# Properties

 Label 729.2.g.b.28.7 Level $729$ Weight $2$ Character 729.28 Analytic conductor $5.821$ Analytic rank $0$ Dimension $144$ CM no Inner twists $2$

# Learn more

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(28,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([44]))

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

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

chi := DirichletCharacter("729.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$729 = 3^{6}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 729.g (of order $$27$$, degree $$18$$, 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: $$5.82109430735$$ Analytic rank: $$0$$ Dimension: $$144$$ Relative dimension: $$8$$ over $$\Q(\zeta_{27})$$ Twist minimal: no (minimal twist has level 81) Sato-Tate group: $\mathrm{SU}(2)[C_{27}]$

## Embedding invariants

 Embedding label 28.7 Character $$\chi$$ $$=$$ 729.28 Dual form 729.2.g.b.703.7

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(1.29056 - 0.848814i) q^{2} +(0.152898 - 0.354458i) q^{4} +(-0.349244 + 0.370177i) q^{5} +(-3.96148 - 0.463031i) q^{7} +(0.432916 + 2.45519i) q^{8} +O(q^{10})$$ $$q+(1.29056 - 0.848814i) q^{2} +(0.152898 - 0.354458i) q^{4} +(-0.349244 + 0.370177i) q^{5} +(-3.96148 - 0.463031i) q^{7} +(0.432916 + 2.45519i) q^{8} +(-0.136509 + 0.774179i) q^{10} +(-1.09805 + 3.66773i) q^{11} +(-0.181020 + 3.10799i) q^{13} +(-5.50556 + 2.76500i) q^{14} +(3.17252 + 3.36268i) q^{16} +(1.41129 - 0.513668i) q^{17} +(6.30242 + 2.29389i) q^{19} +(0.0778134 + 0.180392i) q^{20} +(1.69613 + 5.66546i) q^{22} +(-1.17843 + 0.137739i) q^{23} +(0.275664 + 4.73298i) q^{25} +(2.40449 + 4.16470i) q^{26} +(-0.769829 + 1.33338i) q^{28} +(-6.17988 - 3.10365i) q^{29} +(-0.0276800 - 0.0371807i) q^{31} +(2.09689 + 0.496972i) q^{32} +(1.38535 - 1.86084i) q^{34} +(1.55493 - 1.30474i) q^{35} +(-2.33905 - 1.96269i) q^{37} +(10.0807 - 2.38918i) q^{38} +(-1.06005 - 0.697205i) q^{40} +(-4.96389 - 3.26480i) q^{41} +(0.231769 - 0.0549304i) q^{43} +(1.13217 + 0.950001i) q^{44} +(-1.40392 + 1.17803i) q^{46} +(2.82910 - 3.80014i) q^{47} +(8.66765 + 2.05427i) q^{49} +(4.37318 + 5.87420i) q^{50} +(1.07397 + 0.539370i) q^{52} +(-6.81173 + 11.7983i) q^{53} +(-0.974224 - 1.68741i) q^{55} +(-0.578162 - 9.92665i) q^{56} +(-10.6099 + 1.24012i) q^{58} +(-0.400604 - 1.33811i) q^{59} +(-0.124364 - 0.288308i) q^{61} +(-0.0672822 - 0.0244887i) q^{62} +(-5.56048 + 2.02385i) q^{64} +(-1.08729 - 1.15246i) q^{65} +(4.90826 - 2.46502i) q^{67} +(0.0337102 - 0.578782i) q^{68} +(0.899246 - 3.00369i) q^{70} +(2.03991 - 11.5689i) q^{71} +(2.70207 + 15.3242i) q^{73} +(-4.68464 - 0.547556i) q^{74} +(1.77672 - 1.88321i) q^{76} +(6.04817 - 14.0212i) q^{77} +(11.6941 - 7.69136i) q^{79} -2.35277 q^{80} -9.17740 q^{82} +(0.587346 - 0.386304i) q^{83} +(-0.302737 + 0.701823i) q^{85} +(0.252487 - 0.267620i) q^{86} +(-9.48034 - 1.10809i) q^{88} +(-2.00921 - 11.3948i) q^{89} +(2.15620 - 12.2284i) q^{91} +(-0.131358 + 0.438765i) q^{92} +(0.425507 - 7.30568i) q^{94} +(-3.05023 + 1.53188i) q^{95} +(8.92799 + 9.46312i) q^{97} +(12.9298 - 4.70606i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10})$$ 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 $$144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} + 63 q^{20} + 9 q^{22} - 36 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} + 45 q^{29} + 9 q^{31} - 63 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} + 9 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} - 63 q^{47} + 9 q^{49} + 225 q^{50} + 27 q^{52} - 45 q^{53} - 9 q^{55} - 99 q^{56} + 9 q^{58} + 117 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} - 81 q^{65} + 36 q^{67} + 18 q^{68} + 63 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} + 90 q^{76} - 81 q^{77} + 63 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} + 63 q^{85} - 81 q^{86} + 90 q^{88} + 81 q^{89} - 18 q^{91} + 63 q^{92} + 63 q^{94} - 153 q^{95} + 36 q^{97} - 81 q^{98}+O(q^{100})$$ 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 + 63 * q^20 + 9 * q^22 - 36 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 + 45 * q^29 + 9 * q^31 - 63 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 - 63 * q^47 + 9 * q^49 + 225 * q^50 + 27 * q^52 - 45 * q^53 - 9 * q^55 - 99 * q^56 + 9 * q^58 + 117 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 - 81 * q^65 + 36 * q^67 + 18 * q^68 + 63 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 + 90 * q^76 - 81 * q^77 + 63 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 + 63 * q^85 - 81 * q^86 + 90 * q^88 + 81 * q^89 - 18 * q^91 + 63 * q^92 + 63 * q^94 - 153 * q^95 + 36 * q^97 - 81 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$$.

 $$n$$ $$2$$ $$\chi(n)$$ $$e\left(\frac{22}{27}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.29056 0.848814i 0.912563 0.600202i −0.00404373 0.999992i $$-0.501287\pi$$
0.916607 + 0.399790i $$0.130917\pi$$
$$3$$ 0 0
$$4$$ 0.152898 0.354458i 0.0764491 0.177229i
$$5$$ −0.349244 + 0.370177i −0.156187 + 0.165548i −0.800742 0.599010i $$-0.795561\pi$$
0.644555 + 0.764558i $$0.277043\pi$$
$$6$$ 0 0
$$7$$ −3.96148 0.463031i −1.49730 0.175009i −0.672358 0.740226i $$-0.734718\pi$$
−0.824942 + 0.565217i $$0.808793\pi$$
$$8$$ 0.432916 + 2.45519i 0.153059 + 0.868041i
$$9$$ 0 0
$$10$$ −0.136509 + 0.774179i −0.0431678 + 0.244817i
$$11$$ −1.09805 + 3.66773i −0.331074 + 1.10586i 0.616775 + 0.787140i $$0.288439\pi$$
−0.947848 + 0.318723i $$0.896746\pi$$
$$12$$ 0 0
$$13$$ −0.181020 + 3.10799i −0.0502059 + 0.862002i 0.875373 + 0.483448i $$0.160616\pi$$
−0.925579 + 0.378554i $$0.876421\pi$$
$$14$$ −5.50556 + 2.76500i −1.47142 + 0.738976i
$$15$$ 0 0
$$16$$ 3.17252 + 3.36268i 0.793131 + 0.840669i
$$17$$ 1.41129 0.513668i 0.342288 0.124583i −0.165156 0.986268i $$-0.552813\pi$$
0.507444 + 0.861685i $$0.330590\pi$$
$$18$$ 0 0
$$19$$ 6.30242 + 2.29389i 1.44587 + 0.526255i 0.941436 0.337192i $$-0.109477\pi$$
0.504439 + 0.863447i $$0.331699\pi$$
$$20$$ 0.0778134 + 0.180392i 0.0173996 + 0.0403368i
$$21$$ 0 0
$$22$$ 1.69613 + 5.66546i 0.361616 + 1.20788i
$$23$$ −1.17843 + 0.137739i −0.245720 + 0.0287206i −0.238062 0.971250i $$-0.576512\pi$$
−0.00765887 + 0.999971i $$0.502438\pi$$
$$24$$ 0 0
$$25$$ 0.275664 + 4.73298i 0.0551329 + 0.946595i
$$26$$ 2.40449 + 4.16470i 0.471559 + 0.816765i
$$27$$ 0 0
$$28$$ −0.769829 + 1.33338i −0.145484 + 0.251986i
$$29$$ −6.17988 3.10365i −1.14757 0.576333i −0.229722 0.973256i $$-0.573782\pi$$
−0.917852 + 0.396923i $$0.870078\pi$$
$$30$$ 0 0
$$31$$ −0.0276800 0.0371807i −0.00497148 0.00667785i 0.799631 0.600492i $$-0.205029\pi$$
−0.804602 + 0.593814i $$0.797621\pi$$
$$32$$ 2.09689 + 0.496972i 0.370681 + 0.0878530i
$$33$$ 0 0
$$34$$ 1.38535 1.86084i 0.237585 0.319132i
$$35$$ 1.55493 1.30474i 0.262831 0.220541i
$$36$$ 0 0
$$37$$ −2.33905 1.96269i −0.384537 0.322665i 0.429943 0.902856i $$-0.358533\pi$$
−0.814481 + 0.580191i $$0.802978\pi$$
$$38$$ 10.0807 2.38918i 1.63531 0.387576i
$$39$$ 0 0
$$40$$ −1.06005 0.697205i −0.167608 0.110238i
$$41$$ −4.96389 3.26480i −0.775229 0.509876i 0.0991780 0.995070i $$-0.468379\pi$$
−0.874407 + 0.485194i $$0.838749\pi$$
$$42$$ 0 0
$$43$$ 0.231769 0.0549304i 0.0353445 0.00837680i −0.212906 0.977073i $$-0.568293\pi$$
0.248250 + 0.968696i $$0.420145\pi$$
$$44$$ 1.13217 + 0.950001i 0.170681 + 0.143218i
$$45$$ 0 0
$$46$$ −1.40392 + 1.17803i −0.206997 + 0.173691i
$$47$$ 2.82910 3.80014i 0.412666 0.554307i −0.546387 0.837533i $$-0.683997\pi$$
0.959053 + 0.283226i $$0.0914046\pi$$
$$48$$ 0 0
$$49$$ 8.66765 + 2.05427i 1.23824 + 0.293467i
$$50$$ 4.37318 + 5.87420i 0.618461 + 0.830737i
$$51$$ 0 0
$$52$$ 1.07397 + 0.539370i 0.148933 + 0.0747972i
$$53$$ −6.81173 + 11.7983i −0.935663 + 1.62062i −0.162216 + 0.986755i $$0.551864\pi$$
−0.773447 + 0.633860i $$0.781469\pi$$
$$54$$ 0 0
$$55$$ −0.974224 1.68741i −0.131364 0.227530i
$$56$$ −0.578162 9.92665i −0.0772601 1.32650i
$$57$$ 0 0
$$58$$ −10.6099 + 1.24012i −1.39315 + 0.162836i
$$59$$ −0.400604 1.33811i −0.0521543 0.174207i 0.927944 0.372719i $$-0.121574\pi$$
−0.980099 + 0.198512i $$0.936389\pi$$
$$60$$ 0 0
$$61$$ −0.124364 0.288308i −0.0159232 0.0369141i 0.910069 0.414457i $$-0.136028\pi$$
−0.925992 + 0.377543i $$0.876769\pi$$
$$62$$ −0.0672822 0.0244887i −0.00854485 0.00311007i
$$63$$ 0 0
$$64$$ −5.56048 + 2.02385i −0.695060 + 0.252981i
$$65$$ −1.08729 1.15246i −0.134861 0.142945i
$$66$$ 0 0
$$67$$ 4.90826 2.46502i 0.599639 0.301150i −0.122966 0.992411i $$-0.539241\pi$$
0.722605 + 0.691261i $$0.242944\pi$$
$$68$$ 0.0337102 0.578782i 0.00408797 0.0701877i
$$69$$ 0 0
$$70$$ 0.899246 3.00369i 0.107480 0.359010i
$$71$$ 2.03991 11.5689i 0.242093 1.37298i −0.585054 0.810994i $$-0.698927\pi$$
0.827147 0.561985i $$-0.189962\pi$$
$$72$$ 0 0
$$73$$ 2.70207 + 15.3242i 0.316253 + 1.79356i 0.565106 + 0.825019i $$0.308835\pi$$
−0.248853 + 0.968541i $$0.580053\pi$$
$$74$$ −4.68464 0.547556i −0.544579 0.0636521i
$$75$$ 0 0
$$76$$ 1.77672 1.88321i 0.203804 0.216019i
$$77$$ 6.04817 14.0212i 0.689253 1.59787i
$$78$$ 0 0
$$79$$ 11.6941 7.69136i 1.31569 0.865346i 0.319093 0.947723i $$-0.396622\pi$$
0.996601 + 0.0823774i $$0.0262513\pi$$
$$80$$ −2.35277 −0.263048
$$81$$ 0 0
$$82$$ −9.17740 −1.01347
$$83$$ 0.587346 0.386304i 0.0644696 0.0424023i −0.516865 0.856067i $$-0.672901\pi$$
0.581335 + 0.813665i $$0.302531\pi$$
$$84$$ 0 0
$$85$$ −0.302737 + 0.701823i −0.0328364 + 0.0761234i
$$86$$ 0.252487 0.267620i 0.0272263 0.0288582i
$$87$$ 0 0
$$88$$ −9.48034 1.10809i −1.01061 0.118123i
$$89$$ −2.00921 11.3948i −0.212976 1.20785i −0.884384 0.466760i $$-0.845421\pi$$
0.671408 0.741088i $$-0.265690\pi$$
$$90$$ 0 0
$$91$$ 2.15620 12.2284i 0.226032 1.28189i
$$92$$ −0.131358 + 0.438765i −0.0136950 + 0.0457444i
$$93$$ 0 0
$$94$$ 0.425507 7.30568i 0.0438877 0.753523i
$$95$$ −3.05023 + 1.53188i −0.312947 + 0.157168i
$$96$$ 0 0
$$97$$ 8.92799 + 9.46312i 0.906500 + 0.960834i 0.999393 0.0348418i $$-0.0110927\pi$$
−0.0928924 + 0.995676i $$0.529611\pi$$
$$98$$ 12.9298 4.70606i 1.30611 0.475384i
$$99$$ 0 0
$$100$$ 1.71979 + 0.625952i 0.171979 + 0.0625952i
$$101$$ 4.89713 + 11.3528i 0.487283 + 1.12965i 0.967585 + 0.252545i $$0.0812677\pi$$
−0.480302 + 0.877103i $$0.659473\pi$$
$$102$$ 0 0
$$103$$ 0.599460 + 2.00234i 0.0590666 + 0.197296i 0.982430 0.186631i $$-0.0597567\pi$$
−0.923364 + 0.383927i $$0.874572\pi$$
$$104$$ −7.70907 + 0.901062i −0.755937 + 0.0883564i
$$105$$ 0 0
$$106$$ 1.22359 + 21.0082i 0.118846 + 2.04050i
$$107$$ −0.831363 1.43996i −0.0803709 0.139207i 0.823038 0.567986i $$-0.192277\pi$$
−0.903409 + 0.428779i $$0.858944\pi$$
$$108$$ 0 0
$$109$$ −2.14981 + 3.72357i −0.205914 + 0.356654i −0.950424 0.310958i $$-0.899350\pi$$
0.744510 + 0.667612i $$0.232683\pi$$
$$110$$ −2.68959 1.35076i −0.256442 0.128790i
$$111$$ 0 0
$$112$$ −11.0109 14.7902i −1.04043 1.39754i
$$113$$ 13.8508 + 3.28270i 1.30297 + 0.308810i 0.822784 0.568354i $$-0.192420\pi$$
0.480189 + 0.877165i $$0.340568\pi$$
$$114$$ 0 0
$$115$$ 0.360573 0.484334i 0.0336236 0.0451644i
$$116$$ −2.04501 + 1.71596i −0.189874 + 0.159323i
$$117$$ 0 0
$$118$$ −1.65281 1.38687i −0.152154 0.127672i
$$119$$ −5.82865 + 1.38142i −0.534312 + 0.126634i
$$120$$ 0 0
$$121$$ −3.05618 2.01008i −0.277834 0.182735i
$$122$$ −0.405219 0.266517i −0.0366868 0.0241293i
$$123$$ 0 0
$$124$$ −0.0174112 + 0.00412654i −0.00156357 + 0.000370574i
$$125$$ −3.79760 3.18657i −0.339668 0.285015i
$$126$$ 0 0
$$127$$ 14.1754 11.8946i 1.25787 1.05548i 0.261961 0.965078i $$-0.415631\pi$$
0.995906 0.0903976i $$-0.0288138\pi$$
$$128$$ −8.03198 + 10.7888i −0.709933 + 0.953606i
$$129$$ 0 0
$$130$$ −2.38143 0.564410i −0.208865 0.0495020i
$$131$$ 3.31614 + 4.45435i 0.289732 + 0.389178i 0.923029 0.384731i $$-0.125706\pi$$
−0.633296 + 0.773909i $$0.718299\pi$$
$$132$$ 0 0
$$133$$ −23.9048 12.0054i −2.07281 1.04100i
$$134$$ 4.24205 7.34745i 0.366458 0.634723i
$$135$$ 0 0
$$136$$ 1.87212 + 3.24261i 0.160533 + 0.278052i
$$137$$ 0.173481 + 2.97856i 0.0148215 + 0.254475i 0.997577 + 0.0695670i $$0.0221618\pi$$
−0.982756 + 0.184908i $$0.940801\pi$$
$$138$$ 0 0
$$139$$ 5.85385 0.684217i 0.496517 0.0580345i 0.135851 0.990729i $$-0.456623\pi$$
0.360667 + 0.932695i $$0.382549\pi$$
$$140$$ −0.224730 0.750649i −0.0189931 0.0634415i
$$141$$ 0 0
$$142$$ −7.18724 16.6619i −0.603140 1.39824i
$$143$$ −11.2005 4.07665i −0.936633 0.340907i
$$144$$ 0 0
$$145$$ 3.30719 1.20372i 0.274647 0.0999633i
$$146$$ 16.4946 + 17.4832i 1.36510 + 1.44692i
$$147$$ 0 0
$$148$$ −1.05333 + 0.529002i −0.0865831 + 0.0434837i
$$149$$ 0.316650 5.43668i 0.0259410 0.445390i −0.960182 0.279375i $$-0.909873\pi$$
0.986123 0.166015i $$-0.0530901\pi$$
$$150$$ 0 0
$$151$$ 4.27673 14.2853i 0.348035 1.16252i −0.587482 0.809237i $$-0.699881\pi$$
0.935517 0.353281i $$-0.114934\pi$$
$$152$$ −2.90352 + 16.4667i −0.235507 + 1.33563i
$$153$$ 0 0
$$154$$ −4.09590 23.2290i −0.330057 1.87185i
$$155$$ 0.0234305 + 0.00273864i 0.00188199 + 0.000219973i
$$156$$ 0 0
$$157$$ −5.75380 + 6.09867i −0.459203 + 0.486727i −0.915055 0.403329i $$-0.867853\pi$$
0.455852 + 0.890056i $$0.349335\pi$$
$$158$$ 8.56345 19.8523i 0.681272 1.57937i
$$159$$ 0 0
$$160$$ −0.916293 + 0.602656i −0.0724394 + 0.0476441i
$$161$$ 4.73212 0.372944
$$162$$ 0 0
$$163$$ 3.04537 0.238531 0.119266 0.992862i $$-0.461946\pi$$
0.119266 + 0.992862i $$0.461946\pi$$
$$164$$ −1.91620 + 1.26031i −0.149630 + 0.0984134i
$$165$$ 0 0
$$166$$ 0.430105 0.997096i 0.0333826 0.0773896i
$$167$$ −14.4823 + 15.3503i −1.12067 + 1.18785i −0.140422 + 0.990092i $$0.544846\pi$$
−0.980252 + 0.197753i $$0.936635\pi$$
$$168$$ 0 0
$$169$$ 3.28526 + 0.383992i 0.252712 + 0.0295378i
$$170$$ 0.205018 + 1.16271i 0.0157241 + 0.0891760i
$$171$$ 0 0
$$172$$ 0.0159666 0.0905513i 0.00121744 0.00690447i
$$173$$ 0.486058 1.62355i 0.0369543 0.123436i −0.937522 0.347925i $$-0.886886\pi$$
0.974477 + 0.224489i $$0.0720714\pi$$
$$174$$ 0 0
$$175$$ 1.09947 18.8773i 0.0831125 1.42699i
$$176$$ −15.8170 + 7.94358i −1.19225 + 0.598770i
$$177$$ 0 0
$$178$$ −12.2651 13.0002i −0.919307 0.974409i
$$179$$ −11.3362 + 4.12604i −0.847308 + 0.308395i −0.728942 0.684575i $$-0.759988\pi$$
−0.118366 + 0.992970i $$0.537765\pi$$
$$180$$ 0 0
$$181$$ −7.09567 2.58261i −0.527417 0.191964i 0.0645678 0.997913i $$-0.479433\pi$$
−0.591985 + 0.805949i $$0.701655\pi$$
$$182$$ −7.59697 17.6117i −0.563125 1.30547i
$$183$$ 0 0
$$184$$ −0.848339 2.83365i −0.0625404 0.208899i
$$185$$ 1.54344 0.180403i 0.113476 0.0132635i
$$186$$ 0 0
$$187$$ 0.334333 + 5.74027i 0.0244488 + 0.419770i
$$188$$ −0.914425 1.58383i −0.0666913 0.115513i
$$189$$ 0 0
$$190$$ −2.63622 + 4.56607i −0.191251 + 0.331257i
$$191$$ 11.5732 + 5.81226i 0.837404 + 0.420560i 0.815190 0.579193i $$-0.196632\pi$$
0.0222137 + 0.999753i $$0.492929\pi$$
$$192$$ 0 0
$$193$$ 10.7961 + 14.5016i 0.777118 + 1.04385i 0.997653 + 0.0684715i $$0.0218122\pi$$
−0.220535 + 0.975379i $$0.570780\pi$$
$$194$$ 19.5545 + 4.63451i 1.40393 + 0.332738i
$$195$$ 0 0
$$196$$ 2.05342 2.75822i 0.146673 0.197016i
$$197$$ −7.47510 + 6.27235i −0.532579 + 0.446886i −0.868991 0.494828i $$-0.835231\pi$$
0.336412 + 0.941715i $$0.390786\pi$$
$$198$$ 0 0
$$199$$ −6.35460 5.33214i −0.450465 0.377985i 0.389143 0.921177i $$-0.372771\pi$$
−0.839609 + 0.543192i $$0.817216\pi$$
$$200$$ −11.5010 + 2.72579i −0.813245 + 0.192743i
$$201$$ 0 0
$$202$$ 15.9565 + 10.4947i 1.12269 + 0.738407i
$$203$$ 23.0444 + 15.1565i 1.61740 + 1.06378i
$$204$$ 0 0
$$205$$ 2.94216 0.697305i 0.205490 0.0487019i
$$206$$ 2.47325 + 2.07530i 0.172320 + 0.144593i
$$207$$ 0 0
$$208$$ −11.0255 + 9.25146i −0.764478 + 0.641473i
$$209$$ −15.3337 + 20.5968i −1.06066 + 1.42471i
$$210$$ 0 0
$$211$$ −11.0335 2.61499i −0.759577 0.180023i −0.167464 0.985878i $$-0.553558\pi$$
−0.592113 + 0.805855i $$0.701706\pi$$
$$212$$ 3.14049 + 4.21840i 0.215689 + 0.289721i
$$213$$ 0 0
$$214$$ −2.29519 1.15269i −0.156896 0.0787960i
$$215$$ −0.0606102 + 0.104980i −0.00413358 + 0.00715957i
$$216$$ 0 0
$$217$$ 0.0924381 + 0.160108i 0.00627511 + 0.0108688i
$$218$$ 0.386170 + 6.63028i 0.0261547 + 0.449059i
$$219$$ 0 0
$$220$$ −0.747071 + 0.0873201i −0.0503676 + 0.00588712i
$$221$$ 1.34100 + 4.47926i 0.0902057 + 0.301308i
$$222$$ 0 0
$$223$$ 7.49598 + 17.3776i 0.501968 + 1.16369i 0.961319 + 0.275438i $$0.0888227\pi$$
−0.459351 + 0.888255i $$0.651918\pi$$
$$224$$ −8.07667 2.93967i −0.539646 0.196415i
$$225$$ 0 0
$$226$$ 20.6617 7.52023i 1.37439 0.500239i
$$227$$ −7.61638 8.07290i −0.505517 0.535817i 0.423479 0.905906i $$-0.360809\pi$$
−0.928996 + 0.370089i $$0.879327\pi$$
$$228$$ 0 0
$$229$$ 2.72124 1.36666i 0.179825 0.0903113i −0.356609 0.934254i $$-0.616067\pi$$
0.536434 + 0.843942i $$0.319771\pi$$
$$230$$ 0.0542316 0.931121i 0.00357593 0.0613963i
$$231$$ 0 0
$$232$$ 4.94468 16.5164i 0.324634 1.08435i
$$233$$ 2.47370 14.0290i 0.162057 0.919073i −0.789989 0.613121i $$-0.789914\pi$$
0.952047 0.305953i $$-0.0989750\pi$$
$$234$$ 0 0
$$235$$ 0.418679 + 2.37444i 0.0273116 + 0.154892i
$$236$$ −0.535556 0.0625975i −0.0348617 0.00407475i
$$237$$ 0 0
$$238$$ −6.34966 + 6.73024i −0.411587 + 0.436257i
$$239$$ 3.14737 7.29642i 0.203586 0.471966i −0.785581 0.618759i $$-0.787636\pi$$
0.989167 + 0.146793i $$0.0468950\pi$$
$$240$$ 0 0
$$241$$ −3.02761 + 1.99129i −0.195026 + 0.128270i −0.643266 0.765643i $$-0.722421\pi$$
0.448241 + 0.893913i $$0.352051\pi$$
$$242$$ −5.65036 −0.363219
$$243$$ 0 0
$$244$$ −0.121208 −0.00775955
$$245$$ −3.78757 + 2.49112i −0.241979 + 0.159152i
$$246$$ 0 0
$$247$$ −8.27026 + 19.1726i −0.526224 + 1.21993i
$$248$$ 0.0793026 0.0840558i 0.00503572 0.00533755i
$$249$$ 0 0
$$250$$ −7.60584 0.888995i −0.481035 0.0562250i
$$251$$ 0.441351 + 2.50303i 0.0278578 + 0.157990i 0.995563 0.0940939i $$-0.0299954\pi$$
−0.967706 + 0.252083i $$0.918884\pi$$
$$252$$ 0 0
$$253$$ 0.788785 4.47342i 0.0495905 0.281242i
$$254$$ 8.19794 27.3830i 0.514384 1.71816i
$$255$$ 0 0
$$256$$ −0.519916 + 8.92662i −0.0324948 + 0.557914i
$$257$$ 25.0214 12.5662i 1.56079 0.783860i 0.561739 0.827314i $$-0.310133\pi$$
0.999055 + 0.0434541i $$0.0138362\pi$$
$$258$$ 0 0
$$259$$ 8.35731 + 8.85823i 0.519298 + 0.550424i
$$260$$ −0.574742 + 0.209189i −0.0356440 + 0.0129733i
$$261$$ 0 0
$$262$$ 8.06059 + 2.93381i 0.497985 + 0.181252i
$$263$$ 0.974610 + 2.25940i 0.0600970 + 0.139321i 0.945618 0.325278i $$-0.105458\pi$$
−0.885521 + 0.464599i $$0.846199\pi$$
$$264$$ 0 0
$$265$$ −1.98849 6.64202i −0.122152 0.408016i
$$266$$ −41.0410 + 4.79700i −2.51638 + 0.294123i
$$267$$ 0 0
$$268$$ −0.123282 2.11667i −0.00753064 0.129296i
$$269$$ 5.65271 + 9.79078i 0.344652 + 0.596954i 0.985290 0.170888i $$-0.0546637\pi$$
−0.640639 + 0.767842i $$0.721330\pi$$
$$270$$ 0 0
$$271$$ 2.14084 3.70804i 0.130047 0.225248i −0.793648 0.608378i $$-0.791821\pi$$
0.923694 + 0.383130i $$0.125154\pi$$
$$272$$ 6.20465 + 3.11609i 0.376212 + 0.188941i
$$273$$ 0 0
$$274$$ 2.75213 + 3.69675i 0.166262 + 0.223329i
$$275$$ −17.6620 4.18597i −1.06506 0.252423i
$$276$$ 0 0
$$277$$ 11.2400 15.0980i 0.675349 0.907151i −0.323893 0.946094i $$-0.604992\pi$$
0.999241 + 0.0389429i $$0.0123990\pi$$
$$278$$ 6.97397 5.85185i 0.418271 0.350971i
$$279$$ 0 0
$$280$$ 3.87654 + 3.25280i 0.231668 + 0.194392i
$$281$$ 13.2369 3.13720i 0.789647 0.187150i 0.184046 0.982918i $$-0.441081\pi$$
0.605602 + 0.795768i $$0.292932\pi$$
$$282$$ 0 0
$$283$$ −13.9445 9.17147i −0.828917 0.545187i 0.0626713 0.998034i $$-0.480038\pi$$
−0.891588 + 0.452847i $$0.850408\pi$$
$$284$$ −3.78880 2.49193i −0.224824 0.147869i
$$285$$ 0 0
$$286$$ −17.9152 + 4.24599i −1.05935 + 0.251071i
$$287$$ 18.1527 + 15.2319i 1.07152 + 0.899110i
$$288$$ 0 0
$$289$$ −11.2949 + 9.47752i −0.664404 + 0.557501i
$$290$$ 3.24639 4.36066i 0.190634 0.256067i
$$291$$ 0 0
$$292$$ 5.84492 + 1.38527i 0.342048 + 0.0810669i
$$293$$ 15.1735 + 20.3815i 0.886444 + 1.19070i 0.980771 + 0.195160i $$0.0625225\pi$$
−0.0943276 + 0.995541i $$0.530070\pi$$
$$294$$ 0 0
$$295$$ 0.635248 + 0.319033i 0.0369855 + 0.0185748i
$$296$$ 3.80617 6.59249i 0.221229 0.383181i
$$297$$ 0 0
$$298$$ −4.20607 7.28513i −0.243651 0.422016i
$$299$$ −0.214772 3.68749i −0.0124206 0.213253i
$$300$$ 0 0
$$301$$ −0.943585 + 0.110289i −0.0543874 + 0.00635697i
$$302$$ −6.60616 22.0661i −0.380142 1.26976i
$$303$$ 0 0
$$304$$ 12.2809 + 28.4704i 0.704361 + 1.63289i
$$305$$ 0.150158 + 0.0546532i 0.00859805 + 0.00312943i
$$306$$ 0 0
$$307$$ −9.43080 + 3.43253i −0.538244 + 0.195905i −0.596816 0.802378i $$-0.703568\pi$$
0.0585714 + 0.998283i $$0.481345\pi$$
$$308$$ −4.04518 4.28764i −0.230496 0.244311i
$$309$$ 0 0
$$310$$ 0.0325631 0.0163538i 0.00184946 0.000928834i
$$311$$ 1.56707 26.9055i 0.0888602 1.52567i −0.599543 0.800342i $$-0.704651\pi$$
0.688403 0.725328i $$-0.258312\pi$$
$$312$$ 0 0
$$313$$ −3.73743 + 12.4839i −0.211252 + 0.705631i 0.785028 + 0.619460i $$0.212648\pi$$
−0.996280 + 0.0861711i $$0.972537\pi$$
$$314$$ −2.24898 + 12.7546i −0.126917 + 0.719784i
$$315$$ 0 0
$$316$$ −0.938250 5.32108i −0.0527807 0.299334i
$$317$$ 9.42954 + 1.10216i 0.529616 + 0.0619032i 0.376699 0.926336i $$-0.377059\pi$$
0.152917 + 0.988239i $$0.451133\pi$$
$$318$$ 0 0
$$319$$ 18.1691 19.2582i 1.01728 1.07825i
$$320$$ 1.19278 2.76518i 0.0666785 0.154578i
$$321$$ 0 0
$$322$$ 6.10709 4.01669i 0.340335 0.223842i
$$323$$ 10.0729 0.560468
$$324$$ 0 0
$$325$$ −14.7599 −0.818735
$$326$$ 3.93023 2.58495i 0.217675 0.143167i
$$327$$ 0 0
$$328$$ 5.86675 13.6007i 0.323937 0.750971i
$$329$$ −12.9670 + 13.7442i −0.714894 + 0.757744i
$$330$$ 0 0
$$331$$ 23.3551 + 2.72982i 1.28371 + 0.150045i 0.730452 0.682964i $$-0.239309\pi$$
0.553261 + 0.833008i $$0.313383\pi$$
$$332$$ −0.0471242 0.267255i −0.00258628 0.0146675i
$$333$$ 0 0
$$334$$ −5.66068 + 32.1033i −0.309739 + 1.75661i
$$335$$ −0.801686 + 2.67782i −0.0438008 + 0.146305i
$$336$$ 0 0
$$337$$ 0.180721 3.10287i 0.00984453 0.169024i −0.989802 0.142448i $$-0.954503\pi$$
0.999647 0.0265759i $$-0.00846036\pi$$
$$338$$ 4.56576 2.29301i 0.248344 0.124723i
$$339$$ 0 0
$$340$$ 0.202479 + 0.214615i 0.0109810 + 0.0116391i
$$341$$ 0.166763 0.0606967i 0.00903071 0.00328691i
$$342$$ 0 0
$$343$$ −7.15012 2.60243i −0.386070 0.140518i
$$344$$ 0.235201 + 0.545258i 0.0126812 + 0.0293983i
$$345$$ 0 0
$$346$$ −0.750803 2.50786i −0.0403634 0.134823i
$$347$$ −22.1439 + 2.58826i −1.18875 + 0.138945i −0.687386 0.726292i $$-0.741242\pi$$
−0.501363 + 0.865237i $$0.667168\pi$$
$$348$$ 0 0
$$349$$ −0.175177 3.00767i −0.00937701 0.160997i −0.999746 0.0225430i $$-0.992824\pi$$
0.990369 0.138454i $$-0.0442133\pi$$
$$350$$ −14.6043 25.2955i −0.780635 1.35210i
$$351$$ 0 0
$$352$$ −4.12524 + 7.14512i −0.219876 + 0.380836i
$$353$$ −1.93406 0.971320i −0.102939 0.0516981i 0.396584 0.917998i $$-0.370195\pi$$
−0.499524 + 0.866300i $$0.666492\pi$$
$$354$$ 0 0
$$355$$ 3.57013 + 4.79551i 0.189483 + 0.254519i
$$356$$ −4.34619 1.03007i −0.230348 0.0545934i
$$357$$ 0 0
$$358$$ −11.1278 + 14.9472i −0.588123 + 0.789986i
$$359$$ 0.496794 0.416860i 0.0262198 0.0220010i −0.629584 0.776933i $$-0.716774\pi$$
0.655803 + 0.754932i $$0.272330\pi$$
$$360$$ 0 0
$$361$$ 19.9037 + 16.7012i 1.04756 + 0.879011i
$$362$$ −11.3495 + 2.68989i −0.596518 + 0.141377i
$$363$$ 0 0
$$364$$ −4.00479 2.63399i −0.209908 0.138059i
$$365$$ −6.61635 4.35164i −0.346315 0.227775i
$$366$$ 0 0
$$367$$ −9.21403 + 2.18376i −0.480968 + 0.113992i −0.463946 0.885864i $$-0.653567\pi$$
−0.0170223 + 0.999855i $$0.505419\pi$$
$$368$$ −4.20178 3.52571i −0.219033 0.183790i
$$369$$ 0 0
$$370$$ 1.83878 1.54292i 0.0955935 0.0802124i
$$371$$ 32.4475 43.5846i 1.68459 2.26280i
$$372$$ 0 0
$$373$$ −4.75011 1.12580i −0.245951 0.0582915i 0.105791 0.994388i $$-0.466263\pi$$
−0.351742 + 0.936097i $$0.614411\pi$$
$$374$$ 5.30390 + 7.12437i 0.274258 + 0.368392i
$$375$$ 0 0
$$376$$ 10.5548 + 5.30083i 0.544323 + 0.273369i
$$377$$ 10.7648 18.6452i 0.554415 0.960275i
$$378$$ 0 0
$$379$$ 13.0190 + 22.5495i 0.668739 + 1.15829i 0.978257 + 0.207396i $$0.0664989\pi$$
−0.309518 + 0.950894i $$0.600168\pi$$
$$380$$ 0.0766134 + 1.31540i 0.00393018 + 0.0674787i
$$381$$ 0 0
$$382$$ 19.8694 2.32240i 1.01661 0.118824i
$$383$$ −2.30331 7.69359i −0.117694 0.393124i 0.878760 0.477263i $$-0.158371\pi$$
−0.996454 + 0.0841390i $$0.973186\pi$$
$$384$$ 0 0
$$385$$ 3.07805 + 7.13573i 0.156872 + 0.363670i
$$386$$ 26.2422 + 9.55136i 1.33569 + 0.486152i
$$387$$ 0 0
$$388$$ 4.71935 1.71770i 0.239589 0.0872032i
$$389$$ −15.6093 16.5449i −0.791422 0.838858i 0.198555 0.980090i $$-0.436375\pi$$
−0.989977 + 0.141231i $$0.954894\pi$$
$$390$$ 0 0
$$391$$ −1.59236 + 0.799714i −0.0805291 + 0.0404433i
$$392$$ −1.29126 + 22.1700i −0.0652184 + 1.11976i
$$393$$ 0 0
$$394$$ −4.32300 + 14.4398i −0.217789 + 0.727467i
$$395$$ −1.23695 + 7.01507i −0.0622375 + 0.352967i
$$396$$ 0 0
$$397$$ 4.29294 + 24.3465i 0.215456 + 1.22191i 0.880113 + 0.474765i $$0.157467\pi$$
−0.664656 + 0.747149i $$0.731422\pi$$
$$398$$ −12.7270 1.48757i −0.637946 0.0745652i
$$399$$ 0 0
$$400$$ −15.0409 + 15.9424i −0.752046 + 0.797122i
$$401$$ 6.72403 15.5880i 0.335782 0.778430i −0.663754 0.747951i $$-0.731038\pi$$
0.999535 0.0304785i $$-0.00970310\pi$$
$$402$$ 0 0
$$403$$ 0.120568 0.0792988i 0.00600592 0.00395015i
$$404$$ 4.77286 0.237459
$$405$$ 0 0
$$406$$ 42.6052 2.11446
$$407$$ 9.76702 6.42387i 0.484133 0.318419i
$$408$$ 0 0
$$409$$ 4.47516 10.3746i 0.221282 0.512990i −0.771023 0.636808i $$-0.780255\pi$$
0.992305 + 0.123818i $$0.0395138\pi$$
$$410$$ 3.20515 3.39726i 0.158291 0.167779i
$$411$$ 0 0
$$412$$ 0.801401 + 0.0936703i 0.0394822 + 0.00461481i
$$413$$ 0.967401 + 5.48640i 0.0476027 + 0.269968i
$$414$$ 0 0
$$415$$ −0.0621265 + 0.352337i −0.00304967 + 0.0172955i
$$416$$ −1.92416 + 6.42715i −0.0943398 + 0.315117i
$$417$$ 0 0
$$418$$ −2.30625 + 39.5969i −0.112803 + 1.93675i
$$419$$ −28.9814 + 14.5550i −1.41584 + 0.711059i −0.981814 0.189843i $$-0.939202\pi$$
−0.434021 + 0.900903i $$0.642906\pi$$
$$420$$ 0 0
$$421$$ 0.455943 + 0.483271i 0.0222213 + 0.0235532i 0.738389 0.674375i $$-0.235587\pi$$
−0.716168 + 0.697928i $$0.754105\pi$$
$$422$$ −16.4590 + 5.99059i −0.801212 + 0.291617i
$$423$$ 0 0
$$424$$ −31.9159 11.6164i −1.54997 0.564144i
$$425$$ 2.82022 + 6.53801i 0.136801 + 0.317140i
$$426$$ 0 0
$$427$$ 0.359170 + 1.19971i 0.0173815 + 0.0580581i
$$428$$ −0.637521 + 0.0745155i −0.0308157 + 0.00360184i
$$429$$ 0 0
$$430$$ 0.0108874 + 0.186930i 0.000525037 + 0.00901454i
$$431$$ 15.1861 + 26.3031i 0.731488 + 1.26698i 0.956247 + 0.292561i $$0.0945073\pi$$
−0.224759 + 0.974414i $$0.572159\pi$$
$$432$$ 0 0
$$433$$ 5.68299 9.84323i 0.273107 0.473035i −0.696549 0.717510i $$-0.745282\pi$$
0.969656 + 0.244474i $$0.0786153\pi$$
$$434$$ 0.255198 + 0.128165i 0.0122499 + 0.00615214i
$$435$$ 0 0
$$436$$ 0.991149 + 1.33134i 0.0474674 + 0.0637598i
$$437$$ −7.74294 1.83511i −0.370395 0.0877853i
$$438$$ 0 0
$$439$$ −4.28247 + 5.75236i −0.204391 + 0.274545i −0.892485 0.451076i $$-0.851040\pi$$
0.688094 + 0.725621i $$0.258448\pi$$
$$440$$ 3.72114 3.12241i 0.177399 0.148855i
$$441$$ 0 0
$$442$$ 5.53271 + 4.64249i 0.263164 + 0.220821i
$$443$$ 1.69953 0.402796i 0.0807471 0.0191374i −0.190044 0.981776i $$-0.560863\pi$$
0.270791 + 0.962638i $$0.412715\pi$$
$$444$$ 0 0
$$445$$ 4.91981 + 3.23581i 0.233221 + 0.153392i
$$446$$ 24.4244 + 16.0642i 1.15653 + 0.760661i
$$447$$ 0 0
$$448$$ 22.9649 5.44277i 1.08499 0.257147i
$$449$$ −25.6694 21.5392i −1.21142 1.01650i −0.999229 0.0392691i $$-0.987497\pi$$
−0.212187 0.977229i $$-0.568059\pi$$
$$450$$ 0 0
$$451$$ 17.4250 14.6213i 0.820510 0.688490i
$$452$$ 3.28134 4.40761i 0.154341 0.207316i
$$453$$ 0 0
$$454$$ −16.6818 3.95366i −0.782915 0.185554i
$$455$$ 3.77365 + 5.06889i 0.176911 + 0.237633i
$$456$$ 0 0
$$457$$ 10.2116 + 5.12846i 0.477679 + 0.239899i 0.671312 0.741175i $$-0.265731\pi$$
−0.193634 + 0.981074i $$0.562027\pi$$
$$458$$ 2.35188 4.07358i 0.109896 0.190346i
$$459$$ 0 0
$$460$$ −0.116545 0.201862i −0.00543394 0.00941186i
$$461$$ 0.967981 + 16.6196i 0.0450834 + 0.774051i 0.942776 + 0.333428i $$0.108205\pi$$
−0.897692 + 0.440623i $$0.854758\pi$$
$$462$$ 0 0
$$463$$ 4.54546 0.531288i 0.211245 0.0246910i −0.00981201 0.999952i $$-0.503123\pi$$
0.221057 + 0.975261i $$0.429049\pi$$
$$464$$ −9.16922 30.6273i −0.425670 1.42184i
$$465$$ 0 0
$$466$$ −8.71560 20.2050i −0.403742 0.935980i
$$467$$ 31.8531 + 11.5936i 1.47398 + 0.536486i 0.949179 0.314736i $$-0.101916\pi$$
0.524805 + 0.851222i $$0.324138\pi$$
$$468$$ 0 0
$$469$$ −20.5854 + 7.49246i −0.950544 + 0.345970i
$$470$$ 2.55579 + 2.70898i 0.117890 + 0.124956i
$$471$$ 0 0
$$472$$ 3.11189 1.56285i 0.143236 0.0719360i
$$473$$ −0.0530238 + 0.910384i −0.00243804 + 0.0418595i
$$474$$ 0 0
$$475$$ −9.11959 + 30.4616i −0.418436 + 1.39767i
$$476$$ −0.401537 + 2.27723i −0.0184044 + 0.104377i
$$477$$ 0 0
$$478$$ −2.13144 12.0880i −0.0974898 0.552892i
$$479$$ 8.62453 + 1.00806i 0.394065 + 0.0460596i 0.310818 0.950469i $$-0.399397\pi$$
0.0832467 + 0.996529i $$0.473471\pi$$
$$480$$ 0 0
$$481$$ 6.52345 6.91445i 0.297444 0.315272i
$$482$$ −2.21708 + 5.13976i −0.100985 + 0.234110i
$$483$$ 0 0
$$484$$ −1.17977 + 0.775949i −0.0536261 + 0.0352704i
$$485$$ −6.62108 −0.300648
$$486$$ 0 0
$$487$$ −21.3432 −0.967154 −0.483577 0.875302i $$-0.660663\pi$$
−0.483577 + 0.875302i $$0.660663\pi$$
$$488$$ 0.654012 0.430150i 0.0296057 0.0194720i
$$489$$ 0 0
$$490$$ −2.77358 + 6.42989i −0.125298 + 0.290473i
$$491$$ 2.89262 3.06600i 0.130542 0.138366i −0.658805 0.752314i $$-0.728938\pi$$
0.789347 + 0.613947i $$0.210419\pi$$
$$492$$ 0 0
$$493$$ −10.3158 1.20575i −0.464602 0.0543042i
$$494$$ 5.60073 + 31.7633i 0.251989 + 1.42910i
$$495$$ 0 0
$$496$$ 0.0372113 0.211036i 0.00167084 0.00947578i
$$497$$ −13.4379 + 44.8856i −0.602770 + 2.01339i
$$498$$ 0 0
$$499$$ −1.76905 + 30.3734i −0.0791936 + 1.35970i 0.691445 + 0.722429i $$0.256975\pi$$
−0.770638 + 0.637273i $$0.780062\pi$$
$$500$$ −1.71015 + 0.858870i −0.0764803 + 0.0384098i
$$501$$ 0 0
$$502$$ 2.69419 + 2.85568i 0.120248 + 0.127455i
$$503$$ 11.9111 4.33528i 0.531089 0.193301i −0.0625356 0.998043i $$-0.519919\pi$$
0.593624 + 0.804742i $$0.297696\pi$$
$$504$$ 0 0
$$505$$ −5.91285 2.15210i −0.263118 0.0957673i
$$506$$ −2.77913 6.44275i −0.123547 0.286415i
$$507$$ 0 0
$$508$$ −2.04874 6.84326i −0.0908981 0.303621i
$$509$$ −3.48848 + 0.407744i −0.154624 + 0.0180730i −0.193053 0.981188i $$-0.561839\pi$$
0.0384287 + 0.999261i $$0.487765\pi$$
$$510$$ 0 0
$$511$$ −3.60862 61.9577i −0.159636 2.74085i
$$512$$ −6.54427 11.3350i −0.289219 0.500941i
$$513$$ 0 0
$$514$$ 21.6252 37.4560i 0.953849 1.65211i
$$515$$ −0.950578 0.477398i −0.0418875 0.0210367i
$$516$$ 0 0
$$517$$ 10.8314 + 14.5491i 0.476364 + 0.639869i
$$518$$ 18.3046 + 4.33827i 0.804258 + 0.190613i
$$519$$ 0 0
$$520$$ 2.35880 3.16841i 0.103440 0.138944i
$$521$$ −6.50992 + 5.46247i −0.285205 + 0.239315i −0.774154 0.632997i $$-0.781825\pi$$
0.488950 + 0.872312i $$0.337380\pi$$
$$522$$ 0 0
$$523$$ −9.72249 8.15814i −0.425135 0.356730i 0.404978 0.914327i $$-0.367279\pi$$
−0.830112 + 0.557596i $$0.811724\pi$$
$$524$$ 2.08591 0.494370i 0.0911234 0.0215966i
$$525$$ 0 0
$$526$$ 3.17560 + 2.08863i 0.138463 + 0.0910685i
$$527$$ −0.0581631 0.0382545i −0.00253362 0.00166639i
$$528$$ 0 0
$$529$$ −21.0103 + 4.97953i −0.913491 + 0.216501i
$$530$$ −8.20411 6.88406i −0.356364 0.299025i
$$531$$ 0 0
$$532$$ −7.91043 + 6.63763i −0.342960 + 0.287778i
$$533$$ 11.0455 14.8367i 0.478435 0.642650i
$$534$$ 0 0
$$535$$ 0.823391 + 0.195147i 0.0355983 + 0.00843695i
$$536$$ 8.17695 + 10.9836i 0.353191 + 0.474417i
$$537$$ 0 0
$$538$$ 15.6057 + 7.83748i 0.672810 + 0.337898i
$$539$$ −17.0520 + 29.5349i −0.734481 + 1.27216i
$$540$$ 0 0
$$541$$ −6.14520 10.6438i −0.264203 0.457612i 0.703152 0.711040i $$-0.251775\pi$$
−0.967354 + 0.253427i $$0.918442\pi$$
$$542$$ −0.384559 6.60262i −0.0165182 0.283607i
$$543$$ 0 0
$$544$$ 3.21460 0.375733i 0.137825 0.0161094i
$$545$$ −0.627575 2.09625i −0.0268824 0.0897933i
$$546$$ 0 0
$$547$$ −10.6521 24.6944i −0.455452 1.05586i −0.979000 0.203861i $$-0.934651\pi$$
0.523548 0.851996i $$-0.324608\pi$$
$$548$$ 1.08230 + 0.393924i 0.0462335 + 0.0168276i
$$549$$ 0 0
$$550$$ −26.3469 + 9.58950i −1.12344 + 0.408898i
$$551$$ −31.8287 33.7365i −1.35595 1.43722i
$$552$$ 0 0
$$553$$ −49.8875 + 25.0545i −2.12143 + 1.06542i
$$554$$ 1.69055 29.0256i 0.0718245 1.23318i
$$555$$ 0 0
$$556$$ 0.652517 2.17956i 0.0276729 0.0924339i
$$557$$ −3.81879 + 21.6574i −0.161807 + 0.917654i 0.790488 + 0.612477i $$0.209827\pi$$
−0.952296 + 0.305177i $$0.901284\pi$$
$$558$$ 0 0
$$559$$ 0.128768 + 0.730281i 0.00544631 + 0.0308876i
$$560$$ 9.32047 + 1.08941i 0.393862 + 0.0460358i
$$561$$ 0 0
$$562$$ 14.4201 15.2844i 0.608275 0.644734i
$$563$$ −18.7536 + 43.4757i −0.790370 + 1.83228i −0.333505 + 0.942748i $$0.608232\pi$$
−0.456865 + 0.889536i $$0.651028\pi$$
$$564$$ 0 0
$$565$$ −6.05249 + 3.98079i −0.254630 + 0.167473i
$$566$$ −25.7811 −1.08366
$$567$$ 0 0
$$568$$ 29.2870 1.22886
$$569$$ −14.4816 + 9.52469i −0.607099 + 0.399296i −0.815508 0.578746i $$-0.803542\pi$$
0.208408 + 0.978042i $$0.433172\pi$$
$$570$$ 0 0
$$571$$ 14.1217 32.7377i 0.590973 1.37003i −0.315967 0.948770i $$-0.602329\pi$$
0.906940 0.421260i $$-0.138412\pi$$
$$572$$ −3.15754 + 3.34680i −0.132023 + 0.139937i
$$573$$ 0 0
$$574$$ 36.3561 + 4.24942i 1.51747 + 0.177367i
$$575$$ −0.976768 5.53953i −0.0407341 0.231014i
$$576$$ 0 0
$$577$$ −0.228884 + 1.29807i −0.00952858 + 0.0540393i −0.989201 0.146563i $$-0.953179\pi$$
0.979673 + 0.200602i $$0.0642899\pi$$
$$578$$ −6.53204 + 21.8185i −0.271697 + 0.907532i
$$579$$ 0 0
$$580$$ 0.0789958 1.35630i 0.00328012 0.0563175i
$$581$$ −2.50563 + 1.25838i −0.103951 + 0.0522063i
$$582$$ 0 0
$$583$$ −35.7933 37.9386i −1.48241 1.57126i
$$584$$ −36.4540 + 13.2682i −1.50848 + 0.549041i
$$585$$ 0 0
$$586$$ 36.8824 + 13.4241i 1.52360 + 0.554544i
$$587$$ −1.99538 4.62581i −0.0823582 0.190928i 0.872061 0.489397i $$-0.162783\pi$$
−0.954419 + 0.298469i $$0.903524\pi$$
$$588$$ 0 0
$$589$$ −0.0891625 0.297824i −0.00367388 0.0122716i
$$590$$ 1.09062 0.127476i 0.0449003 0.00524809i
$$591$$ 0 0
$$592$$ −0.820774 14.0922i −0.0337336 0.579184i
$$593$$ −13.0012 22.5187i −0.533895 0.924732i −0.999216 0.0395907i $$-0.987395\pi$$
0.465321 0.885142i $$-0.345939\pi$$
$$594$$ 0 0
$$595$$ 1.52425 2.64009i 0.0624883 0.108233i
$$596$$ −1.87866 0.943497i −0.0769528 0.0386472i
$$597$$ 0 0
$$598$$ −3.40717 4.57663i −0.139330 0.187152i
$$599$$ 17.4587 + 4.13779i 0.713344 + 0.169066i 0.571236 0.820786i $$-0.306464\pi$$
0.142108 + 0.989851i $$0.454612\pi$$
$$600$$ 0 0
$$601$$ −20.4833 + 27.5138i −0.835531 + 1.12231i 0.155389 + 0.987853i $$0.450337\pi$$
−0.990919 + 0.134459i $$0.957070\pi$$
$$602$$ −1.12414 + 0.943264i −0.0458164 + 0.0384446i
$$603$$ 0 0
$$604$$ −4.40962 3.70011i −0.179425 0.150555i
$$605$$ 1.81144 0.429319i 0.0736455 0.0174543i
$$606$$ 0 0
$$607$$ 1.64151 + 1.07964i 0.0666267 + 0.0438211i 0.582385 0.812913i $$-0.302120\pi$$
−0.515759 + 0.856734i $$0.672490\pi$$
$$608$$ 12.0755 + 7.94216i 0.489725 + 0.322097i
$$609$$ 0 0
$$610$$ 0.240179 0.0569234i 0.00972456 0.00230476i
$$611$$ 11.2987 + 9.48071i 0.457095 + 0.383549i
$$612$$ 0 0
$$613$$ −1.60067 + 1.34312i −0.0646505 + 0.0542482i −0.674540 0.738238i $$-0.735658\pi$$
0.609890 + 0.792486i $$0.291214\pi$$
$$614$$ −9.25743 + 12.4349i −0.373599 + 0.501831i
$$615$$ 0 0
$$616$$ 37.0431 + 8.77938i 1.49251 + 0.353731i
$$617$$ 24.8220 + 33.3418i 0.999298 + 1.34229i 0.938928 + 0.344113i $$0.111820\pi$$
0.0603694 + 0.998176i $$0.480772\pi$$
$$618$$ 0 0
$$619$$ −6.28378 3.15583i −0.252567 0.126844i 0.318012 0.948087i $$-0.396985\pi$$
−0.570579 + 0.821243i $$0.693281\pi$$
$$620$$ 0.00455322 0.00788641i 0.000182862 0.000316726i
$$621$$ 0 0
$$622$$ −20.8154 36.0533i −0.834620 1.44561i
$$623$$ 2.68331 + 46.0707i 0.107505 + 1.84578i
$$624$$ 0 0
$$625$$ −21.0388 + 2.45908i −0.841553 + 0.0983634i
$$626$$ 5.77312 + 19.2836i 0.230740 + 0.770727i
$$627$$ 0 0
$$628$$ 1.28198 + 2.97195i 0.0511564 + 0.118594i
$$629$$ −4.30925 1.56844i −0.171821 0.0625378i
$$630$$ 0 0
$$631$$ 6.32771 2.30310i 0.251902 0.0916848i −0.212983 0.977056i $$-0.568318\pi$$
0.464885 + 0.885371i $$0.346096\pi$$
$$632$$ 23.9463 + 25.3816i 0.952534 + 1.00963i
$$633$$ 0 0
$$634$$ 13.1049 6.58153i 0.520463 0.261386i
$$635$$ −0.547578 + 9.40155i −0.0217300 + 0.373089i
$$636$$ 0 0
$$637$$ −7.95367 + 26.5671i −0.315136 + 1.05263i
$$638$$ 7.10175 40.2760i 0.281161 1.59454i
$$639$$ 0 0
$$640$$ −1.18865 6.74119i −0.0469857 0.266469i
$$641$$ 12.9949 + 1.51889i 0.513270 + 0.0599926i 0.368786 0.929515i $$-0.379774\pi$$
0.144484 + 0.989507i $$0.453848\pi$$
$$642$$ 0 0
$$643$$ 1.79987 1.90775i 0.0709800 0.0752344i −0.690910 0.722941i $$-0.742790\pi$$
0.761890 + 0.647706i $$0.224272\pi$$
$$644$$ 0.723533 1.67734i 0.0285112 0.0660964i
$$645$$ 0 0
$$646$$ 12.9996 8.54998i 0.511463 0.336394i
$$647$$ −2.94663 −0.115844 −0.0579219 0.998321i $$-0.518447\pi$$
−0.0579219 + 0.998321i $$0.518447\pi$$
$$648$$ 0 0
$$649$$ 5.34772 0.209916
$$650$$ −19.0486 + 12.5285i −0.747147 + 0.491406i
$$651$$ 0 0
$$652$$ 0.465631 1.07945i 0.0182355 0.0422747i
$$653$$ 24.1758 25.6248i 0.946071 1.00278i −0.0539200 0.998545i $$-0.517172\pi$$
0.999991 0.00423147i $$-0.00134692\pi$$
$$654$$ 0 0
$$655$$ −2.80704 0.328096i −0.109680 0.0128198i
$$656$$ −4.76957 27.0496i −0.186221 1.05611i
$$657$$ 0 0
$$658$$ −5.06840 + 28.7443i −0.197587 + 1.12057i
$$659$$ 4.81941 16.0979i 0.187738 0.627087i −0.811357 0.584550i $$-0.801271\pi$$
0.999095 0.0425366i $$-0.0135439\pi$$
$$660$$ 0 0
$$661$$ 0.169220 2.90540i 0.00658190 0.113007i −0.993417 0.114555i $$-0.963456\pi$$
0.999999 + 0.00154821i $$0.000492812\pi$$
$$662$$ 32.4583 16.3012i 1.26153 0.633562i
$$663$$ 0 0
$$664$$ 1.20272 + 1.27481i 0.0466746 + 0.0494722i
$$665$$ 12.7928 4.65618i 0.496082 0.180559i
$$666$$ 0 0
$$667$$ 7.71007 + 2.80623i 0.298535 + 0.108658i
$$668$$ 3.22673 + 7.48041i 0.124846 + 0.289426i
$$669$$ 0 0
$$670$$ 1.23835 + 4.13637i 0.0478415 + 0.159802i
$$671$$ 1.19399 0.139558i 0.0460936 0.00538757i
$$672$$ 0 0
$$673$$ −0.176906 3.03736i −0.00681923 0.117082i −1.00000 0.000496017i $$-0.999842\pi$$
0.993181 0.116586i $$-0.0371949\pi$$
$$674$$ −2.40053 4.15783i −0.0924648 0.160154i
$$675$$ 0 0
$$676$$ 0.638419 1.10577i 0.0245546 0.0425298i
$$677$$ −33.4519 16.8002i −1.28566 0.645684i −0.331072 0.943605i $$-0.607410\pi$$
−0.954590 + 0.297921i $$0.903707\pi$$
$$678$$ 0 0
$$679$$ −30.9864 41.6219i −1.18915 1.59730i
$$680$$ −1.85417 0.439446i −0.0711042 0.0168520i
$$681$$ 0 0
$$682$$ 0.163697 0.219883i 0.00626829 0.00841977i
$$683$$ 23.8512 20.0135i 0.912641 0.765797i −0.0599783 0.998200i $$-0.519103\pi$$
0.972620 + 0.232403i $$0.0746587\pi$$
$$684$$ 0 0
$$685$$ −1.16318 0.976025i −0.0444429 0.0372920i
$$686$$ −11.4366 + 2.71053i −0.436653 + 0.103489i
$$687$$ 0 0
$$688$$ 0.920007 + 0.605098i 0.0350749 + 0.0230691i
$$689$$ −35.4358 23.3065i −1.35000 0.887907i
$$690$$ 0 0
$$691$$ 10.4258 2.47095i 0.396615 0.0939995i −0.0274683 0.999623i $$-0.508745\pi$$
0.424083 + 0.905623i $$0.360596\pi$$
$$692$$ −0.501162 0.420525i −0.0190513 0.0159859i
$$693$$ 0 0
$$694$$ −26.3811 + 22.1364i −1.00141 + 0.840286i
$$695$$ −1.79114 + 2.40592i −0.0679419 + 0.0912618i
$$696$$ 0 0
$$697$$ −8.68251 2.05779i −0.328874 0.0779445i
$$698$$ −2.77903 3.73289i −0.105188 0.141292i
$$699$$ 0 0
$$700$$ −6.52308 3.27602i −0.246549 0.123822i
$$701$$ 10.3580 17.9406i 0.391216 0.677607i −0.601394 0.798953i $$-0.705388\pi$$
0.992610 + 0.121346i $$0.0387210\pi$$
$$702$$ 0 0
$$703$$ −10.2395 17.7353i −0.386188 0.668898i
$$704$$ −1.31727 22.6166i −0.0496464 0.852396i
$$705$$ 0 0
$$706$$ −3.32048 + 0.388109i −0.124968 + 0.0146067i
$$707$$ −14.1432 47.2416i −0.531910 1.77670i
$$708$$ 0 0
$$709$$ −7.20452 16.7019i −0.270571 0.627255i 0.727708 0.685887i $$-0.240585\pi$$
−0.998280 + 0.0586319i $$0.981326\pi$$
$$710$$ 8.67796 + 3.15852i 0.325678 + 0.118537i
$$711$$ 0 0
$$712$$ 27.1066 9.86600i 1.01586 0.369744i
$$713$$ 0.0377403 + 0.0400024i 0.00141339 + 0.00149810i
$$714$$ 0 0
$$715$$ 5.42080 2.72243i 0.202726 0.101813i
$$716$$ −0.270778 + 4.64907i −0.0101194 + 0.173744i
$$717$$ 0 0
$$718$$ 0.287306 0.959668i 0.0107222 0.0358145i
$$719$$ 5.53156 31.3710i 0.206292 1.16994i −0.689101 0.724666i $$-0.741994\pi$$
0.895393 0.445277i $$-0.146895\pi$$
$$720$$ 0 0
$$721$$ −1.44761 8.20980i −0.0539118 0.305749i
$$722$$ 39.8631 + 4.65933i 1.48355 + 0.173402i
$$723$$ 0 0
$$724$$ −2.00034 + 2.12024i −0.0743421 + 0.0787981i
$$725$$ 12.9859 30.1048i 0.482285 1.11806i
$$726$$ 0 0
$$727$$ −7.91945 + 5.20870i −0.293716 + 0.193180i −0.687811 0.725890i $$-0.741428\pi$$
0.394095 + 0.919070i $$0.371058\pi$$
$$728$$ 30.9566 1.14733
$$729$$ 0 0
$$730$$ −12.2325 −0.452746
$$731$$ 0.298878 0.196575i 0.0110544 0.00727060i
$$732$$ 0 0
$$733$$ −16.6921 + 38.6967i −0.616538 + 1.42930i 0.268271 + 0.963343i $$0.413548\pi$$
−0.884809 + 0.465953i $$0.845712\pi$$
$$734$$ −10.0376 + 10.6393i −0.370496 + 0.392703i
$$735$$ 0 0
$$736$$ −2.53950 0.296824i −0.0936070 0.0109411i
$$737$$ 3.65153 + 20.7089i 0.134506 + 0.762821i
$$738$$ 0 0
$$739$$ 8.32565 47.2171i 0.306264 1.73691i −0.311232 0.950334i $$-0.600742\pi$$
0.617496 0.786574i $$-0.288147\pi$$
$$740$$ 0.172045 0.574669i 0.00632449 0.0211253i
$$741$$ 0 0
$$742$$ 4.88024 83.7904i 0.179159 3.07604i
$$743$$ 9.21372 4.62730i 0.338019 0.169759i −0.271690 0.962385i $$-0.587583\pi$$
0.609709 + 0.792625i $$0.291286\pi$$
$$744$$ 0 0
$$745$$ 1.90195 + 2.01594i 0.0696819 + 0.0738585i
$$746$$ −7.08589 + 2.57905i −0.259433 + 0.0944258i
$$747$$ 0 0
$$748$$ 2.08580 + 0.759170i 0.0762645 + 0.0277580i
$$749$$ 2.62669 + 6.08934i 0.0959770 + 0.222500i
$$750$$ 0 0
$$751$$ −7.18583 24.0023i −0.262215 0.875858i −0.983141 0.182847i $$-0.941469\pi$$
0.720927 0.693011i $$-0.243716\pi$$
$$752$$ 21.7540 2.54268i 0.793287 0.0927220i
$$753$$ 0 0
$$754$$ −1.93368 33.2000i −0.0704205 1.20907i
$$755$$ 3.79446 + 6.57219i 0.138094 + 0.239187i
$$756$$ 0 0
$$757$$ 3.05875 5.29791i 0.111172 0.192556i −0.805071 0.593178i $$-0.797873\pi$$
0.916243 + 0.400623i $$0.131206\pi$$
$$758$$ 35.9421 + 18.0508i 1.30547 + 0.655634i
$$759$$ 0 0
$$760$$ −5.08156 6.82572i −0.184328 0.247595i
$$761$$ −43.6455 10.3442i −1.58215 0.374976i −0.656790 0.754073i $$-0.728086\pi$$
−0.925357 + 0.379097i $$0.876234\pi$$
$$762$$ 0 0
$$763$$ 10.2406 13.7555i 0.370733 0.497981i
$$764$$ 3.82972 3.21351i 0.138554 0.116261i
$$765$$ 0 0
$$766$$ −9.50299 7.97396i −0.343357 0.288111i
$$767$$ 4.23136 1.00285i 0.152785 0.0362108i
$$768$$ 0 0
$$769$$ −31.6906 20.8432i −1.14279 0.751626i −0.170490 0.985359i $$-0.554535\pi$$
−0.972301 + 0.233734i $$0.924906\pi$$
$$770$$ 10.0293 + 6.59639i 0.361431 + 0.237717i
$$771$$ 0 0
$$772$$ 6.79092 1.60948i 0.244411 0.0579264i
$$773$$ −11.7711 9.87712i −0.423377 0.355255i 0.406069 0.913842i $$-0.366899\pi$$
−0.829446 + 0.558587i $$0.811344\pi$$
$$774$$ 0 0
$$775$$ 0.168345 0.141258i 0.00604713 0.00507415i
$$776$$ −19.3687 + 26.0167i −0.695295 + 0.933944i
$$777$$ 0 0
$$778$$ −34.1882 8.10276i −1.22571 0.290498i
$$779$$ −23.7954 31.9628i −0.852559 1.14518i
$$780$$ 0 0
$$781$$ 40.1918 + 20.1851i 1.43818 + 0.722279i
$$782$$ −1.37623 + 2.38370i −0.0492138 + 0.0852408i