LMFDB - Embedded newform 162.7.d.f.107.2

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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.2
Root			$-0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	162.107
Dual form			162.7.d.f.53.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.89898 - 2.82843i) q^{2} +(16.0000 + 27.7128i) q^{4} +(-21.4919 + 12.4084i) q^{5} +(3.09808 - 5.36603i) q^{7} -181.019i q^{8} +O(q^{10})$	\(q+(-4.89898 - 2.82843i) q^{2} +(16.0000 + 27.7128i) q^{4} +(-21.4919 + 12.4084i) q^{5} +(3.09808 - 5.36603i) q^{7} -181.019i q^{8} +140.385 q^{10} +(-113.360 - 65.4483i) q^{11} +(461.004 + 798.482i) q^{13} +(-30.3548 + 17.5254i) q^{14} +(-512.000 + 886.810i) q^{16} -3384.11i q^{17} +5403.30 q^{19} +(-687.742 - 397.068i) q^{20} +(370.232 + 641.260i) q^{22} +(2045.32 - 1180.87i) q^{23} +(-7504.56 + 12998.3i) q^{25} -5215.66i q^{26} +198.277 q^{28} +(-30256.9 - 17468.8i) q^{29} +(-2330.16 - 4035.96i) q^{31} +(5016.55 - 2896.31i) q^{32} +(-9571.71 + 16578.7i) q^{34} +153.768i q^{35} +6916.74 q^{37} +(-26470.6 - 15282.8i) q^{38} +(2246.16 + 3890.46i) q^{40} +(46637.1 - 26926.0i) q^{41} +(-61566.4 + 106636. i) q^{43} -4188.69i q^{44} -13360.0 q^{46} +(-83183.9 - 48026.3i) q^{47} +(58805.3 + 101854. i) q^{49} +(73529.4 - 42452.2i) q^{50} +(-14752.1 + 25551.4i) q^{52} +132310. i q^{53} +3248.43 q^{55} +(-971.354 - 560.812i) q^{56} +(98818.5 + 171159. i) q^{58} +(25181.5 - 14538.6i) q^{59} +(-160333. + 277705. i) q^{61} +26362.8i q^{62} -32768.0 q^{64} +(-19815.7 - 11440.6i) q^{65} +(264909. + 458837. i) q^{67} +(93783.3 - 54145.8i) q^{68} +(434.923 - 753.308i) q^{70} +628518. i q^{71} -68777.7 q^{73} +(-33885.0 - 19563.5i) q^{74} +(86452.7 + 149741. i) q^{76} +(-702.395 + 405.528i) q^{77} +(-235877. + 408551. i) q^{79} -25412.4i q^{80} -304633. q^{82} +(-29055.1 - 16775.0i) q^{83} +(41991.3 + 72731.1i) q^{85} +(603225. - 348272. i) q^{86} +(-11847.4 + 20520.3i) q^{88} +1.01543e6i q^{89} +5712.90 q^{91} +(65450.3 + 37787.7i) q^{92} +(271678. + 470559. i) q^{94} +(-116127. + 67046.1i) q^{95} +(-209094. + 362162. i) q^{97} -665306. i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 128 q^{4} + 4 q^{7}+O(q^{10}) $ 8 * q + 128 * q^4 + 4 * q^7	$ 8 q + 128 q^{4} + 4 q^{7} + 5280 q^{10} - 3836 q^{13} - 4096 q^{16} + 20488 q^{19} + 27072 q^{22} + 25700 q^{25} + 256 q^{28} + 40096 q^{31} - 60528 q^{34} - 40400 q^{37} + 84480 q^{40} - 184940 q^{43} + 325440 q^{46} + 470484 q^{49} + 122752 q^{52} + 1899720 q^{55} - 24624 q^{58} - 609056 q^{61} - 262144 q^{64} + 2008972 q^{67} - 8160 q^{70} + 1051648 q^{73} + 327808 q^{76} + 848716 q^{79} + 1411584 q^{82} + 987840 q^{85} - 866304 q^{88} + 70520 q^{91} + 1965408 q^{94} - 3621728 q^{97}+O(q^{100}) $ 8 * q + 128 * q^4 + 4 * q^7 + 5280 * q^10 - 3836 * q^13 - 4096 * q^16 + 20488 * q^19 + 27072 * q^22 + 25700 * q^25 + 256 * q^28 + 40096 * q^31 - 60528 * q^34 - 40400 * q^37 + 84480 * q^40 - 184940 * q^43 + 325440 * q^46 + 470484 * q^49 + 122752 * q^52 + 1899720 * q^55 - 24624 * q^58 - 609056 * q^61 - 262144 * q^64 + 2008972 * q^67 - 8160 * q^70 + 1051648 * q^73 + 327808 * q^76 + 848716 * q^79 + 1411584 * q^82 + 987840 * q^85 - 866304 * q^88 + 70520 * q^91 + 1965408 * q^94 - 3621728 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$83$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

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

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−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
$5$	−21.4919	+	12.4084i	−0.171936	+	0.0992670i	−0.583498	−	0.812114i	$-0.698316\pi$
$5$	−21.4919	+	12.4084i	−0.171936	+	0.0992670i	0.411563	+	0.911381i	$0.364983\pi$
$6$		0			0
$7$	3.09808	−	5.36603i	0.00903229	−	0.0156444i	−0.861474	−	0.507802i	$-0.830458\pi$
$7$	3.09808	−	5.36603i	0.00903229	−	0.0156444i	0.870506	+	0.492157i	$0.163792\pi$
$8$		−	181.019i		−	0.353553i
$9$		0			0
$10$	140.385			0.140385
$11$	−113.360	−	65.4483i	−0.0851689	−	0.0491723i	0.456811	−	0.889564i	$-0.348992\pi$
$11$	−113.360	−	65.4483i	−0.0851689	−	0.0491723i	−0.541980	+	0.840392i	$0.682325\pi$
$12$		0			0
$13$	461.004	+	798.482i	0.209833	+	0.363442i	0.951662	−	0.307148i	$-0.0993746\pi$
$13$	461.004	+	798.482i	0.209833	+	0.363442i	−0.741829	+	0.670589i	$0.766041\pi$
$14$	−30.3548	+	17.5254i	−0.0110623	+	0.00638680i
$15$		0			0
$16$	−512.000	+	886.810i	−0.125000	+	0.216506i
$17$		−	3384.11i		−	0.688808i	−0.938822	−	0.344404i	$-0.888081\pi$
$17$		−	3384.11i		−	0.688808i	0.938822	−	0.344404i	$-0.111919\pi$
$18$		0			0
$19$	5403.30			0.787767			0.393884	−	0.919160i	$-0.371131\pi$
$19$	5403.30			0.787767			0.393884	+	0.919160i	$0.371131\pi$
$20$	−687.742	−	397.068i	−0.0859678	−	0.0496335i
$21$		0			0
$22$	370.232	+	641.260i	0.0347701	+	0.0602235i
$23$	2045.32	−	1180.87i	0.168104	−	0.0970549i	−0.413588	−	0.910464i	$-0.635724\pi$
$23$	2045.32	−	1180.87i	0.168104	−	0.0970549i	0.581692	+	0.813409i	$0.302391\pi$
$24$		0			0
$25$	−7504.56	+	12998.3i	−0.480292	+	0.831890i
$26$		−	5215.66i		−	0.296749i
$27$		0			0
$28$	198.277			0.00903229
$29$	−30256.9	−	17468.8i	−1.24060	−	0.716258i	−0.271380	−	0.962472i	$-0.587480\pi$
$29$	−30256.9	−	17468.8i	−1.24060	−	0.716258i	−0.969215	+	0.246214i	$0.920813\pi$
$30$		0			0
$31$	−2330.16	−	4035.96i	−0.0782170	−	0.135476i	0.824264	−	0.566206i	$-0.191589\pi$
$31$	−2330.16	−	4035.96i	−0.0782170	−	0.135476i	−0.902481	+	0.430730i	$0.858256\pi$
$32$	5016.55	−	2896.31i	0.153093	−	0.0883883i
$33$		0			0
$34$	−9571.71	+	16578.7i	−0.243530	+	0.421807i
$35$			153.768i			0.00358643i
$36$		0			0
$37$	6916.74			0.136551			0.0682757	−	0.997666i	$-0.478250\pi$
$37$	6916.74			0.136551			0.0682757	+	0.997666i	$0.478250\pi$
$38$	−26470.6	−	15282.8i	−0.482407	−	0.278518i
$39$		0			0
$40$	2246.16	+	3890.46i	0.0350962	+	0.0607884i
$41$	46637.1	−	26926.0i	0.676675	−	0.390679i	−0.121926	−	0.992539i	$-0.538907\pi$
$41$	46637.1	−	26926.0i	0.676675	−	0.390679i	0.798601	+	0.601860i	$0.205574\pi$
$42$		0			0
$43$	−61566.4	+	106636.i	−0.774352	+	1.34122i	0.160805	+	0.986986i	$0.448591\pi$
$43$	−61566.4	+	106636.i	−0.774352	+	1.34122i	−0.935158	+	0.354231i	$0.884743\pi$
$44$		−	4188.69i		−	0.0491723i
$45$		0			0
$46$	−13360.0			−0.137256
$47$	−83183.9	−	48026.3i	−0.801209	−	0.462578i	0.0426847	−	0.999089i	$-0.486409\pi$
$47$	−83183.9	−	48026.3i	−0.801209	−	0.462578i	−0.843894	+	0.536510i	$0.819742\pi$
$48$		0			0
$49$	58805.3	+	101854.i	0.499837	+	0.865743i
$50$	73529.4	−	42452.2i	0.588235	−	0.339618i
$51$		0			0
$52$	−14752.1	+	25551.4i	−0.104917	+	0.181721i
$53$			132310.i			0.888722i	0.895848	+	0.444361i	$0.146569\pi$
$53$			132310.i			0.888722i	−0.895848	+	0.444361i	$0.853431\pi$
$54$		0			0
$55$	3248.43			0.0195247
$56$	−971.354	−	560.812i	−0.00553113	−	0.00319340i
$57$		0			0
$58$	98818.5	+	171159.i	0.506471	+	0.877233i
$59$	25181.5	−	14538.6i	0.122610	−	0.0707889i	−0.437441	−	0.899247i	$-0.644115\pi$
$59$	25181.5	−	14538.6i	0.122610	−	0.0707889i	0.560051	+	0.828458i	$0.310782\pi$
$60$		0			0
$61$	−160333.	+	277705.i	−0.706372	+	1.22347i	0.259822	+	0.965657i	$0.416336\pi$
$61$	−160333.	+	277705.i	−0.706372	+	1.22347i	−0.966194	+	0.257816i	$0.916997\pi$
$62$			26362.8i			0.110616i
$63$		0			0
$64$	−32768.0			−0.125000
$65$	−19815.7	−	11440.6i	−0.0721556	−	0.0416590i
$66$		0			0
$67$	264909.	+	458837.i	0.880791	+	1.52558i	0.850463	+	0.526036i	$0.176322\pi$
$67$	264909.	+	458837.i	0.880791	+	1.52558i	0.0303290	+	0.999540i	$0.490345\pi$
$68$	93783.3	−	54145.8i	0.298262	−	0.172202i
$69$		0			0
$70$	434.923	−	753.308i	0.00126800	−	0.00219623i
$71$			628518.i			1.75607i	0.478594	+	0.878036i	$0.341146\pi$
$71$			628518.i			1.75607i	−0.478594	+	0.878036i	$0.658854\pi$
$72$		0			0
$73$	−68777.7			−0.176799			−0.0883994	−	0.996085i	$-0.528175\pi$
$73$	−68777.7			−0.176799			−0.0883994	+	0.996085i	$0.528175\pi$
$74$	−33885.0	−	19563.5i	−0.0836203	−	0.0482782i
$75$		0			0
$76$	86452.7	+	149741.i	0.196942	+	0.341113i
$77$	−702.395	+	405.528i	−0.00153854	+	0.000888277i
$78$		0			0
$79$	−235877.	+	408551.i	−0.478415	+	0.828638i	−0.999694	−	0.0247478i	$-0.992122\pi$
$79$	−235877.	+	408551.i	−0.478415	+	0.828638i	0.521279	+	0.853386i	$0.325455\pi$
$80$		−	25412.4i		−	0.0496335i
$81$		0			0
$82$	−304633.			−0.552503
$83$	−29055.1	−	16775.0i	−0.0508146	−	0.0293378i	0.474377	−	0.880322i	$-0.342673\pi$
$83$	−29055.1	−	16775.0i	−0.0508146	−	0.0293378i	−0.525192	+	0.850984i	$0.676007\pi$
$84$		0			0
$85$	41991.3	+	72731.1i	0.0683759	+	0.118431i
$86$	603225.	−	348272.i	0.948384	−	0.547550i
$87$		0			0
$88$	−11847.4	+	20520.3i	−0.0173850	+	0.0301118i
$89$			1.01543e6i			1.44039i	0.693772	+	0.720195i	$0.255947\pi$
$89$			1.01543e6i			1.44039i	−0.693772	+	0.720195i	$0.744053\pi$
$90$		0			0
$91$	5712.90			0.00758110
$92$	65450.3	+	37787.7i	0.0840520	+	0.0485275i
$93$		0			0
$94$	271678.	+	470559.i	0.327092	+	0.566540i
$95$	−116127.	+	67046.1i	−0.135445	+	0.0781993i
$96$		0			0
$97$	−209094.	+	362162.i	−0.229101	+	0.396815i	−0.957542	−	0.288294i	$-0.906912\pi$
$97$	−209094.	+	362162.i	−0.229101	+	0.396815i	0.728441	+	0.685109i	$0.240245\pi$
$98$		−	665306.i		−	0.706876i
$99$		0			0
$100$	−480292.			−0.480292
$101$	−581679.	−	335833.i	−0.564572	−	0.325956i	0.190406	−	0.981705i	$-0.439019\pi$
$101$	−581679.	−	335833.i	−0.564572	−	0.325956i	−0.754979	+	0.655749i	$0.772353\pi$
$102$		0			0
$103$	−350999.	−	607949.i	−0.321214	−	0.556359i	0.659525	−	0.751683i	$-0.270758\pi$
$103$	−350999.	−	607949.i	−0.321214	−	0.556359i	−0.980739	+	0.195324i	$0.937424\pi$
$104$	144541.	−	83450.6i	0.128496	−	0.0741872i
$105$		0			0
$106$	374230.	−	648185.i	0.314211	−	0.544229i
$107$		−	350565.i		−	0.286166i	−0.989711	−	0.143083i	$-0.954298\pi$
$107$		−	350565.i		−	0.286166i	0.989711	−	0.143083i	$-0.0457016\pi$
$108$		0			0
$109$	724369.			0.559345			0.279673	−	0.960095i	$-0.409774\pi$
$109$	724369.			0.559345			0.279673	+	0.960095i	$0.409774\pi$
$110$	−15914.0	−	9187.95i	−0.0119564	−	0.00690304i
$111$		0			0
$112$	3172.43	+	5494.81i	0.00225807	+	0.00391110i
$113$	−1.09419e6	+	631732.i	−0.758330	+	0.437822i	−0.828696	−	0.559699i	$-0.810917\pi$
$113$	−1.09419e6	+	631732.i	−0.758330	+	0.437822i	0.0703658	+	0.997521i	$0.477583\pi$
$114$		0			0
$115$	−29305.3	+	50758.2i	−0.0192687	+	0.0333744i
$116$		−	1.11800e6i		−	0.716258i
$117$		0			0
$118$	−164485.			−0.100111
$119$	−18159.2	−	10484.2i	−0.0107760	−	0.00622151i
$120$		0			0
$121$	−877214.	−	1.51938e6i	−0.495164	−	0.857650i
$122$	1.57094e6	−	906981.i	0.865126	−	0.499481i
$123$		0			0
$124$	74565.2	−	129151.i	0.0391085	−	0.0677379i
$125$		−	760240.i		−	0.389243i
$126$		0			0
$127$	2.67398e6			1.30541			0.652706	−	0.757611i	$-0.273634\pi$
$127$	2.67398e6			1.30541			0.652706	+	0.757611i	$0.273634\pi$
$128$	160530.	+	92681.9i	0.0765466	+	0.0441942i
$129$		0			0
$130$	64717.9	+	112095.i	0.0294574	+	0.0510217i
$131$	−3.10743e6	+	1.79407e6i	−1.38225	+	0.798043i	−0.992426	−	0.122846i	$-0.960798\pi$
$131$	−3.10743e6	+	1.79407e6i	−1.38225	+	0.798043i	−0.389825	+	0.920889i	$0.627465\pi$
$132$		0			0
$133$	16739.8	−	28994.2i	0.00711534	−	0.0123241i
$134$		−	2.99711e6i		−	1.24563i
$135$		0			0
$136$	−612590.			−0.243530
$137$	1.32548e6	+	765268.i	0.515481	+	0.297613i	0.735084	−	0.677976i	$-0.237143\pi$
$137$	1.32548e6	+	765268.i	0.515481	+	0.297613i	−0.219603	+	0.975589i	$0.570476\pi$
$138$		0			0
$139$	−1.76383e6	−	3.05504e6i	−0.656769	−	1.13756i	−0.981447	−	0.191732i	$-0.938589\pi$
$139$	−1.76383e6	−	3.05504e6i	−0.656769	−	1.13756i	0.324679	−	0.945824i	$-0.394744\pi$
$140$	−4261.35	+	2460.29i	−0.00155297	+	0.000896609i
$141$		0			0
$142$	1.77772e6	−	3.07909e6i	0.620865	−	1.07537i
$143$		−	120688.i		−	0.0412719i
$144$		0			0
$145$	867039.			0.284403
$146$	336941.	+	194533.i	0.108267	+	0.0625078i
$147$		0			0
$148$	110668.	+	191682.i	0.0341379	+	0.0591285i
$149$	−2.07440e6	+	1.19765e6i	−0.627094	+	0.362053i	−0.779626	−	0.626246i	$-0.784591\pi$
$149$	−2.07440e6	+	1.19765e6i	−0.627094	+	0.362053i	0.152532	+	0.988299i	$0.451257\pi$
$150$		0			0
$151$	1.50837e6	−	2.61258e6i	0.438105	−	0.758820i	−0.559438	−	0.828872i	$-0.688983\pi$
$151$	1.50837e6	−	2.61258e6i	0.438105	−	0.758820i	0.997543	+	0.0700517i	$0.0223164\pi$
$152$		−	978101.i		−	0.278518i
$153$		0			0
$154$	4588.02			0.00125621
$155$	100159.	+	57827.1i	0.0268966	+	0.0155287i
$156$		0			0
$157$	−2.79226e6	−	4.83633e6i	−0.721533	−	1.24973i	−0.960385	−	0.278676i	$-0.910104\pi$
$157$	−2.79226e6	−	4.83633e6i	−0.721533	−	1.24973i	0.238852	−	0.971056i	$-0.423229\pi$
$158$	2.31111e6	−	1.33432e6i	0.585936	−	0.338290i
$159$		0			0
$160$	−71877.0	+	124495.i	−0.0175481	+	0.0303942i
$161$		−	14633.7i		−	0.00350651i
$162$		0			0
$163$	−2.46039e6			−0.568121			−0.284061	−	0.958806i	$-0.591682\pi$
$163$	−2.46039e6			−0.568121			−0.284061	+	0.958806i	$0.591682\pi$
$164$	1.49239e6	+	861631.i	0.338338	+	0.195339i
$165$		0			0
$166$	94893.6	+	164361.i	0.0207450	+	0.0359313i
$167$	−3.48381e6	+	2.01138e6i	−0.748005	+	0.431861i	−0.824973	−	0.565173i	$-0.808810\pi$
$167$	−3.48381e6	+	2.01138e6i	−0.748005	+	0.431861i	0.0769675	+	0.997034i	$0.475476\pi$
$168$		0			0
$169$	1.98836e6	−	3.44393e6i	0.411940	−	0.713501i
$170$		−	475078.i		−	0.0966981i
$171$		0			0
$172$	−3.94025e6			−0.774352
$173$	3.58412e6	+	2.06929e6i	0.692220	+	0.399653i	0.804443	−	0.594030i	$-0.202464\pi$
$173$	3.58412e6	+	2.06929e6i	0.692220	+	0.399653i	−0.112223	+	0.993683i	$0.535797\pi$
$174$		0			0
$175$	46499.4	+	80539.4i	0.00867628	+	0.0150278i
$176$	116080.	−	67019.1i	0.0212922	−	0.0122931i
$177$		0			0
$178$	2.87207e6	−	4.97457e6i	0.509254	−	0.882055i
$179$			4.64610e6i			0.810083i	0.914298	+	0.405042i	$0.132743\pi$
$179$			4.64610e6i			0.810083i	−0.914298	+	0.405042i	$0.867257\pi$
$180$		0			0
$181$	2.01455e6			0.339737			0.169868	−	0.985467i	$-0.445666\pi$
$181$	2.01455e6			0.339737			0.169868	+	0.985467i	$0.445666\pi$
$182$	−27987.4	−	16158.5i	−0.00464246	−	0.00268032i
$183$		0			0
$184$	−213760.	−	370243.i	−0.0343141	−	0.0594337i
$185$	−148654.	+	85825.5i	−0.0234780	+	0.0135551i
$186$		0			0
$187$	−221484.	+	383622.i	−0.0338703	+	0.0586650i
$188$		−	3.07368e6i		−	0.462578i
$189$		0			0
$190$	758540.			0.110591
$191$	3.29614e6	+	1.90303e6i	0.473049	+	0.273115i	0.717515	−	0.696543i	$-0.245279\pi$
$191$	3.29614e6	+	1.90303e6i	0.473049	+	0.273115i	−0.244466	+	0.969658i	$0.578613\pi$
$192$		0			0
$193$	647738.	+	1.12191e6i	0.0901005	+	0.156059i	0.907553	−	0.419937i	$-0.137948\pi$
$193$	647738.	+	1.12191e6i	0.0901005	+	0.156059i	−0.817453	+	0.575996i	$0.804614\pi$
$194$	2.04870e6	−	1.18282e6i	0.280590	−	0.161999i
$195$		0			0
$196$	−1.88177e6	+	3.25932e6i	−0.249918	+	0.432871i
$197$			5.99463e6i			0.784086i	0.919947	+	0.392043i	$0.128231\pi$
$197$			5.99463e6i			0.784086i	−0.919947	+	0.392043i	$0.871769\pi$
$198$		0			0
$199$	−1.04921e6			−0.133139			−0.0665694	−	0.997782i	$-0.521205\pi$
$199$	−1.04921e6			−0.133139			−0.0665694	+	0.997782i	$0.521205\pi$
$200$	2.35294e6	+	1.35847e6i	0.294118	+	0.169809i
$201$		0			0
$202$	1.89976e6	+	3.29047e6i	0.230486	+	0.399213i
$203$	−187476.	+	108239.i	−0.0224108	+	0.0129389i
$204$		0			0
$205$	−668215.	+	1.15738e6i	−0.0775630	+	0.134343i
$206$			3.97110e6i			0.454265i
$207$		0			0
$208$	−944135.			−0.104917
$209$	−612517.	−	353637.i	−0.0670933	−	0.0387363i
$210$		0			0
$211$	2.77104e6	+	4.79958e6i	0.294982	+	0.510923i	0.974981	−	0.222290i	$-0.0713532\pi$
$211$	2.77104e6	+	4.79958e6i	0.294982	+	0.510923i	−0.679999	+	0.733213i	$0.738020\pi$
$212$	−3.66669e6	+	2.11696e6i	−0.384828	+	0.222180i
$213$		0			0
$214$	−991549.	+	1.71741e6i	−0.101175	+	0.175240i
$215$		−	3.05576e6i		−	0.307471i
$216$		0			0
$217$	−28876.1			−0.00282592
$218$	−3.54867e6	−	2.04882e6i	−0.342528	−	0.197758i
$219$		0			0
$220$	51974.9	+	90023.1i	0.00488119	+	0.00845446i
$221$	2.70215e6	−	1.56009e6i	0.250342	−	0.144535i
$222$		0			0
$223$	−2.06883e6	+	3.58332e6i	−0.186557	+	0.323125i	−0.944100	−	0.329659i	$-0.893066\pi$
$223$	−2.06883e6	+	3.58332e6i	−0.186557	+	0.323125i	0.757543	+	0.652785i	$0.226399\pi$
$224$		−	35891.9i		−	0.00319340i
$225$		0			0
$226$	7.14723e6			0.619174
$227$	−1.27830e7	−	7.38025e6i	−1.09283	−	0.630948i	−0.158504	−	0.987358i	$-0.550667\pi$
$227$	−1.27830e7	−	7.38025e6i	−1.09283	−	0.630948i	−0.934329	+	0.356410i	$0.884000\pi$
$228$		0			0
$229$	7.31735e6	+	1.26740e7i	0.609323	+	1.05538i	0.991352	+	0.131228i	$0.0418919\pi$
$229$	7.31735e6	+	1.26740e7i	0.609323	+	1.05538i	−0.382030	+	0.924150i	$0.624775\pi$
$230$	287132.	−	165776.i	0.0235992	−	0.0136250i
$231$		0			0
$232$	−3.16219e6	+	5.47708e6i	−0.253235	+	0.438617i
$233$		−	1.51778e6i		−	0.119989i	−0.998199	−	0.0599946i	$-0.980892\pi$
$233$		−	1.51778e6i		−	0.119989i	0.998199	−	0.0599946i	$-0.0191083\pi$
$234$		0			0
$235$	2.38371e6			0.183675
$236$	805809.	+	465234.i	0.0613050	+	0.0353945i
$237$		0			0
$238$	59307.8	+	102724.i	0.00439927	+	0.00761977i
$239$	1.20904e7	−	6.98040e6i	0.885619	−	0.511312i	0.0131121	−	0.999914i	$-0.495826\pi$
$239$	1.20904e7	−	6.98040e6i	0.885619	−	0.511312i	0.872507	+	0.488602i	$0.162493\pi$
$240$		0			0
$241$	−1.26582e7	+	2.19246e7i	−0.904317	+	1.56632i	−0.0824864	+	0.996592i	$0.526286\pi$
$241$	−1.26582e7	+	2.19246e7i	−0.904317	+	1.56632i	−0.821831	+	0.569731i	$0.807047\pi$
$242$			9.92454e6i			0.700268i
$243$		0			0
$244$	−1.02613e7			−0.706372
$245$	−2.52768e6	−	1.45936e6i	−0.171879	−	0.0992346i
$246$		0			0
$247$	2.49094e6	+	4.31443e6i	0.165300	+	0.286308i
$248$	−730587.	+	421805.i	−0.0478979	+	0.0276539i
$249$		0			0
$250$	−2.15028e6	+	3.72440e6i	−0.137618	+	0.238361i
$251$		−	3.58400e6i		−	0.226645i	−0.993558	−	0.113323i	$-0.963851\pi$
$251$		−	3.58400e6i		−	0.226645i	0.993558	−	0.113323i	$-0.0361494\pi$
$252$		0			0
$253$	−309143.			−0.0190896
$254$	−1.30998e7	−	7.56317e6i	−0.799398	−	0.461533i
$255$		0			0
$256$	−524288.	−	908093.i	−0.0312500	−	0.0541266i
$257$	2.00837e7	−	1.15953e7i	1.18316	−	0.683098i	0.226417	−	0.974031i	$-0.427299\pi$
$257$	2.00837e7	−	1.15953e7i	1.18316	−	0.683098i	0.956743	+	0.290933i	$0.0939656\pi$
$258$		0			0
$259$	21428.6	−	37115.4i	0.00123337	−	0.00213626i
$260$		−	732199.i		−	0.0416590i
$261$		0			0
$262$	2.02976e7			1.12860
$263$	−1.72997e7	−	9.98800e6i	−0.950981	−	0.549049i	−0.0575954	−	0.998340i	$-0.518343\pi$
$263$	−1.72997e7	−	9.98800e6i	−0.950981	−	0.549049i	−0.893386	+	0.449291i	$0.851677\pi$
$264$		0			0
$265$	−1.64176e6	−	2.84360e6i	−0.0882208	−	0.152803i
$266$	−164016.	+	94694.7i	−0.00871448	+	0.00503131i
$267$		0			0
$268$	−8.47710e6	+	1.46828e7i	−0.440396	+	0.762788i
$269$		−	1.05394e7i		−	0.541453i	−0.962656	−	0.270726i	$-0.912736\pi$
$269$		−	1.05394e7i		−	0.541453i	0.962656	−	0.270726i	$-0.0872639\pi$
$270$		0			0
$271$	−2.76838e7			−1.39097			−0.695485	−	0.718540i	$-0.744811\pi$
$271$	−2.76838e7			−1.39097			−0.695485	+	0.718540i	$0.744811\pi$
$272$	3.00106e6	+	1.73267e6i	0.149131	+	0.0861010i
$273$		0			0
$274$	−4.32901e6	−	7.49806e6i	−0.210444	−	0.364500i
$275$	1.70143e6	−	982322.i	0.0818119	−	0.0472341i
$276$		0			0
$277$	−4.08298e6	+	7.07192e6i	−0.192104	+	0.332735i	−0.945947	−	0.324320i	$-0.894865\pi$
$277$	−4.08298e6	+	7.07192e6i	−0.192104	+	0.332735i	0.753843	+	0.657055i	$0.228198\pi$
$278$			1.99555e7i			0.928811i
$279$		0			0
$280$	27835.1			0.00126800
$281$	−3.85847e6	−	2.22769e6i	−0.173899	−	0.100400i	0.410524	−	0.911850i	$-0.365346\pi$
$281$	−3.85847e6	−	2.22769e6i	−0.173899	−	0.100400i	−0.584423	+	0.811449i	$0.698679\pi$
$282$		0			0
$283$	1.59414e7	+	2.76112e7i	0.703341	+	1.21822i	0.967287	+	0.253685i	$0.0816426\pi$
$283$	1.59414e7	+	2.76112e7i	0.703341	+	1.21822i	−0.263946	+	0.964537i	$0.585024\pi$
$284$	−1.74180e7	+	1.00563e7i	−0.760402	+	0.439018i
$285$		0			0
$286$	−341356.	+	591246.i	−0.0145918	+	0.0252738i
$287$		−	333675.i		−	0.0141149i
$288$		0			0
$289$	1.26854e7			0.525544
$290$	−4.24760e6	−	2.45236e6i	−0.174161	−	0.100552i
$291$		0			0
$292$	−1.10044e6	−	1.90602e6i	−0.0441997	−	0.0765561i
$293$	3.09320e7	−	1.78586e7i	1.22972	−	0.709977i	0.262746	−	0.964865i	$-0.415372\pi$
$293$	3.09320e7	−	1.78586e7i	1.22972	−	0.709977i	0.966971	+	0.254888i	$0.0820385\pi$
$294$		0			0
$295$	−360800.	+	624924.i	−0.0140540	+	0.0243423i
$296$		−	1.25206e6i		−	0.0482782i
$297$		0			0
$298$	1.35499e7			0.512020
$299$	1.88580e6	+	1.08877e6i	0.0705476	+	0.0407307i
$300$		0			0
$301$	381475.	+	660734.i	0.0139884	+	0.0242285i
$302$	−1.47790e7	+	8.53265e6i	−0.536567	+	0.309787i
$303$		0			0
$304$	−2.76649e6	+	4.79170e6i	−0.0984709	+	0.170557i
$305$		−	7.95789e6i		−	0.280478i
$306$		0			0
$307$	−5.01121e6			−0.173192			−0.0865959	−	0.996244i	$-0.527599\pi$
$307$	−5.01121e6			−0.173192			−0.0865959	+	0.996244i	$0.527599\pi$
$308$	−22476.6	−	12976.9i	−0.000769270	−	0.000444138i
$309$		0			0
$310$	−327119.	−	566587.i	−0.0109805	−	0.0190187i
$311$	−2.52550e7	+	1.45810e7i	−0.839587	+	0.484736i	−0.857124	−	0.515111i	$-0.827751\pi$
$311$	−2.52550e7	+	1.45810e7i	−0.839587	+	0.484736i	0.0175371	+	0.999846i	$0.494417\pi$
$312$		0			0
$313$	1.53413e7	−	2.65719e7i	0.500298	−	0.866541i	−0.499702	−	0.866197i	$-0.666557\pi$
$313$	1.53413e7	−	2.65719e7i	0.500298	−	0.866541i	1.00000		0.000343995i	$-0.000109497\pi$
$314$			3.15908e7i			1.02040i
$315$		0			0
$316$	−1.50961e7			−0.478415
$317$	4.39431e7	+	2.53706e7i	1.37947	+	0.796439i	0.992096	−	0.125483i	$-0.0400479\pi$
$317$	4.39431e7	+	2.53706e7i	1.37947	+	0.796439i	0.387377	+	0.921922i	$0.373381\pi$
$318$		0			0
$319$	2.28661e6	+	3.96052e6i	0.0704401	+	0.122006i
$320$	704248.	−	406598.i	0.0214919	−	0.0124084i
$321$		0			0
$322$	−41390.3	+	71690.0i	−0.00123974	+	0.00214729i
$323$		−	1.82854e7i		−	0.542620i
$324$		0			0
$325$	−1.38385e7			−0.403125
$326$	1.20534e7	+	6.95903e6i	0.347902	+	0.200861i
$327$		0			0
$328$	−4.87412e6	−	8.44223e6i	−0.138126	−	0.239241i
$329$	−515420.	+	297578.i	−0.0144735	+	0.00835628i
$330$		0			0
$331$	2.10713e7	−	3.64966e7i	0.581042	−	1.00639i	−0.414314	−	0.910134i	$-0.635978\pi$
$331$	2.10713e7	−	3.64966e7i	0.581042	−	1.00639i	0.995356	−	0.0962608i	$-0.0306883\pi$
$332$		−	1.07360e6i		−	0.0293378i
$333$		0			0
$334$	2.27561e7			0.610744
$335$	−1.13868e7	−	6.57419e6i	−0.302879	−	0.174867i
$336$		0			0
$337$	−30716.4	−	53202.3i	−0.000802565	−	0.00139008i	0.865624	−	0.500695i	$-0.166922\pi$
$337$	−30716.4	−	53202.3i	−0.000802565	−	0.00139008i	−0.866426	+	0.499305i	$0.833589\pi$
$338$	−1.94818e7	+	1.12478e7i	−0.504521	+	0.291286i
$339$		0			0
$340$	−1.34372e6	+	2.32740e6i	−0.0341879	+	0.0592153i
$341$			610021.i			0.0153844i
$342$		0			0
$343$	1.45770e6			0.0361233
$344$	1.93032e7	+	1.11447e7i	0.474192	+	0.273775i
$345$		0			0
$346$	−1.17057e7	−	2.02748e7i	−0.282598	−	0.489473i
$347$	2.10694e7	−	1.21644e7i	0.504271	−	0.291141i	−0.226205	−	0.974080i	$-0.572632\pi$
$347$	2.10694e7	−	1.21644e7i	0.504271	−	0.291141i	0.730476	+	0.682939i	$0.239298\pi$
$348$		0			0
$349$	1.26014e7	−	2.18263e7i	0.296444	−	0.513456i	−0.678876	−	0.734253i	$-0.737532\pi$
$349$	1.26014e7	−	2.18263e7i	0.296444	−	0.513456i	0.975320	+	0.220797i	$0.0708658\pi$
$350$		−	526081.i		−	0.0122701i
$351$		0			0
$352$	−758234.			−0.0173850
$353$	5.98516e7	+	3.45553e7i	1.36067	+	0.785581i	0.989713	−	0.143070i	$-0.0456974\pi$
$353$	5.98516e7	+	3.45553e7i	1.36067	+	0.785581i	0.370954	+	0.928651i	$0.379031\pi$
$354$		0			0
$355$	−7.79888e6	−	1.35081e7i	−0.174320	−	0.301931i
$356$	−2.81404e7	+	1.62469e7i	−0.623707	+	0.360097i
$357$		0			0
$358$	1.31412e7	−	2.27612e7i	0.286408	−	0.496073i
$359$		−	1.41061e7i		−	0.304876i	−0.988313	−	0.152438i	$-0.951288\pi$
$359$		−	1.41061e7i		−	0.304876i	0.988313	−	0.152438i	$-0.0487124\pi$
$360$		0			0
$361$	−1.78503e7			−0.379423
$362$	−9.86925e6	−	5.69801e6i	−0.208046	−	0.120115i
$363$		0			0
$364$	91406.4	+	158320.i	0.00189527	+	0.00328271i
$365$	1.47817e6	−	853420.i	0.0303980	−	0.0175503i
$366$		0			0
$367$	4.07223e7	−	7.05331e7i	0.823823	−	1.42690i	−0.0789923	−	0.996875i	$-0.525170\pi$
$367$	4.07223e7	−	7.05331e7i	0.823823	−	1.42690i	0.902815	−	0.430028i	$-0.141496\pi$
$368$			2.41842e6i			0.0485275i
$369$		0			0
$370$	971005.			0.0191697
$371$	709980.	+	409907.i	0.0139035	+	0.00802719i
$372$		0			0
$373$	−3.79860e7	−	6.57937e7i	−0.731977	−	1.26782i	−0.956037	−	0.293246i	$-0.905265\pi$
$373$	−3.79860e7	−	6.57937e7i	−0.731977	−	1.26782i	0.224060	−	0.974575i	$-0.428069\pi$
$374$	2.17010e6	−	1.25291e6i	0.0414824	−	0.0239499i
$375$		0			0
$376$	−8.69368e6	+	1.50579e7i	−0.163546	+	0.283270i
$377$		−	3.22127e7i		−	0.601179i
$378$		0			0
$379$	−4.48086e7			−0.823083			−0.411541	−	0.911391i	$-0.635009\pi$
$379$	−4.48086e7			−0.823083			−0.411541	+	0.911391i	$0.635009\pi$
$380$	−3.71607e6	−	2.14548e6i	−0.0677226	−	0.0390996i
$381$		0			0
$382$	−1.07652e7	−	1.86458e7i	−0.193121	−	0.334496i
$383$	−7.76185e7	+	4.48131e7i	−1.38156	+	0.797643i	−0.992344	−	0.123504i	$-0.960587\pi$
$383$	−7.76185e7	+	4.48131e7i	−1.38156	+	0.797643i	−0.389214	+	0.921147i	$0.627253\pi$
$384$		0			0
$385$	10063.9	−	17431.2i	0.000176353	−	0.000305453i
$386$		−	7.32832e6i		−	0.127421i
$387$		0			0
$388$	−1.33820e7			−0.229101
$389$	−3.03701e7	−	1.75342e7i	−0.515938	−	0.297877i	0.219333	−	0.975650i	$-0.429612\pi$
$389$	−3.03701e7	−	1.75342e7i	−0.515938	−	0.297877i	−0.735271	+	0.677773i	$0.762945\pi$
$390$		0			0
$391$	−3.99619e6	−	6.92160e6i	−0.0668522	−	0.115791i
$392$	1.84375e7	−	1.06449e7i	0.306086	−	0.176719i
$393$		0			0
$394$	1.69554e7	−	2.93676e7i	0.277216	−	0.480152i
$395$		−	1.17074e7i		−	0.189963i
$396$		0			0
$397$	8.17666e7			1.30679			0.653393	−	0.757019i	$-0.273345\pi$
$397$	8.17666e7			1.30679			0.653393	+	0.757019i	$0.273345\pi$
$398$	5.14008e6	+	2.96762e6i	0.0815305	+	0.0470717i
$399$		0			0
$400$	−7.68467e6	−	1.33102e7i	−0.120073	−	0.207973i
$401$	5.28941e7	−	3.05384e7i	0.820303	−	0.473602i	−0.0302179	−	0.999543i	$-0.509620\pi$
$401$	5.28941e7	−	3.05384e7i	0.820303	−	0.473602i	0.850521	+	0.525941i	$0.176287\pi$
$402$		0			0
$403$	2.14843e6	−	3.72119e6i	0.0328251	−	0.0568547i
$404$		−	2.14933e7i		−	0.325956i
$405$		0			0
$406$	1.22459e6			0.0182984
$407$	−784080.	−	452689.i	−0.0116299	−	0.00671455i
$408$		0			0
$409$	−3.34641e7	−	5.79615e7i	−0.489113	−	0.847168i	0.510809	−	0.859694i	$-0.329346\pi$
$409$	−3.34641e7	−	5.79615e7i	−0.489113	−	0.847168i	−0.999922	+	0.0125261i	$0.996013\pi$
$410$	6.54714e6	−	3.78000e6i	0.0949949	−	0.0548453i
$411$		0			0
$412$	1.12320e7	−	1.94544e7i	0.160607	−	0.278180i
$413$		−	180166.i		−	0.00255755i
$414$		0			0
$415$	832601.			0.0116491
$416$	4.62530e6	+	2.67042e6i	0.0642480	+	0.0370936i
$417$		0			0
$418$	2.00047e6	+	3.46492e6i	0.0273907	+	0.0474421i
$419$	−8.43503e7	+	4.86997e7i	−1.14669	+	0.662040i	−0.948078	−	0.318039i	$-0.896976\pi$
$419$	−8.43503e7	+	4.86997e7i	−1.14669	+	0.662040i	−0.198609	+	0.980079i	$0.563642\pi$
$420$		0			0
$421$	−3.79673e7	+	6.57613e7i	−0.508819	+	0.881300i	0.491129	+	0.871087i	$0.336584\pi$
$421$	−3.79673e7	+	6.57613e7i	−0.508819	+	0.881300i	−0.999948	+	0.0102133i	$0.996749\pi$
$422$		−	3.13507e7i		−	0.417167i
$423$		0			0
$424$	2.39507e7			0.314211
$425$	4.39877e7	+	2.53963e7i	0.573012	+	0.330829i
$426$		0			0
$427$	993448.	+	1.72070e6i	0.0127603	+	0.0221015i
$428$	9.71515e6	−	5.60905e6i	0.123913	−	0.0715415i
$429$		0			0
$430$	−8.64299e6	+	1.49701e7i	−0.108707	+	0.188287i
$431$		−	1.10356e8i		−	1.37836i	−0.724590	−	0.689180i	$-0.757971\pi$
$431$		−	1.10356e8i		−	1.37836i	0.724590	−	0.689180i	$-0.242029\pi$
$432$		0			0
$433$	7.04803e7			0.868168			0.434084	−	0.900872i	$-0.357072\pi$
$433$	7.04803e7			0.868168			0.434084	+	0.900872i	$0.357072\pi$
$434$	141463.	+	81673.9i	0.00173051	+	0.000999112i
$435$		0			0
$436$	1.15899e7	+	2.00743e7i	0.139836	+	0.242204i
$437$	1.10515e7	−	6.38057e6i	0.132427	−	0.0764567i
$438$		0			0
$439$	5.59868e6	−	9.69720e6i	0.0661747	−	0.114618i	−0.831040	−	0.556213i	$-0.812254\pi$
$439$	5.59868e6	−	9.69720e6i	0.0661747	−	0.114618i	0.897214	+	0.441595i	$0.145587\pi$
$440$		−	588029.i		−	0.00690304i
$441$		0			0
$442$	−1.76504e7			−0.204403
$443$	−1.34069e8	−	7.74049e7i	−1.54212	−	0.890343i	−0.998705	−	0.0508793i	$-0.983798\pi$
$443$	−1.34069e8	−	7.74049e7i	−1.54212	−	0.890343i	−0.543415	−	0.839464i	$-0.682869\pi$
$444$		0			0
$445$	−1.25998e7	−	2.18236e7i	−0.142983	−	0.247654i
$446$	2.02703e7	−	1.17031e7i	0.228484	−	0.131915i
$447$		0			0
$448$	−101518.	+	175834.i	−0.00112904	+	0.00195555i
$449$			9.20846e7i			1.01730i	0.860974	+	0.508648i	$0.169855\pi$
$449$			9.20846e7i			1.01730i	−0.860974	+	0.508648i	$0.830145\pi$
$450$		0			0
$451$	−7.04904e6			−0.0768423
$452$	−3.50142e7	−	2.02154e7i	−0.379165	−	0.218911i
$453$		0			0
$454$	4.17490e7	+	7.23114e7i	0.446147	+	0.772750i
$455$	−122781.	+	70887.8i	−0.00130346	+	0.000752553i
$456$		0			0
$457$	−4.18331e7	+	7.24571e7i	−0.438300	+	0.759159i	−0.997559	−	0.0698349i	$-0.977753\pi$
$457$	−4.18331e7	+	7.24571e7i	−0.438300	+	0.759159i	0.559258	+	0.828994i	$0.311086\pi$
$458$		−	8.27864e7i		−	0.861712i
$459$		0			0
$460$	−1.87554e6			−0.0192687
$461$	1.03069e8	+	5.95070e7i	1.05203	+	0.607387i	0.923216	−	0.384282i	$-0.125551\pi$
$461$	1.03069e8	+	5.95070e7i	1.05203	+	0.607387i	0.128809	+	0.991669i	$0.458884\pi$
$462$		0			0
$463$	5.67866e7	+	9.83573e7i	0.572141	+	0.990977i	0.996346	+	0.0854109i	$0.0272203\pi$
$463$	5.67866e7	+	9.83573e7i	0.572141	+	0.990977i	−0.424205	+	0.905566i	$0.639446\pi$
$464$	3.09830e7	−	1.78881e7i	0.310149	−	0.179065i
$465$		0			0
$466$	−4.29294e6	+	7.43559e6i	−0.0424226	+	0.0734781i
$467$			1.34722e8i			1.32278i	0.750044	+	0.661388i	$0.230032\pi$
$467$			1.34722e8i			1.32278i	−0.750044	+	0.661388i	$0.769968\pi$
$468$		0			0
$469$	3.28284e6			0.0318223
$470$	−1.16778e7	−	6.74215e6i	−0.112478	−	0.0649389i
$471$		0			0
$472$	−2.63176e6	−	4.55834e6i	−0.0250277	−	0.0433492i
$473$	1.39583e7	−	8.05884e6i	0.131901	−	0.0761534i
$474$		0			0
$475$	−4.05494e7	+	7.02336e7i	−0.378358	+	0.655336i
$476$		−	670991.i		−	0.00622151i
$477$		0			0
$478$	−7.89742e7			−0.723105
$479$	−1.39409e8	−	8.04877e7i	−1.26848	−	0.732357i	−0.293779	−	0.955873i	$-0.594913\pi$
$479$	−1.39409e8	−	8.04877e7i	−1.26848	−	0.732357i	−0.974700	+	0.223516i	$0.928246\pi$
$480$		0			0
$481$	3.18864e6	+	5.52289e6i	0.0286530	+	0.0496285i
$482$	1.24025e8	−	7.16056e7i	1.10756	−	0.639449i
$483$		0			0
$484$	2.80708e7	−	4.86201e7i	0.247582	−	0.428825i
$485$		−	1.03781e7i		−	0.0909687i
$486$		0			0
$487$	1.14964e7			0.0995351			0.0497676	−	0.998761i	$-0.484152\pi$
$487$	1.14964e7			0.0995351			0.0497676	+	0.998761i	$0.484152\pi$
$488$	5.02700e7	+	2.90234e7i	0.432563	+	0.249740i
$489$		0			0
$490$	8.25537e6	+	1.42987e7i	0.0701695	+	0.121537i
$491$	−1.20638e8	+	6.96503e7i	−1.01915	+	0.588408i	−0.913858	−	0.406033i	$-0.866912\pi$
$491$	−1.20638e8	+	6.96503e7i	−1.01915	+	0.588408i	−0.105294	+	0.994441i	$0.533578\pi$
$492$		0			0
$493$	−5.91164e7	+	1.02393e8i	−0.493364	+	0.854532i
$494$		−	2.81818e7i		−	0.233769i
$495$		0			0
$496$	4.77217e6			0.0391085
$497$	3.37264e6	+	1.94720e6i	0.0274727	+	0.0158614i
$498$		0			0
$499$	4.67348e7	+	8.09470e7i	0.376130	+	0.651477i	0.990496	−	0.137545i	$-0.0439211\pi$
$499$	4.67348e7	+	8.09470e7i	0.376130	+	0.651477i	−0.614365	+	0.789022i	$0.710588\pi$
$500$	2.10684e7	−	1.21638e7i	0.168547	−	0.0973107i
$501$		0			0
$502$	−1.01371e7	+	1.75579e7i	−0.0801313	+	0.138791i
$503$			2.32808e8i			1.82934i	0.404200	+	0.914671i	$0.367550\pi$
$503$			2.32808e8i			1.82934i	−0.404200	+	0.914671i	$0.632450\pi$
$504$		0			0
$505$	1.66686e7			0.129427
$506$	1.51449e6	+	874389.i	0.0116900	+	0.00674921i
$507$		0			0
$508$	4.27837e7	+	7.41036e7i	0.326353	+	0.565260i
$509$	1.48895e8	−	8.59645e7i	1.12908	−	0.651877i	0.185380	−	0.982667i	$-0.440648\pi$
$509$	1.48895e8	−	8.59645e7i	1.12908	−	0.651877i	0.943705	+	0.330790i	$0.107315\pi$
$510$		0			0
$511$	−213079.	+	369063.i	−0.00159690	+	0.00276591i
$512$			5.93164e6i			0.0441942i
$513$		0			0
$514$	−1.31186e8			−0.966046
$515$	1.50873e7	+	8.71067e6i	0.110456	+	0.0637719i
$516$		0			0
$517$	6.28648e6	+	1.08885e7i	0.0454921	+	0.0787946i
$518$	−209956.	+	121218.i	−0.00151057	+	0.000872126i
$519$		0			0
$520$	−2.07097e6	+	3.58703e6i	−0.0147287	+	0.0255108i
$521$			2.02142e8i			1.42937i	0.699447	+	0.714684i	$0.253430\pi$
$521$			2.02142e8i			1.42937i	−0.699447	+	0.714684i	$0.746570\pi$
$522$		0			0
$523$	−8.40337e7			−0.587419			−0.293710	−	0.955895i	$-0.594890\pi$
$523$	−8.40337e7			−0.587419			−0.293710	+	0.955895i	$0.594890\pi$
$524$	−9.94376e7	−	5.74103e7i	−0.691125	−	0.399021i
$525$		0			0
$526$	5.65006e7	+	9.78620e7i	0.388236	+	0.672445i
$527$	−1.36581e7	+	7.88553e6i	−0.0933168	+	0.0538765i
$528$		0			0
$529$	−7.12291e7	+	1.23372e8i	−0.481161	+	0.833395i
$530$			1.85743e7i			0.124763i
$531$		0			0
$532$	1.07135e6			0.00711534
$533$	4.29998e7	+	2.48259e7i	0.283978	+	0.163955i
$534$		0			0
$535$	4.34995e6	+	7.53433e6i	0.0284068	+	0.0492021i
$536$	8.30583e7	−	4.79537e7i	0.539372	−	0.311407i
$537$		0			0
$538$	−2.98100e7	+	5.16325e7i	−0.191432	+	0.331571i
$539$		−	1.53948e7i		−	0.0983125i
$540$		0			0
$541$	5.27746e7			0.333299			0.166649	−	0.986016i	$-0.446705\pi$
$541$	5.27746e7			0.333299			0.166649	+	0.986016i	$0.446705\pi$
$542$	1.35622e8	+	7.83016e7i	0.851792	+	0.491782i
$543$		0			0
$544$	−9.80144e6	−	1.69766e7i	−0.0608826	−	0.105452i
$545$	−1.55681e7	+	8.98824e6i	−0.0961713	+	0.0555246i
$546$		0			0
$547$	−3.12323e7	+	5.40959e7i	−0.190828	+	0.330523i	−0.945525	−	0.325550i	$-0.894451\pi$
$547$	−3.12323e7	+	5.40959e7i	−0.190828	+	0.330523i	0.754697	+	0.656073i	$0.227784\pi$
$548$			4.89771e7i			0.297613i
$549$		0			0
$550$	−1.11137e7			−0.0667991
$551$	−1.63487e8	−	9.43892e7i	−0.977300	−	0.564245i
$552$		0			0
$553$	1.46153e6	+	2.53144e6i	0.00864236	+	0.0149690i
$554$	4.00048e7	−	2.30968e7i	0.235279	−	0.135838i
$555$		0			0
$556$	5.64426e7	−	9.77614e7i	0.328384	−	0.568778i
$557$			1.98446e8i			1.14836i	0.818730	+	0.574178i	$0.194678\pi$
$557$			1.98446e8i			1.14836i	−0.818730	+	0.574178i	$0.805322\pi$
$558$		0			0
$559$	−1.13529e8			−0.649939
$560$	−136363.	−	78729.4i	−0.000776486	−	0.000448304i
$561$		0			0
$562$	1.26017e7	+	2.18268e7i	0.0709938	+	0.122965i
$563$	−8.55525e7	+	4.93937e7i	−0.479410	+	0.276788i	−0.720171	−	0.693797i	$-0.755937\pi$
$563$	−8.55525e7	+	4.93937e7i	−0.479410	+	0.276788i	0.240760	+	0.970585i	$0.422603\pi$
$564$		0			0
$565$	1.56775e7	−	2.71543e7i	0.0869226	−	0.150554i
$566$		−	1.80356e8i		−	0.994674i
$567$		0			0
$568$	1.13774e8			0.620865
$569$	1.42132e8	+	8.20597e7i	0.771531	+	0.445444i	0.833421	−	0.552639i	$-0.186379\pi$
$569$	1.42132e8	+	8.20597e7i	0.771531	+	0.445444i	−0.0618893	+	0.998083i	$0.519713\pi$
$570$		0			0
$571$	9.76077e7	+	1.69061e8i	0.524295	+	0.908106i	0.999600	+	0.0282845i	$0.00900442\pi$
$571$	9.76077e7	+	1.69061e8i	0.524295	+	0.908106i	−0.475305	+	0.879821i	$0.657662\pi$
$572$	3.34459e6	−	1.93100e6i	0.0178713	−	0.0103180i
$573$		0			0
$574$	−943775.	+	1.63467e6i	−0.00499037	+	0.00864357i
$575$			3.54476e7i			0.186459i
$576$		0			0
$577$	1.93319e8			1.00634			0.503172	−	0.864186i	$-0.332166\pi$
$577$	1.93319e8			1.00634			0.503172	+	0.864186i	$0.332166\pi$
$578$	−6.21453e7	−	3.58796e7i	−0.321829	−	0.185808i
$579$		0			0
$580$	1.38726e7	+	2.40281e7i	0.0711008	+	0.123150i
$581$	−180030.	+	103940.i	−0.000917944	+	0.000529975i
$582$		0			0
$583$	8.65948e6	−	1.49987e7i	0.0437005	−	0.0756915i
$584$			1.24501e7i			0.0625078i
$585$		0			0
$586$	−2.02047e8			−1.00406
$587$	−2.90014e7	−	1.67440e7i	−0.143385	−	0.0827835i	0.426591	−	0.904445i	$-0.359714\pi$
$587$	−2.90014e7	−	1.67440e7i	−0.143385	−	0.0827835i	−0.569976	+	0.821661i	$0.693048\pi$
$588$		0			0
$589$	−1.25906e7	−	2.18075e7i	−0.0616168	−	0.106723i
$590$	3.53510e6	−	2.04099e6i	0.0172126	−	0.00993769i
$591$		0			0
$592$	−3.54137e6	+	6.13383e6i	−0.0170689	+	0.0295642i
$593$		−	3.75231e8i		−	1.79943i	−0.436479	−	0.899715i	$-0.643775\pi$
$593$		−	3.75231e8i		−	1.79943i	0.436479	−	0.899715i	$-0.356225\pi$
$594$		0			0
$595$	520369.			0.00247036
$596$	−6.63806e7	−	3.83249e7i	−0.313547	−	0.181026i
$597$		0			0
$598$	−6.15900e6	−	1.06677e7i	−0.0288009	−	0.0498847i
$599$	−2.57196e8	+	1.48492e8i	−1.19670	+	0.690913i	−0.959817	−	0.280626i	$-0.909458\pi$
$599$	−2.57196e8	+	1.48492e8i	−1.19670	+	0.690913i	−0.236879	+	0.971539i	$0.576125\pi$
$600$		0			0
$601$	−7.77944e7	+	1.34744e8i	−0.358365	+	0.620706i	−0.987688	−	0.156438i	$-0.949999\pi$
$601$	−7.77944e7	+	1.34744e8i	−0.358365	+	0.620706i	0.629323	+	0.777144i	$0.283332\pi$
$602$		−	4.31590e6i		−	0.0197825i
$603$		0			0
$604$	9.65360e7			0.438105
$605$	3.77060e7	+	2.17696e7i	0.170273	+	0.0983069i
$606$		0			0
$607$	−1.11404e8	−	1.92958e8i	−0.498122	−	0.862773i	0.501875	−	0.864940i	$-0.332644\pi$
$607$	−1.11404e8	−	1.92958e8i	−0.498122	−	0.862773i	−0.999998	+	0.00216674i	$0.999310\pi$
$608$	2.71059e7	−	1.56496e7i	0.120602	−	0.0696294i
$609$		0			0
$610$	−2.25083e7	+	3.89855e7i	−0.0991639	+	0.171757i
$611$		−	8.85611e7i		−	0.388257i
$612$		0			0
$613$	1.22144e8			0.530262			0.265131	−	0.964212i	$-0.414585\pi$
$613$	1.22144e8			0.530262			0.265131	+	0.964212i	$0.414585\pi$
$614$	2.45498e7	+	1.41738e7i	0.106058	+	0.0612326i
$615$		0			0
$616$	73408.4	+	127147.i	0.000314053	+	0.000543956i
$617$	3.26624e8	−	1.88577e8i	1.39057	−	0.802846i	0.397191	−	0.917736i	$-0.369985\pi$
$617$	3.26624e8	−	1.88577e8i	1.39057	−	0.802846i	0.993378	+	0.114890i	$0.0366516\pi$
$618$		0			0
$619$	2.18072e8	−	3.77712e8i	0.919450	−	1.59253i	0.119198	−	0.992871i	$-0.461968\pi$
$619$	2.18072e8	−	3.77712e8i	0.919450	−	1.59253i	0.800252	−	0.599663i	$-0.204699\pi$
$620$			3.70093e6i			0.0155287i
$621$		0			0
$622$	1.64965e8			0.685520
$623$	5.44882e6	+	3.14588e6i	0.0225340	+	0.0130100i
$624$		0			0
$625$	−1.07825e8	−	1.86759e8i	−0.441653	−	0.764966i
$626$	−1.50313e8	+	8.67834e7i	−0.612737	+	0.353764i
$627$		0			0
$628$	8.93522e7	−	1.54763e8i	0.360767	−	0.624866i
$629$		−	2.34070e7i		−	0.0940577i
$630$		0			0
$631$	−8.46175e7			−0.336800			−0.168400	−	0.985719i	$-0.553860\pi$
$631$	−8.46175e7			−0.336800			−0.168400	+	0.985719i	$0.553860\pi$
$632$	7.39556e7	+	4.26983e7i	0.292968	+	0.169145i
$633$		0			0
$634$	−1.43518e8	−	2.48580e8i	−0.563167	−	0.975434i
$635$	−5.74691e7	+	3.31798e7i	−0.224447	+	0.129584i
$636$		0			0
$637$	−5.42189e7	+	9.39099e7i	−0.209765	+	0.363323i
$638$		−	2.58700e7i		−	0.0996173i
$639$		0			0
$640$	−4.60013e6			−0.0175481
$641$	9.93835e7	+	5.73791e7i	0.377347	+	0.217861i	0.676663	−	0.736293i	$-0.263425\pi$
$641$	9.93835e7	+	5.73791e7i	0.377347	+	0.217861i	−0.299317	+	0.954154i	$0.596759\pi$
$642$		0			0
$643$	−1.03843e7	−	1.79862e7i	−0.0390612	−	0.0676560i	0.845834	−	0.533446i	$-0.179103\pi$
$643$	−1.03843e7	−	1.79862e7i	−0.0390612	−	0.0676560i	−0.884895	+	0.465790i	$0.845770\pi$
$644$	405540.	−	234139.i	0.00151836	−	0.000876628i
$645$		0			0
$646$	−5.17188e7	+	8.95796e7i	−0.191845	+	0.332286i
$647$		−	5.18773e8i		−	1.91542i	−0.287734	−	0.957710i	$-0.592902\pi$
$647$		−	5.18773e8i		−	1.91542i	0.287734	−	0.957710i	$-0.407098\pi$
$648$		0			0
$649$	−3.80610e6			−0.0139234
$650$	6.77946e7	+	3.91413e7i	0.246863	+	0.142526i
$651$		0			0
$652$	−3.93662e7	−	6.81843e7i	−0.142030	−	0.246004i
$653$	−1.08224e8	+	6.24831e7i	−0.388673	+	0.224400i	−0.681585	−	0.731739i	$-0.738709\pi$
$653$	−1.08224e8	+	6.24831e7i	−0.388673	+	0.224400i	0.292912	+	0.956139i	$0.405376\pi$
$654$		0			0
$655$	4.45231e7	−	7.71162e7i	0.158439	−	0.274424i
$656$			5.51444e7i			0.195339i
$657$		0			0
$658$	3.36671e6			0.0118176
$659$	−4.37563e8	−	2.52627e8i	−1.52892	−	0.882721i	−0.999408	−	0.0344179i	$-0.989042\pi$
$659$	−4.37563e8	−	2.52627e8i	−1.52892	−	0.882721i	−0.529511	−	0.848303i	$-0.677624\pi$
$660$		0			0
$661$	−2.09467e8	−	3.62807e8i	−0.725289	−	1.25624i	−0.958855	−	0.283896i	$-0.908373\pi$
$661$	−2.09467e8	−	3.62807e8i	−0.725289	−	1.25624i	0.233567	−	0.972341i	$-0.424960\pi$
$662$	−2.06456e8	+	1.19197e8i	−0.711629	+	0.410859i
$663$		0			0
$664$	−3.03659e6	+	5.25954e6i	−0.0103725	+	0.0179657i
$665$			830856.i			0.00282528i
$666$		0			0
$667$	−8.25134e7			−0.278065
$668$	−1.11482e8	−	6.43641e7i	−0.374003	−	0.215931i
$669$		0			0
$670$	3.71893e7	+	6.44137e7i	0.123650	+	0.214168i
$671$	3.63506e7	−	2.09871e7i	0.120322	−	0.0694679i
$672$		0			0
$673$	1.99125e8	−	3.44894e8i	0.653250	−	1.13146i	−0.329079	−	0.944302i	$-0.606738\pi$
$673$	1.99125e8	−	3.44894e8i	0.653250	−	1.13146i	0.982329	−	0.187160i	$-0.0599284\pi$
$674$			347516.i			0.00113500i
$675$		0			0
$676$	1.27255e8			0.411940
$677$	4.73100e8	+	2.73145e8i	1.52471	+	0.880292i	0.999571	+	0.0292753i	$0.00931996\pi$
$677$	4.73100e8	+	2.73145e8i	1.52471	+	0.880292i	0.525139	+	0.851017i	$0.324013\pi$
$678$		0			0
$679$	1.29558e6	+	2.24401e6i	0.00413862	+	0.00716829i
$680$	1.31657e7	−	7.60124e6i	0.0418715	−	0.0241745i
$681$		0			0
$682$	1.72540e6	−	2.98848e6i	0.00543922	−	0.00942101i
$683$		−	3.24992e7i		−	0.102002i	−0.998699	−	0.0510012i	$-0.983759\pi$
$683$		−	3.24992e7i		−	0.102002i	0.998699	−	0.0510012i	$-0.0162412\pi$
$684$		0			0
$685$	−3.79829e7			−0.118173
$686$	−7.14126e6	−	4.12301e6i	−0.0221209	−	0.0127715i
$687$		0			0
$688$	−6.30440e7	−	1.09195e8i	−0.193588	−	0.335304i
$689$	−1.05647e8	+	6.09955e7i	−0.322999	+	0.186483i
$690$		0			0
$691$	1.43850e8	−	2.49156e8i	0.435989	−	0.755156i	−0.561386	−	0.827554i	$-0.689732\pi$
$691$	1.43850e8	−	2.49156e8i	0.435989	−	0.755156i	0.997376	+	0.0723981i	$0.0230652\pi$
$692$			1.32435e8i			0.399653i
$693$		0			0
$694$	−1.37625e8			−0.411736
$695$	7.58163e7	+	4.37725e7i	0.225844	+	0.130391i
$696$		0			0
$697$	−9.11205e7	−	1.57825e8i	−0.269103	−	0.466099i
$698$	−1.23468e8	+	7.12843e7i	−0.363068	+	0.209618i
$699$		0			0
$700$	−1.48798e6	+	2.57726e6i	−0.00433814	+	0.00751388i
$701$		−	2.82907e8i		−	0.821278i	−0.911798	−	0.410639i	$-0.865306\pi$
$701$		−	2.82907e8i		−	0.821278i	0.911798	−	0.410639i	$-0.134694\pi$
$702$		0			0
$703$	3.73732e7			0.107571
$704$	3.71457e6	+	2.14461e6i	0.0106461	+	0.00614654i
$705$		0			0
$706$	−1.95475e8	−	3.38572e8i	−0.555490	−	0.962137i
$707$	−3.60417e6	+	2.08087e6i	−0.0101988	+	0.00588826i
$708$		0			0
$709$	1.19975e8	−	2.07803e8i	0.336629	−	0.583059i	−0.647167	−	0.762348i	$-0.724046\pi$
$709$	1.19975e8	−	2.07803e8i	0.336629	−	0.583059i	0.983796	+	0.179289i	$0.0573798\pi$
$710$			8.82343e7i			0.246526i
$711$		0			0
$712$	1.83812e8			0.509254
$713$	−9.53187e6	−	5.50323e6i	−0.0262972	−	0.0151827i
$714$		0			0
$715$	1.49754e6	+	2.59381e6i	0.00409694	+	0.00709611i
$716$	−1.28757e8	+	7.43376e7i	−0.350776	+	0.202521i
$717$		0			0
$718$	−3.98980e7	+	6.91054e7i	−0.107790	+	0.186698i
$719$			2.12836e7i			0.0572611i	0.999590	+	0.0286305i	$0.00911463\pi$
$719$			2.12836e7i			0.0572611i	−0.999590	+	0.0286305i	$0.990885\pi$
$720$		0			0
$721$	−4.34969e6			−0.0116052
$722$	8.74482e7	+	5.04882e7i	0.232348	+	0.134146i
$723$		0			0
$724$	3.22328e7	+	5.58289e7i	0.0849342	+	0.147110i
$725$	4.54129e8	−	2.62192e8i	1.19170	−	0.688026i
$726$		0			0
$727$	8.88685e7	−	1.53925e8i	0.231283	−	0.400595i	−0.726903	−	0.686741i	$-0.759041\pi$
$727$	8.88685e7	−	1.53925e8i	0.231283	−	0.400595i	0.958186	+	0.286146i	$0.0923742\pi$
$728$		−	1.03414e6i		−	0.00268032i
$729$		0			0
$730$	−9.65535e6			−0.0248199
$731$	3.60869e8	+	2.08348e8i	0.923841	+	0.533380i
$732$		0			0
$733$	2.61308e8	+	4.52599e8i	0.663501	+	1.14922i	0.979690	+	0.200520i	$0.0642633\pi$
$733$	2.61308e8	+	4.52599e8i	0.663501	+	1.14922i	−0.316189	+	0.948696i	$0.602403\pi$
$734$	−3.98995e8	+	2.30360e8i	−1.00897	+	0.582531i
$735$		0			0
$736$	6.84031e6	−	1.18478e7i	0.0171570	−	0.0297169i
$737$		−	6.93515e7i		−	0.173242i
$738$		0			0
$739$	−5.12661e8			−1.27027			−0.635137	−	0.772400i	$-0.719056\pi$
$739$	−5.12661e8			−1.27027			−0.635137	+	0.772400i	$0.719056\pi$
$740$	−4.75693e6	−	2.74642e6i	−0.0117390	−	0.00677753i
$741$		0			0
$742$	−2.31879e6	−	4.01625e6i	−0.00567608	−	0.00983127i
$743$	−9.47357e7	+	5.46957e7i	−0.230966	+	0.133348i	−0.611017	−	0.791617i	$-0.709239\pi$
$743$	−9.47357e7	+	5.46957e7i	−0.230966	+	0.133348i	0.380052	+	0.924965i	$0.375906\pi$
$744$		0			0
$745$	2.97219e7	−	5.14798e7i	0.0718798	−	0.124500i
$746$			4.29763e8i			1.03517i
$747$		0			0
$748$	−1.41750e7			−0.0338703
$749$	−1.88114e6	−	1.08608e6i	−0.00447689	−	0.00258473i
$750$		0			0
$751$	1.80758e8	+	3.13082e8i	0.426755	+	0.739161i	0.996583	−	0.0826034i	$-0.0263235\pi$
$751$	1.80758e8	+	3.13082e8i	0.426755	+	0.739161i	−0.569828	+	0.821764i	$0.692990\pi$
$752$	8.51803e7	−	4.91789e7i	0.200302	−	0.115645i
$753$		0			0
$754$	−9.11114e7	+	1.57810e8i	−0.212549	+	0.368145i
$755$			7.48659e7i			0.173958i
$756$		0			0
$757$	8.46631e7			0.195167			0.0975835	−	0.995227i	$-0.468889\pi$
$757$	8.46631e7			0.195167			0.0975835	+	0.995227i	$0.468889\pi$
$758$	2.19516e8	+	1.26738e8i	0.504033	+	0.291004i
$759$		0			0
$760$	1.21366e7	+	2.10213e7i	0.0276476	+	0.0478871i
$761$	8.57072e7	−	4.94831e7i	0.194475	−	0.112280i	−0.399601	−	0.916689i	$-0.630851\pi$
$761$	8.57072e7	−	4.94831e7i	0.194475	−	0.112280i	0.594076	+	0.804409i	$0.297518\pi$
$762$		0			0
$763$	2.24415e6	−	3.88698e6i	0.00505217	−	0.00875062i
$764$			1.21794e8i			0.273115i
$765$		0			0
$766$	5.07002e8			1.12804
$767$	2.32175e7	+	1.34047e7i	0.0514553	+	0.0297077i
$768$		0			0
$769$	2.70757e7	+	4.68965e7i	0.0595390	+	0.103124i	0.894259	−	0.447551i	$-0.147704\pi$
$769$	2.70757e7	+	4.68965e7i	0.0595390	+	0.103124i	−0.834720	+	0.550675i	$0.814370\pi$
$770$	−98605.5	+	56929.9i	−0.000215988	+	0.000124701i
$771$		0			0
$772$	−2.07276e7	+	3.59013e7i	−0.0450503	+	0.0780293i
$773$		−	9.36821e7i		−	0.202823i	−0.994845	−	0.101412i	$-0.967664\pi$
$773$		−	9.36821e7i		−	0.202823i	0.994845	−	0.101412i	$-0.0323359\pi$
$774$		0			0
$775$	6.99474e7			0.150268
$776$	6.55583e7	+	3.78501e7i	0.140295	+	0.0809995i
$777$		0			0
$778$	9.91884e7	+	1.71799e8i	0.210631	+	0.364824i
$779$	2.51994e8	−	1.45489e8i	0.533063	−	0.307764i
$780$		0			0
$781$	4.11354e7	−	7.12486e7i	0.0863501	−	0.149563i
$782$			4.52117e7i			0.0945432i
$783$		0			0
$784$	−1.20433e8			−0.249918
$785$	1.20022e8	+	6.92947e7i	0.248114	+	0.143249i
$786$		0			0
$787$	1.59674e8	+	2.76563e8i	0.327574	+	0.567374i	0.982030	−	0.188726i	$-0.0604357\pi$
$787$	1.59674e8	+	2.76563e8i	0.327574	+	0.567374i	−0.654456	+	0.756100i	$0.727102\pi$
$788$	−1.66128e8	+	9.59140e7i	−0.339519	+	0.196021i
$789$		0			0
$790$	−3.31135e7	+	5.73543e7i	−0.0671621	+	0.116328i
$791$			7.82862e6i			0.0158181i
$792$		0			0
$793$	−2.95656e8			−0.592881
$794$	−4.00573e8	−	2.31271e8i	−0.800240	−	0.462019i
$795$		0			0
$796$	−1.67874e7	−	2.90767e7i	−0.0332847	−	0.0576508i
$797$	2.16214e8	−	1.24831e8i	0.427080	−	0.246575i	−0.271022	−	0.962573i	$-0.587362\pi$
$797$	2.16214e8	−	1.24831e8i	0.427080	−	0.246575i	0.698102	+	0.715998i	$0.254028\pi$
$798$		0			0
$799$	−1.62526e8	+	2.81504e8i	−0.318627	+	0.551879i
$800$			8.69422e7i			0.169809i
$801$		0			0
$802$	−3.45503e8			−0.669775
$803$	7.79663e6	+	4.50139e6i	0.0150578	+	0.00869360i
$804$		0			0
$805$	181580.	+	314506.i	0.000348081	+	0.000602894i
$806$	−2.10502e7	+	1.21533e7i	−0.0402023	+	0.0232108i
$807$		0			0
$808$	−6.07922e7	+	1.05295e8i	−0.115243	+	0.199606i
$809$			3.16268e8i			0.597323i	0.954359	+	0.298661i	$0.0965401\pi$
$809$			3.16268e8i			0.597323i	−0.954359	+	0.298661i	$0.903460\pi$
$810$		0			0
$811$	1.23239e8			0.231038			0.115519	−	0.993305i	$-0.463147\pi$
$811$	1.23239e8			0.231038			0.115519	+	0.993305i	$0.463147\pi$
$812$	−5.99924e6	−	3.46366e6i	−0.0112054	−	0.00646945i
$813$		0			0
$814$	2.56080e6	+	4.43543e6i	0.00474790	+	0.00822361i
$815$	5.28786e7	−	3.05294e7i	0.0976802	−	0.0563957i
$816$		0			0
$817$	−3.32662e8	+	5.76187e8i	−0.610009	+	1.05657i
$818$			3.78603e8i			0.691710i
$819$		0			0
$820$	−4.27658e7			−0.0775630
$821$	−4.83629e8	−	2.79223e8i	−0.873943	−	0.504571i	−0.00528613	−	0.999986i	$-0.501683\pi$
$821$	−4.83629e8	−	2.79223e8i	−0.873943	−	0.504571i	−0.868656	+	0.495415i	$0.835016\pi$
$822$		0			0
$823$	2.33574e8	+	4.04562e8i	0.419010	+	0.725747i	0.995840	−	0.0911171i	$-0.0290438\pi$
$823$	2.33574e8	+	4.04562e8i	0.419010	+	0.725747i	−0.576830	+	0.816864i	$0.695710\pi$
$824$	−1.10050e8	+	6.35377e7i	−0.196703	+	0.113566i
$825$		0			0
$826$	−509587.	+	882631.i	−0.000904229	+	0.00156617i
$827$			2.65712e8i			0.469780i	0.972022	+	0.234890i	$0.0754730\pi$
$827$			2.65712e8i			0.469780i	−0.972022	+	0.234890i	$0.924527\pi$
$828$		0			0
$829$	−4.35459e8			−0.764335			−0.382167	−	0.924093i	$-0.624822\pi$
$829$	−4.35459e8			−0.764335			−0.382167	+	0.924093i	$0.624822\pi$
$830$	−4.07889e6	−	2.35495e6i	−0.00713359	−	0.00411858i
$831$		0			0
$832$	−1.51062e7	−	2.61646e7i	−0.0262292	−	0.0454302i
$833$	3.44685e8	−	1.99004e8i	0.596330	−	0.344291i
$834$		0			0
$835$	4.99158e7	−	8.64568e7i	0.0857391	−	0.148504i
$836$		−	2.26327e7i		−	0.0387363i
$837$		0			0
$838$	5.50974e8			0.936266
$839$	−7.95763e8	−	4.59434e8i	−1.34740	−	0.777925i	−0.359524	−	0.933136i	$-0.617061\pi$
$839$	−7.95763e8	−	4.59434e8i	−1.34740	−	0.777925i	−0.987881	+	0.155211i	$0.950394\pi$
$840$		0			0
$841$	3.12907e8	+	5.41972e8i	0.526051	+	0.911147i
$842$	3.72002e8	−	2.14775e8i	0.623173	−	0.359789i
$843$		0			0
$844$	−8.86732e7	+	1.53586e8i	−0.147491	+	0.255462i
$845$			9.86891e7i			0.163568i
$846$		0			0
$847$	−1.08707e7			−0.0178899
$848$	−1.17334e8	−	6.77428e7i	−0.192414	−	0.111090i
$849$		0			0
$850$	−1.43663e8	−	2.48832e8i	−0.233931	−	0.405181i
$851$	1.41470e7	−	8.16775e6i	0.0229548	−	0.0132530i
$852$		0			0
$853$	−3.48121e8	+	6.02964e8i	−0.560897	+	0.971503i	0.436521	+	0.899694i	$0.356210\pi$
$853$	−3.48121e8	+	6.02964e8i	−0.560897	+	0.971503i	−0.997418	+	0.0718085i	$0.977123\pi$
$854$		−	1.12396e7i		−	0.0180458i
$855$		0			0
$856$	−6.34591e7			−0.101175
$857$	2.23831e8	+	1.29229e8i	0.355614	+	0.205314i	0.667155	−	0.744919i	$-0.267512\pi$
$857$	2.23831e8	+	1.29229e8i	0.355614	+	0.205314i	−0.311541	+	0.950233i	$0.600845\pi$
$858$		0			0
$859$	−1.96911e8	−	3.41061e8i	−0.310664	−	0.538087i	0.667842	−	0.744303i	$-0.267218\pi$
$859$	−1.96911e8	−	3.41061e8i	−0.310664	−	0.538087i	−0.978506	+	0.206217i	$0.933885\pi$
$860$	8.46836e7	−	4.88921e7i	0.133139	−	0.0768676i
$861$		0			0
$862$	−3.12133e8	+	5.40630e8i	−0.487324	+	0.844069i
$863$		−	4.97185e8i		−	0.773545i	−0.922175	−	0.386773i	$-0.873590\pi$
$863$		−	4.97185e8i		−	0.773545i	0.922175	−	0.386773i	$-0.126410\pi$
$864$		0			0
$865$	−1.02706e8			−0.158690
$866$	−3.45281e8	−	1.99348e8i	−0.531642	−	0.306944i
$867$		0			0
$868$	−462018.	−	800238.i	−0.000706479	−	0.00122366i
$869$	5.34780e7	−	3.08755e7i	0.0814921	−	0.0470495i
$870$		0			0
$871$	−2.44248e8	+	4.23051e8i	−0.369639	+	0.640233i
$872$		−	1.31125e8i		−	0.197758i
$873$		0			0
$874$	−7.21879e7			−0.108126
$875$	−4.07947e6	−	2.35528e6i	−0.00608946	−	0.00351575i
$876$		0			0
$877$	−2.87178e7	−	4.97407e7i	−0.0425748	−	0.0737417i	0.843953	−	0.536417i	$-0.180223\pi$
$877$	−2.87178e7	−	4.97407e7i	−0.0425748	−	0.0737417i	−0.886528	+	0.462676i	$0.846889\pi$
$878$	−5.48556e7	+	3.16709e7i	−0.0810471	+	0.0467926i
$879$		0			0
$880$	−1.66320e6	+	2.88074e6i	−0.00244059	+	0.00422723i
$881$			2.82313e8i			0.412861i	0.978461	+	0.206430i	$0.0661847\pi$
$881$			2.82313e8i			0.412861i	−0.978461	+	0.206430i	$0.933815\pi$
$882$		0			0
$883$	5.96066e8			0.865789			0.432895	−	0.901445i	$-0.357492\pi$
$883$	5.96066e8			0.865789			0.432895	+	0.901445i	$0.357492\pi$
$884$	8.64688e7	+	4.99228e7i	0.125171	+	0.0722674i
$885$		0			0
$886$	4.37868e8	+	7.58410e8i	0.629568	+	1.09044i
$887$	7.03514e8	−	4.06174e8i	1.00810	−	0.582025i	0.0974628	−	0.995239i	$-0.468927\pi$
$887$	7.03514e8	−	4.06174e8i	1.00810	−	0.582025i	0.910634	+	0.413214i	$0.135594\pi$
$888$		0			0
$889$	8.28421e6	−	1.43487e7i	0.0117909	−	0.0204224i
$890$			1.42551e8i			0.202209i
$891$		0			0
$892$	−1.32405e8			−0.186557
$893$	−4.49467e8	−	2.59500e8i	−0.631166	−	0.364404i
$894$		0			0
$895$	−5.76506e7	−	9.98537e7i	−0.0804145	−	0.139282i
$896$	994667.	−	574271.i	0.00138278	−	0.000798349i
$897$		0			0
$898$	2.60454e8	−	4.51120e8i	0.359669	−	0.622965i
$899$			1.62821e8i			0.224094i
$900$		0			0
$901$	4.47753e8			0.612158
$902$	3.45331e7	+	1.99377e7i	0.0470561	+	0.0271678i
$903$		0			0
$904$	1.14356e8	+	1.98070e8i	0.154793	+	0.268110i
$905$	−4.32966e7	+	2.49973e7i	−0.0584128	+	0.0337247i
$906$		0			0
$907$	−4.94339e8	+	8.56220e8i	−0.662526	+	1.14753i	0.317424	+	0.948284i	$0.397182\pi$
$907$	−4.94339e8	+	8.56220e8i	−0.662526	+	1.14753i	−0.979950	+	0.199245i	$0.936151\pi$
$908$		−	4.72336e8i		−	0.630948i
$909$		0			0
$910$	802004.			0.00106427
$911$	−4.44753e8	−	2.56778e8i	−0.588252	−	0.339628i	0.176154	−	0.984363i	$-0.443634\pi$
$911$	−4.44753e8	−	2.56778e8i	−0.588252	−	0.339628i	−0.764406	+	0.644735i	$0.776968\pi$
$912$		0			0
$913$	2.19579e6	+	3.80322e6i	0.00288521	+	0.00499734i
$914$	4.09879e8	−	2.36644e8i	0.536806	−	0.309925i
$915$		0			0
$916$	−2.34155e8	+	4.05569e8i	−0.304661	+	0.527689i
$917$			2.22327e7i			0.0288326i
$918$		0			0
$919$	−5.30833e8			−0.683929			−0.341965	−	0.939713i	$-0.611092\pi$
$919$	−5.30833e8			−0.683929			−0.341965	+	0.939713i	$0.611092\pi$
$920$	9.18822e6	+	5.30482e6i	0.0117996	+	0.00681251i
$921$		0			0
$922$	−3.36623e8	−	5.83047e8i	−0.429487	−	0.743894i
$923$	−5.01860e8	+	2.89749e8i	−0.638230	+	0.368482i
$924$		0			0
$925$	−5.19071e7	+	8.99058e7i	−0.0655846	+	0.113596i
$926$		−	6.42467e8i		−	0.809129i
$927$		0			0
$928$	−2.02380e8			−0.253235
$929$	−7.91295e8	−	4.56854e8i	−0.986941	−	0.569810i	−0.0825823	−	0.996584i	$-0.526317\pi$
$929$	−7.91295e8	−	4.56854e8i	−0.986941	−	0.569810i	−0.904358	+	0.426774i	$0.859650\pi$
$930$		0			0
$931$	3.17742e8	+	5.50346e8i	0.393755	+	0.682004i
$932$	4.20621e7	−	2.42845e7i	0.0519569	−	0.0299973i
$933$		0			0
$934$	3.81050e8	−	6.59998e8i	0.467672	−	0.810032i
$935$		−	1.09931e7i		−	0.0134488i
$936$		0			0
$937$	9.47917e8			1.15226			0.576131	−	0.817357i	$-0.304562\pi$
$937$	9.47917e8			1.15226			0.576131	+	0.817357i	$0.304562\pi$
$938$	−1.60826e7	−	9.28527e6i	−0.0194871	−	0.0112509i
$939$		0			0
$940$	3.81394e7	+	6.60594e7i	0.0459188	+	0.0795336i
$941$	−8.63034e8	+	4.98273e8i	−1.03576	+	0.597996i	−0.918629	−	0.395120i	$-0.870703\pi$
$941$	−8.63034e8	+	4.98273e8i	−1.03576	+	0.597996i	−0.117131	+	0.993117i	$0.537370\pi$
$942$		0			0
$943$	6.35920e7	−	1.10145e8i	0.0758346	−	0.131349i
$944$			2.97750e7i			0.0353945i
$945$		0			0
$946$	−9.11754e7			−0.107697
$947$	1.28817e9	+	7.43725e8i	1.51678	+	0.875714i	0.999806	+	0.0197138i	$0.00627550\pi$
$947$	1.28817e9	+	7.43725e8i	1.51678	+	0.875714i	0.516975	+	0.856000i	$0.327058\pi$
$948$		0			0
$949$	−3.17068e7	−	5.49178e7i	−0.0370983	−	0.0642561i
$950$	3.97301e8	−	2.29382e8i	0.463392	−	0.267540i
$951$		0			0
$952$	−1.89785e6	+	3.28717e6i	−0.00219964	+	0.00380988i
$953$		−	4.53743e8i		−	0.524241i	−0.965035	−	0.262121i	$-0.915578\pi$
$953$		−	4.53743e8i		−	0.524241i	0.965035	−	0.262121i	$-0.0844218\pi$
$954$		0			0
$955$	−9.44541e7			−0.108445
$956$	3.86893e8	+	2.23373e8i	0.442810	+	0.255656i
$957$		0			0
$958$	4.55307e8	+	7.88615e8i	0.517855	+	0.896950i
$959$	8.21289e6	−	4.74172e6i	0.00931194	−	0.00537625i
$960$		0			0
$961$	4.32893e8	−	7.49792e8i	0.487764	−	0.844832i
$962$		−	3.60754e7i		−	0.0405215i
$963$		0			0
$964$	−8.10125e8			−0.904317
$965$	−2.78423e7	−	1.60747e7i	−0.0309830	−	0.0178880i
$966$		0			0
$967$	−5.04639e8	−	8.74060e8i	−0.558086	−	0.966634i	−0.997656	−	0.0684252i	$-0.978203\pi$
$967$	−5.04639e8	−	8.74060e8i	−0.558086	−	0.966634i	0.439570	−	0.898208i	$-0.355131\pi$
$968$	−2.75037e8	+	1.58793e8i	−0.303225	+	0.175067i
$969$		0			0
$970$	−2.93537e7	+	5.08420e7i	−0.0321623	+	0.0557067i
$971$			6.88293e8i			0.751823i	0.926656	+	0.375912i	$0.122670\pi$
$971$			6.88293e8i			0.751823i	−0.926656	+	0.375912i	$0.877330\pi$
$972$		0			0
$973$	−2.18579e7			−0.0237285
$974$	−5.63208e7	−	3.25168e7i	−0.0609526	−	0.0351910i
$975$		0			0
$976$	−1.64181e8	−	2.84370e8i	−0.176593	−	0.305868i
$977$	−6.66620e8	+	3.84873e8i	−0.714816	+	0.412699i	−0.812842	−	0.582484i	$-0.802081\pi$
$977$	−6.66620e8	+	3.84873e8i	−0.714816	+	0.412699i	0.0980254	+	0.995184i	$0.468747\pi$
$978$		0			0
$979$	6.64582e7	−	1.15109e8i	0.0708272	−	0.122676i
$980$		−	9.33988e7i		−	0.0992346i
$981$		0			0
$982$	7.88003e8			0.832135
$983$	7.49309e8	+	4.32614e8i	0.788861	+	0.455449i	0.839561	−	0.543265i	$-0.182812\pi$
$983$	7.49309e8	+	4.32614e8i	0.788861	+	0.455449i	−0.0507003	+	0.998714i	$0.516145\pi$
$984$		0			0
$985$	−7.43836e7	−	1.28836e8i	−0.0778338	−	0.134812i
$986$	5.79220e8	−	3.34413e8i	0.604245	−	0.348861i
$987$		0			0
$988$	−7.97100e7	+	1.38062e8i	−0.0826499	+	0.143154i
$989$			2.90807e8i			0.300619i
$990$		0			0
$991$	1.48536e9			1.52620			0.763101	−	0.646280i	$-0.223676\pi$
$991$	1.48536e9			1.52620			0.763101	+	0.646280i	$0.223676\pi$
$992$	−2.33788e7	−	1.34977e7i	−0.0239490	−	0.0138269i
$993$		0			0
$994$	−1.10150e7	−	1.90785e7i	−0.0112157	−	0.0194261i
$995$	2.25496e7	−	1.30190e7i	0.0228913	−	0.0132163i
$996$		0			0
$997$	2.94090e8	−	5.09379e8i	0.296753	−	0.513991i	−0.678638	−	0.734473i	$-0.737430\pi$
$997$	2.94090e8	−	5.09379e8i	0.296753	−	0.513991i	0.975391	+	0.220482i	$0.0707630\pi$
$998$		−	5.28744e8i		−	0.531929i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.7.d.f.107.2		8
3.2	odd	2	inner	162.7.d.f.107.3		8
9.2	odd	6		162.7.b.a.161.1	✓	4
9.4	even	3	inner	162.7.d.f.53.3		8
9.5	odd	6	inner	162.7.d.f.53.2		8
9.7	even	3		162.7.b.a.161.4	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.7.b.a.161.1	✓	4	9.2	odd	6
162.7.b.a.161.4	yes	4	9.7	even	3
162.7.d.f.53.2		8	9.5	odd	6	inner
162.7.d.f.53.3		8	9.4	even	3	inner
162.7.d.f.107.2		8	1.1	even	1	trivial
162.7.d.f.107.3		8	3.2	odd	2	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)

\(f(q)\)	\(=\)	\(q+(-4.89898 - 2.82843i) q^{2} +(16.0000 + 27.7128i) q^{4} +(-21.4919 + 12.4084i) q^{5} +(3.09808 - 5.36603i) q^{7} -181.019i q^{8} +O(q^{10})\)	\(q+(-4.89898 - 2.82843i) q^{2} +(16.0000 + 27.7128i) q^{4} +(-21.4919 + 12.4084i) q^{5} +(3.09808 - 5.36603i) q^{7} -181.019i q^{8} +140.385 q^{10} +(-113.360 - 65.4483i) q^{11} +(461.004 + 798.482i) q^{13} +(-30.3548 + 17.5254i) q^{14} +(-512.000 + 886.810i) q^{16} -3384.11i q^{17} +5403.30 q^{19} +(-687.742 - 397.068i) q^{20} +(370.232 + 641.260i) q^{22} +(2045.32 - 1180.87i) q^{23} +(-7504.56 + 12998.3i) q^{25} -5215.66i q^{26} +198.277 q^{28} +(-30256.9 - 17468.8i) q^{29} +(-2330.16 - 4035.96i) q^{31} +(5016.55 - 2896.31i) q^{32} +(-9571.71 + 16578.7i) q^{34} +153.768i q^{35} +6916.74 q^{37} +(-26470.6 - 15282.8i) q^{38} +(2246.16 + 3890.46i) q^{40} +(46637.1 - 26926.0i) q^{41} +(-61566.4 + 106636. i) q^{43} -4188.69i q^{44} -13360.0 q^{46} +(-83183.9 - 48026.3i) q^{47} +(58805.3 + 101854. i) q^{49} +(73529.4 - 42452.2i) q^{50} +(-14752.1 + 25551.4i) q^{52} +132310. i q^{53} +3248.43 q^{55} +(-971.354 - 560.812i) q^{56} +(98818.5 + 171159. i) q^{58} +(25181.5 - 14538.6i) q^{59} +(-160333. + 277705. i) q^{61} +26362.8i q^{62} -32768.0 q^{64} +(-19815.7 - 11440.6i) q^{65} +(264909. + 458837. i) q^{67} +(93783.3 - 54145.8i) q^{68} +(434.923 - 753.308i) q^{70} +628518. i q^{71} -68777.7 q^{73} +(-33885.0 - 19563.5i) q^{74} +(86452.7 + 149741. i) q^{76} +(-702.395 + 405.528i) q^{77} +(-235877. + 408551. i) q^{79} -25412.4i q^{80} -304633. q^{82} +(-29055.1 - 16775.0i) q^{83} +(41991.3 + 72731.1i) q^{85} +(603225. - 348272. i) q^{86} +(-11847.4 + 20520.3i) q^{88} +1.01543e6i q^{89} +5712.90 q^{91} +(65450.3 + 37787.7i) q^{92} +(271678. + 470559. i) q^{94} +(-116127. + 67046.1i) q^{95} +(-209094. + 362162. i) q^{97} -665306. i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 128 q^{4} + 4 q^{7}+O(q^{10}) \) 8 * q + 128 * q^4 + 4 * q^7	\( 8 q + 128 q^{4} + 4 q^{7} + 5280 q^{10} - 3836 q^{13} - 4096 q^{16} + 20488 q^{19} + 27072 q^{22} + 25700 q^{25} + 256 q^{28} + 40096 q^{31} - 60528 q^{34} - 40400 q^{37} + 84480 q^{40} - 184940 q^{43} + 325440 q^{46} + 470484 q^{49} + 122752 q^{52} + 1899720 q^{55} - 24624 q^{58} - 609056 q^{61} - 262144 q^{64} + 2008972 q^{67} - 8160 q^{70} + 1051648 q^{73} + 327808 q^{76} + 848716 q^{79} + 1411584 q^{82} + 987840 q^{85} - 866304 q^{88} + 70520 q^{91} + 1965408 q^{94} - 3621728 q^{97}+O(q^{100}) \) 8 * q + 128 * q^4 + 4 * q^7 + 5280 * q^10 - 3836 * q^13 - 4096 * q^16 + 20488 * q^19 + 27072 * q^22 + 25700 * q^25 + 256 * q^28 + 40096 * q^31 - 60528 * q^34 - 40400 * q^37 + 84480 * q^40 - 184940 * q^43 + 325440 * q^46 + 470484 * q^49 + 122752 * q^52 + 1899720 * q^55 - 24624 * q^58 - 609056 * q^61 - 262144 * q^64 + 2008972 * q^67 - 8160 * q^70 + 1051648 * q^73 + 327808 * q^76 + 848716 * q^79 + 1411584 * q^82 + 987840 * q^85 - 866304 * q^88 + 70520 * q^91 + 1965408 * q^94 - 3621728 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more