.345073 + 0.938576i $$0.387854\pi$$
$$158$$ 19.8476 3.65196i 1.57899 0.290534i
$$159$$ 32.1075 2.54629
$$160$$ −3.49673 12.1562i −0.276441 0.961031i
$$161$$ 0 0
$$162$$ −5.29696 28.7878i −0.416168 2.26178i
$$163$$ −3.41606 −0.267566 −0.133783 0.991011i $$-0.542713\pi$$
−0.133783 + 0.991011i $$0.542713\pi$$
$$164$$ 2.33548 + 6.13155i 0.182370 + 0.478793i
$$165$$ −26.0080 18.9523i −2.02472 1.47543i
$$166$$ 15.7250 2.89340i 1.22050 0.224572i
$$167$$ 11.6381i 0.900581i 0.892882 + 0.450290i $$0.148680\pi$$
−0.892882 + 0.450290i $$0.851320\pi$$
$$168$$ 0 0
$$169$$ −8.04812 −0.619086
$$170$$ −3.46205 + 7.20798i −0.265527 + 0.552827i
$$171$$ −37.2804 −2.85090
$$172$$ 12.4542 4.74376i 0.949626 0.361708i
$$173$$ 8.21670 0.624704 0.312352 0.949966i $$-0.398883\pi$$
0.312352 + 0.949966i $$0.398883\pi$$
$$174$$ −10.2388 + 1.88395i −0.776205 + 0.142822i
$$175$$ 0 0
$$176$$ 12.0196 + 13.4890i 0.906013 + 1.01677i
$$177$$ 10.2063i 0.767151i
$$178$$ 21.1623 3.89387i 1.58618 0.291858i
$$179$$ 15.5937i 1.16553i −0.812641 0.582764i $$-0.801971\pi$$
0.812641 0.582764i $$-0.198029\pi$$
$$180$$ 30.8625 + 8.40224i 2.30035 + 0.626266i
$$181$$ 15.8536i 1.17839i −0.807990 0.589196i $$-0.799445\pi$$
0.807990 0.589196i $$-0.200555\pi$$
$$182$$ 0 0
$$183$$ 19.2824 1.42540
$$184$$ −2.51814 4.14529i −0.185640 0.305595i
$$185$$ 0.443484 0.608588i 0.0326056 0.0447442i
$$186$$ 20.4982 3.77167i 1.50300 0.276552i
$$187$$ 11.4214i 0.835217i
$$188$$ −1.02972 2.70342i −0.0751001 0.197167i
$$189$$ 0 0
$$190$$ 7.13647 14.8581i 0.517734 1.07792i
$$191$$ 11.2516i 0.814137i 0.913398 + 0.407068i $$0.133449\pi$$
−0.913398 + 0.407068i $$0.866551\pi$$
$$192$$ −22.6212 11.7483i −1.63255 0.847863i
$$193$$ 24.8339i 1.78758i 0.448484 + 0.893791i $$0.351964\pi$$
−0.448484 + 0.893791i $$0.648036\pi$$
$$194$$ 1.14985 + 6.24919i 0.0825546 + 0.448666i
$$195$$ 9.33717 12.8133i 0.668649 0.917579i
$$196$$ 0 0
$$197$$ 13.9890i 0.996672i 0.866984 + 0.498336i $$0.166055\pi$$
−0.866984 + 0.498336i $$0.833945\pi$$
$$198$$ −44.9322 + 8.26753i −3.19319 + 0.587548i
$$199$$ 19.5440 1.38544 0.692719 0.721208i $$-0.256413\pi$$
0.692719 + 0.721208i $$0.256413\pi$$
$$200$$ −9.25662 + 10.6918i −0.654542 + 0.756026i
$$201$$ 35.5253i 2.50576i
$$202$$ −1.02151 + 0.187959i −0.0718734 + 0.0132247i
$$203$$ 0 0
$$204$$ 5.73572 + 15.0585i 0.401581 + 1.05431i
$$205$$ 4.32024 5.92862i 0.301739 0.414072i
$$206$$ −16.4709 + 3.03065i −1.14758 + 0.211156i
$$207$$ 12.2647 0.852455
$$208$$ −6.64559 + 5.92168i −0.460789 + 0.410595i
$$209$$ 23.5434i 1.62853i
$$210$$ 0 0
$$211$$ 3.60453i 0.248146i −0.992273 0.124073i $$-0.960404\pi$$
0.992273 0.124073i $$-0.0395957\pi$$
$$212$$ 7.17370 + 18.8338i 0.492692 + 1.29351i
$$213$$ −29.1717 −1.99882
$$214$$ 1.27692 + 6.93978i 0.0872885 + 0.474394i
$$215$$ −12.0420 8.77514i −0.821260 0.598460i
$$216$$ 31.9818 19.4280i 2.17609 1.32191i
$$217$$ 0 0
$$218$$ −2.89595 15.7388i −0.196138 1.06597i
$$219$$ 10.3238i 0.697619i
$$220$$ 5.30621 19.4904i 0.357745 1.31404i
$$221$$ 5.62696 0.378511
$$222$$ −0.274607 1.49243i −0.0184304 0.100165i
$$223$$ 1.51767i 0.101631i −0.998708 0.0508154i $$-0.983818\pi$$
0.998708 0.0508154i $$-0.0161820\pi$$
$$224$$ 0 0
$$225$$ −10.9544 34.0421i −0.730293 2.26947i
$$226$$ −2.19080 + 0.403108i −0.145730 + 0.0268144i
$$227$$ 15.5593i 1.03271i 0.856375 + 0.516354i $$0.172711\pi$$
−0.856375 + 0.516354i $$0.827289\pi$$
$$228$$ −11.8233 31.0407i −0.783015 2.05572i
$$229$$ 19.2013i 1.26885i −0.772982 0.634427i $$-0.781236\pi$$
0.772982 0.634427i $$-0.218764\pi$$
$$230$$ −2.34779 + 4.88810i −0.154809 + 0.322311i
$$231$$ 0 0
$$232$$ −3.39274 5.58503i −0.222744 0.366675i
$$233$$ 3.14543i 0.206064i 0.994678 + 0.103032i $$0.0328544\pi$$
−0.994678 + 0.103032i $$0.967146\pi$$
$$234$$ −4.07315 22.1367i −0.266270 1.44712i
$$235$$ −1.90481 + 2.61394i −0.124256 + 0.170515i
$$236$$ −5.98685 + 2.28037i −0.389711 + 0.148439i
$$237$$ −45.4678 −2.95345
$$238$$ 0 0
$$239$$ 3.75292i 0.242756i 0.992606 + 0.121378i $$0.0387314\pi$$
−0.992606 + 0.121378i $$0.961269\pi$$
$$240$$ 2.79192 + 28.3617i 0.180218 + 1.83074i
$$241$$ 7.43129i 0.478691i 0.970934 + 0.239346i $$0.0769329\pi$$
−0.970934 + 0.239346i $$0.923067\pi$$
$$242$$ 2.40603 + 13.0762i 0.154665 + 0.840572i
$$243$$ 26.2581i 1.68446i
$$244$$ 4.30823 + 11.3108i 0.275806 + 0.724099i
$$245$$ 0 0
$$246$$ −2.67511 14.5387i −0.170559 0.926951i
$$247$$ −11.5991 −0.738032
$$248$$ 6.79227 + 11.1812i 0.431309 + 0.710009i
$$249$$ −36.0236 −2.28290
$$250$$ 15.6644 + 2.15070i 0.990706 + 0.136022i
$$251$$ 5.77378 0.364438 0.182219 0.983258i $$-0.441672\pi$$
0.182219 + 0.983258i $$0.441672\pi$$
$$252$$ 0 0
$$253$$ 7.74544i 0.486952i
$$254$$ −4.35379 23.6619i −0.273181 1.48468i
$$255$$ 10.6101 14.5601i 0.664430 0.911790i
$$256$$ 1.83718 15.8942i 0.114824 0.993386i
$$257$$ 14.8503 0.926336 0.463168 0.886270i $$-0.346713\pi$$
0.463168 + 0.886270i $$0.346713\pi$$
$$258$$ −29.5305 + 5.43361i −1.83849 + 0.338282i
$$259$$ 0 0
$$260$$ 9.60227 + 2.61420i 0.595508 + 0.162126i
$$261$$ 16.5245 1.02284
$$262$$ 2.29270 + 12.4603i 0.141643 + 0.769800i
$$263$$ −25.0905 −1.54715 −0.773573 0.633707i $$-0.781533\pi$$
−0.773573 + 0.633707i $$0.781533\pi$$
$$264$$ −21.1338 34.7898i −1.30069 2.14116i
$$265$$ 13.2701 18.2104i 0.815176 1.11866i
$$266$$ 0 0
$$267$$ −48.4796 −2.96690
$$268$$ 20.8386 7.93735i 1.27292 0.484851i
$$269$$ 29.7861i 1.81609i 0.418871 + 0.908046i $$0.362426\pi$$
−0.418871 + 0.908046i $$0.637574\pi$$
$$270$$ −37.7127 18.1137i −2.29512 1.10237i
$$271$$ 1.90002 0.115418 0.0577091 0.998333i $$-0.481620\pi$$
0.0577091 + 0.998333i $$0.481620\pi$$
$$272$$ −7.55157 + 6.72897i −0.457881 + 0.408004i
$$273$$ 0 0
$$274$$ −11.5752 + 2.12984i −0.699284 + 0.128668i
$$275$$ −21.4984 + 6.91795i −1.29640 + 0.417168i
$$276$$ 3.88968 + 10.2119i 0.234131 + 0.614686i
$$277$$ 0.261529i 0.0157138i 0.999969 + 0.00785689i $$0.00250095\pi$$
−0.999969 + 0.00785689i $$0.997499\pi$$
$$278$$ −3.99196 21.6954i −0.239422 1.30120i
$$279$$ −33.0820 −1.98057
$$280$$ 0 0
$$281$$ 5.36553 0.320080 0.160040 0.987110i $$-0.448838\pi$$
0.160040 + 0.987110i $$0.448838\pi$$
$$282$$ 1.17947 + 6.41013i 0.0702361 + 0.381718i
$$283$$ 14.9849i 0.890757i 0.895342 + 0.445378i $$0.146931\pi$$
−0.895342 + 0.445378i $$0.853069\pi$$
$$284$$ −6.51778 17.1117i −0.386759 1.01539i
$$285$$ −21.8710 + 30.0133i −1.29553 + 1.77784i
$$286$$ −13.9798 + 2.57229i −0.826644 + 0.152103i
$$287$$ 0 0
$$288$$ 31.9383 + 24.8372i 1.88198 + 1.46355i
$$289$$ −10.6059 −0.623878
$$290$$ −3.16322 + 6.58582i −0.185751 + 0.386733i
$$291$$ 14.3159i 0.839215i
$$292$$ −6.05579 + 2.30663i −0.354388 + 0.134985i
$$293$$ 23.2770 1.35986 0.679928 0.733279i $$-0.262011\pi$$
0.679928 + 0.733279i $$0.262011\pi$$
$$294$$ 0 0
$$295$$ 5.78871 + 4.21828i 0.337031 + 0.245598i
$$296$$ 0.814082 0.494531i 0.0473176 0.0287440i
$$297$$ 59.7577 3.46749
$$298$$ −0.643344 3.49643i −0.0372679 0.202543i
$$299$$ 3.81593 0.220681
$$300$$ 24.8702 19.9172i 1.43588 1.14992i
$$301$$ 0 0
$$302$$ 17.7127 3.25914i 1.01925 0.187542i
$$303$$ 2.34013 0.134437
$$304$$ 15.5663 13.8707i 0.892791 0.795539i
$$305$$ 7.96948 10.9364i 0.456331 0.626219i
$$306$$ −4.62843 25.1545i −0.264590 1.43799i
$$307$$ 5.70758i 0.325749i 0.986647 + 0.162874i $$0.0520765\pi$$
−0.986647 + 0.162874i $$0.947923\pi$$
$$308$$ 0 0
$$309$$ 37.7324 2.14652
$$310$$ 6.33278 13.1848i 0.359678 0.748847i
$$311$$ 32.0916 1.81975 0.909873 0.414886i $$-0.136179\pi$$
0.909873 + 0.414886i $$0.136179\pi$$
$$312$$ 17.1398 10.4119i 0.970351 0.589460i
$$313$$ 28.1435 1.59077 0.795384 0.606106i $$-0.207269\pi$$
0.795384 + 0.606106i $$0.207269\pi$$
$$314$$ −2.21306 12.0275i −0.124890 0.678751i
$$315$$ 0 0
$$316$$ −10.1588 26.6707i −0.571475 1.50034i
$$317$$ 13.3985i 0.752533i 0.926511 + 0.376267i $$0.122792\pi$$
−0.926511 + 0.376267i $$0.877208\pi$$
$$318$$ −8.21692 44.6571i −0.460782 2.50425i
$$319$$ 10.4356i 0.584280i
$$320$$ −16.0127 + 7.97449i −0.895139 + 0.445787i
$$321$$ 15.8980i 0.887338i
$$322$$ 0 0
$$323$$ −13.1804 −0.733375
$$324$$ −38.6843 + 14.7347i −2.14913 + 0.818595i
$$325$$ −3.40825 10.5915i −0.189056 0.587513i
$$326$$ 0.874236 + 4.75128i 0.0484194 + 0.263149i
$$327$$ 36.0552i 1.99386i
$$328$$ 7.93046 4.81752i 0.437886 0.266003i
$$329$$ 0 0
$$330$$ −19.7041 + 41.0239i −1.08468 + 2.25829i
$$331$$ 22.7117i 1.24835i −0.781286 0.624173i $$-0.785436\pi$$
0.781286 0.624173i $$-0.214564\pi$$
$$332$$ −8.04867 21.1309i −0.441728 1.15971i
$$333$$ 2.40863i 0.131992i
$$334$$ 16.1870 2.97841i 0.885712 0.162971i
$$335$$ −20.1489 14.6827i −1.10085 0.802203i
$$336$$ 0 0
$$337$$ 8.84953i 0.482065i −0.970517 0.241032i $$-0.922514\pi$$
0.970517 0.241032i $$-0.0774860\pi$$
$$338$$ 2.05967 + 11.1938i 0.112031 + 0.608865i
$$339$$ 5.01880 0.272584
$$340$$ 10.9113 + 2.97059i 0.591750 + 0.161103i
$$341$$ 20.8920i 1.13137i
$$342$$ 9.54077 + 51.8520i 0.515906 + 2.80383i
$$343$$ 0 0
$$344$$ −9.78521 16.1081i −0.527583 0.868492i
$$345$$ 7.19524 9.87395i 0.387379 0.531596i
$$346$$ −2.10281 11.4283i −0.113048 0.614390i
$$347$$ 16.7339 0.898325 0.449163 0.893450i $$-0.351722\pi$$
0.449163 + 0.893450i $$0.351722\pi$$
$$348$$ 5.24064 + 13.7587i 0.280928 + 0.737545i
$$349$$ 3.86908i 0.207107i −0.994624 0.103554i $$-0.966979\pi$$
0.994624 0.103554i $$-0.0330213\pi$$
$$350$$ 0 0
$$351$$ 29.4407i 1.57143i
$$352$$ 15.6853 20.1698i 0.836029 1.07505i
$$353$$ 7.90229 0.420597 0.210298 0.977637i $$-0.432556\pi$$
0.210298 + 0.977637i $$0.432556\pi$$
$$354$$ 14.1956 2.61198i 0.754485 0.138825i
$$355$$ −12.0568 + 16.5454i −0.639907 + 0.878137i
$$356$$ −10.8317 28.4374i −0.574079 1.50718i
$$357$$ 0 0
$$358$$ −21.6887 + 3.99073i −1.14629 + 0.210917i
$$359$$ 4.16127i 0.219623i 0.993952 + 0.109812i $$0.0350248\pi$$
−0.993952 + 0.109812i $$0.964975\pi$$
$$360$$ 3.78808 45.0758i 0.199649 2.37570i
$$361$$ 8.16920 0.429958
$$362$$ −22.0503 + 4.05725i −1.15894 + 0.213244i
$$363$$ 29.9556i 1.57226i
$$364$$ 0 0
$$365$$ 5.85537 + 4.26686i 0.306484 + 0.223338i
$$366$$ −4.93475 26.8193i −0.257943 1.40186i
$$367$$ 27.3777i 1.42910i 0.699583 + 0.714551i $$0.253369\pi$$
−0.699583 + 0.714551i $$0.746631\pi$$
$$368$$ −5.12110 + 4.56326i −0.266956 + 0.237876i
$$369$$ 23.4639i 1.22148i
$$370$$ −0.959959 0.461076i −0.0499059 0.0239702i
$$371$$ 0 0
$$372$$ −10.4918 27.5450i −0.543973 1.42814i
$$373$$ 29.3085i 1.51754i −0.651360 0.758768i $$-0.725801\pi$$
0.651360 0.758768i $$-0.274199\pi$$
$$374$$ −15.8857 + 2.92296i −0.821428 + 0.151143i
$$375$$ −33.8328 11.1522i −1.74712 0.575895i
$$376$$ −3.49656 + 2.12406i −0.180321 + 0.109540i
$$377$$ 5.14127 0.264789
$$378$$ 0 0
$$379$$ 21.4131i 1.09992i 0.835192 + 0.549958i $$0.185356\pi$$
−0.835192 + 0.549958i $$0.814644\pi$$
$$380$$ −22.4920 6.12339i −1.15381 0.314123i
$$381$$ 54.2057i 2.77704i
$$382$$ 15.6494 2.87950i 0.800695 0.147328i
$$383$$ 19.2892i 0.985633i −0.870133 0.492817i $$-0.835967\pi$$
0.870133 0.492817i $$-0.164033\pi$$
$$384$$ −10.5511 + 34.4697i −0.538435 + 1.75902i
$$385$$ 0 0
$$386$$ 34.5406 6.35547i 1.75807 0.323485i
$$387$$ 47.6592 2.42265
$$388$$ 8.39751 3.19858i 0.426319 0.162383i
$$389$$ 15.5064 0.786203 0.393102 0.919495i $$-0.371402\pi$$
0.393102 + 0.919495i $$0.371402\pi$$
$$390$$ −20.2111 9.70758i −1.02343 0.491562i
$$391$$ 4.33615 0.219288
$$392$$ 0 0
$$393$$ 28.5446i 1.43989i
$$394$$ 19.4567 3.58004i 0.980217 0.180360i
$$395$$ −18.7920 + 25.7880i −0.945526 + 1.29754i
$$396$$ 22.9980 + 60.3788i 1.15570 + 3.03415i
$$397$$ −23.0690 −1.15780 −0.578899 0.815399i $$-0.696518\pi$$
−0.578899 + 0.815399i $$0.696518\pi$$
$$398$$ −5.00169 27.1831i −0.250712 1.36256i
$$399$$ 0 0
$$400$$ 17.2398 + 10.1385i 0.861991 + 0.506923i
$$401$$ 36.6133 1.82838 0.914191 0.405283i $$-0.132827\pi$$
0.914191 + 0.405283i $$0.132827\pi$$
$$402$$ −49.4109 + 9.09162i −2.46439 + 0.453449i
$$403$$ −10.2928 −0.512722
$$404$$ 0.522850 + 1.37268i 0.0260128 + 0.0682936i
$$405$$ 37.4040 + 27.2567i 1.85862 + 1.35439i
$$406$$ 0 0
$$407$$ 1.52111 0.0753984
$$408$$ 19.4764 11.8314i 0.964228 0.585740i
$$409$$ 30.9997i 1.53284i −0.642341 0.766419i $$-0.722037\pi$$
0.642341 0.766419i $$-0.277963\pi$$
$$410$$ −9.35154 4.49162i −0.461839 0.221825i
$$411$$ 26.5170 1.30799
$$412$$ 8.43046 + 22.1332i 0.415339 + 1.09043i
$$413$$ 0 0
$$414$$ −3.13877 17.0585i −0.154262 0.838381i
$$415$$ −14.8886 + 20.4315i −0.730855 + 1.00294i
$$416$$ 9.93699 + 7.72764i 0.487201 + 0.378879i
$$417$$ 49.7008i 2.43386i
$$418$$ 32.7457 6.02522i 1.60165 0.294703i
$$419$$ 11.9532 0.583953 0.291977 0.956425i $$-0.405687\pi$$
0.291977 + 0.956425i $$0.405687\pi$$
$$420$$ 0 0
$$421$$ 13.5052 0.658205 0.329103 0.944294i $$-0.393254\pi$$
0.329103 + 0.944294i $$0.393254\pi$$
$$422$$ −5.01341 + 0.922469i −0.244049 + 0.0449051i
$$423$$ 10.3453i 0.503006i
$$424$$ 24.3593 14.7976i 1.18299 0.718634i
$$425$$ −3.87289 12.0355i −0.187863 0.583806i
$$426$$ 7.46561 + 40.5740i 0.361710 + 1.96581i
$$427$$ 0 0
$$428$$ 9.32551 3.55205i 0.450765 0.171695i
$$429$$ 32.0256 1.54621
$$430$$ −9.12325 + 18.9946i −0.439962 + 0.915999i
$$431$$ 35.5892i 1.71427i 0.515090 + 0.857136i $$0.327758\pi$$
−0.515090 + 0.857136i $$0.672242\pi$$
$$432$$ −35.2065 39.5103i −1.69387 1.90094i
$$433$$ −16.8799 −0.811199 −0.405599 0.914051i $$-0.632937\pi$$
−0.405599 + 0.914051i $$0.632937\pi$$
$$434$$ 0 0
$$435$$ 9.69428 13.3034i 0.464805 0.637847i
$$436$$ −21.1495 + 8.05574i −1.01288 + 0.385800i
$$437$$ −8.93827 −0.427576
$$438$$ 14.3590 2.64206i 0.686101 0.126243i
$$439$$ −23.5676 −1.12482 −0.562410 0.826858i $$-0.690126\pi$$
−0.562410 + 0.826858i $$0.690126\pi$$
$$440$$ −28.4664 2.39226i −1.35708 0.114046i
$$441$$ 0 0
$$442$$ −1.44005 7.82635i −0.0684962 0.372261i
$$443$$ −8.93347 −0.424442 −0.212221 0.977222i $$-0.568070\pi$$
−0.212221 + 0.977222i $$0.568070\pi$$
$$444$$ −2.00549 + 0.763883i −0.0951764 + 0.0362523i
$$445$$ −20.0368 + 27.4962i −0.949834 + 1.30345i
$$446$$ −2.11087 + 0.388401i −0.0999528 + 0.0183913i
$$447$$ 8.00978i 0.378850i
$$448$$ 0 0
$$449$$ −33.1350 −1.56374 −0.781868 0.623445i $$-0.785733\pi$$
−0.781868 + 0.623445i $$0.785733\pi$$
$$450$$ −44.5445 + 23.9481i −2.09985 + 1.12892i
$$451$$ 14.8180 0.697752
$$452$$ 1.12134 + 2.94395i 0.0527433 + 0.138472i
$$453$$ −40.5771 −1.90648
$$454$$ 21.6409 3.98193i 1.01566 0.186881i
$$455$$ 0 0
$$456$$ −40.1476 + 24.3885i −1.88008 + 1.14209i
$$457$$ 24.6492i 1.15304i −0.817082 0.576521i $$-0.804410\pi$$
0.817082 0.576521i $$-0.195590\pi$$
$$458$$ −26.7064 + 4.91397i −1.24791 + 0.229615i
$$459$$ 33.4543i 1.56151i
$$460$$ 7.39953 + 2.01450i 0.345005 + 0.0939268i
$$461$$ 38.2341i 1.78074i 0.455239 + 0.890369i $$0.349554\pi$$
−0.455239 + 0.890369i $$0.650446\pi$$
$$462$$ 0 0
$$463$$ −14.6319 −0.680004 −0.340002 0.940425i $$-0.610428\pi$$
−0.340002 + 0.940425i $$0.610428\pi$$
$$464$$ −6.89975 + 6.14816i −0.320313 + 0.285421i
$$465$$ −19.4080 + 26.6333i −0.900022 + 1.23509i
$$466$$ 4.37487 0.804976i 0.202662 0.0372898i
$$467$$ 8.52322i 0.394408i −0.980363 0.197204i $$-0.936814\pi$$
0.980363 0.197204i $$-0.0631861\pi$$
$$468$$ −29.7467 + 11.3304i −1.37504 + 0.523748i
$$469$$ 0 0
$$470$$ 4.12312 + 1.98037i 0.190185 + 0.0913476i
$$471$$ 27.5531i 1.26958i
$$472$$ 4.70383 + 7.74331i 0.216511 + 0.356415i
$$473$$ 30.0979i 1.38390i
$$474$$ 11.6361 + 63.2395i 0.534463 + 2.90469i
$$475$$ 7.98335 + 24.8092i 0.366301 + 1.13832i
$$476$$ 0 0
$$477$$ 72.0721i 3.29995i
$$478$$ 5.21981 0.960446i 0.238748 0.0439298i
$$479$$ −39.2249 −1.79223 −0.896115 0.443823i $$-0.853622\pi$$
−0.896115 + 0.443823i $$0.853622\pi$$
$$480$$ 38.7327 11.1415i 1.76790 0.508537i
$$481$$ 0.749400i 0.0341697i
$$482$$ 10.3359 1.90181i 0.470788 0.0866251i
$$483$$ 0 0
$$484$$ 17.5715 6.69292i 0.798706 0.304224i
$$485$$ −8.11959 5.91682i −0.368691 0.268669i
$$486$$ 36.5215 6.71996i 1.65665 0.304824i
$$487$$ 25.5876 1.15948 0.579742 0.814800i $$-0.303153\pi$$
0.579742 + 0.814800i $$0.303153\pi$$
$$488$$ 14.6292 8.88682i 0.662233 0.402287i
$$489$$ 10.8844i 0.492212i
$$490$$ 0 0
$$491$$ 40.7008i 1.83680i −0.395654 0.918400i $$-0.629482\pi$$
0.395654 0.918400i $$-0.370518\pi$$
$$492$$ −19.5367 + 7.44144i −0.880782 + 0.335486i
$$493$$ 5.84217 0.263118
$$494$$ 2.96843 + 16.1328i 0.133556 + 0.725847i
$$495$$ 42.5424 58.3805i 1.91214 2.62401i
$$496$$ 13.8133 12.3086i 0.620236 0.552673i
$$497$$ 0 0
$$498$$ 9.21913 + 50.1039i 0.413119 + 2.24521i
$$499$$ 15.9072i 0.712106i −0.934466 0.356053i $$-0.884122\pi$$
0.934466 0.356053i $$-0.115878\pi$$
$$500$$ −1.01751 22.3375i −0.0455042 0.998964i
$$501$$ −37.0819 −1.65670
$$502$$ −1.47762 8.03055i −0.0659495 0.358421i
$$503$$ 9.64379i 0.429995i 0.976615 + 0.214998i $$0.0689744\pi$$
−0.976615 + 0.214998i $$0.931026\pi$$
$$504$$ 0 0
$$505$$ 0.967182 1.32725i 0.0430391 0.0590620i
$$506$$ −10.7729 + 1.98221i −0.478912 + 0.0881199i
$$507$$ 25.6434i 1.13886i
$$508$$ −31.7963 + 12.1111i −1.41073 + 0.537342i
$$509$$ 3.77669i 0.167399i 0.996491 + 0.0836995i $$0.0266736\pi$$
−0.996491 + 0.0836995i $$0.973326\pi$$
$$510$$ −22.9665 11.0310i −1.01697 0.488460i
$$511$$ 0 0
$$512$$ −22.5768 + 1.51235i −0.997764 + 0.0668372i
$$513$$ 68.9606i 3.04469i
$$514$$ −3.80048 20.6548i −0.167632 0.911043i
$$515$$ 15.5949 21.4007i 0.687193 0.943028i
$$516$$ 15.1148 + 39.6824i 0.665394 + 1.74692i
$$517$$ −6.53330 −0.287334
$$518$$ 0 0
$$519$$ 26.1805i 1.14920i
$$520$$ 1.17859 14.0245i 0.0516845 0.615015i
$$521$$ 0.0914926i 0.00400837i −0.999998 0.00200418i $$-0.999362\pi$$
0.999998 0.00200418i $$-0.000637952\pi$$
$$522$$ −4.22893 22.9833i −0.185095 1.00595i
$$523$$ 15.0818i 0.659480i −0.944072 0.329740i $$-0.893039\pi$$
0.944072 0.329740i $$-0.106961\pi$$
$$524$$ 16.7439 6.37767i 0.731459 0.278610i
$$525$$ 0 0
$$526$$ 6.42115 + 34.8975i 0.279975 + 1.52160i
$$527$$ −11.6960 −0.509487
$$528$$ −42.9794 + 38.2976i −1.87044 + 1.66669i
$$529$$ −20.0594 −0.872150
$$530$$ −28.7243 13.7965i −1.24770 0.599283i
$$531$$ −22.9102 −0.994217
$$532$$ 0 0
$$533$$ 7.30035i 0.316213i
$$534$$ 12.4069 + 67.4286i 0.536898 + 2.91792i
$$535$$ −9.01687 6.57068i −0.389833 0.284075i
$$536$$ −16.3728 26.9524i −0.707197 1.16417i
$$537$$ 49.6855 2.14409
$$538$$ 41.4285 7.62284i 1.78611 0.328644i
$$539$$ 0 0
$$540$$ −15.5423 + 57.0889i −0.668835 + 2.45671i
$$541$$ −27.4738 −1.18119 −0.590596 0.806968i $$-0.701107\pi$$
−0.590596 + 0.806968i $$0.701107\pi$$
$$542$$ −0.486253 2.64268i −0.0208864 0.113513i
$$543$$ 50.5138 2.16775
$$544$$ 11.2917 + 8.78114i 0.484127 + 0.376488i
$$545$$ 20.4495 + 14.9017i 0.875960 + 0.638320i
$$546$$ 0 0
$$547$$ −18.3722 −0.785540 −0.392770 0.919637i $$-0.628483\pi$$
−0.392770 + 0.919637i $$0.628483\pi$$
$$548$$ 5.92464 + 15.5545i 0.253088 + 0.664455i
$$549$$ 43.2835i 1.84730i
$$550$$ 15.1238 + 28.1309i 0.644880 + 1.19950i
$$551$$ −12.0427 −0.513036
$$552$$ 13.2080 8.02345i 0.562168 0.341501i
$$553$$ 0 0
$$554$$ 0.363752 0.0669304i 0.0154543 0.00284360i
$$555$$ 1.93912 + 1.41305i 0.0823109 + 0.0599807i
$$556$$ −29.1538 + 11.1045i −1.23640 + 0.470938i
$$557$$ 13.9550i 0.591294i 0.955297 + 0.295647i $$0.0955351\pi$$
−0.955297 + 0.295647i $$0.904465\pi$$
$$558$$ 8.46632 + 46.0126i 0.358408 + 1.94787i
$$559$$ 14.8283 0.627168
$$560$$ 0 0
$$561$$ 36.3916 1.53645
$$562$$ −1.37314 7.46272i −0.0579225 0.314796i
$$563$$ 18.5730i 0.782760i −0.920229 0.391380i $$-0.871998\pi$$
0.920229 0.391380i $$-0.128002\pi$$
$$564$$ 8.61378 3.28095i 0.362706 0.138153i
$$565$$ 2.07428 2.84652i 0.0872657 0.119754i
$$566$$ 20.8419 3.83491i 0.876051 0.161193i
$$567$$ 0 0
$$568$$ −22.1320 + 13.4446i −0.928640 + 0.564122i
$$569$$ 8.08905 0.339111 0.169555 0.985521i $$-0.445767\pi$$
0.169555 + 0.985521i $$0.445767\pi$$
$$570$$ 47.3417 + 22.7386i 1.98293 + 0.952416i
$$571$$ 0.840877i 0.0351896i −0.999845 0.0175948i $$-0.994399\pi$$
0.999845 0.0175948i $$-0.00560089\pi$$
$$572$$ 7.15541 + 18.7857i 0.299183 + 0.785471i
$$573$$ −35.8505 −1.49767
$$574$$ 0 0
$$575$$ −2.62640 8.16186i −0.109529 0.340373i
$$576$$ 26.3716 50.7782i 1.09882 2.11576i
$$577$$ 46.1975 1.92323 0.961614 0.274404i $$-0.0884807\pi$$
0.961614 + 0.274404i $$0.0884807\pi$$
$$578$$ 2.71426 + 14.7514i 0.112898 + 0.613578i
$$579$$ −79.1271 −3.28841
$$580$$ 9.96952 + 2.71418i 0.413962 + 0.112700i
$$581$$ 0 0
$$582$$ −19.9115 + 3.66373i −0.825360 + 0.151866i
$$583$$ 45.5152 1.88505
$$584$$ 4.75800 + 7.83248i 0.196887 + 0.324110i
$$585$$ 28.7622 + 20.9593i 1.18917 + 0.866560i
$$586$$ −5.95703 32.3751i −0.246083 1.33740i
$$587$$ 2.72072i 0.112296i 0.998422 + 0.0561482i $$0.0178819\pi$$
−0.998422 + 0.0561482i $$0.982118\pi$$
$$588$$ 0 0
$$589$$ 24.1095 0.993414
$$590$$ 4.38562 9.13085i 0.180553 0.375911i
$$591$$ −44.5724 −1.83346
$$592$$ −0.896165 1.00572i −0.0368322 0.0413348i
$$593$$ −34.7891 −1.42862 −0.714308 0.699831i $$-0.753259\pi$$
−0.714308 + 0.699831i $$0.753259\pi$$
$$594$$ −15.2932 83.1149i −0.627486 3.41025i
$$595$$ 0 0
$$596$$ −4.69842 + 1.78961i −0.192455 + 0.0733052i
$$597$$ 62.2722i 2.54863i
$$598$$ −0.976570 5.30744i −0.0399349 0.217037i
$$599$$ 11.7189i 0.478821i 0.970918 + 0.239411i $$0.0769542\pi$$
−0.970918 + 0.239411i $$0.923046\pi$$
$$600$$ −34.0669 29.4940i −1.39078 1.20409i
$$601$$ 17.1738i 0.700532i 0.936650 + 0.350266i $$0.113909\pi$$
−0.936650 + 0.350266i $$0.886091\pi$$
$$602$$ 0 0
$$603$$ 79.7442 3.24743
$$604$$ −9.06605 23.8019i −0.368892 0.968485i
$$605$$ −16.9900 12.3808i −0.690740 0.503349i
$$606$$ −0.598884 3.25480i −0.0243280 0.132217i
$$607$$ 16.6117i 0.674247i 0.941460 + 0.337123i $$0.109454\pi$$
−0.941460 + 0.337123i $$0.890546\pi$$
$$608$$ −23.2760 18.1009i −0.943966 0.734088i
$$609$$ 0 0
$$610$$ −17.2507 8.28563i −0.698458 0.335475i
$$611$$ 3.21874i 0.130216i
$$612$$ −33.8020 + 12.8750i −1.36637 + 0.520443i
$$613$$ 32.9900i 1.33245i −0.745750 0.666226i $$-0.767908\pi$$
0.745750 0.666226i $$-0.232092\pi$$
$$614$$ 7.93847 1.46068i 0.320371 0.0589483i
$$615$$ 18.8901 + 13.7654i 0.761722 + 0.555074i
$$616$$ 0 0
$$617$$ 23.9885i 0.965739i 0.875692 + 0.482870i $$0.160405\pi$$
−0.875692 + 0.482870i $$0.839595\pi$$
$$618$$ −9.65644 52.4806i −0.388439 2.11108i
$$619$$ −31.3184 −1.25879 −0.629396 0.777085i $$-0.716698\pi$$
−0.629396 + 0.777085i $$0.716698\pi$$
$$620$$ −19.9590 5.43379i −0.801572 0.218226i
$$621$$ 22.6870i 0.910400i
$$622$$ −8.21286 44.6351i −0.329306 1.78970i
$$623$$ 0 0
$$624$$ −18.8680 21.1746i −0.755325 0.847660i
$$625$$ −20.3084 + 14.5798i −0.812335 + 0.583191i
$$626$$ −7.20248 39.1439i −0.287869 1.56450i
$$627$$ −75.0154 −2.99583
$$628$$ −16.1623 + 6.15614i −0.644944 + 0.245657i
$$629$$ 0.851564i 0.0339541i
$$630$$ 0 0
$$631$$ 37.4842i 1.49222i −0.665821 0.746112i $$-0.731919\pi$$
0.665821 0.746112i $$-0.268081\pi$$
$$632$$ −34.4955 + 20.9550i −1.37216 + 0.833546i
$$633$$ 11.4850 0.456486
$$634$$ 18.6355 3.42893i 0.740109 0.136180i
$$635$$ 30.7439 + 22.4034i 1.22004 + 0.889051i
$$636$$ −60.0092 + 22.8573i −2.37952 + 0.906349i
$$637$$ 0 0
$$638$$ −14.5145 + 2.67067i −0.574634 + 0.105733i
$$639$$ 65.4822i 2.59044i
$$640$$ 15.1894 + 20.2307i 0.600414 + 0.799690i
$$641$$ 35.6213 1.40696 0.703479 0.710716i $$-0.251629\pi$$
0.703479 + 0.710716i $$0.251629\pi$$
$$642$$ −22.1119 + 4.06860i −0.872688 + 0.160575i
$$643$$ 2.55684i 0.100832i 0.998728 + 0.0504159i $$0.0160547\pi$$
−0.998728 + 0.0504159i $$0.983945\pi$$
$$644$$ 0 0
$$645$$ 27.9599 38.3690i 1.10092 1.51078i
$$646$$ 3.37311 + 18.3321i 0.132713 + 0.721267i
$$647$$ 17.7876i 0.699301i −0.936880 0.349651i $$-0.886300\pi$$
0.936880 0.349651i $$-0.113700\pi$$
$$648$$ 30.3940 + 50.0338i 1.19399 + 1.96551i
$$649$$ 14.4683i 0.567931i
$$650$$ −13.8592 + 7.45100i −0.543602 + 0.292252i
$$651$$ 0 0
$$652$$ 6.38465 2.43189i 0.250042 0.0952401i
$$653$$ 13.0090i 0.509081i 0.967062 + 0.254541i $$0.0819242\pi$$
−0.967062 + 0.254541i $$0.918076\pi$$
$$654$$ 50.1480 9.22723i 1.96094 0.360813i
$$655$$ −16.1897 11.7976i −0.632584 0.460970i
$$656$$ −8.73008 9.79730i −0.340852 0.382520i
$$657$$ −23.1740 −0.904104
$$658$$ 0 0
$$659$$ 5.68280i 0.221370i 0.993856 + 0.110685i $$0.0353045\pi$$
−0.993856 + 0.110685i $$0.964695\pi$$
$$660$$ 62.1013 + 16.9069i 2.41729 + 0.658102i
$$661$$ 16.1645i 0.628727i −0.949303 0.314364i $$-0.898209\pi$$
0.949303 0.314364i $$-0.101791\pi$$
$$662$$ −31.5889 + 5.81235i −1.22774 + 0.225904i
$$663$$ 17.9290i 0.696303i
$$664$$ −27.3304 + 16.6024i −1.06063 + 0.644299i
$$665$$ 0 0
$$666$$ 3.35008 0.616415i 0.129813 0.0238856i
$$667$$ 3.96187 0.153404
$$668$$ −8.28512 21.7517i −0.320561 0.841597i
$$669$$ 4.83569 0.186959
$$670$$ −15.2652 + 31.7820i −0.589745 + 1.22785i
$$671$$ 27.3346 1.05524
$$672$$ 0 0
$$673$$ 32.4901i 1.25240i −0.779662 0.626200i $$-0.784609\pi$$
0.779662 0.626200i $$-0.215391\pi$$
$$674$$ −12.3085 + 2.26477i −0.474106 + 0.0872355i
$$675$$ 62.9705 20.2633i 2.42373 0.779933i
$$676$$ 15.0420 5.72944i 0.578539 0.220363i
$$677$$ 18.1326 0.696891 0.348446 0.937329i $$-0.386710\pi$$
0.348446 + 0.937329i $$0.386710\pi$$
$$678$$ −1.28441 6.98047i −0.0493273 0.268083i
$$679$$ 0 0
$$680$$ 1.33926 15.9364i 0.0513584 0.611134i
$$681$$ −49.5760 −1.89976
$$682$$ 29.0580 5.34668i 1.11269 0.204735i
$$683$$ −8.81555 −0.337318 −0.168659 0.985674i $$-0.553944\pi$$
−0.168659 + 0.985674i $$0.553944\pi$$
$$684$$ 69.6774 26.5398i 2.66418 1.01478i
$$685$$ 10.9596 15.0397i 0.418744 0.574637i
$$686$$ 0 0
$$687$$ 61.1801 2.33417
$$688$$ −19.9000 + 17.7323i −0.758680 + 0.676037i
$$689$$ 22.4239i 0.854281i
$$690$$ −15.5747 7.48067i −0.592920 0.284784i
$$691$$ 9.13188 0.347393 0.173697 0.984799i $$-0.444429\pi$$
0.173697 + 0.984799i $$0.444429\pi$$
$$692$$ −15.3571 + 5.84945i −0.583789 + 0.222363i
$$693$$ 0 0
$$694$$ −4.28254 23.2747i −0.162563 0.883494i
$$695$$ 28.1889 + 20.5415i 1.06927 + 0.779184i
$$696$$ 17.7953 10.8101i 0.674530 0.409757i
$$697$$ 8.29559i 0.314218i
$$698$$ −5.38137 + 0.990173i −0.203688 + 0.0374786i
$$699$$ −10.0221 −0.379072
$$700$$ 0 0
$$701$$ −23.3178 −0.880700 −0.440350 0.897826i $$-0.645146\pi$$
−0.440350 + 0.897826i $$0.645146\pi$$
$$702$$ 40.9480 7.53444i 1.54548 0.284369i
$$703$$ 1.75536i 0.0662047i
$$704$$ −32.0676 16.6543i −1.20859 0.627683i
$$705$$ −8.32870 6.06920i −0.313677 0.228579i
$$706$$ −2.02235 10.9910i −0.0761121 0.413653i
$$707$$ 0 0
$$708$$ −7.26583 19.0756i −0.273067 0.716906i
$$709$$ 0.346485 0.0130125 0.00650625 0.999979i $$-0.497929\pi$$
0.00650625 + 0.999979i $$0.497929\pi$$
$$710$$ 26.0979 + 12.5351i 0.979438 + 0.470432i
$$711$$ 102.062i 3.82763i
$$712$$ −36.7806 + 22.3431i −1.37841 + 0.837343i
$$713$$ −7.93167 −0.297043
$$714$$ 0 0
$$715$$ 13.2363 18.1640i 0.495009 0.679295i
$$716$$ 11.1011 + 29.1448i 0.414869 + 1.08919i
$$717$$ −11.9578 −0.446571
$$718$$ 5.78776 1.06495i 0.215997 0.0397436i
$$719$$ −40.3315 −1.50411 −0.752056 0.659099i $$-0.770938\pi$$
−0.752056 + 0.659099i $$0.770938\pi$$
$$720$$ −63.6638 + 6.26707i −2.37261 + 0.233560i
$$721$$ 0 0
$$722$$ −2.09066 11.3623i −0.0778062 0.422859i
$$723$$ −23.6780 −0.880594
$$724$$ 11.2862 + 29.6306i 0.419448 + 1.10121i
$$725$$ −3.53860 10.9966i −0.131420 0.408405i
$$726$$ −41.6642 + 7.66623i −1.54630 + 0.284520i
$$727$$ 19.5590i 0.725402i −0.931906 0.362701i $$-0.881855\pi$$
0.931906 0.362701i $$-0.118145\pi$$
$$728$$ 0 0
$$729$$ −21.5718 −0.798957
$$730$$ 4.43613 9.23600i 0.164188 0.341840i
$$731$$ 16.8498 0.623211
$$732$$ −36.0391 + 13.7271i −1.33204 + 0.507369i
$$733$$ 19.6314 0.725101 0.362550 0.931964i $$-0.381906\pi$$
0.362550 + 0.931964i $$0.381906\pi$$
$$734$$ 38.0786 7.00647i 1.40551 0.258614i
$$735$$ 0 0
$$736$$ 7.65746 + 5.95493i 0.282258 + 0.219502i
$$737$$ 50.3603i 1.85505i
$$738$$ 32.6351 6.00486i 1.20131 0.221042i
$$739$$ 0.386471i 0.0142166i 0.999975 + 0.00710828i $$0.00226265\pi$$
−0.999975 + 0.00710828i $$0.997737\pi$$
$$740$$ −0.395623 + 1.45317i −0.0145434 + 0.0534197i
$$741$$ 36.9577i 1.35767i
$$742$$ 0 0
$$743$$ −51.2724 −1.88100 −0.940502 0.339789i $$-0.889644\pi$$
−0.940502 + 0.339789i $$0.889644\pi$$
$$744$$ −35.6263 + 21.6419i −1.30612 + 0.793431i
$$745$$ 4.54292 + 3.31047i 0.166440 + 0.121286i
$$746$$ −40.7642 + 7.50061i −1.49248 + 0.274617i
$$747$$ 80.8626i 2.95861i
$$748$$ 8.13089 + 21.3468i 0.297295 + 0.780515i
$$749$$ 0 0
$$750$$ −6.85267 + 49.9109i −0.250224 + 1.82249i
$$751$$ 6.96844i 0.254282i −0.991885 0.127141i $$-0.959420\pi$$
0.991885 0.127141i $$-0.0405801\pi$$
$$752$$ 3.84912 + 4.31966i 0.140363 + 0.157522i
$$753$$ 18.3967i 0.670415i
$$754$$ −1.31575 7.15082i −0.0479168 0.260417i
$$755$$ −16.7706 + 23.0141i −0.610345 + 0.837570i
$$756$$ 0 0
$$757$$ 15.8945i 0.577696i −0.957375 0.288848i $$-0.906728\pi$$
0.957375 0.288848i $$-0.0932722\pi$$
$$758$$ 29.7827 5.48003i 1.08176 0.199044i
$$759$$ 24.6790 0.895790
$$760$$ −2.76068 + 32.8504i −0.100140 + 1.19161i
$$761$$ 15.2848i 0.554074i −0.960859 0.277037i $$-0.910648\pi$$
0.960859 0.277037i $$-0.0893524\pi$$
$$762$$ 75.3929 13.8723i 2.73120 0.502540i
$$763$$ 0 0
$$764$$ −8.00999 21.0293i −0.289791 0.760815i
$$765$$ 32.6833 + 23.8166i 1.18167 + 0.861092i
$$766$$ −26.8287 + 4.93649i −0.969360 + 0.178362i
$$767$$ −7.12807 −0.257380
$$768$$ 50.6429 + 5.85374i 1.82742 + 0.211229i
$$769$$ 7.67597i 0.276803i −0.990376 0.138401i $$-0.955804\pi$$
0.990376 0.138401i $$-0.0441964\pi$$
$$770$$ 0 0
$$771$$ 47.3169i 1.70408i
$$772$$ −17.6792 46.4148i −0.636288 1.67050i
$$773$$ −18.7437 −0.674162 −0.337081 0.941476i $$-0.609440\pi$$
−0.337081 + 0.941476i $$0.609440\pi$$
$$774$$ −12.1969 66.2875i −0.438409 2.38265i
$$775$$ 7.08429 + 22.0153i 0.254475 + 0.790812i
$$776$$ −6.59788 10.8612i −0.236850 0.389895i
$$777$$ 0 0
$$778$$ −3.96837 21.5672i −0.142273 0.773223i
$$779$$ 17.1000i 0.612672i
$$780$$ −8.32951 + 30.5953i −0.298244 + 1.09549i
$$781$$ −41.3535 −1.47975
$$782$$ −1.10970 6.03100i −0.0396829 0.215668i
$$783$$ 30.5667i 1.09236i
$$784$$ 0 0
$$785$$ 15.6273 + 11.3878i 0.557764 + 0.406448i
$$786$$ −39.7017 + 7.30513i −1.41611