LMFDB - Embedded newform 931.2.a.o.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [931,2,Mod(1,931)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(931, 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("931.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 931 = 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	931.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:	$7.43407242818$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 6x^{5} + 18x^{4} + 4x^{3} - 12x^{2} - x + 1 $ x^7 - 3x^6 - 6x^5 + 18x^4 + 4x^3 - 12*x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 133)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$0.273704$ of defining polynomial
Character	$\chi$	$=$	931.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.269662 q^{2} -1.39869 q^{3} -1.92728 q^{4} -3.37987 q^{5} -0.377172 q^{6} -1.05904 q^{8} -1.04367 q^{9} +O(q^{10})$	\(q+0.269662 q^{2} -1.39869 q^{3} -1.92728 q^{4} -3.37987 q^{5} -0.377172 q^{6} -1.05904 q^{8} -1.04367 q^{9} -0.911422 q^{10} -1.57977 q^{11} +2.69567 q^{12} -2.85128 q^{13} +4.72739 q^{15} +3.56898 q^{16} -6.37987 q^{17} -0.281439 q^{18} -1.00000 q^{19} +6.51397 q^{20} -0.426004 q^{22} +2.28675 q^{23} +1.48126 q^{24} +6.42355 q^{25} -0.768880 q^{26} +5.65584 q^{27} +8.17998 q^{29} +1.27479 q^{30} -4.99520 q^{31} +3.08049 q^{32} +2.20960 q^{33} -1.72041 q^{34} +2.01146 q^{36} -10.6332 q^{37} -0.269662 q^{38} +3.98805 q^{39} +3.57941 q^{40} +0.539323 q^{41} +2.79641 q^{43} +3.04466 q^{44} +3.52749 q^{45} +0.616648 q^{46} +9.04650 q^{47} -4.99189 q^{48} +1.73218 q^{50} +8.92345 q^{51} +5.49522 q^{52} +2.71175 q^{53} +1.52516 q^{54} +5.33943 q^{55} +1.39869 q^{57} +2.20583 q^{58} +9.03126 q^{59} -9.11101 q^{60} -6.41110 q^{61} -1.34701 q^{62} -6.30728 q^{64} +9.63696 q^{65} +0.595846 q^{66} +0.976982 q^{67} +12.2958 q^{68} -3.19845 q^{69} -10.9930 q^{71} +1.10529 q^{72} -3.06631 q^{73} -2.86736 q^{74} -8.98453 q^{75} +1.92728 q^{76} +1.07542 q^{78} +0.692355 q^{79} -12.0627 q^{80} -4.77972 q^{81} +0.145435 q^{82} -4.23017 q^{83} +21.5632 q^{85} +0.754085 q^{86} -11.4412 q^{87} +1.67304 q^{88} +4.04045 q^{89} +0.951228 q^{90} -4.40721 q^{92} +6.98672 q^{93} +2.43949 q^{94} +3.37987 q^{95} -4.30864 q^{96} -15.0254 q^{97} +1.64877 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 2 q^{2} + 2 q^{3} + 10 q^{4} + 2 q^{5} + 4 q^{6} + 12 q^{8} + 15 q^{9}+O(q^{10}) $ 7 * q + 2 * q^2 + 2 * q^3 + 10 * q^4 + 2 * q^5 + 4 * q^6 + 12 * q^8 + 15 * q^9	$ 7 q + 2 q^{2} + 2 q^{3} + 10 q^{4} + 2 q^{5} + 4 q^{6} + 12 q^{8} + 15 q^{9} + 7 q^{11} + 22 q^{12} - 6 q^{13} + 2 q^{15} + 24 q^{16} - 19 q^{17} - 12 q^{18} - 7 q^{19} + 8 q^{20} - 6 q^{22} - q^{23} - 20 q^{24} - 3 q^{25} - 12 q^{26} + 14 q^{27} + 24 q^{29} - 20 q^{30} + 26 q^{32} + 14 q^{33} - 6 q^{34} + 46 q^{36} + 8 q^{37} - 2 q^{38} + 16 q^{39} + 10 q^{40} + 4 q^{41} + 4 q^{43} + 26 q^{44} - 14 q^{45} - 16 q^{46} - 5 q^{47} + 28 q^{48} + 16 q^{50} - 4 q^{51} - 42 q^{52} + 20 q^{53} + 24 q^{54} + 30 q^{55} - 2 q^{57} + 16 q^{59} - 44 q^{60} - 5 q^{61} - 24 q^{62} + 32 q^{64} + 26 q^{65} - 68 q^{66} - 4 q^{67} - 22 q^{68} + 36 q^{69} + 12 q^{71} - 3 q^{73} - 4 q^{74} - 18 q^{75} - 10 q^{76} - 14 q^{78} - 20 q^{79} + 4 q^{80} + 27 q^{81} + 48 q^{82} + 11 q^{83} + 26 q^{85} + 36 q^{86} + 16 q^{87} - 32 q^{88} + 10 q^{89} - 32 q^{90} - 30 q^{92} - 4 q^{93} - 16 q^{94} - 2 q^{95} + 12 q^{96} + 4 q^{97} + 15 q^{99}+O(q^{100}) $ 7 * q + 2 * q^2 + 2 * q^3 + 10 * q^4 + 2 * q^5 + 4 * q^6 + 12 * q^8 + 15 * q^9 + 7 * q^11 + 22 * q^12 - 6 * q^13 + 2 * q^15 + 24 * q^16 - 19 * q^17 - 12 * q^18 - 7 * q^19 + 8 * q^20 - 6 * q^22 - q^23 - 20 * q^24 - 3 * q^25 - 12 * q^26 + 14 * q^27 + 24 * q^29 - 20 * q^30 + 26 * q^32 + 14 * q^33 - 6 * q^34 + 46 * q^36 + 8 * q^37 - 2 * q^38 + 16 * q^39 + 10 * q^40 + 4 * q^41 + 4 * q^43 + 26 * q^44 - 14 * q^45 - 16 * q^46 - 5 * q^47 + 28 * q^48 + 16 * q^50 - 4 * q^51 - 42 * q^52 + 20 * q^53 + 24 * q^54 + 30 * q^55 - 2 * q^57 + 16 * q^59 - 44 * q^60 - 5 * q^61 - 24 * q^62 + 32 * q^64 + 26 * q^65 - 68 * q^66 - 4 * q^67 - 22 * q^68 + 36 * q^69 + 12 * q^71 - 3 * q^73 - 4 * q^74 - 18 * q^75 - 10 * q^76 - 14 * q^78 - 20 * q^79 + 4 * q^80 + 27 * q^81 + 48 * q^82 + 11 * q^83 + 26 * q^85 + 36 * q^86 + 16 * q^87 - 32 * q^88 + 10 * q^89 - 32 * q^90 - 30 * q^92 - 4 * q^93 - 16 * q^94 - 2 * q^95 + 12 * q^96 + 4 * q^97 + 15 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0.269662	0.190680	0.0953398	−	0.995445i	$-0.469606\pi$
$2$	0.269662	0.190680	0.0953398	+	0.995445i	$0.469606\pi$
$3$	−1.39869	−0.807532	−0.403766	−	0.914862i	$-0.632299\pi$
$3$	−1.39869	−0.807532	−0.403766	+	0.914862i	$0.632299\pi$
$4$	−1.92728	−0.963641
$5$	−3.37987	−1.51153	−0.755763	−	0.654845i	$-0.772734\pi$
$5$	−3.37987	−1.51153	−0.755763	+	0.654845i	$0.772734\pi$
$6$	−0.377172	−0.153980
$7$	0	0
$7$	0	0
$8$	−1.05904	−0.374426
$9$	−1.04367	−0.347892
$10$	−0.911422	−0.288217
$11$	−1.57977	−0.476319	−0.238159	−	0.971226i	$-0.576544\pi$
$11$	−1.57977	−0.476319	−0.238159	+	0.971226i	$0.576544\pi$
$12$	2.69567	0.778171
$13$	−2.85128	−0.790802	−0.395401	−	0.918509i	$-0.629394\pi$
$13$	−2.85128	−0.790802	−0.395401	+	0.918509i	$0.629394\pi$
$14$	0	0
$15$	4.72739	1.22061
$16$	3.56898	0.892246
$17$	−6.37987	−1.54735	−0.773673	−	0.633585i	$-0.781583\pi$
$17$	−6.37987	−1.54735	−0.773673	+	0.633585i	$0.781583\pi$
$18$	−0.281439	−0.0663358
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	6.51397	1.45657
$21$	0	0
$22$	−0.426004	−0.0908243
$23$	2.28675	0.476820	0.238410	−	0.971165i	$-0.423374\pi$
$23$	2.28675	0.476820	0.238410	+	0.971165i	$0.423374\pi$
$24$	1.48126	0.302361
$25$	6.42355	1.28471
$26$	−0.768880	−0.150790
$27$	5.65584	1.08847
$28$	0	0
$29$	8.17998	1.51898	0.759492	−	0.650517i	$-0.225448\pi$
$29$	8.17998	1.51898	0.759492	+	0.650517i	$0.225448\pi$
$30$	1.27479	0.232745
$31$	−4.99520	−0.897165	−0.448582	−	0.893742i	$-0.648071\pi$
$31$	−4.99520	−0.897165	−0.448582	+	0.893742i	$0.648071\pi$
$32$	3.08049	0.544559
$33$	2.20960	0.384643
$34$	−1.72041	−0.295047
$35$	0	0
$36$	2.01146	0.335243
$37$	−10.6332	−1.74809	−0.874043	−	0.485849i	$-0.838510\pi$
$37$	−10.6332	−1.74809	−0.874043	+	0.485849i	$0.838510\pi$
$38$	−0.269662	−0.0437449
$39$	3.98805	0.638598
$40$	3.57941	0.565955
$41$	0.539323	0.0842281	0.0421141	−	0.999113i	$-0.486591\pi$
$41$	0.539323	0.0842281	0.0421141	+	0.999113i	$0.486591\pi$
$42$	0	0
$43$	2.79641	0.426449	0.213224	−	0.977003i	$-0.431603\pi$
$43$	2.79641	0.426449	0.213224	+	0.977003i	$0.431603\pi$
$44$	3.04466	0.459000
$45$	3.52749	0.525847
$46$	0.616648	0.0909198
$47$	9.04650	1.31957	0.659784	−	0.751456i	$-0.270648\pi$
$47$	9.04650	1.31957	0.659784	+	0.751456i	$0.270648\pi$
$48$	−4.99189	−0.720517
$49$	0	0
$50$	1.73218	0.244968
$51$	8.92345	1.24953
$52$	5.49522	0.762050
$53$	2.71175	0.372487	0.186244	−	0.982504i	$-0.440369\pi$
$53$	2.71175	0.372487	0.186244	+	0.982504i	$0.440369\pi$
$54$	1.52516	0.207548
$55$	5.33943	0.719968
$56$	0	0
$57$	1.39869	0.185261
$58$	2.20583	0.289639
$59$	9.03126	1.17577	0.587885	−	0.808945i	$-0.299961\pi$
$59$	9.03126	1.17577	0.587885	+	0.808945i	$0.299961\pi$
$60$	−9.11101	−1.17623
$61$	−6.41110	−0.820857	−0.410428	−	0.911893i	$-0.634621\pi$
$61$	−6.41110	−0.820857	−0.410428	+	0.911893i	$0.634621\pi$
$62$	−1.34701	−0.171071
$63$	0	0
$64$	−6.30728	−0.788410
$65$	9.63696	1.19532
$66$	0.595846	0.0733435
$67$	0.976982	0.119357	0.0596787	−	0.998218i	$-0.480992\pi$
$67$	0.976982	0.119357	0.0596787	+	0.998218i	$0.480992\pi$
$68$	12.2958	1.49109
$69$	−3.19845	−0.385048
$70$	0	0
$71$	−10.9930	−1.30463	−0.652314	−	0.757949i	$-0.726202\pi$
$71$	−10.9930	−1.30463	−0.652314	+	0.757949i	$0.726202\pi$
$72$	1.10529	0.130260
$73$	−3.06631	−0.358885	−0.179442	−	0.983768i	$-0.557429\pi$
$73$	−3.06631	−0.358885	−0.179442	+	0.983768i	$0.557429\pi$
$74$	−2.86736	−0.333324
$75$	−8.98453	−1.03744
$76$	1.92728	0.221074
$77$	0	0
$78$	1.07542	0.121768
$79$	0.692355	0.0778960	0.0389480	−	0.999241i	$-0.487599\pi$
$79$	0.692355	0.0778960	0.0389480	+	0.999241i	$0.487599\pi$
$80$	−12.0627	−1.34865
$81$	−4.77972	−0.531080
$82$	0.145435	0.0160606
$83$	−4.23017	−0.464322	−0.232161	−	0.972677i	$-0.574580\pi$
$83$	−4.23017	−0.464322	−0.232161	+	0.972677i	$0.574580\pi$
$84$	0	0
$85$	21.5632	2.33885
$86$	0.754085	0.0813150
$87$	−11.4412	−1.22663
$88$	1.67304	0.178346
$89$	4.04045	0.428287	0.214143	−	0.976802i	$-0.431304\pi$
$89$	4.04045	0.428287	0.214143	+	0.976802i	$0.431304\pi$
$90$	0.951228	0.100268
$91$	0	0
$92$	−4.40721	−0.459483
$93$	6.98672	0.724489
$94$	2.43949	0.251614
$95$	3.37987	0.346768
$96$	−4.30864	−0.439749
$97$	−15.0254	−1.52559	−0.762797	−	0.646638i	$-0.776174\pi$
$97$	−15.0254	−1.52559	−0.762797	+	0.646638i	$0.776174\pi$
$98$	0	0
$99$	1.64877	0.165707
$100$	−12.3800	−1.23800
$101$	12.6208	1.25582	0.627910	−	0.778286i	$-0.283911\pi$
$101$	12.6208	1.25582	0.627910	+	0.778286i	$0.283911\pi$
$102$	2.40631	0.238260
$103$	−4.08349	−0.402358	−0.201179	−	0.979554i	$-0.564477\pi$
$103$	−4.08349	−0.402358	−0.201179	+	0.979554i	$0.564477\pi$
$104$	3.01961	0.296097
$105$	0	0
$106$	0.731254	0.0710257
$107$	4.98544	0.481960	0.240980	−	0.970530i	$-0.422531\pi$
$107$	4.98544	0.481960	0.240980	+	0.970530i	$0.422531\pi$
$108$	−10.9004	−1.04889
$109$	10.9154	1.04551	0.522755	−	0.852483i	$-0.324904\pi$
$109$	10.9154	1.04551	0.522755	+	0.852483i	$0.324904\pi$
$110$	1.43984	0.137283
$111$	14.8725	1.41164
$112$	0	0
$113$	−18.5659	−1.74654	−0.873268	−	0.487240i	$-0.838004\pi$
$113$	−18.5659	−1.74654	−0.873268	+	0.487240i	$0.838004\pi$
$114$	0.377172	0.0353254
$115$	−7.72892	−0.720726
$116$	−15.7651	−1.46376
$117$	2.97581	0.275113
$118$	2.43538	0.224195
$119$	0	0
$120$	−5.00648	−0.457027
$121$	−8.50432	−0.773120
$122$	−1.72883	−0.156521
$123$	−0.754344	−0.0680169
$124$	9.62716	0.864545
$125$	−4.81142	−0.430346
$126$	0	0
$127$	−16.9441	−1.50355	−0.751774	−	0.659421i	$-0.770801\pi$
$127$	−16.9441	−1.50355	−0.751774	+	0.659421i	$0.770801\pi$
$128$	−7.86182	−0.694893
$129$	−3.91130	−0.344371
$130$	2.59872	0.227923
$131$	−3.40206	−0.297239	−0.148620	−	0.988894i	$-0.547483\pi$
$131$	−3.40206	−0.297239	−0.148620	+	0.988894i	$0.547483\pi$
$132$	−4.25853	−0.370658
$133$	0	0
$134$	0.263455	0.0227590
$135$	−19.1160	−1.64524
$136$	6.75652	0.579367
$137$	1.75370	0.149829	0.0749143	−	0.997190i	$-0.476132\pi$
$137$	1.75370	0.149829	0.0749143	+	0.997190i	$0.476132\pi$
$138$	−0.862498	−0.0734207
$139$	19.4952	1.65356	0.826780	−	0.562525i	$-0.190170\pi$
$139$	19.4952	1.65356	0.826780	+	0.562525i	$0.190170\pi$
$140$	0	0
$141$	−12.6532	−1.06559
$142$	−2.96439	−0.248766
$143$	4.50437	0.376674
$144$	−3.72486	−0.310405
$145$	−27.6473	−2.29598
$146$	−0.826867	−0.0684320
$147$	0	0
$148$	20.4932	1.68453
$149$	−3.84117	−0.314681	−0.157340	−	0.987544i	$-0.550292\pi$
$149$	−3.84117	−0.314681	−0.157340	+	0.987544i	$0.550292\pi$
$150$	−2.42278	−0.197819
$151$	−14.6285	−1.19045	−0.595223	−	0.803560i	$-0.702936\pi$
$151$	−14.6285	−1.19045	−0.595223	+	0.803560i	$0.702936\pi$
$152$	1.05904	0.0858993
$153$	6.65851	0.538309
$154$	0	0
$155$	16.8832	1.35609
$156$	−7.68609	−0.615380
$157$	8.84191	0.705661	0.352831	−	0.935687i	$-0.385219\pi$
$157$	8.84191	0.705661	0.352831	+	0.935687i	$0.385219\pi$
$158$	0.186701	0.0148532
$159$	−3.79289	−0.300796
$160$	−10.4117	−0.823115
$161$	0	0
$162$	−1.28891	−0.101266
$163$	12.4932	0.978542	0.489271	−	0.872132i	$-0.337263\pi$
$163$	12.4932	0.978542	0.489271	+	0.872132i	$0.337263\pi$
$164$	−1.03943	−0.0811657
$165$	−7.46819	−0.581398
$166$	−1.14072	−0.0885367
$167$	−2.57371	−0.199160	−0.0995799	−	0.995030i	$-0.531750\pi$
$167$	−2.57371	−0.199160	−0.0995799	+	0.995030i	$0.531750\pi$
$168$	0	0
$169$	−4.87021	−0.374632
$170$	5.81476	0.445972
$171$	1.04367	0.0798118
$172$	−5.38947	−0.410944
$173$	2.74850	0.208965	0.104482	−	0.994527i	$-0.466681\pi$
$173$	2.74850	0.208965	0.104482	+	0.994527i	$0.466681\pi$
$174$	−3.08526	−0.233893
$175$	0	0
$176$	−5.63818	−0.424994
$177$	−12.6319	−0.949472
$178$	1.08955	0.0816655
$179$	5.21062	0.389460	0.194730	−	0.980857i	$-0.437617\pi$
$179$	5.21062	0.389460	0.194730	+	0.980857i	$0.437617\pi$
$180$	−6.79847	−0.506728
$181$	−2.25178	−0.167373	−0.0836866	−	0.996492i	$-0.526669\pi$
$181$	−2.25178	−0.167373	−0.0836866	+	0.996492i	$0.526669\pi$
$182$	0	0
$183$	8.96712	0.662868
$184$	−2.42175	−0.178534
$185$	35.9388	2.64228
$186$	1.88405	0.138145
$187$	10.0787	0.737030
$188$	−17.4352	−1.27159
$189$	0	0
$190$	0.911422	0.0661215
$191$	1.36251	0.0985880	0.0492940	−	0.998784i	$-0.484303\pi$
$191$	1.36251	0.0985880	0.0492940	+	0.998784i	$0.484303\pi$
$192$	8.82191	0.636666
$193$	27.6160	1.98784	0.993920	−	0.110105i	$-0.0351188\pi$
$193$	27.6160	1.98784	0.993920	+	0.110105i	$0.0351188\pi$
$194$	−4.05176	−0.290899
$195$	−13.4791	−0.965258
$196$	0	0
$197$	10.4969	0.747874	0.373937	−	0.927454i	$-0.378008\pi$
$197$	10.4969	0.747874	0.373937	+	0.927454i	$0.378008\pi$
$198$	0.444609	0.0315970
$199$	6.23932	0.442294	0.221147	−	0.975240i	$-0.429020\pi$
$199$	6.23932	0.442294	0.221147	+	0.975240i	$0.429020\pi$
$200$	−6.80278	−0.481029
$201$	−1.36649	−0.0963849
$202$	3.40335	0.239459
$203$	0	0
$204$	−17.1980	−1.20410
$205$	−1.82284	−0.127313
$206$	−1.10116	−0.0767215
$207$	−2.38662	−0.165882
$208$	−10.1762	−0.705590
$209$	1.57977	0.109275
$210$	0	0
$211$	−24.5399	−1.68940	−0.844698	−	0.535243i	$-0.820220\pi$
$211$	−24.5399	−1.68940	−0.844698	+	0.535243i	$0.820220\pi$
$212$	−5.22631	−0.358944
$213$	15.3757	1.05353
$214$	1.34438	0.0919000
$215$	−9.45152	−0.644588
$216$	−5.98974	−0.407550
$217$	0	0
$218$	2.94348	0.199357
$219$	4.28881	0.289811
$220$	−10.2906	−0.693791
$221$	18.1908	1.22365
$222$	4.01054	0.269170
$223$	15.5804	1.04334	0.521670	−	0.853147i	$-0.325309\pi$
$223$	15.5804	1.04334	0.521670	+	0.853147i	$0.325309\pi$
$224$	0	0
$225$	−6.70410	−0.446940
$226$	−5.00652	−0.333029
$227$	10.2592	0.680930	0.340465	−	0.940257i	$-0.389416\pi$
$227$	10.2592	0.680930	0.340465	+	0.940257i	$0.389416\pi$
$228$	−2.69567	−0.178525
$229$	20.9056	1.38148	0.690741	−	0.723102i	$-0.257284\pi$
$229$	20.9056	1.38148	0.690741	+	0.723102i	$0.257284\pi$
$230$	−2.08419	−0.137428
$231$	0	0
$232$	−8.66290	−0.568747
$233$	7.99028	0.523461	0.261730	−	0.965141i	$-0.415707\pi$
$233$	7.99028	0.523461	0.261730	+	0.965141i	$0.415707\pi$
$234$	0.802461	0.0524585
$235$	−30.5760	−1.99456
$236$	−17.4058	−1.13302
$237$	−0.968387	−0.0629035
$238$	0	0
$239$	18.8239	1.21762	0.608809	−	0.793317i	$-0.291648\pi$
$239$	18.8239	1.21762	0.608809	+	0.793317i	$0.291648\pi$
$240$	16.8720	1.08908
$241$	12.1098	0.780060	0.390030	−	0.920802i	$-0.372465\pi$
$241$	12.1098	0.780060	0.390030	+	0.920802i	$0.372465\pi$
$242$	−2.29329	−0.147418
$243$	−10.2822	−0.659602
$244$	12.3560	0.791012
$245$	0	0
$246$	−0.203418	−0.0129694
$247$	2.85128	0.181423
$248$	5.29010	0.335922
$249$	5.91669	0.374955
$250$	−1.29745	−0.0820582
$251$	−15.5940	−0.984286	−0.492143	−	0.870514i	$-0.663786\pi$
$251$	−15.5940	−0.984286	−0.492143	+	0.870514i	$0.663786\pi$
$252$	0	0
$253$	−3.61254	−0.227118
$254$	−4.56918	−0.286696
$255$	−30.1601	−1.88870
$256$	10.4945	0.655908
$257$	30.0734	1.87593	0.937963	−	0.346735i	$-0.112710\pi$
$257$	30.0734	1.87593	0.937963	+	0.346735i	$0.112710\pi$
$258$	−1.05473	−0.0656645
$259$	0	0
$260$	−18.5731	−1.15186
$261$	−8.53724	−0.528442
$262$	−0.917404	−0.0566774
$263$	−5.04888	−0.311327	−0.155663	−	0.987810i	$-0.549752\pi$
$263$	−5.04888	−0.311327	−0.155663	+	0.987810i	$0.549752\pi$
$264$	−2.34005	−0.144020
$265$	−9.16537	−0.563024
$266$	0	0
$267$	−5.65132	−0.345855
$268$	−1.88292	−0.115018
$269$	−3.61281	−0.220277	−0.110138	−	0.993916i	$-0.535129\pi$
$269$	−3.61281	−0.220277	−0.110138	+	0.993916i	$0.535129\pi$
$270$	−5.15485	−0.313714
$271$	−8.19089	−0.497561	−0.248781	−	0.968560i	$-0.580030\pi$
$271$	−8.19089	−0.497561	−0.248781	+	0.968560i	$0.580030\pi$
$272$	−22.7697	−1.38061
$273$	0	0
$274$	0.472905	0.0285693
$275$	−10.1477	−0.611931
$276$	6.16431	0.371048
$277$	−12.7017	−0.763173	−0.381587	−	0.924333i	$-0.624622\pi$
$277$	−12.7017	−0.763173	−0.381587	+	0.924333i	$0.624622\pi$
$278$	5.25710	0.315300
$279$	5.21337	0.312116
$280$	0	0
$281$	11.6373	0.694226	0.347113	−	0.937823i	$-0.387162\pi$
$281$	11.6373	0.694226	0.347113	+	0.937823i	$0.387162\pi$
$282$	−3.41209	−0.203187
$283$	−21.7734	−1.29429	−0.647146	−	0.762366i	$-0.724038\pi$
$283$	−21.7734	−1.29429	−0.647146	+	0.762366i	$0.724038\pi$
$284$	21.1866	1.25719
$285$	−4.72739	−0.280026
$286$	1.21465	0.0718240
$287$	0	0
$288$	−3.21503	−0.189448
$289$	23.7028	1.39428
$290$	−7.45541	−0.437797
$291$	21.0158	1.23197
$292$	5.90965	0.345836
$293$	0.850550	0.0496897	0.0248448	−	0.999691i	$-0.492091\pi$
$293$	0.850550	0.0496897	0.0248448	+	0.999691i	$0.492091\pi$
$294$	0	0
$295$	−30.5245	−1.77721
$296$	11.2609	0.654529
$297$	−8.93492	−0.518457
$298$	−1.03582	−0.0600032
$299$	−6.52016	−0.377070
$300$	17.3157	0.999725
$301$	0	0
$302$	−3.94473	−0.226994
$303$	−17.6526	−1.01412
$304$	−3.56898	−0.204695
$305$	21.6687	1.24075
$306$	1.79555	0.102644
$307$	21.8941	1.24956	0.624781	−	0.780800i	$-0.285188\pi$
$307$	21.8941	1.24956	0.624781	+	0.780800i	$0.285188\pi$
$308$	0	0
$309$	5.71152	0.324917
$310$	4.55274	0.258578
$311$	1.91981	0.108863	0.0544314	−	0.998518i	$-0.482665\pi$
$311$	1.91981	0.108863	0.0544314	+	0.998518i	$0.482665\pi$
$312$	−4.22349	−0.239108
$313$	−10.3278	−0.583764	−0.291882	−	0.956454i	$-0.594281\pi$
$313$	−10.3278	−0.583764	−0.291882	+	0.956454i	$0.594281\pi$
$314$	2.38432	0.134555
$315$	0	0
$316$	−1.33436	−0.0750638
$317$	16.9578	0.952445	0.476223	−	0.879325i	$-0.342006\pi$
$317$	16.9578	0.952445	0.476223	+	0.879325i	$0.342006\pi$
$318$	−1.02280	−0.0573556
$319$	−12.9225	−0.723521
$320$	21.3178	1.19170
$321$	−6.97307	−0.389199
$322$	0	0
$323$	6.37987	0.354986
$324$	9.21187	0.511771
$325$	−18.3153	−1.01595
$326$	3.36893	0.186588
$327$	−15.2673	−0.844283
$328$	−0.571163	−0.0315372
$329$	0	0
$330$	−2.01388	−0.110861
$331$	−16.5087	−0.907398	−0.453699	−	0.891155i	$-0.649896\pi$
$331$	−16.5087	−0.907398	−0.453699	+	0.891155i	$0.649896\pi$
$332$	8.15274	0.447440
$333$	11.0976	0.608144
$334$	−0.694032	−0.0379757
$335$	−3.30208	−0.180412
$336$	0	0
$337$	7.11897	0.387795	0.193898	−	0.981022i	$-0.437887\pi$
$337$	7.11897	0.387795	0.193898	+	0.981022i	$0.437887\pi$
$338$	−1.31331	−0.0714346
$339$	25.9679	1.41038
$340$	−41.5583	−2.25382
$341$	7.89127	0.427336
$342$	0.281439	0.0152185
$343$	0	0
$344$	−2.96150	−0.159674
$345$	10.8103	0.582009
$346$	0.741166	0.0398453
$347$	−18.5879	−0.997851	−0.498926	−	0.866645i	$-0.666272\pi$
$347$	−18.5879	−0.997851	−0.498926	+	0.866645i	$0.666272\pi$
$348$	22.0505	1.18203
$349$	19.2917	1.03266	0.516330	−	0.856389i	$-0.327298\pi$
$349$	19.2917	1.03266	0.516330	+	0.856389i	$0.327298\pi$
$350$	0	0
$351$	−16.1264	−0.860761
$352$	−4.86647	−0.259384
$353$	−17.3488	−0.923385	−0.461693	−	0.887040i	$-0.652758\pi$
$353$	−17.3488	−0.923385	−0.461693	+	0.887040i	$0.652758\pi$
$354$	−3.40634	−0.181045
$355$	37.1549	1.97198
$356$	−7.78708	−0.412715
$357$	0	0
$358$	1.40511	0.0742621
$359$	−31.0859	−1.64065	−0.820326	−	0.571896i	$-0.806208\pi$
$359$	−31.0859	−1.64065	−0.820326	+	0.571896i	$0.806208\pi$
$360$	−3.73574	−0.196891
$361$	1.00000	0.0526316
$362$	−0.607218	−0.0319147
$363$	11.8949	0.624320
$364$	0	0
$365$	10.3638	0.542464
$366$	2.41809	0.126395
$367$	9.20277	0.480381	0.240190	−	0.970726i	$-0.422790\pi$
$367$	9.20277	0.480381	0.240190	+	0.970726i	$0.422790\pi$
$368$	8.16137	0.425441
$369$	−0.562878	−0.0293023
$370$	9.69132	0.503828
$371$	0	0
$372$	−13.4654	−0.698148
$373$	−18.9700	−0.982227	−0.491114	−	0.871095i	$-0.663410\pi$
$373$	−18.9700	−0.982227	−0.491114	+	0.871095i	$0.663410\pi$
$374$	2.71785	0.140537
$375$	6.72966	0.347518
$376$	−9.58058	−0.494081
$377$	−23.3234	−1.20122
$378$	0	0
$379$	31.0591	1.59540	0.797699	−	0.603056i	$-0.206051\pi$
$379$	31.0591	1.59540	0.797699	+	0.603056i	$0.206051\pi$
$380$	−6.51397	−0.334160
$381$	23.6995	1.21416
$382$	0.367417	0.0187987
$383$	−13.9670	−0.713679	−0.356839	−	0.934166i	$-0.616146\pi$
$383$	−13.9670	−0.713679	−0.356839	+	0.934166i	$0.616146\pi$
$384$	10.9962	0.561148
$385$	0	0
$386$	7.44696	0.379040
$387$	−2.91854	−0.148358
$388$	28.9581	1.47012
$389$	0.367141	0.0186148	0.00930739	−	0.999957i	$-0.497037\pi$
$389$	0.367141	0.0186148	0.00930739	+	0.999957i	$0.497037\pi$
$390$	−3.63479	−0.184055
$391$	−14.5892	−0.737806
$392$	0	0
$393$	4.75841	0.240030
$394$	2.83061	0.142604
$395$	−2.34007	−0.117742
$396$	−3.17764	−0.159682
$397$	−20.2532	−1.01648	−0.508240	−	0.861216i	$-0.669704\pi$
$397$	−20.2532	−1.01648	−0.508240	+	0.861216i	$0.669704\pi$
$398$	1.68251	0.0843364
$399$	0	0
$400$	22.9255	1.14628
$401$	26.2654	1.31163	0.655815	−	0.754922i	$-0.272325\pi$
$401$	26.2654	1.31163	0.655815	+	0.754922i	$0.272325\pi$
$402$	−0.368491	−0.0183786
$403$	14.2427	0.709480
$404$	−24.3239	−1.21016
$405$	16.1548	0.802741
$406$	0	0
$407$	16.7980	0.832646
$408$	−9.45026	−0.467858
$409$	−0.0743039	−0.00367409	−0.00183705	−	0.999998i	$-0.500585\pi$
$409$	−0.0743039	−0.00367409	−0.00183705	+	0.999998i	$0.500585\pi$
$410$	−0.491551	−0.0242760
$411$	−2.45288	−0.120991
$412$	7.87004	0.387729
$413$	0	0
$414$	−0.643580	−0.0316302
$415$	14.2975	0.701835
$416$	−8.78334	−0.430639
$417$	−27.2677	−1.33530
$418$	0.426004	0.0208365
$419$	−14.9914	−0.732379	−0.366189	−	0.930540i	$-0.619338\pi$
$419$	−14.9914	−0.732379	−0.366189	+	0.930540i	$0.619338\pi$
$420$	0	0
$421$	14.4311	0.703330	0.351665	−	0.936126i	$-0.385616\pi$
$421$	14.4311	0.703330	0.351665	+	0.936126i	$0.385616\pi$
$422$	−6.61747	−0.322133
$423$	−9.44160	−0.459066
$424$	−2.87184	−0.139469
$425$	−40.9814	−1.98789
$426$	4.14625	0.200886
$427$	0	0
$428$	−9.60835	−0.464437
$429$	−6.30020	−0.304176
$430$	−2.54871	−0.122910
$431$	22.4651	1.08211	0.541053	−	0.840988i	$-0.318026\pi$
$431$	22.4651	1.08211	0.541053	+	0.840988i	$0.318026\pi$
$432$	20.1856	0.971179
$433$	11.9702	0.575250	0.287625	−	0.957743i	$-0.407134\pi$
$433$	11.9702	0.575250	0.287625	+	0.957743i	$0.407134\pi$
$434$	0	0
$435$	38.6699	1.85408
$436$	−21.0372	−1.00750
$437$	−2.28675	−0.109390
$438$	1.15653	0.0552611
$439$	7.92106	0.378052	0.189026	−	0.981972i	$-0.439467\pi$
$439$	7.92106	0.378052	0.189026	+	0.981972i	$0.439467\pi$
$440$	−5.65465	−0.269575
$441$	0	0
$442$	4.90536	0.233324
$443$	31.0130	1.47347	0.736735	−	0.676182i	$-0.236366\pi$
$443$	31.0130	1.47347	0.736735	+	0.676182i	$0.236366\pi$
$444$	−28.6635	−1.36031
$445$	−13.6562	−0.647366
$446$	4.20143	0.198944
$447$	5.37259	0.254115
$448$	0	0
$449$	17.3687	0.819681	0.409840	−	0.912157i	$-0.365584\pi$
$449$	17.3687	0.819681	0.409840	+	0.912157i	$0.365584\pi$
$450$	−1.80784	−0.0852223
$451$	−0.852007	−0.0401194
$452$	35.7818	1.68303
$453$	20.4606	0.961324
$454$	2.76652	0.129839
$455$	0	0
$456$	−1.48126	−0.0693664
$457$	−3.08249	−0.144193	−0.0720963	−	0.997398i	$-0.522969\pi$
$457$	−3.08249	−0.144193	−0.0720963	+	0.997398i	$0.522969\pi$
$458$	5.63744	0.263420
$459$	−36.0835	−1.68423
$460$	14.8958	0.694521
$461$	39.9179	1.85916	0.929580	−	0.368620i	$-0.120170\pi$
$461$	39.9179	1.85916	0.929580	+	0.368620i	$0.120170\pi$
$462$	0	0
$463$	25.7081	1.19476	0.597379	−	0.801959i	$-0.296209\pi$
$463$	25.7081	1.19476	0.597379	+	0.801959i	$0.296209\pi$
$464$	29.1942	1.35531
$465$	−23.6142	−1.09508
$466$	2.15467	0.0998133
$467$	19.2441	0.890512	0.445256	−	0.895403i	$-0.353113\pi$
$467$	19.2441	0.890512	0.445256	+	0.895403i	$0.353113\pi$
$468$	−5.73522	−0.265111
$469$	0	0
$470$	−8.24518	−0.380322
$471$	−12.3671	−0.569844
$472$	−9.56444	−0.440239
$473$	−4.41769	−0.203126
$474$	−0.261137	−0.0119944
$475$	−6.42355	−0.294733
$476$	0	0
$477$	−2.83018	−0.129585
$478$	5.07608	0.232175
$479$	−22.1279	−1.01105	−0.505525	−	0.862812i	$-0.668701\pi$
$479$	−22.1279	−1.01105	−0.505525	+	0.862812i	$0.668701\pi$
$480$	14.5627	0.664692
$481$	30.3182	1.38239
$482$	3.26555	0.148742
$483$	0	0
$484$	16.3902	0.745011
$485$	50.7838	2.30597
$486$	−2.77271	−0.125773
$487$	−5.26256	−0.238469	−0.119235	−	0.992866i	$-0.538044\pi$
$487$	−5.26256	−0.238469	−0.119235	+	0.992866i	$0.538044\pi$
$488$	6.78959	0.307350
$489$	−17.4741	−0.790204
$490$	0	0
$491$	−15.7852	−0.712375	−0.356188	−	0.934414i	$-0.615924\pi$
$491$	−15.7852	−0.712375	−0.356188	+	0.934414i	$0.615924\pi$
$492$	1.45383	0.0655439
$493$	−52.1872	−2.35039
$494$	0.768880	0.0345936
$495$	−5.57262	−0.250471
$496$	−17.8278	−0.800491
$497$	0	0
$498$	1.59550	0.0714963
$499$	7.99870	0.358071	0.179035	−	0.983843i	$-0.442702\pi$
$499$	7.99870	0.358071	0.179035	+	0.983843i	$0.442702\pi$
$500$	9.27296	0.414699
$501$	3.59982	0.160828
$502$	−4.20511	−0.187683
$503$	−3.70541	−0.165216	−0.0826079	−	0.996582i	$-0.526325\pi$
$503$	−3.70541	−0.165216	−0.0826079	+	0.996582i	$0.526325\pi$
$504$	0	0
$505$	−42.6568	−1.89820
$506$	−0.974163	−0.0433068
$507$	6.81190	0.302527
$508$	32.6561	1.44888
$509$	−0.946137	−0.0419368	−0.0209684	−	0.999780i	$-0.506675\pi$
$509$	−0.946137	−0.0419368	−0.0209684	+	0.999780i	$0.506675\pi$
$510$	−8.13303	−0.360137
$511$	0	0
$512$	18.5536	0.819961
$513$	−5.65584	−0.249711
$514$	8.10964	0.357701
$515$	13.8017	0.608175
$516$	7.53819	0.331850
$517$	−14.2914	−0.628535
$518$	0	0
$519$	−3.84430	−0.168746
$520$	−10.2059	−0.447558
$521$	6.06750	0.265822	0.132911	−	0.991128i	$-0.457568\pi$
$521$	6.06750	0.265822	0.132911	+	0.991128i	$0.457568\pi$
$522$	−2.30216	−0.100763
$523$	−10.5923	−0.463169	−0.231584	−	0.972815i	$-0.574391\pi$
$523$	−10.5923	−0.463169	−0.231584	+	0.972815i	$0.574391\pi$
$524$	6.55673	0.286432
$525$	0	0
$526$	−1.36149	−0.0593637
$527$	31.8688	1.38822
$528$	7.88604	0.343196
$529$	−17.7708	−0.772643
$530$	−2.47155	−0.107357
$531$	−9.42569	−0.409040
$532$	0	0
$533$	−1.53776	−0.0666078
$534$	−1.52394	−0.0659475
$535$	−16.8501	−0.728495
$536$	−1.03466	−0.0446905
$537$	−7.28803	−0.314502
$538$	−0.974235	−0.0420022
$539$	0	0
$540$	36.8420	1.58543
$541$	16.1842	0.695814	0.347907	−	0.937529i	$-0.386893\pi$
$541$	16.1842	0.695814	0.347907	+	0.937529i	$0.386893\pi$
$542$	−2.20877	−0.0948748
$543$	3.14953	0.135159
$544$	−19.6532	−0.842622
$545$	−36.8928	−1.58032
$546$	0	0
$547$	−41.6886	−1.78247	−0.891237	−	0.453538i	$-0.850162\pi$
$547$	−41.6886	−1.78247	−0.891237	+	0.453538i	$0.850162\pi$
$548$	−3.37987	−0.144381
$549$	6.69110	0.285569
$550$	−2.73645	−0.116683
$551$	−8.17998	−0.348479
$552$	3.38727	0.144172
$553$	0	0
$554$	−3.42517	−0.145521
$555$	−50.2672	−2.13372
$556$	−37.5727	−1.59344
$557$	18.3788	0.778733	0.389366	−	0.921083i	$-0.372694\pi$
$557$	18.3788	0.778733	0.389366	+	0.921083i	$0.372694\pi$
$558$	1.40584	0.0595141
$559$	−7.97335	−0.337237
$560$	0	0
$561$	−14.0970	−0.595176
$562$	3.13814	0.132375
$563$	−6.75866	−0.284844	−0.142422	−	0.989806i	$-0.545489\pi$
$563$	−6.75866	−0.284844	−0.142422	+	0.989806i	$0.545489\pi$
$564$	24.3863	1.02685
$565$	62.7505	2.63993
$566$	−5.87144	−0.246795
$567$	0	0
$568$	11.6420	0.488487
$569$	37.0223	1.55205	0.776027	−	0.630699i	$-0.217232\pi$
$569$	37.0223	1.55205	0.776027	+	0.630699i	$0.217232\pi$
$570$	−1.27479	−0.0533953
$571$	−19.0336	−0.796530	−0.398265	−	0.917270i	$-0.630388\pi$
$571$	−19.0336	−0.796530	−0.398265	+	0.917270i	$0.630388\pi$
$572$	−8.68119	−0.362979
$573$	−1.90573	−0.0796130
$574$	0	0
$575$	14.6890	0.612575
$576$	6.58275	0.274281
$577$	−13.4773	−0.561066	−0.280533	−	0.959844i	$-0.590511\pi$
$577$	−13.4773	−0.561066	−0.280533	+	0.959844i	$0.590511\pi$
$578$	6.39173	0.265861
$579$	−38.6261	−1.60524
$580$	53.2841	2.21250
$581$	0	0
$582$	5.66714	0.234911
$583$	−4.28394	−0.177423
$584$	3.24734	0.134376
$585$	−10.0579	−0.415841
$586$	0.229361	0.00947480
$587$	−14.4778	−0.597562	−0.298781	−	0.954322i	$-0.596580\pi$
$587$	−14.4778	−0.597562	−0.298781	+	0.954322i	$0.596580\pi$
$588$	0	0
$589$	4.99520	0.205824
$590$	−8.23129	−0.338877
$591$	−14.6819	−0.603932
$592$	−37.9497	−1.55972
$593$	−24.8304	−1.01966	−0.509832	−	0.860274i	$-0.670292\pi$
$593$	−24.8304	−1.01966	−0.509832	+	0.860274i	$0.670292\pi$
$594$	−2.40941	−0.0988591
$595$	0	0
$596$	7.40302	0.303239
$597$	−8.72686	−0.357167
$598$	−1.75824	−0.0718996
$599$	38.0432	1.55440	0.777202	−	0.629251i	$-0.216638\pi$
$599$	38.0432	1.55440	0.777202	+	0.629251i	$0.216638\pi$
$600$	9.51496	0.388446
$601$	16.1254	0.657768	0.328884	−	0.944370i	$-0.393328\pi$
$601$	16.1254	0.657768	0.328884	+	0.944370i	$0.393328\pi$
$602$	0	0
$603$	−1.01965	−0.0415234
$604$	28.1932	1.14716
$605$	28.7435	1.16859
$606$	−4.76023	−0.193371
$607$	2.04060	0.0828254	0.0414127	−	0.999142i	$-0.486814\pi$
$607$	2.04060	0.0828254	0.0414127	+	0.999142i	$0.486814\pi$
$608$	−3.08049	−0.124930
$609$	0	0
$610$	5.84322	0.236585
$611$	−25.7941	−1.04352
$612$	−12.8328	−0.518737
$613$	6.31135	0.254913	0.127456	−	0.991844i	$-0.459319\pi$
$613$	6.31135	0.254913	0.127456	+	0.991844i	$0.459319\pi$
$614$	5.90399	0.238266
$615$	2.54959	0.102809
$616$	0	0
$617$	−36.7747	−1.48049	−0.740246	−	0.672336i	$-0.765291\pi$
$617$	−36.7747	−1.48049	−0.740246	+	0.672336i	$0.765291\pi$
$618$	1.54018	0.0619551
$619$	48.4768	1.94845	0.974224	−	0.225585i	$-0.0724292\pi$
$619$	48.4768	1.94845	0.974224	+	0.225585i	$0.0724292\pi$
$620$	−32.5386	−1.30678
$621$	12.9335	0.519002
$622$	0.517700	0.0207579
$623$	0	0
$624$	14.2333	0.569787
$625$	−15.8558	−0.634231
$626$	−2.78502	−0.111312
$627$	−2.20960	−0.0882431
$628$	−17.0409	−0.680004
$629$	67.8384	2.70489
$630$	0	0
$631$	41.4306	1.64933	0.824663	−	0.565624i	$-0.191365\pi$
$631$	41.4306	1.64933	0.824663	+	0.565624i	$0.191365\pi$
$632$	−0.733229	−0.0291663
$633$	34.3236	1.36424
$634$	4.57287	0.181612
$635$	57.2690	2.27265
$636$	7.30997	0.289859
$637$	0	0
$638$	−3.48470	−0.137961
$639$	11.4731	0.453869
$640$	26.5719	1.05035
$641$	−13.3666	−0.527950	−0.263975	−	0.964530i	$-0.585034\pi$
$641$	−13.3666	−0.527950	−0.263975	+	0.964530i	$0.585034\pi$
$642$	−1.88037	−0.0742122
$643$	−21.2566	−0.838278	−0.419139	−	0.907922i	$-0.637668\pi$
$643$	−21.2566	−0.838278	−0.419139	+	0.907922i	$0.637668\pi$
$644$	0	0
$645$	13.2197	0.520526
$646$	1.72041	0.0676885
$647$	−25.5902	−1.00605	−0.503026	−	0.864271i	$-0.667780\pi$
$647$	−25.5902	−1.00605	−0.503026	+	0.864271i	$0.667780\pi$
$648$	5.06190	0.198850
$649$	−14.2673	−0.560041
$650$	−4.93894	−0.193721
$651$	0	0
$652$	−24.0779	−0.942963
$653$	41.8766	1.63876	0.819379	−	0.573252i	$-0.194318\pi$
$653$	41.8766	1.63876	0.819379	+	0.573252i	$0.194318\pi$
$654$	−4.11700	−0.160988
$655$	11.4985	0.449285
$656$	1.92484	0.0751522
$657$	3.20023	0.124853
$658$	0	0
$659$	−16.3252	−0.635940	−0.317970	−	0.948101i	$-0.603001\pi$
$659$	−16.3252	−0.635940	−0.317970	+	0.948101i	$0.603001\pi$
$660$	14.3933	0.560259
$661$	−7.79570	−0.303218	−0.151609	−	0.988441i	$-0.548445\pi$
$661$	−7.79570	−0.303218	−0.151609	+	0.988441i	$0.548445\pi$
$662$	−4.45175	−0.173022
$663$	−25.4432	−0.988133
$664$	4.47991	0.173854
$665$	0	0
$666$	2.99259	0.115961
$667$	18.7055	0.724282
$668$	4.96027	0.191919
$669$	−21.7921	−0.842531
$670$	−0.890443	−0.0344008
$671$	10.1281	0.390990
$672$	0	0
$673$	−12.5226	−0.482709	−0.241355	−	0.970437i	$-0.577592\pi$
$673$	−12.5226	−0.482709	−0.241355	+	0.970437i	$0.577592\pi$
$674$	1.91971	0.0739446
$675$	36.3305	1.39836
$676$	9.38627	0.361011
$677$	1.71203	0.0657988	0.0328994	−	0.999459i	$-0.489526\pi$
$677$	1.71203	0.0657988	0.0328994	+	0.999459i	$0.489526\pi$
$678$	7.00255	0.268931
$679$	0	0
$680$	−22.8362	−0.875728
$681$	−14.3495	−0.549873
$682$	2.12797	0.0814843
$683$	−28.6546	−1.09644	−0.548218	−	0.836335i	$-0.684694\pi$
$683$	−28.6546	−1.09644	−0.548218	+	0.836335i	$0.684694\pi$
$684$	−2.01146	−0.0769099
$685$	−5.92728	−0.226470
$686$	0	0
$687$	−29.2404	−1.11559
$688$	9.98035	0.380497
$689$	−7.73195	−0.294564
$690$	2.91513	0.110977
$691$	−5.86980	−0.223298	−0.111649	−	0.993748i	$-0.535613\pi$
$691$	−5.86980	−0.223298	−0.111649	+	0.993748i	$0.535613\pi$
$692$	−5.29714	−0.201367
$693$	0	0
$694$	−5.01244	−0.190270
$695$	−65.8913	−2.49940
$696$	12.1167	0.459282
$697$	−3.44081	−0.130330
$698$	5.20223	0.196907
$699$	−11.1759	−0.422712
$700$	0	0
$701$	31.9494	1.20671	0.603355	−	0.797473i	$-0.293830\pi$
$701$	31.9494	1.20671	0.603355	+	0.797473i	$0.293830\pi$
$702$	−4.34866	−0.164130
$703$	10.6332	0.401038
$704$	9.96405	0.375534
$705$	42.7663	1.61067
$706$	−4.67831	−0.176071
$707$	0	0
$708$	24.3452	0.914950
$709$	−36.4280	−1.36808	−0.684041	−	0.729443i	$-0.739779\pi$
$709$	−36.4280	−1.36808	−0.684041	+	0.729443i	$0.739779\pi$
$710$	10.0193	0.376016
$711$	−0.722593	−0.0270994
$712$	−4.27898	−0.160362
$713$	−11.4228	−0.427786
$714$	0	0
$715$	−15.2242	−0.569352
$716$	−10.0423	−0.375300
$717$	−26.3288	−0.983265
$718$	−8.38268	−0.312839
$719$	46.7674	1.74413	0.872065	−	0.489391i	$-0.162781\pi$
$719$	46.7674	1.74413	0.872065	+	0.489391i	$0.162781\pi$
$720$	12.5896	0.469185
$721$	0	0
$722$	0.269662	0.0100358
$723$	−16.9378	−0.629924
$724$	4.33981	0.161288
$725$	52.5445	1.95145
$726$	3.20759	0.119045
$727$	−32.7260	−1.21374	−0.606870	−	0.794801i	$-0.707575\pi$
$727$	−32.7260	−1.21374	−0.606870	+	0.794801i	$0.707575\pi$
$728$	0	0
$729$	28.7207	1.06373
$730$	2.79471	0.103437
$731$	−17.8408	−0.659864
$732$	−17.2822	−0.638767
$733$	−43.8720	−1.62045	−0.810225	−	0.586119i	$-0.800655\pi$
$733$	−43.8720	−1.62045	−0.810225	+	0.586119i	$0.800655\pi$
$734$	2.48163	0.0915988
$735$	0	0
$736$	7.04431	0.259657
$737$	−1.54341	−0.0568522
$738$	−0.151787	−0.00558734
$739$	19.2926	0.709688	0.354844	−	0.934925i	$-0.384534\pi$
$739$	19.2926	0.709688	0.354844	+	0.934925i	$0.384534\pi$
$740$	−69.2643	−2.54621
$741$	−3.98805	−0.146505
$742$	0	0
$743$	−4.09248	−0.150138	−0.0750692	−	0.997178i	$-0.523918\pi$
$743$	−4.09248	−0.150138	−0.0750692	+	0.997178i	$0.523918\pi$
$744$	−7.39920	−0.271268
$745$	12.9827	0.475648
$746$	−5.11547	−0.187291
$747$	4.41493	0.161534
$748$	−19.4246	−0.710233
$749$	0	0
$750$	1.81473	0.0662646
$751$	−36.3681	−1.32709	−0.663546	−	0.748136i	$-0.730949\pi$
$751$	−36.3681	−1.32709	−0.663546	+	0.748136i	$0.730949\pi$
$752$	32.2868	1.17738
$753$	21.8112	0.794843
$754$	−6.28942	−0.229047
$755$	49.4423	1.79939
$756$	0	0
$757$	−17.7179	−0.643968	−0.321984	−	0.946745i	$-0.604350\pi$
$757$	−17.7179	−0.643968	−0.321984	+	0.946745i	$0.604350\pi$
$758$	8.37544	0.304210
$759$	5.05281	0.183405
$760$	−3.57941	−0.129839
$761$	33.4435	1.21232	0.606162	−	0.795341i	$-0.292708\pi$
$761$	33.4435	1.21232	0.606162	+	0.795341i	$0.292708\pi$
$762$	6.39085	0.231516
$763$	0	0
$764$	−2.62595	−0.0950034
$765$	−22.5049	−0.813668
$766$	−3.76635	−0.136084
$767$	−25.7506	−0.929801
$768$	−14.6786	−0.529667
$769$	−39.2814	−1.41652	−0.708262	−	0.705949i	$-0.750521\pi$
$769$	−39.2814	−1.41652	−0.708262	+	0.705949i	$0.750521\pi$
$770$	0	0
$771$	−42.0633	−1.51487
$772$	−53.2237	−1.91556
$773$	45.5487	1.63827	0.819136	−	0.573599i	$-0.194453\pi$
$773$	45.5487	1.63827	0.819136	+	0.573599i	$0.194453\pi$
$774$	−0.787019	−0.0282888
$775$	−32.0869	−1.15260
$776$	15.9124	0.571222
$777$	0	0
$778$	0.0990038	0.00354946
$779$	−0.539323	−0.0193233
$780$	25.9780	0.930162
$781$	17.3664	0.621419
$782$	−3.93414	−0.140684
$783$	46.2646	1.65336
$784$	0	0
$785$	−29.8845	−1.06663
$786$	1.28316	0.0457689
$787$	7.78709	0.277580	0.138790	−	0.990322i	$-0.455679\pi$
$787$	7.78709	0.277580	0.138790	+	0.990322i	$0.455679\pi$
$788$	−20.2305	−0.720682
$789$	7.06180	0.251407
$790$	−0.631027	−0.0224509
$791$	0	0
$792$	−1.74611	−0.0620452
$793$	18.2798	0.649136
$794$	−5.46151	−0.193822
$795$	12.8195	0.454660
$796$	−12.0249	−0.426213
$797$	−23.1468	−0.819903	−0.409951	−	0.912107i	$-0.634454\pi$
$797$	−23.1468	−0.819903	−0.409951	+	0.912107i	$0.634454\pi$
$798$	0	0
$799$	−57.7155	−2.04183
$800$	19.7877	0.699601
$801$	−4.21691	−0.148997
$802$	7.08276	0.250101
$803$	4.84407	0.170944
$804$	2.63362	0.0928805
$805$	0	0
$806$	3.84071	0.135283
$807$	5.05318	0.177881
$808$	−13.3659	−0.470212
$809$	8.18092	0.287626	0.143813	−	0.989605i	$-0.454064\pi$
$809$	8.18092	0.287626	0.143813	+	0.989605i	$0.454064\pi$
$810$	4.35634	0.153066
$811$	11.5745	0.406437	0.203218	−	0.979133i	$-0.434860\pi$
$811$	11.5745	0.406437	0.203218	+	0.979133i	$0.434860\pi$
$812$	0	0
$813$	11.4565	0.401797
$814$	4.52977	0.158769
$815$	−42.2254	−1.47909
$816$	31.8476	1.11489
$817$	−2.79641	−0.0978340
$818$	−0.0200369	−0.000700574 0
$819$	0	0
$820$	3.51314	0.122684
$821$	23.3664	0.815493	0.407746	−	0.913095i	$-0.366315\pi$
$821$	23.3664	0.815493	0.407746	+	0.913095i	$0.366315\pi$
$822$	−0.661447	−0.0230706
$823$	−10.9605	−0.382060	−0.191030	−	0.981584i	$-0.561183\pi$
$823$	−10.9605	−0.382060	−0.191030	+	0.981584i	$0.561183\pi$
$824$	4.32457	0.150653
$825$	14.1935	0.494154
$826$	0	0
$827$	−26.1767	−0.910254	−0.455127	−	0.890427i	$-0.650406\pi$
$827$	−26.1767	−0.910254	−0.455127	+	0.890427i	$0.650406\pi$
$828$	4.59969	0.159850
$829$	31.5098	1.09438	0.547190	−	0.837009i	$-0.315698\pi$
$829$	31.5098	1.09438	0.547190	+	0.837009i	$0.315698\pi$
$830$	3.85548	0.133826
$831$	17.7657	0.616287
$832$	17.9838	0.623476
$833$	0	0
$834$	−7.35304	−0.254615
$835$	8.69883	0.301035
$836$	−3.04466	−0.105302
$837$	−28.2520	−0.976533
$838$	−4.04261	−0.139650
$839$	−12.9797	−0.448109	−0.224054	−	0.974577i	$-0.571929\pi$
$839$	−12.9797	−0.448109	−0.224054	+	0.974577i	$0.571929\pi$
$840$	0	0
$841$	37.9120	1.30731
$842$	3.89152	0.134111
$843$	−16.2770	−0.560610
$844$	47.2953	1.62797
$845$	16.4607	0.566265
$846$	−2.54604	−0.0875346
$847$	0	0
$848$	9.67819	0.332350
$849$	30.4541	1.04518
$850$	−11.0511	−0.379050
$851$	−24.3154	−0.833522
$852$	−29.6334	−1.01522
$853$	−27.5739	−0.944114	−0.472057	−	0.881568i	$-0.656488\pi$
$853$	−27.5739	−0.944114	−0.472057	+	0.881568i	$0.656488\pi$
$854$	0	0
$855$	−3.52749	−0.120638
$856$	−5.27976	−0.180459
$857$	−17.8109	−0.608410	−0.304205	−	0.952607i	$-0.598391\pi$
$857$	−17.8109	−0.608410	−0.304205	+	0.952607i	$0.598391\pi$
$858$	−1.69892	−0.0580002
$859$	8.87343	0.302758	0.151379	−	0.988476i	$-0.451629\pi$
$859$	8.87343	0.302758	0.151379	+	0.988476i	$0.451629\pi$
$860$	18.2157	0.621152
$861$	0	0
$862$	6.05798	0.206336
$863$	−50.1569	−1.70736	−0.853680	−	0.520799i	$-0.825634\pi$
$863$	−50.1569	−1.70736	−0.853680	+	0.520799i	$0.825634\pi$
$864$	17.4228	0.592734
$865$	−9.28960	−0.315856
$866$	3.22790	0.109688
$867$	−33.1528	−1.12593
$868$	0	0
$869$	−1.09376	−0.0371033
$870$	10.4278	0.353535
$871$	−2.78565	−0.0943881
$872$	−11.5599	−0.391467
$873$	15.6816	0.530741
$874$	−0.616648	−0.0208584
$875$	0	0
$876$	−8.26576	−0.279274
$877$	11.0522	0.373207	0.186603	−	0.982435i	$-0.440252\pi$
$877$	11.0522	0.373207	0.186603	+	0.982435i	$0.440252\pi$
$878$	2.13601	0.0720867
$879$	−1.18965	−0.0401260
$880$	19.0563	0.642389
$881$	−24.5640	−0.827581	−0.413791	−	0.910372i	$-0.635795\pi$
$881$	−24.5640	−0.827581	−0.413791	+	0.910372i	$0.635795\pi$
$882$	0	0
$883$	−37.3221	−1.25599	−0.627994	−	0.778219i	$-0.716124\pi$
$883$	−37.3221	−1.25599	−0.627994	+	0.778219i	$0.716124\pi$
$884$	−35.0588	−1.17916
$885$	42.6942	1.43515
$886$	8.36300	0.280961
$887$	15.7383	0.528439	0.264220	−	0.964463i	$-0.414886\pi$
$887$	15.7383	0.528439	0.264220	+	0.964463i	$0.414886\pi$
$888$	−15.7505	−0.528553
$889$	0	0
$890$	−3.68255	−0.123439
$891$	7.55086	0.252963
$892$	−30.0278	−1.00541
$893$	−9.04650	−0.302729
$894$	1.44878	0.0484545
$895$	−17.6113	−0.588679
$896$	0	0
$897$	9.11966	0.304497
$898$	4.68368	0.156296
$899$	−40.8606	−1.36278
$900$	12.9207	0.430690
$901$	−17.3006	−0.576367
$902$	−0.229754	−0.00764996
$903$	0	0
$904$	19.6620	0.653949
$905$	7.61072	0.252989
$906$	5.51745	0.183305
$907$	−18.3306	−0.608659	−0.304329	−	0.952567i	$-0.598432\pi$
$907$	−18.3306	−0.608659	−0.304329	+	0.952567i	$0.598432\pi$
$908$	−19.7725	−0.656172
$909$	−13.1720	−0.436889
$910$	0	0
$911$	50.2669	1.66542	0.832708	−	0.553712i	$-0.186789\pi$
$911$	50.2669	1.66542	0.832708	+	0.553712i	$0.186789\pi$
$912$	4.99189	0.165298
$913$	6.68271	0.221165
$914$	−0.831228	−0.0274946
$915$	−30.3077	−1.00194
$916$	−40.2910	−1.33125
$917$	0	0
$918$	−9.73034	−0.321149
$919$	−41.4268	−1.36655	−0.683273	−	0.730163i	$-0.739444\pi$
$919$	−41.4268	−1.36655	−0.683273	+	0.730163i	$0.739444\pi$
$920$	8.18522	0.269859
$921$	−30.6230	−1.00906
$922$	10.7643	0.354504
$923$	31.3441	1.03170
$924$	0	0
$925$	−68.3028	−2.24578
$926$	6.93249	0.227816
$927$	4.26183	0.139977
$928$	25.1984	0.827177
$929$	−47.5742	−1.56086	−0.780429	−	0.625244i	$-0.784999\pi$
$929$	−47.5742	−1.56086	−0.780429	+	0.625244i	$0.784999\pi$
$930$	−6.36785	−0.208810
$931$	0	0
$932$	−15.3995	−0.504428
$933$	−2.68522	−0.0879102
$934$	5.18940	0.169802
$935$	−34.0649	−1.11404
$936$	−3.15149	−0.103010
$937$	−23.8222	−0.778239	−0.389119	−	0.921187i	$-0.627221\pi$
$937$	−23.8222	−0.778239	−0.389119	+	0.921187i	$0.627221\pi$
$938$	0	0
$939$	14.4454	0.471408
$940$	58.9286	1.92204
$941$	22.0786	0.719743	0.359871	−	0.933002i	$-0.382821\pi$
$941$	22.0786	0.719743	0.359871	+	0.933002i	$0.382821\pi$
$942$	−3.33492	−0.108658
$943$	1.23330	0.0401617
$944$	32.2324	1.04908
$945$	0	0
$946$	−1.19128	−0.0387319
$947$	15.6653	0.509053	0.254527	−	0.967066i	$-0.418080\pi$
$947$	15.6653	0.509053	0.254527	+	0.967066i	$0.418080\pi$
$948$	1.86636	0.0606164
$949$	8.74292	0.283807
$950$	−1.73218	−0.0561995
$951$	−23.7187	−0.769130
$952$	0	0
$953$	−9.89901	−0.320660	−0.160330	−	0.987063i	$-0.551256\pi$
$953$	−9.89901	−0.320660	−0.160330	+	0.987063i	$0.551256\pi$
$954$	−0.763192	−0.0247092
$955$	−4.60512	−0.149018
$956$	−36.2790	−1.17335
$957$	18.0745	0.584266
$958$	−5.96704	−0.192786
$959$	0	0
$960$	−29.8169	−0.962337
$961$	−6.04796	−0.195096
$962$	8.17565	0.263593
$963$	−5.20317	−0.167670
$964$	−23.3390	−0.751698
$965$	−93.3384	−3.00467
$966$	0	0
$967$	16.7558	0.538830	0.269415	−	0.963024i	$-0.413170\pi$
$967$	16.7558	0.538830	0.269415	+	0.963024i	$0.413170\pi$
$968$	9.00640	0.289477
$969$	−8.92345	−0.286662
$970$	13.6944	0.439702
$971$	−43.6184	−1.39978	−0.699891	−	0.714250i	$-0.746768\pi$
$971$	−43.6184	−1.39978	−0.699891	+	0.714250i	$0.746768\pi$
$972$	19.8167	0.635620
$973$	0	0
$974$	−1.41911	−0.0454712
$975$	25.6174	0.820414
$976$	−22.8811	−0.732406
$977$	−56.5875	−1.81040	−0.905198	−	0.424991i	$-0.860277\pi$
$977$	−56.5875	−1.81040	−0.905198	+	0.424991i	$0.860277\pi$
$978$	−4.71208	−0.150676
$979$	−6.38298	−0.204001
$980$	0	0
$981$	−11.3922	−0.363724
$982$	−4.25666	−0.135835
$983$	−5.55415	−0.177150	−0.0885750	−	0.996070i	$-0.528231\pi$
$983$	−5.55415	−0.177150	−0.0885750	+	0.996070i	$0.528231\pi$
$984$	0.798879	0.0254673
$985$	−35.4782	−1.13043
$986$	−14.0729	−0.448172
$987$	0	0
$988$	−5.49522	−0.174826
$989$	6.39469	0.203339
$990$	−1.50272	−0.0477597
$991$	−12.9285	−0.410687	−0.205343	−	0.978690i	$-0.565831\pi$
$991$	−12.9285	−0.410687	−0.205343	+	0.978690i	$0.565831\pi$
$992$	−15.3877	−0.488559
$993$	23.0904	0.732753
$994$	0	0
$995$	−21.0881	−0.668539
$996$	−11.4031	−0.361322
$997$	−12.2253	−0.387179	−0.193589	−	0.981083i	$-0.562013\pi$
$997$	−12.2253	−0.387179	−0.193589	+	0.981083i	$0.562013\pi$
$998$	2.15694	0.0682768
$999$	−60.1396	−1.90273

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.a.o.1.4		7
3.2	odd	2		8379.2.a.ck.1.4		7
7.2	even	3		931.2.f.p.704.4		14
7.3	odd	6		133.2.f.d.58.4	yes	14
7.4	even	3		931.2.f.p.324.4		14
7.5	odd	6		133.2.f.d.39.4	✓	14
7.6	odd	2		931.2.a.n.1.4		7
21.5	even	6		1197.2.j.l.172.4		14
21.17	even	6		1197.2.j.l.856.4		14
21.20	even	2		8379.2.a.cl.1.4		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.2.f.d.39.4	✓	14	7.5	odd	6
133.2.f.d.58.4	yes	14	7.3	odd	6
931.2.a.n.1.4		7	7.6	odd	2
931.2.a.o.1.4		7	1.1	even	1	trivial
931.2.f.p.324.4		14	7.4	even	3
931.2.f.p.704.4		14	7.2	even	3
1197.2.j.l.172.4		14	21.5	even	6
1197.2.j.l.856.4		14	21.17	even	6
8379.2.a.ck.1.4		7	3.2	odd	2
8379.2.a.cl.1.4		7	21.20	even	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:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	931.a (trivial)

\(f(q)\)	\(=\)	\(q+0.269662 q^{2} -1.39869 q^{3} -1.92728 q^{4} -3.37987 q^{5} -0.377172 q^{6} -1.05904 q^{8} -1.04367 q^{9} +O(q^{10})\)	\(q+0.269662 q^{2} -1.39869 q^{3} -1.92728 q^{4} -3.37987 q^{5} -0.377172 q^{6} -1.05904 q^{8} -1.04367 q^{9} -0.911422 q^{10} -1.57977 q^{11} +2.69567 q^{12} -2.85128 q^{13} +4.72739 q^{15} +3.56898 q^{16} -6.37987 q^{17} -0.281439 q^{18} -1.00000 q^{19} +6.51397 q^{20} -0.426004 q^{22} +2.28675 q^{23} +1.48126 q^{24} +6.42355 q^{25} -0.768880 q^{26} +5.65584 q^{27} +8.17998 q^{29} +1.27479 q^{30} -4.99520 q^{31} +3.08049 q^{32} +2.20960 q^{33} -1.72041 q^{34} +2.01146 q^{36} -10.6332 q^{37} -0.269662 q^{38} +3.98805 q^{39} +3.57941 q^{40} +0.539323 q^{41} +2.79641 q^{43} +3.04466 q^{44} +3.52749 q^{45} +0.616648 q^{46} +9.04650 q^{47} -4.99189 q^{48} +1.73218 q^{50} +8.92345 q^{51} +5.49522 q^{52} +2.71175 q^{53} +1.52516 q^{54} +5.33943 q^{55} +1.39869 q^{57} +2.20583 q^{58} +9.03126 q^{59} -9.11101 q^{60} -6.41110 q^{61} -1.34701 q^{62} -6.30728 q^{64} +9.63696 q^{65} +0.595846 q^{66} +0.976982 q^{67} +12.2958 q^{68} -3.19845 q^{69} -10.9930 q^{71} +1.10529 q^{72} -3.06631 q^{73} -2.86736 q^{74} -8.98453 q^{75} +1.92728 q^{76} +1.07542 q^{78} +0.692355 q^{79} -12.0627 q^{80} -4.77972 q^{81} +0.145435 q^{82} -4.23017 q^{83} +21.5632 q^{85} +0.754085 q^{86} -11.4412 q^{87} +1.67304 q^{88} +4.04045 q^{89} +0.951228 q^{90} -4.40721 q^{92} +6.98672 q^{93} +2.43949 q^{94} +3.37987 q^{95} -4.30864 q^{96} -15.0254 q^{97} +1.64877 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 2 q^{2} + 2 q^{3} + 10 q^{4} + 2 q^{5} + 4 q^{6} + 12 q^{8} + 15 q^{9}+O(q^{10}) \) 7 * q + 2 * q^2 + 2 * q^3 + 10 * q^4 + 2 * q^5 + 4 * q^6 + 12 * q^8 + 15 * q^9	\( 7 q + 2 q^{2} + 2 q^{3} + 10 q^{4} + 2 q^{5} + 4 q^{6} + 12 q^{8} + 15 q^{9} + 7 q^{11} + 22 q^{12} - 6 q^{13} + 2 q^{15} + 24 q^{16} - 19 q^{17} - 12 q^{18} - 7 q^{19} + 8 q^{20} - 6 q^{22} - q^{23} - 20 q^{24} - 3 q^{25} - 12 q^{26} + 14 q^{27} + 24 q^{29} - 20 q^{30} + 26 q^{32} + 14 q^{33} - 6 q^{34} + 46 q^{36} + 8 q^{37} - 2 q^{38} + 16 q^{39} + 10 q^{40} + 4 q^{41} + 4 q^{43} + 26 q^{44} - 14 q^{45} - 16 q^{46} - 5 q^{47} + 28 q^{48} + 16 q^{50} - 4 q^{51} - 42 q^{52} + 20 q^{53} + 24 q^{54} + 30 q^{55} - 2 q^{57} + 16 q^{59} - 44 q^{60} - 5 q^{61} - 24 q^{62} + 32 q^{64} + 26 q^{65} - 68 q^{66} - 4 q^{67} - 22 q^{68} + 36 q^{69} + 12 q^{71} - 3 q^{73} - 4 q^{74} - 18 q^{75} - 10 q^{76} - 14 q^{78} - 20 q^{79} + 4 q^{80} + 27 q^{81} + 48 q^{82} + 11 q^{83} + 26 q^{85} + 36 q^{86} + 16 q^{87} - 32 q^{88} + 10 q^{89} - 32 q^{90} - 30 q^{92} - 4 q^{93} - 16 q^{94} - 2 q^{95} + 12 q^{96} + 4 q^{97} + 15 q^{99}+O(q^{100}) \) 7 * q + 2 * q^2 + 2 * q^3 + 10 * q^4 + 2 * q^5 + 4 * q^6 + 12 * q^8 + 15 * q^9 + 7 * q^11 + 22 * q^12 - 6 * q^13 + 2 * q^15 + 24 * q^16 - 19 * q^17 - 12 * q^18 - 7 * q^19 + 8 * q^20 - 6 * q^22 - q^23 - 20 * q^24 - 3 * q^25 - 12 * q^26 + 14 * q^27 + 24 * q^29 - 20 * q^30 + 26 * q^32 + 14 * q^33 - 6 * q^34 + 46 * q^36 + 8 * q^37 - 2 * q^38 + 16 * q^39 + 10 * q^40 + 4 * q^41 + 4 * q^43 + 26 * q^44 - 14 * q^45 - 16 * q^46 - 5 * q^47 + 28 * q^48 + 16 * q^50 - 4 * q^51 - 42 * q^52 + 20 * q^53 + 24 * q^54 + 30 * q^55 - 2 * q^57 + 16 * q^59 - 44 * q^60 - 5 * q^61 - 24 * q^62 + 32 * q^64 + 26 * q^65 - 68 * q^66 - 4 * q^67 - 22 * q^68 + 36 * q^69 + 12 * q^71 - 3 * q^73 - 4 * q^74 - 18 * q^75 - 10 * q^76 - 14 * q^78 - 20 * q^79 + 4 * q^80 + 27 * q^81 + 48 * q^82 + 11 * q^83 + 26 * q^85 + 36 * q^86 + 16 * q^87 - 32 * q^88 + 10 * q^89 - 32 * q^90 - 30 * q^92 - 4 * q^93 - 16 * q^94 - 2 * q^95 + 12 * q^96 + 4 * q^97 + 15 * q^99

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