# Properties

 Label 100.9.b.c.51.1 Level $100$ Weight $9$ Character 100.51 Analytic conductor $40.738$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [100,9,Mod(51,100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(100, 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("100.51");

S:= CuspForms(chi, 9);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$100 = 2^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$9$$ Character orbit: $$[\chi]$$ $$=$$ 100.b (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: $$40.7378610061$$ 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 51.1 Root $$0.500000 + 3.12250i$$ of defining polynomial Character $$\chi$$ $$=$$ 100.51 Dual form 100.9.b.c.51.2

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(10.0000 - 12.4900i) q^{2} -99.9200i q^{3} +(-56.0000 - 249.800i) q^{4} +(-1248.00 - 999.200i) q^{6} -1398.88i q^{7} +(-3680.00 - 1798.56i) q^{8} -3423.00 q^{9} +O(q^{10})$$ $$q+(10.0000 - 12.4900i) q^{2} -99.9200i q^{3} +(-56.0000 - 249.800i) q^{4} +(-1248.00 - 999.200i) q^{6} -1398.88i q^{7} +(-3680.00 - 1798.56i) q^{8} -3423.00 q^{9} -18485.2i q^{11} +(-24960.0 + 5595.52i) q^{12} +5470.00 q^{13} +(-17472.0 - 13988.8i) q^{14} +(-59264.0 + 27977.6i) q^{16} -73090.0 q^{17} +(-34230.0 + 42753.3i) q^{18} -19484.4i q^{19} -139776. q^{21} +(-230880. - 184852. i) q^{22} +237210. i q^{23} +(-179712. + 367705. i) q^{24} +(54700.0 - 68320.3i) q^{26} -313549. i q^{27} +(-349440. + 78337.3i) q^{28} -128222. q^{29} -67945.6i q^{31} +(-243200. + 1.01998e6i) q^{32} -1.84704e6 q^{33} +(-730900. + 912894. i) q^{34} +(191688. + 855065. i) q^{36} +3.47203e6 q^{37} +(-243360. - 194844. i) q^{38} -546562. i q^{39} +2.14688e6 q^{41} +(-1.39776e6 + 1.74580e6i) q^{42} +5.92815e6i q^{43} +(-4.61760e6 + 1.03517e6i) q^{44} +(2.96275e6 + 2.37210e6i) q^{46} -7.62629e6i q^{47} +(2.79552e6 + 5.92166e6i) q^{48} +3.80794e6 q^{49} +7.30315e6i q^{51} +(-306320. - 1.36641e6i) q^{52} -824290. q^{53} +(-3.91622e6 - 3.13549e6i) q^{54} +(-2.51597e6 + 5.14788e6i) q^{56} -1.94688e6 q^{57} +(-1.28222e6 + 1.60149e6i) q^{58} -3.72552e6i q^{59} -1.47461e7 q^{61} +(-848640. - 679456. i) q^{62} +4.78836e6i q^{63} +(1.03076e7 + 1.32374e7i) q^{64} +(-1.84704e7 + 2.30695e7i) q^{66} -1.52567e7i q^{67} +(4.09304e6 + 1.82579e7i) q^{68} +2.37020e7 q^{69} -1.19604e6i q^{71} +(1.25966e7 + 6.15647e6i) q^{72} +5.72563e6 q^{73} +(3.47203e7 - 4.33656e7i) q^{74} +(-4.86720e6 + 1.09113e6i) q^{76} -2.58586e7 q^{77} +(-6.82656e6 - 5.46562e6i) q^{78} +3.59132e7i q^{79} -5.37881e7 q^{81} +(2.14688e7 - 2.68145e7i) q^{82} +5.19603e7i q^{83} +(7.82746e6 + 3.49160e7i) q^{84} +(7.40426e7 + 5.92815e7i) q^{86} +1.28119e7i q^{87} +(-3.32467e7 + 6.80255e7i) q^{88} -8.33242e7 q^{89} -7.65187e6i q^{91} +(5.92550e7 - 1.32838e7i) q^{92} -6.78912e6 q^{93} +(-9.52524e7 - 7.62629e7i) q^{94} +(1.01917e8 + 2.43005e7i) q^{96} -1.20619e8 q^{97} +(3.80794e7 - 4.75611e7i) q^{98} +6.32748e7i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 20 q^{2} - 112 q^{4} - 2496 q^{6} - 7360 q^{8} - 6846 q^{9}+O(q^{10})$$ 2 * q + 20 * q^2 - 112 * q^4 - 2496 * q^6 - 7360 * q^8 - 6846 * q^9 $$2 q + 20 q^{2} - 112 q^{4} - 2496 q^{6} - 7360 q^{8} - 6846 q^{9} - 49920 q^{12} + 10940 q^{13} - 34944 q^{14} - 118528 q^{16} - 146180 q^{17} - 68460 q^{18} - 279552 q^{21} - 461760 q^{22} - 359424 q^{24} + 109400 q^{26} - 698880 q^{28} - 256444 q^{29} - 486400 q^{32} - 3694080 q^{33} - 1461800 q^{34} + 383376 q^{36} + 6944060 q^{37} - 486720 q^{38} + 4293764 q^{41} - 2795520 q^{42} - 9235200 q^{44} + 5925504 q^{46} + 5591040 q^{48} + 7615874 q^{49} - 612640 q^{52} - 1648580 q^{53} - 7832448 q^{54} - 5031936 q^{56} - 3893760 q^{57} - 2564440 q^{58} - 29492156 q^{61} - 1697280 q^{62} + 20615168 q^{64} - 36940800 q^{66} + 8186080 q^{68} + 47404032 q^{69} + 25193280 q^{72} + 11451260 q^{73} + 69440600 q^{74} - 9734400 q^{76} - 51717120 q^{77} - 13653120 q^{78} - 107576190 q^{81} + 42937640 q^{82} + 15654912 q^{84} + 148085184 q^{86} - 66493440 q^{88} - 166648444 q^{89} + 118510080 q^{92} - 13578240 q^{93} - 190504704 q^{94} + 203833344 q^{96} - 241238020 q^{97} + 76158740 q^{98}+O(q^{100})$$ 2 * q + 20 * q^2 - 112 * q^4 - 2496 * q^6 - 7360 * q^8 - 6846 * q^9 - 49920 * q^12 + 10940 * q^13 - 34944 * q^14 - 118528 * q^16 - 146180 * q^17 - 68460 * q^18 - 279552 * q^21 - 461760 * q^22 - 359424 * q^24 + 109400 * q^26 - 698880 * q^28 - 256444 * q^29 - 486400 * q^32 - 3694080 * q^33 - 1461800 * q^34 + 383376 * q^36 + 6944060 * q^37 - 486720 * q^38 + 4293764 * q^41 - 2795520 * q^42 - 9235200 * q^44 + 5925504 * q^46 + 5591040 * q^48 + 7615874 * q^49 - 612640 * q^52 - 1648580 * q^53 - 7832448 * q^54 - 5031936 * q^56 - 3893760 * q^57 - 2564440 * q^58 - 29492156 * q^61 - 1697280 * q^62 + 20615168 * q^64 - 36940800 * q^66 + 8186080 * q^68 + 47404032 * q^69 + 25193280 * q^72 + 11451260 * q^73 + 69440600 * q^74 - 9734400 * q^76 - 51717120 * q^77 - 13653120 * q^78 - 107576190 * q^81 + 42937640 * q^82 + 15654912 * q^84 + 148085184 * q^86 - 66493440 * q^88 - 166648444 * q^89 + 118510080 * q^92 - 13578240 * q^93 - 190504704 * q^94 + 203833344 * q^96 - 241238020 * q^97 + 76158740 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$$.

 $$n$$ $$51$$ $$77$$ $$\chi(n)$$ $$-1$$ $$1$$

## 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
$$3$$ 99.9200i 1.23358i −0.787128 0.616790i $$-0.788433\pi$$
0.787128 0.616790i $$-0.211567\pi$$
$$4$$ −56.0000 249.800i −0.218750 0.975781i
$$5$$ 0 0
$$6$$ −1248.00 999.200i −0.962963 0.770987i
$$7$$ 1398.88i 0.582624i −0.956628 0.291312i $$-0.905908\pi$$
0.956628 0.291312i $$-0.0940917\pi$$
$$8$$ −3680.00 1798.56i −0.898438 0.439101i
$$9$$ −3423.00 −0.521719
$$10$$ 0 0
$$11$$ 18485.2i 1.26256i −0.775554 0.631282i $$-0.782529\pi$$
0.775554 0.631282i $$-0.217471\pi$$
$$12$$ −24960.0 + 5595.52i −1.20370 + 0.269846i
$$13$$ 5470.00 0.191520 0.0957600 0.995404i $$-0.469472\pi$$
0.0957600 + 0.995404i $$0.469472\pi$$
$$14$$ −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 $$0.644155\pi$$
$$18$$ −34230.0 + 42753.3i −0.326075 + 0.407267i
$$19$$ 19484.4i 0.149511i −0.997202 0.0747554i $$-0.976182\pi$$
0.997202 0.0747554i $$-0.0238176\pi$$
$$20$$ 0 0
$$21$$ −139776. −0.718713
$$22$$ −230880. 184852.i −0.985588 0.789102i
$$23$$ 237210.i 0.847660i 0.905742 + 0.423830i $$0.139315\pi$$
−0.905742 + 0.423830i $$0.860685\pi$$
$$24$$ −179712. + 367705.i −0.541667 + 1.10829i
$$25$$ 0 0
$$26$$ 54700.0 68320.3i 0.119700 0.149505i
$$27$$ 313549.i 0.589997i
$$28$$ −349440. + 78337.3i −0.568513 + 0.127449i
$$29$$ −128222. −0.181289 −0.0906443 0.995883i $$-0.528893\pi$$
−0.0906443 + 0.995883i $$0.528893\pi$$
$$30$$ 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
$$33$$ −1.84704e6 −1.55747
$$34$$ −730900. + 912894.i −0.546943 + 0.683132i
$$35$$ 0 0
$$36$$ 191688. + 855065.i 0.114126 + 0.509084i
$$37$$ 3.47203e6 1.85258 0.926289 0.376813i $$-0.122980\pi$$
0.926289 + 0.376813i $$0.122980\pi$$
$$38$$ −243360. 194844.i −0.116712 0.0934442i
$$39$$ 546562.i 0.236255i
$$40$$ 0 0
$$41$$ 2.14688e6 0.759754 0.379877 0.925037i $$-0.375966\pi$$
0.379877 + 0.925037i $$0.375966\pi$$
$$42$$ −1.39776e6 + 1.74580e6i −0.449196 + 0.561045i
$$43$$ 5.92815e6i 1.73399i 0.498321 + 0.866993i $$0.333950\pi$$
−0.498321 + 0.866993i $$0.666050\pi$$
$$44$$ −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 $$-0.285511\pi$$
$$48$$ 2.79552e6 + 5.92166e6i 0.526620 + 1.11552i
$$49$$ 3.80794e6 0.660550
$$50$$ 0 0
$$51$$ 7.30315e6i 1.07952i
$$52$$ −306320. 1.36641e6i −0.0418950 0.186881i
$$53$$ −824290. −0.104466 −0.0522332 0.998635i $$-0.516634\pi$$
−0.0522332 + 0.998635i $$0.516634\pi$$
$$54$$ −3.91622e6 3.13549e6i −0.460567 0.368748i
$$55$$ 0 0
$$56$$ −2.51597e6 + 5.14788e6i −0.255831 + 0.523451i
$$57$$ −1.94688e6 −0.184433
$$58$$ −1.28222e6 + 1.60149e6i −0.113305 + 0.141518i
$$59$$ 3.72552e6i 0.307453i −0.988113 0.153726i $$-0.950873\pi$$
0.988113 0.153726i $$-0.0491274\pi$$
$$60$$ 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
$$63$$ 4.78836e6i 0.303966i
$$64$$ 1.03076e7 + 1.32374e7i 0.614380 + 0.789010i
$$65$$ 0 0
$$66$$ −1.84704e7 + 2.30695e7i −0.973421 + 1.21580i
$$67$$ 1.52567e7i 0.757113i −0.925578 0.378557i $$-0.876421\pi$$
0.925578 0.378557i $$-0.123579\pi$$
$$68$$ 4.09304e6 + 1.82579e7i 0.191430 + 0.853915i
$$69$$ 2.37020e7 1.04566
$$70$$ 0 0
$$71$$ 1.19604e6i 0.0470666i −0.999723 0.0235333i $$-0.992508\pi$$
0.999723 0.0235333i $$-0.00749158\pi$$
$$72$$ 1.25966e7 + 6.15647e6i 0.468732 + 0.229088i
$$73$$ 5.72563e6 0.201619 0.100810 0.994906i $$-0.467857\pi$$
0.100810 + 0.994906i $$0.467857\pi$$
$$74$$ 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
$$78$$ −6.82656e6 5.46562e6i −0.184427 0.147659i
$$79$$ 3.59132e7i 0.922032i 0.887392 + 0.461016i $$0.152515\pi$$
−0.887392 + 0.461016i $$0.847485\pi$$
$$80$$ 0 0
$$81$$ −5.37881e7 −1.24953
$$82$$ 2.14688e7 2.68145e7i 0.474846 0.593082i
$$83$$ 5.19603e7i 1.09486i 0.836851 + 0.547431i $$0.184394\pi$$
−0.836851 + 0.547431i $$0.815606\pi$$
$$84$$ 7.82746e6 + 3.49160e7i 0.157218 + 0.701306i
$$85$$ 0 0
$$86$$ 7.40426e7 + 5.92815e7i 1.35359 + 1.08374i
$$87$$ 1.28119e7i 0.223634i
$$88$$ −3.32467e7 + 6.80255e7i −0.554393 + 1.13433i
$$89$$ −8.33242e7 −1.32804 −0.664020 0.747715i $$-0.731151\pi$$
−0.664020 + 0.747715i $$0.731151\pi$$
$$90$$ 0 0
$$91$$ 7.65187e6i 0.111584i
$$92$$ 5.92550e7 1.32838e7i 0.827130 0.185426i
$$93$$ −6.78912e6 −0.0907573
$$94$$ −9.52524e7 7.62629e7i −1.22001 0.976792i
$$95$$ 0 0
$$96$$ 1.01917e8 + 2.43005e7i 1.19994 + 0.286109i
$$97$$ −1.20619e8 −1.36248 −0.681238 0.732062i $$-0.738558\pi$$
−0.681238 + 0.732062i $$0.738558\pi$$
$$98$$ 3.80794e7 4.75611e7i 0.412844 0.515641i
$$99$$ 6.32748e7i 0.658704i
$$100$$ 0 0
$$101$$ 2.77246e7 0.266428 0.133214 0.991087i $$-0.457470\pi$$
0.133214 + 0.991087i $$0.457470\pi$$
$$102$$ 9.12163e7 + 7.30315e7i 0.842698 + 0.674698i
$$103$$ 1.04501e8i 0.928477i −0.885710 0.464238i $$-0.846328\pi$$
0.885710 0.464238i $$-0.153672\pi$$
$$104$$ −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 $$-0.125005\pi$$
$$108$$ −7.83245e7 + 1.75587e7i −0.575708 + 0.129062i
$$109$$ −5.90716e7 −0.418478 −0.209239 0.977865i $$-0.567099\pi$$
−0.209239 + 0.977865i $$0.567099\pi$$
$$110$$ 0 0
$$111$$ 3.46925e8i 2.28530i
$$112$$ 3.91373e7 + 8.29032e7i 0.248724 + 0.526865i
$$113$$ −5.50849e7 −0.337846 −0.168923 0.985629i $$-0.554029\pi$$
−0.168923 + 0.985629i $$0.554029\pi$$
$$114$$ −1.94688e7 + 2.43165e7i −0.115271 + 0.143973i
$$115$$ 0 0
$$116$$ 7.18043e6 + 3.20298e7i 0.0396569 + 0.176898i
$$117$$ −1.87238e7 −0.0999196
$$118$$ −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
$$123$$ 2.14516e8i 0.937217i
$$124$$ −1.69728e7 + 3.80495e6i −0.0717905 + 0.0160939i
$$125$$ 0 0
$$126$$ 5.98067e7 + 4.78836e7i 0.237283 + 0.189979i
$$127$$ 2.57160e8i 0.988529i −0.869312 0.494264i $$-0.835438\pi$$
0.869312 0.494264i $$-0.164562\pi$$
$$128$$ 2.68411e8 + 3.63229e6i 0.999908 + 0.0135313i
$$129$$ 5.92341e8 2.13901
$$130$$ 0 0
$$131$$ 3.12175e8i 1.06002i −0.847992 0.530009i $$-0.822188\pi$$
0.847992 0.530009i $$-0.177812\pi$$
$$132$$ 1.03434e8 + 4.61390e8i 0.340697 + 1.51975i
$$133$$ −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 $$0.602027\pi$$
$$138$$ 2.37020e8 2.96038e8i 0.653535 0.816265i
$$139$$ 2.95030e8i 0.790328i −0.918611 0.395164i $$-0.870688\pi$$
0.918611 0.395164i $$-0.129312\pi$$
$$140$$ 0 0
$$141$$ −7.62019e8 −1.92792
$$142$$ −1.49386e7 1.19604e7i −0.0367414 0.0294166i
$$143$$ 1.01114e8i 0.241806i
$$144$$ 2.02861e8 9.57673e7i 0.471789 0.222724i
$$145$$ 0 0
$$146$$ 5.72563e7 7.15131e7i 0.126012 0.157389i
$$147$$ 3.80489e8i 0.814841i
$$148$$ −1.94434e8 8.67313e8i −0.405252 1.80771i
$$149$$ 4.03603e8 0.818859 0.409429 0.912342i $$-0.365728\pi$$
0.409429 + 0.912342i $$0.365728\pi$$
$$150$$ 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
$$153$$ 2.50187e8 0.456561
$$154$$ −2.58586e8 + 3.22973e8i −0.459750 + 0.574227i
$$155$$ 0 0
$$156$$ −1.36531e8 + 3.06075e7i −0.230533 + 0.0516808i
$$157$$ 2.71319e8 0.446561 0.223281 0.974754i $$-0.428323\pi$$
0.223281 + 0.974754i $$0.428323\pi$$
$$158$$ 4.48556e8 + 3.59132e8i 0.719761 + 0.576270i
$$159$$ 8.23630e7i 0.128868i
$$160$$ 0 0
$$161$$ 3.31828e8 0.493867
$$162$$ −5.37881e8 + 6.71813e8i −0.780955 + 0.975413i
$$163$$ 5.78509e8i 0.819520i −0.912193 0.409760i $$-0.865612\pi$$
0.912193 0.409760i $$-0.134388\pi$$
$$164$$ −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 $$-0.0972958\pi$$
$$168$$ 5.14376e8 + 2.51395e8i 0.645719 + 0.315588i
$$169$$ −7.85810e8 −0.963320
$$170$$ 0 0
$$171$$ 6.66951e7i 0.0780026i
$$172$$ 1.48085e9 3.31976e8i 1.69199 0.379309i
$$173$$ 2.06197e8 0.230196 0.115098 0.993354i $$-0.463282\pi$$
0.115098 + 0.993354i $$0.463282\pi$$
$$174$$ 1.60021e8 + 1.28119e8i 0.174574 + 0.139771i
$$175$$ 0 0
$$176$$ 5.17171e8 + 1.09551e9i 0.538994 + 1.14173i
$$177$$ −3.72253e8 −0.379268
$$178$$ −8.33242e8 + 1.04072e9i −0.830025 + 1.03670i
$$179$$ 1.41911e8i 0.138230i 0.997609 + 0.0691152i $$0.0220176\pi$$
−0.997609 + 0.0691152i $$0.977982\pi$$
$$180$$ 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
$$183$$ 1.47343e9i 1.31379i
$$184$$ 4.26636e8 8.72933e8i 0.372209 0.761569i
$$185$$ 0 0
$$186$$ −6.78912e7 + 8.47961e7i −0.0567233 + 0.0708474i
$$187$$ 1.35108e9i 1.10488i
$$188$$ −1.90505e9 + 4.27072e8i −1.52502 + 0.341877i
$$189$$ −4.38617e8 −0.343747
$$190$$ 0 0
$$191$$ 9.92461e8i 0.745727i 0.927886 + 0.372864i $$0.121624\pi$$
−0.927886 + 0.372864i $$0.878376\pi$$
$$192$$ 1.32268e9 1.02993e9i 0.973307 0.757887i
$$193$$ −1.17593e9 −0.847526 −0.423763 0.905773i $$-0.639291\pi$$
−0.423763 + 0.905773i $$0.639291\pi$$
$$194$$ −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 $$0.691565\pi$$
$$198$$ 7.90302e8 + 6.32748e8i 0.514200 + 0.411690i
$$199$$ 2.49036e9i 1.58800i 0.607919 + 0.793999i $$0.292004\pi$$
−0.607919 + 0.793999i $$0.707996\pi$$
$$200$$ 0 0
$$201$$ −1.52445e9 −0.933960
$$202$$ 2.77246e8 3.46281e8i 0.166518 0.207981i
$$203$$ 1.79367e8i 0.105623i
$$204$$ 1.82433e9 4.08976e8i 1.05337 0.236144i
$$205$$ 0 0
$$206$$ −1.30522e9 1.04501e9i −0.724792 0.580298i
$$207$$ 8.11970e8i 0.442241i
$$208$$ −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
$$213$$ −1.19508e8 −0.0580604
$$214$$ −1.25309e9 1.00328e9i −0.597486 0.478371i
$$215$$ 0 0
$$216$$ −5.63936e8 + 1.15386e9i −0.259069 + 0.530076i
$$217$$ −9.50477e7 −0.0428650
$$218$$ −5.90716e8 + 7.37804e8i −0.261549 + 0.326674i
$$219$$ 5.72105e8i 0.248713i
$$220$$ 0 0
$$221$$ −3.99802e8 −0.167601
$$222$$ −4.33309e9 3.46925e9i −1.78396 1.42831i
$$223$$ 1.47920e9i 0.598147i 0.954230 + 0.299073i $$0.0966776\pi$$
−0.954230 + 0.299073i $$0.903322\pi$$
$$224$$ 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 $$0.954891\pi$$
$$228$$ 1.09025e8 + 4.86330e8i 0.0403448 + 0.179967i
$$229$$ −2.84784e9 −1.03556 −0.517778 0.855515i $$-0.673241\pi$$
−0.517778 + 0.855515i $$0.673241\pi$$
$$230$$ 0 0
$$231$$ 2.58379e9i 0.907421i
$$232$$ 4.71857e8 + 2.30615e8i 0.162876 + 0.0796041i
$$233$$ −2.20621e8 −0.0748553 −0.0374276 0.999299i $$-0.511916\pi$$
−0.0374276 + 0.999299i $$0.511916\pi$$
$$234$$ −1.87238e8 + 2.33860e8i −0.0624498 + 0.0779997i
$$235$$ 0 0
$$236$$ −9.30634e8 + 2.08629e8i −0.300007 + 0.0672553i
$$237$$ 3.58845e9 1.13740
$$238$$ 1.27703e9 + 1.02244e9i 0.398009 + 0.318662i
$$239$$ 4.04493e9i 1.23971i −0.784717 0.619855i $$-0.787192\pi$$
0.784717 0.619855i $$-0.212808\pi$$
$$240$$ 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
$$243$$ 3.31731e9i 0.951395i
$$244$$ 8.25780e8 + 3.68357e9i 0.232973 + 1.03922i
$$245$$ 0 0
$$246$$ −2.67931e9 2.14516e9i −0.731615 0.585760i
$$247$$ 1.06580e8i 0.0286343i
$$248$$ −1.22204e8 + 2.50040e8i −0.0323057 + 0.0661001i
$$249$$ 5.19187e9 1.35060
$$250$$ 0 0
$$251$$ 5.21367e9i 1.31356i 0.754084 + 0.656778i $$0.228081\pi$$
−0.754084 + 0.656778i $$0.771919\pi$$
$$252$$ 1.19613e9 2.68148e8i 0.296604 0.0664926i
$$253$$ 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 $$0.251674\pi$$
$$258$$ 5.92341e9 7.39833e9i 1.33688 1.66976i
$$259$$ 4.85695e9i 1.07936i
$$260$$ 0 0
$$261$$ 4.38904e8 0.0945818
$$262$$ −3.89907e9 3.12175e9i −0.827477 0.662512i
$$263$$ 6.96916e9i 1.45666i −0.685228 0.728329i $$-0.740297\pi$$
0.685228 0.728329i $$-0.259703\pi$$
$$264$$ 6.79711e9 + 3.32201e9i 1.39929 + 0.683889i
$$265$$ 0 0
$$266$$ −2.72563e8 + 3.40431e8i −0.0544428 + 0.0679991i
$$267$$ 8.32575e9i 1.63824i
$$268$$ −3.81112e9 + 8.54374e8i −0.738777 + 0.165619i
$$269$$ 2.70720e9 0.517025 0.258513 0.966008i $$-0.416768\pi$$
0.258513 + 0.966008i $$0.416768\pi$$
$$270$$ 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
$$273$$ −7.64575e8 −0.137648
$$274$$ −2.21980e9 + 2.77253e9i −0.393832 + 0.491897i
$$275$$ 0 0
$$276$$ −1.32731e9 5.92076e9i −0.228737 1.02033i
$$277$$ 8.22965e9 1.39786 0.698928 0.715192i $$-0.253661\pi$$
0.698928 + 0.715192i $$0.253661\pi$$
$$278$$ −3.68493e9 2.95030e9i −0.616949 0.493955i
$$279$$ 2.32578e8i 0.0383841i
$$280$$ 0 0
$$281$$ 3.08105e9 0.494167 0.247083 0.968994i $$-0.420528\pi$$
0.247083 + 0.968994i $$0.420528\pi$$
$$282$$ −7.62019e9 + 9.51761e9i −1.20495 + 1.50498i
$$283$$ 1.17112e9i 0.182582i −0.995824 0.0912908i $$-0.970901\pi$$
0.995824 0.0912908i $$-0.0290993\pi$$
$$284$$ −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
$$288$$ 8.32474e8 3.49140e9i 0.121004 0.507493i
$$289$$ −1.63361e9 −0.234184
$$290$$ 0 0
$$291$$ 1.20522e10i 1.68072i
$$292$$ −3.20635e8 1.43026e9i −0.0441042 0.196736i
$$293$$ −4.80980e9 −0.652614 −0.326307 0.945264i $$-0.605804\pi$$
−0.326307 + 0.945264i $$0.605804\pi$$
$$294$$ −4.75231e9 3.80489e9i −0.636085 0.509275i
$$295$$ 0 0
$$296$$ −1.27771e10 6.24465e9i −1.66443 0.813470i
$$297$$ −5.79601e9 −0.744909
$$298$$ 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
$$303$$ 2.77025e9i 0.328661i
$$304$$ 5.45126e8 + 1.15472e9i 0.0638268 + 0.135202i
$$305$$ 0 0
$$306$$ 2.50187e9 3.12484e9i 0.285351 0.356403i
$$307$$ 3.49176e9i 0.393089i 0.980495 + 0.196545i $$0.0629721\pi$$
−0.980495 + 0.196545i $$0.937028\pi$$
$$308$$ 1.44808e9 + 6.45947e9i 0.160912 + 0.717784i
$$309$$ −1.04417e10 −1.14535
$$310$$ 0 0
$$311$$ 1.29807e10i 1.38757i −0.720182 0.693785i $$-0.755942\pi$$
0.720182 0.693785i $$-0.244058\pi$$
$$312$$ −9.83025e8 + 2.01135e9i −0.103740 + 0.212260i
$$313$$ 6.31165e9 0.657606 0.328803 0.944399i $$-0.393355\pi$$
0.328803 + 0.944399i $$0.393355\pi$$
$$314$$ 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 $$0.806837\pi$$
$$318$$ 1.02871e9 + 8.23630e8i 0.100597 + 0.0805423i
$$319$$ 2.37021e9i 0.228888i
$$320$$ 0 0
$$321$$ −1.00247e10 −0.944175
$$322$$ 3.31828e9 4.14453e9i 0.308667 0.385525i
$$323$$ 1.42411e9i 0.130838i
$$324$$ 3.01213e9 + 1.34363e10i 0.273334 + 1.21927i
$$325$$ 0 0
$$326$$ −7.22557e9 5.78509e9i −0.639738 0.512200i
$$327$$ 5.90243e9i 0.516226i
$$328$$ −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
$$333$$ −1.18848e10 −0.966526
$$334$$ −5.84680e9 4.68118e9i −0.469821 0.376158i
$$335$$ 0 0
$$336$$ 8.28368e9 3.91060e9i 0.649930 0.306822i
$$337$$ 3.56226e8 0.0276189 0.0138095 0.999905i $$-0.495604\pi$$
0.0138095 + 0.999905i $$0.495604\pi$$
$$338$$ −7.85810e9 + 9.81476e9i −0.602075 + 0.751992i
$$339$$ 5.50408e9i 0.416760i
$$340$$ 0 0
$$341$$ −1.25599e9 −0.0928897
$$342$$ 8.33021e8 + 6.66951e8i 0.0608908 + 0.0487517i
$$343$$ 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 $$0.814300\pi$$
$$348$$ 3.20042e9 7.17469e8i 0.218218 0.0489199i
$$349$$ 1.03634e10 0.698553 0.349277 0.937020i $$-0.386427\pi$$
0.349277 + 0.937020i $$0.386427\pi$$
$$350$$ 0 0
$$351$$ 1.71511e9i 0.112996i
$$352$$ 1.88546e10 + 4.49560e9i 1.22814 + 0.292831i
$$353$$ 1.30979e10 0.843536 0.421768 0.906704i $$-0.361410\pi$$
0.421768 + 0.906704i $$0.361410\pi$$
$$354$$ −3.72253e9 + 4.64944e9i −0.237042 + 0.296066i
$$355$$ 0 0
$$356$$ 4.66616e9 + 2.08144e10i 0.290509 + 1.29588i
$$357$$ 1.02162e10 0.628952
$$358$$ 1.77247e9 + 1.41911e9i 0.107906 + 0.0863940i
$$359$$ 3.31454e9i 0.199547i 0.995010 + 0.0997737i $$0.0318119\pi$$
−0.995010 + 0.0997737i $$0.968188\pi$$
$$360$$ 0 0
$$361$$ 1.66039e10 0.977647
$$362$$ 4.82566e9 6.02724e9i 0.281010 0.350982i
$$363$$ 1.27242e10i 0.732829i
$$364$$ −1.91144e9 + 4.28505e8i −0.108882 + 0.0244090i
$$365$$ 0 0
$$366$$ 1.84031e10 + 1.47343e10i 1.02557 + 0.821116i
$$367$$ 1.96628e10i 1.08388i −0.840418 0.541939i $$-0.817691\pi$$
0.840418 0.541939i $$-0.182309\pi$$
$$368$$ −6.63656e9 1.40580e10i −0.361870 0.766536i
$$369$$ −7.34878e9 −0.396378
$$370$$ 0 0
$$371$$ 1.15308e9i 0.0608646i
$$372$$ 3.80191e8 + 1.69592e9i 0.0198532 + 0.0885593i
$$373$$ 2.10063e10 1.08521 0.542606 0.839987i $$-0.317438\pi$$
0.542606 + 0.839987i $$0.317438\pi$$
$$374$$ 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
$$378$$ −4.38617e9 + 5.47833e9i −0.214842 + 0.268337i
$$379$$ 3.04816e9i 0.147734i 0.997268 + 0.0738670i $$0.0235340\pi$$
−0.997268 + 0.0738670i $$0.976466\pi$$
$$380$$ 0 0
$$381$$ −2.56955e10 −1.21943
$$382$$ 1.23958e10 + 9.92461e9i 0.582133 + 0.466080i
$$383$$ 2.23357e10i 1.03802i 0.854770 + 0.519008i $$0.173698\pi$$
−0.854770 + 0.519008i $$0.826302\pi$$
$$384$$ 3.62938e8 2.68196e10i 0.0166920 1.23347i
$$385$$ 0 0
$$386$$ −1.17593e10 + 1.46874e10i −0.529704 + 0.661599i
$$387$$ 2.02921e10i 0.904654i
$$388$$ 6.75466e9 + 3.01306e10i 0.298042 + 1.32948i
$$389$$ 3.13680e10 1.36990 0.684948 0.728592i $$-0.259825\pi$$
0.684948 + 0.728592i $$0.259825\pi$$
$$390$$ 0 0
$$391$$ 1.73377e10i 0.741795i
$$392$$ −1.40132e10 6.84880e9i −0.593463 0.290048i
$$393$$ −3.11926e10 −1.30762
$$394$$ −1.70538e10 + 2.13002e10i −0.707680 + 0.883892i
$$395$$ 0 0
$$396$$ 1.58060e10 3.54339e9i 0.642751 0.144091i
$$397$$ −7.65788e9 −0.308281 −0.154140 0.988049i $$-0.549261\pi$$
−0.154140 + 0.988049i $$0.549261\pi$$
$$398$$ 3.11046e10 + 2.49036e10i 1.23963 + 0.992499i
$$399$$ 2.72345e9i 0.107455i
$$400$$ 0 0
$$401$$ −3.26120e10 −1.26125 −0.630623 0.776089i $$-0.717201\pi$$
−0.630623 + 0.776089i $$0.717201\pi$$
$$402$$ −1.52445e10 + 1.90403e10i −0.583725 + 0.729072i
$$403$$ 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
$$408$$ 1.31352e10 2.68756e10i 0.474018 0.969879i
$$409$$ 2.26168e10 0.808236 0.404118 0.914707i $$-0.367578\pi$$
0.404118 + 0.914707i $$0.367578\pi$$
$$410$$ 0 0
$$411$$ 2.21802e10i 0.777318i
$$412$$ −2.61043e10 + 5.85205e9i −0.905990 + 0.203104i
$$413$$ −5.21155e9 −0.179129
$$414$$ −1.01415e10 8.11970e9i −0.345224 0.276400i
$$415$$ 0 0
$$416$$ −1.33030e9 + 5.57931e9i −0.0444199 + 0.186297i
$$417$$ −2.94794e10 −0.974932
$$418$$ −3.60173e9 + 4.49856e9i −0.117979 + 0.147356i
$$419$$ 4.94503e10i 1.60440i −0.597054 0.802201i $$-0.703662\pi$$
0.597054 0.802201i $$-0.296338\pi$$
$$420$$ 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
$$423$$ 2.61048e10i 0.815378i
$$424$$ 3.03339e9 + 1.48253e9i 0.0938565 + 0.0458713i
$$425$$ 0 0
$$426$$ −1.19508e9 + 1.49266e9i −0.0362878 + 0.0453234i
$$427$$ 2.06280e10i 0.620505i
$$428$$ −2.50618e10 + 5.61834e9i −0.746857 + 0.167430i
$$429$$ −1.01033e10 −0.298287
$$430$$ 0 0
$$431$$ 3.06956e10i 0.889544i −0.895644 0.444772i $$-0.853285\pi$$
0.895644 0.444772i $$-0.146715\pi$$
$$432$$ 8.77234e9 + 1.85822e10i 0.251872 + 0.533533i
$$433$$ −2.88433e9 −0.0820529 −0.0410265 0.999158i $$-0.513063\pi$$
−0.0410265 + 0.999158i $$0.513063\pi$$
$$434$$ −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
$$438$$ −7.14559e9 5.72105e9i −0.194152 0.155446i
$$439$$ 6.92422e10i 1.86429i 0.362088 + 0.932144i $$0.382064\pi$$
−0.362088 + 0.932144i $$0.617936\pi$$
$$440$$ 0 0
$$441$$ −1.30346e10 −0.344621
$$442$$ −3.99802e9 + 4.99353e9i −0.104751 + 0.130833i
$$443$$ 2.06609e10i 0.536455i −0.963356 0.268228i $$-0.913562\pi$$
0.963356 0.268228i $$-0.0864379\pi$$
$$444$$ −8.66619e10 + 1.94278e10i −2.22996 + 0.499910i
$$445$$ 0 0
$$446$$ 1.84752e10 + 1.47920e10i 0.466928 + 0.373842i
$$447$$ 4.03280e10i 1.01013i
$$448$$ 1.85175e10 1.44191e10i 0.459696 0.357952i
$$449$$ 2.11092e10 0.519382 0.259691 0.965692i $$-0.416379\pi$$
0.259691 + 0.965692i $$0.416379\pi$$
$$450$$ 0 0
$$451$$ 3.96855e10i 0.959237i
$$452$$ 3.08476e9 + 1.37602e10i 0.0739039 + 0.329664i
$$453$$ −8.36315e10 −1.98599
$$454$$ 9.36818e9 + 7.50054e9i 0.220512 + 0.176551i
$$455$$ 0 0
$$456$$ 7.16452e9 + 3.50158e9i 0.165702 + 0.0809850i
$$457$$ 2.06831e10 0.474188 0.237094 0.971487i $$-0.423805\pi$$
0.237094 + 0.971487i $$0.423805\pi$$
$$458$$ −2.84784e10 + 3.55695e10i −0.647223 + 0.808381i
$$459$$ 2.29173e10i 0.516312i
$$460$$ 0 0
$$461$$ 7.65072e10 1.69394 0.846971 0.531640i $$-0.178424\pi$$
0.846971 + 0.531640i $$0.178424\pi$$
$$462$$ 3.22715e10 + 2.58379e10i 0.708355 + 0.567138i
$$463$$ 3.41303e9i 0.0742704i −0.999310 0.0371352i $$-0.988177\pi$$
0.999310 0.0371352i $$-0.0118232\pi$$
$$464$$ 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 $$-0.0650002\pi$$
$$468$$ 1.04853e9 + 4.67721e9i 0.0218574 + 0.0974997i
$$469$$ −2.13423e10 −0.441112
$$470$$ 0 0
$$471$$ 2.71102e10i 0.550869i
$$472$$ −6.70056e9 + 1.37099e10i −0.135003 + 0.276227i
$$473$$ 1.09583e11 2.18927
$$474$$ 3.58845e10 4.48197e10i 0.710875 0.887883i
$$475$$ 0 0
$$476$$ 2.55406e10 5.72567e9i 0.497511 0.111532i
$$477$$ 2.82154e9 0.0545021
$$478$$ −5.05212e10 4.04493e10i −0.967748 0.774818i
$$479$$ 2.43887e10i 0.463282i −0.972801 0.231641i $$-0.925590\pi$$
0.972801 0.231641i $$-0.0744095\pi$$
$$480$$ 0 0
$$481$$ 1.89920e10 0.354806
$$482$$ 6.17983e10 7.71861e10i 1.14496 1.43005i
$$483$$ 3.31563e10i 0.609224i
$$484$$ 7.13124e9 + 3.18104e10i 0.129952 + 0.579679i
$$485$$ 0 0
$$486$$ 4.14332e10 + 3.31731e10i 0.742683 + 0.594622i
$$487$$ 9.30801e10i 1.65478i 0.561626 + 0.827391i $$0.310176\pi$$
−0.561626 + 0.827391i $$0.689824\pi$$
$$488$$ 5.42656e10 + 2.65217e10i 0.956853 + 0.467651i
$$489$$ −5.78046e10 −1.01094
$$490$$ 0 0
$$491$$ 2.12850e9i 0.0366225i −0.999832 0.0183113i $$-0.994171\pi$$
0.999832 0.0183113i $$-0.00582898\pi$$
$$492$$ −5.35862e10 + 1.20129e10i −0.914518 + 0.205016i
$$493$$ 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
$$498$$ 5.19187e10 6.48464e10i 0.844124 1.05431i
$$499$$ 1.04101e10i 0.167901i 0.996470 + 0.0839503i $$0.0267537\pi$$
−0.996470 + 0.0839503i $$0.973246\pi$$
$$500$$ 0 0
$$501$$ −4.67744e10 −0.742433
$$502$$ 6.51187e10 + 5.21367e10i 1.02539 + 0.820973i
$$503$$ 3.93019e10i 0.613962i −0.951716 0.306981i $$-0.900681\pi$$
0.951716 0.306981i $$-0.0993188\pi$$
$$504$$ 8.61216e9 1.76212e10i 0.133472 0.273094i
$$505$$ 0 0
$$506$$ 4.38487e10 5.47670e10i 0.668890 0.835444i
$$507$$ 7.85181e10i 1.18833i
$$508$$ −6.42387e10 + 1.44010e10i −0.964587 + 0.216241i
$$509$$ −3.25113e10 −0.484354 −0.242177 0.970232i $$-0.577861\pi$$
−0.242177 + 0.970232i $$0.577861\pi$$
$$510$$ 0 0
$$511$$ 8.00947e9i 0.117468i
$$512$$ −1.41237e10 6.72524e10i −0.205526 0.978652i
$$513$$ −6.10931e9 −0.0882110
$$514$$ 6.13693e10 7.66503e10i 0.879223 1.09815i
$$515$$ 0 0
$$516$$ −3.31711e10 1.47967e11i −0.467908 2.08720i
$$517$$ −1.40973e11 −1.97322
$$518$$ −6.06633e10 4.85695e10i −0.842572 0.674598i
$$519$$ 2.06032e10i 0.283965i
$$520$$ 0 0
$$521$$ 1.84550e9 0.0250475 0.0125237 0.999922i $$-0.496013\pi$$
0.0125237 + 0.999922i $$0.496013\pi$$
$$522$$ 4.38904e9 5.48191e9i 0.0591136 0.0738329i
$$523$$ 6.23770e10i 0.833715i −0.908972 0.416858i $$-0.863131\pi$$
0.908972 0.416858i $$-0.136869\pi$$
$$524$$ −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
$$528$$ 1.09463e11 5.16757e10i 1.40842 0.664892i
$$529$$ 2.20424e10 0.281473
$$530$$ 0 0
$$531$$ 1.27524e10i 0.160404i
$$532$$ 1.52635e9 + 6.80863e9i 0.0190550 + 0.0849988i
$$533$$ 1.17434e10 0.145508
$$534$$ 1.03989e11 + 8.32575e10i 1.27885 + 1.02390i
$$535$$ 0 0
$$536$$ −2.74400e10 + 5.61446e10i −0.332449 + 0.680219i
$$537$$ 1.41797e10 0.170518
$$538$$ 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
$$543$$ 4.82179e10i 0.554638i
$$544$$ 1.77755e10 7.45506e10i 0.202967 0.851246i
$$545$$ 0 0
$$546$$ −7.64575e9 + 9.54954e9i −0.0860299 + 0.107451i
$$547$$ 1.41531e9i 0.0158089i −0.999969 0.00790445i $$-0.997484\pi$$
0.999969 0.00790445i $$-0.00251609\pi$$
$$548$$ 1.24309e10 + 5.54506e10i 0.137841 + 0.614871i
$$549$$ 5.04758e10 0.555641
$$550$$ 0 0
$$551$$ 2.49833e9i 0.0271046i
$$552$$ −8.72234e10 4.26295e10i −0.939457 0.459149i
$$553$$ 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 $$0.246666\pi$$
$$558$$ 2.90489e9 + 2.32578e9i 0.0299636 + 0.0239901i
$$559$$ 3.24270e10i 0.332093i
$$560$$ 0 0
$$561$$ 1.35000e11 1.36296
$$562$$ 3.08105e10 3.84823e10i 0.308854 0.385759i
$$563$$ 1.06415e11i 1.05918i 0.848255 + 0.529589i $$0.177654\pi$$
−0.848255 + 0.529589i $$0.822346\pi$$
$$564$$ 4.26731e10 + 1.90352e11i 0.421733 + 1.88123i
$$565$$ 0 0
$$566$$ −1.46273e10 1.17112e10i −0.142528 0.114113i
$$567$$ 7.52431e10i 0.728005i
$$568$$ −2.15115e9 + 4.40143e9i −0.0206670 + 0.0422864i
$$569$$ 4.02429e10 0.383919 0.191960 0.981403i $$-0.438516\pi$$
0.191960 + 0.981403i $$0.438516\pi$$
$$570$$ 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
$$573$$ 9.91667e10 0.919914
$$574$$ −3.75103e10 3.00323e10i −0.345544 0.276657i
$$575$$ 0 0
$$576$$ −3.52829e10 4.53116e10i −0.320534 0.411642i
$$577$$ −4.96477e9 −0.0447915 −0.0223958 0.999749i $$-0.507129\pi$$
−0.0223958 + 0.999749i $$0.507129\pi$$
$$578$$ −1.63361e10 + 2.04038e10i −0.146365 + 0.182810i
$$579$$ 1.17499e11i 1.04549i
$$580$$ 0 0
$$581$$ 7.26862e10 0.637892
$$582$$ 1.50533e11 + 1.20522e11i 1.31201 + 1.05045i
$$583$$ 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 $$-0.223637\pi$$
$$588$$ −9.50461e10 + 2.13074e10i −0.795106 + 0.178246i
$$589$$ −1.32388e9 −0.0109999
$$590$$ 0 0
$$591$$ 1.70402e11i 1.39677i
$$592$$ −2.05766e11 + 9.71390e10i −1.67528 + 0.790873i
$$593$$ −2.06036e11 −1.66619 −0.833094 0.553131i $$-0.813433\pi$$
−0.833094 + 0.553131i $$0.813433\pi$$
$$594$$ −5.79601e10 + 7.23922e10i −0.465568 + 0.581495i
$$595$$ 0 0
$$596$$ −2.26017e10 1.00820e11i −0.179125 0.799027i
$$597$$ 2.48837e11 1.95892
$$598$$ 1.62063e10 + 1.29754e10i 0.126730 + 0.101465i
$$599$$ 2.30634e11i 1.79150i −0.444558 0.895750i $$-0.646639\pi$$
0.444558 0.895750i $$-0.353361\pi$$
$$600$$ 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
$$603$$ 5.22236e10i 0.395001i
$$604$$ −2.09079e11 + 4.68711e10i −1.57095 + 0.352174i
$$605$$ 0 0
$$606$$ −3.46004e10 2.77025e10i −0.256561 0.205413i
$$607$$ 1.97883e11i 1.45765i 0.684700 + 0.728825i $$0.259933\pi$$
−0.684700 + 0.728825i $$0.740067\pi$$
$$608$$ 1.98738e10 + 4.73860e9i 0.145434 + 0.0346766i
$$609$$ 1.79224e10 0.130294
$$610$$ 0 0
$$611$$ 4.17158e10i 0.299320i
$$612$$ −1.40105e10 6.24967e10i −0.0998728 0.445504i
$$613$$ −1.27158e11 −0.900538 −0.450269 0.892893i $$-0.648672\pi$$
−0.450269 + 0.892893i $$0.648672\pi$$
$$614$$ 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 $$0.444067\pi$$
$$618$$ −1.04417e11 + 1.30417e11i −0.715844 + 0.894089i
$$619$$ 7.06748e10i 0.481395i −0.970600 0.240698i $$-0.922624\pi$$
0.970600 0.240698i $$-0.0773762\pi$$
$$620$$ 0 0
$$621$$ 7.43769e10 0.500117
$$622$$ −1.62128e11 1.29807e11i −1.08317 0.867231i
$$623$$ 1.16561e11i 0.773748i
$$624$$ 1.52915e10 + 3.23915e10i 0.100858 + 0.213645i
$$625$$ 0 0
$$626$$ 6.31165e10 7.88325e10i 0.411004 0.513343i
$$627$$ 3.59885e10i 0.232859i
$$628$$ −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
$$633$$ 1.46657e11 0.913454
$$634$$ −1.65902e11 + 2.07211e11i −1.02682 + 1.28250i
$$635$$ 0 0
$$636$$ 2.05743e10 4.61233e9i 0.125747 0.0281898i
$$637$$ 2.08294e10 0.126508
$$638$$ 2.96039e10 + 2.37021e10i 0.178676 + 0.143055i
$$639$$ 4.09405e9i 0.0245556i
$$640$$ 0 0
$$641$$ 1.12013e11 0.663490 0.331745 0.943369i $$-0.392363\pi$$
0.331745 + 0.943369i $$0.392363\pi$$
$$642$$ −1.00247e11 + 1.25209e11i −0.590109 + 0.737046i
$$643$$ 2.65913e11i 1.55559i 0.628518 + 0.777795i $$0.283662\pi$$
−0.628518 + 0.777795i $$0.716338\pi$$
$$644$$ −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 $$-0.282803\pi$$
$$648$$ 1.97940e11 + 9.67411e10i 1.12262 + 0.548670i
$$649$$ −6.88669e10 −0.388179
$$650$$ 0 0
$$651$$ 9.49716e9i 0.0528774i
$$652$$ −1.44511e11 + 3.23965e10i −0.799672 + 0.179270i
$$653$$ −3.03789e11 −1.67078 −0.835391 0.549656i $$-0.814759\pi$$
−0.835391 + 0.549656i $$0.814759\pi$$
$$654$$ 7.37213e10 + 5.90243e10i 0.402979 + 0.322641i
$$655$$ 0 0
$$656$$ −1.27233e11 + 6.00646e10i −0.687043 + 0.324342i
$$657$$ −1.95988e10 −0.105189
$$658$$ −1.06683e11 + 1.33247e11i −0.569102 + 0.710808i
$$659$$ 4.18575e10i 0.221938i 0.993824 + 0.110969i $$0.0353954\pi$$
−0.993824 + 0.110969i $$0.964605\pi$$
$$660$$ 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
$$663$$ 3.99482e10i 0.206749i
$$664$$ 9.34537e10 1.91214e11i 0.480755 0.983665i
$$665$$ 0 0
$$666$$ −1.18848e11 + 1.48441e11i −0.604079 + 0.754494i
$$667$$ 3.04155e10i 0.153671i
$$668$$ −1.16936e11 + 2.62146e10i −0.587276 + 0.131655i
$$669$$ 1.47802e11 0.737862
$$670$$ 0 0
$$671$$ 2.72584e11i 1.34465i
$$672$$ 3.39935e10 1.42569e11i 0.166694 0.699115i
$$673$$ 3.15336e11 1.53714 0.768569 0.639767i $$-0.220969\pi$$
0.768569 + 0.639767i $$0.220969\pi$$
$$674$$ 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 $$0.481257\pi$$
$$678$$ 6.87460e10 + 5.50408e10i 0.325333 + 0.260475i
$$679$$ 1.68731e11i 0.793811i
$$680$$ 0 0
$$681$$ 7.49454e10 0.348463
$$682$$ −1.25599e10 + 1.56873e10i −0.0580561 + 0.0725120i
$$683$$ 7.20843e10i 0.331251i −0.986189 0.165626i $$-0.947036\pi$$
0.986189 0.165626i $$-0.0529644\pi$$
$$684$$ 1.66604e10 3.73492e9i 0.0761135 0.0170631i
$$685$$ 0 0
$$686$$ −1.67255e11 1.33911e11i −0.755235 0.604672i
$$687$$ 2.84556e11i 1.27744i
$$688$$ −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
$$693$$ 8.85139e10 0.383776
$$694$$ 1.99503e11 + 1.59731e11i 0.860028 + 0.688573i
$$695$$ 0 0
$$696$$ 2.30430e10 4.71479e10i 0.0981980 0.200921i
$$697$$ −1.56916e11 −0.664867
$$698$$ 1.03634e11 1.29438e11i 0.436596 0.545308i
$$699$$ 2.20444e10i 0.0923400i
$$700$$ 0 0
$$701$$ −2.87925e11 −1.19236 −0.596180 0.802851i $$-0.703315\pi$$
−0.596180 + 0.802851i $$0.703315\pi$$
$$702$$ −2.14217e10 1.71511e10i −0.0882077 0.0706227i
$$703$$ 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
$$708$$ 2.08462e10 + 9.29889e10i 0.0829648 + 0.370082i
$$709$$ 2.51685e11 0.996030 0.498015 0.867168i $$-0.334062\pi$$
0.498015 + 0.867168i $$0.334062\pi$$
$$710$$ 0 0
$$711$$ 1.22931e11i 0.481042i
$$712$$ 3.06633e11 + 1.49864e11i 1.19316 + 0.583144i
$$713$$ 1.61174e10 0.0623643
$$714$$ 1.02162e11 1.27601e11i 0.393095 0.490976i
$$715$$ 0 0
$$716$$ 3.54493e10 7.94701e9i 0.134883 0.0302379i
$$717$$ −4.04170e11 −1.52928
$$718$$ 4.13986e10 + 3.31454e10i 0.155772 + 0.124717i
$$719$$ 1.38856e11i 0.519574i −0.965666 0.259787i $$-0.916348\pi$$
0.965666 0.259787i $$-0.0836524\pi$$
$$720$$ 0 0
$$721$$ −1.46184e11 −0.540953
$$722$$ 1.66039e11 2.07383e11i 0.611029 0.763175i
$$723$$ 6.17489e11i 2.25983i
$$724$$ −2.70237e10 1.20545e11i −0.0983536 0.438727i
$$725$$ 0 0
$$726$$ 1.58925e11 + 1.27242e11i 0.572064 + 0.458018i
$$727$$ 1.79083e11i 0.641088i 0.947234 + 0.320544i $$0.103866\pi$$
−0.947234 + 0.320544i $$0.896134\pi$$
$$728$$ −1.37623e10 + 2.81589e10i −0.0489967 + 0.100251i
$$729$$ −2.14381e10 −0.0759061
$$730$$ 0 0
$$731$$ 4.33289e11i 1.51743i
$$732$$ 3.68062e11 8.25119e10i 1.28197 0.287391i
$$733$$ −2.17618e11 −0.753839 −0.376920 0.926246i $$-0.623017\pi$$
−0.376920 + 0.926246i $$0.623017\pi$$
$$734$$ −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
$$738$$ −7.34878e10 + 9.17862e10i −0.247736 + 0.309423i
$$739$$ 4.84950e11i 1.62599i 0.582268 + 0.812997i $$0.302166\pi$$
−0.582268 + 0.812997i $$0.697834\pi$$
$$740$$ 0 0
$$741$$ −1.06494e10 −0.0353227
$$742$$ 1.44020e10 + 1.15308e10i 0.0475124 + 0.0380404i
$$743$$ 2.03509e11i 0.667771i −0.942614 0.333886i $$-0.891640\pi$$
0.942614 0.333886i $$-0.108360\pi$$
$$744$$ 2.49840e10 + 1.22106e10i 0.0815398 + 0.0398517i
$$745$$ 0 0
$$746$$ 2.10063e11 2.62369e11i 0.678258 0.847144i
$$747$$ 1.77860e11i 0.571210i
$$748$$ 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
$$753$$ 5.20950e11 1.62038
$$754$$ −7.01374e9 + 8.76016e9i −0.0217002 + 0.0271036i
$$755$$ 0 0
$$756$$ 2.45626e10 + 1.09567e11i 0.0751946 + 0.335421i
$$757$$ 3.84882e11 1.17204 0.586022 0.810295i $$-0.300693\pi$$
0.586022 + 0.810295i $$0.300693\pi$$
$$758$$ 3.80715e10 + 3.04816e10i 0.115325 + 0.0923338i
$$759$$ 4.38136e11i 1.32021i
$$760$$ 0 0
$$761$$ 2.39209e11 0.713244 0.356622 0.934249i $$-0.383928\pi$$
0.356622 + 0.934249i $$0.383928\pi$$
$$762$$ −2.56955e11 + 3.20936e11i −0.762143 + 0.951916i
$$763$$ 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