LMFDB - Embedded newform 80.6.n.d.63.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,6,Mod(47,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1]))

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

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

chi := DirichletCharacter("80.47");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	80.n (of order $4$, degree $2$, 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:	$12.8307055850$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 271 x^{18} + 109637 x^{16} + 25993614 x^{14} + 5522961902 x^{12} + 881545050522 x^{10} + \cdots + 57\!\cdots\!24 $ x^20 + 271x^18 + 109637x^16 + 25993614x^14 + 5522961902x^12 + 881545050522x^10 + 133816049059481x^8 + 14779507781220031x^6 + 824105698447750789x^4 + 12044868290803250652*x^2 + 579398322543528055824
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{65}\cdot 3^{4}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			63.9
Root			$-3.75557 - 3.81117i$ of defining polynomial
Character	$\chi$	$=$	80.63
Dual form			80.6.n.d.47.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(17.2921 - 17.2921i) q^{3} +(46.1930 - 31.4834i) q^{5} +(-154.079 - 154.079i) q^{7} -355.037i q^{9} +O(q^{10})$	\(q+(17.2921 - 17.2921i) q^{3} +(46.1930 - 31.4834i) q^{5} +(-154.079 - 154.079i) q^{7} -355.037i q^{9} +127.489i q^{11} +(335.067 + 335.067i) q^{13} +(254.362 - 1343.19i) q^{15} +(-1155.01 + 1155.01i) q^{17} -28.2166 q^{19} -5328.70 q^{21} +(2783.04 - 2783.04i) q^{23} +(1142.60 - 2908.63i) q^{25} +(-1937.35 - 1937.35i) q^{27} +3388.31i q^{29} -5384.41i q^{31} +(2204.56 + 2204.56i) q^{33} +(-11968.3 - 2266.45i) q^{35} +(11534.0 - 11534.0i) q^{37} +11588.1 q^{39} -11147.8 q^{41} +(1437.07 - 1437.07i) q^{43} +(-11177.7 - 16400.2i) q^{45} +(219.040 + 219.040i) q^{47} +30673.4i q^{49} +39945.1i q^{51} +(22745.6 + 22745.6i) q^{53} +(4013.79 + 5889.12i) q^{55} +(-487.926 + 487.926i) q^{57} +22196.6 q^{59} -1431.25 q^{61} +(-54703.5 + 54703.5i) q^{63} +(26026.8 + 4928.73i) q^{65} +(28948.2 + 28948.2i) q^{67} -96249.3i q^{69} -24188.3i q^{71} +(28574.8 + 28574.8i) q^{73} +(-30538.4 - 70054.3i) q^{75} +(19643.4 - 19643.4i) q^{77} -23417.0 q^{79} +19271.9 q^{81} +(18919.5 - 18919.5i) q^{83} +(-16989.8 + 89716.9i) q^{85} +(58591.1 + 58591.1i) q^{87} -8179.53i q^{89} -103253. i q^{91} +(-93107.9 - 93107.9i) q^{93} +(-1303.41 + 888.354i) q^{95} +(-76747.2 + 76747.2i) q^{97} +45263.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 44 q^{5}+O(q^{10}) $ 20 * q - 44 * q^5	$ 20 q - 44 q^{5} + 804 q^{13} - 2236 q^{17} - 4520 q^{21} + 948 q^{25} - 11096 q^{33} + 44260 q^{37} - 6760 q^{41} - 92816 q^{45} + 182452 q^{53} - 34288 q^{57} - 41080 q^{61} - 155772 q^{65} + 264372 q^{73} + 399304 q^{77} - 520220 q^{81} - 344796 q^{85} + 713496 q^{93} + 374772 q^{97}+O(q^{100}) $ 20 * q - 44 * q^5 + 804 * q^13 - 2236 * q^17 - 4520 * q^21 + 948 * q^25 - 11096 * q^33 + 44260 * q^37 - 6760 * q^41 - 92816 * q^45 + 182452 * q^53 - 34288 * q^57 - 41080 * q^61 - 155772 * q^65 + 264372 * q^73 + 399304 * q^77 - 520220 * q^81 - 344796 * q^85 + 713496 * q^93 + 374772 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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
$3$	17.2921	−	17.2921i	1.10929	−	1.10929i	0.116048	−	0.993244i	$-0.462977\pi$
$3$	17.2921	−	17.2921i	1.10929	−	1.10929i	0.993244	−	0.116048i	$-0.0370227\pi$
$4$		0			0
$5$	46.1930	−	31.4834i	0.826326	−	0.563192i
$5$	46.1930	−	31.4834i	0.826326	−	0.563192i
$6$		0			0
$7$	−154.079	−	154.079i	−1.18849	−	1.18849i	−0.977484	−	0.211011i	$-0.932324\pi$
$7$	−154.079	−	154.079i	−1.18849	−	1.18849i	−0.211011	−	0.977484i	$-0.567676\pi$
$8$		0			0
$9$		−	355.037i		−	1.46106i
$10$		0			0
$11$			127.489i			0.317682i	0.987304	+	0.158841i	$0.0507757\pi$
$11$			127.489i			0.317682i	−0.987304	+	0.158841i	$0.949224\pi$
$12$		0			0
$13$	335.067	+	335.067i	0.549887	+	0.549887i	0.926408	−	0.376521i	$-0.122880\pi$
$13$	335.067	+	335.067i	0.549887	+	0.549887i	−0.376521	+	0.926408i	$0.622880\pi$
$14$		0			0
$15$	254.362	−	1343.19i	0.291893	−	1.54138i
$16$		0			0
$17$	−1155.01	+	1155.01i	−0.969310	+	0.969310i	−0.999543	−	0.0302331i	$-0.990375\pi$
$17$	−1155.01	+	1155.01i	−0.969310	+	0.969310i	0.0302331	+	0.999543i	$0.490375\pi$
$18$		0			0
$19$	−28.2166			−0.0179317			−0.00896584	−	0.999960i	$-0.502854\pi$
$19$	−28.2166			−0.0179317			−0.00896584	+	0.999960i	$0.502854\pi$
$20$		0			0
$21$	−5328.70			−2.63677
$22$		0			0
$23$	2783.04	−	2783.04i	1.09698	−	1.09698i	0.102219	−	0.994762i	$-0.467406\pi$
$23$	2783.04	−	2783.04i	1.09698	−	1.09698i	0.994762	−	0.102219i	$-0.0325943\pi$
$24$		0			0
$25$	1142.60	−	2908.63i	0.365631	−	0.930760i
$26$		0			0
$27$	−1937.35	−	1937.35i	−0.511446	−	0.511446i
$28$		0			0
$29$			3388.31i			0.748149i	0.927399	+	0.374074i	$0.122040\pi$
$29$			3388.31i			0.748149i	−0.927399	+	0.374074i	$0.877960\pi$
$30$		0			0
$31$		−	5384.41i		−	1.00631i	−0.864195	−	0.503157i	$-0.832172\pi$
$31$		−	5384.41i		−	1.00631i	0.864195	−	0.503157i	$-0.167828\pi$
$32$		0			0
$33$	2204.56	+	2204.56i	0.352402	+	0.352402i
$34$		0			0
$35$	−11968.3	−	2266.45i	−1.65143	−	0.312734i
$36$		0			0
$37$	11534.0	−	11534.0i	1.38508	−	1.38508i	0.549757	−	0.835324i	$-0.314720\pi$
$37$	11534.0	−	11534.0i	1.38508	−	1.38508i	0.835324	−	0.549757i	$-0.185280\pi$
$38$		0			0
$39$	11588.1			1.21997
$40$		0			0
$41$	−11147.8			−1.03569			−0.517844	−	0.855475i	$-0.673265\pi$
$41$	−11147.8			−1.03569			−0.517844	+	0.855475i	$0.673265\pi$
$42$		0			0
$43$	1437.07	−	1437.07i	0.118524	−	0.118524i	−0.645357	−	0.763881i	$-0.723291\pi$
$43$	1437.07	−	1437.07i	0.118524	−	0.118524i	0.763881	+	0.645357i	$0.223291\pi$
$44$		0			0
$45$	−11177.7	−	16400.2i	−0.822855	−	1.20731i
$46$		0			0
$47$	219.040	+	219.040i	0.0144637	+	0.0144637i	0.714302	−	0.699838i	$-0.246744\pi$
$47$	219.040	+	219.040i	0.0144637	+	0.0144637i	−0.699838	+	0.714302i	$0.746744\pi$
$48$		0			0
$49$			30673.4i			1.82504i
$50$		0			0
$51$			39945.1i			2.15049i
$52$		0			0
$53$	22745.6	+	22745.6i	1.11226	+	1.11226i	0.992844	+	0.119421i	$0.0381037\pi$
$53$	22745.6	+	22745.6i	1.11226	+	1.11226i	0.119421	+	0.992844i	$0.461896\pi$
$54$		0			0
$55$	4013.79	+	5889.12i	0.178916	+	0.262509i
$56$		0			0
$57$	−487.926	+	487.926i	−0.0198915	+	0.0198915i
$58$		0			0
$59$	22196.6			0.830149			0.415074	−	0.909787i	$-0.363756\pi$
$59$	22196.6			0.830149			0.415074	+	0.909787i	$0.363756\pi$
$60$		0			0
$61$	−1431.25			−0.0492484			−0.0246242	−	0.999697i	$-0.507839\pi$
$61$	−1431.25			−0.0492484			−0.0246242	+	0.999697i	$0.507839\pi$
$62$		0			0
$63$	−54703.5	+	54703.5i	−1.73646	+	1.73646i
$64$		0			0
$65$	26026.8	+	4928.73i	0.764078	+	0.144694i
$66$		0			0
$67$	28948.2	+	28948.2i	0.787835	+	0.787835i	0.981139	−	0.193304i	$-0.0619204\pi$
$67$	28948.2	+	28948.2i	0.787835	+	0.787835i	−0.193304	+	0.981139i	$0.561920\pi$
$68$		0			0
$69$		−	96249.3i		−	2.43374i
$70$		0			0
$71$		−	24188.3i		−	0.569456i	−0.958608	−	0.284728i	$-0.908097\pi$
$71$		−	24188.3i		−	0.569456i	0.958608	−	0.284728i	$-0.0919032\pi$
$72$		0			0
$73$	28574.8	+	28574.8i	0.627591	+	0.627591i	0.947461	−	0.319871i	$-0.103639\pi$
$73$	28574.8	+	28574.8i	0.627591	+	0.627591i	−0.319871	+	0.947461i	$0.603639\pi$
$74$		0			0
$75$	−30538.4	−	70054.3i	−0.626894	−	1.43808i
$76$		0			0
$77$	19643.4	−	19643.4i	0.377563	−	0.377563i
$78$		0			0
$79$	−23417.0			−0.422147			−0.211073	−	0.977470i	$-0.567696\pi$
$79$	−23417.0			−0.422147			−0.211073	+	0.977470i	$0.567696\pi$
$80$		0			0
$81$	19271.9			0.326371
$82$		0			0
$83$	18919.5	−	18919.5i	0.301450	−	0.301450i	−0.540131	−	0.841581i	$-0.681625\pi$
$83$	18919.5	−	18919.5i	0.301450	−	0.301450i	0.841581	+	0.540131i	$0.181625\pi$
$84$		0			0
$85$	−16989.8	+	89716.9i	−0.255059	+	1.34687i
$86$		0			0
$87$	58591.1	+	58591.1i	0.829915	+	0.829915i
$88$		0			0
$89$		−	8179.53i		−	0.109459i	−0.998501	−	0.0547297i	$-0.982570\pi$
$89$		−	8179.53i		−	0.109459i	0.998501	−	0.0547297i	$-0.0174297\pi$
$90$		0			0
$91$		−	103253.i		−	1.30708i
$92$		0			0
$93$	−93107.9	−	93107.9i	−1.11630	−	1.11630i
$94$		0			0
$95$	−1303.41	+	888.354i	−0.0148174	+	0.0100990i
$96$		0			0
$97$	−76747.2	+	76747.2i	−0.828196	+	0.828196i	−0.987267	−	0.159071i	$-0.949150\pi$
$97$	−76747.2	+	76747.2i	−0.828196	+	0.828196i	0.159071	+	0.987267i	$0.449150\pi$
$98$		0			0
$99$	45263.4			0.464151
$100$		0			0
$101$	−1379.60			−0.0134570			−0.00672851	−	0.999977i	$-0.502142\pi$
$101$	−1379.60			−0.0134570			−0.00672851	+	0.999977i	$0.502142\pi$
$102$		0			0
$103$	−127370.	+	127370.i	−1.18297	+	1.18297i	−0.203994	+	0.978972i	$0.565392\pi$
$103$	−127370.	+	127370.i	−1.18297	+	1.18297i	−0.978972	+	0.203994i	$0.934608\pi$
$104$		0			0
$105$	−246149.	+	167765.i	−2.17884	+	1.48501i
$106$		0			0
$107$	17327.3	+	17327.3i	0.146309	+	0.146309i	0.776467	−	0.630158i	$-0.217010\pi$
$107$	17327.3	+	17327.3i	0.146309	+	0.146309i	−0.630158	+	0.776467i	$0.717010\pi$
$108$		0			0
$109$		−	105777.i		−	0.852759i	−0.904544	−	0.426379i	$-0.859789\pi$
$109$		−	105777.i		−	0.852759i	0.904544	−	0.426379i	$-0.140211\pi$
$110$		0			0
$111$		−	398895.i		−	3.07292i
$112$		0			0
$113$	63449.7	+	63449.7i	0.467449	+	0.467449i	0.901087	−	0.433638i	$-0.142770\pi$
$113$	63449.7	+	63449.7i	0.467449	+	0.467449i	−0.433638	+	0.901087i	$0.642770\pi$
$114$		0			0
$115$	40937.6	−	216176.i	0.288654	−	1.52428i
$116$		0			0
$117$	118961.	−	118961.i	0.803416	−	0.803416i
$118$		0			0
$119$	355924.			2.30404
$120$		0			0
$121$	144797.			0.899078
$122$		0			0
$123$	−192769.	+	192769.i	−1.14888	+	1.14888i
$124$		0			0
$125$	−38793.3	−	170331.i	−0.222066	−	0.975032i
$126$		0			0
$127$	−150685.	−	150685.i	−0.829009	−	0.829009i	0.158370	−	0.987380i	$-0.449376\pi$
$127$	−150685.	−	150685.i	−0.829009	−	0.829009i	−0.987380	+	0.158370i	$0.949376\pi$
$128$		0			0
$129$		−	49700.1i		−	0.262956i
$130$		0			0
$131$			218406.i			1.11195i	0.831199	+	0.555976i	$0.187655\pi$
$131$			218406.i			1.11195i	−0.831199	+	0.555976i	$0.812345\pi$
$132$		0			0
$133$	4347.58	+	4347.58i	0.0213117	+	0.0213117i
$134$		0			0
$135$	−150487.	−	28497.9i	−0.710663	−	0.134579i
$136$		0			0
$137$	48858.6	−	48858.6i	0.222403	−	0.222403i	−0.587107	−	0.809509i	$-0.699733\pi$
$137$	48858.6	−	48858.6i	0.222403	−	0.222403i	0.809509	+	0.587107i	$0.199733\pi$
$138$		0			0
$139$	−356608.			−1.56550			−0.782752	−	0.622334i	$-0.786185\pi$
$139$	−356608.			−1.56550			−0.782752	+	0.622334i	$0.786185\pi$
$140$		0			0
$141$	7575.36			0.0320889
$142$		0			0
$143$	−42717.5	+	42717.5i	−0.174689	+	0.174689i
$144$		0			0
$145$	106675.	+	156516.i	0.421351	+	0.618215i
$146$		0			0
$147$	530409.	+	530409.i	2.02450	+	2.02450i
$148$		0			0
$149$		−	39079.0i		−	0.144204i	−0.997397	−	0.0721022i	$-0.977029\pi$
$149$		−	39079.0i		−	0.144204i	0.997397	−	0.0721022i	$-0.0229708\pi$
$150$		0			0
$151$			355671.i			1.26942i	0.772750	+	0.634711i	$0.218881\pi$
$151$			355671.i			1.26942i	−0.772750	+	0.634711i	$0.781119\pi$
$152$		0			0
$153$	410070.	+	410070.i	1.41622	+	1.41622i
$154$		0			0
$155$	−169519.	−	248722.i	−0.566748	−	0.831544i
$156$		0			0
$157$	−37305.0	+	37305.0i	−0.120786	+	0.120786i	−0.764916	−	0.644130i	$-0.777220\pi$
$157$	−37305.0	+	37305.0i	−0.120786	+	0.120786i	0.644130	+	0.764916i	$0.277220\pi$
$158$		0			0
$159$	786641.			2.46765
$160$		0			0
$161$	−857612.			−2.60751
$162$		0			0
$163$	−180954.	+	180954.i	−0.533458	+	0.533458i	−0.921600	−	0.388142i	$-0.873117\pi$
$163$	−180954.	+	180954.i	−0.533458	+	0.533458i	0.388142	+	0.921600i	$0.373117\pi$
$164$		0			0
$165$	171243.	+	32428.4i	0.489668	+	0.0927291i
$166$		0			0
$167$	174882.	+	174882.i	0.485236	+	0.485236i	0.906799	−	0.421563i	$-0.138518\pi$
$167$	174882.	+	174882.i	0.485236	+	0.485236i	−0.421563	+	0.906799i	$0.638518\pi$
$168$		0			0
$169$		−	146753.i		−	0.395249i
$170$		0			0
$171$			10017.9i			0.0261992i
$172$		0			0
$173$	376164.	+	376164.i	0.955568	+	0.955568i	0.999054	−	0.0434856i	$-0.0138463\pi$
$173$	376164.	+	376164.i	0.955568	+	0.955568i	−0.0434856	+	0.999054i	$0.513846\pi$
$174$		0			0
$175$	−624206.	+	272107.i	−1.54075	+	0.671653i
$176$		0			0
$177$	383826.	−	383826.i	0.920877	−	0.920877i
$178$		0			0
$179$	−384984.			−0.898070			−0.449035	−	0.893514i	$-0.648232\pi$
$179$	−384984.			−0.898070			−0.449035	+	0.893514i	$0.648232\pi$
$180$		0			0
$181$	−332337.			−0.754020			−0.377010	−	0.926209i	$-0.623048\pi$
$181$	−332337.			−0.754020			−0.377010	+	0.926209i	$0.623048\pi$
$182$		0			0
$183$	−24749.5	+	24749.5i	−0.0546308	+	0.0546308i
$184$		0			0
$185$	169661.	−	895919.i	0.364463	−	1.92460i
$186$		0			0
$187$	−147251.	−	147251.i	−0.307932	−	0.307932i
$188$		0			0
$189$			597010.i			1.21570i
$190$		0			0
$191$			164553.i			0.326378i	0.986595	+	0.163189i	$0.0521781\pi$
$191$			164553.i			0.326378i	−0.986595	+	0.163189i	$0.947822\pi$
$192$		0			0
$193$	−58078.0	−	58078.0i	−0.112232	−	0.112232i	0.648760	−	0.760993i	$-0.275288\pi$
$193$	−58078.0	−	58078.0i	−0.112232	−	0.112232i	−0.760993	+	0.648760i	$0.775288\pi$
$194$		0			0
$195$	535288.	−	364831.i	1.00809	−	0.687077i
$196$		0			0
$197$	386719.	−	386719.i	0.709954	−	0.709954i	−0.256571	−	0.966525i	$-0.582593\pi$
$197$	386719.	−	386719.i	0.709954	−	0.709954i	0.966525	+	0.256571i	$0.0825929\pi$
$198$		0			0
$199$	−14055.2			−0.0251596			−0.0125798	−	0.999921i	$-0.504004\pi$
$199$	−14055.2			−0.0251596			−0.0125798	+	0.999921i	$0.504004\pi$
$200$		0			0
$201$	1.00115e6			1.74788
$202$		0			0
$203$	522066.	−	522066.i	0.889171	−	0.889171i
$204$		0			0
$205$	−514950.	+	350970.i	−0.855816	+	0.583291i
$206$		0			0
$207$	−988080.	−	988080.i	−1.60275	−	1.60275i
$208$		0			0
$209$		−	3597.32i		−	0.00569657i
$210$		0			0
$211$		−	438963.i		−	0.678768i	−0.940648	−	0.339384i	$-0.889781\pi$
$211$		−	438963.i		−	0.678768i	0.940648	−	0.339384i	$-0.110219\pi$
$212$		0			0
$213$	−418268.	−	418268.i	−0.631692	−	0.631692i
$214$		0			0
$215$	21138.9	−	111627.i	0.0311878	−	0.164691i
$216$		0			0
$217$	−829622.	+	829622.i	−1.19600	+	1.19600i
$218$		0			0
$219$	988240.			1.39236
$220$		0			0
$221$	−774010.			−1.06602
$222$		0			0
$223$	−413890.	+	413890.i	−0.557343	+	0.557343i	−0.928550	−	0.371207i	$-0.878944\pi$
$223$	−413890.	+	413890.i	−0.557343	+	0.557343i	0.371207	+	0.928550i	$0.378944\pi$
$224$		0			0
$225$	−1.03267e6	−	405663.i	−1.35989	−	0.534207i
$226$		0			0
$227$	165742.	+	165742.i	0.213485	+	0.213485i	0.805746	−	0.592261i	$-0.201765\pi$
$227$	165742.	+	165742.i	0.213485	+	0.213485i	−0.592261	+	0.805746i	$0.701765\pi$
$228$		0			0
$229$			590717.i			0.744373i	0.928158	+	0.372187i	$0.121392\pi$
$229$			590717.i			0.744373i	−0.928158	+	0.372187i	$0.878608\pi$
$230$		0			0
$231$		−	679352.i		−	0.837655i
$232$		0			0
$233$	−849795.	−	849795.i	−1.02547	−	1.02547i	−0.999667	−	0.0258063i	$-0.991785\pi$
$233$	−849795.	−	849795.i	−1.02547	−	1.02547i	−0.0258063	−	0.999667i	$-0.508215\pi$
$234$		0			0
$235$	17014.3	+	3222.02i	0.0200976	+	0.00380591i
$236$		0			0
$237$	−404930.	+	404930.i	−0.468284	+	0.468284i
$238$		0			0
$239$	−72025.5			−0.0815627			−0.0407814	−	0.999168i	$-0.512985\pi$
$239$	−72025.5			−0.0815627			−0.0407814	+	0.999168i	$0.512985\pi$
$240$		0			0
$241$	358847.			0.397985			0.198992	−	0.980001i	$-0.436233\pi$
$241$	358847.			0.397985			0.198992	+	0.980001i	$0.436233\pi$
$242$		0			0
$243$	804029.	−	804029.i	0.873486	−	0.873486i
$244$		0			0
$245$	965703.	+	1.41690e6i	1.02785	+	1.50808i
$246$		0			0
$247$	−9454.46	−	9454.46i	−0.00986040	−	0.00986040i
$248$		0			0
$249$		−	654318.i		−	0.668791i
$250$		0			0
$251$			209249.i			0.209642i	0.994491	+	0.104821i	$0.0334270\pi$
$251$			209249.i			0.209642i	−0.994491	+	0.104821i	$0.966573\pi$
$252$		0			0
$253$	354807.	+	354807.i	0.348491	+	0.348491i
$254$		0			0
$255$	1.25761e6	+	1.84519e6i	1.21114	+	1.77701i
$256$		0			0
$257$	−228218.	+	228218.i	−0.215535	+	0.215535i	−0.806614	−	0.591079i	$-0.798702\pi$
$257$	−228218.	+	228218.i	−0.215535	+	0.215535i	0.591079	+	0.806614i	$0.298702\pi$
$258$		0			0
$259$	−3.55428e6			−3.29232
$260$		0			0
$261$	1.20297e6			1.09309
$262$		0			0
$263$	945242.	−	945242.i	0.842663	−	0.842663i	−0.146542	−	0.989204i	$-0.546814\pi$
$263$	945242.	−	945242.i	0.842663	−	0.842663i	0.989204	+	0.146542i	$0.0468143\pi$
$264$		0			0
$265$	1.76680e6	+	334581.i	1.54551	+	0.292675i
$266$		0			0
$267$	−141442.	−	141442.i	−0.121422	−	0.121422i
$268$		0			0
$269$		−	1.56559e6i		−	1.31916i	−0.751635	−	0.659579i	$-0.770735\pi$
$269$		−	1.56559e6i		−	1.31916i	0.751635	−	0.659579i	$-0.229265\pi$
$270$		0			0
$271$		−	990821.i		−	0.819543i	−0.912188	−	0.409772i	$-0.865608\pi$
$271$		−	990821.i		−	0.819543i	0.912188	−	0.409772i	$-0.134392\pi$
$272$		0			0
$273$	−1.78547e6	−	1.78547e6i	−1.44993	−	1.44993i
$274$		0			0
$275$	370819.	+	145669.i	0.295685	+	0.116154i
$276$		0			0
$277$	−174283.	+	174283.i	−0.136476	+	0.136476i	−0.772044	−	0.635569i	$-0.780766\pi$
$277$	−174283.	+	174283.i	−0.136476	+	0.136476i	0.635569	+	0.772044i	$0.280766\pi$
$278$		0			0
$279$	−1.91166e6			−1.47028
$280$		0			0
$281$	2.17766e6			1.64522			0.822609	−	0.568607i	$-0.192517\pi$
$281$	2.17766e6			1.64522			0.822609	+	0.568607i	$0.192517\pi$
$282$		0			0
$283$	−502126.	+	502126.i	−0.372689	+	0.372689i	−0.868456	−	0.495767i	$-0.834887\pi$
$283$	−502126.	+	502126.i	−0.372689	+	0.372689i	0.495767	+	0.868456i	$0.334887\pi$
$284$		0			0
$285$	−7177.24	+	37900.3i	−0.00523414	+	0.0276396i
$286$		0			0
$287$	1.71763e6	+	1.71763e6i	1.23091	+	1.23091i
$288$		0			0
$289$		−	1.24823e6i		−	0.879123i
$290$		0			0
$291$			2.65425e6i			1.83742i
$292$		0			0
$293$	45772.5	+	45772.5i	0.0311484	+	0.0311484i	0.722509	−	0.691361i	$-0.242989\pi$
$293$	45772.5	+	45772.5i	0.0311484	+	0.0311484i	−0.691361	+	0.722509i	$0.742989\pi$
$294$		0			0
$295$	1.02533e6	−	698823.i	0.685974	−	0.467533i
$296$		0			0
$297$	246992.	−	246992.i	0.162477	−	0.162477i
$298$		0			0
$299$	1.86501e6			1.20643
$300$		0			0
$301$	−442844.			−0.281731
$302$		0			0
$303$	−23856.2	+	23856.2i	−0.0149277	+	0.0149277i
$304$		0			0
$305$	−66114.0	+	45060.7i	−0.0406953	+	0.0277363i
$306$		0			0
$307$	−1.39565e6	−	1.39565e6i	−0.845144	−	0.845144i	0.144379	−	0.989523i	$-0.453882\pi$
$307$	−1.39565e6	−	1.39565e6i	−0.845144	−	0.845144i	−0.989523	+	0.144379i	$0.953882\pi$
$308$		0			0
$309$			4.40498e6i			2.62451i
$310$		0			0
$311$			1.84115e6i			1.07942i	0.841852	+	0.539709i	$0.181466\pi$
$311$			1.84115e6i			1.07942i	−0.841852	+	0.539709i	$0.818534\pi$
$312$		0			0
$313$	2.22340e6	+	2.22340e6i	1.28279	+	1.28279i	0.939073	+	0.343718i	$0.111686\pi$
$313$	2.22340e6	+	2.22340e6i	1.28279	+	1.28279i	0.343718	+	0.939073i	$0.388314\pi$
$314$		0			0
$315$	−804672.	+	4.24918e6i	−0.456922	+	2.41284i
$316$		0			0
$317$	−1.35501e6	+	1.35501e6i	−0.757344	+	0.757344i	−0.975838	−	0.218495i	$-0.929885\pi$
$317$	−1.35501e6	+	1.35501e6i	−0.757344	+	0.757344i	0.218495	+	0.975838i	$0.429885\pi$
$318$		0			0
$319$	−431973.			−0.237673
$320$		0			0
$321$	599254.			0.324600
$322$		0			0
$323$	32590.4	−	32590.4i	0.0173814	−	0.0173814i
$324$		0			0
$325$	1.35743e6	−	591738.i	0.712868	−	0.310757i
$326$		0			0
$327$	−1.82912e6	−	1.82912e6i	−0.945958	−	0.945958i
$328$		0			0
$329$		−	67498.9i		−	0.0343801i
$330$		0			0
$331$			2.40493e6i			1.20652i	0.797546	+	0.603258i	$0.206131\pi$
$331$			2.40493e6i			1.20652i	−0.797546	+	0.603258i	$0.793869\pi$
$332$		0			0
$333$	−4.09499e6	−	4.09499e6i	−2.02368	−	2.02368i
$334$		0			0
$335$	2.24859e6	+	425819.i	1.09471	+	0.207307i
$336$		0			0
$337$	−1.72476e6	+	1.72476e6i	−0.827284	+	0.827284i	−0.987140	−	0.159856i	$-0.948897\pi$
$337$	−1.72476e6	+	1.72476e6i	−0.827284	+	0.827284i	0.159856	+	0.987140i	$0.448897\pi$
$338$		0			0
$339$	2.19436e6			1.03707
$340$		0			0
$341$	686454.			0.319687
$342$		0			0
$343$	2.13652e6	−	2.13652e6i	0.980554	−	0.980554i
$344$		0			0
$345$	−3.03025e6	−	4.44605e6i	−1.37066	−	2.01107i
$346$		0			0
$347$	−2.06948e6	−	2.06948e6i	−0.922653	−	0.922653i	0.0745635	−	0.997216i	$-0.476244\pi$
$347$	−2.06948e6	−	2.06948e6i	−0.922653	−	0.922653i	−0.997216	+	0.0745635i	$0.976244\pi$
$348$		0			0
$349$			1.88338e6i			0.827702i	0.910345	+	0.413851i	$0.135817\pi$
$349$			1.88338e6i			0.827702i	−0.910345	+	0.413851i	$0.864183\pi$
$350$		0			0
$351$		−	1.29829e6i		−	0.562475i
$352$		0			0
$353$	1.77943e6	+	1.77943e6i	0.760054	+	0.760054i	0.976332	−	0.216278i	$-0.0693916\pi$
$353$	1.77943e6	+	1.77943e6i	0.760054	+	0.760054i	−0.216278	+	0.976332i	$0.569392\pi$
$354$		0			0
$355$	−761530.	−	1.11733e6i	−0.320713	−	0.470556i
$356$		0			0
$357$	6.15469e6	−	6.15469e6i	2.55585	−	2.55585i
$358$		0			0
$359$	−4.50238e6			−1.84377			−0.921884	−	0.387466i	$-0.873350\pi$
$359$	−4.50238e6			−1.84377			−0.921884	+	0.387466i	$0.873350\pi$
$360$		0			0
$361$	−2.47530e6			−0.999678
$362$		0			0
$363$	2.50386e6	−	2.50386e6i	0.997340	−	0.997340i
$364$		0			0
$365$	2.21959e6	+	420327.i	0.872049	+	0.165141i
$366$		0			0
$367$	604369.	+	604369.i	0.234227	+	0.234227i	0.814455	−	0.580227i	$-0.197036\pi$
$367$	604369.	+	604369.i	0.234227	+	0.234227i	−0.580227	+	0.814455i	$0.697036\pi$
$368$		0			0
$369$			3.95787e6i			1.51320i
$370$		0			0
$371$		−	7.00922e6i		−	2.64384i
$372$		0			0
$373$	87601.5	+	87601.5i	0.0326016	+	0.0326016i	0.723220	−	0.690618i	$-0.242661\pi$
$373$	87601.5	+	87601.5i	0.0326016	+	0.0326016i	−0.690618	+	0.723220i	$0.742661\pi$
$374$		0			0
$375$	−3.61621e6	−	2.27457e6i	−1.32793	−	0.835258i
$376$		0			0
$377$	−1.13531e6	+	1.13531e6i	−0.411397	+	0.411397i
$378$		0			0
$379$	2.48550e6			0.888824			0.444412	−	0.895823i	$-0.353413\pi$
$379$	2.48550e6			0.888824			0.444412	+	0.895823i	$0.353413\pi$
$380$		0			0
$381$	−5.21132e6			−1.83923
$382$		0			0
$383$	601337.	−	601337.i	0.209470	−	0.209470i	−0.594572	−	0.804042i	$-0.702679\pi$
$383$	601337.	−	601337.i	0.209470	−	0.209470i	0.804042	+	0.594572i	$0.202679\pi$
$384$		0			0
$385$	288948.	−	1.52583e6i	0.0993499	−	0.524630i
$386$		0			0
$387$	−510213.	−	510213.i	−0.173171	−	0.173171i
$388$		0			0
$389$		−	3.73874e6i		−	1.25271i	−0.779537	−	0.626356i	$-0.784546\pi$
$389$		−	3.73874e6i		−	1.25271i	0.779537	−	0.626356i	$-0.215454\pi$
$390$		0			0
$391$			6.42886e6i			2.12663i
$392$		0			0
$393$	3.77670e6	+	3.77670e6i	1.23348	+	1.23348i
$394$		0			0
$395$	−1.08170e6	+	737246.i	−0.348831	+	0.237750i
$396$		0			0
$397$	−209001.	+	209001.i	−0.0665538	+	0.0665538i	−0.739600	−	0.673046i	$-0.764985\pi$
$397$	−209001.	+	209001.i	−0.0665538	+	0.0665538i	0.673046	+	0.739600i	$0.264985\pi$
$398$		0			0
$399$	150358.			0.0472818
$400$		0			0
$401$	−3.88404e6			−1.20621			−0.603104	−	0.797662i	$-0.706070\pi$
$401$	−3.88404e6			−1.20621			−0.603104	+	0.797662i	$0.706070\pi$
$402$		0			0
$403$	1.80414e6	−	1.80414e6i	0.553359	−	0.553359i
$404$		0			0
$405$	890227.	−	606743.i	0.269689	−	0.183809i
$406$		0			0
$407$	1.47046e6	+	1.47046e6i	0.440015	+	0.440015i
$408$		0			0
$409$		−	1.17358e6i		−	0.346899i	−0.984843	−	0.173450i	$-0.944509\pi$
$409$		−	1.17358e6i		−	0.346899i	0.984843	−	0.173450i	$-0.0554913\pi$
$410$		0			0
$411$		−	1.68974e6i		−	0.493419i
$412$		0			0
$413$	−3.42002e6	−	3.42002e6i	−0.986627	−	0.986627i
$414$		0			0
$415$	278300.	−	1.46960e6i	0.0793219	−	0.418870i
$416$		0			0
$417$	−6.16652e6	+	6.16652e6i	−1.73660	+	1.73660i
$418$		0			0
$419$	−1.60340e6			−0.446177			−0.223089	−	0.974798i	$-0.571614\pi$
$419$	−1.60340e6			−0.446177			−0.223089	+	0.974798i	$0.571614\pi$
$420$		0			0
$421$	−3.71020e6			−1.02022			−0.510108	−	0.860111i	$-0.670394\pi$
$421$	−3.71020e6			−1.02022			−0.510108	+	0.860111i	$0.670394\pi$
$422$		0			0
$423$	77767.4	−	77767.4i	0.0211323	−	0.0211323i
$424$		0			0
$425$	2.03978e6	+	4.67919e6i	0.547786	+	1.25660i
$426$		0			0
$427$	220526.	+	220526.i	0.0585315	+	0.0585315i
$428$		0			0
$429$			1.47735e6i			0.387562i
$430$		0			0
$431$			2.29101e6i			0.594065i	0.954867	+	0.297033i	$0.0959971\pi$
$431$			2.29101e6i			0.594065i	−0.954867	+	0.297033i	$0.904003\pi$
$432$		0			0
$433$	−972567.	−	972567.i	−0.249287	−	0.249287i	0.571391	−	0.820678i	$-0.306404\pi$
$433$	−972567.	−	972567.i	−0.249287	−	0.249287i	−0.820678	+	0.571391i	$0.806404\pi$
$434$		0			0
$435$	4.55115e6	+	861857.i	1.15318	+	0.218380i
$436$		0			0
$437$	−78527.9	+	78527.9i	−0.0196707	+	0.0196707i
$438$		0			0
$439$	3.49284e6			0.865002			0.432501	−	0.901633i	$-0.357631\pi$
$439$	3.49284e6			0.865002			0.432501	+	0.901633i	$0.357631\pi$
$440$		0			0
$441$	1.08902e7			2.66648
$442$		0			0
$443$	−4.91464e6	+	4.91464e6i	−1.18982	+	1.18982i	−0.212707	+	0.977116i	$0.568228\pi$
$443$	−4.91464e6	+	4.91464e6i	−1.18982	+	1.18982i	−0.977116	+	0.212707i	$0.931772\pi$
$444$		0			0
$445$	−257519.	−	377837.i	−0.0616466	−	0.0904492i
$446$		0			0
$447$	−675761.	−	675761.i	−0.159965	−	0.159965i
$448$		0			0
$449$		−	3.79845e6i		−	0.889182i	−0.895734	−	0.444591i	$-0.853349\pi$
$449$		−	3.79845e6i		−	0.889182i	0.895734	−	0.444591i	$-0.146651\pi$
$450$		0			0
$451$		−	1.42122e6i		−	0.329019i
$452$		0			0
$453$	6.15031e6	+	6.15031e6i	1.40816	+	1.40816i
$454$		0			0
$455$	−3.25076e6	−	4.76959e6i	−0.736134	−	1.08007i
$456$		0			0
$457$	4.14446e6	−	4.14446e6i	0.928276	−	0.928276i	−0.0693189	−	0.997595i	$-0.522083\pi$
$457$	4.14446e6	−	4.14446e6i	0.928276	−	0.928276i	0.997595	+	0.0693189i	$0.0220826\pi$
$458$		0			0
$459$	4.47532e6			0.991499
$460$		0			0
$461$	1.33612e6			0.292815			0.146407	−	0.989224i	$-0.453229\pi$
$461$	1.33612e6			0.292815			0.146407	+	0.989224i	$0.453229\pi$
$462$		0			0
$463$	−3.66263e6	+	3.66263e6i	−0.794036	+	0.794036i	−0.982148	−	0.188112i	$-0.939763\pi$
$463$	−3.66263e6	+	3.66263e6i	−0.794036	+	0.794036i	0.188112	+	0.982148i	$0.439763\pi$
$464$		0			0
$465$	−7.23229e6	−	1.36959e6i	−1.55111	−	0.293736i
$466$		0			0
$467$	4.58287e6	+	4.58287e6i	0.972401	+	0.972401i	0.999629	−	0.0272279i	$-0.00866797\pi$
$467$	4.58287e6	+	4.58287e6i	0.972401	+	0.972401i	−0.0272279	+	0.999629i	$0.508668\pi$
$468$		0			0
$469$		−	8.92061e6i		−	1.87267i
$470$		0			0
$471$			1.29017e6i			0.267975i
$472$		0			0
$473$	183211.	+	183211.i	0.0376530	+	0.0376530i
$474$		0			0
$475$	−32240.2	+	82071.6i	−0.00655637	+	0.0166901i
$476$		0			0
$477$	8.07553e6	−	8.07553e6i	1.62508	−	1.62508i
$478$		0			0
$479$	−7.00075e6			−1.39414			−0.697069	−	0.717004i	$-0.745513\pi$
$479$	−7.00075e6			−1.39414			−0.697069	+	0.717004i	$0.745513\pi$
$480$		0			0
$481$	7.72932e6			1.52328
$482$		0			0
$483$	−1.48300e7	+	1.48300e7i	−2.89249	+	2.89249i
$484$		0			0
$485$	−1.12893e6	+	5.96145e6i	−0.217927	+	1.15079i
$486$		0			0
$487$	3.98892e6	+	3.98892e6i	0.762137	+	0.762137i	0.976708	−	0.214571i	$-0.0688355\pi$
$487$	3.98892e6	+	3.98892e6i	0.762137	+	0.762137i	−0.214571	+	0.976708i	$0.568835\pi$
$488$		0			0
$489$			6.25818e6i			1.18352i
$490$		0			0
$491$		−	2.30379e6i		−	0.431260i	−0.976475	−	0.215630i	$-0.930819\pi$
$491$		−	2.30379e6i		−	0.431260i	0.976475	−	0.215630i	$-0.0691805\pi$
$492$		0			0
$493$	−3.91352e6	−	3.91352e6i	−0.725188	−	0.725188i
$494$		0			0
$495$	2.09085e6	−	1.42504e6i	0.383540	−	0.261406i
$496$		0			0
$497$	−3.72690e6	+	3.72690e6i	−0.676795	+	0.676795i
$498$		0			0
$499$	2.47982e6			0.445829			0.222914	−	0.974838i	$-0.428443\pi$
$499$	2.47982e6			0.445829			0.222914	+	0.974838i	$0.428443\pi$
$500$		0			0
$501$	6.04816e6			1.07654
$502$		0			0
$503$	4.08077e6	−	4.08077e6i	0.719154	−	0.719154i	−0.249278	−	0.968432i	$-0.580193\pi$
$503$	4.08077e6	−	4.08077e6i	0.719154	−	0.719154i	0.968432	+	0.249278i	$0.0801934\pi$
$504$		0			0
$505$	−63727.8	+	43434.3i	−0.0111199	+	0.00757887i
$506$		0			0
$507$	−2.53768e6	−	2.53768e6i	−0.438446	−	0.438446i
$508$		0			0
$509$			2.80205e6i			0.479382i	0.970849	+	0.239691i	$0.0770461\pi$
$509$			2.80205e6i			0.479382i	−0.970849	+	0.239691i	$0.922954\pi$
$510$		0			0
$511$		−	8.80554e6i		−	1.49178i
$512$		0			0
$513$	54665.6	+	54665.6i	0.00917109	+	0.00917109i
$514$		0			0
$515$	−1.87357e6	+	9.89361e6i	−0.311280	+	1.64375i
$516$		0			0
$517$	−27925.3	+	27925.3i	−0.00459485	+	0.00459485i
$518$		0			0
$519$	1.30094e7			2.12001
$520$		0			0
$521$	144765.			0.0233652			0.0116826	−	0.999932i	$-0.496281\pi$
$521$	144765.			0.0233652			0.0116826	+	0.999932i	$0.496281\pi$
$522$		0			0
$523$	3.79906e6	−	3.79906e6i	0.607327	−	0.607327i	−0.334920	−	0.942247i	$-0.608709\pi$
$523$	3.79906e6	−	3.79906e6i	0.607327	−	0.607327i	0.942247	+	0.334920i	$0.108709\pi$
$524$		0			0
$525$	−6.08855e6	+	1.54992e7i	−0.964085	+	2.45420i
$526$		0			0
$527$	6.21903e6	+	6.21903e6i	0.975430	+	0.975430i
$528$		0			0
$529$		−	9.05423e6i		−	1.40674i
$530$		0			0
$531$		−	7.88060e6i		−	1.21289i
$532$		0			0
$533$	−3.73526e6	−	3.73526e6i	−0.569511	−	0.569511i
$534$		0			0
$535$	1.34593e6	+	254880.i	0.203300	+	0.0384991i
$536$		0			0
$537$	−6.65720e6	+	6.65720e6i	−0.996221	+	0.996221i
$538$		0			0
$539$	−3.91053e6			−0.579781
$540$		0			0
$541$	−1.17321e7			−1.72339			−0.861695	−	0.507426i	$-0.830597\pi$
$541$	−1.17321e7			−1.72339			−0.861695	+	0.507426i	$0.830597\pi$
$542$		0			0
$543$	−5.74683e6	+	5.74683e6i	−0.836428	+	0.836428i
$544$		0			0
$545$	−3.33023e6	−	4.88618e6i	−0.480267	−	0.704657i
$546$		0			0
$547$	5.24186e6	+	5.24186e6i	0.749060	+	0.749060i	0.974303	−	0.225243i	$-0.0723174\pi$
$547$	5.24186e6	+	5.24186e6i	0.749060	+	0.749060i	−0.225243	+	0.974303i	$0.572317\pi$
$548$		0			0
$549$			508148.i			0.0719547i
$550$		0			0
$551$		−	95606.6i		−	0.0134156i
$552$		0			0
$553$	3.60806e6	+	3.60806e6i	0.501719	+	0.501719i
$554$		0			0
$555$	−1.25586e7	−	1.84262e7i	−1.73064	−	2.53923i
$556$		0			0
$557$	7.61782e6	−	7.61782e6i	1.04038	−	1.04038i	0.0412325	−	0.999150i	$-0.486872\pi$
$557$	7.61782e6	−	7.61782e6i	1.04038	−	1.04038i	0.999150	−	0.0412325i	$-0.0131284\pi$
$558$		0			0
$559$	963030.			0.130350
$560$		0			0
$561$	−5.09258e6			−0.683173
$562$		0			0
$563$	86277.5	−	86277.5i	0.0114717	−	0.0114717i	−0.701348	−	0.712819i	$-0.747418\pi$
$563$	86277.5	−	86277.5i	0.0114717	−	0.0114717i	0.712819	+	0.701348i	$0.247418\pi$
$564$		0			0
$565$	4.92855e6	+	933326.i	0.649528	+	0.123002i
$566$		0			0
$567$	−2.96938e6	−	2.96938e6i	−0.387890	−	0.387890i
$568$		0			0
$569$		−	5.02097e6i		−	0.650140i	−0.945690	−	0.325070i	$-0.894612\pi$
$569$		−	5.02097e6i		−	0.650140i	0.945690	−	0.325070i	$-0.105388\pi$
$570$		0			0
$571$			8.08321e6i			1.03751i	0.854922	+	0.518756i	$0.173605\pi$
$571$			8.08321e6i			1.03751i	−0.854922	+	0.518756i	$0.826395\pi$
$572$		0			0
$573$	2.84547e6	+	2.84547e6i	0.362049	+	0.362049i
$574$		0			0
$575$	−4.91492e6	−	1.12747e7i	−0.619936	−	1.42212i
$576$		0			0
$577$	−3.25025e6	+	3.25025e6i	−0.406422	+	0.406422i	−0.880489	−	0.474067i	$-0.842786\pi$
$577$	−3.25025e6	+	3.25025e6i	−0.406422	+	0.406422i	0.474067	+	0.880489i	$0.342786\pi$
$578$		0			0
$579$	−2.00859e6			−0.248997
$580$		0			0
$581$	−5.83018e6			−0.716542
$582$		0			0
$583$	−2.89982e6	+	2.89982e6i	−0.353346	+	0.353346i
$584$		0			0
$585$	1.74988e6	−	9.24047e6i	0.211407	−	1.11636i
$586$		0			0
$587$	−3.79350e6	−	3.79350e6i	−0.454407	−	0.454407i	0.442407	−	0.896814i	$-0.354125\pi$
$587$	−3.79350e6	−	3.79350e6i	−0.454407	−	0.454407i	−0.896814	+	0.442407i	$0.854125\pi$
$588$		0			0
$589$			151930.i			0.0180449i
$590$		0			0
$591$		−	1.33744e7i		−	1.57509i
$592$		0			0
$593$	1.01322e7	+	1.01322e7i	1.18323	+	1.18323i	0.978904	+	0.204321i	$0.0654987\pi$
$593$	1.01322e7	+	1.01322e7i	1.18323	+	1.18323i	0.204321	+	0.978904i	$0.434501\pi$
$594$		0			0
$595$	1.64412e7	−	1.12057e7i	1.90389	−	1.29762i
$596$		0			0
$597$	−243044.	+	243044.i	−0.0279093	+	0.0279093i
$598$		0			0
$599$	1.84016e6			0.209550			0.104775	−	0.994496i	$-0.466588\pi$
$599$	1.84016e6			0.209550			0.104775	+	0.994496i	$0.466588\pi$
$600$		0			0
$601$	2.07660e6			0.234513			0.117257	−	0.993102i	$-0.462590\pi$
$601$	2.07660e6			0.234513			0.117257	+	0.993102i	$0.462590\pi$
$602$		0			0
$603$	1.02777e7	−	1.02777e7i	1.15107	−	1.15107i
$604$		0			0
$605$	6.68864e6	−	4.55871e6i	0.742932	−	0.506353i
$606$		0			0
$607$	−7.47671e6	−	7.47671e6i	−0.823643	−	0.823643i	0.162986	−	0.986628i	$-0.447888\pi$
$607$	−7.47671e6	−	7.47671e6i	−0.823643	−	0.823643i	−0.986628	+	0.162986i	$0.947888\pi$
$608$		0			0
$609$		−	1.80553e7i		−	1.97270i
$610$		0			0
$611$			146786.i			0.0159068i
$612$		0			0
$613$	421185.	+	421185.i	0.0452712	+	0.0452712i	0.729380	−	0.684109i	$-0.239809\pi$
$613$	421185.	+	421185.i	0.0452712	+	0.0452712i	−0.684109	+	0.729380i	$0.739809\pi$
$614$		0			0
$615$	−2.83557e6	+	1.49736e7i	−0.302310	+	1.59639i
$616$		0			0
$617$	4.79146e6	−	4.79146e6i	0.506705	−	0.506705i	−0.406808	−	0.913514i	$-0.633358\pi$
$617$	4.79146e6	−	4.79146e6i	0.506705	−	0.506705i	0.913514	+	0.406808i	$0.133358\pi$
$618$		0			0
$619$	8.81805e6			0.925009			0.462505	−	0.886617i	$-0.346951\pi$
$619$	8.81805e6			0.925009			0.462505	+	0.886617i	$0.346951\pi$
$620$		0			0
$621$	−1.07835e7			−1.12209
$622$		0			0
$623$	−1.26029e6	+	1.26029e6i	−0.130092	+	0.130092i
$624$		0			0
$625$	−7.15458e6	−	6.64676e6i	−0.732629	−	0.680629i
$626$		0			0
$627$	−62205.4	−	62205.4i	−0.00631915	−	0.00631915i
$628$		0			0
$629$			2.66437e7i			2.68515i
$630$		0			0
$631$			4.57807e6i			0.457730i	0.973458	+	0.228865i	$0.0735014\pi$
$631$			4.57807e6i			0.457730i	−0.973458	+	0.228865i	$0.926499\pi$
$632$		0			0
$633$	−7.59061e6	−	7.59061e6i	−0.752952	−	0.752952i
$634$		0			0
$635$	−1.17046e7	−	2.21652e6i	−1.15192	−	0.218141i
$636$		0			0
$637$	−1.02777e7	+	1.02777e7i	−1.00356	+	1.00356i
$638$		0			0
$639$	−8.58774e6			−0.832007
$640$		0			0
$641$	−1.62758e7			−1.56458			−0.782288	−	0.622917i	$-0.785947\pi$
$641$	−1.62758e7			−1.56458			−0.782288	+	0.622917i	$0.785947\pi$
$642$		0			0
$643$	2.99416e6	−	2.99416e6i	0.285593	−	0.285593i	−0.549742	−	0.835335i	$-0.685274\pi$
$643$	2.99416e6	−	2.99416e6i	0.285593	−	0.285593i	0.835335	+	0.549742i	$0.185274\pi$
$644$		0			0
$645$	−1.56473e6	−	2.29580e6i	−0.148094	−	0.217287i
$646$		0			0
$647$	−4.92387e6	−	4.92387e6i	−0.462430	−	0.462430i	0.437021	−	0.899451i	$-0.356033\pi$
$647$	−4.92387e6	−	4.92387e6i	−0.462430	−	0.462430i	−0.899451	+	0.437021i	$0.856033\pi$
$648$		0			0
$649$			2.82983e6i			0.263723i
$650$		0			0
$651$			2.86919e7i			2.65342i
$652$		0			0
$653$	1.05307e7	+	1.05307e7i	0.966441	+	0.966441i	0.999455	−	0.0330138i	$-0.0105105\pi$
$653$	1.05307e7	+	1.05307e7i	0.966441	+	0.966441i	−0.0330138	+	0.999455i	$0.510511\pi$
$654$		0			0
$655$	6.87615e6	+	1.00888e7i	0.626241	+	0.918835i
$656$		0			0
$657$	1.01451e7	−	1.01451e7i	0.916945	−	0.916945i
$658$		0			0
$659$	1.29023e7			1.15732			0.578659	−	0.815570i	$-0.303576\pi$
$659$	1.29023e7			1.15732			0.578659	+	0.815570i	$0.303576\pi$
$660$		0			0
$661$	6.60437e6			0.587933			0.293967	−	0.955816i	$-0.405025\pi$
$661$	6.60437e6			0.587933			0.293967	+	0.955816i	$0.405025\pi$
$662$		0			0
$663$	−1.33843e7	+	1.33843e7i	−1.18253	+	1.18253i
$664$		0			0
$665$	337704.	+	63951.5i	0.0296130	+	0.00560785i
$666$		0			0
$667$	9.42978e6	+	9.42978e6i	0.820705	+	0.820705i
$668$		0			0
$669$			1.43141e7i			1.23651i
$670$		0			0
$671$		−	182470.i		−	0.0156453i
$672$		0			0
$673$	1.01077e7	+	1.01077e7i	0.860230	+	0.860230i	0.991365	−	0.131135i	$-0.0418621\pi$
$673$	1.01077e7	+	1.01077e7i	0.860230	+	0.860230i	−0.131135	+	0.991365i	$0.541862\pi$
$674$		0			0
$675$	−7.84865e6	+	3.42143e6i	−0.663034	+	0.289033i
$676$		0			0
$677$	5.24850e6	−	5.24850e6i	0.440112	−	0.440112i	−0.451938	−	0.892050i	$-0.649267\pi$
$677$	5.24850e6	−	5.24850e6i	0.440112	−	0.440112i	0.892050	+	0.451938i	$0.149267\pi$
$678$		0			0
$679$	2.36502e7			1.96861
$680$		0			0
$681$	5.73207e6			0.473635
$682$		0			0
$683$	1.03798e7	−	1.03798e7i	0.851407	−	0.851407i	−0.138900	−	0.990306i	$-0.544357\pi$
$683$	1.03798e7	−	1.03798e7i	0.851407	−	0.851407i	0.990306	+	0.138900i	$0.0443565\pi$
$684$		0			0
$685$	718695.	−	3.79516e6i	0.0585218	−	0.309032i
$686$		0			0
$687$	1.02148e7	+	1.02148e7i	0.825727	+	0.825727i
$688$		0			0
$689$			1.52426e7i			1.22324i
$690$		0			0
$691$		−	6.06155e6i		−	0.482935i	−0.970409	−	0.241468i	$-0.922371\pi$
$691$		−	6.06155e6i		−	0.482935i	0.970409	−	0.241468i	$-0.0776288\pi$
$692$		0			0
$693$	−6.97412e6	−	6.97412e6i	−0.551641	−	0.551641i
$694$		0			0
$695$	−1.64728e7	+	1.12272e7i	−1.29362	+	0.881679i
$696$		0			0
$697$	1.28758e7	−	1.28758e7i	1.00390	−	1.00390i
$698$		0			0
$699$	−2.93896e7			−2.27510
$700$		0			0
$701$	2.87503e6			0.220977			0.110489	−	0.993877i	$-0.464758\pi$
$701$	2.87503e6			0.220977			0.110489	+	0.993877i	$0.464758\pi$
$702$		0			0
$703$	−325450.	+	325450.i	−0.0248368	+	0.0248368i
$704$		0			0
$705$	349929.	−	238498.i	0.0265159	−	0.0180722i
$706$		0			0
$707$	212566.	+	212566.i	0.0159936	+	0.0159936i
$708$		0			0
$709$			528547.i			0.0394883i	0.999805	+	0.0197441i	$0.00628516\pi$
$709$			528547.i			0.0394883i	−0.999805	+	0.0197441i	$0.993715\pi$
$710$		0			0
$711$			8.31390e6i			0.616780i
$712$		0			0
$713$	−1.49850e7	−	1.49850e7i	−1.10391	−	1.10391i
$714$		0			0
$715$	−628360.	+	3.31814e6i	−0.0459667	+	0.242733i
$716$		0			0
$717$	−1.24548e6	+	1.24548e6i	−0.0904769	+	0.0904769i
$718$		0			0
$719$	−1.66055e7			−1.19793			−0.598963	−	0.800777i	$-0.704420\pi$
$719$	−1.66055e7			−1.19793			−0.598963	+	0.800777i	$0.704420\pi$
$720$		0			0
$721$	3.92498e7			2.81190
$722$		0			0
$723$	6.20523e6	−	6.20523e6i	0.441481	−	0.441481i
$724$		0			0
$725$	9.85532e6	+	3.87147e6i	0.696347	+	0.273546i
$726$		0			0
$727$	−1.54075e7	−	1.54075e7i	−1.08118	−	1.08118i	−0.996400	−	0.0847783i	$-0.972982\pi$
$727$	−1.54075e7	−	1.54075e7i	−1.08118	−	1.08118i	−0.0847783	−	0.996400i	$-0.527018\pi$
$728$		0			0
$729$		−	2.31237e7i		−	1.61153i
$730$		0			0
$731$			3.31966e6i			0.229773i
$732$		0			0
$733$	−1.69113e7	−	1.69113e7i	−1.16256	−	1.16256i	−0.983913	−	0.178650i	$-0.942827\pi$
$733$	−1.69113e7	−	1.69113e7i	−1.16256	−	1.16256i	−0.178650	−	0.983913i	$-0.557173\pi$
$734$		0			0
$735$	4.12003e7	+	7.80215e6i	2.81308	+	0.532716i
$736$		0			0
$737$	−3.69059e6	+	3.69059e6i	−0.250281	+	0.250281i
$738$		0			0
$739$	−2.76180e7			−1.86029			−0.930147	−	0.367187i	$-0.880321\pi$
$739$	−2.76180e7			−1.86029			−0.930147	+	0.367187i	$0.880321\pi$
$740$		0			0
$741$	−326976.			−0.0218761
$742$		0			0
$743$	1.71922e7	−	1.71922e7i	1.14251	−	1.14251i	0.154521	−	0.987990i	$-0.450617\pi$
$743$	1.71922e7	−	1.71922e7i	1.14251	−	1.14251i	0.987990	−	0.154521i	$-0.0493833\pi$
$744$		0			0
$745$	−1.23034e6	−	1.80518e6i	−0.0812147	−	0.119160i
$746$		0			0
$747$	−6.71712e6	−	6.71712e6i	−0.440435	−	0.440435i
$748$		0			0
$749$		−	5.33954e6i		−	0.347776i
$750$		0			0
$751$		−	1.11896e7i		−	0.723961i	−0.932186	−	0.361981i	$-0.882101\pi$
$751$		−	1.11896e7i		−	0.723961i	0.932186	−	0.361981i	$-0.117899\pi$
$752$		0			0
$753$	3.61836e6	+	3.61836e6i	0.232554	+	0.232554i
$754$		0			0
$755$	1.11977e7	+	1.64295e7i	0.714928	+	1.04896i
$756$		0			0
$757$	−1.17247e6	+	1.17247e6i	−0.0743637	+	0.0743637i	−0.743310	−	0.668947i	$-0.766745\pi$
$757$	−1.17247e6	+	1.17247e6i	−0.0743637	+	0.0743637i	0.668947	+	0.743310i	$0.266745\pi$
$758$		0			0
$759$	1.22708e7			0.773156
$760$		0			0
$761$	−9.79138e6			−0.612890			−0.306445	−	0.951888i	$-0.599140\pi$
$761$	−9.79138e6			−0.612890			−0.306445	+	0.951888i	$0.599140\pi$
$762$		0			0
$763$	−1.62980e7	+	1.62980e7i	−1.01350	+	1.01350i
$764$		0			0
$765$	3.18528e7	+	6.03200e6i	1.96786	+	0.372656i
$766$		0			0
$767$	7.43734e6	+	7.43734e6i	0.456488	+	0.456488i
$768$		0			0
$769$			1.10059e7i			0.671138i	0.942016	+	0.335569i	$0.108929\pi$
$769$			1.10059e7i			0.671138i	−0.942016	+	0.335569i	$0.891071\pi$
$770$		0			0
$771$			7.89277e6i			0.478182i
$772$		0			0
$773$	8.90959e6	+	8.90959e6i	0.536302	+	0.536302i	0.922441	−	0.386139i	$-0.126191\pi$
$773$	8.90959e6	+	8.90959e6i	0.536302	+	0.536302i	−0.386139	+	0.922441i	$0.626191\pi$
$774$		0			0
$775$	−1.56612e7	−	6.15220e6i	−0.936637	−	0.367939i
$776$		0			0
$777$	−6.14612e7	+	6.14612e7i	−3.65215	+	3.65215i
$778$		0			0
$779$	314553.			0.0185716
$780$		0			0
$781$	3.08375e6			0.180906
$782$		0			0
$783$	6.56435e6	−	6.56435e6i	0.382638	−	0.382638i
$784$		0			0
$785$	−548745.	+	2.89772e6i	−0.0317831	+	0.167835i
$786$		0			0
$787$	−4.88094e6	−	4.88094e6i	−0.280910	−	0.280910i	0.552562	−	0.833472i	$-0.313650\pi$
$787$	−4.88094e6	−	4.88094e6i	−0.280910	−	0.280910i	−0.833472	+	0.552562i	$0.813650\pi$
$788$		0			0
$789$		−	3.26905e7i		−	1.86952i
$790$		0			0
$791$		−	1.95525e7i		−	1.11112i
$792$		0			0
$793$	−479566.	−	479566.i	−0.0270811	−	0.0270811i
$794$		0			0
$795$	3.63373e7	−	2.47661e7i	2.03909	−	1.38976i
$796$		0			0
$797$	7.86412e6	−	7.86412e6i	0.438535	−	0.438535i	−0.452984	−	0.891519i	$-0.649640\pi$
$797$	7.86412e6	−	7.86412e6i	0.438535	−	0.438535i	0.891519	+	0.452984i	$0.149640\pi$
$798$		0			0
$799$	−505987.			−0.0280396
$800$		0			0
$801$	−2.90403e6			−0.159926
$802$		0			0
$803$	−3.64299e6	+	3.64299e6i	−0.199374	+	0.199374i
$804$		0			0
$805$	−3.96157e7	+	2.70005e7i	−2.15466	+	1.46853i
$806$		0			0
$807$	−2.70724e7	−	2.70724e7i	−1.46333	−	1.46333i
$808$		0			0
$809$			3.59398e6i			0.193065i	0.995330	+	0.0965327i	$0.0307752\pi$
$809$			3.59398e6i			0.193065i	−0.995330	+	0.0965327i	$0.969225\pi$
$810$		0			0
$811$			1.96828e7i			1.05084i	0.850844	+	0.525418i	$0.176091\pi$
$811$			1.96828e7i			1.05084i	−0.850844	+	0.525418i	$0.823909\pi$
$812$		0			0
$813$	−1.71334e7	−	1.71334e7i	−0.909113	−	0.909113i
$814$		0			0
$815$	−2.66178e6	+	1.40559e7i	−0.140371	+	0.741249i
$816$		0			0
$817$	−40549.3	+	40549.3i	−0.00212534	+	0.00212534i
$818$		0			0
$819$	−3.66587e7			−1.90971
$820$		0			0
$821$	−6.87305e6			−0.355870			−0.177935	−	0.984042i	$-0.556942\pi$
$821$	−6.87305e6			−0.355870			−0.177935	+	0.984042i	$0.556942\pi$
$822$		0			0
$823$	2.46199e7	−	2.46199e7i	1.26703	−	1.26703i	0.319415	−	0.947615i	$-0.396514\pi$
$823$	2.46199e7	−	2.46199e7i	1.26703	−	1.26703i	0.947615	−	0.319415i	$-0.103486\pi$
$824$		0			0
$825$	8.93117e6	−	3.89333e6i	0.456850	−	0.199153i
$826$		0			0
$827$	2.64914e7	+	2.64914e7i	1.34692	+	1.34692i	0.888988	+	0.457931i	$0.151409\pi$
$827$	2.64914e7	+	2.64914e7i	1.34692	+	1.34692i	0.457931	+	0.888988i	$0.348591\pi$
$828$		0			0
$829$		−	4.71839e6i		−	0.238456i	−0.992867	−	0.119228i	$-0.961958\pi$
$829$		−	4.71839e6i		−	0.238456i	0.992867	−	0.119228i	$-0.0380419\pi$
$830$		0			0
$831$			6.02745e6i			0.302782i
$832$		0			0
$833$	−3.54280e7	−	3.54280e7i	−1.76903	−	1.76903i
$834$		0			0
$835$	1.35842e7	+	2.57246e6i	0.674245	+	0.127683i
$836$		0			0
$837$	−1.04315e7	+	1.04315e7i	−0.514675	+	0.514675i
$838$		0			0
$839$	−2.18851e6			−0.107336			−0.0536678	−	0.998559i	$-0.517091\pi$
$839$	−2.18851e6			−0.107336			−0.0536678	+	0.998559i	$0.517091\pi$
$840$		0			0
$841$	9.03051e6			0.440273
$842$		0			0
$843$	3.76564e7	−	3.76564e7i	1.82503	−	1.82503i
$844$		0			0
$845$	−4.62028e6	−	6.77897e6i	−0.222601	−	0.326605i
$846$		0			0
$847$	−2.23102e7	−	2.23102e7i	−1.06855	−	1.06855i
$848$		0			0
$849$			1.73657e7i			0.826842i
$850$		0			0
$851$		−	6.41990e7i		−	3.03882i
$852$		0			0
$853$	−1.82806e7	−	1.82806e7i	−0.860238	−	0.860238i	0.131127	−	0.991366i	$-0.458140\pi$
$853$	−1.82806e7	−	1.82806e7i	−0.860238	−	0.860238i	−0.991366	+	0.131127i	$0.958140\pi$
$854$		0			0
$855$	315398.	+	462759.i	0.0147552	+	0.0216491i
$856$		0			0
$857$	2.39122e7	−	2.39122e7i	1.11216	−	1.11216i	0.119303	−	0.992858i	$-0.461934\pi$
$857$	2.39122e7	−	2.39122e7i	1.11216	−	1.11216i	0.992858	−	0.119303i	$-0.0380660\pi$
$858$		0			0
$859$	−1.15768e7			−0.535309			−0.267654	−	0.963515i	$-0.586249\pi$
$859$	−1.15768e7			−0.535309			−0.267654	+	0.963515i	$0.586249\pi$
$860$		0			0
$861$	5.94032e7			2.73088
$862$		0			0
$863$	3.08022e6	−	3.08022e6i	0.140784	−	0.140784i	−0.633202	−	0.773987i	$-0.718260\pi$
$863$	3.08022e6	−	3.08022e6i	0.140784	−	0.140784i	0.773987	+	0.633202i	$0.218260\pi$
$864$		0			0
$865$	2.92191e7	+	5.53325e6i	1.32778	+	0.251443i
$866$		0			0
$867$	−2.15846e7	−	2.15846e7i	−0.975204	−	0.975204i
$868$		0			0
$869$		−	2.98542e6i		−	0.134108i
$870$		0			0
$871$			1.93992e7i			0.866440i
$872$		0			0
$873$	2.72481e7	+	2.72481e7i	1.21004	+	1.21004i
$874$		0			0
$875$	−2.02671e7	+	3.22216e7i	−0.894895	+	1.42274i
$876$		0			0
$877$	−1.24010e7	+	1.24010e7i	−0.544449	+	0.544449i	−0.924830	−	0.380381i	$-0.875793\pi$
$877$	−1.24010e7	+	1.24010e7i	−0.544449	+	0.544449i	0.380381	+	0.924830i	$0.375793\pi$
$878$		0			0
$879$	1.58301e6			0.0691053
$880$		0			0
$881$	8.61119e6			0.373786			0.186893	−	0.982380i	$-0.440158\pi$
$881$	8.61119e6			0.373786			0.186893	+	0.982380i	$0.440158\pi$
$882$		0			0
$883$	−2.44433e7	+	2.44433e7i	−1.05502	+	1.05502i	−0.0566197	+	0.998396i	$0.518032\pi$
$883$	−2.44433e7	+	2.44433e7i	−1.05502	+	1.05502i	−0.998396	+	0.0566197i	$0.981968\pi$
$884$		0			0
$885$	5.64596e6	−	2.98143e7i	0.242315	−	1.27958i
$886$		0			0
$887$	1.94644e7	+	1.94644e7i	0.830678	+	0.830678i	0.987609	−	0.156932i	$-0.0501603\pi$
$887$	1.94644e7	+	1.94644e7i	0.830678	+	0.830678i	−0.156932	+	0.987609i	$0.550160\pi$
$888$		0			0
$889$			4.64345e7i			1.97055i
$890$		0			0
$891$			2.45696e6i			0.103682i
$892$		0			0
$893$	−6180.58	−	6180.58i	−0.000259359	−	0.000259359i
$894$		0			0
$895$	−1.77836e7	+	1.21206e7i	−0.742099	+	0.505785i
$896$		0			0
$897$	3.22500e7	−	3.22500e7i	1.33828	−	1.33828i
$898$		0			0
$899$	1.82440e7			0.752873
$900$		0			0
$901$	−5.25427e7			−2.15626
$902$		0			0
$903$	−7.65772e6	+	7.65772e6i	−0.312522	+	0.312522i
$904$		0			0
$905$	−1.53517e7	+	1.04631e7i	−0.623066	+	0.424658i
$906$		0			0
$907$	−2.02098e7	−	2.02098e7i	−0.815724	−	0.815724i	0.169761	−	0.985485i	$-0.445700\pi$
$907$	−2.02098e7	−	2.02098e7i	−0.815724	−	0.815724i	−0.985485	+	0.169761i	$0.945700\pi$
$908$		0			0
$909$			489807.i			0.0196614i
$910$		0			0
$911$			2.45272e7i			0.979155i	0.871960	+	0.489577i	$0.162849\pi$
$911$			2.45272e7i			0.979155i	−0.871960	+	0.489577i	$0.837151\pi$
$912$		0			0
$913$	2.41204e6	+	2.41204e6i	0.0957650	+	0.0957650i
$914$		0			0
$915$	−364057.	+	1.92245e6i	−0.0143753	+	0.0759105i
$916$		0			0
$917$	3.36516e7	−	3.36516e7i	1.32155	−	1.32155i
$918$		0			0
$919$	−1.34572e7			−0.525613			−0.262806	−	0.964849i	$-0.584648\pi$
$919$	−1.34572e7			−0.525613			−0.262806	+	0.964849i	$0.584648\pi$
$920$		0			0
$921$	−4.82676e7			−1.87502
$922$		0			0
$923$	8.10471e6	−	8.10471e6i	0.313136	−	0.313136i
$924$		0			0
$925$	−2.03694e7	−	4.67268e7i	−0.782751	−	1.79561i
$926$		0			0
$927$	4.52208e7	+	4.52208e7i	1.72838	+	1.72838i
$928$		0			0
$929$			1.09539e7i			0.416417i	0.978084	+	0.208209i	$0.0667633\pi$
$929$			1.09539e7i			0.416417i	−0.978084	+	0.208209i	$0.933237\pi$
$930$		0			0
$931$		−	865500.i		−	0.0327260i
$932$		0			0
$933$	3.18375e7	+	3.18375e7i	1.19739	+	1.19739i
$934$		0			0
$935$	−1.14379e7	−	2.16602e6i	−0.427877	−	0.0810276i
$936$		0			0
$937$	−2.46236e7	+	2.46236e7i	−0.916224	+	0.916224i	−0.996752	−	0.0805282i	$-0.974339\pi$
$937$	−2.46236e7	+	2.46236e7i	−0.916224	+	0.916224i	0.0805282	+	0.996752i	$0.474339\pi$
$938$		0			0
$939$	7.68946e7			2.84598
$940$		0			0
$941$	2.79774e7			1.02999			0.514995	−	0.857193i	$-0.327794\pi$
$941$	2.79774e7			1.02999			0.514995	+	0.857193i	$0.327794\pi$
$942$		0			0
$943$	−3.10247e7	+	3.10247e7i	−1.13613	+	1.13613i
$944$		0			0
$945$	1.87959e7	+	2.75777e7i	0.684673	+	1.00457i
$946$		0			0
$947$	1.34277e7	+	1.34277e7i	0.486550	+	0.486550i	0.907216	−	0.420666i	$-0.138204\pi$
$947$	1.34277e7	+	1.34277e7i	0.486550	+	0.486550i	−0.420666	+	0.907216i	$0.638204\pi$
$948$		0			0
$949$			1.91490e7i			0.690208i
$950$		0			0
$951$			4.68619e7i			1.68023i
$952$		0			0
$953$	−2.47107e7	−	2.47107e7i	−0.881359	−	0.881359i	0.112313	−	0.993673i	$-0.464174\pi$
$953$	−2.47107e7	−	2.47107e7i	−0.881359	−	0.881359i	−0.993673	+	0.112313i	$0.964174\pi$
$954$		0			0
$955$	5.18067e6	+	7.60119e6i	0.183814	+	0.269695i
$956$		0			0
$957$	−7.46974e6	+	7.46974e6i	−0.263649	+	0.263649i
$958$		0			0
$959$	−1.50561e7			−0.528648
$960$		0			0
$961$	−362678.			−0.0126681
$962$		0			0
$963$	6.15184e6	−	6.15184e6i	0.213766	−	0.213766i
$964$		0			0
$965$	−4.51129e6	−	854309.i	−0.155949	−	0.0295323i
$966$		0			0
$967$	−2.49726e7	−	2.49726e7i	−0.858811	−	0.858811i	0.132387	−	0.991198i	$-0.457736\pi$
$967$	−2.49726e7	−	2.49726e7i	−0.858811	−	0.858811i	−0.991198	+	0.132387i	$0.957736\pi$
$968$		0			0
$969$		−	1.12712e6i		−	0.0385620i
$970$		0			0
$971$			1.77496e7i			0.604143i	0.953285	+	0.302071i	$0.0976781\pi$
$971$			1.77496e7i			0.604143i	−0.953285	+	0.302071i	$0.902322\pi$
$972$		0			0
$973$	5.49457e7	+	5.49457e7i	1.86059	+	1.86059i
$974$		0			0
$975$	1.32405e7	−	3.37053e7i	0.446058	−	1.13550i
$976$		0			0
$977$	−2.06328e7	+	2.06328e7i	−0.691548	+	0.691548i	−0.962572	−	0.271024i	$-0.912638\pi$
$977$	−2.06328e7	+	2.06328e7i	−0.691548	+	0.691548i	0.271024	+	0.962572i	$0.412638\pi$
$978$		0			0
$979$	1.04280e6			0.0347733
$980$		0			0
$981$	−3.75548e7			−1.24593
$982$		0			0
$983$	1.82547e7	−	1.82547e7i	0.602546	−	0.602546i	−0.338442	−	0.940987i	$-0.609900\pi$
$983$	1.82547e7	−	1.82547e7i	0.602546	−	0.602546i	0.940987	+	0.338442i	$0.109900\pi$
$984$		0			0
$985$	5.68852e6	−	3.00390e7i	0.186814	−	0.986494i
$986$		0			0
$987$	−1.16720e6	−	1.16720e6i	−0.0381375	−	0.0381375i
$988$		0			0
$989$		−	7.99884e6i		−	0.260038i
$990$		0			0
$991$			3.83326e7i			1.23989i	0.784644	+	0.619947i	$0.212846\pi$
$991$			3.83326e7i			1.23989i	−0.784644	+	0.619947i	$0.787154\pi$
$992$		0			0
$993$	4.15865e7	+	4.15865e7i	1.33838	+	1.33838i
$994$		0			0
$995$	−649252.	+	442504.i	−0.0207900	+	0.0141697i
$996$		0			0
$997$	1.22874e7	−	1.22874e7i	0.391491	−	0.391491i	−0.483727	−	0.875219i	$-0.660717\pi$
$997$	1.22874e7	−	1.22874e7i	0.391491	−	0.391491i	0.875219	+	0.483727i	$0.160717\pi$
$998$		0			0
$999$	−4.46909e7			−1.41679

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.6.n.d.63.9	yes	20
4.3	odd	2	inner	80.6.n.d.63.2	yes	20
5.2	odd	4	inner	80.6.n.d.47.2	✓	20
5.3	odd	4		400.6.n.g.207.9		20
5.4	even	2		400.6.n.g.143.2		20
20.3	even	4		400.6.n.g.207.2		20
20.7	even	4	inner	80.6.n.d.47.9	yes	20
20.19	odd	2		400.6.n.g.143.9		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.n.d.47.2	✓	20	5.2	odd	4	inner
80.6.n.d.47.9	yes	20	20.7	even	4	inner
80.6.n.d.63.2	yes	20	4.3	odd	2	inner
80.6.n.d.63.9	yes	20	1.1	even	1	trivial
400.6.n.g.143.2		20	5.4	even	2
400.6.n.g.143.9		20	20.19	odd	2
400.6.n.g.207.2		20	20.3	even	4
400.6.n.g.207.9		20	5.3	odd	4

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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	80.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(17.2921 - 17.2921i) q^{3} +(46.1930 - 31.4834i) q^{5} +(-154.079 - 154.079i) q^{7} -355.037i q^{9} +O(q^{10})\)	\(q+(17.2921 - 17.2921i) q^{3} +(46.1930 - 31.4834i) q^{5} +(-154.079 - 154.079i) q^{7} -355.037i q^{9} +127.489i q^{11} +(335.067 + 335.067i) q^{13} +(254.362 - 1343.19i) q^{15} +(-1155.01 + 1155.01i) q^{17} -28.2166 q^{19} -5328.70 q^{21} +(2783.04 - 2783.04i) q^{23} +(1142.60 - 2908.63i) q^{25} +(-1937.35 - 1937.35i) q^{27} +3388.31i q^{29} -5384.41i q^{31} +(2204.56 + 2204.56i) q^{33} +(-11968.3 - 2266.45i) q^{35} +(11534.0 - 11534.0i) q^{37} +11588.1 q^{39} -11147.8 q^{41} +(1437.07 - 1437.07i) q^{43} +(-11177.7 - 16400.2i) q^{45} +(219.040 + 219.040i) q^{47} +30673.4i q^{49} +39945.1i q^{51} +(22745.6 + 22745.6i) q^{53} +(4013.79 + 5889.12i) q^{55} +(-487.926 + 487.926i) q^{57} +22196.6 q^{59} -1431.25 q^{61} +(-54703.5 + 54703.5i) q^{63} +(26026.8 + 4928.73i) q^{65} +(28948.2 + 28948.2i) q^{67} -96249.3i q^{69} -24188.3i q^{71} +(28574.8 + 28574.8i) q^{73} +(-30538.4 - 70054.3i) q^{75} +(19643.4 - 19643.4i) q^{77} -23417.0 q^{79} +19271.9 q^{81} +(18919.5 - 18919.5i) q^{83} +(-16989.8 + 89716.9i) q^{85} +(58591.1 + 58591.1i) q^{87} -8179.53i q^{89} -103253. i q^{91} +(-93107.9 - 93107.9i) q^{93} +(-1303.41 + 888.354i) q^{95} +(-76747.2 + 76747.2i) q^{97} +45263.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 44 q^{5}+O(q^{10}) \) 20 * q - 44 * q^5	\( 20 q - 44 q^{5} + 804 q^{13} - 2236 q^{17} - 4520 q^{21} + 948 q^{25} - 11096 q^{33} + 44260 q^{37} - 6760 q^{41} - 92816 q^{45} + 182452 q^{53} - 34288 q^{57} - 41080 q^{61} - 155772 q^{65} + 264372 q^{73} + 399304 q^{77} - 520220 q^{81} - 344796 q^{85} + 713496 q^{93} + 374772 q^{97}+O(q^{100}) \) 20 * q - 44 * q^5 + 804 * q^13 - 2236 * q^17 - 4520 * q^21 + 948 * q^25 - 11096 * q^33 + 44260 * q^37 - 6760 * q^41 - 92816 * q^45 + 182452 * q^53 - 34288 * q^57 - 41080 * q^61 - 155772 * q^65 + 264372 * q^73 + 399304 * q^77 - 520220 * q^81 - 344796 * q^85 + 713496 * q^93 + 374772 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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