LMFDB - Embedded newform 847.1.bb.a.279.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,1,Mod(20,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(110))

chi = DirichletCharacter(H, H._module([55, 76]))

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

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

chi := DirichletCharacter("847.20");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	847.bb (of order $110$, 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:	$0.422708065700$
Analytic rank:	$0$
Dimension:	$40$
Coefficient field:	$\Q(\zeta_{55})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{40} - x^{39} + x^{35} - x^{34} + x^{30} - x^{28} + x^{25} - x^{23} + x^{20} - x^{17} + x^{15} + \cdots + 1 $ x^40 - x^39 + x^35 - x^34 + x^30 - x^28 + x^25 - x^23 + x^20 - x^17 + x^15 - x^12 + x^10 - x^6 + x^5 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{55}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{55} - \cdots)$

Embedding invariants

Embedding label			279.1
Root			$-0.362808 - 0.931864i$ of defining polynomial
Character	$\chi$	$=$	847.279
Dual form			847.1.bb.a.762.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.374706 - 0.962424i) q^{2} +(-0.0491151 + 0.0450774i) q^{4} +(0.516397 - 0.856349i) q^{7} +(-0.865041 - 0.425312i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.374706 - 0.962424i) q^{2} +(-0.0491151 + 0.0450774i) q^{4} +(0.516397 - 0.856349i) q^{7} +(-0.865041 - 0.425312i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(-0.998369 + 0.0570888i) q^{11} +(-1.01767 - 0.176114i) q^{14} +(-0.0908996 + 1.05832i) q^{16} +(-0.262555 + 0.998864i) q^{18} +(0.429039 + 0.939463i) q^{22} +(1.20642 - 1.39228i) q^{23} +(-0.0285561 + 0.999592i) q^{25} +(0.0132391 + 0.0653376i) q^{28} +(-0.0398036 - 1.39331i) q^{29} +(0.127721 - 0.0375023i) q^{32} +(0.0662308 - 0.00759928i) q^{36} +(0.614005 + 0.0704506i) q^{37} +(-0.0243572 + 0.169408i) q^{43} +(0.0464616 - 0.0478078i) q^{44} +(-1.79201 - 0.639389i) q^{46} +(-0.466667 - 0.884433i) q^{49} +(0.972732 - 0.347070i) q^{50} +(0.161197 + 1.87678i) q^{53} +(-0.810921 + 0.521147i) q^{56} +(-1.32604 + 0.560388i) q^{58} +(-0.921124 + 0.389270i) q^{63} +(0.564692 + 0.732306i) q^{64} +(1.02742 + 0.660282i) q^{67} +(0.374083 - 0.133472i) q^{71} +(0.449841 + 0.852543i) q^{72} +(-0.162268 - 0.617332i) q^{74} +(-0.466667 + 0.884433i) q^{77} +(0.812697 - 1.54023i) q^{79} +(0.309017 + 0.951057i) q^{81} +(0.172169 - 0.0400362i) q^{86} +(0.887911 + 0.375234i) q^{88} +(0.00350708 + 0.122764i) q^{92} +(-0.676337 + 0.780534i) q^{98} +(0.841254 + 0.540641i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 2 q^{2} + 3 q^{4} + q^{7} - q^{8} - 10 q^{9}+O(q^{10}) $ 40 * q + 2 * q^2 + 3 * q^4 + q^7 - q^8 - 10 * q^9	$ 40 q + 2 q^{2} + 3 q^{4} + q^{7} - q^{8} - 10 q^{9} + q^{11} - 3 q^{14} - 3 q^{18} + 2 q^{22} - 9 q^{23} + q^{25} - 2 q^{28} + 2 q^{29} - 4 q^{32} + 3 q^{36} - 3 q^{37} + 2 q^{43} - 13 q^{44} - q^{46} + q^{49} + 2 q^{50} - 3 q^{53} - 7 q^{56} - 12 q^{58} + q^{63} - 9 q^{64} + 2 q^{67} - 3 q^{71} - q^{72} + 4 q^{74} + q^{77} - 3 q^{79} - 10 q^{81} - q^{86} - 12 q^{88} - 4 q^{92} - 9 q^{98} - 4 q^{99}+O(q^{100}) $ 40 * q + 2 * q^2 + 3 * q^4 + q^7 - q^8 - 10 * q^9 + q^11 - 3 * q^14 - 3 * q^18 + 2 * q^22 - 9 * q^23 + q^25 - 2 * q^28 + 2 * q^29 - 4 * q^32 + 3 * q^36 - 3 * q^37 + 2 * q^43 - 13 * q^44 - q^46 + q^49 + 2 * q^50 - 3 * q^53 - 7 * q^56 - 12 * q^58 + q^63 - 9 * q^64 + 2 * q^67 - 3 * q^71 - q^72 + 4 * q^74 + q^77 - 3 * q^79 - 10 * q^81 - q^86 - 12 * q^88 - 4 * q^92 - 9 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$-1$	$e\left(\frac{21}{55}\right)$

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 $

$2$	−0.374706	−	0.962424i	−0.374706	−	0.962424i	−0.985354	−	0.170522i	$-0.945455\pi$
$2$	−0.374706	−	0.962424i	−0.374706	−	0.962424i	0.610648	−	0.791902i	$-0.290909\pi$
$3$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$3$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$4$	−0.0491151	+	0.0450774i	−0.0491151	+	0.0450774i
$5$		0			0		−0.696938	−	0.717132i	$-0.745455\pi$
$5$		0			0		0.696938	+	0.717132i	$0.254545\pi$
$6$		0			0
$7$	0.516397	−	0.856349i	0.516397	−	0.856349i
$7$	0.516397	−	0.856349i	0.516397	−	0.856349i
$8$	−0.865041	−	0.425312i	−0.865041	−	0.425312i
$9$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$10$		0			0
$11$	−0.998369	+	0.0570888i	−0.998369	+	0.0570888i
$11$	−0.998369	+	0.0570888i	−0.998369	+	0.0570888i
$12$		0			0
$13$		0			0		0.198590	−	0.980083i	$-0.436364\pi$
$13$		0			0		−0.198590	+	0.980083i	$0.563636\pi$
$14$	−1.01767	−	0.176114i	−1.01767	−	0.176114i
$15$		0			0
$16$	−0.0908996	+	1.05832i	−0.0908996	+	1.05832i
$17$		0			0		0.610648	−	0.791902i	$-0.290909\pi$
$17$		0			0		−0.610648	+	0.791902i	$0.709091\pi$
$18$	−0.262555	+	0.998864i	−0.262555	+	0.998864i
$19$		0			0		0.564443	−	0.825472i	$-0.309091\pi$
$19$		0			0		−0.564443	+	0.825472i	$0.690909\pi$
$20$		0			0
$21$		0			0
$22$	0.429039	+	0.939463i	0.429039	+	0.939463i
$23$	1.20642	−	1.39228i	1.20642	−	1.39228i	0.309017	−	0.951057i	$-0.400000\pi$
$23$	1.20642	−	1.39228i	1.20642	−	1.39228i	0.897398	−	0.441221i	$-0.145455\pi$
$24$		0			0
$25$	−0.0285561	+	0.999592i	−0.0285561	+	0.999592i
$26$		0			0
$27$		0			0
$28$	0.0132391	+	0.0653376i	0.0132391	+	0.0653376i
$29$	−0.0398036	−	1.39331i	−0.0398036	−	1.39331i	−0.736741	−	0.676175i	$-0.763636\pi$
$29$	−0.0398036	−	1.39331i	−0.0398036	−	1.39331i	0.696938	−	0.717132i	$-0.254545\pi$
$30$		0			0
$31$		0			0		0.870746	−	0.491733i	$-0.163636\pi$
$31$		0			0		−0.870746	+	0.491733i	$0.836364\pi$
$32$	0.127721	−	0.0375023i	0.127721	−	0.0375023i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	0.0662308	−	0.00759928i	0.0662308	−	0.00759928i
$37$	0.614005	+	0.0704506i	0.614005	+	0.0704506i	0.415415	−	0.909632i	$-0.363636\pi$
$37$	0.614005	+	0.0704506i	0.614005	+	0.0704506i	0.198590	+	0.980083i	$0.436364\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.774142	−	0.633012i	$-0.218182\pi$
$41$		0			0		−0.774142	+	0.633012i	$0.781818\pi$
$42$		0			0
$43$	−0.0243572	+	0.169408i	−0.0243572	+	0.169408i	−0.998369	−	0.0570888i	$-0.981818\pi$
$43$	−0.0243572	+	0.169408i	−0.0243572	+	0.169408i	0.974012	+	0.226497i	$0.0727273\pi$
$44$	0.0464616	−	0.0478078i	0.0464616	−	0.0478078i
$45$		0			0
$46$	−1.79201	−	0.639389i	−1.79201	−	0.639389i
$47$		0			0		−0.254218	−	0.967147i	$-0.581818\pi$
$47$		0			0		0.254218	+	0.967147i	$0.418182\pi$
$48$		0			0
$49$	−0.466667	−	0.884433i	−0.466667	−	0.884433i
$50$	0.972732	−	0.347070i	0.972732	−	0.347070i
$51$		0			0
$52$		0			0
$53$	0.161197	+	1.87678i	0.161197	+	1.87678i	0.415415	+	0.909632i	$0.363636\pi$
$53$	0.161197	+	1.87678i	0.161197	+	1.87678i	−0.254218	+	0.967147i	$0.581818\pi$
$54$		0			0
$55$		0			0
$56$	−0.810921	+	0.521147i	−0.810921	+	0.521147i
$57$		0			0
$58$	−1.32604	+	0.560388i	−1.32604	+	0.560388i
$59$		0			0		−0.774142	−	0.633012i	$-0.781818\pi$
$59$		0			0		0.774142	+	0.633012i	$0.218182\pi$
$60$		0			0
$61$		0			0		0.362808	−	0.931864i	$-0.381818\pi$
$61$		0			0		−0.362808	+	0.931864i	$0.618182\pi$
$62$		0			0
$63$	−0.921124	+	0.389270i	−0.921124	+	0.389270i
$64$	0.564692	+	0.732306i	0.564692	+	0.732306i
$65$		0			0
$66$		0			0
$67$	1.02742	+	0.660282i	1.02742	+	0.660282i	0.941844	−	0.336049i	$-0.109091\pi$
$67$	1.02742	+	0.660282i	1.02742	+	0.660282i	0.0855750	+	0.996332i	$0.472727\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	0.374083	−	0.133472i	0.374083	−	0.133472i	−0.142315	−	0.989821i	$-0.545455\pi$
$71$	0.374083	−	0.133472i	0.374083	−	0.133472i	0.516397	+	0.856349i	$0.327273\pi$
$72$	0.449841	+	0.852543i	0.449841	+	0.852543i
$73$		0			0		−0.921124	−	0.389270i	$-0.872727\pi$
$73$		0			0		0.921124	+	0.389270i	$0.127273\pi$
$74$	−0.162268	−	0.617332i	−0.162268	−	0.617332i
$75$		0			0
$76$		0			0
$77$	−0.466667	+	0.884433i	−0.466667	+	0.884433i
$78$		0			0
$79$	0.812697	−	1.54023i	0.812697	−	1.54023i	−0.0285561	−	0.999592i	$-0.509091\pi$
$79$	0.812697	−	1.54023i	0.812697	−	1.54023i	0.841254	−	0.540641i	$-0.181818\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.309017	+	0.951057i
$82$		0			0
$83$		0			0		−0.974012	−	0.226497i	$-0.927273\pi$
$83$		0			0		0.974012	+	0.226497i	$0.0727273\pi$
$84$		0			0
$85$		0			0
$86$	0.172169	−	0.0400362i	0.172169	−	0.0400362i
$87$		0			0
$88$	0.887911	+	0.375234i	0.887911	+	0.375234i
$89$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$89$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$90$		0			0
$91$		0			0
$92$	0.00350708	+	0.122764i	0.00350708	+	0.122764i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		0.696938	−	0.717132i	$-0.254545\pi$
$97$		0			0		−0.696938	+	0.717132i	$0.745455\pi$
$98$	−0.676337	+	0.780534i	−0.676337	+	0.780534i
$99$	0.841254	+	0.540641i	0.841254	+	0.540641i
$100$	−0.0436565	−	0.0503823i	−0.0436565	−	0.0503823i
$101$		0			0		−0.998369	−	0.0570888i	$-0.981818\pi$
$101$		0			0		0.998369	+	0.0570888i	$0.0181818\pi$
$102$		0			0
$103$		0			0		0.254218	−	0.967147i	$-0.418182\pi$
$103$		0			0		−0.254218	+	0.967147i	$0.581818\pi$
$104$		0			0
$105$		0			0
$106$	1.74586	−	0.858380i	1.74586	−	0.858380i
$107$	0.0562756	+	0.00973888i	0.0562756	+	0.00973888i	0.198590	−	0.980083i	$-0.436364\pi$
$107$	0.0562756	+	0.00973888i	0.0562756	+	0.00973888i	−0.142315	+	0.989821i	$0.545455\pi$
$108$		0			0
$109$	−0.211212	−	0.462490i	−0.211212	−	0.462490i	0.774142	−	0.633012i	$-0.218182\pi$
$109$	−0.211212	−	0.462490i	−0.211212	−	0.462490i	−0.985354	+	0.170522i	$0.945455\pi$
$110$		0			0
$111$		0			0
$112$	0.859355	+	0.624358i	0.859355	+	0.624358i
$113$	−0.651166	−	0.320157i	−0.651166	−	0.320157i	0.0855750	−	0.996332i	$-0.472727\pi$
$113$	−0.651166	−	0.320157i	−0.651166	−	0.320157i	−0.736741	+	0.676175i	$0.763636\pi$
$114$		0			0
$115$		0			0
$116$	0.0647617	+	0.0666382i	0.0647617	+	0.0666382i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.993482	−	0.113991i	0.993482	−	0.113991i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	0.719794	+	0.740650i	0.719794	+	0.740650i
$127$	1.96749	−	0.112505i	1.96749	−	0.112505i	0.974012	−	0.226497i	$-0.0727273\pi$
$127$	1.96749	−	0.112505i	1.96749	−	0.112505i	0.993482	+	0.113991i	$0.0363636\pi$
$128$	0.561935	−	0.931864i	0.561935	−	0.931864i
$129$		0			0
$130$		0			0
$131$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$131$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$132$		0			0
$133$		0			0
$134$	0.250492	−	1.23623i	0.250492	−	1.23623i
$135$		0			0
$136$		0			0
$137$	−0.126093	+	1.46808i	−0.126093	+	1.46808i	0.610648	+	0.791902i	$0.290909\pi$
$137$	−0.126093	+	1.46808i	−0.126093	+	1.46808i	−0.736741	+	0.676175i	$0.763636\pi$
$138$		0			0
$139$		0			0		0.254218	−	0.967147i	$-0.418182\pi$
$139$		0			0		−0.254218	+	0.967147i	$0.581818\pi$
$140$		0			0
$141$		0			0
$142$	−0.268628	−	0.310013i	−0.268628	−	0.310013i
$143$		0			0
$144$	0.695607	−	0.802773i	0.695607	−	0.802773i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	−0.0333327	+	0.0242176i	−0.0333327	+	0.0242176i
$149$	0.334130	+	1.64900i	0.334130	+	1.64900i	0.696938	+	0.717132i	$0.254545\pi$
$149$	0.334130	+	1.64900i	0.334130	+	1.64900i	−0.362808	+	0.931864i	$0.618182\pi$
$150$		0			0
$151$	−1.32230	−	1.21360i	−1.32230	−	1.21360i	−0.959493	−	0.281733i	$-0.909091\pi$
$151$	−1.32230	−	1.21360i	−1.32230	−	1.21360i	−0.362808	−	0.931864i	$-0.618182\pi$
$152$		0			0
$153$		0			0
$154$	1.02606	+	0.117730i	1.02606	+	0.117730i
$155$		0			0
$156$		0			0
$157$		0			0		0.993482	−	0.113991i	$-0.0363636\pi$
$157$		0			0		−0.993482	+	0.113991i	$0.963636\pi$
$158$	−1.78688	−	0.205025i	−1.78688	−	0.205025i
$159$		0			0
$160$		0			0
$161$	−0.569286	−	1.75208i	−0.569286	−	1.75208i
$162$	0.799530	−	0.653772i	0.799530	−	0.653772i
$163$	0.0266524	−	0.0505118i	0.0266524	−	0.0505118i	−0.870746	−	0.491733i	$-0.836364\pi$
$163$	0.0266524	−	0.0505118i	0.0266524	−	0.0505118i	0.897398	+	0.441221i	$0.145455\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		−0.941844	−	0.336049i	$-0.890909\pi$
$167$		0			0		0.941844	+	0.336049i	$0.109091\pi$
$168$		0			0
$169$	−0.921124	−	0.389270i	−0.921124	−	0.389270i
$170$		0			0
$171$		0			0
$172$	−0.00644017	−	0.00941845i	−0.00644017	−	0.00941845i
$173$		0			0		−0.516397	−	0.856349i	$-0.672727\pi$
$173$		0			0		0.516397	+	0.856349i	$0.327273\pi$
$174$		0			0
$175$	0.841254	+	0.540641i	0.841254	+	0.540641i
$176$	0.0303328	−	1.06179i	0.0303328	−	1.06179i
$177$		0			0
$178$		0			0
$179$	1.81527	−	0.767138i	1.81527	−	0.767138i	0.841254	−	0.540641i	$-0.181818\pi$
$179$	1.81527	−	0.767138i	1.81527	−	0.767138i	0.974012	−	0.226497i	$-0.0727273\pi$
$180$		0			0
$181$		0			0		0.362808	−	0.931864i	$-0.381818\pi$
$181$		0			0		−0.362808	+	0.931864i	$0.618182\pi$
$182$		0			0
$183$		0			0
$184$	−1.63575	+	0.691274i	−1.63575	+	0.691274i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	0.982973	+	1.43755i	0.982973	+	1.43755i	0.897398	+	0.441221i	$0.145455\pi$
$191$	0.982973	+	1.43755i	0.982973	+	1.43755i	0.0855750	+	0.996332i	$0.472727\pi$
$192$		0			0
$193$	0.338621	+	0.641758i	0.338621	+	0.641758i	0.993482	−	0.113991i	$-0.0363636\pi$
$193$	0.338621	+	0.641758i	0.338621	+	0.641758i	−0.654861	+	0.755750i	$0.727273\pi$
$194$		0			0
$195$		0			0
$196$	0.0627884	+	0.0224029i	0.0627884	+	0.0224029i
$197$	0.209698	+	1.45848i	0.209698	+	1.45848i	0.774142	+	0.633012i	$0.218182\pi$
$197$	0.209698	+	1.45848i	0.209698	+	1.45848i	−0.564443	+	0.825472i	$0.690909\pi$
$198$	0.205103	−	1.01222i	0.205103	−	1.01222i
$199$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$199$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$200$	0.449841	−	0.852543i	0.449841	−	0.852543i
$201$		0			0
$202$		0			0
$203$	−1.21371	−	0.685414i	−1.21371	−	0.685414i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−1.79437	+	0.417263i	−1.79437	+	0.417263i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−1.73014	+	0.977055i	−1.73014	+	0.977055i	−0.809017	+	0.587785i	$0.800000\pi$
$211$	−1.73014	+	0.977055i	−1.73014	+	0.977055i	−0.921124	+	0.389270i	$0.872727\pi$
$212$	−0.0925176	−	0.0849119i	−0.0925176	−	0.0849119i
$213$		0			0
$214$	−0.0117139	−	0.0578103i	−0.0117139	−	0.0578103i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−0.365969	+	0.376574i	−0.365969	+	0.376574i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.564443	−	0.825472i	$-0.309091\pi$
$223$		0			0		−0.564443	+	0.825472i	$0.690909\pi$
$224$	0.0338398	−	0.128740i	0.0338398	−	0.128740i
$225$	0.610648	−	0.791902i	0.610648	−	0.791902i
$226$	−0.0641309	+	0.746663i	−0.0641309	+	0.746663i
$227$		0			0		0.897398	−	0.441221i	$-0.145455\pi$
$227$		0			0		−0.897398	+	0.441221i	$0.854545\pi$
$228$		0			0
$229$		0			0		0.198590	−	0.980083i	$-0.436364\pi$
$229$		0			0		−0.198590	+	0.980083i	$0.563636\pi$
$230$		0			0
$231$		0			0
$232$	−0.558158	+	1.22220i	−0.558158	+	1.22220i
$233$	1.55249	+	1.12795i	1.55249	+	1.12795i	0.941844	+	0.336049i	$0.109091\pi$
$233$	1.55249	+	1.12795i	1.55249	+	1.12795i	0.610648	+	0.791902i	$0.290909\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.377401	−	1.16152i	0.377401	−	1.16152i	−0.564443	−	0.825472i	$-0.690909\pi$
$239$	0.377401	−	1.16152i	0.377401	−	1.16152i	0.941844	−	0.336049i	$-0.109091\pi$
$240$		0			0
$241$		0			0		1.00000			$0$
$241$		0			0		−1.00000			$\pi$
$242$	−0.481972	−	0.913438i	−0.481972	−	0.913438i
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$251$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$252$	0.0276938	−	0.0606409i	0.0276938	−	0.0606409i
$253$	−1.12496	+	1.45888i	−1.12496	+	1.45888i
$254$	−0.845509	−	1.85141i	−0.845509	−	1.85141i
$255$		0			0
$256$	−0.196211	−	0.0339556i	−0.196211	−	0.0339556i
$257$		0			0		0.897398	−	0.441221i	$-0.145455\pi$
$257$		0			0		−0.897398	+	0.441221i	$0.854545\pi$
$258$		0			0
$259$	0.377401	−	0.489423i	0.377401	−	0.489423i
$260$		0			0
$261$	−0.786763	+	1.15060i	−0.786763	+	1.15060i
$262$		0			0
$263$	−0.260098	−	0.300169i	−0.260098	−	0.300169i	0.610648	−	0.791902i	$-0.290909\pi$
$263$	−0.260098	−	0.300169i	−0.260098	−	0.300169i	−0.870746	+	0.491733i	$0.836364\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−0.0802257	+	0.0138836i	−0.0802257	+	0.0138836i
$269$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$269$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$270$		0			0
$271$		0			0		−0.0285561	−	0.999592i	$-0.509091\pi$
$271$		0			0		0.0285561	+	0.999592i	$0.490909\pi$
$272$		0			0
$273$		0			0
$274$	1.46016	−	0.428742i	1.46016	−	0.428742i
$275$	−0.0285561	−	0.999592i	−0.0285561	−	0.999592i
$276$		0			0
$277$	−1.09955	+	0.255689i	−1.09955	+	0.255689i	−0.736741	−	0.676175i	$-0.763636\pi$
$277$	−1.09955	+	0.255689i	−1.09955	+	0.255689i	−0.362808	+	0.931864i	$0.618182\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−1.64021	−	0.926272i	−1.64021	−	0.926272i	−0.985354	−	0.170522i	$-0.945455\pi$
$281$	−1.64021	−	0.926272i	−1.64021	−	0.926272i	−0.654861	−	0.755750i	$-0.727273\pi$
$282$		0			0
$283$		0			0		0.774142	−	0.633012i	$-0.218182\pi$
$283$		0			0		−0.774142	+	0.633012i	$0.781818\pi$
$284$	−0.0123565	+	0.0234182i	−0.0123565	+	0.0234182i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.125372	−	0.0447326i	−0.125372	−	0.0447326i
$289$	−0.254218	−	0.967147i	−0.254218	−	0.967147i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		−0.564443	−	0.825472i	$-0.690909\pi$
$293$		0			0		0.564443	+	0.825472i	$0.309091\pi$
$294$		0			0
$295$		0			0
$296$	−0.501177	−	0.322087i	−0.501177	−	0.322087i
$297$		0			0
$298$	1.46183	−	0.939463i	1.46183	−	0.939463i
$299$		0			0
$300$		0			0
$301$	0.132494	+	0.108340i	0.132494	+	0.108340i
$302$	−0.672521	+	1.72736i	−0.672521	+	1.72736i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$307$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$308$	−0.0169476	−	0.0644752i	−0.0169476	−	0.0644752i
$309$		0			0
$310$		0			0
$311$		0			0		−0.516397	−	0.856349i	$-0.672727\pi$
$311$		0			0		0.516397	+	0.856349i	$0.327273\pi$
$312$		0			0
$313$		0			0		0.941844	−	0.336049i	$-0.109091\pi$
$313$		0			0		−0.941844	+	0.336049i	$0.890909\pi$
$314$		0			0
$315$		0			0
$316$	0.0295140	+	0.112283i	0.0295140	+	0.112283i
$317$	−1.52394	−	0.543739i	−1.52394	−	0.543739i	−0.564443	−	0.825472i	$-0.690909\pi$
$317$	−1.52394	−	0.543739i	−1.52394	−	0.543739i	−0.959493	+	0.281733i	$0.909091\pi$
$318$		0			0
$319$	0.119281	+	1.38876i	0.119281	+	1.38876i
$320$		0			0
$321$		0			0
$322$	−1.47293	+	1.20441i	−1.47293	+	1.20441i
$323$		0			0
$324$	−0.0580486	−	0.0327815i	−0.0580486	−	0.0327815i
$325$		0			0
$326$	−0.0586006	−	0.00672379i	−0.0586006	−	0.00672379i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−1.48557	+	0.436202i	−1.48557	+	0.436202i	−0.921124	−	0.389270i	$-0.872727\pi$
$331$	−1.48557	+	0.436202i	−1.48557	+	0.436202i	−0.564443	+	0.825472i	$0.690909\pi$
$332$		0			0
$333$	−0.455331	−	0.417899i	−0.455331	−	0.417899i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−1.52561	+	0.264017i	−1.52561	+	0.264017i	−0.870746	−	0.491733i	$-0.836364\pi$
$337$	−1.52561	+	0.264017i	−1.52561	+	0.264017i	−0.654861	+	0.755750i	$0.727273\pi$
$338$	−0.0294925	+	1.03237i	−0.0294925	+	1.03237i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.998369	−	0.0570888i	−0.998369	−	0.0570888i
$344$	0.0931212	−	0.136185i	0.0931212	−	0.136185i
$345$		0			0
$346$		0			0
$347$	0.166702	−	1.94088i	0.166702	−	1.94088i	−0.142315	−	0.989821i	$-0.545455\pi$
$347$	0.166702	−	1.94088i	0.166702	−	1.94088i	0.309017	−	0.951057i	$-0.400000\pi$
$348$		0			0
$349$		0			0		−0.985354	−	0.170522i	$-0.945455\pi$
$349$		0			0		0.985354	+	0.170522i	$0.0545455\pi$
$350$	0.205103	−	1.01222i	0.205103	−	1.01222i
$351$		0			0
$352$	−0.125372	+	0.0447326i	−0.125372	+	0.0447326i
$353$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$353$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−1.41850	−	1.45960i	−1.41850	−	1.45960i
$359$	−1.14068	+	1.04691i	−1.14068	+	1.04691i	−0.142315	+	0.989821i	$0.545455\pi$
$359$	−1.14068	+	1.04691i	−1.14068	+	1.04691i	−0.998369	+	0.0570888i	$0.981818\pi$
$360$		0			0
$361$	−0.362808	−	0.931864i	−0.362808	−	0.931864i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.736741	−	0.676175i	$-0.236364\pi$
$367$		0			0		−0.736741	+	0.676175i	$0.763636\pi$
$368$	1.36382	+	1.40334i	1.36382	+	1.40334i
$369$		0			0
$370$		0			0
$371$	1.69042	+	0.831123i	1.69042	+	0.831123i
$372$		0			0
$373$	−0.544078	+	1.19136i	−0.544078	+	1.19136i	0.415415	+	0.909632i	$0.363636\pi$
$373$	−0.544078	+	1.19136i	−0.544078	+	1.19136i	−0.959493	+	0.281733i	$0.909091\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.153590	−	1.78821i	0.153590	−	1.78821i	−0.362808	−	0.931864i	$-0.618182\pi$
$379$	0.153590	−	1.78821i	0.153590	−	1.78821i	0.516397	−	0.856349i	$-0.327273\pi$
$380$		0			0
$381$		0			0
$382$	1.01521	−	1.48470i	1.01521	−	1.48470i
$383$		0			0		−0.998369	−	0.0570888i	$-0.981818\pi$
$383$		0			0		0.998369	+	0.0570888i	$0.0181818\pi$
$384$		0			0
$385$		0			0
$386$	0.490760	−	0.566368i	0.490760	−	0.566368i
$387$	0.119281	−	0.122737i	0.119281	−	0.122737i
$388$		0			0
$389$	−1.76851	+	0.306053i	−1.76851	+	0.306053i	−0.959493	−	0.281733i	$-0.909091\pi$
$389$	−1.76851	+	0.306053i	−1.76851	+	0.306053i	−0.809017	+	0.587785i	$0.800000\pi$
$390$		0			0
$391$		0			0
$392$	0.0275264	+	0.963550i	0.0275264	+	0.963550i
$393$		0			0
$394$	1.32511	−	0.748322i	1.32511	−	0.748322i
$395$		0			0
$396$	−0.0656890	+	0.0113679i	−0.0656890	+	0.0113679i
$397$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$397$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$398$		0			0
$399$		0			0
$400$	−1.05530	−	0.121084i	−1.05530	−	0.121084i
$401$	1.93533	+	0.450041i	1.93533	+	0.450041i	0.993482	+	0.113991i	$0.0363636\pi$
$401$	1.93533	+	0.450041i	1.93533	+	0.450041i	0.941844	+	0.336049i	$0.109091\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	−0.204875	+	1.42493i	−0.204875	+	1.42493i
$407$	−0.617026	−	0.0352828i	−0.617026	−	0.0352828i
$408$		0			0
$409$		0			0		−0.941844	−	0.336049i	$-0.890909\pi$
$409$		0			0		0.941844	+	0.336049i	$0.109091\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	1.07395	+	1.57060i	1.07395	+	1.57060i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$419$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$420$		0			0
$421$	−1.42616	+	0.602700i	−1.42616	+	0.602700i	−0.959493	−	0.281733i	$-0.909091\pi$
$421$	−1.42616	+	0.602700i	−1.42616	+	0.602700i	−0.466667	+	0.884433i	$0.654545\pi$
$422$	1.58864	+	1.29902i	1.58864	+	1.29902i
$423$		0			0
$424$	0.658775	−	1.69205i	0.658775	−	1.69205i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−0.00320299	+	0.00205844i	−0.00320299	+	0.00205844i
$429$		0			0
$430$		0			0
$431$	−0.0966045	−	1.12475i	−0.0966045	−	1.12475i	−0.870746	−	0.491733i	$-0.836364\pi$
$431$	−0.0966045	−	1.12475i	−0.0966045	−	1.12475i	0.774142	−	0.633012i	$-0.218182\pi$
$432$		0			0
$433$		0			0		−0.564443	−	0.825472i	$-0.690909\pi$
$433$		0			0		0.564443	+	0.825472i	$0.309091\pi$
$434$		0			0
$435$		0			0
$436$	0.0312216	+	0.0131944i	0.0312216	+	0.0131944i
$437$		0			0
$438$		0			0
$439$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$439$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$440$		0			0
$441$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$442$		0			0
$443$	1.50805	−	1.23312i	1.50805	−	1.23312i	0.610648	−	0.791902i	$-0.290909\pi$
$443$	1.50805	−	1.23312i	1.50805	−	1.23312i	0.897398	−	0.441221i	$-0.145455\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	0.918715	−	0.105413i	0.918715	−	0.105413i
$449$	−0.495223	+	0.115159i	−0.495223	+	0.115159i	−0.466667	−	0.884433i	$-0.654545\pi$
$449$	−0.495223	+	0.115159i	−0.495223	+	0.115159i	−0.0285561	+	0.999592i	$0.509091\pi$
$450$	−0.990959	−	0.290972i	−0.990959	−	0.290972i
$451$		0			0
$452$	0.0464139	−	0.0136284i	0.0464139	−	0.0136284i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$457$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$461$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$462$		0			0
$463$	1.30759	+	1.50903i	1.30759	+	1.50903i	0.696938	+	0.717132i	$0.254545\pi$
$463$	1.30759	+	1.50903i	1.30759	+	1.50903i	0.610648	+	0.791902i	$0.290909\pi$
$464$	1.47819	+	0.0845259i	1.47819	+	0.0845259i
$465$		0			0
$466$	0.503840	−	1.91681i	0.503840	−	1.91681i
$467$		0			0		0.610648	−	0.791902i	$-0.290909\pi$
$467$		0			0		−0.610648	+	0.791902i	$0.709091\pi$
$468$		0			0
$469$	1.09599	−	0.538861i	1.09599	−	0.538861i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.0146462	−	0.170522i	0.0146462	−	0.170522i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	0.972732	−	1.61310i	0.972732	−	1.61310i
$478$	−1.25929	+	0.0720089i	−1.25929	+	0.0720089i
$479$		0			0		−0.696938	−	0.717132i	$-0.745455\pi$
$479$		0			0		0.696938	+	0.717132i	$0.254545\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−0.0436565	+	0.0503823i	−0.0436565	+	0.0503823i
$485$		0			0
$486$		0			0
$487$	0.0528883	−	0.162773i	0.0528883	−	0.162773i	−0.921124	−	0.389270i	$-0.872727\pi$
$487$	0.0528883	−	0.162773i	0.0528883	−	0.162773i	0.974012	+	0.226497i	$0.0727273\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−0.676337	+	1.12158i	−0.676337	+	1.12158i	0.309017	+	0.951057i	$0.400000\pi$
$491$	−0.676337	+	1.12158i	−0.676337	+	1.12158i	−0.985354	+	0.170522i	$0.945455\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.0788763	−	0.389270i	0.0788763	−	0.389270i
$498$		0			0
$499$	−1.45202	+	0.713911i	−1.45202	+	0.713911i	−0.985354	−	0.170522i	$-0.945455\pi$
$499$	−1.45202	+	0.713911i	−1.45202	+	0.713911i	−0.466667	+	0.884433i	$0.654545\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		0.564443	−	0.825472i	$-0.309091\pi$
$503$		0			0		−0.564443	+	0.825472i	$0.690909\pi$
$504$	0.962371	+	0.0550304i	0.962371	+	0.0550304i
$505$		0			0
$506$	1.82559	+	0.536042i	1.82559	+	0.536042i
$507$		0			0
$508$	−0.0915622	+	0.0942153i	−0.0915622	+	0.0942153i
$509$		0			0		0.0285561	−	0.999592i	$-0.490909\pi$
$509$		0			0		−0.0285561	+	0.999592i	$0.509091\pi$
$510$		0			0
$511$		0			0
$512$	−0.175261	−	0.864948i	−0.175261	−	0.864948i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	−0.612447	−	0.179831i	−0.612447	−	0.179831i
$519$		0			0
$520$		0			0
$521$		0			0		−0.993482	−	0.113991i	$-0.963636\pi$
$521$		0			0		0.993482	+	0.113991i	$0.0363636\pi$
$522$	1.40218	+	0.326062i	1.40218	+	0.326062i
$523$		0			0		−0.870746	−	0.491733i	$-0.836364\pi$
$523$		0			0		0.870746	+	0.491733i	$0.163636\pi$
$524$		0			0
$525$		0			0
$526$	−0.191430	+	0.362800i	−0.191430	+	0.362800i
$527$		0			0
$528$		0			0
$529$	−0.340684	−	2.36951i	−0.340684	−	2.36951i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	−0.607934	−	1.00815i	−0.607934	−	1.00815i
$537$		0			0
$538$		0			0
$539$	0.516397	+	0.856349i	0.516397	+	0.856349i
$540$		0			0
$541$	1.21334	+	1.57348i	1.21334	+	1.57348i	0.696938	+	0.717132i	$0.254545\pi$
$541$	1.21334	+	1.57348i	1.21334	+	1.57348i	0.516397	+	0.856349i	$0.327273\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	1.76762	−	0.747004i	1.76762	−	0.747004i	0.774142	−	0.633012i	$-0.218182\pi$
$547$	1.76762	−	0.747004i	1.76762	−	0.747004i	0.993482	−	0.113991i	$-0.0363636\pi$
$548$	−0.0599841	−	0.0777887i	−0.0599841	−	0.0777887i
$549$		0			0
$550$	−0.951332	+	0.402036i	−0.951332	+	0.402036i
$551$		0			0
$552$		0			0
$553$	−0.899302	−	1.49133i	−0.899302	−	1.49133i
$554$	0.658089	+	0.962424i	0.658089	+	0.962424i
$555$		0			0
$556$		0			0
$557$	1.49041	+	0.629852i	1.49041	+	0.629852i	0.974012	−	0.226497i	$-0.0727273\pi$
$557$	1.49041	+	0.629852i	1.49041	+	0.629852i	0.516397	+	0.856349i	$0.327273\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−0.276868	+	1.92566i	−0.276868	+	1.92566i
$563$		0			0		0.466667	−	0.884433i	$-0.345455\pi$
$563$		0			0		−0.466667	+	0.884433i	$0.654545\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.974012	+	0.226497i	0.974012	+	0.226497i
$568$	−0.380364	−	0.0436427i	−0.380364	−	0.0436427i
$569$	−0.282774	+	0.0324453i	−0.282774	+	0.0324453i	−0.254218	−	0.967147i	$-0.581818\pi$
$569$	−0.282774	+	0.0324453i	−0.282774	+	0.0324453i	−0.0285561	+	0.999592i	$0.509091\pi$
$570$		0			0
$571$	1.41380	+	0.415128i	1.41380	+	0.415128i	0.897398	−	0.441221i	$-0.145455\pi$
$571$	1.41380	+	0.415128i	1.41380	+	0.415128i	0.516397	+	0.856349i	$0.327273\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	1.35726	+	1.24568i	1.35726	+	1.24568i
$576$	−0.0264070	−	0.924365i	−0.0264070	−	0.924365i
$577$		0			0		−0.198590	−	0.980083i	$-0.563636\pi$
$577$		0			0		0.198590	+	0.980083i	$0.436364\pi$
$578$	−0.835549	+	0.607062i	−0.835549	+	0.607062i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−0.268077	−	1.86452i	−0.268077	−	1.86452i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		0.254218	−	0.967147i	$-0.418182\pi$
$587$		0			0		−0.254218	+	0.967147i	$0.581818\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−0.130372	+	0.643413i	−0.130372	+	0.643413i
$593$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$593$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$594$		0			0
$595$		0			0
$596$	−0.0907433	−	0.0659289i	−0.0907433	−	0.0659289i
$597$		0			0
$598$		0			0
$599$	0.507607	−	0.0290260i	0.507607	−	0.0290260i	0.198590	−	0.980083i	$-0.436364\pi$
$599$	0.507607	−	0.0290260i	0.507607	−	0.0290260i	0.309017	+	0.951057i	$0.400000\pi$
$600$		0			0
$601$		0			0		0.736741	−	0.676175i	$-0.236364\pi$
$601$		0			0		−0.736741	+	0.676175i	$0.763636\pi$
$602$	0.0546227	−	0.168111i	0.0546227	−	0.168111i
$603$	−0.443096	−	1.13808i	−0.443096	−	1.13808i
$604$	0.119651			0.119651
$605$		0			0
$606$		0			0
$607$		0			0		−0.362808	−	0.931864i	$-0.618182\pi$
$607$		0			0		0.362808	+	0.931864i	$0.381818\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	1.74815	+	0.859509i	1.74815	+	0.859509i	0.974012	+	0.226497i	$0.0727273\pi$
$613$	1.74815	+	0.859509i	1.74815	+	0.859509i	0.774142	+	0.633012i	$0.218182\pi$
$614$		0			0
$615$		0			0
$616$	0.779846	−	0.566592i	0.779846	−	0.566592i
$617$	−0.829475	−	1.81630i	−0.829475	−	1.81630i	−0.466667	−	0.884433i	$-0.654545\pi$
$617$	−0.829475	−	1.81630i	−0.829475	−	1.81630i	−0.362808	−	0.931864i	$-0.618182\pi$
$618$		0			0
$619$		0			0		−0.985354	−	0.170522i	$-0.945455\pi$
$619$		0			0		0.985354	+	0.170522i	$0.0545455\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.998369	−	0.0570888i	−0.998369	−	0.0570888i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−1.95786	+	0.338821i	−1.95786	+	0.338821i	−0.959493	+	0.281733i	$0.909091\pi$
$631$	−1.95786	+	0.338821i	−1.95786	+	0.338821i	−0.998369	+	0.0570888i	$0.981818\pi$
$632$	−1.35810	+	0.986715i	−1.35810	+	0.986715i
$633$		0			0
$634$	0.0477199	+	1.67042i	0.0477199	+	1.67042i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	1.29188	−	0.635176i	1.29188	−	0.635176i
$639$	−0.381092	−	0.111899i	−0.381092	−	0.111899i
$640$		0			0
$641$	1.93533	−	0.222058i	1.93533	−	0.222058i	0.941844	−	0.336049i	$-0.109091\pi$
$641$	1.93533	−	0.222058i	1.93533	−	0.222058i	0.993482	+	0.113991i	$0.0363636\pi$
$642$		0			0
$643$		0			0		−0.974012	−	0.226497i	$-0.927273\pi$
$643$		0			0		0.974012	+	0.226497i	$0.0727273\pi$
$644$	0.106940	+	0.0603917i	0.106940	+	0.0603917i
$645$		0			0
$646$		0			0
$647$		0			0		0.466667	−	0.884433i	$-0.345455\pi$
$647$		0			0		−0.466667	+	0.884433i	$0.654545\pi$
$648$	0.137183	−	0.954132i	0.137183	−	0.954132i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	0.000967910		0.00368231i	0.000967910		0.00368231i
$653$	1.81527	+	0.767138i	1.81527	+	0.767138i	0.974012	+	0.226497i	$0.0727273\pi$
$653$	1.81527	+	0.767138i	1.81527	+	0.767138i	0.841254	+	0.540641i	$0.181818\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−0.239446	−	0.153882i	−0.239446	−	0.153882i	0.415415	−	0.909632i	$-0.363636\pi$
$659$	−0.239446	−	0.153882i	−0.239446	−	0.153882i	−0.654861	+	0.755750i	$0.727273\pi$
$660$		0			0
$661$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$661$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$662$	0.976462	+	1.26630i	0.976462	+	1.26630i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−0.231581	+	0.594811i	−0.231581	+	0.594811i
$667$	−1.98789	−	1.62549i	−1.98789	−	1.62549i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.166702	+	1.94088i	0.166702	+	1.94088i	0.309017	+	0.951057i	$0.400000\pi$
$673$	0.166702	+	1.94088i	0.166702	+	1.94088i	−0.142315	+	0.989821i	$0.545455\pi$
$674$	0.825750	+	1.36935i	0.825750	+	1.36935i
$675$		0			0
$676$	0.0627884	−	0.0224029i	0.0627884	−	0.0224029i
$677$		0			0		−0.466667	−	0.884433i	$-0.654545\pi$
$677$		0			0		0.466667	+	0.884433i	$0.345455\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−0.282774	+	1.96674i	−0.282774	+	1.96674i	−0.0285561	+	0.999592i	$0.509091\pi$
$683$	−0.282774	+	1.96674i	−0.282774	+	1.96674i	−0.254218	+	0.967147i	$0.581818\pi$
$684$		0			0
$685$		0			0
$686$	0.319151	+	0.982246i	0.319151	+	0.982246i
$687$		0			0
$688$	−0.177075	−	0.0411769i	−0.177075	−	0.0411769i
$689$		0			0
$690$		0			0
$691$		0			0		0.974012	−	0.226497i	$-0.0727273\pi$
$691$		0			0		−0.974012	+	0.226497i	$0.927273\pi$
$692$		0			0
$693$	0.897398	−	0.441221i	0.897398	−	0.441221i
$694$	−1.93041	+	0.566820i	−1.93041	+	0.566820i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−0.0656890	+	0.0113679i	−0.0656890	+	0.0113679i
$701$	−0.0512523	+	1.79406i	−0.0512523	+	1.79406i	0.415415	+	0.909632i	$0.363636\pi$
$701$	−0.0512523	+	1.79406i	−0.0512523	+	1.79406i	−0.466667	+	0.884433i	$0.654545\pi$
$702$		0			0
$703$		0			0
$704$	−0.605577	−	0.698874i	−0.605577	−	0.698874i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	1.18956	−	1.54264i	1.18956	−	1.54264i	0.415415	−	0.909632i	$-0.363636\pi$
$709$	1.18956	−	1.54264i	1.18956	−	1.54264i	0.774142	−	0.633012i	$-0.218182\pi$
$710$		0			0
$711$	−1.56281	+	0.768383i	−1.56281	+	0.768383i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−0.0545764	+	0.119506i	−0.0545764	+	0.119506i
$717$		0			0
$718$	1.43499	+	0.705539i	1.43499	+	0.705539i
$719$		0			0		0.516397	−	0.856349i	$-0.327273\pi$
$719$		0			0		−0.516397	+	0.856349i	$0.672727\pi$
$720$		0			0
$721$		0			0
$722$	−0.760903	+	0.698350i	−0.760903	+	0.698350i
$723$		0			0
$724$		0			0
$725$	1.39388			1.39388
$726$		0			0
$727$		0			0		1.00000			$0$
$727$		0			0		−1.00000			$\pi$
$728$		0			0
$729$	0.309017	−	0.951057i	0.309017	−	0.951057i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.516397	−	0.856349i	$-0.327273\pi$
$733$		0			0		−0.516397	+	0.856349i	$0.672727\pi$
$734$		0			0
$735$		0			0
$736$	0.101871	−	0.223067i	0.101871	−	0.223067i
$737$	−1.06344	−	0.600551i	−1.06344	−	0.600551i
$738$		0			0
$739$	−0.321326	+	1.58581i	−0.321326	+	1.58581i	0.415415	+	0.909632i	$0.363636\pi$
$739$	−0.321326	+	1.58581i	−0.321326	+	1.58581i	−0.736741	+	0.676175i	$0.763636\pi$
$740$		0			0
$741$		0			0
$742$	0.166483	−	1.93833i	0.166483	−	1.93833i
$743$	−0.988049	+	1.28132i	−0.988049	+	1.28132i	−0.0285561	+	0.999592i	$0.509091\pi$
$743$	−0.988049	+	1.28132i	−0.988049	+	1.28132i	−0.959493	+	0.281733i	$0.909091\pi$
$744$		0			0
$745$		0			0
$746$	1.35047	+	0.0772225i	1.35047	+	0.0772225i
$747$		0			0
$748$		0			0
$749$	0.0374005	−	0.0431624i	0.0374005	−	0.0431624i
$750$		0			0
$751$	0.0420768	−	1.47288i	0.0420768	−	1.47288i	−0.654861	−	0.755750i	$-0.727273\pi$
$751$	0.0420768	−	1.47288i	0.0420768	−	1.47288i	0.696938	−	0.717132i	$-0.254545\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	1.73865	−	0.981862i	1.73865	−	0.981862i	0.841254	−	0.540641i	$-0.181818\pi$
$757$	1.73865	−	0.981862i	1.73865	−	0.981862i	0.897398	−	0.441221i	$-0.145455\pi$
$758$	−1.77857	+	0.522236i	−1.77857	+	0.522236i
$759$		0			0
$760$		0			0
$761$		0			0		0.974012	−	0.226497i	$-0.0727273\pi$
$761$		0			0		−0.974012	+	0.226497i	$0.927273\pi$
$762$		0			0
$763$	−0.505123	−	0.0579574i	−0.505123	−	0.0579574i
$764$	−0.113080	−	0.0262956i	−0.113080	−	0.0262956i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$769$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$770$		0			0
$771$		0			0
$772$	−0.0455602	−	0.0162559i	−0.0455602	−	0.0162559i
$773$		0			0		−0.254218	−	0.967147i	$-0.581818\pi$
$773$		0			0		0.254218	+	0.967147i	$0.418182\pi$
$774$	−0.162820	−	0.0688085i	−0.162820	−	0.0688085i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	0.957224	+	1.58738i	0.957224	+	1.58738i
$779$		0			0
$780$		0			0
$781$	−0.365853	+	0.154611i	−0.365853	+	0.154611i
$782$		0			0
$783$		0			0
$784$	0.978437	−	0.413491i	0.978437	−	0.413491i
$785$		0			0
$786$		0			0
$787$		0			0		0.362808	−	0.931864i	$-0.381818\pi$
$787$		0			0		−0.362808	+	0.931864i	$0.618182\pi$
$788$	−0.0760441	−	0.0621810i	−0.0760441	−	0.0621810i
$789$		0			0
$790$		0			0
$791$	−0.610427	+	0.392297i	−0.610427	+	0.392297i
$792$	−0.497778	−	0.825472i	−0.497778	−	0.825472i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.941844	−	0.336049i	$-0.109091\pi$
$797$		0			0		−0.941844	+	0.336049i	$0.890909\pi$
$798$		0			0
$799$		0			0
$800$	0.0338398	+	0.128740i	0.0338398	+	0.128740i
$801$		0			0
$802$	−0.292048	−	2.03124i	−0.292048	−	2.03124i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−1.91949	−	0.446359i	−1.91949	−	0.446359i	−0.998369	−	0.0570888i	$-0.981818\pi$
$809$	−1.91949	−	0.446359i	−1.91949	−	0.446359i	−0.921124	−	0.389270i	$-0.872727\pi$
$810$		0			0
$811$		0			0		0.993482	−	0.113991i	$-0.0363636\pi$
$811$		0			0		−0.993482	+	0.113991i	$0.963636\pi$
$812$	0.0905083	−	0.0210468i	0.0905083	−	0.0210468i
$813$		0			0
$814$	0.197246	+	0.607062i	0.197246	+	0.607062i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−0.818662	+	0.141675i	−0.818662	+	0.141675i	−0.564443	−	0.825472i	$-0.690909\pi$
$821$	−0.818662	+	0.141675i	−0.818662	+	0.141675i	−0.254218	+	0.967147i	$0.581818\pi$
$822$		0			0
$823$	−1.12767	+	1.16034i	−1.12767	+	1.16034i	−0.142315	+	0.989821i	$0.545455\pi$
$823$	−1.12767	+	1.16034i	−1.12767	+	1.16034i	−0.985354	+	0.170522i	$0.945455\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1.67976	−	0.0960523i	−1.67976	−	0.0960523i	−0.809017	−	0.587785i	$-0.800000\pi$
$827$	−1.67976	−	0.0960523i	−1.67976	−	0.0960523i	−0.870746	+	0.491733i	$0.836364\pi$
$828$	0.0693216	−	0.101380i	0.0693216	−	0.101380i
$829$		0			0		0.254218	−	0.967147i	$-0.418182\pi$
$829$		0			0		−0.254218	+	0.967147i	$0.581818\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.897398	−	0.441221i	$-0.854545\pi$
$839$		0			0		0.897398	+	0.441221i	$0.145455\pi$
$840$		0			0
$841$	−0.941350	+	0.0538283i	−0.941350	+	0.0538283i
$842$	1.11444	+	1.14674i	1.11444	+	1.14674i
$843$		0			0
$844$	0.0409329	−	0.125978i	0.0409329	−	0.125978i
$845$		0			0
$846$		0			0
$847$	0.415415	−	0.909632i	0.415415	−	0.909632i
$848$	−2.00089			−2.00089
$849$		0			0
$850$		0			0
$851$	0.838832	−	0.769873i	0.838832	−	0.769873i
$852$		0			0
$853$		0			0		0.998369	−	0.0570888i	$-0.0181818\pi$
$853$		0			0		−0.998369	+	0.0570888i	$0.981818\pi$
$854$		0			0
$855$		0			0
$856$	−0.0445387	−	0.0323592i	−0.0445387	−	0.0323592i
$857$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$857$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$858$		0			0
$859$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$859$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$860$		0			0
$861$		0			0
$862$	−1.04628	+	0.514423i	−1.04628	+	0.514423i
$863$	0.0710983	−	0.827782i	0.0710983	−	0.827782i	−0.870746	−	0.491733i	$-0.836364\pi$
$863$	0.0710983	−	0.827782i	0.0710983	−	0.827782i	0.941844	−	0.336049i	$-0.109091\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−0.723442	+	1.58412i	−0.723442	+	1.58412i
$870$		0			0
$871$		0			0
$872$	−0.0139954	+	0.489904i	−0.0139954	+	0.489904i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−0.292620	−	0.268564i	−0.292620	−	0.268564i	0.516397	−	0.856349i	$-0.327273\pi$
$877$	−0.292620	−	0.268564i	−0.292620	−	0.268564i	−0.809017	+	0.587785i	$0.800000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$881$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$882$	1.00595	−	0.233925i	1.00595	−	0.233925i
$883$	−1.90648	+	0.218748i	−1.90648	+	0.218748i	−0.985354	−	0.170522i	$-0.945455\pi$
$883$	−1.90648	+	0.218748i	−1.90648	+	0.218748i	−0.921124	+	0.389270i	$0.872727\pi$
$884$		0			0
$885$		0			0
$886$	−1.75186	−	0.989322i	−1.75186	−	0.989322i
$887$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$887$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$888$		0			0
$889$	0.919665	−	1.74296i	0.919665	−	1.74296i
$890$		0			0
$891$	−0.362808	−	0.931864i	−0.362808	−	0.931864i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−0.507819	−	0.962424i	−0.507819	−	0.962424i
$897$		0			0
$898$	0.296395	+	0.433464i	0.296395	+	0.433464i
$899$		0			0
$900$	0.00570489	+	0.0664208i	0.00570489	+	0.0664208i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	0.427119	+	0.553898i	0.427119	+	0.553898i
$905$		0			0
$906$		0			0
$907$	0.263259	−	0.676175i	0.263259	−	0.676175i	−0.736741	−	0.676175i	$-0.763636\pi$
$907$	0.263259	−	0.676175i	0.263259	−	0.676175i	1.00000			$0$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	1.02742	+	1.33238i	1.02742	+	1.33238i	0.941844	+	0.336049i	$0.109091\pi$
$911$	1.02742	+	1.33238i	1.02742	+	1.33238i	0.0855750	+	0.996332i	$0.472727\pi$
$912$		0			0
$913$		0			0
$914$	0.536974	+	0.345092i	0.536974	+	0.345092i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	0.435557	+	0.825472i	0.435557	+	0.825472i	1.00000			$0$
$919$	0.435557	+	0.825472i	0.435557	+	0.825472i	−0.564443	+	0.825472i	$0.690909\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−0.0879554	+	0.611743i	−0.0879554	+	0.611743i
$926$	0.962371	−	1.82390i	0.962371	−	1.82390i
$927$		0			0
$928$	−0.0573360	−	0.176462i	−0.0573360	−	0.176462i
$929$		0			0		−0.870746	−	0.491733i	$-0.836364\pi$
$929$		0			0		0.870746	+	0.491733i	$0.163636\pi$
$930$		0			0
$931$		0			0
$932$	−0.127096	+	0.0145829i	−0.127096	+	0.0145829i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.870746	−	0.491733i	$-0.163636\pi$
$937$		0			0		−0.870746	+	0.491733i	$0.836364\pi$
$938$	−0.929287	−	0.852892i	−0.929287	−	0.852892i
$939$		0			0
$940$		0			0
$941$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$941$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	−0.169603	+	0.0497999i	−0.169603	+	0.0497999i
$947$	0.186393	+	0.215109i	0.186393	+	0.215109i	0.841254	−	0.540641i	$-0.181818\pi$
$947$	0.186393	+	0.215109i	0.186393	+	0.215109i	−0.654861	+	0.755750i	$0.727273\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	1.78310	−	0.876690i	1.78310	−	0.876690i	0.841254	−	0.540641i	$-0.181818\pi$
$953$	1.78310	−	0.876690i	1.78310	−	0.876690i	0.941844	−	0.336049i	$-0.109091\pi$
$954$	−1.91697	−	0.331745i	−1.91697	−	0.331745i
$955$		0			0
$956$	0.0338223	+	0.0740605i	0.0338223	+	0.0740605i
$957$		0			0
$958$		0			0
$959$	1.19207	+	0.866091i	1.19207	+	0.866091i
$960$		0			0
$961$	0.516397	−	0.856349i	0.516397	−	0.856349i
$962$		0			0
$963$	−0.0398036	−	0.0409569i	−0.0398036	−	0.0409569i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−0.508437			−0.508437			−0.254218	−	0.967147i	$-0.581818\pi$
$967$	−0.508437			−0.508437			−0.254218	+	0.967147i	$0.581818\pi$
$968$	−0.907885	−	0.323933i	−0.907885	−	0.323933i
$969$		0			0
$970$		0			0
$971$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$971$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$972$		0			0
$973$		0			0
$974$	−0.176475	+	0.0100912i	−0.176475	+	0.0100912i
$975$		0			0
$976$		0			0
$977$	−1.25259	−	0.910058i	−1.25259	−	0.910058i	−0.254218	−	0.967147i	$-0.581818\pi$
$977$	−1.25259	−	0.910058i	−1.25259	−	0.910058i	−0.998369	+	0.0570888i	$0.981818\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−0.100971	+	0.498310i	−0.100971	+	0.498310i
$982$	1.33286	+	0.230661i	1.33286	+	0.230661i
$983$		0			0		0.897398	−	0.441221i	$-0.145455\pi$
$983$		0			0		−0.897398	+	0.441221i	$0.854545\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.206478	+	0.238288i	0.206478	+	0.238288i
$990$		0			0
$991$	0.186393	−	0.215109i	0.186393	−	0.215109i	−0.654861	−	0.755750i	$-0.727273\pi$
$991$	0.186393	−	0.215109i	0.186393	−	0.215109i	0.841254	+	0.540641i	$0.181818\pi$
$992$		0			0
$993$		0			0
$994$	−0.404199	+	0.0699493i	−0.404199	+	0.0699493i
$995$		0			0
$996$		0			0
$997$		0			0		−0.0285561	−	0.999592i	$-0.509091\pi$
$997$		0			0		0.0285561	+	0.999592i	$0.490909\pi$
$998$	1.23117	+	1.12995i	1.23117	+	1.12995i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.1.bb.a.279.1	✓	40
7.6	odd	2	CM	847.1.bb.a.279.1	✓	40
121.36	even	55	inner	847.1.bb.a.762.1	yes	40
847.762	odd	110	inner	847.1.bb.a.762.1	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.1.bb.a.279.1	✓	40	1.1	even	1	trivial
847.1.bb.a.279.1	✓	40	7.6	odd	2	CM
847.1.bb.a.762.1	yes	40	121.36	even	55	inner
847.1.bb.a.762.1	yes	40	847.762	odd	110	inner

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	847.bb (of order \(110\), degree \(40\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.374706 - 0.962424i) q^{2} +(-0.0491151 + 0.0450774i) q^{4} +(0.516397 - 0.856349i) q^{7} +(-0.865041 - 0.425312i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.374706 - 0.962424i) q^{2} +(-0.0491151 + 0.0450774i) q^{4} +(0.516397 - 0.856349i) q^{7} +(-0.865041 - 0.425312i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(-0.998369 + 0.0570888i) q^{11} +(-1.01767 - 0.176114i) q^{14} +(-0.0908996 + 1.05832i) q^{16} +(-0.262555 + 0.998864i) q^{18} +(0.429039 + 0.939463i) q^{22} +(1.20642 - 1.39228i) q^{23} +(-0.0285561 + 0.999592i) q^{25} +(0.0132391 + 0.0653376i) q^{28} +(-0.0398036 - 1.39331i) q^{29} +(0.127721 - 0.0375023i) q^{32} +(0.0662308 - 0.00759928i) q^{36} +(0.614005 + 0.0704506i) q^{37} +(-0.0243572 + 0.169408i) q^{43} +(0.0464616 - 0.0478078i) q^{44} +(-1.79201 - 0.639389i) q^{46} +(-0.466667 - 0.884433i) q^{49} +(0.972732 - 0.347070i) q^{50} +(0.161197 + 1.87678i) q^{53} +(-0.810921 + 0.521147i) q^{56} +(-1.32604 + 0.560388i) q^{58} +(-0.921124 + 0.389270i) q^{63} +(0.564692 + 0.732306i) q^{64} +(1.02742 + 0.660282i) q^{67} +(0.374083 - 0.133472i) q^{71} +(0.449841 + 0.852543i) q^{72} +(-0.162268 - 0.617332i) q^{74} +(-0.466667 + 0.884433i) q^{77} +(0.812697 - 1.54023i) q^{79} +(0.309017 + 0.951057i) q^{81} +(0.172169 - 0.0400362i) q^{86} +(0.887911 + 0.375234i) q^{88} +(0.00350708 + 0.122764i) q^{92} +(-0.676337 + 0.780534i) q^{98} +(0.841254 + 0.540641i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 2 q^{2} + 3 q^{4} + q^{7} - q^{8} - 10 q^{9}+O(q^{10}) \) 40 * q + 2 * q^2 + 3 * q^4 + q^7 - q^8 - 10 * q^9	\( 40 q + 2 q^{2} + 3 q^{4} + q^{7} - q^{8} - 10 q^{9} + q^{11} - 3 q^{14} - 3 q^{18} + 2 q^{22} - 9 q^{23} + q^{25} - 2 q^{28} + 2 q^{29} - 4 q^{32} + 3 q^{36} - 3 q^{37} + 2 q^{43} - 13 q^{44} - q^{46} + q^{49} + 2 q^{50} - 3 q^{53} - 7 q^{56} - 12 q^{58} + q^{63} - 9 q^{64} + 2 q^{67} - 3 q^{71} - q^{72} + 4 q^{74} + q^{77} - 3 q^{79} - 10 q^{81} - q^{86} - 12 q^{88} - 4 q^{92} - 9 q^{98} - 4 q^{99}+O(q^{100}) \) 40 * q + 2 * q^2 + 3 * q^4 + q^7 - q^8 - 10 * q^9 + q^11 - 3 * q^14 - 3 * q^18 + 2 * q^22 - 9 * q^23 + q^25 - 2 * q^28 + 2 * q^29 - 4 * q^32 + 3 * q^36 - 3 * q^37 + 2 * q^43 - 13 * q^44 - q^46 + q^49 + 2 * q^50 - 3 * q^53 - 7 * q^56 - 12 * q^58 + q^63 - 9 * q^64 + 2 * q^67 - 3 * q^71 - q^72 + 4 * q^74 + q^77 - 3 * q^79 - 10 * q^81 - q^86 - 12 * q^88 - 4 * q^92 - 9 * q^98 - 4 * q^99

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