LMFDB - Embedded newform 1475.2.a.o.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1475,2,Mod(1,1475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1475, 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("1475.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1475 = 5^{2} \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1475.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:	$11.7779342981$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 10x^{5} + 7x^{4} + 27x^{3} - 11x^{2} - 10x - 1 $ x^7 - x^6 - 10x^5 + 7x^4 + 27x^3 - 11x^2 - 10*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 295)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.373339$ of defining polynomial
Character	$\chi$	$=$	1475.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.373339 q^{2} +0.532704 q^{3} -1.86062 q^{4} +0.198879 q^{6} -4.48402 q^{7} -1.44132 q^{8} -2.71623 q^{9} +O(q^{10})$	\(q+0.373339 q^{2} +0.532704 q^{3} -1.86062 q^{4} +0.198879 q^{6} -4.48402 q^{7} -1.44132 q^{8} -2.71623 q^{9} +3.82475 q^{11} -0.991158 q^{12} +4.31442 q^{13} -1.67406 q^{14} +3.18314 q^{16} -4.80996 q^{17} -1.01407 q^{18} +7.95383 q^{19} -2.38866 q^{21} +1.42793 q^{22} -6.00702 q^{23} -0.767796 q^{24} +1.61074 q^{26} -3.04505 q^{27} +8.34305 q^{28} +4.73093 q^{29} -5.70684 q^{31} +4.07103 q^{32} +2.03746 q^{33} -1.79575 q^{34} +5.05386 q^{36} +9.56710 q^{37} +2.96947 q^{38} +2.29831 q^{39} +1.30200 q^{41} -0.891778 q^{42} +3.81466 q^{43} -7.11640 q^{44} -2.24265 q^{46} +3.95883 q^{47} +1.69567 q^{48} +13.1065 q^{49} -2.56228 q^{51} -8.02749 q^{52} +7.47175 q^{53} -1.13684 q^{54} +6.46290 q^{56} +4.23703 q^{57} +1.76624 q^{58} +1.00000 q^{59} +9.52658 q^{61} -2.13058 q^{62} +12.1796 q^{63} -4.84640 q^{64} +0.760662 q^{66} +5.71115 q^{67} +8.94950 q^{68} -3.19996 q^{69} +15.1030 q^{71} +3.91495 q^{72} +0.770299 q^{73} +3.57177 q^{74} -14.7990 q^{76} -17.1503 q^{77} +0.858048 q^{78} -3.89812 q^{79} +6.52657 q^{81} +0.486088 q^{82} -9.31691 q^{83} +4.44438 q^{84} +1.42416 q^{86} +2.52019 q^{87} -5.51268 q^{88} -2.13321 q^{89} -19.3460 q^{91} +11.1768 q^{92} -3.04005 q^{93} +1.47799 q^{94} +2.16865 q^{96} -6.95969 q^{97} +4.89315 q^{98} -10.3889 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - q^{2} - 3 q^{3} + 7 q^{4} + 8 q^{6} + 4 q^{7} - 6 q^{8} + 16 q^{9}+O(q^{10}) $ 7 * q - q^2 - 3 * q^3 + 7 * q^4 + 8 * q^6 + 4 * q^7 - 6 * q^8 + 16 * q^9	$ 7 q - q^{2} - 3 q^{3} + 7 q^{4} + 8 q^{6} + 4 q^{7} - 6 q^{8} + 16 q^{9} + 3 q^{11} - 10 q^{12} + 9 q^{13} + 14 q^{14} + 7 q^{16} - 24 q^{17} + 16 q^{18} + 3 q^{19} + 9 q^{21} + 12 q^{22} - 3 q^{23} - 5 q^{24} - q^{26} - 18 q^{27} + 29 q^{28} + 4 q^{29} - q^{31} - 18 q^{32} - 8 q^{33} - 21 q^{34} - 5 q^{36} + 24 q^{37} + 13 q^{38} - 3 q^{39} + 45 q^{41} + 19 q^{43} - 27 q^{44} + 16 q^{46} - 16 q^{47} + 17 q^{48} + 13 q^{49} + 15 q^{51} + 5 q^{52} + 7 q^{53} - 18 q^{54} + 3 q^{56} + 8 q^{57} + 27 q^{58} + 7 q^{59} + 9 q^{61} - 29 q^{62} + 32 q^{63} - 32 q^{64} - 47 q^{66} + 16 q^{67} - 16 q^{68} - 10 q^{69} + 15 q^{71} + 51 q^{72} - 5 q^{73} - 10 q^{74} - 10 q^{76} + 3 q^{77} + 76 q^{78} + q^{79} + 31 q^{81} - 26 q^{82} - 23 q^{83} - 17 q^{84} - 2 q^{86} + 17 q^{87} + 22 q^{88} + 7 q^{89} - 12 q^{91} - 47 q^{92} + 20 q^{93} + 53 q^{94} + 19 q^{96} + 4 q^{97} + 68 q^{98} + 9 q^{99}+O(q^{100}) $ 7 * q - q^2 - 3 * q^3 + 7 * q^4 + 8 * q^6 + 4 * q^7 - 6 * q^8 + 16 * q^9 + 3 * q^11 - 10 * q^12 + 9 * q^13 + 14 * q^14 + 7 * q^16 - 24 * q^17 + 16 * q^18 + 3 * q^19 + 9 * q^21 + 12 * q^22 - 3 * q^23 - 5 * q^24 - q^26 - 18 * q^27 + 29 * q^28 + 4 * q^29 - q^31 - 18 * q^32 - 8 * q^33 - 21 * q^34 - 5 * q^36 + 24 * q^37 + 13 * q^38 - 3 * q^39 + 45 * q^41 + 19 * q^43 - 27 * q^44 + 16 * q^46 - 16 * q^47 + 17 * q^48 + 13 * q^49 + 15 * q^51 + 5 * q^52 + 7 * q^53 - 18 * q^54 + 3 * q^56 + 8 * q^57 + 27 * q^58 + 7 * q^59 + 9 * q^61 - 29 * q^62 + 32 * q^63 - 32 * q^64 - 47 * q^66 + 16 * q^67 - 16 * q^68 - 10 * q^69 + 15 * q^71 + 51 * q^72 - 5 * q^73 - 10 * q^74 - 10 * q^76 + 3 * q^77 + 76 * q^78 + q^79 + 31 * q^81 - 26 * q^82 - 23 * q^83 - 17 * q^84 - 2 * q^86 + 17 * q^87 + 22 * q^88 + 7 * q^89 - 12 * q^91 - 47 * q^92 + 20 * q^93 + 53 * q^94 + 19 * q^96 + 4 * q^97 + 68 * q^98 + 9 * 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 $

$2$	0.373339	0.263990	0.131995	−	0.991250i	$-0.457862\pi$
$2$	0.373339	0.263990	0.131995	+	0.991250i	$0.457862\pi$
$3$	0.532704	0.307557	0.153778	−	0.988105i	$-0.450856\pi$
$3$	0.532704	0.307557	0.153778	+	0.988105i	$0.450856\pi$
$4$	−1.86062	−0.930309
$5$	0	0
$5$	0	0
$6$	0.198879	0.0811920
$7$	−4.48402	−1.69480	−0.847401	−	0.530954i	$-0.821834\pi$
$7$	−4.48402	−1.69480	−0.847401	+	0.530954i	$0.821834\pi$
$8$	−1.44132	−0.509583
$9$	−2.71623	−0.905409
$10$	0	0
$11$	3.82475	1.15320	0.576602	−	0.817025i	$-0.304378\pi$
$11$	3.82475	1.15320	0.576602	+	0.817025i	$0.304378\pi$
$12$	−0.991158	−0.286123
$13$	4.31442	1.19661	0.598303	−	0.801270i	$-0.295842\pi$
$13$	4.31442	1.19661	0.598303	+	0.801270i	$0.295842\pi$
$14$	−1.67406	−0.447411
$15$	0	0
$16$	3.18314	0.795784
$17$	−4.80996	−1.16659	−0.583294	−	0.812261i	$-0.698236\pi$
$17$	−4.80996	−1.16659	−0.583294	+	0.812261i	$0.698236\pi$
$18$	−1.01407	−0.239019
$19$	7.95383	1.82473	0.912367	−	0.409374i	$-0.134253\pi$
$19$	7.95383	1.82473	0.912367	+	0.409374i	$0.134253\pi$
$20$	0	0
$21$	−2.38866	−0.521247
$22$	1.42793	0.304435
$23$	−6.00702	−1.25255	−0.626275	−	0.779602i	$-0.715421\pi$
$23$	−6.00702	−1.25255	−0.626275	+	0.779602i	$0.715421\pi$
$24$	−0.767796	−0.156726
$25$	0	0
$26$	1.61074	0.315892
$27$	−3.04505	−0.586021
$28$	8.34305	1.57669
$29$	4.73093	0.878513	0.439256	−	0.898362i	$-0.355242\pi$
$29$	4.73093	0.878513	0.439256	+	0.898362i	$0.355242\pi$
$30$	0	0
$31$	−5.70684	−1.02498	−0.512489	−	0.858694i	$-0.671277\pi$
$31$	−5.70684	−1.02498	−0.512489	+	0.858694i	$0.671277\pi$
$32$	4.07103	0.719662
$33$	2.03746	0.354676
$34$	−1.79575	−0.307968
$35$	0	0
$36$	5.05386	0.842310
$37$	9.56710	1.57282	0.786411	−	0.617704i	$-0.211937\pi$
$37$	9.56710	1.57282	0.786411	+	0.617704i	$0.211937\pi$
$38$	2.96947	0.481712
$39$	2.29831	0.368024
$40$	0	0
$41$	1.30200	0.203339	0.101669	−	0.994818i	$-0.467582\pi$
$41$	1.30200	0.203339	0.101669	+	0.994818i	$0.467582\pi$
$42$	−0.891778	−0.137604
$43$	3.81466	0.581730	0.290865	−	0.956764i	$-0.406057\pi$
$43$	3.81466	0.581730	0.290865	+	0.956764i	$0.406057\pi$
$44$	−7.11640	−1.07284
$45$	0	0
$46$	−2.24265	−0.330661
$47$	3.95883	0.577455	0.288727	−	0.957411i	$-0.406768\pi$
$47$	3.95883	0.577455	0.288727	+	0.957411i	$0.406768\pi$
$48$	1.69567	0.244749
$49$	13.1065	1.87235
$50$	0	0
$51$	−2.56228	−0.358792
$52$	−8.02749	−1.11321
$53$	7.47175	1.02632	0.513162	−	0.858292i	$-0.328474\pi$
$53$	7.47175	1.02632	0.513162	+	0.858292i	$0.328474\pi$
$54$	−1.13684	−0.154704
$55$	0	0
$56$	6.46290	0.863642
$57$	4.23703	0.561209
$58$	1.76624	0.231919
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	0	0
$61$	9.52658	1.21975	0.609877	−	0.792496i	$-0.291219\pi$
$61$	9.52658	1.21975	0.609877	+	0.792496i	$0.291219\pi$
$62$	−2.13058	−0.270584
$63$	12.1796	1.53449
$64$	−4.84640	−0.605800
$65$	0	0
$66$	0.760662	0.0936310
$67$	5.71115	0.697727	0.348864	−	0.937173i	$-0.386568\pi$
$67$	5.71115	0.697727	0.348864	+	0.937173i	$0.386568\pi$
$68$	8.94950	1.08529
$69$	−3.19996	−0.385230
$70$	0	0
$71$	15.1030	1.79240	0.896198	−	0.443655i	$-0.146318\pi$
$71$	15.1030	1.79240	0.896198	+	0.443655i	$0.146318\pi$
$72$	3.91495	0.461381
$73$	0.770299	0.0901567	0.0450784	−	0.998983i	$-0.485646\pi$
$73$	0.770299	0.0901567	0.0450784	+	0.998983i	$0.485646\pi$
$74$	3.57177	0.415210
$75$	0	0
$76$	−14.7990	−1.69757
$77$	−17.1503	−1.95445
$78$	0.858048	0.0971548
$79$	−3.89812	−0.438573	−0.219286	−	0.975661i	$-0.570373\pi$
$79$	−3.89812	−0.438573	−0.219286	+	0.975661i	$0.570373\pi$
$80$	0	0
$81$	6.52657	0.725174
$82$	0.486088	0.0536795
$83$	−9.31691	−1.02266	−0.511332	−	0.859383i	$-0.670848\pi$
$83$	−9.31691	−1.02266	−0.511332	+	0.859383i	$0.670848\pi$
$84$	4.44438	0.484921
$85$	0	0
$86$	1.42416	0.153571
$87$	2.52019	0.270192
$88$	−5.51268	−0.587654
$89$	−2.13321	−0.226120	−0.113060	−	0.993588i	$-0.536065\pi$
$89$	−2.13321	−0.226120	−0.113060	+	0.993588i	$0.536065\pi$
$90$	0	0
$91$	−19.3460	−2.02801
$92$	11.1768	1.16526
$93$	−3.04005	−0.315239
$94$	1.47799	0.152443
$95$	0	0
$96$	2.16865	0.221337
$97$	−6.95969	−0.706649	−0.353325	−	0.935501i	$-0.614949\pi$
$97$	−6.95969	−0.706649	−0.353325	+	0.935501i	$0.614949\pi$
$98$	4.89315	0.494283
$99$	−10.3889	−1.04412
$100$	0	0
$101$	−9.40732	−0.936064	−0.468032	−	0.883712i	$-0.655037\pi$
$101$	−9.40732	−0.936064	−0.468032	+	0.883712i	$0.655037\pi$
$102$	−0.956600	−0.0947175
$103$	−0.107012	−0.0105442	−0.00527208	−	0.999986i	$-0.501678\pi$
$103$	−0.107012	−0.0105442	−0.00527208	+	0.999986i	$0.501678\pi$
$104$	−6.21846	−0.609770
$105$	0	0
$106$	2.78949	0.270939
$107$	4.50122	0.435149	0.217575	−	0.976044i	$-0.430185\pi$
$107$	4.50122	0.435149	0.217575	+	0.976044i	$0.430185\pi$
$108$	5.66568	0.545181
$109$	−2.81849	−0.269963	−0.134981	−	0.990848i	$-0.543097\pi$
$109$	−2.81849	−0.269963	−0.134981	+	0.990848i	$0.543097\pi$
$110$	0	0
$111$	5.09643	0.483732
$112$	−14.2733	−1.34870
$113$	−4.86145	−0.457326	−0.228663	−	0.973506i	$-0.573435\pi$
$113$	−4.86145	−0.457326	−0.228663	+	0.973506i	$0.573435\pi$
$114$	1.58185	0.148154
$115$	0	0
$116$	−8.80246	−0.817288
$117$	−11.7189	−1.08342
$118$	0.373339	0.0343686
$119$	21.5680	1.97713
$120$	0	0
$121$	3.62870	0.329882
$122$	3.55664	0.322003
$123$	0.693582	0.0625382
$124$	10.6182	0.953547
$125$	0	0
$126$	4.54713	0.405090
$127$	7.79391	0.691598	0.345799	−	0.938309i	$-0.387608\pi$
$127$	7.79391	0.691598	0.345799	+	0.938309i	$0.387608\pi$
$128$	−9.95140	−0.879588
$129$	2.03208	0.178915
$130$	0	0
$131$	18.8605	1.64785	0.823926	−	0.566697i	$-0.191779\pi$
$131$	18.8605	1.64785	0.823926	+	0.566697i	$0.191779\pi$
$132$	−3.79093	−0.329958
$133$	−35.6651	−3.09256
$134$	2.13219	0.184193
$135$	0	0
$136$	6.93269	0.594473
$137$	−7.94912	−0.679139	−0.339569	−	0.940581i	$-0.610281\pi$
$137$	−7.94912	−0.679139	−0.339569	+	0.940581i	$0.610281\pi$
$138$	−1.19467	−0.101697
$139$	−14.2536	−1.20897	−0.604486	−	0.796616i	$-0.706622\pi$
$139$	−14.2536	−1.20897	−0.604486	+	0.796616i	$0.706622\pi$
$140$	0	0
$141$	2.10888	0.177600
$142$	5.63853	0.473175
$143$	16.5016	1.37993
$144$	−8.64612	−0.720510
$145$	0	0
$146$	0.287583	0.0238005
$147$	6.98186	0.575854
$148$	−17.8007	−1.46321
$149$	−6.40463	−0.524688	−0.262344	−	0.964974i	$-0.584495\pi$
$149$	−6.40463	−0.524688	−0.262344	+	0.964974i	$0.584495\pi$
$150$	0	0
$151$	−3.26584	−0.265770	−0.132885	−	0.991131i	$-0.542424\pi$
$151$	−3.26584	−0.265770	−0.132885	+	0.991131i	$0.542424\pi$
$152$	−11.4640	−0.929853
$153$	13.0650	1.05624
$154$	−6.40286	−0.515957
$155$	0	0
$156$	−4.27627	−0.342376
$157$	16.7824	1.33938	0.669691	−	0.742640i	$-0.266426\pi$
$157$	16.7824	1.33938	0.669691	+	0.742640i	$0.266426\pi$
$158$	−1.45532	−0.115779
$159$	3.98023	0.315652
$160$	0	0
$161$	26.9356	2.12282
$162$	2.43662	0.191439
$163$	6.15521	0.482113	0.241057	−	0.970511i	$-0.422506\pi$
$163$	6.15521	0.482113	0.241057	+	0.970511i	$0.422506\pi$
$164$	−2.42253	−0.189168
$165$	0	0
$166$	−3.47836	−0.269973
$167$	−0.457392	−0.0353940	−0.0176970	−	0.999843i	$-0.505633\pi$
$167$	−0.457392	−0.0353940	−0.0176970	+	0.999843i	$0.505633\pi$
$168$	3.44281	0.265619
$169$	5.61424	0.431865
$170$	0	0
$171$	−21.6044	−1.65213
$172$	−7.09762	−0.541188
$173$	15.9908	1.21576	0.607878	−	0.794030i	$-0.292021\pi$
$173$	15.9908	1.21576	0.607878	+	0.794030i	$0.292021\pi$
$174$	0.940883	0.0713282
$175$	0	0
$176$	12.1747	0.917702
$177$	0.532704	0.0400405
$178$	−0.796410	−0.0596935
$179$	−17.7992	−1.33038	−0.665188	−	0.746676i	$-0.731649\pi$
$179$	−17.7992	−1.33038	−0.665188	+	0.746676i	$0.731649\pi$
$180$	0	0
$181$	0.435111	0.0323415	0.0161708	−	0.999869i	$-0.494852\pi$
$181$	0.435111	0.0323415	0.0161708	+	0.999869i	$0.494852\pi$
$182$	−7.22260	−0.535375
$183$	5.07484	0.375143
$184$	8.65803	0.638279
$185$	0	0
$186$	−1.13497	−0.0832200
$187$	−18.3969	−1.34531
$188$	−7.36587	−0.537212
$189$	13.6541	0.993189
$190$	0	0
$191$	18.3124	1.32504	0.662518	−	0.749046i	$-0.269488\pi$
$191$	18.3124	1.32504	0.662518	+	0.749046i	$0.269488\pi$
$192$	−2.58170	−0.186318
$193$	17.8986	1.28837	0.644186	−	0.764869i	$-0.277196\pi$
$193$	17.8986	1.28837	0.644186	+	0.764869i	$0.277196\pi$
$194$	−2.59832	−0.186549
$195$	0	0
$196$	−24.3861	−1.74187
$197$	−13.6218	−0.970512	−0.485256	−	0.874372i	$-0.661274\pi$
$197$	−13.6218	−0.970512	−0.485256	+	0.874372i	$0.661274\pi$
$198$	−3.87857	−0.275638
$199$	−0.913774	−0.0647757	−0.0323879	−	0.999475i	$-0.510311\pi$
$199$	−0.913774	−0.0647757	−0.0323879	+	0.999475i	$0.510311\pi$
$200$	0	0
$201$	3.04235	0.214591
$202$	−3.51212	−0.247112
$203$	−21.2136	−1.48890
$204$	4.76743	0.333787
$205$	0	0
$206$	−0.0399516	−0.00278356
$207$	16.3164	1.13407
$208$	13.7334	0.952240
$209$	30.4214	2.10429
$210$	0	0
$211$	−15.5468	−1.07029	−0.535145	−	0.844761i	$-0.679743\pi$
$211$	−15.5468	−1.07029	−0.535145	+	0.844761i	$0.679743\pi$
$212$	−13.9021	−0.954798
$213$	8.04542	0.551263
$214$	1.68048	0.114875
$215$	0	0
$216$	4.38889	0.298626
$217$	25.5896	1.73713
$218$	−1.05225	−0.0712676
$219$	0.410341	0.0277283
$220$	0	0
$221$	−20.7522	−1.39594
$222$	1.90269	0.127700
$223$	−22.1071	−1.48040	−0.740201	−	0.672385i	$-0.765270\pi$
$223$	−22.1071	−1.48040	−0.740201	+	0.672385i	$0.765270\pi$
$224$	−18.2546	−1.21968
$225$	0	0
$226$	−1.81497	−0.120730
$227$	25.3022	1.67936	0.839682	−	0.543078i	$-0.182741\pi$
$227$	25.3022	1.67936	0.839682	+	0.543078i	$0.182741\pi$
$228$	−7.88350	−0.522098
$229$	6.23659	0.412125	0.206063	−	0.978539i	$-0.433935\pi$
$229$	6.23659	0.412125	0.206063	+	0.978539i	$0.433935\pi$
$230$	0	0
$231$	−9.13600	−0.601105
$232$	−6.81878	−0.447675
$233$	1.97525	0.129403	0.0647014	−	0.997905i	$-0.479391\pi$
$233$	1.97525	0.129403	0.0647014	+	0.997905i	$0.479391\pi$
$234$	−4.37514	−0.286012
$235$	0	0
$236$	−1.86062	−0.121116
$237$	−2.07654	−0.134886
$238$	8.05216	0.521944
$239$	−2.59733	−0.168008	−0.0840038	−	0.996465i	$-0.526771\pi$
$239$	−2.59733	−0.168008	−0.0840038	+	0.996465i	$0.526771\pi$
$240$	0	0
$241$	−18.8663	−1.21528	−0.607641	−	0.794211i	$-0.707884\pi$
$241$	−18.8663	−1.21528	−0.607641	+	0.794211i	$0.707884\pi$
$242$	1.35473	0.0870856
$243$	12.6119	0.809053
$244$	−17.7253	−1.13475
$245$	0	0
$246$	0.258941	0.0165095
$247$	34.3162	2.18349
$248$	8.22537	0.522312
$249$	−4.96315	−0.314527
$250$	0	0
$251$	2.13831	0.134969	0.0674846	−	0.997720i	$-0.478503\pi$
$251$	2.13831	0.134969	0.0674846	+	0.997720i	$0.478503\pi$
$252$	−22.6616	−1.42755
$253$	−22.9753	−1.44445
$254$	2.90977	0.182575
$255$	0	0
$256$	5.97756	0.373597
$257$	−7.11695	−0.443943	−0.221972	−	0.975053i	$-0.571249\pi$
$257$	−7.11695	−0.443943	−0.221972	+	0.975053i	$0.571249\pi$
$258$	0.758655	0.0472318
$259$	−42.8991	−2.66562
$260$	0	0
$261$	−12.8503	−0.795413
$262$	7.04137	0.435017
$263$	−1.86948	−0.115277	−0.0576386	−	0.998338i	$-0.518357\pi$
$263$	−1.86948	−0.115277	−0.0576386	+	0.998338i	$0.518357\pi$
$264$	−2.93662	−0.180737
$265$	0	0
$266$	−13.3152	−0.816406
$267$	−1.13637	−0.0695447
$268$	−10.6263	−0.649102
$269$	14.0265	0.855211	0.427605	−	0.903965i	$-0.359357\pi$
$269$	14.0265	0.855211	0.427605	+	0.903965i	$0.359357\pi$
$270$	0	0
$271$	32.1451	1.95268	0.976339	−	0.216246i	$-0.0693814\pi$
$271$	32.1451	1.95268	0.976339	+	0.216246i	$0.0693814\pi$
$272$	−15.3108	−0.928352
$273$	−10.3057	−0.623727
$274$	−2.96771	−0.179286
$275$	0	0
$276$	5.95391	0.358383
$277$	25.9400	1.55858	0.779292	−	0.626661i	$-0.215579\pi$
$277$	25.9400	1.55858	0.779292	+	0.626661i	$0.215579\pi$
$278$	−5.32141	−0.319157
$279$	15.5011	0.928025
$280$	0	0
$281$	−6.90884	−0.412147	−0.206073	−	0.978537i	$-0.566069\pi$
$281$	−6.90884	−0.412147	−0.206073	+	0.978537i	$0.566069\pi$
$282$	0.787328	0.0468847
$283$	−21.9066	−1.30221	−0.651105	−	0.758988i	$-0.725694\pi$
$283$	−21.9066	−1.30221	−0.651105	+	0.758988i	$0.725694\pi$
$284$	−28.1009	−1.66748
$285$	0	0
$286$	6.16068	0.364289
$287$	−5.83821	−0.344619
$288$	−11.0578	−0.651589
$289$	6.13574	0.360926
$290$	0	0
$291$	−3.70745	−0.217335
$292$	−1.43323	−0.0838736
$293$	16.1180	0.941625	0.470812	−	0.882233i	$-0.343961\pi$
$293$	16.1180	0.941625	0.470812	+	0.882233i	$0.343961\pi$
$294$	2.60660	0.152020
$295$	0	0
$296$	−13.7892	−0.801483
$297$	−11.6466	−0.675802
$298$	−2.39110	−0.138512
$299$	−25.9168	−1.49881
$300$	0	0
$301$	−17.1050	−0.985916
$302$	−1.21926	−0.0701608
$303$	−5.01132	−0.287893
$304$	25.3181	1.45209
$305$	0	0
$306$	4.87765	0.278837
$307$	−1.63385	−0.0932490	−0.0466245	−	0.998912i	$-0.514846\pi$
$307$	−1.63385	−0.0932490	−0.0466245	+	0.998912i	$0.514846\pi$
$308$	31.9101	1.81825
$309$	−0.0570054	−0.00324293
$310$	0	0
$311$	−23.0263	−1.30570	−0.652851	−	0.757486i	$-0.726427\pi$
$311$	−23.0263	−1.30570	−0.652851	+	0.757486i	$0.726427\pi$
$312$	−3.31259	−0.187539
$313$	5.63776	0.318665	0.159332	−	0.987225i	$-0.449066\pi$
$313$	5.63776	0.318665	0.159332	+	0.987225i	$0.449066\pi$
$314$	6.26553	0.353584
$315$	0	0
$316$	7.25291	0.408008
$317$	18.0172	1.01195	0.505974	−	0.862549i	$-0.331133\pi$
$317$	18.0172	1.01195	0.505974	+	0.862549i	$0.331133\pi$
$318$	1.48597	0.0833292
$319$	18.0946	1.01310
$320$	0	0
$321$	2.39782	0.133833
$322$	10.0561	0.560405
$323$	−38.2576	−2.12871
$324$	−12.1435	−0.674636
$325$	0	0
$326$	2.29798	0.127273
$327$	−1.50142	−0.0830289
$328$	−1.87660	−0.103618
$329$	−17.7515	−0.978671
$330$	0	0
$331$	−9.03045	−0.496359	−0.248179	−	0.968714i	$-0.579832\pi$
$331$	−9.03045	−0.496359	−0.248179	+	0.968714i	$0.579832\pi$
$332$	17.3352	0.951393
$333$	−25.9864	−1.42405
$334$	−0.170762	−0.00934368
$335$	0	0
$336$	−7.60341	−0.414800
$337$	3.23828	0.176400	0.0882002	−	0.996103i	$-0.471888\pi$
$337$	3.23828	0.176400	0.0882002	+	0.996103i	$0.471888\pi$
$338$	2.09601	0.114008
$339$	−2.58971	−0.140654
$340$	0	0
$341$	−21.8272	−1.18201
$342$	−8.06576	−0.436146
$343$	−27.3815	−1.47846
$344$	−5.49814	−0.296440
$345$	0	0
$346$	5.96998	0.320948
$347$	3.52433	0.189196	0.0945981	−	0.995516i	$-0.469843\pi$
$347$	3.52433	0.189196	0.0945981	+	0.995516i	$0.469843\pi$
$348$	−4.68910	−0.251362
$349$	22.4009	1.19909	0.599547	−	0.800340i	$-0.295348\pi$
$349$	22.4009	1.19909	0.599547	+	0.800340i	$0.295348\pi$
$350$	0	0
$351$	−13.1377	−0.701236
$352$	15.5706	0.829918
$353$	13.7726	0.733044	0.366522	−	0.930409i	$-0.380548\pi$
$353$	13.7726	0.733044	0.366522	+	0.930409i	$0.380548\pi$
$354$	0.198879	0.0105703
$355$	0	0
$356$	3.96909	0.210361
$357$	11.4893	0.608081
$358$	−6.64514	−0.351206
$359$	−17.6891	−0.933594	−0.466797	−	0.884365i	$-0.654592\pi$
$359$	−17.6891	−0.933594	−0.466797	+	0.884365i	$0.654592\pi$
$360$	0	0
$361$	44.2634	2.32965
$362$	0.162444	0.00853785
$363$	1.93302	0.101457
$364$	35.9955	1.88667
$365$	0	0
$366$	1.89464	0.0990342
$367$	20.2776	1.05848	0.529241	−	0.848472i	$-0.322477\pi$
$367$	20.2776	1.05848	0.529241	+	0.848472i	$0.322477\pi$
$368$	−19.1212	−0.996760
$369$	−3.53654	−0.184105
$370$	0	0
$371$	−33.5035	−1.73941
$372$	5.65638	0.293270
$373$	11.5133	0.596134	0.298067	−	0.954545i	$-0.403658\pi$
$373$	11.5133	0.596134	0.298067	+	0.954545i	$0.403658\pi$
$374$	−6.86827	−0.355150
$375$	0	0
$376$	−5.70594	−0.294261
$377$	20.4113	1.05123
$378$	5.09760	0.262192
$379$	26.0724	1.33925	0.669624	−	0.742701i	$-0.266455\pi$
$379$	26.0724	1.33925	0.669624	+	0.742701i	$0.266455\pi$
$380$	0	0
$381$	4.15184	0.212705
$382$	6.83672	0.349797
$383$	−18.9978	−0.970741	−0.485370	−	0.874309i	$-0.661315\pi$
$383$	−18.9978	−0.970741	−0.485370	+	0.874309i	$0.661315\pi$
$384$	−5.30115	−0.270523
$385$	0	0
$386$	6.68225	0.340118
$387$	−10.3615	−0.526703
$388$	12.9493	0.657402
$389$	22.8774	1.15993	0.579964	−	0.814642i	$-0.303066\pi$
$389$	22.8774	1.15993	0.579964	+	0.814642i	$0.303066\pi$
$390$	0	0
$391$	28.8936	1.46121
$392$	−18.8906	−0.954118
$393$	10.0471	0.506808
$394$	−5.08554	−0.256206
$395$	0	0
$396$	19.3297	0.971356
$397$	33.8649	1.69963	0.849814	−	0.527082i	$-0.176714\pi$
$397$	33.8649	1.69963	0.849814	+	0.527082i	$0.176714\pi$
$398$	−0.341147	−0.0171002
$399$	−18.9990	−0.951137
$400$	0	0
$401$	8.21019	0.409997	0.204999	−	0.978762i	$-0.434281\pi$
$401$	8.21019	0.409997	0.204999	+	0.978762i	$0.434281\pi$
$402$	1.13583	0.0566499
$403$	−24.6217	−1.22649
$404$	17.5034	0.870828
$405$	0	0
$406$	−7.91987	−0.393056
$407$	36.5917	1.81378
$408$	3.69307	0.182834
$409$	18.7409	0.926678	0.463339	−	0.886181i	$-0.346651\pi$
$409$	18.7409	0.926678	0.463339	+	0.886181i	$0.346651\pi$
$410$	0	0
$411$	−4.23452	−0.208874
$412$	0.199108	0.00980933
$413$	−4.48402	−0.220644
$414$	6.09156	0.299384
$415$	0	0
$416$	17.5641	0.861152
$417$	−7.59293	−0.371827
$418$	11.3575	0.555513
$419$	−4.73086	−0.231118	−0.115559	−	0.993301i	$-0.536866\pi$
$419$	−4.73086	−0.231118	−0.115559	+	0.993301i	$0.536866\pi$
$420$	0	0
$421$	28.0810	1.36858	0.684292	−	0.729209i	$-0.260112\pi$
$421$	28.0810	1.36858	0.684292	+	0.729209i	$0.260112\pi$
$422$	−5.80424	−0.282546
$423$	−10.7531	−0.522833
$424$	−10.7692	−0.522997
$425$	0	0
$426$	3.00367	0.145528
$427$	−42.7174	−2.06724
$428$	−8.37505	−0.404823
$429$	8.79045	0.424407
$430$	0	0
$431$	−36.9887	−1.78168	−0.890841	−	0.454315i	$-0.849884\pi$
$431$	−36.9887	−1.78168	−0.890841	+	0.454315i	$0.849884\pi$
$432$	−9.69282	−0.466346
$433$	6.56721	0.315600	0.157800	−	0.987471i	$-0.449560\pi$
$433$	6.56721	0.315600	0.157800	+	0.987471i	$0.449560\pi$
$434$	9.55359	0.458587
$435$	0	0
$436$	5.24414	0.251149
$437$	−47.7788	−2.28557
$438$	0.153196	0.00732000
$439$	16.2440	0.775285	0.387643	−	0.921810i	$-0.373290\pi$
$439$	16.2440	0.775285	0.387643	+	0.921810i	$0.373290\pi$
$440$	0	0
$441$	−35.6001	−1.69524
$442$	−7.74761	−0.368516
$443$	13.4169	0.637456	0.318728	−	0.947846i	$-0.396744\pi$
$443$	13.4169	0.637456	0.318728	+	0.947846i	$0.396744\pi$
$444$	−9.48251	−0.450020
$445$	0	0
$446$	−8.25345	−0.390812
$447$	−3.41177	−0.161371
$448$	21.7314	1.02671
$449$	12.1183	0.571899	0.285949	−	0.958245i	$-0.407691\pi$
$449$	12.1183	0.571899	0.285949	+	0.958245i	$0.407691\pi$
$450$	0	0
$451$	4.97984	0.234491
$452$	9.04530	0.425455
$453$	−1.73972	−0.0817394
$454$	9.44628	0.443336
$455$	0	0
$456$	−6.10691	−0.285982
$457$	−32.0214	−1.49790	−0.748949	−	0.662628i	$-0.769441\pi$
$457$	−32.0214	−1.49790	−0.748949	+	0.662628i	$0.769441\pi$
$458$	2.32836	0.108797
$459$	14.6466	0.683645
$460$	0	0
$461$	−21.0866	−0.982102	−0.491051	−	0.871131i	$-0.663387\pi$
$461$	−21.0866	−0.982102	−0.491051	+	0.871131i	$0.663387\pi$
$462$	−3.41082	−0.158686
$463$	18.3779	0.854092	0.427046	−	0.904230i	$-0.359554\pi$
$463$	18.3779	0.854092	0.427046	+	0.904230i	$0.359554\pi$
$464$	15.0592	0.699106
$465$	0	0
$466$	0.737437	0.0341611
$467$	−17.2653	−0.798943	−0.399472	−	0.916746i	$-0.630806\pi$
$467$	−17.2653	−0.798943	−0.399472	+	0.916746i	$0.630806\pi$
$468$	21.8045	1.00791
$469$	−25.6089	−1.18251
$470$	0	0
$471$	8.94005	0.411936
$472$	−1.44132	−0.0663421
$473$	14.5901	0.670854
$474$	−0.775254	−0.0356086
$475$	0	0
$476$	−40.1298	−1.83935
$477$	−20.2950	−0.929242
$478$	−0.969685	−0.0443524
$479$	−23.9355	−1.09364	−0.546820	−	0.837250i	$-0.684162\pi$
$479$	−23.9355	−1.09364	−0.546820	+	0.837250i	$0.684162\pi$
$480$	0	0
$481$	41.2765	1.88205
$482$	−7.04351	−0.320823
$483$	14.3487	0.652889
$484$	−6.75162	−0.306892
$485$	0	0
$486$	4.70851	0.213582
$487$	10.8817	0.493095	0.246548	−	0.969131i	$-0.420704\pi$
$487$	10.8817	0.493095	0.246548	+	0.969131i	$0.420704\pi$
$488$	−13.7308	−0.621566
$489$	3.27890	0.148277
$490$	0	0
$491$	−36.1097	−1.62961	−0.814804	−	0.579736i	$-0.803156\pi$
$491$	−36.1097	−1.62961	−0.814804	+	0.579736i	$0.803156\pi$
$492$	−1.29049	−0.0581798
$493$	−22.7556	−1.02486
$494$	12.8116	0.576419
$495$	0	0
$496$	−18.1656	−0.815661
$497$	−67.7221	−3.03775
$498$	−1.85294	−0.0830321
$499$	2.56775	0.114948	0.0574742	−	0.998347i	$-0.481695\pi$
$499$	2.56775	0.114948	0.0574742	+	0.998347i	$0.481695\pi$
$500$	0	0
$501$	−0.243654	−0.0108857
$502$	0.798316	0.0356306
$503$	2.50280	0.111594	0.0557972	−	0.998442i	$-0.482230\pi$
$503$	2.50280	0.111594	0.0557972	+	0.998442i	$0.482230\pi$
$504$	−17.5547	−0.781949
$505$	0	0
$506$	−8.57759	−0.381320
$507$	2.99073	0.132823
$508$	−14.5015	−0.643400
$509$	−10.1055	−0.447917	−0.223959	−	0.974599i	$-0.571898\pi$
$509$	−10.1055	−0.447917	−0.223959	+	0.974599i	$0.571898\pi$
$510$	0	0
$511$	−3.45404	−0.152798
$512$	22.1345	0.978214
$513$	−24.2198	−1.06933
$514$	−2.65703	−0.117197
$515$	0	0
$516$	−3.78093	−0.166446
$517$	15.1415	0.665924
$518$	−16.0159	−0.703698
$519$	8.51835	0.373914
$520$	0	0
$521$	34.8960	1.52882	0.764411	−	0.644729i	$-0.223030\pi$
$521$	34.8960	1.52882	0.764411	+	0.644729i	$0.223030\pi$
$522$	−4.79751	−0.209981
$523$	4.96750	0.217214	0.108607	−	0.994085i	$-0.465361\pi$
$523$	4.96750	0.217214	0.108607	+	0.994085i	$0.465361\pi$
$524$	−35.0922	−1.53301
$525$	0	0
$526$	−0.697950	−0.0304321
$527$	27.4497	1.19573
$528$	6.48550	0.282245
$529$	13.0843	0.568883
$530$	0	0
$531$	−2.71623	−0.117874
$532$	66.3592	2.87704
$533$	5.61739	0.243316
$534$	−0.424251	−0.0183591
$535$	0	0
$536$	−8.23158	−0.355550
$537$	−9.48171	−0.409166
$538$	5.23664	0.225767
$539$	50.1289	2.15920
$540$	0	0
$541$	−38.8901	−1.67202	−0.836008	−	0.548717i	$-0.815116\pi$
$541$	−38.8901	−1.67202	−0.836008	+	0.548717i	$0.815116\pi$
$542$	12.0010	0.515488
$543$	0.231785	0.00994685
$544$	−19.5815	−0.839549
$545$	0	0
$546$	−3.84751	−0.164658
$547$	−2.33115	−0.0996729	−0.0498365	−	0.998757i	$-0.515870\pi$
$547$	−2.33115	−0.0996729	−0.0498365	+	0.998757i	$0.515870\pi$
$548$	14.7903	0.631809
$549$	−25.8763	−1.10438
$550$	0	0
$551$	37.6290	1.60305
$552$	4.61217	0.196307
$553$	17.4793	0.743293
$554$	9.68441	0.411451
$555$	0	0
$556$	26.5205	1.12472
$557$	29.2231	1.23822	0.619112	−	0.785303i	$-0.287493\pi$
$557$	29.2231	1.23822	0.619112	+	0.785303i	$0.287493\pi$
$558$	5.78715	0.244990
$559$	16.4580	0.696101
$560$	0	0
$561$	−9.80009	−0.413760
$562$	−2.57934	−0.108803
$563$	12.4191	0.523403	0.261701	−	0.965149i	$-0.415716\pi$
$563$	12.4191	0.523403	0.261701	+	0.965149i	$0.415716\pi$
$564$	−3.92383	−0.165223
$565$	0	0
$566$	−8.17857	−0.343771
$567$	−29.2653	−1.22903
$568$	−21.7682	−0.913374
$569$	−3.12988	−0.131211	−0.0656056	−	0.997846i	$-0.520898\pi$
$569$	−3.12988	−0.131211	−0.0656056	+	0.997846i	$0.520898\pi$
$570$	0	0
$571$	9.28786	0.388685	0.194342	−	0.980934i	$-0.437743\pi$
$571$	9.28786	0.388685	0.194342	+	0.980934i	$0.437743\pi$
$572$	−30.7031	−1.28376
$573$	9.75506	0.407524
$574$	−2.17963	−0.0909761
$575$	0	0
$576$	13.1639	0.548497
$577$	−14.8994	−0.620271	−0.310135	−	0.950692i	$-0.600374\pi$
$577$	−14.8994	−0.620271	−0.310135	+	0.950692i	$0.600374\pi$
$578$	2.29071	0.0952810
$579$	9.53467	0.396247
$580$	0	0
$581$	41.7772	1.73321
$582$	−1.38414	−0.0573743
$583$	28.5775	1.18356
$584$	−1.11025	−0.0459423
$585$	0	0
$586$	6.01748	0.248580
$587$	−0.0277559	−0.00114561	−0.000572804	−	1.00000i	$-0.500182\pi$
$587$	−0.0277559	−0.00114561	−0.000572804		1.00000i	$0.500182\pi$
$588$	−12.9906	−0.535722
$589$	−45.3912	−1.87031
$590$	0	0
$591$	−7.25638	−0.298487
$592$	30.4534	1.25163
$593$	−34.4017	−1.41271	−0.706354	−	0.707859i	$-0.749661\pi$
$593$	−34.4017	−1.41271	−0.706354	+	0.707859i	$0.749661\pi$
$594$	−4.34812	−0.178405
$595$	0	0
$596$	11.9166	0.488122
$597$	−0.486771	−0.0199222
$598$	−9.67576	−0.395671
$599$	−36.3506	−1.48525	−0.742623	−	0.669710i	$-0.766419\pi$
$599$	−36.3506	−1.48525	−0.742623	+	0.669710i	$0.766419\pi$
$600$	0	0
$601$	−3.63256	−0.148175	−0.0740876	−	0.997252i	$-0.523604\pi$
$601$	−3.63256	−0.148175	−0.0740876	+	0.997252i	$0.523604\pi$
$602$	−6.38596	−0.260272
$603$	−15.5128	−0.631729
$604$	6.07648	0.247248
$605$	0	0
$606$	−1.87092	−0.0760009
$607$	−29.7647	−1.20811	−0.604057	−	0.796941i	$-0.706450\pi$
$607$	−29.7647	−1.20811	−0.604057	+	0.796941i	$0.706450\pi$
$608$	32.3802	1.31319
$609$	−11.3006	−0.457922
$610$	0	0
$611$	17.0801	0.690986
$612$	−24.3089	−0.982628
$613$	40.0010	1.61563	0.807813	−	0.589439i	$-0.200651\pi$
$613$	40.0010	1.61563	0.807813	+	0.589439i	$0.200651\pi$
$614$	−0.609981	−0.0246168
$615$	0	0
$616$	24.7190	0.995956
$617$	−13.5813	−0.546763	−0.273381	−	0.961906i	$-0.588142\pi$
$617$	−13.5813	−0.546763	−0.273381	+	0.961906i	$0.588142\pi$
$618$	−0.0212823	−0.000856101 0
$619$	2.40088	0.0964996	0.0482498	−	0.998835i	$-0.484636\pi$
$619$	2.40088	0.0964996	0.0482498	+	0.998835i	$0.484636\pi$
$620$	0	0
$621$	18.2917	0.734021
$622$	−8.59661	−0.344693
$623$	9.56537	0.383228
$624$	7.31583	0.292868
$625$	0	0
$626$	2.10479	0.0841245
$627$	16.2056	0.647189
$628$	−31.2257	−1.24604
$629$	−46.0174	−1.83483
$630$	0	0
$631$	−32.3532	−1.28796	−0.643979	−	0.765043i	$-0.722718\pi$
$631$	−32.3532	−1.28796	−0.643979	+	0.765043i	$0.722718\pi$
$632$	5.61843	0.223489
$633$	−8.28186	−0.329174
$634$	6.72653	0.267145
$635$	0	0
$636$	−7.40568	−0.293654
$637$	56.5468	2.24047
$638$	6.75543	0.267450
$639$	−41.0231	−1.62285
$640$	0	0
$641$	−30.2889	−1.19634	−0.598170	−	0.801369i	$-0.704105\pi$
$641$	−30.2889	−1.19634	−0.598170	+	0.801369i	$0.704105\pi$
$642$	0.895197	0.0353306
$643$	−37.2524	−1.46909	−0.734545	−	0.678560i	$-0.762604\pi$
$643$	−37.2524	−1.46909	−0.734545	+	0.678560i	$0.762604\pi$
$644$	−50.1169	−1.97488
$645$	0	0
$646$	−14.2831	−0.561959
$647$	6.56638	0.258151	0.129076	−	0.991635i	$-0.458799\pi$
$647$	6.56638	0.258151	0.129076	+	0.991635i	$0.458799\pi$
$648$	−9.40686	−0.369537
$649$	3.82475	0.150134
$650$	0	0
$651$	13.6317	0.534267
$652$	−11.4525	−0.448514
$653$	24.1370	0.944554	0.472277	−	0.881450i	$-0.343432\pi$
$653$	24.1370	0.944554	0.472277	+	0.881450i	$0.343432\pi$
$654$	−0.560539	−0.0219188
$655$	0	0
$656$	4.14446	0.161814
$657$	−2.09231	−0.0816287
$658$	−6.62732	−0.258360
$659$	49.0389	1.91028	0.955142	−	0.296150i	$-0.0957027\pi$
$659$	49.0389	1.91028	0.955142	+	0.296150i	$0.0957027\pi$
$660$	0	0
$661$	32.7731	1.27473	0.637364	−	0.770563i	$-0.280025\pi$
$661$	32.7731	1.27473	0.637364	+	0.770563i	$0.280025\pi$
$662$	−3.37142	−0.131034
$663$	−11.0548	−0.429332
$664$	13.4286	0.521132
$665$	0	0
$666$	−9.70173	−0.375935
$667$	−28.4188	−1.10038
$668$	0.851031	0.0329274
$669$	−11.7765	−0.455308
$670$	0	0
$671$	36.4368	1.40663
$672$	−9.72428	−0.375122
$673$	5.08459	0.195997	0.0979983	−	0.995187i	$-0.468756\pi$
$673$	5.08459	0.195997	0.0979983	+	0.995187i	$0.468756\pi$
$674$	1.20898	0.0465680
$675$	0	0
$676$	−10.4460	−0.401768
$677$	11.0477	0.424599	0.212299	−	0.977205i	$-0.431905\pi$
$677$	11.0477	0.424599	0.212299	+	0.977205i	$0.431905\pi$
$678$	−0.966839	−0.0371312
$679$	31.2074	1.19763
$680$	0	0
$681$	13.4786	0.516500
$682$	−8.14895	−0.312039
$683$	15.1998	0.581603	0.290801	−	0.956783i	$-0.406078\pi$
$683$	15.1998	0.581603	0.290801	+	0.956783i	$0.406078\pi$
$684$	40.1975	1.53699
$685$	0	0
$686$	−10.2226	−0.390300
$687$	3.32225	0.126752
$688$	12.1426	0.462931
$689$	32.2363	1.22810
$690$	0	0
$691$	−27.7036	−1.05390	−0.526948	−	0.849898i	$-0.676664\pi$
$691$	−27.7036	−1.05390	−0.526948	+	0.849898i	$0.676664\pi$
$692$	−29.7527	−1.13103
$693$	46.5840	1.76958
$694$	1.31577	0.0499460
$695$	0	0
$696$	−3.63239	−0.137685
$697$	−6.26259	−0.237212
$698$	8.36313	0.316549
$699$	1.05222	0.0397987
$700$	0	0
$701$	37.7338	1.42519	0.712594	−	0.701577i	$-0.247520\pi$
$701$	37.7338	1.42519	0.712594	+	0.701577i	$0.247520\pi$
$702$	−4.90480	−0.185120
$703$	76.0950	2.86998
$704$	−18.5363	−0.698612
$705$	0	0
$706$	5.14186	0.193517
$707$	42.1826	1.58644
$708$	−0.991158	−0.0372500
$709$	−21.7629	−0.817323	−0.408661	−	0.912686i	$-0.634004\pi$
$709$	−21.7629	−0.817323	−0.408661	+	0.912686i	$0.634004\pi$
$710$	0	0
$711$	10.5882	0.397088
$712$	3.07464	0.115227
$713$	34.2811	1.28384
$714$	4.28942	0.160527
$715$	0	0
$716$	33.1175	1.23766
$717$	−1.38361	−0.0516718
$718$	−6.60402	−0.246460
$719$	−8.45908	−0.315470	−0.157735	−	0.987481i	$-0.550419\pi$
$719$	−8.45908	−0.315470	−0.157735	+	0.987481i	$0.550419\pi$
$720$	0	0
$721$	0.479842	0.0178703
$722$	16.5252	0.615006
$723$	−10.0501	−0.373768
$724$	−0.809575	−0.0300876
$725$	0	0
$726$	0.721671	0.0267837
$727$	22.6688	0.840737	0.420369	−	0.907353i	$-0.361901\pi$
$727$	22.6688	0.840737	0.420369	+	0.907353i	$0.361901\pi$
$728$	27.8837	1.03344
$729$	−12.8613	−0.476345
$730$	0	0
$731$	−18.3484	−0.678639
$732$	−9.44234	−0.348999
$733$	−39.3814	−1.45459	−0.727293	−	0.686327i	$-0.759222\pi$
$733$	−39.3814	−1.45459	−0.727293	+	0.686327i	$0.759222\pi$
$734$	7.57041	0.279429
$735$	0	0
$736$	−24.4547	−0.901414
$737$	21.8437	0.804623
$738$	−1.32033	−0.0486019
$739$	3.30895	0.121722	0.0608608	−	0.998146i	$-0.480615\pi$
$739$	3.30895	0.121722	0.0608608	+	0.998146i	$0.480615\pi$
$740$	0	0
$741$	18.2804	0.671545
$742$	−12.5081	−0.459189
$743$	−35.2417	−1.29289	−0.646447	−	0.762959i	$-0.723746\pi$
$743$	−35.2417	−1.29289	−0.646447	+	0.762959i	$0.723746\pi$
$744$	4.38169	0.160640
$745$	0	0
$746$	4.29834	0.157374
$747$	25.3068	0.925929
$748$	34.2296	1.25156
$749$	−20.1836	−0.737491
$750$	0	0
$751$	−9.96125	−0.363491	−0.181746	−	0.983346i	$-0.558175\pi$
$751$	−9.96125	−0.363491	−0.181746	+	0.983346i	$0.558175\pi$
$752$	12.6015	0.459529
$753$	1.13909	0.0415107
$754$	7.62031	0.277515
$755$	0	0
$756$	−25.4051	−0.923973
$757$	−35.3975	−1.28654	−0.643271	−	0.765638i	$-0.722423\pi$
$757$	−35.3975	−1.28654	−0.643271	+	0.765638i	$0.722423\pi$
$758$	9.73382	0.353548
$759$	−12.2391	−0.444249
$760$	0	0
$761$	51.6137	1.87099	0.935497	−	0.353335i	$-0.114952\pi$
$761$	51.6137	1.87099	0.935497	+	0.353335i	$0.114952\pi$
$762$	1.55004	0.0561522
$763$	12.6382	0.457533
$764$	−34.0723	−1.23269
$765$	0	0
$766$	−7.09260	−0.256266
$767$	4.31442	0.155785
$768$	3.18427	0.114902
$769$	5.56394	0.200641	0.100320	−	0.994955i	$-0.468013\pi$
$769$	5.56394	0.200641	0.100320	+	0.994955i	$0.468013\pi$
$770$	0	0
$771$	−3.79123	−0.136538
$772$	−33.3025	−1.19858
$773$	−47.3546	−1.70323	−0.851613	−	0.524171i	$-0.824375\pi$
$773$	−47.3546	−1.70323	−0.851613	+	0.524171i	$0.824375\pi$
$774$	−3.86834	−0.139045
$775$	0	0
$776$	10.0311	0.360097
$777$	−22.8525	−0.819829
$778$	8.54101	0.306210
$779$	10.3559	0.371039
$780$	0	0
$781$	57.7651	2.06700
$782$	10.7871	0.385745
$783$	−14.4060	−0.514827
$784$	41.7196	1.48999
$785$	0	0
$786$	3.75096	0.133792
$787$	−1.87574	−0.0668630	−0.0334315	−	0.999441i	$-0.510644\pi$
$787$	−1.87574	−0.0668630	−0.0334315	+	0.999441i	$0.510644\pi$
$788$	25.3449	0.902876
$789$	−0.995880	−0.0354543
$790$	0	0
$791$	21.7988	0.775077
$792$	14.9737	0.532067
$793$	41.1017	1.45956
$794$	12.6431	0.448686
$795$	0	0
$796$	1.70018	0.0602614
$797$	28.3869	1.00552	0.502758	−	0.864427i	$-0.332319\pi$
$797$	28.3869	1.00552	0.502758	+	0.864427i	$0.332319\pi$
$798$	−7.09305	−0.251091
$799$	−19.0418	−0.673652
$800$	0	0
$801$	5.79428	0.204731
$802$	3.06518	0.108235
$803$	2.94620	0.103969
$804$	−5.66065	−0.199636
$805$	0	0
$806$	−9.19224	−0.323783
$807$	7.47197	0.263026
$808$	13.5589	0.477002
$809$	19.2175	0.675650	0.337825	−	0.941209i	$-0.390309\pi$
$809$	19.2175	0.675650	0.337825	+	0.941209i	$0.390309\pi$
$810$	0	0
$811$	−4.94378	−0.173600	−0.0867998	−	0.996226i	$-0.527664\pi$
$811$	−4.94378	−0.173600	−0.0867998	+	0.996226i	$0.527664\pi$
$812$	39.4704	1.38514
$813$	17.1238	0.600559
$814$	13.6611	0.478822
$815$	0	0
$816$	−8.15610	−0.285521
$817$	30.3411	1.06150
$818$	6.99671	0.244634
$819$	52.5480	1.83618
$820$	0	0
$821$	11.3606	0.396488	0.198244	−	0.980153i	$-0.436476\pi$
$821$	11.3606	0.396488	0.198244	+	0.980153i	$0.436476\pi$
$822$	−1.58091	−0.0551406
$823$	23.2345	0.809903	0.404951	−	0.914338i	$-0.367288\pi$
$823$	23.2345	0.809903	0.404951	+	0.914338i	$0.367288\pi$
$824$	0.154238	0.00537312
$825$	0	0
$826$	−1.67406	−0.0582480
$827$	−24.8100	−0.862729	−0.431364	−	0.902178i	$-0.641968\pi$
$827$	−24.8100	−0.862729	−0.431364	+	0.902178i	$0.641968\pi$
$828$	−30.3587	−1.05504
$829$	55.6555	1.93299	0.966497	−	0.256678i	$-0.0826280\pi$
$829$	55.6555	1.93299	0.966497	+	0.256678i	$0.0826280\pi$
$830$	0	0
$831$	13.8183	0.479353
$832$	−20.9094	−0.724904
$833$	−63.0416	−2.18426
$834$	−2.83474	−0.0981589
$835$	0	0
$836$	−56.6026	−1.95764
$837$	17.3776	0.600659
$838$	−1.76621	−0.0610128
$839$	12.7273	0.439394	0.219697	−	0.975568i	$-0.429493\pi$
$839$	12.7273	0.439394	0.219697	+	0.975568i	$0.429493\pi$
$840$	0	0
$841$	−6.61826	−0.228216
$842$	10.4837	0.361293
$843$	−3.68037	−0.126759
$844$	28.9267	0.995700
$845$	0	0
$846$	−4.01454	−0.138023
$847$	−16.2712	−0.559084
$848$	23.7836	0.816732
$849$	−11.6697	−0.400503
$850$	0	0
$851$	−57.4698	−1.97004
$852$	−14.9695	−0.512845
$853$	4.12905	0.141376	0.0706879	−	0.997498i	$-0.477481\pi$
$853$	4.12905	0.141376	0.0706879	+	0.997498i	$0.477481\pi$
$854$	−15.9481	−0.545731
$855$	0	0
$856$	−6.48769	−0.221745
$857$	−46.1854	−1.57766	−0.788831	−	0.614610i	$-0.789313\pi$
$857$	−46.1854	−1.57766	−0.788831	+	0.614610i	$0.789313\pi$
$858$	3.28182	0.112039
$859$	52.9762	1.80753	0.903763	−	0.428034i	$-0.140793\pi$
$859$	52.9762	1.80753	0.903763	+	0.428034i	$0.140793\pi$
$860$	0	0
$861$	−3.11004	−0.105990
$862$	−13.8093	−0.470347
$863$	−19.0050	−0.646937	−0.323468	−	0.946239i	$-0.604849\pi$
$863$	−19.0050	−0.646937	−0.323468	+	0.946239i	$0.604849\pi$
$864$	−12.3965	−0.421737
$865$	0	0
$866$	2.45179	0.0833153
$867$	3.26853	0.111005
$868$	−47.6125	−1.61607
$869$	−14.9093	−0.505764
$870$	0	0
$871$	24.6403	0.834905
$872$	4.06235	0.137568
$873$	18.9041	0.639807
$874$	−17.8377	−0.603369
$875$	0	0
$876$	−0.763488	−0.0257959
$877$	26.9242	0.909165	0.454583	−	0.890705i	$-0.349788\pi$
$877$	26.9242	0.909165	0.454583	+	0.890705i	$0.349788\pi$
$878$	6.06452	0.204668
$879$	8.58613	0.289603
$880$	0	0
$881$	28.1884	0.949692	0.474846	−	0.880069i	$-0.342504\pi$
$881$	28.1884	0.949692	0.474846	+	0.880069i	$0.342504\pi$
$882$	−13.2909	−0.447528
$883$	18.4582	0.621169	0.310584	−	0.950546i	$-0.399475\pi$
$883$	18.4582	0.621169	0.310584	+	0.950546i	$0.399475\pi$
$884$	38.6119	1.29866
$885$	0	0
$886$	5.00905	0.168282
$887$	−0.131642	−0.00442010	−0.00221005	−	0.999998i	$-0.500703\pi$
$887$	−0.131642	−0.00442010	−0.00221005	+	0.999998i	$0.500703\pi$
$888$	−7.34558	−0.246501
$889$	−34.9481	−1.17212
$890$	0	0
$891$	24.9625	0.836275
$892$	41.1329	1.37723
$893$	31.4879	1.05370
$894$	−1.27375	−0.0426004
$895$	0	0
$896$	44.6223	1.49073
$897$	−13.8060	−0.460969
$898$	4.52424	0.150976
$899$	−26.9987	−0.900456
$900$	0	0
$901$	−35.9388	−1.19730
$902$	1.85917	0.0619035
$903$	−9.11190	−0.303225
$904$	7.00689	0.233046
$905$	0	0
$906$	−0.649507	−0.0215784
$907$	−51.6609	−1.71537	−0.857685	−	0.514175i	$-0.828098\pi$
$907$	−51.6609	−1.71537	−0.857685	+	0.514175i	$0.828098\pi$
$908$	−47.0777	−1.56233
$909$	25.5524	0.847520
$910$	0	0
$911$	4.65252	0.154145	0.0770724	−	0.997026i	$-0.475443\pi$
$911$	4.65252	0.154145	0.0770724	+	0.997026i	$0.475443\pi$
$912$	13.4871	0.446601
$913$	−35.6348	−1.17934
$914$	−11.9548	−0.395431
$915$	0	0
$916$	−11.6039	−0.383404
$917$	−84.5710	−2.79278
$918$	5.46814	0.180476
$919$	−1.56207	−0.0515280	−0.0257640	−	0.999668i	$-0.508202\pi$
$919$	−1.56207	−0.0515280	−0.0257640	+	0.999668i	$0.508202\pi$
$920$	0	0
$921$	−0.870360	−0.0286793
$922$	−7.87246	−0.259266
$923$	65.1607	2.14479
$924$	16.9986	0.559213
$925$	0	0
$926$	6.86117	0.225472
$927$	0.290668	0.00954678
$928$	19.2598	0.632232
$929$	−34.4541	−1.13040	−0.565201	−	0.824953i	$-0.691201\pi$
$929$	−34.4541	−1.13040	−0.565201	+	0.824953i	$0.691201\pi$
$930$	0	0
$931$	104.247	3.41654
$932$	−3.67518	−0.120385
$933$	−12.2662	−0.401577
$934$	−6.44581	−0.210913
$935$	0	0
$936$	16.8907	0.552091
$937$	−4.30928	−0.140778	−0.0703890	−	0.997520i	$-0.522424\pi$
$937$	−4.30928	−0.140778	−0.0703890	+	0.997520i	$0.522424\pi$
$938$	−9.56080	−0.312171
$939$	3.00325	0.0980075
$940$	0	0
$941$	−17.3471	−0.565499	−0.282749	−	0.959194i	$-0.591246\pi$
$941$	−17.3471	−0.565499	−0.282749	+	0.959194i	$0.591246\pi$
$942$	3.33767	0.108747
$943$	−7.82117	−0.254692
$944$	3.18314	0.103602
$945$	0	0
$946$	5.44705	0.177099
$947$	−34.1314	−1.10912	−0.554560	−	0.832144i	$-0.687114\pi$
$947$	−34.1314	−1.10912	−0.554560	+	0.832144i	$0.687114\pi$
$948$	3.86365	0.125486
$949$	3.32340	0.107882
$950$	0	0
$951$	9.59784	0.311231
$952$	−31.0863	−1.00751
$953$	3.28945	0.106556	0.0532778	−	0.998580i	$-0.483033\pi$
$953$	3.28945	0.106556	0.0532778	+	0.998580i	$0.483033\pi$
$954$	−7.57689	−0.245311
$955$	0	0
$956$	4.83265	0.156299
$957$	9.63908	0.311587
$958$	−8.93605	−0.288711
$959$	35.6440	1.15101
$960$	0	0
$961$	1.56800	0.0505807
$962$	15.4101	0.496842
$963$	−12.2263	−0.393988
$964$	35.1029	1.13059
$965$	0	0
$966$	5.35693	0.172356
$967$	14.6798	0.472072	0.236036	−	0.971744i	$-0.424152\pi$
$967$	14.6798	0.472072	0.236036	+	0.971744i	$0.424152\pi$
$968$	−5.23011	−0.168102
$969$	−20.3800	−0.654699
$970$	0	0
$971$	−6.98258	−0.224082	−0.112041	−	0.993704i	$-0.535739\pi$
$971$	−6.98258	−0.224082	−0.112041	+	0.993704i	$0.535739\pi$
$972$	−23.4659	−0.752670
$973$	63.9134	2.04897
$974$	4.06255	0.130172
$975$	0	0
$976$	30.3244	0.970660
$977$	37.9354	1.21366	0.606830	−	0.794832i	$-0.292441\pi$
$977$	37.9354	1.21366	0.606830	+	0.794832i	$0.292441\pi$
$978$	1.22414	0.0391437
$979$	−8.15899	−0.260763
$980$	0	0
$981$	7.65567	0.244427
$982$	−13.4812	−0.430201
$983$	−12.8407	−0.409553	−0.204777	−	0.978809i	$-0.565647\pi$
$983$	−12.8407	−0.409553	−0.204777	+	0.978809i	$0.565647\pi$
$984$	−0.999673	−0.0318684
$985$	0	0
$986$	−8.49556	−0.270554
$987$	−9.45628	−0.300997
$988$	−63.8493	−2.03132
$989$	−22.9147	−0.728646
$990$	0	0
$991$	−46.3539	−1.47248	−0.736240	−	0.676720i	$-0.763401\pi$
$991$	−46.3539	−1.47248	−0.736240	+	0.676720i	$0.763401\pi$
$992$	−23.2327	−0.737638
$993$	−4.81055	−0.152658
$994$	−25.2833	−0.801938
$995$	0	0
$996$	9.23453	0.292607
$997$	9.74916	0.308759	0.154379	−	0.988012i	$-0.450662\pi$
$997$	9.74916	0.308759	0.154379	+	0.988012i	$0.450662\pi$
$998$	0.958642	0.0303453
$999$	−29.1323	−0.921706

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1475.2.a.o.1.5		7
5.2	odd	4		1475.2.b.h.1299.9		14
5.3	odd	4		1475.2.b.h.1299.6		14
5.4	even	2		295.2.a.d.1.3	✓	7
15.14	odd	2		2655.2.a.w.1.5		7
20.19	odd	2		4720.2.a.bc.1.5		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
295.2.a.d.1.3	✓	7	5.4	even	2
1475.2.a.o.1.5		7	1.1	even	1	trivial
1475.2.b.h.1299.6		14	5.3	odd	4
1475.2.b.h.1299.9		14	5.2	odd	4
2655.2.a.w.1.5		7	15.14	odd	2
4720.2.a.bc.1.5		7	20.19	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:	\( N \)	\(=\)	\( 1475 = 5^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1475.a (trivial)

\(f(q)\)	\(=\)	\(q+0.373339 q^{2} +0.532704 q^{3} -1.86062 q^{4} +0.198879 q^{6} -4.48402 q^{7} -1.44132 q^{8} -2.71623 q^{9} +O(q^{10})\)	\(q+0.373339 q^{2} +0.532704 q^{3} -1.86062 q^{4} +0.198879 q^{6} -4.48402 q^{7} -1.44132 q^{8} -2.71623 q^{9} +3.82475 q^{11} -0.991158 q^{12} +4.31442 q^{13} -1.67406 q^{14} +3.18314 q^{16} -4.80996 q^{17} -1.01407 q^{18} +7.95383 q^{19} -2.38866 q^{21} +1.42793 q^{22} -6.00702 q^{23} -0.767796 q^{24} +1.61074 q^{26} -3.04505 q^{27} +8.34305 q^{28} +4.73093 q^{29} -5.70684 q^{31} +4.07103 q^{32} +2.03746 q^{33} -1.79575 q^{34} +5.05386 q^{36} +9.56710 q^{37} +2.96947 q^{38} +2.29831 q^{39} +1.30200 q^{41} -0.891778 q^{42} +3.81466 q^{43} -7.11640 q^{44} -2.24265 q^{46} +3.95883 q^{47} +1.69567 q^{48} +13.1065 q^{49} -2.56228 q^{51} -8.02749 q^{52} +7.47175 q^{53} -1.13684 q^{54} +6.46290 q^{56} +4.23703 q^{57} +1.76624 q^{58} +1.00000 q^{59} +9.52658 q^{61} -2.13058 q^{62} +12.1796 q^{63} -4.84640 q^{64} +0.760662 q^{66} +5.71115 q^{67} +8.94950 q^{68} -3.19996 q^{69} +15.1030 q^{71} +3.91495 q^{72} +0.770299 q^{73} +3.57177 q^{74} -14.7990 q^{76} -17.1503 q^{77} +0.858048 q^{78} -3.89812 q^{79} +6.52657 q^{81} +0.486088 q^{82} -9.31691 q^{83} +4.44438 q^{84} +1.42416 q^{86} +2.52019 q^{87} -5.51268 q^{88} -2.13321 q^{89} -19.3460 q^{91} +11.1768 q^{92} -3.04005 q^{93} +1.47799 q^{94} +2.16865 q^{96} -6.95969 q^{97} +4.89315 q^{98} -10.3889 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - q^{2} - 3 q^{3} + 7 q^{4} + 8 q^{6} + 4 q^{7} - 6 q^{8} + 16 q^{9}+O(q^{10}) \) 7 * q - q^2 - 3 * q^3 + 7 * q^4 + 8 * q^6 + 4 * q^7 - 6 * q^8 + 16 * q^9	\( 7 q - q^{2} - 3 q^{3} + 7 q^{4} + 8 q^{6} + 4 q^{7} - 6 q^{8} + 16 q^{9} + 3 q^{11} - 10 q^{12} + 9 q^{13} + 14 q^{14} + 7 q^{16} - 24 q^{17} + 16 q^{18} + 3 q^{19} + 9 q^{21} + 12 q^{22} - 3 q^{23} - 5 q^{24} - q^{26} - 18 q^{27} + 29 q^{28} + 4 q^{29} - q^{31} - 18 q^{32} - 8 q^{33} - 21 q^{34} - 5 q^{36} + 24 q^{37} + 13 q^{38} - 3 q^{39} + 45 q^{41} + 19 q^{43} - 27 q^{44} + 16 q^{46} - 16 q^{47} + 17 q^{48} + 13 q^{49} + 15 q^{51} + 5 q^{52} + 7 q^{53} - 18 q^{54} + 3 q^{56} + 8 q^{57} + 27 q^{58} + 7 q^{59} + 9 q^{61} - 29 q^{62} + 32 q^{63} - 32 q^{64} - 47 q^{66} + 16 q^{67} - 16 q^{68} - 10 q^{69} + 15 q^{71} + 51 q^{72} - 5 q^{73} - 10 q^{74} - 10 q^{76} + 3 q^{77} + 76 q^{78} + q^{79} + 31 q^{81} - 26 q^{82} - 23 q^{83} - 17 q^{84} - 2 q^{86} + 17 q^{87} + 22 q^{88} + 7 q^{89} - 12 q^{91} - 47 q^{92} + 20 q^{93} + 53 q^{94} + 19 q^{96} + 4 q^{97} + 68 q^{98} + 9 q^{99}+O(q^{100}) \) 7 * q - q^2 - 3 * q^3 + 7 * q^4 + 8 * q^6 + 4 * q^7 - 6 * q^8 + 16 * q^9 + 3 * q^11 - 10 * q^12 + 9 * q^13 + 14 * q^14 + 7 * q^16 - 24 * q^17 + 16 * q^18 + 3 * q^19 + 9 * q^21 + 12 * q^22 - 3 * q^23 - 5 * q^24 - q^26 - 18 * q^27 + 29 * q^28 + 4 * q^29 - q^31 - 18 * q^32 - 8 * q^33 - 21 * q^34 - 5 * q^36 + 24 * q^37 + 13 * q^38 - 3 * q^39 + 45 * q^41 + 19 * q^43 - 27 * q^44 + 16 * q^46 - 16 * q^47 + 17 * q^48 + 13 * q^49 + 15 * q^51 + 5 * q^52 + 7 * q^53 - 18 * q^54 + 3 * q^56 + 8 * q^57 + 27 * q^58 + 7 * q^59 + 9 * q^61 - 29 * q^62 + 32 * q^63 - 32 * q^64 - 47 * q^66 + 16 * q^67 - 16 * q^68 - 10 * q^69 + 15 * q^71 + 51 * q^72 - 5 * q^73 - 10 * q^74 - 10 * q^76 + 3 * q^77 + 76 * q^78 + q^79 + 31 * q^81 - 26 * q^82 - 23 * q^83 - 17 * q^84 - 2 * q^86 + 17 * q^87 + 22 * q^88 + 7 * q^89 - 12 * q^91 - 47 * q^92 + 20 * q^93 + 53 * q^94 + 19 * q^96 + 4 * q^97 + 68 * q^98 + 9 * q^99

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