LMFDB - Embedded newform 162.13.d.c.107.4

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 - 4x^7 - 18478x^6 + 55448x^5 + 128029439x^4 - 256151296x^3 - 394230846230x^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

Display 100 coefficients 10 coefficients

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 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \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
$2$	39.1918	+	22.6274i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	1024.00	+	1773.62i	0.250000	+	0.433013i
$5$	23434.3	−	13529.8i	1.49980	−	0.865908i	0.499797	−	0.866143i	$-0.333408\pi$
$5$	23434.3	−	13529.8i	1.49980	−	0.865908i	1.00000		0.000234889i	$7.47674e-5\pi$
$6$		0			0
$7$	−19253.5	+	33348.0i	−0.163652	+	0.283453i	−0.936176	−	0.351533i	$-0.885661\pi$
$7$	−19253.5	+	33348.0i	−0.163652	+	0.283453i	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	$-0.236932\pi$
$11$	915145.	+	528359.i	0.516575	+	0.298245i	−0.218957	+	0.975735i	$0.570265\pi$
$12$		0			0
$13$	−3.18495e6	−	5.51649e6i	−0.659845	−	1.14289i	−0.980655	−	0.195742i	$-0.937289\pi$
$13$	−3.18495e6	−	5.51649e6i	−0.659845	−	1.14289i	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	$-0.983205\pi$
$17$		−	2.54594e6i		−	0.105476i	0.998608	−	0.0527382i	$-0.0167949\pi$
$18$		0			0
$19$	1.58076e6			0.0336003			0.0168002	−	0.999859i	$-0.494652\pi$
$19$	1.58076e6			0.0336003			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	$-0.525623\pi$
$23$	1.09932e8	−	6.34695e7i	0.742607	−	0.428744i	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	$-0.590741\pi$
$29$	−7.45261e8	−	4.30277e8i	−1.25291	−	0.723369i	−0.971687	+	0.236273i	$0.924074\pi$
$30$		0			0
$31$	3.60891e8	+	6.25081e8i	0.406636	+	0.704314i	0.994510	−	0.104638i	$-0.0333684\pi$
$31$	3.60891e8	+	6.25081e8i	0.406636	+	0.704314i	−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	$-0.204523\pi$
$37$	4.10816e9			1.60117			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	$-0.723774\pi$
$41$	−1.46816e9	+	8.47640e8i	−0.309079	+	0.178447i	0.337435	+	0.941349i	$0.390441\pi$
$42$		0			0
$43$	5.93232e9	−	1.02751e10i	0.938456	−	1.62545i	0.170104	−	0.985426i	$-0.445590\pi$
$43$	5.93232e9	−	1.02751e10i	0.938456	−	1.62545i	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	$-0.467867\pi$
$47$	−7.65810e9	−	4.42141e9i	−0.710451	−	0.410179i	−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	$-0.890883\pi$
$53$		−	1.49000e10i		−	0.672251i	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	$-0.405496\pi$
$59$	5.34412e10	−	3.08543e10i	1.26696	−	0.731482i	0.974412	+	0.224768i	$0.0721624\pi$
$60$		0			0
$61$	−3.07148e10	+	5.31996e10i	−0.596168	+	1.03259i	0.397212	+	0.917727i	$0.369978\pi$
$61$	−3.07148e10	+	5.31996e10i	−0.596168	+	1.03259i	−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	$-0.987793\pi$
$67$	−4.81995e10	−	8.34839e10i	−0.532836	−	0.922899i	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	$0.270579\pi$
$71$			1.92487e11i			1.50263i	−0.659946	+	0.751313i	$0.729421\pi$
$72$		0			0
$73$	−2.52890e11			−1.67107			−0.835535	−	0.549437i	$-0.814842\pi$
$73$	−2.52890e11			−1.67107			−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	$-0.649550\pi$
$79$	1.32683e11	−	2.29813e11i	0.545823	−	0.945393i	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	$-0.986321\pi$
$83$	−5.02122e11	−	2.89900e11i	−1.53582	−	0.886706i	−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	$-0.913213\pi$
$89$		−	2.67660e11i		−	0.538571i	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	$-0.515062\pi$
$97$	7.00867e11	−	1.21394e12i	0.841405	−	1.45736i	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	$-0.176458\pi$
$101$	8.69896e11	+	5.02234e11i	0.819481	+	0.473128i	−0.0307565	+	0.999527i	$0.509792\pi$
$102$		0			0
$103$	2.89077e11	+	5.00696e11i	0.242098	+	0.419325i	0.961312	−	0.275463i	$-0.0888312\pi$
$103$	2.89077e11	+	5.00696e11i	0.242098	+	0.419325i	−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	$0.0104512\pi$
$107$			9.85301e10i			0.0656547i	−0.999461	+	0.0328274i	$0.989549\pi$
$108$		0			0
$109$	7.74413e11			0.461757			0.230879	−	0.972983i	$-0.425840\pi$
$109$	7.74413e11			0.461757			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	$-0.903943\pi$
$113$	−2.44593e12	+	1.41216e12i	−1.17482	+	0.678285i	−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	$-0.456270\pi$
$127$	1.14926e12			0.273902			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	$-0.244737\pi$
$131$	8.49167e12	−	4.90267e12i	1.68022	−	0.970073i	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	$-0.0843085\pi$
$137$	8.07299e12	+	4.66094e12i	1.22099	+	0.704937i	0.255859	+	0.966714i	$0.417642\pi$
$138$		0			0
$139$	1.88951e12	+	3.27272e12i	0.261975	+	0.453753i	0.966767	−	0.255661i	$-0.0822930\pi$
$139$	1.88951e12	+	3.27272e12i	0.261975	+	0.453753i	−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	$-0.574261\pi$
$149$	5.42513e12	−	3.13220e12i	0.495784	−	0.286241i	0.726971	+	0.686668i	$0.240928\pi$
$150$		0			0
$151$	3.57828e12	−	6.19776e12i	0.301865	−	0.522845i	−0.674694	−	0.738098i	$-0.735724\pi$
$151$	3.57828e12	−	6.19776e12i	0.301865	−	0.522845i	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	$-0.0378702\pi$
$157$	5.89570e12	+	1.02117e13i	0.393675	+	0.681865i	−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	$-0.539688\pi$
$163$	−4.66492e12			−0.248724			−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	$-0.438527\pi$
$167$	2.46814e13	−	1.42498e13i	1.13781	−	0.656915i	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	$-0.476378\pi$
$173$	−2.01716e13	−	1.16461e13i	−0.752426	−	0.434413i	−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	$0.0165036\pi$
$179$			3.40943e12i			0.103649i	−0.998656	+	0.0518243i	$0.983496\pi$
$180$		0			0
$181$	3.21987e13			0.915730			0.457865	−	0.889022i	$-0.348614\pi$
$181$	3.21987e13			0.915730			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	$-0.328124\pi$
$191$	1.37615e12	+	7.94519e11i	0.0283442	+	0.0163645i	−0.485761	+	0.874092i	$0.661457\pi$
$192$		0			0
$193$	1.93962e13	+	3.35952e13i	0.375295	+	0.650030i	0.990371	−	0.138438i	$-0.0442081\pi$
$193$	1.93962e13	+	3.35952e13i	0.375295	+	0.650030i	−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	$0.0461216\pi$
$197$			1.68796e13i			0.288778i	−0.989521	+	0.144389i	$0.953878\pi$
$198$		0			0
$199$	−4.66159e12			−0.0750613			−0.0375306	−	0.999295i	$-0.511949\pi$
$199$	−4.66159e12			−0.0750613			−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	$-0.995407\pi$
$211$	−4.52210e13	−	7.83251e13i	−0.512443	−	0.887578i	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	$0.368130\pi$
$223$	−7.27416e13	+	1.25992e14i	−0.591499	+	1.02451i	−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	$-0.353726\pi$
$227$	−1.51717e13	−	8.75941e12i	−0.110887	−	0.0640206i	−0.554418	+	0.832239i	$0.687059\pi$
$228$		0			0
$229$	−3.91608e13	−	6.78285e13i	−0.271543	−	0.470326i	0.697714	−	0.716376i	$-0.254201\pi$
$229$	−3.91608e13	−	6.78285e13i	−0.271543	−	0.470326i	−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	$-0.898126\pi$
$233$		−	1.00679e14i		−	0.629224i	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	$-0.541745\pi$
$239$	1.23461e14	−	7.12804e13i	0.662435	−	0.382457i	0.793204	+	0.608956i	$0.208411\pi$
$240$		0			0
$241$	5.62222e13	−	9.73798e13i	0.286950	−	0.497012i	−0.686130	−	0.727479i	$-0.740692\pi$
$241$	5.62222e13	−	9.73798e13i	0.286950	−	0.497012i	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	$-0.841154\pi$
$251$		−	2.39343e14i		−	0.957148i	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	$-0.601864\pi$
$257$	1.00902e14	−	5.82558e13i	0.350188	−	0.202181i	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	$-0.392829\pi$
$263$	−1.06512e14	−	6.14948e13i	−0.321858	−	0.185825i	−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	$0.0732191\pi$
$269$			1.72775e14i			0.456003i	−0.973661	+	0.228001i	$0.926781\pi$
$270$		0			0
$271$	6.56137e14			1.65645			0.828225	−	0.560395i	$-0.189351\pi$
$271$	6.56137e14			1.65645			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	$-0.941333\pi$
$277$	−1.50345e14	+	2.60404e14i	−0.332820	+	0.576461i	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	$-0.0864189\pi$
$281$	5.97080e14	+	3.44724e14i	1.21282	+	0.700219i	0.249444	+	0.968389i	$0.419752\pi$
$282$		0			0
$283$	−1.24503e14	−	2.15646e14i	−0.242360	−	0.419781i	0.719026	−	0.694983i	$-0.244588\pi$
$283$	−1.24503e14	−	2.15646e14i	−0.242360	−	0.419781i	−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	$-0.788172\pi$
$293$	−4.08239e14	+	2.35697e14i	−0.645221	+	0.372519i	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	$-0.823095\pi$
$307$	−1.42240e15			−1.69900			−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	$-0.515783\pi$
$311$	7.15366e14	−	4.13017e14i	0.790617	−	0.456463i	0.840180	+	0.542308i	$0.182450\pi$
$312$		0			0
$313$	−6.74228e14	+	1.16780e15i	−0.717036	+	1.24194i	0.245133	+	0.969489i	$0.421168\pi$
$313$	−6.74228e14	+	1.16780e15i	−0.717036	+	1.24194i	−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	$-0.125680\pi$
$317$	1.06697e15	+	6.16014e14i	1.05147	+	0.607064i	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	$0.437027\pi$
$331$	−9.87477e14	+	1.71036e15i	−0.750860	+	1.30053i	−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	$-0.216810\pi$
$337$	−2.29797e14	−	3.98019e14i	−0.156879	−	0.271722i	−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	$-0.917709\pi$
$347$	−2.14506e15	+	1.23845e15i	−1.22875	+	0.709417i	−0.261979	+	0.965074i	$0.584375\pi$
$348$		0			0
$349$	−4.54506e13	+	7.87227e13i	−0.0251528	+	0.0435660i	−0.878328	−	0.478059i	$-0.841341\pi$
$349$	−4.54506e13	+	7.87227e13i	−0.0251528	+	0.0435660i	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	$-0.573755\pi$
$353$	−2.29734e15	−	1.32637e15i	−1.18734	−	0.685513i	−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	$-0.848182\pi$
$359$		−	1.96552e15i		−	0.918145i	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	$-0.937368\pi$
$367$	−7.84452e14	+	1.35871e15i	−0.321048	+	0.556071i	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	$-0.970048\pi$
$373$	−1.55974e15	−	2.70154e15i	−0.579159	−	1.00313i	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	$-0.502710\pi$
$379$	−5.04620e13			−0.0170266			−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	$-0.952165\pi$
$383$	−4.27200e15	+	2.46644e15i	−1.35344	+	0.781409i	−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	$-0.315886\pi$
$389$	3.28797e14	+	1.89831e14i	0.0948922	+	0.0547860i	−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	$-0.183884\pi$
$397$	6.55958e15			1.67546			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	$-0.715637\pi$
$401$	−1.10355e15	+	6.37137e14i	−0.265416	+	0.153238i	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	$-0.0642824\pi$
$409$	1.47982e15	+	2.56312e15i	0.316132	+	0.547557i	−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	$-0.634879\pi$
$419$	9.34387e14	−	5.39468e14i	0.172680	−	0.0996969i	0.583849	+	0.811862i	$0.301546\pi$
$420$		0			0
$421$	−2.23817e15	+	3.87663e15i	−0.401977	+	0.696245i	−0.993964	−	0.109703i	$-0.965010\pi$
$421$	−2.23817e15	+	3.87663e15i	−0.401977	+	0.696245i	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	$0.210257\pi$
$431$			7.86574e15i			1.22709i	−0.789660	+	0.613544i	$0.789743\pi$
$432$		0			0
$433$	−5.34544e15			−0.811066			−0.405533	−	0.914080i	$-0.632914\pi$
$433$	−5.34544e15			−0.811066			−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	$-0.962363\pi$
$439$	−2.82271e15	+	4.88908e15i	−0.394348	+	0.683030i	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	$-0.627971\pi$
$443$	−1.04600e16	−	6.03907e15i	−1.38391	−	0.799001i	−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	$0.361066\pi$
$449$			1.48510e16i			1.81250i	−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	$-0.978226\pi$
$457$	−4.00489e15	+	6.93667e15i	−0.439636	+	0.761472i	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	$-0.0989876\pi$
$461$	1.11637e16	+	6.44534e15i	1.16306	+	0.671491i	0.211022	+	0.977481i	$0.432321\pi$
$462$		0			0
$463$	−4.51163e15	−	7.81437e15i	−0.457981	−	0.793247i	0.540873	−	0.841104i	$-0.318094\pi$
$463$	−4.51163e15	−	7.81437e15i	−0.457981	−	0.793247i	−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	$0.0409059\pi$
$467$			2.65871e15i			0.256312i	−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	$-0.316015\pi$
$479$	1.13766e15	+	6.56827e14i	0.0941887	+	0.0543798i	−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	$-0.640114\pi$
$487$	−1.13689e16			−0.852207			−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	$-0.412091\pi$
$491$	1.74056e16	−	1.00491e16i	1.24222	−	0.717198i	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	$0.0465403\pi$
$499$	9.58475e15	+	1.66013e16i	0.620837	+	1.07532i	−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	$0.0351703\pi$
$503$			3.57174e15i			0.220532i	−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	$-0.664465\pi$
$509$	2.08346e14	−	1.20289e14i	0.0119806	−	0.00691702i	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	$-0.908698\pi$
$521$		−	1.13166e16i		−	0.565835i	0.959144	−	0.282917i	$-0.0913022\pi$
$522$		0			0
$523$	1.60120e16			0.782414			0.391207	−	0.920303i	$-0.372058\pi$
$523$	1.60120e16			0.782414			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	$-0.588710\pi$
$541$	−1.37943e16			−0.550195			−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	$-0.803327\pi$
$547$	2.52139e15	−	4.36718e15i	0.0941274	−	0.163034i	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	$-0.683740\pi$
$557$		−	5.00485e16i		−	1.67595i	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	$-0.828928\pi$
$563$	−2.69154e16	+	1.55396e16i	−0.845181	+	0.487966i	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	$-0.387221\pi$
$569$	−9.90375e15	−	5.71793e15i	−0.291827	−	0.168487i	−0.638766	+	0.769401i	$0.720555\pi$
$570$		0			0
$571$	2.61075e16	+	4.52196e16i	0.753267	+	1.30470i	0.946231	+	0.323491i	$0.104857\pi$
$571$	2.61075e16	+	4.52196e16i	0.753267	+	1.30470i	−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	$-0.592297\pi$
$577$	−2.11018e16			−0.571828			−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	$-0.0804898\pi$
$587$	5.05498e16	+	2.91849e16i	1.23564	+	0.713395i	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	$0.0207888\pi$
$593$			5.67583e15i			0.130527i	−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	$-0.678017\pi$
$599$	−2.85237e15	+	1.64682e15i	−0.0617511	+	0.0356520i	0.468807	+	0.883301i	$0.344684\pi$
$600$		0			0
$601$	−1.68791e16	+	2.92355e16i	−0.358182	+	0.620389i	−0.987657	−	0.156632i	$-0.949936\pi$
$601$	−1.68791e16	+	2.92355e16i	−0.358182	+	0.620389i	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	$-0.230713\pi$
$607$	−9.99643e15	−	1.73143e16i	−0.199854	−	0.346157i	−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	$-0.495568\pi$
$613$	1.47766e15			0.0278491			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	$-0.612164\pi$
$617$	1.62823e16	−	9.40058e15i	0.295124	−	0.170390i	0.640250	+	0.768166i	$0.278831\pi$
$618$		0			0
$619$	1.24568e16	−	2.15758e16i	0.221443	−	0.383551i	−0.733803	−	0.679362i	$-0.762257\pi$
$619$	1.24568e16	−	2.15758e16i	0.221443	−	0.383551i	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	$-0.321266\pi$
$631$	6.72198e16			1.06493			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	$-0.413074\pi$
$641$	−2.97844e16	−	1.71960e16i	−0.429379	−	0.247902i	−0.699082	+	0.715042i	$0.746408\pi$
$642$		0			0
$643$	4.23528e16	+	7.33572e16i	0.599261	+	1.03795i	0.992930	+	0.118698i	$0.0378722\pi$
$643$	4.23528e16	+	7.33572e16i	0.599261	+	1.03795i	−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	$0.339793\pi$
$647$			1.28516e17i			1.75199i	−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	$-0.343004\pi$
$653$	1.14204e17	−	6.59359e16i	1.47300	−	0.850438i	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	$-0.310450\pi$
$659$	1.01901e16	+	5.88324e15i	0.124413	+	0.0718297i	−0.436502	+	0.899703i	$0.643783\pi$
$660$		0			0
$661$	3.54190e16	+	6.13475e16i	0.424647	+	0.735510i	0.996387	−	0.0849247i	$-0.0270650\pi$
$661$	3.54190e16	+	6.13475e16i	0.424647	+	0.735510i	−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	$-0.993735\pi$
$673$	−4.48652e16	+	7.77089e16i	−0.482858	+	0.836335i	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	$-0.515479\pi$
$677$	−9.03018e16	−	5.21358e16i	−0.937917	−	0.541507i	−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	$0.0265714\pi$
$683$			1.69283e16i			0.166759i	−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	$-0.915674\pi$
$691$	−2.78470e16	+	4.82324e16i	−0.255805	+	0.443068i	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	$0.0167310\pi$
$701$			1.24684e16i			0.105076i	−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	$-0.623499\pi$
$709$	7.78003e16	−	1.34754e17i	0.612497	−	1.06088i	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	$0.278056\pi$
$719$			2.11824e17i			1.53321i	−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	$0.364124\pi$
$727$	−8.58243e16	+	1.48652e17i	−0.581304	+	1.00685i	−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	$-0.940141\pi$
$733$	−1.01296e17	−	1.75450e17i	−0.653086	−	1.13118i	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	$-0.550290\pi$
$739$	−5.12528e16			−0.314667			−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	$-0.797787\pi$
$743$	−1.16670e17	+	6.73595e16i	−0.693468	+	0.400374i	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	$-0.152176\pi$
$751$	8.16463e15	+	1.41416e16i	0.0455090	+	0.0788239i	−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	$-0.392585\pi$
$757$	1.24607e17			0.662169			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	$0.733343\pi$
$761$	−3.19948e17	+	1.84722e17i	−1.64729	+	0.951066i	−0.978141	+	0.207942i	$0.933323\pi$
$762$		0			0
$763$	−1.49101e16	+	2.58251e16i	−0.0755674	+	0.130887i
$764$			3.25435e15i			0.0163645i

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	162.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(39.1918 + 22.6274i) q^{2} +(1024.00 + 1773.62i) q^{4} +(23434.3 - 13529.8i) q^{5} +(-19253.5 + 33348.0i) q^{7} +92681.9i q^{8} +O(q^{10})\)	\(q+(39.1918 + 22.6274i) q^{2} +(1024.00 + 1773.62i) q^{4} +(23434.3 - 13529.8i) q^{5} +(-19253.5 + 33348.0i) q^{7} +92681.9i q^{8} +1.22458e6 q^{10} +(915145. + 528359. i) q^{11} +(-3.18495e6 - 5.51649e6i) q^{13} +(-1.50916e6 + 871312. i) q^{14} +(-2.09715e6 + 3.63237e6i) q^{16} -2.54594e6i q^{17} +1.58076e6 q^{19} +(4.79935e7 + 2.77091e7i) q^{20} +(2.39108e7 + 4.14147e7i) q^{22} +(1.09932e8 - 6.34695e7i) q^{23} +(2.44041e8 - 4.22692e8i) q^{25} -2.88268e8i q^{26} -7.88622e7 q^{28} +(-7.45261e8 - 4.30277e8i) q^{29} +(3.60891e8 + 6.25081e8i) q^{31} +(-1.64382e8 + 9.49063e7i) q^{32} +(5.76081e7 - 9.97802e7i) q^{34} +1.04198e9i q^{35} +4.10816e9 q^{37} +(6.19527e7 + 3.57684e7i) q^{38} +(1.25397e9 + 2.17194e9i) q^{40} +(-1.46816e9 + 8.47640e8i) q^{41} +(5.93232e9 - 1.02751e10i) q^{43} +2.16416e9i q^{44} +5.74461e9 q^{46} +(-7.65810e9 - 4.42141e9i) q^{47} +(6.17925e9 + 1.07028e10i) q^{49} +(1.91289e10 - 1.10440e10i) q^{50} +(6.52277e9 - 1.12978e10i) q^{52} -1.49000e10i q^{53} +2.85944e10 q^{55} +(-3.09075e9 - 1.78445e9i) q^{56} +(-1.94721e10 - 3.37267e10i) q^{58} +(5.34412e10 - 3.08543e10i) q^{59} +(-3.07148e10 + 5.31996e10i) q^{61} +3.26641e10i q^{62} -8.58993e9 q^{64} +(-1.49274e11 - 8.61835e10i) q^{65} +(-4.81995e10 - 8.34839e10i) q^{67} +(4.51554e9 - 2.60705e9i) q^{68} +(-2.35774e10 + 4.08372e10i) q^{70} +1.92487e11i q^{71} -2.52890e11 q^{73} +(1.61006e11 + 9.29570e10i) q^{74} +(1.61869e9 + 2.80366e9i) q^{76} +(-3.52394e10 + 2.03455e10i) q^{77} +(1.32683e11 - 2.29813e11i) q^{79} +1.13496e11i q^{80} -7.67196e10 q^{82} +(-5.02122e11 - 2.89900e11i) q^{83} +(-3.44461e10 - 5.96625e10i) q^{85} +(4.64997e11 - 2.68466e11i) q^{86} +(-4.89693e10 + 8.48174e10i) q^{88} -2.67660e11i q^{89} +2.45285e11 q^{91} +(2.25142e11 + 1.29986e11i) q^{92} +(-2.00090e11 - 3.46566e11i) q^{94} +(3.70439e10 - 2.13873e10i) q^{95} +(7.00867e11 - 1.21394e12i) q^{97} +5.59282e11i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8192 q^{4} - 271484 q^{7}+O(q^{10}) \) 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

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