LMFDB - Embedded newform 162.7.d.g.53.7

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			53.7
Root			$11.9992 + 12.7063i$ of defining polynomial
Character	$\chi$	$=$	162.53
Dual form			162.7.d.g.107.7

$q$-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	0.766532	−	0.642206i	$-0.221981\pi$
$5$	74.2039	+	42.8417i	0.593631	+	0.342733i	−0.172901	+	0.984939i	$0.555314\pi$
$6$		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	−0.891798	−	0.452434i	$-0.850556\pi$
$11$	−1258.96	+	726.862i	−0.945877	+	0.546102i	−0.0540793	+	0.998537i	$0.517222\pi$
$12$		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	$0.173340\pi$
$17$			5090.31i			1.03609i	−0.855353	+	0.518045i	$0.826660\pi$
$18$		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	0.0149399	−	0.999888i	$-0.495244\pi$
$23$	−10263.1	−	5925.40i	−0.843519	−	0.487006i	−0.858459	+	0.512883i	$0.828578\pi$
$24$		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	−0.748301	−	0.663360i	$-0.769130\pi$
$29$	−13364.3	+	7715.89i	−0.547964	+	0.316367i	0.200336	+	0.979727i	$0.435797\pi$
$30$		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	0.395048	−	0.918661i	$-0.370728\pi$
$41$	−13991.8	−	8078.17i	−0.203012	−	0.117209i	−0.598060	+	0.801452i	$0.704061\pi$
$42$		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	0.342150	−	0.939645i	$-0.388845\pi$
$47$	137771.	−	79542.3i	1.32698	−	0.766134i	0.984832	+	0.173512i	$0.0555114\pi$
$48$		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	$0.168201\pi$
$53$			150118.i			1.00834i	−0.863606	+	0.504168i	$0.831799\pi$
$54$		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	0.0369813	−	0.999316i	$-0.488226\pi$
$59$	−166349.	−	96041.6i	−0.809961	−	0.467631i	−0.846942	+	0.531685i	$0.821559\pi$
$60$		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	$-0.588457\pi$
$71$		−	688359.i		−	1.92327i	0.274334	−	0.961635i	$-0.411543\pi$
$72$		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	0.196859	−	0.980432i	$-0.436926\pi$
$83$	654334.	−	377780.i	1.14437	−	0.660701i	0.947508	+	0.319731i	$0.103593\pi$
$84$		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	$0.212007\pi$
$89$			871169.i			1.23575i	−0.786274	+	0.617877i	$0.787993\pi$
$90$		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	−0.125594	−	0.992082i	$-0.540084\pi$
$101$	691103.	−	399008.i	0.670778	−	0.387274i	0.796371	+	0.604808i	$0.206750\pi$
$102$		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	$-0.862473\pi$
$107$		−	1.02594e6i		−	0.837474i	0.908108	−	0.418737i	$-0.137527\pi$
$108$		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	0.605375	−	0.795940i	$-0.293023\pi$
$113$	315645.	+	182238.i	0.218758	+	0.126300i	−0.386617	+	0.922240i	$0.626356\pi$
$114$		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	0.470339	−	0.882486i	$-0.344132\pi$
$131$	−132069.	−	76249.8i	−0.0587470	−	0.0339176i	−0.529086	+	0.848568i	$0.677465\pi$
$132$		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	−0.917071	−	0.398725i	$-0.869453\pi$
$137$	−2.64927e6	+	1.52955e6i	−1.03030	+	0.594844i	−0.113230	+	0.993569i	$0.536120\pi$
$138$		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	−0.0919153	−	0.995767i	$-0.529299\pi$
$149$	−3.30872e6	−	1.91029e6i	−1.00023	−	0.577484i	−0.908317	+	0.418282i	$0.862632\pi$
$150$		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	0.635671	−	0.771960i	$-0.280723\pi$
$167$	1.32724e6	+	766280.i	0.284970	+	0.164527i	−0.350701	+	0.936487i	$0.614057\pi$
$168$		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	0.139227	−	0.990261i	$-0.455538\pi$
$173$	5.52168e6	−	3.18794e6i	1.06643	−	0.615704i	0.927204	+	0.374556i	$0.122205\pi$
$174$		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	$0.0199776\pi$
$179$			719446.i			0.125441i	−0.998031	+	0.0627204i	$0.980022\pi$
$180$		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	−0.621503	−	0.783412i	$-0.713478\pi$
$191$	−1.76845e6	+	1.02101e6i	−0.253800	+	0.146532i	0.367703	+	0.929943i	$0.380144\pi$
$192$		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	$-0.754027\pi$
$197$		−	1.06745e7i		−	1.39621i	0.715995	−	0.698105i	$-0.245973\pi$
$198$		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	−0.359785	−	0.933035i	$-0.617150\pi$
$227$	3.13896e6	−	1.81228e6i	0.268354	−	0.154934i	0.628139	+	0.778101i	$0.283817\pi$
$228$		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	$0.372369\pi$
$233$			2.32921e7i			1.84137i	−0.390308	+	0.920684i	$0.627631\pi$
$234$		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	−0.108611	−	0.994084i	$-0.534640\pi$
$239$	−1.39771e7	−	8.06968e6i	−1.02382	−	0.591102i	−0.915208	+	0.402982i	$0.867974\pi$
$240$		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	$0.188998\pi$
$251$			1.76943e7i			1.11896i	−0.828845	+	0.559478i	$0.811002\pi$
$252$		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	0.997526	−	0.0703044i	$-0.0223971\pi$
$257$	2.43654e7	+	1.40674e7i	1.43540	+	0.828730i	0.437877	+	0.899035i	$0.355730\pi$
$258$		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	−0.433875	−	0.900973i	$-0.642854\pi$
$263$	2.35495e6	−	1.35963e6i	0.129454	−	0.0747402i	0.563328	+	0.826233i	$0.309521\pi$
$264$		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	$0.175678\pi$
$269$			2.04116e7i			1.04863i	−0.851525	+	0.524314i	$0.824322\pi$
$270$		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	−0.176699	−	0.984265i	$-0.556542\pi$
$281$	1.30321e7	−	7.52411e6i	0.587350	−	0.339107i	0.764049	+	0.645158i	$0.223209\pi$
$282$		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	−0.0690059	−	0.997616i	$-0.521983\pi$
$293$	−2.43355e7	−	1.40501e7i	−0.967470	−	0.558569i	−0.898464	+	0.439047i	$0.855316\pi$
$294$		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	0.819453	−	0.573146i	$-0.194277\pi$
$311$	2.20434e7	+	1.27268e7i	0.732820	+	0.423094i	−0.0866330	+	0.996240i	$0.527611\pi$
$312$		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	−0.122796	−	0.992432i	$-0.539186\pi$
$317$	2.15110e7	−	1.24194e7i	0.675278	−	0.389872i	0.798074	+	0.602560i	$0.205853\pi$
$318$		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	−0.104609	−	0.994513i	$-0.533359\pi$
$347$	−4.25418e7	−	2.45615e7i	−1.01819	−	0.587851i	−0.913578	+	0.406663i	$0.866692\pi$
$348$		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	−0.571933	−	0.820301i	$-0.693806\pi$
$353$	−6.48799e6	+	3.74584e6i	−0.147498	+	0.0851579i	0.424435	+	0.905459i	$0.360473\pi$
$354$		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	$0.110289\pi$
$359$			3.14246e7i			0.679183i	−0.940573	+	0.339592i	$0.889711\pi$
$360$		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	0.432358	−	0.901702i	$-0.357682\pi$
$383$	−7.43620e6	−	4.29329e6i	−0.132359	−	0.0764178i	−0.564718	+	0.825284i	$0.691015\pi$
$384$		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	0.184590	−	0.982816i	$-0.440904\pi$
$389$	6.64001e7	−	3.83361e7i	1.12803	−	0.651268i	0.943438	+	0.331548i	$0.107571\pi$
$390$		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	0.605343	−	0.795965i	$-0.293036\pi$
$401$	1.41013e7	+	8.14136e6i	0.218688	+	0.126260i	−0.386655	+	0.922225i	$0.626369\pi$
$402$		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	0.362897	−	0.931829i	$-0.381788\pi$
$419$	−1.93201e7	−	1.11544e7i	−0.262643	−	0.151637i	−0.625540	+	0.780192i	$0.715121\pi$
$420$		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	$-0.772747\pi$
$431$		−	1.04853e8i		−	1.30963i	0.755791	−	0.654813i	$-0.227253\pi$
$432$		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	−0.593673	−	0.804706i	$-0.702323\pi$
$443$	−1.68325e7	+	9.71822e6i	−0.193614	+	0.111783i	0.400059	+	0.916489i	$0.368989\pi$
$444$		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	$0.240681\pi$
$449$			1.24211e8i			1.37221i	−0.727503	+	0.686105i	$0.759319\pi$
$450$		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	−0.335351	−	0.942093i	$-0.608855\pi$
$461$	3.06507e7	−	1.76962e7i	0.312851	−	0.180624i	0.648201	+	0.761469i	$0.275521\pi$
$462$		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	$0.177968\pi$
$467$			1.08045e8i			1.06085i	−0.847731	+	0.530427i	$0.822032\pi$
$468$		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	−0.918320	−	0.395840i	$-0.870454\pi$
$479$	−1.13713e8	+	6.56521e7i	−1.03467	+	0.597368i	−0.116353	+	0.993208i	$0.537120\pi$
$480$		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	$-0.955564\pi$
$491$	−1.90093e8	−	1.09750e8i	−1.60591	−	0.927173i	−0.615640	−	0.788028i	$-0.711102\pi$
$492$		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	$0.0226657\pi$
$503$			1.81087e7i			0.142293i	−0.997466	+	0.0711463i	$0.977334\pi$
$504$		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	−0.0118029	−	0.999930i	$-0.503757\pi$
$509$	−1.16531e8	−	6.72795e7i	−0.883669	−	0.510187i	−0.871867	+	0.489744i	$0.837090\pi$
$510$		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	$-0.920674\pi$
$521$		−	6.97595e7i		−	0.493276i	0.969108	−	0.246638i	$-0.0793259\pi$
$522$		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	$0.206167\pi$
$557$			2.08528e8i			1.20670i	−0.797477	+	0.603349i	$0.793833\pi$
$558$		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	$-0.997591\pi$
$563$	−2.68842e8	−	1.55216e8i	−1.50651	−	0.869785i	−0.506540	−	0.862216i	$-0.669076\pi$
$564$		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	−0.868138	−	0.496323i	$-0.834683\pi$
$569$	−1.60710e8	+	9.27857e7i	−0.872378	+	0.503668i	−0.00424037	+	0.999991i	$0.501350\pi$
$570$		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	0.356691	−	0.934222i	$-0.383905\pi$
$587$	2.71860e8	−	1.56958e8i	1.34410	−	0.776015i	0.987406	+	0.158207i	$0.0505714\pi$
$588$		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	$-0.738786\pi$
$593$		−	3.05107e8i		−	1.46315i	0.681762	−	0.731574i	$-0.261214\pi$
$594$		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	0.619297	−	0.785156i	$-0.287418\pi$
$599$	5.35114e7	+	3.08948e7i	0.248981	+	0.143749i	−0.370317	+	0.928906i	$0.620751\pi$
$600$		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	0.592796	−	0.805353i	$-0.298024\pi$
$617$	4.50365e7	+	2.60018e7i	0.191738	+	0.110700i	−0.401058	+	0.916053i	$0.631357\pi$
$618$		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	−0.860703	−	0.509107i	$-0.829976\pi$
$641$	−2.23909e8	+	1.29274e8i	−0.850155	+	0.490837i	0.0105483	+	0.999944i	$0.496642\pi$
$642$		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	$-0.831865\pi$
$647$		−	2.73001e8i		−	1.00798i	0.863709	−	0.503990i	$-0.168135\pi$
$648$		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	$0.0137895\pi$
$653$	4.27719e8	+	2.46944e8i	1.53610	+	0.886867i	0.537036	+	0.843559i	$0.319544\pi$
$654$		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	−0.926079	−	0.377330i	$-0.876842\pi$
$659$	−3.04033e8	+	1.75533e8i	−1.06234	+	0.613343i	−0.136262	+	0.990673i	$0.543509\pi$
$660$		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	−0.299323	−	0.954152i	$-0.596761\pi$
$677$	1.17083e8	−	6.75978e7i	0.377335	−	0.217854i	0.676658	+	0.736297i	$0.263428\pi$
$678$		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	$0.0774935\pi$
$683$			1.53606e8i			0.482110i	−0.970511	+	0.241055i	$0.922507\pi$
$684$		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	$0.0814881\pi$
$701$			1.74451e8i			0.506431i	−0.967410	+	0.253215i	$0.918512\pi$
$702$		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	$0.300552\pi$
$719$			6.02172e8i			1.62007i	−0.586382	+	0.810035i	$0.699448\pi$
$720$		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	0.885732	−	0.464197i	$-0.153657\pi$
$743$	3.80062e8	+	2.19429e8i	0.926591	+	0.534968i	0.0408594	+	0.999165i	$0.486990\pi$
$744$		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	0.831781	−	0.555103i	$-0.187321\pi$
$761$	3.37998e8	+	1.95143e8i	0.766938	+	0.442792i	−0.0648430	+	0.997895i	$0.520655\pi$
$762$		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	$0.000682879\pi$
$773$			1.98181e6i			0.00429065i	−0.999998	+	0.00214533i	$0.999317\pi$
$774$		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	0.776245	−	0.630431i	$-0.217122\pi$
$797$	3.13071e8	+	1.80752e8i	0.618399	+	0.357033i	−0.157847	+	0.987464i	$0.550455\pi$
$798$		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	$0.0654396\pi$
$809$			2.16174e8i			0.408279i	−0.978942	+	0.204140i	$0.934560\pi$
$810$		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	0.150188	−	0.988657i	$-0.452012\pi$
$821$	5.98480e8	−	3.45533e8i	1.08148	−	0.624396i	0.931297	+	0.364262i	$0.118679\pi$
$822$		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	$0.0994743\pi$
$827$			3.47789e8i			0.614892i	−0.951566	+	0.307446i	$0.900526\pi$
$828$		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	−0.622340	−	0.782747i	$-0.713818\pi$
$839$	−1.50973e8	+	8.71645e7i	−0.255632	+	0.147589i	0.366709	+	0.930336i	$0.380485\pi$
$840$		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	−0.891954	−	0.452127i	$-0.850665\pi$
$857$	−5.95671e8	+	3.43911e8i	−0.946377	+	0.546391i	−0.0544235	+	0.998518i	$0.517332\pi$
$858$		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	$0.282101\pi$
$863$			9.95858e8i			1.54941i	−0.632326	+	0.774703i	$0.717899\pi$
$864$		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	$0.114827\pi$
$881$			4.82715e8i			0.705932i	−0.935636	+	0.352966i	$0.885173\pi$
$882$		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	0.956236	−	0.292596i	$-0.0945191\pi$
$887$	8.24149e8	+	4.75822e8i	1.18096	+	0.681827i	0.224723	+	0.974423i	$0.427852\pi$
$888$		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	−0.400850	−	0.916144i	$-0.631285\pi$
$911$	1.45261e8	−	8.38663e7i	0.192129	−	0.110926i	0.592979	+	0.805218i	$0.297952\pi$
$912$		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	−0.769295	−	0.638893i	$-0.779392\pi$
$929$	−4.81576e8	+	2.78038e8i	−0.600645	+	0.346783i	0.168650	+	0.985676i	$0.446059\pi$
$930$		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	0.568258	−	0.822850i	$-0.307618\pi$
$941$	1.16468e8	+	6.72428e7i	0.139778	+	0.0807006i	−0.428480	+	0.903551i	$0.640951\pi$
$942$		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	−0.168067	−	0.985776i	$-0.553753\pi$
$947$	5.10930e8	−	2.94986e8i	0.601606	−	0.347337i	0.769673	+	0.638438i	$0.220419\pi$
$948$		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	$0.0928791\pi$
$953$			4.97962e8i			0.575331i	−0.957731	+	0.287665i	$0.907121\pi$
$954$		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	$-0.810490\pi$
$971$		−	1.02684e9i		−	1.12162i	0.827944	−	0.560810i	$-0.189510\pi$
$972$		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	0.624638	−	0.780915i	$-0.285247\pi$
$977$	2.43089e8	+	1.40348e8i	0.260665	+	0.150495i	−0.363973	+	0.931409i	$0.618580\pi$
$978$		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	−0.391469	−	0.920191i	$-0.628033\pi$
$983$	1.99191e8	−	1.15003e8i	0.209705	−	0.121073i	0.601174	+	0.799118i	$0.294700\pi$
$984$		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.53.7		16
3.2	odd	2	inner	162.7.d.g.53.2		16
9.2	odd	6	inner	162.7.d.g.107.7		16
9.4	even	3		162.7.b.b.161.6	yes	8
9.5	odd	6		162.7.b.b.161.3	✓	8
9.7	even	3	inner	162.7.d.g.107.2		16

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