# Properties

 Label 99.8.j.a.8.12 Level $99$ Weight $8$ Character 99.8 Analytic conductor $30.926$ Analytic rank $0$ Dimension $112$ CM no 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 8.12 Character $$\chi$$ $$=$$ 99.8 Dual form 99.8.j.a.62.12

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-4.02244 + 2.92248i) q^{2} +(-31.9150 + 98.2243i) q^{4} +(-62.7155 + 86.3205i) q^{5} +(522.505 + 169.772i) q^{7} +(-355.346 - 1093.64i) q^{8} +O(q^{10})$$ $$q+(-4.02244 + 2.92248i) q^{2} +(-31.9150 + 98.2243i) q^{4} +(-62.7155 + 86.3205i) q^{5} +(522.505 + 169.772i) q^{7} +(-355.346 - 1093.64i) q^{8} -530.504i q^{10} +(2359.01 + 3731.25i) q^{11} +(7244.34 + 9970.97i) q^{13} +(-2597.90 + 844.109i) q^{14} +(-6069.49 - 4409.74i) q^{16} +(13260.5 + 9634.35i) q^{17} +(5470.54 - 1777.49i) q^{19} +(-6477.21 - 8915.11i) q^{20} +(-20393.5 - 8114.61i) q^{22} -67520.8i q^{23} +(20624.0 + 63474.0i) q^{25} +(-58279.8 - 18936.3i) q^{26} +(-33351.5 + 45904.4i) q^{28} +(4970.94 - 15299.0i) q^{29} +(-209670. + 152334. i) q^{31} +184492. q^{32} -81495.9 q^{34} +(-47424.0 + 34455.6i) q^{35} +(32368.4 - 99619.6i) q^{37} +(-16810.3 + 23137.3i) q^{38} +(116689. + 37914.7i) q^{40} +(-202479. - 623167. i) q^{41} +990652. i q^{43} +(-441787. + 112629. i) q^{44} +(197328. + 271598. i) q^{46} +(-997288. + 324038. i) q^{47} +(-422071. - 306653. i) q^{49} +(-268460. - 195048. i) q^{50} +(-1.21059e6 + 393346. i) q^{52} +(275492. + 379182. i) q^{53} +(-470030. - 30376.8i) q^{55} -631761. i q^{56} +(24715.6 + 76066.7i) q^{58} +(-1.50482e6 - 488946. i) q^{59} +(-1.25749e6 + 1.73079e6i) q^{61} +(398193. - 1.22551e6i) q^{62} +(34787.6 - 25274.7i) q^{64} -1.31503e6 q^{65} -301833. q^{67} +(-1.36954e6 + 995027. i) q^{68} +(90064.8 - 277191. i) q^{70} +(2.46871e6 - 3.39788e6i) q^{71} +(-2.18986e6 - 711530. i) q^{73} +(160936. + 495310. i) q^{74} +594068. i q^{76} +(599131. + 2.35009e6i) q^{77} +(1.39018e6 + 1.91342e6i) q^{79} +(761302. - 247362. i) q^{80} +(2.63565e6 + 1.91491e6i) q^{82} +(399457. + 290223. i) q^{83} +(-1.66328e6 + 540434. i) q^{85} +(-2.89516e6 - 3.98484e6i) q^{86} +(3.24239e6 - 3.90579e6i) q^{88} +8.78877e6i q^{89} +(2.09241e6 + 6.43977e6i) q^{91} +(6.63218e6 + 2.15492e6i) q^{92} +(3.06454e6 - 4.21797e6i) q^{94} +(-189654. + 583696. i) q^{95} +(1.01865e7 - 7.40089e6i) q^{97} +2.59394e6 q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$112 q - 1792 q^{4}+O(q^{10})$$ 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 $$\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$$.

 $$n$$ $$46$$ $$56$$ $$\chi(n)$$ $$e\left(\frac{3}{10}\right)$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −4.02244 + 2.92248i −0.355537 + 0.258313i −0.751188 0.660088i $$-0.770519\pi$$
0.395651 + 0.918401i $$0.370519\pi$$
$$3$$ 0 0
$$4$$ −31.9150 + 98.2243i −0.249336 + 0.767377i
$$5$$ −62.7155 + 86.3205i −0.224378 + 0.308830i −0.906333 0.422564i $$-0.861130\pi$$
0.681955 + 0.731394i $$0.261130\pi$$
$$6$$ 0 0
$$7$$ 522.505 + 169.772i 0.575768 + 0.187078i 0.582404 0.812900i $$-0.302112\pi$$
−0.00663590 + 0.999978i $$0.502112\pi$$
$$8$$ −355.346 1093.64i −0.245378 0.755196i
$$9$$ 0 0
$$10$$ 530.504i 0.167760i
$$11$$ 2359.01 + 3731.25i 0.534386 + 0.845241i
$$12$$ 0 0
$$13$$ 7244.34 + 9970.97i 0.914528 + 1.25874i 0.965597 + 0.260044i $$0.0837372\pi$$
−0.0510690 + 0.998695i $$0.516263\pi$$
$$14$$ −2597.90 + 844.109i −0.253031 + 0.0822149i
$$15$$ 0 0
$$16$$ −6069.49 4409.74i −0.370452 0.269149i
$$17$$ 13260.5 + 9634.35i 0.654621 + 0.475610i 0.864842 0.502044i $$-0.167418\pi$$
−0.210221 + 0.977654i $$0.567418\pi$$
$$18$$ 0 0
$$19$$ 5470.54 1777.49i 0.182975 0.0594523i −0.216096 0.976372i $$-0.569333\pi$$
0.399072 + 0.916920i $$0.369333\pi$$
$$20$$ −6477.21 8915.11i −0.181043 0.249185i
$$21$$ 0 0
$$22$$ −20393.5 8114.61i −0.408330 0.162476i
$$23$$ 67520.8i 1.15715i −0.815629 0.578575i $$-0.803609\pi$$
0.815629 0.578575i $$-0.196391\pi$$
$$24$$ 0 0
$$25$$ 20624.0 + 63474.0i 0.263987 + 0.812467i
$$26$$ −58279.8 18936.3i −0.650297 0.211294i
$$27$$ 0 0
$$28$$ −33351.5 + 45904.4i −0.287119 + 0.395186i
$$29$$ 4970.94 15299.0i 0.0378482 0.116485i −0.930347 0.366679i $$-0.880495\pi$$
0.968196 + 0.250195i $$0.0804946\pi$$
$$30$$ 0 0
$$31$$ −209670. + 152334.i −1.26407 + 0.918401i −0.998950 0.0458148i $$-0.985412\pi$$
−0.265120 + 0.964215i $$0.585412\pi$$
$$32$$ 184492. 0.995295
$$33$$ 0 0
$$34$$ −81495.9 −0.355598
$$35$$ −47424.0 + 34455.6i −0.186965 + 0.135838i
$$36$$ 0 0
$$37$$ 32368.4 99619.6i 0.105055 0.323325i −0.884689 0.466182i $$-0.845629\pi$$
0.989743 + 0.142858i $$0.0456291\pi$$
$$38$$ −16810.3 + 23137.3i −0.0496972 + 0.0684023i
$$39$$ 0 0
$$40$$ 116689. + 37914.7i 0.288285 + 0.0936693i
$$41$$ −202479. 623167.i −0.458815 1.41209i −0.866598 0.499007i $$-0.833698\pi$$
0.407783 0.913079i $$-0.366302\pi$$
$$42$$ 0 0
$$43$$ 990652.i 1.90012i 0.312065 + 0.950061i $$0.398979\pi$$
−0.312065 + 0.950061i $$0.601021\pi$$
$$44$$ −441787. + 112629.i −0.781860 + 0.199327i
$$45$$ 0 0
$$46$$ 197328. + 271598.i 0.298907 + 0.411410i
$$47$$ −997288. + 324038.i −1.40113 + 0.455254i −0.909556 0.415582i $$-0.863578\pi$$
−0.491573 + 0.870837i $$0.663578\pi$$
$$48$$ 0 0
$$49$$ −422071. 306653.i −0.512507 0.372358i
$$50$$ −268460. 195048.i −0.303728 0.220671i
$$51$$ 0 0
$$52$$ −1.21059e6 + 393346.i −1.19395 + 0.387939i
$$53$$ 275492. + 379182.i 0.254181 + 0.349850i 0.916970 0.398956i $$-0.130627\pi$$
−0.662789 + 0.748806i $$0.730627\pi$$
$$54$$ 0 0
$$55$$ −470030. 30376.8i −0.380940 0.0246191i
$$56$$ 631761.i 0.480723i
$$57$$ 0 0
$$58$$ 24715.6 + 76066.7i 0.0166331 + 0.0511913i
$$59$$ −1.50482e6 488946.i −0.953900 0.309941i −0.209601 0.977787i $$-0.567216\pi$$
−0.744299 + 0.667846i $$0.767216\pi$$
$$60$$ 0 0
$$61$$ −1.25749e6 + 1.73079e6i −0.709333 + 0.976313i 0.290478 + 0.956882i $$0.406186\pi$$
−0.999811 + 0.0194312i $$0.993814\pi$$
$$62$$ 398193. 1.22551e6i 0.212189 0.653051i
$$63$$ 0 0
$$64$$ 34787.6 25274.7i 0.0165880 0.0120519i
$$65$$ −1.31503e6 −0.593936
$$66$$ 0 0
$$67$$ −301833. −0.122604 −0.0613021 0.998119i $$-0.519525\pi$$
−0.0613021 + 0.998119i $$0.519525\pi$$
$$68$$ −1.36954e6 + 995027.i −0.528193 + 0.383755i
$$69$$ 0 0
$$70$$ 90064.8 277191.i 0.0313843 0.0965909i
$$71$$ 2.46871e6 3.39788e6i 0.818587 1.12669i −0.171354 0.985210i $$-0.554814\pi$$
0.989941 0.141479i $$-0.0451858\pi$$
$$72$$ 0 0
$$73$$ −2.18986e6 711530.i −0.658851 0.214074i −0.0395381 0.999218i $$-0.512589\pi$$
−0.619313 + 0.785145i $$0.712589\pi$$
$$74$$ 160936. + 495310.i 0.0461681 + 0.142091i
$$75$$ 0 0
$$76$$ 594068.i 0.155235i
$$77$$ 599131. + 2.35009e6i 0.149556 + 0.586634i
$$78$$ 0 0
$$79$$ 1.39018e6 + 1.91342e6i 0.317232 + 0.436632i 0.937619 0.347663i $$-0.113025\pi$$
−0.620388 + 0.784295i $$0.713025\pi$$
$$80$$ 761302. 247362.i 0.166243 0.0540155i
$$81$$ 0 0
$$82$$ 2.63565e6 + 1.91491e6i 0.527885 + 0.383531i
$$83$$ 399457. + 290223.i 0.0766826 + 0.0557132i 0.625466 0.780251i $$-0.284909\pi$$
−0.548783 + 0.835965i $$0.684909\pi$$
$$84$$ 0 0
$$85$$ −1.66328e6 + 540434.i −0.293765 + 0.0954501i
$$86$$ −2.89516e6 3.98484e6i −0.490826 0.675564i
$$87$$ 0 0
$$88$$ 3.24239e6 3.90579e6i 0.507196 0.610970i
$$89$$ 8.78877e6i 1.32149i 0.750612 + 0.660743i $$0.229759\pi$$
−0.750612 + 0.660743i $$0.770241\pi$$
$$90$$ 0 0
$$91$$ 2.09241e6 + 6.43977e6i 0.291073 + 0.895830i
$$92$$ 6.63218e6 + 2.15492e6i 0.887971 + 0.288519i
$$93$$ 0 0
$$94$$ 3.06454e6 4.21797e6i 0.380555 0.523789i
$$95$$ −189654. + 583696.i −0.0226950 + 0.0698480i
$$96$$ 0 0
$$97$$ 1.01865e7 7.40089e6i 1.13324 0.823347i 0.147077 0.989125i $$-0.453013\pi$$
0.986163 + 0.165778i $$0.0530135\pi$$
$$98$$ 2.59394e6 0.278400
$$99$$ 0 0
$$100$$ −6.89290e6 −0.689290
$$101$$ 1.73397e6 1.25980e6i 0.167462 0.121669i −0.500898 0.865507i $$-0.666997\pi$$
0.668360 + 0.743838i $$0.266997\pi$$
$$102$$ 0 0
$$103$$ 4.86869e6 1.49843e7i 0.439017 1.35116i −0.449896 0.893081i $$-0.648539\pi$$
0.888913 0.458075i $$-0.151461\pi$$
$$104$$ 8.33042e6 1.14658e7i 0.726190 0.999515i
$$105$$ 0 0
$$106$$ −2.21630e6 720119.i −0.180741 0.0587265i
$$107$$ 5.31756e6 + 1.63658e7i 0.419632 + 1.29150i 0.908041 + 0.418881i $$0.137577\pi$$
−0.488409 + 0.872615i $$0.662423\pi$$
$$108$$ 0 0
$$109$$ 5.66270e6i 0.418823i −0.977828 0.209412i $$-0.932845\pi$$
0.977828 0.209412i $$-0.0671548\pi$$
$$110$$ 1.97944e6 1.25146e6i 0.141798 0.0896486i
$$111$$ 0 0
$$112$$ −2.42269e6 3.33454e6i −0.162942 0.224271i
$$113$$ −1.14660e6 + 372554.i −0.0747548 + 0.0242893i −0.346156 0.938177i $$-0.612513\pi$$
0.271401 + 0.962466i $$0.412513\pi$$
$$114$$ 0 0
$$115$$ 5.82843e6 + 4.23460e6i 0.357363 + 0.259639i
$$116$$ 1.34408e6 + 976533.i 0.0799509 + 0.0580877i
$$117$$ 0 0
$$118$$ 7.48199e6 2.43105e6i 0.419209 0.136209i
$$119$$ 5.29306e6 + 7.28527e6i 0.287933 + 0.396306i
$$120$$ 0 0
$$121$$ −8.35733e6 + 1.76041e7i −0.428863 + 0.903369i
$$122$$ 1.06370e7i 0.530345i
$$123$$ 0 0
$$124$$ −8.27131e6 2.54565e7i −0.389581 1.19901i
$$125$$ −1.47004e7 4.77644e6i −0.673198 0.218735i
$$126$$ 0 0
$$127$$ 1.25456e7 1.72675e7i 0.543473 0.748027i −0.445635 0.895215i $$-0.647022\pi$$
0.989109 + 0.147188i $$0.0470222\pi$$
$$128$$ −7.36348e6 + 2.26625e7i −0.310347 + 0.955151i
$$129$$ 0 0
$$130$$ 5.28964e6 3.84315e6i 0.211166 0.153421i
$$131$$ 2.57846e7 1.00210 0.501051 0.865418i $$-0.332947\pi$$
0.501051 + 0.865418i $$0.332947\pi$$
$$132$$ 0 0
$$133$$ 3.16015e6 0.116474
$$134$$ 1.21411e6 882101.i 0.0435903 0.0316702i
$$135$$ 0 0
$$136$$ 5.82444e6 1.79258e7i 0.198549 0.611072i
$$137$$ −4.53268e6 + 6.23870e6i −0.150603 + 0.207287i −0.877652 0.479298i $$-0.840891\pi$$
0.727049 + 0.686585i $$0.240891\pi$$
$$138$$ 0 0
$$139$$ −1.05337e6 342260.i −0.0332681 0.0108095i 0.292336 0.956316i $$-0.405568\pi$$
−0.325604 + 0.945506i $$0.605568\pi$$
$$140$$ −1.87084e6 5.75784e6i −0.0576219 0.177342i
$$141$$ 0 0
$$142$$ 2.08825e7i 0.612031i
$$143$$ −2.01148e7 + 5.05521e7i −0.575227 + 1.44565i
$$144$$ 0 0
$$145$$ 1.00886e6 + 1.38858e6i 0.0274817 + 0.0378253i
$$146$$ 1.08880e7 3.53773e6i 0.289544 0.0940785i
$$147$$ 0 0
$$148$$ 8.75203e6 + 6.35872e6i 0.221918 + 0.161233i
$$149$$ −4.64780e7 3.37683e7i −1.15105 0.836290i −0.162434 0.986719i $$-0.551934\pi$$
−0.988621 + 0.150429i $$0.951934\pi$$
$$150$$ 0 0
$$151$$ 2.02320e7 6.57378e6i 0.478212 0.155380i −0.0599858 0.998199i $$-0.519106\pi$$
0.538197 + 0.842819i $$0.319106\pi$$
$$152$$ −3.88786e6 5.35118e6i −0.0897963 0.123594i
$$153$$ 0 0
$$154$$ −9.27806e6 7.70217e6i −0.204708 0.169938i
$$155$$ 2.76526e7i 0.596451i
$$156$$ 0 0
$$157$$ 1.06707e7 + 3.28410e7i 0.220061 + 0.677279i 0.998755 + 0.0498754i $$0.0158824\pi$$
−0.778694 + 0.627404i $$0.784118\pi$$
$$158$$ −1.11838e7 3.63385e6i −0.225575 0.0732938i
$$159$$ 0 0
$$160$$ −1.15705e7 + 1.59254e7i −0.223322 + 0.307377i
$$161$$ 1.14631e7 3.52799e7i 0.216478 0.666250i
$$162$$ 0 0
$$163$$ −5.83562e7 + 4.23983e7i −1.05543 + 0.766817i −0.973238 0.229800i $$-0.926193\pi$$
−0.0821947 + 0.996616i $$0.526193\pi$$
$$164$$ 6.76723e7 1.19800
$$165$$ 0 0
$$166$$ −2.45496e6 −0.0416549
$$167$$ −3.98206e7 + 2.89314e7i −0.661607 + 0.480686i −0.867205 0.497951i $$-0.834086\pi$$
0.205598 + 0.978636i $$0.434086\pi$$
$$168$$ 0 0
$$169$$ −2.75495e7 + 8.47888e7i −0.439047 + 1.35125i
$$170$$ 5.11106e6 7.03477e6i 0.0797884 0.109819i
$$171$$ 0 0
$$172$$ −9.73060e7 3.16166e7i −1.45811 0.473769i
$$173$$ −2.70065e6 8.31174e6i −0.0396558 0.122048i 0.929269 0.369404i $$-0.120438\pi$$
−0.968925 + 0.247356i $$0.920438\pi$$
$$174$$ 0 0
$$175$$ 3.66669e7i 0.517179i
$$176$$ 2.13589e6 3.30494e7i 0.0295314 0.456951i
$$177$$ 0 0
$$178$$ −2.56849e7 3.53523e7i −0.341357 0.469837i
$$179$$ 9.76633e6 3.17327e6i 0.127276 0.0413544i −0.244687 0.969602i $$-0.578685\pi$$
0.371962 + 0.928248i $$0.378685\pi$$
$$180$$ 0 0
$$181$$ 8.33240e7 + 6.05384e7i 1.04447 + 0.758851i 0.971153 0.238458i $$-0.0766420\pi$$
0.0733155 + 0.997309i $$0.476642\pi$$
$$182$$ −2.72367e7 1.97886e7i −0.334891 0.243313i
$$183$$ 0 0
$$184$$ −7.38435e7 + 2.39932e7i −0.873876 + 0.283940i
$$185$$ 6.56922e6 + 9.04175e6i 0.0762803 + 0.104991i
$$186$$ 0 0
$$187$$ −4.66647e6 + 7.22059e7i −0.0521846 + 0.807472i
$$188$$ 1.08300e8i 1.18870i
$$189$$ 0 0
$$190$$ −942963. 2.90214e6i −0.00997372 0.0306959i
$$191$$ −7.55063e7 2.45335e7i −0.784091 0.254767i −0.110505 0.993876i $$-0.535247\pi$$
−0.673586 + 0.739109i $$0.735247\pi$$
$$192$$ 0 0
$$193$$ 2.96666e7 4.08325e7i 0.297041 0.408842i −0.634244 0.773133i $$-0.718689\pi$$
0.931285 + 0.364291i $$0.118689\pi$$
$$194$$ −1.93455e7 + 5.95393e7i −0.190228 + 0.585461i
$$195$$ 0 0
$$196$$ 4.35911e7 3.16708e7i 0.413525 0.300444i
$$197$$ −9.93802e7 −0.926121 −0.463061 0.886327i $$-0.653249\pi$$
−0.463061 + 0.886327i $$0.653249\pi$$
$$198$$ 0 0
$$199$$ −6.47610e7 −0.582542 −0.291271 0.956641i $$-0.594078\pi$$
−0.291271 + 0.956641i $$0.594078\pi$$
$$200$$ 6.20892e7 4.51104e7i 0.548796 0.398723i
$$201$$ 0 0
$$202$$ −3.29305e6 + 1.01350e7i −0.0281105 + 0.0865153i
$$203$$ 5.19468e6 7.14987e6i 0.0435836 0.0599876i
$$204$$ 0 0
$$205$$ 6.64908e7 + 2.16042e7i 0.539042 + 0.175145i
$$206$$ 2.42072e7 + 7.45020e7i 0.192934 + 0.593790i
$$207$$ 0 0
$$208$$ 9.24643e7i 0.712447i
$$209$$ 1.95373e7 + 1.62189e7i 0.148031 + 0.122888i
$$210$$ 0 0
$$211$$ 7.03862e7 + 9.68783e7i 0.515821 + 0.709967i 0.984887 0.173196i $$-0.0554095\pi$$
−0.469066 + 0.883163i $$0.655409\pi$$
$$212$$ −4.60372e7 + 1.49584e7i −0.331843 + 0.107822i
$$213$$ 0 0
$$214$$ −6.92181e7 5.02899e7i −0.482805 0.350778i
$$215$$ −8.55136e7 6.21293e7i −0.586814 0.426345i
$$216$$ 0 0
$$217$$ −1.35416e8 + 4.39993e7i −0.899624 + 0.292305i
$$218$$ 1.65491e7 + 2.27779e7i 0.108187 + 0.148907i
$$219$$ 0 0
$$220$$ 1.79848e7 4.51989e7i 0.113874 0.286186i
$$221$$ 2.02015e8i 1.25896i
$$222$$ 0 0
$$223$$ 7.43830e7 + 2.28927e8i 0.449166 + 1.38239i 0.877850 + 0.478936i $$0.158977\pi$$
−0.428684 + 0.903455i $$0.641023\pi$$
$$224$$ 9.63978e7 + 3.13215e7i 0.573059 + 0.186198i
$$225$$ 0 0
$$226$$ 3.52337e6 4.84950e6i 0.0203038 0.0279458i
$$227$$ −5.21424e7 + 1.60478e8i −0.295870 + 0.910594i 0.687058 + 0.726602i $$0.258902\pi$$
−0.982928 + 0.183991i $$0.941098\pi$$
$$228$$ 0 0
$$229$$ 1.65121e8 1.19967e8i 0.908611 0.660145i −0.0320518 0.999486i $$-0.510204\pi$$
0.940663 + 0.339341i $$0.110204\pi$$
$$230$$ −3.58200e7 −0.194124
$$231$$ 0 0
$$232$$ −1.84980e7 −0.0972560
$$233$$ 2.22697e7 1.61799e7i 0.115337 0.0837972i −0.528622 0.848858i $$-0.677291\pi$$
0.643959 + 0.765060i $$0.277291\pi$$
$$234$$ 0 0
$$235$$ 3.45743e7 1.06409e8i 0.173786 0.534859i
$$236$$ 9.60528e7 1.32205e8i 0.475683 0.654722i
$$237$$ 0 0
$$238$$ −4.25820e7 1.38357e7i −0.204742 0.0665247i
$$239$$ −9.36313e7 2.88168e8i −0.443638 1.36538i −0.883971 0.467542i $$-0.845140\pi$$
0.440333 0.897834i $$-0.354860\pi$$
$$240$$ 0 0
$$241$$ 3.98774e8i 1.83513i −0.397582 0.917567i $$-0.630151\pi$$
0.397582 0.917567i $$-0.369849\pi$$
$$242$$ −1.78307e7 9.52356e7i −0.0808750 0.431962i
$$243$$ 0 0
$$244$$ −1.29872e8 1.78754e8i −0.572338 0.787756i
$$245$$ 5.29409e7 1.72015e7i 0.229990 0.0747284i
$$246$$ 0 0
$$247$$ 5.73537e7 + 4.16699e7i 0.242171 + 0.175947i
$$248$$ 2.41105e8 + 1.75173e8i 1.00375 + 0.729266i
$$249$$ 0 0
$$250$$ 7.30903e7 2.37485e7i 0.295849 0.0961271i
$$251$$ 1.34314e8 + 1.84868e8i 0.536122 + 0.737909i 0.988048 0.154147i $$-0.0492628\pi$$
−0.451926 + 0.892056i $$0.649263\pi$$
$$252$$ 0 0
$$253$$ 2.51937e8 1.59282e8i 0.978071 0.618365i
$$254$$ 1.06122e8i 0.406337i
$$255$$ 0 0
$$256$$ −3.49105e7 1.07443e8i −0.130052 0.400258i
$$257$$ 2.07079e7 + 6.72841e6i 0.0760975 + 0.0247256i 0.346818 0.937932i $$-0.387262\pi$$
−0.270721 + 0.962658i $$0.587262\pi$$
$$258$$ 0 0
$$259$$ 3.38253e7 4.65565e7i 0.120974 0.166506i
$$260$$ 4.19693e7 1.29168e8i 0.148090 0.455773i
$$261$$ 0 0
$$262$$ −1.03717e8 + 7.53550e7i −0.356284 + 0.258856i
$$263$$ 2.55504e8 0.866068 0.433034 0.901378i $$-0.357443\pi$$
0.433034 + 0.901378i $$0.357443\pi$$
$$264$$ 0 0
$$265$$ −5.00088e7 −0.165077
$$266$$ −1.27115e7 + 9.23546e6i −0.0414106 + 0.0300866i
$$267$$ 0 0
$$268$$ 9.63301e6 2.96474e7i 0.0305696 0.0940837i
$$269$$ −1.84859e8 + 2.54436e8i −0.579037 + 0.796977i −0.993589 0.113049i $$-0.963938\pi$$
0.414552 + 0.910026i $$0.363938\pi$$
$$270$$ 0 0
$$271$$ 1.99405e7 + 6.47907e6i 0.0608617 + 0.0197752i 0.339290 0.940682i $$-0.389813\pi$$
−0.278428 + 0.960457i $$0.589813\pi$$
$$272$$ −3.79997e7 1.16951e8i −0.114496 0.352381i
$$273$$ 0 0
$$274$$ 3.83415e7i 0.112601i
$$275$$ −1.88186e8 + 2.26689e8i −0.545660 + 0.657303i
$$276$$ 0 0
$$277$$ 3.58592e8 + 4.93560e8i 1.01373 + 1.39528i 0.916509 + 0.400014i $$0.130995\pi$$
0.0972190 + 0.995263i $$0.469005\pi$$
$$278$$ 5.23735e6 1.70172e6i 0.0146203 0.00475041i
$$279$$ 0 0
$$280$$ 5.45339e7 + 3.96212e7i 0.148461 + 0.107864i
$$281$$ 2.70813e8 + 1.96757e8i 0.728110 + 0.529003i 0.888965 0.457975i $$-0.151425\pi$$
−0.160855 + 0.986978i $$0.551425\pi$$
$$282$$ 0 0
$$283$$ 1.14375e8 3.71626e7i 0.299970 0.0974662i −0.155165 0.987889i $$-0.549591\pi$$
0.455135 + 0.890422i $$0.349591\pi$$
$$284$$ 2.54966e8 + 3.50930e8i 0.660492 + 0.909089i
$$285$$ 0 0
$$286$$ −6.68266e7 2.62128e8i −0.168915 0.662570i
$$287$$ 3.59984e8i 0.898868i
$$288$$ 0 0
$$289$$ −4.37803e7 1.34742e8i −0.106693 0.328368i
$$290$$ −8.11617e6 2.63710e6i −0.0195415 0.00634942i
$$291$$ 0 0
$$292$$ 1.39779e8 1.92389e8i 0.328550 0.452211i
$$293$$ 4.66040e7 1.43432e8i 0.108240 0.333127i −0.882238 0.470805i $$-0.843964\pi$$
0.990477 + 0.137677i $$0.0439637\pi$$
$$294$$ 0 0
$$295$$ 1.36582e8 9.92325e7i 0.309753 0.225049i
$$296$$ −1.20450e8 −0.269952
$$297$$ 0 0
$$298$$ 2.85642e8 0.625267
$$299$$ 6.73248e8 4.89143e8i 1.45655 1.05825i
$$300$$ 0 0
$$301$$ −1.68185e8 + 5.17621e8i −0.355472 + 1.09403i
$$302$$ −6.21704e7 + 8.55703e7i −0.129885 + 0.178772i
$$303$$ 0 0
$$304$$ −4.10416e7 1.33352e7i −0.0837851 0.0272234i
$$305$$ −7.05382e7 2.17094e8i −0.142356 0.438126i
$$306$$ 0 0
$$307$$ 1.90006e8i 0.374785i −0.982285 0.187393i $$-0.939996\pi$$
0.982285 0.187393i $$-0.0600036\pi$$
$$308$$ −2.49957e8 1.61541e7i −0.487459 0.0315032i
$$309$$ 0 0
$$310$$ 8.08140e7 + 1.11231e8i 0.154071 + 0.212061i
$$311$$ −6.73627e8 + 2.18875e8i −1.26987 + 0.412605i −0.865001 0.501771i $$-0.832682\pi$$
−0.404867 + 0.914376i $$0.632682\pi$$
$$312$$ 0 0
$$313$$ 7.58465e7 + 5.51057e7i 0.139807 + 0.101576i 0.655491 0.755203i $$-0.272462\pi$$
−0.515683 + 0.856779i $$0.672462\pi$$
$$314$$ −1.38899e8 1.00916e8i −0.253190 0.183953i
$$315$$ 0 0
$$316$$ −2.32312e8 + 7.54827e7i −0.414158 + 0.134568i
$$317$$ 5.07216e8 + 6.98124e8i 0.894306 + 1.23091i 0.972249 + 0.233948i $$0.0751646\pi$$
−0.0779434 + 0.996958i $$0.524835\pi$$
$$318$$ 0 0
$$319$$ 6.88108e7 1.75426e7i 0.118683 0.0302570i
$$320$$ 4.58800e6i 0.00782705i
$$321$$ 0 0
$$322$$ 5.69949e7 + 1.75412e8i 0.0951350 + 0.292796i
$$323$$ 8.96672e7 + 2.91346e7i 0.148056 + 0.0481062i
$$324$$ 0 0
$$325$$ −4.83491e8 + 6.65468e8i −0.781262 + 1.07531i
$$326$$ 1.10827e8 3.41089e8i 0.177167 0.545263i
$$327$$ 0 0
$$328$$ −6.09571e8 + 4.42880e8i −0.953819 + 0.692990i
$$329$$ −5.76101e8 −0.891893
$$330$$ 0 0
$$331$$ −8.83832e8 −1.33959 −0.669795 0.742546i $$-0.733618\pi$$
−0.669795 + 0.742546i $$0.733618\pi$$
$$332$$ −4.12556e7 + 2.99739e7i −0.0618727 + 0.0449532i
$$333$$ 0 0
$$334$$ 7.56249e7 2.32749e8i 0.111059 0.341803i
$$335$$ 1.89296e7 2.60544e7i 0.0275097 0.0378638i
$$336$$ 0 0
$$337$$ −3.32549e8 1.08052e8i −0.473316 0.153790i 0.0626392 0.998036i $$-0.480048\pi$$
−0.535955 + 0.844247i $$0.680048\pi$$
$$338$$ −1.36977e8 4.21571e8i −0.192947 0.593830i
$$339$$ 0 0
$$340$$ 1.80623e8i 0.249228i
$$341$$ −1.06301e9 4.22975e8i −1.45177 0.577663i
$$342$$ 0 0
$$343$$ −4.34417e8 5.97923e8i −0.581269 0.800048i
$$344$$ 1.08342e9 3.52024e8i 1.43497 0.466248i
$$345$$ 0 0
$$346$$ 3.51541e7 + 2.55409e7i 0.0456257 + 0.0331490i
$$347$$ −7.30955e8 5.31070e8i −0.939155 0.682336i 0.00906197 0.999959i $$-0.497115\pi$$
−0.948217 + 0.317623i $$0.897115\pi$$
$$348$$ 0 0
$$349$$ 4.54869e8 1.47796e8i 0.572793 0.186112i −0.00827654 0.999966i $$-0.502635\pi$$
0.581069 + 0.813854i $$0.302635\pi$$
$$350$$ −1.07158e8 1.47490e8i −0.133594 0.183876i
$$351$$ 0 0
$$352$$ 4.35217e8 + 6.88385e8i 0.531871 + 0.841263i
$$353$$ 3.87310e8i 0.468649i −0.972158 0.234325i $$-0.924712\pi$$
0.972158 0.234325i $$-0.0752878\pi$$
$$354$$ 0 0
$$355$$ 1.38481e8 + 4.26200e8i 0.164282 + 0.505608i
$$356$$ −8.63270e8 2.80493e8i −1.01408 0.329494i
$$357$$ 0 0
$$358$$ −3.00107e7 + 4.13062e7i −0.0345689 + 0.0475800i
$$359$$ −4.38160e8 + 1.34852e9i −0.499806 + 1.53825i 0.309524 + 0.950892i $$0.399830\pi$$
−0.809330 + 0.587354i $$0.800170\pi$$
$$360$$ 0 0
$$361$$ −6.96390e8 + 5.05957e8i −0.779072 + 0.566029i
$$362$$ −5.12088e8 −0.567368
$$363$$ 0 0
$$364$$ −6.99321e8 −0.760014
$$365$$ 1.98758e8 1.44406e8i 0.213944 0.155439i
$$366$$ 0 0
$$367$$ −3.45614e8 + 1.06369e9i −0.364972 + 1.12327i 0.585026 + 0.811015i $$0.301084\pi$$
−0.949998 + 0.312255i $$0.898916\pi$$
$$368$$ −2.97749e8 + 4.09816e8i −0.311446 + 0.428669i
$$369$$ 0 0
$$370$$ −5.28486e7 1.71716e7i −0.0542410 0.0176240i
$$371$$ 7.95713e7 + 2.44895e8i 0.0808999 + 0.248984i
$$372$$ 0 0
$$373$$ 1.48070e9i 1.47736i −0.674056 0.738680i $$-0.735449\pi$$
0.674056 0.738680i $$-0.264551\pi$$
$$374$$ −1.92249e8 3.04082e8i −0.190027 0.300566i
$$375$$ 0 0
$$376$$ 7.08763e8 + 9.75529e8i 0.687613 + 0.946418i
$$377$$ 1.88557e8 6.12658e7i 0.181237 0.0588876i
$$378$$ 0 0
$$379$$ 3.75058e8 + 2.72496e8i 0.353884 + 0.257112i 0.750497 0.660874i $$-0.229814\pi$$
−0.396613 + 0.917986i $$0.629814\pi$$
$$380$$ −5.12803e7 3.72573e7i −0.0479411 0.0348312i
$$381$$ 0 0
$$382$$ 3.75418e8 1.21981e8i 0.344583 0.111962i
$$383$$ −2.12243e8 2.92127e8i −0.193035 0.265690i 0.701518 0.712652i $$-0.252506\pi$$
−0.894553 + 0.446961i $$0.852506\pi$$
$$384$$ 0 0
$$385$$ −2.40436e8 9.56701e7i −0.214727 0.0854405i
$$386$$ 2.50946e8i 0.222088i
$$387$$ 0 0
$$388$$ 4.01846e8 + 1.23676e9i 0.349260 + 1.07491i
$$389$$ 1.68289e9 + 5.46804e8i 1.44955 + 0.470987i 0.924860 0.380308i $$-0.124182\pi$$
0.524688 + 0.851295i $$0.324182\pi$$
$$390$$ 0 0
$$391$$ 6.50518e8 8.95362e8i 0.550352 0.757495i
$$392$$ −1.85387e8 + 5.70562e8i −0.155445 + 0.478412i
$$393$$ 0 0
$$394$$ 3.99751e8 2.90436e8i 0.329270 0.239229i
$$395$$ −2.52353e8 −0.206025
$$396$$ 0 0
$$397$$ 1.09879e8 0.0881347 0.0440674 0.999029i $$-0.485968\pi$$
0.0440674 + 0.999029i $$0.485968\pi$$
$$398$$ 2.60497e8 1.89262e8i 0.207115 0.150478i
$$399$$ 0 0
$$400$$ 1.54727e8 4.76201e8i 0.120881 0.372032i
$$401$$ 1.08934e9 1.49935e9i 0.843643 1.16118i −0.141585 0.989926i $$-0.545220\pi$$
0.985228 0.171249i $$-0.0547802\pi$$
$$402$$ 0 0
$$403$$ −3.03785e9 9.87056e8i −2.31205 0.751232i
$$404$$ 6.84036e7 + 2.10525e8i 0.0516112 + 0.158843i
$$405$$ 0 0
$$406$$ 4.39412e7i 0.0325860i
$$407$$ 4.48063e8 1.14229e8i 0.329427 0.0839838i
$$408$$ 0 0
$$409$$ 9.76214e8 + 1.34364e9i 0.705527 + 0.971074i 0.999882 + 0.0153779i $$0.00489513\pi$$
−0.294355 + 0.955696i $$0.595105\pi$$
$$410$$ −3.30593e8 + 1.07416e8i −0.236892 + 0.0769708i
$$411$$ 0 0
$$412$$ 1.31644e9 + 9.56447e8i 0.927384 + 0.673784i
$$413$$ −7.03268e8 5.10954e8i −0.491242 0.356908i
$$414$$ 0 0
$$415$$ −5.01043e7 + 1.62799e7i −0.0344118 + 0.0111811i
$$416$$ 1.33652e9 + 1.83956e9i 0.910224 + 1.25282i
$$417$$ 0 0
$$418$$ −1.25987e8 8.14218e6i −0.0843739 0.00545285i
$$419$$ 3.09054e8i 0.205251i −0.994720 0.102626i $$-0.967276\pi$$
0.994720 0.102626i $$-0.0327243\pi$$
$$420$$ 0 0
$$421$$ −1.76149e8 5.42132e8i −0.115052 0.354093i 0.876906 0.480662i $$-0.159604\pi$$
−0.991958 + 0.126569i $$0.959604\pi$$
$$422$$ −5.66249e8 1.83985e8i −0.366787 0.119176i
$$423$$ 0 0
$$424$$ 3.16794e8 4.36030e8i 0.201835 0.277802i
$$425$$ −3.38046e8 + 1.04040e9i −0.213606 + 0.657413i
$$426$$ 0 0
$$427$$ −9.50884e8 + 6.90858e8i −0.591058 + 0.429429i
$$428$$ −1.77722e9 −1.09569
$$429$$ 0 0
$$430$$ 5.25545e8 0.318765
$$431$$ 1.49843e9 1.08867e9i 0.901498 0.654977i −0.0373521 0.999302i $$-0.511892\pi$$
0.938850 + 0.344325i $$0.111892\pi$$
$$432$$ 0 0
$$433$$ 6.58379e8 2.02628e9i 0.389734 1.19948i −0.543254 0.839569i $$-0.682808\pi$$
0.932987 0.359909i $$-0.117192\pi$$
$$434$$ 4.16116e8 5.72735e8i 0.244343 0.336310i
$$435$$ 0 0
$$436$$ 5.56214e8 + 1.80725e8i 0.321395 + 0.104428i
$$437$$ −1.20017e8 3.69375e8i −0.0687952 0.211730i
$$438$$ 0 0
$$439$$ 2.61260e8i 0.147383i −0.997281 0.0736914i $$-0.976522\pi$$
0.997281 0.0736914i $$-0.0234780\pi$$
$$440$$ 1.33802e8 + 5.24839e8i 0.0748821 + 0.293725i
$$441$$ 0 0
$$442$$ −5.90384e8 8.12593e8i −0.325204 0.447605i
$$443$$ 3.00676e9 9.76957e8i 1.64318 0.533903i 0.665938 0.746007i $$-0.268032\pi$$
0.977247 + 0.212104i $$0.0680317\pi$$
$$444$$ 0 0
$$445$$ −7.58651e8 5.51192e8i −0.408114 0.296513i
$$446$$ −9.68236e8 7.03465e8i −0.516784 0.375466i
$$447$$ 0 0
$$448$$ 2.24676e7 7.30018e6i 0.0118055 0.00383584i
$$449$$ 1.98044e9 + 2.72584e9i 1.03252 + 1.42115i 0.903036 + 0.429564i $$0.141333\pi$$
0.129486 + 0.991581i $$0.458667\pi$$
$$450$$ 0 0
$$451$$ 1.84755e9 2.22556e9i 0.948369 1.14241i
$$452$$ 1.24514e8i 0.0634213i
$$453$$ 0 0
$$454$$ −2.59253e8 7.97898e8i −0.130025 0.400177i
$$455$$ −6.87111e8 2.23256e8i −0.341969 0.111113i
$$456$$ 0 0
$$457$$ 2.07094e9 2.85040e9i 1.01499 1.39701i 0.0993250 0.995055i $$-0.468332\pi$$
0.915660 0.401953i $$-0.131668\pi$$
$$458$$ −3.13588e8 + 9.65124e8i −0.152521 + 0.469412i
$$459$$ 0 0
$$460$$ −6.01955e8 + 4.37346e8i −0.288344 + 0.209494i
$$461$$ 3.06840e9 1.45868 0.729338 0.684153i $$-0.239828\pi$$
0.729338 + 0.684153i $$0.239828\pi$$
$$462$$ 0 0
$$463$$ 9.23554e8 0.432443 0.216221 0.976344i $$-0.430627\pi$$
0.216221 + 0.976344i $$0.430627\pi$$
$$464$$ −9.76355e7 + 7.09364e7i −0.0453727 + 0.0329652i
$$465$$ 0 0
$$466$$ −4.22932e7 + 1.30165e8i −0.0193607 + 0.0595860i
$$467$$ 9.89025e8 1.36128e9i 0.449364 0.618496i −0.522897 0.852396i $$-0.675149\pi$$
0.972261 + 0.233900i $$0.0751487\pi$$
$$468$$ 0 0
$$469$$ −1.57709e8 5.12429e7i −0.0705916 0.0229366i
$$470$$ 1.71904e8 + 5.29065e8i 0.0763735 + 0.235053i
$$471$$ 0 0
$$472$$ 1.81948e9i 0.796435i
$$473$$ −3.69637e9 + 2.33696e9i −1.60606 + 1.01540i
$$474$$ 0 0
$$475$$ 2.25648e8 + 3.10578e8i 0.0966060 + 0.132967i
$$476$$ −8.84518e8 + 2.87397e8i −0.375909 + 0.122140i
$$477$$ 0 0
$$478$$ 1.21879e9 + 8.85502e8i 0.510424 + 0.370845i
$$479$$ −1.50652e9 1.09455e9i −0.626328 0.455054i 0.228798 0.973474i $$-0.426520\pi$$
−0.855126 + 0.518420i $$0.826520\pi$$
$$480$$ 0 0
$$481$$ 1.22779e9 3.98934e8i 0.503057 0.163453i
$$482$$ 1.16541e9 + 1.60405e9i 0.474038 + 0.652458i
$$483$$ 0 0
$$484$$ −1.46243e9 1.38273e9i −0.586294 0.554342i
$$485$$ 1.34345e9i 0.534719i
$$486$$ 0 0
$$487$$ 3.01827e8 + 9.28929e8i 0.118415 + 0.364444i 0.992644 0.121070i $$-0.0386324\pi$$
−0.874229 + 0.485514i $$0.838632\pi$$
$$488$$ 2.33970e9 + 7.60215e8i 0.911363 + 0.296120i
$$489$$ 0 0
$$490$$ −1.62681e8 + 2.23911e8i −0.0624668 + 0.0859782i
$$491$$ −9.38771e8 + 2.88924e9i −0.357910 + 1.10153i 0.596392 + 0.802693i $$0.296600\pi$$
−0.954303 + 0.298842i $$0.903400\pi$$
$$492$$ 0 0
$$493$$ 2.13313e8 1.54981e8i 0.0801776 0.0582524i
$$494$$ −3.52481e8 −0.131550
$$495$$ 0 0
$$496$$ 1.94435e9 0.715464
$$497$$ 1.86678e9 1.35629e9i 0.682095 0.495571i
$$498$$ 0 0
$$499$$ 4.17712e8 1.28558e9i 0.150496 0.463179i −0.847181 0.531305i $$-0.821702\pi$$
0.997677 + 0.0681259i $$0.0217020\pi$$
$$500$$ 9.38324e8 1.29149e9i 0.335705 0.462058i
$$501$$ 0 0
$$502$$ −1.08054e9 3.51089e8i −0.381223 0.123867i
$$503$$ −1.03043e9 3.17133e9i −0.361018 1.11110i −0.952437 0.304735i $$-0.901432\pi$$
0.591419 0.806365i $$-0.298568\pi$$
$$504$$ 0 0
$$505$$ 2.28687e8i 0.0790171i
$$506$$ −5.47905e8 + 1.37698e9i −0.188009 + 0.472500i
$$507$$ 0 0
$$508$$ 1.29570e9 + 1.78337e9i 0.438511 + 0.603559i
$$509$$ −6.82900e8 + 2.21888e8i −0.229533 + 0.0745798i −0.421525 0.906817i $$-0.638505\pi$$
0.191992 + 0.981396i $$0.438505\pi$$
$$510$$ 0 0
$$511$$ −1.02342e9 7.43556e8i −0.339297 0.246513i
$$512$$ −2.01314e9 1.46263e9i −0.662870 0.481603i
$$513$$ 0 0
$$514$$ −1.02960e8 + 3.34537e7i −0.0334424 + 0.0108661i
$$515$$ 9.88109e8 + 1.36002e9i 0.318772 + 0.438751i
$$516$$ 0 0
$$517$$ −3.56168e9 2.95672e9i −1.13354 0.941009i
$$518$$ 2.86124e8i 0.0904484i
$$519$$ 0 0
$$520$$ 4.67291e8 + 1.43817e9i 0.145739 + 0.448538i
$$521$$ −3.65924e9 1.18896e9i −1.13360 0.368328i −0.318655 0.947871i $$-0.603231\pi$$
−0.814942 + 0.579543i $$0.803231\pi$$
$$522$$ 0 0
$$523$$ 3.37554e8 4.64604e8i 0.103178 0.142013i −0.754306 0.656523i $$-0.772026\pi$$
0.857484 + 0.514511i $$0.172026\pi$$
$$524$$ −8.22917e8 + 2.53268e9i −0.249860 + 0.768990i
$$525$$ 0 0
$$526$$ −1.02775e9 + 7.46703e8i −0.307919 + 0.223716i
$$527$$ −4.24798e9 −1.26429
$$528$$ 0 0
$$529$$ −1.15423e9 −0.338998
$$530$$ 2.01158e8 1.46149e8i 0.0586909 0.0426414i
$$531$$ 0 0
$$532$$ −1.00856e8 + 3.10404e8i −0.0290410 + 0.0893791i
$$533$$ 4.74676e9 6.53335e9i 1.35785 1.86892i
$$534$$ 0 0
$$535$$ −1.74619e9 5.67373e8i −0.493009 0.160188i
$$536$$ 1.07255e8 + 3.30097e8i 0.0300844 + 0.0925903i
$$537$$ 0 0
$$538$$ 1.56370e9i 0.432927i
$$539$$ 1.48530e8 2.29825e9i 0.0408557 0.632174i
$$540$$ 0 0
$$541$$ 2.27912e9 + 3.13694e9i 0.618838 + 0.851757i 0.997268 0.0738729i $$-0.0235359\pi$$
−0.378430 + 0.925630i $$0.623536\pi$$
$$542$$ −9.91445e7 + 3.22140e7i −0.0267468 + 0.00869055i
$$543$$ 0 0
$$544$$ 2.44646e9 + 1.77746e9i 0.651541 + 0.473372i
$$545$$ 4.88807e8 + 3.55139e8i 0.129345 + 0.0939747i
$$546$$ 0 0
$$547$$ −2.61894e9 + 8.50944e8i −0.684178 + 0.222303i −0.630424 0.776251i $$-0.717119\pi$$
−0.0537544 + 0.998554i $$0.517119\pi$$
$$548$$ −4.68132e8 6.44328e8i −0.121517 0.167253i
$$549$$ 0 0
$$550$$ 9.44728e7 1.46181e9i 0.0242124 0.374646i
$$551$$ 9.25294e7i 0.0235640i
$$552$$ 0 0
$$553$$ 4.01531e8 + 1.23579e9i 0.100967 + 0.310746i
$$554$$ −2.88483e9 9.37339e8i −0.720836 0.234214i
$$555$$ 0 0
$$556$$ 6.72364e7 9.25430e7i 0.0165899 0.0228340i
$$557$$ −1.38404e9 + 4.25964e9i −0.339357 + 1.04443i 0.625180 + 0.780481i $$0.285026\pi$$
−0.964536 + 0.263951i $$0.914974\pi$$
$$558$$ 0 0
$$559$$ −9.87776e9 + 7.17661e9i −2.39176 + 1.73771i
$$560$$ 4.39780e8 0.105822
$$561$$ 0 0
$$562$$ −1.66435e9 −0.395518
$$563$$ 4.16183e9 3.02375e9i 0.982891 0.714112i 0.0245382 0.999699i $$-0.492188\pi$$
0.958353 + 0.285587i $$0.0921885\pi$$
$$564$$ 0 0
$$565$$ 3.97508e7 1.22340e8i 0.00927206 0.0285365i
$$566$$ −3.51459e8 + 4.83742e8i −0.0814737 + 0.112139i
$$567$$ 0 0
$$568$$ −4.59331e9 1.49246e9i −1.05173 0.341729i
$$569$$ 4.50072e8 + 1.38518e9i 0.102421 + 0.315219i 0.989116 0.147135i $$-0.0470050\pi$$
−0.886696 + 0.462354i $$0.847005\pi$$
$$570$$ 0 0
$$571$$ 6.99471e8i 0.157233i −0.996905 0.0786165i $$-0.974950\pi$$
0.996905 0.0786165i $$-0.0250502\pi$$
$$572$$ −4.32348e9 3.58913e9i −0.965933 0.801868i
$$573$$ 0 0
$$574$$ 1.05204e9 + 1.44801e9i 0.232189 + 0.319581i
$$575$$ 4.28581e9 1.39255e9i 0.940147 0.305472i
$$576$$ 0 0
$$577$$ 6.56396e9 + 4.76900e9i 1.42250 + 1.03350i 0.991353 + 0.131219i $$0.0418891\pi$$
0.431142 + 0.902284i $$0.358111\pi$$
$$578$$ 5.69884e8 + 4.14045e8i 0.122755 + 0.0891867i
$$579$$ 0 0
$$580$$ −1.68590e8 + 5.47781e7i −0.0358784 + 0.0116576i
$$581$$ 1.59447e8 + 2.19459e8i 0.0337286 + 0.0464235i
$$582$$ 0 0
$$583$$ −7.64936e8 + 1.92242e9i −0.159877 + 0.401799i
$$584$$ 2.64776e9i 0.550091i
$$585$$ 0 0
$$586$$ 2.31715e8 + 7.13147e8i 0.0475678 + 0.146399i
$$587$$ 1.01774e9 + 3.30682e8i 0.207683 + 0.0674804i 0.411011 0.911630i $$-0.365176\pi$$
−0.203328 + 0.979111i $$0.565176\pi$$
$$588$$ 0 0
$$589$$ −8.76237e8 + 1.20604e9i −0.176693 + 0.243196i
$$590$$ −2.59388e8 + 7.98314e8i −0.0519957 + 0.160026i
$$591$$ 0 0
$$592$$ −6.35756e8 + 4.61904e8i −0.125940 + 0.0915009i
$$593$$ −9.77682e9 −1.92534 −0.962668 0.270686i $$-0.912749\pi$$
−0.962668 + 0.270686i $$0.912749\pi$$
$$594$$ 0 0
$$595$$ −9.60825e8 −0.186997
$$596$$ 4.80021e9 3.48756e9i 0.928749 0.674776i
$$597$$ 0 0
$$598$$ −1.27859e9 + 3.93510e9i −0.244499 + 0.752491i
$$599$$ 1.23412e9 1.69863e9i 0.234620 0.322927i −0.675431 0.737423i $$-0.736042\pi$$
0.910051 + 0.414497i $$0.136042\pi$$
$$600$$ 0 0
$$601$$ 4.23944e9 + 1.37748e9i 0.796614 + 0.258836i 0.678918 0.734214i $$-0.262449\pi$$
0.117696 + 0.993050i $$0.462449\pi$$
$$602$$ −8.36218e8 2.57362e9i −0.156218 0.480791i
$$603$$ 0 0
$$604$$ 2.19708e9i 0.405710i
$$605$$ −9.95462e8 1.82546e9i −0.182760 0.335142i
$$606$$ 0 0
$$607$$ −2.67567e8 3.68275e8i −0.0485593 0.0668362i 0.784047 0.620702i $$-0.213152\pi$$
−0.832606 + 0.553865i $$0.813152\pi$$
$$608$$ 1.00927e9 3.27931e8i 0.182114 0.0591725i
$$609$$ 0 0
$$610$$ 9.18189e8 + 6.67103e8i 0.163786 + 0.118998i
$$611$$ −1.04557e10 7.59648e9i −1.85442 1.34731i
$$612$$ 0 0
$$613$$ 7.20021e9 2.33949e9i 1.26251 0.410213i 0.400119 0.916463i $$-0.368969\pi$$
0.862387 + 0.506250i $$0.168969\pi$$
$$614$$ 5.55287e8 + 7.64287e8i 0.0968118 + 0.133250i
$$615$$ 0 0
$$616$$ 2.35726e9 1.49033e9i 0.406326 0.256891i
$$617$$ 1.06436e10i 1.82428i 0.409880 + 0.912140i $$0.365571\pi$$
−0.409880 + 0.912140i $$0.634429\pi$$
$$618$$ 0 0
$$619$$ 4.81512e8 + 1.48194e9i 0.0815999 + 0.251139i 0.983530 0.180742i $$-0.0578500\pi$$
−0.901931 + 0.431881i $$0.857850\pi$$
$$620$$ 2.71616e9 + 8.82533e8i 0.457703 + 0.148717i
$$621$$ 0 0
$$622$$ 2.06997e9 2.84907e9i 0.344904 0.474719i
$$623$$ −1.49209e9 + 4.59217e9i −0.247222 + 0.760870i
$$624$$ 0 0
$$625$$ −2.88405e9 + 2.09539e9i −0.472523 + 0.343308i
$$626$$ −4.66133e8 −0.0759451
$$627$$ 0 0
$$628$$ −3.56634e9 −0.574598
$$629$$ 1.38899e9 1.00916e9i 0.222547 0.161690i
$$630$$ 0 0
$$631$$ −1.25665e9 + 3.86758e9i −0.199119 + 0.612825i 0.800785 + 0.598952i $$0.204416\pi$$
−0.999904 + 0.0138730i $$0.995584\pi$$
$$632$$ 1.59860e9 2.20028e9i 0.251901 0.346712i
$$633$$ 0 0
$$634$$ −4.08050e9 1.32583e9i −0.635917 0.206622i
$$635$$ 7.03738e8 + 2.16588e9i 0.109069 + 0.335681i
$$636$$ 0 0
$$637$$ 6.42996e9i 0.985644i
$$638$$ −2.25520e8 + 2.71662e8i −0.0343805 + 0.0414149i
$$639$$ 0 0
$$640$$ −1.49443e9 2.05691e9i −0.225344 0.310159i
$$641$$ 8.39651e9 2.72819e9i 1.25920 0.409140i 0.397992 0.917389i $$-0.369707\pi$$
0.861210 + 0.508249i $$0.169707\pi$$
$$642$$ 0 0
$$643$$ −3.09641e9 2.24967e9i −0.459324 0.333719i 0.333942 0.942594i $$-0.391621\pi$$
−0.793266 + 0.608875i $$0.791621\pi$$
$$644$$ 3.09950e9 + 2.25192e9i 0.457289 + 0.332240i
$$645$$ 0 0
$$646$$ −4.45826e8 + 1.44858e8i −0.0650657 + 0.0211411i
$$647$$ 7.27301e9 + 1.00104e10i 1.05572 + 1.45308i 0.883742 + 0.467975i $$0.155016\pi$$
0.171980 + 0.985101i $$0.444984\pi$$
$$648$$ 0 0
$$649$$ −1.72550e9 6.76830e9i −0.247776 0.971903i
$$650$$ 4.08980e9i 0.584124i
$$651$$ 0 0
$$652$$ −2.30210e9 7.08514e9i −0.325280 1.00111i
$$653$$ −5.23074e9 1.69957e9i −0.735135 0.238860i −0.0825623 0.996586i $$-0.526310\pi$$
−0.652573 + 0.757726i $$0.726310\pi$$
$$654$$ 0 0
$$655$$ −1.61710e9 + 2.22574e9i −0.224849 + 0.309479i
$$656$$ −1.51906e9 + 4.67519e9i −0.210093 + 0.646600i
$$657$$ 0 0
$$658$$ 2.31733e9 1.68364e9i 0.317101 0.230387i
$$659$$ −9.55087e9 −1.30000 −0.650001 0.759934i $$-0.725231\pi$$
−0.650001 + 0.759934i $$0.725231\pi$$
$$660$$ 0 0
$$661$$ 1.04063e10 1.40149 0.700744 0.713412i $$-0.252851\pi$$
0.700744 + 0.713412i $$0.252851\pi$$
$$662$$ 3.55516e9 2.58298e9i 0.476273 0.346033i
$$663$$ 0 0
$$664$$ 1.75454e8 5.39992e8i 0.0232581 0.0715812i
$$665$$ −1.98191e8 + 2.72786e8i −0.0261341 + 0.0359705i
$$666$$ 0 0
$$667$$ −1.03300e9 3.35642e8i −0.134790 0.0437961i
$$668$$ −1.57089e9 4.83469e9i −0.203905 0.627554i
$$669$$ 0 0
$$670$$ 1.60124e8i 0.0205681i
$$671$$ −9.42443e9 6.09075e8i −1.20428 0.0778291i
$$672$$ 0 0
$$673$$ 3.45295e9 + 4.75258e9i 0.436654 + 0.601003i 0.969464 0.245232i $$-0.0788640\pi$$
−0.532810 + 0.846235i $$0.678864\pi$$
$$674$$ 1.65344e9 5.37234e8i 0.208007 0.0675856i
$$675$$ 0 0
$$676$$ −7.44907e9 5.41207e9i −0.927446 0.673829i
$$677$$ 6.62226e9 + 4.81136e9i 0.820250 + 0.595946i 0.916784 0.399383i $$-0.130776\pi$$
−0.0965344 + 0.995330i $$0.530776\pi$$
$$678$$ 0 0
$$679$$ 6.57894e9 2.13763e9i 0.806514 0.262052i
$$680$$ 1.18208e9 + 1.62700e9i 0.144167 + 0.198429i
$$681$$ 0 0
$$682$$ 5.51204e9 1.40523e9i 0.665376 0.169630i
$$683$$ 1.49778e10i 1.79877i −0.437162 0.899383i $$-0.644016\pi$$
0.437162 0.899383i $$-0.355984\pi$$
$$684$$ 0 0
$$685$$ −2.54259e8 7.82528e8i −0.0302245 0.0930214i
$$686$$ 3.49483e9 + 1.13554e9i 0.413325 + 0.134297i
$$687$$ 0 0
$$688$$ 4.36852e9 6.01275e9i 0.511416 0.703904i
$$689$$ −1.78506e9 + 5.49384e9i −0.207915 + 0.639895i
$$690$$ 0 0
$$691$$ −1.08108e10 + 7.85450e9i −1.24648 + 0.905619i −0.998012 0.0630218i $$-0.979926\pi$$
−0.248465 + 0.968641i $$0.579926\pi$$
$$692$$ 9.02606e8 0.103544
$$693$$ 0 0
$$694$$ 4.49226e9 0.510161
$$695$$ 9.56065e7 6.94622e7i 0.0108029 0.00784877i
$$696$$ 0 0
$$697$$ 3.31882e9 1.02143e10i 0.371253 1.14260i
$$698$$ −1.39775e9 + 1.92384e9i −0.155574 + 0.214129i
$$699$$ 0 0
$$700$$ −3.60158e9 1.17022e9i −0.396871 0.128951i
$$701$$ 1.57726e9 + 4.85432e9i 0.172938 + 0.532249i 0.999533 0.0305480i $$-0.00972525\pi$$
−0.826595 + 0.562797i $$0.809725\pi$$
$$702$$ 0 0
$$703$$ 6.02507e8i 0.0654061i
$$704$$ 1.76370e8 + 7.01782e7i 0.0190512 + 0.00758050i
$$705$$ 0 0
$$706$$ 1.13191e9 + 1.55793e9i 0.121058 + 0.166622i
$$707$$ 1.11989e9 3.63874e8i 0.119181 0.0387242i
$$708$$ 0 0
$$709$$ 6.79294e9 + 4.93536e9i 0.715807 + 0.520064i 0.885042 0.465512i $$-0.154130\pi$$
−0.169235 + 0.985576i $$0.554130\pi$$
$$710$$ −1.80259e9 1.30966e9i −0.189013 0.137326i
$$711$$ 0 0
$$712$$ 9.61176e9 3.12305e9i 0.997982 0.324264i
$$713$$ 1.02857e10 + 1.41571e10i 1.06273 + 1.46272i
$$714$$ 0 0
$$715$$ −3.10217e9 4.90672e9i −0.317391 0.502019i
$$716$$ 1.06057e9i 0.107980i
$$717$$ 0 0
$$718$$ −2.17853e9 6.70484e9i −0.219649 0.676010i
$$719$$ 1.59643e10 + 5.18710e9i 1.60176 + 0.520443i 0.967542 0.252711i $$-0.0813221\pi$$
0.634218 + 0.773154i $$0.281322\pi$$
$$720$$ 0 0
$$721$$ 5.08783e9 7.00280e9i 0.505544 0.695822i
$$722$$ 1.32254e9 4.07037e9i 0.130776 0.402488i
$$723$$ 0 0
$$724$$ −8.60563e9 + 6.25236e9i −0.842748 + 0.612292i
$$725$$ 1.07361e9 0.104632
$$726$$ 0 0
$$727$$ 6.26269e9 0.604492 0.302246 0.953230i $$-0.402264\pi$$
0.302246 + 0.953230i $$0.402264\pi$$
$$728$$ 6.29927e9 4.57669e9i 0.605105 0.439634i
$$729$$ 0 0
$$730$$ −3.77469e8 + 1.16173e9i −0.0359130 + 0.110529i
$$731$$ −9.54428e9 + 1.31366e10i −0.903717 + 1.24386i
$$732$$ 0 0
$$733$$ 2.88905e9 + 9.38708e8i 0.270951 + 0.0880373i 0.441341 0.897339i $$-0.354503\pi$$
−0.170390 + 0.985377i $$0.554503\pi$$
$$734$$ −1.71840e9 5.28868e9i −0.160394 0.493641i
$$735$$ 0 0
$$736$$ 1.24570e10i 1.15171i
$$737$$ −7.12027e8 1.12622e9i −0.0655180 0.103630i
$$738$$ 0 0
$$739$$ 4.99971e9 + 6.88151e9i 0.455711 + 0.627232i 0.973612 0.228208i $$-0.0732866\pi$$
−0.517901 + 0.855440i $$0.673287\pi$$
$$740$$ −1.09778e9 + 3.56689e8i −0.0995870 + 0.0323578i
$$741$$ 0 0
$$742$$ −1.03577e9 7.52532e8i −0.0930787 0.0676256i
$$743$$ −3.09446e9 2.24826e9i −0.276773 0.201088i 0.440735 0.897637i $$-0.354718\pi$$
−0.717509 + 0.696549i $$0.754718\pi$$
$$744$$ 0 0
$$745$$ 5.82979e9 1.89421e9i 0.516543 0.167835i
$$746$$ 4.32731e9 + 5.95603e9i 0.381621 + 0.525256i
$$747$$ 0 0
$$748$$ −6.94344e9 2.76281e9i −0.606624 0.241377i
$$749$$ 9.45397e9i 0.822106i
$$750$$ 0 0
$$751$$ 6.62110e9 + 2.03776e10i 0.570414 + 1.75555i 0.651289 + 0.758830i $$0.274229\pi$$
−0.0808748 + 0.996724i $$0.525771\pi$$
$$752$$ 7.48195e9 + 2.43103e9i 0.641582 + 0.208463i
$$753$$ 0 0
$$754$$ −5.79411e8 + 7.97491e8i −0.0492251 + 0.0677526i
$$755$$ −7.01410e8 + 2.15872e9i −0.0593141 + 0.182550i
$$756$$ 0 0
$$757$$ 4.48701e9 3.26000e9i 0.375942 0.273138i −0.383728 0.923446i $$-0.625360\pi$$
0.759671 + 0.650308i $$0.225360\pi$$
$$758$$ −2.30501e9 −0.192234
$$759$$ 0 0
$$760$$ 7.05746e8 0.0583178
$$761$$ 2.82352e9 2.05140e9i 0.232244 0.168735i −0.465577 0.885007i $$-0.654153\pi$$
0.697821 + 0.716272i $$0.254153\pi$$
$$762$$ 0 0
$$763$$ 9.61369e8 2.95879e9i 0.0783527 0.241145i
$$764$$ 4.81957e9 6.63357e9i 0.391004 0.538171i
$$765$$ 0 0
$$766$$ 1.70747e9 + 5.54790e8i 0.137262 + 0.0445993i
$$767$$ −6.02616e9 1.85466e10i −0.482233 1.48416i
$$768$$ 0 0
$$769$$ 8.62193e9i 0.683695i 0.939755 + 0.341848i $$0.111053\pi$$
−0.939755 + 0.341848i $$0.888947\pi$$
$$770$$ 1.24673e9 3.17841e8i 0.0984138 0.0250895i
$$771$$ 0 0
$$772$$ 3.06394e9 + 4.21715e9i 0.239673 + 0.329882i
$$773$$ −1.28237e10 + 4.16667e9i −0.998584 + 0.324459i −0.762299 0.647225i $$-0.775930\pi$$