LMFDB - Embedded newform 392.6.i.q.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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 638 x^{10} - 2656 x^{9} + 153618 x^{8} + 1282848 x^{7} - 13837748 x^{6} - 207709824 x^{5} + \cdots + 219426904900 $ x^12 - 638x^10 - 2656x^9 + 153618x^8 + 1282848x^7 - 13837748x^6 - 207709824x^5 - 203803319x^4 + 10050168544x^3 + 71643260322x^2 + 203689025120x + 219426904900
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{8}\cdot 7^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.2
Root			$-10.2798 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	392.361
Dual form			392.6.i.q.177.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-8.18310 + 14.1736i) q^{3} +(-25.5066 - 44.1787i) q^{5} +(-12.4264 - 21.5232i) q^{9} +(136.714 - 236.796i) q^{11} -369.233 q^{13} +834.891 q^{15} +(518.115 - 897.401i) q^{17} +(1091.92 + 1891.27i) q^{19} +(506.952 + 878.067i) q^{23} +(261.331 - 452.639i) q^{25} -3570.24 q^{27} -212.806 q^{29} +(-114.856 + 198.936i) q^{31} +(2237.49 + 3875.45i) q^{33} +(4559.37 + 7897.06i) q^{37} +(3021.47 - 5233.34i) q^{39} -16772.9 q^{41} +16121.9 q^{43} +(-633.909 + 1097.96i) q^{45} +(-562.734 - 974.683i) q^{47} +(8479.58 + 14687.1i) q^{51} +(-17082.1 + 29587.0i) q^{53} -13948.4 q^{55} -35741.3 q^{57} +(-5595.60 + 9691.86i) q^{59} +(-17996.6 - 31171.0i) q^{61} +(9417.86 + 16312.2i) q^{65} +(28759.3 - 49812.5i) q^{67} -16593.8 q^{69} -20951.5 q^{71} +(-28213.5 + 48867.2i) q^{73} +(4277.00 + 7407.98i) q^{75} +(-24080.5 - 41708.7i) q^{79} +(32235.3 - 55833.2i) q^{81} -64392.7 q^{83} -52861.3 q^{85} +(1741.41 - 3016.21i) q^{87} +(-31248.1 - 54123.3i) q^{89} +(-1879.76 - 3255.83i) q^{93} +(55702.4 - 96479.4i) q^{95} +35202.8 q^{97} -6795.46 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 122 q^{9} - 248 q^{11} - 752 q^{15} + 2904 q^{23} - 1510 q^{25} - 816 q^{29} + 18648 q^{37} + 15240 q^{39} - 21168 q^{43} - 3016 q^{51} + 66772 q^{53} - 112528 q^{57} + 55316 q^{65} + 169632 q^{67}+ \cdots - 347024 q^{99}+O(q^{100}) $ 12 * q + 122 * q^9 - 248 * q^11 - 752 * q^15 + 2904 * q^23 - 1510 * q^25 - 816 * q^29 + 18648 * q^37 + 15240 * q^39 - 21168 * q^43 - 3016 * q^51 + 66772 * q^53 - 112528 * q^57 + 55316 * q^65 + 169632 * q^67 - 109760 * q^71 - 50576 * q^79 + 270194 * q^81 - 812152 * q^85 + 164944 * q^93 + 551912 * q^95 - 347024 * 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
$3$	−8.18310	+	14.1736i	−0.524946	+	0.909234i	0.474632	+	0.880185i	$0.342581\pi$
$3$	−8.18310	+	14.1736i	−0.524946	+	0.909234i	−0.999578	+	0.0290493i	$0.990752\pi$
$4$		0			0
$5$	−25.5066	−	44.1787i	−0.456275	−	0.790292i	0.542485	−	0.840065i	$-0.317483\pi$
$5$	−25.5066	−	44.1787i	−0.456275	−	0.790292i	−0.998761	+	0.0497735i	$0.984150\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−12.4264	−	21.5232i	−0.0511375	−	0.0885727i
$10$		0			0
$11$	136.714	−	236.796i	0.340668	−	0.590055i	−0.643889	−	0.765119i	$-0.722680\pi$
$11$	136.714	−	236.796i	0.340668	−	0.590055i	0.984557	+	0.175064i	$0.0560133\pi$
$12$		0			0
$13$	−369.233			−0.605957			−0.302979	−	0.952997i	$-0.597981\pi$
$13$	−369.233			−0.605957			−0.302979	+	0.952997i	$0.597981\pi$
$14$		0			0
$15$	834.891			0.958080
$16$		0			0
$17$	518.115	−	897.401i	0.434814	−	0.753120i	−0.562466	−	0.826820i	$-0.690147\pi$
$17$	518.115	−	897.401i	0.434814	−	0.753120i	0.997280	+	0.0737000i	$0.0234807\pi$
$18$		0			0
$19$	1091.92	+	1891.27i	0.693918	+	1.20190i	0.970544	+	0.240924i	$0.0774505\pi$
$19$	1091.92	+	1891.27i	0.693918	+	1.20190i	−0.276626	+	0.960978i	$0.589216\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	506.952	+	878.067i	0.199824	+	0.346105i	0.948471	−	0.316863i	$-0.102630\pi$
$23$	506.952	+	878.067i	0.199824	+	0.346105i	−0.748647	+	0.662968i	$0.769296\pi$
$24$		0			0
$25$	261.331	−	452.639i	0.0836260	−	0.144844i
$26$		0			0
$27$	−3570.24			−0.942515
$28$		0			0
$29$	−212.806			−0.0469881			−0.0234941	−	0.999724i	$-0.507479\pi$
$29$	−212.806			−0.0469881			−0.0234941	+	0.999724i	$0.507479\pi$
$30$		0			0
$31$	−114.856	+	198.936i	−0.0214659	+	0.0371800i	−0.876559	−	0.481295i	$-0.840167\pi$
$31$	−114.856	+	198.936i	−0.0214659	+	0.0371800i	0.855093	+	0.518475i	$0.173500\pi$
$32$		0			0
$33$	2237.49	+	3875.45i	0.357665	+	0.619495i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	4559.37	+	7897.06i	0.547521	+	0.948333i	0.998444	+	0.0557706i	$0.0177616\pi$
$37$	4559.37	+	7897.06i	0.547521	+	0.948333i	−0.450923	+	0.892563i	$0.648905\pi$
$38$		0			0
$39$	3021.47	−	5233.34i	0.318095	−	0.550957i
$40$		0			0
$41$	−16772.9			−1.55829			−0.779144	−	0.626845i	$-0.784346\pi$
$41$	−16772.9			−1.55829			−0.779144	+	0.626845i	$0.784346\pi$
$42$		0			0
$43$	16121.9			1.32968			0.664838	−	0.746987i	$-0.268500\pi$
$43$	16121.9			1.32968			0.664838	+	0.746987i	$0.268500\pi$
$44$		0			0
$45$	−633.909	+	1097.96i	−0.0466655	+	0.0808270i
$46$		0			0
$47$	−562.734	−	974.683i	−0.0371585	−	0.0643604i	0.846848	−	0.531835i	$-0.178497\pi$
$47$	−562.734	−	974.683i	−0.0371585	−	0.0643604i	−0.884007	+	0.467474i	$0.845164\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	8479.58	+	14687.1i	0.456508	+	0.790696i
$52$		0			0
$53$	−17082.1	+	29587.0i	−0.835315	+	1.44681i	0.0584585	+	0.998290i	$0.481381\pi$
$53$	−17082.1	+	29587.0i	−0.835315	+	1.44681i	−0.893774	+	0.448518i	$0.851952\pi$
$54$		0			0
$55$	−13948.4			−0.621754
$56$		0			0
$57$	−35741.3			−1.45708
$58$		0			0
$59$	−5595.60	+	9691.86i	−0.209275	+	0.362474i	−0.951486	−	0.307691i	$-0.900444\pi$
$59$	−5595.60	+	9691.86i	−0.209275	+	0.362474i	0.742212	+	0.670166i	$0.233777\pi$
$60$		0			0
$61$	−17996.6	−	31171.0i	−0.619248	−	1.07257i	−0.989623	−	0.143687i	$-0.954104\pi$
$61$	−17996.6	−	31171.0i	−0.619248	−	1.07257i	0.370375	−	0.928882i	$-0.379229\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	9417.86	+	16312.2i	0.276483	+	0.478883i
$66$		0			0
$67$	28759.3	−	49812.5i	0.782692	−	1.35566i	−0.147676	−	0.989036i	$-0.547179\pi$
$67$	28759.3	−	49812.5i	0.782692	−	1.35566i	0.930368	−	0.366627i	$-0.119488\pi$
$68$		0			0
$69$	−16593.8			−0.419587
$70$		0			0
$71$	−20951.5			−0.493253			−0.246627	−	0.969111i	$-0.579322\pi$
$71$	−20951.5			−0.493253			−0.246627	+	0.969111i	$0.579322\pi$
$72$		0			0
$73$	−28213.5	+	48867.2i	−0.619655	+	1.07327i	0.369894	+	0.929074i	$0.379394\pi$
$73$	−28213.5	+	48867.2i	−0.619655	+	1.07327i	−0.989549	+	0.144200i	$0.953939\pi$
$74$		0			0
$75$	4277.00	+	7407.98i	0.0877983	+	0.152071i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−24080.5	−	41708.7i	−0.434108	−	0.751898i	0.563114	−	0.826379i	$-0.309603\pi$
$79$	−24080.5	−	41708.7i	−0.434108	−	0.751898i	−0.997222	+	0.0744813i	$0.976270\pi$
$80$		0			0
$81$	32235.3	−	55833.2i	0.545907	−	0.945539i
$82$		0			0
$83$	−64392.7			−1.02599			−0.512993	−	0.858393i	$-0.671463\pi$
$83$	−64392.7			−1.02599			−0.512993	+	0.858393i	$0.671463\pi$
$84$		0			0
$85$	−52861.3			−0.793580
$86$		0			0
$87$	1741.41	−	3016.21i	0.0246662	−	0.0427232i
$88$		0			0
$89$	−31248.1	−	54123.3i	−0.418166	−	0.724285i	0.577589	−	0.816328i	$-0.303994\pi$
$89$	−31248.1	−	54123.3i	−0.418166	−	0.724285i	−0.995755	+	0.0920428i	$0.970660\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−1879.76	−	3255.83i	−0.0225369	−	0.0390350i
$94$		0			0
$95$	55702.4	−	96479.4i	0.633235	−	1.09680i
$96$		0			0
$97$	35202.8			0.379881			0.189941	−	0.981796i	$-0.439170\pi$
$97$	35202.8			0.379881			0.189941	+	0.981796i	$0.439170\pi$
$98$		0			0
$99$	−6795.46			−0.0696837
$100$		0			0
$101$	−41169.3	+	71307.3i	−0.401578	+	0.695554i	−0.993917	−	0.110135i	$-0.964872\pi$
$101$	−41169.3	+	71307.3i	−0.401578	+	0.695554i	0.592338	+	0.805689i	$0.298205\pi$
$102$		0			0
$103$	−49420.9	−	85599.6i	−0.459006	−	0.795021i	0.539903	−	0.841727i	$-0.318461\pi$
$103$	−49420.9	−	85599.6i	−0.459006	−	0.795021i	−0.998909	+	0.0467062i	$0.985128\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−108201.	−	187410.i	−0.913633	−	1.58246i	−0.808890	−	0.587960i	$-0.799931\pi$
$107$	−108201.	−	187410.i	−0.913633	−	1.58246i	−0.104743	−	0.994499i	$-0.533402\pi$
$108$		0			0
$109$	90929.2	−	157494.i	0.733056	−	1.26969i	−0.222515	−	0.974929i	$-0.571427\pi$
$109$	90929.2	−	157494.i	0.733056	−	1.26969i	0.955571	−	0.294761i	$-0.0952399\pi$
$110$		0			0
$111$	−149239.			−1.14968
$112$		0			0
$113$	−191197.			−1.40859			−0.704296	−	0.709907i	$-0.748737\pi$
$113$	−191197.			−1.40859			−0.704296	+	0.709907i	$0.748737\pi$
$114$		0			0
$115$	25861.2	−	44792.9i	0.182349	−	0.315838i
$116$		0			0
$117$	4588.24	+	7947.06i	0.0309871	+	0.0536712i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	43143.9	+	74727.5i	0.267890	+	0.463999i
$122$		0			0
$123$	137254.	−	237731.i	0.818018	−	1.41685i
$124$		0			0
$125$	−186079.			−1.06518
$126$		0			0
$127$	−136702.			−0.752083			−0.376041	−	0.926603i	$-0.622715\pi$
$127$	−136702.			−0.752083			−0.376041	+	0.926603i	$0.622715\pi$
$128$		0			0
$129$	−131927.	+	228505.i	−0.698009	+	1.20899i
$130$		0			0
$131$	−42710.8	−	73977.3i	−0.217450	−	0.376635i	0.736578	−	0.676353i	$-0.236441\pi$
$131$	−42710.8	−	73977.3i	−0.217450	−	0.376635i	−0.954028	+	0.299718i	$0.903107\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	91064.6	+	157729.i	0.430046	+	0.744862i
$136$		0			0
$137$	20639.6	−	35748.9i	0.0939508	−	0.162728i	−0.815219	−	0.579152i	$-0.803384\pi$
$137$	20639.6	−	35748.9i	0.0939508	−	0.162728i	0.909170	+	0.416425i	$0.136717\pi$
$138$		0			0
$139$	−245593.			−1.07815			−0.539075	−	0.842258i	$-0.681226\pi$
$139$	−245593.			−1.07815			−0.539075	+	0.842258i	$0.681226\pi$
$140$		0			0
$141$	18419.6			0.0780249
$142$		0			0
$143$	−50479.4	+	87432.8i	−0.206431	+	0.357548i
$144$		0			0
$145$	5427.94	+	9401.47i	0.0214395	+	0.0371343i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	163829.	+	283760.i	0.604539	+	1.04709i	0.992124	+	0.125259i	$0.0399761\pi$
$149$	163829.	+	283760.i	0.604539	+	1.04709i	−0.387585	+	0.921834i	$0.626691\pi$
$150$		0			0
$151$	−186335.	+	322742.i	−0.665047	+	1.15190i	0.314226	+	0.949348i	$0.398255\pi$
$151$	−186335.	+	322742.i	−0.665047	+	1.15190i	−0.979273	+	0.202547i	$0.935078\pi$
$152$		0			0
$153$	−25753.2			−0.0889412
$154$		0			0
$155$	11718.3			0.0391774
$156$		0			0
$157$	−105494.	+	182721.i	−0.341569	+	0.591616i	−0.984724	−	0.174120i	$-0.944292\pi$
$157$	−105494.	+	182721.i	−0.341569	+	0.591616i	0.643155	+	0.765736i	$0.277625\pi$
$158$		0			0
$159$	−279568.	−	484227.i	−0.876991	−	1.51899i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	96410.4	+	166988.i	0.284220	+	0.492284i	0.972420	−	0.233238i	$-0.0749320\pi$
$163$	96410.4	+	166988.i	0.284220	+	0.492284i	−0.688200	+	0.725521i	$0.741599\pi$
$164$		0			0
$165$	114141.	−	197699.i	0.326388	−	0.565320i
$166$		0			0
$167$	−507788.			−1.40893			−0.704467	−	0.709736i	$-0.748814\pi$
$167$	−507788.			−1.40893			−0.704467	+	0.709736i	$0.748814\pi$
$168$		0			0
$169$	−234960.			−0.632816
$170$		0			0
$171$	27137.4	−	47003.3i	0.0709704	−	0.122924i
$172$		0			0
$173$	281838.	+	488157.i	0.715951	+	1.24006i	0.962591	+	0.270957i	$0.0873402\pi$
$173$	281838.	+	488157.i	0.715951	+	1.24006i	−0.246640	+	0.969107i	$0.579327\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−91578.7	−	158619.i	−0.219716	−	0.380559i
$178$		0			0
$179$	−95157.5	+	164818.i	−0.221978	+	0.384478i	−0.955409	−	0.295287i	$-0.904585\pi$
$179$	−95157.5	+	164818.i	−0.221978	+	0.384478i	0.733430	+	0.679765i	$0.237918\pi$
$180$		0			0
$181$	−428708.			−0.972670			−0.486335	−	0.873772i	$-0.661667\pi$
$181$	−428708.			−0.972670			−0.486335	+	0.873772i	$0.661667\pi$
$182$		0			0
$183$	589071.			1.30029
$184$		0			0
$185$	232588.	−	402854.i	0.499640	−	0.865402i
$186$		0			0
$187$	−141667.	−	245375.i	−0.296255	−	0.513129i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	115837.	+	200636.i	0.229755	+	0.397947i	0.957735	−	0.287650i	$-0.0928741\pi$
$191$	115837.	+	200636.i	0.229755	+	0.397947i	−0.727980	+	0.685598i	$0.759541\pi$
$192$		0			0
$193$	210903.	−	365296.i	0.407559	−	0.705913i	−0.587057	−	0.809546i	$-0.699713\pi$
$193$	210903.	−	365296.i	0.407559	−	0.705913i	0.994616	+	0.103633i	$0.0330468\pi$
$194$		0			0
$195$	−308269.			−0.580555
$196$		0			0
$197$	−708516.			−1.30072			−0.650360	−	0.759626i	$-0.725382\pi$
$197$	−708516.			−1.30072			−0.650360	+	0.759626i	$0.725382\pi$
$198$		0			0
$199$	−321283.	+	556479.i	−0.575116	+	0.996130i	0.420913	+	0.907101i	$0.361710\pi$
$199$	−321283.	+	556479.i	−0.575116	+	0.996130i	−0.996029	+	0.0890289i	$0.971624\pi$
$200$		0			0
$201$	470681.	+	815243.i	0.821743	+	1.42330i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	427818.	+	741003.i	0.711008	+	1.23150i
$206$		0			0
$207$	12599.2	−	21822.4i	0.0204370	−	0.0353979i
$208$		0			0
$209$	597126.			0.945584
$210$		0			0
$211$	916183.			1.41669			0.708347	−	0.705864i	$-0.249441\pi$
$211$	916183.			1.41669			0.708347	+	0.705864i	$0.249441\pi$
$212$		0			0
$213$	171449.	−	296958.i	0.258931	−	0.448482i
$214$		0			0
$215$	−411215.	−	712245.i	−0.606698	−	1.05083i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−461748.	−	799771.i	−0.650571	−	1.12682i
$220$		0			0
$221$	−191305.	+	331350.i	−0.263479	+	0.456359i
$222$		0			0
$223$	965140.			1.29966			0.649828	−	0.760081i	$-0.274841\pi$
$223$	965140.			1.29966			0.649828	+	0.760081i	$0.274841\pi$
$224$		0			0
$225$	−12989.6			−0.0171057
$226$		0			0
$227$	446701.	−	773709.i	0.575377	−	0.996582i	−0.420624	−	0.907235i	$-0.638189\pi$
$227$	446701.	−	773709.i	0.575377	−	0.996582i	0.996001	−	0.0893469i	$-0.0284780\pi$
$228$		0			0
$229$	608766.	+	1.05441e6i	0.767117	+	1.32869i	0.939120	+	0.343589i	$0.111643\pi$
$229$	608766.	+	1.05441e6i	0.767117	+	1.32869i	−0.172003	+	0.985096i	$0.555024\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−622536.	−	1.07826e6i	−0.751234	−	1.30117i	−0.947225	−	0.320569i	$-0.896126\pi$
$233$	−622536.	−	1.07826e6i	−0.751234	−	1.30117i	0.195992	−	0.980606i	$-0.437207\pi$
$234$		0			0
$235$	−28706.8	+	49721.6i	−0.0339090	+	0.0587321i
$236$		0			0
$237$	788214.			0.911535
$238$		0			0
$239$	−223953.			−0.253607			−0.126803	−	0.991928i	$-0.540472\pi$
$239$	−223953.			−0.253607			−0.126803	+	0.991928i	$0.540472\pi$
$240$		0			0
$241$	−200762.	+	347729.i	−0.222658	+	0.385655i	−0.955614	−	0.294621i	$-0.904807\pi$
$241$	−200762.	+	347729.i	−0.222658	+	0.385655i	0.732956	+	0.680276i	$0.238140\pi$
$242$		0			0
$243$	93784.9	+	162440.i	0.101887	+	0.176473i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−403174.	−	698318.i	−0.420485	−	0.728301i
$248$		0			0
$249$	526932.	−	912674.i	0.538588	−	0.932862i
$250$		0			0
$251$	406156.			0.406920			0.203460	−	0.979083i	$-0.434781\pi$
$251$	406156.			0.406920			0.203460	+	0.979083i	$0.434781\pi$
$252$		0			0
$253$	277230.			0.272295
$254$		0			0
$255$	432570.	−	749232.i	0.416587	−	0.721549i
$256$		0			0
$257$	−415486.	−	719642.i	−0.392395	−	0.679648i	0.600370	−	0.799722i	$-0.295020\pi$
$257$	−415486.	−	719642.i	−0.392395	−	0.679648i	−0.992765	+	0.120075i	$0.961687\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	2644.41	+	4580.25i	0.00240285	+	0.00416186i
$262$		0			0
$263$	−829724.	+	1.43712e6i	−0.739681	+	1.28117i	0.212958	+	0.977061i	$0.431690\pi$
$263$	−829724.	+	1.43712e6i	−0.739681	+	1.28117i	−0.952639	+	0.304104i	$0.901643\pi$
$264$		0			0
$265$	1.74282e6			1.52453
$266$		0			0
$267$	1.02283e6			0.878059
$268$		0			0
$269$	−52758.3	+	91380.1i	−0.0444539	+	0.0769965i	−0.887396	−	0.461007i	$-0.847488\pi$
$269$	−52758.3	+	91380.1i	−0.0444539	+	0.0769965i	0.842942	+	0.538004i	$0.180821\pi$
$270$		0			0
$271$	−877475.	−	1.51983e6i	−0.725791	−	1.25711i	−0.958648	−	0.284596i	$-0.908141\pi$
$271$	−877475.	−	1.51983e6i	−0.725791	−	1.25711i	0.232857	−	0.972511i	$-0.425193\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−71455.4	−	123764.i	−0.0569775	−	0.0986879i
$276$		0			0
$277$	−1.07500e6	+	1.86196e6i	−0.841803	+	1.45805i	0.0465659	+	0.998915i	$0.485172\pi$
$277$	−1.07500e6	+	1.86196e6i	−0.841803	+	1.45805i	−0.888369	+	0.459130i	$0.848161\pi$
$278$		0			0
$279$	5708.98			0.00439084
$280$		0			0
$281$	−1.94418e6			−1.46883			−0.734415	−	0.678701i	$-0.762543\pi$
$281$	−1.94418e6			−1.46883			−0.734415	+	0.678701i	$0.762543\pi$
$282$		0			0
$283$	214228.	−	371055.i	0.159005	−	0.275405i	−0.775505	−	0.631341i	$-0.782505\pi$
$283$	214228.	−	371055.i	0.159005	−	0.275405i	0.934510	+	0.355936i	$0.115838\pi$
$284$		0			0
$285$	911638.	+	1.57900e6i	0.664829	+	1.15152i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	173043.	+	299719.i	0.121873	+	0.211091i
$290$		0			0
$291$	−288068.	+	498949.i	−0.199417	+	0.345401i
$292$		0			0
$293$	1.75383e6			1.19349			0.596746	−	0.802430i	$-0.296460\pi$
$293$	1.75383e6			1.19349			0.596746	+	0.802430i	$0.296460\pi$
$294$		0			0
$295$	570898.			0.381947
$296$		0			0
$297$	−488103.	+	845419.i	−0.321085	+	0.556136i
$298$		0			0
$299$	−187183.	−	324211.i	−0.121085	−	0.209725i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−673786.	−	1.16703e6i	−0.421614	−	0.730257i
$304$		0			0
$305$	−918060.	+	1.59013e6i	−0.565095	+	0.978774i
$306$		0			0
$307$	2.02249e6			1.22473			0.612364	−	0.790576i	$-0.290219\pi$
$307$	2.02249e6			1.22473			0.612364	+	0.790576i	$0.290219\pi$
$308$		0			0
$309$	1.61767e6			0.963813
$310$		0			0
$311$	713124.	−	1.23517e6i	0.418085	−	0.724144i	−0.577662	−	0.816276i	$-0.696035\pi$
$311$	713124.	−	1.23517e6i	0.418085	−	0.724144i	0.995747	+	0.0921321i	$0.0293682\pi$
$312$		0			0
$313$	26636.8	+	46136.3i	0.0153681	+	0.0266184i	0.873607	−	0.486632i	$-0.161775\pi$
$313$	26636.8	+	46136.3i	0.0153681	+	0.0266184i	−0.858239	+	0.513250i	$0.828441\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.31241e6	+	2.27315e6i	0.733533	+	1.27052i	0.955364	+	0.295432i	$0.0954634\pi$
$317$	1.31241e6	+	2.27315e6i	0.733533	+	1.27052i	−0.221831	+	0.975085i	$0.571203\pi$
$318$		0			0
$319$	−29093.6	+	50391.5i	−0.0160074	+	0.0277256i
$320$		0			0
$321$	3.54168e6			1.91843
$322$		0			0
$323$	2.26297e6			1.20690
$324$		0			0
$325$	−96492.1	+	167129.i	−0.0506738	+	0.0877696i
$326$		0			0
$327$	1.48817e6	+	2.57758e6i	0.769630	+	1.33304i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−651741.	−	1.12885e6i	−0.326968	−	0.566325i	0.654941	−	0.755680i	$-0.272694\pi$
$331$	−651741.	−	1.12885e6i	−0.326968	−	0.566325i	−0.981909	+	0.189355i	$0.939360\pi$
$332$		0			0
$333$	113313.	−	196264.i	0.0559976	−	0.0969907i
$334$		0			0
$335$	−2.93420e6			−1.42849
$336$		0			0
$337$	−1.33530e6			−0.640476			−0.320238	−	0.947337i	$-0.603763\pi$
$337$	−1.33530e6			−0.640476			−0.320238	+	0.947337i	$0.603763\pi$
$338$		0			0
$339$	1.56459e6	−	2.70994e6i	0.739435	−	1.28074i
$340$		0			0
$341$	31404.9	+	54394.8i	0.0146255	+	0.0253321i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	423250.	+	733090.i	0.191447	+	0.331596i
$346$		0			0
$347$	−862296.	+	1.49354e6i	−0.384443	+	0.665876i	−0.991692	−	0.128636i	$-0.958940\pi$
$347$	−862296.	+	1.49354e6i	−0.384443	+	0.665876i	0.607248	+	0.794512i	$0.292273\pi$
$348$		0			0
$349$	−2.97845e6			−1.30896			−0.654481	−	0.756079i	$-0.727113\pi$
$349$	−2.97845e6			−1.30896			−0.654481	+	0.756079i	$0.727113\pi$
$350$		0			0
$351$	1.31825e6			0.571124
$352$		0			0
$353$	−259227.	+	448995.i	−0.110725	+	0.191781i	−0.916063	−	0.401035i	$-0.868650\pi$
$353$	−259227.	+	448995.i	−0.110725	+	0.191781i	0.805338	+	0.592816i	$0.201984\pi$
$354$		0			0
$355$	534401.	+	925610.i	0.225059	+	0.389814i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	126728.	+	219499.i	0.0518961	+	0.0898868i	0.890806	−	0.454383i	$-0.150140\pi$
$359$	126728.	+	219499.i	0.0518961	+	0.0898868i	−0.838910	+	0.544270i	$0.816807\pi$
$360$		0			0
$361$	−1.14655e6	+	1.98588e6i	−0.463045	+	0.802018i
$362$		0			0
$363$	−1.41221e6			−0.562512
$364$		0			0
$365$	2.87852e6			1.13093
$366$		0			0
$367$	319805.	−	553919.i	0.123943	−	0.214675i	−0.797377	−	0.603482i	$-0.793779\pi$
$367$	319805.	−	553919.i	0.123943	−	0.214675i	0.921319	+	0.388807i	$0.127113\pi$
$368$		0			0
$369$	208426.	+	361005.i	0.0796869	+	0.138022i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	1.55000e6	+	2.68468e6i	0.576845	+	0.999125i	0.995838	+	0.0911357i	$0.0290497\pi$
$373$	1.55000e6	+	2.68468e6i	0.576845	+	0.999125i	−0.418993	+	0.907989i	$0.637617\pi$
$374$		0			0
$375$	1.52270e6	−	2.63740e6i	0.559160	−	0.968494i
$376$		0			0
$377$	78574.8			0.0284728
$378$		0			0
$379$	−746368.			−0.266904			−0.133452	−	0.991055i	$-0.542606\pi$
$379$	−746368.			−0.266904			−0.133452	+	0.991055i	$0.542606\pi$
$380$		0			0
$381$	1.11865e6	−	1.93755e6i	0.394803	−	0.683819i
$382$		0			0
$383$	562243.	+	973833.i	0.195852	+	0.339225i	0.947179	−	0.320704i	$-0.103920\pi$
$383$	562243.	+	973833.i	0.195852	+	0.339225i	−0.751328	+	0.659929i	$0.770586\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−200338.	−	346995.i	−0.0679963	−	0.117773i
$388$		0			0
$389$	−442986.	+	767274.i	−0.148428	+	0.257085i	−0.930647	−	0.365919i	$-0.880755\pi$
$389$	−442986.	+	767274.i	−0.148428	+	0.257085i	0.782219	+	0.623004i	$0.214088\pi$
$390$		0			0
$391$	1.05064e6			0.347545
$392$		0			0
$393$	1.39803e6			0.456599
$394$		0			0
$395$	−1.22842e6	+	2.12769e6i	−0.396146	+	0.686145i
$396$		0			0
$397$	885186.	+	1.53319e6i	0.281876	+	0.488224i	0.971847	−	0.235614i	$-0.0757100\pi$
$397$	885186.	+	1.53319e6i	0.281876	+	0.488224i	−0.689971	+	0.723837i	$0.742377\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−2.03855e6	−	3.53087e6i	−0.633082	−	1.09653i	−0.986918	−	0.161222i	$-0.948456\pi$
$401$	−2.03855e6	−	3.53087e6i	−0.633082	−	1.09653i	0.353836	−	0.935307i	$-0.384877\pi$
$402$		0			0
$403$	42408.6	−	73453.8i	0.0130074	−	0.0225295i
$404$		0			0
$405$	−3.28884e6			−0.996336
$406$		0			0
$407$	2.49332e6			0.746092
$408$		0			0
$409$	174515.	−	302269.i	0.0515852	−	0.0893482i	−0.839080	−	0.544008i	$-0.816906\pi$
$409$	174515.	−	302269.i	0.0515852	−	0.0893482i	0.890665	+	0.454660i	$0.150239\pi$
$410$		0			0
$411$	337793.	+	585074.i	0.0986383	+	0.170847i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	1.64244e6	+	2.84478e6i	0.468132	+	0.810829i
$416$		0			0
$417$	2.00971e6	−	3.48093e6i	0.565971	−	0.980291i
$418$		0			0
$419$	3.72353e6			1.03614			0.518072	−	0.855337i	$-0.326650\pi$
$419$	3.72353e6			1.03614			0.518072	+	0.855337i	$0.326650\pi$
$420$		0			0
$421$	−5.31261e6			−1.46084			−0.730421	−	0.682998i	$-0.760676\pi$
$421$	−5.31261e6			−1.46084			−0.730421	+	0.682998i	$0.760676\pi$
$422$		0			0
$423$	−13985.5	+	24223.6i	−0.00380038	+	0.00658246i
$424$		0			0
$425$	−270799.	−	469038.i	−0.0727235	−	0.125961i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−826156.	−	1.43094e6i	−0.216730	−	0.375387i
$430$		0			0
$431$	1.86623e6	−	3.23240e6i	0.483917	−	0.838169i	−0.515912	−	0.856642i	$-0.672547\pi$
$431$	1.86623e6	−	3.23240e6i	0.483917	−	0.838169i	0.999829	+	0.0184721i	$0.00588019\pi$
$432$		0			0
$433$	1.39251e6			0.356927			0.178464	−	0.983947i	$-0.442887\pi$
$433$	1.39251e6			0.356927			0.178464	+	0.983947i	$0.442887\pi$
$434$		0			0
$435$	−177670.			−0.0450184
$436$		0			0
$437$	−1.10711e6	+	1.91756e6i	−0.277323	+	0.480337i
$438$		0			0
$439$	−1.54520e6	−	2.67637e6i	−0.382670	−	0.662804i	0.608773	−	0.793345i	$-0.291662\pi$
$439$	−1.54520e6	−	2.67637e6i	−0.382670	−	0.662804i	−0.991443	+	0.130541i	$0.958329\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	2.08533e6	+	3.61190e6i	0.504853	+	0.874432i	0.999984	+	0.00561334i	$0.00178679\pi$
$443$	2.08533e6	+	3.61190e6i	0.504853	+	0.874432i	−0.495131	+	0.868818i	$0.664880\pi$
$444$		0			0
$445$	−1.59406e6	+	2.76100e6i	−0.381598	+	0.660946i
$446$		0			0
$447$	−5.36251e6			−1.26940
$448$		0			0
$449$	−4.50893e6			−1.05550			−0.527749	−	0.849400i	$-0.676964\pi$
$449$	−4.50893e6			−1.05550			−0.527749	+	0.849400i	$0.676964\pi$
$450$		0			0
$451$	−2.29309e6	+	3.97175e6i	−0.530860	+	0.919476i
$452$		0			0
$453$	−3.04960e6	−	5.28206e6i	−0.698228	−	1.20937i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−260662.	−	451480.i	−0.0583831	−	0.101122i	0.835357	−	0.549708i	$-0.185261\pi$
$457$	−260662.	−	451480.i	−0.0583831	−	0.101122i	−0.893740	+	0.448586i	$0.851928\pi$
$458$		0			0
$459$	−1.84980e6	+	3.20394e6i	−0.409819	+	0.709827i
$460$		0			0
$461$	−4.45956e6			−0.977327			−0.488663	−	0.872472i	$-0.662515\pi$
$461$	−4.45956e6			−0.977327			−0.488663	+	0.872472i	$0.662515\pi$
$462$		0			0
$463$	−7.41318e6			−1.60713			−0.803567	−	0.595214i	$-0.797067\pi$
$463$	−7.41318e6			−1.60713			−0.803567	+	0.595214i	$0.797067\pi$
$464$		0			0
$465$	−95892.2	+	166090.i	−0.0205660	+	0.0356214i
$466$		0			0
$467$	−3.03835e6	−	5.26258e6i	−0.644682	−	1.11662i	−0.984375	−	0.176086i	$-0.943656\pi$
$467$	−3.03835e6	−	5.26258e6i	−0.644682	−	1.11662i	0.339692	−	0.940537i	$-0.389677\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−1.72654e6	−	2.99045e6i	−0.358611	−	0.621133i
$472$		0			0
$473$	2.20410e6	−	3.81761e6i	0.452979	−	0.784583i
$474$		0			0
$475$	1.14142e6			0.232118
$476$		0			0
$477$	849074.			0.170864
$478$		0			0
$479$	−3.91094e6	+	6.77395e6i	−0.778829	+	1.34897i	0.153788	+	0.988104i	$0.450853\pi$
$479$	−3.91094e6	+	6.77395e6i	−0.778829	+	1.34897i	−0.932617	+	0.360868i	$0.882480\pi$
$480$		0			0
$481$	−1.68347e6	−	2.91585e6i	−0.331774	−	0.574649i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−897902.	−	1.55521e6i	−0.173330	−	0.300217i
$486$		0			0
$487$	3.82244e6	−	6.62066e6i	0.730328	−	1.26497i	−0.226415	−	0.974031i	$-0.572701\pi$
$487$	3.82244e6	−	6.62066e6i	0.730328	−	1.26497i	0.956743	−	0.290934i	$-0.0939661\pi$
$488$		0			0
$489$	−3.15575e6			−0.596801
$490$		0			0
$491$	−4.62867e6			−0.866468			−0.433234	−	0.901282i	$-0.642628\pi$
$491$	−4.62867e6			−0.866468			−0.433234	+	0.901282i	$0.642628\pi$
$492$		0			0
$493$	−110258.	+	190972.i	−0.0204311	+	0.0353877i
$494$		0			0
$495$	173329.	+	300214.i	0.0317949	+	0.0550704i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−172391.	−	298589.i	−0.0309929	−	0.0536813i	0.850113	−	0.526600i	$-0.176534\pi$
$499$	−172391.	−	298589.i	−0.0309929	−	0.0536813i	−0.881106	+	0.472919i	$0.843200\pi$
$500$		0			0
$501$	4.15528e6	−	7.19715e6i	0.739615	−	1.28105i
$502$		0			0
$503$	2.44839e6			0.431479			0.215740	−	0.976451i	$-0.430784\pi$
$503$	2.44839e6			0.431479			0.215740	+	0.976451i	$0.430784\pi$
$504$		0			0
$505$	4.20035e6			0.732921
$506$		0			0
$507$	1.92270e6	−	3.33022e6i	0.332194	−	0.575378i
$508$		0			0
$509$	−2.19922e6	−	3.80916e6i	−0.376248	−	0.651681i	0.614265	−	0.789100i	$-0.289453\pi$
$509$	−2.19922e6	−	3.80916e6i	−0.376248	−	0.651681i	−0.990513	+	0.137419i	$0.956119\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−3.89843e6	−	6.75228e6i	−0.654029	−	1.13281i
$514$		0			0
$515$	−2.52112e6	+	4.36670e6i	−0.418866	+	0.725497i
$516$		0			0
$517$	−307735.			−0.0506349
$518$		0			0
$519$	−9.22522e6			−1.50334
$520$		0			0
$521$	1.95115e6	−	3.37948e6i	0.314916	−	0.545451i	−0.664503	−	0.747285i	$-0.731357\pi$
$521$	1.95115e6	−	3.37948e6i	0.314916	−	0.545451i	0.979420	+	0.201834i	$0.0646902\pi$
$522$		0			0
$523$	1.47797e6	+	2.55992e6i	0.236272	+	0.409235i	0.959642	−	0.281226i	$-0.0907410\pi$
$523$	1.47797e6	+	2.55992e6i	0.236272	+	0.409235i	−0.723370	+	0.690461i	$0.757408\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	119017.	+	206144.i	0.0186673	+	0.0323328i
$528$		0			0
$529$	2.70417e6	−	4.68376e6i	0.420141	−	0.727705i
$530$		0			0
$531$	278133.			0.0428071
$532$		0			0
$533$	6.19310e6			0.944256
$534$		0			0
$535$	−5.51967e6	+	9.56035e6i	−0.833736	+	1.44407i
$536$		0			0
$537$	−1.55737e6	−	2.69744e6i	−0.233053	−	0.403661i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	824975.	+	1.42890e6i	0.121185	+	0.209898i	0.920235	−	0.391366i	$-0.127997\pi$
$541$	824975.	+	1.42890e6i	0.121185	+	0.209898i	−0.799050	+	0.601264i	$0.794664\pi$
$542$		0			0
$543$	3.50817e6	−	6.07632e6i	0.510600	−	0.884385i
$544$		0			0
$545$	−9.27716e6			−1.33790
$546$		0			0
$547$	−8.86766e6			−1.26719			−0.633594	−	0.773666i	$-0.718421\pi$
$547$	−8.86766e6			−1.26719			−0.633594	+	0.773666i	$0.718421\pi$
$548$		0			0
$549$	−447265.	+	774686.i	−0.0633336	+	0.109697i
$550$		0			0
$551$	−232368.	−	402472.i	−0.0326059	−	0.0564751i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	3.80658e6	+	6.59319e6i	0.524569	+	0.908579i
$556$		0			0
$557$	3.14791e6	−	5.45234e6i	0.429917	−	0.744637i	−0.566949	−	0.823753i	$-0.691876\pi$
$557$	3.14791e6	−	5.45234e6i	0.429917	−	0.744637i	0.996865	+	0.0791157i	$0.0252096\pi$
$558$		0			0
$559$	−5.95275e6			−0.805727
$560$		0			0
$561$	4.63711e6			0.622072
$562$		0			0
$563$	−4.17685e6	+	7.23451e6i	−0.555364	+	0.961918i	0.442511	+	0.896763i	$0.354088\pi$
$563$	−4.17685e6	+	7.23451e6i	−0.555364	+	0.961918i	−0.997875	+	0.0651553i	$0.979246\pi$
$564$		0			0
$565$	4.87678e6	+	8.44683e6i	0.642705	+	1.11320i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	1.24399e6	+	2.15465e6i	0.161078	+	0.278995i	0.935255	−	0.353973i	$-0.115170\pi$
$569$	1.24399e6	+	2.15465e6i	0.161078	+	0.278995i	−0.774178	+	0.632968i	$0.781836\pi$
$570$		0			0
$571$	−1.22087e6	+	2.11461e6i	−0.156704	+	0.271419i	−0.933678	−	0.358113i	$-0.883420\pi$
$571$	−1.22087e6	+	2.11461e6i	−0.156704	+	0.271419i	0.776974	+	0.629532i	$0.216754\pi$
$572$		0			0
$573$	−3.79164e6			−0.482436
$574$		0			0
$575$	529930.			0.0668419
$576$		0			0
$577$	1.07028e6	−	1.85378e6i	0.133831	−	0.231803i	−0.791319	−	0.611403i	$-0.790605\pi$
$577$	1.07028e6	−	1.85378e6i	0.133831	−	0.231803i	0.925150	+	0.379601i	$0.123939\pi$
$578$		0			0
$579$	3.45169e6	+	5.97850e6i	0.427893	+	0.741133i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	4.67072e6	+	8.08992e6i	0.569131	+	0.985764i
$584$		0			0
$585$	234060.	−	405404.i	0.0282773	−	0.0489777i
$586$		0			0
$587$	−16057.9			−0.00192350			−0.000961752	−	1.00000i	$-0.500306\pi$
$587$	−16057.9			−0.00192350			−0.000961752		1.00000i	$0.500306\pi$
$588$		0			0
$589$	−501655.			−0.0595823
$590$		0			0
$591$	5.79786e6	−	1.00422e7i	0.682809	−	1.18266i
$592$		0			0
$593$	−6.08574e6	−	1.05408e7i	−0.710684	−	1.23094i	−0.964601	−	0.263715i	$-0.915052\pi$
$593$	−6.08574e6	−	1.05408e7i	−0.710684	−	1.23094i	0.253917	−	0.967226i	$-0.418281\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−5.25819e6	−	9.10745e6i	−0.603810	−	1.04583i
$598$		0			0
$599$	3.80405e6	−	6.58881e6i	0.433191	−	0.750308i	−0.563955	−	0.825805i	$-0.690721\pi$
$599$	3.80405e6	−	6.58881e6i	0.433191	−	0.750308i	0.997146	+	0.0754969i	$0.0240543\pi$
$600$		0			0
$601$	−1.38834e7			−1.56786			−0.783932	−	0.620847i	$-0.786789\pi$
$601$	−1.38834e7			−1.56786			−0.783932	+	0.620847i	$0.786789\pi$
$602$		0			0
$603$	−1.42950e6			−0.160100
$604$		0			0
$605$	2.20091e6	−	3.81208e6i	0.244463	−	0.423422i
$606$		0			0
$607$	4.64229e6	+	8.04068e6i	0.511400	+	0.885771i	0.999913	+	0.0132139i	$0.00420623\pi$
$607$	4.64229e6	+	8.04068e6i	0.511400	+	0.885771i	−0.488513	+	0.872557i	$0.662460\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	207780.	+	359885.i	0.0225165	+	0.0389997i
$612$		0			0
$613$	815932.	−	1.41323e6i	0.0877006	−	0.151902i	−0.818838	−	0.574024i	$-0.805381\pi$
$613$	815932.	−	1.41323e6i	0.0877006	−	0.151902i	0.906539	+	0.422122i	$0.138715\pi$
$614$		0			0
$615$	−1.40035e7			−1.49297
$616$		0			0
$617$	8.30019e6			0.877758			0.438879	−	0.898546i	$-0.355376\pi$
$617$	8.30019e6			0.877758			0.438879	+	0.898546i	$0.355376\pi$
$618$		0			0
$619$	4.83445e6	−	8.37351e6i	0.507131	−	0.878377i	−0.492835	−	0.870123i	$-0.664039\pi$
$619$	4.83445e6	−	8.37351e6i	0.507131	−	0.878377i	0.999966	−	0.00825399i	$-0.00262736\pi$
$620$		0			0
$621$	−1.80994e6	−	3.13491e6i	−0.188337	−	0.326209i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	3.92956e6	+	6.80621e6i	0.402387	+	0.696955i
$626$		0			0
$627$	−4.88635e6	+	8.46340e6i	−0.496381	+	0.859757i
$628$		0			0
$629$	9.44911e6			0.952279
$630$		0			0
$631$	−8.91041e6			−0.890891			−0.445445	−	0.895309i	$-0.646955\pi$
$631$	−8.91041e6			−0.890891			−0.445445	+	0.895309i	$0.646955\pi$
$632$		0			0
$633$	−7.49722e6	+	1.29856e7i	−0.743688	+	1.28811i
$634$		0			0
$635$	3.48680e6	+	6.03931e6i	0.343157	+	0.594365i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	260352.	+	450943.i	0.0252237	+	0.0436887i
$640$		0			0
$641$	−5.47351e6	+	9.48040e6i	−0.526164	+	0.911342i	0.473372	+	0.880863i	$0.343037\pi$
$641$	−5.47351e6	+	9.48040e6i	−0.526164	+	0.911342i	−0.999535	+	0.0304793i	$0.990297\pi$
$642$		0			0
$643$	1.81902e7			1.73504			0.867522	−	0.497399i	$-0.165712\pi$
$643$	1.81902e7			1.73504			0.867522	+	0.497399i	$0.165712\pi$
$644$		0			0
$645$	1.34601e7			1.27394
$646$		0			0
$647$	−1.17441e6	+	2.03414e6i	−0.110296	+	0.191038i	−0.915890	−	0.401430i	$-0.868513\pi$
$647$	−1.17441e6	+	2.03414e6i	−0.110296	+	0.191038i	0.805594	+	0.592468i	$0.201846\pi$
$648$		0			0
$649$	1.53000e6	+	2.65003e6i	0.142587	+	0.246967i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	2.55317e6	+	4.42223e6i	0.234314	+	0.405843i	0.959073	−	0.283159i	$-0.0913824\pi$
$653$	2.55317e6	+	4.42223e6i	0.234314	+	0.405843i	−0.724759	+	0.689002i	$0.758049\pi$
$654$		0			0
$655$	−2.17881e6	+	3.77381e6i	−0.198434	+	0.343698i
$656$		0			0
$657$	1.40237e6			0.126750
$658$		0			0
$659$	1.94777e7			1.74713			0.873563	−	0.486711i	$-0.161803\pi$
$659$	1.94777e7			1.74713			0.873563	+	0.486711i	$0.161803\pi$
$660$		0			0
$661$	819130.	−	1.41877e6i	0.0729204	−	0.126302i	−0.827260	−	0.561820i	$-0.810101\pi$
$661$	819130.	−	1.41877e6i	0.0729204	−	0.126302i	0.900180	+	0.435518i	$0.143435\pi$
$662$		0			0
$663$	−3.13094e6	−	5.42294e6i	−0.276624	−	0.479128i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−107882.	−	186858.i	−0.00938935	−	0.0162628i
$668$		0			0
$669$	−7.89785e6	+	1.36795e7i	−0.682250	+	1.18169i
$670$		0			0
$671$	−9.84154e6			−0.843834
$672$		0			0
$673$	−989610.			−0.0842222			−0.0421111	−	0.999113i	$-0.513408\pi$
$673$	−989610.			−0.0842222			−0.0421111	+	0.999113i	$0.513408\pi$
$674$		0			0
$675$	−933016.	+	1.61603e6i	−0.0788188	+	0.136518i
$676$		0			0
$677$	−9.48196e6	−	1.64232e7i	−0.795108	−	1.37717i	−0.922770	−	0.385350i	$-0.874081\pi$
$677$	−9.48196e6	−	1.64232e7i	−0.795108	−	1.37717i	0.127662	−	0.991818i	$-0.459253\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	7.31081e6	+	1.26627e7i	0.604084	+	1.04630i
$682$		0			0
$683$	1.80547e6	−	3.12716e6i	0.148094	−	0.256506i	−0.782429	−	0.622740i	$-0.786019\pi$
$683$	1.80547e6	−	3.12716e6i	0.148094	−	0.256506i	0.930523	+	0.366233i	$0.119353\pi$
$684$		0			0
$685$	−2.10578e6			−0.171470
$686$		0			0
$687$	−1.99264e7			−1.61078
$688$		0			0
$689$	6.30725e6	−	1.09245e7i	0.506165	−	0.876704i
$690$		0			0
$691$	9.59174e6	+	1.66134e7i	0.764192	+	1.32362i	0.940673	+	0.339315i	$0.110195\pi$
$691$	9.59174e6	+	1.66134e7i	0.764192	+	1.32362i	−0.176481	+	0.984304i	$0.556471\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	6.26424e6	+	1.08500e7i	0.491933	+	0.852053i
$696$		0			0
$697$	−8.69027e6	+	1.50520e7i	−0.677566	+	1.17358i
$698$		0			0
$699$	2.03771e7			1.57743
$700$		0			0
$701$	−1.10240e7			−0.847314			−0.423657	−	0.905823i	$-0.639254\pi$
$701$	−1.10240e7			−0.847314			−0.423657	+	0.905823i	$0.639254\pi$
$702$		0			0
$703$	−9.95697e6	+	1.72460e7i	−0.759869	+	1.31613i
$704$		0			0
$705$	−469821.	−	813755.i	−0.0356008	−	0.0616624i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−1.02669e7	−	1.77827e7i	−0.767047	−	1.32856i	−0.939158	−	0.343486i	$-0.888392\pi$
$709$	−1.02669e7	−	1.77827e7i	−0.767047	−	1.32856i	0.172111	−	0.985078i	$-0.444941\pi$
$710$		0			0
$711$	−598469.	+	1.03658e6i	−0.0443984	+	0.0769003i
$712$		0			0
$713$	−232906.			−0.0171576
$714$		0			0
$715$	5.15022e6			0.376756
$716$		0			0
$717$	1.83263e6	−	3.17420e6i	0.133130	−	0.230588i
$718$		0			0
$719$	4.04561e6	+	7.00719e6i	0.291851	+	0.505501i	0.974247	−	0.225481i	$-0.0723955\pi$
$719$	4.04561e6	+	7.00719e6i	0.291851	+	0.505501i	−0.682396	+	0.730982i	$0.739062\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−3.28571e6	−	5.69101e6i	−0.233767	−	0.404896i
$724$		0			0
$725$	−55612.8	+	96324.1i	−0.00392943	+	0.00680597i
$726$		0			0
$727$	1.58746e7			1.11396			0.556978	−	0.830527i	$-0.311961\pi$
$727$	1.58746e7			1.11396			0.556978	+	0.830527i	$0.311961\pi$
$728$		0			0
$729$	1.25965e7			0.877875
$730$		0			0
$731$	8.35301e6	−	1.44678e7i	0.578162	−	1.00141i
$732$		0			0
$733$	−2.26273e6	−	3.91917e6i	−0.155551	−	0.269423i	0.777708	−	0.628625i	$-0.216382\pi$
$733$	−2.26273e6	−	3.91917e6i	−0.155551	−	0.269423i	−0.933260	+	0.359203i	$0.883049\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−7.86361e6	−	1.36202e7i	−0.533277	−	0.923663i
$738$		0			0
$739$	5.35216e6	−	9.27022e6i	0.360511	−	0.624423i	−0.627534	−	0.778589i	$-0.715936\pi$
$739$	5.35216e6	−	9.27022e6i	0.360511	−	0.624423i	0.988045	+	0.154166i	$0.0492690\pi$
$740$		0			0
$741$	1.31969e7			0.882928
$742$		0			0
$743$	1.76704e7			1.17429			0.587144	−	0.809482i	$-0.300252\pi$
$743$	1.76704e7			1.17429			0.587144	+	0.809482i	$0.300252\pi$
$744$		0			0
$745$	8.35741e6	−	1.44755e7i	0.551672	−	0.955525i
$746$		0			0
$747$	800170.	+	1.38593e6i	0.0524663	+	0.0908744i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−5.88974e6	−	1.02013e7i	−0.381062	−	0.660019i	0.610152	−	0.792284i	$-0.291108\pi$
$751$	−5.88974e6	−	1.02013e7i	−0.381062	−	0.660019i	−0.991214	+	0.132265i	$0.957775\pi$
$752$		0			0
$753$	−3.32362e6	+	5.75668e6i	−0.213611	+	0.369985i
$754$		0			0
$755$	1.90111e7			1.21378
$756$		0			0
$757$	−2.89421e7			−1.83565			−0.917827	−	0.396981i	$-0.870058\pi$
$757$	−2.89421e7			−1.83565			−0.917827	+	0.396981i	$0.870058\pi$
$758$		0			0
$759$	−2.26860e6	+	3.92934e6i	−0.142940	+	0.247580i
$760$		0			0
$761$	6.68358e6	+	1.15763e7i	0.418358	+	0.724616i	0.995774	−	0.0918330i	$-0.0292726\pi$
$761$	6.68358e6	+	1.15763e7i	0.418358	+	0.724616i	−0.577417	+	0.816449i	$0.695939\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	656876.	+	1.13774e6i	0.0405816	+	0.0702895i
$766$		0			0
$767$	2.06608e6	−	3.57855e6i	0.126811	−	0.219644i
$768$		0			0
$769$	2.23666e7			1.36390			0.681952	−	0.731397i	$-0.261131\pi$
$769$	2.23666e7			1.36390			0.681952	+	0.731397i	$0.261131\pi$
$770$		0			0
$771$	1.35999e7			0.823945
$772$		0			0
$773$	2.83865e6	−	4.91669e6i	0.170869	−	0.295954i	−0.767855	−	0.640624i	$-0.778676\pi$
$773$	2.83865e6	−	4.91669e6i	0.170869	−	0.295954i	0.938724	+	0.344670i	$0.112009\pi$
$774$		0			0
$775$	60030.9	+	103976.i	0.00359021	+	0.00621843i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−1.83147e7	−	3.17220e7i	−1.08132	−	1.87291i
$780$		0			0
$781$	−2.86437e6	+	4.96124e6i	−0.168036	+	0.291047i
$782$		0			0
$783$	759768.			0.0442870
$784$		0			0
$785$	1.07632e7			0.623399
$786$		0			0
$787$	7.80962e6	−	1.35267e7i	0.449462	−	0.778491i	−0.548889	−	0.835895i	$-0.684949\pi$
$787$	7.80962e6	−	1.35267e7i	0.449462	−	0.778491i	0.998351	+	0.0574044i	$0.0182824\pi$
$788$		0			0
$789$	−1.35794e7	−	2.35203e7i	−0.776586	−	1.34509i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	6.64492e6	+	1.15093e7i	0.375238	+	0.649931i
$794$		0			0
$795$	−1.42617e7	+	2.47019e7i	−0.800299	+	1.38616i
$796$		0			0
$797$	1.18054e7			0.658317			0.329159	−	0.944275i	$-0.393235\pi$
$797$	1.18054e7			0.658317			0.329159	+	0.944275i	$0.393235\pi$
$798$		0			0
$799$	−1.16624e6			−0.0646282
$800$		0			0
$801$	−776603.	+	1.34512e6i	−0.0427679	+	0.0740762i
$802$		0			0
$803$	7.71437e6	+	1.33617e7i	0.422194	+	0.731261i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−863454.	−	1.49555e6i	−0.0466719	−	0.0808380i
$808$		0			0
$809$	−8.14192e6	+	1.41022e7i	−0.437376	+	0.757558i	−0.997486	−	0.0708601i	$-0.977426\pi$
$809$	−8.14192e6	+	1.41022e7i	−0.437376	+	0.757558i	0.560110	+	0.828418i	$0.310759\pi$
$810$		0			0
$811$	2.34229e7			1.25051			0.625257	−	0.780419i	$-0.284994\pi$
$811$	2.34229e7			1.25051			0.625257	+	0.780419i	$0.284994\pi$
$812$		0			0
$813$	2.87219e7			1.52401
$814$		0			0
$815$	4.91819e6	−	8.51856e6i	0.259365	−	0.449234i
$816$		0			0
$817$	1.76039e7	+	3.04909e7i	0.922687	+	1.59814i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.38005e7	−	2.39032e7i	−0.714559	−	1.23765i	−0.963129	−	0.269039i	$-0.913294\pi$
$821$	−1.38005e7	−	2.39032e7i	−0.714559	−	1.23765i	0.248570	−	0.968614i	$-0.420039\pi$
$822$		0			0
$823$	1.85631e7	−	3.21523e7i	0.955325	−	1.65467i	0.221703	−	0.975114i	$-0.428839\pi$
$823$	1.85631e7	−	3.21523e7i	0.955325	−	1.65467i	0.733622	−	0.679557i	$-0.237828\pi$
$824$		0			0
$825$	2.33891e6			0.119640
$826$		0			0
$827$	1.18296e7			0.601459			0.300729	−	0.953710i	$-0.402770\pi$
$827$	1.18296e7			0.601459			0.300729	+	0.953710i	$0.402770\pi$
$828$		0			0
$829$	−1.28307e7	+	2.22235e7i	−0.648433	+	1.12312i	0.335064	+	0.942195i	$0.391242\pi$
$829$	−1.28307e7	+	2.22235e7i	−0.648433	+	1.12312i	−0.983497	+	0.180924i	$0.942091\pi$
$830$		0			0
$831$	−1.75937e7	−	3.04732e7i	−0.883803	−	1.53079i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	1.29519e7	+	2.24334e7i	0.642862	+	1.11347i
$836$		0			0
$837$	410063.	−	710250.i	0.0202319	−	0.0350427i
$838$		0			0
$839$	−2.86405e7			−1.40467			−0.702336	−	0.711845i	$-0.747860\pi$
$839$	−2.86405e7			−1.40467			−0.702336	+	0.711845i	$0.747860\pi$
$840$		0			0
$841$	−2.04659e7			−0.997792
$842$		0			0
$843$	1.59095e7	−	2.75560e7i	0.771057	−	1.33551i
$844$		0			0
$845$	5.99302e6	+	1.03802e7i	0.288738	+	0.500109i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	3.50611e6	+	6.07276e6i	0.166938	+	0.289146i
$850$		0			0
$851$	−4.62276e6	+	8.00686e6i	−0.218815	+	0.378999i
$852$		0			0
$853$	3.22929e7			1.51962			0.759809	−	0.650146i	$-0.225292\pi$
$853$	3.22929e7			1.51962			0.759809	+	0.650146i	$0.225292\pi$
$854$		0			0
$855$	−2.76872e6			−0.129528
$856$		0			0
$857$	8.64886e6	−	1.49803e7i	0.402260	−	0.696735i	−0.591738	−	0.806130i	$-0.701558\pi$
$857$	8.64886e6	−	1.49803e7i	0.402260	−	0.696735i	0.993998	+	0.109395i	$0.0348914\pi$
$858$		0			0
$859$	1.89527e7	+	3.28271e7i	0.876372	+	1.51792i	0.855294	+	0.518143i	$0.173376\pi$
$859$	1.89527e7	+	3.28271e7i	0.876372	+	1.51792i	0.0210779	+	0.999778i	$0.493290\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−3.86830e6	−	6.70009e6i	−0.176804	−	0.306234i	0.763980	−	0.645240i	$-0.223243\pi$
$863$	−3.86830e6	−	6.70009e6i	−0.176804	−	0.306234i	−0.940784	+	0.339006i	$0.889909\pi$
$864$		0			0
$865$	1.43774e7	−	2.49024e7i	0.653342	−	1.13162i
$866$		0			0
$867$	−5.66410e6			−0.255908
$868$		0			0
$869$	−1.31686e7			−0.591548
$870$		0			0
$871$	−1.06189e7	+	1.83924e7i	−0.474278	+	0.821474i
$872$		0			0
$873$	−437444.	−	757675.i	−0.0194262	−	0.0336471i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−539376.	−	934226.i	−0.0236806	−	0.0410160i	0.853942	−	0.520368i	$-0.174205\pi$
$877$	−539376.	−	934226.i	−0.0236806	−	0.0410160i	−0.877623	+	0.479352i	$0.840872\pi$
$878$		0			0
$879$	−1.43518e7	+	2.48581e7i	−0.626519	+	1.08516i
$880$		0			0
$881$	−1.88089e7			−0.816440			−0.408220	−	0.912884i	$-0.633850\pi$
$881$	−1.88089e7			−0.816440			−0.408220	+	0.912884i	$0.633850\pi$
$882$		0			0
$883$	3.12763e7			1.34994			0.674968	−	0.737847i	$-0.264158\pi$
$883$	3.12763e7			1.34994			0.674968	+	0.737847i	$0.264158\pi$
$884$		0			0
$885$	−4.67172e6	+	8.09165e6i	−0.200502	+	0.347279i
$886$		0			0
$887$	−1.34552e7	−	2.33051e7i	−0.574223	−	0.994584i	−0.996126	−	0.0879427i	$-0.971971\pi$
$887$	−1.34552e7	−	2.33051e7i	−0.574223	−	0.994584i	0.421902	−	0.906641i	$-0.361363\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−8.81404e6	−	1.52664e7i	−0.371947	−	0.644231i
$892$		0			0
$893$	1.22892e6	−	2.12856e6i	0.0515699	−	0.0893218i
$894$		0			0
$895$	9.70857e6			0.405133
$896$		0			0
$897$	6.12696e6			0.254252
$898$		0			0
$899$	24442.0	−	42334.7i	0.00100864	−	0.00174702i
$900$		0			0
$901$	1.77009e7	+	3.06589e7i	0.726414	+	1.25819i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1.09349e7	+	1.89398e7i	0.443805	+	0.768693i
$906$		0			0
$907$	−2.27362e7	+	3.93803e7i	−0.917699	+	1.58950i	−0.114798	+	0.993389i	$0.536622\pi$
$907$	−2.27362e7	+	3.93803e7i	−0.917699	+	1.58950i	−0.802901	+	0.596112i	$0.796711\pi$
$908$		0			0
$909$	2.04635e6			0.0821428
$910$		0			0
$911$	−4.44792e7			−1.77567			−0.887833	−	0.460165i	$-0.847790\pi$
$911$	−4.44792e7			−1.77567			−0.887833	+	0.460165i	$0.847790\pi$
$912$		0			0
$913$	−8.80340e6	+	1.52479e7i	−0.349521	+	0.605389i
$914$		0			0
$915$	−1.50252e7	−	2.60244e7i	−0.593289	−	1.02761i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	2.25980e7	+	3.91410e7i	0.882637	+	1.52877i	0.848398	+	0.529359i	$0.177567\pi$
$919$	2.25980e7	+	3.91410e7i	0.882637	+	1.52877i	0.0342388	+	0.999414i	$0.489099\pi$
$920$		0			0
$921$	−1.65502e7	+	2.86658e7i	−0.642916	+	1.11356i
$922$		0			0
$923$	7.73599e6			0.298890
$924$		0			0
$925$	4.76602e6			0.183148
$926$		0			0
$927$	−1.22825e6	+	2.12739e6i	−0.0469448	+	0.0813107i
$928$		0			0
$929$	98709.7	+	170970.i	0.00375250	+	0.00649952i	0.867896	−	0.496747i	$-0.165472\pi$
$929$	98709.7	+	170970.i	0.00375250	+	0.00649952i	−0.864143	+	0.503246i	$0.832139\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	1.16711e7	+	2.02150e7i	0.438944	+	0.760274i
$934$		0			0
$935$	−7.22689e6	+	1.25173e7i	−0.270348	+	0.468256i
$936$		0			0
$937$	−2.35263e7			−0.875394			−0.437697	−	0.899122i	$-0.644206\pi$
$937$	−2.35263e7			−0.875394			−0.437697	+	0.899122i	$0.644206\pi$
$938$		0			0
$939$	−871888.			−0.0322698
$940$		0			0
$941$	2.28962e7	−	3.96573e7i	0.842925	−	1.45999i	−0.0444861	−	0.999010i	$-0.514165\pi$
$941$	2.28962e7	−	3.96573e7i	0.842925	−	1.45999i	0.887411	−	0.460979i	$-0.152502\pi$
$942$		0			0
$943$	−8.50304e6	−	1.47277e7i	−0.311383	−	0.539331i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−4.39479e6	−	7.61200e6i	−0.159244	−	0.275819i	0.775352	−	0.631529i	$-0.217572\pi$
$947$	−4.39479e6	−	7.61200e6i	−0.159244	−	0.275819i	−0.934596	+	0.355710i	$0.884239\pi$
$948$		0			0
$949$	1.04174e7	−	1.80434e7i	0.375484	−	0.650358i
$950$		0			0
$951$	−4.29582e7			−1.54026
$952$		0			0
$953$	2.97668e7			1.06170			0.530848	−	0.847467i	$-0.321874\pi$
$953$	2.97668e7			1.06170			0.530848	+	0.847467i	$0.321874\pi$
$954$		0			0
$955$	5.90922e6	−	1.02351e7i	0.209663	−	0.363147i
$956$		0			0
$957$	−476151.	−	824718.i	−0.0168060	−	0.0291089i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	1.42882e7	+	2.47479e7i	0.499078	+	0.864429i
$962$		0			0
$963$	−2.68910e6	+	4.65766e6i	−0.0934418	+	0.161846i
$964$		0			0
$965$	−2.15177e7			−0.743836
$966$		0			0
$967$	1.40282e7			0.482433			0.241217	−	0.970471i	$-0.422454\pi$
$967$	1.40282e7			0.482433			0.241217	+	0.970471i	$0.422454\pi$
$968$		0			0
$969$	−1.85181e7	+	3.20743e7i	−0.633559	+	1.09736i
$970$		0			0
$971$	−1.02223e7	−	1.77055e7i	−0.347936	−	0.602643i	0.637946	−	0.770081i	$-0.279784\pi$
$971$	−1.02223e7	−	1.77055e7i	−0.347936	−	0.602643i	−0.985883	+	0.167437i	$0.946451\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−1.57921e6	−	2.73527e6i	−0.0532020	−	0.0921486i
$976$		0			0
$977$	1.06439e7	−	1.84358e7i	0.356750	−	0.617909i	−0.630666	−	0.776055i	$-0.717218\pi$
$977$	1.06439e7	−	1.84358e7i	0.356750	−	0.617909i	0.987416	+	0.158145i	$0.0505514\pi$
$978$		0			0
$979$	−1.70882e7			−0.569824
$980$		0			0
$981$	−4.51969e6			−0.149946
$982$		0			0
$983$	−2.02194e7	+	3.50210e7i	−0.667396	+	1.15596i	0.311234	+	0.950333i	$0.399258\pi$
$983$	−2.02194e7	+	3.50210e7i	−0.667396	+	1.15596i	−0.978630	+	0.205630i	$0.934076\pi$
$984$		0			0
$985$	1.80718e7	+	3.13013e7i	0.593487	+	1.02795i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	8.17305e6	+	1.41561e7i	0.265701	+	0.460208i
$990$		0			0
$991$	1.23687e7	−	2.14231e7i	0.400072	−	0.692946i	−0.593662	−	0.804715i	$-0.702318\pi$
$991$	1.23687e7	−	2.14231e7i	0.400072	−	0.692946i	0.993734	+	0.111769i	$0.0356517\pi$
$992$		0			0
$993$	2.13331e7			0.686562
$994$		0			0
$995$	3.27793e7			1.04964
$996$		0			0
$997$	−1.04615e7	+	1.81198e7i	−0.333316	+	0.577320i	−0.983160	−	0.182748i	$-0.941501\pi$
$997$	−1.04615e7	+	1.81198e7i	−0.333316	+	0.577320i	0.649844	+	0.760067i	$0.274834\pi$
$998$		0			0
$999$	−1.62781e7	−	2.81944e7i	−0.516046	−	0.893819i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.6.i.q.361.2		12
7.2	even	3	inner	392.6.i.q.177.2		12
7.3	odd	6		392.6.a.m.1.2	✓	6
7.4	even	3		392.6.a.m.1.5	yes	6
7.5	odd	6	inner	392.6.i.q.177.5		12
7.6	odd	2	inner	392.6.i.q.361.5		12
28.3	even	6		784.6.a.bn.1.5		6
28.11	odd	6		784.6.a.bn.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
392.6.a.m.1.2	✓	6	7.3	odd	6
392.6.a.m.1.5	yes	6	7.4	even	3
392.6.i.q.177.2		12	7.2	even	3	inner
392.6.i.q.177.5		12	7.5	odd	6	inner
392.6.i.q.361.2		12	1.1	even	1	trivial
392.6.i.q.361.5		12	7.6	odd	2	inner
784.6.a.bn.1.2		6	28.11	odd	6
784.6.a.bn.1.5		6	28.3	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)

\(f(q)\)	\(=\)	\(q+(-8.18310 + 14.1736i) q^{3} +(-25.5066 - 44.1787i) q^{5} +(-12.4264 - 21.5232i) q^{9} +(136.714 - 236.796i) q^{11} -369.233 q^{13} +834.891 q^{15} +(518.115 - 897.401i) q^{17} +(1091.92 + 1891.27i) q^{19} +(506.952 + 878.067i) q^{23} +(261.331 - 452.639i) q^{25} -3570.24 q^{27} -212.806 q^{29} +(-114.856 + 198.936i) q^{31} +(2237.49 + 3875.45i) q^{33} +(4559.37 + 7897.06i) q^{37} +(3021.47 - 5233.34i) q^{39} -16772.9 q^{41} +16121.9 q^{43} +(-633.909 + 1097.96i) q^{45} +(-562.734 - 974.683i) q^{47} +(8479.58 + 14687.1i) q^{51} +(-17082.1 + 29587.0i) q^{53} -13948.4 q^{55} -35741.3 q^{57} +(-5595.60 + 9691.86i) q^{59} +(-17996.6 - 31171.0i) q^{61} +(9417.86 + 16312.2i) q^{65} +(28759.3 - 49812.5i) q^{67} -16593.8 q^{69} -20951.5 q^{71} +(-28213.5 + 48867.2i) q^{73} +(4277.00 + 7407.98i) q^{75} +(-24080.5 - 41708.7i) q^{79} +(32235.3 - 55833.2i) q^{81} -64392.7 q^{83} -52861.3 q^{85} +(1741.41 - 3016.21i) q^{87} +(-31248.1 - 54123.3i) q^{89} +(-1879.76 - 3255.83i) q^{93} +(55702.4 - 96479.4i) q^{95} +35202.8 q^{97} -6795.46 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 122 q^{9} - 248 q^{11} - 752 q^{15} + 2904 q^{23} - 1510 q^{25} - 816 q^{29} + 18648 q^{37} + 15240 q^{39} - 21168 q^{43} - 3016 q^{51} + 66772 q^{53} - 112528 q^{57} + 55316 q^{65} + 169632 q^{67}+ \cdots - 347024 q^{99}+O(q^{100}) \) 12 * q + 122 * q^9 - 248 * q^11 - 752 * q^15 + 2904 * q^23 - 1510 * q^25 - 816 * q^29 + 18648 * q^37 + 15240 * q^39 - 21168 * q^43 - 3016 * q^51 + 66772 * q^53 - 112528 * q^57 + 55316 * q^65 + 169632 * q^67 - 109760 * q^71 - 50576 * q^79 + 270194 * q^81 - 812152 * q^85 + 164944 * q^93 + 551912 * q^95 - 347024 * q^99

Introduction

L-functions

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