# Properties

 Label 192.9.e.f.65.1 Level $192$ Weight $9$ Character 192.65 Analytic conductor $78.217$ 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] = [192,9,Mod(65,192)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(192, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("192.65");

S:= CuspForms(chi, 9);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$192 = 2^{6} \cdot 3$$ Weight: $$k$$ $$=$$ $$9$$ Character orbit: $$[\chi]$$ $$=$$ 192.e (of order $$2$$, degree $$1$$, not 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: $$78.2166931317$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\sqrt{-14})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} + 14$$ x^2 + 14 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2\cdot 3$$ Twist minimal: no (minimal twist has level 3) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 65.1 Root $$3.74166i$$ of defining polynomial Character $$\chi$$ $$=$$ 192.65 Dual form 192.9.e.f.65.2

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(45.0000 - 67.3498i) q^{3} +224.499i q^{5} +1750.00 q^{7} +(-2511.00 - 6061.48i) q^{9} +O(q^{10})$$ $$q+(45.0000 - 67.3498i) q^{3} +224.499i q^{5} +1750.00 q^{7} +(-2511.00 - 6061.48i) q^{9} +6959.48i q^{11} -25730.0 q^{13} +(15120.0 + 10102.5i) q^{15} +74893.0i q^{17} +18938.0 q^{19} +(78750.0 - 117862. i) q^{21} +470461. i q^{23} +340225. q^{25} +(-521235. - 103651. i) q^{27} -460897. i q^{29} +351478. q^{31} +(468720. + 313177. i) q^{33} +392874. i q^{35} -1.33517e6 q^{37} +(-1.15785e6 + 1.73291e6i) q^{39} +1.87547e6i q^{41} -3.52615e6 q^{43} +(1.36080e6 - 563718. i) q^{45} +4.08104e6i q^{47} -2.70230e6 q^{49} +(5.04403e6 + 3.37019e6i) q^{51} +6.60177e6i q^{53} -1.56240e6 q^{55} +(852210. - 1.27547e6i) q^{57} +1.37149e7i q^{59} -753602. q^{61} +(-4.39425e6 - 1.06076e7i) q^{63} -5.77637e6i q^{65} +2.26889e6 q^{67} +(3.16855e7 + 2.11707e7i) q^{69} -1.70220e7i q^{71} +2.76728e7 q^{73} +(1.53101e7 - 2.29141e7i) q^{75} +1.21791e7i q^{77} +2.29810e7 q^{79} +(-3.04365e7 + 3.04408e7i) q^{81} -4.63952e7i q^{83} -1.68134e7 q^{85} +(-3.10414e7 - 2.07404e7i) q^{87} +7.26152e7i q^{89} -4.50275e7 q^{91} +(1.58165e7 - 2.36720e7i) q^{93} +4.25157e6i q^{95} +1.47271e8 q^{97} +(4.21848e7 - 1.74753e7i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 90 q^{3} + 3500 q^{7} - 5022 q^{9}+O(q^{10})$$ 2 * q + 90 * q^3 + 3500 * q^7 - 5022 * q^9 $$2 q + 90 q^{3} + 3500 q^{7} - 5022 q^{9} - 51460 q^{13} + 30240 q^{15} + 37876 q^{19} + 157500 q^{21} + 680450 q^{25} - 1042470 q^{27} + 702956 q^{31} + 937440 q^{33} - 2670340 q^{37} - 2315700 q^{39} - 7052300 q^{43} + 2721600 q^{45} - 5404602 q^{49} + 10088064 q^{51} - 3124800 q^{55} + 1704420 q^{57} - 1507204 q^{61} - 8788500 q^{63} + 4537780 q^{67} + 63370944 q^{69} + 55345540 q^{73} + 30620250 q^{75} + 45961964 q^{79} - 60872958 q^{81} - 33626880 q^{85} - 62082720 q^{87} - 90055000 q^{91} + 31633020 q^{93} + 294542020 q^{97} + 84369600 q^{99}+O(q^{100})$$ 2 * q + 90 * q^3 + 3500 * q^7 - 5022 * q^9 - 51460 * q^13 + 30240 * q^15 + 37876 * q^19 + 157500 * q^21 + 680450 * q^25 - 1042470 * q^27 + 702956 * q^31 + 937440 * q^33 - 2670340 * q^37 - 2315700 * q^39 - 7052300 * q^43 + 2721600 * q^45 - 5404602 * q^49 + 10088064 * q^51 - 3124800 * q^55 + 1704420 * q^57 - 1507204 * q^61 - 8788500 * q^63 + 4537780 * q^67 + 63370944 * q^69 + 55345540 * q^73 + 30620250 * q^75 + 45961964 * q^79 - 60872958 * q^81 - 33626880 * q^85 - 62082720 * q^87 - 90055000 * q^91 + 31633020 * q^93 + 294542020 * q^97 + 84369600 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$$.

 $$n$$ $$65$$ $$127$$ $$133$$ $$\chi(n)$$ $$-1$$ $$1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 45.0000 67.3498i 0.555556 0.831479i
$$4$$ 0 0
$$5$$ 224.499i 0.359199i 0.983740 + 0.179600i $$0.0574802\pi$$
−0.983740 + 0.179600i $$0.942520\pi$$
$$6$$ 0 0
$$7$$ 1750.00 0.728863 0.364431 0.931230i $$-0.381263\pi$$
0.364431 + 0.931230i $$0.381263\pi$$
$$8$$ 0 0
$$9$$ −2511.00 6061.48i −0.382716 0.923866i
$$10$$ 0 0
$$11$$ 6959.48i 0.475342i 0.971346 + 0.237671i $$0.0763840\pi$$
−0.971346 + 0.237671i $$0.923616\pi$$
$$12$$ 0 0
$$13$$ −25730.0 −0.900879 −0.450439 0.892807i $$-0.648733\pi$$
−0.450439 + 0.892807i $$0.648733\pi$$
$$14$$ 0 0
$$15$$ 15120.0 + 10102.5i 0.298667 + 0.199555i
$$16$$ 0 0
$$17$$ 74893.0i 0.896697i 0.893859 + 0.448348i $$0.147988\pi$$
−0.893859 + 0.448348i $$0.852012\pi$$
$$18$$ 0 0
$$19$$ 18938.0 0.145318 0.0726590 0.997357i $$-0.476852\pi$$
0.0726590 + 0.997357i $$0.476852\pi$$
$$20$$ 0 0
$$21$$ 78750.0 117862.i 0.404924 0.606035i
$$22$$ 0 0
$$23$$ 470461.i 1.68117i 0.541678 + 0.840586i $$0.317789\pi$$
−0.541678 + 0.840586i $$0.682211\pi$$
$$24$$ 0 0
$$25$$ 340225. 0.870976
$$26$$ 0 0
$$27$$ −521235. 103651.i −0.980796 0.195038i
$$28$$ 0 0
$$29$$ 460897.i 0.651647i −0.945431 0.325823i $$-0.894359\pi$$
0.945431 0.325823i $$-0.105641\pi$$
$$30$$ 0 0
$$31$$ 351478. 0.380585 0.190292 0.981727i $$-0.439056\pi$$
0.190292 + 0.981727i $$0.439056\pi$$
$$32$$ 0 0
$$33$$ 468720. + 313177.i 0.395237 + 0.264079i
$$34$$ 0 0
$$35$$ 392874.i 0.261807i
$$36$$ 0 0
$$37$$ −1.33517e6 −0.712409 −0.356205 0.934408i $$-0.615929\pi$$
−0.356205 + 0.934408i $$0.615929\pi$$
$$38$$ 0 0
$$39$$ −1.15785e6 + 1.73291e6i −0.500488 + 0.749062i
$$40$$ 0 0
$$41$$ 1.87547e6i 0.663704i 0.943331 + 0.331852i $$0.107673\pi$$
−0.943331 + 0.331852i $$0.892327\pi$$
$$42$$ 0 0
$$43$$ −3.52615e6 −1.03140 −0.515700 0.856769i $$-0.672468\pi$$
−0.515700 + 0.856769i $$0.672468\pi$$
$$44$$ 0 0
$$45$$ 1.36080e6 563718.i 0.331852 0.137471i
$$46$$ 0 0
$$47$$ 4.08104e6i 0.836333i 0.908370 + 0.418167i $$0.137327\pi$$
−0.908370 + 0.418167i $$0.862673\pi$$
$$48$$ 0 0
$$49$$ −2.70230e6 −0.468759
$$50$$ 0 0
$$51$$ 5.04403e6 + 3.37019e6i 0.745585 + 0.498165i
$$52$$ 0 0
$$53$$ 6.60177e6i 0.836675i 0.908292 + 0.418337i $$0.137387\pi$$
−0.908292 + 0.418337i $$0.862613\pi$$
$$54$$ 0 0
$$55$$ −1.56240e6 −0.170742
$$56$$ 0 0
$$57$$ 852210. 1.27547e6i 0.0807323 0.120829i
$$58$$ 0 0
$$59$$ 1.37149e7i 1.13184i 0.824461 + 0.565919i $$0.191479\pi$$
−0.824461 + 0.565919i $$0.808521\pi$$
$$60$$ 0 0
$$61$$ −753602. −0.0544280 −0.0272140 0.999630i $$-0.508664\pi$$
−0.0272140 + 0.999630i $$0.508664\pi$$
$$62$$ 0 0
$$63$$ −4.39425e6 1.06076e7i −0.278948 0.673372i
$$64$$ 0 0
$$65$$ 5.77637e6i 0.323595i
$$66$$ 0 0
$$67$$ 2.26889e6 0.112594 0.0562969 0.998414i $$-0.482071\pi$$
0.0562969 + 0.998414i $$0.482071\pi$$
$$68$$ 0 0
$$69$$ 3.16855e7 + 2.11707e7i 1.39786 + 0.933985i
$$70$$ 0 0
$$71$$ 1.70220e7i 0.669849i −0.942245 0.334925i $$-0.891289\pi$$
0.942245 0.334925i $$-0.108711\pi$$
$$72$$ 0 0
$$73$$ 2.76728e7 0.974454 0.487227 0.873275i $$-0.338008\pi$$
0.487227 + 0.873275i $$0.338008\pi$$
$$74$$ 0 0
$$75$$ 1.53101e7 2.29141e7i 0.483876 0.724199i
$$76$$ 0 0
$$77$$ 1.21791e7i 0.346459i
$$78$$ 0 0
$$79$$ 2.29810e7 0.590011 0.295006 0.955496i $$-0.404678\pi$$
0.295006 + 0.955496i $$0.404678\pi$$
$$80$$ 0 0
$$81$$ −3.04365e7 + 3.04408e7i −0.707057 + 0.707157i
$$82$$ 0 0
$$83$$ 4.63952e7i 0.977599i −0.872396 0.488799i $$-0.837435\pi$$
0.872396 0.488799i $$-0.162565\pi$$
$$84$$ 0 0
$$85$$ −1.68134e7 −0.322093
$$86$$ 0 0
$$87$$ −3.10414e7 2.07404e7i −0.541831 0.362026i
$$88$$ 0 0
$$89$$ 7.26152e7i 1.15736i 0.815555 + 0.578679i $$0.196432\pi$$
−0.815555 + 0.578679i $$0.803568\pi$$
$$90$$ 0 0
$$91$$ −4.50275e7 −0.656617
$$92$$ 0 0
$$93$$ 1.58165e7 2.36720e7i 0.211436 0.316448i
$$94$$ 0 0
$$95$$ 4.25157e6i 0.0521981i
$$96$$ 0 0
$$97$$ 1.47271e8 1.66353 0.831764 0.555129i $$-0.187331\pi$$
0.831764 + 0.555129i $$0.187331\pi$$
$$98$$ 0 0
$$99$$ 4.21848e7 1.74753e7i 0.439152 0.181921i
$$100$$ 0 0
$$101$$ 1.03545e8i 0.995045i 0.867451 + 0.497522i $$0.165757\pi$$
−0.867451 + 0.497522i $$0.834243\pi$$
$$102$$ 0 0
$$103$$ 1.66064e8 1.47545 0.737726 0.675100i $$-0.235899\pi$$
0.737726 + 0.675100i $$0.235899\pi$$
$$104$$ 0 0
$$105$$ 2.64600e7 + 1.76793e7i 0.217687 + 0.145448i
$$106$$ 0 0
$$107$$ 2.25540e7i 0.172063i −0.996292 0.0860316i $$-0.972581\pi$$
0.996292 0.0860316i $$-0.0274186\pi$$
$$108$$ 0 0
$$109$$ 1.09975e8 0.779091 0.389546 0.921007i $$-0.372632\pi$$
0.389546 + 0.921007i $$0.372632\pi$$
$$110$$ 0 0
$$111$$ −6.00826e7 + 8.99235e7i −0.395783 + 0.592354i
$$112$$ 0 0
$$113$$ 2.87748e8i 1.76481i 0.470490 + 0.882405i $$0.344077\pi$$
−0.470490 + 0.882405i $$0.655923\pi$$
$$114$$ 0 0
$$115$$ −1.05618e8 −0.603876
$$116$$ 0 0
$$117$$ 6.46080e7 + 1.55962e8i 0.344781 + 0.832291i
$$118$$ 0 0
$$119$$ 1.31063e8i 0.653569i
$$120$$ 0 0
$$121$$ 1.65924e8 0.774050
$$122$$ 0 0
$$123$$ 1.26312e8 + 8.43961e7i 0.551856 + 0.368724i
$$124$$ 0 0
$$125$$ 1.64075e8i 0.672053i
$$126$$ 0 0
$$127$$ −2.75994e8 −1.06092 −0.530462 0.847708i $$-0.677982\pi$$
−0.530462 + 0.847708i $$0.677982\pi$$
$$128$$ 0 0
$$129$$ −1.58677e8 + 2.37486e8i −0.573000 + 0.857588i
$$130$$ 0 0
$$131$$ 2.89118e8i 0.981725i 0.871237 + 0.490862i $$0.163318\pi$$
−0.871237 + 0.490862i $$0.836682\pi$$
$$132$$ 0 0
$$133$$ 3.31415e7 0.105917
$$134$$ 0 0
$$135$$ 2.32697e7 1.17017e8i 0.0700576 0.352301i
$$136$$ 0 0
$$137$$ 2.07562e8i 0.589205i −0.955620 0.294602i $$-0.904813\pi$$
0.955620 0.294602i $$-0.0951872\pi$$
$$138$$ 0 0
$$139$$ −1.42668e8 −0.382180 −0.191090 0.981573i $$-0.561202\pi$$
−0.191090 + 0.981573i $$0.561202\pi$$
$$140$$ 0 0
$$141$$ 2.74857e8 + 1.83647e8i 0.695394 + 0.464630i
$$142$$ 0 0
$$143$$ 1.79067e8i 0.428226i
$$144$$ 0 0
$$145$$ 1.03471e8 0.234071
$$146$$ 0 0
$$147$$ −1.21604e8 + 1.82000e8i −0.260422 + 0.389763i
$$148$$ 0 0
$$149$$ 8.19236e8i 1.66213i 0.556179 + 0.831063i $$0.312267\pi$$
−0.556179 + 0.831063i $$0.687733\pi$$
$$150$$ 0 0
$$151$$ −4.23861e8 −0.815296 −0.407648 0.913139i $$-0.633651\pi$$
−0.407648 + 0.913139i $$0.633651\pi$$
$$152$$ 0 0
$$153$$ 4.53963e8 1.88056e8i 0.828428 0.343180i
$$154$$ 0 0
$$155$$ 7.89066e7i 0.136706i
$$156$$ 0 0
$$157$$ 7.59851e8 1.25063 0.625316 0.780371i $$-0.284970\pi$$
0.625316 + 0.780371i $$0.284970\pi$$
$$158$$ 0 0
$$159$$ 4.44628e8 + 2.97079e8i 0.695678 + 0.464819i
$$160$$ 0 0
$$161$$ 8.23307e8i 1.22534i
$$162$$ 0 0
$$163$$ 6.68160e8 0.946520 0.473260 0.880923i $$-0.343077\pi$$
0.473260 + 0.880923i $$0.343077\pi$$
$$164$$ 0 0
$$165$$ −7.03080e7 + 1.05227e8i −0.0948569 + 0.141969i
$$166$$ 0 0
$$167$$ 1.96306e8i 0.252387i −0.992006 0.126194i $$-0.959724\pi$$
0.992006 0.126194i $$-0.0402761\pi$$
$$168$$ 0 0
$$169$$ −1.53698e8 −0.188417
$$170$$ 0 0
$$171$$ −4.75533e7 1.14792e8i −0.0556156 0.134254i
$$172$$ 0 0
$$173$$ 1.02319e9i 1.14228i −0.820852 0.571141i $$-0.806501\pi$$
0.820852 0.571141i $$-0.193499\pi$$
$$174$$ 0 0
$$175$$ 5.95394e8 0.634822
$$176$$ 0 0
$$177$$ 9.23696e8 + 6.17170e8i 0.941100 + 0.628799i
$$178$$ 0 0
$$179$$ 1.28895e9i 1.25552i −0.778408 0.627759i $$-0.783972\pi$$
0.778408 0.627759i $$-0.216028\pi$$
$$180$$ 0 0
$$181$$ −4.71707e8 −0.439499 −0.219749 0.975556i $$-0.570524\pi$$
−0.219749 + 0.975556i $$0.570524\pi$$
$$182$$ 0 0
$$183$$ −3.39121e7 + 5.07550e7i −0.0302378 + 0.0452558i
$$184$$ 0 0
$$185$$ 2.99745e8i 0.255897i
$$186$$ 0 0
$$187$$ −5.21217e8 −0.426238
$$188$$ 0 0
$$189$$ −9.12161e8 1.81390e8i −0.714866 0.142156i
$$190$$ 0 0
$$191$$ 1.61787e8i 0.121565i 0.998151 + 0.0607827i $$0.0193597\pi$$
−0.998151 + 0.0607827i $$0.980640\pi$$
$$192$$ 0 0
$$193$$ −1.58840e9 −1.14480 −0.572401 0.819974i $$-0.693988\pi$$
−0.572401 + 0.819974i $$0.693988\pi$$
$$194$$ 0 0
$$195$$ −3.89038e8 2.59937e8i −0.269062 0.179775i
$$196$$ 0 0
$$197$$ 5.37769e8i 0.357052i 0.983935 + 0.178526i $$0.0571328\pi$$
−0.983935 + 0.178526i $$0.942867\pi$$
$$198$$ 0 0
$$199$$ −6.47586e8 −0.412938 −0.206469 0.978453i $$-0.566197\pi$$
−0.206469 + 0.978453i $$0.566197\pi$$
$$200$$ 0 0
$$201$$ 1.02100e8 1.52809e8i 0.0625521 0.0936194i
$$202$$ 0 0
$$203$$ 8.06570e8i 0.474961i
$$204$$ 0 0
$$205$$ −4.21042e8 −0.238402
$$206$$ 0 0
$$207$$ 2.85169e9 1.18133e9i 1.55318 0.643412i
$$208$$ 0 0
$$209$$ 1.31799e8i 0.0690758i
$$210$$ 0 0
$$211$$ 5.81104e7 0.0293173 0.0146586 0.999893i $$-0.495334\pi$$
0.0146586 + 0.999893i $$0.495334\pi$$
$$212$$ 0 0
$$213$$ −1.14643e9 7.65990e8i −0.556966 0.372139i
$$214$$ 0 0
$$215$$ 7.91619e8i 0.370478i
$$216$$ 0 0
$$217$$ 6.15086e8 0.277394
$$218$$ 0 0
$$219$$ 1.24527e9 1.86376e9i 0.541363 0.810238i
$$220$$ 0 0
$$221$$ 1.92700e9i 0.807815i
$$222$$ 0 0
$$223$$ −4.40200e9 −1.78004 −0.890021 0.455920i $$-0.849310\pi$$
−0.890021 + 0.455920i $$0.849310\pi$$
$$224$$ 0 0
$$225$$ −8.54305e8 2.06227e9i −0.333336 0.804665i
$$226$$ 0 0
$$227$$ 3.53592e9i 1.33168i 0.746095 + 0.665839i $$0.231926\pi$$
−0.746095 + 0.665839i $$0.768074\pi$$
$$228$$ 0 0
$$229$$ 1.86569e9 0.678420 0.339210 0.940711i $$-0.389840\pi$$
0.339210 + 0.940711i $$0.389840\pi$$
$$230$$ 0 0
$$231$$ 8.20260e8 + 5.48059e8i 0.288074 + 0.192477i
$$232$$ 0 0
$$233$$ 2.72132e9i 0.923328i −0.887055 0.461664i $$-0.847253\pi$$
0.887055 0.461664i $$-0.152747\pi$$
$$234$$ 0 0
$$235$$ −9.16191e8 −0.300410
$$236$$ 0 0
$$237$$ 1.03414e9 1.54777e9i 0.327784 0.490582i
$$238$$ 0 0
$$239$$ 2.27461e9i 0.697132i 0.937284 + 0.348566i $$0.113331\pi$$
−0.937284 + 0.348566i $$0.886669\pi$$
$$240$$ 0 0
$$241$$ −1.74667e9 −0.517778 −0.258889 0.965907i $$-0.583356\pi$$
−0.258889 + 0.965907i $$0.583356\pi$$
$$242$$ 0 0
$$243$$ 6.80540e8 + 3.41973e9i 0.195177 + 0.980768i
$$244$$ 0 0
$$245$$ 6.06665e8i 0.168378i
$$246$$ 0 0
$$247$$ −4.87275e8 −0.130914
$$248$$ 0 0
$$249$$ −3.12471e9 2.08778e9i −0.812853 0.543110i
$$250$$ 0 0
$$251$$ 1.37549e9i 0.346547i 0.984874 + 0.173274i $$0.0554345\pi$$
−0.984874 + 0.173274i $$0.944566\pi$$
$$252$$ 0 0
$$253$$ −3.27417e9 −0.799132
$$254$$ 0 0
$$255$$ −7.56605e8 + 1.13238e9i −0.178940 + 0.267813i
$$256$$ 0 0
$$257$$ 7.93672e9i 1.81932i −0.415356 0.909659i $$-0.636343\pi$$
0.415356 0.909659i $$-0.363657\pi$$
$$258$$ 0 0
$$259$$ −2.33655e9 −0.519249
$$260$$ 0 0
$$261$$ −2.79372e9 + 1.15731e9i −0.602034 + 0.249396i
$$262$$ 0 0
$$263$$ 3.22555e8i 0.0674187i −0.999432 0.0337093i $$-0.989268\pi$$
0.999432 0.0337093i $$-0.0107320\pi$$
$$264$$ 0 0
$$265$$ −1.48209e9 −0.300533
$$266$$ 0 0
$$267$$ 4.89062e9 + 3.26769e9i 0.962319 + 0.642977i
$$268$$ 0 0
$$269$$ 3.47314e9i 0.663304i −0.943402 0.331652i $$-0.892394\pi$$
0.943402 0.331652i $$-0.107606\pi$$
$$270$$ 0 0
$$271$$ 1.44216e9 0.267385 0.133693 0.991023i $$-0.457317\pi$$
0.133693 + 0.991023i $$0.457317\pi$$
$$272$$ 0 0
$$273$$ −2.02624e9 + 3.03259e9i −0.364787 + 0.545964i
$$274$$ 0 0
$$275$$ 2.36779e9i 0.414012i
$$276$$ 0 0
$$277$$ −3.38046e9 −0.574192 −0.287096 0.957902i $$-0.592690\pi$$
−0.287096 + 0.957902i $$0.592690\pi$$
$$278$$ 0 0
$$279$$ −8.82561e8 2.13048e9i −0.145656 0.351609i
$$280$$ 0 0
$$281$$ 4.02262e9i 0.645184i 0.946538 + 0.322592i $$0.104554\pi$$
−0.946538 + 0.322592i $$0.895446\pi$$
$$282$$ 0 0
$$283$$ −1.04253e10 −1.62533 −0.812666 0.582730i $$-0.801984\pi$$
−0.812666 + 0.582730i $$0.801984\pi$$
$$284$$ 0 0
$$285$$ 2.86343e8 + 1.91321e8i 0.0434017 + 0.0289990i
$$286$$ 0 0
$$287$$ 3.28207e9i 0.483749i
$$288$$ 0 0
$$289$$ 1.36679e9 0.195935
$$290$$ 0 0
$$291$$ 6.62720e9 9.91868e9i 0.924183 1.38319i
$$292$$ 0 0
$$293$$ 1.03927e10i 1.41012i −0.709146 0.705061i $$-0.750919\pi$$
0.709146 0.705061i $$-0.249081\pi$$
$$294$$ 0 0
$$295$$ −3.07899e9 −0.406555
$$296$$ 0 0
$$297$$ 7.21360e8 3.62753e9i 0.0927099 0.466213i
$$298$$ 0 0
$$299$$ 1.21050e10i 1.51453i
$$300$$ 0 0
$$301$$ −6.17076e9 −0.751749
$$302$$ 0 0
$$303$$ 6.97372e9 + 4.65951e9i 0.827359 + 0.552803i
$$304$$ 0 0
$$305$$ 1.69183e8i 0.0195505i
$$306$$ 0 0
$$307$$ −2.99309e9 −0.336951 −0.168476 0.985706i $$-0.553884\pi$$
−0.168476 + 0.985706i $$0.553884\pi$$
$$308$$ 0 0
$$309$$ 7.47286e9 1.11843e10i 0.819696 1.22681i
$$310$$ 0 0
$$311$$ 6.44832e9i 0.689295i −0.938732 0.344647i $$-0.887998\pi$$
0.938732 0.344647i $$-0.112002\pi$$
$$312$$ 0 0
$$313$$ 3.27737e7 0.00341467 0.00170733 0.999999i $$-0.499457\pi$$
0.00170733 + 0.999999i $$0.499457\pi$$
$$314$$ 0 0
$$315$$ 2.38140e9 9.86507e8i 0.241875 0.100198i
$$316$$ 0 0
$$317$$ 1.17797e10i 1.16653i 0.812282 + 0.583264i $$0.198225\pi$$
−0.812282 + 0.583264i $$0.801775\pi$$
$$318$$ 0 0
$$319$$ 3.20761e9 0.309755
$$320$$ 0 0
$$321$$ −1.51901e9 1.01493e9i −0.143067 0.0955907i
$$322$$ 0 0
$$323$$ 1.41832e9i 0.130306i
$$324$$ 0 0
$$325$$ −8.75399e9 −0.784644
$$326$$ 0 0
$$327$$ 4.94888e9 7.40680e9i 0.432829 0.647798i
$$328$$ 0 0
$$329$$ 7.14182e9i 0.609573i
$$330$$ 0 0
$$331$$ −1.20100e10 −1.00053 −0.500265 0.865872i $$-0.666764\pi$$
−0.500265 + 0.865872i $$0.666764\pi$$
$$332$$ 0 0
$$333$$ 3.35261e9 + 8.09311e9i 0.272651 + 0.658171i
$$334$$ 0 0
$$335$$ 5.09365e8i 0.0404436i
$$336$$ 0 0
$$337$$ 1.59214e10 1.23441 0.617207 0.786801i $$-0.288264\pi$$
0.617207 + 0.786801i $$0.288264\pi$$
$$338$$ 0 0
$$339$$ 1.93798e10 + 1.29486e10i 1.46740 + 0.980451i
$$340$$ 0 0
$$341$$ 2.44611e9i 0.180908i
$$342$$ 0 0
$$343$$ −1.48174e10 −1.07052
$$344$$ 0 0
$$345$$ −4.75282e9 + 7.11337e9i −0.335487 + 0.502110i
$$346$$ 0 0
$$347$$ 4.94792e9i 0.341275i −0.985334 0.170638i $$-0.945417\pi$$
0.985334 0.170638i $$-0.0545828\pi$$
$$348$$ 0 0
$$349$$ 7.29567e9 0.491772 0.245886 0.969299i $$-0.420921\pi$$
0.245886 + 0.969299i $$0.420921\pi$$
$$350$$ 0 0
$$351$$ 1.34114e10 + 2.66695e9i 0.883578 + 0.175706i
$$352$$ 0 0
$$353$$ 6.93875e9i 0.446871i −0.974719 0.223436i $$-0.928273\pi$$
0.974719 0.223436i $$-0.0717272\pi$$
$$354$$ 0 0
$$355$$ 3.82143e9 0.240609
$$356$$ 0 0
$$357$$ 8.82706e9 + 5.89782e9i 0.543429 + 0.363094i
$$358$$ 0 0
$$359$$ 1.60096e10i 0.963838i −0.876216 0.481919i $$-0.839940\pi$$
0.876216 0.481919i $$-0.160060\pi$$
$$360$$ 0 0
$$361$$ −1.66249e10 −0.978883
$$362$$ 0 0
$$363$$ 7.46660e9 1.11750e10i 0.430028 0.643607i
$$364$$ 0 0
$$365$$ 6.21252e9i 0.350023i
$$366$$ 0 0
$$367$$ −1.36364e10 −0.751686 −0.375843 0.926683i $$-0.622647\pi$$
−0.375843 + 0.926683i $$0.622647\pi$$
$$368$$ 0 0
$$369$$ 1.13681e10 4.70930e9i 0.613173 0.254010i
$$370$$ 0 0
$$371$$ 1.15531e10i 0.609821i
$$372$$ 0 0
$$373$$ 2.44062e10 1.26085 0.630427 0.776248i $$-0.282880\pi$$
0.630427 + 0.776248i $$0.282880\pi$$
$$374$$ 0 0
$$375$$ 1.10505e10 + 7.38339e9i 0.558798 + 0.373363i
$$376$$ 0 0
$$377$$ 1.18589e10i 0.587055i
$$378$$ 0 0
$$379$$ −1.98392e10 −0.961542 −0.480771 0.876846i $$-0.659643\pi$$
−0.480771 + 0.876846i $$0.659643\pi$$
$$380$$ 0 0
$$381$$ −1.24197e10 + 1.85881e10i −0.589403 + 0.882137i
$$382$$ 0 0
$$383$$ 1.51133e10i 0.702366i 0.936307 + 0.351183i $$0.114220\pi$$
−0.936307 + 0.351183i $$0.885780\pi$$
$$384$$ 0 0
$$385$$ −2.73420e9 −0.124448
$$386$$ 0 0
$$387$$ 8.85416e9 + 2.13737e10i 0.394733 + 0.952875i
$$388$$ 0 0
$$389$$ 1.79991e10i 0.786056i 0.919527 + 0.393028i $$0.128572\pi$$
−0.919527 + 0.393028i $$0.871428\pi$$
$$390$$ 0 0
$$391$$ −3.52342e10 −1.50750
$$392$$ 0 0
$$393$$ 1.94720e10 + 1.30103e10i 0.816284 + 0.545403i
$$394$$ 0 0
$$395$$ 5.15922e9i 0.211931i
$$396$$ 0 0
$$397$$ 2.35673e10 0.948739 0.474370 0.880326i $$-0.342676\pi$$
0.474370 + 0.880326i $$0.342676\pi$$
$$398$$ 0 0
$$399$$ 1.49137e9 2.23207e9i 0.0588428 0.0880678i
$$400$$ 0 0
$$401$$ 1.37692e10i 0.532515i 0.963902 + 0.266257i $$0.0857871\pi$$
−0.963902 + 0.266257i $$0.914213\pi$$
$$402$$ 0 0
$$403$$ −9.04353e9 −0.342861
$$404$$ 0 0
$$405$$ −6.83394e9 6.83297e9i −0.254010 0.253974i
$$406$$ 0 0
$$407$$ 9.29209e9i 0.338638i
$$408$$ 0 0
$$409$$ 3.58480e10 1.28107 0.640533 0.767931i $$-0.278714\pi$$
0.640533 + 0.767931i $$0.278714\pi$$
$$410$$ 0 0
$$411$$ −1.39793e10 9.34031e9i −0.489912 0.327336i
$$412$$ 0 0
$$413$$ 2.40011e10i 0.824955i
$$414$$ 0 0
$$415$$ 1.04157e10 0.351153
$$416$$ 0 0
$$417$$ −6.42007e9 + 9.60868e9i −0.212322 + 0.317775i
$$418$$ 0 0
$$419$$ 2.23996e10i 0.726750i 0.931643 + 0.363375i $$0.118376\pi$$
−0.931643 + 0.363375i $$0.881624\pi$$
$$420$$ 0 0
$$421$$ 1.49535e10 0.476008 0.238004 0.971264i $$-0.423507\pi$$
0.238004 + 0.971264i $$0.423507\pi$$
$$422$$ 0 0
$$423$$ 2.47372e10 1.02475e10i 0.772660 0.320078i
$$424$$ 0 0
$$425$$ 2.54805e10i 0.781001i
$$426$$ 0 0
$$427$$ −1.31880e9 −0.0396706
$$428$$ 0 0
$$429$$ −1.20602e10 8.05804e9i −0.356061 0.237903i
$$430$$ 0 0
$$431$$ 6.40436e10i 1.85595i 0.372640 + 0.927976i $$0.378453\pi$$
−0.372640 + 0.927976i $$0.621547\pi$$
$$432$$ 0 0
$$433$$ −5.22954e9 −0.148769 −0.0743843 0.997230i $$-0.523699\pi$$
−0.0743843 + 0.997230i $$0.523699\pi$$
$$434$$ 0 0
$$435$$ 4.65620e9 6.96877e9i 0.130039 0.194625i
$$436$$ 0 0
$$437$$ 8.90959e9i 0.244305i
$$438$$ 0 0
$$439$$ −4.34801e10 −1.17066 −0.585332 0.810793i $$-0.699036\pi$$
−0.585332 + 0.810793i $$0.699036\pi$$
$$440$$ 0 0
$$441$$ 6.78548e9 + 1.63800e10i 0.179402 + 0.433070i
$$442$$ 0 0
$$443$$ 3.78737e10i 0.983383i −0.870770 0.491691i $$-0.836379\pi$$
0.870770 0.491691i $$-0.163621\pi$$
$$444$$ 0 0
$$445$$ −1.63021e10 −0.415722
$$446$$ 0 0
$$447$$ 5.51754e10 + 3.68656e10i 1.38202 + 0.923403i
$$448$$ 0 0
$$449$$ 2.95505e10i 0.727076i 0.931579 + 0.363538i $$0.118431\pi$$
−0.931579 + 0.363538i $$0.881569\pi$$
$$450$$ 0 0
$$451$$ −1.30523e10 −0.315486
$$452$$ 0 0
$$453$$ −1.90737e10 + 2.85469e10i −0.452942 + 0.677902i
$$454$$ 0 0
$$455$$ 1.01086e10i 0.235856i
$$456$$ 0 0
$$457$$ −2.02181e10 −0.463529 −0.231764 0.972772i $$-0.574450\pi$$
−0.231764 + 0.972772i $$0.574450\pi$$
$$458$$ 0 0
$$459$$ 7.76277e9 3.90369e10i 0.174890 0.879476i
$$460$$ 0 0
$$461$$ 7.01826e10i 1.55391i −0.629556 0.776955i $$-0.716763\pi$$
0.629556 0.776955i $$-0.283237\pi$$
$$462$$ 0 0
$$463$$ −4.16009e9 −0.0905271 −0.0452635 0.998975i $$-0.514413\pi$$
−0.0452635 + 0.998975i $$0.514413\pi$$
$$464$$ 0 0
$$465$$ 5.31435e9 + 3.55080e9i 0.113668 + 0.0759476i
$$466$$ 0 0
$$467$$ 2.88138e10i 0.605806i 0.953021 + 0.302903i $$0.0979558\pi$$
−0.953021 + 0.302903i $$0.902044\pi$$
$$468$$ 0 0
$$469$$ 3.97056e9 0.0820654
$$470$$ 0 0
$$471$$ 3.41933e10 5.11758e10i 0.694796 1.03988i
$$472$$ 0 0
$$473$$ 2.45402e10i 0.490268i
$$474$$ 0 0
$$475$$ 6.44318e9 0.126569
$$476$$ 0 0
$$477$$ 4.00165e10 1.65770e10i 0.772975 0.320209i
$$478$$ 0 0
$$479$$ 4.47149e10i 0.849395i −0.905335 0.424698i $$-0.860380\pi$$
0.905335 0.424698i $$-0.139620\pi$$
$$480$$ 0 0
$$481$$ 3.43539e10 0.641795
$$482$$ 0 0
$$483$$ 5.54496e10 + 3.70488e10i 1.01885 + 0.680747i
$$484$$ 0 0
$$485$$ 3.30623e10i 0.597538i
$$486$$ 0 0
$$487$$ −5.72836e10 −1.01839 −0.509195 0.860651i $$-0.670057\pi$$
−0.509195 + 0.860651i $$0.670057\pi$$
$$488$$ 0 0
$$489$$ 3.00672e10 4.50005e10i 0.525845 0.787012i
$$490$$ 0 0
$$491$$ 7.25262e10i 1.24787i −0.781477 0.623934i $$-0.785533\pi$$
0.781477 0.623934i $$-0.214467\pi$$
$$492$$ 0 0
$$493$$ 3.45180e10 0.584330
$$494$$ 0 0
$$495$$ 3.92319e9 + 9.47046e9i 0.0653459 + 0.157743i
$$496$$ 0 0
$$497$$ 2.97885e10i 0.488228i
$$498$$ 0 0
$$499$$ −2.64368e10 −0.426389 −0.213195 0.977010i $$-0.568387\pi$$
−0.213195 + 0.977010i $$0.568387\pi$$
$$500$$ 0 0
$$501$$ −1.32212e10 8.83376e9i −0.209855 0.140215i
$$502$$ 0 0
$$503$$ 7.52828e10i 1.17604i −0.808845 0.588022i $$-0.799907\pi$$
0.808845 0.588022i $$-0.200093\pi$$
$$504$$ 0 0
$$505$$ −2.32457e10 −0.357419
$$506$$ 0 0
$$507$$ −6.91640e9 + 1.03515e10i −0.104676 + 0.156665i
$$508$$ 0 0
$$509$$ 6.45184e10i 0.961197i 0.876941 + 0.480599i $$0.159581\pi$$
−0.876941 + 0.480599i $$0.840419\pi$$
$$510$$ 0 0
$$511$$ 4.84273e10 0.710243
$$512$$ 0 0
$$513$$ −9.87115e9 1.96295e9i −0.142527 0.0283426i
$$514$$ 0 0
$$515$$ 3.72812e10i 0.529981i
$$516$$ 0 0
$$517$$ −2.84019e10 −0.397544
$$518$$ 0 0
$$519$$ −6.89119e10 4.60437e10i −0.949783 0.634601i
$$520$$ 0 0
$$521$$ 7.65146e10i 1.03847i −0.854632 0.519235i $$-0.826217\pi$$
0.854632 0.519235i $$-0.173783\pi$$
$$522$$ 0 0
$$523$$ −8.46771e10 −1.13177 −0.565886 0.824483i $$-0.691466\pi$$
−0.565886 + 0.824483i $$0.691466\pi$$
$$524$$ 0 0
$$525$$ 2.67927e10 4.00997e10i 0.352679 0.527842i
$$526$$ 0 0
$$527$$ 2.63232e10i 0.341269i
$$528$$ 0 0
$$529$$ −1.43023e11 −1.82634
$$530$$ 0 0
$$531$$ 8.31326e10 3.44381e10i 1.04567 0.433173i
$$532$$ 0 0
$$533$$ 4.82558e10i 0.597917i
$$534$$ 0 0
$$535$$ 5.06336e9 0.0618050
$$536$$ 0 0
$$537$$ −8.68104e10 5.80026e10i −1.04394 0.697510i
$$538$$ 0 0
$$539$$ 1.88066e10i 0.222821i
$$540$$ 0 0
$$541$$ −1.43470e11 −1.67483 −0.837415 0.546568i $$-0.815934\pi$$
−0.837415 + 0.546568i $$0.815934\pi$$
$$542$$ 0 0
$$543$$ −2.12268e10 + 3.17694e10i −0.244166 + 0.365434i
$$544$$ 0 0
$$545$$ 2.46893e10i 0.279849i
$$546$$ 0 0
$$547$$ 1.64171e11 1.83378 0.916892 0.399134i $$-0.130689\pi$$
0.916892 + 0.399134i $$0.130689\pi$$
$$548$$ 0 0
$$549$$ 1.89229e9 + 4.56795e9i 0.0208305 + 0.0502842i
$$550$$ 0 0
$$551$$ 8.72847e9i 0.0946961i
$$552$$ 0 0
$$553$$ 4.02167e10 0.430037
$$554$$ 0 0
$$555$$ −2.01878e10 1.34885e10i −0.212773 0.142165i
$$556$$ 0 0
$$557$$ 1.54420e11i 1.60429i −0.597130 0.802145i $$-0.703692\pi$$
0.597130 0.802145i $$-0.296308\pi$$
$$558$$ 0 0
$$559$$ 9.07278e10 0.929166
$$560$$ 0 0
$$561$$ −2.34547e10 + 3.51039e10i −0.236799 + 0.354408i
$$562$$ 0 0
$$563$$ 1.54622e11i 1.53900i 0.638646 + 0.769500i $$0.279495\pi$$
−0.638646 + 0.769500i $$0.720505\pi$$
$$564$$ 0 0
$$565$$ −6.45992e10 −0.633919
$$566$$ 0 0
$$567$$ −5.32638e10 + 5.32714e10i −0.515348 + 0.515420i
$$568$$ 0 0
$$569$$ 1.15380e11i 1.10073i −0.834925 0.550364i $$-0.814489\pi$$
0.834925 0.550364i $$-0.185511\pi$$
$$570$$ 0 0
$$571$$ −1.63410e11 −1.53722 −0.768608 0.639720i $$-0.779050\pi$$
−0.768608 + 0.639720i $$0.779050\pi$$
$$572$$ 0 0
$$573$$ 1.08963e10 + 7.28041e9i 0.101079 + 0.0675363i
$$574$$ 0 0
$$575$$ 1.60063e11i 1.46426i
$$576$$ 0 0
$$577$$ 7.42282e10 0.669678 0.334839 0.942275i $$-0.391318\pi$$
0.334839 + 0.942275i $$0.391318\pi$$
$$578$$ 0 0
$$579$$ −7.14779e10 + 1.06978e11i −0.636001 + 0.951879i
$$580$$ 0 0
$$581$$ 8.11916e10i 0.712535i
$$582$$ 0 0
$$583$$ −4.59449e10 −0.397707
$$584$$ 0 0
$$585$$ −3.50134e10 + 1.45045e10i −0.298958 + 0.123845i
$$586$$ 0 0
$$587$$ 6.72877e10i 0.566739i −0.959011 0.283369i $$-0.908548\pi$$
0.959011 0.283369i $$-0.0914523\pi$$
$$588$$ 0 0
$$589$$ 6.65629e9 0.0553059
$$590$$ 0 0
$$591$$ 3.62187e10 + 2.41996e10i 0.296881 + 0.198362i
$$592$$ 0 0
$$593$$ 2.36444e10i 0.191210i −0.995419 0.0956048i $$-0.969521\pi$$
0.995419 0.0956048i $$-0.0304785\pi$$
$$594$$ 0 0
$$595$$ −2.94235e10 −0.234761
$$596$$ 0 0
$$597$$ −2.91414e10 + 4.36148e10i −0.229410 + 0.343350i
$$598$$ 0 0
$$599$$ 3.03370e10i 0.235649i −0.993034 0.117825i $$-0.962408\pi$$
0.993034 0.117825i $$-0.0375921\pi$$
$$600$$ 0 0
$$601$$ 3.37911e10 0.259003 0.129501 0.991579i $$-0.458662\pi$$
0.129501 + 0.991579i $$0.458662\pi$$
$$602$$ 0 0
$$603$$ −5.69718e9 1.37528e10i −0.0430914 0.104022i
$$604$$ 0 0
$$605$$ 3.72500e10i 0.278038i
$$606$$ 0 0
$$607$$ 3.82366e10 0.281660 0.140830 0.990034i $$-0.455023\pi$$
0.140830 + 0.990034i $$0.455023\pi$$
$$608$$ 0 0
$$609$$ −5.43224e10 3.62957e10i −0.394920 0.263867i
$$610$$ 0 0
$$611$$ 1.05005e11i 0.753435i
$$612$$ 0 0
$$613$$ −1.08066e11 −0.765330 −0.382665 0.923887i $$-0.624994\pi$$
−0.382665 + 0.923887i $$0.624994\pi$$
$$614$$ 0 0
$$615$$ −1.89469e10 + 2.83571e10i −0.132445 + 0.198226i
$$616$$ 0 0
$$617$$ 4.72538e9i 0.0326059i −0.999867 0.0163029i $$-0.994810\pi$$
0.999867 0.0163029i $$-0.00518962\pi$$
$$618$$ 0 0
$$619$$ 2.29845e10 0.156557 0.0782786 0.996932i $$-0.475058\pi$$
0.0782786 + 0.996932i $$0.475058\pi$$
$$620$$ 0 0
$$621$$ 4.87639e10 2.45221e11i 0.327893 1.64889i
$$622$$ 0 0
$$623$$ 1.27077e11i 0.843555i
$$624$$ 0 0
$$625$$ 9.60656e10 0.629575
$$626$$ 0 0
$$627$$ 8.87662e9 + 5.93094e9i 0.0574351 + 0.0383754i
$$628$$ 0 0
$$629$$ 9.99949e10i 0.638815i
$$630$$ 0 0
$$631$$ 1.01892e11 0.642722 0.321361 0.946957i $$-0.395860\pi$$
0.321361 + 0.946957i $$0.395860\pi$$
$$632$$ 0 0
$$633$$ 2.61497e9 3.91372e9i 0.0162874 0.0243767i
$$634$$ 0 0
$$635$$ 6.19605e10i 0.381083i
$$636$$ 0 0
$$637$$ 6.95302e10 0.422295
$$638$$ 0 0
$$639$$ −1.03179e11 + 4.27422e10i −0.618851 + 0.256362i
$$640$$ 0 0
$$641$$ 1.17803e11i 0.697791i 0.937162 + 0.348896i $$0.113443\pi$$
−0.937162 + 0.348896i $$0.886557\pi$$
$$642$$ 0 0
$$643$$ −2.62680e10 −0.153668 −0.0768339 0.997044i $$-0.524481\pi$$
−0.0768339 + 0.997044i $$0.524481\pi$$
$$644$$ 0 0
$$645$$ −5.33154e10 3.56228e10i −0.308045 0.205821i
$$646$$ 0 0
$$647$$ 3.10527e11i 1.77208i −0.463612 0.886038i $$-0.653447\pi$$
0.463612 0.886038i $$-0.346553\pi$$
$$648$$ 0 0
$$649$$ −9.54486e10 −0.538010
$$650$$ 0 0
$$651$$ 2.76789e10 4.14260e10i 0.154108 0.230648i
$$652$$ 0 0
$$653$$ 3.48345e10i 0.191583i −0.995401 0.0957914i $$-0.969462\pi$$
0.995401 0.0957914i $$-0.0305382\pi$$
$$654$$ 0 0
$$655$$ −6.49068e10 −0.352635
$$656$$ 0 0
$$657$$ −6.94863e10 1.67738e11i −0.372939 0.900265i
$$658$$ 0 0
$$659$$ 3.77120e10i 0.199957i 0.994990 + 0.0999787i $$0.0318775\pi$$
−0.994990 + 0.0999787i $$0.968123\pi$$
$$660$$ 0 0
$$661$$ 1.39619e11 0.731372 0.365686 0.930738i $$-0.380834\pi$$
0.365686 + 0.930738i $$0.380834\pi$$
$$662$$ 0 0
$$663$$ −1.29783e11 8.67149e10i −0.671682 0.448786i
$$664$$ 0 0
$$665$$ 7.44025e9i 0.0380453i
$$666$$ 0 0
$$667$$ 2.16834e11 1.09553
$$668$$ 0 0
$$669$$ −1.98090e11 + 2.96474e11i −0.988912 + 1.48007i
$$670$$ 0 0
$$671$$ 5.24468e9i 0.0258719i
$$672$$ 0 0
$$673$$ −1.29783e11 −0.632642 −0.316321 0.948652i $$-0.602448\pi$$
−0.316321 + 0.948652i $$0.602448\pi$$
$$674$$ 0 0
$$675$$ −1.77337e11 3.52648e10i −0.854249 0.169874i
$$676$$ 0 0
$$677$$ 3.40648e11i 1.62163i 0.585306 + 0.810813i $$0.300975\pi$$
−0.585306 + 0.810813i $$0.699025\pi$$
$$678$$ 0 0
$$679$$ 2.57724e11 1.21248
$$680$$ 0 0
$$681$$ 2.38144e11 + 1.59117e11i 1.10726 + 0.739821i
$$682$$ 0 0
$$683$$ 1.02876e11i 0.472750i 0.971662 + 0.236375i $$0.0759593\pi$$
−0.971662 + 0.236375i $$0.924041\pi$$
$$684$$ 0 0
$$685$$ 4.65976e10 0.211642
$$686$$ 0 0
$$687$$ 8.39562e10 1.25654e11i 0.376900 0.564092i
$$688$$ 0 0
$$689$$ 1.69863e11i 0.753742i
$$690$$ 0 0
$$691$$ 3.58259e11 1.57140 0.785698 0.618611i $$-0.212304\pi$$
0.785698 + 0.618611i $$0.212304\pi$$
$$692$$ 0 0
$$693$$ 7.38234e10 3.05817e10i 0.320082 0.132595i
$$694$$ 0 0
$$695$$ 3.20289e10i 0.137279i
$$696$$ 0 0
$$697$$ −1.40459e11 −0.595141
$$698$$ 0 0
$$699$$ −1.83280e11 1.22459e11i −0.767728 0.512960i
$$700$$ 0 0
$$701$$ 2.49323e11i 1.03250i 0.856438 + 0.516250i $$0.172673\pi$$
−0.856438 + 0.516250i $$0.827327\pi$$
$$702$$ 0 0
$$703$$ −2.52854e10 −0.103526
$$704$$ 0 0
$$705$$ −4.12286e10 + 6.17053e10i −0.166895 + 0.249785i
$$706$$ 0 0
$$707$$ 1.81203e11i 0.725251i
$$708$$ 0 0
$$709$$ 3.88874e11 1.53895 0.769474 0.638678i $$-0.220518\pi$$
0.769474 + 0.638678i $$0.220518\pi$$
$$710$$ 0 0
$$711$$ −5.77052e10 1.39299e11i −0.225807 0.545091i
$$712$$ 0 0
$$713$$ 1.65357e11i 0.639829i
$$714$$ 0 0
$$715$$ 4.02006e10 0.153818
$$716$$ 0 0
$$717$$ 1.53195e11 + 1.02357e11i 0.579651 + 0.387296i
$$718$$ 0 0
$$719$$ 3.35735e10i 0.125626i −0.998025 0.0628132i $$-0.979993\pi$$
0.998025 0.0628132i $$-0.0200072\pi$$
$$720$$ 0 0
$$721$$ 2.90611e11 1.07540
$$722$$ 0 0
$$723$$ −7.86002e10 + 1.17638e11i −0.287654 + 0.430521i
$$724$$ 0 0
$$725$$ 1.56809e11i 0.567569i
$$726$$ 0 0
$$727$$ −2.53113e11 −0.906102 −0.453051 0.891485i $$-0.649664\pi$$
−0.453051 + 0.891485i $$0.649664\pi$$
$$728$$ 0 0
$$729$$ 2.60942e11 + 1.08053e11i 0.923920 + 0.382586i
$$730$$ 0 0
$$731$$ 2.64084e11i 0.924853i
$$732$$ 0 0
$$733$$ −2.07602e11 −0.719144 −0.359572 0.933117i $$-0.617077\pi$$
−0.359572 + 0.933117i $$0.617077\pi$$
$$734$$ 0 0
$$735$$ −4.08588e10 2.72999e10i −0.140003 0.0935432i
$$736$$ 0 0
$$737$$ 1.57903e10i 0.0535205i
$$738$$ 0 0
$$739$$ 4.15014e11 1.39151 0.695753 0.718281i $$-0.255071\pi$$
0.695753 + 0.718281i $$0.255071\pi$$
$$740$$ 0 0
$$741$$ −2.19274e10 + 3.28179e10i −0.0727300 + 0.108852i
$$742$$ 0 0
$$743$$ 3.30690e11i 1.08509i 0.840027 + 0.542545i $$0.182539\pi$$
−0.840027 + 0.542545i $$0.817461\pi$$
$$744$$ 0 0
$$745$$ −1.83918e11 −0.597034
$$746$$ 0 0
$$747$$ −2.81224e11 + 1.16498e11i −0.903170 + 0.374143i
$$748$$ 0 0
$$749$$ 3.94695e10i 0.125411i
$$750$$ 0 0
$$751$$ 4.77978e11 1.50262 0.751308 0.659952i $$-0.229423\pi$$
0.751308 + 0.659952i $$0.229423\pi$$
$$752$$ 0 0
$$753$$ 9.26390e10 + 6.18970e10i 0.288147 + 0.192526i
$$754$$ 0 0
$$755$$ 9.51565e10i 0.292854i
$$756$$ 0 0
$$757$$ 8.95066e10 0.272566 0.136283 0.990670i $$-0.456484\pi$$
0.136283 + 0.990670i $$0.456484\pi$$
$$758$$ 0 0
$$759$$ −1.47337e11 + 2.20514e11i −0.443962 + 0.664462i
$$760$$ 0 0
$$761$$ 5.71473e11i 1.70395i 0.523581 + 0.851976i $$0.324596\pi$$
−0.523581 + 0.851976i $$0.675404\pi$$
$$762$$ 0 0
$$763$$ 1.92456e11 0.567851
$$764$$ 0 0
$$765$$ 4.22185e10 + 1.01914e11i 0.123270 + 0.297570i
$$766$$ 0 0
$$767$$ 3.52884e11i 1.01965i
$$768$$ 0 0
$$769$$ 2.56194e11 0.732596 0.366298 0.930498i $$-0.380625\pi$$
0.366298 + 0.930498i $$0.380625\pi$$
$$770$$ 0 0
$$771$$ −5.34537e11 3.57152e11i −1.51273 1.01073i
$$772$$ 0 0
$$773$$ 1.00523e11i 0.281543i 0.990042 + 0.140772i $$0.0449584\pi$$
−0.990042 + 0.140772i $$0.955042\pi$$
$$774$$ 0 0
$$775$$ 1.19582e11 0.331480
$$776$$ 0 0
$$777$$ −1.05145e11 + 1.57366e11i −0.288472 + 0.431745i
$$778$$ 0 0
$$779$$ 3.55176e10i 0.0964482i
$$780$$ 0 0
$$781$$ 1.18464e11 0.318408
$$782$$ 0 0
$$783$$