# Properties

 Label 1045.2.b.d.419.13 Level $1045$ Weight $2$ Character 1045.419 Analytic conductor $8.344$ Analytic rank $0$ Dimension $22$ Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,2,Mod(419,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

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

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

chi := DirichletCharacter("1045.419");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1045 = 5 \cdot 11 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1045.b (of order $$2$$, degree $$1$$, 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: $$8.34436701122$$ Analytic rank: $$0$$ Dimension: $$22$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 419.13 Character $$\chi$$ $$=$$ 1045.419 Dual form 1045.2.b.d.419.10

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+0.790175i q^{2} -2.57534i q^{3} +1.37562 q^{4} +(1.76786 + 1.36919i) q^{5} +2.03497 q^{6} +0.0669205i q^{7} +2.66733i q^{8} -3.63236 q^{9} +O(q^{10})$$ $$q+0.790175i q^{2} -2.57534i q^{3} +1.37562 q^{4} +(1.76786 + 1.36919i) q^{5} +2.03497 q^{6} +0.0669205i q^{7} +2.66733i q^{8} -3.63236 q^{9} +(-1.08190 + 1.39692i) q^{10} -1.00000 q^{11} -3.54270i q^{12} -4.14913i q^{13} -0.0528789 q^{14} +(3.52613 - 4.55283i) q^{15} +0.643589 q^{16} -6.61558i q^{17} -2.87020i q^{18} +1.00000 q^{19} +(2.43191 + 1.88349i) q^{20} +0.172343 q^{21} -0.790175i q^{22} -2.21109i q^{23} +6.86928 q^{24} +(1.25064 + 4.84106i) q^{25} +3.27854 q^{26} +1.62854i q^{27} +0.0920574i q^{28} -2.56775 q^{29} +(3.59753 + 2.78626i) q^{30} +8.77193 q^{31} +5.84321i q^{32} +2.57534i q^{33} +5.22747 q^{34} +(-0.0916269 + 0.118306i) q^{35} -4.99676 q^{36} +11.4277i q^{37} +0.790175i q^{38} -10.6854 q^{39} +(-3.65209 + 4.71546i) q^{40} +10.9830 q^{41} +0.136181i q^{42} -3.95978i q^{43} -1.37562 q^{44} +(-6.42149 - 4.97339i) q^{45} +1.74715 q^{46} -8.97459i q^{47} -1.65746i q^{48} +6.99552 q^{49} +(-3.82529 + 0.988221i) q^{50} -17.0374 q^{51} -5.70765i q^{52} +3.13641i q^{53} -1.28683 q^{54} +(-1.76786 - 1.36919i) q^{55} -0.178499 q^{56} -2.57534i q^{57} -2.02897i q^{58} -10.3362 q^{59} +(4.85062 - 6.26298i) q^{60} +2.76550 q^{61} +6.93135i q^{62} -0.243079i q^{63} -3.32998 q^{64} +(5.68095 - 7.33507i) q^{65} -2.03497 q^{66} +15.2686i q^{67} -9.10056i q^{68} -5.69431 q^{69} +(-0.0934823 - 0.0724013i) q^{70} -4.11096 q^{71} -9.68871i q^{72} -7.16167i q^{73} -9.02987 q^{74} +(12.4674 - 3.22081i) q^{75} +1.37562 q^{76} -0.0669205i q^{77} -8.44334i q^{78} -8.94984 q^{79} +(1.13777 + 0.881196i) q^{80} -6.70304 q^{81} +8.67846i q^{82} -3.78408i q^{83} +0.237079 q^{84} +(9.05799 - 11.6954i) q^{85} +3.12892 q^{86} +6.61283i q^{87} -2.66733i q^{88} -0.223450 q^{89} +(3.92985 - 5.07410i) q^{90} +0.277662 q^{91} -3.04163i q^{92} -22.5907i q^{93} +7.09149 q^{94} +(1.76786 + 1.36919i) q^{95} +15.0482 q^{96} +14.1106i q^{97} +5.52768i q^{98} +3.63236 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$22 q - 32 q^{4} + 7 q^{5} - 12 q^{6} - 34 q^{9}+O(q^{10})$$ 22 * q - 32 * q^4 + 7 * q^5 - 12 * q^6 - 34 * q^9 $$22 q - 32 q^{4} + 7 q^{5} - 12 q^{6} - 34 q^{9} + 2 q^{10} - 22 q^{11} + 8 q^{14} - 23 q^{15} + 40 q^{16} + 22 q^{19} - 22 q^{20} - 22 q^{21} + 22 q^{24} + 13 q^{25} + 16 q^{26} + 10 q^{29} - 22 q^{30} + 76 q^{31} - 56 q^{34} - 2 q^{35} + 104 q^{36} + 8 q^{39} - 20 q^{40} + 6 q^{41} + 32 q^{44} - 12 q^{45} + 88 q^{46} - 28 q^{49} - 20 q^{50} + 8 q^{51} - 38 q^{54} - 7 q^{55} + 44 q^{56} - 40 q^{59} + 78 q^{60} - 6 q^{61} - 140 q^{64} - 22 q^{65} + 12 q^{66} - 74 q^{69} - 24 q^{70} + 62 q^{71} + 26 q^{74} + 13 q^{75} - 32 q^{76} - 102 q^{79} + 142 q^{80} + 94 q^{81} + 38 q^{84} + 26 q^{85} + 28 q^{86} - 54 q^{89} + 118 q^{90} + 88 q^{91} - 36 q^{94} + 7 q^{95} + 2 q^{96} + 34 q^{99}+O(q^{100})$$ 22 * q - 32 * q^4 + 7 * q^5 - 12 * q^6 - 34 * q^9 + 2 * q^10 - 22 * q^11 + 8 * q^14 - 23 * q^15 + 40 * q^16 + 22 * q^19 - 22 * q^20 - 22 * q^21 + 22 * q^24 + 13 * q^25 + 16 * q^26 + 10 * q^29 - 22 * q^30 + 76 * q^31 - 56 * q^34 - 2 * q^35 + 104 * q^36 + 8 * q^39 - 20 * q^40 + 6 * q^41 + 32 * q^44 - 12 * q^45 + 88 * q^46 - 28 * q^49 - 20 * q^50 + 8 * q^51 - 38 * q^54 - 7 * q^55 + 44 * q^56 - 40 * q^59 + 78 * q^60 - 6 * q^61 - 140 * q^64 - 22 * q^65 + 12 * q^66 - 74 * q^69 - 24 * q^70 + 62 * q^71 + 26 * q^74 + 13 * q^75 - 32 * q^76 - 102 * q^79 + 142 * q^80 + 94 * q^81 + 38 * q^84 + 26 * q^85 + 28 * q^86 - 54 * q^89 + 118 * q^90 + 88 * q^91 - 36 * q^94 + 7 * q^95 + 2 * q^96 + 34 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times$$.

 $$n$$ $$496$$ $$761$$ $$837$$ $$\chi(n)$$ $$1$$ $$1$$ $$-1$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.790175i 0.558738i 0.960184 + 0.279369i $$0.0901252\pi$$
−0.960184 + 0.279369i $$0.909875\pi$$
$$3$$ 2.57534i 1.48687i −0.668807 0.743436i $$-0.733195\pi$$
0.668807 0.743436i $$-0.266805\pi$$
$$4$$ 1.37562 0.687812
$$5$$ 1.76786 + 1.36919i 0.790610 + 0.612320i
$$6$$ 2.03497 0.830771
$$7$$ 0.0669205i 0.0252936i 0.999920 + 0.0126468i $$0.00402570\pi$$
−0.999920 + 0.0126468i $$0.995974\pi$$
$$8$$ 2.66733i 0.943044i
$$9$$ −3.63236 −1.21079
$$10$$ −1.08190 + 1.39692i −0.342127 + 0.441744i
$$11$$ −1.00000 −0.301511
$$12$$ 3.54270i 1.02269i
$$13$$ 4.14913i 1.15076i −0.817885 0.575381i $$-0.804854\pi$$
0.817885 0.575381i $$-0.195146\pi$$
$$14$$ −0.0528789 −0.0141325
$$15$$ 3.52613 4.55283i 0.910442 1.17553i
$$16$$ 0.643589 0.160897
$$17$$ 6.61558i 1.60451i −0.596978 0.802257i $$-0.703632\pi$$
0.596978 0.802257i $$-0.296368\pi$$
$$18$$ 2.87020i 0.676512i
$$19$$ 1.00000 0.229416
$$20$$ 2.43191 + 1.88349i 0.543791 + 0.421161i
$$21$$ 0.172343 0.0376083
$$22$$ 0.790175i 0.168466i
$$23$$ 2.21109i 0.461045i −0.973067 0.230522i $$-0.925957\pi$$
0.973067 0.230522i $$-0.0740435\pi$$
$$24$$ 6.86928 1.40219
$$25$$ 1.25064 + 4.84106i 0.250127 + 0.968213i
$$26$$ 3.27854 0.642974
$$27$$ 1.62854i 0.313413i
$$28$$ 0.0920574i 0.0173972i
$$29$$ −2.56775 −0.476820 −0.238410 0.971165i $$-0.576626\pi$$
−0.238410 + 0.971165i $$0.576626\pi$$
$$30$$ 3.59753 + 2.78626i 0.656816 + 0.508698i
$$31$$ 8.77193 1.57548 0.787742 0.616005i $$-0.211250\pi$$
0.787742 + 0.616005i $$0.211250\pi$$
$$32$$ 5.84321i 1.03294i
$$33$$ 2.57534i 0.448309i
$$34$$ 5.22747 0.896503
$$35$$ −0.0916269 + 0.118306i −0.0154878 + 0.0199973i
$$36$$ −4.99676 −0.832794
$$37$$ 11.4277i 1.87870i 0.342960 + 0.939350i $$0.388570\pi$$
−0.342960 + 0.939350i $$0.611430\pi$$
$$38$$ 0.790175i 0.128183i
$$39$$ −10.6854 −1.71104
$$40$$ −3.65209 + 4.71546i −0.577445 + 0.745580i
$$41$$ 10.9830 1.71525 0.857626 0.514274i $$-0.171939\pi$$
0.857626 + 0.514274i $$0.171939\pi$$
$$42$$ 0.136181i 0.0210132i
$$43$$ 3.95978i 0.603861i −0.953330 0.301931i $$-0.902369\pi$$
0.953330 0.301931i $$-0.0976311\pi$$
$$44$$ −1.37562 −0.207383
$$45$$ −6.42149 4.97339i −0.957260 0.741390i
$$46$$ 1.74715 0.257603
$$47$$ 8.97459i 1.30908i −0.756028 0.654539i $$-0.772863\pi$$
0.756028 0.654539i $$-0.227137\pi$$
$$48$$ 1.65746i 0.239234i
$$49$$ 6.99552 0.999360
$$50$$ −3.82529 + 0.988221i −0.540977 + 0.139756i
$$51$$ −17.0374 −2.38571
$$52$$ 5.70765i 0.791508i
$$53$$ 3.13641i 0.430819i 0.976524 + 0.215410i $$0.0691087\pi$$
−0.976524 + 0.215410i $$0.930891\pi$$
$$54$$ −1.28683 −0.175116
$$55$$ −1.76786 1.36919i −0.238378 0.184622i
$$56$$ −0.178499 −0.0238530
$$57$$ 2.57534i 0.341112i
$$58$$ 2.02897i 0.266417i
$$59$$ −10.3362 −1.34566 −0.672828 0.739799i $$-0.734921\pi$$
−0.672828 + 0.739799i $$0.734921\pi$$
$$60$$ 4.85062 6.26298i 0.626213 0.808547i
$$61$$ 2.76550 0.354086 0.177043 0.984203i $$-0.443347\pi$$
0.177043 + 0.984203i $$0.443347\pi$$
$$62$$ 6.93135i 0.880283i
$$63$$ 0.243079i 0.0306251i
$$64$$ −3.32998 −0.416248
$$65$$ 5.68095 7.33507i 0.704635 0.909804i
$$66$$ −2.03497 −0.250487
$$67$$ 15.2686i 1.86535i 0.360713 + 0.932677i $$0.382533\pi$$
−0.360713 + 0.932677i $$0.617467\pi$$
$$68$$ 9.10056i 1.10360i
$$69$$ −5.69431 −0.685514
$$70$$ −0.0934823 0.0724013i −0.0111733 0.00865360i
$$71$$ −4.11096 −0.487881 −0.243940 0.969790i $$-0.578440\pi$$
−0.243940 + 0.969790i $$0.578440\pi$$
$$72$$ 9.68871i 1.14183i
$$73$$ 7.16167i 0.838210i −0.907938 0.419105i $$-0.862344\pi$$
0.907938 0.419105i $$-0.137656\pi$$
$$74$$ −9.02987 −1.04970
$$75$$ 12.4674 3.22081i 1.43961 0.371907i
$$76$$ 1.37562 0.157795
$$77$$ 0.0669205i 0.00762630i
$$78$$ 8.44334i 0.956020i
$$79$$ −8.94984 −1.00694 −0.503468 0.864014i $$-0.667943\pi$$
−0.503468 + 0.864014i $$0.667943\pi$$
$$80$$ 1.13777 + 0.881196i 0.127207 + 0.0985207i
$$81$$ −6.70304 −0.744782
$$82$$ 8.67846i 0.958376i
$$83$$ 3.78408i 0.415357i −0.978197 0.207679i $$-0.933409\pi$$
0.978197 0.207679i $$-0.0665908\pi$$
$$84$$ 0.237079 0.0258674
$$85$$ 9.05799 11.6954i 0.982477 1.26854i
$$86$$ 3.12892 0.337400
$$87$$ 6.61283i 0.708970i
$$88$$ 2.66733i 0.284339i
$$89$$ −0.223450 −0.0236856 −0.0118428 0.999930i $$-0.503770\pi$$
−0.0118428 + 0.999930i $$0.503770\pi$$
$$90$$ 3.92985 5.07410i 0.414242 0.534857i
$$91$$ 0.277662 0.0291069
$$92$$ 3.04163i 0.317112i
$$93$$ 22.5907i 2.34254i
$$94$$ 7.09149 0.731431
$$95$$ 1.76786 + 1.36919i 0.181378 + 0.140476i
$$96$$ 15.0482 1.53585
$$97$$ 14.1106i 1.43272i 0.697732 + 0.716359i $$0.254193\pi$$
−0.697732 + 0.716359i $$0.745807\pi$$
$$98$$ 5.52768i 0.558380i
$$99$$ 3.63236 0.365066
$$100$$ 1.72041 + 6.65948i 0.172041 + 0.665948i
$$101$$ −11.6761 −1.16182 −0.580909 0.813968i $$-0.697303\pi$$
−0.580909 + 0.813968i $$0.697303\pi$$
$$102$$ 13.4625i 1.33298i
$$103$$ 11.6529i 1.14820i 0.818786 + 0.574098i $$0.194647\pi$$
−0.818786 + 0.574098i $$0.805353\pi$$
$$104$$ 11.0671 1.08522
$$105$$ 0.304677 + 0.235970i 0.0297335 + 0.0230283i
$$106$$ −2.47831 −0.240715
$$107$$ 2.72445i 0.263382i 0.991291 + 0.131691i $$0.0420407\pi$$
−0.991291 + 0.131691i $$0.957959\pi$$
$$108$$ 2.24026i 0.215569i
$$109$$ 3.96882 0.380144 0.190072 0.981770i $$-0.439128\pi$$
0.190072 + 0.981770i $$0.439128\pi$$
$$110$$ 1.08190 1.39692i 0.103155 0.133191i
$$111$$ 29.4301 2.79339
$$112$$ 0.0430693i 0.00406967i
$$113$$ 2.81732i 0.265031i −0.991181 0.132516i $$-0.957695\pi$$
0.991181 0.132516i $$-0.0423055\pi$$
$$114$$ 2.03497 0.190592
$$115$$ 3.02741 3.90890i 0.282307 0.364506i
$$116$$ −3.53226 −0.327962
$$117$$ 15.0711i 1.39333i
$$118$$ 8.16739i 0.751869i
$$119$$ 0.442718 0.0405839
$$120$$ 12.1439 + 9.40535i 1.10858 + 0.858587i
$$121$$ 1.00000 0.0909091
$$122$$ 2.18523i 0.197841i
$$123$$ 28.2848i 2.55036i
$$124$$ 12.0669 1.08364
$$125$$ −4.41739 + 10.2707i −0.395104 + 0.918637i
$$126$$ 0.192075 0.0171114
$$127$$ 1.05561i 0.0936707i −0.998903 0.0468353i $$-0.985086\pi$$
0.998903 0.0468353i $$-0.0149136\pi$$
$$128$$ 9.05516i 0.800371i
$$129$$ −10.1978 −0.897864
$$130$$ 5.79599 + 4.48894i 0.508342 + 0.393706i
$$131$$ −18.2156 −1.59151 −0.795753 0.605621i $$-0.792925\pi$$
−0.795753 + 0.605621i $$0.792925\pi$$
$$132$$ 3.54270i 0.308352i
$$133$$ 0.0669205i 0.00580274i
$$134$$ −12.0648 −1.04224
$$135$$ −2.22978 + 2.87903i −0.191909 + 0.247787i
$$136$$ 17.6460 1.51313
$$137$$ 7.14378i 0.610334i 0.952299 + 0.305167i $$0.0987123\pi$$
−0.952299 + 0.305167i $$0.901288\pi$$
$$138$$ 4.49950i 0.383023i
$$139$$ −2.25667 −0.191408 −0.0957041 0.995410i $$-0.530510\pi$$
−0.0957041 + 0.995410i $$0.530510\pi$$
$$140$$ −0.126044 + 0.162744i −0.0106527 + 0.0137544i
$$141$$ −23.1126 −1.94643
$$142$$ 3.24837i 0.272598i
$$143$$ 4.14913i 0.346968i
$$144$$ −2.33775 −0.194812
$$145$$ −4.53942 3.51574i −0.376978 0.291967i
$$146$$ 5.65897 0.468340
$$147$$ 18.0158i 1.48592i
$$148$$ 15.7202i 1.29219i
$$149$$ −5.60288 −0.459006 −0.229503 0.973308i $$-0.573710\pi$$
−0.229503 + 0.973308i $$0.573710\pi$$
$$150$$ 2.54500 + 9.85140i 0.207799 + 0.804364i
$$151$$ −20.8631 −1.69782 −0.848908 0.528541i $$-0.822739\pi$$
−0.848908 + 0.528541i $$0.822739\pi$$
$$152$$ 2.66733i 0.216349i
$$153$$ 24.0302i 1.94273i
$$154$$ 0.0528789 0.00426110
$$155$$ 15.5075 + 12.0104i 1.24559 + 0.964701i
$$156$$ −14.6991 −1.17687
$$157$$ 0.664796i 0.0530565i −0.999648 0.0265282i $$-0.991555\pi$$
0.999648 0.0265282i $$-0.00844519\pi$$
$$158$$ 7.07194i 0.562613i
$$159$$ 8.07732 0.640573
$$160$$ −8.00047 + 10.3300i −0.632493 + 0.816655i
$$161$$ 0.147967 0.0116615
$$162$$ 5.29657i 0.416138i
$$163$$ 0.357030i 0.0279647i −0.999902 0.0139824i $$-0.995549\pi$$
0.999902 0.0139824i $$-0.00445087\pi$$
$$164$$ 15.1084 1.17977
$$165$$ −3.52613 + 4.55283i −0.274509 + 0.354437i
$$166$$ 2.99009 0.232076
$$167$$ 12.2396i 0.947127i −0.880760 0.473563i $$-0.842967\pi$$
0.880760 0.473563i $$-0.157033\pi$$
$$168$$ 0.459696i 0.0354663i
$$169$$ −4.21530 −0.324253
$$170$$ 9.24141 + 7.15740i 0.708784 + 0.548947i
$$171$$ −3.63236 −0.277774
$$172$$ 5.44717i 0.415343i
$$173$$ 14.4260i 1.09679i 0.836220 + 0.548394i $$0.184761\pi$$
−0.836220 + 0.548394i $$0.815239\pi$$
$$174$$ −5.22529 −0.396128
$$175$$ −0.323966 + 0.0836932i −0.0244896 + 0.00632661i
$$176$$ −0.643589 −0.0485124
$$177$$ 26.6191i 2.00082i
$$178$$ 0.176564i 0.0132341i
$$179$$ −8.72275 −0.651969 −0.325984 0.945375i $$-0.605696\pi$$
−0.325984 + 0.945375i $$0.605696\pi$$
$$180$$ −8.83356 6.84152i −0.658415 0.509937i
$$181$$ −13.9631 −1.03787 −0.518936 0.854813i $$-0.673672\pi$$
−0.518936 + 0.854813i $$0.673672\pi$$
$$182$$ 0.219401i 0.0162631i
$$183$$ 7.12209i 0.526480i
$$184$$ 5.89772 0.434786
$$185$$ −15.6467 + 20.2025i −1.15037 + 1.48532i
$$186$$ 17.8506 1.30887
$$187$$ 6.61558i 0.483779i
$$188$$ 12.3457i 0.900400i
$$189$$ −0.108983 −0.00792733
$$190$$ −1.08190 + 1.39692i −0.0784892 + 0.101343i
$$191$$ 4.76262 0.344611 0.172306 0.985044i $$-0.444878\pi$$
0.172306 + 0.985044i $$0.444878\pi$$
$$192$$ 8.57582i 0.618907i
$$193$$ 5.69191i 0.409713i 0.978792 + 0.204856i $$0.0656727\pi$$
−0.978792 + 0.204856i $$0.934327\pi$$
$$194$$ −11.1499 −0.800514
$$195$$ −18.8903 14.6304i −1.35276 1.04770i
$$196$$ 9.62321 0.687372
$$197$$ 19.1425i 1.36385i 0.731424 + 0.681923i $$0.238856\pi$$
−0.731424 + 0.681923i $$0.761144\pi$$
$$198$$ 2.87020i 0.203976i
$$199$$ −21.1279 −1.49772 −0.748859 0.662730i $$-0.769398\pi$$
−0.748859 + 0.662730i $$0.769398\pi$$
$$200$$ −12.9127 + 3.33586i −0.913068 + 0.235881i
$$201$$ 39.3217 2.77354
$$202$$ 9.22619i 0.649152i
$$203$$ 0.171835i 0.0120605i
$$204$$ −23.4370 −1.64092
$$205$$ 19.4163 + 15.0378i 1.35609 + 1.05028i
$$206$$ −9.20784 −0.641541
$$207$$ 8.03149i 0.558227i
$$208$$ 2.67034i 0.185155i
$$209$$ −1.00000 −0.0691714
$$210$$ −0.186458 + 0.240748i −0.0128668 + 0.0166132i
$$211$$ 21.9394 1.51037 0.755187 0.655510i $$-0.227546\pi$$
0.755187 + 0.655510i $$0.227546\pi$$
$$212$$ 4.31452i 0.296323i
$$213$$ 10.5871i 0.725416i
$$214$$ −2.15279 −0.147162
$$215$$ 5.42169 7.00033i 0.369757 0.477418i
$$216$$ −4.34386 −0.295562
$$217$$ 0.587022i 0.0398496i
$$218$$ 3.13606i 0.212401i
$$219$$ −18.4437 −1.24631
$$220$$ −2.43191 1.88349i −0.163959 0.126985i
$$221$$ −27.4489 −1.84641
$$222$$ 23.2549i 1.56077i
$$223$$ 23.0514i 1.54363i −0.635844 0.771817i $$-0.719348\pi$$
0.635844 0.771817i $$-0.280652\pi$$
$$224$$ −0.391031 −0.0261268
$$225$$ −4.54276 17.5845i −0.302851 1.17230i
$$226$$ 2.22618 0.148083
$$227$$ 12.1150i 0.804101i −0.915618 0.402050i $$-0.868298\pi$$
0.915618 0.402050i $$-0.131702\pi$$
$$228$$ 3.54270i 0.234621i
$$229$$ 17.0184 1.12461 0.562303 0.826931i $$-0.309915\pi$$
0.562303 + 0.826931i $$0.309915\pi$$
$$230$$ 3.08871 + 2.39218i 0.203664 + 0.157736i
$$231$$ −0.172343 −0.0113393
$$232$$ 6.84905i 0.449662i
$$233$$ 2.08834i 0.136812i 0.997658 + 0.0684060i $$0.0217913\pi$$
−0.997658 + 0.0684060i $$0.978209\pi$$
$$234$$ −11.9088 −0.778505
$$235$$ 12.2879 15.8658i 0.801575 1.03497i
$$236$$ −14.2187 −0.925558
$$237$$ 23.0488i 1.49718i
$$238$$ 0.349825i 0.0226758i
$$239$$ 16.8870 1.09233 0.546165 0.837677i $$-0.316087\pi$$
0.546165 + 0.837677i $$0.316087\pi$$
$$240$$ 2.26938 2.93015i 0.146488 0.189140i
$$241$$ 19.6461 1.26551 0.632757 0.774351i $$-0.281923\pi$$
0.632757 + 0.774351i $$0.281923\pi$$
$$242$$ 0.790175i 0.0507944i
$$243$$ 22.1482i 1.42081i
$$244$$ 3.80429 0.243545
$$245$$ 12.3671 + 9.57820i 0.790104 + 0.611929i
$$246$$ 22.3500 1.42498
$$247$$ 4.14913i 0.264003i
$$248$$ 23.3976i 1.48575i
$$249$$ −9.74529 −0.617583
$$250$$ −8.11562 3.49051i −0.513277 0.220759i
$$251$$ 21.9810 1.38743 0.693714 0.720251i $$-0.255973\pi$$
0.693714 + 0.720251i $$0.255973\pi$$
$$252$$ 0.334386i 0.0210643i
$$253$$ 2.21109i 0.139010i
$$254$$ 0.834120 0.0523374
$$255$$ −30.1196 23.3274i −1.88616 1.46082i
$$256$$ −13.8151 −0.863445
$$257$$ 27.5365i 1.71768i −0.512246 0.858839i $$-0.671186\pi$$
0.512246 0.858839i $$-0.328814\pi$$
$$258$$ 8.05802i 0.501671i
$$259$$ −0.764746 −0.0475190
$$260$$ 7.81485 10.0903i 0.484657 0.625774i
$$261$$ 9.32701 0.577327
$$262$$ 14.3935i 0.889235i
$$263$$ 21.4214i 1.32090i 0.750871 + 0.660449i $$0.229634\pi$$
−0.750871 + 0.660449i $$0.770366\pi$$
$$264$$ −6.86928 −0.422775
$$265$$ −4.29435 + 5.54473i −0.263800 + 0.340610i
$$266$$ −0.0528789 −0.00324221
$$267$$ 0.575459i 0.0352175i
$$268$$ 21.0038i 1.28301i
$$269$$ −8.06510 −0.491738 −0.245869 0.969303i $$-0.579073\pi$$
−0.245869 + 0.969303i $$0.579073\pi$$
$$270$$ −2.27494 1.76192i −0.138448 0.107227i
$$271$$ −14.7370 −0.895211 −0.447606 0.894231i $$-0.647723\pi$$
−0.447606 + 0.894231i $$0.647723\pi$$
$$272$$ 4.25772i 0.258162i
$$273$$ 0.715073i 0.0432782i
$$274$$ −5.64483 −0.341017
$$275$$ −1.25064 4.84106i −0.0754162 0.291927i
$$276$$ −7.83323 −0.471505
$$277$$ 32.5834i 1.95775i 0.204470 + 0.978873i $$0.434453\pi$$
−0.204470 + 0.978873i $$0.565547\pi$$
$$278$$ 1.78316i 0.106947i
$$279$$ −31.8628 −1.90758
$$280$$ −0.315561 0.244399i −0.0188584 0.0146057i
$$281$$ −16.8550 −1.00548 −0.502741 0.864437i $$-0.667675\pi$$
−0.502741 + 0.864437i $$0.667675\pi$$
$$282$$ 18.2630i 1.08754i
$$283$$ 6.26244i 0.372263i −0.982525 0.186132i $$-0.940405\pi$$
0.982525 0.186132i $$-0.0595951\pi$$
$$284$$ −5.65513 −0.335570
$$285$$ 3.52613 4.55283i 0.208870 0.269686i
$$286$$ −3.27854 −0.193864
$$287$$ 0.734986i 0.0433848i
$$288$$ 21.2247i 1.25067i
$$289$$ −26.7659 −1.57447
$$290$$ 2.77805 3.58693i 0.163133 0.210632i
$$291$$ 36.3396 2.13027
$$292$$ 9.85177i 0.576531i
$$293$$ 7.67080i 0.448133i 0.974574 + 0.224067i $$0.0719333\pi$$
−0.974574 + 0.224067i $$0.928067\pi$$
$$294$$ 14.2356 0.830240
$$295$$ −18.2729 14.1522i −1.06389 0.823973i
$$296$$ −30.4814 −1.77170
$$297$$ 1.62854i 0.0944976i
$$298$$ 4.42725i 0.256464i
$$299$$ −9.17411 −0.530553
$$300$$ 17.1504 4.43062i 0.990180 0.255802i
$$301$$ 0.264991 0.0152738
$$302$$ 16.4855i 0.948634i
$$303$$ 30.0700i 1.72748i
$$304$$ 0.643589 0.0369124
$$305$$ 4.88901 + 3.78649i 0.279944 + 0.216814i
$$306$$ −18.9880 −1.08547
$$307$$ 0.00440478i 0.000251394i −1.00000 0.000125697i $$-0.999960\pi$$
1.00000 0.000125697i $$-4.00106e-5\pi$$
$$308$$ 0.0920574i 0.00524546i
$$309$$ 30.0102 1.70722
$$310$$ −9.49034 + 12.2536i −0.539015 + 0.695960i
$$311$$ 12.0604 0.683883 0.341942 0.939721i $$-0.388915\pi$$
0.341942 + 0.939721i $$0.388915\pi$$
$$312$$ 28.5015i 1.61358i
$$313$$ 16.4882i 0.931967i −0.884793 0.465983i $$-0.845701\pi$$
0.884793 0.465983i $$-0.154299\pi$$
$$314$$ 0.525305 0.0296447
$$315$$ 0.332822 0.429730i 0.0187524 0.0242125i
$$316$$ −12.3116 −0.692582
$$317$$ 25.9591i 1.45801i 0.684508 + 0.729005i $$0.260017\pi$$
−0.684508 + 0.729005i $$0.739983\pi$$
$$318$$ 6.38249i 0.357912i
$$319$$ 2.56775 0.143767
$$320$$ −5.88693 4.55938i −0.329089 0.254877i
$$321$$ 7.01637 0.391616
$$322$$ 0.116920i 0.00651570i
$$323$$ 6.61558i 0.368101i
$$324$$ −9.22086 −0.512270
$$325$$ 20.0862 5.18906i 1.11418 0.287837i
$$326$$ 0.282116 0.0156249
$$327$$ 10.2210i 0.565225i
$$328$$ 29.2952i 1.61756i
$$329$$ 0.600584 0.0331113
$$330$$ −3.59753 2.78626i −0.198037 0.153378i
$$331$$ 25.4456 1.39862 0.699310 0.714819i $$-0.253491\pi$$
0.699310 + 0.714819i $$0.253491\pi$$
$$332$$ 5.20548i 0.285688i
$$333$$ 41.5095i 2.27470i
$$334$$ 9.67140 0.529196
$$335$$ −20.9056 + 26.9927i −1.14219 + 1.47477i
$$336$$ 0.110918 0.00605107
$$337$$ 28.8344i 1.57071i −0.619046 0.785355i $$-0.712480\pi$$
0.619046 0.785355i $$-0.287520\pi$$
$$338$$ 3.33082i 0.181173i
$$339$$ −7.25555 −0.394067
$$340$$ 12.4604 16.0885i 0.675760 0.872520i
$$341$$ −8.77193 −0.475026
$$342$$ 2.87020i 0.155203i
$$343$$ 0.936587i 0.0505710i
$$344$$ 10.5621 0.569468
$$345$$ −10.0667 7.79659i −0.541974 0.419754i
$$346$$ −11.3991 −0.612817
$$347$$ 20.2741i 1.08837i −0.838965 0.544185i $$-0.816839\pi$$
0.838965 0.544185i $$-0.183161\pi$$
$$348$$ 9.09677i 0.487638i
$$349$$ −23.5879 −1.26263 −0.631316 0.775525i $$-0.717485\pi$$
−0.631316 + 0.775525i $$0.717485\pi$$
$$350$$ −0.0661323 0.255990i −0.00353492 0.0136832i
$$351$$ 6.75703 0.360664
$$352$$ 5.84321i 0.311444i
$$353$$ 26.1715i 1.39297i 0.717573 + 0.696484i $$0.245253\pi$$
−0.717573 + 0.696484i $$0.754747\pi$$
$$354$$ −21.0338 −1.11793
$$355$$ −7.26759 5.62868i −0.385723 0.298739i
$$356$$ −0.307383 −0.0162913
$$357$$ 1.14015i 0.0603431i
$$358$$ 6.89249i 0.364280i
$$359$$ −32.5322 −1.71698 −0.858492 0.512828i $$-0.828598\pi$$
−0.858492 + 0.512828i $$0.828598\pi$$
$$360$$ 13.2657 17.1283i 0.699163 0.902739i
$$361$$ 1.00000 0.0526316
$$362$$ 11.0333i 0.579898i
$$363$$ 2.57534i 0.135170i
$$364$$ 0.381958 0.0200201
$$365$$ 9.80569 12.6608i 0.513253 0.662697i
$$366$$ 5.62770 0.294164
$$367$$ 9.12225i 0.476178i −0.971243 0.238089i $$-0.923479\pi$$
0.971243 0.238089i $$-0.0765210\pi$$
$$368$$ 1.42304i 0.0741808i
$$369$$ −39.8941 −2.07680
$$370$$ −15.9635 12.3636i −0.829903 0.642753i
$$371$$ −0.209890 −0.0108970
$$372$$ 31.0763i 1.61123i
$$373$$ 32.3890i 1.67704i 0.544872 + 0.838519i $$0.316578\pi$$
−0.544872 + 0.838519i $$0.683422\pi$$
$$374$$ −5.22747 −0.270306
$$375$$ 26.4504 + 11.3763i 1.36589 + 0.587468i
$$376$$ 23.9382 1.23452
$$377$$ 10.6539i 0.548706i
$$378$$ 0.0861155i 0.00442930i
$$379$$ 20.8497 1.07098 0.535489 0.844542i $$-0.320127\pi$$
0.535489 + 0.844542i $$0.320127\pi$$
$$380$$ 2.43191 + 1.88349i 0.124754 + 0.0966210i
$$381$$ −2.71856 −0.139276
$$382$$ 3.76330i 0.192547i
$$383$$ 14.8606i 0.759342i 0.925122 + 0.379671i $$0.123963\pi$$
−0.925122 + 0.379671i $$0.876037\pi$$
$$384$$ 23.3201 1.19005
$$385$$ 0.0916269 0.118306i 0.00466974 0.00602943i
$$386$$ −4.49760 −0.228922
$$387$$ 14.3834i 0.731147i
$$388$$ 19.4109i 0.985441i
$$389$$ 2.79047 0.141482 0.0707412 0.997495i $$-0.477464\pi$$
0.0707412 + 0.997495i $$0.477464\pi$$
$$390$$ 11.5605 14.9266i 0.585391 0.755839i
$$391$$ −14.6277 −0.739753
$$392$$ 18.6594i 0.942441i
$$393$$ 46.9114i 2.36637i
$$394$$ −15.1259 −0.762032
$$395$$ −15.8220 12.2540i −0.796093 0.616567i
$$396$$ 4.99676 0.251097
$$397$$ 9.55809i 0.479707i −0.970809 0.239853i $$-0.922901\pi$$
0.970809 0.239853i $$-0.0770994\pi$$
$$398$$ 16.6947i 0.836832i
$$399$$ 0.172343 0.00862793
$$400$$ 0.804896 + 3.11566i 0.0402448 + 0.155783i
$$401$$ −9.84081 −0.491427 −0.245713 0.969343i $$-0.579022\pi$$
−0.245713 + 0.969343i $$0.579022\pi$$
$$402$$ 31.0710i 1.54968i
$$403$$ 36.3959i 1.81301i
$$404$$ −16.0620 −0.799113
$$405$$ −11.8500 9.17773i −0.588832 0.456045i
$$406$$ 0.135780 0.00673864
$$407$$ 11.4277i 0.566449i
$$408$$ 45.4443i 2.24983i
$$409$$ −5.23929 −0.259066 −0.129533 0.991575i $$-0.541348\pi$$
−0.129533 + 0.991575i $$0.541348\pi$$
$$410$$ −11.8825 + 15.3423i −0.586833 + 0.757701i
$$411$$ 18.3976 0.907488
$$412$$ 16.0300i 0.789743i
$$413$$ 0.691702i 0.0340364i
$$414$$ −6.34628 −0.311902
$$415$$ 5.18113 6.68972i 0.254332 0.328385i
$$416$$ 24.2443 1.18867
$$417$$ 5.81168i 0.284599i
$$418$$ 0.790175i 0.0386487i
$$419$$ 11.2351 0.548870 0.274435 0.961606i $$-0.411509\pi$$
0.274435 + 0.961606i $$0.411509\pi$$
$$420$$ 0.419122 + 0.324606i 0.0204510 + 0.0158392i
$$421$$ 34.2914 1.67126 0.835630 0.549292i $$-0.185103\pi$$
0.835630 + 0.549292i $$0.185103\pi$$
$$422$$ 17.3360i 0.843903i
$$423$$ 32.5989i 1.58501i
$$424$$ −8.36586 −0.406282
$$425$$ 32.0265 8.27369i 1.55351 0.401333i
$$426$$ −8.36566 −0.405318
$$427$$ 0.185069i 0.00895610i
$$428$$ 3.74782i 0.181158i
$$429$$ 10.6854 0.515897
$$430$$ 5.53148 + 4.28409i 0.266752 + 0.206597i
$$431$$ 24.2325 1.16724 0.583620 0.812027i $$-0.301636\pi$$
0.583620 + 0.812027i $$0.301636\pi$$
$$432$$ 1.04811i 0.0504273i
$$433$$ 11.5535i 0.555228i 0.960693 + 0.277614i $$0.0895436\pi$$
−0.960693 + 0.277614i $$0.910456\pi$$
$$434$$ −0.463850 −0.0222655
$$435$$ −9.05422 + 11.6905i −0.434117 + 0.560518i
$$436$$ 5.45960 0.261467
$$437$$ 2.21109i 0.105771i
$$438$$ 14.5738i 0.696361i
$$439$$ 38.1975 1.82307 0.911534 0.411225i $$-0.134899\pi$$
0.911534 + 0.411225i $$0.134899\pi$$
$$440$$ 3.65209 4.71546i 0.174106 0.224801i
$$441$$ −25.4103 −1.21001
$$442$$ 21.6894i 1.03166i
$$443$$ 19.8322i 0.942256i −0.882065 0.471128i $$-0.843847\pi$$
0.882065 0.471128i $$-0.156153\pi$$
$$444$$ 40.4848 1.92132
$$445$$ −0.395027 0.305945i −0.0187261 0.0145032i
$$446$$ 18.2146 0.862487
$$447$$ 14.4293i 0.682483i
$$448$$ 0.222844i 0.0105284i
$$449$$ −19.6541 −0.927532 −0.463766 0.885958i $$-0.653502\pi$$
−0.463766 + 0.885958i $$0.653502\pi$$
$$450$$ 13.8948 3.58958i 0.655008 0.169214i
$$451$$ −10.9830 −0.517168
$$452$$ 3.87557i 0.182292i
$$453$$ 53.7295i 2.52443i
$$454$$ 9.57296 0.449282
$$455$$ 0.490867 + 0.380172i 0.0230122 + 0.0178227i
$$456$$ 6.86928 0.321684
$$457$$ 12.6434i 0.591432i 0.955276 + 0.295716i $$0.0955581\pi$$
−0.955276 + 0.295716i $$0.904442\pi$$
$$458$$ 13.4475i 0.628360i
$$459$$ 10.7738 0.502876
$$460$$ 4.16457 5.37717i 0.194174 0.250712i
$$461$$ −2.24816 −0.104707 −0.0523536 0.998629i $$-0.516672\pi$$
−0.0523536 + 0.998629i $$0.516672\pi$$
$$462$$ 0.136181i 0.00633571i
$$463$$ 16.2839i 0.756778i −0.925647 0.378389i $$-0.876478\pi$$
0.925647 0.378389i $$-0.123522\pi$$
$$464$$ −1.65258 −0.0767190
$$465$$ 30.9309 39.9371i 1.43439 1.85204i
$$466$$ −1.65016 −0.0764420
$$467$$ 2.08404i 0.0964378i −0.998837 0.0482189i $$-0.984645\pi$$
0.998837 0.0482189i $$-0.0153545\pi$$
$$468$$ 20.7322i 0.958347i
$$469$$ −1.02178 −0.0471815
$$470$$ 12.5367 + 9.70960i 0.578277 + 0.447870i
$$471$$ −1.71207 −0.0788881
$$472$$ 27.5700i 1.26901i
$$473$$ 3.95978i 0.182071i
$$474$$ −18.2126 −0.836533
$$475$$ 1.25064 + 4.84106i 0.0573831 + 0.222123i
$$476$$ 0.609014 0.0279141
$$477$$ 11.3926i 0.521630i
$$478$$ 13.3437i 0.610326i
$$479$$ −16.3963 −0.749164 −0.374582 0.927194i $$-0.622214\pi$$
−0.374582 + 0.927194i $$0.622214\pi$$
$$480$$ 26.6031 + 20.6039i 1.21426 + 0.940435i
$$481$$ 47.4150 2.16194
$$482$$ 15.5238i 0.707090i
$$483$$ 0.381066i 0.0173391i
$$484$$ 1.37562 0.0625284
$$485$$ −19.3201 + 24.9456i −0.877283 + 1.13272i
$$486$$ −17.5010 −0.793859
$$487$$ 6.55183i 0.296892i −0.988921 0.148446i $$-0.952573\pi$$
0.988921 0.148446i $$-0.0474271\pi$$
$$488$$ 7.37651i 0.333919i
$$489$$ −0.919471 −0.0415799
$$490$$ −7.56845 + 9.77215i −0.341908 + 0.441461i
$$491$$ 29.7599 1.34305 0.671524 0.740983i $$-0.265640\pi$$
0.671524 + 0.740983i $$0.265640\pi$$
$$492$$ 38.9093i 1.75417i
$$493$$ 16.9872i 0.765064i
$$494$$ 3.27854 0.147508
$$495$$ 6.42149 + 4.97339i 0.288625 + 0.223537i
$$496$$ 5.64552 0.253491
$$497$$ 0.275107i 0.0123403i
$$498$$ 7.70048i 0.345067i
$$499$$ 25.0420 1.12104 0.560518 0.828142i $$-0.310602\pi$$
0.560518 + 0.828142i $$0.310602\pi$$
$$500$$ −6.07667 + 14.1286i −0.271757 + 0.631849i
$$501$$ −31.5210 −1.40826
$$502$$ 17.3688i 0.775208i
$$503$$ 14.9942i 0.668560i 0.942474 + 0.334280i $$0.108493\pi$$
−0.942474 + 0.334280i $$0.891507\pi$$
$$504$$ 0.648374 0.0288809
$$505$$ −20.6417 15.9868i −0.918545 0.711405i
$$506$$ −1.74715 −0.0776703
$$507$$ 10.8558i 0.482123i
$$508$$ 1.45213i 0.0644278i
$$509$$ 21.5572 0.955506 0.477753 0.878494i $$-0.341451\pi$$
0.477753 + 0.878494i $$0.341451\pi$$
$$510$$ 18.4327 23.7998i 0.816214 1.05387i
$$511$$ 0.479263 0.0212013
$$512$$ 7.19396i 0.317931i
$$513$$ 1.62854i 0.0719019i
$$514$$ 21.7586 0.959731
$$515$$ −15.9551 + 20.6007i −0.703064 + 0.907775i
$$516$$ −14.0283 −0.617562
$$517$$ 8.97459i 0.394702i
$$518$$ 0.604283i 0.0265507i
$$519$$ 37.1518 1.63078
$$520$$ 19.5651 + 15.1530i 0.857985 + 0.664502i
$$521$$ −34.7658 −1.52312 −0.761558 0.648097i $$-0.775565\pi$$
−0.761558 + 0.648097i $$0.775565\pi$$
$$522$$ 7.36996i 0.322575i
$$523$$ 26.7047i 1.16771i 0.811856 + 0.583857i $$0.198457\pi$$
−0.811856 + 0.583857i $$0.801543\pi$$
$$524$$ −25.0579 −1.09466
$$525$$ 0.215538 + 0.834323i 0.00940686 + 0.0364128i
$$526$$ −16.9266 −0.738036
$$527$$ 58.0314i 2.52789i
$$528$$ 1.65746i 0.0721316i
$$529$$ 18.1111 0.787438
$$530$$ −4.38130 3.39328i −0.190312 0.147395i
$$531$$ 37.5447 1.62930
$$532$$ 0.0920574i 0.00399120i
$$533$$ 45.5698i 1.97385i
$$534$$ −0.454713 −0.0196773
$$535$$ −3.73029 + 4.81644i −0.161274 + 0.208233i
$$536$$ −40.7264 −1.75911
$$537$$ 22.4640i 0.969394i
$$538$$ 6.37284i 0.274753i
$$539$$ −6.99552 −0.301318
$$540$$ −3.06734 + 3.96046i −0.131997 + 0.170431i
$$541$$ 9.54398 0.410328 0.205164 0.978728i $$-0.434227\pi$$
0.205164 + 0.978728i $$0.434227\pi$$
$$542$$ 11.6448i 0.500188i
$$543$$ 35.9598i 1.54318i
$$544$$ 38.6563 1.65737
$$545$$ 7.01630 + 5.43407i 0.300545 + 0.232770i
$$546$$ 0.565033 0.0241812
$$547$$ 27.6080i 1.18043i −0.807245 0.590217i $$-0.799042\pi$$
0.807245 0.590217i $$-0.200958\pi$$
$$548$$ 9.82715i 0.419795i
$$549$$ −10.0453 −0.428723
$$550$$ 3.82529 0.988221i 0.163111 0.0421379i
$$551$$ −2.56775 −0.109390
$$552$$ 15.1886i 0.646470i
$$553$$ 0.598928i 0.0254690i
$$554$$ −25.7466 −1.09387
$$555$$ 52.0283 + 40.2955i 2.20848 + 1.71045i
$$556$$ −3.10433 −0.131653
$$557$$ 14.9783i 0.634651i −0.948317 0.317325i $$-0.897215\pi$$
0.948317 0.317325i $$-0.102785\pi$$
$$558$$ 25.1772i 1.06583i
$$559$$ −16.4297 −0.694900
$$560$$ −0.0589701 + 0.0761404i −0.00249194 + 0.00321752i
$$561$$ 17.0374 0.719318
$$562$$ 13.3184i 0.561801i
$$563$$ 0.475683i 0.0200476i 0.999950 + 0.0100238i $$0.00319073\pi$$
−0.999950 + 0.0100238i $$0.996809\pi$$
$$564$$ −31.7942 −1.33878
$$565$$ 3.85745 4.98062i 0.162284 0.209536i
$$566$$ 4.94842 0.207998
$$567$$ 0.448571i 0.0188382i
$$568$$ 10.9653i 0.460093i
$$569$$ 9.06417 0.379990 0.189995 0.981785i $$-0.439153\pi$$
0.189995 + 0.981785i $$0.439153\pi$$
$$570$$ 3.59753 + 2.78626i 0.150684 + 0.116703i
$$571$$ 4.75692 0.199071 0.0995355 0.995034i $$-0.468264\pi$$
0.0995355 + 0.995034i $$0.468264\pi$$
$$572$$ 5.70765i 0.238649i
$$573$$ 12.2654i 0.512393i
$$574$$ −0.580767 −0.0242408
$$575$$ 10.7040 2.76527i 0.446389 0.115320i
$$576$$ 12.0957 0.503987
$$577$$ 24.9499i 1.03868i −0.854569 0.519338i $$-0.826178\pi$$
0.854569 0.519338i $$-0.173822\pi$$
$$578$$ 21.1498i 0.879715i
$$579$$ 14.6586 0.609190
$$580$$ −6.24454 4.83634i −0.259290 0.200818i
$$581$$ 0.253233 0.0105059
$$582$$ 28.7147i 1.19026i
$$583$$ 3.13641i 0.129897i
$$584$$ 19.1026 0.790470
$$585$$ −20.6353 + 26.6436i −0.853163 + 1.10158i
$$586$$ −6.06127 −0.250389
$$587$$ 19.3052i 0.796810i −0.917210 0.398405i $$-0.869564\pi$$
0.917210 0.398405i $$-0.130436\pi$$
$$588$$ 24.7830i 1.02203i
$$589$$ 8.77193 0.361441
$$590$$ 11.1827 14.4388i 0.460385 0.594435i
$$591$$ 49.2983 2.02786
$$592$$ 7.35473i 0.302278i
$$593$$ 6.49883i 0.266875i −0.991057 0.133437i $$-0.957398\pi$$
0.991057 0.133437i $$-0.0426015\pi$$
$$594$$ 1.28683 0.0527994
$$595$$ 0.782662 + 0.606165i 0.0320860 + 0.0248504i
$$596$$ −7.70746 −0.315710
$$597$$ 54.4115i 2.22691i
$$598$$ 7.24915i 0.296440i
$$599$$ −8.10308 −0.331083 −0.165541 0.986203i $$-0.552937\pi$$
−0.165541 + 0.986203i $$0.552937\pi$$
$$600$$ 8.59097 + 33.2546i 0.350725 + 1.35761i
$$601$$ −34.2650 −1.39770 −0.698848 0.715270i $$-0.746304\pi$$
−0.698848 + 0.715270i $$0.746304\pi$$
$$602$$ 0.209389i 0.00853405i
$$603$$ 55.4610i 2.25855i
$$604$$ −28.6998 −1.16778
$$605$$ 1.76786 + 1.36919i 0.0718736 + 0.0556655i
$$606$$ −23.7605 −0.965206
$$607$$ 16.9455i 0.687797i 0.939007 + 0.343898i $$0.111748\pi$$
−0.939007 + 0.343898i $$0.888252\pi$$
$$608$$ 5.84321i 0.236974i
$$609$$ −0.442534 −0.0179324
$$610$$ −2.99199 + 3.86317i −0.121142 + 0.156415i
$$611$$ −37.2367 −1.50644
$$612$$ 33.0565i 1.33623i
$$613$$ 1.47243i 0.0594709i −0.999558 0.0297354i $$-0.990534\pi$$
0.999558 0.0297354i $$-0.00946648\pi$$
$$614$$ 0.00348055 0.000140464
$$615$$ 38.7273 50.0036i 1.56164 2.01634i
$$616$$ 0.178499 0.00719194
$$617$$ 19.4675i 0.783731i 0.920022 + 0.391866i $$0.128170\pi$$
−0.920022 + 0.391866i $$0.871830\pi$$
$$618$$ 23.7133i 0.953889i
$$619$$ −21.8377 −0.877732 −0.438866 0.898552i $$-0.644620\pi$$
−0.438866 + 0.898552i $$0.644620\pi$$
$$620$$ 21.3325 + 16.5218i 0.856734 + 0.663533i
$$621$$ 3.60086 0.144497
$$622$$ 9.52983i 0.382112i
$$623$$ 0.0149534i 0.000599094i
$$624$$ −6.87702 −0.275301
$$625$$ −21.8718 + 12.1088i −0.874873 + 0.484353i
$$626$$ 13.0285 0.520725
$$627$$ 2.57534i 0.102849i
$$628$$ 0.914509i 0.0364929i
$$629$$ 75.6008 3.01440
$$630$$ 0.339561 + 0.262987i 0.0135285 + 0.0104777i
$$631$$ 0.393330 0.0156582 0.00782912 0.999969i $$-0.497508\pi$$
0.00782912 + 0.999969i $$0.497508\pi$$
$$632$$ 23.8722i 0.949585i
$$633$$ 56.5015i 2.24573i
$$634$$ −20.5123 −0.814646
$$635$$ 1.44534 1.86618i 0.0573565 0.0740569i
$$636$$ 11.1114 0.440594
$$637$$ 29.0253i 1.15003i
$$638$$ 2.02897i 0.0803278i
$$639$$ 14.9325 0.590720
$$640$$ −12.3982 + 16.0082i −0.490083 + 0.632781i
$$641$$ 2.08000 0.0821549 0.0410774 0.999156i $$-0.486921\pi$$
0.0410774 + 0.999156i $$0.486921\pi$$
$$642$$ 5.54416i 0.218811i
$$643$$ 15.7787i 0.622250i 0.950369 + 0.311125i $$0.100706\pi$$
−0.950369 + 0.311125i $$0.899294\pi$$
$$644$$ 0.203548 0.00802090
$$645$$ −18.0282 13.9627i −0.709860 0.549780i
$$646$$ 5.22747 0.205672
$$647$$ 6.67760i 0.262524i −0.991348 0.131262i $$-0.958097\pi$$
0.991348 0.131262i $$-0.0419028\pi$$
$$648$$ 17.8792i 0.702363i
$$649$$ 10.3362 0.405731
$$650$$ 4.10026 + 15.8716i 0.160825 + 0.622536i
$$651$$ 1.51178 0.0592513
$$652$$ 0.491138i 0.0192345i
$$653$$ 6.00890i 0.235147i 0.993064 + 0.117573i $$0.0375115\pi$$
−0.993064 + 0.117573i $$0.962488\pi$$
$$654$$ 8.07641 0.315813
$$655$$ −32.2026 24.9407i −1.25826 0.974512i
$$656$$ 7.06852 0.275979
$$657$$ 26.0138i 1.01489i
$$658$$ 0.474566i 0.0185005i
$$659$$ −14.3389 −0.558566 −0.279283 0.960209i $$-0.590097\pi$$
−0.279283 + 0.960209i $$0.590097\pi$$
$$660$$ −4.85062 + 6.26298i −0.188810 + 0.243786i
$$661$$ −4.17451 −0.162370 −0.0811849 0.996699i $$-0.525870\pi$$
−0.0811849 + 0.996699i $$0.525870\pi$$
$$662$$ 20.1065i 0.781462i
$$663$$ 70.6902i 2.74538i
$$664$$ 10.0934 0.391700
$$665$$ −0.0916269 + 0.118306i −0.00355314 + 0.00458770i
$$666$$ 32.7997 1.27096
$$667$$ 5.67754i 0.219835i
$$668$$ 16.8371i 0.651445i
$$669$$ −59.3651 −2.29519
$$670$$ −21.3289 16.5191i −0.824008 0.638187i
$$671$$ −2.76550 −0.106761
$$672$$ 1.00704i 0.0388473i
$$673$$ 1.71412i 0.0660745i −0.999454 0.0330373i $$-0.989482\pi$$
0.999454 0.0330373i $$-0.0105180\pi$$
$$674$$ 22.7842 0.877615
$$675$$ −7.88387 + 2.03671i −0.303450 + 0.0783931i
$$676$$ −5.79866 −0.223025
$$677$$ 0.206434i 0.00793392i −0.999992 0.00396696i $$-0.998737\pi$$
0.999992 0.00396696i $$-0.00126273\pi$$
$$678$$ 5.73315i 0.220180i
$$679$$ −0.944291 −0.0362386
$$680$$ 31.1955 + 24.1607i 1.19629 + 0.926520i
$$681$$ −31.2002 −1.19559
$$682$$ 6.93135i 0.265415i
$$683$$ 29.3173i 1.12179i −0.827886 0.560897i $$-0.810456\pi$$
0.827886 0.560897i $$-0.189544\pi$$
$$684$$ −4.99676 −0.191056
$$685$$ −9.78119 + 12.6292i −0.373720 + 0.482536i
$$686$$ −0.740068 −0.0282559
$$687$$ 43.8280i 1.67214i
$$688$$ 2.54847i 0.0971596i
$$689$$ 13.0134 0.495771
$$690$$ 6.16067 7.95447i 0.234533 0.302821i
$$691$$ −44.8795 −1.70730 −0.853649 0.520849i $$-0.825615\pi$$
−0.853649 + 0.520849i $$0.825615\pi$$
$$692$$ 19.8448i 0.754384i
$$693$$ 0.243079i 0.00923382i
$$694$$ 16.0201 0.608114
$$695$$ −3.98947 3.08981i −0.151329 0.117203i
$$696$$ −17.6386 −0.668590
$$697$$ 72.6587i 2.75215i
$$698$$ 18.6386i 0.705481i
$$699$$ 5.37819 0.203422
$$700$$ −0.445656 + 0.115130i −0.0168442 + 0.00435152i
$$701$$ 7.13370 0.269436 0.134718 0.990884i $$-0.456987\pi$$
0.134718 + 0.990884i $$0.456987\pi$$
$$702$$ 5.33924i 0.201517i
$$703$$ 11.4277i 0.431003i
$$704$$ 3.32998 0.125503
$$705$$ −40.8597 31.6455i −1.53887 1.19184i
$$706$$ −20.6800 −0.778304
$$707$$ 0.781373i 0.0293865i
$$708$$ 36.6179i 1.37619i
$$709$$ 37.5143 1.40888 0.704440 0.709763i $$-0.251198\pi$$
0.704440 + 0.709763i $$0.251198\pi$$
$$710$$ 4.44764 5.74266i 0.166917 0.215518i
$$711$$ 32.5090 1.21918
$$712$$ 0.596015i 0.0223366i
$$713$$ 19.3955i 0.726369i
$$714$$ 0.900916 0.0337160
$$715$$ −5.68095 + 7.33507i −0.212456 + 0.274316i
$$716$$ −11.9992 −0.448432
$$717$$ 43.4898i 1.62415i
$$718$$ 25.7061i 0.959343i
$$719$$ 9.92990 0.370323 0.185161 0.982708i $$-0.440719\pi$$
0.185161 + 0.982708i $$0.440719\pi$$
$$720$$ −4.13280 3.20082i −0.154021 0.119288i
$$721$$ −0.779819 −0.0290420
$$722$$ 0.790175i 0.0294073i
$$723$$ 50.5952i 1.88166i
$$724$$ −19.2080 −0.713860
$$725$$ −3.21133 12.4307i −0.119266 0.461663i
$$726$$ 2.03497 0.0755247
$$727$$ 16.4750i 0.611025i −0.952188 0.305513i $$-0.901172\pi$$
0.952188 0.305513i $$-0.0988278\pi$$
$$728$$ 0.740617i 0.0274491i
$$729$$ 36.9300 1.36778
$$730$$ 10.0043 + 7.74821i 0.370274 + 0.286774i
$$731$$ −26.1963 −0.968904
$$732$$ 9.79732i 0.362119i
$$733$$ 35.6615i 1.31719i −0.752498 0.658594i $$-0.771151\pi$$
0.752498 0.658594i $$-0.228849\pi$$
$$734$$ 7.20817 0.266059
$$735$$ 24.6671 31.8494i 0.909859 1.17478i
$$736$$ 12.9199 0.476233
$$737$$ 15.2686i 0.562425i
$$738$$ 31.5233i 1.16039i
$$739$$ −12.0150 −0.441977 −0.220989 0.975276i $$-0.570928\pi$$
−0.220989 + 0.975276i $$0.570928\pi$$
$$740$$ −21.5239 + 27.7911i −0.791236 + 1.02162i
$$741$$ −10.6854 −0.392538
$$742$$ 0.165850i 0.00608854i
$$743$$ 6.68005i 0.245067i −0.992464 0.122534i $$-0.960898\pi$$
0.992464 0.122534i $$-0.0391019\pi$$
$$744$$ 60.2568 2.20912
$$745$$ −9.90509 7.67141i −0.362894 0.281059i
$$746$$ −25.5930 −0.937025
$$747$$ 13.7452i 0.502909i
$$748$$ 9.10056i 0.332749i
$$749$$ −0.182321 −0.00666188
$$750$$ −8.98924 + 20.9005i −0.328241 + 0.763177i
$$751$$ −6.22015 −0.226976 −0.113488 0.993539i $$-0.536202\pi$$
−0.113488 + 0.993539i $$0.536202\pi$$
$$752$$ 5.77595i 0.210627i
$$753$$ 56.6084i 2.06293i
$$754$$ −8.41848 −0.306583
$$755$$ −36.8830 28.5656i −1.34231 1.03961i
$$756$$ −0.149919 −0.00545251
$$757$$ 14.2550i 0.518105i −0.965863 0.259053i $$-0.916590\pi$$
0.965863 0.259053i $$-0.0834103\pi$$
$$758$$ 16.4749i 0.598396i
$$759$$ 5.69431 0.206690
$$760$$ −3.65209 + 4.71546i −0.132475 + 0.171048i
$$761$$ −3.46765 −0.125702 −0.0628512 0.998023i $$-0.520019\pi$$
−0.0628512 + 0.998023i $$0.520019\pi$$
$$762$$ 2.14814i 0.0778189i
$$763$$ 0.265595i 0.00961519i
$$764$$ 6.55158 0.237028
$$765$$ −32.9019 + 42.4819i −1.18957 + 1.53594i
$$766$$ −11.7425 −0.424273
$$767$$ 42.8862i 1.54853i
$$768$$ 35.5786i 1.28383i
$$769$$ 38.6283 1.39297 0.696485 0.717571i $$-0.254746\pi$$
0.696485 + 0.717571i $$0.254746\pi$$
$$770$$ 0.0934823 + 0.0724013i 0.00336887 + 0.00260916i
$$771$$ −70.9157 −2.55397
$$772$$ 7.82993i 0.281805i
$$773$$ 27.8564i 1.00193i −0.865469 0.500963i $$-0.832979\pi$$
0.865469 0.500963i $$-0.167021\pi$$
$$774$$ −11.3654 −0.408520
$$775$$ 10.9705 + 42.4655i 0.394072 + 1.52540i
$$776$$ −37.6378 −1.35112
$$777$$ 1.96948i 0.0706547i
$$778$$ 2.20496i 0.0790515i
$$779$$ 10.9830 0.393506
$$780$$ −25.9859 20.1259i −0.930445 0.720622i
$$781$$ 4.11096 0.147102
$$782$$ 11.5584i 0.413328i