LMFDB - Embedded newform 162.7.d.g.53.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,7,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, 7, names="a")

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

chi := DirichletCharacter("162.53");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 7 $
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:	$37.2687615464$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 485774x^{12} + 87183614355x^{8} + 6839940225440174x^{4} + 198392288899684017121 $ x^16 + 485774x^12 + 87183614355x^8 + 6839940225440174*x^4 + 198392288899684017121
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{36} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			53.2
Root			$-11.9992 - 12.7063i$ of defining polynomial
Character	$\chi$	$=$	162.53
Dual form			162.7.d.g.107.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.89898 + 2.82843i) q^{2} +(16.0000 - 27.7128i) q^{4} +(-74.2039 - 42.8417i) q^{5} +(282.029 + 488.488i) q^{7} +181.019i q^{8} +O(q^{10})$	\(q+(-4.89898 + 2.82843i) q^{2} +(16.0000 - 27.7128i) q^{4} +(-74.2039 - 42.8417i) q^{5} +(282.029 + 488.488i) q^{7} +181.019i q^{8} +484.698 q^{10} +(1258.96 - 726.862i) q^{11} +(-420.311 + 728.001i) q^{13} +(-2763.31 - 1595.40i) q^{14} +(-512.000 - 886.810i) q^{16} -5090.31i q^{17} -6688.88 q^{19} +(-2374.53 + 1370.93i) q^{20} +(-4111.75 + 7121.77i) q^{22} +(10263.1 + 5925.40i) q^{23} +(-4141.68 - 7173.61i) q^{25} -4755.28i q^{26} +18049.9 q^{28} +(13364.3 - 7715.89i) q^{29} +(-16541.1 + 28650.0i) q^{31} +(5016.55 + 2896.31i) q^{32} +(14397.6 + 24937.3i) q^{34} -48330.3i q^{35} +84382.4 q^{37} +(32768.7 - 18919.0i) q^{38} +(7755.17 - 13432.3i) q^{40} +(13991.8 + 8078.17i) q^{41} +(33055.4 + 57253.7i) q^{43} -46519.2i q^{44} -67038.2 q^{46} +(-137771. + 79542.3i) q^{47} +(-100256. + 173649. i) q^{49} +(40580.1 + 23428.9i) q^{50} +(13450.0 + 23296.0i) q^{52} -150118. i q^{53} -124560. q^{55} +(-88425.8 + 51052.7i) q^{56} +(-43647.6 + 75599.9i) q^{58} +(166349. + 96041.6i) q^{59} +(191244. + 331244. i) q^{61} -187141. i q^{62} -32768.0 q^{64} +(62377.5 - 36013.7i) q^{65} +(-118774. + 205723. i) q^{67} +(-141067. - 81445.0i) q^{68} +(136699. + 236769. i) q^{70} +688359. i q^{71} +379634. q^{73} +(-413387. + 238669. i) q^{74} +(-107022. + 185368. i) q^{76} +(710128. + 409992. i) q^{77} +(385496. + 667698. i) q^{79} +87739.7i q^{80} -91394.1 q^{82} +(-654334. + 377780. i) q^{83} +(-218077. + 377721. i) q^{85} +(-323876. - 186990. i) q^{86} +(131576. + 227897. i) q^{88} -871169. i q^{89} -474160. q^{91} +(328419. - 189613. i) q^{92} +(449959. - 779352. i) q^{94} +(496341. + 286563. i) q^{95} +(-606631. - 1.05072e6i) q^{97} -1.13427e6i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 256 q^{4} - 964 q^{7}+O(q^{10}) $ 16 * q + 256 * q^4 - 964 * q^7	$ 16 q + 256 q^{4} - 964 q^{7} - 1536 q^{10} - 4540 q^{13} - 8192 q^{16} - 47368 q^{19} - 27072 q^{22} + 32392 q^{25} - 61696 q^{28} - 77056 q^{31} + 52608 q^{34} - 22696 q^{37} - 24576 q^{40} + 226604 q^{43} - 325440 q^{46} - 1298088 q^{49} + 145280 q^{52} - 2921832 q^{55} - 867456 q^{58} + 327476 q^{61} - 524288 q^{64} - 1713292 q^{67} + 176352 q^{70} - 4378432 q^{73} - 757888 q^{76} + 1326884 q^{79} - 2317632 q^{82} - 3483180 q^{85} + 866304 q^{88} + 2260648 q^{91} + 26400 q^{94} + 2200064 q^{97}+O(q^{100}) $ 16 * q + 256 * q^4 - 964 * q^7 - 1536 * q^10 - 4540 * q^13 - 8192 * q^16 - 47368 * q^19 - 27072 * q^22 + 32392 * q^25 - 61696 * q^28 - 77056 * q^31 + 52608 * q^34 - 22696 * q^37 - 24576 * q^40 + 226604 * q^43 - 325440 * q^46 - 1298088 * q^49 + 145280 * q^52 - 2921832 * q^55 - 867456 * q^58 + 327476 * q^61 - 524288 * q^64 - 1713292 * q^67 + 176352 * q^70 - 4378432 * q^73 - 757888 * q^76 + 1326884 * q^79 - 2317632 * q^82 - 3483180 * q^85 + 866304 * q^88 + 2260648 * q^91 + 26400 * q^94 + 2200064 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$83$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−4.89898	+	2.82843i	−0.612372	+	0.353553i
$2$	−4.89898	+	2.82843i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	16.0000	−	27.7128i	0.250000	−	0.433013i
$5$	−74.2039	−	42.8417i	−0.593631	−	0.342733i	0.172901	−	0.984939i	$-0.444686\pi$
$5$	−74.2039	−	42.8417i	−0.593631	−	0.342733i	−0.766532	+	0.642206i	$0.778019\pi$
$6$		0			0
$7$	282.029	+	488.488i	0.822242	+	1.42416i	0.904009	+	0.427513i	$0.140610\pi$
$7$	282.029	+	488.488i	0.822242	+	1.42416i	−0.0817675	+	0.996651i	$0.526056\pi$
$8$			181.019i			0.353553i
$9$		0			0
$10$	484.698			0.484698
$11$	1258.96	−	726.862i	0.945877	−	0.546102i	0.0540793	−	0.998537i	$-0.482778\pi$
$11$	1258.96	−	726.862i	0.945877	−	0.546102i	0.891798	+	0.452434i	$0.149444\pi$
$12$		0			0
$13$	−420.311	+	728.001i	−0.191312	+	0.331361i	−0.945685	−	0.325084i	$-0.894607\pi$
$13$	−420.311	+	728.001i	−0.191312	+	0.331361i	0.754374	+	0.656445i	$0.227941\pi$
$14$	−2763.31	−	1595.40i	−1.00704	−	0.581413i
$15$		0			0
$16$	−512.000	−	886.810i	−0.125000	−	0.216506i
$17$		−	5090.31i		−	1.03609i	−0.855353	−	0.518045i	$-0.826660\pi$
$17$		−	5090.31i		−	1.03609i	0.855353	−	0.518045i	$-0.173340\pi$
$18$		0			0
$19$	−6688.88			−0.975198			−0.487599	−	0.873068i	$-0.662127\pi$
$19$	−6688.88			−0.975198			−0.487599	+	0.873068i	$0.662127\pi$
$20$	−2374.53	+	1370.93i	−0.296816	+	0.171367i
$21$		0			0
$22$	−4111.75	+	7121.77i	−0.386153	+	0.668836i
$23$	10263.1	+	5925.40i	0.843519	+	0.487006i	0.858459	−	0.512883i	$-0.171422\pi$
$23$	10263.1	+	5925.40i	0.843519	+	0.487006i	−0.0149399	+	0.999888i	$0.504756\pi$
$24$		0			0
$25$	−4141.68	−	7173.61i	−0.265068	−	0.459111i
$26$		−	4755.28i		−	0.270555i
$27$		0			0
$28$	18049.9			0.822242
$29$	13364.3	−	7715.89i	0.547964	−	0.316367i	−0.200336	−	0.979727i	$-0.564203\pi$
$29$	13364.3	−	7715.89i	0.547964	−	0.316367i	0.748301	+	0.663360i	$0.230870\pi$
$30$		0			0
$31$	−16541.1	+	28650.0i	−0.555239	+	0.961701i	0.442646	+	0.896696i	$0.354040\pi$
$31$	−16541.1	+	28650.0i	−0.555239	+	0.961701i	−0.997885	+	0.0650051i	$0.979294\pi$
$32$	5016.55	+	2896.31i	0.153093	+	0.0883883i
$33$		0			0
$34$	14397.6	+	24937.3i	0.366313	+	0.634473i
$35$		−	48330.3i		−	1.12724i
$36$		0			0
$37$	84382.4			1.66589			0.832945	−	0.553355i	$-0.186653\pi$
$37$	84382.4			1.66589			0.832945	+	0.553355i	$0.186653\pi$
$38$	32768.7	−	18919.0i	0.597184	−	0.344784i
$39$		0			0
$40$	7755.17	−	13432.3i	0.121175	−	0.209880i
$41$	13991.8	+	8078.17i	0.203012	+	0.117209i	0.598060	−	0.801452i	$-0.295939\pi$
$41$	13991.8	+	8078.17i	0.203012	+	0.117209i	−0.395048	+	0.918661i	$0.629272\pi$
$42$		0			0
$43$	33055.4	+	57253.7i	0.415755	+	0.720109i	0.995507	−	0.0946837i	$-0.0301840\pi$
$43$	33055.4	+	57253.7i	0.415755	+	0.720109i	−0.579752	+	0.814793i	$0.696851\pi$
$44$		−	46519.2i		−	0.546102i
$45$		0			0
$46$	−67038.2			−0.688730
$47$	−137771.	+	79542.3i	−1.32698	+	0.766134i	−0.984832	−	0.173512i	$-0.944489\pi$
$47$	−137771.	+	79542.3i	−1.32698	+	0.766134i	−0.342150	+	0.939645i	$0.611155\pi$
$48$		0			0
$49$	−100256.	+	173649.i	−0.852163	+	1.47599i
$50$	40580.1	+	23428.9i	0.324640	+	0.187431i
$51$		0			0
$52$	13450.0	+	23296.0i	0.0956558	+	0.165681i
$53$		−	150118.i		−	1.00834i	−0.863606	−	0.504168i	$-0.831799\pi$
$53$		−	150118.i		−	1.00834i	0.863606	−	0.504168i	$-0.168201\pi$
$54$		0			0
$55$	−124560.			−0.748670
$56$	−88425.8	+	51052.7i	−0.503518	+	0.290706i
$57$		0			0
$58$	−43647.6	+	75599.9i	−0.223706	+	0.387469i
$59$	166349.	+	96041.6i	0.809961	+	0.467631i	0.846942	−	0.531685i	$-0.178441\pi$
$59$	166349.	+	96041.6i	0.809961	+	0.467631i	−0.0369813	+	0.999316i	$0.511774\pi$
$60$		0			0
$61$	191244.	+	331244.i	0.842554	+	1.45935i	0.887728	+	0.460368i	$0.152282\pi$
$61$	191244.	+	331244.i	0.842554	+	1.45935i	−0.0451740	+	0.998979i	$0.514384\pi$
$62$		−	187141.i		−	0.785226i
$63$		0			0
$64$	−32768.0			−0.125000
$65$	62377.5	−	36013.7i	0.227137	−	0.131138i
$66$		0			0
$67$	−118774.	+	205723.i	−0.394910	+	0.684004i	−0.993090	−	0.117358i	$-0.962558\pi$
$67$	−118774.	+	205723.i	−0.394910	+	0.684004i	0.598180	+	0.801362i	$0.295891\pi$
$68$	−141067.	−	81445.0i	−0.448640	−	0.259022i
$69$		0			0
$70$	136699.	+	236769.i	0.398539	+	0.690290i
$71$			688359.i			1.92327i	0.274334	+	0.961635i	$0.411543\pi$
$71$			688359.i			1.92327i	−0.274334	+	0.961635i	$0.588457\pi$
$72$		0			0
$73$	379634.			0.975880			0.487940	−	0.872877i	$-0.337749\pi$
$73$	379634.			0.975880			0.487940	+	0.872877i	$0.337749\pi$
$74$	−413387.	+	238669.i	−1.02015	+	0.588981i
$75$		0			0
$76$	−107022.	+	185368.i	−0.243799	+	0.422273i
$77$	710128.	+	409992.i	1.55548	+	0.898056i
$78$		0			0
$79$	385496.	+	667698.i	0.781877	+	1.35425i	0.930847	+	0.365408i	$0.119071\pi$
$79$	385496.	+	667698.i	0.781877	+	1.35425i	−0.148971	+	0.988842i	$0.547596\pi$
$80$			87739.7i			0.171367i
$81$		0			0
$82$	−91394.1			−0.165759
$83$	−654334.	+	377780.i	−1.14437	+	0.660701i	−0.947508	−	0.319731i	$-0.896407\pi$
$83$	−654334.	+	377780.i	−1.14437	+	0.660701i	−0.196859	+	0.980432i	$0.563074\pi$
$84$		0			0
$85$	−218077.	+	377721.i	−0.355102	+	0.615056i
$86$	−323876.	−	186990.i	−0.509194	−	0.293983i
$87$		0			0
$88$	131576.	+	227897.i	0.193076	+	0.334418i
$89$		−	871169.i		−	1.23575i	−0.786274	−	0.617877i	$-0.787993\pi$
$89$		−	871169.i		−	1.23575i	0.786274	−	0.617877i	$-0.212007\pi$
$90$		0			0
$91$	−474160.			−0.629217
$92$	328419.	−	189613.i	0.421759	−	0.243503i
$93$		0			0
$94$	449959.	−	779352.i	0.541738	−	0.938318i
$95$	496341.	+	286563.i	0.578908	+	0.334233i
$96$		0			0
$97$	−606631.	−	1.05072e6i	−0.664675	−	1.15125i	−0.979373	−	0.202059i	$-0.935237\pi$
$97$	−606631.	−	1.05072e6i	−0.664675	−	1.15125i	0.314698	−	0.949192i	$-0.398097\pi$
$98$		−	1.13427e6i		−	1.20514i
$99$		0			0
$100$	−265068.			−0.265068
$101$	−691103.	+	399008.i	−0.670778	+	0.387274i	−0.796371	−	0.604808i	$-0.793250\pi$
$101$	−691103.	+	399008.i	−0.670778	+	0.387274i	0.125594	+	0.992082i	$0.459916\pi$
$102$		0			0
$103$	−371948.	+	644233.i	−0.340385	+	0.589564i	−0.984504	−	0.175361i	$-0.943891\pi$
$103$	−371948.	+	644233.i	−0.340385	+	0.589564i	0.644119	+	0.764925i	$0.277224\pi$
$104$	−131782.	−	76084.5i	−0.117154	−	0.0676389i
$105$		0			0
$106$	424598.	+	735425.i	0.356501	+	0.617477i
$107$			1.02594e6i			0.837474i	0.908108	+	0.418737i	$0.137527\pi$
$107$			1.02594e6i			0.837474i	−0.908108	+	0.418737i	$0.862473\pi$
$108$		0			0
$109$	1.09355e6			0.844421			0.422210	−	0.906498i	$-0.361254\pi$
$109$	1.09355e6			0.844421			0.422210	+	0.906498i	$0.361254\pi$
$110$	610217.	−	352309.i	0.458465	−	0.264695i
$111$		0			0
$112$	288798.	−	500212.i	0.205560	−	0.356041i
$113$	−315645.	−	182238.i	−0.218758	−	0.126300i	0.386617	−	0.922240i	$-0.373644\pi$
$113$	−315645.	−	182238.i	−0.218758	−	0.126300i	−0.605375	+	0.795940i	$0.706977\pi$
$114$		0			0
$115$	−507708.	−	879376.i	−0.333826	−	0.578204i
$116$		−	493817.i		−	0.316367i
$117$		0			0
$118$	−1.08659e6			−0.661330
$119$	2.48656e6	−	1.43561e6i	1.47556	−	0.851916i
$120$		0			0
$121$	170877.	−	295967.i	0.0964555	−	0.167066i
$122$	−1.87380e6	−	1.08184e6i	−1.03191	−	0.595776i
$123$		0			0
$124$	529316.	+	916801.i	0.277619	+	0.480851i
$125$			2.04855e6i			1.04886i
$126$		0			0
$127$	2.27969e6			1.11292			0.556461	−	0.830874i	$-0.312159\pi$
$127$	2.27969e6			1.11292			0.556461	+	0.830874i	$0.312159\pi$
$128$	160530.	−	92681.9i	0.0765466	−	0.0441942i
$129$		0			0
$130$	−203724.	+	352861.i	−0.0927283	+	0.160610i
$131$	132069.	+	76249.8i	0.0587470	+	0.0339176i	0.529086	−	0.848568i	$-0.322535\pi$
$131$	132069.	+	76249.8i	0.0587470	+	0.0339176i	−0.470339	+	0.882486i	$0.655868\pi$
$132$		0			0
$133$	−1.88646e6	−	3.26744e6i	−0.801848	−	1.38884i
$134$		−	1.34378e6i		−	0.558487i
$135$		0			0
$136$	921444.			0.366313
$137$	2.64927e6	−	1.52955e6i	1.03030	−	0.594844i	0.113230	−	0.993569i	$-0.463880\pi$
$137$	2.64927e6	−	1.52955e6i	1.03030	−	0.594844i	0.917071	+	0.398725i	$0.130547\pi$
$138$		0			0
$139$	−311009.	+	538683.i	−0.115805	+	0.200581i	−0.918101	−	0.396346i	$-0.870278\pi$
$139$	−311009.	+	538683.i	−0.115805	+	0.200581i	0.802296	+	0.596926i	$0.203612\pi$
$140$	−1.33937e6	−	773286.i	−0.488109	−	0.281810i
$141$		0			0
$142$	−1.94697e6	−	3.37226e6i	−0.679978	−	1.17776i
$143$			1.22203e6i			0.417903i
$144$		0			0
$145$	−1.32225e6			−0.433719
$146$	−1.85982e6	+	1.07377e6i	−0.597602	+	0.345026i
$147$		0			0
$148$	1.35012e6	−	2.33847e6i	0.416473	−	0.721352i
$149$	3.30872e6	+	1.91029e6i	1.00023	+	0.577484i	0.908317	−	0.418282i	$-0.137368\pi$
$149$	3.30872e6	+	1.91029e6i	1.00023	+	0.577484i	0.0919153	+	0.995767i	$0.470701\pi$
$150$		0			0
$151$	−2.42965e6	−	4.20828e6i	−0.705688	−	1.22229i	−0.966443	−	0.256883i	$-0.917305\pi$
$151$	−2.42965e6	−	4.20828e6i	−0.705688	−	1.22229i	0.260754	−	0.965405i	$-0.416029\pi$
$152$		−	1.21082e6i		−	0.344784i
$153$		0			0
$154$	−4.63853e6			−1.27004
$155$	2.45483e6	−	1.41730e6i	0.659214	−	0.380597i
$156$		0			0
$157$	2.69987e6	−	4.67631e6i	0.697660	−	1.20838i	−0.271615	−	0.962406i	$-0.587558\pi$
$157$	2.69987e6	−	4.67631e6i	0.697660	−	1.20838i	0.969276	−	0.245977i	$-0.0791088\pi$
$158$	−3.77707e6	−	2.18069e6i	−0.957599	−	0.552870i
$159$		0			0
$160$	−248165.	−	429835.i	−0.0605873	−	0.104940i
$161$			6.68454e6i			1.60175i
$162$		0			0
$163$	−1.13788e6			−0.262744			−0.131372	−	0.991333i	$-0.541938\pi$
$163$	−1.13788e6			−0.262744			−0.131372	+	0.991333i	$0.541938\pi$
$164$	447738.	−	258501.i	0.101506	−	0.0586046i
$165$		0			0
$166$	2.13705e6	−	3.70147e6i	0.467186	−	0.809190i
$167$	−1.32724e6	−	766280.i	−0.284970	−	0.164527i	0.350701	−	0.936487i	$-0.385943\pi$
$167$	−1.32724e6	−	766280.i	−0.284970	−	0.164527i	−0.635671	+	0.771960i	$0.719277\pi$
$168$		0			0
$169$	2.06008e6	+	3.56816e6i	0.426800	+	0.739239i
$170$		−	2.46726e6i		−	0.502191i
$171$		0			0
$172$	2.11555e6			0.415755
$173$	−5.52168e6	+	3.18794e6i	−1.06643	+	0.615704i	−0.927204	−	0.374556i	$-0.877795\pi$
$173$	−5.52168e6	+	3.18794e6i	−1.06643	+	0.615704i	−0.139227	+	0.990261i	$0.544462\pi$
$174$		0			0
$175$	2.33615e6	−	4.04633e6i	0.435900	−	0.755000i
$176$	−1.28918e6	−	744307.i	−0.236469	−	0.136526i
$177$		0			0
$178$	2.46404e6	+	4.26784e6i	0.436905	+	0.756742i
$179$		−	719446.i		−	0.125441i	−0.998031	−	0.0627204i	$-0.980022\pi$
$179$		−	719446.i		−	0.125441i	0.998031	−	0.0627204i	$-0.0199776\pi$
$180$		0			0
$181$	7.41982e6			1.25129			0.625645	−	0.780108i	$-0.284836\pi$
$181$	7.41982e6			1.25129			0.625645	+	0.780108i	$0.284836\pi$
$182$	2.32290e6	−	1.34113e6i	0.385315	−	0.222462i
$183$		0			0
$184$	−1.07261e6	+	1.85782e6i	−0.172183	+	0.298229i
$185$	−6.26150e6	−	3.61508e6i	−0.988925	−	0.570956i
$186$		0			0
$187$	−3.69995e6	−	6.40851e6i	−0.565811	−	0.980014i
$188$			5.09071e6i			0.766134i
$189$		0			0
$190$	−3.24209e6			−0.472676
$191$	1.76845e6	−	1.02101e6i	0.253800	−	0.146532i	−0.367703	−	0.929943i	$-0.619856\pi$
$191$	1.76845e6	−	1.02101e6i	0.253800	−	0.146532i	0.621503	+	0.783412i	$0.286522\pi$
$192$		0			0
$193$	−2.10449e6	+	3.64508e6i	−0.292735	+	0.507032i	−0.974456	−	0.224581i	$-0.927899\pi$
$193$	−2.10449e6	+	3.64508e6i	−0.292735	+	0.507032i	0.681720	+	0.731613i	$0.261232\pi$
$194$	5.94374e6	+	3.43162e6i	0.814057	+	0.469996i
$195$		0			0
$196$	3.20820e6	+	5.55676e6i	0.426081	+	0.737995i
$197$			1.06745e7i			1.39621i	0.715995	+	0.698105i	$0.245973\pi$
$197$			1.06745e7i			1.39621i	−0.715995	+	0.698105i	$0.754027\pi$
$198$		0			0
$199$	−3.53584e6			−0.448676			−0.224338	−	0.974511i	$-0.572022\pi$
$199$	−3.53584e6			−0.448676			−0.224338	+	0.974511i	$0.572022\pi$
$200$	1.29856e6	−	749725.i	0.162320	−	0.0937156i
$201$		0			0
$202$	2.25713e6	−	3.90947e6i	0.273844	−	0.474311i
$203$	7.53824e6	+	4.35221e6i	0.901118	+	0.520261i
$204$		0			0
$205$	−692164.	−	1.19886e6i	−0.0803429	−	0.139158i
$206$		−	4.20811e6i		−	0.481377i
$207$		0			0
$208$	860798.			0.0956558
$209$	−8.42105e6	+	4.86189e6i	−0.922417	+	0.532558i
$210$		0			0
$211$	−3.60241e6	+	6.23956e6i	−0.383483	+	0.664212i	−0.991557	−	0.129668i	$-0.958609\pi$
$211$	−3.60241e6	+	6.23956e6i	−0.383483	+	0.664212i	0.608075	+	0.793880i	$0.291942\pi$
$212$	−4.16019e6	−	2.40189e6i	−0.436622	−	0.252084i
$213$		0			0
$214$	−2.90180e6	−	5.02607e6i	−0.296092	−	0.512846i
$215$		−	5.66460e6i		−	0.569973i
$216$		0			0
$217$	−1.86603e7			−1.82616
$218$	−5.35728e6	+	3.09302e6i	−0.517100	+	0.298548i
$219$		0			0
$220$	−1.99296e6	+	3.45191e6i	−0.187167	+	0.324184i
$221$	3.70575e6	+	2.13952e6i	0.343320	+	0.198216i
$222$		0			0
$223$	6.54953e6	+	1.13441e7i	0.590603	+	1.02295i	0.994151	+	0.107996i	$0.0344435\pi$
$223$	6.54953e6	+	1.13441e7i	0.590603	+	1.02295i	−0.403548	+	0.914958i	$0.632223\pi$
$224$			3.26737e6i			0.290706i
$225$		0			0
$226$	2.06179e6			0.178615
$227$	−3.13896e6	+	1.81228e6i	−0.268354	+	0.154934i	−0.628139	−	0.778101i	$-0.716183\pi$
$227$	−3.13896e6	+	1.81228e6i	−0.268354	+	0.154934i	0.359785	+	0.933035i	$0.382850\pi$
$228$		0			0
$229$	−6.64918e6	+	1.15167e7i	−0.553683	+	0.959007i	0.444321	+	0.895867i	$0.353445\pi$
$229$	−6.64918e6	+	1.15167e7i	−0.553683	+	0.959007i	−0.998005	+	0.0631401i	$0.979889\pi$
$230$	4.97450e6	+	2.87203e6i	0.408852	+	0.236051i
$231$		0			0
$232$	1.39672e6	+	2.41920e6i	0.111853	+	0.193735i
$233$		−	2.32921e7i		−	1.84137i	−0.390308	−	0.920684i	$-0.627631\pi$
$233$		−	2.32921e7i		−	1.84137i	0.390308	−	0.920684i	$-0.372369\pi$
$234$		0			0
$235$	1.36309e7			1.05032
$236$	5.32317e6	−	3.07333e6i	0.404981	−	0.233816i
$237$		0			0
$238$	−8.12106e6	+	1.40661e7i	−0.602396	+	1.04338i
$239$	1.39771e7	+	8.06968e6i	1.02382	+	0.591102i	0.915208	−	0.402982i	$-0.132026\pi$
$239$	1.39771e7	+	8.06968e6i	1.02382	+	0.591102i	0.108611	+	0.994084i	$0.465360\pi$
$240$		0			0
$241$	5.59767e6	+	9.69545e6i	0.399904	+	0.692655i	0.993714	−	0.111951i	$-0.0357100\pi$
$241$	5.59767e6	+	9.69545e6i	0.399904	+	0.692655i	−0.593809	+	0.804606i	$0.702377\pi$
$242$			1.93325e6i			0.136409i
$243$		0			0
$244$	1.22396e7			0.842554
$245$	1.48788e7	−	8.59028e6i	1.01174	−	0.584129i
$246$		0			0
$247$	2.81141e6	−	4.86951e6i	0.186567	−	0.323143i
$248$	−5.18621e6	−	2.99426e6i	−0.340013	−	0.196306i
$249$		0			0
$250$	−5.79417e6	−	1.00358e7i	−0.370827	−	0.642291i
$251$		−	1.76943e7i		−	1.11896i	−0.828845	−	0.559478i	$-0.811002\pi$
$251$		−	1.76943e7i		−	1.11896i	0.828845	−	0.559478i	$-0.188998\pi$
$252$		0			0
$253$	1.72278e7			1.06382
$254$	−1.11682e7	+	6.44794e6i	−0.681523	+	0.393477i
$255$		0			0
$256$	−524288.	+	908093.i	−0.0312500	+	0.0541266i
$257$	−2.43654e7	−	1.40674e7i	−1.43540	−	0.828730i	−0.437877	−	0.899035i	$-0.644270\pi$
$257$	−2.43654e7	−	1.40674e7i	−1.43540	−	0.828730i	−0.997526	+	0.0703044i	$0.977603\pi$
$258$		0			0
$259$	2.37983e7	+	4.12198e7i	1.36976	+	2.37250i
$260$		−	2.30488e6i		−	0.131138i
$261$		0			0
$262$	−862668.			−0.0479667
$263$	−2.35495e6	+	1.35963e6i	−0.129454	+	0.0747402i	−0.563328	−	0.826233i	$-0.690479\pi$
$263$	−2.35495e6	+	1.35963e6i	−0.129454	+	0.0747402i	0.433875	+	0.900973i	$0.357146\pi$
$264$		0			0
$265$	−6.43130e6	+	1.11393e7i	−0.345590	+	0.598580i
$266$	1.84834e7	+	1.06714e7i	0.982059	+	0.566992i
$267$		0			0
$268$	3.80078e6	+	6.58314e6i	0.197455	+	0.342002i
$269$		−	2.04116e7i		−	1.04863i	−0.851525	−	0.524314i	$-0.824322\pi$
$269$		−	2.04116e7i		−	1.04863i	0.851525	−	0.524314i	$-0.175678\pi$
$270$		0			0
$271$	−1.14647e7			−0.576044			−0.288022	−	0.957624i	$-0.592998\pi$
$271$	−1.14647e7			−0.576044			−0.288022	+	0.957624i	$0.592998\pi$
$272$	−4.51414e6	+	2.60624e6i	−0.224320	+	0.129511i
$273$		0			0
$274$	−8.65247e6	+	1.49865e7i	−0.420618	+	0.728532i
$275$	−1.04284e7	−	6.02087e6i	−0.501443	−	0.289508i
$276$		0			0
$277$	−1.06342e7	−	1.84189e7i	−0.500340	−	0.866614i	−1.00000		0.000392228i	$-0.999875\pi$
$277$	−1.06342e7	−	1.84189e7i	−0.500340	−	0.866614i	0.499660	−	0.866221i	$-0.333458\pi$
$278$		−	3.51866e6i		−	0.163773i
$279$		0			0
$280$	8.74873e6			0.398539
$281$	−1.30321e7	+	7.52411e6i	−0.587350	+	0.339107i	−0.764049	−	0.645158i	$-0.776791\pi$
$281$	−1.30321e7	+	7.52411e6i	−0.587350	+	0.339107i	0.176699	+	0.984265i	$0.443458\pi$
$282$		0			0
$283$	8.53876e6	−	1.47896e7i	0.376735	−	0.652524i	−0.613850	−	0.789422i	$-0.710380\pi$
$283$	8.53876e6	−	1.47896e7i	0.376735	−	0.652524i	0.990585	+	0.136899i	$0.0437135\pi$
$284$	1.90764e7	+	1.10137e7i	0.832800	+	0.480817i
$285$		0			0
$286$	−3.45643e6	−	5.98672e6i	−0.147751	−	0.255912i
$287$			9.11311e6i			0.385497i
$288$		0			0
$289$	−1.77368e6			−0.0734822
$290$	6.47765e6	−	3.73987e6i	0.265597	−	0.153343i
$291$		0			0
$292$	6.07414e6	−	1.05207e7i	0.243970	−	0.422568i
$293$	2.43355e7	+	1.40501e7i	0.967470	+	0.558569i	0.898464	−	0.439047i	$-0.144684\pi$
$293$	2.43355e7	+	1.40501e7i	0.967470	+	0.558569i	0.0690059	+	0.997616i	$0.478017\pi$
$294$		0			0
$295$	−8.22917e6	−	1.42533e7i	−0.320546	−	0.555201i
$296$			1.52748e7i			0.588981i
$297$		0			0
$298$	−2.16125e7			−0.816686
$299$	−8.62739e6	+	4.98103e6i	−0.322750	+	0.186340i
$300$		0			0
$301$	−1.86452e7	+	3.22944e7i	−0.683702	+	1.18421i
$302$	2.38056e7	+	1.37442e7i	0.864288	+	0.498997i
$303$		0			0
$304$	3.42471e6	+	5.93177e6i	0.121900	+	0.211136i
$305$		−	3.27728e7i		−	1.15509i
$306$		0			0
$307$	−2.48453e7			−0.858676			−0.429338	−	0.903144i	$-0.641253\pi$
$307$	−2.48453e7			−0.858676			−0.429338	+	0.903144i	$0.641253\pi$
$308$	2.27241e7	−	1.31198e7i	0.777740	−	0.449028i
$309$		0			0
$310$	−8.01744e6	+	1.38866e7i	−0.269123	+	0.466135i
$311$	−2.20434e7	−	1.27268e7i	−0.732820	−	0.423094i	0.0866330	−	0.996240i	$-0.472389\pi$
$311$	−2.20434e7	−	1.27268e7i	−0.732820	−	0.423094i	−0.819453	+	0.573146i	$0.805723\pi$
$312$		0			0
$313$	9.01887e6	+	1.56211e7i	0.294116	+	0.509425i	0.974779	−	0.223172i	$-0.0716413\pi$
$313$	9.01887e6	+	1.56211e7i	0.294116	+	0.509425i	−0.680663	+	0.732597i	$0.738308\pi$
$314$			3.05455e7i			0.986641i
$315$		0			0
$316$	2.46717e7			0.781877
$317$	−2.15110e7	+	1.24194e7i	−0.675278	+	0.389872i	−0.798074	−	0.602560i	$-0.794147\pi$
$317$	−2.15110e7	+	1.24194e7i	−0.675278	+	0.389872i	0.122796	+	0.992432i	$0.460814\pi$
$318$		0			0
$319$	1.12168e7	−	1.94280e7i	0.345538	−	0.598489i
$320$	2.43151e6	+	1.40384e6i	0.0742039	+	0.0428417i
$321$		0			0
$322$	−1.89067e7	−	3.27474e7i	−0.566303	−	0.980865i
$323$			3.40485e7i			1.01039i
$324$		0			0
$325$	6.96319e6			0.202842
$326$	5.57443e6	−	3.21840e6i	0.160897	−	0.0928939i
$327$		0			0
$328$	−1.46231e6	+	2.53279e6i	−0.0414397	+	0.0717756i
$329$	−7.77110e7	−	4.48664e7i	−2.18220	−	1.25989i
$330$		0			0
$331$	1.59873e7	+	2.76909e7i	0.440851	+	0.763577i	0.997753	−	0.0670017i	$-0.0213433\pi$
$331$	1.59873e7	+	2.76909e7i	0.440851	+	0.763577i	−0.556902	+	0.830578i	$0.688010\pi$
$332$			2.41779e7i			0.660701i
$333$		0			0
$334$	8.66947e6			0.232677
$335$	1.76270e7	−	1.01770e7i	0.468862	−	0.270698i
$336$		0			0
$337$	3.51718e7	−	6.09193e7i	0.918977	−	1.59171i	0.118004	−	0.993013i	$-0.462350\pi$
$337$	3.51718e7	−	6.09193e7i	0.918977	−	1.59171i	0.800972	−	0.598701i	$-0.204316\pi$
$338$	−2.01846e7	−	1.16536e7i	−0.522721	−	0.301793i
$339$		0			0
$340$	6.97847e6	+	1.20871e7i	0.177551	+	0.307528i
$341$			4.80924e7i			1.21287i
$342$		0			0
$343$	−4.67397e7			−1.15825
$344$	−1.03640e7	+	5.98367e6i	−0.254597	+	0.146992i
$345$		0			0
$346$	1.80337e7	−	3.12353e7i	0.435369	−	0.754081i
$347$	4.25418e7	+	2.45615e7i	1.01819	+	0.587851i	0.913578	−	0.406663i	$-0.133308\pi$
$347$	4.25418e7	+	2.45615e7i	1.01819	+	0.587851i	0.104609	+	0.994513i	$0.466641\pi$
$348$		0			0
$349$	−1.74695e7	−	3.02580e7i	−0.410964	−	0.711811i	0.584031	−	0.811731i	$-0.301475\pi$
$349$	−1.74695e7	−	3.02580e7i	−0.410964	−	0.711811i	−0.994995	+	0.0999204i	$0.968141\pi$
$350$			2.64305e7i			0.616455i
$351$		0			0
$352$	8.42087e6			0.193076
$353$	6.48799e6	−	3.74584e6i	0.147498	−	0.0851579i	−0.424435	−	0.905459i	$-0.639527\pi$
$353$	6.48799e6	−	3.74584e6i	0.147498	−	0.0851579i	0.571933	+	0.820301i	$0.306194\pi$
$354$		0			0
$355$	2.94905e7	−	5.10790e7i	0.659168	−	1.14171i
$356$	−2.41425e7	−	1.39387e7i	−0.535098	−	0.308939i
$357$		0			0
$358$	2.03490e6	+	3.52455e6i	0.0443500	+	0.0768165i
$359$		−	3.14246e7i		−	0.679183i	−0.940573	−	0.339592i	$-0.889711\pi$
$359$		−	3.14246e7i		−	0.679183i	0.940573	−	0.339592i	$-0.110289\pi$
$360$		0			0
$361$	−2.30477e6			−0.0489898
$362$	−3.63496e7	+	2.09864e7i	−0.766255	+	0.442398i
$363$		0			0
$364$	−7.58656e6	+	1.31403e7i	−0.157304	+	0.272459i
$365$	−2.81703e7	−	1.62641e7i	−0.579313	−	0.334466i
$366$		0			0
$367$	−2.31642e7	−	4.01216e7i	−0.468618	−	0.811671i	0.530738	−	0.847536i	$-0.321915\pi$
$367$	−2.31642e7	−	4.01216e7i	−0.468618	−	0.811671i	−0.999357	+	0.0358651i	$0.988581\pi$
$368$		−	1.21352e7i		−	0.243503i
$369$		0			0
$370$	4.09000e7			0.807454
$371$	7.33309e7	−	4.23376e7i	1.43604	−	0.829096i
$372$		0			0
$373$	3.64132e6	−	6.30695e6i	0.0701669	−	0.121533i	−0.828807	−	0.559534i	$-0.810980\pi$
$373$	3.64132e6	−	6.30695e6i	0.0701669	−	0.121533i	0.898974	+	0.438001i	$0.144313\pi$
$374$	3.62520e7	+	2.09301e7i	0.692974	+	0.400089i
$375$		0			0
$376$	−1.43987e7	−	2.49393e7i	−0.270869	−	0.469159i
$377$			1.29723e7i			0.242099i
$378$		0			0
$379$	−6.01546e7			−1.10497			−0.552486	−	0.833522i	$-0.686321\pi$
$379$	−6.01546e7			−1.10497			−0.552486	+	0.833522i	$0.686321\pi$
$380$	1.58829e7	−	9.17001e6i	0.289454	−	0.167116i
$381$		0			0
$382$	−5.77573e6	+	1.00039e7i	−0.103614	+	0.179464i
$383$	7.43620e6	+	4.29329e6i	0.132359	+	0.0764178i	0.564718	−	0.825284i	$-0.308985\pi$
$383$	7.43620e6	+	4.29329e6i	0.132359	+	0.0764178i	−0.432358	+	0.901702i	$0.642318\pi$
$384$		0			0
$385$	−3.51295e7	−	6.08461e7i	−0.615588	−	1.06623i
$386$		−	2.38096e7i		−	0.413990i
$387$		0			0
$388$	−3.88244e7			−0.664675
$389$	−6.64001e7	+	3.83361e7i	−1.12803	+	0.651268i	−0.943438	−	0.331548i	$-0.892429\pi$
$389$	−6.64001e7	+	3.83361e7i	−1.12803	+	0.651268i	−0.184590	+	0.982816i	$0.559096\pi$
$390$		0			0
$391$	3.01621e7	−	5.22423e7i	0.504582	−	0.873961i
$392$	−3.14338e7	−	1.81483e7i	−0.521841	−	0.301285i
$393$		0			0
$394$	−3.01922e7	−	5.22944e7i	−0.493635	−	0.855001i
$395$		−	6.60611e7i		−	1.07190i
$396$		0			0
$397$	6.57190e7			1.05031			0.525157	−	0.851005i	$-0.324006\pi$
$397$	6.57190e7			1.05031			0.525157	+	0.851005i	$0.324006\pi$
$398$	1.73220e7	−	1.00009e7i	0.274757	−	0.158631i
$399$		0			0
$400$	−4.24108e6	+	7.34577e6i	−0.0662669	+	0.114778i
$401$	−1.41013e7	−	8.14136e6i	−0.218688	−	0.126260i	0.386655	−	0.922225i	$-0.373631\pi$
$401$	−1.41013e7	−	8.14136e6i	−0.218688	−	0.126260i	−0.605343	+	0.795965i	$0.706964\pi$
$402$		0			0
$403$	−1.39048e7	−	2.40839e7i	−0.212447	−	0.367969i
$404$			2.55365e7i			0.387274i
$405$		0			0
$406$	−4.92396e7			−0.735760
$407$	1.06234e8	−	6.13344e7i	1.57573	−	0.909747i
$408$		0			0
$409$	2.30924e7	−	3.99972e7i	0.337519	−	0.584601i	−0.646446	−	0.762960i	$-0.723745\pi$
$409$	2.30924e7	−	3.99972e7i	0.337519	−	0.584601i	0.983966	+	0.178359i	$0.0570788\pi$
$410$	6.78180e6	+	3.91547e6i	0.0983996	+	0.0568110i
$411$		0			0
$412$	1.19023e7	+	2.06154e7i	0.170193	+	0.294782i
$413$			1.08346e8i			1.53802i
$414$		0			0
$415$	6.47389e7			0.905777
$416$	−4.21703e6	+	2.43470e6i	−0.0585770	+	0.0338194i
$417$		0			0
$418$	2.75030e7	−	4.76366e7i	0.376575	−	0.652247i
$419$	1.93201e7	+	1.11544e7i	0.262643	+	0.151637i	0.625540	−	0.780192i	$-0.284879\pi$
$419$	1.93201e7	+	1.11544e7i	0.262643	+	0.151637i	−0.362897	+	0.931829i	$0.618212\pi$
$420$		0			0
$421$	2.39889e6	+	4.15500e6i	0.0321487	+	0.0556832i	0.881652	−	0.471900i	$-0.156432\pi$
$421$	2.39889e6	+	4.15500e6i	0.0321487	+	0.0556832i	−0.849503	+	0.527583i	$0.823098\pi$
$422$		−	4.07566e7i		−	0.542326i
$423$		0			0
$424$	2.71743e7			0.356501
$425$	−3.65159e7	+	2.10825e7i	−0.475680	+	0.274634i
$426$		0			0
$427$	−1.07873e8	+	1.86841e8i	−1.38557	+	2.39987i
$428$	2.84317e7	+	1.64151e7i	0.362637	+	0.209369i
$429$		0			0
$430$	1.60219e7	+	2.77508e7i	0.201516	+	0.349035i
$431$			1.04853e8i			1.30963i	0.755791	+	0.654813i	$0.227253\pi$
$431$			1.04853e8i			1.30963i	−0.755791	+	0.654813i	$0.772747\pi$
$432$		0			0
$433$	1.10290e8			1.35854			0.679270	−	0.733889i	$-0.262297\pi$
$433$	1.10290e8			1.35854			0.679270	+	0.733889i	$0.262297\pi$
$434$	9.14164e7	−	5.27793e7i	1.11829	−	0.645645i
$435$		0			0
$436$	1.74968e7	−	3.03053e7i	0.211105	−	0.365645i
$437$	−6.86486e7	−	3.96343e7i	−0.822597	−	0.474927i
$438$		0			0
$439$	4.67573e6	+	8.09860e6i	0.0552657	+	0.0957231i	0.892335	−	0.451374i	$-0.149066\pi$
$439$	4.67573e6	+	8.09860e6i	0.0552657	+	0.0957231i	−0.837069	+	0.547097i	$0.815733\pi$
$440$		−	2.25478e7i		−	0.264695i
$441$		0			0
$442$	−2.42059e7			−0.280320
$443$	1.68325e7	−	9.71822e6i	0.193614	−	0.111783i	−0.400059	−	0.916489i	$-0.631011\pi$
$443$	1.68325e7	−	9.71822e6i	0.193614	−	0.111783i	0.593673	+	0.804706i	$0.297677\pi$
$444$		0			0
$445$	−3.73223e7	+	6.46442e7i	−0.423534	+	0.733583i
$446$	−6.41721e7	−	3.70498e7i	−0.723338	−	0.417620i
$447$		0			0
$448$	−9.24152e6	−	1.60068e7i	−0.102780	−	0.178021i
$449$		−	1.24211e8i		−	1.37221i	−0.727503	−	0.686105i	$-0.759319\pi$
$449$		−	1.24211e8i		−	1.37221i	0.727503	−	0.686105i	$-0.240681\pi$
$450$		0			0
$451$	2.34869e7			0.256033
$452$	−1.01006e7	+	5.83161e6i	−0.109379	+	0.0631500i
$453$		0			0
$454$	1.02518e7	−	1.77566e7i	0.109555	−	0.189755i
$455$	3.51845e7	+	2.03138e7i	0.373523	+	0.215654i
$456$		0			0
$457$	8.76082e6	+	1.51742e7i	0.0917902	+	0.158985i	0.908264	−	0.418397i	$-0.137408\pi$
$457$	8.76082e6	+	1.51742e7i	0.0917902	+	0.158985i	−0.816474	+	0.577382i	$0.804074\pi$
$458$		−	7.52268e7i		−	0.783026i
$459$		0			0
$460$	−3.24933e7			−0.333826
$461$	−3.06507e7	+	1.76962e7i	−0.312851	+	0.180624i	−0.648201	−	0.761469i	$-0.724479\pi$
$461$	−3.06507e7	+	1.76962e7i	−0.312851	+	0.180624i	0.335351	+	0.942093i	$0.391145\pi$
$462$		0			0
$463$	1.54307e6	−	2.67267e6i	0.0155468	−	0.0269279i	−0.858147	−	0.513404i	$-0.828384\pi$
$463$	1.54307e6	−	2.67267e6i	0.0155468	−	0.0269279i	0.873694	+	0.486476i	$0.161718\pi$
$464$	−1.36850e7	−	7.90107e6i	−0.136991	−	0.0790919i
$465$		0			0
$466$	6.58800e7	+	1.14107e8i	0.651022	+	1.12760i
$467$		−	1.08045e8i		−	1.06085i	−0.847731	−	0.530427i	$-0.822032\pi$
$467$		−	1.08045e8i		−	1.06085i	0.847731	−	0.530427i	$-0.177968\pi$
$468$		0			0
$469$	−1.33991e8			−1.29885
$470$	−6.67775e7	+	3.85540e7i	−0.643186	+	0.371343i
$471$		0			0
$472$	−1.73854e7	+	3.01124e7i	−0.165333	+	0.286364i
$473$	8.32311e7	+	4.80535e7i	0.786507	+	0.454090i
$474$		0			0
$475$	2.77032e7	+	4.79834e7i	0.258493	+	0.447724i
$476$		−	9.18793e7i		−	0.851916i
$477$		0			0
$478$	−9.12980e7			−0.835944
$479$	1.13713e8	−	6.56521e7i	1.03467	−	0.597368i	0.116353	−	0.993208i	$-0.462880\pi$
$479$	1.13713e8	−	6.56521e7i	1.03467	−	0.597368i	0.918320	+	0.395840i	$0.129546\pi$
$480$		0			0
$481$	−3.54669e7	+	6.14304e7i	−0.318704	+	0.552012i
$482$	−5.48457e7	−	3.16652e7i	−0.489781	−	0.282775i
$483$		0			0
$484$	−5.46806e6	−	9.47096e6i	−0.0482278	−	0.0835329i
$485$			1.03956e8i			0.911225i
$486$		0			0
$487$	−4.65915e7			−0.403385			−0.201692	−	0.979449i	$-0.564644\pi$
$487$	−4.65915e7			−0.403385			−0.201692	+	0.979449i	$0.564644\pi$
$488$	−5.99616e7	+	3.46188e7i	−0.515957	+	0.297888i
$489$		0			0
$490$	−4.85939e7	+	8.41672e7i	−0.413042	+	0.715409i
$491$	1.90093e8	+	1.09750e8i	1.60591	+	0.927173i	0.990272	+	0.139146i	$0.0444356\pi$
$491$	1.90093e8	+	1.09750e8i	1.60591	+	0.927173i	0.615640	+	0.788028i	$0.288898\pi$
$492$		0			0
$493$	−3.92762e7	−	6.80284e7i	−0.327785	−	0.567740i
$494$			3.18075e7i			0.263845i
$495$		0			0
$496$	3.38762e7			0.277619
$497$	−3.36255e8	+	1.94137e8i	−2.73905	+	1.58139i
$498$		0			0
$499$	6.67232e7	−	1.15568e8i	0.537001	−	0.930114i	−0.462062	−	0.886848i	$-0.652890\pi$
$499$	6.67232e7	−	1.15568e8i	0.537001	−	0.930114i	0.999064	−	0.0432661i	$-0.0137763\pi$
$500$	5.67710e7	+	3.27768e7i	0.454168	+	0.262214i
$501$		0			0
$502$	5.00471e7	+	8.66841e7i	0.395610	+	0.685217i
$503$		−	1.81087e7i		−	0.142293i	−0.997466	−	0.0711463i	$-0.977334\pi$
$503$		−	1.81087e7i		−	0.142293i	0.997466	−	0.0711463i	$-0.0226657\pi$
$504$		0			0
$505$	6.83767e7			0.530926
$506$	−8.43986e7	+	4.87276e7i	−0.651454	+	0.376117i
$507$		0			0
$508$	3.64750e7	−	6.31766e7i	0.278230	−	0.481909i
$509$	1.16531e8	+	6.72795e7i	0.883669	+	0.510187i	0.871867	−	0.489744i	$-0.162910\pi$
$509$	1.16531e8	+	6.72795e7i	0.883669	+	0.510187i	0.0118029	+	0.999930i	$0.496243\pi$
$510$		0			0
$511$	1.07068e8	+	1.85447e8i	0.802409	+	1.38981i
$512$		−	5.93164e6i		−	0.0441942i
$513$		0			0
$514$	1.59154e8			1.17200
$515$	5.52000e7	−	3.18697e7i	0.404127	−	0.233323i
$516$		0			0
$517$	−1.15633e8	+	2.00281e8i	−0.836775	+	1.44934i
$518$	−2.33174e8	−	1.34623e8i	−1.67761	−	0.968570i
$519$		0			0
$520$	6.51917e6	+	1.12915e7i	0.0463642	+	0.0803051i
$521$			6.97595e7i			0.493276i	0.969108	+	0.246638i	$0.0793259\pi$
$521$			6.97595e7i			0.493276i	−0.969108	+	0.246638i	$0.920674\pi$
$522$		0			0
$523$	−1.49134e7			−0.104249			−0.0521245	−	0.998641i	$-0.516599\pi$
$523$	−1.49134e7			−0.104249			−0.0521245	+	0.998641i	$0.516599\pi$
$524$	4.22619e6	−	2.43999e6i	0.0293735	−	0.0169588i
$525$		0			0
$526$	7.69125e6	−	1.33216e7i	0.0528493	−	0.0915377i
$527$	1.45838e8	+	8.41994e7i	0.996409	+	0.575277i
$528$		0			0
$529$	−3.79722e6	−	6.57697e6i	−0.0256507	−	0.0444282i
$530$		−	7.27619e7i		−	0.488738i
$531$		0			0
$532$	−1.20733e8			−0.801848
$533$	−1.17618e7	+	6.79070e6i	−0.0776771	+	0.0448469i
$534$		0			0
$535$	4.39531e7	−	7.61289e7i	0.287030	−	0.497151i
$536$	−3.72399e7	−	2.15005e7i	−0.241832	−	0.139622i
$537$		0			0
$538$	5.77329e7	+	9.99962e7i	0.370746	+	0.642151i
$539$			2.91490e8i			1.86147i
$540$		0			0
$541$	2.00053e8			1.26344			0.631718	−	0.775198i	$-0.282350\pi$
$541$	2.00053e8			1.26344			0.631718	+	0.775198i	$0.282350\pi$
$542$	5.61654e7	−	3.24271e7i	0.352753	−	0.203662i
$543$		0			0
$544$	1.47431e7	−	2.55358e7i	0.0915783	−	0.158618i
$545$	−8.11456e7	−	4.68495e7i	−0.501275	−	0.289411i
$546$		0			0
$547$	1.29618e8	+	2.24505e8i	0.791962	+	1.37172i	0.924751	+	0.380573i	$0.124273\pi$
$547$	1.29618e8	+	2.24505e8i	0.791962	+	1.37172i	−0.132789	+	0.991144i	$0.542393\pi$
$548$		−	9.78915e7i		−	0.594844i
$549$		0			0
$550$	6.81183e7			0.409427
$551$	−8.93922e7	+	5.16106e7i	−0.534374	+	0.308521i
$552$		0			0
$553$	−2.17442e8	+	3.76620e8i	−1.28578	+	2.22704i
$554$	1.04193e8	+	6.01560e7i	0.612788	+	0.353794i
$555$		0			0
$556$	9.95229e6	+	1.72379e7i	0.0579027	+	0.100290i
$557$		−	2.08528e8i		−	1.20670i	−0.797477	−	0.603349i	$-0.793833\pi$
$557$		−	2.08528e8i		−	1.20670i	0.797477	−	0.603349i	$-0.206167\pi$
$558$		0			0
$559$	−5.55743e7			−0.318155
$560$	−4.28598e7	+	2.47451e7i	−0.244054	+	0.140905i
$561$		0			0
$562$	4.25628e7	−	7.37209e7i	0.239785	−	0.415319i
$563$	2.68842e8	+	1.55216e8i	1.50651	+	0.869785i	0.999971	+	0.00756824i	$0.00240907\pi$
$563$	2.68842e8	+	1.55216e8i	1.50651	+	0.869785i	0.506540	+	0.862216i	$0.330924\pi$
$564$		0			0
$565$	1.56147e7	+	2.70455e7i	0.0865744	+	0.149951i
$566$			9.66051e7i			0.532783i
$567$		0			0
$568$	−1.24606e8			−0.679978
$569$	1.60710e8	−	9.27857e7i	0.872378	−	0.503668i	0.00424037	−	0.999991i	$-0.498650\pi$
$569$	1.60710e8	−	9.27857e7i	0.872378	−	0.503668i	0.868138	+	0.496323i	$0.165317\pi$
$570$		0			0
$571$	4.02359e7	−	6.96906e7i	0.216125	−	0.374340i	−0.737495	−	0.675353i	$-0.763991\pi$
$571$	4.02359e7	−	6.96906e7i	0.216125	−	0.374340i	0.953620	+	0.301013i	$0.0973247\pi$
$572$	3.38660e7	+	1.95525e7i	0.180957	+	0.104476i
$573$		0			0
$574$	−2.57758e7	−	4.46449e7i	−0.136294	−	0.236068i
$575$		−	9.81645e7i		−	0.516358i
$576$		0			0
$577$	8.84457e7			0.460415			0.230207	−	0.973142i	$-0.426060\pi$
$577$	8.84457e7			0.460415			0.230207	+	0.973142i	$0.426060\pi$
$578$	8.68923e6	−	5.01673e6i	0.0449984	−	0.0259799i
$579$		0			0
$580$	−2.11559e7	+	3.66431e7i	−0.108430	+	0.187806i
$581$	−3.69082e8	−	2.13090e8i	−1.88189	−	1.08651i
$582$		0			0
$583$	−1.09115e8	−	1.88993e8i	−0.550655	−	0.953762i
$584$			6.87211e7i			0.345026i
$585$		0			0
$586$	−1.58959e8			−0.789936
$587$	−2.71860e8	+	1.56958e8i	−1.34410	+	0.776015i	−0.987406	−	0.158207i	$-0.949429\pi$
$587$	−2.71860e8	+	1.56958e8i	−1.34410	+	0.776015i	−0.356691	+	0.934222i	$0.616095\pi$
$588$		0			0
$589$	1.10642e8	−	1.91637e8i	0.541467	−	0.937849i
$590$	8.06290e7	+	4.65512e7i	0.392587	+	0.226660i
$591$		0			0
$592$	−4.32038e7	−	7.48311e7i	−0.208236	−	0.360676i
$593$			3.05107e8i			1.46315i	0.681762	+	0.731574i	$0.261214\pi$
$593$			3.05107e8i			1.46315i	−0.681762	+	0.731574i	$0.738786\pi$
$594$		0			0
$595$	−2.46016e8			−1.16792
$596$	1.05879e8	−	6.11292e7i	0.500116	−	0.288742i
$597$		0			0
$598$	2.81769e7	−	4.88039e7i	0.131762	−	0.228219i
$599$	−5.35114e7	−	3.08948e7i	−0.248981	−	0.143749i	0.370317	−	0.928906i	$-0.379249\pi$
$599$	−5.35114e7	−	3.08948e7i	−0.248981	−	0.143749i	−0.619297	+	0.785156i	$0.712582\pi$
$600$		0			0
$601$	−1.89951e8	−	3.29004e8i	−0.875019	−	1.51558i	−0.856743	−	0.515744i	$-0.827515\pi$
$601$	−1.89951e8	−	3.29004e8i	−0.875019	−	1.51558i	−0.0182764	−	0.999833i	$-0.505818\pi$
$602$		−	2.10946e8i		−	0.966901i
$603$		0			0
$604$	−1.55498e8			−0.705688
$605$	−2.53595e7	+	1.46413e7i	−0.114518	+	0.0661170i
$606$		0			0
$607$	−2.70882e7	+	4.69182e7i	−0.121120	+	0.209785i	−0.920209	−	0.391426i	$-0.871982\pi$
$607$	−2.70882e7	+	4.69182e7i	−0.121120	+	0.209785i	0.799090	+	0.601212i	$0.205315\pi$
$608$	−3.35551e7	−	1.93731e7i	−0.149296	−	0.0861961i
$609$		0			0
$610$	9.26955e7	+	1.60553e8i	0.408384	+	0.707343i
$611$		−	1.33730e8i		−	0.586281i
$612$		0			0
$613$	4.26874e7			0.185318			0.0926592	−	0.995698i	$-0.470463\pi$
$613$	4.26874e7			0.185318			0.0926592	+	0.995698i	$0.470463\pi$
$614$	1.21717e8	−	7.02732e7i	0.525830	−	0.303588i
$615$		0			0
$616$	−7.42165e7	+	1.28547e8i	−0.317511	+	0.549945i
$617$	−4.50365e7	−	2.60018e7i	−0.191738	−	0.110700i	0.401058	−	0.916053i	$-0.368643\pi$
$617$	−4.50365e7	−	2.60018e7i	−0.191738	−	0.110700i	−0.592796	+	0.805353i	$0.701976\pi$
$618$		0			0
$619$	3.23743e7	+	5.60739e7i	0.136499	+	0.236423i	0.926169	−	0.377109i	$-0.123082\pi$
$619$	3.23743e7	+	5.60739e7i	0.136499	+	0.236423i	−0.789670	+	0.613531i	$0.789748\pi$
$620$		−	9.07070e7i		−	0.380597i
$621$		0			0
$622$	1.43987e8			0.598345
$623$	4.25556e8	−	2.45695e8i	1.75992	−	1.01609i
$624$		0			0
$625$	2.30494e7	−	3.99227e7i	0.0944103	−	0.163524i
$626$	−8.83666e7	−	5.10185e7i	−0.360218	−	0.207972i
$627$		0			0
$628$	−8.63959e7	−	1.49642e8i	−0.348830	−	0.604191i
$629$		−	4.29532e8i		−	1.72601i
$630$		0			0
$631$	4.62024e7			0.183898			0.0919489	−	0.995764i	$-0.470690\pi$
$631$	4.62024e7			0.183898			0.0919489	+	0.995764i	$0.470690\pi$
$632$	−1.20866e8	+	6.97822e7i	−0.478800	+	0.276435i
$633$		0			0
$634$	7.02546e7	−	1.21685e8i	0.275681	−	0.477494i
$635$	−1.69162e8	−	9.76657e7i	−0.660665	−	0.381435i
$636$		0			0
$637$	−8.42776e7	−	1.45973e8i	−0.326057	−	0.564748i
$638$			1.26903e8i			0.488665i
$639$		0			0
$640$	−1.58826e7			−0.0605873
$641$	2.23909e8	−	1.29274e8i	0.850155	−	0.490837i	−0.0105483	−	0.999944i	$-0.503358\pi$
$641$	2.23909e8	−	1.29274e8i	0.850155	−	0.490837i	0.860703	+	0.509107i	$0.170024\pi$
$642$		0			0
$643$	1.12067e8	−	1.94105e8i	0.421545	−	0.730137i	−0.574546	−	0.818472i	$-0.694821\pi$
$643$	1.12067e8	−	1.94105e8i	0.421545	−	0.730137i	0.996091	+	0.0883351i	$0.0281546\pi$
$644$	1.85247e8	+	1.06953e8i	0.693576	+	0.400437i
$645$		0			0
$646$	−9.63036e7	−	1.66803e8i	−0.357228	−	0.618736i
$647$			2.73001e8i			1.00798i	0.863709	+	0.503990i	$0.168135\pi$
$647$			2.73001e8i			1.00798i	−0.863709	+	0.503990i	$0.831865\pi$
$648$		0			0
$649$	2.79236e8			1.02150
$650$	−3.41125e7	+	1.96949e7i	−0.124215	+	0.0717155i
$651$		0			0
$652$	−1.82060e7	+	3.15337e7i	−0.0656859	+	0.113771i
$653$	−4.27719e8	−	2.46944e8i	−1.53610	−	0.886867i	−0.999062	−	0.0433076i	$-0.986210\pi$
$653$	−4.27719e8	−	2.46944e8i	−1.53610	−	0.886867i	−0.537036	−	0.843559i	$-0.680456\pi$
$654$		0			0
$655$	−6.53333e6	−	1.13161e7i	−0.0232494	−	0.0402691i
$656$		−	1.65441e7i		−	0.0586046i
$657$		0			0
$658$	5.07606e8			1.78176
$659$	3.04033e8	−	1.75533e8i	1.06234	−	0.613343i	0.136262	−	0.990673i	$-0.456491\pi$
$659$	3.04033e8	−	1.75533e8i	1.06234	−	0.613343i	0.926079	+	0.377330i	$0.123158\pi$
$660$		0			0
$661$	5.79524e6	−	1.00377e7i	0.0200663	−	0.0347559i	−0.855818	−	0.517277i	$-0.826946\pi$
$661$	5.79524e6	−	1.00377e7i	0.0200663	−	0.0347559i	0.875884	+	0.482521i	$0.160279\pi$
$662$	−1.56643e8	−	9.04380e7i	−0.539930	−	0.311729i
$663$		0			0
$664$	−6.83855e7	−	1.18447e8i	−0.233593	−	0.404595i
$665$			3.23276e8i			1.09928i
$666$		0			0
$667$	1.82879e8			0.616291
$668$	−4.24715e7	+	2.45210e7i	−0.142485	+	0.0822637i
$669$		0			0
$670$	−5.75697e7	+	9.97137e7i	−0.191412	+	0.331536i
$671$	4.81538e8	+	2.78016e8i	1.59391	+	0.920242i
$672$		0			0
$673$	6.26015e7	+	1.08429e8i	0.205371	+	0.355713i	0.950251	−	0.311485i	$-0.100827\pi$
$673$	6.26015e7	+	1.08429e8i	0.205371	+	0.355713i	−0.744880	+	0.667199i	$0.767493\pi$
$674$			3.97923e8i			1.29963i
$675$		0			0
$676$	1.31845e8			0.426800
$677$	−1.17083e8	+	6.75978e7i	−0.377335	+	0.217854i	−0.676658	−	0.736297i	$-0.736572\pi$
$677$	−1.17083e8	+	6.75978e7i	−0.377335	+	0.217854i	0.299323	+	0.954152i	$0.403239\pi$
$678$		0			0
$679$	3.42175e8	−	5.92664e8i	1.09305	−	1.89321i
$680$	−6.83748e7	−	3.94762e7i	−0.217455	−	0.125548i
$681$		0			0
$682$	−1.36026e8	−	2.35604e8i	−0.428814	−	0.742727i
$683$		−	1.53606e8i		−	0.482110i	−0.970511	−	0.241055i	$-0.922507\pi$
$683$		−	1.53606e8i		−	0.482110i	0.970511	−	0.241055i	$-0.0774935\pi$
$684$		0			0
$685$	−2.62115e8			−0.815492
$686$	2.28977e8	−	1.32200e8i	0.709282	−	0.409504i
$687$		0			0
$688$	3.38488e7	−	5.86278e7i	0.103939	−	0.180027i
$689$	1.09286e8	+	6.30963e7i	0.334123	+	0.192906i
$690$		0			0
$691$	−1.58932e8	−	2.75279e8i	−0.481702	−	0.834332i	0.518077	−	0.855334i	$-0.326648\pi$
$691$	−1.58932e8	−	2.75279e8i	−0.481702	−	0.834332i	−0.999779	+	0.0210014i	$0.993315\pi$
$692$			2.04028e8i			0.615704i
$693$		0			0
$694$	−2.77882e8			−0.831346
$695$	4.61562e7	−	2.66483e7i	0.137491	−	0.0793807i
$696$		0			0
$697$	4.11204e7	−	7.12226e7i	0.121439	−	0.210339i
$698$	1.71165e8	+	9.88224e7i	0.503326	+	0.290596i
$699$		0			0
$700$	−7.47568e7	−	1.29483e8i	−0.217950	−	0.377500i
$701$		−	1.74451e8i		−	0.506431i	−0.967410	−	0.253215i	$-0.918512\pi$
$701$		−	1.74451e8i		−	0.506431i	0.967410	−	0.253215i	$-0.0814881\pi$
$702$		0			0
$703$	−5.64424e8			−1.62457
$704$	−4.12537e7	+	2.38178e7i	−0.118235	+	0.0682628i
$705$		0			0
$706$	−2.11897e7	+	3.67016e7i	−0.0602158	+	0.104297i
$707$	−3.89822e8	−	2.25064e8i	−1.10308	−	0.636865i
$708$		0			0
$709$	−3.92293e7	−	6.79471e7i	−0.110071	−	0.190648i	0.805728	−	0.592286i	$-0.201774\pi$
$709$	−3.92293e7	−	6.79471e7i	−0.110071	−	0.190648i	−0.915799	+	0.401638i	$0.868441\pi$
$710$			3.33646e8i			0.932205i
$711$		0			0
$712$	1.57698e8			0.436905
$713$	−3.39526e8	+	1.96025e8i	−0.936708	+	0.540809i
$714$		0			0
$715$	5.23540e7	−	9.06797e7i	0.143229	−	0.248080i
$716$	−1.99379e7	−	1.15111e7i	−0.0543175	−	0.0313602i
$717$		0			0
$718$	8.88823e7	+	1.53949e8i	0.240128	+	0.415913i
$719$		−	6.02172e8i		−	1.62007i	−0.586382	−	0.810035i	$-0.699448\pi$
$719$		−	6.02172e8i		−	1.62007i	0.586382	−	0.810035i	$-0.300552\pi$
$720$		0			0
$721$	−4.19600e8			−1.11952
$722$	1.12910e7	−	6.51886e6i	0.0300000	−	0.0173205i
$723$		0			0
$724$	1.18717e8	−	2.05624e8i	0.312822	−	0.541824i
$725$	−1.10701e8	−	6.39135e7i	−0.290495	−	0.167718i
$726$		0			0
$727$	−9.44192e7	−	1.63539e8i	−0.245729	−	0.425616i	0.716607	−	0.697477i	$-0.245694\pi$
$727$	−9.44192e7	−	1.63539e8i	−0.245729	−	0.425616i	−0.962336	+	0.271861i	$0.912361\pi$
$728$		−	8.58321e7i		−	0.222462i
$729$		0			0
$730$	1.84008e8			0.473007
$731$	2.91439e8	−	1.68262e8i	0.746098	−	0.430760i
$732$		0			0
$733$	1.33412e8	−	2.31076e8i	0.338752	−	0.586735i	−0.645447	−	0.763805i	$-0.723329\pi$
$733$	1.33412e8	−	2.31076e8i	0.338752	−	0.586735i	0.984198	+	0.177070i	$0.0566620\pi$
$734$	2.26962e8	+	1.31037e8i	0.573938	+	0.331363i
$735$		0			0
$736$	3.43236e7	+	5.94502e7i	0.0860913	+	0.149114i
$737$			3.45330e8i			0.862645i
$738$		0			0
$739$	−6.75150e7			−0.167289			−0.0836444	−	0.996496i	$-0.526656\pi$
$739$	−6.75150e7			−0.167289			−0.0836444	+	0.996496i	$0.526656\pi$
$740$	−2.00368e8	+	1.15683e8i	−0.494463	+	0.285478i
$741$		0			0
$742$	−2.39498e8	+	4.14822e8i	−0.586259	+	1.01543i
$743$	−3.80062e8	−	2.19429e8i	−0.926591	−	0.534968i	−0.0408594	−	0.999165i	$-0.513010\pi$
$743$	−3.80062e8	−	2.19429e8i	−0.926591	−	0.534968i	−0.885732	+	0.464197i	$0.846343\pi$
$744$		0			0
$745$	−1.63680e8	−	2.83502e8i	−0.395846	−	0.685626i
$746$			4.11968e7i			0.0992310i
$747$		0			0
$748$	−2.36797e8			−0.565811
$749$	−5.01161e8	+	2.89345e8i	−1.19270	+	0.688606i
$750$		0			0
$751$	−1.71057e8	+	2.96279e8i	−0.403851	+	0.699490i	−0.994187	−	0.107668i	$-0.965662\pi$
$751$	−1.71057e8	+	2.96279e8i	−0.403851	+	0.699490i	0.590336	+	0.807157i	$0.298995\pi$
$752$	1.41078e8	+	8.14513e7i	0.331746	+	0.191533i
$753$		0			0
$754$	−3.66912e7	−	6.35510e7i	−0.0855949	−	0.148255i
$755$			4.16361e8i			0.967452i
$756$		0			0
$757$	8.84203e7			0.203828			0.101914	−	0.994793i	$-0.467503\pi$
$757$	8.84203e7			0.203828			0.101914	+	0.994793i	$0.467503\pi$
$758$	2.94696e8	−	1.70143e8i	0.676654	−	0.390666i
$759$		0			0
$760$	−5.18734e7	+	8.98474e7i	−0.118169	+	0.204675i
$761$	−3.37998e8	−	1.95143e8i	−0.766938	−	0.442792i	0.0648430	−	0.997895i	$-0.479345\pi$
$761$	−3.37998e8	−	1.95143e8i	−0.766938	−	0.442792i	−0.831781	+	0.555103i	$0.812679\pi$
$762$		0			0
$763$	3.08412e8	+	5.34186e8i	0.694318	+	1.20259i
$764$		−	6.53449e7i		−	0.146532i
$765$		0			0
$766$	−4.85731e7			−0.108071
$767$	−1.39837e8	+	8.07348e7i	−0.309910	+	0.178927i
$768$		0			0
$769$	−6.85245e7	+	1.18688e8i	−0.150684	+	0.260992i	−0.931479	−	0.363795i	$-0.881481\pi$
$769$	−6.85245e7	+	1.18688e8i	−0.150684	+	0.260992i	0.780795	+	0.624787i	$0.214814\pi$
$770$	3.44197e8	+	1.98722e8i	0.753938	+	0.435286i
$771$		0			0
$772$	6.73437e7	+	1.16643e8i	0.146368	+	0.253516i
$773$		−	1.98181e6i		−	0.00429065i	−0.999998	−	0.00214533i	$-0.999317\pi$
$773$		−	1.98181e6i		−	0.00429065i	0.999998	−	0.00214533i	$-0.000682879\pi$
$774$		0			0
$775$	2.74032e8			0.588703
$776$	1.90200e8	−	1.09812e8i	0.407029	−	0.234998i
$777$		0			0
$778$	2.16862e8	−	3.75616e8i	0.460516	−	0.797637i
$779$	−9.35895e7	−	5.40339e7i	−0.197977	−	0.114302i
$780$		0			0
$781$	5.00342e8	+	8.66618e8i	1.05030	+	1.81918i
$782$			3.41245e8i			0.713586i
$783$		0			0
$784$	2.05325e8			0.426081
$785$	−4.00682e8	+	2.31334e8i	−0.828306	+	0.478223i
$786$		0			0
$787$	6.08666e7	−	1.05424e8i	0.124869	−	0.216280i	−0.796813	−	0.604226i	$-0.793482\pi$
$787$	6.08666e7	−	1.05424e8i	0.124869	−	0.216280i	0.921682	+	0.387947i	$0.126816\pi$
$788$	2.95822e8	+	1.70793e8i	0.604577	+	0.349053i
$789$		0			0
$790$	1.86849e8	+	3.23632e8i	0.378974	+	0.656402i
$791$		−	2.05585e8i		−	0.415396i
$792$		0			0
$793$	−3.21528e8			−0.644762
$794$	−3.21956e8	+	1.85881e8i	−0.643184	+	0.371342i
$795$		0			0
$796$	−5.65734e7	+	9.79880e7i	−0.112169	+	0.194283i
$797$	−3.13071e8	−	1.80752e8i	−0.618399	−	0.357033i	0.157847	−	0.987464i	$-0.449545\pi$
$797$	−3.13071e8	−	1.80752e8i	−0.618399	−	0.357033i	−0.776245	+	0.630431i	$0.782878\pi$
$798$		0			0
$799$	4.04895e8	+	7.01298e8i	0.793783	+	1.37487i
$800$		−	4.79824e7i		−	0.0937156i
$801$		0			0
$802$	9.21090e7			0.178558
$803$	4.77945e8	−	2.75941e8i	0.923062	−	0.532930i
$804$		0			0
$805$	2.86377e8	−	4.96019e8i	0.548972	−	0.950847i
$806$	1.36239e8	+	7.86576e7i	0.260193	+	0.150223i
$807$		0			0
$808$	−7.22283e7	−	1.25103e8i	−0.136922	−	0.237156i
$809$		−	2.16174e8i		−	0.408279i	−0.978942	−	0.204140i	$-0.934560\pi$
$809$		−	2.16174e8i		−	0.408279i	0.978942	−	0.204140i	$-0.0654396\pi$
$810$		0			0
$811$	−4.81616e6			−0.00902897			−0.00451449	−	0.999990i	$-0.501437\pi$
$811$	−4.81616e6			−0.00902897			−0.00451449	+	0.999990i	$0.501437\pi$
$812$	2.41224e8	−	1.39271e8i	0.450559	−	0.260131i
$813$		0			0
$814$	−3.46960e8	+	6.00951e8i	−0.643288	+	1.11421i
$815$	8.44348e7	+	4.87485e7i	0.155973	+	0.0900509i
$816$		0			0
$817$	−2.21104e8	−	3.82963e8i	−0.405443	−	0.702249i
$818$			2.61260e8i			0.477325i
$819$		0			0
$820$	−4.42985e7			−0.0803429
$821$	−5.98480e8	+	3.45533e8i	−1.08148	+	0.624396i	−0.931297	−	0.364262i	$-0.881321\pi$
$821$	−5.98480e8	+	3.45533e8i	−1.08148	+	0.624396i	−0.150188	+	0.988657i	$0.547988\pi$
$822$		0			0
$823$	−5.07158e8	+	8.78423e8i	−0.909795	+	1.57581i	−0.0954466	+	0.995435i	$0.530428\pi$
$823$	−5.07158e8	+	8.78423e8i	−0.909795	+	1.57581i	−0.814348	+	0.580376i	$0.802905\pi$
$824$	−1.16619e8	−	6.73298e7i	−0.208442	−	0.120344i
$825$		0			0
$826$	−3.06449e8	−	5.30785e8i	−0.543774	−	0.941843i
$827$		−	3.47789e8i		−	0.614892i	−0.951566	−	0.307446i	$-0.900526\pi$
$827$		−	3.47789e8i		−	0.614892i	0.951566	−	0.307446i	$-0.0994743\pi$
$828$		0			0
$829$	5.07108e8			0.890096			0.445048	−	0.895507i	$-0.353187\pi$
$829$	5.07108e8			0.890096			0.445048	+	0.895507i	$0.353187\pi$
$830$	−3.17155e8	+	1.83109e8i	−0.554673	+	0.320240i
$831$		0			0
$832$	1.37728e7	−	2.38551e7i	0.0239139	−	0.0414202i
$833$	8.83926e8	+	5.10335e8i	1.52926	+	0.882917i
$834$		0			0
$835$	6.56574e7	+	1.13722e8i	0.112778	+	0.195337i
$836$			3.11161e8i			0.532558i
$837$		0			0
$838$	−1.26198e8			−0.214447
$839$	1.50973e8	−	8.71645e7i	0.255632	−	0.147589i	−0.366709	−	0.930336i	$-0.619515\pi$
$839$	1.50973e8	−	8.71645e7i	0.255632	−	0.147589i	0.622340	+	0.782747i	$0.286182\pi$
$840$		0			0
$841$	−1.78342e8	+	3.08897e8i	−0.299823	+	0.519309i
$842$	−2.35042e7	−	1.35702e7i	−0.0393740	−	0.0227326i
$843$		0			0
$844$	1.15277e8	+	1.99666e8i	0.191741	+	0.332106i
$845$		−	3.53029e8i		−	0.585114i
$846$		0			0
$847$	1.92769e8			0.317239
$848$	−1.33126e8	+	7.68604e7i	−0.218311	+	0.126042i
$849$		0			0
$850$	1.19260e8	−	2.06565e8i	0.194196	−	0.336357i
$851$	8.66024e8	+	4.99999e8i	1.40521	+	0.811299i
$852$		0			0
$853$	1.57292e8	+	2.72438e8i	0.253431	+	0.438955i	0.964468	−	0.264199i	$-0.0851076\pi$
$853$	1.57292e8	+	2.72438e8i	0.253431	+	0.438955i	−0.711037	+	0.703154i	$0.751774\pi$
$854$		−	1.22044e9i		−	1.95949i
$855$		0			0
$856$	−1.85715e8			−0.296092
$857$	5.95671e8	−	3.43911e8i	0.946377	−	0.546391i	0.0544235	−	0.998518i	$-0.482668\pi$
$857$	5.95671e8	−	3.43911e8i	0.946377	−	0.546391i	0.891954	+	0.452127i	$0.149335\pi$
$858$		0			0
$859$	−3.94171e8	+	6.82724e8i	−0.621877	+	1.07712i	0.367258	+	0.930119i	$0.380296\pi$
$859$	−3.94171e8	+	6.82724e8i	−0.621877	+	1.07712i	−0.989136	+	0.147004i	$0.953037\pi$
$860$	−1.56982e8	−	9.06336e7i	−0.246805	−	0.142493i
$861$		0			0
$862$	−2.96568e8	−	5.13670e8i	−0.463023	−	0.801979i
$863$		−	9.95858e8i		−	1.54941i	−0.632326	−	0.774703i	$-0.717899\pi$
$863$		−	9.95858e8i		−	1.54941i	0.632326	−	0.774703i	$-0.282101\pi$
$864$		0			0
$865$	5.46307e8			0.844089
$866$	−5.40308e8	+	3.11947e8i	−0.831932	+	0.480316i
$867$		0			0
$868$	−2.98565e8	+	5.17129e8i	−0.456540	+	0.790751i
$869$	9.70649e8	+	5.60405e8i	1.47912	+	0.853969i
$870$		0			0
$871$	−9.98445e7	−	1.72936e8i	−0.151102	−	0.261716i
$872$			1.97954e8i			0.298548i
$873$		0			0
$874$	4.48411e8			0.671648
$875$	−1.00069e9	+	5.77750e8i	−1.49374	+	0.862414i
$876$		0			0
$877$	1.09546e8	−	1.89739e8i	0.162404	−	0.281292i	−0.773326	−	0.634008i	$-0.781409\pi$
$877$	1.09546e8	−	1.89739e8i	0.162404	−	0.281292i	0.935730	+	0.352716i	$0.114742\pi$
$878$	−4.58126e7	−	2.64499e7i	−0.0676864	−	0.0390788i
$879$		0			0
$880$	6.37747e7	+	1.10461e8i	0.0935837	+	0.162092i
$881$		−	4.82715e8i		−	0.705932i	−0.935636	−	0.352966i	$-0.885173\pi$
$881$		−	4.82715e8i		−	0.705932i	0.935636	−	0.352966i	$-0.114827\pi$
$882$		0			0
$883$	−7.75993e8			−1.12713			−0.563567	−	0.826070i	$-0.690571\pi$
$883$	−7.75993e8			−1.12713			−0.563567	+	0.826070i	$0.690571\pi$
$884$	1.18584e8	−	6.84645e7i	0.171660	−	0.0991080i
$885$		0			0
$886$	−5.49746e7	+	9.52187e7i	−0.0790425	+	0.136906i
$887$	−8.24149e8	−	4.75822e8i	−1.18096	−	0.681827i	−0.224723	−	0.974423i	$-0.572148\pi$
$887$	−8.24149e8	−	4.75822e8i	−1.18096	−	0.681827i	−0.956236	+	0.292596i	$0.905481\pi$
$888$		0			0
$889$	6.42938e8	+	1.11360e9i	0.915091	+	1.58498i
$890$		−	4.22254e8i		−	0.598968i
$891$		0			0
$892$	4.19170e8			0.590603
$893$	9.21536e8	−	5.32049e8i	1.29407	−	0.747132i
$894$		0			0
$895$	−3.08222e7	+	5.33857e7i	−0.0429927	+	0.0744656i
$896$	9.05481e7	+	5.22780e7i	0.125880	+	0.0726766i
$897$		0			0
$898$	3.51321e8	+	6.08506e8i	0.485149	+	0.840303i
$899$			5.10517e8i			0.702638i
$900$		0			0
$901$	−7.64147e8			−1.04473
$902$	−1.15062e8	+	6.64309e7i	−0.156787	+	0.0905212i
$903$		0			0
$904$	3.29886e7	−	5.71379e7i	0.0446538	−	0.0773426i
$905$	−5.50580e8	−	3.17877e8i	−0.742805	−	0.428859i
$906$		0			0
$907$	−2.46790e8	−	4.27452e8i	−0.330754	−	0.572883i	0.651906	−	0.758300i	$-0.273970\pi$
$907$	−2.46790e8	−	4.27452e8i	−0.330754	−	0.572883i	−0.982660	+	0.185417i	$0.940636\pi$
$908$			1.15986e8i			0.154934i
$909$		0			0
$910$	−2.29824e8			−0.304980
$911$	−1.45261e8	+	8.38663e7i	−0.192129	+	0.110926i	−0.592979	−	0.805218i	$-0.702048\pi$
$911$	−1.45261e8	+	8.38663e7i	−0.192129	+	0.110926i	0.400850	+	0.916144i	$0.368715\pi$
$912$		0			0
$913$	−5.49188e8	+	9.51222e8i	−0.721620	+	1.24988i
$914$	−8.58382e7	−	4.95587e7i	−0.112420	−	0.0649054i
$915$		0			0
$916$	2.12774e8	+	3.68535e8i	0.276842	+	0.479504i
$917$			8.60186e7i			0.111554i
$918$		0			0
$919$	7.11908e8			0.917227			0.458614	−	0.888636i	$-0.348346\pi$
$919$	7.11908e8			0.917227			0.458614	+	0.888636i	$0.348346\pi$
$920$	1.59184e8	−	9.19050e7i	0.204426	−	0.118025i
$921$		0			0
$922$	1.00105e8	−	1.73386e8i	0.127721	−	0.221219i
$923$	−5.01126e8	−	2.89325e8i	−0.637297	−	0.367944i
$924$		0			0
$925$	−3.49485e8	−	6.05326e8i	−0.441574	−	0.764829i
$926$			1.74578e7i			0.0219865i
$927$		0			0
$928$	8.93904e7			0.111853
$929$	4.81576e8	−	2.78038e8i	0.600645	−	0.346783i	−0.168650	−	0.985676i	$-0.553941\pi$
$929$	4.81576e8	−	2.78038e8i	0.600645	−	0.346783i	0.769295	+	0.638893i	$0.220608\pi$
$930$		0			0
$931$	6.70601e8	−	1.16152e9i	0.831027	−	1.43938i
$932$	−6.45489e8	−	3.72673e8i	−0.797336	−	0.460342i
$933$		0			0
$934$	3.05599e8	+	5.29312e8i	0.375069	+	0.649638i
$935$			6.34049e8i			0.775689i
$936$		0			0
$937$	1.14269e9			1.38902			0.694509	−	0.719484i	$-0.255622\pi$
$937$	1.14269e9			1.38902			0.694509	+	0.719484i	$0.255622\pi$
$938$	6.56420e8	−	3.78984e8i	0.795378	−	0.459212i
$939$		0			0
$940$	2.18094e8	−	3.77750e8i	0.262579	−	0.454801i
$941$	−1.16468e8	−	6.72428e7i	−0.139778	−	0.0807006i	0.428480	−	0.903551i	$-0.359049\pi$
$941$	−1.16468e8	−	6.72428e7i	−0.139778	−	0.0807006i	−0.568258	+	0.822850i	$0.692382\pi$
$942$		0			0
$943$	9.57328e7	+	1.65814e8i	0.114163	+	0.197736i
$944$		−	1.96693e8i		−	0.233816i
$945$		0			0
$946$	−5.43663e8			−0.642180
$947$	−5.10930e8	+	2.94986e8i	−0.601606	+	0.347337i	−0.769673	−	0.638438i	$-0.779581\pi$
$947$	−5.10930e8	+	2.94986e8i	−0.601606	+	0.347337i	0.168067	+	0.985776i	$0.446247\pi$
$948$		0			0
$949$	−1.59564e8	+	2.76374e8i	−0.186697	+	0.323369i
$950$	−2.71435e8	−	1.56713e8i	−0.316589	−	0.182782i
$951$		0			0
$952$	2.59874e8	+	4.50115e8i	0.301198	+	0.521690i
$953$		−	4.97962e8i		−	0.575331i	−0.957731	−	0.287665i	$-0.907121\pi$
$953$		−	4.97962e8i		−	0.575331i	0.957731	−	0.287665i	$-0.0928791\pi$
$954$		0			0
$955$	−1.74968e8			−0.200885
$956$	4.47267e8	−	2.58230e8i	0.511909	−	0.295551i
$957$		0			0
$958$	−3.71384e8	+	6.43257e8i	−0.422403	+	0.731624i
$959$	1.49434e9	+	8.62757e8i	1.69431	+	0.978212i
$960$		0			0
$961$	−1.03465e8	−	1.79206e8i	−0.116580	−	0.201922i
$962$		−	4.01262e8i		−	0.450716i
$963$		0			0
$964$	3.58251e8			0.399904
$965$	3.12323e8	−	1.80320e8i	0.347554	−	0.200660i
$966$		0			0
$967$	−8.29987e8	+	1.43758e9i	−0.917893	+	1.58984i	−0.115284	+	0.993333i	$0.536778\pi$
$967$	−8.29987e8	+	1.43758e9i	−0.917893	+	1.58984i	−0.802609	+	0.596505i	$0.796556\pi$
$968$	5.35758e7	+	3.09320e7i	0.0590667	+	0.0341022i
$969$		0			0
$970$	−2.94033e8	−	5.09280e8i	−0.322167	−	0.558009i
$971$			1.02684e9i			1.12162i	0.827944	+	0.560810i	$0.189510\pi$
$971$			1.02684e9i			1.12162i	−0.827944	+	0.560810i	$0.810490\pi$
$972$		0			0
$973$	−3.50854e8			−0.380880
$974$	2.28251e8	−	1.31781e8i	0.247022	−	0.142618i
$975$		0			0
$976$	1.95834e8	−	3.39194e8i	0.210639	−	0.364837i
$977$	−2.43089e8	−	1.40348e8i	−0.260665	−	0.150495i	0.363973	−	0.931409i	$-0.381420\pi$
$977$	−2.43089e8	−	1.40348e8i	−0.260665	−	0.150495i	−0.624638	+	0.780915i	$0.714753\pi$
$978$		0			0
$979$	−6.33220e8	−	1.09677e9i	−0.674849	−	1.16887i
$980$		−	5.49778e8i		−	0.584129i
$981$		0			0
$982$	−1.24168e9			−1.31122
$983$	−1.99191e8	+	1.15003e8i	−0.209705	+	0.121073i	−0.601174	−	0.799118i	$-0.705300\pi$
$983$	−1.99191e8	+	1.15003e8i	−0.209705	+	0.121073i	0.391469	+	0.920191i	$0.371967\pi$
$984$		0			0
$985$	4.57315e8	−	7.92093e8i	0.478528	−	0.828834i
$986$	3.84827e8	+	2.22180e8i	0.401453	+	0.231779i
$987$		0			0
$988$	−8.99652e7	−	1.55824e8i	−0.0932833	−	0.161571i
$989$			7.83467e8i			0.809901i
$990$		0			0
$991$	8.95079e7			0.0919688			0.0459844	−	0.998942i	$-0.485358\pi$
$991$	8.95079e7			0.0919688			0.0459844	+	0.998942i	$0.485358\pi$
$992$	−1.65959e8	+	9.58163e7i	−0.170006	+	0.0981532i
$993$		0			0
$994$	1.09821e9	−	1.90215e9i	1.11821	−	1.93680i
$995$	2.62373e8	+	1.51481e8i	0.266348	+	0.153776i
$996$		0			0
$997$	−6.22328e8	−	1.07790e9i	−0.627963	−	1.08766i	−0.987960	−	0.154710i	$-0.950556\pi$
$997$	−6.22328e8	−	1.07790e9i	−0.627963	−	1.08766i	0.359997	−	0.932953i	$-0.382778\pi$
$998$			7.54887e8i			0.759435i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.7.d.g.53.2		16
3.2	odd	2	inner	162.7.d.g.53.7		16
9.2	odd	6	inner	162.7.d.g.107.2		16
9.4	even	3		162.7.b.b.161.3	✓	8
9.5	odd	6		162.7.b.b.161.6	yes	8
9.7	even	3	inner	162.7.d.g.107.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.7.b.b.161.3	✓	8	9.4	even	3
162.7.b.b.161.6	yes	8	9.5	odd	6
162.7.d.g.53.2		16	1.1	even	1	trivial
162.7.d.g.53.7		16	3.2	odd	2	inner
162.7.d.g.107.2		16	9.2	odd	6	inner
162.7.d.g.107.7		16	9.7	even	3	inner

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:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	162.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.89898 + 2.82843i) q^{2} +(16.0000 - 27.7128i) q^{4} +(-74.2039 - 42.8417i) q^{5} +(282.029 + 488.488i) q^{7} +181.019i q^{8} +O(q^{10})\)	\(q+(-4.89898 + 2.82843i) q^{2} +(16.0000 - 27.7128i) q^{4} +(-74.2039 - 42.8417i) q^{5} +(282.029 + 488.488i) q^{7} +181.019i q^{8} +484.698 q^{10} +(1258.96 - 726.862i) q^{11} +(-420.311 + 728.001i) q^{13} +(-2763.31 - 1595.40i) q^{14} +(-512.000 - 886.810i) q^{16} -5090.31i q^{17} -6688.88 q^{19} +(-2374.53 + 1370.93i) q^{20} +(-4111.75 + 7121.77i) q^{22} +(10263.1 + 5925.40i) q^{23} +(-4141.68 - 7173.61i) q^{25} -4755.28i q^{26} +18049.9 q^{28} +(13364.3 - 7715.89i) q^{29} +(-16541.1 + 28650.0i) q^{31} +(5016.55 + 2896.31i) q^{32} +(14397.6 + 24937.3i) q^{34} -48330.3i q^{35} +84382.4 q^{37} +(32768.7 - 18919.0i) q^{38} +(7755.17 - 13432.3i) q^{40} +(13991.8 + 8078.17i) q^{41} +(33055.4 + 57253.7i) q^{43} -46519.2i q^{44} -67038.2 q^{46} +(-137771. + 79542.3i) q^{47} +(-100256. + 173649. i) q^{49} +(40580.1 + 23428.9i) q^{50} +(13450.0 + 23296.0i) q^{52} -150118. i q^{53} -124560. q^{55} +(-88425.8 + 51052.7i) q^{56} +(-43647.6 + 75599.9i) q^{58} +(166349. + 96041.6i) q^{59} +(191244. + 331244. i) q^{61} -187141. i q^{62} -32768.0 q^{64} +(62377.5 - 36013.7i) q^{65} +(-118774. + 205723. i) q^{67} +(-141067. - 81445.0i) q^{68} +(136699. + 236769. i) q^{70} +688359. i q^{71} +379634. q^{73} +(-413387. + 238669. i) q^{74} +(-107022. + 185368. i) q^{76} +(710128. + 409992. i) q^{77} +(385496. + 667698. i) q^{79} +87739.7i q^{80} -91394.1 q^{82} +(-654334. + 377780. i) q^{83} +(-218077. + 377721. i) q^{85} +(-323876. - 186990. i) q^{86} +(131576. + 227897. i) q^{88} -871169. i q^{89} -474160. q^{91} +(328419. - 189613. i) q^{92} +(449959. - 779352. i) q^{94} +(496341. + 286563. i) q^{95} +(-606631. - 1.05072e6i) q^{97} -1.13427e6i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 256 q^{4} - 964 q^{7}+O(q^{10}) \) 16 * q + 256 * q^4 - 964 * q^7	\( 16 q + 256 q^{4} - 964 q^{7} - 1536 q^{10} - 4540 q^{13} - 8192 q^{16} - 47368 q^{19} - 27072 q^{22} + 32392 q^{25} - 61696 q^{28} - 77056 q^{31} + 52608 q^{34} - 22696 q^{37} - 24576 q^{40} + 226604 q^{43} - 325440 q^{46} - 1298088 q^{49} + 145280 q^{52} - 2921832 q^{55} - 867456 q^{58} + 327476 q^{61} - 524288 q^{64} - 1713292 q^{67} + 176352 q^{70} - 4378432 q^{73} - 757888 q^{76} + 1326884 q^{79} - 2317632 q^{82} - 3483180 q^{85} + 866304 q^{88} + 2260648 q^{91} + 26400 q^{94} + 2200064 q^{97}+O(q^{100}) \) 16 * q + 256 * q^4 - 964 * q^7 - 1536 * q^10 - 4540 * q^13 - 8192 * q^16 - 47368 * q^19 - 27072 * q^22 + 32392 * q^25 - 61696 * q^28 - 77056 * q^31 + 52608 * q^34 - 22696 * q^37 - 24576 * q^40 + 226604 * q^43 - 325440 * q^46 - 1298088 * q^49 + 145280 * q^52 - 2921832 * q^55 - 867456 * q^58 + 327476 * q^61 - 524288 * q^64 - 1713292 * q^67 + 176352 * q^70 - 4378432 * q^73 - 757888 * q^76 + 1326884 * q^79 - 2317632 * q^82 - 3483180 * q^85 + 866304 * q^88 + 2260648 * q^91 + 26400 * q^94 + 2200064 * q^97

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