LMFDB - Embedded newform 392.6.i.o.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 = [10,0,5,0,-81,0,0,0,-390] 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:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 200 x^{8} - 198 x^{7} + 34197 x^{6} - 16185 x^{5} + 1170401 x^{4} + 2020497 x^{3} + \cdots + 13068225 $ x^10 + 200x^8 - 198x^7 + 34197x^6 - 16185x^5 + 1170401x^4 + 2020497x^3 + 33316924x^2 + 20977845x + 13068225
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{18}\cdot 3\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$6.16047 - 10.6702i$ of defining polynomial
Character	$\chi$	$=$	392.361
Dual form			392.6.i.o.177.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-11.8209 + 20.4745i) q^{3} +(10.0228 + 17.3600i) q^{5} +(-157.969 - 273.611i) q^{9} +(-29.3766 + 50.8817i) q^{11} +691.185 q^{13} -473.916 q^{15} +(-263.388 + 456.202i) q^{17} +(63.7838 + 110.477i) q^{19} +(-1134.30 - 1964.67i) q^{23} +(1361.59 - 2358.34i) q^{25} +1724.41 q^{27} +8636.30 q^{29} +(5145.41 - 8912.12i) q^{31} +(-694.517 - 1202.94i) q^{33} +(2361.55 + 4090.33i) q^{37} +(-8170.46 + 14151.6i) q^{39} +6676.64 q^{41} +22926.7 q^{43} +(3166.59 - 5484.70i) q^{45} +(-12056.0 - 20881.6i) q^{47} +(-6226.99 - 10785.5i) q^{51} +(4121.48 - 7138.61i) q^{53} -1177.74 q^{55} -3015.94 q^{57} +(-18067.1 + 31293.2i) q^{59} +(-7827.42 - 13557.5i) q^{61} +(6927.61 + 11999.0i) q^{65} +(-14685.9 + 25436.7i) q^{67} +53634.1 q^{69} -9025.02 q^{71} +(-2217.71 + 3841.19i) q^{73} +(32190.5 + 55755.6i) q^{75} +(-4100.81 - 7102.81i) q^{79} +(18002.4 - 31181.1i) q^{81} -54575.9 q^{83} -10559.5 q^{85} +(-102089. + 176824. i) q^{87} +(43466.9 + 75286.9i) q^{89} +(121647. + 210699. i) q^{93} +(-1278.58 + 2214.57i) q^{95} +157783. q^{97} +18562.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 5 q^{3} - 81 q^{5} - 390 q^{9} - 361 q^{11} + 684 q^{13} - 2098 q^{15} - 1809 q^{17} - 1277 q^{19} - 911 q^{23} - 3940 q^{25} - 9502 q^{27} + 10884 q^{29} - 2187 q^{31} + 5553 q^{33} + 8181 q^{37}+ \cdots + 499596 q^{99}+O(q^{100}) $ 10 * q + 5 * q^3 - 81 * q^5 - 390 * q^9 - 361 * q^11 + 684 * q^13 - 2098 * q^15 - 1809 * q^17 - 1277 * q^19 - 911 * q^23 - 3940 * q^25 - 9502 * q^27 + 10884 * q^29 - 2187 * q^31 + 5553 * q^33 + 8181 * q^37 + 3422 * q^39 + 33156 * q^41 + 12664 * q^43 - 41310 * q^45 - 16101 * q^47 + 67865 * q^51 - 16047 * q^53 + 91258 * q^55 + 44694 * q^57 - 71027 * q^59 - 31093 * q^61 + 64370 * q^65 - 47981 * q^67 + 274498 * q^69 + 45024 * q^71 - 123333 * q^73 + 45460 * q^75 + 212481 * q^79 - 52917 * q^81 + 174920 * q^83 + 444282 * q^85 - 318070 * q^87 - 129045 * q^89 + 252835 * q^93 - 300417 * q^95 + 656548 * q^97 + 499596 * 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
$3$	−11.8209	+	20.4745i	−0.758314	+	1.31344i	0.185396	+	0.982664i	$0.440643\pi$
$3$	−11.8209	+	20.4745i	−0.758314	+	1.31344i	−0.943710	+	0.330774i	$0.892690\pi$
$4$		0			0
$5$	10.0228	+	17.3600i	0.179293	+	0.310545i	0.941639	−	0.336625i	$-0.109286\pi$
$5$	10.0228	+	17.3600i	0.179293	+	0.310545i	−0.762345	+	0.647170i	$0.775952\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−157.969	−	273.611i	−0.650080	−	1.12597i
$10$		0			0
$11$	−29.3766	+	50.8817i	−0.0732014	+	0.126789i	−0.900303	−	0.435264i	$-0.856655\pi$
$11$	−29.3766	+	50.8817i	−0.0732014	+	0.126789i	0.827101	+	0.562053i	$0.189988\pi$
$12$		0			0
$13$	691.185			1.13432			0.567160	−	0.823607i	$-0.308042\pi$
$13$	691.185			1.13432			0.567160	+	0.823607i	$0.308042\pi$
$14$		0			0
$15$	−473.916			−0.543842
$16$		0			0
$17$	−263.388	+	456.202i	−0.221041	+	0.382855i	−0.955124	−	0.296205i	$-0.904279\pi$
$17$	−263.388	+	456.202i	−0.221041	+	0.382855i	0.734083	+	0.679060i	$0.237612\pi$
$18$		0			0
$19$	63.7838	+	110.477i	0.0405346	+	0.0702080i	0.885581	−	0.464485i	$-0.153761\pi$
$19$	63.7838	+	110.477i	0.0405346	+	0.0702080i	−0.845046	+	0.534693i	$0.820427\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1134.30	−	1964.67i	−0.447105	−	0.774408i	0.551091	−	0.834445i	$-0.314212\pi$
$23$	−1134.30	−	1964.67i	−0.447105	−	0.774408i	−0.998196	+	0.0600366i	$0.980878\pi$
$24$		0			0
$25$	1361.59	−	2358.34i	0.435708	−	0.754668i
$26$		0			0
$27$	1724.41			0.455230
$28$		0			0
$29$	8636.30			1.90692			0.953461	−	0.301518i	$-0.0974933\pi$
$29$	8636.30			1.90692			0.953461	+	0.301518i	$0.0974933\pi$
$30$		0			0
$31$	5145.41	−	8912.12i	0.961648	−	1.66562i	0.243283	−	0.969955i	$-0.421776\pi$
$31$	5145.41	−	8912.12i	0.961648	−	1.66562i	0.718364	−	0.695667i	$-0.244891\pi$
$32$		0			0
$33$	−694.517	−	1202.94i	−0.111019	−	0.192291i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	2361.55	+	4090.33i	0.283592	+	0.491195i	0.972267	−	0.233875i	$-0.0751407\pi$
$37$	2361.55	+	4090.33i	0.283592	+	0.491195i	−0.688675	+	0.725070i	$0.741807\pi$
$38$		0			0
$39$	−8170.46	+	14151.6i	−0.860171	+	1.48986i
$40$		0			0
$41$	6676.64			0.620295			0.310147	−	0.950688i	$-0.399622\pi$
$41$	6676.64			0.620295			0.310147	+	0.950688i	$0.399622\pi$
$42$		0			0
$43$	22926.7			1.89091			0.945455	−	0.325754i	$-0.105618\pi$
$43$	22926.7			1.89091			0.945455	+	0.325754i	$0.105618\pi$
$44$		0			0
$45$	3166.59	−	5484.70i	0.233110	−	0.403758i
$46$		0			0
$47$	−12056.0	−	20881.6i	−0.796085	−	1.37886i	−0.922148	−	0.386837i	$-0.873568\pi$
$47$	−12056.0	−	20881.6i	−0.796085	−	1.37886i	0.126064	−	0.992022i	$-0.459766\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−6226.99	−	10785.5i	−0.335238	−	0.580649i
$52$		0			0
$53$	4121.48	−	7138.61i	0.201541	−	0.349079i	−0.747484	−	0.664280i	$-0.768738\pi$
$53$	4121.48	−	7138.61i	0.201541	−	0.349079i	0.949025	+	0.315200i	$0.102072\pi$
$54$		0			0
$55$	−1177.74			−0.0524981
$56$		0			0
$57$	−3015.94			−0.122952
$58$		0			0
$59$	−18067.1	+	31293.2i	−0.675709	+	1.17036i	0.300553	+	0.953765i	$0.402829\pi$
$59$	−18067.1	+	31293.2i	−0.675709	+	1.17036i	−0.976261	+	0.216596i	$0.930504\pi$
$60$		0			0
$61$	−7827.42	−	13557.5i	−0.269336	−	0.466504i	0.699355	−	0.714775i	$-0.253471\pi$
$61$	−7827.42	−	13557.5i	−0.269336	−	0.466504i	−0.968691	+	0.248271i	$0.920138\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	6927.61	+	11999.0i	0.203376	+	0.352258i
$66$		0			0
$67$	−14685.9	+	25436.7i	−0.399680	+	0.692267i	−0.993686	−	0.112194i	$-0.964212\pi$
$67$	−14685.9	+	25436.7i	−0.399680	+	0.692267i	0.594006	+	0.804461i	$0.297546\pi$
$68$		0			0
$69$	53634.1			1.35618
$70$		0			0
$71$	−9025.02			−0.212472			−0.106236	−	0.994341i	$-0.533880\pi$
$71$	−9025.02			−0.212472			−0.106236	+	0.994341i	$0.533880\pi$
$72$		0			0
$73$	−2217.71	+	3841.19i	−0.0487077	+	0.0843642i	−0.889351	−	0.457224i	$-0.848844\pi$
$73$	−2217.71	+	3841.19i	−0.0487077	+	0.0843642i	0.840644	+	0.541589i	$0.182177\pi$
$74$		0			0
$75$	32190.5	+	55755.6i	0.660807	+	1.14455i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−4100.81	−	7102.81i	−0.0739268	−	0.128045i	0.826692	−	0.562654i	$-0.190220\pi$
$79$	−4100.81	−	7102.81i	−0.0739268	−	0.128045i	−0.900619	+	0.434609i	$0.856886\pi$
$80$		0			0
$81$	18002.4	−	31181.1i	0.304872	−	0.528054i
$82$		0			0
$83$	−54575.9			−0.869572			−0.434786	−	0.900534i	$-0.643176\pi$
$83$	−54575.9			−0.869572			−0.434786	+	0.900534i	$0.643176\pi$
$84$		0			0
$85$	−10559.5			−0.158525
$86$		0			0
$87$	−102089.	+	176824.i	−1.44604	+	2.50462i
$88$		0			0
$89$	43466.9	+	75286.9i	0.581680	+	1.00750i	0.995280	+	0.0970406i	$0.0309377\pi$
$89$	43466.9	+	75286.9i	0.581680	+	1.00750i	−0.413601	+	0.910458i	$0.635729\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	121647.	+	210699.i	1.45846	+	2.52613i
$94$		0			0
$95$	−1278.58	+	2214.57i	−0.0145352	+	0.0251757i
$96$		0			0
$97$	157783.			1.70268			0.851338	−	0.524617i	$-0.175792\pi$
$97$	157783.			1.70268			0.851338	+	0.524617i	$0.175792\pi$
$98$		0			0
$99$	18562.4			0.190347
$100$		0			0
$101$	−38890.9	+	67361.1i	−0.379354	+	0.657061i	−0.990968	−	0.134095i	$-0.957187\pi$
$101$	−38890.9	+	67361.1i	−0.379354	+	0.657061i	0.611614	+	0.791156i	$0.290521\pi$
$102$		0			0
$103$	−53503.2	−	92670.2i	−0.496920	−	0.860690i	0.503074	−	0.864243i	$-0.332202\pi$
$103$	−53503.2	−	92670.2i	−0.496920	−	0.860690i	−0.999994	+	0.00355302i	$0.998869\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	80198.2	+	138907.i	0.677182	+	1.17291i	0.975826	+	0.218549i	$0.0701323\pi$
$107$	80198.2	+	138907.i	0.677182	+	1.17291i	−0.298644	+	0.954365i	$0.596534\pi$
$108$		0			0
$109$	−40088.3	+	69435.0i	−0.323185	+	0.559773i	−0.981143	−	0.193281i	$-0.938087\pi$
$109$	−40088.3	+	69435.0i	−0.323185	+	0.559773i	0.657958	+	0.753055i	$0.271420\pi$
$110$		0			0
$111$	−111663.			−0.860206
$112$		0			0
$113$	−99679.0			−0.734358			−0.367179	−	0.930150i	$-0.619676\pi$
$113$	−99679.0			−0.734358			−0.367179	+	0.930150i	$0.619676\pi$
$114$		0			0
$115$	22737.8	−	39383.0i	0.160326	−	0.277693i
$116$		0			0
$117$	−109186.	−	189116.i	−0.737399	−	1.27721i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	78799.5	+	136485.i	0.489283	+	0.847463i
$122$		0			0
$123$	−78924.2	+	136701.i	−0.470378	+	0.814719i
$124$		0			0
$125$	117230.			0.671065
$126$		0			0
$127$	−120594.			−0.663463			−0.331732	−	0.943374i	$-0.607633\pi$
$127$	−120594.			−0.663463			−0.331732	+	0.943374i	$0.607633\pi$
$128$		0			0
$129$	−271015.	+	469412.i	−1.43390	+	2.48359i
$130$		0			0
$131$	25113.9	+	43498.5i	0.127860	+	0.221460i	0.922847	−	0.385166i	$-0.125856\pi$
$131$	25113.9	+	43498.5i	0.127860	+	0.221460i	−0.794987	+	0.606626i	$0.792522\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	17283.4	+	29935.8i	0.0816197	+	0.141370i
$136$		0			0
$137$	104113.	−	180329.i	0.473917	−	0.820849i	−0.525637	−	0.850709i	$-0.676173\pi$
$137$	104113.	−	180329.i	0.473917	−	0.820849i	0.999554	+	0.0298603i	$0.00950626\pi$
$138$		0			0
$139$	215032.			0.943988			0.471994	−	0.881602i	$-0.343534\pi$
$139$	215032.			0.943988			0.471994	+	0.881602i	$0.343534\pi$
$140$		0			0
$141$	570054.			2.41473
$142$		0			0
$143$	−20304.6	+	35168.7i	−0.0830338	+	0.143819i
$144$		0			0
$145$	86559.9	+	149926.i	0.341898	+	0.592185i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−191763.	−	332143.i	−0.707618	−	1.22563i	−0.965738	−	0.259518i	$-0.916436\pi$
$149$	−191763.	−	332143.i	−0.707618	−	1.22563i	0.258120	−	0.966113i	$-0.416897\pi$
$150$		0			0
$151$	−205459.	+	355866.i	−0.733302	+	1.27012i	0.222162	+	0.975010i	$0.428689\pi$
$151$	−205459.	+	355866.i	−0.733302	+	1.27012i	−0.955464	+	0.295107i	$0.904645\pi$
$152$		0			0
$153$	166429.			0.574778
$154$		0			0
$155$	206286.			0.689668
$156$		0			0
$157$	164855.	−	285538.i	0.533769	−	0.924515i	−0.465453	−	0.885073i	$-0.654108\pi$
$157$	164855.	−	285538.i	0.533769	−	0.924515i	0.999222	−	0.0394426i	$-0.0125582\pi$
$158$		0			0
$159$	97439.6	+	168770.i	0.305663	+	0.529424i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	190916.	+	330676.i	0.562824	+	0.974840i	0.997248	+	0.0741318i	$0.0236185\pi$
$163$	190916.	+	330676.i	0.562824	+	0.974840i	−0.434424	+	0.900708i	$0.643048\pi$
$164$		0			0
$165$	13922.0	−	24113.6i	0.0398100	−	0.0689530i
$166$		0			0
$167$	195870.			0.543471			0.271735	−	0.962372i	$-0.412402\pi$
$167$	195870.			0.543471			0.271735	+	0.962372i	$0.412402\pi$
$168$		0			0
$169$	106443.			0.286683
$170$		0			0
$171$	20151.8	−	34903.9i	0.0527015	−	0.0912816i
$172$		0			0
$173$	−265993.	−	460714.i	−0.675703	−	1.17035i	−0.976263	−	0.216588i	$-0.930507\pi$
$173$	−265993.	−	460714.i	−0.675703	−	1.17035i	0.300560	−	0.953763i	$-0.402826\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−427141.	−	739830.i	−1.02480	−	1.77500i
$178$		0			0
$179$	187306.	−	324423.i	0.436937	−	0.756796i	−0.560515	−	0.828144i	$-0.689397\pi$
$179$	187306.	−	324423.i	0.436937	−	0.756796i	0.997451	+	0.0713479i	$0.0227301\pi$
$180$		0			0
$181$	148562.			0.337063			0.168532	−	0.985696i	$-0.446097\pi$
$181$	148562.			0.337063			0.168532	+	0.985696i	$0.446097\pi$
$182$		0			0
$183$	370110.			0.816965
$184$		0			0
$185$	−47338.8	+	81993.1i	−0.101692	+	0.176136i
$186$		0			0
$187$	−15474.9	−	26803.3i	−0.0323611	−	0.0560510i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	308445.	+	534243.i	0.611779	+	1.05963i	0.990940	+	0.134302i	$0.0428792\pi$
$191$	308445.	+	534243.i	0.611779	+	1.05963i	−0.379161	+	0.925331i	$0.623788\pi$
$192$		0			0
$193$	−34975.5	+	60579.3i	−0.0675882	+	0.117066i	−0.897839	−	0.440324i	$-0.854864\pi$
$193$	−34975.5	+	60579.3i	−0.0675882	+	0.117066i	0.830251	+	0.557390i	$0.188197\pi$
$194$		0			0
$195$	−327563.			−0.616892
$196$		0			0
$197$	440150.			0.808045			0.404022	−	0.914749i	$-0.367612\pi$
$197$	440150.			0.808045			0.404022	+	0.914749i	$0.367612\pi$
$198$		0			0
$199$	175205.	−	303463.i	0.313627	−	0.543217i	−0.665518	−	0.746382i	$-0.731789\pi$
$199$	175205.	−	303463.i	0.313627	−	0.543217i	0.979145	+	0.203165i	$0.0651227\pi$
$200$		0			0
$201$	−347202.	−	601371.i	−0.606166	−	1.04991i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	66918.6	+	115906.i	0.111215	+	0.192630i
$206$		0			0
$207$	−358370.	+	620715.i	−0.581308	+	1.00685i
$208$		0			0
$209$	−7494.99			−0.0118688
$210$		0			0
$211$	−637860.			−0.986323			−0.493161	−	0.869938i	$-0.664159\pi$
$211$	−637860.			−0.986323			−0.493161	+	0.869938i	$0.664159\pi$
$212$		0			0
$213$	106684.	−	184783.i	0.161121	−	0.279069i
$214$		0			0
$215$	229790.	+	398008.i	0.339027	+	0.587213i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−52430.8	−	90812.9i	−0.0738714	−	0.127949i
$220$		0			0
$221$	−182050.	+	315320.i	−0.250732	+	0.434280i
$222$		0			0
$223$	−56418.4			−0.0759729			−0.0379864	−	0.999278i	$-0.512094\pi$
$223$	−56418.4			−0.0759729			−0.0379864	+	0.999278i	$0.512094\pi$
$224$		0			0
$225$	−860356.			−1.13298
$226$		0			0
$227$	146749.	−	254177.i	0.189022	−	0.327395i	−0.755903	−	0.654684i	$-0.772802\pi$
$227$	146749.	−	254177.i	0.189022	−	0.327395i	0.944924	+	0.327289i	$0.106135\pi$
$228$		0			0
$229$	−310287.	−	537433.i	−0.390998	−	0.677229i	0.601583	−	0.798810i	$-0.294537\pi$
$229$	−310287.	−	537433.i	−0.390998	−	0.677229i	−0.992581	+	0.121581i	$0.961203\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	362161.	+	627282.i	0.437031	+	0.756960i	0.997459	−	0.0712431i	$-0.0226966\pi$
$233$	362161.	+	627282.i	0.437031	+	0.756960i	−0.560428	+	0.828203i	$0.689363\pi$
$234$		0			0
$235$	241670.	−	418585.i	0.285465	−	0.494440i
$236$		0			0
$237$	193902.			0.224239
$238$		0			0
$239$	−272208.			−0.308252			−0.154126	−	0.988051i	$-0.549256\pi$
$239$	−272208.			−0.308252			−0.154126	+	0.988051i	$0.549256\pi$
$240$		0			0
$241$	−425007.	+	736134.i	−0.471361	+	0.816421i	−0.999463	−	0.0327596i	$-0.989570\pi$
$241$	−425007.	+	736134.i	−0.471361	+	0.816421i	0.528102	+	0.849181i	$0.322904\pi$
$242$		0			0
$243$	635127.	+	1.10007e6i	0.689993	+	1.19510i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	44086.4	+	76359.8i	0.0459793	+	0.0796384i
$248$		0			0
$249$	645138.	−	1.11741e6i	0.659409	−	1.14213i
$250$		0			0
$251$	−1.62295e6			−1.62601			−0.813003	−	0.582260i	$-0.802169\pi$
$251$	−1.62295e6			−1.62601			−0.813003	+	0.582260i	$0.802169\pi$
$252$		0			0
$253$	133288.			0.130915
$254$		0			0
$255$	124824.	−	216201.i	0.120212	−	0.208213i
$256$		0			0
$257$	649381.	+	1.12476e6i	0.613292	+	1.06225i	0.990682	+	0.136198i	$0.0434883\pi$
$257$	649381.	+	1.12476e6i	0.613292	+	1.06225i	−0.377390	+	0.926054i	$0.623178\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−1.36427e6	−	2.36299e6i	−1.23965	−	2.14714i
$262$		0			0
$263$	794069.	−	1.37537e6i	0.707895	−	1.22611i	−0.257742	−	0.966214i	$-0.582978\pi$
$263$	794069.	−	1.37537e6i	0.707895	−	1.22611i	0.965637	−	0.259896i	$-0.0836884\pi$
$264$		0			0
$265$	165235.			0.144540
$266$		0			0
$267$	−2.05528e6			−1.76438
$268$		0			0
$269$	425303.	−	736646.i	0.358358	−	0.620695i	−0.629328	−	0.777139i	$-0.716670\pi$
$269$	425303.	−	736646.i	0.358358	−	0.620695i	0.987687	+	0.156445i	$0.0500033\pi$
$270$		0			0
$271$	879810.	+	1.52388e6i	0.727722	+	1.26045i	0.957844	+	0.287290i	$0.0927544\pi$
$271$	879810.	+	1.52388e6i	0.727722	+	1.26045i	−0.230121	+	0.973162i	$0.573912\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	79997.5	+	138560.i	0.0637888	+	0.110486i
$276$		0			0
$277$	872894.	−	1.51190e6i	0.683537	−	1.18392i	−0.290357	−	0.956918i	$-0.593774\pi$
$277$	872894.	−	1.51190e6i	0.683537	−	1.18392i	0.973894	−	0.227003i	$-0.0728926\pi$
$278$		0			0
$279$	−3.25127e6			−2.50059
$280$		0			0
$281$	−2.07171e6			−1.56518			−0.782588	−	0.622541i	$-0.786101\pi$
$281$	−2.07171e6			−1.56518			−0.782588	+	0.622541i	$0.786101\pi$
$282$		0			0
$283$	157468.	−	272742.i	0.116876	−	0.202436i	−0.801652	−	0.597791i	$-0.796045\pi$
$283$	157468.	−	272742.i	0.116876	−	0.202436i	0.918528	+	0.395355i	$0.129379\pi$
$284$		0			0
$285$	−30228.1	−	52356.7i	−0.0220444	−	0.0381821i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	571182.	+	989316.i	0.402281	+	0.696772i
$290$		0			0
$291$	−1.86515e6	+	3.23053e6i	−1.29116	+	2.23636i
$292$		0			0
$293$	2.07017e6			1.40876			0.704381	−	0.709822i	$-0.251225\pi$
$293$	2.07017e6			1.40876			0.704381	+	0.709822i	$0.251225\pi$
$294$		0			0
$295$	−724334.			−0.484600
$296$		0			0
$297$	−50657.2	+	87740.9i	−0.0333235	+	0.0577180i
$298$		0			0
$299$	−784013.	−	1.35795e6i	−0.507160	−	0.878427i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−919455.	−	1.59254e6i	−0.575339	−	0.996517i
$304$		0			0
$305$	156905.	−	271768.i	0.0965803	−	0.167282i
$306$		0			0
$307$	1.16092e6			0.703000			0.351500	−	0.936188i	$-0.385672\pi$
$307$	1.16092e6			0.703000			0.351500	+	0.936188i	$0.385672\pi$
$308$		0			0
$309$	2.52983e6			1.50728
$310$		0			0
$311$	331687.	−	574499.i	0.194459	−	0.336813i	−0.752264	−	0.658862i	$-0.771038\pi$
$311$	331687.	−	574499.i	0.194459	−	0.336813i	0.946723	+	0.322049i	$0.104372\pi$
$312$		0			0
$313$	−310346.	−	537535.i	−0.179054	−	0.310131i	0.762502	−	0.646985i	$-0.223971\pi$
$313$	−310346.	−	537535.i	−0.179054	−	0.310131i	−0.941557	+	0.336854i	$0.890637\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−911696.	−	1.57910e6i	−0.509568	−	0.882597i	−0.999939	−	0.0110832i	$-0.996472\pi$
$317$	−911696.	−	1.57910e6i	−0.509568	−	0.882597i	0.490371	−	0.871514i	$-0.336861\pi$
$318$		0			0
$319$	−253705.	+	439430.i	−0.139589	+	0.241776i
$320$		0			0
$321$	−3.79207e6			−2.05407
$322$		0			0
$323$	−67199.5			−0.0358393
$324$		0			0
$325$	941108.	−	1.63005e6i	0.494232	−	0.856036i
$326$		0			0
$327$	−947764.	−	1.64157e6i	−0.490152	−	0.848968i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−670564.	−	1.16145e6i	−0.336411	−	0.582681i	0.647344	−	0.762198i	$-0.275880\pi$
$331$	−670564.	−	1.16145e6i	−0.336411	−	0.582681i	−0.983755	+	0.179517i	$0.942546\pi$
$332$		0			0
$333$	746106.	−	1.29229e6i	0.368714	−	0.638632i
$334$		0			0
$335$	−588774.			−0.286640
$336$		0			0
$337$	320075.			0.153524			0.0767621	−	0.997049i	$-0.475542\pi$
$337$	320075.			0.153524			0.0767621	+	0.997049i	$0.475542\pi$
$338$		0			0
$339$	1.17830e6	−	2.04088e6i	0.556874	−	0.964533i
$340$		0			0
$341$	302309.	+	523615.i	0.140788	+	0.243852i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	537564.	+	931088.i	0.243155	+	0.421156i
$346$		0			0
$347$	−348783.	+	604110.i	−0.155500	+	0.269335i	−0.933241	−	0.359251i	$-0.883032\pi$
$347$	−348783.	+	604110.i	−0.155500	+	0.269335i	0.777741	+	0.628585i	$0.216366\pi$
$348$		0			0
$349$	2.08445e6			0.916068			0.458034	−	0.888935i	$-0.348554\pi$
$349$	2.08445e6			0.916068			0.458034	+	0.888935i	$0.348554\pi$
$350$		0			0
$351$	1.19189e6			0.516377
$352$		0			0
$353$	1.56859e6	−	2.71688e6i	0.669998	−	1.16047i	−0.307906	−	0.951417i	$-0.599628\pi$
$353$	1.56859e6	−	2.71688e6i	0.669998	−	1.16047i	0.977904	−	0.209054i	$-0.0670385\pi$
$354$		0			0
$355$	−90456.0	−	156674.i	−0.0380949	−	0.0659823i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	902646.	+	1.56343e6i	0.369642	+	0.640239i	0.989510	−	0.144468i	$-0.0461470\pi$
$359$	902646.	+	1.56343e6i	0.369642	+	0.640239i	−0.619867	+	0.784707i	$0.712814\pi$
$360$		0			0
$361$	1.22991e6	−	2.13027e6i	0.496714	−	0.860334i
$362$		0			0
$363$	−3.72594e6			−1.48412
$364$		0			0
$365$	−88910.6			−0.0349318
$366$		0			0
$367$	790678.	−	1.36949e6i	0.306432	−	0.530756i	−0.671147	−	0.741324i	$-0.734198\pi$
$367$	790678.	−	1.36949e6i	0.306432	−	0.530756i	0.977579	+	0.210568i	$0.0675314\pi$
$368$		0			0
$369$	−1.05470e6	−	1.82680e6i	−0.403241	−	0.698434i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−850482.	−	1.47308e6i	−0.316514	−	0.548219i	0.663244	−	0.748403i	$-0.269179\pi$
$373$	−850482.	−	1.47308e6i	−0.316514	−	0.548219i	−0.979758	+	0.200185i	$0.935846\pi$
$374$		0			0
$375$	−1.38577e6	+	2.40023e6i	−0.508878	+	0.881402i
$376$		0			0
$377$	5.96928e6			2.16306
$378$		0			0
$379$	4.93679e6			1.76541			0.882707	−	0.469923i	$-0.155718\pi$
$379$	4.93679e6			1.76541			0.882707	+	0.469923i	$0.155718\pi$
$380$		0			0
$381$	1.42554e6	−	2.46910e6i	0.503113	−	0.871418i
$382$		0			0
$383$	224225.	+	388369.i	0.0781065	+	0.135284i	0.902433	−	0.430830i	$-0.141779\pi$
$383$	224225.	+	388369.i	0.0781065	+	0.135284i	−0.824326	+	0.566115i	$0.808446\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−3.62172e6	−	6.27300e6i	−1.22924	−	2.12911i
$388$		0			0
$389$	−122538.	+	212242.i	−0.0410579	+	0.0711143i	−0.885824	−	0.464021i	$-0.846406\pi$
$389$	−122538.	+	212242.i	−0.0410579	+	0.0711143i	0.844766	+	0.535136i	$0.179739\pi$
$390$		0			0
$391$	1.19505e6			0.395315
$392$		0			0
$393$	−1.18748e6			−0.387833
$394$		0			0
$395$	82203.2	−	142380.i	0.0265092	−	0.0459152i
$396$		0			0
$397$	1.53370e6	+	2.65645e6i	0.488387	+	0.845911i	0.999911	−	0.0133582i	$-0.00425218\pi$
$397$	1.53370e6	+	2.65645e6i	0.488387	+	0.845911i	−0.511524	+	0.859269i	$0.670919\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	2.25843e6	+	3.91172e6i	0.701368	+	1.21480i	0.967986	+	0.251002i	$0.0807602\pi$
$401$	2.25843e6	+	3.91172e6i	0.701368	+	1.21480i	−0.266619	+	0.963802i	$0.585906\pi$
$402$		0			0
$403$	3.55643e6	−	6.15992e6i	1.09082	−	1.88935i
$404$		0			0
$405$	721738.			0.218646
$406$		0			0
$407$	−277497.			−0.0830372
$408$		0			0
$409$	−2.54149e6	+	4.40199e6i	−0.751243	+	1.30119i	0.195978	+	0.980608i	$0.437212\pi$
$409$	−2.54149e6	+	4.40199e6i	−0.751243	+	1.30119i	−0.947221	+	0.320582i	$0.896121\pi$
$410$		0			0
$411$	2.46142e6	+	4.26331e6i	0.718756	+	1.24492i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−547003.	−	947438.i	−0.155908	−	0.270041i
$416$		0			0
$417$	−2.54188e6	+	4.40267e6i	−0.715839	+	1.23987i
$418$		0			0
$419$	−2.14263e6			−0.596227			−0.298114	−	0.954530i	$-0.596357\pi$
$419$	−2.14263e6			−0.596227			−0.298114	+	0.954530i	$0.596357\pi$
$420$		0			0
$421$	3.63121e6			0.998497			0.499248	−	0.866459i	$-0.333609\pi$
$421$	3.63121e6			0.998497			0.499248	+	0.866459i	$0.333609\pi$
$422$		0			0
$423$	−3.80896e6	+	6.59732e6i	−1.03504	+	1.79274i
$424$		0			0
$425$	717251.	+	1.24232e6i	0.192619	+	0.333626i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−480040.	−	831454.i	−0.125931	−	0.218120i
$430$		0			0
$431$	−979639.	+	1.69678e6i	−0.254023	+	0.439981i	−0.964630	−	0.263609i	$-0.915087\pi$
$431$	−979639.	+	1.69678e6i	−0.254023	+	0.439981i	0.710607	+	0.703589i	$0.248421\pi$
$432$		0			0
$433$	−2.49301e6			−0.639005			−0.319502	−	0.947585i	$-0.603516\pi$
$433$	−2.49301e6			−0.639005			−0.319502	+	0.947585i	$0.603516\pi$
$434$		0			0
$435$	−4.09288e6			−1.03706
$436$		0			0
$437$	144700.	−	250628.i	0.0362465	−	0.0627807i
$438$		0			0
$439$	−2.01049e6	−	3.48227e6i	−0.497898	−	0.862384i	0.502099	−	0.864810i	$-0.332561\pi$
$439$	−2.01049e6	−	3.48227e6i	−0.497898	−	0.862384i	−0.999997	+	0.00242560i	$0.999228\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	2.23277e6	+	3.86727e6i	0.540548	+	0.936257i	0.998873	+	0.0474721i	$0.0151165\pi$
$443$	2.23277e6	+	3.86727e6i	0.540548	+	0.936257i	−0.458324	+	0.888785i	$0.651550\pi$
$444$		0			0
$445$	−871321.	+	1.50917e6i	−0.208583	+	0.361276i
$446$		0			0
$447$	9.06727e6			2.14639
$448$		0			0
$449$	−3.68564e6			−0.862774			−0.431387	−	0.902167i	$-0.641976\pi$
$449$	−3.68564e6			−0.862774			−0.431387	+	0.902167i	$0.641976\pi$
$450$		0			0
$451$	−196137.	+	339719.i	−0.0454064	+	0.0786463i
$452$		0			0
$453$	−4.85744e6	−	8.41333e6i	−1.11215	−	1.92629i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	1.06717e6	+	1.84840e6i	0.239025	+	0.414004i	0.960435	−	0.278505i	$-0.0898387\pi$
$457$	1.06717e6	+	1.84840e6i	0.239025	+	0.414004i	−0.721409	+	0.692509i	$0.756505\pi$
$458$		0			0
$459$	−454189.	+	786678.i	−0.100625	+	0.174287i
$460$		0			0
$461$	−3.11136e6			−0.681865			−0.340932	−	0.940088i	$-0.610743\pi$
$461$	−3.11136e6			−0.681865			−0.340932	+	0.940088i	$0.610743\pi$
$462$		0			0
$463$	−4.03151e6			−0.874009			−0.437004	−	0.899459i	$-0.643961\pi$
$463$	−4.03151e6			−0.874009			−0.437004	+	0.899459i	$0.643961\pi$
$464$		0			0
$465$	−2.43849e6	+	4.22359e6i	−0.522985	+	0.905836i
$466$		0			0
$467$	−232500.	−	402701.i	−0.0493322	−	0.0854458i	0.840305	−	0.542114i	$-0.182376\pi$
$467$	−232500.	−	402701.i	−0.0493322	−	0.0854458i	−0.889637	+	0.456668i	$0.849043\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	3.89749e6	+	6.75065e6i	0.809529	+	1.40215i
$472$		0			0
$473$	−673508.	+	1.16655e6i	−0.138417	+	0.239746i
$474$		0			0
$475$	347389.			0.0706450
$476$		0			0
$477$	−2.60427e6			−0.524071
$478$		0			0
$479$	−1.94096e6	+	3.36184e6i	−0.386525	+	0.669481i	−0.991980	−	0.126399i	$-0.959658\pi$
$479$	−1.94096e6	+	3.36184e6i	−0.386525	+	0.669481i	0.605454	+	0.795880i	$0.292991\pi$
$480$		0			0
$481$	1.63227e6	+	2.82717e6i	0.321684	+	0.557173i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	1.58143e6	+	2.73912e6i	0.305279	+	0.528758i
$486$		0			0
$487$	1.88615e6	−	3.26691e6i	0.360375	−	0.624187i	−0.627648	−	0.778498i	$-0.715982\pi$
$487$	1.88615e6	−	3.26691e6i	0.360375	−	0.624187i	0.988022	+	0.154310i	$0.0493155\pi$
$488$		0			0
$489$	−9.02722e6			−1.70719
$490$		0			0
$491$	3.97153e6			0.743455			0.371727	−	0.928342i	$-0.378766\pi$
$491$	3.97153e6			0.743455			0.371727	+	0.928342i	$0.378766\pi$
$492$		0			0
$493$	−2.27470e6	+	3.93989e6i	−0.421509	+	0.730074i
$494$		0			0
$495$	186047.	+	322243.i	0.0341279	+	0.0591113i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	4.65183e6	+	8.05721e6i	0.836320	+	1.44855i	0.892951	+	0.450154i	$0.148631\pi$
$499$	4.65183e6	+	8.05721e6i	0.836320	+	1.44855i	−0.0566309	+	0.998395i	$0.518036\pi$
$500$		0			0
$501$	−2.31536e6	+	4.01033e6i	−0.412121	+	0.713815i
$502$		0			0
$503$	2.66706e6			0.470016			0.235008	−	0.971993i	$-0.424488\pi$
$503$	2.66706e6			0.470016			0.235008	+	0.971993i	$0.424488\pi$
$504$		0			0
$505$	−1.55918e6			−0.272063
$506$		0			0
$507$	−1.25826e6	+	2.17937e6i	−0.217396	+	0.376541i
$508$		0			0
$509$	2.96997e6	+	5.14414e6i	0.508110	+	0.880072i	0.999956	+	0.00939004i	$0.00298899\pi$
$509$	2.96997e6	+	5.14414e6i	0.508110	+	0.880072i	−0.491846	+	0.870682i	$0.663678\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	109989.	+	190507.i	0.0184526	+	0.0319608i
$514$		0			0
$515$	1.07250e6	−	1.85763e6i	0.178189	−	0.308632i
$516$		0			0
$517$	1.41666e6			0.233098
$518$		0			0
$519$	1.25772e7			2.04958
$520$		0			0
$521$	−3.24712e6	+	5.62417e6i	−0.524087	+	0.907745i	0.475520	+	0.879705i	$0.342260\pi$
$521$	−3.24712e6	+	5.62417e6i	−0.524087	+	0.907745i	−0.999607	+	0.0280404i	$0.991073\pi$
$522$		0			0
$523$	−2.63401e6	−	4.56225e6i	−0.421079	−	0.729331i	0.574966	−	0.818177i	$-0.305015\pi$
$523$	−2.63401e6	−	4.56225e6i	−0.421079	−	0.729331i	−0.996045	+	0.0888467i	$0.971682\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	2.71048e6	+	4.69469e6i	0.425128	+	0.736343i
$528$		0			0
$529$	644886.	−	1.11697e6i	0.100194	−	0.173542i
$530$		0			0
$531$	1.14162e7			1.75706
$532$		0			0
$533$	4.61479e6			0.703613
$534$		0			0
$535$	−1.60762e6	+	2.78448e6i	−0.242828	+	0.420591i
$536$		0			0
$537$	4.42826e6	+	7.66997e6i	0.662670	+	1.14778i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	1.97097e6	+	3.41382e6i	0.289526	+	0.501473i	0.973697	−	0.227848i	$-0.0731691\pi$
$541$	1.97097e6	+	3.41382e6i	0.289526	+	0.501473i	−0.684171	+	0.729322i	$0.739836\pi$
$542$		0			0
$543$	−1.75614e6	+	3.04173e6i	−0.255600	+	0.442712i
$544$		0			0
$545$	−1.60719e6			−0.231780
$546$		0			0
$547$	−1.04260e7			−1.48987			−0.744934	−	0.667138i	$-0.767519\pi$
$547$	−1.04260e7			−1.48987			−0.744934	+	0.667138i	$0.767519\pi$
$548$		0			0
$549$	−2.47299e6	+	4.28334e6i	−0.350180	+	0.606529i
$550$		0			0
$551$	550856.	+	954110.i	0.0772963	+	0.133881i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−1.11918e6	−	1.93847e6i	−0.154229	−	0.267133i
$556$		0			0
$557$	−4.55443e6	+	7.88851e6i	−0.622008	+	1.07735i	0.367103	+	0.930180i	$0.380350\pi$
$557$	−4.55443e6	+	7.88851e6i	−0.622008	+	1.07735i	−0.989111	+	0.147170i	$0.952984\pi$
$558$		0			0
$559$	1.58466e7			2.14490
$560$		0			0
$561$	731710.			0.0981594
$562$		0			0
$563$	4.76306e6	−	8.24986e6i	0.633308	−	1.09692i	−0.353563	−	0.935411i	$-0.615030\pi$
$563$	4.76306e6	−	8.24986e6i	0.633308	−	1.09692i	0.986871	−	0.161511i	$-0.0516366\pi$
$564$		0			0
$565$	−999063.	−	1.73043e6i	−0.131665	−	0.228051i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−6.34557e6	−	1.09909e7i	−0.821656	−	1.42315i	−0.904448	−	0.426584i	$-0.859717\pi$
$569$	−6.34557e6	−	1.09909e7i	−0.821656	−	1.42315i	0.0827916	−	0.996567i	$-0.473616\pi$
$570$		0			0
$571$	2.00433e6	−	3.47160e6i	0.257264	−	0.445594i	−0.708244	−	0.705968i	$-0.750512\pi$
$571$	2.00433e6	−	3.47160e6i	0.257264	−	0.445594i	0.965508	+	0.260373i	$0.0838457\pi$
$572$		0			0
$573$	−1.45845e7			−1.85568
$574$		0			0
$575$	−6.17781e6			−0.779228
$576$		0			0
$577$	721529.	−	1.24973e6i	0.0902224	−	0.156270i	−0.817382	−	0.576096i	$-0.804576\pi$
$577$	721529.	−	1.24973e6i	0.0902224	−	0.156270i	0.907605	+	0.419826i	$0.137909\pi$
$578$		0			0
$579$	−826887.	−	1.43221e6i	−0.102506	−	0.177546i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	242150.	+	419416.i	0.0295062	+	0.0511062i
$584$		0			0
$585$	2.18870e6	−	3.79094e6i	0.264421	−	0.457991i
$586$		0			0
$587$	3.38345e6			0.405289			0.202645	−	0.979252i	$-0.435046\pi$
$587$	3.38345e6			0.405289			0.202645	+	0.979252i	$0.435046\pi$
$588$		0			0
$589$	1.31278e6			0.155920
$590$		0			0
$591$	−5.20299e6	+	9.01185e6i	−0.612752	+	1.06132i
$592$		0			0
$593$	−2.47333e6	−	4.28394e6i	−0.288832	−	0.500272i	0.684699	−	0.728826i	$-0.259934\pi$
$593$	−2.47333e6	−	4.28394e6i	−0.288832	−	0.500272i	−0.973531	+	0.228554i	$0.926600\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	4.14217e6	+	7.17444e6i	0.475655	+	0.823858i
$598$		0			0
$599$	6.48207e6	−	1.12273e7i	0.738153	−	1.27852i	−0.215173	−	0.976576i	$-0.569031\pi$
$599$	6.48207e6	−	1.12273e7i	0.738153	−	1.27852i	0.953326	−	0.301943i	$-0.0976353\pi$
$600$		0			0
$601$	1.52347e7			1.72047			0.860235	−	0.509897i	$-0.170317\pi$
$601$	1.52347e7			1.72047			0.860235	+	0.509897i	$0.170317\pi$
$602$		0			0
$603$	9.27967e6			1.03930
$604$		0			0
$605$	−1.57958e6	+	2.73592e6i	−0.175450	+	0.303889i
$606$		0			0
$607$	−3.25303e6	−	5.63441e6i	−0.358357	−	0.620693i	0.629329	−	0.777139i	$-0.283330\pi$
$607$	−3.25303e6	−	5.63441e6i	−0.358357	−	0.620693i	−0.987687	+	0.156446i	$0.949996\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−8.33294e6	−	1.44331e7i	−0.903015	−	1.56407i
$612$		0			0
$613$	−3.64137e6	+	6.30704e6i	−0.391394	+	0.677914i	−0.992634	−	0.121155i	$-0.961340\pi$
$613$	−3.64137e6	+	6.30704e6i	−0.391394	+	0.677914i	0.601240	+	0.799068i	$0.294674\pi$
$614$		0			0
$615$	−3.16416e6			−0.337343
$616$		0			0
$617$	1.34924e7			1.42684			0.713422	−	0.700734i	$-0.247144\pi$
$617$	1.34924e7			1.42684			0.713422	+	0.700734i	$0.247144\pi$
$618$		0			0
$619$	3.52824e6	−	6.11109e6i	0.370111	−	0.641051i	−0.619472	−	0.785019i	$-0.712653\pi$
$619$	3.52824e6	−	6.11109e6i	0.370111	−	0.641051i	0.989582	+	0.143969i	$0.0459864\pi$
$620$		0			0
$621$	−1.95600e6	−	3.38790e6i	−0.203536	−	0.352534i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−3.07998e6	−	5.33469e6i	−0.315390	−	0.546272i
$626$		0			0
$627$	88597.9	−	153456.i	0.00900025	−	0.0155889i
$628$		0			0
$629$	−2.48802e6			−0.250742
$630$		0			0
$631$	1.46502e7			1.46477			0.732384	−	0.680891i	$-0.238407\pi$
$631$	1.46502e7			1.46477			0.732384	+	0.680891i	$0.238407\pi$
$632$		0			0
$633$	7.54010e6	−	1.30598e7i	0.747942	−	1.29547i
$634$		0			0
$635$	−1.20869e6	−	2.09351e6i	−0.118955	−	0.206035i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	1.42568e6	+	2.46935e6i	0.138124	+	0.239238i
$640$		0			0
$641$	−9.95195e6	+	1.72373e7i	−0.956673	+	1.65701i	−0.226179	+	0.974086i	$0.572623\pi$
$641$	−9.95195e6	+	1.72373e7i	−0.956673	+	1.65701i	−0.730493	+	0.682920i	$0.760710\pi$
$642$		0			0
$643$	−5.52786e6			−0.527266			−0.263633	−	0.964623i	$-0.584921\pi$
$643$	−5.52786e6			−0.527266			−0.263633	+	0.964623i	$0.584921\pi$
$644$		0			0
$645$	−1.08653e7			−1.02836
$646$		0			0
$647$	907539.	−	1.57190e6i	0.0852323	−	0.147627i	−0.820258	−	0.571994i	$-0.806170\pi$
$647$	907539.	−	1.57190e6i	0.0852323	−	0.147627i	0.905490	+	0.424367i	$0.139503\pi$
$648$		0			0
$649$	−1.06150e6	−	1.83857e6i	−0.0989256	−	0.171344i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	7.96257e6	+	1.37916e7i	0.730753	+	1.26570i	0.956562	+	0.291529i	$0.0941641\pi$
$653$	7.96257e6	+	1.37916e7i	0.730753	+	1.26570i	−0.225809	+	0.974172i	$0.572503\pi$
$654$		0			0
$655$	−503423.	+	871954.i	−0.0458490	+	0.0794128i
$656$		0			0
$657$	1.40132e6			0.126656
$658$		0			0
$659$	38652.4			0.00346707			0.00173353	−	0.999998i	$-0.499448\pi$
$659$	38652.4			0.00346707			0.00173353	+	0.999998i	$0.499448\pi$
$660$		0			0
$661$	7.62719e6	−	1.32107e7i	0.678986	−	1.17604i	−0.296300	−	0.955095i	$-0.595753\pi$
$661$	7.62719e6	−	1.32107e7i	0.678986	−	1.17604i	0.975287	−	0.220944i	$-0.0709137\pi$
$662$		0			0
$663$	−4.30400e6	−	7.45475e6i	−0.380267	−	0.658642i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−9.79618e6	−	1.69675e7i	−0.852594	−	1.47674i
$668$		0			0
$669$	666918.	−	1.15514e6i	0.0576113	−	0.0997856i
$670$		0			0
$671$	919771.			0.0788631
$672$		0			0
$673$	2.71207e6			0.230815			0.115407	−	0.993318i	$-0.463183\pi$
$673$	2.71207e6			0.230815			0.115407	+	0.993318i	$0.463183\pi$
$674$		0			0
$675$	2.34793e6	−	4.06674e6i	0.198347	−	0.343548i
$676$		0			0
$677$	6.36003e6	+	1.10159e7i	0.533319	+	0.923736i	0.999243	+	0.0389113i	$0.0123890\pi$
$677$	6.36003e6	+	1.10159e7i	0.533319	+	0.923736i	−0.465923	+	0.884825i	$0.654278\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	3.46943e6	+	6.00923e6i	0.286676	+	0.496537i
$682$		0			0
$683$	2.45454e6	−	4.25139e6i	0.201335	−	0.348722i	−0.747624	−	0.664122i	$-0.768805\pi$
$683$	2.45454e6	−	4.25139e6i	0.201335	−	0.348722i	0.948959	+	0.315400i	$0.102139\pi$
$684$		0			0
$685$	4.17401e6			0.339881
$686$		0			0
$687$	1.46715e7			1.18600
$688$		0			0
$689$	2.84871e6	−	4.93410e6i	0.228612	−	0.395968i
$690$		0			0
$691$	−3.79933e6	−	6.58063e6i	−0.302699	−	0.524291i	0.674047	−	0.738688i	$-0.264554\pi$
$691$	−3.79933e6	−	6.58063e6i	−0.302699	−	0.524291i	−0.976746	+	0.214398i	$0.931221\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	2.15523e6	+	3.73296e6i	0.169251	+	0.293151i
$696$		0			0
$697$	−1.75855e6	+	3.04589e6i	−0.137111	+	0.237483i
$698$		0			0
$699$	−1.71244e7			−1.32563
$700$		0			0
$701$	−3.72699e6			−0.286460			−0.143230	−	0.989689i	$-0.545749\pi$
$701$	−3.72699e6			−0.286460			−0.143230	+	0.989689i	$0.545749\pi$
$702$		0			0
$703$	−301258.	+	521793.i	−0.0229906	+	0.0398208i
$704$		0			0
$705$	5.71354e6	+	9.89614e6i	0.432945	+	0.749882i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−47116.3	−	81607.9i	−0.00352011	−	0.00609701i	0.864260	−	0.503045i	$-0.167787\pi$
$709$	−47116.3	−	81607.9i	−0.00352011	−	0.00609701i	−0.867780	+	0.496948i	$0.834454\pi$
$710$		0			0
$711$	−1.29560e6	+	2.24405e6i	−0.0961166	+	0.166479i
$712$		0			0
$713$	−2.33458e7			−1.71983
$714$		0			0
$715$	−814037.			−0.0595497
$716$		0			0
$717$	3.21775e6	−	5.57331e6i	0.233751	−	0.404869i
$718$		0			0
$719$	7.61953e6	+	1.31974e7i	0.549675	+	0.952065i	0.998297	+	0.0583433i	$0.0185818\pi$
$719$	7.61953e6	+	1.31974e7i	0.549675	+	0.952065i	−0.448622	+	0.893722i	$0.648085\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−1.00480e7	−	1.74036e7i	−0.714879	−	1.23821i
$724$		0			0
$725$	1.17591e7	−	2.03673e7i	0.830860	−	1.43909i
$726$		0			0
$727$	−3.09483e6			−0.217171			−0.108585	−	0.994087i	$-0.534632\pi$
$727$	−3.09483e6			−0.217171			−0.108585	+	0.994087i	$0.534632\pi$
$728$		0			0
$729$	−2.12820e7			−1.48318
$730$		0			0
$731$	−6.03862e6	+	1.04592e7i	−0.417969	+	0.723944i
$732$		0			0
$733$	−3.05582e6	−	5.29284e6i	−0.210072	−	0.363856i	0.741665	−	0.670771i	$-0.234037\pi$
$733$	−3.05582e6	−	5.29284e6i	−0.210072	−	0.363856i	−0.951737	+	0.306915i	$0.900703\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−862841.	−	1.49448e6i	−0.0585143	−	0.101350i
$738$		0			0
$739$	1.83910e6	−	3.18542e6i	0.123878	−	0.214563i	−0.797416	−	0.603430i	$-0.793800\pi$
$739$	1.83910e6	−	3.18542e6i	0.123878	−	0.214563i	0.921294	+	0.388867i	$0.127133\pi$
$740$		0			0
$741$	−2.08457e6			−0.139467
$742$		0			0
$743$	−2.68224e7			−1.78249			−0.891243	−	0.453526i	$-0.850166\pi$
$743$	−2.68224e7			−1.78249			−0.891243	+	0.453526i	$0.850166\pi$
$744$		0			0
$745$	3.84400e6	−	6.65801e6i	0.253742	−	0.439495i
$746$		0			0
$747$	8.62132e6	+	1.49326e7i	0.565291	+	0.979113i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−7.88734e6	−	1.36613e7i	−0.510306	−	0.883876i	−0.999929	−	0.0119415i	$-0.996199\pi$
$751$	−7.88734e6	−	1.36613e7i	−0.510306	−	0.883876i	0.489623	−	0.871934i	$-0.337135\pi$
$752$		0			0
$753$	1.91848e7	−	3.32291e7i	1.23302	−	2.13566i
$754$		0			0
$755$	−8.23710e6			−0.525905
$756$		0			0
$757$	−2.33178e7			−1.47893			−0.739466	−	0.673194i	$-0.764922\pi$
$757$	−2.33178e7			−1.47893			−0.739466	+	0.673194i	$0.764922\pi$
$758$		0			0
$759$	−1.57559e6	+	2.72900e6i	−0.0992745	+	0.171948i
$760$		0			0
$761$	−2.92286e6	−	5.06253e6i	−0.182956	−	0.316888i	0.759930	−	0.650005i	$-0.225233\pi$
$761$	−2.92286e6	−	5.06253e6i	−0.182956	−	0.316888i	−0.942886	+	0.333116i	$0.891900\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	1.66808e6	+	2.88921e6i	0.103054	+	0.178495i
$766$		0			0
$767$	−1.24877e7	+	2.16294e7i	−0.766470	+	1.32757i
$768$		0			0
$769$	1.79261e7			1.09313			0.546563	−	0.837418i	$-0.315936\pi$
$769$	1.79261e7			1.09313			0.546563	+	0.837418i	$0.315936\pi$
$770$		0			0
$771$	−3.07052e7			−1.86027
$772$		0			0
$773$	−1.07768e7	+	1.86659e7i	−0.648694	+	1.12357i	0.334741	+	0.942310i	$0.391351\pi$
$773$	−1.07768e7	+	1.86659e7i	−0.648694	+	1.12357i	−0.983435	+	0.181261i	$0.941982\pi$
$774$		0			0
$775$	−1.40119e7	−	2.42692e7i	−0.837995	−	1.45145i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	425861.	+	737613.i	0.0251434	+	0.0435497i
$780$		0			0
$781$	265124.	−	459209.i	0.0155533	−	0.0269391i
$782$		0			0
$783$	1.48925e7			0.868088
$784$		0			0
$785$	6.60924e6			0.382805
$786$		0			0
$787$	1.28444e6	−	2.22472e6i	0.0739228	−	0.128038i	−0.826695	−	0.562651i	$-0.809781\pi$
$787$	1.28444e6	−	2.22472e6i	0.0739228	−	0.128038i	0.900617	+	0.434613i	$0.143115\pi$
$788$		0			0
$789$	1.87733e7	+	3.25163e7i	1.07361	+	1.85955i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−5.41020e6	−	9.37074e6i	−0.305513	−	0.529165i
$794$		0			0
$795$	−1.95324e6	+	3.38310e6i	−0.109607	+	0.189844i
$796$		0			0
$797$	−2.63767e7			−1.47087			−0.735437	−	0.677593i	$-0.763023\pi$
$797$	−2.63767e7			−1.47087			−0.735437	+	0.677593i	$0.763023\pi$
$798$		0			0
$799$	1.27016e7			0.703871
$800$		0			0
$801$	1.37329e7	−	2.37861e7i	0.756277	−	1.30991i
$802$		0			0
$803$	−130297.	−	225682.i	−0.00713094	−	0.0123512i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	1.00550e7	+	1.74157e7i	0.543496	+	0.941363i
$808$		0			0
$809$	−1.14428e7	+	1.98195e7i	−0.614696	+	1.06468i	0.375742	+	0.926724i	$0.377388\pi$
$809$	−1.14428e7	+	1.98195e7i	−0.614696	+	1.06468i	−0.990438	+	0.137960i	$0.955945\pi$
$810$		0			0
$811$	−1.52953e6			−0.0816592			−0.0408296	−	0.999166i	$-0.513000\pi$
$811$	−1.52953e6			−0.0816592			−0.0408296	+	0.999166i	$0.513000\pi$
$812$		0			0
$813$	−4.16007e7			−2.20737
$814$		0			0
$815$	−3.82702e6	+	6.62860e6i	−0.201821	+	0.349565i
$816$		0			0
$817$	1.46235e6	+	2.53287e6i	0.0766473	+	0.132757i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−7.93743e6	−	1.37480e7i	−0.410982	−	0.711841i	0.584016	−	0.811742i	$-0.301481\pi$
$821$	−7.93743e6	−	1.37480e7i	−0.410982	−	0.711841i	−0.994997	+	0.0999014i	$0.968147\pi$
$822$		0			0
$823$	1.55476e7	−	2.69292e7i	0.800136	−	1.38588i	−0.119391	−	0.992847i	$-0.538094\pi$
$823$	1.55476e7	−	2.69292e7i	0.800136	−	1.38588i	0.919526	−	0.393028i	$-0.128573\pi$
$824$		0			0
$825$	−3.78258e6			−0.193488
$826$		0			0
$827$	−4.81422e6			−0.244772			−0.122386	−	0.992483i	$-0.539055\pi$
$827$	−4.81422e6			−0.244772			−0.122386	+	0.992483i	$0.539055\pi$
$828$		0			0
$829$	−1.27178e7	+	2.20278e7i	−0.642724	+	1.11323i	0.342099	+	0.939664i	$0.388862\pi$
$829$	−1.27178e7	+	2.20278e7i	−0.642724	+	1.11323i	−0.984822	+	0.173566i	$0.944471\pi$
$830$		0			0
$831$	2.06369e7	+	3.57441e7i	1.03667	+	1.79557i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	1.96316e6	+	3.40030e6i	0.0974407	+	0.168772i
$836$		0			0
$837$	8.87280e6	−	1.53681e7i	0.437771	−	0.758242i
$838$		0			0
$839$	−2.74688e7			−1.34721			−0.673605	−	0.739091i	$-0.735255\pi$
$839$	−2.74688e7			−1.34721			−0.673605	+	0.739091i	$0.735255\pi$
$840$		0			0
$841$	5.40745e7			2.63635
$842$		0			0
$843$	2.44896e7	−	4.24172e7i	1.18689	−	2.05576i
$844$		0			0
$845$	1.06686e6	+	1.84786e6i	0.0514004	+	0.0890281i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	3.72284e6	+	6.44815e6i	0.177258	+	0.307019i
$850$		0			0
$851$	5.35743e6	−	9.27935e6i	0.253590	−	0.439231i
$852$		0			0
$853$	5.98613e6			0.281691			0.140846	−	0.990032i	$-0.455018\pi$
$853$	5.98613e6			0.281691			0.140846	+	0.990032i	$0.455018\pi$
$854$		0			0
$855$	807909.			0.0377961
$856$		0			0
$857$	6.52973e6	−	1.13098e7i	0.303699	−	0.526022i	−0.673272	−	0.739395i	$-0.735112\pi$
$857$	6.52973e6	−	1.13098e7i	0.303699	−	0.526022i	0.976971	+	0.213373i	$0.0684450\pi$
$858$		0			0
$859$	−3.75674e6	−	6.50687e6i	−0.173712	−	0.300877i	0.766003	−	0.642837i	$-0.222243\pi$
$859$	−3.75674e6	−	6.50687e6i	−0.173712	−	0.300877i	−0.939715	+	0.341960i	$0.888909\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	417499.	+	723130.i	0.0190822	+	0.0330514i	0.875409	−	0.483383i	$-0.160592\pi$
$863$	417499.	+	723130.i	0.0190822	+	0.0330514i	−0.856327	+	0.516435i	$0.827259\pi$
$864$		0			0
$865$	5.33200e6	−	9.23529e6i	0.242298	−	0.419672i
$866$		0			0
$867$	−2.70076e7			−1.22022
$868$		0			0
$869$	481871.			0.0216462
$870$		0			0
$871$	−1.01507e7	+	1.75814e7i	−0.453366	+	0.785252i
$872$		0			0
$873$	−2.49250e7	−	4.31713e7i	−1.10688	−	1.91716i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−6.78393e6	−	1.17501e7i	−0.297840	−	0.515873i	0.677802	−	0.735245i	$-0.262933\pi$
$877$	−6.78393e6	−	1.17501e7i	−0.297840	−	0.515873i	−0.975641	+	0.219371i	$0.929599\pi$
$878$		0			0
$879$	−2.44714e7	+	4.23857e7i	−1.06828	+	1.85032i
$880$		0			0
$881$	1.02028e7			0.442873			0.221436	−	0.975175i	$-0.428926\pi$
$881$	1.02028e7			0.442873			0.221436	+	0.975175i	$0.428926\pi$
$882$		0			0
$883$	−2.57631e7			−1.11198			−0.555989	−	0.831190i	$-0.687660\pi$
$883$	−2.57631e7			−1.11198			−0.555989	+	0.831190i	$0.687660\pi$
$884$		0			0
$885$	8.56231e6	−	1.48303e7i	0.367479	−	0.636492i
$886$		0			0
$887$	−8.55282e6	−	1.48139e7i	−0.365006	−	0.632209i	0.623771	−	0.781607i	$-0.285600\pi$
$887$	−8.55282e6	−	1.48139e7i	−0.365006	−	0.632209i	−0.988777	+	0.149398i	$0.952266\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	1.05770e6	+	1.83199e6i	0.0446342	+	0.0773086i
$892$		0			0
$893$	1.53796e6	−	2.66382e6i	0.0645380	−	0.111783i
$894$		0			0
$895$	7.50931e6			0.313359
$896$		0			0
$897$	3.70711e7			1.53835
$898$		0			0
$899$	4.44373e7	−	7.69677e7i	1.83379	−	3.17621i
$900$		0			0
$901$	2.17110e6	+	3.76045e6i	0.0890979	+	0.154322i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1.48901e6	+	2.57904e6i	0.0604332	+	0.104673i
$906$		0			0
$907$	1.20645e6	−	2.08963e6i	0.0486958	−	0.0843435i	−0.840650	−	0.541579i	$-0.817827\pi$
$907$	1.20645e6	−	2.08963e6i	0.0486958	−	0.0843435i	0.889346	+	0.457235i	$0.151160\pi$
$908$		0			0
$909$	2.45743e7			0.986442
$910$		0			0
$911$	2.36633e7			0.944668			0.472334	−	0.881420i	$-0.343412\pi$
$911$	2.36633e7			0.944668			0.472334	+	0.881420i	$0.343412\pi$
$912$		0			0
$913$	1.60325e6	−	2.77691e6i	0.0636539	−	0.110252i
$914$		0			0
$915$	3.70954e6	+	6.42511e6i	0.146476	+	0.253704i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−1.81079e6	−	3.13639e6i	−0.0707262	−	0.122501i	0.828494	−	0.559999i	$-0.189198\pi$
$919$	−1.81079e6	−	3.13639e6i	−0.0707262	−	0.122501i	−0.899220	+	0.437497i	$0.855865\pi$
$920$		0			0
$921$	−1.37231e7	+	2.37692e7i	−0.533095	+	0.923347i
$922$		0			0
$923$	−6.23796e6			−0.241012
$924$		0			0
$925$	1.28618e7			0.494252
$926$		0			0
$927$	−1.69037e7	+	2.92781e7i	−0.646075	+	1.11903i
$928$		0			0
$929$	−1.60670e7	−	2.78289e7i	−0.610796	−	1.05793i	−0.991107	−	0.133070i	$-0.957516\pi$
$929$	−1.60670e7	−	2.78289e7i	−0.610796	−	1.05793i	0.380311	−	0.924859i	$-0.375817\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	7.84172e6	+	1.35822e7i	0.294922	+	0.510820i
$934$		0			0
$935$	310203.	−	537288.i	0.0116043	−	0.0200992i
$936$		0			0
$937$	−1.50936e7			−0.561621			−0.280811	−	0.959763i	$-0.590603\pi$
$937$	−1.50936e7			−0.561621			−0.280811	+	0.959763i	$0.590603\pi$
$938$		0			0
$939$	1.46743e7			0.543118
$940$		0			0
$941$	−1.94317e7	+	3.36567e7i	−0.715379	+	1.23907i	0.247434	+	0.968905i	$0.420413\pi$
$941$	−1.94317e7	+	3.36567e7i	−0.715379	+	1.23907i	−0.962813	+	0.270169i	$0.912921\pi$
$942$		0			0
$943$	−7.57333e6	−	1.31174e7i	−0.277337	−	0.480362i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−9.71303e6	−	1.68235e7i	−0.351949	−	0.609593i	0.634642	−	0.772806i	$-0.281148\pi$
$947$	−9.71303e6	−	1.68235e7i	−0.351949	−	0.609593i	−0.986591	+	0.163213i	$0.947814\pi$
$948$		0			0
$949$	−1.53285e6	+	2.65497e6i	−0.0552501	+	0.0956960i
$950$		0			0
$951$	4.31084e7			1.54565
$952$		0			0
$953$	−3.32921e7			−1.18743			−0.593717	−	0.804674i	$-0.702340\pi$
$953$	−3.32921e7			−1.18743			−0.593717	+	0.804674i	$0.702340\pi$
$954$		0			0
$955$	−6.18297e6	+	1.07092e7i	−0.219376	+	0.379970i
$956$		0			0
$957$	−5.99806e6	−	1.03889e7i	−0.211705	−	0.366684i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−3.86360e7	−	6.69194e7i	−1.34953	−	2.33746i
$962$		0			0
$963$	2.53377e7	−	4.38862e7i	0.880445	−	1.52497i
$964$		0			0
$965$	−1.40221e6			−0.0484724
$966$		0			0
$967$	1.99707e7			0.686796			0.343398	−	0.939190i	$-0.388422\pi$
$967$	1.99707e7			0.686796			0.343398	+	0.939190i	$0.388422\pi$
$968$		0			0
$969$	794362.	−	1.37587e6i	0.0271775	−	0.0470727i
$970$		0			0
$971$	2.46369e7	+	4.26723e7i	0.838567	+	1.45244i	0.891093	+	0.453820i	$0.149939\pi$
$971$	2.46369e7	+	4.26723e7i	0.838567	+	1.45244i	−0.0525266	+	0.998620i	$0.516727\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	2.22496e7	+	3.85374e7i	0.749566	+	1.29829i
$976$		0			0
$977$	−2.37696e7	+	4.11702e7i	−0.796684	+	1.37990i	0.125081	+	0.992147i	$0.460081\pi$
$977$	−2.37696e7	+	4.11702e7i	−0.796684	+	1.37990i	−0.921765	+	0.387750i	$0.873252\pi$
$978$		0			0
$979$	−5.10764e6			−0.170319
$980$		0			0
$981$	2.53309e7			0.840385
$982$		0			0
$983$	−9.14729e6	+	1.58436e7i	−0.301932	+	0.522961i	−0.976573	−	0.215184i	$-0.930965\pi$
$983$	−9.14729e6	+	1.58436e7i	−0.301932	+	0.522961i	0.674642	+	0.738145i	$0.264298\pi$
$984$		0			0
$985$	4.41154e6	+	7.64101e6i	0.144877	+	0.250934i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−2.60058e7	−	4.50434e7i	−0.845435	−	1.46434i
$990$		0			0
$991$	−2.80880e6	+	4.86498e6i	−0.0908524	+	0.157361i	−0.907870	−	0.419252i	$-0.862292\pi$
$991$	−2.80880e6	+	4.86498e6i	−0.0908524	+	0.157361i	0.817018	+	0.576613i	$0.195626\pi$
$992$		0			0
$993$	3.17068e7			1.02042
$994$		0			0
$995$	7.02416e6			0.224925
$996$		0			0
$997$	−9.85754e6	+	1.70738e7i	−0.314073	+	0.543990i	−0.979240	−	0.202704i	$-0.935027\pi$
$997$	−9.85754e6	+	1.70738e7i	−0.314073	+	0.543990i	0.665167	+	0.746695i	$0.268360\pi$
$998$		0			0
$999$	4.07229e6	+	7.05341e6i	0.129099	+	0.223607i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.6.i.o.361.1		10
7.2	even	3	inner	392.6.i.o.177.1		10
7.3	odd	6		392.6.a.k.1.1		5
7.4	even	3		392.6.a.j.1.5		5
7.5	odd	6		56.6.i.b.9.5	✓	10
7.6	odd	2		56.6.i.b.25.5	yes	10
21.5	even	6		504.6.s.b.289.3		10
21.20	even	2		504.6.s.b.361.3		10
28.3	even	6		784.6.a.bk.1.5		5
28.11	odd	6		784.6.a.bl.1.1		5
28.19	even	6		112.6.i.f.65.1		10
28.27	even	2		112.6.i.f.81.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.6.i.b.9.5	✓	10	7.5	odd	6
56.6.i.b.25.5	yes	10	7.6	odd	2
112.6.i.f.65.1		10	28.19	even	6
112.6.i.f.81.1		10	28.27	even	2
392.6.a.j.1.5		5	7.4	even	3
392.6.a.k.1.1		5	7.3	odd	6
392.6.i.o.177.1		10	7.2	even	3	inner
392.6.i.o.361.1		10	1.1	even	1	trivial
504.6.s.b.289.3		10	21.5	even	6
504.6.s.b.361.3		10	21.20	even	2
784.6.a.bk.1.5		5	28.3	even	6
784.6.a.bl.1.1		5	28.11	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)

\(f(q)\)	\(=\)	\(q+(-11.8209 + 20.4745i) q^{3} +(10.0228 + 17.3600i) q^{5} +(-157.969 - 273.611i) q^{9} +(-29.3766 + 50.8817i) q^{11} +691.185 q^{13} -473.916 q^{15} +(-263.388 + 456.202i) q^{17} +(63.7838 + 110.477i) q^{19} +(-1134.30 - 1964.67i) q^{23} +(1361.59 - 2358.34i) q^{25} +1724.41 q^{27} +8636.30 q^{29} +(5145.41 - 8912.12i) q^{31} +(-694.517 - 1202.94i) q^{33} +(2361.55 + 4090.33i) q^{37} +(-8170.46 + 14151.6i) q^{39} +6676.64 q^{41} +22926.7 q^{43} +(3166.59 - 5484.70i) q^{45} +(-12056.0 - 20881.6i) q^{47} +(-6226.99 - 10785.5i) q^{51} +(4121.48 - 7138.61i) q^{53} -1177.74 q^{55} -3015.94 q^{57} +(-18067.1 + 31293.2i) q^{59} +(-7827.42 - 13557.5i) q^{61} +(6927.61 + 11999.0i) q^{65} +(-14685.9 + 25436.7i) q^{67} +53634.1 q^{69} -9025.02 q^{71} +(-2217.71 + 3841.19i) q^{73} +(32190.5 + 55755.6i) q^{75} +(-4100.81 - 7102.81i) q^{79} +(18002.4 - 31181.1i) q^{81} -54575.9 q^{83} -10559.5 q^{85} +(-102089. + 176824. i) q^{87} +(43466.9 + 75286.9i) q^{89} +(121647. + 210699. i) q^{93} +(-1278.58 + 2214.57i) q^{95} +157783. q^{97} +18562.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 5 q^{3} - 81 q^{5} - 390 q^{9} - 361 q^{11} + 684 q^{13} - 2098 q^{15} - 1809 q^{17} - 1277 q^{19} - 911 q^{23} - 3940 q^{25} - 9502 q^{27} + 10884 q^{29} - 2187 q^{31} + 5553 q^{33} + 8181 q^{37}+ \cdots + 499596 q^{99}+O(q^{100}) \) 10 * q + 5 * q^3 - 81 * q^5 - 390 * q^9 - 361 * q^11 + 684 * q^13 - 2098 * q^15 - 1809 * q^17 - 1277 * q^19 - 911 * q^23 - 3940 * q^25 - 9502 * q^27 + 10884 * q^29 - 2187 * q^31 + 5553 * q^33 + 8181 * q^37 + 3422 * q^39 + 33156 * q^41 + 12664 * q^43 - 41310 * q^45 - 16101 * q^47 + 67865 * q^51 - 16047 * q^53 + 91258 * q^55 + 44694 * q^57 - 71027 * q^59 - 31093 * q^61 + 64370 * q^65 - 47981 * q^67 + 274498 * q^69 + 45024 * q^71 - 123333 * q^73 + 45460 * q^75 + 212481 * q^79 - 52917 * q^81 + 174920 * q^83 + 444282 * q^85 - 318070 * q^87 - 129045 * q^89 + 252835 * q^93 - 300417 * q^95 + 656548 * q^97 + 499596 * q^99

Introduction

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