# Properties

 Label 675.2.u.b.49.4 Level $675$ Weight $2$ Character 675.49 Analytic conductor $5.390$ Analytic rank $0$ Dimension $24$ CM no Inner twists $4$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(49,675)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([14, 9]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("675.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$675 = 3^{3} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 675.u (of order $$18$$, degree $$6$$, not minimal)

## Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

 Self dual: no Analytic conductor: $$5.38990213644$$ Analytic rank: $$0$$ Dimension: $$24$$ Relative dimension: $$4$$ over $$\Q(\zeta_{18})$$ Twist minimal: no (minimal twist has level 27) Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

## Embedding invariants

 Embedding label 49.4 Character $$\chi$$ $$=$$ 675.49 Dual form 675.2.u.b.124.4

## $q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(1.36054 + 1.62143i) q^{2} +(-1.42389 - 0.986166i) q^{3} +(-0.430663 + 2.44241i) q^{4} +(-0.338267 - 3.65046i) q^{6} +(0.957561 - 0.168844i) q^{7} +(-0.880031 + 0.508086i) q^{8} +(1.05495 + 2.80839i) q^{9} +O(q^{10})$$ $$q+(1.36054 + 1.62143i) q^{2} +(-1.42389 - 0.986166i) q^{3} +(-0.430663 + 2.44241i) q^{4} +(-0.338267 - 3.65046i) q^{6} +(0.957561 - 0.168844i) q^{7} +(-0.880031 + 0.508086i) q^{8} +(1.05495 + 2.80839i) q^{9} +(0.297791 + 0.108387i) q^{11} +(3.02185 - 3.05303i) q^{12} +(0.973200 - 1.15981i) q^{13} +(1.57657 + 1.32290i) q^{14} +(2.63991 + 0.960847i) q^{16} +(1.01731 + 0.587342i) q^{17} +(-3.11830 + 5.53146i) q^{18} +(3.11040 + 5.38737i) q^{19} +(-1.52997 - 0.703898i) q^{21} +(0.229414 + 0.630310i) q^{22} +(2.12988 + 0.375556i) q^{23} +(1.75413 + 0.144396i) q^{24} +3.20463 q^{26} +(1.26740 - 5.03922i) q^{27} +2.41147i q^{28} +(3.37436 - 2.83142i) q^{29} +(-1.50609 + 8.54146i) q^{31} +(2.72885 + 7.49746i) q^{32} +(-0.317135 - 0.448003i) q^{33} +(0.431752 + 2.44859i) q^{34} +(-7.31359 + 1.36716i) q^{36} +(-3.86823 - 2.23332i) q^{37} +(-4.50341 + 12.3730i) q^{38} +(-2.52950 + 0.691717i) q^{39} +(4.47767 + 3.75721i) q^{41} +(-0.940269 - 3.43842i) q^{42} +(1.91223 - 5.25381i) q^{43} +(-0.392973 + 0.680649i) q^{44} +(2.28885 + 3.96441i) q^{46} +(-2.43845 + 0.429965i) q^{47} +(-2.81139 - 3.97153i) q^{48} +(-5.68943 + 2.07078i) q^{49} +(-0.869320 - 1.83955i) q^{51} +(2.41362 + 2.87645i) q^{52} -10.8920i q^{53} +(9.89507 - 4.80105i) q^{54} +(-0.756896 + 0.635111i) q^{56} +(0.883963 - 10.7384i) q^{57} +(9.18189 + 1.61901i) q^{58} +(-1.62023 + 0.589715i) q^{59} +(0.176214 + 0.999361i) q^{61} +(-15.8985 + 9.17898i) q^{62} +(1.48436 + 2.51109i) q^{63} +(-5.63455 + 9.75933i) q^{64} +(0.294929 - 1.12374i) q^{66} +(0.550580 - 0.656156i) q^{67} +(-1.87265 + 2.23174i) q^{68} +(-2.66237 - 2.63517i) q^{69} +(4.79788 - 8.31018i) q^{71} +(-2.35530 - 1.93547i) q^{72} +(-13.1998 + 7.62091i) q^{73} +(-1.64171 - 9.31057i) q^{74} +(-14.4977 + 5.27674i) q^{76} +(0.303453 + 0.0535070i) q^{77} +(-4.56306 - 3.16030i) q^{78} +(8.59024 - 7.20807i) q^{79} +(-6.77415 + 5.92544i) q^{81} +12.3721i q^{82} +(3.01141 + 3.58886i) q^{83} +(2.37811 - 3.43369i) q^{84} +(11.1203 - 4.04747i) q^{86} +(-7.59698 + 0.703969i) q^{87} +(-0.317135 + 0.0559194i) q^{88} +(-7.74976 - 13.4230i) q^{89} +(0.736071 - 1.27491i) q^{91} +(-1.83453 + 5.04032i) q^{92} +(10.5678 - 10.6769i) q^{93} +(-4.01476 - 3.36879i) q^{94} +(3.50815 - 13.3667i) q^{96} +(1.89804 - 5.21481i) q^{97} +(-11.0983 - 6.40762i) q^{98} +(0.00976156 + 0.950656i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$24 q + 12 q^{4}+O(q^{10})$$ 24 * q + 12 * q^4 $$24 q + 12 q^{4} + 6 q^{11} - 30 q^{14} + 6 q^{19} - 24 q^{21} + 36 q^{24} - 60 q^{26} + 12 q^{29} + 6 q^{31} - 18 q^{34} + 36 q^{36} - 66 q^{39} + 30 q^{41} - 6 q^{44} - 6 q^{46} - 24 q^{49} - 36 q^{51} + 108 q^{54} - 66 q^{56} + 24 q^{59} + 24 q^{61} - 24 q^{64} - 18 q^{66} - 18 q^{69} + 54 q^{71} - 66 q^{74} - 96 q^{76} + 84 q^{79} + 72 q^{81} - 12 q^{84} + 102 q^{86} - 18 q^{89} + 12 q^{91} + 30 q^{94} + 54 q^{99}+O(q^{100})$$ 24 * q + 12 * q^4 + 6 * q^11 - 30 * q^14 + 6 * q^19 - 24 * q^21 + 36 * q^24 - 60 * q^26 + 12 * q^29 + 6 * q^31 - 18 * q^34 + 36 * q^36 - 66 * q^39 + 30 * q^41 - 6 * q^44 - 6 * q^46 - 24 * q^49 - 36 * q^51 + 108 * q^54 - 66 * q^56 + 24 * q^59 + 24 * q^61 - 24 * q^64 - 18 * q^66 - 18 * q^69 + 54 * q^71 - 66 * q^74 - 96 * q^76 + 84 * q^79 + 72 * q^81 - 12 * q^84 + 102 * q^86 - 18 * q^89 + 12 * q^91 + 30 * q^94 + 54 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$$.

 $$n$$ $$326$$ $$352$$ $$\chi(n)$$ $$e\left(\frac{7}{9}\right)$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.36054 + 1.62143i 0.962046 + 1.14652i 0.989153 + 0.146889i $$0.0469262\pi$$
−0.0271067 + 0.999633i $$0.508629\pi$$
$$3$$ −1.42389 0.986166i −0.822086 0.569363i
$$4$$ −0.430663 + 2.44241i −0.215332 + 1.22121i
$$5$$ 0 0
$$6$$ −0.338267 3.65046i −0.138097 1.49029i
$$7$$ 0.957561 0.168844i 0.361924 0.0638170i 0.0102706 0.999947i $$-0.496731\pi$$
0.351653 + 0.936130i $$0.385620\pi$$
$$8$$ −0.880031 + 0.508086i −0.311138 + 0.179636i
$$9$$ 1.05495 + 2.80839i 0.351651 + 0.936131i
$$10$$ 0 0
$$11$$ 0.297791 + 0.108387i 0.0897872 + 0.0326799i 0.386523 0.922280i $$-0.373676\pi$$
−0.296736 + 0.954960i $$0.595898\pi$$
$$12$$ 3.02185 3.05303i 0.872332 0.881335i
$$13$$ 0.973200 1.15981i 0.269917 0.321675i −0.614011 0.789297i $$-0.710445\pi$$
0.883928 + 0.467623i $$0.154889\pi$$
$$14$$ 1.57657 + 1.32290i 0.421355 + 0.353559i
$$15$$ 0 0
$$16$$ 2.63991 + 0.960847i 0.659977 + 0.240212i
$$17$$ 1.01731 + 0.587342i 0.246733 + 0.142451i 0.618267 0.785968i $$-0.287835\pi$$
−0.371534 + 0.928419i $$0.621168\pi$$
$$18$$ −3.11830 + 5.53146i −0.734991 + 1.30378i
$$19$$ 3.11040 + 5.38737i 0.713575 + 1.23595i 0.963507 + 0.267685i $$0.0862586\pi$$
−0.249931 + 0.968264i $$0.580408\pi$$
$$20$$ 0 0
$$21$$ −1.52997 0.703898i −0.333868 0.153603i
$$22$$ 0.229414 + 0.630310i 0.0489113 + 0.134383i
$$23$$ 2.12988 + 0.375556i 0.444112 + 0.0783089i 0.391232 0.920292i $$-0.372049\pi$$
0.0528796 + 0.998601i $$0.483160\pi$$
$$24$$ 1.75413 + 0.144396i 0.358060 + 0.0294747i
$$25$$ 0 0
$$26$$ 3.20463 0.628480
$$27$$ 1.26740 5.03922i 0.243912 0.969797i
$$28$$ 2.41147i 0.455726i
$$29$$ 3.37436 2.83142i 0.626602 0.525782i −0.273269 0.961938i $$-0.588105\pi$$
0.899871 + 0.436156i $$0.143660\pi$$
$$30$$ 0 0
$$31$$ −1.50609 + 8.54146i −0.270502 + 1.53409i 0.482395 + 0.875954i $$0.339767\pi$$
−0.752897 + 0.658138i $$0.771344\pi$$
$$32$$ 2.72885 + 7.49746i 0.482398 + 1.32538i
$$33$$ −0.317135 0.448003i −0.0552061 0.0779872i
$$34$$ 0.431752 + 2.44859i 0.0740449 + 0.419930i
$$35$$ 0 0
$$36$$ −7.31359 + 1.36716i −1.21893 + 0.227859i
$$37$$ −3.86823 2.23332i −0.635933 0.367156i 0.147113 0.989120i $$-0.453002\pi$$
−0.783046 + 0.621964i $$0.786335\pi$$
$$38$$ −4.50341 + 12.3730i −0.730550 + 2.00717i
$$39$$ −2.52950 + 0.691717i −0.405045 + 0.110763i
$$40$$ 0 0
$$41$$ 4.47767 + 3.75721i 0.699295 + 0.586778i 0.921573 0.388205i $$-0.126905\pi$$
−0.222278 + 0.974983i $$0.571349\pi$$
$$42$$ −0.940269 3.43842i −0.145087 0.530560i
$$43$$ 1.91223 5.25381i 0.291613 0.801199i −0.704219 0.709983i $$-0.748702\pi$$
0.995831 0.0912158i $$-0.0290753\pi$$
$$44$$ −0.392973 + 0.680649i −0.0592429 + 0.102612i
$$45$$ 0 0
$$46$$ 2.28885 + 3.96441i 0.337473 + 0.584521i
$$47$$ −2.43845 + 0.429965i −0.355685 + 0.0627168i −0.348636 0.937258i $$-0.613355\pi$$
−0.00704911 + 0.999975i $$0.502244\pi$$
$$48$$ −2.81139 3.97153i −0.405790 0.573241i
$$49$$ −5.68943 + 2.07078i −0.812776 + 0.295826i
$$50$$ 0 0
$$51$$ −0.869320 1.83955i −0.121729 0.257588i
$$52$$ 2.41362 + 2.87645i 0.334710 + 0.398891i
$$53$$ 10.8920i 1.49613i −0.663628 0.748063i $$-0.730984\pi$$
0.663628 0.748063i $$-0.269016\pi$$
$$54$$ 9.89507 4.80105i 1.34655 0.653340i
$$55$$ 0 0
$$56$$ −0.756896 + 0.635111i −0.101145 + 0.0848703i
$$57$$ 0.883963 10.7384i 0.117084 1.42234i
$$58$$ 9.18189 + 1.61901i 1.20564 + 0.212587i
$$59$$ −1.62023 + 0.589715i −0.210936 + 0.0767743i −0.445327 0.895368i $$-0.646913\pi$$
0.234391 + 0.972142i $$0.424690\pi$$
$$60$$ 0 0
$$61$$ 0.176214 + 0.999361i 0.0225619 + 0.127955i 0.994008 0.109304i $$-0.0348621\pi$$
−0.971446 + 0.237259i $$0.923751\pi$$
$$62$$ −15.8985 + 9.17898i −2.01911 + 1.16573i
$$63$$ 1.48436 + 2.51109i 0.187012 + 0.316367i
$$64$$ −5.63455 + 9.75933i −0.704319 + 1.21992i
$$65$$ 0 0
$$66$$ 0.294929 1.12374i 0.0363033 0.138322i
$$67$$ 0.550580 0.656156i 0.0672641 0.0801622i −0.731363 0.681988i $$-0.761116\pi$$
0.798627 + 0.601826i $$0.205560\pi$$
$$68$$ −1.87265 + 2.23174i −0.227092 + 0.270638i
$$69$$ −2.66237 2.63517i −0.320512 0.317238i
$$70$$ 0 0
$$71$$ 4.79788 8.31018i 0.569404 0.986237i −0.427221 0.904147i $$-0.640507\pi$$
0.996625 0.0820894i $$-0.0261593\pi$$
$$72$$ −2.35530 1.93547i −0.277574 0.228097i
$$73$$ −13.1998 + 7.62091i −1.54492 + 0.891960i −0.546404 + 0.837522i $$0.684004\pi$$
−0.998517 + 0.0544385i $$0.982663\pi$$
$$74$$ −1.64171 9.31057i −0.190844 1.08233i
$$75$$ 0 0
$$76$$ −14.4977 + 5.27674i −1.66300 + 0.605284i
$$77$$ 0.303453 + 0.0535070i 0.0345817 + 0.00609768i
$$78$$ −4.56306 3.16030i −0.516664 0.357833i
$$79$$ 8.59024 7.20807i 0.966478 0.810971i −0.0155168 0.999880i $$-0.504939\pi$$
0.981995 + 0.188908i $$0.0604949\pi$$
$$80$$ 0 0
$$81$$ −6.77415 + 5.92544i −0.752684 + 0.658382i
$$82$$ 12.3721i 1.36626i
$$83$$ 3.01141 + 3.58886i 0.330546 + 0.393929i 0.905563 0.424212i $$-0.139449\pi$$
−0.575017 + 0.818141i $$0.695005\pi$$
$$84$$ 2.37811 3.43369i 0.259474 0.374646i
$$85$$ 0 0
$$86$$ 11.1203 4.04747i 1.19914 0.436450i
$$87$$ −7.59698 + 0.703969i −0.814482 + 0.0754734i
$$88$$ −0.317135 + 0.0559194i −0.0338067 + 0.00596103i
$$89$$ −7.74976 13.4230i −0.821473 1.42283i −0.904586 0.426292i $$-0.859820\pi$$
0.0831130 0.996540i $$-0.473514\pi$$
$$90$$ 0 0
$$91$$ 0.736071 1.27491i 0.0771612 0.133647i
$$92$$ −1.83453 + 5.04032i −0.191263 + 0.525490i
$$93$$ 10.5678 10.6769i 1.09583 1.10714i
$$94$$ −4.01476 3.36879i −0.414091 0.347464i
$$95$$ 0 0
$$96$$ 3.50815 13.3667i 0.358049 1.36423i
$$97$$ 1.89804 5.21481i 0.192716 0.529484i −0.805270 0.592908i $$-0.797980\pi$$
0.997987 + 0.0634241i $$0.0202021\pi$$
$$98$$ −11.0983 6.40762i −1.12110 0.647267i
$$99$$ 0.00976156 + 0.950656i 0.000981074 + 0.0955445i
$$100$$ 0 0
$$101$$ −1.76063 9.98501i −0.175189 0.993546i −0.937926 0.346836i $$-0.887256\pi$$
0.762737 0.646709i $$-0.223855\pi$$
$$102$$ 1.79995 3.91231i 0.178221 0.387377i
$$103$$ 3.37002 + 9.25906i 0.332058 + 0.912323i 0.987576 + 0.157143i $$0.0502283\pi$$
−0.655518 + 0.755180i $$0.727549\pi$$
$$104$$ −0.267160 + 1.51514i −0.0261972 + 0.148572i
$$105$$ 0 0
$$106$$ 17.6605 14.8189i 1.71534 1.43934i
$$107$$ 5.17080i 0.499880i −0.968261 0.249940i $$-0.919589\pi$$
0.968261 0.249940i $$-0.0804109\pi$$
$$108$$ 11.7620 + 5.26573i 1.13180 + 0.506695i
$$109$$ 7.31065 0.700234 0.350117 0.936706i $$-0.386142\pi$$
0.350117 + 0.936706i $$0.386142\pi$$
$$110$$ 0 0
$$111$$ 3.30552 + 6.99473i 0.313746 + 0.663911i
$$112$$ 2.69010 + 0.474338i 0.254191 + 0.0448207i
$$113$$ −3.54868 9.74991i −0.333832 0.917195i −0.987105 0.160073i $$-0.948827\pi$$
0.653274 0.757122i $$-0.273395\pi$$
$$114$$ 18.6142 13.1768i 1.74338 1.23412i
$$115$$ 0 0
$$116$$ 5.46229 + 9.46096i 0.507161 + 0.878428i
$$117$$ 4.28390 + 1.50958i 0.396046 + 0.139561i
$$118$$ −3.16056 1.82475i −0.290953 0.167982i
$$119$$ 1.07330 + 0.390650i 0.0983894 + 0.0358108i
$$120$$ 0 0
$$121$$ −8.34956 7.00611i −0.759051 0.636919i
$$122$$ −1.38064 + 1.64539i −0.124998 + 0.148966i
$$123$$ −2.67050 9.76560i −0.240790 0.880535i
$$124$$ −20.2132 7.35699i −1.81520 0.660677i
$$125$$ 0 0
$$126$$ −2.05201 + 5.82321i −0.182808 + 0.518773i
$$127$$ −4.52709 + 2.61372i −0.401714 + 0.231930i −0.687223 0.726446i $$-0.741171\pi$$
0.285509 + 0.958376i $$0.407837\pi$$
$$128$$ −7.77522 + 1.37098i −0.687239 + 0.121179i
$$129$$ −7.90395 + 5.59510i −0.695904 + 0.492621i
$$130$$ 0 0
$$131$$ −1.25622 + 7.12440i −0.109757 + 0.622461i 0.879457 + 0.475979i $$0.157906\pi$$
−0.989213 + 0.146482i $$0.953205\pi$$
$$132$$ 1.23079 0.581636i 0.107126 0.0506249i
$$133$$ 3.88802 + 4.63357i 0.337134 + 0.401781i
$$134$$ 1.81300 0.156619
$$135$$ 0 0
$$136$$ −1.19368 −0.102357
$$137$$ −7.23092 8.61748i −0.617779 0.736241i 0.362907 0.931825i $$-0.381784\pi$$
−0.980687 + 0.195584i $$0.937340\pi$$
$$138$$ 0.650482 7.90210i 0.0553727 0.672671i
$$139$$ −1.62885 + 9.23766i −0.138157 + 0.783528i 0.834452 + 0.551081i $$0.185784\pi$$
−0.972609 + 0.232447i $$0.925327\pi$$
$$140$$ 0 0
$$141$$ 3.89612 + 1.79249i 0.328112 + 0.150955i
$$142$$ 20.0021 3.52690i 1.67854 0.295971i
$$143$$ 0.415518 0.239900i 0.0347474 0.0200614i
$$144$$ 0.0865360 + 8.42754i 0.00721133 + 0.702295i
$$145$$ 0 0
$$146$$ −30.3156 11.0340i −2.50894 0.913179i
$$147$$ 10.1433 + 2.66215i 0.836605 + 0.219570i
$$148$$ 7.12060 8.48600i 0.585310 0.697545i
$$149$$ −14.5941 12.2459i −1.19560 1.00322i −0.999745 0.0225899i $$-0.992809\pi$$
−0.195851 0.980634i $$-0.562747\pi$$
$$150$$ 0 0
$$151$$ −3.77193 1.37287i −0.306955 0.111723i 0.183950 0.982936i $$-0.441112\pi$$
−0.490905 + 0.871213i $$0.663334\pi$$
$$152$$ −5.47450 3.16070i −0.444041 0.256367i
$$153$$ −0.576279 + 3.47661i −0.0465894 + 0.281068i
$$154$$ 0.326102 + 0.564825i 0.0262780 + 0.0455149i
$$155$$ 0 0
$$156$$ −0.600093 6.47599i −0.0480459 0.518494i
$$157$$ 2.48851 + 6.83713i 0.198605 + 0.545662i 0.998516 0.0544560i $$-0.0173425\pi$$
−0.799911 + 0.600118i $$0.795120\pi$$
$$158$$ 23.3747 + 4.12159i 1.85959 + 0.327896i
$$159$$ −10.7413 + 15.5090i −0.851839 + 1.22994i
$$160$$ 0 0
$$161$$ 2.10290 0.165732
$$162$$ −18.8242 2.92200i −1.47897 0.229574i
$$163$$ 12.4492i 0.975094i 0.873097 + 0.487547i $$0.162108\pi$$
−0.873097 + 0.487547i $$0.837892\pi$$
$$164$$ −11.1050 + 9.31823i −0.867157 + 0.727632i
$$165$$ 0 0
$$166$$ −1.72194 + 9.76558i −0.133648 + 0.757956i
$$167$$ −0.797553 2.19126i −0.0617165 0.169565i 0.905002 0.425408i $$-0.139869\pi$$
−0.966718 + 0.255843i $$0.917647\pi$$
$$168$$ 1.70407 0.157906i 0.131472 0.0121827i
$$169$$ 1.85937 + 10.5450i 0.143029 + 0.811157i
$$170$$ 0 0
$$171$$ −11.8485 + 14.4187i −0.906081 + 1.10262i
$$172$$ 12.0085 + 6.93308i 0.915636 + 0.528643i
$$173$$ −1.22521 + 3.36623i −0.0931509 + 0.255930i −0.977514 0.210869i $$-0.932371\pi$$
0.884363 + 0.466799i $$0.154593\pi$$
$$174$$ −11.4774 11.3602i −0.870101 0.861213i
$$175$$ 0 0
$$176$$ 0.681996 + 0.572262i 0.0514074 + 0.0431359i
$$177$$ 2.88859 + 0.758123i 0.217120 + 0.0569840i
$$178$$ 11.2205 30.8281i 0.841014 2.31067i
$$179$$ −9.99785 + 17.3168i −0.747275 + 1.29432i 0.201850 + 0.979416i $$0.435305\pi$$
−0.949124 + 0.314901i $$0.898029\pi$$
$$180$$ 0 0
$$181$$ −4.86616 8.42844i −0.361699 0.626481i 0.626542 0.779388i $$-0.284470\pi$$
−0.988241 + 0.152907i $$0.951136\pi$$
$$182$$ 3.06863 0.541082i 0.227462 0.0401077i
$$183$$ 0.734626 1.59676i 0.0543051 0.118036i
$$184$$ −2.06518 + 0.751664i −0.152247 + 0.0554134i
$$185$$ 0 0
$$186$$ 31.6897 + 2.60862i 2.32360 + 0.191274i
$$187$$ 0.239284 + 0.285168i 0.0174982 + 0.0208535i
$$188$$ 6.14088i 0.447869i
$$189$$ 0.362776 5.03935i 0.0263881 0.366559i
$$190$$ 0 0
$$191$$ −13.6023 + 11.4137i −0.984227 + 0.825864i −0.984722 0.174135i $$-0.944287\pi$$
0.000494763 1.00000i $$0.499843\pi$$
$$192$$ 17.6473 8.33965i 1.27359 0.601862i
$$193$$ 10.4235 + 1.83795i 0.750303 + 0.132299i 0.535706 0.844404i $$-0.320045\pi$$
0.214596 + 0.976703i $$0.431156\pi$$
$$194$$ 11.0378 4.01743i 0.792467 0.288434i
$$195$$ 0 0
$$196$$ −2.60748 14.7878i −0.186249 1.05627i
$$197$$ −12.2620 + 7.07945i −0.873628 + 0.504390i −0.868552 0.495597i $$-0.834949\pi$$
−0.00507615 + 0.999987i $$0.501616\pi$$
$$198$$ −1.52814 + 1.30923i −0.108600 + 0.0930431i
$$199$$ 3.77010 6.53000i 0.267255 0.462899i −0.700897 0.713263i $$-0.747217\pi$$
0.968152 + 0.250363i $$0.0805501\pi$$
$$200$$ 0 0
$$201$$ −1.43105 + 0.391333i −0.100938 + 0.0276025i
$$202$$ 13.7946 16.4397i 0.970582 1.15669i
$$203$$ 2.75308 3.28100i 0.193229 0.230281i
$$204$$ 4.86732 1.33101i 0.340780 0.0931896i
$$205$$ 0 0
$$206$$ −10.4278 + 18.0616i −0.726543 + 1.25841i
$$207$$ 1.19222 + 6.37775i 0.0828648 + 0.443284i
$$208$$ 3.68356 2.12670i 0.255409 0.147460i
$$209$$ 0.342328 + 1.94144i 0.0236793 + 0.134292i
$$210$$ 0 0
$$211$$ −4.89922 + 1.78317i −0.337276 + 0.122758i −0.505106 0.863058i $$-0.668546\pi$$
0.167829 + 0.985816i $$0.446324\pi$$
$$212$$ 26.6027 + 4.69077i 1.82708 + 0.322163i
$$213$$ −15.0269 + 7.10131i −1.02963 + 0.486573i
$$214$$ 8.38408 7.03508i 0.573124 0.480908i
$$215$$ 0 0
$$216$$ 1.44500 + 5.07862i 0.0983199 + 0.345556i
$$217$$ 8.43326i 0.572487i
$$218$$ 9.94643 + 11.8537i 0.673657 + 0.802833i
$$219$$ 26.3106 + 2.16583i 1.77791 + 0.146353i
$$220$$ 0 0
$$221$$ 1.67125 0.608285i 0.112420 0.0409177i
$$222$$ −6.84416 + 14.8763i −0.459350 + 0.998430i
$$223$$ −17.4250 + 3.07250i −1.16686 + 0.205750i −0.723326 0.690506i $$-0.757388\pi$$
−0.443537 + 0.896256i $$0.646277\pi$$
$$224$$ 3.87894 + 6.71853i 0.259173 + 0.448901i
$$225$$ 0 0
$$226$$ 10.9807 19.0191i 0.730423 1.26513i
$$227$$ 5.39434 14.8208i 0.358035 0.983692i −0.621676 0.783275i $$-0.713548\pi$$
0.979711 0.200418i $$-0.0642299\pi$$
$$228$$ 25.8470 + 6.78365i 1.71176 + 0.449258i
$$229$$ 1.35350 + 1.13572i 0.0894415 + 0.0750504i 0.686412 0.727213i $$-0.259185\pi$$
−0.596971 + 0.802263i $$0.703629\pi$$
$$230$$ 0 0
$$231$$ −0.379318 0.375443i −0.0249573 0.0247024i
$$232$$ −1.53093 + 4.20620i −0.100511 + 0.276151i
$$233$$ 12.0364 + 6.94920i 0.788529 + 0.455257i 0.839444 0.543446i $$-0.182881\pi$$
−0.0509157 + 0.998703i $$0.516214\pi$$
$$234$$ 3.38073 + 8.99987i 0.221005 + 0.588340i
$$235$$ 0 0
$$236$$ −0.742554 4.21123i −0.0483362 0.274128i
$$237$$ −19.3400 + 1.79212i −1.25627 + 0.116411i
$$238$$ 0.826858 + 2.27177i 0.0535973 + 0.147257i
$$239$$ 3.44391 19.5314i 0.222768 1.26338i −0.644138 0.764909i $$-0.722784\pi$$
0.866906 0.498471i $$-0.166105\pi$$
$$240$$ 0 0
$$241$$ 14.8419 12.4538i 0.956050 0.802221i −0.0242563 0.999706i $$-0.507722\pi$$
0.980306 + 0.197485i $$0.0632773\pi$$
$$242$$ 23.0703i 1.48301i
$$243$$ 15.4892 1.75676i 0.993629 0.112696i
$$244$$ −2.51674 −0.161118
$$245$$ 0 0
$$246$$ 12.2009 17.6165i 0.777901 1.12319i
$$247$$ 9.27540 + 1.63550i 0.590179 + 0.104065i
$$248$$ −3.01439 8.28198i −0.191414 0.525906i
$$249$$ −0.748720 8.07992i −0.0474482 0.512044i
$$250$$ 0 0
$$251$$ 2.73786 + 4.74212i 0.172812 + 0.299320i 0.939402 0.342818i $$-0.111381\pi$$
−0.766590 + 0.642137i $$0.778048\pi$$
$$252$$ −6.77237 + 2.54399i −0.426619 + 0.160256i
$$253$$ 0.593554 + 0.342689i 0.0373164 + 0.0215447i
$$254$$ −10.3972 3.78428i −0.652380 0.237447i
$$255$$ 0 0
$$256$$ 4.46383 + 3.74560i 0.278989 + 0.234100i
$$257$$ −7.43395 + 8.85943i −0.463717 + 0.552636i −0.946332 0.323196i $$-0.895243\pi$$
0.482615 + 0.875833i $$0.339687\pi$$
$$258$$ −19.8257 5.20333i −1.23429 0.323945i
$$259$$ −4.08115 1.48542i −0.253590 0.0922993i
$$260$$ 0 0
$$261$$ 11.5115 + 6.48951i 0.712546 + 0.401691i
$$262$$ −13.2608 + 7.65614i −0.819257 + 0.472998i
$$263$$ −6.37952 + 1.12488i −0.393378 + 0.0693632i −0.366839 0.930285i $$-0.619560\pi$$
−0.0265395 + 0.999648i $$0.508449\pi$$
$$264$$ 0.506712 + 0.233124i 0.0311860 + 0.0143478i
$$265$$ 0 0
$$266$$ −2.22318 + 12.6083i −0.136312 + 0.773064i
$$267$$ −2.20245 + 26.7554i −0.134788 + 1.63741i
$$268$$ 1.36549 + 1.62733i 0.0834106 + 0.0994048i
$$269$$ 13.8387 0.843758 0.421879 0.906652i $$-0.361371\pi$$
0.421879 + 0.906652i $$0.361371\pi$$
$$270$$ 0 0
$$271$$ 1.94536 0.118172 0.0590860 0.998253i $$-0.481181\pi$$
0.0590860 + 0.998253i $$0.481181\pi$$
$$272$$ 2.12125 + 2.52800i 0.128619 + 0.153283i
$$273$$ −2.30536 + 1.08945i −0.139527 + 0.0659366i
$$274$$ 4.13466 23.4488i 0.249784 1.41660i
$$275$$ 0 0
$$276$$ 7.58277 5.36774i 0.456429 0.323100i
$$277$$ 12.2832 2.16586i 0.738026 0.130134i 0.208016 0.978125i $$-0.433299\pi$$
0.530010 + 0.847991i $$0.322188\pi$$
$$278$$ −17.1943 + 9.92713i −1.03125 + 0.595390i
$$279$$ −25.5766 + 4.78114i −1.53123 + 0.286239i
$$280$$ 0 0
$$281$$ −9.16752 3.33670i −0.546888 0.199051i 0.0537751 0.998553i $$-0.482875\pi$$
−0.600663 + 0.799502i $$0.705097\pi$$
$$282$$ 2.39442 + 8.75602i 0.142585 + 0.521414i
$$283$$ −17.0797 + 20.3547i −1.01528 + 1.20996i −0.0377246 + 0.999288i $$0.512011\pi$$
−0.977556 + 0.210676i $$0.932433\pi$$
$$284$$ 18.2306 + 15.2973i 1.08179 + 0.907728i
$$285$$ 0 0
$$286$$ 0.954309 + 0.347340i 0.0564295 + 0.0205386i
$$287$$ 4.92202 + 2.84173i 0.290538 + 0.167742i
$$288$$ −18.1770 + 15.5732i −1.07109 + 0.917657i
$$289$$ −7.81006 13.5274i −0.459415 0.795730i
$$290$$ 0 0
$$291$$ −7.84527 + 5.55356i −0.459898 + 0.325556i
$$292$$ −12.9287 35.5214i −0.756598 2.07873i
$$293$$ 12.0712 + 2.12849i 0.705210 + 0.124347i 0.514741 0.857346i $$-0.327888\pi$$
0.190469 + 0.981693i $$0.438999\pi$$
$$294$$ 9.48386 + 20.0686i 0.553110 + 1.17042i
$$295$$ 0 0
$$296$$ 4.53888 0.263817
$$297$$ 0.923606 1.36326i 0.0535930 0.0791044i
$$298$$ 40.3243i 2.33592i
$$299$$ 2.50838 2.10478i 0.145063 0.121723i
$$300$$ 0 0
$$301$$ 0.944004 5.35371i 0.0544115 0.308583i
$$302$$ −2.90585 7.98375i −0.167213 0.459413i
$$303$$ −7.33993 + 15.9539i −0.421668 + 0.916526i
$$304$$ 3.03473 + 17.2108i 0.174053 + 0.987106i
$$305$$ 0 0
$$306$$ −6.42113 + 3.79567i −0.367071 + 0.216984i
$$307$$ −22.9271 13.2370i −1.30852 0.755475i −0.326671 0.945138i $$-0.605927\pi$$
−0.981849 + 0.189663i $$0.939260\pi$$
$$308$$ −0.261372 + 0.718114i −0.0148931 + 0.0409184i
$$309$$ 4.33242 16.5073i 0.246463 0.939070i
$$310$$ 0 0
$$311$$ −13.5280 11.3513i −0.767100 0.643673i 0.172865 0.984946i $$-0.444698\pi$$
−0.939964 + 0.341272i $$0.889142\pi$$
$$312$$ 1.87459 1.89394i 0.106128 0.107223i
$$313$$ 3.29954 9.06541i 0.186501 0.512407i −0.810841 0.585266i $$-0.800990\pi$$
0.997342 + 0.0728589i $$0.0232123\pi$$
$$314$$ −7.70019 + 13.3371i −0.434547 + 0.752657i
$$315$$ 0 0
$$316$$ 13.9056 + 24.0852i 0.782250 + 1.35490i
$$317$$ −3.65412 + 0.644320i −0.205236 + 0.0361886i −0.275321 0.961352i $$-0.588784\pi$$
0.0700850 + 0.997541i $$0.477673\pi$$
$$318$$ −39.7606 + 3.68439i −2.22967 + 0.206610i
$$319$$ 1.31174 0.477435i 0.0734434 0.0267312i
$$320$$ 0 0
$$321$$ −5.09927 + 7.36268i −0.284614 + 0.410945i
$$322$$ 2.86108 + 3.40971i 0.159442 + 0.190016i
$$323$$ 7.30748i 0.406599i
$$324$$ −11.5550 19.0972i −0.641944 1.06095i
$$325$$ 0 0
$$326$$ −20.1854 + 16.9376i −1.11797 + 0.938085i
$$327$$ −10.4096 7.20952i −0.575652 0.398687i
$$328$$ −5.84948 1.03142i −0.322983 0.0569507i
$$329$$ −2.26237 + 0.823435i −0.124728 + 0.0453974i
$$330$$ 0 0
$$331$$ −0.245329 1.39133i −0.0134845 0.0764745i 0.977323 0.211755i $$-0.0679177\pi$$
−0.990807 + 0.135280i $$0.956807\pi$$
$$332$$ −10.0624 + 5.80953i −0.552246 + 0.318839i
$$333$$ 2.19126 13.2196i 0.120080 0.724427i
$$334$$ 2.46786 4.27446i 0.135035 0.233888i
$$335$$ 0 0
$$336$$ −3.36265 3.32830i −0.183447 0.181573i
$$337$$ −8.34986 + 9.95097i −0.454846 + 0.542064i −0.943918 0.330179i $$-0.892891\pi$$
0.489073 + 0.872243i $$0.337335\pi$$
$$338$$ −14.5683 + 17.3618i −0.792409 + 0.944356i
$$339$$ −4.56209 + 17.3824i −0.247779 + 0.944084i
$$340$$ 0 0
$$341$$ −1.37428 + 2.38033i −0.0744215 + 0.128902i
$$342$$ −39.4992 + 0.405587i −2.13587 + 0.0219316i
$$343$$ −10.9928 + 6.34669i −0.593555 + 0.342689i
$$344$$ 0.986567 + 5.59510i 0.0531921 + 0.301667i
$$345$$ 0 0
$$346$$ −7.12504 + 2.59330i −0.383045 + 0.139417i
$$347$$ 4.72753 + 0.833591i 0.253787 + 0.0447495i 0.299094 0.954224i $$-0.403316\pi$$
−0.0453070 + 0.998973i $$0.514427\pi$$
$$348$$ 1.55236 18.8581i 0.0832152 1.01090i
$$349$$ 17.2954 14.5126i 0.925803 0.776841i −0.0492565 0.998786i $$-0.515685\pi$$
0.975059 + 0.221946i $$0.0712407\pi$$
$$350$$ 0 0
$$351$$ −4.61112 6.37412i −0.246123 0.340225i
$$352$$ 2.52845i 0.134767i
$$353$$ −19.0950 22.7565i −1.01632 1.21121i −0.977276 0.211972i $$-0.932012\pi$$
−0.0390490 0.999237i $$-0.512433\pi$$
$$354$$ 2.70080 + 5.71509i 0.143546 + 0.303754i
$$355$$ 0 0
$$356$$ 36.1220 13.1473i 1.91446 0.696807i
$$357$$ −1.14302 1.61470i −0.0604952 0.0854589i
$$358$$ −41.6804 + 7.34937i −2.20288 + 0.388427i
$$359$$ 6.70991 + 11.6219i 0.354136 + 0.613381i 0.986970 0.160906i $$-0.0514418\pi$$
−0.632834 + 0.774288i $$0.718108\pi$$
$$360$$ 0 0
$$361$$ −9.84920 + 17.0593i −0.518379 + 0.897858i
$$362$$ 7.04550 19.3573i 0.370303 1.01740i
$$363$$ 4.97970 + 18.2100i 0.261366 + 0.955778i
$$364$$ 2.79686 + 2.34685i 0.146595 + 0.123008i
$$365$$ 0 0
$$366$$ 3.58852 0.981314i 0.187575 0.0512941i
$$367$$ 2.71905 7.47054i 0.141933 0.389959i −0.848275 0.529556i $$-0.822359\pi$$
0.990208 + 0.139597i $$0.0445808\pi$$
$$368$$ 5.26184 + 3.03793i 0.274293 + 0.158363i
$$369$$ −5.82801 + 16.5387i −0.303394 + 0.860973i
$$370$$ 0 0
$$371$$ −1.83904 10.4297i −0.0954782 0.541484i
$$372$$ 21.5262 + 30.4091i 1.11608 + 1.57664i
$$373$$ 3.90604 + 10.7318i 0.202247 + 0.555670i 0.998804 0.0488939i $$-0.0155696\pi$$
−0.796557 + 0.604564i $$0.793347\pi$$
$$374$$ −0.136823 + 0.775963i −0.00707496 + 0.0401241i
$$375$$ 0 0
$$376$$ 1.92745 1.61733i 0.0994009 0.0834072i
$$377$$ 6.66917i 0.343480i
$$378$$ 8.66451 6.26801i 0.445654 0.322392i
$$379$$ 24.1705 1.24155 0.620777 0.783987i $$-0.286817\pi$$
0.620777 + 0.783987i $$0.286817\pi$$
$$380$$ 0 0
$$381$$ 9.02366 + 0.742807i 0.462296 + 0.0380551i
$$382$$ −37.0129 6.52637i −1.89374 0.333918i
$$383$$ −3.22979 8.87378i −0.165035 0.453429i 0.829416 0.558631i $$-0.188673\pi$$
−0.994451 + 0.105202i $$0.966451\pi$$
$$384$$ 12.4231 + 5.71553i 0.633964 + 0.291669i
$$385$$ 0 0
$$386$$ 11.2015 + 19.4016i 0.570143 + 0.987516i
$$387$$ 16.7721 0.172220i 0.852573 0.00875442i
$$388$$ 11.9193 + 6.88162i 0.605111 + 0.349361i
$$389$$ −2.39406 0.871367i −0.121384 0.0441801i 0.280614 0.959821i $$-0.409462\pi$$
−0.401998 + 0.915641i $$0.631684\pi$$
$$390$$ 0 0
$$391$$ 1.94617 + 1.63303i 0.0984218 + 0.0825857i
$$392$$ 3.95474 4.71308i 0.199745 0.238046i
$$393$$ 8.81457 8.90554i 0.444636 0.449225i
$$394$$ −28.1617 10.2500i −1.41876 0.516388i
$$395$$ 0 0
$$396$$ −2.32610 0.385571i −0.116891 0.0193757i
$$397$$ −3.18279 + 1.83759i −0.159740 + 0.0922258i −0.577739 0.816222i $$-0.696065\pi$$
0.417999 + 0.908447i $$0.362731\pi$$
$$398$$ 15.7173 2.77138i 0.787836 0.138917i
$$399$$ −0.966669 10.4319i −0.0483940 0.522251i
$$400$$ 0 0
$$401$$ 2.80420 15.9034i 0.140035 0.794177i −0.831186 0.555995i $$-0.812337\pi$$
0.971220 0.238182i $$-0.0765516\pi$$
$$402$$ −2.58151 1.78791i −0.128754 0.0891731i
$$403$$ 8.44078 + 10.0593i 0.420465 + 0.501091i
$$404$$ 25.1458 1.25105
$$405$$ 0 0
$$406$$ 9.06558 0.449917
$$407$$ −0.909859 1.08433i −0.0451000 0.0537481i
$$408$$ 1.69968 + 1.17717i 0.0841465 + 0.0582785i
$$409$$ −1.59443 + 9.04248i −0.0788396 + 0.447122i 0.919677 + 0.392676i $$0.128450\pi$$
−0.998517 + 0.0544462i $$0.982661\pi$$
$$410$$ 0 0
$$411$$ 1.79780 + 19.4013i 0.0886792 + 0.956994i
$$412$$ −24.0658 + 4.24345i −1.18564 + 0.209060i
$$413$$ −1.45190 + 0.838253i −0.0714432 + 0.0412477i
$$414$$ −8.71900 + 10.6103i −0.428515 + 0.521466i
$$415$$ 0 0
$$416$$ 11.3514 + 4.13157i 0.556548 + 0.202567i
$$417$$ 11.4292 11.5471i 0.559689 0.565466i
$$418$$ −2.68215 + 3.19646i −0.131188 + 0.156344i
$$419$$ 5.34613 + 4.48594i 0.261176 + 0.219152i 0.763967 0.645256i $$-0.223249\pi$$
−0.502791 + 0.864408i $$0.667694\pi$$
$$420$$ 0 0
$$421$$ −28.9525 10.5379i −1.41106 0.513584i −0.479619 0.877477i $$-0.659225\pi$$
−0.931441 + 0.363894i $$0.881447\pi$$
$$422$$ −9.55686 5.51765i −0.465221 0.268595i
$$423$$ −3.77996 6.39454i −0.183788 0.310913i
$$424$$ 5.53405 + 9.58526i 0.268757 + 0.465502i
$$425$$ 0 0
$$426$$ −31.9589 14.7034i −1.54842 0.712383i
$$427$$ 0.337472 + 0.927196i 0.0163314 + 0.0448702i
$$428$$ 12.6292 + 2.22687i 0.610457 + 0.107640i
$$429$$ −0.828236 0.0681784i −0.0399876 0.00329169i
$$430$$ 0 0
$$431$$ 27.8971 1.34376 0.671879 0.740661i $$-0.265487\pi$$
0.671879 + 0.740661i $$0.265487\pi$$
$$432$$ 8.18774 12.0853i 0.393933 0.581453i
$$433$$ 19.1706i 0.921278i 0.887588 + 0.460639i $$0.152380\pi$$
−0.887588 + 0.460639i $$0.847620\pi$$
$$434$$ −13.6739 + 11.4738i −0.656369 + 0.550759i
$$435$$ 0 0
$$436$$ −3.14843 + 17.8556i −0.150782 + 0.855130i
$$437$$ 4.60154 + 12.6426i 0.220121 + 0.604778i
$$438$$ 32.2849 + 45.6075i 1.54263 + 2.17921i
$$439$$ 4.12397 + 23.3882i 0.196826 + 1.11626i 0.909794 + 0.415060i $$0.136239\pi$$
−0.712968 + 0.701197i $$0.752649\pi$$
$$440$$ 0 0
$$441$$ −11.8177 13.7936i −0.562746 0.656838i
$$442$$ 3.26009 + 1.88221i 0.155067 + 0.0895278i
$$443$$ 7.98900 21.9496i 0.379569 1.04286i −0.591967 0.805962i $$-0.701648\pi$$
0.971536 0.236894i $$-0.0761294\pi$$
$$444$$ −18.5076 + 5.06108i −0.878332 + 0.240188i
$$445$$ 0 0
$$446$$ −28.6892 24.0731i −1.35847 1.13989i
$$447$$ 8.70396 + 31.8291i 0.411683 + 1.50546i
$$448$$ −3.74762 + 10.2965i −0.177059 + 0.486464i
$$449$$ 2.40953 4.17343i 0.113713 0.196956i −0.803552 0.595235i $$-0.797059\pi$$
0.917264 + 0.398279i $$0.130392\pi$$
$$450$$ 0 0
$$451$$ 0.926176 + 1.60418i 0.0436119 + 0.0755380i
$$452$$ 25.3416 4.46841i 1.19197 0.210176i
$$453$$ 4.01695 + 5.67457i 0.188733 + 0.266615i
$$454$$ 31.3701 11.4178i 1.47227 0.535863i
$$455$$ 0 0
$$456$$ 4.67813 + 9.89928i 0.219074 + 0.463576i
$$457$$ 3.14555 + 3.74872i 0.147142 + 0.175358i 0.834581 0.550885i $$-0.185710\pi$$
−0.687439 + 0.726242i $$0.741265\pi$$
$$458$$ 3.73978i 0.174749i
$$459$$ 4.24908 4.38203i 0.198330 0.204535i
$$460$$ 0 0
$$461$$ 21.4419 17.9919i 0.998650 0.837967i 0.0118535 0.999930i $$-0.496227\pi$$
0.986797 + 0.161963i $$0.0517824\pi$$
$$462$$ 0.0926768 1.12584i 0.00431171 0.0523789i
$$463$$ −27.0579 4.77104i −1.25749 0.221729i −0.495093 0.868840i $$-0.664866\pi$$
−0.762396 + 0.647111i $$0.775977\pi$$
$$464$$ 11.6285 4.23245i 0.539842 0.196486i
$$465$$ 0 0
$$466$$ 5.10832 + 28.9707i 0.236639 + 1.34204i
$$467$$ 18.4000 10.6232i 0.851450 0.491585i −0.00968963 0.999953i $$-0.503084\pi$$
0.861140 + 0.508368i $$0.169751\pi$$
$$468$$ −5.53194 + 9.81292i −0.255714 + 0.453602i
$$469$$ 0.416426 0.721272i 0.0192288 0.0333052i
$$470$$ 0 0
$$471$$ 3.19917 12.1894i 0.147410 0.561659i
$$472$$ 1.12623 1.34218i 0.0518387 0.0617790i
$$473$$ 1.13889 1.35728i 0.0523662 0.0624076i
$$474$$ −29.2186 28.9201i −1.34205 1.32834i
$$475$$ 0 0
$$476$$ −1.41636 + 2.45321i −0.0649188 + 0.112443i
$$477$$ 30.5889 11.4905i 1.40057 0.526113i
$$478$$ 36.3543 20.9892i 1.66281 0.960022i
$$479$$ 7.23745 + 41.0456i 0.330688 + 1.87542i 0.466248 + 0.884654i $$0.345606\pi$$
−0.135560 + 0.990769i $$0.543283\pi$$
$$480$$ 0 0
$$481$$ −6.35480 + 2.31296i −0.289754 + 0.105462i
$$482$$ 40.3859 + 7.12113i 1.83953 + 0.324358i
$$483$$ −2.99431 2.07381i −0.136246 0.0943618i
$$484$$ 20.7077 17.3758i 0.941258 0.789809i
$$485$$ 0 0
$$486$$ 23.9220 + 22.7244i 1.08513 + 1.03080i
$$487$$ 4.02801i 0.182527i −0.995827 0.0912634i $$-0.970909\pi$$
0.995827 0.0912634i $$-0.0290905\pi$$
$$488$$ −0.662836 0.789937i −0.0300052 0.0357588i
$$489$$ 12.2769 17.7263i 0.555183 0.801611i
$$490$$ 0 0
$$491$$ 36.2922 13.2093i 1.63784 0.596126i 0.651184 0.758920i $$-0.274273\pi$$
0.986660 + 0.162793i $$0.0520504\pi$$
$$492$$ 25.0017 2.31677i 1.12716 0.104448i
$$493$$ 5.09577 0.898521i 0.229502 0.0404674i
$$494$$ 9.96769 + 17.2645i 0.448468 + 0.776769i
$$495$$ 0 0
$$496$$ −12.1830 + 21.1015i −0.547032 + 0.947487i
$$497$$ 3.19114 8.76759i 0.143142 0.393280i
$$498$$ 12.0823 12.2070i 0.541423 0.547011i
$$499$$ 3.11922 + 2.61734i 0.139636 + 0.117168i 0.709930 0.704272i $$-0.248726\pi$$
−0.570295 + 0.821440i $$0.693171\pi$$
$$500$$ 0 0
$$501$$ −1.02531 + 3.90664i −0.0458076 + 0.174536i
$$502$$ −3.96403 + 10.8911i −0.176923 + 0.486093i
$$503$$ 2.96695 + 1.71297i 0.132290 + 0.0763775i 0.564684 0.825307i $$-0.308998\pi$$
−0.432395 + 0.901684i $$0.642331\pi$$
$$504$$ −2.58213 1.45565i −0.115017 0.0648398i
$$505$$ 0 0
$$506$$ 0.251909 + 1.42865i 0.0111987 + 0.0635111i
$$507$$ 7.75161 16.8487i 0.344261 0.748276i
$$508$$ −4.43412 12.1827i −0.196732 0.540518i
$$509$$ 2.12952 12.0771i 0.0943893 0.535308i −0.900543 0.434766i $$-0.856831\pi$$
0.994933 0.100542i $$-0.0320578\pi$$
$$510$$ 0 0
$$511$$ −11.3529 + 9.52619i −0.502222 + 0.421414i
$$512$$ 28.1241i 1.24292i
$$513$$ 31.0903 8.84601i 1.37267 0.390561i
$$514$$ −24.4791 −1.07973
$$515$$ 0 0
$$516$$ −10.2616 21.7143i −0.451742 0.955920i
$$517$$ −0.772750 0.136257i −0.0339855 0.00599257i
$$518$$ −3.14407 8.63825i −0.138142 0.379543i
$$519$$ 5.06423 3.58490i 0.222295 0.157360i
$$520$$ 0 0
$$521$$ −7.04117 12.1957i −0.308479 0.534302i 0.669551 0.742766i $$-0.266487\pi$$
−0.978030 + 0.208465i $$0.933153\pi$$
$$522$$ 5.13962 + 27.4943i 0.224955 + 1.20339i
$$523$$ −8.46897 4.88956i −0.370322 0.213806i 0.303277 0.952902i $$-0.401919\pi$$
−0.673599 + 0.739097i $$0.735253\pi$$
$$524$$ −16.8597 6.13643i −0.736520 0.268071i
$$525$$ 0 0
$$526$$ −10.5035 8.81348i −0.457974 0.384286i
$$527$$ −6.54892 + 7.80469i −0.285275 + 0.339978i
$$528$$ −0.406744 1.48740i −0.0177013 0.0647309i
$$529$$ −17.2176 6.26668i −0.748590 0.272464i
$$530$$ 0 0
$$531$$ −3.36541 3.92812i −0.146047 0.170466i
$$532$$ −12.9915 + 7.50065i −0.563254 + 0.325195i
$$533$$ 8.71534 1.53675i 0.377503 0.0665640i
$$534$$ −46.3785 + 32.8307i −2.00699 + 1.42072i
$$535$$ 0 0
$$536$$ −0.151144 + 0.857180i −0.00652843 + 0.0370245i
$$537$$ 31.3131 14.7977i 1.35126 0.638569i
$$538$$ 18.8280 + 22.4384i 0.811734 + 0.967387i
$$539$$ −1.91871 −0.0826445
$$540$$ 0 0
$$541$$ 40.9454 1.76038 0.880189 0.474623i $$-0.157416\pi$$
0.880189 + 0.474623i $$0.157416\pi$$
$$542$$ 2.64674 + 3.15426i 0.113687 + 0.135487i
$$543$$ −1.38294 + 16.8001i −0.0593477 + 0.720959i
$$544$$ −1.62750 + 9.22999i −0.0697783 + 0.395732i
$$545$$ 0 0
$$546$$ −4.90300 2.25573i −0.209829 0.0965365i
$$547$$ 1.09341 0.192798i 0.0467508 0.00824343i −0.150224 0.988652i $$-0.547999\pi$$
0.196975 + 0.980409i $$0.436888\pi$$
$$548$$ 24.1615 13.9497i 1.03213 0.595900i
$$549$$ −2.62070 + 1.54916i −0.111849 + 0.0661164i
$$550$$ 0 0
$$551$$ 25.7495 + 9.37206i 1.09697 + 0.399263i
$$552$$ 3.68186 + 0.966321i 0.156711 + 0.0411293i
$$553$$ 7.00864 8.35257i 0.298038 0.355188i
$$554$$ 20.2236 + 16.9696i 0.859216 + 0.720968i
$$555$$ 0 0
$$556$$ −21.8607 7.95664i −0.927100 0.337437i
$$557$$ 30.3458 + 17.5201i 1.28579 + 0.742352i 0.977901 0.209070i $$-0.0670437\pi$$
0.307890 + 0.951422i $$0.400377\pi$$
$$558$$ −42.5503 34.9657i −1.80130 1.48022i
$$559$$ −4.23247 7.33084i −0.179014 0.310062i
$$560$$ 0 0
$$561$$ −0.0594925 0.642022i −0.00251178 0.0271062i
$$562$$ −7.06254 19.4042i −0.297915 0.818516i
$$563$$ −38.1822 6.73255i −1.60919 0.283743i −0.704463 0.709741i $$-0.748812\pi$$
−0.904724 + 0.425998i $$0.859923\pi$$
$$564$$ −6.05593 + 8.74396i −0.255001 + 0.368187i
$$565$$ 0 0
$$566$$ −56.2413 −2.36400
$$567$$ −5.48619 + 6.81774i −0.230398 + 0.286318i
$$568$$ 9.75095i 0.409141i
$$569$$ 26.0213 21.8344i 1.09087 0.915347i 0.0940904 0.995564i $$-0.470006\pi$$
0.996777 + 0.0802169i $$0.0255613\pi$$
$$570$$ 0 0
$$571$$ 1.75191 9.93559i 0.0733153 0.415792i −0.925956 0.377631i $$-0.876739\pi$$
0.999272 0.0381610i $$-0.0121500\pi$$
$$572$$ 0.406986 + 1.11818i 0.0170169 + 0.0467536i
$$573$$ 30.6240 2.83775i 1.27934 0.118549i
$$574$$ 2.08894 + 11.8470i 0.0871908 + 0.494484i
$$575$$ 0 0
$$576$$ −33.3522 5.52842i −1.38968 0.230351i
$$577$$ −10.5069 6.06615i −0.437407 0.252537i 0.265090 0.964224i $$-0.414598\pi$$
−0.702497 + 0.711687i $$0.747932\pi$$
$$578$$ 11.3078 31.0680i 0.470344 1.29226i
$$579$$ −13.0295 12.8964i −0.541487 0.535956i
$$580$$ 0 0
$$581$$ 3.48957 + 2.92810i 0.144772 + 0.121478i
$$582$$ −19.6785 5.16470i −0.815700 0.214084i
$$583$$ 1.18055 3.24352i 0.0488932 0.134333i
$$584$$ 7.74416 13.4133i 0.320456 0.555046i
$$585$$ 0 0
$$586$$ 12.9722 + 22.4685i 0.535877 + 0.928167i
$$587$$ 31.2669 5.51319i 1.29052 0.227554i 0.514079 0.857743i $$-0.328134\pi$$
0.776442 + 0.630189i $$0.217023\pi$$
$$588$$ −10.8704 + 23.6276i −0.448288 + 0.974387i
$$589$$ −50.7006 + 18.4535i −2.08908 + 0.760363i
$$590$$ 0 0
$$591$$ 24.4412 + 2.01195i 1.00538 + 0.0827605i
$$592$$ −8.06588 9.61254i −0.331506 0.395073i
$$593$$ 13.4906i 0.553993i 0.960871 + 0.276996i $$0.0893390\pi$$
−0.960871 + 0.276996i $$0.910661\pi$$
$$594$$ 3.46703 0.357210i 0.142254 0.0146565i
$$595$$ 0 0
$$596$$ 36.1947 30.3710i 1.48259 1.24404i
$$597$$ −11.8079 + 5.58009i −0.483265 + 0.228378i
$$598$$ 6.82550 + 1.20352i 0.279115 + 0.0492156i
$$599$$ −39.8715 + 14.5120i −1.62911 + 0.592946i −0.985086 0.172063i $$-0.944957\pi$$
−0.644020 + 0.765009i $$0.722735\pi$$
$$600$$ 0 0
$$601$$ −3.43906 19.5039i −0.140282 0.795579i −0.971035 0.238938i $$-0.923201\pi$$
0.830753 0.556641i $$-0.187910\pi$$
$$602$$ 9.96501 5.75330i 0.406144 0.234487i
$$603$$ 2.42358 + 0.854034i 0.0986958 + 0.0347789i
$$604$$ 4.97755 8.62136i 0.202533 0.350798i
$$605$$ 0 0
$$606$$ −35.8543 + 9.80470i −1.45648 + 0.398289i
$$607$$ −23.1397 + 27.5769i −0.939213 + 1.11931i 0.0534715 + 0.998569i $$0.482971\pi$$
−0.992684 + 0.120741i $$0.961473\pi$$
$$608$$ −31.9038 + 38.0215i −1.29387 + 1.54197i
$$609$$ −7.15571 + 1.95680i −0.289964 + 0.0792934i
$$610$$ 0 0
$$611$$ −1.87442 + 3.24659i −0.0758310 + 0.131343i
$$612$$ −8.24315 2.90476i −0.333209 0.117418i
$$613$$ 22.9175 13.2314i 0.925627 0.534411i 0.0402013 0.999192i $$-0.487200\pi$$
0.885426 + 0.464780i $$0.153867\pi$$
$$614$$ −9.73045 55.1841i −0.392689 2.22705i
$$615$$ 0 0
$$616$$ −0.294234 + 0.107093i −0.0118550 + 0.00431488i
$$617$$ −48.3705 8.52903i −1.94732 0.343366i −0.999713 0.0239406i $$-0.992379\pi$$
−0.947611 0.319425i $$-0.896510\pi$$
$$618$$ 32.6599 15.4342i 1.31377 0.620853i
$$619$$ 18.5430 15.5595i 0.745307 0.625387i −0.188950 0.981987i $$-0.560508\pi$$
0.934257 + 0.356600i $$0.116064\pi$$
$$620$$ 0 0
$$621$$ 4.59193 10.2570i 0.184268 0.411598i
$$622$$ 37.3785i 1.49874i
$$623$$ −9.68725 11.5448i −0.388111 0.462533i
$$624$$ −7.34229 0.604400i −0.293927 0.0241954i
$$625$$ 0 0
$$626$$ 19.1881 6.98388i 0.766909 0.279132i
$$627$$ 1.42714 3.10199i 0.0569945 0.123882i
$$628$$ −17.7708 + 3.13347i −0.709132 + 0.125039i
$$629$$ −2.62345 4.54395i −0.104604 0.181179i
$$630$$ 0 0
$$631$$ −8.84842 + 15.3259i −0.352250 + 0.610115i −0.986643 0.162895i $$-0.947917\pi$$
0.634393 + 0.773010i $$0.281250\pi$$
$$632$$ −3.89736 + 10.7079i −0.155029 + 0.425938i
$$633$$ 8.73447 + 2.29240i 0.347164 + 0.0911147i
$$634$$ −6.01629 5.04827i −0.238937 0.200492i
$$635$$ 0 0
$$636$$ −33.2535 32.9138i −1.31859 1.30512i
$$637$$ −3.13523 + 8.61398i −0.124222 + 0.341298i
$$638$$ 2.55880 + 1.47732i 0.101304 + 0.0584878i
$$639$$ 28.3998 + 4.70751i 1.12348 + 0.186226i
$$640$$ 0 0
$$641$$ 6.60738 + 37.4723i 0.260976 + 1.48007i 0.780254 + 0.625463i $$0.215090\pi$$
−0.519278 + 0.854605i $$0.673799\pi$$
$$642$$ −18.8758 + 1.74911i −0.744968 + 0.0690319i
$$643$$ −16.0553 44.1115i −0.633158 1.73959i −0.672220 0.740352i $$-0.734659\pi$$
0.0390615 0.999237i $$-0.487563\pi$$
$$644$$ −0.905644 + 5.13616i −0.0356874 + 0.202393i
$$645$$ 0 0
$$646$$ −11.8485 + 9.94211i −0.466175 + 0.391167i
$$647$$ 28.2333i 1.10997i 0.831862 + 0.554983i $$0.187275\pi$$
−0.831862 + 0.554983i $$0.812725\pi$$
$$648$$ 2.95083 8.65643i 0.115920 0.340057i
$$649$$ −0.546406 −0.0214483
$$650$$ 0 0
$$651$$ 8.31660 12.0081i 0.325953 0.470634i
$$652$$ −30.4060 5.36140i −1.19079 0.209969i
$$653$$ −12.0758 33.1779i −0.472562 1.29835i −0.915687 0.401893i $$-0.868353\pi$$
0.443125 0.896460i $$-0.353870\pi$$
$$654$$ −2.47295 26.6872i −0.0967001 1.04355i
$$655$$ 0 0
$$656$$ 8.21052 + 14.2210i 0.320567 + 0.555239i
$$657$$ −35.3277 29.0306i −1.37826 1.13259i
$$658$$ −4.41318 2.54795i −0.172044 0.0993295i
$$659$$ 39.1793 + 14.2601i 1.52621 + 0.555494i 0.962689 0.270609i $$-0.0872250\pi$$
0.563519 + 0.826103i $$0.309447\pi$$
$$660$$ 0 0
$$661$$ 0.975874 + 0.818856i 0.0379571 + 0.0318498i 0.661569 0.749884i $$-0.269891\pi$$
−0.623612 + 0.781734i $$0.714335\pi$$
$$662$$ 1.92216 2.29075i 0.0747070 0.0890324i
$$663$$ −2.97956 0.781997i −0.115716 0.0303702i
$$664$$ −4.47359 1.62825i −0.173609 0.0631885i
$$665$$ 0 0
$$666$$ 24.4158 14.4328i 0.946095 0.559258i
$$667$$ 8.25035 4.76334i 0.319455 0.184437i
$$668$$ 5.69543 1.00426i 0.220363 0.0388559i
$$669$$ 27.8413 + 12.8090i 1.07641 + 0.495226i
$$670$$ 0 0
$$671$$ −0.0558427 + 0.316700i −0.00215578 + 0.0122261i
$$672$$ 1.10238 13.3918i 0.0425252 0.516598i
$$673$$ 22.9043 + 27.2963i 0.882896 + 1.05219i 0.998266 + 0.0588715i $$0.0187502\pi$$
−0.115370 + 0.993323i $$0.536805\pi$$
$$674$$ −27.4951 −1.05907
$$675$$ 0 0
$$676$$ −26.5561 −1.02139
$$677$$ −11.5714 13.7902i −0.444725 0.530002i 0.496386 0.868102i $$-0.334660\pi$$
−0.941110 + 0.338100i $$0.890216\pi$$
$$678$$ −34.3913 + 16.2524i −1.32079 + 0.624169i
$$679$$ 0.936996 5.31397i 0.0359586 0.203931i
$$680$$ 0 0
$$681$$ −22.2968 + 15.7836i −0.854414 + 0.604828i
$$682$$ −5.72929 + 1.01023i −0.219386 + 0.0386836i
$$683$$ 34.4344 19.8807i 1.31760 0.760715i 0.334255 0.942483i $$-0.391515\pi$$
0.983341 + 0.181768i $$0.0581820\pi$$
$$684$$ −30.1136 35.1486i −1.15142 1.34394i
$$685$$ 0 0
$$686$$ −25.2468 9.18909i −0.963928 0.350841i
$$687$$ −0.807229 2.95192i −0.0307977 0.112623i
$$688$$ 10.0962 12.0322i 0.384915 0.458724i
$$689$$ −12.6327 10.6001i −0.481266 0.403830i
$$690$$ 0 0
$$691$$ 15.8251 + 5.75986i 0.602015 + 0.219115i 0.625006 0.780620i $$-0.285097\pi$$
−0.0229909 + 0.999736i $$0.507319\pi$$
$$692$$ −7.69408 4.44218i −0.292485 0.168866i
$$693$$ 0.169860 + 0.908663i 0.00645244 + 0.0345173i
$$694$$ 5.08038 + 8.79948i 0.192849 + 0.334024i
$$695$$ 0 0
$$696$$ 6.32790 4.47944i 0.239859 0.169793i
$$697$$ 2.34839 + 6.45216i 0.0889518 + 0.244393i
$$698$$ 47.0622 + 8.29833i 1.78133 + 0.314097i
$$699$$ −10.2854 21.7648i −0.389031 0.823220i
$$700$$ 0 0
$$701$$ −8.96921 −0.338762 −0.169381 0.985551i $$-0.554177\pi$$
−0.169381 + 0.985551i $$0.554177\pi$$
$$702$$ 4.06156 16.1488i 0.153294 0.609498i
$$703$$ 27.7861i 1.04797i
$$704$$ −2.73570 + 2.29552i −0.103106 + 0.0865158i
$$705$$ 0 0
$$706$$ 10.9186 61.9223i 0.410926 2.33048i
$$707$$ −3.37181 9.26398i −0.126810 0.348408i
$$708$$ −3.09566 + 6.72864i −0.116342 + 0.252878i
$$709$$ −3.15026 17.8660i −0.118311 0.670973i −0.985058 0.172225i $$-0.944904\pi$$
0.866747 0.498748i $$-0.166207\pi$$
$$710$$ 0 0
$$711$$ 29.3054 + 16.5206i 1.09904 + 0.619572i
$$712$$ 13.6401 + 7.87509i 0.511183 + 0.295131i
$$713$$ −6.41560 + 17.6267i −0.240266 + 0.660125i
$$714$$ 1.06299 4.05019i 0.0397814 0.151574i
$$715$$ 0 0
$$716$$ −37.9890 31.8766i −1.41972 1.19128i
$$717$$ −24.1650 + 24.4144i −0.902457 + 0.911771i
$$718$$ −9.71498 + 26.6917i −0.362560 + 0.996125i
$$719$$ 15.7860 27.3421i 0.588718 1.01969i −0.405683 0.914014i $$-0.632966\pi$$
0.994401 0.105675i $$-0.0337004\pi$$
$$720$$ 0 0
$$721$$ 4.79034 + 8.29711i 0.178402 + 0.309001i
$$722$$ −41.0606 + 7.24010i −1.52812 + 0.269449i
$$723$$ −33.4148 + 3.09636i −1.24271 + 0.115155i
$$724$$ 22.6814 8.25536i 0.842948 0.306808i
$$725$$ 0 0
$$726$$ −22.7511 + 32.8497i −0.844374 + 1.21916i
$$727$$ −24.6890 29.4232i −0.915664 1.09125i −0.995530 0.0944407i $$-0.969894\pi$$
0.0798662 0.996806i $$-0.474551\pi$$
$$728$$ 1.49595i 0.0554436i
$$729$$ −23.7874 12.7734i −0.881014 0.473090i
$$730$$ 0 0
$$731$$ 5.03111 4.22160i 0.186082 0.156142i
$$732$$ 3.58358 + 2.48193i 0.132453 + 0.0917346i
$$733$$ −29.8695 5.26680i −1.10326 0.194534i −0.407778 0.913081i $$-0.633696\pi$$
−0.695478 + 0.718547i $$0.744807\pi$$
$$734$$ 15.8123 5.75521i 0.583643 0.212429i
$$735$$ 0 0
$$736$$ 2.99643 + 16.9936i 0.110450 + 0.626391i
$$737$$ 0.235076 0.135721i 0.00865915 0.00499936i
$$738$$ −34.7456 + 13.0519i −1.27900 + 0.480448i
$$739$$ 5.00127 8.66245i 0.183975 0.318653i −0.759256 0.650792i $$-0.774437\pi$$
0.943230 + 0.332139i $$0.107770\pi$$
$$740$$ 0 0
$$741$$ −11.5943 11.4759i −0.425928 0.421577i
$$742$$ 14.4089 17.1719i 0.528969 0.630400i
$$743$$ −23.3163 + 27.7873i −0.855394 + 1.01942i 0.144160 + 0.989554i $$0.453952\pi$$
−0.999554 + 0.0298642i $$0.990493\pi$$
$$744$$ −3.87523 + 14.7654i −0.142073 + 0.541324i
$$745$$ 0 0
$$746$$ −12.0865 + 20.9344i −0.442517 + 0.766461i
$$747$$ −6.90205 + 12.2433i −0.252533 + 0.447960i
$$748$$ −0.799548 + 0.461619i −0.0292344 + 0.0168785i
$$749$$ −0.873058 4.95136i −0.0319008 0.180919i
$$750$$ 0 0
$$751$$ 13.6766 4.97788i 0.499067 0.181646i −0.0802073 0.996778i $$-0.525558\pi$$
0.579274 + 0.815133i $$0.303336\pi$$
$$752$$ −6.85041 1.20791i −0.249809 0.0440480i
$$753$$ 0.778089 9.45226i 0.0283551 0.344460i
$$754$$ 10.8136 9.07366i 0.393807 0.330443i
$$755$$ 0 0
$$756$$ 12.1519 + 3.05631i 0.441962 + 0.111157i
$$757$$ 45.5754i 1.65646i 0.560385 + 0.828232i $$0.310653\pi$$
−0.560385 + 0.828232i $$0.689347\pi$$
$$758$$ 32.8849 + 39.1907i 1.19443 + 1.42347i
$$759$$ −0.507211 1.07330i −0.0184106 0.0389582i
$$760$$ 0 0
$$761$$ −20.9040 + 7.60843i −0.757769 + 0.275805i −0.691871 0.722021i $$-0.743213\pi$$
−0.0658978 + 0.997826i $$0.520991\pi$$
$$762$$ 11.0726 + 15.6418i 0.401119 + 0.566643i
$$763$$ 7.00040 1.23436i 0.253431 0.0446868i
$$764$$ −22.0189 38.1379i −0.796616 1.37978i
$$765$$ 0 0
$$766$$ 9.99393 17.3100i 0.361096 0.625436i
$$767$$ −0.892846 + 2.45307i −0.0322388 + 0.0885754i
$$768$$ −2.66224 9.73542i −0.0960654 0.351297i
$$769$$ −10.4679 8.78365i −0.377484 0.316747i 0.434230 0.900802i $$-0.357021\pi$$
−0.811714 + 0.584056i $$0.801465\pi$$
$$770$$ 0 0
$$771$$ 19.3220 5.28379i 0.695866 0.190291i
$$772$$ −8.97807 + 24.6670i −0.323128 + 0.887786i
$$773$$ 17.8869 + 10.3270i 0.643345 + 0.371436i 0.785902 0.618351i $$-0.212199\pi$$
−0.142557 + 0.989787i $$0.545532\pi$$
$$774$$ 23.0983 + 26.9604i 0.830252 + 0.969072i
$$775$$ 0 0
$$776$$ 0.979243 + 5.55356i 0.0351528 + 0.199361i
$$777$$ 4.34626 +