LMFDB - Embedded newform 931.2.a.o.1.5

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			1.5
Root			$2.27137$ 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)

$f(q)$	$=$	$q+1.13506 q^{2} +2.19453 q^{3} -0.711632 q^{4} +1.83111 q^{5} +2.49093 q^{6} -3.07787 q^{8} +1.81594 q^{9} +O(q^{10})$	\(q+1.13506 q^{2} +2.19453 q^{3} -0.711632 q^{4} +1.83111 q^{5} +2.49093 q^{6} -3.07787 q^{8} +1.81594 q^{9} +2.07842 q^{10} +4.13788 q^{11} -1.56170 q^{12} +4.73726 q^{13} +4.01841 q^{15} -2.07032 q^{16} -1.16889 q^{17} +2.06121 q^{18} -1.00000 q^{19} -1.30307 q^{20} +4.69676 q^{22} -0.834902 q^{23} -6.75447 q^{24} -1.64705 q^{25} +5.37709 q^{26} -2.59844 q^{27} +3.47567 q^{29} +4.56115 q^{30} -7.88792 q^{31} +3.80581 q^{32} +9.08069 q^{33} -1.32677 q^{34} -1.29228 q^{36} +9.51182 q^{37} -1.13506 q^{38} +10.3961 q^{39} -5.63591 q^{40} +2.27013 q^{41} +8.77566 q^{43} -2.94465 q^{44} +3.32519 q^{45} -0.947667 q^{46} -4.49711 q^{47} -4.54336 q^{48} -1.86951 q^{50} -2.56517 q^{51} -3.37119 q^{52} -7.62095 q^{53} -2.94939 q^{54} +7.57690 q^{55} -2.19453 q^{57} +3.94511 q^{58} -3.26159 q^{59} -2.85963 q^{60} -7.85276 q^{61} -8.95328 q^{62} +8.46046 q^{64} +8.67443 q^{65} +10.3072 q^{66} -11.7522 q^{67} +0.831823 q^{68} -1.83221 q^{69} -8.72597 q^{71} -5.58925 q^{72} -7.69908 q^{73} +10.7965 q^{74} -3.61450 q^{75} +0.711632 q^{76} +11.8002 q^{78} -6.90625 q^{79} -3.79097 q^{80} -11.1502 q^{81} +2.57674 q^{82} +15.0920 q^{83} -2.14037 q^{85} +9.96093 q^{86} +7.62745 q^{87} -12.7359 q^{88} -3.40801 q^{89} +3.77430 q^{90} +0.594143 q^{92} -17.3102 q^{93} -5.10451 q^{94} -1.83111 q^{95} +8.35195 q^{96} -3.04535 q^{97} +7.51417 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.13506	0.802611	0.401305	−	0.915944i	$-0.368557\pi$
$2$	1.13506	0.802611	0.401305	+	0.915944i	$0.368557\pi$
$3$	2.19453	1.26701	0.633505	−	0.773738i	$-0.281616\pi$
$3$	2.19453	1.26701	0.633505	+	0.773738i	$0.281616\pi$
$4$	−0.711632	−0.355816
$5$	1.83111	0.818895	0.409448	−	0.912334i	$-0.365721\pi$
$5$	1.83111	0.818895	0.409448	+	0.912334i	$0.365721\pi$
$6$	2.49093	1.01692
$7$	0	0
$7$	0	0
$8$	−3.07787	−1.08819
$9$	1.81594	0.605315
$10$	2.07842	0.657254
$11$	4.13788	1.24762	0.623809	−	0.781576i	$-0.285584\pi$
$11$	4.13788	1.24762	0.623809	+	0.781576i	$0.285584\pi$
$12$	−1.56170	−0.450823
$13$	4.73726	1.31388	0.656940	−	0.753943i	$-0.271850\pi$
$13$	4.73726	1.31388	0.656940	+	0.753943i	$0.271850\pi$
$14$	0	0
$15$	4.01841	1.03755
$16$	−2.07032	−0.517579
$17$	−1.16889	−0.283498	−0.141749	−	0.989903i	$-0.545273\pi$
$17$	−1.16889	−0.283498	−0.141749	+	0.989903i	$0.545273\pi$
$18$	2.06121	0.485832
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−1.30307	−0.291376
$21$	0	0
$22$	4.69676	1.00135
$23$	−0.834902	−0.174089	−0.0870446	−	0.996204i	$-0.527742\pi$
$23$	−0.834902	−0.174089	−0.0870446	+	0.996204i	$0.527742\pi$
$24$	−6.75447	−1.37875
$25$	−1.64705	−0.329410
$26$	5.37709	1.05453
$27$	−2.59844	−0.500070
$28$	0	0
$29$	3.47567	0.645416	0.322708	−	0.946499i	$-0.395407\pi$
$29$	3.47567	0.645416	0.322708	+	0.946499i	$0.395407\pi$
$30$	4.56115	0.832748
$31$	−7.88792	−1.41671	−0.708356	−	0.705856i	$-0.750563\pi$
$31$	−7.88792	−1.41671	−0.708356	+	0.705856i	$0.750563\pi$
$32$	3.80581	0.672778
$33$	9.08069	1.58075
$34$	−1.32677	−0.227539
$35$	0	0
$36$	−1.29228	−0.215381
$37$	9.51182	1.56373	0.781867	−	0.623446i	$-0.214268\pi$
$37$	9.51182	1.56373	0.781867	+	0.623446i	$0.214268\pi$
$38$	−1.13506	−0.184132
$39$	10.3961	1.66470
$40$	−5.63591	−0.891116
$41$	2.27013	0.354534	0.177267	−	0.984163i	$-0.443274\pi$
$41$	2.27013	0.354534	0.177267	+	0.984163i	$0.443274\pi$
$42$	0	0
$43$	8.77566	1.33828	0.669138	−	0.743138i	$-0.266663\pi$
$43$	8.77566	1.33828	0.669138	+	0.743138i	$0.266663\pi$
$44$	−2.94465	−0.443923
$45$	3.32519	0.495690
$46$	−0.947667	−0.139726
$47$	−4.49711	−0.655972	−0.327986	−	0.944683i	$-0.606370\pi$
$47$	−4.49711	−0.655972	−0.327986	+	0.944683i	$0.606370\pi$
$48$	−4.54336	−0.655778
$49$	0	0
$50$	−1.86951	−0.264388
$51$	−2.56517	−0.359195
$52$	−3.37119	−0.467500
$53$	−7.62095	−1.04682	−0.523409	−	0.852082i	$-0.675340\pi$
$53$	−7.62095	−1.04682	−0.523409	+	0.852082i	$0.675340\pi$
$54$	−2.94939	−0.401361
$55$	7.57690	1.02167
$56$	0	0
$57$	−2.19453	−0.290672
$58$	3.94511	0.518018
$59$	−3.26159	−0.424623	−0.212312	−	0.977202i	$-0.568099\pi$
$59$	−3.26159	−0.424623	−0.212312	+	0.977202i	$0.568099\pi$
$60$	−2.85963	−0.369177
$61$	−7.85276	−1.00544	−0.502722	−	0.864448i	$-0.667668\pi$
$61$	−7.85276	−1.00544	−0.502722	+	0.864448i	$0.667668\pi$
$62$	−8.95328	−1.13707
$63$	0	0
$64$	8.46046	1.05756
$65$	8.67443	1.07593
$66$	10.3072	1.26872
$67$	−11.7522	−1.43577	−0.717883	−	0.696164i	$-0.754889\pi$
$67$	−11.7522	−1.43577	−0.717883	+	0.696164i	$0.754889\pi$
$68$	0.831823	0.100873
$69$	−1.83221	−0.220573
$70$	0	0
$71$	−8.72597	−1.03558	−0.517791	−	0.855507i	$-0.673246\pi$
$71$	−8.72597	−1.03558	−0.517791	+	0.855507i	$0.673246\pi$
$72$	−5.58925	−0.658699
$73$	−7.69908	−0.901109	−0.450555	−	0.892749i	$-0.648774\pi$
$73$	−7.69908	−0.901109	−0.450555	+	0.892749i	$0.648774\pi$
$74$	10.7965	1.25507
$75$	−3.61450	−0.417366
$76$	0.711632	0.0816298
$77$	0	0
$78$	11.8002	1.33611
$79$	−6.90625	−0.777014	−0.388507	−	0.921446i	$-0.627009\pi$
$79$	−6.90625	−0.777014	−0.388507	+	0.921446i	$0.627009\pi$
$80$	−3.79097	−0.423843
$81$	−11.1502	−1.23891
$82$	2.57674	0.284553
$83$	15.0920	1.65656	0.828280	−	0.560315i	$-0.189320\pi$
$83$	15.0920	1.65656	0.828280	+	0.560315i	$0.189320\pi$
$84$	0	0
$85$	−2.14037	−0.232156
$86$	9.96093	1.07411
$87$	7.62745	0.817749
$88$	−12.7359	−1.35765
$89$	−3.40801	−0.361248	−0.180624	−	0.983552i	$-0.557812\pi$
$89$	−3.40801	−0.361248	−0.180624	+	0.983552i	$0.557812\pi$
$90$	3.77430	0.397846
$91$	0	0
$92$	0.594143	0.0619437
$93$	−17.3102	−1.79499
$94$	−5.10451	−0.526490
$95$	−1.83111	−0.187868
$96$	8.35195	0.852417
$97$	−3.04535	−0.309209	−0.154604	−	0.987976i	$-0.549410\pi$
$97$	−3.04535	−0.309209	−0.154604	+	0.987976i	$0.549410\pi$
$98$	0	0
$99$	7.51417	0.755202
$100$	1.17209	0.117209
$101$	−11.9906	−1.19311	−0.596557	−	0.802571i	$-0.703465\pi$
$101$	−11.9906	−1.19311	−0.596557	+	0.802571i	$0.703465\pi$
$102$	−2.91163	−0.288294
$103$	14.4675	1.42553	0.712764	−	0.701404i	$-0.247443\pi$
$103$	14.4675	1.42553	0.712764	+	0.701404i	$0.247443\pi$
$104$	−14.5807	−1.42976
$105$	0	0
$106$	−8.65025	−0.840187
$107$	−4.64077	−0.448640	−0.224320	−	0.974516i	$-0.572016\pi$
$107$	−4.64077	−0.448640	−0.224320	+	0.974516i	$0.572016\pi$
$108$	1.84913	0.177933
$109$	7.76669	0.743914	0.371957	−	0.928250i	$-0.378687\pi$
$109$	7.76669	0.743914	0.371957	+	0.928250i	$0.378687\pi$
$110$	8.60026	0.820003
$111$	20.8739	1.98127
$112$	0	0
$113$	16.3900	1.54184	0.770921	−	0.636931i	$-0.219796\pi$
$113$	16.3900	1.54184	0.770921	+	0.636931i	$0.219796\pi$
$114$	−2.49093	−0.233297
$115$	−1.52879	−0.142561
$116$	−2.47340	−0.229649
$117$	8.60261	0.795312
$118$	−3.70211	−0.340807
$119$	0	0
$120$	−12.3682	−1.12905
$121$	6.12208	0.556553
$122$	−8.91338	−0.806980
$123$	4.98185	0.449198
$124$	5.61330	0.504089
$125$	−12.1715	−1.08865
$126$	0	0
$127$	−9.55496	−0.847866	−0.423933	−	0.905694i	$-0.639351\pi$
$127$	−9.55496	−0.847866	−0.423933	+	0.905694i	$0.639351\pi$
$128$	1.99154	0.176029
$129$	19.2584	1.69561
$130$	9.84603	0.863554
$131$	−20.1432	−1.75992	−0.879961	−	0.475046i	$-0.842431\pi$
$131$	−20.1432	−1.75992	−0.879961	+	0.475046i	$0.842431\pi$
$132$	−6.46211	−0.562455
$133$	0	0
$134$	−13.3395	−1.15236
$135$	−4.75802	−0.409505
$136$	3.59771	0.308501
$137$	−2.57311	−0.219835	−0.109918	−	0.993941i	$-0.535059\pi$
$137$	−2.57311	−0.219835	−0.109918	+	0.993941i	$0.535059\pi$
$138$	−2.07968	−0.177034
$139$	0.592800	0.0502806	0.0251403	−	0.999684i	$-0.491997\pi$
$139$	0.592800	0.0502806	0.0251403	+	0.999684i	$0.491997\pi$
$140$	0	0
$141$	−9.86903	−0.831123
$142$	−9.90453	−0.831170
$143$	19.6022	1.63922
$144$	−3.75958	−0.313298
$145$	6.36432	0.528528
$146$	−8.73894	−0.723240
$147$	0	0
$148$	−6.76892	−0.556402
$149$	14.5460	1.19165	0.595827	−	0.803113i	$-0.296824\pi$
$149$	14.5460	1.19165	0.595827	+	0.803113i	$0.296824\pi$
$150$	−4.10268	−0.334982
$151$	23.5597	1.91726	0.958632	−	0.284649i	$-0.0918769\pi$
$151$	23.5597	1.91726	0.958632	+	0.284649i	$0.0918769\pi$
$152$	3.07787	0.249648
$153$	−2.12265	−0.171606
$154$	0	0
$155$	−14.4436	−1.16014
$156$	−7.39816	−0.592327
$157$	−0.391072	−0.0312109	−0.0156055	−	0.999878i	$-0.504968\pi$
$157$	−0.391072	−0.0312109	−0.0156055	+	0.999878i	$0.504968\pi$
$158$	−7.83903	−0.623640
$159$	−16.7244	−1.32633
$160$	6.96884	0.550935
$161$	0	0
$162$	−12.6562	−0.994361
$163$	−4.73291	−0.370710	−0.185355	−	0.982672i	$-0.559343\pi$
$163$	−4.73291	−0.370710	−0.185355	+	0.982672i	$0.559343\pi$
$164$	−1.61549	−0.126149
$165$	16.6277	1.29447
$166$	17.1303	1.32957
$167$	−24.4555	−1.89242	−0.946212	−	0.323547i	$-0.895125\pi$
$167$	−24.4555	−1.89242	−0.946212	+	0.323547i	$0.895125\pi$
$168$	0	0
$169$	9.44167	0.726283
$170$	−2.42945	−0.186331
$171$	−1.81594	−0.138869
$172$	−6.24505	−0.476180
$173$	−9.56007	−0.726839	−0.363419	−	0.931626i	$-0.618391\pi$
$173$	−9.56007	−0.726839	−0.363419	+	0.931626i	$0.618391\pi$
$174$	8.65764	0.656334
$175$	0	0
$176$	−8.56672	−0.645741
$177$	−7.15765	−0.538002
$178$	−3.86831	−0.289942
$179$	4.05719	0.303249	0.151624	−	0.988438i	$-0.451550\pi$
$179$	4.05719	0.303249	0.151624	+	0.988438i	$0.451550\pi$
$180$	−2.36631	−0.176374
$181$	7.19110	0.534510	0.267255	−	0.963626i	$-0.413883\pi$
$181$	7.19110	0.534510	0.267255	+	0.963626i	$0.413883\pi$
$182$	0	0
$183$	−17.2331	−1.27391
$184$	2.56972	0.189442
$185$	17.4172	1.28053
$186$	−19.6482	−1.44068
$187$	−4.83675	−0.353698
$188$	3.20029	0.233405
$189$	0	0
$190$	−2.07842	−0.150784
$191$	−4.60668	−0.333328	−0.166664	−	0.986014i	$-0.553299\pi$
$191$	−4.60668	−0.333328	−0.166664	+	0.986014i	$0.553299\pi$
$192$	18.5667	1.33994
$193$	−18.7579	−1.35022	−0.675111	−	0.737717i	$-0.735904\pi$
$193$	−18.7579	−1.35022	−0.675111	+	0.737717i	$0.735904\pi$
$194$	−3.45667	−0.248174
$195$	19.0363	1.36322
$196$	0	0
$197$	2.23257	0.159064	0.0795321	−	0.996832i	$-0.474657\pi$
$197$	2.23257	0.159064	0.0795321	+	0.996832i	$0.474657\pi$
$198$	8.52905	0.606134
$199$	6.30872	0.447213	0.223607	−	0.974679i	$-0.428217\pi$
$199$	6.30872	0.447213	0.223607	+	0.974679i	$0.428217\pi$
$200$	5.06941	0.358462
$201$	−25.7906	−1.81913
$202$	−13.6101	−0.957606
$203$	0	0
$204$	1.82546	0.127808
$205$	4.15684	0.290326
$206$	16.4215	1.14414
$207$	−1.51614	−0.105379
$208$	−9.80763	−0.680037
$209$	−4.13788	−0.286223
$210$	0	0
$211$	19.2973	1.32848	0.664241	−	0.747519i	$-0.268755\pi$
$211$	19.2973	1.32848	0.664241	+	0.747519i	$0.268755\pi$
$212$	5.42331	0.372474
$213$	−19.1494	−1.31209
$214$	−5.26756	−0.360083
$215$	16.0692	1.09591
$216$	7.99767	0.544172
$217$	0	0
$218$	8.81569	0.597074
$219$	−16.8958	−1.14171
$220$	−5.39197	−0.363526
$221$	−5.53736	−0.372483
$222$	23.6932	1.59019
$223$	−1.58264	−0.105981	−0.0529906	−	0.998595i	$-0.516875\pi$
$223$	−1.58264	−0.105981	−0.0529906	+	0.998595i	$0.516875\pi$
$224$	0	0
$225$	−2.99095	−0.199397
$226$	18.6037	1.23750
$227$	−2.42883	−0.161207	−0.0806036	−	0.996746i	$-0.525685\pi$
$227$	−2.42883	−0.161207	−0.0806036	+	0.996746i	$0.525685\pi$
$228$	1.56170	0.103426
$229$	−2.80764	−0.185534	−0.0927669	−	0.995688i	$-0.529571\pi$
$229$	−2.80764	−0.185534	−0.0927669	+	0.995688i	$0.529571\pi$
$230$	−1.73528	−0.114421
$231$	0	0
$232$	−10.6977	−0.702337
$233$	22.1168	1.44892	0.724461	−	0.689316i	$-0.242089\pi$
$233$	22.1168	1.44892	0.724461	+	0.689316i	$0.242089\pi$
$234$	9.76450	0.638326
$235$	−8.23469	−0.537172
$236$	2.32105	0.151088
$237$	−15.1559	−0.984485
$238$	0	0
$239$	13.0161	0.841944	0.420972	−	0.907074i	$-0.361689\pi$
$239$	13.0161	0.841944	0.420972	+	0.907074i	$0.361689\pi$
$240$	−8.31938	−0.537013
$241$	11.4453	0.737254	0.368627	−	0.929577i	$-0.379828\pi$
$241$	11.4453	0.737254	0.368627	+	0.929577i	$0.379828\pi$
$242$	6.94895	0.446695
$243$	−16.6740	−1.06964
$244$	5.58828	0.357753
$245$	0	0
$246$	5.65471	0.360531
$247$	−4.73726	−0.301425
$248$	24.2780	1.54165
$249$	33.1197	2.09888
$250$	−13.8154	−0.873761
$251$	2.29536	0.144882	0.0724411	−	0.997373i	$-0.476921\pi$
$251$	2.29536	0.144882	0.0724411	+	0.997373i	$0.476921\pi$
$252$	0	0
$253$	−3.45473	−0.217197
$254$	−10.8455	−0.680506
$255$	−4.69710	−0.294144
$256$	−14.6604	−0.916275
$257$	12.9349	0.806857	0.403428	−	0.915011i	$-0.367818\pi$
$257$	12.9349	0.806857	0.403428	+	0.915011i	$0.367818\pi$
$258$	21.8595	1.36091
$259$	0	0
$260$	−6.17301	−0.382834
$261$	6.31163	0.390680
$262$	−22.8638	−1.41253
$263$	18.8105	1.15990	0.579951	−	0.814651i	$-0.303072\pi$
$263$	18.8105	1.15990	0.579951	+	0.814651i	$0.303072\pi$
$264$	−27.9492	−1.72016
$265$	−13.9548	−0.857234
$266$	0	0
$267$	−7.47897	−0.457705
$268$	8.36328	0.510868
$269$	3.19124	0.194573	0.0972866	−	0.995256i	$-0.468984\pi$
$269$	3.19124	0.194573	0.0972866	+	0.995256i	$0.468984\pi$
$270$	−5.40065	−0.328673
$271$	0.534528	0.0324703	0.0162351	−	0.999868i	$-0.494832\pi$
$271$	0.534528	0.0324703	0.0162351	+	0.999868i	$0.494832\pi$
$272$	2.41998	0.146733
$273$	0	0
$274$	−2.92064	−0.176442
$275$	−6.81531	−0.410978
$276$	1.30386	0.0784833
$277$	26.8067	1.61066	0.805328	−	0.592829i	$-0.201989\pi$
$277$	26.8067	1.61066	0.805328	+	0.592829i	$0.201989\pi$
$278$	0.672865	0.0403557
$279$	−14.3240	−0.857557
$280$	0	0
$281$	1.86099	0.111017	0.0555087	−	0.998458i	$-0.482322\pi$
$281$	1.86099	0.111017	0.0555087	+	0.998458i	$0.482322\pi$
$282$	−11.2020	−0.667068
$283$	−12.4410	−0.739543	−0.369771	−	0.929123i	$-0.620564\pi$
$283$	−12.4410	−0.739543	−0.369771	+	0.929123i	$0.620564\pi$
$284$	6.20968	0.368477
$285$	−4.01841	−0.238030
$286$	22.2498	1.31566
$287$	0	0
$288$	6.91114	0.407243
$289$	−15.6337	−0.919629
$290$	7.22391	0.424202
$291$	−6.68311	−0.391771
$292$	5.47891	0.320629
$293$	−4.08101	−0.238415	−0.119208	−	0.992869i	$-0.538035\pi$
$293$	−4.08101	−0.238415	−0.119208	+	0.992869i	$0.538035\pi$
$294$	0	0
$295$	−5.97232	−0.347722
$296$	−29.2762	−1.70164
$297$	−10.7520	−0.623897
$298$	16.5106	0.956434
$299$	−3.95515	−0.228732
$300$	2.57219	0.148506
$301$	0	0
$302$	26.7418	1.53882
$303$	−26.3138	−1.51169
$304$	2.07032	0.118741
$305$	−14.3792	−0.823353
$306$	−2.40934	−0.137733
$307$	13.6881	0.781223	0.390612	−	0.920556i	$-0.372264\pi$
$307$	13.6881	0.781223	0.390612	+	0.920556i	$0.372264\pi$
$308$	0	0
$309$	31.7494	1.80616
$310$	−16.3944	−0.931140
$311$	−13.0057	−0.737488	−0.368744	−	0.929531i	$-0.620212\pi$
$311$	−13.0057	−0.737488	−0.368744	+	0.929531i	$0.620212\pi$
$312$	−31.9977	−1.81151
$313$	1.65165	0.0933571	0.0466785	−	0.998910i	$-0.485136\pi$
$313$	1.65165	0.0933571	0.0466785	+	0.998910i	$0.485136\pi$
$314$	−0.443891	−0.0250502
$315$	0	0
$316$	4.91471	0.276474
$317$	35.0878	1.97073	0.985363	−	0.170471i	$-0.0545290\pi$
$317$	35.0878	1.97073	0.985363	+	0.170471i	$0.0545290\pi$
$318$	−18.9832	−1.06453
$319$	14.3819	0.805233
$320$	15.4920	0.866029
$321$	−10.1843	−0.568431
$322$	0	0
$323$	1.16889	0.0650390
$324$	7.93483	0.440824
$325$	−7.80252	−0.432806
$326$	−5.37215	−0.297536
$327$	17.0442	0.942547
$328$	−6.98716	−0.385801
$329$	0	0
$330$	18.8735	1.03895
$331$	−16.5046	−0.907174	−0.453587	−	0.891212i	$-0.649856\pi$
$331$	−16.5046	−0.907174	−0.453587	+	0.891212i	$0.649856\pi$
$332$	−10.7399	−0.589430
$333$	17.2729	0.946551
$334$	−27.7585	−1.51888
$335$	−21.5196	−1.17574
$336$	0	0
$337$	−10.0546	−0.547710	−0.273855	−	0.961771i	$-0.588299\pi$
$337$	−10.0546	−0.547710	−0.273855	+	0.961771i	$0.588299\pi$
$338$	10.7169	0.582922
$339$	35.9683	1.95353
$340$	1.52316	0.0826047
$341$	−32.6393	−1.76752
$342$	−2.06121	−0.111458
$343$	0	0
$344$	−27.0104	−1.45630
$345$	−3.35498	−0.180626
$346$	−10.8513	−0.583368
$347$	−27.7296	−1.48860	−0.744301	−	0.667845i	$-0.767217\pi$
$347$	−27.7296	−1.48860	−0.744301	+	0.667845i	$0.767217\pi$
$348$	−5.42794	−0.290968
$349$	−21.4865	−1.15014	−0.575072	−	0.818103i	$-0.695026\pi$
$349$	−21.4865	−1.15014	−0.575072	+	0.818103i	$0.695026\pi$
$350$	0	0
$351$	−12.3095	−0.657032
$352$	15.7480	0.839371
$353$	31.2690	1.66428	0.832140	−	0.554566i	$-0.187116\pi$
$353$	31.2690	1.66428	0.832140	+	0.554566i	$0.187116\pi$
$354$	−8.12438	−0.431806
$355$	−15.9782	−0.848034
$356$	2.42525	0.128538
$357$	0	0
$358$	4.60517	0.243391
$359$	−1.16328	−0.0613957	−0.0306979	−	0.999529i	$-0.509773\pi$
$359$	−1.16328	−0.0613957	−0.0306979	+	0.999529i	$0.509773\pi$
$360$	−10.2345	−0.539406
$361$	1.00000	0.0526316
$362$	8.16235	0.429004
$363$	13.4351	0.705158
$364$	0	0
$365$	−14.0978	−0.737914
$366$	−19.5606	−1.02245
$367$	10.6069	0.553675	0.276838	−	0.960917i	$-0.410714\pi$
$367$	10.6069	0.553675	0.276838	+	0.960917i	$0.410714\pi$
$368$	1.72851	0.0901049
$369$	4.12242	0.214605
$370$	19.7696	1.02777
$371$	0	0
$372$	12.3185	0.638686
$373$	0.424629	0.0219864	0.0109932	−	0.999940i	$-0.496501\pi$
$373$	0.424629	0.0219864	0.0109932	+	0.999940i	$0.496501\pi$
$374$	−5.49001	−0.283882
$375$	−26.7106	−1.37933
$376$	13.8415	0.713823
$377$	16.4652	0.848000
$378$	0	0
$379$	−0.337918	−0.0173577	−0.00867885	−	0.999962i	$-0.502763\pi$
$379$	−0.337918	−0.0173577	−0.00867885	+	0.999962i	$0.502763\pi$
$380$	1.30307	0.0668463
$381$	−20.9686	−1.07425
$382$	−5.22887	−0.267532
$383$	27.9380	1.42756	0.713782	−	0.700368i	$-0.246981\pi$
$383$	27.9380	1.42756	0.713782	+	0.700368i	$0.246981\pi$
$384$	4.37049	0.223031
$385$	0	0
$386$	−21.2914	−1.08370
$387$	15.9361	0.810079
$388$	2.16717	0.110021
$389$	30.8591	1.56462	0.782308	−	0.622892i	$-0.214042\pi$
$389$	30.8591	1.56462	0.782308	+	0.622892i	$0.214042\pi$
$390$	21.6074	1.09413
$391$	0.975912	0.0493540
$392$	0	0
$393$	−44.2048	−2.22984
$394$	2.53411	0.127667
$395$	−12.6461	−0.636293
$396$	−5.34732	−0.268713
$397$	−28.7758	−1.44422	−0.722109	−	0.691779i	$-0.756827\pi$
$397$	−28.7758	−1.44422	−0.722109	+	0.691779i	$0.756827\pi$
$398$	7.16079	0.358938
$399$	0	0
$400$	3.40991	0.170496
$401$	12.4489	0.621668	0.310834	−	0.950464i	$-0.399392\pi$
$401$	12.4489	0.621668	0.310834	+	0.950464i	$0.399392\pi$
$402$	−29.2740	−1.46005
$403$	−37.3671	−1.86139
$404$	8.53293	0.424529
$405$	−20.4172	−1.01454
$406$	0	0
$407$	39.3588	1.95094
$408$	7.89526	0.390874
$409$	−17.8715	−0.883689	−0.441845	−	0.897092i	$-0.645676\pi$
$409$	−17.8715	−0.883689	−0.441845	+	0.897092i	$0.645676\pi$
$410$	4.71828	0.233019
$411$	−5.64675	−0.278534
$412$	−10.2956	−0.507225
$413$	0	0
$414$	−1.72091	−0.0845781
$415$	27.6350	1.35655
$416$	18.0291	0.883950
$417$	1.30091	0.0637060
$418$	−4.69676	−0.229726
$419$	−20.2060	−0.987126	−0.493563	−	0.869710i	$-0.664306\pi$
$419$	−20.2060	−0.987126	−0.493563	+	0.869710i	$0.664306\pi$
$420$	0	0
$421$	7.33097	0.357290	0.178645	−	0.983914i	$-0.442829\pi$
$421$	7.33097	0.357290	0.178645	+	0.983914i	$0.442829\pi$
$422$	21.9037	1.06625
$423$	−8.16651	−0.397069
$424$	23.4563	1.13914
$425$	1.92523	0.0933873
$426$	−21.7358	−1.05310
$427$	0	0
$428$	3.30252	0.159633
$429$	43.0176	2.07691
$430$	18.2395	0.879588
$431$	−7.60358	−0.366252	−0.183126	−	0.983089i	$-0.558622\pi$
$431$	−7.60358	−0.366252	−0.183126	+	0.983089i	$0.558622\pi$
$432$	5.37959	0.258826
$433$	25.0990	1.20618	0.603092	−	0.797672i	$-0.293935\pi$
$433$	25.0990	1.20618	0.603092	+	0.797672i	$0.293935\pi$
$434$	0	0
$435$	13.9667	0.669651
$436$	−5.52703	−0.264697
$437$	0.834902	0.0399388
$438$	−19.1778	−0.916352
$439$	35.8632	1.71166	0.855829	−	0.517259i	$-0.173047\pi$
$439$	35.8632	1.71166	0.855829	+	0.517259i	$0.173047\pi$
$440$	−23.3207	−1.11177
$441$	0	0
$442$	−6.28525	−0.298959
$443$	29.1136	1.38323	0.691615	−	0.722266i	$-0.256899\pi$
$443$	29.1136	1.38323	0.691615	+	0.722266i	$0.256899\pi$
$444$	−14.8546	−0.704967
$445$	−6.24043	−0.295825
$446$	−1.79639	−0.0850617
$447$	31.9215	1.50984
$448$	0	0
$449$	−8.10596	−0.382544	−0.191272	−	0.981537i	$-0.561261\pi$
$449$	−8.10596	−0.382544	−0.191272	+	0.981537i	$0.561261\pi$
$450$	−3.39492	−0.160038
$451$	9.39352	0.442323
$452$	−11.6637	−0.548612
$453$	51.7024	2.42919
$454$	−2.75688	−0.129387
$455$	0	0
$456$	6.75447	0.316307
$457$	−12.2443	−0.572764	−0.286382	−	0.958115i	$-0.592453\pi$
$457$	−12.2443	−0.572764	−0.286382	+	0.958115i	$0.592453\pi$
$458$	−3.18684	−0.148911
$459$	3.03730	0.141769
$460$	1.08794	0.0507254
$461$	35.0498	1.63243	0.816216	−	0.577747i	$-0.196068\pi$
$461$	35.0498	1.63243	0.816216	+	0.577747i	$0.196068\pi$
$462$	0	0
$463$	28.8700	1.34170	0.670852	−	0.741591i	$-0.265929\pi$
$463$	28.8700	1.34170	0.670852	+	0.741591i	$0.265929\pi$
$464$	−7.19574	−0.334054
$465$	−31.6969	−1.46991
$466$	25.1040	1.16292
$467$	34.8463	1.61249	0.806247	−	0.591580i	$-0.201496\pi$
$467$	34.8463	1.61249	0.806247	+	0.591580i	$0.201496\pi$
$468$	−6.12189	−0.282985
$469$	0	0
$470$	−9.34689	−0.431140
$471$	−0.858217	−0.0395446
$472$	10.0388	0.462072
$473$	36.3127	1.66966
$474$	−17.2030	−0.790158
$475$	1.64705	0.0755719
$476$	0	0
$477$	−13.8392	−0.633654
$478$	14.7741	0.675753
$479$	18.8948	0.863326	0.431663	−	0.902035i	$-0.357927\pi$
$479$	18.8948	0.863326	0.431663	+	0.902035i	$0.357927\pi$
$480$	15.2933	0.698040
$481$	45.0600	2.05456
$482$	12.9911	0.591728
$483$	0	0
$484$	−4.35667	−0.198030
$485$	−5.57636	−0.253210
$486$	−18.9261	−0.858505
$487$	−0.314082	−0.0142324	−0.00711620	−	0.999975i	$-0.502265\pi$
$487$	−0.314082	−0.0142324	−0.00711620	+	0.999975i	$0.502265\pi$
$488$	24.1698	1.09412
$489$	−10.3865	−0.469693
$490$	0	0
$491$	37.2050	1.67904	0.839519	−	0.543330i	$-0.182837\pi$
$491$	37.2050	1.67904	0.839519	+	0.543330i	$0.182837\pi$
$492$	−3.54525	−0.159832
$493$	−4.06269	−0.182974
$494$	−5.37709	−0.241927
$495$	13.7592	0.618432
$496$	16.3305	0.733260
$497$	0	0
$498$	37.5930	1.68458
$499$	−30.3987	−1.36083	−0.680416	−	0.732826i	$-0.738201\pi$
$499$	−30.3987	−1.36083	−0.680416	+	0.732826i	$0.738201\pi$
$500$	8.66160	0.387358
$501$	−53.6683	−2.39772
$502$	2.60538	0.116284
$503$	12.1197	0.540390	0.270195	−	0.962806i	$-0.412912\pi$
$503$	12.1197	0.540390	0.270195	+	0.962806i	$0.412912\pi$
$504$	0	0
$505$	−21.9561	−0.977036
$506$	−3.92133	−0.174325
$507$	20.7200	0.920207
$508$	6.79962	0.301684
$509$	3.72098	0.164929	0.0824647	−	0.996594i	$-0.473721\pi$
$509$	3.72098	0.164929	0.0824647	+	0.996594i	$0.473721\pi$
$510$	−5.33150	−0.236083
$511$	0	0
$512$	−20.6236	−0.911441
$513$	2.59844	0.114724
$514$	14.6819	0.647592
$515$	26.4916	1.16736
$516$	−13.7049	−0.603325
$517$	−18.6085	−0.818402
$518$	0	0
$519$	−20.9798	−0.920912
$520$	−26.6988	−1.17082
$521$	−8.36054	−0.366282	−0.183141	−	0.983087i	$-0.558626\pi$
$521$	−8.36054	−0.366282	−0.183141	+	0.983087i	$0.558626\pi$
$522$	7.16410	0.313564
$523$	−13.5948	−0.594459	−0.297229	−	0.954806i	$-0.596063\pi$
$523$	−13.5948	−0.594459	−0.297229	+	0.954806i	$0.596063\pi$
$524$	14.3346	0.626209
$525$	0	0
$526$	21.3511	0.930950
$527$	9.22014	0.401636
$528$	−18.7999	−0.818161
$529$	−22.3029	−0.969693
$530$	−15.8395	−0.688025
$531$	−5.92287	−0.257031
$532$	0	0
$533$	10.7542	0.465816
$534$	−8.48910	−0.367359
$535$	−8.49774	−0.367389
$536$	36.1719	1.56239
$537$	8.90361	0.384219
$538$	3.62226	0.156167
$539$	0	0
$540$	3.38596	0.145708
$541$	−17.8176	−0.766038	−0.383019	−	0.923740i	$-0.625116\pi$
$541$	−17.8176	−0.766038	−0.383019	+	0.923740i	$0.625116\pi$
$542$	0.606723	0.0260610
$543$	15.7811	0.677230
$544$	−4.44859	−0.190732
$545$	14.2216	0.609188
$546$	0	0
$547$	−22.1622	−0.947587	−0.473793	−	0.880636i	$-0.657116\pi$
$547$	−22.1622	−0.947587	−0.473793	+	0.880636i	$0.657116\pi$
$548$	1.83111	0.0782210
$549$	−14.2602	−0.608610
$550$	−7.73580	−0.329856
$551$	−3.47567	−0.148069
$552$	5.63932	0.240026
$553$	0	0
$554$	30.4273	1.29273
$555$	38.2224	1.62245
$556$	−0.421855	−0.0178906
$557$	20.2402	0.857606	0.428803	−	0.903398i	$-0.358935\pi$
$557$	20.2402	0.857606	0.428803	+	0.903398i	$0.358935\pi$
$558$	−16.2587	−0.688284
$559$	41.5726	1.75834
$560$	0	0
$561$	−10.6144	−0.448139
$562$	2.11234	0.0891037
$563$	−37.3471	−1.57399	−0.786995	−	0.616959i	$-0.788364\pi$
$563$	−37.3471	−1.57399	−0.786995	+	0.616959i	$0.788364\pi$
$564$	7.02312	0.295727
$565$	30.0118	1.26261
$566$	−14.1214	−0.593565
$567$	0	0
$568$	26.8574	1.12691
$569$	5.01882	0.210400	0.105200	−	0.994451i	$-0.466452\pi$
$569$	5.01882	0.210400	0.105200	+	0.994451i	$0.466452\pi$
$570$	−4.56115	−0.191045
$571$	−11.1874	−0.468177	−0.234089	−	0.972215i	$-0.575211\pi$
$571$	−11.1874	−0.468177	−0.234089	+	0.972215i	$0.575211\pi$
$572$	−13.9496	−0.583262
$573$	−10.1095	−0.422329
$574$	0	0
$575$	1.37513	0.0573467
$576$	15.3637	0.640156
$577$	18.9610	0.789356	0.394678	−	0.918819i	$-0.370856\pi$
$577$	18.9610	0.789356	0.394678	+	0.918819i	$0.370856\pi$
$578$	−17.7452	−0.738104
$579$	−41.1646	−1.71074
$580$	−4.52906	−0.188059
$581$	0	0
$582$	−7.58575	−0.314439
$583$	−31.5346	−1.30603
$584$	23.6968	0.980580
$585$	15.7523	0.651277
$586$	−4.63221	−0.191355
$587$	−35.2670	−1.45562	−0.727812	−	0.685777i	$-0.759463\pi$
$587$	−35.2670	−1.45562	−0.727812	+	0.685777i	$0.759463\pi$
$588$	0	0
$589$	7.88792	0.325016
$590$	−6.77896	−0.279085
$591$	4.89944	0.201536
$592$	−19.6925	−0.809355
$593$	−16.0376	−0.658585	−0.329293	−	0.944228i	$-0.606810\pi$
$593$	−16.0376	−0.658585	−0.329293	+	0.944228i	$0.606810\pi$
$594$	−12.2042	−0.500746
$595$	0	0
$596$	−10.3514	−0.424010
$597$	13.8446	0.566624
$598$	−4.48935	−0.183583
$599$	4.77170	0.194966	0.0974831	−	0.995237i	$-0.468921\pi$
$599$	4.77170	0.194966	0.0974831	+	0.995237i	$0.468921\pi$
$600$	11.1250	0.454175
$601$	−3.18521	−0.129928	−0.0649638	−	0.997888i	$-0.520693\pi$
$601$	−3.18521	−0.129928	−0.0649638	+	0.997888i	$0.520693\pi$
$602$	0	0
$603$	−21.3414	−0.869090
$604$	−16.7659	−0.682193
$605$	11.2102	0.455759
$606$	−29.8678	−1.21330
$607$	−32.6945	−1.32703	−0.663514	−	0.748164i	$-0.730936\pi$
$607$	−32.6945	−1.32703	−0.663514	+	0.748164i	$0.730936\pi$
$608$	−3.80581	−0.154346
$609$	0	0
$610$	−16.3213	−0.660832
$611$	−21.3040	−0.861868
$612$	1.51054	0.0610601
$613$	−8.69213	−0.351072	−0.175536	−	0.984473i	$-0.556166\pi$
$613$	−8.69213	−0.351072	−0.175536	+	0.984473i	$0.556166\pi$
$614$	15.5369	0.627018
$615$	9.12230	0.367846
$616$	0	0
$617$	33.5546	1.35086	0.675429	−	0.737425i	$-0.263959\pi$
$617$	33.5546	1.35086	0.675429	+	0.737425i	$0.263959\pi$
$618$	36.0375	1.44964
$619$	−26.0101	−1.04544	−0.522718	−	0.852506i	$-0.675082\pi$
$619$	−26.0101	−1.04544	−0.522718	+	0.852506i	$0.675082\pi$
$620$	10.2785	0.412796
$621$	2.16944	0.0870568
$622$	−14.7623	−0.591915
$623$	0	0
$624$	−21.5231	−0.861614
$625$	−14.0520	−0.562079
$626$	1.87473	0.0749294
$627$	−9.08069	−0.362648
$628$	0.278299	0.0111053
$629$	−11.1183	−0.443316
$630$	0	0
$631$	−6.86026	−0.273102	−0.136551	−	0.990633i	$-0.543602\pi$
$631$	−6.86026	−0.273102	−0.136551	+	0.990633i	$0.543602\pi$
$632$	21.2566	0.845541
$633$	42.3485	1.68320
$634$	39.8268	1.58173
$635$	−17.4961	−0.694313
$636$	11.9016	0.471929
$637$	0	0
$638$	16.3244	0.646289
$639$	−15.8459	−0.626854
$640$	3.64672	0.144149
$641$	35.0868	1.38585	0.692923	−	0.721012i	$-0.256323\pi$
$641$	35.0868	1.38585	0.692923	+	0.721012i	$0.256323\pi$
$642$	−11.5598	−0.456229
$643$	12.6069	0.497166	0.248583	−	0.968611i	$-0.420035\pi$
$643$	12.6069	0.497166	0.248583	+	0.968611i	$0.420035\pi$
$644$	0	0
$645$	35.2642	1.38853
$646$	1.32677	0.0522010
$647$	−16.3733	−0.643701	−0.321850	−	0.946791i	$-0.604305\pi$
$647$	−16.3733	−0.643701	−0.321850	+	0.946791i	$0.604305\pi$
$648$	34.3188	1.34817
$649$	−13.4961	−0.529768
$650$	−8.85635	−0.347374
$651$	0	0
$652$	3.36809	0.131905
$653$	43.9868	1.72134	0.860668	−	0.509167i	$-0.170046\pi$
$653$	43.9868	1.72134	0.860668	+	0.509167i	$0.170046\pi$
$654$	19.3463	0.756498
$655$	−36.8844	−1.44119
$656$	−4.69988	−0.183499
$657$	−13.9811	−0.545455
$658$	0	0
$659$	7.67382	0.298930	0.149465	−	0.988767i	$-0.452245\pi$
$659$	7.67382	0.298930	0.149465	+	0.988767i	$0.452245\pi$
$660$	−11.8328	−0.460592
$661$	5.24677	0.204076	0.102038	−	0.994781i	$-0.467464\pi$
$661$	5.24677	0.204076	0.102038	+	0.994781i	$0.467464\pi$
$662$	−18.7337	−0.728107
$663$	−12.1519	−0.471940
$664$	−46.4512	−1.80266
$665$	0	0
$666$	19.6059	0.759712
$667$	−2.90185	−0.112360
$668$	17.4033	0.673355
$669$	−3.47314	−0.134279
$670$	−24.4261	−0.943663
$671$	−32.4938	−1.25441
$672$	0	0
$673$	−3.86577	−0.149015	−0.0745073	−	0.997220i	$-0.523738\pi$
$673$	−3.86577	−0.149015	−0.0745073	+	0.997220i	$0.523738\pi$
$674$	−11.4126	−0.439598
$675$	4.27976	0.164728
$676$	−6.71900	−0.258423
$677$	−1.43146	−0.0550153	−0.0275077	−	0.999622i	$-0.508757\pi$
$677$	−1.43146	−0.0550153	−0.0275077	+	0.999622i	$0.508757\pi$
$678$	40.8263	1.56792
$679$	0	0
$680$	6.58778	0.252630
$681$	−5.33013	−0.204251
$682$	−37.0476	−1.41863
$683$	−25.8187	−0.987925	−0.493962	−	0.869483i	$-0.664452\pi$
$683$	−25.8187	−0.987925	−0.493962	+	0.869483i	$0.664452\pi$
$684$	1.29228	0.0494117
$685$	−4.71163	−0.180022
$686$	0	0
$687$	−6.16143	−0.235073
$688$	−18.1684	−0.692663
$689$	−36.1024	−1.37539
$690$	−3.80811	−0.144972
$691$	−19.3172	−0.734862	−0.367431	−	0.930051i	$-0.619763\pi$
$691$	−19.3172	−0.734862	−0.367431	+	0.930051i	$0.619763\pi$
$692$	6.80325	0.258621
$693$	0	0
$694$	−31.4748	−1.19477
$695$	1.08548	0.0411746
$696$	−23.4763	−0.889868
$697$	−2.65354	−0.100510
$698$	−24.3885	−0.923117
$699$	48.5359	1.83580
$700$	0	0
$701$	33.3256	1.25869	0.629345	−	0.777126i	$-0.283323\pi$
$701$	33.3256	1.25869	0.629345	+	0.777126i	$0.283323\pi$
$702$	−13.9721	−0.527341
$703$	−9.51182	−0.358745
$704$	35.0084	1.31943
$705$	−18.0712	−0.680603
$706$	35.4923	1.33577
$707$	0	0
$708$	5.09361	0.191430
$709$	37.3750	1.40365	0.701824	−	0.712351i	$-0.252369\pi$
$709$	37.3750	1.40365	0.701824	+	0.712351i	$0.252369\pi$
$710$	−18.1362	−0.680641
$711$	−12.5414	−0.470338
$712$	10.4894	0.393108
$713$	6.58564	0.246634
$714$	0	0
$715$	35.8938	1.34235
$716$	−2.88723	−0.107901
$717$	28.5643	1.06675
$718$	−1.32040	−0.0492769
$719$	−17.6638	−0.658748	−0.329374	−	0.944200i	$-0.606838\pi$
$719$	−17.6638	−0.658748	−0.329374	+	0.944200i	$0.606838\pi$
$720$	−6.88419	−0.256558
$721$	0	0
$722$	1.13506	0.0422427
$723$	25.1169	0.934108
$724$	−5.11742	−0.190187
$725$	−5.72461	−0.212607
$726$	15.2496	0.565967
$727$	18.7835	0.696640	0.348320	−	0.937376i	$-0.386752\pi$
$727$	18.7835	0.696640	0.348320	+	0.937376i	$0.386752\pi$
$728$	0	0
$729$	−3.14108	−0.116336
$730$	−16.0019	−0.592258
$731$	−10.2578	−0.379399
$732$	12.2636	0.453277
$733$	17.3943	0.642474	0.321237	−	0.946999i	$-0.395901\pi$
$733$	17.3943	0.642474	0.321237	+	0.946999i	$0.395901\pi$
$734$	12.0395	0.444386
$735$	0	0
$736$	−3.17748	−0.117123
$737$	−48.6294	−1.79129
$738$	4.67921	0.172244
$739$	−28.1262	−1.03464	−0.517319	−	0.855793i	$-0.673070\pi$
$739$	−28.1262	−1.03464	−0.517319	+	0.855793i	$0.673070\pi$
$740$	−12.3946	−0.455635
$741$	−10.3961	−0.381908
$742$	0	0
$743$	−32.3940	−1.18842	−0.594211	−	0.804310i	$-0.702535\pi$
$743$	−32.3940	−1.18842	−0.594211	+	0.804310i	$0.702535\pi$
$744$	53.2787	1.95329
$745$	26.6352	0.975840
$746$	0.481980	0.0176465
$747$	27.4062	1.00274
$748$	3.44199	0.125851
$749$	0	0
$750$	−30.3182	−1.10706
$751$	−5.91823	−0.215959	−0.107980	−	0.994153i	$-0.534438\pi$
$751$	−5.91823	−0.215959	−0.107980	+	0.994153i	$0.534438\pi$
$752$	9.31044	0.339517
$753$	5.03724	0.183567
$754$	18.6890	0.680614
$755$	43.1404	1.57004
$756$	0	0
$757$	−23.7464	−0.863078	−0.431539	−	0.902094i	$-0.642029\pi$
$757$	−23.7464	−0.863078	−0.431539	+	0.902094i	$0.642029\pi$
$758$	−0.383559	−0.0139315
$759$	−7.58149	−0.275191
$760$	5.63591	0.204436
$761$	0.606289	0.0219780	0.0109890	−	0.999940i	$-0.496502\pi$
$761$	0.606289	0.0219780	0.0109890	+	0.999940i	$0.496502\pi$
$762$	−23.8007	−0.862208
$763$	0	0
$764$	3.27826	0.118603
$765$	−3.88679	−0.140527
$766$	31.7114	1.14578
$767$	−15.4510	−0.557904
$768$	−32.1726	−1.16093
$769$	−48.3067	−1.74199	−0.870993	−	0.491296i	$-0.836523\pi$
$769$	−48.3067	−1.74199	−0.870993	+	0.491296i	$0.836523\pi$
$770$	0	0
$771$	28.3860	1.02230
$772$	13.3487	0.480430
$773$	3.31978	0.119404	0.0597021	−	0.998216i	$-0.480985\pi$
$773$	3.31978	0.119404	0.0597021	+	0.998216i	$0.480985\pi$
$774$	18.0885	0.650178
$775$	12.9918	0.466679
$776$	9.37321	0.336479
$777$	0	0
$778$	35.0270	1.25578
$779$	−2.27013	−0.0813357
$780$	−13.5468	−0.485054
$781$	−36.1071	−1.29201
$782$	1.10772	0.0396120
$783$	−9.03132	−0.322753
$784$	0	0
$785$	−0.716094	−0.0255585
$786$	−50.1753	−1.78969
$787$	37.2734	1.32865	0.664327	−	0.747442i	$-0.268718\pi$
$787$	37.2734	1.32865	0.664327	+	0.747442i	$0.268718\pi$
$788$	−1.58877	−0.0565976
$789$	41.2800	1.46961
$790$	−14.3541	−0.510696
$791$	0	0
$792$	−23.1277	−0.821806
$793$	−37.2006	−1.32103
$794$	−32.6624	−1.15914
$795$	−30.6241	−1.08612
$796$	−4.48949	−0.159126
$797$	32.2508	1.14238	0.571191	−	0.820817i	$-0.306482\pi$
$797$	32.2508	1.14238	0.571191	+	0.820817i	$0.306482\pi$
$798$	0	0
$799$	5.25665	0.185967
$800$	−6.26836	−0.221620
$801$	−6.18876	−0.218669
$802$	14.1303	0.498957
$803$	−31.8579	−1.12424
$804$	18.3534	0.647276
$805$	0	0
$806$	−42.4141	−1.49397
$807$	7.00326	0.246526
$808$	36.9057	1.29834
$809$	−4.37072	−0.153666	−0.0768332	−	0.997044i	$-0.524481\pi$
$809$	−4.37072	−0.153666	−0.0768332	+	0.997044i	$0.524481\pi$
$810$	−23.1748	−0.814278
$811$	−24.3955	−0.856644	−0.428322	−	0.903626i	$-0.640895\pi$
$811$	−24.3955	−0.856644	−0.428322	+	0.903626i	$0.640895\pi$
$812$	0	0
$813$	1.17304	0.0411402
$814$	44.6747	1.56585
$815$	−8.66645	−0.303573
$816$	5.31071	0.185912
$817$	−8.77566	−0.307022
$818$	−20.2853	−0.709258
$819$	0	0
$820$	−2.95814	−0.103303
$821$	−22.4555	−0.783702	−0.391851	−	0.920029i	$-0.628165\pi$
$821$	−22.4555	−0.783702	−0.391851	+	0.920029i	$0.628165\pi$
$822$	−6.40942	−0.223554
$823$	33.3905	1.16392	0.581960	−	0.813218i	$-0.302286\pi$
$823$	33.3905	1.16392	0.581960	+	0.813218i	$0.302286\pi$
$824$	−44.5292	−1.55125
$825$	−14.9564	−0.520714
$826$	0	0
$827$	−44.6022	−1.55097	−0.775486	−	0.631365i	$-0.782495\pi$
$827$	−44.6022	−1.55097	−0.775486	+	0.631365i	$0.782495\pi$
$828$	1.07893	0.0374955
$829$	32.2868	1.12137	0.560684	−	0.828030i	$-0.310538\pi$
$829$	32.2868	1.12137	0.560684	+	0.828030i	$0.310538\pi$
$830$	31.3675	1.08878
$831$	58.8279	2.04072
$832$	40.0794	1.38950
$833$	0	0
$834$	1.47662	0.0511311
$835$	−44.7806	−1.54970
$836$	2.94465	0.101843
$837$	20.4963	0.708455
$838$	−22.9350	−0.792278
$839$	5.17125	0.178531	0.0892657	−	0.996008i	$-0.471548\pi$
$839$	5.17125	0.178531	0.0892657	+	0.996008i	$0.471548\pi$
$840$	0	0
$841$	−16.9197	−0.583438
$842$	8.32111	0.286764
$843$	4.08399	0.140660
$844$	−13.7326	−0.472695
$845$	17.2887	0.594749
$846$	−9.26950	−0.318692
$847$	0	0
$848$	15.7778	0.541811
$849$	−27.3022	−0.937008
$850$	2.18525	0.0749536
$851$	−7.94144	−0.272229
$852$	13.6273	0.466864
$853$	3.86988	0.132502	0.0662511	−	0.997803i	$-0.478896\pi$
$853$	3.86988	0.132502	0.0662511	+	0.997803i	$0.478896\pi$
$854$	0	0
$855$	−3.32519	−0.113719
$856$	14.2837	0.488207
$857$	14.7977	0.505481	0.252741	−	0.967534i	$-0.418668\pi$
$857$	14.7977	0.505481	0.252741	+	0.967534i	$0.418668\pi$
$858$	48.8277	1.66695
$859$	−37.6674	−1.28520	−0.642598	−	0.766204i	$-0.722143\pi$
$859$	−37.6674	−1.28520	−0.642598	+	0.766204i	$0.722143\pi$
$860$	−11.4353	−0.389942
$861$	0	0
$862$	−8.63054	−0.293957
$863$	0.671748	0.0228666	0.0114333	−	0.999935i	$-0.496361\pi$
$863$	0.671748	0.0228666	0.0114333	+	0.999935i	$0.496361\pi$
$864$	−9.88916	−0.336436
$865$	−17.5055	−0.595205
$866$	28.4890	0.968096
$867$	−34.3085	−1.16518
$868$	0	0
$869$	−28.5773	−0.969417
$870$	15.8531	0.537469
$871$	−55.6735	−1.88642
$872$	−23.9049	−0.809522
$873$	−5.53019	−0.187169
$874$	0.947667	0.0320553
$875$	0	0
$876$	12.0236	0.406240
$877$	2.39645	0.0809224	0.0404612	−	0.999181i	$-0.487117\pi$
$877$	2.39645	0.0809224	0.0404612	+	0.999181i	$0.487117\pi$
$878$	40.7070	1.37380
$879$	−8.95589	−0.302075
$880$	−15.6866	−0.528794
$881$	4.30698	0.145106	0.0725530	−	0.997365i	$-0.476885\pi$
$881$	4.30698	0.145106	0.0725530	+	0.997365i	$0.476885\pi$
$882$	0	0
$883$	−29.6998	−0.999479	−0.499739	−	0.866176i	$-0.666571\pi$
$883$	−29.6998	−0.999479	−0.499739	+	0.866176i	$0.666571\pi$
$884$	3.94056	0.132535
$885$	−13.1064	−0.440567
$886$	33.0458	1.11020
$887$	53.8320	1.80750	0.903751	−	0.428058i	$-0.140802\pi$
$887$	53.8320	1.80750	0.903751	+	0.428058i	$0.140802\pi$
$888$	−64.2473	−2.15600
$889$	0	0
$890$	−7.08328	−0.237432
$891$	−46.1381	−1.54569
$892$	1.12626	0.0377098
$893$	4.49711	0.150490
$894$	36.2330	1.21181
$895$	7.42914	0.248329
$896$	0	0
$897$	−8.67969	−0.289806
$898$	−9.20078	−0.307034
$899$	−27.4158	−0.914368
$900$	2.12846	0.0709486
$901$	8.90808	0.296771
$902$	10.6622	0.355014
$903$	0	0
$904$	−50.4463	−1.67782
$905$	13.1677	0.437708
$906$	58.6855	1.94970
$907$	0.718141	0.0238455	0.0119227	−	0.999929i	$-0.496205\pi$
$907$	0.718141	0.0238455	0.0119227	+	0.999929i	$0.496205\pi$
$908$	1.72843	0.0573601
$909$	−21.7744	−0.722210
$910$	0	0
$911$	−51.2647	−1.69848	−0.849238	−	0.528010i	$-0.822939\pi$
$911$	−51.2647	−1.69848	−0.849238	+	0.528010i	$0.822939\pi$
$912$	4.54336	0.150446
$913$	62.4488	2.06675
$914$	−13.8981	−0.459707
$915$	−31.5556	−1.04320
$916$	1.99800	0.0660159
$917$	0	0
$918$	3.44753	0.113785
$919$	24.0222	0.792420	0.396210	−	0.918160i	$-0.370325\pi$
$919$	24.0222	0.792420	0.396210	+	0.918160i	$0.370325\pi$
$920$	4.70544	0.155134
$921$	30.0390	0.989818
$922$	39.7837	1.31021
$923$	−41.3372	−1.36063
$924$	0	0
$925$	−15.6665	−0.515110
$926$	32.7693	1.07687
$927$	26.2722	0.862893
$928$	13.2277	0.434222
$929$	24.6046	0.807251	0.403626	−	0.914924i	$-0.367750\pi$
$929$	24.6046	0.807251	0.403626	+	0.914924i	$0.367750\pi$
$930$	−35.9780	−1.17976
$931$	0	0
$932$	−15.7390	−0.515549
$933$	−28.5414	−0.934404
$934$	39.5527	1.29420
$935$	−8.85660	−0.289642
$936$	−26.4777	−0.865452
$937$	−2.90609	−0.0949377	−0.0474688	−	0.998873i	$-0.515115\pi$
$937$	−2.90609	−0.0949377	−0.0474688	+	0.998873i	$0.515115\pi$
$938$	0	0
$939$	3.62460	0.118284
$940$	5.86007	0.191134
$941$	−3.64954	−0.118972	−0.0594858	−	0.998229i	$-0.518946\pi$
$941$	−3.64954	−0.118972	−0.0594858	+	0.998229i	$0.518946\pi$
$942$	−0.974130	−0.0317389
$943$	−1.89533	−0.0617205
$944$	6.75252	0.219776
$945$	0	0
$946$	41.2172	1.34009
$947$	−36.4871	−1.18567	−0.592836	−	0.805323i	$-0.701992\pi$
$947$	−36.4871	−1.18567	−0.592836	+	0.805323i	$0.701992\pi$
$948$	10.7855	0.350295
$949$	−36.4726	−1.18395
$950$	1.86951	0.0606548
$951$	77.0010	2.49693
$952$	0	0
$953$	8.22124	0.266312	0.133156	−	0.991095i	$-0.457489\pi$
$953$	8.22124	0.266312	0.133156	+	0.991095i	$0.457489\pi$
$954$	−15.7084	−0.508578
$955$	−8.43532	−0.272960
$956$	−9.26270	−0.299577
$957$	31.5615	1.02024
$958$	21.4468	0.692915
$959$	0	0
$960$	33.9976	1.09727
$961$	31.2192	1.00707
$962$	51.1459	1.64901
$963$	−8.42738	−0.271569
$964$	−8.14481	−0.262327
$965$	−34.3476	−1.10569
$966$	0	0
$967$	−44.4422	−1.42917	−0.714583	−	0.699551i	$-0.753383\pi$
$967$	−44.4422	−1.42917	−0.714583	+	0.699551i	$0.753383\pi$
$968$	−18.8430	−0.605637
$969$	2.56517	0.0824051
$970$	−6.32952	−0.203229
$971$	57.6556	1.85026	0.925129	−	0.379653i	$-0.123957\pi$
$971$	57.6556	1.85026	0.925129	+	0.379653i	$0.123957\pi$
$972$	11.8658	0.380595
$973$	0	0
$974$	−0.356502	−0.0114231
$975$	−17.1228	−0.548369
$976$	16.2577	0.520396
$977$	29.1680	0.933168	0.466584	−	0.884477i	$-0.345485\pi$
$977$	29.1680	0.933168	0.466584	+	0.884477i	$0.345485\pi$
$978$	−11.7893	−0.376981
$979$	−14.1019	−0.450700
$980$	0	0
$981$	14.1039	0.450303
$982$	42.2300	1.34761
$983$	27.6877	0.883099	0.441549	−	0.897237i	$-0.354429\pi$
$983$	27.6877	0.883099	0.441549	+	0.897237i	$0.354429\pi$
$984$	−15.3335	−0.488814
$985$	4.08808	0.130257
$986$	−4.61141	−0.146857
$987$	0	0
$988$	3.37119	0.107252
$989$	−7.32682	−0.232979
$990$	15.6176	0.496360
$991$	16.6411	0.528623	0.264312	−	0.964437i	$-0.414855\pi$
$991$	16.6411	0.528623	0.264312	+	0.964437i	$0.414855\pi$
$992$	−30.0199	−0.953133
$993$	−36.2197	−1.14940
$994$	0	0
$995$	11.5519	0.366221
$996$	−23.5691	−0.746814
$997$	−28.2236	−0.893851	−0.446925	−	0.894571i	$-0.647481\pi$
$997$	−28.2236	−0.893851	−0.446925	+	0.894571i	$0.647481\pi$
$998$	−34.5044	−1.09222
$999$	−24.7159	−0.781976

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.a.o.1.5		7
3.2	odd	2		8379.2.a.ck.1.3		7
7.2	even	3		931.2.f.p.704.3		14
7.3	odd	6		133.2.f.d.58.3	yes	14
7.4	even	3		931.2.f.p.324.3		14
7.5	odd	6		133.2.f.d.39.3	✓	14
7.6	odd	2		931.2.a.n.1.5		7
21.5	even	6		1197.2.j.l.172.5		14
21.17	even	6		1197.2.j.l.856.5		14
21.20	even	2		8379.2.a.cl.1.3		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.2.f.d.39.3	✓	14	7.5	odd	6
133.2.f.d.58.3	yes	14	7.3	odd	6
931.2.a.n.1.5		7	7.6	odd	2
931.2.a.o.1.5		7	1.1	even	1	trivial
931.2.f.p.324.3		14	7.4	even	3
931.2.f.p.704.3		14	7.2	even	3
1197.2.j.l.172.5		14	21.5	even	6
1197.2.j.l.856.5		14	21.17	even	6
8379.2.a.ck.1.3		7	3.2	odd	2
8379.2.a.cl.1.3		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)

\(f(q)\)	\(=\)	\(q+1.13506 q^{2} +2.19453 q^{3} -0.711632 q^{4} +1.83111 q^{5} +2.49093 q^{6} -3.07787 q^{8} +1.81594 q^{9} +O(q^{10})\)	\(q+1.13506 q^{2} +2.19453 q^{3} -0.711632 q^{4} +1.83111 q^{5} +2.49093 q^{6} -3.07787 q^{8} +1.81594 q^{9} +2.07842 q^{10} +4.13788 q^{11} -1.56170 q^{12} +4.73726 q^{13} +4.01841 q^{15} -2.07032 q^{16} -1.16889 q^{17} +2.06121 q^{18} -1.00000 q^{19} -1.30307 q^{20} +4.69676 q^{22} -0.834902 q^{23} -6.75447 q^{24} -1.64705 q^{25} +5.37709 q^{26} -2.59844 q^{27} +3.47567 q^{29} +4.56115 q^{30} -7.88792 q^{31} +3.80581 q^{32} +9.08069 q^{33} -1.32677 q^{34} -1.29228 q^{36} +9.51182 q^{37} -1.13506 q^{38} +10.3961 q^{39} -5.63591 q^{40} +2.27013 q^{41} +8.77566 q^{43} -2.94465 q^{44} +3.32519 q^{45} -0.947667 q^{46} -4.49711 q^{47} -4.54336 q^{48} -1.86951 q^{50} -2.56517 q^{51} -3.37119 q^{52} -7.62095 q^{53} -2.94939 q^{54} +7.57690 q^{55} -2.19453 q^{57} +3.94511 q^{58} -3.26159 q^{59} -2.85963 q^{60} -7.85276 q^{61} -8.95328 q^{62} +8.46046 q^{64} +8.67443 q^{65} +10.3072 q^{66} -11.7522 q^{67} +0.831823 q^{68} -1.83221 q^{69} -8.72597 q^{71} -5.58925 q^{72} -7.69908 q^{73} +10.7965 q^{74} -3.61450 q^{75} +0.711632 q^{76} +11.8002 q^{78} -6.90625 q^{79} -3.79097 q^{80} -11.1502 q^{81} +2.57674 q^{82} +15.0920 q^{83} -2.14037 q^{85} +9.96093 q^{86} +7.62745 q^{87} -12.7359 q^{88} -3.40801 q^{89} +3.77430 q^{90} +0.594143 q^{92} -17.3102 q^{93} -5.10451 q^{94} -1.83111 q^{95} +8.35195 q^{96} -3.04535 q^{97} +7.51417 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 2 q^{2} + 2 q^{3} + 10 q^{4} + 2 q^{5} + 4 q^{6} + 12 q^{8} + 15 q^{9}+O(q^{10}) \) 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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