# Properties

 Label 162.13.d.c.107.4 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 107.4 Root $$-68.6972 - 0.707107i$$ of defining polynomial Character $$\chi$$ $$=$$ 162.107 Dual form 162.13.d.c.53.4

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(39.1918 + 22.6274i) q^{2} +(1024.00 + 1773.62i) q^{4} +(23434.3 - 13529.8i) q^{5} +(-19253.5 + 33348.0i) q^{7} +92681.9i q^{8} +O(q^{10})$$ $$q+(39.1918 + 22.6274i) q^{2} +(1024.00 + 1773.62i) q^{4} +(23434.3 - 13529.8i) q^{5} +(-19253.5 + 33348.0i) q^{7} +92681.9i q^{8} +1.22458e6 q^{10} +(915145. + 528359. i) q^{11} +(-3.18495e6 - 5.51649e6i) q^{13} +(-1.50916e6 + 871312. i) q^{14} +(-2.09715e6 + 3.63237e6i) q^{16} -2.54594e6i q^{17} +1.58076e6 q^{19} +(4.79935e7 + 2.77091e7i) q^{20} +(2.39108e7 + 4.14147e7i) q^{22} +(1.09932e8 - 6.34695e7i) q^{23} +(2.44041e8 - 4.22692e8i) q^{25} -2.88268e8i q^{26} -7.88622e7 q^{28} +(-7.45261e8 - 4.30277e8i) q^{29} +(3.60891e8 + 6.25081e8i) q^{31} +(-1.64382e8 + 9.49063e7i) q^{32} +(5.76081e7 - 9.97802e7i) q^{34} +1.04198e9i q^{35} +4.10816e9 q^{37} +(6.19527e7 + 3.57684e7i) q^{38} +(1.25397e9 + 2.17194e9i) q^{40} +(-1.46816e9 + 8.47640e8i) q^{41} +(5.93232e9 - 1.02751e10i) q^{43} +2.16416e9i q^{44} +5.74461e9 q^{46} +(-7.65810e9 - 4.42141e9i) q^{47} +(6.17925e9 + 1.07028e10i) q^{49} +(1.91289e10 - 1.10440e10i) q^{50} +(6.52277e9 - 1.12978e10i) q^{52} -1.49000e10i q^{53} +2.85944e10 q^{55} +(-3.09075e9 - 1.78445e9i) q^{56} +(-1.94721e10 - 3.37267e10i) q^{58} +(5.34412e10 - 3.08543e10i) q^{59} +(-3.07148e10 + 5.31996e10i) q^{61} +3.26641e10i q^{62} -8.58993e9 q^{64} +(-1.49274e11 - 8.61835e10i) q^{65} +(-4.81995e10 - 8.34839e10i) q^{67} +(4.51554e9 - 2.60705e9i) q^{68} +(-2.35774e10 + 4.08372e10i) q^{70} +1.92487e11i q^{71} -2.52890e11 q^{73} +(1.61006e11 + 9.29570e10i) q^{74} +(1.61869e9 + 2.80366e9i) q^{76} +(-3.52394e10 + 2.03455e10i) q^{77} +(1.32683e11 - 2.29813e11i) q^{79} +1.13496e11i q^{80} -7.67196e10 q^{82} +(-5.02122e11 - 2.89900e11i) q^{83} +(-3.44461e10 - 5.96625e10i) q^{85} +(4.64997e11 - 2.68466e11i) q^{86} +(-4.89693e10 + 8.48174e10i) q^{88} -2.67660e11i q^{89} +2.45285e11 q^{91} +(2.25142e11 + 1.29986e11i) q^{92} +(-2.00090e11 - 3.46566e11i) q^{94} +(3.70439e10 - 2.13873e10i) q^{95} +(7.00867e11 - 1.21394e12i) q^{97} +5.59282e11i q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q + 8192 q^{4} - 271484 q^{7}+O(q^{10})$$ 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
$$5$$ 23434.3 13529.8i 1.49980 0.865908i 0.499797 0.866143i $$-0.333408\pi$$
1.00000 0.000234889i $$7.47674e-5\pi$$
$$6$$ 0 0
$$7$$ −19253.5 + 33348.0i −0.163652 + 0.283453i −0.936176 0.351533i $$-0.885661\pi$$
0.772524 + 0.634986i $$0.218994\pi$$
$$8$$ 92681.9i 0.353553i
$$9$$ 0 0
$$10$$ 1.22458e6 1.22458
$$11$$ 915145. + 528359.i 0.516575 + 0.298245i 0.735532 0.677490i $$-0.236932\pi$$
−0.218957 + 0.975735i $$0.570265\pi$$
$$12$$ 0 0
$$13$$ −3.18495e6 5.51649e6i −0.659845 1.14289i −0.980655 0.195742i $$-0.937289\pi$$
0.320810 0.947143i $$-0.396045\pi$$
$$14$$ −1.50916e6 + 871312.i −0.200432 + 0.115719i
$$15$$ 0 0
$$16$$ −2.09715e6 + 3.63237e6i −0.125000 + 0.216506i
$$17$$ 2.54594e6i 0.105476i −0.998608 0.0527382i $$-0.983205\pi$$
0.998608 0.0527382i $$-0.0167949\pi$$
$$18$$ 0 0
$$19$$ 1.58076e6 0.0336003 0.0168002 0.999859i $$-0.494652\pi$$
0.0168002 + 0.999859i $$0.494652\pi$$
$$20$$ 4.79935e7 + 2.77091e7i 0.749898 + 0.432954i
$$21$$ 0 0
$$22$$ 2.39108e7 + 4.14147e7i 0.210891 + 0.365274i
$$23$$ 1.09932e8 6.34695e7i 0.742607 0.428744i −0.0804097 0.996762i $$-0.525623\pi$$
0.823016 + 0.568018i $$0.192290\pi$$
$$24$$ 0 0
$$25$$ 2.44041e8 4.22692e8i 0.999593 1.73135i
$$26$$ 2.88268e8i 0.933162i
$$27$$ 0 0
$$28$$ −7.88622e7 −0.163652
$$29$$ −7.45261e8 4.30277e8i −1.25291 0.723369i −0.281225 0.959642i $$-0.590741\pi$$
−0.971687 + 0.236273i $$0.924074\pi$$
$$30$$ 0 0
$$31$$ 3.60891e8 + 6.25081e8i 0.406636 + 0.704314i 0.994510 0.104638i $$-0.0333684\pi$$
−0.587874 + 0.808952i $$0.700035\pi$$
$$32$$ −1.64382e8 + 9.49063e7i −0.153093 + 0.0883883i
$$33$$ 0 0
$$34$$ 5.76081e7 9.97802e7i 0.0372915 0.0645908i
$$35$$ 1.04198e9i 0.566829i
$$36$$ 0 0
$$37$$ 4.10816e9 1.60117 0.800584 0.599221i $$-0.204523\pi$$
0.800584 + 0.599221i $$0.204523\pi$$
$$38$$ 6.19527e7 + 3.57684e7i 0.0205759 + 0.0118795i
$$39$$ 0 0
$$40$$ 1.25397e9 + 2.17194e9i 0.306145 + 0.530258i
$$41$$ −1.46816e9 + 8.47640e8i −0.309079 + 0.178447i −0.646514 0.762902i $$-0.723774\pi$$
0.337435 + 0.941349i $$0.390441\pi$$
$$42$$ 0 0
$$43$$ 5.93232e9 1.02751e10i 0.938456 1.62545i 0.170104 0.985426i $$-0.445590\pi$$
0.768352 0.640027i $$-0.221077\pi$$
$$44$$ 2.16416e9i 0.298245i
$$45$$ 0 0
$$46$$ 5.74461e9 0.606336
$$47$$ −7.65810e9 4.42141e9i −0.710451 0.410179i 0.100777 0.994909i $$-0.467867\pi$$
−0.811228 + 0.584730i $$0.801200\pi$$
$$48$$ 0 0
$$49$$ 6.17925e9 + 1.07028e10i 0.446436 + 0.773250i
$$50$$ 1.91289e10 1.10440e10i 1.22425 0.706819i
$$51$$ 0 0
$$52$$ 6.52277e9 1.12978e10i 0.329923 0.571443i
$$53$$ 1.49000e10i 0.672251i −0.941817 0.336125i $$-0.890883\pi$$
0.941817 0.336125i $$-0.109117\pi$$
$$54$$ 0 0
$$55$$ 2.85944e10 1.03301
$$56$$ −3.09075e9 1.78445e9i −0.100216 0.0578596i
$$57$$ 0 0
$$58$$ −1.94721e10 3.37267e10i −0.511499 0.885943i
$$59$$ 5.34412e10 3.08543e10i 1.26696 0.731482i 0.292551 0.956250i $$-0.405496\pi$$
0.974412 + 0.224768i $$0.0721624\pi$$
$$60$$ 0 0
$$61$$ −3.07148e10 + 5.31996e10i −0.596168 + 1.03259i 0.397212 + 0.917727i $$0.369978\pi$$
−0.993381 + 0.114867i $$0.963356\pi$$
$$62$$ 3.26641e10i 0.575070i
$$63$$ 0 0
$$64$$ −8.58993e9 −0.125000
$$65$$ −1.49274e11 8.61835e10i −1.97927 1.14273i
$$66$$ 0 0
$$67$$ −4.81995e10 8.34839e10i −0.532836 0.922899i −0.999265 0.0383400i $$-0.987793\pi$$
0.466429 0.884559i $$-0.345540\pi$$
$$68$$ 4.51554e9 2.60705e9i 0.0456726 0.0263691i
$$69$$ 0 0
$$70$$ −2.35774e10 + 4.08372e10i −0.200404 + 0.347111i
$$71$$ 1.92487e11i 1.50263i 0.659946 + 0.751313i $$0.270579\pi$$
−0.659946 + 0.751313i $$0.729421\pi$$
$$72$$ 0 0
$$73$$ −2.52890e11 −1.67107 −0.835535 0.549437i $$-0.814842\pi$$
−0.835535 + 0.549437i $$0.814842\pi$$
$$74$$ 1.61006e11 + 9.29570e10i 0.980511 + 0.566098i
$$75$$ 0 0
$$76$$ 1.61869e9 + 2.80366e9i 0.00840008 + 0.0145494i
$$77$$ −3.52394e10 + 2.03455e10i −0.169077 + 0.0976166i
$$78$$ 0 0
$$79$$ 1.32683e11 2.29813e11i 0.545823 0.945393i −0.452731 0.891647i $$-0.649550\pi$$
0.998555 0.0537465i $$-0.0171163\pi$$
$$80$$ 1.13496e11i 0.432954i
$$81$$ 0 0
$$82$$ −7.67196e10 −0.252362
$$83$$ −5.02122e11 2.89900e11i −1.53582 0.886706i −0.999077 0.0429604i $$-0.986321\pi$$
−0.536743 0.843746i $$-0.680346\pi$$
$$84$$ 0 0
$$85$$ −3.44461e10 5.96625e10i −0.0913328 0.158193i
$$86$$ 4.64997e11 2.68466e11i 1.14937 0.663589i
$$87$$ 0 0
$$88$$ −4.89693e10 + 8.48174e10i −0.105445 + 0.182637i
$$89$$ 2.67660e11i 0.538571i −0.963060 0.269285i $$-0.913213\pi$$
0.963060 0.269285i $$-0.0867875\pi$$
$$90$$ 0 0
$$91$$ 2.45285e11 0.431939
$$92$$ 2.25142e11 + 1.29986e11i 0.371303 + 0.214372i
$$93$$ 0 0
$$94$$ −2.00090e11 3.46566e11i −0.290040 0.502364i
$$95$$ 3.70439e10 2.13873e10i 0.0503936 0.0290948i
$$96$$ 0 0
$$97$$ 7.00867e11 1.21394e12i 0.841405 1.45736i −0.0473023 0.998881i $$-0.515062\pi$$
0.888707 0.458475i $$-0.151604\pi$$
$$98$$ 5.59282e11i 0.631356i
$$99$$ 0 0
$$100$$ 9.99593e11 0.999593
$$101$$ 8.69896e11 + 5.02234e11i 0.819481 + 0.473128i 0.850237 0.526399i $$-0.176458\pi$$
−0.0307565 + 0.999527i $$0.509792\pi$$
$$102$$ 0 0
$$103$$ 2.89077e11 + 5.00696e11i 0.242098 + 0.419325i 0.961312 0.275463i $$-0.0888312\pi$$
−0.719214 + 0.694789i $$0.755498\pi$$
$$104$$ 5.11279e11 2.95187e11i 0.404071 0.233290i
$$105$$ 0 0
$$106$$ 3.37149e11 5.83959e11i 0.237677 0.411668i
$$107$$ 9.85301e10i 0.0656547i 0.999461 + 0.0328274i $$0.0104512\pi$$
−0.999461 + 0.0328274i $$0.989549\pi$$
$$108$$ 0 0
$$109$$ 7.74413e11 0.461757 0.230879 0.972983i $$-0.425840\pi$$
0.230879 + 0.972983i $$0.425840\pi$$
$$110$$ 1.12067e12 + 6.47017e11i 0.632587 + 0.365224i
$$111$$ 0 0
$$112$$ −8.07549e10 1.39872e11i −0.0409129 0.0708633i
$$113$$ −2.44593e12 + 1.41216e12i −1.17482 + 0.678285i −0.954812 0.297212i $$-0.903943\pi$$
−0.220013 + 0.975497i $$0.570610\pi$$
$$114$$ 0 0
$$115$$ 1.71746e12 2.97473e12i 0.742506 1.28606i
$$116$$ 1.76241e12i 0.723369i
$$117$$ 0 0
$$118$$ 2.79261e12 1.03447
$$119$$ 8.49020e10 + 4.90182e10i 0.0298976 + 0.0172614i
$$120$$ 0 0
$$121$$ −1.01089e12 1.75091e12i −0.322100 0.557893i
$$122$$ −2.40754e12 + 1.38999e12i −0.730154 + 0.421555i
$$123$$ 0 0
$$124$$ −7.39104e11 + 1.28017e12i −0.203318 + 0.352157i
$$125$$ 6.60098e12i 1.73041i
$$126$$ 0 0
$$127$$ 1.14926e12 0.273902 0.136951 0.990578i $$-0.456270\pi$$
0.136951 + 0.990578i $$0.456270\pi$$
$$128$$ −3.36655e11 1.94368e11i −0.0765466 0.0441942i
$$129$$ 0 0
$$130$$ −3.90022e12 6.75538e12i −0.808032 1.39955i
$$131$$ 8.49167e12 4.90267e12i 1.68022 0.970073i 0.718702 0.695318i $$-0.244737\pi$$
0.961514 0.274755i $$-0.0885967\pi$$
$$132$$ 0 0
$$133$$ −3.04350e10 + 5.27150e10i −0.00549875 + 0.00952411i
$$134$$ 4.36252e12i 0.753544i
$$135$$ 0 0
$$136$$ 2.35963e11 0.0372915
$$137$$ 8.07299e12 + 4.66094e12i 1.22099 + 0.704937i 0.965128 0.261777i $$-0.0843085\pi$$
0.255859 + 0.966714i $$0.417642\pi$$
$$138$$ 0 0
$$139$$ 1.88951e12 + 3.27272e12i 0.261975 + 0.453753i 0.966767 0.255661i $$-0.0822930\pi$$
−0.704792 + 0.709414i $$0.748960\pi$$
$$140$$ −1.84808e12 + 1.06699e12i −0.245444 + 0.141707i
$$141$$ 0 0
$$142$$ −4.35548e12 + 7.54391e12i −0.531258 + 0.920167i
$$143$$ 6.73118e12i 0.787182i
$$144$$ 0 0
$$145$$ −2.32863e13 −2.50548
$$146$$ −9.91123e12 5.72225e12i −1.02332 0.590812i
$$147$$ 0 0
$$148$$ 4.20675e12 + 7.28631e12i 0.400292 + 0.693326i
$$149$$ 5.42513e12 3.13220e12i 0.495784 0.286241i −0.231187 0.972909i $$-0.574261\pi$$
0.726971 + 0.686668i $$0.240928\pi$$
$$150$$ 0 0
$$151$$ 3.57828e12 6.19776e12i 0.301865 0.522845i −0.674694 0.738098i $$-0.735724\pi$$
0.976558 + 0.215253i $$0.0690576\pi$$
$$152$$ 1.46507e11i 0.0118795i
$$153$$ 0 0
$$154$$ −1.84146e12 −0.138051
$$155$$ 1.69145e13 + 9.76557e12i 1.21974 + 0.704218i
$$156$$ 0 0
$$157$$ 5.89570e12 + 1.02117e13i 0.393675 + 0.681865i 0.992931 0.118692i $$-0.0378702\pi$$
−0.599256 + 0.800557i $$0.704537\pi$$
$$158$$ 1.04002e13 6.00454e12i 0.668494 0.385955i
$$159$$ 0 0
$$160$$ −2.56813e12 + 4.44813e12i −0.153072 + 0.265129i
$$161$$ 4.88803e12i 0.280659i
$$162$$ 0 0
$$163$$ −4.66492e12 −0.248724 −0.124362 0.992237i $$-0.539688\pi$$
−0.124362 + 0.992237i $$0.539688\pi$$
$$164$$ −3.00678e12 1.73597e12i −0.154539 0.0892233i
$$165$$ 0 0
$$166$$ −1.31194e13 2.27234e13i −0.626996 1.08599i
$$167$$ 2.46814e13 1.42498e13i 1.13781 0.656915i 0.191923 0.981410i $$-0.438527\pi$$
0.945888 + 0.324494i $$0.105194\pi$$
$$168$$ 0 0
$$169$$ −8.63873e12 + 1.49627e13i −0.370791 + 0.642229i
$$170$$ 3.11771e12i 0.129164i
$$171$$ 0 0
$$172$$ 2.42988e13 0.938456
$$173$$ −2.01716e13 1.16461e13i −0.752426 0.434413i 0.0741439 0.997248i $$-0.476378\pi$$
−0.826570 + 0.562834i $$0.809711\pi$$
$$174$$ 0 0
$$175$$ 9.39728e12 + 1.62766e13i 0.327170 + 0.566675i
$$176$$ −3.83840e12 + 2.21610e12i −0.129144 + 0.0745612i
$$177$$ 0 0
$$178$$ 6.05645e12 1.04901e13i 0.190414 0.329806i
$$179$$ 3.40943e12i 0.103649i 0.998656 + 0.0518243i $$0.0165036\pi$$
−0.998656 + 0.0518243i $$0.983496\pi$$
$$180$$ 0 0
$$181$$ 3.21987e13 0.915730 0.457865 0.889022i $$-0.348614\pi$$
0.457865 + 0.889022i $$0.348614\pi$$
$$182$$ 9.61317e12 + 5.55016e12i 0.264508 + 0.152714i
$$183$$ 0 0
$$184$$ 5.88248e12 + 1.01887e13i 0.151584 + 0.262551i
$$185$$ 9.62719e13 5.55826e13i 2.40143 1.38646i
$$186$$ 0 0
$$187$$ 1.34517e12 2.32991e12i 0.0314578 0.0544865i
$$188$$ 1.81101e13i 0.410179i
$$189$$ 0 0
$$190$$ 1.93576e12 0.0411462
$$191$$ 1.37615e12 + 7.94519e11i 0.0283442 + 0.0163645i 0.514105 0.857727i $$-0.328124\pi$$
−0.485761 + 0.874092i $$0.661457\pi$$
$$192$$ 0 0
$$193$$ 1.93962e13 + 3.35952e13i 0.375295 + 0.650030i 0.990371 0.138438i $$-0.0442081\pi$$
−0.615076 + 0.788468i $$0.710875\pi$$
$$194$$ 5.49365e13 3.17176e13i 1.03051 0.594963i
$$195$$ 0 0
$$196$$ −1.26551e13 + 2.19193e13i −0.223218 + 0.386625i
$$197$$ 1.68796e13i 0.288778i 0.989521 + 0.144389i $$0.0461216\pi$$
−0.989521 + 0.144389i $$0.953878\pi$$
$$198$$ 0 0
$$199$$ −4.66159e12 −0.0750613 −0.0375306 0.999295i $$-0.511949\pi$$
−0.0375306 + 0.999295i $$0.511949\pi$$
$$200$$ 3.91759e13 + 2.26182e13i 0.612123 + 0.353410i
$$201$$ 0 0
$$202$$ 2.27285e13 + 3.93670e13i 0.334552 + 0.579461i
$$203$$ 2.86977e13 1.65686e13i 0.410082 0.236761i
$$204$$ 0 0
$$205$$ −2.29368e13 + 3.97277e13i −0.309037 + 0.535267i
$$206$$ 2.61643e13i 0.342378i
$$207$$ 0 0
$$208$$ 2.67173e13 0.329923
$$209$$ 1.44662e12 + 8.35207e11i 0.0173571 + 0.0100211i
$$210$$ 0 0
$$211$$ −4.52210e13 7.83251e13i −0.512443 0.887578i −0.999896 0.0144282i $$-0.995407\pi$$
0.487453 0.873149i $$-0.337926\pi$$
$$212$$ 2.64270e13 1.52576e13i 0.291093 0.168063i
$$213$$ 0 0
$$214$$ −2.22948e12 + 3.86157e12i −0.0232125 + 0.0402052i
$$215$$ 3.21053e14i 3.25047i
$$216$$ 0 0
$$217$$ −2.77936e13 −0.266187
$$218$$ 3.03507e13 + 1.75230e13i 0.282768 + 0.163256i
$$219$$ 0 0
$$220$$ 2.92807e13 + 5.07156e13i 0.258253 + 0.447307i
$$221$$ −1.40447e13 + 8.10869e12i −0.120547 + 0.0695981i
$$222$$ 0 0
$$223$$ −7.27416e13 + 1.25992e14i −0.591499 + 1.02451i 0.402532 + 0.915406i $$0.368130\pi$$
−0.994031 + 0.109100i $$0.965203\pi$$
$$224$$ 7.30909e12i 0.0578596i
$$225$$ 0 0
$$226$$ −1.27814e14 −0.959240
$$227$$ −1.51717e13 8.75941e12i −0.110887 0.0640206i 0.443531 0.896259i $$-0.353726\pi$$
−0.554418 + 0.832239i $$0.687059\pi$$
$$228$$ 0 0
$$229$$ −3.91608e13 6.78285e13i −0.271543 0.470326i 0.697714 0.716376i $$-0.254201\pi$$
−0.969257 + 0.246050i $$0.920867\pi$$
$$230$$ 1.34621e14 7.77234e13i 0.909380 0.525031i
$$231$$ 0 0
$$232$$ 3.98789e13 6.90722e13i 0.255750 0.442971i
$$233$$ 1.00679e14i 0.629224i −0.949220 0.314612i $$-0.898126\pi$$
0.949220 0.314612i $$-0.101874\pi$$
$$234$$ 0 0
$$235$$ −2.39283e14 −1.42071
$$236$$ 1.09448e14 + 6.31896e13i 0.633482 + 0.365741i
$$237$$ 0 0
$$238$$ 2.21831e12 + 3.84223e12i 0.0122056 + 0.0211408i
$$239$$ 1.23461e14 7.12804e13i 0.662435 0.382457i −0.130769 0.991413i $$-0.541745\pi$$
0.793204 + 0.608956i $$0.208411\pi$$
$$240$$ 0 0
$$241$$ 5.62222e13 9.73798e13i 0.286950 0.497012i −0.686130 0.727479i $$-0.740692\pi$$
0.973080 + 0.230467i $$0.0740254\pi$$
$$242$$ 9.14951e13i 0.455518i
$$243$$ 0 0
$$244$$ −1.25808e14 −0.596168
$$245$$ 2.89613e14 + 1.67208e14i 1.33913 + 0.773145i
$$246$$ 0 0
$$247$$ −5.03462e12 8.72022e12i −0.0221710 0.0384013i
$$248$$ −5.79337e13 + 3.34480e13i −0.249013 + 0.143767i
$$249$$ 0 0
$$250$$ 1.49363e14 2.58704e14i 0.611791 1.05965i
$$251$$ 2.39343e14i 0.957148i −0.878047 0.478574i $$-0.841154\pi$$
0.878047 0.478574i $$-0.158846\pi$$
$$252$$ 0 0
$$253$$ 1.34139e14 0.511483
$$254$$ 4.50415e13 + 2.60047e13i 0.167730 + 0.0968389i
$$255$$ 0 0
$$256$$ −8.79609e12 1.52353e13i −0.0312500 0.0541266i
$$257$$ 1.00902e14 5.82558e13i 0.350188 0.202181i −0.314580 0.949231i $$-0.601864\pi$$
0.664768 + 0.747050i $$0.268530\pi$$
$$258$$ 0 0
$$259$$ −7.90962e13 + 1.36999e14i −0.262034 + 0.453856i
$$260$$ 3.53007e14i 1.14273i
$$261$$ 0 0
$$262$$ 4.43739e14 1.37189
$$263$$ −1.06512e14 6.14948e13i −0.321858 0.185825i 0.330362 0.943854i $$-0.392829\pi$$
−0.652221 + 0.758029i $$0.726162\pi$$
$$264$$ 0 0
$$265$$ −2.01594e14 3.49172e14i −0.582107 1.00824i
$$266$$ −2.38561e12 + 1.37733e12i −0.00673456 + 0.00388820i
$$267$$ 0 0
$$268$$ 9.87125e13 1.70975e14i 0.266418 0.461449i
$$269$$ 1.72775e14i 0.456003i 0.973661 + 0.228001i $$0.0732191\pi$$
−0.973661 + 0.228001i $$0.926781\pi$$
$$270$$ 0 0
$$271$$ 6.56137e14 1.65645 0.828225 0.560395i $$-0.189351\pi$$
0.828225 + 0.560395i $$0.189351\pi$$
$$272$$ 9.24782e12 + 5.33923e12i 0.0228363 + 0.0131845i
$$273$$ 0 0
$$274$$ 2.10930e14 + 3.65342e14i 0.498466 + 0.863368i
$$275$$ 4.46666e14 2.57883e14i 1.03273 0.596247i
$$276$$ 0 0
$$277$$ −1.50345e14 + 2.60404e14i −0.332820 + 0.576461i −0.983064 0.183265i $$-0.941333\pi$$
0.650244 + 0.759726i $$0.274667\pi$$
$$278$$ 1.71018e14i 0.370488i
$$279$$ 0 0
$$280$$ −9.65729e13 −0.200404
$$281$$ 5.97080e14 + 3.44724e14i 1.21282 + 0.700219i 0.963372 0.268170i $$-0.0864189\pi$$
0.249444 + 0.968389i $$0.419752\pi$$
$$282$$ 0 0
$$283$$ −1.24503e14 2.15646e14i −0.242360 0.419781i 0.719026 0.694983i $$-0.244588\pi$$
−0.961386 + 0.275203i $$0.911255\pi$$
$$284$$ −3.41398e14 + 1.97106e14i −0.650656 + 0.375656i
$$285$$ 0 0
$$286$$ 1.52309e14 2.63807e14i 0.278311 0.482048i
$$287$$ 6.52800e13i 0.116812i
$$288$$ 0 0
$$289$$ 5.76140e14 0.988875
$$290$$ −9.12631e14 5.26908e14i −1.53429 0.885822i
$$291$$ 0 0
$$292$$ −2.58959e14 4.48531e14i −0.417767 0.723595i
$$293$$ −4.08239e14 + 2.35697e14i −0.645221 + 0.372519i −0.786623 0.617434i $$-0.788172\pi$$
0.141402 + 0.989952i $$0.454839\pi$$
$$294$$ 0 0
$$295$$ 8.34906e14 1.44610e15i 1.26679 2.19415i
$$296$$ 3.80752e14i 0.566098i
$$297$$ 0 0
$$298$$ 2.83494e14 0.404806
$$299$$ −7.00258e14 4.04294e14i −0.980011 0.565810i
$$300$$ 0 0
$$301$$ 2.28435e14 + 3.95662e14i 0.307160 + 0.532016i
$$302$$ 2.80478e14 1.61934e14i 0.369707 0.213451i
$$303$$ 0 0
$$304$$ −3.31509e12 + 5.74190e12i −0.00420004 + 0.00727468i
$$305$$ 1.66226e15i 2.06491i
$$306$$ 0 0
$$307$$ −1.42240e15 −1.69900 −0.849498 0.527591i $$-0.823095\pi$$
−0.849498 + 0.527591i $$0.823095\pi$$
$$308$$ −7.21703e13 4.16675e13i −0.0845384 0.0488083i
$$309$$ 0 0
$$310$$ 4.41939e14 + 7.65461e14i 0.497958 + 0.862488i
$$311$$ 7.15366e14 4.13017e14i 0.790617 0.456463i −0.0495630 0.998771i $$-0.515783\pi$$
0.840180 + 0.542308i $$0.182450\pi$$
$$312$$ 0 0
$$313$$ −6.74228e14 + 1.16780e15i −0.717036 + 1.24194i 0.245133 + 0.969489i $$0.421168\pi$$
−0.962169 + 0.272453i $$0.912165\pi$$
$$314$$ 5.33618e14i 0.556740i
$$315$$ 0 0
$$316$$ 5.43469e14 0.545823
$$317$$ 1.06697e15 + 6.16014e14i 1.05147 + 0.607064i 0.923059 0.384657i $$-0.125680\pi$$
0.128407 + 0.991722i $$0.459014\pi$$
$$318$$ 0 0
$$319$$ −4.54681e14 7.87531e14i −0.431482 0.747349i
$$320$$ −2.01299e14 + 1.16220e14i −0.187475 + 0.108238i
$$321$$ 0 0
$$322$$ −1.10604e14 + 1.91571e14i −0.0992279 + 0.171868i
$$323$$ 4.02452e12i 0.00354404i
$$324$$ 0 0
$$325$$ −3.10903e15 −2.63831
$$326$$ −1.82827e14 1.05555e14i −0.152312 0.0879373i
$$327$$ 0 0
$$328$$ −7.85609e13 1.36071e14i −0.0630904 0.109276i
$$329$$ 2.94890e14 1.70255e14i 0.232533 0.134253i
$$330$$ 0 0
$$331$$ −9.87477e14 + 1.71036e15i −0.750860 + 1.30053i 0.196547 + 0.980494i $$0.437027\pi$$
−0.947406 + 0.320033i $$0.896306\pi$$
$$332$$ 1.18743e15i 0.886706i
$$333$$ 0 0
$$334$$ 1.28974e15 0.929019
$$335$$ −2.25904e15 1.30426e15i −1.59829 0.922773i
$$336$$ 0 0
$$337$$ −2.29797e14 3.98019e14i −0.156879 0.271722i 0.776863 0.629670i $$-0.216810\pi$$
−0.933742 + 0.357948i $$0.883477\pi$$
$$338$$ −6.77135e14 + 3.90944e14i −0.454125 + 0.262189i
$$339$$ 0 0
$$340$$ 7.05457e13 1.22189e14i 0.0456664 0.0790966i
$$341$$ 7.62720e14i 0.485108i
$$342$$ 0 0
$$343$$ −1.00887e15 −0.619544
$$344$$ 9.52314e14 + 5.49819e14i 0.574685 + 0.331794i
$$345$$ 0 0
$$346$$ −5.27041e14 9.12862e14i −0.307177 0.532045i
$$347$$ −2.14506e15 + 1.23845e15i −1.22875 + 0.709417i −0.966768 0.255656i $$-0.917709\pi$$
−0.261979 + 0.965074i $$0.584375\pi$$
$$348$$ 0 0
$$349$$ −4.54506e13 + 7.87227e13i −0.0251528 + 0.0435660i −0.878328 0.478059i $$-0.841341\pi$$
0.853175 + 0.521625i $$0.174674\pi$$
$$350$$ 8.50544e14i 0.462689i
$$351$$ 0 0
$$352$$ −2.00578e14 −0.105445
$$353$$ −2.29734e15 1.32637e15i −1.18734 0.685513i −0.229642 0.973275i $$-0.573755\pi$$
−0.957702 + 0.287762i $$0.907089\pi$$
$$354$$ 0 0
$$355$$ 2.60431e15 + 4.51080e15i 1.30114 + 2.25363i
$$356$$ 4.74726e14 2.74083e14i 0.233208 0.134643i
$$357$$ 0 0
$$358$$ −7.71466e13 + 1.33622e14i −0.0366453 + 0.0634715i
$$359$$ 1.96552e15i 0.918145i −0.888399 0.459073i $$-0.848182\pi$$
0.888399 0.459073i $$-0.151818\pi$$
$$360$$ 0 0
$$361$$ −2.21082e15 −0.998871
$$362$$ 1.26193e15 + 7.28574e14i 0.560768 + 0.323759i
$$363$$ 0 0
$$364$$ 2.51172e14 + 4.35042e14i 0.107985 + 0.187035i
$$365$$ −5.92631e15 + 3.42156e15i −2.50626 + 1.44699i
$$366$$ 0 0
$$367$$ −7.84452e14 + 1.35871e15i −0.321048 + 0.556071i −0.980705 0.195496i $$-0.937368\pi$$
0.659657 + 0.751567i $$0.270702\pi$$
$$368$$ 5.32421e14i 0.214372i
$$369$$ 0 0
$$370$$ 5.03076e15 1.96076
$$371$$ 4.96885e14 + 2.86877e14i 0.190552 + 0.110015i
$$372$$ 0 0
$$373$$ −1.55974e15 2.70154e15i −0.579159 1.00313i −0.995576 0.0939592i $$-0.970048\pi$$
0.416417 0.909174i $$-0.363286\pi$$
$$374$$ 1.05440e14 6.08756e13i 0.0385278 0.0222440i
$$375$$ 0 0
$$376$$ 4.09784e14 7.09767e14i 0.145020 0.251182i
$$377$$ 5.48163e15i 1.90925i
$$378$$ 0 0
$$379$$ −5.04620e13 −0.0170266 −0.00851332 0.999964i $$-0.502710\pi$$
−0.00851332 + 0.999964i $$0.502710\pi$$
$$380$$ 7.58660e13 + 4.38012e13i 0.0251968 + 0.0145474i
$$381$$ 0 0
$$382$$ 3.59558e13 + 6.22773e13i 0.0115715 + 0.0200424i
$$383$$ −4.27200e15 + 2.46644e15i −1.35344 + 0.781409i −0.988730 0.149712i $$-0.952165\pi$$
−0.364710 + 0.931121i $$0.618832\pi$$
$$384$$ 0 0
$$385$$ −5.50541e14 + 9.53565e14i −0.169054 + 0.292810i
$$386$$ 1.75554e15i 0.530747i
$$387$$ 0 0
$$388$$ 2.87075e15 0.841405
$$389$$ 3.28797e14 + 1.89831e14i 0.0948922 + 0.0547860i 0.546695 0.837332i $$-0.315886\pi$$
−0.451803 + 0.892118i $$0.649219\pi$$
$$390$$ 0 0
$$391$$ −1.61590e14 2.79882e14i −0.0452224 0.0783275i
$$392$$ −9.91954e14 + 5.72705e14i −0.273385 + 0.157839i
$$393$$ 0 0
$$394$$ −3.81941e14 + 6.61541e14i −0.102098 + 0.176840i
$$395$$ 7.18069e15i 1.89053i
$$396$$ 0 0
$$397$$ 6.55958e15 1.67546 0.837728 0.546088i $$-0.183884\pi$$
0.837728 + 0.546088i $$0.183884\pi$$
$$398$$ −1.82696e14 1.05480e14i −0.0459655 0.0265382i
$$399$$ 0 0
$$400$$ 1.02358e15 + 1.77290e15i 0.249898 + 0.432837i
$$401$$ −1.10355e15 + 6.37137e14i −0.265416 + 0.153238i −0.626803 0.779178i $$-0.715637\pi$$
0.361387 + 0.932416i $$0.382303\pi$$
$$402$$ 0 0
$$403$$ 2.29884e15 3.98170e15i 0.536633 0.929476i
$$404$$ 2.05715e15i 0.473128i
$$405$$ 0 0
$$406$$ 1.49962e15 0.334831
$$407$$ 3.75956e15 + 2.17058e15i 0.827124 + 0.477540i
$$408$$ 0 0
$$409$$ 1.47982e15 + 2.56312e15i 0.316132 + 0.547557i 0.979678 0.200579i $$-0.0642824\pi$$
−0.663545 + 0.748136i $$0.730949\pi$$
$$410$$ −1.79787e15 + 1.03800e15i −0.378491 + 0.218522i
$$411$$ 0 0
$$412$$ −5.92030e14 + 1.02543e15i −0.121049 + 0.209663i
$$413$$ 2.37621e15i 0.478833i
$$414$$ 0 0
$$415$$ −1.56892e16 −3.07122
$$416$$ 1.04710e15 + 6.04543e14i 0.202035 + 0.116645i
$$417$$ 0 0
$$418$$ 3.77971e13 + 6.54666e13i 0.00708600 + 0.0122733i
$$419$$ 9.34387e14 5.39468e14i 0.172680 0.0996969i −0.411169 0.911559i $$-0.634879\pi$$
0.583849 + 0.811862i $$0.301546\pi$$
$$420$$ 0 0
$$421$$ −2.23817e15 + 3.87663e15i −0.401977 + 0.696245i −0.993964 0.109703i $$-0.965010\pi$$
0.591987 + 0.805947i $$0.298343\pi$$
$$422$$ 4.09294e15i 0.724704i
$$423$$ 0 0
$$424$$ 1.38096e15 0.237677
$$425$$ −1.07615e15 6.21315e14i −0.182616 0.105433i
$$426$$ 0 0
$$427$$ −1.18273e15 2.04855e15i −0.195128 0.337971i
$$428$$ −1.74755e14 + 1.00895e14i −0.0284293 + 0.0164137i
$$429$$ 0 0
$$430$$ 7.26459e15 1.25826e16i 1.14921 1.99050i
$$431$$ 7.86574e15i 1.22709i 0.789660 + 0.613544i $$0.210257\pi$$
−0.789660 + 0.613544i $$0.789743\pi$$
$$432$$ 0 0
$$433$$ −5.34544e15 −0.811066 −0.405533 0.914080i $$-0.632914\pi$$
−0.405533 + 0.914080i $$0.632914\pi$$
$$434$$ −1.08928e15 6.28897e14i −0.163005 0.0941112i
$$435$$ 0 0
$$436$$ 7.92999e14 + 1.37352e15i 0.115439 + 0.199947i
$$437$$ 1.73776e14 1.00330e14i 0.0249518 0.0144059i
$$438$$ 0 0
$$439$$ −2.82271e15 + 4.88908e15i −0.394348 + 0.683030i −0.993018 0.117966i $$-0.962363\pi$$
0.598670 + 0.800996i $$0.295696\pi$$
$$440$$ 2.65018e15i 0.365224i
$$441$$ 0 0
$$442$$ −7.33915e14 −0.0984266
$$443$$ −1.04600e16 6.03907e15i −1.38391 0.799001i −0.391290 0.920267i $$-0.627971\pi$$
−0.992620 + 0.121266i $$0.961305\pi$$
$$444$$ 0 0
$$445$$ −3.62138e15 6.27242e15i −0.466353 0.807747i
$$446$$ −5.70175e15 + 3.29191e15i −0.724435 + 0.418253i
$$447$$ 0 0
$$448$$ 1.65386e14 2.86457e14i 0.0204565 0.0354316i
$$449$$ 1.48510e16i 1.81250i 0.422746 + 0.906248i $$0.361066\pi$$
−0.422746 + 0.906248i $$0.638934\pi$$
$$450$$ 0 0
$$451$$ −1.79143e15 −0.212883
$$452$$ −5.00926e15 2.89210e15i −0.587412 0.339143i
$$453$$ 0 0
$$454$$ −3.96406e14 6.86595e14i −0.0452694 0.0784089i
$$455$$ 5.74809e15 3.31866e15i 0.647821 0.374019i
$$456$$ 0 0
$$457$$ −4.00489e15 + 6.93667e15i −0.439636 + 0.761472i −0.997661 0.0683522i $$-0.978226\pi$$
0.558025 + 0.829824i $$0.311559\pi$$
$$458$$ 3.54443e15i 0.384020i
$$459$$ 0 0
$$460$$ 7.03472e15 0.742506
$$461$$ 1.11637e16 + 6.44534e15i 1.16306 + 0.671491i 0.952035 0.305990i $$-0.0989876\pi$$
0.211022 + 0.977481i $$0.432321\pi$$
$$462$$ 0 0
$$463$$ −4.51163e15 7.81437e15i −0.457981 0.793247i 0.540873 0.841104i $$-0.318094\pi$$
−0.998854 + 0.0478576i $$0.984761\pi$$
$$464$$ 3.12585e15 1.80471e15i 0.313228 0.180842i
$$465$$ 0 0
$$466$$ 2.27811e15 3.94581e15i 0.222464 0.385319i
$$467$$ 2.65871e15i 0.256312i 0.991754 + 0.128156i $$0.0409059\pi$$
−0.991754 + 0.128156i $$0.959094\pi$$
$$468$$ 0 0
$$469$$ 3.71203e15 0.348798
$$470$$ −9.37795e15 5.41436e15i −0.870003 0.502296i
$$471$$ 0 0
$$472$$ 2.85963e15 + 4.95303e15i 0.258618 + 0.447939i
$$473$$ 1.08579e16 6.26879e15i 0.969566 0.559779i
$$474$$ 0 0
$$475$$ 3.85770e14 6.68173e14i 0.0335866 0.0581738i
$$476$$ 2.00779e14i 0.0172614i
$$477$$ 0 0
$$478$$ 6.45156e15 0.540876
$$479$$ 1.13766e15 + 6.56827e14i 0.0941887 + 0.0543798i 0.546354 0.837554i $$-0.316015\pi$$
−0.452166 + 0.891934i $$0.649348\pi$$
$$480$$ 0 0
$$481$$ −1.30843e16 2.26626e16i −1.05652 1.82995i
$$482$$ 4.40691e15 2.54433e15i 0.351440 0.202904i
$$483$$ 0 0
$$484$$ 2.07030e15 3.58586e15i 0.161050 0.278947i
$$485$$ 3.79304e16i 2.91432i
$$486$$ 0 0
$$487$$ −1.13689e16 −0.852207 −0.426104 0.904674i $$-0.640114\pi$$
−0.426104 + 0.904674i $$0.640114\pi$$
$$488$$ −4.93064e15 2.84671e15i −0.365077 0.210777i
$$489$$ 0 0
$$490$$ 7.56698e15 + 1.31064e16i 0.546696 + 0.946906i
$$491$$ 1.74056e16 1.00491e16i 1.24222 0.717198i 0.272677 0.962106i $$-0.412091\pi$$
0.969546 + 0.244908i $$0.0787578\pi$$
$$492$$ 0 0
$$493$$ −1.09546e15 + 1.89739e15i −0.0762984 + 0.132153i
$$494$$ 4.55682e14i 0.0313545i
$$495$$ 0 0
$$496$$ −3.02737e15 −0.203318
$$497$$ −6.41904e15 3.70604e15i −0.425924 0.245907i
$$498$$ 0 0
$$499$$ 9.58475e15 + 1.66013e16i 0.620837 + 1.07532i 0.989330 + 0.145690i $$0.0465403\pi$$
−0.368494 + 0.929630i $$0.620126\pi$$
$$500$$ 1.17076e16 6.75940e15i 0.749288 0.432602i
$$501$$ 0 0
$$502$$ 5.41572e15 9.38031e15i 0.338403 0.586131i
$$503$$ 3.57174e15i 0.220532i 0.993902 + 0.110266i $$0.0351703\pi$$
−0.993902 + 0.110266i $$0.964830\pi$$
$$504$$ 0 0
$$505$$ 2.71805e16 1.63874
$$506$$ 5.25715e15 + 3.03521e15i 0.313218 + 0.180837i
$$507$$ 0 0
$$508$$ 1.17684e15 + 2.03835e15i 0.0684754 + 0.118603i
$$509$$ 2.08346e14 1.20289e14i 0.0119806 0.00691702i −0.493998 0.869463i $$-0.664465\pi$$
0.505978 + 0.862546i $$0.331132\pi$$
$$510$$ 0 0
$$511$$ 4.86901e15 8.43337e15i 0.273473 0.473670i
$$512$$ 7.96131e14i 0.0441942i
$$513$$ 0 0
$$514$$ 5.27271e15 0.285927
$$515$$ 1.35487e16 + 7.82232e15i 0.726194 + 0.419268i
$$516$$ 0 0
$$517$$ −4.67218e15 8.09245e15i −0.244667 0.423776i
$$518$$ −6.19985e15 + 3.57949e15i −0.320924 + 0.185286i
$$519$$ 0 0
$$520$$ 7.98765e15 1.38350e16i 0.404016 0.699777i
$$521$$ 1.13166e16i 0.565835i −0.959144 0.282917i $$-0.908698\pi$$
0.959144 0.282917i $$-0.0913022\pi$$
$$522$$ 0 0
$$523$$ 1.60120e16 0.782414 0.391207 0.920303i $$-0.372058\pi$$
0.391207 + 0.920303i $$0.372058\pi$$
$$524$$ 1.73909e16 + 1.00407e16i 0.840108 + 0.485037i
$$525$$ 0 0
$$526$$ −2.78294e15 4.82019e15i −0.131398 0.227588i
$$527$$ 1.59142e15 9.18808e14i 0.0742885 0.0428905i
$$528$$ 0 0
$$529$$ −2.90055e15 + 5.02390e15i −0.132357 + 0.229249i
$$530$$ 1.82462e16i 0.823224i
$$531$$ 0 0
$$532$$ −1.24662e14 −0.00549875
$$533$$ 9.35199e15 + 5.39938e15i 0.407888 + 0.235494i
$$534$$ 0 0
$$535$$ 1.33309e15 + 2.30899e15i 0.0568510 + 0.0984688i
$$536$$ 7.73745e15 4.46722e15i 0.326294 0.188386i
$$537$$ 0 0
$$538$$ −3.90946e15 + 6.77138e15i −0.161221 + 0.279244i
$$539$$ 1.30595e16i 0.532589i
$$540$$ 0 0
$$541$$ −1.37943e16 −0.550195 −0.275098 0.961416i $$-0.588710\pi$$
−0.275098 + 0.961416i $$0.588710\pi$$
$$542$$ 2.57152e16 + 1.48467e16i 1.01436 + 0.585644i
$$543$$ 0 0
$$544$$ 2.41626e14 + 4.18509e14i 0.00932288 + 0.0161477i
$$545$$ 1.81479e16 1.04777e16i 0.692542 0.399839i
$$546$$ 0 0
$$547$$ 2.52139e15 4.36718e15i 0.0941274 0.163034i −0.815117 0.579297i $$-0.803327\pi$$
0.909244 + 0.416263i $$0.136661\pi$$
$$548$$ 1.90912e16i 0.704937i
$$549$$ 0 0
$$550$$ 2.33409e16 0.843221
$$551$$ −1.17808e15 6.80163e14i −0.0420982 0.0243054i
$$552$$ 0 0
$$553$$ 5.10920e15 + 8.84940e15i 0.178650 + 0.309430i
$$554$$ −1.17846e16 + 6.80382e15i −0.407619 + 0.235339i
$$555$$ 0 0
$$556$$ −3.86971e15 + 6.70253e15i −0.130987 + 0.226877i
$$557$$ 5.00485e16i 1.67595i −0.545711 0.837974i $$-0.683740\pi$$
0.545711 0.837974i $$-0.316260\pi$$
$$558$$ 0 0
$$559$$ −7.55765e16 −2.47694
$$560$$ −3.78487e15 2.18520e15i −0.122722 0.0708536i
$$561$$ 0 0
$$562$$ 1.56004e16 + 2.70208e16i 0.495130 + 0.857590i
$$563$$ −2.69154e16 + 1.55396e16i −0.845181 + 0.487966i −0.859022 0.511938i $$-0.828928\pi$$
0.0138407 + 0.999904i $$0.495594\pi$$
$$564$$ 0 0
$$565$$ −3.82124e16 + 6.61859e16i −1.17466 + 2.03458i
$$566$$ 1.12687e16i 0.342749i
$$567$$ 0 0
$$568$$ −1.78400e16 −0.531258
$$569$$ −9.90375e15 5.71793e15i −0.291827 0.168487i 0.346938 0.937888i $$-0.387221\pi$$
−0.638766 + 0.769401i $$0.720555\pi$$
$$570$$ 0 0
$$571$$ 2.61075e16 + 4.52196e16i 0.753267 + 1.30470i 0.946231 + 0.323491i $$0.104857\pi$$
−0.192964 + 0.981206i $$0.561810\pi$$
$$572$$ 1.19386e16 6.89273e15i 0.340860 0.196795i
$$573$$ 0 0
$$574$$ 1.47712e15 2.55844e15i 0.0412994 0.0715327i
$$575$$ 6.19567e16i 1.71428i
$$576$$ 0 0
$$577$$ −2.11018e16 −0.571828 −0.285914 0.958255i $$-0.592297\pi$$
−0.285914 + 0.958255i $$0.592297\pi$$
$$578$$ 2.25800e16 + 1.30366e16i 0.605560 + 0.349620i
$$579$$ 0 0
$$580$$ −2.38451e16 4.13010e16i −0.626371 1.08491i
$$581$$ 1.93352e16 1.11632e16i 0.502679 0.290222i
$$582$$ 0 0
$$583$$ 7.87255e15 1.36357e16i 0.200495 0.347268i
$$584$$ 2.34383e16i 0.590812i
$$585$$ 0 0
$$586$$ −2.13328e16 −0.526821
$$587$$ 5.05498e16 + 2.91849e16i 1.23564 + 0.713395i 0.968199 0.250180i $$-0.0804898\pi$$
0.267437 + 0.963575i $$0.413823\pi$$
$$588$$ 0 0
$$589$$ 5.70480e14 + 9.88101e14i 0.0136631 + 0.0236652i
$$590$$ 6.54430e16 3.77835e16i 1.55150 0.895757i
$$591$$ 0 0
$$592$$ −8.61543e15 + 1.49224e16i −0.200146 + 0.346663i
$$593$$ 5.67583e15i 0.130527i 0.997868 + 0.0652637i $$0.0207888\pi$$
−0.997868 + 0.0652637i $$0.979211\pi$$
$$594$$ 0 0
$$595$$ 2.65283e15 0.0597871
$$596$$ 1.11107e16 + 6.41474e15i 0.247892 + 0.143120i
$$597$$ 0 0
$$598$$ −1.82963e16 3.16901e16i −0.400088 0.692972i
$$599$$ −2.85237e15 + 1.64682e15i −0.0617511 + 0.0356520i −0.530558 0.847649i $$-0.678017\pi$$
0.468807 + 0.883301i $$0.344684\pi$$
$$600$$ 0 0
$$601$$ −1.68791e16 + 2.92355e16i −0.358182 + 0.620389i −0.987657 0.156632i $$-0.949936\pi$$
0.629475 + 0.777020i $$0.283270\pi$$
$$602$$ 2.06756e16i 0.434390i
$$603$$ 0 0
$$604$$ 1.46566e16 0.301865
$$605$$ −4.73789e16 2.73542e16i −0.966169 0.557818i
$$606$$ 0 0
$$607$$ −9.99643e15 1.73143e16i −0.199854 0.346157i 0.748627 0.662992i $$-0.230713\pi$$
−0.948481 + 0.316834i $$0.897380\pi$$
$$608$$ −2.59849e14 + 1.50024e14i −0.00514397 + 0.00296988i
$$609$$ 0 0
$$610$$ −3.76127e16 + 6.51471e16i −0.730055 + 1.26449i
$$611$$ 5.63278e16i 1.08262i
$$612$$ 0 0
$$613$$ 1.47766e15 0.0278491 0.0139246 0.999903i $$-0.495568\pi$$
0.0139246 + 0.999903i $$0.495568\pi$$
$$614$$ −5.57466e16 3.21853e16i −1.04042 0.600686i
$$615$$ 0 0
$$616$$ −1.88566e15 3.26605e15i −0.0345127 0.0597777i
$$617$$ 1.62823e16 9.40058e15i 0.295124 0.170390i −0.345126 0.938556i $$-0.612164\pi$$
0.640250 + 0.768166i $$0.278831\pi$$
$$618$$ 0 0
$$619$$ 1.24568e16 2.15758e16i 0.221443 0.383551i −0.733803 0.679362i $$-0.762257\pi$$
0.955246 + 0.295811i $$0.0955899\pi$$
$$620$$ 3.99998e16i 0.704218i
$$621$$ 0 0
$$622$$ 3.73820e16 0.645536
$$623$$ 8.92590e15 + 5.15337e15i 0.152660 + 0.0881380i
$$624$$ 0 0
$$625$$ −2.97296e16 5.14931e16i −0.498780 0.863912i
$$626$$ −5.28485e16 + 3.05121e16i −0.878186 + 0.507021i
$$627$$ 0 0
$$628$$ −1.20744e16 + 2.09135e16i −0.196837 + 0.340932i
$$629$$ 1.04591e16i 0.168885i
$$630$$ 0 0
$$631$$ 6.72198e16 1.06493 0.532465 0.846452i $$-0.321266\pi$$
0.532465 + 0.846452i $$0.321266\pi$$
$$632$$ 2.12995e16 + 1.22973e16i 0.334247 + 0.192978i
$$633$$ 0 0
$$634$$ 2.78776e16 + 4.82854e16i 0.429259 + 0.743499i
$$635$$ 2.69321e16 1.55492e16i 0.410797 0.237174i
$$636$$ 0 0
$$637$$ 3.93612e16 6.81756e16i 0.589158 1.02045i
$$638$$ 4.11531e16i 0.610208i
$$639$$ 0 0
$$640$$ −1.05191e16 −0.153072
$$641$$ −2.97844e16 1.71960e16i −0.429379 0.247902i 0.269703 0.962944i $$-0.413074\pi$$
−0.699082 + 0.715042i $$0.746408\pi$$
$$642$$ 0 0
$$643$$ 4.23528e16 + 7.33572e16i 0.599261 + 1.03795i 0.992930 + 0.118698i $$0.0378722\pi$$
−0.393669 + 0.919252i $$0.628795\pi$$
$$644$$ −8.66951e15 + 5.00534e15i −0.121529 + 0.0701647i
$$645$$ 0 0
$$646$$ 9.10644e13 1.57728e14i 0.00125301 0.00217027i
$$647$$ 1.28516e17i 1.75199i 0.482323 + 0.875994i $$0.339793\pi$$
−0.482323 + 0.875994i $$0.660207\pi$$
$$648$$ 0 0
$$649$$ 6.52086e16 0.872643
$$650$$ −1.21849e17 7.03494e16i −1.61563 0.932782i
$$651$$ 0 0
$$652$$ −4.77687e15 8.27379e15i −0.0621811 0.107701i
$$653$$ 1.14204e17 6.59359e16i 1.47300 0.850438i 0.473464 0.880813i $$-0.343004\pi$$
0.999539 + 0.0303751i $$0.00967019\pi$$
$$654$$ 0 0
$$655$$ 1.32664e17 2.29781e17i 1.67999 2.90983i
$$656$$ 7.11052e15i 0.0892233i
$$657$$ 0 0
$$658$$ 1.54097e16 0.189862
$$659$$ 1.01901e16 + 5.88324e15i 0.124413 + 0.0718297i 0.560915 0.827874i $$-0.310450\pi$$
−0.436502 + 0.899703i $$0.643783\pi$$
$$660$$ 0 0
$$661$$ 3.54190e16 + 6.13475e16i 0.424647 + 0.735510i 0.996387 0.0849247i $$-0.0270650\pi$$
−0.571741 + 0.820434i $$0.693732\pi$$
$$662$$ −7.74020e16 + 4.46881e16i −0.919612 + 0.530938i
$$663$$ 0 0
$$664$$ 2.68685e16 4.65376e16i 0.313498 0.542994i
$$665$$ 1.64712e15i 0.0190456i
$$666$$ 0 0
$$667$$ −1.09238e17 −1.24056
$$668$$ 5.05474e16 + 2.91836e16i 0.568905 + 0.328458i
$$669$$ 0 0
$$670$$ −5.90240e16 1.02233e17i −0.652499 1.13016i
$$671$$ −5.62170e16 + 3.24569e16i −0.615932 + 0.355608i
$$672$$ 0 0
$$673$$ −4.48652e16 + 7.77089e16i −0.482858 + 0.836335i −0.999806 0.0196819i $$-0.993735\pi$$
0.516948 + 0.856017i $$0.327068\pi$$
$$674$$ 2.07988e16i 0.221860i
$$675$$ 0 0
$$676$$ −3.53842e16 −0.370791
$$677$$ −9.03018e16 5.21358e16i −0.937917 0.541507i −0.0486104 0.998818i $$-0.515479\pi$$
−0.889307 + 0.457311i $$0.848813\pi$$
$$678$$ 0 0
$$679$$ 2.69882e16 + 4.67450e16i 0.275395 + 0.476997i
$$680$$ 5.52963e15 3.19253e15i 0.0559297 0.0322910i
$$681$$ 0 0
$$682$$ −1.72584e16 + 2.98924e16i −0.171512 + 0.297067i
$$683$$ 1.69283e16i 0.166759i 0.996518 + 0.0833797i $$0.0265714\pi$$
−0.996518 + 0.0833797i $$0.973429\pi$$
$$684$$ 0 0
$$685$$ 2.52247e17 2.44164
$$686$$ −3.95396e16 2.28282e16i −0.379391 0.219042i
$$687$$ 0 0
$$688$$ 2.48820e16 + 4.30968e16i 0.234614 + 0.406363i
$$689$$ −8.21957e16 + 4.74557e16i −0.768306 + 0.443581i
$$690$$ 0 0
$$691$$ −2.78470e16 + 4.82324e16i −0.255805 + 0.443068i −0.965114 0.261830i $$-0.915674\pi$$
0.709309 + 0.704898i $$0.249007\pi$$
$$692$$ 4.77023e16i 0.434413i
$$693$$ 0 0
$$694$$ −1.12092e17 −1.00327
$$695$$ 8.85585e16 + 5.11293e16i 0.785817 + 0.453692i
$$696$$ 0 0
$$697$$ 2.15804e15 + 3.73784e15i 0.0188219 + 0.0326005i
$$698$$ −3.56258e15 + 2.05686e15i −0.0308058 + 0.0177857i
$$699$$ 0 0
$$700$$ −1.92456e16 + 3.33344e16i −0.163585 + 0.283338i
$$701$$ 1.24684e16i 0.105076i 0.998619 + 0.0525379i $$0.0167310\pi$$
−0.998619 + 0.0525379i $$0.983269\pi$$
$$702$$ 0 0
$$703$$ 6.49399e15 0.0537997
$$704$$ −7.86103e15 4.53857e15i −0.0645719 0.0372806i
$$705$$ 0 0
$$706$$ −6.00246e16 1.03966e17i −0.484731 0.839579i
$$707$$ −3.34970e16 + 1.93395e16i −0.268219 + 0.154856i
$$708$$ 0 0
$$709$$ 7.78003e16 1.34754e17i 0.612497 1.06088i −0.378321 0.925674i $$-0.623499\pi$$
0.990818 0.135201i $$-0.0431681\pi$$
$$710$$ 2.35715e17i 1.84008i
$$711$$ 0 0
$$712$$ 2.48072e16 0.190414
$$713$$ 7.93472e16 + 4.58111e16i 0.603941 + 0.348685i
$$714$$ 0 0
$$715$$ −9.10716e16 1.57741e17i −0.681627 1.18061i
$$716$$ −6.04703e15 + 3.49126e15i −0.0448812 + 0.0259122i
$$717$$ 0 0
$$718$$ 4.44747e16 7.70325e16i 0.324613 0.562247i
$$719$$ 2.11824e17i 1.53321i 0.642118 + 0.766606i $$0.278056\pi$$
−0.642118 + 0.766606i $$0.721944\pi$$
$$720$$ 0 0
$$721$$ −2.22629e16 −0.158479
$$722$$ −8.66459e16 5.00251e16i −0.611681 0.353154i
$$723$$ 0 0
$$724$$ 3.29715e16 + 5.71083e16i 0.228933 + 0.396523i
$$725$$ −3.63749e17 + 2.10011e17i −2.50480 + 1.44615i
$$726$$ 0 0
$$727$$ −8.58243e16 + 1.48652e17i −0.581304 + 1.00685i 0.414021 + 0.910267i $$0.364124\pi$$
−0.995325 + 0.0965813i $$0.969209\pi$$
$$728$$ 2.27335e16i 0.152714i
$$729$$ 0 0
$$730$$ −3.09684e17 −2.04636
$$731$$ −2.61598e16 1.51034e16i −0.171447 0.0989850i
$$732$$ 0 0
$$733$$ −1.01296e17 1.75450e17i −0.653086 1.13118i −0.982370 0.186947i $$-0.940141\pi$$
0.329285 0.944231i $$-0.393192\pi$$
$$734$$ −6.14882e16 + 3.55002e16i −0.393202 + 0.227015i
$$735$$ 0 0
$$736$$ −1.20473e16 + 2.08666e16i −0.0757920 + 0.131276i
$$737$$ 1.01866e17i 0.635662i
$$738$$ 0 0
$$739$$ −5.12528e16 −0.314667 −0.157333 0.987546i $$-0.550290\pi$$
−0.157333 + 0.987546i $$0.550290\pi$$
$$740$$ 1.97165e17 + 1.13833e17i 1.20071 + 0.693232i
$$741$$ 0 0
$$742$$ 1.29826e16 + 2.24864e16i 0.0777923 + 0.134740i
$$743$$ −1.16670e17 + 6.73595e16i −0.693468 + 0.400374i −0.804910 0.593397i $$-0.797787\pi$$
0.111442 + 0.993771i $$0.464453\pi$$
$$744$$ 0 0
$$745$$ 8.47561e16 1.46802e17i 0.495717 0.858606i
$$746$$ 1.41171e17i 0.819055i
$$747$$ 0 0
$$748$$ 5.50983e15 0.0314578
$$749$$ −3.28578e15 1.89704e15i −0.0186100 0.0107445i
$$750$$ 0 0
$$751$$ 8.16463e15 + 1.41416e16i 0.0455090 + 0.0788239i 0.887883 0.460070i $$-0.152176\pi$$
−0.842374 + 0.538894i $$0.818842\pi$$
$$752$$ 3.21204e16 1.85447e16i 0.177613 0.102545i
$$753$$ 0 0
$$754$$ −1.24035e17 + 2.14835e17i −0.675020 + 1.16917i
$$755$$ 1.93654e17i 1.04555i
$$756$$ 0 0
$$757$$ 1.24607e17 0.662169 0.331084 0.943601i $$-0.392585\pi$$
0.331084 + 0.943601i $$0.392585\pi$$
$$758$$ −1.97770e15 1.14182e15i −0.0104266 0.00601982i
$$759$$ 0 0
$$760$$ 1.98222e15 + 3.43330e15i 0.0102866 + 0.0178168i
$$761$$ −3.19948e17 + 1.84722e17i −1.64729 + 0.951066i −0.669154 + 0.743124i $$0.733343\pi$$
−0.978141 + 0.207942i $$0.933323\pi$$
$$762$$ 0 0
$$763$$ −1.49101e16 + 2.58251e16i −0.0755674 + 0.130887i
$$764$$ 3.25435e15i 0.0163645i