Properties

 Label 405.2.j.d.379.2 Level $405$ Weight $2$ Character 405.379 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(109,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("405.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$405 = 3^{4} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 405.j (of order $$6$$, degree $$2$$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

 Self dual: no Analytic conductor: $$3.23394128186$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ 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: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

 Embedding label 379.2 Root $$-1.18614 - 1.26217i$$ of defining polynomial Character $$\chi$$ $$=$$ 405.379 Dual form 405.2.j.d.109.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(2.18614 + 1.26217i) q^{2} +(2.18614 + 3.78651i) q^{4} +(-0.686141 - 2.12819i) q^{5} +(3.00000 + 1.73205i) q^{7} +5.98844i q^{8} +O(q^{10})$$ $$q+(2.18614 + 1.26217i) q^{2} +(2.18614 + 3.78651i) q^{4} +(-0.686141 - 2.12819i) q^{5} +(3.00000 + 1.73205i) q^{7} +5.98844i q^{8} +(1.18614 - 5.51856i) q^{10} +(0.686141 - 1.18843i) q^{11} +(-3.55842 + 2.05446i) q^{13} +(4.37228 + 7.57301i) q^{14} +(-3.18614 + 5.51856i) q^{16} -2.52434i q^{17} -5.37228 q^{19} +(6.55842 - 7.25061i) q^{20} +(3.00000 - 1.73205i) q^{22} +(4.37228 - 2.52434i) q^{23} +(-4.05842 + 2.92048i) q^{25} -10.3723 q^{26} +15.1460i q^{28} +(-2.87228 + 4.97494i) q^{29} +(-0.313859 - 0.543620i) q^{31} +(-3.55842 + 2.05446i) q^{32} +(3.18614 - 5.51856i) q^{34} +(1.62772 - 7.57301i) q^{35} -7.57301i q^{37} +(-11.7446 - 6.78073i) q^{38} +(12.7446 - 4.10891i) q^{40} +(-0.686141 - 1.18843i) q^{41} +(3.00000 + 1.73205i) q^{43} +6.00000 q^{44} +12.7446 q^{46} +(-7.37228 - 4.25639i) q^{47} +(2.50000 + 4.33013i) q^{49} +(-12.5584 + 1.26217i) q^{50} +(-15.5584 - 8.98266i) q^{52} -5.34363i q^{53} +(-3.00000 - 0.644810i) q^{55} +(-10.3723 + 17.9653i) q^{56} +(-12.5584 + 7.25061i) q^{58} +(-3.68614 - 6.38458i) q^{59} +(-1.81386 + 3.14170i) q^{61} -1.58457i q^{62} +2.37228 q^{64} +(6.81386 + 6.16337i) q^{65} +(7.11684 - 4.10891i) q^{67} +(9.55842 - 5.51856i) q^{68} +(13.1168 - 14.5012i) q^{70} +4.11684 q^{71} +7.57301i q^{73} +(9.55842 - 16.5557i) q^{74} +(-11.7446 - 20.3422i) q^{76} +(4.11684 - 2.37686i) q^{77} +(-2.37228 + 4.10891i) q^{79} +(13.9307 + 2.99422i) q^{80} -3.46410i q^{82} +(4.62772 + 2.67181i) q^{83} +(-5.37228 + 1.73205i) q^{85} +(4.37228 + 7.57301i) q^{86} +(7.11684 + 4.10891i) q^{88} -3.00000 q^{89} -14.2337 q^{91} +(19.1168 + 11.0371i) q^{92} +(-10.7446 - 18.6101i) q^{94} +(3.68614 + 11.4333i) q^{95} +(16.1168 + 9.30506i) q^{97} +12.6217i q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 3 q^{2} + 3 q^{4} + 3 q^{5} + 12 q^{7}+O(q^{10})$$ 4 * q + 3 * q^2 + 3 * q^4 + 3 * q^5 + 12 * q^7 $$4 q + 3 q^{2} + 3 q^{4} + 3 q^{5} + 12 q^{7} - q^{10} - 3 q^{11} + 3 q^{13} + 6 q^{14} - 7 q^{16} - 10 q^{19} + 9 q^{20} + 12 q^{22} + 6 q^{23} + q^{25} - 30 q^{26} - 7 q^{31} + 3 q^{32} + 7 q^{34} + 18 q^{35} - 24 q^{38} + 28 q^{40} + 3 q^{41} + 12 q^{43} + 24 q^{44} + 28 q^{46} - 18 q^{47} + 10 q^{49} - 33 q^{50} - 45 q^{52} - 12 q^{55} - 30 q^{56} - 33 q^{58} - 9 q^{59} - 13 q^{61} - 2 q^{64} + 33 q^{65} - 6 q^{67} + 21 q^{68} + 18 q^{70} - 18 q^{71} + 21 q^{74} - 24 q^{76} - 18 q^{77} + 2 q^{79} + 27 q^{80} + 30 q^{83} - 10 q^{85} + 6 q^{86} - 6 q^{88} - 12 q^{89} + 12 q^{91} + 42 q^{92} - 20 q^{94} + 9 q^{95} + 30 q^{97}+O(q^{100})$$ 4 * q + 3 * q^2 + 3 * q^4 + 3 * q^5 + 12 * q^7 - q^10 - 3 * q^11 + 3 * q^13 + 6 * q^14 - 7 * q^16 - 10 * q^19 + 9 * q^20 + 12 * q^22 + 6 * q^23 + q^25 - 30 * q^26 - 7 * q^31 + 3 * q^32 + 7 * q^34 + 18 * q^35 - 24 * q^38 + 28 * q^40 + 3 * q^41 + 12 * q^43 + 24 * q^44 + 28 * q^46 - 18 * q^47 + 10 * q^49 - 33 * q^50 - 45 * q^52 - 12 * q^55 - 30 * q^56 - 33 * q^58 - 9 * q^59 - 13 * q^61 - 2 * q^64 + 33 * q^65 - 6 * q^67 + 21 * q^68 + 18 * q^70 - 18 * q^71 + 21 * q^74 - 24 * q^76 - 18 * q^77 + 2 * q^79 + 27 * q^80 + 30 * q^83 - 10 * q^85 + 6 * q^86 - 6 * q^88 - 12 * q^89 + 12 * q^91 + 42 * q^92 - 20 * q^94 + 9 * q^95 + 30 * q^97

Character values

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

 $$n$$ $$82$$ $$326$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$

Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 2.18614 + 1.26217i 1.54583 + 0.892488i 0.998453 + 0.0556054i $$0.0177089\pi$$
0.547382 + 0.836883i $$0.315624\pi$$
$$3$$ 0 0
$$4$$ 2.18614 + 3.78651i 1.09307 + 1.89325i
$$5$$ −0.686141 2.12819i −0.306851 0.951757i
$$6$$ 0 0
$$7$$ 3.00000 + 1.73205i 1.13389 + 0.654654i 0.944911 0.327327i $$-0.106148\pi$$
0.188982 + 0.981981i $$0.439481\pi$$
$$8$$ 5.98844i 2.11723i
$$9$$ 0 0
$$10$$ 1.18614 5.51856i 0.375091 1.74512i
$$11$$ 0.686141 1.18843i 0.206879 0.358325i −0.743851 0.668346i $$-0.767003\pi$$
0.950730 + 0.310021i $$0.100336\pi$$
$$12$$ 0 0
$$13$$ −3.55842 + 2.05446i −0.986929 + 0.569804i −0.904355 0.426781i $$-0.859647\pi$$
−0.0825739 + 0.996585i $$0.526314\pi$$
$$14$$ 4.37228 + 7.57301i 1.16854 + 2.02397i
$$15$$ 0 0
$$16$$ −3.18614 + 5.51856i −0.796535 + 1.37964i
$$17$$ 2.52434i 0.612242i −0.951993 0.306121i $$-0.900969\pi$$
0.951993 0.306121i $$-0.0990312\pi$$
$$18$$ 0 0
$$19$$ −5.37228 −1.23249 −0.616243 0.787556i $$-0.711346\pi$$
−0.616243 + 0.787556i $$0.711346\pi$$
$$20$$ 6.55842 7.25061i 1.46651 1.62129i
$$21$$ 0 0
$$22$$ 3.00000 1.73205i 0.639602 0.369274i
$$23$$ 4.37228 2.52434i 0.911684 0.526361i 0.0307112 0.999528i $$-0.490223\pi$$
0.880972 + 0.473167i $$0.156889\pi$$
$$24$$ 0 0
$$25$$ −4.05842 + 2.92048i −0.811684 + 0.584096i
$$26$$ −10.3723 −2.03417
$$27$$ 0 0
$$28$$ 15.1460i 2.86233i
$$29$$ −2.87228 + 4.97494i −0.533369 + 0.923823i 0.465871 + 0.884853i $$0.345741\pi$$
−0.999240 + 0.0389701i $$0.987592\pi$$
$$30$$ 0 0
$$31$$ −0.313859 0.543620i −0.0563708 0.0976371i 0.836463 0.548023i $$-0.184620\pi$$
−0.892834 + 0.450386i $$0.851286\pi$$
$$32$$ −3.55842 + 2.05446i −0.629046 + 0.363180i
$$33$$ 0 0
$$34$$ 3.18614 5.51856i 0.546419 0.946425i
$$35$$ 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 $$-0.213882\pi$$
$$38$$ −11.7446 6.78073i −1.90522 1.09998i
$$39$$ 0 0
$$40$$ 12.7446 4.10891i 2.01509 0.649676i
$$41$$ −0.686141 1.18843i −0.107157 0.185602i 0.807460 0.589922i $$-0.200841\pi$$
−0.914617 + 0.404320i $$0.867508\pi$$
$$42$$ 0 0
$$43$$ 3.00000 + 1.73205i 0.457496 + 0.264135i 0.710991 0.703201i $$-0.248247\pi$$
−0.253495 + 0.967337i $$0.581580\pi$$
$$44$$ 6.00000 0.904534
$$45$$ 0 0
$$46$$ 12.7446 1.87908
$$47$$ −7.37228 4.25639i −1.07536 0.620858i −0.145717 0.989326i $$-0.546549\pi$$
−0.929640 + 0.368468i $$0.879882\pi$$
$$48$$ 0 0
$$49$$ 2.50000 + 4.33013i 0.357143 + 0.618590i
$$50$$ −12.5584 + 1.26217i −1.77603 + 0.178498i
$$51$$ 0 0
$$52$$ −15.5584 8.98266i −2.15756 1.24567i
$$53$$ 5.34363i 0.734004i −0.930220 0.367002i $$-0.880384\pi$$
0.930220 0.367002i $$-0.119616\pi$$
$$54$$ 0 0
$$55$$ −3.00000 0.644810i −0.404520 0.0869462i
$$56$$ −10.3723 + 17.9653i −1.38605 + 2.40072i
$$57$$ 0 0
$$58$$ −12.5584 + 7.25061i −1.64900 + 0.952052i
$$59$$ −3.68614 6.38458i −0.479895 0.831202i 0.519839 0.854264i $$-0.325992\pi$$
−0.999734 + 0.0230621i $$0.992658\pi$$
$$60$$ 0 0
$$61$$ −1.81386 + 3.14170i −0.232241 + 0.402253i −0.958467 0.285203i $$-0.907939\pi$$
0.726226 + 0.687456i $$0.241272\pi$$
$$62$$ 1.58457i 0.201241i
$$63$$ 0 0
$$64$$ 2.37228 0.296535
$$65$$ 6.81386 + 6.16337i 0.845155 + 0.764472i
$$66$$ 0 0
$$67$$ 7.11684 4.10891i 0.869461 0.501983i 0.00229183 0.999997i $$-0.499270\pi$$
0.867169 + 0.498014i $$0.165937\pi$$
$$68$$ 9.55842 5.51856i 1.15913 0.669223i
$$69$$ 0 0
$$70$$ 13.1168 14.5012i 1.56776 1.73323i
$$71$$ 4.11684 0.488579 0.244290 0.969702i $$-0.421445\pi$$
0.244290 + 0.969702i $$0.421445\pi$$
$$72$$ 0 0
$$73$$ 7.57301i 0.886354i 0.896434 + 0.443177i $$0.146149\pi$$
−0.896434 + 0.443177i $$0.853851\pi$$
$$74$$ 9.55842 16.5557i 1.11114 1.92456i
$$75$$ 0 0
$$76$$ −11.7446 20.3422i −1.34719 2.33341i
$$77$$ 4.11684 2.37686i 0.469158 0.270868i
$$78$$ 0 0
$$79$$ −2.37228 + 4.10891i −0.266903 + 0.462289i −0.968060 0.250717i $$-0.919334\pi$$
0.701158 + 0.713006i $$0.252667\pi$$
$$80$$ 13.9307 + 2.99422i 1.55750 + 0.334764i
$$81$$ 0 0
$$82$$ 3.46410i 0.382546i
$$83$$ 4.62772 + 2.67181i 0.507958 + 0.293270i 0.731994 0.681311i $$-0.238590\pi$$
−0.224036 + 0.974581i $$0.571923\pi$$
$$84$$ 0 0
$$85$$ −5.37228 + 1.73205i −0.582706 + 0.187867i
$$86$$ 4.37228 + 7.57301i 0.471475 + 0.816619i
$$87$$ 0 0
$$88$$ 7.11684 + 4.10891i 0.758658 + 0.438011i
$$89$$ −3.00000 −0.317999 −0.159000 0.987279i $$-0.550827\pi$$
−0.159000 + 0.987279i $$0.550827\pi$$
$$90$$ 0 0
$$91$$ −14.2337 −1.49210
$$92$$ 19.1168 + 11.0371i 1.99307 + 1.15070i
$$93$$ 0 0
$$94$$ −10.7446 18.6101i −1.10822 1.91949i
$$95$$ 3.68614 + 11.4333i 0.378190 + 1.17303i
$$96$$ 0 0
$$97$$ 16.1168 + 9.30506i 1.63642 + 0.944786i 0.982053 + 0.188607i $$0.0603973\pi$$
0.654365 + 0.756179i $$0.272936\pi$$
$$98$$ 12.6217i 1.27498i
$$99$$ 0 0
$$100$$ −19.9307 8.98266i −1.99307 0.898266i
$$101$$ −5.31386 + 9.20387i −0.528749 + 0.915820i 0.470689 + 0.882299i $$0.344005\pi$$
−0.999438 + 0.0335207i $$0.989328\pi$$
$$102$$ 0 0
$$103$$ −6.00000 + 3.46410i −0.591198 + 0.341328i −0.765571 0.643352i $$-0.777543\pi$$
0.174373 + 0.984680i $$0.444210\pi$$
$$104$$ −12.3030 21.3094i −1.20641 2.08956i
$$105$$ 0 0
$$106$$ 6.74456 11.6819i 0.655090 1.13465i
$$107$$ 13.2665i 1.28252i 0.767323 + 0.641260i $$0.221588\pi$$
−0.767323 + 0.641260i $$0.778412\pi$$
$$108$$ 0 0
$$109$$ 1.74456 0.167099 0.0835494 0.996504i $$-0.473374\pi$$
0.0835494 + 0.996504i $$0.473374\pi$$
$$110$$ −5.74456 5.19615i −0.547723 0.495434i
$$111$$ 0 0
$$112$$ −19.1168 + 11.0371i −1.80637 + 1.04291i
$$113$$ −8.18614 + 4.72627i −0.770087 + 0.444610i −0.832906 0.553415i $$-0.813324\pi$$
0.0628184 + 0.998025i $$0.479991\pi$$
$$114$$ 0 0
$$115$$ −8.37228 7.57301i −0.780719 0.706187i
$$116$$ −25.1168 −2.33204
$$117$$ 0 0
$$118$$ 18.6101i 1.71320i
$$119$$ 4.37228 7.57301i 0.400806 0.694217i
$$120$$ 0 0
$$121$$ 4.55842 + 7.89542i 0.414402 + 0.717765i
$$122$$ −7.93070 + 4.57879i −0.718012 + 0.414545i
$$123$$ 0 0
$$124$$ 1.37228 2.37686i 0.123235 0.213448i
$$125$$ 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 $$0.847461\pi$$
$$128$$ 12.3030 + 7.10313i 1.08744 + 0.627834i
$$129$$ 0 0
$$130$$ 7.11684 + 22.0742i 0.624189 + 1.93604i
$$131$$ −0.686141 1.18843i −0.0599484 0.103834i 0.834494 0.551018i $$-0.185760\pi$$
−0.894442 + 0.447184i $$0.852427\pi$$
$$132$$ 0 0
$$133$$ −16.1168 9.30506i −1.39751 0.806851i
$$134$$ 20.7446 1.79206
$$135$$ 0 0
$$136$$ 15.1168 1.29626
$$137$$ −1.93070 1.11469i −0.164951 0.0952346i 0.415252 0.909706i $$-0.363693\pi$$
−0.580203 + 0.814472i $$0.697027\pi$$
$$138$$ 0 0
$$139$$ −3.05842 5.29734i −0.259412 0.449315i 0.706673 0.707541i $$-0.250195\pi$$
−0.966085 + 0.258226i $$0.916862\pi$$
$$140$$ 32.2337 10.3923i 2.72424 0.878310i
$$141$$ 0 0
$$142$$ 9.00000 + 5.19615i 0.755263 + 0.436051i
$$143$$ 5.63858i 0.471522i
$$144$$ 0 0
$$145$$ 12.5584 + 2.69927i 1.04292 + 0.224162i
$$146$$ −9.55842 + 16.5557i −0.791061 + 1.37016i
$$147$$ 0 0
$$148$$ 28.6753 16.5557i 2.35709 1.36087i
$$149$$ −8.18614 14.1788i −0.670635 1.16157i −0.977724 0.209893i $$-0.932688\pi$$
0.307090 0.951681i $$-0.400645\pi$$
$$150$$ 0 0
$$151$$ −9.05842 + 15.6896i −0.737164 + 1.27681i 0.216603 + 0.976260i $$0.430502\pi$$
−0.953767 + 0.300546i $$0.902831\pi$$
$$152$$ 32.1716i 2.60946i
$$153$$ 0 0
$$154$$ 12.0000 0.966988
$$155$$ −0.941578 + 1.04095i −0.0756294 + 0.0836114i
$$156$$ 0 0
$$157$$ 18.5584 10.7147i 1.48112 0.855127i 0.481352 0.876527i $$-0.340146\pi$$
0.999771 + 0.0214003i $$0.00681243\pi$$
$$158$$ −10.3723 + 5.98844i −0.825174 + 0.476415i
$$159$$ 0 0
$$160$$ 6.81386 + 6.16337i 0.538683 + 0.487257i
$$161$$ 17.4891 1.37834
$$162$$ 0 0
$$163$$ 4.75372i 0.372340i −0.982518 0.186170i $$-0.940392\pi$$
0.982518 0.186170i $$-0.0596076\pi$$
$$164$$ 3.00000 5.19615i 0.234261 0.405751i
$$165$$ 0 0
$$166$$ 6.74456 + 11.6819i 0.523480 + 0.906693i
$$167$$ 0.255437 0.147477i 0.0197663 0.0114121i −0.490084 0.871675i $$-0.663034\pi$$
0.509851 + 0.860263i $$0.329701\pi$$
$$168$$ 0 0
$$169$$ 1.94158 3.36291i 0.149352 0.258686i
$$170$$ −13.9307 2.99422i −1.06844 0.229646i
$$171$$ 0 0
$$172$$ 15.1460i 1.15487i
$$173$$ −6.81386 3.93398i −0.518048 0.299095i 0.218088 0.975929i $$-0.430018\pi$$
−0.736136 + 0.676834i $$0.763351\pi$$
$$174$$ 0 0
$$175$$ −17.2337 + 1.73205i −1.30274 + 0.130931i
$$176$$ 4.37228 + 7.57301i 0.329573 + 0.570837i
$$177$$ 0 0
$$178$$ −6.55842 3.78651i −0.491575 0.283811i
$$179$$ −22.1168 −1.65309 −0.826545 0.562870i $$-0.809697\pi$$
−0.826545 + 0.562870i $$0.809697\pi$$
$$180$$ 0 0
$$181$$ 14.8614 1.10464 0.552320 0.833632i $$-0.313743\pi$$
0.552320 + 0.833632i $$0.313743\pi$$
$$182$$ −31.1168 17.9653i −2.30653 1.33168i
$$183$$ 0 0
$$184$$ 15.1168 + 26.1831i 1.11443 + 1.93025i
$$185$$ −16.1168 + 5.19615i −1.18493 + 0.382029i
$$186$$ 0 0
$$187$$ −3.00000 1.73205i −0.219382 0.126660i
$$188$$ 37.2203i 2.71457i
$$189$$ 0 0
$$190$$ −6.37228 + 29.6472i −0.462294 + 2.15084i
$$191$$ 6.68614 11.5807i 0.483792 0.837953i −0.516035 0.856568i $$-0.672592\pi$$
0.999827 + 0.0186152i $$0.00592573\pi$$
$$192$$ 0 0
$$193$$ 18.5584 10.7147i 1.33586 0.771262i 0.349673 0.936872i $$-0.386293\pi$$
0.986191 + 0.165610i $$0.0529593\pi$$
$$194$$ 23.4891 + 40.6844i 1.68642 + 2.92097i
$$195$$ 0 0
$$196$$ −10.9307 + 18.9325i −0.780765 + 1.35232i
$$197$$ 23.0140i 1.63968i 0.572593 + 0.819840i $$0.305937\pi$$
−0.572593 + 0.819840i $$0.694063\pi$$
$$198$$ 0 0
$$199$$ −16.0000 −1.13421 −0.567105 0.823646i $$-0.691937\pi$$
−0.567105 + 0.823646i $$0.691937\pi$$
$$200$$ −17.4891 24.3036i −1.23667 1.71853i
$$201$$ 0 0
$$202$$ −23.2337 + 13.4140i −1.63472 + 0.943804i
$$203$$ −17.2337 + 9.94987i −1.20957 + 0.698344i
$$204$$ 0 0
$$205$$ −2.05842 + 2.27567i −0.143766 + 0.158940i
$$206$$ −17.4891 −1.21853
$$207$$ 0 0
$$208$$ 26.1831i 1.81547i
$$209$$ −3.68614 + 6.38458i −0.254976 + 0.441631i
$$210$$ 0 0
$$211$$ −13.4307 23.2627i −0.924608 1.60147i −0.792191 0.610273i $$-0.791060\pi$$
−0.132417 0.991194i $$-0.542274\pi$$
$$212$$ 20.2337 11.6819i 1.38966 0.802318i
$$213$$ 0 0
$$214$$ −16.7446 + 29.0024i −1.14463 + 1.98257i
$$215$$ 1.62772 7.57301i 0.111009 0.516475i
$$216$$ 0 0
$$217$$ 2.17448i 0.147613i
$$218$$ 3.81386 + 2.20193i 0.258307 + 0.149134i
$$219$$ 0 0
$$220$$ −4.11684 12.7692i −0.277558 0.860897i
$$221$$ 5.18614 + 8.98266i 0.348858 + 0.604239i
$$222$$ 0 0
$$223$$ −1.11684 0.644810i −0.0747894 0.0431797i 0.462139 0.886808i $$-0.347082\pi$$
−0.536928 + 0.843628i $$0.680415\pi$$
$$224$$ −14.2337 −0.951028
$$225$$ 0 0
$$226$$ −23.8614 −1.58724
$$227$$ −0.255437 0.147477i −0.0169540 0.00978838i 0.491499 0.870878i $$-0.336449\pi$$
−0.508453 + 0.861090i $$0.669782\pi$$
$$228$$ 0 0
$$229$$ 11.3030 + 19.5773i 0.746922 + 1.29371i 0.949291 + 0.314398i $$0.101803\pi$$
−0.202369 + 0.979309i $$0.564864\pi$$
$$230$$ −8.74456 27.1229i −0.576599 1.78843i
$$231$$ 0 0
$$232$$ −29.7921 17.2005i −1.95595 1.12927i
$$233$$ 9.45254i 0.619257i −0.950858 0.309628i $$-0.899795\pi$$
0.950858 0.309628i $$-0.100205\pi$$
$$234$$ 0 0
$$235$$ −4.00000 + 18.6101i −0.260931 + 1.21399i
$$236$$ 16.1168 27.9152i 1.04912 1.81712i
$$237$$ 0 0
$$238$$ 19.1168 11.0371i 1.23916 0.715430i
$$239$$ 11.4891 + 19.8997i 0.743170 + 1.28721i 0.951045 + 0.309052i $$0.100012\pi$$
−0.207875 + 0.978155i $$0.566655\pi$$
$$240$$ 0 0
$$241$$ 12.2446 21.2082i 0.788742 1.36614i −0.137997 0.990433i $$-0.544066\pi$$
0.926738 0.375708i $$-0.122600\pi$$
$$242$$ 23.0140i 1.47940i
$$243$$ 0 0
$$244$$ −15.8614 −1.01542
$$245$$ 7.50000 8.29156i 0.479157 0.529728i
$$246$$ 0 0
$$247$$ 19.1168 11.0371i 1.21638 0.702275i
$$248$$ 3.25544 1.87953i 0.206720 0.119350i
$$249$$ 0 0
$$250$$ 11.3030 + 25.8607i 0.714864 + 1.63558i
$$251$$ −14.2337 −0.898422 −0.449211 0.893426i $$-0.648295\pi$$
−0.449211 + 0.893426i $$0.648295\pi$$
$$252$$ 0 0
$$253$$ 6.92820i 0.435572i
$$254$$ −13.1168 + 22.7190i −0.823024 + 1.42552i
$$255$$ 0 0
$$256$$ 15.5584 + 26.9480i 0.972401 + 1.68425i
$$257$$ 19.9307 11.5070i 1.24324 0.717787i 0.273490 0.961875i $$-0.411822\pi$$
0.969753 + 0.244088i $$0.0784886\pi$$
$$258$$ 0 0
$$259$$ 13.1168 22.7190i 0.815041 1.41169i
$$260$$ −8.44158 + 39.2747i −0.523524 + 2.43571i
$$261$$ 0 0
$$262$$ 3.46410i 0.214013i
$$263$$ 22.9783 + 13.2665i 1.41690 + 0.818047i 0.996025 0.0890715i $$-0.0283900\pi$$
0.420874 + 0.907119i $$0.361723\pi$$
$$264$$ 0 0
$$265$$ −11.3723 + 3.66648i −0.698594 + 0.225230i
$$266$$ −23.4891 40.6844i −1.44021 2.49452i
$$267$$ 0 0
$$268$$ 31.1168 + 17.9653i 1.90076 + 1.09741i
$$269$$ 5.23369 0.319104 0.159552 0.987190i $$-0.448995\pi$$
0.159552 + 0.987190i $$0.448995\pi$$
$$270$$ 0 0
$$271$$ 16.7446 1.01716 0.508580 0.861015i $$-0.330171\pi$$
0.508580 + 0.861015i $$0.330171\pi$$
$$272$$ 13.9307 + 8.04290i 0.844673 + 0.487672i
$$273$$ 0 0
$$274$$ −2.81386 4.87375i −0.169991 0.294434i
$$275$$ 0.686141 + 6.82701i 0.0413758 + 0.411684i
$$276$$ 0 0
$$277$$ −1.88316 1.08724i −0.113148 0.0653260i 0.442358 0.896839i $$-0.354142\pi$$
−0.555506 + 0.831513i $$0.687475\pi$$
$$278$$ 15.4410i 0.926088i
$$279$$ 0 0
$$280$$ 45.3505 + 9.74749i 2.71021 + 0.582524i
$$281$$ 2.18614 3.78651i 0.130414 0.225884i −0.793422 0.608672i $$-0.791703\pi$$
0.923836 + 0.382788i $$0.125036\pi$$
$$282$$ 0 0
$$283$$ −24.0000 + 13.8564i −1.42665 + 0.823678i −0.996855 0.0792477i $$-0.974748\pi$$
−0.429797 + 0.902926i $$0.641415\pi$$
$$284$$ 9.00000 + 15.5885i 0.534052 + 0.925005i
$$285$$ 0 0
$$286$$ −7.11684 + 12.3267i −0.420828 + 0.728895i
$$287$$ 4.75372i 0.280603i
$$288$$ 0 0
$$289$$ 10.6277 0.625160
$$290$$ 24.0475 + 21.7518i 1.41212 + 1.27731i
$$291$$ 0 0
$$292$$ −28.6753 + 16.5557i −1.67809 + 0.968847i
$$293$$ −2.18614 + 1.26217i −0.127716 + 0.0737367i −0.562497 0.826800i $$-0.690159\pi$$
0.434781 + 0.900536i $$0.356826\pi$$
$$294$$ 0 0
$$295$$ −11.0584 + 12.2255i −0.643846 + 0.711799i
$$296$$ 45.3505 2.63595
$$297$$ 0 0
$$298$$ 41.3292i 2.39413i
$$299$$ −10.3723 + 17.9653i −0.599845 + 1.03896i
$$300$$ 0 0
$$301$$ 6.00000 + 10.3923i 0.345834 + 0.599002i
$$302$$ −39.6060 + 22.8665i −2.27907 + 1.31582i
$$303$$ 0 0
$$304$$ 17.1168 29.6472i 0.981718 1.70039i
$$305$$ 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 $$-0.0433138\pi$$
$$308$$ 18.0000 + 10.3923i 1.02565 + 0.592157i
$$309$$ 0 0
$$310$$ −3.37228 + 1.08724i −0.191533 + 0.0617511i
$$311$$ 6.43070 + 11.1383i 0.364652 + 0.631595i 0.988720 0.149774i $$-0.0478547\pi$$
−0.624068 + 0.781370i $$0.714521\pi$$
$$312$$ 0 0
$$313$$ 4.67527 + 2.69927i 0.264262 + 0.152572i 0.626277 0.779601i $$-0.284578\pi$$
−0.362015 + 0.932172i $$0.617911\pi$$
$$314$$ 54.0951 3.05276
$$315$$ 0 0
$$316$$ −20.7446 −1.16697
$$317$$ −6.04755 3.49155i −0.339664 0.196105i 0.320459 0.947262i $$-0.396163\pi$$
−0.660123 + 0.751157i $$0.729496\pi$$
$$318$$ 0 0
$$319$$ 3.94158 + 6.82701i 0.220686 + 0.382239i
$$320$$ −1.62772 5.04868i −0.0909922 0.282230i
$$321$$ 0 0
$$322$$ 38.2337 + 22.0742i 2.13068 + 1.23015i
$$323$$ 13.5615i 0.754579i
$$324$$ 0 0
$$325$$ 8.44158 18.7302i 0.468254 1.03896i
$$326$$ 6.00000 10.3923i 0.332309 0.575577i
$$327$$ 0 0
$$328$$ 7.11684 4.10891i 0.392962 0.226877i
$$329$$ −14.7446 25.5383i −0.812894 1.40797i
$$330$$ 0 0
$$331$$ 4.05842 7.02939i 0.223071 0.386370i −0.732668 0.680586i $$-0.761725\pi$$
0.955739 + 0.294216i $$0.0950585\pi$$
$$332$$ 23.3639i 1.28226i
$$333$$ 0 0
$$334$$ 0.744563 0.0407407
$$335$$ −13.6277 12.3267i −0.744562 0.673481i
$$336$$ 0 0
$$337$$ −6.00000 + 3.46410i −0.326841 + 0.188702i −0.654438 0.756116i $$-0.727095\pi$$
0.327597 + 0.944818i $$0.393761\pi$$
$$338$$ 8.48913 4.90120i 0.461748 0.266590i
$$339$$ 0 0
$$340$$ −18.3030 16.5557i −0.992619 0.897857i
$$341$$ −0.861407 −0.0466478
$$342$$ 0 0
$$343$$ 6.92820i 0.374088i
$$344$$ −10.3723 + 17.9653i −0.559236 + 0.968625i
$$345$$ 0 0
$$346$$ −9.93070 17.2005i −0.533878 0.924704i
$$347$$ 20.4891 11.8294i 1.09991 0.635036i 0.163715 0.986508i $$-0.447652\pi$$
0.936198 + 0.351472i $$0.114319\pi$$
$$348$$ 0 0
$$349$$ 6.80298 11.7831i 0.364155 0.630736i −0.624485 0.781037i $$-0.714691\pi$$
0.988640 + 0.150301i $$0.0480244\pi$$
$$350$$ −39.8614 17.9653i −2.13068 0.960287i
$$351$$ 0 0
$$352$$ 5.63858i 0.300537i
$$353$$ −7.37228 4.25639i −0.392387 0.226545i 0.290807 0.956782i $$-0.406076\pi$$
−0.683194 + 0.730237i $$0.739410\pi$$
$$354$$ 0 0
$$355$$ −2.82473 8.76144i −0.149921 0.465009i
$$356$$ −6.55842 11.3595i −0.347596 0.602053i
$$357$$ 0 0
$$358$$ −48.3505 27.9152i −2.55541 1.47536i
$$359$$ −28.1168 −1.48395 −0.741975 0.670427i $$-0.766111\pi$$
−0.741975 + 0.670427i $$0.766111\pi$$
$$360$$ 0 0
$$361$$ 9.86141 0.519021
$$362$$ 32.4891 + 18.7576i 1.70759 + 0.985878i
$$363$$ 0 0
$$364$$ −31.1168 53.8960i −1.63097 2.82492i
$$365$$ 16.1168 5.19615i 0.843594 0.271979i
$$366$$ 0 0
$$367$$ 20.2337 + 11.6819i 1.05619 + 0.609792i 0.924376 0.381483i $$-0.124586\pi$$
0.131814 + 0.991274i $$0.457920\pi$$
$$368$$ 32.1716i 1.67706i
$$369$$ 0 0
$$370$$ −41.7921 8.98266i −2.17267 0.466986i
$$371$$ 9.25544 16.0309i 0.480518 0.832282i
$$372$$ 0 0
$$373$$ −10.1168 + 5.84096i −0.523830 + 0.302434i −0.738500 0.674253i $$-0.764466\pi$$
0.214670 + 0.976687i $$0.431132\pi$$
$$374$$ −4.37228 7.57301i −0.226085 0.391591i
$$375$$ 0 0
$$376$$ 25.4891 44.1485i 1.31450 2.27678i
$$377$$ 23.6039i 1.21566i
$$378$$ 0 0
$$379$$ −21.4891 −1.10382 −0.551911 0.833903i $$-0.686101\pi$$
−0.551911 + 0.833903i $$0.686101\pi$$
$$380$$ −35.2337 + 38.9523i −1.80745 + 1.99821i
$$381$$ 0 0
$$382$$ 29.2337 16.8781i 1.49573 0.863558i
$$383$$ 30.6060 17.6704i 1.56389 0.902913i 0.567035 0.823694i $$-0.308090\pi$$
0.996857 0.0792196i $$-0.0252428\pi$$
$$384$$ 0 0
$$385$$ −7.88316 7.13058i −0.401763 0.363408i
$$386$$ 54.0951 2.75337
$$387$$ 0 0
$$388$$ 81.3687i 4.13087i
$$389$$ 11.7446 20.3422i 0.595473 1.03139i −0.398007 0.917382i $$-0.630298\pi$$
0.993480 0.114007i $$-0.0363686\pi$$
$$390$$ 0 0
$$391$$ −6.37228 11.0371i −0.322260 0.558171i
$$392$$ −25.9307 + 14.9711i −1.30970 + 0.756155i
$$393$$ 0 0
$$394$$ −29.0475 + 50.3118i −1.46339 + 2.53467i
$$395$$ 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 $$0.899895\pi$$
$$398$$ −34.9783 20.1947i −1.75330 1.01227i
$$399$$ 0 0
$$400$$ −3.18614 31.7017i −0.159307 1.58508i
$$401$$ 9.81386 + 16.9981i 0.490081 + 0.848845i 0.999935 0.0114161i $$-0.00363395\pi$$
−0.509854 + 0.860261i $$0.670301\pi$$
$$402$$ 0 0
$$403$$ 2.23369 + 1.28962i 0.111268 + 0.0642406i
$$404$$ −46.4674 −2.31184
$$405$$ 0 0
$$406$$ −50.2337 −2.49306
$$407$$ −9.00000 5.19615i −0.446113 0.257564i
$$408$$ 0 0
$$409$$ −2.93070 5.07613i −0.144914 0.250998i 0.784427 0.620221i $$-0.212957\pi$$
−0.929341 + 0.369223i $$0.879624\pi$$
$$410$$ −7.37228 + 2.37686i −0.364091 + 0.117385i
$$411$$ 0 0
$$412$$ −26.2337 15.1460i −1.29244 0.746191i
$$413$$ 25.5383i 1.25666i
$$414$$ 0 0
$$415$$ 2.51087 11.6819i 0.123254 0.573443i
$$416$$ 8.44158 14.6212i 0.413882 0.716865i
$$417$$ 0 0
$$418$$ −16.1168 + 9.30506i −0.788301 + 0.455126i
$$419$$ −2.74456 4.75372i −0.134081 0.232235i 0.791165 0.611602i $$-0.209475\pi$$
−0.925246 + 0.379368i $$0.876141\pi$$
$$420$$ 0 0
$$421$$ 5.12772 8.88147i 0.249910 0.432856i −0.713591 0.700563i $$-0.752932\pi$$
0.963501 + 0.267706i $$0.0862657\pi$$
$$422$$ 67.8073i 3.30081i
$$423$$ 0 0
$$424$$ 32.0000 1.55406
$$425$$ 7.37228 + 10.2448i 0.357608 + 0.496947i
$$426$$ 0 0
$$427$$ −10.8832 + 6.28339i −0.526673 + 0.304075i
$$428$$ −50.2337 + 29.0024i −2.42814 + 1.40189i
$$429$$ 0 0
$$430$$ 13.1168 14.5012i 0.632550 0.699311i
$$431$$ −18.3505 −0.883914 −0.441957 0.897036i $$-0.645716\pi$$
−0.441957 + 0.897036i $$0.645716\pi$$
$$432$$ 0 0
$$433$$ 2.81929i 0.135487i −0.997703 0.0677433i $$-0.978420\pi$$
0.997703 0.0677433i $$-0.0215799\pi$$
$$434$$ 2.74456 4.75372i 0.131743 0.228186i
$$435$$ 0 0
$$436$$ 3.81386 + 6.60580i 0.182651 + 0.316360i
$$437$$ −23.4891 + 13.5615i −1.12364 + 0.648732i
$$438$$ 0 0
$$439$$ 1.56930 2.71810i 0.0748984 0.129728i −0.826144 0.563460i $$-0.809470\pi$$
0.901042 + 0.433732i $$0.142803\pi$$
$$440$$ 3.86141 17.9653i 0.184085 0.856463i
$$441$$ 0 0
$$442$$ 26.1831i 1.24541i
$$443$$ −21.6060 12.4742i −1.02653 0.592668i −0.110542 0.993871i $$-0.535259\pi$$
−0.915989 + 0.401204i $$0.868592\pi$$
$$444$$ 0 0
$$445$$ 2.05842 + 6.38458i 0.0975786 + 0.302658i
$$446$$ −1.62772 2.81929i −0.0770747 0.133497i
$$447$$ 0 0
$$448$$ 7.11684 + 4.10891i 0.336239 + 0.194128i
$$449$$ −28.1168 −1.32692 −0.663458 0.748214i $$-0.730912\pi$$
−0.663458 + 0.748214i $$0.730912\pi$$
$$450$$ 0 0
$$451$$ −1.88316 −0.0886744
$$452$$ −35.7921 20.6646i −1.68352 0.971980i
$$453$$ 0 0
$$454$$ −0.372281 0.644810i −0.0174720 0.0302624i
$$455$$ 9.76631 + 30.2921i 0.457852 + 1.42011i
$$456$$ 0 0
$$457$$ −7.67527 4.43132i −0.359034 0.207288i 0.309623 0.950859i $$-0.399797\pi$$
−0.668657 + 0.743571i $$0.733130\pi$$
$$458$$ 57.0651i 2.66648i
$$459$$ 0 0
$$460$$ 10.3723 48.2574i 0.483610 2.25001i
$$461$$ −19.5475 + 33.8573i −0.910420 + 1.57689i −0.0969482 + 0.995289i $$0.530908\pi$$
−0.813472 + 0.581604i $$0.802425\pi$$
$$462$$ 0 0
$$463$$ 12.0000 6.92820i 0.557687 0.321981i −0.194529 0.980897i $$-0.562318\pi$$
0.752217 + 0.658916i $$0.228985\pi$$
$$464$$ −18.3030 31.7017i −0.849695 1.47171i
$$465$$ 0 0
$$466$$ 11.9307 20.6646i 0.552679 0.957268i
$$467$$ 14.8511i 0.687226i −0.939111 0.343613i $$-0.888349\pi$$
0.939111 0.343613i $$-0.111651\pi$$
$$468$$ 0 0
$$469$$ 28.4674 1.31450
$$470$$ −32.2337 + 35.6357i −1.48683 + 1.64375i
$$471$$ 0 0
$$472$$ 38.2337 22.0742i 1.75985 1.01605i
$$473$$ 4.11684 2.37686i 0.189293 0.109288i
$$474$$ 0 0
$$475$$ 21.8030 15.6896i 1.00039 0.719890i
$$476$$ 38.2337 1.75244
$$477$$ 0 0
$$478$$ 58.0049i 2.65308i
$$479$$ 10.8030 18.7113i 0.493601 0.854942i −0.506372 0.862315i $$-0.669014\pi$$
0.999973 + 0.00737327i $$0.00234701\pi$$
$$480$$ 0 0
$$481$$ 15.5584 + 26.9480i 0.709403 + 1.22872i
$$482$$ 53.5367 30.9094i 2.43853 1.40789i
$$483$$ 0 0
$$484$$ −19.9307 + 34.5210i −0.905941 + 1.56914i
$$485$$ 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 $$-0.240780\pi$$
$$488$$ −18.8139 10.8622i −0.851663 0.491708i
$$489$$ 0 0
$$490$$ 26.8614 8.66025i 1.21347 0.391230i
$$491$$ −18.6861 32.3653i −0.843294 1.46063i −0.887095 0.461587i $$-0.847280\pi$$
0.0438011 0.999040i $$-0.486053\pi$$
$$492$$ 0 0
$$493$$ 12.5584 + 7.25061i 0.565603 + 0.326551i
$$494$$ 55.7228 2.50709
$$495$$ 0 0
$$496$$ 4.00000 0.179605
$$497$$ 12.3505 + 7.13058i 0.553997 + 0.319850i
$$498$$ 0 0
$$499$$ −9.31386 16.1321i −0.416946 0.722171i 0.578685 0.815551i $$-0.303566\pi$$
−0.995631 + 0.0933802i $$0.970233\pi$$
$$500$$ −5.44158 + 48.5798i −0.243355 + 2.17255i
$$501$$ 0 0
$$502$$ −31.1168 17.9653i −1.38881 0.801831i
$$503$$ 10.0974i 0.450219i −0.974334 0.225109i $$-0.927726\pi$$
0.974334 0.225109i $$-0.0722739\pi$$
$$504$$ 0 0
$$505$$ 23.2337 + 4.99377i 1.03389 + 0.222220i
$$506$$ 8.74456 15.1460i 0.388743 0.673323i
$$507$$ 0 0
$$508$$ −39.3505 + 22.7190i −1.74590 + 1.00799i
$$509$$ −11.7446 20.3422i −0.520569 0.901651i −0.999714 0.0239157i $$-0.992387\pi$$
0.479145 0.877736i $$-0.340947\pi$$
$$510$$ 0 0
$$511$$ −13.1168 + 22.7190i −0.580255 + 1.00503i
$$512$$ 50.1369i 2.21576i
$$513$$ 0 0
$$514$$ 58.0951 2.56246
$$515$$ 11.4891 + 10.3923i 0.506271 + 0.457940i
$$516$$ 0 0
$$517$$ −10.1168 + 5.84096i −0.444938 + 0.256885i
$$518$$ 57.3505 33.1113i 2.51984 1.45483i
$$519$$ 0 0
$$520$$ −36.9090 + 40.8044i −1.61856 + 1.78939i
$$521$$ 18.0000 0.788594 0.394297 0.918983i $$-0.370988\pi$$
0.394297 + 0.918983i $$0.370988\pi$$
$$522$$ 0 0
$$523$$ 15.1460i 0.662290i 0.943580 + 0.331145i $$0.107435\pi$$
−0.943580 + 0.331145i $$0.892565\pi$$
$$524$$ 3.00000 5.19615i 0.131056 0.226995i
$$525$$ 0 0
$$526$$ 33.4891 + 58.0049i 1.46020 + 2.52913i
$$527$$ −1.37228 + 0.792287i −0.0597775 + 0.0345126i
$$528$$ 0 0
$$529$$ 1.24456 2.15565i 0.0541114 0.0937237i
$$530$$ −29.4891 6.33830i −1.28093 0.275318i
$$531$$ 0 0
$$532$$ 81.3687i 3.52778i
$$533$$ 4.88316 + 2.81929i 0.211513 + 0.122117i
$$534$$ 0 0
$$535$$ 28.2337 9.10268i 1.22065 0.393543i
$$536$$ 24.6060 + 42.6188i 1.06282 + 1.84085i
$$537$$ 0 0
$$538$$ 11.4416 + 6.60580i 0.493281 + 0.284796i
$$539$$ 6.86141 0.295542
$$540$$ 0 0
$$541$$ −15.2337 −0.654947 −0.327474 0.944860i $$-0.606197\pi$$
−0.327474 + 0.944860i $$0.606197\pi$$
$$542$$ 36.6060 + 21.1345i 1.57236 + 0.907803i
$$543$$ 0 0
$$544$$ 5.18614 + 8.98266i 0.222354 + 0.385128i
$$545$$ −1.19702 3.71277i −0.0512745 0.159038i
$$546$$ 0 0
$$547$$ −6.00000 3.46410i −0.256541 0.148114i 0.366214 0.930531i $$-0.380654\pi$$
−0.622756 + 0.782416i $$0.713987\pi$$
$$548$$ 9.74749i 0.416392i
$$549$$ 0 0
$$550$$ −7.11684 + 15.7908i −0.303463 + 0.673324i
$$551$$ 15.4307 26.7268i 0.657370 1.13860i
$$552$$ 0 0
$$553$$ −14.2337 + 8.21782i −0.605278 + 0.349457i
$$554$$ −2.74456 4.75372i −0.116605 0.201966i
$$555$$ 0 0
$$556$$ 13.3723 23.1615i 0.567111 0.982265i
$$557$$ 21.7244i 0.920491i 0.887792 + 0.460246i $$0.152239\pi$$
−0.887792 + 0.460246i $$0.847761\pi$$
$$558$$ 0 0
$$559$$ −14.2337 −0.602021
$$560$$ 36.6060 + 33.1113i 1.54688 + 1.39921i
$$561$$ 0 0
$$562$$ 9.55842 5.51856i 0.403198 0.232786i
$$563$$ −0.861407 + 0.497333i −0.0363040 + 0.0209601i −0.518042 0.855355i $$-0.673339\pi$$
0.481738 + 0.876315i $$0.340006\pi$$
$$564$$ 0 0
$$565$$ 15.6753 + 14.1788i 0.659463 + 0.596507i
$$566$$ −69.9565 −2.94049
$$567$$ 0 0
$$568$$ 24.6535i 1.03444i
$$569$$ 1.24456 2.15565i 0.0521748 0.0903694i −0.838758 0.544504i $$-0.816718\pi$$
0.890933 + 0.454134i $$0.150051\pi$$
$$570$$ 0 0
$$571$$ −16.4307 28.4588i −0.687604 1.19096i −0.972611 0.232439i $$-0.925329\pi$$
0.285007 0.958525i $$-0.408004\pi$$
$$572$$ −21.3505 + 12.3267i −0.892711 + 0.515407i
$$573$$ 0 0
$$574$$ 6.00000 10.3923i 0.250435 0.433766i
$$575$$ −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 $$-0.200979\pi$$
$$578$$ 23.2337 + 13.4140i 0.966394 + 0.557948i
$$579$$ 0 0
$$580$$ 17.2337 + 53.4535i 0.715590 + 2.21954i
$$581$$ 9.25544 + 16.0309i 0.383980 + 0.665073i
$$582$$ 0 0
$$583$$ −6.35053 3.66648i −0.263012 0.151850i
$$584$$ −45.3505 −1.87662
$$585$$ 0 0
$$586$$ −6.37228 −0.263237
$$587$$ −8.48913 4.90120i −0.350384 0.202294i 0.314471 0.949267i $$-0.398173\pi$$
−0.664854 + 0.746973i $$0.731506\pi$$
$$588$$ 0 0
$$589$$ 1.68614 + 2.92048i 0.0694762 + 0.120336i
$$590$$ −39.6060 + 12.7692i −1.63055 + 0.525698i
$$591$$ 0 0
$$592$$ 41.7921 + 24.1287i 1.71765 + 0.991683i
$$593$$ 38.1600i 1.56704i 0.621364 + 0.783522i $$0.286579\pi$$
−0.621364 + 0.783522i $$0.713421\pi$$
$$594$$ 0 0
$$595$$ −19.1168 4.10891i −0.783714 0.168449i
$$596$$ 35.7921 61.9938i 1.46610 2.53936i
$$597$$ 0 0
$$598$$ −45.3505 + 26.1831i −1.85452 + 1.07071i
$$599$$ −3.68614 6.38458i −0.150612 0.260867i 0.780841 0.624730i $$-0.214791\pi$$
−0.931452 + 0.363863i $$0.881458\pi$$
$$600$$ 0 0
$$601$$ −13.9891 + 24.2299i −0.570628 + 0.988357i 0.425873 + 0.904783i $$0.359967\pi$$
−0.996502 + 0.0835744i $$0.973366\pi$$
$$602$$ 30.2921i 1.23461i
$$603$$ 0 0
$$604$$ −79.2119 −3.22309
$$605$$ 13.6753 15.1186i 0.555979 0.614657i
$$606$$ 0 0
$$607$$ −31.4674 + 18.1677i −1.27722 + 0.737404i −0.976337 0.216256i $$-0.930615\pi$$
−0.300885 + 0.953661i $$0.597282\pi$$
$$608$$ 19.1168 11.0371i 0.775290 0.447614i
$$609$$ 0 0
$$610$$ 15.1861 + 13.7364i 0.614869 + 0.556170i
$$611$$ 34.9783 1.41507
$$612$$ 0 0
$$613$$ 9.50744i 0.384002i 0.981395 + 0.192001i $$0.0614977\pi$$
−0.981395 + 0.192001i $$0.938502\pi$$
$$614$$ 6.00000 10.3923i 0.242140 0.419399i
$$615$$ 0 0
$$616$$ 14.2337 + 24.6535i 0.573492 + 0.993317i
$$617$$ −19.4198 + 11.2120i −0.781813 + 0.451380i −0.837072 0.547092i $$-0.815735\pi$$
0.0552595 + 0.998472i $$0.482401\pi$$
$$618$$ 0 0
$$619$$ 2.00000 3.46410i 0.0803868 0.139234i −0.823029 0.567999i $$-0.807718\pi$$
0.903416 + 0.428765i $$0.141051\pi$$
$$620$$ −6.00000 1.28962i −0.240966 0.0517924i
$$621$$ 0 0
$$622$$ 32.4665i 1.30179i
$$623$$ −9.00000 5.19615i −0.360577 0.208179i
$$624$$ 0 0
$$625$$ 7.94158 23.7051i 0.317663 0.948204i
$$626$$ 6.81386 + 11.8020i 0.272337 + 0.471701i
$$627$$ 0 0
$$628$$ 81.1426 + 46.8477i 3.23794 + 1.86943i
$$629$$ −19.1168 −0.762238
$$630$$ 0 0
$$631$$ 0.627719 0.0249891 0.0124945 0.999922i $$-0.496023\pi$$
0.0124945 + 0.999922i $$0.496023\pi$$
$$632$$ −24.6060 14.2063i −0.978773 0.565095i
$$633$$ 0 0
$$634$$ −8.81386 15.2661i −0.350043 0.606292i
$$635$$ 22.1168 7.13058i 0.877680 0.282969i
$$636$$ 0 0
$$637$$ −17.7921 10.2723i −0.704949 0.407003i
$$638$$ 19.8997i 0.787839i
$$639$$ 0 0
$$640$$ 6.67527 31.0569i 0.263863 1.22763i
$$641$$ −18.9891 + 32.8901i −0.750025 + 1.29908i 0.197784 + 0.980246i $$0.436625\pi$$
−0.947810 + 0.318836i $$0.896708\pi$$
$$642$$ 0 0
$$643$$ 16.1168 9.30506i 0.635586 0.366956i −0.147326 0.989088i $$-0.547067\pi$$
0.782912 + 0.622132i $$0.213733\pi$$
$$644$$ 38.2337 + 66.2227i 1.50662 + 2.60954i
$$645$$ 0 0
$$646$$ −17.1168 + 29.6472i −0.673453 + 1.16646i
$$647$$ 4.45877i 0.175292i −0.996152 0.0876461i $$-0.972066\pi$$
0.996152 0.0876461i $$-0.0279345\pi$$
$$648$$ 0 0
$$649$$ −10.1168 −0.397121
$$650$$ 42.0951 30.2921i 1.65111 1.18815i
$$651$$ 0 0
$$652$$ 18.0000 10.3923i 0.704934 0.406994i
$$653$$ 17.4891 10.0974i 0.684402 0.395140i −0.117109 0.993119i $$-0.537363\pi$$
0.801512 + 0.597979i $$0.204029\pi$$
$$654$$ 0 0
$$655$$ −2.05842 + 2.27567i −0.0804292 + 0.0889178i
$$656$$ 8.74456 0.341418
$$657$$ 0 0
$$658$$ 74.4405i 2.90199i
$$659$$ −16.3723 + 28.3576i −0.637774 + 1.10466i 0.348147 + 0.937440i $$0.386811\pi$$
−0.985920 + 0.167216i $$0.946522\pi$$
$$660$$ 0 0
$$661$$ −9.61684 16.6569i −0.374052 0.647877i 0.616133 0.787642i $$-0.288698\pi$$
−0.990185 + 0.139765i $$0.955365\pi$$
$$662$$ 17.7446 10.2448i 0.689662 0.398177i
$$663$$ 0 0
$$664$$ −16.0000 + 27.7128i −0.620920 + 1.07547i
$$665$$ −8.74456 + 40.6844i −0.339100 + 1.57767i
$$666$$ 0 0
$$667$$ 29.0024i 1.12298i
$$668$$ 1.11684 + 0.644810i 0.0432120 + 0.0249485i
$$669$$ 0 0
$$670$$ −14.2337 44.1485i −0.549895 1.70560i
$$671$$ 2.48913 + 4.31129i 0.0960916 + 0.166436i
$$672$$ 0 0
$$673$$ −16.6753 9.62747i −0.642784 0.371112i 0.142902 0.989737i $$-0.454357\pi$$
−0.785686 + 0.618625i $$0.787690\pi$$
$$674$$ −17.4891 −0.673656
$$675$$ 0 0
$$676$$ 16.9783 0.653010
$$677$$ 22.9783 + 13.2665i 0.883126 + 0.509873i 0.871688 0.490062i $$-0.163026\pi$$
0.0114381 + 0.999935i $$0.496359\pi$$
$$678$$ 0 0
$$679$$ 32.2337 + 55.8304i 1.23702 + 2.14257i
$$680$$ −10.3723 32.1716i −0.397759 1.23372i
$$681$$ 0 0
$$682$$ −1.88316 1.08724i −0.0721098 0.0416326i
$$683$$ 0.589907i 0.0225722i −0.999936 0.0112861i $$-0.996407\pi$$
0.999936 0.0112861i $$-0.00359255\pi$$
$$684$$ 0 0
$$685$$ −1.04755 + 4.87375i −0.0400247 + 0.186216i
$$686$$ 8.74456 15.1460i 0.333869 0.578278i
$$687$$ 0 0
$$688$$ −19.1168 + 11.0371i −0.728823 + 0.420786i
$$689$$ 10.9783 + 19.0149i 0.418238 + 0.724410i
$$690$$ 0 0
$$691$$ 5.86141 10.1523i 0.222978 0.386210i −0.732733 0.680517i $$-0.761755\pi$$
0.955711 + 0.294307i $$0.0950887\pi$$
$$692$$ 34.4010i 1.30773i
$$693$$ 0 0
$$694$$ 59.7228 2.26705
$$695$$ −9.17527 + 10.1436i −0.348038 + 0.384770i
$$696$$ 0 0
$$697$$ −3.00000 + 1.73205i −0.113633 + 0.0656061i
$$698$$ 29.7446 17.1730i 1.12585 0.650009i
$$699$$ 0 0
$$700$$ −44.2337 61.4690i −1.67188 2.32331i
$$701$$ 17.2337 0.650907 0.325454 0.945558i $$-0.394483\pi$$
0.325454 + 0.945558i $$0.394483\pi$$
$$702$$ 0 0
$$703$$ 40.6844i 1.53444i
$$704$$ 1.62772 2.81929i 0.0613470 0.106256i
$$705$$ 0 0
$$706$$ −10.7446 18.6101i −0.404377 0.700401i
$$707$$ −31.8832 + 18.4077i −1.19909 + 0.692295i
$$708$$ 0 0
$$709$$ 0.324734 0.562456i 0.0121956 0.0211235i −0.859863 0.510525i $$-0.829451\pi$$
0.872059 + 0.489401i $$0.162785\pi$$
$$710$$ 4.88316 22.7190i 0.183262 0.852630i
$$711$$ 0 0
$$712$$ 17.9653i 0.673279i
$$713$$ −2.74456 1.58457i −0.102785 0.0593428i
$$714$$ 0 0
$$715$$ 12.0000 3.86886i 0.448775 0.144687i
$$716$$ −48.3505 83.7456i −1.80694 3.12972i
$$717$$ 0 0
$$718$$ −61.4674 35.4882i −2.29394 1.32441i
$$719$$ 28.1168 1.04858 0.524291 0.851539i $$-0.324331\pi$$
0.524291 + 0.851539i $$0.324331\pi$$
$$720$$ 0 0
$$721$$ −24.0000 −0.893807
$$722$$ 21.5584 + 12.4468i 0.802321 + 0.463220i
$$723$$ 0 0
$$724$$ 32.4891 + 56.2728i 1.20745 + 2.09136i
$$725$$ −2.87228 28.5788i −0.106674 1.06139i
$$726$$ 0 0
$$727$$ −9.35053 5.39853i −0.346792 0.200220i 0.316479 0.948599i $$-0.397499\pi$$
−0.663271 + 0.748379i $$0.730833\pi$$
$$728$$ 85.2376i 3.15911i
$$729$$ 0 0
$$730$$ 41.7921 + 8.98266i 1.54680 + 0.332463i
$$731$$ 4.37228 7.57301i 0.161715 0.280098i
$$732$$ 0 0
$$733$$ 20.2337 11.6819i 0.747348 0.431482i −0.0773867 0.997001i $$-0.524658\pi$$
0.824735 + 0.565519i $$0.191324\pi$$
$$734$$ 29.4891 + 51.0767i 1.08846 + 1.88527i
$$735$$ 0 0
$$736$$ −10.3723 + 17.9653i −0.382327 + 0.662210i
$$737$$ 11.2772i 0.415400i
$$738$$ 0 0
$$739$$ −11.3723 −0.418336 −0.209168 0.977880i $$-0.567076\pi$$
−0.209168 + 0.977880i $$0.567076\pi$$
$$740$$ −54.9090 49.6670i −2.01849 1.82580i
$$741$$ 0 0
$$742$$ 40.4674 23.3639i 1.48560 0.857714i
$$743$$ −36.8614 + 21.2819i −1.35231 + 0.780759i −0.988573 0.150742i $$-0.951834\pi$$
−0.363741 + 0.931500i $$0.618501\pi$$
$$744$$ 0 0
$$745$$ −24.5584 + 27.1504i −0.899751 + 0.994712i
$$746$$ −29.4891 −1.07967
$$747$$ 0 0
$$748$$ 15.1460i 0.553794i
$$749$$ −22.9783 + 39.7995i −0.839607 + 1.45424i
$$750$$ 0 0
$$751$$ 17.8614 + 30.9369i 0.651772 + 1.12890i 0.982693 + 0.185244i $$0.0593074\pi$$
−0.330921 + 0.943659i $$0.607359\pi$$
$$752$$ 46.9783 27.1229i 1.71312 0.989071i
$$753$$ 0 0
$$754$$ 29.7921 51.6014i 1.08496 1.87921i
$$755$$ 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 $$0.727428\pi$$
$$758$$ −46.9783 27.1229i −1.70633 0.985148i
$$759$$ 0 0
$$760$$ −68.4674 + 22.0742i −2.48357 + 0.800716i
$$761$$ 4.75544 + 8.23666i 0.172384 + 0.298579i 0.939253 0.343226i $$-0.111520\pi$$
−0.766869 + 0.641804i $$0.778186\pi$$
$$762$$ 0 0
$$763$$ 5.23369 + 3.02167i 0.189472 + 0.109392i
$$764$$ 58.4674 2.11528
$$765$$ 0 0
$$766$$ 89.2119 3.22336
$$767$$ 26.2337 + 15.1460i 0.947244 + 0.546891i
$$768$$ 0 0
$$769$$ 3.24456 + 5.61975i 0.117002 + 0.202653i 0.918578 0.395239i $$-0.129338\pi$$
−0.801576 + 0.597892i $$0.796005\pi$$
$$770$$ −8.23369 25.5383i −0.296722 0.920338i
$$771$$ 0 0
$$772$$ 81.1426 + 46.8477i 2.92039 + 1.68609i
$$773$$ 18.2603i 0.656776i 0.944543 + 0.328388i $$0.106505\pi$$
−0.944543 + 0.328388i $$0.893495\pi$$
$$774$$ 0 0
$$775$$ 2.86141 + 1.28962i 0.102785 + 0.0463245i
$$776$$ −55.7228 + 96.5147i −2.00033 + 3.46468i
$$777$$ 0 0
$$778$$ 51.3505 29.6472i 1.84101 1.06291i
$$779$$ 3.68614 + 6.38458i 0.132070 + 0.228751i
$$780$$ 0 0