# Properties

 Label 729.2.e.q.163.2 Level $729$ Weight $2$ Character 729.163 Analytic conductor $5.821$ Analytic rank $0$ Dimension $12$ CM no Inner twists $4$

# Learn more

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(82,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$729 = 3^{6}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 729.e (of order $$9$$, 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: $$5.82109430735$$ Analytic rank: $$0$$ Dimension: $$12$$ Relative dimension: $$2$$ over $$\Q(\zeta_{9})$$ Coefficient field: $$\Q(\zeta_{36})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{12} - x^{6} + 1$$ x^12 - x^6 + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{4}]$$ Coefficient ring index: $$3$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

## Embedding invariants

 Embedding label 163.2 Root $$0.342020 - 0.939693i$$ of defining polynomial Character $$\chi$$ $$=$$ 729.163 Dual form 729.2.e.q.568.2

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(1.20805 - 0.439693i) q^{2} +(-0.266044 + 0.223238i) q^{4} +(-0.0775297 - 0.439693i) q^{5} +(-2.70574 - 2.27038i) q^{7} +(-1.50881 + 2.61334i) q^{8} +O(q^{10})$$ $$q+(1.20805 - 0.439693i) q^{2} +(-0.266044 + 0.223238i) q^{4} +(-0.0775297 - 0.439693i) q^{5} +(-2.70574 - 2.27038i) q^{7} +(-1.50881 + 2.61334i) q^{8} +(-0.286989 - 0.497079i) q^{10} +(0.482753 - 2.73783i) q^{11} +(-3.09240 - 1.12554i) q^{13} +(-4.26692 - 1.55303i) q^{14} +(-0.553033 + 3.13641i) q^{16} +(-3.51968 - 6.09627i) q^{17} +(2.59240 - 4.49016i) q^{19} +(0.118782 + 0.0996702i) q^{20} +(-0.620615 - 3.51968i) q^{22} +(-5.57445 + 4.67752i) q^{23} +(4.51114 - 1.64192i) q^{25} -4.23065 q^{26} +1.22668 q^{28} +(3.40090 - 1.23783i) q^{29} +(-1.48293 + 1.24432i) q^{31} +(-0.337044 - 1.91147i) q^{32} +(-6.93242 - 5.81699i) q^{34} +(-0.788496 + 1.36571i) q^{35} +(1.61334 + 2.79439i) q^{37} +(1.15744 - 6.56418i) q^{38} +(1.26604 + 0.460802i) q^{40} +(-4.56769 - 1.66250i) q^{41} +(-1.00000 + 5.67128i) q^{43} +(0.482753 + 0.836152i) q^{44} +(-4.67752 + 8.10170i) q^{46} +(-2.31164 - 1.93969i) q^{47} +(0.950837 + 5.39246i) q^{49} +(4.72773 - 3.96703i) q^{50} +(1.07398 - 0.390896i) q^{52} -8.77141 q^{53} -1.24123 q^{55} +(10.0157 - 3.64543i) q^{56} +(3.56418 - 2.99070i) q^{58} +(-0.514654 - 2.91875i) q^{59} +(6.04189 + 5.06975i) q^{61} +(-1.24432 + 2.15523i) q^{62} +(-4.43242 - 7.67717i) q^{64} +(-0.255139 + 1.44697i) q^{65} +(8.86959 + 3.22826i) q^{67} +(2.29731 + 0.836152i) q^{68} +(-0.352044 + 1.99654i) q^{70} +(2.65366 + 4.59627i) q^{71} +(0.777189 - 1.34613i) q^{73} +(3.17766 + 2.66637i) q^{74} +(0.312681 + 1.77330i) q^{76} +(-7.52211 + 6.31180i) q^{77} +(11.1839 - 4.07061i) q^{79} +1.42193 q^{80} -6.24897 q^{82} +(-15.2768 + 5.56031i) q^{83} +(-2.40760 + 2.02022i) q^{85} +(1.28558 + 7.29086i) q^{86} +(6.42649 + 5.39246i) q^{88} +(9.21291 - 15.9572i) q^{89} +(5.81180 + 10.0663i) q^{91} +(0.438852 - 2.48886i) q^{92} +(-3.64543 - 1.32683i) q^{94} +(-2.17528 - 0.791737i) q^{95} +(1.75624 - 9.96016i) q^{97} +(3.51968 + 6.09627i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$12 q + 6 q^{4} - 12 q^{7}+O(q^{10})$$ 12 * q + 6 * q^4 - 12 * q^7 $$12 q + 6 q^{4} - 12 q^{7} + 12 q^{10} - 30 q^{13} + 18 q^{16} + 24 q^{19} - 30 q^{22} + 42 q^{25} - 12 q^{28} + 24 q^{31} - 36 q^{34} + 6 q^{37} + 6 q^{40} - 12 q^{43} - 6 q^{46} - 12 q^{49} - 18 q^{52} - 60 q^{55} + 6 q^{58} + 60 q^{61} - 6 q^{64} + 78 q^{67} - 66 q^{70} - 12 q^{73} + 48 q^{76} + 6 q^{79} - 24 q^{82} - 36 q^{85} - 24 q^{88} - 12 q^{94} + 6 q^{97}+O(q^{100})$$ 12 * q + 6 * q^4 - 12 * q^7 + 12 * q^10 - 30 * q^13 + 18 * q^16 + 24 * q^19 - 30 * q^22 + 42 * q^25 - 12 * q^28 + 24 * q^31 - 36 * q^34 + 6 * q^37 + 6 * q^40 - 12 * q^43 - 6 * q^46 - 12 * q^49 - 18 * q^52 - 60 * q^55 + 6 * q^58 + 60 * q^61 - 6 * q^64 + 78 * q^67 - 66 * q^70 - 12 * q^73 + 48 * q^76 + 6 * q^79 - 24 * q^82 - 36 * q^85 - 24 * q^88 - 12 * q^94 + 6 * q^97

## Character values

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

 $$n$$ $$2$$ $$\chi(n)$$ $$e\left(\frac{8}{9}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.20805 0.439693i 0.854217 0.310910i 0.122459 0.992474i $$-0.460922\pi$$
0.731759 + 0.681564i $$0.238700\pi$$
$$3$$ 0 0
$$4$$ −0.266044 + 0.223238i −0.133022 + 0.111619i
$$5$$ −0.0775297 0.439693i −0.0346723 0.196637i 0.962552 0.271099i $$-0.0873870\pi$$
−0.997224 + 0.0744624i $$0.976276\pi$$
$$6$$ 0 0
$$7$$ −2.70574 2.27038i −1.02267 0.858124i −0.0327115 0.999465i $$-0.510414\pi$$
−0.989961 + 0.141341i $$0.954859\pi$$
$$8$$ −1.50881 + 2.61334i −0.533446 + 0.923956i
$$9$$ 0 0
$$10$$ −0.286989 0.497079i −0.0907539 0.157190i
$$11$$ 0.482753 2.73783i 0.145555 0.825486i −0.821364 0.570404i $$-0.806787\pi$$
0.966920 0.255081i $$-0.0821023\pi$$
$$12$$ 0 0
$$13$$ −3.09240 1.12554i −0.857676 0.312169i −0.124510 0.992218i $$-0.539736\pi$$
−0.733166 + 0.680050i $$0.761958\pi$$
$$14$$ −4.26692 1.55303i −1.14038 0.415066i
$$15$$ 0 0
$$16$$ −0.553033 + 3.13641i −0.138258 + 0.784102i
$$17$$ −3.51968 6.09627i −0.853648 1.47856i −0.877894 0.478856i $$-0.841052\pi$$
0.0242455 0.999706i $$-0.492282\pi$$
$$18$$ 0 0
$$19$$ 2.59240 4.49016i 0.594736 1.03011i −0.398848 0.917017i $$-0.630590\pi$$
0.993584 0.113097i $$-0.0360769\pi$$
$$20$$ 0.118782 + 0.0996702i 0.0265605 + 0.0222869i
$$21$$ 0 0
$$22$$ −0.620615 3.51968i −0.132316 0.750399i
$$23$$ −5.57445 + 4.67752i −1.16235 + 0.975330i −0.999935 0.0113920i $$-0.996374\pi$$
−0.162418 + 0.986722i $$0.551929\pi$$
$$24$$ 0 0
$$25$$ 4.51114 1.64192i 0.902229 0.328384i
$$26$$ −4.23065 −0.829698
$$27$$ 0 0
$$28$$ 1.22668 0.231821
$$29$$ 3.40090 1.23783i 0.631531 0.229859i −0.00636650 0.999980i $$-0.502027\pi$$
0.637898 + 0.770121i $$0.279804\pi$$
$$30$$ 0 0
$$31$$ −1.48293 + 1.24432i −0.266341 + 0.223487i −0.766171 0.642637i $$-0.777840\pi$$
0.499830 + 0.866124i $$0.333396\pi$$
$$32$$ −0.337044 1.91147i −0.0595816 0.337904i
$$33$$ 0 0
$$34$$ −6.93242 5.81699i −1.18890 0.997606i
$$35$$ −0.788496 + 1.36571i −0.133280 + 0.230848i
$$36$$ 0 0
$$37$$ 1.61334 + 2.79439i 0.265232 + 0.459395i 0.967624 0.252395i $$-0.0812183\pi$$
−0.702393 + 0.711790i $$0.747885\pi$$
$$38$$ 1.15744 6.56418i 0.187762 1.06485i
$$39$$ 0 0
$$40$$ 1.26604 + 0.460802i 0.200179 + 0.0728593i
$$41$$ −4.56769 1.66250i −0.713354 0.259639i −0.0402521 0.999190i $$-0.512816\pi$$
−0.673102 + 0.739550i $$0.735038\pi$$
$$42$$ 0 0
$$43$$ −1.00000 + 5.67128i −0.152499 + 0.864862i 0.808539 + 0.588443i $$0.200259\pi$$
−0.961037 + 0.276419i $$0.910852\pi$$
$$44$$ 0.482753 + 0.836152i 0.0727777 + 0.126055i
$$45$$ 0 0
$$46$$ −4.67752 + 8.10170i −0.689662 + 1.19453i
$$47$$ −2.31164 1.93969i −0.337187 0.282933i 0.458434 0.888729i $$-0.348411\pi$$
−0.795621 + 0.605795i $$0.792855\pi$$
$$48$$ 0 0
$$49$$ 0.950837 + 5.39246i 0.135834 + 0.770352i
$$50$$ 4.72773 3.96703i 0.668602 0.561023i
$$51$$ 0 0
$$52$$ 1.07398 0.390896i 0.148934 0.0542075i
$$53$$ −8.77141 −1.20485 −0.602423 0.798177i $$-0.705798\pi$$
−0.602423 + 0.798177i $$0.705798\pi$$
$$54$$ 0 0
$$55$$ −1.24123 −0.167367
$$56$$ 10.0157 3.64543i 1.33841 0.487141i
$$57$$ 0 0
$$58$$ 3.56418 2.99070i 0.467999 0.392698i
$$59$$ −0.514654 2.91875i −0.0670022 0.379989i −0.999808 0.0196084i $$-0.993758\pi$$
0.932805 0.360380i $$-0.117353\pi$$
$$60$$ 0 0
$$61$$ 6.04189 + 5.06975i 0.773585 + 0.649115i 0.941624 0.336666i $$-0.109299\pi$$
−0.168040 + 0.985780i $$0.553744\pi$$
$$62$$ −1.24432 + 2.15523i −0.158029 + 0.273714i
$$63$$ 0 0
$$64$$ −4.43242 7.67717i −0.554052 0.959647i
$$65$$ −0.255139 + 1.44697i −0.0316461 + 0.179474i
$$66$$ 0 0
$$67$$ 8.86959 + 3.22826i 1.08359 + 0.394395i 0.821244 0.570578i $$-0.193281\pi$$
0.262349 + 0.964973i $$0.415503\pi$$
$$68$$ 2.29731 + 0.836152i 0.278590 + 0.101398i
$$69$$ 0 0
$$70$$ −0.352044 + 1.99654i −0.0420773 + 0.238632i
$$71$$ 2.65366 + 4.59627i 0.314931 + 0.545476i 0.979423 0.201819i $$-0.0646853\pi$$
−0.664492 + 0.747296i $$0.731352\pi$$
$$72$$ 0 0
$$73$$ 0.777189 1.34613i 0.0909631 0.157553i −0.816954 0.576703i $$-0.804339\pi$$
0.907917 + 0.419151i $$0.137672\pi$$
$$74$$ 3.17766 + 2.66637i 0.369396 + 0.309960i
$$75$$ 0 0
$$76$$ 0.312681 + 1.77330i 0.0358670 + 0.203412i
$$77$$ −7.52211 + 6.31180i −0.857225 + 0.719297i
$$78$$ 0 0
$$79$$ 11.1839 4.07061i 1.25829 0.457980i 0.375094 0.926987i $$-0.377610\pi$$
0.883194 + 0.469007i $$0.155388\pi$$
$$80$$ 1.42193 0.158977
$$81$$ 0 0
$$82$$ −6.24897 −0.690083
$$83$$ −15.2768 + 5.56031i −1.67685 + 0.610323i −0.992873 0.119181i $$-0.961973\pi$$
−0.683976 + 0.729504i $$0.739751\pi$$
$$84$$ 0 0
$$85$$ −2.40760 + 2.02022i −0.261141 + 0.219124i
$$86$$ 1.28558 + 7.29086i 0.138627 + 0.786194i
$$87$$ 0 0
$$88$$ 6.42649 + 5.39246i 0.685066 + 0.574839i
$$89$$ 9.21291 15.9572i 0.976567 1.69146i 0.301902 0.953339i $$-0.402378\pi$$
0.674665 0.738125i $$-0.264288\pi$$
$$90$$ 0 0
$$91$$ 5.81180 + 10.0663i 0.609243 + 1.05524i
$$92$$ 0.438852 2.48886i 0.0457535 0.259481i
$$93$$ 0 0
$$94$$ −3.64543 1.32683i −0.375997 0.136852i
$$95$$ −2.17528 0.791737i −0.223179 0.0812305i
$$96$$ 0 0
$$97$$ 1.75624 9.96016i 0.178320 1.01130i −0.755922 0.654661i $$-0.772811\pi$$
0.934242 0.356640i $$-0.116078\pi$$
$$98$$ 3.51968 + 6.09627i 0.355541 + 0.615816i
$$99$$ 0 0
$$100$$ −0.833626 + 1.44388i −0.0833626 + 0.144388i
$$101$$ 1.59397 + 1.33750i 0.158606 + 0.133086i 0.718637 0.695386i $$-0.244766\pi$$
−0.560031 + 0.828472i $$0.689211\pi$$
$$102$$ 0 0
$$103$$ −0.251497 1.42631i −0.0247807 0.140538i 0.969907 0.243475i $$-0.0782873\pi$$
−0.994688 + 0.102936i $$0.967176\pi$$
$$104$$ 7.60727 6.38326i 0.745954 0.625930i
$$105$$ 0 0
$$106$$ −10.5963 + 3.85673i −1.02920 + 0.374598i
$$107$$ 2.23583 0.216146 0.108073 0.994143i $$-0.465532\pi$$
0.108073 + 0.994143i $$0.465532\pi$$
$$108$$ 0 0
$$109$$ −11.5030 −1.10179 −0.550893 0.834576i $$-0.685713\pi$$
−0.550893 + 0.834576i $$0.685713\pi$$
$$110$$ −1.49946 + 0.545759i −0.142968 + 0.0520361i
$$111$$ 0 0
$$112$$ 8.61721 7.23070i 0.814250 0.683237i
$$113$$ −0.293144 1.66250i −0.0275767 0.156395i 0.967910 0.251297i $$-0.0808572\pi$$
−0.995487 + 0.0949023i $$0.969746\pi$$
$$114$$ 0 0
$$115$$ 2.48886 + 2.08840i 0.232087 + 0.194744i
$$116$$ −0.628461 + 1.08853i −0.0583511 + 0.101067i
$$117$$ 0 0
$$118$$ −1.90508 3.29969i −0.175377 0.303761i
$$119$$ −4.31753 + 24.4859i −0.395787 + 2.24462i
$$120$$ 0 0
$$121$$ 3.07398 + 1.11884i 0.279453 + 0.101712i
$$122$$ 9.52801 + 3.46791i 0.862625 + 0.313970i
$$123$$ 0 0
$$124$$ 0.116744 0.662090i 0.0104840 0.0594575i
$$125$$ −2.18788 3.78952i −0.195690 0.338945i
$$126$$ 0 0
$$127$$ 1.33615 2.31428i 0.118564 0.205359i −0.800635 0.599153i $$-0.795504\pi$$
0.919199 + 0.393793i $$0.128837\pi$$
$$128$$ −5.75643 4.83022i −0.508802 0.426935i
$$129$$ 0 0
$$130$$ 0.328001 + 1.86018i 0.0287676 + 0.163149i
$$131$$ 2.23675 1.87686i 0.195426 0.163982i −0.539824 0.841778i $$-0.681509\pi$$
0.735250 + 0.677796i $$0.237065\pi$$
$$132$$ 0 0
$$133$$ −17.2087 + 6.26347i −1.49219 + 0.543111i
$$134$$ 12.1343 1.04824
$$135$$ 0 0
$$136$$ 21.2422 1.82150
$$137$$ −4.37636 + 1.59286i −0.373897 + 0.136087i −0.522132 0.852865i $$-0.674863\pi$$
0.148235 + 0.988952i $$0.452641\pi$$
$$138$$ 0 0
$$139$$ −6.13041 + 5.14403i −0.519975 + 0.436311i −0.864623 0.502421i $$-0.832443\pi$$
0.344648 + 0.938732i $$0.387998\pi$$
$$140$$ −0.0951042 0.539363i −0.00803777 0.0455845i
$$141$$ 0 0
$$142$$ 5.22668 + 4.38571i 0.438613 + 0.368040i
$$143$$ −4.57440 + 7.92309i −0.382530 + 0.662562i
$$144$$ 0 0
$$145$$ −0.807934 1.39938i −0.0670952 0.116212i
$$146$$ 0.346996 1.96791i 0.0287176 0.162865i
$$147$$ 0 0
$$148$$ −1.05303 0.383273i −0.0865588 0.0315048i
$$149$$ 18.9928 + 6.91282i 1.55595 + 0.566320i 0.969804 0.243884i $$-0.0784217\pi$$
0.586147 + 0.810204i $$0.300644\pi$$
$$150$$ 0 0
$$151$$ 1.16385 6.60051i 0.0947126 0.537142i −0.900122 0.435637i $$-0.856523\pi$$
0.994835 0.101505i $$-0.0323657\pi$$
$$152$$ 7.82288 + 13.5496i 0.634520 + 1.09902i
$$153$$ 0 0
$$154$$ −6.31180 + 10.9324i −0.508620 + 0.880955i
$$155$$ 0.662090 + 0.555560i 0.0531804 + 0.0446236i
$$156$$ 0 0
$$157$$ 0.924678 + 5.24411i 0.0737973 + 0.418525i 0.999216 + 0.0395801i $$0.0126020\pi$$
−0.925419 + 0.378945i $$0.876287\pi$$
$$158$$ 11.7209 9.83497i 0.932462 0.782428i
$$159$$ 0 0
$$160$$ −0.814330 + 0.296392i −0.0643784 + 0.0234318i
$$161$$ 25.7028 2.02566
$$162$$ 0 0
$$163$$ 3.81521 0.298830 0.149415 0.988775i $$-0.452261\pi$$
0.149415 + 0.988775i $$0.452261\pi$$
$$164$$ 1.58634 0.577382i 0.123873 0.0450859i
$$165$$ 0 0
$$166$$ −16.0103 + 13.4342i −1.24264 + 1.04270i
$$167$$ 1.58634 + 8.99660i 0.122755 + 0.696178i 0.982616 + 0.185650i $$0.0594389\pi$$
−0.859861 + 0.510528i $$0.829450\pi$$
$$168$$ 0 0
$$169$$ −1.66250 1.39501i −0.127885 0.107308i
$$170$$ −2.02022 + 3.49912i −0.154944 + 0.268370i
$$171$$ 0 0
$$172$$ −1.00000 1.73205i −0.0762493 0.132068i
$$173$$ 1.05471 5.98158i 0.0801884 0.454771i −0.918103 0.396342i $$-0.870280\pi$$
0.998292 0.0584296i $$-0.0186093\pi$$
$$174$$ 0 0
$$175$$ −15.9338 5.79942i −1.20448 0.438395i
$$176$$ 8.31996 + 3.02822i 0.627141 + 0.228261i
$$177$$ 0 0
$$178$$ 4.11334 23.3279i 0.308308 1.74850i
$$179$$ −5.14057 8.90373i −0.384224 0.665496i 0.607437 0.794368i $$-0.292198\pi$$
−0.991661 + 0.128872i $$0.958864\pi$$
$$180$$ 0 0
$$181$$ 11.5706 20.0408i 0.860034 1.48962i −0.0118609 0.999930i $$-0.503776\pi$$
0.871895 0.489693i $$-0.162891\pi$$
$$182$$ 11.4470 + 9.60519i 0.848510 + 0.711984i
$$183$$ 0 0
$$184$$ −3.81315 21.6254i −0.281109 1.59425i
$$185$$ 1.10359 0.926022i 0.0811376 0.0680825i
$$186$$ 0 0
$$187$$ −18.3897 + 6.69329i −1.34478 + 0.489462i
$$188$$ 1.04801 0.0764340
$$189$$ 0 0
$$190$$ −2.97596 −0.215899
$$191$$ −13.7856 + 5.01754i −0.997490 + 0.363057i −0.788616 0.614886i $$-0.789202\pi$$
−0.208874 + 0.977943i $$0.566980\pi$$
$$192$$ 0 0
$$193$$ 17.9572 15.0679i 1.29259 1.08461i 0.301215 0.953556i $$-0.402608\pi$$
0.991375 0.131055i $$-0.0418366\pi$$
$$194$$ −2.25778 12.8045i −0.162099 0.919312i
$$195$$ 0 0
$$196$$ −1.45677 1.22237i −0.104055 0.0873123i
$$197$$ 4.51384 7.81820i 0.321598 0.557024i −0.659220 0.751950i $$-0.729113\pi$$
0.980818 + 0.194926i $$0.0624468\pi$$
$$198$$ 0 0
$$199$$ −1.30200 2.25514i −0.0922966 0.159862i 0.816181 0.577797i $$-0.196087\pi$$
−0.908477 + 0.417935i $$0.862754\pi$$
$$200$$ −2.51557 + 14.2665i −0.177878 + 1.00879i
$$201$$ 0 0
$$202$$ 2.51367 + 0.914901i 0.176861 + 0.0643722i
$$203$$ −12.0123 4.37211i −0.843097 0.306862i
$$204$$ 0 0
$$205$$ −0.376859 + 2.13727i −0.0263210 + 0.149274i
$$206$$ −0.930956 1.61246i −0.0648628 0.112346i
$$207$$ 0 0
$$208$$ 5.24035 9.07656i 0.363353 0.629346i
$$209$$ −11.0418 9.26517i −0.763777 0.640885i
$$210$$ 0 0
$$211$$ −2.84002 16.1066i −0.195515 1.10882i −0.911683 0.410894i $$-0.865217\pi$$
0.716168 0.697928i $$-0.245894\pi$$
$$212$$ 2.33359 1.95811i 0.160271 0.134484i
$$213$$ 0 0
$$214$$ 2.70099 0.983080i 0.184636 0.0672019i
$$215$$ 2.57115 0.175351
$$216$$ 0 0
$$217$$ 6.83750 0.464159
$$218$$ −13.8961 + 5.05778i −0.941165 + 0.342556i
$$219$$ 0 0
$$220$$ 0.330222 0.277089i 0.0222636 0.0186814i
$$221$$ 4.02266 + 22.8136i 0.270593 + 1.53461i
$$222$$ 0 0
$$223$$ 2.83615 + 2.37981i 0.189923 + 0.159364i 0.732791 0.680454i $$-0.238217\pi$$
−0.542868 + 0.839818i $$0.682662\pi$$
$$224$$ −3.42782 + 5.93717i −0.229031 + 0.396694i
$$225$$ 0 0
$$226$$ −1.08512 1.87949i −0.0721813 0.125022i
$$227$$ −1.83386 + 10.4003i −0.121717 + 0.690294i 0.861486 + 0.507781i $$0.169534\pi$$
−0.983203 + 0.182513i $$0.941577\pi$$
$$228$$ 0 0
$$229$$ −12.7096 4.62592i −0.839875 0.305689i −0.113969 0.993484i $$-0.536357\pi$$
−0.725905 + 0.687795i $$0.758579\pi$$
$$230$$ 3.92490 + 1.42855i 0.258801 + 0.0941957i
$$231$$ 0 0
$$232$$ −1.89646 + 10.7554i −0.124509 + 0.706124i
$$233$$ −6.35035 10.9991i −0.416025 0.720576i 0.579510 0.814965i $$-0.303244\pi$$
−0.995535 + 0.0943883i $$0.969910\pi$$
$$234$$ 0 0
$$235$$ −0.673648 + 1.16679i −0.0439440 + 0.0761132i
$$236$$ 0.788496 + 0.661626i 0.0513267 + 0.0430682i
$$237$$ 0 0
$$238$$ 5.55051 + 31.4785i 0.359786 + 2.04045i
$$239$$ −4.48254 + 3.76130i −0.289951 + 0.243298i −0.776147 0.630552i $$-0.782829\pi$$
0.486196 + 0.873850i $$0.338384\pi$$
$$240$$ 0 0
$$241$$ 8.02481 2.92079i 0.516924 0.188145i −0.0703666 0.997521i $$-0.522417\pi$$
0.587290 + 0.809376i $$0.300195\pi$$
$$242$$ 4.20545 0.270337
$$243$$ 0 0
$$244$$ −2.73917 −0.175357
$$245$$ 2.29731 0.836152i 0.146770 0.0534198i
$$246$$ 0 0
$$247$$ −13.0706 + 10.9675i −0.831661 + 0.697846i
$$248$$ −1.01438 5.75284i −0.0644133 0.365306i
$$249$$ 0 0
$$250$$ −4.30928 3.61591i −0.272543 0.228690i
$$251$$ 3.37895 5.85251i 0.213277 0.369407i −0.739461 0.673199i $$-0.764920\pi$$
0.952738 + 0.303792i $$0.0982529\pi$$
$$252$$ 0 0
$$253$$ 10.1152 + 17.5200i 0.635934 + 1.10147i
$$254$$ 0.596559 3.38326i 0.0374315 0.212284i
$$255$$ 0 0
$$256$$ 7.58260 + 2.75984i 0.473912 + 0.172490i
$$257$$ −3.46085 1.25965i −0.215882 0.0785747i 0.231815 0.972760i $$-0.425534\pi$$
−0.447697 + 0.894185i $$0.647756\pi$$
$$258$$ 0 0
$$259$$ 1.97906 11.2238i 0.122973 0.697412i
$$260$$ −0.255139 0.441914i −0.0158231 0.0274064i
$$261$$ 0 0
$$262$$ 1.87686 3.25082i 0.115953 0.200836i
$$263$$ 2.78677 + 2.33837i 0.171839 + 0.144190i 0.724651 0.689116i $$-0.242001\pi$$
−0.552812 + 0.833306i $$0.686445\pi$$
$$264$$ 0 0
$$265$$ 0.680045 + 3.85673i 0.0417748 + 0.236917i
$$266$$ −18.0349 + 15.1331i −1.10579 + 0.927870i
$$267$$ 0 0
$$268$$ −3.08037 + 1.12116i −0.188164 + 0.0684860i
$$269$$ −7.08672 −0.432085 −0.216042 0.976384i $$-0.569315\pi$$
−0.216042 + 0.976384i $$0.569315\pi$$
$$270$$ 0 0
$$271$$ −19.0000 −1.15417 −0.577084 0.816685i $$-0.695809\pi$$
−0.577084 + 0.816685i $$0.695809\pi$$
$$272$$ 21.0669 7.66772i 1.27737 0.464924i
$$273$$ 0 0
$$274$$ −4.58647 + 3.84850i −0.277079 + 0.232497i
$$275$$ −2.31753 13.1434i −0.139752 0.792575i
$$276$$ 0 0
$$277$$ −10.6420 8.92972i −0.639417 0.536535i 0.264422 0.964407i $$-0.414819\pi$$
−0.903839 + 0.427872i $$0.859263\pi$$
$$278$$ −5.14403 + 8.90972i −0.308518 + 0.534369i
$$279$$ 0 0
$$280$$ −2.37939 4.12122i −0.142195 0.246290i
$$281$$ 3.84240 21.7913i 0.229218 1.29996i −0.625236 0.780435i $$-0.714997\pi$$
0.854455 0.519526i $$-0.173891\pi$$
$$282$$ 0 0
$$283$$ 22.3011 + 8.11695i 1.32566 + 0.482502i 0.905269 0.424839i $$-0.139669\pi$$
0.420395 + 0.907341i $$0.361891\pi$$
$$284$$ −1.73205 0.630415i −0.102778 0.0374082i
$$285$$ 0 0
$$286$$ −2.04236 + 11.5828i −0.120767 + 0.684904i
$$287$$ 8.58445 + 14.8687i 0.506724 + 0.877672i
$$288$$ 0 0
$$289$$ −16.2763 + 28.1914i −0.957430 + 1.65832i
$$290$$ −1.59132 1.33527i −0.0934454 0.0784100i
$$291$$ 0 0
$$292$$ 0.0937404 + 0.531628i 0.00548574 + 0.0311112i
$$293$$ 14.2531 11.9598i 0.832674 0.698697i −0.123229 0.992378i $$-0.539325\pi$$
0.955903 + 0.293682i $$0.0948805\pi$$
$$294$$ 0 0
$$295$$ −1.24345 + 0.452579i −0.0723965 + 0.0263502i
$$296$$ −9.73692 −0.565947
$$297$$ 0 0
$$298$$ 25.9837 1.50520
$$299$$ 22.5031 8.19047i 1.30139 0.473667i
$$300$$ 0 0
$$301$$ 15.5817 13.0746i 0.898115 0.753608i
$$302$$ −1.49621 8.48545i −0.0860974 0.488283i
$$303$$ 0 0
$$304$$ 12.6493 + 10.6140i 0.725487 + 0.608756i
$$305$$ 1.76070 3.04963i 0.100818 0.174621i
$$306$$ 0 0
$$307$$ −10.3735 17.9674i −0.592044 1.02545i −0.993957 0.109773i $$-0.964988\pi$$
0.401912 0.915678i $$-0.368346\pi$$
$$308$$ 0.592184 3.35844i 0.0337428 0.191365i
$$309$$ 0 0
$$310$$ 1.04411 + 0.380025i 0.0593015 + 0.0215840i
$$311$$ −19.1561 6.97225i −1.08624 0.395360i −0.264015 0.964519i $$-0.585047\pi$$
−0.822228 + 0.569159i $$0.807269\pi$$
$$312$$ 0 0
$$313$$ −5.18180 + 29.3874i −0.292893 + 1.66108i 0.382753 + 0.923851i $$0.374976\pi$$
−0.675646 + 0.737226i $$0.736135\pi$$
$$314$$ 3.42285 + 5.92855i 0.193163 + 0.334567i
$$315$$ 0 0
$$316$$ −2.06670 + 3.57964i −0.116261 + 0.201370i
$$317$$ 3.30671 + 2.77466i 0.185724 + 0.155841i 0.730909 0.682475i $$-0.239096\pi$$
−0.545186 + 0.838315i $$0.683541\pi$$
$$318$$ 0 0
$$319$$ −1.74716 9.90863i −0.0978221 0.554777i
$$320$$ −3.03195 + 2.54411i −0.169491 + 0.142220i
$$321$$ 0 0
$$322$$ 31.0501 11.3013i 1.73035 0.629797i
$$323$$ −36.4976 −2.03078
$$324$$ 0 0
$$325$$ −15.7983 −0.876332
$$326$$ 4.60894 1.67752i 0.255266 0.0929092i
$$327$$ 0 0
$$328$$ 11.2365 9.42853i 0.620431 0.520603i
$$329$$ 1.85083 + 10.4966i 0.102040 + 0.578696i
$$330$$ 0 0
$$331$$ −2.23601 1.87624i −0.122902 0.103127i 0.579265 0.815139i $$-0.303340\pi$$
−0.702167 + 0.712012i $$0.747784\pi$$
$$332$$ 2.82304 4.88965i 0.154935 0.268355i
$$333$$ 0 0
$$334$$ 5.87211 + 10.1708i 0.321308 + 0.556521i
$$335$$ 0.731788 4.15018i 0.0399819 0.226748i
$$336$$ 0 0
$$337$$ −13.5706 4.93929i −0.739236 0.269060i −0.0551671 0.998477i $$-0.517569\pi$$
−0.684069 + 0.729417i $$0.739791\pi$$
$$338$$ −2.62175 0.954241i −0.142605 0.0519038i
$$339$$ 0 0
$$340$$ 0.189540 1.07494i 0.0102793 0.0582966i
$$341$$ 2.69085 + 4.66069i 0.145718 + 0.252391i
$$342$$ 0 0
$$343$$ −2.69207 + 4.66280i −0.145358 + 0.251767i
$$344$$ −13.3122 11.1702i −0.717745 0.602259i
$$345$$ 0 0
$$346$$ −1.35591 7.68977i −0.0728944 0.413405i
$$347$$ −1.11386 + 0.934640i −0.0597952 + 0.0501741i −0.672195 0.740374i $$-0.734649\pi$$
0.612400 + 0.790548i $$0.290204\pi$$
$$348$$ 0 0
$$349$$ 25.9183 9.43350i 1.38738 0.504964i 0.462971 0.886374i $$-0.346784\pi$$
0.924406 + 0.381410i $$0.124561\pi$$
$$350$$ −21.7987 −1.16519
$$351$$ 0 0
$$352$$ −5.39599 −0.287607
$$353$$ −9.89695 + 3.60220i −0.526762 + 0.191726i −0.591692 0.806164i $$-0.701540\pi$$
0.0649301 + 0.997890i $$0.479318\pi$$
$$354$$ 0 0
$$355$$ 1.81521 1.52314i 0.0963412 0.0808399i
$$356$$ 1.11121 + 6.30200i 0.0588942 + 0.334006i
$$357$$ 0 0
$$358$$ −10.1250 8.49584i −0.535120 0.449019i
$$359$$ −7.35273 + 12.7353i −0.388062 + 0.672143i −0.992189 0.124745i $$-0.960189\pi$$
0.604127 + 0.796888i $$0.293522\pi$$
$$360$$ 0 0
$$361$$ −3.94104 6.82608i −0.207423 0.359267i
$$362$$ 5.16598 29.2977i 0.271518 1.53985i
$$363$$ 0 0
$$364$$ −3.79339 1.38068i −0.198827 0.0723673i
$$365$$ −0.652139 0.237359i −0.0341345 0.0124239i
$$366$$ 0 0
$$367$$ −3.70961 + 21.0382i −0.193640 + 1.09819i 0.720702 + 0.693245i $$0.243819\pi$$
−0.914342 + 0.404942i $$0.867292\pi$$
$$368$$ −11.5878 20.0706i −0.604053 1.04625i
$$369$$ 0 0
$$370$$ 0.926022 1.60392i 0.0481416 0.0833837i
$$371$$ 23.7331 + 19.9145i 1.23216 + 1.03391i
$$372$$ 0 0
$$373$$ 3.92871 + 22.2808i 0.203421 + 1.15366i 0.899905 + 0.436085i $$0.143635\pi$$
−0.696484 + 0.717572i $$0.745253\pi$$
$$374$$ −19.2725 + 16.1716i −0.996560 + 0.836213i
$$375$$ 0 0
$$376$$ 8.55690 3.11446i 0.441289 0.160616i
$$377$$ −11.9101 −0.613404
$$378$$ 0 0
$$379$$ −17.0743 −0.877047 −0.438523 0.898720i $$-0.644498\pi$$
−0.438523 + 0.898720i $$0.644498\pi$$
$$380$$ 0.755466 0.274967i 0.0387546 0.0141055i
$$381$$ 0 0
$$382$$ −14.4474 + 12.1228i −0.739195 + 0.620258i
$$383$$ −6.77082 38.3992i −0.345973 1.96211i −0.258891 0.965906i $$-0.583357\pi$$
−0.0870812 0.996201i $$-0.527754\pi$$
$$384$$ 0 0
$$385$$ 3.35844 + 2.81807i 0.171162 + 0.143622i
$$386$$ 15.0679 26.0984i 0.766936 1.32837i
$$387$$ 0 0
$$388$$ 1.75624 + 3.04190i 0.0891598 + 0.154429i
$$389$$ 1.77330 10.0569i 0.0899101 0.509905i −0.906279 0.422681i $$-0.861089\pi$$
0.996189 0.0872245i $$-0.0277997\pi$$
$$390$$ 0 0
$$391$$ 48.1357 + 17.5200i 2.43433 + 0.886022i
$$392$$ −15.5270 5.65136i −0.784231 0.285437i
$$393$$ 0 0
$$394$$ 2.01532 11.4294i 0.101530 0.575807i
$$395$$ −2.65690 4.60189i −0.133683 0.231546i
$$396$$ 0 0
$$397$$ 0.571452 0.989783i 0.0286803 0.0496758i −0.851329 0.524632i $$-0.824203\pi$$
0.880009 + 0.474956i $$0.157536\pi$$
$$398$$ −2.56445 2.15183i −0.128544 0.107861i
$$399$$ 0 0
$$400$$ 2.65493 + 15.0568i 0.132746 + 0.752841i
$$401$$ −15.7452 + 13.2118i −0.786280 + 0.659767i −0.944822 0.327585i $$-0.893765\pi$$
0.158542 + 0.987352i $$0.449321\pi$$
$$402$$ 0 0
$$403$$ 5.98633 2.17885i 0.298200 0.108536i
$$404$$ −0.722645 −0.0359530
$$405$$ 0 0
$$406$$ −16.4338 −0.815594
$$407$$ 8.42939 3.06805i 0.417830 0.152078i
$$408$$ 0 0
$$409$$ −6.22668 + 5.22481i −0.307890 + 0.258350i −0.783619 0.621242i $$-0.786629\pi$$
0.475730 + 0.879592i $$0.342184\pi$$
$$410$$ 0.484481 + 2.74763i 0.0239268 + 0.135696i
$$411$$ 0 0
$$412$$ 0.385315 + 0.323318i 0.0189831 + 0.0159287i
$$413$$ −5.23416 + 9.06583i −0.257556 + 0.446100i
$$414$$ 0 0
$$415$$ 3.62923 + 6.28602i 0.178152 + 0.308568i
$$416$$ −1.10917 + 6.29039i −0.0543813 + 0.308412i
$$417$$ 0 0
$$418$$ −17.4128 6.33775i −0.851689 0.309989i
$$419$$ −33.6207 12.2369i −1.64248 0.597814i −0.655010 0.755620i $$-0.727336\pi$$
−0.987470 + 0.157806i $$0.949558\pi$$
$$420$$ 0 0
$$421$$ −2.27807 + 12.9196i −0.111026 + 0.629661i 0.877615 + 0.479366i $$0.159133\pi$$
−0.988641 + 0.150295i $$0.951978\pi$$
$$422$$ −10.5128 18.2087i −0.511756 0.886387i
$$423$$ 0 0
$$424$$ 13.2344 22.9227i 0.642720 1.11322i
$$425$$ −25.8874 21.7221i −1.25572 1.05368i
$$426$$ 0 0
$$427$$ −4.83750 27.4348i −0.234103 1.32766i
$$428$$ −0.594831 + 0.499123i −0.0287523 + 0.0241260i
$$429$$ 0 0
$$430$$ 3.10607 1.13052i 0.149788 0.0545183i
$$431$$ 9.48411 0.456833 0.228417 0.973563i $$-0.426645\pi$$
0.228417 + 0.973563i $$0.426645\pi$$
$$432$$ 0 0
$$433$$ 17.6628 0.848820 0.424410 0.905470i $$-0.360481\pi$$
0.424410 + 0.905470i $$0.360481\pi$$
$$434$$ 8.26001 3.00640i 0.396493 0.144312i
$$435$$ 0 0
$$436$$ 3.06031 2.56790i 0.146562 0.122980i
$$437$$ 6.55163 + 37.1562i 0.313407 + 1.77742i
$$438$$ 0 0
$$439$$ −13.5326 11.3552i −0.645874 0.541952i 0.259942 0.965624i $$-0.416297\pi$$
−0.905816 + 0.423672i $$0.860741\pi$$
$$440$$ 1.87278 3.24376i 0.0892814 0.154640i
$$441$$ 0 0
$$442$$ 14.8905 + 25.7912i 0.708270 + 1.22676i
$$443$$ −2.25606 + 12.7947i −0.107188 + 0.607896i 0.883135 + 0.469119i $$0.155428\pi$$
−0.990324 + 0.138777i $$0.955683\pi$$
$$444$$ 0 0
$$445$$ −7.73055 2.81369i −0.366463 0.133382i
$$446$$ 4.47259 + 1.62789i 0.211783 + 0.0770828i
$$447$$ 0 0
$$448$$ −5.43717 + 30.8357i −0.256882 + 1.45685i
$$449$$ 2.31428 + 4.00846i 0.109218 + 0.189171i 0.915454 0.402424i $$-0.131832\pi$$
−0.806236 + 0.591594i $$0.798499\pi$$
$$450$$ 0 0
$$451$$ −6.75671 + 11.7030i −0.318161 + 0.551071i
$$452$$ 0.449123 + 0.376859i 0.0211250 + 0.0177260i
$$453$$ 0 0
$$454$$ 2.35756 + 13.3704i 0.110646 + 0.627504i
$$455$$ 3.97551 3.33585i 0.186375 0.156387i
$$456$$ 0 0
$$457$$ −19.3268 + 7.03439i −0.904070 + 0.329055i −0.751883 0.659297i $$-0.770854\pi$$
−0.152188 + 0.988352i $$0.548632\pi$$
$$458$$ −17.3878 −0.812477
$$459$$ 0 0
$$460$$ −1.12836 −0.0526098
$$461$$ 31.5478 11.4825i 1.46933 0.534791i 0.521410 0.853307i $$-0.325406\pi$$
0.947918 + 0.318515i $$0.103184\pi$$
$$462$$ 0 0
$$463$$ 10.0590 8.44047i 0.467480 0.392262i −0.378395 0.925644i $$-0.623524\pi$$
0.845874 + 0.533382i $$0.179079\pi$$
$$464$$ 2.00152 + 11.3512i 0.0929181 + 0.526965i
$$465$$ 0 0
$$466$$ −12.5077 10.4952i −0.579410 0.486183i
$$467$$ −11.8154 + 20.4648i −0.546750 + 0.946999i 0.451745 + 0.892147i $$0.350802\pi$$
−0.998495 + 0.0548513i $$0.982532\pi$$
$$468$$ 0 0
$$469$$ −16.6694 28.8722i −0.769720 1.33319i
$$470$$ −0.300767 + 1.70574i −0.0138734 + 0.0786798i
$$471$$ 0 0
$$472$$ 8.40420 + 3.05888i 0.386835 + 0.140796i
$$473$$ 15.0442 + 5.47565i 0.691734 + 0.251771i
$$474$$ 0 0
$$475$$ 4.32218 24.5123i 0.198315 1.12470i
$$476$$ −4.31753 7.47818i −0.197894 0.342762i
$$477$$ 0 0
$$478$$ −3.76130 + 6.51476i −0.172038 + 0.297978i
$$479$$ −4.50449 3.77972i −0.205815 0.172700i 0.534054 0.845451i $$-0.320668\pi$$
−0.739869 + 0.672751i $$0.765113\pi$$
$$480$$ 0 0
$$481$$ −1.84389 10.4572i −0.0840743 0.476809i
$$482$$ 8.41009 7.05690i 0.383069 0.321433i
$$483$$ 0 0
$$484$$ −1.06758 + 0.388568i −0.0485264 + 0.0176622i
$$485$$ −4.51557 −0.205041
$$486$$ 0 0
$$487$$ 38.7965 1.75804 0.879020 0.476786i $$-0.158198\pi$$
0.879020 + 0.476786i $$0.158198\pi$$
$$488$$ −22.3651 + 8.14022i −1.01242 + 0.368490i
$$489$$ 0 0
$$490$$ 2.40760 2.02022i 0.108764 0.0912642i
$$491$$ −6.52644 37.0133i −0.294534 1.67039i −0.669090 0.743181i $$-0.733316\pi$$
0.374557 0.927204i $$-0.377795\pi$$
$$492$$ 0 0
$$493$$ −19.5162 16.3760i −0.878965 0.737539i
$$494$$ −10.9675 + 18.9963i −0.493452 + 0.854684i
$$495$$ 0 0
$$496$$ −3.08260 5.33921i −0.138413 0.239738i
$$497$$ 3.25519 18.4611i 0.146015 0.828094i
$$498$$ 0 0
$$499$$ −31.7165 11.5439i −1.41982 0.516774i −0.485827 0.874055i $$-0.661482\pi$$
−0.933997 + 0.357281i $$0.883704\pi$$
$$500$$ 1.42804 + 0.519762i 0.0638637 + 0.0232445i
$$501$$ 0 0
$$502$$ 1.50862 8.55580i 0.0673329 0.381864i
$$503$$ 9.35597 + 16.2050i 0.417162 + 0.722546i 0.995653 0.0931429i $$-0.0296913\pi$$
−0.578491 + 0.815689i $$0.696358\pi$$
$$504$$ 0 0
$$505$$ 0.464508 0.804551i 0.0206703 0.0358020i
$$506$$ 19.9230 + 16.7173i 0.885684 + 0.743177i
$$507$$ 0 0
$$508$$ 0.161160 + 0.913982i 0.00715030 + 0.0405514i
$$509$$ 16.6754 13.9923i 0.739124 0.620198i −0.193478 0.981105i $$-0.561977\pi$$
0.932602 + 0.360906i $$0.117533\pi$$
$$510$$ 0 0
$$511$$ −5.15910 + 1.87776i −0.228225 + 0.0830672i
$$512$$ 25.4026 1.12265
$$513$$ 0 0
$$514$$ −4.73473 −0.208840
$$515$$ −0.607639 + 0.221162i −0.0267758 + 0.00974558i
$$516$$ 0 0
$$517$$ −6.42649 + 5.39246i −0.282637 + 0.237160i
$$518$$ −2.54422 14.4290i −0.111787 0.633975i
$$519$$ 0 0
$$520$$ −3.39646 2.84997i −0.148945 0.124979i
$$521$$ 3.23822 5.60876i 0.141869 0.245724i −0.786332 0.617805i $$-0.788022\pi$$
0.928200 + 0.372081i $$0.121356\pi$$
$$522$$ 0 0
$$523$$ 5.43629 + 9.41593i 0.237712 + 0.411730i 0.960057 0.279803i $$-0.0902691\pi$$
−0.722345 + 0.691533i $$0.756936\pi$$
$$524$$ −0.176090 + 0.998656i −0.00769253 + 0.0436265i
$$525$$ 0 0
$$526$$ 4.39470 + 1.59954i 0.191618 + 0.0697433i
$$527$$ 12.8051 + 4.66069i 0.557801 + 0.203023i
$$528$$ 0 0
$$529$$ 5.20140 29.4986i 0.226148 1.28255i
$$530$$ 2.51730 + 4.36009i 0.109344 + 0.189390i
$$531$$ 0 0
$$532$$ 3.18004 5.50800i 0.137872 0.238802i
$$533$$ 12.2539 + 10.2822i 0.530775 + 0.445373i
$$534$$ 0 0
$$535$$ −0.173343 0.983080i −0.00749429 0.0425022i
$$536$$ −21.8191 + 18.3084i −0.942442 + 0.790802i
$$537$$ 0 0
$$538$$ −8.56108 + 3.11598i −0.369094 + 0.134339i
$$539$$ 15.2226 0.655686
$$540$$ 0 0
$$541$$ 24.6459 1.05961 0.529805 0.848120i $$-0.322265\pi$$
0.529805 + 0.848120i $$0.322265\pi$$
$$542$$ −22.9529 + 8.35416i −0.985910 + 0.358842i
$$543$$ 0 0
$$544$$ −10.4666 + 8.78249i −0.448750 + 0.376546i
$$545$$ 0.891823 + 5.05778i 0.0382015 + 0.216652i
$$546$$ 0 0
$$547$$ 23.6917 + 19.8797i 1.01298 + 0.849993i 0.988729 0.149713i $$-0.0478350\pi$$
0.0242526 + 0.999706i $$0.492279\pi$$
$$548$$ 0.808718 1.40074i 0.0345467 0.0598367i
$$549$$ 0 0
$$550$$ −8.57873 14.8588i −0.365798 0.633581i
$$551$$ 3.25844 18.4795i 0.138814 0.787254i
$$552$$ 0 0
$$553$$ −39.5026 14.3778i −1.67982 0.611405i
$$554$$ −16.7824 6.10829i −0.713015 0.259516i
$$555$$ 0 0
$$556$$ 0.482621 2.73708i 0.0204677 0.116078i
$$557$$ −11.6813 20.2327i −0.494954 0.857286i 0.505029 0.863102i $$-0.331482\pi$$
−0.999983 + 0.00581674i $$0.998148\pi$$
$$558$$ 0 0
$$559$$ 9.47565 16.4123i 0.400777 0.694167i
$$560$$ −3.84737 3.22833i −0.162581 0.136422i
$$561$$ 0 0
$$562$$ −4.93969 28.0144i −0.208368 1.18172i
$$563$$ 25.8063 21.6540i 1.08761 0.912609i 0.0910754 0.995844i $$-0.470970\pi$$
0.996530 + 0.0832347i $$0.0265251\pi$$
$$564$$ 0 0
$$565$$ −0.708263 + 0.257787i −0.0297969 + 0.0108452i
$$566$$ 30.5097 1.28242
$$567$$ 0 0
$$568$$ −16.0155 −0.671995
$$569$$ 28.9386 10.5328i 1.21317 0.441558i 0.345368 0.938467i $$-0.387754\pi$$
0.867803 + 0.496909i $$0.165532\pi$$
$$570$$ 0 0
$$571$$ −22.8858 + 19.2035i −0.957740 + 0.803639i −0.980584 0.196100i $$-0.937172\pi$$
0.0228438 + 0.999739i $$0.492728\pi$$
$$572$$ −0.551740 3.12907i −0.0230694 0.130833i
$$573$$ 0 0
$$574$$ 16.9081 + 14.1876i 0.705729 + 0.592177i
$$575$$ −17.4670 + 30.2538i −0.728425 + 1.26167i
$$576$$ 0 0
$$577$$ −2.40373 4.16339i −0.100069 0.173324i 0.811644 0.584152i $$-0.198573\pi$$
−0.911713 + 0.410828i $$0.865240\pi$$
$$578$$ −7.26698 + 41.2131i −0.302266 + 1.71424i
$$579$$ 0 0
$$580$$ 0.527341 + 0.191936i 0.0218966 + 0.00796973i
$$581$$ 53.9591 + 19.6395i 2.23860 + 0.814784i
$$582$$ 0 0
$$583$$ −4.23442 + 24.0146i −0.175372 + 0.994583i
$$584$$ 2.34527 + 4.06212i 0.0970478 + 0.168092i
$$585$$ 0 0
$$586$$ 11.9598 20.7149i 0.494053 0.855725i
$$587$$ 6.08056 + 5.10220i 0.250972 + 0.210590i 0.759591 0.650402i $$-0.225399\pi$$
−0.508619 + 0.860992i $$0.669844\pi$$
$$588$$ 0 0
$$589$$ 1.74288 + 9.88435i 0.0718141 + 0.407278i
$$590$$ −1.30315 + 1.09347i −0.0536498 + 0.0450176i
$$591$$ 0 0
$$592$$ −9.65657 + 3.51471i −0.396883 + 0.144454i
$$593$$ 36.2753 1.48965 0.744824 0.667261i $$-0.232533\pi$$
0.744824 + 0.667261i $$0.232533\pi$$
$$594$$ 0 0
$$595$$ 11.1010 0.455097
$$596$$ −6.59613 + 2.40080i −0.270188 + 0.0983405i
$$597$$ 0 0
$$598$$ 23.5835 19.7889i 0.964402 0.809230i
$$599$$ 5.84240 + 33.1339i 0.238714 + 1.35381i 0.834650 + 0.550781i $$0.185670\pi$$
−0.595936 + 0.803032i $$0.703219\pi$$
$$600$$ 0 0
$$601$$ −2.28106 1.91404i −0.0930463 0.0780752i 0.595078 0.803668i $$-0.297121\pi$$
−0.688124 + 0.725593i $$0.741566\pi$$
$$602$$ 13.0746 22.6459i 0.532882 0.922978i
$$603$$ 0 0
$$604$$ 1.16385 + 2.01584i 0.0473563 + 0.0820235i
$$605$$ 0.253620 1.43835i 0.0103111 0.0584772i
$$606$$ 0 0
$$607$$ 14.7049 + 5.35213i 0.596852 + 0.217236i 0.622740 0.782429i $$-0.286019\pi$$
−0.0258885 + 0.999665i $$0.508242\pi$$
$$608$$ −9.45658 3.44191i −0.383515 0.139588i
$$609$$ 0 0
$$610$$ 0.786112 4.45826i 0.0318287 0.180510i
$$611$$ 4.96529 + 8.60014i 0.200874 + 0.347924i
$$612$$ 0 0
$$613$$ 0.533433 0.923933i 0.0215452 0.0373173i −0.855052 0.518543i $$-0.826475\pi$$
0.876597 + 0.481225i $$0.159808\pi$$
$$614$$ −20.4317 17.1442i −0.824557 0.691886i
$$615$$ 0 0
$$616$$ −5.14543 29.1812i −0.207315 1.17574i
$$617$$ −10.0122 + 8.40121i −0.403075 + 0.338220i −0.821681 0.569948i $$-0.806963\pi$$
0.418606 + 0.908168i $$0.362519\pi$$
$$618$$ 0 0
$$619$$ −19.2802 + 7.01741i −0.774936 + 0.282054i −0.699059 0.715064i $$-0.746398\pi$$
−0.0758765 + 0.997117i $$0.524175\pi$$
$$620$$ −0.300167 −0.0120550
$$621$$ 0 0
$$622$$ −26.2071 −1.05081
$$623$$ −61.1568 + 22.2592i −2.45019 + 0.891798i
$$624$$ 0 0
$$625$$ 16.8910 14.1732i 0.675640 0.566929i
$$626$$ 6.66159 + 37.7798i 0.266251 + 1.50998i
$$627$$ 0 0
$$628$$ −1.41669 1.18874i −0.0565320 0.0474360i
$$629$$ 11.3569 19.6707i 0.452829 0.784323i
$$630$$ 0 0
$$631$$ 5.15611 + 8.93064i 0.205261 + 0.355523i 0.950216 0.311592i $$-0.100862\pi$$
−0.744955 + 0.667115i $$0.767529\pi$$
$$632$$ −6.23654 + 35.3692i −0.248076 + 1.40691i
$$633$$ 0 0
$$634$$ 5.21466 + 1.89798i 0.207101 + 0.0753785i
$$635$$ −1.12116 0.408071i −0.0444921 0.0161938i
$$636$$ 0 0
$$637$$ 3.12907 17.7458i 0.123978 0.703116i
$$638$$ −6.46740 11.2019i −0.256047 0.443486i
$$639$$ 0 0
$$640$$ −1.67752 + 2.90555i −0.0663097 + 0.114852i
$$641$$ 2.68588 + 2.25372i 0.106086 + 0.0890165i 0.694288 0.719698i $$-0.255720\pi$$
−0.588202 + 0.808714i $$0.700164\pi$$
$$642$$ 0 0
$$643$$ 5.47889 + 31.0723i 0.216066 + 1.22537i 0.879046 + 0.476736i $$0.158180\pi$$
−0.662980 + 0.748637i $$0.730708\pi$$
$$644$$ −6.83807 + 5.73783i −0.269458 + 0.226102i
$$645$$ 0 0
$$646$$ −44.0908 + 16.0477i −1.73473 + 0.631390i
$$647$$ −3.04628 −0.119762 −0.0598808 0.998206i $$-0.519072\pi$$
−0.0598808 + 0.998206i $$0.519072\pi$$
$$648$$ 0 0
$$649$$ −8.23947 −0.323428
$$650$$ −19.0851 + 6.94639i −0.748578 + 0.272460i
$$651$$ 0 0
$$652$$ −1.01501 + 0.851698i −0.0397510 + 0.0333551i
$$653$$ −5.33749 30.2704i −0.208872 1.18457i −0.891229 0.453553i $$-0.850156\pi$$
0.682357 0.731019i $$-0.260955\pi$$
$$654$$ 0 0
$$655$$ −0.998656 0.837972i −0.0390207 0.0327423i
$$656$$ 7.74038 13.4067i 0.302211 0.523445i
$$657$$ 0 0
$$658$$ 6.85117 + 11.8666i 0.267086 + 0.462607i
$$659$$ −5.76233 + 32.6798i −0.224469 + 1.27302i 0.639230 + 0.769016i $$0.279253\pi$$
−0.863699 + 0.504009i $$0.831858\pi$$
$$660$$ 0 0
$$661$$ 14.0086 + 5.09872i 0.544872 + 0.198317i 0.599767 0.800175i $$-0.295260\pi$$
−0.0548946 + 0.998492i $$0.517482\pi$$
$$662$$ −3.52618 1.28342i −0.137049 0.0498817i
$$663$$ 0 0
$$664$$ 8.51889 48.3130i 0.330597 1.87491i
$$665$$ 4.08819 + 7.08095i 0.158533 + 0.274587i
$$666$$ 0 0
$$667$$ −13.1682 + 22.8080i −0.509874 + 0.883128i
$$668$$ −2.43042 2.03936i −0.0940357 0.0789053i
$$669$$ 0 0
$$670$$ −0.940769 5.33537i −0.0363451 0.206123i
$$671$$ 16.7968 14.0942i 0.648434 0.544101i
$$672$$ 0 0
$$673$$ −6.47343 + 2.35614i −0.249532 + 0.0908224i −0.463758 0.885962i $$-0.653499\pi$$
0.214226 + 0.976784i $$0.431277\pi$$
$$674$$ −18.5656 −0.715122
$$675$$ 0 0
$$676$$ 0.753718 0.0289892
$$677$$ 12.3938 4.51098i 0.476333 0.173371i −0.0926859 0.995695i $$-0.529545\pi$$
0.569019 + 0.822324i $$0.307323\pi$$
$$678$$ 0 0
$$679$$ −27.3653 + 22.9622i −1.05018 + 0.881209i
$$680$$ −1.64690 9.34002i −0.0631557 0.358174i
$$681$$ 0 0
$$682$$ 5.29994 + 4.44718i 0.202945 + 0.170291i
$$683$$ 1.68907 2.92556i 0.0646305 0.111943i −0.831900 0.554926i $$-0.812746\pi$$
0.896530 + 0.442983i $$0.146080\pi$$
$$684$$ 0 0
$$685$$ 1.03967 + 1.80076i 0.0397237 + 0.0688034i
$$686$$ −1.20194 + 6.81655i −0.0458904 + 0.260257i
$$687$$ 0 0
$$688$$ −17.2344 6.27282i −0.657056 0.239149i
$$689$$ 27.1247 + 9.87258i 1.03337 + 0.376115i
$$690$$ 0 0
$$691$$ 4.06599 23.0594i 0.154678 0.877220i −0.804403 0.594085i $$-0.797514\pi$$
0.959080 0.283135i $$-0.0913745\pi$$
$$692$$ 1.05471 + 1.82682i 0.0400942 + 0.0694452i
$$693$$ 0 0
$$694$$ −0.934640 + 1.61884i −0.0354785 + 0.0614505i
$$695$$ 2.73708 + 2.29668i 0.103823 + 0.0871182i
$$696$$ 0 0
$$697$$ 5.94175 + 33.6974i 0.225060 + 1.27638i
$$698$$ 27.1627 22.7922i 1.02812 0.862698i
$$699$$ 0 0
$$700$$ 5.53374 2.01412i 0.209156 0.0761264i
$$701$$ 45.5001 1.71852 0.859258 0.511543i $$-0.170926\pi$$
0.859258 + 0.511543i $$0.170926\pi$$
$$702$$ 0 0
$$703$$ 16.7297 0.630972
$$704$$ −23.1585 + 8.42902i −0.872820 + 0.317680i
$$705$$ 0 0
$$706$$ −10.3721 + 8.70323i −0.390360 + 0.327551i
$$707$$ −1.27622 7.23783i −0.0479973 0.272206i
$$708$$ 0 0
$$709$$ 29.5822 + 24.8224i 1.11098 + 0.932225i 0.998114 0.0613851i $$-0.0195518\pi$$
0.112868 + 0.993610i $$0.463996\pi$$
$$710$$ 1.52314 2.63816i 0.0571624 0.0990082i
$$711$$ 0 0
$$712$$ 27.8011 + 48.1530i 1.04189 + 1.80461i
$$713$$ 2.44615 13.8728i 0.0916092 0.519541i
$$714$$ 0 0
$$715$$ 3.83837 + 1.39705i 0.143547 + 0.0522468i
$$716$$ 3.35527 + 1.22122i 0.125392 + 0.0456391i
$$717$$ 0 0
$$718$$ −3.28281 + 18.6178i −0.122514 + 0.694809i
$$719$$ 24.6591 + 42.7108i 0.919630 + 1.59285i 0.799978 + 0.600030i $$0.204845\pi$$
0.119652 + 0.992816i $$0.461822\pi$$
$$720$$ 0 0
$$721$$ −2.55778 + 4.43021i −0.0952567 + 0.164990i
$$722$$ −7.76233 6.51337i −0.288884 0.242402i
$$723$$ 0 0
$$724$$ 1.39558 + 7.91474i 0.0518664 + 0.294149i
$$725$$ 13.3095 11.1680i 0.494304 0.414770i
$$726$$ 0 0
$$727$$ 30.3469 11.0454i 1.12550 0.409650i 0.288846 0.957376i $$-0.406729\pi$$
0.836658 + 0.547726i $$0.184506\pi$$
$$728$$ −35.0757 −1.29999
$$729$$ 0 0
$$730$$ −0.892178 −0.0330210
$$731$$ 38.0933 13.8648i 1.40893 0.512810i
$$732$$ 0 0
$$733$$ 30.2328 25.3684i 1.11668 0.937002i 0.118243 0.992985i $$-0.462274\pi$$
0.998432 + 0.0559830i $$0.0178293\pi$$
$$734$$ 4.76898 + 27.0462i 0.176026 + 0.998294i
$$735$$ 0 0
$$736$$ 10.8198 + 9.07888i 0.398823 + 0.334652i
$$737$$ 13.1202 22.7249i 0.483290 0.837083i
$$738$$ 0 0
$$739$$ −17.6545 30.5785i −0.649432 1.12485i −0.983259 0.182215i $$-0.941673\pi$$
0.333827 0.942634i $$-0.391660\pi$$
$$740$$ −0.0868809 + 0.492726i −0.00319381 + 0.0181130i
$$741$$ 0 0
$$742$$ 37.4270 + 13.6223i 1.37399 + 0.500090i
$$743$$ 44.5514 + 16.2154i 1.63443 + 0.594884i 0.986053 0.166433i $$-0.0532251\pi$$
0.648379 + 0.761318i $$0.275447\pi$$
$$744$$ 0 0
$$745$$ 1.56701 8.88695i 0.0574108 0.325593i
$$746$$ 14.5428 + 25.1888i 0.532449 + 0.922228i
$$747$$ 0 0
$$748$$ 3.39827 5.88598i 0.124253 0.215213i
$$749$$ −6.04958 5.07620i −0.221047 0.185480i
$$750$$ 0 0
$$751$$ −1.55035 8.79244i −0.0565729 0.320841i 0.943368 0.331749i $$-0.107639\pi$$
−0.999941 + 0.0109084i $$0.996528\pi$$
$$752$$ 7.36208 6.17752i 0.268467 0.225271i
$$753$$ 0 0
$$754$$ −14.3880 + 5.23680i −0.523980 + 0.190713i
$$755$$ −2.99243 −0.108906
$$756$$ 0 0
$$757$$ −3.63816 −0.132231 −0.0661155 0.997812i $$-0.521061\pi$$
−0.0661155 + 0.997812i $$0.521061\pi$$
$$758$$ −20.6265 + 7.50744i −0.749189 + 0.272682i
$$759$$ 0 0
$$760$$ 5.35117 4.49016i 0.194107 0.162875i
$$761$$ −1.16150 6.58718i −0.0421043 0.238785i 0.956492 0.291760i $$-0.0942408\pi$$
−0.998596 + 0.0529748i $$0.983130\pi$$
$$762$$ 0 0
$$763$$ 31.1241 + 26.1162i 1.12677 + 0.945470i
$$764$$ 2.54747 4.41235i 0.0921643 0.159633i
$$765$$ 0 0
$$766$$ −25.0633 43.4109i −0.905574 1.56850i
$$767$$ −1.69365 + 9.60519i −0.0611543 + 0.346823i
$$768$$ 0 0
$$769$$ 20.1763 + 7.34359i 0.727577 + 0.264816i 0.679139 0.734010i $$-0.262353\pi$$
0.0484383 + 0.998826i $$0.484576\pi$$
$$770$$ 5.29623 + 1.92767i 0.190863 + 0.0694684i
$$771$$ 0 0
$$772$$ −1.41370 + 8.01747i −0.0508800 + 0.288555i
$$773$$ 5.12208 + 8.87170i 0.184228 + 0.319093i 0.943316 0.331895i $$-0.107688\pi$$
−0.759088 + 0.650988i $$0.774355\pi$$
$$774$$ 0 0
$$775$$ −4.64661 + 8.04817i −0.166911 + 0.289099i
$$776$$ 23.3794 + 19.6177i 0.839273 + 0.704234i
$$777$$ 0 0
$$778$$ −2.27972 12.9289i −0.0817317 0.463524i
$$779$$ −19.3062 + 16.1998i −0.691716 + 0.580418i
$$780$$ 0