LMFDB - Embedded newform 392.6.i.h.361.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [392,6,Mod(177,392)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("392.177"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(392, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	392.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,-14,0,42,0,0,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$62.8704573667$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{193})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 49x^{2} + 48x + 2304 $ x^4 - x^3 + 49x^2 + 48x + 2304
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$3.72311 - 6.44862i$ of defining polynomial
Character	$\chi$	$=$	392.361
Dual form			392.6.i.h.177.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-10.4462 + 18.0934i) q^{3} +(45.2311 + 78.3426i) q^{5} +(-96.7471 - 167.571i) q^{9} +(276.247 - 478.474i) q^{11} +593.172 q^{13} -1889.98 q^{15} +(-711.096 + 1231.65i) q^{17} +(159.499 + 276.260i) q^{19} +(-329.977 - 571.537i) q^{23} +(-2529.21 + 4380.71i) q^{25} -1034.30 q^{27} -8185.27 q^{29} +(-4799.02 + 8312.14i) q^{31} +(5771.48 + 9996.49i) q^{33} +(-2590.28 - 4486.50i) q^{37} +(-6196.40 + 10732.5i) q^{39} +2192.46 q^{41} +7458.29 q^{43} +(8751.96 - 15158.8i) q^{45} +(-9780.88 - 16941.0i) q^{47} +(-14856.5 - 25732.3i) q^{51} +(-18284.8 + 31670.2i) q^{53} +49979.9 q^{55} -6664.63 q^{57} +(8180.87 - 14169.7i) q^{59} +(-5446.57 - 9433.74i) q^{61} +(26829.8 + 46470.6i) q^{65} +(-4017.95 + 6959.30i) q^{67} +13788.0 q^{69} +55983.3 q^{71} +(-38876.3 + 67335.6i) q^{73} +(-52841.3 - 91523.8i) q^{75} +(1604.22 + 2778.58i) q^{79} +(34314.0 - 59433.7i) q^{81} -76626.9 q^{83} -128655. q^{85} +(85505.2 - 148099. i) q^{87} +(-42144.3 - 72996.1i) q^{89} +(-100263. - 173661. i) q^{93} +(-14428.6 + 24991.1i) q^{95} -101273. q^{97} -106904. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 14 q^{3} + 42 q^{5} + 2 q^{9} + 716 q^{11} + 1428 q^{13} - 4448 q^{15} - 1344 q^{17} - 1946 q^{19} + 1792 q^{23} - 4282 q^{25} + 3976 q^{27} - 2400 q^{29} - 6804 q^{31} + 10416 q^{33} - 14640 q^{37}+ \cdots - 149880 q^{99}+O(q^{100}) $ 4 * q - 14 * q^3 + 42 * q^5 + 2 * q^9 + 716 * q^11 + 1428 * q^13 - 4448 * q^15 - 1344 * q^17 - 1946 * q^19 + 1792 * q^23 - 4282 * q^25 + 3976 * q^27 - 2400 * q^29 - 6804 * q^31 + 10416 * q^33 - 14640 * q^37 - 11560 * q^39 - 15792 * q^41 + 1048 * q^43 + 26978 * q^45 - 18396 * q^47 - 30252 * q^51 - 45132 * q^53 + 84112 * q^55 - 44552 * q^57 + 22582 * q^59 - 52822 * q^61 + 47804 * q^65 - 9848 * q^67 + 61376 * q^69 - 1680 * q^71 - 122052 * q^73 - 111034 * q^75 - 31704 * q^79 + 41954 * q^81 - 73948 * q^83 - 264888 * q^85 + 219156 * q^87 - 210588 * q^89 - 219784 * q^93 - 138624 * q^95 + 88480 * q^97 - 149880 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	−10.4462	+	18.0934i	−0.670125	+	1.16069i	0.307743	+	0.951470i	$0.400426\pi$
$3$	−10.4462	+	18.0934i	−0.670125	+	1.16069i	−0.977868	+	0.209222i	$0.932907\pi$
$4$		0			0
$5$	45.2311	+	78.3426i	0.809119	+	1.40143i	0.913475	+	0.406895i	$0.133388\pi$
$5$	45.2311	+	78.3426i	0.809119	+	1.40143i	−0.104356	+	0.994540i	$0.533278\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−96.7471	−	167.571i	−0.398136	−	0.689592i
$10$		0			0
$11$	276.247	−	478.474i	0.688361	−	1.19228i	−0.284007	−	0.958822i	$-0.591664\pi$
$11$	276.247	−	478.474i	0.688361	−	1.19228i	0.972368	−	0.233453i	$-0.0750027\pi$
$12$		0			0
$13$	593.172			0.973469			0.486734	−	0.873550i	$-0.338188\pi$
$13$	593.172			0.973469			0.486734	+	0.873550i	$0.338188\pi$
$14$		0			0
$15$	−1889.98			−2.16884
$16$		0			0
$17$	−711.096	+	1231.65i	−0.596769	+	1.03363i	0.396526	+	0.918023i	$0.370216\pi$
$17$	−711.096	+	1231.65i	−0.596769	+	1.03363i	−0.993295	+	0.115610i	$0.963118\pi$
$18$		0			0
$19$	159.499	+	276.260i	0.101361	+	0.175563i	0.912246	−	0.409643i	$-0.134347\pi$
$19$	159.499	+	276.260i	0.101361	+	0.175563i	−0.810884	+	0.585206i	$0.801013\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−329.977	−	571.537i	−0.130066	−	0.225281i	0.793636	−	0.608393i	$-0.208186\pi$
$23$	−329.977	−	571.537i	−0.130066	−	0.225281i	−0.923702	+	0.383112i	$0.874852\pi$
$24$		0			0
$25$	−2529.21	+	4380.71i	−0.809346	+	1.40183i
$26$		0			0
$27$	−1034.30			−0.273046
$28$		0			0
$29$	−8185.27			−1.80733			−0.903667	−	0.428237i	$-0.859135\pi$
$29$	−8185.27			−1.80733			−0.903667	+	0.428237i	$0.859135\pi$
$30$		0			0
$31$	−4799.02	+	8312.14i	−0.896908	+	1.55349i	−0.0654826	+	0.997854i	$0.520859\pi$
$31$	−4799.02	+	8312.14i	−0.896908	+	1.55349i	−0.831425	+	0.555636i	$0.812475\pi$
$32$		0			0
$33$	5771.48	+	9996.49i	0.922576	+	1.59795i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−2590.28	−	4486.50i	−0.311059	−	0.538770i	0.667533	−	0.744580i	$-0.267350\pi$
$37$	−2590.28	−	4486.50i	−0.311059	−	0.538770i	−0.978592	+	0.205810i	$0.934017\pi$
$38$		0			0
$39$	−6196.40	+	10732.5i	−0.652346	+	1.12990i
$40$		0			0
$41$	2192.46			0.203691			0.101846	−	0.994800i	$-0.467525\pi$
$41$	2192.46			0.203691			0.101846	+	0.994800i	$0.467525\pi$
$42$		0			0
$43$	7458.29			0.615131			0.307566	−	0.951527i	$-0.400486\pi$
$43$	7458.29			0.615131			0.307566	+	0.951527i	$0.400486\pi$
$44$		0			0
$45$	8751.96	−	15158.8i	0.644279	−	1.11592i
$46$		0			0
$47$	−9780.88	−	16941.0i	−0.645853	−	1.11865i	−0.984104	−	0.177594i	$-0.943169\pi$
$47$	−9780.88	−	16941.0i	−0.645853	−	1.11865i	0.338251	−	0.941056i	$-0.390165\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−14856.5	−	25732.3i	−0.799820	−	1.38533i
$52$		0			0
$53$	−18284.8	+	31670.2i	−0.894129	+	1.54868i	−0.0592509	+	0.998243i	$0.518871\pi$
$53$	−18284.8	+	31670.2i	−0.894129	+	1.54868i	−0.834878	+	0.550434i	$0.814462\pi$
$54$		0			0
$55$	49979.9			2.22786
$56$		0			0
$57$	−6664.63			−0.271700
$58$		0			0
$59$	8180.87	−	14169.7i	0.305963	−	0.529944i	−0.671512	−	0.740994i	$-0.734355\pi$
$59$	8180.87	−	14169.7i	0.305963	−	0.529944i	0.977475	+	0.211050i	$0.0676881\pi$
$60$		0			0
$61$	−5446.57	−	9433.74i	−0.187412	−	0.324608i	0.756974	−	0.653445i	$-0.226677\pi$
$61$	−5446.57	−	9433.74i	−0.187412	−	0.324608i	−0.944387	+	0.328837i	$0.893343\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	26829.8	+	46470.6i	0.787652	+	1.36425i
$66$		0			0
$67$	−4017.95	+	6959.30i	−0.109350	+	0.189399i	−0.915507	−	0.402302i	$-0.868210\pi$
$67$	−4017.95	+	6959.30i	−0.109350	+	0.189399i	0.806157	+	0.591701i	$0.201544\pi$
$68$		0			0
$69$	13788.0			0.348642
$70$		0			0
$71$	55983.3			1.31799			0.658996	−	0.752146i	$-0.270981\pi$
$71$	55983.3			1.31799			0.658996	+	0.752146i	$0.270981\pi$
$72$		0			0
$73$	−38876.3	+	67335.6i	−0.853841	+	1.47890i	0.0238742	+	0.999715i	$0.492400\pi$
$73$	−38876.3	+	67335.6i	−0.853841	+	1.47890i	−0.877716	+	0.479182i	$0.840933\pi$
$74$		0			0
$75$	−52841.3	−	91523.8i	−1.08473	−	1.87880i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	1604.22	+	2778.58i	0.0289198	+	0.0500906i	0.880123	−	0.474746i	$-0.157460\pi$
$79$	1604.22	+	2778.58i	0.0289198	+	0.0500906i	−0.851203	+	0.524836i	$0.824127\pi$
$80$		0			0
$81$	34314.0	−	59433.7i	0.581111	−	1.00651i
$82$		0			0
$83$	−76626.9			−1.22092			−0.610458	−	0.792049i	$-0.709015\pi$
$83$	−76626.9			−1.22092			−0.610458	+	0.792049i	$0.709015\pi$
$84$		0			0
$85$	−128655.			−1.93143
$86$		0			0
$87$	85505.2	−	148099.i	1.21114	−	2.09776i
$88$		0			0
$89$	−42144.3	−	72996.1i	−0.563980	−	0.976843i	−0.997144	−	0.0755272i	$-0.975936\pi$
$89$	−42144.3	−	72996.1i	−0.563980	−	0.976843i	0.433163	−	0.901315i	$-0.357397\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−100263.	−	173661.i	−1.20208	−	2.08207i
$94$		0			0
$95$	−14428.6	+	24991.1i	−0.164027	+	0.284103i
$96$		0			0
$97$	−101273.			−1.09286			−0.546428	−	0.837506i	$-0.684013\pi$
$97$	−101273.			−1.09286			−0.546428	+	0.837506i	$0.684013\pi$
$98$		0			0
$99$	−106904.			−1.09625
$100$		0			0
$101$	38728.3	−	67079.3i	0.377767	−	0.654312i	−0.612970	−	0.790106i	$-0.710025\pi$
$101$	38728.3	−	67079.3i	0.377767	−	0.654312i	0.990737	+	0.135794i	$0.0433586\pi$
$102$		0			0
$103$	−28358.4	−	49118.3i	−0.263384	−	0.456194i	0.703755	−	0.710443i	$-0.251505\pi$
$103$	−28358.4	−	49118.3i	−0.263384	−	0.456194i	−0.967139	+	0.254248i	$0.918172\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	19349.6	+	33514.5i	0.163385	+	0.282991i	0.936081	−	0.351786i	$-0.114425\pi$
$107$	19349.6	+	33514.5i	0.163385	+	0.282991i	−0.772696	+	0.634777i	$0.781092\pi$
$108$		0			0
$109$	8297.63	−	14371.9i	0.0668941	−	0.115864i	−0.830639	−	0.556812i	$-0.812024\pi$
$109$	8297.63	−	14371.9i	0.0668941	−	0.115864i	0.897533	+	0.440948i	$0.145358\pi$
$110$		0			0
$111$	108235.			0.833794
$112$		0			0
$113$	−76723.9			−0.565242			−0.282621	−	0.959232i	$-0.591204\pi$
$113$	−76723.9			−0.565242			−0.282621	+	0.959232i	$0.591204\pi$
$114$		0			0
$115$	29850.4	−	51702.5i	0.210478	−	0.364558i
$116$		0			0
$117$	−57387.6	−	99398.3i	−0.387573	−	0.671296i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−72099.4	−	124880.i	−0.447681	−	0.775406i
$122$		0			0
$123$	−22902.9	+	39669.0i	−0.136499	+	0.236423i
$124$		0			0
$125$	−174901.			−1.00119
$126$		0			0
$127$	68539.3			0.377077			0.188539	−	0.982066i	$-0.439625\pi$
$127$	68539.3			0.377077			0.188539	+	0.982066i	$0.439625\pi$
$128$		0			0
$129$	−77910.9	+	134946.i	−0.412215	+	0.713978i
$130$		0			0
$131$	47968.1	+	83083.2i	0.244216	+	0.422995i	0.961911	−	0.273363i	$-0.0881360\pi$
$131$	47968.1	+	83083.2i	0.244216	+	0.422995i	−0.717695	+	0.696358i	$0.754803\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−46782.4	−	81029.5i	−0.220927	−	0.382656i
$136$		0			0
$137$	−145648.	+	252269.i	−0.662983	+	1.14832i	0.316845	+	0.948477i	$0.397376\pi$
$137$	−145648.	+	252269.i	−0.662983	+	1.14832i	−0.979828	+	0.199842i	$0.935957\pi$
$138$		0			0
$139$	281554.			1.23602			0.618009	−	0.786171i	$-0.287939\pi$
$139$	281554.			1.23602			0.618009	+	0.786171i	$0.287939\pi$
$140$		0			0
$141$	408693.			1.73121
$142$		0			0
$143$	163862.	−	283817.i	0.670097	−	1.16064i
$144$		0			0
$145$	−370229.	−	641256.i	−1.46235	−	2.53286i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	64141.4	+	111096.i	0.236686	+	0.409952i	0.959761	−	0.280817i	$-0.0906054\pi$
$149$	64141.4	+	111096.i	0.236686	+	0.409952i	−0.723075	+	0.690769i	$0.757272\pi$
$150$		0			0
$151$	−9508.87	+	16469.8i	−0.0339380	+	0.0587824i	−0.882496	−	0.470321i	$-0.844138\pi$
$151$	−9508.87	+	16469.8i	−0.0339380	+	0.0587824i	0.848558	+	0.529103i	$0.177472\pi$
$152$		0			0
$153$	275186.			0.950381
$154$		0			0
$155$	−868259.			−2.90282
$156$		0			0
$157$	−136494.	+	236415.i	−0.441941	+	0.765465i	−0.997834	−	0.0657895i	$-0.979043\pi$
$157$	−136494.	+	236415.i	−0.441941	+	0.765465i	0.555892	+	0.831254i	$0.312377\pi$
$158$		0			0
$159$	−382014.	−	661668.i	−1.19836	−	2.07562i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−157925.	−	273533.i	−0.465565	−	0.806383i	0.533661	−	0.845698i	$-0.320816\pi$
$163$	−157925.	−	273533.i	−0.465565	−	0.806383i	−0.999227	+	0.0393152i	$0.987482\pi$
$164$		0			0
$165$	−522101.	+	904305.i	−1.49295	+	2.58586i
$166$		0			0
$167$	588655.			1.63331			0.816657	−	0.577123i	$-0.195825\pi$
$167$	588655.			1.63331			0.816657	+	0.577123i	$0.195825\pi$
$168$		0			0
$169$	−19440.5			−0.0523590
$170$		0			0
$171$	30862.1	−	53454.7i	0.0807114	−	0.139796i
$172$		0			0
$173$	359128.	+	622028.i	0.912292	+	1.58014i	0.810818	+	0.585298i	$0.199022\pi$
$173$	359128.	+	622028.i	0.912292	+	1.58014i	0.101474	+	0.994838i	$0.467644\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	170918.	+	296039.i	0.410068	+	0.710258i
$178$		0			0
$179$	−26818.6	+	46451.2i	−0.0625610	+	0.108359i	−0.895609	−	0.444841i	$-0.853260\pi$
$179$	−26818.6	+	46451.2i	−0.0625610	+	0.108359i	0.833048	+	0.553200i	$0.186593\pi$
$180$		0			0
$181$	392213.			0.889867			0.444934	−	0.895564i	$-0.353227\pi$
$181$	392213.			0.889867			0.444934	+	0.895564i	$0.353227\pi$
$182$		0			0
$183$	227584.			0.502359
$184$		0			0
$185$	234323.	−	405859.i	0.503367	−	0.871858i
$186$		0			0
$187$	392876.	+	680482.i	0.821584	+	1.42303i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−197754.	−	342521.i	−0.392232	−	0.679365i	0.600512	−	0.799616i	$-0.294963\pi$
$191$	−197754.	−	342521.i	−0.392232	−	0.679365i	−0.992744	+	0.120251i	$0.961630\pi$
$192$		0			0
$193$	281446.	−	487478.i	0.543878	−	0.942024i	−0.454799	−	0.890594i	$-0.650289\pi$
$193$	281446.	−	487478.i	0.543878	−	0.942024i	0.998677	−	0.0514299i	$-0.0163779\pi$
$194$		0			0
$195$	−1.12108e6			−2.11130
$196$		0			0
$197$	402202.			0.738378			0.369189	−	0.929354i	$-0.379635\pi$
$197$	402202.			0.738378			0.369189	+	0.929354i	$0.379635\pi$
$198$		0			0
$199$	−227987.	+	394886.i	−0.408111	+	0.706869i	−0.994678	−	0.103032i	$-0.967146\pi$
$199$	−227987.	+	394886.i	−0.408111	+	0.706869i	0.586567	+	0.809901i	$0.300479\pi$
$200$		0			0
$201$	−83944.9	−	145397.i	−0.146556	−	0.253843i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	99167.4	+	171763.i	0.164810	+	0.285460i
$206$		0			0
$207$	−63848.6	+	110589.i	−0.103568	+	0.179385i
$208$		0			0
$209$	176244.			0.279093
$210$		0			0
$211$	−1.18264e6			−1.82871			−0.914356	−	0.404911i	$-0.867302\pi$
$211$	−1.18264e6			−1.82871			−0.914356	+	0.404911i	$0.867302\pi$
$212$		0			0
$213$	−584814.	+	1.01293e6i	−0.883220	+	1.52978i
$214$		0			0
$215$	337347.	+	584301.i	0.497714	+	0.862066i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−812220.	−	1.40681e6i	−1.14436	−	1.98209i
$220$		0			0
$221$	−421802.	+	730582.i	−0.580935	+	1.00621i
$222$		0			0
$223$	−931112.			−1.25383			−0.626917	−	0.779086i	$-0.715683\pi$
$223$	−931112.			−1.25383			−0.626917	+	0.779086i	$0.715683\pi$
$224$		0			0
$225$	978774.			1.28892
$226$		0			0
$227$	96326.7	−	166843.i	0.124074	−	0.214903i	−0.797296	−	0.603588i	$-0.793737\pi$
$227$	96326.7	−	166843.i	0.124074	−	0.214903i	0.921371	+	0.388685i	$0.127071\pi$
$228$		0			0
$229$	−391967.	−	678907.i	−0.493925	−	0.855503i	0.506051	−	0.862504i	$-0.331105\pi$
$229$	−391967.	−	678907.i	−0.493925	−	0.855503i	−0.999975	+	0.00700082i	$0.997772\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	699881.	+	1.21223e6i	0.844568	+	1.46283i	0.885996	+	0.463693i	$0.153476\pi$
$233$	699881.	+	1.21223e6i	0.844568	+	1.46283i	−0.0414277	+	0.999142i	$0.513191\pi$
$234$		0			0
$235$	884800.	−	1.53252e6i	1.04514	−	1.81024i
$236$		0			0
$237$	−67032.0			−0.0775196
$238$		0			0
$239$	−643631.			−0.728857			−0.364429	−	0.931231i	$-0.618736\pi$
$239$	−643631.			−0.728857			−0.364429	+	0.931231i	$0.618736\pi$
$240$		0			0
$241$	−29378.2	+	50884.5i	−0.0325824	+	0.0564343i	−0.881857	−	0.471517i	$-0.843706\pi$
$241$	−29378.2	+	50884.5i	−0.0325824	+	0.0564343i	0.849274	+	0.527952i	$0.177040\pi$
$242$		0			0
$243$	591237.	+	1.02405e6i	0.642312	+	1.11252i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	94610.1	+	163869.i	0.0986722	+	0.170905i
$248$		0			0
$249$	800461.	−	1.38644e6i	0.818167	−	1.41711i
$250$		0			0
$251$	641680.			0.642886			0.321443	−	0.946929i	$-0.395832\pi$
$251$	641680.			0.642886			0.321443	+	0.946929i	$0.395832\pi$
$252$		0			0
$253$	−364621.			−0.358129
$254$		0			0
$255$	1.34395e6	−	2.32780e6i	1.29430	−	2.24179i
$256$		0			0
$257$	405335.	+	702061.i	0.382809	+	0.663044i	0.991463	−	0.130392i	$-0.0416235\pi$
$257$	405335.	+	702061.i	0.382809	+	0.663044i	−0.608654	+	0.793436i	$0.708290\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	791902.	+	1.37161e6i	0.719565	+	1.24632i
$262$		0			0
$263$	1.02031e6	−	1.76722e6i	0.909581	−	1.57544i	0.0949342	−	0.995484i	$-0.469736\pi$
$263$	1.02031e6	−	1.76722e6i	0.909581	−	1.57544i	0.814647	−	0.579957i	$-0.196931\pi$
$264$		0			0
$265$	−3.30817e6			−2.89383
$266$		0			0
$267$	1.76100e6			1.51175
$268$		0			0
$269$	−641499.	+	1.11111e6i	−0.540524	+	0.936216i	0.458349	+	0.888772i	$0.348441\pi$
$269$	−641499.	+	1.11111e6i	−0.540524	+	0.936216i	−0.998874	+	0.0474437i	$0.984893\pi$
$270$		0			0
$271$	−11255.6	−	19495.3i	−0.00930994	−	0.0161253i	0.861333	−	0.508041i	$-0.169630\pi$
$271$	−11255.6	−	19495.3i	−0.00930994	−	0.0161253i	−0.870643	+	0.491916i	$0.836297\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.39737e6	+	2.42032e6i	1.11424	+	1.92993i
$276$		0			0
$277$	−184105.	+	318879.i	−0.144167	+	0.249705i	−0.929062	−	0.369924i	$-0.879384\pi$
$277$	−184105.	+	318879.i	−0.144167	+	0.249705i	0.784895	+	0.619629i	$0.212717\pi$
$278$		0			0
$279$	1.85716e6			1.42837
$280$		0			0
$281$	2.03709e6			1.53902			0.769511	−	0.638634i	$-0.220500\pi$
$281$	2.03709e6			1.53902			0.769511	+	0.638634i	$0.220500\pi$
$282$		0			0
$283$	−328205.	+	568468.i	−0.243601	+	0.421929i	−0.961737	−	0.273973i	$-0.911662\pi$
$283$	−328205.	+	568468.i	−0.243601	+	0.421929i	0.718136	+	0.695902i	$0.244995\pi$
$284$		0			0
$285$	−301449.	−	522125.i	−0.219837	−	0.380769i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−301387.	−	522017.i	−0.212265	−	0.367654i
$290$		0			0
$291$	1.05792e6	−	1.83237e6i	0.732351	−	1.26847i
$292$		0			0
$293$	962295.			0.654846			0.327423	−	0.944878i	$-0.393820\pi$
$293$	962295.			0.654846			0.327423	+	0.944878i	$0.393820\pi$
$294$		0			0
$295$	1.48012e6			0.990243
$296$		0			0
$297$	−285722.	+	494884.i	−0.187954	+	0.325546i
$298$		0			0
$299$	−195733.	−	339019.i	−0.126615	−	0.219304i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	809128.	+	1.40145e6i	0.506303	+	0.876943i
$304$		0			0
$305$	492709.	−	853397.i	0.303278	−	0.525293i
$306$		0			0
$307$	296468.			0.179528			0.0897638	−	0.995963i	$-0.471389\pi$
$307$	296468.			0.179528			0.0897638	+	0.995963i	$0.471389\pi$
$308$		0			0
$309$	1.18495e6			0.706001
$310$		0			0
$311$	560317.	−	970497.i	0.328498	−	0.568975i	−0.653716	−	0.756740i	$-0.726791\pi$
$311$	560317.	−	970497.i	0.328498	−	0.568975i	0.982214	+	0.187765i	$0.0601243\pi$
$312$		0			0
$313$	874540.	+	1.51475e6i	0.504567	+	0.873935i	0.999986	+	0.00528142i	$0.00168114\pi$
$313$	874540.	+	1.51475e6i	0.504567	+	0.873935i	−0.495419	+	0.868654i	$0.664986\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.58749e6	−	2.74961e6i	−0.887284	−	1.53682i	−0.843073	−	0.537799i	$-0.819256\pi$
$317$	−1.58749e6	−	2.74961e6i	−0.887284	−	1.53682i	−0.0442112	−	0.999022i	$-0.514077\pi$
$318$		0			0
$319$	−2.26116e6	+	3.91644e6i	−1.24410	+	2.15484i
$320$		0			0
$321$	−808520.			−0.437954
$322$		0			0
$323$	−453675.			−0.241957
$324$		0			0
$325$	−1.50025e6	+	2.59852e6i	−0.787873	+	1.36464i
$326$		0			0
$327$	173358.	+	300264.i	0.0896549	+	0.155287i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−439202.	−	760721.i	−0.220341	−	0.381641i	0.734571	−	0.678532i	$-0.237384\pi$
$331$	−439202.	−	760721.i	−0.220341	−	0.381641i	−0.954911	+	0.296891i	$0.904050\pi$
$332$		0			0
$333$	−501205.	+	868112.i	−0.247688	+	0.429008i
$334$		0			0
$335$	−726946.			−0.353908
$336$		0			0
$337$	2.05261e6			0.984536			0.492268	−	0.870444i	$-0.336168\pi$
$337$	2.05261e6			0.984536			0.492268	+	0.870444i	$0.336168\pi$
$338$		0			0
$339$	801475.	−	1.38819e6i	0.378783	−	0.656072i
$340$		0			0
$341$	2.65143e6	+	4.59241e6i	1.23479	+	2.13872i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	623649.	+	1.08019e6i	0.282093	+	0.488599i
$346$		0			0
$347$	−238091.	+	412385.i	−0.106150	+	0.183857i	−0.914207	−	0.405247i	$-0.867186\pi$
$347$	−238091.	+	412385.i	−0.106150	+	0.183857i	0.808058	+	0.589103i	$0.200519\pi$
$348$		0			0
$349$	−351681.			−0.154556			−0.0772780	−	0.997010i	$-0.524623\pi$
$349$	−351681.			−0.154556			−0.0772780	+	0.997010i	$0.524623\pi$
$350$		0			0
$351$	−613515.			−0.265802
$352$		0			0
$353$	−868608.	+	1.50447e6i	−0.371011	+	0.642611i	−0.989721	−	0.143009i	$-0.954322\pi$
$353$	−868608.	+	1.50447e6i	−0.371011	+	0.642611i	0.618710	+	0.785619i	$0.287656\pi$
$354$		0			0
$355$	2.53219e6	+	4.38588e6i	1.06641	+	1.84708i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	848653.	+	1.46991e6i	0.347531	+	0.601942i	0.985810	−	0.167863i	$-0.0536867\pi$
$359$	848653.	+	1.46991e6i	0.347531	+	0.601942i	−0.638279	+	0.769805i	$0.720353\pi$
$360$		0			0
$361$	1.18717e6	−	2.05624e6i	0.479452	−	0.830435i
$362$		0			0
$363$	3.01267e6			1.20001
$364$		0			0
$365$	−7.03366e6			−2.76344
$366$		0			0
$367$	−559599.	+	969254.i	−0.216876	+	0.375640i	−0.953851	−	0.300279i	$-0.902920\pi$
$367$	−559599.	+	969254.i	−0.216876	+	0.375640i	0.736975	+	0.675920i	$0.236253\pi$
$368$		0			0
$369$	−212114.	−	367393.i	−0.0810968	−	0.140464i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	418911.	+	725575.i	0.155901	+	0.270029i	0.933387	−	0.358872i	$-0.116838\pi$
$373$	418911.	+	725575.i	0.155901	+	0.270029i	−0.777486	+	0.628901i	$0.783505\pi$
$374$		0			0
$375$	1.82705e6	−	3.16455e6i	0.670924	−	1.16207i
$376$		0			0
$377$	−4.85527e6			−1.75938
$378$		0			0
$379$	−1.94713e6			−0.696300			−0.348150	−	0.937439i	$-0.613190\pi$
$379$	−1.94713e6			−0.696300			−0.348150	+	0.937439i	$0.613190\pi$
$380$		0			0
$381$	−715976.	+	1.24011e6i	−0.252689	+	0.437670i
$382$		0			0
$383$	−101032.	−	174992.i	−0.0351933	−	0.0609566i	0.847892	−	0.530169i	$-0.177871\pi$
$383$	−101032.	−	174992.i	−0.0351933	−	0.0609566i	−0.883086	+	0.469212i	$0.844538\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−721568.	−	1.24979e6i	−0.244906	−	0.424190i
$388$		0			0
$389$	−1.61870e6	+	2.80368e6i	−0.542367	+	0.939408i	0.456400	+	0.889775i	$0.349139\pi$
$389$	−1.61870e6	+	2.80368e6i	−0.542367	+	0.939408i	−0.998768	+	0.0496333i	$0.984195\pi$
$390$		0			0
$391$	938581.			0.310477
$392$		0			0
$393$	−2.00434e6			−0.654622
$394$		0			0
$395$	−145121.	+	251357.i	−0.0467991	+	0.0810584i
$396$		0			0
$397$	411960.	+	713536.i	0.131183	+	0.227216i	0.924133	−	0.382071i	$-0.124789\pi$
$397$	411960.	+	713536.i	0.131183	+	0.227216i	−0.792950	+	0.609287i	$0.791456\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−1.19668e6	−	2.07272e6i	−0.371637	−	0.643693i	0.618181	−	0.786036i	$-0.287870\pi$
$401$	−1.19668e6	−	2.07272e6i	−0.371637	−	0.643693i	−0.989817	+	0.142342i	$0.954537\pi$
$402$		0			0
$403$	−2.84664e6	+	4.93052e6i	−0.873112	+	1.51227i
$404$		0			0
$405$	6.20825e6			1.88075
$406$		0			0
$407$	−2.86223e6			−0.856483
$408$		0			0
$409$	−290900.	+	503854.i	−0.0859876	+	0.148935i	−0.905812	−	0.423681i	$-0.860738\pi$
$409$	−290900.	+	503854.i	−0.0859876	+	0.148935i	0.819824	+	0.572616i	$0.194071\pi$
$410$		0			0
$411$	−3.04294e6	−	5.27052e6i	−0.888563	−	1.53904i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−3.46592e6	−	6.00315e6i	−0.987866	−	1.71103i
$416$		0			0
$417$	−2.94118e6	+	5.09427e6i	−0.828288	+	1.43464i
$418$		0			0
$419$	−3.11898e6			−0.867915			−0.433957	−	0.900933i	$-0.642883\pi$
$419$	−3.11898e6			−0.867915			−0.433957	+	0.900933i	$0.642883\pi$
$420$		0			0
$421$	−1.14481e6			−0.314796			−0.157398	−	0.987535i	$-0.550311\pi$
$421$	−1.14481e6			−0.314796			−0.157398	+	0.987535i	$0.550311\pi$
$422$		0			0
$423$	−1.89254e6	+	3.27798e6i	−0.514275	+	0.890750i
$424$		0			0
$425$	−3.59702e6	−	6.23022e6i	−0.965985	−	1.67313i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	3.42348e6	+	5.92963e6i	0.898099	+	1.55555i
$430$		0			0
$431$	2.15506e6	−	3.73267e6i	0.558812	−	0.967891i	−0.438784	−	0.898593i	$-0.644591\pi$
$431$	2.15506e6	−	3.73267e6i	0.558812	−	0.967891i	0.997596	−	0.0692985i	$-0.0220761\pi$
$432$		0			0
$433$	2.79301e6			0.715901			0.357950	−	0.933741i	$-0.383476\pi$
$433$	2.79301e6			0.715901			0.357950	+	0.933741i	$0.383476\pi$
$434$		0			0
$435$	1.54700e7			3.91982
$436$		0			0
$437$	105262.	−	182319.i	0.0263674	−	0.0456696i
$438$		0			0
$439$	126234.	+	218643.i	0.0312618	+	0.0541470i	0.881233	−	0.472682i	$-0.156714\pi$
$439$	126234.	+	218643.i	0.0312618	+	0.0541470i	−0.849971	+	0.526829i	$0.823381\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	1.71641e6	+	2.97291e6i	0.415539	+	0.719734i	0.995485	−	0.0949208i	$-0.0302598\pi$
$443$	1.71641e6	+	2.97291e6i	0.415539	+	0.719734i	−0.579946	+	0.814655i	$0.696926\pi$
$444$		0			0
$445$	3.81247e6	−	6.60339e6i	0.912654	−	1.58076i
$446$		0			0
$447$	−2.68014e6			−0.634437
$448$		0			0
$449$	−1.68031e6			−0.393345			−0.196673	−	0.980469i	$-0.563014\pi$
$449$	−1.68031e6			−0.393345			−0.196673	+	0.980469i	$0.563014\pi$
$450$		0			0
$451$	605661.	−	1.04904e6i	0.140213	−	0.242856i
$452$		0			0
$453$	−198663.	−	344095.i	−0.0454855	−	0.0787831i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	1.47293e6	+	2.55118e6i	0.329906	+	0.571414i	0.982493	−	0.186300i	$-0.0596495\pi$
$457$	1.47293e6	+	2.55118e6i	0.329906	+	0.571414i	−0.652587	+	0.757714i	$0.726316\pi$
$458$		0			0
$459$	735484.	−	1.27390e6i	0.162945	−	0.282229i
$460$		0			0
$461$	1.91583e6			0.419860			0.209930	−	0.977716i	$-0.432676\pi$
$461$	1.91583e6			0.419860			0.209930	+	0.977716i	$0.432676\pi$
$462$		0			0
$463$	−3.75401e6			−0.813847			−0.406924	−	0.913462i	$-0.633398\pi$
$463$	−3.75401e6			−0.813847			−0.406924	+	0.913462i	$0.633398\pi$
$464$		0			0
$465$	9.07003e6	−	1.57097e7i	1.94525	−	3.36928i
$466$		0			0
$467$	−1.05297e6	−	1.82380e6i	−0.223421	−	0.386976i	0.732424	−	0.680849i	$-0.238389\pi$
$467$	−1.05297e6	−	1.82380e6i	−0.223421	−	0.386976i	−0.955845	+	0.293873i	$0.905056\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−2.85169e6	−	4.93928e6i	−0.592312	−	1.02592i
$472$		0			0
$473$	2.06033e6	−	3.56860e6i	0.423432	−	0.733406i
$474$		0			0
$475$	−1.61362e6			−0.328146
$476$		0			0
$477$	7.07600e6			1.42394
$478$		0			0
$479$	−137463.	+	238093.i	−0.0273745	+	0.0474141i	−0.879388	−	0.476106i	$-0.842048\pi$
$479$	−137463.	+	238093.i	−0.0273745	+	0.0474141i	0.852014	+	0.523520i	$0.175381\pi$
$480$		0			0
$481$	−1.53648e6	−	2.66126e6i	−0.302806	−	0.524476i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−4.58068e6	−	7.93396e6i	−0.884250	−	1.53157i
$486$		0			0
$487$	−3.83564e6	+	6.64353e6i	−0.732851	+	1.26934i	0.222809	+	0.974862i	$0.428477\pi$
$487$	−3.83564e6	+	6.64353e6i	−0.732851	+	1.26934i	−0.955660	+	0.294473i	$0.904856\pi$
$488$		0			0
$489$	6.59886e6			1.24795
$490$		0			0
$491$	−2.42352e6			−0.453673			−0.226837	−	0.973933i	$-0.572838\pi$
$491$	−2.42352e6			−0.453673			−0.226837	+	0.973933i	$0.572838\pi$
$492$		0			0
$493$	5.82052e6	−	1.00814e7i	1.07856	−	1.86812i
$494$		0			0
$495$	−4.83541e6	−	8.37517e6i	−0.886993	−	1.53632i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	4.11158e6	+	7.12147e6i	0.739193	+	1.28032i	0.952859	+	0.303413i	$0.0981262\pi$
$499$	4.11158e6	+	7.12147e6i	0.739193	+	1.28032i	−0.213666	+	0.976907i	$0.568540\pi$
$500$		0			0
$501$	−6.14922e6	+	1.06508e7i	−1.09453	+	1.89577i
$502$		0			0
$503$	−2.98186e6			−0.525493			−0.262746	−	0.964865i	$-0.584628\pi$
$503$	−2.98186e6			−0.525493			−0.262746	+	0.964865i	$0.584628\pi$
$504$		0			0
$505$	7.00689e6			1.22263
$506$		0			0
$507$	203080.	−	351745.i	0.0350871	−	0.0607726i
$508$		0			0
$509$	−3.13433e6	−	5.42883e6i	−0.536230	−	0.928777i	−0.999103	−	0.0423525i	$-0.986515\pi$
$509$	−3.13433e6	−	5.42883e6i	−0.536230	−	0.928777i	0.462873	−	0.886425i	$-0.346819\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−164969.	−	285735.i	−0.0276763	−	0.0479368i
$514$		0			0
$515$	2.56537e6	−	4.44335e6i	0.426218	−	0.738231i
$516$		0			0
$517$	−1.08078e7			−1.77832
$518$		0			0
$519$	−1.50061e7			−2.44540
$520$		0			0
$521$	−2.06067e6	+	3.56919e6i	−0.332594	+	0.576070i	−0.983020	−	0.183500i	$-0.941257\pi$
$521$	−2.06067e6	+	3.56919e6i	−0.332594	+	0.576070i	0.650426	+	0.759570i	$0.274591\pi$
$522$		0			0
$523$	−2.35234e6	−	4.07438e6i	−0.376051	−	0.651339i	0.614433	−	0.788969i	$-0.289385\pi$
$523$	−2.35234e6	−	4.07438e6i	−0.376051	−	0.651339i	−0.990484	+	0.137630i	$0.956052\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−6.82512e6	−	1.18215e7i	−1.07049	−	1.85415i
$528$		0			0
$529$	3.00040e6	−	5.19685e6i	0.466166	−	0.807423i
$530$		0			0
$531$	−3.16590e6			−0.487261
$532$		0			0
$533$	1.30051e6			0.198287
$534$		0			0
$535$	−1.75041e6	+	3.03179e6i	−0.264396	+	0.457947i
$536$		0			0
$537$	−560307.	−	970479.i	−0.0838475	−	0.145228i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−2.23920e6	−	3.87841e6i	−0.328927	−	0.569719i	0.653372	−	0.757037i	$-0.273354\pi$
$541$	−2.23920e6	−	3.87841e6i	−0.328927	−	0.569719i	−0.982299	+	0.187318i	$0.940020\pi$
$542$		0			0
$543$	−4.09714e6	+	7.09646e6i	−0.596323	+	1.03286i
$544$		0			0
$545$	1.50124e6			0.216501
$546$		0			0
$547$	−6.49187e6			−0.927687			−0.463843	−	0.885917i	$-0.653530\pi$
$547$	−6.49187e6			−0.927687			−0.463843	+	0.885917i	$0.653530\pi$
$548$		0			0
$549$	−1.05388e6	+	1.82537e6i	−0.149231	+	0.258476i
$550$		0			0
$551$	−1.30554e6	−	2.26126e6i	−0.183194	−	0.317301i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	4.89557e6	+	8.47938e6i	0.674638	+	1.16851i
$556$		0			0
$557$	1.25429e6	−	2.17249e6i	0.171301	−	0.296702i	−0.767574	−	0.640960i	$-0.778536\pi$
$557$	1.25429e6	−	2.17249e6i	0.171301	−	0.296702i	0.938875	+	0.344259i	$0.111870\pi$
$558$		0			0
$559$	4.42404e6			0.598811
$560$		0			0
$561$	−1.64163e7			−2.20226
$562$		0			0
$563$	−1.76351e6	+	3.05449e6i	−0.234480	+	0.406132i	−0.959122	−	0.282994i	$-0.908672\pi$
$563$	−1.76351e6	+	3.05449e6i	−0.234480	+	0.406132i	0.724641	+	0.689126i	$0.242006\pi$
$564$		0			0
$565$	−3.47031e6	−	6.01075e6i	−0.457348	−	0.792150i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−4.87641e6	−	8.44620e6i	−0.631422	−	1.09366i	−0.987261	−	0.159108i	$-0.949138\pi$
$569$	−4.87641e6	−	8.44620e6i	−0.631422	−	1.09366i	0.355839	−	0.934547i	$-0.384195\pi$
$570$		0			0
$571$	−850427.	+	1.47298e6i	−0.109156	+	0.189063i	−0.915428	−	0.402481i	$-0.868148\pi$
$571$	−850427.	+	1.47298e6i	−0.109156	+	0.189063i	0.806273	+	0.591544i	$0.201481\pi$
$572$		0			0
$573$	8.26314e6			1.05138
$574$		0			0
$575$	3.33832e6			0.421074
$576$		0			0
$577$	−5.85328e6	+	1.01382e7i	−0.731914	+	1.26771i	0.224150	+	0.974555i	$0.428039\pi$
$577$	−5.85328e6	+	1.01382e7i	−0.731914	+	1.26771i	−0.956064	+	0.293157i	$0.905294\pi$
$578$		0			0
$579$	5.88009e6	+	1.01846e7i	0.728933	+	1.26255i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	1.01022e7	+	1.74976e7i	1.23097	+	2.13210i
$584$		0			0
$585$	5.19141e6	−	8.99179e6i	0.627185	−	1.08632i
$586$		0			0
$587$	3.75683e6			0.450015			0.225007	−	0.974357i	$-0.427759\pi$
$587$	3.75683e6			0.450015			0.225007	+	0.974357i	$0.427759\pi$
$588$		0			0
$589$	−3.06175e6			−0.363648
$590$		0			0
$591$	−4.20149e6	+	7.27720e6i	−0.494806	+	0.857029i
$592$		0			0
$593$	4.32169e6	+	7.48539e6i	0.504681	+	0.874133i	0.999985	+	0.00541364i	$0.00172322\pi$
$593$	4.32169e6	+	7.48539e6i	0.504681	+	0.874133i	−0.495304	+	0.868720i	$0.664943\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−4.76321e6	−	8.25013e6i	−0.546971	−	0.947382i
$598$		0			0
$599$	−4.65965e6	+	8.07075e6i	−0.530623	+	0.919067i	0.468738	+	0.883337i	$0.344709\pi$
$599$	−4.65965e6	+	8.07075e6i	−0.530623	+	0.919067i	−0.999361	+	0.0357296i	$0.988625\pi$
$600$		0			0
$601$	−910438.			−0.102817			−0.0514084	−	0.998678i	$-0.516371\pi$
$601$	−910438.			−0.102817			−0.0514084	+	0.998678i	$0.516371\pi$
$602$		0			0
$603$	1.55490e6			0.174144
$604$		0			0
$605$	6.52227e6	−	1.12969e7i	0.724454	−	1.25479i
$606$		0			0
$607$	2.85087e6	+	4.93784e6i	0.314054	+	0.543958i	0.979236	−	0.202723i	$-0.0649792\pi$
$607$	2.85087e6	+	4.93784e6i	0.314054	+	0.543958i	−0.665182	+	0.746682i	$0.731646\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−5.80174e6	−	1.00489e7i	−0.628717	−	1.08897i
$612$		0			0
$613$	−8.06637e6	+	1.39714e7i	−0.867016	+	1.50172i	−0.00198504	+	0.999998i	$0.500632\pi$
$613$	−8.06637e6	+	1.39714e7i	−0.867016	+	1.50172i	−0.865031	+	0.501718i	$0.832701\pi$
$614$		0			0
$615$	−4.14370e6			−0.441774
$616$		0			0
$617$	−5.53575e6			−0.585415			−0.292708	−	0.956202i	$-0.594556\pi$
$617$	−5.53575e6			−0.585415			−0.292708	+	0.956202i	$0.594556\pi$
$618$		0			0
$619$	−9.42242e6	+	1.63201e7i	−0.988407	+	1.71197i	−0.362716	+	0.931900i	$0.618151\pi$
$619$	−9.42242e6	+	1.63201e7i	−0.988407	+	1.71197i	−0.625691	+	0.780071i	$0.715183\pi$
$620$		0			0
$621$	341294.	+	591139.i	0.0355140	+	0.0615121i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−7189.06	−	12451.8i	−0.000736160	−	0.00127507i
$626$		0			0
$627$	−1.84109e6	+	3.18885e6i	−0.187027	+	0.323941i
$628$		0			0
$629$	7.36776e6			0.742521
$630$		0			0
$631$	2.63269e6			0.263224			0.131612	−	0.991301i	$-0.457985\pi$
$631$	2.63269e6			0.263224			0.131612	+	0.991301i	$0.457985\pi$
$632$		0			0
$633$	1.23541e7	−	2.13979e7i	1.22547	−	2.12257i
$634$		0			0
$635$	3.10011e6	+	5.36954e6i	0.305100	+	0.528449i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−5.41622e6	−	9.38118e6i	−0.524740	−	0.908877i
$640$		0			0
$641$	−7.14693e6	+	1.23788e7i	−0.687028	+	1.18997i	0.285767	+	0.958299i	$0.407752\pi$
$641$	−7.14693e6	+	1.23788e7i	−0.687028	+	1.18997i	−0.972795	+	0.231668i	$0.925582\pi$
$642$		0			0
$643$	1.63874e7			1.56308			0.781542	−	0.623853i	$-0.214434\pi$
$643$	1.63874e7			1.56308			0.781542	+	0.623853i	$0.214434\pi$
$644$		0			0
$645$	−1.40960e7			−1.33412
$646$		0			0
$647$	5.96516e6	−	1.03320e7i	0.560224	−	0.970336i	−0.437253	−	0.899339i	$-0.644049\pi$
$647$	5.96516e6	−	1.03320e7i	0.560224	−	0.970336i	0.997477	−	0.0709972i	$-0.0226181\pi$
$648$		0			0
$649$	−4.51988e6	−	7.82867e6i	−0.421226	−	0.729585i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−1.73931e6	−	3.01257e6i	−0.159622	−	0.276474i	0.775110	−	0.631826i	$-0.217694\pi$
$653$	−1.73931e6	−	3.01257e6i	−0.159622	−	0.276474i	−0.934733	+	0.355352i	$0.884361\pi$
$654$		0			0
$655$	−4.33930e6	+	7.51589e6i	−0.395200	+	0.684506i
$656$		0			0
$657$	1.50447e7			1.35978
$658$		0			0
$659$	2.09397e7			1.87826			0.939131	−	0.343560i	$-0.111633\pi$
$659$	2.09397e7			1.87826			0.939131	+	0.343560i	$0.111633\pi$
$660$		0			0
$661$	−5.12829e6	+	8.88246e6i	−0.456530	+	0.790733i	−0.998775	−	0.0494878i	$-0.984241\pi$
$661$	−5.12829e6	+	8.88246e6i	−0.456530	+	0.790733i	0.542245	+	0.840220i	$0.317574\pi$
$662$		0			0
$663$	−8.81247e6	−	1.52637e7i	−0.778599	−	1.34857i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	2.70095e6	+	4.67818e6i	0.235073	+	0.407158i
$668$		0			0
$669$	9.72661e6	−	1.68470e7i	0.840226	−	1.45531i
$670$		0			0
$671$	−6.01840e6			−0.516029
$672$		0			0
$673$	716398.			0.0609701			0.0304851	−	0.999535i	$-0.490295\pi$
$673$	716398.			0.0609701			0.0304851	+	0.999535i	$0.490295\pi$
$674$		0			0
$675$	2.61595e6	−	4.53096e6i	0.220989	−	0.382764i
$676$		0			0
$677$	472813.	+	818935.i	0.0396476	+	0.0686717i	0.885168	−	0.465271i	$-0.154043\pi$
$677$	472813.	+	818935.i	0.0396476	+	0.0686717i	−0.845521	+	0.533943i	$0.820710\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	2.01250e6	+	3.48575e6i	0.166291	+	0.288024i
$682$		0			0
$683$	−1.78496e6	+	3.09164e6i	−0.146412	+	0.253593i	−0.929899	−	0.367815i	$-0.880106\pi$
$683$	−1.78496e6	+	3.09164e6i	−0.146412	+	0.253593i	0.783487	+	0.621408i	$0.213439\pi$
$684$		0			0
$685$	−2.63512e7			−2.14573
$686$		0			0
$687$	1.63783e7			1.32397
$688$		0			0
$689$	−1.08460e7	+	1.87859e7i	−0.870407	+	1.50759i
$690$		0			0
$691$	4.83905e6	+	8.38149e6i	0.385536	+	0.667768i	0.991843	−	0.127462i	$-0.0406831\pi$
$691$	4.83905e6	+	8.38149e6i	0.385536	+	0.667768i	−0.606307	+	0.795231i	$0.707350\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	1.27350e7	+	2.20577e7i	1.00009	+	1.73220i
$696$		0			0
$697$	−1.55905e6	+	2.70035e6i	−0.121556	+	0.210542i
$698$		0			0
$699$	−2.92445e7			−2.26387
$700$		0			0
$701$	2.52404e7			1.94000			0.970000	−	0.243105i	$-0.0781659\pi$
$701$	2.52404e7			1.94000			0.970000	+	0.243105i	$0.0781659\pi$
$702$		0			0
$703$	826293.	−	1.43118e6i	0.0630588	−	0.109221i
$704$		0			0
$705$	1.84856e7	+	3.20181e7i	1.40075	+	2.42618i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	8.73720e6	+	1.51333e7i	0.652765	+	1.13062i	0.982449	+	0.186531i	$0.0597245\pi$
$709$	8.73720e6	+	1.51333e7i	0.652765	+	1.13062i	−0.329684	+	0.944091i	$0.606942\pi$
$710$		0			0
$711$	310407.	−	537640.i	0.0230280	−	0.0398857i
$712$		0			0
$713$	6.33426e6			0.466629
$714$		0			0
$715$	2.96466e7			2.16875
$716$		0			0
$717$	6.72352e6	−	1.16455e7i	0.488426	−	0.845978i
$718$		0			0
$719$	−4.86681e6	−	8.42955e6i	−0.351093	−	0.608110i	0.635348	−	0.772226i	$-0.280856\pi$
$719$	−4.86681e6	−	8.42955e6i	−0.351093	−	0.608110i	−0.986441	+	0.164115i	$0.947523\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−613782.	−	1.06310e6i	−0.0436685	−	0.0756361i
$724$		0			0
$725$	2.07023e7	−	3.58573e7i	1.46276	−	2.53357i
$726$		0			0
$727$	1.60454e7			1.12594			0.562971	−	0.826477i	$-0.309658\pi$
$727$	1.60454e7			1.12594			0.562971	+	0.826477i	$0.309658\pi$
$728$		0			0
$729$	−8.02815e6			−0.559496
$730$		0			0
$731$	−5.30356e6	+	9.18603e6i	−0.367091	+	0.635820i
$732$		0			0
$733$	5.22668e6	+	9.05288e6i	0.359307	+	0.622339i	0.987845	−	0.155440i	$-0.0496796\pi$
$733$	5.22668e6	+	9.05288e6i	0.359307	+	0.622339i	−0.628538	+	0.777779i	$0.716346\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	2.21990e6	+	3.84497e6i	0.150544	+	0.260750i
$738$		0			0
$739$	3.73819e6	−	6.47474e6i	0.251797	−	0.436125i	−0.712224	−	0.701953i	$-0.752312\pi$
$739$	3.73819e6	−	6.47474e6i	0.251797	−	0.436125i	0.964021	+	0.265827i	$0.0856451\pi$
$740$		0			0
$741$	−3.95327e6			−0.264491
$742$		0			0
$743$	−1.33998e7			−0.890483			−0.445241	−	0.895411i	$-0.646882\pi$
$743$	−1.33998e7			−0.890483			−0.445241	+	0.895411i	$0.646882\pi$
$744$		0			0
$745$	−5.80237e6	+	1.00500e7i	−0.383014	+	0.663400i
$746$		0			0
$747$	7.41343e6	+	1.28404e7i	0.486091	+	0.841934i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−4.56952e6	−	7.91463e6i	−0.295645	−	0.512072i	0.679490	−	0.733685i	$-0.262201\pi$
$751$	−4.56952e6	−	7.91463e6i	−0.295645	−	0.512072i	−0.975135	+	0.221613i	$0.928868\pi$
$752$		0			0
$753$	−6.70313e6	+	1.16102e7i	−0.430815	+	0.746193i
$754$		0			0
$755$	−1.72039e6			−0.109840
$756$		0			0
$757$	−1.16376e7			−0.738117			−0.369059	−	0.929406i	$-0.620320\pi$
$757$	−1.16376e7			−0.738117			−0.369059	+	0.929406i	$0.620320\pi$
$758$		0			0
$759$	3.80891e6	−	6.59722e6i	0.239992	−	0.415678i
$760$		0			0
$761$	−4.03536e6	−	6.98945e6i	−0.252593	−	0.437503i	0.711646	−	0.702538i	$-0.247950\pi$
$761$	−4.03536e6	−	6.98945e6i	−0.252593	−	0.437503i	−0.964239	+	0.265035i	$0.914617\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	1.24470e7	+	2.15588e7i	0.768971	+	1.33190i
$766$		0			0
$767$	4.85266e6	−	8.40505e6i	0.297846	−	0.515884i
$768$		0			0
$769$	1.30085e7			0.793255			0.396628	−	0.917980i	$-0.370180\pi$
$769$	1.30085e7			0.793255			0.396628	+	0.917980i	$0.370180\pi$
$770$		0			0
$771$	−1.69369e7			−1.02612
$772$		0			0
$773$	1.18819e7	−	2.05800e7i	0.715214	−	1.23879i	−0.247663	−	0.968846i	$-0.579663\pi$
$773$	1.18819e7	−	2.05800e7i	0.715214	−	1.23879i	0.962877	−	0.269941i	$-0.0870041\pi$
$774$		0			0
$775$	−2.42754e7	−	4.20462e7i	−1.45182	−	2.51462i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	349694.	+	605689.i	0.0206464	+	0.0357607i
$780$		0			0
$781$	1.54652e7	−	2.67866e7i	0.907254	−	1.57141i
$782$		0			0
$783$	8.46600e6			0.493485
$784$		0			0
$785$	−2.46951e7			−1.43033
$786$		0			0
$787$	−1.42470e7	+	2.46765e7i	−0.819947	+	1.42019i	0.0857729	+	0.996315i	$0.472664\pi$
$787$	−1.42470e7	+	2.46765e7i	−0.819947	+	1.42019i	−0.905720	+	0.423876i	$0.860669\pi$
$788$		0			0
$789$	2.13167e7	+	3.69216e7i	1.21907	+	2.11149i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−3.23075e6	−	5.59582e6i	−0.182440	−	0.315996i
$794$		0			0
$795$	3.45578e7	−	5.98559e7i	1.93923	−	3.35884i
$796$		0			0
$797$	−1.43450e7			−0.799938			−0.399969	−	0.916529i	$-0.630979\pi$
$797$	−1.43450e7			−0.799938			−0.399969	+	0.916529i	$0.630979\pi$
$798$		0			0
$799$	2.78206e7			1.54170
$800$		0			0
$801$	−8.15468e6	+	1.41243e7i	−0.449082	+	0.777833i
$802$		0			0
$803$	2.14789e7	+	3.72026e7i	1.17550	+	2.03603i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−1.34025e7	−	2.32138e7i	−0.724438	−	1.25476i
$808$		0			0
$809$	1.79642e6	−	3.11149e6i	0.0965020	−	0.167146i	−0.813733	−	0.581240i	$-0.802568\pi$
$809$	1.79642e6	−	3.11149e6i	0.0965020	−	0.167146i	0.910234	+	0.414093i	$0.135901\pi$
$810$		0			0
$811$	−3.52968e7			−1.88445			−0.942223	−	0.334988i	$-0.891268\pi$
$811$	−3.52968e7			−1.88445			−0.942223	+	0.334988i	$0.891268\pi$
$812$		0			0
$813$	470316.			0.0249553
$814$		0			0
$815$	1.42862e7	−	2.47444e7i	0.753395	−	1.30492i
$816$		0			0
$817$	1.18959e6	+	2.06042e6i	0.0623506	+	0.107994i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−5.22792e6	−	9.05502e6i	−0.270689	−	0.468847i	0.698349	−	0.715757i	$-0.253918\pi$
$821$	−5.22792e6	−	9.05502e6i	−0.270689	−	0.468847i	−0.969038	+	0.246910i	$0.920585\pi$
$822$		0			0
$823$	−2.49595e6	+	4.32311e6i	−0.128451	+	0.222483i	−0.923076	−	0.384616i	$-0.874334\pi$
$823$	−2.49595e6	+	4.32311e6i	−0.128451	+	0.222483i	0.794626	+	0.607099i	$0.207667\pi$
$824$		0			0
$825$	−5.83890e7			−2.98673
$826$		0			0
$827$	−2.06198e7			−1.04839			−0.524193	−	0.851599i	$-0.675633\pi$
$827$	−2.06198e7			−1.04839			−0.524193	+	0.851599i	$0.675633\pi$
$828$		0			0
$829$	−253421.	+	438939.i	−0.0128073	+	0.0221829i	−0.872358	−	0.488868i	$-0.837410\pi$
$829$	−253421.	+	438939.i	−0.0128073	+	0.0221829i	0.859551	+	0.511050i	$0.170743\pi$
$830$		0			0
$831$	−3.84640e6	−	6.66217e6i	−0.193220	−	0.334667i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	2.66255e7	+	4.61168e7i	1.32155	+	2.28898i
$836$		0			0
$837$	4.96361e6	−	8.59722e6i	0.244897	−	0.424174i
$838$		0			0
$839$	4.41851e6			0.216706			0.108353	−	0.994112i	$-0.465442\pi$
$839$	4.41851e6			0.216706			0.108353	+	0.994112i	$0.465442\pi$
$840$		0			0
$841$	4.64876e7			2.26645
$842$		0			0
$843$	−2.12799e7	+	3.68579e7i	−1.03134	+	1.78633i
$844$		0			0
$845$	−879316.	−	1.52302e6i	−0.0423646	−	0.0733777i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−6.85700e6	−	1.18767e7i	−0.326486	−	0.565491i
$850$		0			0
$851$	−1.70947e6	+	2.96088e6i	−0.0809164	+	0.140151i
$852$		0			0
$853$	1.11737e7			0.525806			0.262903	−	0.964822i	$-0.415320\pi$
$853$	1.11737e7			0.525806			0.262903	+	0.964822i	$0.415320\pi$
$854$		0			0
$855$	5.58370e6			0.261220
$856$		0			0
$857$	1.06154e7	−	1.83864e7i	0.493724	−	0.855155i	−0.506250	−	0.862387i	$-0.668969\pi$
$857$	1.06154e7	−	1.83864e7i	0.493724	−	0.855155i	0.999974	+	0.00723167i	$0.00230193\pi$
$858$		0			0
$859$	1.82114e7	+	3.15432e7i	0.842096	+	1.45855i	0.888119	+	0.459613i	$0.152012\pi$
$859$	1.82114e7	+	3.15432e7i	0.842096	+	1.45855i	−0.0460234	+	0.998940i	$0.514655\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	1.26649e7	+	2.19362e7i	0.578861	+	1.00262i	0.995610	+	0.0935954i	$0.0298360\pi$
$863$	1.26649e7	+	2.19362e7i	0.578861	+	1.00262i	−0.416749	+	0.909022i	$0.636831\pi$
$864$		0			0
$865$	−3.24875e7	+	5.62700e7i	−1.47631	+	2.55704i
$866$		0			0
$867$	1.25934e7			0.568978
$868$		0			0
$869$	1.77264e6			0.0796290
$870$		0			0
$871$	−2.38334e6	+	4.12806e6i	−0.106449	+	0.184374i
$872$		0			0
$873$	9.79784e6	+	1.69704e7i	0.435106	+	0.753625i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	288569.	+	499816.i	0.0126692	+	0.0219438i	0.872291	−	0.488988i	$-0.162634\pi$
$877$	288569.	+	499816.i	0.0126692	+	0.0219438i	−0.859621	+	0.510932i	$0.829300\pi$
$878$		0			0
$879$	−1.00524e7	+	1.74112e7i	−0.438829	+	0.760074i
$880$		0			0
$881$	2.15071e7			0.933561			0.466781	−	0.884373i	$-0.345414\pi$
$881$	2.15071e7			0.933561			0.466781	+	0.884373i	$0.345414\pi$
$882$		0			0
$883$	−3.71948e6			−0.160539			−0.0802695	−	0.996773i	$-0.525578\pi$
$883$	−3.71948e6			−0.160539			−0.0802695	+	0.996773i	$0.525578\pi$
$884$		0			0
$885$	−1.54617e7	+	2.67804e7i	−0.663587	+	1.14937i
$886$		0			0
$887$	9.08802e6	+	1.57409e7i	0.387847	+	0.671770i	0.992160	−	0.124977i	$-0.0398856\pi$
$887$	9.08802e6	+	1.57409e7i	0.387847	+	0.671770i	−0.604313	+	0.796747i	$0.706552\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−1.89583e7	−	3.28368e7i	−0.800028	−	1.38569i
$892$		0			0
$893$	3.12007e6	−	5.40413e6i	0.130929	−	0.226776i
$894$		0			0
$895$	−4.85214e6			−0.202477
$896$		0			0
$897$	8.17868e6			0.339392
$898$		0			0
$899$	3.92813e7	−	6.80371e7i	1.62101	−	2.80767i
$900$		0			0
$901$	−2.60045e7	−	4.50411e7i	−1.06718	−	1.84840i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1.77402e7	+	3.07270e7i	0.720008	+	1.24709i
$906$		0			0
$907$	6.77151e6	−	1.17286e7i	0.273317	−	0.473400i	−0.696392	−	0.717662i	$-0.745212\pi$
$907$	6.77151e6	−	1.17286e7i	0.273317	−	0.473400i	0.969709	+	0.244262i	$0.0785458\pi$
$908$		0			0
$909$	−1.49874e7			−0.601612
$910$		0			0
$911$	−412746.			−0.0164773			−0.00823866	−	0.999966i	$-0.502622\pi$
$911$	−412746.			−0.0164773			−0.00823866	+	0.999966i	$0.502622\pi$
$912$		0			0
$913$	−2.11680e7	+	3.66640e7i	−0.840431	+	1.45567i
$914$		0			0
$915$	1.02939e7	+	1.78295e7i	0.406468	+	0.704024i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−1.39529e7	−	2.41672e7i	−0.544976	−	0.943925i	−0.998608	−	0.0527367i	$-0.983206\pi$
$919$	−1.39529e7	−	2.41672e7i	−0.544976	−	0.943925i	0.453633	−	0.891189i	$-0.350128\pi$
$920$		0			0
$921$	−3.09697e6	+	5.36411e6i	−0.120306	+	0.208376i
$922$		0			0
$923$	3.32077e7			1.28302
$924$		0			0
$925$	2.62054e7			1.00702
$926$		0			0
$927$	−5.48719e6	+	9.50410e6i	−0.209725	+	0.363255i
$928$		0			0
$929$	−9.74202e6	−	1.68737e7i	−0.370348	−	0.641461i	0.619271	−	0.785177i	$-0.287428\pi$
$929$	−9.74202e6	−	1.68737e7i	−0.370348	−	0.641461i	−0.989619	+	0.143716i	$0.954095\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	1.17064e7	+	2.02761e7i	0.440270	+	0.762569i
$934$		0			0
$935$	−3.55405e7	+	6.15579e7i	−1.32952	+	2.30279i
$936$		0			0
$937$	1.89631e7			0.705602			0.352801	−	0.935698i	$-0.385229\pi$
$937$	1.89631e7			0.705602			0.352801	+	0.935698i	$0.385229\pi$
$938$		0			0
$939$	−3.65425e7			−1.35249
$940$		0			0
$941$	−1.15249e7	+	1.99617e7i	−0.424290	+	0.734891i	−0.996354	−	0.0853175i	$-0.972810\pi$
$941$	−1.15249e7	+	1.99617e7i	−0.424290	+	0.734891i	0.572064	+	0.820209i	$0.306143\pi$
$942$		0			0
$943$	−723461.	−	1.25307e6i	−0.0264933	−	0.0458877i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1.74655e7	+	3.02511e7i	0.632858	+	1.09614i	0.986965	+	0.160937i	$0.0514517\pi$
$947$	1.74655e7	+	3.02511e7i	0.632858	+	1.09614i	−0.354107	+	0.935205i	$0.615215\pi$
$948$		0			0
$949$	−2.30603e7	+	3.99416e7i	−0.831188	+	1.43966i
$950$		0			0
$951$	6.63331e7			2.37837
$952$		0			0
$953$	2.74501e7			0.979066			0.489533	−	0.871985i	$-0.337167\pi$
$953$	2.74501e7			0.979066			0.489533	+	0.871985i	$0.337167\pi$
$954$		0			0
$955$	1.78893e7	−	3.09852e7i	0.634724	−	1.09937i
$956$		0			0
$957$	−4.72411e7	−	8.18240e7i	−1.66740	−	2.88803i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−3.17465e7	−	5.49866e7i	−1.10889	−	1.92065i
$962$		0			0
$963$	3.74403e6	−	6.48486e6i	0.130099	−	0.225338i
$964$		0			0
$965$	5.09204e7			1.76025
$966$		0			0
$967$	−9.37608e6			−0.322445			−0.161222	−	0.986918i	$-0.551544\pi$
$967$	−9.37608e6			−0.322445			−0.161222	+	0.986918i	$0.551544\pi$
$968$		0			0
$969$	4.73919e6	−	8.20852e6i	0.162142	−	0.280838i
$970$		0			0
$971$	3.61679e6	+	6.26447e6i	0.123105	+	0.213224i	0.920991	−	0.389585i	$-0.127381\pi$
$971$	3.61679e6	+	6.26447e6i	0.123105	+	0.213224i	−0.797886	+	0.602809i	$0.794048\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−3.13440e7	−	5.42893e7i	−1.05595	−	1.82895i
$976$		0			0
$977$	1.44011e7	−	2.49434e7i	0.482680	−	0.836026i	−0.517122	−	0.855912i	$-0.672997\pi$
$977$	1.44011e7	−	2.49434e7i	0.482680	−	0.836026i	0.999802	+	0.0198853i	$0.00633011\pi$
$978$		0			0
$979$	−4.65690e7			−1.55289
$980$		0			0
$981$	−3.21109e6			−0.106532
$982$		0			0
$983$	2.60924e7	−	4.51934e7i	0.861252	−	1.49173i	−0.00946931	−	0.999955i	$-0.503014\pi$
$983$	2.60924e7	−	4.51934e7i	0.861252	−	1.49173i	0.870721	−	0.491777i	$-0.163652\pi$
$984$		0			0
$985$	1.81921e7	+	3.15096e7i	0.597436	+	1.03479i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−2.46106e6	−	4.26268e6i	−0.0800077	−	0.138577i
$990$		0			0
$991$	1.94789e7	−	3.37385e7i	0.630058	−	1.09129i	−0.357481	−	0.933920i	$-0.616364\pi$
$991$	1.94789e7	−	3.37385e7i	0.630058	−	1.09129i	0.987539	−	0.157373i	$-0.0503024\pi$
$992$		0			0
$993$	1.83520e7			0.590624
$994$		0			0
$995$	−4.12485e7			−1.32084
$996$		0			0
$997$	−1.50858e7	+	2.61294e7i	−0.480652	+	0.832514i	−0.999754	−	0.0221985i	$-0.992933\pi$
$997$	−1.50858e7	+	2.61294e7i	−0.480652	+	0.832514i	0.519101	+	0.854713i	$0.326267\pi$
$998$		0			0
$999$	2.67912e6	+	4.64037e6i	0.0849334	+	0.147109i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.6.i.h.361.1		4
7.2	even	3	inner	392.6.i.h.177.1		4
7.3	odd	6		56.6.a.d.1.1	✓	2
7.4	even	3		392.6.a.e.1.2		2
7.5	odd	6		392.6.i.k.177.2		4
7.6	odd	2		392.6.i.k.361.2		4
21.17	even	6		504.6.a.m.1.1		2
28.3	even	6		112.6.a.j.1.2		2
28.11	odd	6		784.6.a.q.1.1		2
56.3	even	6		448.6.a.r.1.1		2
56.45	odd	6		448.6.a.x.1.2		2
84.59	odd	6		1008.6.a.bi.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.6.a.d.1.1	✓	2	7.3	odd	6
112.6.a.j.1.2		2	28.3	even	6
392.6.a.e.1.2		2	7.4	even	3
392.6.i.h.177.1		4	7.2	even	3	inner
392.6.i.h.361.1		4	1.1	even	1	trivial
392.6.i.k.177.2		4	7.5	odd	6
392.6.i.k.361.2		4	7.6	odd	2
448.6.a.r.1.1		2	56.3	even	6
448.6.a.x.1.2		2	56.45	odd	6
504.6.a.m.1.1		2	21.17	even	6
784.6.a.q.1.1		2	28.11	odd	6
1008.6.a.bi.1.1		2	84.59	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	392.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-10.4462 + 18.0934i) q^{3} +(45.2311 + 78.3426i) q^{5} +(-96.7471 - 167.571i) q^{9} +(276.247 - 478.474i) q^{11} +593.172 q^{13} -1889.98 q^{15} +(-711.096 + 1231.65i) q^{17} +(159.499 + 276.260i) q^{19} +(-329.977 - 571.537i) q^{23} +(-2529.21 + 4380.71i) q^{25} -1034.30 q^{27} -8185.27 q^{29} +(-4799.02 + 8312.14i) q^{31} +(5771.48 + 9996.49i) q^{33} +(-2590.28 - 4486.50i) q^{37} +(-6196.40 + 10732.5i) q^{39} +2192.46 q^{41} +7458.29 q^{43} +(8751.96 - 15158.8i) q^{45} +(-9780.88 - 16941.0i) q^{47} +(-14856.5 - 25732.3i) q^{51} +(-18284.8 + 31670.2i) q^{53} +49979.9 q^{55} -6664.63 q^{57} +(8180.87 - 14169.7i) q^{59} +(-5446.57 - 9433.74i) q^{61} +(26829.8 + 46470.6i) q^{65} +(-4017.95 + 6959.30i) q^{67} +13788.0 q^{69} +55983.3 q^{71} +(-38876.3 + 67335.6i) q^{73} +(-52841.3 - 91523.8i) q^{75} +(1604.22 + 2778.58i) q^{79} +(34314.0 - 59433.7i) q^{81} -76626.9 q^{83} -128655. q^{85} +(85505.2 - 148099. i) q^{87} +(-42144.3 - 72996.1i) q^{89} +(-100263. - 173661. i) q^{93} +(-14428.6 + 24991.1i) q^{95} -101273. q^{97} -106904. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 14 q^{3} + 42 q^{5} + 2 q^{9} + 716 q^{11} + 1428 q^{13} - 4448 q^{15} - 1344 q^{17} - 1946 q^{19} + 1792 q^{23} - 4282 q^{25} + 3976 q^{27} - 2400 q^{29} - 6804 q^{31} + 10416 q^{33} - 14640 q^{37}+ \cdots - 149880 q^{99}+O(q^{100}) \) 4 * q - 14 * q^3 + 42 * q^5 + 2 * q^9 + 716 * q^11 + 1428 * q^13 - 4448 * q^15 - 1344 * q^17 - 1946 * q^19 + 1792 * q^23 - 4282 * q^25 + 3976 * q^27 - 2400 * q^29 - 6804 * q^31 + 10416 * q^33 - 14640 * q^37 - 11560 * q^39 - 15792 * q^41 + 1048 * q^43 + 26978 * q^45 - 18396 * q^47 - 30252 * q^51 - 45132 * q^53 + 84112 * q^55 - 44552 * q^57 + 22582 * q^59 - 52822 * q^61 + 47804 * q^65 - 9848 * q^67 + 61376 * q^69 - 1680 * q^71 - 122052 * q^73 - 111034 * q^75 - 31704 * q^79 + 41954 * q^81 - 73948 * q^83 - 264888 * q^85 + 219156 * q^87 - 210588 * q^89 - 219784 * q^93 - 138624 * q^95 + 88480 * q^97 - 149880 * q^99

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