# Properties

 Label 400.2.l.g.301.1 Level $400$ Weight $2$ Character 400.301 Analytic conductor $3.194$ Analytic rank $0$ Dimension $12$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$400 = 2^{4} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 400.l (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$3.19401608085$$ Analytic rank: $$0$$ Dimension: $$12$$ Relative dimension: $$6$$ over $$\Q(i)$$ Coefficient field: 12.0.4767670494822400.1 Defining polynomial: $$x^{12} - 4 x^{11} + 7 x^{10} - 4 x^{9} - 8 x^{8} + 24 x^{7} - 38 x^{6} + 48 x^{5} - 32 x^{4} - 32 x^{3} + 112 x^{2} - 128 x + 64$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 301.1 Root $$-1.41313 + 0.0554252i$$ of defining polynomial Character $$\chi$$ $$=$$ 400.301 Dual form 400.2.l.g.101.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.41313 + 0.0554252i) q^{2} +(0.488516 + 0.488516i) q^{3} +(1.99386 - 0.156646i) q^{4} +(-0.717411 - 0.663259i) q^{6} +4.71540i q^{7} +(-2.80889 + 0.331870i) q^{8} -2.52270i q^{9} +O(q^{10})$$ $$q+(-1.41313 + 0.0554252i) q^{2} +(0.488516 + 0.488516i) q^{3} +(1.99386 - 0.156646i) q^{4} +(-0.717411 - 0.663259i) q^{6} +4.71540i q^{7} +(-2.80889 + 0.331870i) q^{8} -2.52270i q^{9} +(-3.91360 + 3.91360i) q^{11} +(1.05055 + 0.897506i) q^{12} +(0.0878822 + 0.0878822i) q^{13} +(-0.261352 - 6.66346i) q^{14} +(3.95092 - 0.624658i) q^{16} -4.67442 q^{17} +(0.139821 + 3.56490i) q^{18} +(1.81249 + 1.81249i) q^{19} +(-2.30355 + 2.30355i) q^{21} +(5.31350 - 5.74732i) q^{22} -1.63007i q^{23} +(-1.53431 - 1.21006i) q^{24} +(-0.129060 - 0.119318i) q^{26} +(2.69793 - 2.69793i) q^{27} +(0.738648 + 9.40184i) q^{28} +(3.26362 + 3.26362i) q^{29} -2.12875 q^{31} +(-5.54854 + 1.10170i) q^{32} -3.82371 q^{33} +(6.60555 - 0.259081i) q^{34} +(-0.395171 - 5.02991i) q^{36} +(-3.97797 + 3.97797i) q^{37} +(-2.66173 - 2.46082i) q^{38} +0.0858637i q^{39} +8.25504i q^{41} +(3.12753 - 3.38288i) q^{42} +(-2.27336 + 2.27336i) q^{43} +(-7.19010 + 8.41620i) q^{44} +(0.0903468 + 2.30349i) q^{46} +4.06129 q^{47} +(2.23524 + 1.62493i) q^{48} -15.2350 q^{49} +(-2.28353 - 2.28353i) q^{51} +(0.188991 + 0.161458i) q^{52} +(5.03938 - 5.03938i) q^{53} +(-3.66298 + 3.96205i) q^{54} +(-1.56490 - 13.2450i) q^{56} +1.77086i q^{57} +(-4.79280 - 4.43103i) q^{58} +(-5.16453 + 5.16453i) q^{59} +(7.12726 + 7.12726i) q^{61} +(3.00819 - 0.117986i) q^{62} +11.8956 q^{63} +(7.77972 - 1.86437i) q^{64} +(5.40339 - 0.211930i) q^{66} +(7.49920 + 7.49920i) q^{67} +(-9.32012 + 0.732228i) q^{68} +(0.796314 - 0.796314i) q^{69} -4.54072i q^{71} +(0.837210 + 7.08600i) q^{72} -8.30557i q^{73} +(5.40090 - 5.84186i) q^{74} +(3.89776 + 3.32992i) q^{76} +(-18.4542 - 18.4542i) q^{77} +(-0.00475901 - 0.121336i) q^{78} +11.5317 q^{79} -4.93215 q^{81} +(-0.457537 - 11.6654i) q^{82} +(1.16919 + 1.16919i) q^{83} +(-4.23211 + 4.95379i) q^{84} +(3.08655 - 3.33855i) q^{86} +3.18866i q^{87} +(9.69406 - 12.2917i) q^{88} -3.24572i q^{89} +(-0.414400 + 0.414400i) q^{91} +(-0.255343 - 3.25012i) q^{92} +(-1.03993 - 1.03993i) q^{93} +(-5.73912 + 0.225098i) q^{94} +(-3.24875 - 2.17235i) q^{96} +13.9581 q^{97} +(21.5290 - 0.844405i) q^{98} +(9.87285 + 9.87285i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$12q + 4q^{2} + 2q^{3} + 2q^{4} + 6q^{6} - 8q^{8} + O(q^{10})$$ $$12q + 4q^{2} + 2q^{3} + 2q^{4} + 6q^{6} - 8q^{8} - 2q^{11} + 8q^{12} - 4q^{13} + 14q^{14} + 2q^{16} - 8q^{17} + 18q^{18} - 14q^{19} - 20q^{21} + 2q^{22} - 14q^{24} - 16q^{26} - 10q^{27} + 26q^{28} - 4q^{31} - 16q^{32} + 28q^{33} - 6q^{34} + 2q^{36} + 8q^{37} + 10q^{38} + 10q^{42} - 44q^{44} - 10q^{46} + 8q^{47} - 28q^{48} + 4q^{49} + 10q^{51} - 12q^{52} - 16q^{53} + 10q^{54} + 6q^{56} - 60q^{58} + 20q^{59} + 4q^{61} - 18q^{62} - 8q^{63} + 38q^{64} + 32q^{66} + 50q^{67} - 60q^{68} - 14q^{72} + 10q^{74} + 60q^{76} - 8q^{77} + 4q^{78} + 12q^{79} - 8q^{81} + 42q^{82} - 2q^{83} + 34q^{84} + 6q^{86} + 30q^{88} - 2q^{92} - 44q^{93} + 32q^{94} - 34q^{96} + 64q^{98} + 12q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$$.

 $$n$$ $$101$$ $$177$$ $$351$$ $$\chi(n)$$ $$e\left(\frac{3}{4}\right)$$ $$1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.41313 + 0.0554252i −0.999232 + 0.0391915i
$$3$$ 0.488516 + 0.488516i 0.282045 + 0.282045i 0.833924 0.551879i $$-0.186089\pi$$
−0.551879 + 0.833924i $$0.686089\pi$$
$$4$$ 1.99386 0.156646i 0.996928 0.0783229i
$$5$$ 0 0
$$6$$ −0.717411 0.663259i −0.292882 0.270774i
$$7$$ 4.71540i 1.78226i 0.453753 + 0.891128i $$0.350085\pi$$
−0.453753 + 0.891128i $$0.649915\pi$$
$$8$$ −2.80889 + 0.331870i −0.993093 + 0.117334i
$$9$$ 2.52270i 0.840901i
$$10$$ 0 0
$$11$$ −3.91360 + 3.91360i −1.17999 + 1.17999i −0.200249 + 0.979745i $$0.564175\pi$$
−0.979745 + 0.200249i $$0.935825\pi$$
$$12$$ 1.05055 + 0.897506i 0.303269 + 0.259088i
$$13$$ 0.0878822 + 0.0878822i 0.0243741 + 0.0243741i 0.719189 0.694815i $$-0.244514\pi$$
−0.694815 + 0.719189i $$0.744514\pi$$
$$14$$ −0.261352 6.66346i −0.0698493 1.78089i
$$15$$ 0 0
$$16$$ 3.95092 0.624658i 0.987731 0.156165i
$$17$$ −4.67442 −1.13371 −0.566857 0.823816i $$-0.691841\pi$$
−0.566857 + 0.823816i $$0.691841\pi$$
$$18$$ 0.139821 + 3.56490i 0.0329562 + 0.840255i
$$19$$ 1.81249 + 1.81249i 0.415813 + 0.415813i 0.883758 0.467945i $$-0.155005\pi$$
−0.467945 + 0.883758i $$0.655005\pi$$
$$20$$ 0 0
$$21$$ −2.30355 + 2.30355i −0.502676 + 0.502676i
$$22$$ 5.31350 5.74732i 1.13284 1.22533i
$$23$$ 1.63007i 0.339893i −0.985453 0.169946i $$-0.945641\pi$$
0.985453 0.169946i $$-0.0543594\pi$$
$$24$$ −1.53431 1.21006i −0.313190 0.247003i
$$25$$ 0 0
$$26$$ −0.129060 0.119318i −0.0253107 0.0234002i
$$27$$ 2.69793 2.69793i 0.519217 0.519217i
$$28$$ 0.738648 + 9.40184i 0.139591 + 1.77678i
$$29$$ 3.26362 + 3.26362i 0.606039 + 0.606039i 0.941909 0.335869i $$-0.109030\pi$$
−0.335869 + 0.941909i $$0.609030\pi$$
$$30$$ 0 0
$$31$$ −2.12875 −0.382334 −0.191167 0.981557i $$-0.561227\pi$$
−0.191167 + 0.981557i $$0.561227\pi$$
$$32$$ −5.54854 + 1.10170i −0.980852 + 0.194755i
$$33$$ −3.82371 −0.665622
$$34$$ 6.60555 0.259081i 1.13284 0.0444320i
$$35$$ 0 0
$$36$$ −0.395171 5.02991i −0.0658618 0.838318i
$$37$$ −3.97797 + 3.97797i −0.653974 + 0.653974i −0.953948 0.299973i $$-0.903022\pi$$
0.299973 + 0.953948i $$0.403022\pi$$
$$38$$ −2.66173 2.46082i −0.431790 0.399197i
$$39$$ 0.0858637i 0.0137492i
$$40$$ 0 0
$$41$$ 8.25504i 1.28922i 0.764511 + 0.644611i $$0.222980\pi$$
−0.764511 + 0.644611i $$0.777020\pi$$
$$42$$ 3.12753 3.38288i 0.482589 0.521990i
$$43$$ −2.27336 + 2.27336i −0.346685 + 0.346685i −0.858873 0.512188i $$-0.828835\pi$$
0.512188 + 0.858873i $$0.328835\pi$$
$$44$$ −7.19010 + 8.41620i −1.08395 + 1.26879i
$$45$$ 0 0
$$46$$ 0.0903468 + 2.30349i 0.0133209 + 0.339631i
$$47$$ 4.06129 0.592400 0.296200 0.955126i $$-0.404281\pi$$
0.296200 + 0.955126i $$0.404281\pi$$
$$48$$ 2.23524 + 1.62493i 0.322630 + 0.234539i
$$49$$ −15.2350 −2.17643
$$50$$ 0 0
$$51$$ −2.28353 2.28353i −0.319758 0.319758i
$$52$$ 0.188991 + 0.161458i 0.0262083 + 0.0223902i
$$53$$ 5.03938 5.03938i 0.692211 0.692211i −0.270507 0.962718i $$-0.587191\pi$$
0.962718 + 0.270507i $$0.0871912\pi$$
$$54$$ −3.66298 + 3.96205i −0.498469 + 0.539167i
$$55$$ 0 0
$$56$$ −1.56490 13.2450i −0.209119 1.76994i
$$57$$ 1.77086i 0.234556i
$$58$$ −4.79280 4.43103i −0.629325 0.581822i
$$59$$ −5.16453 + 5.16453i −0.672365 + 0.672365i −0.958261 0.285896i $$-0.907709\pi$$
0.285896 + 0.958261i $$0.407709\pi$$
$$60$$ 0 0
$$61$$ 7.12726 + 7.12726i 0.912552 + 0.912552i 0.996472 0.0839206i $$-0.0267442\pi$$
−0.0839206 + 0.996472i $$0.526744\pi$$
$$62$$ 3.00819 0.117986i 0.382041 0.0149843i
$$63$$ 11.8956 1.49870
$$64$$ 7.77972 1.86437i 0.972466 0.233047i
$$65$$ 0 0
$$66$$ 5.40339 0.211930i 0.665111 0.0260868i
$$67$$ 7.49920 + 7.49920i 0.916173 + 0.916173i 0.996748 0.0805758i $$-0.0256759\pi$$
−0.0805758 + 0.996748i $$0.525676\pi$$
$$68$$ −9.32012 + 0.732228i −1.13023 + 0.0887957i
$$69$$ 0.796314 0.796314i 0.0958649 0.0958649i
$$70$$ 0 0
$$71$$ 4.54072i 0.538884i −0.963017 0.269442i $$-0.913161\pi$$
0.963017 0.269442i $$-0.0868393\pi$$
$$72$$ 0.837210 + 7.08600i 0.0986662 + 0.835093i
$$73$$ 8.30557i 0.972093i −0.873933 0.486047i $$-0.838439\pi$$
0.873933 0.486047i $$-0.161561\pi$$
$$74$$ 5.40090 5.84186i 0.627842 0.679102i
$$75$$ 0 0
$$76$$ 3.89776 + 3.32992i 0.447104 + 0.381968i
$$77$$ −18.4542 18.4542i −2.10305 2.10305i
$$78$$ −0.00475901 0.121336i −0.000538852 0.0137386i
$$79$$ 11.5317 1.29742 0.648709 0.761037i $$-0.275309\pi$$
0.648709 + 0.761037i $$0.275309\pi$$
$$80$$ 0 0
$$81$$ −4.93215 −0.548017
$$82$$ −0.457537 11.6654i −0.0505266 1.28823i
$$83$$ 1.16919 + 1.16919i 0.128335 + 0.128335i 0.768357 0.640022i $$-0.221075\pi$$
−0.640022 + 0.768357i $$0.721075\pi$$
$$84$$ −4.23211 + 4.95379i −0.461761 + 0.540503i
$$85$$ 0 0
$$86$$ 3.08655 3.33855i 0.332831 0.360006i
$$87$$ 3.18866i 0.341861i
$$88$$ 9.69406 12.2917i 1.03339 1.31030i
$$89$$ 3.24572i 0.344046i −0.985093 0.172023i $$-0.944970\pi$$
0.985093 0.172023i $$-0.0550304\pi$$
$$90$$ 0 0
$$91$$ −0.414400 + 0.414400i −0.0434409 + 0.0434409i
$$92$$ −0.255343 3.25012i −0.0266214 0.338848i
$$93$$ −1.03993 1.03993i −0.107835 0.107835i
$$94$$ −5.73912 + 0.225098i −0.591945 + 0.0232171i
$$95$$ 0 0
$$96$$ −3.24875 2.17235i −0.331574 0.221714i
$$97$$ 13.9581 1.41723 0.708613 0.705598i $$-0.249321\pi$$
0.708613 + 0.705598i $$0.249321\pi$$
$$98$$ 21.5290 0.844405i 2.17476 0.0852978i
$$99$$ 9.87285 + 9.87285i 0.992258 + 0.992258i
$$100$$ 0 0
$$101$$ 13.4088 13.4088i 1.33422 1.33422i 0.432672 0.901552i $$-0.357571\pi$$
0.901552 0.432672i $$-0.142429\pi$$
$$102$$ 3.35348 + 3.10035i 0.332044 + 0.306981i
$$103$$ 13.7638i 1.35618i −0.734977 0.678092i $$-0.762807\pi$$
0.734977 0.678092i $$-0.237193\pi$$
$$104$$ −0.276017 0.217686i −0.0270657 0.0213459i
$$105$$ 0 0
$$106$$ −6.84197 + 7.40059i −0.664551 + 0.718808i
$$107$$ 0.327996 0.327996i 0.0317086 0.0317086i −0.691075 0.722783i $$-0.742862\pi$$
0.722783 + 0.691075i $$0.242862\pi$$
$$108$$ 4.95666 5.80190i 0.476955 0.558288i
$$109$$ −0.149698 0.149698i −0.0143385 0.0143385i 0.699901 0.714240i $$-0.253227\pi$$
−0.714240 + 0.699901i $$0.753227\pi$$
$$110$$ 0 0
$$111$$ −3.88660 −0.368900
$$112$$ 2.94551 + 18.6302i 0.278325 + 1.76039i
$$113$$ −5.97999 −0.562550 −0.281275 0.959627i $$-0.590757\pi$$
−0.281275 + 0.959627i $$0.590757\pi$$
$$114$$ −0.0981502 2.50245i −0.00919261 0.234376i
$$115$$ 0 0
$$116$$ 7.01843 + 5.99596i 0.651644 + 0.556711i
$$117$$ 0.221701 0.221701i 0.0204962 0.0204962i
$$118$$ 7.01189 7.58439i 0.645497 0.698199i
$$119$$ 22.0418i 2.02057i
$$120$$ 0 0
$$121$$ 19.6325i 1.78477i
$$122$$ −10.4668 9.67669i −0.947615 0.876086i
$$123$$ −4.03272 + 4.03272i −0.363618 + 0.363618i
$$124$$ −4.24442 + 0.333459i −0.381160 + 0.0299455i
$$125$$ 0 0
$$126$$ −16.8100 + 0.659314i −1.49755 + 0.0587364i
$$127$$ 2.73076 0.242315 0.121158 0.992633i $$-0.461339\pi$$
0.121158 + 0.992633i $$0.461339\pi$$
$$128$$ −10.8904 + 3.06579i −0.962585 + 0.270980i
$$129$$ −2.22115 −0.195561
$$130$$ 0 0
$$131$$ −0.813555 0.813555i −0.0710806 0.0710806i 0.670673 0.741753i $$-0.266006\pi$$
−0.741753 + 0.670673i $$0.766006\pi$$
$$132$$ −7.62392 + 0.598967i −0.663577 + 0.0521334i
$$133$$ −8.54661 + 8.54661i −0.741085 + 0.741085i
$$134$$ −11.0130 10.1817i −0.951375 0.879563i
$$135$$ 0 0
$$136$$ 13.1299 1.55130i 1.12588 0.133023i
$$137$$ 0.199812i 0.0170711i 0.999964 + 0.00853557i $$0.00271699\pi$$
−0.999964 + 0.00853557i $$0.997283\pi$$
$$138$$ −1.08116 + 1.16943i −0.0920342 + 0.0995484i
$$139$$ −11.6301 + 11.6301i −0.986448 + 0.986448i −0.999909 0.0134610i $$-0.995715\pi$$
0.0134610 + 0.999909i $$0.495715\pi$$
$$140$$ 0 0
$$141$$ 1.98400 + 1.98400i 0.167083 + 0.167083i
$$142$$ 0.251670 + 6.41661i 0.0211197 + 0.538470i
$$143$$ −0.687871 −0.0575227
$$144$$ −1.57583 9.96701i −0.131319 0.830585i
$$145$$ 0 0
$$146$$ 0.460338 + 11.7368i 0.0380978 + 0.971346i
$$147$$ −7.44256 7.44256i −0.613852 0.613852i
$$148$$ −7.30837 + 8.55463i −0.600744 + 0.703186i
$$149$$ −1.13384 + 1.13384i −0.0928880 + 0.0928880i −0.752024 0.659136i $$-0.770922\pi$$
0.659136 + 0.752024i $$0.270922\pi$$
$$150$$ 0 0
$$151$$ 7.12216i 0.579593i −0.957088 0.289797i $$-0.906412\pi$$
0.957088 0.289797i $$-0.0935877\pi$$
$$152$$ −5.69259 4.48957i −0.461730 0.364152i
$$153$$ 11.7922i 0.953341i
$$154$$ 27.1009 + 25.0553i 2.18386 + 2.01901i
$$155$$ 0 0
$$156$$ 0.0134502 + 0.171200i 0.00107688 + 0.0137070i
$$157$$ 5.32145 + 5.32145i 0.424698 + 0.424698i 0.886818 0.462120i $$-0.152911\pi$$
−0.462120 + 0.886818i $$0.652911\pi$$
$$158$$ −16.2957 + 0.639147i −1.29642 + 0.0508478i
$$159$$ 4.92363 0.390469
$$160$$ 0 0
$$161$$ 7.68643 0.605775
$$162$$ 6.96976 0.273365i 0.547596 0.0214776i
$$163$$ 12.3010 + 12.3010i 0.963488 + 0.963488i 0.999357 0.0358685i $$-0.0114197\pi$$
−0.0358685 + 0.999357i $$0.511420\pi$$
$$164$$ 1.29312 + 16.4594i 0.100975 + 1.28526i
$$165$$ 0 0
$$166$$ −1.71702 1.58741i −0.133266 0.123207i
$$167$$ 9.86820i 0.763624i 0.924240 + 0.381812i $$0.124700\pi$$
−0.924240 + 0.381812i $$0.875300\pi$$
$$168$$ 5.70594 7.23490i 0.440223 0.558184i
$$169$$ 12.9846i 0.998812i
$$170$$ 0 0
$$171$$ 4.57237 4.57237i 0.349658 0.349658i
$$172$$ −4.17665 + 4.88887i −0.318466 + 0.372773i
$$173$$ 13.4089 + 13.4089i 1.01946 + 1.01946i 0.999807 + 0.0196525i $$0.00625599\pi$$
0.0196525 + 0.999807i $$0.493744\pi$$
$$174$$ −0.176732 4.50599i −0.0133980 0.341598i
$$175$$ 0 0
$$176$$ −13.0177 + 17.9070i −0.981243 + 1.34979i
$$177$$ −5.04591 −0.379274
$$178$$ 0.179895 + 4.58662i 0.0134837 + 0.343782i
$$179$$ 0.419587 + 0.419587i 0.0313614 + 0.0313614i 0.722614 0.691252i $$-0.242941\pi$$
−0.691252 + 0.722614i $$0.742941\pi$$
$$180$$ 0 0
$$181$$ −14.2605 + 14.2605i −1.05998 + 1.05998i −0.0618956 + 0.998083i $$0.519715\pi$$
−0.998083 + 0.0618956i $$0.980285\pi$$
$$182$$ 0.562632 0.608568i 0.0417050 0.0451101i
$$183$$ 6.96356i 0.514761i
$$184$$ 0.540971 + 4.57868i 0.0398809 + 0.337545i
$$185$$ 0 0
$$186$$ 1.52719 + 1.41191i 0.111979 + 0.103526i
$$187$$ 18.2938 18.2938i 1.33777 1.33777i
$$188$$ 8.09762 0.636183i 0.590580 0.0463984i
$$189$$ 12.7218 + 12.7218i 0.925377 + 0.925377i
$$190$$ 0 0
$$191$$ 17.3304 1.25399 0.626993 0.779025i $$-0.284285\pi$$
0.626993 + 0.779025i $$0.284285\pi$$
$$192$$ 4.71130 + 2.88974i 0.340008 + 0.208549i
$$193$$ −16.8667 −1.21409 −0.607045 0.794667i $$-0.707645\pi$$
−0.607045 + 0.794667i $$0.707645\pi$$
$$194$$ −19.7245 + 0.773628i −1.41614 + 0.0555432i
$$195$$ 0 0
$$196$$ −30.3765 + 2.38650i −2.16975 + 0.170464i
$$197$$ 3.58908 3.58908i 0.255712 0.255712i −0.567596 0.823307i $$-0.692126\pi$$
0.823307 + 0.567596i $$0.192126\pi$$
$$198$$ −14.4988 13.4044i −1.03038 0.952608i
$$199$$ 6.64501i 0.471052i −0.971868 0.235526i $$-0.924319\pi$$
0.971868 0.235526i $$-0.0756813\pi$$
$$200$$ 0 0
$$201$$ 7.32695i 0.516803i
$$202$$ −18.2051 + 19.6915i −1.28091 + 1.38549i
$$203$$ −15.3893 + 15.3893i −1.08012 + 1.08012i
$$204$$ −4.91073 4.19532i −0.343820 0.293731i
$$205$$ 0 0
$$206$$ 0.762860 + 19.4500i 0.0531510 + 1.35514i
$$207$$ −4.11218 −0.285816
$$208$$ 0.402112 + 0.292320i 0.0278815 + 0.0202687i
$$209$$ −14.1867 −0.981314
$$210$$ 0 0
$$211$$ 1.90906 + 1.90906i 0.131425 + 0.131425i 0.769759 0.638334i $$-0.220376\pi$$
−0.638334 + 0.769759i $$0.720376\pi$$
$$212$$ 9.25839 10.8372i 0.635869 0.744301i
$$213$$ 2.21821 2.21821i 0.151989 0.151989i
$$214$$ −0.445321 + 0.481680i −0.0304415 + 0.0329270i
$$215$$ 0 0
$$216$$ −6.68282 + 8.47355i −0.454709 + 0.576552i
$$217$$ 10.0379i 0.681418i
$$218$$ 0.219839 + 0.203245i 0.0148894 + 0.0137655i
$$219$$ 4.05740 4.05740i 0.274174 0.274174i
$$220$$ 0 0
$$221$$ −0.410798 0.410798i −0.0276333 0.0276333i
$$222$$ 5.49226 0.215416i 0.368617 0.0144578i
$$223$$ −24.1071 −1.61433 −0.807165 0.590326i $$-0.798999\pi$$
−0.807165 + 0.590326i $$0.798999\pi$$
$$224$$ −5.19497 26.1636i −0.347103 1.74813i
$$225$$ 0 0
$$226$$ 8.45048 0.331442i 0.562118 0.0220472i
$$227$$ −6.67411 6.67411i −0.442977 0.442977i 0.450035 0.893011i $$-0.351412\pi$$
−0.893011 + 0.450035i $$0.851412\pi$$
$$228$$ 0.277397 + 3.53084i 0.0183711 + 0.233835i
$$229$$ 16.0807 16.0807i 1.06264 1.06264i 0.0647388 0.997902i $$-0.479379\pi$$
0.997902 0.0647388i $$-0.0206214\pi$$
$$230$$ 0 0
$$231$$ 18.0303i 1.18631i
$$232$$ −10.2503 8.08406i −0.672962 0.530744i
$$233$$ 16.4976i 1.08079i −0.841411 0.540396i $$-0.818274\pi$$
0.841411 0.540396i $$-0.181726\pi$$
$$234$$ −0.301004 + 0.325579i −0.0196772 + 0.0212838i
$$235$$ 0 0
$$236$$ −9.48833 + 11.1063i −0.617638 + 0.722961i
$$237$$ 5.63342 + 5.63342i 0.365930 + 0.365930i
$$238$$ 1.22167 + 31.1478i 0.0791891 + 2.01901i
$$239$$ 5.25917 0.340188 0.170094 0.985428i $$-0.445593\pi$$
0.170094 + 0.985428i $$0.445593\pi$$
$$240$$ 0 0
$$241$$ −14.1126 −0.909075 −0.454538 0.890728i $$-0.650196\pi$$
−0.454538 + 0.890728i $$0.650196\pi$$
$$242$$ 1.08813 + 27.7432i 0.0699479 + 1.78340i
$$243$$ −10.5032 10.5032i −0.673782 0.673782i
$$244$$ 15.3272 + 13.0943i 0.981222 + 0.838275i
$$245$$ 0 0
$$246$$ 5.47523 5.92226i 0.349088 0.377589i
$$247$$ 0.318571i 0.0202702i
$$248$$ 5.97942 0.706468i 0.379693 0.0448608i
$$249$$ 1.14234i 0.0723927i
$$250$$ 0 0
$$251$$ −9.98825 + 9.98825i −0.630453 + 0.630453i −0.948182 0.317729i $$-0.897080\pi$$
0.317729 + 0.948182i $$0.397080\pi$$
$$252$$ 23.7181 1.86339i 1.49410 0.117383i
$$253$$ 6.37943 + 6.37943i 0.401071 + 0.401071i
$$254$$ −3.85890 + 0.151353i −0.242129 + 0.00949671i
$$255$$ 0 0
$$256$$ 15.2196 4.93595i 0.951225 0.308497i
$$257$$ 8.44760 0.526947 0.263474 0.964667i $$-0.415132\pi$$
0.263474 + 0.964667i $$0.415132\pi$$
$$258$$ 3.13877 0.123108i 0.195411 0.00766435i
$$259$$ −18.7577 18.7577i −1.16555 1.16555i
$$260$$ 0 0
$$261$$ 8.23315 8.23315i 0.509619 0.509619i
$$262$$ 1.19475 + 1.10457i 0.0738118 + 0.0682403i
$$263$$ 18.3064i 1.12882i 0.825494 + 0.564410i $$0.190896\pi$$
−0.825494 + 0.564410i $$0.809104\pi$$
$$264$$ 10.7404 1.26897i 0.661024 0.0781000i
$$265$$ 0 0
$$266$$ 11.6037 12.5511i 0.711472 0.769560i
$$267$$ 1.58559 1.58559i 0.0970364 0.0970364i
$$268$$ 16.1270 + 13.7776i 0.985115 + 0.841601i
$$269$$ 13.5631 + 13.5631i 0.826955 + 0.826955i 0.987094 0.160140i $$-0.0511945\pi$$
−0.160140 + 0.987094i $$0.551194\pi$$
$$270$$ 0 0
$$271$$ −2.24520 −0.136386 −0.0681930 0.997672i $$-0.521723\pi$$
−0.0681930 + 0.997672i $$0.521723\pi$$
$$272$$ −18.4683 + 2.91991i −1.11980 + 0.177046i
$$273$$ −0.404882 −0.0245046
$$274$$ −0.0110746 0.282360i −0.000669044 0.0170580i
$$275$$ 0 0
$$276$$ 1.46300 1.71247i 0.0880620 0.103079i
$$277$$ −7.28255 + 7.28255i −0.437566 + 0.437566i −0.891192 0.453626i $$-0.850130\pi$$
0.453626 + 0.891192i $$0.350130\pi$$
$$278$$ 15.7901 17.0793i 0.947030 1.02435i
$$279$$ 5.37020i 0.321506i
$$280$$ 0 0
$$281$$ 6.04084i 0.360367i −0.983633 0.180183i $$-0.942331\pi$$
0.983633 0.180183i $$-0.0576691\pi$$
$$282$$ −2.91361 2.69369i −0.173503 0.160407i
$$283$$ 15.1350 15.1350i 0.899682 0.899682i −0.0957259 0.995408i $$-0.530517\pi$$
0.995408 + 0.0957259i $$0.0305172\pi$$
$$284$$ −0.711284 9.05354i −0.0422070 0.537229i
$$285$$ 0 0
$$286$$ 0.972049 0.0381254i 0.0574785 0.00225440i
$$287$$ −38.9259 −2.29772
$$288$$ 2.77927 + 13.9973i 0.163770 + 0.824800i
$$289$$ 4.85021 0.285306
$$290$$ 0 0
$$291$$ 6.81873 + 6.81873i 0.399721 + 0.399721i
$$292$$ −1.30103 16.5601i −0.0761371 0.969107i
$$293$$ 10.7777 10.7777i 0.629637 0.629637i −0.318339 0.947977i $$-0.603125\pi$$
0.947977 + 0.318339i $$0.103125\pi$$
$$294$$ 10.9298 + 10.1048i 0.637438 + 0.589322i
$$295$$ 0 0
$$296$$ 9.85351 12.4939i 0.572724 0.726190i
$$297$$ 21.1172i 1.22534i
$$298$$ 1.53942 1.66511i 0.0891762 0.0964571i
$$299$$ 0.143254 0.143254i 0.00828459 0.00828459i
$$300$$ 0 0
$$301$$ −10.7198 10.7198i −0.617881 0.617881i
$$302$$ 0.394747 + 10.0645i 0.0227152 + 0.579148i
$$303$$ 13.1008 0.752621
$$304$$ 8.29319 + 6.02882i 0.475647 + 0.345776i
$$305$$ 0 0
$$306$$ −0.653584 16.6639i −0.0373629 0.952609i
$$307$$ −7.94378 7.94378i −0.453376 0.453376i 0.443098 0.896473i $$-0.353880\pi$$
−0.896473 + 0.443098i $$0.853880\pi$$
$$308$$ −39.6858 33.9042i −2.26131 1.93187i
$$309$$ 6.72382 6.72382i 0.382505 0.382505i
$$310$$ 0 0
$$311$$ 31.1649i 1.76720i 0.468244 + 0.883599i $$0.344887\pi$$
−0.468244 + 0.883599i $$0.655113\pi$$
$$312$$ −0.0284956 0.241182i −0.00161325 0.0136542i
$$313$$ 5.35842i 0.302876i 0.988467 + 0.151438i $$0.0483903\pi$$
−0.988467 + 0.151438i $$0.951610\pi$$
$$314$$ −7.81482 7.22494i −0.441016 0.407727i
$$315$$ 0 0
$$316$$ 22.9925 1.80639i 1.29343 0.101617i
$$317$$ 8.88165 + 8.88165i 0.498843 + 0.498843i 0.911078 0.412235i $$-0.135252\pi$$
−0.412235 + 0.911078i $$0.635252\pi$$
$$318$$ −6.95771 + 0.272893i −0.390169 + 0.0153031i
$$319$$ −25.5450 −1.43025
$$320$$ 0 0
$$321$$ 0.320463 0.0178865
$$322$$ −10.8619 + 0.426022i −0.605310 + 0.0237413i
$$323$$ −8.47233 8.47233i −0.471413 0.471413i
$$324$$ −9.83400 + 0.772600i −0.546333 + 0.0429222i
$$325$$ 0 0
$$326$$ −18.0646 16.7011i −1.00051 0.924987i
$$327$$ 0.146260i 0.00808817i
$$328$$ −2.73960 23.1875i −0.151269 1.28032i
$$329$$ 19.1506i 1.05581i
$$330$$ 0 0
$$331$$ 6.07281 6.07281i 0.333792 0.333792i −0.520233 0.854025i $$-0.674155\pi$$
0.854025 + 0.520233i $$0.174155\pi$$
$$332$$ 2.51435 + 2.14805i 0.137993 + 0.117890i
$$333$$ 10.0352 + 10.0352i 0.549928 + 0.549928i
$$334$$ −0.546947 13.9450i −0.0299276 0.763038i
$$335$$ 0 0
$$336$$ −7.66222 + 10.5401i −0.418008 + 0.575009i
$$337$$ 22.0227 1.19965 0.599827 0.800130i $$-0.295236\pi$$
0.599827 + 0.800130i $$0.295236\pi$$
$$338$$ 0.719672 + 18.3488i 0.0391450 + 0.998044i
$$339$$ −2.92132 2.92132i −0.158664 0.158664i
$$340$$ 0 0
$$341$$ 8.33106 8.33106i 0.451152 0.451152i
$$342$$ −6.20792 + 6.71477i −0.335686 + 0.363093i
$$343$$ 38.8315i 2.09670i
$$344$$ 5.63117 7.14009i 0.303612 0.384968i
$$345$$ 0 0
$$346$$ −19.6917 18.2053i −1.05863 0.978722i
$$347$$ −11.8920 + 11.8920i −0.638395 + 0.638395i −0.950159 0.311765i $$-0.899080\pi$$
0.311765 + 0.950159i $$0.399080\pi$$
$$348$$ 0.499490 + 6.35773i 0.0267755 + 0.340810i
$$349$$ −8.65696 8.65696i −0.463396 0.463396i 0.436371 0.899767i $$-0.356264\pi$$
−0.899767 + 0.436371i $$0.856264\pi$$
$$350$$ 0 0
$$351$$ 0.474200 0.0253109
$$352$$ 17.4031 26.0263i 0.927589 1.38721i
$$353$$ 26.6153 1.41659 0.708296 0.705916i $$-0.249464\pi$$
0.708296 + 0.705916i $$0.249464\pi$$
$$354$$ 7.13051 0.279671i 0.378983 0.0148643i
$$355$$ 0 0
$$356$$ −0.508429 6.47151i −0.0269467 0.342989i
$$357$$ 10.7678 10.7678i 0.569890 0.569890i
$$358$$ −0.616185 0.569674i −0.0325664 0.0301082i
$$359$$ 4.85032i 0.255990i 0.991775 + 0.127995i $$0.0408542\pi$$
−0.991775 + 0.127995i $$0.959146\pi$$
$$360$$ 0 0
$$361$$ 12.4298i 0.654199i
$$362$$ 19.3616 20.9424i 1.01762 1.10071i
$$363$$ 9.59078 9.59078i 0.503385 0.503385i
$$364$$ −0.761340 + 0.891168i −0.0399051 + 0.0467099i
$$365$$ 0 0
$$366$$ −0.385957 9.84039i −0.0201743 0.514365i
$$367$$ 15.6741 0.818182 0.409091 0.912494i $$-0.365846\pi$$
0.409091 + 0.912494i $$0.365846\pi$$
$$368$$ −1.01823 6.44027i −0.0530792 0.335722i
$$369$$ 20.8250 1.08411
$$370$$ 0 0
$$371$$ 23.7627 + 23.7627i 1.23370 + 1.23370i
$$372$$ −2.23637 1.91057i −0.115950 0.0990582i
$$373$$ −5.44481 + 5.44481i −0.281922 + 0.281922i −0.833875 0.551953i $$-0.813883\pi$$
0.551953 + 0.833875i $$0.313883\pi$$
$$374$$ −24.8375 + 26.8654i −1.28432 + 1.38918i
$$375$$ 0 0
$$376$$ −11.4077 + 1.34782i −0.588308 + 0.0695085i
$$377$$ 0.573629i 0.0295434i
$$378$$ −18.6827 17.2724i −0.960933 0.888399i
$$379$$ −17.4103 + 17.4103i −0.894309 + 0.894309i −0.994925 0.100616i $$-0.967919\pi$$
0.100616 + 0.994925i $$0.467919\pi$$
$$380$$ 0 0
$$381$$ 1.33402 + 1.33402i 0.0683438 + 0.0683438i
$$382$$ −24.4901 + 0.960543i −1.25302 + 0.0491457i
$$383$$ 9.04928 0.462396 0.231198 0.972907i $$-0.425735\pi$$
0.231198 + 0.972907i $$0.425735\pi$$
$$384$$ −6.81782 3.82245i −0.347921 0.195064i
$$385$$ 0 0
$$386$$ 23.8348 0.934839i 1.21316 0.0475821i
$$387$$ 5.73503 + 5.73503i 0.291528 + 0.291528i
$$388$$ 27.8303 2.18647i 1.41287 0.111001i
$$389$$ −15.3617 + 15.3617i −0.778871 + 0.778871i −0.979639 0.200768i $$-0.935656\pi$$
0.200768 + 0.979639i $$0.435656\pi$$
$$390$$ 0 0
$$391$$ 7.61962i 0.385341i
$$392$$ 42.7935 5.05605i 2.16140 0.255369i
$$393$$ 0.794869i 0.0400959i
$$394$$ −4.87291 + 5.27076i −0.245493 + 0.265537i
$$395$$ 0 0
$$396$$ 21.2316 + 18.1385i 1.06693 + 0.911494i
$$397$$ 9.44519 + 9.44519i 0.474041 + 0.474041i 0.903220 0.429179i $$-0.141197\pi$$
−0.429179 + 0.903220i $$0.641197\pi$$
$$398$$ 0.368301 + 9.39024i 0.0184613 + 0.470690i
$$399$$ −8.35031 −0.418038
$$400$$ 0 0
$$401$$ −21.5765 −1.07748 −0.538739 0.842473i $$-0.681099\pi$$
−0.538739 + 0.842473i $$0.681099\pi$$
$$402$$ −0.406098 10.3539i −0.0202543 0.516406i
$$403$$ −0.187079 0.187079i −0.00931907 0.00931907i
$$404$$ 24.6347 28.8356i 1.22562 1.43462i
$$405$$ 0 0
$$406$$ 20.8941 22.6000i 1.03696 1.12162i
$$407$$ 31.1363i 1.54337i
$$408$$ 7.17202 + 5.65635i 0.355068 + 0.280031i
$$409$$ 4.17336i 0.206359i 0.994663 + 0.103180i $$0.0329017\pi$$
−0.994663 + 0.103180i $$0.967098\pi$$
$$410$$ 0 0
$$411$$ −0.0976116 + 0.0976116i −0.00481482 + 0.00481482i
$$412$$ −2.15604 27.4430i −0.106220 1.35202i
$$413$$ −24.3529 24.3529i −1.19833 1.19833i
$$414$$ 5.81103 0.227918i 0.285597 0.0112016i
$$415$$ 0 0
$$416$$ −0.584438 0.390798i −0.0286544 0.0191604i
$$417$$ −11.3629 −0.556445
$$418$$ 20.0476 0.786300i 0.980560 0.0384592i
$$419$$ 27.1191 + 27.1191i 1.32485 + 1.32485i 0.909794 + 0.415060i $$0.136239\pi$$
0.415060 + 0.909794i $$0.363761\pi$$
$$420$$ 0 0
$$421$$ −26.9594 + 26.9594i −1.31392 + 1.31392i −0.395421 + 0.918500i $$0.629401\pi$$
−0.918500 + 0.395421i $$0.870599\pi$$
$$422$$ −2.80355 2.59193i −0.136475 0.126173i
$$423$$ 10.2454i 0.498150i
$$424$$ −12.4826 + 15.8275i −0.606210 + 0.768650i
$$425$$ 0 0
$$426$$ −3.01167 + 3.25756i −0.145916 + 0.157829i
$$427$$ −33.6079 + 33.6079i −1.62640 + 1.62640i
$$428$$ 0.602598 0.705357i 0.0291277 0.0340947i
$$429$$ −0.336036 0.336036i −0.0162240 0.0162240i
$$430$$ 0 0
$$431$$ −22.4059 −1.07925 −0.539626 0.841905i $$-0.681434\pi$$
−0.539626 + 0.841905i $$0.681434\pi$$
$$432$$ 8.97403 12.3446i 0.431763 0.593930i
$$433$$ 16.8061 0.807649 0.403824 0.914837i $$-0.367681\pi$$
0.403824 + 0.914837i $$0.367681\pi$$
$$434$$ 0.556353 + 14.1848i 0.0267058 + 0.680894i
$$435$$ 0 0
$$436$$ −0.321925 0.275026i −0.0154174 0.0131714i
$$437$$ 2.95448 2.95448i 0.141332 0.141332i
$$438$$ −5.50874 + 5.95851i −0.263218 + 0.284708i
$$439$$ 9.08322i 0.433519i −0.976225 0.216759i $$-0.930451\pi$$
0.976225 0.216759i $$-0.0695487\pi$$
$$440$$ 0 0
$$441$$ 38.4335i 1.83017i
$$442$$ 0.603279 + 0.557742i 0.0286951 + 0.0265291i
$$443$$ −12.5397 + 12.5397i −0.595781 + 0.595781i −0.939187 0.343406i $$-0.888419\pi$$
0.343406 + 0.939187i $$0.388419\pi$$
$$444$$ −7.74933 + 0.608820i −0.367767 + 0.0288933i
$$445$$ 0 0
$$446$$ 34.0664 1.33614i 1.61309 0.0632681i
$$447$$ −1.10780 −0.0523972
$$448$$ 8.79127 + 36.6845i 0.415349 + 1.73318i
$$449$$ 18.0707 0.852811 0.426406 0.904532i $$-0.359780\pi$$
0.426406 + 0.904532i $$0.359780\pi$$
$$450$$ 0 0
$$451$$ −32.3069 32.3069i −1.52127 1.52127i
$$452$$ −11.9232 + 0.936740i −0.560822 + 0.0440605i
$$453$$ 3.47929 3.47929i 0.163471 0.163471i
$$454$$ 9.80129 + 9.06146i 0.459997 + 0.425275i
$$455$$ 0 0
$$456$$ −0.587695 4.97415i −0.0275213 0.232936i
$$457$$ 18.6637i 0.873052i 0.899692 + 0.436526i $$0.143791\pi$$
−0.899692 + 0.436526i $$0.856209\pi$$
$$458$$ −21.8328 + 23.6153i −1.02018 + 1.10347i
$$459$$ −12.6113 + 12.6113i −0.588643 + 0.588643i
$$460$$ 0 0
$$461$$ −0.831229 0.831229i −0.0387142 0.0387142i 0.687485 0.726199i $$-0.258715\pi$$
−0.726199 + 0.687485i $$0.758715\pi$$
$$462$$ 0.999335 + 25.4791i 0.0464933 + 1.18540i
$$463$$ −7.82533 −0.363674 −0.181837 0.983329i $$-0.558204\pi$$
−0.181837 + 0.983329i $$0.558204\pi$$
$$464$$ 14.9330 + 10.8557i 0.693246 + 0.503962i
$$465$$ 0 0
$$466$$ 0.914382 + 23.3132i 0.0423579 + 1.07996i
$$467$$ −8.75068 8.75068i −0.404933 0.404933i 0.475034 0.879967i $$-0.342436\pi$$
−0.879967 + 0.475034i $$0.842436\pi$$
$$468$$ 0.407311 0.476768i 0.0188280 0.0220386i
$$469$$ −35.3617 + 35.3617i −1.63285 + 1.63285i
$$470$$ 0 0
$$471$$ 5.19922i 0.239568i
$$472$$ 12.7926 16.2206i 0.588829 0.746612i
$$473$$ 17.7941i 0.818172i
$$474$$ −8.27297 7.64850i −0.379990 0.351307i
$$475$$ 0 0
$$476$$ −3.45275 43.9481i −0.158257 2.01436i
$$477$$ −12.7129 12.7129i −0.582082 0.582082i
$$478$$ −7.43188 + 0.291491i −0.339926 + 0.0133325i
$$479$$ 2.10417 0.0961421 0.0480710 0.998844i $$-0.484693\pi$$
0.0480710 + 0.998844i $$0.484693\pi$$
$$480$$ 0 0
$$481$$ −0.699186 −0.0318801
$$482$$ 19.9430 0.782196i 0.908377 0.0356281i
$$483$$ 3.75494 + 3.75494i 0.170856 + 0.170856i
$$484$$ −3.07534 39.1443i −0.139788 1.77929i
$$485$$ 0 0
$$486$$ 15.4245 + 14.2602i 0.699671 + 0.646858i
$$487$$ 4.87183i 0.220764i 0.993889 + 0.110382i $$0.0352074\pi$$
−0.993889 + 0.110382i $$0.964793\pi$$
$$488$$ −22.3850 17.6544i −1.01332 0.799175i
$$489$$ 12.0185i 0.543494i
$$490$$ 0 0
$$491$$ 14.3582 14.3582i 0.647975 0.647975i −0.304528 0.952503i $$-0.598499\pi$$
0.952503 + 0.304528i $$0.0984987\pi$$
$$492$$ −7.40895 + 8.67237i −0.334021 + 0.390981i
$$493$$ −15.2555 15.2555i −0.687075 0.687075i
$$494$$ −0.0176569 0.450181i −0.000794419 0.0202546i
$$495$$ 0 0
$$496$$ −8.41052 + 1.32974i −0.377644 + 0.0597071i
$$497$$ 21.4113 0.960429
$$498$$ −0.0633143 1.61427i −0.00283718 0.0723370i
$$499$$ −25.1060 25.1060i −1.12390 1.12390i −0.991150 0.132748i $$-0.957620\pi$$
−0.132748 0.991150i $$-0.542380\pi$$
$$500$$ 0 0
$$501$$ −4.82077 + 4.82077i −0.215376 + 0.215376i
$$502$$ 13.5611 14.6683i 0.605260 0.654677i
$$503$$ 18.8868i 0.842120i 0.907033 + 0.421060i $$0.138342\pi$$
−0.907033 + 0.421060i $$0.861658\pi$$
$$504$$ −33.4133 + 3.94778i −1.48835 + 0.175848i
$$505$$ 0 0
$$506$$ −9.36852 8.66136i −0.416482 0.385044i
$$507$$ 6.34316 6.34316i 0.281710 0.281710i
$$508$$ 5.44473 0.427761i 0.241571 0.0189788i
$$509$$ −22.9756 22.9756i −1.01837 1.01837i −0.999828 0.0185459i $$-0.994096\pi$$
−0.0185459 0.999828i $$-0.505904\pi$$
$$510$$ 0 0
$$511$$ 39.1641 1.73252
$$512$$ −21.2337 + 7.81868i −0.938404 + 0.345540i
$$513$$ 9.77993 0.431794
$$514$$ −11.9375 + 0.468210i −0.526542 + 0.0206519i
$$515$$ 0 0
$$516$$ −4.42865 + 0.347933i −0.194961 + 0.0153169i
$$517$$ −15.8942 + 15.8942i −0.699028 + 0.699028i
$$518$$ 27.5467 + 25.4674i 1.21033 + 1.11897i
$$519$$ 13.1009i 0.575066i
$$520$$ 0 0
$$521$$ 20.2089i 0.885367i −0.896678 0.442683i $$-0.854027\pi$$
0.896678 0.442683i $$-0.145973\pi$$
$$522$$ −11.1782 + 12.0908i −0.489255 + 0.529201i
$$523$$ 3.93445 3.93445i 0.172042 0.172042i −0.615834 0.787876i $$-0.711181\pi$$
0.787876 + 0.615834i $$0.211181\pi$$
$$524$$ −1.74955 1.49467i −0.0764295 0.0652951i
$$525$$ 0 0
$$526$$ −1.01464 25.8693i −0.0442402 1.12795i
$$527$$ 9.95066 0.433458
$$528$$ −15.1072 + 2.38851i −0.657456 + 0.103947i
$$529$$ 20.3429 0.884473
$$530$$ 0 0
$$531$$ 13.0286 + 13.0286i 0.565393 + 0.565393i
$$532$$ −15.7019 + 18.3795i −0.680765 + 0.796853i
$$533$$ −0.725471 + 0.725471i −0.0314237 + 0.0314237i
$$534$$ −2.15276 + 2.32852i −0.0931589 + 0.100765i
$$535$$ 0 0
$$536$$ −23.5532 18.5757i −1.01734 0.802346i
$$537$$ 0.409950i 0.0176906i
$$538$$ −19.9181 18.4146i −0.858729 0.793910i
$$539$$ 59.6238 59.6238i 2.56818 2.56818i
$$540$$ 0 0
$$541$$ −3.17895 3.17895i −0.136674 0.136674i 0.635460 0.772134i $$-0.280811\pi$$
−0.772134 + 0.635460i $$0.780811\pi$$
$$542$$ 3.17275 0.124440i 0.136281 0.00534518i
$$543$$ −13.9330 −0.597923
$$544$$ 25.9362 5.14982i 1.11201 0.220797i
$$545$$ 0 0
$$546$$ 0.572150 0.0224407i 0.0244857 0.000960372i
$$547$$ 1.32918 + 1.32918i 0.0568317 + 0.0568317i 0.734951 0.678120i $$-0.237205\pi$$
−0.678120 + 0.734951i $$0.737205\pi$$
$$548$$ 0.0312998 + 0.398397i 0.00133706 + 0.0170187i
$$549$$ 17.9800 17.9800i 0.767366 0.767366i
$$550$$ 0 0
$$551$$ 11.8306i 0.503998i
$$552$$ −1.97249 + 2.50103i −0.0839545 + 0.106451i
$$553$$ 54.3766i 2.31233i
$$554$$ 9.88754 10.6948i 0.420081 0.454379i
$$555$$ 0 0
$$556$$ −21.3669 + 25.0105i −0.906157 + 1.06068i
$$557$$ 24.9082 + 24.9082i 1.05539 + 1.05539i 0.998373 + 0.0570196i $$0.0181598\pi$$
0.0570196 + 0.998373i $$0.481840\pi$$
$$558$$ −0.297645 7.58878i −0.0126003 0.321259i
$$559$$ −0.399576 −0.0169003
$$560$$ 0 0
$$561$$ 17.8736 0.754625
$$562$$ 0.334815 + 8.53648i 0.0141233 + 0.360090i
$$563$$ 3.80804 + 3.80804i 0.160490 + 0.160490i 0.782784 0.622294i $$-0.213799\pi$$
−0.622294 + 0.782784i $$0.713799\pi$$
$$564$$ 4.26660 + 3.64503i 0.179656 + 0.153484i
$$565$$ 0 0
$$566$$ −20.5488 + 22.2265i −0.863731 + 0.934251i
$$567$$ 23.2571i 0.976706i
$$568$$ 1.50693 + 12.7544i 0.0632293 + 0.535162i
$$569$$ 8.43971i 0.353811i 0.984228 + 0.176905i $$0.0566087\pi$$
−0.984228 + 0.176905i $$0.943391\pi$$
$$570$$ 0 0
$$571$$ −21.2821 + 21.2821i −0.890629 + 0.890629i −0.994582 0.103953i $$-0.966851\pi$$
0.103953 + 0.994582i $$0.466851\pi$$
$$572$$ −1.37152 + 0.107752i −0.0573460 + 0.00450534i
$$573$$ 8.46619 + 8.46619i 0.353680 + 0.353680i
$$574$$ 55.0072 2.15747i 2.29596 0.0900512i
$$575$$ 0 0
$$576$$ −4.70326 19.6259i −0.195969 0.817748i
$$577$$ −36.3491 −1.51323 −0.756615 0.653860i $$-0.773148\pi$$
−0.756615 + 0.653860i $$0.773148\pi$$
$$578$$ −6.85396 + 0.268824i −0.285087 + 0.0111816i
$$579$$ −8.23964 8.23964i −0.342428 0.342428i
$$580$$ 0 0
$$581$$ −5.51321 + 5.51321i −0.228726 + 0.228726i
$$582$$ −10.0137 9.25780i −0.415080 0.383748i
$$583$$ 39.4442i 1.63361i
$$584$$ 2.75637 + 23.3294i 0.114059 + 0.965379i
$$585$$ 0 0
$$586$$ −14.6328 + 15.8275i −0.604477 + 0.653830i
$$587$$ −6.55994 + 6.55994i −0.270758 + 0.270758i −0.829405 0.558647i $$-0.811321\pi$$
0.558647 + 0.829405i $$0.311321\pi$$
$$588$$ −16.0052 13.6735i −0.660044 0.563887i
$$589$$ −3.85833 3.85833i −0.158980 0.158980i
$$590$$ 0 0
$$591$$ 3.50665 0.144244
$$592$$ −13.2318 + 18.2015i −0.543823 + 0.748078i
$$593$$ −1.40974 −0.0578911 −0.0289455 0.999581i $$-0.509215\pi$$
−0.0289455 + 0.999581i $$0.509215\pi$$
$$594$$ −1.17043 29.8413i −0.0480231 1.22440i
$$595$$ 0 0
$$596$$ −2.08311 + 2.43833i −0.0853274 + 0.0998779i
$$597$$ 3.24619 3.24619i 0.132858 0.132858i
$$598$$ −0.194496 + 0.210376i −0.00795354 + 0.00860291i
$$599$$ 23.3593i 0.954435i 0.878785 + 0.477218i $$0.158355\pi$$
−0.878785 + 0.477218i $$0.841645\pi$$
$$600$$ 0 0
$$601$$ 20.4138i 0.832695i 0.909206 + 0.416347i $$0.136690\pi$$
−0.909206 + 0.416347i $$0.863310\pi$$
$$602$$ 15.7426 + 14.5543i 0.641622 + 0.593190i
$$603$$ 18.9183 18.9183i 0.770411 0.770411i
$$604$$ −1.11566 14.2006i −0.0453954 0.577813i
$$605$$ 0 0
$$606$$ −18.5131 + 0.726115i −0.752043 + 0.0294964i
$$607$$ 0.758240 0.0307760 0.0153880 0.999882i $$-0.495102\pi$$
0.0153880 + 0.999882i $$0.495102\pi$$
$$608$$ −12.0535 8.05983i −0.488833 0.326869i
$$609$$ −15.0358 −0.609283
$$610$$ 0 0
$$611$$ 0.356915 + 0.356915i 0.0144392 + 0.0144392i
$$612$$ 1.84719 + 23.5119i 0.0746684 + 0.950413i
$$613$$ 12.0341 12.0341i 0.486052 0.486052i −0.421006 0.907058i $$-0.638323\pi$$
0.907058 + 0.421006i $$0.138323\pi$$
$$614$$ 11.6659 + 10.7853i 0.470796 + 0.435259i
$$615$$ 0 0
$$616$$ 57.9602 + 45.7114i 2.33528 + 1.84176i
$$617$$ 32.6899i 1.31605i −0.752998 0.658023i $$-0.771393\pi$$
0.752998 0.658023i $$-0.228607\pi$$
$$618$$ −9.12894 + 9.87428i −0.367220 + 0.397202i
$$619$$ 26.3836 26.3836i 1.06045 1.06045i 0.0623934 0.998052i $$-0.480127\pi$$
0.998052 0.0623934i $$-0.0198733\pi$$
$$620$$ 0 0
$$621$$ −4.39781 4.39781i −0.176478 0.176478i
$$622$$ −1.72732 44.0399i −0.0692592 1.76584i
$$623$$ 15.3049 0.613178
$$624$$ 0.0536355 + 0.339241i 0.00214714 + 0.0135805i
$$625$$ 0 0
$$626$$ −0.296991 7.57213i −0.0118702 0.302643i
$$627$$ −6.93042 6.93042i −0.276774 0.276774i
$$628$$ 11.4438 + 9.77662i 0.456657 + 0.390130i
$$629$$ 18.5947 18.5947i 0.741420 0.741420i
$$630$$ 0 0
$$631$$ 6.08765i 0.242345i 0.992631 + 0.121173i $$0.0386655\pi$$
−0.992631 + 0.121173i $$0.961335\pi$$
$$632$$ −32.3913 + 3.82703i −1.28846 + 0.152231i
$$633$$ 1.86521i 0.0741354i
$$634$$ −13.0432 12.0586i −0.518010 0.478909i
$$635$$ 0 0
$$636$$ 9.81701 0.771266i 0.389270 0.0305827i
$$637$$ −1.33889 1.33889i −0.0530487 0.0530487i
$$638$$ 36.0983 1.41584i 1.42915 0.0560535i
$$639$$ −11.4549 −0.453149
$$640$$ 0 0
$$641$$ 11.1680 0.441111 0.220555 0.975374i $$-0.429213\pi$$
0.220555 + 0.975374i $$0.429213\pi$$
$$642$$ −0.452855 + 0.0177617i −0.0178728 + 0.000700999i
$$643$$ −21.9585 21.9585i −0.865957 0.865957i 0.126065 0.992022i $$-0.459765\pi$$
−0.992022 + 0.126065i $$0.959765\pi$$
$$644$$ 15.3256 1.20405i 0.603914 0.0474460i
$$645$$ 0 0
$$646$$ 12.4421 + 11.5029i 0.489526 + 0.452575i
$$647$$ 36.9848i 1.45402i 0.686625 + 0.727011i $$0.259091\pi$$
−0.686625 + 0.727011i $$0.740909\pi$$
$$648$$ 13.8539 1.63683i 0.544231 0.0643009i
$$649$$ 40.4238i 1.58677i
$$650$$ 0 0
$$651$$ 4.90368 4.90368i 0.192190 0.192190i
$$652$$ 26.4533 + 22.5995i 1.03599 + 0.885065i
$$653$$ −18.4157 18.4157i −0.720663 0.720663i 0.248077 0.968740i $$-0.420201\pi$$
−0.968740 + 0.248077i $$0.920201\pi$$
$$654$$ 0.00810646 + 0.206683i 0.000316988 + 0.00808196i
$$655$$ 0 0
$$656$$ 5.15658 + 32.6150i 0.201331 + 1.27340i
$$657$$ −20.9525 −0.817435
$$658$$ −1.06143 27.0622i −0.0413787 1.05500i
$$659$$ −15.5421 15.5421i −0.605434 0.605434i 0.336316 0.941749i $$-0.390819\pi$$
−0.941749 + 0.336316i $$0.890819\pi$$
$$660$$ 0 0
$$661$$ 29.6677 29.6677i 1.15394 1.15394i 0.168185 0.985755i $$-0.446209\pi$$
0.985755 0.168185i $$-0.0537906\pi$$
$$662$$ −8.24507 + 8.91825i −0.320454 + 0.346617i
$$663$$ 0.401363i 0.0155877i
$$664$$ −3.67215 2.89611i −0.142507 0.112391i
$$665$$ 0 0
$$666$$ −14.7373 13.6249i −0.571058 0.527953i
$$667$$ 5.31992 5.31992i 0.205988 0.205988i
$$668$$ 1.54581 + 19.6758i 0.0598092 + 0.761278i
$$669$$ −11.7767 11.7767i −0.455313 0.455313i
$$670$$ 0 0
$$671$$ −55.7864 −2.15361
$$672$$ 10.2435 15.3192i 0.395152 0.590949i
$$673$$ −29.2198 −1.12634 −0.563171 0.826340i $$-0.690419\pi$$
−0.563171 + 0.826340i $$0.690419\pi$$
$$674$$ −31.1209 + 1.22061i −1.19873 + 0.0470163i
$$675$$ 0 0
$$676$$ −2.03397 25.8893i −0.0782298 0.995743i
$$677$$ 17.2591 17.2591i 0.663320 0.663320i −0.292841 0.956161i $$-0.594601\pi$$
0.956161 + 0.292841i $$0.0946006\pi$$
$$678$$ 4.29011 + 3.96628i 0.164761 + 0.152324i
$$679$$ 65.8179i 2.52586i
$$680$$ 0 0
$$681$$ 6.52082i 0.249878i
$$682$$ −11.3111 + 12.2346i −0.433124 + 0.468487i
$$683$$ 1.10407 1.10407i 0.0422459 0.0422459i −0.685668 0.727914i $$-0.740490\pi$$
0.727914 + 0.685668i $$0.240490\pi$$
$$684$$ 8.40041 9.83289i 0.321198 0.375970i
$$685$$ 0 0
$$686$$ 2.15224 + 54.8738i 0.0821731 + 2.09509i
$$687$$ 15.7113 0.599425
$$688$$ −7.56181 + 10.4020i −0.288291 + 0.396571i
$$689$$ 0.885743 0.0337441
$$690$$ 0 0
$$691$$ −28.4233 28.4233i −1.08127 1.08127i −0.996391 0.0848830i $$-0.972948\pi$$
−0.0848830 0.996391i $$-0.527052\pi$$
$$692$$ 28.8359 + 24.6350i 1.09617 + 0.936481i
$$693$$ −46.5545 + 46.5545i −1.76846 + 1.76846i
$$694$$ 16.1458 17.4640i 0.612885 0.662924i
$$695$$ 0 0
$$696$$ −1.05822 8.95660i −0.0401118 0.339499i
$$697$$ 38.5875i 1.46161i
$$698$$ 12.7132 + 11.7536i 0.481201 + 0.444879i
$$699$$ 8.05933 8.05933i 0.304832 0.304832i
$$700$$ 0 0
$$701$$ −23.7991 23.7991i −0.898880 0.898880i 0.0964573 0.995337i $$-0.469249\pi$$
−0.995337 + 0.0964573i $$0.969249\pi$$
$$702$$ −0.670105 + 0.0262826i −0.0252915 + 0.000991974i
$$703$$ −14.4200 −0.543862
$$704$$ −23.1503 + 37.7431i −0.872510 + 1.42250i
$$705$$ 0 0
$$706$$ −37.6109 + 1.47516i −1.41550 + 0.0555184i
$$707$$ 63.2278 + 63.2278i 2.37793 + 2.37793i
$$708$$ −10.0608 + 0.790421i −0.378109 + 0.0297058i
$$709$$ 1.49921 1.49921i 0.0563039 0.0563039i −0.678394 0.734698i $$-0.737324\pi$$
0.734698 + 0.678394i $$0.237324\pi$$
$$710$$ 0 0
$$711$$ 29.0911i 1.09100i
$$712$$ 1.07716 + 9.11688i 0.0403682 + 0.341670i
$$713$$ 3.47000i 0.129953i
$$714$$ −14.6194 + 15.8130i −0.547118 + 0.591787i
$$715$$ 0 0
$$716$$ 0.902323 + 0.770870i 0.0337214 + 0.0288088i
$$717$$ 2.56919 + 2.56919i 0.0959482 + 0.0959482i
$$718$$ −0.268830 6.85412i −0.0100327 0.255794i
$$719$$ 7.37612 0.275083 0.137541 0.990496i $$-0.456080\pi$$
0.137541 + 0.990496i $$0.456080\pi$$
$$720$$ 0 0
$$721$$ 64.9017 2.41707
$$722$$ 0.688923 + 17.5649i 0.0256391 + 0.653696i
$$723$$ −6.89425 6.89425i −0.256400 0.256400i
$$724$$ −26.1996 + 30.6673i −0.973702 + 1.13974i
$$725$$ 0 0
$$726$$ −13.0214 + 14.0846i −0.483270 + 0.522727i
$$727$$ 30.1470i 1.11809i −0.829137 0.559045i $$-0.811168\pi$$
0.829137 0.559045i $$-0.188832\pi$$
$$728$$ 1.02648 1.30153i 0.0380438 0.0482380i
$$729$$ 4.53447i 0.167943i
$$730$$ 0 0
$$731$$ 10.6267 10.6267i 0.393041 0.393041i
$$732$$ 1.09081 + 13.8843i 0.0403176 + 0.513180i
$$733$$ −1.43297 1.43297i −0.0529279 0.0529279i 0.680147 0.733075i $$-0.261916\pi$$
−0.733075 + 0.680147i $$0.761916\pi$$
$$734$$ −22.1495 + 0.868740i −0.817553 + 0.0320658i
$$735$$ 0 0
$$736$$ 1.79585 + 9.04449i 0.0661959 + 0.333384i
$$737$$ −58.6977 −2.16216
$$738$$ −29.4284 + 1.15423i −1.08328 + 0.0424879i
$$739$$ 31.0001 + 31.0001i 1.14036 + 1.14036i 0.988385 + 0.151973i $$0.0485626\pi$$
0.151973 + 0.988385i $$0.451437\pi$$
$$740$$ 0 0
$$741$$ −0.155627 + 0.155627i −0.00571710 + 0.00571710i
$$742$$ −34.8968 32.2626i −1.28110 1.18440i
$$743$$ 38.5395i 1.41388i 0.707276 + 0.706938i $$0.249924\pi$$
−0.707276 + 0.706938i $$0.750076\pi$$
$$744$$ 3.26616 + 2.57592i 0.119743 + 0.0944378i
$$745$$ 0 0
$$746$$ 7.39243 7.99599i 0.270656 0.292754i
$$747$$ 2.94952 2.94952i 0.107917 0.107917i
$$748$$ 33.6096 39.3408i 1.22889 1.43844i
$$749$$ 1.54664 + 1.54664i 0.0565128 + 0.0565128i
$$750$$ 0 0
$$751$$ 26.9523 0.983503 0.491751 0.870736i $$-0.336357\pi$$
0.491751 + 0.870736i $$0.336357\pi$$
$$752$$ 16.0458 2.53692i 0.585132 0.0925118i
$$753$$ −9.75884 −0.355632
$$754$$ −0.0317935 0.810610i −0.00115785 0.0295207i
$$755$$ 0 0
$$756$$ 27.3583 + 23.3727i 0.995012 + 0.850056i
$$757$$ 17.0688 17.0688i 0.620377 0.620377i −0.325251 0.945628i $$-0.605449\pi$$
0.945628 + 0.325251i $$0.105449\pi$$
$$758$$ 23.6380 25.5680i 0.858573 0.928671i
$$759$$ 6.23290i 0.226240i
$$760$$ 0 0
$$761$$ 6.89608i 0.249983i 0.992158 + 0.124991i $$0.0398903\pi$$
−0.992158 + 0.124991i $$0.960110\pi$$
$$762$$ −1.95907 1.81120i −0.0709698 0.0656128i
$$763$$ 0.705886 0.705886i 0.0255548 0.0255548i
$$764$$ 34.5544 2.71474i 1.25013 0.0982158i
$$765$$ 0 0
$$766$$ −12.7878 + 0.501558i −0.462041 + 0.0181220i
$$767$$ −0.907741 −0.0327766
$$768$$ 9.84631 + 5.02373i 0.355298 + 0.181278i
$$769$$ 11.8443 0.427117 0.213558 0.976930i $$-0.431495\pi$$
0.213558 + 0.976930i $$0.431495\pi$$
$$770$$ 0 0
$$771$$ 4.12679 + 4.12679i 0.148623 + 0.148623i
$$772$$ −33.6297 + 2.64209i −1.21036 + 0.0950910i
$$773$$ −3.58865 + 3.58865i −0.129075 + 0.129075i −0.768693 0.639618i $$-0.779093\pi$$
0.639618 + 0.768693i $$0.279093\pi$$
$$774$$ −8.42219 7.78646i −0.302729 0.279878i
$$775$$ 0 0
$$776$$ −39.2066 + 4.63226i −1.40744 + 0.166288i
$$777$$ 18.3269i 0.657474i
$$778$$ 20.8567 22.5595i 0.747748 0.808798i
$$779$$ −14.9622 + 14.9622i −0.536075 + 0.536075i
$$780$$ 0 0
$$781$$ 17.7705 + 17.7705i 0.635880 + 0.635880i
$$782$$ −0.422319 10.7675i −0.0151021 0.385045i
$$783$$ 17.6100 0.629332 <