LMFDB - Embedded newform 1875.2.a.j.1.5

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:	$1$
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			1.5
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	$-0.223295\pi$
$2$	2.16056	1.52775	0.763873	+	0.645366i	$0.223295\pi$
$3$	−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	$-0.703756\pi$
$7$	−3.16056	−1.19458	−0.597290	+	0.802026i	$0.703756\pi$
$8$	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	$-0.759019\pi$
$13$	−5.24144	−1.45371	−0.726857	+	0.686789i	$0.759019\pi$
$14$	−6.82858	−1.82501
$15$	0	0
$16$	−2.21771	−0.554428
$17$	1.29068	0.313037	0.156518	−	0.987675i	$-0.449973\pi$
$17$	1.29068	0.313037	0.156518	+	0.987675i	$0.449973\pi$
$18$	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	$-0.734423\pi$
$23$	−6.44244	−1.34334	−0.671671	+	0.740850i	$0.734423\pi$
$24$	−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	$-0.662895\pi$
$37$	−5.95751	−0.979408	−0.489704	+	0.871889i	$0.662895\pi$
$38$	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	$-0.723943\pi$
$43$	−8.48426	−1.29384	−0.646919	+	0.762559i	$0.723943\pi$
$44$	4.10435	0.618754
$45$	0	0
$46$	−13.9193	−2.05228
$47$	0.753070	0.109847	0.0549233	−	0.998491i	$-0.482509\pi$
$47$	0.753070	0.109847	0.0549233	+	0.998491i	$0.482509\pi$
$48$	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	$-0.266454\pi$
$53$	9.74991	1.33925	0.669626	+	0.742698i	$0.266454\pi$
$54$	−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	$-0.537000\pi$
$67$	−1.89864	−0.231956	−0.115978	+	0.993252i	$0.537000\pi$
$68$	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	$-0.424576\pi$
$73$	4.01123	0.469478	0.234739	+	0.972058i	$0.424576\pi$
$74$	−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	$-0.243390\pi$
$83$	13.1488	1.44327	0.721636	+	0.692272i	$0.243390\pi$
$84$	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	$-0.326856\pi$
$97$	10.1939	1.03504	0.517518	+	0.855673i	$0.326856\pi$
$98$	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	$-0.578216\pi$
$103$	−4.93756	−0.486512	−0.243256	+	0.969962i	$0.578216\pi$
$104$	−7.56494	−0.741803
$105$	0	0
$106$	21.0653	2.04604
$107$	15.3059	1.47967	0.739837	−	0.672786i	$-0.234902\pi$
$107$	15.3059	1.47967	0.739837	+	0.672786i	$0.234902\pi$
$108$	−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	$-0.638665\pi$
$113$	−8.97143	−0.843961	−0.421981	+	0.906605i	$0.638665\pi$
$114$	−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	$-0.353382\pi$
$127$	10.0185	0.888995	0.444497	+	0.895780i	$0.353382\pi$
$128$	−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	$-0.628229\pi$
$137$	−9.17732	−0.784071	−0.392036	+	0.919950i	$0.628229\pi$
$138$	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	$-0.254961\pi$
$157$	17.4417	1.39200	0.696001	+	0.718041i	$0.254961\pi$
$158$	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	$-0.719697\pi$
$163$	−16.2574	−1.27338	−0.636689	+	0.771120i	$0.719697\pi$
$164$	−22.7641	−1.77757
$165$	0	0
$166$	28.4089	2.20496
$167$	−11.3906	−0.881430	−0.440715	−	0.897647i	$-0.645275\pi$
$167$	−11.3906	−0.881430	−0.440715	+	0.897647i	$0.645275\pi$
$168$	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	$-0.382928\pi$
$173$	9.45845	0.719113	0.359556	+	0.933123i	$0.382928\pi$
$174$	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	$-0.710387\pi$
$193$	−17.0562	−1.22774	−0.613868	+	0.789409i	$0.710387\pi$
$194$	22.0246	1.58127
$195$	0	0
$196$	7.97508	0.569648
$197$	−4.40523	−0.313860	−0.156930	−	0.987610i	$-0.550160\pi$
$197$	−4.40523	−0.313860	−0.156930	+	0.987610i	$0.550160\pi$
$198$	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	$-0.508224\pi$
$223$	−0.771557	−0.0516673	−0.0258336	+	0.999666i	$0.508224\pi$
$224$	24.2671	1.62141
$225$	0	0
$226$	−19.3833	−1.28936
$227$	11.4314	0.758727	0.379363	−	0.925248i	$-0.376143\pi$
$227$	11.4314	0.758727	0.379363	+	0.925248i	$0.376143\pi$
$228$	−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	$-0.764118\pi$
$233$	−22.5229	−1.47553	−0.737763	+	0.675059i	$0.764118\pi$
$234$	−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	$-0.690329\pi$
$257$	−18.0492	−1.12588	−0.562939	+	0.826498i	$0.690329\pi$
$258$	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	$-0.700511\pi$
$263$	−19.1066	−1.17817	−0.589083	+	0.808072i	$0.700511\pi$
$264$	−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	$-0.660058\pi$
$277$	−16.0413	−0.963826	−0.481913	+	0.876219i	$0.660058\pi$
$278$	−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	$-0.510692\pi$
$283$	−1.12995	−0.0671685	−0.0335843	+	0.999436i	$0.510692\pi$
$284$	−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	$-0.522134\pi$
$293$	−2.37857	−0.138958	−0.0694789	+	0.997583i	$0.522134\pi$
$294$	−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	$-0.473686\pi$
$307$	2.89366	0.165150	0.0825748	+	0.996585i	$0.473686\pi$
$308$	−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	$-0.274384\pi$
$313$	23.0318	1.30184	0.650918	+	0.759148i	$0.274384\pi$
$314$	37.6839	2.12663
$315$	0	0
$316$	4.31816	0.242916
$317$	−20.7750	−1.16684	−0.583419	−	0.812171i	$-0.698285\pi$
$317$	−20.7750	−1.16684	−0.583419	+	0.812171i	$0.698285\pi$
$318$	−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	$-0.298649\pi$
$337$	21.7064	1.18243	0.591213	+	0.806516i	$0.298649\pi$
$338$	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	$-0.514657\pi$
$347$	−1.71494	−0.0920626	−0.0460313	+	0.998940i	$0.514657\pi$
$348$	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	$-0.364161\pi$
$353$	15.5536	0.827833	0.413916	+	0.910315i	$0.364161\pi$
$354$	−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	$-0.237847\pi$
$367$	28.1068	1.46716	0.733581	+	0.679602i	$0.237847\pi$
$368$	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	$-0.580870\pi$
$373$	−9.70825	−0.502674	−0.251337	+	0.967900i	$0.580870\pi$
$374$	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	$-0.613217\pi$
$383$	−13.6299	−0.696458	−0.348229	+	0.937410i	$0.613217\pi$
$384$	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	$-0.311646\pi$
$397$	22.2281	1.11560	0.557799	+	0.829976i	$0.311646\pi$
$398$	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	$-0.504204\pi$
$433$	−0.549678	−0.0264158	−0.0132079	+	0.999913i	$0.504204\pi$
$434$	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	$-0.836905\pi$
$443$	−36.6893	−1.74316	−0.871580	+	0.490253i	$0.836905\pi$
$444$	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	$-0.691320\pi$
$457$	−24.1784	−1.13102	−0.565509	+	0.824742i	$0.691320\pi$
$458$	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	$-0.342533\pi$
$463$	20.4314	0.949530	0.474765	+	0.880113i	$0.342533\pi$
$464$	5.24181	0.243345
$465$	0	0
$466$	−48.6622	−2.25423
$467$	31.2124	1.44434	0.722169	−	0.691716i	$-0.243145\pi$
$467$	31.2124	1.44434	0.722169	+	0.691716i	$0.243145\pi$
$468$	−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	$-0.448301\pi$
$487$	7.13702	0.323409	0.161705	+	0.986839i	$0.448301\pi$
$488$	−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	$-0.771613\pi$
$503$	−33.7963	−1.50690	−0.753452	+	0.657503i	$0.771613\pi$
$504$	−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	$-0.549131\pi$
$523$	−7.03174	−0.307477	−0.153738	+	0.988112i	$0.549131\pi$
$524$	−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	$-0.108663\pi$
$547$	44.0769	1.88459	0.942296	+	0.334782i	$0.108663\pi$
$548$	−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	$-0.566962\pi$
$557$	−9.85667	−0.417641	−0.208820	+	0.977954i	$0.566962\pi$
$558$	−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	$-0.584093\pi$
$563$	−12.3917	−0.522249	−0.261125	+	0.965305i	$0.584093\pi$
$564$	−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	$-0.739234\pi$
$577$	−32.8024	−1.36558	−0.682790	+	0.730614i	$0.739234\pi$
$578$	−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	$-0.374316\pi$
$587$	18.6395	0.769334	0.384667	+	0.923055i	$0.374316\pi$
$588$	−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	$-0.489810\pi$
$593$	1.55882	0.0640129	0.0320064	+	0.999488i	$0.489810\pi$
$594$	−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	$-0.331812\pi$
$607$	24.8410	1.00827	0.504133	+	0.863626i	$0.331812\pi$
$608$	−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	$-0.525390\pi$
$613$	−3.94558	−0.159360	−0.0796802	+	0.996820i	$0.525390\pi$
$614$	6.25192	0.252307
$615$	0	0
$616$	−7.01737	−0.282738
$617$	−17.4821	−0.703801	−0.351900	−	0.936037i	$-0.614464\pi$
$617$	−17.4821	−0.703801	−0.351900	+	0.936037i	$0.614464\pi$
$618$	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	$-0.364603\pi$
$643$	20.9276	0.825303	0.412651	+	0.910889i	$0.364603\pi$
$644$	54.3254	2.14072
$645$	0	0
$646$	15.1864	0.597499
$647$	−1.84667	−0.0726002	−0.0363001	−	0.999341i	$-0.511557\pi$
$647$	−1.84667	−0.0726002	−0.0363001	+	0.999341i	$0.511557\pi$
$648$	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	$-0.617320\pi$
$653$	−18.4133	−0.720567	−0.360284	+	0.932843i	$0.617320\pi$
$654$	−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	$-0.378077\pi$
$673$	19.3911	0.747473	0.373736	+	0.927535i	$0.378077\pi$
$674$	46.8981	1.80645
$675$	0	0
$676$	38.6133	1.48513
$677$	−45.6836	−1.75576	−0.877882	−	0.478876i	$-0.841044\pi$
$677$	−45.6836	−1.75576	−0.877882	+	0.478876i	$0.841044\pi$
$678$	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	$-0.428831\pi$
$683$	11.5893	0.443451	0.221725	+	0.975109i	$0.428831\pi$
$684$	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	$-0.343667\pi$
$727$	25.4328	0.943251	0.471625	+	0.881799i	$0.343667\pi$
$728$	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	$-0.611733\pi$
$733$	−18.6190	−0.687708	−0.343854	+	0.939023i	$0.611733\pi$
$734$	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	$-0.786500\pi$
$743$	−42.7061	−1.56674	−0.783368	+	0.621558i	$0.786500\pi$
$744$	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	$-0.0884737\pi$
$757$	52.9153	1.92324	0.961620	+	0.274383i	$0.0884737\pi$
$758$	−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	$-0.617181\pi$
$773$	−20.0112	−0.719754	−0.359877	+	0.933000i	$0.617181\pi$
$774$	−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	$-0.448761\pi$
$787$	8.99272	0.320556	0.160278	+	0.987072i	$0.448761\pi$
$788$	−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	$-0.733149\pi$
$797$	−37.7564	−1.33740	−0.668700	+	0.743533i	$0.733149\pi$
$798$	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	$-0.654743\pi$
$823$	−26.8070	−0.934433	−0.467217	+	0.884143i	$0.654743\pi$
$824$	−7.12635	−0.248258
$825$	0	0
$826$	−28.0839	−0.977163
$827$	−21.3649	−0.742929	−0.371465	−	0.928447i	$-0.621144\pi$
$827$	−21.3649	−0.742929	−0.371465	+	0.928447i	$0.621144\pi$
$828$	−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	$-0.972998\pi$
$853$	−58.2023	−1.99281	−0.996404	+	0.0847260i	$0.972998\pi$
$854$	73.0245	2.49885
$855$	0	0
$856$	22.0909	0.755051
$857$	−3.22045	−0.110008	−0.0550042	−	0.998486i	$-0.517517\pi$
$857$	−3.22045	−0.110008	−0.0550042	+	0.998486i	$0.517517\pi$
$858$	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	$-0.380793\pi$
$863$	21.4924	0.731611	0.365806	+	0.930691i	$0.380793\pi$
$864$	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	$-0.416389\pi$
$877$	15.3793	0.519321	0.259661	+	0.965700i	$0.416389\pi$
$878$	−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	$-0.466102\pi$
$883$	6.31708	0.212587	0.106293	+	0.994335i	$0.466102\pi$
$884$	−18.0492	−0.607062
$885$	0	0
$886$	−79.2694	−2.66311
$887$	0.0721586	0.00242285	0.00121142	−	0.999999i	$-0.499614\pi$
$887$	0.0721586	0.00242285	0.00121142	+	0.999999i	$0.499614\pi$
$888$	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	$-0.639120\pi$
$907$	−25.4951	−0.846550	−0.423275	+	0.906001i	$0.639120\pi$
$908$	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	$-0.326573\pi$
$937$	31.7296	1.03656	0.518280	+	0.855211i	$0.326573\pi$
$938$	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	$-0.550994\pi$
$947$	−9.81789	−0.319038	−0.159519	+	0.987195i	$0.550994\pi$
$948$	−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	$-0.170320\pi$
$953$	53.1118	1.72046	0.860230	+	0.509906i	$0.170320\pi$
$954$	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	$-0.512529\pi$
$967$	−2.44732	−0.0787004	−0.0393502	+	0.999225i	$0.512529\pi$
$968$	−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	$-0.376256\pi$
$977$	23.6950	0.758070	0.379035	+	0.925382i	$0.376256\pi$
$978$	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	$-0.433783\pi$
$983$	12.9505	0.413057	0.206529	+	0.978441i	$0.433783\pi$
$984$	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	$-0.842232\pi$
$997$	−55.5513	−1.75933	−0.879663	+	0.475597i	$0.842232\pi$
$998$	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.j.1.5		6
3.2	odd	2		5625.2.a.p.1.2		6
5.2	odd	4		1875.2.b.f.1249.10		12
5.3	odd	4		1875.2.b.f.1249.3		12
5.4	even	2		1875.2.a.k.1.2		6
15.14	odd	2		5625.2.a.q.1.5		6
25.3	odd	20		375.2.i.d.49.1		24
25.4	even	10		375.2.g.c.76.3		12
25.6	even	5		75.2.g.c.61.1	yes	12
25.8	odd	20		375.2.i.d.199.6		24
25.17	odd	20		375.2.i.d.199.1		24
25.19	even	10		375.2.g.c.301.3		12
25.21	even	5		75.2.g.c.16.1	✓	12
25.22	odd	20		375.2.i.d.49.6		24
75.56	odd	10		225.2.h.d.136.3		12
75.71	odd	10		225.2.h.d.91.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.c.16.1	✓	12	25.21	even	5
75.2.g.c.61.1	yes	12	25.6	even	5
225.2.h.d.91.3		12	75.71	odd	10
225.2.h.d.136.3		12	75.56	odd	10
375.2.g.c.76.3		12	25.4	even	10
375.2.g.c.301.3		12	25.19	even	10
375.2.i.d.49.1		24	25.3	odd	20
375.2.i.d.49.6		24	25.22	odd	20
375.2.i.d.199.1		24	25.17	odd	20
375.2.i.d.199.6		24	25.8	odd	20
1875.2.a.j.1.5		6	1.1	even	1	trivial
1875.2.a.k.1.2		6	5.4	even	2
1875.2.b.f.1249.3		12	5.3	odd	4
1875.2.b.f.1249.10		12	5.2	odd	4
5625.2.a.p.1.2		6	3.2	odd	2
5625.2.a.q.1.5		6	15.14	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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