Properties

 Label 99.8.j.a.62.4 Level $99$ Weight $8$ Character 99.62 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 62.4 Character $$\chi$$ $$=$$ 99.62 Dual form 99.8.j.a.8.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-14.7879 - 10.7440i) q^{2} +(63.6930 + 196.027i) q^{4} +(194.917 + 268.280i) q^{5} +(-72.5991 + 23.5889i) q^{7} +(441.228 - 1357.96i) q^{8} +O(q^{10})$$ $$q+(-14.7879 - 10.7440i) q^{2} +(63.6930 + 196.027i) q^{4} +(194.917 + 268.280i) q^{5} +(-72.5991 + 23.5889i) q^{7} +(441.228 - 1357.96i) q^{8} -6061.48i q^{10} +(4373.83 + 597.324i) q^{11} +(5506.28 - 7578.75i) q^{13} +(1327.03 + 431.177i) q^{14} +(229.262 - 166.569i) q^{16} +(-9949.29 + 7228.58i) q^{17} +(-20612.9 - 6697.54i) q^{19} +(-40175.3 + 55296.5i) q^{20} +(-58261.9 - 55825.6i) q^{22} +88301.0i q^{23} +(-9839.67 + 30283.4i) q^{25} +(-162852. + 52913.9i) q^{26} +(-9248.11 - 12728.9i) q^{28} +(21088.6 + 64904.1i) q^{29} +(39589.7 + 28763.6i) q^{31} -187944. q^{32} +224793. q^{34} +(-20479.2 - 14879.0i) q^{35} +(12353.9 + 38021.3i) q^{37} +(232862. + 320508. i) q^{38} +(450317. - 146317. i) q^{40} +(129634. - 398974. i) q^{41} -273270. i q^{43} +(161491. + 895433. i) q^{44} +(948707. - 1.30578e6i) q^{46} +(1.12068e6 + 364132. i) q^{47} +(-661546. + 480641. i) q^{49} +(470873. - 342109. i) q^{50} +(1.83635e6 + 596666. i) q^{52} +(431286. - 593614. i) q^{53} +(692283. + 1.28984e6i) q^{55} +108995. i q^{56} +(385475. - 1.18637e6i) q^{58} +(-1.86916e6 + 607326. i) q^{59} +(1.39569e6 + 1.92100e6i) q^{61} +(-276411. - 850705. i) q^{62} +(2.74995e6 + 1.99795e6i) q^{64} +3.10649e6 q^{65} -369220. q^{67} +(-2.05070e6 - 1.48992e6i) q^{68} +(142984. + 440058. i) q^{70} +(2.08693e6 + 2.87241e6i) q^{71} +(-1.18339e6 + 384506. i) q^{73} +(225814. - 694984. i) q^{74} -4.46727e6i q^{76} +(-331626. + 59808.5i) q^{77} +(2.54246e6 - 3.49939e6i) q^{79} +(89374.2 + 29039.4i) q^{80} +(-6.20360e6 + 4.50718e6i) q^{82} +(-2.09707e6 + 1.52361e6i) q^{83} +(-3.87857e6 - 1.26022e6i) q^{85} +(-2.93601e6 + 4.04107e6i) q^{86} +(2.74100e6 - 5.67593e6i) q^{88} +6.18536e6i q^{89} +(-220977. + 680097. i) q^{91} +(-1.73094e7 + 5.62416e6i) q^{92} +(-1.26603e7 - 1.74254e7i) q^{94} +(-2.22099e6 - 6.83550e6i) q^{95} +(-7.39031e6 - 5.36938e6i) q^{97} +1.49469e7 q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$112 q - 1792 q^{4}+O(q^{10})$$ 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −14.7879 10.7440i −1.30708 0.949646i −0.307077 0.951685i $$-0.599351\pi$$
−0.999998 + 0.00203905i $$0.999351\pi$$
$$3$$ 0 0
$$4$$ 63.6930 + 196.027i 0.497601 + 1.53146i
$$5$$ 194.917 + 268.280i 0.697356 + 0.959828i 0.999977 + 0.00671741i $$0.00213823\pi$$
−0.302621 + 0.953111i $$0.597862\pi$$
$$6$$ 0 0
$$7$$ −72.5991 + 23.5889i −0.0799997 + 0.0259935i −0.348743 0.937218i $$-0.613392\pi$$
0.268744 + 0.963212i $$0.413392\pi$$
$$8$$ 441.228 1357.96i 0.304683 0.937719i
$$9$$ 0 0
$$10$$ 6061.48i 1.91681i
$$11$$ 4373.83 + 597.324i 0.990803 + 0.135312i
$$12$$ 0 0
$$13$$ 5506.28 7578.75i 0.695115 0.956744i −0.304876 0.952392i $$-0.598615\pi$$
0.999991 0.00435150i $$-0.00138513\pi$$
$$14$$ 1327.03 + 431.177i 0.129250 + 0.0419959i
$$15$$ 0 0
$$16$$ 229.262 166.569i 0.0139931 0.0101665i
$$17$$ −9949.29 + 7228.58i −0.491157 + 0.356847i −0.805629 0.592420i $$-0.798173\pi$$
0.314472 + 0.949267i $$0.398173\pi$$
$$18$$ 0 0
$$19$$ −20612.9 6697.54i −0.689448 0.224015i −0.0567209 0.998390i $$-0.518065\pi$$
−0.632727 + 0.774375i $$0.718065\pi$$
$$20$$ −40175.3 + 55296.5i −1.12293 + 1.54558i
$$21$$ 0 0
$$22$$ −58261.9 55825.6i −1.16656 1.11777i
$$23$$ 88301.0i 1.51328i 0.653834 + 0.756638i $$0.273160\pi$$
−0.653834 + 0.756638i $$0.726840\pi$$
$$24$$ 0 0
$$25$$ −9839.67 + 30283.4i −0.125948 + 0.387628i
$$26$$ −162852. + 52913.9i −1.81713 + 0.590423i
$$27$$ 0 0
$$28$$ −9248.11 12728.9i −0.0796159 0.109582i
$$29$$ 21088.6 + 64904.1i 0.160567 + 0.494173i 0.998682 0.0513193i $$-0.0163426\pi$$
−0.838116 + 0.545493i $$0.816343\pi$$
$$30$$ 0 0
$$31$$ 39589.7 + 28763.6i 0.238680 + 0.173411i 0.700695 0.713461i $$-0.252873\pi$$
−0.462015 + 0.886872i $$0.652873\pi$$
$$32$$ −187944. −1.01392
$$33$$ 0 0
$$34$$ 224793. 0.980858
$$35$$ −20479.2 14879.0i −0.0807375 0.0586592i
$$36$$ 0 0
$$37$$ 12353.9 + 38021.3i 0.0400956 + 0.123402i 0.969101 0.246665i $$-0.0793348\pi$$
−0.929005 + 0.370067i $$0.879335\pi$$
$$38$$ 232862. + 320508.i 0.688425 + 0.947536i
$$39$$ 0 0
$$40$$ 450317. 146317.i 1.11252 0.361480i
$$41$$ 129634. 398974.i 0.293749 0.904067i −0.689889 0.723915i $$-0.742341\pi$$
0.983639 0.180153i $$-0.0576592\pi$$
$$42$$ 0 0
$$43$$ 273270.i 0.524145i −0.965048 0.262073i $$-0.915594\pi$$
0.965048 0.262073i $$-0.0844060\pi$$
$$44$$ 161491. + 895433.i 0.285800 + 1.58471i
$$45$$ 0 0
$$46$$ 948707. 1.30578e6i 1.43708 1.97797i
$$47$$ 1.12068e6 + 364132.i 1.57449 + 0.511583i 0.960630 0.277832i $$-0.0896158\pi$$
0.613860 + 0.789415i $$0.289616\pi$$
$$48$$ 0 0
$$49$$ −661546. + 480641.i −0.803293 + 0.583626i
$$50$$ 470873. 342109.i 0.532732 0.387053i
$$51$$ 0 0
$$52$$ 1.83635e6 + 596666.i 1.81110 + 0.588464i
$$53$$ 431286. 593614.i 0.397924 0.547695i −0.562298 0.826935i $$-0.690082\pi$$
0.960221 + 0.279240i $$0.0900825\pi$$
$$54$$ 0 0
$$55$$ 692283. + 1.28984e6i 0.561066 + 1.04536i
$$56$$ 108995.i 0.0829370i
$$57$$ 0 0
$$58$$ 385475. 1.18637e6i 0.259417 0.798403i
$$59$$ −1.86916e6 + 607326.i −1.18485 + 0.384982i −0.834167 0.551512i $$-0.814051\pi$$
−0.350684 + 0.936494i $$0.614051\pi$$
$$60$$ 0 0
$$61$$ 1.39569e6 + 1.92100e6i 0.787288 + 1.08361i 0.994440 + 0.105300i $$0.0335804\pi$$
−0.207152 + 0.978309i $$0.566420\pi$$
$$62$$ −276411. 850705.i −0.147294 0.453323i
$$63$$ 0 0
$$64$$ 2.74995e6 + 1.99795e6i 1.31128 + 0.952698i
$$65$$ 3.10649e6 1.40305
$$66$$ 0 0
$$67$$ −369220. −0.149977 −0.0749884 0.997184i $$-0.523892\pi$$
−0.0749884 + 0.997184i $$0.523892\pi$$
$$68$$ −2.05070e6 1.48992e6i −0.790897 0.574620i
$$69$$ 0 0
$$70$$ 142984. + 440058.i 0.0498245 + 0.153344i
$$71$$ 2.08693e6 + 2.87241e6i 0.691995 + 0.952449i 0.999999 + 0.00106427i $$0.000338768\pi$$
−0.308005 + 0.951385i $$0.599661\pi$$
$$72$$ 0 0
$$73$$ −1.18339e6 + 384506.i −0.356039 + 0.115684i −0.481575 0.876405i $$-0.659935\pi$$
0.125536 + 0.992089i $$0.459935\pi$$
$$74$$ 225814. 694984.i 0.0647799 0.199372i
$$75$$ 0 0
$$76$$ 4.46727e6i 1.16733i
$$77$$ −331626. + 59808.5i −0.0827811 + 0.0149295i
$$78$$ 0 0
$$79$$ 2.54246e6 3.49939e6i 0.580174 0.798542i −0.413540 0.910486i $$-0.635708\pi$$
0.993714 + 0.111944i $$0.0357078\pi$$
$$80$$ 89374.2 + 29039.4i 0.0195163 + 0.00634122i
$$81$$ 0 0
$$82$$ −6.20360e6 + 4.50718e6i −1.24250 + 0.902726i
$$83$$ −2.09707e6 + 1.52361e6i −0.402569 + 0.292484i −0.770587 0.637335i $$-0.780037\pi$$
0.368017 + 0.929819i $$0.380037\pi$$
$$84$$ 0 0
$$85$$ −3.87857e6 1.26022e6i −0.685023 0.222578i
$$86$$ −2.93601e6 + 4.04107e6i −0.497752 + 0.685097i
$$87$$ 0 0
$$88$$ 2.74100e6 5.67593e6i 0.428765 0.887867i
$$89$$ 6.18536e6i 0.930037i 0.885301 + 0.465018i $$0.153952\pi$$
−0.885301 + 0.465018i $$0.846048\pi$$
$$90$$ 0 0
$$91$$ −220977. + 680097.i −0.0307399 + 0.0946076i
$$92$$ −1.73094e7 + 5.62416e6i −2.31752 + 0.753009i
$$93$$ 0 0
$$94$$ −1.26603e7 1.74254e7i −1.57215 2.16388i
$$95$$ −2.22099e6 6.83550e6i −0.265775 0.817970i
$$96$$ 0 0
$$97$$ −7.39031e6 5.36938e6i −0.822170 0.597342i 0.0951629 0.995462i $$-0.469663\pi$$
−0.917333 + 0.398120i $$0.869663\pi$$
$$98$$ 1.49469e7 1.60420
$$99$$ 0 0
$$100$$ −6.56308e6 −0.656308
$$101$$ 8.99227e6 + 6.53326e6i 0.868449 + 0.630965i 0.930170 0.367128i $$-0.119659\pi$$
−0.0617212 + 0.998093i $$0.519659\pi$$
$$102$$ 0 0
$$103$$ 3.84333e6 + 1.18286e7i 0.346559 + 1.06660i 0.960744 + 0.277437i $$0.0894850\pi$$
−0.614185 + 0.789162i $$0.710515\pi$$
$$104$$ −7.86212e6 1.08213e7i −0.685367 0.943326i
$$105$$ 0 0
$$106$$ −1.27556e7 + 4.14455e6i −1.04023 + 0.337992i
$$107$$ −470632. + 1.44846e6i −0.0371397 + 0.114304i −0.967908 0.251306i $$-0.919140\pi$$
0.930768 + 0.365611i $$0.119140\pi$$
$$108$$ 0 0
$$109$$ 2.42278e7i 1.79193i 0.444121 + 0.895967i $$0.353516\pi$$
−0.444121 + 0.895967i $$0.646484\pi$$
$$110$$ 3.62067e6 2.65119e7i 0.259367 1.89918i
$$111$$ 0 0
$$112$$ −12715.1 + 17500.8i −0.000855176 + 0.00117705i
$$113$$ −1.43236e7 4.65400e6i −0.933848 0.303426i −0.197713 0.980260i $$-0.563351\pi$$
−0.736135 + 0.676834i $$0.763351\pi$$
$$114$$ 0 0
$$115$$ −2.36894e7 + 1.72114e7i −1.45249 + 1.05529i
$$116$$ −1.13798e7 + 8.26787e6i −0.676908 + 0.491803i
$$117$$ 0 0
$$118$$ 3.41660e7 + 1.11012e7i 1.91429 + 0.621989i
$$119$$ 551795. 759481.i 0.0300168 0.0413145i
$$120$$ 0 0
$$121$$ 1.87736e7 + 5.22519e6i 0.963381 + 0.268135i
$$122$$ 4.34028e7i 2.16400i
$$123$$ 0 0
$$124$$ −3.11685e6 + 9.59268e6i −0.146805 + 0.451819i
$$125$$ 1.45969e7 4.74281e6i 0.668459 0.217196i
$$126$$ 0 0
$$127$$ −469790. 646611.i −0.0203512 0.0280111i 0.798720 0.601703i $$-0.205511\pi$$
−0.819071 + 0.573692i $$0.805511\pi$$
$$128$$ −1.17658e7 3.62115e7i −0.495893 1.52620i
$$129$$ 0 0
$$130$$ −4.59384e7 3.33762e7i −1.83389 1.33240i
$$131$$ 4.37657e7 1.70092 0.850460 0.526039i $$-0.176324\pi$$
0.850460 + 0.526039i $$0.176324\pi$$
$$132$$ 0 0
$$133$$ 1.65447e6 0.0609786
$$134$$ 5.45998e6 + 3.96691e6i 0.196031 + 0.142425i
$$135$$ 0 0
$$136$$ 5.42623e6 + 1.67002e7i 0.184974 + 0.569293i
$$137$$ 3.35338e7 + 4.61553e7i 1.11419 + 1.53355i 0.815091 + 0.579333i $$0.196687\pi$$
0.299102 + 0.954221i $$0.403313\pi$$
$$138$$ 0 0
$$139$$ 2.50224e7 8.13027e6i 0.790273 0.256775i 0.114053 0.993475i $$-0.463617\pi$$
0.676220 + 0.736699i $$0.263617\pi$$
$$140$$ 1.61231e6 4.96217e6i 0.0496592 0.152835i
$$141$$ 0 0
$$142$$ 6.48987e7i 1.90207i
$$143$$ 2.86105e7 2.98591e7i 0.818181 0.853887i
$$144$$ 0 0
$$145$$ −1.33020e7 + 1.83086e7i −0.362349 + 0.498731i
$$146$$ 2.16309e7 + 7.02832e6i 0.575229 + 0.186903i
$$147$$ 0 0
$$148$$ −6.66634e6 + 4.84338e6i −0.169033 + 0.122810i
$$149$$ −4.90229e7 + 3.56172e7i −1.21408 + 0.882081i −0.995595 0.0937595i $$-0.970112\pi$$
−0.218485 + 0.975840i $$0.570112\pi$$
$$150$$ 0 0
$$151$$ 6.61252e7 + 2.14854e7i 1.56296 + 0.507837i 0.957597 0.288112i $$-0.0930276\pi$$
0.605364 + 0.795949i $$0.293028\pi$$
$$152$$ −1.81900e7 + 2.50364e7i −0.420127 + 0.578255i
$$153$$ 0 0
$$154$$ 5.54663e6 + 2.67856e6i 0.122379 + 0.0590988i
$$155$$ 1.62276e7i 0.350021i
$$156$$ 0 0
$$157$$ −9.68557e6 + 2.98091e7i −0.199745 + 0.614752i 0.800143 + 0.599809i $$0.204757\pi$$
−0.999888 + 0.0149434i $$0.995243\pi$$
$$158$$ −7.51950e7 + 2.44323e7i −1.51666 + 0.492794i
$$159$$ 0 0
$$160$$ −3.66335e7 5.04217e7i −0.707063 0.973189i
$$161$$ −2.08292e6 6.41058e6i −0.0393353 0.121062i
$$162$$ 0 0
$$163$$ 3.21683e6 + 2.33717e6i 0.0581797 + 0.0422701i 0.616495 0.787359i $$-0.288552\pi$$
−0.558315 + 0.829629i $$0.688552\pi$$
$$164$$ 8.64664e7 1.53071
$$165$$ 0 0
$$166$$ 4.73810e7 0.803944
$$167$$ −8.53648e7 6.20211e7i −1.41831 1.03046i −0.992048 0.125862i $$-0.959830\pi$$
−0.426262 0.904600i $$-0.640170\pi$$
$$168$$ 0 0
$$169$$ −7.72790e6 2.37840e7i −0.123157 0.379037i
$$170$$ 4.38159e7 + 6.03074e7i 0.684007 + 0.941455i
$$171$$ 0 0
$$172$$ 5.35682e7 1.74054e7i 0.802707 0.260815i
$$173$$ −2.78623e7 + 8.57512e7i −0.409124 + 1.25915i 0.508278 + 0.861193i $$0.330282\pi$$
−0.917402 + 0.397961i $$0.869718\pi$$
$$174$$ 0 0
$$175$$ 2.43066e6i 0.0342839i
$$176$$ 1.10225e6 591599.i 0.0152400 0.00817962i
$$177$$ 0 0
$$178$$ 6.64556e7 9.14683e7i 0.883205 1.21563i
$$179$$ −1.14626e8 3.72441e7i −1.49381 0.485369i −0.555606 0.831446i $$-0.687514\pi$$
−0.938206 + 0.346077i $$0.887514\pi$$
$$180$$ 0 0
$$181$$ −9.53899e7 + 6.93048e7i −1.19571 + 0.868737i −0.993856 0.110677i $$-0.964698\pi$$
−0.201858 + 0.979415i $$0.564698\pi$$
$$182$$ 1.05748e7 7.68301e6i 0.130023 0.0944673i
$$183$$ 0 0
$$184$$ 1.19909e8 + 3.89609e7i 1.41903 + 0.461070i
$$185$$ −7.79239e6 + 1.07253e7i −0.0904835 + 0.124540i
$$186$$ 0 0
$$187$$ −4.78343e7 + 2.56736e7i −0.534926 + 0.287106i
$$188$$ 2.42876e8i 2.66583i
$$189$$ 0 0
$$190$$ −4.05970e7 + 1.24945e8i −0.429394 + 1.32154i
$$191$$ −9.64312e7 + 3.13324e7i −1.00138 + 0.325370i −0.763419 0.645904i $$-0.776481\pi$$
−0.237966 + 0.971274i $$0.576481\pi$$
$$192$$ 0 0
$$193$$ −1.02374e7 1.40906e7i −0.102504 0.141084i 0.754684 0.656089i $$-0.227790\pi$$
−0.857188 + 0.515004i $$0.827790\pi$$
$$194$$ 5.15983e7 + 1.58803e8i 0.507375 + 1.56154i
$$195$$ 0 0
$$196$$ −1.36354e8 9.90673e7i −1.29352 0.939797i
$$197$$ 1.27719e6 0.0119021 0.00595105 0.999982i $$-0.498106\pi$$
0.00595105 + 0.999982i $$0.498106\pi$$
$$198$$ 0 0
$$199$$ 1.89402e8 1.70372 0.851861 0.523768i $$-0.175474\pi$$
0.851861 + 0.523768i $$0.175474\pi$$
$$200$$ 3.67822e7 + 2.67238e7i 0.325111 + 0.236207i
$$201$$ 0 0
$$202$$ −6.27830e7 1.93226e8i −0.535935 1.64944i
$$203$$ −3.06203e6 4.21452e6i −0.0256906 0.0353600i
$$204$$ 0 0
$$205$$ 1.32305e8 4.29884e7i 1.07260 0.348508i
$$206$$ 7.02515e7 2.16212e8i 0.559913 1.72323i
$$207$$ 0 0
$$208$$ 2.65469e6i 0.0204547i
$$209$$ −8.61567e7 4.16065e7i −0.652795 0.315245i
$$210$$ 0 0
$$211$$ 9.01787e7 1.24120e8i 0.660869 0.909608i −0.338641 0.940916i $$-0.609967\pi$$
0.999510 + 0.0313077i $$0.00996719\pi$$
$$212$$ 1.43834e8 + 4.67346e7i 1.03678 + 0.336870i
$$213$$ 0 0
$$214$$ 2.25219e7 1.63631e7i 0.157093 0.114135i
$$215$$ 7.33128e7 5.32649e7i 0.503089 0.365516i
$$216$$ 0 0
$$217$$ −3.55268e6 1.15434e6i −0.0236019 0.00766872i
$$218$$ 2.60304e8 3.58278e8i 1.70170 2.34219i
$$219$$ 0 0
$$220$$ −2.08750e8 + 2.17860e8i −1.32174 + 1.37942i
$$221$$ 1.15206e8i 0.717961i
$$222$$ 0 0
$$223$$ 4.53676e7 1.39627e8i 0.273955 0.843145i −0.715540 0.698572i $$-0.753819\pi$$
0.989494 0.144573i $$-0.0461809\pi$$
$$224$$ 1.36446e7 4.43339e6i 0.0811133 0.0263553i
$$225$$ 0 0
$$226$$ 1.61812e8 + 2.22715e8i 0.932463 + 1.28342i
$$227$$ −2.81273e7 8.65669e7i −0.159602 0.491203i 0.838996 0.544137i $$-0.183143\pi$$
−0.998598 + 0.0529337i $$0.983143\pi$$
$$228$$ 0 0
$$229$$ 5.17047e7 + 3.75657e7i 0.284515 + 0.206713i 0.720885 0.693055i $$-0.243736\pi$$
−0.436369 + 0.899768i $$0.643736\pi$$
$$230$$ 5.35235e8 2.90066
$$231$$ 0 0
$$232$$ 9.74422e7 0.512317
$$233$$ −1.95276e8 1.41876e8i −1.01135 0.734792i −0.0468612 0.998901i $$-0.514922\pi$$
−0.964493 + 0.264110i $$0.914922\pi$$
$$234$$ 0 0
$$235$$ 1.20751e8 + 3.71632e8i 0.606948 + 1.86800i
$$236$$ −2.38104e8 3.27723e8i −1.17917 1.62298i
$$237$$ 0 0
$$238$$ −1.63198e7 + 5.30261e6i −0.0784683 + 0.0254959i
$$239$$ −6.81816e7 + 2.09841e8i −0.323054 + 0.994257i 0.649258 + 0.760568i $$0.275080\pi$$
−0.972311 + 0.233689i $$0.924920\pi$$
$$240$$ 0 0
$$241$$ 3.16216e8i 1.45521i −0.685998 0.727603i $$-0.740634\pi$$
0.685998 0.727603i $$-0.259366\pi$$
$$242$$ −2.21482e8 2.78973e8i −1.00458 1.26534i
$$243$$ 0 0
$$244$$ −2.87672e8 + 3.95946e8i −1.26775 + 1.74491i
$$245$$ −2.57893e8 8.37945e7i −1.12036 0.364028i
$$246$$ 0 0
$$247$$ −1.64259e8 + 1.19341e8i −0.693571 + 0.503909i
$$248$$ 5.65280e7 4.10700e7i 0.235333 0.170979i
$$249$$ 0 0
$$250$$ −2.66814e8 8.66930e7i −1.07999 0.350909i
$$251$$ −849631. + 1.16942e6i −0.00339135 + 0.00466779i −0.810709 0.585449i $$-0.800918\pi$$
0.807318 + 0.590117i $$0.200918\pi$$
$$252$$ 0 0
$$253$$ −5.27443e7 + 3.86214e8i −0.204764 + 1.49936i
$$254$$ 1.46094e7i 0.0559391i
$$255$$ 0 0
$$256$$ −8.06160e7 + 2.48110e8i −0.300318 + 0.924283i
$$257$$ 2.83614e8 9.21519e7i 1.04223 0.338640i 0.262613 0.964901i $$-0.415416\pi$$
0.779613 + 0.626261i $$0.215416\pi$$
$$258$$ 0 0
$$259$$ −1.79376e6 2.46890e6i −0.00641528 0.00882987i
$$260$$ 1.97862e8 + 6.08956e8i 0.698161 + 2.14872i
$$261$$ 0 0
$$262$$ −6.47201e8 4.70219e8i −2.22323 1.61527i
$$263$$ −3.08584e8 −1.04599 −0.522996 0.852335i $$-0.675186\pi$$
−0.522996 + 0.852335i $$0.675186\pi$$
$$264$$ 0 0
$$265$$ 2.43320e8 0.803188
$$266$$ −2.44660e7 1.77756e7i −0.0797035 0.0579080i
$$267$$ 0 0
$$268$$ −2.35167e7 7.23771e7i −0.0746286 0.229683i
$$269$$ −2.57083e8 3.53845e8i −0.805269 1.10836i −0.992036 0.125954i $$-0.959801\pi$$
0.186767 0.982404i $$-0.440199\pi$$
$$270$$ 0 0
$$271$$ 9.85469e7 3.20198e7i 0.300781 0.0977296i −0.154739 0.987955i $$-0.549454\pi$$
0.455519 + 0.890226i $$0.349454\pi$$
$$272$$ −1.07694e6 + 3.31448e6i −0.00324489 + 0.00998675i
$$273$$ 0 0
$$274$$ 1.04282e9i 3.06256i
$$275$$ −6.11261e7 + 1.26577e8i −0.177240 + 0.367020i
$$276$$ 0 0
$$277$$ −7.39417e7 + 1.01772e8i −0.209031 + 0.287706i −0.900640 0.434566i $$-0.856902\pi$$
0.691609 + 0.722272i $$0.256902\pi$$
$$278$$ −4.57380e8 1.48612e8i −1.27679 0.414855i
$$279$$ 0 0
$$280$$ −2.92412e7 + 2.12450e7i −0.0796052 + 0.0578366i
$$281$$ 1.30972e8 9.51567e7i 0.352133 0.255839i −0.397630 0.917546i $$-0.630167\pi$$
0.749763 + 0.661706i $$0.230167\pi$$
$$282$$ 0 0
$$283$$ −2.04333e8 6.63917e7i −0.535901 0.174125i 0.0285482 0.999592i $$-0.490912\pi$$
−0.564450 + 0.825467i $$0.690912\pi$$
$$284$$ −4.30146e8 + 5.92046e8i −1.11430 + 1.53370i
$$285$$ 0 0
$$286$$ −7.43895e8 + 1.34161e8i −1.88031 + 0.339113i
$$287$$ 3.20231e7i 0.0799607i
$$288$$ 0 0
$$289$$ −8.00657e7 + 2.46417e8i −0.195121 + 0.600521i
$$290$$ 3.93415e8 1.27828e8i 0.947236 0.307775i
$$291$$ 0 0
$$292$$ −1.50747e8 2.07486e8i −0.354331 0.487695i
$$293$$ 1.77785e8 + 5.47165e8i 0.412912 + 1.27081i 0.914105 + 0.405478i $$0.132895\pi$$
−0.501193 + 0.865336i $$0.667105\pi$$
$$294$$ 0 0
$$295$$ −5.27264e8 3.83080e8i −1.19578 0.868785i
$$296$$ 5.70824e7 0.127933
$$297$$ 0 0
$$298$$ 1.10762e9 2.42456
$$299$$ 6.69211e8 + 4.86210e8i 1.44782 + 1.05190i
$$300$$ 0 0
$$301$$ 6.44612e6 + 1.98391e7i 0.0136244 + 0.0419315i
$$302$$ −7.47012e8 1.02817e9i −1.56064 2.14804i
$$303$$ 0 0
$$304$$ −5.84136e6 + 1.89797e6i −0.0119249 + 0.00387465i
$$305$$ −2.43323e8 + 7.48870e8i −0.491059 + 1.51132i
$$306$$ 0 0
$$307$$ 1.06336e8i 0.209746i −0.994486 0.104873i $$-0.966556\pi$$
0.994486 0.104873i $$-0.0334436\pi$$
$$308$$ −3.28463e7 6.11983e7i −0.0640560 0.119347i
$$309$$ 0 0
$$310$$ 1.74350e8 2.39972e8i 0.332396 0.457504i
$$311$$ −2.88639e8 9.37846e7i −0.544119 0.176795i 0.0240440 0.999711i $$-0.492346\pi$$
−0.568163 + 0.822916i $$0.692346\pi$$
$$312$$ 0 0
$$313$$ 6.64300e7 4.82642e7i 0.122450 0.0889652i −0.524875 0.851180i $$-0.675888\pi$$
0.647325 + 0.762214i $$0.275888\pi$$
$$314$$ 4.63498e8 3.36751e8i 0.844879 0.613840i
$$315$$ 0 0
$$316$$ 8.47911e8 + 2.75503e8i 1.51163 + 0.491158i
$$317$$ 6.54888e8 9.01376e8i 1.15467 1.58927i 0.425477 0.904969i $$-0.360106\pi$$
0.729197 0.684303i $$-0.239894\pi$$
$$318$$ 0 0
$$319$$ 5.34692e7 + 2.96476e8i 0.0922224 + 0.511355i
$$320$$ 1.12719e9i 1.92297i
$$321$$ 0 0
$$322$$ −3.80733e7 + 1.17178e8i −0.0635514 + 0.195591i
$$323$$ 2.53497e8 8.23663e7i 0.418567 0.136001i
$$324$$ 0 0
$$325$$ 1.75330e8 + 2.41321e8i 0.283312 + 0.389946i
$$326$$ −2.24595e7 6.91234e7i −0.0359037 0.110500i
$$327$$ 0 0
$$328$$ −4.84593e8 3.52077e8i −0.758260 0.550908i
$$329$$ −8.99500e7 −0.139256
$$330$$ 0 0
$$331$$ 5.26497e8 0.797991 0.398996 0.916953i $$-0.369359\pi$$
0.398996 + 0.916953i $$0.369359\pi$$
$$332$$ −4.32238e8 3.14039e8i −0.648246 0.470978i
$$333$$ 0 0
$$334$$ 5.96007e8 + 1.83432e9i 0.875263 + 2.69378i
$$335$$ −7.19673e7 9.90545e7i −0.104587 0.143952i
$$336$$ 0 0
$$337$$ −5.61134e8 + 1.82324e8i −0.798661 + 0.259501i −0.679788 0.733409i $$-0.737928\pi$$
−0.118873 + 0.992909i $$0.537928\pi$$
$$338$$ −1.41257e8 + 4.34744e8i −0.198976 + 0.612385i
$$339$$ 0 0
$$340$$ 8.40571e8i 1.15984i
$$341$$ 1.55977e8 + 1.49455e8i 0.213020 + 0.204113i
$$342$$ 0 0
$$343$$ 7.36412e7 1.01358e8i 0.0985352 0.135622i
$$344$$ −3.71090e8 1.20574e8i −0.491501 0.159698i
$$345$$ 0 0
$$346$$ 1.33334e9 9.68725e8i 1.73051 1.25729i
$$347$$ 5.28779e8 3.84180e8i 0.679393 0.493608i −0.193763 0.981048i $$-0.562069\pi$$
0.873156 + 0.487440i $$0.162069\pi$$
$$348$$ 0 0
$$349$$ 1.50436e9 + 4.88797e8i 1.89437 + 0.615517i 0.975045 + 0.222009i $$0.0712615\pi$$
0.919321 + 0.393508i $$0.128739\pi$$
$$350$$ −2.61150e7 + 3.59442e7i −0.0325576 + 0.0448116i
$$351$$ 0 0
$$352$$ −8.22035e8 1.12264e8i −1.00460 0.137195i
$$353$$ 3.80307e8i 0.460175i −0.973170 0.230088i $$-0.926099\pi$$
0.973170 0.230088i $$-0.0739012\pi$$
$$354$$ 0 0
$$355$$ −3.63833e8 + 1.11976e9i −0.431621 + 1.32839i
$$356$$ −1.21250e9 + 3.93964e8i −1.42431 + 0.462787i
$$357$$ 0 0
$$358$$ 1.29492e9 + 1.78230e9i 1.49160 + 2.05301i
$$359$$ 4.32632e8 + 1.33150e9i 0.493501 + 1.51884i 0.819280 + 0.573394i $$0.194374\pi$$
−0.325779 + 0.945446i $$0.605626\pi$$
$$360$$ 0 0
$$361$$ −3.43123e8 2.49293e8i −0.383861 0.278892i
$$362$$ 2.15523e9 2.38788
$$363$$ 0 0
$$364$$ −1.47392e8 −0.160184
$$365$$ −3.33818e8 2.42533e8i −0.359323 0.261063i
$$366$$ 0 0
$$367$$ −2.45330e8 7.55048e8i −0.259071 0.797340i −0.993000 0.118113i $$-0.962315\pi$$
0.733929 0.679226i $$-0.237685\pi$$
$$368$$ 1.47082e7 + 2.02441e7i 0.0153848 + 0.0211754i
$$369$$ 0 0
$$370$$ 2.30465e8 7.48828e7i 0.236537 0.0768557i
$$371$$ −1.73083e7 + 5.32694e7i −0.0175973 + 0.0541589i
$$372$$ 0 0
$$373$$ 1.12986e9i 1.12731i −0.826010 0.563655i $$-0.809395\pi$$
0.826010 0.563655i $$-0.190605\pi$$
$$374$$ 9.83205e8 + 1.34274e8i 0.971837 + 0.132722i
$$375$$ 0 0
$$376$$ 9.88954e8 1.36118e9i 0.959441 1.32056i
$$377$$ 6.08012e8 + 1.97555e8i 0.584409 + 0.189886i
$$378$$ 0 0
$$379$$ −2.95684e8 + 2.14827e8i −0.278991 + 0.202699i −0.718477 0.695551i $$-0.755161\pi$$
0.439486 + 0.898249i $$0.355161\pi$$
$$380$$ 1.19848e9 8.70746e8i 1.12044 0.814046i
$$381$$ 0 0
$$382$$ 1.76265e9 + 5.72719e8i 1.61787 + 0.525678i
$$383$$ 4.78842e8 6.59069e8i 0.435508 0.599426i −0.533698 0.845675i $$-0.679198\pi$$
0.969207 + 0.246249i $$0.0791982\pi$$
$$384$$ 0 0
$$385$$ −8.06850e7 7.73111e7i −0.0720577 0.0690445i
$$386$$ 3.18361e8i 0.281750i
$$387$$ 0 0
$$388$$ 5.81831e8 1.79069e9i 0.505692 1.55636i
$$389$$ −4.48316e7 + 1.45667e7i −0.0386154 + 0.0125469i −0.328261 0.944587i $$-0.606463\pi$$
0.289646 + 0.957134i $$0.406463\pi$$
$$390$$ 0 0
$$391$$ −6.38291e8 8.78532e8i −0.540008 0.743257i
$$392$$ 3.60800e8 + 1.11043e9i 0.302527 + 0.931084i
$$393$$ 0 0
$$394$$ −1.88869e7 1.37222e7i −0.0155570 0.0113028i
$$395$$ 1.43438e9 1.17105
$$396$$ 0 0
$$397$$ −1.78256e9 −1.42980 −0.714902 0.699224i $$-0.753529\pi$$
−0.714902 + 0.699224i $$0.753529\pi$$
$$398$$ −2.80085e9 2.03494e9i −2.22689 1.61793i
$$399$$ 0 0
$$400$$ 2.78840e6 + 8.58182e6i 0.00217844 + 0.00670455i
$$401$$ −8.77578e8 1.20788e9i −0.679643 0.935448i 0.320287 0.947321i $$-0.396221\pi$$
−0.999930 + 0.0118727i $$0.996221\pi$$
$$402$$ 0 0
$$403$$ 4.35984e8 1.41660e8i 0.331820 0.107815i
$$404$$ −7.07951e8 + 2.17885e9i −0.534156 + 1.64396i
$$405$$ 0 0
$$406$$ 9.52223e7i 0.0706151i
$$407$$ 3.13227e7 + 1.73678e8i 0.0230292 + 0.127692i
$$408$$ 0 0
$$409$$ 7.90411e7 1.08791e8i 0.0571244 0.0786250i −0.779499 0.626403i $$-0.784526\pi$$
0.836623 + 0.547778i $$0.184526\pi$$
$$410$$ −2.41837e9 7.85777e8i −1.73292 0.563061i
$$411$$ 0 0
$$412$$ −2.07392e9 + 1.50679e9i −1.46101 + 1.06148i
$$413$$ 1.21373e8 8.81827e7i 0.0847807 0.0615968i
$$414$$ 0 0
$$415$$ −8.17511e8 2.65625e8i −0.561468 0.182432i
$$416$$ −1.03487e9 + 1.42438e9i −0.704791 + 0.970062i
$$417$$ 0 0
$$418$$ 8.27053e8 + 1.54094e9i 0.553881 + 1.03197i
$$419$$ 2.46822e9i 1.63921i 0.572930 + 0.819604i $$0.305807\pi$$
−0.572930 + 0.819604i $$0.694193\pi$$
$$420$$ 0 0
$$421$$ −2.15144e8 + 6.62146e8i −0.140521 + 0.432480i −0.996408 0.0846833i $$-0.973012\pi$$
0.855887 + 0.517164i $$0.173012\pi$$
$$422$$ −2.66710e9 + 8.66593e8i −1.72761 + 0.561335i
$$423$$ 0 0
$$424$$ −6.15810e8 8.47590e8i −0.392343 0.540014i
$$425$$ −1.21008e8 3.72425e8i −0.0764634 0.235330i
$$426$$ 0 0
$$427$$ −1.46640e8 1.06540e8i −0.0911496 0.0662240i
$$428$$ −3.13913e8 −0.193533
$$429$$ 0 0
$$430$$ −1.65642e9 −1.00469
$$431$$ 4.45542e8 + 3.23706e8i 0.268052 + 0.194751i 0.713689 0.700463i $$-0.247023\pi$$
−0.445637 + 0.895214i $$0.647023\pi$$
$$432$$ 0 0
$$433$$ −3.42794e8 1.05501e9i −0.202920 0.624524i −0.999792 0.0203762i $$-0.993514\pi$$
0.796872 0.604148i $$-0.206486\pi$$
$$434$$ 4.01344e7 + 5.52402e7i 0.0235669 + 0.0324370i
$$435$$ 0 0
$$436$$ −4.74931e9 + 1.54314e9i −2.74427 + 0.891669i
$$437$$ 5.91399e8 1.82014e9i 0.338997 1.04333i
$$438$$ 0 0
$$439$$ 1.80506e9i 1.01828i 0.860684 + 0.509139i $$0.170036\pi$$
−0.860684 + 0.509139i $$0.829964\pi$$
$$440$$ 2.05701e9 3.70980e8i 1.15120 0.207618i
$$441$$ 0 0
$$442$$ 1.23777e9 1.70365e9i 0.681809 0.938429i
$$443$$ 1.17482e8 + 3.81722e7i 0.0642034 + 0.0208609i 0.340943 0.940084i $$-0.389254\pi$$
−0.276739 + 0.960945i $$0.589254\pi$$
$$444$$ 0 0
$$445$$ −1.65941e9 + 1.20563e9i −0.892675 + 0.648567i
$$446$$ −2.17104e9 + 1.57736e9i −1.15877 + 0.841895i
$$447$$ 0 0
$$448$$ −2.46773e8 8.01815e7i −0.129666 0.0421309i
$$449$$ −1.68117e9 + 2.31393e9i −0.876494 + 1.20639i 0.100886 + 0.994898i $$0.467832\pi$$
−0.977380 + 0.211492i $$0.932168\pi$$
$$450$$ 0 0
$$451$$ 8.05315e8 1.66761e9i 0.413379 0.856005i
$$452$$ 3.10423e9i 1.58114i
$$453$$ 0 0
$$454$$ −5.14133e8 + 1.58234e9i −0.257858 + 0.793604i
$$455$$ −2.25529e8 + 7.32787e7i −0.112244 + 0.0364702i
$$456$$ 0 0
$$457$$ −1.49764e9 2.06132e9i −0.734007 1.01027i −0.998941 0.0460069i $$-0.985350\pi$$
0.264935 0.964266i $$-0.414650\pi$$
$$458$$ −3.60996e8 1.11103e9i −0.175579 0.540378i
$$459$$ 0 0
$$460$$ −4.88274e9 3.54752e9i −2.33890 1.69931i
$$461$$ 1.43615e9 0.682726 0.341363 0.939932i $$-0.389112\pi$$
0.341363 + 0.939932i $$0.389112\pi$$
$$462$$ 0 0
$$463$$ 3.63234e9 1.70080 0.850399 0.526138i $$-0.176360\pi$$
0.850399 + 0.526138i $$0.176360\pi$$
$$464$$ 1.56458e7 + 1.13674e7i 0.00727085 + 0.00528258i
$$465$$ 0 0
$$466$$ 1.36339e9 + 4.19610e9i 0.624124 + 1.92086i
$$467$$ 1.00506e8 + 1.38334e8i 0.0456648 + 0.0628521i 0.831239 0.555916i $$-0.187632\pi$$
−0.785574 + 0.618768i $$0.787632\pi$$
$$468$$ 0 0
$$469$$ 2.68051e7 8.70950e6i 0.0119981 0.00389842i
$$470$$ 2.20718e9 6.79299e9i 0.980606 3.01800i
$$471$$ 0 0
$$472$$ 2.80621e9i 1.22835i
$$473$$ 1.63231e8 1.19523e9i 0.0709230 0.519325i
$$474$$ 0 0
$$475$$ 4.05648e8 5.58327e8i 0.173669 0.239035i
$$476$$ 1.84024e8 + 5.97931e7i 0.0782079 + 0.0254113i
$$477$$ 0 0
$$478$$ 3.26280e9 2.37056e9i 1.36645 0.992782i
$$479$$ 1.95205e9 1.41825e9i 0.811551 0.589626i −0.102729 0.994709i $$-0.532757\pi$$
0.914280 + 0.405083i $$0.132757\pi$$
$$480$$ 0 0
$$481$$ 3.56178e8 + 1.15729e8i 0.145935 + 0.0474171i
$$482$$ −3.39743e9 + 4.67616e9i −1.38193 + 1.90206i
$$483$$ 0 0
$$484$$ 1.71468e8 + 4.01293e9i 0.0687425 + 1.60880i
$$485$$ 3.02926e9i 1.20570i
$$486$$ 0 0
$$487$$ 1.16512e9 3.58586e9i 0.457107 1.40683i −0.411538 0.911393i $$-0.635008\pi$$
0.868644 0.495436i $$-0.164992\pi$$
$$488$$ 3.22446e9 1.04769e9i 1.25599 0.408097i
$$489$$ 0 0
$$490$$ 2.91340e9 + 4.00995e9i 1.11870 + 1.53976i
$$491$$ −1.15909e9 3.56732e9i −0.441909 1.36006i −0.885838 0.463994i $$-0.846416\pi$$
0.443929 0.896062i $$-0.353584\pi$$
$$492$$ 0 0
$$493$$ −6.78981e8 4.93309e8i −0.255208 0.185419i
$$494$$ 3.71125e9 1.38508
$$495$$ 0 0
$$496$$ 1.38675e7 0.00510286
$$497$$ −2.19266e8 1.59306e8i −0.0801168 0.0582083i
$$498$$ 0 0
$$499$$ −1.50366e9 4.62778e9i −0.541748 1.66733i −0.728600 0.684940i $$-0.759828\pi$$
0.186852 0.982388i $$-0.440172\pi$$
$$500$$ 1.85944e9 + 2.55930e9i 0.665253 + 0.915642i
$$501$$ 0 0
$$502$$ 2.51285e7 8.16473e6i 0.00886549 0.00288057i
$$503$$ 9.71261e8 2.98923e9i 0.340289 1.04730i −0.623769 0.781609i $$-0.714399\pi$$
0.964058 0.265693i $$-0.0856007\pi$$
$$504$$ 0 0
$$505$$ 3.68589e9i 1.27357i
$$506$$ 4.92946e9 5.14459e9i 1.69150 1.76532i
$$507$$ 0 0
$$508$$ 9.68307e7 1.33276e8i 0.0327710 0.0451055i
$$509$$ 3.07026e9 + 9.97588e8i 1.03196 + 0.335304i 0.775565 0.631268i $$-0.217465\pi$$
0.256395 + 0.966572i $$0.417465\pi$$
$$510$$ 0 0
$$511$$ 7.68429e7 5.58297e7i 0.0254760 0.0185094i
$$512$$ −8.49894e7 + 6.17484e7i −0.0279847 + 0.0203320i
$$513$$ 0 0
$$514$$ −5.18413e9 1.68443e9i −1.68386 0.547118i
$$515$$ −2.42424e9 + 3.33667e9i −0.782077 + 1.07644i
$$516$$ 0 0
$$517$$ 4.68417e9 + 2.26206e9i 1.49079 + 0.719925i
$$518$$ 5.57820e7i 0.0176335i
$$519$$ 0 0
$$520$$ 1.37067e9 4.21850e9i 0.427487 1.31567i
$$521$$ −1.64022e7 + 5.32940e6i −0.00508125 + 0.00165100i −0.311557 0.950228i $$-0.600850\pi$$
0.306475 + 0.951879i $$0.400850\pi$$
$$522$$ 0 0
$$523$$ −2.28534e9 3.14550e9i −0.698546 0.961466i −0.999968 0.00797495i $$-0.997461\pi$$
0.301423 0.953491i $$-0.402539\pi$$
$$524$$ 2.78757e9 + 8.57924e9i 0.846380 + 2.60489i
$$525$$ 0 0
$$526$$ 4.56330e9 + 3.31543e9i 1.36719 + 0.993321i
$$527$$ −6.01809e8 −0.179111
$$528$$ 0 0
$$529$$ −4.39225e9 −1.29001
$$530$$ −3.59818e9 2.61423e9i −1.04983 0.762744i
$$531$$ 0 0
$$532$$ 1.05378e8 + 3.24320e8i 0.0303430 + 0.0933862i
$$533$$ −2.30992e9 3.17933e9i −0.660771 0.909474i
$$534$$ 0 0
$$535$$ −4.80327e8 + 1.56068e8i −0.135612 + 0.0440630i
$$536$$ −1.62911e8 + 5.01387e8i −0.0456954 + 0.140636i
$$537$$ 0 0
$$538$$ 7.99472e9i 2.21343i
$$539$$ −3.18059e9 + 1.70709e9i −0.874876 + 0.469564i
$$540$$ 0 0
$$541$$ −1.06024e8 + 1.45930e8i −0.0287882 + 0.0396236i −0.823168 0.567797i $$-0.807796\pi$$
0.794380 + 0.607421i $$0.207796\pi$$
$$542$$ −1.80132e9 5.85284e8i −0.485952 0.157895i
$$543$$ 0 0
$$544$$ 1.86991e9 1.35857e9i 0.497995 0.361814i
$$545$$ −6.49985e9 + 4.72242e9i −1.71995 + 1.24962i
$$546$$ 0 0
$$547$$ 4.64326e9 + 1.50869e9i 1.21302 + 0.394134i 0.844535 0.535501i $$-0.179877\pi$$
0.368484 + 0.929634i $$0.379877\pi$$
$$548$$ −6.91180e9 + 9.51328e9i −1.79415 + 2.46944i
$$549$$ 0 0
$$550$$ 2.26387e9 1.21506e9i 0.580205 0.311408i
$$551$$ 1.47910e9i 0.376676i
$$552$$ 0 0
$$553$$ −1.02033e8 + 3.14026e8i −0.0256569 + 0.0789638i
$$554$$ 2.18688e9 7.10560e8i 0.546438 0.177548i
$$555$$ 0 0
$$556$$ 3.18750e9 + 4.38722e9i 0.786482 + 1.08250i
$$557$$ −1.37870e8 4.24321e8i −0.0338047 0.104040i 0.932730 0.360575i $$-0.117419\pi$$
−0.966535 + 0.256534i $$0.917419\pi$$
$$558$$ 0 0
$$559$$ −2.07104e9 1.50470e9i −0.501473 0.364341i
$$560$$ −7.17349e6 −0.00172613
$$561$$ 0 0
$$562$$ −2.95916e9 −0.703221
$$563$$ −1.07591e9 7.81691e8i −0.254094 0.184610i 0.453445 0.891284i $$-0.350195\pi$$
−0.707539 + 0.706674i $$0.750195\pi$$
$$564$$ 0 0
$$565$$ −1.54333e9 4.74987e9i −0.359988 1.10793i
$$566$$ 2.30833e9 + 3.17714e9i 0.535106 + 0.736511i
$$567$$ 0 0
$$568$$ 4.82143e9 1.56658e9i 1.10397 0.358701i
$$569$$ 5.16896e8 1.59084e9i 0.117628 0.362021i −0.874858 0.484379i $$-0.839046\pi$$
0.992486 + 0.122358i $$0.0390455\pi$$
$$570$$ 0 0
$$571$$ 1.64546e9i 0.369881i 0.982750 + 0.184940i $$0.0592092\pi$$
−0.982750 + 0.184940i $$0.940791\pi$$
$$572$$ 7.67547e9 + 3.70661e9i 1.71482 + 0.828115i
$$573$$ 0 0
$$574$$ 3.44056e8 4.73553e8i 0.0759343 0.104515i
$$575$$ −2.67406e9 8.68853e8i −0.586588 0.190594i
$$576$$ 0 0
$$577$$ 1.48214e9 1.07684e9i 0.321200 0.233365i −0.415488 0.909599i $$-0.636389\pi$$
0.736687 + 0.676234i $$0.236389\pi$$
$$578$$ 3.83151e9 2.78375e9i 0.825319 0.599630i
$$579$$ 0 0
$$580$$ −4.43621e9 1.44141e9i −0.944092 0.306754i
$$581$$ 1.16305e8 1.60081e8i 0.0246027 0.0338628i
$$582$$ 0 0
$$583$$ 2.24095e9 2.33875e9i 0.468374 0.488814i
$$584$$ 1.77665e9i 0.369111i
$$585$$ 0 0
$$586$$ 3.24969e9 1.00015e10i 0.667115 2.05317i
$$587$$ −5.54757e8 + 1.80251e8i −0.113206 + 0.0367828i −0.365072 0.930979i $$-0.618956\pi$$
0.251866 + 0.967762i $$0.418956\pi$$
$$588$$ 0 0
$$589$$ −6.23413e8 8.58055e8i −0.125711 0.173026i
$$590$$ 3.68130e9 + 1.13299e10i 0.737936 + 2.27113i
$$591$$ 0 0
$$592$$ 9.16544e6 + 6.65908e6i 0.00181563 + 0.00131913i
$$593$$ −6.34419e9 −1.24935 −0.624676 0.780884i $$-0.714769\pi$$
−0.624676 + 0.780884i $$0.714769\pi$$
$$594$$ 0 0
$$595$$ 3.11308e8 0.0605872
$$596$$ −1.01044e10 7.34124e9i −1.95500 1.42039i
$$597$$ 0 0
$$598$$ −4.67235e9 1.43800e10i −0.893473 2.74983i
$$599$$ 4.39871e9 + 6.05430e9i 0.836241 + 1.15099i 0.986729 + 0.162375i $$0.0519155\pi$$
−0.150488 + 0.988612i $$0.548085\pi$$
$$600$$ 0 0
$$601$$ −2.91754e9 + 9.47966e8i −0.548222 + 0.178128i −0.570015 0.821634i $$-0.693063\pi$$
0.0217930 + 0.999763i $$0.493063\pi$$
$$602$$ 1.17827e8 3.62636e8i 0.0220120 0.0677459i
$$603$$ 0 0
$$604$$ 1.43308e10i 2.64631i
$$605$$ 2.25747e9 + 6.05506e9i 0.414457 + 1.11167i
$$606$$ 0 0
$$607$$ 2.70175e9 3.71864e9i 0.490325 0.674875i −0.490123 0.871653i $$-0.663048\pi$$
0.980448 + 0.196779i $$0.0630480\pi$$
$$608$$ 3.87407e9 + 1.25876e9i 0.699045 + 0.227134i
$$609$$ 0 0
$$610$$ 1.16441e10 8.45993e9i 2.07707 1.50908i
$$611$$ 8.93045e9 6.48835e9i 1.58391 1.15077i
$$612$$ 0 0
$$613$$ −2.67774e9 8.70050e8i −0.469522 0.152557i 0.0646934 0.997905i $$-0.479393\pi$$
−0.534216 + 0.845348i $$0.679393\pi$$
$$614$$ −1.14247e9 + 1.57248e9i −0.199185 + 0.274154i
$$615$$ 0 0
$$616$$ −6.51053e7 + 4.76725e8i −0.0112223 + 0.0821742i
$$617$$ 7.32574e9i 1.25561i 0.778373 + 0.627803i $$0.216046\pi$$
−0.778373 + 0.627803i $$0.783954\pi$$
$$618$$ 0 0
$$619$$ −1.50954e8 + 4.64590e8i −0.0255816 + 0.0787322i −0.963032 0.269386i $$-0.913179\pi$$
0.937451 + 0.348118i $$0.113179\pi$$
$$620$$ −3.18105e9 + 1.03359e9i −0.536044 + 0.174171i
$$621$$ 0 0
$$622$$ 3.26074e9 + 4.48802e9i 0.543312 + 0.747805i
$$623$$ −1.45906e8 4.49052e8i −0.0241749 0.0744026i
$$624$$ 0 0
$$625$$ 6.13013e9 + 4.45380e9i 1.00436 + 0.729711i
$$626$$ −1.50091e9 −0.244537
$$627$$ 0 0
$$628$$ −6.46029e9 −1.04086
$$629$$ −3.97752e8 2.88984e8i −0.0637288 0.0463017i
$$630$$ 0 0
$$631$$ 1.30938e9 + 4.02987e9i 0.207474 + 0.638539i 0.999603 + 0.0281853i $$0.00897286\pi$$
−0.792129 + 0.610354i $$0.791027\pi$$
$$632$$ −3.63023e9 4.99659e9i −0.572038 0.787343i
$$633$$ 0 0
$$634$$ −1.93688e10 + 6.29330e9i −3.01849 + 0.980767i
$$635$$ 8.19028e7 2.52071e8i 0.0126938 0.0390674i
$$636$$ 0 0
$$637$$ 7.66024e9i 1.17423i
$$638$$ 2.39465e9 4.95872e9i 0.365064 0.755958i
$$639$$ 0 0
$$640$$ 7.42147e9 1.02148e10i 1.11908 1.54028i
$$641$$ −9.19294e9 2.98697e9i −1.37864 0.447948i −0.476418 0.879219i $$-0.658065\pi$$
−0.902222 + 0.431271i $$0.858065\pi$$
$$642$$ 0 0
$$643$$ 1.04351e10 7.58156e9i 1.54796 1.12466i 0.602871 0.797839i $$-0.294023\pi$$
0.945087 0.326818i $$-0.105977\pi$$
$$644$$ 1.12398e9 8.16617e8i 0.165828 0.120481i
$$645$$ 0 0
$$646$$ −4.63363e9 1.50556e9i −0.676250 0.219727i
$$647$$ −9.00612e8 + 1.23959e9i −0.130729 + 0.179933i −0.869364 0.494173i $$-0.835471\pi$$
0.738634 + 0.674106i $$0.235471\pi$$
$$648$$ 0 0
$$649$$ −8.53814e9 + 1.53985e9i −1.22605 + 0.221117i
$$650$$ 5.45238e9i 0.778734i
$$651$$ 0 0
$$652$$ −2.53257e8 + 7.79446e8i −0.0357846 + 0.110134i
$$653$$ 1.09247e10 3.54965e9i 1.53537 0.498872i 0.585276 0.810834i $$-0.300986\pi$$
0.950094 + 0.311963i $$0.100986\pi$$
$$654$$ 0 0
$$655$$ 8.53067e9 + 1.17415e10i 1.18615 + 1.63259i
$$656$$ −3.67363e7 1.13063e8i −0.00508080 0.0156371i
$$657$$ 0 0
$$658$$ 1.33017e9 + 9.66424e8i 0.182019 + 0.132244i
$$659$$ 1.09359e7 0.00148852 0.000744262 1.00000i $$-0.499763\pi$$
0.000744262 1.00000i $$0.499763\pi$$
$$660$$ 0 0
$$661$$ −3.76410e9 −0.506939 −0.253469 0.967343i $$-0.581572\pi$$
−0.253469 + 0.967343i $$0.581572\pi$$
$$662$$ −7.78577e9 5.65669e9i −1.04303 0.757809i
$$663$$ 0 0
$$664$$ 1.14372e9 + 3.52001e9i 0.151611 + 0.466612i
$$665$$ 3.22483e8 + 4.43860e8i 0.0425238 + 0.0585289i
$$666$$ 0 0
$$667$$ −5.73110e9 + 1.86215e9i −0.747821 + 0.242982i
$$668$$ 6.72067e9 2.06841e10i 0.872358 2.68484i
$$669$$ 0 0
$$670$$ 2.23802e9i 0.287477i
$$671$$ 4.95704e9 + 9.23580e9i 0.633422 + 1.18017i
$$672$$ 0 0
$$673$$ −3.59607e9 + 4.94957e9i −0.454753 + 0.625914i −0.973410 0.229068i $$-0.926432\pi$$
0.518657 + 0.854982i $$0.326432\pi$$
$$674$$ 1.02569e10 + 3.33266e9i 1.29034 + 0.419258i
$$675$$ 0 0
$$676$$ 4.17009e9 3.02975e9i 0.519197 0.377219i
$$677$$ 6.01956e9 4.37347e9i 0.745597 0.541708i −0.148862 0.988858i $$-0.547561\pi$$
0.894459 + 0.447150i $$0.147561\pi$$
$$678$$ 0 0
$$679$$ 6.63188e8 + 2.15483e8i 0.0813004 + 0.0264161i
$$680$$ −3.42267e9 + 4.71090e9i −0.417430 + 0.574543i
$$681$$ 0 0
$$682$$ −7.00827e8 3.88594e9i −0.0845990 0.469085i
$$683$$ 6.55957e9i 0.787777i −0.919158 0.393888i $$-0.871130\pi$$
0.919158 0.393888i $$-0.128870\pi$$
$$684$$ 0 0
$$685$$ −5.84624e9 + 1.79929e10i −0.694960 + 2.13887i
$$686$$ −2.17799e9 + 7.07673e8i −0.257586 + 0.0836947i
$$687$$ 0 0
$$688$$ −4.55182e7 6.26504e7i −0.00532875 0.00733439i
$$689$$ −2.12407e9 6.53722e9i −0.247401 0.761422i
$$690$$ 0 0
$$691$$ 3.46227e9 + 2.51548e9i 0.399197 + 0.290034i 0.769214 0.638992i $$-0.220648\pi$$
−0.370017 + 0.929025i $$0.620648\pi$$
$$692$$ −1.85842e10 −2.13192
$$693$$ 0 0
$$694$$ −1.19472e10 −1.35677
$$695$$ 7.05848e9 + 5.12829e9i 0.797562 + 0.579463i
$$696$$ 0 0
$$697$$ 1.59424e9 + 4.90658e9i 0.178336 + 0.548863i
$$698$$ −1.69947e10 2.33912e10i −1.89156 2.60350i
$$699$$ 0 0
$$700$$ 4.76474e8 1.54816e8i 0.0525044 0.0170597i
$$701$$ −1.74200e9 + 5.36131e9i −0.191000 + 0.587838i 0.809000 + 0.587809i $$0.200009\pi$$
−1.00000 2.93357e-5i $$0.999991\pi$$
$$702$$ 0 0
$$703$$ 8.66470e8i 0.0940611i
$$704$$ 1.08344e10 + 1.03813e10i 1.17031 + 1.12137i
$$705$$ 0 0
$$706$$ −4.08603e9 + 5.62393e9i −0.437003 + 0.601483i
$$707$$ −8.06943e8 2.62192e8i −0.0858766 0.0279030i
$$708$$ 0 0
$$709$$ −7.18831e9 + 5.22261e9i −0.757469 + 0.550334i −0.898133 0.439724i $$-0.855076\pi$$
0.140664 + 0.990057i $$0.455076\pi$$
$$710$$ 1.74110e10 1.26499e10i 1.82566 1.32642i
$$711$$ 0 0
$$712$$ 8.39948e9 + 2.72916e9i 0.872113 + 0.283367i
$$713$$ −2.53986e9 + 3.49581e9i −0.262419 + 0.361189i
$$714$$ 0 0
$$715$$ 1.35873e10 + 1.85558e9i 1.39015 + 0.189850i
$$716$$ 2.48419e10i 2.52923i
$$717$$ 0 0
$$718$$ 7.90800e9 2.43383e10i 0.797317 2.45389i
$$719$$ 1.28303e10 4.16881e9i 1.28732 0.418274i 0.416164 0.909289i $$-0.363374\pi$$
0.871151 + 0.491015i $$0.163374\pi$$
$$720$$ 0 0
$$721$$ −5.58045e8 7.68083e8i −0.0554492 0.0763193i
$$722$$ 2.39564e9 + 7.37303e9i 0.236887 + 0.729064i
$$723$$ 0 0
$$724$$ −1.96613e10 1.42848e10i −1.92543 1.39890i
$$725$$ −2.17302e9 −0.211778
$$726$$ 0 0
$$727$$ −3.88356e9 −0.374852 −0.187426 0.982279i $$-0.560014\pi$$
−0.187426 + 0.982279i $$0.560014\pi$$
$$728$$ 8.26045e8 + 6.00157e8i 0.0793494 + 0.0576507i
$$729$$ 0 0
$$730$$ 2.33068e9 + 7.17309e9i 0.221744 + 0.682459i
$$731$$ 1.97535e9 + 2.71884e9i 0.187040 + 0.257438i
$$732$$ 0 0
$$733$$ −6.86357e9 + 2.23011e9i −0.643704 + 0.209152i −0.612636 0.790365i $$-0.709891\pi$$
−0.0310677 + 0.999517i $$0.509891\pi$$
$$734$$ −4.48434e9 + 1.38014e10i −0.418564 + 1.28821i
$$735$$ 0 0
$$736$$ 1.65957e10i 1.53434i
$$737$$ −1.61491e9 2.20544e8i −0.148597 0.0202936i
$$738$$ 0 0
$$739$$ −1.29510e9 + 1.78255e9i −0.118045 + 0.162475i −0.863950 0.503577i $$-0.832017\pi$$
0.745905 + 0.666052i $$0.232017\pi$$
$$740$$ −2.59877e9 8.44390e8i −0.235752 0.0766006i
$$741$$ 0 0
$$742$$ 8.28280e8 6.01781e8i 0.0744327 0.0540785i
$$743$$ −6.12290e9 + 4.44855e9i −0.547641 + 0.397885i −0.826915 0.562327i $$-0.809906\pi$$
0.279274 + 0.960212i $$0.409906\pi$$
$$744$$ 0 0
$$745$$ −1.91108e10 6.20947e9i −1.69329 0.550184i
$$746$$ −1.21392e10 + 1.67082e10i −1.07055 + 1.47348i
$$747$$ 0 0
$$748$$ −8.07943e9 7.74157e9i −0.705870 0.676353i
$$749$$ 1.16258e8i 0.0101097i
$$750$$ 0 0
$$751$$ 5.75420e9 1.77096e10i 0.495730 1.52570i −0.320086 0.947389i $$-0.603712\pi$$
0.815816 0.578312i $$-0.196288\pi$$
$$752$$ 3.17583e8 1.03189e8i 0.0272330 0.00884852i
$$753$$ 0 0
$$754$$ −6.86866e9 9.45390e9i −0.583542 0.803177i
$$755$$ 7.12483e9 + 2.19280e10i 0.602504 + 1.85432i
$$756$$ 0 0
$$757$$ 1.80582e10 + 1.31200e10i 1.51300 + 1.09926i 0.964825 + 0.262894i $$0.0846770\pi$$
0.548174 + 0.836364i $$0.315323\pi$$
$$758$$ 6.68063e9 0.557154
$$759$$ 0 0
$$760$$ −1.02623e10 −0.848003
$$761$$ −1.01033e10 7.34046e9i −0.831029 0.603778i 0.0888215 0.996048i $$-0.471690\pi$$
−0.919850 + 0.392270i $$0.871690\pi$$
$$762$$ 0 0
$$763$$ −5.71508e8 1.75892e9i −0.0465786 0.143354i
$$764$$ −1.22840e10 1.69074e10i −0.996581 1.37168i
$$765$$ 0 0
$$766$$ −1.41621e10 + 4.60154e9i −1.13848 + 0.369916i
$$767$$ −5.68934e9 + 1.75100e10i −0.455279 + 1.40121i
$$768$$ 0 0
$$769$$ 1.17360e10i 0.930630i −0.885145 0.465315i $$-0.845941\pi$$
0.885145 0.465315i $$-0.154059\pi$$
$$770$$ 3.62528e8 + 2.01015e9i 0.0286170 + 0.158676i
$$771$$ 0 0
$$772$$ 2.11008e9 2.90428e9i 0.165059 0.227184i
$$773$$ −4.38016e9 1.42320e9i −0.341084 0.110825i 0.133466 0.991053i $$-0.457389\pi$$