LMFDB - Embedded newform 2175.2.a.w.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2175,2,Mod(1,2175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2175, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2175.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2175 = 3 \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2175.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:	$17.3674624396$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.246832.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 5x^{3} + 6x^{2} + 7x - 2 $ x^5 - 2x^4 - 5x^3 + 6x^2 + 7x - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 435)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$2.71457$ of defining polynomial
Character	$\chi$	$=$	2175.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.71457 q^{2} -1.00000 q^{3} +0.939748 q^{4} -1.71457 q^{6} +0.654317 q^{7} -1.81788 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.71457 q^{2} -1.00000 q^{3} +0.939748 q^{4} -1.71457 q^{6} +0.654317 q^{7} -1.81788 q^{8} +1.00000 q^{9} +0.163559 q^{11} -0.939748 q^{12} -2.65432 q^{13} +1.12187 q^{14} -4.99637 q^{16} +3.86328 q^{17} +1.71457 q^{18} -3.47954 q^{19} -0.654317 q^{21} +0.280433 q^{22} -7.69972 q^{23} +1.81788 q^{24} -4.55101 q^{26} -1.00000 q^{27} +0.614893 q^{28} +1.00000 q^{29} +5.05274 q^{31} -4.93087 q^{32} -0.163559 q^{33} +6.62385 q^{34} +0.939748 q^{36} -10.5904 q^{37} -5.96591 q^{38} +2.65432 q^{39} -6.17417 q^{41} -1.12187 q^{42} +10.5547 q^{43} +0.153704 q^{44} -13.2017 q^{46} -10.3036 q^{47} +4.99637 q^{48} -6.57187 q^{49} -3.86328 q^{51} -2.49439 q^{52} -4.04766 q^{53} -1.71457 q^{54} -1.18947 q^{56} +3.47954 q^{57} +1.71457 q^{58} -0.328734 q^{59} -5.72054 q^{61} +8.66328 q^{62} +0.654317 q^{63} +1.53842 q^{64} -0.280433 q^{66} -3.51985 q^{67} +3.63050 q^{68} +7.69972 q^{69} +11.7457 q^{71} -1.81788 q^{72} +1.12143 q^{73} -18.1580 q^{74} -3.26989 q^{76} +0.107019 q^{77} +4.55101 q^{78} -12.4074 q^{79} +1.00000 q^{81} -10.5860 q^{82} -7.89306 q^{83} -0.614893 q^{84} +18.0968 q^{86} -1.00000 q^{87} -0.297329 q^{88} +5.04702 q^{89} -1.73677 q^{91} -7.23579 q^{92} -5.05274 q^{93} -17.6663 q^{94} +4.93087 q^{96} -8.49076 q^{97} -11.2679 q^{98} +0.163559 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 3 q^{2} - 5 q^{3} + 5 q^{4} + 3 q^{6} - 8 q^{7} - 9 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q - 3 * q^2 - 5 * q^3 + 5 * q^4 + 3 * q^6 - 8 * q^7 - 9 * q^8 + 5 * q^9	$ 5 q - 3 q^{2} - 5 q^{3} + 5 q^{4} + 3 q^{6} - 8 q^{7} - 9 q^{8} + 5 q^{9} + 12 q^{11} - 5 q^{12} - 2 q^{13} + 6 q^{14} + q^{16} - 3 q^{18} - 2 q^{19} + 8 q^{21} - 14 q^{22} - 8 q^{23} + 9 q^{24} - 5 q^{27} + 6 q^{28} + 5 q^{29} + 2 q^{31} - q^{32} - 12 q^{33} + 4 q^{34} + 5 q^{36} - 16 q^{37} + 14 q^{38} + 2 q^{39} - 14 q^{41} - 6 q^{42} + 20 q^{44} - 6 q^{46} - 2 q^{47} - q^{48} - 7 q^{49} - 16 q^{52} - 26 q^{53} + 3 q^{54} - 2 q^{56} + 2 q^{57} - 3 q^{58} + 4 q^{59} - 12 q^{61} - 8 q^{63} - 9 q^{64} + 14 q^{66} - 12 q^{67} + 20 q^{68} + 8 q^{69} + 30 q^{71} - 9 q^{72} + 12 q^{73} + 2 q^{74} - 44 q^{76} - 18 q^{77} - 18 q^{79} + 5 q^{81} - 10 q^{82} - 2 q^{83} - 6 q^{84} + 30 q^{86} - 5 q^{87} - 42 q^{88} - 22 q^{89} - 12 q^{91} - 20 q^{92} - 2 q^{93} - 50 q^{94} + q^{96} - 20 q^{97} + 9 q^{98} + 12 q^{99}+O(q^{100}) $ 5 * q - 3 * q^2 - 5 * q^3 + 5 * q^4 + 3 * q^6 - 8 * q^7 - 9 * q^8 + 5 * q^9 + 12 * q^11 - 5 * q^12 - 2 * q^13 + 6 * q^14 + q^16 - 3 * q^18 - 2 * q^19 + 8 * q^21 - 14 * q^22 - 8 * q^23 + 9 * q^24 - 5 * q^27 + 6 * q^28 + 5 * q^29 + 2 * q^31 - q^32 - 12 * q^33 + 4 * q^34 + 5 * q^36 - 16 * q^37 + 14 * q^38 + 2 * q^39 - 14 * q^41 - 6 * q^42 + 20 * q^44 - 6 * q^46 - 2 * q^47 - q^48 - 7 * q^49 - 16 * q^52 - 26 * q^53 + 3 * q^54 - 2 * q^56 + 2 * q^57 - 3 * q^58 + 4 * q^59 - 12 * q^61 - 8 * q^63 - 9 * q^64 + 14 * q^66 - 12 * q^67 + 20 * q^68 + 8 * q^69 + 30 * q^71 - 9 * q^72 + 12 * q^73 + 2 * q^74 - 44 * q^76 - 18 * q^77 - 18 * q^79 + 5 * q^81 - 10 * q^82 - 2 * q^83 - 6 * q^84 + 30 * q^86 - 5 * q^87 - 42 * q^88 - 22 * q^89 - 12 * q^91 - 20 * q^92 - 2 * q^93 - 50 * q^94 + q^96 - 20 * q^97 + 9 * 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 $

$2$	1.71457	1.21238	0.606192	−	0.795319i	$-0.292696\pi$
$2$	1.71457	1.21238	0.606192	+	0.795319i	$0.292696\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.939748	0.469874
$5$	0	0
$5$	0	0
$6$	−1.71457	−0.699970
$7$	0.654317	0.247309	0.123654	−	0.992325i	$-0.460539\pi$
$7$	0.654317	0.247309	0.123654	+	0.992325i	$0.460539\pi$
$8$	−1.81788	−0.642716
$9$	1.00000	0.333333
$10$	0	0
$11$	0.163559	0.0493148	0.0246574	−	0.999696i	$-0.492151\pi$
$11$	0.163559	0.0493148	0.0246574	+	0.999696i	$0.492151\pi$
$12$	−0.939748	−0.271282
$13$	−2.65432	−0.736175	−0.368088	−	0.929791i	$-0.619987\pi$
$13$	−2.65432	−0.736175	−0.368088	+	0.929791i	$0.619987\pi$
$14$	1.12187	0.299833
$15$	0	0
$16$	−4.99637	−1.24909
$17$	3.86328	0.936982	0.468491	−	0.883468i	$-0.344798\pi$
$17$	3.86328	0.936982	0.468491	+	0.883468i	$0.344798\pi$
$18$	1.71457	0.404128
$19$	−3.47954	−0.798260	−0.399130	−	0.916894i	$-0.630688\pi$
$19$	−3.47954	−0.798260	−0.399130	+	0.916894i	$0.630688\pi$
$20$	0	0
$21$	−0.654317	−0.142784
$22$	0.280433	0.0597884
$23$	−7.69972	−1.60550	−0.802751	−	0.596314i	$-0.796631\pi$
$23$	−7.69972	−1.60550	−0.802751	+	0.596314i	$0.796631\pi$
$24$	1.81788	0.371072
$25$	0	0
$26$	−4.55101	−0.892527
$27$	−1.00000	−0.192450
$28$	0.614893	0.116204
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	0	0
$31$	5.05274	0.907499	0.453750	−	0.891129i	$-0.350086\pi$
$31$	5.05274	0.907499	0.453750	+	0.891129i	$0.350086\pi$
$32$	−4.93087	−0.871663
$33$	−0.163559	−0.0284719
$34$	6.62385	1.13598
$35$	0	0
$36$	0.939748	0.156625
$37$	−10.5904	−1.74106	−0.870528	−	0.492118i	$-0.836223\pi$
$37$	−10.5904	−1.74106	−0.870528	+	0.492118i	$0.836223\pi$
$38$	−5.96591	−0.967798
$39$	2.65432	0.425031
$40$	0	0
$41$	−6.17417	−0.964244	−0.482122	−	0.876104i	$-0.660134\pi$
$41$	−6.17417	−0.964244	−0.482122	+	0.876104i	$0.660134\pi$
$42$	−1.12187	−0.173109
$43$	10.5547	1.60958	0.804790	−	0.593559i	$-0.202278\pi$
$43$	10.5547	1.60958	0.804790	+	0.593559i	$0.202278\pi$
$44$	0.153704	0.0231717
$45$	0	0
$46$	−13.2017	−1.94648
$47$	−10.3036	−1.50294	−0.751470	−	0.659767i	$-0.770655\pi$
$47$	−10.3036	−1.50294	−0.751470	+	0.659767i	$0.770655\pi$
$48$	4.99637	0.721164
$49$	−6.57187	−0.938838
$50$	0	0
$51$	−3.86328	−0.540967
$52$	−2.49439	−0.345909
$53$	−4.04766	−0.555989	−0.277995	−	0.960583i	$-0.589670\pi$
$53$	−4.04766	−0.555989	−0.277995	+	0.960583i	$0.589670\pi$
$54$	−1.71457	−0.233323
$55$	0	0
$56$	−1.18947	−0.158949
$57$	3.47954	0.460876
$58$	1.71457	0.225134
$59$	−0.328734	−0.0427975	−0.0213988	−	0.999771i	$-0.506812\pi$
$59$	−0.328734	−0.0427975	−0.0213988	+	0.999771i	$0.506812\pi$
$60$	0	0
$61$	−5.72054	−0.732441	−0.366220	−	0.930528i	$-0.619348\pi$
$61$	−5.72054	−0.732441	−0.366220	+	0.930528i	$0.619348\pi$
$62$	8.66328	1.10024
$63$	0.654317	0.0824362
$64$	1.53842	0.192303
$65$	0	0
$66$	−0.280433	−0.0345189
$67$	−3.51985	−0.430019	−0.215009	−	0.976612i	$-0.568978\pi$
$67$	−3.51985	−0.430019	−0.215009	+	0.976612i	$0.568978\pi$
$68$	3.63050	0.440263
$69$	7.69972	0.926937
$70$	0	0
$71$	11.7457	1.39396	0.696981	−	0.717090i	$-0.254526\pi$
$71$	11.7457	1.39396	0.696981	+	0.717090i	$0.254526\pi$
$72$	−1.81788	−0.214239
$73$	1.12143	0.131253	0.0656267	−	0.997844i	$-0.479095\pi$
$73$	1.12143	0.131253	0.0656267	+	0.997844i	$0.479095\pi$
$74$	−18.1580	−2.11083
$75$	0	0
$76$	−3.26989	−0.375082
$77$	0.107019	0.0121960
$78$	4.55101	0.515300
$79$	−12.4074	−1.39594	−0.697970	−	0.716127i	$-0.745913\pi$
$79$	−12.4074	−1.39594	−0.697970	+	0.716127i	$0.745913\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−10.5860	−1.16903
$83$	−7.89306	−0.866376	−0.433188	−	0.901304i	$-0.642611\pi$
$83$	−7.89306	−0.866376	−0.433188	+	0.901304i	$0.642611\pi$
$84$	−0.614893	−0.0670903
$85$	0	0
$86$	18.0968	1.95143
$87$	−1.00000	−0.107211
$88$	−0.297329	−0.0316954
$89$	5.04702	0.534983	0.267491	−	0.963560i	$-0.413805\pi$
$89$	5.04702	0.534983	0.267491	+	0.963560i	$0.413805\pi$
$90$	0	0
$91$	−1.73677	−0.182062
$92$	−7.23579	−0.754383
$93$	−5.05274	−0.523945
$94$	−17.6663	−1.82214
$95$	0	0
$96$	4.93087	0.503255
$97$	−8.49076	−0.862106	−0.431053	−	0.902327i	$-0.641858\pi$
$97$	−8.49076	−0.862106	−0.431053	+	0.902327i	$0.641858\pi$
$98$	−11.2679	−1.13823
$99$	0.163559	0.0164383
$100$	0	0
$101$	1.81126	0.180227	0.0901136	−	0.995931i	$-0.471277\pi$
$101$	1.81126	0.180227	0.0901136	+	0.995931i	$0.471277\pi$
$102$	−6.62385	−0.655859
$103$	−5.80807	−0.572286	−0.286143	−	0.958187i	$-0.592373\pi$
$103$	−5.80807	−0.572286	−0.286143	+	0.958187i	$0.592373\pi$
$104$	4.82522	0.473152
$105$	0	0
$106$	−6.94000	−0.674072
$107$	−3.48568	−0.336973	−0.168487	−	0.985704i	$-0.553888\pi$
$107$	−3.48568	−0.336973	−0.168487	+	0.985704i	$0.553888\pi$
$108$	−0.939748	−0.0904273
$109$	8.11029	0.776825	0.388412	−	0.921486i	$-0.373024\pi$
$109$	8.11029	0.776825	0.388412	+	0.921486i	$0.373024\pi$
$110$	0	0
$111$	10.5904	1.00520
$112$	−3.26921	−0.308911
$113$	−2.06715	−0.194461	−0.0972307	−	0.995262i	$-0.530998\pi$
$113$	−2.06715	−0.194461	−0.0972307	+	0.995262i	$0.530998\pi$
$114$	5.96591	0.558758
$115$	0	0
$116$	0.939748	0.0872534
$117$	−2.65432	−0.245392
$118$	−0.563637	−0.0518870
$119$	2.52781	0.231724
$120$	0	0
$121$	−10.9732	−0.997568
$122$	−9.80827	−0.887999
$123$	6.17417	0.556706
$124$	4.74830	0.426410
$125$	0	0
$126$	1.12187	0.0999443
$127$	12.9962	1.15323	0.576613	−	0.817017i	$-0.304374\pi$
$127$	12.9962	1.15323	0.576613	+	0.817017i	$0.304374\pi$
$128$	12.4995	1.10481
$129$	−10.5547	−0.929292
$130$	0	0
$131$	8.69003	0.759251	0.379626	−	0.925140i	$-0.376053\pi$
$131$	8.69003	0.759251	0.379626	+	0.925140i	$0.376053\pi$
$132$	−0.153704	−0.0133782
$133$	−2.27672	−0.197417
$134$	−6.03504	−0.521348
$135$	0	0
$136$	−7.02295	−0.602213
$137$	−14.4550	−1.23498	−0.617489	−	0.786580i	$-0.711850\pi$
$137$	−14.4550	−1.23498	−0.617489	+	0.786580i	$0.711850\pi$
$138$	13.2017	1.12380
$139$	−1.72208	−0.146065	−0.0730324	−	0.997330i	$-0.523268\pi$
$139$	−1.72208	−0.146065	−0.0730324	+	0.997330i	$0.523268\pi$
$140$	0	0
$141$	10.3036	0.867723
$142$	20.1389	1.69002
$143$	−0.434137	−0.0363043
$144$	−4.99637	−0.416364
$145$	0	0
$146$	1.92277	0.159129
$147$	6.57187	0.542039
$148$	−9.95234	−0.818077
$149$	16.1461	1.32274	0.661369	−	0.750060i	$-0.269976\pi$
$149$	16.1461	1.32274	0.661369	+	0.750060i	$0.269976\pi$
$150$	0	0
$151$	−0.733083	−0.0596574	−0.0298287	−	0.999555i	$-0.509496\pi$
$151$	−0.733083	−0.0596574	−0.0298287	+	0.999555i	$0.509496\pi$
$152$	6.32536	0.513055
$153$	3.86328	0.312327
$154$	0.183492	0.0147862
$155$	0	0
$156$	2.49439	0.199711
$157$	−10.8270	−0.864085	−0.432043	−	0.901853i	$-0.642207\pi$
$157$	−10.8270	−0.864085	−0.432043	+	0.901853i	$0.642207\pi$
$158$	−21.2733	−1.69241
$159$	4.04766	0.321000
$160$	0	0
$161$	−5.03806	−0.397054
$162$	1.71457	0.134709
$163$	13.5528	1.06154	0.530768	−	0.847517i	$-0.321904\pi$
$163$	13.5528	1.06154	0.530768	+	0.847517i	$0.321904\pi$
$164$	−5.80216	−0.453073
$165$	0	0
$166$	−13.5332	−1.05038
$167$	−18.4671	−1.42902	−0.714512	−	0.699623i	$-0.753351\pi$
$167$	−18.4671	−1.42902	−0.714512	+	0.699623i	$0.753351\pi$
$168$	1.18947	0.0917694
$169$	−5.95460	−0.458046
$170$	0	0
$171$	−3.47954	−0.266087
$172$	9.91878	0.756300
$173$	8.92785	0.678772	0.339386	−	0.940647i	$-0.389781\pi$
$173$	8.92785	0.678772	0.339386	+	0.940647i	$0.389781\pi$
$174$	−1.71457	−0.129981
$175$	0	0
$176$	−0.817200	−0.0615987
$177$	0.328734	0.0247092
$178$	8.65346	0.648604
$179$	−1.86896	−0.139693	−0.0698465	−	0.997558i	$-0.522251\pi$
$179$	−1.86896	−0.139693	−0.0698465	+	0.997558i	$0.522251\pi$
$180$	0	0
$181$	16.8852	1.25507	0.627533	−	0.778590i	$-0.284065\pi$
$181$	16.8852	1.25507	0.627533	+	0.778590i	$0.284065\pi$
$182$	−2.97780	−0.220730
$183$	5.72054	0.422875
$184$	13.9971	1.03188
$185$	0	0
$186$	−8.66328	−0.635222
$187$	0.631872	0.0462071
$188$	−9.68282	−0.706192
$189$	−0.654317	−0.0475946
$190$	0	0
$191$	7.58677	0.548960	0.274480	−	0.961593i	$-0.411494\pi$
$191$	7.58677	0.548960	0.274480	+	0.961593i	$0.411494\pi$
$192$	−1.53842	−0.111026
$193$	−27.2794	−1.96362	−0.981808	−	0.189876i	$-0.939191\pi$
$193$	−27.2794	−1.96362	−0.981808	+	0.189876i	$0.939191\pi$
$194$	−14.5580	−1.04520
$195$	0	0
$196$	−6.17590	−0.441136
$197$	9.70626	0.691542	0.345771	−	0.938319i	$-0.387617\pi$
$197$	9.70626	0.691542	0.345771	+	0.938319i	$0.387617\pi$
$198$	0.280433	0.0199295
$199$	22.9520	1.62703	0.813513	−	0.581547i	$-0.197552\pi$
$199$	22.9520	1.62703	0.813513	+	0.581547i	$0.197552\pi$
$200$	0	0
$201$	3.51985	0.248271
$202$	3.10553	0.218504
$203$	0.654317	0.0459241
$204$	−3.63050	−0.254186
$205$	0	0
$206$	−9.95834	−0.693831
$207$	−7.69972	−0.535167
$208$	13.2619	0.919551
$209$	−0.569108	−0.0393660
$210$	0	0
$211$	18.0020	1.23931	0.619655	−	0.784874i	$-0.287273\pi$
$211$	18.0020	1.23931	0.619655	+	0.784874i	$0.287273\pi$
$212$	−3.80378	−0.261245
$213$	−11.7457	−0.804804
$214$	−5.97644	−0.408541
$215$	0	0
$216$	1.81788	0.123691
$217$	3.30610	0.224432
$218$	13.9057	0.941810
$219$	−1.12143	−0.0757792
$220$	0	0
$221$	−10.2544	−0.689783
$222$	18.1580	1.21869
$223$	19.1383	1.28160	0.640799	−	0.767708i	$-0.278603\pi$
$223$	19.1383	1.28160	0.640799	+	0.767708i	$0.278603\pi$
$224$	−3.22635	−0.215570
$225$	0	0
$226$	−3.54428	−0.235762
$227$	13.3621	0.886872	0.443436	−	0.896306i	$-0.353759\pi$
$227$	13.3621	0.886872	0.443436	+	0.896306i	$0.353759\pi$
$228$	3.26989	0.216554
$229$	7.45145	0.492405	0.246203	−	0.969218i	$-0.420817\pi$
$229$	7.45145	0.492405	0.246203	+	0.969218i	$0.420817\pi$
$230$	0	0
$231$	−0.107019	−0.00704135
$232$	−1.81788	−0.119349
$233$	−21.5080	−1.40904	−0.704518	−	0.709687i	$-0.748837\pi$
$233$	−21.5080	−1.40904	−0.704518	+	0.709687i	$0.748837\pi$
$234$	−4.55101	−0.297509
$235$	0	0
$236$	−0.308927	−0.0201094
$237$	12.4074	0.805946
$238$	4.33410	0.280938
$239$	24.1169	1.55999	0.779997	−	0.625784i	$-0.215221\pi$
$239$	24.1169	1.55999	0.779997	+	0.625784i	$0.215221\pi$
$240$	0	0
$241$	−7.22805	−0.465600	−0.232800	−	0.972525i	$-0.574789\pi$
$241$	−7.22805	−0.465600	−0.232800	+	0.972525i	$0.574789\pi$
$242$	−18.8144	−1.20944
$243$	−1.00000	−0.0641500
$244$	−5.37587	−0.344155
$245$	0	0
$246$	10.5860	0.674942
$247$	9.23579	0.587659
$248$	−9.18526	−0.583264
$249$	7.89306	0.500203
$250$	0	0
$251$	−8.74458	−0.551953	−0.275977	−	0.961164i	$-0.589001\pi$
$251$	−8.74458	−0.551953	−0.275977	+	0.961164i	$0.589001\pi$
$252$	0.614893	0.0387346
$253$	−1.25936	−0.0791750
$254$	22.2829	1.39815
$255$	0	0
$256$	18.3544	1.14715
$257$	10.1877	0.635494	0.317747	−	0.948176i	$-0.397074\pi$
$257$	10.1877	0.635494	0.317747	+	0.948176i	$0.397074\pi$
$258$	−18.0968	−1.12666
$259$	−6.92950	−0.430578
$260$	0	0
$261$	1.00000	0.0618984
$262$	14.8997	0.920504
$263$	−11.6794	−0.720184	−0.360092	−	0.932917i	$-0.617255\pi$
$263$	−11.6794	−0.720184	−0.360092	+	0.932917i	$0.617255\pi$
$264$	0.297329	0.0182994
$265$	0	0
$266$	−3.90359	−0.239345
$267$	−5.04702	−0.308872
$268$	−3.30778	−0.202055
$269$	23.0385	1.40468	0.702342	−	0.711839i	$-0.252138\pi$
$269$	23.0385	1.40468	0.702342	+	0.711839i	$0.252138\pi$
$270$	0	0
$271$	−4.45505	−0.270625	−0.135312	−	0.990803i	$-0.543204\pi$
$271$	−4.45505	−0.270625	−0.135312	+	0.990803i	$0.543204\pi$
$272$	−19.3024	−1.17038
$273$	1.73677	0.105114
$274$	−24.7842	−1.49727
$275$	0	0
$276$	7.23579	0.435543
$277$	−15.7000	−0.943321	−0.471661	−	0.881780i	$-0.656345\pi$
$277$	−15.7000	−0.943321	−0.471661	+	0.881780i	$0.656345\pi$
$278$	−2.95262	−0.177087
$279$	5.05274	0.302500
$280$	0	0
$281$	13.4721	0.803677	0.401838	−	0.915711i	$-0.368371\pi$
$281$	13.4721	0.803677	0.401838	+	0.915711i	$0.368371\pi$
$282$	17.6663	1.05201
$283$	−5.86481	−0.348627	−0.174313	−	0.984690i	$-0.555771\pi$
$283$	−5.86481	−0.348627	−0.174313	+	0.984690i	$0.555771\pi$
$284$	11.0380	0.654986
$285$	0	0
$286$	−0.744357	−0.0440148
$287$	−4.03987	−0.238466
$288$	−4.93087	−0.290554
$289$	−2.07510	−0.122065
$290$	0	0
$291$	8.49076	0.497737
$292$	1.05386	0.0616726
$293$	10.3642	0.605485	0.302742	−	0.953072i	$-0.402098\pi$
$293$	10.3642	0.605485	0.302742	+	0.953072i	$0.402098\pi$
$294$	11.2679	0.657159
$295$	0	0
$296$	19.2521	1.11901
$297$	−0.163559	−0.00949064
$298$	27.6836	1.60367
$299$	20.4375	1.18193
$300$	0	0
$301$	6.90614	0.398063
$302$	−1.25692	−0.0723277
$303$	−1.81126	−0.104054
$304$	17.3850	0.997101
$305$	0	0
$306$	6.62385	0.378660
$307$	16.0760	0.917504	0.458752	−	0.888564i	$-0.348297\pi$
$307$	16.0760	0.917504	0.458752	+	0.888564i	$0.348297\pi$
$308$	0.100571	0.00573057
$309$	5.80807	0.330410
$310$	0	0
$311$	16.9976	0.963846	0.481923	−	0.876214i	$-0.339939\pi$
$311$	16.9976	0.963846	0.481923	+	0.876214i	$0.339939\pi$
$312$	−4.82522	−0.273174
$313$	−25.2391	−1.42660	−0.713300	−	0.700858i	$-0.752800\pi$
$313$	−25.2391	−1.42660	−0.713300	+	0.700858i	$0.752800\pi$
$314$	−18.5636	−1.04760
$315$	0	0
$316$	−11.6598	−0.655916
$317$	−3.06731	−0.172277	−0.0861386	−	0.996283i	$-0.527453\pi$
$317$	−3.06731	−0.172277	−0.0861386	+	0.996283i	$0.527453\pi$
$318$	6.94000	0.389176
$319$	0.163559	0.00915753
$320$	0	0
$321$	3.48568	0.194552
$322$	−8.63810	−0.481382
$323$	−13.4424	−0.747955
$324$	0.939748	0.0522082
$325$	0	0
$326$	23.2372	1.28699
$327$	−8.11029	−0.448500
$328$	11.2239	0.619735
$329$	−6.74185	−0.371690
$330$	0	0
$331$	−19.9971	−1.09914	−0.549571	−	0.835447i	$-0.685209\pi$
$331$	−19.9971	−1.09914	−0.549571	+	0.835447i	$0.685209\pi$
$332$	−7.41749	−0.407088
$333$	−10.5904	−0.580352
$334$	−31.6631	−1.73253
$335$	0	0
$336$	3.26921	0.178350
$337$	6.45613	0.351688	0.175844	−	0.984418i	$-0.443735\pi$
$337$	6.45613	0.351688	0.175844	+	0.984418i	$0.443735\pi$
$338$	−10.2096	−0.555328
$339$	2.06715	0.112272
$340$	0	0
$341$	0.826420	0.0447531
$342$	−5.96591	−0.322599
$343$	−8.88031	−0.479491
$344$	−19.1872	−1.03450
$345$	0	0
$346$	15.3074	0.822932
$347$	14.9415	0.802099	0.401050	−	0.916056i	$-0.368645\pi$
$347$	14.9415	0.802099	0.401050	+	0.916056i	$0.368645\pi$
$348$	−0.939748	−0.0503758
$349$	−12.1055	−0.647992	−0.323996	−	0.946058i	$-0.605026\pi$
$349$	−12.1055	−0.647992	−0.323996	+	0.946058i	$0.605026\pi$
$350$	0	0
$351$	2.65432	0.141677
$352$	−0.806487	−0.0429859
$353$	18.1937	0.968355	0.484178	−	0.874970i	$-0.339119\pi$
$353$	18.1937	0.968355	0.484178	+	0.874970i	$0.339119\pi$
$354$	0.563637	0.0299570
$355$	0	0
$356$	4.74292	0.251374
$357$	−2.52781	−0.133786
$358$	−3.20447	−0.169361
$359$	−35.1010	−1.85256	−0.926279	−	0.376838i	$-0.877011\pi$
$359$	−35.1010	−1.85256	−0.926279	+	0.376838i	$0.877011\pi$
$360$	0	0
$361$	−6.89283	−0.362780
$362$	28.9508	1.52162
$363$	10.9732	0.575946
$364$	−1.63212	−0.0855464
$365$	0	0
$366$	9.80827	0.512686
$367$	−23.1943	−1.21073	−0.605367	−	0.795946i	$-0.706974\pi$
$367$	−23.1943	−1.21073	−0.605367	+	0.795946i	$0.706974\pi$
$368$	38.4706	2.00542
$369$	−6.17417	−0.321415
$370$	0	0
$371$	−2.64845	−0.137501
$372$	−4.74830	−0.246188
$373$	4.99469	0.258615	0.129308	−	0.991605i	$-0.458725\pi$
$373$	4.99469	0.258615	0.129308	+	0.991605i	$0.458725\pi$
$374$	1.08339	0.0560207
$375$	0	0
$376$	18.7307	0.965964
$377$	−2.65432	−0.136704
$378$	−1.12187	−0.0577029
$379$	−28.7738	−1.47801	−0.739006	−	0.673699i	$-0.764704\pi$
$379$	−28.7738	−1.47801	−0.739006	+	0.673699i	$0.764704\pi$
$380$	0	0
$381$	−12.9962	−0.665816
$382$	13.0080	0.665550
$383$	24.9482	1.27479	0.637396	−	0.770537i	$-0.280012\pi$
$383$	24.9482	1.27479	0.637396	+	0.770537i	$0.280012\pi$
$384$	−12.4995	−0.637861
$385$	0	0
$386$	−46.7725	−2.38066
$387$	10.5547	0.536527
$388$	−7.97917	−0.405081
$389$	31.0949	1.57657	0.788286	−	0.615308i	$-0.210969\pi$
$389$	31.0949	1.57657	0.788286	+	0.615308i	$0.210969\pi$
$390$	0	0
$391$	−29.7461	−1.50433
$392$	11.9468	0.603407
$393$	−8.69003	−0.438354
$394$	16.6421	0.838414
$395$	0	0
$396$	0.153704	0.00772391
$397$	12.1948	0.612038	0.306019	−	0.952025i	$-0.401003\pi$
$397$	12.1948	0.612038	0.306019	+	0.952025i	$0.401003\pi$
$398$	39.3528	1.97258
$399$	2.27672	0.113979
$400$	0	0
$401$	4.33039	0.216249	0.108125	−	0.994137i	$-0.465515\pi$
$401$	4.33039	0.216249	0.108125	+	0.994137i	$0.465515\pi$
$402$	6.03504	0.301000
$403$	−13.4116	−0.668078
$404$	1.70213	0.0846841
$405$	0	0
$406$	1.12187	0.0556776
$407$	−1.73216	−0.0858599
$408$	7.02295	0.347688
$409$	5.12178	0.253256	0.126628	−	0.991950i	$-0.459585\pi$
$409$	5.12178	0.253256	0.126628	+	0.991950i	$0.459585\pi$
$410$	0	0
$411$	14.4550	0.713015
$412$	−5.45812	−0.268902
$413$	−0.215096	−0.0105842
$414$	−13.2017	−0.648828
$415$	0	0
$416$	13.0881	0.641697
$417$	1.72208	0.0843306
$418$	−0.975776	−0.0477267
$419$	14.1945	0.693445	0.346723	−	0.937968i	$-0.387295\pi$
$419$	14.1945	0.693445	0.346723	+	0.937968i	$0.387295\pi$
$420$	0	0
$421$	4.83364	0.235577	0.117789	−	0.993039i	$-0.462419\pi$
$421$	4.83364	0.235577	0.117789	+	0.993039i	$0.462419\pi$
$422$	30.8657	1.50252
$423$	−10.3036	−0.500980
$424$	7.35815	0.357343
$425$	0	0
$426$	−20.1389	−0.975731
$427$	−3.74305	−0.181139
$428$	−3.27566	−0.158335
$429$	0.434137	0.0209603
$430$	0	0
$431$	−18.0910	−0.871411	−0.435706	−	0.900089i	$-0.643501\pi$
$431$	−18.0910	−0.871411	−0.435706	+	0.900089i	$0.643501\pi$
$432$	4.99637	0.240388
$433$	1.71005	0.0821798	0.0410899	−	0.999155i	$-0.486917\pi$
$433$	1.71005	0.0821798	0.0410899	+	0.999155i	$0.486917\pi$
$434$	5.66853	0.272098
$435$	0	0
$436$	7.62163	0.365010
$437$	26.7914	1.28161
$438$	−1.92277	−0.0918734
$439$	24.3533	1.16232	0.581160	−	0.813789i	$-0.302599\pi$
$439$	24.3533	1.16232	0.581160	+	0.813789i	$0.302599\pi$
$440$	0	0
$441$	−6.57187	−0.312946
$442$	−17.5818	−0.836281
$443$	−18.9066	−0.898280	−0.449140	−	0.893461i	$-0.648270\pi$
$443$	−18.9066	−0.898280	−0.449140	+	0.893461i	$0.648270\pi$
$444$	9.95234	0.472317
$445$	0	0
$446$	32.8140	1.55379
$447$	−16.1461	−0.763684
$448$	1.00661	0.0475581
$449$	25.2808	1.19307	0.596537	−	0.802586i	$-0.296543\pi$
$449$	25.2808	1.19307	0.596537	+	0.802586i	$0.296543\pi$
$450$	0	0
$451$	−1.00984	−0.0475515
$452$	−1.94260	−0.0913723
$453$	0.733083	0.0344432
$454$	22.9102	1.07523
$455$	0	0
$456$	−6.32536	−0.296212
$457$	−4.25835	−0.199197	−0.0995986	−	0.995028i	$-0.531756\pi$
$457$	−4.25835	−0.199197	−0.0995986	+	0.995028i	$0.531756\pi$
$458$	12.7760	0.596984
$459$	−3.86328	−0.180322
$460$	0	0
$461$	2.48353	0.115670	0.0578349	−	0.998326i	$-0.481580\pi$
$461$	2.48353	0.115670	0.0578349	+	0.998326i	$0.481580\pi$
$462$	−0.183492	−0.00853682
$463$	−27.4876	−1.27746	−0.638728	−	0.769433i	$-0.720539\pi$
$463$	−27.4876	−1.27746	−0.638728	+	0.769433i	$0.720539\pi$
$464$	−4.99637	−0.231951
$465$	0	0
$466$	−36.8769	−1.70829
$467$	6.24698	0.289076	0.144538	−	0.989499i	$-0.453830\pi$
$467$	6.24698	0.289076	0.144538	+	0.989499i	$0.453830\pi$
$468$	−2.49439	−0.115303
$469$	−2.30310	−0.106347
$470$	0	0
$471$	10.8270	0.498880
$472$	0.597598	0.0275067
$473$	1.72632	0.0793761
$474$	21.2733	0.977116
$475$	0	0
$476$	2.37550	0.108881
$477$	−4.04766	−0.185330
$478$	41.3501	1.89131
$479$	−11.5736	−0.528812	−0.264406	−	0.964412i	$-0.585176\pi$
$479$	−11.5736	−0.528812	−0.264406	+	0.964412i	$0.585176\pi$
$480$	0	0
$481$	28.1104	1.28172
$482$	−12.3930	−0.564485
$483$	5.03806	0.229240
$484$	−10.3121	−0.468731
$485$	0	0
$486$	−1.71457	−0.0777744
$487$	31.1947	1.41357	0.706783	−	0.707431i	$-0.250146\pi$
$487$	31.1947	1.41357	0.706783	+	0.707431i	$0.250146\pi$
$488$	10.3992	0.470751
$489$	−13.5528	−0.612878
$490$	0	0
$491$	−7.93512	−0.358107	−0.179053	−	0.983839i	$-0.557303\pi$
$491$	−7.93512	−0.358107	−0.179053	+	0.983839i	$0.557303\pi$
$492$	5.80216	0.261582
$493$	3.86328	0.173993
$494$	15.8354	0.712469
$495$	0	0
$496$	−25.2454	−1.13355
$497$	7.68543	0.344739
$498$	13.5332	0.606437
$499$	−32.8984	−1.47274	−0.736368	−	0.676581i	$-0.763461\pi$
$499$	−32.8984	−1.47274	−0.736368	+	0.676581i	$0.763461\pi$
$500$	0	0
$501$	18.4671	0.825047
$502$	−14.9932	−0.669179
$503$	40.7038	1.81489	0.907446	−	0.420168i	$-0.138029\pi$
$503$	40.7038	1.81489	0.907446	+	0.420168i	$0.138029\pi$
$504$	−1.18947	−0.0529831
$505$	0	0
$506$	−2.15925	−0.0959905
$507$	5.95460	0.264453
$508$	12.2132	0.541871
$509$	−36.9407	−1.63737	−0.818684	−	0.574245i	$-0.805296\pi$
$509$	−36.9407	−1.63737	−0.818684	+	0.574245i	$0.805296\pi$
$510$	0	0
$511$	0.733771	0.0324601
$512$	6.47089	0.285976
$513$	3.47954	0.153625
$514$	17.4676	0.770462
$515$	0	0
$516$	−9.91878	−0.436650
$517$	−1.68525	−0.0741172
$518$	−11.8811	−0.522026
$519$	−8.92785	−0.391889
$520$	0	0
$521$	−33.2555	−1.45695	−0.728476	−	0.685072i	$-0.759771\pi$
$521$	−33.2555	−1.45695	−0.728476	+	0.685072i	$0.759771\pi$
$522$	1.71457	0.0750447
$523$	0.341001	0.0149109	0.00745547	−	0.999972i	$-0.497627\pi$
$523$	0.341001	0.0149109	0.00745547	+	0.999972i	$0.497627\pi$
$524$	8.16644	0.356752
$525$	0	0
$526$	−20.0252	−0.873139
$527$	19.5201	0.850310
$528$	0.817200	0.0355640
$529$	36.2856	1.57764
$530$	0	0
$531$	−0.328734	−0.0142658
$532$	−2.13954	−0.0927609
$533$	16.3882	0.709852
$534$	−8.65346	−0.374472
$535$	0	0
$536$	6.39866	0.276380
$537$	1.86896	0.0806518
$538$	39.5012	1.70302
$539$	−1.07489	−0.0462986
$540$	0	0
$541$	−18.4196	−0.791919	−0.395960	−	0.918268i	$-0.629588\pi$
$541$	−18.4196	−0.791919	−0.395960	+	0.918268i	$0.629588\pi$
$542$	−7.63849	−0.328101
$543$	−16.8852	−0.724613
$544$	−19.0493	−0.816732
$545$	0	0
$546$	2.97780	0.127438
$547$	−42.5936	−1.82117	−0.910586	−	0.413320i	$-0.864369\pi$
$547$	−42.5936	−1.82117	−0.910586	+	0.413320i	$0.864369\pi$
$548$	−13.5841	−0.580284
$549$	−5.72054	−0.244147
$550$	0	0
$551$	−3.47954	−0.148233
$552$	−13.9971	−0.595757
$553$	−8.11836	−0.345228
$554$	−26.9187	−1.14367
$555$	0	0
$556$	−1.61832	−0.0686321
$557$	−17.5805	−0.744908	−0.372454	−	0.928051i	$-0.621484\pi$
$557$	−17.5805	−0.744908	−0.372454	+	0.928051i	$0.621484\pi$
$558$	8.66328	0.366746
$559$	−28.0156	−1.18493
$560$	0	0
$561$	−0.631872	−0.0266777
$562$	23.0988	0.974365
$563$	−6.29621	−0.265354	−0.132677	−	0.991159i	$-0.542357\pi$
$563$	−6.29621	−0.265354	−0.132677	+	0.991159i	$0.542357\pi$
$564$	9.68282	0.407720
$565$	0	0
$566$	−10.0556	−0.422669
$567$	0.654317	0.0274787
$568$	−21.3523	−0.895921
$569$	−42.3981	−1.77742	−0.888710	−	0.458469i	$-0.848398\pi$
$569$	−42.3981	−1.77742	−0.888710	+	0.458469i	$0.848398\pi$
$570$	0	0
$571$	−18.4882	−0.773708	−0.386854	−	0.922141i	$-0.626438\pi$
$571$	−18.4882	−0.773708	−0.386854	+	0.922141i	$0.626438\pi$
$572$	−0.407979	−0.0170585
$573$	−7.58677	−0.316942
$574$	−6.92663	−0.289112
$575$	0	0
$576$	1.53842	0.0641009
$577$	22.0727	0.918897	0.459448	−	0.888204i	$-0.348047\pi$
$577$	22.0727	0.918897	0.459448	+	0.888204i	$0.348047\pi$
$578$	−3.55791	−0.147990
$579$	27.2794	1.13369
$580$	0	0
$581$	−5.16457	−0.214262
$582$	14.5580	0.603448
$583$	−0.662030	−0.0274185
$584$	−2.03862	−0.0843587
$585$	0	0
$586$	17.7702	0.734080
$587$	44.1932	1.82405	0.912024	−	0.410136i	$-0.134519\pi$
$587$	44.1932	1.82405	0.912024	+	0.410136i	$0.134519\pi$
$588$	6.17590	0.254690
$589$	−17.5812	−0.724421
$590$	0	0
$591$	−9.70626	−0.399262
$592$	52.9137	2.17474
$593$	−17.4159	−0.715184	−0.357592	−	0.933878i	$-0.616402\pi$
$593$	−17.4159	−0.715184	−0.357592	+	0.933878i	$0.616402\pi$
$594$	−0.280433	−0.0115063
$595$	0	0
$596$	15.1732	0.621520
$597$	−22.9520	−0.939364
$598$	35.0415	1.43295
$599$	7.70544	0.314836	0.157418	−	0.987532i	$-0.449683\pi$
$599$	7.70544	0.314836	0.157418	+	0.987532i	$0.449683\pi$
$600$	0	0
$601$	−31.5500	−1.28695	−0.643476	−	0.765466i	$-0.722508\pi$
$601$	−31.5500	−1.28695	−0.643476	+	0.765466i	$0.722508\pi$
$602$	11.8410	0.482605
$603$	−3.51985	−0.143340
$604$	−0.688913	−0.0280315
$605$	0	0
$606$	−3.10553	−0.126154
$607$	13.2516	0.537864	0.268932	−	0.963159i	$-0.413329\pi$
$607$	13.2516	0.537864	0.268932	+	0.963159i	$0.413329\pi$
$608$	17.1571	0.695814
$609$	−0.654317	−0.0265143
$610$	0	0
$611$	27.3491	1.10643
$612$	3.63050	0.146754
$613$	−29.4609	−1.18991	−0.594957	−	0.803758i	$-0.702831\pi$
$613$	−29.4609	−1.18991	−0.594957	+	0.803758i	$0.702831\pi$
$614$	27.5634	1.11237
$615$	0	0
$616$	−0.194548	−0.00783855
$617$	5.61068	0.225877	0.112939	−	0.993602i	$-0.463974\pi$
$617$	5.61068	0.225877	0.112939	+	0.993602i	$0.463974\pi$
$618$	9.95834	0.400583
$619$	40.5248	1.62883	0.814415	−	0.580282i	$-0.197058\pi$
$619$	40.5248	1.62883	0.814415	+	0.580282i	$0.197058\pi$
$620$	0	0
$621$	7.69972	0.308979
$622$	29.1436	1.16855
$623$	3.30235	0.132306
$624$	−13.2619	−0.530903
$625$	0	0
$626$	−43.2743	−1.72959
$627$	0.569108	0.0227280
$628$	−10.1746	−0.406011
$629$	−40.9138	−1.63134
$630$	0	0
$631$	−20.2197	−0.804935	−0.402467	−	0.915434i	$-0.631847\pi$
$631$	−20.2197	−0.804935	−0.402467	+	0.915434i	$0.631847\pi$
$632$	22.5551	0.897193
$633$	−18.0020	−0.715516
$634$	−5.25911	−0.208866
$635$	0	0
$636$	3.80378	0.150830
$637$	17.4438	0.691149
$638$	0.280433	0.0111024
$639$	11.7457	0.464654
$640$	0	0
$641$	−44.0804	−1.74107	−0.870535	−	0.492107i	$-0.836227\pi$
$641$	−44.0804	−1.74107	−0.870535	+	0.492107i	$0.836227\pi$
$642$	5.97644	0.235871
$643$	−3.56303	−0.140512	−0.0702561	−	0.997529i	$-0.522382\pi$
$643$	−3.56303	−0.140512	−0.0702561	+	0.997529i	$0.522382\pi$
$644$	−4.73450	−0.186566
$645$	0	0
$646$	−23.0479	−0.906809
$647$	40.7523	1.60214	0.801069	−	0.598573i	$-0.204265\pi$
$647$	40.7523	1.60214	0.801069	+	0.598573i	$0.204265\pi$
$648$	−1.81788	−0.0714129
$649$	−0.0537673	−0.00211055
$650$	0	0
$651$	−3.30610	−0.129576
$652$	12.7362	0.498788
$653$	11.6902	0.457472	0.228736	−	0.973489i	$-0.426541\pi$
$653$	11.6902	0.457472	0.228736	+	0.973489i	$0.426541\pi$
$654$	−13.9057	−0.543754
$655$	0	0
$656$	30.8484	1.20443
$657$	1.12143	0.0437511
$658$	−11.5594	−0.450631
$659$	−28.1795	−1.09772	−0.548858	−	0.835915i	$-0.684937\pi$
$659$	−28.1795	−1.09772	−0.548858	+	0.835915i	$0.684937\pi$
$660$	0	0
$661$	−20.6736	−0.804108	−0.402054	−	0.915616i	$-0.631704\pi$
$661$	−20.6736	−0.804108	−0.402054	+	0.915616i	$0.631704\pi$
$662$	−34.2865	−1.33258
$663$	10.2544	0.398246
$664$	14.3486	0.556834
$665$	0	0
$666$	−18.1580	−0.703610
$667$	−7.69972	−0.298134
$668$	−17.3544	−0.671461
$669$	−19.1383	−0.739931
$670$	0	0
$671$	−0.935645	−0.0361202
$672$	3.22635	0.124459
$673$	−44.7915	−1.72659	−0.863293	−	0.504703i	$-0.831602\pi$
$673$	−44.7915	−1.72659	−0.863293	+	0.504703i	$0.831602\pi$
$674$	11.0695	0.426380
$675$	0	0
$676$	−5.59582	−0.215224
$677$	−16.8746	−0.648542	−0.324271	−	0.945964i	$-0.605119\pi$
$677$	−16.8746	−0.648542	−0.324271	+	0.945964i	$0.605119\pi$
$678$	3.54428	0.136117
$679$	−5.55565	−0.213206
$680$	0	0
$681$	−13.3621	−0.512036
$682$	1.41695	0.0542580
$683$	28.6207	1.09514	0.547571	−	0.836759i	$-0.315553\pi$
$683$	28.6207	1.09514	0.547571	+	0.836759i	$0.315553\pi$
$684$	−3.26989	−0.125027
$685$	0	0
$686$	−15.2259	−0.581328
$687$	−7.45145	−0.284290
$688$	−52.7353	−2.01051
$689$	10.7438	0.409305
$690$	0	0
$691$	−28.5928	−1.08772	−0.543861	−	0.839175i	$-0.683038\pi$
$691$	−28.5928	−1.08772	−0.543861	+	0.839175i	$0.683038\pi$
$692$	8.38993	0.318937
$693$	0.107019	0.00406532
$694$	25.6182	0.972452
$695$	0	0
$696$	1.81788	0.0689064
$697$	−23.8525	−0.903479
$698$	−20.7557	−0.785615
$699$	21.5080	0.813507
$700$	0	0
$701$	49.6636	1.87577	0.937885	−	0.346946i	$-0.112781\pi$
$701$	49.6636	1.87577	0.937885	+	0.346946i	$0.112781\pi$
$702$	4.55101	0.171767
$703$	36.8498	1.38982
$704$	0.251622	0.00948336
$705$	0	0
$706$	31.1944	1.17402
$707$	1.18514	0.0445717
$708$	0.308927	0.0116102
$709$	−19.4755	−0.731419	−0.365710	−	0.930729i	$-0.619174\pi$
$709$	−19.4755	−0.731419	−0.365710	+	0.930729i	$0.619174\pi$
$710$	0	0
$711$	−12.4074	−0.465313
$712$	−9.17485	−0.343842
$713$	−38.9047	−1.45699
$714$	−4.33410	−0.162200
$715$	0	0
$716$	−1.75636	−0.0656381
$717$	−24.1169	−0.900663
$718$	−60.1830	−2.24601
$719$	−34.3195	−1.27990	−0.639951	−	0.768415i	$-0.721046\pi$
$719$	−34.3195	−1.27990	−0.639951	+	0.768415i	$0.721046\pi$
$720$	0	0
$721$	−3.80032	−0.141531
$722$	−11.8182	−0.439829
$723$	7.22805	0.268814
$724$	15.8678	0.589723
$725$	0	0
$726$	18.8144	0.698268
$727$	−19.3206	−0.716560	−0.358280	−	0.933614i	$-0.616637\pi$
$727$	−19.3206	−0.716560	−0.358280	+	0.933614i	$0.616637\pi$
$728$	3.15722	0.117014
$729$	1.00000	0.0370370
$730$	0	0
$731$	40.7758	1.50815
$732$	5.37587	0.198698
$733$	−3.10588	−0.114718	−0.0573591	−	0.998354i	$-0.518268\pi$
$733$	−3.10588	−0.114718	−0.0573591	+	0.998354i	$0.518268\pi$
$734$	−39.7683	−1.46787
$735$	0	0
$736$	37.9663	1.39946
$737$	−0.575703	−0.0212063
$738$	−10.5860	−0.389678
$739$	38.7106	1.42399	0.711997	−	0.702183i	$-0.247791\pi$
$739$	38.7106	1.42399	0.711997	+	0.702183i	$0.247791\pi$
$740$	0	0
$741$	−9.23579	−0.339285
$742$	−4.54096	−0.166704
$743$	8.41130	0.308581	0.154290	−	0.988026i	$-0.450691\pi$
$743$	8.41130	0.308581	0.154290	+	0.988026i	$0.450691\pi$
$744$	9.18526	0.336748
$745$	0	0
$746$	8.56373	0.313541
$747$	−7.89306	−0.288792
$748$	0.593801	0.0217115
$749$	−2.28074	−0.0833364
$750$	0	0
$751$	−30.5930	−1.11635	−0.558177	−	0.829722i	$-0.688499\pi$
$751$	−30.5930	−1.11635	−0.558177	+	0.829722i	$0.688499\pi$
$752$	51.4808	1.87731
$753$	8.74458	0.318670
$754$	−4.55101	−0.165738
$755$	0	0
$756$	−0.614893	−0.0223634
$757$	41.6526	1.51389	0.756945	−	0.653479i	$-0.226691\pi$
$757$	41.6526	1.51389	0.756945	+	0.653479i	$0.226691\pi$
$758$	−49.3347	−1.79192
$759$	1.25936	0.0457117
$760$	0	0
$761$	−28.3957	−1.02934	−0.514671	−	0.857388i	$-0.672086\pi$
$761$	−28.3957	−1.02934	−0.514671	+	0.857388i	$0.672086\pi$
$762$	−22.2829	−0.807224
$763$	5.30670	0.192115
$764$	7.12965	0.257942
$765$	0	0
$766$	42.7753	1.54554
$767$	0.872565	0.0315065
$768$	−18.3544	−0.662306
$769$	−48.6782	−1.75538	−0.877690	−	0.479229i	$-0.840916\pi$
$769$	−48.6782	−1.75538	−0.877690	+	0.479229i	$0.840916\pi$
$770$	0	0
$771$	−10.1877	−0.366902
$772$	−25.6358	−0.922652
$773$	54.9974	1.97812	0.989060	−	0.147513i	$-0.0471267\pi$
$773$	54.9974	1.97812	0.989060	+	0.147513i	$0.0471267\pi$
$774$	18.0968	0.650476
$775$	0	0
$776$	15.4351	0.554089
$777$	6.92950	0.248595
$778$	53.3143	1.91141
$779$	21.4833	0.769717
$780$	0	0
$781$	1.92112	0.0687429
$782$	−51.0018	−1.82382
$783$	−1.00000	−0.0357371
$784$	32.8355	1.17270
$785$	0	0
$786$	−14.8997	−0.531453
$787$	−32.7472	−1.16731	−0.583655	−	0.812002i	$-0.698378\pi$
$787$	−32.7472	−1.16731	−0.583655	+	0.812002i	$0.698378\pi$
$788$	9.12143	0.324938
$789$	11.6794	0.415798
$790$	0	0
$791$	−1.35257	−0.0480920
$792$	−0.297329	−0.0105651
$793$	15.1841	0.539205
$794$	20.9088	0.742025
$795$	0	0
$796$	21.5691	0.764497
$797$	−6.54714	−0.231912	−0.115956	−	0.993254i	$-0.536993\pi$
$797$	−6.54714	−0.231912	−0.115956	+	0.993254i	$0.536993\pi$
$798$	3.90359	0.138186
$799$	−39.8058	−1.40823
$800$	0	0
$801$	5.04702	0.178328
$802$	7.42475	0.262177
$803$	0.183420	0.00647274
$804$	3.30778	0.116656
$805$	0	0
$806$	−22.9951	−0.809967
$807$	−23.0385	−0.810995
$808$	−3.29265	−0.115835
$809$	40.5849	1.42689	0.713444	−	0.700712i	$-0.247134\pi$
$809$	40.5849	1.42689	0.713444	+	0.700712i	$0.247134\pi$
$810$	0	0
$811$	15.4588	0.542832	0.271416	−	0.962462i	$-0.412508\pi$
$811$	15.4588	0.542832	0.271416	+	0.962462i	$0.412508\pi$
$812$	0.614893	0.0215785
$813$	4.45505	0.156245
$814$	−2.96990	−0.104095
$815$	0	0
$816$	19.3024	0.675717
$817$	−36.7255	−1.28486
$818$	8.78165	0.307043
$819$	−1.73677	−0.0606875
$820$	0	0
$821$	−22.4828	−0.784656	−0.392328	−	0.919825i	$-0.628330\pi$
$821$	−22.4828	−0.784656	−0.392328	+	0.919825i	$0.628330\pi$
$822$	24.7842	0.864448
$823$	−45.1129	−1.57254	−0.786268	−	0.617886i	$-0.787989\pi$
$823$	−45.1129	−1.57254	−0.786268	+	0.617886i	$0.787989\pi$
$824$	10.5584	0.367818
$825$	0	0
$826$	−0.368798	−0.0128321
$827$	−9.44115	−0.328301	−0.164150	−	0.986435i	$-0.552488\pi$
$827$	−9.44115	−0.328301	−0.164150	+	0.986435i	$0.552488\pi$
$828$	−7.23579	−0.251461
$829$	−55.4844	−1.92705	−0.963527	−	0.267612i	$-0.913765\pi$
$829$	−55.4844	−1.92705	−0.963527	+	0.267612i	$0.913765\pi$
$830$	0	0
$831$	15.7000	0.544627
$832$	−4.08346	−0.141568
$833$	−25.3889	−0.879675
$834$	2.95262	0.102241
$835$	0	0
$836$	−0.534818	−0.0184971
$837$	−5.05274	−0.174648
$838$	24.3374	0.840721
$839$	36.6797	1.26632	0.633162	−	0.774019i	$-0.281757\pi$
$839$	36.6797	1.26632	0.633162	+	0.774019i	$0.281757\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	8.28762	0.285610
$843$	−13.4721	−0.464003
$844$	16.9174	0.582319
$845$	0	0
$846$	−17.6663	−0.607380
$847$	−7.17998	−0.246707
$848$	20.2236	0.694482
$849$	5.86481	0.201280
$850$	0	0
$851$	81.5433	2.79527
$852$	−11.0380	−0.378156
$853$	16.2128	0.555114	0.277557	−	0.960709i	$-0.410475\pi$
$853$	16.2128	0.555114	0.277557	+	0.960709i	$0.410475\pi$
$854$	−6.41772	−0.219610
$855$	0	0
$856$	6.33653	0.216578
$857$	−52.9150	−1.80754	−0.903772	−	0.428015i	$-0.859213\pi$
$857$	−52.9150	−1.80754	−0.903772	+	0.428015i	$0.859213\pi$
$858$	0.744357	0.0254119
$859$	−13.7986	−0.470803	−0.235401	−	0.971898i	$-0.575641\pi$
$859$	−13.7986	−0.470803	−0.235401	+	0.971898i	$0.575641\pi$
$860$	0	0
$861$	4.03987	0.137678
$862$	−31.0182	−1.05648
$863$	4.25394	0.144806	0.0724029	−	0.997375i	$-0.476933\pi$
$863$	4.25394	0.144806	0.0724029	+	0.997375i	$0.476933\pi$
$864$	4.93087	0.167752
$865$	0	0
$866$	2.93200	0.0996334
$867$	2.07510	0.0704743
$868$	3.10690	0.105455
$869$	−2.02934	−0.0688405
$870$	0	0
$871$	9.34281	0.316569
$872$	−14.7435	−0.499278
$873$	−8.49076	−0.287369
$874$	45.9358	1.55380
$875$	0	0
$876$	−1.05386	−0.0356067
$877$	−49.9185	−1.68563	−0.842814	−	0.538205i	$-0.819103\pi$
$877$	−49.9185	−1.68563	−0.842814	+	0.538205i	$0.819103\pi$
$878$	41.7554	1.40918
$879$	−10.3642	−0.349577
$880$	0	0
$881$	−11.5561	−0.389334	−0.194667	−	0.980869i	$-0.562363\pi$
$881$	−11.5561	−0.389334	−0.194667	+	0.980869i	$0.562363\pi$
$882$	−11.2679	−0.379411
$883$	−10.5007	−0.353375	−0.176688	−	0.984267i	$-0.556538\pi$
$883$	−10.5007	−0.353375	−0.176688	+	0.984267i	$0.556538\pi$
$884$	−9.63651	−0.324111
$885$	0	0
$886$	−32.4167	−1.08906
$887$	13.1447	0.441356	0.220678	−	0.975347i	$-0.429173\pi$
$887$	13.1447	0.441356	0.220678	+	0.975347i	$0.429173\pi$
$888$	−19.2521	−0.646058
$889$	8.50364	0.285203
$890$	0	0
$891$	0.163559	0.00547942
$892$	17.9852	0.602190
$893$	35.8519	1.19974
$894$	−27.6836	−0.925877
$895$	0	0
$896$	8.17862	0.273228
$897$	−20.4375	−0.682388
$898$	43.3456	1.44646
$899$	5.05274	0.168518
$900$	0	0
$901$	−15.6372	−0.520952
$902$	−1.73144	−0.0576506
$903$	−6.90614	−0.229822
$904$	3.75783	0.124983
$905$	0	0
$906$	1.25692	0.0417584
$907$	8.45271	0.280668	0.140334	−	0.990104i	$-0.455182\pi$
$907$	8.45271	0.280668	0.140334	+	0.990104i	$0.455182\pi$
$908$	12.5570	0.416718
$909$	1.81126	0.0600757
$910$	0	0
$911$	−23.3000	−0.771965	−0.385982	−	0.922506i	$-0.626137\pi$
$911$	−23.3000	−0.771965	−0.385982	+	0.922506i	$0.626137\pi$
$912$	−17.3850	−0.575676
$913$	−1.29098	−0.0427252
$914$	−7.30123	−0.241503
$915$	0	0
$916$	7.00248	0.231368
$917$	5.68603	0.187769
$918$	−6.62385	−0.218620
$919$	−37.7491	−1.24523	−0.622614	−	0.782529i	$-0.713929\pi$
$919$	−37.7491	−1.24523	−0.622614	+	0.782529i	$0.713929\pi$
$920$	0	0
$921$	−16.0760	−0.529721
$922$	4.25819	0.140236
$923$	−31.1769	−1.02620
$924$	−0.100571	−0.00330855
$925$	0	0
$926$	−47.1294	−1.54877
$927$	−5.80807	−0.190762
$928$	−4.93087	−0.161864
$929$	34.3843	1.12811	0.564055	−	0.825737i	$-0.309240\pi$
$929$	34.3843	1.12811	0.564055	+	0.825737i	$0.309240\pi$
$930$	0	0
$931$	22.8671	0.749437
$932$	−20.2121	−0.662069
$933$	−16.9976	−0.556476
$934$	10.7109	0.350471
$935$	0	0
$936$	4.82522	0.157717
$937$	8.85110	0.289153	0.144576	−	0.989494i	$-0.453818\pi$
$937$	8.85110	0.289153	0.144576	+	0.989494i	$0.453818\pi$
$938$	−3.94883	−0.128934
$939$	25.2391	0.823648
$940$	0	0
$941$	−20.4890	−0.667921	−0.333960	−	0.942587i	$-0.608385\pi$
$941$	−20.4890	−0.667921	−0.333960	+	0.942587i	$0.608385\pi$
$942$	18.5636	0.604834
$943$	47.5394	1.54810
$944$	1.64248	0.0534581
$945$	0	0
$946$	2.95989	0.0962343
$947$	38.8206	1.26150	0.630750	−	0.775986i	$-0.282747\pi$
$947$	38.8206	1.26150	0.630750	+	0.775986i	$0.282747\pi$
$948$	11.6598	0.378693
$949$	−2.97663	−0.0966255
$950$	0	0
$951$	3.06731	0.0994643
$952$	−4.59524	−0.148933
$953$	−33.3755	−1.08114	−0.540570	−	0.841299i	$-0.681791\pi$
$953$	−33.3755	−1.08114	−0.540570	+	0.841299i	$0.681791\pi$
$954$	−6.94000	−0.224691
$955$	0	0
$956$	22.6638	0.733000
$957$	−0.163559	−0.00528710
$958$	−19.8437	−0.641122
$959$	−9.45818	−0.305421
$960$	0	0
$961$	−5.46979	−0.176445
$962$	48.1972	1.55394
$963$	−3.48568	−0.112324
$964$	−6.79254	−0.218773
$965$	0	0
$966$	8.63810	0.277926
$967$	−14.2745	−0.459036	−0.229518	−	0.973304i	$-0.573715\pi$
$967$	−14.2745	−0.459036	−0.229518	+	0.973304i	$0.573715\pi$
$968$	19.9480	0.641153
$969$	13.4424	0.431832
$970$	0	0
$971$	58.2228	1.86846	0.934229	−	0.356675i	$-0.116090\pi$
$971$	58.2228	1.86846	0.934229	+	0.356675i	$0.116090\pi$
$972$	−0.939748	−0.0301424
$973$	−1.12679	−0.0361231
$974$	53.4854	1.71378
$975$	0	0
$976$	28.5820	0.914886
$977$	−57.0456	−1.82505	−0.912526	−	0.409019i	$-0.865871\pi$
$977$	−57.0456	−1.82505	−0.912526	+	0.409019i	$0.865871\pi$
$978$	−23.2372	−0.743043
$979$	0.825483	0.0263826
$980$	0	0
$981$	8.11029	0.258942
$982$	−13.6053	−0.434163
$983$	−2.76691	−0.0882506	−0.0441253	−	0.999026i	$-0.514050\pi$
$983$	−2.76691	−0.0882506	−0.0441253	+	0.999026i	$0.514050\pi$
$984$	−11.2239	−0.357804
$985$	0	0
$986$	6.62385	0.210946
$987$	6.74185	0.214595
$988$	8.67932	0.276126
$989$	−81.2684	−2.58418
$990$	0	0
$991$	26.2090	0.832557	0.416278	−	0.909237i	$-0.363334\pi$
$991$	26.2090	0.832557	0.416278	+	0.909237i	$0.363334\pi$
$992$	−24.9144	−0.791034
$993$	19.9971	0.634590
$994$	13.1772	0.417955
$995$	0	0
$996$	7.41749	0.235032
$997$	−53.0937	−1.68149	−0.840747	−	0.541428i	$-0.817884\pi$
$997$	−53.0937	−1.68149	−0.840747	+	0.541428i	$0.817884\pi$
$998$	−56.4066	−1.78552
$999$	10.5904	0.335067

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2175.2.a.w.1.5		5
3.2	odd	2		6525.2.a.bs.1.1		5
5.2	odd	4		435.2.c.e.349.8	yes	10
5.3	odd	4		435.2.c.e.349.3	✓	10
5.4	even	2		2175.2.a.z.1.1		5
15.2	even	4		1305.2.c.j.784.3		10
15.8	even	4		1305.2.c.j.784.8		10
15.14	odd	2		6525.2.a.bl.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.2.c.e.349.3	✓	10	5.3	odd	4
435.2.c.e.349.8	yes	10	5.2	odd	4
1305.2.c.j.784.3		10	15.2	even	4
1305.2.c.j.784.8		10	15.8	even	4
2175.2.a.w.1.5		5	1.1	even	1	trivial
2175.2.a.z.1.1		5	5.4	even	2
6525.2.a.bl.1.5		5	15.14	odd	2
6525.2.a.bs.1.1		5	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2175 = 3 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2175.a (trivial)

\(f(q)\)	\(=\)	\(q+1.71457 q^{2} -1.00000 q^{3} +0.939748 q^{4} -1.71457 q^{6} +0.654317 q^{7} -1.81788 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.71457 q^{2} -1.00000 q^{3} +0.939748 q^{4} -1.71457 q^{6} +0.654317 q^{7} -1.81788 q^{8} +1.00000 q^{9} +0.163559 q^{11} -0.939748 q^{12} -2.65432 q^{13} +1.12187 q^{14} -4.99637 q^{16} +3.86328 q^{17} +1.71457 q^{18} -3.47954 q^{19} -0.654317 q^{21} +0.280433 q^{22} -7.69972 q^{23} +1.81788 q^{24} -4.55101 q^{26} -1.00000 q^{27} +0.614893 q^{28} +1.00000 q^{29} +5.05274 q^{31} -4.93087 q^{32} -0.163559 q^{33} +6.62385 q^{34} +0.939748 q^{36} -10.5904 q^{37} -5.96591 q^{38} +2.65432 q^{39} -6.17417 q^{41} -1.12187 q^{42} +10.5547 q^{43} +0.153704 q^{44} -13.2017 q^{46} -10.3036 q^{47} +4.99637 q^{48} -6.57187 q^{49} -3.86328 q^{51} -2.49439 q^{52} -4.04766 q^{53} -1.71457 q^{54} -1.18947 q^{56} +3.47954 q^{57} +1.71457 q^{58} -0.328734 q^{59} -5.72054 q^{61} +8.66328 q^{62} +0.654317 q^{63} +1.53842 q^{64} -0.280433 q^{66} -3.51985 q^{67} +3.63050 q^{68} +7.69972 q^{69} +11.7457 q^{71} -1.81788 q^{72} +1.12143 q^{73} -18.1580 q^{74} -3.26989 q^{76} +0.107019 q^{77} +4.55101 q^{78} -12.4074 q^{79} +1.00000 q^{81} -10.5860 q^{82} -7.89306 q^{83} -0.614893 q^{84} +18.0968 q^{86} -1.00000 q^{87} -0.297329 q^{88} +5.04702 q^{89} -1.73677 q^{91} -7.23579 q^{92} -5.05274 q^{93} -17.6663 q^{94} +4.93087 q^{96} -8.49076 q^{97} -11.2679 q^{98} +0.163559 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 3 q^{2} - 5 q^{3} + 5 q^{4} + 3 q^{6} - 8 q^{7} - 9 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q - 3 * q^2 - 5 * q^3 + 5 * q^4 + 3 * q^6 - 8 * q^7 - 9 * q^8 + 5 * q^9	\( 5 q - 3 q^{2} - 5 q^{3} + 5 q^{4} + 3 q^{6} - 8 q^{7} - 9 q^{8} + 5 q^{9} + 12 q^{11} - 5 q^{12} - 2 q^{13} + 6 q^{14} + q^{16} - 3 q^{18} - 2 q^{19} + 8 q^{21} - 14 q^{22} - 8 q^{23} + 9 q^{24} - 5 q^{27} + 6 q^{28} + 5 q^{29} + 2 q^{31} - q^{32} - 12 q^{33} + 4 q^{34} + 5 q^{36} - 16 q^{37} + 14 q^{38} + 2 q^{39} - 14 q^{41} - 6 q^{42} + 20 q^{44} - 6 q^{46} - 2 q^{47} - q^{48} - 7 q^{49} - 16 q^{52} - 26 q^{53} + 3 q^{54} - 2 q^{56} + 2 q^{57} - 3 q^{58} + 4 q^{59} - 12 q^{61} - 8 q^{63} - 9 q^{64} + 14 q^{66} - 12 q^{67} + 20 q^{68} + 8 q^{69} + 30 q^{71} - 9 q^{72} + 12 q^{73} + 2 q^{74} - 44 q^{76} - 18 q^{77} - 18 q^{79} + 5 q^{81} - 10 q^{82} - 2 q^{83} - 6 q^{84} + 30 q^{86} - 5 q^{87} - 42 q^{88} - 22 q^{89} - 12 q^{91} - 20 q^{92} - 2 q^{93} - 50 q^{94} + q^{96} - 20 q^{97} + 9 q^{98} + 12 q^{99}+O(q^{100}) \) 5 * q - 3 * q^2 - 5 * q^3 + 5 * q^4 + 3 * q^6 - 8 * q^7 - 9 * q^8 + 5 * q^9 + 12 * q^11 - 5 * q^12 - 2 * q^13 + 6 * q^14 + q^16 - 3 * q^18 - 2 * q^19 + 8 * q^21 - 14 * q^22 - 8 * q^23 + 9 * q^24 - 5 * q^27 + 6 * q^28 + 5 * q^29 + 2 * q^31 - q^32 - 12 * q^33 + 4 * q^34 + 5 * q^36 - 16 * q^37 + 14 * q^38 + 2 * q^39 - 14 * q^41 - 6 * q^42 + 20 * q^44 - 6 * q^46 - 2 * q^47 - q^48 - 7 * q^49 - 16 * q^52 - 26 * q^53 + 3 * q^54 - 2 * q^56 + 2 * q^57 - 3 * q^58 + 4 * q^59 - 12 * q^61 - 8 * q^63 - 9 * q^64 + 14 * q^66 - 12 * q^67 + 20 * q^68 + 8 * q^69 + 30 * q^71 - 9 * q^72 + 12 * q^73 + 2 * q^74 - 44 * q^76 - 18 * q^77 - 18 * q^79 + 5 * q^81 - 10 * q^82 - 2 * q^83 - 6 * q^84 + 30 * q^86 - 5 * q^87 - 42 * q^88 - 22 * q^89 - 12 * q^91 - 20 * q^92 - 2 * q^93 - 50 * q^94 + q^96 - 20 * q^97 + 9 * q^98 + 12 * q^99

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