# Properties

 Label 99.8.j.a.62.1 Level $99$ Weight $8$ Character 99.62 Analytic conductor $30.926$ Analytic rank $0$ Dimension $112$ Inner twists $4$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,8,Mod(8,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 3]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("99.8");

S:= CuspForms(chi, 8);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$99 = 3^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$8$$ Character orbit: $$[\chi]$$ $$=$$ 99.j (of order $$10$$, degree $$4$$, 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: $$30.9261175229$$ Analytic rank: $$0$$ Dimension: $$112$$ Relative dimension: $$28$$ over $$\Q(\zeta_{10})$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

## Embedding invariants

 Embedding label 62.1 Character $$\chi$$ $$=$$ 99.62 Dual form 99.8.j.a.8.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-17.5311 - 12.7371i) q^{2} +(105.552 + 324.855i) q^{4} +(-159.065 - 218.934i) q^{5} +(-1136.60 + 369.305i) q^{7} +(1430.14 - 4401.52i) q^{8} +O(q^{10})$$ $$q+(-17.5311 - 12.7371i) q^{2} +(105.552 + 324.855i) q^{4} +(-159.065 - 218.934i) q^{5} +(-1136.60 + 369.305i) q^{7} +(1430.14 - 4401.52i) q^{8} +5864.17i q^{10} +(4216.26 + 1307.78i) q^{11} +(6830.31 - 9401.11i) q^{13} +(24629.8 + 8002.70i) q^{14} +(-45763.1 + 33248.9i) q^{16} +(-4812.95 + 3496.81i) q^{17} +(29060.5 + 9442.31i) q^{19} +(54332.1 - 74781.8i) q^{20} +(-57258.3 - 76629.7i) q^{22} -96563.1i q^{23} +(1511.50 - 4651.91i) q^{25} +(-239485. + 77813.5i) q^{26} +(-239941. - 330250. i) q^{28} +(-24030.4 - 73957.8i) q^{29} +(-127217. - 92428.6i) q^{31} +633383. q^{32} +128915. q^{34} +(261647. + 190098. i) q^{35} +(135597. + 417323. i) q^{37} +(-389194. - 535679. i) q^{38} +(-1.19113e6 + 387020. i) q^{40} +(-7872.79 + 24230.0i) q^{41} +44925.2i q^{43} +(20194.4 + 1.50771e6i) q^{44} +(-1.22993e6 + 1.69286e6i) q^{46} +(208893. + 67873.6i) q^{47} +(489222. - 355441. i) q^{49} +(-85750.0 + 62301.0i) q^{50} +(3.77494e6 + 1.22655e6i) q^{52} +(487319. - 670738. i) q^{53} +(-384341. - 1.13111e6i) q^{55} +5.53094e6i q^{56} +(-520729. + 1.60264e6i) q^{58} +(-1.99174e6 + 647157. i) q^{59} +(500336. + 688653. i) q^{61} +(1.05298e6 + 3.24075e6i) q^{62} +(-5.24622e6 - 3.81160e6i) q^{64} -3.14468e6 q^{65} -2.90295e6 q^{67} +(-1.64397e6 - 1.19441e6i) q^{68} +(-2.16567e6 - 6.66524e6i) q^{70} +(-2.16301e6 - 2.97713e6i) q^{71} +(5.27787e6 - 1.71488e6i) q^{73} +(2.93833e6 - 9.04324e6i) q^{74} +1.04371e7i q^{76} +(-5.27519e6 + 70656.2i) q^{77} +(-4.80416e6 + 6.61236e6i) q^{79} +(1.45586e7 + 4.73038e6i) q^{80} +(446638. - 324501. i) q^{82} +(707866. - 514295. i) q^{83} +(1.53114e6 + 497498. i) q^{85} +(572216. - 787588. i) q^{86} +(1.17861e7 - 1.66876e7i) q^{88} +3.06496e6i q^{89} +(-4.29148e6 + 1.32078e7i) q^{91} +(3.13690e7 - 1.01924e7i) q^{92} +(-2.79762e6 - 3.85059e6i) q^{94} +(-2.55525e6 - 7.86426e6i) q^{95} +(-2.33105e6 - 1.69361e6i) q^{97} -1.31039e7 q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$112 q - 1792 q^{4}+O(q^{10})$$ 112 * q - 1792 * q^4 $$112 q - 1792 q^{4} - 134096 q^{16} + 401484 q^{22} - 68552 q^{25} + 1493020 q^{28} - 398144 q^{31} - 729944 q^{34} + 685476 q^{37} - 399360 q^{40} - 1410880 q^{46} + 2923872 q^{49} + 6472520 q^{52} + 1445488 q^{55} + 13215936 q^{58} - 7843440 q^{61} - 12806712 q^{64} + 1864032 q^{67} - 1233728 q^{70} + 53841940 q^{73} - 53845440 q^{79} - 36360204 q^{82} + 41703500 q^{85} + 21474024 q^{88} + 27611736 q^{91} - 94707560 q^{94} - 27695460 q^{97}+O(q^{100})$$ 112 * q - 1792 * q^4 - 134096 * q^16 + 401484 * q^22 - 68552 * q^25 + 1493020 * q^28 - 398144 * q^31 - 729944 * q^34 + 685476 * q^37 - 399360 * q^40 - 1410880 * q^46 + 2923872 * q^49 + 6472520 * q^52 + 1445488 * q^55 + 13215936 * q^58 - 7843440 * q^61 - 12806712 * q^64 + 1864032 * q^67 - 1233728 * q^70 + 53841940 * q^73 - 53845440 * q^79 - 36360204 * q^82 + 41703500 * q^85 + 21474024 * q^88 + 27611736 * q^91 - 94707560 * q^94 - 27695460 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$$.

 $$n$$ $$46$$ $$56$$ $$\chi(n)$$ $$e\left(\frac{7}{10}\right)$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −17.5311 12.7371i −1.54954 1.12581i −0.943975 0.330016i $$-0.892946\pi$$
−0.605569 0.795793i $$-0.707054\pi$$
$$3$$ 0 0
$$4$$ 105.552 + 324.855i 0.824622 + 2.53793i
$$5$$ −159.065 218.934i −0.569088 0.783282i 0.423359 0.905962i $$-0.360851\pi$$
−0.992446 + 0.122680i $$0.960851\pi$$
$$6$$ 0 0
$$7$$ −1136.60 + 369.305i −1.25247 + 0.406951i −0.858804 0.512304i $$-0.828792\pi$$
−0.393662 + 0.919255i $$0.628792\pi$$
$$8$$ 1430.14 4401.52i 0.987560 3.03940i
$$9$$ 0 0
$$10$$ 5864.17i 1.85441i
$$11$$ 4216.26 + 1307.78i 0.955110 + 0.296252i
$$12$$ 0 0
$$13$$ 6830.31 9401.11i 0.862261 1.18680i −0.118765 0.992922i $$-0.537894\pi$$
0.981026 0.193878i $$-0.0621064\pi$$
$$14$$ 24629.8 + 8002.70i 2.39890 + 0.779450i
$$15$$ 0 0
$$16$$ −45763.1 + 33248.9i −2.79316 + 2.02935i
$$17$$ −4812.95 + 3496.81i −0.237596 + 0.172624i −0.700212 0.713935i $$-0.746911\pi$$
0.462615 + 0.886559i $$0.346911\pi$$
$$18$$ 0 0
$$19$$ 29060.5 + 9442.31i 0.971997 + 0.315821i 0.751622 0.659594i $$-0.229272\pi$$
0.220375 + 0.975415i $$0.429272\pi$$
$$20$$ 54332.1 74781.8i 1.51863 2.09021i
$$21$$ 0 0
$$22$$ −57258.3 76629.7i −1.14646 1.53433i
$$23$$ 96563.1i 1.65487i −0.561561 0.827435i $$-0.689799\pi$$
0.561561 0.827435i $$-0.310201\pi$$
$$24$$ 0 0
$$25$$ 1511.50 4651.91i 0.0193472 0.0595445i
$$26$$ −239485. + 77813.5i −2.67222 + 0.868257i
$$27$$ 0 0
$$28$$ −239941. 330250.i −2.06562 2.84309i
$$29$$ −24030.4 73957.8i −0.182965 0.563107i 0.816943 0.576719i $$-0.195667\pi$$
−0.999907 + 0.0136116i $$0.995667\pi$$
$$30$$ 0 0
$$31$$ −127217. 92428.6i −0.766972 0.557238i 0.134069 0.990972i $$-0.457196\pi$$
−0.901041 + 0.433734i $$0.857196\pi$$
$$32$$ 633383. 3.41697
$$33$$ 0 0
$$34$$ 128915. 0.562508
$$35$$ 261647. + 190098.i 1.03152 + 0.749443i
$$36$$ 0 0
$$37$$ 135597. + 417323.i 0.440091 + 1.35446i 0.887778 + 0.460271i $$0.152248\pi$$
−0.447687 + 0.894190i $$0.647752\pi$$
$$38$$ −389194. 535679.i −1.15060 1.58366i
$$39$$ 0 0
$$40$$ −1.19113e6 + 387020.i −2.94271 + 0.956145i
$$41$$ −7872.79 + 24230.0i −0.0178396 + 0.0549047i −0.959580 0.281436i $$-0.909189\pi$$
0.941740 + 0.336341i $$0.109189\pi$$
$$42$$ 0 0
$$43$$ 44925.2i 0.0861689i 0.999071 + 0.0430845i $$0.0137185\pi$$
−0.999071 + 0.0430845i $$0.986282\pi$$
$$44$$ 20194.4 + 1.50771e6i 0.0357393 + 2.66829i
$$45$$ 0 0
$$46$$ −1.22993e6 + 1.69286e6i −1.86307 + 2.56429i
$$47$$ 208893. + 67873.6i 0.293482 + 0.0953582i 0.452058 0.891989i $$-0.350690\pi$$
−0.158575 + 0.987347i $$0.550690\pi$$
$$48$$ 0 0
$$49$$ 489222. 355441.i 0.594046 0.431599i
$$50$$ −85750.0 + 62301.0i −0.0970150 + 0.0704855i
$$51$$ 0 0
$$52$$ 3.77494e6 + 1.22655e6i 3.72305 + 1.20969i
$$53$$ 487319. 670738.i 0.449623 0.618853i −0.522694 0.852521i $$-0.675073\pi$$
0.972316 + 0.233668i $$0.0750729\pi$$
$$54$$ 0 0
$$55$$ −384341. 1.13111e6i −0.311492 0.916714i
$$56$$ 5.53094e6i 4.20863i
$$57$$ 0 0
$$58$$ −520729. + 1.60264e6i −0.350440 + 1.07854i
$$59$$ −1.99174e6 + 647157.i −1.26256 + 0.410230i −0.862405 0.506218i $$-0.831043\pi$$
−0.400153 + 0.916448i $$0.631043\pi$$
$$60$$ 0 0
$$61$$ 500336. + 688653.i 0.282233 + 0.388460i 0.926472 0.376364i $$-0.122826\pi$$
−0.644239 + 0.764824i $$0.722826\pi$$
$$62$$ 1.05298e6 + 3.24075e6i 0.561113 + 1.72693i
$$63$$ 0 0
$$64$$ −5.24622e6 3.81160e6i −2.50159 1.81751i
$$65$$ −3.14468e6 −1.42030
$$66$$ 0 0
$$67$$ −2.90295e6 −1.17917 −0.589587 0.807705i $$-0.700710\pi$$
−0.589587 + 0.807705i $$0.700710\pi$$
$$68$$ −1.64397e6 1.19441e6i −0.634034 0.460653i
$$69$$ 0 0
$$70$$ −2.16567e6 6.66524e6i −0.754655 2.32259i
$$71$$ −2.16301e6 2.97713e6i −0.717223 0.987173i −0.999611 0.0278726i $$-0.991127\pi$$
0.282389 0.959300i $$-0.408873\pi$$
$$72$$ 0 0
$$73$$ 5.27787e6 1.71488e6i 1.58792 0.515946i 0.623838 0.781554i $$-0.285573\pi$$
0.964081 + 0.265608i $$0.0855727\pi$$
$$74$$ 2.93833e6 9.04324e6i 0.842925 2.59426i
$$75$$ 0 0
$$76$$ 1.04371e7i 2.72729i
$$77$$ −5.27519e6 + 70656.2i −1.31680 + 0.0176373i
$$78$$ 0 0
$$79$$ −4.80416e6 + 6.61236e6i −1.09628 + 1.50890i −0.256062 + 0.966660i $$0.582425\pi$$
−0.840221 + 0.542244i $$0.817575\pi$$
$$80$$ 1.45586e7 + 4.73038e6i 3.17911 + 1.03295i
$$81$$ 0 0
$$82$$ 446638. 324501.i 0.0894555 0.0649932i
$$83$$ 707866. 514295.i 0.135887 0.0987276i −0.517765 0.855523i $$-0.673236\pi$$
0.653652 + 0.756795i $$0.273236\pi$$
$$84$$ 0 0
$$85$$ 1.53114e6 + 497498.i 0.270426 + 0.0878668i
$$86$$ 572216. 787588.i 0.0970098 0.133523i
$$87$$ 0 0
$$88$$ 1.17861e7 1.66876e7i 1.84366 2.61039i
$$89$$ 3.06496e6i 0.460851i 0.973090 + 0.230425i $$0.0740118\pi$$
−0.973090 + 0.230425i $$0.925988\pi$$
$$90$$ 0 0
$$91$$ −4.29148e6 + 1.32078e7i −0.596983 + 1.83732i
$$92$$ 3.13690e7 1.01924e7i 4.19994 1.36464i
$$93$$ 0 0
$$94$$ −2.79762e6 3.85059e6i −0.347409 0.478167i
$$95$$ −2.55525e6 7.86426e6i −0.305775 0.941077i
$$96$$ 0 0
$$97$$ −2.33105e6 1.69361e6i −0.259328 0.188413i 0.450522 0.892765i $$-0.351238\pi$$
−0.709851 + 0.704352i $$0.751238\pi$$
$$98$$ −1.31039e7 −1.40640
$$99$$ 0 0
$$100$$ 1.67074e6 0.167074
$$101$$ 1.93406e6 + 1.40517e6i 0.186786 + 0.135708i 0.677249 0.735754i $$-0.263172\pi$$
−0.490463 + 0.871462i $$0.663172\pi$$
$$102$$ 0 0
$$103$$ −1.45103e6 4.46580e6i −0.130841 0.402688i 0.864079 0.503357i $$-0.167902\pi$$
−0.994920 + 0.100668i $$0.967902\pi$$
$$104$$ −3.16109e7 4.35086e7i −2.75562 3.79279i
$$105$$ 0 0
$$106$$ −1.70865e7 + 5.55173e6i −1.39342 + 0.452750i
$$107$$ −6.16946e6 + 1.89876e7i −0.486860 + 1.49840i 0.342409 + 0.939551i $$0.388757\pi$$
−0.829269 + 0.558850i $$0.811243\pi$$
$$108$$ 0 0
$$109$$ 2.58835e6i 0.191439i −0.995408 0.0957196i $$-0.969485\pi$$
0.995408 0.0957196i $$-0.0305152\pi$$
$$110$$ −7.66906e6 + 2.47249e7i −0.549374 + 1.77117i
$$111$$ 0 0
$$112$$ 3.97356e7 5.46913e7i 2.67249 3.67837i
$$113$$ −1.92026e7 6.23930e6i −1.25195 0.406782i −0.393328 0.919398i $$-0.628676\pi$$
−0.858618 + 0.512617i $$0.828676\pi$$
$$114$$ 0 0
$$115$$ −2.11409e7 + 1.53598e7i −1.29623 + 0.941766i
$$116$$ 2.14891e7 1.56127e7i 1.27825 0.928701i
$$117$$ 0 0
$$118$$ 4.31603e7 + 1.40236e7i 2.41823 + 0.785731i
$$119$$ 4.17902e6 5.75193e6i 0.227332 0.312896i
$$120$$ 0 0
$$121$$ 1.60666e7 + 1.10279e7i 0.824470 + 0.565906i
$$122$$ 1.84457e7i 0.919676i
$$123$$ 0 0
$$124$$ 1.65979e7 5.10830e7i 0.781766 2.40603i
$$125$$ −2.13661e7 + 6.94227e6i −0.978453 + 0.317919i
$$126$$ 0 0
$$127$$ −6.54024e6 9.00187e6i −0.283322 0.389960i 0.643509 0.765439i $$-0.277478\pi$$
−0.926831 + 0.375479i $$0.877478\pi$$
$$128$$ 1.83703e7 + 5.65379e7i 0.774250 + 2.38290i
$$129$$ 0 0
$$130$$ 5.51297e7 + 4.00541e7i 2.20082 + 1.59899i
$$131$$ −4.76925e7 −1.85354 −0.926768 0.375635i $$-0.877425\pi$$
−0.926768 + 0.375635i $$0.877425\pi$$
$$132$$ 0 0
$$133$$ −3.65173e7 −1.34592
$$134$$ 5.08919e7 + 3.69751e7i 1.82718 + 1.32753i
$$135$$ 0 0
$$136$$ 8.50808e6 + 2.61852e7i 0.290032 + 0.892626i
$$137$$ −1.07934e7 1.48558e7i −0.358621 0.493599i 0.591143 0.806567i $$-0.298677\pi$$
−0.949764 + 0.312968i $$0.898677\pi$$
$$138$$ 0 0
$$139$$ 2.64308e7 8.58790e6i 0.834755 0.271228i 0.139708 0.990193i $$-0.455384\pi$$
0.695047 + 0.718964i $$0.255384\pi$$
$$140$$ −3.41368e7 + 1.05062e8i −1.05142 + 3.23593i
$$141$$ 0 0
$$142$$ 7.97427e7i 2.33712i
$$143$$ 4.10930e7 3.07050e7i 1.17515 0.878078i
$$144$$ 0 0
$$145$$ −1.23695e7 + 1.70251e7i −0.336949 + 0.463770i
$$146$$ −1.14369e8 3.71608e7i −3.04141 0.988213i
$$147$$ 0 0
$$148$$ −1.21257e8 + 8.80983e7i −3.07461 + 2.23384i
$$149$$ 1.17024e7 8.50229e6i 0.289816 0.210564i −0.433371 0.901215i $$-0.642676\pi$$
0.723188 + 0.690651i $$0.242676\pi$$
$$150$$ 0 0
$$151$$ 5.99320e6 + 1.94731e6i 0.141658 + 0.0460273i 0.378988 0.925402i $$-0.376272\pi$$
−0.237330 + 0.971429i $$0.576272\pi$$
$$152$$ 8.31210e7 1.14406e8i 1.91981 2.64239i
$$153$$ 0 0
$$154$$ 9.33798e7 + 6.59519e7i 2.06030 + 1.45514i
$$155$$ 4.25543e7i 0.917873i
$$156$$ 0 0
$$157$$ 2.93418e7 9.03048e7i 0.605115 1.86235i 0.109118 0.994029i $$-0.465197\pi$$
0.495997 0.868324i $$-0.334803\pi$$
$$158$$ 1.68444e8 5.47309e7i 3.39748 1.10391i
$$159$$ 0 0
$$160$$ −1.00749e8 1.38669e8i −1.94456 2.67645i
$$161$$ 3.56612e7 + 1.09754e8i 0.673451 + 2.07267i
$$162$$ 0 0
$$163$$ −5.15716e7 3.74689e7i −0.932725 0.677665i 0.0139332 0.999903i $$-0.495565\pi$$
−0.946659 + 0.322238i $$0.895565\pi$$
$$164$$ −8.70220e6 −0.154055
$$165$$ 0 0
$$166$$ −1.89603e7 −0.321711
$$167$$ −6.07288e7 4.41220e7i −1.00899 0.733074i −0.0449932 0.998987i $$-0.514327\pi$$
−0.963997 + 0.265913i $$0.914327\pi$$
$$168$$ 0 0
$$169$$ −2.23374e7 6.87476e7i −0.355984 1.09561i
$$170$$ −2.05059e7 2.82239e7i −0.320116 0.440602i
$$171$$ 0 0
$$172$$ −1.45942e7 + 4.74193e6i −0.218690 + 0.0710568i
$$173$$ −9.85562e6 + 3.03325e7i −0.144718 + 0.445396i −0.996975 0.0777277i $$-0.975234\pi$$
0.852257 + 0.523124i $$0.175234\pi$$
$$174$$ 0 0
$$175$$ 5.84558e6i 0.0824508i
$$176$$ −2.36432e8 + 8.03377e7i −3.26897 + 1.11077i
$$177$$ 0 0
$$178$$ 3.90387e7 5.37322e7i 0.518830 0.714109i
$$179$$ −1.31379e7 4.26878e6i −0.171215 0.0556311i 0.222155 0.975011i $$-0.428691\pi$$
−0.393370 + 0.919380i $$0.628691\pi$$
$$180$$ 0 0
$$181$$ 3.71801e7 2.70129e7i 0.466054 0.338608i −0.329848 0.944034i $$-0.606997\pi$$
0.795901 + 0.605426i $$0.206997\pi$$
$$182$$ 2.43463e8 1.76886e8i 2.99353 2.17493i
$$183$$ 0 0
$$184$$ −4.25024e8 1.38099e8i −5.02981 1.63428i
$$185$$ 6.97976e7 9.60682e7i 0.810475 1.11552i
$$186$$ 0 0
$$187$$ −2.48657e7 + 8.44919e6i −0.278071 + 0.0944864i
$$188$$ 7.50241e7i 0.823471i
$$189$$ 0 0
$$190$$ −5.53714e7 + 1.70416e8i −0.585663 + 1.80248i
$$191$$ 2.27515e6 739241.i 0.0236262 0.00767661i −0.297180 0.954821i $$-0.596046\pi$$
0.320806 + 0.947145i $$0.396046\pi$$
$$192$$ 0 0
$$193$$ 1.67196e7 + 2.30126e7i 0.167408 + 0.230417i 0.884476 0.466586i $$-0.154516\pi$$
−0.717068 + 0.697003i $$0.754516\pi$$
$$194$$ 1.92942e7 + 5.93815e7i 0.189724 + 0.583909i
$$195$$ 0 0
$$196$$ 1.67105e8 + 1.21409e8i 1.58523 + 1.15174i
$$197$$ −9.82844e7 −0.915910 −0.457955 0.888975i $$-0.651418\pi$$
−0.457955 + 0.888975i $$0.651418\pi$$
$$198$$ 0 0
$$199$$ −1.30437e8 −1.17332 −0.586660 0.809833i $$-0.699557\pi$$
−0.586660 + 0.809833i $$0.699557\pi$$
$$200$$ −1.83138e7 1.33058e7i −0.161873 0.117607i
$$201$$ 0 0
$$202$$ −1.60083e7 4.92684e7i −0.136652 0.420571i
$$203$$ 5.46260e7 + 7.51862e7i 0.458314 + 0.630815i
$$204$$ 0 0
$$205$$ 6.55705e6 2.13051e6i 0.0531581 0.0172721i
$$206$$ −3.14432e7 + 9.67722e7i −0.250606 + 0.771286i
$$207$$ 0 0
$$208$$ 6.57324e8i 5.06475i
$$209$$ 1.10178e8 + 7.78160e7i 0.834801 + 0.589600i
$$210$$ 0 0
$$211$$ −1.65709e7 + 2.28080e7i −0.121439 + 0.167147i −0.865408 0.501067i $$-0.832941\pi$$
0.743969 + 0.668214i $$0.232941\pi$$
$$212$$ 2.69330e8 + 8.75105e7i 1.94137 + 0.630790i
$$213$$ 0 0
$$214$$ 3.50005e8 2.54293e8i 2.44132 1.77373i
$$215$$ 9.83566e6 7.14602e6i 0.0674946 0.0490377i
$$216$$ 0 0
$$217$$ 1.78730e8 + 5.80728e7i 1.18738 + 0.385802i
$$218$$ −3.29681e7 + 4.53766e7i −0.215524 + 0.296643i
$$219$$ 0 0
$$220$$ 3.26877e8 2.44245e8i 2.06969 1.54649i
$$221$$ 6.91314e7i 0.430826i
$$222$$ 0 0
$$223$$ 5.23558e7 1.61134e8i 0.316153 0.973019i −0.659124 0.752034i $$-0.729073\pi$$
0.975277 0.220985i $$-0.0709272\pi$$
$$224$$ −7.19906e8 + 2.33912e8i −4.27965 + 1.39054i
$$225$$ 0 0
$$226$$ 2.57172e8 + 3.53967e8i 1.48199 + 2.03978i
$$227$$ −4.91950e6 1.51407e7i −0.0279145 0.0859121i 0.936129 0.351658i $$-0.114382\pi$$
−0.964043 + 0.265746i $$0.914382\pi$$
$$228$$ 0 0
$$229$$ −2.53269e8 1.84011e8i −1.39366 1.01256i −0.995452 0.0952612i $$-0.969631\pi$$
−0.398210 0.917294i $$-0.630369\pi$$
$$230$$ 5.66263e8 3.06881
$$231$$ 0 0
$$232$$ −3.59893e8 −1.89219
$$233$$ 1.35704e8 + 9.85944e7i 0.702822 + 0.510630i 0.880850 0.473395i $$-0.156972\pi$$
−0.178028 + 0.984025i $$0.556972\pi$$
$$234$$ 0 0
$$235$$ −1.83678e7 5.65301e7i −0.0923249 0.284147i
$$236$$ −4.20464e8 5.78719e8i −2.08227 2.86600i
$$237$$ 0 0
$$238$$ −1.46526e8 + 4.76091e7i −0.704522 + 0.228913i
$$239$$ −2.29398e7 + 7.06015e7i −0.108692 + 0.334519i −0.990579 0.136941i $$-0.956273\pi$$
0.881887 + 0.471460i $$0.156273\pi$$
$$240$$ 0 0
$$241$$ 2.87762e6i 0.0132426i −0.999978 0.00662131i $$-0.997892\pi$$
0.999978 0.00662131i $$-0.00210764\pi$$
$$242$$ −1.41201e8 3.97973e8i −0.640449 1.80509i
$$243$$ 0 0
$$244$$ −1.70901e8 + 2.35225e8i −0.753147 + 1.03662i
$$245$$ −1.55636e8 5.05692e7i −0.676128 0.219687i
$$246$$ 0 0
$$247$$ 2.87260e8 2.08707e8i 1.21293 0.881246i
$$248$$ −5.88764e8 + 4.27762e8i −2.45110 + 1.78083i
$$249$$ 0 0
$$250$$ 4.62995e8 + 1.50436e8i 1.87407 + 0.608923i
$$251$$ −4.12073e7 + 5.67170e7i −0.164481 + 0.226389i −0.883300 0.468809i $$-0.844683\pi$$
0.718818 + 0.695198i $$0.244683\pi$$
$$252$$ 0 0
$$253$$ 1.26284e8 4.07136e8i 0.490258 1.58058i
$$254$$ 2.41116e8i 0.923226i
$$255$$ 0 0
$$256$$ 1.41581e8 4.35741e8i 0.527429 1.62326i
$$257$$ −1.74191e8 + 5.65980e7i −0.640116 + 0.207986i −0.611051 0.791591i $$-0.709253\pi$$
−0.0290651 + 0.999578i $$0.509253\pi$$
$$258$$ 0 0
$$259$$ −3.08239e8 4.24255e8i −1.10240 1.51732i
$$260$$ −3.31927e8 1.02156e9i −1.17121 3.60462i
$$261$$ 0 0
$$262$$ 8.36102e8 + 6.07464e8i 2.87213 + 2.08673i
$$263$$ 4.22481e8 1.43206 0.716031 0.698069i $$-0.245957\pi$$
0.716031 + 0.698069i $$0.245957\pi$$
$$264$$ 0 0
$$265$$ −2.24363e8 −0.740611
$$266$$ 6.40188e8 + 4.65124e8i 2.08556 + 1.51525i
$$267$$ 0 0
$$268$$ −3.06411e8 9.43037e8i −0.972374 2.99266i
$$269$$ 3.25147e8 + 4.47527e8i 1.01847 + 1.40180i 0.913273 + 0.407348i $$0.133546\pi$$
0.105194 + 0.994452i $$0.466454\pi$$
$$270$$ 0 0
$$271$$ −1.61700e8 + 5.25394e7i −0.493534 + 0.160359i −0.545201 0.838306i $$-0.683547\pi$$
0.0516669 + 0.998664i $$0.483547\pi$$
$$272$$ 1.03991e8 3.20050e8i 0.313331 0.964332i
$$273$$ 0 0
$$274$$ 3.97915e8i 1.16859i
$$275$$ 1.24566e7 1.76370e7i 0.0361188 0.0511399i
$$276$$ 0 0
$$277$$ −2.36819e8 + 3.25953e8i −0.669479 + 0.921459i −0.999748 0.0224276i $$-0.992860\pi$$
0.330269 + 0.943887i $$0.392860\pi$$
$$278$$ −5.72746e8 1.86096e8i −1.59884 0.519495i
$$279$$ 0 0
$$280$$ 1.21091e9 8.79778e8i 3.29654 2.39508i
$$281$$ −5.61350e6 + 4.07844e6i −0.0150925 + 0.0109653i −0.595306 0.803499i $$-0.702969\pi$$
0.580213 + 0.814464i $$0.302969\pi$$
$$282$$ 0 0
$$283$$ −2.85926e8 9.29028e7i −0.749895 0.243656i −0.0909590 0.995855i $$-0.528993\pi$$
−0.658936 + 0.752199i $$0.728993\pi$$
$$284$$ 7.38824e8 1.01690e9i 1.91393 2.63430i
$$285$$ 0 0
$$286$$ −1.11150e9 + 1.48875e7i −2.80949 + 0.0376304i
$$287$$ 3.04473e7i 0.0760261i
$$288$$ 0 0
$$289$$ −1.15865e8 + 3.56595e8i −0.282364 + 0.869027i
$$290$$ 4.33701e8 1.40918e8i 1.04423 0.339292i
$$291$$ 0 0
$$292$$ 1.11417e9 + 1.53353e9i 2.61887 + 3.60456i
$$293$$ −6.61585e6 2.03615e7i −0.0153656 0.0472904i 0.943080 0.332567i $$-0.107915\pi$$
−0.958445 + 0.285276i $$0.907915\pi$$
$$294$$ 0 0
$$295$$ 4.58501e8 + 3.33121e8i 1.03983 + 0.755482i
$$296$$ 2.03078e9 4.55136
$$297$$ 0 0
$$298$$ −3.13450e8 −0.686138
$$299$$ −9.07801e8 6.59556e8i −1.96400 1.42693i
$$300$$ 0 0
$$301$$ −1.65911e7 5.10622e7i −0.0350665 0.107924i
$$302$$ −8.02643e7 1.10474e8i −0.167687 0.230801i
$$303$$ 0 0
$$304$$ −1.64384e9 + 5.34117e8i −3.35585 + 1.09038i
$$305$$ 7.11837e7 2.19081e8i 0.143659 0.442135i
$$306$$ 0 0
$$307$$ 4.78004e8i 0.942860i 0.881904 + 0.471430i $$0.156262\pi$$
−0.881904 + 0.471430i $$0.843738\pi$$
$$308$$ −5.79758e8 1.70621e9i −1.13063 3.32740i
$$309$$ 0 0
$$310$$ 5.42017e8 7.46023e8i 1.03335 1.42228i
$$311$$ 3.13450e8 + 1.01846e8i 0.590891 + 0.191992i 0.589174 0.808006i $$-0.299453\pi$$
0.00171734 + 0.999999i $$0.499453\pi$$
$$312$$ 0 0
$$313$$ −3.59369e8 + 2.61097e8i −0.662422 + 0.481278i −0.867480 0.497472i $$-0.834262\pi$$
0.205058 + 0.978750i $$0.434262\pi$$
$$314$$ −1.66461e9 + 1.20941e9i −3.03431 + 2.20455i
$$315$$ 0 0
$$316$$ −2.65514e9 8.62708e8i −4.73351 1.53801i
$$317$$ 2.32784e7 3.20399e7i 0.0410436 0.0564916i −0.788002 0.615673i $$-0.788884\pi$$
0.829046 + 0.559181i $$0.188884\pi$$
$$318$$ 0 0
$$319$$ −4.59754e6 3.43252e8i −0.00792972 0.592033i
$$320$$ 1.75487e9i 2.99378i
$$321$$ 0 0
$$322$$ 7.72766e8 2.37833e9i 1.28989 3.96987i
$$323$$ −1.72884e8 + 5.61736e7i −0.285461 + 0.0927520i
$$324$$ 0 0
$$325$$ −3.34091e7 4.59837e7i −0.0539851 0.0743041i
$$326$$ 4.26861e8 + 1.31374e9i 0.682378 + 2.10014i
$$327$$ 0 0
$$328$$ 9.53894e7 + 6.93045e7i 0.149259 + 0.108443i
$$329$$ −2.62495e8 −0.406383
$$330$$ 0 0
$$331$$ 1.19903e9 1.81732 0.908660 0.417536i $$-0.137106\pi$$
0.908660 + 0.417536i $$0.137106\pi$$
$$332$$ 2.41787e8 + 1.75669e8i 0.362619 + 0.263458i
$$333$$ 0 0
$$334$$ 5.02656e8 + 1.54701e9i 0.738173 + 2.27186i
$$335$$ 4.61758e8 + 6.35555e8i 0.671054 + 0.923626i
$$336$$ 0 0
$$337$$ 8.68206e8 2.82097e8i 1.23571 0.401508i 0.382933 0.923776i $$-0.374914\pi$$
0.852781 + 0.522268i $$0.174914\pi$$
$$338$$ −4.84044e8 + 1.48973e9i −0.681830 + 2.09846i
$$339$$ 0 0
$$340$$ 5.49910e8i 0.758779i
$$341$$ −4.15504e8 5.56076e8i −0.567460 0.759440i
$$342$$ 0 0
$$343$$ 1.53720e8 2.11578e8i 0.205684 0.283100i
$$344$$ 1.97739e8 + 6.42493e7i 0.261902 + 0.0850970i
$$345$$ 0 0
$$346$$ 5.59127e8 4.06230e8i 0.725678 0.527236i
$$347$$ −6.60456e8 + 4.79850e8i −0.848576 + 0.616527i −0.924753 0.380568i $$-0.875729\pi$$
0.0761768 + 0.997094i $$0.475729\pi$$
$$348$$ 0 0
$$349$$ −8.31786e8 2.70264e8i −1.04742 0.340329i −0.265767 0.964037i $$-0.585625\pi$$
−0.781657 + 0.623708i $$0.785625\pi$$
$$350$$ 7.44557e7 1.02479e8i 0.0928239 0.127761i
$$351$$ 0 0
$$352$$ 2.67051e9 + 8.28328e8i 3.26359 + 1.01229i
$$353$$ 4.10173e8i 0.496313i −0.968720 0.248157i $$-0.920175\pi$$
0.968720 0.248157i $$-0.0798248\pi$$
$$354$$ 0 0
$$355$$ −3.07735e8 + 9.47112e8i −0.365072 + 1.12358i
$$356$$ −9.95668e8 + 3.23512e8i −1.16961 + 0.380028i
$$357$$ 0 0
$$358$$ 1.75951e8 + 2.42175e8i 0.202675 + 0.278958i
$$359$$ −3.25759e8 1.00258e9i −0.371592 1.14364i −0.945749 0.324897i $$-0.894670\pi$$
0.574158 0.818745i $$-0.305330\pi$$
$$360$$ 0 0
$$361$$ 3.21954e7 + 2.33913e7i 0.0360179 + 0.0261686i
$$362$$ −9.95874e8 −1.10338
$$363$$ 0 0
$$364$$ −4.74359e9 −5.15528
$$365$$ −1.21497e9 8.82726e8i −1.30780 0.950169i
$$366$$ 0 0
$$367$$ 4.01854e8 + 1.23678e9i 0.424363 + 1.30606i 0.903603 + 0.428371i $$0.140912\pi$$
−0.479240 + 0.877684i $$0.659088\pi$$
$$368$$ 3.21061e9 + 4.41903e9i 3.35831 + 4.62232i
$$369$$ 0 0
$$370$$ −2.44726e9 + 7.95162e8i −2.51173 + 0.816111i
$$371$$ −3.06182e8 + 9.42333e8i −0.311295 + 0.958066i
$$372$$ 0 0
$$373$$ 5.29458e8i 0.528263i 0.964487 + 0.264132i $$0.0850853\pi$$
−0.964487 + 0.264132i $$0.914915\pi$$
$$374$$ 5.43541e8 + 1.68593e8i 0.537257 + 0.166644i
$$375$$ 0 0
$$376$$ 5.97493e8 8.22379e8i 0.579663 0.797838i
$$377$$ −8.59421e8 2.79243e8i −0.826059 0.268403i
$$378$$ 0 0
$$379$$ −5.76636e8 + 4.18950e8i −0.544082 + 0.395299i −0.825599 0.564258i $$-0.809162\pi$$
0.281517 + 0.959556i $$0.409162\pi$$
$$380$$ 2.28503e9 1.66017e9i 2.13624 1.55207i
$$381$$ 0 0
$$382$$ −4.93016e7 1.60191e7i −0.0452522 0.0147033i
$$383$$ 2.17749e8 2.99705e8i 0.198043 0.272583i −0.698433 0.715676i $$-0.746119\pi$$
0.896476 + 0.443093i $$0.146119\pi$$
$$384$$ 0 0
$$385$$ 8.54567e8 + 1.14368e9i 0.763191 + 1.02139i
$$386$$ 6.16396e8i 0.545512i
$$387$$ 0 0
$$388$$ 3.04130e8 9.36014e8i 0.264331 0.813526i
$$389$$ −1.12923e9 + 3.66909e8i −0.972656 + 0.316035i −0.751888 0.659291i $$-0.770856\pi$$
−0.220768 + 0.975326i $$0.570856\pi$$
$$390$$ 0 0
$$391$$ 3.37663e8 + 4.64753e8i 0.285670 + 0.393191i
$$392$$ −8.64822e8 2.66165e9i −0.725146 2.23177i
$$393$$ 0 0
$$394$$ 1.72303e9 + 1.25186e9i 1.41924 + 1.03114i
$$395$$ 2.21184e9 1.80578
$$396$$ 0 0
$$397$$ 3.08823e8 0.247709 0.123855 0.992300i $$-0.460474\pi$$
0.123855 + 0.992300i $$0.460474\pi$$
$$398$$ 2.28671e9 + 1.66139e9i 1.81811 + 1.32093i
$$399$$ 0 0
$$400$$ 8.54999e7 + 2.63142e8i 0.0667968 + 0.205579i
$$401$$ −1.11081e9 1.52891e9i −0.860273 1.18406i −0.981504 0.191440i $$-0.938684\pi$$
0.121231 0.992624i $$-0.461316\pi$$
$$402$$ 0 0
$$403$$ −1.73786e9 + 5.64666e8i −1.32266 + 0.429758i
$$404$$ −2.52334e8 + 7.76605e8i −0.190389 + 0.585957i
$$405$$ 0 0
$$406$$ 2.01387e9i 1.49345i
$$407$$ 2.59426e7 + 1.93688e9i 0.0190736 + 1.42404i
$$408$$ 0 0
$$409$$ 1.25202e8 1.72325e8i 0.0904854 0.124542i −0.761374 0.648313i $$-0.775475\pi$$
0.851860 + 0.523770i $$0.175475\pi$$
$$410$$ −1.42089e8 4.61674e7i −0.101816 0.0330820i
$$411$$ 0 0
$$412$$ 1.29758e9 9.42745e8i 0.914099 0.664131i
$$413$$ 2.02483e9 1.47112e9i 1.41437 1.02760i
$$414$$ 0 0
$$415$$ −2.25193e8 7.31697e7i −0.154663 0.0502531i
$$416$$ 4.32620e9 5.95451e9i 2.94632 4.05527i
$$417$$ 0 0
$$418$$ −9.40392e8 2.76755e9i −0.629784 1.85344i
$$419$$ 2.09860e9i 1.39374i 0.717198 + 0.696869i $$0.245424\pi$$
−0.717198 + 0.696869i $$0.754576\pi$$
$$420$$ 0 0
$$421$$ 4.94540e8 1.52204e9i 0.323009 0.994118i −0.649323 0.760513i $$-0.724948\pi$$
0.972331 0.233605i $$-0.0750524\pi$$
$$422$$ 5.81013e8 1.88783e8i 0.376351 0.122284i
$$423$$ 0 0
$$424$$ −2.25533e9 3.10419e9i −1.43691 1.97774i
$$425$$ 8.99210e6 + 2.76748e7i 0.00568198 + 0.0174873i
$$426$$ 0 0
$$427$$ −8.23007e8 5.97949e8i −0.511571 0.371678i
$$428$$ −6.81942e9 −4.20431
$$429$$ 0 0
$$430$$ −2.63449e8 −0.159793
$$431$$ −1.99131e8 1.44677e8i −0.119803 0.0870419i 0.526270 0.850317i $$-0.323590\pi$$
−0.646073 + 0.763275i $$0.723590\pi$$
$$432$$ 0 0
$$433$$ 3.99678e7 + 1.23008e8i 0.0236593 + 0.0728159i 0.962189 0.272383i $$-0.0878116\pi$$
−0.938530 + 0.345198i $$0.887812\pi$$
$$434$$ −2.39365e9 3.29458e9i −1.40555 1.93457i
$$435$$ 0 0
$$436$$ 8.40838e8 2.73205e8i 0.485858 0.157865i
$$437$$ 9.11779e8 2.80617e9i 0.522643 1.60853i
$$438$$ 0 0
$$439$$ 2.22822e9i 1.25699i 0.777813 + 0.628496i $$0.216329\pi$$
−0.777813 + 0.628496i $$0.783671\pi$$
$$440$$ −5.52824e9 + 7.40456e7i −3.09387 + 0.0414395i
$$441$$ 0 0
$$442$$ 8.80532e8 1.21195e9i 0.485028 0.667584i
$$443$$ −1.97258e8 6.40930e7i −0.107801 0.0350265i 0.254620 0.967041i $$-0.418050\pi$$
−0.362421 + 0.932015i $$0.618050\pi$$
$$444$$ 0 0
$$445$$ 6.71025e8 4.87528e8i 0.360976 0.262265i
$$446$$ −2.97024e9 + 2.15800e9i −1.58533 + 1.15181i
$$447$$ 0 0
$$448$$ 7.37051e9 + 2.39483e9i 3.87280 + 1.25835i
$$449$$ −1.16804e9 + 1.60766e9i −0.608967 + 0.838171i −0.996492 0.0836879i $$-0.973330\pi$$
0.387525 + 0.921859i $$0.373330\pi$$
$$450$$ 0 0
$$451$$ −6.48813e7 + 9.18640e7i −0.0333044 + 0.0471550i
$$452$$ 6.89662e9i 3.51279i
$$453$$ 0 0
$$454$$ −1.06604e8 + 3.28092e8i −0.0534659 + 0.164551i
$$455$$ 3.57426e9 1.16135e9i 1.77888 0.577993i
$$456$$ 0 0
$$457$$ −1.15785e9 1.59364e9i −0.567473 0.781060i 0.424779 0.905297i $$-0.360352\pi$$
−0.992253 + 0.124237i $$0.960352\pi$$
$$458$$ 2.09632e9 + 6.45181e9i 1.01960 + 3.13800i
$$459$$ 0 0
$$460$$ −7.22116e9 5.24648e9i −3.45903 2.51313i
$$461$$ 2.20731e9 1.04933 0.524663 0.851310i $$-0.324191\pi$$
0.524663 + 0.851310i $$0.324191\pi$$
$$462$$ 0 0
$$463$$ 1.66274e9 0.778556 0.389278 0.921120i $$-0.372725\pi$$
0.389278 + 0.921120i $$0.372725\pi$$
$$464$$ 3.55872e9 + 2.58556e9i 1.65379 + 1.20155i
$$465$$ 0 0
$$466$$ −1.12323e9 3.45693e9i −0.514181 1.58249i
$$467$$ −2.26326e8 3.11511e8i −0.102831 0.141535i 0.754500 0.656300i $$-0.227879\pi$$
−0.857331 + 0.514765i $$0.827879\pi$$
$$468$$ 0 0
$$469$$ 3.29951e9 1.07208e9i 1.47688 0.479866i
$$470$$ −3.98022e8 + 1.22499e9i −0.176834 + 0.544238i
$$471$$ 0 0
$$472$$ 9.69222e9i 4.24254i
$$473$$ −5.87524e7 + 1.89417e8i −0.0255277 + 0.0823008i
$$474$$ 0 0
$$475$$ 8.78496e7 1.20915e8i 0.0376108 0.0517668i
$$476$$ 2.30964e9 + 7.50449e8i 0.981569 + 0.318931i
$$477$$ 0 0
$$478$$ 1.30142e9 9.45535e8i 0.545028 0.395986i
$$479$$ 6.79822e8 4.93919e8i 0.282632 0.205344i −0.437433 0.899251i $$-0.644112\pi$$
0.720064 + 0.693907i $$0.244112\pi$$
$$480$$ 0 0
$$481$$ 4.84947e9 + 1.57569e9i 1.98695 + 0.645599i
$$482$$ −3.66525e7 + 5.04478e7i −0.0149087 + 0.0205200i
$$483$$ 0 0
$$484$$ −1.88661e9 + 6.38331e9i −0.756352 + 2.55910i
$$485$$ 7.79739e8i 0.310351i
$$486$$ 0 0
$$487$$ −3.75506e8 + 1.15569e9i −0.147321 + 0.453408i −0.997302 0.0734053i $$-0.976613\pi$$
0.849981 + 0.526813i $$0.176613\pi$$
$$488$$ 3.74667e9 1.21737e9i 1.45941 0.474190i
$$489$$ 0 0
$$490$$ 2.08436e9 + 2.86888e9i 0.800364 + 1.10161i
$$491$$ 2.09309e8 + 6.44187e8i 0.0797999 + 0.245599i 0.982995 0.183631i $$-0.0587851\pi$$
−0.903195 + 0.429230i $$0.858785\pi$$
$$492$$ 0 0
$$493$$ 3.74273e8 + 2.71925e8i 0.140678 + 0.102208i
$$494$$ −7.69430e9 −2.87160
$$495$$ 0 0
$$496$$ 8.89500e9 3.27311
$$497$$ 3.55795e9 + 2.58500e9i 1.30003 + 0.944526i
$$498$$ 0 0
$$499$$ −8.02086e8 2.46857e9i −0.288981 0.889391i −0.985177 0.171540i $$-0.945126\pi$$
0.696197 0.717851i $$-0.254874\pi$$
$$500$$ −4.51045e9 6.20811e9i −1.61371 2.22108i
$$501$$ 0 0
$$502$$ 1.44482e9 4.69450e8i 0.509742 0.165625i
$$503$$ 1.50959e9 4.64604e9i 0.528897 1.62778i −0.227581 0.973759i $$-0.573081\pi$$
0.756478 0.654019i $$-0.226919\pi$$
$$504$$ 0 0
$$505$$ 6.46944e8i 0.223536i
$$506$$ −7.39961e9 + 5.52905e9i −2.53911 + 1.89724i
$$507$$ 0 0
$$508$$ 2.23396e9 3.07479e9i 0.756055 1.04062i
$$509$$ 3.81563e9 + 1.23977e9i 1.28249 + 0.416707i 0.869457 0.494009i $$-0.164469\pi$$
0.413034 + 0.910716i $$0.364469\pi$$
$$510$$ 0 0
$$511$$ −5.36553e9 + 3.89828e9i −1.77885 + 1.29241i
$$512$$ −1.87609e9 + 1.36306e9i −0.617746 + 0.448819i
$$513$$ 0 0
$$514$$ 3.77464e9 + 1.22646e9i 1.22604 + 0.398365i
$$515$$ −7.46908e8 + 1.02803e9i −0.240958 + 0.331651i
$$516$$ 0 0
$$517$$ 7.91986e8 + 5.59360e8i 0.252058 + 0.178022i
$$518$$ 1.13637e10i 3.59225i
$$519$$ 0 0
$$520$$ −4.49734e9 + 1.38414e10i −1.40263 + 4.31686i
$$521$$ −3.64272e9 + 1.18359e9i −1.12848 + 0.366665i −0.812998 0.582266i $$-0.802166\pi$$
−0.315482 + 0.948932i $$0.602166\pi$$
$$522$$ 0 0
$$523$$ −5.38305e6 7.40914e6i −0.00164540 0.00226471i 0.808193 0.588917i $$-0.200446\pi$$
−0.809839 + 0.586652i $$0.800446\pi$$
$$524$$ −5.03403e9 1.54931e10i −1.52847 4.70414i
$$525$$ 0 0
$$526$$ −7.40655e9 5.38117e9i −2.21904 1.61223i
$$527$$ 9.35495e8 0.278422
$$528$$ 0 0
$$529$$ −5.91961e9 −1.73860
$$530$$ 3.93332e9 + 2.85772e9i 1.14761 + 0.833787i
$$531$$ 0 0
$$532$$ −3.85446e9 1.18628e10i −1.10987 3.41584i
$$533$$ 1.74015e8 + 2.39511e8i 0.0497785 + 0.0685142i
$$534$$ 0 0
$$535$$ 5.13839e9 1.66956e9i 1.45074 0.471373i
$$536$$ −4.15163e9 + 1.27774e10i −1.16451 + 3.58398i
$$537$$ 0 0
$$538$$ 1.19871e10i 3.31875i
$$539$$ 2.52753e9 8.58835e8i 0.695241 0.236238i
$$540$$ 0 0
$$541$$ −3.00104e8 + 4.13058e8i −0.0814857 + 0.112155i −0.847814 0.530294i $$-0.822082\pi$$
0.766328 + 0.642449i $$0.222082\pi$$
$$542$$ 3.50397e9 + 1.13851e9i 0.945286 + 0.307142i
$$543$$ 0 0
$$544$$ −3.04844e9 + 2.21482e9i −0.811861 + 0.589851i
$$545$$ −5.66678e8 + 4.11716e8i −0.149951 + 0.108946i
$$546$$ 0 0
$$547$$ 7.85767e8 + 2.55311e8i 0.205276 + 0.0666982i 0.409850 0.912153i $$-0.365581\pi$$
−0.204574 + 0.978851i $$0.565581\pi$$
$$548$$ 3.68672e9 5.07433e9i 0.956991 1.31719i
$$549$$ 0 0
$$550$$ −4.43021e8 + 1.50535e8i −0.113541 + 0.0385805i
$$551$$ 2.37615e9i 0.605123i
$$552$$ 0 0
$$553$$ 3.01845e9 9.28984e9i 0.759008 2.33599i
$$554$$ 8.30339e9 2.69793e9i 2.07478 0.674135i
$$555$$ 0 0
$$556$$ 5.57964e9 + 7.67971e9i 1.37672 + 1.89489i
$$557$$ 7.09812e8 + 2.18458e9i 0.174040 + 0.535641i 0.999588 0.0286909i $$-0.00913384\pi$$
−0.825548 + 0.564332i $$0.809134\pi$$
$$558$$ 0 0
$$559$$ 4.22347e8 + 3.06853e8i 0.102265 + 0.0743001i
$$560$$ −1.82943e10 −4.40208
$$561$$ 0 0
$$562$$ 1.50358e8 0.0357314
$$563$$ 1.97074e9 + 1.43183e9i 0.465426 + 0.338152i 0.795656 0.605749i $$-0.207126\pi$$
−0.330230 + 0.943900i $$0.607126\pi$$
$$564$$ 0 0
$$565$$ 1.68846e9 + 5.19655e9i 0.393842 + 1.21212i
$$566$$ 3.82927e9 + 5.27054e9i 0.887685 + 1.22179i
$$567$$ 0 0
$$568$$ −1.61973e10 + 5.26281e9i −3.70871 + 1.20503i
$$569$$ −5.41073e8 + 1.66525e9i −0.123130 + 0.378954i −0.993556 0.113345i $$-0.963843\pi$$
0.870426 + 0.492299i $$0.163843\pi$$
$$570$$ 0 0
$$571$$ 1.90437e9i 0.428079i −0.976825 0.214039i $$-0.931338\pi$$
0.976825 0.214039i $$-0.0686621\pi$$
$$572$$ 1.43121e10 + 1.01083e10i 3.19755 + 2.25835i
$$573$$ 0 0
$$574$$ −3.87810e8 + 5.33775e8i −0.0855909 + 0.117806i
$$575$$ −4.49203e8 1.45955e8i −0.0985384 0.0320171i
$$576$$ 0 0
$$577$$ −1.77768e9 + 1.29156e9i −0.385246 + 0.279898i −0.763505 0.645802i $$-0.776523\pi$$
0.378258 + 0.925700i $$0.376523\pi$$
$$578$$ 6.57322e9 4.77572e9i 1.41589 1.02871i
$$579$$ 0 0
$$580$$ −6.83632e9 2.22125e9i −1.45487 0.472716i
$$581$$ −6.14631e8 + 8.45968e8i −0.130016 + 0.178952i
$$582$$ 0 0
$$583$$ 2.93185e9 2.19070e9i 0.612775 0.457871i
$$584$$ 2.56831e10i 5.33584i
$$585$$ 0 0
$$586$$ −1.43363e8 + 4.41226e8i −0.0294303 + 0.0905773i
$$587$$ −6.05080e8 + 1.96602e8i −0.123475 + 0.0401195i −0.370103 0.928991i $$-0.620678\pi$$
0.246628 + 0.969110i $$0.420678\pi$$
$$588$$ 0 0
$$589$$ −2.82425e9 3.88724e9i −0.569507 0.783859i
$$590$$ −3.79504e9 1.16799e10i −0.760737 2.34131i
$$591$$ 0 0
$$592$$ −2.00809e10 1.45896e10i −3.97792 2.89013i
$$593$$ −6.60675e9 −1.30106 −0.650528 0.759482i $$-0.725453\pi$$
−0.650528 + 0.759482i $$0.725453\pi$$
$$594$$ 0 0
$$595$$ −1.92403e9 −0.374457
$$596$$ 3.99722e9 + 2.90415e9i 0.773385 + 0.561897i
$$597$$ 0 0
$$598$$ 7.51392e9 + 2.31255e10i 1.43685 + 4.42218i
$$599$$ −1.24334e9 1.71131e9i −0.236372 0.325338i 0.674309 0.738450i $$-0.264442\pi$$
−0.910680 + 0.413112i $$0.864442\pi$$
$$600$$ 0 0
$$601$$ 8.93339e9 2.90264e9i 1.67863 0.545421i 0.693988 0.719987i $$-0.255852\pi$$
0.984646 + 0.174566i $$0.0558522\pi$$
$$602$$ −3.59523e8 + 1.10650e9i −0.0671644 + 0.206711i
$$603$$ 0 0
$$604$$ 2.15246e9i 0.397471i
$$605$$ −1.41243e8 5.27167e9i −0.0259313 0.967842i
$$606$$ 0 0
$$607$$ −2.29038e9 + 3.15244e9i −0.415669 + 0.572120i −0.964590 0.263755i $$-0.915039\pi$$
0.548920 + 0.835875i $$0.315039\pi$$
$$608$$ 1.84064e10 + 5.98061e9i 3.32129 + 1.07915i
$$609$$ 0 0
$$610$$ −4.03838e9 + 2.93406e9i −0.720365 + 0.523376i
$$611$$ 2.06489e9 1.50023e9i 0.366229 0.266081i
$$612$$ 0 0
$$613$$ −7.47637e9 2.42922e9i −1.31093 0.425947i −0.431559 0.902085i $$-0.642036\pi$$
−0.879371 + 0.476138i $$0.842036\pi$$
$$614$$ 6.08837e9 8.37993e9i 1.06148 1.46100i
$$615$$ 0 0
$$616$$ −7.23327e9 + 2.33199e10i −1.24681 + 4.01970i
$$617$$ 9.21072e7i 0.0157868i 0.999969 + 0.00789342i $$0.00251258\pi$$
−0.999969 + 0.00789342i $$0.997487\pi$$
$$618$$ 0 0
$$619$$ −2.79979e8 + 8.61686e8i −0.0474469 + 0.146026i −0.971973 0.235092i $$-0.924461\pi$$
0.924526 + 0.381118i $$0.124461\pi$$
$$620$$ −1.38240e10 + 4.49167e9i −2.32949 + 0.756898i
$$621$$ 0 0
$$622$$ −4.19790e9 5.77792e9i −0.699465 0.962731i
$$623$$ −1.13191e9 3.48365e9i −0.187544 0.577200i
$$624$$ 0 0
$$625$$ 4.60934e9 + 3.34888e9i 0.755194 + 0.548681i
$$626$$ 9.62573e9 1.56828
$$627$$ 0 0
$$628$$ 3.24330e10 5.22551
$$629$$ −2.11192e9 1.53440e9i −0.338377 0.245845i
$$630$$ 0 0
$$631$$ −4.00569e8 1.23282e9i −0.0634708 0.195343i 0.914292 0.405055i $$-0.132748\pi$$
−0.977763 + 0.209712i $$0.932748\pi$$
$$632$$ 2.22338e10 + 3.06022e10i 3.50351 + 4.82217i
$$633$$ 0 0
$$634$$ −8.16190e8 + 2.65196e8i −0.127198 + 0.0413290i
$$635$$ −9.30492e8 + 2.86376e9i −0.144213 + 0.443842i
$$636$$ 0 0
$$637$$ 7.02700e9i 1.07716i
$$638$$ −4.29143e9 + 6.07614e9i −0.654229 + 0.926308i
$$639$$ 0 0
$$640$$ 9.45600e9 1.30151e10i 1.42586 1.96253i
$$641$$ −7.59910e9 2.46910e9i −1.13962 0.370284i −0.322394 0.946605i $$-0.604488\pi$$
−0.817223 + 0.576321i $$0.804488\pi$$
$$642$$ 0 0
$$643$$ −6.35425e9 + 4.61663e9i −0.942597 + 0.684837i −0.949044 0.315142i $$-0.897948\pi$$
0.00644744 + 0.999979i $$0.497948\pi$$
$$644$$ −3.18900e10 + 2.31694e10i −4.70494 + 3.41834i
$$645$$ 0 0
$$646$$ 3.74634e9 + 1.21726e9i 0.546756 + 0.177652i
$$647$$ −4.68346e9 + 6.44623e9i −0.679833 + 0.935710i −0.999932 0.0116744i $$-0.996284\pi$$
0.320099 + 0.947384i $$0.396284\pi$$
$$648$$ 0 0
$$649$$ −9.24406e9 + 1.23815e8i −1.32741 + 0.0177795i
$$650$$ 1.23168e9i 0.175914i
$$651$$ 0 0
$$652$$ 6.72849e9 2.07082e10i 0.950717 2.92601i
$$653$$ 6.71408e9 2.18154e9i 0.943606 0.306596i 0.203491 0.979077i $$-0.434771\pi$$
0.740115 + 0.672481i $$0.234771\pi$$
$$654$$ 0 0
$$655$$ 7.58621e9 + 1.04415e10i 1.05482 + 1.45184i
$$656$$ −4.45335e8 1.37060e9i −0.0615919 0.189560i
$$657$$ 0 0
$$658$$ 4.60182e9 + 3.34342e9i 0.629708 + 0.457510i
$$659$$ −9.53571e8 −0.129794 −0.0648969 0.997892i $$-0.520672\pi$$
−0.0648969 + 0.997892i $$0.520672\pi$$
$$660$$ 0 0
$$661$$ 1.14191e9 0.153790 0.0768950 0.997039i $$-0.475499\pi$$
0.0768950 + 0.997039i $$0.475499\pi$$
$$662$$ −2.10203e10 1.52721e10i −2.81602 2.04596i
$$663$$ 0 0
$$664$$ −1.25133e9 3.85120e9i −0.165876 0.510514i
$$665$$ 5.80862e9 + 7.99488e9i 0.765945 + 1.05423i
$$666$$ 0 0
$$667$$ −7.14160e9 + 2.32045e9i −0.931869 + 0.302783i
$$668$$ 7.92322e9 2.43852e10i 1.02845 3.16525i
$$669$$ 0 0
$$670$$ 1.70234e10i 2.18668i
$$671$$ 1.20894e9 + 3.55787e9i 0.154481 + 0.454634i
$$672$$ 0 0
$$673$$ 4.42077e9 6.08466e9i 0.559042 0.769456i −0.432162 0.901796i $$-0.642249\pi$$
0.991204 + 0.132340i $$0.0422491\pi$$
$$674$$ −1.88137e10 6.11294e9i −2.36682 0.769025i
$$675$$ 0 0
$$676$$ 1.99752e10 1.45128e10i 2.48701 1.80692i
$$677$$ −2.97784e9 + 2.16353e9i −0.368843 + 0.267980i −0.756731 0.653727i $$-0.773205\pi$$
0.387888 + 0.921706i $$0.373205\pi$$
$$678$$ 0 0
$$679$$ 3.27494e9 + 1.06409e9i 0.401475 + 0.130447i
$$680$$ 4.37949e9 6.02785e9i 0.534124 0.735159i
$$681$$ 0 0
$$682$$ 2.01459e8 + 1.50409e10i 0.0243188 + 1.81564i
$$683$$ 1.16210e10i 1.39564i 0.716274 + 0.697819i $$0.245846\pi$$
−0.716274 + 0.697819i $$0.754154\pi$$
$$684$$ 0 0
$$685$$ −1.53559e9 + 4.72607e9i −0.182541 + 0.561802i
$$686$$ −5.38976e9 + 1.75124e9i −0.637434 + 0.207115i
$$687$$ 0 0
$$688$$ −1.49371e9 2.05592e9i −0.174867 0.240684i
$$689$$ −2.97714e9 9.16269e9i −0.346762 1.06722i
$$690$$ 0 0
$$691$$ −8.66267e9 6.29380e9i −0.998800 0.725671i −0.0369695 0.999316i $$-0.511770\pi$$
−0.961831 + 0.273646i $$0.911770\pi$$
$$692$$ −1.08939e10 −1.24972
$$693$$ 0 0
$$694$$ 1.76904e10 2.00900
$$695$$ −6.08440e9 4.42057e9i −0.687497 0.499496i
$$696$$ 0 0
$$697$$ −4.68363e7 1.44147e8i −0.00523923 0.0161247i
$$698$$ 1.11397e10 + 1.53325e10i 1.23988 + 1.70655i
$$699$$ 0 0
$$700$$ −1.89896e9 + 6.17011e8i −0.209254 + 0.0679907i
$$701$$ 1.03788e9 3.19426e9i 0.113798 0.350233i −0.877897 0.478850i $$-0.841054\pi$$
0.991694 + 0.128617i $$0.0410538\pi$$
$$702$$ 0 0
$$703$$ 1.34080e10i 1.45552i
$$704$$ −1.71347e10 2.29316e10i −1.85085 2.47703i
$$705$$ 0 0
$$706$$ −5.22441e9 + 7.19078e9i −0.558754 + 0.769059i
$$707$$ −2.71719e9 8.82869e8i −0.289170 0.0939569i
$$708$$ 0 0
$$709$$ 6.22477e9 4.52256e9i 0.655936 0.476565i −0.209352 0.977840i $$-0.567136\pi$$
0.865288 + 0.501275i $$0.167136\pi$$
$$710$$ 1.74584e10 1.26843e10i 1.83063 1.33003i
$$711$$ 0 0
$$712$$ 1.34905e10 + 4.38333e9i 1.40071 + 0.455118i
$$713$$ −8.92520e9 + 1.22845e10i −0.922156 + 1.26924i
$$714$$ 0 0
$$715$$ −1.32588e10 4.11256e9i −1.35654 0.420767i
$$716$$ 4.71850e9i 0.480406i
$$717$$ 0 0
$$718$$ −7.05908e9 + 2.17256e10i −0.711725 + 2.19046i
$$719$$ 1.06843e10 3.47155e9i 1.07200 0.348315i 0.280736 0.959785i $$-0.409422\pi$$
0.791267 + 0.611470i $$0.209422\pi$$
$$720$$ 0 0
$$721$$ 3.29849e9 + 4.53998e9i 0.327749 + 0.451108i
$$722$$ −2.66483e8 8.20151e8i −0.0263506 0.0810987i
$$723$$ 0 0
$$724$$ 1.26997e10 + 9.22687e9i 1.24368 + 0.903586i
$$725$$ −3.80367e8 −0.0370698
$$726$$ 0 0
$$727$$ −1.94517e10 −1.87753 −0.938766 0.344555i $$-0.888030\pi$$
−0.938766 + 0.344555i $$0.888030\pi$$
$$728$$ 5.19970e10 + 3.77780e10i 4.99480 + 3.62894i
$$729$$ 0 0
$$730$$ 1.00564e10 + 3.09503e10i 0.956778 + 2.94466i
$$731$$ −1.57095e8 2.16223e8i −0.0148748 0.0204734i
$$732$$ 0 0
$$733$$ 1.07247e10 3.48465e9i 1.00582 0.326810i 0.240630 0.970617i $$-0.422646\pi$$
0.765188 + 0.643807i $$0.222646\pi$$
$$734$$ 8.70803e9 2.68006e10i 0.812800 2.50154i
$$735$$ 0 0
$$736$$ 6.11615e10i 5.65465i
$$737$$ −1.22396e10 3.79643e9i −1.12624 0.349333i
$$738$$ 0 0
$$739$$ −5.56409e9 + 7.65831e9i −0.507153 + 0.698036i −0.983436 0.181256i $$-0.941984\pi$$
0.476283 + 0.879292i $$0.341984\pi$$
$$740$$ 3.85754e10 + 1.25339e10i 3.49945 + 1.13704i
$$741$$ 0 0
$$742$$ 1.73703e10 1.26202e10i 1.56096 1.13411i
$$743$$ −1.50128e10 + 1.09075e10i −1.34277 + 0.975579i −0.343432 + 0.939178i $$0.611589\pi$$
−0.999337 + 0.0364014i $$0.988411\pi$$
$$744$$ 0 0
$$745$$ −3.72288e9 1.20964e9i −0.329862 0.107179i
$$746$$ 6.74374e9 9.28197e9i 0.594724 0.818567i
$$747$$ 0 0
$$748$$ −5.36937e9 7.18592e9i −0.469103 0.627808i
$$749$$ 2.38599e10i 2.07482i
$$750$$ 0 0
$$751$$ 2.23307e9 6.87268e9i 0.192381 0.592088i −0.807616 0.589709i $$-0.799243\pi$$
0.999997 0.00237963i $$-0.000757460\pi$$
$$752$$ −1.18163e10 + 3.83936e9i −1.01326 + 0.329228i
$$753$$ 0 0
$$754$$ 1.15098e10 + 1.58419e10i 0.977844 + 1.34589i
$$755$$ −5.26976e8 1.62186e9i −0.0445632 0.137151i
$$756$$ 0 0
$$757$$ −1.31201e10 9.53234e9i −1.09927 0.798664i −0.118326 0.992975i $$-0.537753\pi$$
−0.980940 + 0.194311i $$0.937753\pi$$
$$758$$ 1.54453e10 1.28811
$$759$$ 0 0
$$760$$ −3.82690e10 −3.16228
$$761$$ −6.76120e9 4.91230e9i −0.556131 0.404053i 0.273910 0.961755i $$-0.411683\pi$$
−0.830041 + 0.557702i $$0.811683\pi$$
$$762$$ 0 0
$$763$$ 9.55892e8 + 2.94193e9i 0.0779063 + 0.239771i
$$764$$ 4.80292e8 + 6.61065e8i 0.0389653 + 0.0536312i
$$765$$ 0 0
$$766$$ −7.63474e9 + 2.48068e9i −0.613753 + 0.199420i
$$767$$ −7.52023e9 + 2.31449e10i −0.601793 + 1.85213i
$$768$$ 0 0
$$769$$ 1.87910e9i 0.149007i 0.997221 + 0.0745036i $$0.0237372\pi$$
−0.997221 + 0.0745036i $$0.976263\pi$$
$$770$$ −4.14340e8 3.09346e10i −0.0327069 2.44190i
$$771$$ 0 0
$$772$$ −5.71097e9 + 7.86047e9i −0.446734 + 0.614877i
$$773$$ −1.80238e10 5.85629e9i −1.40352 0.456031i −0.493193 0.869920i $$-0.664170\pi$$
−0.910327