LMFDB - Embedded newform 616.2.bi.b.349.2

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			349.2
Root			$1.10362 + 0.884319i$ of defining polynomial
Character	$\chi$	$=$	616.349
Dual form			616.2.bi.b.293.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.10362 - 0.884319i) q^{2} +(0.435959 - 1.95191i) q^{4} +(-2.51626 - 0.817582i) q^{7} +(-1.24498 - 2.53969i) q^{8} +(2.42705 - 1.76336i) q^{9} +O(q^{10})$	\(q+(1.10362 - 0.884319i) q^{2} +(0.435959 - 1.95191i) q^{4} +(-2.51626 - 0.817582i) q^{7} +(-1.24498 - 2.53969i) q^{8} +(2.42705 - 1.76336i) q^{9} +(3.17317 - 0.964887i) q^{11} +(-3.50000 + 1.32288i) q^{14} +(-3.61988 - 1.70190i) q^{16} +(1.11917 - 4.09236i) q^{18} +(2.64871 - 3.87096i) q^{22} -7.50465 q^{23} +(-1.54508 - 4.75528i) q^{25} +(-2.69283 + 4.55507i) q^{28} +(1.42225 - 4.37724i) q^{29} +(-5.50000 + 1.32288i) q^{32} +(-2.38381 - 5.50613i) q^{36} +(8.53732 + 2.77394i) q^{37} +6.59794 q^{43} +(-0.500000 - 6.61438i) q^{44} +(-8.28229 + 6.63651i) q^{46} +(5.66312 + 4.11450i) q^{49} +(-5.91038 - 3.88168i) q^{50} +(8.48743 + 11.6819i) q^{53} +(1.05627 + 7.40839i) q^{56} +(-2.30125 - 6.08854i) q^{58} +(-7.54878 + 2.45275i) q^{63} +(-4.90007 + 6.32371i) q^{64} +15.1939i q^{67} +(7.95588 + 5.78028i) q^{71} +(-7.50000 - 3.96863i) q^{72} +(11.8750 - 4.48833i) q^{74} +(-8.77339 - 0.166419i) q^{77} +(-4.78485 - 6.58577i) q^{79} +(2.78115 - 8.55951i) q^{81} +(7.28162 - 5.83468i) q^{86} +(-6.40103 - 6.85761i) q^{88} +(-3.27172 + 14.6484i) q^{92} +(9.88847 - 0.467160i) q^{98} +(6.00000 - 7.93725i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 28 q^{14} - q^{16} - 3 q^{18} - 9 q^{22} + 16 q^{23} + 10 q^{25} - 7 q^{28} - 4 q^{29} - 44 q^{32} - 9 q^{36} + 30 q^{37} + 24 q^{43} - 4 q^{44} - 23 q^{46} + 14 q^{49} - 5 q^{50} + 50 q^{53} - 7 q^{56} + 2 q^{58} - 9 q^{64} + 48 q^{71} - 60 q^{72} - 28 q^{74} - 14 q^{77} + 40 q^{79} - 18 q^{81} - 12 q^{86} + 17 q^{88} - 24 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 - 28 * q^14 - q^16 - 3 * q^18 - 9 * q^22 + 16 * q^23 + 10 * q^25 - 7 * q^28 - 4 * q^29 - 44 * q^32 - 9 * q^36 + 30 * q^37 + 24 * q^43 - 4 * q^44 - 23 * q^46 + 14 * q^49 - 5 * q^50 + 50 * q^53 - 7 * q^56 + 2 * q^58 - 9 * q^64 + 48 * q^71 - 60 * q^72 - 28 * q^74 - 14 * q^77 + 40 * q^79 - 18 * q^81 - 12 * q^86 + 17 * q^88 - 24 * q^92 - 7 * q^98 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$57$	$309$	$353$	$463$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$-1$	$-1$	$1$

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 $

$2$	1.10362	−	0.884319i	0.780378	−	0.625308i
$2$	1.10362	−	0.884319i	0.780378	−	0.625308i
$3$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$3$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$4$	0.435959	−	1.95191i	0.217979	−	0.975953i
$5$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$5$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$6$		0			0
$7$	−2.51626	−	0.817582i	−0.951057	−	0.309017i
$7$	−2.51626	−	0.817582i	−0.951057	−	0.309017i
$8$	−1.24498	−	2.53969i	−0.440165	−	0.897917i
$9$	2.42705	−	1.76336i	0.809017	−	0.587785i
$10$		0			0
$11$	3.17317	−	0.964887i	0.956746	−	0.290924i
$11$	3.17317	−	0.964887i	0.956746	−	0.290924i
$12$		0			0
$13$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$13$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$14$	−3.50000	+	1.32288i	−0.935414	+	0.353553i
$15$		0			0
$16$	−3.61988	−	1.70190i	−0.904970	−	0.425475i
$17$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$17$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$18$	1.11917	−	4.09236i	0.263792	−	0.964580i
$19$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$19$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$20$		0			0
$21$		0			0
$22$	2.64871	−	3.87096i	0.564706	−	0.825292i
$23$	−7.50465			−1.56483			−0.782414	−	0.622758i	$-0.786012\pi$
$23$	−7.50465			−1.56483			−0.782414	+	0.622758i	$0.786012\pi$
$24$		0			0
$25$	−1.54508	−	4.75528i	−0.309017	−	0.951057i
$26$		0			0
$27$		0			0
$28$	−2.69283	+	4.55507i	−0.508897	+	0.860828i
$29$	1.42225	−	4.37724i	0.264105	−	0.812833i	−0.727793	−	0.685797i	$-0.759454\pi$
$29$	1.42225	−	4.37724i	0.264105	−	0.812833i	0.991898	−	0.127036i	$-0.0405463\pi$
$30$		0			0
$31$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$31$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$32$	−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
$37$	8.53732	+	2.77394i	1.40353	+	0.456033i	0.910330	−	0.413884i	$-0.135828\pi$
$37$	8.53732	+	2.77394i	1.40353	+	0.456033i	0.493197	+	0.869918i	$0.335828\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$41$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$42$		0			0
$43$	6.59794			1.00618			0.503088	−	0.864235i	$-0.332197\pi$
$43$	6.59794			1.00618			0.503088	+	0.864235i	$0.332197\pi$
$44$	−0.500000	−	6.61438i	−0.0753778	−	0.997155i
$45$		0			0
$46$	−8.28229	+	6.63651i	−1.22116	+	0.978500i
$47$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$47$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$48$		0			0
$49$	5.66312	+	4.11450i	0.809017	+	0.587785i
$50$	−5.91038	−	3.88168i	−0.835853	−	0.548953i
$51$		0			0
$52$		0			0
$53$	8.48743	+	11.6819i	1.16584	+	1.60464i	0.686803	+	0.726844i	$0.259014\pi$
$53$	8.48743	+	11.6819i	1.16584	+	1.60464i	0.479036	+	0.877795i	$0.340986\pi$
$54$		0			0
$55$		0			0
$56$	1.05627	+	7.40839i	0.141151	+	0.989988i
$57$		0			0
$58$	−2.30125	−	6.08854i	−0.302169	−	0.799464i
$59$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$59$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$60$		0			0
$61$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$61$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$62$		0			0
$63$	−7.54878	+	2.45275i	−0.951057	+	0.309017i
$64$	−4.90007	+	6.32371i	−0.612509	+	0.790464i
$65$		0			0
$66$		0			0
$67$			15.1939i			1.85623i	0.372295	+	0.928114i	$0.378571\pi$
$67$			15.1939i			1.85623i	−0.372295	+	0.928114i	$0.621429\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	7.95588	+	5.78028i	0.944189	+	0.685993i	0.949425	−	0.313993i	$-0.101667\pi$
$71$	7.95588	+	5.78028i	0.944189	+	0.685993i	−0.00523645	+	0.999986i	$0.501667\pi$
$72$	−7.50000	−	3.96863i	−0.883883	−	0.467707i
$73$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$73$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$74$	11.8750	−	4.48833i	1.38044	−	0.521758i
$75$		0			0
$76$		0			0
$77$	−8.77339	−	0.166419i	−0.999820	−	0.0189652i
$78$		0			0
$79$	−4.78485	−	6.58577i	−0.538337	−	0.740957i	0.450035	−	0.893011i	$-0.351411\pi$
$79$	−4.78485	−	6.58577i	−0.538337	−	0.740957i	−0.988372	+	0.152053i	$0.951411\pi$
$80$		0			0
$81$	2.78115	−	8.55951i	0.309017	−	0.951057i
$82$		0			0
$83$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$83$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$84$		0			0
$85$		0			0
$86$	7.28162	−	5.83468i	0.785197	−	0.629170i
$87$		0			0
$88$	−6.40103	−	6.85761i	−0.682352	−	0.731023i
$89$		0			0		1.00000			$0$
$89$		0			0		−1.00000			$\pi$
$90$		0			0
$91$		0			0
$92$	−3.27172	+	14.6484i	−0.341100	+	1.52720i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$97$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$98$	9.88847	−	0.467160i	0.998886	−	0.0471903i
$99$	6.00000	−	7.93725i	0.603023	−	0.797724i
$100$	−9.95546	+	0.942755i	−0.995546	+	0.0942755i
$101$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$101$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$102$		0			0
$103$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$103$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$104$		0			0
$105$		0			0
$106$	19.6975	+	5.38684i	1.91319	+	0.523217i
$107$	−0.354696	−	1.09164i	−0.0342898	−	0.105533i	0.932447	−	0.361308i	$-0.117670\pi$
$107$	−0.354696	−	1.09164i	−0.0342898	−	0.105533i	−0.966736	+	0.255774i	$0.917670\pi$
$108$		0			0
$109$	4.50273			0.431283			0.215642	−	0.976473i	$-0.430816\pi$
$109$	4.50273			0.431283			0.215642	+	0.976473i	$0.430816\pi$
$110$		0			0
$111$		0			0
$112$	7.71711	+	7.24197i	0.729199	+	0.684302i
$113$	4.34450	+	13.3710i	0.408696	+	1.25784i	0.917769	+	0.397114i	$0.129988\pi$
$113$	4.34450	+	13.3710i	0.408696	+	1.25784i	−0.509073	+	0.860724i	$0.670012\pi$
$114$		0			0
$115$		0			0
$116$	−7.92392	−	4.68440i	−0.735717	−	0.434935i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	9.13799	−	6.12350i	0.830726	−	0.556682i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	−6.16198	+	9.38243i	−0.548953	+	0.835853i
$127$	−11.8276	+	16.2794i	−1.04953	+	1.44456i	−0.160322	+	0.987065i	$0.551253\pi$
$127$	−11.8276	+	16.2794i	−1.04953	+	1.44456i	−0.889212	+	0.457495i	$0.848747\pi$
$128$	0.184357	+	11.3122i	0.0162950	+	0.999867i
$129$		0			0
$130$		0			0
$131$		0			0		1.00000			$0$
$131$		0			0		−1.00000			$\pi$
$132$		0			0
$133$		0			0
$134$	13.4362	+	16.7683i	1.16072	+	1.44856i
$135$		0			0
$136$		0			0
$137$	18.7856	+	13.6485i	1.60496	+	1.16607i	0.877051	+	0.480397i	$0.159507\pi$
$137$	18.7856	+	13.6485i	1.60496	+	1.16607i	0.727909	+	0.685674i	$0.240493\pi$
$138$		0			0
$139$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$139$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$140$		0			0
$141$		0			0
$142$	13.8919	−	0.656294i	1.16578	−	0.0550750i
$143$		0			0
$144$	−11.7867	+	2.25253i	−0.982224	+	0.187711i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	9.13640	−	15.4547i	0.751007	−	1.27037i
$149$	−17.7984	−	12.9313i	−1.45810	−	1.05937i	−0.983853	−	0.178979i	$-0.942720\pi$
$149$	−17.7984	−	12.9313i	−1.45810	−	1.05937i	−0.474247	−	0.880392i	$-0.657280\pi$
$150$		0			0
$151$	−20.1531	+	6.54813i	−1.64003	+	0.532879i	−0.976546	−	0.215308i	$-0.930924\pi$
$151$	−20.1531	+	6.54813i	−1.64003	+	0.532879i	−0.663487	+	0.748187i	$0.730924\pi$
$152$		0			0
$153$		0			0
$154$	−9.82966	+	7.57481i	−0.792097	+	0.610396i
$155$		0			0
$156$		0			0
$157$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$157$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$158$	−11.1046	−	3.03687i	−0.883433	−	0.241600i
$159$		0			0
$160$		0			0
$161$	18.8837	+	6.13567i	1.48824	+	0.483559i
$162$	−4.50000	−	11.9059i	−0.353553	−	0.935414i
$163$	−14.0637	−	19.3570i	−1.10156	−	1.51616i	−0.833307	−	0.552811i	$-0.813555\pi$
$163$	−14.0637	−	19.3570i	−1.10156	−	1.51616i	−0.268249	−	0.963350i	$-0.586445\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$167$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$168$		0			0
$169$	4.01722	−	12.3637i	0.309017	−	0.951057i
$170$		0			0
$171$		0			0
$172$	2.87643	−	12.8786i	0.219326	−	0.981981i
$173$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$173$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$174$		0			0
$175$			13.2288i			1.00000i
$176$	−13.1286	−	1.90764i	−0.989608	−	0.143794i
$177$		0			0
$178$		0			0
$179$	11.3937	−	3.70204i	0.851605	−	0.276703i	0.149487	−	0.988764i	$-0.452238\pi$
$179$	11.3937	−	3.70204i	0.851605	−	0.276703i	0.702118	+	0.712060i	$0.252238\pi$
$180$		0			0
$181$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$181$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$182$		0			0
$183$		0			0
$184$	9.34311	+	19.0595i	0.688783	+	1.40509i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	6.80563	−	20.9456i	0.492438	−	1.51557i	−0.328474	−	0.944513i	$-0.606534\pi$
$191$	6.80563	−	20.9456i	0.492438	−	1.51557i	0.820912	−	0.571055i	$-0.193466\pi$
$192$		0			0
$193$	3.84619	−	5.29383i	0.276855	−	0.381058i	−0.647834	−	0.761781i	$-0.724325\pi$
$193$	3.84619	−	5.29383i	0.276855	−	0.381058i	0.924689	+	0.380724i	$0.124325\pi$
$194$		0			0
$195$		0			0
$196$	10.5000	−	9.26013i	0.750000	−	0.661438i
$197$	18.0995			1.28953			0.644767	−	0.764379i	$-0.276954\pi$
$197$	18.0995			1.28953			0.644767	+	0.764379i	$0.276954\pi$
$198$	−0.397341	−	14.0656i	−0.0282378	−	0.999601i
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$	−10.1534	+	9.84425i	−0.717951	+	0.696094i
$201$		0			0
$202$		0			0
$203$	−7.15750	+	9.85146i	−0.502358	+	0.691437i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−18.2142	+	13.2334i	−1.26597	+	0.919783i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−17.3570	+	12.6106i	−1.19490	+	0.868148i	−0.993774	−	0.111417i	$-0.964461\pi$
$211$	−17.3570	+	12.6106i	−1.19490	+	0.868148i	−0.201129	+	0.979565i	$0.564461\pi$
$212$	26.5022	−	11.4738i	1.82018	−	0.788026i
$213$		0			0
$214$	−1.35681	−	0.891096i	−0.0927497	−	0.0609140i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	4.96931	−	3.98185i	0.336564	−	0.269685i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$223$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$224$	14.9210	+	1.16800i	0.996950	+	0.0780405i
$225$	−12.1353	−	8.81678i	−0.809017	−	0.587785i
$226$	16.6189	+	10.9146i	1.10547	+	0.726028i
$227$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$227$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$228$		0			0
$229$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$229$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$230$		0			0
$231$		0			0
$232$	−12.8875	+	1.83748i	−0.846106	+	0.120636i
$233$	−12.4411	−	17.1237i	−0.815042	−	1.12181i	−0.990526	−	0.137326i	$-0.956149\pi$
$233$	−12.4411	−	17.1237i	−0.815042	−	1.12181i	0.175484	−	0.984482i	$-0.443851\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	29.3012	−	9.52055i	1.89534	−	0.615833i	0.921614	−	0.388108i	$-0.126871\pi$
$239$	29.3012	−	9.52055i	1.89534	−	0.615833i	0.973726	−	0.227725i	$-0.0731287\pi$
$240$		0			0
$241$		0			0			−	1.00000i	$-0.5\pi$
$241$		0			0				1.00000i	$0.5\pi$
$242$	4.66974	−	14.8389i	0.300183	−	0.953882i
$243$		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		−0.587785	−	0.809017i	$-0.700000\pi$
$251$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$252$	1.49658	+	15.8038i	0.0942755	+	0.995546i
$253$	−23.8135	+	7.24115i	−1.49714	+	0.455247i
$254$	1.34291	+	28.4257i	0.0842618	+	1.78358i
$255$		0			0
$256$	10.2071	+	12.3214i	0.637941	+	0.770085i
$257$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$257$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$258$		0			0
$259$	−19.2142	−	13.9599i	−1.19391	−	0.867427i
$260$		0			0
$261$	−4.26675	−	13.1317i	−0.264105	−	0.812833i
$262$		0			0
$263$		−	14.5282i		−	0.895848i	−0.894072	−	0.447924i	$-0.852164\pi$
$263$		−	14.5282i		−	0.895848i	0.894072	−	0.447924i	$-0.147836\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	29.6571	+	6.62391i	1.81159	+	0.404620i
$269$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$269$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$270$		0			0
$271$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$271$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$272$		0			0
$273$		0			0
$274$	32.8018	−	1.54965i	1.98163	−	0.0936180i
$275$	−9.49113	−	13.5985i	−0.572336	−	0.820019i
$276$		0			0
$277$	−21.9284	+	15.9319i	−1.31755	+	0.957254i	−0.317588	+	0.948229i	$0.602873\pi$
$277$	−21.9284	+	15.9319i	−1.31755	+	0.957254i	−0.999959	+	0.00902525i	$0.997127\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−19.0478	+	26.2171i	−1.13630	+	1.56398i	−0.360782	+	0.932650i	$0.617490\pi$
$281$	−19.0478	+	26.2171i	−1.13630	+	1.56398i	−0.775515	+	0.631329i	$0.782510\pi$
$282$		0			0
$283$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$283$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$284$	14.7510	−	13.0092i	0.875311	−	0.771952i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−11.0161	+	12.9091i	−0.649129	+	0.760679i
$289$	−5.25329	−	16.1680i	−0.309017	−	0.951057i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$293$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$294$		0			0
$295$		0			0
$296$	−3.58379	−	25.1357i	−0.208304	−	1.46098i
$297$		0			0
$298$	−31.0780	+	1.46822i	−1.80030	+	0.0850516i
$299$		0			0
$300$		0			0
$301$	−16.6021	−	5.39436i	−0.956930	−	0.310925i
$302$	−16.4507	+	25.0484i	−0.946632	+	1.44137i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$	−4.14967	+	17.0523i	−0.236449	+	0.971644i
$309$		0			0
$310$		0			0
$311$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$311$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$312$		0			0
$313$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$313$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$314$		0			0
$315$		0			0
$316$	−14.9408	+	6.46845i	−0.840486	+	0.363879i
$317$	−6.71419	−	9.24129i	−0.377107	−	0.519043i	0.577708	−	0.816243i	$-0.303947\pi$
$317$	−6.71419	−	9.24129i	−0.377107	−	0.519043i	−0.954815	+	0.297200i	$0.903947\pi$
$318$		0			0
$319$	0.289499	−	15.2620i	0.0162088	−	0.854509i
$320$		0			0
$321$		0			0
$322$	26.2663	−	9.92772i	1.46376	−	0.553250i
$323$		0			0
$324$	−15.4949	−	9.16014i	−0.860828	−	0.508897i
$325$		0			0
$326$	−32.6388	−	8.92603i	−1.80770	−	0.494367i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$			35.8732i			1.97177i	0.167426	+	0.985885i	$0.446455\pi$
$331$			35.8732i			1.97177i	−0.167426	+	0.985885i	$0.553545\pi$
$332$		0			0
$333$	25.6120	−	8.32183i	1.40353	−	0.456033i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−20.9147	−	6.79560i	−1.13930	−	0.370180i	−0.322195	−	0.946673i	$-0.604421\pi$
$337$	−20.9147	−	6.79560i	−1.13930	−	0.370180i	−0.817102	+	0.576493i	$0.804421\pi$
$338$	−6.50000	−	17.1974i	−0.353553	−	0.935414i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−10.8859	−	14.9832i	−0.587785	−	0.809017i
$344$	−8.21427	−	16.7567i	−0.442884	−	0.903462i
$345$		0			0
$346$		0			0
$347$	20.2318	+	14.6993i	1.08610	+	0.789100i	0.978737	−	0.205120i	$-0.0657585\pi$
$347$	20.2318	+	14.6993i	1.08610	+	0.789100i	0.107366	+	0.994220i	$0.465758\pi$
$348$		0			0
$349$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$349$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$350$	11.6984	+	14.5995i	0.625308	+	0.780378i
$351$		0			0
$352$	−16.1760	+	9.50459i	−0.862183	+	0.506596i
$353$		0			0		1.00000			$0$
$353$		0			0		−1.00000			$\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	9.30055	−	14.1613i	0.491549	−	0.748449i
$359$	18.1220	+	5.88820i	0.956443	+	0.310767i	0.745331	−	0.666695i	$-0.232292\pi$
$359$	18.1220	+	5.88820i	0.956443	+	0.310767i	0.211112	+	0.977462i	$0.432292\pi$
$360$		0			0
$361$	−15.3713	+	11.1679i	−0.809017	+	0.587785i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$367$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$368$	27.1659	+	12.7722i	1.41612	+	0.665796i
$369$		0			0
$370$		0			0
$371$	−11.8056	−	36.3340i	−0.612918	−	1.88637i
$372$		0			0
$373$	−22.0000			−1.13912			−0.569558	−	0.821951i	$-0.692886\pi$
$373$	−22.0000			−1.13912			−0.569558	+	0.821951i	$0.692886\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.0196740	−	0.0270790i	0.00101059	−	0.00139095i	−0.808511	−	0.588481i	$-0.799726\pi$
$379$	0.0196740	−	0.0270790i	0.00101059	−	0.00139095i	0.809522	+	0.587090i	$0.199726\pi$
$380$		0			0
$381$		0			0
$382$	−11.0117	−	29.1343i	−0.563409	−	1.49064i
$383$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$383$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$384$		0			0
$385$		0			0
$386$	−0.436697	−	9.24364i	−0.0222273	−	0.470489i
$387$	16.0135	−	11.6345i	0.814013	−	0.591415i
$388$		0			0
$389$	31.2611	+	10.1573i	1.58500	+	0.514997i	0.963338	−	0.268290i	$-0.0864585\pi$
$389$	31.2611	+	10.1573i	1.58500	+	0.514997i	0.621660	+	0.783287i	$0.286458\pi$
$390$		0			0
$391$		0			0
$392$	3.39911	−	19.5050i	0.171681	−	0.985153i
$393$		0			0
$394$	19.9750	−	16.0057i	1.00632	−	0.806356i
$395$		0			0
$396$	−12.8770	−	15.1718i	−0.647095	−	0.762409i
$397$		0			0			−	1.00000i	$-0.5\pi$
$397$		0			0				1.00000i	$0.5\pi$
$398$		0			0
$399$		0			0
$400$	−2.50000	+	19.8431i	−0.125000	+	0.992157i
$401$	−7.78557	−	5.65655i	−0.388793	−	0.282475i	0.376168	−	0.926552i	$-0.377242\pi$
$401$	−7.78557	−	5.65655i	−0.388793	−	0.282475i	−0.764961	+	0.644077i	$0.777242\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	0.812664	+	17.2018i	0.0403318	+	0.853711i
$407$	29.7669	+	0.564636i	1.47549	+	0.0279880i
$408$		0			0
$409$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$409$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	−8.39902	+	30.7118i	−0.412789	+	1.50940i
$415$		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
$421$	−14.1864	+	4.60945i	−0.691404	+	0.224651i	−0.633581	−	0.773676i	$-0.718416\pi$
$421$	−14.1864	+	4.60945i	−0.691404	+	0.224651i	−0.0578225	+	0.998327i	$0.518416\pi$
$422$	−8.00374	+	29.2664i	−0.389616	+	1.42467i
$423$		0			0
$424$	19.1019	−	36.0992i	0.927671	−	1.75313i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−2.28542	+	0.216423i	−0.110470	+	0.0104612i
$429$		0			0
$430$		0			0
$431$	−13.0829	−	18.0071i	−0.630182	−	0.867371i	0.367862	−	0.929880i	$-0.380090\pi$
$431$	−13.0829	−	18.0071i	−0.630182	−	0.867371i	−0.998044	+	0.0625092i	$0.980090\pi$
$432$		0			0
$433$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$433$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$434$		0			0
$435$		0			0
$436$	1.96300	−	8.78891i	0.0940109	−	0.420912i
$437$		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
$443$	17.3194	−	5.62742i	0.822870	−	0.267367i	0.132831	−	0.991139i	$-0.457593\pi$
$443$	17.3194	−	5.62742i	0.822870	−	0.267367i	0.690039	+	0.723772i	$0.257593\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	17.5000	−	11.9059i	0.826797	−	0.562500i
$449$	−32.0711	+	23.3010i	−1.51353	+	1.09964i	−0.548950	+	0.835855i	$0.684972\pi$
$449$	−32.0711	+	23.3010i	−1.51353	+	1.09964i	−0.964580	+	0.263790i	$0.915028\pi$
$450$	−21.1896	+	1.00106i	−0.998886	+	0.0471903i
$451$		0			0
$452$	27.9930	−	2.65086i	1.31668	−	0.124686i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−11.0431	+	15.1995i	−0.516575	+	0.711004i	−0.985011	−	0.172493i	$-0.944818\pi$
$457$	−11.0431	+	15.1995i	−0.516575	+	0.711004i	0.468436	+	0.883497i	$0.344818\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		1.00000			$0$
$461$		0			0		−1.00000			$\pi$
$462$		0			0
$463$	41.6915			1.93757			0.968784	−	0.247907i	$-0.0797429\pi$
$463$	41.6915			1.93757			0.968784	+	0.247907i	$0.0797429\pi$
$464$	−12.5980	+	13.4245i	−0.584848	+	0.623219i
$465$		0			0
$466$	−28.8730	−	7.89616i	−1.33752	−	0.365782i
$467$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$467$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$468$		0			0
$469$	12.4223	−	38.2318i	0.573606	−	1.76538i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	20.9364	−	6.36627i	0.962655	−	0.292721i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	41.1989	+	13.3863i	1.88637	+	0.612918i
$478$	23.9183	−	36.4187i	1.09400	−	1.66575i
$479$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$479$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−7.96871	−	20.5061i	−0.362214	−	0.932095i
$485$		0			0
$486$		0			0
$487$	0.727878	+	2.24018i	0.0329833	+	0.101512i	0.966193	−	0.257821i	$-0.0830043\pi$
$487$	0.727878	+	2.24018i	0.0329833	+	0.101512i	−0.933210	+	0.359333i	$0.883004\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−13.5967	+	41.8465i	−0.613613	+	1.88851i	−0.193249	+	0.981150i	$0.561903\pi$
$491$	−13.5967	+	41.8465i	−0.613613	+	1.88851i	−0.420363	+	0.907356i	$0.638097\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−15.2932	−	21.0493i	−0.685993	−	0.944189i
$498$		0			0
$499$	−40.4816	−	13.1533i	−1.81220	−	0.588821i	−0.999985	−	0.00546838i	$-0.998259\pi$
$499$	−40.4816	−	13.1533i	−1.81220	−	0.588821i	−0.812219	−	0.583352i	$-0.801741\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$503$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$504$	15.6273	+	16.1180i	0.696094	+	0.717951i
$505$		0			0
$506$	−19.8776	+	29.0502i	−0.883668	+	1.29144i
$507$		0			0
$508$	26.6194	+	30.1836i	1.18105	+	1.33918i
$509$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$509$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$510$		0			0
$511$		0			0
$512$	22.1607	+	4.57181i	0.979376	+	0.202047i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	−33.5502	+	1.58501i	−1.47411	+	0.0696414i
$519$		0			0
$520$		0			0
$521$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$521$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$522$	−16.3215	−	10.7193i	−0.714373	−	0.469169i
$523$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$523$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$524$		0			0
$525$		0			0
$526$	−12.8476	−	16.0336i	−0.560181	−	0.699100i
$527$		0			0
$528$		0			0
$529$	33.3198			1.44869
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	38.5878	−	18.9160i	1.66674	−	0.817048i
$537$		0			0
$538$		0			0
$539$	21.9401	+	7.59172i	0.945025	+	0.326998i
$540$		0			0
$541$	−32.9284	+	23.9239i	−1.41570	+	1.02857i	−0.423238	+	0.906019i	$0.639107\pi$
$541$	−32.9284	+	23.9239i	−1.41570	+	1.02857i	−0.992463	+	0.122548i	$0.960893\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−13.5967	−	41.8465i	−0.581355	−	1.78923i	−0.613440	−	0.789741i	$-0.710215\pi$
$547$	−13.5967	−	41.8465i	−0.581355	−	1.78923i	0.0320849	−	0.999485i	$-0.489785\pi$
$548$	34.8304	−	30.7175i	1.48788	−	1.31219i
$549$		0			0
$550$	−22.5000	−	6.61438i	−0.959403	−	0.282038i
$551$		0			0
$552$		0			0
$553$	6.65550	+	20.4835i	0.283021	+	0.871048i
$554$	−10.1117	+	36.9744i	−0.429606	+	1.57089i
$555$		0			0
$556$		0			0
$557$	9.57775	−	29.4773i	0.405822	−	1.24899i	−0.514384	−	0.857560i	$-0.671980\pi$
$557$	9.57775	−	29.4773i	0.405822	−	1.24899i	0.920207	−	0.391433i	$-0.128020\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	2.16269	+	45.7781i	0.0912276	+	1.93103i
$563$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$563$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−13.9962	+	19.2641i	−0.587785	+	0.809017i
$568$	4.77527	−	27.4018i	0.200366	−	1.14975i
$569$	−40.2601	+	13.0813i	−1.68779	+	0.548397i	−0.986398	−	0.164375i	$-0.947439\pi$
$569$	−40.2601	+	13.0813i	−1.68779	+	0.548397i	−0.701395	+	0.712773i	$0.747439\pi$
$570$		0			0
$571$	44.0566			1.84371			0.921856	−	0.387534i	$-0.126673\pi$
$571$	44.0566			1.84371			0.921856	+	0.387534i	$0.126673\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	11.5953	+	35.6868i	0.483559	+	1.48824i
$576$	−0.741773	+	23.9885i	−0.0309072	+	0.999522i
$577$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$577$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$578$	−20.0953	−	13.1977i	−0.835853	−	0.548953i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	38.2038	+	28.8794i	1.58224	+	1.19606i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$587$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−26.1831	−	24.5710i	−1.07612	−	1.00986i
$593$		0			0			−	1.00000i	$-0.5\pi$
$593$		0			0				1.00000i	$0.5\pi$
$594$		0			0
$595$		0			0
$596$	−33.0000	+	29.1033i	−1.35173	+	1.19212i
$597$		0			0
$598$		0			0
$599$	20.4997	+	14.8939i	0.837597	+	0.608550i	0.921698	−	0.387907i	$-0.126802\pi$
$599$	20.4997	+	14.8939i	0.837597	+	0.608550i	−0.0841014	+	0.996457i	$0.526802\pi$
$600$		0			0
$601$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$601$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$602$	−23.0928	+	8.72825i	−0.941191	+	0.355737i
$603$	26.7922	+	36.8763i	1.09106	+	1.50172i
$604$	3.99543	+	42.1916i	0.162572	+	1.71675i
$605$		0			0
$606$		0			0
$607$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$607$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	15.2668	+	46.9862i	0.616618	+	1.89776i	0.372644	+	0.927974i	$0.378451\pi$
$613$	15.2668	+	46.9862i	0.616618	+	1.89776i	0.243974	+	0.969782i	$0.421549\pi$
$614$		0			0
$615$		0			0
$616$	10.5000	+	22.4889i	0.423057	+	0.906103i
$617$	−45.9166			−1.84853			−0.924266	−	0.381749i	$-0.875322\pi$
$617$	−45.9166			−1.84853			−0.924266	+	0.381749i	$0.875322\pi$
$618$		0			0
$619$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$619$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−20.2254	+	14.6946i	−0.809017	+	0.587785i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	12.4683	−	38.3736i	0.496357	−	1.52763i	−0.318475	−	0.947931i	$-0.603171\pi$
$631$	12.4683	−	38.3736i	0.496357	−	1.52763i	0.814832	−	0.579698i	$-0.196829\pi$
$632$	−10.7688	+	20.3512i	−0.428361	+	0.809526i
$633$		0			0
$634$	−15.5822	−	4.26140i	−0.618847	−	0.169242i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	−13.1770	−	17.0995i	−0.521683	−	0.676976i
$639$	29.5020			1.16708
$640$		0			0
$641$	15.3445	+	47.2255i	0.606071	+	1.86530i	0.489251	+	0.872143i	$0.337270\pi$
$641$	15.3445	+	47.2255i	0.606071	+	1.86530i	0.116820	+	0.993153i	$0.462730\pi$
$642$		0			0
$643$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$643$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$644$	20.2088	−	34.1842i	0.796336	−	1.34705i
$645$		0			0
$646$		0			0
$647$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$647$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$648$	−25.2010	+	3.59311i	−0.989988	+	0.141151i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−43.9143	+	19.0122i	−1.71982	+	0.744575i
$653$	48.3357	+	15.7052i	1.89152	+	0.614593i	0.978326	+	0.207072i	$0.0663936\pi$
$653$	48.3357	+	15.7052i	1.89152	+	0.614593i	0.913196	+	0.407520i	$0.133606\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	44.0000			1.71400			0.856998	−	0.515319i	$-0.172327\pi$
$659$	44.0000			1.71400			0.856998	+	0.515319i	$0.172327\pi$
$660$		0			0
$661$		0			0			−	1.00000i	$-0.5\pi$
$661$		0			0				1.00000i	$0.5\pi$
$662$	31.7234	+	39.5904i	1.23296	+	1.53873i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	20.9067	−	31.8333i	0.810120	−	1.23351i
$667$	−10.6735	+	32.8497i	−0.413280	+	1.27194i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−30.4948	−	41.9725i	−1.17549	−	1.61792i	−0.597281	−	0.802032i	$-0.703752\pi$
$673$	−30.4948	−	41.9725i	−1.17549	−	1.61792i	−0.578208	−	0.815890i	$-0.696248\pi$
$674$	−29.0914	+	10.9955i	−1.12056	+	0.423532i
$675$		0			0
$676$	−22.3815	−	13.2313i	−0.860828	−	0.508897i
$677$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$677$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$			47.8198i			1.82977i	0.403711	+	0.914886i	$0.367720\pi$
$683$			47.8198i			1.82977i	−0.403711	+	0.914886i	$0.632280\pi$
$684$		0			0
$685$		0			0
$686$	−25.2639	−	6.90914i	−0.964580	−	0.263792i
$687$		0			0
$688$	−23.8837	−	11.2290i	−0.910559	−	0.428103i
$689$		0			0
$690$		0			0
$691$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$691$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$692$		0			0
$693$	−21.5869	+	15.0667i	−0.820019	+	0.572336i
$694$	35.3272	−	1.66896i	1.34100	−	0.0633528i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	25.8213	+	5.76719i	0.975953	+	0.217979i
$701$	15.3604	+	47.2743i	0.580153	+	1.78553i	0.617922	+	0.786239i	$0.287975\pi$
$701$	15.3604	+	47.2743i	0.580153	+	1.78553i	−0.0377695	+	0.999286i	$0.512025\pi$
$702$		0			0
$703$		0			0
$704$	−9.44708	+	24.7942i	−0.356050	+	0.934467i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	27.2355	−	37.4865i	1.02285	−	1.40784i	0.112667	−	0.993633i	$-0.464061\pi$
$709$	27.2355	−	37.4865i	1.02285	−	1.40784i	0.910185	−	0.414202i	$-0.135939\pi$
$710$		0			0
$711$	−23.2261	−	7.54663i	−0.871048	−	0.283021i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−2.25885	−	23.8534i	−0.0844172	−	0.891443i
$717$		0			0
$718$	25.2069	−	9.52730i	0.940712	−	0.355556i
$719$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$719$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$720$		0			0
$721$		0			0
$722$	−7.08811	+	25.9183i	−0.263792	+	0.964580i
$723$		0			0
$724$		0			0
$725$	−23.0125			−0.854663
$726$		0			0
$727$		0			0		1.00000			$0$
$727$		0			0		−1.00000			$\pi$
$728$		0			0
$729$	−8.34346	−	25.6785i	−0.309017	−	0.951057i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$733$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$734$		0			0
$735$		0			0
$736$	41.2756	−	9.92772i	1.52144	−	0.365941i
$737$	14.6604	+	48.2128i	0.540022	+	1.77594i
$738$		0			0
$739$	41.5832	−	30.2120i	1.52966	−	1.11137i	0.573238	−	0.819389i	$-0.305687\pi$
$739$	41.5832	−	30.2120i	1.52966	−	1.11137i	0.956425	−	0.291977i	$-0.0943129\pi$
$740$		0			0
$741$		0			0
$742$	−45.1598	−	29.6590i	−1.65787	−	1.08882i
$743$	31.4335	−	43.2645i	1.15318	−	1.58722i	0.419453	−	0.907777i	$-0.362222\pi$
$743$	31.4335	−	43.2645i	1.15318	−	1.58722i	0.733729	−	0.679442i	$-0.237778\pi$
$744$		0			0
$745$		0			0
$746$	−24.2797	+	19.4550i	−0.888942	+	0.712299i
$747$		0			0
$748$		0			0
$749$			3.03685i			0.110964i
$750$		0			0
$751$	−3.19208	−	9.82420i	−0.116481	−	0.358490i	0.875772	−	0.482724i	$-0.160353\pi$
$751$	−3.19208	−	9.82420i	−0.116481	−	0.358490i	−0.992253	+	0.124234i	$0.960353\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−23.6891	−	32.6052i	−0.860994	−	1.18506i	−0.981332	−	0.192323i	$-0.938398\pi$
$757$	−23.6891	−	32.6052i	−0.860994	−	1.18506i	0.120338	−	0.992733i	$-0.461602\pi$
$758$	−0.00223379	−	0.0472831i	−8.11350e−5	−	0.00171740i
$759$		0			0
$760$		0			0
$761$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$761$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$762$		0			0
$763$	−11.3300	−	3.68135i	−0.410175	−	0.133274i
$764$	−37.9168	−	22.4154i	−1.37178	−	0.810959i
$765$		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
$772$	−8.65627	−	9.81529i	−0.311546	−	0.353260i
$773$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$773$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$774$	7.38425	−	27.0012i	0.265421	−	0.970537i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	43.4827	−	16.4349i	1.55893	−	0.589220i
$779$		0			0
$780$		0			0
$781$	30.8227	+	10.6653i	1.10292	+	0.381634i
$782$		0			0
$783$		0			0
$784$	−13.4973	−	24.5321i	−0.482048	−	0.876145i
$785$		0			0
$786$		0			0
$787$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$787$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$788$	7.89062	−	35.3285i	0.281092	−	1.25853i
$789$		0			0
$790$		0			0
$791$		−	37.1969i		−	1.32257i
$792$	−27.6280	−	5.35646i	−0.981719	−	0.190334i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$797$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$798$		0			0
$799$		0			0
$800$	14.7886	+	24.1101i	0.522856	+	0.852421i
$801$		0			0
$802$	−13.5945	+	0.642245i	−0.480039	+	0.0226785i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	13.5536	−	18.6550i	0.476521	−	0.655874i	−0.501311	−	0.865267i	$-0.667149\pi$
$809$	13.5536	−	18.6550i	0.476521	−	0.655874i	0.977832	+	0.209393i	$0.0671487\pi$
$810$		0			0
$811$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$811$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$812$	16.1088	+	18.2656i	0.565306	+	0.640997i
$813$		0			0
$814$	33.3507	−	25.7003i	1.16894	−	0.900795i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	6.79837	−	20.9232i	0.237265	−	0.730226i	−0.759548	−	0.650451i	$-0.774580\pi$
$821$	6.79837	−	20.9232i	0.237265	−	0.730226i	0.996813	−	0.0797750i	$-0.0254202\pi$
$822$		0			0
$823$	−43.5906	+	31.6704i	−1.51947	+	1.10396i	−0.557725	+	0.830026i	$0.688326\pi$
$823$	−43.5906	+	31.6704i	−1.51947	+	1.10396i	−0.961748	+	0.273936i	$0.911674\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	35.5967	−	25.8626i	1.23782	−	0.899329i	0.240369	−	0.970682i	$-0.422732\pi$
$827$	35.5967	−	25.8626i	1.23782	−	0.899329i	0.997451	+	0.0713526i	$0.0227315\pi$
$828$	17.8897	+	41.3216i	0.621710	+	1.43602i
$829$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$829$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$830$		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		−0.309017	−	0.951057i	$-0.600000\pi$
$839$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$840$		0			0
$841$	6.32408	+	4.59471i	0.218072	+	0.158438i
$842$	−11.5802	+	17.6324i	−0.399080	+	0.607653i
$843$		0			0
$844$	17.0477	+	39.3769i	0.586807	+	1.35541i
$845$		0			0
$846$		0			0
$847$	−28.0000	+	7.93725i	−0.962091	+	0.272727i
$848$	−10.8420	−	56.7320i	−0.372315	−	1.94819i
$849$		0			0
$850$		0			0
$851$	−64.0696	−	20.8175i	−2.19628	−	0.713614i
$852$		0			0
$853$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$853$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$854$		0			0
$855$		0			0
$856$	−2.33085	+	2.25989i	−0.0796668	+	0.0772414i
$857$		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
$862$	−30.3626	−	8.30353i	−1.03415	−	0.282819i
$863$	6.47214	+	4.70228i	0.220314	+	0.160068i	0.692468	−	0.721449i	$-0.256523\pi$
$863$	6.47214	+	4.70228i	0.220314	+	0.160068i	−0.472154	+	0.881516i	$0.656523\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−21.5376	−	16.2809i	−0.730615	−	0.552293i
$870$		0			0
$871$		0			0
$872$	−5.60579	−	11.4355i	−0.189836	−	0.387257i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	6.73325	+	20.7228i	0.227366	+	0.699759i	0.998043	+	0.0625337i	$0.0199181\pi$
$877$	6.73325	+	20.7228i	0.227366	+	0.699759i	−0.770677	+	0.637226i	$0.780082\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	23.1760	−	18.5707i	0.780378	−	0.625308i
$883$	−55.3577	+	17.9868i	−1.86293	+	0.605304i	−0.869072	+	0.494686i	$0.835283\pi$
$883$	−55.3577	+	17.9868i	−1.86293	+	0.605304i	−0.993863	+	0.110619i	$0.964717\pi$
$884$		0			0
$885$		0			0
$886$	14.1376	−	21.5264i	0.474963	−	0.723194i
$887$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$887$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$888$		0			0
$889$	43.0711	−	31.2930i	1.44456	−	1.04953i
$890$		0			0
$891$	0.566103	−	29.8443i	0.0189652	−	0.999820i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	8.78477	−	28.6152i	0.293478	−	0.955966i
$897$		0			0
$898$	−14.7888	+	54.0767i	−0.493509	+	1.80456i
$899$		0			0
$900$	−22.5000	+	19.8431i	−0.750000	+	0.661438i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	28.5494	−	27.6803i	0.949540	−	0.920632i
$905$		0			0
$906$		0			0
$907$	−23.2457	+	31.9950i	−0.771862	+	1.06238i	0.224271	+	0.974527i	$0.428000\pi$
$907$	−23.2457	+	31.9950i	−0.771862	+	1.06238i	−0.996134	+	0.0878507i	$0.972000\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	12.9443	−	9.40456i	0.428863	−	0.311587i	−0.352331	−	0.935875i	$-0.614611\pi$
$911$	12.9443	−	9.40456i	0.428863	−	0.311587i	0.781194	+	0.624288i	$0.214611\pi$
$912$		0			0
$913$		0			0
$914$	1.25384	+	26.5402i	0.0414732	+	0.877870i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−1.03022	+	1.41798i	−0.0339839	+	0.0467748i	−0.825671	−	0.564152i	$-0.809203\pi$
$919$	−1.03022	+	1.41798i	−0.0339839	+	0.0467748i	0.791687	+	0.610927i	$0.209203\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$		−	44.8833i		−	1.47576i
$926$	46.0116	−	36.8686i	1.51203	−	1.21158i
$927$		0			0
$928$	−2.03184	+	25.9563i	−0.0666984	+	0.852056i
$929$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$929$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$930$		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		−0.587785	−	0.809017i	$-0.700000\pi$
$937$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$938$	−20.0996	−	53.1786i	−0.656276	−	1.73634i
$939$		0			0
$940$		0			0
$941$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$941$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	17.4760	−	25.5404i	0.568194	−	0.830389i
$947$		−	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
$953$	−58.6820	−	19.0669i	−1.90090	−	0.617639i	−0.961495	−	0.274822i	$-0.911381\pi$
$953$	−58.6820	−	19.0669i	−1.90090	−	0.617639i	−0.939402	−	0.342817i	$-0.888619\pi$
$954$	57.3057	−	21.6595i	1.85534	−	0.701253i
$955$		0			0
$956$	−5.80909	−	61.3438i	−0.187880	−	1.98400i
$957$		0			0
$958$		0			0
$959$	−36.1106	−	49.7019i	−1.16607	−	1.60496i
$960$		0			0
$961$	9.57953	−	29.4828i	0.309017	−	0.951057i
$962$		0			0
$963$	−2.78582	−	2.02402i	−0.0897719	−	0.0652231i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			23.3258i			0.750107i	0.927003	+	0.375053i	$0.122376\pi$
$967$			23.3258i			0.750107i	−0.927003	+	0.375053i	$0.877624\pi$
$968$	−26.9284	−	15.5841i	−0.865511	−	0.500891i
$969$		0			0
$970$		0			0
$971$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$971$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$972$		0			0
$973$		0			0
$974$	2.78433	+	1.82863i	0.0892158	+	0.0585931i
$975$		0			0
$976$		0			0
$977$	−21.0711	+	15.3091i	−0.674126	+	0.489781i	−0.871404	−	0.490567i	$-0.836790\pi$
$977$	−21.0711	+	15.3091i	−0.674126	+	0.489781i	0.197278	+	0.980348i	$0.436790\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	10.9284	−	7.93992i	0.348916	−	0.253502i
$982$	22.0000	+	58.2065i	0.702048	+	1.85744i
$983$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$983$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−49.5152			−1.57449
$990$		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
$994$	−35.4922	−	9.70635i	−1.12574	−	0.307867i
$995$		0			0
$996$		0			0
$997$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$997$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$998$	−56.3080	+	21.2824i	−1.78240	+	0.673683i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	616.2.bi.b.349.2	yes	8
7.6	odd	2	CM	616.2.bi.b.349.2	yes	8
8.5	even	2		616.2.bi.a.349.1	yes	8
11.7	odd	10		616.2.bi.a.293.1	✓	8
56.13	odd	2		616.2.bi.a.349.1	yes	8
77.62	even	10		616.2.bi.a.293.1	✓	8
88.29	odd	10	inner	616.2.bi.b.293.2	yes	8
616.293	even	10	inner	616.2.bi.b.293.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
616.2.bi.a.293.1	✓	8	11.7	odd	10
616.2.bi.a.293.1	✓	8	77.62	even	10
616.2.bi.a.349.1	yes	8	8.5	even	2
616.2.bi.a.349.1	yes	8	56.13	odd	2
616.2.bi.b.293.2	yes	8	88.29	odd	10	inner
616.2.bi.b.293.2	yes	8	616.293	even	10	inner
616.2.bi.b.349.2	yes	8	1.1	even	1	trivial
616.2.bi.b.349.2	yes	8	7.6	odd	2	CM

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.10362 - 0.884319i) q^{2} +(0.435959 - 1.95191i) q^{4} +(-2.51626 - 0.817582i) q^{7} +(-1.24498 - 2.53969i) q^{8} +(2.42705 - 1.76336i) q^{9} +O(q^{10})\)	\(q+(1.10362 - 0.884319i) q^{2} +(0.435959 - 1.95191i) q^{4} +(-2.51626 - 0.817582i) q^{7} +(-1.24498 - 2.53969i) q^{8} +(2.42705 - 1.76336i) q^{9} +(3.17317 - 0.964887i) q^{11} +(-3.50000 + 1.32288i) q^{14} +(-3.61988 - 1.70190i) q^{16} +(1.11917 - 4.09236i) q^{18} +(2.64871 - 3.87096i) q^{22} -7.50465 q^{23} +(-1.54508 - 4.75528i) q^{25} +(-2.69283 + 4.55507i) q^{28} +(1.42225 - 4.37724i) q^{29} +(-5.50000 + 1.32288i) q^{32} +(-2.38381 - 5.50613i) q^{36} +(8.53732 + 2.77394i) q^{37} +6.59794 q^{43} +(-0.500000 - 6.61438i) q^{44} +(-8.28229 + 6.63651i) q^{46} +(5.66312 + 4.11450i) q^{49} +(-5.91038 - 3.88168i) q^{50} +(8.48743 + 11.6819i) q^{53} +(1.05627 + 7.40839i) q^{56} +(-2.30125 - 6.08854i) q^{58} +(-7.54878 + 2.45275i) q^{63} +(-4.90007 + 6.32371i) q^{64} +15.1939i q^{67} +(7.95588 + 5.78028i) q^{71} +(-7.50000 - 3.96863i) q^{72} +(11.8750 - 4.48833i) q^{74} +(-8.77339 - 0.166419i) q^{77} +(-4.78485 - 6.58577i) q^{79} +(2.78115 - 8.55951i) q^{81} +(7.28162 - 5.83468i) q^{86} +(-6.40103 - 6.85761i) q^{88} +(-3.27172 + 14.6484i) q^{92} +(9.88847 - 0.467160i) q^{98} +(6.00000 - 7.93725i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 3 q^{4} - 5 q^{8} + 6 q^{9}+O(q^{10}) \) 8 * q + q^2 + 3 * q^4 - 5 * q^8 + 6 * q^9	\( 8 q + q^{2} + 3 q^{4} - 5 q^{8} + 6 q^{9} + 4 q^{11} - 28 q^{14} - q^{16} - 3 q^{18} - 9 q^{22} + 16 q^{23} + 10 q^{25} - 7 q^{28} - 4 q^{29} - 44 q^{32} - 9 q^{36} + 30 q^{37} + 24 q^{43} - 4 q^{44} - 23 q^{46} + 14 q^{49} - 5 q^{50} + 50 q^{53} - 7 q^{56} + 2 q^{58} - 9 q^{64} + 48 q^{71} - 60 q^{72} - 28 q^{74} - 14 q^{77} + 40 q^{79} - 18 q^{81} - 12 q^{86} + 17 q^{88} - 24 q^{92} - 7 q^{98} + 48 q^{99}+O(q^{100}) \) 8 * q + q^2 + 3 * q^4 - 5 * q^8 + 6 * q^9 + 4 * q^11 - 28 * q^14 - q^16 - 3 * q^18 - 9 * q^22 + 16 * q^23 + 10 * q^25 - 7 * q^28 - 4 * q^29 - 44 * q^32 - 9 * q^36 + 30 * q^37 + 24 * q^43 - 4 * q^44 - 23 * q^46 + 14 * q^49 - 5 * q^50 + 50 * q^53 - 7 * q^56 + 2 * q^58 - 9 * q^64 + 48 * q^71 - 60 * q^72 - 28 * q^74 - 14 * q^77 + 40 * q^79 - 18 * q^81 - 12 * q^86 + 17 * q^88 - 24 * q^92 - 7 * q^98 + 48 * q^99

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