# Properties

 Label 567.2.w.a.37.10 Level $567$ Weight $2$ Character 567.37 Analytic conductor $4.528$ Analytic rank $0$ Dimension $132$ Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(37,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([14, 6]))

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

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

chi := DirichletCharacter("567.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$567 = 3^{4} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 567.w (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: $$4.52751779461$$ Analytic rank: $$0$$ Dimension: $$132$$ Relative dimension: $$22$$ over $$\Q(\zeta_{9})$$ Twist minimal: no (minimal twist has level 189) Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

## Embedding invariants

 Embedding label 37.10 Character $$\chi$$ $$=$$ 567.37 Dual form 567.2.w.a.46.10

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-0.0910389 - 0.516307i) q^{2} +(1.62110 - 0.590032i) q^{4} +(-0.0290567 + 0.164789i) q^{5} +(-0.352779 + 2.62213i) q^{7} +(-0.976493 - 1.69134i) q^{8} +O(q^{10})$$ $$q+(-0.0910389 - 0.516307i) q^{2} +(1.62110 - 0.590032i) q^{4} +(-0.0290567 + 0.164789i) q^{5} +(-0.352779 + 2.62213i) q^{7} +(-0.976493 - 1.69134i) q^{8} +0.0877269 q^{10} +(0.765229 + 4.33983i) q^{11} +(2.84925 + 2.39080i) q^{13} +(1.38594 - 0.0565734i) q^{14} +(1.85872 - 1.55965i) q^{16} +5.82553 q^{17} -2.90577 q^{19} +(0.0501268 + 0.284283i) q^{20} +(2.17102 - 0.790186i) q^{22} +(-3.96175 - 3.32431i) q^{23} +(4.67215 + 1.70052i) q^{25} +(0.974996 - 1.68874i) q^{26} +(0.975250 + 4.45888i) q^{28} +(4.36652 - 3.66395i) q^{29} +(-4.90997 + 1.78708i) q^{31} +(-3.96662 - 3.32839i) q^{32} +(-0.530350 - 3.00776i) q^{34} +(-0.421846 - 0.134324i) q^{35} +(-1.57282 - 2.72421i) q^{37} +(0.264538 + 1.50027i) q^{38} +(0.307087 - 0.111770i) q^{40} +(-0.151822 - 0.127394i) q^{41} +(-0.469933 - 0.171042i) q^{43} +(3.80115 + 6.58378i) q^{44} +(-1.35569 + 2.34812i) q^{46} +(2.74267 + 0.998251i) q^{47} +(-6.75109 - 1.85006i) q^{49} +(0.452646 - 2.56708i) q^{50} +(6.02956 + 2.19458i) q^{52} +(-2.31775 - 4.01446i) q^{53} -0.737389 q^{55} +(4.77938 - 1.96382i) q^{56} +(-2.28925 - 1.92091i) q^{58} +(2.66671 + 2.23764i) q^{59} +(8.98407 + 3.26993i) q^{61} +(1.36968 + 2.37236i) q^{62} +(1.06902 - 1.85160i) q^{64} +(-0.476766 + 0.400054i) q^{65} +(2.47407 - 14.0311i) q^{67} +(9.44377 - 3.43725i) q^{68} +(-0.0309482 + 0.230031i) q^{70} +(3.85452 - 6.67622i) q^{71} +(-6.89159 + 11.9366i) q^{73} +(-1.26334 + 1.06007i) q^{74} +(-4.71055 + 1.71450i) q^{76} +(-11.6495 + 0.475528i) q^{77} +(-0.654200 - 3.71015i) q^{79} +(0.203004 + 0.351613i) q^{80} +(-0.0519526 + 0.0899846i) q^{82} +(-13.0814 + 10.9766i) q^{83} +(-0.169271 + 0.959981i) q^{85} +(-0.0455279 + 0.258201i) q^{86} +(6.59287 - 5.53207i) q^{88} +7.43742 q^{89} +(-7.27413 + 6.62766i) q^{91} +(-8.38384 - 3.05147i) q^{92} +(0.265714 - 1.50694i) q^{94} +(0.0844320 - 0.478838i) q^{95} +(-4.44029 - 1.61613i) q^{97} +(-0.340587 + 3.65407i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10})$$ 132 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 6 * q^7 + 6 * q^8 $$132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8} - 6 q^{10} - 3 q^{11} - 12 q^{13} - 15 q^{14} - 9 q^{16} + 54 q^{17} - 6 q^{19} + 18 q^{20} - 12 q^{22} - 3 q^{25} - 30 q^{26} - 12 q^{28} + 30 q^{29} - 3 q^{31} - 51 q^{32} - 18 q^{34} + 12 q^{35} + 3 q^{37} + 57 q^{38} - 66 q^{40} - 12 q^{43} - 3 q^{44} + 3 q^{46} + 21 q^{47} + 12 q^{49} + 39 q^{50} + 9 q^{52} - 9 q^{53} - 24 q^{55} - 57 q^{56} - 3 q^{58} + 18 q^{59} + 33 q^{61} - 75 q^{62} - 30 q^{64} - 81 q^{65} - 3 q^{67} - 6 q^{68} - 42 q^{70} + 18 q^{71} + 21 q^{73} + 93 q^{74} - 24 q^{76} - 87 q^{77} + 15 q^{79} - 102 q^{80} - 6 q^{82} + 42 q^{83} - 63 q^{85} - 159 q^{86} + 57 q^{88} + 150 q^{89} + 6 q^{91} + 66 q^{92} + 33 q^{94} + 147 q^{95} - 12 q^{97} - 99 q^{98}+O(q^{100})$$ 132 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 6 * q^7 + 6 * q^8 - 6 * q^10 - 3 * q^11 - 12 * q^13 - 15 * q^14 - 9 * q^16 + 54 * q^17 - 6 * q^19 + 18 * q^20 - 12 * q^22 - 3 * q^25 - 30 * q^26 - 12 * q^28 + 30 * q^29 - 3 * q^31 - 51 * q^32 - 18 * q^34 + 12 * q^35 + 3 * q^37 + 57 * q^38 - 66 * q^40 - 12 * q^43 - 3 * q^44 + 3 * q^46 + 21 * q^47 + 12 * q^49 + 39 * q^50 + 9 * q^52 - 9 * q^53 - 24 * q^55 - 57 * q^56 - 3 * q^58 + 18 * q^59 + 33 * q^61 - 75 * q^62 - 30 * q^64 - 81 * q^65 - 3 * q^67 - 6 * q^68 - 42 * q^70 + 18 * q^71 + 21 * q^73 + 93 * q^74 - 24 * q^76 - 87 * q^77 + 15 * q^79 - 102 * q^80 - 6 * q^82 + 42 * q^83 - 63 * q^85 - 159 * q^86 + 57 * q^88 + 150 * q^89 + 6 * q^91 + 66 * q^92 + 33 * q^94 + 147 * q^95 - 12 * q^97 - 99 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$$.

 $$n$$ $$325$$ $$407$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{9}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.0910389 0.516307i −0.0643742 0.365084i −0.999929 0.0119032i $$-0.996211\pi$$
0.935555 0.353181i $$-0.114900\pi$$
$$3$$ 0 0
$$4$$ 1.62110 0.590032i 0.810550 0.295016i
$$5$$ −0.0290567 + 0.164789i −0.0129945 + 0.0736957i −0.990615 0.136679i $$-0.956357\pi$$
0.977621 + 0.210374i $$0.0674683\pi$$
$$6$$ 0 0
$$7$$ −0.352779 + 2.62213i −0.133338 + 0.991071i
$$8$$ −0.976493 1.69134i −0.345243 0.597978i
$$9$$ 0 0
$$10$$ 0.0877269 0.0277417
$$11$$ 0.765229 + 4.33983i 0.230725 + 1.30851i 0.851432 + 0.524465i $$0.175735\pi$$
−0.620707 + 0.784043i $$0.713154\pi$$
$$12$$ 0 0
$$13$$ 2.84925 + 2.39080i 0.790238 + 0.663089i 0.945804 0.324737i $$-0.105276\pi$$
−0.155566 + 0.987825i $$0.549720\pi$$
$$14$$ 1.38594 0.0565734i 0.370408 0.0151199i
$$15$$ 0 0
$$16$$ 1.85872 1.55965i 0.464679 0.389912i
$$17$$ 5.82553 1.41290 0.706449 0.707764i $$-0.250296\pi$$
0.706449 + 0.707764i $$0.250296\pi$$
$$18$$ 0 0
$$19$$ −2.90577 −0.666630 −0.333315 0.942816i $$-0.608167\pi$$
−0.333315 + 0.942816i $$0.608167\pi$$
$$20$$ 0.0501268 + 0.284283i 0.0112087 + 0.0635676i
$$21$$ 0 0
$$22$$ 2.17102 0.790186i 0.462863 0.168468i
$$23$$ −3.96175 3.32431i −0.826083 0.693166i 0.128305 0.991735i $$-0.459046\pi$$
−0.954388 + 0.298569i $$0.903491\pi$$
$$24$$ 0 0
$$25$$ 4.67215 + 1.70052i 0.934430 + 0.340105i
$$26$$ 0.974996 1.68874i 0.191212 0.331190i
$$27$$ 0 0
$$28$$ 0.975250 + 4.45888i 0.184305 + 0.842649i
$$29$$ 4.36652 3.66395i 0.810843 0.680378i −0.139966 0.990156i $$-0.544699\pi$$
0.950809 + 0.309778i $$0.100255\pi$$
$$30$$ 0 0
$$31$$ −4.90997 + 1.78708i −0.881856 + 0.320969i −0.742959 0.669337i $$-0.766578\pi$$
−0.138898 + 0.990307i $$0.544356\pi$$
$$32$$ −3.96662 3.32839i −0.701206 0.588382i
$$33$$ 0 0
$$34$$ −0.530350 3.00776i −0.0909543 0.515827i
$$35$$ −0.421846 0.134324i −0.0713050 0.0227049i
$$36$$ 0 0
$$37$$ −1.57282 2.72421i −0.258570 0.447857i 0.707289 0.706925i $$-0.249918\pi$$
−0.965859 + 0.259068i $$0.916585\pi$$
$$38$$ 0.264538 + 1.50027i 0.0429138 + 0.243376i
$$39$$ 0 0
$$40$$ 0.307087 0.111770i 0.0485546 0.0176724i
$$41$$ −0.151822 0.127394i −0.0237106 0.0198956i 0.630855 0.775900i $$-0.282704\pi$$
−0.654566 + 0.756005i $$0.727149\pi$$
$$42$$ 0 0
$$43$$ −0.469933 0.171042i −0.0716641 0.0260836i 0.305939 0.952051i $$-0.401030\pi$$
−0.377603 + 0.925967i $$0.623252\pi$$
$$44$$ 3.80115 + 6.58378i 0.573045 + 0.992543i
$$45$$ 0 0
$$46$$ −1.35569 + 2.34812i −0.199886 + 0.346212i
$$47$$ 2.74267 + 0.998251i 0.400060 + 0.145610i 0.534211 0.845351i $$-0.320609\pi$$
−0.134152 + 0.990961i $$0.542831\pi$$
$$48$$ 0 0
$$49$$ −6.75109 1.85006i −0.964442 0.264294i
$$50$$ 0.452646 2.56708i 0.0640138 0.363040i
$$51$$ 0 0
$$52$$ 6.02956 + 2.19458i 0.836150 + 0.304334i
$$53$$ −2.31775 4.01446i −0.318368 0.551429i 0.661780 0.749698i $$-0.269801\pi$$
−0.980148 + 0.198269i $$0.936468\pi$$
$$54$$ 0 0
$$55$$ −0.737389 −0.0994295
$$56$$ 4.77938 1.96382i 0.638672 0.262427i
$$57$$ 0 0
$$58$$ −2.28925 1.92091i −0.300593 0.252227i
$$59$$ 2.66671 + 2.23764i 0.347177 + 0.291316i 0.799655 0.600460i $$-0.205016\pi$$
−0.452479 + 0.891775i $$0.649460\pi$$
$$60$$ 0 0
$$61$$ 8.98407 + 3.26993i 1.15029 + 0.418672i 0.845620 0.533785i $$-0.179231\pi$$
0.304672 + 0.952457i $$0.401453\pi$$
$$62$$ 1.36968 + 2.37236i 0.173950 + 0.301290i
$$63$$ 0 0
$$64$$ 1.06902 1.85160i 0.133628 0.231450i
$$65$$ −0.476766 + 0.400054i −0.0591356 + 0.0496206i
$$66$$ 0 0
$$67$$ 2.47407 14.0311i 0.302255 1.71418i −0.333895 0.942610i $$-0.608363\pi$$
0.636150 0.771565i $$-0.280526\pi$$
$$68$$ 9.44377 3.43725i 1.14523 0.416828i
$$69$$ 0 0
$$70$$ −0.0309482 + 0.230031i −0.00369901 + 0.0274940i
$$71$$ 3.85452 6.67622i 0.457447 0.792321i −0.541378 0.840779i $$-0.682097\pi$$
0.998825 + 0.0484578i $$0.0154306\pi$$
$$72$$ 0 0
$$73$$ −6.89159 + 11.9366i −0.806599 + 1.39707i 0.108607 + 0.994085i $$0.465361\pi$$
−0.915206 + 0.402986i $$0.867972\pi$$
$$74$$ −1.26334 + 1.06007i −0.146860 + 0.123230i
$$75$$ 0 0
$$76$$ −4.71055 + 1.71450i −0.540337 + 0.196666i
$$77$$ −11.6495 + 0.475528i −1.32759 + 0.0541915i
$$78$$ 0 0
$$79$$ −0.654200 3.71015i −0.0736033 0.417425i −0.999239 0.0390088i $$-0.987580\pi$$
0.925636 0.378416i $$-0.123531\pi$$
$$80$$ 0.203004 + 0.351613i 0.0226965 + 0.0393115i
$$81$$ 0 0
$$82$$ −0.0519526 + 0.0899846i −0.00573721 + 0.00993713i
$$83$$ −13.0814 + 10.9766i −1.43587 + 1.20484i −0.493739 + 0.869610i $$0.664370\pi$$
−0.942135 + 0.335232i $$0.891185\pi$$
$$84$$ 0 0
$$85$$ −0.169271 + 0.959981i −0.0183600 + 0.104125i
$$86$$ −0.0455279 + 0.258201i −0.00490940 + 0.0278426i
$$87$$ 0 0
$$88$$ 6.59287 5.53207i 0.702802 0.589721i
$$89$$ 7.43742 0.788365 0.394182 0.919032i $$-0.371028\pi$$
0.394182 + 0.919032i $$0.371028\pi$$
$$90$$ 0 0
$$91$$ −7.27413 + 6.62766i −0.762536 + 0.694767i
$$92$$ −8.38384 3.05147i −0.874076 0.318138i
$$93$$ 0 0
$$94$$ 0.265714 1.50694i 0.0274063 0.155429i
$$95$$ 0.0844320 0.478838i 0.00866254 0.0491277i
$$96$$ 0 0
$$97$$ −4.44029 1.61613i −0.450843 0.164094i 0.106612 0.994301i $$-0.466000\pi$$
−0.557455 + 0.830207i $$0.688222\pi$$
$$98$$ −0.340587 + 3.65407i −0.0344045 + 0.369117i
$$99$$ 0 0
$$100$$ 8.57739 0.857739
$$101$$ −8.08668 + 6.78553i −0.804655 + 0.675185i −0.949326 0.314294i $$-0.898232\pi$$
0.144671 + 0.989480i $$0.453788\pi$$
$$102$$ 0 0
$$103$$ 1.97305 11.1897i 0.194410 1.10256i −0.718845 0.695170i $$-0.755329\pi$$
0.913256 0.407387i $$-0.133560\pi$$
$$104$$ 1.26138 7.15363i 0.123688 0.701471i
$$105$$ 0 0
$$106$$ −1.86169 + 1.56214i −0.180823 + 0.151729i
$$107$$ −3.33654 + 5.77905i −0.322555 + 0.558682i −0.981015 0.193934i $$-0.937875\pi$$
0.658459 + 0.752616i $$0.271208\pi$$
$$108$$ 0 0
$$109$$ 4.03004 + 6.98023i 0.386008 + 0.668585i 0.991908 0.126955i $$-0.0405205\pi$$
−0.605901 + 0.795540i $$0.707187\pi$$
$$110$$ 0.0671311 + 0.380719i 0.00640070 + 0.0363002i
$$111$$ 0 0
$$112$$ 3.43388 + 5.42400i 0.324471 + 0.512519i
$$113$$ −19.4781 + 7.08946i −1.83235 + 0.666921i −0.840136 + 0.542376i $$0.817525\pi$$
−0.992214 + 0.124544i $$0.960253\pi$$
$$114$$ 0 0
$$115$$ 0.662923 0.556258i 0.0618179 0.0518714i
$$116$$ 4.91672 8.51602i 0.456506 0.790692i
$$117$$ 0 0
$$118$$ 0.912535 1.58056i 0.0840056 0.145502i
$$119$$ −2.05512 + 15.2753i −0.188393 + 1.40028i
$$120$$ 0 0
$$121$$ −7.91191 + 2.87970i −0.719264 + 0.261791i
$$122$$ 0.870391 4.93623i 0.0788015 0.446905i
$$123$$ 0 0
$$124$$ −6.90511 + 5.79408i −0.620097 + 0.520324i
$$125$$ −0.834311 + 1.44507i −0.0746230 + 0.129251i
$$126$$ 0 0
$$127$$ −9.57031 16.5763i −0.849228 1.47091i −0.881898 0.471440i $$-0.843735\pi$$
0.0326704 0.999466i $$-0.489599\pi$$
$$128$$ −10.7849 3.92538i −0.953258 0.346958i
$$129$$ 0 0
$$130$$ 0.249955 + 0.209737i 0.0219225 + 0.0183952i
$$131$$ −6.04416 5.07165i −0.528081 0.443112i 0.339357 0.940658i $$-0.389790\pi$$
−0.867438 + 0.497545i $$0.834235\pi$$
$$132$$ 0 0
$$133$$ 1.02509 7.61930i 0.0888869 0.660677i
$$134$$ −7.46961 −0.645276
$$135$$ 0 0
$$136$$ −5.68859 9.85293i −0.487793 0.844882i
$$137$$ 2.08979 + 0.760623i 0.178543 + 0.0649844i 0.429745 0.902950i $$-0.358604\pi$$
−0.251202 + 0.967935i $$0.580826\pi$$
$$138$$ 0 0
$$139$$ 1.70860 9.68995i 0.144921 0.821891i −0.822509 0.568753i $$-0.807426\pi$$
0.967430 0.253138i $$-0.0814627\pi$$
$$140$$ −0.763110 + 0.0311498i −0.0644946 + 0.00263264i
$$141$$ 0 0
$$142$$ −3.79789 1.38232i −0.318712 0.116002i
$$143$$ −8.19534 + 14.1947i −0.685329 + 1.18702i
$$144$$ 0 0
$$145$$ 0.476900 + 0.826015i 0.0396044 + 0.0685968i
$$146$$ 6.79035 + 2.47148i 0.561973 + 0.204541i
$$147$$ 0 0
$$148$$ −4.15707 3.48820i −0.341709 0.286728i
$$149$$ 13.6915 4.98332i 1.12166 0.408249i 0.286399 0.958110i $$-0.407542\pi$$
0.835256 + 0.549861i $$0.185319\pi$$
$$150$$ 0 0
$$151$$ −0.638711 3.62231i −0.0519776 0.294779i 0.947727 0.319082i $$-0.103375\pi$$
−0.999705 + 0.0243026i $$0.992263\pi$$
$$152$$ 2.83747 + 4.91464i 0.230149 + 0.398630i
$$153$$ 0 0
$$154$$ 1.30608 + 5.97145i 0.105247 + 0.481193i
$$155$$ −0.151823 0.861033i −0.0121947 0.0691599i
$$156$$ 0 0
$$157$$ −9.90610 8.31221i −0.790593 0.663386i 0.155299 0.987867i $$-0.450366\pi$$
−0.945892 + 0.324481i $$0.894810\pi$$
$$158$$ −1.85602 + 0.675537i −0.147657 + 0.0537428i
$$159$$ 0 0
$$160$$ 0.663738 0.556942i 0.0524731 0.0440301i
$$161$$ 10.1144 9.21547i 0.797124 0.726281i
$$162$$ 0 0
$$163$$ −5.79198 + 10.0320i −0.453663 + 0.785767i −0.998610 0.0527032i $$-0.983216\pi$$
0.544947 + 0.838470i $$0.316550\pi$$
$$164$$ −0.321285 0.116938i −0.0250881 0.00913133i
$$165$$ 0 0
$$166$$ 6.85824 + 5.75475i 0.532303 + 0.446655i
$$167$$ −11.8334 + 4.30699i −0.915693 + 0.333285i −0.756524 0.653966i $$-0.773104\pi$$
−0.159170 + 0.987251i $$0.550882\pi$$
$$168$$ 0 0
$$169$$ 0.144844 + 0.821452i 0.0111419 + 0.0631887i
$$170$$ 0.511056 0.0391962
$$171$$ 0 0
$$172$$ −0.862728 −0.0657824
$$173$$ 12.4806 10.4724i 0.948880 0.796204i −0.0302289 0.999543i $$-0.509624\pi$$
0.979108 + 0.203339i $$0.0651792\pi$$
$$174$$ 0 0
$$175$$ −6.10722 + 11.6511i −0.461663 + 0.880738i
$$176$$ 8.19094 + 6.87302i 0.617415 + 0.518073i
$$177$$ 0 0
$$178$$ −0.677095 3.83999i −0.0507504 0.287820i
$$179$$ −3.97648 −0.297216 −0.148608 0.988896i $$-0.547479\pi$$
−0.148608 + 0.988896i $$0.547479\pi$$
$$180$$ 0 0
$$181$$ −0.0601490 0.104181i −0.00447084 0.00774372i 0.863781 0.503867i $$-0.168090\pi$$
−0.868252 + 0.496123i $$0.834756\pi$$
$$182$$ 4.08414 + 3.15231i 0.302736 + 0.233665i
$$183$$ 0 0
$$184$$ −1.75389 + 9.94682i −0.129299 + 0.733289i
$$185$$ 0.494619 0.180027i 0.0363651 0.0132358i
$$186$$ 0 0
$$187$$ 4.45786 + 25.2818i 0.325991 + 1.84879i
$$188$$ 5.03514 0.367226
$$189$$ 0 0
$$190$$ −0.254914 −0.0184934
$$191$$ 2.28213 + 12.9426i 0.165129 + 0.936493i 0.948931 + 0.315482i $$0.102166\pi$$
−0.783802 + 0.621010i $$0.786723\pi$$
$$192$$ 0 0
$$193$$ −5.65411 + 2.05793i −0.406992 + 0.148133i −0.537400 0.843327i $$-0.680593\pi$$
0.130408 + 0.991460i $$0.458371\pi$$
$$194$$ −0.430183 + 2.43969i −0.0308853 + 0.175159i
$$195$$ 0 0
$$196$$ −12.0358 + 0.984231i −0.859700 + 0.0703022i
$$197$$ −7.14867 12.3819i −0.509321 0.882171i −0.999942 0.0107972i $$-0.996563\pi$$
0.490620 0.871374i $$-0.336770\pi$$
$$198$$ 0 0
$$199$$ 1.31297 0.0930741 0.0465371 0.998917i $$-0.485181\pi$$
0.0465371 + 0.998917i $$0.485181\pi$$
$$200$$ −1.68617 9.56273i −0.119230 0.676187i
$$201$$ 0 0
$$202$$ 4.23962 + 3.55747i 0.298299 + 0.250302i
$$203$$ 8.06692 + 12.7421i 0.566187 + 0.894323i
$$204$$ 0 0
$$205$$ 0.0254045 0.0213169i 0.00177432 0.00148884i
$$206$$ −5.95696 −0.415041
$$207$$ 0 0
$$208$$ 9.02474 0.625753
$$209$$ −2.22358 12.6105i −0.153808 0.872290i
$$210$$ 0 0
$$211$$ 18.9172 6.88531i 1.30232 0.474005i 0.404566 0.914509i $$-0.367423\pi$$
0.897751 + 0.440504i $$0.145200\pi$$
$$212$$ −6.12597 5.14030i −0.420733 0.353037i
$$213$$ 0 0
$$214$$ 3.28752 + 1.19656i 0.224730 + 0.0817952i
$$215$$ 0.0418404 0.0724697i 0.00285349 0.00494239i
$$216$$ 0 0
$$217$$ −2.95382 13.5050i −0.200519 0.916779i
$$218$$ 3.23705 2.71621i 0.219241 0.183965i
$$219$$ 0 0
$$220$$ −1.19538 + 0.435083i −0.0805926 + 0.0293333i
$$221$$ 16.5984 + 13.9277i 1.11653 + 0.936877i
$$222$$ 0 0
$$223$$ 2.38617 + 13.5327i 0.159790 + 0.906214i 0.954275 + 0.298930i $$0.0966297\pi$$
−0.794485 + 0.607284i $$0.792259\pi$$
$$224$$ 10.1268 9.22680i 0.676625 0.616492i
$$225$$ 0 0
$$226$$ 5.43361 + 9.41129i 0.361439 + 0.626030i
$$227$$ −2.30630 13.0797i −0.153074 0.868128i −0.960525 0.278193i $$-0.910265\pi$$
0.807451 0.589935i $$-0.200847\pi$$
$$228$$ 0 0
$$229$$ 13.3651 4.86451i 0.883192 0.321456i 0.139695 0.990195i $$-0.455388\pi$$
0.743497 + 0.668739i $$0.233166\pi$$
$$230$$ −0.347552 0.291631i −0.0229169 0.0192296i
$$231$$ 0 0
$$232$$ −10.4609 3.80744i −0.686788 0.249971i
$$233$$ −10.2255 17.7111i −0.669897 1.16030i −0.977933 0.208921i $$-0.933005\pi$$
0.308036 0.951375i $$-0.400328\pi$$
$$234$$ 0 0
$$235$$ −0.244193 + 0.422955i −0.0159294 + 0.0275905i
$$236$$ 5.64329 + 2.05399i 0.367347 + 0.133703i
$$237$$ 0 0
$$238$$ 8.07384 0.329570i 0.523349 0.0213629i
$$239$$ −0.879905 + 4.99019i −0.0569163 + 0.322788i −0.999951 0.00990621i $$-0.996847\pi$$
0.943035 + 0.332695i $$0.107958\pi$$
$$240$$ 0 0
$$241$$ −5.26663 1.91690i −0.339254 0.123478i 0.166775 0.985995i $$-0.446665\pi$$
−0.506028 + 0.862517i $$0.668887\pi$$
$$242$$ 2.20710 + 3.82281i 0.141878 + 0.245740i
$$243$$ 0 0
$$244$$ 16.4934 1.05588
$$245$$ 0.501033 1.05875i 0.0320098 0.0676408i
$$246$$ 0 0
$$247$$ −8.27925 6.94712i −0.526796 0.442035i
$$248$$ 7.81711 + 6.55933i 0.496387 + 0.416518i
$$249$$ 0 0
$$250$$ 0.822055 + 0.299203i 0.0519913 + 0.0189233i
$$251$$ −3.77146 6.53236i −0.238053 0.412319i 0.722103 0.691786i $$-0.243176\pi$$
−0.960155 + 0.279467i $$0.909842\pi$$
$$252$$ 0 0
$$253$$ 11.3953 19.7372i 0.716414 1.24087i
$$254$$ −7.68718 + 6.45031i −0.482337 + 0.404728i
$$255$$ 0 0
$$256$$ −0.302321 + 1.71455i −0.0188950 + 0.107159i
$$257$$ 7.73949 2.81694i 0.482776 0.175716i −0.0891550 0.996018i $$-0.528417\pi$$
0.571931 + 0.820302i $$0.306194\pi$$
$$258$$ 0 0
$$259$$ 7.69808 3.16310i 0.478335 0.196545i
$$260$$ −0.536841 + 0.929835i −0.0332934 + 0.0576659i
$$261$$ 0 0
$$262$$ −2.06828 + 3.58236i −0.127779 + 0.221319i
$$263$$ 7.23383 6.06990i 0.446057 0.374286i −0.391913 0.920002i $$-0.628187\pi$$
0.837970 + 0.545716i $$0.183742\pi$$
$$264$$ 0 0
$$265$$ 0.728884 0.265292i 0.0447750 0.0162968i
$$266$$ −4.02722 + 0.164389i −0.246925 + 0.0100794i
$$267$$ 0 0
$$268$$ −4.26811 24.2056i −0.260716 1.47860i
$$269$$ 7.22050 + 12.5063i 0.440242 + 0.762521i 0.997707 0.0676791i $$-0.0215594\pi$$
−0.557465 + 0.830200i $$0.688226\pi$$
$$270$$ 0 0
$$271$$ −0.0795025 + 0.137702i −0.00482943 + 0.00836482i −0.868430 0.495812i $$-0.834871\pi$$
0.863601 + 0.504177i $$0.168204\pi$$
$$272$$ 10.8280 9.08577i 0.656544 0.550906i
$$273$$ 0 0
$$274$$ 0.202463 1.14822i 0.0122312 0.0693666i
$$275$$ −3.80472 + 21.5776i −0.229433 + 1.30118i
$$276$$ 0 0
$$277$$ −7.95742 + 6.67707i −0.478115 + 0.401186i −0.849744 0.527195i $$-0.823244\pi$$
0.371629 + 0.928381i $$0.378799\pi$$
$$278$$ −5.15854 −0.309389
$$279$$ 0 0
$$280$$ 0.184742 + 0.844650i 0.0110405 + 0.0504775i
$$281$$ 15.0687 + 5.48457i 0.898924 + 0.327182i 0.749822 0.661640i $$-0.230139\pi$$
0.149103 + 0.988822i $$0.452361\pi$$
$$282$$ 0 0
$$283$$ 0.0723941 0.410567i 0.00430338 0.0244057i −0.982580 0.185838i $$-0.940500\pi$$
0.986884 + 0.161432i $$0.0516112\pi$$
$$284$$ 2.30937 13.0971i 0.137036 0.777170i
$$285$$ 0 0
$$286$$ 8.07495 + 2.93904i 0.477482 + 0.173789i
$$287$$ 0.387602 0.353154i 0.0228794 0.0208460i
$$288$$ 0 0
$$289$$ 16.9368 0.996283
$$290$$ 0.383061 0.321427i 0.0224941 0.0188748i
$$291$$ 0 0
$$292$$ −4.12899 + 23.4166i −0.241631 + 1.37036i
$$293$$ 5.33332 30.2467i 0.311576 1.76703i −0.279234 0.960223i $$-0.590081\pi$$
0.590810 0.806811i $$-0.298808\pi$$
$$294$$ 0 0
$$295$$ −0.446223 + 0.374426i −0.0259801 + 0.0217999i
$$296$$ −3.07170 + 5.32034i −0.178539 + 0.309239i
$$297$$ 0 0
$$298$$ −3.81939 6.61537i −0.221251 0.383218i
$$299$$ −3.34025 18.9435i −0.193172 1.09553i
$$300$$ 0 0
$$301$$ 0.614275 1.17188i 0.0354062 0.0675463i
$$302$$ −1.81208 + 0.659543i −0.104273 + 0.0379524i
$$303$$ 0 0
$$304$$ −5.40100 + 4.53198i −0.309769 + 0.259927i
$$305$$ −0.799895 + 1.38546i −0.0458018 + 0.0793311i
$$306$$ 0 0
$$307$$ −3.38224 + 5.85821i −0.193035 + 0.334346i −0.946254 0.323423i $$-0.895166\pi$$
0.753220 + 0.657769i $$0.228500\pi$$
$$308$$ −18.6045 + 7.64448i −1.06009 + 0.435585i
$$309$$ 0 0
$$310$$ −0.430736 + 0.156775i −0.0244642 + 0.00890423i
$$311$$ −0.660957 + 3.74847i −0.0374794 + 0.212556i −0.997796 0.0663558i $$-0.978863\pi$$
0.960317 + 0.278912i $$0.0899739\pi$$
$$312$$ 0 0
$$313$$ 13.6497 11.4534i 0.771526 0.647387i −0.169573 0.985518i $$-0.554239\pi$$
0.941099 + 0.338131i $$0.109795\pi$$
$$314$$ −3.38981 + 5.87133i −0.191298 + 0.331338i
$$315$$ 0 0
$$316$$ −3.24963 5.62853i −0.182806 0.316630i
$$317$$ 9.06781 + 3.30041i 0.509299 + 0.185370i 0.583872 0.811846i $$-0.301537\pi$$
−0.0745729 + 0.997216i $$0.523759\pi$$
$$318$$ 0 0
$$319$$ 19.2423 + 16.1462i 1.07736 + 0.904014i
$$320$$ 0.274061 + 0.229964i 0.0153205 + 0.0128554i
$$321$$ 0 0
$$322$$ −5.67882 4.38316i −0.316468 0.244264i
$$323$$ −16.9277 −0.941880
$$324$$ 0 0
$$325$$ 9.24649 + 16.0154i 0.512903 + 0.888374i
$$326$$ 5.70689 + 2.07714i 0.316076 + 0.115042i
$$327$$ 0 0
$$328$$ −0.0672125 + 0.381181i −0.00371119 + 0.0210472i
$$329$$ −3.58510 + 6.83947i −0.197653 + 0.377072i
$$330$$ 0 0
$$331$$ −13.0406 4.74638i −0.716775 0.260885i −0.0422189 0.999108i $$-0.513443\pi$$
−0.674556 + 0.738224i $$0.735665\pi$$
$$332$$ −14.7298 + 25.5127i −0.808401 + 1.40019i
$$333$$ 0 0
$$334$$ 3.30103 + 5.71755i 0.180624 + 0.312850i
$$335$$ 2.24028 + 0.815396i 0.122400 + 0.0445498i
$$336$$ 0 0
$$337$$ 24.4425 + 20.5097i 1.33147 + 1.11723i 0.983733 + 0.179639i $$0.0574930\pi$$
0.347734 + 0.937593i $$0.386951\pi$$
$$338$$ 0.410936 0.149568i 0.0223519 0.00813544i
$$339$$ 0 0
$$340$$ 0.292015 + 1.65610i 0.0158367 + 0.0898146i
$$341$$ −11.5129 19.9409i −0.623457 1.07986i
$$342$$ 0 0
$$343$$ 7.23273 17.0496i 0.390531 0.920590i
$$344$$ 0.169598 + 0.961836i 0.00914409 + 0.0518587i
$$345$$ 0 0
$$346$$ −6.54321 5.49041i −0.351765 0.295166i
$$347$$ 22.1987 8.07967i 1.19169 0.433739i 0.331373 0.943500i $$-0.392488\pi$$
0.860316 + 0.509761i $$0.170266\pi$$
$$348$$ 0 0
$$349$$ 0.379417 0.318369i 0.0203097 0.0170419i −0.632576 0.774498i $$-0.718003\pi$$
0.652886 + 0.757456i $$0.273558\pi$$
$$350$$ 6.57153 + 2.09251i 0.351263 + 0.111849i
$$351$$ 0 0
$$352$$ 11.4093 19.7614i 0.608116 1.05329i
$$353$$ −20.6890 7.53018i −1.10116 0.400791i −0.273419 0.961895i $$-0.588155\pi$$
−0.827745 + 0.561104i $$0.810377\pi$$
$$354$$ 0 0
$$355$$ 0.988165 + 0.829169i 0.0524464 + 0.0440077i
$$356$$ 12.0568 4.38832i 0.639009 0.232580i
$$357$$ 0 0
$$358$$ 0.362015 + 2.05309i 0.0191331 + 0.108509i
$$359$$ 33.3784 1.76164 0.880822 0.473448i $$-0.156991\pi$$
0.880822 + 0.473448i $$0.156991\pi$$
$$360$$ 0 0
$$361$$ −10.5565 −0.555605
$$362$$ −0.0483136 + 0.0405399i −0.00253931 + 0.00213073i
$$363$$ 0 0
$$364$$ −7.88157 + 15.0361i −0.413106 + 0.788104i
$$365$$ −1.76677 1.48249i −0.0924767 0.0775972i
$$366$$ 0 0
$$367$$ 5.35778 + 30.3855i 0.279674 + 1.58611i 0.723713 + 0.690101i $$0.242434\pi$$
−0.444039 + 0.896007i $$0.646455\pi$$
$$368$$ −12.5485 −0.654136
$$369$$ 0 0
$$370$$ −0.137979 0.238986i −0.00717317 0.0124243i
$$371$$ 11.3441 4.66122i 0.588955 0.241999i
$$372$$ 0 0
$$373$$ −2.46530 + 13.9814i −0.127648 + 0.723929i 0.852051 + 0.523458i $$0.175358\pi$$
−0.979700 + 0.200471i $$0.935753\pi$$
$$374$$ 12.6473 4.60326i 0.653978 0.238029i
$$375$$ 0 0
$$376$$ −0.989823 5.61357i −0.0510462 0.289498i
$$377$$ 21.2011 1.09191
$$378$$ 0 0
$$379$$ −31.8848 −1.63781 −0.818907 0.573926i $$-0.805420\pi$$
−0.818907 + 0.573926i $$0.805420\pi$$
$$380$$ −0.145657 0.826062i −0.00747205 0.0423761i
$$381$$ 0 0
$$382$$ 6.47459 2.35656i 0.331269 0.120572i
$$383$$ −2.72859 + 15.4746i −0.139425 + 0.790716i 0.832251 + 0.554399i $$0.187052\pi$$
−0.971676 + 0.236318i $$0.924059\pi$$
$$384$$ 0 0
$$385$$ 0.260135 1.93353i 0.0132577 0.0985417i
$$386$$ 1.57727 + 2.73191i 0.0802808 + 0.139050i
$$387$$ 0 0
$$388$$ −8.15173 −0.413841
$$389$$ −4.01215 22.7541i −0.203424 1.15368i −0.899900 0.436096i $$-0.856361\pi$$
0.696476 0.717580i $$-0.254750\pi$$
$$390$$ 0 0
$$391$$ −23.0793 19.3658i −1.16717 0.979373i
$$392$$ 3.46333 + 13.2249i 0.174924 + 0.667960i
$$393$$ 0 0
$$394$$ −5.74204 + 4.81814i −0.289280 + 0.242734i
$$395$$ 0.630400 0.0317189
$$396$$ 0 0
$$397$$ 6.26112 0.314237 0.157118 0.987580i $$-0.449780\pi$$
0.157118 + 0.987580i $$0.449780\pi$$
$$398$$ −0.119532 0.677897i −0.00599158 0.0339799i
$$399$$ 0 0
$$400$$ 11.3364 4.12612i 0.566821 0.206306i
$$401$$ −22.5668 18.9358i −1.12693 0.945607i −0.127996 0.991775i $$-0.540855\pi$$
−0.998934 + 0.0461680i $$0.985299\pi$$
$$402$$ 0 0
$$403$$ −18.2623 6.64692i −0.909708 0.331107i
$$404$$ −9.10564 + 15.7714i −0.453022 + 0.784658i
$$405$$ 0 0
$$406$$ 5.84446 5.32504i 0.290056 0.264277i
$$407$$ 10.6190 8.91042i 0.526365 0.441673i
$$408$$ 0 0
$$409$$ 16.2666 5.92057i 0.804334 0.292754i 0.0930527 0.995661i $$-0.470337\pi$$
0.711281 + 0.702908i $$0.248115\pi$$
$$410$$ −0.0133189 0.0111758i −0.000657771 0.000551936i
$$411$$ 0 0
$$412$$ −3.40379 19.3038i −0.167692 0.951031i
$$413$$ −6.80813 + 6.20307i −0.335006 + 0.305233i
$$414$$ 0 0
$$415$$ −1.42872 2.47462i −0.0701331 0.121474i
$$416$$ −3.34436 18.9668i −0.163971 0.929924i
$$417$$ 0 0
$$418$$ −6.30849 + 2.29610i −0.308558 + 0.112306i
$$419$$ 8.30352 + 6.96748i 0.405653 + 0.340384i 0.822674 0.568513i $$-0.192481\pi$$
−0.417021 + 0.908897i $$0.636926\pi$$
$$420$$ 0 0
$$421$$ 3.82428 + 1.39192i 0.186384 + 0.0678382i 0.433526 0.901141i $$-0.357269\pi$$
−0.247142 + 0.968979i $$0.579491\pi$$
$$422$$ −5.27714 9.14028i −0.256887 0.444942i
$$423$$ 0 0
$$424$$ −4.52654 + 7.84019i −0.219828 + 0.380754i
$$425$$ 27.2178 + 9.90646i 1.32026 + 0.480534i
$$426$$ 0 0
$$427$$ −11.7436 + 22.4038i −0.568311 + 1.08420i
$$428$$ −1.99903 + 11.3371i −0.0966270 + 0.547999i
$$429$$ 0 0
$$430$$ −0.0412257 0.0150049i −0.00198808 0.000723603i
$$431$$ 0.857208 + 1.48473i 0.0412902 + 0.0715168i 0.885932 0.463815i $$-0.153520\pi$$
−0.844642 + 0.535332i $$0.820187\pi$$
$$432$$ 0 0
$$433$$ −7.74104 −0.372011 −0.186005 0.982549i $$-0.559554\pi$$
−0.186005 + 0.982549i $$0.559554\pi$$
$$434$$ −6.70382 + 2.75456i −0.321794 + 0.132223i
$$435$$ 0 0
$$436$$ 10.6517 + 8.93780i 0.510122 + 0.428043i
$$437$$ 11.5119 + 9.65967i 0.550691 + 0.462085i
$$438$$ 0 0
$$439$$ 7.29847 + 2.65643i 0.348337 + 0.126784i 0.510263 0.860019i $$-0.329548\pi$$
−0.161926 + 0.986803i $$0.551770\pi$$
$$440$$ 0.720056 + 1.24717i 0.0343273 + 0.0594566i
$$441$$ 0 0
$$442$$ 5.67987 9.83782i 0.270164 0.467937i
$$443$$ 11.5210 9.66731i 0.547381 0.459308i −0.326672 0.945138i $$-0.605927\pi$$
0.874053 + 0.485830i $$0.161483\pi$$
$$444$$ 0 0
$$445$$ −0.216107 + 1.22560i −0.0102444 + 0.0580991i
$$446$$ 6.76978 2.46400i 0.320558 0.116674i
$$447$$ 0 0
$$448$$ 4.47801 + 3.45632i 0.211566 + 0.163296i
$$449$$ 5.62232 9.73814i 0.265334 0.459571i −0.702317 0.711864i $$-0.747851\pi$$
0.967651 + 0.252293i $$0.0811846\pi$$
$$450$$ 0 0
$$451$$ 0.436688 0.756366i 0.0205628 0.0356159i
$$452$$ −27.3930 + 22.9855i −1.28846 + 1.08115i
$$453$$ 0 0
$$454$$ −6.54316 + 2.38152i −0.307086 + 0.111770i
$$455$$ −0.880800 1.39127i −0.0412925 0.0652238i
$$456$$ 0 0
$$457$$ 1.37539 + 7.80022i 0.0643380 + 0.364879i 0.999930 + 0.0117969i $$0.00375515\pi$$
−0.935592 + 0.353082i $$0.885134\pi$$
$$458$$ −3.72833 6.45766i −0.174213 0.301746i
$$459$$ 0 0
$$460$$ 0.746454 1.29290i 0.0348036 0.0602816i
$$461$$ −31.5097 + 26.4397i −1.46755 + 1.23142i −0.549179 + 0.835705i $$0.685059\pi$$
−0.918373 + 0.395717i $$0.870496\pi$$
$$462$$ 0 0
$$463$$ −1.09506 + 6.21042i −0.0508919 + 0.288623i −0.999623 0.0274624i $$-0.991257\pi$$
0.948731 + 0.316085i $$0.102368\pi$$
$$464$$ 2.40166 13.6205i 0.111494 0.632314i
$$465$$ 0 0
$$466$$ −8.21347 + 6.89192i −0.380482 + 0.319262i
$$467$$ −22.0979 −1.02257 −0.511285 0.859411i $$-0.670830\pi$$
−0.511285 + 0.859411i $$0.670830\pi$$
$$468$$ 0 0
$$469$$ 35.9186 + 11.4372i 1.65857 + 0.528121i
$$470$$ 0.240606 + 0.0875734i 0.0110983 + 0.00403946i
$$471$$ 0 0
$$472$$ 1.18057 6.69535i 0.0543402 0.308178i
$$473$$ 0.382685 2.17031i 0.0175959 0.0997911i
$$474$$ 0 0
$$475$$ −13.5762 4.94133i −0.622919 0.226724i
$$476$$ 5.68135 + 25.9753i 0.260404 + 1.19058i
$$477$$ 0 0
$$478$$ 2.65658 0.121509
$$479$$ 26.7411 22.4384i 1.22183 1.02524i 0.223104 0.974795i $$-0.428381\pi$$
0.998727 0.0504428i $$-0.0160633\pi$$
$$480$$ 0 0
$$481$$ 2.03168 11.5222i 0.0926367 0.525369i
$$482$$ −0.510240 + 2.89371i −0.0232408 + 0.131805i
$$483$$ 0 0
$$484$$ −11.1269 + 9.33656i −0.505767 + 0.424389i
$$485$$ 0.395340 0.684750i 0.0179515 0.0310929i
$$486$$ 0 0
$$487$$ 4.47185 + 7.74547i 0.202639 + 0.350981i 0.949378 0.314136i $$-0.101715\pi$$
−0.746739 + 0.665117i $$0.768382\pi$$
$$488$$ −3.24233 18.3881i −0.146773 0.832392i
$$489$$ 0 0
$$490$$ −0.592252 0.162300i −0.0267552 0.00733196i
$$491$$ −12.0705 + 4.39330i −0.544734 + 0.198267i −0.599705 0.800221i $$-0.704715\pi$$
0.0549715 + 0.998488i $$0.482493\pi$$
$$492$$ 0 0
$$493$$ 25.4373 21.3444i 1.14564 0.961305i
$$494$$ −2.83312 + 4.90710i −0.127468 + 0.220781i
$$495$$ 0 0
$$496$$ −6.33901 + 10.9795i −0.284630 + 0.492994i
$$497$$ 16.1461 + 12.4623i 0.724252 + 0.559009i
$$498$$ 0 0
$$499$$ −27.5613 + 10.0315i −1.23381 + 0.449071i −0.874902 0.484300i $$-0.839074\pi$$
−0.358911 + 0.933372i $$0.616852\pi$$
$$500$$ −0.499864 + 2.83487i −0.0223546 + 0.126779i
$$501$$ 0 0
$$502$$ −3.02936 + 2.54193i −0.135207 + 0.113452i
$$503$$ −19.2874 + 33.4067i −0.859982 + 1.48953i 0.0119637 + 0.999928i $$0.496192\pi$$
−0.871945 + 0.489603i $$0.837142\pi$$
$$504$$ 0 0
$$505$$ −0.883206 1.52976i −0.0393021 0.0680733i
$$506$$ −11.2279 4.08661i −0.499139 0.181672i
$$507$$ 0 0
$$508$$ −25.2950 21.2250i −1.12228 0.941707i
$$509$$ 7.19261 + 6.03532i 0.318807 + 0.267511i 0.788121 0.615521i $$-0.211054\pi$$
−0.469314 + 0.883031i $$0.655499\pi$$
$$510$$ 0 0
$$511$$ −28.8680 22.2816i −1.27705 0.985679i
$$512$$ −22.0413 −0.974098
$$513$$ 0 0
$$514$$ −2.15900 3.73951i −0.0952296 0.164942i
$$515$$ 1.78661 + 0.650272i 0.0787274 + 0.0286544i
$$516$$ 0 0
$$517$$ −2.23347 + 12.6666i −0.0982277 + 0.557077i
$$518$$ −2.33396 3.68661i −0.102548 0.161980i
$$519$$ 0 0
$$520$$ 1.14219 + 0.415722i 0.0500881 + 0.0182306i
$$521$$ −10.8653 + 18.8192i −0.476016 + 0.824483i −0.999622 0.0274767i $$-0.991253\pi$$
0.523607 + 0.851960i $$0.324586\pi$$
$$522$$ 0 0
$$523$$ −6.95293 12.0428i −0.304031 0.526596i 0.673014 0.739629i $$-0.264999\pi$$
−0.977045 + 0.213033i $$0.931666\pi$$
$$524$$ −12.7906 4.65541i −0.558761 0.203372i
$$525$$ 0 0
$$526$$ −3.79250 3.18228i −0.165361 0.138754i
$$527$$ −28.6032 + 10.4107i −1.24597 + 0.453497i
$$528$$ 0 0
$$529$$ 0.650571 + 3.68957i 0.0282857 + 0.160416i
$$530$$ −0.203329 0.352176i −0.00883205 0.0152976i
$$531$$ 0 0
$$532$$ −2.83385 12.9565i −0.122863 0.561735i
$$533$$ −0.128005 0.725952i −0.00554451 0.0314445i
$$534$$ 0 0
$$535$$ −0.855373 0.717743i −0.0369810 0.0310307i
$$536$$ −26.1473 + 9.51683i −1.12939 + 0.411064i
$$537$$ 0 0
$$538$$ 5.79974 4.86656i 0.250044 0.209812i
$$539$$ 2.86281 30.7143i 0.123310 1.32296i
$$540$$ 0 0
$$541$$ 6.05930 10.4950i 0.260510 0.451216i −0.705868 0.708344i $$-0.749443\pi$$
0.966377 + 0.257128i $$0.0827760\pi$$
$$542$$ 0.0783346 + 0.0285115i 0.00336476 + 0.00122467i
$$543$$ 0 0
$$544$$ −23.1077 19.3896i −0.990734 0.831324i
$$545$$ −1.26736 + 0.461282i −0.0542878 + 0.0197591i
$$546$$ 0 0
$$547$$ 3.20992 + 18.2043i 0.137246 + 0.778361i 0.973269 + 0.229667i $$0.0737637\pi$$
−0.836023 + 0.548694i $$0.815125\pi$$
$$548$$ 3.83656 0.163890
$$549$$ 0 0
$$550$$ 11.4871 0.489810
$$551$$ −12.6881 + 10.6466i −0.540532 + 0.453560i
$$552$$ 0 0
$$553$$ 9.95928 0.406533i 0.423512 0.0172875i
$$554$$ 4.17186 + 3.50060i 0.177245 + 0.148726i
$$555$$ 0 0
$$556$$ −2.94757 16.7165i −0.125005 0.708938i
$$557$$ −10.8392 −0.459270 −0.229635 0.973277i $$-0.573753\pi$$
−0.229635 + 0.973277i $$0.573753\pi$$
$$558$$ 0 0
$$559$$ −0.930028 1.61086i −0.0393360 0.0681319i
$$560$$ −0.993590 + 0.408260i −0.0419868 + 0.0172522i
$$561$$ 0 0
$$562$$ 1.45988 8.27940i 0.0615814 0.349245i
$$563$$ 13.5783 4.94209i 0.572257 0.208284i −0.0396511 0.999214i $$-0.512625\pi$$
0.611908 + 0.790929i $$0.290402\pi$$
$$564$$ 0 0
$$565$$ −0.602293 3.41577i −0.0253386 0.143703i
$$566$$ −0.218570 −0.00918717
$$567$$ 0 0
$$568$$ −15.0556 −0.631721
$$569$$ 3.93291 + 22.3046i 0.164876 + 0.935058i 0.949192 + 0.314697i $$0.101903\pi$$
−0.784316 + 0.620361i $$0.786986\pi$$
$$570$$ 0 0
$$571$$ 12.2245 4.44936i 0.511580 0.186200i −0.0733150 0.997309i $$-0.523358\pi$$
0.584895 + 0.811109i $$0.301136\pi$$
$$572$$ −4.91011 + 27.8466i −0.205302 + 1.16433i
$$573$$ 0 0
$$574$$ −0.217623 0.167971i −0.00908341 0.00701097i
$$575$$ −12.8568 22.2687i −0.536168 0.928670i
$$576$$ 0 0
$$577$$ −35.9124 −1.49505 −0.747527 0.664231i $$-0.768759\pi$$
−0.747527 + 0.664231i $$0.768759\pi$$
$$578$$ −1.54191 8.74460i −0.0641350 0.363728i
$$579$$ 0 0
$$580$$ 1.26048 + 1.05767i 0.0523385 + 0.0439172i
$$581$$ −24.1673 38.1735i −1.00263 1.58370i
$$582$$ 0 0
$$583$$ 15.6485 13.1306i 0.648093 0.543815i
$$584$$ 26.9184 1.11389
$$585$$ 0 0
$$586$$ −16.1022 −0.665174
$$587$$ −2.72345 15.4454i −0.112409 0.637501i −0.988001 0.154450i $$-0.950640\pi$$
0.875592 0.483051i $$-0.160472\pi$$
$$588$$ 0 0
$$589$$ 14.2672 5.19285i 0.587872 0.213968i
$$590$$ 0.233942 + 0.196301i 0.00963126 + 0.00808158i
$$591$$ 0 0
$$592$$ −7.17223 2.61048i −0.294777 0.107290i
$$593$$ −5.12430 + 8.87554i −0.210430 + 0.364475i −0.951849 0.306567i $$-0.900820\pi$$
0.741419 + 0.671042i $$0.234153\pi$$
$$594$$ 0 0
$$595$$ −2.45748 0.782509i −0.100747 0.0320798i
$$596$$ 19.2550 16.1569i 0.788718 0.661813i
$$597$$ 0 0
$$598$$ −9.47659 + 3.44920i −0.387526 + 0.141048i
$$599$$ −2.14768 1.80211i −0.0877517 0.0736324i 0.597857 0.801603i $$-0.296019\pi$$
−0.685608 + 0.727971i $$0.740464\pi$$
$$600$$ 0 0
$$601$$ −4.55665 25.8420i −0.185870 1.05412i −0.924833 0.380373i $$-0.875796\pi$$
0.738963 0.673746i $$-0.235316\pi$$
$$602$$ −0.660975 0.210468i −0.0269393 0.00857802i
$$603$$ 0 0
$$604$$ −3.17269 5.49527i −0.129095 0.223599i
$$605$$ −0.244648 1.38747i −0.00994635 0.0564085i
$$606$$ 0 0
$$607$$ 28.6778 10.4379i 1.16400 0.423660i 0.313472 0.949597i $$-0.398508\pi$$
0.850523 + 0.525938i $$0.176285\pi$$
$$608$$ 11.5261 + 9.67154i 0.467445 + 0.392233i
$$609$$ 0 0
$$610$$ 0.788144 + 0.286861i 0.0319110 + 0.0116147i
$$611$$ 5.42792 + 9.40144i 0.219590 + 0.380342i
$$612$$ 0 0
$$613$$ 12.8303 22.2228i 0.518212 0.897570i −0.481564 0.876411i $$-0.659931\pi$$
0.999776 0.0211587i $$-0.00673554\pi$$
$$614$$ 3.33255 + 1.21295i 0.134491 + 0.0489507i
$$615$$ 0 0
$$616$$ 12.1800 + 19.2389i 0.490745 + 0.775158i
$$617$$ −6.93374 + 39.3232i −0.279142 + 1.58309i 0.446348 + 0.894860i $$0.352724\pi$$
−0.725490 + 0.688233i $$0.758387\pi$$
$$618$$ 0 0
$$619$$ 45.7767 + 16.6614i 1.83992 + 0.669677i 0.989682 + 0.143283i $$0.0457661\pi$$
0.850241 + 0.526394i $$0.176456\pi$$
$$620$$ −0.754158 1.30624i −0.0302877 0.0524599i
$$621$$ 0 0
$$622$$ 1.99554 0.0800138
$$623$$ −2.62376 + 19.5018i −0.105119 + 0.781325i
$$624$$ 0 0
$$625$$ 18.8300 + 15.8002i 0.753199 + 0.632009i
$$626$$ −7.15615 6.00472i −0.286017 0.239997i
$$627$$ 0 0
$$628$$ −20.9632 7.63000i −0.836525 0.304470i
$$629$$ −9.16253 15.8700i −0.365334 0.632777i
$$630$$ 0 0
$$631$$ −4.78233 + 8.28324i −0.190382 + 0.329751i −0.945377 0.325980i $$-0.894306\pi$$
0.754995 + 0.655730i $$0.227639\pi$$
$$632$$ −5.63630 + 4.72941i −0.224200 + 0.188126i
$$633$$ 0 0
$$634$$ 0.878504 4.98224i 0.0348898 0.197870i
$$635$$ 3.00966 1.09543i 0.119435 0.0434707i
$$636$$ 0 0
$$637$$ −14.8124 21.4118i −0.586889 0.848366i
$$638$$ 6.58461 11.4049i 0.260687 0.451523i
$$639$$ 0 0
$$640$$ 0.960230 1.66317i 0.0379564 0.0657425i
$$641$$ −17.8850 + 15.0073i −0.706416 + 0.592753i −0.923591 0.383379i $$-0.874760\pi$$
0.217175 + 0.976133i $$0.430316\pi$$
$$642$$ 0 0
$$643$$ 8.05707 2.93253i 0.317740 0.115648i −0.178227 0.983989i $$-0.557036\pi$$
0.495967 + 0.868342i $$0.334814\pi$$
$$644$$ 10.9590 20.9070i 0.431844 0.823851i
$$645$$ 0 0
$$646$$ 1.54108 + 8.73988i 0.0606328 + 0.343866i
$$647$$ −23.6773 41.0103i −0.930852 1.61228i −0.781869 0.623443i $$-0.785734\pi$$
−0.148983 0.988840i $$-0.547600\pi$$
$$648$$ 0 0
$$649$$ −7.67032 + 13.2854i −0.301086 + 0.521497i
$$650$$ 7.42708 6.23206i 0.291314 0.244441i
$$651$$ 0 0
$$652$$ −3.47017 + 19.6803i −0.135902 + 0.770741i
$$653$$ 6.09997 34.5947i 0.238710 1.35379i −0.595947 0.803024i $$-0.703223\pi$$
0.834657 0.550770i $$-0.185666\pi$$
$$654$$ 0 0
$$655$$ 1.01137 0.848643i 0.0395176 0.0331592i
$$656$$ −0.480883 −0.0187753
$$657$$ 0 0
$$658$$ 3.85765 + 1.22835i 0.150387 + 0.0478862i
$$659$$ 32.0994 + 11.6832i 1.25042 + 0.455114i 0.880542 0.473968i $$-0.157179\pi$$
0.369874 + 0.929082i $$0.379401\pi$$
$$660$$ 0 0
$$661$$ 1.35395 7.67861i 0.0526624 0.298663i −0.947089 0.320972i $$-0.895990\pi$$
0.999751 + 0.0223085i $$0.00710159\pi$$
$$662$$ −1.26339 + 7.16505i −0.0491031 + 0.278478i
$$663$$ 0 0
$$664$$ 31.3391 + 11.4065i 1.21619 + 0.442658i
$$665$$ 1.22579 + 0.390315i 0.0475340 + 0.0151358i
$$666$$ 0 0
$$667$$ −29.4792 −1.14144
$$668$$ −16.6418 + 13.9641i −0.643891 + 0.540289i
$$669$$ 0 0
$$670$$ 0.217042 1.23091i 0.00838507 0.0475541i
$$671$$ −7.31608 + 41.4915i −0.282434 + 1.60176i
$$672$$ 0 0
$$673$$ −36.7385 + 30.8273i −1.41617 + 1.18830i −0.462809 + 0.886458i $$0.653158\pi$$
−0.953357 + 0.301846i $$0.902397\pi$$
$$674$$ 8.36408 14.4870i 0.322172 0.558019i
$$675$$ 0 0
$$676$$ 0.719490 + 1.24619i 0.0276727 + 0.0479305i
$$677$$ −0.667582 3.78605i −0.0256573 0.145510i 0.969288 0.245928i $$-0.0790928\pi$$
−0.994945 + 0.100419i $$0.967982\pi$$
$$678$$ 0 0
$$679$$ 5.80415 11.0729i 0.222743 0.424938i
$$680$$ 1.78894 0.651122i 0.0686028 0.0249694i
$$681$$ 0 0
$$682$$ −9.24751 + 7.75958i −0.354105 + 0.297130i
$$683$$ −12.9081 + 22.3575i −0.493916 + 0.855487i −0.999975 0.00701138i $$-0.997768\pi$$
0.506060 + 0.862498i $$0.331102\pi$$
$$684$$ 0 0
$$685$$ −0.186064 + 0.322273i −0.00710915 + 0.0123134i
$$686$$ −9.46128 2.18214i −0.361233 0.0833145i
$$687$$ 0 0
$$688$$ −1.14024 + 0.415012i −0.0434711 + 0.0158222i
$$689$$ 2.99394 16.9795i 0.114060 0.646866i
$$690$$ 0 0
$$691$$ −23.7181 + 19.9018i −0.902278 + 0.757101i −0.970634 0.240560i $$-0.922669\pi$$
0.0683562 + 0.997661i $$0.478225\pi$$
$$692$$ 14.0532 24.3408i 0.534221 0.925298i
$$693$$ 0 0
$$694$$ −6.19254 10.7258i −0.235066 0.407146i
$$695$$ 1.54715 + 0.563115i 0.0586866 + 0.0213602i
$$696$$ 0 0
$$697$$ −0.884443 0.742136i −0.0335007 0.0281104i
$$698$$ −0.198918 0.166912i −0.00752915 0.00631771i
$$699$$ 0 0
$$700$$ −3.02592 + 22.4910i −0.114369 + 0.850080i
$$701$$ 16.6949 0.630556 0.315278 0.948999i $$-0.397902\pi$$
0.315278 + 0.948999i $$0.397902\pi$$
$$702$$ 0 0
$$703$$ 4.57026 + 7.91593i 0.172371 + 0.298555i
$$704$$ 8.85369 + 3.22248i 0.333686 + 0.121452i
$$705$$ 0 0
$$706$$ −2.00438 + 11.3674i −0.0754360 + 0.427819i
$$707$$ −14.9397 23.5981i −0.561866 0.887497i
$$708$$ 0 0
$$709$$ 13.9167 + 5.06528i 0.522654 + 0.190230i 0.589855 0.807509i $$-0.299185\pi$$
−0.0672014 + 0.997739i $$0.521407\pi$$
$$710$$ 0.338145 0.585684i 0.0126903 0.0219803i
$$711$$ 0 0
$$712$$ −7.26259 12.5792i −0.272177 0.471424i
$$713$$ 25.3929 + 9.24225i 0.950971 + 0.346125i
$$714$$ 0 0
$$715$$ −2.10100 1.76295i −0.0785730 0.0659306i
$$716$$ −6.44627 + 2.34625i −0.240909 + 0.0876835i
$$717$$ 0 0
$$718$$ −3.03873 17.2335i −0.113404 0.643149i
$$719$$ 18.8263 + 32.6081i 0.702102 + 1.21608i 0.967727 + 0.252000i $$0.0810883\pi$$
−0.265625 + 0.964076i $$0.585578\pi$$
$$720$$ 0 0
$$721$$ 28.6448 + 9.12108i 1.06679 + 0.339687i
$$722$$ 0.961052 + 5.45040i 0.0357666 + 0.202843i
$$723$$ 0 0
$$724$$ −0.158978 0.133398i −0.00590836 0.00495770i
$$725$$ 26.6317 9.69314i 0.989076 0.359994i
$$726$$ 0 0
$$727$$ 2.73015 2.29087i 0.101256 0.0849635i −0.590755 0.806851i $$-0.701170\pi$$
0.692010 + 0.721888i $$0.256725\pi$$
$$728$$ 18.3127 + 5.83114i 0.678715 + 0.216117i
$$729$$ 0 0
$$730$$ −0.604577 + 1.04716i −0.0223764 + 0.0387571i
$$731$$ −2.73761 0.996408i −0.101254 0.0368535i
$$732$$ 0 0
$$733$$ −33.4801 28.0931i −1.23661 1.03764i −0.997781 0.0665826i $$-0.978790\pi$$
−0.238834 0.971060i $$-0.576765\pi$$
$$734$$ 15.2005 5.53252i 0.561060 0.204209i
$$735$$ 0 0
$$736$$ 4.65019 + 26.3725i 0.171408 + 0.972104i
$$737$$ 62.7859 2.31275
$$738$$ 0 0
$$739$$ 13.4386 0.494348 0.247174 0.968971i $$-0.420498\pi$$
0.247174 + 0.968971i $$0.420498\pi$$
$$740$$ 0.695606 0.583683i 0.0255710 0.0214566i
$$741$$ 0 0
$$742$$ −3.43938 5.43268i −0.126263 0.199440i
$$743$$ 28.4384 + 23.8627i 1.04331 + 0.875437i 0.992374 0.123265i $$-0.0393365\pi$$
0.0509315 + 0.998702i $$0.483781\pi$$
$$744$$ 0 0
$$745$$ 0.423363 + 2.40101i 0.0155108 + 0.0879662i
$$746$$ 7.44314 0.272513
$$747$$ 0 0
$$748$$ 22.1437 + 38.3540i 0.809654 + 1.40236i
$$749$$ −13.9763 10.7875i −0.510685 0.394168i
$$750$$ 0 0
$$751$$ 5.74504 32.5818i 0.209640 1.18893i −0.680330 0.732906i $$-0.738164\pi$$
0.889970 0.456020i $$-0.150725\pi$$
$$752$$ 6.65476 2.42214i 0.242674 0.0883262i
$$753$$ 0 0
$$754$$ −1.93012 10.9463i −0.0702909 0.398640i
$$755$$ 0.615474 0.0223994
$$756$$ 0 0
$$757$$ 50.3539 1.83014 0.915072 0.403291i $$-0.132134\pi$$
0.915072 + 0.403291i $$0.132134\pi$$
$$758$$ 2.90276 + 16.4624i 0.105433 + 0.597940i
$$759$$ 0 0
$$760$$ −0.892323 + 0.324779i −0.0323680 + 0.0117810i
$$761$$ 5.20712 29.5310i 0.188758 1.07050i −0.732274 0.681011i $$-0.761541\pi$$
0.921031 0.389488i $$-0.127348\pi$$
$$762$$ 0 0
$$763$$ −19.7248 + 8.10479i −0.714084 + 0.293413i
$$764$$ 11.3361 + 19.6347i 0.410126 + 0.710358i
$$765$$ 0 0
$$766$$ 8.23807 0.297654
$$767$$ 2.24837 + 12.7512i 0.0811841 + 0.460418i
$$768$$ 0 0
$$769$$ −17.8704 14.9950i −0.644423 0.540735i 0.260950 0.965352i $$-0.415964\pi$$
−0.905373 + 0.424617i $$0.860409\pi$$
$$770$$ −1.02198 + 0.0417166i −0.0368295 + 0.00150336i
$$771$$ 0 0
$$772$$ −7.95164 + 6.67222i −0.286186 + 0.240138i
$$773$$ 37.6553 1.35437 0.677184 0.735814i $$-0.263200\pi$$
0.677184 + 0.735814i $$0.263200\pi$$
$$774$$ 0 0
$$775$$ −25.9791 −0.933197
$$776$$ 1.60249 + 9.08817i 0.0575260 + 0.326246i
$$777$$ 0 0
$$778$$ −11.3828 + 4.14301i −0.408094 + 0.148534i
$$779$$ 0.441160 + 0.370177i 0.0158062 + 0.0132630i
$$780$$ 0 0
$$781$$ 31.9232 + 11.6191i 1.14230 + 0.415764i
$$782$$ −7.89761 + 13.6791i −0.282418 + 0.489162i
$$783$$ 0