LMFDB - Embedded newform 162.13.d.c.107.2

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			107.2
Root			$69.6972 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	162.107
Dual form			162.13.d.c.53.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

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
$5$	12529.2	−	7233.73i	0.801868	−	0.462959i	−0.0422557	−	0.999107i	$-0.513454\pi$
$5$	12529.2	−	7233.73i	0.801868	−	0.462959i	0.844124	+	0.536148i	$0.180121\pi$
$6$		0			0
$7$	−48617.5	+	84208.1i	−0.413242	+	0.715757i	−0.995242	−	0.0974322i	$-0.968937\pi$
$7$	−48617.5	+	84208.1i	−0.413242	+	0.715757i	0.582000	+	0.813189i	$0.302270\pi$
$8$		−	92681.9i		−	0.353553i
$9$		0			0
$10$	−654723.			−0.654723
$11$	1.20670e6	+	696690.i	0.681152	+	0.393263i	0.800289	−	0.599614i	$-0.204679\pi$
$11$	1.20670e6	+	696690.i	0.681152	+	0.393263i	−0.119137	+	0.992878i	$0.538013\pi$
$12$		0			0
$13$	3.01088e6	+	5.21499e6i	0.623782	+	1.08042i	0.988775	+	0.149412i	$0.0477379\pi$
$13$	3.01088e6	+	5.21499e6i	0.623782	+	1.08042i	−0.364993	+	0.931010i	$0.618929\pi$
$14$	3.81082e6	−	2.20018e6i	0.506116	−	0.292206i
$15$		0			0
$16$	−2.09715e6	+	3.63237e6i	−0.125000	+	0.216506i
$17$			2.96631e7i			1.22892i	0.788948	+	0.614460i	$0.210626\pi$
$17$			2.96631e7i			1.22892i	−0.788948	+	0.614460i	$0.789374\pi$
$18$		0			0
$19$	−4.55192e7			−0.967550			−0.483775	−	0.875192i	$-0.660735\pi$
$19$	−4.55192e7			−0.967550			−0.483775	+	0.875192i	$0.660735\pi$
$20$	2.56598e7	+	1.48147e7i	0.400934	+	0.231479i
$21$		0			0
$22$	−3.15286e7	−	5.46091e7i	−0.278079	−	0.481647i
$23$	8.46661e7	−	4.88820e7i	0.571930	−	0.330204i	−0.185990	−	0.982552i	$-0.559549\pi$
$23$	8.46661e7	−	4.88820e7i	0.571930	−	0.330204i	0.757920	+	0.652348i	$0.226216\pi$
$24$		0			0
$25$	−1.74165e7	+	3.01663e7i	−0.0713381	+	0.123561i
$26$		−	2.72513e8i		−	0.882161i
$27$		0			0
$28$	−1.99137e8			−0.413242
$29$	4.17778e8	+	2.41204e8i	0.702356	+	0.405505i	0.808224	−	0.588875i	$-0.200429\pi$
$29$	4.17778e8	+	2.41204e8i	0.702356	+	0.405505i	−0.105869	+	0.994380i	$0.533762\pi$
$30$		0			0
$31$	2.34743e8	+	4.06586e8i	0.264498	+	0.458124i	0.967432	−	0.253131i	$-0.0814605\pi$
$31$	2.34743e8	+	4.06586e8i	0.264498	+	0.458124i	−0.702934	+	0.711255i	$0.748127\pi$
$32$	1.64382e8	−	9.49063e7i	0.153093	−	0.0883883i
$33$		0			0
$34$	6.71200e8	−	1.16255e9i	0.434489	−	0.752557i
$35$			1.40675e9i			0.765257i
$36$		0			0
$37$	−4.39480e9			−1.71289			−0.856444	−	0.516240i	$-0.827331\pi$
$37$	−4.39480e9			−1.71289			−0.856444	+	0.516240i	$0.827331\pi$
$38$	1.78398e9	+	1.02998e9i	0.592501	+	0.342081i
$39$		0			0
$40$	−6.70436e8	−	1.16123e9i	−0.163681	−	0.283503i
$41$	−4.92680e9	+	2.84449e9i	−1.03720	+	0.598827i	−0.919039	−	0.394167i	$-0.871033\pi$
$41$	−4.92680e9	+	2.84449e9i	−1.03720	+	0.598827i	−0.118160	+	0.992995i	$0.537700\pi$
$42$		0			0
$43$	−2.15314e9	+	3.72934e9i	−0.340613	+	0.589959i	−0.984547	−	0.175122i	$-0.943968\pi$
$43$	−2.15314e9	+	3.72934e9i	−0.340613	+	0.589959i	0.643934	+	0.765081i	$0.277301\pi$
$44$			2.85364e9i			0.393263i
$45$		0			0
$46$	−4.42430e9			−0.466979
$47$	3.32101e9	+	1.91738e9i	0.308094	+	0.177878i	0.646073	−	0.763276i	$-0.276410\pi$
$47$	3.32101e9	+	1.91738e9i	0.308094	+	0.177878i	−0.337979	+	0.941153i	$0.609743\pi$
$48$		0			0
$49$	2.19331e9	+	3.79893e9i	0.158462	+	0.274464i
$50$	1.36517e9	−	7.88182e8i	0.0873710	−	0.0504437i
$51$		0			0
$52$	−6.16627e9	+	1.06803e10i	−0.311891	+	0.540211i
$53$		−	2.52870e10i		−	1.14089i	−0.821337	−	0.570443i	$-0.806772\pi$
$53$		−	2.52870e10i		−	1.14089i	0.821337	−	0.570443i	$-0.193228\pi$
$54$		0			0
$55$	2.01587e10			0.728259
$56$	7.80456e9	+	4.50597e9i	0.253058	+	0.146103i
$57$		0			0
$58$	−1.09156e10	−	1.89065e10i	−0.286735	−	0.496640i
$59$	−5.60254e10	+	3.23463e10i	−1.32823	+	0.766854i	−0.985026	−	0.172407i	$-0.944846\pi$
$59$	−5.60254e10	+	3.23463e10i	−1.32823	+	0.766854i	−0.343204	+	0.939261i	$0.611512\pi$
$60$		0			0
$61$	1.61241e10	−	2.79278e10i	0.312966	−	0.542072i	−0.666037	−	0.745918i	$-0.732011\pi$
$61$	1.61241e10	−	2.79278e10i	0.312966	−	0.542072i	0.979003	+	0.203846i	$0.0653442\pi$
$62$		−	2.12465e10i		−	0.374056i
$63$		0			0
$64$	−8.58993e9			−0.125000
$65$	7.54477e10	+	4.35597e10i	1.00038	+	0.577571i
$66$		0			0
$67$	−2.90443e10	−	5.03063e10i	−0.321079	−	0.556126i	0.659632	−	0.751589i	$-0.270712\pi$
$67$	−2.90443e10	−	5.03063e10i	−0.321079	−	0.556126i	−0.980711	+	0.195463i	$0.937379\pi$
$68$	−5.26111e10	+	3.03750e10i	−0.532138	+	0.307230i
$69$		0			0
$70$	3.18310e10	−	5.51329e10i	0.270559	−	0.468622i
$71$		−	3.98191e10i		−	0.310843i	−0.987848	−	0.155422i	$-0.950326\pi$
$71$		−	3.98191e10i		−	0.310843i	0.987848	−	0.155422i	$-0.0496736\pi$
$72$		0			0
$73$	1.63455e11			1.08009			0.540045	−	0.841636i	$-0.318407\pi$
$73$	1.63455e11			1.08009			0.540045	+	0.841636i	$0.318407\pi$
$74$	1.72240e11	+	9.94430e10i	1.04893	+	0.605597i
$75$		0			0
$76$	−4.66117e10	−	8.07338e10i	−0.241887	−	0.418961i
$77$	−1.17334e11	+	6.77427e10i	−0.562962	+	0.325026i
$78$		0			0
$79$	9.35920e10	−	1.62106e11i	0.385014	−	0.666863i	−0.606757	−	0.794887i	$-0.707530\pi$
$79$	9.35920e10	−	1.62106e11i	0.385014	−	0.666863i	0.991771	+	0.128024i	$0.0408633\pi$
$80$			6.06809e10i			0.231479i
$81$		0			0
$82$	2.57454e11			0.846870
$83$	−6.69378e10	−	3.86466e10i	−0.204740	−	0.118207i	0.394124	−	0.919057i	$-0.371048\pi$
$83$	−6.69378e10	−	3.86466e10i	−0.204740	−	0.118207i	−0.598865	+	0.800850i	$0.704381\pi$
$84$		0			0
$85$	2.14575e11	+	3.71655e11i	0.568939	+	0.985432i
$86$	1.68771e11	−	9.74399e10i	0.417164	−	0.240850i
$87$		0			0
$88$	6.45706e10	−	1.11839e11i	0.139040	−	0.240824i
$89$		−	9.19946e11i		−	1.85107i	−0.378665	−	0.925534i	$-0.623617\pi$
$89$		−	9.19946e11i		−	1.85107i	0.378665	−	0.925534i	$-0.376383\pi$
$90$		0			0
$91$	−5.85525e11			−1.03109
$92$	1.73396e11	+	1.00110e11i	0.285965	+	0.165102i
$93$		0			0
$94$	−8.67709e10	−	1.50292e11i	−0.125779	−	0.217855i
$95$	−5.70319e11	+	3.29274e11i	−0.775848	+	0.447936i
$96$		0			0
$97$	7.16954e11	−	1.24180e12i	0.860718	−	1.49081i	−0.0105198	−	0.999945i	$-0.503349\pi$
$97$	7.16954e11	−	1.24180e12i	0.860718	−	1.49081i	0.871237	−	0.490862i	$-0.163318\pi$
$98$		−	1.98516e11i		−	0.224099i
$99$		0			0
$100$	−7.13381e10			−0.0713381
$101$	−8.20501e11	−	4.73716e11i	−0.772949	−	0.446262i	0.0609766	−	0.998139i	$-0.480579\pi$
$101$	−8.20501e11	−	4.73716e11i	−0.772949	−	0.446262i	−0.833926	+	0.551877i	$0.813912\pi$
$102$		0			0
$103$	−9.26886e11	−	1.60541e12i	−0.776252	−	1.34451i	−0.934088	−	0.357043i	$-0.883785\pi$
$103$	−9.26886e11	−	1.60541e12i	−0.776252	−	1.34451i	0.157836	−	0.987465i	$-0.449548\pi$
$104$	4.83335e11	−	2.79054e11i	0.381987	−	0.220540i
$105$		0			0
$106$	−5.72180e11	+	9.91044e11i	−0.403364	+	0.698647i
$107$			2.27324e12i			1.51475i	0.652977	+	0.757377i	$0.273520\pi$
$107$			2.27324e12i			1.51475i	−0.652977	+	0.757377i	$0.726480\pi$
$108$		0			0
$109$	−2.04503e11			−0.121938			−0.0609692	−	0.998140i	$-0.519419\pi$
$109$	−2.04503e11			−0.121938			−0.0609692	+	0.998140i	$0.519419\pi$
$110$	−7.90056e11	−	4.56139e11i	−0.445966	−	0.257478i
$111$		0			0
$112$	−2.03917e11	−	3.53194e11i	−0.103311	−	0.178939i
$113$	−2.45337e11	+	1.41645e11i	−0.117840	+	0.0680349i	−0.557761	−	0.830001i	$-0.688340\pi$
$113$	−2.45337e11	+	1.41645e11i	−0.117840	+	0.0680349i	0.439922	+	0.898036i	$0.355006\pi$
$114$		0			0
$115$	7.07199e11	−	1.22490e12i	0.305742	−	0.529560i
$116$			9.87971e11i			0.405505i
$117$		0			0
$118$	2.92765e12			1.08450
$119$	−2.49787e12	−	1.44215e12i	−0.879607	−	0.507842i
$120$		0			0
$121$	−5.98460e11	−	1.03656e12i	−0.190688	−	0.330281i
$122$	−1.26387e12	+	7.29693e11i	−0.383303	+	0.221300i
$123$		0			0
$124$	−4.80753e11	+	8.32689e11i	−0.132249	+	0.229062i
$125$			4.03604e12i			1.05802i
$126$		0			0
$127$	−3.29909e12			−0.786271			−0.393136	−	0.919480i	$-0.628610\pi$
$127$	−3.29909e12			−0.786271			−0.393136	+	0.919480i	$0.628610\pi$
$128$	3.36655e11	+	1.94368e11i	0.0765466	+	0.0441942i
$129$		0			0
$130$	−1.97129e12	−	3.41437e12i	−0.408404	−	0.707377i
$131$	6.04050e12	−	3.48748e12i	1.19521	−	0.690056i	0.235728	−	0.971819i	$-0.424253\pi$
$131$	6.04050e12	−	3.48748e12i	1.19521	−	0.690056i	0.959484	+	0.281763i	$0.0909193\pi$
$132$		0			0
$133$	2.21303e12	−	3.83309e12i	0.399833	−	0.692530i
$134$			2.62879e12i			0.454075i
$135$		0			0
$136$	2.74924e12			0.434489
$137$	2.35726e12	+	1.36097e12i	0.356520	+	0.205837i	0.667553	−	0.744562i	$-0.267342\pi$
$137$	2.35726e12	+	1.36097e12i	0.356520	+	0.205837i	−0.311033	+	0.950399i	$0.600675\pi$
$138$		0			0
$139$	5.02531e12	+	8.70410e12i	0.696746	+	1.20680i	0.969589	+	0.244740i	$0.0787027\pi$
$139$	5.02531e12	+	8.70410e12i	0.696746	+	1.20680i	−0.272843	+	0.962059i	$0.587964\pi$
$140$	−2.49503e12	+	1.44051e12i	−0.331366	+	0.191314i
$141$		0			0
$142$	−9.01004e11	+	1.56058e12i	−0.109900	+	0.190352i
$143$			8.39059e12i			0.981242i
$144$		0			0
$145$	6.97922e12			0.750929
$146$	−6.40609e12	−	3.69856e12i	−0.661418	−	0.381870i
$147$		0			0
$148$	−4.50028e12	−	7.79471e12i	−0.428222	−	0.741702i
$149$	−1.40788e13	+	8.12840e12i	−1.28661	+	0.742827i	−0.978049	−	0.208376i	$-0.933182\pi$
$149$	−1.40788e13	+	8.12840e12i	−1.28661	+	0.742827i	−0.308565	+	0.951203i	$0.599849\pi$
$150$		0			0
$151$	4.73231e12	−	8.19660e12i	0.399219	−	0.691468i	−0.594410	−	0.804162i	$-0.702614\pi$
$151$	4.73231e12	−	8.19660e12i	0.399219	−	0.691468i	0.993630	+	0.112694i	$0.0359478\pi$
$152$			4.21881e12i			0.342081i
$153$		0			0
$154$	6.13137e12			0.459656
$155$	5.88227e12	+	3.39613e12i	0.424185	+	0.244903i
$156$		0			0
$157$	9.22889e12	+	1.59849e13i	0.616242	+	1.06736i	0.990165	+	0.139903i	$0.0446792\pi$
$157$	9.22889e12	+	1.59849e13i	0.616242	+	1.06736i	−0.373923	+	0.927460i	$0.621987\pi$
$158$	−7.33609e12	+	4.23549e12i	−0.471544	+	0.272246i
$159$		0			0
$160$	1.37305e12	−	2.37820e12i	0.0818403	−	0.141752i
$161$			9.50609e12i			0.545817i
$162$		0			0
$163$	−1.76328e13			−0.940145			−0.470073	−	0.882628i	$-0.655772\pi$
$163$	−1.76328e13			−0.940145			−0.470073	+	0.882628i	$0.655772\pi$
$164$	−1.00901e13	−	5.82552e12i	−0.518600	−	0.299414i
$165$		0			0
$166$	1.74894e12	+	3.02926e12i	0.0835848	+	0.144773i
$167$	−3.53071e13	+	2.03845e13i	−1.62766	+	0.939728i	−0.642867	+	0.765978i	$0.722255\pi$
$167$	−3.53071e13	+	2.03845e13i	−1.62766	+	0.939728i	−0.984790	+	0.173750i	$0.944412\pi$
$168$		0			0
$169$	−6.48170e12	+	1.12266e13i	−0.278207	+	0.481869i
$170$		−	1.94211e13i		−	0.804602i
$171$		0			0
$172$	−8.81925e12			−0.340613
$173$	−2.65381e13	−	1.53218e13i	−0.989905	−	0.571522i	−0.0846590	−	0.996410i	$-0.526980\pi$
$173$	−2.65381e13	−	1.53218e13i	−0.989905	−	0.571522i	−0.905246	+	0.424888i	$0.860313\pi$
$174$		0			0
$175$	−1.69350e12	−	2.93322e12i	−0.0589599	−	0.102121i
$176$	−5.06128e12	+	2.92213e12i	−0.170288	+	0.0983158i
$177$		0			0
$178$	−2.08160e13	+	3.60544e13i	−0.654451	+	1.13354i
$179$		−	2.05014e13i		−	0.623254i	−0.950204	−	0.311627i	$-0.899126\pi$
$179$		−	2.05014e13i		−	0.623254i	0.950204	−	0.311627i	$-0.100874\pi$
$180$		0			0
$181$	−4.90808e13			−1.39585			−0.697927	−	0.716169i	$-0.745894\pi$
$181$	−4.90808e13			−1.39585			−0.697927	+	0.716169i	$0.745894\pi$
$182$	2.29478e13	+	1.32489e13i	0.631412	+	0.364546i
$183$		0			0
$184$	−4.53048e12	−	7.84702e12i	−0.116745	−	0.202208i
$185$	−5.50633e13	+	3.17908e13i	−1.37351	+	0.792997i
$186$		0			0
$187$	−2.06660e13	+	3.57946e13i	−0.483289	+	0.837081i
$188$			7.85361e12i			0.177878i
$189$		0			0
$190$	2.98025e13			0.633477
$191$	3.85302e13	+	2.22454e13i	0.793600	+	0.458185i	0.841228	−	0.540680i	$-0.181833\pi$
$191$	3.85302e13	+	2.22454e13i	0.793600	+	0.458185i	−0.0476285	+	0.998865i	$0.515166\pi$
$192$		0			0
$193$	−2.82943e12	−	4.90072e12i	−0.0547464	−	0.0948235i	0.837353	−	0.546662i	$-0.184102\pi$
$193$	−2.82943e12	−	4.90072e12i	−0.0547464	−	0.0948235i	−0.892100	+	0.451838i	$0.850768\pi$
$194$	−5.61975e13	+	3.24456e13i	−1.05416	+	0.608619i
$195$		0			0
$196$	−4.49190e12	+	7.78021e12i	−0.0792308	+	0.137232i
$197$			4.31845e13i			0.738806i	0.929269	+	0.369403i	$0.120438\pi$
$197$			4.31845e13i			0.738806i	−0.929269	+	0.369403i	$0.879562\pi$
$198$		0			0
$199$	4.74962e13			0.764787			0.382394	−	0.924000i	$-0.375100\pi$
$199$	4.74962e13			0.764787			0.382394	+	0.924000i	$0.375100\pi$
$200$	2.79587e12	+	1.61420e12i	0.0436855	+	0.0252218i
$201$		0			0
$202$	2.14380e13	+	3.71316e13i	0.315555	+	0.546558i
$203$	−4.06226e13	+	2.34535e13i	−0.580486	+	0.335144i
$204$		0			0
$205$	−4.11526e13	+	7.12784e13i	−0.554465	+	0.960361i
$206$			8.38921e13i			1.09779i
$207$		0			0
$208$	−2.52571e13			−0.311891
$209$	−5.49282e13	−	3.17128e13i	−0.659049	−	0.380502i
$210$		0			0
$211$	−1.39456e13	−	2.41545e13i	−0.158031	−	0.273718i	0.776127	−	0.630576i	$-0.217181\pi$
$211$	−1.39456e13	−	2.41545e13i	−0.158031	−	0.273718i	−0.934159	+	0.356858i	$0.883848\pi$
$212$	4.48495e13	−	2.58939e13i	0.494018	−	0.285221i
$213$		0			0
$214$	5.14375e13	−	8.90924e13i	0.535547	−	0.927594i
$215$			6.23009e13i			0.630759i
$216$		0			0
$217$	−4.56505e13			−0.437207
$218$	8.01484e12	+	4.62737e12i	0.0746717	+	0.0431117i
$219$		0			0
$220$	2.06425e13	+	3.57538e13i	0.182065	+	0.315345i
$221$	−1.54693e14	+	8.93120e13i	−1.32775	+	0.766578i
$222$		0			0
$223$	5.37603e13	−	9.31156e13i	0.437152	−	0.757170i	−0.560316	−	0.828279i	$-0.689320\pi$
$223$	5.37603e13	−	9.31156e13i	0.437152	−	0.757170i	0.997469	+	0.0711088i	$0.0226538\pi$
$224$			1.84564e13i			0.146103i
$225$		0			0
$226$	1.28203e13			0.0962159
$227$	−2.29884e14	−	1.32723e14i	−1.68017	−	0.970047i	−0.961544	−	0.274650i	$-0.911438\pi$
$227$	−2.29884e14	−	1.32723e14i	−1.68017	−	0.970047i	−0.718626	−	0.695397i	$-0.755229\pi$
$228$		0			0
$229$	3.94551e13	+	6.83382e13i	0.273583	+	0.473860i	0.969777	−	0.243994i	$-0.0784577\pi$
$229$	3.94551e13	+	6.83382e13i	0.273583	+	0.473860i	−0.696193	+	0.717854i	$0.745124\pi$
$230$	−5.54328e13	+	3.20042e13i	−0.374455	+	0.216192i
$231$		0			0
$232$	2.23552e13	−	3.87204e13i	0.143368	−	0.248320i
$233$			3.12595e14i			1.95365i	0.214040	+	0.976825i	$0.431338\pi$
$233$			3.12595e14i			1.95365i	−0.214040	+	0.976825i	$0.568662\pi$
$234$		0			0
$235$	5.54794e13			0.329401
$236$	−1.14740e14	−	6.62452e13i	−0.664115	−	0.383427i
$237$		0			0
$238$	6.52642e13	+	1.13041e14i	0.359098	+	0.621976i
$239$	−2.32962e14	+	1.34501e14i	−1.24996	+	0.721667i	−0.971102	−	0.238664i	$-0.923291\pi$
$239$	−2.32962e14	+	1.34501e14i	−1.24996	+	0.721667i	−0.278862	+	0.960331i	$0.589957\pi$
$240$		0			0
$241$	−1.04212e14	+	1.80500e14i	−0.531880	+	0.921244i	0.467427	+	0.884032i	$0.345181\pi$
$241$	−1.04212e14	+	1.80500e14i	−0.531880	+	0.921244i	−0.999307	+	0.0372122i	$0.988152\pi$
$242$			5.41664e13i			0.269673i
$243$		0			0
$244$	6.60443e13			0.312966
$245$	5.49609e13	+	3.17317e13i	0.254131	+	0.146722i
$246$		0			0
$247$	−1.37053e14	−	2.37382e14i	−0.603540	−	1.04536i
$248$	3.76832e13	−	2.17564e13i	0.161971	−	0.0935141i
$249$		0			0
$250$	9.13252e13	−	1.58180e14i	0.374068	−	0.647905i
$251$			2.11752e14i			0.846809i	0.905941	+	0.423404i	$0.139165\pi$
$251$			2.11752e14i			0.846809i	−0.905941	+	0.423404i	$0.860835\pi$
$252$		0			0
$253$	1.36222e14			0.519428
$254$	1.29298e14	+	7.46500e13i	0.481491	+	0.277989i
$255$		0			0
$256$	−8.79609e12	−	1.52353e13i	−0.0312500	−	0.0541266i
$257$	2.71787e14	−	1.56916e14i	0.943255	−	0.544589i	0.0522760	−	0.998633i	$-0.483352\pi$
$257$	2.71787e14	−	1.56916e14i	0.943255	−	0.544589i	0.890979	+	0.454044i	$0.150019\pi$
$258$		0			0
$259$	2.13664e14	−	3.70078e14i	0.707838	−	1.22601i
$260$			1.78421e14i			0.577571i
$261$		0			0
$262$	−3.15651e14			−0.975886
$263$	−3.99989e14	−	2.30934e14i	−1.20869	−	0.697835i	−0.246214	−	0.969216i	$-0.579187\pi$
$263$	−3.99989e14	−	2.30934e14i	−1.20869	−	0.697835i	−0.962472	+	0.271380i	$0.912520\pi$
$264$		0			0
$265$	−1.82919e14	−	3.16826e14i	−0.528183	−	0.914840i
$266$	−1.73466e14	+	1.00150e14i	−0.489693	+	0.282724i
$267$		0			0
$268$	5.94828e13	−	1.03027e14i	0.160540	−	0.278063i
$269$			1.40054e14i			0.369642i	0.982772	+	0.184821i	$0.0591706\pi$
$269$			1.40054e14i			0.369642i	−0.982772	+	0.184821i	$0.940829\pi$
$270$		0			0
$271$	1.78016e14			0.449411			0.224706	−	0.974427i	$-0.427858\pi$
$271$	1.78016e14			0.449411			0.224706	+	0.974427i	$0.427858\pi$
$272$	−1.07748e14	−	6.22081e13i	−0.266069	−	0.153615i
$273$		0			0
$274$	−6.15903e13	−	1.06678e14i	−0.145549	−	0.252098i
$275$	−4.20332e13	+	2.42679e13i	−0.0971842	+	0.0561093i
$276$		0			0
$277$	−2.70621e14	+	4.68729e14i	−0.599077	+	1.03763i	0.393880	+	0.919162i	$0.371132\pi$
$277$	−2.70621e14	+	4.68729e14i	−0.599077	+	1.03763i	−0.992958	+	0.118471i	$0.962201\pi$
$278$		−	4.54839e14i		−	0.985347i
$279$		0			0
$280$	1.30380e14			0.270559
$281$	5.26175e14	+	3.03787e14i	1.06879	+	0.617066i	0.927850	−	0.372953i	$-0.121655\pi$
$281$	5.26175e14	+	3.03787e14i	1.06879	+	0.617066i	0.140939	+	0.990018i	$0.454988\pi$
$282$		0			0
$283$	−2.46102e13	−	4.26261e13i	−0.0479067	−	0.0829769i	0.841078	−	0.540914i	$-0.181922\pi$
$283$	−2.46102e13	−	4.26261e13i	−0.0479067	−	0.0829769i	−0.888984	+	0.457937i	$0.848588\pi$
$284$	7.06240e13	−	4.07748e13i	0.134599	−	0.0777108i
$285$		0			0
$286$	1.89857e14	−	3.28843e14i	0.346921	−	0.600886i
$287$		−	5.53169e14i		−	0.989843i
$288$		0			0
$289$	−2.97279e14			−0.510243
$290$	−2.73528e14	−	1.57922e14i	−0.459848	−	0.265493i
$291$		0			0
$292$	1.67378e14	+	2.89907e14i	0.270023	+	0.467693i
$293$	−5.49782e14	+	3.17417e14i	−0.868931	+	0.501677i	−0.866993	−	0.498321i	$-0.833950\pi$
$293$	−5.49782e14	+	3.17417e14i	−0.868931	+	0.501677i	−0.00193795	+	0.999998i	$0.500617\pi$
$294$		0			0
$295$	−4.67969e14	+	8.10546e14i	−0.710044	+	1.22983i
$296$			4.07319e14i			0.605597i
$297$		0			0
$298$	7.35699e14			1.05052
$299$	5.09838e14	+	2.94355e14i	0.713519	+	0.411950i
$300$		0			0
$301$	−2.09361e14	−	3.62623e14i	−0.281511	−	0.487592i
$302$	−3.70936e14	+	2.14160e14i	−0.488942	+	0.282291i
$303$		0			0
$304$	9.54608e13	−	1.65343e14i	0.120944	−	0.209481i
$305$		−	4.66550e14i		−	0.579561i
$306$		0			0
$307$	−1.14005e15			−1.36174			−0.680871	−	0.732403i	$-0.738399\pi$
$307$	−1.14005e15			−1.36174			−0.680871	+	0.732403i	$0.738399\pi$
$308$	−2.40300e14	−	1.38737e14i	−0.281481	−	0.162513i
$309$		0			0
$310$	−1.53691e14	−	2.66201e14i	−0.173173	−	0.299944i
$311$	6.83695e14	−	3.94731e14i	0.755614	−	0.436254i	−0.0721048	−	0.997397i	$-0.522972\pi$
$311$	6.83695e14	−	3.94731e14i	0.755614	−	0.436254i	0.827719	+	0.561143i	$0.189638\pi$
$312$		0			0
$313$	5.76629e14	−	9.98750e14i	0.613240	−	1.06216i	−0.377451	−	0.926030i	$-0.623199\pi$
$313$	5.76629e14	−	9.98750e14i	0.613240	−	1.06216i	0.990691	−	0.136133i	$-0.0434673\pi$
$314$		−	8.35304e14i		−	0.871498i
$315$		0			0
$316$	3.83353e14			0.385014
$317$	9.76548e14	+	5.63810e14i	0.962361	+	0.555619i	0.896899	−	0.442236i	$-0.145815\pi$
$317$	9.76548e14	+	5.63810e14i	0.962361	+	0.555619i	0.0654618	+	0.997855i	$0.479148\pi$
$318$		0			0
$319$	3.36089e14	+	5.82123e14i	0.318941	+	0.552421i
$320$	−1.07625e14	+	6.21373e13i	−0.100234	+	0.0578699i
$321$		0			0
$322$	2.15098e14	−	3.72561e14i	0.192975	−	0.334243i
$323$		−	1.35024e15i		−	1.18904i
$324$		0			0
$325$	−2.09756e14			−0.177998
$326$	6.91061e14	+	3.98984e14i	0.575719	+	0.332392i
$327$		0			0
$328$	2.63633e14	+	4.56626e14i	0.211717	+	0.366705i
$329$	−3.22918e14	+	1.86437e14i	−0.254635	+	0.147013i
$330$		0			0
$331$	6.91154e14	−	1.19711e15i	0.525541	−	0.910264i	−0.474016	−	0.880516i	$-0.657196\pi$
$331$	6.91154e14	−	1.19711e15i	0.525541	−	0.910264i	0.999557	−	0.0297477i	$-0.00947039\pi$
$332$		−	1.58296e14i		−	0.118207i
$333$		0			0
$334$	1.84500e15			1.32898
$335$	−7.27804e14	−	4.20198e14i	−0.514927	−	0.297293i
$336$		0			0
$337$	2.46463e14	+	4.26886e14i	0.168256	+	0.291429i	0.937807	−	0.347157i	$-0.112853\pi$
$337$	2.46463e14	+	4.26886e14i	0.168256	+	0.291429i	−0.769550	+	0.638586i	$0.779520\pi$
$338$	5.08059e14	−	2.93328e14i	0.340733	−	0.196722i
$339$		0			0
$340$	−4.39450e14	+	7.61150e14i	−0.284470	+	0.492716i
$341$			6.54172e14i			0.416069i
$342$		0			0
$343$	−1.77239e15			−1.08842
$344$	3.45643e14	+	1.99557e14i	0.208582	+	0.120425i
$345$		0			0
$346$	6.93385e14	+	1.20098e15i	0.404127	+	0.699968i
$347$	2.19672e15	−	1.26828e15i	1.25834	−	0.726504i	0.285590	−	0.958352i	$-0.407810\pi$
$347$	2.19672e15	−	1.26828e15i	1.25834	−	0.726504i	0.972752	+	0.231848i	$0.0744771\pi$
$348$		0			0
$349$	−1.16998e15	+	2.02647e15i	−0.647481	+	1.12147i	0.336241	+	0.941776i	$0.390844\pi$
$349$	−1.16998e15	+	2.02647e15i	−0.647481	+	1.12147i	−0.983723	+	0.179694i	$0.942489\pi$
$350$			1.53278e14i			0.0833818i
$351$		0			0
$352$	2.64481e14			0.139040
$353$	−9.07166e14	−	5.23753e14i	−0.468855	−	0.270694i	0.246905	−	0.969040i	$-0.420586\pi$
$353$	−9.07166e14	−	5.23753e14i	−0.468855	−	0.270694i	−0.715760	+	0.698346i	$0.753920\pi$
$354$		0			0
$355$	−2.88041e14	−	4.98901e14i	−0.143908	−	0.249255i
$356$	1.63163e15	−	9.42025e14i	0.801536	−	0.462767i
$357$		0			0
$358$	−4.63894e14	+	8.03487e14i	−0.220354	+	0.381664i
$359$		−	1.80008e15i		−	0.840861i	−0.907325	−	0.420431i	$-0.861879\pi$
$359$		−	1.80008e15i		−	0.840861i	0.907325	−	0.420431i	$-0.138121\pi$
$360$		0			0
$361$	−1.41314e14			−0.0638472
$362$	1.92357e15	+	1.11057e15i	0.854783	+	0.493509i
$363$		0			0
$364$	−5.99578e14	−	1.03850e15i	−0.257773	−	0.446476i
$365$	2.04796e15	−	1.18239e15i	0.866091	−	0.500038i
$366$		0			0
$367$	−1.63875e15	+	2.83839e15i	−0.670680	+	1.16165i	0.307032	+	0.951699i	$0.400664\pi$
$367$	−1.63875e15	+	2.83839e15i	−0.670680	+	1.16165i	−0.977712	+	0.209952i	$0.932669\pi$
$368$			4.10052e14i			0.165102i
$369$		0			0
$370$	2.87738e15			1.12147
$371$	2.12937e15	+	1.22939e15i	0.816596	+	0.471462i
$372$		0			0
$373$	7.38996e14	+	1.27998e15i	0.274403	+	0.475280i	0.969984	−	0.243167i	$-0.0781864\pi$
$373$	7.38996e14	+	1.27998e15i	0.274403	+	0.475280i	−0.695581	+	0.718448i	$0.744853\pi$
$374$	1.61988e15	−	9.35237e14i	0.591906	−	0.341737i
$375$		0			0
$376$	1.77707e14	−	3.07797e14i	0.0628893	−	0.108928i
$377$			2.90494e15i			1.01179i
$378$		0			0
$379$	−5.85878e15			−1.97684			−0.988420	−	0.151741i	$-0.951512\pi$
$379$	−5.85878e15			−1.97684			−0.988420	+	0.151741i	$0.951512\pi$
$380$	−1.16801e15	−	6.74353e14i	−0.387924	−	0.223968i
$381$		0			0
$382$	−1.00671e15	−	1.74368e15i	−0.323986	−	0.561160i
$383$	1.51358e15	−	8.73864e14i	0.479526	−	0.276854i	−0.240693	−	0.970601i	$-0.577375\pi$
$383$	1.51358e15	−	8.73864e14i	0.479526	−	0.276854i	0.720219	+	0.693747i	$0.244041\pi$
$384$		0			0
$385$	−9.80065e14	+	1.69752e15i	−0.300947	+	0.521256i
$386$			2.56091e14i			0.0774230i
$387$		0			0
$388$	2.93664e15			0.860718
$389$	−1.79778e14	−	1.03795e14i	−0.0518846	−	0.0299556i	0.473833	−	0.880615i	$-0.342870\pi$
$389$	−1.79778e14	−	1.03795e14i	−0.0518846	−	0.0299556i	−0.525718	+	0.850659i	$0.676203\pi$
$390$		0			0
$391$	1.44999e15	+	2.51146e15i	0.405794	+	0.702856i
$392$	3.52092e14	−	2.03280e14i	0.0970375	−	0.0560246i
$393$		0			0
$394$	9.77153e14	−	1.69248e15i	0.261207	−	0.452424i
$395$		−	2.70808e15i		−	0.712982i
$396$		0			0
$397$	−4.92065e15			−1.25684			−0.628419	−	0.777875i	$-0.716297\pi$
$397$	−4.92065e15			−1.25684			−0.628419	+	0.777875i	$0.716297\pi$
$398$	−1.86146e15	−	1.07472e15i	−0.468334	−	0.270393i
$399$		0			0
$400$	−7.30502e13	−	1.26527e14i	−0.0178345	−	0.0308903i
$401$	5.83715e15	−	3.37008e15i	1.40389	−	0.810538i	0.409104	−	0.912488i	$-0.365841\pi$
$401$	5.83715e15	−	3.37008e15i	1.40389	−	0.810538i	0.994790	+	0.101949i	$0.0325079\pi$
$402$		0			0
$403$	−1.41356e15	+	2.44836e15i	−0.329978	+	0.571538i
$404$		−	1.94034e15i		−	0.446262i
$405$		0			0
$406$	2.12277e15			0.473965
$407$	−5.30322e15	−	3.06181e15i	−1.16674	−	0.673616i
$408$		0			0
$409$	−2.42365e15	−	4.19789e15i	−0.517763	−	0.896791i	−0.999787	−	0.0206335i	$-0.993432\pi$
$409$	−2.42365e15	−	4.19789e15i	−0.517763	−	0.896791i	0.482024	−	0.876158i	$-0.339902\pi$
$410$	3.22569e15	−	1.86235e15i	0.679078	−	0.392066i
$411$		0			0
$412$	1.89826e15	−	3.28789e15i	0.388126	−	0.672254i
$413$		−	6.29039e15i		−	1.26759i
$414$		0			0
$415$	−1.11824e15			−0.218900
$416$	9.89870e14	+	5.71502e14i	0.190993	+	0.110270i
$417$		0			0
$418$	1.43516e15	+	2.48577e15i	0.269056	+	0.466018i
$419$	4.45459e15	−	2.57186e15i	0.823234	−	0.475294i	−0.0282963	−	0.999600i	$-0.509008\pi$
$419$	4.45459e15	−	2.57186e15i	0.823234	−	0.475294i	0.851530	+	0.524305i	$0.175675\pi$
$420$		0			0
$421$	−8.05297e13	+	1.39482e14i	−0.0144632	+	0.0250509i	−0.873166	−	0.487422i	$-0.837937\pi$
$421$	−8.05297e13	+	1.39482e14i	−0.0144632	+	0.0250509i	0.858703	+	0.512473i	$0.171271\pi$
$422$			1.26221e15i			0.223490i
$423$		0			0
$424$	−2.34365e15			−0.403364
$425$	−8.94828e14	−	5.16629e14i	−0.151847	−	0.0876688i
$426$		0			0
$427$	1.56783e15	+	2.71556e15i	0.258661	+	0.448014i
$428$	−4.03186e15	+	2.32780e15i	−0.655908	+	0.378689i
$429$		0			0
$430$	1.40971e15	−	2.44169e15i	0.223007	−	0.386260i
$431$		−	6.68591e15i		−	1.04303i	−0.853242	−	0.521515i	$-0.825367\pi$
$431$		−	6.68591e15i		−	1.04303i	0.853242	−	0.521515i	$-0.174633\pi$
$432$		0			0
$433$	5.39263e15			0.818226			0.409113	−	0.912484i	$-0.365838\pi$
$433$	5.39263e15			0.818226			0.409113	+	0.912484i	$0.365838\pi$
$434$	1.78913e15	+	1.03295e15i	0.267733	+	0.154576i
$435$		0			0
$436$	−2.09411e14	−	3.62710e14i	−0.0304846	−	0.0528009i
$437$	−3.85394e15	+	2.22507e15i	−0.553371	+	0.319489i
$438$		0			0
$439$	5.03987e15	−	8.72931e15i	0.704096	−	1.21953i	−0.262920	−	0.964818i	$-0.584686\pi$
$439$	5.03987e15	−	8.72931e15i	0.704096	−	1.21953i	0.967017	−	0.254713i	$-0.0819811\pi$
$440$		−	1.86834e15i		−	0.257478i
$441$		0			0
$442$	8.08360e15			1.08410
$443$	8.85904e15	+	5.11477e15i	1.17210	+	0.676712i	0.954174	−	0.299254i	$-0.0967378\pi$
$443$	8.85904e15	+	5.11477e15i	1.17210	+	0.676712i	0.217925	+	0.975965i	$0.430071\pi$
$444$		0			0
$445$	−6.65464e15	−	1.15262e16i	−0.856968	−	1.48431i
$446$	−4.21393e15	+	2.43291e15i	−0.535400	+	0.309113i
$447$		0			0
$448$	4.17622e14	−	7.23342e14i	0.0516553	−	0.0894696i
$449$			7.99330e15i			0.975547i	0.872970	+	0.487773i	$0.162191\pi$
$449$			7.99330e15i			0.975547i	−0.872970	+	0.487773i	$0.837809\pi$
$450$		0			0
$451$	−7.92692e15			−0.941987
$452$	−5.02450e14	−	2.90090e14i	−0.0589199	−	0.0340174i
$453$		0			0
$454$	6.00638e15	+	1.04034e16i	0.685927	+	1.18806i
$455$	−7.33616e15	+	4.23553e15i	−0.826800	+	0.477353i
$456$		0			0
$457$	−4.13927e15	+	7.16943e15i	−0.454388	+	0.787023i	−0.998653	−	0.0518906i	$-0.983475\pi$
$457$	−4.13927e15	+	7.16943e15i	−0.454388	+	0.787023i	0.544265	+	0.838913i	$0.316809\pi$
$458$		−	3.57106e15i		−	0.386905i
$459$		0			0
$460$	2.89669e15			0.305742
$461$	1.09173e16	+	6.30311e15i	1.13739	+	0.656673i	0.945783	−	0.324799i	$-0.105297\pi$
$461$	1.09173e16	+	6.30311e15i	1.13739	+	0.656673i	0.191607	+	0.981472i	$0.438630\pi$
$462$		0			0
$463$	3.48265e15	+	6.03212e15i	0.353528	+	0.612328i	0.986865	−	0.161548i	$-0.0516486\pi$
$463$	3.48265e15	+	6.03212e15i	0.353528	+	0.612328i	−0.633337	+	0.773876i	$0.718315\pi$
$464$	−1.75229e15	+	1.01168e15i	−0.175589	+	0.101376i
$465$		0			0
$466$	7.07322e15	−	1.22512e16i	0.690720	−	1.19636i
$467$			1.26089e16i			1.21556i	0.794106	+	0.607779i	$0.207939\pi$
$467$			1.26089e16i			1.21556i	−0.794106	+	0.607779i	$0.792061\pi$
$468$		0			0
$469$	5.64826e15			0.530734
$470$	−2.17434e15	−	1.25536e15i	−0.201716	−	0.116461i
$471$		0			0
$472$	2.99792e15	+	5.19254e15i	0.271124	+	0.469600i
$473$	−5.19640e15	+	3.00014e15i	−0.464019	+	0.267901i
$474$		0			0
$475$	7.92787e14	−	1.37315e15i	0.0690232	−	0.119552i
$476$		−	5.90704e15i		−	0.507842i
$477$		0			0
$478$	1.21736e16			1.02059
$479$	3.32071e15	+	1.91721e15i	0.274927	+	0.158729i	0.631125	−	0.775681i	$-0.282594\pi$
$479$	3.32071e15	+	1.91721e15i	0.274927	+	0.158729i	−0.356197	+	0.934411i	$0.615927\pi$
$480$		0			0
$481$	−1.32322e16	−	2.29188e16i	−1.06847	−	1.85064i
$482$	8.16849e15	−	4.71608e15i	0.651418	−	0.376096i
$483$		0			0
$484$	1.22565e15	−	2.12288e15i	0.0953439	−	0.165141i
$485$		−	2.07450e16i		−	1.59391i
$486$		0			0
$487$	1.99630e15			0.149641			0.0748207	−	0.997197i	$-0.476162\pi$
$487$	1.99630e15			0.149641			0.0748207	+	0.997197i	$0.476162\pi$
$488$	−2.58840e15	−	1.49441e15i	−0.191651	−	0.110650i
$489$		0			0
$490$	−1.43601e15	−	2.48725e15i	−0.103748	−	0.179698i
$491$	−5.72082e15	+	3.30292e15i	−0.408290	+	0.235727i	−0.690055	−	0.723757i	$-0.742414\pi$
$491$	−5.72082e15	+	3.30292e15i	−0.408290	+	0.235727i	0.281764	+	0.959484i	$0.409080\pi$
$492$		0			0
$493$	−7.15486e15	+	1.23926e16i	−0.498333	+	0.863139i
$494$			1.24046e16i			0.853534i
$495$		0			0
$496$	−1.96916e15			−0.132249
$497$	3.35309e15	+	1.93591e15i	0.222488	+	0.128454i
$498$		0			0
$499$	−1.00653e16	−	1.74336e16i	−0.651963	−	1.12923i	−0.982646	−	0.185491i	$-0.940612\pi$
$499$	−1.00653e16	−	1.74336e16i	−0.651963	−	1.12923i	0.330683	−	0.943742i	$-0.392721\pi$
$500$	−7.15841e15	+	4.13291e15i	−0.458138	+	0.264506i
$501$		0			0
$502$	4.79140e15	−	8.29895e15i	0.299392	−	0.518562i
$503$			1.72099e16i			1.06260i	0.847184	+	0.531300i	$0.178296\pi$
$503$			1.72099e16i			1.06260i	−0.847184	+	0.531300i	$0.821704\pi$
$504$		0			0
$505$	−1.37070e16			−0.826404
$506$	−5.33881e15	−	3.08236e15i	−0.318084	−	0.183646i
$507$		0			0
$508$	−3.37827e15	−	5.85134e15i	−0.196568	−	0.340465i
$509$	−1.39053e16	+	8.02821e15i	−0.799600	+	0.461649i	−0.843331	−	0.537394i	$-0.819409\pi$
$509$	−1.39053e16	+	8.02821e15i	−0.799600	+	0.461649i	0.0437313	+	0.999043i	$0.486075\pi$
$510$		0			0
$511$	−7.94677e15	+	1.37642e16i	−0.446339	+	0.773082i
$512$			7.96131e14i			0.0441942i
$513$		0			0
$514$	−1.42024e16			−0.770165
$515$	−2.32263e16	−	1.34097e16i	−1.24490	−	0.718746i
$516$		0			0
$517$	2.67165e15	+	4.62743e15i	0.139906	+	0.242324i
$518$	−1.67478e16	+	9.66935e15i	−0.866920	+	0.500517i
$519$		0			0
$520$	4.03720e15	−	6.99263e15i	0.204202	−	0.353688i
$521$			2.27894e16i			1.13948i	0.821825	+	0.569740i	$0.192956\pi$
$521$			2.27894e16i			1.13948i	−0.821825	+	0.569740i	$0.807044\pi$
$522$		0			0
$523$	−2.36146e16			−1.15390			−0.576952	−	0.816778i	$-0.695758\pi$
$523$	−2.36146e16			−1.15390			−0.576952	+	0.816778i	$0.695758\pi$
$524$	1.23709e16	+	7.14236e15i	0.597606	+	0.345028i
$525$		0			0
$526$	1.04509e16	+	1.81014e16i	0.493444	+	0.854670i
$527$	−1.20606e16	+	6.96320e15i	−0.562997	+	0.325046i
$528$		0			0
$529$	−6.17841e15	+	1.07013e16i	−0.281931	+	0.488319i
$530$			1.65560e16i			0.746964i
$531$		0			0
$532$	9.06459e15			0.399833
$533$	−2.96680e16	−	1.71288e16i	−1.29397	−	0.747075i
$534$		0			0
$535$	1.64440e16	+	2.84818e16i	0.701269	+	1.21463i
$536$	−4.66248e15	+	2.69188e15i	−0.196620	+	0.113519i
$537$		0			0
$538$	3.16906e15	−	5.48897e15i	0.130688	−	0.226359i
$539$			6.11224e15i			0.249269i
$540$		0			0
$541$	1.91409e16			0.763449			0.381724	−	0.924276i	$-0.375330\pi$
$541$	1.91409e16			0.763449			0.381724	+	0.924276i	$0.375330\pi$
$542$	−6.97678e15	−	4.02805e15i	−0.275207	−	0.158891i
$543$		0			0
$544$	2.81522e15	+	4.87610e15i	0.108622	+	0.188139i
$545$	−2.56226e15	+	1.47932e15i	−0.0977785	+	0.0564525i
$546$		0			0
$547$	4.53225e15	−	7.85009e15i	0.169196	−	0.293056i	−0.768941	−	0.639319i	$-0.779216\pi$
$547$	4.53225e15	−	7.85009e15i	0.169196	−	0.293056i	0.938137	+	0.346263i	$0.112550\pi$
$548$			5.57452e15i			0.205837i
$549$		0			0
$550$	2.19648e15			0.0793506
$551$	−1.90169e16	−	1.09794e16i	−0.679564	−	0.392347i
$552$		0			0
$553$	9.10043e15	+	1.57624e16i	0.318208	+	0.551152i
$554$	2.12123e16	−	1.22469e16i	0.733717	−	0.423612i
$555$		0			0
$556$	−1.02918e16	+	1.78260e16i	−0.348373	+	0.603399i
$557$			2.68418e16i			0.898837i	0.893321	+	0.449419i	$0.148369\pi$
$557$			2.68418e16i			0.898837i	−0.893321	+	0.449419i	$0.851631\pi$
$558$		0			0
$559$	−2.59313e16			−0.849873
$560$	−5.10982e15	−	2.95016e15i	−0.165683	−	0.0956571i
$561$		0			0
$562$	−1.37478e16	−	2.38119e16i	−0.436331	−	0.755748i
$563$	−1.00983e16	+	5.83025e15i	−0.317101	+	0.183078i	−0.650100	−	0.759849i	$-0.725273\pi$
$563$	−1.00983e16	+	5.83025e15i	−0.317101	+	0.183078i	0.332999	+	0.942927i	$0.391939\pi$
$564$		0			0
$565$	−2.04925e15	+	3.54940e15i	−0.0629947	+	0.109110i
$566$			2.22746e15i			0.0677503i
$567$		0			0
$568$	−3.69051e15			−0.109900
$569$	−1.76847e16	−	1.02103e16i	−0.521104	−	0.300860i	0.216282	−	0.976331i	$-0.430607\pi$
$569$	−1.76847e16	−	1.02103e16i	−0.521104	−	0.300860i	−0.737386	+	0.675471i	$0.763940\pi$
$570$		0			0
$571$	4.38932e15	+	7.60252e15i	0.126643	+	0.219352i	0.922374	−	0.386298i	$-0.126246\pi$
$571$	4.38932e15	+	7.60252e15i	0.126643	+	0.219352i	−0.795731	+	0.605650i	$0.792913\pi$
$572$	−1.48817e16	+	8.59196e15i	−0.424890	+	0.245311i
$573$		0			0
$574$	−1.25168e16	+	2.16797e16i	−0.349962	+	0.606153i
$575$			3.40542e15i			0.0942245i
$576$		0			0
$577$	3.12644e16			0.847219			0.423609	−	0.905845i	$-0.360763\pi$
$577$	3.12644e16			0.847219			0.423609	+	0.905845i	$0.360763\pi$
$578$	1.16509e16	+	6.72666e15i	0.312459	+	0.180398i
$579$		0			0
$580$	7.14672e15	+	1.23785e16i	0.187732	+	0.325162i
$581$	6.50870e15	−	3.75780e15i	0.169215	−	0.0976961i
$582$		0			0
$583$	1.76172e16	−	3.05139e16i	0.448669	−	0.777117i
$584$		−	1.51493e16i		−	0.381870i
$585$		0			0
$586$	2.87293e16			0.709479
$587$	1.38519e16	+	7.99742e15i	0.338596	+	0.195488i	0.659651	−	0.751572i	$-0.270704\pi$
$587$	1.38519e16	+	7.99742e15i	0.338596	+	0.195488i	−0.321055	+	0.947061i	$0.604037\pi$
$588$		0			0
$589$	−1.06853e16	−	1.85075e16i	−0.255915	−	0.443257i
$590$	3.66811e16	−	2.11779e16i	0.869622	−	0.502077i
$591$		0			0
$592$	9.21657e15	−	1.59636e16i	0.214111	−	0.370851i
$593$			2.23212e16i			0.513322i	0.966501	+	0.256661i	$0.0826224\pi$
$593$			2.23212e16i			0.513322i	−0.966501	+	0.256661i	$0.917378\pi$
$594$		0			0
$595$	−4.17285e16			−0.940439
$596$	−2.88334e16	−	1.66470e16i	−0.643307	−	0.371413i
$597$		0			0
$598$	−1.33210e16	−	2.30727e16i	−0.291293	−	0.504534i
$599$	−2.09928e16	+	1.21202e16i	−0.454475	+	0.262391i	−0.709718	−	0.704485i	$-0.751178\pi$
$599$	−2.09928e16	+	1.21202e16i	−0.454475	+	0.262391i	0.255243	+	0.966877i	$0.417845\pi$
$600$		0			0
$601$	−3.65059e16	+	6.32300e16i	−0.774669	+	1.34177i	0.160312	+	0.987066i	$0.448750\pi$
$601$	−3.65059e16	+	6.32300e16i	−0.774669	+	1.34177i	−0.934980	+	0.354699i	$0.884583\pi$
$602$			1.89492e16i			0.398117i
$603$		0			0
$604$	1.93835e16			0.399219
$605$	−1.49964e16	−	8.65820e15i	−0.305813	−	0.176561i
$606$		0			0
$607$	2.61136e16	+	4.52301e16i	0.522077	+	0.904265i	0.999670	+	0.0256833i	$0.00817616\pi$
$607$	2.61136e16	+	4.52301e16i	0.522077	+	0.904265i	−0.477593	+	0.878581i	$0.658491\pi$
$608$	−7.48256e15	+	4.32006e15i	−0.148125	+	0.0855201i
$609$		0			0
$610$	−1.05568e16	+	1.82849e16i	−0.204906	+	0.354907i
$611$			2.30920e16i			0.443828i
$612$		0			0
$613$	8.18124e16			1.54190			0.770950	−	0.636895i	$-0.219782\pi$
$613$	8.18124e16			1.54190			0.770950	+	0.636895i	$0.219782\pi$
$614$	4.46808e16	+	2.57965e16i	0.833893	+	0.481449i
$615$		0			0
$616$	6.27852e15	+	1.08747e16i	0.114914	+	0.199037i
$617$	−6.09006e16	+	3.51610e16i	−1.10385	+	0.637309i	−0.937230	−	0.348712i	$-0.886619\pi$
$617$	−6.09006e16	+	3.51610e16i	−1.10385	+	0.637309i	−0.166622	+	0.986021i	$0.553286\pi$
$618$		0			0
$619$	2.93637e16	−	5.08594e16i	0.521995	−	0.904122i	−0.477677	−	0.878535i	$-0.658521\pi$
$619$	2.93637e16	−	5.08594e16i	0.521995	−	0.904122i	0.999673	−	0.0255868i	$-0.00814543\pi$
$620$			1.39106e16i			0.244903i
$621$		0			0
$622$	−3.57270e16			−0.616956
$623$	7.74669e16	+	4.47255e16i	1.32491	+	0.764939i
$624$		0			0
$625$	2.49436e16	+	4.32035e16i	0.418484	+	0.724835i
$626$	−4.51983e16	+	2.60952e16i	−0.751062	+	0.433626i
$627$		0			0
$628$	−1.89008e16	+	3.27371e16i	−0.308121	+	0.533682i
$629$		−	1.30364e17i		−	2.10500i
$630$		0			0
$631$	−7.07787e16			−1.12131			−0.560656	−	0.828049i	$-0.689451\pi$
$631$	−7.07787e16			−1.12131			−0.560656	+	0.828049i	$0.689451\pi$
$632$	−1.50243e16	−	8.67429e15i	−0.235772	−	0.136123i
$633$		0			0
$634$	−2.55151e16	−	4.41935e16i	−0.392882	−	0.680492i
$635$	−4.13350e16	+	2.38648e16i	−0.630486	+	0.364011i
$636$		0			0
$637$	−1.32076e16	+	2.28762e16i	−0.197691	+	0.342411i
$638$		−	3.04193e16i		−	0.451050i
$639$		0			0
$640$	5.62403e15			0.0818403
$641$	7.18335e15	+	4.14731e15i	0.103557	+	0.0597886i	0.550884	−	0.834582i	$-0.314291\pi$
$641$	7.18335e15	+	4.14731e15i	0.103557	+	0.0597886i	−0.447327	+	0.894370i	$0.647624\pi$
$642$		0			0
$643$	−4.02701e16	−	6.97498e16i	−0.569792	−	0.986909i	−0.996586	−	0.0825600i	$-0.973690\pi$
$643$	−4.02701e16	−	6.97498e16i	−0.569792	−	0.986909i	0.426794	−	0.904349i	$-0.359643\pi$
$644$	−1.68602e16	+	9.73424e15i	−0.236346	+	0.136454i
$645$		0			0
$646$	−3.05525e16	+	5.29185e16i	−0.420390	+	0.728136i
$647$			7.39646e16i			1.00832i	0.863610	+	0.504160i	$0.168198\pi$
$647$			7.39646e16i			1.00832i	−0.863610	+	0.504160i	$0.831802\pi$
$648$		0			0
$649$	−9.01414e16			−1.20630
$650$	8.22073e15	+	4.74624e15i	0.109001	+	0.0629317i
$651$		0			0
$652$	−1.80560e16	−	3.12738e16i	−0.235036	−	0.407095i
$653$	9.93720e16	−	5.73725e16i	1.28170	−	0.739988i	0.304538	−	0.952500i	$-0.401498\pi$
$653$	9.93720e16	−	5.73725e16i	1.28170	−	0.739988i	0.977158	+	0.212513i	$0.0681647\pi$
$654$		0			0
$655$	5.04550e16	−	8.73907e16i	0.638935	−	1.10667i
$656$		−	2.38613e16i		−	0.299414i
$657$		0			0
$658$	1.68744e16			0.207908
$659$	1.51010e16	+	8.71858e15i	0.184371	+	0.106447i	0.589345	−	0.807882i	$-0.299386\pi$
$659$	1.51010e16	+	8.71858e15i	0.184371	+	0.106447i	−0.404973	+	0.914328i	$0.632719\pi$
$660$		0			0
$661$	−1.73419e16	−	3.00371e16i	−0.207916	−	0.360121i	0.743142	−	0.669134i	$-0.233335\pi$
$661$	−1.73419e16	−	3.00371e16i	−0.207916	−	0.360121i	−0.951058	+	0.309013i	$0.900001\pi$
$662$	−5.41752e16	+	3.12780e16i	−0.643654	+	0.371614i
$663$		0			0
$664$	−3.58184e15	+	6.20392e15i	−0.0417924	+	0.0723866i
$665$		−	6.40340e16i		−	0.740424i
$666$		0			0
$667$	4.71621e16			0.535597
$668$	−7.23089e16	−	4.17475e16i	−0.813828	−	0.469864i
$669$		0			0
$670$	1.90160e16	+	3.29366e16i	0.210218	+	0.364108i
$671$	3.89140e16	−	2.24670e16i	0.426354	−	0.246156i
$672$		0			0
$673$	1.33393e16	−	2.31043e16i	0.143563	−	0.248658i	−0.785273	−	0.619149i	$-0.787478\pi$
$673$	1.33393e16	−	2.31043e16i	0.143563	−	0.248658i	0.928836	+	0.370492i	$0.120811\pi$
$674$		−	2.23073e16i		−	0.237951i
$675$		0			0
$676$	−2.65490e16			−0.278207
$677$	3.99632e16	+	2.30728e16i	0.415076	+	0.239645i	0.692969	−	0.720968i	$-0.256302\pi$
$677$	3.99632e16	+	2.30728e16i	0.415076	+	0.239645i	−0.277892	+	0.960612i	$0.589636\pi$
$678$		0			0
$679$	6.97130e16	+	1.20747e17i	0.711370	+	1.23213i
$680$	3.44457e16	−	1.98872e16i	0.348403	−	0.201150i
$681$		0			0
$682$	1.48022e16	−	2.56382e16i	0.147103	−	0.254789i
$683$		−	1.03018e17i		−	1.01482i	−0.861706	−	0.507408i	$-0.830604\pi$
$683$		−	1.03018e17i		−	1.01482i	0.861706	−	0.507408i	$-0.169396\pi$
$684$		0			0
$685$	3.93795e16			0.381177
$686$	6.94633e16	+	4.01047e16i	0.666516	+	0.384813i
$687$		0			0
$688$	−9.03092e15	−	1.56420e16i	−0.0851532	−	0.147490i
$689$	1.31871e17	−	7.61360e16i	1.23264	−	0.711664i
$690$		0			0
$691$	7.44211e16	−	1.28901e17i	0.683640	−	1.18410i	−0.290221	−	0.956959i	$-0.593729\pi$
$691$	7.44211e16	−	1.28901e17i	0.683640	−	1.18410i	0.973862	−	0.227141i	$-0.0729377\pi$
$692$		−	6.27580e16i		−	0.571522i
$693$		0			0
$694$	−1.14792e17			−1.02743
$695$	1.25926e17	+	7.27035e16i	1.11740	+	0.645129i
$696$		0			0
$697$	−8.43765e16	−	1.46144e17i	−0.735911	−	1.27463i
$698$	9.17076e16	−	5.29474e16i	0.792999	−	0.457838i
$699$		0			0
$700$	3.46828e15	−	6.00724e15i	0.0294799	−	0.0510607i
$701$			9.48887e15i			0.0799662i	0.999200	+	0.0399831i	$0.0127304\pi$
$701$			9.48887e15i			0.0799662i	−0.999200	+	0.0399831i	$0.987270\pi$
$702$		0			0
$703$	2.00048e17			1.65730
$704$	−1.03655e16	−	5.98452e15i	−0.0851440	−	0.0491579i
$705$		0			0
$706$	2.37023e16	+	4.10537e16i	0.191409	+	0.331531i
$707$	7.97815e16	−	4.60619e16i	0.638830	−	0.368829i
$708$		0			0
$709$	8.47181e16	−	1.46736e17i	0.666959	−	1.15521i	−0.311791	−	0.950151i	$-0.600929\pi$
$709$	8.47181e16	−	1.46736e17i	0.666959	−	1.15521i	0.978750	−	0.205056i	$-0.0657377\pi$
$710$			2.60705e16i			0.203516i
$711$		0			0
$712$	−8.52623e16			−0.654451
$713$	3.97495e16	+	2.29494e16i	0.302548	+	0.174676i
$714$		0			0
$715$	6.06953e16	+	1.05127e17i	0.454275	+	0.786827i
$716$	3.63617e16	−	2.09934e16i	0.269877	−	0.155814i
$717$		0			0
$718$	−4.07311e16	+	7.05483e16i	−0.297289	+	0.514920i
$719$			1.16432e16i			0.0842754i	0.999112	+	0.0421377i	$0.0134168\pi$
$719$			1.16432e16i			0.0842754i	−0.999112	+	0.0421377i	$0.986583\pi$
$720$		0			0
$721$	1.80252e17			1.28312
$722$	5.53835e15	+	3.19757e15i	0.0390983	+	0.0225734i
$723$		0			0
$724$	−5.02587e16	−	8.70507e16i	−0.348964	−	0.604423i
$725$	−1.45525e16	+	8.40187e15i	−0.100209	+	0.0578560i
$726$		0			0
$727$	−2.28530e16	+	3.95826e16i	−0.154788	+	0.268101i	−0.932982	−	0.359923i	$-0.882803\pi$
$727$	−2.28530e16	+	3.95826e16i	−0.154788	+	0.268101i	0.778194	+	0.628024i	$0.216136\pi$
$728$			5.42676e16i			0.364546i
$729$		0			0
$730$	−1.07018e17			−0.707160
$731$	−1.10624e17	−	6.38688e16i	−0.725012	−	0.418586i
$732$		0			0
$733$	1.04080e16	+	1.80272e16i	0.0671032	+	0.116226i	0.897625	−	0.440760i	$-0.145291\pi$
$733$	1.04080e16	+	1.80272e16i	0.0671032	+	0.116226i	−0.830522	+	0.556986i	$0.811958\pi$
$734$	1.28451e17	−	7.41612e16i	0.821412	−	0.474242i
$735$		0			0
$736$	9.27842e15	−	1.60707e16i	0.0583723	−	0.101104i
$737$		−	8.09396e16i		−	0.505075i
$738$		0			0
$739$	2.08350e17			1.27917			0.639584	−	0.768721i	$-0.279107\pi$
$739$	2.08350e17			1.27917			0.639584	+	0.768721i	$0.279107\pi$
$740$	−1.12770e17	−	6.51076e16i	−0.686755	−	0.396498i
$741$		0			0
$742$	−5.56359e16	−	9.63642e16i	−0.333374	−	0.577421i
$743$	2.70067e17	−	1.55923e17i	1.60523	−	0.926783i	0.614818	−	0.788669i	$-0.289229\pi$
$743$	2.70067e17	−	1.55923e17i	1.60523	−	0.926783i	0.990416	−	0.138114i	$-0.0441040\pi$
$744$		0			0
$745$	−1.17597e17	+	2.03685e17i	−0.687797	+	1.19130i
$746$		−	6.68863e16i		−	0.388065i
$747$		0			0
$748$	−8.46480e16			−0.483289
$749$	−1.91425e17	−	1.10519e17i	−1.08420	−	0.625961i
$750$		0			0
$751$	−1.30877e17	−	2.26686e17i	−0.729499	−	1.26353i	−0.957095	−	0.289774i	$-0.906420\pi$
$751$	−1.30877e17	−	2.26686e17i	−0.729499	−	1.26353i	0.227596	−	0.973756i	$-0.426914\pi$
$752$	−1.39293e16	+	8.04209e15i	−0.0770234	+	0.0444695i
$753$		0			0
$754$	6.57313e16	−	1.13850e17i	0.357721	−	0.619590i
$755$		−	1.36929e17i		−	0.739289i
$756$		0			0
$757$	1.02581e17			0.545119			0.272559	−	0.962139i	$-0.412130\pi$
$757$	1.02581e17			0.545119			0.272559	+	0.962139i	$0.412130\pi$
$758$	2.29616e17	+	1.32569e17i	1.21056	+	0.698919i
$759$		0			0
$760$	3.05177e16	+	5.28583e16i	0.158369	+	0.274304i
$761$	−1.48043e16	+	8.54727e15i	−0.0762220	+	0.0440068i	−0.537627	−	0.843183i	$-0.680679\pi$
$761$	−1.48043e16	+	8.54727e15i	−0.0762220	+	0.0440068i	0.461405	+	0.887190i	$0.347346\pi$
$762$		0			0
$763$	9.94243e15	−	1.72208e16i	0.0503901	−	0.0872782i
$764$			9.11173e16i			0.458185i

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)

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

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