LMFDB - Embedded newform 336.6.q.h.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,6,Mod(193,336)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("336.193");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	336.q (of order $3$, 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:	$53.8889634572$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{505})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 127x^{2} + 126x + 15876 $ x^4 - x^3 + 127x^2 + 126x + 15876
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 7 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.1
Root			$-5.36805 - 9.29774i$ of defining polynomial
Character	$\chi$	$=$	336.289
Dual form			336.6.q.h.193.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.50000 + 7.79423i) q^{3} +(-43.5764 + 75.4765i) q^{5} +(113.236 + 63.1236i) q^{7} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})$	\(q+(4.50000 + 7.79423i) q^{3} +(-43.5764 + 75.4765i) q^{5} +(113.236 + 63.1236i) q^{7} +(-40.5000 + 70.1481i) q^{9} +(-239.035 - 414.020i) q^{11} -436.153 q^{13} -784.374 q^{15} +(-1129.53 - 1956.40i) q^{17} +(1332.06 - 2307.20i) q^{19} +(17.5629 + 1166.64i) q^{21} +(-1284.31 + 2224.48i) q^{23} +(-2235.30 - 3871.65i) q^{25} -729.000 q^{27} -708.010 q^{29} +(2754.57 + 4771.05i) q^{31} +(2151.31 - 3726.18i) q^{33} +(-9698.76 + 5795.97i) q^{35} +(457.815 - 792.959i) q^{37} +(-1962.69 - 3399.47i) q^{39} +8866.08 q^{41} +7915.62 q^{43} +(-3529.69 - 6113.59i) q^{45} +(9786.25 - 16950.3i) q^{47} +(8837.83 + 14295.7i) q^{49} +(10165.7 - 17607.6i) q^{51} +(-4123.94 - 7142.87i) q^{53} +41665.0 q^{55} +23977.1 q^{57} +(-16095.3 - 27877.9i) q^{59} +(-14210.0 + 24612.5i) q^{61} +(-9014.06 + 5386.79i) q^{63} +(19005.9 - 32919.3i) q^{65} +(-4841.21 - 8385.21i) q^{67} -23117.5 q^{69} -28568.4 q^{71} +(1556.44 + 2695.83i) q^{73} +(20117.7 - 34844.8i) q^{75} +(-932.921 - 61970.7i) q^{77} +(-3395.03 + 5880.37i) q^{79} +(-3280.50 - 5681.99i) q^{81} -14482.3 q^{83} +196883. q^{85} +(-3186.05 - 5518.39i) q^{87} +(-13732.3 + 23785.0i) q^{89} +(-49388.2 - 27531.5i) q^{91} +(-24791.1 + 42939.5i) q^{93} +(116093. + 201079. i) q^{95} -91212.8 q^{97} +38723.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 18 q^{3} - 17 q^{5} + 408 q^{7} - 162 q^{9}+O(q^{10}) $ 4 * q + 18 * q^3 - 17 * q^5 + 408 * q^7 - 162 * q^9	$ 4 q + 18 q^{3} - 17 q^{5} + 408 q^{7} - 162 q^{9} + 145 q^{11} - 1430 q^{13} - 306 q^{15} - 1372 q^{17} + 1081 q^{19} + 2295 q^{21} - 4508 q^{23} - 6267 q^{25} - 2916 q^{27} + 15730 q^{29} + 8816 q^{31} - 1305 q^{33} - 24278 q^{35} + 14573 q^{37} - 6435 q^{39} + 14700 q^{41} + 11842 q^{43} - 1377 q^{45} + 44808 q^{47} + 17014 q^{49} + 12348 q^{51} - 9417 q^{53} + 170750 q^{55} + 19458 q^{57} - 5077 q^{59} - 42368 q^{61} - 12393 q^{63} + 18450 q^{65} + 30501 q^{67} - 81144 q^{69} - 183488 q^{71} + 85665 q^{73} + 56403 q^{75} + 154585 q^{77} + 94646 q^{79} - 13122 q^{81} - 67682 q^{83} + 518224 q^{85} + 70785 q^{87} - 27558 q^{89} - 149395 q^{91} - 79344 q^{93} + 343246 q^{95} - 93342 q^{97} - 23490 q^{99}+O(q^{100}) $ 4 * q + 18 * q^3 - 17 * q^5 + 408 * q^7 - 162 * q^9 + 145 * q^11 - 1430 * q^13 - 306 * q^15 - 1372 * q^17 + 1081 * q^19 + 2295 * q^21 - 4508 * q^23 - 6267 * q^25 - 2916 * q^27 + 15730 * q^29 + 8816 * q^31 - 1305 * q^33 - 24278 * q^35 + 14573 * q^37 - 6435 * q^39 + 14700 * q^41 + 11842 * q^43 - 1377 * q^45 + 44808 * q^47 + 17014 * q^49 + 12348 * q^51 - 9417 * q^53 + 170750 * q^55 + 19458 * q^57 - 5077 * q^59 - 42368 * q^61 - 12393 * q^63 + 18450 * q^65 + 30501 * q^67 - 81144 * q^69 - 183488 * q^71 + 85665 * q^73 + 56403 * q^75 + 154585 * q^77 + 94646 * q^79 - 13122 * q^81 - 67682 * q^83 + 518224 * q^85 + 70785 * q^87 - 27558 * q^89 - 149395 * q^91 - 79344 * q^93 + 343246 * q^95 - 93342 * q^97 - 23490 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	4.50000	+	7.79423i	0.288675	+	0.500000i
$3$	4.50000	+	7.79423i	0.288675	+	0.500000i
$4$		0			0
$5$	−43.5764	+	75.4765i	−0.779518	+	1.35016i	0.152702	+	0.988272i	$0.451202\pi$
$5$	−43.5764	+	75.4765i	−0.779518	+	1.35016i	−0.932220	+	0.361892i	$0.882131\pi$
$6$		0			0
$7$	113.236	+	63.1236i	0.873454	+	0.486907i
$7$	113.236	+	63.1236i	0.873454	+	0.486907i
$8$		0			0
$9$	−40.5000	+	70.1481i	−0.166667	+	0.288675i
$10$		0			0
$11$	−239.035	−	414.020i	−0.595633	−	1.03167i	−0.993457	−	0.114205i	$-0.963568\pi$
$11$	−239.035	−	414.020i	−0.595633	−	1.03167i	0.397824	−	0.917462i	$-0.369765\pi$
$12$		0			0
$13$	−436.153			−0.715781			−0.357891	−	0.933764i	$-0.616504\pi$
$13$	−436.153			−0.715781			−0.357891	+	0.933764i	$0.616504\pi$
$14$		0			0
$15$	−784.374			−0.900109
$16$		0			0
$17$	−1129.53	−	1956.40i	−0.947926	−	1.64186i	−0.749784	−	0.661682i	$-0.769843\pi$
$17$	−1129.53	−	1956.40i	−0.947926	−	1.64186i	−0.198142	−	0.980173i	$-0.563491\pi$
$18$		0			0
$19$	1332.06	−	2307.20i	0.846526	−	1.46623i	−0.0377632	−	0.999287i	$-0.512023\pi$
$19$	1332.06	−	2307.20i	0.846526	−	1.46623i	0.884289	−	0.466939i	$-0.154643\pi$
$20$		0			0
$21$	17.5629	+	1166.64i	0.00869058	+	0.577285i
$22$		0			0
$23$	−1284.31	+	2224.48i	−0.506231	+	0.876818i	0.493743	+	0.869608i	$0.335628\pi$
$23$	−1284.31	+	2224.48i	−0.506231	+	0.876818i	−0.999974	+	0.00720994i	$0.997705\pi$
$24$		0			0
$25$	−2235.30	−	3871.65i	−0.715295	−	1.23893i
$26$		0			0
$27$	−729.000			−0.192450
$28$		0			0
$29$	−708.010			−0.156331			−0.0781654	−	0.996940i	$-0.524906\pi$
$29$	−708.010			−0.156331			−0.0781654	+	0.996940i	$0.524906\pi$
$30$		0			0
$31$	2754.57	+	4771.05i	0.514813	+	0.891682i	0.999852	+	0.0171898i	$0.00547195\pi$
$31$	2754.57	+	4771.05i	0.514813	+	0.891682i	−0.485039	+	0.874492i	$0.661195\pi$
$32$		0			0
$33$	2151.31	−	3726.18i	0.343889	−	0.595633i
$34$		0			0
$35$	−9698.76	+	5795.97i	−1.33828	+	0.799753i
$36$		0			0
$37$	457.815	−	792.959i	0.0549776	−	0.0952240i	−0.837227	−	0.546856i	$-0.815825\pi$
$37$	457.815	−	792.959i	0.0549776	−	0.0952240i	0.892204	+	0.451632i	$0.149158\pi$
$38$		0			0
$39$	−1962.69	−	3399.47i	−0.206628	−	0.357891i
$40$		0			0
$41$	8866.08			0.823706			0.411853	−	0.911250i	$-0.364882\pi$
$41$	8866.08			0.823706			0.411853	+	0.911250i	$0.364882\pi$
$42$		0			0
$43$	7915.62			0.652851			0.326425	−	0.945223i	$-0.394156\pi$
$43$	7915.62			0.652851			0.326425	+	0.945223i	$0.394156\pi$
$44$		0			0
$45$	−3529.69	−	6113.59i	−0.259839	−	0.450055i
$46$		0			0
$47$	9786.25	−	16950.3i	0.646207	−	1.11926i	−0.337814	−	0.941213i	$-0.609688\pi$
$47$	9786.25	−	16950.3i	0.646207	−	1.11926i	0.984021	−	0.178051i	$-0.0569791\pi$
$48$		0			0
$49$	8837.83	+	14295.7i	0.525842	+	0.850582i
$50$		0			0
$51$	10165.7	−	17607.6i	0.547285	−	0.947926i
$52$		0			0
$53$	−4123.94	−	7142.87i	−0.201661	−	0.349287i	0.747403	−	0.664371i	$-0.231301\pi$
$53$	−4123.94	−	7142.87i	−0.201661	−	0.349287i	−0.949064	+	0.315084i	$0.897967\pi$
$54$		0			0
$55$	41665.0			1.85723
$56$		0			0
$57$	23977.1			0.977484
$58$		0			0
$59$	−16095.3	−	27877.9i	−0.601961	−	1.04263i	−0.992524	−	0.122051i	$-0.961053\pi$
$59$	−16095.3	−	27877.9i	−0.601961	−	1.04263i	0.390562	−	0.920576i	$-0.372281\pi$
$60$		0			0
$61$	−14210.0	+	24612.5i	−0.488957	+	0.846898i	−0.999919	−	0.0127053i	$-0.995956\pi$
$61$	−14210.0	+	24612.5i	−0.488957	+	0.846898i	0.510963	+	0.859603i	$0.329289\pi$
$62$		0			0
$63$	−9014.06	+	5386.79i	−0.286134	+	0.170993i
$64$		0			0
$65$	19005.9	−	32919.3i	0.557964	−	0.966422i
$66$		0			0
$67$	−4841.21	−	8385.21i	−0.131755	−	0.228206i	0.792598	−	0.609744i	$-0.208728\pi$
$67$	−4841.21	−	8385.21i	−0.131755	−	0.228206i	−0.924353	+	0.381538i	$0.875394\pi$
$68$		0			0
$69$	−23117.5			−0.584545
$70$		0			0
$71$	−28568.4			−0.672574			−0.336287	−	0.941760i	$-0.609171\pi$
$71$	−28568.4			−0.672574			−0.336287	+	0.941760i	$0.609171\pi$
$72$		0			0
$73$	1556.44	+	2695.83i	0.0341842	+	0.0592087i	0.882611	−	0.470103i	$-0.155783\pi$
$73$	1556.44	+	2695.83i	0.0341842	+	0.0592087i	−0.848427	+	0.529312i	$0.822450\pi$
$74$		0			0
$75$	20117.7	−	34844.8i	0.412976	−	0.715295i
$76$		0			0
$77$	−932.921	−	61970.7i	−0.0179316	−	1.19113i
$78$		0			0
$79$	−3395.03	+	5880.37i	−0.0612035	+	0.106008i	−0.895004	−	0.446059i	$-0.852827\pi$
$79$	−3395.03	+	5880.37i	−0.0612035	+	0.106008i	0.833800	+	0.552066i	$0.186161\pi$
$80$		0			0
$81$	−3280.50	−	5681.99i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−14482.3			−0.230750			−0.115375	−	0.993322i	$-0.536807\pi$
$83$	−14482.3			−0.230750			−0.115375	+	0.993322i	$0.536807\pi$
$84$		0			0
$85$	196883.			2.95570
$86$		0			0
$87$	−3186.05	−	5518.39i	−0.0451288	−	0.0781654i
$88$		0			0
$89$	−13732.3	+	23785.0i	−0.183767	+	0.318294i	−0.943160	−	0.332338i	$-0.892163\pi$
$89$	−13732.3	+	23785.0i	−0.183767	+	0.318294i	0.759393	+	0.650632i	$0.225496\pi$
$90$		0			0
$91$	−49388.2	−	27531.5i	−0.625202	−	0.348519i
$92$		0			0
$93$	−24791.1	+	42939.5i	−0.297227	+	0.514813i
$94$		0			0
$95$	116093.	+	201079.i	1.31976	+	2.28590i
$96$		0			0
$97$	−91212.8			−0.984298			−0.492149	−	0.870511i	$-0.663788\pi$
$97$	−91212.8			−0.984298			−0.492149	+	0.870511i	$0.663788\pi$
$98$		0			0
$99$	38723.6			0.397089
$100$		0			0
$101$	−53856.1	−	93281.5i	−0.525329	−	0.909897i	−0.999565	−	0.0294990i	$-0.990609\pi$
$101$	−53856.1	−	93281.5i	−0.525329	−	0.909897i	0.474236	−	0.880398i	$-0.342725\pi$
$102$		0			0
$103$	−25000.7	+	43302.4i	−0.232198	+	0.402179i	−0.958455	−	0.285245i	$-0.907925\pi$
$103$	−25000.7	+	43302.4i	−0.232198	+	0.402179i	0.726257	+	0.687424i	$0.241258\pi$
$104$		0			0
$105$	−88819.5	−	49512.5i	−0.786204	−	0.438270i
$106$		0			0
$107$	86342.9	−	149550.i	0.729066	−	1.26278i	−0.228212	−	0.973612i	$-0.573288\pi$
$107$	86342.9	−	149550.i	0.729066	−	1.26278i	0.957278	−	0.289169i	$-0.0933788\pi$
$108$		0			0
$109$	−74850.1	−	129644.i	−0.603429	−	1.04517i	−0.992298	−	0.123876i	$-0.960467\pi$
$109$	−74850.1	−	129644.i	−0.603429	−	1.04517i	0.388869	−	0.921293i	$-0.372866\pi$
$110$		0			0
$111$	8240.67			0.0634826
$112$		0			0
$113$	143442.			1.05677			0.528384	−	0.849005i	$-0.322798\pi$
$113$	143442.			1.05677			0.528384	+	0.849005i	$0.322798\pi$
$114$		0			0
$115$	−111931.	−	193870.i	−0.789232	−	1.36699i
$116$		0			0
$117$	17664.2	−	30595.3i	0.119297	−	0.206628i
$118$		0			0
$119$	−4408.40	−	292835.i	−0.0285373	−	1.89564i
$120$		0			0
$121$	−33749.5	+	58455.8i	−0.209558	+	0.362965i
$122$		0			0
$123$	39897.4	+	69104.2i	0.237783	+	0.411853i
$124$		0			0
$125$	117272.			0.671306
$126$		0			0
$127$	337908.			1.85904			0.929520	−	0.368771i	$-0.120221\pi$
$127$	337908.			1.85904			0.929520	+	0.368771i	$0.120221\pi$
$128$		0			0
$129$	35620.3	+	61696.2i	0.188462	+	0.326425i
$130$		0			0
$131$	−9338.19	+	16174.2i	−0.0475428	+	0.0823465i	−0.888817	−	0.458261i	$-0.848472\pi$
$131$	−9338.19	+	16174.2i	−0.0475428	+	0.0823465i	0.841275	+	0.540608i	$0.181806\pi$
$132$		0			0
$133$	296476.	−	177174.i	1.45332	−	0.868501i
$134$		0			0
$135$	31767.2	−	55022.3i	0.150018	−	0.259839i
$136$		0			0
$137$	−51319.4	−	88887.8i	−0.233604	−	0.404614i	0.725262	−	0.688473i	$-0.241719\pi$
$137$	−51319.4	−	88887.8i	−0.233604	−	0.404614i	−0.958866	+	0.283859i	$0.908385\pi$
$138$		0			0
$139$	202436.			0.888692			0.444346	−	0.895855i	$-0.353436\pi$
$139$	202436.			0.888692			0.444346	+	0.895855i	$0.353436\pi$
$140$		0			0
$141$	176153.			0.746176
$142$		0			0
$143$	104256.	+	180576.i	0.426343	+	0.738448i
$144$		0			0
$145$	30852.5	−	53438.1i	0.121863	−	0.211072i
$146$		0			0
$147$	−71654.0	+	133215.i	−0.273494	+	0.508463i
$148$		0			0
$149$	46808.9	−	81075.3i	0.172728	−	0.299173i	−0.766645	−	0.642072i	$-0.778075\pi$
$149$	46808.9	−	81075.3i	0.172728	−	0.299173i	0.939373	+	0.342898i	$0.111409\pi$
$150$		0			0
$151$	−94589.0	−	163833.i	−0.337597	−	0.584735i	0.646383	−	0.763013i	$-0.276281\pi$
$151$	−94589.0	−	163833.i	−0.337597	−	0.584735i	−0.983980	+	0.178278i	$0.942947\pi$
$152$		0			0
$153$	182983.			0.631951
$154$		0			0
$155$	−480136.			−1.60522
$156$		0			0
$157$	−263263.	−	455985.i	−0.852395	−	1.47639i	−0.879041	−	0.476747i	$-0.841816\pi$
$157$	−263263.	−	455985.i	−0.852395	−	1.47639i	0.0266453	−	0.999645i	$-0.491518\pi$
$158$		0			0
$159$	37115.4	−	64285.8i	0.116429	−	0.201661i
$160$		0			0
$161$	−285847.	+	170822.i	−0.869098	+	0.519372i
$162$		0			0
$163$	97546.2	−	168955.i	0.287569	−	0.498083i	−0.685660	−	0.727922i	$-0.740486\pi$
$163$	97546.2	−	168955.i	0.287569	−	0.498083i	0.973229	+	0.229838i	$0.0738197\pi$
$164$		0			0
$165$	187493.	+	324747.i	0.536135	+	0.928613i
$166$		0			0
$167$	−240814.			−0.668175			−0.334087	−	0.942542i	$-0.608428\pi$
$167$	−240814.			−0.668175			−0.334087	+	0.942542i	$0.608428\pi$
$168$		0			0
$169$	−181064.			−0.487657
$170$		0			0
$171$	107897.	+	186883.i	0.282175	+	0.488742i
$172$		0			0
$173$	−268635.	+	465289.i	−0.682412	+	1.18197i	0.291830	+	0.956470i	$0.405736\pi$
$173$	−268635.	+	465289.i	−0.682412	+	1.18197i	−0.974243	+	0.225503i	$0.927598\pi$
$174$		0			0
$175$	−8724.08	−	579511.i	−0.0215340	−	1.43043i
$176$		0			0
$177$	144858.	−	250901.i	0.347543	−	0.601961i
$178$		0			0
$179$	−92946.6	−	160988.i	−0.216821	−	0.375545i	0.737013	−	0.675878i	$-0.236235\pi$
$179$	−92946.6	−	160988.i	−0.216821	−	0.375545i	−0.953834	+	0.300333i	$0.902902\pi$
$180$		0			0
$181$	1575.22			0.00357392			0.00178696	−	0.999998i	$-0.499431\pi$
$181$	1575.22			0.00357392			0.00178696	+	0.999998i	$0.499431\pi$
$182$		0			0
$183$	−255780.			−0.564598
$184$		0			0
$185$	39899.8	+	69108.5i	0.0857120	+	0.148458i
$186$		0			0
$187$	−539992.	+	935294.i	−1.12923	+	1.95589i
$188$		0			0
$189$	−82549.1	−	46017.1i	−0.168096	−	0.0937054i
$190$		0			0
$191$	98662.3	−	170888.i	0.195690	−	0.338944i	−0.751437	−	0.659805i	$-0.770639\pi$
$191$	98662.3	−	170888.i	0.195690	−	0.338944i	0.947126	+	0.320861i	$0.103972\pi$
$192$		0			0
$193$	228859.	+	396395.i	0.442256	+	0.766010i	0.997857	−	0.0654391i	$-0.0208448\pi$
$193$	228859.	+	396395.i	0.442256	+	0.766010i	−0.555600	+	0.831450i	$0.687511\pi$
$194$		0			0
$195$	342107.			0.644281
$196$		0			0
$197$	−280464.			−0.514887			−0.257443	−	0.966293i	$-0.582880\pi$
$197$	−280464.			−0.514887			−0.257443	+	0.966293i	$0.582880\pi$
$198$		0			0
$199$	60513.6	+	104813.i	0.108323	+	0.187621i	0.915091	−	0.403248i	$-0.132119\pi$
$199$	60513.6	+	104813.i	0.108323	+	0.187621i	−0.806768	+	0.590868i	$0.798785\pi$
$200$		0			0
$201$	43570.9	−	75466.9i	0.0760687	−	0.131755i
$202$		0			0
$203$	−80172.3	−	44692.1i	−0.136548	−	0.0761186i
$204$		0			0
$205$	−386351.	+	669180.i	−0.642093	+	1.11214i
$206$		0			0
$207$	−104029.	−	180183.i	−0.168744	−	0.292273i
$208$		0			0
$209$	−1.27363e6			−2.01688
$210$		0			0
$211$	270026.			0.417541			0.208770	−	0.977965i	$-0.433054\pi$
$211$	270026.			0.417541			0.208770	+	0.977965i	$0.433054\pi$
$212$		0			0
$213$	−128558.	−	222669.i	−0.194155	−	0.336287i
$214$		0			0
$215$	−344934.	+	597443.i	−0.508909	+	0.881456i
$216$		0			0
$217$	10750.7	+	714134.i	0.0154985	+	1.02951i
$218$		0			0
$219$	−14007.9	+	24262.5i	−0.0197362	+	0.0341842i
$220$		0			0
$221$	492646.	+	853289.i	0.678507	+	1.17521i
$222$		0			0
$223$	−83646.2			−0.112638			−0.0563189	−	0.998413i	$-0.517936\pi$
$223$	−83646.2			−0.112638			−0.0563189	+	0.998413i	$0.517936\pi$
$224$		0			0
$225$	362118.			0.476864
$226$		0			0
$227$	52225.9	+	90457.9i	0.0672700	+	0.116515i	0.897699	−	0.440610i	$-0.145238\pi$
$227$	52225.9	+	90457.9i	0.0672700	+	0.116515i	−0.830429	+	0.557125i	$0.811904\pi$
$228$		0			0
$229$	781460.	−	1.35353e6i	0.984732	−	1.70561i	0.341610	−	0.939842i	$-0.389028\pi$
$229$	781460.	−	1.35353e6i	0.984732	−	1.70561i	0.643122	−	0.765764i	$-0.277639\pi$
$230$		0			0
$231$	478816.	−	286140.i	0.590389	−	0.352816i
$232$		0			0
$233$	449041.	−	777761.i	0.541871	−	0.938548i	−0.456926	−	0.889505i	$-0.651049\pi$
$233$	449041.	−	777761.i	0.541871	−	0.938548i	0.998797	−	0.0490433i	$-0.0156172\pi$
$234$		0			0
$235$	852898.	+	1.47726e6i	1.00746	+	1.74497i
$236$		0			0
$237$	−61110.6			−0.0706718
$238$		0			0
$239$	884007.			1.00106			0.500531	−	0.865719i	$-0.333138\pi$
$239$	884007.			1.00106			0.500531	+	0.865719i	$0.333138\pi$
$240$		0			0
$241$	230213.	+	398741.i	0.255322	+	0.442230i	0.964983	−	0.262313i	$-0.0844853\pi$
$241$	230213.	+	398741.i	0.255322	+	0.442230i	−0.709661	+	0.704543i	$0.751152\pi$
$242$		0			0
$243$	29524.5	−	51137.9i	0.0320750	−	0.0555556i
$244$		0			0
$245$	−1.46411e6	+	44092.1i	−1.55833	+	0.0469295i
$246$		0			0
$247$	−580982.	+	1.00629e6i	−0.605927	+	1.04950i
$248$		0			0
$249$	−65170.2	−	112878.i	−0.0666117	−	0.115375i
$250$		0			0
$251$	−1.89967e6			−1.90324			−0.951621	−	0.307276i	$-0.900583\pi$
$251$	−1.89967e6			−1.90324			−0.951621	+	0.307276i	$0.900583\pi$
$252$		0			0
$253$	1.22797e6			1.20611
$254$		0			0
$255$	885972.	+	1.53455e6i	0.853237	+	1.47785i
$256$		0			0
$257$	−375239.	+	649932.i	−0.354384	+	0.613812i	−0.987012	−	0.160644i	$-0.948643\pi$
$257$	−375239.	+	649932.i	−0.354384	+	0.613812i	0.632628	+	0.774456i	$0.281976\pi$
$258$		0			0
$259$	101896.	−	60892.6i	0.0943856	−	0.0564047i
$260$		0			0
$261$	28674.4	−	49665.6i	0.0260551	−	0.0451288i
$262$		0			0
$263$	−701464.	−	1.21497e6i	−0.625340	−	1.08312i	−0.988475	−	0.151384i	$-0.951627\pi$
$263$	−701464.	−	1.21497e6i	−0.625340	−	1.08312i	0.363136	−	0.931736i	$-0.381706\pi$
$264$		0			0
$265$	718824.			0.628794
$266$		0			0
$267$	−247181.			−0.212196
$268$		0			0
$269$	−406758.	−	704525.i	−0.342732	−	0.593630i	0.642207	−	0.766531i	$-0.278019\pi$
$269$	−406758.	−	704525.i	−0.342732	−	0.593630i	−0.984939	+	0.172902i	$0.944686\pi$
$270$		0			0
$271$	−76671.1	+	132798.i	−0.0634174	+	0.109842i	−0.895991	−	0.444072i	$-0.853533\pi$
$271$	−76671.1	+	132798.i	−0.0634174	+	0.109842i	0.832573	+	0.553915i	$0.186867\pi$
$272$		0			0
$273$	−7660.12	−	508835.i	−0.00622055	−	0.413210i
$274$		0			0
$275$	−1.06863e6	+	1.85092e6i	−0.852107	+	1.47589i
$276$		0			0
$277$	241957.	+	419082.i	0.189469	+	0.328170i	0.945073	−	0.326858i	$-0.105990\pi$
$277$	241957.	+	419082.i	0.189469	+	0.328170i	−0.755604	+	0.655029i	$0.772657\pi$
$278$		0			0
$279$	−446240.			−0.343209
$280$		0			0
$281$	845997.			0.639151			0.319575	−	0.947561i	$-0.396460\pi$
$281$	845997.			0.639151			0.319575	+	0.947561i	$0.396460\pi$
$282$		0			0
$283$	−757643.	−	1.31228e6i	−0.562340	−	0.974001i	−0.997292	−	0.0735474i	$-0.976568\pi$
$283$	−757643.	−	1.31228e6i	−0.562340	−	0.974001i	0.434952	−	0.900454i	$-0.356765\pi$
$284$		0			0
$285$	−1.04484e6	+	1.80971e6i	−0.761966	+	1.31976i
$286$		0			0
$287$	1.00396e6	+	559659.i	0.719469	+	0.401068i
$288$		0			0
$289$	−1.84173e6	+	3.18998e6i	−1.29713	+	2.24669i
$290$		0			0
$291$	−410458.	−	710933.i	−0.284142	−	0.492149i
$292$		0			0
$293$	−2.17685e6			−1.48135			−0.740676	−	0.671862i	$-0.765495\pi$
$293$	−2.17685e6			−1.48135			−0.740676	+	0.671862i	$0.765495\pi$
$294$		0			0
$295$	2.80550e6			1.87696
$296$		0			0
$297$	174256.	+	301821.i	0.114630	+	0.198544i
$298$		0			0
$299$	560153.	−	970214.i	0.362351	−	0.627610i
$300$		0			0
$301$	896334.	+	499662.i	0.570235	+	0.317878i
$302$		0			0
$303$	484705.	−	839534.i	0.303299	−	0.525329i
$304$		0			0
$305$	−1.23844e6	−	2.14504e6i	−0.762300	−	1.32034i
$306$		0			0
$307$	−2.52205e6			−1.52724			−0.763621	−	0.645665i	$-0.776580\pi$
$307$	−2.52205e6			−1.52724			−0.763621	+	0.645665i	$0.776580\pi$
$308$		0			0
$309$	−450012.			−0.268119
$310$		0			0
$311$	151874.	+	263053.i	0.0890394	+	0.154221i	0.907105	−	0.420904i	$-0.138287\pi$
$311$	151874.	+	263053.i	0.0890394	+	0.154221i	−0.818066	+	0.575124i	$0.804954\pi$
$312$		0			0
$313$	862415.	−	1.49375e6i	0.497571	−	0.861819i	−0.502425	−	0.864621i	$-0.667559\pi$
$313$	862415.	−	1.49375e6i	0.497571	−	0.861819i	0.999996	+	0.00280229i	$0.000891999\pi$
$314$		0			0
$315$	−13775.9	−	915086.i	−0.00782247	−	0.519620i
$316$		0			0
$317$	−1.72168e6	+	2.98205e6i	−0.962289	+	1.66673i	−0.245560	+	0.969381i	$0.578972\pi$
$317$	−1.72168e6	+	2.98205e6i	−0.962289	+	1.66673i	−0.716729	+	0.697352i	$0.754362\pi$
$318$		0			0
$319$	169239.	+	293130.i	0.0931158	+	0.161281i
$320$		0			0
$321$	1.55417e6			0.841853
$322$		0			0
$323$	−6.01840e6			−3.20978
$324$		0			0
$325$	974931.	+	1.68863e6i	0.511995	+	0.886801i
$326$		0			0
$327$	673651.	−	1.16680e6i	0.348390	−	0.603429i
$328$		0			0
$329$	2.17812e6	−	1.30164e6i	1.10941	−	0.662982i
$330$		0			0
$331$	681794.	−	1.18090e6i	0.342045	−	0.592439i	−0.642768	−	0.766061i	$-0.722214\pi$
$331$	681794.	−	1.18090e6i	0.342045	−	0.592439i	0.984812	+	0.173622i	$0.0555472\pi$
$332$		0			0
$333$	37083.0	+	64229.7i	0.0183259	+	0.0317413i
$334$		0			0
$335$	843848.			0.410821
$336$		0			0
$337$	−3.63708e6			−1.74453			−0.872265	−	0.489034i	$-0.837349\pi$
$337$	−3.63708e6			−1.74453			−0.872265	+	0.489034i	$0.837349\pi$
$338$		0			0
$339$	645488.	+	1.11802e6i	0.305063	+	0.528384i
$340$		0			0
$341$	1.31687e6	−	2.28089e6i	0.613279	−	1.06223i
$342$		0			0
$343$	98363.6	+	2.17667e6i	0.0451439	+	0.998980i
$344$		0			0
$345$	1.00738e6	−	1.74483e6i	0.455663	−	0.789232i
$346$		0			0
$347$	−882075.	−	1.52780e6i	−0.393262	−	0.681149i	0.599616	−	0.800288i	$-0.295320\pi$
$347$	−882075.	−	1.52780e6i	−0.393262	−	0.681149i	−0.992878	+	0.119139i	$0.961987\pi$
$348$		0			0
$349$	−3.15882e6			−1.38823			−0.694114	−	0.719865i	$-0.744204\pi$
$349$	−3.15882e6			−1.38823			−0.694114	+	0.719865i	$0.744204\pi$
$350$		0			0
$351$	317955.			0.137752
$352$		0			0
$353$	885852.	+	1.53434e6i	0.378377	+	0.655368i	0.990826	−	0.135142i	$-0.0431490\pi$
$353$	885852.	+	1.53434e6i	0.378377	+	0.655368i	−0.612449	+	0.790510i	$0.709816\pi$
$354$		0			0
$355$	1.24491e6	−	2.15624e6i	0.524283	−	0.908085i
$356$		0			0
$357$	2.26258e6	−	1.35212e6i	0.939580	−	0.561492i
$358$		0			0
$359$	−742627.	+	1.28627e6i	−0.304113	+	0.526739i	−0.977063	−	0.212949i	$-0.931693\pi$
$359$	−742627.	+	1.28627e6i	−0.304113	+	0.526739i	0.672951	+	0.739687i	$0.265027\pi$
$360$		0			0
$361$	−2.31073e6	−	4.00230e6i	−0.933213	−	1.61637i
$362$		0			0
$363$	−607491.			−0.241977
$364$		0			0
$365$	−271296.			−0.106589
$366$		0			0
$367$	265152.	+	459257.i	0.102761	+	0.177988i	0.912821	−	0.408359i	$-0.133899\pi$
$367$	265152.	+	459257.i	0.102761	+	0.177988i	−0.810060	+	0.586347i	$0.800566\pi$
$368$		0			0
$369$	−359076.	+	621938.i	−0.137284	+	0.237783i
$370$		0			0
$371$	−16095.2	−	1.06915e6i	−0.00607102	−	0.403277i
$372$		0			0
$373$	1.72357e6	−	2.98531e6i	0.641442	−	1.11101i	−0.343669	−	0.939091i	$-0.611670\pi$
$373$	1.72357e6	−	2.98531e6i	0.641442	−	1.11101i	0.985111	−	0.171919i	$-0.0549967\pi$
$374$		0			0
$375$	527726.	+	914048.i	0.193789	+	0.335653i
$376$		0			0
$377$	308801.			0.111899
$378$		0			0
$379$	1.59447e6			0.570189			0.285094	−	0.958499i	$-0.407975\pi$
$379$	1.59447e6			0.570189			0.285094	+	0.958499i	$0.407975\pi$
$380$		0			0
$381$	1.52058e6	+	2.63373e6i	0.536659	+	0.929520i
$382$		0			0
$383$	−1.09098e6	+	1.88963e6i	−0.380032	+	0.658235i	−0.991066	−	0.133369i	$-0.957420\pi$
$383$	−1.09098e6	+	1.88963e6i	−0.380032	+	0.658235i	0.611035	+	0.791604i	$0.290754\pi$
$384$		0			0
$385$	4.71798e6	+	2.63004e6i	1.62220	+	0.904297i
$386$		0			0
$387$	−320583.	+	555265.i	−0.108808	+	0.188462i
$388$		0			0
$389$	−1.05746e6	−	1.83157e6i	−0.354314	−	0.613689i	0.632687	−	0.774408i	$-0.281952\pi$
$389$	−1.05746e6	−	1.83157e6i	−0.354314	−	0.613689i	−0.987000	+	0.160719i	$0.948619\pi$
$390$		0			0
$391$	5.80263e6			1.91948
$392$		0			0
$393$	−168087.			−0.0548976
$394$		0			0
$395$	−295887.	−	512490.i	−0.0954185	−	0.165270i
$396$		0			0
$397$	245781.	−	425705.i	0.0782658	−	0.135560i	−0.824236	−	0.566246i	$-0.808395\pi$
$397$	245781.	−	425705.i	0.0782658	−	0.135560i	0.902502	+	0.430686i	$0.141728\pi$
$398$		0			0
$399$	2.71507e6	+	1.51352e6i	0.853787	+	0.475944i
$400$		0			0
$401$	1.36060e6	−	2.35663e6i	0.422542	−	0.731865i	−0.573645	−	0.819104i	$-0.694471\pi$
$401$	1.36060e6	−	2.35663e6i	0.422542	−	0.731865i	0.996187	+	0.0872390i	$0.0278044\pi$
$402$		0			0
$403$	−1.20141e6	−	2.08091e6i	−0.368493	−	0.638249i
$404$		0			0
$405$	571809.			0.173226
$406$		0			0
$407$	−437734.			−0.130986
$408$		0			0
$409$	−1.59954e6	−	2.77048e6i	−0.472810	−	0.818931i	0.526706	−	0.850048i	$-0.323427\pi$
$409$	−1.59954e6	−	2.77048e6i	−0.472810	−	0.818931i	−0.999516	+	0.0311168i	$0.990094\pi$
$410$		0			0
$411$	461874.	−	799990.i	0.134871	−	0.233604i
$412$		0			0
$413$	−62817.8	−	4.17277e6i	−0.0181221	−	1.20379i
$414$		0			0
$415$	631084.	−	1.09307e6i	0.179874	−	0.311550i
$416$		0			0
$417$	910963.	+	1.57783e6i	0.256543	+	0.444346i
$418$		0			0
$419$	4.89012e6			1.36077			0.680385	−	0.732855i	$-0.261812\pi$
$419$	4.89012e6			1.36077			0.680385	+	0.732855i	$0.261812\pi$
$420$		0			0
$421$	4.98359e6			1.37037			0.685184	−	0.728370i	$-0.259722\pi$
$421$	4.98359e6			1.37037			0.685184	+	0.728370i	$0.259722\pi$
$422$		0			0
$423$	792686.	+	1.37297e6i	0.215402	+	0.373088i
$424$		0			0
$425$	−5.04966e6	+	8.74627e6i	−1.35609	+	2.34882i
$426$		0			0
$427$	−3.16272e6	+	1.89003e6i	−0.839442	+	0.501649i
$428$		0			0
$429$	−938300.	+	1.62518e6i	−0.246149	+	0.426343i
$430$		0			0
$431$	874395.	+	1.51450e6i	0.226733	+	0.392713i	0.956838	−	0.290622i	$-0.0938623\pi$
$431$	874395.	+	1.51450e6i	0.226733	+	0.392713i	−0.730105	+	0.683335i	$0.760529\pi$
$432$		0			0
$433$	5.36175e6			1.37432			0.687159	−	0.726507i	$-0.258858\pi$
$433$	5.36175e6			1.37432			0.687159	+	0.726507i	$0.258858\pi$
$434$		0			0
$435$	555345.			0.140715
$436$		0			0
$437$	3.42155e6	+	5.92630e6i	0.857075	+	1.48450i
$438$		0			0
$439$	3.08724e6	−	5.34726e6i	0.764555	−	1.32425i	−0.175926	−	0.984403i	$-0.556292\pi$
$439$	3.08724e6	−	5.34726e6i	0.764555	−	1.32425i	0.940481	−	0.339845i	$-0.110375\pi$
$440$		0			0
$441$	−1.36075e6	+	40979.4i	−0.333182	+	0.0100339i
$442$		0			0
$443$	−1.79138e6	+	3.10277e6i	−0.433690	+	0.751173i	−0.997188	−	0.0749446i	$-0.976122\pi$
$443$	−1.79138e6	+	3.10277e6i	−0.433690	+	0.751173i	0.563498	+	0.826118i	$0.309455\pi$
$444$		0			0
$445$	−1.19681e6	−	2.07293e6i	−0.286499	−	0.496232i
$446$		0			0
$447$	842560.			0.199449
$448$		0			0
$449$	−4.93126e6			−1.15436			−0.577182	−	0.816616i	$-0.695848\pi$
$449$	−4.93126e6			−1.15436			−0.577182	+	0.816616i	$0.695848\pi$
$450$		0			0
$451$	−2.11930e6	−	3.67073e6i	−0.490626	−	0.849790i
$452$		0			0
$453$	851301.	−	1.47450e6i	0.194912	−	0.337597i
$454$		0			0
$455$	4.23014e6	−	2.52793e6i	0.957914	−	0.572448i
$456$		0			0
$457$	2.13615e6	−	3.69991e6i	0.478454	−	0.828707i	−0.521241	−	0.853410i	$-0.674531\pi$
$457$	2.13615e6	−	3.69991e6i	0.478454	−	0.828707i	0.999695	+	0.0247028i	$0.00786393\pi$
$458$		0			0
$459$	823425.	+	1.42621e6i	0.182428	+	0.315975i
$460$		0			0
$461$	−4.13355e6			−0.905882			−0.452941	−	0.891541i	$-0.649625\pi$
$461$	−4.13355e6			−0.905882			−0.452941	+	0.891541i	$0.649625\pi$
$462$		0			0
$463$	7.66515e6			1.66176			0.830880	−	0.556452i	$-0.187838\pi$
$463$	7.66515e6			1.66176			0.830880	+	0.556452i	$0.187838\pi$
$464$		0			0
$465$	−2.16061e6	−	3.74229e6i	−0.463388	−	0.802611i
$466$		0			0
$467$	−312336.	+	540982.i	−0.0662720	+	0.114787i	−0.897258	−	0.441508i	$-0.854444\pi$
$467$	−312336.	+	540982.i	−0.0662720	+	0.114787i	0.830986	+	0.556294i	$0.187777\pi$
$468$		0			0
$469$	−18894.6	−	1.25510e6i	−0.00396648	−	0.263480i
$470$		0			0
$471$	2.36937e6	−	4.10387e6i	0.492131	−	0.852395i
$472$		0			0
$473$	−1.89211e6	−	3.27722e6i	−0.388860	−	0.673524i
$474$		0			0
$475$	−1.19102e7			−2.42206
$476$		0			0
$477$	668078.			0.134441
$478$		0			0
$479$	−3.65034e6	−	6.32257e6i	−0.726933	−	1.25909i	−0.958173	−	0.286189i	$-0.907612\pi$
$479$	−3.65034e6	−	6.32257e6i	−0.726933	−	1.25909i	0.231240	−	0.972897i	$-0.425722\pi$
$480$		0			0
$481$	−199677.	+	345851.i	−0.0393519	+	0.0681595i
$482$		0			0
$483$	−2.61774e6	−	1.45926e6i	−0.510573	−	0.284619i
$484$		0			0
$485$	3.97472e6	−	6.88442e6i	0.767277	−	1.32896i
$486$		0			0
$487$	−4.22861e6	−	7.32417e6i	−0.807933	−	1.39938i	−0.914293	−	0.405054i	$-0.867253\pi$
$487$	−4.22861e6	−	7.32417e6i	−0.807933	−	1.39938i	0.106360	−	0.994328i	$-0.466080\pi$
$488$		0			0
$489$	1.75583e6			0.332056
$490$		0			0
$491$	2.09490e6			0.392156			0.196078	−	0.980588i	$-0.437179\pi$
$491$	2.09490e6			0.392156			0.196078	+	0.980588i	$0.437179\pi$
$492$		0			0
$493$	799717.	+	1.38515e6i	0.148190	+	0.256673i
$494$		0			0
$495$	−1.68743e6	+	2.92272e6i	−0.309538	+	0.536135i
$496$		0			0
$497$	−3.23497e6	−	1.80334e6i	−0.587462	−	0.327481i
$498$		0			0
$499$	−2.96233e6	+	5.13091e6i	−0.532577	+	0.922451i	0.466699	+	0.884416i	$0.345443\pi$
$499$	−2.96233e6	+	5.13091e6i	−0.532577	+	0.922451i	−0.999276	+	0.0380347i	$0.987890\pi$
$500$		0			0
$501$	−1.08366e6	−	1.87696e6i	−0.192885	−	0.334087i
$502$		0			0
$503$	−4.80370e6			−0.846557			−0.423278	−	0.906000i	$-0.639121\pi$
$503$	−4.80370e6			−0.846557			−0.423278	+	0.906000i	$0.639121\pi$
$504$		0			0
$505$	9.38741e6			1.63801
$506$		0			0
$507$	−814787.	−	1.41125e6i	−0.140775	−	0.243829i
$508$		0			0
$509$	2.60141e6	−	4.50578e6i	0.445056	−	0.770860i	−0.553000	−	0.833181i	$-0.686517\pi$
$509$	2.60141e6	−	4.50578e6i	0.445056	−	0.770860i	0.998056	+	0.0623214i	$0.0198504\pi$
$510$		0			0
$511$	6074.58	+	403513.i	0.00102912	+	0.0683606i
$512$		0			0
$513$	−971073.	+	1.68195e6i	−0.162914	+	0.282175i
$514$		0			0
$515$	−2.17888e6	−	3.77392e6i	−0.362005	−	0.627011i
$516$		0			0
$517$	−9.35701e6			−1.53961
$518$		0			0
$519$	−4.83542e6			−0.787982
$520$		0			0
$521$	3.40577e6	+	5.89896e6i	0.549693	+	0.952097i	0.998295	+	0.0583651i	$0.0185887\pi$
$521$	3.40577e6	+	5.89896e6i	0.549693	+	0.952097i	−0.448602	+	0.893732i	$0.648078\pi$
$522$		0			0
$523$	−5.36153e6	+	9.28645e6i	−0.857106	+	1.48455i	0.0175707	+	0.999846i	$0.494407\pi$
$523$	−5.36153e6	+	9.28645e6i	−0.857106	+	1.48455i	−0.874677	+	0.484706i	$0.838927\pi$
$524$		0			0
$525$	4.47758e6	−	2.67579e6i	0.708998	−	0.423696i
$526$		0			0
$527$	6.22272e6	−	1.07781e7i	0.976009	−	1.69050i
$528$		0			0
$529$	−80709.4	−	139793.i	−0.0125396	−	0.0217193i
$530$		0			0
$531$	2.60744e6			0.401308
$532$		0			0
$533$	−3.86696e6			−0.589593
$534$		0			0
$535$	7.52502e6	+	1.30337e7i	1.13664	+	1.96872i
$536$		0			0
$537$	836519.	−	1.44889e6i	0.125182	−	0.216821i
$538$		0			0
$539$	3.80617e6	−	7.07621e6i	0.564308	−	1.04913i
$540$		0			0
$541$	−6.39450e6	+	1.10756e7i	−0.939320	+	1.62695i	−0.172576	+	0.984996i	$0.555209\pi$
$541$	−6.39450e6	+	1.10756e7i	−0.939320	+	1.62695i	−0.766744	+	0.641954i	$0.778124\pi$
$542$		0			0
$543$	7088.48	+	12277.6i	0.00103170	+	0.00178696i
$544$		0			0
$545$	1.30468e7			1.88153
$546$		0			0
$547$	1.14426e7			1.63514			0.817570	−	0.575829i	$-0.195321\pi$
$547$	1.14426e7			1.63514			0.817570	+	0.575829i	$0.195321\pi$
$548$		0			0
$549$	−1.15101e6	−	1.99361e6i	−0.162986	−	0.282299i
$550$		0			0
$551$	−943113.	+	1.63352e6i	−0.132338	+	0.229216i
$552$		0			0
$553$	−755631.	+	451564.i	−0.105074	+	0.0627923i
$554$		0			0
$555$	−359098.	+	621977.i	−0.0494858	+	0.0857120i
$556$		0			0
$557$	1.45344e6	+	2.51743e6i	0.198499	+	0.343811i	0.948042	−	0.318145i	$-0.103060\pi$
$557$	1.45344e6	+	2.51743e6i	0.198499	+	0.343811i	−0.749543	+	0.661956i	$0.769727\pi$
$558$		0			0
$559$	−3.45242e6			−0.467298
$560$		0			0
$561$	−9.71986e6			−1.30393
$562$		0			0
$563$	1.71348e6	+	2.96783e6i	0.227828	+	0.394610i	0.957164	−	0.289546i	$-0.0935042\pi$
$563$	1.71348e6	+	2.96783e6i	0.227828	+	0.394610i	−0.729336	+	0.684156i	$0.760171\pi$
$564$		0			0
$565$	−6.25067e6	+	1.08265e7i	−0.823769	+	1.42681i
$566$		0			0
$567$	−12803.4	−	850484.i	−0.00167250	−	0.111099i
$568$		0			0
$569$	832615.	−	1.44213e6i	0.107811	−	0.186734i	−0.807072	−	0.590453i	$-0.798949\pi$
$569$	832615.	−	1.44213e6i	0.107811	−	0.186734i	0.914883	+	0.403719i	$0.132283\pi$
$570$		0			0
$571$	−7.48756e6	−	1.29688e7i	−0.961060	−	1.66460i	−0.719848	−	0.694131i	$-0.755789\pi$
$571$	−7.48756e6	−	1.29688e7i	−0.961060	−	1.66460i	−0.241211	−	0.970473i	$-0.577545\pi$
$572$		0			0
$573$	1.77592e6			0.225963
$574$		0			0
$575$	1.14832e7			1.44842
$576$		0			0
$577$	−5.60924e6	−	9.71549e6i	−0.701398	−	1.21486i	−0.967976	−	0.251044i	$-0.919226\pi$
$577$	−5.60924e6	−	9.71549e6i	−0.701398	−	1.21486i	0.266577	−	0.963814i	$-0.414107\pi$
$578$		0			0
$579$	−2.05973e6	+	3.56755e6i	−0.255337	+	0.442256i
$580$		0			0
$581$	−1.63992e6	−	914172.i	−0.201549	−	0.112354i
$582$		0			0
$583$	−1.97153e6	+	3.41478e6i	−0.240232	+	0.416094i
$584$		0			0
$585$	1.53948e6	+	2.66646e6i	0.185988	+	0.322141i
$586$		0			0
$587$	−1.13200e6			−0.135597			−0.0677984	−	0.997699i	$-0.521597\pi$
$587$	−1.13200e6			−0.135597			−0.0677984	+	0.997699i	$0.521597\pi$
$588$		0			0
$589$	1.46770e7			1.74321
$590$		0			0
$591$	−1.26209e6	−	2.18600e6i	−0.148635	−	0.257443i
$592$		0			0
$593$	−5.86391e6	+	1.01566e7i	−0.684779	+	1.18607i	0.288727	+	0.957412i	$0.406768\pi$
$593$	−5.86391e6	+	1.01566e7i	−0.684779	+	1.18607i	−0.973506	+	0.228661i	$0.926565\pi$
$594$		0			0
$595$	2.22942e7	+	1.24279e7i	2.58167	+	1.43915i
$596$		0			0
$597$	−544622.	+	943314.i	−0.0625402	+	0.108323i
$598$		0			0
$599$	1.02415e6	+	1.77388e6i	0.116626	+	0.202003i	0.918429	−	0.395586i	$-0.129459\pi$
$599$	1.02415e6	+	1.77388e6i	0.116626	+	0.202003i	−0.801802	+	0.597589i	$0.796125\pi$
$600$		0			0
$601$	−5.75746e6			−0.650196			−0.325098	−	0.945680i	$-0.605397\pi$
$601$	−5.75746e6			−0.650196			−0.325098	+	0.945680i	$0.605397\pi$
$602$		0			0
$603$	784275.			0.0878366
$604$		0			0
$605$	−2.94136e6	−	5.09459e6i	−0.326708	−	0.565875i
$606$		0			0
$607$	−2.48898e6	+	4.31105e6i	−0.274189	+	0.474910i	−0.969930	−	0.243383i	$-0.921743\pi$
$607$	−2.48898e6	+	4.31105e6i	−0.274189	+	0.474910i	0.695741	+	0.718293i	$0.255076\pi$
$608$		0			0
$609$	−12434.7	−	825996.i	−0.00135861	−	0.0902474i
$610$		0			0
$611$	−4.26830e6	+	7.39291e6i	−0.462543	+	0.801148i
$612$		0			0
$613$	2.28153e6	+	3.95172e6i	0.245230	+	0.424752i	0.962196	−	0.272357i	$-0.0878030\pi$
$613$	2.28153e6	+	3.95172e6i	0.245230	+	0.424752i	−0.716966	+	0.697108i	$0.754470\pi$
$614$		0			0
$615$	−6.95433e6			−0.741425
$616$		0			0
$617$	1.41767e7			1.49921			0.749603	−	0.661888i	$-0.230244\pi$
$617$	1.41767e7			1.49921			0.749603	+	0.661888i	$0.230244\pi$
$618$		0			0
$619$	−3.77397e6	−	6.53671e6i	−0.395888	−	0.685698i	0.597326	−	0.801998i	$-0.296230\pi$
$619$	−3.77397e6	−	6.53671e6i	−0.395888	−	0.685698i	−0.993214	+	0.116301i	$0.962896\pi$
$620$		0			0
$621$	936259.	−	1.62165e6i	0.0974242	−	0.168744i
$622$		0			0
$623$	−3.05639e6	+	1.82649e6i	−0.315492	+	0.188537i
$624$		0			0
$625$	1.87500e6	−	3.24760e6i	0.192000	−	0.332554i
$626$		0			0
$627$	−5.73136e6	−	9.92700e6i	−0.582222	−	1.00844i
$628$		0			0
$629$	−2.06846e6			−0.208459
$630$		0			0
$631$	87076.0			0.00870612			0.00435306	−	0.999991i	$-0.498614\pi$
$631$	87076.0			0.00870612			0.00435306	+	0.999991i	$0.498614\pi$
$632$		0			0
$633$	1.21512e6	+	2.10464e6i	0.120534	+	0.208770i
$634$		0			0
$635$	−1.47248e7	+	2.55041e7i	−1.44915	+	2.51001i
$636$		0			0
$637$	−3.85464e6	−	6.23512e6i	−0.376388	−	0.608831i
$638$		0			0
$639$	1.15702e6	−	2.00402e6i	0.112096	−	0.194155i
$640$		0			0
$641$	−6.76673e6	−	1.17203e7i	−0.650480	−	1.12666i	−0.983007	−	0.183570i	$-0.941235\pi$
$641$	−6.76673e6	−	1.17203e7i	−0.650480	−	1.12666i	0.332527	−	0.943094i	$-0.392099\pi$
$642$		0			0
$643$	595140.			0.0567664			0.0283832	−	0.999597i	$-0.490964\pi$
$643$	595140.			0.0567664			0.0283832	+	0.999597i	$0.490964\pi$
$644$		0			0
$645$	−6.20881e6			−0.587637
$646$		0			0
$647$	1.95405e6	+	3.38451e6i	0.183516	+	0.317859i	0.943076	−	0.332579i	$-0.107919\pi$
$647$	1.95405e6	+	3.38451e6i	0.183516	+	0.317859i	−0.759559	+	0.650438i	$0.774585\pi$
$648$		0			0
$649$	−7.69466e6	+	1.33275e7i	−0.717096	+	1.24205i
$650$		0			0
$651$	−5.51774e6	+	3.29740e6i	−0.510281	+	0.304943i
$652$		0			0
$653$	2.59227e6	−	4.48995e6i	0.237902	−	0.412058i	−0.722210	−	0.691674i	$-0.756874\pi$
$653$	2.59227e6	−	4.48995e6i	0.237902	−	0.412058i	0.960112	+	0.279616i	$0.0902070\pi$
$654$		0			0
$655$	−813848.	−	1.40963e6i	−0.0741208	−	0.128381i
$656$		0			0
$657$	−252143.			−0.0227894
$658$		0			0
$659$	−2.73626e6			−0.245439			−0.122719	−	0.992441i	$-0.539162\pi$
$659$	−2.73626e6			−0.245439			−0.122719	+	0.992441i	$0.539162\pi$
$660$		0			0
$661$	−2.99560e6	−	5.18852e6i	−0.266673	−	0.461892i	0.701327	−	0.712839i	$-0.252591\pi$
$661$	−2.99560e6	−	5.18852e6i	−0.266673	−	0.461892i	−0.968001	+	0.250948i	$0.919258\pi$
$662$		0			0
$663$	−4.43382e6	+	7.67960e6i	−0.391736	+	0.678507i
$664$		0			0
$665$	453095.	+	3.00976e7i	0.0397315	+	2.63923i
$666$		0			0
$667$	909302.	−	1.57496e6i	0.0791395	−	0.137074i
$668$		0			0
$669$	−376408.	−	651958.i	−0.0325157	−	0.0563189i
$670$		0			0
$671$	1.35867e7			1.16495
$672$		0			0
$673$	−6.70138e6			−0.570330			−0.285165	−	0.958478i	$-0.592048\pi$
$673$	−6.70138e6			−0.570330			−0.285165	+	0.958478i	$0.592048\pi$
$674$		0			0
$675$	1.62953e6	+	2.82243e6i	0.137659	+	0.238432i
$676$		0			0
$677$	3.66332e6	−	6.34506e6i	0.307188	−	0.532065i	−0.670558	−	0.741857i	$-0.733945\pi$
$677$	3.66332e6	−	6.34506e6i	0.307188	−	0.532065i	0.977746	+	0.209792i	$0.0672788\pi$
$678$		0			0
$679$	−1.03286e7	−	5.75768e6i	−0.859738	−	0.479262i
$680$		0			0
$681$	−470033.	+	814121.i	−0.0388383	+	0.0672700i
$682$		0			0
$683$	95655.4	+	165680.i	0.00784617	+	0.0135900i	0.869922	−	0.493190i	$-0.164169\pi$
$683$	95655.4	+	165680.i	0.00784617	+	0.0135900i	−0.862076	+	0.506780i	$0.830836\pi$
$684$		0			0
$685$	8.94524e6			0.728393
$686$		0			0
$687$	1.40663e7			1.13707
$688$		0			0
$689$	1.79867e6	+	3.11538e6i	0.144345	+	0.250013i
$690$		0			0
$691$	−5.14617e6	+	8.91343e6i	−0.410005	+	0.710150i	−0.994890	−	0.100967i	$-0.967806\pi$
$691$	−5.14617e6	+	8.91343e6i	−0.410005	+	0.710150i	0.584885	+	0.811116i	$0.301140\pi$
$692$		0			0
$693$	4.38491e6	+	2.44437e6i	0.346839	+	0.193346i
$694$		0			0
$695$	−8.82144e6	+	1.52792e7i	−0.692751	+	1.19988i
$696$		0			0
$697$	−1.00145e7	−	1.73456e7i	−0.780812	−	1.35241i
$698$		0			0
$699$	8.08273e6			0.625699
$700$		0			0
$701$	7.48444e6			0.575260			0.287630	−	0.957742i	$-0.407133\pi$
$701$	7.48444e6			0.575260			0.287630	+	0.957742i	$0.407133\pi$
$702$		0			0
$703$	−1.21968e6	−	2.11254e6i	−0.0930799	−	0.161219i
$704$		0			0
$705$	−7.67609e6	+	1.32954e7i	−0.581657	+	1.00746i
$706$		0			0
$707$	−210194.	−	1.39624e7i	−0.0158151	−	1.05054i
$708$		0			0
$709$	−8.33927e6	+	1.44440e7i	−0.623035	+	1.07913i	0.365882	+	0.930661i	$0.380767\pi$
$709$	−8.33927e6	+	1.44440e7i	−0.623035	+	1.07913i	−0.988917	+	0.148468i	$0.952566\pi$
$710$		0			0
$711$	−274998.	−	476310.i	−0.0204012	−	0.0353359i
$712$		0			0
$713$	−1.41508e7			−1.04246
$714$		0			0
$715$	−1.81723e7			−1.32937
$716$		0			0
$717$	3.97803e6	+	6.89015e6i	0.288982	+	0.500531i
$718$		0			0
$719$	−6.96941e6	+	1.20714e7i	−0.502775	+	0.870832i	0.497220	+	0.867625i	$0.334354\pi$
$719$	−6.96941e6	+	1.20714e7i	−0.502775	+	0.870832i	−0.999995	+	0.00320738i	$0.998979\pi$
$720$		0			0
$721$	−5.56438e6	+	3.32527e6i	−0.398638	+	0.238226i
$722$		0			0
$723$	−2.07192e6	+	3.58867e6i	−0.147410	+	0.255322i
$724$		0			0
$725$	1.58261e6	+	2.74117e6i	0.111823	+	0.193683i
$726$		0			0
$727$	−1.05038e7			−0.737075			−0.368537	−	0.929613i	$-0.620141\pi$
$727$	−1.05038e7			−0.737075			−0.368537	+	0.929613i	$0.620141\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$		0			0
$731$	−8.94091e6	−	1.54861e7i	−0.618854	−	1.07189i
$732$		0			0
$733$	−9.65313e6	+	1.67197e7i	−0.663603	+	1.14939i	0.316059	+	0.948739i	$0.397640\pi$
$733$	−9.65313e6	+	1.67197e7i	−0.663603	+	1.14939i	−0.979662	+	0.200654i	$0.935693\pi$
$734$		0			0
$735$	−6.93217e6	−	1.12132e7i	−0.473316	−	0.765617i
$736$		0			0
$737$	−2.31443e6	+	4.00871e6i	−0.156955	+	0.271854i
$738$		0			0
$739$	−5.47367e6	−	9.48067e6i	−0.368695	−	0.638599i	0.620667	−	0.784075i	$-0.286862\pi$
$739$	−5.47367e6	−	9.48067e6i	−0.368695	−	0.638599i	−0.989362	+	0.145476i	$0.953529\pi$
$740$		0			0
$741$	−1.04577e7			−0.699665
$742$		0			0
$743$	1.37335e7			0.912661			0.456331	−	0.889810i	$-0.349163\pi$
$743$	1.37335e7			0.912661			0.456331	+	0.889810i	$0.349163\pi$
$744$		0			0
$745$	4.07952e6	+	7.06594e6i	0.269289	+	0.466422i
$746$		0			0
$747$	586532.	−	1.01590e6i	0.0384583	−	0.0666117i
$748$		0			0
$749$	1.92173e7	−	1.14842e7i	1.25166	−	0.747992i
$750$		0			0
$751$	−3.45643e6	+	5.98671e6i	−0.223629	+	0.387336i	−0.955907	−	0.293669i	$-0.905124\pi$
$751$	−3.45643e6	+	5.98671e6i	−0.223629	+	0.387336i	0.732278	+	0.681005i	$0.238457\pi$
$752$		0			0
$753$	−8.54851e6	−	1.48065e7i	−0.549418	−	0.951621i
$754$		0			0
$755$	1.64874e7			1.05265
$756$		0			0
$757$	6.68202e6			0.423807			0.211904	−	0.977291i	$-0.432034\pi$
$757$	6.68202e6			0.423807			0.211904	+	0.977291i	$0.432034\pi$
$758$		0			0
$759$	5.52588e6	+	9.57110e6i	0.348175	+	0.603056i
$760$		0			0
$761$	−1.17430e7	+	2.03394e7i	−0.735049	+	1.27314i	0.219653	+	0.975578i	$0.429508\pi$
$761$	−1.17430e7	+	2.03394e7i	−0.735049	+	1.27314i	−0.954702	+	0.297564i	$0.903826\pi$
$762$		0			0
$763$	−292130.	−	1.94052e7i	−0.0181662	−	1.20672i
$764$		0			0
$765$	−7.97375e6	+	1.38109e7i	−0.492617	+	0.853237i
$766$		0			0
$767$	7.02000e6	+	1.21590e7i	0.430873	+	0.746293i
$768$		0			0
$769$	1.24562e7			0.759571			0.379785	−	0.925075i	$-0.375998\pi$
$769$	1.24562e7			0.759571			0.379785	+	0.925075i	$0.375998\pi$
$770$		0			0
$771$	−6.75429e6			−0.409208
$772$		0			0
$773$	186979.	+	323856.i	0.0112549	+	0.0194941i	0.871598	−	0.490221i	$-0.163084\pi$
$773$	186979.	+	323856.i	0.0112549	+	0.0194941i	−0.860343	+	0.509715i	$0.829751\pi$
$774$		0			0
$775$	1.23146e7	−	2.13295e7i	0.736487	−	1.27563i
$776$		0			0
$777$	933141.	+	520180.i	0.0554491	+	0.0309102i
$778$		0			0
$779$	1.18102e7	−	2.04558e7i	0.697288	−	1.20774i
$780$		0			0
$781$	6.82883e6	+	1.18279e7i	0.400607	+	0.693872i
$782$		0			0
$783$	516140.			0.0300859
$784$		0			0
$785$	4.58882e7			2.65783
$786$		0			0
$787$	1.51910e7	+	2.63116e7i	0.874278	+	1.51429i	0.857530	+	0.514433i	$0.171998\pi$
$787$	1.51910e7	+	2.63116e7i	0.874278	+	1.51429i	0.0167471	+	0.999860i	$0.494669\pi$
$788$		0			0
$789$	6.31317e6	−	1.09347e7i	0.361040	−	0.625340i
$790$		0			0
$791$	1.62428e7	+	9.05456e6i	0.923038	+	0.514548i
$792$		0			0
$793$	6.19774e6	−	1.07348e7i	0.349986	−	0.606193i
$794$		0			0
$795$	3.23471e6	+	5.60268e6i	0.181517	+	0.314397i
$796$		0			0
$797$	−1.17189e7			−0.653492			−0.326746	−	0.945112i	$-0.605952\pi$
$797$	−1.17189e7			−0.653492			−0.326746	+	0.945112i	$0.605952\pi$
$798$		0			0
$799$	−4.42153e7			−2.45023
$800$		0			0
$801$	−1.11232e6	−	1.92659e6i	−0.0612557	−	0.106098i
$802$		0			0
$803$	744085.	−	1.28879e6i	0.0407224	−	0.0705333i
$804$		0			0
$805$	−436851.	−	2.90185e7i	−0.0237599	−	1.57829i
$806$		0			0
$807$	3.66082e6	−	6.34073e6i	0.197877	−	0.342732i
$808$		0			0
$809$	1.11718e6	+	1.93502e6i	0.0600141	+	0.103947i	0.894471	−	0.447125i	$-0.147552\pi$
$809$	1.11718e6	+	1.93502e6i	0.0600141	+	0.103947i	−0.834457	+	0.551072i	$0.814219\pi$
$810$		0			0
$811$	−3.29804e6			−0.176077			−0.0880387	−	0.996117i	$-0.528060\pi$
$811$	−3.29804e6			−0.176077			−0.0880387	+	0.996117i	$0.528060\pi$
$812$		0			0
$813$	−1.38008e6			−0.0732281
$814$		0			0
$815$	8.50142e6	+	1.47249e7i	0.448330	+	0.776530i
$816$		0			0
$817$	1.05441e7	−	1.82629e7i	0.552655	−	0.957227i
$818$		0			0
$819$	3.93151e6	−	2.34946e6i	0.204809	−	0.122394i
$820$		0			0
$821$	−857472.	+	1.48519e6i	−0.0443979	+	0.0768994i	−0.887370	−	0.461057i	$-0.847470\pi$
$821$	−857472.	+	1.48519e6i	−0.0443979	+	0.0768994i	0.842973	+	0.537957i	$0.180804\pi$
$822$		0			0
$823$	4.86968e6	+	8.43454e6i	0.250612	+	0.434072i	0.963694	−	0.267008i	$-0.0860350\pi$
$823$	4.86968e6	+	8.43454e6i	0.250612	+	0.434072i	−0.713083	+	0.701080i	$0.752702\pi$
$824$		0			0
$825$	−1.92353e7			−0.983929
$826$		0			0
$827$	2.95256e7			1.50119			0.750593	−	0.660765i	$-0.229768\pi$
$827$	2.95256e7			1.50119			0.750593	+	0.660765i	$0.229768\pi$
$828$		0			0
$829$	−8.67496e6	−	1.50255e7i	−0.438411	−	0.759350i	0.559156	−	0.829062i	$-0.311125\pi$
$829$	−8.67496e6	−	1.50255e7i	−0.438411	−	0.759350i	−0.997567	+	0.0697124i	$0.977792\pi$
$830$		0			0
$831$	−2.17761e6	+	3.77174e6i	−0.109390	+	0.189469i
$832$		0			0
$833$	1.79856e7	−	3.34377e7i	0.898074	−	1.66965i
$834$		0			0
$835$	1.04938e7	−	1.81758e7i	0.520854	−	0.902145i
$836$		0			0
$837$	−2.00808e6	−	3.47810e6i	−0.0990758	−	0.171604i
$838$		0			0
$839$	−2.22091e7			−1.08924			−0.544622	−	0.838681i	$-0.683327\pi$
$839$	−2.22091e7			−1.08924			−0.544622	+	0.838681i	$0.683327\pi$
$840$		0			0
$841$	−2.00099e7			−0.975561
$842$		0			0
$843$	3.80699e6	+	6.59390e6i	0.184507	+	0.319575i
$844$		0			0
$845$	7.89010e6	−	1.36661e7i	0.380138	−	0.658418i
$846$		0			0
$847$	−7.51160e6	+	4.48892e6i	−0.359769	+	0.214998i
$848$		0			0
$849$	6.81879e6	−	1.18105e7i	0.324667	−	0.562340i
$850$		0			0
$851$	1.17595e6	+	2.03680e6i	0.0556627	+	0.0964106i
$852$		0			0
$853$	−1.55354e7			−0.731053			−0.365527	−	0.930801i	$-0.619111\pi$
$853$	−1.55354e7			−0.731053			−0.365527	+	0.930801i	$0.619111\pi$
$854$		0			0
$855$	−1.88070e7			−0.879843
$856$		0			0
$857$	1.43558e7	+	2.48650e7i	0.667690	+	1.15647i	0.978548	+	0.206017i	$0.0660503\pi$
$857$	1.43558e7	+	2.48650e7i	0.667690	+	1.15647i	−0.310858	+	0.950456i	$0.600616\pi$
$858$		0			0
$859$	5.79540e6	−	1.00379e7i	0.267979	−	0.464153i	−0.700361	−	0.713789i	$-0.746978\pi$
$859$	5.79540e6	−	1.00379e7i	0.267979	−	0.464153i	0.968340	+	0.249636i	$0.0803110\pi$
$860$		0			0
$861$	155714.	+	1.03436e7i	0.00715848	+	0.475513i
$862$		0			0
$863$	3.88252e6	−	6.72471e6i	0.177454	−	0.307360i	−0.763554	−	0.645744i	$-0.776547\pi$
$863$	3.88252e6	−	6.72471e6i	0.177454	−	0.307360i	0.941008	+	0.338385i	$0.109881\pi$
$864$		0			0
$865$	−2.34122e7	−	4.05512e7i	−1.06390	−	1.84274i
$866$		0			0
$867$	−3.31512e7			−1.49779
$868$		0			0
$869$	3.24612e6			0.145819
$870$		0			0
$871$	2.11151e6	+	3.65723e6i	0.0943076	+	0.163346i
$872$		0			0
$873$	3.69412e6	−	6.39840e6i	0.164050	−	0.284142i
$874$		0			0
$875$	1.32795e7	+	7.40265e6i	0.586355	+	0.326864i
$876$		0			0
$877$	−1.25395e7	+	2.17190e7i	−0.550529	+	0.953544i	0.447707	+	0.894180i	$0.352241\pi$
$877$	−1.25395e7	+	2.17190e7i	−0.550529	+	0.953544i	−0.998236	+	0.0593640i	$0.981093\pi$
$878$		0			0
$879$	−9.79580e6	−	1.69668e7i	−0.427630	−	0.740676i
$880$		0			0
$881$	6.69476e6			0.290600			0.145300	−	0.989388i	$-0.453585\pi$
$881$	6.69476e6			0.290600			0.145300	+	0.989388i	$0.453585\pi$
$882$		0			0
$883$	−6.82227e6			−0.294460			−0.147230	−	0.989102i	$-0.547036\pi$
$883$	−6.82227e6			−0.294460			−0.147230	+	0.989102i	$0.547036\pi$
$884$		0			0
$885$	1.26247e7	+	2.18667e7i	0.541831	+	0.938479i
$886$		0			0
$887$	9.05626e6	−	1.56859e7i	0.386491	−	0.669422i	−0.605484	−	0.795858i	$-0.707020\pi$
$887$	9.05626e6	−	1.56859e7i	0.386491	−	0.669422i	0.991975	+	0.126435i	$0.0403536\pi$
$888$		0			0
$889$	3.82634e7	+	2.13299e7i	1.62379	+	0.905181i
$890$		0			0
$891$	−1.56831e6	+	2.71638e6i	−0.0661815	+	0.114630i
$892$		0			0
$893$	−2.60718e7	−	4.51576e7i	−1.09406	−	1.89497i
$894$		0			0
$895$	1.62011e7			0.676062
$896$		0			0
$897$	1.00828e7			0.418406
$898$		0			0
$899$	−1.95026e6	−	3.37796e6i	−0.0804811	−	0.139397i
$900$		0			0
$901$	−9.31620e6	+	1.61361e7i	−0.382320	+	0.662197i
$902$		0			0
$903$	139021.	+	9.23471e6i	0.00567365	+	0.376881i
$904$		0			0
$905$	−68642.3	+	118892.i	−0.00278593	+	0.00482537i
$906$		0			0
$907$	9.66832e6	+	1.67460e7i	0.390241	+	0.675917i	0.992481	−	0.122398i	$-0.0390584\pi$
$907$	9.66832e6	+	1.67460e7i	0.390241	+	0.675917i	−0.602240	+	0.798315i	$0.705725\pi$
$908$		0			0
$909$	8.72469e6			0.350220
$910$		0			0
$911$	4.70161e6			0.187694			0.0938471	−	0.995587i	$-0.470084\pi$
$911$	4.70161e6			0.187694			0.0938471	+	0.995587i	$0.470084\pi$
$912$		0			0
$913$	3.46176e6	+	5.99595e6i	0.137442	+	0.238057i
$914$		0			0
$915$	1.11460e7	−	1.93054e7i	0.440114	−	0.762300i
$916$		0			0
$917$	−2.07839e6	+	1.24205e6i	−0.0816215	+	0.0487769i
$918$		0			0
$919$	6.88634e6	−	1.19275e7i	0.268967	−	0.465865i	−0.699628	−	0.714507i	$-0.746651\pi$
$919$	6.88634e6	−	1.19275e7i	0.268967	−	0.465865i	0.968595	+	0.248642i	$0.0799843\pi$
$920$		0			0
$921$	−1.13492e7	−	1.96574e7i	−0.440877	−	0.763621i
$922$		0			0
$923$	1.24602e7			0.481416
$924$		0			0
$925$	−4.09341e6			−0.157301
$926$		0			0
$927$	−2.02505e6	−	3.50750e6i	−0.0773994	−	0.134060i
$928$		0			0
$929$	1.07422e7	−	1.86060e7i	0.408370	−	0.707317i	−0.586337	−	0.810067i	$-0.699431\pi$
$929$	1.07422e7	−	1.86060e7i	0.408370	−	0.707317i	0.994707	+	0.102750i	$0.0327641\pi$
$930$		0			0
$931$	4.47556e7	−	1.34783e6i	1.69228	−	0.0509636i
$932$		0			0
$933$	−1.36687e6	+	2.36748e6i	−0.0514069	+	0.0890394i
$934$		0			0
$935$	−4.70618e7	−	8.15134e7i	−1.76051	−	3.04930i
$936$		0			0
$937$	−2.27448e7			−0.846318			−0.423159	−	0.906055i	$-0.639079\pi$
$937$	−2.27448e7			−0.846318			−0.423159	+	0.906055i	$0.639079\pi$
$938$		0			0
$939$	1.55235e7			0.574546
$940$		0			0
$941$	9.59286e6	+	1.66153e7i	0.353162	+	0.611695i	0.986802	−	0.161934i	$-0.0517731\pi$
$941$	9.59286e6	+	1.66153e7i	0.353162	+	0.611695i	−0.633639	+	0.773628i	$0.718440\pi$
$942$		0			0
$943$	−1.13868e7	+	1.97224e7i	−0.416985	+	0.722240i
$944$		0			0
$945$	7.07040e6	−	4.22526e6i	0.257552	−	0.153912i
$946$		0			0
$947$	−547729.	+	948695.i	−0.0198468	+	0.0343757i	−0.875778	−	0.482714i	$-0.839651\pi$
$947$	−547729.	+	948695.i	−0.0198468	+	0.0343757i	0.855931	+	0.517089i	$0.172985\pi$
$948$		0			0
$949$	−678845.	−	1.17579e6i	−0.0244684	−	0.0423805i
$950$		0			0
$951$	−3.09903e7			−1.11116
$952$		0			0
$953$	−276787.			−0.00987218			−0.00493609	−	0.999988i	$-0.501571\pi$
$953$	−276787.			−0.00987218			−0.00493609	+	0.999988i	$0.501571\pi$
$954$		0			0
$955$	8.59869e6	+	1.48934e7i	0.305087	+	0.528426i
$956$		0			0
$957$	−1.52315e6	+	2.63817e6i	−0.0537604	+	0.0931158i
$958$		0			0
$959$	−200293.	−	1.33048e7i	−0.00703265	−	0.467155i
$960$		0			0
$961$	−860726.	+	1.49082e6i	−0.0300647	+	0.0520735i
$962$		0			0
$963$	6.99377e6	+	1.21136e7i	0.243022	+	0.420927i
$964$		0			0
$965$	−3.98913e7			−1.37899
$966$		0			0
$967$	1.39867e7			0.481005			0.240502	−	0.970649i	$-0.422688\pi$
$967$	1.39867e7			0.481005			0.240502	+	0.970649i	$0.422688\pi$
$968$		0			0
$969$	−2.70828e7	−	4.69088e7i	−0.926582	−	1.60489i
$970$		0			0
$971$	1.35991e7	−	2.35544e7i	0.462874	−	0.801721i	−0.536229	−	0.844073i	$-0.680152\pi$
$971$	1.35991e7	−	2.35544e7i	0.462874	−	0.801721i	0.999103	+	0.0423515i	$0.0134849\pi$
$972$		0			0
$973$	2.29231e7	+	1.27785e7i	0.776231	+	0.432711i
$974$		0			0
$975$	−8.77438e6	+	1.51977e7i	−0.295600	+	0.511995i
$976$		0			0
$977$	2.31696e7	+	4.01309e7i	0.776571	+	1.34506i	0.933907	+	0.357516i	$0.116376\pi$
$977$	2.31696e7	+	4.01309e7i	0.776571	+	1.34506i	−0.157335	+	0.987545i	$0.550290\pi$
$978$		0			0
$979$	1.31300e7			0.437831
$980$		0			0
$981$	1.21257e7			0.402286
$982$		0			0
$983$	2.25001e6	+	3.89713e6i	0.0742679	+	0.128636i	0.900768	−	0.434301i	$-0.143005\pi$
$983$	2.25001e6	+	3.89713e6i	0.0742679	+	0.128636i	−0.826500	+	0.562937i	$0.809671\pi$
$984$		0			0
$985$	1.22216e7	−	2.11684e7i	0.401363	−	0.695182i
$986$		0			0
$987$	1.99468e7	+	1.11194e7i	0.651750	+	0.363319i
$988$		0			0
$989$	−1.01661e7	+	1.76082e7i	−0.330493	+	0.572431i
$990$		0			0
$991$	−2.08406e7	−	3.60969e7i	−0.674101	−	1.16758i	−0.976731	−	0.214469i	$-0.931198\pi$
$991$	−2.08406e7	−	3.60969e7i	−0.674101	−	1.16758i	0.302629	−	0.953108i	$-0.402136\pi$
$992$		0			0
$993$	1.22723e7			0.394959
$994$		0			0
$995$	−1.05478e7			−0.337758
$996$		0			0
$997$	1.68904e7	+	2.92550e7i	0.538147	+	0.932099i	0.999004	+	0.0446240i	$0.0142090\pi$
$997$	1.68904e7	+	2.92550e7i	0.538147	+	0.932099i	−0.460856	+	0.887475i	$0.652458\pi$
$998$		0			0
$999$	−333747.	+	578067.i	−0.0105804	+	0.0183259i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.6.q.h.289.1		4
4.3	odd	2		42.6.e.d.37.1	yes	4
7.4	even	3	inner	336.6.q.h.193.1		4
12.11	even	2		126.6.g.g.37.2		4
28.3	even	6		294.6.e.y.67.2		4
28.11	odd	6		42.6.e.d.25.1	✓	4
28.19	even	6		294.6.a.o.1.1		2
28.23	odd	6		294.6.a.p.1.2		2
28.27	even	2		294.6.e.y.79.2		4
84.11	even	6		126.6.g.g.109.2		4
84.23	even	6		882.6.a.bm.1.1		2
84.47	odd	6		882.6.a.bs.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.6.e.d.25.1	✓	4	28.11	odd	6
42.6.e.d.37.1	yes	4	4.3	odd	2
126.6.g.g.37.2		4	12.11	even	2
126.6.g.g.109.2		4	84.11	even	6
294.6.a.o.1.1		2	28.19	even	6
294.6.a.p.1.2		2	28.23	odd	6
294.6.e.y.67.2		4	28.3	even	6
294.6.e.y.79.2		4	28.27	even	2
336.6.q.h.193.1		4	7.4	even	3	inner
336.6.q.h.289.1		4	1.1	even	1	trivial
882.6.a.bm.1.1		2	84.23	even	6
882.6.a.bs.1.2		2	84.47	odd	6

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	336.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(4.50000 + 7.79423i) q^{3} +(-43.5764 + 75.4765i) q^{5} +(113.236 + 63.1236i) q^{7} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\)	\(q+(4.50000 + 7.79423i) q^{3} +(-43.5764 + 75.4765i) q^{5} +(113.236 + 63.1236i) q^{7} +(-40.5000 + 70.1481i) q^{9} +(-239.035 - 414.020i) q^{11} -436.153 q^{13} -784.374 q^{15} +(-1129.53 - 1956.40i) q^{17} +(1332.06 - 2307.20i) q^{19} +(17.5629 + 1166.64i) q^{21} +(-1284.31 + 2224.48i) q^{23} +(-2235.30 - 3871.65i) q^{25} -729.000 q^{27} -708.010 q^{29} +(2754.57 + 4771.05i) q^{31} +(2151.31 - 3726.18i) q^{33} +(-9698.76 + 5795.97i) q^{35} +(457.815 - 792.959i) q^{37} +(-1962.69 - 3399.47i) q^{39} +8866.08 q^{41} +7915.62 q^{43} +(-3529.69 - 6113.59i) q^{45} +(9786.25 - 16950.3i) q^{47} +(8837.83 + 14295.7i) q^{49} +(10165.7 - 17607.6i) q^{51} +(-4123.94 - 7142.87i) q^{53} +41665.0 q^{55} +23977.1 q^{57} +(-16095.3 - 27877.9i) q^{59} +(-14210.0 + 24612.5i) q^{61} +(-9014.06 + 5386.79i) q^{63} +(19005.9 - 32919.3i) q^{65} +(-4841.21 - 8385.21i) q^{67} -23117.5 q^{69} -28568.4 q^{71} +(1556.44 + 2695.83i) q^{73} +(20117.7 - 34844.8i) q^{75} +(-932.921 - 61970.7i) q^{77} +(-3395.03 + 5880.37i) q^{79} +(-3280.50 - 5681.99i) q^{81} -14482.3 q^{83} +196883. q^{85} +(-3186.05 - 5518.39i) q^{87} +(-13732.3 + 23785.0i) q^{89} +(-49388.2 - 27531.5i) q^{91} +(-24791.1 + 42939.5i) q^{93} +(116093. + 201079. i) q^{95} -91212.8 q^{97} +38723.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 18 q^{3} - 17 q^{5} + 408 q^{7} - 162 q^{9}+O(q^{10}) \) 4 * q + 18 * q^3 - 17 * q^5 + 408 * q^7 - 162 * q^9	\( 4 q + 18 q^{3} - 17 q^{5} + 408 q^{7} - 162 q^{9} + 145 q^{11} - 1430 q^{13} - 306 q^{15} - 1372 q^{17} + 1081 q^{19} + 2295 q^{21} - 4508 q^{23} - 6267 q^{25} - 2916 q^{27} + 15730 q^{29} + 8816 q^{31} - 1305 q^{33} - 24278 q^{35} + 14573 q^{37} - 6435 q^{39} + 14700 q^{41} + 11842 q^{43} - 1377 q^{45} + 44808 q^{47} + 17014 q^{49} + 12348 q^{51} - 9417 q^{53} + 170750 q^{55} + 19458 q^{57} - 5077 q^{59} - 42368 q^{61} - 12393 q^{63} + 18450 q^{65} + 30501 q^{67} - 81144 q^{69} - 183488 q^{71} + 85665 q^{73} + 56403 q^{75} + 154585 q^{77} + 94646 q^{79} - 13122 q^{81} - 67682 q^{83} + 518224 q^{85} + 70785 q^{87} - 27558 q^{89} - 149395 q^{91} - 79344 q^{93} + 343246 q^{95} - 93342 q^{97} - 23490 q^{99}+O(q^{100}) \) 4 * q + 18 * q^3 - 17 * q^5 + 408 * q^7 - 162 * q^9 + 145 * q^11 - 1430 * q^13 - 306 * q^15 - 1372 * q^17 + 1081 * q^19 + 2295 * q^21 - 4508 * q^23 - 6267 * q^25 - 2916 * q^27 + 15730 * q^29 + 8816 * q^31 - 1305 * q^33 - 24278 * q^35 + 14573 * q^37 - 6435 * q^39 + 14700 * q^41 + 11842 * q^43 - 1377 * q^45 + 44808 * q^47 + 17014 * q^49 + 12348 * q^51 - 9417 * q^53 + 170750 * q^55 + 19458 * q^57 - 5077 * q^59 - 42368 * q^61 - 12393 * q^63 + 18450 * q^65 + 30501 * q^67 - 81144 * q^69 - 183488 * q^71 + 85665 * q^73 + 56403 * q^75 + 154585 * q^77 + 94646 * q^79 - 13122 * q^81 - 67682 * q^83 + 518224 * q^85 + 70785 * q^87 - 27558 * q^89 - 149395 * q^91 - 79344 * q^93 + 343246 * q^95 - 93342 * q^97 - 23490 * q^99

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