# Properties

 Label 162.13.d.c.107.3 Level $162$ Weight $13$ Character 162.107 Analytic conductor $148.067$ Analytic rank $0$ Dimension $8$ CM no Inner twists $4$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,13,Mod(53,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 13, names="a")

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

chi := DirichletCharacter("162.53");

S:= CuspForms(chi, 13);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$162 = 2 \cdot 3^{4}$$ Weight: $$k$$ $$=$$ $$13$$ Character orbit: $$[\chi]$$ $$=$$ 162.d (of order $$6$$, degree $$2$$, 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: $$148.066998399$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{8} - 4 x^{7} - 18478 x^{6} + 55448 x^{5} + 128029439 x^{4} - 256151296 x^{3} - 394230846230 x^{2} + 394358931120 x + 455189180292012$$ x^8 - 4*x^7 - 18478*x^6 + 55448*x^5 + 128029439*x^4 - 256151296*x^3 - 394230846230*x^2 + 394358931120*x + 455189180292012 Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{24}\cdot 3^{12}$$ Twist minimal: no (minimal twist has level 54) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 107.3 Root $$67.2477 - 0.707107i$$ of defining polynomial Character $$\chi$$ $$=$$ 162.107 Dual form 162.13.d.c.53.3

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(39.1918 + 22.6274i) q^{2} +(1024.00 + 1773.62i) q^{4} +(-12529.2 + 7233.73i) q^{5} +(-48617.5 + 84208.1i) q^{7} +92681.9i q^{8} +O(q^{10})$$ $$q+(39.1918 + 22.6274i) q^{2} +(1024.00 + 1773.62i) q^{4} +(-12529.2 + 7233.73i) q^{5} +(-48617.5 + 84208.1i) q^{7} +92681.9i q^{8} -654723. q^{10} +(-1.20670e6 - 696690. i) q^{11} +(3.01088e6 + 5.21499e6i) q^{13} +(-3.81082e6 + 2.20018e6i) q^{14} +(-2.09715e6 + 3.63237e6i) q^{16} -2.96631e7i q^{17} -4.55192e7 q^{19} +(-2.56598e7 - 1.48147e7i) q^{20} +(-3.15286e7 - 5.46091e7i) q^{22} +(-8.46661e7 + 4.88820e7i) q^{23} +(-1.74165e7 + 3.01663e7i) q^{25} +2.72513e8i q^{26} -1.99137e8 q^{28} +(-4.17778e8 - 2.41204e8i) q^{29} +(2.34743e8 + 4.06586e8i) q^{31} +(-1.64382e8 + 9.49063e7i) q^{32} +(6.71200e8 - 1.16255e9i) q^{34} -1.40675e9i q^{35} -4.39480e9 q^{37} +(-1.78398e9 - 1.02998e9i) q^{38} +(-6.70436e8 - 1.16123e9i) q^{40} +(4.92680e9 - 2.84449e9i) q^{41} +(-2.15314e9 + 3.72934e9i) q^{43} -2.85364e9i q^{44} -4.42430e9 q^{46} +(-3.32101e9 - 1.91738e9i) q^{47} +(2.19331e9 + 3.79893e9i) q^{49} +(-1.36517e9 + 7.88182e8i) q^{50} +(-6.16627e9 + 1.06803e10i) q^{52} +2.52870e10i q^{53} +2.01587e10 q^{55} +(-7.80456e9 - 4.50597e9i) q^{56} +(-1.09156e10 - 1.89065e10i) q^{58} +(5.60254e10 - 3.23463e10i) q^{59} +(1.61241e10 - 2.79278e10i) q^{61} +2.12465e10i q^{62} -8.58993e9 q^{64} +(-7.54477e10 - 4.35597e10i) q^{65} +(-2.90443e10 - 5.03063e10i) q^{67} +(5.26111e10 - 3.03750e10i) q^{68} +(3.18310e10 - 5.51329e10i) q^{70} +3.98191e10i q^{71} +1.63455e11 q^{73} +(-1.72240e11 - 9.94430e10i) q^{74} +(-4.66117e10 - 8.07338e10i) q^{76} +(1.17334e11 - 6.77427e10i) q^{77} +(9.35920e10 - 1.62106e11i) q^{79} -6.06809e10i q^{80} +2.57454e11 q^{82} +(6.69378e10 + 3.86466e10i) q^{83} +(2.14575e11 + 3.71655e11i) q^{85} +(-1.68771e11 + 9.74399e10i) q^{86} +(6.45706e10 - 1.11839e11i) q^{88} +9.19946e11i q^{89} -5.85525e11 q^{91} +(-1.73396e11 - 1.00110e11i) q^{92} +(-8.67709e10 - 1.50292e11i) q^{94} +(5.70319e11 - 3.29274e11i) q^{95} +(7.16954e11 - 1.24180e12i) q^{97} +1.98516e11i q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q + 8192 q^{4} - 271484 q^{7}+O(q^{10})$$ 8 * q + 8192 * q^4 - 271484 * q^7 $$8 q + 8192 q^{4} - 271484 q^{7} + 2279424 q^{10} - 696284 q^{13} - 16777216 q^{16} - 175753928 q^{19} - 30471168 q^{22} + 906499004 q^{25} - 1111998464 q^{28} + 2382534136 q^{31} + 2915232768 q^{34} - 1146574280 q^{37} + 2334130176 q^{40} + 15116732344 q^{43} + 5281241088 q^{46} + 33490260096 q^{49} + 1425989632 q^{52} + 195012288000 q^{55} - 121550997504 q^{58} - 58362866396 q^{61} - 68719476736 q^{64} - 308975155100 q^{67} + 33014547456 q^{70} - 357741406856 q^{73} - 179972022272 q^{76} + 905099168836 q^{79} + 722937556992 q^{82} + 720516135168 q^{85} + 62404952064 q^{88} - 1360962234040 q^{91} - 1147443557376 q^{94} + 5671281236356 q^{97}+O(q^{100})$$ 8 * q + 8192 * q^4 - 271484 * q^7 + 2279424 * q^10 - 696284 * q^13 - 16777216 * q^16 - 175753928 * q^19 - 30471168 * q^22 + 906499004 * q^25 - 1111998464 * q^28 + 2382534136 * q^31 + 2915232768 * q^34 - 1146574280 * q^37 + 2334130176 * q^40 + 15116732344 * q^43 + 5281241088 * q^46 + 33490260096 * q^49 + 1425989632 * q^52 + 195012288000 * q^55 - 121550997504 * q^58 - 58362866396 * q^61 - 68719476736 * q^64 - 308975155100 * q^67 + 33014547456 * q^70 - 357741406856 * q^73 - 179972022272 * q^76 + 905099168836 * q^79 + 722937556992 * q^82 + 720516135168 * q^85 + 62404952064 * q^88 - 1360962234040 * q^91 - 1147443557376 * q^94 + 5671281236356 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$$.

 $$n$$ $$83$$ $$\chi(n)$$ $$e\left(\frac{1}{6}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 39.1918 + 22.6274i 0.612372 + 0.353553i
$$3$$ 0 0
$$4$$ 1024.00 + 1773.62i 0.250000 + 0.433013i
$$5$$ −12529.2 + 7233.73i −0.801868 + 0.462959i −0.844124 0.536148i $$-0.819879\pi$$
0.0422557 + 0.999107i $$0.486546\pi$$
$$6$$ 0 0
$$7$$ −48617.5 + 84208.1i −0.413242 + 0.715757i −0.995242 0.0974322i $$-0.968937\pi$$
0.582000 + 0.813189i $$0.302270\pi$$
$$8$$ 92681.9i 0.353553i
$$9$$ 0 0
$$10$$ −654723. −0.654723
$$11$$ −1.20670e6 696690.i −0.681152 0.393263i 0.119137 0.992878i $$-0.461987\pi$$
−0.800289 + 0.599614i $$0.795321\pi$$
$$12$$ 0 0
$$13$$ 3.01088e6 + 5.21499e6i 0.623782 + 1.08042i 0.988775 + 0.149412i $$0.0477379\pi$$
−0.364993 + 0.931010i $$0.618929\pi$$
$$14$$ −3.81082e6 + 2.20018e6i −0.506116 + 0.292206i
$$15$$ 0 0
$$16$$ −2.09715e6 + 3.63237e6i −0.125000 + 0.216506i
$$17$$ 2.96631e7i 1.22892i −0.788948 0.614460i $$-0.789374\pi$$
0.788948 0.614460i $$-0.210626\pi$$
$$18$$ 0 0
$$19$$ −4.55192e7 −0.967550 −0.483775 0.875192i $$-0.660735\pi$$
−0.483775 + 0.875192i $$0.660735\pi$$
$$20$$ −2.56598e7 1.48147e7i −0.400934 0.231479i
$$21$$ 0 0
$$22$$ −3.15286e7 5.46091e7i −0.278079 0.481647i
$$23$$ −8.46661e7 + 4.88820e7i −0.571930 + 0.330204i −0.757920 0.652348i $$-0.773784\pi$$
0.185990 + 0.982552i $$0.440451\pi$$
$$24$$ 0 0
$$25$$ −1.74165e7 + 3.01663e7i −0.0713381 + 0.123561i
$$26$$ 2.72513e8i 0.882161i
$$27$$ 0 0
$$28$$ −1.99137e8 −0.413242
$$29$$ −4.17778e8 2.41204e8i −0.702356 0.405505i 0.105869 0.994380i $$-0.466238\pi$$
−0.808224 + 0.588875i $$0.799571\pi$$
$$30$$ 0 0
$$31$$ 2.34743e8 + 4.06586e8i 0.264498 + 0.458124i 0.967432 0.253131i $$-0.0814605\pi$$
−0.702934 + 0.711255i $$0.748127\pi$$
$$32$$ −1.64382e8 + 9.49063e7i −0.153093 + 0.0883883i
$$33$$ 0 0
$$34$$ 6.71200e8 1.16255e9i 0.434489 0.752557i
$$35$$ 1.40675e9i 0.765257i
$$36$$ 0 0
$$37$$ −4.39480e9 −1.71289 −0.856444 0.516240i $$-0.827331\pi$$
−0.856444 + 0.516240i $$0.827331\pi$$
$$38$$ −1.78398e9 1.02998e9i −0.592501 0.342081i
$$39$$ 0 0
$$40$$ −6.70436e8 1.16123e9i −0.163681 0.283503i
$$41$$ 4.92680e9 2.84449e9i 1.03720 0.598827i 0.118160 0.992995i $$-0.462300\pi$$
0.919039 + 0.394167i $$0.128967\pi$$
$$42$$ 0 0
$$43$$ −2.15314e9 + 3.72934e9i −0.340613 + 0.589959i −0.984547 0.175122i $$-0.943968\pi$$
0.643934 + 0.765081i $$0.277301\pi$$
$$44$$ 2.85364e9i 0.393263i
$$45$$ 0 0
$$46$$ −4.42430e9 −0.466979
$$47$$ −3.32101e9 1.91738e9i −0.308094 0.177878i 0.337979 0.941153i $$-0.390257\pi$$
−0.646073 + 0.763276i $$0.723590\pi$$
$$48$$ 0 0
$$49$$ 2.19331e9 + 3.79893e9i 0.158462 + 0.274464i
$$50$$ −1.36517e9 + 7.88182e8i −0.0873710 + 0.0504437i
$$51$$ 0 0
$$52$$ −6.16627e9 + 1.06803e10i −0.311891 + 0.540211i
$$53$$ 2.52870e10i 1.14089i 0.821337 + 0.570443i $$0.193228\pi$$
−0.821337 + 0.570443i $$0.806772\pi$$
$$54$$ 0 0
$$55$$ 2.01587e10 0.728259
$$56$$ −7.80456e9 4.50597e9i −0.253058 0.146103i
$$57$$ 0 0
$$58$$ −1.09156e10 1.89065e10i −0.286735 0.496640i
$$59$$ 5.60254e10 3.23463e10i 1.32823 0.766854i 0.343204 0.939261i $$-0.388488\pi$$
0.985026 + 0.172407i $$0.0551545\pi$$
$$60$$ 0 0
$$61$$ 1.61241e10 2.79278e10i 0.312966 0.542072i −0.666037 0.745918i $$-0.732011\pi$$
0.979003 + 0.203846i $$0.0653442\pi$$
$$62$$ 2.12465e10i 0.374056i
$$63$$ 0 0
$$64$$ −8.58993e9 −0.125000
$$65$$ −7.54477e10 4.35597e10i −1.00038 0.577571i
$$66$$ 0 0
$$67$$ −2.90443e10 5.03063e10i −0.321079 0.556126i 0.659632 0.751589i $$-0.270712\pi$$
−0.980711 + 0.195463i $$0.937379\pi$$
$$68$$ 5.26111e10 3.03750e10i 0.532138 0.307230i
$$69$$ 0 0
$$70$$ 3.18310e10 5.51329e10i 0.270559 0.468622i
$$71$$ 3.98191e10i 0.310843i 0.987848 + 0.155422i $$0.0496736\pi$$
−0.987848 + 0.155422i $$0.950326\pi$$
$$72$$ 0 0
$$73$$ 1.63455e11 1.08009 0.540045 0.841636i $$-0.318407\pi$$
0.540045 + 0.841636i $$0.318407\pi$$
$$74$$ −1.72240e11 9.94430e10i −1.04893 0.605597i
$$75$$ 0 0
$$76$$ −4.66117e10 8.07338e10i −0.241887 0.418961i
$$77$$ 1.17334e11 6.77427e10i 0.562962 0.325026i
$$78$$ 0 0
$$79$$ 9.35920e10 1.62106e11i 0.385014 0.666863i −0.606757 0.794887i $$-0.707530\pi$$
0.991771 + 0.128024i $$0.0408633\pi$$
$$80$$ 6.06809e10i 0.231479i
$$81$$ 0 0
$$82$$ 2.57454e11 0.846870
$$83$$ 6.69378e10 + 3.86466e10i 0.204740 + 0.118207i 0.598865 0.800850i $$-0.295619\pi$$
−0.394124 + 0.919057i $$0.628952\pi$$
$$84$$ 0 0
$$85$$ 2.14575e11 + 3.71655e11i 0.568939 + 0.985432i
$$86$$ −1.68771e11 + 9.74399e10i −0.417164 + 0.240850i
$$87$$ 0 0
$$88$$ 6.45706e10 1.11839e11i 0.139040 0.240824i
$$89$$ 9.19946e11i 1.85107i 0.378665 + 0.925534i $$0.376383\pi$$
−0.378665 + 0.925534i $$0.623617\pi$$
$$90$$ 0 0
$$91$$ −5.85525e11 −1.03109
$$92$$ −1.73396e11 1.00110e11i −0.285965 0.165102i
$$93$$ 0 0
$$94$$ −8.67709e10 1.50292e11i −0.125779 0.217855i
$$95$$ 5.70319e11 3.29274e11i 0.775848 0.447936i
$$96$$ 0 0
$$97$$ 7.16954e11 1.24180e12i 0.860718 1.49081i −0.0105198 0.999945i $$-0.503349\pi$$
0.871237 0.490862i $$-0.163318\pi$$
$$98$$ 1.98516e11i 0.224099i
$$99$$ 0 0
$$100$$ −7.13381e10 −0.0713381
$$101$$ 8.20501e11 + 4.73716e11i 0.772949 + 0.446262i 0.833926 0.551877i $$-0.186088\pi$$
−0.0609766 + 0.998139i $$0.519421\pi$$
$$102$$ 0 0
$$103$$ −9.26886e11 1.60541e12i −0.776252 1.34451i −0.934088 0.357043i $$-0.883785\pi$$
0.157836 0.987465i $$-0.449548\pi$$
$$104$$ −4.83335e11 + 2.79054e11i −0.381987 + 0.220540i
$$105$$ 0 0
$$106$$ −5.72180e11 + 9.91044e11i −0.403364 + 0.698647i
$$107$$ 2.27324e12i 1.51475i −0.652977 0.757377i $$-0.726480\pi$$
0.652977 0.757377i $$-0.273520\pi$$
$$108$$ 0 0
$$109$$ −2.04503e11 −0.121938 −0.0609692 0.998140i $$-0.519419\pi$$
−0.0609692 + 0.998140i $$0.519419\pi$$
$$110$$ 7.90056e11 + 4.56139e11i 0.445966 + 0.257478i
$$111$$ 0 0
$$112$$ −2.03917e11 3.53194e11i −0.103311 0.178939i
$$113$$ 2.45337e11 1.41645e11i 0.117840 0.0680349i −0.439922 0.898036i $$-0.644994\pi$$
0.557761 + 0.830001i $$0.311660\pi$$
$$114$$ 0 0
$$115$$ 7.07199e11 1.22490e12i 0.305742 0.529560i
$$116$$ 9.87971e11i 0.405505i
$$117$$ 0 0
$$118$$ 2.92765e12 1.08450
$$119$$ 2.49787e12 + 1.44215e12i 0.879607 + 0.507842i
$$120$$ 0 0
$$121$$ −5.98460e11 1.03656e12i −0.190688 0.330281i
$$122$$ 1.26387e12 7.29693e11i 0.383303 0.221300i
$$123$$ 0 0
$$124$$ −4.80753e11 + 8.32689e11i −0.132249 + 0.229062i
$$125$$ 4.03604e12i 1.05802i
$$126$$ 0 0
$$127$$ −3.29909e12 −0.786271 −0.393136 0.919480i $$-0.628610\pi$$
−0.393136 + 0.919480i $$0.628610\pi$$
$$128$$ −3.36655e11 1.94368e11i −0.0765466 0.0441942i
$$129$$ 0 0
$$130$$ −1.97129e12 3.41437e12i −0.408404 0.707377i
$$131$$ −6.04050e12 + 3.48748e12i −1.19521 + 0.690056i −0.959484 0.281763i $$-0.909081\pi$$
−0.235728 + 0.971819i $$0.575747\pi$$
$$132$$ 0 0
$$133$$ 2.21303e12 3.83309e12i 0.399833 0.692530i
$$134$$ 2.62879e12i 0.454075i
$$135$$ 0 0
$$136$$ 2.74924e12 0.434489
$$137$$ −2.35726e12 1.36097e12i −0.356520 0.205837i 0.311033 0.950399i $$-0.399325\pi$$
−0.667553 + 0.744562i $$0.732658\pi$$
$$138$$ 0 0
$$139$$ 5.02531e12 + 8.70410e12i 0.696746 + 1.20680i 0.969589 + 0.244740i $$0.0787027\pi$$
−0.272843 + 0.962059i $$0.587964\pi$$
$$140$$ 2.49503e12 1.44051e12i 0.331366 0.191314i
$$141$$ 0 0
$$142$$ −9.01004e11 + 1.56058e12i −0.109900 + 0.190352i
$$143$$ 8.39059e12i 0.981242i
$$144$$ 0 0
$$145$$ 6.97922e12 0.750929
$$146$$ 6.40609e12 + 3.69856e12i 0.661418 + 0.381870i
$$147$$ 0 0
$$148$$ −4.50028e12 7.79471e12i −0.428222 0.741702i
$$149$$ 1.40788e13 8.12840e12i 1.28661 0.742827i 0.308565 0.951203i $$-0.400151\pi$$
0.978049 + 0.208376i $$0.0668179\pi$$
$$150$$ 0 0
$$151$$ 4.73231e12 8.19660e12i 0.399219 0.691468i −0.594410 0.804162i $$-0.702614\pi$$
0.993630 + 0.112694i $$0.0359478\pi$$
$$152$$ 4.21881e12i 0.342081i
$$153$$ 0 0
$$154$$ 6.13137e12 0.459656
$$155$$ −5.88227e12 3.39613e12i −0.424185 0.244903i
$$156$$ 0 0
$$157$$ 9.22889e12 + 1.59849e13i 0.616242 + 1.06736i 0.990165 + 0.139903i $$0.0446792\pi$$
−0.373923 + 0.927460i $$0.621987\pi$$
$$158$$ 7.33609e12 4.23549e12i 0.471544 0.272246i
$$159$$ 0 0
$$160$$ 1.37305e12 2.37820e12i 0.0818403 0.141752i
$$161$$ 9.50609e12i 0.545817i
$$162$$ 0 0
$$163$$ −1.76328e13 −0.940145 −0.470073 0.882628i $$-0.655772\pi$$
−0.470073 + 0.882628i $$0.655772\pi$$
$$164$$ 1.00901e13 + 5.82552e12i 0.518600 + 0.299414i
$$165$$ 0 0
$$166$$ 1.74894e12 + 3.02926e12i 0.0835848 + 0.144773i
$$167$$ 3.53071e13 2.03845e13i 1.62766 0.939728i 0.642867 0.765978i $$-0.277745\pi$$
0.984790 0.173750i $$-0.0555884\pi$$
$$168$$ 0 0
$$169$$ −6.48170e12 + 1.12266e13i −0.278207 + 0.481869i
$$170$$ 1.94211e13i 0.804602i
$$171$$ 0 0
$$172$$ −8.81925e12 −0.340613
$$173$$ 2.65381e13 + 1.53218e13i 0.989905 + 0.571522i 0.905246 0.424888i $$-0.139687\pi$$
0.0846590 + 0.996410i $$0.473020\pi$$
$$174$$ 0 0
$$175$$ −1.69350e12 2.93322e12i −0.0589599 0.102121i
$$176$$ 5.06128e12 2.92213e12i 0.170288 0.0983158i
$$177$$ 0 0
$$178$$ −2.08160e13 + 3.60544e13i −0.654451 + 1.13354i
$$179$$ 2.05014e13i 0.623254i 0.950204 + 0.311627i $$0.100874\pi$$
−0.950204 + 0.311627i $$0.899126\pi$$
$$180$$ 0 0
$$181$$ −4.90808e13 −1.39585 −0.697927 0.716169i $$-0.745894\pi$$
−0.697927 + 0.716169i $$0.745894\pi$$
$$182$$ −2.29478e13 1.32489e13i −0.631412 0.364546i
$$183$$ 0 0
$$184$$ −4.53048e12 7.84702e12i −0.116745 0.202208i
$$185$$ 5.50633e13 3.17908e13i 1.37351 0.792997i
$$186$$ 0 0
$$187$$ −2.06660e13 + 3.57946e13i −0.483289 + 0.837081i
$$188$$ 7.85361e12i 0.177878i
$$189$$ 0 0
$$190$$ 2.98025e13 0.633477
$$191$$ −3.85302e13 2.22454e13i −0.793600 0.458185i 0.0476285 0.998865i $$-0.484834\pi$$
−0.841228 + 0.540680i $$0.818167\pi$$
$$192$$ 0 0
$$193$$ −2.82943e12 4.90072e12i −0.0547464 0.0948235i 0.837353 0.546662i $$-0.184102\pi$$
−0.892100 + 0.451838i $$0.850768\pi$$
$$194$$ 5.61975e13 3.24456e13i 1.05416 0.608619i
$$195$$ 0 0
$$196$$ −4.49190e12 + 7.78021e12i −0.0792308 + 0.137232i
$$197$$ 4.31845e13i 0.738806i −0.929269 0.369403i $$-0.879562\pi$$
0.929269 0.369403i $$-0.120438\pi$$
$$198$$ 0 0
$$199$$ 4.74962e13 0.764787 0.382394 0.924000i $$-0.375100\pi$$
0.382394 + 0.924000i $$0.375100\pi$$
$$200$$ −2.79587e12 1.61420e12i −0.0436855 0.0252218i
$$201$$ 0 0
$$202$$ 2.14380e13 + 3.71316e13i 0.315555 + 0.546558i
$$203$$ 4.06226e13 2.34535e13i 0.580486 0.335144i
$$204$$ 0 0
$$205$$ −4.11526e13 + 7.12784e13i −0.554465 + 0.960361i
$$206$$ 8.38921e13i 1.09779i
$$207$$ 0 0
$$208$$ −2.52571e13 −0.311891
$$209$$ 5.49282e13 + 3.17128e13i 0.659049 + 0.380502i
$$210$$ 0 0
$$211$$ −1.39456e13 2.41545e13i −0.158031 0.273718i 0.776127 0.630576i $$-0.217181\pi$$
−0.934159 + 0.356858i $$0.883848\pi$$
$$212$$ −4.48495e13 + 2.58939e13i −0.494018 + 0.285221i
$$213$$ 0 0
$$214$$ 5.14375e13 8.90924e13i 0.535547 0.927594i
$$215$$ 6.23009e13i 0.630759i
$$216$$ 0 0
$$217$$ −4.56505e13 −0.437207
$$218$$ −8.01484e12 4.62737e12i −0.0746717 0.0431117i
$$219$$ 0 0
$$220$$ 2.06425e13 + 3.57538e13i 0.182065 + 0.315345i
$$221$$ 1.54693e14 8.93120e13i 1.32775 0.766578i
$$222$$ 0 0
$$223$$ 5.37603e13 9.31156e13i 0.437152 0.757170i −0.560316 0.828279i $$-0.689320\pi$$
0.997469 + 0.0711088i $$0.0226538\pi$$
$$224$$ 1.84564e13i 0.146103i
$$225$$ 0 0
$$226$$ 1.28203e13 0.0962159
$$227$$ 2.29884e14 + 1.32723e14i 1.68017 + 0.970047i 0.961544 + 0.274650i $$0.0885619\pi$$
0.718626 + 0.695397i $$0.244771\pi$$
$$228$$ 0 0
$$229$$ 3.94551e13 + 6.83382e13i 0.273583 + 0.473860i 0.969777 0.243994i $$-0.0784577\pi$$
−0.696193 + 0.717854i $$0.745124\pi$$
$$230$$ 5.54328e13 3.20042e13i 0.374455 0.216192i
$$231$$ 0 0
$$232$$ 2.23552e13 3.87204e13i 0.143368 0.248320i
$$233$$ 3.12595e14i 1.95365i −0.214040 0.976825i $$-0.568662\pi$$
0.214040 0.976825i $$-0.431338\pi$$
$$234$$ 0 0
$$235$$ 5.54794e13 0.329401
$$236$$ 1.14740e14 + 6.62452e13i 0.664115 + 0.383427i
$$237$$ 0 0
$$238$$ 6.52642e13 + 1.13041e14i 0.359098 + 0.621976i
$$239$$ 2.32962e14 1.34501e14i 1.24996 0.721667i 0.278862 0.960331i $$-0.410043\pi$$
0.971102 + 0.238664i $$0.0767094\pi$$
$$240$$ 0 0
$$241$$ −1.04212e14 + 1.80500e14i −0.531880 + 0.921244i 0.467427 + 0.884032i $$0.345181\pi$$
−0.999307 + 0.0372122i $$0.988152\pi$$
$$242$$ 5.41664e13i 0.269673i
$$243$$ 0 0
$$244$$ 6.60443e13 0.312966
$$245$$ −5.49609e13 3.17317e13i −0.254131 0.146722i
$$246$$ 0 0
$$247$$ −1.37053e14 2.37382e14i −0.603540 1.04536i
$$248$$ −3.76832e13 + 2.17564e13i −0.161971 + 0.0935141i
$$249$$ 0 0
$$250$$ 9.13252e13 1.58180e14i 0.374068 0.647905i
$$251$$ 2.11752e14i 0.846809i −0.905941 0.423404i $$-0.860835\pi$$
0.905941 0.423404i $$-0.139165\pi$$
$$252$$ 0 0
$$253$$ 1.36222e14 0.519428
$$254$$ −1.29298e14 7.46500e13i −0.481491 0.277989i
$$255$$ 0 0
$$256$$ −8.79609e12 1.52353e13i −0.0312500 0.0541266i
$$257$$ −2.71787e14 + 1.56916e14i −0.943255 + 0.544589i −0.890979 0.454044i $$-0.849981\pi$$
−0.0522760 + 0.998633i $$0.516648\pi$$
$$258$$ 0 0
$$259$$ 2.13664e14 3.70078e14i 0.707838 1.22601i
$$260$$ 1.78421e14i 0.577571i
$$261$$ 0 0
$$262$$ −3.15651e14 −0.975886
$$263$$ 3.99989e14 + 2.30934e14i 1.20869 + 0.697835i 0.962472 0.271380i $$-0.0874801\pi$$
0.246214 + 0.969216i $$0.420813\pi$$
$$264$$ 0 0
$$265$$ −1.82919e14 3.16826e14i −0.528183 0.914840i
$$266$$ 1.73466e14 1.00150e14i 0.489693 0.282724i
$$267$$ 0 0
$$268$$ 5.94828e13 1.03027e14i 0.160540 0.278063i
$$269$$ 1.40054e14i 0.369642i −0.982772 0.184821i $$-0.940829\pi$$
0.982772 0.184821i $$-0.0591706\pi$$
$$270$$ 0 0
$$271$$ 1.78016e14 0.449411 0.224706 0.974427i $$-0.427858\pi$$
0.224706 + 0.974427i $$0.427858\pi$$
$$272$$ 1.07748e14 + 6.22081e13i 0.266069 + 0.153615i
$$273$$ 0 0
$$274$$ −6.15903e13 1.06678e14i −0.145549 0.252098i
$$275$$ 4.20332e13 2.42679e13i 0.0971842 0.0561093i
$$276$$ 0 0
$$277$$ −2.70621e14 + 4.68729e14i −0.599077 + 1.03763i 0.393880 + 0.919162i $$0.371132\pi$$
−0.992958 + 0.118471i $$0.962201\pi$$
$$278$$ 4.54839e14i 0.985347i
$$279$$ 0 0
$$280$$ 1.30380e14 0.270559
$$281$$ −5.26175e14 3.03787e14i −1.06879 0.617066i −0.140939 0.990018i $$-0.545012\pi$$
−0.927850 + 0.372953i $$0.878345\pi$$
$$282$$ 0 0
$$283$$ −2.46102e13 4.26261e13i −0.0479067 0.0829769i 0.841078 0.540914i $$-0.181922\pi$$
−0.888984 + 0.457937i $$0.848588\pi$$
$$284$$ −7.06240e13 + 4.07748e13i −0.134599 + 0.0777108i
$$285$$ 0 0
$$286$$ 1.89857e14 3.28843e14i 0.346921 0.600886i
$$287$$ 5.53169e14i 0.989843i
$$288$$ 0 0
$$289$$ −2.97279e14 −0.510243
$$290$$ 2.73528e14 + 1.57922e14i 0.459848 + 0.265493i
$$291$$ 0 0
$$292$$ 1.67378e14 + 2.89907e14i 0.270023 + 0.467693i
$$293$$ 5.49782e14 3.17417e14i 0.868931 0.501677i 0.00193795 0.999998i $$-0.499383\pi$$
0.866993 + 0.498321i $$0.166050\pi$$
$$294$$ 0 0
$$295$$ −4.67969e14 + 8.10546e14i −0.710044 + 1.22983i
$$296$$ 4.07319e14i 0.605597i
$$297$$ 0 0
$$298$$ 7.35699e14 1.05052
$$299$$ −5.09838e14 2.94355e14i −0.713519 0.411950i
$$300$$ 0 0
$$301$$ −2.09361e14 3.62623e14i −0.281511 0.487592i
$$302$$ 3.70936e14 2.14160e14i 0.488942 0.282291i
$$303$$ 0 0
$$304$$ 9.54608e13 1.65343e14i 0.120944 0.209481i
$$305$$ 4.66550e14i 0.579561i
$$306$$ 0 0
$$307$$ −1.14005e15 −1.36174 −0.680871 0.732403i $$-0.738399\pi$$
−0.680871 + 0.732403i $$0.738399\pi$$
$$308$$ 2.40300e14 + 1.38737e14i 0.281481 + 0.162513i
$$309$$ 0 0
$$310$$ −1.53691e14 2.66201e14i −0.173173 0.299944i
$$311$$ −6.83695e14 + 3.94731e14i −0.755614 + 0.436254i −0.827719 0.561143i $$-0.810362\pi$$
0.0721048 + 0.997397i $$0.477028\pi$$
$$312$$ 0 0
$$313$$ 5.76629e14 9.98750e14i 0.613240 1.06216i −0.377451 0.926030i $$-0.623199\pi$$
0.990691 0.136133i $$-0.0434673\pi$$
$$314$$ 8.35304e14i 0.871498i
$$315$$ 0 0
$$316$$ 3.83353e14 0.385014
$$317$$ −9.76548e14 5.63810e14i −0.962361 0.555619i −0.0654618 0.997855i $$-0.520852\pi$$
−0.896899 + 0.442236i $$0.854185\pi$$
$$318$$ 0 0
$$319$$ 3.36089e14 + 5.82123e14i 0.318941 + 0.552421i
$$320$$ 1.07625e14 6.21373e13i 0.100234 0.0578699i
$$321$$ 0 0
$$322$$ 2.15098e14 3.72561e14i 0.192975 0.334243i
$$323$$ 1.35024e15i 1.18904i
$$324$$ 0 0
$$325$$ −2.09756e14 −0.177998
$$326$$ −6.91061e14 3.98984e14i −0.575719 0.332392i
$$327$$ 0 0
$$328$$ 2.63633e14 + 4.56626e14i 0.211717 + 0.366705i
$$329$$ 3.22918e14 1.86437e14i 0.254635 0.147013i
$$330$$ 0 0
$$331$$ 6.91154e14 1.19711e15i 0.525541 0.910264i −0.474016 0.880516i $$-0.657196\pi$$
0.999557 0.0297477i $$-0.00947039\pi$$
$$332$$ 1.58296e14i 0.118207i
$$333$$ 0 0
$$334$$ 1.84500e15 1.32898
$$335$$ 7.27804e14 + 4.20198e14i 0.514927 + 0.297293i
$$336$$ 0 0
$$337$$ 2.46463e14 + 4.26886e14i 0.168256 + 0.291429i 0.937807 0.347157i $$-0.112853\pi$$
−0.769550 + 0.638586i $$0.779520\pi$$
$$338$$ −5.08059e14 + 2.93328e14i −0.340733 + 0.196722i
$$339$$ 0 0
$$340$$ −4.39450e14 + 7.61150e14i −0.284470 + 0.492716i
$$341$$ 6.54172e14i 0.416069i
$$342$$ 0 0
$$343$$ −1.77239e15 −1.08842
$$344$$ −3.45643e14 1.99557e14i −0.208582 0.120425i
$$345$$ 0 0
$$346$$ 6.93385e14 + 1.20098e15i 0.404127 + 0.699968i
$$347$$ −2.19672e15 + 1.26828e15i −1.25834 + 0.726504i −0.972752 0.231848i $$-0.925523\pi$$
−0.285590 + 0.958352i $$0.592190\pi$$
$$348$$ 0 0
$$349$$ −1.16998e15 + 2.02647e15i −0.647481 + 1.12147i 0.336241 + 0.941776i $$0.390844\pi$$
−0.983723 + 0.179694i $$0.942489\pi$$
$$350$$ 1.53278e14i 0.0833818i
$$351$$ 0 0
$$352$$ 2.64481e14 0.139040
$$353$$ 9.07166e14 + 5.23753e14i 0.468855 + 0.270694i 0.715760 0.698346i $$-0.246080\pi$$
−0.246905 + 0.969040i $$0.579414\pi$$
$$354$$ 0 0
$$355$$ −2.88041e14 4.98901e14i −0.143908 0.249255i
$$356$$ −1.63163e15 + 9.42025e14i −0.801536 + 0.462767i
$$357$$ 0 0
$$358$$ −4.63894e14 + 8.03487e14i −0.220354 + 0.381664i
$$359$$ 1.80008e15i 0.840861i 0.907325 + 0.420431i $$0.138121\pi$$
−0.907325 + 0.420431i $$0.861879\pi$$
$$360$$ 0 0
$$361$$ −1.41314e14 −0.0638472
$$362$$ −1.92357e15 1.11057e15i −0.854783 0.493509i
$$363$$ 0 0
$$364$$ −5.99578e14 1.03850e15i −0.257773 0.446476i
$$365$$ −2.04796e15 + 1.18239e15i −0.866091 + 0.500038i
$$366$$ 0 0
$$367$$ −1.63875e15 + 2.83839e15i −0.670680 + 1.16165i 0.307032 + 0.951699i $$0.400664\pi$$
−0.977712 + 0.209952i $$0.932669\pi$$
$$368$$ 4.10052e14i 0.165102i
$$369$$ 0 0
$$370$$ 2.87738e15 1.12147
$$371$$ −2.12937e15 1.22939e15i −0.816596 0.471462i
$$372$$ 0 0
$$373$$ 7.38996e14 + 1.27998e15i 0.274403 + 0.475280i 0.969984 0.243167i $$-0.0781864\pi$$
−0.695581 + 0.718448i $$0.744853\pi$$
$$374$$ −1.61988e15 + 9.35237e14i −0.591906 + 0.341737i
$$375$$ 0 0
$$376$$ 1.77707e14 3.07797e14i 0.0628893 0.108928i
$$377$$ 2.90494e15i 1.01179i
$$378$$ 0 0
$$379$$ −5.85878e15 −1.97684 −0.988420 0.151741i $$-0.951512\pi$$
−0.988420 + 0.151741i $$0.951512\pi$$
$$380$$ 1.16801e15 + 6.74353e14i 0.387924 + 0.223968i
$$381$$ 0 0
$$382$$ −1.00671e15 1.74368e15i −0.323986 0.561160i
$$383$$ −1.51358e15 + 8.73864e14i −0.479526 + 0.276854i −0.720219 0.693747i $$-0.755959\pi$$
0.240693 + 0.970601i $$0.422625\pi$$
$$384$$ 0 0
$$385$$ −9.80065e14 + 1.69752e15i −0.300947 + 0.521256i
$$386$$ 2.56091e14i 0.0774230i
$$387$$ 0 0
$$388$$ 2.93664e15 0.860718
$$389$$ 1.79778e14 + 1.03795e14i 0.0518846 + 0.0299556i 0.525718 0.850659i $$-0.323797\pi$$
−0.473833 + 0.880615i $$0.657130\pi$$
$$390$$ 0 0
$$391$$ 1.44999e15 + 2.51146e15i 0.405794 + 0.702856i
$$392$$ −3.52092e14 + 2.03280e14i −0.0970375 + 0.0560246i
$$393$$ 0 0
$$394$$ 9.77153e14 1.69248e15i 0.261207 0.452424i
$$395$$ 2.70808e15i 0.712982i
$$396$$ 0 0
$$397$$ −4.92065e15 −1.25684 −0.628419 0.777875i $$-0.716297\pi$$
−0.628419 + 0.777875i $$0.716297\pi$$
$$398$$ 1.86146e15 + 1.07472e15i 0.468334 + 0.270393i
$$399$$ 0 0
$$400$$ −7.30502e13 1.26527e14i −0.0178345 0.0308903i
$$401$$ −5.83715e15 + 3.37008e15i −1.40389 + 0.810538i −0.994790 0.101949i $$-0.967492\pi$$
−0.409104 + 0.912488i $$0.634159\pi$$
$$402$$ 0 0
$$403$$ −1.41356e15 + 2.44836e15i −0.329978 + 0.571538i
$$404$$ 1.94034e15i 0.446262i
$$405$$ 0 0
$$406$$ 2.12277e15 0.473965
$$407$$ 5.30322e15 + 3.06181e15i 1.16674 + 0.673616i
$$408$$ 0 0
$$409$$ −2.42365e15 4.19789e15i −0.517763 0.896791i −0.999787 0.0206335i $$-0.993432\pi$$
0.482024 0.876158i $$-0.339902\pi$$
$$410$$ −3.22569e15 + 1.86235e15i −0.679078 + 0.392066i
$$411$$ 0 0
$$412$$ 1.89826e15 3.28789e15i 0.388126 0.672254i
$$413$$ 6.29039e15i 1.26759i
$$414$$ 0 0
$$415$$ −1.11824e15 −0.218900
$$416$$ −9.89870e14 5.71502e14i −0.190993 0.110270i
$$417$$ 0 0
$$418$$ 1.43516e15 + 2.48577e15i 0.269056 + 0.466018i
$$419$$ −4.45459e15 + 2.57186e15i −0.823234 + 0.475294i −0.851530 0.524305i $$-0.824325\pi$$
0.0282963 + 0.999600i $$0.490992\pi$$
$$420$$ 0 0
$$421$$ −8.05297e13 + 1.39482e14i −0.0144632 + 0.0250509i −0.873166 0.487422i $$-0.837937\pi$$
0.858703 + 0.512473i $$0.171271\pi$$
$$422$$ 1.26221e15i 0.223490i
$$423$$ 0 0
$$424$$ −2.34365e15 −0.403364
$$425$$ 8.94828e14 + 5.16629e14i 0.151847 + 0.0876688i
$$426$$ 0 0
$$427$$ 1.56783e15 + 2.71556e15i 0.258661 + 0.448014i
$$428$$ 4.03186e15 2.32780e15i 0.655908 0.378689i
$$429$$ 0 0
$$430$$ 1.40971e15 2.44169e15i 0.223007 0.386260i
$$431$$ 6.68591e15i 1.04303i 0.853242 + 0.521515i $$0.174633\pi$$
−0.853242 + 0.521515i $$0.825367\pi$$
$$432$$ 0 0
$$433$$ 5.39263e15 0.818226 0.409113 0.912484i $$-0.365838\pi$$
0.409113 + 0.912484i $$0.365838\pi$$
$$434$$ −1.78913e15 1.03295e15i −0.267733 0.154576i
$$435$$ 0 0
$$436$$ −2.09411e14 3.62710e14i −0.0304846 0.0528009i
$$437$$ 3.85394e15 2.22507e15i 0.553371 0.319489i
$$438$$ 0 0
$$439$$ 5.03987e15 8.72931e15i 0.704096 1.21953i −0.262920 0.964818i $$-0.584686\pi$$
0.967017 0.254713i $$-0.0819811\pi$$
$$440$$ 1.86834e15i 0.257478i
$$441$$ 0 0
$$442$$ 8.08360e15 1.08410
$$443$$ −8.85904e15 5.11477e15i −1.17210 0.676712i −0.217925 0.975965i $$-0.569929\pi$$
−0.954174 + 0.299254i $$0.903262\pi$$
$$444$$ 0 0
$$445$$ −6.65464e15 1.15262e16i −0.856968 1.48431i
$$446$$ 4.21393e15 2.43291e15i 0.535400 0.309113i
$$447$$ 0 0
$$448$$ 4.17622e14 7.23342e14i 0.0516553 0.0894696i
$$449$$ 7.99330e15i 0.975547i −0.872970 0.487773i $$-0.837809\pi$$
0.872970 0.487773i $$-0.162191\pi$$
$$450$$ 0 0
$$451$$ −7.92692e15 −0.941987
$$452$$ 5.02450e14 + 2.90090e14i 0.0589199 + 0.0340174i
$$453$$ 0 0
$$454$$ 6.00638e15 + 1.04034e16i 0.685927 + 1.18806i
$$455$$ 7.33616e15 4.23553e15i 0.826800 0.477353i
$$456$$ 0 0
$$457$$ −4.13927e15 + 7.16943e15i −0.454388 + 0.787023i −0.998653 0.0518906i $$-0.983475\pi$$
0.544265 + 0.838913i $$0.316809\pi$$
$$458$$ 3.57106e15i 0.386905i
$$459$$ 0 0
$$460$$ 2.89669e15 0.305742
$$461$$ −1.09173e16 6.30311e15i −1.13739 0.656673i −0.191607 0.981472i $$-0.561370\pi$$
−0.945783 + 0.324799i $$0.894703\pi$$
$$462$$ 0 0
$$463$$ 3.48265e15 + 6.03212e15i 0.353528 + 0.612328i 0.986865 0.161548i $$-0.0516486\pi$$
−0.633337 + 0.773876i $$0.718315\pi$$
$$464$$ 1.75229e15 1.01168e15i 0.175589 0.101376i
$$465$$ 0 0
$$466$$ 7.07322e15 1.22512e16i 0.690720 1.19636i
$$467$$ 1.26089e16i 1.21556i −0.794106 0.607779i $$-0.792061\pi$$
0.794106 0.607779i $$-0.207939\pi$$
$$468$$ 0 0
$$469$$ 5.64826e15 0.530734
$$470$$ 2.17434e15 + 1.25536e15i 0.201716 + 0.116461i
$$471$$ 0 0
$$472$$ 2.99792e15 + 5.19254e15i 0.271124 + 0.469600i
$$473$$ 5.19640e15 3.00014e15i 0.464019 0.267901i
$$474$$ 0 0
$$475$$ 7.92787e14 1.37315e15i 0.0690232 0.119552i
$$476$$ 5.90704e15i 0.507842i
$$477$$ 0 0
$$478$$ 1.21736e16 1.02059
$$479$$ −3.32071e15 1.91721e15i −0.274927 0.158729i 0.356197 0.934411i $$-0.384073\pi$$
−0.631125 + 0.775681i $$0.717406\pi$$
$$480$$ 0 0
$$481$$ −1.32322e16 2.29188e16i −1.06847 1.85064i
$$482$$ −8.16849e15 + 4.71608e15i −0.651418 + 0.376096i
$$483$$ 0 0
$$484$$ 1.22565e15 2.12288e15i 0.0953439 0.165141i
$$485$$ 2.07450e16i 1.59391i
$$486$$ 0 0
$$487$$ 1.99630e15 0.149641 0.0748207 0.997197i $$-0.476162\pi$$
0.0748207 + 0.997197i $$0.476162\pi$$
$$488$$ 2.58840e15 + 1.49441e15i 0.191651 + 0.110650i
$$489$$ 0 0
$$490$$ −1.43601e15 2.48725e15i −0.103748 0.179698i
$$491$$ 5.72082e15 3.30292e15i 0.408290 0.235727i −0.281764 0.959484i $$-0.590920\pi$$
0.690055 + 0.723757i $$0.257586\pi$$
$$492$$ 0 0
$$493$$ −7.15486e15 + 1.23926e16i −0.498333 + 0.863139i
$$494$$ 1.24046e16i 0.853534i
$$495$$ 0 0
$$496$$ −1.96916e15 −0.132249
$$497$$ −3.35309e15 1.93591e15i −0.222488 0.128454i
$$498$$ 0 0
$$499$$ −1.00653e16 1.74336e16i −0.651963 1.12923i −0.982646 0.185491i $$-0.940612\pi$$
0.330683 0.943742i $$-0.392721\pi$$
$$500$$ 7.15841e15 4.13291e15i 0.458138 0.264506i
$$501$$ 0 0
$$502$$ 4.79140e15 8.29895e15i 0.299392 0.518562i
$$503$$ 1.72099e16i 1.06260i −0.847184 0.531300i $$-0.821704\pi$$
0.847184 0.531300i $$-0.178296\pi$$
$$504$$ 0 0
$$505$$ −1.37070e16 −0.826404
$$506$$ 5.33881e15 + 3.08236e15i 0.318084 + 0.183646i
$$507$$ 0 0
$$508$$ −3.37827e15 5.85134e15i −0.196568 0.340465i
$$509$$ 1.39053e16 8.02821e15i 0.799600 0.461649i −0.0437313 0.999043i $$-0.513925\pi$$
0.843331 + 0.537394i $$0.180591\pi$$
$$510$$ 0 0
$$511$$ −7.94677e15 + 1.37642e16i −0.446339 + 0.773082i
$$512$$ 7.96131e14i 0.0441942i
$$513$$ 0 0
$$514$$ −1.42024e16 −0.770165
$$515$$ 2.32263e16 + 1.34097e16i 1.24490 + 0.718746i
$$516$$ 0 0
$$517$$ 2.67165e15 + 4.62743e15i 0.139906 + 0.242324i
$$518$$ 1.67478e16 9.66935e15i 0.866920 0.500517i
$$519$$ 0 0
$$520$$ 4.03720e15 6.99263e15i 0.204202 0.353688i
$$521$$ 2.27894e16i 1.13948i −0.821825 0.569740i $$-0.807044\pi$$
0.821825 0.569740i $$-0.192956\pi$$
$$522$$ 0 0
$$523$$ −2.36146e16 −1.15390 −0.576952 0.816778i $$-0.695758\pi$$
−0.576952 + 0.816778i $$0.695758\pi$$
$$524$$ −1.23709e16 7.14236e15i −0.597606 0.345028i
$$525$$ 0 0
$$526$$ 1.04509e16 + 1.81014e16i 0.493444 + 0.854670i
$$527$$ 1.20606e16 6.96320e15i 0.562997 0.325046i
$$528$$ 0 0
$$529$$ −6.17841e15 + 1.07013e16i −0.281931 + 0.488319i
$$530$$ 1.65560e16i 0.746964i
$$531$$ 0 0
$$532$$ 9.06459e15 0.399833
$$533$$ 2.96680e16 + 1.71288e16i 1.29397 + 0.747075i
$$534$$ 0 0
$$535$$ 1.64440e16 + 2.84818e16i 0.701269 + 1.21463i
$$536$$ 4.66248e15 2.69188e15i 0.196620 0.113519i
$$537$$ 0 0
$$538$$ 3.16906e15 5.48897e15i 0.130688 0.226359i
$$539$$ 6.11224e15i 0.249269i
$$540$$ 0 0
$$541$$ 1.91409e16 0.763449 0.381724 0.924276i $$-0.375330\pi$$
0.381724 + 0.924276i $$0.375330\pi$$
$$542$$ 6.97678e15 + 4.02805e15i 0.275207 + 0.158891i
$$543$$ 0 0
$$544$$ 2.81522e15 + 4.87610e15i 0.108622 + 0.188139i
$$545$$ 2.56226e15 1.47932e15i 0.0977785 0.0564525i
$$546$$ 0 0
$$547$$ 4.53225e15 7.85009e15i 0.169196 0.293056i −0.768941 0.639319i $$-0.779216\pi$$
0.938137 + 0.346263i $$0.112550\pi$$
$$548$$ 5.57452e15i 0.205837i
$$549$$ 0 0
$$550$$ 2.19648e15 0.0793506
$$551$$ 1.90169e16 + 1.09794e16i 0.679564 + 0.392347i
$$552$$ 0 0
$$553$$ 9.10043e15 + 1.57624e16i 0.318208 + 0.551152i
$$554$$ −2.12123e16 + 1.22469e16i −0.733717 + 0.423612i
$$555$$ 0 0
$$556$$ −1.02918e16 + 1.78260e16i −0.348373 + 0.603399i
$$557$$ 2.68418e16i 0.898837i −0.893321 0.449419i $$-0.851631\pi$$
0.893321 0.449419i $$-0.148369\pi$$
$$558$$ 0 0
$$559$$ −2.59313e16 −0.849873
$$560$$ 5.10982e15 + 2.95016e15i 0.165683 + 0.0956571i
$$561$$ 0 0
$$562$$ −1.37478e16 2.38119e16i −0.436331 0.755748i
$$563$$ 1.00983e16 5.83025e15i 0.317101 0.183078i −0.332999 0.942927i $$-0.608061\pi$$
0.650100 + 0.759849i $$0.274727\pi$$
$$564$$ 0 0
$$565$$ −2.04925e15 + 3.54940e15i −0.0629947 + 0.109110i
$$566$$ 2.22746e15i 0.0677503i
$$567$$ 0 0
$$568$$ −3.69051e15 −0.109900
$$569$$ 1.76847e16 + 1.02103e16i 0.521104 + 0.300860i 0.737386 0.675471i $$-0.236060\pi$$
−0.216282 + 0.976331i $$0.569393\pi$$
$$570$$ 0 0
$$571$$ 4.38932e15 + 7.60252e15i 0.126643 + 0.219352i 0.922374 0.386298i $$-0.126246\pi$$
−0.795731 + 0.605650i $$0.792913\pi$$
$$572$$ 1.48817e16 8.59196e15i 0.424890 0.245311i
$$573$$ 0 0
$$574$$ −1.25168e16 + 2.16797e16i −0.349962 + 0.606153i
$$575$$ 3.40542e15i 0.0942245i
$$576$$ 0 0
$$577$$ 3.12644e16 0.847219 0.423609 0.905845i $$-0.360763\pi$$
0.423609 + 0.905845i $$0.360763\pi$$
$$578$$ −1.16509e16 6.72666e15i −0.312459 0.180398i
$$579$$ 0 0
$$580$$ 7.14672e15 + 1.23785e16i 0.187732 + 0.325162i
$$581$$ −6.50870e15 + 3.75780e15i −0.169215 + 0.0976961i
$$582$$ 0 0
$$583$$ 1.76172e16 3.05139e16i 0.448669 0.777117i
$$584$$ 1.51493e16i 0.381870i
$$585$$ 0 0
$$586$$ 2.87293e16 0.709479
$$587$$ −1.38519e16 7.99742e15i −0.338596 0.195488i 0.321055 0.947061i $$-0.395963\pi$$
−0.659651 + 0.751572i $$0.729296\pi$$
$$588$$ 0 0
$$589$$ −1.06853e16 1.85075e16i −0.255915 0.443257i
$$590$$ −3.66811e16 + 2.11779e16i −0.869622 + 0.502077i
$$591$$ 0 0
$$592$$ 9.21657e15 1.59636e16i 0.214111 0.370851i
$$593$$ 2.23212e16i 0.513322i −0.966501 0.256661i $$-0.917378\pi$$
0.966501 0.256661i $$-0.0826224\pi$$
$$594$$ 0 0
$$595$$ −4.17285e16 −0.940439
$$596$$ 2.88334e16 + 1.66470e16i 0.643307 + 0.371413i
$$597$$ 0 0
$$598$$ −1.33210e16 2.30727e16i −0.291293 0.504534i
$$599$$ 2.09928e16 1.21202e16i 0.454475 0.262391i −0.255243 0.966877i $$-0.582155\pi$$
0.709718 + 0.704485i $$0.248822\pi$$
$$600$$ 0 0
$$601$$ −3.65059e16 + 6.32300e16i −0.774669 + 1.34177i 0.160312 + 0.987066i $$0.448750\pi$$
−0.934980 + 0.354699i $$0.884583\pi$$
$$602$$ 1.89492e16i 0.398117i
$$603$$ 0 0
$$604$$ 1.93835e16 0.399219
$$605$$ 1.49964e16 + 8.65820e15i 0.305813 + 0.176561i
$$606$$ 0 0
$$607$$ 2.61136e16 + 4.52301e16i 0.522077 + 0.904265i 0.999670 + 0.0256833i $$0.00817616\pi$$
−0.477593 + 0.878581i $$0.658491\pi$$
$$608$$ 7.48256e15 4.32006e15i 0.148125 0.0855201i
$$609$$ 0 0
$$610$$ −1.05568e16 + 1.82849e16i −0.204906 + 0.354907i
$$611$$ 2.30920e16i 0.443828i
$$612$$ 0 0
$$613$$ 8.18124e16 1.54190 0.770950 0.636895i $$-0.219782\pi$$
0.770950 + 0.636895i $$0.219782\pi$$
$$614$$ −4.46808e16 2.57965e16i −0.833893 0.481449i
$$615$$ 0 0
$$616$$ 6.27852e15 + 1.08747e16i 0.114914 + 0.199037i
$$617$$ 6.09006e16 3.51610e16i 1.10385 0.637309i 0.166622 0.986021i $$-0.446714\pi$$
0.937230 + 0.348712i $$0.113381\pi$$
$$618$$ 0 0
$$619$$ 2.93637e16 5.08594e16i 0.521995 0.904122i −0.477677 0.878535i $$-0.658521\pi$$
0.999673 0.0255868i $$-0.00814543\pi$$
$$620$$ 1.39106e16i 0.244903i
$$621$$ 0 0
$$622$$ −3.57270e16 −0.616956
$$623$$ −7.74669e16 4.47255e16i −1.32491 0.764939i
$$624$$ 0 0
$$625$$ 2.49436e16 + 4.32035e16i 0.418484 + 0.724835i
$$626$$ 4.51983e16 2.60952e16i 0.751062 0.433626i
$$627$$ 0 0
$$628$$ −1.89008e16 + 3.27371e16i −0.308121 + 0.533682i
$$629$$ 1.30364e17i 2.10500i
$$630$$ 0 0
$$631$$ −7.07787e16 −1.12131 −0.560656 0.828049i $$-0.689451\pi$$
−0.560656 + 0.828049i $$0.689451\pi$$
$$632$$ 1.50243e16 + 8.67429e15i 0.235772 + 0.136123i
$$633$$ 0 0
$$634$$ −2.55151e16 4.41935e16i −0.392882 0.680492i
$$635$$ 4.13350e16 2.38648e16i 0.630486 0.364011i
$$636$$ 0 0
$$637$$ −1.32076e16 + 2.28762e16i −0.197691 + 0.342411i
$$638$$ 3.04193e16i 0.451050i
$$639$$ 0 0
$$640$$ 5.62403e15 0.0818403
$$641$$ −7.18335e15 4.14731e15i −0.103557 0.0597886i 0.447327 0.894370i $$-0.352376\pi$$
−0.550884 + 0.834582i $$0.685709\pi$$
$$642$$ 0 0
$$643$$ −4.02701e16 6.97498e16i −0.569792 0.986909i −0.996586 0.0825600i $$-0.973690\pi$$
0.426794 0.904349i $$-0.359643\pi$$
$$644$$ 1.68602e16 9.73424e15i 0.236346 0.136454i
$$645$$ 0 0
$$646$$ −3.05525e16 + 5.29185e16i −0.420390 + 0.728136i
$$647$$ 7.39646e16i 1.00832i −0.863610 0.504160i $$-0.831802\pi$$
0.863610 0.504160i $$-0.168198\pi$$
$$648$$ 0 0
$$649$$ −9.01414e16 −1.20630
$$650$$ −8.22073e15 4.74624e15i −0.109001 0.0629317i
$$651$$ 0 0
$$652$$ −1.80560e16 3.12738e16i −0.235036 0.407095i
$$653$$ −9.93720e16 + 5.73725e16i −1.28170 + 0.739988i −0.977158 0.212513i $$-0.931835\pi$$
−0.304538 + 0.952500i $$0.598502\pi$$
$$654$$ 0 0
$$655$$ 5.04550e16 8.73907e16i 0.638935 1.10667i
$$656$$ 2.38613e16i 0.299414i
$$657$$ 0 0
$$658$$ 1.68744e16 0.207908
$$659$$ −1.51010e16 8.71858e15i −0.184371 0.106447i 0.404973 0.914328i $$-0.367281\pi$$
−0.589345 + 0.807882i $$0.700614\pi$$
$$660$$ 0 0
$$661$$ −1.73419e16 3.00371e16i −0.207916 0.360121i 0.743142 0.669134i $$-0.233335\pi$$
−0.951058 + 0.309013i $$0.900001\pi$$
$$662$$ 5.41752e16 3.12780e16i 0.643654 0.371614i
$$663$$ 0 0
$$664$$ −3.58184e15 + 6.20392e15i −0.0417924 + 0.0723866i
$$665$$ 6.40340e16i 0.740424i
$$666$$ 0 0
$$667$$ 4.71621e16 0.535597
$$668$$ 7.23089e16 + 4.17475e16i 0.813828 + 0.469864i
$$669$$ 0 0
$$670$$ 1.90160e16 + 3.29366e16i 0.210218 + 0.364108i
$$671$$ −3.89140e16 + 2.24670e16i −0.426354 + 0.246156i
$$672$$ 0 0
$$673$$ 1.33393e16 2.31043e16i 0.143563 0.248658i −0.785273 0.619149i $$-0.787478\pi$$
0.928836 + 0.370492i $$0.120811\pi$$
$$674$$ 2.23073e16i 0.237951i
$$675$$ 0 0
$$676$$ −2.65490e16 −0.278207
$$677$$ −3.99632e16 2.30728e16i −0.415076 0.239645i 0.277892 0.960612i $$-0.410364\pi$$
−0.692969 + 0.720968i $$0.743698\pi$$
$$678$$ 0 0
$$679$$ 6.97130e16 + 1.20747e17i 0.711370 + 1.23213i
$$680$$ −3.44457e16 + 1.98872e16i −0.348403 + 0.201150i
$$681$$ 0 0
$$682$$ 1.48022e16 2.56382e16i 0.147103 0.254789i
$$683$$ 1.03018e17i 1.01482i 0.861706 + 0.507408i $$0.169396\pi$$
−0.861706 + 0.507408i $$0.830604\pi$$
$$684$$ 0 0
$$685$$ 3.93795e16 0.381177
$$686$$ −6.94633e16 4.01047e16i −0.666516 0.384813i
$$687$$ 0 0
$$688$$ −9.03092e15 1.56420e16i −0.0851532 0.147490i
$$689$$ −1.31871e17 + 7.61360e16i −1.23264 + 0.711664i
$$690$$ 0 0
$$691$$ 7.44211e16 1.28901e17i 0.683640 1.18410i −0.290221 0.956959i $$-0.593729\pi$$
0.973862 0.227141i $$-0.0729377\pi$$
$$692$$ 6.27580e16i 0.571522i
$$693$$ 0 0
$$694$$ −1.14792e17 −1.02743
$$695$$ −1.25926e17 7.27035e16i −1.11740 0.645129i
$$696$$ 0 0
$$697$$ −8.43765e16 1.46144e17i −0.735911 1.27463i
$$698$$ −9.17076e16 + 5.29474e16i −0.792999 + 0.457838i
$$699$$ 0 0
$$700$$ 3.46828e15 6.00724e15i 0.0294799 0.0510607i
$$701$$ 9.48887e15i 0.0799662i −0.999200 0.0399831i $$-0.987270\pi$$
0.999200 0.0399831i $$-0.0127304\pi$$
$$702$$ 0 0
$$703$$ 2.00048e17 1.65730
$$704$$ 1.03655e16 + 5.98452e15i 0.0851440 + 0.0491579i
$$705$$ 0 0
$$706$$ 2.37023e16 + 4.10537e16i 0.191409 + 0.331531i
$$707$$ −7.97815e16 + 4.60619e16i −0.638830 + 0.368829i
$$708$$ 0 0
$$709$$ 8.47181e16 1.46736e17i 0.666959 1.15521i −0.311791 0.950151i $$-0.600929\pi$$
0.978750 0.205056i $$-0.0657377\pi$$
$$710$$ 2.60705e16i 0.203516i
$$711$$ 0 0
$$712$$ −8.52623e16 −0.654451
$$713$$ −3.97495e16 2.29494e16i −0.302548 0.174676i
$$714$$ 0 0
$$715$$ 6.06953e16 + 1.05127e17i 0.454275 + 0.786827i
$$716$$ −3.63617e16 + 2.09934e16i −0.269877 + 0.155814i
$$717$$ 0 0
$$718$$ −4.07311e16 + 7.05483e16i −0.297289 + 0.514920i
$$719$$ 1.16432e16i 0.0842754i −0.999112 0.0421377i $$-0.986583\pi$$
0.999112 0.0421377i $$-0.0134168\pi$$
$$720$$ 0 0
$$721$$ 1.80252e17 1.28312
$$722$$ −5.53835e15 3.19757e15i −0.0390983 0.0225734i
$$723$$ 0 0
$$724$$ −5.02587e16 8.70507e16i −0.348964 0.604423i
$$725$$ 1.45525e16 8.40187e15i 0.100209 0.0578560i
$$726$$ 0 0
$$727$$ −2.28530e16 + 3.95826e16i −0.154788 + 0.268101i −0.932982 0.359923i $$-0.882803\pi$$
0.778194 + 0.628024i $$0.216136\pi$$
$$728$$ 5.42676e16i 0.364546i
$$729$$ 0 0
$$730$$ −1.07018e17 −0.707160
$$731$$ 1.10624e17 + 6.38688e16i 0.725012 + 0.418586i
$$732$$ 0 0
$$733$$ 1.04080e16 + 1.80272e16i 0.0671032 + 0.116226i 0.897625 0.440760i $$-0.145291\pi$$
−0.830522 + 0.556986i $$0.811958\pi$$
$$734$$ −1.28451e17 + 7.41612e16i −0.821412 + 0.474242i
$$735$$ 0 0
$$736$$ 9.27842e15 1.60707e16i 0.0583723 0.101104i
$$737$$ 8.09396e16i 0.505075i
$$738$$ 0 0
$$739$$ 2.08350e17 1.27917 0.639584 0.768721i $$-0.279107\pi$$
0.639584 + 0.768721i $$0.279107\pi$$
$$740$$ 1.12770e17 + 6.51076e16i 0.686755 + 0.396498i
$$741$$ 0 0
$$742$$ −5.56359e16 9.63642e16i −0.333374 0.577421i
$$743$$ −2.70067e17 + 1.55923e17i −1.60523 + 0.926783i −0.614818 + 0.788669i $$0.710771\pi$$
−0.990416 + 0.138114i $$0.955896\pi$$
$$744$$ 0 0
$$745$$ −1.17597e17 + 2.03685e17i −0.687797 + 1.19130i
$$746$$ 6.68863e16i 0.388065i
$$747$$ 0 0
$$748$$ −8.46480e16 −0.483289
$$749$$ 1.91425e17 + 1.10519e17i 1.08420 + 0.625961i
$$750$$ 0 0
$$751$$ −1.30877e17 2.26686e17i −0.729499 1.26353i −0.957095 0.289774i $$-0.906420\pi$$
0.227596 0.973756i $$-0.426914\pi$$
$$752$$ 1.39293e16 8.04209e15i 0.0770234 0.0444695i
$$753$$ 0 0
$$754$$ 6.57313e16 1.13850e17i 0.357721 0.619590i
$$755$$ 1.36929e17i 0.739289i
$$756$$ 0 0
$$757$$ 1.02581e17 0.545119 0.272559 0.962139i $$-0.412130\pi$$
0.272559 + 0.962139i $$0.412130\pi$$
$$758$$ −2.29616e17 1.32569e17i −1.21056 0.698919i
$$759$$ 0 0
$$760$$ 3.05177e16 + 5.28583e16i 0.158369 + 0.274304i
$$761$$ 1.48043e16 8.54727e15i 0.0762220 0.0440068i −0.461405 0.887190i $$-0.652654\pi$$
0.537627 + 0.843183i $$0.319321\pi$$
$$762$$ 0 0
$$763$$ 9.94243e15 1.72208e16i 0.0503901 0.0872782i
$$764$$ 9.11173e16i