LMFDB - Embedded newform 1875.2.a.o.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:	$8$
Coefficient field:	8.8.13366265625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 12x^{6} + 10x^{5} + 41x^{4} - 20x^{3} - 48x^{2} + 8x + 16 $ x^8 - x^7 - 12x^6 + 10x^5 + 41x^4 - 20x^3 - 48x^2 + 8x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.52260$ 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)

$f(q)$	$=$	$q-1.52260 q^{2} +1.00000 q^{3} +0.318310 q^{4} -1.52260 q^{6} -0.990985 q^{7} +2.56054 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.52260 q^{2} +1.00000 q^{3} +0.318310 q^{4} -1.52260 q^{6} -0.990985 q^{7} +2.56054 q^{8} +1.00000 q^{9} +5.97349 q^{11} +0.318310 q^{12} +4.02992 q^{13} +1.50887 q^{14} -4.53530 q^{16} +0.476176 q^{17} -1.52260 q^{18} +2.82322 q^{19} -0.990985 q^{21} -9.09523 q^{22} -1.74696 q^{23} +2.56054 q^{24} -6.13596 q^{26} +1.00000 q^{27} -0.315440 q^{28} -1.41641 q^{29} +8.76141 q^{31} +1.78436 q^{32} +5.97349 q^{33} -0.725025 q^{34} +0.318310 q^{36} -8.06031 q^{37} -4.29864 q^{38} +4.02992 q^{39} -5.50296 q^{41} +1.50887 q^{42} -6.82255 q^{43} +1.90142 q^{44} +2.65993 q^{46} -9.62845 q^{47} -4.53530 q^{48} -6.01795 q^{49} +0.476176 q^{51} +1.28276 q^{52} +6.57994 q^{53} -1.52260 q^{54} -2.53746 q^{56} +2.82322 q^{57} +2.15662 q^{58} +13.0760 q^{59} +12.2013 q^{61} -13.3401 q^{62} -0.990985 q^{63} +6.35373 q^{64} -9.09523 q^{66} +11.3195 q^{67} +0.151571 q^{68} -1.74696 q^{69} -5.43047 q^{71} +2.56054 q^{72} -4.08935 q^{73} +12.2726 q^{74} +0.898661 q^{76} -5.91964 q^{77} -6.13596 q^{78} +15.0070 q^{79} +1.00000 q^{81} +8.37881 q^{82} -2.29898 q^{83} -0.315440 q^{84} +10.3880 q^{86} -1.41641 q^{87} +15.2954 q^{88} +6.26920 q^{89} -3.99359 q^{91} -0.556076 q^{92} +8.76141 q^{93} +14.6603 q^{94} +1.78436 q^{96} +13.2541 q^{97} +9.16293 q^{98} +5.97349 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 8 q^{3} + 9 q^{4} + q^{6} + 12 q^{7} + 3 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + q^2 + 8 * q^3 + 9 * q^4 + q^6 + 12 * q^7 + 3 * q^8 + 8 * q^9	$ 8 q + q^{2} + 8 q^{3} + 9 q^{4} + q^{6} + 12 q^{7} + 3 q^{8} + 8 q^{9} + 12 q^{11} + 9 q^{12} + 14 q^{13} + 16 q^{14} + 15 q^{16} - q^{17} + q^{18} + 16 q^{19} + 12 q^{21} + 18 q^{22} - 4 q^{23} + 3 q^{24} - 34 q^{26} + 8 q^{27} - 21 q^{28} + 2 q^{29} + 13 q^{31} - 18 q^{32} + 12 q^{33} - 37 q^{34} + 9 q^{36} - 8 q^{37} - 24 q^{38} + 14 q^{39} - 12 q^{41} + 16 q^{42} + 20 q^{43} + 47 q^{44} + 33 q^{46} - 15 q^{47} + 15 q^{48} + 30 q^{49} - q^{51} - q^{52} - 4 q^{53} + q^{54} + 60 q^{56} + 16 q^{57} + 2 q^{58} + 14 q^{59} + 10 q^{61} + 4 q^{62} + 12 q^{63} + 41 q^{64} + 18 q^{66} + 19 q^{67} - 33 q^{68} - 4 q^{69} + 21 q^{71} + 3 q^{72} - 19 q^{73} - 9 q^{74} - q^{76} - 11 q^{77} - 34 q^{78} + 10 q^{79} + 8 q^{81} + 24 q^{82} - 27 q^{83} - 21 q^{84} + 42 q^{86} + 2 q^{87} + 53 q^{88} - 9 q^{89} - 12 q^{91} - 63 q^{92} + 13 q^{93} + 14 q^{94} - 18 q^{96} + 24 q^{97} - 24 q^{98} + 12 q^{99}+O(q^{100}) $ 8 * q + q^2 + 8 * q^3 + 9 * q^4 + q^6 + 12 * q^7 + 3 * q^8 + 8 * q^9 + 12 * q^11 + 9 * q^12 + 14 * q^13 + 16 * q^14 + 15 * q^16 - q^17 + q^18 + 16 * q^19 + 12 * q^21 + 18 * q^22 - 4 * q^23 + 3 * q^24 - 34 * q^26 + 8 * q^27 - 21 * q^28 + 2 * q^29 + 13 * q^31 - 18 * q^32 + 12 * q^33 - 37 * q^34 + 9 * q^36 - 8 * q^37 - 24 * q^38 + 14 * q^39 - 12 * q^41 + 16 * q^42 + 20 * q^43 + 47 * q^44 + 33 * q^46 - 15 * q^47 + 15 * q^48 + 30 * q^49 - q^51 - q^52 - 4 * q^53 + q^54 + 60 * q^56 + 16 * q^57 + 2 * q^58 + 14 * q^59 + 10 * q^61 + 4 * q^62 + 12 * q^63 + 41 * q^64 + 18 * q^66 + 19 * q^67 - 33 * q^68 - 4 * q^69 + 21 * q^71 + 3 * q^72 - 19 * q^73 - 9 * q^74 - q^76 - 11 * q^77 - 34 * q^78 + 10 * q^79 + 8 * q^81 + 24 * q^82 - 27 * q^83 - 21 * q^84 + 42 * q^86 + 2 * q^87 + 53 * q^88 - 9 * q^89 - 12 * q^91 - 63 * q^92 + 13 * q^93 + 14 * q^94 - 18 * q^96 + 24 * q^97 - 24 * q^98 + 12 * 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 $

$2$	−1.52260	−1.07664	−0.538320	−	0.842740i	$-0.680941\pi$
$2$	−1.52260	−1.07664	−0.538320	+	0.842740i	$0.680941\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.318310	0.159155
$5$	0	0
$5$	0	0
$6$	−1.52260	−0.621599
$7$	−0.990985	−0.374557	−0.187279	−	0.982307i	$-0.559967\pi$
$7$	−0.990985	−0.374557	−0.187279	+	0.982307i	$0.559967\pi$
$8$	2.56054	0.905288
$9$	1.00000	0.333333
$10$	0	0
$11$	5.97349	1.80107	0.900537	−	0.434779i	$-0.143174\pi$
$11$	5.97349	1.80107	0.900537	+	0.434779i	$0.143174\pi$
$12$	0.318310	0.0918882
$13$	4.02992	1.11770	0.558850	−	0.829269i	$-0.311243\pi$
$13$	4.02992	1.11770	0.558850	+	0.829269i	$0.311243\pi$
$14$	1.50887	0.403263
$15$	0	0
$16$	−4.53530	−1.13382
$17$	0.476176	0.115490	0.0577448	−	0.998331i	$-0.481609\pi$
$17$	0.476176	0.115490	0.0577448	+	0.998331i	$0.481609\pi$
$18$	−1.52260	−0.358880
$19$	2.82322	0.647692	0.323846	−	0.946110i	$-0.395024\pi$
$19$	2.82322	0.647692	0.323846	+	0.946110i	$0.395024\pi$
$20$	0	0
$21$	−0.990985	−0.216251
$22$	−9.09523	−1.93911
$23$	−1.74696	−0.364267	−0.182134	−	0.983274i	$-0.558300\pi$
$23$	−1.74696	−0.364267	−0.182134	+	0.983274i	$0.558300\pi$
$24$	2.56054	0.522668
$25$	0	0
$26$	−6.13596	−1.20336
$27$	1.00000	0.192450
$28$	−0.315440	−0.0596127
$29$	−1.41641	−0.263020	−0.131510	−	0.991315i	$-0.541983\pi$
$29$	−1.41641	−0.263020	−0.131510	+	0.991315i	$0.541983\pi$
$30$	0	0
$31$	8.76141	1.57360	0.786798	−	0.617211i	$-0.211737\pi$
$31$	8.76141	1.57360	0.786798	+	0.617211i	$0.211737\pi$
$32$	1.78436	0.315434
$33$	5.97349	1.03985
$34$	−0.725025	−0.124341
$35$	0	0
$36$	0.318310	0.0530517
$37$	−8.06031	−1.32511	−0.662553	−	0.749015i	$-0.730527\pi$
$37$	−8.06031	−1.32511	−0.662553	+	0.749015i	$0.730527\pi$
$38$	−4.29864	−0.697332
$39$	4.02992	0.645304
$40$	0	0
$41$	−5.50296	−0.859418	−0.429709	−	0.902967i	$-0.641384\pi$
$41$	−5.50296	−0.859418	−0.429709	+	0.902967i	$0.641384\pi$
$42$	1.50887	0.232824
$43$	−6.82255	−1.04043	−0.520214	−	0.854036i	$-0.674148\pi$
$43$	−6.82255	−1.04043	−0.520214	+	0.854036i	$0.674148\pi$
$44$	1.90142	0.286650
$45$	0	0
$46$	2.65993	0.392185
$47$	−9.62845	−1.40445	−0.702227	−	0.711953i	$-0.747811\pi$
$47$	−9.62845	−1.40445	−0.702227	+	0.711953i	$0.747811\pi$
$48$	−4.53530	−0.654614
$49$	−6.01795	−0.859707
$50$	0	0
$51$	0.476176	0.0666779
$52$	1.28276	0.177887
$53$	6.57994	0.903824	0.451912	−	0.892063i	$-0.350742\pi$
$53$	6.57994	0.903824	0.451912	+	0.892063i	$0.350742\pi$
$54$	−1.52260	−0.207200
$55$	0	0
$56$	−2.53746	−0.339082
$57$	2.82322	0.373945
$58$	2.15662	0.283179
$59$	13.0760	1.70235	0.851177	−	0.524879i	$-0.175889\pi$
$59$	13.0760	1.70235	0.851177	+	0.524879i	$0.175889\pi$
$60$	0	0
$61$	12.2013	1.56222	0.781108	−	0.624397i	$-0.214655\pi$
$61$	12.2013	1.56222	0.781108	+	0.624397i	$0.214655\pi$
$62$	−13.3401	−1.69420
$63$	−0.990985	−0.124852
$64$	6.35373	0.794216
$65$	0	0
$66$	−9.09523	−1.11955
$67$	11.3195	1.38289	0.691445	−	0.722429i	$-0.256974\pi$
$67$	11.3195	1.38289	0.691445	+	0.722429i	$0.256974\pi$
$68$	0.151571	0.0183807
$69$	−1.74696	−0.210310
$70$	0	0
$71$	−5.43047	−0.644478	−0.322239	−	0.946658i	$-0.604436\pi$
$71$	−5.43047	−0.644478	−0.322239	+	0.946658i	$0.604436\pi$
$72$	2.56054	0.301763
$73$	−4.08935	−0.478622	−0.239311	−	0.970943i	$-0.576922\pi$
$73$	−4.08935	−0.478622	−0.239311	+	0.970943i	$0.576922\pi$
$74$	12.2726	1.42666
$75$	0	0
$76$	0.898661	0.103083
$77$	−5.91964	−0.674605
$78$	−6.13596	−0.694761
$79$	15.0070	1.68842	0.844212	−	0.536009i	$-0.180069\pi$
$79$	15.0070	1.68842	0.844212	+	0.536009i	$0.180069\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	8.37881	0.925284
$83$	−2.29898	−0.252346	−0.126173	−	0.992008i	$-0.540269\pi$
$83$	−2.29898	−0.252346	−0.126173	+	0.992008i	$0.540269\pi$
$84$	−0.315440	−0.0344174
$85$	0	0
$86$	10.3880	1.12017
$87$	−1.41641	−0.151855
$88$	15.2954	1.63049
$89$	6.26920	0.664533	0.332267	−	0.943185i	$-0.392187\pi$
$89$	6.26920	0.664533	0.332267	+	0.943185i	$0.392187\pi$
$90$	0	0
$91$	−3.99359	−0.418642
$92$	−0.556076	−0.0579749
$93$	8.76141	0.908516
$94$	14.6603	1.51209
$95$	0	0
$96$	1.78436	0.182116
$97$	13.2541	1.34575	0.672875	−	0.739756i	$-0.265059\pi$
$97$	13.2541	1.34575	0.672875	+	0.739756i	$0.265059\pi$
$98$	9.16293	0.925595
$99$	5.97349	0.600358
$100$	0	0
$101$	−6.41452	−0.638269	−0.319134	−	0.947709i	$-0.603392\pi$
$101$	−6.41452	−0.638269	−0.319134	+	0.947709i	$0.603392\pi$
$102$	−0.725025	−0.0717882
$103$	9.38309	0.924543	0.462272	−	0.886738i	$-0.347034\pi$
$103$	9.38309	0.924543	0.462272	+	0.886738i	$0.347034\pi$
$104$	10.3188	1.01184
$105$	0	0
$106$	−10.0186	−0.973094
$107$	−13.4108	−1.29647	−0.648234	−	0.761441i	$-0.724492\pi$
$107$	−13.4108	−1.29647	−0.648234	+	0.761441i	$0.724492\pi$
$108$	0.318310	0.0306294
$109$	2.81573	0.269698	0.134849	−	0.990866i	$-0.456945\pi$
$109$	2.81573	0.269698	0.134849	+	0.990866i	$0.456945\pi$
$110$	0	0
$111$	−8.06031	−0.765050
$112$	4.49441	0.424682
$113$	−19.4252	−1.82737	−0.913685	−	0.406423i	$-0.866776\pi$
$113$	−19.4252	−1.82737	−0.913685	+	0.406423i	$0.866776\pi$
$114$	−4.29864	−0.402605
$115$	0	0
$116$	−0.450857	−0.0418610
$117$	4.02992	0.372566
$118$	−19.9096	−1.83282
$119$	−0.471883	−0.0432574
$120$	0	0
$121$	24.6825	2.24387
$122$	−18.5777	−1.68194
$123$	−5.50296	−0.496185
$124$	2.78884	0.250446
$125$	0	0
$126$	1.50887	0.134421
$127$	6.42366	0.570008	0.285004	−	0.958526i	$-0.408005\pi$
$127$	6.42366	0.570008	0.285004	+	0.958526i	$0.408005\pi$
$128$	−13.2429	−1.17052
$129$	−6.82255	−0.600692
$130$	0	0
$131$	−7.30057	−0.637853	−0.318927	−	0.947779i	$-0.603322\pi$
$131$	−7.30057	−0.637853	−0.318927	+	0.947779i	$0.603322\pi$
$132$	1.90142	0.165497
$133$	−2.79777	−0.242598
$134$	−17.2350	−1.48888
$135$	0	0
$136$	1.21927	0.104551
$137$	−7.84860	−0.670552	−0.335276	−	0.942120i	$-0.608829\pi$
$137$	−7.84860	−0.670552	−0.335276	+	0.942120i	$0.608829\pi$
$138$	2.65993	0.226428
$139$	−17.0514	−1.44628	−0.723138	−	0.690703i	$-0.757301\pi$
$139$	−17.0514	−1.44628	−0.723138	+	0.690703i	$0.757301\pi$
$140$	0	0
$141$	−9.62845	−0.810862
$142$	8.26844	0.693872
$143$	24.0727	2.01306
$144$	−4.53530	−0.377942
$145$	0	0
$146$	6.22644	0.515304
$147$	−6.01795	−0.496352
$148$	−2.56568	−0.210897
$149$	2.84365	0.232961	0.116480	−	0.993193i	$-0.462839\pi$
$149$	2.84365	0.232961	0.116480	+	0.993193i	$0.462839\pi$
$150$	0	0
$151$	11.5744	0.941915	0.470958	−	0.882156i	$-0.343908\pi$
$151$	11.5744	0.941915	0.470958	+	0.882156i	$0.343908\pi$
$152$	7.22898	0.586348
$153$	0.476176	0.0384965
$154$	9.01324	0.726307
$155$	0	0
$156$	1.28276	0.102703
$157$	4.77270	0.380903	0.190452	−	0.981697i	$-0.439005\pi$
$157$	4.77270	0.380903	0.190452	+	0.981697i	$0.439005\pi$
$158$	−22.8497	−1.81783
$159$	6.57994	0.521823
$160$	0	0
$161$	1.73122	0.136439
$162$	−1.52260	−0.119627
$163$	2.98657	0.233926	0.116963	−	0.993136i	$-0.462684\pi$
$163$	2.98657	0.233926	0.116963	+	0.993136i	$0.462684\pi$
$164$	−1.75165	−0.136781
$165$	0	0
$166$	3.50043	0.271686
$167$	18.6105	1.44012	0.720060	−	0.693912i	$-0.244114\pi$
$167$	18.6105	1.44012	0.720060	+	0.693912i	$0.244114\pi$
$168$	−2.53746	−0.195769
$169$	3.24028	0.249252
$170$	0	0
$171$	2.82322	0.215897
$172$	−2.17169	−0.165589
$173$	16.3578	1.24366	0.621829	−	0.783153i	$-0.286390\pi$
$173$	16.3578	1.24366	0.621829	+	0.783153i	$0.286390\pi$
$174$	2.15662	0.163493
$175$	0	0
$176$	−27.0915	−2.04210
$177$	13.0760	0.982855
$178$	−9.54548	−0.715464
$179$	−15.2266	−1.13809	−0.569045	−	0.822307i	$-0.692687\pi$
$179$	−15.2266	−1.13809	−0.569045	+	0.822307i	$0.692687\pi$
$180$	0	0
$181$	−3.44321	−0.255932	−0.127966	−	0.991779i	$-0.540845\pi$
$181$	−3.44321	−0.255932	−0.127966	+	0.991779i	$0.540845\pi$
$182$	6.08064	0.450727
$183$	12.2013	0.901945
$184$	−4.47317	−0.329767
$185$	0	0
$186$	−13.3401	−0.978145
$187$	2.84443	0.208005
$188$	−3.06483	−0.223526
$189$	−0.990985	−0.0720836
$190$	0	0
$191$	15.1752	1.09804	0.549020	−	0.835809i	$-0.315001\pi$
$191$	15.1752	1.09804	0.549020	+	0.835809i	$0.315001\pi$
$192$	6.35373	0.458541
$193$	14.0304	1.00993	0.504965	−	0.863140i	$-0.331505\pi$
$193$	14.0304	1.00993	0.504965	+	0.863140i	$0.331505\pi$
$194$	−20.1807	−1.44889
$195$	0	0
$196$	−1.91557	−0.136827
$197$	23.7871	1.69476	0.847382	−	0.530984i	$-0.178177\pi$
$197$	23.7871	1.69476	0.847382	+	0.530984i	$0.178177\pi$
$198$	−9.09523	−0.646370
$199$	−15.9445	−1.13028	−0.565139	−	0.824996i	$-0.691177\pi$
$199$	−15.9445	−1.13028	−0.565139	+	0.824996i	$0.691177\pi$
$200$	0	0
$201$	11.3195	0.798412
$202$	9.76675	0.687186
$203$	1.40364	0.0985162
$204$	0.151571	0.0106121
$205$	0	0
$206$	−14.2867	−0.995401
$207$	−1.74696	−0.121422
$208$	−18.2769	−1.26728
$209$	16.8645	1.16654
$210$	0	0
$211$	−6.49016	−0.446801	−0.223401	−	0.974727i	$-0.571716\pi$
$211$	−6.49016	−0.446801	−0.223401	+	0.974727i	$0.571716\pi$
$212$	2.09446	0.143848
$213$	−5.43047	−0.372090
$214$	20.4192	1.39583
$215$	0	0
$216$	2.56054	0.174223
$217$	−8.68243	−0.589402
$218$	−4.28723	−0.290368
$219$	−4.08935	−0.276332
$220$	0	0
$221$	1.91895	0.129083
$222$	12.2726	0.823684
$223$	10.7454	0.719562	0.359781	−	0.933037i	$-0.382851\pi$
$223$	10.7454	0.719562	0.359781	+	0.933037i	$0.382851\pi$
$224$	−1.76828	−0.118148
$225$	0	0
$226$	29.5768	1.96742
$227$	−6.84922	−0.454599	−0.227299	−	0.973825i	$-0.572990\pi$
$227$	−6.84922	−0.454599	−0.227299	+	0.973825i	$0.572990\pi$
$228$	0.898661	0.0595153
$229$	2.21379	0.146291	0.0731457	−	0.997321i	$-0.476696\pi$
$229$	2.21379	0.146291	0.0731457	+	0.997321i	$0.476696\pi$
$230$	0	0
$231$	−5.91964	−0.389484
$232$	−3.62677	−0.238109
$233$	−9.39682	−0.615606	−0.307803	−	0.951450i	$-0.599594\pi$
$233$	−9.39682	−0.615606	−0.307803	+	0.951450i	$0.599594\pi$
$234$	−6.13596	−0.401120
$235$	0	0
$236$	4.16223	0.270938
$237$	15.0070	0.974812
$238$	0.718489	0.0465727
$239$	−0.737315	−0.0476930	−0.0238465	−	0.999716i	$-0.507591\pi$
$239$	−0.737315	−0.0476930	−0.0238465	+	0.999716i	$0.507591\pi$
$240$	0	0
$241$	−4.21895	−0.271767	−0.135883	−	0.990725i	$-0.543387\pi$
$241$	−4.21895	−0.271767	−0.135883	+	0.990725i	$0.543387\pi$
$242$	−37.5816	−2.41584
$243$	1.00000	0.0641500
$244$	3.88379	0.248634
$245$	0	0
$246$	8.37881	0.534213
$247$	11.3774	0.723925
$248$	22.4339	1.42456
$249$	−2.29898	−0.145692
$250$	0	0
$251$	−9.82121	−0.619909	−0.309955	−	0.950751i	$-0.600314\pi$
$251$	−9.82121	−0.619909	−0.309955	+	0.950751i	$0.600314\pi$
$252$	−0.315440	−0.0198709
$253$	−10.4355	−0.656072
$254$	−9.78067	−0.613694
$255$	0	0
$256$	7.45620	0.466012
$257$	0.0383881	0.00239458	0.00119729	−	0.999999i	$-0.499619\pi$
$257$	0.0383881	0.00239458	0.00119729	+	0.999999i	$0.499619\pi$
$258$	10.3880	0.646729
$259$	7.98764	0.496328
$260$	0	0
$261$	−1.41641	−0.0876735
$262$	11.1158	0.686739
$263$	−14.2706	−0.879965	−0.439982	−	0.898006i	$-0.645015\pi$
$263$	−14.2706	−0.879965	−0.439982	+	0.898006i	$0.645015\pi$
$264$	15.2954	0.941364
$265$	0	0
$266$	4.25989	0.261191
$267$	6.26920	0.383669
$268$	3.60309	0.220094
$269$	21.4090	1.30533	0.652666	−	0.757646i	$-0.273651\pi$
$269$	21.4090	1.30533	0.652666	+	0.757646i	$0.273651\pi$
$270$	0	0
$271$	6.22804	0.378327	0.189163	−	0.981946i	$-0.439422\pi$
$271$	6.22804	0.378327	0.189163	+	0.981946i	$0.439422\pi$
$272$	−2.15960	−0.130945
$273$	−3.99359	−0.241703
$274$	11.9503	0.721943
$275$	0	0
$276$	−0.556076	−0.0334718
$277$	−14.0431	−0.843768	−0.421884	−	0.906650i	$-0.638631\pi$
$277$	−14.0431	−0.843768	−0.421884	+	0.906650i	$0.638631\pi$
$278$	25.9624	1.55712
$279$	8.76141	0.524532
$280$	0	0
$281$	−0.516993	−0.0308412	−0.0154206	−	0.999881i	$-0.504909\pi$
$281$	−0.516993	−0.0308412	−0.0154206	+	0.999881i	$0.504909\pi$
$282$	14.6603	0.873007
$283$	0.977154	0.0580858	0.0290429	−	0.999578i	$-0.490754\pi$
$283$	0.977154	0.0580858	0.0290429	+	0.999578i	$0.490754\pi$
$284$	−1.72857	−0.102572
$285$	0	0
$286$	−36.6531	−2.16734
$287$	5.45335	0.321901
$288$	1.78436	0.105145
$289$	−16.7733	−0.986662
$290$	0	0
$291$	13.2541	0.776969
$292$	−1.30168	−0.0761751
$293$	2.75561	0.160984	0.0804922	−	0.996755i	$-0.474351\pi$
$293$	2.75561	0.160984	0.0804922	+	0.996755i	$0.474351\pi$
$294$	9.16293	0.534393
$295$	0	0
$296$	−20.6387	−1.19960
$297$	5.97349	0.346617
$298$	−4.32974	−0.250815
$299$	−7.04013	−0.407141
$300$	0	0
$301$	6.76104	0.389700
$302$	−17.6233	−1.01410
$303$	−6.41452	−0.368505
$304$	−12.8042	−0.734369
$305$	0	0
$306$	−0.725025	−0.0414469
$307$	16.1940	0.924241	0.462120	−	0.886817i	$-0.347089\pi$
$307$	16.1940	0.924241	0.462120	+	0.886817i	$0.347089\pi$
$308$	−1.88428	−0.107367
$309$	9.38309	0.533785
$310$	0	0
$311$	8.20094	0.465033	0.232516	−	0.972593i	$-0.425304\pi$
$311$	8.20094	0.465033	0.232516	+	0.972593i	$0.425304\pi$
$312$	10.3188	0.584186
$313$	20.0065	1.13083	0.565416	−	0.824806i	$-0.308716\pi$
$313$	20.0065	1.13083	0.565416	+	0.824806i	$0.308716\pi$
$314$	−7.26691	−0.410096
$315$	0	0
$316$	4.77689	0.268721
$317$	−6.52708	−0.366597	−0.183299	−	0.983057i	$-0.558678\pi$
$317$	−6.52708	−0.366597	−0.183299	+	0.983057i	$0.558678\pi$
$318$	−10.0186	−0.561816
$319$	−8.46090	−0.473719
$320$	0	0
$321$	−13.4108	−0.748516
$322$	−2.63595	−0.146896
$323$	1.34435	0.0748017
$324$	0.318310	0.0176839
$325$	0	0
$326$	−4.54735	−0.251854
$327$	2.81573	0.155710
$328$	−14.0906	−0.778021
$329$	9.54165	0.526048
$330$	0	0
$331$	33.2523	1.82771	0.913857	−	0.406037i	$-0.133090\pi$
$331$	33.2523	1.82771	0.913857	+	0.406037i	$0.133090\pi$
$332$	−0.731789	−0.0401621
$333$	−8.06031	−0.441702
$334$	−28.3363	−1.55049
$335$	0	0
$336$	4.49441	0.245190
$337$	16.9653	0.924160	0.462080	−	0.886838i	$-0.347103\pi$
$337$	16.9653	0.924160	0.462080	+	0.886838i	$0.347103\pi$
$338$	−4.93365	−0.268355
$339$	−19.4252	−1.05503
$340$	0	0
$341$	52.3362	2.83416
$342$	−4.29864	−0.232444
$343$	12.9006	0.696567
$344$	−17.4694	−0.941888
$345$	0	0
$346$	−24.9063	−1.33897
$347$	−20.1449	−1.08144	−0.540719	−	0.841203i	$-0.681848\pi$
$347$	−20.1449	−1.08144	−0.540719	+	0.841203i	$0.681848\pi$
$348$	−0.450857	−0.0241685
$349$	−29.8420	−1.59741	−0.798703	−	0.601725i	$-0.794480\pi$
$349$	−29.8420	−1.59741	−0.798703	+	0.601725i	$0.794480\pi$
$350$	0	0
$351$	4.02992	0.215101
$352$	10.6589	0.568120
$353$	0.982924	0.0523157	0.0261579	−	0.999658i	$-0.491673\pi$
$353$	0.982924	0.0523157	0.0261579	+	0.999658i	$0.491673\pi$
$354$	−19.9096	−1.05818
$355$	0	0
$356$	1.99555	0.105764
$357$	−0.471883	−0.0249747
$358$	23.1840	1.22531
$359$	−33.4999	−1.76806	−0.884030	−	0.467431i	$-0.845180\pi$
$359$	−33.4999	−1.76806	−0.884030	+	0.467431i	$0.845180\pi$
$360$	0	0
$361$	−11.0294	−0.580495
$362$	5.24263	0.275546
$363$	24.6825	1.29550
$364$	−1.27120	−0.0666290
$365$	0	0
$366$	−18.5777	−0.971071
$367$	0.352799	0.0184160	0.00920798	−	0.999958i	$-0.497069\pi$
$367$	0.352799	0.0184160	0.00920798	+	0.999958i	$0.497069\pi$
$368$	7.92300	0.413015
$369$	−5.50296	−0.286473
$370$	0	0
$371$	−6.52062	−0.338534
$372$	2.78884	0.144595
$373$	−24.2811	−1.25723	−0.628614	−	0.777718i	$-0.716377\pi$
$373$	−24.2811	−1.25723	−0.628614	+	0.777718i	$0.716377\pi$
$374$	−4.33093	−0.223947
$375$	0	0
$376$	−24.6540	−1.27144
$377$	−5.70802	−0.293978
$378$	1.50887	0.0776081
$379$	−36.4446	−1.87203	−0.936017	−	0.351956i	$-0.885517\pi$
$379$	−36.4446	−1.87203	−0.936017	+	0.351956i	$0.885517\pi$
$380$	0	0
$381$	6.42366	0.329094
$382$	−23.1058	−1.18219
$383$	6.63250	0.338905	0.169453	−	0.985538i	$-0.445800\pi$
$383$	6.63250	0.338905	0.169453	+	0.985538i	$0.445800\pi$
$384$	−13.2429	−0.675799
$385$	0	0
$386$	−21.3627	−1.08733
$387$	−6.82255	−0.346810
$388$	4.21891	0.214183
$389$	2.94097	0.149113	0.0745566	−	0.997217i	$-0.476246\pi$
$389$	2.94097	0.149113	0.0745566	+	0.997217i	$0.476246\pi$
$390$	0	0
$391$	−0.831862	−0.0420690
$392$	−15.4092	−0.778282
$393$	−7.30057	−0.368265
$394$	−36.2183	−1.82465
$395$	0	0
$396$	1.90142	0.0955500
$397$	−9.44435	−0.473998	−0.236999	−	0.971510i	$-0.576164\pi$
$397$	−9.44435	−0.473998	−0.236999	+	0.971510i	$0.576164\pi$
$398$	24.2771	1.21690
$399$	−2.79777	−0.140064
$400$	0	0
$401$	24.3968	1.21832	0.609159	−	0.793048i	$-0.291507\pi$
$401$	24.3968	1.21832	0.609159	+	0.793048i	$0.291507\pi$
$402$	−17.2350	−0.859603
$403$	35.3078	1.75881
$404$	−2.04181	−0.101584
$405$	0	0
$406$	−2.13718	−0.106067
$407$	−48.1481	−2.38661
$408$	1.21927	0.0603627
$409$	13.6073	0.672836	0.336418	−	0.941713i	$-0.390784\pi$
$409$	13.6073	0.672836	0.336418	+	0.941713i	$0.390784\pi$
$410$	0	0
$411$	−7.84860	−0.387143
$412$	2.98673	0.147146
$413$	−12.9582	−0.637629
$414$	2.65993	0.130728
$415$	0	0
$416$	7.19085	0.352560
$417$	−17.0514	−0.835008
$418$	−25.6779	−1.25595
$419$	25.0654	1.22452	0.612262	−	0.790655i	$-0.290260\pi$
$419$	25.0654	1.22452	0.612262	+	0.790655i	$0.290260\pi$
$420$	0	0
$421$	−5.56078	−0.271016	−0.135508	−	0.990776i	$-0.543267\pi$
$421$	−5.56078	−0.271016	−0.135508	+	0.990776i	$0.543267\pi$
$422$	9.88192	0.481044
$423$	−9.62845	−0.468151
$424$	16.8482	0.818221
$425$	0	0
$426$	8.26844	0.400607
$427$	−12.0913	−0.585139
$428$	−4.26878	−0.206339
$429$	24.0727	1.16224
$430$	0	0
$431$	24.2599	1.16856	0.584279	−	0.811553i	$-0.301377\pi$
$431$	24.2599	1.16856	0.584279	+	0.811553i	$0.301377\pi$
$432$	−4.53530	−0.218205
$433$	38.8459	1.86681	0.933407	−	0.358821i	$-0.116821\pi$
$433$	38.8459	1.86681	0.933407	+	0.358821i	$0.116821\pi$
$434$	13.2199	0.634574
$435$	0	0
$436$	0.896274	0.0429238
$437$	−4.93207	−0.235933
$438$	6.22644	0.297511
$439$	−9.22879	−0.440466	−0.220233	−	0.975447i	$-0.570682\pi$
$439$	−9.22879	−0.440466	−0.220233	+	0.975447i	$0.570682\pi$
$440$	0	0
$441$	−6.01795	−0.286569
$442$	−2.92179	−0.138976
$443$	−5.30591	−0.252091	−0.126046	−	0.992024i	$-0.540229\pi$
$443$	−5.30591	−0.252091	−0.126046	+	0.992024i	$0.540229\pi$
$444$	−2.56568	−0.121762
$445$	0	0
$446$	−16.3609	−0.774710
$447$	2.84365	0.134500
$448$	−6.29645	−0.297479
$449$	−22.2199	−1.04862	−0.524311	−	0.851527i	$-0.675677\pi$
$449$	−22.2199	−1.04862	−0.524311	+	0.851527i	$0.675677\pi$
$450$	0	0
$451$	−32.8719	−1.54788
$452$	−6.18324	−0.290835
$453$	11.5744	0.543815
$454$	10.4286	0.489440
$455$	0	0
$456$	7.22898	0.338528
$457$	−6.77157	−0.316761	−0.158380	−	0.987378i	$-0.550627\pi$
$457$	−6.77157	−0.316761	−0.158380	+	0.987378i	$0.550627\pi$
$458$	−3.37072	−0.157503
$459$	0.476176	0.0222260
$460$	0	0
$461$	33.9340	1.58046	0.790231	−	0.612809i	$-0.209960\pi$
$461$	33.9340	1.58046	0.790231	+	0.612809i	$0.209960\pi$
$462$	9.01324	0.419334
$463$	−28.8896	−1.34262	−0.671308	−	0.741179i	$-0.734267\pi$
$463$	−28.8896	−1.34262	−0.671308	+	0.741179i	$0.734267\pi$
$464$	6.42384	0.298219
$465$	0	0
$466$	14.3076	0.662786
$467$	−31.2100	−1.44423	−0.722113	−	0.691776i	$-0.756829\pi$
$467$	−31.2100	−1.44423	−0.722113	+	0.691776i	$0.756829\pi$
$468$	1.28276	0.0592958
$469$	−11.2174	−0.517972
$470$	0	0
$471$	4.77270	0.219914
$472$	33.4817	1.54112
$473$	−40.7544	−1.87389
$474$	−22.8497	−1.04952
$475$	0	0
$476$	−0.150205	−0.00688464
$477$	6.57994	0.301275
$478$	1.12264	0.0513482
$479$	−14.6580	−0.669741	−0.334870	−	0.942264i	$-0.608693\pi$
$479$	−14.6580	−0.669741	−0.334870	+	0.942264i	$0.608693\pi$
$480$	0	0
$481$	−32.4824	−1.48107
$482$	6.42377	0.292595
$483$	1.73122	0.0787730
$484$	7.85670	0.357123
$485$	0	0
$486$	−1.52260	−0.0690665
$487$	5.55868	0.251888	0.125944	−	0.992037i	$-0.459804\pi$
$487$	5.55868	0.251888	0.125944	+	0.992037i	$0.459804\pi$
$488$	31.2419	1.41425
$489$	2.98657	0.135057
$490$	0	0
$491$	−17.4593	−0.787925	−0.393962	−	0.919127i	$-0.628896\pi$
$491$	−17.4593	−0.787925	−0.393962	+	0.919127i	$0.628896\pi$
$492$	−1.75165	−0.0789704
$493$	−0.674459	−0.0303761
$494$	−17.3232	−0.779407
$495$	0	0
$496$	−39.7356	−1.78418
$497$	5.38152	0.241394
$498$	3.50043	0.156858
$499$	16.3254	0.730825	0.365412	−	0.930846i	$-0.380928\pi$
$499$	16.3254	0.730825	0.365412	+	0.930846i	$0.380928\pi$
$500$	0	0
$501$	18.6105	0.831454
$502$	14.9538	0.667420
$503$	−16.7612	−0.747345	−0.373672	−	0.927561i	$-0.621902\pi$
$503$	−16.7612	−0.747345	−0.373672	+	0.927561i	$0.621902\pi$
$504$	−2.53746	−0.113027
$505$	0	0
$506$	15.8890	0.706354
$507$	3.24028	0.143906
$508$	2.04472	0.0907196
$509$	8.35851	0.370485	0.185242	−	0.982693i	$-0.440693\pi$
$509$	8.35851	0.370485	0.185242	+	0.982693i	$0.440693\pi$
$510$	0	0
$511$	4.05248	0.179271
$512$	15.1330	0.668791
$513$	2.82322	0.124648
$514$	−0.0584497	−0.00257811
$515$	0	0
$516$	−2.17169	−0.0956031
$517$	−57.5154	−2.52953
$518$	−12.1620	−0.534367
$519$	16.3578	0.718026
$520$	0	0
$521$	−45.6262	−1.99892	−0.999460	−	0.0328599i	$-0.989538\pi$
$521$	−45.6262	−1.99892	−0.999460	+	0.0328599i	$0.989538\pi$
$522$	2.15662	0.0943928
$523$	−26.6701	−1.16620	−0.583102	−	0.812399i	$-0.698161\pi$
$523$	−26.6701	−1.16620	−0.583102	+	0.812399i	$0.698161\pi$
$524$	−2.32384	−0.101518
$525$	0	0
$526$	21.7285	0.947406
$527$	4.17197	0.181734
$528$	−27.0915	−1.17901
$529$	−19.9481	−0.867309
$530$	0	0
$531$	13.0760	0.567451
$532$	−0.890559	−0.0386106
$533$	−22.1765	−0.960571
$534$	−9.54548	−0.413073
$535$	0	0
$536$	28.9839	1.25191
$537$	−15.2266	−0.657076
$538$	−32.5974	−1.40537
$539$	−35.9481	−1.54840
$540$	0	0
$541$	−0.225005	−0.00967370	−0.00483685	−	0.999988i	$-0.501540\pi$
$541$	−0.225005	−0.00967370	−0.00483685	+	0.999988i	$0.501540\pi$
$542$	−9.48282	−0.407322
$543$	−3.44321	−0.147762
$544$	0.849670	0.0364293
$545$	0	0
$546$	6.08064	0.260228
$547$	8.58474	0.367057	0.183529	−	0.983014i	$-0.441248\pi$
$547$	8.58474	0.367057	0.183529	+	0.983014i	$0.441248\pi$
$548$	−2.49829	−0.106722
$549$	12.2013	0.520738
$550$	0	0
$551$	−3.99884	−0.170356
$552$	−4.47317	−0.190391
$553$	−14.8718	−0.632411
$554$	21.3820	0.908435
$555$	0	0
$556$	−5.42762	−0.230182
$557$	−20.6736	−0.875968	−0.437984	−	0.898983i	$-0.644307\pi$
$557$	−20.6736	−0.875968	−0.437984	+	0.898983i	$0.644307\pi$
$558$	−13.3401	−0.564732
$559$	−27.4943	−1.16289
$560$	0	0
$561$	2.84443	0.120092
$562$	0.787174	0.0332049
$563$	12.6162	0.531708	0.265854	−	0.964013i	$-0.414346\pi$
$563$	12.6162	0.531708	0.265854	+	0.964013i	$0.414346\pi$
$564$	−3.06483	−0.129053
$565$	0	0
$566$	−1.48781	−0.0625375
$567$	−0.990985	−0.0416175
$568$	−13.9049	−0.583439
$569$	10.9897	0.460714	0.230357	−	0.973106i	$-0.426011\pi$
$569$	10.9897	0.460714	0.230357	+	0.973106i	$0.426011\pi$
$570$	0	0
$571$	0.276517	0.0115719	0.00578593	−	0.999983i	$-0.498158\pi$
$571$	0.276517	0.0115719	0.00578593	+	0.999983i	$0.498158\pi$
$572$	7.66258	0.320389
$573$	15.1752	0.633953
$574$	−8.30327	−0.346572
$575$	0	0
$576$	6.35373	0.264739
$577$	−15.7460	−0.655515	−0.327757	−	0.944762i	$-0.606293\pi$
$577$	−15.7460	−0.655515	−0.327757	+	0.944762i	$0.606293\pi$
$578$	25.5390	1.06228
$579$	14.0304	0.583083
$580$	0	0
$581$	2.27826	0.0945180
$582$	−20.1807	−0.836517
$583$	39.3052	1.62785
$584$	−10.4709	−0.433291
$585$	0	0
$586$	−4.19569	−0.173322
$587$	−11.3751	−0.469501	−0.234751	−	0.972056i	$-0.575427\pi$
$587$	−11.3751	−0.469501	−0.234751	+	0.972056i	$0.575427\pi$
$588$	−1.91557	−0.0789969
$589$	24.7354	1.01921
$590$	0	0
$591$	23.7871	0.978473
$592$	36.5559	1.50244
$593$	−30.4617	−1.25091	−0.625457	−	0.780259i	$-0.715087\pi$
$593$	−30.4617	−1.25091	−0.625457	+	0.780259i	$0.715087\pi$
$594$	−9.09523	−0.373182
$595$	0	0
$596$	0.905161	0.0370769
$597$	−15.9445	−0.652566
$598$	10.7193	0.438345
$599$	3.09493	0.126455	0.0632277	−	0.997999i	$-0.479861\pi$
$599$	3.09493	0.126455	0.0632277	+	0.997999i	$0.479861\pi$
$600$	0	0
$601$	9.19481	0.375064	0.187532	−	0.982258i	$-0.439951\pi$
$601$	9.19481	0.375064	0.187532	+	0.982258i	$0.439951\pi$
$602$	−10.2944	−0.419567
$603$	11.3195	0.460964
$604$	3.68426	0.149911
$605$	0	0
$606$	9.76675	0.396747
$607$	37.9938	1.54212	0.771060	−	0.636762i	$-0.219727\pi$
$607$	37.9938	1.54212	0.771060	+	0.636762i	$0.219727\pi$
$608$	5.03766	0.204304
$609$	1.40364	0.0568784
$610$	0	0
$611$	−38.8019	−1.56976
$612$	0.151571	0.00612691
$613$	−24.7188	−0.998381	−0.499191	−	0.866492i	$-0.666369\pi$
$613$	−24.7188	−0.998381	−0.499191	+	0.866492i	$0.666369\pi$
$614$	−24.6570	−0.995075
$615$	0	0
$616$	−15.1575	−0.610712
$617$	29.8302	1.20092	0.600460	−	0.799655i	$-0.294984\pi$
$617$	29.8302	1.20092	0.600460	+	0.799655i	$0.294984\pi$
$618$	−14.2867	−0.574695
$619$	−20.9427	−0.841757	−0.420878	−	0.907117i	$-0.638278\pi$
$619$	−20.9427	−0.841757	−0.420878	+	0.907117i	$0.638278\pi$
$620$	0	0
$621$	−1.74696	−0.0701032
$622$	−12.4867	−0.500673
$623$	−6.21268	−0.248906
$624$	−18.2769	−0.731662
$625$	0	0
$626$	−30.4618	−1.21750
$627$	16.8645	0.673503
$628$	1.51920	0.0606226
$629$	−3.83812	−0.153036
$630$	0	0
$631$	18.1871	0.724017	0.362009	−	0.932175i	$-0.382091\pi$
$631$	18.1871	0.724017	0.362009	+	0.932175i	$0.382091\pi$
$632$	38.4261	1.52851
$633$	−6.49016	−0.257961
$634$	9.93813	0.394693
$635$	0	0
$636$	2.09446	0.0830507
$637$	−24.2519	−0.960894
$638$	12.8826	0.510025
$639$	−5.43047	−0.214826
$640$	0	0
$641$	3.94506	0.155821	0.0779103	−	0.996960i	$-0.475175\pi$
$641$	3.94506	0.155821	0.0779103	+	0.996960i	$0.475175\pi$
$642$	20.4192	0.805883
$643$	23.1026	0.911077	0.455538	−	0.890216i	$-0.349447\pi$
$643$	23.1026	0.911077	0.455538	+	0.890216i	$0.349447\pi$
$644$	0.551063	0.0217149
$645$	0	0
$646$	−2.04691	−0.0805345
$647$	−9.35622	−0.367831	−0.183916	−	0.982942i	$-0.558877\pi$
$647$	−9.35622	−0.367831	−0.183916	+	0.982942i	$0.558877\pi$
$648$	2.56054	0.100588
$649$	78.1095	3.06607
$650$	0	0
$651$	−8.68243	−0.340291
$652$	0.950655	0.0372305
$653$	2.29702	0.0898892	0.0449446	−	0.998989i	$-0.485689\pi$
$653$	2.29702	0.0898892	0.0449446	+	0.998989i	$0.485689\pi$
$654$	−4.28723	−0.167644
$655$	0	0
$656$	24.9576	0.974429
$657$	−4.08935	−0.159541
$658$	−14.5281	−0.566365
$659$	−17.5619	−0.684116	−0.342058	−	0.939679i	$-0.611124\pi$
$659$	−17.5619	−0.684116	−0.342058	+	0.939679i	$0.611124\pi$
$660$	0	0
$661$	−6.88170	−0.267667	−0.133834	−	0.991004i	$-0.542729\pi$
$661$	−6.88170	−0.267667	−0.133834	+	0.991004i	$0.542729\pi$
$662$	−50.6300	−1.96779
$663$	1.91895	0.0745259
$664$	−5.88664	−0.228446
$665$	0	0
$666$	12.2726	0.475554
$667$	2.47441	0.0958097
$668$	5.92390	0.229202
$669$	10.7454	0.415440
$670$	0	0
$671$	72.8842	2.81367
$672$	−1.76828	−0.0682128
$673$	−12.4307	−0.479168	−0.239584	−	0.970876i	$-0.577011\pi$
$673$	−12.4307	−0.479168	−0.239584	+	0.970876i	$0.577011\pi$
$674$	−25.8314	−0.994989
$675$	0	0
$676$	1.03141	0.0396697
$677$	−6.61696	−0.254310	−0.127155	−	0.991883i	$-0.540585\pi$
$677$	−6.61696	−0.254310	−0.127155	+	0.991883i	$0.540585\pi$
$678$	29.5768	1.13589
$679$	−13.1346	−0.504060
$680$	0	0
$681$	−6.84922	−0.262463
$682$	−79.6870	−3.05137
$683$	−18.6885	−0.715097	−0.357549	−	0.933895i	$-0.616387\pi$
$683$	−18.6885	−0.715097	−0.357549	+	0.933895i	$0.616387\pi$
$684$	0.898661	0.0343612
$685$	0	0
$686$	−19.6424	−0.749952
$687$	2.21379	0.0844614
$688$	30.9423	1.17966
$689$	26.5166	1.01020
$690$	0	0
$691$	−18.4352	−0.701306	−0.350653	−	0.936505i	$-0.614040\pi$
$691$	−18.4352	−0.701306	−0.350653	+	0.936505i	$0.614040\pi$
$692$	5.20684	0.197934
$693$	−5.91964	−0.224868
$694$	30.6727	1.16432
$695$	0	0
$696$	−3.62677	−0.137472
$697$	−2.62038	−0.0992538
$698$	45.4375	1.71983
$699$	−9.39682	−0.355420
$700$	0	0
$701$	14.9443	0.564437	0.282219	−	0.959350i	$-0.408930\pi$
$701$	14.9443	0.564437	0.282219	+	0.959350i	$0.408930\pi$
$702$	−6.13596	−0.231587
$703$	−22.7561	−0.858261
$704$	37.9539	1.43044
$705$	0	0
$706$	−1.49660	−0.0563253
$707$	6.35670	0.239068
$708$	4.16223	0.156426
$709$	44.4198	1.66822	0.834110	−	0.551598i	$-0.185982\pi$
$709$	44.4198	1.66822	0.834110	+	0.551598i	$0.185982\pi$
$710$	0	0
$711$	15.0070	0.562808
$712$	16.0525	0.601594
$713$	−15.3059	−0.573209
$714$	0.718489	0.0268888
$715$	0	0
$716$	−4.84678	−0.181133
$717$	−0.737315	−0.0275355
$718$	51.0070	1.90356
$719$	−38.9409	−1.45225	−0.726125	−	0.687563i	$-0.758681\pi$
$719$	−38.9409	−1.45225	−0.726125	+	0.687563i	$0.758681\pi$
$720$	0	0
$721$	−9.29850	−0.346294
$722$	16.7934	0.624984
$723$	−4.21895	−0.156905
$724$	−1.09601	−0.0407328
$725$	0	0
$726$	−37.5816	−1.39479
$727$	2.48415	0.0921320	0.0460660	−	0.998938i	$-0.485332\pi$
$727$	2.48415	0.0921320	0.0460660	+	0.998938i	$0.485332\pi$
$728$	−10.2258	−0.378992
$729$	1.00000	0.0370370
$730$	0	0
$731$	−3.24873	−0.120159
$732$	3.88379	0.143549
$733$	−31.7905	−1.17421	−0.587105	−	0.809511i	$-0.699733\pi$
$733$	−31.7905	−1.17421	−0.587105	+	0.809511i	$0.699733\pi$
$734$	−0.537172	−0.0198274
$735$	0	0
$736$	−3.11722	−0.114902
$737$	67.6166	2.49069
$738$	8.37881	0.308428
$739$	−32.4392	−1.19329	−0.596647	−	0.802504i	$-0.703501\pi$
$739$	−32.4392	−1.19329	−0.596647	+	0.802504i	$0.703501\pi$
$740$	0	0
$741$	11.3774	0.417958
$742$	9.92829	0.364479
$743$	−2.02921	−0.0744447	−0.0372223	−	0.999307i	$-0.511851\pi$
$743$	−2.02921	−0.0744447	−0.0372223	+	0.999307i	$0.511851\pi$
$744$	22.4339	0.822468
$745$	0	0
$746$	36.9704	1.35358
$747$	−2.29898	−0.0841154
$748$	0.905410	0.0331051
$749$	13.2899	0.485602
$750$	0	0
$751$	−31.8934	−1.16381	−0.581904	−	0.813257i	$-0.697692\pi$
$751$	−31.8934	−1.16381	−0.581904	+	0.813257i	$0.697692\pi$
$752$	43.6679	1.59241
$753$	−9.82121	−0.357905
$754$	8.69102	0.316508
$755$	0	0
$756$	−0.315440	−0.0114725
$757$	39.2724	1.42738	0.713689	−	0.700463i	$-0.247023\pi$
$757$	39.2724	1.42738	0.713689	+	0.700463i	$0.247023\pi$
$758$	55.4905	2.01551
$759$	−10.4355	−0.378783
$760$	0	0
$761$	14.2422	0.516278	0.258139	−	0.966108i	$-0.416891\pi$
$761$	14.2422	0.516278	0.258139	+	0.966108i	$0.416891\pi$
$762$	−9.78067	−0.354316
$763$	−2.79034	−0.101017
$764$	4.83042	0.174758
$765$	0	0
$766$	−10.0987	−0.364879
$767$	52.6954	1.90272
$768$	7.45620	0.269052
$769$	−6.86409	−0.247526	−0.123763	−	0.992312i	$-0.539496\pi$
$769$	−6.86409	−0.247526	−0.123763	+	0.992312i	$0.539496\pi$
$770$	0	0
$771$	0.0383881	0.00138251
$772$	4.46601	0.160735
$773$	−8.46681	−0.304530	−0.152265	−	0.988340i	$-0.548657\pi$
$773$	−8.46681	−0.304530	−0.152265	+	0.988340i	$0.548657\pi$
$774$	10.3880	0.373389
$775$	0	0
$776$	33.9377	1.21829
$777$	7.98764	0.286555
$778$	−4.47792	−0.160541
$779$	−15.5361	−0.556638
$780$	0	0
$781$	−32.4389	−1.16075
$782$	1.26659	0.0452932
$783$	−1.41641	−0.0506183
$784$	27.2932	0.974757
$785$	0	0
$786$	11.1158	0.396489
$787$	−14.9960	−0.534551	−0.267275	−	0.963620i	$-0.586123\pi$
$787$	−14.9960	−0.534551	−0.267275	+	0.963620i	$0.586123\pi$
$788$	7.57169	0.269730
$789$	−14.2706	−0.508048
$790$	0	0
$791$	19.2501	0.684455
$792$	15.2954	0.543497
$793$	49.1703	1.74609
$794$	14.3800	0.510326
$795$	0	0
$796$	−5.07530	−0.179889
$797$	−10.9127	−0.386549	−0.193274	−	0.981145i	$-0.561911\pi$
$797$	−10.9127	−0.386549	−0.193274	+	0.981145i	$0.561911\pi$
$798$	4.25989	0.150798
$799$	−4.58483	−0.162200
$800$	0	0
$801$	6.26920	0.221511
$802$	−37.1465	−1.31169
$803$	−24.4277	−0.862033
$804$	3.60309	0.127071
$805$	0	0
$806$	−53.7597	−1.89360
$807$	21.4090	0.753633
$808$	−16.4246	−0.577817
$809$	13.8729	0.487746	0.243873	−	0.969807i	$-0.421582\pi$
$809$	13.8729	0.487746	0.243873	+	0.969807i	$0.421582\pi$
$810$	0	0
$811$	13.1036	0.460129	0.230065	−	0.973175i	$-0.426106\pi$
$811$	13.1036	0.460129	0.230065	+	0.973175i	$0.426106\pi$
$812$	0.446793	0.0156793
$813$	6.22804	0.218427
$814$	73.3103	2.56953
$815$	0	0
$816$	−2.15960	−0.0756011
$817$	−19.2616	−0.673878
$818$	−20.7184	−0.724403
$819$	−3.99359	−0.139547
$820$	0	0
$821$	15.5589	0.543011	0.271505	−	0.962437i	$-0.412479\pi$
$821$	15.5589	0.543011	0.271505	+	0.962437i	$0.412479\pi$
$822$	11.9503	0.416814
$823$	45.2205	1.57629	0.788144	−	0.615491i	$-0.211042\pi$
$823$	45.2205	1.57629	0.788144	+	0.615491i	$0.211042\pi$
$824$	24.0258	0.836978
$825$	0	0
$826$	19.7301	0.686497
$827$	−25.6349	−0.891411	−0.445706	−	0.895180i	$-0.647047\pi$
$827$	−25.6349	−0.891411	−0.445706	+	0.895180i	$0.647047\pi$
$828$	−0.556076	−0.0193250
$829$	14.6302	0.508129	0.254064	−	0.967187i	$-0.418232\pi$
$829$	14.6302	0.508129	0.254064	+	0.967187i	$0.418232\pi$
$830$	0	0
$831$	−14.0431	−0.487150
$832$	25.6050	0.887695
$833$	−2.86560	−0.0992872
$834$	25.9624	0.899004
$835$	0	0
$836$	5.36814	0.185661
$837$	8.76141	0.302839
$838$	−38.1645	−1.31837
$839$	37.4349	1.29240	0.646199	−	0.763169i	$-0.276358\pi$
$839$	37.4349	1.29240	0.646199	+	0.763169i	$0.276358\pi$
$840$	0	0
$841$	−26.9938	−0.930820
$842$	8.46684	0.291787
$843$	−0.516993	−0.0178062
$844$	−2.06588	−0.0711106
$845$	0	0
$846$	14.6603	0.504031
$847$	−24.4600	−0.840457
$848$	−29.8420	−1.02478
$849$	0.977154	0.0335358
$850$	0	0
$851$	14.0811	0.482693
$852$	−1.72857	−0.0592200
$853$	−4.45661	−0.152591	−0.0762956	−	0.997085i	$-0.524309\pi$
$853$	−4.45661	−0.152591	−0.0762956	+	0.997085i	$0.524309\pi$
$854$	18.4102	0.629984
$855$	0	0
$856$	−34.3388	−1.17368
$857$	48.0738	1.64217	0.821084	−	0.570807i	$-0.193370\pi$
$857$	48.0738	1.64217	0.821084	+	0.570807i	$0.193370\pi$
$858$	−36.6531	−1.25132
$859$	−40.5317	−1.38292	−0.691461	−	0.722414i	$-0.743033\pi$
$859$	−40.5317	−1.38292	−0.691461	+	0.722414i	$0.743033\pi$
$860$	0	0
$861$	5.45335	0.185850
$862$	−36.9381	−1.25812
$863$	7.99001	0.271983	0.135992	−	0.990710i	$-0.456578\pi$
$863$	7.99001	0.271983	0.135992	+	0.990710i	$0.456578\pi$
$864$	1.78436	0.0607053
$865$	0	0
$866$	−59.1467	−2.00989
$867$	−16.7733	−0.569650
$868$	−2.76370	−0.0938062
$869$	89.6444	3.04098
$870$	0	0
$871$	45.6165	1.54566
$872$	7.20979	0.244154
$873$	13.2541	0.448583
$874$	7.50957	0.254015
$875$	0	0
$876$	−1.30168	−0.0439797
$877$	30.7432	1.03812	0.519062	−	0.854737i	$-0.326281\pi$
$877$	30.7432	1.03812	0.519062	+	0.854737i	$0.326281\pi$
$878$	14.0518	0.474224
$879$	2.75561	0.0929444
$880$	0	0
$881$	−35.1508	−1.18426	−0.592130	−	0.805843i	$-0.701713\pi$
$881$	−35.1508	−1.18426	−0.592130	+	0.805843i	$0.701713\pi$
$882$	9.16293	0.308532
$883$	−35.8185	−1.20539	−0.602694	−	0.797972i	$-0.705906\pi$
$883$	−35.8185	−1.20539	−0.602694	+	0.797972i	$0.705906\pi$
$884$	0.610821	0.0205441
$885$	0	0
$886$	8.07877	0.271412
$887$	−30.3154	−1.01789	−0.508946	−	0.860798i	$-0.669965\pi$
$887$	−30.3154	−1.01789	−0.508946	+	0.860798i	$0.669965\pi$
$888$	−20.6387	−0.692591
$889$	−6.36575	−0.213501
$890$	0	0
$891$	5.97349	0.200119
$892$	3.42035	0.114522
$893$	−27.1833	−0.909654
$894$	−4.32974	−0.144808
$895$	0	0
$896$	13.1235	0.438426
$897$	−7.04013	−0.235063
$898$	33.8320	1.12899
$899$	−12.4097	−0.413888
$900$	0	0
$901$	3.13321	0.104382
$902$	50.0507	1.66651
$903$	6.76104	0.224993
$904$	−49.7390	−1.65430
$905$	0	0
$906$	−17.6233	−0.585493
$907$	−6.79755	−0.225709	−0.112854	−	0.993612i	$-0.535999\pi$
$907$	−6.79755	−0.225709	−0.112854	+	0.993612i	$0.535999\pi$
$908$	−2.18018	−0.0723517
$909$	−6.41452	−0.212756
$910$	0	0
$911$	−34.3310	−1.13744	−0.568719	−	0.822532i	$-0.692561\pi$
$911$	−34.3310	−1.13744	−0.568719	+	0.822532i	$0.692561\pi$
$912$	−12.8042	−0.423988
$913$	−13.7329	−0.454494
$914$	10.3104	0.341037
$915$	0	0
$916$	0.704672	0.0232830
$917$	7.23475	0.238913
$918$	−0.725025	−0.0239294
$919$	6.72902	0.221970	0.110985	−	0.993822i	$-0.464599\pi$
$919$	6.72902	0.221970	0.110985	+	0.993822i	$0.464599\pi$
$920$	0	0
$921$	16.1940	0.533611
$922$	−51.6679	−1.70159
$923$	−21.8844	−0.720333
$924$	−1.88428	−0.0619883
$925$	0	0
$926$	43.9874	1.44551
$927$	9.38309	0.308181
$928$	−2.52739	−0.0829656
$929$	−4.70020	−0.154209	−0.0771043	−	0.997023i	$-0.524567\pi$
$929$	−4.70020	−0.154209	−0.0771043	+	0.997023i	$0.524567\pi$
$930$	0	0
$931$	−16.9900	−0.556825
$932$	−2.99110	−0.0979768
$933$	8.20094	0.268487
$934$	47.5203	1.55491
$935$	0	0
$936$	10.3188	0.337280
$937$	1.41847	0.0463395	0.0231698	−	0.999732i	$-0.492624\pi$
$937$	1.41847	0.0463395	0.0231698	+	0.999732i	$0.492624\pi$
$938$	17.0796	0.557669
$939$	20.0065	0.652886
$940$	0	0
$941$	−48.7929	−1.59060	−0.795302	−	0.606213i	$-0.792688\pi$
$941$	−48.7929	−1.59060	−0.795302	+	0.606213i	$0.792688\pi$
$942$	−7.26691	−0.236769
$943$	9.61347	0.313058
$944$	−59.3037	−1.93017
$945$	0	0
$946$	62.0526	2.01751
$947$	−38.1885	−1.24096	−0.620480	−	0.784222i	$-0.713062\pi$
$947$	−38.1885	−1.24096	−0.620480	+	0.784222i	$0.713062\pi$
$948$	4.77689	0.155146
$949$	−16.4798	−0.534955
$950$	0	0
$951$	−6.52708	−0.211655
$952$	−1.20828	−0.0391604
$953$	−8.25677	−0.267463	−0.133731	−	0.991018i	$-0.542696\pi$
$953$	−8.25677	−0.267463	−0.133731	+	0.991018i	$0.542696\pi$
$954$	−10.0186	−0.324365
$955$	0	0
$956$	−0.234695	−0.00759057
$957$	−8.46090	−0.273502
$958$	22.3183	0.721070
$959$	7.77785	0.251160
$960$	0	0
$961$	45.7623	1.47620
$962$	49.4577	1.59458
$963$	−13.4108	−0.432156
$964$	−1.34293	−0.0432530
$965$	0	0
$966$	−2.63595	−0.0848102
$967$	43.3033	1.39254	0.696270	−	0.717780i	$-0.254842\pi$
$967$	43.3033	1.39254	0.696270	+	0.717780i	$0.254842\pi$
$968$	63.2007	2.03135
$969$	1.34435	0.0431868
$970$	0	0
$971$	−35.1452	−1.12786	−0.563932	−	0.825821i	$-0.690712\pi$
$971$	−35.1452	−1.12786	−0.563932	+	0.825821i	$0.690712\pi$
$972$	0.318310	0.0102098
$973$	16.8976	0.541713
$974$	−8.46364	−0.271192
$975$	0	0
$976$	−55.3365	−1.77128
$977$	40.4411	1.29383	0.646913	−	0.762563i	$-0.276059\pi$
$977$	40.4411	1.29383	0.646913	+	0.762563i	$0.276059\pi$
$978$	−4.54735	−0.145408
$979$	37.4490	1.19687
$980$	0	0
$981$	2.81573	0.0898993
$982$	26.5835	0.848312
$983$	−58.9585	−1.88048	−0.940241	−	0.340509i	$-0.889401\pi$
$983$	−58.9585	−1.88048	−0.940241	+	0.340509i	$0.889401\pi$
$984$	−14.0906	−0.449190
$985$	0	0
$986$	1.02693	0.0327042
$987$	9.54165	0.303714
$988$	3.62153	0.115216
$989$	11.9187	0.378994
$990$	0	0
$991$	11.0145	0.349888	0.174944	−	0.984578i	$-0.444026\pi$
$991$	11.0145	0.349888	0.174944	+	0.984578i	$0.444026\pi$
$992$	15.6335	0.496365
$993$	33.2523	1.05523
$994$	−8.19390	−0.259895
$995$	0	0
$996$	−0.731789	−0.0231876
$997$	52.8873	1.67496	0.837479	−	0.546469i	$-0.184029\pi$
$997$	52.8873	1.67496	0.837479	+	0.546469i	$0.184029\pi$
$998$	−24.8570	−0.786836
$999$	−8.06031	−0.255017

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1875.2.a.o.1.2	yes	8
3.2	odd	2		5625.2.a.u.1.7		8
5.2	odd	4		1875.2.b.g.1249.4		16
5.3	odd	4		1875.2.b.g.1249.13		16
5.4	even	2		1875.2.a.n.1.7	✓	8
15.14	odd	2		5625.2.a.bc.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1875.2.a.n.1.7	✓	8	5.4	even	2
1875.2.a.o.1.2	yes	8	1.1	even	1	trivial
1875.2.b.g.1249.4		16	5.2	odd	4
1875.2.b.g.1249.13		16	5.3	odd	4
5625.2.a.u.1.7		8	3.2	odd	2
5625.2.a.bc.1.2		8	15.14	odd	2

Overview	Random
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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)

\(f(q)\)	\(=\)	\(q-1.52260 q^{2} +1.00000 q^{3} +0.318310 q^{4} -1.52260 q^{6} -0.990985 q^{7} +2.56054 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.52260 q^{2} +1.00000 q^{3} +0.318310 q^{4} -1.52260 q^{6} -0.990985 q^{7} +2.56054 q^{8} +1.00000 q^{9} +5.97349 q^{11} +0.318310 q^{12} +4.02992 q^{13} +1.50887 q^{14} -4.53530 q^{16} +0.476176 q^{17} -1.52260 q^{18} +2.82322 q^{19} -0.990985 q^{21} -9.09523 q^{22} -1.74696 q^{23} +2.56054 q^{24} -6.13596 q^{26} +1.00000 q^{27} -0.315440 q^{28} -1.41641 q^{29} +8.76141 q^{31} +1.78436 q^{32} +5.97349 q^{33} -0.725025 q^{34} +0.318310 q^{36} -8.06031 q^{37} -4.29864 q^{38} +4.02992 q^{39} -5.50296 q^{41} +1.50887 q^{42} -6.82255 q^{43} +1.90142 q^{44} +2.65993 q^{46} -9.62845 q^{47} -4.53530 q^{48} -6.01795 q^{49} +0.476176 q^{51} +1.28276 q^{52} +6.57994 q^{53} -1.52260 q^{54} -2.53746 q^{56} +2.82322 q^{57} +2.15662 q^{58} +13.0760 q^{59} +12.2013 q^{61} -13.3401 q^{62} -0.990985 q^{63} +6.35373 q^{64} -9.09523 q^{66} +11.3195 q^{67} +0.151571 q^{68} -1.74696 q^{69} -5.43047 q^{71} +2.56054 q^{72} -4.08935 q^{73} +12.2726 q^{74} +0.898661 q^{76} -5.91964 q^{77} -6.13596 q^{78} +15.0070 q^{79} +1.00000 q^{81} +8.37881 q^{82} -2.29898 q^{83} -0.315440 q^{84} +10.3880 q^{86} -1.41641 q^{87} +15.2954 q^{88} +6.26920 q^{89} -3.99359 q^{91} -0.556076 q^{92} +8.76141 q^{93} +14.6603 q^{94} +1.78436 q^{96} +13.2541 q^{97} +9.16293 q^{98} +5.97349 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 8 q^{3} + 9 q^{4} + q^{6} + 12 q^{7} + 3 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + q^2 + 8 * q^3 + 9 * q^4 + q^6 + 12 * q^7 + 3 * q^8 + 8 * q^9	\( 8 q + q^{2} + 8 q^{3} + 9 q^{4} + q^{6} + 12 q^{7} + 3 q^{8} + 8 q^{9} + 12 q^{11} + 9 q^{12} + 14 q^{13} + 16 q^{14} + 15 q^{16} - q^{17} + q^{18} + 16 q^{19} + 12 q^{21} + 18 q^{22} - 4 q^{23} + 3 q^{24} - 34 q^{26} + 8 q^{27} - 21 q^{28} + 2 q^{29} + 13 q^{31} - 18 q^{32} + 12 q^{33} - 37 q^{34} + 9 q^{36} - 8 q^{37} - 24 q^{38} + 14 q^{39} - 12 q^{41} + 16 q^{42} + 20 q^{43} + 47 q^{44} + 33 q^{46} - 15 q^{47} + 15 q^{48} + 30 q^{49} - q^{51} - q^{52} - 4 q^{53} + q^{54} + 60 q^{56} + 16 q^{57} + 2 q^{58} + 14 q^{59} + 10 q^{61} + 4 q^{62} + 12 q^{63} + 41 q^{64} + 18 q^{66} + 19 q^{67} - 33 q^{68} - 4 q^{69} + 21 q^{71} + 3 q^{72} - 19 q^{73} - 9 q^{74} - q^{76} - 11 q^{77} - 34 q^{78} + 10 q^{79} + 8 q^{81} + 24 q^{82} - 27 q^{83} - 21 q^{84} + 42 q^{86} + 2 q^{87} + 53 q^{88} - 9 q^{89} - 12 q^{91} - 63 q^{92} + 13 q^{93} + 14 q^{94} - 18 q^{96} + 24 q^{97} - 24 q^{98} + 12 q^{99}+O(q^{100}) \) 8 * q + q^2 + 8 * q^3 + 9 * q^4 + q^6 + 12 * q^7 + 3 * q^8 + 8 * q^9 + 12 * q^11 + 9 * q^12 + 14 * q^13 + 16 * q^14 + 15 * q^16 - q^17 + q^18 + 16 * q^19 + 12 * q^21 + 18 * q^22 - 4 * q^23 + 3 * q^24 - 34 * q^26 + 8 * q^27 - 21 * q^28 + 2 * q^29 + 13 * q^31 - 18 * q^32 + 12 * q^33 - 37 * q^34 + 9 * q^36 - 8 * q^37 - 24 * q^38 + 14 * q^39 - 12 * q^41 + 16 * q^42 + 20 * q^43 + 47 * q^44 + 33 * q^46 - 15 * q^47 + 15 * q^48 + 30 * q^49 - q^51 - q^52 - 4 * q^53 + q^54 + 60 * q^56 + 16 * q^57 + 2 * q^58 + 14 * q^59 + 10 * q^61 + 4 * q^62 + 12 * q^63 + 41 * q^64 + 18 * q^66 + 19 * q^67 - 33 * q^68 - 4 * q^69 + 21 * q^71 + 3 * q^72 - 19 * q^73 - 9 * q^74 - q^76 - 11 * q^77 - 34 * q^78 + 10 * q^79 + 8 * q^81 + 24 * q^82 - 27 * q^83 - 21 * q^84 + 42 * q^86 + 2 * q^87 + 53 * q^88 - 9 * q^89 - 12 * q^91 - 63 * q^92 + 13 * q^93 + 14 * q^94 - 18 * q^96 + 24 * q^97 - 24 * q^98 + 12 * q^99

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