LMFDB - Embedded newform 833.2.a.j.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [833,2,Mod(1,833)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(833, 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("833.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 833 = 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	833.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:	$6.65153848837$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 9x^{6} + 16x^{5} + 25x^{4} - 36x^{3} - 21x^{2} + 18x + 1 $ x^8 - 2x^7 - 9x^6 + 16x^5 + 25x^4 - 36x^3 - 21x^2 + 18*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-0.971912$ of defining polynomial
Character	$\chi$	$=$	833.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.971912 q^{2} +1.65046 q^{3} -1.05539 q^{4} -2.99258 q^{5} +1.60411 q^{6} -2.96957 q^{8} -0.275972 q^{9} +O(q^{10})$	\(q+0.971912 q^{2} +1.65046 q^{3} -1.05539 q^{4} -2.99258 q^{5} +1.60411 q^{6} -2.96957 q^{8} -0.275972 q^{9} -2.90852 q^{10} +1.75633 q^{11} -1.74188 q^{12} -1.15844 q^{13} -4.93913 q^{15} -0.775385 q^{16} -1.00000 q^{17} -0.268220 q^{18} -8.19160 q^{19} +3.15832 q^{20} +1.70699 q^{22} +2.00160 q^{23} -4.90116 q^{24} +3.95551 q^{25} -1.12590 q^{26} -5.40687 q^{27} -8.40252 q^{29} -4.80041 q^{30} -1.49124 q^{31} +5.18553 q^{32} +2.89875 q^{33} -0.971912 q^{34} +0.291257 q^{36} +0.0964009 q^{37} -7.96151 q^{38} -1.91195 q^{39} +8.88665 q^{40} -7.95695 q^{41} +8.56198 q^{43} -1.85360 q^{44} +0.825866 q^{45} +1.94538 q^{46} -1.22068 q^{47} -1.27974 q^{48} +3.84441 q^{50} -1.65046 q^{51} +1.22260 q^{52} +8.80167 q^{53} -5.25500 q^{54} -5.25594 q^{55} -13.5199 q^{57} -8.16651 q^{58} +2.31045 q^{59} +5.21270 q^{60} -8.19772 q^{61} -1.44936 q^{62} +6.59065 q^{64} +3.46670 q^{65} +2.81733 q^{66} -0.640991 q^{67} +1.05539 q^{68} +3.30357 q^{69} +11.5495 q^{71} +0.819517 q^{72} +16.5037 q^{73} +0.0936932 q^{74} +6.52842 q^{75} +8.64530 q^{76} -1.85825 q^{78} -8.79507 q^{79} +2.32040 q^{80} -8.09592 q^{81} -7.73346 q^{82} +12.0558 q^{83} +2.99258 q^{85} +8.32149 q^{86} -13.8681 q^{87} -5.21553 q^{88} +0.421332 q^{89} +0.802669 q^{90} -2.11247 q^{92} -2.46124 q^{93} -1.18639 q^{94} +24.5140 q^{95} +8.55852 q^{96} -4.53118 q^{97} -0.484696 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 8 q^{3} + 6 q^{4} - 4 q^{5} + 6 q^{6} - 6 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 - 8 * q^3 + 6 * q^4 - 4 * q^5 + 6 * q^6 - 6 * q^8 + 8 * q^9	$ 8 q - 2 q^{2} - 8 q^{3} + 6 q^{4} - 4 q^{5} + 6 q^{6} - 6 q^{8} + 8 q^{9} - 12 q^{10} + 4 q^{11} - 20 q^{12} - 12 q^{13} - 4 q^{15} - 6 q^{16} - 8 q^{17} - 6 q^{18} - 16 q^{19} + 18 q^{20} + 8 q^{22} - 4 q^{23} + 8 q^{24} + 8 q^{25} - 8 q^{26} - 20 q^{27} + 10 q^{30} - 28 q^{31} - 4 q^{32} - 16 q^{33} + 2 q^{34} + 20 q^{36} + 8 q^{37} - 8 q^{38} + 20 q^{39} - 26 q^{40} - 4 q^{41} - 8 q^{43} - 4 q^{44} + 20 q^{45} - 16 q^{46} - 28 q^{47} + 6 q^{48} - 32 q^{50} + 8 q^{51} - 32 q^{52} - 8 q^{53} + 14 q^{54} - 44 q^{55} - 16 q^{57} - 32 q^{58} + 8 q^{59} - 42 q^{60} - 8 q^{61} + 24 q^{62} - 22 q^{64} - 16 q^{66} - 20 q^{67} - 6 q^{68} - 4 q^{69} + 40 q^{71} - 40 q^{72} - 8 q^{73} + 4 q^{74} - 16 q^{75} + 12 q^{76} + 4 q^{79} + 32 q^{80} + 4 q^{81} + 10 q^{82} + 4 q^{83} + 4 q^{85} + 14 q^{86} - 16 q^{87} + 24 q^{88} + 4 q^{89} - 26 q^{90} - 28 q^{92} + 32 q^{93} - 8 q^{94} + 4 q^{95} + 52 q^{96} - 40 q^{97} + 8 q^{99}+O(q^{100}) $ 8 * q - 2 * q^2 - 8 * q^3 + 6 * q^4 - 4 * q^5 + 6 * q^6 - 6 * q^8 + 8 * q^9 - 12 * q^10 + 4 * q^11 - 20 * q^12 - 12 * q^13 - 4 * q^15 - 6 * q^16 - 8 * q^17 - 6 * q^18 - 16 * q^19 + 18 * q^20 + 8 * q^22 - 4 * q^23 + 8 * q^24 + 8 * q^25 - 8 * q^26 - 20 * q^27 + 10 * q^30 - 28 * q^31 - 4 * q^32 - 16 * q^33 + 2 * q^34 + 20 * q^36 + 8 * q^37 - 8 * q^38 + 20 * q^39 - 26 * q^40 - 4 * q^41 - 8 * q^43 - 4 * q^44 + 20 * q^45 - 16 * q^46 - 28 * q^47 + 6 * q^48 - 32 * q^50 + 8 * q^51 - 32 * q^52 - 8 * q^53 + 14 * q^54 - 44 * q^55 - 16 * q^57 - 32 * q^58 + 8 * q^59 - 42 * q^60 - 8 * q^61 + 24 * q^62 - 22 * q^64 - 16 * q^66 - 20 * q^67 - 6 * q^68 - 4 * q^69 + 40 * q^71 - 40 * q^72 - 8 * q^73 + 4 * q^74 - 16 * q^75 + 12 * q^76 + 4 * q^79 + 32 * q^80 + 4 * q^81 + 10 * q^82 + 4 * q^83 + 4 * q^85 + 14 * q^86 - 16 * q^87 + 24 * q^88 + 4 * q^89 - 26 * q^90 - 28 * q^92 + 32 * q^93 - 8 * q^94 + 4 * q^95 + 52 * q^96 - 40 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.971912	0.687246	0.343623	−	0.939108i	$-0.388346\pi$
$2$	0.971912	0.687246	0.343623	+	0.939108i	$0.388346\pi$
$3$	1.65046	0.952895	0.476448	−	0.879203i	$-0.341924\pi$
$3$	1.65046	0.952895	0.476448	+	0.879203i	$0.341924\pi$
$4$	−1.05539	−0.527693
$5$	−2.99258	−1.33832	−0.669160	−	0.743118i	$-0.733346\pi$
$5$	−2.99258	−1.33832	−0.669160	+	0.743118i	$0.733346\pi$
$6$	1.60411	0.654873
$7$	0	0
$7$	0	0
$8$	−2.96957	−1.04990
$9$	−0.275972	−0.0919906
$10$	−2.90852	−0.919755
$11$	1.75633	0.529552	0.264776	−	0.964310i	$-0.414702\pi$
$11$	1.75633	0.529552	0.264776	+	0.964310i	$0.414702\pi$
$12$	−1.74188	−0.502837
$13$	−1.15844	−0.321292	−0.160646	−	0.987012i	$-0.551358\pi$
$13$	−1.15844	−0.321292	−0.160646	+	0.987012i	$0.551358\pi$
$14$	0	0
$15$	−4.93913	−1.27528
$16$	−0.775385	−0.193846
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−0.268220	−0.0632201
$19$	−8.19160	−1.87928	−0.939641	−	0.342163i	$-0.888841\pi$
$19$	−8.19160	−1.87928	−0.939641	+	0.342163i	$0.888841\pi$
$20$	3.15832	0.706223
$21$	0	0
$22$	1.70699	0.363932
$23$	2.00160	0.417363	0.208682	−	0.977984i	$-0.433083\pi$
$23$	2.00160	0.417363	0.208682	+	0.977984i	$0.433083\pi$
$24$	−4.90116	−1.00045
$25$	3.95551	0.791101
$26$	−1.12590	−0.220807
$27$	−5.40687	−1.04055
$28$	0	0
$29$	−8.40252	−1.56031	−0.780154	−	0.625587i	$-0.784860\pi$
$29$	−8.40252	−1.56031	−0.780154	+	0.625587i	$0.784860\pi$
$30$	−4.80041	−0.876430
$31$	−1.49124	−0.267835	−0.133918	−	0.990992i	$-0.542756\pi$
$31$	−1.49124	−0.267835	−0.133918	+	0.990992i	$0.542756\pi$
$32$	5.18553	0.916681
$33$	2.89875	0.504608
$34$	−0.971912	−0.166682
$35$	0	0
$36$	0.291257	0.0485428
$37$	0.0964009	0.0158482	0.00792410	−	0.999969i	$-0.497478\pi$
$37$	0.0964009	0.0158482	0.00792410	+	0.999969i	$0.497478\pi$
$38$	−7.96151	−1.29153
$39$	−1.91195	−0.306158
$40$	8.88665	1.40510
$41$	−7.95695	−1.24267	−0.621334	−	0.783546i	$-0.713409\pi$
$41$	−7.95695	−1.24267	−0.621334	+	0.783546i	$0.713409\pi$
$42$	0	0
$43$	8.56198	1.30569	0.652845	−	0.757491i	$-0.273575\pi$
$43$	8.56198	1.30569	0.652845	+	0.757491i	$0.273575\pi$
$44$	−1.85360	−0.279441
$45$	0.825866	0.123113
$46$	1.94538	0.286831
$47$	−1.22068	−0.178054	−0.0890272	−	0.996029i	$-0.528376\pi$
$47$	−1.22068	−0.178054	−0.0890272	+	0.996029i	$0.528376\pi$
$48$	−1.27974	−0.184715
$49$	0	0
$50$	3.84441	0.543681
$51$	−1.65046	−0.231111
$52$	1.22260	0.169544
$53$	8.80167	1.20900	0.604501	−	0.796604i	$-0.293372\pi$
$53$	8.80167	1.20900	0.604501	+	0.796604i	$0.293372\pi$
$54$	−5.25500	−0.715115
$55$	−5.25594	−0.708710
$56$	0	0
$57$	−13.5199	−1.79076
$58$	−8.16651	−1.07232
$59$	2.31045	0.300795	0.150398	−	0.988626i	$-0.451945\pi$
$59$	2.31045	0.300795	0.150398	+	0.988626i	$0.451945\pi$
$60$	5.21270	0.672956
$61$	−8.19772	−1.04961	−0.524805	−	0.851222i	$-0.675862\pi$
$61$	−8.19772	−1.04961	−0.524805	+	0.851222i	$0.675862\pi$
$62$	−1.44936	−0.184069
$63$	0	0
$64$	6.59065	0.823831
$65$	3.46670	0.429992
$66$	2.81733	0.346789
$67$	−0.640991	−0.0783096	−0.0391548	−	0.999233i	$-0.512467\pi$
$67$	−0.640991	−0.0783096	−0.0391548	+	0.999233i	$0.512467\pi$
$68$	1.05539	0.127984
$69$	3.30357	0.397704
$70$	0	0
$71$	11.5495	1.37068	0.685338	−	0.728225i	$-0.259655\pi$
$71$	11.5495	1.37068	0.685338	+	0.728225i	$0.259655\pi$
$72$	0.819517	0.0965810
$73$	16.5037	1.93161	0.965804	−	0.259275i	$-0.0834836\pi$
$73$	16.5037	1.93161	0.965804	+	0.259275i	$0.0834836\pi$
$74$	0.0936932	0.0108916
$75$	6.52842	0.753837
$76$	8.64530	0.991684
$77$	0	0
$78$	−1.85825	−0.210406
$79$	−8.79507	−0.989523	−0.494761	−	0.869029i	$-0.664745\pi$
$79$	−8.79507	−0.989523	−0.494761	+	0.869029i	$0.664745\pi$
$80$	2.32040	0.259428
$81$	−8.09592	−0.899547
$82$	−7.73346	−0.854018
$83$	12.0558	1.32329	0.661646	−	0.749816i	$-0.269858\pi$
$83$	12.0558	1.32329	0.661646	+	0.749816i	$0.269858\pi$
$84$	0	0
$85$	2.99258	0.324590
$86$	8.32149	0.897330
$87$	−13.8681	−1.48681
$88$	−5.21553	−0.555977
$89$	0.421332	0.0446611	0.0223306	−	0.999751i	$-0.492891\pi$
$89$	0.421332	0.0446611	0.0223306	+	0.999751i	$0.492891\pi$
$90$	0.802669	0.0846088
$91$	0	0
$92$	−2.11247	−0.220240
$93$	−2.46124	−0.255219
$94$	−1.18639	−0.122367
$95$	24.5140	2.51508
$96$	8.55852	0.873501
$97$	−4.53118	−0.460072	−0.230036	−	0.973182i	$-0.573884\pi$
$97$	−4.53118	−0.460072	−0.230036	+	0.973182i	$0.573884\pi$
$98$	0	0
$99$	−0.484696	−0.0487138
$100$	−4.17459	−0.417459
$101$	4.44307	0.442102	0.221051	−	0.975262i	$-0.429051\pi$
$101$	4.44307	0.442102	0.221051	+	0.975262i	$0.429051\pi$
$102$	−1.60411	−0.158830
$103$	−4.09228	−0.403225	−0.201612	−	0.979465i	$-0.564618\pi$
$103$	−4.09228	−0.403225	−0.201612	+	0.979465i	$0.564618\pi$
$104$	3.44005	0.337325
$105$	0	0
$106$	8.55445	0.830882
$107$	19.4341	1.87876	0.939382	−	0.342873i	$-0.111400\pi$
$107$	19.4341	1.87876	0.939382	+	0.342873i	$0.111400\pi$
$108$	5.70634	0.549093
$109$	−7.54345	−0.722532	−0.361266	−	0.932463i	$-0.617655\pi$
$109$	−7.54345	−0.722532	−0.361266	+	0.932463i	$0.617655\pi$
$110$	−5.10831	−0.487058
$111$	0.159106	0.0151017
$112$	0	0
$113$	−15.5499	−1.46281	−0.731404	−	0.681944i	$-0.761135\pi$
$113$	−15.5499	−1.46281	−0.731404	+	0.681944i	$0.761135\pi$
$114$	−13.1402	−1.23069
$115$	−5.98995	−0.558566
$116$	8.86791	0.823365
$117$	0.319695	0.0295558
$118$	2.24556	0.206720
$119$	0	0
$120$	14.6671	1.33892
$121$	−7.91532	−0.719575
$122$	−7.96746	−0.721340
$123$	−13.1327	−1.18413
$124$	1.57384	0.141335
$125$	3.12572	0.279573
$126$	0	0
$127$	−5.57747	−0.494921	−0.247460	−	0.968898i	$-0.579596\pi$
$127$	−5.57747	−0.494921	−0.247460	+	0.968898i	$0.579596\pi$
$128$	−3.96553	−0.350506
$129$	14.1312	1.24419
$130$	3.36933	0.295510
$131$	−3.08454	−0.269497	−0.134749	−	0.990880i	$-0.543023\pi$
$131$	−3.08454	−0.269497	−0.134749	+	0.990880i	$0.543023\pi$
$132$	−3.05930	−0.266278
$133$	0	0
$134$	−0.622987	−0.0538179
$135$	16.1805	1.39259
$136$	2.96957	0.254638
$137$	−17.5624	−1.50046	−0.750228	−	0.661180i	$-0.770056\pi$
$137$	−17.5624	−1.50046	−0.750228	+	0.661180i	$0.770056\pi$
$138$	3.21078	0.273320
$139$	11.7587	0.997356	0.498678	−	0.866787i	$-0.333819\pi$
$139$	11.7587	0.997356	0.498678	+	0.866787i	$0.333819\pi$
$140$	0	0
$141$	−2.01469	−0.169667
$142$	11.2251	0.941991
$143$	−2.03459	−0.170141
$144$	0.213984	0.0178320
$145$	25.1452	2.08819
$146$	16.0401	1.32749
$147$	0	0
$148$	−0.101740	−0.00836299
$149$	−13.4616	−1.10282	−0.551409	−	0.834235i	$-0.685910\pi$
$149$	−13.4616	−1.10282	−0.551409	+	0.834235i	$0.685910\pi$
$150$	6.34505	0.518071
$151$	−23.0099	−1.87252	−0.936258	−	0.351314i	$-0.885735\pi$
$151$	−23.0099	−1.87252	−0.936258	+	0.351314i	$0.885735\pi$
$152$	24.3255	1.97306
$153$	0.275972	0.0223110
$154$	0	0
$155$	4.46266	0.358450
$156$	2.01785	0.161557
$157$	−23.2649	−1.85674	−0.928370	−	0.371659i	$-0.878789\pi$
$157$	−23.2649	−1.85674	−0.928370	+	0.371659i	$0.878789\pi$
$158$	−8.54804	−0.680045
$159$	14.5268	1.15205
$160$	−15.5181	−1.22681
$161$	0	0
$162$	−7.86853	−0.618210
$163$	17.7706	1.39190	0.695952	−	0.718089i	$-0.254983\pi$
$163$	17.7706	1.39190	0.695952	+	0.718089i	$0.254983\pi$
$164$	8.39766	0.655747
$165$	−8.67473	−0.675327
$166$	11.7171	0.909427
$167$	−2.59952	−0.201157	−0.100579	−	0.994929i	$-0.532069\pi$
$167$	−2.59952	−0.201157	−0.100579	+	0.994929i	$0.532069\pi$
$168$	0	0
$169$	−11.6580	−0.896771
$170$	2.90852	0.223073
$171$	2.26065	0.172876
$172$	−9.03620	−0.689004
$173$	−19.0015	−1.44466	−0.722329	−	0.691549i	$-0.756929\pi$
$173$	−19.0015	−1.44466	−0.722329	+	0.691549i	$0.756929\pi$
$174$	−13.4785	−1.02180
$175$	0	0
$176$	−1.36183	−0.102652
$177$	3.81331	0.286626
$178$	0.409498	0.0306931
$179$	−3.14824	−0.235311	−0.117655	−	0.993054i	$-0.537538\pi$
$179$	−3.14824	−0.235311	−0.117655	+	0.993054i	$0.537538\pi$
$180$	−0.871608	−0.0649659
$181$	1.45702	0.108300	0.0541499	−	0.998533i	$-0.482755\pi$
$181$	1.45702	0.108300	0.0541499	+	0.998533i	$0.482755\pi$
$182$	0	0
$183$	−13.5300	−1.00017
$184$	−5.94390	−0.438190
$185$	−0.288487	−0.0212100
$186$	−2.39211	−0.175398
$187$	−1.75633	−0.128435
$188$	1.28829	0.0939581
$189$	0	0
$190$	23.8254	1.72848
$191$	−15.6760	−1.13427	−0.567137	−	0.823623i	$-0.691949\pi$
$191$	−15.6760	−1.13427	−0.567137	+	0.823623i	$0.691949\pi$
$192$	10.8776	0.785025
$193$	−17.7568	−1.27816	−0.639080	−	0.769140i	$-0.720685\pi$
$193$	−17.7568	−1.27816	−0.639080	+	0.769140i	$0.720685\pi$
$194$	−4.40391	−0.316182
$195$	5.72167	0.409737
$196$	0	0
$197$	−0.736946	−0.0525052	−0.0262526	−	0.999655i	$-0.508357\pi$
$197$	−0.736946	−0.0525052	−0.0262526	+	0.999655i	$0.508357\pi$
$198$	−0.471082	−0.0334784
$199$	−14.1722	−1.00464	−0.502322	−	0.864681i	$-0.667521\pi$
$199$	−14.1722	−1.00464	−0.502322	+	0.864681i	$0.667521\pi$
$200$	−11.7461	−0.830578
$201$	−1.05793	−0.0746208
$202$	4.31827	0.303833
$203$	0	0
$204$	1.74188	0.121956
$205$	23.8118	1.66309
$206$	−3.97734	−0.277114
$207$	−0.552386	−0.0383935
$208$	0.898233	0.0622813
$209$	−14.3871	−0.995178
$210$	0	0
$211$	13.5325	0.931618	0.465809	−	0.884885i	$-0.345763\pi$
$211$	13.5325	0.931618	0.465809	+	0.884885i	$0.345763\pi$
$212$	−9.28917	−0.637983
$213$	19.0621	1.30611
$214$	18.8882	1.29117
$215$	−25.6224	−1.74743
$216$	16.0561	1.09248
$217$	0	0
$218$	−7.33157	−0.496557
$219$	27.2387	1.84062
$220$	5.54705	0.373982
$221$	1.15844	0.0779248
$222$	0.154637	0.0103786
$223$	−18.9408	−1.26837	−0.634185	−	0.773181i	$-0.718664\pi$
$223$	−18.9408	−1.26837	−0.634185	+	0.773181i	$0.718664\pi$
$224$	0	0
$225$	−1.09161	−0.0727739
$226$	−15.1131	−1.00531
$227$	5.97724	0.396724	0.198362	−	0.980129i	$-0.436438\pi$
$227$	5.97724	0.396724	0.198362	+	0.980129i	$0.436438\pi$
$228$	14.2688	0.944971
$229$	−7.47623	−0.494043	−0.247022	−	0.969010i	$-0.579452\pi$
$229$	−7.47623	−0.494043	−0.247022	+	0.969010i	$0.579452\pi$
$230$	−5.82171	−0.383872
$231$	0	0
$232$	24.9519	1.63817
$233$	10.9000	0.714082	0.357041	−	0.934089i	$-0.383786\pi$
$233$	10.9000	0.714082	0.357041	+	0.934089i	$0.383786\pi$
$234$	0.310716	0.0203121
$235$	3.65298	0.238294
$236$	−2.43842	−0.158728
$237$	−14.5159	−0.942912
$238$	0	0
$239$	23.7540	1.53652	0.768259	−	0.640139i	$-0.221123\pi$
$239$	23.7540	1.53652	0.768259	+	0.640139i	$0.221123\pi$
$240$	3.82973	0.247208
$241$	−0.441643	−0.0284487	−0.0142244	−	0.999899i	$-0.504528\pi$
$241$	−0.441643	−0.0284487	−0.0142244	+	0.999899i	$0.504528\pi$
$242$	−7.69299	−0.494524
$243$	2.85859	0.183378
$244$	8.65176	0.553872
$245$	0	0
$246$	−12.7638	−0.813789
$247$	9.48943	0.603798
$248$	4.42835	0.281201
$249$	19.8976	1.26096
$250$	3.03793	0.192135
$251$	−19.1440	−1.20836	−0.604179	−	0.796849i	$-0.706499\pi$
$251$	−19.1440	−1.20836	−0.604179	+	0.796849i	$0.706499\pi$
$252$	0	0
$253$	3.51547	0.221016
$254$	−5.42081	−0.340132
$255$	4.93913	0.309301
$256$	−17.0354	−1.06472
$257$	4.29692	0.268034	0.134017	−	0.990979i	$-0.457212\pi$
$257$	4.29692	0.268034	0.134017	+	0.990979i	$0.457212\pi$
$258$	13.7343	0.855061
$259$	0	0
$260$	−3.65871	−0.226904
$261$	2.31886	0.143534
$262$	−2.99790	−0.185211
$263$	4.30077	0.265197	0.132598	−	0.991170i	$-0.457668\pi$
$263$	4.30077	0.265197	0.132598	+	0.991170i	$0.457668\pi$
$264$	−8.60804	−0.529788
$265$	−26.3397	−1.61803
$266$	0	0
$267$	0.695393	0.0425574
$268$	0.676494	0.0413234
$269$	9.14530	0.557599	0.278799	−	0.960349i	$-0.410064\pi$
$269$	9.14530	0.557599	0.278799	+	0.960349i	$0.410064\pi$
$270$	15.7260	0.957053
$271$	11.5486	0.701525	0.350762	−	0.936465i	$-0.385923\pi$
$271$	11.5486	0.701525	0.350762	+	0.936465i	$0.385923\pi$
$272$	0.775385	0.0470146
$273$	0	0
$274$	−17.0691	−1.03118
$275$	6.94716	0.418929
$276$	−3.48655	−0.209866
$277$	10.3020	0.618984	0.309492	−	0.950902i	$-0.399841\pi$
$277$	10.3020	0.618984	0.309492	+	0.950902i	$0.399841\pi$
$278$	11.4284	0.685429
$279$	0.411541	0.0246383
$280$	0	0
$281$	23.2865	1.38916	0.694578	−	0.719417i	$-0.255591\pi$
$281$	23.2865	1.38916	0.694578	+	0.719417i	$0.255591\pi$
$282$	−1.95810	−0.116603
$283$	−10.4976	−0.624019	−0.312010	−	0.950079i	$-0.601002\pi$
$283$	−10.4976	−0.624019	−0.312010	+	0.950079i	$0.601002\pi$
$284$	−12.1892	−0.723297
$285$	40.4594	2.39661
$286$	−1.97744	−0.116929
$287$	0	0
$288$	−1.43106	−0.0843260
$289$	1.00000	0.0588235
$290$	24.4389	1.43510
$291$	−7.47855	−0.438400
$292$	−17.4177	−1.01930
$293$	32.5564	1.90197	0.950983	−	0.309242i	$-0.100075\pi$
$293$	32.5564	1.90197	0.950983	+	0.309242i	$0.100075\pi$
$294$	0	0
$295$	−6.91420	−0.402560
$296$	−0.286269	−0.0166390
$297$	−9.49623	−0.551027
$298$	−13.0835	−0.757907
$299$	−2.31873	−0.134096
$300$	−6.89001	−0.397795
$301$	0	0
$302$	−22.3636	−1.28688
$303$	7.33312	0.421277
$304$	6.35164	0.364292
$305$	24.5323	1.40471
$306$	0.268220	0.0153331
$307$	16.0501	0.916025	0.458012	−	0.888946i	$-0.348562\pi$
$307$	16.0501	0.916025	0.458012	+	0.888946i	$0.348562\pi$
$308$	0	0
$309$	−6.75416	−0.384231
$310$	4.33731	0.246343
$311$	4.74583	0.269112	0.134556	−	0.990906i	$-0.457039\pi$
$311$	4.74583	0.269112	0.134556	+	0.990906i	$0.457039\pi$
$312$	5.67768	0.321435
$313$	10.6286	0.600766	0.300383	−	0.953819i	$-0.402886\pi$
$313$	10.6286	0.600766	0.300383	+	0.953819i	$0.402886\pi$
$314$	−22.6114	−1.27604
$315$	0	0
$316$	9.28220	0.522165
$317$	10.9446	0.614709	0.307354	−	0.951595i	$-0.400556\pi$
$317$	10.9446	0.614709	0.307354	+	0.951595i	$0.400556\pi$
$318$	14.1188	0.791744
$319$	−14.7576	−0.826265
$320$	−19.7230	−1.10255
$321$	32.0752	1.79027
$322$	0	0
$323$	8.19160	0.455793
$324$	8.54433	0.474685
$325$	−4.58220	−0.254175
$326$	17.2715	0.956579
$327$	−12.4502	−0.688497
$328$	23.6287	1.30468
$329$	0	0
$330$	−8.43108	−0.464115
$331$	−27.8769	−1.53225	−0.766125	−	0.642691i	$-0.777818\pi$
$331$	−27.8769	−1.53225	−0.766125	+	0.642691i	$0.777818\pi$
$332$	−12.7235	−0.698293
$333$	−0.0266039	−0.00145789
$334$	−2.52651	−0.138244
$335$	1.91822	0.104803
$336$	0	0
$337$	17.6568	0.961826	0.480913	−	0.876768i	$-0.340305\pi$
$337$	17.6568	0.961826	0.480913	+	0.876768i	$0.340305\pi$
$338$	−11.3306	−0.616302
$339$	−25.6645	−1.39390
$340$	−3.15832	−0.171284
$341$	−2.61911	−0.141833
$342$	2.19715	0.118808
$343$	0	0
$344$	−25.4254	−1.37084
$345$	−9.88619	−0.532255
$346$	−18.4678	−0.992835
$347$	1.10582	0.0593635	0.0296818	−	0.999559i	$-0.490551\pi$
$347$	1.10582	0.0593635	0.0296818	+	0.999559i	$0.490551\pi$
$348$	14.6362	0.784580
$349$	−31.7887	−1.70161	−0.850804	−	0.525482i	$-0.823885\pi$
$349$	−31.7887	−1.70161	−0.850804	+	0.525482i	$0.823885\pi$
$350$	0	0
$351$	6.26351	0.334321
$352$	9.10748	0.485430
$353$	−5.42032	−0.288495	−0.144247	−	0.989542i	$-0.546076\pi$
$353$	−5.42032	−0.288495	−0.144247	+	0.989542i	$0.546076\pi$
$354$	3.70621	0.196983
$355$	−34.5628	−1.83440
$356$	−0.444668	−0.0235674
$357$	0	0
$358$	−3.05982	−0.161716
$359$	−19.7634	−1.04307	−0.521536	−	0.853229i	$-0.674641\pi$
$359$	−19.7634	−1.04307	−0.521536	+	0.853229i	$0.674641\pi$
$360$	−2.45247	−0.129256
$361$	48.1023	2.53170
$362$	1.41610	0.0744286
$363$	−13.0639	−0.685679
$364$	0	0
$365$	−49.3884	−2.58511
$366$	−13.1500	−0.687361
$367$	−18.1163	−0.945665	−0.472832	−	0.881152i	$-0.656768\pi$
$367$	−18.1163	−0.945665	−0.472832	+	0.881152i	$0.656768\pi$
$368$	−1.55201	−0.0809043
$369$	2.19589	0.114314
$370$	−0.280384	−0.0145765
$371$	0	0
$372$	2.59756	0.134677
$373$	−28.6647	−1.48420	−0.742102	−	0.670287i	$-0.766171\pi$
$373$	−28.6647	−1.48420	−0.742102	+	0.670287i	$0.766171\pi$
$374$	−1.70699	−0.0882666
$375$	5.15889	0.266404
$376$	3.62489	0.186939
$377$	9.73378	0.501315
$378$	0	0
$379$	26.9402	1.38383	0.691913	−	0.721981i	$-0.256768\pi$
$379$	26.9402	1.38383	0.691913	+	0.721981i	$0.256768\pi$
$380$	−25.8717	−1.32719
$381$	−9.20541	−0.471607
$382$	−15.2357	−0.779525
$383$	27.0519	1.38229	0.691144	−	0.722717i	$-0.257107\pi$
$383$	27.0519	1.38229	0.691144	+	0.722717i	$0.257107\pi$
$384$	−6.54496	−0.333996
$385$	0	0
$386$	−17.2580	−0.878410
$387$	−2.36287	−0.120111
$388$	4.78215	0.242777
$389$	−20.5002	−1.03940	−0.519700	−	0.854349i	$-0.673956\pi$
$389$	−20.5002	−1.03940	−0.519700	+	0.854349i	$0.673956\pi$
$390$	5.56096	0.281590
$391$	−2.00160	−0.101225
$392$	0	0
$393$	−5.09092	−0.256803
$394$	−0.716246	−0.0360840
$395$	26.3199	1.32430
$396$	0.511542	0.0257060
$397$	11.9050	0.597494	0.298747	−	0.954332i	$-0.403431\pi$
$397$	11.9050	0.597494	0.298747	+	0.954332i	$0.403431\pi$
$398$	−13.7742	−0.690437
$399$	0	0
$400$	−3.06704	−0.153352
$401$	−6.32642	−0.315926	−0.157963	−	0.987445i	$-0.550493\pi$
$401$	−6.32642	−0.315926	−0.157963	+	0.987445i	$0.550493\pi$
$402$	−1.02822	−0.0512828
$403$	1.72751	0.0860534
$404$	−4.68916	−0.233294
$405$	24.2277	1.20388
$406$	0	0
$407$	0.169311	0.00839245
$408$	4.90116	0.242644
$409$	2.54401	0.125793	0.0628967	−	0.998020i	$-0.479966\pi$
$409$	2.54401	0.125793	0.0628967	+	0.998020i	$0.479966\pi$
$410$	23.1430	1.14295
$411$	−28.9861	−1.42978
$412$	4.31894	0.212779
$413$	0	0
$414$	−0.536871	−0.0263858
$415$	−36.0778	−1.77099
$416$	−6.00710	−0.294522
$417$	19.4072	0.950376
$418$	−13.9830	−0.683931
$419$	−1.23758	−0.0604598	−0.0302299	−	0.999543i	$-0.509624\pi$
$419$	−1.23758	−0.0604598	−0.0302299	+	0.999543i	$0.509624\pi$
$420$	0	0
$421$	−12.1490	−0.592106	−0.296053	−	0.955172i	$-0.595670\pi$
$421$	−12.1490	−0.592106	−0.296053	+	0.955172i	$0.595670\pi$
$422$	13.1524	0.640250
$423$	0.336873	0.0163793
$424$	−26.1372	−1.26933
$425$	−3.95551	−0.191870
$426$	18.5266	0.897619
$427$	0	0
$428$	−20.5105	−0.991411
$429$	−3.35802	−0.162126
$430$	−24.9027	−1.20091
$431$	−16.2269	−0.781624	−0.390812	−	0.920471i	$-0.627806\pi$
$431$	−16.2269	−0.781624	−0.390812	+	0.920471i	$0.627806\pi$
$432$	4.19241	0.201707
$433$	−5.55847	−0.267123	−0.133562	−	0.991041i	$-0.542641\pi$
$433$	−5.55847	−0.267123	−0.133562	+	0.991041i	$0.542641\pi$
$434$	0	0
$435$	41.5012	1.98983
$436$	7.96126	0.381275
$437$	−16.3963	−0.784343
$438$	26.4736	1.26496
$439$	−36.7625	−1.75458	−0.877290	−	0.479961i	$-0.840651\pi$
$439$	−36.7625	−1.75458	−0.877290	+	0.479961i	$0.840651\pi$
$440$	15.6079	0.744076
$441$	0	0
$442$	1.12590	0.0535535
$443$	−34.3789	−1.63339	−0.816694	−	0.577070i	$-0.804196\pi$
$443$	−34.3789	−1.63339	−0.816694	+	0.577070i	$0.804196\pi$
$444$	−0.167918	−0.00796906
$445$	−1.26087	−0.0597709
$446$	−18.4088	−0.871682
$447$	−22.2179	−1.05087
$448$	0	0
$449$	−33.5795	−1.58472	−0.792358	−	0.610056i	$-0.791147\pi$
$449$	−33.5795	−1.58472	−0.792358	+	0.610056i	$0.791147\pi$
$450$	−1.06095	−0.0500135
$451$	−13.9750	−0.658057
$452$	16.4111	0.771914
$453$	−37.9769	−1.78431
$454$	5.80936	0.272647
$455$	0	0
$456$	40.1483	1.88012
$457$	23.6692	1.10720	0.553599	−	0.832784i	$-0.313254\pi$
$457$	23.6692	1.10720	0.553599	+	0.832784i	$0.313254\pi$
$458$	−7.26624	−0.339529
$459$	5.40687	0.252371
$460$	6.32172	0.294752
$461$	35.9193	1.67293	0.836464	−	0.548022i	$-0.184619\pi$
$461$	35.9193	1.67293	0.836464	+	0.548022i	$0.184619\pi$
$462$	0	0
$463$	−6.92180	−0.321683	−0.160842	−	0.986980i	$-0.551421\pi$
$463$	−6.92180	−0.321683	−0.160842	+	0.986980i	$0.551421\pi$
$464$	6.51519	0.302460
$465$	7.36546	0.341565
$466$	10.5938	0.490750
$467$	9.61747	0.445044	0.222522	−	0.974928i	$-0.428571\pi$
$467$	9.61747	0.445044	0.222522	+	0.974928i	$0.428571\pi$
$468$	−0.337402	−0.0155964
$469$	0	0
$470$	3.55037	0.163766
$471$	−38.3978	−1.76928
$472$	−6.86104	−0.315805
$473$	15.0376	0.691431
$474$	−14.1082	−0.648012
$475$	−32.4019	−1.48670
$476$	0	0
$477$	−2.42901	−0.111217
$478$	23.0868	1.05597
$479$	32.3487	1.47805	0.739026	−	0.673677i	$-0.235286\pi$
$479$	32.3487	1.47805	0.739026	+	0.673677i	$0.235286\pi$
$480$	−25.6120	−1.16902
$481$	−0.111674	−0.00509190
$482$	−0.429238	−0.0195513
$483$	0	0
$484$	8.35372	0.379715
$485$	13.5599	0.615723
$486$	2.77830	0.126026
$487$	3.11809	0.141294	0.0706470	−	0.997501i	$-0.477494\pi$
$487$	3.11809	0.141294	0.0706470	+	0.997501i	$0.477494\pi$
$488$	24.3437	1.10199
$489$	29.3298	1.32634
$490$	0	0
$491$	29.5680	1.33439	0.667193	−	0.744885i	$-0.267496\pi$
$491$	29.5680	1.33439	0.667193	+	0.744885i	$0.267496\pi$
$492$	13.8600	0.624858
$493$	8.40252	0.378431
$494$	9.22290	0.414958
$495$	1.45049	0.0651947
$496$	1.15629	0.0519189
$497$	0	0
$498$	19.3387	0.866588
$499$	−15.4566	−0.691931	−0.345965	−	0.938247i	$-0.612449\pi$
$499$	−15.4566	−0.691931	−0.345965	+	0.938247i	$0.612449\pi$
$500$	−3.29885	−0.147529
$501$	−4.29042	−0.191682
$502$	−18.6063	−0.830439
$503$	−15.6125	−0.696129	−0.348065	−	0.937471i	$-0.613161\pi$
$503$	−15.6125	−0.696129	−0.348065	+	0.937471i	$0.613161\pi$
$504$	0	0
$505$	−13.2962	−0.591674
$506$	3.41673	0.151892
$507$	−19.2411	−0.854529
$508$	5.88639	0.261166
$509$	−3.57893	−0.158633	−0.0793165	−	0.996849i	$-0.525274\pi$
$509$	−3.57893	−0.158633	−0.0793165	+	0.996849i	$0.525274\pi$
$510$	4.80041	0.212566
$511$	0	0
$512$	−8.62590	−0.381214
$513$	44.2909	1.95549
$514$	4.17623	0.184205
$515$	12.2465	0.539644
$516$	−14.9139	−0.656549
$517$	−2.14391	−0.0942891
$518$	0	0
$519$	−31.3613	−1.37661
$520$	−10.2946	−0.451449
$521$	13.2352	0.579846	0.289923	−	0.957050i	$-0.406370\pi$
$521$	13.2352	0.579846	0.289923	+	0.957050i	$0.406370\pi$
$522$	2.25373	0.0986429
$523$	−6.00569	−0.262610	−0.131305	−	0.991342i	$-0.541917\pi$
$523$	−6.00569	−0.262610	−0.131305	+	0.991342i	$0.541917\pi$
$524$	3.25538	0.142212
$525$	0	0
$526$	4.17997	0.182255
$527$	1.49124	0.0649596
$528$	−2.24765	−0.0978163
$529$	−18.9936	−0.825808
$530$	−25.5998	−1.11199
$531$	−0.637619	−0.0276703
$532$	0	0
$533$	9.21761	0.399259
$534$	0.675861	0.0292474
$535$	−58.1580	−2.51439
$536$	1.90347	0.0822173
$537$	−5.19606	−0.224226
$538$	8.88843	0.383207
$539$	0	0
$540$	−17.0767	−0.734862
$541$	−20.3333	−0.874197	−0.437098	−	0.899414i	$-0.643994\pi$
$541$	−20.3333	−0.874197	−0.437098	+	0.899414i	$0.643994\pi$
$542$	11.2242	0.482120
$543$	2.40477	0.103198
$544$	−5.18553	−0.222328
$545$	22.5743	0.966979
$546$	0	0
$547$	20.2018	0.863765	0.431882	−	0.901930i	$-0.357850\pi$
$547$	20.2018	0.863765	0.431882	+	0.901930i	$0.357850\pi$
$548$	18.5351	0.791780
$549$	2.26234	0.0965542
$550$	6.75203	0.287907
$551$	68.8301	2.93226
$552$	−9.81018	−0.417549
$553$	0	0
$554$	10.0126	0.425394
$555$	−0.476137	−0.0202109
$556$	−12.4099	−0.526298
$557$	−5.23930	−0.221996	−0.110998	−	0.993821i	$-0.535405\pi$
$557$	−5.23930	−0.221996	−0.110998	+	0.993821i	$0.535405\pi$
$558$	0.399982	0.0169326
$559$	−9.91850	−0.419508
$560$	0	0
$561$	−2.89875	−0.122385
$562$	22.6324	0.954692
$563$	28.0661	1.18285	0.591423	−	0.806361i	$-0.298566\pi$
$563$	28.0661	1.18285	0.591423	+	0.806361i	$0.298566\pi$
$564$	2.12627	0.0895323
$565$	46.5341	1.95771
$566$	−10.2028	−0.428855
$567$	0	0
$568$	−34.2971	−1.43907
$569$	14.0616	0.589495	0.294747	−	0.955575i	$-0.404765\pi$
$569$	14.0616	0.589495	0.294747	+	0.955575i	$0.404765\pi$
$570$	39.3230	1.64706
$571$	−17.6118	−0.737033	−0.368516	−	0.929621i	$-0.620134\pi$
$571$	−17.6118	−0.737033	−0.368516	+	0.929621i	$0.620134\pi$
$572$	2.14728	0.0897823
$573$	−25.8726	−1.08084
$574$	0	0
$575$	7.91736	0.330177
$576$	−1.81883	−0.0757847
$577$	11.6400	0.484578	0.242289	−	0.970204i	$-0.422102\pi$
$577$	11.6400	0.484578	0.242289	+	0.970204i	$0.422102\pi$
$578$	0.971912	0.0404262
$579$	−29.3069	−1.21795
$580$	−26.5379	−1.10193
$581$	0	0
$582$	−7.26849	−0.301289
$583$	15.4586	0.640230
$584$	−49.0087	−2.02800
$585$	−0.956713	−0.0395552
$586$	31.6420	1.30712
$587$	0.734456	0.0303142	0.0151571	−	0.999885i	$-0.495175\pi$
$587$	0.734456	0.0303142	0.0151571	+	0.999885i	$0.495175\pi$
$588$	0	0
$589$	12.2157	0.503338
$590$	−6.71999	−0.276658
$591$	−1.21630	−0.0500320
$592$	−0.0747478	−0.00307211
$593$	−30.2196	−1.24097	−0.620486	−	0.784217i	$-0.713065\pi$
$593$	−30.2196	−1.24097	−0.620486	+	0.784217i	$0.713065\pi$
$594$	−9.22950	−0.378691
$595$	0	0
$596$	14.2072	0.581950
$597$	−23.3908	−0.957320
$598$	−2.25360	−0.0921566
$599$	3.13349	0.128031	0.0640154	−	0.997949i	$-0.479609\pi$
$599$	3.13349	0.128031	0.0640154	+	0.997949i	$0.479609\pi$
$600$	−19.3866	−0.791454
$601$	−41.1110	−1.67695	−0.838477	−	0.544938i	$-0.816553\pi$
$601$	−41.1110	−1.67695	−0.838477	+	0.544938i	$0.816553\pi$
$602$	0	0
$603$	0.176896	0.00720374
$604$	24.2843	0.988114
$605$	23.6872	0.963021
$606$	7.12715	0.289521
$607$	−22.9391	−0.931067	−0.465534	−	0.885030i	$-0.654138\pi$
$607$	−22.9391	−0.931067	−0.465534	+	0.885030i	$0.654138\pi$
$608$	−42.4778	−1.72270
$609$	0	0
$610$	23.8432	0.965384
$611$	1.41408	0.0572075
$612$	−0.291257	−0.0117734
$613$	36.4850	1.47361	0.736807	−	0.676103i	$-0.236333\pi$
$613$	36.4850	1.47361	0.736807	+	0.676103i	$0.236333\pi$
$614$	15.5992	0.629534
$615$	39.3005	1.58475
$616$	0	0
$617$	12.2175	0.491857	0.245929	−	0.969288i	$-0.420907\pi$
$617$	12.2175	0.491857	0.245929	+	0.969288i	$0.420907\pi$
$618$	−6.56445	−0.264061
$619$	41.4810	1.66726	0.833630	−	0.552323i	$-0.186258\pi$
$619$	41.4810	1.66726	0.833630	+	0.552323i	$0.186258\pi$
$620$	−4.70983	−0.189151
$621$	−10.8224	−0.434289
$622$	4.61253	0.184946
$623$	0	0
$624$	1.48250	0.0593475
$625$	−29.1315	−1.16526
$626$	10.3301	0.412874
$627$	−23.7454	−0.948300
$628$	24.5534	0.979789
$629$	−0.0964009	−0.00384375
$630$	0	0
$631$	−9.80572	−0.390359	−0.195180	−	0.980767i	$-0.562529\pi$
$631$	−9.80572	−0.390359	−0.195180	+	0.980767i	$0.562529\pi$
$632$	26.1176	1.03890
$633$	22.3349	0.887734
$634$	10.6372	0.422456
$635$	16.6910	0.662362
$636$	−15.3314	−0.607931
$637$	0	0
$638$	−14.3431	−0.567847
$639$	−3.18734	−0.126089
$640$	11.8671	0.469090
$641$	23.1993	0.916319	0.458159	−	0.888870i	$-0.348509\pi$
$641$	23.1993	0.916319	0.458159	+	0.888870i	$0.348509\pi$
$642$	31.1743	1.23035
$643$	6.36392	0.250969	0.125484	−	0.992096i	$-0.459952\pi$
$643$	6.36392	0.250969	0.125484	+	0.992096i	$0.459952\pi$
$644$	0	0
$645$	−42.2888	−1.66512
$646$	7.96151	0.313242
$647$	0.0111346	0.000437746 0	0.000218873	−	1.00000i	$-0.499930\pi$
$647$	0.0111346	0.000437746 0	0.000218873		1.00000i	$0.499930\pi$
$648$	24.0414	0.944435
$649$	4.05790	0.159287
$650$	−4.45349	−0.174680
$651$	0	0
$652$	−18.7549	−0.734498
$653$	19.3517	0.757292	0.378646	−	0.925542i	$-0.376390\pi$
$653$	19.3517	0.757292	0.378646	+	0.925542i	$0.376390\pi$
$654$	−12.1005	−0.473167
$655$	9.23071	0.360674
$656$	6.16970	0.240886
$657$	−4.55454	−0.177690
$658$	0	0
$659$	−39.0362	−1.52064	−0.760318	−	0.649551i	$-0.774957\pi$
$659$	−39.0362	−1.52064	−0.760318	+	0.649551i	$0.774957\pi$
$660$	9.15520	0.356366
$661$	−46.0480	−1.79106	−0.895530	−	0.445002i	$-0.853203\pi$
$661$	−46.0480	−1.79106	−0.895530	+	0.445002i	$0.853203\pi$
$662$	−27.0939	−1.05303
$663$	1.91195	0.0742542
$664$	−35.8004	−1.38933
$665$	0	0
$666$	−0.0258567	−0.00100193
$667$	−16.8185	−0.651216
$668$	2.74350	0.106149
$669$	−31.2611	−1.20862
$670$	1.86434	0.0720256
$671$	−14.3979	−0.555823
$672$	0	0
$673$	2.02205	0.0779443	0.0389722	−	0.999240i	$-0.487592\pi$
$673$	2.02205	0.0779443	0.0389722	+	0.999240i	$0.487592\pi$
$674$	17.1608	0.661010
$675$	−21.3869	−0.823183
$676$	12.3037	0.473220
$677$	17.7365	0.681670	0.340835	−	0.940123i	$-0.389290\pi$
$677$	17.7365	0.681670	0.340835	+	0.940123i	$0.389290\pi$
$678$	−24.9436	−0.957954
$679$	0	0
$680$	−8.88665	−0.340788
$681$	9.86522	0.378036
$682$	−2.54555	−0.0974740
$683$	−32.3540	−1.23799	−0.618996	−	0.785394i	$-0.712460\pi$
$683$	−32.3540	−1.23799	−0.618996	+	0.785394i	$0.712460\pi$
$684$	−2.38586	−0.0912256
$685$	52.5567	2.00809
$686$	0	0
$687$	−12.3392	−0.470772
$688$	−6.63883	−0.253103
$689$	−10.1962	−0.388443
$690$	−9.60851	−0.365790
$691$	34.6857	1.31951	0.659753	−	0.751483i	$-0.270661\pi$
$691$	34.6857	1.31951	0.659753	+	0.751483i	$0.270661\pi$
$692$	20.0540	0.762337
$693$	0	0
$694$	1.07476	0.0407973
$695$	−35.1887	−1.33478
$696$	41.1821	1.56100
$697$	7.95695	0.301391
$698$	−30.8958	−1.16942
$699$	17.9900	0.680445
$700$	0	0
$701$	−18.5691	−0.701345	−0.350673	−	0.936498i	$-0.614047\pi$
$701$	−18.5691	−0.701345	−0.350673	+	0.936498i	$0.614047\pi$
$702$	6.08758	0.229761
$703$	−0.789677	−0.0297832
$704$	11.5753	0.436262
$705$	6.02910	0.227069
$706$	−5.26808	−0.198267
$707$	0	0
$708$	−4.02452	−0.151251
$709$	28.5834	1.07347	0.536737	−	0.843750i	$-0.319657\pi$
$709$	28.5834	1.07347	0.536737	+	0.843750i	$0.319657\pi$
$710$	−33.5920	−1.26069
$711$	2.42719	0.0910268
$712$	−1.25117	−0.0468897
$713$	−2.98488	−0.111785
$714$	0	0
$715$	6.08866	0.227703
$716$	3.32261	0.124172
$717$	39.2051	1.46414
$718$	−19.2083	−0.716847
$719$	9.87923	0.368433	0.184217	−	0.982886i	$-0.441025\pi$
$719$	9.87923	0.368433	0.184217	+	0.982886i	$0.441025\pi$
$720$	−0.640364	−0.0238650
$721$	0	0
$722$	46.7512	1.73990
$723$	−0.728915	−0.0271086
$724$	−1.53772	−0.0571491
$725$	−33.2362	−1.23436
$726$	−12.6970	−0.471230
$727$	−30.9667	−1.14849	−0.574246	−	0.818683i	$-0.694705\pi$
$727$	−30.9667	−1.14849	−0.574246	+	0.818683i	$0.694705\pi$
$728$	0	0
$729$	29.0058	1.07429
$730$	−48.0012	−1.77660
$731$	−8.56198	−0.316676
$732$	14.2794	0.527782
$733$	−11.6666	−0.430917	−0.215458	−	0.976513i	$-0.569125\pi$
$733$	−11.6666	−0.430917	−0.215458	+	0.976513i	$0.569125\pi$
$734$	−17.6075	−0.649904
$735$	0	0
$736$	10.3794	0.382589
$737$	−1.12579	−0.0414690
$738$	2.13422	0.0785616
$739$	−39.0011	−1.43468	−0.717340	−	0.696723i	$-0.754641\pi$
$739$	−39.0011	−1.43468	−0.717340	+	0.696723i	$0.754641\pi$
$740$	0.304465	0.0111924
$741$	15.6620	0.575357
$742$	0	0
$743$	26.0603	0.956059	0.478030	−	0.878344i	$-0.341351\pi$
$743$	26.0603	0.956059	0.478030	+	0.878344i	$0.341351\pi$
$744$	7.30883	0.267955
$745$	40.2849	1.47592
$746$	−27.8596	−1.02001
$747$	−3.32705	−0.121730
$748$	1.85360	0.0677744
$749$	0	0
$750$	5.01399	0.183085
$751$	−26.1285	−0.953442	−0.476721	−	0.879055i	$-0.658175\pi$
$751$	−26.1285	−0.953442	−0.476721	+	0.879055i	$0.658175\pi$
$752$	0.946496	0.0345152
$753$	−31.5964	−1.15144
$754$	9.46037	0.344527
$755$	68.8587	2.50603
$756$	0	0
$757$	−4.95833	−0.180214	−0.0901068	−	0.995932i	$-0.528721\pi$
$757$	−4.95833	−0.180214	−0.0901068	+	0.995932i	$0.528721\pi$
$758$	26.1835	0.951028
$759$	5.80215	0.210605
$760$	−72.7959	−2.64058
$761$	45.6636	1.65530	0.827651	−	0.561243i	$-0.189677\pi$
$761$	45.6636	1.65530	0.827651	+	0.561243i	$0.189677\pi$
$762$	−8.94685	−0.324110
$763$	0	0
$764$	16.5442	0.598549
$765$	−0.825866	−0.0298593
$766$	26.2921	0.949971
$767$	−2.67651	−0.0966431
$768$	−28.1164	−1.01456
$769$	32.5805	1.17488	0.587441	−	0.809267i	$-0.300136\pi$
$769$	32.5805	1.17488	0.587441	+	0.809267i	$0.300136\pi$
$770$	0	0
$771$	7.09190	0.255409
$772$	18.7403	0.674477
$773$	12.9902	0.467224	0.233612	−	0.972330i	$-0.424946\pi$
$773$	12.9902	0.467224	0.233612	+	0.972330i	$0.424946\pi$
$774$	−2.29650	−0.0825459
$775$	−5.89863	−0.211885
$776$	13.4556	0.483030
$777$	0	0
$778$	−19.9244	−0.714324
$779$	65.1802	2.33532
$780$	−6.03857	−0.216216
$781$	20.2847	0.725844
$782$	−1.94538	−0.0695668
$783$	45.4313	1.62358
$784$	0	0
$785$	69.6219	2.48491
$786$	−4.94792	−0.176487
$787$	13.8911	0.495163	0.247581	−	0.968867i	$-0.420364\pi$
$787$	13.8911	0.495163	0.247581	+	0.968867i	$0.420364\pi$
$788$	0.777763	0.0277067
$789$	7.09826	0.252705
$790$	25.5806	0.910119
$791$	0	0
$792$	1.43934	0.0511447
$793$	9.49652	0.337231
$794$	11.5706	0.410625
$795$	−43.4727	−1.54182
$796$	14.9572	0.530144
$797$	−14.3920	−0.509792	−0.254896	−	0.966968i	$-0.582041\pi$
$797$	−14.3920	−0.509792	−0.254896	+	0.966968i	$0.582041\pi$
$798$	0	0
$799$	1.22068	0.0431845
$800$	20.5114	0.725187
$801$	−0.116276	−0.00410840
$802$	−6.14872	−0.217119
$803$	28.9858	1.02289
$804$	1.11653	0.0393769
$805$	0	0
$806$	1.67899	0.0591398
$807$	15.0940	0.531333
$808$	−13.1940	−0.464163
$809$	−0.0887004	−0.00311854	−0.00155927	−	0.999999i	$-0.500496\pi$
$809$	−0.0887004	−0.00311854	−0.00155927	+	0.999999i	$0.500496\pi$
$810$	23.5472	0.827363
$811$	−27.8030	−0.976295	−0.488147	−	0.872761i	$-0.662327\pi$
$811$	−27.8030	−0.976295	−0.488147	+	0.872761i	$0.662327\pi$
$812$	0	0
$813$	19.0605	0.668479
$814$	0.164556	0.00576768
$815$	−53.1799	−1.86281
$816$	1.27974	0.0448000
$817$	−70.1363	−2.45376
$818$	2.47256	0.0864509
$819$	0	0
$820$	−25.1306	−0.877600
$821$	6.19788	0.216308	0.108154	−	0.994134i	$-0.465506\pi$
$821$	6.19788	0.216308	0.108154	+	0.994134i	$0.465506\pi$
$822$	−28.1719	−0.982608
$823$	16.2905	0.567850	0.283925	−	0.958847i	$-0.408363\pi$
$823$	16.2905	0.567850	0.283925	+	0.958847i	$0.408363\pi$
$824$	12.1523	0.423346
$825$	11.4660	0.399196
$826$	0	0
$827$	8.82581	0.306904	0.153452	−	0.988156i	$-0.450961\pi$
$827$	8.82581	0.306904	0.153452	+	0.988156i	$0.450961\pi$
$828$	0.582981	0.0202600
$829$	−3.73773	−0.129817	−0.0649084	−	0.997891i	$-0.520676\pi$
$829$	−3.73773	−0.129817	−0.0649084	+	0.997891i	$0.520676\pi$
$830$	−35.0644	−1.21710
$831$	17.0030	0.589827
$832$	−7.63484	−0.264690
$833$	0	0
$834$	18.8621	0.653142
$835$	7.77927	0.269213
$836$	15.1840	0.525149
$837$	8.06297	0.278697
$838$	−1.20282	−0.0415507
$839$	−31.2204	−1.07785	−0.538924	−	0.842355i	$-0.681169\pi$
$839$	−31.2204	−1.07785	−0.538924	+	0.842355i	$0.681169\pi$
$840$	0	0
$841$	41.6024	1.43456
$842$	−11.8078	−0.406922
$843$	38.4335	1.32372
$844$	−14.2821	−0.491609
$845$	34.8875	1.20017
$846$	0.327411	0.0112566
$847$	0	0
$848$	−6.82469	−0.234361
$849$	−17.3259	−0.594625
$850$	−3.84441	−0.131862
$851$	0.192956	0.00661446
$852$	−20.1178	−0.689226
$853$	48.6338	1.66519	0.832596	−	0.553881i	$-0.186854\pi$
$853$	48.6338	1.66519	0.832596	+	0.553881i	$0.186854\pi$
$854$	0	0
$855$	−6.76516	−0.231364
$856$	−57.7108	−1.97252
$857$	−2.65832	−0.0908065	−0.0454033	−	0.998969i	$-0.514457\pi$
$857$	−2.65832	−0.0908065	−0.0454033	+	0.998969i	$0.514457\pi$
$858$	−3.26370	−0.111421
$859$	1.02458	0.0349582	0.0174791	−	0.999847i	$-0.494436\pi$
$859$	1.02458	0.0349582	0.0174791	+	0.999847i	$0.494436\pi$
$860$	27.0415	0.922108
$861$	0	0
$862$	−15.7712	−0.537168
$863$	−14.5516	−0.495342	−0.247671	−	0.968844i	$-0.579665\pi$
$863$	−14.5516	−0.495342	−0.247671	+	0.968844i	$0.579665\pi$
$864$	−28.0375	−0.953855
$865$	56.8635	1.93342
$866$	−5.40234	−0.183579
$867$	1.65046	0.0560527
$868$	0	0
$869$	−15.4470	−0.524004
$870$	40.3355	1.36750
$871$	0.742547	0.0251602
$872$	22.4008	0.758586
$873$	1.25048	0.0423223
$874$	−15.9358	−0.539036
$875$	0	0
$876$	−28.7473	−0.971283
$877$	11.3461	0.383130	0.191565	−	0.981480i	$-0.438644\pi$
$877$	11.3461	0.383130	0.191565	+	0.981480i	$0.438644\pi$
$878$	−35.7299	−1.20583
$879$	53.7332	1.81238
$880$	4.07537	0.137381
$881$	32.2301	1.08586	0.542930	−	0.839778i	$-0.317315\pi$
$881$	32.2301	1.08586	0.542930	+	0.839778i	$0.317315\pi$
$882$	0	0
$883$	−16.2677	−0.547450	−0.273725	−	0.961808i	$-0.588256\pi$
$883$	−16.2677	−0.547450	−0.273725	+	0.961808i	$0.588256\pi$
$884$	−1.22260	−0.0411204
$885$	−11.4116	−0.383598
$886$	−33.4132	−1.12254
$887$	−15.5054	−0.520621	−0.260311	−	0.965525i	$-0.583825\pi$
$887$	−15.5054	−0.520621	−0.260311	+	0.965525i	$0.583825\pi$
$888$	−0.472476	−0.0158553
$889$	0	0
$890$	−1.22545	−0.0410773
$891$	−14.2191	−0.476357
$892$	19.9899	0.669311
$893$	9.99932	0.334614
$894$	−21.5938	−0.722206
$895$	9.42135	0.314921
$896$	0	0
$897$	−3.82698	−0.127779
$898$	−32.6364	−1.08909
$899$	12.5302	0.417906
$900$	1.15207	0.0384023
$901$	−8.80167	−0.293226
$902$	−13.5825	−0.452247
$903$	0	0
$904$	46.1764	1.53580
$905$	−4.36026	−0.144940
$906$	−36.9102	−1.22626
$907$	4.22916	0.140427	0.0702135	−	0.997532i	$-0.477632\pi$
$907$	4.22916	0.140427	0.0702135	+	0.997532i	$0.477632\pi$
$908$	−6.30830	−0.209348
$909$	−1.22616	−0.0406692
$910$	0	0
$911$	21.0906	0.698764	0.349382	−	0.936980i	$-0.386392\pi$
$911$	21.0906	0.698764	0.349382	+	0.936980i	$0.386392\pi$
$912$	10.4831	0.347132
$913$	21.1739	0.700752
$914$	23.0044	0.760917
$915$	40.4896	1.33855
$916$	7.89032	0.260703
$917$	0	0
$918$	5.25500	0.173441
$919$	−3.75811	−0.123968	−0.0619842	−	0.998077i	$-0.519743\pi$
$919$	−3.75811	−0.123968	−0.0619842	+	0.998077i	$0.519743\pi$
$920$	17.7876	0.586439
$921$	26.4900	0.872876
$922$	34.9104	1.14971
$923$	−13.3794	−0.440387
$924$	0	0
$925$	0.381314	0.0125375
$926$	−6.72738	−0.221076
$927$	1.12935	0.0370929
$928$	−43.5715	−1.43031
$929$	37.6313	1.23464	0.617322	−	0.786711i	$-0.288218\pi$
$929$	37.6313	1.23464	0.617322	+	0.786711i	$0.288218\pi$
$930$	7.15858	0.234739
$931$	0	0
$932$	−11.5037	−0.376816
$933$	7.83282	0.256435
$934$	9.34734	0.305854
$935$	5.25594	0.171888
$936$	−0.949357	−0.0310307
$937$	−40.6345	−1.32747	−0.663736	−	0.747967i	$-0.731030\pi$
$937$	−40.6345	−1.32747	−0.663736	+	0.747967i	$0.731030\pi$
$938$	0	0
$939$	17.5422	0.572467
$940$	−3.85530	−0.125746
$941$	1.67458	0.0545898	0.0272949	−	0.999627i	$-0.491311\pi$
$941$	1.67458	0.0545898	0.0272949	+	0.999627i	$0.491311\pi$
$942$	−37.3193	−1.21593
$943$	−15.9267	−0.518644
$944$	−1.79149	−0.0583080
$945$	0	0
$946$	14.6153	0.475183
$947$	−25.7544	−0.836906	−0.418453	−	0.908239i	$-0.637427\pi$
$947$	−25.7544	−0.836906	−0.418453	+	0.908239i	$0.637427\pi$
$948$	15.3199	0.497568
$949$	−19.1184	−0.620610
$950$	−31.4918	−1.02173
$951$	18.0636	0.585753
$952$	0	0
$953$	−4.59720	−0.148918	−0.0744590	−	0.997224i	$-0.523723\pi$
$953$	−4.59720	−0.148918	−0.0744590	+	0.997224i	$0.523723\pi$
$954$	−2.36079	−0.0764333
$955$	46.9116	1.51802
$956$	−25.0697	−0.810811
$957$	−24.3568	−0.787344
$958$	31.4401	1.01578
$959$	0	0
$960$	−32.5521	−1.05061
$961$	−28.7762	−0.928264
$962$	−0.108537	−0.00349939
$963$	−5.36326	−0.172829
$964$	0.466104	0.0150122
$965$	53.1385	1.71059
$966$	0	0
$967$	−53.3191	−1.71463	−0.857313	−	0.514796i	$-0.827868\pi$
$967$	−53.3191	−1.71463	−0.857313	+	0.514796i	$0.827868\pi$
$968$	23.5051	0.755482
$969$	13.5199	0.434323
$970$	13.1790	0.423153
$971$	41.9243	1.34541	0.672707	−	0.739909i	$-0.265131\pi$
$971$	41.9243	1.34541	0.672707	+	0.739909i	$0.265131\pi$
$972$	−3.01692	−0.0967676
$973$	0	0
$974$	3.03051	0.0971037
$975$	−7.56275	−0.242202
$976$	6.35639	0.203463
$977$	−0.0538462	−0.00172269	−0.000861346	−	1.00000i	$-0.500274\pi$
$977$	−0.0538462	−0.00172269	−0.000861346		1.00000i	$0.500274\pi$
$978$	28.5060	0.911520
$979$	0.739996	0.0236504
$980$	0	0
$981$	2.08178	0.0664661
$982$	28.7375	0.917050
$983$	−42.4395	−1.35361	−0.676804	−	0.736163i	$-0.736636\pi$
$983$	−42.4395	−1.35361	−0.676804	+	0.736163i	$0.736636\pi$
$984$	38.9983	1.24322
$985$	2.20537	0.0702688
$986$	8.16651	0.260075
$987$	0	0
$988$	−10.0150	−0.318620
$989$	17.1377	0.544947
$990$	1.40975	0.0448048
$991$	26.8616	0.853288	0.426644	−	0.904420i	$-0.359696\pi$
$991$	26.8616	0.853288	0.426644	+	0.904420i	$0.359696\pi$
$992$	−7.73289	−0.245520
$993$	−46.0097	−1.46007
$994$	0	0
$995$	42.4115	1.34454
$996$	−20.9997	−0.665400
$997$	8.16845	0.258697	0.129349	−	0.991599i	$-0.458711\pi$
$997$	8.16845	0.258697	0.129349	+	0.991599i	$0.458711\pi$
$998$	−15.0224	−0.475526
$999$	−0.521227	−0.0164909

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	833.2.a.j.1.6	✓	8
3.2	odd	2		7497.2.a.cg.1.3		8
7.2	even	3		833.2.e.l.18.3		16
7.3	odd	6		833.2.e.k.324.3		16
7.4	even	3		833.2.e.l.324.3		16
7.5	odd	6		833.2.e.k.18.3		16
7.6	odd	2		833.2.a.k.1.6	yes	8
21.20	even	2		7497.2.a.cf.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
833.2.a.j.1.6	✓	8	1.1	even	1	trivial
833.2.a.k.1.6	yes	8	7.6	odd	2
833.2.e.k.18.3		16	7.5	odd	6
833.2.e.k.324.3		16	7.3	odd	6
833.2.e.l.18.3		16	7.2	even	3
833.2.e.l.324.3		16	7.4	even	3
7497.2.a.cf.1.3		8	21.20	even	2
7497.2.a.cg.1.3		8	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 833 = 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	833.a (trivial)

\(f(q)\)	\(=\)	\(q+0.971912 q^{2} +1.65046 q^{3} -1.05539 q^{4} -2.99258 q^{5} +1.60411 q^{6} -2.96957 q^{8} -0.275972 q^{9} +O(q^{10})\)	\(q+0.971912 q^{2} +1.65046 q^{3} -1.05539 q^{4} -2.99258 q^{5} +1.60411 q^{6} -2.96957 q^{8} -0.275972 q^{9} -2.90852 q^{10} +1.75633 q^{11} -1.74188 q^{12} -1.15844 q^{13} -4.93913 q^{15} -0.775385 q^{16} -1.00000 q^{17} -0.268220 q^{18} -8.19160 q^{19} +3.15832 q^{20} +1.70699 q^{22} +2.00160 q^{23} -4.90116 q^{24} +3.95551 q^{25} -1.12590 q^{26} -5.40687 q^{27} -8.40252 q^{29} -4.80041 q^{30} -1.49124 q^{31} +5.18553 q^{32} +2.89875 q^{33} -0.971912 q^{34} +0.291257 q^{36} +0.0964009 q^{37} -7.96151 q^{38} -1.91195 q^{39} +8.88665 q^{40} -7.95695 q^{41} +8.56198 q^{43} -1.85360 q^{44} +0.825866 q^{45} +1.94538 q^{46} -1.22068 q^{47} -1.27974 q^{48} +3.84441 q^{50} -1.65046 q^{51} +1.22260 q^{52} +8.80167 q^{53} -5.25500 q^{54} -5.25594 q^{55} -13.5199 q^{57} -8.16651 q^{58} +2.31045 q^{59} +5.21270 q^{60} -8.19772 q^{61} -1.44936 q^{62} +6.59065 q^{64} +3.46670 q^{65} +2.81733 q^{66} -0.640991 q^{67} +1.05539 q^{68} +3.30357 q^{69} +11.5495 q^{71} +0.819517 q^{72} +16.5037 q^{73} +0.0936932 q^{74} +6.52842 q^{75} +8.64530 q^{76} -1.85825 q^{78} -8.79507 q^{79} +2.32040 q^{80} -8.09592 q^{81} -7.73346 q^{82} +12.0558 q^{83} +2.99258 q^{85} +8.32149 q^{86} -13.8681 q^{87} -5.21553 q^{88} +0.421332 q^{89} +0.802669 q^{90} -2.11247 q^{92} -2.46124 q^{93} -1.18639 q^{94} +24.5140 q^{95} +8.55852 q^{96} -4.53118 q^{97} -0.484696 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 8 q^{3} + 6 q^{4} - 4 q^{5} + 6 q^{6} - 6 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 - 8 * q^3 + 6 * q^4 - 4 * q^5 + 6 * q^6 - 6 * q^8 + 8 * q^9	\( 8 q - 2 q^{2} - 8 q^{3} + 6 q^{4} - 4 q^{5} + 6 q^{6} - 6 q^{8} + 8 q^{9} - 12 q^{10} + 4 q^{11} - 20 q^{12} - 12 q^{13} - 4 q^{15} - 6 q^{16} - 8 q^{17} - 6 q^{18} - 16 q^{19} + 18 q^{20} + 8 q^{22} - 4 q^{23} + 8 q^{24} + 8 q^{25} - 8 q^{26} - 20 q^{27} + 10 q^{30} - 28 q^{31} - 4 q^{32} - 16 q^{33} + 2 q^{34} + 20 q^{36} + 8 q^{37} - 8 q^{38} + 20 q^{39} - 26 q^{40} - 4 q^{41} - 8 q^{43} - 4 q^{44} + 20 q^{45} - 16 q^{46} - 28 q^{47} + 6 q^{48} - 32 q^{50} + 8 q^{51} - 32 q^{52} - 8 q^{53} + 14 q^{54} - 44 q^{55} - 16 q^{57} - 32 q^{58} + 8 q^{59} - 42 q^{60} - 8 q^{61} + 24 q^{62} - 22 q^{64} - 16 q^{66} - 20 q^{67} - 6 q^{68} - 4 q^{69} + 40 q^{71} - 40 q^{72} - 8 q^{73} + 4 q^{74} - 16 q^{75} + 12 q^{76} + 4 q^{79} + 32 q^{80} + 4 q^{81} + 10 q^{82} + 4 q^{83} + 4 q^{85} + 14 q^{86} - 16 q^{87} + 24 q^{88} + 4 q^{89} - 26 q^{90} - 28 q^{92} + 32 q^{93} - 8 q^{94} + 4 q^{95} + 52 q^{96} - 40 q^{97} + 8 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 - 8 * q^3 + 6 * q^4 - 4 * q^5 + 6 * q^6 - 6 * q^8 + 8 * q^9 - 12 * q^10 + 4 * q^11 - 20 * q^12 - 12 * q^13 - 4 * q^15 - 6 * q^16 - 8 * q^17 - 6 * q^18 - 16 * q^19 + 18 * q^20 + 8 * q^22 - 4 * q^23 + 8 * q^24 + 8 * q^25 - 8 * q^26 - 20 * q^27 + 10 * q^30 - 28 * q^31 - 4 * q^32 - 16 * q^33 + 2 * q^34 + 20 * q^36 + 8 * q^37 - 8 * q^38 + 20 * q^39 - 26 * q^40 - 4 * q^41 - 8 * q^43 - 4 * q^44 + 20 * q^45 - 16 * q^46 - 28 * q^47 + 6 * q^48 - 32 * q^50 + 8 * q^51 - 32 * q^52 - 8 * q^53 + 14 * q^54 - 44 * q^55 - 16 * q^57 - 32 * q^58 + 8 * q^59 - 42 * q^60 - 8 * q^61 + 24 * q^62 - 22 * q^64 - 16 * q^66 - 20 * q^67 - 6 * q^68 - 4 * q^69 + 40 * q^71 - 40 * q^72 - 8 * q^73 + 4 * q^74 - 16 * q^75 + 12 * q^76 + 4 * q^79 + 32 * q^80 + 4 * q^81 + 10 * q^82 + 4 * q^83 + 4 * q^85 + 14 * q^86 - 16 * q^87 + 24 * q^88 + 4 * q^89 - 26 * q^90 - 28 * q^92 + 32 * q^93 - 8 * q^94 + 4 * q^95 + 52 * q^96 - 40 * q^97 + 8 * q^99

Introduction

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