# Properties

 Label 405.2.b.a.244.4 Level $405$ Weight $2$ Character 405.244 Analytic conductor $3.234$ Analytic rank $0$ Dimension $4$ Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,2,Mod(244,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("405.244");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$405 = 3^{4} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 405.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: $$3.23394128186$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\sqrt{-3}, \sqrt{-11})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{4} - x^{3} - 2x^{2} - 3x + 9$$ x^4 - x^3 - 2*x^2 - 3*x + 9 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 244.4 Root $$-1.18614 - 1.26217i$$ of defining polynomial Character $$\chi$$ $$=$$ 405.244 Dual form 405.2.b.a.244.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+2.52434i q^{2} -4.37228 q^{4} +(-2.18614 - 0.469882i) q^{5} -3.46410i q^{7} -5.98844i q^{8} +O(q^{10})$$ $$q+2.52434i q^{2} -4.37228 q^{4} +(-2.18614 - 0.469882i) q^{5} -3.46410i q^{7} -5.98844i q^{8} +(1.18614 - 5.51856i) q^{10} +1.37228 q^{11} -4.10891i q^{13} +8.74456 q^{14} +6.37228 q^{16} +2.52434i q^{17} -5.37228 q^{19} +(9.55842 + 2.05446i) q^{20} +3.46410i q^{22} -5.04868i q^{23} +(4.55842 + 2.05446i) q^{25} +10.3723 q^{26} +15.1460i q^{28} -5.74456 q^{29} +0.627719 q^{31} +4.10891i q^{32} -6.37228 q^{34} +(-1.62772 + 7.57301i) q^{35} -7.57301i q^{37} -13.5615i q^{38} +(-2.81386 + 13.0916i) q^{40} -1.37228 q^{41} -3.46410i q^{43} -6.00000 q^{44} +12.7446 q^{46} -8.51278i q^{47} -5.00000 q^{49} +(-5.18614 + 11.5070i) q^{50} +17.9653i q^{52} +5.34363i q^{53} +(-3.00000 - 0.644810i) q^{55} -20.7446 q^{56} -14.5012i q^{58} -7.37228 q^{59} +3.62772 q^{61} +1.58457i q^{62} +2.37228 q^{64} +(-1.93070 + 8.98266i) q^{65} +8.21782i q^{67} -11.0371i q^{68} +(-19.1168 - 4.10891i) q^{70} -4.11684 q^{71} +7.57301i q^{73} +19.1168 q^{74} +23.4891 q^{76} -4.75372i q^{77} +4.74456 q^{79} +(-13.9307 - 2.99422i) q^{80} -3.46410i q^{82} +5.34363i q^{83} +(1.18614 - 5.51856i) q^{85} +8.74456 q^{86} -8.21782i q^{88} +3.00000 q^{89} -14.2337 q^{91} +22.0742i q^{92} +21.4891 q^{94} +(11.7446 + 2.52434i) q^{95} -18.6101i q^{97} -12.6217i q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 6 q^{4} - 3 q^{5}+O(q^{10})$$ 4 * q - 6 * q^4 - 3 * q^5 $$4 q - 6 q^{4} - 3 q^{5} - q^{10} - 6 q^{11} + 12 q^{14} + 14 q^{16} - 10 q^{19} + 21 q^{20} + q^{25} + 30 q^{26} + 14 q^{31} - 14 q^{34} - 18 q^{35} - 17 q^{40} + 6 q^{41} - 24 q^{44} + 28 q^{46} - 20 q^{49} - 15 q^{50} - 12 q^{55} - 60 q^{56} - 18 q^{59} + 26 q^{61} - 2 q^{64} + 21 q^{65} - 42 q^{70} + 18 q^{71} + 42 q^{74} + 48 q^{76} - 4 q^{79} - 27 q^{80} - q^{85} + 12 q^{86} + 12 q^{89} + 12 q^{91} + 40 q^{94} + 24 q^{95}+O(q^{100})$$ 4 * q - 6 * q^4 - 3 * q^5 - q^10 - 6 * q^11 + 12 * q^14 + 14 * q^16 - 10 * q^19 + 21 * q^20 + q^25 + 30 * q^26 + 14 * q^31 - 14 * q^34 - 18 * q^35 - 17 * q^40 + 6 * q^41 - 24 * q^44 + 28 * q^46 - 20 * q^49 - 15 * q^50 - 12 * q^55 - 60 * q^56 - 18 * q^59 + 26 * q^61 - 2 * q^64 + 21 * q^65 - 42 * q^70 + 18 * q^71 + 42 * q^74 + 48 * q^76 - 4 * q^79 - 27 * q^80 - q^85 + 12 * q^86 + 12 * q^89 + 12 * q^91 + 40 * q^94 + 24 * q^95

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$$.

 $$n$$ $$82$$ $$326$$ $$\chi(n)$$ $$-1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 2.52434i 1.78498i 0.451071 + 0.892488i $$0.351042\pi$$
−0.451071 + 0.892488i $$0.648958\pi$$
$$3$$ 0 0
$$4$$ −4.37228 −2.18614
$$5$$ −2.18614 0.469882i −0.977672 0.210138i
$$6$$ 0 0
$$7$$ 3.46410i 1.30931i −0.755929 0.654654i $$-0.772814\pi$$
0.755929 0.654654i $$-0.227186\pi$$
$$8$$ 5.98844i 2.11723i
$$9$$ 0 0
$$10$$ 1.18614 5.51856i 0.375091 1.74512i
$$11$$ 1.37228 0.413758 0.206879 0.978366i $$-0.433669\pi$$
0.206879 + 0.978366i $$0.433669\pi$$
$$12$$ 0 0
$$13$$ 4.10891i 1.13961i −0.821781 0.569804i $$-0.807019\pi$$
0.821781 0.569804i $$-0.192981\pi$$
$$14$$ 8.74456 2.33708
$$15$$ 0 0
$$16$$ 6.37228 1.59307
$$17$$ 2.52434i 0.612242i 0.951993 + 0.306121i $$0.0990312\pi$$
−0.951993 + 0.306121i $$0.900969\pi$$
$$18$$ 0 0
$$19$$ −5.37228 −1.23249 −0.616243 0.787556i $$-0.711346\pi$$
−0.616243 + 0.787556i $$0.711346\pi$$
$$20$$ 9.55842 + 2.05446i 2.13733 + 0.459390i
$$21$$ 0 0
$$22$$ 3.46410i 0.738549i
$$23$$ 5.04868i 1.05272i −0.850261 0.526361i $$-0.823556\pi$$
0.850261 0.526361i $$-0.176444\pi$$
$$24$$ 0 0
$$25$$ 4.55842 + 2.05446i 0.911684 + 0.410891i
$$26$$ 10.3723 2.03417
$$27$$ 0 0
$$28$$ 15.1460i 2.86233i
$$29$$ −5.74456 −1.06674 −0.533369 0.845883i $$-0.679074\pi$$
−0.533369 + 0.845883i $$0.679074\pi$$
$$30$$ 0 0
$$31$$ 0.627719 0.112742 0.0563708 0.998410i $$-0.482047\pi$$
0.0563708 + 0.998410i $$0.482047\pi$$
$$32$$ 4.10891i 0.726360i
$$33$$ 0 0
$$34$$ −6.37228 −1.09284
$$35$$ −1.62772 + 7.57301i −0.275135 + 1.28007i
$$36$$ 0 0
$$37$$ 7.57301i 1.24500i −0.782621 0.622498i $$-0.786118\pi$$
0.782621 0.622498i $$-0.213882\pi$$
$$38$$ 13.5615i 2.19996i
$$39$$ 0 0
$$40$$ −2.81386 + 13.0916i −0.444910 + 2.06996i
$$41$$ −1.37228 −0.214314 −0.107157 0.994242i $$-0.534175\pi$$
−0.107157 + 0.994242i $$0.534175\pi$$
$$42$$ 0 0
$$43$$ 3.46410i 0.528271i −0.964486 0.264135i $$-0.914913\pi$$
0.964486 0.264135i $$-0.0850865\pi$$
$$44$$ −6.00000 −0.904534
$$45$$ 0 0
$$46$$ 12.7446 1.87908
$$47$$ 8.51278i 1.24172i −0.783923 0.620858i $$-0.786784\pi$$
0.783923 0.620858i $$-0.213216\pi$$
$$48$$ 0 0
$$49$$ −5.00000 −0.714286
$$50$$ −5.18614 + 11.5070i −0.733431 + 1.62734i
$$51$$ 0 0
$$52$$ 17.9653i 2.49134i
$$53$$ 5.34363i 0.734004i 0.930220 + 0.367002i $$0.119616\pi$$
−0.930220 + 0.367002i $$0.880384\pi$$
$$54$$ 0 0
$$55$$ −3.00000 0.644810i −0.404520 0.0869462i
$$56$$ −20.7446 −2.77211
$$57$$ 0 0
$$58$$ 14.5012i 1.90410i
$$59$$ −7.37228 −0.959789 −0.479895 0.877326i $$-0.659325\pi$$
−0.479895 + 0.877326i $$0.659325\pi$$
$$60$$ 0 0
$$61$$ 3.62772 0.464482 0.232241 0.972658i $$-0.425394\pi$$
0.232241 + 0.972658i $$0.425394\pi$$
$$62$$ 1.58457i 0.201241i
$$63$$ 0 0
$$64$$ 2.37228 0.296535
$$65$$ −1.93070 + 8.98266i −0.239474 + 1.11416i
$$66$$ 0 0
$$67$$ 8.21782i 1.00397i 0.864877 + 0.501983i $$0.167396\pi$$
−0.864877 + 0.501983i $$0.832604\pi$$
$$68$$ 11.0371i 1.33845i
$$69$$ 0 0
$$70$$ −19.1168 4.10891i −2.28490 0.491109i
$$71$$ −4.11684 −0.488579 −0.244290 0.969702i $$-0.578555\pi$$
−0.244290 + 0.969702i $$0.578555\pi$$
$$72$$ 0 0
$$73$$ 7.57301i 0.886354i 0.896434 + 0.443177i $$0.146149\pi$$
−0.896434 + 0.443177i $$0.853851\pi$$
$$74$$ 19.1168 2.22229
$$75$$ 0 0
$$76$$ 23.4891 2.69439
$$77$$ 4.75372i 0.541737i
$$78$$ 0 0
$$79$$ 4.74456 0.533805 0.266903 0.963724i $$-0.414000\pi$$
0.266903 + 0.963724i $$0.414000\pi$$
$$80$$ −13.9307 2.99422i −1.55750 0.334764i
$$81$$ 0 0
$$82$$ 3.46410i 0.382546i
$$83$$ 5.34363i 0.586540i 0.956030 + 0.293270i $$0.0947434\pi$$
−0.956030 + 0.293270i $$0.905257\pi$$
$$84$$ 0 0
$$85$$ 1.18614 5.51856i 0.128655 0.598572i
$$86$$ 8.74456 0.942950
$$87$$ 0 0
$$88$$ 8.21782i 0.876023i
$$89$$ 3.00000 0.317999 0.159000 0.987279i $$-0.449173\pi$$
0.159000 + 0.987279i $$0.449173\pi$$
$$90$$ 0 0
$$91$$ −14.2337 −1.49210
$$92$$ 22.0742i 2.30140i
$$93$$ 0 0
$$94$$ 21.4891 2.21643
$$95$$ 11.7446 + 2.52434i 1.20497 + 0.258992i
$$96$$ 0 0
$$97$$ 18.6101i 1.88957i −0.327688 0.944786i $$-0.606269\pi$$
0.327688 0.944786i $$-0.393731\pi$$
$$98$$ 12.6217i 1.27498i
$$99$$ 0 0
$$100$$ −19.9307 8.98266i −1.99307 0.898266i
$$101$$ −10.6277 −1.05750 −0.528749 0.848778i $$-0.677339\pi$$
−0.528749 + 0.848778i $$0.677339\pi$$
$$102$$ 0 0
$$103$$ 6.92820i 0.682656i −0.939944 0.341328i $$-0.889123\pi$$
0.939944 0.341328i $$-0.110877\pi$$
$$104$$ −24.6060 −2.41281
$$105$$ 0 0
$$106$$ −13.4891 −1.31018
$$107$$ 13.2665i 1.28252i −0.767323 0.641260i $$-0.778412\pi$$
0.767323 0.641260i $$-0.221588\pi$$
$$108$$ 0 0
$$109$$ 1.74456 0.167099 0.0835494 0.996504i $$-0.473374\pi$$
0.0835494 + 0.996504i $$0.473374\pi$$
$$110$$ 1.62772 7.57301i 0.155197 0.722058i
$$111$$ 0 0
$$112$$ 22.0742i 2.08582i
$$113$$ 9.45254i 0.889220i 0.895724 + 0.444610i $$0.146658\pi$$
−0.895724 + 0.444610i $$0.853342\pi$$
$$114$$ 0 0
$$115$$ −2.37228 + 11.0371i −0.221216 + 1.02922i
$$116$$ 25.1168 2.33204
$$117$$ 0 0
$$118$$ 18.6101i 1.71320i
$$119$$ 8.74456 0.801613
$$120$$ 0 0
$$121$$ −9.11684 −0.828804
$$122$$ 9.15759i 0.829089i
$$123$$ 0 0
$$124$$ −2.74456 −0.246469
$$125$$ −9.00000 6.63325i −0.804984 0.593296i
$$126$$ 0 0
$$127$$ 10.3923i 0.922168i 0.887357 + 0.461084i $$0.152539\pi$$
−0.887357 + 0.461084i $$0.847461\pi$$
$$128$$ 14.2063i 1.25567i
$$129$$ 0 0
$$130$$ −22.6753 4.87375i −1.98875 0.427456i
$$131$$ −1.37228 −0.119897 −0.0599484 0.998201i $$-0.519094\pi$$
−0.0599484 + 0.998201i $$0.519094\pi$$
$$132$$ 0 0
$$133$$ 18.6101i 1.61370i
$$134$$ −20.7446 −1.79206
$$135$$ 0 0
$$136$$ 15.1168 1.29626
$$137$$ 2.22938i 0.190469i −0.995455 0.0952346i $$-0.969640\pi$$
0.995455 0.0952346i $$-0.0303601\pi$$
$$138$$ 0 0
$$139$$ 6.11684 0.518824 0.259412 0.965767i $$-0.416471\pi$$
0.259412 + 0.965767i $$0.416471\pi$$
$$140$$ 7.11684 33.1113i 0.601483 2.79842i
$$141$$ 0 0
$$142$$ 10.3923i 0.872103i
$$143$$ 5.63858i 0.471522i
$$144$$ 0 0
$$145$$ 12.5584 + 2.69927i 1.04292 + 0.224162i
$$146$$ −19.1168 −1.58212
$$147$$ 0 0
$$148$$ 33.1113i 2.72174i
$$149$$ −16.3723 −1.34127 −0.670635 0.741788i $$-0.733978\pi$$
−0.670635 + 0.741788i $$0.733978\pi$$
$$150$$ 0 0
$$151$$ 18.1168 1.47433 0.737164 0.675714i $$-0.236165\pi$$
0.737164 + 0.675714i $$0.236165\pi$$
$$152$$ 32.1716i 2.60946i
$$153$$ 0 0
$$154$$ 12.0000 0.966988
$$155$$ −1.37228 0.294954i −0.110224 0.0236912i
$$156$$ 0 0
$$157$$ 21.4294i 1.71025i 0.518419 + 0.855127i $$0.326521\pi$$
−0.518419 + 0.855127i $$0.673479\pi$$
$$158$$ 11.9769i 0.952829i
$$159$$ 0 0
$$160$$ 1.93070 8.98266i 0.152635 0.710142i
$$161$$ −17.4891 −1.37834
$$162$$ 0 0
$$163$$ 4.75372i 0.372340i −0.982518 0.186170i $$-0.940392\pi$$
0.982518 0.186170i $$-0.0596076\pi$$
$$164$$ 6.00000 0.468521
$$165$$ 0 0
$$166$$ −13.4891 −1.04696
$$167$$ 0.294954i 0.0228242i −0.999935 0.0114121i $$-0.996367\pi$$
0.999935 0.0114121i $$-0.00363266\pi$$
$$168$$ 0 0
$$169$$ −3.88316 −0.298704
$$170$$ 13.9307 + 2.99422i 1.06844 + 0.229646i
$$171$$ 0 0
$$172$$ 15.1460i 1.15487i
$$173$$ 7.86797i 0.598190i −0.954223 0.299095i $$-0.903315\pi$$
0.954223 0.299095i $$-0.0966848\pi$$
$$174$$ 0 0
$$175$$ 7.11684 15.7908i 0.537983 1.19368i
$$176$$ 8.74456 0.659146
$$177$$ 0 0
$$178$$ 7.57301i 0.567621i
$$179$$ 22.1168 1.65309 0.826545 0.562870i $$-0.190303\pi$$
0.826545 + 0.562870i $$0.190303\pi$$
$$180$$ 0 0
$$181$$ 14.8614 1.10464 0.552320 0.833632i $$-0.313743\pi$$
0.552320 + 0.833632i $$0.313743\pi$$
$$182$$ 35.9306i 2.66336i
$$183$$ 0 0
$$184$$ −30.2337 −2.22886
$$185$$ −3.55842 + 16.5557i −0.261620 + 1.21720i
$$186$$ 0 0
$$187$$ 3.46410i 0.253320i
$$188$$ 37.2203i 2.71457i
$$189$$ 0 0
$$190$$ −6.37228 + 29.6472i −0.462294 + 2.15084i
$$191$$ 13.3723 0.967584 0.483792 0.875183i $$-0.339259\pi$$
0.483792 + 0.875183i $$0.339259\pi$$
$$192$$ 0 0
$$193$$ 21.4294i 1.54252i 0.636518 + 0.771262i $$0.280374\pi$$
−0.636518 + 0.771262i $$0.719626\pi$$
$$194$$ 46.9783 3.37284
$$195$$ 0 0
$$196$$ 21.8614 1.56153
$$197$$ 23.0140i 1.63968i −0.572593 0.819840i $$-0.694063\pi$$
0.572593 0.819840i $$-0.305937\pi$$
$$198$$ 0 0
$$199$$ −16.0000 −1.13421 −0.567105 0.823646i $$-0.691937\pi$$
−0.567105 + 0.823646i $$0.691937\pi$$
$$200$$ 12.3030 27.2978i 0.869952 1.93025i
$$201$$ 0 0
$$202$$ 26.8280i 1.88761i
$$203$$ 19.8997i 1.39669i
$$204$$ 0 0
$$205$$ 3.00000 + 0.644810i 0.209529 + 0.0450355i
$$206$$ 17.4891 1.21853
$$207$$ 0 0
$$208$$ 26.1831i 1.81547i
$$209$$ −7.37228 −0.509951
$$210$$ 0 0
$$211$$ 26.8614 1.84922 0.924608 0.380921i $$-0.124393\pi$$
0.924608 + 0.380921i $$0.124393\pi$$
$$212$$ 23.3639i 1.60464i
$$213$$ 0 0
$$214$$ 33.4891 2.28927
$$215$$ −1.62772 + 7.57301i −0.111009 + 0.516475i
$$216$$ 0 0
$$217$$ 2.17448i 0.147613i
$$218$$ 4.40387i 0.298267i
$$219$$ 0 0
$$220$$ 13.1168 + 2.81929i 0.884337 + 0.190077i
$$221$$ 10.3723 0.697715
$$222$$ 0 0
$$223$$ 1.28962i 0.0863594i 0.999067 + 0.0431797i $$0.0137488\pi$$
−0.999067 + 0.0431797i $$0.986251\pi$$
$$224$$ 14.2337 0.951028
$$225$$ 0 0
$$226$$ −23.8614 −1.58724
$$227$$ 0.294954i 0.0195768i −0.999952 0.00978838i $$-0.996884\pi$$
0.999952 0.00978838i $$-0.00311579\pi$$
$$228$$ 0 0
$$229$$ −22.6060 −1.49384 −0.746922 0.664911i $$-0.768469\pi$$
−0.746922 + 0.664911i $$0.768469\pi$$
$$230$$ −27.8614 5.98844i −1.83713 0.394866i
$$231$$ 0 0
$$232$$ 34.4010i 2.25853i
$$233$$ 9.45254i 0.619257i 0.950858 + 0.309628i $$0.100205\pi$$
−0.950858 + 0.309628i $$0.899795\pi$$
$$234$$ 0 0
$$235$$ −4.00000 + 18.6101i −0.260931 + 1.21399i
$$236$$ 32.2337 2.09823
$$237$$ 0 0
$$238$$ 22.0742i 1.43086i
$$239$$ 22.9783 1.48634 0.743170 0.669103i $$-0.233321\pi$$
0.743170 + 0.669103i $$0.233321\pi$$
$$240$$ 0 0
$$241$$ −24.4891 −1.57748 −0.788742 0.614725i $$-0.789267\pi$$
−0.788742 + 0.614725i $$0.789267\pi$$
$$242$$ 23.0140i 1.47940i
$$243$$ 0 0
$$244$$ −15.8614 −1.01542
$$245$$ 10.9307 + 2.34941i 0.698337 + 0.150098i
$$246$$ 0 0
$$247$$ 22.0742i 1.40455i
$$248$$ 3.75906i 0.238700i
$$249$$ 0 0
$$250$$ 16.7446 22.7190i 1.05902 1.43688i
$$251$$ 14.2337 0.898422 0.449211 0.893426i $$-0.351705\pi$$
0.449211 + 0.893426i $$0.351705\pi$$
$$252$$ 0 0
$$253$$ 6.92820i 0.435572i
$$254$$ −26.2337 −1.64605
$$255$$ 0 0
$$256$$ −31.1168 −1.94480
$$257$$ 23.0140i 1.43557i −0.696263 0.717787i $$-0.745155\pi$$
0.696263 0.717787i $$-0.254845\pi$$
$$258$$ 0 0
$$259$$ −26.2337 −1.63008
$$260$$ 8.44158 39.2747i 0.523524 2.43571i
$$261$$ 0 0
$$262$$ 3.46410i 0.214013i
$$263$$ 26.5330i 1.63609i 0.575151 + 0.818047i $$0.304943\pi$$
−0.575151 + 0.818047i $$0.695057\pi$$
$$264$$ 0 0
$$265$$ 2.51087 11.6819i 0.154242 0.717615i
$$266$$ −46.9783 −2.88042
$$267$$ 0 0
$$268$$ 35.9306i 2.19481i
$$269$$ −5.23369 −0.319104 −0.159552 0.987190i $$-0.551005\pi$$
−0.159552 + 0.987190i $$0.551005\pi$$
$$270$$ 0 0
$$271$$ 16.7446 1.01716 0.508580 0.861015i $$-0.330171\pi$$
0.508580 + 0.861015i $$0.330171\pi$$
$$272$$ 16.0858i 0.975344i
$$273$$ 0 0
$$274$$ 5.62772 0.339983
$$275$$ 6.25544 + 2.81929i 0.377217 + 0.170010i
$$276$$ 0 0
$$277$$ 2.17448i 0.130652i 0.997864 + 0.0653260i $$0.0208087\pi$$
−0.997864 + 0.0653260i $$0.979191\pi$$
$$278$$ 15.4410i 0.926088i
$$279$$ 0 0
$$280$$ 45.3505 + 9.74749i 2.71021 + 0.582524i
$$281$$ 4.37228 0.260828 0.130414 0.991460i $$-0.458369\pi$$
0.130414 + 0.991460i $$0.458369\pi$$
$$282$$ 0 0
$$283$$ 27.7128i 1.64736i −0.567058 0.823678i $$-0.691918\pi$$
0.567058 0.823678i $$-0.308082\pi$$
$$284$$ 18.0000 1.06810
$$285$$ 0 0
$$286$$ 14.2337 0.841656
$$287$$ 4.75372i 0.280603i
$$288$$ 0 0
$$289$$ 10.6277 0.625160
$$290$$ −6.81386 + 31.7017i −0.400124 + 1.86159i
$$291$$ 0 0
$$292$$ 33.1113i 1.93769i
$$293$$ 2.52434i 0.147473i 0.997278 + 0.0737367i $$0.0234924\pi$$
−0.997278 + 0.0737367i $$0.976508\pi$$
$$294$$ 0 0
$$295$$ 16.1168 + 3.46410i 0.938359 + 0.201688i
$$296$$ −45.3505 −2.63595
$$297$$ 0 0
$$298$$ 41.3292i 2.39413i
$$299$$ −20.7446 −1.19969
$$300$$ 0 0
$$301$$ −12.0000 −0.691669
$$302$$ 45.7330i 2.63164i
$$303$$ 0 0
$$304$$ −34.2337 −1.96344
$$305$$ −7.93070 1.70460i −0.454111 0.0976051i
$$306$$ 0 0
$$307$$ 4.75372i 0.271309i −0.990756 0.135655i $$-0.956686\pi$$
0.990756 0.135655i $$-0.0433138\pi$$
$$308$$ 20.7846i 1.18431i
$$309$$ 0 0
$$310$$ 0.744563 3.46410i 0.0422883 0.196748i
$$311$$ 12.8614 0.729303 0.364652 0.931144i $$-0.381188\pi$$
0.364652 + 0.931144i $$0.381188\pi$$
$$312$$ 0 0
$$313$$ 5.39853i 0.305143i −0.988292 0.152572i $$-0.951245\pi$$
0.988292 0.152572i $$-0.0487554\pi$$
$$314$$ −54.0951 −3.05276
$$315$$ 0 0
$$316$$ −20.7446 −1.16697
$$317$$ 6.98311i 0.392210i −0.980583 0.196105i $$-0.937171\pi$$
0.980583 0.196105i $$-0.0628294\pi$$
$$318$$ 0 0
$$319$$ −7.88316 −0.441372
$$320$$ −5.18614 1.11469i −0.289914 0.0623132i
$$321$$ 0 0
$$322$$ 44.1485i 2.46030i
$$323$$ 13.5615i 0.754579i
$$324$$ 0 0
$$325$$ 8.44158 18.7302i 0.468254 1.03896i
$$326$$ 12.0000 0.664619
$$327$$ 0 0
$$328$$ 8.21782i 0.453753i
$$329$$ −29.4891 −1.62579
$$330$$ 0 0
$$331$$ −8.11684 −0.446142 −0.223071 0.974802i $$-0.571608\pi$$
−0.223071 + 0.974802i $$0.571608\pi$$
$$332$$ 23.3639i 1.28226i
$$333$$ 0 0
$$334$$ 0.744563 0.0407407
$$335$$ 3.86141 17.9653i 0.210971 0.981550i
$$336$$ 0 0
$$337$$ 6.92820i 0.377403i −0.982034 0.188702i $$-0.939572\pi$$
0.982034 0.188702i $$-0.0604279\pi$$
$$338$$ 9.80240i 0.533180i
$$339$$ 0 0
$$340$$ −5.18614 + 24.1287i −0.281258 + 1.30856i
$$341$$ 0.861407 0.0466478
$$342$$ 0 0
$$343$$ 6.92820i 0.374088i
$$344$$ −20.7446 −1.11847
$$345$$ 0 0
$$346$$ 19.8614 1.06776
$$347$$ 23.6588i 1.27007i −0.772483 0.635036i $$-0.780985\pi$$
0.772483 0.635036i $$-0.219015\pi$$
$$348$$ 0 0
$$349$$ −13.6060 −0.728311 −0.364155 0.931338i $$-0.618642\pi$$
−0.364155 + 0.931338i $$0.618642\pi$$
$$350$$ 39.8614 + 17.9653i 2.13068 + 0.960287i
$$351$$ 0 0
$$352$$ 5.63858i 0.300537i
$$353$$ 8.51278i 0.453089i −0.974001 0.226545i $$-0.927257\pi$$
0.974001 0.226545i $$-0.0727429\pi$$
$$354$$ 0 0
$$355$$ 9.00000 + 1.93443i 0.477670 + 0.102669i
$$356$$ −13.1168 −0.695191
$$357$$ 0 0
$$358$$ 55.8304i 2.95073i
$$359$$ 28.1168 1.48395 0.741975 0.670427i $$-0.233889\pi$$
0.741975 + 0.670427i $$0.233889\pi$$
$$360$$ 0 0
$$361$$ 9.86141 0.519021
$$362$$ 37.5152i 1.97176i
$$363$$ 0 0
$$364$$ 62.2337 3.26193
$$365$$ 3.55842 16.5557i 0.186256 0.866564i
$$366$$ 0 0
$$367$$ 23.3639i 1.21958i −0.792562 0.609792i $$-0.791253\pi$$
0.792562 0.609792i $$-0.208747\pi$$
$$368$$ 32.1716i 1.67706i
$$369$$ 0 0
$$370$$ −41.7921 8.98266i −2.17267 0.466986i
$$371$$ 18.5109 0.961037
$$372$$ 0 0
$$373$$ 11.6819i 0.604867i −0.953170 0.302434i $$-0.902201\pi$$
0.953170 0.302434i $$-0.0977990\pi$$
$$374$$ −8.74456 −0.452171
$$375$$ 0 0
$$376$$ −50.9783 −2.62900
$$377$$ 23.6039i 1.21566i
$$378$$ 0 0
$$379$$ −21.4891 −1.10382 −0.551911 0.833903i $$-0.686101\pi$$
−0.551911 + 0.833903i $$0.686101\pi$$
$$380$$ −51.3505 11.0371i −2.63423 0.566192i
$$381$$ 0 0
$$382$$ 33.7562i 1.72712i
$$383$$ 35.3407i 1.80583i −0.429822 0.902913i $$-0.641424\pi$$
0.429822 0.902913i $$-0.358576\pi$$
$$384$$ 0 0
$$385$$ −2.23369 + 10.3923i −0.113839 + 0.529641i
$$386$$ −54.0951 −2.75337
$$387$$ 0 0
$$388$$ 81.3687i 4.13087i
$$389$$ 23.4891 1.19095 0.595473 0.803375i $$-0.296965\pi$$
0.595473 + 0.803375i $$0.296965\pi$$
$$390$$ 0 0
$$391$$ 12.7446 0.644520
$$392$$ 29.9422i 1.51231i
$$393$$ 0 0
$$394$$ 58.0951 2.92679
$$395$$ −10.3723 2.22938i −0.521886 0.112172i
$$396$$ 0 0
$$397$$ 12.3267i 0.618661i 0.950955 + 0.309331i $$0.100105\pi$$
−0.950955 + 0.309331i $$0.899895\pi$$
$$398$$ 40.3894i 2.02454i
$$399$$ 0 0
$$400$$ 29.0475 + 13.0916i 1.45238 + 0.654579i
$$401$$ 19.6277 0.980161 0.490081 0.871677i $$-0.336967\pi$$
0.490081 + 0.871677i $$0.336967\pi$$
$$402$$ 0 0
$$403$$ 2.57924i 0.128481i
$$404$$ 46.4674 2.31184
$$405$$ 0 0
$$406$$ −50.2337 −2.49306
$$407$$ 10.3923i 0.515127i
$$408$$ 0 0
$$409$$ 5.86141 0.289828 0.144914 0.989444i $$-0.453709\pi$$
0.144914 + 0.989444i $$0.453709\pi$$
$$410$$ −1.62772 + 7.57301i −0.0803873 + 0.374004i
$$411$$ 0 0
$$412$$ 30.2921i 1.49238i
$$413$$ 25.5383i 1.25666i
$$414$$ 0 0
$$415$$ 2.51087 11.6819i 0.123254 0.573443i
$$416$$ 16.8832 0.827765
$$417$$ 0 0
$$418$$ 18.6101i 0.910251i
$$419$$ −5.48913 −0.268161 −0.134081 0.990970i $$-0.542808\pi$$
−0.134081 + 0.990970i $$0.542808\pi$$
$$420$$ 0 0
$$421$$ −10.2554 −0.499819 −0.249910 0.968269i $$-0.580401\pi$$
−0.249910 + 0.968269i $$0.580401\pi$$
$$422$$ 67.8073i 3.30081i
$$423$$ 0 0
$$424$$ 32.0000 1.55406
$$425$$ −5.18614 + 11.5070i −0.251565 + 0.558171i
$$426$$ 0 0
$$427$$ 12.5668i 0.608149i
$$428$$ 58.0049i 2.80377i
$$429$$ 0 0
$$430$$ −19.1168 4.10891i −0.921896 0.198149i
$$431$$ 18.3505 0.883914 0.441957 0.897036i $$-0.354284\pi$$
0.441957 + 0.897036i $$0.354284\pi$$
$$432$$ 0 0
$$433$$ 2.81929i 0.135487i −0.997703 0.0677433i $$-0.978420\pi$$
0.997703 0.0677433i $$-0.0215799\pi$$
$$434$$ 5.48913 0.263486
$$435$$ 0 0
$$436$$ −7.62772 −0.365301
$$437$$ 27.1229i 1.29746i
$$438$$ 0 0
$$439$$ −3.13859 −0.149797 −0.0748984 0.997191i $$-0.523863\pi$$
−0.0748984 + 0.997191i $$0.523863\pi$$
$$440$$ −3.86141 + 17.9653i −0.184085 + 0.856463i
$$441$$ 0 0
$$442$$ 26.1831i 1.24541i
$$443$$ 24.9484i 1.18534i −0.805447 0.592668i $$-0.798075\pi$$
0.805447 0.592668i $$-0.201925\pi$$
$$444$$ 0 0
$$445$$ −6.55842 1.40965i −0.310899 0.0668236i
$$446$$ −3.25544 −0.154149
$$447$$ 0 0
$$448$$ 8.21782i 0.388256i
$$449$$ 28.1168 1.32692 0.663458 0.748214i $$-0.269088\pi$$
0.663458 + 0.748214i $$0.269088\pi$$
$$450$$ 0 0
$$451$$ −1.88316 −0.0886744
$$452$$ 41.3292i 1.94396i
$$453$$ 0 0
$$454$$ 0.744563 0.0349441
$$455$$ 31.1168 + 6.68815i 1.45878 + 0.313545i
$$456$$ 0 0
$$457$$ 8.86263i 0.414577i 0.978280 + 0.207288i $$0.0664638\pi$$
−0.978280 + 0.207288i $$0.933536\pi$$
$$458$$ 57.0651i 2.66648i
$$459$$ 0 0
$$460$$ 10.3723 48.2574i 0.483610 2.25001i
$$461$$ −39.0951 −1.82084 −0.910420 0.413685i $$-0.864241\pi$$
−0.910420 + 0.413685i $$0.864241\pi$$
$$462$$ 0 0
$$463$$ 13.8564i 0.643962i 0.946746 + 0.321981i $$0.104349\pi$$
−0.946746 + 0.321981i $$0.895651\pi$$
$$464$$ −36.6060 −1.69939
$$465$$ 0 0
$$466$$ −23.8614 −1.10536
$$467$$ 14.8511i 0.687226i 0.939111 + 0.343613i $$0.111651\pi$$
−0.939111 + 0.343613i $$0.888349\pi$$
$$468$$ 0 0
$$469$$ 28.4674 1.31450
$$470$$ −46.9783 10.0974i −2.16695 0.465756i
$$471$$ 0 0
$$472$$ 44.1485i 2.03210i
$$473$$ 4.75372i 0.218576i
$$474$$ 0 0
$$475$$ −24.4891 11.0371i −1.12364 0.506418i
$$476$$ −38.2337 −1.75244
$$477$$ 0 0
$$478$$ 58.0049i 2.65308i
$$479$$ 21.6060 0.987202 0.493601 0.869688i $$-0.335680\pi$$
0.493601 + 0.869688i $$0.335680\pi$$
$$480$$ 0 0
$$481$$ −31.1168 −1.41881
$$482$$ 61.8188i 2.81577i
$$483$$ 0 0
$$484$$ 39.8614 1.81188
$$485$$ −8.74456 + 40.6844i −0.397070 + 1.84738i
$$486$$ 0 0
$$487$$ 30.2921i 1.37266i −0.727288 0.686332i $$-0.759220\pi$$
0.727288 0.686332i $$-0.240780\pi$$
$$488$$ 21.7244i 0.983416i
$$489$$ 0 0
$$490$$ −5.93070 + 27.5928i −0.267922 + 1.24652i
$$491$$ −37.3723 −1.68659 −0.843294 0.537453i $$-0.819387\pi$$
−0.843294 + 0.537453i $$0.819387\pi$$
$$492$$ 0 0
$$493$$ 14.5012i 0.653102i
$$494$$ −55.7228 −2.50709
$$495$$ 0 0
$$496$$ 4.00000 0.179605
$$497$$ 14.2612i 0.639701i
$$498$$ 0 0
$$499$$ 18.6277 0.833891 0.416946 0.908931i $$-0.363101\pi$$
0.416946 + 0.908931i $$0.363101\pi$$
$$500$$ 39.3505 + 29.0024i 1.75981 + 1.29703i
$$501$$ 0 0
$$502$$ 35.9306i 1.60366i
$$503$$ 10.0974i 0.450219i 0.974334 + 0.225109i $$0.0722739\pi$$
−0.974334 + 0.225109i $$0.927726\pi$$
$$504$$ 0 0
$$505$$ 23.2337 + 4.99377i 1.03389 + 0.222220i
$$506$$ 17.4891 0.777486
$$507$$ 0 0
$$508$$ 45.4381i 2.01599i
$$509$$ −23.4891 −1.04114 −0.520569 0.853820i $$-0.674280\pi$$
−0.520569 + 0.853820i $$0.674280\pi$$
$$510$$ 0 0
$$511$$ 26.2337 1.16051
$$512$$ 50.1369i 2.21576i
$$513$$ 0 0
$$514$$ 58.0951 2.56246
$$515$$ −3.25544 + 15.1460i −0.143452 + 0.667414i
$$516$$ 0 0
$$517$$ 11.6819i 0.513770i
$$518$$ 66.2227i 2.90966i
$$519$$ 0 0
$$520$$ 53.7921 + 11.5619i 2.35894 + 0.507023i
$$521$$ −18.0000 −0.788594 −0.394297 0.918983i $$-0.629012\pi$$
−0.394297 + 0.918983i $$0.629012\pi$$
$$522$$ 0 0
$$523$$ 15.1460i 0.662290i 0.943580 + 0.331145i $$0.107435\pi$$
−0.943580 + 0.331145i $$0.892565\pi$$
$$524$$ 6.00000 0.262111
$$525$$ 0 0
$$526$$ −66.9783 −2.92039
$$527$$ 1.58457i 0.0690251i
$$528$$ 0 0
$$529$$ −2.48913 −0.108223
$$530$$ 29.4891 + 6.33830i 1.28093 + 0.275318i
$$531$$ 0 0
$$532$$ 81.3687i 3.52778i
$$533$$ 5.63858i 0.244234i
$$534$$ 0 0
$$535$$ −6.23369 + 29.0024i −0.269506 + 1.25388i
$$536$$ 49.2119 2.12563
$$537$$ 0 0
$$538$$ 13.2116i 0.569592i
$$539$$ −6.86141 −0.295542
$$540$$ 0 0
$$541$$ −15.2337 −0.654947 −0.327474 0.944860i $$-0.606197\pi$$
−0.327474 + 0.944860i $$0.606197\pi$$
$$542$$ 42.2689i 1.81561i
$$543$$ 0 0
$$544$$ −10.3723 −0.444708
$$545$$ −3.81386 0.819738i −0.163368 0.0351137i
$$546$$ 0 0
$$547$$ 6.92820i 0.296229i 0.988970 + 0.148114i $$0.0473203\pi$$
−0.988970 + 0.148114i $$0.952680\pi$$
$$548$$ 9.74749i 0.416392i
$$549$$ 0 0
$$550$$ −7.11684 + 15.7908i −0.303463 + 0.673324i
$$551$$ 30.8614 1.31474
$$552$$ 0 0
$$553$$ 16.4356i 0.698915i
$$554$$ −5.48913 −0.233211
$$555$$ 0 0
$$556$$ −26.7446 −1.13422
$$557$$ 21.7244i 0.920491i −0.887792 0.460246i $$-0.847761\pi$$
0.887792 0.460246i $$-0.152239\pi$$
$$558$$ 0 0
$$559$$ −14.2337 −0.602021
$$560$$ −10.3723 + 48.2574i −0.438309 + 2.03925i
$$561$$ 0 0
$$562$$ 11.0371i 0.465573i
$$563$$ 0.994667i 0.0419202i 0.999780 + 0.0209601i $$0.00667230\pi$$
−0.999780 + 0.0209601i $$0.993328\pi$$
$$564$$ 0 0
$$565$$ 4.44158 20.6646i 0.186859 0.869366i
$$566$$ 69.9565 2.94049
$$567$$ 0 0
$$568$$ 24.6535i 1.03444i
$$569$$ 2.48913 0.104350 0.0521748 0.998638i $$-0.483385\pi$$
0.0521748 + 0.998638i $$0.483385\pi$$
$$570$$ 0 0
$$571$$ 32.8614 1.37521 0.687604 0.726086i $$-0.258663\pi$$
0.687604 + 0.726086i $$0.258663\pi$$
$$572$$ 24.6535i 1.03081i
$$573$$ 0 0
$$574$$ −12.0000 −0.500870
$$575$$ 10.3723 23.0140i 0.432554 0.959750i
$$576$$ 0 0
$$577$$ 28.3576i 1.18054i −0.807205 0.590272i $$-0.799021\pi$$
0.807205 0.590272i $$-0.200979\pi$$
$$578$$ 26.8280i 1.11590i
$$579$$ 0 0
$$580$$ −54.9090 11.8020i −2.27997 0.490049i
$$581$$ 18.5109 0.767960
$$582$$ 0 0
$$583$$ 7.33296i 0.303700i
$$584$$ 45.3505 1.87662
$$585$$ 0 0
$$586$$ −6.37228 −0.263237
$$587$$ 9.80240i 0.404588i −0.979325 0.202294i $$-0.935160\pi$$
0.979325 0.202294i $$-0.0648397\pi$$
$$588$$ 0 0
$$589$$ −3.37228 −0.138952
$$590$$ −8.74456 + 40.6844i −0.360008 + 1.67495i
$$591$$ 0 0
$$592$$ 48.2574i 1.98337i
$$593$$ 38.1600i 1.56704i −0.621364 0.783522i $$-0.713421\pi$$
0.621364 0.783522i $$-0.286579\pi$$
$$594$$ 0 0
$$595$$ −19.1168 4.10891i −0.783714 0.168449i
$$596$$ 71.5842 2.93220
$$597$$ 0 0
$$598$$ 52.3663i 2.14142i
$$599$$ −7.37228 −0.301223 −0.150612 0.988593i $$-0.548124\pi$$
−0.150612 + 0.988593i $$0.548124\pi$$
$$600$$ 0 0
$$601$$ 27.9783 1.14126 0.570628 0.821208i $$-0.306700\pi$$
0.570628 + 0.821208i $$0.306700\pi$$
$$602$$ 30.2921i 1.23461i
$$603$$ 0 0
$$604$$ −79.2119 −3.22309
$$605$$ 19.9307 + 4.28384i 0.810298 + 0.174163i
$$606$$ 0 0
$$607$$ 36.3354i 1.47481i −0.675452 0.737404i $$-0.736051\pi$$
0.675452 0.737404i $$-0.263949\pi$$
$$608$$ 22.0742i 0.895228i
$$609$$ 0 0
$$610$$ 4.30298 20.0198i 0.174223 0.810577i
$$611$$ −34.9783 −1.41507
$$612$$ 0 0
$$613$$ 9.50744i 0.384002i 0.981395 + 0.192001i $$0.0614977\pi$$
−0.981395 + 0.192001i $$0.938502\pi$$
$$614$$ 12.0000 0.484281
$$615$$ 0 0
$$616$$ −28.4674 −1.14698
$$617$$ 22.4241i 0.902760i 0.892332 + 0.451380i $$0.149068\pi$$
−0.892332 + 0.451380i $$0.850932\pi$$
$$618$$ 0 0
$$619$$ −4.00000 −0.160774 −0.0803868 0.996764i $$-0.525616\pi$$
−0.0803868 + 0.996764i $$0.525616\pi$$
$$620$$ 6.00000 + 1.28962i 0.240966 + 0.0517924i
$$621$$ 0 0
$$622$$ 32.4665i 1.30179i
$$623$$ 10.3923i 0.416359i
$$624$$ 0 0
$$625$$ 16.5584 + 18.7302i 0.662337 + 0.749206i
$$626$$ 13.6277 0.544673
$$627$$ 0 0
$$628$$ 93.6955i 3.73886i
$$629$$ 19.1168 0.762238
$$630$$ 0 0
$$631$$ 0.627719 0.0249891 0.0124945 0.999922i $$-0.496023\pi$$
0.0124945 + 0.999922i $$0.496023\pi$$
$$632$$ 28.4125i 1.13019i
$$633$$ 0 0
$$634$$ 17.6277 0.700086
$$635$$ 4.88316 22.7190i 0.193782 0.901578i
$$636$$ 0 0
$$637$$ 20.5446i 0.814005i
$$638$$ 19.8997i 0.787839i
$$639$$ 0 0
$$640$$ 6.67527 31.0569i 0.263863 1.22763i
$$641$$ −37.9783 −1.50005 −0.750025 0.661409i $$-0.769959\pi$$
−0.750025 + 0.661409i $$0.769959\pi$$
$$642$$ 0 0
$$643$$ 18.6101i 0.733912i 0.930238 + 0.366956i $$0.119600\pi$$
−0.930238 + 0.366956i $$0.880400\pi$$
$$644$$ 76.4674 3.01324
$$645$$ 0 0
$$646$$ 34.2337 1.34691
$$647$$ 4.45877i 0.175292i 0.996152 + 0.0876461i $$0.0279345\pi$$
−0.996152 + 0.0876461i $$0.972066\pi$$
$$648$$ 0 0
$$649$$ −10.1168 −0.397121
$$650$$ 47.2812 + 21.3094i 1.85452 + 0.835823i
$$651$$ 0 0
$$652$$ 20.7846i 0.813988i
$$653$$ 20.1947i 0.790280i −0.918621 0.395140i $$-0.870696\pi$$
0.918621 0.395140i $$-0.129304\pi$$
$$654$$ 0 0
$$655$$ 3.00000 + 0.644810i 0.117220 + 0.0251948i
$$656$$ −8.74456 −0.341418
$$657$$ 0 0
$$658$$ 74.4405i 2.90199i
$$659$$ −32.7446 −1.27555 −0.637774 0.770224i $$-0.720144\pi$$
−0.637774 + 0.770224i $$0.720144\pi$$
$$660$$ 0 0
$$661$$ 19.2337 0.748104 0.374052 0.927408i $$-0.377968\pi$$
0.374052 + 0.927408i $$0.377968\pi$$
$$662$$ 20.4897i 0.796353i
$$663$$ 0 0
$$664$$ 32.0000 1.24184
$$665$$ 8.74456 40.6844i 0.339100 1.57767i
$$666$$ 0 0
$$667$$ 29.0024i 1.12298i
$$668$$ 1.28962i 0.0498969i
$$669$$ 0 0
$$670$$ 45.3505 + 9.74749i 1.75204 + 0.376579i
$$671$$ 4.97825 0.192183
$$672$$ 0 0
$$673$$ 19.2549i 0.742223i 0.928588 + 0.371112i $$0.121023\pi$$
−0.928588 + 0.371112i $$0.878977\pi$$
$$674$$ 17.4891 0.673656
$$675$$ 0 0
$$676$$ 16.9783 0.653010
$$677$$ 26.5330i 1.01975i 0.860250 + 0.509873i $$0.170308\pi$$
−0.860250 + 0.509873i $$0.829692\pi$$
$$678$$ 0 0
$$679$$ −64.4674 −2.47403
$$680$$ −33.0475 7.10313i −1.26732 0.272393i
$$681$$ 0 0
$$682$$ 2.17448i 0.0832652i
$$683$$ 0.589907i 0.0225722i 0.999936 + 0.0112861i $$0.00359255\pi$$
−0.999936 + 0.0112861i $$0.996407\pi$$
$$684$$ 0 0
$$685$$ −1.04755 + 4.87375i −0.0400247 + 0.186216i
$$686$$ 17.4891 0.667738
$$687$$ 0 0
$$688$$ 22.0742i 0.841572i
$$689$$ 21.9565 0.836476
$$690$$ 0 0
$$691$$ −11.7228 −0.445957 −0.222978 0.974823i $$-0.571578\pi$$
−0.222978 + 0.974823i $$0.571578\pi$$
$$692$$ 34.4010i 1.30773i
$$693$$ 0 0
$$694$$ 59.7228 2.26705
$$695$$ −13.3723 2.87419i −0.507240 0.109024i
$$696$$ 0 0
$$697$$ 3.46410i 0.131212i
$$698$$ 34.3461i 1.30002i
$$699$$ 0 0
$$700$$ −31.1168 + 69.0420i −1.17611 + 2.60954i
$$701$$ −17.2337 −0.650907 −0.325454 0.945558i $$-0.605517\pi$$
−0.325454 + 0.945558i $$0.605517\pi$$
$$702$$ 0 0
$$703$$ 40.6844i 1.53444i
$$704$$ 3.25544 0.122694
$$705$$ 0 0
$$706$$ 21.4891 0.808754
$$707$$ 36.8155i 1.38459i
$$708$$ 0 0
$$709$$ −0.649468 −0.0243913 −0.0121956 0.999926i $$-0.503882\pi$$
−0.0121956 + 0.999926i $$0.503882\pi$$
$$710$$ −4.88316 + 22.7190i −0.183262 + 0.852630i
$$711$$ 0 0
$$712$$ 17.9653i 0.673279i
$$713$$ 3.16915i 0.118686i
$$714$$ 0 0
$$715$$ −2.64947 + 12.3267i −0.0990845 + 0.460994i
$$716$$ −96.7011 −3.61389
$$717$$ 0 0
$$718$$ 70.9764i 2.64882i
$$719$$ −28.1168 −1.04858 −0.524291 0.851539i $$-0.675669\pi$$
−0.524291 + 0.851539i $$0.675669\pi$$
$$720$$ 0 0
$$721$$ −24.0000 −0.893807
$$722$$ 24.8935i 0.926441i
$$723$$ 0 0
$$724$$ −64.9783 −2.41490
$$725$$ −26.1861 11.8020i −0.972529 0.438313i
$$726$$ 0 0
$$727$$ 10.7971i 0.400441i 0.979751 + 0.200220i $$0.0641658\pi$$
−0.979751 + 0.200220i $$0.935834\pi$$
$$728$$ 85.2376i 3.15911i
$$729$$ 0 0
$$730$$ 41.7921 + 8.98266i 1.54680 + 0.332463i
$$731$$ 8.74456 0.323429
$$732$$ 0 0
$$733$$ 23.3639i 0.862964i 0.902122 + 0.431482i $$0.142009\pi$$
−0.902122 + 0.431482i $$0.857991\pi$$
$$734$$ 58.9783 2.17693
$$735$$ 0 0
$$736$$ 20.7446 0.764655
$$737$$ 11.2772i 0.415400i
$$738$$ 0 0
$$739$$ −11.3723 −0.418336 −0.209168 0.977880i $$-0.567076\pi$$
−0.209168 + 0.977880i $$0.567076\pi$$
$$740$$ 15.5584 72.3861i 0.571939 2.66096i
$$741$$ 0 0
$$742$$ 46.7277i 1.71543i
$$743$$ 42.5639i 1.56152i 0.624833 + 0.780759i $$0.285167\pi$$
−0.624833 + 0.780759i $$0.714833\pi$$
$$744$$ 0 0
$$745$$ 35.7921 + 7.69304i 1.31132 + 0.281851i
$$746$$ 29.4891 1.07967
$$747$$ 0 0
$$748$$ 15.1460i 0.553794i
$$749$$ −45.9565 −1.67921
$$750$$ 0 0
$$751$$ −35.7228 −1.30354 −0.651772 0.758415i $$-0.725974\pi$$
−0.651772 + 0.758415i $$0.725974\pi$$
$$752$$ 54.2458i 1.97814i
$$753$$ 0 0
$$754$$ −59.5842 −2.16993
$$755$$ −39.6060 8.51278i −1.44141 0.309812i
$$756$$ 0 0
$$757$$ 41.5692i 1.51086i 0.655230 + 0.755429i $$0.272572\pi$$
−0.655230 + 0.755429i $$0.727428\pi$$
$$758$$ 54.2458i 1.97030i
$$759$$ 0 0
$$760$$ 15.1168 70.3316i 0.548346 2.55120i
$$761$$ 9.51087 0.344769 0.172384 0.985030i $$-0.444853\pi$$
0.172384 + 0.985030i $$0.444853\pi$$
$$762$$ 0 0
$$763$$ 6.04334i 0.218784i
$$764$$ −58.4674 −2.11528
$$765$$ 0 0
$$766$$ 89.2119 3.22336
$$767$$ 30.2921i 1.09378i
$$768$$ 0 0
$$769$$ −6.48913 −0.234004 −0.117002 0.993132i $$-0.537328\pi$$
−0.117002 + 0.993132i $$0.537328\pi$$
$$770$$ −26.2337 5.63858i −0.945396 0.203200i
$$771$$ 0 0
$$772$$ 93.6955i 3.37217i
$$773$$ 18.2603i 0.656776i −0.944543 0.328388i $$-0.893495\pi$$
0.944543 0.328388i $$-0.106505\pi$$
$$774$$ 0 0
$$775$$ 2.86141 + 1.28962i 0.102785 + 0.0463245i
$$776$$ −111.446 −4.00066
$$777$$ 0 0
$$778$$ 59.2945i 2.12581i
$$779$$ 7.37228 0.264139
$$780$$ 0 0
$$781$$ −5.64947 −0.202154
$$782$$ 32.1716i 1.15045i
$$783$$ 0 0
$$784$$ −31.8614 −1.13791
$$785$$ 10.0693 46.8477i 0.359389 1.67207i
$$786$$ 0 0
$$787$$ 17.3205i 0.617409i −0.951158 0.308705i $$-0.900105\pi$$
0.951158 0.308705i $$-0.0998955\pi$$
$$788$$ 100.624i 3.58457i
$$789$$ 0 0
$$790$$ 5.62772 26.1831i 0.200225