LMFDB - Embedded newform 616.2.bi.a.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			$-0.373058 - 1.36412i$ of defining polynomial
Character	$\chi$	$=$	616.349
Dual form			616.2.bi.a.293.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.373058 - 1.36412i) q^{2} +(-1.72166 - 1.01779i) q^{4} +(2.51626 + 0.817582i) q^{7} +(-2.03067 + 1.96885i) q^{8} +(2.42705 - 1.76336i) q^{9} +O(q^{10})$	\(q+(0.373058 - 1.36412i) q^{2} +(-1.72166 - 1.01779i) q^{4} +(2.51626 + 0.817582i) q^{7} +(-2.03067 + 1.96885i) q^{8} +(2.42705 - 1.76336i) q^{9} +(-0.0629004 - 3.31603i) q^{11} +(2.05399 - 3.12748i) q^{14} +(1.92819 + 3.50458i) q^{16} +(-1.50000 - 3.96863i) q^{18} +(-4.54693 - 1.15127i) q^{22} +2.56038 q^{23} +(-1.54508 - 4.75528i) q^{25} +(-3.50000 - 3.96863i) q^{28} +(2.42225 - 7.45492i) q^{29} +(5.50000 - 1.32288i) q^{32} +(-5.97328 + 0.565653i) q^{36} +(-2.31678 - 0.752769i) q^{37} -12.8185 q^{43} +(-3.26674 + 5.77308i) q^{44} +(0.955172 - 3.49267i) q^{46} +(5.66312 + 4.11450i) q^{49} +(-7.06319 + 0.333686i) q^{50} +(1.57760 + 2.17138i) q^{53} +(-6.71939 + 3.29390i) q^{56} +(-9.26578 - 6.08536i) q^{58} +(7.54878 - 2.45275i) q^{63} +(0.247258 - 7.99618i) q^{64} +10.4916i q^{67} +(12.9884 + 9.43662i) q^{71} +(-1.45676 + 8.35930i) q^{72} +(-1.89116 + 2.87955i) q^{74} +(2.55285 - 8.39541i) q^{77} +(10.3127 + 14.1942i) q^{79} +(2.78115 - 8.55951i) q^{81} +(-4.78204 + 17.4860i) q^{86} +(6.65649 + 6.60992i) q^{88} +(-4.40809 - 2.60594i) q^{92} +(7.72535 - 6.19024i) q^{98} +(-6.00000 - 7.93725i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/616\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.373058	−	1.36412i	0.263792	−	0.964580i
$2$	0.373058	−	1.36412i	0.263792	−	0.964580i
$3$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$3$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$4$	−1.72166	−	1.01779i	−0.860828	−	0.508897i
$5$		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
$8$	−2.03067	+	1.96885i	−0.717951	+	0.696094i
$9$	2.42705	−	1.76336i	0.809017	−	0.587785i
$10$		0			0
$11$	−0.0629004	−	3.31603i	−0.0189652	−	0.999820i
$11$	−0.0629004	−	3.31603i	−0.0189652	−	0.999820i
$12$		0			0
$13$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$13$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$14$	2.05399	−	3.12748i	0.548953	−	0.835853i
$15$		0			0
$16$	1.92819	+	3.50458i	0.482048	+	0.876145i
$17$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$17$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$18$	−1.50000	−	3.96863i	−0.353553	−	0.935414i
$19$		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
$22$	−4.54693	−	1.15127i	−0.969409	−	0.245451i
$23$	2.56038			0.533877			0.266938	−	0.963714i	$-0.413988\pi$
$23$	2.56038			0.533877			0.266938	+	0.963714i	$0.413988\pi$
$24$		0			0
$25$	−1.54508	−	4.75528i	−0.309017	−	0.951057i
$26$		0			0
$27$		0			0
$28$	−3.50000	−	3.96863i	−0.661438	−	0.750000i
$29$	2.42225	−	7.45492i	0.449801	−	1.38434i	−0.427331	−	0.904095i	$-0.640546\pi$
$29$	2.42225	−	7.45492i	0.449801	−	1.38434i	0.877132	−	0.480249i	$-0.159454\pi$
$30$		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
$36$	−5.97328	+	0.565653i	−0.995546	+	0.0942755i
$37$	−2.31678	−	0.752769i	−0.380877	−	0.123754i	0.112320	−	0.993672i	$-0.464172\pi$
$37$	−2.31678	−	0.752769i	−0.380877	−	0.123754i	−0.493197	+	0.869918i	$0.664172\pi$
$38$		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
$43$	−12.8185			−1.95480			−0.977399	−	0.211402i	$-0.932197\pi$
$43$	−12.8185			−1.95480			−0.977399	+	0.211402i	$0.932197\pi$
$44$	−3.26674	+	5.77308i	−0.492480	+	0.870324i
$45$		0			0
$46$	0.955172	−	3.49267i	0.140832	−	0.514966i
$47$		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
$50$	−7.06319	+	0.333686i	−0.998886	+	0.0471903i
$51$		0			0
$52$		0			0
$53$	1.57760	+	2.17138i	0.216700	+	0.298263i	0.903503	−	0.428581i	$-0.140986\pi$
$53$	1.57760	+	2.17138i	0.216700	+	0.298263i	−0.686803	+	0.726844i	$0.740986\pi$
$54$		0			0
$55$		0			0
$56$	−6.71939	+	3.29390i	−0.897917	+	0.440165i
$57$		0			0
$58$	−9.26578	−	6.08536i	−1.21666	−	0.799048i
$59$		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
$64$	0.247258	−	7.99618i	0.0309072	−	0.999522i
$65$		0			0
$66$		0			0
$67$			10.4916i			1.28175i	0.767644	+	0.640877i	$0.221429\pi$
$67$			10.4916i			1.28175i	−0.767644	+	0.640877i	$0.778571\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	12.9884	+	9.43662i	1.54144	+	1.11992i	0.949425	+	0.313993i	$0.101667\pi$
$71$	12.9884	+	9.43662i	1.54144	+	1.11992i	0.592014	+	0.805928i	$0.298333\pi$
$72$	−1.45676	+	8.35930i	−0.171681	+	0.985153i
$73$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$73$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$74$	−1.89116	+	2.87955i	−0.219843	+	0.334741i
$75$		0			0
$76$		0			0
$77$	2.55285	−	8.39541i	0.290924	−	0.956746i
$78$		0			0
$79$	10.3127	+	14.1942i	1.16027	+	1.59698i	0.710235	+	0.703964i	$0.248589\pi$
$79$	10.3127	+	14.1942i	1.16027	+	1.59698i	0.450035	+	0.893011i	$0.351411\pi$
$80$		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
$86$	−4.78204	+	17.4860i	−0.515660	+	1.88556i
$87$		0			0
$88$	6.65649	+	6.60992i	0.709585	+	0.704620i
$89$		0			0		1.00000			$0$
$89$		0			0		−1.00000			$\pi$
$90$		0			0
$91$		0			0
$92$	−4.40809	−	2.60594i	−0.459576	−	0.271688i
$93$		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	$0.800000\pi$
$98$	7.72535	−	6.19024i	0.780378	−	0.625308i
$99$	−6.00000	−	7.93725i	−0.603023	−	0.797724i
$100$	−2.17979	+	9.75953i	−0.217979	+	0.975953i
$101$		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
$106$	3.55057	−	1.34199i	0.344862	−	0.130346i
$107$	3.46496	+	10.6641i	0.334971	+	1.03093i	0.966736	+	0.255774i	$0.0823304\pi$
$107$	3.46496	+	10.6641i	0.334971	+	1.03093i	−0.631766	+	0.775159i	$0.717670\pi$
$108$		0			0
$109$	15.6273			1.49683			0.748414	−	0.663232i	$-0.230816\pi$
$109$	15.6273			1.49683			0.748414	+	0.663232i	$0.230816\pi$
$110$		0			0
$111$		0			0
$112$	1.98655	+	10.3949i	0.187711	+	0.982224i
$113$	−3.34450	−	10.2933i	−0.314624	−	0.968314i	−0.975909	−	0.218179i	$-0.929988\pi$
$113$	−3.34450	−	10.2933i	−0.314624	−	0.968314i	0.661285	−	0.750135i	$-0.270012\pi$
$114$		0			0
$115$		0			0
$116$	−11.7579	+	10.3695i	−1.09169	+	0.962779i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−10.9921	+	0.417159i	−0.999281	+	0.0379235i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	−0.529710	−	11.2125i	−0.0471903	−	0.998886i
$127$	−6.06090	+	8.34211i	−0.537818	+	0.740242i	−0.988297	−	0.152545i	$-0.951253\pi$
$127$	−6.06090	+	8.34211i	−0.537818	+	0.740242i	0.450479	+	0.892787i	$0.351253\pi$
$128$	−10.8155	−	3.32033i	−0.955966	−	0.293478i
$129$		0			0
$130$		0			0
$131$		0			0		1.00000			$0$
$131$		0			0		−1.00000			$\pi$
$132$		0			0
$133$		0			0
$134$	14.3118	+	3.91398i	1.23635	+	0.338116i
$135$		0			0
$136$		0			0
$137$	−13.7856	−	10.0158i	−1.17778	−	0.855708i	−0.185861	−	0.982576i	$-0.559507\pi$
$137$	−13.7856	−	10.0158i	−1.17778	−	0.855708i	−0.991920	+	0.126868i	$0.959507\pi$
$138$		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
$142$	17.7181	−	14.1973i	1.48687	−	1.19141i
$143$		0			0
$144$	10.8596	+	5.10570i	0.904970	+	0.425475i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	3.22254	+	3.65402i	0.264891	+	0.300358i
$149$	17.7984	+	12.9313i	1.45810	+	1.05937i	0.983853	+	0.178979i	$0.0572796\pi$
$149$	17.7984	+	12.9313i	1.45810	+	1.05937i	0.474247	+	0.880392i	$0.342720\pi$
$150$		0			0
$151$	−23.2633	+	7.55872i	−1.89314	+	0.615120i	−0.916597	+	0.399811i	$0.869076\pi$
$151$	−23.2633	+	7.55872i	−1.89314	+	0.615120i	−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		0.951057	−	0.309017i	$-0.100000\pi$
$157$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$158$	23.2099	−	8.77251i	1.84648	−	0.697904i
$159$		0			0
$160$		0			0
$161$	6.44258	+	2.09332i	0.507747	+	0.164977i
$162$	−10.6387	−	6.98703i	−0.835853	−	0.548953i
$163$	8.29696	+	11.4198i	0.649868	+	0.894467i	0.999093	−	0.0425718i	$-0.0135551\pi$
$163$	8.29696	+	11.4198i	0.649868	+	0.894467i	−0.349225	+	0.937039i	$0.613555\pi$
$164$		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
$172$	22.0690	+	13.0466i	1.68274	+	0.994791i
$173$		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
$176$	11.5000	−	6.61438i	0.866845	−	0.498578i
$177$		0			0
$178$		0			0
$179$	4.15763	−	1.35090i	0.310756	−	0.100971i	−0.149487	−	0.988764i	$-0.547762\pi$
$179$	4.15763	−	1.35090i	0.310756	−	0.100971i	0.460243	+	0.887793i	$0.347762\pi$
$180$		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
$184$	−5.19930	+	5.04101i	−0.383297	+	0.371628i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−2.80563	+	8.63483i	−0.203008	+	0.624795i	0.796781	+	0.604268i	$0.206534\pi$
$191$	−2.80563	+	8.63483i	−0.203008	+	0.624795i	−0.999789	+	0.0205267i	$0.993466\pi$
$192$		0			0
$193$	−16.2839	+	22.4128i	−1.17214	+	1.61331i	−0.524305	+	0.851530i	$0.675675\pi$
$193$	−16.2839	+	22.4128i	−1.17214	+	1.61331i	−0.647834	+	0.761781i	$0.724325\pi$
$194$		0			0
$195$		0			0
$196$	−5.56223	−	12.8476i	−0.397302	−	0.917688i
$197$	2.03059			0.144674			0.0723369	−	0.997380i	$-0.476954\pi$
$197$	2.03059			0.144674			0.0723369	+	0.997380i	$0.476954\pi$
$198$	−13.0657	+	5.22367i	−0.928541	+	0.371230i
$199$		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
$203$	12.1900	−	16.7781i	0.855572	−	1.17759i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	6.21418	−	4.51486i	0.431915	−	0.313805i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−23.3570	+	16.9698i	−1.60796	+	1.16825i	−0.738490	+	0.674264i	$0.764461\pi$
$211$	−23.3570	+	16.9698i	−1.60796	+	1.16825i	−0.869469	+	0.493987i	$0.835539\pi$
$212$	−0.506067	−	5.34405i	−0.0347568	−	0.367031i
$213$		0			0
$214$	15.8397	−	0.748315i	1.08278	−	0.0511537i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	5.82991	−	21.3176i	0.394851	−	1.44381i
$219$		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
$226$	−15.2890	+	0.722299i	−1.01701	+	0.0480466i
$227$		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
$232$	9.75883	+	19.9075i	0.640698	+	1.30699i
$233$	12.4411	+	17.1237i	0.815042	+	1.12181i	0.990526	+	0.137326i	$0.0438509\pi$
$233$	12.4411	+	17.1237i	0.815042	+	1.12181i	−0.175484	+	0.984482i	$0.556149\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−11.4127	+	3.70821i	−0.738226	+	0.239864i	−0.653907	−	0.756575i	$-0.726871\pi$
$239$	−11.4127	+	3.70821i	−0.738226	+	0.239864i	−0.0843185	+	0.996439i	$0.526871\pi$
$240$		0			0
$241$		0			0			−	1.00000i	$-0.5\pi$
$241$		0			0				1.00000i	$0.5\pi$
$242$	−3.53163	+	15.1502i	−0.227022	+	0.973890i
$243$		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	$0.300000\pi$
$252$	−15.4928	−	3.46031i	−0.975953	−	0.217979i
$253$	−0.161049	−	8.49030i	−0.0101251	−	0.533781i
$254$	9.11858	+	11.3799i	0.572151	+	0.714038i
$255$		0			0
$256$	−8.56415	+	13.5150i	−0.535259	+	0.844688i
$257$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$257$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$258$		0			0
$259$	−5.21418	−	3.78832i	−0.323993	−	0.235395i
$260$		0			0
$261$	−7.26675	−	22.3648i	−0.449801	−	1.38434i
$262$		0			0
$263$		−	23.0900i		−	1.42379i	−0.702284	−	0.711897i	$-0.747836\pi$
$263$		−	23.0900i		−	1.42379i	0.702284	−	0.711897i	$-0.252164\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	10.6783	−	18.0629i	0.652280	−	1.10337i
$269$		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
$274$	−18.8056	+	15.0687i	−1.13609	+	0.910334i
$275$	−15.6715	+	5.42265i	−0.945025	+	0.326998i
$276$		0			0
$277$	−26.9284	+	19.5646i	−1.61797	+	1.17552i	−0.803679	+	0.595063i	$0.797127\pi$
$277$	−26.9284	+	19.5646i	−1.61797	+	1.17552i	−0.814289	+	0.580460i	$0.802873\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	1.08226	−	1.48960i	0.0645620	−	0.0888620i	−0.775515	−	0.631329i	$-0.782510\pi$
$281$	1.08226	−	1.48960i	0.0645620	−	0.0888620i	0.840077	+	0.542467i	$0.182510\pi$
$282$		0			0
$283$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$283$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$284$	−12.7570	−	29.4661i	−0.756989	−	1.74849i
$285$		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
$296$	6.18672	−	3.03277i	0.359596	−	0.176276i
$297$		0			0
$298$	24.2797	−	19.4550i	1.40648	−	1.12700i
$299$		0			0
$300$		0			0
$301$	−32.2546	−	10.4802i	−1.85912	−	0.604066i
$302$	1.63243	+	34.5539i	0.0939356	+	1.98835i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$	−12.9399	+	11.8557i	−0.737321	+	0.675543i
$309$		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
$316$	−3.30813	−	34.9338i	−0.186097	−	1.96518i
$317$	16.7792	+	23.0946i	0.942415	+	1.29712i	0.954815	+	0.297200i	$0.0960529\pi$
$317$	16.7792	+	23.0946i	0.942415	+	1.29712i	−0.0123997	+	0.999923i	$0.503947\pi$
$318$		0			0
$319$	−24.8731	−	7.56333i	−1.39263	−	0.423465i
$320$		0			0
$321$		0			0
$322$	5.25901	−	8.00754i	0.293073	−	0.446243i
$323$		0			0
$324$	−13.5000	+	11.9059i	−0.750000	+	0.661438i
$325$		0			0
$326$	18.6732	−	7.05782i	1.03421	−	0.390896i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$		−	32.6029i		−	1.79202i	−0.444038	−	0.896008i	$-0.646455\pi$
$331$		−	32.6029i		−	1.79202i	0.444038	−	0.896008i	$-0.353545\pi$
$332$		0			0
$333$	−6.95035	+	2.25831i	−0.380877	+	0.123754i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−33.3558	−	10.8380i	−1.81701	−	0.590381i	−0.999904	−	0.0138879i	$-0.995579\pi$
$337$	−33.3558	−	10.8380i	−1.81701	−	0.590381i	−0.817102	−	0.576493i	$-0.804421\pi$
$338$	−15.3670	−	10.0924i	−0.835853	−	0.548953i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	10.8859	+	14.9832i	0.587785	+	0.809017i
$344$	26.0301	−	25.2376i	1.40345	−	1.36072i
$345$		0			0
$346$		0			0
$347$	14.9958	+	10.8951i	0.805016	+	0.584878i	0.912381	−	0.409342i	$-0.134242\pi$
$347$	14.9958	+	10.8951i	0.805016	+	0.584878i	−0.107366	+	0.994220i	$0.534242\pi$
$348$		0			0
$349$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$349$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$350$	−18.0456	−	4.93510i	−0.964580	−	0.263792i
$351$		0			0
$352$	−4.73265	−	18.1549i	−0.252251	−	0.967662i
$353$		0			0		1.00000			$0$
$353$		0			0		−1.00000			$\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−0.291748	−	6.17548i	−0.0154194	−	0.326384i
$359$	−3.64987	−	1.18591i	−0.192633	−	0.0625901i	0.211112	−	0.977462i	$-0.432292\pi$
$359$	−3.64987	−	1.18591i	−0.192633	−	0.0625901i	−0.403745	+	0.914872i	$0.632292\pi$
$360$		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	$0.600000\pi$
$368$	4.93691	+	8.97306i	0.257354	+	0.467753i
$369$		0			0
$370$		0			0
$371$	2.19437	+	6.75359i	0.113926	+	0.350629i
$372$		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
$379$	13.4361	−	18.4932i	0.690165	−	0.949931i	−0.309834	−	0.950791i	$-0.600274\pi$
$379$	13.4361	−	18.4932i	0.690165	−	0.949931i	1.00000		0.000859657i	$0.000273637\pi$
$380$		0			0
$381$		0			0
$382$	10.7323	+	7.04851i	0.549112	+	0.360633i
$383$		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
$386$	24.4990	+	30.5745i	1.24697	+	1.55620i
$387$	−31.1111	+	22.6035i	−1.58147	+	1.14900i
$388$		0			0
$389$	−37.4816	−	12.1785i	−1.90039	−	0.617475i	−0.963338	−	0.268290i	$-0.913542\pi$
$389$	−37.4816	−	12.1785i	−1.90039	−	0.617475i	−0.937054	−	0.349185i	$-0.886458\pi$
$390$		0			0
$391$		0			0
$392$	−19.6008	+	2.79464i	−0.989988	+	0.141151i
$393$		0			0
$394$	0.757530	−	2.76998i	0.0381638	−	0.139549i
$395$		0			0
$396$	2.25144	+	19.7720i	0.113139	+	0.993579i
$397$		0			0			−	1.00000i	$-0.5\pi$
$397$		0			0				1.00000i	$0.5\pi$
$398$		0			0
$399$		0			0
$400$	13.6860	−	14.5840i	0.684302	−	0.729199i
$401$	24.7856	+	18.0078i	1.23773	+	0.899265i	0.997445	−	0.0714367i	$-0.0227584\pi$
$401$	24.7856	+	18.0078i	1.23773	+	0.899265i	0.240287	+	0.970702i	$0.422758\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	−18.3398	−	22.8879i	−0.910190	−	1.13591i
$407$	−2.35048	+	7.72987i	−0.116509	+	0.383155i
$408$		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
$414$	−3.84057	−	10.1612i	−0.188754	−	0.499396i
$415$		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
$421$	32.8480	−	10.6730i	1.60091	−	0.520169i	0.633581	−	0.773676i	$-0.281584\pi$
$421$	32.8480	−	10.6730i	1.60091	−	0.520169i	0.967333	+	0.253507i	$0.0815842\pi$
$422$	14.4354	+	38.1925i	0.702704	+	1.85918i
$423$		0			0
$424$	−7.47872	−	1.30331i	−0.363199	−	0.0632941i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	4.88834	−	21.8865i	0.236287	−	1.05792i
$429$		0			0
$430$		0			0
$431$	−22.6942	−	31.2358i	−1.09314	−	1.50458i	−0.844177	−	0.536065i	$-0.819910\pi$
$431$	−22.6942	−	31.2358i	−1.09314	−	1.50458i	−0.248963	−	0.968513i	$-0.580090\pi$
$432$		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
$436$	−26.9049	−	15.9054i	−1.28851	−	0.761731i
$437$		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
$443$	39.6801	−	12.8928i	1.88526	−	0.612557i	0.901582	−	0.432608i	$-0.142407\pi$
$443$	39.6801	−	12.8928i	1.88526	−	0.612557i	0.983676	−	0.179949i	$-0.0575933\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	7.15970	−	19.9183i	0.338264	−	0.941051i
$449$	33.0711	−	24.0276i	1.56072	−	1.13393i	0.625310	−	0.780376i	$-0.284972\pi$
$449$	33.0711	−	24.0276i	1.56072	−	1.13393i	0.935413	−	0.353556i	$-0.115028\pi$
$450$	−16.5543	+	13.2648i	−0.780378	+	0.625308i
$451$		0			0
$452$	−4.71840	+	21.1256i	−0.221935	+	0.993663i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	4.33490	−	5.96648i	0.202778	−	0.279100i	−0.695501	−	0.718525i	$-0.744818\pi$
$457$	4.33490	−	5.96648i	0.202778	−	0.279100i	0.898279	+	0.439425i	$0.144818\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		1.00000			$0$
$461$		0			0		−1.00000			$\pi$
$462$		0			0
$463$	23.0299			1.07029			0.535145	−	0.844760i	$-0.320257\pi$
$463$	23.0299			1.07029			0.535145	+	0.844760i	$0.320257\pi$
$464$	30.7969	−	5.88555i	1.42971	−	0.273230i
$465$		0			0
$466$	28.0000	−	10.5830i	1.29707	−	0.490248i
$467$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$467$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$468$		0			0
$469$	−8.57775	+	26.3996i	−0.396084	+	1.21902i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.806287	+	42.5064i	0.0370731	+	1.95445i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	7.65785	+	2.48818i	0.350629	+	0.113926i
$478$	0.800847	+	16.9517i	0.0366299	+	0.775352i
$479$		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
$484$	19.3492	+	10.4695i	0.879507	+	0.475885i
$485$		0			0
$486$		0			0
$487$	−12.7279	−	39.1724i	−0.576755	−	1.77507i	−0.630123	−	0.776495i	$-0.716996\pi$
$487$	−12.7279	−	39.1724i	−0.576755	−	1.77507i	0.0533681	−	0.998575i	$-0.483004\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	13.5967	−	41.8465i	0.613613	−	1.88851i	0.193249	−	0.981150i	$-0.438097\pi$
$491$	13.5967	−	41.8465i	0.613613	−	1.88851i	0.420363	−	0.907356i	$-0.361903\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	24.9670	+	34.3641i	1.11992	+	1.54144i
$498$		0			0
$499$	−0.232351	−	0.0754955i	−0.0104015	−	0.00337964i	0.303812	−	0.952732i	$-0.401741\pi$
$499$	−0.232351	−	0.0754955i	−0.0104015	−	0.00337964i	−0.314213	+	0.949352i	$0.601741\pi$
$500$		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	$0.900000\pi$
$504$	−10.5000	+	19.8431i	−0.467707	+	0.883883i
$505$		0			0
$506$	−11.6419	−	2.94769i	−0.517545	−	0.131041i
$507$		0			0
$508$	18.9253	−	8.19349i	0.839675	−	0.363527i
$509$		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
$512$	15.2412	+	16.7244i	0.673571	+	0.739122i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	−7.11292	+	5.69951i	−0.312524	+	0.250422i
$519$		0			0
$520$		0			0
$521$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$521$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$522$	−33.2192	+	1.56937i	−1.45396	+	0.0686896i
$523$		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
$526$	−31.4976	−	8.61393i	−1.37336	−	0.375585i
$527$		0			0
$528$		0			0
$529$	−16.4444			−0.714976
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	−20.6564	−	21.3050i	−0.892221	−	0.920236i
$537$		0			0
$538$		0			0
$539$	13.2876	−	19.0379i	0.572336	−	0.820019i
$540$		0			0
$541$	−15.9284	+	11.5726i	−0.684814	+	0.497546i	−0.874951	−	0.484211i	$-0.839107\pi$
$541$	−15.9284	+	11.5726i	−0.684814	+	0.497546i	0.190138	+	0.981757i	$0.439107\pi$
$542$		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	$0.289785\pi$
$547$	13.5967	+	41.8465i	0.581355	+	1.78923i	−0.0320849	+	0.999485i	$0.510215\pi$
$548$	13.5400	+	31.2746i	0.578399	+	1.33599i
$549$		0			0
$550$	1.55079	+	23.4007i	0.0661259	+	0.997811i
$551$		0			0
$552$		0			0
$553$	14.3445	+	44.1478i	0.609990	+	1.87736i
$554$	16.6426	+	44.0323i	0.707078	+	1.87075i
$555$		0			0
$556$		0			0
$557$	−13.4223	+	41.3094i	−0.568719	+	1.75034i	0.0879152	+	0.996128i	$0.471980\pi$
$557$	−13.4223	+	41.3094i	−0.568719	+	1.75034i	−0.656634	+	0.754209i	$0.728020\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−1.62825	−	2.03204i	−0.0686835	−	0.0857163i
$563$		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
$568$	−44.9545	+	6.40952i	−1.88625	+	0.268938i
$569$	40.2601	−	13.0813i	1.68779	−	0.548397i	0.701395	−	0.712773i	$-0.252561\pi$
$569$	40.2601	−	13.0813i	1.68779	−	0.548397i	0.986398	+	0.164375i	$0.0525608\pi$
$570$		0			0
$571$	46.5287			1.94717			0.973583	−	0.228332i	$-0.0733271\pi$
$571$	46.5287			1.94717			0.973583	+	0.228332i	$0.0733271\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−3.95601	−	12.1753i	−0.164977	−	0.507747i
$576$	−13.5000	−	19.8431i	−0.562500	−	0.826797i
$577$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$577$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$578$	−24.0148	+	1.13453i	−0.998886	+	0.0471903i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	7.10114	−	5.36796i	0.294099	−	0.222318i
$584$		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
$592$	−1.82907	−	9.57083i	−0.0751742	−	0.393359i
$593$		0			0			−	1.00000i	$-0.5\pi$
$593$		0			0				1.00000i	$0.5\pi$
$594$		0			0
$595$		0			0
$596$	−17.4813	−	40.3783i	−0.716061	−	1.65396i
$597$		0			0
$598$		0			0
$599$	−36.4997	−	26.5186i	−1.49134	−	1.08352i	−0.973676	−	0.227937i	$-0.926802\pi$
$599$	−36.4997	−	26.5186i	−1.49134	−	1.08352i	−0.517663	−	0.855584i	$-0.673198\pi$
$600$		0			0
$601$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$601$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$602$	−26.3290	+	40.0895i	−1.07309	+	1.63393i
$603$	18.5004	+	25.4637i	0.753396	+	1.03696i
$604$	47.7447	+	10.6638i	1.94270	+	0.433903i
$605$		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
$613$	−3.73325	−	11.4898i	−0.150784	−	0.464067i	0.846925	−	0.531712i	$-0.178451\pi$
$613$	−3.73325	−	11.4898i	−0.150784	−	0.464067i	−0.997709	+	0.0676456i	$0.978451\pi$
$614$		0			0
$615$		0			0
$616$	11.3453	+	22.0745i	0.457115	+	0.889407i
$617$	3.84770			0.154902			0.0774512	−	0.996996i	$-0.475322\pi$
$617$	3.84770			0.154902			0.0774512	+	0.996996i	$0.475322\pi$
$618$		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
$631$	−15.5241	+	47.7782i	−0.618003	+	1.90202i	−0.299528	+	0.954087i	$0.596829\pi$
$631$	−15.5241	+	47.7782i	−0.618003	+	1.90202i	−0.318475	+	0.947931i	$0.603171\pi$
$632$	−48.8880	−	8.51964i	−1.94466	−	0.338893i
$633$		0			0
$634$	37.7635	−	14.2733i	1.49978	−	0.566864i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	−19.5964	+	31.1084i	−0.775830	+	1.23159i
$639$	48.1636			1.90532
$640$		0			0
$641$	7.65550	+	23.5612i	0.302374	+	0.930611i	0.980644	+	0.195799i	$0.0627300\pi$
$641$	7.65550	+	23.5612i	0.302374	+	0.930611i	−0.678270	+	0.734813i	$0.737270\pi$
$642$		0			0
$643$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$643$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$644$	−8.96134	−	10.1612i	−0.353126	−	0.400407i
$645$		0			0
$646$		0			0
$647$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$647$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$648$	11.2048	+	22.8572i	0.440165	+	0.897917i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−2.66152	−	28.1055i	−0.104233	−	1.10070i
$653$	−42.1152	−	13.6840i	−1.64809	−	0.535498i	−0.669768	−	0.742571i	$-0.733606\pi$
$653$	−42.1152	−	13.6840i	−1.64809	−	0.535498i	−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	$0.5\pi$
$662$	−44.4743	−	12.1628i	−1.72854	−	0.472720i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	0.487718	+	10.3236i	0.0188987	+	0.400032i
$667$	6.20189	−	19.0874i	0.240138	−	0.739069i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	9.76533	+	13.4408i	0.376426	+	0.518106i	0.954633	−	0.297784i	$-0.0962476\pi$
$673$	9.76533	+	13.4408i	0.376426	+	0.518106i	−0.578208	+	0.815890i	$0.696248\pi$
$674$	−27.2279	+	41.4582i	−1.04878	+	1.59691i
$675$		0			0
$676$	−19.5000	+	17.1974i	−0.750000	+	0.661438i
$677$		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
$683$		−	51.0901i		−	1.95491i	−0.211147	−	0.977454i	$-0.567720\pi$
$683$		−	51.0901i		−	1.95491i	0.211147	−	0.977454i	$-0.432280\pi$
$684$		0			0
$685$		0			0
$686$	24.5000	−	9.26013i	0.935414	−	0.353553i
$687$		0			0
$688$	−24.7165	−	44.9233i	−0.942307	−	1.71269i
$689$		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
$693$	−8.60820	−	24.8777i	−0.326998	−	0.945025i
$694$	20.4565	−	16.3916i	0.776518	−	0.622215i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−13.4641	+	22.7754i	−0.508897	+	0.860828i
$701$	15.7423	+	48.4499i	0.594579	+	1.82993i	0.556810	+	0.830640i	$0.312025\pi$
$701$	15.7423	+	48.4499i	0.594579	+	1.82993i	0.0377695	+	0.999286i	$0.487975\pi$
$702$		0			0
$703$		0			0
$704$	−26.5311	−	0.316950i	−0.999929	−	0.0119455i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	23.0896	−	31.7802i	0.867150	−	1.19353i	−0.112667	−	0.993633i	$-0.535939\pi$
$709$	23.0896	−	31.7802i	0.867150	−	1.19353i	0.979817	−	0.199896i	$-0.0640606\pi$
$710$		0			0
$711$	50.0589	+	16.2651i	1.87736	+	0.609990i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−8.53295	−	1.90583i	−0.318891	−	0.0712244i
$717$		0			0
$718$	−2.97934	+	4.53645i	−0.111188	+	0.169299i
$719$		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
$722$	9.50000	+	25.1346i	0.353553	+	0.935414i
$723$		0			0
$724$		0			0
$725$	−39.1928			−1.45559
$726$		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
$736$	14.0821	−	3.38707i	0.519073	−	0.124849i
$737$	34.7905	−	0.659926i	1.28152	−	0.0243087i
$738$		0			0
$739$	−26.4857	+	19.2430i	−0.974291	+	0.707864i	−0.956425	−	0.291977i	$-0.905687\pi$
$739$	−26.4857	+	19.2430i	−0.974291	+	0.707864i	−0.0178655	+	0.999840i	$0.505687\pi$
$740$		0			0
$741$		0			0
$742$	10.0313	−	0.473910i	0.368262	−	0.0173978i
$743$	−3.79415	+	5.22220i	−0.139194	+	0.191584i	−0.872923	−	0.487858i	$-0.837778\pi$
$743$	−3.79415	+	5.22220i	−0.139194	+	0.191584i	0.733729	+	0.679442i	$0.237778\pi$
$744$		0			0
$745$		0			0
$746$	8.20728	−	30.0107i	0.300490	−	1.09877i
$747$		0			0
$748$		0			0
$749$			29.6664i			1.08399i
$750$		0			0
$751$	12.3593	+	38.0379i	0.450996	+	1.38802i	0.875772	+	0.482724i	$0.160353\pi$
$751$	12.3593	+	38.0379i	0.450996	+	1.38802i	−0.424777	+	0.905298i	$0.639647\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	13.6240	+	18.7519i	0.495174	+	0.681548i	0.981332	−	0.192323i	$-0.0616021\pi$
$757$	13.6240	+	18.7519i	0.495174	+	0.681548i	−0.486158	+	0.873871i	$0.661602\pi$
$758$	−20.2145	−	25.2275i	−0.734224	−	0.916303i
$759$		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
$763$	39.3224	+	12.7766i	1.42357	+	0.462545i
$764$	13.6188	−	12.0107i	0.492711	−	0.434530i
$765$		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
$772$	50.8469	−	22.0135i	1.83002	−	0.792285i
$773$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$773$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$774$	19.2277	+	50.8717i	0.691126	+	1.82855i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−30.5958	+	46.5862i	−1.09691	+	1.67019i
$779$		0			0
$780$		0			0
$781$	30.4751	−	43.6635i	1.09049	−	1.56240i
$782$		0			0
$783$		0			0
$784$	−3.50000	+	27.7804i	−0.125000	+	0.992157i
$785$		0			0
$786$		0			0
$787$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$787$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$788$	−3.49598	−	2.06673i	−0.124539	−	0.0736241i
$789$		0			0
$790$		0			0
$791$		−	28.6351i		−	1.01815i
$792$	27.8113	+	4.30486i	0.988231	+	0.152966i
$793$		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
$802$	33.8113	−	27.0926i	1.19392	−	0.956672i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	28.9316	−	39.8210i	1.01718	−	1.40003i	0.103022	−	0.994679i	$-0.467149\pi$
$809$	28.9316	−	39.8210i	1.01718	−	1.40003i	0.914160	−	0.405353i	$-0.132851\pi$
$810$		0			0
$811$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$811$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$812$	−38.0637	+	16.4792i	−1.33577	+	0.578307i
$813$		0			0
$814$	9.66762	+	6.09003i	0.338850	+	0.213455i
$815$		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	$0.225420\pi$
$821$	−6.79837	+	20.9232i	−0.237265	+	0.730226i	−0.996813	+	0.0797750i	$0.974580\pi$
$822$		0			0
$823$	1.70206	−	1.23662i	0.0593301	−	0.0431058i	−0.557725	−	0.830026i	$-0.688326\pi$
$823$	1.70206	−	1.23662i	0.0593301	−	0.0431058i	0.617055	+	0.786920i	$0.288326\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−35.5967	+	25.8626i	−1.23782	+	0.899329i	−0.997451	−	0.0713526i	$-0.977268\pi$
$827$	−35.5967	+	25.8626i	−1.23782	+	0.899329i	−0.240369	+	0.970682i	$0.577268\pi$
$828$	−15.2939	+	1.44829i	−0.531499	+	0.0503315i
$829$		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
$841$	−26.2471	−	19.0696i	−0.905071	−	0.657573i
$842$	−2.30500	−	48.7903i	−0.0794355	−	1.68143i
$843$		0			0
$844$	57.4844	−	5.44362i	1.97870	−	0.187377i
$845$		0			0
$846$		0			0
$847$	−28.0000	−	7.93725i	−0.962091	−	0.272727i
$848$	−4.56787	+	9.71568i	−0.156861	+	0.333638i
$849$		0			0
$850$		0			0
$851$	−5.93185	−	1.92738i	−0.203341	−	0.0660696i
$852$		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
$856$	−28.0321	−	14.8332i	−0.958119	−	0.506989i
$857$		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
$862$	−51.0757	+	19.3048i	−1.73965	+	0.657525i
$863$	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
$869$	46.4198	−	35.0901i	1.57468	−	1.19035i
$870$		0			0
$871$		0			0
$872$	−31.7340	+	30.7679i	−1.07465	+	1.04193i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−18.2668	−	56.2193i	−0.616824	−	1.89839i	−0.367885	−	0.929871i	$-0.619918\pi$
$877$	−18.2668	−	56.2193i	−0.616824	−	1.89839i	−0.248939	−	0.968519i	$-0.580082\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	7.83422	−	28.6466i	0.263792	−	0.964580i
$883$	−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
$886$	−2.78442	−	58.9382i	−0.0935443	−	1.98007i
$887$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$887$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$888$		0			0
$889$	−22.0711	+	16.0356i	−0.740242	+	0.537818i
$890$		0			0
$891$	−28.5585	−	8.68399i	−0.956746	−	0.290924i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−24.5000	−	17.1974i	−0.818488	−	0.574524i
$897$		0			0
$898$	−20.4391	−	54.0767i	−0.682061	−	1.80456i
$899$		0			0
$900$	11.9191	+	27.5306i	0.397302	+	0.917688i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	27.0576	+	14.3175i	0.899922	+	0.476194i
$905$		0			0
$906$		0			0
$907$	18.2132	−	25.0684i	0.604760	−	0.832381i	−0.391373	−	0.920232i	$-0.628000\pi$
$907$	18.2132	−	25.0684i	0.604760	−	0.832381i	0.996134	+	0.0878507i	$0.0279999\pi$
$908$		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
$914$	−6.52183	−	8.13918i	−0.215723	−	0.269220i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	34.1974	−	47.0687i	1.12807	−	1.55265i	0.336381	−	0.941726i	$-0.390797\pi$
$919$	34.1974	−	47.0687i	1.12807	−	1.55265i	0.791687	−	0.610927i	$-0.209203\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$			12.1801i			0.400478i
$926$	8.59149	−	31.4156i	0.282334	−	1.03238i
$927$		0			0
$928$	3.46045	−	44.2064i	0.113595	−	1.45115i
$929$		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
$932$	−3.99087	−	42.1435i	−0.130725	−	1.38046i
$933$		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	$0.300000\pi$
$938$	32.8123	+	21.5497i	1.07136	+	0.703622i
$939$		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
$946$	58.2847	+	14.7575i	1.89500	+	0.479808i
$947$		−	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
$953$	−46.2410	−	15.0246i	−1.49789	−	0.486694i	−0.558489	−	0.829512i	$-0.688619\pi$
$953$	−46.2410	−	15.0246i	−1.49789	−	0.486694i	−0.939402	+	0.342817i	$0.888619\pi$
$954$	6.25101	−	9.51799i	0.202384	−	0.308156i
$955$		0			0
$956$	23.4229	+	5.23151i	0.757551	+	0.169199i
$957$		0			0
$958$		0			0
$959$	−26.4993	−	36.4732i	−0.855708	−	1.17778i
$960$		0			0
$961$	9.57953	−	29.4828i	0.309017	−	0.951057i
$962$		0			0
$963$	27.2142	+	19.7723i	0.876965	+	0.637152i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			52.7587i			1.69661i	0.529511	+	0.848303i	$0.322376\pi$
$967$			52.7587i			1.69661i	−0.529511	+	0.848303i	$0.677624\pi$
$968$	21.5000	−	22.4889i	0.691036	−	0.722820i
$969$		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
$974$	−58.1841	+	2.74879i	−1.86434	+	0.0880769i
$975$		0			0
$976$		0			0
$977$	44.0711	−	32.0196i	1.40996	−	1.02440i	0.416632	−	0.909075i	$-0.363210\pi$
$977$	44.0711	−	32.0196i	1.40996	−	1.02440i	0.993328	−	0.115321i	$-0.0367898\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	37.9284	−	27.5566i	1.21096	−	0.879813i
$982$	−52.0113	−	34.1588i	−1.65975	−	1.09005i
$983$		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
$989$	−32.8202			−1.04362
$990$		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
$994$	56.1909	−	21.2382i	1.78227	−	0.673633i
$995$		0			0
$996$		0			0
$997$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$997$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$998$	−0.189666	+	0.288791i	−0.00600376	+	0.00914153i
$999$		0			0

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.373058 - 1.36412i) q^{2} +(-1.72166 - 1.01779i) q^{4} +(2.51626 + 0.817582i) q^{7} +(-2.03067 + 1.96885i) q^{8} +(2.42705 - 1.76336i) q^{9} +O(q^{10})\)	\(q+(0.373058 - 1.36412i) q^{2} +(-1.72166 - 1.01779i) q^{4} +(2.51626 + 0.817582i) q^{7} +(-2.03067 + 1.96885i) q^{8} +(2.42705 - 1.76336i) q^{9} +(-0.0629004 - 3.31603i) q^{11} +(2.05399 - 3.12748i) q^{14} +(1.92819 + 3.50458i) q^{16} +(-1.50000 - 3.96863i) q^{18} +(-4.54693 - 1.15127i) q^{22} +2.56038 q^{23} +(-1.54508 - 4.75528i) q^{25} +(-3.50000 - 3.96863i) q^{28} +(2.42225 - 7.45492i) q^{29} +(5.50000 - 1.32288i) q^{32} +(-5.97328 + 0.565653i) q^{36} +(-2.31678 - 0.752769i) q^{37} -12.8185 q^{43} +(-3.26674 + 5.77308i) q^{44} +(0.955172 - 3.49267i) q^{46} +(5.66312 + 4.11450i) q^{49} +(-7.06319 + 0.333686i) q^{50} +(1.57760 + 2.17138i) q^{53} +(-6.71939 + 3.29390i) q^{56} +(-9.26578 - 6.08536i) q^{58} +(7.54878 - 2.45275i) q^{63} +(0.247258 - 7.99618i) q^{64} +10.4916i q^{67} +(12.9884 + 9.43662i) q^{71} +(-1.45676 + 8.35930i) q^{72} +(-1.89116 + 2.87955i) q^{74} +(2.55285 - 8.39541i) q^{77} +(10.3127 + 14.1942i) q^{79} +(2.78115 - 8.55951i) q^{81} +(-4.78204 + 17.4860i) q^{86} +(6.65649 + 6.60992i) q^{88} +(-4.40809 - 2.60594i) q^{92} +(7.72535 - 6.19024i) q^{98} +(-6.00000 - 7.93725i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} + 3 q^{4} + 5 q^{8} + 6 q^{9}+O(q^{10}) \) 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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