LMFDB - Embedded newform 1175.2.a.k.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1175,2,Mod(1,1175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1175, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1175.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1175 = 5^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1175.a (trivial)

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:	yes
Analytic conductor:	$9.38242223750$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 23 x^{11} - x^{10} + 200 x^{9} + 11 x^{8} - 816 x^{7} - 19 x^{6} + 1581 x^{5} - 102 x^{4} + \cdots - 117 $ x^13 - 23x^11 - x^10 + 200x^9 + 11x^8 - 816x^7 - 19x^6 + 1581x^5 - 102x^4 - 1309x^3 + 300x^2 + 341x - 117
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.09045$ of defining polynomial
Character	$\chi$	$=$	1175.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.09045 q^{2} -0.807628 q^{3} +2.36999 q^{4} +1.68831 q^{6} -0.424369 q^{7} -0.773439 q^{8} -2.34774 q^{9} +O(q^{10})$	\(q-2.09045 q^{2} -0.807628 q^{3} +2.36999 q^{4} +1.68831 q^{6} -0.424369 q^{7} -0.773439 q^{8} -2.34774 q^{9} +5.89732 q^{11} -1.91407 q^{12} -4.73827 q^{13} +0.887122 q^{14} -3.12314 q^{16} +3.30225 q^{17} +4.90783 q^{18} +4.30350 q^{19} +0.342732 q^{21} -12.3281 q^{22} -6.48440 q^{23} +0.624652 q^{24} +9.90511 q^{26} +4.31898 q^{27} -1.00575 q^{28} -5.81090 q^{29} +10.3459 q^{31} +8.07564 q^{32} -4.76285 q^{33} -6.90319 q^{34} -5.56410 q^{36} -3.43456 q^{37} -8.99626 q^{38} +3.82676 q^{39} -12.1630 q^{41} -0.716465 q^{42} +6.61860 q^{43} +13.9766 q^{44} +13.5553 q^{46} -1.00000 q^{47} +2.52233 q^{48} -6.81991 q^{49} -2.66699 q^{51} -11.2296 q^{52} +10.0218 q^{53} -9.02863 q^{54} +0.328224 q^{56} -3.47563 q^{57} +12.1474 q^{58} -1.21323 q^{59} +4.23512 q^{61} -21.6277 q^{62} +0.996306 q^{63} -10.6355 q^{64} +9.95650 q^{66} -2.80775 q^{67} +7.82628 q^{68} +5.23699 q^{69} +1.98732 q^{71} +1.81583 q^{72} +10.1431 q^{73} +7.17979 q^{74} +10.1992 q^{76} -2.50264 q^{77} -7.99965 q^{78} -1.84218 q^{79} +3.55508 q^{81} +25.4263 q^{82} -5.54132 q^{83} +0.812271 q^{84} -13.8359 q^{86} +4.69305 q^{87} -4.56122 q^{88} -2.77463 q^{89} +2.01077 q^{91} -15.3680 q^{92} -8.35566 q^{93} +2.09045 q^{94} -6.52212 q^{96} +17.6076 q^{97} +14.2567 q^{98} -13.8454 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 20 q^{4} + 5 q^{6} - 3 q^{8} + 27 q^{9}+O(q^{10}) $ 13 * q + 20 * q^4 + 5 * q^6 - 3 * q^8 + 27 * q^9	$ 13 q + 20 q^{4} + 5 q^{6} - 3 q^{8} + 27 q^{9} + 9 q^{11} + q^{12} + 2 q^{13} - 4 q^{14} + 34 q^{16} - 5 q^{17} + 7 q^{18} + 16 q^{19} + 26 q^{21} - 15 q^{22} + 10 q^{23} - 8 q^{24} + 3 q^{26} - 15 q^{27} + 30 q^{28} + 10 q^{29} + 15 q^{31} - 36 q^{32} + 22 q^{33} + q^{34} + 57 q^{36} - 5 q^{37} + 42 q^{38} - 2 q^{39} + 24 q^{41} - 62 q^{42} + 2 q^{43} - 6 q^{44} + 50 q^{46} - 13 q^{47} + 67 q^{48} + 39 q^{49} + 9 q^{51} - 36 q^{52} - 4 q^{53} - 34 q^{54} - 9 q^{56} + 5 q^{57} + 27 q^{58} - 25 q^{59} + 22 q^{61} - 2 q^{62} + 7 q^{63} + 53 q^{64} + 2 q^{66} + 4 q^{67} - 5 q^{68} + 5 q^{69} - 6 q^{71} - 66 q^{72} + 3 q^{73} - 49 q^{74} + 63 q^{76} + 8 q^{77} + 59 q^{78} + 37 q^{79} + 49 q^{81} - 48 q^{82} - 27 q^{83} - 2 q^{84} + 3 q^{86} + 35 q^{87} + 44 q^{88} + 32 q^{89} + 12 q^{91} - 29 q^{92} - 56 q^{93} - 11 q^{96} - 25 q^{97} + 61 q^{98} + 36 q^{99}+O(q^{100}) $ 13 * q + 20 * q^4 + 5 * q^6 - 3 * q^8 + 27 * q^9 + 9 * q^11 + q^12 + 2 * q^13 - 4 * q^14 + 34 * q^16 - 5 * q^17 + 7 * q^18 + 16 * q^19 + 26 * q^21 - 15 * q^22 + 10 * q^23 - 8 * q^24 + 3 * q^26 - 15 * q^27 + 30 * q^28 + 10 * q^29 + 15 * q^31 - 36 * q^32 + 22 * q^33 + q^34 + 57 * q^36 - 5 * q^37 + 42 * q^38 - 2 * q^39 + 24 * q^41 - 62 * q^42 + 2 * q^43 - 6 * q^44 + 50 * q^46 - 13 * q^47 + 67 * q^48 + 39 * q^49 + 9 * q^51 - 36 * q^52 - 4 * q^53 - 34 * q^54 - 9 * q^56 + 5 * q^57 + 27 * q^58 - 25 * q^59 + 22 * q^61 - 2 * q^62 + 7 * q^63 + 53 * q^64 + 2 * q^66 + 4 * q^67 - 5 * q^68 + 5 * q^69 - 6 * q^71 - 66 * q^72 + 3 * q^73 - 49 * q^74 + 63 * q^76 + 8 * q^77 + 59 * q^78 + 37 * q^79 + 49 * q^81 - 48 * q^82 - 27 * q^83 - 2 * q^84 + 3 * q^86 + 35 * q^87 + 44 * q^88 + 32 * q^89 + 12 * q^91 - 29 * q^92 - 56 * q^93 - 11 * q^96 - 25 * q^97 + 61 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−2.09045	−1.47817	−0.739086	−	0.673611i	$-0.764742\pi$
$2$	−2.09045	−1.47817	−0.739086	+	0.673611i	$0.764742\pi$
$3$	−0.807628	−0.466284	−0.233142	−	0.972443i	$-0.574901\pi$
$3$	−0.807628	−0.466284	−0.233142	+	0.972443i	$0.574901\pi$
$4$	2.36999	1.18499
$5$	0	0
$5$	0	0
$6$	1.68831	0.689249
$7$	−0.424369	−0.160396	−0.0801982	−	0.996779i	$-0.525555\pi$
$7$	−0.424369	−0.160396	−0.0801982	+	0.996779i	$0.525555\pi$
$8$	−0.773439	−0.273452
$9$	−2.34774	−0.782579
$10$	0	0
$11$	5.89732	1.77811	0.889055	−	0.457800i	$-0.151363\pi$
$11$	5.89732	1.77811	0.889055	+	0.457800i	$0.151363\pi$
$12$	−1.91407	−0.552544
$13$	−4.73827	−1.31416	−0.657079	−	0.753822i	$-0.728208\pi$
$13$	−4.73827	−1.31416	−0.657079	+	0.753822i	$0.728208\pi$
$14$	0.887122	0.237093
$15$	0	0
$16$	−3.12314	−0.780784
$17$	3.30225	0.800913	0.400456	−	0.916316i	$-0.368852\pi$
$17$	3.30225	0.800913	0.400456	+	0.916316i	$0.368852\pi$
$18$	4.90783	1.15679
$19$	4.30350	0.987291	0.493646	−	0.869663i	$-0.335664\pi$
$19$	4.30350	0.987291	0.493646	+	0.869663i	$0.335664\pi$
$20$	0	0
$21$	0.342732	0.0747903
$22$	−12.3281	−2.62835
$23$	−6.48440	−1.35209	−0.676046	−	0.736859i	$-0.736308\pi$
$23$	−6.48440	−1.35209	−0.676046	+	0.736859i	$0.736308\pi$
$24$	0.624652	0.127506
$25$	0	0
$26$	9.90511	1.94255
$27$	4.31898	0.831189
$28$	−1.00575	−0.190069
$29$	−5.81090	−1.07906	−0.539529	−	0.841967i	$-0.681398\pi$
$29$	−5.81090	−1.07906	−0.539529	+	0.841967i	$0.681398\pi$
$30$	0	0
$31$	10.3459	1.85818	0.929092	−	0.369850i	$-0.120591\pi$
$31$	10.3459	1.85818	0.929092	+	0.369850i	$0.120591\pi$
$32$	8.07564	1.42759
$33$	−4.76285	−0.829105
$34$	−6.90319	−1.18389
$35$	0	0
$36$	−5.56410	−0.927351
$37$	−3.43456	−0.564639	−0.282319	−	0.959320i	$-0.591104\pi$
$37$	−3.43456	−0.564639	−0.282319	+	0.959320i	$0.591104\pi$
$38$	−8.99626	−1.45939
$39$	3.82676	0.612772
$40$	0	0
$41$	−12.1630	−1.89955	−0.949774	−	0.312936i	$-0.898687\pi$
$41$	−12.1630	−1.89955	−0.949774	+	0.312936i	$0.898687\pi$
$42$	−0.716465	−0.110553
$43$	6.61860	1.00933	0.504664	−	0.863316i	$-0.331616\pi$
$43$	6.61860	1.00933	0.504664	+	0.863316i	$0.331616\pi$
$44$	13.9766	2.10705
$45$	0	0
$46$	13.5553	1.99862
$47$	−1.00000	−0.145865
$47$	−1.00000	−0.145865
$48$	2.52233	0.364067
$49$	−6.81991	−0.974273
$50$	0	0
$51$	−2.66699	−0.373453
$52$	−11.2296	−1.55727
$53$	10.0218	1.37660	0.688301	−	0.725425i	$-0.258357\pi$
$53$	10.0218	1.37660	0.688301	+	0.725425i	$0.258357\pi$
$54$	−9.02863	−1.22864
$55$	0	0
$56$	0.328224	0.0438607
$57$	−3.47563	−0.460358
$58$	12.1474	1.59503
$59$	−1.21323	−0.157949	−0.0789745	−	0.996877i	$-0.525165\pi$
$59$	−1.21323	−0.157949	−0.0789745	+	0.996877i	$0.525165\pi$
$60$	0	0
$61$	4.23512	0.542252	0.271126	−	0.962544i	$-0.412604\pi$
$61$	4.23512	0.542252	0.271126	+	0.962544i	$0.412604\pi$
$62$	−21.6277	−2.74671
$63$	0.996306	0.125523
$64$	−10.6355	−1.32943
$65$	0	0
$66$	9.95650	1.22556
$67$	−2.80775	−0.343022	−0.171511	−	0.985182i	$-0.554865\pi$
$67$	−2.80775	−0.343022	−0.171511	+	0.985182i	$0.554865\pi$
$68$	7.82628	0.949076
$69$	5.23699	0.630459
$70$	0	0
$71$	1.98732	0.235851	0.117926	−	0.993022i	$-0.462376\pi$
$71$	1.98732	0.235851	0.117926	+	0.993022i	$0.462376\pi$
$72$	1.81583	0.213998
$73$	10.1431	1.18716	0.593581	−	0.804774i	$-0.297714\pi$
$73$	10.1431	1.18716	0.593581	+	0.804774i	$0.297714\pi$
$74$	7.17979	0.834633
$75$	0	0
$76$	10.1992	1.16993
$77$	−2.50264	−0.285202
$78$	−7.99965	−0.905782
$79$	−1.84218	−0.207261	−0.103631	−	0.994616i	$-0.533046\pi$
$79$	−1.84218	−0.207261	−0.103631	+	0.994616i	$0.533046\pi$
$80$	0	0
$81$	3.55508	0.395008
$82$	25.4263	2.80786
$83$	−5.54132	−0.608239	−0.304119	−	0.952634i	$-0.598362\pi$
$83$	−5.54132	−0.608239	−0.304119	+	0.952634i	$0.598362\pi$
$84$	0.812271	0.0886260
$85$	0	0
$86$	−13.8359	−1.49196
$87$	4.69305	0.503148
$88$	−4.56122	−0.486228
$89$	−2.77463	−0.294110	−0.147055	−	0.989128i	$-0.546979\pi$
$89$	−2.77463	−0.294110	−0.147055	+	0.989128i	$0.546979\pi$
$90$	0	0
$91$	2.01077	0.210786
$92$	−15.3680	−1.60222
$93$	−8.35566	−0.866442
$94$	2.09045	0.215614
$95$	0	0
$96$	−6.52212	−0.665661
$97$	17.6076	1.78778	0.893889	−	0.448288i	$-0.147966\pi$
$97$	17.6076	1.78778	0.893889	+	0.448288i	$0.147966\pi$
$98$	14.2567	1.44014
$99$	−13.8454	−1.39151
$100$	0	0
$101$	−1.08344	−0.107806	−0.0539030	−	0.998546i	$-0.517166\pi$
$101$	−1.08344	−0.107806	−0.0539030	+	0.998546i	$0.517166\pi$
$102$	5.57521	0.552028
$103$	9.96609	0.981988	0.490994	−	0.871163i	$-0.336634\pi$
$103$	9.96609	0.981988	0.490994	+	0.871163i	$0.336634\pi$
$104$	3.66476	0.359359
$105$	0	0
$106$	−20.9501	−2.03486
$107$	7.78547	0.752649	0.376325	−	0.926488i	$-0.377188\pi$
$107$	7.78547	0.752649	0.376325	+	0.926488i	$0.377188\pi$
$108$	10.2359	0.984953
$109$	18.2389	1.74697	0.873485	−	0.486851i	$-0.161854\pi$
$109$	18.2389	1.74697	0.873485	+	0.486851i	$0.161854\pi$
$110$	0	0
$111$	2.77385	0.263282
$112$	1.32536	0.125235
$113$	17.5106	1.64726	0.823629	−	0.567128i	$-0.191946\pi$
$113$	17.5106	1.64726	0.823629	+	0.567128i	$0.191946\pi$
$114$	7.26564	0.680489
$115$	0	0
$116$	−13.7718	−1.27868
$117$	11.1242	1.02843
$118$	2.53620	0.233476
$119$	−1.40137	−0.128463
$120$	0	0
$121$	23.7784	2.16168
$122$	−8.85332	−0.801542
$123$	9.82322	0.885730
$124$	24.5197	2.20193
$125$	0	0
$126$	−2.08273	−0.185544
$127$	10.5533	0.936451	0.468226	−	0.883609i	$-0.344893\pi$
$127$	10.5533	0.936451	0.468226	+	0.883609i	$0.344893\pi$
$128$	6.08164	0.537546
$129$	−5.34537	−0.470634
$130$	0	0
$131$	11.3994	0.995972	0.497986	−	0.867185i	$-0.334073\pi$
$131$	11.3994	0.995972	0.497986	+	0.867185i	$0.334073\pi$
$132$	−11.2879	−0.982484
$133$	−1.82627	−0.158358
$134$	5.86947	0.507045
$135$	0	0
$136$	−2.55409	−0.219011
$137$	−4.89569	−0.418267	−0.209134	−	0.977887i	$-0.567064\pi$
$137$	−4.89569	−0.418267	−0.209134	+	0.977887i	$0.567064\pi$
$138$	−10.9477	−0.931928
$139$	13.2181	1.12114	0.560572	−	0.828106i	$-0.310581\pi$
$139$	13.2181	1.12114	0.560572	+	0.828106i	$0.310581\pi$
$140$	0	0
$141$	0.807628	0.0680146
$142$	−4.15440	−0.348629
$143$	−27.9431	−2.33672
$144$	7.33230	0.611025
$145$	0	0
$146$	−21.2037	−1.75483
$147$	5.50795	0.454288
$148$	−8.13987	−0.669093
$149$	6.16721	0.505238	0.252619	−	0.967566i	$-0.418708\pi$
$149$	6.16721	0.505238	0.252619	+	0.967566i	$0.418708\pi$
$150$	0	0
$151$	−11.9559	−0.972960	−0.486480	−	0.873692i	$-0.661719\pi$
$151$	−11.9559	−0.972960	−0.486480	+	0.873692i	$0.661719\pi$
$152$	−3.32850	−0.269977
$153$	−7.75281	−0.626777
$154$	5.23165	0.421578
$155$	0	0
$156$	9.06936	0.726130
$157$	8.97250	0.716083	0.358042	−	0.933706i	$-0.383445\pi$
$157$	8.97250	0.716083	0.358042	+	0.933706i	$0.383445\pi$
$158$	3.85098	0.306368
$159$	−8.09390	−0.641888
$160$	0	0
$161$	2.75178	0.216871
$162$	−7.43171	−0.583890
$163$	−1.61139	−0.126213	−0.0631067	−	0.998007i	$-0.520101\pi$
$163$	−1.61139	−0.126213	−0.0631067	+	0.998007i	$0.520101\pi$
$164$	−28.8263	−2.25095
$165$	0	0
$166$	11.5839	0.899081
$167$	−14.7952	−1.14489	−0.572445	−	0.819943i	$-0.694005\pi$
$167$	−14.7952	−1.14489	−0.572445	+	0.819943i	$0.694005\pi$
$168$	−0.265083	−0.0204516
$169$	9.45116	0.727012
$170$	0	0
$171$	−10.1035	−0.772633
$172$	15.6860	1.19605
$173$	6.82566	0.518946	0.259473	−	0.965750i	$-0.416451\pi$
$173$	6.82566	0.518946	0.259473	+	0.965750i	$0.416451\pi$
$174$	−9.81060	−0.743739
$175$	0	0
$176$	−18.4181	−1.38832
$177$	0.979839	0.0736492
$178$	5.80022	0.434745
$179$	24.8399	1.85662	0.928311	−	0.371804i	$-0.121261\pi$
$179$	24.8399	1.85662	0.928311	+	0.371804i	$0.121261\pi$
$180$	0	0
$181$	10.4226	0.774705	0.387353	−	0.921932i	$-0.373390\pi$
$181$	10.4226	0.774705	0.387353	+	0.921932i	$0.373390\pi$
$182$	−4.20342	−0.311578
$183$	−3.42041	−0.252844
$184$	5.01529	0.369732
$185$	0	0
$186$	17.4671	1.28075
$187$	19.4744	1.42411
$188$	−2.36999	−0.172849
$189$	−1.83284	−0.133320
$190$	0	0
$191$	−16.6819	−1.20706	−0.603529	−	0.797341i	$-0.706239\pi$
$191$	−16.6819	−1.20706	−0.603529	+	0.797341i	$0.706239\pi$
$192$	8.58950	0.619894
$193$	−0.166953	−0.0120176	−0.00600879	−	0.999982i	$-0.501913\pi$
$193$	−0.166953	−0.0120176	−0.00600879	+	0.999982i	$0.501913\pi$
$194$	−36.8078	−2.64264
$195$	0	0
$196$	−16.1631	−1.15451
$197$	6.14271	0.437650	0.218825	−	0.975764i	$-0.429778\pi$
$197$	6.14271	0.437650	0.218825	+	0.975764i	$0.429778\pi$
$198$	28.9431	2.05689
$199$	18.4106	1.30509	0.652547	−	0.757748i	$-0.273700\pi$
$199$	18.4106	1.30509	0.652547	+	0.757748i	$0.273700\pi$
$200$	0	0
$201$	2.26762	0.159946
$202$	2.26487	0.159356
$203$	2.46597	0.173077
$204$	−6.32073	−0.442540
$205$	0	0
$206$	−20.8336	−1.45155
$207$	15.2237	1.05812
$208$	14.7982	1.02607
$209$	25.3791	1.75551
$210$	0	0
$211$	6.73132	0.463403	0.231702	−	0.972787i	$-0.425571\pi$
$211$	6.73132	0.463403	0.231702	+	0.972787i	$0.425571\pi$
$212$	23.7516	1.63126
$213$	−1.60502	−0.109974
$214$	−16.2751	−1.11255
$215$	0	0
$216$	−3.34047	−0.227290
$217$	−4.39049	−0.298046
$218$	−38.1275	−2.58232
$219$	−8.19187	−0.553555
$220$	0	0
$221$	−15.6469	−1.05253
$222$	−5.79860	−0.389177
$223$	−10.7316	−0.718640	−0.359320	−	0.933214i	$-0.616991\pi$
$223$	−10.7316	−0.718640	−0.359320	+	0.933214i	$0.616991\pi$
$224$	−3.42705	−0.228979
$225$	0	0
$226$	−36.6051	−2.43493
$227$	3.13946	0.208373	0.104187	−	0.994558i	$-0.466776\pi$
$227$	3.13946	0.208373	0.104187	+	0.994558i	$0.466776\pi$
$228$	−8.23720	−0.545522
$229$	−16.7319	−1.10568	−0.552839	−	0.833288i	$-0.686456\pi$
$229$	−16.7319	−1.10568	−0.552839	+	0.833288i	$0.686456\pi$
$230$	0	0
$231$	2.02120	0.132985
$232$	4.49438	0.295071
$233$	−17.7978	−1.16597	−0.582987	−	0.812481i	$-0.698116\pi$
$233$	−17.7978	−1.16597	−0.582987	+	0.812481i	$0.698116\pi$
$234$	−23.2546	−1.52020
$235$	0	0
$236$	−2.87534	−0.187169
$237$	1.48779	0.0966426
$238$	2.92950	0.189891
$239$	−8.08833	−0.523191	−0.261595	−	0.965178i	$-0.584249\pi$
$239$	−8.08833	−0.523191	−0.261595	+	0.965178i	$0.584249\pi$
$240$	0	0
$241$	−4.04626	−0.260642	−0.130321	−	0.991472i	$-0.541601\pi$
$241$	−4.04626	−0.260642	−0.130321	+	0.991472i	$0.541601\pi$
$242$	−49.7076	−3.19533
$243$	−15.8281	−1.01538
$244$	10.0372	0.642565
$245$	0	0
$246$	−20.5350	−1.30926
$247$	−20.3911	−1.29746
$248$	−8.00195	−0.508124
$249$	4.47533	0.283612
$250$	0	0
$251$	−0.802795	−0.0506720	−0.0253360	−	0.999679i	$-0.508066\pi$
$251$	−0.802795	−0.0506720	−0.0253360	+	0.999679i	$0.508066\pi$
$252$	2.36123	0.148744
$253$	−38.2406	−2.40417
$254$	−22.0611	−1.38424
$255$	0	0
$256$	8.55756	0.534848
$257$	7.48934	0.467172	0.233586	−	0.972336i	$-0.424954\pi$
$257$	7.48934	0.467172	0.233586	+	0.972336i	$0.424954\pi$
$258$	11.1742	0.695678
$259$	1.45752	0.0905660
$260$	0	0
$261$	13.6425	0.844448
$262$	−23.8299	−1.47222
$263$	9.99405	0.616259	0.308130	−	0.951344i	$-0.400297\pi$
$263$	9.99405	0.616259	0.308130	+	0.951344i	$0.400297\pi$
$264$	3.68377	0.226721
$265$	0	0
$266$	3.81773	0.234080
$267$	2.24087	0.137139
$268$	−6.65434	−0.406479
$269$	−7.26099	−0.442710	−0.221355	−	0.975193i	$-0.571048\pi$
$269$	−7.26099	−0.442710	−0.221355	+	0.975193i	$0.571048\pi$
$270$	0	0
$271$	−2.80352	−0.170302	−0.0851509	−	0.996368i	$-0.527137\pi$
$271$	−2.80352	−0.170302	−0.0851509	+	0.996368i	$0.527137\pi$
$272$	−10.3134	−0.625340
$273$	−1.62396	−0.0982863
$274$	10.2342	0.618271
$275$	0	0
$276$	12.4116	0.747090
$277$	−28.3549	−1.70368	−0.851842	−	0.523799i	$-0.824514\pi$
$277$	−28.3549	−1.70368	−0.851842	+	0.523799i	$0.824514\pi$
$278$	−27.6318	−1.65724
$279$	−24.2895	−1.45417
$280$	0	0
$281$	2.01022	0.119920	0.0599599	−	0.998201i	$-0.480903\pi$
$281$	2.01022	0.119920	0.0599599	+	0.998201i	$0.480903\pi$
$282$	−1.68831	−0.100537
$283$	−7.12600	−0.423597	−0.211798	−	0.977313i	$-0.567932\pi$
$283$	−7.12600	−0.423597	−0.211798	+	0.977313i	$0.567932\pi$
$284$	4.70992	0.279482
$285$	0	0
$286$	58.4137	3.45407
$287$	5.16162	0.304681
$288$	−18.9595	−1.11720
$289$	−6.09516	−0.358539
$290$	0	0
$291$	−14.2204	−0.833613
$292$	24.0391	1.40678
$293$	28.9365	1.69049	0.845245	−	0.534379i	$-0.179455\pi$
$293$	28.9365	1.69049	0.845245	+	0.534379i	$0.179455\pi$
$294$	−11.5141	−0.671516
$295$	0	0
$296$	2.65643	0.154402
$297$	25.4704	1.47795
$298$	−12.8923	−0.746828
$299$	30.7248	1.77686
$300$	0	0
$301$	−2.80873	−0.161892
$302$	24.9933	1.43820
$303$	0.875014	0.0502682
$304$	−13.4404	−0.770861
$305$	0	0
$306$	16.2069	0.926485
$307$	10.8290	0.618046	0.309023	−	0.951055i	$-0.399998\pi$
$307$	10.8290	0.618046	0.309023	+	0.951055i	$0.399998\pi$
$308$	−5.93122	−0.337963
$309$	−8.04890	−0.457886
$310$	0	0
$311$	−28.7716	−1.63149	−0.815745	−	0.578412i	$-0.803672\pi$
$311$	−28.7716	−1.63149	−0.815745	+	0.578412i	$0.803672\pi$
$312$	−2.95977	−0.167564
$313$	7.38126	0.417213	0.208607	−	0.978000i	$-0.433107\pi$
$313$	7.38126	0.417213	0.208607	+	0.978000i	$0.433107\pi$
$314$	−18.7566	−1.05849
$315$	0	0
$316$	−4.36594	−0.245603
$317$	−23.8675	−1.34053	−0.670266	−	0.742121i	$-0.733820\pi$
$317$	−23.8675	−1.34053	−0.670266	+	0.742121i	$0.733820\pi$
$318$	16.9199	0.948822
$319$	−34.2688	−1.91868
$320$	0	0
$321$	−6.28776	−0.350949
$322$	−5.75246	−0.320572
$323$	14.2112	0.790734
$324$	8.42548	0.468082
$325$	0	0
$326$	3.36852	0.186565
$327$	−14.7303	−0.814585
$328$	9.40738	0.519436
$329$	0.424369	0.0233962
$330$	0	0
$331$	22.4348	1.23313	0.616563	−	0.787305i	$-0.288524\pi$
$331$	22.4348	1.23313	0.616563	+	0.787305i	$0.288524\pi$
$332$	−13.1328	−0.720759
$333$	8.06345	0.441874
$334$	30.9287	1.69234
$335$	0	0
$336$	−1.07040	−0.0583951
$337$	3.12992	0.170498	0.0852489	−	0.996360i	$-0.472831\pi$
$337$	3.12992	0.170498	0.0852489	+	0.996360i	$0.472831\pi$
$338$	−19.7572	−1.07465
$339$	−14.1421	−0.768091
$340$	0	0
$341$	61.0133	3.30405
$342$	21.1209	1.14208
$343$	5.86474	0.316666
$344$	−5.11909	−0.276003
$345$	0	0
$346$	−14.2687	−0.767091
$347$	−16.2938	−0.874697	−0.437348	−	0.899292i	$-0.644082\pi$
$347$	−16.2938	−0.874697	−0.437348	+	0.899292i	$0.644082\pi$
$348$	11.1225	0.596227
$349$	−24.6308	−1.31846	−0.659228	−	0.751943i	$-0.729117\pi$
$349$	−24.6308	−1.31846	−0.659228	+	0.751943i	$0.729117\pi$
$350$	0	0
$351$	−20.4645	−1.09231
$352$	47.6247	2.53840
$353$	23.2972	1.23998	0.619991	−	0.784609i	$-0.287136\pi$
$353$	23.2972	1.23998	0.619991	+	0.784609i	$0.287136\pi$
$354$	−2.04830	−0.108866
$355$	0	0
$356$	−6.57583	−0.348518
$357$	1.13179	0.0599005
$358$	−51.9266	−2.74441
$359$	14.5257	0.766640	0.383320	−	0.923616i	$-0.374781\pi$
$359$	14.5257	0.766640	0.383320	+	0.923616i	$0.374781\pi$
$360$	0	0
$361$	−0.479871	−0.0252564
$362$	−21.7879	−1.14515
$363$	−19.2041	−1.00796
$364$	4.76550	0.249780
$365$	0	0
$366$	7.15019	0.373746
$367$	21.6012	1.12757	0.563787	−	0.825920i	$-0.309344\pi$
$367$	21.6012	1.12757	0.563787	+	0.825920i	$0.309344\pi$
$368$	20.2517	1.05569
$369$	28.5556	1.48655
$370$	0	0
$371$	−4.25295	−0.220802
$372$	−19.8028	−1.02673
$373$	−6.74153	−0.349063	−0.174532	−	0.984652i	$-0.555841\pi$
$373$	−6.74153	−0.349063	−0.174532	+	0.984652i	$0.555841\pi$
$374$	−40.7103	−2.10508
$375$	0	0
$376$	0.773439	0.0398871
$377$	27.5336	1.41805
$378$	3.83147	0.197069
$379$	22.0390	1.13207	0.566033	−	0.824383i	$-0.308477\pi$
$379$	22.0390	1.13207	0.566033	+	0.824383i	$0.308477\pi$
$380$	0	0
$381$	−8.52312	−0.436653
$382$	34.8727	1.78424
$383$	6.02442	0.307833	0.153917	−	0.988084i	$-0.450811\pi$
$383$	6.02442	0.307833	0.153917	+	0.988084i	$0.450811\pi$
$384$	−4.91170	−0.250649
$385$	0	0
$386$	0.349008	0.0177640
$387$	−15.5387	−0.789878
$388$	41.7297	2.11851
$389$	−8.84529	−0.448474	−0.224237	−	0.974535i	$-0.571989\pi$
$389$	−8.84529	−0.448474	−0.224237	+	0.974535i	$0.571989\pi$
$390$	0	0
$391$	−21.4131	−1.08291
$392$	5.27479	0.266417
$393$	−9.20649	−0.464406
$394$	−12.8410	−0.646923
$395$	0	0
$396$	−32.8133	−1.64893
$397$	−19.5603	−0.981701	−0.490851	−	0.871244i	$-0.663314\pi$
$397$	−19.5603	−0.981701	−0.490851	+	0.871244i	$0.663314\pi$
$398$	−38.4865	−1.92915
$399$	1.47495	0.0738398
$400$	0	0
$401$	11.4380	0.571187	0.285594	−	0.958351i	$-0.407809\pi$
$401$	11.4380	0.571187	0.285594	+	0.958351i	$0.407809\pi$
$402$	−4.74035	−0.236427
$403$	−49.0217	−2.44195
$404$	−2.56773	−0.127749
$405$	0	0
$406$	−5.15498	−0.255837
$407$	−20.2547	−1.00399
$408$	2.06275	0.102122
$409$	4.34064	0.214631	0.107316	−	0.994225i	$-0.465774\pi$
$409$	4.34064	0.214631	0.107316	+	0.994225i	$0.465774\pi$
$410$	0	0
$411$	3.95390	0.195032
$412$	23.6195	1.16365
$413$	0.514857	0.0253344
$414$	−31.8243	−1.56408
$415$	0	0
$416$	−38.2645	−1.87607
$417$	−10.6753	−0.522772
$418$	−53.0539	−2.59495
$419$	14.5052	0.708626	0.354313	−	0.935127i	$-0.384715\pi$
$419$	14.5052	0.708626	0.354313	+	0.935127i	$0.384715\pi$
$420$	0	0
$421$	30.1225	1.46808	0.734041	−	0.679105i	$-0.237632\pi$
$421$	30.1225	1.46808	0.734041	+	0.679105i	$0.237632\pi$
$422$	−14.0715	−0.684990
$423$	2.34774	0.114151
$424$	−7.75127	−0.376435
$425$	0	0
$426$	3.35521	0.162560
$427$	−1.79725	−0.0869752
$428$	18.4515	0.891885
$429$	22.5676	1.08958
$430$	0	0
$431$	−23.4270	−1.12844	−0.564220	−	0.825625i	$-0.690823\pi$
$431$	−23.4270	−1.12844	−0.564220	+	0.825625i	$0.690823\pi$
$432$	−13.4888	−0.648979
$433$	−7.38254	−0.354782	−0.177391	−	0.984140i	$-0.556766\pi$
$433$	−7.38254	−0.354782	−0.177391	+	0.984140i	$0.556766\pi$
$434$	9.17810	0.440563
$435$	0	0
$436$	43.2260	2.07015
$437$	−27.9056	−1.33491
$438$	17.1247	0.818250
$439$	17.9107	0.854829	0.427414	−	0.904056i	$-0.359425\pi$
$439$	17.9107	0.854829	0.427414	+	0.904056i	$0.359425\pi$
$440$	0	0
$441$	16.0114	0.762445
$442$	32.7091	1.55581
$443$	−37.8962	−1.80050	−0.900252	−	0.435369i	$-0.856618\pi$
$443$	−37.8962	−1.80050	−0.900252	+	0.435369i	$0.856618\pi$
$444$	6.57399	0.311988
$445$	0	0
$446$	22.4338	1.06227
$447$	−4.98082	−0.235584
$448$	4.51336	0.213236
$449$	28.6560	1.35236	0.676181	−	0.736736i	$-0.263634\pi$
$449$	28.6560	1.35236	0.676181	+	0.736736i	$0.263634\pi$
$450$	0	0
$451$	−71.7294	−3.37761
$452$	41.4999	1.95199
$453$	9.65595	0.453676
$454$	−6.56289	−0.308012
$455$	0	0
$456$	2.68819	0.125886
$457$	36.3792	1.70175	0.850873	−	0.525371i	$-0.176074\pi$
$457$	36.3792	1.70175	0.850873	+	0.525371i	$0.176074\pi$
$458$	34.9773	1.63438
$459$	14.2624	0.665710
$460$	0	0
$461$	−0.463152	−0.0215711	−0.0107856	−	0.999942i	$-0.503433\pi$
$461$	−0.463152	−0.0215711	−0.0107856	+	0.999942i	$0.503433\pi$
$462$	−4.22523	−0.196575
$463$	36.5111	1.69681	0.848407	−	0.529344i	$-0.177562\pi$
$463$	36.5111	1.69681	0.848407	+	0.529344i	$0.177562\pi$
$464$	18.1482	0.842511
$465$	0	0
$466$	37.2055	1.72351
$467$	14.2290	0.658438	0.329219	−	0.944254i	$-0.393214\pi$
$467$	14.2290	0.658438	0.329219	+	0.944254i	$0.393214\pi$
$468$	26.3642	1.21869
$469$	1.19152	0.0550194
$470$	0	0
$471$	−7.24644	−0.333898
$472$	0.938360	0.0431915
$473$	39.0320	1.79470
$474$	−3.11016	−0.142854
$475$	0	0
$476$	−3.32123	−0.152228
$477$	−23.5286	−1.07730
$478$	16.9083	0.773366
$479$	25.6849	1.17357	0.586786	−	0.809742i	$-0.300393\pi$
$479$	25.6849	1.17357	0.586786	+	0.809742i	$0.300393\pi$
$480$	0	0
$481$	16.2739	0.742025
$482$	8.45851	0.385274
$483$	−2.22241	−0.101123
$484$	56.3546	2.56157
$485$	0	0
$486$	33.0879	1.50090
$487$	−17.0688	−0.773460	−0.386730	−	0.922193i	$-0.626396\pi$
$487$	−17.0688	−0.773460	−0.386730	+	0.922193i	$0.626396\pi$
$488$	−3.27561	−0.148280
$489$	1.30140	0.0588514
$490$	0	0
$491$	−13.8416	−0.624662	−0.312331	−	0.949973i	$-0.601110\pi$
$491$	−13.8416	−0.624662	−0.312331	+	0.949973i	$0.601110\pi$
$492$	23.2809	1.04958
$493$	−19.1890	−0.864231
$494$	42.6267	1.91786
$495$	0	0
$496$	−32.3117	−1.45084
$497$	−0.843356	−0.0378297
$498$	−9.35545	−0.419228
$499$	−40.8063	−1.82674	−0.913371	−	0.407128i	$-0.866530\pi$
$499$	−40.8063	−1.82674	−0.913371	+	0.407128i	$0.866530\pi$
$500$	0	0
$501$	11.9491	0.533844
$502$	1.67820	0.0749019
$503$	−13.3124	−0.593572	−0.296786	−	0.954944i	$-0.595915\pi$
$503$	−13.3124	−0.593572	−0.296786	+	0.954944i	$0.595915\pi$
$504$	−0.770582	−0.0343245
$505$	0	0
$506$	79.9402	3.55377
$507$	−7.63302	−0.338994
$508$	25.0111	1.10969
$509$	−13.3069	−0.589818	−0.294909	−	0.955525i	$-0.595289\pi$
$509$	−13.3069	−0.589818	−0.294909	+	0.955525i	$0.595289\pi$
$510$	0	0
$511$	−4.30442	−0.190416
$512$	−30.0524	−1.32814
$513$	18.5868	0.820625
$514$	−15.6561	−0.690561
$515$	0	0
$516$	−12.6685	−0.557698
$517$	−5.89732	−0.259364
$518$	−3.04688	−0.133872
$519$	−5.51260	−0.241976
$520$	0	0
$521$	−24.0268	−1.05264	−0.526318	−	0.850288i	$-0.676428\pi$
$521$	−24.0268	−1.05264	−0.526318	+	0.850288i	$0.676428\pi$
$522$	−28.5189	−1.24824
$523$	−15.6907	−0.686109	−0.343054	−	0.939316i	$-0.611461\pi$
$523$	−15.6907	−0.686109	−0.343054	+	0.939316i	$0.611461\pi$
$524$	27.0165	1.18022
$525$	0	0
$526$	−20.8921	−0.910937
$527$	34.1648	1.48824
$528$	14.8750	0.647352
$529$	19.0475	0.828152
$530$	0	0
$531$	2.84834	0.123608
$532$	−4.32824	−0.187653
$533$	57.6317	2.49631
$534$	−4.68443	−0.202715
$535$	0	0
$536$	2.17163	0.0938000
$537$	−20.0614	−0.865714
$538$	15.1787	0.654402
$539$	−40.2192	−1.73236
$540$	0	0
$541$	16.2581	0.698991	0.349496	−	0.936938i	$-0.386353\pi$
$541$	16.2581	0.698991	0.349496	+	0.936938i	$0.386353\pi$
$542$	5.86063	0.251736
$543$	−8.41758	−0.361233
$544$	26.6678	1.14337
$545$	0	0
$546$	3.39480	0.145284
$547$	−8.15907	−0.348857	−0.174428	−	0.984670i	$-0.555808\pi$
$547$	−8.15907	−0.348857	−0.174428	+	0.984670i	$0.555808\pi$
$548$	−11.6027	−0.495644
$549$	−9.94295	−0.424355
$550$	0	0
$551$	−25.0072	−1.06534
$552$	−4.05049	−0.172400
$553$	0.781762	0.0332439
$554$	59.2746	2.51834
$555$	0	0
$556$	31.3267	1.32855
$557$	14.6923	0.622532	0.311266	−	0.950323i	$-0.399247\pi$
$557$	14.6923	0.622532	0.311266	+	0.950323i	$0.399247\pi$
$558$	50.7760	2.14952
$559$	−31.3607	−1.32642
$560$	0	0
$561$	−15.7281	−0.664041
$562$	−4.20227	−0.177262
$563$	−32.2329	−1.35846	−0.679228	−	0.733927i	$-0.737685\pi$
$563$	−32.2329	−1.35846	−0.679228	+	0.733927i	$0.737685\pi$
$564$	1.91407	0.0805968
$565$	0	0
$566$	14.8966	0.626149
$567$	−1.50866	−0.0633579
$568$	−1.53707	−0.0644941
$569$	29.8446	1.25115	0.625574	−	0.780164i	$-0.284865\pi$
$569$	29.8446	1.25115	0.625574	+	0.780164i	$0.284865\pi$
$570$	0	0
$571$	40.4798	1.69403	0.847014	−	0.531570i	$-0.178398\pi$
$571$	40.4798	1.69403	0.847014	+	0.531570i	$0.178398\pi$
$572$	−66.2247	−2.76900
$573$	13.4728	0.562833
$574$	−10.7901	−0.450370
$575$	0	0
$576$	24.9693	1.04039
$577$	−41.2724	−1.71819	−0.859096	−	0.511815i	$-0.828973\pi$
$577$	−41.2724	−1.71819	−0.859096	+	0.511815i	$0.828973\pi$
$578$	12.7416	0.529982
$579$	0.134836	0.00560361
$580$	0	0
$581$	2.35156	0.0975592
$582$	29.7270	1.23222
$583$	59.1019	2.44775
$584$	−7.84509	−0.324632
$585$	0	0
$586$	−60.4904	−2.49884
$587$	5.69992	0.235261	0.117630	−	0.993057i	$-0.462470\pi$
$587$	5.69992	0.235261	0.117630	+	0.993057i	$0.462470\pi$
$588$	13.0538	0.538329
$589$	44.5237	1.83457
$590$	0	0
$591$	−4.96103	−0.204070
$592$	10.7266	0.440861
$593$	−15.2550	−0.626446	−0.313223	−	0.949680i	$-0.601409\pi$
$593$	−15.2550	−0.626446	−0.313223	+	0.949680i	$0.601409\pi$
$594$	−53.2447	−2.18466
$595$	0	0
$596$	14.6162	0.598703
$597$	−14.8689	−0.608545
$598$	−64.2288	−2.62651
$599$	−14.1584	−0.578498	−0.289249	−	0.957254i	$-0.593406\pi$
$599$	−14.1584	−0.578498	−0.289249	+	0.957254i	$0.593406\pi$
$600$	0	0
$601$	29.1333	1.18837	0.594185	−	0.804328i	$-0.297475\pi$
$601$	29.1333	1.18837	0.594185	+	0.804328i	$0.297475\pi$
$602$	5.87151	0.239305
$603$	6.59187	0.268442
$604$	−28.3354	−1.15295
$605$	0	0
$606$	−1.82917	−0.0743051
$607$	−20.0553	−0.814020	−0.407010	−	0.913424i	$-0.633429\pi$
$607$	−20.0553	−0.814020	−0.407010	+	0.913424i	$0.633429\pi$
$608$	34.7535	1.40944
$609$	−1.99158	−0.0807031
$610$	0	0
$611$	4.73827	0.191690
$612$	−18.3741	−0.742727
$613$	23.4862	0.948598	0.474299	−	0.880364i	$-0.342702\pi$
$613$	23.4862	0.948598	0.474299	+	0.880364i	$0.342702\pi$
$614$	−22.6376	−0.913579
$615$	0	0
$616$	1.93564	0.0779892
$617$	4.56078	0.183610	0.0918050	−	0.995777i	$-0.470736\pi$
$617$	4.56078	0.183610	0.0918050	+	0.995777i	$0.470736\pi$
$618$	16.8258	0.676834
$619$	34.4300	1.38386	0.691930	−	0.721964i	$-0.256761\pi$
$619$	34.4300	1.38386	0.691930	+	0.721964i	$0.256761\pi$
$620$	0	0
$621$	−28.0060	−1.12384
$622$	60.1457	2.41162
$623$	1.17747	0.0471741
$624$	−11.9515	−0.478442
$625$	0	0
$626$	−15.4302	−0.616713
$627$	−20.4969	−0.818568
$628$	21.2647	0.848554
$629$	−11.3418	−0.452226
$630$	0	0
$631$	2.33775	0.0930643	0.0465322	−	0.998917i	$-0.485183\pi$
$631$	2.33775	0.0930643	0.0465322	+	0.998917i	$0.485183\pi$
$632$	1.42481	0.0566760
$633$	−5.43641	−0.216078
$634$	49.8938	1.98154
$635$	0	0
$636$	−19.1824	−0.760634
$637$	32.3145	1.28035
$638$	71.6372	2.83615
$639$	−4.66570	−0.184572
$640$	0	0
$641$	−20.2244	−0.798815	−0.399407	−	0.916774i	$-0.630784\pi$
$641$	−20.2244	−0.798815	−0.399407	+	0.916774i	$0.630784\pi$
$642$	13.1443	0.518763
$643$	0.189290	0.00746488	0.00373244	−	0.999993i	$-0.498812\pi$
$643$	0.189290	0.00746488	0.00373244	+	0.999993i	$0.498812\pi$
$644$	6.52168	0.256990
$645$	0	0
$646$	−29.7079	−1.16884
$647$	1.26748	0.0498299	0.0249149	−	0.999690i	$-0.492069\pi$
$647$	1.26748	0.0498299	0.0249149	+	0.999690i	$0.492069\pi$
$648$	−2.74964	−0.108016
$649$	−7.15481	−0.280851
$650$	0	0
$651$	3.54588	0.138974
$652$	−3.81896	−0.149562
$653$	−2.22854	−0.0872095	−0.0436047	−	0.999049i	$-0.513884\pi$
$653$	−2.22854	−0.0872095	−0.0436047	+	0.999049i	$0.513884\pi$
$654$	30.7929	1.20410
$655$	0	0
$656$	37.9868	1.48314
$657$	−23.8134	−0.929048
$658$	−0.887122	−0.0345836
$659$	41.4110	1.61314	0.806571	−	0.591137i	$-0.201321\pi$
$659$	41.4110	1.61314	0.806571	+	0.591137i	$0.201321\pi$
$660$	0	0
$661$	−11.2338	−0.436945	−0.218473	−	0.975843i	$-0.570107\pi$
$661$	−11.2338	−0.436945	−0.218473	+	0.975843i	$0.570107\pi$
$662$	−46.8988	−1.82277
$663$	12.6369	0.490777
$664$	4.28587	0.166324
$665$	0	0
$666$	−16.8563	−0.653166
$667$	37.6803	1.45899
$668$	−35.0645	−1.35669
$669$	8.66713	0.335090
$670$	0	0
$671$	24.9759	0.964183
$672$	2.76778	0.106770
$673$	5.22751	0.201506	0.100753	−	0.994911i	$-0.467875\pi$
$673$	5.22751	0.201506	0.100753	+	0.994911i	$0.467875\pi$
$674$	−6.54295	−0.252025
$675$	0	0
$676$	22.3991	0.861504
$677$	−12.7618	−0.490475	−0.245238	−	0.969463i	$-0.578866\pi$
$677$	−12.7618	−0.490475	−0.245238	+	0.969463i	$0.578866\pi$
$678$	29.5633	1.13537
$679$	−7.47210	−0.286753
$680$	0	0
$681$	−2.53552	−0.0971613
$682$	−127.545	−4.88396
$683$	7.57295	0.289771	0.144885	−	0.989448i	$-0.453719\pi$
$683$	7.57295	0.289771	0.144885	+	0.989448i	$0.453719\pi$
$684$	−23.9451	−0.915565
$685$	0	0
$686$	−12.2599	−0.468087
$687$	13.5132	0.515560
$688$	−20.6708	−0.788067
$689$	−47.4860	−1.80907
$690$	0	0
$691$	−6.70480	−0.255063	−0.127531	−	0.991835i	$-0.540705\pi$
$691$	−6.70480	−0.255063	−0.127531	+	0.991835i	$0.540705\pi$
$692$	16.1767	0.614947
$693$	5.87554	0.223193
$694$	34.0614	1.29295
$695$	0	0
$696$	−3.62979	−0.137587
$697$	−40.1654	−1.52137
$698$	51.4895	1.94891
$699$	14.3740	0.543676
$700$	0	0
$701$	8.09493	0.305741	0.152871	−	0.988246i	$-0.451148\pi$
$701$	8.09493	0.305741	0.152871	+	0.988246i	$0.451148\pi$
$702$	42.7800	1.61463
$703$	−14.7807	−0.557463
$704$	−62.7208	−2.36388
$705$	0	0
$706$	−48.7016	−1.83291
$707$	0.459776	0.0172917
$708$	2.32220	0.0872738
$709$	31.8519	1.19622	0.598112	−	0.801412i	$-0.295918\pi$
$709$	31.8519	1.19622	0.598112	+	0.801412i	$0.295918\pi$
$710$	0	0
$711$	4.32495	0.162198
$712$	2.14601	0.0804250
$713$	−67.0872	−2.51243
$714$	−2.36595	−0.0885433
$715$	0	0
$716$	58.8703	2.20009
$717$	6.53237	0.243956
$718$	−30.3654	−1.13323
$719$	−19.3047	−0.719943	−0.359972	−	0.932963i	$-0.617214\pi$
$719$	−19.3047	−0.719943	−0.359972	+	0.932963i	$0.617214\pi$
$720$	0	0
$721$	−4.22930	−0.157507
$722$	1.00315	0.0373332
$723$	3.26787	0.121534
$724$	24.7014	0.918020
$725$	0	0
$726$	40.1453	1.48993
$727$	8.91576	0.330667	0.165334	−	0.986238i	$-0.447130\pi$
$727$	8.91576	0.330667	0.165334	+	0.986238i	$0.447130\pi$
$728$	−1.55521	−0.0576399
$729$	2.11802	0.0784452
$730$	0	0
$731$	21.8563	0.808383
$732$	−8.10631	−0.299618
$733$	−29.0119	−1.07158	−0.535789	−	0.844352i	$-0.679986\pi$
$733$	−29.0119	−1.07158	−0.535789	+	0.844352i	$0.679986\pi$
$734$	−45.1563	−1.66675
$735$	0	0
$736$	−52.3657	−1.93023
$737$	−16.5582	−0.609930
$738$	−59.6941	−2.19737
$739$	−29.5801	−1.08812	−0.544061	−	0.839045i	$-0.683114\pi$
$739$	−29.5801	−1.08812	−0.544061	+	0.839045i	$0.683114\pi$
$740$	0	0
$741$	16.4685	0.604984
$742$	8.89058	0.326383
$743$	−33.7059	−1.23655	−0.618274	−	0.785963i	$-0.712168\pi$
$743$	−33.7059	−1.23655	−0.618274	+	0.785963i	$0.712168\pi$
$744$	6.46260	0.236930
$745$	0	0
$746$	14.0928	0.515975
$747$	13.0096	0.475995
$748$	46.1541	1.68756
$749$	−3.30391	−0.120722
$750$	0	0
$751$	6.61046	0.241219	0.120610	−	0.992700i	$-0.461515\pi$
$751$	6.61046	0.241219	0.120610	+	0.992700i	$0.461515\pi$
$752$	3.12314	0.113889
$753$	0.648360	0.0236275
$754$	−57.5577	−2.09613
$755$	0	0
$756$	−4.34381	−0.157983
$757$	−18.6772	−0.678833	−0.339417	−	0.940636i	$-0.610230\pi$
$757$	−18.6772	−0.678833	−0.339417	+	0.940636i	$0.610230\pi$
$758$	−46.0714	−1.67339
$759$	30.8842	1.12103
$760$	0	0
$761$	−27.6470	−1.00220	−0.501101	−	0.865389i	$-0.667071\pi$
$761$	−27.6470	−1.00220	−0.501101	+	0.865389i	$0.667071\pi$
$762$	17.8172	0.645448
$763$	−7.74002	−0.280208
$764$	−39.5358	−1.43036
$765$	0	0
$766$	−12.5937	−0.455031
$767$	5.74860	0.207570
$768$	−6.91133	−0.249391
$769$	−6.09456	−0.219775	−0.109888	−	0.993944i	$-0.535049\pi$
$769$	−6.09456	−0.219775	−0.109888	+	0.993944i	$0.535049\pi$
$770$	0	0
$771$	−6.04860	−0.217835
$772$	−0.395677	−0.0142407
$773$	23.4880	0.844805	0.422402	−	0.906408i	$-0.361187\pi$
$773$	23.4880	0.844805	0.422402	+	0.906408i	$0.361187\pi$
$774$	32.4830	1.16758
$775$	0	0
$776$	−13.6184	−0.488872
$777$	−1.17714	−0.0422295
$778$	18.4906	0.662922
$779$	−52.3437	−1.87541
$780$	0	0
$781$	11.7199	0.419370
$782$	44.7631	1.60072
$783$	−25.0972	−0.896901
$784$	21.2995	0.760697
$785$	0	0
$786$	19.2457	0.686472
$787$	15.7531	0.561538	0.280769	−	0.959775i	$-0.409411\pi$
$787$	15.7531	0.561538	0.280769	+	0.959775i	$0.409411\pi$
$788$	14.5582	0.518613
$789$	−8.07147	−0.287352
$790$	0	0
$791$	−7.43095	−0.264214
$792$	10.7085	0.380512
$793$	−20.0671	−0.712605
$794$	40.8898	1.45112
$795$	0	0
$796$	43.6329	1.54653
$797$	−46.6282	−1.65165	−0.825827	−	0.563923i	$-0.809291\pi$
$797$	−46.6282	−1.65165	−0.825827	+	0.563923i	$0.809291\pi$
$798$	−3.08331	−0.109148
$799$	−3.30225	−0.116825
$800$	0	0
$801$	6.51409	0.230164
$802$	−23.9106	−0.844313
$803$	59.8173	2.11091
$804$	5.37423	0.189535
$805$	0	0
$806$	102.478	3.60962
$807$	5.86418	0.206429
$808$	0.837972	0.0294798
$809$	33.9847	1.19484	0.597419	−	0.801929i	$-0.296193\pi$
$809$	33.9847	1.19484	0.597419	+	0.801929i	$0.296193\pi$
$810$	0	0
$811$	−3.17987	−0.111660	−0.0558301	−	0.998440i	$-0.517781\pi$
$811$	−3.17987	−0.111660	−0.0558301	+	0.998440i	$0.517781\pi$
$812$	5.84431	0.205095
$813$	2.26420	0.0794091
$814$	42.3415	1.48407
$815$	0	0
$816$	8.32937	0.291586
$817$	28.4832	0.996500
$818$	−9.07391	−0.317262
$819$	−4.72076	−0.164957
$820$	0	0
$821$	−43.1101	−1.50455	−0.752276	−	0.658848i	$-0.771044\pi$
$821$	−43.1101	−1.50455	−0.752276	+	0.658848i	$0.771044\pi$
$822$	−8.26544	−0.288290
$823$	8.82702	0.307690	0.153845	−	0.988095i	$-0.450834\pi$
$823$	8.82702	0.307690	0.153845	+	0.988095i	$0.450834\pi$
$824$	−7.70817	−0.268527
$825$	0	0
$826$	−1.07628	−0.0374487
$827$	−31.6764	−1.10150	−0.550748	−	0.834672i	$-0.685657\pi$
$827$	−31.6764	−1.10150	−0.550748	+	0.834672i	$0.685657\pi$
$828$	36.0799	1.25386
$829$	7.96237	0.276545	0.138272	−	0.990394i	$-0.455845\pi$
$829$	7.96237	0.276545	0.138272	+	0.990394i	$0.455845\pi$
$830$	0	0
$831$	22.9003	0.794401
$832$	50.3937	1.74709
$833$	−22.5210	−0.780308
$834$	22.3162	0.772747
$835$	0	0
$836$	60.1482	2.08027
$837$	44.6839	1.54450
$838$	−30.3224	−1.04747
$839$	−6.43833	−0.222276	−0.111138	−	0.993805i	$-0.535450\pi$
$839$	−6.43833	−0.222276	−0.111138	+	0.993805i	$0.535450\pi$
$840$	0	0
$841$	4.76661	0.164366
$842$	−62.9697	−2.17008
$843$	−1.62351	−0.0559167
$844$	15.9531	0.549130
$845$	0	0
$846$	−4.90783	−0.168735
$847$	−10.0908	−0.346725
$848$	−31.2995	−1.07483
$849$	5.75516	0.197517
$850$	0	0
$851$	22.2711	0.763444
$852$	−3.80387	−0.130318
$853$	30.6106	1.04809	0.524043	−	0.851692i	$-0.324423\pi$
$853$	30.6106	1.04809	0.524043	+	0.851692i	$0.324423\pi$
$854$	3.75707	0.128564
$855$	0	0
$856$	−6.02159	−0.205814
$857$	29.6799	1.01384	0.506922	−	0.861992i	$-0.330783\pi$
$857$	29.6799	1.01384	0.506922	+	0.861992i	$0.330783\pi$
$858$	−47.1765	−1.61058
$859$	−17.1547	−0.585311	−0.292655	−	0.956218i	$-0.594539\pi$
$859$	−17.1547	−0.585311	−0.292655	+	0.956218i	$0.594539\pi$
$860$	0	0
$861$	−4.16867	−0.142068
$862$	48.9730	1.66803
$863$	11.2260	0.382138	0.191069	−	0.981577i	$-0.438805\pi$
$863$	11.2260	0.382138	0.191069	+	0.981577i	$0.438805\pi$
$864$	34.8786	1.18659
$865$	0	0
$866$	15.4328	0.524429
$867$	4.92262	0.167181
$868$	−10.4054	−0.353182
$869$	−10.8639	−0.368533
$870$	0	0
$871$	13.3039	0.450785
$872$	−14.1067	−0.477713
$873$	−41.3379	−1.39908
$874$	58.3354	1.97322
$875$	0	0
$876$	−19.4146	−0.655959
$877$	−19.8245	−0.669425	−0.334713	−	0.942320i	$-0.608639\pi$
$877$	−19.8245	−0.669425	−0.334713	+	0.942320i	$0.608639\pi$
$878$	−37.4414	−1.26358
$879$	−23.3700	−0.788249
$880$	0	0
$881$	−38.3201	−1.29104	−0.645518	−	0.763745i	$-0.723358\pi$
$881$	−38.3201	−1.29104	−0.645518	+	0.763745i	$0.723358\pi$
$882$	−33.4710	−1.12703
$883$	−11.0266	−0.371076	−0.185538	−	0.982637i	$-0.559403\pi$
$883$	−11.0266	−0.371076	−0.185538	+	0.982637i	$0.559403\pi$
$884$	−37.0830	−1.24724
$885$	0	0
$886$	79.2202	2.66146
$887$	57.5815	1.93340	0.966699	−	0.255916i	$-0.0823769\pi$
$887$	57.5815	1.93340	0.966699	+	0.255916i	$0.0823769\pi$
$888$	−2.14541	−0.0719951
$889$	−4.47848	−0.150203
$890$	0	0
$891$	20.9654	0.702368
$892$	−25.4337	−0.851583
$893$	−4.30350	−0.144011
$894$	10.4122	0.348234
$895$	0	0
$896$	−2.58086	−0.0862204
$897$	−24.8142	−0.828523
$898$	−59.9040	−1.99902
$899$	−60.1192	−2.00509
$900$	0	0
$901$	33.0945	1.10254
$902$	149.947	4.99268
$903$	2.26841	0.0754879
$904$	−13.5434	−0.450446
$905$	0	0
$906$	−20.1853	−0.670611
$907$	−11.1726	−0.370981	−0.185491	−	0.982646i	$-0.559387\pi$
$907$	−11.1726	−0.370981	−0.185491	+	0.982646i	$0.559387\pi$
$908$	7.44048	0.246921
$909$	2.54362	0.0843666
$910$	0	0
$911$	−40.5709	−1.34417	−0.672087	−	0.740472i	$-0.734602\pi$
$911$	−40.5709	−1.34417	−0.672087	+	0.740472i	$0.734602\pi$
$912$	10.8549	0.359441
$913$	−32.6789	−1.08152
$914$	−76.0489	−2.51547
$915$	0	0
$916$	−39.6545	−1.31022
$917$	−4.83756	−0.159750
$918$	−29.8148	−0.984034
$919$	18.7412	0.618214	0.309107	−	0.951027i	$-0.399970\pi$
$919$	18.7412	0.618214	0.309107	+	0.951027i	$0.399970\pi$
$920$	0	0
$921$	−8.74584	−0.288185
$922$	0.968196	0.0318858
$923$	−9.41645	−0.309946
$924$	4.79022	0.157587
$925$	0	0
$926$	−76.3246	−2.50818
$927$	−23.3978	−0.768483
$928$	−46.9268	−1.54045
$929$	−33.7121	−1.10606	−0.553029	−	0.833162i	$-0.686528\pi$
$929$	−33.7121	−1.10606	−0.553029	+	0.833162i	$0.686528\pi$
$930$	0	0
$931$	−29.3495	−0.961891
$932$	−42.1806	−1.38167
$933$	23.2368	0.760738
$934$	−29.7450	−0.973285
$935$	0	0
$936$	−8.60389	−0.281227
$937$	13.9422	0.455471	0.227735	−	0.973723i	$-0.426868\pi$
$937$	13.9422	0.455471	0.227735	+	0.973723i	$0.426868\pi$
$938$	−2.49082	−0.0813282
$939$	−5.96131	−0.194540
$940$	0	0
$941$	−3.11593	−0.101576	−0.0507882	−	0.998709i	$-0.516173\pi$
$941$	−3.11593	−0.101576	−0.0507882	+	0.998709i	$0.516173\pi$
$942$	15.1483	0.493560
$943$	78.8701	2.56836
$944$	3.78908	0.123324
$945$	0	0
$946$	−81.5946	−2.65287
$947$	−4.94780	−0.160782	−0.0803909	−	0.996763i	$-0.525617\pi$
$947$	−4.94780	−0.160782	−0.0803909	+	0.996763i	$0.525617\pi$
$948$	3.52605	0.114521
$949$	−48.0608	−1.56012
$950$	0	0
$951$	19.2761	0.625069
$952$	1.08388	0.0351286
$953$	25.9745	0.841398	0.420699	−	0.907200i	$-0.361785\pi$
$953$	25.9745	0.841398	0.420699	+	0.907200i	$0.361785\pi$
$954$	49.1854	1.59244
$955$	0	0
$956$	−19.1692	−0.619977
$957$	27.6764	0.894652
$958$	−53.6929	−1.73474
$959$	2.07758	0.0670885
$960$	0	0
$961$	76.0382	2.45284
$962$	−34.0197	−1.09684
$963$	−18.2782	−0.589008
$964$	−9.58958	−0.308860
$965$	0	0
$966$	4.64585	0.149478
$967$	−44.5002	−1.43103	−0.715515	−	0.698598i	$-0.753808\pi$
$967$	−44.5002	−1.43103	−0.715515	+	0.698598i	$0.753808\pi$
$968$	−18.3912	−0.591115
$969$	−11.4774	−0.368707
$970$	0	0
$971$	−48.0753	−1.54281	−0.771405	−	0.636345i	$-0.780446\pi$
$971$	−48.0753	−1.54281	−0.771405	+	0.636345i	$0.780446\pi$
$972$	−37.5125	−1.20321
$973$	−5.60935	−0.179827
$974$	35.6815	1.14331
$975$	0	0
$976$	−13.2269	−0.423382
$977$	−54.6084	−1.74708	−0.873538	−	0.486756i	$-0.838180\pi$
$977$	−54.6084	−1.74708	−0.873538	+	0.486756i	$0.838180\pi$
$978$	−2.72052	−0.0869925
$979$	−16.3629	−0.522960
$980$	0	0
$981$	−42.8201	−1.36714
$982$	28.9351	0.923357
$983$	9.17638	0.292681	0.146341	−	0.989234i	$-0.453250\pi$
$983$	9.17638	0.292681	0.146341	+	0.989234i	$0.453250\pi$
$984$	−7.59767	−0.242205
$985$	0	0
$986$	40.1138	1.27748
$987$	−0.342732	−0.0109093
$988$	−48.3267	−1.53748
$989$	−42.9177	−1.36470
$990$	0	0
$991$	39.7431	1.26248	0.631240	−	0.775588i	$-0.282546\pi$
$991$	39.7431	1.26248	0.631240	+	0.775588i	$0.282546\pi$
$992$	83.5500	2.65272
$993$	−18.1190	−0.574988
$994$	1.76300	0.0559188
$995$	0	0
$996$	10.6065	0.336079
$997$	−29.0703	−0.920666	−0.460333	−	0.887746i	$-0.652270\pi$
$997$	−29.0703	−0.920666	−0.460333	+	0.887746i	$0.652270\pi$
$998$	85.3037	2.70024
$999$	−14.8338	−0.469321

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1175.2.a.k.1.3	✓	13
5.2	odd	4		1175.2.c.h.424.6		26
5.3	odd	4		1175.2.c.h.424.21		26
5.4	even	2		1175.2.a.l.1.11	yes	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1175.2.a.k.1.3	✓	13	1.1	even	1	trivial
1175.2.a.l.1.11	yes	13	5.4	even	2
1175.2.c.h.424.6		26	5.2	odd	4
1175.2.c.h.424.21		26	5.3	odd	4

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:	\( N \)	\(=\)	\( 1175 = 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1175.a (trivial)

\(f(q)\)	\(=\)	\(q-2.09045 q^{2} -0.807628 q^{3} +2.36999 q^{4} +1.68831 q^{6} -0.424369 q^{7} -0.773439 q^{8} -2.34774 q^{9} +O(q^{10})\)	\(q-2.09045 q^{2} -0.807628 q^{3} +2.36999 q^{4} +1.68831 q^{6} -0.424369 q^{7} -0.773439 q^{8} -2.34774 q^{9} +5.89732 q^{11} -1.91407 q^{12} -4.73827 q^{13} +0.887122 q^{14} -3.12314 q^{16} +3.30225 q^{17} +4.90783 q^{18} +4.30350 q^{19} +0.342732 q^{21} -12.3281 q^{22} -6.48440 q^{23} +0.624652 q^{24} +9.90511 q^{26} +4.31898 q^{27} -1.00575 q^{28} -5.81090 q^{29} +10.3459 q^{31} +8.07564 q^{32} -4.76285 q^{33} -6.90319 q^{34} -5.56410 q^{36} -3.43456 q^{37} -8.99626 q^{38} +3.82676 q^{39} -12.1630 q^{41} -0.716465 q^{42} +6.61860 q^{43} +13.9766 q^{44} +13.5553 q^{46} -1.00000 q^{47} +2.52233 q^{48} -6.81991 q^{49} -2.66699 q^{51} -11.2296 q^{52} +10.0218 q^{53} -9.02863 q^{54} +0.328224 q^{56} -3.47563 q^{57} +12.1474 q^{58} -1.21323 q^{59} +4.23512 q^{61} -21.6277 q^{62} +0.996306 q^{63} -10.6355 q^{64} +9.95650 q^{66} -2.80775 q^{67} +7.82628 q^{68} +5.23699 q^{69} +1.98732 q^{71} +1.81583 q^{72} +10.1431 q^{73} +7.17979 q^{74} +10.1992 q^{76} -2.50264 q^{77} -7.99965 q^{78} -1.84218 q^{79} +3.55508 q^{81} +25.4263 q^{82} -5.54132 q^{83} +0.812271 q^{84} -13.8359 q^{86} +4.69305 q^{87} -4.56122 q^{88} -2.77463 q^{89} +2.01077 q^{91} -15.3680 q^{92} -8.35566 q^{93} +2.09045 q^{94} -6.52212 q^{96} +17.6076 q^{97} +14.2567 q^{98} -13.8454 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 20 q^{4} + 5 q^{6} - 3 q^{8} + 27 q^{9}+O(q^{10}) \) 13 * q + 20 * q^4 + 5 * q^6 - 3 * q^8 + 27 * q^9	\( 13 q + 20 q^{4} + 5 q^{6} - 3 q^{8} + 27 q^{9} + 9 q^{11} + q^{12} + 2 q^{13} - 4 q^{14} + 34 q^{16} - 5 q^{17} + 7 q^{18} + 16 q^{19} + 26 q^{21} - 15 q^{22} + 10 q^{23} - 8 q^{24} + 3 q^{26} - 15 q^{27} + 30 q^{28} + 10 q^{29} + 15 q^{31} - 36 q^{32} + 22 q^{33} + q^{34} + 57 q^{36} - 5 q^{37} + 42 q^{38} - 2 q^{39} + 24 q^{41} - 62 q^{42} + 2 q^{43} - 6 q^{44} + 50 q^{46} - 13 q^{47} + 67 q^{48} + 39 q^{49} + 9 q^{51} - 36 q^{52} - 4 q^{53} - 34 q^{54} - 9 q^{56} + 5 q^{57} + 27 q^{58} - 25 q^{59} + 22 q^{61} - 2 q^{62} + 7 q^{63} + 53 q^{64} + 2 q^{66} + 4 q^{67} - 5 q^{68} + 5 q^{69} - 6 q^{71} - 66 q^{72} + 3 q^{73} - 49 q^{74} + 63 q^{76} + 8 q^{77} + 59 q^{78} + 37 q^{79} + 49 q^{81} - 48 q^{82} - 27 q^{83} - 2 q^{84} + 3 q^{86} + 35 q^{87} + 44 q^{88} + 32 q^{89} + 12 q^{91} - 29 q^{92} - 56 q^{93} - 11 q^{96} - 25 q^{97} + 61 q^{98} + 36 q^{99}+O(q^{100}) \) 13 * q + 20 * q^4 + 5 * q^6 - 3 * q^8 + 27 * q^9 + 9 * q^11 + q^12 + 2 * q^13 - 4 * q^14 + 34 * q^16 - 5 * q^17 + 7 * q^18 + 16 * q^19 + 26 * q^21 - 15 * q^22 + 10 * q^23 - 8 * q^24 + 3 * q^26 - 15 * q^27 + 30 * q^28 + 10 * q^29 + 15 * q^31 - 36 * q^32 + 22 * q^33 + q^34 + 57 * q^36 - 5 * q^37 + 42 * q^38 - 2 * q^39 + 24 * q^41 - 62 * q^42 + 2 * q^43 - 6 * q^44 + 50 * q^46 - 13 * q^47 + 67 * q^48 + 39 * q^49 + 9 * q^51 - 36 * q^52 - 4 * q^53 - 34 * q^54 - 9 * q^56 + 5 * q^57 + 27 * q^58 - 25 * q^59 + 22 * q^61 - 2 * q^62 + 7 * q^63 + 53 * q^64 + 2 * q^66 + 4 * q^67 - 5 * q^68 + 5 * q^69 - 6 * q^71 - 66 * q^72 + 3 * q^73 - 49 * q^74 + 63 * q^76 + 8 * q^77 + 59 * q^78 + 37 * q^79 + 49 * q^81 - 48 * q^82 - 27 * q^83 - 2 * q^84 + 3 * q^86 + 35 * q^87 + 44 * q^88 + 32 * q^89 + 12 * q^91 - 29 * q^92 - 56 * q^93 - 11 * q^96 - 25 * q^97 + 61 * q^98 + 36 * q^99

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