LMFDB - Embedded newform 392.6.i.l.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,6,Mod(177,392)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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:	$\Q(\sqrt{-3}, \sqrt{-59})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 14x^{2} - 15x + 225 $ x^4 - x^3 - 14x^2 - 15x + 225
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.2
Root			$-3.07603 - 2.35330i$ of defining polynomial
Character	$\chi$	$=$	392.361
Dual form			392.6.i.l.177.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(13.1521 - 22.7800i) q^{3} +(48.7603 + 84.4554i) q^{5} +(-224.454 - 388.765i) q^{9} +(-203.088 + 351.758i) q^{11} -905.594 q^{13} +2565.20 q^{15} +(-179.912 + 311.617i) q^{17} +(-906.626 - 1570.32i) q^{19} +(1081.71 + 1873.58i) q^{23} +(-3192.64 + 5529.82i) q^{25} -5416.22 q^{27} -4090.26 q^{29} +(-2225.77 + 3855.14i) q^{31} +(5342.04 + 9252.69i) q^{33} +(-4467.84 - 7738.53i) q^{37} +(-11910.4 + 20629.5i) q^{39} -3415.04 q^{41} -8694.80 q^{43} +(21888.9 - 37912.7i) q^{45} +(-7102.26 - 12301.5i) q^{47} +(4732.44 + 8196.83i) q^{51} +(7308.18 - 12658.1i) q^{53} -39610.5 q^{55} -47696.1 q^{57} +(-10698.4 + 18530.2i) q^{59} +(-27041.0 - 46836.3i) q^{61} +(-44157.0 - 76482.2i) q^{65} +(-22486.6 + 38947.9i) q^{67} +56907.0 q^{69} +5700.89 q^{71} +(-23825.4 + 41266.8i) q^{73} +(83979.7 + 145457. i) q^{75} +(-2904.60 - 5030.91i) q^{79} +(-16692.2 + 28911.8i) q^{81} +27058.2 q^{83} -35090.4 q^{85} +(-53795.3 + 93176.3i) q^{87} +(48122.6 + 83350.8i) q^{89} +(58546.9 + 101406. i) q^{93} +(88414.8 - 153139. i) q^{95} +101968. q^{97} +182335. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 26 q^{3} + 62 q^{5} - 206 q^{9} - 972 q^{11} + 156 q^{13} + 5152 q^{15} - 560 q^{17} - 2642 q^{19} - 2272 q^{23} - 4522 q^{25} - 11128 q^{27} - 15616 q^{29} - 5444 q^{31} + 10512 q^{33} - 576 q^{37}+ \cdots + 89784 q^{99}+O(q^{100}) $ 4 * q + 26 * q^3 + 62 * q^5 - 206 * q^9 - 972 * q^11 + 156 * q^13 + 5152 * q^15 - 560 * q^17 - 2642 * q^19 - 2272 * q^23 - 4522 * q^25 - 11128 * q^27 - 15616 * q^29 - 5444 * q^31 + 10512 * q^33 - 576 * q^37 - 24120 * q^39 - 33776 * q^41 - 16792 * q^43 + 52406 * q^45 + 4532 * q^47 + 9404 * q^51 - 1420 * q^53 - 39024 * q^55 - 94888 * q^57 - 34146 * q^59 - 19106 * q^61 - 123252 * q^65 - 56952 * q^67 + 116512 * q^69 - 14448 * q^71 - 128828 * q^73 + 168526 * q^75 - 52808 * q^79 - 92366 * q^81 - 168972 * q^83 - 55960 * q^85 - 106460 * q^87 + 130972 * q^89 + 116792 * q^93 + 147392 * q^95 + 389248 * q^97 + 89784 * 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
$3$	13.1521	−	22.7800i	0.843706	−	1.46134i	−0.0430351	−	0.999074i	$-0.513703\pi$
$3$	13.1521	−	22.7800i	0.843706	−	1.46134i	0.886741	−	0.462267i	$-0.152964\pi$
$4$		0			0
$5$	48.7603	+	84.4554i	0.872251	+	1.51078i	0.859662	+	0.510863i	$0.170674\pi$
$5$	48.7603	+	84.4554i	0.872251	+	1.51078i	0.0125893	+	0.999921i	$0.495993\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−224.454	−	388.765i	−0.923678	−	1.59986i
$10$		0			0
$11$	−203.088	+	351.758i	−0.506060	+	0.876521i	0.493916	+	0.869510i	$0.335565\pi$
$11$	−203.088	+	351.758i	−0.506060	+	0.876521i	−0.999975	+	0.00701124i	$0.997768\pi$
$12$		0			0
$13$	−905.594			−1.48619			−0.743096	−	0.669185i	$-0.766643\pi$
$13$	−905.594			−1.48619			−0.743096	+	0.669185i	$0.766643\pi$
$14$		0			0
$15$	2565.20			2.94369
$16$		0			0
$17$	−179.912	+	311.617i	−0.150987	+	0.261517i	−0.931590	−	0.363510i	$-0.881578\pi$
$17$	−179.912	+	311.617i	−0.150987	+	0.261517i	0.780604	+	0.625026i	$0.214912\pi$
$18$		0			0
$19$	−906.626	−	1570.32i	−0.576162	−	0.997941i	−0.995914	−	0.0903028i	$-0.971217\pi$
$19$	−906.626	−	1570.32i	−0.576162	−	0.997941i	0.419753	−	0.907639i	$-0.362117\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1081.71	+	1873.58i	0.426376	+	0.738504i	0.996548	−	0.0830210i	$-0.0264569\pi$
$23$	1081.71	+	1873.58i	0.426376	+	0.738504i	−0.570172	+	0.821525i	$0.693124\pi$
$24$		0			0
$25$	−3192.64	+	5529.82i	−1.02165	+	1.76954i
$26$		0			0
$27$	−5416.22			−1.42984
$28$		0			0
$29$	−4090.26			−0.903141			−0.451571	−	0.892235i	$-0.649136\pi$
$29$	−4090.26			−0.903141			−0.451571	+	0.892235i	$0.649136\pi$
$30$		0			0
$31$	−2225.77	+	3855.14i	−0.415983	+	0.720504i	−0.995531	−	0.0944341i	$-0.969896\pi$
$31$	−2225.77	+	3855.14i	−0.415983	+	0.720504i	0.579548	+	0.814938i	$0.303229\pi$
$32$		0			0
$33$	5342.04	+	9252.69i	0.853931	+	1.47905i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−4467.84	−	7738.53i	−0.536530	−	0.929296i	−0.999088	−	0.0427075i	$-0.986402\pi$
$37$	−4467.84	−	7738.53i	−0.536530	−	0.929296i	0.462558	−	0.886589i	$-0.346932\pi$
$38$		0			0
$39$	−11910.4	+	20629.5i	−1.25391	+	2.17183i
$40$		0			0
$41$	−3415.04			−0.317275			−0.158637	−	0.987337i	$-0.550710\pi$
$41$	−3415.04			−0.317275			−0.158637	+	0.987337i	$0.550710\pi$
$42$		0			0
$43$	−8694.80			−0.717114			−0.358557	−	0.933508i	$-0.616731\pi$
$43$	−8694.80			−0.717114			−0.358557	+	0.933508i	$0.616731\pi$
$44$		0			0
$45$	21888.9	−	37912.7i	1.61136	−	2.79096i
$46$		0			0
$47$	−7102.26	−	12301.5i	−0.468977	−	0.812293i	0.530394	−	0.847751i	$-0.322044\pi$
$47$	−7102.26	−	12301.5i	−0.468977	−	0.812293i	−0.999371	+	0.0354588i	$0.988711\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	4732.44	+	8196.83i	0.254777	+	0.441286i
$52$		0			0
$53$	7308.18	−	12658.1i	0.357371	−	0.618985i	−0.630150	−	0.776474i	$-0.717006\pi$
$53$	7308.18	−	12658.1i	0.357371	−	0.618985i	0.987521	+	0.157489i	$0.0503397\pi$
$54$		0			0
$55$	−39610.5			−1.76564
$56$		0			0
$57$	−47696.1			−1.94444
$58$		0			0
$59$	−10698.4	+	18530.2i	−0.400119	+	0.693027i	−0.993740	−	0.111718i	$-0.964365\pi$
$59$	−10698.4	+	18530.2i	−0.400119	+	0.693027i	0.593620	+	0.804745i	$0.297698\pi$
$60$		0			0
$61$	−27041.0	−	46836.3i	−0.930460	−	1.61160i	−0.782536	−	0.622605i	$-0.786074\pi$
$61$	−27041.0	−	46836.3i	−0.930460	−	1.61160i	−0.147924	−	0.988999i	$-0.547259\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−44157.0	−	76482.2i	−1.29633	−	2.24531i
$66$		0			0
$67$	−22486.6	+	38947.9i	−0.611978	+	1.05998i	0.378928	+	0.925426i	$0.376293\pi$
$67$	−22486.6	+	38947.9i	−0.611978	+	1.05998i	−0.990907	+	0.134552i	$0.957041\pi$
$68$		0			0
$69$	56907.0			1.43894
$70$		0			0
$71$	5700.89			0.134214			0.0671069	−	0.997746i	$-0.478623\pi$
$71$	5700.89			0.134214			0.0671069	+	0.997746i	$0.478623\pi$
$72$		0			0
$73$	−23825.4	+	41266.8i	−0.523279	+	0.906345i	0.476354	+	0.879253i	$0.341958\pi$
$73$	−23825.4	+	41266.8i	−0.523279	+	0.906345i	−0.999633	+	0.0270917i	$0.991375\pi$
$74$		0			0
$75$	83979.7	+	145457.i	1.72394	+	2.98594i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−2904.60	−	5030.91i	−0.0523623	−	0.0906941i	0.838656	−	0.544661i	$-0.183342\pi$
$79$	−2904.60	−	5030.91i	−0.0523623	−	0.0906941i	−0.891018	+	0.453967i	$0.850008\pi$
$80$		0			0
$81$	−16692.2	+	28911.8i	−0.282684	+	0.489623i
$82$		0			0
$83$	27058.2			0.431126			0.215563	−	0.976490i	$-0.430841\pi$
$83$	27058.2			0.431126			0.215563	+	0.976490i	$0.430841\pi$
$84$		0			0
$85$	−35090.4			−0.526794
$86$		0			0
$87$	−53795.3	+	93176.3i	−0.761985	+	1.31980i
$88$		0			0
$89$	48122.6	+	83350.8i	0.643982	+	1.11541i	0.984536	+	0.175185i	$0.0560523\pi$
$89$	48122.6	+	83350.8i	0.643982	+	1.11541i	−0.340553	+	0.940225i	$0.610614\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	58546.9	+	101406.i	0.701935	+	1.21579i
$94$		0			0
$95$	88414.8	−	153139.i	1.00512	−	1.74091i
$96$		0			0
$97$	101968.			1.10036			0.550182	−	0.835045i	$-0.314558\pi$
$97$	101968.			1.10036			0.550182	+	0.835045i	$0.314558\pi$
$98$		0			0
$99$	182335.			1.86974
$100$		0			0
$101$	10928.4	−	18928.6i	0.106599	−	0.184635i	−0.807791	−	0.589469i	$-0.799337\pi$
$101$	10928.4	−	18928.6i	0.106599	−	0.184635i	0.914390	+	0.404833i	$0.132670\pi$
$102$		0			0
$103$	68053.2	+	117872.i	0.632056	+	1.09475i	0.987131	+	0.159915i	$0.0511219\pi$
$103$	68053.2	+	117872.i	0.632056	+	1.09475i	−0.355075	+	0.934838i	$0.615545\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−13697.4	−	23724.5i	−0.115658	−	0.200326i	0.802384	−	0.596808i	$-0.203564\pi$
$107$	−13697.4	−	23724.5i	−0.115658	−	0.200326i	−0.918043	+	0.396481i	$0.870231\pi$
$108$		0			0
$109$	−44284.8	+	76703.5i	−0.357016	+	0.618371i	−0.987461	−	0.157864i	$-0.949539\pi$
$109$	−44284.8	+	76703.5i	−0.357016	+	0.618371i	0.630444	+	0.776234i	$0.282873\pi$
$110$		0			0
$111$	−235046.			−1.81069
$112$		0			0
$113$	18947.6			0.139591			0.0697955	−	0.997561i	$-0.477765\pi$
$113$	18947.6			0.139591			0.0697955	+	0.997561i	$0.477765\pi$
$114$		0			0
$115$	−105489.	+	182713.i	−0.743813	+	1.28832i
$116$		0			0
$117$	203264.	+	352063.i	1.37276	+	2.37770i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−1963.64	−	3401.13i	−0.0121927	−	0.0211183i
$122$		0			0
$123$	−44914.8	+	77794.7i	−0.267687	+	0.463647i
$124$		0			0
$125$	−317945.			−1.82002
$126$		0			0
$127$	−188535.			−1.03725			−0.518625	−	0.855002i	$-0.673556\pi$
$127$	−188535.			−1.03725			−0.518625	+	0.855002i	$0.673556\pi$
$128$		0			0
$129$	−114355.	+	198068.i	−0.605033	+	1.04795i
$130$		0			0
$131$	107081.	+	185469.i	0.545171	+	0.944264i	0.998596	+	0.0529693i	$0.0168686\pi$
$131$	107081.	+	185469.i	0.545171	+	0.944264i	−0.453425	+	0.891294i	$0.649798\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−264097.	−	457429.i	−1.24718	−	2.16018i
$136$		0			0
$137$	22451.9	−	38887.9i	0.102200	−	0.177016i	−0.810391	−	0.585890i	$-0.800745\pi$
$137$	22451.9	−	38887.9i	0.102200	−	0.177016i	0.912591	+	0.408874i	$0.134078\pi$
$138$		0			0
$139$	262924.			1.15423			0.577116	−	0.816662i	$-0.304178\pi$
$139$	262924.			1.15423			0.577116	+	0.816662i	$0.304178\pi$
$140$		0			0
$141$	−373638.			−1.58272
$142$		0			0
$143$	183915.	−	318550.i	0.752102	−	1.30268i
$144$		0			0
$145$	−199442.	−	345444.i	−0.787766	−	1.36445i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−104882.	−	181661.i	−0.387022	−	0.670342i	0.605025	−	0.796206i	$-0.293163\pi$
$149$	−104882.	−	181661.i	−0.387022	−	0.670342i	−0.992047	+	0.125864i	$0.959830\pi$
$150$		0			0
$151$	−165333.	+	286364.i	−0.590087	+	1.02206i	0.404133	+	0.914700i	$0.367573\pi$
$151$	−165333.	+	286364.i	−0.590087	+	1.02206i	−0.994220	+	0.107360i	$0.965760\pi$
$152$		0			0
$153$	161528.			0.557853
$154$		0			0
$155$	−434117.			−1.45137
$156$		0			0
$157$	255040.	−	441742.i	0.825769	−	1.43027i	−0.0755611	−	0.997141i	$-0.524075\pi$
$157$	255040.	−	441742.i	0.825769	−	1.43027i	0.901330	−	0.433133i	$-0.142592\pi$
$158$		0			0
$159$	−192235.	−	332961.i	−0.603032	−	1.04448i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−69.3984	−	120.201i	−0.000204588	−	0.000354357i	0.865923	−	0.500177i	$-0.166732\pi$
$163$	−69.3984	−	120.201i	−0.000204588	−	0.000354357i	−0.866128	+	0.499823i	$0.833398\pi$
$164$		0			0
$165$	−520960.	+	902329.i	−1.48968	+	2.58021i
$166$		0			0
$167$	527469.			1.46354			0.731772	−	0.681549i	$-0.238693\pi$
$167$	527469.			1.46354			0.731772	+	0.681549i	$0.238693\pi$
$168$		0			0
$169$	448807.			1.20877
$170$		0			0
$171$	−406991.	+	704930.i	−1.06438	+	1.84355i
$172$		0			0
$173$	172808.	+	299312.i	0.438984	+	0.760342i	0.997611	−	0.0690762i	$-0.0220052\pi$
$173$	172808.	+	299312.i	0.438984	+	0.760342i	−0.558627	+	0.829419i	$0.688672\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	281413.	+	487421.i	0.675166	+	1.16942i
$178$		0			0
$179$	−174764.	+	302699.i	−0.407679	+	0.706121i	−0.994629	−	0.103502i	$-0.966995\pi$
$179$	−174764.	+	302699.i	−0.407679	+	0.706121i	0.586950	+	0.809623i	$0.300328\pi$
$180$		0			0
$181$	−469274.			−1.06471			−0.532353	−	0.846522i	$-0.678692\pi$
$181$	−469274.			−1.06471			−0.532353	+	0.846522i	$0.678692\pi$
$182$		0			0
$183$	−1.42258e6			−3.14014
$184$		0			0
$185$	435707.	−	754667.i	0.935977	−	1.62116i
$186$		0			0
$187$	−73076.0	−	126571.i	−0.152817	−	0.264686i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−425662.	−	737268.i	−0.844270	−	1.46232i	−0.886254	−	0.463200i	$-0.846701\pi$
$191$	−425662.	−	737268.i	−0.844270	−	1.46232i	0.0419839	−	0.999118i	$-0.486632\pi$
$192$		0			0
$193$	−61442.9	+	106422.i	−0.118735	+	0.205655i	−0.919267	−	0.393635i	$-0.871217\pi$
$193$	−61442.9	+	106422.i	−0.118735	+	0.205655i	0.800532	+	0.599290i	$0.204551\pi$
$194$		0			0
$195$	−2.32303e6			−4.37489
$196$		0			0
$197$	744847.			1.36742			0.683709	−	0.729755i	$-0.260366\pi$
$197$	744847.			1.36742			0.683709	+	0.729755i	$0.260366\pi$
$198$		0			0
$199$	−163369.	+	282963.i	−0.292440	+	0.506521i	−0.974386	−	0.224882i	$-0.927800\pi$
$199$	−163369.	+	282963.i	−0.292440	+	0.506521i	0.681946	+	0.731402i	$0.261134\pi$
$200$		0			0
$201$	591490.	+	1.02449e6i	1.03266	+	1.78862i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−166518.	−	288418.i	−0.276744	−	0.479334i
$206$		0			0
$207$	485589.	−	841065.i	0.787668	−	1.36428i
$208$		0			0
$209$	736498.			1.16629
$210$		0			0
$211$	336421.			0.520209			0.260104	−	0.965581i	$-0.416243\pi$
$211$	336421.			0.520209			0.260104	+	0.965581i	$0.416243\pi$
$212$		0			0
$213$	74978.5	−	129867.i	0.113237	−	0.196132i
$214$		0			0
$215$	−423961.	−	734322.i	−0.625504	−	1.08340i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	626706.	+	1.08549e6i	0.882986	+	1.52938i
$220$		0			0
$221$	162928.	−	282199.i	0.224395	−	0.388664i
$222$		0			0
$223$	633862.			0.853556			0.426778	−	0.904356i	$-0.359649\pi$
$223$	633862.			0.853556			0.426778	+	0.904356i	$0.359649\pi$
$224$		0			0
$225$	2.86640e6			3.77468
$226$		0			0
$227$	148704.	−	257563.i	0.191539	−	0.331756i	−0.754221	−	0.656620i	$-0.771985\pi$
$227$	148704.	−	257563.i	0.191539	−	0.331756i	0.945761	+	0.324864i	$0.105319\pi$
$228$		0			0
$229$	−297476.	−	515244.i	−0.374855	−	0.649269i	0.615450	−	0.788176i	$-0.288974\pi$
$229$	−297476.	−	515244.i	−0.374855	−	0.649269i	−0.990305	+	0.138907i	$0.955641\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−75447.0	−	130678.i	−0.0910442	−	0.157693i	0.816907	−	0.576770i	$-0.195687\pi$
$233$	−75447.0	−	130678.i	−0.0910442	−	0.157693i	−0.907951	+	0.419077i	$0.862354\pi$
$234$		0			0
$235$	692617.	−	1.19965e6i	0.818132	−	1.41705i
$236$		0			0
$237$	−152806.			−0.176713
$238$		0			0
$239$	−826500.			−0.935941			−0.467970	−	0.883744i	$-0.655015\pi$
$239$	−826500.			−0.935941			−0.467970	+	0.883744i	$0.655015\pi$
$240$		0			0
$241$	−683864.	+	1.18449e6i	−0.758450	+	1.31367i	0.185191	+	0.982703i	$0.440710\pi$
$241$	−683864.	+	1.18449e6i	−0.758450	+	1.31367i	−0.943641	+	0.330971i	$0.892624\pi$
$242$		0			0
$243$	−218996.	−	379313.i	−0.237915	−	0.412080i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	821035.	+	1.42207e6i	0.856287	+	1.48313i
$248$		0			0
$249$	355872.	−	616388.i	0.363743	−	0.630022i
$250$		0			0
$251$	1.73585e6			1.73911			0.869557	−	0.493832i	$-0.164404\pi$
$251$	1.73585e6			1.73911			0.869557	+	0.493832i	$0.164404\pi$
$252$		0			0
$253$	−878730.			−0.863086
$254$		0			0
$255$	−461511.	+	799360.i	−0.444459	+	0.769825i
$256$		0			0
$257$	1.02337e6	+	1.77253e6i	0.966496	+	1.67402i	0.705540	+	0.708670i	$0.250705\pi$
$257$	1.02337e6	+	1.77253e6i	0.966496	+	1.67402i	0.260957	+	0.965351i	$0.415962\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	918074.	+	1.59015e6i	0.834212	+	1.44490i
$262$		0			0
$263$	202868.	−	351378.i	0.180853	−	0.313246i	−0.761318	−	0.648378i	$-0.775448\pi$
$263$	202868.	−	351378.i	0.180853	−	0.313246i	0.942171	+	0.335132i	$0.108781\pi$
$264$		0			0
$265$	1.42540e6			1.24687
$266$		0			0
$267$	2.53165e6			2.17333
$268$		0			0
$269$	740187.	−	1.28204e6i	0.623678	−	1.08024i	−0.365117	−	0.930962i	$-0.618971\pi$
$269$	740187.	−	1.28204e6i	0.623678	−	1.08024i	0.988795	−	0.149281i	$-0.0476958\pi$
$270$		0			0
$271$	−228738.	−	396186.i	−0.189198	−	0.327700i	0.755785	−	0.654819i	$-0.227255\pi$
$271$	−228738.	−	396186.i	−0.189198	−	0.327700i	−0.944983	+	0.327120i	$0.893922\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.29677e6	−	2.24607e6i	−1.03403	−	1.79099i
$276$		0			0
$277$	−729152.	+	1.26293e6i	−0.570977	+	0.988961i	0.425489	+	0.904964i	$0.360102\pi$
$277$	−729152.	+	1.26293e6i	−0.570977	+	0.988961i	−0.996466	+	0.0839974i	$0.973231\pi$
$278$		0			0
$279$	1.99833e6			1.53694
$280$		0			0
$281$	−1.90172e6			−1.43675			−0.718373	−	0.695658i	$-0.755113\pi$
$281$	−1.90172e6			−1.43675			−0.718373	+	0.695658i	$0.755113\pi$
$282$		0			0
$283$	−505935.	+	876305.i	−0.375516	+	0.650413i	−0.990404	−	0.138202i	$-0.955868\pi$
$283$	−505935.	+	876305.i	−0.375516	+	0.650413i	0.614888	+	0.788614i	$0.289201\pi$
$284$		0			0
$285$	−2.32568e6	−	4.02819e6i	−1.69604	−	2.93763i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	645192.	+	1.11750e6i	0.454406	+	0.787054i
$290$		0			0
$291$	1.34110e6	−	2.32285e6i	0.928383	−	1.60801i
$292$		0			0
$293$	1.30915e6			0.890882			0.445441	−	0.895311i	$-0.353047\pi$
$293$	1.30915e6			0.890882			0.445441	+	0.895311i	$0.353047\pi$
$294$		0			0
$295$	−2.08663e6			−1.39602
$296$		0			0
$297$	1.09997e6	−	1.90520e6i	0.723583	−	1.25328i
$298$		0			0
$299$	−979592.	−	1.69670e6i	−0.633676	−	1.09756i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−287463.	−	497900.i	−0.179877	−	0.311556i
$304$		0			0
$305$	2.63705e6	−	4.56751e6i	1.62319	−	2.81145i
$306$		0			0
$307$	−1.83705e6			−1.11244			−0.556219	−	0.831036i	$-0.687748\pi$
$307$	−1.83705e6			−1.11244			−0.556219	+	0.831036i	$0.687748\pi$
$308$		0			0
$309$	3.58016e6			2.13307
$310$		0			0
$311$	−709767.	+	1.22935e6i	−0.416116	+	0.720735i	−0.995545	−	0.0942883i	$-0.969942\pi$
$311$	−709767.	+	1.22935e6i	−0.416116	+	0.720735i	0.579429	+	0.815023i	$0.303276\pi$
$312$		0			0
$313$	−1.33631e6	−	2.31455e6i	−0.770983	−	1.33538i	−0.937025	−	0.349264i	$-0.886432\pi$
$313$	−1.33631e6	−	2.31455e6i	−0.770983	−	1.33538i	0.166041	−	0.986119i	$-0.446902\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−17033.2	−	29502.3i	−0.00952024	−	0.0164895i	0.861226	−	0.508222i	$-0.169697\pi$
$317$	−17033.2	−	29502.3i	−0.00952024	−	0.0164895i	−0.870746	+	0.491733i	$0.836364\pi$
$318$		0			0
$319$	830681.	−	1.43878e6i	0.457043	−	0.791622i
$320$		0			0
$321$	−720595.			−0.390327
$322$		0			0
$323$	652453.			0.347971
$324$		0			0
$325$	2.89124e6	−	5.00777e6i	1.51836	−	2.62988i
$326$		0			0
$327$	1.16487e6	+	2.01762e6i	0.602434	+	1.04345i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−775251.	−	1.34277e6i	−0.388931	−	0.673648i	0.603375	−	0.797458i	$-0.293822\pi$
$331$	−775251.	−	1.34277e6i	−0.388931	−	0.673648i	−0.992306	+	0.123809i	$0.960489\pi$
$332$		0			0
$333$	−2.00565e6	+	3.47389e6i	−0.991161	+	1.71674i
$334$		0			0
$335$	−4.38581e6			−2.13520
$336$		0			0
$337$	−3.49728e6			−1.67747			−0.838736	−	0.544539i	$-0.816705\pi$
$337$	−3.49728e6			−1.67747			−0.838736	+	0.544539i	$0.816705\pi$
$338$		0			0
$339$	249200.	−	431626.i	0.117774	−	0.203990i
$340$		0			0
$341$	−904052.	−	1.56586e6i	−0.421025	−	0.729236i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	2.77481e6	+	4.80611e6i	1.25512	+	2.17393i
$346$		0			0
$347$	−1.62912e6	+	2.82172e6i	−0.726323	+	1.25803i	0.232105	+	0.972691i	$0.425439\pi$
$347$	−1.62912e6	+	2.82172e6i	−0.726323	+	1.25803i	−0.958427	+	0.285337i	$0.907894\pi$
$348$		0			0
$349$	−1.40547e6			−0.617672			−0.308836	−	0.951115i	$-0.599940\pi$
$349$	−1.40547e6			−0.617672			−0.308836	+	0.951115i	$0.599940\pi$
$350$		0			0
$351$	4.90489e6			2.12501
$352$		0			0
$353$	−1.18681e6	+	2.05561e6i	−0.506924	+	0.878018i	0.493044	+	0.870004i	$0.335884\pi$
$353$	−1.18681e6	+	2.05561e6i	−0.506924	+	0.878018i	−0.999968	+	0.00801339i	$0.997449\pi$
$354$		0			0
$355$	277978.	+	481471.i	0.117068	+	0.202768i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	392801.	+	680351.i	0.160856	+	0.278610i	0.935176	−	0.354184i	$-0.115241\pi$
$359$	392801.	+	680351.i	0.160856	+	0.278610i	−0.774320	+	0.632794i	$0.781908\pi$
$360$		0			0
$361$	−405894.	+	703028.i	−0.163925	+	0.283926i
$362$		0			0
$363$	−103304.			−0.0411481
$364$		0			0
$365$	−4.64694e6			−1.82572
$366$		0			0
$367$	1.31344e6	−	2.27494e6i	0.509031	−	0.881667i	−0.490914	−	0.871208i	$-0.663337\pi$
$367$	1.31344e6	−	2.27494e6i	0.509031	−	0.881667i	0.999945	−	0.0104596i	$-0.00332945\pi$
$368$		0			0
$369$	766518.	+	1.32765e6i	0.293060	+	0.507595i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−1.21737e6	−	2.10855e6i	−0.453056	−	0.784717i	0.545518	−	0.838099i	$-0.316333\pi$
$373$	−1.21737e6	−	2.10855e6i	−0.453056	−	0.784717i	−0.998574	+	0.0533826i	$0.983000\pi$
$374$		0			0
$375$	−4.18163e6	+	7.24280e6i	−1.53556	+	2.65967i
$376$		0			0
$377$	3.70411e6			1.34224
$378$		0			0
$379$	83774.3			0.0299580			0.0149790	−	0.999888i	$-0.495232\pi$
$379$	83774.3			0.0299580			0.0149790	+	0.999888i	$0.495232\pi$
$380$		0			0
$381$	−2.47963e6	+	4.29484e6i	−0.875133	+	1.51577i
$382$		0			0
$383$	−877048.	−	1.51909e6i	−0.305511	−	0.529160i	0.671864	−	0.740674i	$-0.265494\pi$
$383$	−877048.	−	1.51909e6i	−0.305511	−	0.529160i	−0.977375	+	0.211514i	$0.932160\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	1.95158e6	+	3.38024e6i	0.662383	+	1.14728i
$388$		0			0
$389$	−1.87797e6	+	3.25274e6i	−0.629238	+	1.08987i	0.358467	+	0.933543i	$0.383300\pi$
$389$	−1.87797e6	+	3.25274e6i	−0.629238	+	1.08987i	−0.987705	+	0.156330i	$0.950034\pi$
$390$		0			0
$391$	−778454.			−0.257508
$392$		0			0
$393$	5.63333e6			1.83985
$394$		0			0
$395$	283259.	−	490618.i	0.0913462	−	0.158216i
$396$		0			0
$397$	501332.	+	868333.i	0.159643	+	0.276509i	0.934740	−	0.355333i	$-0.115632\pi$
$397$	501332.	+	868333.i	0.159643	+	0.276509i	−0.775097	+	0.631842i	$0.782299\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−2.65671e6	−	4.60156e6i	−0.825056	−	1.42904i	−0.901877	−	0.431994i	$-0.857810\pi$
$401$	−2.65671e6	−	4.60156e6i	−0.825056	−	1.42904i	0.0768209	−	0.997045i	$-0.475523\pi$
$402$		0			0
$403$	2.01564e6	−	3.49119e6i	0.618231	−	1.07081i
$404$		0			0
$405$	−3.25567e6			−0.986286
$406$		0			0
$407$	3.62945e6			1.08606
$408$		0			0
$409$	2.29332e6	−	3.97214e6i	0.677884	−	1.17413i	−0.297732	−	0.954649i	$-0.596230\pi$
$409$	2.29332e6	−	3.97214e6i	0.677884	−	1.17413i	0.975617	−	0.219481i	$-0.0704364\pi$
$410$		0			0
$411$	−590579.	−	1.02291e6i	−0.172454	−	0.298699i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	1.31937e6	+	2.28521e6i	0.376050	+	0.651338i
$416$		0			0
$417$	3.45800e6	−	5.98942e6i	0.973833	−	1.68673i
$418$		0			0
$419$	2.29852e6			0.639607			0.319803	−	0.947484i	$-0.396383\pi$
$419$	2.29852e6			0.639607			0.319803	+	0.947484i	$0.396383\pi$
$420$		0			0
$421$	−5554.63			−0.00152739			−0.000763695	−	1.00000i	$-0.500243\pi$
$421$	−5554.63			−0.00152739			−0.000763695		1.00000i	$0.500243\pi$
$422$		0			0
$423$	−3.18826e6	+	5.52222e6i	−0.866368	+	1.50059i
$424$		0			0
$425$	−1.14879e6	−	1.98977e6i	−0.308510	−	0.534355i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−4.83772e6	−	8.37918e6i	−1.26910	−	2.19815i
$430$		0			0
$431$	2.08596e6	−	3.61299e6i	0.540895	−	0.936858i	−0.457957	−	0.888974i	$-0.651419\pi$
$431$	2.08596e6	−	3.61299e6i	0.540895	−	0.936858i	0.998853	−	0.0478842i	$-0.0152479\pi$
$432$		0			0
$433$	1.68030e6			0.430693			0.215347	−	0.976538i	$-0.430912\pi$
$433$	1.68030e6			0.430693			0.215347	+	0.976538i	$0.430912\pi$
$434$		0			0
$435$	−1.04923e7			−2.65857
$436$		0			0
$437$	1.96142e6	−	3.39728e6i	0.491323	−	0.850996i
$438$		0			0
$439$	1.06450e6	+	1.84376e6i	0.263623	+	0.456608i	0.967202	−	0.254009i	$-0.0817493\pi$
$439$	1.06450e6	+	1.84376e6i	0.263623	+	0.456608i	−0.703579	+	0.710617i	$0.748416\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	2.73075e6	+	4.72980e6i	0.661108	+	1.14507i	0.980325	+	0.197391i	$0.0632468\pi$
$443$	2.73075e6	+	4.72980e6i	0.661108	+	1.14507i	−0.319217	+	0.947682i	$0.603420\pi$
$444$		0			0
$445$	−4.69295e6	+	8.12842e6i	−1.12343	+	1.94584i
$446$		0			0
$447$	−5.51767e6			−1.30613
$448$		0			0
$449$	1.17382e6			0.274779			0.137390	−	0.990517i	$-0.456129\pi$
$449$	1.17382e6			0.274779			0.137390	+	0.990517i	$0.456129\pi$
$450$		0			0
$451$	693552.	−	1.20127e6i	0.160560	−	0.278098i
$452$		0			0
$453$	4.34893e6	+	7.53257e6i	0.995719	+	1.72464i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−1.94116e6	−	3.36218e6i	−0.434780	−	0.753062i	0.562497	−	0.826799i	$-0.309841\pi$
$457$	−1.94116e6	−	3.36218e6i	−0.434780	−	0.753062i	−0.997278	+	0.0737374i	$0.976507\pi$
$458$		0			0
$459$	974445.	−	1.68779e6i	0.215887	−	0.373926i
$460$		0			0
$461$	−1.13112e6			−0.247889			−0.123945	−	0.992289i	$-0.539555\pi$
$461$	−1.13112e6			−0.247889			−0.123945	+	0.992289i	$0.539555\pi$
$462$		0			0
$463$	−1.74204e6			−0.377664			−0.188832	−	0.982009i	$-0.560470\pi$
$463$	−1.74204e6			−0.377664			−0.188832	+	0.982009i	$0.560470\pi$
$464$		0			0
$465$	−5.70954e6	+	9.88921e6i	−1.22453	+	2.12094i
$466$		0			0
$467$	−2.48405e6	−	4.30251e6i	−0.527071	−	0.912913i	−0.999502	−	0.0315460i	$-0.989957\pi$
$467$	−2.48405e6	−	4.30251e6i	−0.527071	−	0.912913i	0.472432	−	0.881367i	$-0.343376\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−6.70860e6	−	1.16196e7i	−1.39341	−	2.41346i
$472$		0			0
$473$	1.76581e6	−	3.05846e6i	0.362903	−	0.628566i
$474$		0			0
$475$	1.15781e7			2.35453
$476$		0			0
$477$	−6.56140e6			−1.32038
$478$		0			0
$479$	−864744.	+	1.49778e6i	−0.172206	+	0.298270i	−0.939191	−	0.343396i	$-0.888423\pi$
$479$	−864744.	+	1.49778e6i	−0.172206	+	0.298270i	0.766985	+	0.641665i	$0.221756\pi$
$480$		0			0
$481$	4.04605e6	+	7.00797e6i	0.797386	+	1.38111i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	4.97202e6	+	8.61178e6i	0.959794	+	1.66241i
$486$		0			0
$487$	1.95131e6	−	3.37976e6i	0.372824	−	0.645749i	−0.617175	−	0.786826i	$-0.711723\pi$
$487$	1.95131e6	−	3.37976e6i	0.372824	−	0.645749i	0.989999	+	0.141077i	$0.0450564\pi$
$488$		0			0
$489$	−3650.93			−0.000690448
$490$		0			0
$491$	−8.62067e6			−1.61375			−0.806877	−	0.590720i	$-0.798844\pi$
$491$	−8.62067e6			−1.61375			−0.806877	+	0.590720i	$0.798844\pi$
$492$		0			0
$493$	735888.	−	1.27460e6i	0.136362	−	0.236187i
$494$		0			0
$495$	8.89072e6	+	1.53992e7i	1.63089	+	2.82478i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	3.50893e6	+	6.07765e6i	0.630846	+	1.09266i	0.987379	+	0.158375i	$0.0506256\pi$
$499$	3.50893e6	+	6.07765e6i	0.630846	+	1.09266i	−0.356533	+	0.934283i	$0.616041\pi$
$500$		0			0
$501$	6.93731e6	−	1.20158e7i	1.23480	−	2.13874i
$502$		0			0
$503$	−3.89602e6			−0.686596			−0.343298	−	0.939226i	$-0.611544\pi$
$503$	−3.89602e6			−0.686596			−0.343298	+	0.939226i	$0.611544\pi$
$504$		0			0
$505$	2.13149e6			0.371925
$506$		0			0
$507$	5.90274e6	−	1.02238e7i	1.01984	−	1.76642i
$508$		0			0
$509$	−774023.	−	1.34065e6i	−0.132422	−	0.229361i	0.792188	−	0.610277i	$-0.208942\pi$
$509$	−774023.	−	1.34065e6i	−0.132422	−	0.229361i	−0.924610	+	0.380916i	$0.875609\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	4.91049e6	+	8.50521e6i	0.823818	+	1.42689i
$514$		0			0
$515$	−6.63659e6	+	1.14949e7i	−1.10262	+	1.90980i
$516$		0			0
$517$	5.76952e6			0.949322
$518$		0			0
$519$	9.09113e6			1.48149
$520$		0			0
$521$	−3.55535e6	+	6.15804e6i	−0.573836	+	0.993913i	0.422331	+	0.906442i	$0.361212\pi$
$521$	−3.55535e6	+	6.15804e6i	−0.573836	+	0.993913i	−0.996167	+	0.0874713i	$0.972121\pi$
$522$		0			0
$523$	−2.68665e6	−	4.65341e6i	−0.429493	−	0.743904i	0.567335	−	0.823487i	$-0.307974\pi$
$523$	−2.68665e6	−	4.65341e6i	−0.429493	−	0.743904i	−0.996828	+	0.0795831i	$0.974641\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−800887.	−	1.38718e6i	−0.125616	−	0.217573i
$528$		0			0
$529$	877967.	−	1.52068e6i	0.136408	−	0.236265i
$530$		0			0
$531$	9.60520e6			1.47833
$532$		0			0
$533$	3.09264e6			0.471532
$534$		0			0
$535$	1.33578e6	−	2.31363e6i	0.201767	−	0.349470i
$536$		0			0
$537$	4.59701e6	+	7.96225e6i	0.687922	+	1.19152i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−2.63040e6	−	4.55598e6i	−0.386392	−	0.669251i	0.605569	−	0.795793i	$-0.292945\pi$
$541$	−2.63040e6	−	4.55598e6i	−0.386392	−	0.669251i	−0.991961	+	0.126542i	$0.959612\pi$
$542$		0			0
$543$	−6.17192e6	+	1.06901e7i	−0.898299	+	1.55590i
$544$		0			0
$545$	−8.63736e6			−1.24563
$546$		0			0
$547$	4.26833e6			0.609943			0.304972	−	0.952361i	$-0.401353\pi$
$547$	4.26833e6			0.609943			0.304972	+	0.952361i	$0.401353\pi$
$548$		0			0
$549$	−1.21389e7	+	2.10252e7i	−1.71889	+	2.97721i
$550$		0			0
$551$	3.70834e6	+	6.42303e6i	0.520355	+	0.901282i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−1.14609e7	−	1.98509e7i	−1.57938	−	2.73556i
$556$		0			0
$557$	2.64036e6	−	4.57323e6i	0.360599	−	0.624576i	−0.627461	−	0.778648i	$-0.715906\pi$
$557$	2.64036e6	−	4.57323e6i	0.360599	−	0.624576i	0.988060	+	0.154073i	$0.0492390\pi$
$558$		0			0
$559$	7.87395e6			1.06577
$560$		0			0
$561$	−3.84440e6			−0.515729
$562$		0			0
$563$	−4.49115e6	+	7.77889e6i	−0.597154	+	1.03430i	0.396085	+	0.918214i	$0.370369\pi$
$563$	−4.49115e6	+	7.77889e6i	−0.597154	+	1.03430i	−0.993239	+	0.116087i	$0.962965\pi$
$564$		0			0
$565$	923890.	+	1.60022e6i	0.121758	+	0.210892i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−5.32855e6	−	9.22931e6i	−0.689966	−	1.19506i	−0.971848	−	0.235608i	$-0.924292\pi$
$569$	−5.32855e6	−	9.22931e6i	−0.689966	−	1.19506i	0.281882	−	0.959449i	$-0.409041\pi$
$570$		0			0
$571$	1.76406e6	−	3.05545e6i	0.226425	−	0.392179i	−0.730321	−	0.683104i	$-0.760630\pi$
$571$	1.76406e6	−	3.05545e6i	0.226425	−	0.392179i	0.956746	+	0.290925i	$0.0939630\pi$
$572$		0			0
$573$	−2.23933e7			−2.84926
$574$		0			0
$575$	−1.38141e7			−1.74242
$576$		0			0
$577$	−1.31656e6	+	2.28035e6i	−0.164627	+	0.285143i	−0.936523	−	0.350607i	$-0.885975\pi$
$577$	−1.31656e6	+	2.28035e6i	−0.164627	+	0.285143i	0.771896	+	0.635749i	$0.219309\pi$
$578$		0			0
$579$	1.61620e6	+	2.79935e6i	0.200355	+	0.347025i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	2.96840e6	+	5.14142e6i	0.361702	+	0.626487i
$584$		0			0
$585$	−1.98224e7	+	3.43335e7i	−2.39479	+	4.14790i
$586$		0			0
$587$	−1.04984e7			−1.25755			−0.628776	−	0.777586i	$-0.716444\pi$
$587$	−1.04984e7			−1.25755			−0.628776	+	0.777586i	$0.716444\pi$
$588$		0			0
$589$	8.07176e6			0.958694
$590$		0			0
$591$	9.79627e6	−	1.69676e7i	1.15370	−	1.99826i
$592$		0			0
$593$	−2.23477e6	−	3.87073e6i	−0.260973	−	0.452018i	0.705528	−	0.708682i	$-0.250710\pi$
$593$	−2.23477e6	−	3.87073e6i	−0.260973	−	0.452018i	−0.966501	+	0.256664i	$0.917377\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	4.29728e6	+	7.44310e6i	0.493466	+	0.854709i
$598$		0			0
$599$	−4.22152e6	+	7.31189e6i	−0.480731	+	0.832650i	−0.999756	−	0.0221092i	$-0.992962\pi$
$599$	−4.22152e6	+	7.31189e6i	−0.480731	+	0.832650i	0.519025	+	0.854759i	$0.326295\pi$
$600$		0			0
$601$	−1.38045e7			−1.55896			−0.779481	−	0.626426i	$-0.784517\pi$
$601$	−1.38045e7			−1.55896			−0.779481	+	0.626426i	$0.784517\pi$
$602$		0			0
$603$	2.01888e7			2.26108
$604$		0			0
$605$	191496.	−	331680.i	0.0212702	−	0.0368410i
$606$		0			0
$607$	3.21919e6	+	5.57579e6i	0.354629	+	0.614236i	0.987054	−	0.160386i	$-0.0512738\pi$
$607$	3.21919e6	+	5.57579e6i	0.354629	+	0.614236i	−0.632425	+	0.774621i	$0.717940\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	6.43176e6	+	1.11401e7i	0.696990	+	1.20722i
$612$		0			0
$613$	649869.	−	1.12561e6i	0.0698513	−	0.120986i	−0.828984	−	0.559272i	$-0.811081\pi$
$613$	649869.	−	1.12561e6i	0.0698513	−	0.120986i	0.898836	+	0.438286i	$0.144414\pi$
$614$		0			0
$615$	−8.76024e6			−0.933960
$616$		0			0
$617$	−5.51795e6			−0.583532			−0.291766	−	0.956490i	$-0.594243\pi$
$617$	−5.51795e6			−0.583532			−0.291766	+	0.956490i	$0.594243\pi$
$618$		0			0
$619$	4.68387e6	−	8.11270e6i	0.491335	−	0.851018i	−0.508615	−	0.860994i	$-0.669842\pi$
$619$	4.68387e6	−	8.11270e6i	0.491335	−	0.851018i	0.999950	+	0.00997644i	$0.00317565\pi$
$620$		0			0
$621$	−5.85879e6	−	1.01477e7i	−0.609648	−	1.05594i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−5.52610e6	−	9.57148e6i	−0.565872	−	0.980120i
$626$		0			0
$627$	9.68648e6	−	1.67775e7i	0.984004	−	1.70435i
$628$		0			0
$629$	3.21528e6			0.324035
$630$		0			0
$631$	7.50281e6			0.750154			0.375077	−	0.926994i	$-0.377616\pi$
$631$	7.50281e6			0.750154			0.375077	+	0.926994i	$0.377616\pi$
$632$		0			0
$633$	4.42464e6	−	7.66370e6i	0.438903	−	0.760202i
$634$		0			0
$635$	−9.19304e6	−	1.59228e7i	−0.904742	−	1.56706i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−1.27959e6	−	2.21631e6i	−0.123970	−	0.214723i
$640$		0			0
$641$	−56350.3	+	97601.5i	−0.00541690	+	0.00938235i	−0.868721	−	0.495301i	$-0.835058\pi$
$641$	−56350.3	+	97601.5i	−0.00541690	+	0.00938235i	0.863304	+	0.504684i	$0.168391\pi$
$642$		0			0
$643$	453508.			0.0432572			0.0216286	−	0.999766i	$-0.493115\pi$
$643$	453508.			0.0432572			0.0216286	+	0.999766i	$0.493115\pi$
$644$		0			0
$645$	−2.23039e7			−2.11096
$646$		0			0
$647$	−3.85516e6	+	6.67734e6i	−0.362061	+	0.627108i	−0.988300	−	0.152523i	$-0.951260\pi$
$647$	−3.85516e6	+	6.67734e6i	−0.362061	+	0.627108i	0.626239	+	0.779631i	$0.284593\pi$
$648$		0			0
$649$	−4.34543e6	−	7.52651e6i	−0.404969	−	0.701426i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	2.99333e6	+	5.18459e6i	0.274708	+	0.475808i	0.970061	−	0.242860i	$-0.0780855\pi$
$653$	2.99333e6	+	5.18459e6i	0.274708	+	0.475808i	−0.695354	+	0.718668i	$0.744752\pi$
$654$		0			0
$655$	−1.04426e7	+	1.80871e7i	−0.951052	+	1.64727i
$656$		0			0
$657$	2.13908e7			1.93336
$658$		0			0
$659$	−1.44274e7			−1.29412			−0.647058	−	0.762441i	$-0.724001\pi$
$659$	−1.44274e7			−1.29412			−0.647058	+	0.762441i	$0.724001\pi$
$660$		0			0
$661$	9.01844e6	−	1.56204e7i	0.802838	−	1.39056i	−0.114903	−	0.993377i	$-0.536656\pi$
$661$	9.01844e6	−	1.56204e7i	0.802838	−	1.39056i	0.917741	−	0.397180i	$-0.130011\pi$
$662$		0			0
$663$	−4.28567e6	−	7.42299e6i	−0.378647	−	0.655836i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−4.42448e6	−	7.66343e6i	−0.385077	−	0.666974i
$668$		0			0
$669$	8.33659e6	−	1.44394e7i	0.720150	−	1.24734i
$670$		0			0
$671$	2.19667e7			1.88347
$672$		0			0
$673$	−1.58113e7			−1.34564			−0.672820	−	0.739806i	$-0.734917\pi$
$673$	−1.58113e7			−1.34564			−0.672820	+	0.739806i	$0.734917\pi$
$674$		0			0
$675$	1.72920e7	−	2.99507e7i	1.46079	−	2.53016i
$676$		0			0
$677$	6.39384e6	+	1.10744e7i	0.536154	+	0.928647i	0.999107	+	0.0422633i	$0.0134569\pi$
$677$	6.39384e6	+	1.10744e7i	0.536154	+	0.928647i	−0.462952	+	0.886383i	$0.653210\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−3.91153e6	−	6.77497e6i	−0.323206	−	0.559809i
$682$		0			0
$683$	2.08745e6	−	3.61558e6i	0.171224	−	0.296569i	−0.767624	−	0.640901i	$-0.778561\pi$
$683$	2.08745e6	−	3.61558e6i	0.171224	−	0.296569i	0.938848	+	0.344332i	$0.111894\pi$
$684$		0			0
$685$	4.37906e6			0.356578
$686$		0			0
$687$	−1.56497e7			−1.26507
$688$		0			0
$689$	−6.61824e6	+	1.14631e7i	−0.531122	+	0.919931i
$690$		0			0
$691$	4.15804e6	+	7.20194e6i	0.331279	+	0.573792i	0.982763	−	0.184870i	$-0.0591865\pi$
$691$	4.15804e6	+	7.20194e6i	0.331279	+	0.573792i	−0.651484	+	0.758662i	$0.725853\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	1.28203e7	+	2.22054e7i	1.00678	+	1.74380i
$696$		0			0
$697$	614408.	−	1.06419e6i	0.0479043	−	0.0829727i
$698$		0			0
$699$	−3.96914e6			−0.307258
$700$		0			0
$701$	−1.67718e6			−0.128909			−0.0644546	−	0.997921i	$-0.520531\pi$
$701$	−1.67718e6			−0.128909			−0.0644546	+	0.997921i	$0.520531\pi$
$702$		0			0
$703$	−8.10133e6	+	1.40319e7i	−0.618256	+	1.07085i
$704$		0			0
$705$	−1.82187e7	−	3.15557e7i	−1.38053	−	2.39114i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−8.30467e6	−	1.43841e7i	−0.620450	−	1.07465i	−0.989402	−	0.145202i	$-0.953617\pi$
$709$	−8.30467e6	−	1.43841e7i	−0.620450	−	1.07465i	0.368952	−	0.929448i	$-0.379717\pi$
$710$		0			0
$711$	−1.30390e6	+	2.25842e6i	−0.0967318	+	0.167544i
$712$		0			0
$713$	−9.63057e6			−0.709460
$714$		0			0
$715$	3.58710e7			2.62409
$716$		0			0
$717$	−1.08702e7	+	1.88277e7i	−0.789658	+	1.36773i
$718$		0			0
$719$	1.16401e7	+	2.01613e7i	0.839722	+	1.45444i	0.890127	+	0.455712i	$0.150615\pi$
$719$	1.16401e7	+	2.01613e7i	0.839722	+	1.45444i	−0.0504057	+	0.998729i	$0.516051\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	1.79884e7	+	3.11569e7i	1.27982	+	2.21671i
$724$		0			0
$725$	1.30587e7	−	2.26184e7i	0.922690	−	1.59815i
$726$		0			0
$727$	−1.74527e7			−1.22469			−0.612345	−	0.790591i	$-0.709774\pi$
$727$	−1.74527e7			−1.22469			−0.612345	+	0.790591i	$0.709774\pi$
$728$		0			0
$729$	−1.96334e7			−1.36829
$730$		0			0
$731$	1.56430e6	−	2.70945e6i	0.108275	−	0.187537i
$732$		0			0
$733$	−470338.	−	814649.i	−0.0323333	−	0.0560029i	0.849406	−	0.527740i	$-0.176960\pi$
$733$	−470338.	−	814649.i	−0.0323333	−	0.0560029i	−0.881739	+	0.471737i	$0.843627\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−9.13348e6	−	1.58197e7i	−0.619395	−	1.07282i
$738$		0			0
$739$	−5.69498e6	+	9.86399e6i	−0.383602	+	0.664418i	−0.991574	−	0.129540i	$-0.958650\pi$
$739$	−5.69498e6	+	9.86399e6i	−0.383602	+	0.664418i	0.607972	+	0.793958i	$0.291983\pi$
$740$		0			0
$741$	4.31932e7			2.88982
$742$		0			0
$743$	262087.			0.0174170			0.00870851	−	0.999962i	$-0.497228\pi$
$743$	262087.			0.0174170			0.00870851	+	0.999962i	$0.497228\pi$
$744$		0			0
$745$	1.02282e7	−	1.77157e7i	0.675161	−	1.16941i
$746$		0			0
$747$	−6.07332e6	−	1.05193e7i	−0.398222	−	0.689740i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−553382.	−	958485.i	−0.0358035	−	0.0620134i	0.847568	−	0.530686i	$-0.178066\pi$
$751$	−553382.	−	958485.i	−0.0358035	−	0.0620134i	−0.883372	+	0.468673i	$0.844732\pi$
$752$		0			0
$753$	2.28300e7	−	3.95428e7i	1.46730	−	2.54144i
$754$		0			0
$755$	−3.22467e7			−2.05882
$756$		0			0
$757$	3.07218e7			1.94853			0.974264	−	0.225412i	$-0.0723728\pi$
$757$	3.07218e7			1.94853			0.974264	+	0.225412i	$0.0723728\pi$
$758$		0			0
$759$	−1.15571e7	+	2.00175e7i	−0.728190	+	1.26126i
$760$		0			0
$761$	−5.93175e6	−	1.02741e7i	−0.371297	−	0.643104i	0.618469	−	0.785809i	$-0.287753\pi$
$761$	−5.93175e6	−	1.02741e7i	−0.371297	−	0.643104i	−0.989765	+	0.142705i	$0.954420\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	7.87616e6	+	1.36419e7i	0.486588	+	0.842795i
$766$		0			0
$767$	9.68842e6	−	1.67808e7i	0.594654	−	1.02997i
$768$		0			0
$769$	2.08006e7			1.26841			0.634204	−	0.773166i	$-0.281328\pi$
$769$	2.08006e7			1.26841			0.634204	+	0.773166i	$0.281328\pi$
$770$		0			0
$771$	5.38378e7			3.26175
$772$		0			0
$773$	−5.63165e6	+	9.75430e6i	−0.338990	+	0.587148i	−0.984243	−	0.176821i	$-0.943419\pi$
$773$	−5.63165e6	+	9.75430e6i	−0.338990	+	0.587148i	0.645253	+	0.763969i	$0.276752\pi$
$774$		0			0
$775$	−1.42122e7	−	2.46162e7i	−0.849974	−	1.47220i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	3.09616e6	+	5.36271e6i	0.182802	+	0.316622i
$780$		0			0
$781$	−1.15778e6	+	2.00534e6i	−0.0679202	+	0.117641i
$782$		0			0
$783$	2.21537e7			1.29135
$784$		0			0
$785$	4.97433e7			2.88111
$786$		0			0
$787$	−1.32971e7	+	2.30312e7i	−0.765278	+	1.32550i	0.174821	+	0.984600i	$0.444065\pi$
$787$	−1.32971e7	+	2.30312e7i	−0.765278	+	1.32550i	−0.940099	+	0.340900i	$0.889268\pi$
$788$		0			0
$789$	−5.33628e6	−	9.24270e6i	−0.305173	−	0.528575i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	2.44881e7	+	4.24147e7i	1.38284	+	2.39515i
$794$		0			0
$795$	1.87469e7	−	3.24706e7i	1.05199	−	1.82210i
$796$		0			0
$797$	1.25159e7			0.697938			0.348969	−	0.937134i	$-0.386532\pi$
$797$	1.25159e7			0.697938			0.348969	+	0.937134i	$0.386532\pi$
$798$		0			0
$799$	5.11114e6			0.283237
$800$		0			0
$801$	2.16026e7	−	3.74168e7i	1.18966	−	2.06056i
$802$		0			0
$803$	−9.67728e6	−	1.67615e7i	−0.529620	−	0.917329i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−1.94700e7	−	3.37230e7i	−1.05240	−	1.82281i
$808$		0			0
$809$	−5.12955e6	+	8.88464e6i	−0.275555	+	0.477275i	−0.970275	−	0.242005i	$-0.922195\pi$
$809$	−5.12955e6	+	8.88464e6i	−0.275555	+	0.477275i	0.694720	+	0.719280i	$0.255528\pi$
$810$		0			0
$811$	1.32031e7			0.704892			0.352446	−	0.935832i	$-0.385350\pi$
$811$	1.32031e7			0.704892			0.352446	+	0.935832i	$0.385350\pi$
$812$		0			0
$813$	−1.20335e7			−0.638508
$814$		0			0
$815$	6767.77	−	11722.1i	0.000356904	−	0.000618177i
$816$		0			0
$817$	7.88293e6	+	1.36536e7i	0.413174	+	0.715638i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.44070e7	−	2.49536e7i	−0.745958	−	1.29204i	−0.949746	−	0.313023i	$-0.898658\pi$
$821$	−1.44070e7	−	2.49536e7i	−0.745958	−	1.29204i	0.203787	−	0.979015i	$-0.434675\pi$
$822$		0			0
$823$	−1.36049e7	+	2.35643e7i	−0.700156	+	1.21271i	0.268256	+	0.963348i	$0.413553\pi$
$823$	−1.36049e7	+	2.35643e7i	−0.700156	+	1.21271i	−0.968411	+	0.249358i	$0.919780\pi$
$824$		0			0
$825$	−6.82209e7			−3.48966
$826$		0			0
$827$	3.36307e7			1.70991			0.854954	−	0.518705i	$-0.173586\pi$
$827$	3.36307e7			1.70991			0.854954	+	0.518705i	$0.173586\pi$
$828$		0			0
$829$	1.65417e7	−	2.86511e7i	0.835978	−	1.44796i	−0.0572543	−	0.998360i	$-0.518235\pi$
$829$	1.65417e7	−	2.86511e7i	0.835978	−	1.44796i	0.893232	−	0.449596i	$-0.148432\pi$
$830$		0			0
$831$	1.91797e7	+	3.32202e7i	0.963473	+	1.66878i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	2.57196e7	+	4.45476e7i	1.27658	+	2.21110i
$836$		0			0
$837$	1.20553e7	−	2.08803e7i	0.594789	−	1.03020i
$838$		0			0
$839$	1.85094e7			0.907796			0.453898	−	0.891054i	$-0.350033\pi$
$839$	1.85094e7			0.907796			0.453898	+	0.891054i	$0.350033\pi$
$840$		0			0
$841$	−3.78094e6			−0.184336
$842$		0			0
$843$	−2.50115e7	+	4.33212e7i	−1.21219	+	2.09958i
$844$		0			0
$845$	2.18840e7	+	3.79041e7i	1.05435	+	1.82619i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	1.33082e7	+	2.30504e7i	0.633650	+	1.09751i
$850$		0			0
$851$	9.66585e6	−	1.67417e7i	0.457526	−	0.792459i
$852$		0			0
$853$	1.52810e7			0.719086			0.359543	−	0.933129i	$-0.382933\pi$
$853$	1.52810e7			0.719086			0.359543	+	0.933129i	$0.382933\pi$
$854$		0			0
$855$	−7.93802e7			−3.71361
$856$		0			0
$857$	−2.55315e6	+	4.42218e6i	−0.118747	+	0.205676i	−0.919271	−	0.393624i	$-0.871221\pi$
$857$	−2.55315e6	+	4.42218e6i	−0.118747	+	0.205676i	0.800524	+	0.599300i	$0.204554\pi$
$858$		0			0
$859$	1.16468e7	+	2.01728e7i	0.538546	+	0.932788i	0.998983	+	0.0450959i	$0.0143594\pi$
$859$	1.16468e7	+	2.01728e7i	0.538546	+	0.932788i	−0.460437	+	0.887692i	$0.652307\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−1.21283e7	−	2.10069e7i	−0.554337	−	0.960139i	−0.997955	−	0.0639235i	$-0.979639\pi$
$863$	−1.21283e7	−	2.10069e7i	−0.554337	−	0.960139i	0.443618	−	0.896216i	$-0.353695\pi$
$864$		0			0
$865$	−1.68524e7	+	2.91891e7i	−0.765809	+	1.32642i
$866$		0			0
$867$	3.39424e7			1.53354
$868$		0			0
$869$	2.35955e6			0.105994
$870$		0			0
$871$	2.03637e7	−	3.52709e7i	0.909517	−	1.57533i
$872$		0			0
$873$	−2.28872e7	−	3.96418e7i	−1.01638	−	1.76043i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	1.40670e7	+	2.43647e7i	0.617592	+	1.06970i	0.989924	+	0.141601i	$0.0452250\pi$
$877$	1.40670e7	+	2.43647e7i	0.617592	+	1.06970i	−0.372332	+	0.928100i	$0.621442\pi$
$878$		0			0
$879$	1.72180e7	−	2.98225e7i	0.751642	−	1.30188i
$880$		0			0
$881$	−8.51907e6			−0.369788			−0.184894	−	0.982759i	$-0.559194\pi$
$881$	−8.51907e6			−0.369788			−0.184894	+	0.982759i	$0.559194\pi$
$882$		0			0
$883$	−1.36512e7			−0.589210			−0.294605	−	0.955619i	$-0.595188\pi$
$883$	−1.36512e7			−0.589210			−0.294605	+	0.955619i	$0.595188\pi$
$884$		0			0
$885$	−2.74436e7	+	4.75336e7i	−1.17783	+	2.04006i
$886$		0			0
$887$	−5.13749e6	−	8.89840e6i	−0.219251	−	0.379754i	0.735328	−	0.677711i	$-0.237028\pi$
$887$	−5.13749e6	−	8.89840e6i	−0.219251	−	0.379754i	−0.954579	+	0.297957i	$0.903695\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−6.77996e6	−	1.17432e7i	−0.286110	−	0.495557i
$892$		0			0
$893$	−1.28782e7	+	2.23057e7i	−0.540414	+	0.936024i
$894$		0			0
$895$	−3.40861e7			−1.42239
$896$		0			0
$897$	−5.15346e7			−2.13854
$898$		0			0
$899$	9.10397e6	−	1.57685e7i	0.375692	−	0.650717i
$900$		0			0
$901$	2.62967e6	+	4.55471e6i	0.107917	+	0.186917i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−2.28819e7	−	3.96327e7i	−0.928692	−	1.60854i
$906$		0			0
$907$	−1.54258e7	+	2.67183e7i	−0.622630	+	1.07843i	0.366364	+	0.930472i	$0.380603\pi$
$907$	−1.54258e7	+	2.67183e7i	−0.622630	+	1.07843i	−0.988994	+	0.147955i	$0.952731\pi$
$908$		0			0
$909$	−9.81170e6			−0.393853
$910$		0			0
$911$	1.48424e7			0.592525			0.296263	−	0.955107i	$-0.404260\pi$
$911$	1.48424e7			0.592525			0.296263	+	0.955107i	$0.404260\pi$
$912$		0			0
$913$	−5.49519e6	+	9.51795e6i	−0.218175	+	0.377891i
$914$		0			0
$915$	−6.93654e7	−	1.20144e8i	−2.73899	−	4.74407i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	1.57033e7	+	2.71989e7i	0.613340	+	1.06234i	0.990673	+	0.136258i	$0.0435077\pi$
$919$	1.57033e7	+	2.71989e7i	0.613340	+	1.06234i	−0.377333	+	0.926077i	$0.623159\pi$
$920$		0			0
$921$	−2.41610e7	+	4.18481e7i	−0.938569	+	1.62565i
$922$		0			0
$923$	−5.16269e6			−0.199467
$924$		0			0
$925$	5.70569e7			2.19257
$926$		0			0
$927$	3.05496e7	−	5.29134e7i	1.16763	−	2.02240i
$928$		0			0
$929$	3.87830e6	+	6.71742e6i	0.147436	+	0.255366i	0.930279	−	0.366853i	$-0.119565\pi$
$929$	3.87830e6	+	6.71742e6i	0.147436	+	0.255366i	−0.782843	+	0.622219i	$0.786231\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	1.86698e7	+	3.23371e7i	0.702159	+	1.21618i
$934$		0			0
$935$	7.12642e6	−	1.23433e7i	0.266589	−	0.461746i
$936$		0			0
$937$	2.51058e7			0.934167			0.467084	−	0.884213i	$-0.345305\pi$
$937$	2.51058e7			0.934167			0.467084	+	0.884213i	$0.345305\pi$
$938$		0			0
$939$	−7.03007e7			−2.60193
$940$		0			0
$941$	2.03888e7	−	3.53145e7i	0.750617	−	1.30011i	−0.196907	−	0.980422i	$-0.563090\pi$
$941$	2.03888e7	−	3.53145e7i	0.750617	−	1.30011i	0.947524	−	0.319684i	$-0.103577\pi$
$942$		0			0
$943$	−3.69409e6	−	6.39835e6i	−0.135278	−	0.234309i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.55894e7	−	2.70017e7i	−0.564879	−	0.978399i	−0.997061	−	0.0766123i	$-0.975590\pi$
$947$	−1.55894e7	−	2.70017e7i	−0.564879	−	0.978399i	0.432182	−	0.901786i	$-0.357744\pi$
$948$		0			0
$949$	2.15761e7	−	3.73709e7i	0.777692	−	1.34700i
$950$		0			0
$951$	−896086.			−0.0321291
$952$		0			0
$953$	−2.49371e7			−0.889433			−0.444716	−	0.895671i	$-0.646696\pi$
$953$	−2.49371e7			−0.889433			−0.444716	+	0.895671i	$0.646696\pi$
$954$		0			0
$955$	4.15108e7	−	7.18989e7i	1.47283	−	2.55102i
$956$		0			0
$957$	−2.18503e7	−	3.78459e7i	−0.771220	−	1.33579i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	4.40648e6	+	7.63225e6i	0.153916	+	0.266590i
$962$		0			0
$963$	−6.14885e6	+	1.06501e7i	−0.213662	+	0.370074i
$964$		0			0
$965$	−1.19839e7			−0.414267
$966$		0			0
$967$	−9.62902e6			−0.331143			−0.165572	−	0.986198i	$-0.552947\pi$
$967$	−9.62902e6			−0.331143			−0.165572	+	0.986198i	$0.552947\pi$
$968$		0			0
$969$	8.58111e6	−	1.48629e7i	0.293585	−	0.508504i
$970$		0			0
$971$	2.88493e7	+	4.99685e7i	0.981946	+	1.70078i	0.654791	+	0.755810i	$0.272757\pi$
$971$	2.88493e7	+	4.99685e7i	0.981946	+	1.70078i	0.327155	+	0.944971i	$0.393910\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−7.60514e7	−	1.31725e8i	−2.56210	−	4.43769i
$976$		0			0
$977$	−1.79167e7	+	3.10326e7i	−0.600512	+	1.04012i	0.392231	+	0.919867i	$0.371703\pi$
$977$	−1.79167e7	+	3.10326e7i	−0.600512	+	1.04012i	−0.992744	+	0.120251i	$0.961630\pi$
$978$		0			0
$979$	−3.90924e7			−1.30357
$980$		0			0
$981$	3.97595e7			1.31907
$982$		0			0
$983$	−2.63358e7	+	4.56150e7i	−0.869287	+	1.50565i	−0.00656114	+	0.999978i	$0.502088\pi$
$983$	−2.63358e7	+	4.56150e7i	−0.869287	+	1.50565i	−0.862726	+	0.505671i	$0.831245\pi$
$984$		0			0
$985$	3.63190e7	+	6.29063e7i	1.19273	+	2.06587i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−9.40527e6	−	1.62904e7i	−0.305760	−	0.529592i
$990$		0			0
$991$	−6.84136e6	+	1.18496e7i	−0.221288	+	0.383283i	−0.955199	−	0.295963i	$-0.904360\pi$
$991$	−6.84136e6	+	1.18496e7i	−0.221288	+	0.383283i	0.733911	+	0.679245i	$0.237693\pi$
$992$		0			0
$993$	−4.07846e7			−1.31257
$994$		0			0
$995$	−3.18637e7			−1.02032
$996$		0			0
$997$	−1.71922e7	+	2.97777e7i	−0.547763	+	0.948754i	0.450664	+	0.892694i	$0.351187\pi$
$997$	−1.71922e7	+	2.97777e7i	−0.547763	+	0.948754i	−0.998427	+	0.0560604i	$0.982146\pi$
$998$		0			0
$999$	2.41988e7	+	4.19136e7i	0.767150	+	1.32874i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.6.i.l.361.2		4
7.2	even	3	inner	392.6.i.l.177.2		4
7.3	odd	6		392.6.a.f.1.2		2
7.4	even	3		56.6.a.c.1.1	✓	2
7.5	odd	6		392.6.i.g.177.1		4
7.6	odd	2		392.6.i.g.361.1		4
21.11	odd	6		504.6.a.s.1.2		2
28.3	even	6		784.6.a.p.1.1		2
28.11	odd	6		112.6.a.k.1.2		2
56.11	odd	6		448.6.a.q.1.1		2
56.53	even	6		448.6.a.z.1.2		2
84.11	even	6		1008.6.a.bt.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.6.a.c.1.1	✓	2	7.4	even	3
112.6.a.k.1.2		2	28.11	odd	6
392.6.a.f.1.2		2	7.3	odd	6
392.6.i.g.177.1		4	7.5	odd	6
392.6.i.g.361.1		4	7.6	odd	2
392.6.i.l.177.2		4	7.2	even	3	inner
392.6.i.l.361.2		4	1.1	even	1	trivial
448.6.a.q.1.1		2	56.11	odd	6
448.6.a.z.1.2		2	56.53	even	6
504.6.a.s.1.2		2	21.11	odd	6
784.6.a.p.1.1		2	28.3	even	6
1008.6.a.bt.1.2		2	84.11	even	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:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	392.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(13.1521 - 22.7800i) q^{3} +(48.7603 + 84.4554i) q^{5} +(-224.454 - 388.765i) q^{9} +(-203.088 + 351.758i) q^{11} -905.594 q^{13} +2565.20 q^{15} +(-179.912 + 311.617i) q^{17} +(-906.626 - 1570.32i) q^{19} +(1081.71 + 1873.58i) q^{23} +(-3192.64 + 5529.82i) q^{25} -5416.22 q^{27} -4090.26 q^{29} +(-2225.77 + 3855.14i) q^{31} +(5342.04 + 9252.69i) q^{33} +(-4467.84 - 7738.53i) q^{37} +(-11910.4 + 20629.5i) q^{39} -3415.04 q^{41} -8694.80 q^{43} +(21888.9 - 37912.7i) q^{45} +(-7102.26 - 12301.5i) q^{47} +(4732.44 + 8196.83i) q^{51} +(7308.18 - 12658.1i) q^{53} -39610.5 q^{55} -47696.1 q^{57} +(-10698.4 + 18530.2i) q^{59} +(-27041.0 - 46836.3i) q^{61} +(-44157.0 - 76482.2i) q^{65} +(-22486.6 + 38947.9i) q^{67} +56907.0 q^{69} +5700.89 q^{71} +(-23825.4 + 41266.8i) q^{73} +(83979.7 + 145457. i) q^{75} +(-2904.60 - 5030.91i) q^{79} +(-16692.2 + 28911.8i) q^{81} +27058.2 q^{83} -35090.4 q^{85} +(-53795.3 + 93176.3i) q^{87} +(48122.6 + 83350.8i) q^{89} +(58546.9 + 101406. i) q^{93} +(88414.8 - 153139. i) q^{95} +101968. q^{97} +182335. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 26 q^{3} + 62 q^{5} - 206 q^{9} - 972 q^{11} + 156 q^{13} + 5152 q^{15} - 560 q^{17} - 2642 q^{19} - 2272 q^{23} - 4522 q^{25} - 11128 q^{27} - 15616 q^{29} - 5444 q^{31} + 10512 q^{33} - 576 q^{37}+ \cdots + 89784 q^{99}+O(q^{100}) \) 4 * q + 26 * q^3 + 62 * q^5 - 206 * q^9 - 972 * q^11 + 156 * q^13 + 5152 * q^15 - 560 * q^17 - 2642 * q^19 - 2272 * q^23 - 4522 * q^25 - 11128 * q^27 - 15616 * q^29 - 5444 * q^31 + 10512 * q^33 - 576 * q^37 - 24120 * q^39 - 33776 * q^41 - 16792 * q^43 + 52406 * q^45 + 4532 * q^47 + 9404 * q^51 - 1420 * q^53 - 39024 * q^55 - 94888 * q^57 - 34146 * q^59 - 19106 * q^61 - 123252 * q^65 - 56952 * q^67 + 116512 * q^69 - 14448 * q^71 - 128828 * q^73 + 168526 * q^75 - 52808 * q^79 - 92366 * q^81 - 168972 * q^83 - 55960 * q^85 - 106460 * q^87 + 130972 * q^89 + 116792 * q^93 + 147392 * q^95 + 389248 * q^97 + 89784 * q^99

Introduction

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