# Properties

 Label 729.2.g.d.109.3 Level $729$ Weight $2$ Character 729.109 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 109.3 Character $$\chi$$ $$=$$ 729.109 Dual form 729.2.g.d.622.3

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-0.464338 - 0.492169i) q^{2} +(0.0896686 - 1.53955i) q^{4} +(-0.936797 + 0.109496i) q^{5} +(-1.30528 - 0.655538i) q^{7} +(-1.83603 + 1.54061i) q^{8} +O(q^{10})$$ $$q+(-0.464338 - 0.492169i) q^{2} +(0.0896686 - 1.53955i) q^{4} +(-0.936797 + 0.109496i) q^{5} +(-1.30528 - 0.655538i) q^{7} +(-1.83603 + 1.54061i) q^{8} +(0.488880 + 0.410219i) q^{10} +(2.42430 + 5.62016i) q^{11} +(-5.10531 - 1.20998i) q^{13} +(0.283457 + 0.946811i) q^{14} +(-1.45269 - 0.169795i) q^{16} +(-0.00536485 + 0.0304256i) q^{17} +(0.634963 + 3.60105i) q^{19} +(0.0845732 + 1.45207i) q^{20} +(1.64038 - 3.80282i) q^{22} +(0.0934269 - 0.0469207i) q^{23} +(-3.99963 + 0.947929i) q^{25} +(1.77507 + 3.07451i) q^{26} +(-1.12628 + 1.95077i) q^{28} +(-0.147045 + 0.491165i) q^{29} +(6.82537 + 4.48912i) q^{31} +(3.45346 + 4.63881i) q^{32} +(0.0174656 - 0.0114873i) q^{34} +(1.29456 + 0.471183i) q^{35} +(5.42328 - 1.97391i) q^{37} +(1.47749 - 1.98461i) q^{38} +(1.55129 - 1.64427i) q^{40} +(-3.00983 + 3.19024i) q^{41} +(0.822094 - 1.10426i) q^{43} +(8.86991 - 3.22838i) q^{44} +(-0.0664745 - 0.0241947i) q^{46} +(-4.68685 + 3.08259i) q^{47} +(-2.90608 - 3.90354i) q^{49} +(2.32372 + 1.52833i) q^{50} +(-2.32061 + 7.75138i) q^{52} +(-4.89106 + 8.47157i) q^{53} +(-2.88646 - 4.99950i) q^{55} +(3.40646 - 0.807346i) q^{56} +(0.310015 - 0.155695i) q^{58} +(-2.23761 + 5.18737i) q^{59} +(-0.0998805 - 1.71488i) q^{61} +(-0.959872 - 5.44370i) q^{62} +(0.171556 - 0.972942i) q^{64} +(4.91512 + 0.574495i) q^{65} +(-0.785171 - 2.62265i) q^{67} +(0.0463607 + 0.0109877i) q^{68} +(-0.369213 - 0.855932i) q^{70} +(1.66448 + 1.39666i) q^{71} +(-6.38204 + 5.35517i) q^{73} +(-3.48973 - 1.75261i) q^{74} +(5.60094 - 0.654656i) q^{76} +(0.519830 - 8.92513i) q^{77} +(8.65544 + 9.17423i) q^{79} +1.37947 q^{80} +2.96771 q^{82} +(-12.2319 - 12.9650i) q^{83} +(0.00169430 - 0.0290900i) q^{85} +(-0.925214 + 0.108142i) q^{86} +(-13.1096 - 6.58387i) q^{88} +(-10.6853 + 8.96604i) q^{89} +(5.87068 + 4.92609i) q^{91} +(-0.0638594 - 0.148043i) q^{92} +(3.69344 + 0.875361i) q^{94} +(-0.989131 - 3.30393i) q^{95} +(6.96396 + 0.813970i) q^{97} +(-0.571800 + 3.24284i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10})$$ 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 $$144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} + 45 q^{20} + 9 q^{22} - 45 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} + 36 q^{29} + 9 q^{31} - 99 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} + 18 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} - 99 q^{47} + 9 q^{49} + 126 q^{50} - 27 q^{52} + 45 q^{53} - 9 q^{55} - 225 q^{56} + 9 q^{58} + 72 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} - 81 q^{65} - 45 q^{67} + 117 q^{68} - 99 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} - 153 q^{76} + 81 q^{77} - 99 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} - 99 q^{85} + 81 q^{86} - 153 q^{88} - 81 q^{89} - 18 q^{91} + 207 q^{92} - 99 q^{94} - 171 q^{95} - 45 q^{97} + 81 q^{98}+O(q^{100})$$ 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 + 45 * q^20 + 9 * q^22 - 45 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 + 36 * q^29 + 9 * q^31 - 99 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 + 18 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 - 99 * q^47 + 9 * q^49 + 126 * q^50 - 27 * q^52 + 45 * q^53 - 9 * q^55 - 225 * q^56 + 9 * q^58 + 72 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 - 81 * q^65 - 45 * q^67 + 117 * q^68 - 99 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 - 153 * q^76 + 81 * q^77 - 99 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 - 99 * q^85 + 81 * q^86 - 153 * q^88 - 81 * q^89 - 18 * q^91 + 207 * q^92 - 99 * q^94 - 171 * q^95 - 45 * q^97 + 81 * q^98

## Character values

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

 $$n$$ $$2$$ $$\chi(n)$$ $$e\left(\frac{7}{27}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.464338 0.492169i −0.328336 0.348016i 0.542085 0.840324i $$-0.317635\pi$$
−0.870421 + 0.492308i $$0.836154\pi$$
$$3$$ 0 0
$$4$$ 0.0896686 1.53955i 0.0448343 0.769776i
$$5$$ −0.936797 + 0.109496i −0.418948 + 0.0489680i −0.322956 0.946414i $$-0.604677\pi$$
−0.0959924 + 0.995382i $$0.530602\pi$$
$$6$$ 0 0
$$7$$ −1.30528 0.655538i −0.493351 0.247770i 0.184687 0.982797i $$-0.440873\pi$$
−0.678037 + 0.735027i $$0.737169\pi$$
$$8$$ −1.83603 + 1.54061i −0.649133 + 0.544688i
$$9$$ 0 0
$$10$$ 0.488880 + 0.410219i 0.154598 + 0.129723i
$$11$$ 2.42430 + 5.62016i 0.730955 + 1.69454i 0.719387 + 0.694610i $$0.244423\pi$$
0.0115680 + 0.999933i $$0.496318\pi$$
$$12$$ 0 0
$$13$$ −5.10531 1.20998i −1.41596 0.335588i −0.549773 0.835314i $$-0.685286\pi$$
−0.866184 + 0.499726i $$0.833434\pi$$
$$14$$ 0.283457 + 0.946811i 0.0757570 + 0.253046i
$$15$$ 0 0
$$16$$ −1.45269 0.169795i −0.363172 0.0424488i
$$17$$ −0.00536485 + 0.0304256i −0.00130117 + 0.00737929i −0.985451 0.169957i $$-0.945637\pi$$
0.984150 + 0.177337i $$0.0567481\pi$$
$$18$$ 0 0
$$19$$ 0.634963 + 3.60105i 0.145670 + 0.826138i 0.966826 + 0.255434i $$0.0822184\pi$$
−0.821156 + 0.570704i $$0.806670\pi$$
$$20$$ 0.0845732 + 1.45207i 0.0189111 + 0.324692i
$$21$$ 0 0
$$22$$ 1.64038 3.80282i 0.349729 0.810764i
$$23$$ 0.0934269 0.0469207i 0.0194808 0.00978365i −0.439032 0.898471i $$-0.644679\pi$$
0.458513 + 0.888688i $$0.348382\pi$$
$$24$$ 0 0
$$25$$ −3.99963 + 0.947929i −0.799925 + 0.189586i
$$26$$ 1.77507 + 3.07451i 0.348120 + 0.602961i
$$27$$ 0 0
$$28$$ −1.12628 + 1.95077i −0.212846 + 0.368661i
$$29$$ −0.147045 + 0.491165i −0.0273056 + 0.0912071i −0.970556 0.240875i $$-0.922566\pi$$
0.943251 + 0.332082i $$0.107751\pi$$
$$30$$ 0 0
$$31$$ 6.82537 + 4.48912i 1.22587 + 0.806269i 0.986357 0.164623i $$-0.0526407\pi$$
0.239517 + 0.970892i $$0.423011\pi$$
$$32$$ 3.45346 + 4.63881i 0.610492 + 0.820033i
$$33$$ 0 0
$$34$$ 0.0174656 0.0114873i 0.00299533 0.00197006i
$$35$$ 1.29456 + 0.471183i 0.218821 + 0.0796444i
$$36$$ 0 0
$$37$$ 5.42328 1.97391i 0.891581 0.324509i 0.144707 0.989475i $$-0.453776\pi$$
0.746874 + 0.664965i $$0.231554\pi$$
$$38$$ 1.47749 1.98461i 0.239680 0.321947i
$$39$$ 0 0
$$40$$ 1.55129 1.64427i 0.245281 0.259983i
$$41$$ −3.00983 + 3.19024i −0.470057 + 0.498231i −0.918413 0.395624i $$-0.870528\pi$$
0.448356 + 0.893855i $$0.352010\pi$$
$$42$$ 0 0
$$43$$ 0.822094 1.10426i 0.125368 0.168399i −0.735008 0.678059i $$-0.762821\pi$$
0.860376 + 0.509660i $$0.170229\pi$$
$$44$$ 8.86991 3.22838i 1.33719 0.486697i
$$45$$ 0 0
$$46$$ −0.0664745 0.0241947i −0.00980113 0.00356732i
$$47$$ −4.68685 + 3.08259i −0.683648 + 0.449642i −0.843237 0.537541i $$-0.819353\pi$$
0.159590 + 0.987183i $$0.448983\pi$$
$$48$$ 0 0
$$49$$ −2.90608 3.90354i −0.415154 0.557648i
$$50$$ 2.32372 + 1.52833i 0.328623 + 0.216139i
$$51$$ 0 0
$$52$$ −2.32061 + 7.75138i −0.321811 + 1.07492i
$$53$$ −4.89106 + 8.47157i −0.671839 + 1.16366i 0.305543 + 0.952178i $$0.401162\pi$$
−0.977382 + 0.211481i $$0.932171\pi$$
$$54$$ 0 0
$$55$$ −2.88646 4.99950i −0.389211 0.674132i
$$56$$ 3.40646 0.807346i 0.455208 0.107886i
$$57$$ 0 0
$$58$$ 0.310015 0.155695i 0.0407070 0.0204438i
$$59$$ −2.23761 + 5.18737i −0.291313 + 0.675339i −0.999530 0.0306559i $$-0.990240\pi$$
0.708217 + 0.705994i $$0.249500\pi$$
$$60$$ 0 0
$$61$$ −0.0998805 1.71488i −0.0127884 0.219568i −0.998648 0.0519919i $$-0.983443\pi$$
0.985859 0.167576i $$-0.0535940\pi$$
$$62$$ −0.959872 5.44370i −0.121904 0.691351i
$$63$$ 0 0
$$64$$ 0.171556 0.972942i 0.0214445 0.121618i
$$65$$ 4.91512 + 0.574495i 0.609646 + 0.0712574i
$$66$$ 0 0
$$67$$ −0.785171 2.62265i −0.0959239 0.320408i 0.896537 0.442969i $$-0.146075\pi$$
−0.992461 + 0.122560i $$0.960889\pi$$
$$68$$ 0.0463607 + 0.0109877i 0.00562206 + 0.00133245i
$$69$$ 0 0
$$70$$ −0.369213 0.855932i −0.0441294 0.102303i
$$71$$ 1.66448 + 1.39666i 0.197537 + 0.165753i 0.736191 0.676774i $$-0.236623\pi$$
−0.538654 + 0.842527i $$0.681067\pi$$
$$72$$ 0 0
$$73$$ −6.38204 + 5.35517i −0.746961 + 0.626775i −0.934697 0.355445i $$-0.884329\pi$$
0.187736 + 0.982219i $$0.439885\pi$$
$$74$$ −3.48973 1.75261i −0.405673 0.203737i
$$75$$ 0 0
$$76$$ 5.60094 0.654656i 0.642472 0.0750942i
$$77$$ 0.519830 8.92513i 0.0592401 1.01711i
$$78$$ 0 0
$$79$$ 8.65544 + 9.17423i 0.973813 + 1.03218i 0.999471 + 0.0325105i $$0.0103502\pi$$
−0.0256586 + 0.999671i $$0.508168\pi$$
$$80$$ 1.37947 0.154229
$$81$$ 0 0
$$82$$ 2.96771 0.327729
$$83$$ −12.2319 12.9650i −1.34262 1.42310i −0.822216 0.569176i $$-0.807262\pi$$
−0.520406 0.853919i $$-0.674219\pi$$
$$84$$ 0 0
$$85$$ 0.00169430 0.0290900i 0.000183773 0.00315526i
$$86$$ −0.925214 + 0.108142i −0.0997683 + 0.0116612i
$$87$$ 0 0
$$88$$ −13.1096 6.58387i −1.39748 0.701843i
$$89$$ −10.6853 + 8.96604i −1.13264 + 0.950399i −0.999173 0.0406545i $$-0.987056\pi$$
−0.133468 + 0.991053i $$0.542611\pi$$
$$90$$ 0 0
$$91$$ 5.87068 + 4.92609i 0.615415 + 0.516394i
$$92$$ −0.0638594 0.148043i −0.00665780 0.0154345i
$$93$$ 0 0
$$94$$ 3.69344 + 0.875361i 0.380949 + 0.0902865i
$$95$$ −0.989131 3.30393i −0.101483 0.338976i
$$96$$ 0 0
$$97$$ 6.96396 + 0.813970i 0.707083 + 0.0826461i 0.462031 0.886864i $$-0.347121\pi$$
0.245052 + 0.969510i $$0.421195\pi$$
$$98$$ −0.571800 + 3.24284i −0.0577605 + 0.327576i
$$99$$ 0 0
$$100$$ 1.10074 + 6.24263i 0.110074 + 0.624263i
$$101$$ 0.505324 + 8.67608i 0.0502816 + 0.863302i 0.925306 + 0.379222i $$0.123808\pi$$
−0.875024 + 0.484080i $$0.839154\pi$$
$$102$$ 0 0
$$103$$ −2.03098 + 4.70833i −0.200118 + 0.463926i −0.988492 0.151270i $$-0.951664\pi$$
0.788374 + 0.615196i $$0.210923\pi$$
$$104$$ 11.2376 5.64373i 1.10194 0.553413i
$$105$$ 0 0
$$106$$ 6.44055 1.52644i 0.625561 0.148261i
$$107$$ −4.97642 8.61941i −0.481089 0.833270i 0.518676 0.854971i $$-0.326425\pi$$
−0.999765 + 0.0217011i $$0.993092\pi$$
$$108$$ 0 0
$$109$$ 6.36856 11.0307i 0.609997 1.05655i −0.381243 0.924475i $$-0.624504\pi$$
0.991240 0.132071i $$-0.0421627\pi$$
$$110$$ −1.12031 + 3.74208i −0.106817 + 0.356794i
$$111$$ 0 0
$$112$$ 1.78486 + 1.17392i 0.168654 + 0.110925i
$$113$$ 3.43180 + 4.60971i 0.322837 + 0.433645i 0.933681 0.358106i $$-0.116577\pi$$
−0.610844 + 0.791751i $$0.709170\pi$$
$$114$$ 0 0
$$115$$ −0.0823844 + 0.0541850i −0.00768238 + 0.00505278i
$$116$$ 0.742989 + 0.270426i 0.0689848 + 0.0251084i
$$117$$ 0 0
$$118$$ 3.59207 1.30741i 0.330677 0.120357i
$$119$$ 0.0269478 0.0361972i 0.00247030 0.00331819i
$$120$$ 0 0
$$121$$ −18.1603 + 19.2488i −1.65094 + 1.74989i
$$122$$ −0.797633 + 0.845442i −0.0722143 + 0.0765427i
$$123$$ 0 0
$$124$$ 7.52325 10.1055i 0.675608 0.907499i
$$125$$ 8.07451 2.93888i 0.722206 0.262862i
$$126$$ 0 0
$$127$$ −9.96192 3.62584i −0.883977 0.321741i −0.140163 0.990128i $$-0.544763\pi$$
−0.743814 + 0.668387i $$0.766985\pi$$
$$128$$ 9.10501 5.98846i 0.804777 0.529310i
$$129$$ 0 0
$$130$$ −1.99953 2.68583i −0.175370 0.235563i
$$131$$ −11.9172 7.83807i −1.04121 0.684815i −0.0908184 0.995867i $$-0.528948\pi$$
−0.950393 + 0.311052i $$0.899319\pi$$
$$132$$ 0 0
$$133$$ 1.53182 5.11664i 0.132826 0.443669i
$$134$$ −0.926205 + 1.60423i −0.0800119 + 0.138585i
$$135$$ 0 0
$$136$$ −0.0370239 0.0641273i −0.00317478 0.00549887i
$$137$$ 5.19234 1.23061i 0.443612 0.105138i −0.00273858 0.999996i $$-0.500872\pi$$
0.446350 + 0.894858i $$0.352724\pi$$
$$138$$ 0 0
$$139$$ −3.65867 + 1.83745i −0.310324 + 0.155851i −0.597144 0.802134i $$-0.703698\pi$$
0.286820 + 0.957984i $$0.407402\pi$$
$$140$$ 0.841492 1.95080i 0.0711190 0.164872i
$$141$$ 0 0
$$142$$ −0.0854853 1.46773i −0.00717376 0.123169i
$$143$$ −5.57652 31.6260i −0.466332 2.64470i
$$144$$ 0 0
$$145$$ 0.0839709 0.476223i 0.00697341 0.0395482i
$$146$$ 5.59907 + 0.654437i 0.463382 + 0.0541616i
$$147$$ 0 0
$$148$$ −2.55264 8.52641i −0.209826 0.700867i
$$149$$ −18.3677 4.35323i −1.50474 0.356630i −0.606127 0.795368i $$-0.707278\pi$$
−0.898615 + 0.438738i $$0.855426\pi$$
$$150$$ 0 0
$$151$$ −1.22010 2.82850i −0.0992901 0.230180i 0.861330 0.508046i $$-0.169632\pi$$
−0.960620 + 0.277866i $$0.910373\pi$$
$$152$$ −6.71362 5.63340i −0.544547 0.456929i
$$153$$ 0 0
$$154$$ −4.63405 + 3.88843i −0.373422 + 0.313338i
$$155$$ −6.88553 3.45804i −0.553059 0.277757i
$$156$$ 0 0
$$157$$ 3.40543 0.398037i 0.271783 0.0317668i 0.0208901 0.999782i $$-0.493350\pi$$
0.250893 + 0.968015i $$0.419276\pi$$
$$158$$ 0.496226 8.51988i 0.0394776 0.677805i
$$159$$ 0 0
$$160$$ −3.74312 3.96748i −0.295920 0.313657i
$$161$$ −0.152707 −0.0120350
$$162$$ 0 0
$$163$$ −19.7151 −1.54420 −0.772101 0.635500i $$-0.780794\pi$$
−0.772101 + 0.635500i $$0.780794\pi$$
$$164$$ 4.64165 + 4.91986i 0.362452 + 0.384176i
$$165$$ 0 0
$$166$$ −0.701267 + 12.0403i −0.0544289 + 0.934507i
$$167$$ 19.2117 2.24553i 1.48665 0.173764i 0.666324 0.745663i $$-0.267867\pi$$
0.820324 + 0.571898i $$0.193793\pi$$
$$168$$ 0 0
$$169$$ 12.9829 + 6.52024i 0.998682 + 0.501557i
$$170$$ −0.0151039 + 0.0126737i −0.00115842 + 0.000972029i
$$171$$ 0 0
$$172$$ −1.62635 1.36467i −0.124008 0.104055i
$$173$$ −2.44275 5.66294i −0.185719 0.430545i 0.799765 0.600313i $$-0.204957\pi$$
−0.985484 + 0.169768i $$0.945698\pi$$
$$174$$ 0 0
$$175$$ 5.84205 + 1.38459i 0.441617 + 0.104665i
$$176$$ −2.56748 8.57599i −0.193531 0.646439i
$$177$$ 0 0
$$178$$ 9.37440 + 1.09571i 0.702641 + 0.0821270i
$$179$$ −0.601129 + 3.40917i −0.0449305 + 0.254814i −0.998997 0.0447821i $$-0.985741\pi$$
0.954066 + 0.299596i $$0.0968518\pi$$
$$180$$ 0 0
$$181$$ −3.31327 18.7905i −0.246273 1.39668i −0.817517 0.575904i $$-0.804650\pi$$
0.571244 0.820780i $$-0.306461\pi$$
$$182$$ −0.301511 5.17674i −0.0223494 0.383725i
$$183$$ 0 0
$$184$$ −0.0992477 + 0.230082i −0.00731664 + 0.0169619i
$$185$$ −4.86437 + 2.44298i −0.357636 + 0.179612i
$$186$$ 0 0
$$187$$ −0.184003 + 0.0436095i −0.0134556 + 0.00318904i
$$188$$ 4.32554 + 7.49206i 0.315473 + 0.546415i
$$189$$ 0 0
$$190$$ −1.16680 + 2.02096i −0.0846486 + 0.146616i
$$191$$ 5.71535 19.0906i 0.413548 1.38135i −0.457089 0.889421i $$-0.651108\pi$$
0.870637 0.491926i $$-0.163707\pi$$
$$192$$ 0 0
$$193$$ 8.95424 + 5.88930i 0.644540 + 0.423921i 0.829254 0.558871i $$-0.188765\pi$$
−0.184714 + 0.982792i $$0.559136\pi$$
$$194$$ −2.83302 3.80540i −0.203399 0.273212i
$$195$$ 0 0
$$196$$ −6.27028 + 4.12403i −0.447877 + 0.294573i
$$197$$ 22.2725 + 8.10651i 1.58685 + 0.577565i 0.976679 0.214707i $$-0.0688795\pi$$
0.610169 + 0.792272i $$0.291102\pi$$
$$198$$ 0 0
$$199$$ −8.20833 + 2.98759i −0.581873 + 0.211785i −0.616151 0.787628i $$-0.711309\pi$$
0.0342781 + 0.999412i $$0.489087\pi$$
$$200$$ 5.88303 7.90228i 0.415993 0.558776i
$$201$$ 0 0
$$202$$ 4.03546 4.27733i 0.283934 0.300952i
$$203$$ 0.513913 0.544716i 0.0360696 0.0382316i
$$204$$ 0 0
$$205$$ 2.47028 3.31817i 0.172532 0.231751i
$$206$$ 3.26035 1.18667i 0.227160 0.0826793i
$$207$$ 0 0
$$208$$ 7.21098 + 2.62458i 0.499991 + 0.181982i
$$209$$ −18.6992 + 12.2986i −1.29345 + 0.850714i
$$210$$ 0 0
$$211$$ −4.34616 5.83790i −0.299202 0.401898i 0.626943 0.779065i $$-0.284306\pi$$
−0.926145 + 0.377167i $$0.876898\pi$$
$$212$$ 12.6038 + 8.28968i 0.865635 + 0.569337i
$$213$$ 0 0
$$214$$ −1.93147 + 6.45155i −0.132032 + 0.441019i
$$215$$ −0.649223 + 1.12449i −0.0442766 + 0.0766894i
$$216$$ 0 0
$$217$$ −5.96626 10.3339i −0.405016 0.701508i
$$218$$ −8.38611 + 1.98754i −0.567979 + 0.134614i
$$219$$ 0 0
$$220$$ −7.95581 + 3.99556i −0.536381 + 0.269381i
$$221$$ 0.0642036 0.148841i 0.00431880 0.0100121i
$$222$$ 0 0
$$223$$ −0.0435199 0.747208i −0.00291431 0.0500367i 0.996537 0.0831449i $$-0.0264964\pi$$
−0.999452 + 0.0331082i $$0.989459\pi$$
$$224$$ −1.46684 8.31884i −0.0980071 0.555826i
$$225$$ 0 0
$$226$$ 0.675242 3.82949i 0.0449164 0.254734i
$$227$$ −7.55453 0.882998i −0.501412 0.0586067i −0.138372 0.990380i $$-0.544187\pi$$
−0.363040 + 0.931774i $$0.618261\pi$$
$$228$$ 0 0
$$229$$ 4.47466 + 14.9464i 0.295694 + 0.987686i 0.968739 + 0.248084i $$0.0798009\pi$$
−0.673045 + 0.739602i $$0.735014\pi$$
$$230$$ 0.0649224 + 0.0153869i 0.00428085 + 0.00101458i
$$231$$ 0 0
$$232$$ −0.486715 1.12833i −0.0319544 0.0740786i
$$233$$ −12.6227 10.5917i −0.826940 0.693885i 0.127647 0.991820i $$-0.459258\pi$$
−0.954586 + 0.297935i $$0.903702\pi$$
$$234$$ 0 0
$$235$$ 4.05310 3.40095i 0.264395 0.221854i
$$236$$ 7.78558 + 3.91007i 0.506798 + 0.254524i
$$237$$ 0 0
$$238$$ −0.0303280 + 0.00354483i −0.00196587 + 0.000229777i
$$239$$ −1.12492 + 19.3142i −0.0727653 + 1.24933i 0.742342 + 0.670021i $$0.233715\pi$$
−0.815107 + 0.579310i $$0.803322\pi$$
$$240$$ 0 0
$$241$$ −3.95611 4.19324i −0.254836 0.270110i 0.587308 0.809364i $$-0.300188\pi$$
−0.842143 + 0.539254i $$0.818706\pi$$
$$242$$ 17.9062 1.15105
$$243$$ 0 0
$$244$$ −2.64910 −0.169591
$$245$$ 3.14982 + 3.33862i 0.201235 + 0.213296i
$$246$$ 0 0
$$247$$ 1.11552 19.1528i 0.0709789 1.21866i
$$248$$ −19.4475 + 2.27309i −1.23492 + 0.144341i
$$249$$ 0 0
$$250$$ −5.19572 2.60939i −0.328607 0.165032i
$$251$$ −14.4752 + 12.1462i −0.913668 + 0.766659i −0.972813 0.231591i $$-0.925607\pi$$
0.0591449 + 0.998249i $$0.481163\pi$$
$$252$$ 0 0
$$253$$ 0.490197 + 0.411324i 0.0308184 + 0.0258597i
$$254$$ 2.84116 + 6.58656i 0.178271 + 0.413278i
$$255$$ 0 0
$$256$$ −9.09777 2.15621i −0.568611 0.134763i
$$257$$ 5.19708 + 17.3594i 0.324185 + 1.08285i 0.952410 + 0.304821i $$0.0985965\pi$$
−0.628225 + 0.778032i $$0.716218\pi$$
$$258$$ 0 0
$$259$$ −8.37289 0.978650i −0.520266 0.0608104i
$$260$$ 1.32520 7.51557i 0.0821853 0.466096i
$$261$$ 0 0
$$262$$ 1.67595 + 9.50479i 0.103541 + 0.587208i
$$263$$ −0.504066 8.65448i −0.0310821 0.533658i −0.977529 0.210800i $$-0.932393\pi$$
0.946447 0.322859i $$-0.104644\pi$$
$$264$$ 0 0
$$265$$ 3.65433 8.47169i 0.224484 0.520412i
$$266$$ −3.22953 + 1.62193i −0.198015 + 0.0994470i
$$267$$ 0 0
$$268$$ −4.10812 + 0.973641i −0.250943 + 0.0594746i
$$269$$ −5.59305 9.68745i −0.341014 0.590654i 0.643607 0.765356i $$-0.277437\pi$$
−0.984621 + 0.174702i $$0.944104\pi$$
$$270$$ 0 0
$$271$$ 5.08705 8.81103i 0.309016 0.535232i −0.669131 0.743144i $$-0.733334\pi$$
0.978147 + 0.207912i $$0.0666669\pi$$
$$272$$ 0.0129596 0.0432880i 0.000785790 0.00262472i
$$273$$ 0 0
$$274$$ −3.01667 1.98409i −0.182243 0.119863i
$$275$$ −15.0238 20.1805i −0.905970 1.21693i
$$276$$ 0 0
$$277$$ 1.08784 0.715482i 0.0653618 0.0429892i −0.516408 0.856343i $$-0.672731\pi$$
0.581769 + 0.813354i $$0.302361\pi$$
$$278$$ 2.60319 + 0.947485i 0.156129 + 0.0568264i
$$279$$ 0 0
$$280$$ −3.10276 + 1.12931i −0.185425 + 0.0674894i
$$281$$ −3.82768 + 5.14146i −0.228340 + 0.306714i −0.901497 0.432786i $$-0.857531\pi$$
0.673157 + 0.739500i $$0.264938\pi$$
$$282$$ 0 0
$$283$$ 13.1190 13.9053i 0.779842 0.826584i −0.208629 0.977995i $$-0.566900\pi$$
0.988471 + 0.151411i $$0.0483816\pi$$
$$284$$ 2.29948 2.43731i 0.136449 0.144628i
$$285$$ 0 0
$$286$$ −12.9760 + 17.4297i −0.767284 + 1.03064i
$$287$$ 6.02001 2.19110i 0.355350 0.129337i
$$288$$ 0 0
$$289$$ 15.9739 + 5.81402i 0.939640 + 0.342001i
$$290$$ −0.273373 + 0.179800i −0.0160530 + 0.0105582i
$$291$$ 0 0
$$292$$ 7.67228 + 10.3057i 0.448986 + 0.603093i
$$293$$ 1.52565 + 1.00344i 0.0891296 + 0.0586214i 0.593291 0.804988i $$-0.297828\pi$$
−0.504162 + 0.863609i $$0.668199\pi$$
$$294$$ 0 0
$$295$$ 1.52819 5.10452i 0.0889749 0.297197i
$$296$$ −6.91625 + 11.9793i −0.401999 + 0.696283i
$$297$$ 0 0
$$298$$ 6.38629 + 11.0614i 0.369948 + 0.640769i
$$299$$ −0.533746 + 0.126500i −0.0308673 + 0.00731569i
$$300$$ 0 0
$$301$$ −1.79695 + 0.902464i −0.103575 + 0.0520171i
$$302$$ −0.825565 + 1.91387i −0.0475059 + 0.110131i
$$303$$ 0 0
$$304$$ −0.310963 5.33903i −0.0178349 0.306214i
$$305$$ 0.281340 + 1.59556i 0.0161095 + 0.0913614i
$$306$$ 0 0
$$307$$ −2.60207 + 14.7571i −0.148508 + 0.842232i 0.815975 + 0.578087i $$0.196201\pi$$
−0.964483 + 0.264145i $$0.914910\pi$$
$$308$$ −13.6941 1.60061i −0.780293 0.0912031i
$$309$$ 0 0
$$310$$ 1.49527 + 4.99454i 0.0849255 + 0.283671i
$$311$$ 20.1029 + 4.76447i 1.13993 + 0.270168i 0.756876 0.653558i $$-0.226725\pi$$
0.383053 + 0.923726i $$0.374873\pi$$
$$312$$ 0 0
$$313$$ 8.84187 + 20.4977i 0.499772 + 1.15860i 0.962298 + 0.271996i $$0.0876837\pi$$
−0.462527 + 0.886605i $$0.653057\pi$$
$$314$$ −1.77717 1.49122i −0.100291 0.0841545i
$$315$$ 0 0
$$316$$ 14.9003 12.5028i 0.838208 0.703340i
$$317$$ 10.1518 + 5.09842i 0.570181 + 0.286356i 0.710438 0.703759i $$-0.248497\pi$$
−0.140257 + 0.990115i $$0.544793\pi$$
$$318$$ 0 0
$$319$$ −3.11691 + 0.364315i −0.174514 + 0.0203977i
$$320$$ −0.0541799 + 0.930234i −0.00302875 + 0.0520016i
$$321$$ 0 0
$$322$$ 0.0709075 + 0.0751576i 0.00395152 + 0.00418837i
$$323$$ −0.112971 −0.00628586
$$324$$ 0 0
$$325$$ 21.5663 1.19628
$$326$$ 9.15444 + 9.70314i 0.507017 + 0.537407i
$$327$$ 0 0
$$328$$ 0.611225 10.4943i 0.0337493 0.579453i
$$329$$ 8.13843 0.951245i 0.448686 0.0524439i
$$330$$ 0 0
$$331$$ 12.8748 + 6.46596i 0.707662 + 0.355401i 0.765951 0.642899i $$-0.222268\pi$$
−0.0582896 + 0.998300i $$0.518565\pi$$
$$332$$ −21.0571 + 17.6690i −1.15566 + 0.969714i
$$333$$ 0 0
$$334$$ −10.0259 8.41273i −0.548593 0.460324i
$$335$$ 1.02272 + 2.37092i 0.0558769 + 0.129537i
$$336$$ 0 0
$$337$$ −9.64054 2.28485i −0.525154 0.124464i −0.0405164 0.999179i $$-0.512900\pi$$
−0.484637 + 0.874715i $$0.661048\pi$$
$$338$$ −2.81937 9.41736i −0.153354 0.512237i
$$339$$ 0 0
$$340$$ −0.0446337 0.00521693i −0.00242060 0.000282928i
$$341$$ −8.68281 + 49.2427i −0.470201 + 2.66664i
$$342$$ 0 0
$$343$$ 3.00981 + 17.0695i 0.162514 + 0.921665i
$$344$$ 0.191853 + 3.29398i 0.0103440 + 0.177600i
$$345$$ 0 0
$$346$$ −1.65286 + 3.83176i −0.0888583 + 0.205997i
$$347$$ −3.01890 + 1.51615i −0.162063 + 0.0813912i −0.527982 0.849256i $$-0.677051\pi$$
0.365919 + 0.930647i $$0.380755\pi$$
$$348$$ 0 0
$$349$$ −1.29409 + 0.306704i −0.0692708 + 0.0164175i −0.265105 0.964220i $$-0.585407\pi$$
0.195834 + 0.980637i $$0.437259\pi$$
$$350$$ −2.03123 3.51819i −0.108574 0.188055i
$$351$$ 0 0
$$352$$ −17.6986 + 30.6549i −0.943340 + 1.63391i
$$353$$ −3.38243 + 11.2981i −0.180029 + 0.601338i 0.819569 + 0.572981i $$0.194213\pi$$
−0.999598 + 0.0283577i $$0.990972\pi$$
$$354$$ 0 0
$$355$$ −1.71220 1.12613i −0.0908744 0.0597690i
$$356$$ 12.8455 + 17.2546i 0.680812 + 0.914490i
$$357$$ 0 0
$$358$$ 1.95702 1.28715i 0.103432 0.0680280i
$$359$$ 27.9195 + 10.1619i 1.47353 + 0.536323i 0.949058 0.315102i $$-0.102039\pi$$
0.524477 + 0.851425i $$0.324261\pi$$
$$360$$ 0 0
$$361$$ 5.28976 1.92531i 0.278408 0.101332i
$$362$$ −7.70961 + 10.3558i −0.405208 + 0.544289i
$$363$$ 0 0
$$364$$ 8.11038 8.59650i 0.425100 0.450579i
$$365$$ 5.39230 5.71551i 0.282246 0.299163i
$$366$$ 0 0
$$367$$ −4.79340 + 6.43865i −0.250213 + 0.336095i −0.909429 0.415859i $$-0.863481\pi$$
0.659216 + 0.751954i $$0.270888\pi$$
$$368$$ −0.143687 + 0.0522978i −0.00749021 + 0.00272621i
$$369$$ 0 0
$$370$$ 3.46107 + 1.25973i 0.179933 + 0.0654901i
$$371$$ 11.9377 7.85152i 0.619772 0.407631i
$$372$$ 0 0
$$373$$ −1.78779 2.40142i −0.0925681 0.124341i 0.753426 0.657533i $$-0.228400\pi$$
−0.845994 + 0.533192i $$0.820992\pi$$
$$374$$ 0.106903 + 0.0703110i 0.00552781 + 0.00363570i
$$375$$ 0 0
$$376$$ 3.85612 12.8803i 0.198864 0.664252i
$$377$$ 1.34501 2.32963i 0.0692716 0.119982i
$$378$$ 0 0
$$379$$ 11.0537 + 19.1456i 0.567792 + 0.983444i 0.996784 + 0.0801362i $$0.0255355\pi$$
−0.428992 + 0.903308i $$0.641131\pi$$
$$380$$ −5.17526 + 1.22656i −0.265485 + 0.0629212i
$$381$$ 0 0
$$382$$ −12.0497 + 6.05156i −0.616514 + 0.309625i
$$383$$ 5.68677 13.1834i 0.290580 0.673641i −0.708919 0.705290i $$-0.750817\pi$$
0.999499 + 0.0316494i $$0.0100760\pi$$
$$384$$ 0 0
$$385$$ 0.490290 + 8.41795i 0.0249875 + 0.429018i
$$386$$ −1.25926 7.14162i −0.0640947 0.363499i
$$387$$ 0 0
$$388$$ 1.87760 10.6484i 0.0953206 0.540590i
$$389$$ 18.1068 + 2.11638i 0.918049 + 0.107305i 0.561976 0.827154i $$-0.310041\pi$$
0.356073 + 0.934458i $$0.384115\pi$$
$$390$$ 0 0
$$391$$ 0.000926370 0.00309429i 4.68485e−5 0.000156485i
$$392$$ 11.3495 + 2.68987i 0.573234 + 0.135859i
$$393$$ 0 0
$$394$$ −6.35216 14.7260i −0.320017 0.741884i
$$395$$ −9.11293 7.64665i −0.458521 0.384745i
$$396$$ 0 0
$$397$$ 1.06250 0.891545i 0.0533255 0.0447454i −0.615735 0.787953i $$-0.711141\pi$$
0.669061 + 0.743208i $$0.266697\pi$$
$$398$$ 5.28184 + 2.65264i 0.264754 + 0.132965i
$$399$$ 0 0
$$400$$ 5.97117 0.697930i 0.298558 0.0348965i
$$401$$ −1.28420 + 22.0489i −0.0641301 + 1.10107i 0.800719 + 0.599040i $$0.204451\pi$$
−0.864849 + 0.502031i $$0.832586\pi$$
$$402$$ 0 0
$$403$$ −29.4139 31.1769i −1.46521 1.55303i
$$404$$ 13.4026 0.666803
$$405$$ 0 0
$$406$$ −0.506722 −0.0251482
$$407$$ 24.2414 + 25.6944i 1.20160 + 1.27362i
$$408$$ 0 0
$$409$$ −0.0335717 + 0.576405i −0.00166002 + 0.0285014i −0.999036 0.0438882i $$-0.986025\pi$$
0.997376 + 0.0723896i $$0.0230625\pi$$
$$410$$ −2.78015 + 0.324952i −0.137302 + 0.0160483i
$$411$$ 0 0
$$412$$ 7.06660 + 3.54898i 0.348147 + 0.174846i
$$413$$ 6.32124 5.30415i 0.311048 0.261000i
$$414$$ 0 0
$$415$$ 12.8784 + 10.8062i 0.632175 + 0.530458i
$$416$$ −12.0181 27.8612i −0.589237 1.36601i
$$417$$ 0 0
$$418$$ 14.7357 + 3.49243i 0.720748 + 0.170820i
$$419$$ 3.62277 + 12.1009i 0.176984 + 0.591167i 0.999741 + 0.0227734i $$0.00724962\pi$$
−0.822757 + 0.568393i $$0.807565\pi$$
$$420$$ 0 0
$$421$$ −21.2812 2.48741i −1.03718 0.121229i −0.419578 0.907719i $$-0.637822\pi$$
−0.617602 + 0.786490i $$0.711896\pi$$
$$422$$ −0.855151 + 4.84980i −0.0416281 + 0.236085i
$$423$$ 0 0
$$424$$ −4.07126 23.0892i −0.197718 1.12131i
$$425$$ −0.00738389 0.126777i −0.000358171 0.00614956i
$$426$$ 0 0
$$427$$ −0.993798 + 2.30388i −0.0480932 + 0.111493i
$$428$$ −13.7163 + 6.88856i −0.663000 + 0.332971i
$$429$$ 0 0
$$430$$ 0.854896 0.202614i 0.0412267 0.00977092i
$$431$$ −2.23566 3.87227i −0.107688 0.186521i 0.807145 0.590353i $$-0.201011\pi$$
−0.914833 + 0.403832i $$0.867678\pi$$
$$432$$ 0 0
$$433$$ −4.56671 + 7.90977i −0.219462 + 0.380119i −0.954644 0.297751i $$-0.903763\pi$$
0.735182 + 0.677870i $$0.237097\pi$$
$$434$$ −2.31565 + 7.73481i −0.111155 + 0.371283i
$$435$$ 0 0
$$436$$ −16.4112 10.7938i −0.785955 0.516930i
$$437$$ 0.228287 + 0.306642i 0.0109204 + 0.0146687i
$$438$$ 0 0
$$439$$ −2.38000 + 1.56535i −0.113591 + 0.0747101i −0.605033 0.796200i $$-0.706840\pi$$
0.491442 + 0.870910i $$0.336470\pi$$
$$440$$ 13.0019 + 4.73230i 0.619841 + 0.225604i
$$441$$ 0 0
$$442$$ −0.103067 + 0.0375133i −0.00490239 + 0.00178432i
$$443$$ −7.38778 + 9.92352i −0.351004 + 0.471480i −0.942202 0.335046i $$-0.891248\pi$$
0.591197 + 0.806527i $$0.298655\pi$$
$$444$$ 0 0
$$445$$ 9.02822 9.56936i 0.427979 0.453631i
$$446$$ −0.347544 + 0.368376i −0.0164567 + 0.0174431i
$$447$$ 0 0
$$448$$ −0.861730 + 1.15750i −0.0407129 + 0.0546869i
$$449$$ −16.1389 + 5.87407i −0.761640 + 0.277214i −0.693495 0.720461i $$-0.743930\pi$$
−0.0681449 + 0.997675i $$0.521708\pi$$
$$450$$ 0 0
$$451$$ −25.2264 9.18166i −1.18786 0.432347i
$$452$$ 7.40461 4.87009i 0.348284 0.229070i
$$453$$ 0 0
$$454$$ 3.07327 + 4.12812i 0.144236 + 0.193742i
$$455$$ −6.03902 3.97193i −0.283114 0.186207i
$$456$$ 0 0
$$457$$ −0.253753 + 0.847594i −0.0118701 + 0.0396488i −0.963719 0.266917i $$-0.913995\pi$$
0.951849 + 0.306566i $$0.0991801\pi$$
$$458$$ 5.27840 9.14246i 0.246644 0.427199i
$$459$$ 0 0
$$460$$ 0.0760334 + 0.131694i 0.00354507 + 0.00614025i
$$461$$ −14.8212 + 3.51270i −0.690294 + 0.163603i −0.560768 0.827973i $$-0.689494\pi$$
−0.129526 + 0.991576i $$0.541346\pi$$
$$462$$ 0 0
$$463$$ 30.0591 15.0962i 1.39696 0.701582i 0.418542 0.908197i $$-0.362541\pi$$
0.978422 + 0.206615i $$0.0662449\pi$$
$$464$$ 0.297009 0.688543i 0.0137883 0.0319648i
$$465$$ 0 0
$$466$$ 0.648284 + 11.1306i 0.0300312 + 0.515616i
$$467$$ 1.91520 + 10.8616i 0.0886249 + 0.502617i 0.996515 + 0.0834093i $$0.0265809\pi$$
−0.907890 + 0.419207i $$0.862308\pi$$
$$468$$ 0 0
$$469$$ −0.694378 + 3.93802i −0.0320634 + 0.181841i
$$470$$ −3.55585 0.415619i −0.164019 0.0191711i
$$471$$ 0 0
$$472$$ −3.88340 12.9714i −0.178748 0.597059i
$$473$$ 8.19915 + 1.94323i 0.376997 + 0.0893500i
$$474$$ 0 0
$$475$$ −5.95315 13.8010i −0.273149 0.633232i
$$476$$ −0.0533110 0.0447333i −0.00244351 0.00205035i
$$477$$ 0 0
$$478$$ 10.0282 8.41465i 0.458679 0.384877i
$$479$$ −10.6546 5.35095i −0.486822 0.244491i 0.188418 0.982089i $$-0.439664\pi$$
−0.675241 + 0.737598i $$0.735960\pi$$
$$480$$ 0 0
$$481$$ −30.0759 + 3.51537i −1.37134 + 0.160287i
$$482$$ −0.226809 + 3.89415i −0.0103308 + 0.177374i
$$483$$ 0 0
$$484$$ 28.0062 + 29.6848i 1.27301 + 1.34931i
$$485$$ −6.61294 −0.300278
$$486$$ 0 0
$$487$$ 38.2435 1.73298 0.866489 0.499196i $$-0.166371\pi$$
0.866489 + 0.499196i $$0.166371\pi$$
$$488$$ 2.82534 + 2.99469i 0.127897 + 0.135563i
$$489$$ 0 0
$$490$$ 0.180583 3.10049i 0.00815791 0.140066i
$$491$$ −4.21090 + 0.492183i −0.190035 + 0.0222119i −0.210578 0.977577i $$-0.567535\pi$$
0.0205429 + 0.999789i $$0.493461\pi$$
$$492$$ 0 0
$$493$$ −0.0141551 0.00710897i −0.000637515 0.000320172i
$$494$$ −9.94438 + 8.34432i −0.447419 + 0.375429i
$$495$$ 0 0
$$496$$ −9.15292 7.68021i −0.410978 0.344852i
$$497$$ −1.25705 2.91417i −0.0563863 0.130718i
$$498$$ 0 0
$$499$$ 36.3957 + 8.62595i 1.62930 + 0.386151i 0.940766 0.339056i $$-0.110108\pi$$
0.688531 + 0.725207i $$0.258256\pi$$
$$500$$ −3.80053 12.6946i −0.169965 0.567722i
$$501$$ 0 0
$$502$$ 12.6994 + 1.48434i 0.566800 + 0.0662494i
$$503$$ 0.0594062 0.336909i 0.00264879 0.0150220i −0.983455 0.181154i $$-0.942017\pi$$
0.986104 + 0.166132i $$0.0531278\pi$$
$$504$$ 0 0
$$505$$ −1.42338 8.07239i −0.0633396 0.359217i
$$506$$ −0.0251759 0.432253i −0.00111920 0.0192160i
$$507$$ 0 0
$$508$$ −6.47544 + 15.0118i −0.287301 + 0.666039i
$$509$$ −5.58869 + 2.80675i −0.247714 + 0.124407i −0.568325 0.822804i $$-0.692408\pi$$
0.320610 + 0.947211i $$0.396112\pi$$
$$510$$ 0 0
$$511$$ 11.8409 2.80634i 0.523810 0.124145i
$$512$$ −7.73462 13.3968i −0.341825 0.592059i
$$513$$ 0 0
$$514$$ 6.13058 10.6185i 0.270408 0.468361i
$$515$$ 1.38707 4.63313i 0.0611216 0.204160i
$$516$$ 0 0
$$517$$ −28.6870 18.8677i −1.26165 0.829802i
$$518$$ 3.40619 + 4.57530i 0.149659 + 0.201027i
$$519$$ 0 0
$$520$$ −9.90937 + 6.51749i −0.434554 + 0.285811i
$$521$$ 29.5418 + 10.7523i 1.29425 + 0.471068i 0.895119 0.445827i $$-0.147090\pi$$
0.399129 + 0.916895i $$0.369313\pi$$
$$522$$ 0 0
$$523$$ −20.1279 + 7.32597i −0.880134 + 0.320342i −0.742264 0.670108i $$-0.766248\pi$$
−0.137870 + 0.990450i $$0.544026\pi$$
$$524$$ −13.1357 + 17.6443i −0.573836 + 0.770796i
$$525$$ 0 0
$$526$$ −4.02541 + 4.26669i −0.175516 + 0.186036i
$$527$$ −0.173201 + 0.183583i −0.00754477 + 0.00799698i
$$528$$ 0 0
$$529$$ −13.7281 + 18.4401i −0.596875 + 0.801742i
$$530$$ −5.86635 + 2.13518i −0.254818 + 0.0927461i
$$531$$ 0 0
$$532$$ −7.73997 2.81712i −0.335570 0.122138i
$$533$$ 19.2262 12.6453i 0.832781 0.547729i
$$534$$ 0 0
$$535$$ 5.60568 + 7.52974i 0.242355 + 0.325539i
$$536$$ 5.48208 + 3.60562i 0.236790 + 0.155739i
$$537$$ 0 0
$$538$$ −2.17080 + 7.25097i −0.0935898 + 0.312612i
$$539$$ 14.8933 25.7960i 0.641500 1.11111i
$$540$$ 0 0
$$541$$ 0.188033 + 0.325682i 0.00808416 + 0.0140022i 0.870039 0.492983i $$-0.164093\pi$$
−0.861955 + 0.506985i $$0.830760\pi$$
$$542$$ −6.69862 + 1.58760i −0.287731 + 0.0681934i
$$543$$ 0 0
$$544$$ −0.159666 + 0.0801872i −0.00684562 + 0.00343800i
$$545$$ −4.75823 + 11.0308i −0.203820 + 0.472508i
$$546$$ 0 0
$$547$$ 0.388245 + 6.66590i 0.0166001 + 0.285013i 0.996385 + 0.0849573i $$0.0270754\pi$$
−0.979784 + 0.200056i $$0.935888\pi$$
$$548$$ −1.42899 8.10422i −0.0610436 0.346195i
$$549$$ 0 0
$$550$$ −2.95609 + 16.7648i −0.126048 + 0.714854i
$$551$$ −1.86208 0.217646i −0.0793273 0.00927203i
$$552$$ 0 0
$$553$$ −5.28374 17.6489i −0.224688 0.750509i
$$554$$ −0.857262 0.203175i −0.0364216 0.00863207i
$$555$$ 0 0
$$556$$ 2.50078 + 5.79747i 0.106057 + 0.245867i
$$557$$ 2.30382 + 1.93313i 0.0976160 + 0.0819095i 0.690290 0.723533i $$-0.257483\pi$$
−0.592674 + 0.805443i $$0.701928\pi$$
$$558$$ 0 0
$$559$$ −5.53318 + 4.64289i −0.234028 + 0.196373i
$$560$$ −1.80060 0.904293i −0.0760890 0.0382134i
$$561$$ 0 0
$$562$$ 4.30780 0.503510i 0.181714 0.0212393i
$$563$$ 1.90779 32.7554i 0.0804036 1.38048i −0.681040 0.732246i $$-0.738472\pi$$
0.761444 0.648231i $$-0.224491\pi$$
$$564$$ 0 0
$$565$$ −3.71965 3.94260i −0.156487 0.165866i
$$566$$ −12.9354 −0.543715
$$567$$ 0 0
$$568$$ −5.20773 −0.218511
$$569$$ −17.9432 19.0186i −0.752217 0.797303i 0.232291 0.972646i $$-0.425378\pi$$
−0.984507 + 0.175343i $$0.943896\pi$$
$$570$$ 0 0
$$571$$ 0.0465596 0.799398i 0.00194846 0.0334538i −0.997194 0.0748636i $$-0.976148\pi$$
0.999142 + 0.0414098i $$0.0131849\pi$$
$$572$$ −49.1899 + 5.74947i −2.05673 + 0.240398i
$$573$$ 0 0
$$574$$ −3.87371 1.94545i −0.161685 0.0812015i
$$575$$ −0.329195 + 0.276227i −0.0137284 + 0.0115195i
$$576$$ 0 0
$$577$$ −32.3968 27.1841i −1.34869 1.13169i −0.979300 0.202416i $$-0.935121\pi$$
−0.369395 0.929273i $$-0.620435\pi$$
$$578$$ −4.55579 10.5615i −0.189496 0.439301i
$$579$$ 0 0
$$580$$ −0.725640 0.171980i −0.0301306 0.00714107i
$$581$$ 7.46699 + 24.9415i 0.309783 + 1.03475i
$$582$$ 0 0
$$583$$ −59.4690 6.95093i −2.46296 0.287878i
$$584$$ 3.46737 19.6644i 0.143481 0.813721i
$$585$$ 0 0
$$586$$ −0.214557 1.21681i −0.00886326 0.0502661i
$$587$$ −0.775932 13.3222i −0.0320261 0.549868i −0.975716 0.219037i $$-0.929708\pi$$
0.943690 0.330830i $$-0.107329\pi$$
$$588$$ 0 0
$$589$$ −11.8317 + 27.4289i −0.487516 + 1.13019i
$$590$$ −3.22189 + 1.61809i −0.132643 + 0.0666158i
$$591$$ 0 0
$$592$$ −8.21350 + 1.94664i −0.337573 + 0.0800062i
$$593$$ −17.2045 29.7990i −0.706503 1.22370i −0.966147 0.257994i $$-0.916939\pi$$
0.259644 0.965704i $$-0.416395\pi$$
$$594$$ 0 0
$$595$$ −0.0212812 + 0.0368601i −0.000872443 + 0.00151112i
$$596$$ −8.34903 + 27.8877i −0.341989 + 1.14232i
$$597$$ 0 0
$$598$$ 0.310098 + 0.203954i 0.0126808 + 0.00834032i
$$599$$ −23.9225 32.1334i −0.977445 1.31294i −0.949647 0.313323i $$-0.898558\pi$$
−0.0277982 0.999614i $$-0.508850\pi$$
$$600$$ 0 0
$$601$$ 36.0814 23.7311i 1.47179 0.968013i 0.475708 0.879603i $$-0.342192\pi$$
0.996084 0.0884094i $$-0.0281784\pi$$
$$602$$ 1.27856 + 0.465357i 0.0521101 + 0.0189665i
$$603$$ 0 0
$$604$$ −4.46403 + 1.62477i −0.181639 + 0.0661111i
$$605$$ 14.9049 20.0207i 0.605970 0.813958i
$$606$$ 0 0
$$607$$ −12.0916 + 12.8163i −0.490782 + 0.520199i −0.924671 0.380768i $$-0.875660\pi$$
0.433889 + 0.900967i $$0.357141\pi$$
$$608$$ −14.5118 + 15.3816i −0.588530 + 0.623805i
$$609$$ 0 0
$$610$$ 0.654648 0.879345i 0.0265059 0.0356036i
$$611$$ 27.6577 10.0666i 1.11891 0.407250i
$$612$$ 0 0
$$613$$ 25.9691 + 9.45198i 1.04888 + 0.381762i 0.808241 0.588852i $$-0.200420\pi$$
0.240641 + 0.970614i $$0.422642\pi$$
$$614$$ 8.47123 5.57161i 0.341871 0.224852i
$$615$$ 0 0
$$616$$ 12.7957 + 17.1876i 0.515554 + 0.692509i
$$617$$ −3.68414 2.42310i −0.148318 0.0975503i 0.473181 0.880965i $$-0.343106\pi$$
−0.621499 + 0.783415i $$0.713476\pi$$
$$618$$ 0 0
$$619$$ 7.17467 23.9651i 0.288374 0.963237i −0.683936 0.729542i $$-0.739733\pi$$
0.972310 0.233695i $$-0.0750816\pi$$
$$620$$ −5.94125 + 10.2905i −0.238606 + 0.413278i
$$621$$ 0 0
$$622$$ −6.98959 12.1063i −0.280257 0.485420i
$$623$$ 19.8249 4.69860i 0.794270 0.188245i
$$624$$ 0 0
$$625$$ 11.1237 5.58651i 0.444946 0.223460i
$$626$$ 5.98275 13.8696i 0.239119 0.554339i
$$627$$ 0 0
$$628$$ −0.307439 5.27852i −0.0122681 0.210636i
$$629$$ 0.0309624 + 0.175596i 0.00123455 + 0.00700148i
$$630$$ 0 0
$$631$$ 2.45133 13.9022i 0.0975857 0.553436i −0.896339 0.443370i $$-0.853783\pi$$
0.993924 0.110066i $$-0.0351062\pi$$
$$632$$ −30.0255 3.50948i −1.19435 0.139600i
$$633$$ 0 0
$$634$$ −2.20457 7.36378i −0.0875547 0.292453i
$$635$$ 9.72931 + 2.30589i 0.386096 + 0.0915064i
$$636$$ 0 0
$$637$$ 10.1132 + 23.4450i 0.400700 + 0.928926i
$$638$$ 1.62660 + 1.36488i 0.0643978 + 0.0540362i
$$639$$ 0 0
$$640$$ −7.87383 + 6.60693i −0.311241 + 0.261162i
$$641$$ 30.5703 + 15.3530i 1.20746 + 0.606407i 0.934618 0.355653i $$-0.115742\pi$$
0.272838 + 0.962060i $$0.412038\pi$$
$$642$$ 0 0
$$643$$ 13.3953 1.56569i 0.528260 0.0617447i 0.152217 0.988347i $$-0.451359\pi$$
0.376043 + 0.926602i $$0.377285\pi$$
$$644$$ −0.0136930 + 0.235100i −0.000539581 + 0.00926424i
$$645$$ 0 0
$$646$$ 0.0524565 + 0.0556007i 0.00206387 + 0.00218758i
$$647$$ 3.19249 0.125510 0.0627548 0.998029i $$-0.480011\pi$$
0.0627548 + 0.998029i $$0.480011\pi$$
$$648$$ 0 0
$$649$$ −34.5785 −1.35733
$$650$$ −10.0140 10.6143i −0.392783 0.416325i
$$651$$ 0 0
$$652$$ −1.76782 + 30.3523i −0.0692333 + 1.18869i
$$653$$ 31.9500 3.73442i 1.25030 0.146139i 0.534936 0.844892i $$-0.320336\pi$$
0.715363 + 0.698753i $$0.246261\pi$$
$$654$$ 0 0
$$655$$ 12.0222 + 6.03779i 0.469748 + 0.235916i
$$656$$ 4.91404 4.12337i 0.191861 0.160991i
$$657$$ 0 0
$$658$$ −4.24715 3.56378i −0.165571 0.138931i
$$659$$ 5.78047 + 13.4006i 0.225175 + 0.522015i 0.992926 0.118734i $$-0.0378835\pi$$
−0.767751 + 0.640748i $$0.778624\pi$$
$$660$$ 0 0
$$661$$ −7.58170 1.79690i −0.294894 0.0698912i 0.0805058 0.996754i $$-0.474346\pi$$
−0.375400 + 0.926863i $$0.622495\pi$$
$$662$$ −2.79590 9.33895i −0.108666 0.362969i
$$663$$ 0 0
$$664$$ 42.4320 + 4.95959i 1.64668 + 0.192470i
$$665$$ −0.874754 + 4.96098i −0.0339215 + 0.192378i
$$666$$ 0 0
$$667$$ 0.00930786 + 0.0527875i 0.000360402 + 0.00204394i
$$668$$ −1.73442 29.7788i −0.0671066 1.15218i
$$669$$ 0 0
$$670$$ 0.692009 1.60426i 0.0267346 0.0619778i
$$671$$ 9.39577 4.71873i 0.362720 0.182165i
$$672$$ 0 0
$$673$$ 7.80154 1.84900i 0.300727 0.0712737i −0.0774821 0.996994i $$-0.524688\pi$$
0.378209 + 0.925720i $$0.376540\pi$$
$$674$$ 3.35193 + 5.80572i 0.129112 + 0.223628i
$$675$$ 0 0
$$676$$ 11.2024 19.4031i 0.430862 0.746274i
$$677$$ −2.44329 + 8.16115i −0.0939031 + 0.313658i −0.992017 0.126105i $$-0.959752\pi$$
0.898114 + 0.439763i $$0.144938\pi$$
$$678$$ 0 0
$$679$$ −8.55635 5.62760i −0.328363 0.215968i
$$680$$ 0.0417056 + 0.0560203i 0.00159934 + 0.00214828i
$$681$$ 0 0
$$682$$ 28.2675 18.5918i 1.08242 0.711917i
$$683$$ −13.5460 4.93034i −0.518323 0.188654i 0.0695940 0.997575i $$-0.477830\pi$$
−0.587917 + 0.808921i $$0.700052\pi$$
$$684$$ 0 0
$$685$$ −4.72942 + 1.72137i −0.180702 + 0.0657701i
$$686$$ 7.00350 9.40733i 0.267395 0.359174i
$$687$$ 0 0
$$688$$ −1.38175 + 1.46457i −0.0526786 + 0.0558360i
$$689$$ 35.2208 37.3319i 1.34181 1.42223i
$$690$$ 0 0
$$691$$ 21.7780 29.2530i 0.828475 1.11283i −0.163518 0.986540i $$-0.552284\pi$$
0.991993 0.126294i $$-0.0403084\pi$$
$$692$$ −8.93742 + 3.25296i −0.339750 + 0.123659i
$$693$$ 0 0
$$694$$ 2.14799 + 0.781805i 0.0815366 + 0.0296769i
$$695$$ 3.22623 2.12193i 0.122378 0.0804893i
$$696$$ 0 0
$$697$$ −0.0809176 0.108691i −0.00306497 0.00411697i
$$698$$ 0.751843 + 0.494495i 0.0284577 + 0.0187169i
$$699$$ 0 0
$$700$$ 2.65550 8.86998i 0.100368 0.335254i
$$701$$ −4.76010 + 8.24474i −0.179787 + 0.311399i −0.941807 0.336153i $$-0.890874\pi$$
0.762021 + 0.647553i $$0.224207\pi$$
$$702$$ 0 0
$$703$$ 10.5517 + 18.2761i 0.397966 + 0.689298i
$$704$$ 5.88400 1.39453i 0.221761 0.0525584i
$$705$$ 0 0
$$706$$ 7.13118 3.58141i 0.268385 0.134788i
$$707$$ 5.02791 11.6560i 0.189094 0.438369i
$$708$$ 0 0
$$709$$ −0.695397 11.9395i −0.0261162 0.448398i −0.985865 0.167539i $$-0.946418\pi$$
0.959749 0.280858i $$-0.0906191\pi$$
$$710$$ 0.240792 + 1.36560i 0.00903677 + 0.0512501i
$$711$$ 0 0
$$712$$ 5.80535 32.9238i 0.217565 1.23387i
$$713$$ 0.848306 + 0.0991527i 0.0317693 + 0.00371330i
$$714$$ 0 0
$$715$$ 8.68698 + 29.0165i 0.324875 + 1.08516i
$$716$$ 5.19470 + 1.23117i 0.194135 + 0.0460108i
$$717$$ 0 0
$$718$$ −7.96272 18.4596i −0.297166 0.688908i
$$719$$ −16.3766 13.7416i −0.610743 0.512474i 0.284135 0.958784i $$-0.408294\pi$$
−0.894879 + 0.446310i $$0.852738\pi$$
$$720$$ 0 0
$$721$$ 5.73749 4.81433i 0.213675 0.179295i
$$722$$ −3.40381 1.70946i −0.126677 0.0636195i
$$723$$ 0 0
$$724$$ −29.2260 + 3.41603i −1.08617 + 0.126956i
$$725$$ 0.122536 2.10387i 0.00455088 0.0781356i
$$726$$ 0 0
$$727$$ 5.40837 + 5.73254i 0.200585 + 0.212608i 0.819856 0.572569i $$-0.194053\pi$$
−0.619271 + 0.785177i $$0.712572\pi$$
$$728$$ −18.3679 −0.680760
$$729$$ 0 0
$$730$$ −5.31685 −0.196785
$$731$$ 0.0291875 + 0.0309369i 0.00107954 + 0.00114424i
$$732$$ 0 0
$$733$$ −2.02479 + 34.7644i −0.0747875 + 1.28405i 0.727081 + 0.686551i $$0.240876\pi$$
−0.801869 + 0.597500i $$0.796161\pi$$
$$734$$ 5.39466 0.630545i 0.199120 0.0232738i
$$735$$ 0 0
$$736$$ 0.540303 + 0.271350i 0.0199158 + 0.0100021i
$$737$$ 12.8363 10.7709i 0.472829 0.396751i
$$738$$ 0 0
$$739$$ 33.5899 + 28.1853i 1.23563 + 1.03681i 0.997853 + 0.0654916i $$0.0208615\pi$$
0.237772 + 0.971321i $$0.423583\pi$$
$$740$$ 3.32491 + 7.70801i 0.122226 + 0.283352i
$$741$$ 0 0
$$742$$ −9.40738 2.22959i −0.345356 0.0818508i
$$743$$ −6.12394 20.4554i −0.224666 0.750435i −0.993784 0.111329i $$-0.964489\pi$$
0.769118 0.639107i $$-0.220696\pi$$
$$744$$ 0 0
$$745$$ 17.6835 + 2.06690i 0.647872 + 0.0757254i
$$746$$ −0.351765 + 1.99496i −0.0128790 + 0.0730407i
$$747$$ 0 0
$$748$$ 0.0506397 + 0.287192i 0.00185157 + 0.0105008i
$$749$$ 0.845286 + 14.5130i 0.0308861 + 0.530294i
$$750$$ 0 0
$$751$$ 1.79352 4.15784i 0.0654464 0.151722i −0.882354 0.470587i $$-0.844042\pi$$
0.947800 + 0.318865i $$0.103302\pi$$
$$752$$ 7.33195 3.68224i 0.267369 0.134278i
$$753$$ 0 0
$$754$$ −1.77111 + 0.419761i −0.0645000 + 0.0152868i
$$755$$ 1.45269 + 2.51614i 0.0528689 + 0.0915716i
$$756$$ 0 0
$$757$$ −15.3969 + 26.6682i −0.559610 + 0.969273i 0.437919 + 0.899014i $$0.355716\pi$$
−0.997529 + 0.0702583i $$0.977618\pi$$
$$758$$ 4.29022 14.3303i 0.155828 0.520501i
$$759$$ 0 0
$$760$$ 6.90613 + 4.54224i 0.250512 + 0.164764i
$$761$$ −2.13712 2.87064i −0.0774704 0.104061i 0.761699 0.647931i $$-0.224366\pi$$
−0.839169 + 0.543871i $$0.816958\pi$$
$$762$$ 0 0
$$763$$ −15.5438 + 10.2233i −0.562723 + 0.370109i
$$764$$ −28.8785 10.5109i −1.04479 0.380271i
$$765$$ 0 0
$$766$$ −9.12904 + 3.32270i −0.329846 + 0.120054i
$$767$$ 17.7003 23.7757i 0.639122 0.858489i
$$768$$ 0 0
$$769$$ 10.0226 10.6233i 0.361423 0.383085i −0.520989 0.853563i $$-0.674437\pi$$
0.882412 + 0.470478i $$0.155918\pi$$
$$770$$ 3.91539 4.15008i 0.141101 0.149558i
$$771$$ 0 0
$$772$$ 9.86979 13.2574i 0.355221 0.477145i
$$773$$ −18.7983 + 6.84203i −0.676129 + 0.246091i −0.657184 0.753730i $$-0.728253\pi$$
−0.0189442 + 0.999821i $$0.506030\pi$$
$$774$$ 0 0
$$775$$ −31.5543 11.4848i −1.13346 0.412547i
$$776$$ −14.0400 + 9.23427i −0.504007 + 0.331491i
$$777$$ 0 0
$$778$$ −7.36603 9.89429i −0.264085 0.354728i
$$779$$ −13.3993 8.81289i −0.480081 0.315754i
$$780$$ 0 0
$$781$$ −3.81427 + 12.7406i −0.136485 + 0.455893i
$$782$$ 0.00109277 0.00189273i 3.90772e−5 6.76838e-5i
$$783$$