# Properties

 Label 36.9.d.b.19.1 Level $36$ Weight $9$ Character 36.19 Analytic conductor $14.666$ Analytic rank $0$ Dimension $2$ Inner twists $2$

# Learn more

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [36,9,Mod(19,36)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(36, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("36.19");

S:= CuspForms(chi, 9);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$36 = 2^{2} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$9$$ Character orbit: $$[\chi]$$ $$=$$ 36.d (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

comment: select newform

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

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

 Self dual: no Analytic conductor: $$14.6656299622$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\sqrt{-39})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} - x + 10$$ x^2 - x + 10 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: no (minimal twist has level 4) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 19.1 Root $$0.500000 + 3.12250i$$ of defining polynomial Character $$\chi$$ $$=$$ 36.19 Dual form 36.9.d.b.19.2

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(10.0000 - 12.4900i) q^{2} +(-56.0000 - 249.800i) q^{4} -610.000 q^{5} +1398.88i q^{7} +(-3680.00 - 1798.56i) q^{8} +O(q^{10})$$ $$q+(10.0000 - 12.4900i) q^{2} +(-56.0000 - 249.800i) q^{4} -610.000 q^{5} +1398.88i q^{7} +(-3680.00 - 1798.56i) q^{8} +(-6100.00 + 7618.90i) q^{10} +18485.2i q^{11} -5470.00 q^{13} +(17472.0 + 13988.8i) q^{14} +(-59264.0 + 27977.6i) q^{16} -73090.0 q^{17} -19484.4i q^{19} +(34160.0 + 152378. i) q^{20} +(230880. + 184852. i) q^{22} +237210. i q^{23} -18525.0 q^{25} +(-54700.0 + 68320.3i) q^{26} +(349440. - 78337.3i) q^{28} +128222. q^{29} -67945.6i q^{31} +(-243200. + 1.01998e6i) q^{32} +(-730900. + 912894. i) q^{34} -853317. i q^{35} -3.47203e6 q^{37} +(-243360. - 194844. i) q^{38} +(2.24480e6 + 1.09712e6i) q^{40} -2.14688e6 q^{41} -5.92815e6i q^{43} +(4.61760e6 - 1.03517e6i) q^{44} +(2.96275e6 + 2.37210e6i) q^{46} -7.62629e6i q^{47} +3.80794e6 q^{49} +(-185250. + 231377. i) q^{50} +(306320. + 1.36641e6i) q^{52} -824290. q^{53} -1.12760e7i q^{55} +(2.51597e6 - 5.14788e6i) q^{56} +(1.28222e6 - 1.60149e6i) q^{58} +3.72552e6i q^{59} -1.47461e7 q^{61} +(-848640. - 679456. i) q^{62} +(1.03076e7 + 1.32374e7i) q^{64} +3.33670e6 q^{65} +1.52567e7i q^{67} +(4.09304e6 + 1.82579e7i) q^{68} +(-1.06579e7 - 8.53317e6i) q^{70} +1.19604e6i q^{71} -5.72563e6 q^{73} +(-3.47203e7 + 4.33656e7i) q^{74} +(-4.86720e6 + 1.09113e6i) q^{76} -2.58586e7 q^{77} +3.59132e7i q^{79} +(3.61510e7 - 1.70663e7i) q^{80} +(-2.14688e7 + 2.68145e7i) q^{82} +5.19603e7i q^{83} +4.45849e7 q^{85} +(-7.40426e7 - 5.92815e7i) q^{86} +(3.32467e7 - 6.80255e7i) q^{88} +8.33242e7 q^{89} -7.65187e6i q^{91} +(5.92550e7 - 1.32838e7i) q^{92} +(-9.52524e7 - 7.62629e7i) q^{94} +1.18855e7i q^{95} +1.20619e8 q^{97} +(3.80794e7 - 4.75611e7i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 20 q^{2} - 112 q^{4} - 1220 q^{5} - 7360 q^{8}+O(q^{10})$$ 2 * q + 20 * q^2 - 112 * q^4 - 1220 * q^5 - 7360 * q^8 $$2 q + 20 q^{2} - 112 q^{4} - 1220 q^{5} - 7360 q^{8} - 12200 q^{10} - 10940 q^{13} + 34944 q^{14} - 118528 q^{16} - 146180 q^{17} + 68320 q^{20} + 461760 q^{22} - 37050 q^{25} - 109400 q^{26} + 698880 q^{28} + 256444 q^{29} - 486400 q^{32} - 1461800 q^{34} - 6944060 q^{37} - 486720 q^{38} + 4489600 q^{40} - 4293764 q^{41} + 9235200 q^{44} + 5925504 q^{46} + 7615874 q^{49} - 370500 q^{50} + 612640 q^{52} - 1648580 q^{53} + 5031936 q^{56} + 2564440 q^{58} - 29492156 q^{61} - 1697280 q^{62} + 20615168 q^{64} + 6673400 q^{65} + 8186080 q^{68} - 21315840 q^{70} - 11451260 q^{73} - 69440600 q^{74} - 9734400 q^{76} - 51717120 q^{77} + 72302080 q^{80} - 42937640 q^{82} + 89169800 q^{85} - 148085184 q^{86} + 66493440 q^{88} + 166648444 q^{89} + 118510080 q^{92} - 190504704 q^{94} + 241238020 q^{97} + 76158740 q^{98}+O(q^{100})$$ 2 * q + 20 * q^2 - 112 * q^4 - 1220 * q^5 - 7360 * q^8 - 12200 * q^10 - 10940 * q^13 + 34944 * q^14 - 118528 * q^16 - 146180 * q^17 + 68320 * q^20 + 461760 * q^22 - 37050 * q^25 - 109400 * q^26 + 698880 * q^28 + 256444 * q^29 - 486400 * q^32 - 1461800 * q^34 - 6944060 * q^37 - 486720 * q^38 + 4489600 * q^40 - 4293764 * q^41 + 9235200 * q^44 + 5925504 * q^46 + 7615874 * q^49 - 370500 * q^50 + 612640 * q^52 - 1648580 * q^53 + 5031936 * q^56 + 2564440 * q^58 - 29492156 * q^61 - 1697280 * q^62 + 20615168 * q^64 + 6673400 * q^65 + 8186080 * q^68 - 21315840 * q^70 - 11451260 * q^73 - 69440600 * q^74 - 9734400 * q^76 - 51717120 * q^77 + 72302080 * q^80 - 42937640 * q^82 + 89169800 * q^85 - 148085184 * q^86 + 66493440 * q^88 + 166648444 * q^89 + 118510080 * q^92 - 190504704 * q^94 + 241238020 * q^97 + 76158740 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$$.

 $$n$$ $$19$$ $$29$$ $$\chi(n)$$ $$-1$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 10.0000 12.4900i 0.625000 0.780625i
$$3$$ 0 0
$$4$$ −56.0000 249.800i −0.218750 0.975781i
$$5$$ −610.000 −0.976000 −0.488000 0.872844i $$-0.662273\pi$$
−0.488000 + 0.872844i $$0.662273\pi$$
$$6$$ 0 0
$$7$$ 1398.88i 0.582624i 0.956628 + 0.291312i $$0.0940917\pi$$
−0.956628 + 0.291312i $$0.905908\pi$$
$$8$$ −3680.00 1798.56i −0.898438 0.439101i
$$9$$ 0 0
$$10$$ −6100.00 + 7618.90i −0.610000 + 0.761890i
$$11$$ 18485.2i 1.26256i 0.775554 + 0.631282i $$0.217471\pi$$
−0.775554 + 0.631282i $$0.782529\pi$$
$$12$$ 0 0
$$13$$ −5470.00 −0.191520 −0.0957600 0.995404i $$-0.530528\pi$$
−0.0957600 + 0.995404i $$0.530528\pi$$
$$14$$ 17472.0 + 13988.8i 0.454810 + 0.364140i
$$15$$ 0 0
$$16$$ −59264.0 + 27977.6i −0.904297 + 0.426904i
$$17$$ −73090.0 −0.875109 −0.437555 0.899192i $$-0.644155\pi$$
−0.437555 + 0.899192i $$0.644155\pi$$
$$18$$ 0 0
$$19$$ 19484.4i 0.149511i −0.997202 0.0747554i $$-0.976182\pi$$
0.997202 0.0747554i $$-0.0238176\pi$$
$$20$$ 34160.0 + 152378.i 0.213500 + 0.952362i
$$21$$ 0 0
$$22$$ 230880. + 184852.i 0.985588 + 0.789102i
$$23$$ 237210.i 0.847660i 0.905742 + 0.423830i $$0.139315\pi$$
−0.905742 + 0.423830i $$0.860685\pi$$
$$24$$ 0 0
$$25$$ −18525.0 −0.0474240
$$26$$ −54700.0 + 68320.3i −0.119700 + 0.149505i
$$27$$ 0 0
$$28$$ 349440. 78337.3i 0.568513 0.127449i
$$29$$ 128222. 0.181289 0.0906443 0.995883i $$-0.471107\pi$$
0.0906443 + 0.995883i $$0.471107\pi$$
$$30$$ 0 0
$$31$$ 67945.6i 0.0735723i −0.999323 0.0367862i $$-0.988288\pi$$
0.999323 0.0367862i $$-0.0117120\pi$$
$$32$$ −243200. + 1.01998e6i −0.231934 + 0.972732i
$$33$$ 0 0
$$34$$ −730900. + 912894.i −0.546943 + 0.683132i
$$35$$ 853317.i 0.568641i
$$36$$ 0 0
$$37$$ −3.47203e6 −1.85258 −0.926289 0.376813i $$-0.877020\pi$$
−0.926289 + 0.376813i $$0.877020\pi$$
$$38$$ −243360. 194844.i −0.116712 0.0934442i
$$39$$ 0 0
$$40$$ 2.24480e6 + 1.09712e6i 0.876875 + 0.428563i
$$41$$ −2.14688e6 −0.759754 −0.379877 0.925037i $$-0.624034\pi$$
−0.379877 + 0.925037i $$0.624034\pi$$
$$42$$ 0 0
$$43$$ 5.92815e6i 1.73399i −0.498321 0.866993i $$-0.666050\pi$$
0.498321 0.866993i $$-0.333950\pi$$
$$44$$ 4.61760e6 1.03517e6i 1.23199 0.276186i
$$45$$ 0 0
$$46$$ 2.96275e6 + 2.37210e6i 0.661704 + 0.529787i
$$47$$ 7.62629e6i 1.56287i −0.623989 0.781433i $$-0.714489\pi$$
0.623989 0.781433i $$-0.285511\pi$$
$$48$$ 0 0
$$49$$ 3.80794e6 0.660550
$$50$$ −185250. + 231377.i −0.0296400 + 0.0370203i
$$51$$ 0 0
$$52$$ 306320. + 1.36641e6i 0.0418950 + 0.186881i
$$53$$ −824290. −0.104466 −0.0522332 0.998635i $$-0.516634\pi$$
−0.0522332 + 0.998635i $$0.516634\pi$$
$$54$$ 0 0
$$55$$ 1.12760e7i 1.23226i
$$56$$ 2.51597e6 5.14788e6i 0.255831 0.523451i
$$57$$ 0 0
$$58$$ 1.28222e6 1.60149e6i 0.113305 0.141518i
$$59$$ 3.72552e6i 0.307453i 0.988113 + 0.153726i $$0.0491274\pi$$
−0.988113 + 0.153726i $$0.950873\pi$$
$$60$$ 0 0
$$61$$ −1.47461e7 −1.06502 −0.532509 0.846424i $$-0.678751\pi$$
−0.532509 + 0.846424i $$0.678751\pi$$
$$62$$ −848640. 679456.i −0.0574324 0.0459827i
$$63$$ 0 0
$$64$$ 1.03076e7 + 1.32374e7i 0.614380 + 0.789010i
$$65$$ 3.33670e6 0.186923
$$66$$ 0 0
$$67$$ 1.52567e7i 0.757113i 0.925578 + 0.378557i $$0.123579\pi$$
−0.925578 + 0.378557i $$0.876421\pi$$
$$68$$ 4.09304e6 + 1.82579e7i 0.191430 + 0.853915i
$$69$$ 0 0
$$70$$ −1.06579e7 8.53317e6i −0.443895 0.355400i
$$71$$ 1.19604e6i 0.0470666i 0.999723 + 0.0235333i $$0.00749158\pi$$
−0.999723 + 0.0235333i $$0.992508\pi$$
$$72$$ 0 0
$$73$$ −5.72563e6 −0.201619 −0.100810 0.994906i $$-0.532143\pi$$
−0.100810 + 0.994906i $$0.532143\pi$$
$$74$$ −3.47203e7 + 4.33656e7i −1.15786 + 1.44617i
$$75$$ 0 0
$$76$$ −4.86720e6 + 1.09113e6i −0.145890 + 0.0327055i
$$77$$ −2.58586e7 −0.735600
$$78$$ 0 0
$$79$$ 3.59132e7i 0.922032i 0.887392 + 0.461016i $$0.152515\pi$$
−0.887392 + 0.461016i $$0.847485\pi$$
$$80$$ 3.61510e7 1.70663e7i 0.882594 0.416658i
$$81$$ 0 0
$$82$$ −2.14688e7 + 2.68145e7i −0.474846 + 0.593082i
$$83$$ 5.19603e7i 1.09486i 0.836851 + 0.547431i $$0.184394\pi$$
−0.836851 + 0.547431i $$0.815606\pi$$
$$84$$ 0 0
$$85$$ 4.45849e7 0.854107
$$86$$ −7.40426e7 5.92815e7i −1.35359 1.08374i
$$87$$ 0 0
$$88$$ 3.32467e7 6.80255e7i 0.554393 1.13433i
$$89$$ 8.33242e7 1.32804 0.664020 0.747715i $$-0.268849\pi$$
0.664020 + 0.747715i $$0.268849\pi$$
$$90$$ 0 0
$$91$$ 7.65187e6i 0.111584i
$$92$$ 5.92550e7 1.32838e7i 0.827130 0.185426i
$$93$$ 0 0
$$94$$ −9.52524e7 7.62629e7i −1.22001 0.976792i
$$95$$ 1.18855e7i 0.145923i
$$96$$ 0 0
$$97$$ 1.20619e8 1.36248 0.681238 0.732062i $$-0.261442\pi$$
0.681238 + 0.732062i $$0.261442\pi$$
$$98$$ 3.80794e7 4.75611e7i 0.412844 0.515641i
$$99$$ 0 0
$$100$$ 1.03740e6 + 4.62754e6i 0.0103740 + 0.0462754i
$$101$$ −2.77246e7 −0.266428 −0.133214 0.991087i $$-0.542530\pi$$
−0.133214 + 0.991087i $$0.542530\pi$$
$$102$$ 0 0
$$103$$ 1.04501e8i 0.928477i 0.885710 + 0.464238i $$0.153672\pi$$
−0.885710 + 0.464238i $$0.846328\pi$$
$$104$$ 2.01296e7 + 9.83812e6i 0.172069 + 0.0840967i
$$105$$ 0 0
$$106$$ −8.24290e6 + 1.02954e7i −0.0652915 + 0.0815490i
$$107$$ 1.00328e8i 0.765394i −0.923874 0.382697i $$-0.874995\pi$$
0.923874 0.382697i $$-0.125005\pi$$
$$108$$ 0 0
$$109$$ −5.90716e7 −0.418478 −0.209239 0.977865i $$-0.567099\pi$$
−0.209239 + 0.977865i $$0.567099\pi$$
$$110$$ −1.40837e8 1.12760e8i −0.961934 0.770164i
$$111$$ 0 0
$$112$$ −3.91373e7 8.29032e7i −0.248724 0.526865i
$$113$$ −5.50849e7 −0.337846 −0.168923 0.985629i $$-0.554029\pi$$
−0.168923 + 0.985629i $$0.554029\pi$$
$$114$$ 0 0
$$115$$ 1.44698e8i 0.827316i
$$116$$ −7.18043e6 3.20298e7i −0.0396569 0.176898i
$$117$$ 0 0
$$118$$ 4.65317e7 + 3.72552e7i 0.240005 + 0.192158i
$$119$$ 1.02244e8i 0.509859i
$$120$$ 0 0
$$121$$ −1.27344e8 −0.594067
$$122$$ −1.47461e8 + 1.84178e8i −0.665637 + 0.831380i
$$123$$ 0 0
$$124$$ −1.69728e7 + 3.80495e6i −0.0717905 + 0.0160939i
$$125$$ 2.49581e8 1.02229
$$126$$ 0 0
$$127$$ 2.57160e8i 0.988529i 0.869312 + 0.494264i $$0.164562\pi$$
−0.869312 + 0.494264i $$0.835438\pi$$
$$128$$ 2.68411e8 + 3.63229e6i 0.999908 + 0.0135313i
$$129$$ 0 0
$$130$$ 3.33670e7 4.16754e7i 0.116827 0.145917i
$$131$$ 3.12175e8i 1.06002i 0.847992 + 0.530009i $$0.177812\pi$$
−0.847992 + 0.530009i $$0.822188\pi$$
$$132$$ 0 0
$$133$$ 2.72563e7 0.0871085
$$134$$ 1.90556e8 + 1.52567e8i 0.591021 + 0.473196i
$$135$$ 0 0
$$136$$ 2.68971e8 + 1.31457e8i 0.786231 + 0.384262i
$$137$$ −2.21980e8 −0.630132 −0.315066 0.949070i $$-0.602027\pi$$
−0.315066 + 0.949070i $$0.602027\pi$$
$$138$$ 0 0
$$139$$ 2.95030e8i 0.790328i −0.918611 0.395164i $$-0.870688\pi$$
0.918611 0.395164i $$-0.129312\pi$$
$$140$$ −2.13158e8 + 4.77857e7i −0.554869 + 0.124390i
$$141$$ 0 0
$$142$$ 1.49386e7 + 1.19604e7i 0.0367414 + 0.0294166i
$$143$$ 1.01114e8i 0.241806i
$$144$$ 0 0
$$145$$ −7.82154e7 −0.176938
$$146$$ −5.72563e7 + 7.15131e7i −0.126012 + 0.157389i
$$147$$ 0 0
$$148$$ 1.94434e8 + 8.67313e8i 0.405252 + 1.80771i
$$149$$ −4.03603e8 −0.818859 −0.409429 0.912342i $$-0.634272\pi$$
−0.409429 + 0.912342i $$0.634272\pi$$
$$150$$ 0 0
$$151$$ 8.36985e8i 1.60994i −0.593316 0.804970i $$-0.702181\pi$$
0.593316 0.804970i $$-0.297819\pi$$
$$152$$ −3.50438e7 + 7.17026e7i −0.0656504 + 0.134326i
$$153$$ 0 0
$$154$$ −2.58586e8 + 3.22973e8i −0.459750 + 0.574227i
$$155$$ 4.14468e7i 0.0718066i
$$156$$ 0 0
$$157$$ −2.71319e8 −0.446561 −0.223281 0.974754i $$-0.571677\pi$$
−0.223281 + 0.974754i $$0.571677\pi$$
$$158$$ 4.48556e8 + 3.59132e8i 0.719761 + 0.576270i
$$159$$ 0 0
$$160$$ 1.48352e8 6.22190e8i 0.226367 0.949386i
$$161$$ −3.31828e8 −0.493867
$$162$$ 0 0
$$163$$ 5.78509e8i 0.819520i 0.912193 + 0.409760i $$0.134388\pi$$
−0.912193 + 0.409760i $$0.865612\pi$$
$$164$$ 1.20225e8 + 5.36291e8i 0.166196 + 0.741353i
$$165$$ 0 0
$$166$$ 6.48984e8 + 5.19603e8i 0.854676 + 0.684288i
$$167$$ 4.68118e8i 0.601852i −0.953647 0.300926i $$-0.902704\pi$$
0.953647 0.300926i $$-0.0972958\pi$$
$$168$$ 0 0
$$169$$ −7.85810e8 −0.963320
$$170$$ 4.45849e8 5.56865e8i 0.533817 0.666737i
$$171$$ 0 0
$$172$$ −1.48085e9 + 3.31976e8i −1.69199 + 0.379309i
$$173$$ 2.06197e8 0.230196 0.115098 0.993354i $$-0.463282\pi$$
0.115098 + 0.993354i $$0.463282\pi$$
$$174$$ 0 0
$$175$$ 2.59142e7i 0.0276303i
$$176$$ −5.17171e8 1.09551e9i −0.538994 1.14173i
$$177$$ 0 0
$$178$$ 8.33242e8 1.04072e9i 0.830025 1.03670i
$$179$$ 1.41911e8i 0.138230i −0.997609 0.0691152i $$-0.977982\pi$$
0.997609 0.0691152i $$-0.0220176\pi$$
$$180$$ 0 0
$$181$$ 4.82566e8 0.449616 0.224808 0.974403i $$-0.427824\pi$$
0.224808 + 0.974403i $$0.427824\pi$$
$$182$$ −9.55718e7 7.65187e7i −0.0871053 0.0697400i
$$183$$ 0 0
$$184$$ 4.26636e8 8.72933e8i 0.372209 0.761569i
$$185$$ 2.11794e9 1.80812
$$186$$ 0 0
$$187$$ 1.35108e9i 1.10488i
$$188$$ −1.90505e9 + 4.27072e8i −1.52502 + 0.341877i
$$189$$ 0 0
$$190$$ 1.48450e8 + 1.18855e8i 0.113911 + 0.0912016i
$$191$$ 9.92461e8i 0.745727i −0.927886 0.372864i $$-0.878376\pi$$
0.927886 0.372864i $$-0.121624\pi$$
$$192$$ 0 0
$$193$$ 1.17593e9 0.847526 0.423763 0.905773i $$-0.360709\pi$$
0.423763 + 0.905773i $$0.360709\pi$$
$$194$$ 1.20619e9 1.50653e9i 0.851547 1.06358i
$$195$$ 0 0
$$196$$ −2.13244e8 9.51222e8i −0.144495 0.644552i
$$197$$ −1.70538e9 −1.13229 −0.566144 0.824306i $$-0.691565\pi$$
−0.566144 + 0.824306i $$0.691565\pi$$
$$198$$ 0 0
$$199$$ 2.49036e9i 1.58800i 0.607919 + 0.793999i $$0.292004\pi$$
−0.607919 + 0.793999i $$0.707996\pi$$
$$200$$ 6.81720e7 + 3.33183e7i 0.0426075 + 0.0208239i
$$201$$ 0 0
$$202$$ −2.77246e8 + 3.46281e8i −0.166518 + 0.207981i
$$203$$ 1.79367e8i 0.105623i
$$204$$ 0 0
$$205$$ 1.30960e9 0.741519
$$206$$ 1.30522e9 + 1.04501e9i 0.724792 + 0.580298i
$$207$$ 0 0
$$208$$ 3.24174e8 1.53037e8i 0.173191 0.0817606i
$$209$$ 3.60173e8 0.188767
$$210$$ 0 0
$$211$$ 1.46774e9i 0.740491i 0.928934 + 0.370245i $$0.120726\pi$$
−0.928934 + 0.370245i $$0.879274\pi$$
$$212$$ 4.61602e7 + 2.05908e8i 0.0228520 + 0.101936i
$$213$$ 0 0
$$214$$ −1.25309e9 1.00328e9i −0.597486 0.478371i
$$215$$ 3.61617e9i 1.69237i
$$216$$ 0 0
$$217$$ 9.50477e7 0.0428650
$$218$$ −5.90716e8 + 7.37804e8i −0.261549 + 0.326674i
$$219$$ 0 0
$$220$$ −2.81674e9 + 6.31454e8i −1.20242 + 0.269557i
$$221$$ 3.99802e8 0.167601
$$222$$ 0 0
$$223$$ 1.47920e9i 0.598147i −0.954230 0.299073i $$-0.903322\pi$$
0.954230 0.299073i $$-0.0966776\pi$$
$$224$$ −1.42683e9 3.40208e8i −0.566737 0.135130i
$$225$$ 0 0
$$226$$ −5.50849e8 + 6.88011e8i −0.211154 + 0.263731i
$$227$$ 7.50054e8i 0.282481i 0.989975 + 0.141241i $$0.0451091\pi$$
−0.989975 + 0.141241i $$0.954891\pi$$
$$228$$ 0 0
$$229$$ −2.84784e9 −1.03556 −0.517778 0.855515i $$-0.673241\pi$$
−0.517778 + 0.855515i $$0.673241\pi$$
$$230$$ −1.80728e9 1.44698e9i −0.645823 0.517073i
$$231$$ 0 0
$$232$$ −4.71857e8 2.30615e8i −0.162876 0.0796041i
$$233$$ −2.20621e8 −0.0748553 −0.0374276 0.999299i $$-0.511916\pi$$
−0.0374276 + 0.999299i $$0.511916\pi$$
$$234$$ 0 0
$$235$$ 4.65204e9i 1.52536i
$$236$$ 9.30634e8 2.08629e8i 0.300007 0.0672553i
$$237$$ 0 0
$$238$$ −1.27703e9 1.02244e9i −0.398009 0.318662i
$$239$$ 4.04493e9i 1.23971i 0.784717 + 0.619855i $$0.212808\pi$$
−0.784717 + 0.619855i $$0.787192\pi$$
$$240$$ 0 0
$$241$$ 6.17983e9 1.83193 0.915964 0.401260i $$-0.131427\pi$$
0.915964 + 0.401260i $$0.131427\pi$$
$$242$$ −1.27344e9 + 1.59052e9i −0.371292 + 0.463743i
$$243$$ 0 0
$$244$$ 8.25780e8 + 3.68357e9i 0.232973 + 1.03922i
$$245$$ −2.32284e9 −0.644696
$$246$$ 0 0
$$247$$ 1.06580e8i 0.0286343i
$$248$$ −1.22204e8 + 2.50040e8i −0.0323057 + 0.0661001i
$$249$$ 0 0
$$250$$ 2.49582e9 3.11727e9i 0.638929 0.798022i
$$251$$ 5.21367e9i 1.31356i −0.754084 0.656778i $$-0.771919\pi$$
0.754084 0.656778i $$-0.228081\pi$$
$$252$$ 0 0
$$253$$ −4.38487e9 −1.07022
$$254$$ 3.21193e9 + 2.57160e9i 0.771670 + 0.617830i
$$255$$ 0 0
$$256$$ 2.72948e9 3.31613e9i 0.635506 0.772096i
$$257$$ 6.13693e9 1.40676 0.703378 0.710816i $$-0.251674\pi$$
0.703378 + 0.710816i $$0.251674\pi$$
$$258$$ 0 0
$$259$$ 4.85695e9i 1.07936i
$$260$$ −1.86855e8 8.33507e8i −0.0408895 0.182396i
$$261$$ 0 0
$$262$$ 3.89907e9 + 3.12175e9i 0.827477 + 0.662512i
$$263$$ 6.96916e9i 1.45666i −0.685228 0.728329i $$-0.740297\pi$$
0.685228 0.728329i $$-0.259703\pi$$
$$264$$ 0 0
$$265$$ 5.02817e8 0.101959
$$266$$ 2.72563e8 3.40431e8i 0.0544428 0.0679991i
$$267$$ 0 0
$$268$$ 3.81112e9 8.54374e8i 0.738777 0.165619i
$$269$$ −2.70720e9 −0.517025 −0.258513 0.966008i $$-0.583232\pi$$
−0.258513 + 0.966008i $$0.583232\pi$$
$$270$$ 0 0
$$271$$ 7.99032e9i 1.48145i −0.671808 0.740725i $$-0.734482\pi$$
0.671808 0.740725i $$-0.265518\pi$$
$$272$$ 4.33161e9 2.04488e9i 0.791359 0.373588i
$$273$$ 0 0
$$274$$ −2.21980e9 + 2.77253e9i −0.393832 + 0.491897i
$$275$$ 3.42438e8i 0.0598758i
$$276$$ 0 0
$$277$$ −8.22965e9 −1.39786 −0.698928 0.715192i $$-0.746339\pi$$
−0.698928 + 0.715192i $$0.746339\pi$$
$$278$$ −3.68493e9 2.95030e9i −0.616949 0.493955i
$$279$$ 0 0
$$280$$ −1.53474e9 + 3.14020e9i −0.249691 + 0.510888i
$$281$$ −3.08105e9 −0.494167 −0.247083 0.968994i $$-0.579472\pi$$
−0.247083 + 0.968994i $$0.579472\pi$$
$$282$$ 0 0
$$283$$ 1.17112e9i 0.182582i 0.995824 + 0.0912908i $$0.0290993\pi$$
−0.995824 + 0.0912908i $$0.970901\pi$$
$$284$$ 2.98771e8 6.69784e7i 0.0459267 0.0102958i
$$285$$ 0 0
$$286$$ −1.26291e9 1.01114e9i −0.188760 0.151129i
$$287$$ 3.00323e9i 0.442650i
$$288$$ 0 0
$$289$$ −1.63361e9 −0.234184
$$290$$ −7.82154e8 + 9.76910e8i −0.110586 + 0.138122i
$$291$$ 0 0
$$292$$ 3.20635e8 + 1.43026e9i 0.0441042 + 0.196736i
$$293$$ −4.80980e9 −0.652614 −0.326307 0.945264i $$-0.605804\pi$$
−0.326307 + 0.945264i $$0.605804\pi$$
$$294$$ 0 0
$$295$$ 2.27256e9i 0.300074i
$$296$$ 1.27771e10 + 6.24465e9i 1.66443 + 0.813470i
$$297$$ 0 0
$$298$$ −4.03603e9 + 5.04100e9i −0.511787 + 0.639221i
$$299$$ 1.29754e9i 0.162344i
$$300$$ 0 0
$$301$$ 8.29277e9 1.01026
$$302$$ −1.04539e10 8.36985e9i −1.25676 1.00621i
$$303$$ 0 0
$$304$$ 5.45126e8 + 1.15472e9i 0.0638268 + 0.135202i
$$305$$ 8.99511e9 1.03946
$$306$$ 0 0
$$307$$ 3.49176e9i 0.393089i −0.980495 0.196545i $$-0.937028\pi$$
0.980495 0.196545i $$-0.0629721\pi$$
$$308$$ 1.44808e9 + 6.45947e9i 0.160912 + 0.717784i
$$309$$ 0 0
$$310$$ 5.17670e8 + 4.14468e8i 0.0560540 + 0.0448791i
$$311$$ 1.29807e10i 1.38757i 0.720182 + 0.693785i $$0.244058\pi$$
−0.720182 + 0.693785i $$0.755942\pi$$
$$312$$ 0 0
$$313$$ −6.31165e9 −0.657606 −0.328803 0.944399i $$-0.606645\pi$$
−0.328803 + 0.944399i $$0.606645\pi$$
$$314$$ −2.71319e9 + 3.38877e9i −0.279101 + 0.348597i
$$315$$ 0 0
$$316$$ 8.97112e9 2.01114e9i 0.899702 0.201695i
$$317$$ −1.65902e10 −1.64291 −0.821455 0.570273i $$-0.806837\pi$$
−0.821455 + 0.570273i $$0.806837\pi$$
$$318$$ 0 0
$$319$$ 2.37021e9i 0.228888i
$$320$$ −6.28763e9 8.07481e9i −0.599635 0.770074i
$$321$$ 0 0
$$322$$ −3.31828e9 + 4.14453e9i −0.308667 + 0.385525i
$$323$$ 1.42411e9i 0.130838i
$$324$$ 0 0
$$325$$ 1.01332e8 0.00908264
$$326$$ 7.22557e9 + 5.78509e9i 0.639738 + 0.512200i
$$327$$ 0 0
$$328$$ 7.90053e9 + 3.86129e9i 0.682591 + 0.333609i
$$329$$ 1.06683e10 0.910563
$$330$$ 0 0
$$331$$ 5.48640e9i 0.457062i 0.973537 + 0.228531i $$0.0733922\pi$$
−0.973537 + 0.228531i $$0.926608\pi$$
$$332$$ 1.29797e10 2.90978e9i 1.06834 0.239501i
$$333$$ 0 0
$$334$$ −5.84680e9 4.68118e9i −0.469821 0.376158i
$$335$$ 9.30657e9i 0.738942i
$$336$$ 0 0
$$337$$ −3.56226e8 −0.0276189 −0.0138095 0.999905i $$-0.504396\pi$$
−0.0138095 + 0.999905i $$0.504396\pi$$
$$338$$ −7.85810e9 + 9.81476e9i −0.602075 + 0.751992i
$$339$$ 0 0
$$340$$ −2.49675e9 1.11373e10i −0.186836 0.833421i
$$341$$ 1.25599e9 0.0928897
$$342$$ 0 0
$$343$$ 1.33911e10i 0.967476i
$$344$$ −1.06621e10 + 2.18156e10i −0.761396 + 1.55788i
$$345$$ 0 0
$$346$$ 2.06197e9 2.57540e9i 0.143872 0.179697i
$$347$$ 1.59731e10i 1.10172i 0.834599 + 0.550859i $$0.185700\pi$$
−0.834599 + 0.550859i $$0.814300\pi$$
$$348$$ 0 0
$$349$$ 1.03634e10 0.698553 0.349277 0.937020i $$-0.386427\pi$$
0.349277 + 0.937020i $$0.386427\pi$$
$$350$$ −3.23669e8 2.59142e8i −0.0215689 0.0172690i
$$351$$ 0 0
$$352$$ −1.88546e10 4.49560e9i −1.22814 0.292831i
$$353$$ 1.30979e10 0.843536 0.421768 0.906704i $$-0.361410\pi$$
0.421768 + 0.906704i $$0.361410\pi$$
$$354$$ 0 0
$$355$$ 7.29586e8i 0.0459370i
$$356$$ −4.66616e9 2.08144e10i −0.290509 1.29588i
$$357$$ 0 0
$$358$$ −1.77247e9 1.41911e9i −0.107906 0.0863940i
$$359$$ 3.31454e9i 0.199547i −0.995010 0.0997737i $$-0.968188\pi$$
0.995010 0.0997737i $$-0.0318119\pi$$
$$360$$ 0 0
$$361$$ 1.66039e10 0.977647
$$362$$ 4.82566e9 6.02724e9i 0.281010 0.350982i
$$363$$ 0 0
$$364$$ −1.91144e9 + 4.28505e8i −0.108882 + 0.0244090i
$$365$$ 3.49263e9 0.196780
$$366$$ 0 0
$$367$$ 1.96628e10i 1.08388i 0.840418 + 0.541939i $$0.182309\pi$$
−0.840418 + 0.541939i $$0.817691\pi$$
$$368$$ −6.63656e9 1.40580e10i −0.361870 0.766536i
$$369$$ 0 0
$$370$$ 2.11794e10 2.64530e10i 1.13007 1.41146i
$$371$$ 1.15308e9i 0.0608646i
$$372$$ 0 0
$$373$$ −2.10063e10 −1.08521 −0.542606 0.839987i $$-0.682562\pi$$
−0.542606 + 0.839987i $$0.682562\pi$$
$$374$$ −1.68750e10 1.35108e10i −0.862498 0.690551i
$$375$$ 0 0
$$376$$ −1.37163e10 + 2.80648e10i −0.686257 + 1.40414i
$$377$$ −7.01374e8 −0.0347204
$$378$$ 0 0
$$379$$ 3.04816e9i 0.147734i 0.997268 + 0.0738670i $$0.0235340\pi$$
−0.997268 + 0.0738670i $$0.976466\pi$$
$$380$$ 2.96899e9 6.65587e8i 0.142388 0.0319206i
$$381$$ 0 0
$$382$$ −1.23958e10 9.92461e9i −0.582133 0.466080i
$$383$$ 2.23357e10i 1.03802i 0.854770 + 0.519008i $$0.173698\pi$$
−0.854770 + 0.519008i $$0.826302\pi$$
$$384$$ 0 0
$$385$$ 1.57737e10 0.717945
$$386$$ 1.17593e10 1.46874e10i 0.529704 0.661599i
$$387$$ 0 0
$$388$$ −6.75466e9 3.01306e10i −0.298042 1.32948i
$$389$$ −3.13680e10 −1.36990 −0.684948 0.728592i $$-0.740175\pi$$
−0.684948 + 0.728592i $$0.740175\pi$$
$$390$$ 0 0
$$391$$ 1.73377e10i 0.741795i
$$392$$ −1.40132e10 6.84880e9i −0.593463 0.290048i
$$393$$ 0 0
$$394$$ −1.70538e10 + 2.13002e10i −0.707680 + 0.883892i
$$395$$ 2.19071e10i 0.899904i
$$396$$ 0 0
$$397$$ 7.65788e9 0.308281 0.154140 0.988049i $$-0.450739\pi$$
0.154140 + 0.988049i $$0.450739\pi$$
$$398$$ 3.11046e10 + 2.49036e10i 1.23963 + 0.992499i
$$399$$ 0 0
$$400$$ 1.09787e9 5.18285e8i 0.0428854 0.0202455i
$$401$$ 3.26120e10 1.26125 0.630623 0.776089i $$-0.282799\pi$$
0.630623 + 0.776089i $$0.282799\pi$$
$$402$$ 0 0
$$403$$ 3.71662e8i 0.0140906i
$$404$$ 1.55258e9 + 6.92561e9i 0.0582812 + 0.259976i
$$405$$ 0 0
$$406$$ 2.24029e9 + 1.79367e9i 0.0824520 + 0.0660144i
$$407$$ 6.41811e10i 2.33900i
$$408$$ 0 0
$$409$$ 2.26168e10 0.808236 0.404118 0.914707i $$-0.367578\pi$$
0.404118 + 0.914707i $$0.367578\pi$$
$$410$$ 1.30960e10 1.63569e10i 0.463450 0.578848i
$$411$$ 0 0
$$412$$ 2.61043e10 5.85205e9i 0.905990 0.203104i
$$413$$ −5.21155e9 −0.179129
$$414$$ 0 0
$$415$$ 3.16958e10i 1.06858i
$$416$$ 1.33030e9 5.57931e9i 0.0444199 0.186297i
$$417$$ 0 0
$$418$$ 3.60173e9 4.49856e9i 0.117979 0.147356i
$$419$$ 4.94503e10i 1.60440i 0.597054 + 0.802201i $$0.296338\pi$$
−0.597054 + 0.802201i $$0.703662\pi$$
$$420$$ 0 0
$$421$$ −3.34077e10 −1.06345 −0.531726 0.846916i $$-0.678457\pi$$
−0.531726 + 0.846916i $$0.678457\pi$$
$$422$$ 1.83321e10 + 1.46774e10i 0.578045 + 0.462807i
$$423$$ 0 0
$$424$$ 3.03339e9 + 1.48253e9i 0.0938565 + 0.0458713i
$$425$$ 1.35399e9 0.0415012
$$426$$ 0 0
$$427$$ 2.06280e10i 0.620505i
$$428$$ −2.50618e10 + 5.61834e9i −0.746857 + 0.167430i
$$429$$ 0 0
$$430$$ 4.51660e10 + 3.61617e10i 1.32111 + 1.05773i
$$431$$ 3.06956e10i 0.889544i 0.895644 + 0.444772i $$0.146715\pi$$
−0.895644 + 0.444772i $$0.853285\pi$$
$$432$$ 0 0
$$433$$ 2.88433e9 0.0820529 0.0410265 0.999158i $$-0.486937\pi$$
0.0410265 + 0.999158i $$0.486937\pi$$
$$434$$ 9.50477e8 1.18715e9i 0.0267906 0.0334615i
$$435$$ 0 0
$$436$$ 3.30801e9 + 1.47561e10i 0.0915421 + 0.408343i
$$437$$ 4.62189e9 0.126734
$$438$$ 0 0
$$439$$ 6.92422e10i 1.86429i 0.362088 + 0.932144i $$0.382064\pi$$
−0.362088 + 0.932144i $$0.617936\pi$$
$$440$$ −2.02805e10 + 4.14956e10i −0.541088 + 1.10711i
$$441$$ 0 0
$$442$$ 3.99802e9 4.99353e9i 0.104751 0.130833i
$$443$$ 2.06609e10i 0.536455i −0.963356 0.268228i $$-0.913562\pi$$
0.963356 0.268228i $$-0.0864379\pi$$
$$444$$ 0 0
$$445$$ −5.08278e10 −1.29617
$$446$$ −1.84752e10 1.47920e10i −0.466928 0.373842i
$$447$$ 0 0
$$448$$ −1.85175e10 + 1.44191e10i −0.459696 + 0.357952i
$$449$$ −2.11092e10 −0.519382 −0.259691 0.965692i $$-0.583621\pi$$
−0.259691 + 0.965692i $$0.583621\pi$$
$$450$$ 0 0
$$451$$ 3.96855e10i 0.959237i
$$452$$ 3.08476e9 + 1.37602e10i 0.0739039 + 0.329664i
$$453$$ 0 0
$$454$$ 9.36818e9 + 7.50054e9i 0.220512 + 0.176551i
$$455$$ 4.66764e9i 0.108906i
$$456$$ 0 0
$$457$$ −2.06831e10 −0.474188 −0.237094 0.971487i $$-0.576195\pi$$
−0.237094 + 0.971487i $$0.576195\pi$$
$$458$$ −2.84784e10 + 3.55695e10i −0.647223 + 0.808381i
$$459$$ 0 0
$$460$$ −3.61456e10 + 8.10309e9i −0.807279 + 0.180975i
$$461$$ −7.65072e10 −1.69394 −0.846971 0.531640i $$-0.821576\pi$$
−0.846971 + 0.531640i $$0.821576\pi$$
$$462$$ 0 0
$$463$$ 3.41303e9i 0.0742704i 0.999310 + 0.0371352i $$0.0118232\pi$$
−0.999310 + 0.0371352i $$0.988177\pi$$
$$464$$ −7.59895e9 + 3.58734e9i −0.163939 + 0.0773929i
$$465$$ 0 0
$$466$$ −2.20621e9 + 2.75555e9i −0.0467845 + 0.0584339i
$$467$$ 1.92903e10i 0.405576i −0.979223 0.202788i $$-0.935000\pi$$
0.979223 0.202788i $$-0.0650002\pi$$
$$468$$ 0 0
$$469$$ −2.13423e10 −0.441112
$$470$$ 5.81039e10 + 4.65204e10i 1.19073 + 0.953349i
$$471$$ 0 0
$$472$$ 6.70056e9 1.37099e10i 0.135003 0.276227i
$$473$$ 1.09583e11 2.18927
$$474$$ 0 0
$$475$$ 3.60948e8i 0.00709040i
$$476$$ −2.55406e10 + 5.72567e9i −0.497511 + 0.111532i
$$477$$ 0 0
$$478$$ 5.05212e10 + 4.04493e10i 0.967748 + 0.774818i
$$479$$ 2.43887e10i 0.463282i 0.972801 + 0.231641i $$0.0744095\pi$$
−0.972801 + 0.231641i $$0.925590\pi$$
$$480$$ 0 0
$$481$$ 1.89920e10 0.354806
$$482$$ 6.17983e10 7.71861e10i 1.14496 1.43005i
$$483$$ 0 0
$$484$$ 7.13124e9 + 3.18104e10i 0.129952 + 0.579679i
$$485$$ −7.35776e10 −1.32978
$$486$$ 0 0
$$487$$ 9.30801e10i 1.65478i −0.561626 0.827391i $$-0.689824\pi$$
0.561626 0.827391i $$-0.310176\pi$$
$$488$$ 5.42656e10 + 2.65217e10i 0.956853 + 0.467651i
$$489$$ 0 0
$$490$$ −2.32284e10 + 2.90123e10i −0.402935 + 0.503266i
$$491$$ 2.12850e9i 0.0366225i 0.999832 + 0.0183113i $$0.00582898\pi$$
−0.999832 + 0.0183113i $$0.994171\pi$$
$$492$$ 0 0
$$493$$ −9.37175e9 −0.158647
$$494$$ 1.33118e9 + 1.06580e9i 0.0223526 + 0.0178964i
$$495$$ 0 0
$$496$$ 1.90095e9 + 4.02673e9i 0.0314083 + 0.0665312i
$$497$$ −1.67312e9 −0.0274221
$$498$$ 0 0
$$499$$ 1.04101e10i 0.167901i 0.996470 + 0.0839503i $$0.0267537\pi$$
−0.996470 + 0.0839503i $$0.973246\pi$$
$$500$$ −1.39766e10 6.23454e10i −0.223625 0.997527i
$$501$$ 0 0
$$502$$ −6.51187e10 5.21367e10i −1.02539 0.820973i
$$503$$ 3.93019e10i 0.613962i −0.951716 0.306981i $$-0.900681\pi$$
0.951716 0.306981i $$-0.0993188\pi$$
$$504$$ 0 0
$$505$$ 1.69120e10 0.260034
$$506$$ −4.38487e10 + 5.47670e10i −0.668890 + 0.835444i
$$507$$ 0 0
$$508$$ 6.42387e10 1.44010e10i 0.964587 0.216241i
$$509$$ 3.25113e10 0.484354 0.242177 0.970232i $$-0.422139\pi$$
0.242177 + 0.970232i $$0.422139\pi$$
$$510$$ 0 0
$$511$$ 8.00947e9i 0.117468i
$$512$$ −1.41237e10 6.72524e10i −0.205526 0.978652i
$$513$$ 0 0
$$514$$ 6.13693e10 7.66503e10i 0.879223 1.09815i
$$515$$ 6.37455e10i 0.906194i
$$516$$ 0 0
$$517$$ 1.40973e11 1.97322
$$518$$ −6.06633e10 4.85695e10i −0.842572 0.674598i
$$519$$ 0 0
$$520$$ −1.22791e10 6.00125e9i −0.167939 0.0820783i
$$521$$ −1.84550e9 −0.0250475 −0.0125237 0.999922i $$-0.503987\pi$$
−0.0125237 + 0.999922i $$0.503987\pi$$
$$522$$ 0 0
$$523$$ 6.23770e10i 0.833715i 0.908972 + 0.416858i $$0.136869\pi$$
−0.908972 + 0.416858i $$0.863131\pi$$
$$524$$ 7.79814e10 1.74818e10i 1.03435 0.231879i
$$525$$ 0 0
$$526$$ −8.70448e10 6.96916e10i −1.13710 0.910411i
$$527$$ 4.96614e9i 0.0643838i
$$528$$ 0 0
$$529$$ 2.20424e10 0.281473
$$530$$ 5.02817e9 6.28018e9i 0.0637245 0.0795919i
$$531$$ 0 0
$$532$$ −1.52635e9 6.80863e9i −0.0190550 0.0849988i
$$533$$ 1.17434e10 0.145508
$$534$$ 0 0
$$535$$ 6.11998e10i 0.747025i
$$536$$ 2.74400e10 5.61446e10i 0.332449 0.680219i
$$537$$ 0 0
$$538$$ −2.70720e10 + 3.38130e10i −0.323141 + 0.403603i
$$539$$ 7.03905e10i 0.833986i
$$540$$ 0 0
$$541$$ −7.45917e10 −0.870766 −0.435383 0.900245i $$-0.643387\pi$$
−0.435383 + 0.900245i $$0.643387\pi$$
$$542$$ −9.97991e10 7.99032e10i −1.15646 0.925907i
$$543$$ 0 0
$$544$$ 1.77755e10 7.45506e10i 0.202967 0.851246i
$$545$$ 3.60337e10 0.408435
$$546$$ 0 0
$$547$$ 1.41531e9i 0.0158089i 0.999969 + 0.00790445i $$0.00251609\pi$$
−0.999969 + 0.00790445i $$0.997484\pi$$
$$548$$ 1.24309e10 + 5.54506e10i 0.137841 + 0.614871i
$$549$$ 0 0
$$550$$ −4.27705e9 3.42438e9i −0.0467405 0.0374224i
$$551$$ 2.49833e9i 0.0271046i
$$552$$ 0 0
$$553$$ −5.02383e10 −0.537198
$$554$$ −8.22965e10 + 1.02788e11i −0.873660 + 1.09120i
$$555$$ 0 0
$$556$$ −7.36985e10 + 1.65217e10i −0.771187 + 0.172884i
$$557$$ 1.37543e11 1.42895 0.714475 0.699661i $$-0.246666\pi$$
0.714475 + 0.699661i $$0.246666\pi$$
$$558$$ 0 0
$$559$$ 3.24270e10i 0.332093i
$$560$$ 2.38737e10 + 5.05710e10i 0.242755 + 0.514220i
$$561$$ 0 0
$$562$$ −3.08105e10 + 3.84823e10i −0.308854 + 0.385759i
$$563$$ 1.06415e11i 1.05918i 0.848255 + 0.529589i $$0.177654\pi$$
−0.848255 + 0.529589i $$0.822346\pi$$
$$564$$ 0 0
$$565$$ 3.36018e10 0.329738
$$566$$ 1.46273e10 + 1.17112e10i 0.142528 + 0.114113i
$$567$$ 0 0
$$568$$ 2.15115e9 4.40143e9i 0.0206670 0.0422864i
$$569$$ −4.02429e10 −0.383919 −0.191960 0.981403i $$-0.561484\pi$$
−0.191960 + 0.981403i $$0.561484\pi$$
$$570$$ 0 0
$$571$$ 1.50341e11i 1.41427i 0.707077 + 0.707137i $$0.250014\pi$$
−0.707077 + 0.707137i $$0.749986\pi$$
$$572$$ −2.52583e10 + 5.66238e9i −0.235950 + 0.0528951i
$$573$$ 0 0
$$574$$ −3.75103e10 3.00323e10i −0.345544 0.276657i
$$575$$ 4.39432e9i 0.0401994i
$$576$$ 0 0
$$577$$ 4.96477e9 0.0447915 0.0223958 0.999749i $$-0.492871\pi$$
0.0223958 + 0.999749i $$0.492871\pi$$
$$578$$ −1.63361e10 + 2.04038e10i −0.146365 + 0.182810i
$$579$$ 0 0
$$580$$ 4.38006e9 + 1.95382e10i 0.0387051 + 0.172652i
$$581$$ −7.26862e10 −0.637892
$$582$$ 0 0
$$583$$ 1.52372e10i 0.131895i
$$584$$ 2.10703e10 + 1.02979e10i 0.181142 + 0.0885313i
$$585$$ 0 0
$$586$$ −4.80980e10 + 6.00743e10i −0.407884 + 0.509446i
$$587$$ 1.53440e11i 1.29237i −0.763181 0.646185i $$-0.776363\pi$$
0.763181 0.646185i $$-0.223637\pi$$
$$588$$ 0 0
$$589$$ −1.32388e9 −0.0109999
$$590$$ −2.83843e10 2.27256e10i −0.234245 0.187546i
$$591$$ 0 0
$$592$$ 2.05766e11 9.71390e10i 1.67528 0.790873i
$$593$$ −2.06036e11 −1.66619 −0.833094 0.553131i $$-0.813433\pi$$
−0.833094 + 0.553131i $$0.813433\pi$$
$$594$$ 0 0
$$595$$ 6.23689e10i 0.497623i
$$596$$ 2.26017e10 + 1.00820e11i 0.179125 + 0.799027i
$$597$$ 0 0
$$598$$ −1.62063e10 1.29754e10i −0.126730 0.101465i
$$599$$ 2.30634e11i 1.79150i 0.444558 + 0.895750i $$0.353361\pi$$
−0.444558 + 0.895750i $$0.646639\pi$$
$$600$$ 0 0
$$601$$ 1.01422e11 0.777382 0.388691 0.921368i $$-0.372927\pi$$
0.388691 + 0.921368i $$0.372927\pi$$
$$602$$ 8.29277e10 1.03577e11i 0.631413 0.788635i
$$603$$ 0 0
$$604$$ −2.09079e11 + 4.68711e10i −1.57095 + 0.352174i
$$605$$ 7.76795e10 0.579809
$$606$$ 0 0
$$607$$ 1.97883e11i 1.45765i −0.684700 0.728825i $$-0.740067\pi$$
0.684700 0.728825i $$-0.259933\pi$$
$$608$$ 1.98738e10 + 4.73860e9i 0.145434 + 0.0346766i
$$609$$ 0 0
$$610$$ 8.99511e10 1.12349e11i 0.649661 0.811427i
$$611$$ 4.17158e10i 0.299320i
$$612$$ 0 0
$$613$$ 1.27158e11 0.900538 0.450269 0.892893i $$-0.351328\pi$$
0.450269 + 0.892893i $$0.351328\pi$$
$$614$$ −4.36121e10 3.49176e10i −0.306855 0.245681i
$$615$$ 0 0
$$616$$ 9.51595e10 + 4.65082e10i 0.660890 + 0.323003i
$$617$$ 5.06702e10 0.349632 0.174816 0.984601i $$-0.444067\pi$$
0.174816 + 0.984601i $$0.444067\pi$$
$$618$$ 0 0
$$619$$ 7.06748e10i 0.481395i −0.970600 0.240698i $$-0.922624\pi$$
0.970600 0.240698i $$-0.0773762\pi$$
$$620$$ 1.03534e10 2.32102e9i 0.0700675 0.0157077i
$$621$$ 0 0
$$622$$ 1.62128e11 + 1.29807e11i 1.08317 + 0.867231i
$$623$$ 1.16561e11i 0.773748i
$$624$$ 0 0
$$625$$ −1.45008e11 −0.950327
$$626$$ −6.31165e10 + 7.88325e10i −0.411004 + 0.513343i
$$627$$ 0 0
$$628$$ 1.51938e10 + 6.77754e10i 0.0976853 + 0.435746i
$$629$$ 2.53771e11 1.62121
$$630$$ 0 0
$$631$$ 1.65273e11i 1.04252i 0.853399 + 0.521259i $$0.174537\pi$$
−0.853399 + 0.521259i $$0.825463\pi$$
$$632$$ 6.45921e10 1.32161e11i 0.404866 0.828388i
$$633$$ 0 0
$$634$$ −1.65902e11 + 2.07211e11i −1.02682 + 1.28250i
$$635$$ 1.56868e11i 0.964804i
$$636$$ 0 0
$$637$$ −2.08294e10 −0.126508
$$638$$ 2.96039e10 + 2.37021e10i 0.178676 + 0.143055i
$$639$$ 0 0
$$640$$ −1.63731e11 2.21570e9i −0.975911 0.0132066i
$$641$$ −1.12013e11 −0.663490 −0.331745 0.943369i $$-0.607637\pi$$
−0.331745 + 0.943369i $$0.607637\pi$$
$$642$$ 0 0
$$643$$ 2.65913e11i 1.55559i −0.628518 0.777795i $$-0.716338\pi$$
0.628518 0.777795i $$-0.283662\pi$$
$$644$$ 1.85824e10 + 8.28907e10i 0.108033 + 0.481906i
$$645$$ 0 0
$$646$$ 1.77872e10 + 1.42411e10i 0.102136 + 0.0817739i
$$647$$ 2.71996e11i 1.55219i −0.630614 0.776097i $$-0.717197\pi$$
0.630614 0.776097i $$-0.282803\pi$$
$$648$$ 0 0
$$649$$ −6.88669e10 −0.388179
$$650$$ 1.01332e9 1.26563e9i 0.00567665 0.00709013i
$$651$$ 0 0
$$652$$ 1.44511e11 3.23965e10i 0.799672 0.179270i
$$653$$ −3.03789e11 −1.67078 −0.835391 0.549656i $$-0.814759\pi$$
−0.835391 + 0.549656i $$0.814759\pi$$
$$654$$ 0 0
$$655$$ 1.90427e11i 1.03458i
$$656$$ 1.27233e11 6.00646e10i 0.687043 0.324342i
$$657$$ 0 0
$$658$$ 1.06683e11 1.33247e11i 0.569102 0.710808i
$$659$$ 4.18575e10i 0.221938i −0.993824 0.110969i $$-0.964605\pi$$
0.993824 0.110969i $$-0.0353954\pi$$
$$660$$ 0 0
$$661$$ −2.46529e11 −1.29141 −0.645703 0.763589i $$-0.723435\pi$$
−0.645703 + 0.763589i $$0.723435\pi$$
$$662$$ 6.85251e10 + 5.48640e10i 0.356794 + 0.285664i
$$663$$ 0 0
$$664$$ 9.34537e10 1.91214e11i 0.480755 0.983665i
$$665$$ −1.66264e10 −0.0850179
$$666$$ 0 0
$$667$$ 3.04155e10i 0.153671i
$$668$$ −1.16936e11 + 2.62146e10i −0.587276 + 0.131655i
$$669$$ 0 0
$$670$$ −1.16239e11 9.30657e10i −0.576837 0.461839i
$$671$$ 2.72584e11i 1.34465i
$$672$$ 0 0
$$673$$ −3.15336e11 −1.53714 −0.768569 0.639767i $$-0.779031\pi$$
−0.768569 + 0.639767i $$0.779031\pi$$
$$674$$ −3.56226e9 + 4.44927e9i −0.0172618 + 0.0215600i
$$675$$ 0 0
$$676$$ 4.40053e10 + 1.96295e11i 0.210726 + 0.939989i
$$677$$ 2.47236e10 0.117695 0.0588475 0.998267i $$-0.481257\pi$$
0.0588475 + 0.998267i $$0.481257\pi$$
$$678$$ 0 0
$$679$$ 1.68731e11i 0.793811i
$$680$$ −1.64072e11 8.01886e10i −0.767361 0.375039i
$$681$$ 0 0
$$682$$ 1.25599e10 1.56873e10i 0.0580561 0.0725120i
$$683$$ 7.20843e10i 0.331251i −0.986189 0.165626i $$-0.947036\pi$$
0.986189 0.165626i $$-0.0529644\pi$$
$$684$$ 0 0
$$685$$ 1.35408e11 0.615009
$$686$$ 1.67255e11 + 1.33911e11i 0.755235 + 0.604672i
$$687$$ 0 0
$$688$$ 1.65855e11 + 3.51326e11i 0.740246 + 1.56804i
$$689$$ 4.50887e9 0.0200074
$$690$$ 0 0
$$691$$ 2.95424e11i 1.29578i −0.761732 0.647892i $$-0.775651\pi$$
0.761732 0.647892i $$-0.224349\pi$$
$$692$$ −1.15470e10 5.15080e10i −0.0503554 0.224621i
$$693$$ 0 0
$$694$$ 1.99503e11 + 1.59731e11i 0.860028 + 0.688573i
$$695$$ 1.79968e11i 0.771360i
$$696$$ 0 0
$$697$$ 1.56916e11 0.664867
$$698$$ 1.03634e11 1.29438e11i 0.436596 0.545308i
$$699$$ 0 0
$$700$$ −6.47338e9 + 1.45120e9i −0.0269612 + 0.00604414i
$$701$$ 2.87925e11 1.19236 0.596180 0.802851i $$-0.296685\pi$$
0.596180 + 0.802851i $$0.296685\pi$$
$$702$$ 0 0
$$703$$ 6.76504e10i 0.276980i
$$704$$ −2.44696e11 + 1.90538e11i −0.996176 + 0.775694i
$$705$$ 0 0
$$706$$ 1.30979e11 1.63593e11i 0.527210 0.658485i
$$707$$ 3.87834e10i 0.155227i
$$708$$ 0 0
$$709$$ 2.51685e11 0.996030 0.498015 0.867168i $$-0.334062\pi$$
0.498015 + 0.867168i $$0.334062\pi$$
$$710$$ −9.11252e9 7.29586e9i −0.0358596 0.0287106i
$$711$$ 0 0
$$712$$ −3.06633e11 1.49864e11i −1.19316 0.583144i
$$713$$ 1.61174e10 0.0623643
$$714$$ 0 0
$$715$$ 6.16795e10i 0.236003i
$$716$$ −3.54493e10 + 7.94701e9i −0.134883 + 0.0302379i
$$717$$ 0 0
$$718$$ −4.13986e10 3.31454e10i −0.155772 0.124717i
$$719$$ 1.38856e11i 0.519574i 0.965666 + 0.259787i $$0.0836524\pi$$
−0.965666 + 0.259787i $$0.916348\pi$$
$$720$$ 0 0
$$721$$ −1.46184e11 −0.540953
$$722$$ 1.66039e11 2.07383e11i 0.611029 0.763175i
$$723$$ 0 0
$$724$$ −2.70237e10 1.20545e11i −0.0983536 0.438727i
$$725$$ −2.37531e9 −0.00859743
$$726$$ 0 0
$$727$$ 1.79083e11i 0.641088i −0.947234 0.320544i $$-0.896134\pi$$
0.947234 0.320544i $$-0.103866\pi$$
$$728$$ −1.37623e10 + 2.81589e10i −0.0489967 + 0.100251i
$$729$$ 0 0
$$730$$ 3.49263e10 4.36230e10i 0.122988 0.153612i
$$731$$ 4.33289e11i 1.51743i
$$732$$ 0 0
$$733$$ 2.17618e11 0.753839 0.376920 0.926246i $$-0.376983\pi$$
0.376920 + 0.926246i $$0.376983\pi$$
$$734$$ 2.45588e11 + 1.96628e11i 0.846101 + 0.677423i
$$735$$ 0 0
$$736$$ −2.41950e11 5.76895e10i −0.824546 0.196601i
$$737$$ −2.82023e11 −0.955904
$$738$$ 0 0
$$739$$ 4.84950e11i 1.62599i 0.582268 + 0.812997i $$0.302166\pi$$
−0.582268 + 0.812997i $$0.697834\pi$$
$$740$$ −1.18605e11 5.29061e11i −0.395525 1.76433i
$$741$$ 0 0
$$742$$ −1.44020e10 1.15308e10i −0.0475124 0.0380404i
$$743$$ 2.03509e11i 0.667771i −0.942614 0.333886i $$-0.891640\pi$$
0.942614 0.333886i $$-0.108360\pi$$
$$744$$ 0 0
$$745$$ 2.46198e11 0.799206
$$746$$ −2.10063e11 + 2.62369e11i −0.678258 + 0.847144i
$$747$$ 0 0
$$748$$ −3.37500e11 + 7.56606e10i −1.07812 + 0.241693i
$$749$$ 1.40346e11 0.445937
$$750$$ 0 0
$$751$$ 2.34693e11i 0.737804i 0.929468 + 0.368902i $$0.120266\pi$$
−0.929468 + 0.368902i $$0.879734\pi$$
$$752$$ 2.13365e11 + 4.51965e11i 0.667194 + 1.41330i
$$753$$ 0 0
$$754$$ −7.01374e9 + 8.76016e9i −0.0217002 + 0.0271036i
$$755$$ 5.10561e11i 1.57130i
$$756$$ 0 0
$$757$$ −3.84882e11 −1.17204 −0.586022 0.810295i $$-0.699307\pi$$
−0.586022 + 0.810295i $$0.699307\pi$$
$$758$$ 3.80715e10 + 3.04816e10i 0.115325 + 0.0923338i
$$759$$ 0 0
$$760$$ 2.13767e10 4.37386e10i 0.0640748 0.131102i
$$761$$ −2.39209e11 −0.713244 −0.356622 0.934249i $$-0.616072\pi$$
−0.356622 + 0.934249i $$0.616072\pi$$
$$762$$ 0 0
$$763$$ 8.26340e10i 0.243815i
$$764$$ −2.47917e11 + 5.55778e10i −0.727666 + 0.163128i
$$765$$ 0 0
$$766$$ 2.78972e11 + 2.23357e11i 0.810301 + 0.648760i
$$767$$ 2.03786e10i 0.0588833i
$$768$$ 0 0
$$769$$ 2.08457e11 0.596089 0.298045 0.954552i $$-0.403666\pi$$
0.298045 + 0.954552i $$0.403666\pi$$
$$770$$ 1.57737e11 1.97014e11i 0.448716 0.560446i
$$771$$ 0 0
$$772$$ −6.58522e10 2.93748e11i −0.185396 0.826999i