LMFDB - Embedded newform 2217.1.p.a.1016.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2217,1,Mod(20,2217)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2217, base_ring=CyclotomicField(82))

chi = DirichletCharacter(H, H._module([41, 6]))

N = Newforms(chi, 1, names="a")

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

chi := DirichletCharacter("2217.20");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2217 = 3 \cdot 739 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2217.p (of order $82$, degree $40$, 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:	$1.10642713301$
Analytic rank:	$0$
Dimension:	$40$
Coefficient field:	$\Q(\zeta_{82})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{40} - x^{39} + x^{38} - x^{37} + x^{36} - x^{35} + x^{34} - x^{33} + x^{32} - x^{31} + x^{30} + \cdots + 1 $ x^40 - x^39 + x^38 - x^37 + x^36 - x^35 + x^34 - x^33 + x^32 - x^31 + x^30 - x^29 + x^28 - x^27 + x^26 - x^25 + x^24 - x^23 + x^22 - x^21 + x^20 - x^19 + x^18 - x^17 + x^16 - x^15 + x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{41}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{41} - \cdots)$

Embedding invariants

Embedding label			1016.1
Root			$0.973695 - 0.227854i$ of defining polynomial
Character	$\chi$	$=$	2217.1016
Dual form			2217.1.p.a.731.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.817929 - 0.575319i) q^{3} +(-0.665326 - 0.746553i) q^{4} +(0.444713 - 0.992015i) q^{7} +(0.338017 - 0.941140i) q^{9} +O(q^{10})$	\(q+(0.817929 - 0.575319i) q^{3} +(-0.665326 - 0.746553i) q^{4} +(0.444713 - 0.992015i) q^{7} +(0.338017 - 0.941140i) q^{9} +(-0.973695 - 0.227854i) q^{12} +(0.00293420 + 0.0765493i) q^{13} +(-0.114683 + 0.993402i) q^{16} +(-0.821267 - 1.51028i) q^{19} +(-0.206981 - 1.06725i) q^{21} +(0.338017 + 0.941140i) q^{25} +(-0.264982 - 0.964253i) q^{27} +(-1.03647 + 0.328011i) q^{28} +(0.0258939 + 0.675538i) q^{31} +(-0.927502 + 0.373817i) q^{36} +(-0.139048 + 1.20445i) q^{37} +(0.0464402 + 0.0609238i) q^{39} +(0.455540 - 1.65769i) q^{43} +(0.477720 + 0.878512i) q^{48} +(-0.120998 - 0.135770i) q^{49} +(0.0551959 - 0.0531207i) q^{52} +(-1.54063 - 0.762816i) q^{57} +(-0.0436694 + 0.225171i) q^{61} +(-0.783304 - 0.753855i) q^{63} +(0.817929 - 0.575319i) q^{64} +(-0.449783 + 1.25233i) q^{67} +(-0.521553 + 0.430121i) q^{73} +(0.817929 + 0.575319i) q^{75} +(-0.581098 + 1.61795i) q^{76} +(-0.495976 - 0.650659i) q^{79} +(-0.771489 - 0.636242i) q^{81} +(-0.659049 + 0.864591i) q^{84} +(0.0772429 + 0.0311317i) q^{91} +(0.409829 + 0.537645i) q^{93} +(0.796617 - 1.77700i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - q^{3} - q^{4} - 2 q^{7} - q^{9}+O(q^{10}) $ 40 * q - q^3 - q^4 - 2 * q^7 - q^9	$ 40 q - q^{3} - q^{4} - 2 q^{7} - q^{9} - q^{12} + 39 q^{13} - q^{16} - 2 q^{19} - 2 q^{21} - q^{25} - q^{27} - 2 q^{28} - 2 q^{31} - q^{36} - 2 q^{37} - 2 q^{39} - 2 q^{43} - q^{48} - 3 q^{49} - 2 q^{52} - 2 q^{57} - 2 q^{61} - 2 q^{63} - q^{64} - 2 q^{67} - 2 q^{73} - q^{75} - 2 q^{76} - 2 q^{79} - q^{81} - 2 q^{84} - 4 q^{91} - 2 q^{93} - 2 q^{97}+O(q^{100}) $ 40 * q - q^3 - q^4 - 2 * q^7 - q^9 - q^12 + 39 * q^13 - q^16 - 2 * q^19 - 2 * q^21 - q^25 - q^27 - 2 * q^28 - 2 * q^31 - q^36 - 2 * q^37 - 2 * q^39 - 2 * q^43 - q^48 - 3 * q^49 - 2 * q^52 - 2 * q^57 - 2 * q^61 - 2 * q^63 - q^64 - 2 * q^67 - 2 * q^73 - q^75 - 2 * q^76 - 2 * q^79 - q^81 - 2 * q^84 - 4 * q^91 - 2 * q^93 - 2 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2217\mathbb{Z}\right)^\times$.

$n$	$740$	$742$
$\chi(n)$	$-1$	$e\left(\frac{33}{41}\right)$

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		0.409069	−	0.912504i	$-0.365854\pi$
$2$		0			0		−0.409069	+	0.912504i	$0.634146\pi$
$3$	0.817929	−	0.575319i	0.817929	−	0.575319i
$3$	0.817929	−	0.575319i	0.817929	−	0.575319i
$4$	−0.665326	−	0.746553i	−0.665326	−	0.746553i
$5$		0			0		−0.817929	−	0.575319i	$-0.804878\pi$
$5$		0			0		0.817929	+	0.575319i	$0.195122\pi$
$6$		0			0
$7$	0.444713	−	0.992015i	0.444713	−	0.992015i	−0.543568	−	0.839365i	$-0.682927\pi$
$7$	0.444713	−	0.992015i	0.444713	−	0.992015i	0.988280	−	0.152649i	$-0.0487805\pi$
$8$		0			0
$9$	0.338017	−	0.941140i	0.338017	−	0.941140i
$10$		0			0
$11$		0			0		−0.997066	−	0.0765493i	$-0.975610\pi$
$11$		0			0		0.997066	+	0.0765493i	$0.0243902\pi$
$12$	−0.973695	−	0.227854i	−0.973695	−	0.227854i
$13$	0.00293420	+	0.0765493i	0.00293420	+	0.0765493i	1.00000			$0$
$13$	0.00293420	+	0.0765493i	0.00293420	+	0.0765493i	−0.997066	+	0.0765493i	$0.975610\pi$
$14$		0			0
$15$		0			0
$16$	−0.114683	+	0.993402i	−0.114683	+	0.993402i
$17$		0			0		−0.543568	−	0.839365i	$-0.682927\pi$
$17$		0			0		0.543568	+	0.839365i	$0.317073\pi$
$18$		0			0
$19$	−0.821267	−	1.51028i	−0.821267	−	1.51028i	−0.859570	−	0.511019i	$-0.829268\pi$
$19$	−0.821267	−	1.51028i	−0.821267	−	1.51028i	0.0383027	−	0.999266i	$-0.487805\pi$
$20$		0			0
$21$	−0.206981	−	1.06725i	−0.206981	−	1.06725i
$22$		0			0
$23$		0			0		0.409069	−	0.912504i	$-0.365854\pi$
$23$		0			0		−0.409069	+	0.912504i	$0.634146\pi$
$24$		0			0
$25$	0.338017	+	0.941140i	0.338017	+	0.941140i
$26$		0			0
$27$	−0.264982	−	0.964253i	−0.264982	−	0.964253i
$28$	−1.03647	+	0.328011i	−1.03647	+	0.328011i
$29$		0			0		0.927502	−	0.373817i	$-0.121951\pi$
$29$		0			0		−0.927502	+	0.373817i	$0.878049\pi$
$30$		0			0
$31$	0.0258939	+	0.675538i	0.0258939	+	0.675538i	0.953396	+	0.301721i	$0.0975610\pi$
$31$	0.0258939	+	0.675538i	0.0258939	+	0.675538i	−0.927502	+	0.373817i	$0.878049\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−0.927502	+	0.373817i	−0.927502	+	0.373817i
$37$	−0.139048	+	1.20445i	−0.139048	+	1.20445i	0.720522	+	0.693433i	$0.243902\pi$
$37$	−0.139048	+	1.20445i	−0.139048	+	1.20445i	−0.859570	+	0.511019i	$0.829268\pi$
$38$		0			0
$39$	0.0464402	+	0.0609238i	0.0464402	+	0.0609238i
$40$		0			0
$41$		0			0		0.720522	−	0.693433i	$-0.243902\pi$
$41$		0			0		−0.720522	+	0.693433i	$0.756098\pi$
$42$		0			0
$43$	0.455540	−	1.65769i	0.455540	−	1.65769i	−0.264982	−	0.964253i	$-0.585366\pi$
$43$	0.455540	−	1.65769i	0.455540	−	1.65769i	0.720522	−	0.693433i	$-0.243902\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		0			0		0.988280	−	0.152649i	$-0.0487805\pi$
$47$		0			0		−0.988280	+	0.152649i	$0.951220\pi$
$48$	0.477720	+	0.878512i	0.477720	+	0.878512i
$49$	−0.120998	−	0.135770i	−0.120998	−	0.135770i
$50$		0			0
$51$		0			0
$52$	0.0551959	−	0.0531207i	0.0551959	−	0.0531207i
$53$		0			0		0.114683	−	0.993402i	$-0.463415\pi$
$53$		0			0		−0.114683	+	0.993402i	$0.536585\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−1.54063	−	0.762816i	−1.54063	−	0.762816i
$58$		0			0
$59$		0			0		−0.264982	−	0.964253i	$-0.585366\pi$
$59$		0			0		0.264982	+	0.964253i	$0.414634\pi$
$60$		0			0
$61$	−0.0436694	+	0.225171i	−0.0436694	+	0.225171i	−0.997066	−	0.0765493i	$-0.975610\pi$
$61$	−0.0436694	+	0.225171i	−0.0436694	+	0.225171i	0.953396	+	0.301721i	$0.0975610\pi$
$62$		0			0
$63$	−0.783304	−	0.753855i	−0.783304	−	0.753855i
$64$	0.817929	−	0.575319i	0.817929	−	0.575319i
$65$		0			0
$66$		0			0
$67$	−0.449783	+	1.25233i	−0.449783	+	1.25233i	0.477720	+	0.878512i	$0.341463\pi$
$67$	−0.449783	+	1.25233i	−0.449783	+	1.25233i	−0.927502	+	0.373817i	$0.878049\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0		−0.988280	−	0.152649i	$-0.951220\pi$
$71$		0			0		0.988280	+	0.152649i	$0.0487805\pi$
$72$		0			0
$73$	−0.521553	+	0.430121i	−0.521553	+	0.430121i	−0.859570	−	0.511019i	$-0.829268\pi$
$73$	−0.521553	+	0.430121i	−0.521553	+	0.430121i	0.338017	+	0.941140i	$0.390244\pi$
$74$		0			0
$75$	0.817929	+	0.575319i	0.817929	+	0.575319i
$76$	−0.581098	+	1.61795i	−0.581098	+	1.61795i
$77$		0			0
$78$		0			0
$79$	−0.495976	−	0.650659i	−0.495976	−	0.650659i	0.477720	−	0.878512i	$-0.341463\pi$
$79$	−0.495976	−	0.650659i	−0.495976	−	0.650659i	−0.973695	+	0.227854i	$0.926829\pi$
$80$		0			0
$81$	−0.771489	−	0.636242i	−0.771489	−	0.636242i
$82$		0			0
$83$		0			0		−0.606225	−	0.795293i	$-0.707317\pi$
$83$		0			0		0.606225	+	0.795293i	$0.292683\pi$
$84$	−0.659049	+	0.864591i	−0.659049	+	0.864591i
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		0.0383027	−	0.999266i	$-0.487805\pi$
$89$		0			0		−0.0383027	+	0.999266i	$0.512195\pi$
$90$		0			0
$91$	0.0772429	+	0.0311317i	0.0772429	+	0.0311317i
$92$		0			0
$93$	0.409829	+	0.537645i	0.409829	+	0.537645i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	0.796617	−	1.77700i	0.796617	−	1.77700i	0.190391	−	0.981708i	$-0.439024\pi$
$97$	0.796617	−	1.77700i	0.796617	−	1.77700i	0.606225	−	0.795293i	$-0.292683\pi$
$98$		0			0
$99$		0			0
$100$	0.477720	−	0.878512i	0.477720	−	0.878512i
$101$		0			0		0.114683	−	0.993402i	$-0.463415\pi$
$101$		0			0		−0.114683	+	0.993402i	$0.536585\pi$
$102$		0			0
$103$	0.487097	−	1.35622i	0.487097	−	1.35622i	−0.409069	−	0.912504i	$-0.634146\pi$
$103$	0.487097	−	1.35622i	0.487097	−	1.35622i	0.896166	−	0.443720i	$-0.146341\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		−0.817929	−	0.575319i	$-0.804878\pi$
$107$		0			0		0.817929	+	0.575319i	$0.195122\pi$
$108$	−0.543568	+	0.839365i	−0.543568	+	0.839365i
$109$	0.516023	+	0.120754i	0.516023	+	0.120754i	0.477720	−	0.878512i	$-0.341463\pi$
$109$	0.516023	+	0.120754i	0.516023	+	0.120754i	0.0383027	+	0.999266i	$0.487805\pi$
$110$		0			0
$111$	0.579212	+	1.06515i	0.579212	+	1.06515i
$112$	0.934468	+	0.555546i	0.934468	+	0.555546i
$113$		0			0		−0.927502	−	0.373817i	$-0.878049\pi$
$113$		0			0		0.927502	+	0.373817i	$0.121951\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.0730354	+	0.0231134i	0.0730354	+	0.0231134i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.988280	+	0.152649i	0.988280	+	0.152649i
$122$		0			0
$123$		0			0
$124$	0.487097	−	0.468784i	0.487097	−	0.468784i
$125$		0			0
$126$		0			0
$127$	0.311453	+	0.219071i	0.311453	+	0.219071i	0.720522	−	0.693433i	$-0.243902\pi$
$127$	0.311453	+	0.219071i	0.311453	+	0.219071i	−0.409069	+	0.912504i	$0.634146\pi$
$128$		0			0
$129$	−0.581098	−	1.61795i	−0.581098	−	1.61795i
$130$		0			0
$131$		0			0		0.0383027	−	0.999266i	$-0.487805\pi$
$131$		0			0		−0.0383027	+	0.999266i	$0.512195\pi$
$132$		0			0
$133$	−1.86345	+	0.143066i	−1.86345	+	0.143066i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		0.896166	−	0.443720i	$-0.146341\pi$
$137$		0			0		−0.896166	+	0.443720i	$0.853659\pi$
$138$		0			0
$139$	−0.780009	−	0.246849i	−0.780009	−	0.246849i	−0.114683	−	0.993402i	$-0.536585\pi$
$139$	−0.780009	−	0.246849i	−0.780009	−	0.246849i	−0.665326	+	0.746553i	$0.731707\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	0.896166	+	0.443720i	0.896166	+	0.443720i
$145$		0			0
$146$		0			0
$147$	−0.177079	−	0.0414381i	−0.177079	−	0.0414381i
$148$	0.991699	−	0.697546i	0.991699	−	0.697546i
$149$		0			0		−0.720522	−	0.693433i	$-0.756098\pi$
$149$		0			0		0.720522	+	0.693433i	$0.243902\pi$
$150$		0			0
$151$	0.910913	+	1.67514i	0.910913	+	1.67514i	0.720522	+	0.693433i	$0.243902\pi$
$151$	0.910913	+	1.67514i	0.910913	+	1.67514i	0.190391	+	0.981708i	$0.439024\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$	0.0145850	−	0.0752042i	0.0145850	−	0.0752042i
$157$	1.50239	+	0.351573i	1.50239	+	0.351573i	0.896166	−	0.443720i	$-0.146341\pi$
$157$	1.50239	+	0.351573i	1.50239	+	0.351573i	0.606225	+	0.795293i	$0.292683\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	0.491542	+	1.78869i	0.491542	+	1.78869i	0.606225	+	0.795293i	$0.292683\pi$
$163$	0.491542	+	1.78869i	0.491542	+	1.78869i	−0.114683	+	0.993402i	$0.536585\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		0.771489	−	0.636242i	$-0.219512\pi$
$167$		0			0		−0.771489	+	0.636242i	$0.780488\pi$
$168$		0			0
$169$	0.991215	−	0.0761000i	0.991215	−	0.0761000i
$170$		0			0
$171$	−1.69899	+	0.262425i	−1.69899	+	0.262425i
$172$	−1.54063	+	0.762816i	−1.54063	+	0.762816i
$173$		0			0		0.543568	−	0.839365i	$-0.317073\pi$
$173$		0			0		−0.543568	+	0.839365i	$0.682927\pi$
$174$		0			0
$175$	1.08395	+	0.0832194i	1.08395	+	0.0832194i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		−0.409069	−	0.912504i	$-0.634146\pi$
$179$		0			0		0.409069	+	0.912504i	$0.365854\pi$
$180$		0			0
$181$	−1.33065	+	1.49311i	−1.33065	+	1.49311i	−0.665326	+	0.746553i	$0.731707\pi$
$181$	−1.33065	+	1.49311i	−1.33065	+	1.49311i	−0.665326	+	0.746553i	$0.731707\pi$
$182$		0			0
$183$	0.0938268	+	0.209298i	0.0938268	+	0.209298i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−1.07439	−	0.165950i	−1.07439	−	0.165950i
$190$		0			0
$191$		0			0		−0.927502	−	0.373817i	$-0.878049\pi$
$191$		0			0		0.927502	+	0.373817i	$0.121951\pi$
$192$	0.338017	−	0.941140i	0.338017	−	0.941140i
$193$	−0.379665	+	1.95766i	−0.379665	+	1.95766i	−0.114683	+	0.993402i	$0.536585\pi$
$193$	−0.379665	+	1.95766i	−0.379665	+	1.95766i	−0.264982	+	0.964253i	$0.585366\pi$
$194$		0			0
$195$		0			0
$196$	−0.0208566	+	0.180663i	−0.0208566	+	0.180663i
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$		0			0
$199$	0.212738	−	0.0857412i	0.212738	−	0.0857412i	−0.264982	−	0.964253i	$-0.585366\pi$
$199$	0.212738	−	0.0857412i	0.212738	−	0.0857412i	0.477720	+	0.878512i	$0.341463\pi$
$200$		0			0
$201$	0.352598	+	1.28309i	0.352598	+	1.28309i
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$	−0.0763807	−	0.00586409i	−0.0763807	−	0.00586409i
$209$		0			0
$210$		0			0
$211$	−0.589486	−	1.31496i	−0.589486	−	1.31496i	−0.927502	−	0.373817i	$-0.878049\pi$
$211$	−0.589486	−	1.31496i	−0.589486	−	1.31496i	0.338017	−	0.941140i	$-0.390244\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$	0.681659	+	0.274733i	0.681659	+	0.274733i
$218$		0			0
$219$	−0.179136	+	0.651868i	−0.179136	+	0.651868i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	0.781482	−	1.43712i	0.781482	−	1.43712i	−0.114683	−	0.993402i	$-0.536585\pi$
$223$	0.781482	−	1.43712i	0.781482	−	1.43712i	0.896166	−	0.443720i	$-0.146341\pi$
$224$		0			0
$225$	1.00000			1.00000
$226$		0			0
$227$		0			0		0.606225	−	0.795293i	$-0.292683\pi$
$227$		0			0		−0.606225	+	0.795293i	$0.707317\pi$
$228$	0.455540	+	1.65769i	0.455540	+	1.65769i
$229$	1.42415	−	0.219974i	1.42415	−	0.219974i	0.606225	−	0.795293i	$-0.292683\pi$
$229$	1.42415	−	0.219974i	1.42415	−	0.219974i	0.817929	+	0.575319i	$0.195122\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		−0.606225	−	0.795293i	$-0.707317\pi$
$233$		0			0		0.606225	+	0.795293i	$0.292683\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−0.780009	−	0.246849i	−0.780009	−	0.246849i
$238$		0			0
$239$		0			0		0.896166	−	0.443720i	$-0.146341\pi$
$239$		0			0		−0.896166	+	0.443720i	$0.853659\pi$
$240$		0			0
$241$	1.02658	−	1.15192i	1.02658	−	1.15192i	0.0383027	−	0.999266i	$-0.487805\pi$
$241$	1.02658	−	1.15192i	1.02658	−	1.15192i	0.988280	−	0.152649i	$-0.0487805\pi$
$242$		0			0
$243$	−0.997066	−	0.0765493i	−0.997066	−	0.0765493i
$244$	0.197157	−	0.117211i	0.197157	−	0.117211i
$245$		0			0
$246$		0			0
$247$	0.113201	−	0.0672988i	0.113201	−	0.0672988i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		0			0		−0.114683	−	0.993402i	$-0.536585\pi$
$251$		0			0		0.114683	+	0.993402i	$0.463415\pi$
$252$	−0.0416402	+	1.08634i	−0.0416402	+	1.08634i
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.973695	−	0.227854i	−0.973695	−	0.227854i
$257$		0			0		−0.409069	−	0.912504i	$-0.634146\pi$
$257$		0			0		0.409069	+	0.912504i	$0.365854\pi$
$258$		0			0
$259$	1.13300	+	0.673573i	1.13300	+	0.673573i
$260$		0			0
$261$		0			0
$262$		0			0
$263$		0			0		−0.771489	−	0.636242i	$-0.780488\pi$
$263$		0			0		0.771489	+	0.636242i	$0.219512\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	1.23418	−	0.497420i	1.23418	−	0.497420i
$269$		0			0		0.771489	−	0.636242i	$-0.219512\pi$
$269$		0			0		−0.771489	+	0.636242i	$0.780488\pi$
$270$		0			0
$271$	0.796617	+	1.77700i	0.796617	+	1.77700i	0.606225	+	0.795293i	$0.292683\pi$
$271$	0.796617	+	1.77700i	0.796617	+	1.77700i	0.190391	+	0.981708i	$0.439024\pi$
$272$		0			0
$273$	0.0810898	−	0.0189758i	0.0810898	−	0.0189758i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	1.88445	+	0.596369i	1.88445	+	0.596369i	0.988280	+	0.152649i	$0.0487805\pi$
$277$	1.88445	+	0.596369i	1.88445	+	0.596369i	0.896166	+	0.443720i	$0.146341\pi$
$278$		0			0
$279$	0.644528	+	0.203973i	0.644528	+	0.203973i
$280$		0			0
$281$		0			0		0.264982	−	0.964253i	$-0.414634\pi$
$281$		0			0		−0.264982	+	0.964253i	$0.585366\pi$
$282$		0			0
$283$	−0.523752	−	0.0808985i	−0.523752	−	0.0808985i	−0.114683	−	0.993402i	$-0.536585\pi$
$283$	−0.523752	−	0.0808985i	−0.523752	−	0.0808985i	−0.409069	+	0.912504i	$0.634146\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−0.409069	+	0.912504i	−0.409069	+	0.912504i
$290$		0			0
$291$	−0.370766	−	1.91177i	−0.370766	−	1.91177i
$292$	0.668111	+	0.103196i	0.668111	+	0.103196i
$293$		0			0		−0.606225	−	0.795293i	$-0.707317\pi$
$293$		0			0		0.606225	+	0.795293i	$0.292683\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$	−0.114683	−	0.993402i	−0.114683	−	0.993402i
$301$	−1.44186	−	1.18910i	−1.44186	−	1.18910i
$302$		0			0
$303$		0			0
$304$	1.59451	−	0.642644i	1.59451	−	0.642644i
$305$		0			0
$306$		0			0
$307$	−1.31506	+	0.203123i	−1.31506	+	0.203123i	−0.771489	−	0.636242i	$-0.780488\pi$
$307$	−1.31506	+	0.203123i	−1.31506	+	0.203123i	−0.543568	+	0.839365i	$0.682927\pi$
$308$		0			0
$309$	−0.381850	−	1.38953i	−0.381850	−	1.38953i
$310$		0			0
$311$		0			0		−0.114683	−	0.993402i	$-0.536585\pi$
$311$		0			0		0.114683	+	0.993402i	$0.463415\pi$
$312$		0			0
$313$	−0.0202990	−	0.529574i	−0.0202990	−	0.529574i	−0.973695	−	0.227854i	$-0.926829\pi$
$313$	−0.0202990	−	0.529574i	−0.0202990	−	0.529574i	0.953396	−	0.301721i	$-0.0975610\pi$
$314$		0			0
$315$		0			0
$316$	−0.155766	+	0.803172i	−0.155766	+	0.803172i
$317$		0			0		1.00000			$0$
$317$		0			0		−1.00000			$\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$	0.0383027	+	0.999266i	0.0383027	+	0.999266i
$325$	−0.0710518	+	0.0286364i	−0.0710518	+	0.0286364i
$326$		0			0
$327$	0.491542	−	0.198109i	0.491542	−	0.198109i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−0.379665	−	0.0291486i	−0.379665	−	0.0291486i	−0.114683	−	0.993402i	$-0.536585\pi$
$331$	−0.379665	−	0.0291486i	−0.379665	−	0.0291486i	−0.264982	+	0.964253i	$0.585366\pi$
$332$		0			0
$333$	1.08656	+	0.537988i	1.08656	+	0.537988i
$334$		0			0
$335$		0			0
$336$	1.08395	−	0.0832194i	1.08395	−	0.0832194i
$337$	−1.31506	−	0.203123i	−1.31506	−	0.203123i	−0.543568	−	0.839365i	$-0.682927\pi$
$337$	−1.31506	−	0.203123i	−1.31506	−	0.203123i	−0.771489	+	0.636242i	$0.780488\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	0.847975	−	0.268358i	0.847975	−	0.268358i
$344$		0			0
$345$		0			0
$346$		0			0
$347$		0			0		−0.859570	−	0.511019i	$-0.829268\pi$
$347$		0			0		0.859570	+	0.511019i	$0.170732\pi$
$348$		0			0
$349$	−0.886173	−	0.357160i	−0.886173	−	0.357160i	−0.114683	−	0.993402i	$-0.536585\pi$
$349$	−0.886173	−	0.357160i	−0.886173	−	0.357160i	−0.771489	+	0.636242i	$0.780488\pi$
$350$		0			0
$351$	0.0730354	−	0.0231134i	0.0730354	−	0.0231134i
$352$		0			0
$353$		0			0		−0.817929	−	0.575319i	$-0.804878\pi$
$353$		0			0		0.817929	+	0.575319i	$0.195122\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		0.817929	−	0.575319i	$-0.195122\pi$
$359$		0			0		−0.817929	+	0.575319i	$0.804878\pi$
$360$		0			0
$361$	−1.06291	+	1.64133i	−1.06291	+	1.64133i
$362$		0			0
$363$	0.896166	−	0.443720i	0.896166	−	0.443720i
$364$	−0.0281502	−	0.0783786i	−0.0281502	−	0.0783786i
$365$		0			0
$366$		0			0
$367$	−0.0436694	+	0.225171i	−0.0436694	+	0.225171i	−0.997066	−	0.0765493i	$-0.975610\pi$
$367$	−0.0436694	+	0.225171i	−0.0436694	+	0.225171i	0.953396	+	0.301721i	$0.0975610\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$	0.128711	−	0.663668i	0.128711	−	0.663668i
$373$	0.380782			0.380782			0.190391	−	0.981708i	$-0.439024\pi$
$373$	0.380782			0.380782			0.190391	+	0.981708i	$0.439024\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	1.15595	−	1.51646i	1.15595	−	1.51646i	0.338017	−	0.941140i	$-0.390244\pi$
$379$	1.15595	−	1.51646i	1.15595	−	1.51646i	0.817929	−	0.575319i	$-0.195122\pi$
$380$		0			0
$381$	0.380782			0.380782
$382$		0			0
$383$		0			0		0.771489	−	0.636242i	$-0.219512\pi$
$383$		0			0		−0.771489	+	0.636242i	$0.780488\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−1.40613	−	0.989053i	−1.40613	−	0.989053i
$388$	−1.85664	+	0.587568i	−1.85664	+	0.587568i
$389$		0			0		0.477720	−	0.878512i	$-0.341463\pi$
$389$		0			0		−0.477720	+	0.878512i	$0.658537\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−0.505265	+	1.83863i	−0.505265	+	1.83863i	0.0383027	+	0.999266i	$0.487805\pi$
$397$	−0.505265	+	1.83863i	−0.505265	+	1.83863i	−0.543568	+	0.839365i	$0.682927\pi$
$398$		0			0
$399$	−1.44186	+	1.18910i	−1.44186	+	1.18910i
$400$	−0.973695	+	0.227854i	−0.973695	+	0.227854i
$401$		0			0		0.338017	−	0.941140i	$-0.390244\pi$
$401$		0			0		−0.338017	+	0.941140i	$0.609756\pi$
$402$		0			0
$403$	−0.0516359	+	0.00396432i	−0.0516359	+	0.00396432i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	0.456432	−	0.839365i	0.456432	−	0.839365i	−0.543568	−	0.839365i	$-0.682927\pi$
$409$	0.456432	−	0.839365i	0.456432	−	0.839365i	1.00000			$0$
$410$		0			0
$411$		0			0
$412$	−1.33657	+	0.538687i	−1.33657	+	0.538687i
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−0.780009	+	0.246849i	−0.780009	+	0.246849i
$418$		0			0
$419$		0			0		1.00000			$0$
$419$		0			0		−1.00000			$\pi$
$420$		0			0
$421$	−1.97076	+	0.151304i	−1.97076	+	0.151304i	−0.997066	−	0.0765493i	$-0.975610\pi$
$421$	−1.97076	+	0.151304i	−1.97076	+	0.151304i	−0.973695	+	0.227854i	$0.926829\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$		0			0
$427$	0.203953	+	0.143457i	0.203953	+	0.143457i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.973695	−	0.227854i	$-0.0731707\pi$
$431$		0			0		−0.973695	+	0.227854i	$0.926829\pi$
$432$	0.988280	−	0.152649i	0.988280	−	0.152649i
$433$	−0.353176	+	1.82107i	−0.353176	+	1.82107i	0.190391	+	0.981708i	$0.439024\pi$
$433$	−0.353176	+	1.82107i	−0.353176	+	1.82107i	−0.543568	+	0.839365i	$0.682927\pi$
$434$		0			0
$435$		0			0
$436$	−0.253174	−	0.465579i	−0.253174	−	0.465579i
$437$		0			0
$438$		0			0
$439$	0.124676	+	1.07996i	0.124676	+	1.07996i	0.896166	+	0.443720i	$0.146341\pi$
$439$	0.124676	+	1.07996i	0.124676	+	1.07996i	−0.771489	+	0.636242i	$0.780488\pi$
$440$		0			0
$441$	−0.168678	+	0.0679834i	−0.168678	+	0.0679834i
$442$		0			0
$443$		0			0		−0.190391	−	0.981708i	$-0.560976\pi$
$443$		0			0		0.190391	+	0.981708i	$0.439024\pi$
$444$	0.409829	−	1.14109i	0.409829	−	1.14109i
$445$		0			0
$446$		0			0
$447$		0			0
$448$	−0.206981	−	1.06725i	−0.206981	−	1.06725i
$449$		0			0		0.606225	−	0.795293i	$-0.292683\pi$
$449$		0			0		−0.606225	+	0.795293i	$0.707317\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	1.70880	+	0.846082i	1.70880	+	0.846082i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	0.0258939	+	0.0720965i	0.0258939	+	0.0720965i	0.953396	−	0.301721i	$-0.0975610\pi$
$457$	0.0258939	+	0.0720965i	0.0258939	+	0.0720965i	−0.927502	+	0.373817i	$0.878049\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		0.665326	−	0.746553i	$-0.268293\pi$
$461$		0			0		−0.665326	+	0.746553i	$0.731707\pi$
$462$		0			0
$463$	−0.139048	+	0.182414i	−0.139048	+	0.182414i	−0.859570	−	0.511019i	$-0.829268\pi$
$463$	−0.139048	+	0.182414i	−0.139048	+	0.182414i	0.720522	+	0.693433i	$0.243902\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		0.896166	−	0.443720i	$-0.146341\pi$
$467$		0			0		−0.896166	+	0.443720i	$0.853659\pi$
$468$	−0.0313369	−	0.0699028i	−0.0313369	−	0.0699028i
$469$	1.04230	+	1.00312i	1.04230	+	1.00312i
$470$		0			0
$471$	1.43112	−	0.576792i	1.43112	−	0.576792i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	1.14379	−	1.28343i	1.14379	−	1.28343i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.988280	−	0.152649i	$-0.0487805\pi$
$479$		0			0		−0.988280	+	0.152649i	$0.951220\pi$
$480$		0			0
$481$	−0.0926078	−	0.00710992i	−0.0926078	−	0.00710992i
$482$		0			0
$483$		0			0
$484$	−0.543568	−	0.839365i	−0.543568	−	0.839365i
$485$		0			0
$486$		0			0
$487$	0.0464402	−	1.21156i	0.0464402	−	1.21156i	−0.771489	−	0.636242i	$-0.780488\pi$
$487$	0.0464402	−	1.21156i	0.0464402	−	1.21156i	0.817929	−	0.575319i	$-0.195122\pi$
$488$		0			0
$489$	1.43112	+	1.18023i	1.43112	+	1.18023i
$490$		0			0
$491$		0			0		−0.338017	−	0.941140i	$-0.609756\pi$
$491$		0			0		0.338017	+	0.941140i	$0.390244\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−0.674050	−	0.0517499i	−0.674050	−	0.0517499i
$497$		0			0
$498$		0			0
$499$	−0.205551	+	1.78051i	−0.205551	+	1.78051i	0.338017	+	0.941140i	$0.390244\pi$
$499$	−0.205551	+	1.78051i	−0.205551	+	1.78051i	−0.543568	+	0.839365i	$0.682927\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		0.543568	−	0.839365i	$-0.317073\pi$
$503$		0			0		−0.543568	+	0.839365i	$0.682927\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.766962	−	0.632509i	0.766962	−	0.632509i
$508$	−0.0436694	−	0.378270i	−0.0436694	−	0.378270i
$509$		0			0		−0.114683	−	0.993402i	$-0.536585\pi$
$509$		0			0		0.114683	+	0.993402i	$0.463415\pi$
$510$		0			0
$511$	0.194746	+	0.708668i	0.194746	+	0.708668i
$512$		0			0
$513$	−1.23868	+	1.19211i	−1.23868	+	1.19211i
$514$		0			0
$515$		0			0
$516$	−0.821267	+	1.51028i	−0.821267	+	1.51028i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$		0			0		0.606225	−	0.795293i	$-0.292683\pi$
$521$		0			0		−0.606225	+	0.795293i	$0.707317\pi$
$522$		0			0
$523$	0.723299	+	1.11690i	0.723299	+	1.11690i	0.988280	+	0.152649i	$0.0487805\pi$
$523$	0.723299	+	1.11690i	0.723299	+	1.11690i	−0.264982	+	0.964253i	$0.585366\pi$
$524$		0			0
$525$	0.934468	−	0.555546i	0.934468	−	0.555546i
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−0.665326	−	0.746553i	−0.665326	−	0.746553i
$530$		0			0
$531$		0			0
$532$	1.34661	+	1.29598i	1.34661	+	1.29598i
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−1.26864	−	1.42352i	−1.26864	−	1.42352i	−0.859570	−	0.511019i	$-0.829268\pi$
$541$	−1.26864	−	1.42352i	−1.26864	−	1.42352i	−0.409069	−	0.912504i	$-0.634146\pi$
$542$		0			0
$543$	−0.229367	+	1.98680i	−0.229367	+	1.98680i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	0.668111	−	1.86022i	0.668111	−	1.86022i	0.190391	−	0.981708i	$-0.439024\pi$
$547$	0.668111	−	1.86022i	0.668111	−	1.86022i	0.477720	−	0.878512i	$-0.341463\pi$
$548$		0			0
$549$	0.197157	+	0.117211i	0.197157	+	0.117211i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−0.866030	+	0.202659i	−0.866030	+	0.202659i
$554$		0			0
$555$		0			0
$556$	0.334674	+	0.746553i	0.334674	+	0.746553i
$557$		0			0		0.720522	−	0.693433i	$-0.243902\pi$
$557$		0			0		−0.720522	+	0.693433i	$0.756098\pi$
$558$		0			0
$559$	0.128231	+	0.0300073i	0.128231	+	0.0300073i
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		0.190391	−	0.981708i	$-0.439024\pi$
$563$		0			0		−0.190391	+	0.981708i	$0.560976\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.974253	+	0.482383i	−0.974253	+	0.482383i
$568$		0			0
$569$		0			0		−0.896166	−	0.443720i	$-0.853659\pi$
$569$		0			0		0.896166	+	0.443720i	$0.146341\pi$
$570$		0			0
$571$	−0.635679	−	1.16899i	−0.635679	−	1.16899i	−0.973695	−	0.227854i	$-0.926829\pi$
$571$	−0.635679	−	1.16899i	−0.635679	−	1.16899i	0.338017	−	0.941140i	$-0.390244\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.264982	−	0.964253i	−0.264982	−	0.964253i
$577$	−1.66239	+	0.823102i	−1.66239	+	0.823102i	−0.665326	+	0.746553i	$0.731707\pi$
$577$	−1.66239	+	0.823102i	−1.66239	+	0.823102i	−0.997066	+	0.0765493i	$0.975610\pi$
$578$		0			0
$579$	0.815737	+	1.81965i	0.815737	+	1.81965i
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		−0.720522	−	0.693433i	$-0.756098\pi$
$587$		0			0		0.720522	+	0.693433i	$0.243902\pi$
$588$	0.0868794	+	0.159769i	0.0868794	+	0.159769i
$589$	0.998988	−	0.593904i	0.998988	−	0.593904i
$590$		0			0
$591$		0			0
$592$	−1.18056	−	0.276261i	−1.18056	−	0.276261i
$593$		0			0		−0.264982	−	0.964253i	$-0.585366\pi$
$593$		0			0		0.264982	+	0.964253i	$0.414634\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	0.124676	−	0.192523i	0.124676	−	0.192523i
$598$		0			0
$599$		0			0		−0.953396	−	0.301721i	$-0.902439\pi$
$599$		0			0		0.953396	+	0.301721i	$0.0975610\pi$
$600$		0			0
$601$	−1.59283	−	0.372736i	−1.59283	−	0.372736i	−0.665326	−	0.746553i	$-0.731707\pi$
$601$	−1.59283	−	0.372736i	−1.59283	−	0.372736i	−0.927502	+	0.373817i	$0.878049\pi$
$602$		0			0
$603$	1.02658	+	0.846617i	1.02658	+	0.846617i
$604$	0.644528	−	1.79456i	0.644528	−	1.79456i
$605$		0			0
$606$		0			0
$607$	0.363036	+	0.114890i	0.363036	+	0.114890i	0.477720	−	0.878512i	$-0.341463\pi$
$607$	0.363036	+	0.114890i	0.363036	+	0.114890i	−0.114683	+	0.993402i	$0.536585\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−1.51726	+	0.611512i	−1.51726	+	0.611512i	−0.973695	−	0.227854i	$-0.926829\pi$
$613$	−1.51726	+	0.611512i	−1.51726	+	0.611512i	−0.543568	+	0.839365i	$0.682927\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		0			0		−0.817929	−	0.575319i	$-0.804878\pi$
$617$		0			0		0.817929	+	0.575319i	$0.195122\pi$
$618$		0			0
$619$	−0.505265	+	0.159901i	−0.505265	+	0.159901i	−0.543568	−	0.839365i	$-0.682927\pi$
$619$	−0.505265	+	0.159901i	−0.505265	+	0.159901i	0.0383027	+	0.999266i	$0.487805\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$	−0.0658477	+	0.0391468i	−0.0658477	+	0.0391468i
$625$	−0.771489	+	0.636242i	−0.771489	+	0.636242i
$626$		0			0
$627$		0			0
$628$	−0.737111	−	1.35553i	−0.737111	−	1.35553i
$629$		0			0
$630$		0			0
$631$	−0.659049	+	1.01769i	−0.659049	+	1.01769i	0.338017	+	0.941140i	$0.390244\pi$
$631$	−0.659049	+	1.01769i	−0.659049	+	1.01769i	−0.997066	+	0.0765493i	$0.975610\pi$
$632$		0			0
$633$	−1.23868	−	0.736400i	−1.23868	−	0.736400i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	0.0100381	−	0.00966068i	0.0100381	−	0.00966068i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		0			0		0.953396	−	0.301721i	$-0.0975610\pi$
$641$		0			0		−0.953396	+	0.301721i	$0.902439\pi$
$642$		0			0
$643$	−1.78707	+	0.137202i	−1.78707	+	0.137202i	−0.927502	−	0.373817i	$-0.878049\pi$
$643$	−1.78707	+	0.137202i	−1.78707	+	0.137202i	−0.859570	+	0.511019i	$0.829268\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		0.953396	−	0.301721i	$-0.0975610\pi$
$647$		0			0		−0.953396	+	0.301721i	$0.902439\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	0.715608	−	0.167459i	0.715608	−	0.167459i
$652$	1.00832	−	1.55703i	1.00832	−	1.55703i
$653$		0			0		−0.771489	−	0.636242i	$-0.780488\pi$
$653$		0			0		0.771489	+	0.636242i	$0.219512\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	0.228511	+	0.636242i	0.228511	+	0.636242i
$658$		0			0
$659$		0			0		0.665326	−	0.746553i	$-0.268293\pi$
$659$		0			0		−0.665326	+	0.746553i	$0.731707\pi$
$660$		0			0
$661$	1.94168	−	0.454370i	1.94168	−	0.454370i	0.953396	−	0.301721i	$-0.0975610\pi$
$661$	1.94168	−	0.454370i	1.94168	−	0.454370i	0.988280	−	0.152649i	$-0.0487805\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	−0.187606	−	1.62507i	−0.187606	−	1.62507i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.109573	−	0.949136i	−0.109573	−	0.949136i	−0.927502	−	0.373817i	$-0.878049\pi$
$673$	−0.109573	−	0.949136i	−0.109573	−	0.949136i	0.817929	−	0.575319i	$-0.195122\pi$
$674$		0			0
$675$	0.817929	−	0.575319i	0.817929	−	0.575319i
$676$	−0.716293	−	0.689363i	−0.716293	−	0.689363i
$677$		0			0		−0.927502	−	0.373817i	$-0.878049\pi$
$677$		0			0		0.927502	+	0.373817i	$0.121951\pi$
$678$		0			0
$679$	−1.40855	−	1.58051i	−1.40855	−	1.58051i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		0			0		0.114683	−	0.993402i	$-0.463415\pi$
$683$		0			0		−0.114683	+	0.993402i	$0.536585\pi$
$684$	1.32630	+	1.09379i	1.32630	+	1.09379i
$685$		0			0
$686$		0			0
$687$	1.03830	−	0.999266i	1.03830	−	0.999266i
$688$	1.59451	+	0.642644i	1.59451	+	0.642644i
$689$		0			0
$690$		0			0
$691$	0.781482	+	1.43712i	0.781482	+	1.43712i	0.896166	+	0.443720i	$0.146341\pi$
$691$	0.781482	+	1.43712i	0.781482	+	1.43712i	−0.114683	+	0.993402i	$0.536585\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−0.659049	−	0.864591i	−0.659049	−	0.864591i
$701$		0			0		0.997066	−	0.0765493i	$-0.0243902\pi$
$701$		0			0		−0.997066	+	0.0765493i	$0.975610\pi$
$702$		0			0
$703$	1.93326	−	0.779174i	1.93326	−	0.779174i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−0.155766	+	0.347465i	−0.155766	+	0.347465i	−0.973695	−	0.227854i	$-0.926829\pi$
$709$	−0.155766	+	0.347465i	−0.155766	+	0.347465i	0.817929	+	0.575319i	$0.195122\pi$
$710$		0			0
$711$	−0.780009	+	0.246849i	−0.780009	+	0.246849i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.114683	−	0.993402i	$-0.536585\pi$
$719$		0			0		0.114683	+	0.993402i	$0.463415\pi$
$720$		0			0
$721$	−1.12878	−	1.08634i	−1.12878	−	1.08634i
$722$		0			0
$723$	0.176954	−	1.53280i	0.176954	−	1.53280i
$724$	2.00000			2.00000
$725$		0			0
$726$		0			0
$727$	1.94168	+	0.454370i	1.94168	+	0.454370i	0.988280	+	0.152649i	$0.0487805\pi$
$727$	1.94168	+	0.454370i	1.94168	+	0.454370i	0.953396	+	0.301721i	$0.0975610\pi$
$728$		0			0
$729$	−0.859570	+	0.511019i	−0.859570	+	0.511019i
$730$		0			0
$731$		0			0
$732$	0.0938268	−	0.209298i	0.0938268	−	0.209298i
$733$	−0.206981	−	1.06725i	−0.206981	−	1.06725i	−0.927502	−	0.373817i	$-0.878049\pi$
$733$	−0.206981	−	1.06725i	−0.206981	−	1.06725i	0.720522	−	0.693433i	$-0.243902\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−0.973695	−	0.227854i	−0.973695	−	0.227854i
$739$	−0.973695	−	0.227854i	−0.973695	−	0.227854i
$740$		0			0
$741$	0.0538725	−	0.120173i	0.0538725	−	0.120173i
$742$		0			0
$743$		0			0		−0.665326	−	0.746553i	$-0.731707\pi$
$743$		0			0		0.665326	+	0.746553i	$0.268293\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−1.40314	−	0.328347i	−1.40314	−	0.328347i	−0.543568	−	0.839365i	$-0.682927\pi$
$751$	−1.40314	−	0.328347i	−1.40314	−	0.328347i	−0.859570	+	0.511019i	$0.829268\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$	0.590931	+	0.912504i	0.590931	+	0.912504i
$757$	0.688415	+	0.662533i	0.688415	+	0.662533i	0.953396	−	0.301721i	$-0.0975610\pi$
$757$	0.688415	+	0.662533i	0.688415	+	0.662533i	−0.264982	+	0.964253i	$0.585366\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		0.477720	−	0.878512i	$-0.341463\pi$
$761$		0			0		−0.477720	+	0.878512i	$0.658537\pi$
$762$		0			0
$763$	0.349272	−	0.458201i	0.349272	−	0.458201i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.927502	+	0.373817i	−0.927502	+	0.373817i
$769$	−0.276544	+	0.616883i	−0.276544	+	0.616883i	−0.997066	−	0.0765493i	$-0.975610\pi$
$769$	−0.276544	+	0.616883i	−0.276544	+	0.616883i	0.720522	+	0.693433i	$0.243902\pi$
$770$		0			0
$771$		0			0
$772$	1.71409	−	1.01904i	1.71409	−	1.01904i
$773$		0			0		0.988280	−	0.152649i	$-0.0487805\pi$
$773$		0			0		−0.988280	+	0.152649i	$0.951220\pi$
$774$		0			0
$775$	−0.627023	+	0.252713i	−0.627023	+	0.252713i
$776$		0			0
$777$	1.31423	−	0.100899i	1.31423	−	0.100899i
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.148751	−	0.104629i	0.148751	−	0.104629i
$785$		0			0
$786$		0			0
$787$	−0.253174	−	0.465579i	−0.253174	−	0.465579i	0.720522	−	0.693433i	$-0.243902\pi$
$787$	−0.253174	−	0.465579i	−0.253174	−	0.465579i	−0.973695	+	0.227854i	$0.926829\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−0.0173648	−	0.00268216i	−0.0173648	−	0.00268216i
$794$		0			0
$795$		0			0
$796$	−0.205551	−	0.101775i	−0.205551	−	0.101775i
$797$		0			0		0.0383027	−	0.999266i	$-0.487805\pi$
$797$		0			0		−0.0383027	+	0.999266i	$0.512195\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$		0			0
$803$		0			0
$804$	0.723299	−	1.11690i	0.723299	−	1.11690i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$		0			0		−0.114683	−	0.993402i	$-0.536585\pi$
$809$		0			0		0.114683	+	0.993402i	$0.463415\pi$
$810$		0			0
$811$	0.0464402	−	1.21156i	0.0464402	−	1.21156i	−0.771489	−	0.636242i	$-0.780488\pi$
$811$	0.0464402	−	1.21156i	0.0464402	−	1.21156i	0.817929	−	0.575319i	$-0.195122\pi$
$812$		0			0
$813$	1.67392	+	0.995153i	1.67392	+	0.995153i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−2.87770	+	0.673407i	−2.87770	+	0.673407i
$818$		0			0
$819$	0.0554087	−	0.0621733i	0.0554087	−	0.0621733i
$820$		0			0
$821$		0			0		−0.338017	−	0.941140i	$-0.609756\pi$
$821$		0			0		0.338017	+	0.941140i	$0.390244\pi$
$822$		0			0
$823$	−1.12455	+	1.47527i	−1.12455	+	1.47527i	−0.264982	+	0.964253i	$0.585366\pi$
$823$	−1.12455	+	1.47527i	−1.12455	+	1.47527i	−0.859570	+	0.511019i	$0.829268\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		0.973695	−	0.227854i	$-0.0731707\pi$
$827$		0			0		−0.973695	+	0.227854i	$0.926829\pi$
$828$		0			0
$829$	−0.379665	−	1.95766i	−0.379665	−	1.95766i	−0.264982	−	0.964253i	$-0.585366\pi$
$829$	−0.379665	−	1.95766i	−0.379665	−	1.95766i	−0.114683	−	0.993402i	$-0.536585\pi$
$830$		0			0
$831$	1.88445	−	0.596369i	1.88445	−	0.596369i
$832$	0.0464402	+	0.0609238i	0.0464402	+	0.0609238i
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$	0.644528	−	0.203973i	0.644528	−	0.203973i
$838$		0			0
$839$		0			0		0.477720	−	0.878512i	$-0.341463\pi$
$839$		0			0		−0.477720	+	0.878512i	$0.658537\pi$
$840$		0			0
$841$	0.720522	−	0.693433i	0.720522	−	0.693433i
$842$		0			0
$843$		0			0
$844$	−0.589486	+	1.31496i	−0.589486	+	1.31496i
$845$		0			0
$846$		0			0
$847$	0.590931	−	0.912504i	0.590931	−	0.912504i
$848$		0			0
$849$	−0.474935	+	0.235155i	−0.474935	+	0.235155i
$850$		0			0
$851$		0			0
$852$		0			0
$853$	1.19039	−	0.981708i	1.19039	−	0.981708i	0.190391	−	0.981708i	$-0.439024\pi$
$853$	1.19039	−	0.981708i	1.19039	−	0.981708i	1.00000			$0$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		−0.988280	−	0.152649i	$-0.951220\pi$
$857$		0			0		0.988280	+	0.152649i	$0.0487805\pi$
$858$		0			0
$859$	1.15595	−	0.365821i	1.15595	−	0.365821i	0.338017	−	0.941140i	$-0.390244\pi$
$859$	1.15595	−	0.365821i	1.15595	−	0.365821i	0.817929	+	0.575319i	$0.195122\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.720522	−	0.693433i	$-0.243902\pi$
$863$		0			0		−0.720522	+	0.693433i	$0.756098\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	0.190391	+	0.981708i	0.190391	+	0.981708i
$868$	−0.248422	−	0.691681i	−0.248422	−	0.691681i
$869$		0			0
$870$		0			0
$871$	−0.0971846	−	0.0307559i	−0.0971846	−	0.0307559i
$872$		0			0
$873$	−1.40314	−	1.35038i	−1.40314	−	1.35038i
$874$		0			0
$875$		0			0
$876$	0.605838	−	0.299970i	0.605838	−	0.299970i
$877$	−1.92457	−	0.450366i	−1.92457	−	0.450366i	−0.997066	−	0.0765493i	$-0.975610\pi$
$877$	−1.92457	−	0.450366i	−1.92457	−	0.450366i	−0.927502	−	0.373817i	$-0.878049\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		0.543568	−	0.839365i	$-0.317073\pi$
$881$		0			0		−0.543568	+	0.839365i	$0.682927\pi$
$882$		0			0
$883$	−1.74518	−	0.864096i	−1.74518	−	0.864096i	−0.973695	−	0.227854i	$-0.926829\pi$
$883$	−1.74518	−	0.864096i	−1.74518	−	0.864096i	−0.771489	−	0.636242i	$-0.780488\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		0			0		0.817929	−	0.575319i	$-0.195122\pi$
$887$		0			0		−0.817929	+	0.575319i	$0.804878\pi$
$888$		0			0
$889$	0.355829	−	0.211542i	0.355829	−	0.211542i
$890$		0			0
$891$		0			0
$892$	−1.59283	+	0.372736i	−1.59283	+	0.372736i
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	−0.665326	−	0.746553i	−0.665326	−	0.746553i
$901$		0			0
$902$		0			0
$903$	−1.86345	−	0.143066i	−1.86345	−	0.143066i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−0.635679	−	1.16899i	−0.635679	−	1.16899i	−0.973695	−	0.227854i	$-0.926829\pi$
$907$	−0.635679	−	1.16899i	−0.635679	−	1.16899i	0.338017	−	0.941140i	$-0.390244\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		0			0		0.896166	−	0.443720i	$-0.146341\pi$
$911$		0			0		−0.896166	+	0.443720i	$0.853659\pi$
$912$	0.934468	−	1.44299i	0.934468	−	1.44299i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	−1.11175	−	0.916853i	−1.11175	−	0.916853i
$917$		0			0
$918$		0			0
$919$	1.80621	+	0.422669i	1.80621	+	0.422669i	0.988280	−	0.152649i	$-0.0487805\pi$
$919$	1.80621	+	0.422669i	1.80621	+	0.422669i	0.817929	+	0.575319i	$0.195122\pi$
$920$		0			0
$921$	−0.958763	+	0.922717i	−0.958763	+	0.922717i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−1.18056	+	0.276261i	−1.18056	+	0.276261i
$926$		0			0
$927$	−1.11175	−	0.916853i	−1.11175	−	0.916853i
$928$		0			0
$929$		0			0		−0.859570	−	0.511019i	$-0.829268\pi$
$929$		0			0		0.859570	+	0.511019i	$0.170732\pi$
$930$		0			0
$931$	−0.105680	+	0.294245i	−0.105680	+	0.294245i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−1.31506	−	1.47561i	−1.31506	−	1.47561i	−0.771489	−	0.636242i	$-0.780488\pi$
$937$	−1.31506	−	1.47561i	−1.31506	−	1.47561i	−0.543568	−	0.839365i	$-0.682927\pi$
$938$		0			0
$939$	−0.321277	−	0.421476i	−0.321277	−	0.421476i
$940$		0			0
$941$		0			0		−0.859570	−	0.511019i	$-0.829268\pi$
$941$		0			0		0.859570	+	0.511019i	$0.170732\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		−0.997066	−	0.0765493i	$-0.975610\pi$
$947$		0			0		0.997066	+	0.0765493i	$0.0243902\pi$
$948$	0.334674	+	0.746553i	0.334674	+	0.746553i
$949$	−0.0344558	−	0.0386624i	−0.0344558	−	0.0386624i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		0.859570	−	0.511019i	$-0.170732\pi$
$953$		0			0		−0.859570	+	0.511019i	$0.829268\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.541385	−	0.0415646i	0.541385	−	0.0415646i
$962$		0			0
$963$		0			0
$964$	−1.54298			−1.54298
$965$		0			0
$966$		0			0
$967$	0.491542	+	1.78869i	0.491542	+	1.78869i	0.606225	+	0.795293i	$0.292683\pi$
$967$	0.491542	+	1.78869i	0.491542	+	1.78869i	−0.114683	+	0.993402i	$0.536585\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		0			0		0.771489	−	0.636242i	$-0.219512\pi$
$971$		0			0		−0.771489	+	0.636242i	$0.780488\pi$
$972$	0.606225	+	0.795293i	0.606225	+	0.795293i
$973$	−0.591758	+	0.664004i	−0.591758	+	0.664004i
$974$		0			0
$975$	−0.0416402	+	0.0643000i	−0.0416402	+	0.0643000i
$976$	−0.218678	−	0.0692047i	−0.218678	−	0.0692047i
$977$		0			0		0.264982	−	0.964253i	$-0.414634\pi$
$977$		0			0		−0.264982	+	0.964253i	$0.585366\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	0.288071	−	0.444833i	0.288071	−	0.444833i
$982$		0			0
$983$		0			0		0.859570	−	0.511019i	$-0.170732\pi$
$983$		0			0		−0.859570	+	0.511019i	$0.829268\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	−0.125558	−	0.0397352i	−0.125558	−	0.0397352i
$989$		0			0
$990$		0			0
$991$	0.0766055	−	1.99853i	0.0766055	−	1.99853i	0.0383027	−	0.999266i	$-0.487805\pi$
$991$	0.0766055	−	1.99853i	0.0766055	−	1.99853i	0.0383027	−	0.999266i	$-0.487805\pi$
$992$		0			0
$993$	−0.327309	+	0.194587i	−0.327309	+	0.194587i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−1.78707	−	0.137202i	−1.78707	−	0.137202i	−0.859570	−	0.511019i	$-0.829268\pi$
$997$	−1.78707	−	0.137202i	−1.78707	−	0.137202i	−0.927502	+	0.373817i	$0.878049\pi$
$998$		0			0
$999$	1.19824	−	0.185080i	1.19824	−	0.185080i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2217.1.p.a.1016.1	yes	40
3.2	odd	2	CM	2217.1.p.a.1016.1	yes	40
739.731	even	41	inner	2217.1.p.a.731.1	✓	40
2217.731	odd	82	inner	2217.1.p.a.731.1	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2217.1.p.a.731.1	✓	40	739.731	even	41	inner
2217.1.p.a.731.1	✓	40	2217.731	odd	82	inner
2217.1.p.a.1016.1	yes	40	1.1	even	1	trivial
2217.1.p.a.1016.1	yes	40	3.2	odd	2	CM

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:	\( N \)	\(=\)	\( 2217 = 3 \cdot 739 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2217.p (of order \(82\), degree \(40\), minimal)

\(f(q)\)	\(=\)	\(q+(0.817929 - 0.575319i) q^{3} +(-0.665326 - 0.746553i) q^{4} +(0.444713 - 0.992015i) q^{7} +(0.338017 - 0.941140i) q^{9} +O(q^{10})\)	\(q+(0.817929 - 0.575319i) q^{3} +(-0.665326 - 0.746553i) q^{4} +(0.444713 - 0.992015i) q^{7} +(0.338017 - 0.941140i) q^{9} +(-0.973695 - 0.227854i) q^{12} +(0.00293420 + 0.0765493i) q^{13} +(-0.114683 + 0.993402i) q^{16} +(-0.821267 - 1.51028i) q^{19} +(-0.206981 - 1.06725i) q^{21} +(0.338017 + 0.941140i) q^{25} +(-0.264982 - 0.964253i) q^{27} +(-1.03647 + 0.328011i) q^{28} +(0.0258939 + 0.675538i) q^{31} +(-0.927502 + 0.373817i) q^{36} +(-0.139048 + 1.20445i) q^{37} +(0.0464402 + 0.0609238i) q^{39} +(0.455540 - 1.65769i) q^{43} +(0.477720 + 0.878512i) q^{48} +(-0.120998 - 0.135770i) q^{49} +(0.0551959 - 0.0531207i) q^{52} +(-1.54063 - 0.762816i) q^{57} +(-0.0436694 + 0.225171i) q^{61} +(-0.783304 - 0.753855i) q^{63} +(0.817929 - 0.575319i) q^{64} +(-0.449783 + 1.25233i) q^{67} +(-0.521553 + 0.430121i) q^{73} +(0.817929 + 0.575319i) q^{75} +(-0.581098 + 1.61795i) q^{76} +(-0.495976 - 0.650659i) q^{79} +(-0.771489 - 0.636242i) q^{81} +(-0.659049 + 0.864591i) q^{84} +(0.0772429 + 0.0311317i) q^{91} +(0.409829 + 0.537645i) q^{93} +(0.796617 - 1.77700i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - q^{3} - q^{4} - 2 q^{7} - q^{9}+O(q^{10}) \) 40 * q - q^3 - q^4 - 2 * q^7 - q^9	\( 40 q - q^{3} - q^{4} - 2 q^{7} - q^{9} - q^{12} + 39 q^{13} - q^{16} - 2 q^{19} - 2 q^{21} - q^{25} - q^{27} - 2 q^{28} - 2 q^{31} - q^{36} - 2 q^{37} - 2 q^{39} - 2 q^{43} - q^{48} - 3 q^{49} - 2 q^{52} - 2 q^{57} - 2 q^{61} - 2 q^{63} - q^{64} - 2 q^{67} - 2 q^{73} - q^{75} - 2 q^{76} - 2 q^{79} - q^{81} - 2 q^{84} - 4 q^{91} - 2 q^{93} - 2 q^{97}+O(q^{100}) \) 40 * q - q^3 - q^4 - 2 * q^7 - q^9 - q^12 + 39 * q^13 - q^16 - 2 * q^19 - 2 * q^21 - q^25 - q^27 - 2 * q^28 - 2 * q^31 - q^36 - 2 * q^37 - 2 * q^39 - 2 * q^43 - q^48 - 3 * q^49 - 2 * q^52 - 2 * q^57 - 2 * q^61 - 2 * q^63 - q^64 - 2 * q^67 - 2 * q^73 - q^75 - 2 * q^76 - 2 * q^79 - q^81 - 2 * q^84 - 4 * q^91 - 2 * q^93 - 2 * q^97

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