# Properties

 Label 1045.2.b.b.419.9 Level $1045$ Weight $2$ Character 1045.419 Analytic conductor $8.344$ Analytic rank $0$ Dimension $16$ 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: $$16$$ Coefficient field: $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{16} + 19x^{14} + 144x^{12} + 552x^{10} + 1119x^{8} + 1146x^{6} + 524x^{4} + 83x^{2} + 4$$ x^16 + 19*x^14 + 144*x^12 + 552*x^10 + 1119*x^8 + 1146*x^6 + 524*x^4 + 83*x^2 + 4 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2^{3}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 419.9 Root $$0.301154i$$ of defining polynomial Character $$\chi$$ $$=$$ 1045.419 Dual form 1045.2.b.b.419.8

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+0.301154i q^{2} -1.85377i q^{3} +1.90931 q^{4} +(0.637551 - 2.14325i) q^{5} +0.558272 q^{6} -1.94668i q^{7} +1.17730i q^{8} -0.436480 q^{9} +O(q^{10})$$ $$q+0.301154i q^{2} -1.85377i q^{3} +1.90931 q^{4} +(0.637551 - 2.14325i) q^{5} +0.558272 q^{6} -1.94668i q^{7} +1.17730i q^{8} -0.436480 q^{9} +(0.645450 + 0.192001i) q^{10} -1.00000 q^{11} -3.53942i q^{12} -3.75832i q^{13} +0.586251 q^{14} +(-3.97311 - 1.18188i) q^{15} +3.46406 q^{16} +2.16098i q^{17} -0.131448i q^{18} -1.00000 q^{19} +(1.21728 - 4.09212i) q^{20} -3.60871 q^{21} -0.301154i q^{22} +4.03747i q^{23} +2.18246 q^{24} +(-4.18706 - 2.73286i) q^{25} +1.13183 q^{26} -4.75219i q^{27} -3.71681i q^{28} +2.18930 q^{29} +(0.355927 - 1.19652i) q^{30} +3.21529 q^{31} +3.39783i q^{32} +1.85377i q^{33} -0.650787 q^{34} +(-4.17223 - 1.24111i) q^{35} -0.833374 q^{36} +5.64900i q^{37} -0.301154i q^{38} -6.96707 q^{39} +(2.52326 + 0.750591i) q^{40} -3.52926 q^{41} -1.08678i q^{42} +2.74094i q^{43} -1.90931 q^{44} +(-0.278278 + 0.935486i) q^{45} -1.21590 q^{46} +1.87707i q^{47} -6.42159i q^{48} +3.21044 q^{49} +(0.823014 - 1.26095i) q^{50} +4.00596 q^{51} -7.17578i q^{52} +4.59639i q^{53} +1.43114 q^{54} +(-0.637551 + 2.14325i) q^{55} +2.29184 q^{56} +1.85377i q^{57} +0.659317i q^{58} -3.10100 q^{59} +(-7.58588 - 2.25656i) q^{60} -10.0971 q^{61} +0.968298i q^{62} +0.849687i q^{63} +5.90485 q^{64} +(-8.05502 - 2.39612i) q^{65} -0.558272 q^{66} -12.0622i q^{67} +4.12596i q^{68} +7.48457 q^{69} +(0.373765 - 1.25648i) q^{70} +6.42317 q^{71} -0.513870i q^{72} +10.7452i q^{73} -1.70122 q^{74} +(-5.06611 + 7.76186i) q^{75} -1.90931 q^{76} +1.94668i q^{77} -2.09816i q^{78} -10.8068 q^{79} +(2.20851 - 7.42436i) q^{80} -10.1189 q^{81} -1.06285i q^{82} +8.12591i q^{83} -6.89012 q^{84} +(4.63152 + 1.37773i) q^{85} -0.825447 q^{86} -4.05847i q^{87} -1.17730i q^{88} +11.1151 q^{89} +(-0.281726 - 0.0838046i) q^{90} -7.31624 q^{91} +7.70877i q^{92} -5.96042i q^{93} -0.565288 q^{94} +(-0.637551 + 2.14325i) q^{95} +6.29880 q^{96} -11.4492i q^{97} +0.966837i q^{98} +0.436480 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$16 q - 6 q^{4} + 3 q^{5} - 8 q^{6} - 8 q^{9}+O(q^{10})$$ 16 * q - 6 * q^4 + 3 * q^5 - 8 * q^6 - 8 * q^9 $$16 q - 6 q^{4} + 3 q^{5} - 8 q^{6} - 8 q^{9} + 10 q^{10} - 16 q^{11} + 4 q^{14} + 3 q^{15} - 18 q^{16} - 16 q^{19} - 2 q^{20} - 10 q^{21} + 10 q^{24} - 7 q^{25} - 24 q^{26} + 2 q^{29} + 4 q^{30} - 32 q^{31} - 16 q^{34} - 18 q^{35} + 18 q^{36} + 40 q^{39} - 28 q^{40} + 6 q^{41} + 6 q^{44} + 16 q^{45} + 38 q^{49} - 30 q^{50} - 16 q^{51} + 18 q^{54} - 3 q^{55} + 12 q^{56} + 24 q^{59} - 20 q^{60} - 42 q^{61} + 62 q^{64} - 20 q^{65} + 8 q^{66} + 30 q^{69} - 18 q^{70} - 46 q^{71} - 2 q^{74} - 25 q^{75} + 6 q^{76} + 74 q^{79} - 22 q^{80} - 56 q^{81} + 34 q^{84} - 18 q^{85} + 8 q^{86} + 14 q^{89} - 4 q^{90} - 24 q^{91} + 64 q^{94} - 3 q^{95} + 54 q^{96} + 8 q^{99}+O(q^{100})$$ 16 * q - 6 * q^4 + 3 * q^5 - 8 * q^6 - 8 * q^9 + 10 * q^10 - 16 * q^11 + 4 * q^14 + 3 * q^15 - 18 * q^16 - 16 * q^19 - 2 * q^20 - 10 * q^21 + 10 * q^24 - 7 * q^25 - 24 * q^26 + 2 * q^29 + 4 * q^30 - 32 * q^31 - 16 * q^34 - 18 * q^35 + 18 * q^36 + 40 * q^39 - 28 * q^40 + 6 * q^41 + 6 * q^44 + 16 * q^45 + 38 * q^49 - 30 * q^50 - 16 * q^51 + 18 * q^54 - 3 * q^55 + 12 * q^56 + 24 * q^59 - 20 * q^60 - 42 * q^61 + 62 * q^64 - 20 * q^65 + 8 * q^66 + 30 * q^69 - 18 * q^70 - 46 * q^71 - 2 * q^74 - 25 * q^75 + 6 * q^76 + 74 * q^79 - 22 * q^80 - 56 * q^81 + 34 * q^84 - 18 * q^85 + 8 * q^86 + 14 * q^89 - 4 * q^90 - 24 * q^91 + 64 * q^94 - 3 * q^95 + 54 * q^96 + 8 * 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.301154i 0.212948i 0.994315 + 0.106474i $$0.0339561\pi$$
−0.994315 + 0.106474i $$0.966044\pi$$
$$3$$ 1.85377i 1.07028i −0.844764 0.535139i $$-0.820259\pi$$
0.844764 0.535139i $$-0.179741\pi$$
$$4$$ 1.90931 0.954653
$$5$$ 0.637551 2.14325i 0.285121 0.958491i
$$6$$ 0.558272 0.227914
$$7$$ 1.94668i 0.735776i −0.929870 0.367888i $$-0.880081\pi$$
0.929870 0.367888i $$-0.119919\pi$$
$$8$$ 1.17730i 0.416240i
$$9$$ −0.436480 −0.145493
$$10$$ 0.645450 + 0.192001i 0.204109 + 0.0607161i
$$11$$ −1.00000 −0.301511
$$12$$ 3.53942i 1.02174i
$$13$$ 3.75832i 1.04237i −0.853444 0.521185i $$-0.825490\pi$$
0.853444 0.521185i $$-0.174510\pi$$
$$14$$ 0.586251 0.156682
$$15$$ −3.97311 1.18188i −1.02585 0.305159i
$$16$$ 3.46406 0.866015
$$17$$ 2.16098i 0.524114i 0.965052 + 0.262057i $$0.0844008\pi$$
−0.965052 + 0.262057i $$0.915599\pi$$
$$18$$ 0.131448i 0.0309825i
$$19$$ −1.00000 −0.229416
$$20$$ 1.21728 4.09212i 0.272192 0.915027i
$$21$$ −3.60871 −0.787484
$$22$$ 0.301154i 0.0642063i
$$23$$ 4.03747i 0.841872i 0.907090 + 0.420936i $$0.138298\pi$$
−0.907090 + 0.420936i $$0.861702\pi$$
$$24$$ 2.18246 0.445492
$$25$$ −4.18706 2.73286i −0.837412 0.546573i
$$26$$ 1.13183 0.221971
$$27$$ 4.75219i 0.914559i
$$28$$ 3.71681i 0.702411i
$$29$$ 2.18930 0.406543 0.203271 0.979122i $$-0.434843\pi$$
0.203271 + 0.979122i $$0.434843\pi$$
$$30$$ 0.355927 1.19652i 0.0649830 0.218453i
$$31$$ 3.21529 0.577483 0.288741 0.957407i $$-0.406763\pi$$
0.288741 + 0.957407i $$0.406763\pi$$
$$32$$ 3.39783i 0.600656i
$$33$$ 1.85377i 0.322701i
$$34$$ −0.650787 −0.111609
$$35$$ −4.17223 1.24111i −0.705235 0.209785i
$$36$$ −0.833374 −0.138896
$$37$$ 5.64900i 0.928690i 0.885654 + 0.464345i $$0.153710\pi$$
−0.885654 + 0.464345i $$0.846290\pi$$
$$38$$ 0.301154i 0.0488537i
$$39$$ −6.96707 −1.11562
$$40$$ 2.52326 + 0.750591i 0.398962 + 0.118679i
$$41$$ −3.52926 −0.551177 −0.275589 0.961276i $$-0.588873\pi$$
−0.275589 + 0.961276i $$0.588873\pi$$
$$42$$ 1.08678i 0.167693i
$$43$$ 2.74094i 0.417990i 0.977917 + 0.208995i $$0.0670192\pi$$
−0.977917 + 0.208995i $$0.932981\pi$$
$$44$$ −1.90931 −0.287839
$$45$$ −0.278278 + 0.935486i −0.0414832 + 0.139454i
$$46$$ −1.21590 −0.179275
$$47$$ 1.87707i 0.273799i 0.990585 + 0.136899i $$0.0437137\pi$$
−0.990585 + 0.136899i $$0.956286\pi$$
$$48$$ 6.42159i 0.926877i
$$49$$ 3.21044 0.458634
$$50$$ 0.823014 1.26095i 0.116392 0.178325i
$$51$$ 4.00596 0.560947
$$52$$ 7.17578i 0.995101i
$$53$$ 4.59639i 0.631362i 0.948865 + 0.315681i $$0.102233\pi$$
−0.948865 + 0.315681i $$0.897767\pi$$
$$54$$ 1.43114 0.194754
$$55$$ −0.637551 + 2.14325i −0.0859673 + 0.288996i
$$56$$ 2.29184 0.306259
$$57$$ 1.85377i 0.245538i
$$58$$ 0.659317i 0.0865726i
$$59$$ −3.10100 −0.403715 −0.201858 0.979415i $$-0.564698\pi$$
−0.201858 + 0.979415i $$0.564698\pi$$
$$60$$ −7.58588 2.25656i −0.979332 0.291321i
$$61$$ −10.0971 −1.29281 −0.646403 0.762996i $$-0.723728\pi$$
−0.646403 + 0.762996i $$0.723728\pi$$
$$62$$ 0.968298i 0.122974i
$$63$$ 0.849687i 0.107050i
$$64$$ 5.90485 0.738107
$$65$$ −8.05502 2.39612i −0.999102 0.297202i
$$66$$ −0.558272 −0.0687186
$$67$$ 12.0622i 1.47363i −0.676096 0.736814i $$-0.736329\pi$$
0.676096 0.736814i $$-0.263671\pi$$
$$68$$ 4.12596i 0.500347i
$$69$$ 7.48457 0.901036
$$70$$ 0.373765 1.25648i 0.0446734 0.150179i
$$71$$ 6.42317 0.762291 0.381145 0.924515i $$-0.375530\pi$$
0.381145 + 0.924515i $$0.375530\pi$$
$$72$$ 0.513870i 0.0605601i
$$73$$ 10.7452i 1.25763i 0.777556 + 0.628814i $$0.216459\pi$$
−0.777556 + 0.628814i $$0.783541\pi$$
$$74$$ −1.70122 −0.197763
$$75$$ −5.06611 + 7.76186i −0.584984 + 0.896263i
$$76$$ −1.90931 −0.219012
$$77$$ 1.94668i 0.221845i
$$78$$ 2.09816i 0.237570i
$$79$$ −10.8068 −1.21586 −0.607932 0.793989i $$-0.708001\pi$$
−0.607932 + 0.793989i $$0.708001\pi$$
$$80$$ 2.20851 7.42436i 0.246919 0.830068i
$$81$$ −10.1189 −1.12432
$$82$$ 1.06285i 0.117372i
$$83$$ 8.12591i 0.891934i 0.895049 + 0.445967i $$0.147140\pi$$
−0.895049 + 0.445967i $$0.852860\pi$$
$$84$$ −6.89012 −0.751774
$$85$$ 4.63152 + 1.37773i 0.502358 + 0.149436i
$$86$$ −0.825447 −0.0890103
$$87$$ 4.05847i 0.435114i
$$88$$ 1.17730i 0.125501i
$$89$$ 11.1151 1.17820 0.589101 0.808060i $$-0.299482\pi$$
0.589101 + 0.808060i $$0.299482\pi$$
$$90$$ −0.281726 0.0838046i −0.0296965 0.00883378i
$$91$$ −7.31624 −0.766950
$$92$$ 7.70877i 0.803695i
$$93$$ 5.96042i 0.618066i
$$94$$ −0.565288 −0.0583050
$$95$$ −0.637551 + 2.14325i −0.0654113 + 0.219893i
$$96$$ 6.29880 0.642869
$$97$$ 11.4492i 1.16249i −0.813728 0.581246i $$-0.802565\pi$$
0.813728 0.581246i $$-0.197435\pi$$
$$98$$ 0.966837i 0.0976653i
$$99$$ 0.436480 0.0438679
$$100$$ −7.99438 5.21787i −0.799438 0.521787i
$$101$$ 6.86482 0.683075 0.341537 0.939868i $$-0.389052\pi$$
0.341537 + 0.939868i $$0.389052\pi$$
$$102$$ 1.20641i 0.119453i
$$103$$ 13.7258i 1.35244i −0.736699 0.676220i $$-0.763617\pi$$
0.736699 0.676220i $$-0.236383\pi$$
$$104$$ 4.42468 0.433876
$$105$$ −2.30073 + 7.73437i −0.224529 + 0.754797i
$$106$$ −1.38422 −0.134447
$$107$$ 14.8545i 1.43603i −0.696025 0.718017i $$-0.745050\pi$$
0.696025 0.718017i $$-0.254950\pi$$
$$108$$ 9.07338i 0.873087i
$$109$$ 7.13713 0.683613 0.341806 0.939770i $$-0.388961\pi$$
0.341806 + 0.939770i $$0.388961\pi$$
$$110$$ −0.645450 0.192001i −0.0615412 0.0183066i
$$111$$ 10.4720 0.993956
$$112$$ 6.74342i 0.637193i
$$113$$ 1.22524i 0.115261i −0.998338 0.0576303i $$-0.981646\pi$$
0.998338 0.0576303i $$-0.0183545\pi$$
$$114$$ −0.558272 −0.0522870
$$115$$ 8.65332 + 2.57409i 0.806927 + 0.240036i
$$116$$ 4.18004 0.388107
$$117$$ 1.64043i 0.151658i
$$118$$ 0.933879i 0.0859705i
$$119$$ 4.20673 0.385630
$$120$$ 1.39143 4.67756i 0.127019 0.427000i
$$121$$ 1.00000 0.0909091
$$122$$ 3.04080i 0.275301i
$$123$$ 6.54245i 0.589913i
$$124$$ 6.13897 0.551296
$$125$$ −8.52668 + 7.23158i −0.762649 + 0.646812i
$$126$$ −0.255887 −0.0227962
$$127$$ 1.78182i 0.158111i 0.996870 + 0.0790554i $$0.0251904\pi$$
−0.996870 + 0.0790554i $$0.974810\pi$$
$$128$$ 8.57392i 0.757835i
$$129$$ 5.08109 0.447365
$$130$$ 0.721601 2.42580i 0.0632886 0.212757i
$$131$$ 18.4204 1.60939 0.804697 0.593685i $$-0.202328\pi$$
0.804697 + 0.593685i $$0.202328\pi$$
$$132$$ 3.53942i 0.308067i
$$133$$ 1.94668i 0.168799i
$$134$$ 3.63257 0.313807
$$135$$ −10.1851 3.02976i −0.876597 0.260760i
$$136$$ −2.54413 −0.218157
$$137$$ 13.8926i 1.18693i 0.804861 + 0.593463i $$0.202240\pi$$
−0.804861 + 0.593463i $$0.797760\pi$$
$$138$$ 2.25401i 0.191874i
$$139$$ 4.35165 0.369102 0.184551 0.982823i $$-0.440917\pi$$
0.184551 + 0.982823i $$0.440917\pi$$
$$140$$ −7.96606 2.36965i −0.673255 0.200272i
$$141$$ 3.47967 0.293041
$$142$$ 1.93437i 0.162328i
$$143$$ 3.75832i 0.314286i
$$144$$ −1.51199 −0.125999
$$145$$ 1.39579 4.69222i 0.115914 0.389668i
$$146$$ −3.23596 −0.267810
$$147$$ 5.95142i 0.490865i
$$148$$ 10.7857i 0.886577i
$$149$$ 11.6917 0.957818 0.478909 0.877864i $$-0.341032\pi$$
0.478909 + 0.877864i $$0.341032\pi$$
$$150$$ −2.33752 1.52568i −0.190858 0.124571i
$$151$$ −23.0439 −1.87529 −0.937644 0.347596i $$-0.886998\pi$$
−0.937644 + 0.347596i $$0.886998\pi$$
$$152$$ 1.17730i 0.0954920i
$$153$$ 0.943222i 0.0762550i
$$154$$ −0.586251 −0.0472415
$$155$$ 2.04991 6.89117i 0.164653 0.553512i
$$156$$ −13.3023 −1.06503
$$157$$ 12.2578i 0.978277i −0.872206 0.489138i $$-0.837311\pi$$
0.872206 0.489138i $$-0.162689\pi$$
$$158$$ 3.25452i 0.258916i
$$159$$ 8.52066 0.675732
$$160$$ 7.28240 + 2.16629i 0.575724 + 0.171260i
$$161$$ 7.85967 0.619429
$$162$$ 3.04736i 0.239423i
$$163$$ 8.00570i 0.627055i 0.949579 + 0.313527i $$0.101511\pi$$
−0.949579 + 0.313527i $$0.898489\pi$$
$$164$$ −6.73843 −0.526183
$$165$$ 3.97311 + 1.18188i 0.309306 + 0.0920089i
$$166$$ −2.44715 −0.189936
$$167$$ 5.00463i 0.387270i −0.981074 0.193635i $$-0.937972\pi$$
0.981074 0.193635i $$-0.0620278\pi$$
$$168$$ 4.24855i 0.327782i
$$169$$ −1.12494 −0.0865341
$$170$$ −0.414910 + 1.39480i −0.0318221 + 0.106976i
$$171$$ 0.436480 0.0333784
$$172$$ 5.23330i 0.399035i
$$173$$ 7.15833i 0.544237i 0.962264 + 0.272119i $$0.0877244\pi$$
−0.962264 + 0.272119i $$0.912276\pi$$
$$174$$ 1.22223 0.0926567
$$175$$ −5.32001 + 8.15086i −0.402155 + 0.616147i
$$176$$ −3.46406 −0.261113
$$177$$ 5.74855i 0.432087i
$$178$$ 3.34737i 0.250896i
$$179$$ 4.12217 0.308106 0.154053 0.988063i $$-0.450767\pi$$
0.154053 + 0.988063i $$0.450767\pi$$
$$180$$ −0.531318 + 1.78613i −0.0396021 + 0.133130i
$$181$$ 17.5288 1.30291 0.651454 0.758688i $$-0.274159\pi$$
0.651454 + 0.758688i $$0.274159\pi$$
$$182$$ 2.20332i 0.163321i
$$183$$ 18.7178i 1.38366i
$$184$$ −4.75334 −0.350421
$$185$$ 12.1072 + 3.60152i 0.890141 + 0.264789i
$$186$$ 1.79501 0.131616
$$187$$ 2.16098i 0.158026i
$$188$$ 3.58390i 0.261383i
$$189$$ −9.25099 −0.672911
$$190$$ −0.645450 0.192001i −0.0468258 0.0139292i
$$191$$ −27.5080 −1.99041 −0.995205 0.0978155i $$-0.968814\pi$$
−0.995205 + 0.0978155i $$0.968814\pi$$
$$192$$ 10.9463i 0.789979i
$$193$$ 13.1923i 0.949603i 0.880093 + 0.474802i $$0.157480\pi$$
−0.880093 + 0.474802i $$0.842520\pi$$
$$194$$ 3.44798 0.247551
$$195$$ −4.44186 + 14.9322i −0.318088 + 1.06932i
$$196$$ 6.12970 0.437836
$$197$$ 11.4532i 0.816006i 0.912981 + 0.408003i $$0.133775\pi$$
−0.912981 + 0.408003i $$0.866225\pi$$
$$198$$ 0.131448i 0.00934159i
$$199$$ 19.7562 1.40048 0.700240 0.713907i $$-0.253076\pi$$
0.700240 + 0.713907i $$0.253076\pi$$
$$200$$ 3.21741 4.92944i 0.227505 0.348564i
$$201$$ −22.3605 −1.57719
$$202$$ 2.06737i 0.145460i
$$203$$ 4.26187i 0.299124i
$$204$$ 7.64861 0.535510
$$205$$ −2.25008 + 7.56409i −0.157152 + 0.528299i
$$206$$ 4.13358 0.288000
$$207$$ 1.76228i 0.122487i
$$208$$ 13.0190i 0.902708i
$$209$$ 1.00000 0.0691714
$$210$$ −2.32924 0.692876i −0.160733 0.0478130i
$$211$$ −22.4594 −1.54617 −0.773085 0.634303i $$-0.781287\pi$$
−0.773085 + 0.634303i $$0.781287\pi$$
$$212$$ 8.77591i 0.602732i
$$213$$ 11.9071i 0.815862i
$$214$$ 4.47349 0.305801
$$215$$ 5.87453 + 1.74749i 0.400640 + 0.119178i
$$216$$ 5.59477 0.380676
$$217$$ 6.25914i 0.424898i
$$218$$ 2.14938i 0.145574i
$$219$$ 19.9191 1.34601
$$220$$ −1.21728 + 4.09212i −0.0820690 + 0.275891i
$$221$$ 8.12163 0.546320
$$222$$ 3.15368i 0.211661i
$$223$$ 10.3113i 0.690499i 0.938511 + 0.345249i $$0.112206\pi$$
−0.938511 + 0.345249i $$0.887794\pi$$
$$224$$ 6.61448 0.441949
$$225$$ 1.82757 + 1.19284i 0.121838 + 0.0795226i
$$226$$ 0.368986 0.0245446
$$227$$ 19.9756i 1.32583i 0.748696 + 0.662914i $$0.230680\pi$$
−0.748696 + 0.662914i $$0.769320\pi$$
$$228$$ 3.53942i 0.234404i
$$229$$ 15.7027 1.03767 0.518833 0.854876i $$-0.326367\pi$$
0.518833 + 0.854876i $$0.326367\pi$$
$$230$$ −0.775200 + 2.60599i −0.0511152 + 0.171834i
$$231$$ 3.60871 0.237435
$$232$$ 2.57747i 0.169219i
$$233$$ 21.1823i 1.38770i 0.720120 + 0.693850i $$0.244087\pi$$
−0.720120 + 0.693850i $$0.755913\pi$$
$$234$$ −0.494022 −0.0322953
$$235$$ 4.02304 + 1.19673i 0.262434 + 0.0780659i
$$236$$ −5.92075 −0.385408
$$237$$ 20.0334i 1.30131i
$$238$$ 1.26687i 0.0821193i
$$239$$ 0.429031 0.0277517 0.0138759 0.999904i $$-0.495583\pi$$
0.0138759 + 0.999904i $$0.495583\pi$$
$$240$$ −13.7631 4.09409i −0.888403 0.264272i
$$241$$ 11.9657 0.770781 0.385391 0.922753i $$-0.374067\pi$$
0.385391 + 0.922753i $$0.374067\pi$$
$$242$$ 0.301154i 0.0193589i
$$243$$ 4.50164i 0.288780i
$$244$$ −19.2785 −1.23418
$$245$$ 2.04682 6.88077i 0.130766 0.439596i
$$246$$ −1.97029 −0.125621
$$247$$ 3.75832i 0.239136i
$$248$$ 3.78537i 0.240371i
$$249$$ 15.0636 0.954617
$$250$$ −2.17782 2.56785i −0.137738 0.162405i
$$251$$ 7.13854 0.450581 0.225290 0.974292i $$-0.427667\pi$$
0.225290 + 0.974292i $$0.427667\pi$$
$$252$$ 1.62231i 0.102196i
$$253$$ 4.03747i 0.253834i
$$254$$ −0.536602 −0.0336694
$$255$$ 2.55400 8.58579i 0.159938 0.537663i
$$256$$ 9.22763 0.576727
$$257$$ 6.86772i 0.428397i 0.976790 + 0.214198i $$0.0687139\pi$$
−0.976790 + 0.214198i $$0.931286\pi$$
$$258$$ 1.53019i 0.0952657i
$$259$$ 10.9968 0.683308
$$260$$ −15.3795 4.57492i −0.953796 0.283725i
$$261$$ −0.955585 −0.0591492
$$262$$ 5.54737i 0.342718i
$$263$$ 0.473180i 0.0291775i −0.999894 0.0145888i $$-0.995356\pi$$
0.999894 0.0145888i $$-0.00464391\pi$$
$$264$$ −2.18246 −0.134321
$$265$$ 9.85121 + 2.93043i 0.605155 + 0.180015i
$$266$$ −0.586251 −0.0359454
$$267$$ 20.6049i 1.26100i
$$268$$ 23.0304i 1.40680i
$$269$$ −2.26859 −0.138318 −0.0691591 0.997606i $$-0.522032\pi$$
−0.0691591 + 0.997606i $$0.522032\pi$$
$$270$$ 0.912426 3.06730i 0.0555285 0.186670i
$$271$$ −13.6384 −0.828474 −0.414237 0.910169i $$-0.635952\pi$$
−0.414237 + 0.910169i $$0.635952\pi$$
$$272$$ 7.48575i 0.453891i
$$273$$ 13.5627i 0.820850i
$$274$$ −4.18382 −0.252754
$$275$$ 4.18706 + 2.73286i 0.252489 + 0.164798i
$$276$$ 14.2903 0.860177
$$277$$ 1.64693i 0.0989544i 0.998775 + 0.0494772i $$0.0157555\pi$$
−0.998775 + 0.0494772i $$0.984244\pi$$
$$278$$ 1.31052i 0.0785997i
$$279$$ −1.40341 −0.0840198
$$280$$ 1.46116 4.91198i 0.0873211 0.293547i
$$281$$ 16.7390 0.998565 0.499282 0.866439i $$-0.333597\pi$$
0.499282 + 0.866439i $$0.333597\pi$$
$$282$$ 1.04792i 0.0624025i
$$283$$ 9.91741i 0.589529i −0.955570 0.294764i $$-0.904759\pi$$
0.955570 0.294764i $$-0.0952412\pi$$
$$284$$ 12.2638 0.727723
$$285$$ 3.97311 + 1.18188i 0.235346 + 0.0700082i
$$286$$ −1.13183 −0.0669267
$$287$$ 6.87034i 0.405543i
$$288$$ 1.48308i 0.0873915i
$$289$$ 12.3302 0.725305
$$290$$ 1.41308 + 0.420348i 0.0829791 + 0.0246837i
$$291$$ −21.2243 −1.24419
$$292$$ 20.5158i 1.20060i
$$293$$ 14.1780i 0.828289i −0.910211 0.414144i $$-0.864081\pi$$
0.910211 0.414144i $$-0.135919\pi$$
$$294$$ 1.79230 0.104529
$$295$$ −1.97704 + 6.64622i −0.115108 + 0.386958i
$$296$$ −6.65059 −0.386558
$$297$$ 4.75219i 0.275750i
$$298$$ 3.52100i 0.203966i
$$299$$ 15.1741 0.877541
$$300$$ −9.67276 + 14.8198i −0.558457 + 0.855620i
$$301$$ 5.33574 0.307547
$$302$$ 6.93978i 0.399340i
$$303$$ 12.7258i 0.731079i
$$304$$ −3.46406 −0.198678
$$305$$ −6.43744 + 21.6407i −0.368607 + 1.23914i
$$306$$ 0.284056 0.0162384
$$307$$ 7.49870i 0.427974i 0.976837 + 0.213987i $$0.0686450\pi$$
−0.976837 + 0.213987i $$0.931355\pi$$
$$308$$ 3.71681i 0.211785i
$$309$$ −25.4445 −1.44749
$$310$$ 2.07531 + 0.617339i 0.117869 + 0.0350625i
$$311$$ −22.6904 −1.28666 −0.643328 0.765591i $$-0.722447\pi$$
−0.643328 + 0.765591i $$0.722447\pi$$
$$312$$ 8.20236i 0.464367i
$$313$$ 16.3070i 0.921723i −0.887472 0.460862i $$-0.847540\pi$$
0.887472 0.460862i $$-0.152460\pi$$
$$314$$ 3.69148 0.208322
$$315$$ 1.82109 + 0.541718i 0.102607 + 0.0305224i
$$316$$ −20.6336 −1.16073
$$317$$ 26.5837i 1.49309i 0.665336 + 0.746544i $$0.268288\pi$$
−0.665336 + 0.746544i $$0.731712\pi$$
$$318$$ 2.56603i 0.143896i
$$319$$ −2.18930 −0.122577
$$320$$ 3.76464 12.6556i 0.210450 0.707469i
$$321$$ −27.5368 −1.53696
$$322$$ 2.36697i 0.131906i
$$323$$ 2.16098i 0.120240i
$$324$$ −19.3201 −1.07334
$$325$$ −10.2710 + 15.7363i −0.569731 + 0.872892i
$$326$$ −2.41095 −0.133530
$$327$$ 13.2306i 0.731655i
$$328$$ 4.15501i 0.229422i
$$329$$ 3.65406 0.201455
$$330$$ −0.355927 + 1.19652i −0.0195931 + 0.0658662i
$$331$$ 12.6060 0.692887 0.346444 0.938071i $$-0.387389\pi$$
0.346444 + 0.938071i $$0.387389\pi$$
$$332$$ 15.5148i 0.851487i
$$333$$ 2.46567i 0.135118i
$$334$$ 1.50717 0.0824685
$$335$$ −25.8523 7.69024i −1.41246 0.420163i
$$336$$ −12.5008 −0.681974
$$337$$ 6.18984i 0.337182i 0.985686 + 0.168591i $$0.0539217\pi$$
−0.985686 + 0.168591i $$0.946078\pi$$
$$338$$ 0.338782i 0.0184273i
$$339$$ −2.27131 −0.123361
$$340$$ 8.84298 + 2.63051i 0.479578 + 0.142660i
$$341$$ −3.21529 −0.174118
$$342$$ 0.131448i 0.00710788i
$$343$$ 19.8765i 1.07323i
$$344$$ −3.22693 −0.173984
$$345$$ 4.77179 16.0413i 0.256905 0.863635i
$$346$$ −2.15576 −0.115894
$$347$$ 12.5724i 0.674921i 0.941340 + 0.337460i $$0.109568\pi$$
−0.941340 + 0.337460i $$0.890432\pi$$
$$348$$ 7.74886i 0.415382i
$$349$$ −17.0337 −0.911793 −0.455897 0.890033i $$-0.650681\pi$$
−0.455897 + 0.890033i $$0.650681\pi$$
$$350$$ −2.45467 1.60214i −0.131208 0.0856382i
$$351$$ −17.8602 −0.953308
$$352$$ 3.39783i 0.181105i
$$353$$ 8.51838i 0.453387i −0.973966 0.226694i $$-0.927208\pi$$
0.973966 0.226694i $$-0.0727916\pi$$
$$354$$ −1.73120 −0.0920123
$$355$$ 4.09510 13.7665i 0.217345 0.730649i
$$356$$ 21.2222 1.12477
$$357$$ 7.79833i 0.412731i
$$358$$ 1.24141i 0.0656106i
$$359$$ 6.43010 0.339367 0.169684 0.985499i $$-0.445725\pi$$
0.169684 + 0.985499i $$0.445725\pi$$
$$360$$ −1.10135 0.327618i −0.0580464 0.0172670i
$$361$$ 1.00000 0.0526316
$$362$$ 5.27889i 0.277452i
$$363$$ 1.85377i 0.0972979i
$$364$$ −13.9689 −0.732172
$$365$$ 23.0296 + 6.85059i 1.20543 + 0.358576i
$$366$$ −5.63696 −0.294648
$$367$$ 29.9633i 1.56407i 0.623233 + 0.782037i $$0.285819\pi$$
−0.623233 + 0.782037i $$0.714181\pi$$
$$368$$ 13.9861i 0.729074i
$$369$$ 1.54045 0.0801926
$$370$$ −1.08461 + 3.64615i −0.0563864 + 0.189554i
$$371$$ 8.94769 0.464541
$$372$$ 11.3803i 0.590039i
$$373$$ 34.6611i 1.79469i −0.441334 0.897343i $$-0.645495\pi$$
0.441334 0.897343i $$-0.354505\pi$$
$$374$$ 0.650787 0.0336514
$$375$$ 13.4057 + 15.8065i 0.692269 + 0.816246i
$$376$$ −2.20988 −0.113966
$$377$$ 8.22808i 0.423768i
$$378$$ 2.78598i 0.143295i
$$379$$ −1.82041 −0.0935083 −0.0467542 0.998906i $$-0.514888\pi$$
−0.0467542 + 0.998906i $$0.514888\pi$$
$$380$$ −1.21728 + 4.09212i −0.0624451 + 0.209922i
$$381$$ 3.30309 0.169222
$$382$$ 8.28415i 0.423854i
$$383$$ 17.0353i 0.870463i 0.900319 + 0.435232i $$0.143334\pi$$
−0.900319 + 0.435232i $$0.856666\pi$$
$$384$$ 15.8941 0.811094
$$385$$ 4.17223 + 1.24111i 0.212636 + 0.0632527i
$$386$$ −3.97292 −0.202216
$$387$$ 1.19637i 0.0608147i
$$388$$ 21.8601i 1.10978i
$$389$$ 21.7778 1.10418 0.552090 0.833784i $$-0.313830\pi$$
0.552090 + 0.833784i $$0.313830\pi$$
$$390$$ −4.49689 1.33769i −0.227709 0.0677363i
$$391$$ −8.72488 −0.441236
$$392$$ 3.77966i 0.190902i
$$393$$ 34.1472i 1.72250i
$$394$$ −3.44918 −0.173767
$$395$$ −6.88990 + 23.1618i −0.346669 + 1.16539i
$$396$$ 0.833374 0.0418786
$$397$$ 8.81816i 0.442571i −0.975209 0.221285i $$-0.928975\pi$$
0.975209 0.221285i $$-0.0710252\pi$$
$$398$$ 5.94967i 0.298230i
$$399$$ 3.60871 0.180661
$$400$$ −14.5042 9.46681i −0.725211 0.473340i
$$401$$ −11.0380 −0.551210 −0.275605 0.961271i $$-0.588878\pi$$
−0.275605 + 0.961271i $$0.588878\pi$$
$$402$$ 6.73397i 0.335860i
$$403$$ 12.0841i 0.601950i
$$404$$ 13.1070 0.652099
$$405$$ −6.45133 + 21.6874i −0.320569 + 1.07766i
$$406$$ 1.28348 0.0636980
$$407$$ 5.64900i 0.280011i
$$408$$ 4.71624i 0.233489i
$$409$$ 25.9583 1.28355 0.641777 0.766891i $$-0.278197\pi$$
0.641777 + 0.766891i $$0.278197\pi$$
$$410$$ −2.27796 0.677621i −0.112500 0.0334653i
$$411$$ 25.7538 1.27034
$$412$$ 26.2067i 1.29111i
$$413$$ 6.03665i 0.297044i
$$414$$ 0.530717 0.0260833
$$415$$ 17.4159 + 5.18068i 0.854911 + 0.254309i
$$416$$ 12.7701 0.626106
$$417$$ 8.06698i 0.395042i
$$418$$ 0.301154i 0.0147299i
$$419$$ −8.14823 −0.398067 −0.199034 0.979993i $$-0.563780\pi$$
−0.199034 + 0.979993i $$0.563780\pi$$
$$420$$ −4.39280 + 14.7673i −0.214347 + 0.720569i
$$421$$ −14.7467 −0.718711 −0.359356 0.933201i $$-0.617003\pi$$
−0.359356 + 0.933201i $$0.617003\pi$$
$$422$$ 6.76375i 0.329254i
$$423$$ 0.819304i 0.0398359i
$$424$$ −5.41134 −0.262798
$$425$$ 5.90565 9.04813i 0.286466 0.438899i
$$426$$ 3.58588 0.173736
$$427$$ 19.6559i 0.951216i
$$428$$ 28.3617i 1.37092i
$$429$$ 6.96707 0.336373
$$430$$ −0.526264 + 1.76914i −0.0253787 + 0.0853156i
$$431$$ −28.0178 −1.34957 −0.674785 0.738014i $$-0.735764\pi$$
−0.674785 + 0.738014i $$0.735764\pi$$
$$432$$ 16.4619i 0.792022i
$$433$$ 2.14430i 0.103049i −0.998672 0.0515243i $$-0.983592\pi$$
0.998672 0.0515243i $$-0.0164080\pi$$
$$434$$ 1.88497 0.0904813
$$435$$ −8.69832 2.58748i −0.417053 0.124060i
$$436$$ 13.6270 0.652613
$$437$$ 4.03747i 0.193139i
$$438$$ 5.99873i 0.286631i
$$439$$ −4.98343 −0.237846 −0.118923 0.992903i $$-0.537944\pi$$
−0.118923 + 0.992903i $$0.537944\pi$$
$$440$$ −2.52326 0.750591i −0.120292 0.0357830i
$$441$$ −1.40129 −0.0667281
$$442$$ 2.44586i 0.116338i
$$443$$ 10.3754i 0.492952i −0.969149 0.246476i $$-0.920727\pi$$
0.969149 0.246476i $$-0.0792726\pi$$
$$444$$ 19.9942 0.948883
$$445$$ 7.08646 23.8225i 0.335930 1.12930i
$$446$$ −3.10531 −0.147041
$$447$$ 21.6737i 1.02513i
$$448$$ 11.4949i 0.543081i
$$449$$ −35.9683 −1.69745 −0.848725 0.528835i $$-0.822629\pi$$
−0.848725 + 0.528835i $$0.822629\pi$$
$$450$$ −0.359229 + 0.550380i −0.0169342 + 0.0259451i
$$451$$ 3.52926 0.166186
$$452$$ 2.33935i 0.110034i
$$453$$ 42.7183i 2.00708i
$$454$$ −6.01574 −0.282333
$$455$$ −4.66447 + 15.6805i −0.218674 + 0.735115i
$$456$$ −2.18246 −0.102203
$$457$$ 27.3842i 1.28098i 0.767966 + 0.640490i $$0.221269\pi$$
−0.767966 + 0.640490i $$0.778731\pi$$
$$458$$ 4.72895i 0.220969i
$$459$$ 10.2694 0.479333
$$460$$ 16.5218 + 4.91473i 0.770335 + 0.229151i
$$461$$ −9.58866 −0.446589 −0.223294 0.974751i $$-0.571681\pi$$
−0.223294 + 0.974751i $$0.571681\pi$$
$$462$$ 1.08678i 0.0505615i
$$463$$ 27.4154i 1.27410i −0.770822 0.637050i $$-0.780154\pi$$
0.770822 0.637050i $$-0.219846\pi$$
$$464$$ 7.58387 0.352072
$$465$$ −12.7747 3.80007i −0.592411 0.176224i
$$466$$ −6.37915 −0.295508
$$467$$ 30.6386i 1.41778i −0.705317 0.708892i $$-0.749195\pi$$
0.705317 0.708892i $$-0.250805\pi$$
$$468$$ 3.13208i 0.144781i
$$469$$ −23.4812 −1.08426
$$470$$ −0.360400 + 1.21155i −0.0166240 + 0.0558849i
$$471$$ −22.7231 −1.04703
$$472$$ 3.65082i 0.168043i
$$473$$ 2.74094i 0.126029i
$$474$$ −6.03315 −0.277112
$$475$$ 4.18706 + 2.73286i 0.192115 + 0.125392i
$$476$$ 8.03193 0.368143
$$477$$ 2.00623i 0.0918589i
$$478$$ 0.129205i 0.00590968i
$$479$$ −5.55489 −0.253809 −0.126905 0.991915i $$-0.540504\pi$$
−0.126905 + 0.991915i $$0.540504\pi$$
$$480$$ 4.01581 13.4999i 0.183296 0.616184i
$$481$$ 21.2307 0.968038
$$482$$ 3.60354i 0.164137i
$$483$$ 14.5701i 0.662961i
$$484$$ 1.90931 0.0867866
$$485$$ −24.5386 7.29946i −1.11424 0.331451i
$$486$$ −1.35569 −0.0614953
$$487$$ 15.4839i 0.701642i −0.936442 0.350821i $$-0.885902\pi$$
0.936442 0.350821i $$-0.114098\pi$$
$$488$$ 11.8874i 0.538118i
$$489$$ 14.8408 0.671122
$$490$$ 2.07217 + 0.616407i 0.0936113 + 0.0278464i
$$491$$ −25.8915 −1.16847 −0.584233 0.811586i $$-0.698605\pi$$
−0.584233 + 0.811586i $$0.698605\pi$$
$$492$$ 12.4915i 0.563162i
$$493$$ 4.73103i 0.213075i
$$494$$ −1.13183 −0.0509236
$$495$$ 0.278278 0.935486i 0.0125077 0.0420470i
$$496$$ 11.1380 0.500109
$$497$$ 12.5039i 0.560875i
$$498$$ 4.53647i 0.203284i
$$499$$ 33.9769 1.52102 0.760508 0.649329i $$-0.224950\pi$$
0.760508 + 0.649329i $$0.224950\pi$$
$$500$$ −16.2800 + 13.8073i −0.728065 + 0.617481i
$$501$$ −9.27746 −0.414486
$$502$$ 2.14980i 0.0959504i
$$503$$ 11.0065i 0.490756i −0.969428 0.245378i $$-0.921088\pi$$
0.969428 0.245378i $$-0.0789120\pi$$
$$504$$ −1.00034 −0.0445587
$$505$$ 4.37667 14.7130i 0.194759 0.654721i
$$506$$ 1.21590 0.0540535
$$507$$ 2.08539i 0.0926155i
$$508$$ 3.40204i 0.150941i
$$509$$ 20.0893 0.890443 0.445221 0.895420i $$-0.353125\pi$$
0.445221 + 0.895420i $$0.353125\pi$$
$$510$$ 2.58565 + 0.769149i 0.114494 + 0.0340585i
$$511$$ 20.9174 0.925332
$$512$$ 19.9268i 0.880648i
$$513$$ 4.75219i 0.209814i
$$514$$ −2.06824 −0.0912264
$$515$$ −29.4178 8.75088i −1.29630 0.385610i
$$516$$ 9.70136 0.427079
$$517$$ 1.87707i 0.0825535i
$$518$$ 3.31173i 0.145509i
$$519$$ 13.2699 0.582485
$$520$$ 2.82096 9.48321i 0.123707 0.415866i
$$521$$ −5.13542 −0.224987 −0.112493 0.993652i $$-0.535884\pi$$
−0.112493 + 0.993652i $$0.535884\pi$$
$$522$$ 0.287779i 0.0125957i
$$523$$ 11.4021i 0.498578i 0.968429 + 0.249289i $$0.0801968\pi$$
−0.968429 + 0.249289i $$0.919803\pi$$
$$524$$ 35.1701 1.53641
$$525$$ 15.1099 + 9.86210i 0.659448 + 0.430417i
$$526$$ 0.142500 0.00621330
$$527$$ 6.94816i 0.302667i
$$528$$ 6.42159i 0.279464i
$$529$$ 6.69880 0.291252
$$530$$ −0.882511 + 2.96674i −0.0383338 + 0.128867i
$$531$$ 1.35352 0.0587379
$$532$$ 3.71681i 0.161144i
$$533$$ 13.2641i 0.574530i
$$534$$ 6.20527 0.268528
$$535$$ −31.8369 9.47047i −1.37643 0.409444i
$$536$$ 14.2008 0.613383
$$537$$ 7.64158i 0.329758i
$$538$$ 0.683195i 0.0294546i
$$539$$ −3.21044 −0.138283
$$540$$ −19.4465 5.78474i −0.836846 0.248936i
$$541$$ 31.1731 1.34024 0.670118 0.742254i $$-0.266243\pi$$
0.670118 + 0.742254i $$0.266243\pi$$
$$542$$ 4.10726i 0.176422i
$$543$$ 32.4945i 1.39447i
$$544$$ −7.34262 −0.314812
$$545$$ 4.55028 15.2967i 0.194913 0.655237i
$$546$$ −4.08445 −0.174798
$$547$$ 36.3618i 1.55472i −0.629056 0.777360i $$-0.716558\pi$$
0.629056 0.777360i $$-0.283442\pi$$
$$548$$ 26.5252i 1.13310i
$$549$$ 4.40720 0.188095
$$550$$ −0.823014 + 1.26095i −0.0350934 + 0.0537671i
$$551$$ −2.18930 −0.0932673
$$552$$ 8.81161i 0.375047i
$$553$$ 21.0374i 0.894603i
$$554$$ −0.495980 −0.0210722
$$555$$ 6.67641 22.4441i 0.283398 0.952698i
$$556$$ 8.30863 0.352364
$$557$$ 0.847753i 0.0359204i −0.999839 0.0179602i $$-0.994283\pi$$
0.999839 0.0179602i $$-0.00571722\pi$$
$$558$$ 0.422642i 0.0178919i
$$559$$ 10.3013 0.435700
$$560$$ −14.4528 4.29927i −0.610744 0.181677i
$$561$$ −4.00596 −0.169132
$$562$$ 5.04102i 0.212643i
$$563$$ 39.5533i 1.66697i −0.552541 0.833486i $$-0.686342\pi$$
0.552541 0.833486i $$-0.313658\pi$$
$$564$$ 6.64375 0.279752
$$565$$ −2.62599 0.781151i −0.110476 0.0328633i
$$566$$ 2.98667 0.125539
$$567$$ 19.6983i 0.827251i
$$568$$ 7.56203i 0.317296i
$$569$$ −18.3932 −0.771082 −0.385541 0.922691i $$-0.625985\pi$$
−0.385541 + 0.922691i $$0.625985\pi$$
$$570$$ −0.355927 + 1.19652i −0.0149081 + 0.0501166i
$$571$$ 33.4442 1.39959 0.699797 0.714341i $$-0.253274\pi$$
0.699797 + 0.714341i $$0.253274\pi$$
$$572$$ 7.17578i 0.300034i
$$573$$ 50.9936i 2.13029i
$$574$$ −2.06903 −0.0863597
$$575$$ 11.0339 16.9051i 0.460144 0.704993i
$$576$$ −2.57735 −0.107390
$$577$$ 32.8041i 1.36565i 0.730581 + 0.682826i $$0.239249\pi$$
−0.730581 + 0.682826i $$0.760751\pi$$
$$578$$ 3.71329i 0.154452i
$$579$$ 24.4556 1.01634
$$580$$ 2.66499 8.95889i 0.110658 0.371998i
$$581$$ 15.8185 0.656264
$$582$$ 6.39178i 0.264948i
$$583$$ 4.59639i 0.190363i
$$584$$ −12.6503 −0.523475
$$585$$ 3.51585 + 1.04586i 0.145363 + 0.0432409i
$$586$$ 4.26977 0.176383
$$587$$ 26.2752i 1.08449i −0.840220 0.542246i $$-0.817574\pi$$
0.840220 0.542246i $$-0.182426\pi$$
$$588$$ 11.3631i 0.468606i
$$589$$ −3.21529 −0.132484
$$590$$ −2.00154 0.595395i −0.0824020 0.0245120i
$$591$$ 21.2316 0.873353
$$592$$ 19.5685i 0.804260i
$$593$$ 19.5147i 0.801371i −0.916216 0.400686i $$-0.868772\pi$$
0.916216 0.400686i $$-0.131228\pi$$
$$594$$ −1.43114 −0.0587205
$$595$$ 2.68200 9.01608i 0.109951 0.369623i
$$596$$ 22.3230 0.914384
$$597$$ 36.6236i 1.49890i
$$598$$ 4.56975i 0.186871i
$$599$$ −15.9690 −0.652476 −0.326238 0.945288i $$-0.605781\pi$$
−0.326238 + 0.945288i $$0.605781\pi$$
$$600$$ −9.13807 5.96436i −0.373060 0.243494i
$$601$$ −18.0313 −0.735510 −0.367755 0.929923i $$-0.619874\pi$$
−0.367755 + 0.929923i $$0.619874\pi$$
$$602$$ 1.60688i 0.0654916i
$$603$$ 5.26489i 0.214403i
$$604$$ −43.9979 −1.79025
$$605$$ 0.637551 2.14325i 0.0259201 0.0871356i
$$606$$ 3.83244 0.155682
$$607$$ 9.02312i 0.366237i −0.983091 0.183119i $$-0.941381\pi$$
0.983091 0.183119i $$-0.0586192\pi$$
$$608$$ 3.39783i 0.137800i
$$609$$ −7.90054 −0.320146
$$610$$ −6.51720 1.93866i −0.263874 0.0784942i
$$611$$ 7.05463 0.285400
$$612$$ 1.80090i 0.0727971i
$$613$$ 35.9969i 1.45390i −0.686690 0.726950i $$-0.740937\pi$$
0.686690 0.726950i $$-0.259063\pi$$
$$614$$ −2.25827 −0.0911362
$$615$$ 14.0221 + 4.17114i 0.565426 + 0.168197i
$$616$$ −2.29184 −0.0923407
$$617$$ 44.8507i 1.80562i 0.430037 + 0.902811i $$0.358501\pi$$
−0.430037 + 0.902811i $$0.641499\pi$$
$$618$$ 7.66272i 0.308240i
$$619$$ −36.6485 −1.47303 −0.736514 0.676422i $$-0.763530\pi$$
−0.736514 + 0.676422i $$0.763530\pi$$
$$620$$ 3.91390 13.1574i 0.157186 0.528412i
$$621$$ 19.1868 0.769941
$$622$$ 6.83331i 0.273991i
$$623$$ 21.6376i 0.866892i
$$624$$ −24.1344 −0.966148
$$625$$ 10.0629 + 22.8853i 0.402517 + 0.915413i
$$626$$ 4.91091 0.196279
$$627$$ 1.85377i 0.0740326i
$$628$$ 23.4038i 0.933915i
$$629$$ −12.2074 −0.486739
$$630$$ −0.163141 + 0.548430i −0.00649968 + 0.0218500i
$$631$$ −39.4249 −1.56948 −0.784739 0.619826i $$-0.787203\pi$$
−0.784739 + 0.619826i $$0.787203\pi$$
$$632$$ 12.7229i 0.506091i
$$633$$ 41.6347i 1.65483i
$$634$$ −8.00579 −0.317950
$$635$$ 3.81888 + 1.13600i 0.151548 + 0.0450807i
$$636$$ 16.2686 0.645090
$$637$$ 12.0658i 0.478066i
$$638$$ 0.659317i 0.0261026i
$$639$$ −2.80359 −0.110908
$$640$$ 18.3761 + 5.46631i 0.726378 + 0.216075i
$$641$$ −6.91478 −0.273117 −0.136559 0.990632i $$-0.543604\pi$$
−0.136559 + 0.990632i $$0.543604\pi$$
$$642$$ 8.29283i 0.327292i
$$643$$ 38.8033i 1.53025i 0.643879 + 0.765127i $$0.277324\pi$$
−0.643879 + 0.765127i $$0.722676\pi$$
$$644$$ 15.0065 0.591340
$$645$$ 3.23945 10.8901i 0.127553 0.428796i
$$646$$ 0.650787 0.0256049
$$647$$ 18.4537i 0.725490i 0.931888 + 0.362745i $$0.118160\pi$$
−0.931888 + 0.362745i $$0.881840\pi$$
$$648$$ 11.9131i 0.467989i
$$649$$ 3.10100 0.121725
$$650$$ −4.73905 3.09315i −0.185881 0.121323i
$$651$$ −11.6030 −0.454758
$$652$$ 15.2853i 0.598620i
$$653$$ 12.6249i 0.494052i 0.969009 + 0.247026i $$0.0794533\pi$$
−0.969009 + 0.247026i $$0.920547\pi$$
$$654$$ 3.98446 0.155805
$$655$$ 11.7439 39.4795i 0.458873 1.54259i
$$656$$ −12.2256 −0.477328
$$657$$ 4.69005i 0.182976i
$$658$$ 1.10044i 0.0428994i
$$659$$ −37.4031 −1.45702 −0.728509 0.685036i $$-0.759786\pi$$
−0.728509 + 0.685036i $$0.759786\pi$$
$$660$$ 7.58588 + 2.25656i 0.295280 + 0.0878365i
$$661$$ −12.6089 −0.490431 −0.245215 0.969469i $$-0.578859\pi$$
−0.245215 + 0.969469i $$0.578859\pi$$
$$662$$ 3.79634i 0.147549i
$$663$$ 15.0557i 0.584714i
$$664$$ −9.56666 −0.371259
$$665$$ 4.17223 + 1.24111i 0.161792 + 0.0481281i
$$666$$ 0.742549 0.0287732
$$667$$ 8.83924i 0.342257i
$$668$$ 9.55538i 0.369709i
$$669$$ 19.1149 0.739025
$$670$$ 2.31595 7.78552i 0.0894729 0.300781i
$$671$$ 10.0971 0.389796
$$672$$ 12.2618i 0.473008i
$$673$$ 6.19541i 0.238815i −0.992845 0.119408i $$-0.961900\pi$$
0.992845 0.119408i $$-0.0380996\pi$$
$$674$$ −1.86410 −0.0718023
$$675$$ −12.9871 + 19.8977i −0.499873 + 0.765862i
$$676$$ −2.14786 −0.0826101
$$677$$ 26.5020i 1.01855i −0.860603 0.509276i $$-0.829913\pi$$
0.860603 0.509276i $$-0.170087\pi$$
$$678$$ 0.684016i 0.0262695i
$$679$$ −22.2880 −0.855334
$$680$$ −1.62201 + 5.45270i −0.0622012 + 0.209102i
$$681$$ 37.0303 1.41900
$$682$$ 0.968298i 0.0370780i
$$683$$ 44.3957i 1.69876i 0.527786 + 0.849378i $$0.323022\pi$$
−0.527786 + 0.849378i $$0.676978\pi$$
$$684$$ 0.833374 0.0318648
$$685$$ 29.7754 + 8.85724i 1.13766 + 0.338418i
$$686$$ 5.98588 0.228542
$$687$$ 29.1093i 1.11059i
$$688$$ 9.49480i 0.361986i
$$689$$ 17.2747 0.658113
$$690$$ 4.83091 + 1.43705i 0.183910 + 0.0547074i
$$691$$ −15.0873 −0.573948 −0.286974 0.957938i $$-0.592649\pi$$
−0.286974 + 0.957938i $$0.592649\pi$$
$$692$$ 13.6674i 0.519558i
$$693$$ 0.849687i 0.0322769i
$$694$$ −3.78623 −0.143723
$$695$$ 2.77440 9.32668i 0.105239 0.353781i
$$696$$ 4.77805 0.181112
$$697$$ 7.62664i 0.288880i
$$698$$ 5.12978i 0.194165i
$$699$$ 39.2672 1.48522
$$700$$ −10.1575 + 15.5625i −0.383919 + 0.588207i
$$701$$ 8.66946 0.327441 0.163720 0.986507i $$-0.447650\pi$$
0.163720 + 0.986507i $$0.447650\pi$$
$$702$$ 5.37869i 0.203005i
$$703$$ 5.64900i 0.213056i
$$704$$ −5.90485 −0.222548
$$705$$ 2.21846 7.45780i 0.0835522 0.280877i
$$706$$ 2.56535 0.0965481
$$707$$ 13.3636i 0.502590i
$$708$$ 10.9757i 0.412494i
$$709$$ −42.7639 −1.60603 −0.803015 0.595958i $$-0.796772\pi$$
−0.803015 + 0.595958i $$0.796772\pi$$
$$710$$ 4.14584 + 1.23326i 0.155590 + 0.0462833i
$$711$$ 4.71696 0.176900
$$712$$ 13.0859i 0.490415i
$$713$$ 12.9816i 0.486166i
$$714$$ 2.34850 0.0878904
$$715$$ 8.05502 + 2.39612i 0.301241 + 0.0896097i
$$716$$ 7.87049 0.294134
$$717$$ 0.795327i 0.0297020i
$$718$$ 1.93645i 0.0722677i
$$719$$ −27.6655 −1.03175 −0.515875 0.856664i $$-0.672533\pi$$
−0.515875 + 0.856664i $$0.672533\pi$$
$$720$$ −0.963972 + 3.24058i −0.0359251 + 0.120769i
$$721$$ −26.7197 −0.995093
$$722$$ 0.301154i 0.0112078i
$$723$$ 22.1818i 0.824950i
$$724$$ 33.4679 1.24383
$$725$$ −9.16673 5.98306i −0.340444 0.222205i
$$726$$ 0.558272 0.0207194
$$727$$ 20.9256i 0.776088i −0.921641 0.388044i $$-0.873151\pi$$
0.921641 0.388044i $$-0.126849\pi$$
$$728$$ 8.61344i 0.319235i
$$729$$ −22.0118 −0.815250
$$730$$ −2.06309 + 6.93547i −0.0763582 + 0.256693i
$$731$$ −5.92311 −0.219074
$$732$$ 35.7381i 1.32092i
$$733$$ 27.8171i 1.02745i 0.857956 + 0.513723i $$0.171734\pi$$
−0.857956 + 0.513723i $$0.828266\pi$$
$$734$$ −9.02359 −0.333067
$$735$$ −12.7554 3.79433i −0.470490 0.139956i
$$736$$ −13.7186 −0.505676
$$737$$ 12.0622i 0.444316i
$$738$$ 0.463913i 0.0170769i
$$739$$ −9.45503 −0.347809 −0.173904 0.984763i $$-0.555638\pi$$
−0.173904 + 0.984763i $$0.555638\pi$$
$$740$$ 23.1164 + 6.87641i 0.849776 + 0.252782i
$$741$$ 6.96707 0.255942
$$742$$ 2.69464i 0.0989232i
$$743$$ 5.01586i 0.184014i −0.995758 0.0920070i $$-0.970672\pi$$
0.995758 0.0920070i $$-0.0293282\pi$$
$$744$$ 7.01723 0.257264
$$745$$ 7.45403 25.0582i 0.273094 0.918061i
$$746$$ 10.4384 0.382175
$$747$$ 3.54679i 0.129770i
$$748$$ 4.12596i 0.150860i
$$749$$ −28.9169 −1.05660
$$750$$ −4.76021 + 4.03719i −0.173818 + 0.147417i
$$751$$ −42.5515 −1.55273 −0.776363 0.630286i $$-0.782938\pi$$
−0.776363 + 0.630286i $$0.782938\pi$$
$$752$$ 6.50229i 0.237114i
$$753$$ 13.2332i 0.482246i
$$754$$ 2.47792 0.0902406
$$755$$ −14.6917 + 49.3890i −0.534685 + 1.79745i
$$756$$ −17.6630 −0.642396
$$757$$ 6.77125i 0.246105i −0.992400 0.123053i $$-0.960732\pi$$
0.992400 0.123053i $$-0.0392684\pi$$
$$758$$ 0.548225i 0.0199124i
$$759$$ −7.48457 −0.271673
$$760$$ −2.52326 0.750591i −0.0915283 0.0272268i
$$761$$ 31.5134 1.14236 0.571180 0.820825i $$-0.306486\pi$$
0.571180 + 0.820825i $$0.306486\pi$$
$$762$$ 0.994739i 0.0360356i
$$763$$ 13.8937i 0.502986i
$$764$$ −52.5212 −1.90015
$$765$$ −2.02156 0.601352i −0.0730898 0.0217419i
$$766$$ −5.13025 −0.185364
$$767$$ 11.6545i 0.420821i
$$768$$ 17.1059i 0.617258i
$$769$$ −10.0557 −0.362617 −0.181308 0.983426i $$-0.558033\pi$$
−0.181308 + 0.983426i $$0.558033\pi$$
$$770$$ −0.373765 + 1.25648i −0.0134695 + 0.0452805i
$$771$$ 12.7312 0.458503
$$772$$ 25.1882i 0.906541i
$$773$$ 4.14250i 0.148995i 0.997221 + 0.0744977i $$0.0237353\pi$$
−0.997221 + 0.0744977i $$0.976265\pi$$
$$774$$ 0.360291 0.0129504
$$775$$ −13.4626 8.78694i −0.483591 0.315636i
$$776$$ 13.4792 0.483876
$$777$$ 20.3856i 0.731329i
$$778$$ 6.55849i 0.235133i
$$779$$ 3.52926 0.126449
$$780$$ −8.48087 + 28.5101i −0.303664 + 1.02083i
$$781$$ −6.42317