LMFDB - Embedded newform 931.2.a.o.1.2

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			1.2
Root			$0.862998$ 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)

$f(q)$	$=$	$q-1.40650 q^{2} -3.19504 q^{3} -0.0217491 q^{4} -0.295752 q^{5} +4.49383 q^{6} +2.84360 q^{8} +7.20828 q^{9} +O(q^{10})$	\(q-1.40650 q^{2} -3.19504 q^{3} -0.0217491 q^{4} -0.295752 q^{5} +4.49383 q^{6} +2.84360 q^{8} +7.20828 q^{9} +0.415977 q^{10} -0.372561 q^{11} +0.0694893 q^{12} -3.46904 q^{13} +0.944941 q^{15} -3.95603 q^{16} -3.29575 q^{17} -10.1385 q^{18} -1.00000 q^{19} +0.00643235 q^{20} +0.524008 q^{22} -7.41280 q^{23} -9.08541 q^{24} -4.91253 q^{25} +4.87922 q^{26} -13.4456 q^{27} +3.21894 q^{29} -1.32906 q^{30} +3.96455 q^{31} -0.123026 q^{32} +1.19035 q^{33} +4.63549 q^{34} -0.156774 q^{36} +9.83661 q^{37} +1.40650 q^{38} +11.0837 q^{39} -0.841001 q^{40} -2.81301 q^{41} -6.08278 q^{43} +0.00810286 q^{44} -2.13187 q^{45} +10.4261 q^{46} -6.82129 q^{47} +12.6397 q^{48} +6.90949 q^{50} +10.5301 q^{51} +0.0754486 q^{52} +10.4357 q^{53} +18.9113 q^{54} +0.110186 q^{55} +3.19504 q^{57} -4.52745 q^{58} +4.68799 q^{59} -0.0205516 q^{60} -7.09816 q^{61} -5.57615 q^{62} +8.08509 q^{64} +1.02598 q^{65} -1.67423 q^{66} -7.66601 q^{67} +0.0716797 q^{68} +23.6842 q^{69} +1.88170 q^{71} +20.4974 q^{72} +1.01791 q^{73} -13.8352 q^{74} +15.6957 q^{75} +0.0217491 q^{76} -15.5893 q^{78} -10.6056 q^{79} +1.17001 q^{80} +21.3345 q^{81} +3.95650 q^{82} +12.3958 q^{83} +0.974727 q^{85} +8.55545 q^{86} -10.2847 q^{87} -1.05941 q^{88} +6.18557 q^{89} +2.99848 q^{90} +0.161222 q^{92} -12.6669 q^{93} +9.59417 q^{94} +0.295752 q^{95} +0.393073 q^{96} +0.235136 q^{97} -2.68552 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.40650	−0.994548	−0.497274	−	0.867594i	$-0.665666\pi$
$2$	−1.40650	−0.994548	−0.497274	+	0.867594i	$0.665666\pi$
$3$	−3.19504	−1.84466	−0.922329	−	0.386406i	$-0.873716\pi$
$3$	−3.19504	−1.84466	−0.922329	+	0.386406i	$0.873716\pi$
$4$	−0.0217491	−0.0108746
$5$	−0.295752	−0.132265	−0.0661323	−	0.997811i	$-0.521066\pi$
$5$	−0.295752	−0.132265	−0.0661323	+	0.997811i	$0.521066\pi$
$6$	4.49383	1.83460
$7$	0	0
$7$	0	0
$8$	2.84360	1.00536
$9$	7.20828	2.40276
$10$	0.415977	0.131543
$11$	−0.372561	−0.112331	−0.0561656	−	0.998421i	$-0.517887\pi$
$11$	−0.372561	−0.112331	−0.0561656	+	0.998421i	$0.517887\pi$
$12$	0.0694893	0.0200598
$13$	−3.46904	−0.962140	−0.481070	−	0.876682i	$-0.659752\pi$
$13$	−3.46904	−0.962140	−0.481070	+	0.876682i	$0.659752\pi$
$14$	0	0
$15$	0.944941	0.243983
$16$	−3.95603	−0.989007
$17$	−3.29575	−0.799337	−0.399669	−	0.916660i	$-0.630875\pi$
$17$	−3.29575	−0.799337	−0.399669	+	0.916660i	$0.630875\pi$
$18$	−10.1385	−2.38966
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	0.00643235	0.00143832
$21$	0	0
$22$	0.524008	0.111719
$23$	−7.41280	−1.54568	−0.772838	−	0.634604i	$-0.781163\pi$
$23$	−7.41280	−1.54568	−0.772838	+	0.634604i	$0.781163\pi$
$24$	−9.08541	−1.85455
$25$	−4.91253	−0.982506
$26$	4.87922	0.956894
$27$	−13.4456	−2.58761
$28$	0	0
$29$	3.21894	0.597743	0.298871	−	0.954293i	$-0.403390\pi$
$29$	3.21894	0.597743	0.298871	+	0.954293i	$0.403390\pi$
$30$	−1.32906	−0.242652
$31$	3.96455	0.712054	0.356027	−	0.934476i	$-0.384131\pi$
$31$	3.96455	0.712054	0.356027	+	0.934476i	$0.384131\pi$
$32$	−0.123026	−0.0217482
$33$	1.19035	0.207213
$34$	4.63549	0.794979
$35$	0	0
$36$	−0.156774	−0.0261290
$37$	9.83661	1.61713	0.808564	−	0.588408i	$-0.200245\pi$
$37$	9.83661	1.61713	0.808564	+	0.588408i	$0.200245\pi$
$38$	1.40650	0.228165
$39$	11.0837	1.77482
$40$	−0.841001	−0.132974
$41$	−2.81301	−0.439318	−0.219659	−	0.975577i	$-0.570494\pi$
$41$	−2.81301	−0.439318	−0.219659	+	0.975577i	$0.570494\pi$
$42$	0	0
$43$	−6.08278	−0.927615	−0.463808	−	0.885936i	$-0.653517\pi$
$43$	−6.08278	−0.927615	−0.463808	+	0.885936i	$0.653517\pi$
$44$	0.00810286	0.00122155
$45$	−2.13187	−0.317800
$46$	10.4261	1.53725
$47$	−6.82129	−0.994988	−0.497494	−	0.867468i	$-0.665746\pi$
$47$	−6.82129	−0.994988	−0.497494	+	0.867468i	$0.665746\pi$
$48$	12.6397	1.82438
$49$	0	0
$50$	6.90949	0.977149
$51$	10.5301	1.47450
$52$	0.0754486	0.0104628
$53$	10.4357	1.43345	0.716724	−	0.697356i	$-0.245641\pi$
$53$	10.4357	1.43345	0.716724	+	0.697356i	$0.245641\pi$
$54$	18.9113	2.57351
$55$	0.110186	0.0148574
$56$	0	0
$57$	3.19504	0.423193
$58$	−4.52745	−0.594484
$59$	4.68799	0.610324	0.305162	−	0.952300i	$-0.401289\pi$
$59$	4.68799	0.610324	0.305162	+	0.952300i	$0.401289\pi$
$60$	−0.0205516	−0.00265320
$61$	−7.09816	−0.908827	−0.454413	−	0.890791i	$-0.650151\pi$
$61$	−7.09816	−0.908827	−0.454413	+	0.890791i	$0.650151\pi$
$62$	−5.57615	−0.708172
$63$	0	0
$64$	8.08509	1.01064
$65$	1.02598	0.127257
$66$	−1.67423	−0.206083
$67$	−7.66601	−0.936552	−0.468276	−	0.883582i	$-0.655125\pi$
$67$	−7.66601	−0.936552	−0.468276	+	0.883582i	$0.655125\pi$
$68$	0.0716797	0.00869244
$69$	23.6842	2.85124
$70$	0	0
$71$	1.88170	0.223317	0.111658	−	0.993747i	$-0.464384\pi$
$71$	1.88170	0.223317	0.111658	+	0.993747i	$0.464384\pi$
$72$	20.4974	2.41565
$73$	1.01791	0.119138	0.0595688	−	0.998224i	$-0.481027\pi$
$73$	1.01791	0.119138	0.0595688	+	0.998224i	$0.481027\pi$
$74$	−13.8352	−1.60831
$75$	15.6957	1.81239
$76$	0.0217491	0.00249480
$77$	0	0
$78$	−15.5893	−1.76514
$79$	−10.6056	−1.19323	−0.596614	−	0.802529i	$-0.703487\pi$
$79$	−10.6056	−1.19323	−0.596614	+	0.802529i	$0.703487\pi$
$80$	1.17001	0.130811
$81$	21.3345	2.37050
$82$	3.95650	0.436923
$83$	12.3958	1.36061	0.680306	−	0.732928i	$-0.261847\pi$
$83$	12.3958	1.36061	0.680306	+	0.732928i	$0.261847\pi$
$84$	0	0
$85$	0.974727	0.105724
$86$	8.55545	0.922558
$87$	−10.2847	−1.10263
$88$	−1.05941	−0.112934
$89$	6.18557	0.655669	0.327834	−	0.944735i	$-0.393681\pi$
$89$	6.18557	0.655669	0.327834	+	0.944735i	$0.393681\pi$
$90$	2.99848	0.316067
$91$	0	0
$92$	0.161222	0.0168085
$93$	−12.6669	−1.31350
$94$	9.59417	0.989563
$95$	0.295752	0.0303436
$96$	0.393073	0.0401179
$97$	0.235136	0.0238745	0.0119372	−	0.999929i	$-0.496200\pi$
$97$	0.235136	0.0238745	0.0119372	+	0.999929i	$0.496200\pi$
$98$	0	0
$99$	−2.68552	−0.269905
$100$	0.106843	0.0106843
$101$	−0.771429	−0.0767601	−0.0383800	−	0.999263i	$-0.512220\pi$
$101$	−0.771429	−0.0767601	−0.0383800	+	0.999263i	$0.512220\pi$
$102$	−14.8106	−1.46646
$103$	−10.6191	−1.04633	−0.523167	−	0.852230i	$-0.675250\pi$
$103$	−10.6191	−1.04633	−0.523167	+	0.852230i	$0.675250\pi$
$104$	−9.86456	−0.967300
$105$	0	0
$106$	−14.6778	−1.42563
$107$	8.14803	0.787700	0.393850	−	0.919175i	$-0.371143\pi$
$107$	8.14803	0.787700	0.393850	+	0.919175i	$0.371143\pi$
$108$	0.292431	0.0281392
$109$	6.70289	0.642020	0.321010	−	0.947076i	$-0.395978\pi$
$109$	6.70289	0.642020	0.321010	+	0.947076i	$0.395978\pi$
$110$	−0.154977	−0.0147764
$111$	−31.4284	−2.98305
$112$	0	0
$113$	15.6066	1.46814	0.734072	−	0.679072i	$-0.237617\pi$
$113$	15.6066	1.46814	0.734072	+	0.679072i	$0.237617\pi$
$114$	−4.49383	−0.420886
$115$	2.19235	0.204438
$116$	−0.0700092	−0.00650019
$117$	−25.0058	−2.31179
$118$	−6.59367	−0.606996
$119$	0	0
$120$	2.68703	0.245291
$121$	−10.8612	−0.987382
$122$	9.98359	0.903872
$123$	8.98767	0.810391
$124$	−0.0862254	−0.00774327
$125$	2.93165	0.262215
$126$	0	0
$127$	−3.34348	−0.296686	−0.148343	−	0.988936i	$-0.547394\pi$
$127$	−3.34348	−0.296686	−0.148343	+	0.988936i	$0.547394\pi$
$128$	−11.1257	−0.983378
$129$	19.4347	1.71113
$130$	−1.44304	−0.126563
$131$	15.7131	1.37286	0.686430	−	0.727196i	$-0.259177\pi$
$131$	15.7131	1.37286	0.686430	+	0.727196i	$0.259177\pi$
$132$	−0.0258890	−0.00225335
$133$	0	0
$134$	10.7823	0.931445
$135$	3.97658	0.342249
$136$	−9.37179	−0.803624
$137$	13.5984	1.16179	0.580893	−	0.813980i	$-0.302703\pi$
$137$	13.5984	1.16179	0.580893	+	0.813980i	$0.302703\pi$
$138$	−33.3119	−2.83570
$139$	21.3319	1.80935	0.904675	−	0.426102i	$-0.140114\pi$
$139$	21.3319	1.80935	0.904675	+	0.426102i	$0.140114\pi$
$140$	0	0
$141$	21.7943	1.83541
$142$	−2.64662	−0.222099
$143$	1.29243	0.108078
$144$	−28.5162	−2.37635
$145$	−0.952011	−0.0790602
$146$	−1.43170	−0.118488
$147$	0	0
$148$	−0.213938	−0.0175856
$149$	10.2208	0.837320	0.418660	−	0.908143i	$-0.362500\pi$
$149$	10.2208	0.837320	0.418660	+	0.908143i	$0.362500\pi$
$150$	−22.0761	−1.80251
$151$	−2.58011	−0.209966	−0.104983	−	0.994474i	$-0.533479\pi$
$151$	−2.58011	−0.209966	−0.104983	+	0.994474i	$0.533479\pi$
$152$	−2.84360	−0.230646
$153$	−23.7567	−1.92062
$154$	0	0
$155$	−1.17252	−0.0941795
$156$	−0.241061	−0.0193004
$157$	21.6002	1.72388	0.861941	−	0.507009i	$-0.169249\pi$
$157$	21.6002	1.72388	0.861941	+	0.507009i	$0.169249\pi$
$158$	14.9169	1.18672
$159$	−33.3424	−2.64422
$160$	0.0363853	0.00287651
$161$	0	0
$162$	−30.0070	−2.35758
$163$	−15.4704	−1.21174	−0.605868	−	0.795565i	$-0.707174\pi$
$163$	−15.4704	−1.21174	−0.605868	+	0.795565i	$0.707174\pi$
$164$	0.0611804	0.00477739
$165$	−0.352048	−0.0274069
$166$	−17.4347	−1.35319
$167$	−7.96646	−0.616463	−0.308231	−	0.951311i	$-0.599737\pi$
$167$	−7.96646	−0.616463	−0.308231	+	0.951311i	$0.599737\pi$
$168$	0	0
$169$	−0.965736	−0.0742874
$170$	−1.37096	−0.105148
$171$	−7.20828	−0.551231
$172$	0.132295	0.0100874
$173$	5.61526	0.426920	0.213460	−	0.976952i	$-0.431527\pi$
$173$	5.61526	0.426920	0.213460	+	0.976952i	$0.431527\pi$
$174$	14.4654	1.09662
$175$	0	0
$176$	1.47386	0.111096
$177$	−14.9783	−1.12584
$178$	−8.70002	−0.652094
$179$	7.43709	0.555874	0.277937	−	0.960599i	$-0.410349\pi$
$179$	7.43709	0.555874	0.277937	+	0.960599i	$0.410349\pi$
$180$	0.0463662	0.00345594
$181$	8.99507	0.668598	0.334299	−	0.942467i	$-0.391500\pi$
$181$	8.99507	0.668598	0.334299	+	0.942467i	$0.391500\pi$
$182$	0	0
$183$	22.6789	1.67647
$184$	−21.0790	−1.55396
$185$	−2.90920	−0.213889
$186$	17.8160	1.30633
$187$	1.22787	0.0897906
$188$	0.148357	0.0108201
$189$	0	0
$190$	−0.415977	−0.0301781
$191$	22.1575	1.60326	0.801629	−	0.597822i	$-0.203967\pi$
$191$	22.1575	1.60326	0.801629	+	0.597822i	$0.203967\pi$
$192$	−25.8322	−1.86428
$193$	0.407408	0.0293259	0.0146629	−	0.999892i	$-0.495332\pi$
$193$	0.407408	0.0293259	0.0146629	+	0.999892i	$0.495332\pi$
$194$	−0.330720	−0.0237443
$195$	−3.27804	−0.234745
$196$	0	0
$197$	−20.5203	−1.46201	−0.731006	−	0.682371i	$-0.760949\pi$
$197$	−20.5203	−1.46201	−0.731006	+	0.682371i	$0.760949\pi$
$198$	3.77720	0.268434
$199$	7.01563	0.497325	0.248662	−	0.968590i	$-0.420009\pi$
$199$	7.01563	0.497325	0.248662	+	0.968590i	$0.420009\pi$
$200$	−13.9693	−0.987775
$201$	24.4932	1.72762
$202$	1.08502	0.0763416
$203$	0	0
$204$	−0.229020	−0.0160346
$205$	0.831953	0.0581061
$206$	14.9358	1.04063
$207$	−53.4335	−3.71389
$208$	13.7236	0.951563
$209$	0.372561	0.0257706
$210$	0	0
$211$	−15.2256	−1.04817	−0.524087	−	0.851665i	$-0.675593\pi$
$211$	−15.2256	−1.04817	−0.524087	+	0.851665i	$0.675593\pi$
$212$	−0.226967	−0.0155881
$213$	−6.01211	−0.411943
$214$	−11.4602	−0.783405
$215$	1.79900	0.122691
$216$	−38.2340	−2.60149
$217$	0	0
$218$	−9.42763	−0.638520
$219$	−3.25227	−0.219768
$220$	−0.00239644	−0.000161568 0
$221$	11.4331	0.769074
$222$	44.2041	2.96678
$223$	0.0430042	0.00287977	0.00143989	−	0.999999i	$-0.499542\pi$
$223$	0.0430042	0.00287977	0.00143989	+	0.999999i	$0.499542\pi$
$224$	0	0
$225$	−35.4109	−2.36073
$226$	−21.9507	−1.46014
$227$	−15.7366	−1.04448	−0.522238	−	0.852800i	$-0.674903\pi$
$227$	−15.7366	−1.04448	−0.522238	+	0.852800i	$0.674903\pi$
$228$	−0.0694893	−0.00460204
$229$	10.5762	0.698898	0.349449	−	0.936955i	$-0.386369\pi$
$229$	10.5762	0.698898	0.349449	+	0.936955i	$0.386369\pi$
$230$	−3.08355	−0.203323
$231$	0	0
$232$	9.15338	0.600949
$233$	−0.526501	−0.0344922	−0.0172461	−	0.999851i	$-0.505490\pi$
$233$	−0.526501	−0.0344922	−0.0172461	+	0.999851i	$0.505490\pi$
$234$	35.1708	2.29919
$235$	2.01741	0.131602
$236$	−0.101960	−0.00663701
$237$	33.8854	2.20110
$238$	0	0
$239$	−4.56967	−0.295588	−0.147794	−	0.989018i	$-0.547217\pi$
$239$	−4.56967	−0.295588	−0.147794	+	0.989018i	$0.547217\pi$
$240$	−3.73821	−0.241301
$241$	22.8596	1.47252	0.736258	−	0.676701i	$-0.236591\pi$
$241$	22.8596	1.47252	0.736258	+	0.676701i	$0.236591\pi$
$242$	15.2763	0.981998
$243$	−27.8277	−1.78515
$244$	0.154379	0.00988309
$245$	0	0
$246$	−12.6412	−0.805972
$247$	3.46904	0.220730
$248$	11.2736	0.715873
$249$	−39.6050	−2.50986
$250$	−4.12338	−0.260786
$251$	8.49789	0.536382	0.268191	−	0.963366i	$-0.413574\pi$
$251$	8.49789	0.536382	0.268191	+	0.963366i	$0.413574\pi$
$252$	0	0
$253$	2.76172	0.173628
$254$	4.70261	0.295068
$255$	−3.11429	−0.195024
$256$	−0.521917	−0.0326198
$257$	11.3461	0.707749	0.353875	−	0.935293i	$-0.384864\pi$
$257$	11.3461	0.707749	0.353875	+	0.935293i	$0.384864\pi$
$258$	−27.3350	−1.70180
$259$	0	0
$260$	−0.0223141	−0.00138386
$261$	23.2031	1.43623
$262$	−22.1005	−1.36537
$263$	−4.91687	−0.303187	−0.151594	−	0.988443i	$-0.548441\pi$
$263$	−4.91687	−0.303187	−0.151594	+	0.988443i	$0.548441\pi$
$264$	3.38486	0.208324
$265$	−3.08637	−0.189594
$266$	0	0
$267$	−19.7631	−1.20948
$268$	0.166729	0.0101846
$269$	28.8234	1.75739	0.878696	−	0.477381i	$-0.158414\pi$
$269$	28.8234	1.75739	0.878696	+	0.477381i	$0.158414\pi$
$270$	−5.59307	−0.340383
$271$	2.65446	0.161247	0.0806234	−	0.996745i	$-0.474309\pi$
$271$	2.65446	0.161247	0.0806234	+	0.996745i	$0.474309\pi$
$272$	13.0381	0.790550
$273$	0	0
$274$	−19.1261	−1.15545
$275$	1.83022	0.110366
$276$	−0.515110	−0.0310060
$277$	−3.59970	−0.216285	−0.108143	−	0.994135i	$-0.534490\pi$
$277$	−3.59970	−0.216285	−0.108143	+	0.994135i	$0.534490\pi$
$278$	−30.0034	−1.79949
$279$	28.5776	1.71090
$280$	0	0
$281$	1.35683	0.0809415	0.0404708	−	0.999181i	$-0.487114\pi$
$281$	1.35683	0.0809415	0.0404708	+	0.999181i	$0.487114\pi$
$282$	−30.6538	−1.82540
$283$	6.05006	0.359639	0.179819	−	0.983700i	$-0.442449\pi$
$283$	6.05006	0.359639	0.179819	+	0.983700i	$0.442449\pi$
$284$	−0.0409253	−0.00242847
$285$	−0.944941	−0.0559735
$286$	−1.81781	−0.107489
$287$	0	0
$288$	−0.886807	−0.0522556
$289$	−6.13802	−0.361060
$290$	1.33901	0.0786291
$291$	−0.751270	−0.0440402
$292$	−0.0221387	−0.00129557
$293$	3.98610	0.232871	0.116435	−	0.993198i	$-0.462853\pi$
$293$	3.98610	0.232871	0.116435	+	0.993198i	$0.462853\pi$
$294$	0	0
$295$	−1.38648	−0.0807242
$296$	27.9713	1.62580
$297$	5.00931	0.290670
$298$	−14.3756	−0.832755
$299$	25.7153	1.48716
$300$	−0.341368	−0.0197089
$301$	0	0
$302$	3.62893	0.208822
$303$	2.46475	0.141596
$304$	3.95603	0.226894
$305$	2.09930	0.120206
$306$	33.4139	1.91015
$307$	−17.9160	−1.02252	−0.511259	−	0.859427i	$-0.670821\pi$
$307$	−17.9160	−1.02252	−0.511259	+	0.859427i	$0.670821\pi$
$308$	0	0
$309$	33.9286	1.93013
$310$	1.64916	0.0936660
$311$	−18.8468	−1.06870	−0.534352	−	0.845262i	$-0.679444\pi$
$311$	−18.8468	−1.06870	−0.534352	+	0.845262i	$0.679444\pi$
$312$	31.5177	1.78434
$313$	18.8133	1.06339	0.531694	−	0.846936i	$-0.321556\pi$
$313$	18.8133	1.06339	0.531694	+	0.846936i	$0.321556\pi$
$314$	−30.3807	−1.71448
$315$	0	0
$316$	0.230663	0.0129758
$317$	14.0847	0.791078	0.395539	−	0.918449i	$-0.370558\pi$
$317$	14.0847	0.791078	0.395539	+	0.918449i	$0.370558\pi$
$318$	46.8962	2.62981
$319$	−1.19925	−0.0671452
$320$	−2.39119	−0.133671
$321$	−26.0333	−1.45304
$322$	0	0
$323$	3.29575	0.183381
$324$	−0.464006	−0.0257781
$325$	17.0418	0.945308
$326$	21.7592	1.20513
$327$	−21.4160	−1.18431
$328$	−7.99905	−0.441674
$329$	0	0
$330$	0.495156	0.0272575
$331$	7.13182	0.392000	0.196000	−	0.980604i	$-0.437205\pi$
$331$	7.13182	0.392000	0.196000	+	0.980604i	$0.437205\pi$
$332$	−0.269597	−0.0147961
$333$	70.9051	3.88557
$334$	11.2048	0.613102
$335$	2.26724	0.123873
$336$	0	0
$337$	−6.45355	−0.351547	−0.175774	−	0.984431i	$-0.556243\pi$
$337$	−6.45355	−0.351547	−0.175774	+	0.984431i	$0.556243\pi$
$338$	1.35831	0.0738824
$339$	−49.8637	−2.70822
$340$	−0.0211994	−0.00114970
$341$	−1.47703	−0.0799859
$342$	10.1385	0.548226
$343$	0	0
$344$	−17.2970	−0.932590
$345$	−7.00466	−0.377118
$346$	−7.89788	−0.424593
$347$	4.87230	0.261559	0.130779	−	0.991411i	$-0.458252\pi$
$347$	4.87230	0.261559	0.130779	+	0.991411i	$0.458252\pi$
$348$	0.223682	0.0119906
$349$	−11.2362	−0.601459	−0.300729	−	0.953709i	$-0.597230\pi$
$349$	−11.2362	−0.601459	−0.300729	+	0.953709i	$0.597230\pi$
$350$	0	0
$351$	46.6435	2.48965
$352$	0.0458347	0.00244300
$353$	−6.20110	−0.330051	−0.165026	−	0.986289i	$-0.552771\pi$
$353$	−6.20110	−0.330051	−0.165026	+	0.986289i	$0.552771\pi$
$354$	21.0670	1.11970
$355$	−0.556517	−0.0295369
$356$	−0.134531	−0.00713011
$357$	0	0
$358$	−10.4603	−0.552844
$359$	19.4926	1.02878	0.514390	−	0.857557i	$-0.328018\pi$
$359$	19.4926	1.02878	0.514390	+	0.857557i	$0.328018\pi$
$360$	−6.06217	−0.319504
$361$	1.00000	0.0526316
$362$	−12.6516	−0.664953
$363$	34.7020	1.82138
$364$	0	0
$365$	−0.301050	−0.0157577
$366$	−31.8980	−1.66733
$367$	−23.3201	−1.21730	−0.608649	−	0.793440i	$-0.708288\pi$
$367$	−23.3201	−1.21730	−0.608649	+	0.793440i	$0.708288\pi$
$368$	29.3252	1.52868
$369$	−20.2769	−1.05558
$370$	4.09180	0.212723
$371$	0	0
$372$	0.275494	0.0142837
$373$	−0.251690	−0.0130320	−0.00651601	−	0.999979i	$-0.502074\pi$
$373$	−0.251690	−0.0130320	−0.00651601	+	0.999979i	$0.502074\pi$
$374$	−1.72700	−0.0893010
$375$	−9.36676	−0.483697
$376$	−19.3970	−1.00032
$377$	−11.1667	−0.575112
$378$	0	0
$379$	−6.23458	−0.320249	−0.160125	−	0.987097i	$-0.551190\pi$
$379$	−6.23458	−0.320249	−0.160125	+	0.987097i	$0.551190\pi$
$380$	−0.00643235	−0.000329973 0
$381$	10.6826	0.547284
$382$	−31.1645	−1.59452
$383$	11.5020	0.587723	0.293862	−	0.955848i	$-0.405060\pi$
$383$	11.5020	0.587723	0.293862	+	0.955848i	$0.405060\pi$
$384$	35.5469	1.81400
$385$	0	0
$386$	−0.573021	−0.0291660
$387$	−43.8464	−2.22884
$388$	−0.00511401	−0.000259624 0
$389$	−34.8083	−1.76485	−0.882426	−	0.470452i	$-0.844091\pi$
$389$	−34.8083	−1.76485	−0.882426	+	0.470452i	$0.844091\pi$
$390$	4.61058	0.233466
$391$	24.4307	1.23552
$392$	0	0
$393$	−50.2040	−2.53246
$394$	28.8619	1.45404
$395$	3.13664	0.157822
$396$	0.0584077	0.00293510
$397$	−29.1524	−1.46311	−0.731557	−	0.681780i	$-0.761206\pi$
$397$	−29.1524	−1.46311	−0.731557	+	0.681780i	$0.761206\pi$
$398$	−9.86750	−0.494613
$399$	0	0
$400$	19.4341	0.971706
$401$	−14.5746	−0.727820	−0.363910	−	0.931434i	$-0.618558\pi$
$401$	−14.5746	−0.727820	−0.363910	+	0.931434i	$0.618558\pi$
$402$	−34.4498	−1.71820
$403$	−13.7532	−0.685095
$404$	0.0167779	0.000834732 0
$405$	−6.30973	−0.313533
$406$	0	0
$407$	−3.66473	−0.181654
$408$	29.9432	1.48241
$409$	9.60370	0.474872	0.237436	−	0.971403i	$-0.423693\pi$
$409$	9.60370	0.474872	0.237436	+	0.971403i	$0.423693\pi$
$410$	−1.17015	−0.0577893
$411$	−43.4473	−2.14310
$412$	0.230957	0.0113784
$413$	0	0
$414$	75.1544	3.69364
$415$	−3.66608	−0.179961
$416$	0.426783	0.0209248
$417$	−68.1564	−3.33763
$418$	−0.524008	−0.0256301
$419$	17.2401	0.842234	0.421117	−	0.907006i	$-0.361638\pi$
$419$	17.2401	0.842234	0.421117	+	0.907006i	$0.361638\pi$
$420$	0	0
$421$	15.3528	0.748251	0.374126	−	0.927378i	$-0.377943\pi$
$421$	15.3528	0.748251	0.374126	+	0.927378i	$0.377943\pi$
$422$	21.4149	1.04246
$423$	−49.1698	−2.39072
$424$	29.6748	1.44114
$425$	16.1905	0.785354
$426$	8.45605	0.409697
$427$	0	0
$428$	−0.177212	−0.00856589
$429$	−4.12936	−0.199368
$430$	−2.53029	−0.122022
$431$	−5.98348	−0.288214	−0.144107	−	0.989562i	$-0.546031\pi$
$431$	−5.98348	−0.288214	−0.144107	+	0.989562i	$0.546031\pi$
$432$	53.1913	2.55917
$433$	15.2443	0.732596	0.366298	−	0.930498i	$-0.380625\pi$
$433$	15.2443	0.732596	0.366298	+	0.930498i	$0.380625\pi$
$434$	0	0
$435$	3.04171	0.145839
$436$	−0.145782	−0.00698169
$437$	7.41280	0.354602
$438$	4.57433	0.218570
$439$	31.9500	1.52489	0.762445	−	0.647053i	$-0.223999\pi$
$439$	31.9500	1.52489	0.762445	+	0.647053i	$0.223999\pi$
$440$	0.313324	0.0149371
$441$	0	0
$442$	−16.0807	−0.764881
$443$	33.7439	1.60322	0.801610	−	0.597848i	$-0.203977\pi$
$443$	33.7439	1.60322	0.801610	+	0.597848i	$0.203977\pi$
$444$	0.683539	0.0324393
$445$	−1.82940	−0.0867217
$446$	−0.0604855	−0.00286407
$447$	−32.6559	−1.54457
$448$	0	0
$449$	21.1734	0.999234	0.499617	−	0.866246i	$-0.333474\pi$
$449$	21.1734	0.999234	0.499617	+	0.866246i	$0.333474\pi$
$450$	49.8056	2.34786
$451$	1.04802	0.0493491
$452$	−0.339430	−0.0159654
$453$	8.24356	0.387316
$454$	22.1336	1.03878
$455$	0	0
$456$	9.08541	0.425463
$457$	−8.06009	−0.377035	−0.188518	−	0.982070i	$-0.560368\pi$
$457$	−8.06009	−0.377035	−0.188518	+	0.982070i	$0.560368\pi$
$458$	−14.8755	−0.695088
$459$	44.3135	2.06838
$460$	−0.0476817	−0.00222317
$461$	−12.4647	−0.580537	−0.290268	−	0.956945i	$-0.593745\pi$
$461$	−12.4647	−0.580537	−0.290268	+	0.956945i	$0.593745\pi$
$462$	0	0
$463$	14.8402	0.689685	0.344842	−	0.938661i	$-0.387932\pi$
$463$	14.8402	0.689685	0.344842	+	0.938661i	$0.387932\pi$
$464$	−12.7342	−0.591172
$465$	3.74626	0.173729
$466$	0.740525	0.0343042
$467$	2.49691	0.115543	0.0577715	−	0.998330i	$-0.481601\pi$
$467$	2.49691	0.115543	0.0577715	+	0.998330i	$0.481601\pi$
$468$	0.543855	0.0251397
$469$	0	0
$470$	−2.83750	−0.130884
$471$	−69.0134	−3.17997
$472$	13.3307	0.613597
$473$	2.26620	0.104200
$474$	−47.6600	−2.18909
$475$	4.91253	0.225402
$476$	0	0
$477$	75.2232	3.44424
$478$	6.42726	0.293976
$479$	15.7163	0.718097	0.359049	−	0.933319i	$-0.383101\pi$
$479$	15.7163	0.718097	0.359049	+	0.933319i	$0.383101\pi$
$480$	−0.116252	−0.00530617
$481$	−34.1236	−1.55590
$482$	−32.1521	−1.46449
$483$	0	0
$484$	0.236222	0.0107373
$485$	−0.0695421	−0.00315775
$486$	39.1397	1.77541
$487$	14.8609	0.673412	0.336706	−	0.941610i	$-0.390687\pi$
$487$	14.8609	0.673412	0.336706	+	0.941610i	$0.390687\pi$
$488$	−20.1843	−0.913701
$489$	49.4286	2.23524
$490$	0	0
$491$	−2.79345	−0.126067	−0.0630334	−	0.998011i	$-0.520077\pi$
$491$	−2.79345	−0.126067	−0.0630334	+	0.998011i	$0.520077\pi$
$492$	−0.195474	−0.00881264
$493$	−10.6088	−0.477798
$494$	−4.87922	−0.219527
$495$	0.794250	0.0356989
$496$	−15.6839	−0.704226
$497$	0	0
$498$	55.7045	2.49618
$499$	31.0687	1.39082	0.695412	−	0.718611i	$-0.255222\pi$
$499$	31.0687	1.39082	0.695412	+	0.718611i	$0.255222\pi$
$500$	−0.0637609	−0.00285147
$501$	25.4532	1.13716
$502$	−11.9523	−0.533458
$503$	9.93140	0.442819	0.221410	−	0.975181i	$-0.428934\pi$
$503$	9.93140	0.442819	0.221410	+	0.975181i	$0.428934\pi$
$504$	0	0
$505$	0.228152	0.0101526
$506$	−3.88436	−0.172681
$507$	3.08557	0.137035
$508$	0.0727177	0.00322633
$509$	−14.3464	−0.635894	−0.317947	−	0.948108i	$-0.602993\pi$
$509$	−14.3464	−0.635894	−0.317947	+	0.948108i	$0.602993\pi$
$510$	4.38026	0.193961
$511$	0	0
$512$	22.9854	1.01582
$513$	13.4456	0.593639
$514$	−15.9583	−0.703891
$515$	3.14063	0.138393
$516$	−0.422688	−0.0186078
$517$	2.54134	0.111768
$518$	0	0
$519$	−17.9410	−0.787522
$520$	2.91747	0.127939
$521$	−35.4447	−1.55286	−0.776431	−	0.630203i	$-0.782972\pi$
$521$	−35.4447	−1.55286	−0.776431	+	0.630203i	$0.782972\pi$
$522$	−32.6352	−1.42840
$523$	33.8791	1.48143	0.740714	−	0.671820i	$-0.234487\pi$
$523$	33.8791	1.48143	0.740714	+	0.671820i	$0.234487\pi$
$524$	−0.341746	−0.0149292
$525$	0	0
$526$	6.91559	0.301534
$527$	−13.0662	−0.569171
$528$	−4.70904	−0.204935
$529$	31.9496	1.38911
$530$	4.34099	0.188561
$531$	33.7923	1.46646
$532$	0	0
$533$	9.75844	0.422685
$534$	27.7969	1.20289
$535$	−2.40980	−0.104185
$536$	−21.7990	−0.941574
$537$	−23.7618	−1.02540
$538$	−40.5402	−1.74781
$539$	0	0
$540$	−0.0864871	−0.00372181
$541$	−31.4110	−1.35046	−0.675232	−	0.737606i	$-0.735956\pi$
$541$	−31.4110	−1.35046	−0.675232	+	0.737606i	$0.735956\pi$
$542$	−3.73350	−0.160368
$543$	−28.7396	−1.23333
$544$	0.405464	0.0173841
$545$	−1.98240	−0.0849165
$546$	0	0
$547$	−39.3436	−1.68221	−0.841106	−	0.540870i	$-0.818095\pi$
$547$	−39.3436	−1.68221	−0.841106	+	0.540870i	$0.818095\pi$
$548$	−0.295752	−0.0126339
$549$	−51.1656	−2.18369
$550$	−2.57420	−0.109764
$551$	−3.21894	−0.137132
$552$	67.3483	2.86653
$553$	0	0
$554$	5.06300	0.215106
$555$	9.29501	0.394551
$556$	−0.463951	−0.0196759
$557$	22.2814	0.944091	0.472046	−	0.881574i	$-0.343516\pi$
$557$	22.2814	0.944091	0.472046	+	0.881574i	$0.343516\pi$
$558$	−40.1945	−1.70157
$559$	21.1014	0.892495
$560$	0	0
$561$	−3.92309	−0.165633
$562$	−1.90838	−0.0805002
$563$	22.9600	0.967649	0.483825	−	0.875165i	$-0.339247\pi$
$563$	22.9600	0.967649	0.483825	+	0.875165i	$0.339247\pi$
$564$	−0.474007	−0.0199593
$565$	−4.61569	−0.194183
$566$	−8.50943	−0.357678
$567$	0	0
$568$	5.35080	0.224514
$569$	−5.71545	−0.239604	−0.119802	−	0.992798i	$-0.538226\pi$
$569$	−5.71545	−0.239604	−0.119802	+	0.992798i	$0.538226\pi$
$570$	1.32906	0.0556683
$571$	20.7502	0.868370	0.434185	−	0.900824i	$-0.357036\pi$
$571$	20.7502	0.868370	0.434185	+	0.900824i	$0.357036\pi$
$572$	−0.0281092	−0.00117530
$573$	−70.7940	−2.95746
$574$	0	0
$575$	36.4156	1.51864
$576$	58.2796	2.42832
$577$	−3.83652	−0.159717	−0.0798583	−	0.996806i	$-0.525447\pi$
$577$	−3.83652	−0.159717	−0.0798583	+	0.996806i	$0.525447\pi$
$578$	8.63314	0.359091
$579$	−1.30169	−0.0540962
$580$	0.0207054	0.000859745 0
$581$	0	0
$582$	1.05666	0.0438001
$583$	−3.88792	−0.161021
$584$	2.89453	0.119777
$585$	7.39554	0.305768
$586$	−5.60647	−0.231601
$587$	−36.8951	−1.52282	−0.761412	−	0.648269i	$-0.775493\pi$
$587$	−36.8951	−1.52282	−0.761412	+	0.648269i	$0.775493\pi$
$588$	0	0
$589$	−3.96455	−0.163356
$590$	1.95009	0.0802841
$591$	65.5632	2.69691
$592$	−38.9139	−1.59935
$593$	37.4036	1.53598	0.767990	−	0.640462i	$-0.221257\pi$
$593$	37.4036	1.53598	0.767990	+	0.640462i	$0.221257\pi$
$594$	−7.04561	−0.289085
$595$	0	0
$596$	−0.222293	−0.00910549
$597$	−22.4152	−0.917394
$598$	−36.1687	−1.47905
$599$	−14.1382	−0.577672	−0.288836	−	0.957379i	$-0.593268\pi$
$599$	−14.1382	−0.577672	−0.288836	+	0.957379i	$0.593268\pi$
$600$	44.6323	1.82211
$601$	−42.8102	−1.74627	−0.873133	−	0.487482i	$-0.837916\pi$
$601$	−42.8102	−1.74627	−0.873133	+	0.487482i	$0.837916\pi$
$602$	0	0
$603$	−55.2587	−2.25031
$604$	0.0561151	0.00228329
$605$	3.21223	0.130596
$606$	−3.46667	−0.140824
$607$	−13.3315	−0.541107	−0.270554	−	0.962705i	$-0.587207\pi$
$607$	−13.3315	−0.541107	−0.270554	+	0.962705i	$0.587207\pi$
$608$	0.123026	0.00498937
$609$	0	0
$610$	−2.95267	−0.119550
$611$	23.6634	0.957317
$612$	0.516688	0.0208859
$613$	3.39651	0.137184	0.0685919	−	0.997645i	$-0.478149\pi$
$613$	3.39651	0.137184	0.0685919	+	0.997645i	$0.478149\pi$
$614$	25.1989	1.01694
$615$	−2.65812	−0.107186
$616$	0	0
$617$	−26.1522	−1.05285	−0.526424	−	0.850222i	$-0.676467\pi$
$617$	−26.1522	−1.05285	−0.526424	+	0.850222i	$0.676467\pi$
$618$	−47.7206	−1.91961
$619$	−46.8265	−1.88211	−0.941057	−	0.338247i	$-0.890166\pi$
$619$	−46.8265	−1.88211	−0.941057	+	0.338247i	$0.890166\pi$
$620$	0.0255014	0.00102416
$621$	99.6698	3.99961
$622$	26.5081	1.06288
$623$	0	0
$624$	−43.8476	−1.75531
$625$	23.6956	0.947824
$626$	−26.4609	−1.05759
$627$	−1.19035	−0.0475378
$628$	−0.469785	−0.0187465
$629$	−32.4190	−1.29263
$630$	0	0
$631$	12.1061	0.481935	0.240968	−	0.970533i	$-0.422535\pi$
$631$	12.1061	0.481935	0.240968	+	0.970533i	$0.422535\pi$
$632$	−30.1581	−1.19963
$633$	48.6464	1.93352
$634$	−19.8102	−0.786765
$635$	0.988842	0.0392410
$636$	0.725167	0.0287548
$637$	0	0
$638$	1.68675	0.0667791
$639$	13.5638	0.536577
$640$	3.29044	0.130066
$641$	17.4856	0.690638	0.345319	−	0.938485i	$-0.387771\pi$
$641$	17.4856	0.690638	0.345319	+	0.938485i	$0.387771\pi$
$642$	36.6159	1.44511
$643$	−0.553783	−0.0218391	−0.0109195	−	0.999940i	$-0.503476\pi$
$643$	−0.553783	−0.0218391	−0.0109195	+	0.999940i	$0.503476\pi$
$644$	0	0
$645$	−5.74787	−0.226322
$646$	−4.63549	−0.182381
$647$	−13.1248	−0.515991	−0.257995	−	0.966146i	$-0.583062\pi$
$647$	−13.1248	−0.515991	−0.257995	+	0.966146i	$0.583062\pi$
$648$	60.6667	2.38321
$649$	−1.74656	−0.0685585
$650$	−23.9693	−0.940154
$651$	0	0
$652$	0.336468	0.0131771
$653$	3.42592	0.134067	0.0670333	−	0.997751i	$-0.478647\pi$
$653$	3.42592	0.134067	0.0670333	+	0.997751i	$0.478647\pi$
$654$	30.1217	1.17785
$655$	−4.64719	−0.181581
$656$	11.1283	0.434488
$657$	7.33740	0.286259
$658$	0	0
$659$	3.34771	0.130408	0.0652041	−	0.997872i	$-0.479230\pi$
$659$	3.34771	0.130408	0.0652041	+	0.997872i	$0.479230\pi$
$660$	0.00765673	0.000298038 0
$661$	−25.2423	−0.981810	−0.490905	−	0.871213i	$-0.663334\pi$
$661$	−25.2423	−0.981810	−0.490905	+	0.871213i	$0.663334\pi$
$662$	−10.0309	−0.389863
$663$	−36.5292	−1.41868
$664$	35.2486	1.36791
$665$	0	0
$666$	−99.7282	−3.86439
$667$	−23.8614	−0.923916
$668$	0.173263	0.00670376
$669$	−0.137400	−0.00531219
$670$	−3.18888	−0.123197
$671$	2.64450	0.102090
$672$	0	0
$673$	−5.61847	−0.216576	−0.108288	−	0.994120i	$-0.534537\pi$
$673$	−5.61847	−0.216576	−0.108288	+	0.994120i	$0.534537\pi$
$674$	9.07693	0.349630
$675$	66.0521	2.54235
$676$	0.0210039	0.000807843 0
$677$	51.6090	1.98349	0.991747	−	0.128209i	$-0.0409228\pi$
$677$	51.6090	1.98349	0.991747	+	0.128209i	$0.0409228\pi$
$678$	70.1334	2.69346
$679$	0	0
$680$	2.77173	0.106291
$681$	50.2792	1.92670
$682$	2.07745	0.0795498
$683$	16.4961	0.631207	0.315603	−	0.948891i	$-0.397793\pi$
$683$	16.4961	0.631207	0.315603	+	0.948891i	$0.397793\pi$
$684$	0.156774	0.00599440
$685$	−4.02175	−0.153663
$686$	0	0
$687$	−33.7915	−1.28923
$688$	24.0637	0.917418
$689$	−36.2018	−1.37918
$690$	9.85207	0.375062
$691$	−11.7493	−0.446965	−0.223482	−	0.974708i	$-0.571743\pi$
$691$	−11.7493	−0.446965	−0.223482	+	0.974708i	$0.571743\pi$
$692$	−0.122127	−0.00464257
$693$	0	0
$694$	−6.85290	−0.260133
$695$	−6.30897	−0.239313
$696$	−29.2454	−1.10854
$697$	9.27097	0.351163
$698$	15.8037	0.598180
$699$	1.68219	0.0636263
$700$	0	0
$701$	−28.7953	−1.08758	−0.543792	−	0.839220i	$-0.683012\pi$
$701$	−28.7953	−1.08758	−0.543792	+	0.839220i	$0.683012\pi$
$702$	−65.6042	−2.47607
$703$	−9.83661	−0.370995
$704$	−3.01219	−0.113526
$705$	−6.44572	−0.242760
$706$	8.72187	0.328252
$707$	0	0
$708$	0.325765	0.0122430
$709$	18.1688	0.682345	0.341172	−	0.940001i	$-0.389176\pi$
$709$	18.1688	0.682345	0.341172	+	0.940001i	$0.389176\pi$
$710$	0.782743	0.0293758
$711$	−76.4484	−2.86704
$712$	17.5893	0.659185
$713$	−29.3884	−1.10060
$714$	0	0
$715$	−0.382239	−0.0142949
$716$	−0.161750	−0.00604489
$717$	14.6003	0.545258
$718$	−27.4164	−1.02317
$719$	−34.2823	−1.27851	−0.639256	−	0.768994i	$-0.720758\pi$
$719$	−34.2823	−1.27851	−0.639256	+	0.768994i	$0.720758\pi$
$720$	8.43373	0.314306
$721$	0	0
$722$	−1.40650	−0.0523446
$723$	−73.0373	−2.71629
$724$	−0.195635	−0.00727071
$725$	−15.8132	−0.587286
$726$	−48.8084	−1.81145
$727$	13.1214	0.486646	0.243323	−	0.969945i	$-0.421763\pi$
$727$	13.1214	0.486646	0.243323	+	0.969945i	$0.421763\pi$
$728$	0	0
$729$	24.9070	0.922483
$730$	0.423428	0.0156718
$731$	20.0473	0.741478
$732$	−0.493247	−0.0182309
$733$	6.06773	0.224117	0.112058	−	0.993702i	$-0.464256\pi$
$733$	6.06773	0.224117	0.112058	+	0.993702i	$0.464256\pi$
$734$	32.7997	1.21066
$735$	0	0
$736$	0.911968	0.0336156
$737$	2.85605	0.105204
$738$	28.5196	1.04982
$739$	23.7399	0.873288	0.436644	−	0.899634i	$-0.356167\pi$
$739$	23.7399	0.873288	0.436644	+	0.899634i	$0.356167\pi$
$740$	0.0632726	0.00232595
$741$	−11.0837	−0.407171
$742$	0	0
$743$	−33.1525	−1.21625	−0.608124	−	0.793842i	$-0.708078\pi$
$743$	−33.1525	−1.21625	−0.608124	+	0.793842i	$0.708078\pi$
$744$	−36.0195	−1.32054
$745$	−3.02283	−0.110748
$746$	0.354003	0.0129610
$747$	89.3522	3.26923
$748$	−0.0267050	−0.000976433 0
$749$	0	0
$750$	13.1744	0.481060
$751$	37.5315	1.36954	0.684772	−	0.728757i	$-0.259902\pi$
$751$	37.5315	1.36954	0.684772	+	0.728757i	$0.259902\pi$
$752$	26.9852	0.984050
$753$	−27.1511	−0.989441
$754$	15.7059	0.571977
$755$	0.763074	0.0277711
$756$	0	0
$757$	14.2165	0.516708	0.258354	−	0.966050i	$-0.416820\pi$
$757$	14.2165	0.516708	0.258354	+	0.966050i	$0.416820\pi$
$758$	8.76896	0.318503
$759$	−8.82379	−0.320283
$760$	0.841001	0.0305063
$761$	−51.4365	−1.86457	−0.932285	−	0.361725i	$-0.882188\pi$
$761$	−51.4365	−1.86457	−0.932285	+	0.361725i	$0.882188\pi$
$762$	−15.0250	−0.544300
$763$	0	0
$764$	−0.481905	−0.0174347
$765$	7.02611	0.254029
$766$	−16.1776	−0.584519
$767$	−16.2628	−0.587217
$768$	1.66755	0.0601724
$769$	−29.5161	−1.06438	−0.532188	−	0.846626i	$-0.678630\pi$
$769$	−29.5161	−1.06438	−0.532188	+	0.846626i	$0.678630\pi$
$770$	0	0
$771$	−36.2512	−1.30556
$772$	−0.00886077	−0.000318906 0
$773$	47.3158	1.70183	0.850916	−	0.525301i	$-0.176047\pi$
$773$	47.3158	1.70183	0.850916	+	0.525301i	$0.176047\pi$
$774$	61.6701	2.21669
$775$	−19.4760	−0.699597
$776$	0.668633	0.0240025
$777$	0	0
$778$	48.9580	1.75523
$779$	2.81301	0.100786
$780$	0.0712945	0.00255275
$781$	−0.701047	−0.0250854
$782$	−34.3619	−1.22878
$783$	−43.2807	−1.54673
$784$	0	0
$785$	−6.38830	−0.228008
$786$	70.6120	2.51865
$787$	20.6740	0.736948	0.368474	−	0.929638i	$-0.379880\pi$
$787$	20.6740	0.736948	0.368474	+	0.929638i	$0.379880\pi$
$788$	0.446299	0.0158987
$789$	15.7096	0.559277
$790$	−4.41170	−0.156961
$791$	0	0
$792$	−7.63654	−0.271353
$793$	24.6238	0.874418
$794$	41.0029	1.45514
$795$	9.86109	0.349737
$796$	−0.152584	−0.00540819
$797$	19.0955	0.676398	0.338199	−	0.941075i	$-0.390182\pi$
$797$	19.0955	0.676398	0.338199	+	0.941075i	$0.390182\pi$
$798$	0	0
$799$	22.4813	0.795331
$800$	0.604370	0.0213677
$801$	44.5873	1.57542
$802$	20.4992	0.723851
$803$	−0.379234	−0.0133829
$804$	−0.532705	−0.0187871
$805$	0	0
$806$	19.3439	0.681360
$807$	−92.0919	−3.24179
$808$	−2.19363	−0.0771717
$809$	7.56887	0.266107	0.133054	−	0.991109i	$-0.457522\pi$
$809$	7.56887	0.266107	0.133054	+	0.991109i	$0.457522\pi$
$810$	8.87465	0.311824
$811$	−10.5995	−0.372200	−0.186100	−	0.982531i	$-0.559585\pi$
$811$	−10.5995	−0.372200	−0.186100	+	0.982531i	$0.559585\pi$
$812$	0	0
$813$	−8.48110	−0.297445
$814$	5.15446	0.180664
$815$	4.57541	0.160270
$816$	−41.6572	−1.45829
$817$	6.08278	0.212810
$818$	−13.5076	−0.472283
$819$	0	0
$820$	−0.0180943	−0.000631879 0
$821$	5.17484	0.180603	0.0903016	−	0.995914i	$-0.471217\pi$
$821$	5.17484	0.180603	0.0903016	+	0.995914i	$0.471217\pi$
$822$	61.1088	2.13141
$823$	−11.4852	−0.400348	−0.200174	−	0.979760i	$-0.564151\pi$
$823$	−11.4852	−0.400348	−0.200174	+	0.979760i	$0.564151\pi$
$824$	−30.1965	−1.05195
$825$	−5.84761	−0.203588
$826$	0	0
$827$	−4.29977	−0.149518	−0.0747588	−	0.997202i	$-0.523819\pi$
$827$	−4.29977	−0.149518	−0.0747588	+	0.997202i	$0.523819\pi$
$828$	1.16213	0.0403869
$829$	−56.5964	−1.96567	−0.982837	−	0.184474i	$-0.940942\pi$
$829$	−56.5964	−1.96567	−0.982837	+	0.184474i	$0.940942\pi$
$830$	5.15635	0.178980
$831$	11.5012	0.398972
$832$	−28.0475	−0.972374
$833$	0	0
$834$	95.8621	3.31943
$835$	2.35610	0.0815362
$836$	−0.00810286	−0.000280243 0
$837$	−53.3059	−1.84252
$838$	−24.2483	−0.837642
$839$	8.94673	0.308875	0.154438	−	0.988003i	$-0.450643\pi$
$839$	8.94673	0.308875	0.154438	+	0.988003i	$0.450643\pi$
$840$	0	0
$841$	−18.6384	−0.642703
$842$	−21.5938	−0.744172
$843$	−4.33512	−0.149309
$844$	0.331143	0.0113984
$845$	0.285619	0.00982558
$846$	69.1575	2.37768
$847$	0	0
$848$	−41.2838	−1.41769
$849$	−19.3302	−0.663410
$850$	−22.7720	−0.781072
$851$	−72.9168	−2.49956
$852$	0.130758	0.00447970
$853$	21.1366	0.723702	0.361851	−	0.932236i	$-0.382145\pi$
$853$	21.1366	0.723702	0.361851	+	0.932236i	$0.382145\pi$
$854$	0	0
$855$	2.13187	0.0729083
$856$	23.1697	0.791924
$857$	−57.6877	−1.97058	−0.985288	−	0.170903i	$-0.945332\pi$
$857$	−57.6877	−1.97058	−0.985288	+	0.170903i	$0.945332\pi$
$858$	5.80796	0.198281
$859$	−28.3309	−0.966638	−0.483319	−	0.875444i	$-0.660569\pi$
$859$	−28.3309	−0.966638	−0.483319	+	0.875444i	$0.660569\pi$
$860$	−0.0391266	−0.00133421
$861$	0	0
$862$	8.41578	0.286643
$863$	8.74556	0.297702	0.148851	−	0.988860i	$-0.452442\pi$
$863$	8.74556	0.297702	0.148851	+	0.988860i	$0.452442\pi$
$864$	1.65416	0.0562758
$865$	−1.66073	−0.0564664
$866$	−21.4412	−0.728602
$867$	19.6112	0.666032
$868$	0	0
$869$	3.95124	0.134037
$870$	−4.27818	−0.145044
$871$	26.5937	0.901093
$872$	19.0603	0.645463
$873$	1.69493	0.0573646
$874$	−10.4261	−0.352669
$875$	0	0
$876$	0.0707340	0.00238988
$877$	33.7988	1.14131	0.570653	−	0.821191i	$-0.306690\pi$
$877$	33.7988	1.14131	0.570653	+	0.821191i	$0.306690\pi$
$878$	−44.9378	−1.51658
$879$	−12.7358	−0.429566
$880$	−0.435898	−0.0146941
$881$	7.64434	0.257544	0.128772	−	0.991674i	$-0.458896\pi$
$881$	7.64434	0.257544	0.128772	+	0.991674i	$0.458896\pi$
$882$	0	0
$883$	35.1172	1.18179	0.590894	−	0.806749i	$-0.298775\pi$
$883$	35.1172	1.18179	0.590894	+	0.806749i	$0.298775\pi$
$884$	−0.248660	−0.00836334
$885$	4.42987	0.148909
$886$	−47.4608	−1.59448
$887$	−38.9233	−1.30692	−0.653459	−	0.756962i	$-0.726683\pi$
$887$	−38.9233	−1.30692	−0.653459	+	0.756962i	$0.726683\pi$
$888$	−89.3696	−2.99905
$889$	0	0
$890$	2.57305	0.0862489
$891$	−7.94839	−0.266281
$892$	−0.000935303 0	−3.13163e−5 0
$893$	6.82129	0.228266
$894$	45.9306	1.53615
$895$	−2.19954	−0.0735225
$896$	0	0
$897$	−82.1615	−2.74329
$898$	−29.7804	−0.993786
$899$	12.7617	0.425625
$900$	0.770156	0.0256719
$901$	−34.3934	−1.14581
$902$	−1.47404	−0.0490801
$903$	0	0
$904$	44.3788	1.47602
$905$	−2.66031	−0.0884318
$906$	−11.5946	−0.385204
$907$	−34.8962	−1.15871	−0.579355	−	0.815075i	$-0.696696\pi$
$907$	−34.8962	−1.15871	−0.579355	+	0.815075i	$0.696696\pi$
$908$	0.342258	0.0113582
$909$	−5.56068	−0.184436
$910$	0	0
$911$	15.0789	0.499588	0.249794	−	0.968299i	$-0.419637\pi$
$911$	15.0789	0.499588	0.249794	+	0.968299i	$0.419637\pi$
$912$	−12.6397	−0.418541
$913$	−4.61818	−0.152839
$914$	11.3365	0.374980
$915$	−6.70735	−0.221738
$916$	−0.230024	−0.00760021
$917$	0	0
$918$	−62.3270	−2.05710
$919$	−39.1404	−1.29112	−0.645562	−	0.763708i	$-0.723377\pi$
$919$	−39.1404	−1.29112	−0.645562	+	0.763708i	$0.723377\pi$
$920$	6.23417	0.205534
$921$	57.2422	1.88620
$922$	17.5316	0.577372
$923$	−6.52770	−0.214862
$924$	0	0
$925$	−48.3226	−1.58884
$926$	−20.8729	−0.685925
$927$	−76.5457	−2.51409
$928$	−0.396014	−0.0129998
$929$	−45.5626	−1.49486	−0.747430	−	0.664341i	$-0.768712\pi$
$929$	−45.5626	−1.49486	−0.747430	+	0.664341i	$0.768712\pi$
$930$	−5.26913	−0.172782
$931$	0	0
$932$	0.0114509	0.000375088 0
$933$	60.2163	1.97139
$934$	−3.51191	−0.114913
$935$	−0.363145	−0.0118761
$936$	−71.1065	−2.32419
$937$	34.5829	1.12977	0.564887	−	0.825168i	$-0.308920\pi$
$937$	34.5829	1.12977	0.564887	+	0.825168i	$0.308920\pi$
$938$	0	0
$939$	−60.1091	−1.96159
$940$	−0.0438770	−0.00143111
$941$	−37.4816	−1.22186	−0.610932	−	0.791683i	$-0.709205\pi$
$941$	−37.4816	−1.22186	−0.610932	+	0.791683i	$0.709205\pi$
$942$	97.0676	3.16263
$943$	20.8522	0.679042
$944$	−18.5458	−0.603615
$945$	0	0
$946$	−3.18742	−0.103632
$947$	−31.6815	−1.02951	−0.514755	−	0.857337i	$-0.672117\pi$
$947$	−31.6815	−1.02951	−0.514755	+	0.857337i	$0.672117\pi$
$948$	−0.736978	−0.0239359
$949$	−3.53118	−0.114627
$950$	−6.90949	−0.224173
$951$	−45.0013	−1.45927
$952$	0	0
$953$	48.2237	1.56212	0.781060	−	0.624456i	$-0.214679\pi$
$953$	48.2237	1.56212	0.781060	+	0.624456i	$0.214679\pi$
$954$	−105.802	−3.42546
$955$	−6.55312	−0.212054
$956$	0.0993864	0.00321439
$957$	3.83166	0.123860
$958$	−22.1051	−0.714182
$959$	0	0
$960$	7.63994	0.246578
$961$	−15.2824	−0.492979
$962$	47.9950	1.54742
$963$	58.7333	1.89265
$964$	−0.497176	−0.0160130
$965$	−0.120492	−0.00387877
$966$	0	0
$967$	33.3518	1.07252	0.536260	−	0.844053i	$-0.319836\pi$
$967$	33.3518	1.07252	0.536260	+	0.844053i	$0.319836\pi$
$968$	−30.8849	−0.992677
$969$	−10.5301	−0.338274
$970$	0.0978112	0.00314053
$971$	52.4761	1.68404	0.842019	−	0.539448i	$-0.181367\pi$
$971$	52.4761	1.68404	0.842019	+	0.539448i	$0.181367\pi$
$972$	0.605227	0.0194127
$973$	0	0
$974$	−20.9019	−0.669740
$975$	−54.4492	−1.74377
$976$	28.0805	0.898836
$977$	21.5232	0.688588	0.344294	−	0.938862i	$-0.388118\pi$
$977$	21.5232	0.688588	0.344294	+	0.938862i	$0.388118\pi$
$978$	−69.5215	−2.22305
$979$	−2.30450	−0.0736521
$980$	0	0
$981$	48.3163	1.54262
$982$	3.92900	0.125380
$983$	9.88684	0.315341	0.157671	−	0.987492i	$-0.449602\pi$
$983$	9.88684	0.315341	0.157671	+	0.987492i	$0.449602\pi$
$984$	25.5573	0.814737
$985$	6.06893	0.193372
$986$	14.9214	0.475193
$987$	0	0
$988$	−0.0754486	−0.00240034
$989$	45.0904	1.43379
$990$	−1.11711	−0.0355042
$991$	25.5753	0.812426	0.406213	−	0.913778i	$-0.366849\pi$
$991$	25.5753	0.812426	0.406213	+	0.913778i	$0.366849\pi$
$992$	−0.487743	−0.0154859
$993$	−22.7865	−0.723107
$994$	0	0
$995$	−2.07489	−0.0657784
$996$	0.861374	0.0272937
$997$	5.06941	0.160550	0.0802750	−	0.996773i	$-0.474420\pi$
$997$	5.06941	0.160550	0.0802750	+	0.996773i	$0.474420\pi$
$998$	−43.6982	−1.38324
$999$	−132.259	−4.18450

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.a.o.1.2		7
3.2	odd	2		8379.2.a.ck.1.6		7
7.2	even	3		931.2.f.p.704.6		14
7.3	odd	6		133.2.f.d.58.6	yes	14
7.4	even	3		931.2.f.p.324.6		14
7.5	odd	6		133.2.f.d.39.6	✓	14
7.6	odd	2		931.2.a.n.1.2		7
21.5	even	6		1197.2.j.l.172.2		14
21.17	even	6		1197.2.j.l.856.2		14
21.20	even	2		8379.2.a.cl.1.6		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.2.f.d.39.6	✓	14	7.5	odd	6
133.2.f.d.58.6	yes	14	7.3	odd	6
931.2.a.n.1.2		7	7.6	odd	2
931.2.a.o.1.2		7	1.1	even	1	trivial
931.2.f.p.324.6		14	7.4	even	3
931.2.f.p.704.6		14	7.2	even	3
1197.2.j.l.172.2		14	21.5	even	6
1197.2.j.l.856.2		14	21.17	even	6
8379.2.a.ck.1.6		7	3.2	odd	2
8379.2.a.cl.1.6		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)

\(f(q)\)	\(=\)	\(q-1.40650 q^{2} -3.19504 q^{3} -0.0217491 q^{4} -0.295752 q^{5} +4.49383 q^{6} +2.84360 q^{8} +7.20828 q^{9} +O(q^{10})\)	\(q-1.40650 q^{2} -3.19504 q^{3} -0.0217491 q^{4} -0.295752 q^{5} +4.49383 q^{6} +2.84360 q^{8} +7.20828 q^{9} +0.415977 q^{10} -0.372561 q^{11} +0.0694893 q^{12} -3.46904 q^{13} +0.944941 q^{15} -3.95603 q^{16} -3.29575 q^{17} -10.1385 q^{18} -1.00000 q^{19} +0.00643235 q^{20} +0.524008 q^{22} -7.41280 q^{23} -9.08541 q^{24} -4.91253 q^{25} +4.87922 q^{26} -13.4456 q^{27} +3.21894 q^{29} -1.32906 q^{30} +3.96455 q^{31} -0.123026 q^{32} +1.19035 q^{33} +4.63549 q^{34} -0.156774 q^{36} +9.83661 q^{37} +1.40650 q^{38} +11.0837 q^{39} -0.841001 q^{40} -2.81301 q^{41} -6.08278 q^{43} +0.00810286 q^{44} -2.13187 q^{45} +10.4261 q^{46} -6.82129 q^{47} +12.6397 q^{48} +6.90949 q^{50} +10.5301 q^{51} +0.0754486 q^{52} +10.4357 q^{53} +18.9113 q^{54} +0.110186 q^{55} +3.19504 q^{57} -4.52745 q^{58} +4.68799 q^{59} -0.0205516 q^{60} -7.09816 q^{61} -5.57615 q^{62} +8.08509 q^{64} +1.02598 q^{65} -1.67423 q^{66} -7.66601 q^{67} +0.0716797 q^{68} +23.6842 q^{69} +1.88170 q^{71} +20.4974 q^{72} +1.01791 q^{73} -13.8352 q^{74} +15.6957 q^{75} +0.0217491 q^{76} -15.5893 q^{78} -10.6056 q^{79} +1.17001 q^{80} +21.3345 q^{81} +3.95650 q^{82} +12.3958 q^{83} +0.974727 q^{85} +8.55545 q^{86} -10.2847 q^{87} -1.05941 q^{88} +6.18557 q^{89} +2.99848 q^{90} +0.161222 q^{92} -12.6669 q^{93} +9.59417 q^{94} +0.295752 q^{95} +0.393073 q^{96} +0.235136 q^{97} -2.68552 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 2 q^{2} + 2 q^{3} + 10 q^{4} + 2 q^{5} + 4 q^{6} + 12 q^{8} + 15 q^{9}+O(q^{10}) \) 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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