LMFDB - Embedded newform 1875.2.a.k.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1875,2,Mod(1,1875)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1875, 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("1875.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1875 = 3 \cdot 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1875.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:	$14.9719503790$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.44400625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 11x^{4} - x^{3} + 29x^{2} + 3x - 1 $ x^6 - 11x^4 - x^3 + 29x^2 + 3*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 75)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2.16056$ of defining polynomial
Character	$\chi$	$=$	1875.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.16056 q^{2} +1.00000 q^{3} +2.66802 q^{4} -2.16056 q^{6} +3.16056 q^{7} -1.44329 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.16056 q^{2} +1.00000 q^{3} +2.66802 q^{4} -2.16056 q^{6} +3.16056 q^{7} -1.44329 q^{8} +1.00000 q^{9} +1.53835 q^{11} +2.66802 q^{12} +5.24144 q^{13} -6.82858 q^{14} -2.21771 q^{16} -1.29068 q^{17} -2.16056 q^{18} +5.44587 q^{19} +3.16056 q^{21} -3.32370 q^{22} +6.44244 q^{23} -1.44329 q^{24} -11.3244 q^{26} +1.00000 q^{27} +8.43243 q^{28} -2.36361 q^{29} -4.46542 q^{31} +7.67809 q^{32} +1.53835 q^{33} +2.78860 q^{34} +2.66802 q^{36} +5.95751 q^{37} -11.7661 q^{38} +5.24144 q^{39} -8.53219 q^{41} -6.82858 q^{42} +8.48426 q^{43} +4.10435 q^{44} -13.9193 q^{46} -0.753070 q^{47} -2.21771 q^{48} +2.98914 q^{49} -1.29068 q^{51} +13.9843 q^{52} -9.74991 q^{53} -2.16056 q^{54} -4.56162 q^{56} +5.44587 q^{57} +5.10672 q^{58} +4.11270 q^{59} -10.6939 q^{61} +9.64781 q^{62} +3.16056 q^{63} -12.1535 q^{64} -3.32370 q^{66} +1.89864 q^{67} -3.44357 q^{68} +6.44244 q^{69} -0.0708774 q^{71} -1.44329 q^{72} -4.01123 q^{73} -12.8716 q^{74} +14.5297 q^{76} +4.86205 q^{77} -11.3244 q^{78} +1.61849 q^{79} +1.00000 q^{81} +18.4343 q^{82} -13.1488 q^{83} +8.43243 q^{84} -18.3308 q^{86} -2.36361 q^{87} -2.22029 q^{88} +7.27597 q^{89} +16.5659 q^{91} +17.1885 q^{92} -4.46542 q^{93} +1.62705 q^{94} +7.67809 q^{96} -10.1939 q^{97} -6.45821 q^{98} +1.53835 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{3} + 10 q^{4} + 6 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + 6 * q^3 + 10 * q^4 + 6 * q^7 + 3 * q^8 + 6 * q^9	$ 6 q + 6 q^{3} + 10 q^{4} + 6 q^{7} + 3 q^{8} + 6 q^{9} + 3 q^{11} + 10 q^{12} + 6 q^{13} - 22 q^{14} + 18 q^{16} + 13 q^{17} + 11 q^{19} + 6 q^{21} + 16 q^{22} + 13 q^{23} + 3 q^{24} - 28 q^{26} + 6 q^{27} + 7 q^{28} - 3 q^{29} - 11 q^{31} + 16 q^{32} + 3 q^{33} + 15 q^{34} + 10 q^{36} + 21 q^{37} - 9 q^{38} + 6 q^{39} - q^{41} - 22 q^{42} + 2 q^{43} + 9 q^{44} + 19 q^{46} + 14 q^{47} + 18 q^{48} - 14 q^{49} + 13 q^{51} + 13 q^{52} + 23 q^{53} - 35 q^{56} + 11 q^{57} + 22 q^{58} + 9 q^{59} + 11 q^{61} - 23 q^{62} + 6 q^{63} - 23 q^{64} + 16 q^{66} + 8 q^{67} + 50 q^{68} + 13 q^{69} - 8 q^{71} + 3 q^{72} + 13 q^{73} - 22 q^{74} - 26 q^{76} - 13 q^{77} - 28 q^{78} - 5 q^{79} + 6 q^{81} - 13 q^{82} - 20 q^{83} + 7 q^{84} - 37 q^{86} - 3 q^{87} + 28 q^{88} - 4 q^{89} + 34 q^{91} + 61 q^{92} - 11 q^{93} + 41 q^{94} + 16 q^{96} - 7 q^{97} - 41 q^{98} + 3 q^{99}+O(q^{100}) $ 6 * q + 6 * q^3 + 10 * q^4 + 6 * q^7 + 3 * q^8 + 6 * q^9 + 3 * q^11 + 10 * q^12 + 6 * q^13 - 22 * q^14 + 18 * q^16 + 13 * q^17 + 11 * q^19 + 6 * q^21 + 16 * q^22 + 13 * q^23 + 3 * q^24 - 28 * q^26 + 6 * q^27 + 7 * q^28 - 3 * q^29 - 11 * q^31 + 16 * q^32 + 3 * q^33 + 15 * q^34 + 10 * q^36 + 21 * q^37 - 9 * q^38 + 6 * q^39 - q^41 - 22 * q^42 + 2 * q^43 + 9 * q^44 + 19 * q^46 + 14 * q^47 + 18 * q^48 - 14 * q^49 + 13 * q^51 + 13 * q^52 + 23 * q^53 - 35 * q^56 + 11 * q^57 + 22 * q^58 + 9 * q^59 + 11 * q^61 - 23 * q^62 + 6 * q^63 - 23 * q^64 + 16 * q^66 + 8 * q^67 + 50 * q^68 + 13 * q^69 - 8 * q^71 + 3 * q^72 + 13 * q^73 - 22 * q^74 - 26 * q^76 - 13 * q^77 - 28 * q^78 - 5 * q^79 + 6 * q^81 - 13 * q^82 - 20 * q^83 + 7 * q^84 - 37 * q^86 - 3 * q^87 + 28 * q^88 - 4 * q^89 + 34 * q^91 + 61 * q^92 - 11 * q^93 + 41 * q^94 + 16 * q^96 - 7 * q^97 - 41 * q^98 + 3 * 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 $

$2$	−2.16056	−1.52775	−0.763873	−	0.645366i	$-0.776705\pi$
$2$	−2.16056	−1.52775	−0.763873	+	0.645366i	$0.776705\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.66802	1.33401
$5$	0	0
$5$	0	0
$6$	−2.16056	−0.882045
$7$	3.16056	1.19458	0.597290	−	0.802026i	$-0.296244\pi$
$7$	3.16056	1.19458	0.597290	+	0.802026i	$0.296244\pi$
$8$	−1.44329	−0.510282
$9$	1.00000	0.333333
$10$	0	0
$11$	1.53835	0.463830	0.231915	−	0.972736i	$-0.425501\pi$
$11$	1.53835	0.463830	0.231915	+	0.972736i	$0.425501\pi$
$12$	2.66802	0.770191
$13$	5.24144	1.45371	0.726857	−	0.686789i	$-0.240981\pi$
$13$	5.24144	1.45371	0.726857	+	0.686789i	$0.240981\pi$
$14$	−6.82858	−1.82501
$15$	0	0
$16$	−2.21771	−0.554428
$17$	−1.29068	−0.313037	−0.156518	−	0.987675i	$-0.550027\pi$
$17$	−1.29068	−0.313037	−0.156518	+	0.987675i	$0.550027\pi$
$18$	−2.16056	−0.509249
$19$	5.44587	1.24937	0.624685	−	0.780877i	$-0.285228\pi$
$19$	5.44587	1.24937	0.624685	+	0.780877i	$0.285228\pi$
$20$	0	0
$21$	3.16056	0.689691
$22$	−3.32370	−0.708615
$23$	6.44244	1.34334	0.671671	−	0.740850i	$-0.265577\pi$
$23$	6.44244	1.34334	0.671671	+	0.740850i	$0.265577\pi$
$24$	−1.44329	−0.294611
$25$	0	0
$26$	−11.3244	−2.22090
$27$	1.00000	0.192450
$28$	8.43243	1.59358
$29$	−2.36361	−0.438912	−0.219456	−	0.975622i	$-0.570428\pi$
$29$	−2.36361	−0.438912	−0.219456	+	0.975622i	$0.570428\pi$
$30$	0	0
$31$	−4.46542	−0.802014	−0.401007	−	0.916075i	$-0.631340\pi$
$31$	−4.46542	−0.802014	−0.401007	+	0.916075i	$0.631340\pi$
$32$	7.67809	1.35731
$33$	1.53835	0.267793
$34$	2.78860	0.478241
$35$	0	0
$36$	2.66802	0.444670
$37$	5.95751	0.979408	0.489704	−	0.871889i	$-0.337105\pi$
$37$	5.95751	0.979408	0.489704	+	0.871889i	$0.337105\pi$
$38$	−11.7661	−1.90872
$39$	5.24144	0.839302
$40$	0	0
$41$	−8.53219	−1.33250	−0.666252	−	0.745726i	$-0.732103\pi$
$41$	−8.53219	−1.33250	−0.666252	+	0.745726i	$0.732103\pi$
$42$	−6.82858	−1.05367
$43$	8.48426	1.29384	0.646919	−	0.762559i	$-0.276057\pi$
$43$	8.48426	1.29384	0.646919	+	0.762559i	$0.276057\pi$
$44$	4.10435	0.618754
$45$	0	0
$46$	−13.9193	−2.05228
$47$	−0.753070	−0.109847	−0.0549233	−	0.998491i	$-0.517491\pi$
$47$	−0.753070	−0.109847	−0.0549233	+	0.998491i	$0.517491\pi$
$48$	−2.21771	−0.320099
$49$	2.98914	0.427020
$50$	0	0
$51$	−1.29068	−0.180732
$52$	13.9843	1.93927
$53$	−9.74991	−1.33925	−0.669626	−	0.742698i	$-0.733546\pi$
$53$	−9.74991	−1.33925	−0.669626	+	0.742698i	$0.733546\pi$
$54$	−2.16056	−0.294015
$55$	0	0
$56$	−4.56162	−0.609572
$57$	5.44587	0.721324
$58$	5.10672	0.670546
$59$	4.11270	0.535428	0.267714	−	0.963498i	$-0.413732\pi$
$59$	4.11270	0.535428	0.267714	+	0.963498i	$0.413732\pi$
$60$	0	0
$61$	−10.6939	−1.36922	−0.684610	−	0.728910i	$-0.740027\pi$
$61$	−10.6939	−1.36922	−0.684610	+	0.728910i	$0.740027\pi$
$62$	9.64781	1.22527
$63$	3.16056	0.398193
$64$	−12.1535	−1.51919
$65$	0	0
$66$	−3.32370	−0.409119
$67$	1.89864	0.231956	0.115978	−	0.993252i	$-0.463000\pi$
$67$	1.89864	0.231956	0.115978	+	0.993252i	$0.463000\pi$
$68$	−3.44357	−0.417594
$69$	6.44244	0.775578
$70$	0	0
$71$	−0.0708774	−0.00841160	−0.00420580	−	0.999991i	$-0.501339\pi$
$71$	−0.0708774	−0.00841160	−0.00420580	+	0.999991i	$0.501339\pi$
$72$	−1.44329	−0.170094
$73$	−4.01123	−0.469478	−0.234739	−	0.972058i	$-0.575424\pi$
$73$	−4.01123	−0.469478	−0.234739	+	0.972058i	$0.575424\pi$
$74$	−12.8716	−1.49629
$75$	0	0
$76$	14.5297	1.66667
$77$	4.86205	0.554082
$78$	−11.3244	−1.28224
$79$	1.61849	0.182094	0.0910472	−	0.995847i	$-0.470979\pi$
$79$	1.61849	0.182094	0.0910472	+	0.995847i	$0.470979\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	18.4343	2.03573
$83$	−13.1488	−1.44327	−0.721636	−	0.692272i	$-0.756610\pi$
$83$	−13.1488	−1.44327	−0.721636	+	0.692272i	$0.756610\pi$
$84$	8.43243	0.920054
$85$	0	0
$86$	−18.3308	−1.97666
$87$	−2.36361	−0.253406
$88$	−2.22029	−0.236684
$89$	7.27597	0.771251	0.385626	−	0.922655i	$-0.373986\pi$
$89$	7.27597	0.771251	0.385626	+	0.922655i	$0.373986\pi$
$90$	0	0
$91$	16.5659	1.73658
$92$	17.1885	1.79203
$93$	−4.46542	−0.463043
$94$	1.62705	0.167818
$95$	0	0
$96$	7.67809	0.783642
$97$	−10.1939	−1.03504	−0.517518	−	0.855673i	$-0.673144\pi$
$97$	−10.1939	−1.03504	−0.517518	+	0.855673i	$0.673144\pi$
$98$	−6.45821	−0.652378
$99$	1.53835	0.154610
$100$	0	0
$101$	1.08759	0.108219	0.0541096	−	0.998535i	$-0.482768\pi$
$101$	1.08759	0.108219	0.0541096	+	0.998535i	$0.482768\pi$
$102$	2.78860	0.276112
$103$	4.93756	0.486512	0.243256	−	0.969962i	$-0.421784\pi$
$103$	4.93756	0.486512	0.243256	+	0.969962i	$0.421784\pi$
$104$	−7.56494	−0.741803
$105$	0	0
$106$	21.0653	2.04604
$107$	−15.3059	−1.47967	−0.739837	−	0.672786i	$-0.765098\pi$
$107$	−15.3059	−1.47967	−0.739837	+	0.672786i	$0.765098\pi$
$108$	2.66802	0.256730
$109$	6.65900	0.637816	0.318908	−	0.947786i	$-0.396684\pi$
$109$	6.65900	0.637816	0.318908	+	0.947786i	$0.396684\pi$
$110$	0	0
$111$	5.95751	0.565462
$112$	−7.00922	−0.662309
$113$	8.97143	0.843961	0.421981	−	0.906605i	$-0.361335\pi$
$113$	8.97143	0.843961	0.421981	+	0.906605i	$0.361335\pi$
$114$	−11.7661	−1.10200
$115$	0	0
$116$	−6.30616	−0.585512
$117$	5.24144	0.484571
$118$	−8.88573	−0.817998
$119$	−4.07928	−0.373947
$120$	0	0
$121$	−8.63348	−0.784861
$122$	23.1049	2.09182
$123$	−8.53219	−0.769322
$124$	−11.9138	−1.06989
$125$	0	0
$126$	−6.82858	−0.608338
$127$	−10.0185	−0.888995	−0.444497	−	0.895780i	$-0.646618\pi$
$127$	−10.0185	−0.888995	−0.444497	+	0.895780i	$0.646618\pi$
$128$	10.9023	0.963635
$129$	8.48426	0.746997
$130$	0	0
$131$	−6.37865	−0.557305	−0.278653	−	0.960392i	$-0.589888\pi$
$131$	−6.37865	−0.557305	−0.278653	+	0.960392i	$0.589888\pi$
$132$	4.10435	0.357238
$133$	17.2120	1.49247
$134$	−4.10214	−0.354371
$135$	0	0
$136$	1.86284	0.159737
$137$	9.17732	0.784071	0.392036	−	0.919950i	$-0.371771\pi$
$137$	9.17732	0.784071	0.392036	+	0.919950i	$0.371771\pi$
$138$	−13.9193	−1.18489
$139$	−9.26539	−0.785880	−0.392940	−	0.919564i	$-0.628542\pi$
$139$	−9.26539	−0.785880	−0.392940	+	0.919564i	$0.628542\pi$
$140$	0	0
$141$	−0.753070	−0.0634200
$142$	0.153135	0.0128508
$143$	8.06317	0.674276
$144$	−2.21771	−0.184809
$145$	0	0
$146$	8.66649	0.717244
$147$	2.98914	0.246540
$148$	15.8947	1.30654
$149$	−10.0817	−0.825928	−0.412964	−	0.910747i	$-0.635506\pi$
$149$	−10.0817	−0.825928	−0.412964	+	0.910747i	$0.635506\pi$
$150$	0	0
$151$	10.7375	0.873804	0.436902	−	0.899509i	$-0.356076\pi$
$151$	10.7375	0.873804	0.436902	+	0.899509i	$0.356076\pi$
$152$	−7.86000	−0.637530
$153$	−1.29068	−0.104346
$154$	−10.5048	−0.846497
$155$	0	0
$156$	13.9843	1.11964
$157$	−17.4417	−1.39200	−0.696001	−	0.718041i	$-0.745039\pi$
$157$	−17.4417	−1.39200	−0.696001	+	0.718041i	$0.745039\pi$
$158$	−3.49684	−0.278194
$159$	−9.74991	−0.773218
$160$	0	0
$161$	20.3617	1.60473
$162$	−2.16056	−0.169750
$163$	16.2574	1.27338	0.636689	−	0.771120i	$-0.280303\pi$
$163$	16.2574	1.27338	0.636689	+	0.771120i	$0.280303\pi$
$164$	−22.7641	−1.77757
$165$	0	0
$166$	28.4089	2.20496
$167$	11.3906	0.881430	0.440715	−	0.897647i	$-0.354725\pi$
$167$	11.3906	0.881430	0.440715	+	0.897647i	$0.354725\pi$
$168$	−4.56162	−0.351936
$169$	14.4727	1.11328
$170$	0	0
$171$	5.44587	0.416456
$172$	22.6362	1.72599
$173$	−9.45845	−0.719113	−0.359556	−	0.933123i	$-0.617072\pi$
$173$	−9.45845	−0.719113	−0.359556	+	0.933123i	$0.617072\pi$
$174$	5.10672	0.387140
$175$	0	0
$176$	−3.41162	−0.257161
$177$	4.11270	0.309129
$178$	−15.7202	−1.17828
$179$	4.07747	0.304764	0.152382	−	0.988322i	$-0.451306\pi$
$179$	4.07747	0.304764	0.152382	+	0.988322i	$0.451306\pi$
$180$	0	0
$181$	−11.1202	−0.826558	−0.413279	−	0.910604i	$-0.635617\pi$
$181$	−11.1202	−0.826558	−0.413279	+	0.910604i	$0.635617\pi$
$182$	−35.7916	−2.65305
$183$	−10.6939	−0.790519
$184$	−9.29833	−0.685482
$185$	0	0
$186$	9.64781	0.707412
$187$	−1.98552	−0.145196
$188$	−2.00921	−0.146536
$189$	3.16056	0.229897
$190$	0	0
$191$	3.61135	0.261308	0.130654	−	0.991428i	$-0.458292\pi$
$191$	3.61135	0.261308	0.130654	+	0.991428i	$0.458292\pi$
$192$	−12.1535	−0.877107
$193$	17.0562	1.22774	0.613868	−	0.789409i	$-0.289613\pi$
$193$	17.0562	1.22774	0.613868	+	0.789409i	$0.289613\pi$
$194$	22.0246	1.58127
$195$	0	0
$196$	7.97508	0.569648
$197$	4.40523	0.313860	0.156930	−	0.987610i	$-0.449840\pi$
$197$	4.40523	0.313860	0.156930	+	0.987610i	$0.449840\pi$
$198$	−3.32370	−0.236205
$199$	16.5956	1.17643	0.588214	−	0.808705i	$-0.299831\pi$
$199$	16.5956	1.17643	0.588214	+	0.808705i	$0.299831\pi$
$200$	0	0
$201$	1.89864	0.133920
$202$	−2.34980	−0.165332
$203$	−7.47034	−0.524315
$204$	−3.44357	−0.241098
$205$	0	0
$206$	−10.6679	−0.743267
$207$	6.44244	0.447780
$208$	−11.6240	−0.805980
$209$	8.37767	0.579495
$210$	0	0
$211$	18.5454	1.27671	0.638357	−	0.769740i	$-0.279614\pi$
$211$	18.5454	1.27671	0.638357	+	0.769740i	$0.279614\pi$
$212$	−26.0129	−1.78658
$213$	−0.0708774	−0.00485644
$214$	33.0693	2.26057
$215$	0	0
$216$	−1.44329	−0.0982037
$217$	−14.1132	−0.958069
$218$	−14.3872	−0.974422
$219$	−4.01123	−0.271053
$220$	0	0
$221$	−6.76504	−0.455066
$222$	−12.8716	−0.863882
$223$	0.771557	0.0516673	0.0258336	−	0.999666i	$-0.491776\pi$
$223$	0.771557	0.0516673	0.0258336	+	0.999666i	$0.491776\pi$
$224$	24.2671	1.62141
$225$	0	0
$226$	−19.3833	−1.28936
$227$	−11.4314	−0.758727	−0.379363	−	0.925248i	$-0.623857\pi$
$227$	−11.4314	−0.758727	−0.379363	+	0.925248i	$0.623857\pi$
$228$	14.5297	0.962253
$229$	10.2248	0.675671	0.337835	−	0.941205i	$-0.390305\pi$
$229$	10.2248	0.675671	0.337835	+	0.941205i	$0.390305\pi$
$230$	0	0
$231$	4.86205	0.319899
$232$	3.41139	0.223969
$233$	22.5229	1.47553	0.737763	−	0.675059i	$-0.235882\pi$
$233$	22.5229	1.47553	0.737763	+	0.675059i	$0.235882\pi$
$234$	−11.3244	−0.740302
$235$	0	0
$236$	10.9728	0.714266
$237$	1.61849	0.105132
$238$	8.81353	0.571297
$239$	−0.589074	−0.0381040	−0.0190520	−	0.999818i	$-0.506065\pi$
$239$	−0.589074	−0.0381040	−0.0190520	+	0.999818i	$0.506065\pi$
$240$	0	0
$241$	1.50937	0.0972270	0.0486135	−	0.998818i	$-0.484520\pi$
$241$	1.50937	0.0972270	0.0486135	+	0.998818i	$0.484520\pi$
$242$	18.6531	1.19907
$243$	1.00000	0.0641500
$244$	−28.5317	−1.82655
$245$	0	0
$246$	18.4343	1.17533
$247$	28.5442	1.81622
$248$	6.44492	0.409253
$249$	−13.1488	−0.833274
$250$	0	0
$251$	11.8953	0.750823	0.375412	−	0.926858i	$-0.377501\pi$
$251$	11.8953	0.750823	0.375412	+	0.926858i	$0.377501\pi$
$252$	8.43243	0.531193
$253$	9.91073	0.623082
$254$	21.6455	1.35816
$255$	0	0
$256$	0.752056	0.0470035
$257$	18.0492	1.12588	0.562939	−	0.826498i	$-0.309671\pi$
$257$	18.0492	1.12588	0.562939	+	0.826498i	$0.309671\pi$
$258$	−18.3308	−1.14122
$259$	18.8291	1.16998
$260$	0	0
$261$	−2.36361	−0.146304
$262$	13.7815	0.851421
$263$	19.1066	1.17817	0.589083	−	0.808072i	$-0.299489\pi$
$263$	19.1066	1.17817	0.589083	+	0.808072i	$0.299489\pi$
$264$	−2.22029	−0.136650
$265$	0	0
$266$	−37.1876	−2.28012
$267$	7.27597	0.445282
$268$	5.06562	0.309432
$269$	−22.2250	−1.35508	−0.677542	−	0.735484i	$-0.736955\pi$
$269$	−22.2250	−1.35508	−0.677542	+	0.735484i	$0.736955\pi$
$270$	0	0
$271$	20.2107	1.22772	0.613858	−	0.789417i	$-0.289617\pi$
$271$	20.2107	1.22772	0.613858	+	0.789417i	$0.289617\pi$
$272$	2.86237	0.173556
$273$	16.5659	1.00261
$274$	−19.8281	−1.19786
$275$	0	0
$276$	17.1885	1.03463
$277$	16.0413	0.963826	0.481913	−	0.876219i	$-0.339942\pi$
$277$	16.0413	0.963826	0.481913	+	0.876219i	$0.339942\pi$
$278$	20.0184	1.20063
$279$	−4.46542	−0.267338
$280$	0	0
$281$	8.37308	0.499496	0.249748	−	0.968311i	$-0.419652\pi$
$281$	8.37308	0.499496	0.249748	+	0.968311i	$0.419652\pi$
$282$	1.62705	0.0968896
$283$	1.12995	0.0671685	0.0335843	−	0.999436i	$-0.489308\pi$
$283$	1.12995	0.0671685	0.0335843	+	0.999436i	$0.489308\pi$
$284$	−0.189102	−0.0112211
$285$	0	0
$286$	−17.4210	−1.03012
$287$	−26.9665	−1.59178
$288$	7.67809	0.452436
$289$	−15.3341	−0.902008
$290$	0	0
$291$	−10.1939	−0.597578
$292$	−10.7020	−0.626289
$293$	2.37857	0.138958	0.0694789	−	0.997583i	$-0.477866\pi$
$293$	2.37857	0.138958	0.0694789	+	0.997583i	$0.477866\pi$
$294$	−6.45821	−0.376651
$295$	0	0
$296$	−8.59844	−0.499774
$297$	1.53835	0.0892642
$298$	21.7822	1.26181
$299$	33.7676	1.95283
$300$	0	0
$301$	26.8150	1.54559
$302$	−23.1990	−1.33495
$303$	1.08759	0.0624804
$304$	−12.0774	−0.692686
$305$	0	0
$306$	2.78860	0.159414
$307$	−2.89366	−0.165150	−0.0825748	−	0.996585i	$-0.526314\pi$
$307$	−2.89366	−0.165150	−0.0825748	+	0.996585i	$0.526314\pi$
$308$	12.9720	0.739151
$309$	4.93756	0.280888
$310$	0	0
$311$	−7.14545	−0.405181	−0.202591	−	0.979264i	$-0.564936\pi$
$311$	−7.14545	−0.405181	−0.202591	+	0.979264i	$0.564936\pi$
$312$	−7.56494	−0.428280
$313$	−23.0318	−1.30184	−0.650918	−	0.759148i	$-0.725616\pi$
$313$	−23.0318	−1.30184	−0.650918	+	0.759148i	$0.725616\pi$
$314$	37.6839	2.12663
$315$	0	0
$316$	4.31816	0.242916
$317$	20.7750	1.16684	0.583419	−	0.812171i	$-0.301715\pi$
$317$	20.7750	1.16684	0.583419	+	0.812171i	$0.301715\pi$
$318$	21.0653	1.18128
$319$	−3.63606	−0.203581
$320$	0	0
$321$	−15.3059	−0.854291
$322$	−43.9927	−2.45162
$323$	−7.02890	−0.391098
$324$	2.66802	0.148223
$325$	0	0
$326$	−35.1251	−1.94540
$327$	6.65900	0.368243
$328$	12.3145	0.679953
$329$	−2.38012	−0.131220
$330$	0	0
$331$	−19.2504	−1.05810	−0.529048	−	0.848592i	$-0.677451\pi$
$331$	−19.2504	−1.05810	−0.529048	+	0.848592i	$0.677451\pi$
$332$	−35.0814	−1.92534
$333$	5.95751	0.326469
$334$	−24.6100	−1.34660
$335$	0	0
$336$	−7.00922	−0.382384
$337$	−21.7064	−1.18243	−0.591213	−	0.806516i	$-0.701351\pi$
$337$	−21.7064	−1.18243	−0.591213	+	0.806516i	$0.701351\pi$
$338$	−31.2690	−1.70081
$339$	8.97143	0.487261
$340$	0	0
$341$	−6.86939	−0.371998
$342$	−11.7661	−0.636240
$343$	−12.6766	−0.684470
$344$	−12.2453	−0.660221
$345$	0	0
$346$	20.4356	1.09862
$347$	1.71494	0.0920626	0.0460313	−	0.998940i	$-0.485343\pi$
$347$	1.71494	0.0920626	0.0460313	+	0.998940i	$0.485343\pi$
$348$	−6.30616	−0.338046
$349$	−15.5553	−0.832654	−0.416327	−	0.909215i	$-0.636683\pi$
$349$	−15.5553	−0.832654	−0.416327	+	0.909215i	$0.636683\pi$
$350$	0	0
$351$	5.24144	0.279767
$352$	11.8116	0.629560
$353$	−15.5536	−0.827833	−0.413916	−	0.910315i	$-0.635839\pi$
$353$	−15.5536	−0.827833	−0.413916	+	0.910315i	$0.635839\pi$
$354$	−8.88573	−0.472271
$355$	0	0
$356$	19.4124	1.02886
$357$	−4.07928	−0.215899
$358$	−8.80961	−0.465602
$359$	−24.5371	−1.29502	−0.647508	−	0.762059i	$-0.724189\pi$
$359$	−24.5371	−1.29502	−0.647508	+	0.762059i	$0.724189\pi$
$360$	0	0
$361$	10.6575	0.560924
$362$	24.0259	1.26277
$363$	−8.63348	−0.453140
$364$	44.1981	2.31661
$365$	0	0
$366$	23.1049	1.20771
$367$	−28.1068	−1.46716	−0.733581	−	0.679602i	$-0.762153\pi$
$367$	−28.1068	−1.46716	−0.733581	+	0.679602i	$0.762153\pi$
$368$	−14.2875	−0.744786
$369$	−8.53219	−0.444168
$370$	0	0
$371$	−30.8152	−1.59984
$372$	−11.9138	−0.617703
$373$	9.70825	0.502674	0.251337	−	0.967900i	$-0.419130\pi$
$373$	9.70825	0.502674	0.251337	+	0.967900i	$0.419130\pi$
$374$	4.28984	0.221823
$375$	0	0
$376$	1.08690	0.0560527
$377$	−12.3887	−0.638052
$378$	−6.82858	−0.351224
$379$	−22.2665	−1.14375	−0.571875	−	0.820340i	$-0.693784\pi$
$379$	−22.2665	−1.14375	−0.571875	+	0.820340i	$0.693784\pi$
$380$	0	0
$381$	−10.0185	−0.513261
$382$	−7.80253	−0.399212
$383$	13.6299	0.696458	0.348229	−	0.937410i	$-0.386783\pi$
$383$	13.6299	0.696458	0.348229	+	0.937410i	$0.386783\pi$
$384$	10.9023	0.556355
$385$	0	0
$386$	−36.8510	−1.87567
$387$	8.48426	0.431279
$388$	−27.1976	−1.38075
$389$	19.2304	0.975021	0.487510	−	0.873117i	$-0.337905\pi$
$389$	19.2304	0.975021	0.487510	+	0.873117i	$0.337905\pi$
$390$	0	0
$391$	−8.31515	−0.420515
$392$	−4.31421	−0.217900
$393$	−6.37865	−0.321760
$394$	−9.51777	−0.479498
$395$	0	0
$396$	4.10435	0.206251
$397$	−22.2281	−1.11560	−0.557799	−	0.829976i	$-0.688354\pi$
$397$	−22.2281	−1.11560	−0.557799	+	0.829976i	$0.688354\pi$
$398$	−35.8557	−1.79729
$399$	17.2120	0.861678
$400$	0	0
$401$	4.71728	0.235570	0.117785	−	0.993039i	$-0.462421\pi$
$401$	4.71728	0.235570	0.117785	+	0.993039i	$0.462421\pi$
$402$	−4.10214	−0.204596
$403$	−23.4052	−1.16590
$404$	2.90171	0.144365
$405$	0	0
$406$	16.1401	0.801020
$407$	9.16474	0.454279
$408$	1.86284	0.0922241
$409$	−12.4807	−0.617130	−0.308565	−	0.951203i	$-0.599849\pi$
$409$	−12.4807	−0.617130	−0.308565	+	0.951203i	$0.599849\pi$
$410$	0	0
$411$	9.17732	0.452684
$412$	13.1735	0.649012
$413$	12.9984	0.639611
$414$	−13.9193	−0.684095
$415$	0	0
$416$	40.2442	1.97314
$417$	−9.26539	−0.453728
$418$	−18.1005	−0.885322
$419$	34.9484	1.70734	0.853669	−	0.520815i	$-0.174372\pi$
$419$	34.9484	1.70734	0.853669	+	0.520815i	$0.174372\pi$
$420$	0	0
$421$	−39.5601	−1.92804	−0.964020	−	0.265829i	$-0.914354\pi$
$421$	−39.5601	−1.92804	−0.964020	+	0.265829i	$0.914354\pi$
$422$	−40.0683	−1.95050
$423$	−0.753070	−0.0366155
$424$	14.0720	0.683396
$425$	0	0
$426$	0.153135	0.00741940
$427$	−33.7989	−1.63564
$428$	−40.8364	−1.97390
$429$	8.06317	0.389294
$430$	0	0
$431$	−14.0584	−0.677170	−0.338585	−	0.940936i	$-0.609948\pi$
$431$	−14.0584	−0.677170	−0.338585	+	0.940936i	$0.609948\pi$
$432$	−2.21771	−0.106700
$433$	0.549678	0.0264158	0.0132079	−	0.999913i	$-0.495796\pi$
$433$	0.549678	0.0264158	0.0132079	+	0.999913i	$0.495796\pi$
$434$	30.4925	1.46369
$435$	0	0
$436$	17.7663	0.850853
$437$	35.0847	1.67833
$438$	8.66649	0.414101
$439$	−2.97377	−0.141930	−0.0709651	−	0.997479i	$-0.522608\pi$
$439$	−2.97377	−0.141930	−0.0709651	+	0.997479i	$0.522608\pi$
$440$	0	0
$441$	2.98914	0.142340
$442$	14.6163	0.695225
$443$	36.6893	1.74316	0.871580	−	0.490253i	$-0.163095\pi$
$443$	36.6893	1.74316	0.871580	+	0.490253i	$0.163095\pi$
$444$	15.8947	0.754331
$445$	0	0
$446$	−1.66700	−0.0789345
$447$	−10.0817	−0.476850
$448$	−38.4120	−1.81480
$449$	−17.8432	−0.842071	−0.421036	−	0.907044i	$-0.638333\pi$
$449$	−17.8432	−0.842071	−0.421036	+	0.907044i	$0.638333\pi$
$450$	0	0
$451$	−13.1255	−0.618056
$452$	23.9359	1.12585
$453$	10.7375	0.504491
$454$	24.6982	1.15914
$455$	0	0
$456$	−7.86000	−0.368078
$457$	24.1784	1.13102	0.565509	−	0.824742i	$-0.308680\pi$
$457$	24.1784	1.13102	0.565509	+	0.824742i	$0.308680\pi$
$458$	−22.0912	−1.03225
$459$	−1.29068	−0.0602439
$460$	0	0
$461$	−37.3874	−1.74130	−0.870651	−	0.491901i	$-0.836302\pi$
$461$	−37.3874	−1.74130	−0.870651	+	0.491901i	$0.836302\pi$
$462$	−10.5048	−0.488725
$463$	−20.4314	−0.949530	−0.474765	−	0.880113i	$-0.657467\pi$
$463$	−20.4314	−0.949530	−0.474765	+	0.880113i	$0.657467\pi$
$464$	5.24181	0.243345
$465$	0	0
$466$	−48.6622	−2.25423
$467$	−31.2124	−1.44434	−0.722169	−	0.691716i	$-0.756855\pi$
$467$	−31.2124	−1.44434	−0.722169	+	0.691716i	$0.756855\pi$
$468$	13.9843	0.646422
$469$	6.00078	0.277090
$470$	0	0
$471$	−17.4417	−0.803673
$472$	−5.93584	−0.273219
$473$	13.0518	0.600121
$474$	−3.49684	−0.160615
$475$	0	0
$476$	−10.8836	−0.498849
$477$	−9.74991	−0.446418
$478$	1.27273	0.0582133
$479$	11.0970	0.507033	0.253516	−	0.967331i	$-0.418413\pi$
$479$	11.0970	0.507033	0.253516	+	0.967331i	$0.418413\pi$
$480$	0	0
$481$	31.2259	1.42378
$482$	−3.26108	−0.148538
$483$	20.3617	0.926490
$484$	−23.0343	−1.04701
$485$	0	0
$486$	−2.16056	−0.0980050
$487$	−7.13702	−0.323409	−0.161705	−	0.986839i	$-0.551699\pi$
$487$	−7.13702	−0.323409	−0.161705	+	0.986839i	$0.551699\pi$
$488$	15.4345	0.698688
$489$	16.2574	0.735185
$490$	0	0
$491$	7.23348	0.326442	0.163221	−	0.986590i	$-0.447812\pi$
$491$	7.23348	0.326442	0.163221	+	0.986590i	$0.447812\pi$
$492$	−22.7641	−1.02628
$493$	3.05067	0.137395
$494$	−61.6715	−2.77473
$495$	0	0
$496$	9.90303	0.444659
$497$	−0.224012	−0.0100483
$498$	28.4089	1.27303
$499$	16.0169	0.717014	0.358507	−	0.933527i	$-0.383286\pi$
$499$	16.0169	0.717014	0.358507	+	0.933527i	$0.383286\pi$
$500$	0	0
$501$	11.3906	0.508894
$502$	−25.7005	−1.14707
$503$	33.7963	1.50690	0.753452	−	0.657503i	$-0.228387\pi$
$503$	33.7963	1.50690	0.753452	+	0.657503i	$0.228387\pi$
$504$	−4.56162	−0.203191
$505$	0	0
$506$	−21.4127	−0.951912
$507$	14.4727	0.642753
$508$	−26.7294	−1.18593
$509$	−36.4270	−1.61460	−0.807300	−	0.590142i	$-0.799072\pi$
$509$	−36.4270	−1.61460	−0.807300	+	0.590142i	$0.799072\pi$
$510$	0	0
$511$	−12.6777	−0.560829
$512$	−23.4294	−1.03544
$513$	5.44587	0.240441
$514$	−38.9964	−1.72006
$515$	0	0
$516$	22.6362	0.996502
$517$	−1.15849	−0.0509502
$518$	−40.6813	−1.78743
$519$	−9.45845	−0.415180
$520$	0	0
$521$	25.4993	1.11714	0.558572	−	0.829456i	$-0.311349\pi$
$521$	25.4993	1.11714	0.558572	+	0.829456i	$0.311349\pi$
$522$	5.10672	0.223515
$523$	7.03174	0.307477	0.153738	−	0.988112i	$-0.450869\pi$
$523$	7.03174	0.307477	0.153738	+	0.988112i	$0.450869\pi$
$524$	−17.0184	−0.743450
$525$	0	0
$526$	−41.2811	−1.79994
$527$	5.76345	0.251060
$528$	−3.41162	−0.148472
$529$	18.5050	0.804565
$530$	0	0
$531$	4.11270	0.178476
$532$	45.9220	1.99097
$533$	−44.7210	−1.93708
$534$	−15.7202	−0.680278
$535$	0	0
$536$	−2.74030	−0.118363
$537$	4.07747	0.175956
$538$	48.0185	2.07022
$539$	4.59834	0.198065
$540$	0	0
$541$	−27.1476	−1.16717	−0.583584	−	0.812053i	$-0.698350\pi$
$541$	−27.1476	−1.16717	−0.583584	+	0.812053i	$0.698350\pi$
$542$	−43.6665	−1.87564
$543$	−11.1202	−0.477214
$544$	−9.90999	−0.424887
$545$	0	0
$546$	−35.7916	−1.53174
$547$	−44.0769	−1.88459	−0.942296	−	0.334782i	$-0.891337\pi$
$547$	−44.0769	−1.88459	−0.942296	+	0.334782i	$0.891337\pi$
$548$	24.4853	1.04596
$549$	−10.6939	−0.456407
$550$	0	0
$551$	−12.8719	−0.548363
$552$	−9.29833	−0.395763
$553$	5.11533	0.217526
$554$	−34.6581	−1.47248
$555$	0	0
$556$	−24.7202	−1.04837
$557$	9.85667	0.417641	0.208820	−	0.977954i	$-0.433038\pi$
$557$	9.85667	0.417641	0.208820	+	0.977954i	$0.433038\pi$
$558$	9.64781	0.408425
$559$	44.4697	1.88087
$560$	0	0
$561$	−1.98552	−0.0838289
$562$	−18.0905	−0.763103
$563$	12.3917	0.522249	0.261125	−	0.965305i	$-0.415907\pi$
$563$	12.3917	0.522249	0.261125	+	0.965305i	$0.415907\pi$
$564$	−2.00921	−0.0846028
$565$	0	0
$566$	−2.44132	−0.102616
$567$	3.16056	0.132731
$568$	0.102297	0.00429228
$569$	−11.7158	−0.491150	−0.245575	−	0.969378i	$-0.578977\pi$
$569$	−11.7158	−0.491150	−0.245575	+	0.969378i	$0.578977\pi$
$570$	0	0
$571$	28.9797	1.21276	0.606382	−	0.795173i	$-0.292620\pi$
$571$	28.9797	1.21276	0.606382	+	0.795173i	$0.292620\pi$
$572$	21.5127	0.899491
$573$	3.61135	0.150866
$574$	58.2628	2.43184
$575$	0	0
$576$	−12.1535	−0.506398
$577$	32.8024	1.36558	0.682790	−	0.730614i	$-0.260766\pi$
$577$	32.8024	1.36558	0.682790	+	0.730614i	$0.260766\pi$
$578$	33.1303	1.37804
$579$	17.0562	0.708833
$580$	0	0
$581$	−41.5577	−1.72410
$582$	22.0246	0.912947
$583$	−14.9988	−0.621186
$584$	5.78938	0.239566
$585$	0	0
$586$	−5.13905	−0.212292
$587$	−18.6395	−0.769334	−0.384667	−	0.923055i	$-0.625684\pi$
$587$	−18.6395	−0.769334	−0.384667	+	0.923055i	$0.625684\pi$
$588$	7.97508	0.328887
$589$	−24.3181	−1.00201
$590$	0	0
$591$	4.40523	0.181207
$592$	−13.2120	−0.543012
$593$	−1.55882	−0.0640129	−0.0320064	−	0.999488i	$-0.510190\pi$
$593$	−1.55882	−0.0640129	−0.0320064	+	0.999488i	$0.510190\pi$
$594$	−3.32370	−0.136373
$595$	0	0
$596$	−26.8983	−1.10180
$597$	16.5956	0.679212
$598$	−72.9570	−2.98343
$599$	−31.5470	−1.28898	−0.644489	−	0.764614i	$-0.722930\pi$
$599$	−31.5470	−1.28898	−0.644489	+	0.764614i	$0.722930\pi$
$600$	0	0
$601$	−32.3999	−1.32162	−0.660809	−	0.750554i	$-0.729787\pi$
$601$	−32.3999	−1.32162	−0.660809	+	0.750554i	$0.729787\pi$
$602$	−57.9354	−2.36127
$603$	1.89864	0.0773188
$604$	28.6478	1.16566
$605$	0	0
$606$	−2.34980	−0.0954542
$607$	−24.8410	−1.00827	−0.504133	−	0.863626i	$-0.668188\pi$
$607$	−24.8410	−1.00827	−0.504133	+	0.863626i	$0.668188\pi$
$608$	41.8139	1.69578
$609$	−7.47034	−0.302713
$610$	0	0
$611$	−3.94717	−0.159685
$612$	−3.44357	−0.139198
$613$	3.94558	0.159360	0.0796802	−	0.996820i	$-0.474610\pi$
$613$	3.94558	0.159360	0.0796802	+	0.996820i	$0.474610\pi$
$614$	6.25192	0.252307
$615$	0	0
$616$	−7.01737	−0.282738
$617$	17.4821	0.703801	0.351900	−	0.936037i	$-0.385536\pi$
$617$	17.4821	0.703801	0.351900	+	0.936037i	$0.385536\pi$
$618$	−10.6679	−0.429126
$619$	−14.3869	−0.578260	−0.289130	−	0.957290i	$-0.593366\pi$
$619$	−14.3869	−0.578260	−0.289130	+	0.957290i	$0.593366\pi$
$620$	0	0
$621$	6.44244	0.258526
$622$	15.4382	0.619014
$623$	22.9961	0.921321
$624$	−11.6240	−0.465333
$625$	0	0
$626$	49.7617	1.98888
$627$	8.37767	0.334572
$628$	−46.5349	−1.85694
$629$	−7.68926	−0.306591
$630$	0	0
$631$	−17.6758	−0.703664	−0.351832	−	0.936063i	$-0.614441\pi$
$631$	−17.6758	−0.703664	−0.351832	+	0.936063i	$0.614441\pi$
$632$	−2.33596	−0.0929194
$633$	18.5454	0.737112
$634$	−44.8855	−1.78263
$635$	0	0
$636$	−26.0129	−1.03148
$637$	15.6674	0.620764
$638$	7.85594	0.311019
$639$	−0.0708774	−0.00280387
$640$	0	0
$641$	−2.74127	−0.108274	−0.0541369	−	0.998534i	$-0.517241\pi$
$641$	−2.74127	−0.108274	−0.0541369	+	0.998534i	$0.517241\pi$
$642$	33.0693	1.30514
$643$	−20.9276	−0.825303	−0.412651	−	0.910889i	$-0.635397\pi$
$643$	−20.9276	−0.825303	−0.412651	+	0.910889i	$0.635397\pi$
$644$	54.3254	2.14072
$645$	0	0
$646$	15.1864	0.597499
$647$	1.84667	0.0726002	0.0363001	−	0.999341i	$-0.488443\pi$
$647$	1.84667	0.0726002	0.0363001	+	0.999341i	$0.488443\pi$
$648$	−1.44329	−0.0566980
$649$	6.32678	0.248348
$650$	0	0
$651$	−14.1132	−0.553141
$652$	43.3751	1.69870
$653$	18.4133	0.720567	0.360284	−	0.932843i	$-0.382680\pi$
$653$	18.4133	0.720567	0.360284	+	0.932843i	$0.382680\pi$
$654$	−14.3872	−0.562583
$655$	0	0
$656$	18.9220	0.738778
$657$	−4.01123	−0.156493
$658$	5.14240	0.200472
$659$	−13.3800	−0.521210	−0.260605	−	0.965446i	$-0.583922\pi$
$659$	−13.3800	−0.521210	−0.260605	+	0.965446i	$0.583922\pi$
$660$	0	0
$661$	39.1834	1.52406	0.762030	−	0.647542i	$-0.224203\pi$
$661$	39.1834	1.52406	0.762030	+	0.647542i	$0.224203\pi$
$662$	41.5915	1.61650
$663$	−6.76504	−0.262732
$664$	18.9776	0.736476
$665$	0	0
$666$	−12.8716	−0.498763
$667$	−15.2274	−0.589608
$668$	30.3903	1.17584
$669$	0.771557	0.0298301
$670$	0	0
$671$	−16.4510	−0.635086
$672$	24.2671	0.936122
$673$	−19.3911	−0.747473	−0.373736	−	0.927535i	$-0.621923\pi$
$673$	−19.3911	−0.747473	−0.373736	+	0.927535i	$0.621923\pi$
$674$	46.8981	1.80645
$675$	0	0
$676$	38.6133	1.48513
$677$	45.6836	1.75576	0.877882	−	0.478876i	$-0.158956\pi$
$677$	45.6836	1.75576	0.877882	+	0.478876i	$0.158956\pi$
$678$	−19.3833	−0.744412
$679$	−32.2185	−1.23643
$680$	0	0
$681$	−11.4314	−0.438051
$682$	14.8417	0.568319
$683$	−11.5893	−0.443451	−0.221725	−	0.975109i	$-0.571169\pi$
$683$	−11.5893	−0.443451	−0.221725	+	0.975109i	$0.571169\pi$
$684$	14.5297	0.555557
$685$	0	0
$686$	27.3885	1.04570
$687$	10.2248	0.390099
$688$	−18.8157	−0.717340
$689$	−51.1035	−1.94689
$690$	0	0
$691$	−21.6424	−0.823317	−0.411658	−	0.911338i	$-0.635050\pi$
$691$	−21.6424	−0.823317	−0.411658	+	0.911338i	$0.635050\pi$
$692$	−25.2353	−0.959303
$693$	4.86205	0.184694
$694$	−3.70522	−0.140648
$695$	0	0
$696$	3.41139	0.129308
$697$	11.0124	0.417123
$698$	33.6081	1.27208
$699$	22.5229	0.851896
$700$	0	0
$701$	−8.61904	−0.325537	−0.162768	−	0.986664i	$-0.552042\pi$
$701$	−8.61904	−0.325537	−0.162768	+	0.986664i	$0.552042\pi$
$702$	−11.3244	−0.427413
$703$	32.4438	1.22364
$704$	−18.6964	−0.704648
$705$	0	0
$706$	33.6044	1.26472
$707$	3.43739	0.129276
$708$	10.9728	0.412381
$709$	16.0001	0.600895	0.300447	−	0.953798i	$-0.402864\pi$
$709$	16.0001	0.600895	0.300447	+	0.953798i	$0.402864\pi$
$710$	0	0
$711$	1.61849	0.0606981
$712$	−10.5014	−0.393555
$713$	−28.7682	−1.07738
$714$	8.81353	0.329838
$715$	0	0
$716$	10.8788	0.406558
$717$	−0.589074	−0.0219994
$718$	53.0138	1.97846
$719$	−48.5838	−1.81187	−0.905935	−	0.423416i	$-0.860831\pi$
$719$	−48.5838	−1.81187	−0.905935	+	0.423416i	$0.860831\pi$
$720$	0	0
$721$	15.6055	0.581177
$722$	−23.0263	−0.856949
$723$	1.50937	0.0561340
$724$	−29.6689	−1.10264
$725$	0	0
$726$	18.6531	0.692283
$727$	−25.4328	−0.943251	−0.471625	−	0.881799i	$-0.656333\pi$
$727$	−25.4328	−0.943251	−0.471625	+	0.881799i	$0.656333\pi$
$728$	−23.9094	−0.886143
$729$	1.00000	0.0370370
$730$	0	0
$731$	−10.9505	−0.405019
$732$	−28.5317	−1.05456
$733$	18.6190	0.687708	0.343854	−	0.939023i	$-0.388267\pi$
$733$	18.6190	0.687708	0.343854	+	0.939023i	$0.388267\pi$
$734$	60.7264	2.24145
$735$	0	0
$736$	49.4656	1.82333
$737$	2.92078	0.107588
$738$	18.4343	0.678576
$739$	46.8872	1.72478	0.862388	−	0.506249i	$-0.168968\pi$
$739$	46.8872	1.72478	0.862388	+	0.506249i	$0.168968\pi$
$740$	0	0
$741$	28.5442	1.04860
$742$	66.5780	2.44416
$743$	42.7061	1.56674	0.783368	−	0.621558i	$-0.213500\pi$
$743$	42.7061	1.56674	0.783368	+	0.621558i	$0.213500\pi$
$744$	6.44492	0.236282
$745$	0	0
$746$	−20.9753	−0.767959
$747$	−13.1488	−0.481091
$748$	−5.29742	−0.193693
$749$	−48.3751	−1.76759
$750$	0	0
$751$	−2.64893	−0.0966608	−0.0483304	−	0.998831i	$-0.515390\pi$
$751$	−2.64893	−0.0966608	−0.0483304	+	0.998831i	$0.515390\pi$
$752$	1.67009	0.0609021
$753$	11.8953	0.433488
$754$	26.7666	0.974781
$755$	0	0
$756$	8.43243	0.306685
$757$	−52.9153	−1.92324	−0.961620	−	0.274383i	$-0.911526\pi$
$757$	−52.9153	−1.92324	−0.961620	+	0.274383i	$0.911526\pi$
$758$	48.1080	1.74736
$759$	9.91073	0.359737
$760$	0	0
$761$	50.7787	1.84073	0.920363	−	0.391064i	$-0.127893\pi$
$761$	50.7787	1.84073	0.920363	+	0.391064i	$0.127893\pi$
$762$	21.6455	0.784133
$763$	21.0462	0.761922
$764$	9.63514	0.348587
$765$	0	0
$766$	−29.4483	−1.06401
$767$	21.5565	0.778358
$768$	0.752056	0.0271375
$769$	24.5805	0.886396	0.443198	−	0.896424i	$-0.353844\pi$
$769$	24.5805	0.886396	0.443198	+	0.896424i	$0.353844\pi$
$770$	0	0
$771$	18.0492	0.650026
$772$	45.5064	1.63781
$773$	20.0112	0.719754	0.359877	−	0.933000i	$-0.382819\pi$
$773$	20.0112	0.719754	0.359877	+	0.933000i	$0.382819\pi$
$774$	−18.3308	−0.658885
$775$	0	0
$776$	14.7128	0.528159
$777$	18.8291	0.675489
$778$	−41.5485	−1.48958
$779$	−46.4653	−1.66479
$780$	0	0
$781$	−0.109034	−0.00390155
$782$	17.9654	0.642441
$783$	−2.36361	−0.0844686
$784$	−6.62905	−0.236752
$785$	0	0
$786$	13.7815	0.491568
$787$	−8.99272	−0.320556	−0.160278	−	0.987072i	$-0.551239\pi$
$787$	−8.99272	−0.320556	−0.160278	+	0.987072i	$0.551239\pi$
$788$	11.7532	0.418692
$789$	19.1066	0.680215
$790$	0	0
$791$	28.3547	1.00818
$792$	−2.22029	−0.0788947
$793$	−56.0517	−1.99045
$794$	48.0252	1.70435
$795$	0	0
$796$	44.2773	1.56937
$797$	37.7564	1.33740	0.668700	−	0.743533i	$-0.266851\pi$
$797$	37.7564	1.33740	0.668700	+	0.743533i	$0.266851\pi$
$798$	−37.1876	−1.31643
$799$	0.971976	0.0343860
$800$	0	0
$801$	7.27597	0.257084
$802$	−10.1920	−0.359891
$803$	−6.17067	−0.217758
$804$	5.06562	0.178651
$805$	0	0
$806$	50.5684	1.78120
$807$	−22.2250	−0.782358
$808$	−1.56971	−0.0552223
$809$	−48.9001	−1.71924	−0.859618	−	0.510937i	$-0.829298\pi$
$809$	−48.9001	−1.71924	−0.859618	+	0.510937i	$0.829298\pi$
$810$	0	0
$811$	−18.0551	−0.633999	−0.317000	−	0.948426i	$-0.602675\pi$
$811$	−18.0551	−0.633999	−0.317000	+	0.948426i	$0.602675\pi$
$812$	−19.9310	−0.699441
$813$	20.2107	0.708822
$814$	−19.8010	−0.694024
$815$	0	0
$816$	2.86237	0.100203
$817$	46.2042	1.61648
$818$	26.9653	0.942819
$819$	16.5659	0.578859
$820$	0	0
$821$	50.6097	1.76629	0.883146	−	0.469099i	$-0.155421\pi$
$821$	50.6097	1.76629	0.883146	+	0.469099i	$0.155421\pi$
$822$	−19.8281	−0.691586
$823$	26.8070	0.934433	0.467217	−	0.884143i	$-0.345257\pi$
$823$	26.8070	0.934433	0.467217	+	0.884143i	$0.345257\pi$
$824$	−7.12635	−0.248258
$825$	0	0
$826$	−28.0839	−0.977163
$827$	21.3649	0.742929	0.371465	−	0.928447i	$-0.378856\pi$
$827$	21.3649	0.742929	0.371465	+	0.928447i	$0.378856\pi$
$828$	17.1885	0.597343
$829$	−48.1123	−1.67101	−0.835504	−	0.549484i	$-0.814824\pi$
$829$	−48.1123	−1.67101	−0.835504	+	0.549484i	$0.814824\pi$
$830$	0	0
$831$	16.0413	0.556465
$832$	−63.7021	−2.20847
$833$	−3.85803	−0.133673
$834$	20.0184	0.693182
$835$	0	0
$836$	22.3518	0.773052
$837$	−4.46542	−0.154348
$838$	−75.5080	−2.60838
$839$	−41.8540	−1.44496	−0.722481	−	0.691391i	$-0.756998\pi$
$839$	−41.8540	−1.44496	−0.722481	+	0.691391i	$0.756998\pi$
$840$	0	0
$841$	−23.4133	−0.807357
$842$	85.4719	2.94556
$843$	8.37308	0.288384
$844$	49.4794	1.70315
$845$	0	0
$846$	1.62705	0.0559393
$847$	−27.2866	−0.937579
$848$	21.6225	0.742520
$849$	1.12995	0.0387798
$850$	0	0
$851$	38.3809	1.31568
$852$	−0.189102	−0.00647853
$853$	58.2023	1.99281	0.996404	−	0.0847260i	$-0.0270015\pi$
$853$	58.2023	1.99281	0.996404	+	0.0847260i	$0.0270015\pi$
$854$	73.0245	2.49885
$855$	0	0
$856$	22.0909	0.755051
$857$	3.22045	0.110008	0.0550042	−	0.998486i	$-0.482483\pi$
$857$	3.22045	0.110008	0.0550042	+	0.998486i	$0.482483\pi$
$858$	−17.4210	−0.594742
$859$	49.4431	1.68698	0.843488	−	0.537147i	$-0.180498\pi$
$859$	49.4431	1.68698	0.843488	+	0.537147i	$0.180498\pi$
$860$	0	0
$861$	−26.9665	−0.919016
$862$	30.3740	1.03454
$863$	−21.4924	−0.731611	−0.365806	−	0.930691i	$-0.619207\pi$
$863$	−21.4924	−0.731611	−0.365806	+	0.930691i	$0.619207\pi$
$864$	7.67809	0.261214
$865$	0	0
$866$	−1.18761	−0.0403567
$867$	−15.3341	−0.520775
$868$	−37.6544	−1.27807
$869$	2.48981	0.0844609
$870$	0	0
$871$	9.95163	0.337198
$872$	−9.61090	−0.325466
$873$	−10.1939	−0.345012
$874$	−75.8026	−2.56406
$875$	0	0
$876$	−10.7020	−0.361588
$877$	−15.3793	−0.519321	−0.259661	−	0.965700i	$-0.583611\pi$
$877$	−15.3793	−0.519321	−0.259661	+	0.965700i	$0.583611\pi$
$878$	6.42501	0.216833
$879$	2.37857	0.0802273
$880$	0	0
$881$	18.9275	0.637682	0.318841	−	0.947808i	$-0.396706\pi$
$881$	18.9275	0.637682	0.318841	+	0.947808i	$0.396706\pi$
$882$	−6.45821	−0.217459
$883$	−6.31708	−0.212587	−0.106293	−	0.994335i	$-0.533898\pi$
$883$	−6.31708	−0.212587	−0.106293	+	0.994335i	$0.533898\pi$
$884$	−18.0492	−0.607062
$885$	0	0
$886$	−79.2694	−2.66311
$887$	−0.0721586	−0.00242285	−0.00121142	−	0.999999i	$-0.500386\pi$
$887$	−0.0721586	−0.00242285	−0.00121142	+	0.999999i	$0.500386\pi$
$888$	−8.59844	−0.288545
$889$	−31.6639	−1.06197
$890$	0	0
$891$	1.53835	0.0515367
$892$	2.05853	0.0689246
$893$	−4.10113	−0.137239
$894$	21.7822	0.728505
$895$	0	0
$896$	34.4573	1.15114
$897$	33.7676	1.12747
$898$	38.5512	1.28647
$899$	10.5545	0.352013
$900$	0	0
$901$	12.5840	0.419235
$902$	28.3584	0.944233
$903$	26.8150	0.892348
$904$	−12.9484	−0.430658
$905$	0	0
$906$	−23.1990	−0.770735
$907$	25.4951	0.846550	0.423275	−	0.906001i	$-0.360880\pi$
$907$	25.4951	0.846550	0.423275	+	0.906001i	$0.360880\pi$
$908$	−30.4991	−1.01215
$909$	1.08759	0.0360731
$910$	0	0
$911$	3.55803	0.117883	0.0589414	−	0.998261i	$-0.481227\pi$
$911$	3.55803	0.117883	0.0589414	+	0.998261i	$0.481227\pi$
$912$	−12.0774	−0.399922
$913$	−20.2275	−0.669434
$914$	−52.2389	−1.72791
$915$	0	0
$916$	27.2798	0.901351
$917$	−20.1601	−0.665745
$918$	2.78860	0.0920375
$919$	7.96968	0.262896	0.131448	−	0.991323i	$-0.458037\pi$
$919$	7.96968	0.262896	0.131448	+	0.991323i	$0.458037\pi$
$920$	0	0
$921$	−2.89366	−0.0953492
$922$	80.7776	2.66027
$923$	−0.371499	−0.0122280
$924$	12.9720	0.426749
$925$	0	0
$926$	44.1434	1.45064
$927$	4.93756	0.162171
$928$	−18.1480	−0.595738
$929$	48.5424	1.59263	0.796313	−	0.604885i	$-0.206781\pi$
$929$	48.5424	1.59263	0.796313	+	0.604885i	$0.206781\pi$
$930$	0	0
$931$	16.2785	0.533505
$932$	60.0916	1.96837
$933$	−7.14545	−0.233932
$934$	67.4363	2.20658
$935$	0	0
$936$	−7.56494	−0.247268
$937$	−31.7296	−1.03656	−0.518280	−	0.855211i	$-0.673427\pi$
$937$	−31.7296	−1.03656	−0.518280	+	0.855211i	$0.673427\pi$
$938$	−12.9650	−0.423324
$939$	−23.0318	−0.751616
$940$	0	0
$941$	41.0068	1.33678	0.668392	−	0.743809i	$-0.266983\pi$
$941$	41.0068	1.33678	0.668392	+	0.743809i	$0.266983\pi$
$942$	37.6839	1.22781
$943$	−54.9681	−1.79001
$944$	−9.12079	−0.296856
$945$	0	0
$946$	−28.1991	−0.916833
$947$	9.81789	0.319038	0.159519	−	0.987195i	$-0.449006\pi$
$947$	9.81789	0.319038	0.159519	+	0.987195i	$0.449006\pi$
$948$	4.31816	0.140247
$949$	−21.0246	−0.682487
$950$	0	0
$951$	20.7750	0.673674
$952$	5.88761	0.190818
$953$	−53.1118	−1.72046	−0.860230	−	0.509906i	$-0.829680\pi$
$953$	−53.1118	−1.72046	−0.860230	+	0.509906i	$0.829680\pi$
$954$	21.0653	0.682013
$955$	0	0
$956$	−1.57166	−0.0508311
$957$	−3.63606	−0.117537
$958$	−23.9756	−0.774618
$959$	29.0055	0.936635
$960$	0	0
$961$	−11.0600	−0.356774
$962$	−67.4654	−2.17517
$963$	−15.3059	−0.493225
$964$	4.02702	0.129702
$965$	0	0
$966$	−43.9927	−1.41544
$967$	2.44732	0.0787004	0.0393502	−	0.999225i	$-0.487471\pi$
$967$	2.44732	0.0787004	0.0393502	+	0.999225i	$0.487471\pi$
$968$	12.4606	0.400500
$969$	−7.02890	−0.225801
$970$	0	0
$971$	−47.9683	−1.53938	−0.769688	−	0.638421i	$-0.779588\pi$
$971$	−47.9683	−1.53938	−0.769688	+	0.638421i	$0.779588\pi$
$972$	2.66802	0.0855767
$973$	−29.2838	−0.938796
$974$	15.4200	0.494088
$975$	0	0
$976$	23.7161	0.759134
$977$	−23.6950	−0.758070	−0.379035	−	0.925382i	$-0.623744\pi$
$977$	−23.6950	−0.758070	−0.379035	+	0.925382i	$0.623744\pi$
$978$	−35.1251	−1.12318
$979$	11.1930	0.357730
$980$	0	0
$981$	6.65900	0.212605
$982$	−15.6284	−0.498721
$983$	−12.9505	−0.413057	−0.206529	−	0.978441i	$-0.566217\pi$
$983$	−12.9505	−0.413057	−0.206529	+	0.978441i	$0.566217\pi$
$984$	12.3145	0.392571
$985$	0	0
$986$	−6.59116	−0.209905
$987$	−2.38012	−0.0757602
$988$	76.1565	2.42286
$989$	54.6593	1.73807
$990$	0	0
$991$	44.4967	1.41348	0.706742	−	0.707471i	$-0.250164\pi$
$991$	44.4967	1.41348	0.706742	+	0.707471i	$0.250164\pi$
$992$	−34.2859	−1.08858
$993$	−19.2504	−0.610891
$994$	0.483992	0.0153513
$995$	0	0
$996$	−35.0814	−1.11160
$997$	55.5513	1.75933	0.879663	−	0.475597i	$-0.157768\pi$
$997$	55.5513	1.75933	0.879663	+	0.475597i	$0.157768\pi$
$998$	−34.6054	−1.09542
$999$	5.95751	0.188487

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1875.2.a.k.1.2		6
3.2	odd	2		5625.2.a.q.1.5		6
5.2	odd	4		1875.2.b.f.1249.3		12
5.3	odd	4		1875.2.b.f.1249.10		12
5.4	even	2		1875.2.a.j.1.5		6
15.14	odd	2		5625.2.a.p.1.2		6
25.3	odd	20		375.2.i.d.49.6		24
25.4	even	10		75.2.g.c.16.1	✓	12
25.6	even	5		375.2.g.c.301.3		12
25.8	odd	20		375.2.i.d.199.1		24
25.17	odd	20		375.2.i.d.199.6		24
25.19	even	10		75.2.g.c.61.1	yes	12
25.21	even	5		375.2.g.c.76.3		12
25.22	odd	20		375.2.i.d.49.1		24
75.29	odd	10		225.2.h.d.91.3		12
75.44	odd	10		225.2.h.d.136.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.c.16.1	✓	12	25.4	even	10
75.2.g.c.61.1	yes	12	25.19	even	10
225.2.h.d.91.3		12	75.29	odd	10
225.2.h.d.136.3		12	75.44	odd	10
375.2.g.c.76.3		12	25.21	even	5
375.2.g.c.301.3		12	25.6	even	5
375.2.i.d.49.1		24	25.22	odd	20
375.2.i.d.49.6		24	25.3	odd	20
375.2.i.d.199.1		24	25.8	odd	20
375.2.i.d.199.6		24	25.17	odd	20
1875.2.a.j.1.5		6	5.4	even	2
1875.2.a.k.1.2		6	1.1	even	1	trivial
1875.2.b.f.1249.3		12	5.2	odd	4
1875.2.b.f.1249.10		12	5.3	odd	4
5625.2.a.p.1.2		6	15.14	odd	2
5625.2.a.q.1.5		6	3.2	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:	\( N \)	\(=\)	\( 1875 = 3 \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1875.a (trivial)

\(f(q)\)	\(=\)	\(q-2.16056 q^{2} +1.00000 q^{3} +2.66802 q^{4} -2.16056 q^{6} +3.16056 q^{7} -1.44329 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.16056 q^{2} +1.00000 q^{3} +2.66802 q^{4} -2.16056 q^{6} +3.16056 q^{7} -1.44329 q^{8} +1.00000 q^{9} +1.53835 q^{11} +2.66802 q^{12} +5.24144 q^{13} -6.82858 q^{14} -2.21771 q^{16} -1.29068 q^{17} -2.16056 q^{18} +5.44587 q^{19} +3.16056 q^{21} -3.32370 q^{22} +6.44244 q^{23} -1.44329 q^{24} -11.3244 q^{26} +1.00000 q^{27} +8.43243 q^{28} -2.36361 q^{29} -4.46542 q^{31} +7.67809 q^{32} +1.53835 q^{33} +2.78860 q^{34} +2.66802 q^{36} +5.95751 q^{37} -11.7661 q^{38} +5.24144 q^{39} -8.53219 q^{41} -6.82858 q^{42} +8.48426 q^{43} +4.10435 q^{44} -13.9193 q^{46} -0.753070 q^{47} -2.21771 q^{48} +2.98914 q^{49} -1.29068 q^{51} +13.9843 q^{52} -9.74991 q^{53} -2.16056 q^{54} -4.56162 q^{56} +5.44587 q^{57} +5.10672 q^{58} +4.11270 q^{59} -10.6939 q^{61} +9.64781 q^{62} +3.16056 q^{63} -12.1535 q^{64} -3.32370 q^{66} +1.89864 q^{67} -3.44357 q^{68} +6.44244 q^{69} -0.0708774 q^{71} -1.44329 q^{72} -4.01123 q^{73} -12.8716 q^{74} +14.5297 q^{76} +4.86205 q^{77} -11.3244 q^{78} +1.61849 q^{79} +1.00000 q^{81} +18.4343 q^{82} -13.1488 q^{83} +8.43243 q^{84} -18.3308 q^{86} -2.36361 q^{87} -2.22029 q^{88} +7.27597 q^{89} +16.5659 q^{91} +17.1885 q^{92} -4.46542 q^{93} +1.62705 q^{94} +7.67809 q^{96} -10.1939 q^{97} -6.45821 q^{98} +1.53835 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{3} + 10 q^{4} + 6 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + 6 * q^3 + 10 * q^4 + 6 * q^7 + 3 * q^8 + 6 * q^9	\( 6 q + 6 q^{3} + 10 q^{4} + 6 q^{7} + 3 q^{8} + 6 q^{9} + 3 q^{11} + 10 q^{12} + 6 q^{13} - 22 q^{14} + 18 q^{16} + 13 q^{17} + 11 q^{19} + 6 q^{21} + 16 q^{22} + 13 q^{23} + 3 q^{24} - 28 q^{26} + 6 q^{27} + 7 q^{28} - 3 q^{29} - 11 q^{31} + 16 q^{32} + 3 q^{33} + 15 q^{34} + 10 q^{36} + 21 q^{37} - 9 q^{38} + 6 q^{39} - q^{41} - 22 q^{42} + 2 q^{43} + 9 q^{44} + 19 q^{46} + 14 q^{47} + 18 q^{48} - 14 q^{49} + 13 q^{51} + 13 q^{52} + 23 q^{53} - 35 q^{56} + 11 q^{57} + 22 q^{58} + 9 q^{59} + 11 q^{61} - 23 q^{62} + 6 q^{63} - 23 q^{64} + 16 q^{66} + 8 q^{67} + 50 q^{68} + 13 q^{69} - 8 q^{71} + 3 q^{72} + 13 q^{73} - 22 q^{74} - 26 q^{76} - 13 q^{77} - 28 q^{78} - 5 q^{79} + 6 q^{81} - 13 q^{82} - 20 q^{83} + 7 q^{84} - 37 q^{86} - 3 q^{87} + 28 q^{88} - 4 q^{89} + 34 q^{91} + 61 q^{92} - 11 q^{93} + 41 q^{94} + 16 q^{96} - 7 q^{97} - 41 q^{98} + 3 q^{99}+O(q^{100}) \) 6 * q + 6 * q^3 + 10 * q^4 + 6 * q^7 + 3 * q^8 + 6 * q^9 + 3 * q^11 + 10 * q^12 + 6 * q^13 - 22 * q^14 + 18 * q^16 + 13 * q^17 + 11 * q^19 + 6 * q^21 + 16 * q^22 + 13 * q^23 + 3 * q^24 - 28 * q^26 + 6 * q^27 + 7 * q^28 - 3 * q^29 - 11 * q^31 + 16 * q^32 + 3 * q^33 + 15 * q^34 + 10 * q^36 + 21 * q^37 - 9 * q^38 + 6 * q^39 - q^41 - 22 * q^42 + 2 * q^43 + 9 * q^44 + 19 * q^46 + 14 * q^47 + 18 * q^48 - 14 * q^49 + 13 * q^51 + 13 * q^52 + 23 * q^53 - 35 * q^56 + 11 * q^57 + 22 * q^58 + 9 * q^59 + 11 * q^61 - 23 * q^62 + 6 * q^63 - 23 * q^64 + 16 * q^66 + 8 * q^67 + 50 * q^68 + 13 * q^69 - 8 * q^71 + 3 * q^72 + 13 * q^73 - 22 * q^74 - 26 * q^76 - 13 * q^77 - 28 * q^78 - 5 * q^79 + 6 * q^81 - 13 * q^82 - 20 * q^83 + 7 * q^84 - 37 * q^86 - 3 * q^87 + 28 * q^88 - 4 * q^89 + 34 * q^91 + 61 * q^92 - 11 * q^93 + 41 * q^94 + 16 * q^96 - 7 * q^97 - 41 * q^98 + 3 * q^99

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