LMFDB - Embedded newform 616.2.bi.a.237.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [616,2,Mod(13,616)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(616, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 5, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("616.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 616 = 2^{3} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	616.bi (of order $10$, degree $4$, 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:	$4.91878476451$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.37515625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - x^{6} + 3x^{5} - x^{4} + 6x^{3} - 4x^{2} - 8x + 16 $ x^8 - x^7 - x^6 + 3x^5 - x^4 + 6x^3 - 4x^2 - 8x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{10}]$

Embedding invariants

Embedding label			237.2
Root			$-1.41264 - 0.0667372i$ of defining polynomial
Character	$\chi$	$=$	616.237
Dual form			616.2.bi.a.13.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41264 - 0.0667372i) q^{2} +(1.99109 - 0.188551i) q^{4} +(-1.55513 - 2.14046i) q^{7} +(2.80011 - 0.399234i) q^{8} +(-0.927051 - 2.85317i) q^{9} +O(q^{10})$	\(q+(1.41264 - 0.0667372i) q^{2} +(1.99109 - 0.188551i) q^{4} +(-1.55513 - 2.14046i) q^{7} +(2.80011 - 0.399234i) q^{8} +(-0.927051 - 2.85317i) q^{9} +(3.13429 - 1.08453i) q^{11} +(-2.33969 - 2.91991i) q^{14} +(3.92890 - 0.750845i) q^{16} +(-1.50000 - 3.96863i) q^{18} +(4.35524 - 1.74122i) q^{22} +3.36187 q^{23} +(4.04508 + 2.93893i) q^{25} +(-3.50000 - 3.96863i) q^{28} +(-7.64279 + 5.55281i) q^{29} +(5.50000 - 1.32288i) q^{32} +(-2.38381 - 5.50613i) q^{36} +(2.95957 + 4.07350i) q^{37} -1.32431 q^{43} +(6.03618 - 2.75038i) q^{44} +(4.74910 - 0.224362i) q^{46} +(-2.16312 + 6.65740i) q^{49} +(5.91038 + 3.88168i) q^{50} +(-12.1554 + 3.94951i) q^{53} +(-5.20909 - 5.37265i) q^{56} +(-10.4259 + 8.35417i) q^{58} +(-4.66540 + 6.42137i) q^{63} +(7.68122 - 2.23580i) q^{64} -8.70972i q^{67} +(-0.0272696 + 0.0839271i) q^{71} +(-3.73493 - 7.61908i) q^{72} +(4.45265 + 5.55686i) q^{74} +(-7.19564 - 5.02223i) q^{77} +(2.57067 - 0.835260i) q^{79} +(-7.28115 + 5.29007i) q^{81} +(-1.87078 + 0.0883810i) q^{86} +(8.34338 - 4.28812i) q^{88} +(6.69379 - 0.633884i) q^{92} +(-2.61141 + 9.54885i) q^{98} +(-6.00000 - 7.93725i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} + 3 q^{4} + 5 q^{8} + 6 q^{9}+O(q^{10}) $ 8 * q - q^2 + 3 * q^4 + 5 * q^8 + 6 * q^9	$ 8 q - q^{2} + 3 q^{4} + 5 q^{8} + 6 q^{9} - 4 q^{11} + 7 q^{14} - q^{16} - 12 q^{18} + 5 q^{22} + 16 q^{23} + 10 q^{25} - 28 q^{28} + 4 q^{29} + 44 q^{32} - 9 q^{36} - 30 q^{37} - 24 q^{43} + 13 q^{44} + 8 q^{46} + 14 q^{49} + 5 q^{50} - 50 q^{53} - 7 q^{56} - 73 q^{58} - 9 q^{64} + 48 q^{71} - 15 q^{72} + 28 q^{74} + 14 q^{77} + 40 q^{79} - 18 q^{81} - 17 q^{86} + 3 q^{88} + q^{92} + 7 q^{98} - 48 q^{99}+O(q^{100}) $ 8 * q - q^2 + 3 * q^4 + 5 * q^8 + 6 * q^9 - 4 * q^11 + 7 * q^14 - q^16 - 12 * q^18 + 5 * q^22 + 16 * q^23 + 10 * q^25 - 28 * q^28 + 4 * q^29 + 44 * q^32 - 9 * q^36 - 30 * q^37 - 24 * q^43 + 13 * q^44 + 8 * q^46 + 14 * q^49 + 5 * q^50 - 50 * q^53 - 7 * q^56 - 73 * q^58 - 9 * q^64 + 48 * q^71 - 15 * q^72 + 28 * q^74 + 14 * q^77 + 40 * q^79 - 18 * q^81 - 17 * q^86 + 3 * q^88 + q^92 + 7 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/616\mathbb{Z}\right)^\times$.

$n$	$57$	$309$	$353$	$463$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$-1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.41264	−	0.0667372i	0.998886	−	0.0471903i
$2$	1.41264	−	0.0667372i	0.998886	−	0.0471903i
$3$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$3$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$4$	1.99109	−	0.188551i	0.995546	−	0.0942755i
$5$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$5$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$6$		0			0
$7$	−1.55513	−	2.14046i	−0.587785	−	0.809017i
$7$	−1.55513	−	2.14046i	−0.587785	−	0.809017i
$8$	2.80011	−	0.399234i	0.989988	−	0.141151i
$9$	−0.927051	−	2.85317i	−0.309017	−	0.951057i
$10$		0			0
$11$	3.13429	−	1.08453i	0.945025	−	0.326998i
$11$	3.13429	−	1.08453i	0.945025	−	0.326998i
$12$		0			0
$13$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$13$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$14$	−2.33969	−	2.91991i	−0.625308	−	0.780378i
$15$		0			0
$16$	3.92890	−	0.750845i	0.982224	−	0.187711i
$17$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$17$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$18$	−1.50000	−	3.96863i	−0.353553	−	0.935414i
$19$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$19$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$20$		0			0
$21$		0			0
$22$	4.35524	−	1.74122i	0.928541	−	0.371230i
$23$	3.36187			0.700998			0.350499	−	0.936563i	$-0.386012\pi$
$23$	3.36187			0.700998			0.350499	+	0.936563i	$0.386012\pi$
$24$		0			0
$25$	4.04508	+	2.93893i	0.809017	+	0.587785i
$26$		0			0
$27$		0			0
$28$	−3.50000	−	3.96863i	−0.661438	−	0.750000i
$29$	−7.64279	+	5.55281i	−1.41923	+	1.03113i	−0.427331	+	0.904095i	$0.640546\pi$
$29$	−7.64279	+	5.55281i	−1.41923	+	1.03113i	−0.991898	+	0.127036i	$0.959454\pi$
$30$		0			0
$31$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$31$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$32$	5.50000	−	1.32288i	0.972272	−	0.233854i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−2.38381	−	5.50613i	−0.397302	−	0.917688i
$37$	2.95957	+	4.07350i	0.486550	+	0.669679i	0.979747	−	0.200239i	$-0.0641718\pi$
$37$	2.95957	+	4.07350i	0.486550	+	0.669679i	−0.493197	+	0.869918i	$0.664172\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$41$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$42$		0			0
$43$	−1.32431			−0.201956			−0.100978	−	0.994889i	$-0.532197\pi$
$43$	−1.32431			−0.201956			−0.100978	+	0.994889i	$0.532197\pi$
$44$	6.03618	−	2.75038i	0.909988	−	0.414635i
$45$		0			0
$46$	4.74910	−	0.224362i	0.700217	−	0.0330803i
$47$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$47$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$48$		0			0
$49$	−2.16312	+	6.65740i	−0.309017	+	0.951057i
$50$	5.91038	+	3.88168i	0.835853	+	0.548953i
$51$		0			0
$52$		0			0
$53$	−12.1554	+	3.94951i	−1.66967	+	0.542507i	−0.982863	−	0.184336i	$-0.940986\pi$
$53$	−12.1554	+	3.94951i	−1.66967	+	0.542507i	−0.686803	+	0.726844i	$0.740986\pi$
$54$		0			0
$55$		0			0
$56$	−5.20909	−	5.37265i	−0.696094	−	0.717951i
$57$		0			0
$58$	−10.4259	+	8.35417i	−1.36899	+	1.09696i
$59$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$59$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$60$		0			0
$61$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$61$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$62$		0			0
$63$	−4.66540	+	6.42137i	−0.587785	+	0.809017i
$64$	7.68122	−	2.23580i	0.960153	−	0.279475i
$65$		0			0
$66$		0			0
$67$		−	8.70972i		−	1.06406i	−0.846725	−	0.532031i	$-0.821429\pi$
$67$		−	8.70972i		−	1.06406i	0.846725	−	0.532031i	$-0.178571\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−0.0272696	+	0.0839271i	−0.00323630	+	0.00996031i	−0.952662	−	0.304033i	$-0.901667\pi$
$71$	−0.0272696	+	0.0839271i	−0.00323630	+	0.00996031i	0.949425	+	0.313993i	$0.101667\pi$
$72$	−3.73493	−	7.61908i	−0.440165	−	0.897917i
$73$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$73$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$74$	4.45265	+	5.55686i	0.517610	+	0.645972i
$75$		0			0
$76$		0			0
$77$	−7.19564	−	5.02223i	−0.820019	−	0.572336i
$78$		0			0
$79$	2.57067	−	0.835260i	0.289223	−	0.0939741i	−0.160813	−	0.986985i	$-0.551411\pi$
$79$	2.57067	−	0.835260i	0.289223	−	0.0939741i	0.450035	+	0.893011i	$0.351411\pi$
$80$		0			0
$81$	−7.28115	+	5.29007i	−0.809017	+	0.587785i
$82$		0			0
$83$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$83$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$84$		0			0
$85$		0			0
$86$	−1.87078	+	0.0883810i	−0.201731	+	0.00953037i
$87$		0			0
$88$	8.34338	−	4.28812i	0.889407	−	0.457115i
$89$		0			0		1.00000			$0$
$89$		0			0		−1.00000			$\pi$
$90$		0			0
$91$		0			0
$92$	6.69379	−	0.633884i	0.697876	−	0.0660869i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$97$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$98$	−2.61141	+	9.54885i	−0.263792	+	0.964580i
$99$	−6.00000	−	7.93725i	−0.603023	−	0.797724i
$100$	8.60828	+	5.08897i	0.860828	+	0.508897i
$101$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$101$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$102$		0			0
$103$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$103$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$104$		0			0
$105$		0			0
$106$	−16.9075	+	6.39045i	−1.64220	+	0.620695i
$107$	15.6064	+	11.3387i	1.50873	+	1.09616i	0.966736	+	0.255774i	$0.0823304\pi$
$107$	15.6064	+	11.3387i	1.50873	+	1.09616i	0.541994	+	0.840382i	$0.317670\pi$
$108$		0			0
$109$	−20.7828			−1.99064			−0.995318	−	0.0966592i	$-0.969184\pi$
$109$	−20.7828			−1.99064			−0.995318	+	0.0966592i	$0.969184\pi$
$110$		0			0
$111$		0			0
$112$	−7.71711	−	7.24197i	−0.729199	−	0.684302i
$113$	16.7856	+	12.1954i	1.57905	+	1.14725i	0.917769	+	0.397114i	$0.129988\pi$
$113$	16.7856	+	12.1954i	1.57905	+	1.14725i	0.661285	+	0.750135i	$0.270012\pi$
$114$		0			0
$115$		0			0
$116$	−14.1705	+	12.4972i	−1.31570	+	1.16034i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	8.64759	−	6.79848i	0.786144	−	0.618043i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	−6.16198	+	9.38243i	−0.548953	+	0.835853i
$127$	−3.26991	−	1.06246i	−0.290157	−	0.0942778i	0.160322	−	0.987065i	$-0.448747\pi$
$127$	−3.26991	−	1.06246i	−0.290157	−	0.0942778i	−0.450479	+	0.892787i	$0.648747\pi$
$128$	10.7016	−	3.67100i	0.945895	−	0.324473i
$129$		0			0
$130$		0			0
$131$		0			0		1.00000			$0$
$131$		0			0		−1.00000			$\pi$
$132$		0			0
$133$		0			0
$134$	−0.581262	−	12.3037i	−0.0502134	−	1.06288i
$135$		0			0
$136$		0			0
$137$	−1.34450	+	4.13795i	−0.114869	+	0.353529i	−0.991920	−	0.126868i	$-0.959507\pi$
$137$	−1.34450	+	4.13795i	−0.114869	+	0.353529i	0.877051	+	0.480397i	$0.159507\pi$
$138$		0			0
$139$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$139$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$140$		0			0
$141$		0			0
$142$	−0.0329210	+	0.120378i	−0.00276267	+	0.0101019i
$143$		0			0
$144$	−5.78458	−	10.5137i	−0.482048	−	0.876145i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	6.66084	+	7.55268i	0.547517	+	0.620826i
$149$	−6.79837	+	20.9232i	−0.556944	+	1.71410i	0.133808	+	0.991007i	$0.457280\pi$
$149$	−6.79837	+	20.9232i	−0.556944	+	1.71410i	−0.690752	+	0.723092i	$0.742720\pi$
$150$		0			0
$151$	−10.8081	+	14.8760i	−0.879547	+	1.21059i	0.0969991	+	0.995284i	$0.469076\pi$
$151$	−10.8081	+	14.8760i	−0.879547	+	1.21059i	−0.976546	+	0.215308i	$0.930924\pi$
$152$		0			0
$153$		0			0
$154$	−10.5000	−	6.61438i	−0.846114	−	0.533002i
$155$		0			0
$156$		0			0
$157$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$157$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$158$	3.57568	−	1.35148i	0.284466	−	0.107518i
$159$		0			0
$160$		0			0
$161$	−5.22816	−	7.19594i	−0.412036	−	0.567119i
$162$	−9.93259	+	7.95887i	−0.780378	+	0.625308i
$163$	1.03384	−	0.335914i	0.0809764	−	0.0263108i	−0.268249	−	0.963350i	$-0.586445\pi$
$163$	1.03384	−	0.335914i	0.0809764	−	0.0263108i	0.349225	+	0.937039i	$0.386445\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$167$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$168$		0			0
$169$	−10.5172	+	7.64121i	−0.809017	+	0.587785i
$170$		0			0
$171$		0			0
$172$	−2.63683	+	0.249701i	−0.201057	+	0.0190395i
$173$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$173$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$174$		0			0
$175$		−	13.2288i		−	1.00000i
$176$	11.5000	−	6.61438i	0.866845	−	0.498578i
$177$		0			0
$178$		0			0
$179$	11.1993	−	15.4146i	0.837077	−	1.15214i	−0.149487	−	0.988764i	$-0.547762\pi$
$179$	11.1993	−	15.4146i	0.837077	−	1.15214i	0.986564	−	0.163374i	$-0.0522378\pi$
$180$		0			0
$181$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$181$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$182$		0			0
$183$		0			0
$184$	9.41360	−	1.34217i	0.693980	−	0.0989463i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	22.3570	−	16.2433i	1.61769	−	1.17532i	0.796781	−	0.604268i	$-0.206534\pi$
$191$	22.3570	−	16.2433i	1.61769	−	1.17532i	0.820912	−	0.571055i	$-0.193466\pi$
$192$		0			0
$193$	−10.0606	−	3.26889i	−0.724179	−	0.235300i	−0.0763450	−	0.997081i	$-0.524325\pi$
$193$	−10.0606	−	3.26889i	−0.724179	−	0.235300i	−0.647834	+	0.761781i	$0.724325\pi$
$194$		0			0
$195$		0			0
$196$	−3.05171	+	13.6633i	−0.217979	+	0.975953i
$197$	14.8139			1.05545			0.527724	−	0.849416i	$-0.323046\pi$
$197$	14.8139			1.05545			0.527724	+	0.849416i	$0.323046\pi$
$198$	−9.00554	−	10.8120i	−0.639996	−	0.768378i
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$	12.5000	+	6.61438i	0.883883	+	0.467707i
$201$		0			0
$202$		0			0
$203$	23.7711	+	7.72370i	1.66840	+	0.542097i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−3.11662	−	9.59198i	−0.216620	−	0.666689i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−7.80563	−	24.0233i	−0.537362	−	1.65383i	−0.738490	−	0.674264i	$-0.764461\pi$
$211$	−7.80563	−	24.0233i	−0.537362	−	1.65383i	0.201129	−	0.979565i	$-0.435539\pi$
$212$	−23.4577	+	10.1557i	−1.61108	+	0.697500i
$213$		0			0
$214$	22.8030	+	14.9760i	1.55878	+	1.02374i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−29.3586	+	1.38699i	−1.98842	+	0.0939387i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$223$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$224$	−11.3848	−	9.71527i	−0.760679	−	0.649129i
$225$	4.63525	−	14.2658i	0.309017	−	0.951057i
$226$	24.5258	+	16.1075i	1.63143	+	1.07146i
$227$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$227$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$228$		0			0
$229$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$229$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$230$		0			0
$231$		0			0
$232$	−19.1838	+	18.5997i	−1.25948	+	1.22113i
$233$	20.1301	−	6.54066i	1.31876	−	0.428493i	0.436694	−	0.899610i	$-0.356149\pi$
$233$	20.1301	−	6.54066i	1.31876	−	0.428493i	0.882071	+	0.471117i	$0.156149\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−13.7499	+	18.9251i	−0.889407	+	1.22416i	0.0843185	+	0.996439i	$0.473129\pi$
$239$	−13.7499	+	18.9251i	−0.889407	+	1.22416i	−0.973726	+	0.227725i	$0.926871\pi$
$240$		0			0
$241$		0			0			−	1.00000i	$-0.5\pi$
$241$		0			0				1.00000i	$0.5\pi$
$242$	11.7622	−	10.1809i	0.756103	−	0.654453i
$243$		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		0.951057	−	0.309017i	$-0.100000\pi$
$251$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$252$	−8.07849	+	13.6652i	−0.508897	+	0.860828i
$253$	10.5371	−	3.64605i	0.662461	−	0.229225i
$254$	−4.69010	−	1.28264i	−0.294283	−	0.0804802i
$255$		0			0
$256$	14.8725	−	5.89998i	0.929529	−	0.368749i
$257$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$257$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$258$		0			0
$259$	4.11662	−	12.6697i	0.255795	−	0.787255i
$260$		0			0
$261$	22.9284	+	16.6584i	1.41923	+	1.03113i
$262$		0			0
$263$		−	28.7986i		−	1.77580i	−0.460036	−	0.887900i	$-0.652164\pi$
$263$		−	28.7986i		−	1.77580i	0.460036	−	0.887900i	$-0.347836\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−1.64223	−	17.3419i	−0.100315	−	1.05932i
$269$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$269$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$270$		0			0
$271$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$271$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$272$		0			0
$273$		0			0
$274$	−1.62314	+	5.93515i	−0.0980574	+	0.358556i
$275$	15.8658	+	4.82444i	0.956746	+	0.290924i
$276$		0			0
$277$	−8.26675	−	25.4424i	−0.496701	−	1.52869i	−0.814289	−	0.580460i	$-0.802873\pi$
$277$	−8.26675	−	25.4424i	−0.496701	−	1.52869i	0.317588	−	0.948229i	$-0.397127\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−29.7378	−	9.66238i	−1.77401	−	0.576409i	−0.775515	−	0.631329i	$-0.782510\pi$
$281$	−29.7378	−	9.66238i	−1.77401	−	0.576409i	−0.998491	+	0.0549198i	$0.982510\pi$
$282$		0			0
$283$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$283$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$284$	−0.0384717	+	0.172248i	−0.00228287	+	0.0102211i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−8.87317	−	14.4661i	−0.522856	−	0.852421i
$289$	13.7533	+	9.99235i	0.809017	+	0.587785i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$293$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$294$		0			0
$295$		0			0
$296$	9.91340	+	10.2247i	0.576204	+	0.594297i
$297$		0			0
$298$	−8.20728	+	30.0107i	−0.475435	+	1.73847i
$299$		0			0
$300$		0			0
$301$	2.05949	+	2.83464i	0.118707	+	0.163386i
$302$	−14.2751	+	21.7357i	−0.821439	+	1.25075i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$	−15.2741	−	8.64298i	−0.870324	−	0.492480i
$309$		0			0
$310$		0			0
$311$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$311$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$312$		0			0
$313$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$313$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$314$		0			0
$315$		0			0
$316$	4.96095	−	2.14778i	0.279075	−	0.120822i
$317$	27.6430	−	8.98176i	1.55259	−	0.504466i	0.597772	−	0.801666i	$-0.296053\pi$
$317$	27.6430	−	8.98176i	1.55259	−	0.504466i	0.954815	+	0.297200i	$0.0960529\pi$
$318$		0			0
$319$	−17.9325	+	25.6930i	−1.00403	+	1.43853i
$320$		0			0
$321$		0			0
$322$	−7.86573	−	9.81634i	−0.438340	−	0.547043i
$323$		0			0
$324$	−13.5000	+	11.9059i	−0.750000	+	0.661438i
$325$		0			0
$326$	1.43802	−	0.543521i	0.0796446	−	0.0301028i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$			16.8794i			0.927773i	0.885895	+	0.463887i	$0.153545\pi$
$331$			16.8794i			0.927773i	−0.885895	+	0.463887i	$0.846455\pi$
$332$		0			0
$333$	8.87871	−	12.2205i	0.486550	−	0.669679i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−20.4298	−	28.1192i	−1.11288	−	1.53175i	−0.817102	−	0.576493i	$-0.804421\pi$
$337$	−20.4298	−	28.1192i	−1.11288	−	1.53175i	−0.295779	−	0.955256i	$-0.595579\pi$
$338$	−14.3471	+	11.4962i	−0.780378	+	0.625308i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	17.6138	−	5.72307i	0.951057	−	0.309017i
$344$	−3.70822	+	0.528712i	−0.199934	+	0.0285062i
$345$		0			0
$346$		0			0
$347$	−11.2679	+	34.6790i	−0.604893	+	1.86167i	−0.107366	+	0.994220i	$0.534242\pi$
$347$	−11.2679	+	34.6790i	−0.604893	+	1.86167i	−0.497527	+	0.867448i	$0.665758\pi$
$348$		0			0
$349$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$349$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$350$	−0.882850	−	18.6874i	−0.0471903	−	0.998886i
$351$		0			0
$352$	15.8039	−	10.1112i	0.842351	−	0.538929i
$353$		0			0		1.00000			$0$
$353$		0			0		−1.00000			$\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	14.7919	−	22.5226i	0.781775	−	1.19036i
$359$	−14.8499	−	20.4391i	−0.783747	−	1.07873i	−0.994859	−	0.101273i	$-0.967708\pi$
$359$	−14.8499	−	20.4391i	−0.783747	−	1.07873i	0.211112	−	0.977462i	$-0.432292\pi$
$360$		0			0
$361$	5.87132	+	18.0701i	0.309017	+	0.951057i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$367$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$368$	13.2084	−	2.52424i	0.688537	−	0.131585i
$369$		0			0
$370$		0			0
$371$	27.3570	+	19.8760i	1.42030	+	1.03191i
$372$		0			0
$373$	22.0000			1.13912			0.569558	−	0.821951i	$-0.307114\pi$
$373$	22.0000			1.13912			0.569558	+	0.821951i	$0.307114\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−35.2080	−	11.4398i	−1.80851	−	0.587621i	−0.808511	−	0.588481i	$-0.799726\pi$
$379$	−35.2080	−	11.4398i	−1.80851	−	0.587621i	−1.00000		0.000859657i	$0.999726\pi$
$380$		0			0
$381$		0			0
$382$	30.4983	−	24.4379i	1.56043	−	1.25035i
$383$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$383$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$384$		0			0
$385$		0			0
$386$	−14.4302	−	3.94635i	−0.734476	−	0.200864i
$387$	1.22771	+	3.77849i	0.0624078	+	0.192072i
$388$		0			0
$389$	−18.1612	−	24.9967i	−0.920809	−	1.26739i	−0.963338	−	0.268290i	$-0.913542\pi$
$389$	−18.1612	−	24.9967i	−0.920809	−	1.26739i	0.0425291	−	0.999095i	$-0.486458\pi$
$390$		0			0
$391$		0			0
$392$	−3.39911	+	19.5050i	−0.171681	+	0.985153i
$393$		0			0
$394$	20.9267	−	0.988639i	1.05427	−	0.0498069i
$395$		0			0
$396$	−13.4431	−	14.6725i	−0.675543	−	0.737321i
$397$		0			0			−	1.00000i	$-0.5\pi$
$397$		0			0				1.00000i	$0.5\pi$
$398$		0			0
$399$		0			0
$400$	18.0994	+	8.50951i	0.904970	+	0.425475i
$401$	12.3445	−	37.9925i	0.616455	−	1.89725i	0.240287	−	0.970702i	$-0.422758\pi$
$401$	12.3445	−	37.9925i	0.616455	−	1.89725i	0.376168	−	0.926552i	$-0.377242\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	34.0954	+	9.32438i	1.69213	+	0.462761i
$407$	13.6940	+	9.55779i	0.678786	+	0.473762i
$408$		0			0
$409$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$409$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	−5.04280	−	13.3420i	−0.247840	−	0.655724i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	24.0803	−	33.1437i	1.17360	−	1.61533i	0.540022	−	0.841651i	$-0.318416\pi$
$421$	24.0803	−	33.1437i	1.17360	−	1.61533i	0.633581	−	0.773676i	$-0.281584\pi$
$422$	−12.6298	−	33.4152i	−0.614808	−	1.62663i
$423$		0			0
$424$	−32.4595	+	15.9119i	−1.57637	+	0.772750i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	33.2118	+	19.6339i	1.60535	+	0.949038i
$429$		0			0
$430$		0			0
$431$	38.2455	−	12.4267i	1.84222	−	0.598574i	0.844177	−	0.536065i	$-0.180090\pi$
$431$	38.2455	−	12.4267i	1.84222	−	0.598574i	0.998044	−	0.0625092i	$-0.0199103\pi$
$432$		0			0
$433$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$433$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$434$		0			0
$435$		0			0
$436$	−41.3806	+	3.91863i	−1.98177	+	0.187668i
$437$		0			0
$438$		0			0
$439$		0			0			−	1.00000i	$-0.5\pi$
$439$		0			0				1.00000i	$0.5\pi$
$440$		0			0
$441$	21.0000			1.00000
$442$		0			0
$443$	−4.45246	+	6.12829i	−0.211543	+	0.291164i	−0.901582	−	0.432608i	$-0.857593\pi$
$443$	−4.45246	+	6.12829i	−0.211543	+	0.291164i	0.690039	+	0.723772i	$0.257593\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	−16.7310	−	12.9644i	−0.790464	−	0.612509i
$449$	8.18900	+	25.2032i	0.386463	+	1.18941i	0.935413	+	0.353556i	$0.115028\pi$
$449$	8.18900	+	25.2032i	0.386463	+	1.18941i	−0.548950	+	0.835855i	$0.684972\pi$
$450$	5.59587	−	20.4618i	0.263792	−	0.964580i
$451$		0			0
$452$	35.7211	+	21.1173i	1.68018	+	0.993274i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−29.2170	−	9.49319i	−1.36672	−	0.444073i	−0.468436	−	0.883497i	$-0.655182\pi$
$457$	−29.2170	−	9.49319i	−1.36672	−	0.444073i	−0.898279	+	0.439425i	$0.855182\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		1.00000			$0$
$461$		0			0		−1.00000			$\pi$
$462$		0			0
$463$	−27.4582			−1.27609			−0.638046	−	0.769998i	$-0.720257\pi$
$463$	−27.4582			−1.27609			−0.638046	+	0.769998i	$0.720257\pi$
$464$	−25.8584	+	27.5550i	−1.20045	+	1.27921i
$465$		0			0
$466$	28.0000	−	10.5830i	1.29707	−	0.490248i
$467$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$467$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$468$		0			0
$469$	−18.6428	+	13.5448i	−0.860844	+	0.625440i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−4.15079	+	1.43626i	−0.190853	+	0.0660393i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	22.5373	+	31.0199i	1.03191	+	1.42030i
$478$	−18.1606	+	27.6520i	−0.830647	+	1.26477i
$479$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$479$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	15.9363	−	15.1669i	0.724376	−	0.689405i
$485$		0			0
$486$		0			0
$487$	22.4997	+	16.3470i	1.01956	+	0.740754i	0.966193	−	0.257821i	$-0.0830043\pi$
$487$	22.4997	+	16.3470i	1.01956	+	0.740754i	0.0533681	+	0.998575i	$0.483004\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−35.5967	+	25.8626i	−1.60646	+	1.16716i	−0.733047	+	0.680178i	$0.761903\pi$
$491$	−35.5967	+	25.8626i	−1.60646	+	1.16716i	−0.873412	+	0.486983i	$0.838097\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.222050	−	0.0721485i	0.00996031	−	0.00323630i
$498$		0			0
$499$	−24.9302	−	34.3135i	−1.11603	−	1.53608i	−0.812219	−	0.583352i	$-0.801741\pi$
$499$	−24.9302	−	34.3135i	−1.11603	−	1.53608i	−0.303812	−	0.952732i	$-0.598259\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$503$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$504$	−10.5000	+	19.8431i	−0.467707	+	0.883883i
$505$		0			0
$506$	14.6418	−	5.85376i	0.650905	−	0.260232i
$507$		0			0
$508$	−6.71101	−	1.49891i	−0.297753	−	0.0665032i
$509$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$509$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$510$		0			0
$511$		0			0
$512$	20.6157	−	9.32709i	0.911092	−	0.412203i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	4.96976	−	18.1724i	0.218359	−	0.798449i
$519$		0			0
$520$		0			0
$521$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$521$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$522$	33.5012	+	22.0022i	1.46631	+	0.963008i
$523$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$523$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$524$		0			0
$525$		0			0
$526$	−1.92194	−	40.6821i	−0.0838006	−	1.77382i
$527$		0			0
$528$		0			0
$529$	−11.6978			−0.508602
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	−3.47722	−	24.3882i	−0.150193	−	1.05341i
$537$		0			0
$538$		0			0
$539$	0.440303	+	23.2122i	0.0189652	+	0.999820i
$540$		0			0
$541$	2.73325	+	8.41207i	0.117511	+	0.361663i	0.992463	−	0.122548i	$-0.0391066\pi$
$541$	2.73325	+	8.41207i	0.117511	+	0.361663i	−0.874951	+	0.484211i	$0.839107\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−35.5967	−	25.8626i	−1.52201	−	1.10580i	−0.960482	−	0.278343i	$-0.910215\pi$
$547$	−35.5967	−	25.8626i	−1.52201	−	1.10580i	−0.561525	−	0.827460i	$-0.689785\pi$
$548$	−1.89681	+	8.49255i	−0.0810278	+	0.362784i
$549$		0			0
$550$	22.7347	+	5.75634i	0.969409	+	0.245451i
$551$		0			0
$552$		0			0
$553$	−5.78557	−	4.20346i	−0.246027	−	0.178749i
$554$	−13.3759	−	35.3893i	−0.568287	−	1.50355i
$555$		0			0
$556$		0			0
$557$	−3.35721	+	2.43916i	−0.142250	+	0.103350i	−0.656634	−	0.754209i	$-0.728020\pi$
$557$	−3.35721	+	2.43916i	−0.142250	+	0.103350i	0.514384	+	0.857560i	$0.328020\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−42.6535	−	11.6648i	−1.79923	−	0.492051i
$563$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$563$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	22.6463	+	7.35824i	0.951057	+	0.309017i
$568$	−0.0428512	+	0.245892i	−0.00179800	+	0.0103174i
$569$	−24.8821	+	34.2473i	−1.04311	+	1.43572i	−0.148483	+	0.988915i	$0.547439\pi$
$569$	−24.8821	+	34.2473i	−1.04311	+	1.43572i	−0.894630	+	0.446808i	$0.852561\pi$
$570$		0			0
$571$	−31.2285			−1.30687			−0.653435	−	0.756982i	$-0.726673\pi$
$571$	−31.2285			−1.30687			−0.653435	+	0.756982i	$0.726673\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	13.5990	+	9.88028i	0.567119	+	0.412036i
$576$	−13.5000	−	19.8431i	−0.562500	−	0.826797i
$577$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$577$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$578$	20.0953	+	13.1977i	0.835853	+	0.548953i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−33.8151	+	25.5618i	−1.40048	+	1.05866i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$587$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	14.6864	+	13.7822i	0.603608	+	0.566444i
$593$		0			0			−	1.00000i	$-0.5\pi$
$593$		0			0				1.00000i	$0.5\pi$
$594$		0			0
$595$		0			0
$596$	−9.59109	+	42.9419i	−0.392866	+	1.75897i
$597$		0			0
$598$		0			0
$599$	−14.7279	+	45.3277i	−0.601765	+	1.85204i	−0.0841014	+	0.996457i	$0.526802\pi$
$599$	−14.7279	+	45.3277i	−0.601765	+	1.85204i	−0.517663	+	0.855584i	$0.673198\pi$
$600$		0			0
$601$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$601$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$602$	3.09848	+	3.86687i	0.126285	+	0.157602i
$603$	−24.8503	+	8.07435i	−1.01198	+	0.328813i
$604$	−18.7149	+	31.6574i	−0.761500	+	1.28812i
$605$		0			0
$606$		0			0
$607$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$607$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−33.9284	−	24.6504i	−1.37035	−	0.995620i	−0.997709	−	0.0676456i	$-0.978451\pi$
$613$	−33.9284	−	24.6504i	−1.37035	−	0.995620i	−0.372644	−	0.927974i	$-0.621549\pi$
$614$		0			0
$615$		0			0
$616$	−22.1536	−	11.1901i	−0.892595	−	0.450860i
$617$	48.2946			1.94427			0.972133	−	0.234428i	$-0.0753218\pi$
$617$	48.2946			1.94427			0.972133	+	0.234428i	$0.0753218\pi$
$618$		0			0
$619$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$619$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	7.72542	+	23.7764i	0.309017	+	0.951057i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−33.1185	+	24.0620i	−1.31843	+	0.957892i	−0.318475	+	0.947931i	$0.603171\pi$
$631$	−33.1185	+	24.0620i	−1.31843	+	0.957892i	−0.999950	+	0.00996082i	$0.996829\pi$
$632$	6.86468	−	3.36512i	0.273062	−	0.133857i
$633$		0			0
$634$	38.4502	−	14.5328i	1.52705	−	0.577171i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	−23.6175	+	37.4916i	−0.935026	+	1.48431i
$639$	0.264738			0.0104729
$640$		0			0
$641$	27.7856	+	20.1874i	1.09746	+	0.797354i	0.980644	−	0.195799i	$-0.0627300\pi$
$641$	27.7856	+	20.1874i	1.09746	+	0.797354i	0.116820	+	0.993153i	$0.462730\pi$
$642$		0			0
$643$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$643$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$644$	−11.7665	−	13.3420i	−0.463667	−	0.525749i
$645$		0			0
$646$		0			0
$647$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$647$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$648$	−18.2760	+	17.7197i	−0.717951	+	0.696094i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	1.99513	−	0.863768i	0.0781353	−	0.0338278i
$653$	−12.2421	−	16.8497i	−0.479069	−	0.659382i	0.499257	−	0.866454i	$-0.333606\pi$
$653$	−12.2421	−	16.8497i	−0.479069	−	0.659382i	−0.978326	+	0.207072i	$0.933606\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−44.0000			−1.71400			−0.856998	−	0.515319i	$-0.827673\pi$
$659$	−44.0000			−1.71400			−0.856998	+	0.515319i	$0.827673\pi$
$660$		0			0
$661$		0			0			−	1.00000i	$-0.5\pi$
$661$		0			0				1.00000i	$0.5\pi$
$662$	1.12648	+	23.8444i	0.0437819	+	0.926740i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	11.7268	−	17.8557i	0.454406	−	0.691893i
$667$	−25.6940	+	18.6678i	−0.994877	+	0.722821i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−39.5763	+	12.8591i	−1.52556	+	0.495683i	−0.947348	−	0.320207i	$-0.896248\pi$
$673$	−39.5763	+	12.8591i	−1.52556	+	0.495683i	−0.578208	+	0.815890i	$0.696248\pi$
$674$	−30.7365	−	38.3588i	−1.18393	−	1.47753i
$675$		0			0
$676$	−19.5000	+	17.1974i	−0.750000	+	0.661438i
$677$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$677$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$			34.8457i			1.33334i	0.745355	+	0.666668i	$0.232280\pi$
$683$			34.8457i			1.33334i	−0.745355	+	0.666668i	$0.767720\pi$
$684$		0			0
$685$		0			0
$686$	24.5000	−	9.26013i	0.935414	−	0.353553i
$687$		0			0
$688$	−5.20309	+	0.994355i	−0.198366	+	0.0379094i
$689$		0			0
$690$		0			0
$691$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$691$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$692$		0			0
$693$	−7.65856	+	25.1862i	−0.290924	+	0.956746i
$694$	−13.6031	+	49.7409i	−0.516366	+	1.88814i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−2.49430	−	26.3397i	−0.0942755	−	0.995546i
$701$	26.4716	+	19.2327i	0.999819	+	0.726411i	0.962049	−	0.272876i	$-0.0879747\pi$
$701$	26.4716	+	19.2327i	0.999819	+	0.726411i	0.0377695	+	0.999286i	$0.487975\pi$
$702$		0			0
$703$		0			0
$704$	21.6504	−	15.3382i	0.815981	−	0.578079i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−20.9784	−	6.81629i	−0.787860	−	0.255991i	−0.112667	−	0.993633i	$-0.535939\pi$
$709$	−20.9784	−	6.81629i	−0.787860	−	0.255991i	−0.675192	+	0.737642i	$0.735939\pi$
$710$		0			0
$711$	−4.76628	−	6.56022i	−0.178749	−	0.246027i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	19.3925	−	32.8034i	0.724731	−	1.22592i
$717$		0			0
$718$	−22.3416	−	27.8820i	−0.833779	−	1.04055i
$719$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$719$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$720$		0			0
$721$		0			0
$722$	9.50000	+	25.1346i	0.353553	+	0.935414i
$723$		0			0
$724$		0			0
$725$	−47.2350			−1.75426
$726$		0			0
$727$		0			0		1.00000			$0$
$727$		0			0		−1.00000			$\pi$
$728$		0			0
$729$	21.8435	+	15.8702i	0.809017	+	0.587785i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$733$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$734$		0			0
$735$		0			0
$736$	18.4903	−	4.44733i	0.681561	−	0.163931i
$737$	−9.44596	−	27.2988i	−0.347946	−	1.00556i
$738$		0			0
$739$	−9.63096	−	29.6410i	−0.354281	−	1.09036i	−0.956425	−	0.291977i	$-0.905687\pi$
$739$	−9.63096	−	29.6410i	−0.354281	−	1.09036i	0.602145	−	0.798387i	$-0.294313\pi$
$740$		0			0
$741$		0			0
$742$	39.9720	+	26.2519i	1.46742	+	0.963736i
$743$	47.0663	+	15.2928i	1.72669	+	0.561037i	0.992965	−	0.118405i	$-0.0377783\pi$
$743$	47.0663	+	15.2928i	1.72669	+	0.561037i	0.733729	+	0.679442i	$0.237778\pi$
$744$		0			0
$745$		0			0
$746$	31.0780	−	1.46822i	1.13785	−	0.0537553i
$747$		0			0
$748$		0			0
$749$		−	51.0381i		−	1.86489i
$750$		0			0
$751$	43.9977	+	31.9662i	1.60550	+	1.16646i	0.875772	+	0.482724i	$0.160353\pi$
$751$	43.9977	+	31.9662i	1.60550	+	1.16646i	0.729727	+	0.683739i	$0.239647\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	51.9537	−	16.8808i	1.88829	−	0.613543i	0.906959	−	0.421220i	$-0.138398\pi$
$757$	51.9537	−	16.8808i	1.88829	−	0.613543i	0.981332	−	0.192323i	$-0.0616021\pi$
$758$	−50.4995	−	13.8106i	−1.83423	−	0.501622i
$759$		0			0
$760$		0			0
$761$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$761$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$762$		0			0
$763$	32.3201	+	44.4848i	1.17007	+	1.61046i
$764$	41.4521	−	36.5573i	1.49968	−	1.32260i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0			−	1.00000i	$-0.5\pi$
$769$		0			0				1.00000i	$0.5\pi$
$770$		0			0
$771$		0			0
$772$	−20.6480	−	4.61173i	−0.743137	−	0.165980i
$773$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$773$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$774$	1.98647	+	5.25571i	0.0714022	+	0.188913i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−27.3234	−	34.0993i	−0.979592	−	1.22252i
$779$		0			0
$780$		0			0
$781$	0.00555072	+	0.292627i	0.000198620	+	0.0104710i
$782$		0			0
$783$		0			0
$784$	−3.50000	+	27.7804i	−0.125000	+	0.992157i
$785$		0			0
$786$		0			0
$787$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$787$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$788$	29.4959	−	2.79318i	1.05075	−	0.0995028i
$789$		0			0
$790$		0			0
$791$		−	54.8943i		−	1.95182i
$792$	−19.9695	−	19.8298i	−0.709585	−	0.704620i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$797$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$798$		0			0
$799$		0			0
$800$	26.1358	+	10.8130i	0.924040	+	0.382296i
$801$		0			0
$802$	14.9028	−	54.4934i	0.526236	−	1.92423i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−53.8138	−	17.4852i	−1.89199	−	0.614745i	−0.977832	−	0.209393i	$-0.932851\pi$
$809$	−53.8138	−	17.4852i	−1.89199	−	0.614745i	−0.914160	−	0.405353i	$-0.867149\pi$
$810$		0			0
$811$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$811$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$812$	48.7868	+	10.8965i	1.71208	+	0.382393i
$813$		0			0
$814$	19.9825	+	12.5878i	0.700387	+	0.441202i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	17.7984	−	12.9313i	0.621168	−	0.451305i	−0.232162	−	0.972677i	$-0.574580\pi$
$821$	17.7984	−	12.9313i	0.621168	−	0.451305i	0.853329	+	0.521373i	$0.174580\pi$
$822$		0			0
$823$	−17.0519	−	52.4804i	−0.594393	−	1.82935i	−0.557725	−	0.830026i	$-0.688326\pi$
$823$	−17.0519	−	52.4804i	−0.594393	−	1.82935i	−0.0366680	−	0.999328i	$-0.511674\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	13.5967	+	41.8465i	0.472805	+	1.45514i	0.848895	+	0.528562i	$0.177268\pi$
$827$	13.5967	+	41.8465i	0.472805	+	1.45514i	−0.376090	+	0.926583i	$0.622732\pi$
$828$	−8.01406	−	18.5109i	−0.278508	−	0.643297i
$829$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$829$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$830$		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		−0.809017	−	0.587785i	$-0.800000\pi$
$839$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$840$		0			0
$841$	18.6170	−	57.2972i	0.641965	−	1.97577i
$842$	31.8049	−	48.4272i	1.09607	−	1.66891i
$843$		0			0
$844$	−20.0713	−	46.3607i	−0.690884	−	1.59580i
$845$		0			0
$846$		0			0
$847$	−28.0000	−	7.93725i	−0.962091	−	0.272727i
$848$	−44.7917	+	24.6440i	−1.53815	+	0.846279i
$849$		0			0
$850$		0			0
$851$	9.94968	+	13.6946i	0.341071	+	0.469444i
$852$		0			0
$853$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$853$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$854$		0			0
$855$		0			0
$856$	48.2265	+	25.5191i	1.64835	+	0.872224i
$857$		0			0			−	1.00000i	$-0.5\pi$
$857$		0			0				1.00000i	$0.5\pi$
$858$		0			0
$859$		0			0			−	1.00000i	$-0.5\pi$
$859$		0			0				1.00000i	$0.5\pi$
$860$		0			0
$861$		0			0
$862$	53.1977	−	20.1069i	1.81192	−	0.684842i
$863$	−2.47214	+	7.60845i	−0.0841525	+	0.258995i	−0.984275	−	0.176642i	$-0.943477\pi$
$863$	−2.47214	+	7.60845i	−0.0841525	+	0.258995i	0.900123	+	0.435636i	$0.143477\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	7.15136	−	5.40592i	0.242593	−	0.183383i
$870$		0			0
$871$		0			0
$872$	−58.1942	+	8.29722i	−1.97071	+	0.280979i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	11.9284	+	8.66646i	0.402792	+	0.292645i	0.770677	−	0.637226i	$-0.219918\pi$
$877$	11.9284	+	8.66646i	0.402792	+	0.292645i	−0.367885	+	0.929871i	$0.619918\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	29.6654	−	1.40148i	0.998886	−	0.0471903i
$883$	34.2129	−	47.0901i	1.15136	−	1.58471i	0.412325	−	0.911037i	$-0.364717\pi$
$883$	34.2129	−	47.0901i	1.15136	−	1.58471i	0.739032	−	0.673670i	$-0.235283\pi$
$884$		0			0
$885$		0			0
$886$	−5.88073	+	8.95420i	−0.197567	+	0.300822i
$887$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$887$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$888$		0			0
$889$	2.81100	+	8.65136i	0.0942778	+	0.290157i
$890$		0			0
$891$	−17.0840	+	24.4773i	−0.572336	+	0.820019i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−24.5000	−	17.1974i	−0.818488	−	0.574524i
$897$		0			0
$898$	13.2501	+	35.0564i	0.442161	+	1.16985i
$899$		0			0
$900$	6.53938	−	29.2786i	0.217979	−	0.975953i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	51.8703	+	27.4472i	1.72518	+	0.912879i
$905$		0			0
$906$		0			0
$907$	55.8256	+	18.1389i	1.85366	+	0.602291i	0.996134	+	0.0878507i	$0.0279999\pi$
$907$	55.8256	+	18.1389i	1.85366	+	0.602291i	0.857526	+	0.514440i	$0.172000\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−4.94427	−	15.2169i	−0.163811	−	0.504159i	0.835136	−	0.550044i	$-0.185389\pi$
$911$	−4.94427	−	15.2169i	−0.163811	−	0.504159i	−0.998947	+	0.0458855i	$0.985389\pi$
$912$		0			0
$913$		0			0
$914$	−41.9066	−	11.4606i	−1.38615	−	0.379082i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	32.5305	+	10.5698i	1.07308	+	0.348665i	0.791687	−	0.610927i	$-0.209203\pi$
$919$	32.5305	+	10.5698i	1.07308	+	0.348665i	0.281394	+	0.959592i	$0.409203\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$			25.1756i			0.827769i
$926$	−38.7885	+	1.83249i	−1.27467	+	0.0602192i
$927$		0			0
$928$	−34.6896	+	40.6509i	−1.13874	+	1.33443i
$929$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$929$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$930$		0			0
$931$		0			0
$932$	38.8476	−	16.8186i	1.27249	−	0.550911i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$937$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$938$	−25.4316	+	20.3780i	−0.830370	+	0.665366i
$939$		0			0
$940$		0			0
$941$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$941$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	−5.76771	+	2.30593i	−0.187524	+	0.0749722i
$947$		−	58.2065i		−	1.89146i	−0.324956	−	0.945729i	$-0.605350\pi$
$947$		−	58.2065i		−	1.89146i	0.324956	−	0.945729i	$-0.394650\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−9.97347	−	13.7273i	−0.323072	−	0.444671i	0.616330	−	0.787488i	$-0.288619\pi$
$953$	−9.97347	−	13.7273i	−0.323072	−	0.444671i	−0.939402	+	0.342817i	$0.888619\pi$
$954$	33.9072	+	42.3158i	1.09779	+	1.37002i
$955$		0			0
$956$	−23.8090	+	40.2742i	−0.770037	+	1.30256i
$957$		0			0
$958$		0			0
$959$	10.9480	−	3.55722i	0.353529	−	0.114869i
$960$		0			0
$961$	−25.0795	+	18.2213i	−0.809017	+	0.587785i
$962$		0			0
$963$	17.8834	−	55.0394i	0.576284	−	1.77362i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	62.0397i		−	1.99506i	−0.0702371	−	0.997530i	$-0.522376\pi$
$967$		−	62.0397i		−	1.99506i	0.0702371	−	0.997530i	$-0.477624\pi$
$968$	21.5000	−	22.4889i	0.691036	−	0.722820i
$969$		0			0
$970$		0			0
$971$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$971$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$972$		0			0
$973$		0			0
$974$	32.8750	+	21.5909i	1.05338	+	0.691816i
$975$		0			0
$976$		0			0
$977$	19.1890	+	59.0577i	0.613911	+	1.88942i	0.416632	+	0.909075i	$0.363210\pi$
$977$	19.1890	+	59.0577i	0.613911	+	1.88942i	0.197278	+	0.980348i	$0.436790\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	19.2668	+	59.2970i	0.615140	+	1.89321i
$982$	−48.5593	+	38.9100i	−1.54959	+	1.24167i
$983$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$983$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−4.45217			−0.141571
$990$		0			0
$991$	−24.0000			−0.762385			−0.381193	−	0.924496i	$-0.624487\pi$
$991$	−24.0000			−0.762385			−0.381193	+	0.924496i	$0.624487\pi$
$992$		0			0
$993$		0			0
$994$	0.308861	−	0.116739i	0.00979649	−	0.00370273i
$995$		0			0
$996$		0			0
$997$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$997$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$998$	−37.5074	−	46.8088i	−1.18728	−	1.48171i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	616.2.bi.a.237.2	yes	8
7.6	odd	2	CM	616.2.bi.a.237.2	yes	8
8.5	even	2		616.2.bi.b.237.2	yes	8
11.2	odd	10		616.2.bi.b.13.2	yes	8
56.13	odd	2		616.2.bi.b.237.2	yes	8
77.13	even	10		616.2.bi.b.13.2	yes	8
88.13	odd	10	inner	616.2.bi.a.13.2	✓	8
616.13	even	10	inner	616.2.bi.a.13.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
616.2.bi.a.13.2	✓	8	88.13	odd	10	inner
616.2.bi.a.13.2	✓	8	616.13	even	10	inner
616.2.bi.a.237.2	yes	8	1.1	even	1	trivial
616.2.bi.a.237.2	yes	8	7.6	odd	2	CM
616.2.bi.b.13.2	yes	8	11.2	odd	10
616.2.bi.b.13.2	yes	8	77.13	even	10
616.2.bi.b.237.2	yes	8	8.5	even	2
616.2.bi.b.237.2	yes	8	56.13	odd	2

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:	\( N \)	\(=\)	\( 616 = 2^{3} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	616.bi (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41264 - 0.0667372i) q^{2} +(1.99109 - 0.188551i) q^{4} +(-1.55513 - 2.14046i) q^{7} +(2.80011 - 0.399234i) q^{8} +(-0.927051 - 2.85317i) q^{9} +O(q^{10})\)	\(q+(1.41264 - 0.0667372i) q^{2} +(1.99109 - 0.188551i) q^{4} +(-1.55513 - 2.14046i) q^{7} +(2.80011 - 0.399234i) q^{8} +(-0.927051 - 2.85317i) q^{9} +(3.13429 - 1.08453i) q^{11} +(-2.33969 - 2.91991i) q^{14} +(3.92890 - 0.750845i) q^{16} +(-1.50000 - 3.96863i) q^{18} +(4.35524 - 1.74122i) q^{22} +3.36187 q^{23} +(4.04508 + 2.93893i) q^{25} +(-3.50000 - 3.96863i) q^{28} +(-7.64279 + 5.55281i) q^{29} +(5.50000 - 1.32288i) q^{32} +(-2.38381 - 5.50613i) q^{36} +(2.95957 + 4.07350i) q^{37} -1.32431 q^{43} +(6.03618 - 2.75038i) q^{44} +(4.74910 - 0.224362i) q^{46} +(-2.16312 + 6.65740i) q^{49} +(5.91038 + 3.88168i) q^{50} +(-12.1554 + 3.94951i) q^{53} +(-5.20909 - 5.37265i) q^{56} +(-10.4259 + 8.35417i) q^{58} +(-4.66540 + 6.42137i) q^{63} +(7.68122 - 2.23580i) q^{64} -8.70972i q^{67} +(-0.0272696 + 0.0839271i) q^{71} +(-3.73493 - 7.61908i) q^{72} +(4.45265 + 5.55686i) q^{74} +(-7.19564 - 5.02223i) q^{77} +(2.57067 - 0.835260i) q^{79} +(-7.28115 + 5.29007i) q^{81} +(-1.87078 + 0.0883810i) q^{86} +(8.34338 - 4.28812i) q^{88} +(6.69379 - 0.633884i) q^{92} +(-2.61141 + 9.54885i) q^{98} +(-6.00000 - 7.93725i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} + 3 q^{4} + 5 q^{8} + 6 q^{9}+O(q^{10}) \) 8 * q - q^2 + 3 * q^4 + 5 * q^8 + 6 * q^9	\( 8 q - q^{2} + 3 q^{4} + 5 q^{8} + 6 q^{9} - 4 q^{11} + 7 q^{14} - q^{16} - 12 q^{18} + 5 q^{22} + 16 q^{23} + 10 q^{25} - 28 q^{28} + 4 q^{29} + 44 q^{32} - 9 q^{36} - 30 q^{37} - 24 q^{43} + 13 q^{44} + 8 q^{46} + 14 q^{49} + 5 q^{50} - 50 q^{53} - 7 q^{56} - 73 q^{58} - 9 q^{64} + 48 q^{71} - 15 q^{72} + 28 q^{74} + 14 q^{77} + 40 q^{79} - 18 q^{81} - 17 q^{86} + 3 q^{88} + q^{92} + 7 q^{98} - 48 q^{99}+O(q^{100}) \) 8 * q - q^2 + 3 * q^4 + 5 * q^8 + 6 * q^9 - 4 * q^11 + 7 * q^14 - q^16 - 12 * q^18 + 5 * q^22 + 16 * q^23 + 10 * q^25 - 28 * q^28 + 4 * q^29 + 44 * q^32 - 9 * q^36 - 30 * q^37 - 24 * q^43 + 13 * q^44 + 8 * q^46 + 14 * q^49 + 5 * q^50 - 50 * q^53 - 7 * q^56 - 73 * q^58 - 9 * q^64 + 48 * q^71 - 15 * q^72 + 28 * q^74 + 14 * q^77 + 40 * q^79 - 18 * q^81 - 17 * q^86 + 3 * q^88 + q^92 + 7 * q^98 - 48 * q^99

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