LMFDB - Embedded newform 8673.2.a.ba.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8673,2,Mod(1,8673)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8673, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8673.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8673 = 3 \cdot 7^{2} \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8673.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:	$69.2542536731$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 17 x^{10} + 52 x^{9} + 101 x^{8} - 316 x^{7} - 260 x^{6} + 830 x^{5} + 287 x^{4} + \cdots - 61 $ x^12 - 3x^11 - 17x^10 + 52x^9 + 101x^8 - 316x^7 - 260x^6 + 830x^5 + 287x^4 - 941x^3 - 77x^2 + 360*x - 61
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 1239)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$2.47416$ of defining polynomial
Character	$\chi$	$=$	8673.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.47416 q^{2} +1.00000 q^{3} +4.12148 q^{4} -0.798478 q^{5} +2.47416 q^{6} +5.24888 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.47416 q^{2} +1.00000 q^{3} +4.12148 q^{4} -0.798478 q^{5} +2.47416 q^{6} +5.24888 q^{8} +1.00000 q^{9} -1.97556 q^{10} +0.583974 q^{11} +4.12148 q^{12} -1.18818 q^{13} -0.798478 q^{15} +4.74363 q^{16} -6.24817 q^{17} +2.47416 q^{18} +7.64822 q^{19} -3.29091 q^{20} +1.44485 q^{22} +8.22160 q^{23} +5.24888 q^{24} -4.36243 q^{25} -2.93975 q^{26} +1.00000 q^{27} +1.77215 q^{29} -1.97556 q^{30} +2.75028 q^{31} +1.23874 q^{32} +0.583974 q^{33} -15.4590 q^{34} +4.12148 q^{36} +7.94122 q^{37} +18.9229 q^{38} -1.18818 q^{39} -4.19111 q^{40} +6.17596 q^{41} +3.29864 q^{43} +2.40684 q^{44} -0.798478 q^{45} +20.3416 q^{46} +3.47901 q^{47} +4.74363 q^{48} -10.7934 q^{50} -6.24817 q^{51} -4.89705 q^{52} +5.57579 q^{53} +2.47416 q^{54} -0.466290 q^{55} +7.64822 q^{57} +4.38459 q^{58} +1.00000 q^{59} -3.29091 q^{60} +0.324365 q^{61} +6.80464 q^{62} -6.42241 q^{64} +0.948734 q^{65} +1.44485 q^{66} -3.33737 q^{67} -25.7517 q^{68} +8.22160 q^{69} -7.61512 q^{71} +5.24888 q^{72} +7.70393 q^{73} +19.6479 q^{74} -4.36243 q^{75} +31.5220 q^{76} -2.93975 q^{78} +7.17243 q^{79} -3.78768 q^{80} +1.00000 q^{81} +15.2803 q^{82} +14.4122 q^{83} +4.98902 q^{85} +8.16137 q^{86} +1.77215 q^{87} +3.06521 q^{88} +8.71901 q^{89} -1.97556 q^{90} +33.8851 q^{92} +2.75028 q^{93} +8.60763 q^{94} -6.10693 q^{95} +1.23874 q^{96} -11.1304 q^{97} +0.583974 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} + 12 q^{3} + 19 q^{4} + 4 q^{5} + 3 q^{6} + 12 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 + 12 * q^3 + 19 * q^4 + 4 * q^5 + 3 * q^6 + 12 * q^8 + 12 * q^9	$ 12 q + 3 q^{2} + 12 q^{3} + 19 q^{4} + 4 q^{5} + 3 q^{6} + 12 q^{8} + 12 q^{9} - 2 q^{10} + 2 q^{11} + 19 q^{12} - 9 q^{13} + 4 q^{15} + 33 q^{16} + 5 q^{17} + 3 q^{18} - 7 q^{19} + 15 q^{20} + 24 q^{22} + q^{23} + 12 q^{24} + 30 q^{25} - 3 q^{26} + 12 q^{27} + 11 q^{29} - 2 q^{30} - 13 q^{31} + 22 q^{32} + 2 q^{33} - 8 q^{34} + 19 q^{36} + 7 q^{37} + 4 q^{38} - 9 q^{39} + 20 q^{40} + 21 q^{43} + 23 q^{44} + 4 q^{45} - 7 q^{46} + 18 q^{47} + 33 q^{48} + 52 q^{50} + 5 q^{51} - 23 q^{52} + 15 q^{53} + 3 q^{54} - 20 q^{55} - 7 q^{57} + 27 q^{58} + 12 q^{59} + 15 q^{60} - 30 q^{61} - q^{62} + 88 q^{64} + q^{65} + 24 q^{66} + 19 q^{67} + 25 q^{68} + q^{69} + 18 q^{71} + 12 q^{72} - 19 q^{73} + 3 q^{74} + 30 q^{75} - 62 q^{76} - 3 q^{78} + 16 q^{79} + 47 q^{80} + 12 q^{81} - 19 q^{82} + 37 q^{83} + 48 q^{85} - 8 q^{86} + 11 q^{87} + 46 q^{88} - 23 q^{89} - 2 q^{90} + 19 q^{92} - 13 q^{93} - 13 q^{94} + 20 q^{95} + 22 q^{96} - 9 q^{97} + 2 q^{99}+O(q^{100}) $ 12 * q + 3 * q^2 + 12 * q^3 + 19 * q^4 + 4 * q^5 + 3 * q^6 + 12 * q^8 + 12 * q^9 - 2 * q^10 + 2 * q^11 + 19 * q^12 - 9 * q^13 + 4 * q^15 + 33 * q^16 + 5 * q^17 + 3 * q^18 - 7 * q^19 + 15 * q^20 + 24 * q^22 + q^23 + 12 * q^24 + 30 * q^25 - 3 * q^26 + 12 * q^27 + 11 * q^29 - 2 * q^30 - 13 * q^31 + 22 * q^32 + 2 * q^33 - 8 * q^34 + 19 * q^36 + 7 * q^37 + 4 * q^38 - 9 * q^39 + 20 * q^40 + 21 * q^43 + 23 * q^44 + 4 * q^45 - 7 * q^46 + 18 * q^47 + 33 * q^48 + 52 * q^50 + 5 * q^51 - 23 * q^52 + 15 * q^53 + 3 * q^54 - 20 * q^55 - 7 * q^57 + 27 * q^58 + 12 * q^59 + 15 * q^60 - 30 * q^61 - q^62 + 88 * q^64 + q^65 + 24 * q^66 + 19 * q^67 + 25 * q^68 + q^69 + 18 * q^71 + 12 * q^72 - 19 * q^73 + 3 * q^74 + 30 * q^75 - 62 * q^76 - 3 * q^78 + 16 * q^79 + 47 * q^80 + 12 * q^81 - 19 * q^82 + 37 * q^83 + 48 * q^85 - 8 * q^86 + 11 * q^87 + 46 * q^88 - 23 * q^89 - 2 * q^90 + 19 * q^92 - 13 * q^93 - 13 * q^94 + 20 * q^95 + 22 * q^96 - 9 * q^97 + 2 * 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 $

$2$	2.47416	1.74950	0.874748	−	0.484577i	$-0.161027\pi$
$2$	2.47416	1.74950	0.874748	+	0.484577i	$0.161027\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.12148	2.06074
$5$	−0.798478	−0.357090	−0.178545	−	0.983932i	$-0.557139\pi$
$5$	−0.798478	−0.357090	−0.178545	+	0.983932i	$0.557139\pi$
$6$	2.47416	1.01007
$7$	0	0
$7$	0	0
$8$	5.24888	1.85576
$9$	1.00000	0.333333
$10$	−1.97556	−0.624728
$11$	0.583974	0.176075	0.0880374	−	0.996117i	$-0.471940\pi$
$11$	0.583974	0.176075	0.0880374	+	0.996117i	$0.471940\pi$
$12$	4.12148	1.18977
$13$	−1.18818	−0.329541	−0.164771	−	0.986332i	$-0.552688\pi$
$13$	−1.18818	−0.329541	−0.164771	+	0.986332i	$0.552688\pi$
$14$	0	0
$15$	−0.798478	−0.206166
$16$	4.74363	1.18591
$17$	−6.24817	−1.51540	−0.757702	−	0.652601i	$-0.773678\pi$
$17$	−6.24817	−1.51540	−0.757702	+	0.652601i	$0.773678\pi$
$18$	2.47416	0.583166
$19$	7.64822	1.75462	0.877311	−	0.479922i	$-0.159335\pi$
$19$	7.64822	1.75462	0.877311	+	0.479922i	$0.159335\pi$
$20$	−3.29091	−0.735869
$21$	0	0
$22$	1.44485	0.308042
$23$	8.22160	1.71432	0.857161	−	0.515049i	$-0.172226\pi$
$23$	8.22160	1.71432	0.857161	+	0.515049i	$0.172226\pi$
$24$	5.24888	1.07142
$25$	−4.36243	−0.872487
$26$	−2.93975	−0.576532
$27$	1.00000	0.192450
$28$	0	0
$29$	1.77215	0.329080	0.164540	−	0.986370i	$-0.447386\pi$
$29$	1.77215	0.329080	0.164540	+	0.986370i	$0.447386\pi$
$30$	−1.97556	−0.360687
$31$	2.75028	0.493965	0.246983	−	0.969020i	$-0.420561\pi$
$31$	2.75028	0.493965	0.246983	+	0.969020i	$0.420561\pi$
$32$	1.23874	0.218980
$33$	0.583974	0.101657
$34$	−15.4590	−2.65119
$35$	0	0
$36$	4.12148	0.686913
$37$	7.94122	1.30553	0.652764	−	0.757561i	$-0.273609\pi$
$37$	7.94122	1.30553	0.652764	+	0.757561i	$0.273609\pi$
$38$	18.9229	3.06971
$39$	−1.18818	−0.190261
$40$	−4.19111	−0.662673
$41$	6.17596	0.964523	0.482262	−	0.876027i	$-0.339815\pi$
$41$	6.17596	0.964523	0.482262	+	0.876027i	$0.339815\pi$
$42$	0	0
$43$	3.29864	0.503038	0.251519	−	0.967852i	$-0.419070\pi$
$43$	3.29864	0.503038	0.251519	+	0.967852i	$0.419070\pi$
$44$	2.40684	0.362844
$45$	−0.798478	−0.119030
$46$	20.3416	2.99920
$47$	3.47901	0.507465	0.253733	−	0.967274i	$-0.418342\pi$
$47$	3.47901	0.507465	0.253733	+	0.967274i	$0.418342\pi$
$48$	4.74363	0.684684
$49$	0	0
$50$	−10.7934	−1.52641
$51$	−6.24817	−0.874919
$52$	−4.89705	−0.679099
$53$	5.57579	0.765894	0.382947	−	0.923770i	$-0.374909\pi$
$53$	5.57579	0.765894	0.382947	+	0.923770i	$0.374909\pi$
$54$	2.47416	0.336691
$55$	−0.466290	−0.0628746
$56$	0	0
$57$	7.64822	1.01303
$58$	4.38459	0.575725
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	−3.29091	−0.424854
$61$	0.324365	0.0415307	0.0207654	−	0.999784i	$-0.493390\pi$
$61$	0.324365	0.0415307	0.0207654	+	0.999784i	$0.493390\pi$
$62$	6.80464	0.864191
$63$	0	0
$64$	−6.42241	−0.802801
$65$	0.948734	0.117676
$66$	1.44485	0.177848
$67$	−3.33737	−0.407725	−0.203862	−	0.979000i	$-0.565350\pi$
$67$	−3.33737	−0.407725	−0.203862	+	0.979000i	$0.565350\pi$
$68$	−25.7517	−3.12285
$69$	8.22160	0.989764
$70$	0	0
$71$	−7.61512	−0.903748	−0.451874	−	0.892082i	$-0.649244\pi$
$71$	−7.61512	−0.903748	−0.451874	+	0.892082i	$0.649244\pi$
$72$	5.24888	0.618587
$73$	7.70393	0.901677	0.450838	−	0.892606i	$-0.351125\pi$
$73$	7.70393	0.901677	0.450838	+	0.892606i	$0.351125\pi$
$74$	19.6479	2.28402
$75$	−4.36243	−0.503730
$76$	31.5220	3.61582
$77$	0	0
$78$	−2.93975	−0.332861
$79$	7.17243	0.806961	0.403481	−	0.914988i	$-0.367800\pi$
$79$	7.17243	0.806961	0.403481	+	0.914988i	$0.367800\pi$
$80$	−3.78768	−0.423476
$81$	1.00000	0.111111
$82$	15.2803	1.68743
$83$	14.4122	1.58194	0.790971	−	0.611854i	$-0.209576\pi$
$83$	14.4122	1.58194	0.790971	+	0.611854i	$0.209576\pi$
$84$	0	0
$85$	4.98902	0.541135
$86$	8.16137	0.880063
$87$	1.77215	0.189995
$88$	3.06521	0.326753
$89$	8.71901	0.924214	0.462107	−	0.886824i	$-0.347094\pi$
$89$	8.71901	0.924214	0.462107	+	0.886824i	$0.347094\pi$
$90$	−1.97556	−0.208243
$91$	0	0
$92$	33.8851	3.53277
$93$	2.75028	0.285191
$94$	8.60763	0.887809
$95$	−6.10693	−0.626558
$96$	1.23874	0.126428
$97$	−11.1304	−1.13012	−0.565058	−	0.825051i	$-0.691146\pi$
$97$	−11.1304	−1.13012	−0.565058	+	0.825051i	$0.691146\pi$
$98$	0	0
$99$	0.583974	0.0586916
$100$	−17.9797	−1.79797
$101$	−0.201312	−0.0200313	−0.0100157	−	0.999950i	$-0.503188\pi$
$101$	−0.201312	−0.0200313	−0.0100157	+	0.999950i	$0.503188\pi$
$102$	−15.4590	−1.53067
$103$	−12.7771	−1.25897	−0.629483	−	0.777014i	$-0.716733\pi$
$103$	−12.7771	−1.25897	−0.629483	+	0.777014i	$0.716733\pi$
$104$	−6.23661	−0.611550
$105$	0	0
$106$	13.7954	1.33993
$107$	−19.2940	−1.86522	−0.932610	−	0.360886i	$-0.882474\pi$
$107$	−19.2940	−1.86522	−0.932610	+	0.360886i	$0.882474\pi$
$108$	4.12148	0.396589
$109$	−1.65806	−0.158813	−0.0794067	−	0.996842i	$-0.525303\pi$
$109$	−1.65806	−0.158813	−0.0794067	+	0.996842i	$0.525303\pi$
$110$	−1.15368	−0.109999
$111$	7.94122	0.753747
$112$	0	0
$113$	−9.31517	−0.876297	−0.438149	−	0.898903i	$-0.644366\pi$
$113$	−9.31517	−0.876297	−0.438149	+	0.898903i	$0.644366\pi$
$114$	18.9229	1.77230
$115$	−6.56476	−0.612167
$116$	7.30389	0.678149
$117$	−1.18818	−0.109847
$118$	2.47416	0.227765
$119$	0	0
$120$	−4.19111	−0.382595
$121$	−10.6590	−0.968998
$122$	0.802533	0.0726579
$123$	6.17596	0.556868
$124$	11.3352	1.01793
$125$	7.47569	0.668646
$126$	0	0
$127$	12.1227	1.07572	0.537860	−	0.843034i	$-0.319233\pi$
$127$	12.1227	1.07572	0.537860	+	0.843034i	$0.319233\pi$
$128$	−18.3676	−1.62348
$129$	3.29864	0.290429
$130$	2.34732	0.205874
$131$	10.6603	0.931393	0.465696	−	0.884945i	$-0.345804\pi$
$131$	10.6603	0.931393	0.465696	+	0.884945i	$0.345804\pi$
$132$	2.40684	0.209488
$133$	0	0
$134$	−8.25720	−0.713313
$135$	−0.798478	−0.0687220
$136$	−32.7959	−2.81222
$137$	13.4012	1.14494	0.572471	−	0.819925i	$-0.305985\pi$
$137$	13.4012	1.14494	0.572471	+	0.819925i	$0.305985\pi$
$138$	20.3416	1.73159
$139$	14.6259	1.24056	0.620278	−	0.784382i	$-0.287020\pi$
$139$	14.6259	1.24056	0.620278	+	0.784382i	$0.287020\pi$
$140$	0	0
$141$	3.47901	0.292985
$142$	−18.8410	−1.58110
$143$	−0.693865	−0.0580239
$144$	4.74363	0.395302
$145$	−1.41502	−0.117511
$146$	19.0608	1.57748
$147$	0	0
$148$	32.7295	2.69035
$149$	1.57613	0.129122	0.0645609	−	0.997914i	$-0.479435\pi$
$149$	1.57613	0.129122	0.0645609	+	0.997914i	$0.479435\pi$
$150$	−10.7934	−0.881275
$151$	−20.4528	−1.66443	−0.832214	−	0.554454i	$-0.812927\pi$
$151$	−20.4528	−1.66443	−0.832214	+	0.554454i	$0.812927\pi$
$152$	40.1446	3.25616
$153$	−6.24817	−0.505134
$154$	0	0
$155$	−2.19604	−0.176390
$156$	−4.89705	−0.392078
$157$	3.64011	0.290512	0.145256	−	0.989394i	$-0.453599\pi$
$157$	3.64011	0.290512	0.145256	+	0.989394i	$0.453599\pi$
$158$	17.7458	1.41178
$159$	5.57579	0.442189
$160$	−0.989106	−0.0781957
$161$	0	0
$162$	2.47416	0.194389
$163$	−2.73838	−0.214487	−0.107243	−	0.994233i	$-0.534202\pi$
$163$	−2.73838	−0.214487	−0.107243	+	0.994233i	$0.534202\pi$
$164$	25.4541	1.98763
$165$	−0.466290	−0.0363006
$166$	35.6580	2.76760
$167$	4.46622	0.345607	0.172803	−	0.984956i	$-0.444717\pi$
$167$	4.46622	0.345607	0.172803	+	0.984956i	$0.444717\pi$
$168$	0	0
$169$	−11.5882	−0.891402
$170$	12.3436	0.946715
$171$	7.64822	0.584874
$172$	13.5953	1.03663
$173$	−16.9536	−1.28896	−0.644478	−	0.764623i	$-0.722925\pi$
$173$	−16.9536	−1.28896	−0.644478	+	0.764623i	$0.722925\pi$
$174$	4.38459	0.332395
$175$	0	0
$176$	2.77016	0.208808
$177$	1.00000	0.0751646
$178$	21.5723	1.61691
$179$	16.3749	1.22392	0.611959	−	0.790889i	$-0.290382\pi$
$179$	16.3749	1.22392	0.611959	+	0.790889i	$0.290382\pi$
$180$	−3.29091	−0.245290
$181$	−14.4761	−1.07600	−0.537999	−	0.842945i	$-0.680820\pi$
$181$	−14.4761	−1.07600	−0.537999	+	0.842945i	$0.680820\pi$
$182$	0	0
$183$	0.324365	0.0239778
$184$	43.1542	3.18137
$185$	−6.34088	−0.466191
$186$	6.80464	0.498941
$187$	−3.64877	−0.266824
$188$	14.3387	1.04575
$189$	0	0
$190$	−15.1095	−1.09616
$191$	−22.1840	−1.60518	−0.802589	−	0.596532i	$-0.796545\pi$
$191$	−22.1840	−1.60518	−0.802589	+	0.596532i	$0.796545\pi$
$192$	−6.42241	−0.463498
$193$	14.5248	1.04552	0.522759	−	0.852481i	$-0.324903\pi$
$193$	14.5248	1.04552	0.522759	+	0.852481i	$0.324903\pi$
$194$	−27.5383	−1.97714
$195$	0.948734	0.0679403
$196$	0	0
$197$	−16.6164	−1.18387	−0.591933	−	0.805987i	$-0.701635\pi$
$197$	−16.6164	−1.18387	−0.591933	+	0.805987i	$0.701635\pi$
$198$	1.44485	0.102681
$199$	−22.4467	−1.59121	−0.795604	−	0.605817i	$-0.792846\pi$
$199$	−22.4467	−1.59121	−0.795604	+	0.605817i	$0.792846\pi$
$200$	−22.8979	−1.61913
$201$	−3.33737	−0.235400
$202$	−0.498079	−0.0350447
$203$	0	0
$204$	−25.7517	−1.80298
$205$	−4.93137	−0.344422
$206$	−31.6126	−2.20256
$207$	8.22160	0.571441
$208$	−5.63628	−0.390805
$209$	4.46636	0.308945
$210$	0	0
$211$	−20.5005	−1.41131	−0.705656	−	0.708555i	$-0.749348\pi$
$211$	−20.5005	−1.41131	−0.705656	+	0.708555i	$0.749348\pi$
$212$	22.9805	1.57831
$213$	−7.61512	−0.521779
$214$	−47.7365	−3.26320
$215$	−2.63389	−0.179630
$216$	5.24888	0.357141
$217$	0	0
$218$	−4.10231	−0.277843
$219$	7.70393	0.520583
$220$	−1.92180	−0.129568
$221$	7.42394	0.499388
$222$	19.6479	1.31868
$223$	−18.7261	−1.25399	−0.626996	−	0.779022i	$-0.715716\pi$
$223$	−18.7261	−1.25399	−0.626996	+	0.779022i	$0.715716\pi$
$224$	0	0
$225$	−4.36243	−0.290829
$226$	−23.0472	−1.53308
$227$	1.50542	0.0999185	0.0499592	−	0.998751i	$-0.484091\pi$
$227$	1.50542	0.0999185	0.0499592	+	0.998751i	$0.484091\pi$
$228$	31.5220	2.08759
$229$	12.0184	0.794195	0.397098	−	0.917776i	$-0.370017\pi$
$229$	12.0184	0.794195	0.397098	+	0.917776i	$0.370017\pi$
$230$	−16.2423	−1.07098
$231$	0	0
$232$	9.30182	0.610694
$233$	14.8982	0.976011	0.488005	−	0.872841i	$-0.337725\pi$
$233$	14.8982	0.976011	0.488005	+	0.872841i	$0.337725\pi$
$234$	−2.93975	−0.192177
$235$	−2.77791	−0.181211
$236$	4.12148	0.268285
$237$	7.17243	0.465899
$238$	0	0
$239$	−0.0620078	−0.00401095	−0.00200548	−	0.999998i	$-0.500638\pi$
$239$	−0.0620078	−0.00401095	−0.00200548	+	0.999998i	$0.500638\pi$
$240$	−3.78768	−0.244494
$241$	−20.7596	−1.33724	−0.668621	−	0.743604i	$-0.733115\pi$
$241$	−20.7596	−1.33724	−0.668621	+	0.743604i	$0.733115\pi$
$242$	−26.3720	−1.69526
$243$	1.00000	0.0641500
$244$	1.33686	0.0855840
$245$	0	0
$246$	15.2803	0.974238
$247$	−9.08745	−0.578221
$248$	14.4359	0.916681
$249$	14.4122	0.913334
$250$	18.4961	1.16979
$251$	−2.70554	−0.170772	−0.0853860	−	0.996348i	$-0.527212\pi$
$251$	−2.70554	−0.170772	−0.0853860	+	0.996348i	$0.527212\pi$
$252$	0	0
$253$	4.80120	0.301849
$254$	29.9936	1.88197
$255$	4.98902	0.312425
$256$	−32.5995	−2.03747
$257$	10.4922	0.654484	0.327242	−	0.944941i	$-0.393881\pi$
$257$	10.4922	0.654484	0.327242	+	0.944941i	$0.393881\pi$
$258$	8.16137	0.508105
$259$	0	0
$260$	3.91019	0.242499
$261$	1.77215	0.109693
$262$	26.3753	1.62947
$263$	20.3159	1.25273	0.626365	−	0.779530i	$-0.284542\pi$
$263$	20.3159	1.25273	0.626365	+	0.779530i	$0.284542\pi$
$264$	3.06521	0.188651
$265$	−4.45214	−0.273493
$266$	0	0
$267$	8.71901	0.533595
$268$	−13.7549	−0.840214
$269$	28.9839	1.76718	0.883590	−	0.468261i	$-0.155119\pi$
$269$	28.9839	1.76718	0.883590	+	0.468261i	$0.155119\pi$
$270$	−1.97556	−0.120229
$271$	0.458269	0.0278379	0.0139189	−	0.999903i	$-0.495569\pi$
$271$	0.458269	0.0278379	0.0139189	+	0.999903i	$0.495569\pi$
$272$	−29.6390	−1.79713
$273$	0	0
$274$	33.1567	2.00307
$275$	−2.54755	−0.153623
$276$	33.8851	2.03965
$277$	8.53722	0.512952	0.256476	−	0.966551i	$-0.417439\pi$
$277$	8.53722	0.512952	0.256476	+	0.966551i	$0.417439\pi$
$278$	36.1869	2.17035
$279$	2.75028	0.164655
$280$	0	0
$281$	−28.7774	−1.71672	−0.858359	−	0.513049i	$-0.828516\pi$
$281$	−28.7774	−1.71672	−0.858359	+	0.513049i	$0.828516\pi$
$282$	8.60763	0.512577
$283$	−15.2955	−0.909225	−0.454613	−	0.890689i	$-0.650222\pi$
$283$	−15.2955	−0.909225	−0.454613	+	0.890689i	$0.650222\pi$
$284$	−31.3855	−1.86239
$285$	−6.10693	−0.361743
$286$	−1.71674	−0.101513
$287$	0	0
$288$	1.23874	0.0729935
$289$	22.0396	1.29645
$290$	−3.50100	−0.205586
$291$	−11.1304	−0.652473
$292$	31.7516	1.85812
$293$	−17.0331	−0.995083	−0.497542	−	0.867440i	$-0.665764\pi$
$293$	−17.0331	−0.995083	−0.497542	+	0.867440i	$0.665764\pi$
$294$	0	0
$295$	−0.798478	−0.0464892
$296$	41.6825	2.42275
$297$	0.583974	0.0338856
$298$	3.89960	0.225898
$299$	−9.76873	−0.564940
$300$	−17.9797	−1.03806
$301$	0	0
$302$	−50.6037	−2.91191
$303$	−0.201312	−0.0115651
$304$	36.2803	2.08082
$305$	−0.258998	−0.0148302
$306$	−15.4590	−0.883731
$307$	18.9549	1.08181	0.540906	−	0.841083i	$-0.318082\pi$
$307$	18.9549	1.08181	0.540906	+	0.841083i	$0.318082\pi$
$308$	0	0
$309$	−12.7771	−0.726864
$310$	−5.43336	−0.308594
$311$	−27.4189	−1.55478	−0.777391	−	0.629018i	$-0.783457\pi$
$311$	−27.4189	−1.55478	−0.777391	+	0.629018i	$0.783457\pi$
$312$	−6.23661	−0.353078
$313$	24.1459	1.36481	0.682403	−	0.730977i	$-0.260935\pi$
$313$	24.1459	1.36481	0.682403	+	0.730977i	$0.260935\pi$
$314$	9.00621	0.508250
$315$	0	0
$316$	29.5610	1.66294
$317$	0.400012	0.0224669	0.0112335	−	0.999937i	$-0.496424\pi$
$317$	0.400012	0.0224669	0.0112335	+	0.999937i	$0.496424\pi$
$318$	13.7954	0.773608
$319$	1.03489	0.0579428
$320$	5.12815	0.286672
$321$	−19.2940	−1.07689
$322$	0	0
$323$	−47.7874	−2.65896
$324$	4.12148	0.228971
$325$	5.18335	0.287521
$326$	−6.77520	−0.375244
$327$	−1.65806	−0.0916909
$328$	32.4169	1.78992
$329$	0	0
$330$	−1.15368	−0.0635079
$331$	−4.61192	−0.253494	−0.126747	−	0.991935i	$-0.540454\pi$
$331$	−4.61192	−0.253494	−0.126747	+	0.991935i	$0.540454\pi$
$332$	59.3994	3.25997
$333$	7.94122	0.435176
$334$	11.0502	0.604638
$335$	2.66482	0.145594
$336$	0	0
$337$	−11.6341	−0.633748	−0.316874	−	0.948468i	$-0.602633\pi$
$337$	−11.6341	−0.633748	−0.316874	+	0.948468i	$0.602633\pi$
$338$	−28.6712	−1.55951
$339$	−9.31517	−0.505930
$340$	20.5621	1.11514
$341$	1.60609	0.0869748
$342$	18.9229	1.02324
$343$	0	0
$344$	17.3142	0.933518
$345$	−6.56476	−0.353435
$346$	−41.9459	−2.25502
$347$	−8.12870	−0.436371	−0.218186	−	0.975907i	$-0.570014\pi$
$347$	−8.12870	−0.436371	−0.218186	+	0.975907i	$0.570014\pi$
$348$	7.30389	0.391530
$349$	7.38492	0.395306	0.197653	−	0.980272i	$-0.436668\pi$
$349$	7.38492	0.395306	0.197653	+	0.980272i	$0.436668\pi$
$350$	0	0
$351$	−1.18818	−0.0634203
$352$	0.723392	0.0385569
$353$	−27.2408	−1.44988	−0.724941	−	0.688811i	$-0.758133\pi$
$353$	−27.2408	−1.44988	−0.724941	+	0.688811i	$0.758133\pi$
$354$	2.47416	0.131500
$355$	6.08050	0.322720
$356$	35.9352	1.90456
$357$	0	0
$358$	40.5142	2.14124
$359$	−11.9234	−0.629294	−0.314647	−	0.949209i	$-0.601886\pi$
$359$	−11.9234	−0.629294	−0.314647	+	0.949209i	$0.601886\pi$
$360$	−4.19111	−0.220891
$361$	39.4953	2.07870
$362$	−35.8162	−1.88246
$363$	−10.6590	−0.559451
$364$	0	0
$365$	−6.15141	−0.321980
$366$	0.802533	0.0419491
$367$	−20.1829	−1.05354	−0.526771	−	0.850007i	$-0.676597\pi$
$367$	−20.1829	−1.05354	−0.526771	+	0.850007i	$0.676597\pi$
$368$	39.0002	2.03303
$369$	6.17596	0.321508
$370$	−15.6884	−0.815600
$371$	0	0
$372$	11.3352	0.587704
$373$	33.3530	1.72695	0.863476	−	0.504390i	$-0.168283\pi$
$373$	33.3530	1.72695	0.863476	+	0.504390i	$0.168283\pi$
$374$	−9.02764	−0.466808
$375$	7.47569	0.386043
$376$	18.2609	0.941734
$377$	−2.10563	−0.108446
$378$	0	0
$379$	4.52337	0.232350	0.116175	−	0.993229i	$-0.462937\pi$
$379$	4.52337	0.232350	0.116175	+	0.993229i	$0.462937\pi$
$380$	−25.1696	−1.29117
$381$	12.1227	0.621067
$382$	−54.8868	−2.80826
$383$	−1.80160	−0.0920575	−0.0460287	−	0.998940i	$-0.514657\pi$
$383$	−1.80160	−0.0920575	−0.0460287	+	0.998940i	$0.514657\pi$
$384$	−18.3676	−0.937316
$385$	0	0
$386$	35.9367	1.82913
$387$	3.29864	0.167679
$388$	−45.8735	−2.32888
$389$	21.4676	1.08845	0.544224	−	0.838940i	$-0.316824\pi$
$389$	21.4676	1.08845	0.544224	+	0.838940i	$0.316824\pi$
$390$	2.34732	0.118861
$391$	−51.3699	−2.59789
$392$	0	0
$393$	10.6603	0.537740
$394$	−41.1116	−2.07117
$395$	−5.72702	−0.288158
$396$	2.40684	0.120948
$397$	−15.7566	−0.790800	−0.395400	−	0.918509i	$-0.629394\pi$
$397$	−15.7566	−0.790800	−0.395400	+	0.918509i	$0.629394\pi$
$398$	−55.5369	−2.78381
$399$	0	0
$400$	−20.6938	−1.03469
$401$	25.4203	1.26943	0.634714	−	0.772747i	$-0.281118\pi$
$401$	25.4203	1.26943	0.634714	+	0.772747i	$0.281118\pi$
$402$	−8.25720	−0.411832
$403$	−3.26783	−0.162782
$404$	−0.829703	−0.0412793
$405$	−0.798478	−0.0396767
$406$	0	0
$407$	4.63746	0.229871
$408$	−32.7959	−1.62364
$409$	−24.4519	−1.20907	−0.604535	−	0.796579i	$-0.706641\pi$
$409$	−24.4519	−1.20907	−0.604535	+	0.796579i	$0.706641\pi$
$410$	−12.2010	−0.602564
$411$	13.4012	0.661032
$412$	−52.6606	−2.59440
$413$	0	0
$414$	20.3416	0.999734
$415$	−11.5078	−0.564895
$416$	−1.47184	−0.0721631
$417$	14.6259	0.716235
$418$	11.0505	0.540498
$419$	−31.1428	−1.52143	−0.760713	−	0.649089i	$-0.775150\pi$
$419$	−31.1428	−1.52143	−0.760713	+	0.649089i	$0.775150\pi$
$420$	0	0
$421$	20.9321	1.02017	0.510085	−	0.860124i	$-0.329614\pi$
$421$	20.9321	1.02017	0.510085	+	0.860124i	$0.329614\pi$
$422$	−50.7215	−2.46909
$423$	3.47901	0.169155
$424$	29.2667	1.42131
$425$	27.2572	1.32217
$426$	−18.8410	−0.912851
$427$	0	0
$428$	−79.5197	−3.84373
$429$	−0.693865	−0.0335001
$430$	−6.51667	−0.314262
$431$	14.3575	0.691578	0.345789	−	0.938312i	$-0.387611\pi$
$431$	14.3575	0.691578	0.345789	+	0.938312i	$0.387611\pi$
$432$	4.74363	0.228228
$433$	−32.2479	−1.54973	−0.774867	−	0.632124i	$-0.782183\pi$
$433$	−32.2479	−1.54973	−0.774867	+	0.632124i	$0.782183\pi$
$434$	0	0
$435$	−1.41502	−0.0678452
$436$	−6.83366	−0.327273
$437$	62.8806	3.00799
$438$	19.0608	0.910759
$439$	−2.38828	−0.113986	−0.0569932	−	0.998375i	$-0.518151\pi$
$439$	−2.38828	−0.113986	−0.0569932	+	0.998375i	$0.518151\pi$
$440$	−2.44750	−0.116680
$441$	0	0
$442$	18.3680	0.873678
$443$	−12.0725	−0.573582	−0.286791	−	0.957993i	$-0.592589\pi$
$443$	−12.0725	−0.573582	−0.286791	+	0.957993i	$0.592589\pi$
$444$	32.7295	1.55328
$445$	−6.96194	−0.330027
$446$	−46.3314	−2.19386
$447$	1.57613	0.0745485
$448$	0	0
$449$	5.01953	0.236886	0.118443	−	0.992961i	$-0.462210\pi$
$449$	5.01953	0.236886	0.118443	+	0.992961i	$0.462210\pi$
$450$	−10.7934	−0.508804
$451$	3.60660	0.169828
$452$	−38.3923	−1.80582
$453$	−20.4528	−0.960959
$454$	3.72466	0.174807
$455$	0	0
$456$	40.1446	1.87994
$457$	−22.1919	−1.03809	−0.519046	−	0.854746i	$-0.673713\pi$
$457$	−22.1919	−1.03809	−0.519046	+	0.854746i	$0.673713\pi$
$458$	29.7354	1.38944
$459$	−6.24817	−0.291640
$460$	−27.0565	−1.26152
$461$	−23.4367	−1.09156	−0.545778	−	0.837930i	$-0.683766\pi$
$461$	−23.4367	−1.09156	−0.545778	+	0.837930i	$0.683766\pi$
$462$	0	0
$463$	12.2578	0.569668	0.284834	−	0.958577i	$-0.408061\pi$
$463$	12.2578	0.569668	0.284834	+	0.958577i	$0.408061\pi$
$464$	8.40643	0.390259
$465$	−2.19604	−0.101839
$466$	36.8605	1.70753
$467$	12.6850	0.586994	0.293497	−	0.955960i	$-0.405181\pi$
$467$	12.6850	0.586994	0.293497	+	0.955960i	$0.405181\pi$
$468$	−4.89705	−0.226366
$469$	0	0
$470$	−6.87300	−0.317028
$471$	3.64011	0.167727
$472$	5.24888	0.241599
$473$	1.92632	0.0885723
$474$	17.7458	0.815090
$475$	−33.3649	−1.53088
$476$	0	0
$477$	5.57579	0.255298
$478$	−0.153417	−0.00701714
$479$	5.63561	0.257498	0.128749	−	0.991677i	$-0.458904\pi$
$479$	5.63561	0.257498	0.128749	+	0.991677i	$0.458904\pi$
$480$	−0.989106	−0.0451463
$481$	−9.43558	−0.430226
$482$	−51.3625	−2.33950
$483$	0	0
$484$	−43.9307	−1.99685
$485$	8.88734	0.403553
$486$	2.47416	0.112230
$487$	0.303849	0.0137687	0.00688435	−	0.999976i	$-0.497809\pi$
$487$	0.303849	0.0137687	0.00688435	+	0.999976i	$0.497809\pi$
$488$	1.70256	0.0770711
$489$	−2.73838	−0.123834
$490$	0	0
$491$	13.5028	0.609372	0.304686	−	0.952453i	$-0.401448\pi$
$491$	13.5028	0.609372	0.304686	+	0.952453i	$0.401448\pi$
$492$	25.4541	1.14756
$493$	−11.0727	−0.498690
$494$	−22.4838	−1.01160
$495$	−0.466290	−0.0209582
$496$	13.0463	0.585797
$497$	0	0
$498$	35.6580	1.59788
$499$	0.143829	0.00643868	0.00321934	−	0.999995i	$-0.498975\pi$
$499$	0.143829	0.00643868	0.00321934	+	0.999995i	$0.498975\pi$
$500$	30.8109	1.37791
$501$	4.46622	0.199536
$502$	−6.69394	−0.298765
$503$	−8.61729	−0.384226	−0.192113	−	0.981373i	$-0.561534\pi$
$503$	−8.61729	−0.384226	−0.192113	+	0.981373i	$0.561534\pi$
$504$	0	0
$505$	0.160743	0.00715298
$506$	11.8789	0.528084
$507$	−11.5882	−0.514651
$508$	49.9636	2.21678
$509$	10.5293	0.466702	0.233351	−	0.972393i	$-0.425031\pi$
$509$	10.5293	0.466702	0.233351	+	0.972393i	$0.425031\pi$
$510$	12.3436	0.546586
$511$	0	0
$512$	−43.9214	−1.94107
$513$	7.64822	0.337677
$514$	25.9593	1.14502
$515$	10.2022	0.449564
$516$	13.5953	0.598499
$517$	2.03165	0.0893519
$518$	0	0
$519$	−16.9536	−0.744179
$520$	4.97979	0.218378
$521$	23.4652	1.02803	0.514014	−	0.857782i	$-0.328158\pi$
$521$	23.4652	1.02803	0.514014	+	0.857782i	$0.328158\pi$
$522$	4.38459	0.191908
$523$	−9.23372	−0.403762	−0.201881	−	0.979410i	$-0.564705\pi$
$523$	−9.23372	−0.403762	−0.201881	+	0.979410i	$0.564705\pi$
$524$	43.9361	1.91936
$525$	0	0
$526$	50.2648	2.19165
$527$	−17.1842	−0.748557
$528$	2.77016	0.120556
$529$	44.5947	1.93890
$530$	−11.0153	−0.478475
$531$	1.00000	0.0433963
$532$	0	0
$533$	−7.33815	−0.317850
$534$	21.5723	0.933523
$535$	15.4058	0.666051
$536$	−17.5175	−0.756639
$537$	16.3749	0.706629
$538$	71.7109	3.09168
$539$	0	0
$540$	−3.29091	−0.141618
$541$	−11.0423	−0.474746	−0.237373	−	0.971419i	$-0.576286\pi$
$541$	−11.0423	−0.474746	−0.237373	+	0.971419i	$0.576286\pi$
$542$	1.13383	0.0487023
$543$	−14.4761	−0.621228
$544$	−7.73986	−0.331844
$545$	1.32392	0.0567107
$546$	0	0
$547$	−9.28633	−0.397055	−0.198527	−	0.980095i	$-0.563616\pi$
$547$	−9.28633	−0.397055	−0.198527	+	0.980095i	$0.563616\pi$
$548$	55.2327	2.35943
$549$	0.324365	0.0138436
$550$	−6.30305	−0.268763
$551$	13.5538	0.577412
$552$	43.1542	1.83676
$553$	0	0
$554$	21.1225	0.897408
$555$	−6.34088	−0.269155
$556$	60.2805	2.55646
$557$	−26.5522	−1.12505	−0.562527	−	0.826779i	$-0.690171\pi$
$557$	−26.5522	−1.12505	−0.562527	+	0.826779i	$0.690171\pi$
$558$	6.80464	0.288064
$559$	−3.91937	−0.165772
$560$	0	0
$561$	−3.64877	−0.154051
$562$	−71.2001	−3.00339
$563$	21.3520	0.899878	0.449939	−	0.893059i	$-0.351446\pi$
$563$	21.3520	0.899878	0.449939	+	0.893059i	$0.351446\pi$
$564$	14.3387	0.603766
$565$	7.43795	0.312917
$566$	−37.8436	−1.59069
$567$	0	0
$568$	−39.9709	−1.67714
$569$	25.2096	1.05684	0.528421	−	0.848982i	$-0.322784\pi$
$569$	25.2096	1.05684	0.528421	+	0.848982i	$0.322784\pi$
$570$	−15.1095	−0.632869
$571$	−37.1302	−1.55385	−0.776926	−	0.629592i	$-0.783222\pi$
$571$	−37.1302	−1.55385	−0.776926	+	0.629592i	$0.783222\pi$
$572$	−2.85975	−0.119572
$573$	−22.1840	−0.926750
$574$	0	0
$575$	−35.8662	−1.49572
$576$	−6.42241	−0.267600
$577$	−33.3585	−1.38873	−0.694367	−	0.719621i	$-0.744316\pi$
$577$	−33.3585	−1.38873	−0.694367	+	0.719621i	$0.744316\pi$
$578$	54.5296	2.26813
$579$	14.5248	0.603630
$580$	−5.83199	−0.242160
$581$	0	0
$582$	−27.5383	−1.14150
$583$	3.25612	0.134855
$584$	40.4370	1.67330
$585$	0.948734	0.0392253
$586$	−42.1426	−1.74089
$587$	29.3481	1.21133	0.605663	−	0.795721i	$-0.292908\pi$
$587$	29.3481	1.21133	0.605663	+	0.795721i	$0.292908\pi$
$588$	0	0
$589$	21.0348	0.866722
$590$	−1.97556	−0.0813326
$591$	−16.6164	−0.683506
$592$	37.6702	1.54823
$593$	−30.9562	−1.27122	−0.635609	−	0.772011i	$-0.719251\pi$
$593$	−30.9562	−1.27122	−0.635609	+	0.772011i	$0.719251\pi$
$594$	1.44485	0.0592828
$595$	0	0
$596$	6.49599	0.266086
$597$	−22.4467	−0.918684
$598$	−24.1694	−0.988361
$599$	−3.24716	−0.132675	−0.0663377	−	0.997797i	$-0.521131\pi$
$599$	−3.24716	−0.132675	−0.0663377	+	0.997797i	$0.521131\pi$
$600$	−22.8979	−0.934803
$601$	36.8920	1.50485	0.752427	−	0.658675i	$-0.228883\pi$
$601$	36.8920	1.50485	0.752427	+	0.658675i	$0.228883\pi$
$602$	0	0
$603$	−3.33737	−0.135908
$604$	−84.2960	−3.42995
$605$	8.51095	0.346019
$606$	−0.498079	−0.0202331
$607$	−32.9523	−1.33749	−0.668747	−	0.743490i	$-0.733169\pi$
$607$	−32.9523	−1.33749	−0.668747	+	0.743490i	$0.733169\pi$
$608$	9.47416	0.384228
$609$	0	0
$610$	−0.640804	−0.0259454
$611$	−4.13368	−0.167231
$612$	−25.7517	−1.04095
$613$	47.7345	1.92798	0.963989	−	0.265943i	$-0.0856833\pi$
$613$	47.7345	1.92798	0.963989	+	0.265943i	$0.0856833\pi$
$614$	46.8974	1.89262
$615$	−4.93137	−0.198852
$616$	0	0
$617$	38.7351	1.55942	0.779709	−	0.626142i	$-0.215367\pi$
$617$	38.7351	1.55942	0.779709	+	0.626142i	$0.215367\pi$
$618$	−31.6126	−1.27165
$619$	−6.03266	−0.242473	−0.121237	−	0.992624i	$-0.538686\pi$
$619$	−6.03266	−0.242473	−0.121237	+	0.992624i	$0.538686\pi$
$620$	−9.05093	−0.363494
$621$	8.22160	0.329921
$622$	−67.8387	−2.72009
$623$	0	0
$624$	−5.63628	−0.225632
$625$	15.8430	0.633720
$626$	59.7408	2.38772
$627$	4.46636	0.178369
$628$	15.0026	0.598670
$629$	−49.6180	−1.97840
$630$	0	0
$631$	−34.6985	−1.38133	−0.690663	−	0.723177i	$-0.742681\pi$
$631$	−34.6985	−1.38133	−0.690663	+	0.723177i	$0.742681\pi$
$632$	37.6472	1.49753
$633$	−20.5005	−0.814821
$634$	0.989695	0.0393058
$635$	−9.67974	−0.384129
$636$	22.9805	0.911236
$637$	0	0
$638$	2.56049	0.101371
$639$	−7.61512	−0.301249
$640$	14.6661	0.579728
$641$	31.4143	1.24079	0.620394	−	0.784290i	$-0.286973\pi$
$641$	31.4143	1.24079	0.620394	+	0.784290i	$0.286973\pi$
$642$	−47.7365	−1.88401
$643$	23.1109	0.911406	0.455703	−	0.890132i	$-0.349388\pi$
$643$	23.1109	0.911406	0.455703	+	0.890132i	$0.349388\pi$
$644$	0	0
$645$	−2.63389	−0.103709
$646$	−118.234	−4.65184
$647$	46.4843	1.82749	0.913743	−	0.406292i	$-0.133178\pi$
$647$	46.4843	1.82749	0.913743	+	0.406292i	$0.133178\pi$
$648$	5.24888	0.206196
$649$	0.583974	0.0229230
$650$	12.8244	0.503016
$651$	0	0
$652$	−11.2862	−0.442001
$653$	−9.72740	−0.380663	−0.190331	−	0.981720i	$-0.560956\pi$
$653$	−9.72740	−0.380663	−0.190331	+	0.981720i	$0.560956\pi$
$654$	−4.10231	−0.160413
$655$	−8.51199	−0.332591
$656$	29.2965	1.14383
$657$	7.70393	0.300559
$658$	0	0
$659$	−15.7187	−0.612314	−0.306157	−	0.951981i	$-0.599043\pi$
$659$	−15.7187	−0.612314	−0.306157	+	0.951981i	$0.599043\pi$
$660$	−1.92180	−0.0748062
$661$	−5.10601	−0.198601	−0.0993004	−	0.995058i	$-0.531660\pi$
$661$	−5.10601	−0.198601	−0.0993004	+	0.995058i	$0.531660\pi$
$662$	−11.4106	−0.443487
$663$	7.42394	0.288322
$664$	75.6478	2.93570
$665$	0	0
$666$	19.6479	0.761339
$667$	14.5699	0.564150
$668$	18.4074	0.712205
$669$	−18.7261	−0.723993
$670$	6.59319	0.254717
$671$	0.189421	0.00731252
$672$	0	0
$673$	−3.02815	−0.116727	−0.0583633	−	0.998295i	$-0.518588\pi$
$673$	−3.02815	−0.116727	−0.0583633	+	0.998295i	$0.518588\pi$
$674$	−28.7846	−1.10874
$675$	−4.36243	−0.167910
$676$	−47.7606	−1.83695
$677$	4.71011	0.181024	0.0905122	−	0.995895i	$-0.471150\pi$
$677$	4.71011	0.181024	0.0905122	+	0.995895i	$0.471150\pi$
$678$	−23.0472	−0.885124
$679$	0	0
$680$	26.1868	1.00422
$681$	1.50542	0.0576880
$682$	3.97374	0.152162
$683$	5.95652	0.227920	0.113960	−	0.993485i	$-0.463646\pi$
$683$	5.95652	0.227920	0.113960	+	0.993485i	$0.463646\pi$
$684$	31.5220	1.20527
$685$	−10.7006	−0.408847
$686$	0	0
$687$	12.0184	0.458529
$688$	15.6475	0.596556
$689$	−6.62503	−0.252394
$690$	−16.2423	−0.618333
$691$	5.23748	0.199243	0.0996215	−	0.995025i	$-0.468237\pi$
$691$	5.23748	0.199243	0.0996215	+	0.995025i	$0.468237\pi$
$692$	−69.8738	−2.65620
$693$	0	0
$694$	−20.1117	−0.763430
$695$	−11.6785	−0.442990
$696$	9.30182	0.352585
$697$	−38.5884	−1.46164
$698$	18.2715	0.691586
$699$	14.8982	0.563500
$700$	0	0
$701$	26.2286	0.990642	0.495321	−	0.868710i	$-0.335051\pi$
$701$	26.2286	0.990642	0.495321	+	0.868710i	$0.335051\pi$
$702$	−2.93975	−0.110954
$703$	60.7362	2.29071
$704$	−3.75052	−0.141353
$705$	−2.77791	−0.104622
$706$	−67.3982	−2.53656
$707$	0	0
$708$	4.12148	0.154895
$709$	−37.8113	−1.42003	−0.710017	−	0.704185i	$-0.751313\pi$
$709$	−37.8113	−1.42003	−0.710017	+	0.704185i	$0.751313\pi$
$710$	15.0441	0.564597
$711$	7.17243	0.268987
$712$	45.7651	1.71512
$713$	22.6117	0.846816
$714$	0	0
$715$	0.554036	0.0207198
$716$	67.4888	2.52218
$717$	−0.0620078	−0.00231572
$718$	−29.5005	−1.10095
$719$	17.5848	0.655802	0.327901	−	0.944712i	$-0.393659\pi$
$719$	17.5848	0.655802	0.327901	+	0.944712i	$0.393659\pi$
$720$	−3.78768	−0.141159
$721$	0	0
$722$	97.7177	3.63668
$723$	−20.7596	−0.772057
$724$	−59.6628	−2.21735
$725$	−7.73090	−0.287118
$726$	−26.3720	−0.978758
$727$	−7.73201	−0.286764	−0.143382	−	0.989667i	$-0.545798\pi$
$727$	−7.73201	−0.286764	−0.143382	+	0.989667i	$0.545798\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−15.2196	−0.563303
$731$	−20.6105	−0.762305
$732$	1.33686	0.0494120
$733$	14.3516	0.530090	0.265045	−	0.964236i	$-0.414613\pi$
$733$	14.3516	0.530090	0.265045	+	0.964236i	$0.414613\pi$
$734$	−49.9359	−1.84317
$735$	0	0
$736$	10.1844	0.375403
$737$	−1.94894	−0.0717901
$738$	15.2803	0.562477
$739$	25.7742	0.948118	0.474059	−	0.880493i	$-0.342788\pi$
$739$	25.7742	0.948118	0.474059	+	0.880493i	$0.342788\pi$
$740$	−26.1338	−0.960698
$741$	−9.08745	−0.333836
$742$	0	0
$743$	−25.2969	−0.928052	−0.464026	−	0.885822i	$-0.653596\pi$
$743$	−25.2969	−0.928052	−0.464026	+	0.885822i	$0.653596\pi$
$744$	14.4359	0.529246
$745$	−1.25851	−0.0461081
$746$	82.5207	3.02130
$747$	14.4122	0.527314
$748$	−15.0383	−0.549855
$749$	0	0
$750$	18.4961	0.675381
$751$	3.92364	0.143176	0.0715878	−	0.997434i	$-0.477193\pi$
$751$	3.92364	0.143176	0.0715878	+	0.997434i	$0.477193\pi$
$752$	16.5031	0.601807
$753$	−2.70554	−0.0985953
$754$	−5.20968	−0.189725
$755$	16.3311	0.594351
$756$	0	0
$757$	6.24755	0.227071	0.113536	−	0.993534i	$-0.463782\pi$
$757$	6.24755	0.227071	0.113536	+	0.993534i	$0.463782\pi$
$758$	11.1916	0.406496
$759$	4.80120	0.174273
$760$	−32.0546	−1.16274
$761$	14.9292	0.541183	0.270592	−	0.962694i	$-0.412781\pi$
$761$	14.9292	0.541183	0.270592	+	0.962694i	$0.412781\pi$
$762$	29.9936	1.08656
$763$	0	0
$764$	−91.4309	−3.30785
$765$	4.98902	0.180378
$766$	−4.45745	−0.161054
$767$	−1.18818	−0.0429026
$768$	−32.5995	−1.17633
$769$	18.9884	0.684739	0.342369	−	0.939565i	$-0.388771\pi$
$769$	18.9884	0.684739	0.342369	+	0.939565i	$0.388771\pi$
$770$	0	0
$771$	10.4922	0.377867
$772$	59.8636	2.15454
$773$	12.2957	0.442245	0.221122	−	0.975246i	$-0.429028\pi$
$773$	12.2957	0.442245	0.221122	+	0.975246i	$0.429028\pi$
$774$	8.16137	0.293354
$775$	−11.9979	−0.430978
$776$	−58.4219	−2.09723
$777$	0	0
$778$	53.1142	1.90424
$779$	47.2351	1.69237
$780$	3.91019	0.140007
$781$	−4.44703	−0.159127
$782$	−127.098	−4.54500
$783$	1.77215	0.0633316
$784$	0	0
$785$	−2.90654	−0.103739
$786$	26.3753	0.940774
$787$	−3.59510	−0.128151	−0.0640757	−	0.997945i	$-0.520410\pi$
$787$	−3.59510	−0.128151	−0.0640757	+	0.997945i	$0.520410\pi$
$788$	−68.4840	−2.43964
$789$	20.3159	0.723264
$790$	−14.1696	−0.504131
$791$	0	0
$792$	3.06521	0.108918
$793$	−0.385404	−0.0136861
$794$	−38.9843	−1.38350
$795$	−4.45214	−0.157901
$796$	−92.5138	−3.27906
$797$	7.31778	0.259209	0.129605	−	0.991566i	$-0.458629\pi$
$797$	7.31778	0.259209	0.129605	+	0.991566i	$0.458629\pi$
$798$	0	0
$799$	−21.7374	−0.769015
$800$	−5.40392	−0.191057
$801$	8.71901	0.308071
$802$	62.8939	2.22086
$803$	4.49889	0.158763
$804$	−13.7549	−0.485098
$805$	0	0
$806$	−8.08513	−0.284787
$807$	28.9839	1.02028
$808$	−1.05666	−0.0371733
$809$	5.63887	0.198252	0.0991260	−	0.995075i	$-0.468395\pi$
$809$	5.63887	0.198252	0.0991260	+	0.995075i	$0.468395\pi$
$810$	−1.97556	−0.0694142
$811$	29.2806	1.02818	0.514090	−	0.857736i	$-0.328130\pi$
$811$	29.2806	1.02818	0.514090	+	0.857736i	$0.328130\pi$
$812$	0	0
$813$	0.458269	0.0160722
$814$	11.4738	0.402158
$815$	2.18654	0.0765910
$816$	−29.6390	−1.03757
$817$	25.2287	0.882642
$818$	−60.4980	−2.11526
$819$	0	0
$820$	−20.3245	−0.709763
$821$	32.5035	1.13438	0.567190	−	0.823587i	$-0.308031\pi$
$821$	32.5035	1.13438	0.567190	+	0.823587i	$0.308031\pi$
$822$	33.1567	1.15647
$823$	−10.4333	−0.363681	−0.181841	−	0.983328i	$-0.558205\pi$
$823$	−10.4333	−0.363681	−0.181841	+	0.983328i	$0.558205\pi$
$824$	−67.0655	−2.33634
$825$	−2.54755	−0.0886942
$826$	0	0
$827$	−23.1890	−0.806360	−0.403180	−	0.915121i	$-0.632095\pi$
$827$	−23.1890	−0.806360	−0.403180	+	0.915121i	$0.632095\pi$
$828$	33.8851	1.17759
$829$	−51.6409	−1.79356	−0.896780	−	0.442476i	$-0.854100\pi$
$829$	−51.6409	−1.79356	−0.896780	+	0.442476i	$0.854100\pi$
$830$	−28.4721	−0.988283
$831$	8.53722	0.296153
$832$	7.63097	0.264556
$833$	0	0
$834$	36.1869	1.25305
$835$	−3.56618	−0.123413
$836$	18.4080	0.636655
$837$	2.75028	0.0950637
$838$	−77.0524	−2.66173
$839$	−4.39459	−0.151718	−0.0758590	−	0.997119i	$-0.524170\pi$
$839$	−4.39459	−0.151718	−0.0758590	+	0.997119i	$0.524170\pi$
$840$	0	0
$841$	−25.8595	−0.891706
$842$	51.7895	1.78478
$843$	−28.7774	−0.991148
$844$	−84.4923	−2.90835
$845$	9.25294	0.318311
$846$	8.60763	0.295936
$847$	0	0
$848$	26.4495	0.908278
$849$	−15.2955	−0.524941
$850$	67.4388	2.31313
$851$	65.2895	2.23809
$852$	−31.3855	−1.07525
$853$	21.8650	0.748642	0.374321	−	0.927299i	$-0.377876\pi$
$853$	21.8650	0.748642	0.374321	+	0.927299i	$0.377876\pi$
$854$	0	0
$855$	−6.10693	−0.208853
$856$	−101.272	−3.46140
$857$	9.20574	0.314462	0.157231	−	0.987562i	$-0.449743\pi$
$857$	9.20574	0.314462	0.157231	+	0.987562i	$0.449743\pi$
$858$	−1.71674	−0.0586084
$859$	−21.9366	−0.748468	−0.374234	−	0.927334i	$-0.622094\pi$
$859$	−21.9366	−0.748468	−0.374234	+	0.927334i	$0.622094\pi$
$860$	−10.8555	−0.370170
$861$	0	0
$862$	35.5228	1.20991
$863$	−40.5513	−1.38038	−0.690191	−	0.723627i	$-0.742474\pi$
$863$	−40.5513	−1.38038	−0.690191	+	0.723627i	$0.742474\pi$
$864$	1.23874	0.0421428
$865$	13.5370	0.460273
$866$	−79.7865	−2.71126
$867$	22.0396	0.748504
$868$	0	0
$869$	4.18851	0.142086
$870$	−3.50100	−0.118695
$871$	3.96539	0.134362
$872$	−8.70296	−0.294719
$873$	−11.1304	−0.376706
$874$	155.577	5.26246
$875$	0	0
$876$	31.7516	1.07279
$877$	−28.4277	−0.959934	−0.479967	−	0.877286i	$-0.659351\pi$
$877$	−28.4277	−0.959934	−0.479967	+	0.877286i	$0.659351\pi$
$878$	−5.90899	−0.199419
$879$	−17.0331	−0.574512
$880$	−2.21191	−0.0745634
$881$	−39.2949	−1.32388	−0.661939	−	0.749558i	$-0.730266\pi$
$881$	−39.2949	−1.32388	−0.661939	+	0.749558i	$0.730266\pi$
$882$	0	0
$883$	48.7146	1.63938	0.819689	−	0.572808i	$-0.194146\pi$
$883$	48.7146	1.63938	0.819689	+	0.572808i	$0.194146\pi$
$884$	30.5976	1.02911
$885$	−0.798478	−0.0268405
$886$	−29.8693	−1.00348
$887$	−44.8995	−1.50758	−0.753789	−	0.657116i	$-0.771776\pi$
$887$	−44.8995	−1.50758	−0.753789	+	0.657116i	$0.771776\pi$
$888$	41.6825	1.39877
$889$	0	0
$890$	−17.2250	−0.577382
$891$	0.583974	0.0195639
$892$	−77.1792	−2.58415
$893$	26.6082	0.890410
$894$	3.89960	0.130422
$895$	−13.0750	−0.437049
$896$	0	0
$897$	−9.76873	−0.326168
$898$	12.4191	0.414432
$899$	4.87392	0.162554
$900$	−17.9797	−0.599323
$901$	−34.8385	−1.16064
$902$	8.92332	0.297114
$903$	0	0
$904$	−48.8942	−1.62620
$905$	11.5588	0.384228
$906$	−50.6037	−1.68119
$907$	−30.3678	−1.00835	−0.504173	−	0.863603i	$-0.668203\pi$
$907$	−30.3678	−1.00835	−0.504173	+	0.863603i	$0.668203\pi$
$908$	6.20457	0.205906
$909$	−0.201312	−0.00667710
$910$	0	0
$911$	12.5587	0.416089	0.208044	−	0.978119i	$-0.433290\pi$
$911$	12.5587	0.416089	0.208044	+	0.978119i	$0.433290\pi$
$912$	36.2803	1.20136
$913$	8.41633	0.278540
$914$	−54.9063	−1.81614
$915$	−0.258998	−0.00856223
$916$	49.5334	1.63663
$917$	0	0
$918$	−15.4590	−0.510222
$919$	0.796126	0.0262618	0.0131309	−	0.999914i	$-0.495820\pi$
$919$	0.796126	0.0262618	0.0131309	+	0.999914i	$0.495820\pi$
$920$	−34.4577	−1.13604
$921$	18.9549	0.624584
$922$	−57.9862	−1.90967
$923$	9.04812	0.297823
$924$	0	0
$925$	−34.6430	−1.13906
$926$	30.3278	0.996633
$927$	−12.7771	−0.419655
$928$	2.19524	0.0720622
$929$	15.6111	0.512184	0.256092	−	0.966652i	$-0.417565\pi$
$929$	15.6111	0.512184	0.256092	+	0.966652i	$0.417565\pi$
$930$	−5.43336	−0.178167
$931$	0	0
$932$	61.4024	2.01130
$933$	−27.4189	−0.897654
$934$	31.3849	1.02694
$935$	2.91346	0.0952803
$936$	−6.23661	−0.203850
$937$	−47.7812	−1.56094	−0.780471	−	0.625191i	$-0.785021\pi$
$937$	−47.7812	−1.56094	−0.780471	+	0.625191i	$0.785021\pi$
$938$	0	0
$939$	24.1459	0.787971
$940$	−11.4491	−0.373428
$941$	−28.2698	−0.921568	−0.460784	−	0.887512i	$-0.652432\pi$
$941$	−28.2698	−0.921568	−0.460784	+	0.887512i	$0.652432\pi$
$942$	9.00621	0.293438
$943$	50.7763	1.65350
$944$	4.74363	0.154392
$945$	0	0
$946$	4.76603	0.154957
$947$	−38.0791	−1.23740	−0.618702	−	0.785626i	$-0.712341\pi$
$947$	−38.0791	−1.23740	−0.618702	+	0.785626i	$0.712341\pi$
$948$	29.5610	0.960097
$949$	−9.15364	−0.297140
$950$	−82.5501	−2.67828
$951$	0.400012	0.0129713
$952$	0	0
$953$	−28.9731	−0.938531	−0.469266	−	0.883057i	$-0.655481\pi$
$953$	−28.9731	−0.938531	−0.469266	+	0.883057i	$0.655481\pi$
$954$	13.7954	0.446643
$955$	17.7134	0.573193
$956$	−0.255564	−0.00826552
$957$	1.03489	0.0334533
$958$	13.9434	0.450491
$959$	0	0
$960$	5.12815	0.165510
$961$	−23.4359	−0.755998
$962$	−23.3452	−0.752678
$963$	−19.2940	−0.621740
$964$	−85.5601	−2.75571
$965$	−11.5977	−0.373344
$966$	0	0
$967$	−11.4871	−0.369401	−0.184701	−	0.982795i	$-0.559132\pi$
$967$	−11.4871	−0.369401	−0.184701	+	0.982795i	$0.559132\pi$
$968$	−55.9477	−1.79823
$969$	−47.7874	−1.53515
$970$	21.9887	0.706015
$971$	−8.75392	−0.280927	−0.140463	−	0.990086i	$-0.544859\pi$
$971$	−8.75392	−0.280927	−0.140463	+	0.990086i	$0.544859\pi$
$972$	4.12148	0.132196
$973$	0	0
$974$	0.751771	0.0240883
$975$	5.18335	0.166000
$976$	1.53867	0.0492516
$977$	−20.3898	−0.652328	−0.326164	−	0.945313i	$-0.605756\pi$
$977$	−20.3898	−0.652328	−0.326164	+	0.945313i	$0.605756\pi$
$978$	−6.77520	−0.216647
$979$	5.09168	0.162731
$980$	0	0
$981$	−1.65806	−0.0529378
$982$	33.4081	1.06609
$983$	0.654404	0.0208723	0.0104361	−	0.999946i	$-0.496678\pi$
$983$	0.654404	0.0208723	0.0104361	+	0.999946i	$0.496678\pi$
$984$	32.4169	1.03341
$985$	13.2678	0.422747
$986$	−27.3957	−0.872456
$987$	0	0
$988$	−37.4537	−1.19156
$989$	27.1201	0.862369
$990$	−1.15368	−0.0366663
$991$	58.6761	1.86391	0.931954	−	0.362577i	$-0.118103\pi$
$991$	58.6761	1.86391	0.931954	+	0.362577i	$0.118103\pi$
$992$	3.40689	0.108169
$993$	−4.61192	−0.146355
$994$	0	0
$995$	17.9232	0.568204
$996$	59.3994	1.88214
$997$	24.4530	0.774433	0.387217	−	0.921989i	$-0.373437\pi$
$997$	24.4530	0.774433	0.387217	+	0.921989i	$0.373437\pi$
$998$	0.355857	0.0112644
$999$	7.94122	0.251249

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8673.2.a.ba.1.10		12
7.6	odd	2		1239.2.a.i.1.10	✓	12
21.20	even	2		3717.2.a.q.1.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1239.2.a.i.1.10	✓	12	7.6	odd	2
3717.2.a.q.1.3		12	21.20	even	2
8673.2.a.ba.1.10		12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 8673 = 3 \cdot 7^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8673.a (trivial)

\(f(q)\)	\(=\)	\(q+2.47416 q^{2} +1.00000 q^{3} +4.12148 q^{4} -0.798478 q^{5} +2.47416 q^{6} +5.24888 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.47416 q^{2} +1.00000 q^{3} +4.12148 q^{4} -0.798478 q^{5} +2.47416 q^{6} +5.24888 q^{8} +1.00000 q^{9} -1.97556 q^{10} +0.583974 q^{11} +4.12148 q^{12} -1.18818 q^{13} -0.798478 q^{15} +4.74363 q^{16} -6.24817 q^{17} +2.47416 q^{18} +7.64822 q^{19} -3.29091 q^{20} +1.44485 q^{22} +8.22160 q^{23} +5.24888 q^{24} -4.36243 q^{25} -2.93975 q^{26} +1.00000 q^{27} +1.77215 q^{29} -1.97556 q^{30} +2.75028 q^{31} +1.23874 q^{32} +0.583974 q^{33} -15.4590 q^{34} +4.12148 q^{36} +7.94122 q^{37} +18.9229 q^{38} -1.18818 q^{39} -4.19111 q^{40} +6.17596 q^{41} +3.29864 q^{43} +2.40684 q^{44} -0.798478 q^{45} +20.3416 q^{46} +3.47901 q^{47} +4.74363 q^{48} -10.7934 q^{50} -6.24817 q^{51} -4.89705 q^{52} +5.57579 q^{53} +2.47416 q^{54} -0.466290 q^{55} +7.64822 q^{57} +4.38459 q^{58} +1.00000 q^{59} -3.29091 q^{60} +0.324365 q^{61} +6.80464 q^{62} -6.42241 q^{64} +0.948734 q^{65} +1.44485 q^{66} -3.33737 q^{67} -25.7517 q^{68} +8.22160 q^{69} -7.61512 q^{71} +5.24888 q^{72} +7.70393 q^{73} +19.6479 q^{74} -4.36243 q^{75} +31.5220 q^{76} -2.93975 q^{78} +7.17243 q^{79} -3.78768 q^{80} +1.00000 q^{81} +15.2803 q^{82} +14.4122 q^{83} +4.98902 q^{85} +8.16137 q^{86} +1.77215 q^{87} +3.06521 q^{88} +8.71901 q^{89} -1.97556 q^{90} +33.8851 q^{92} +2.75028 q^{93} +8.60763 q^{94} -6.10693 q^{95} +1.23874 q^{96} -11.1304 q^{97} +0.583974 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} + 12 q^{3} + 19 q^{4} + 4 q^{5} + 3 q^{6} + 12 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 + 12 * q^3 + 19 * q^4 + 4 * q^5 + 3 * q^6 + 12 * q^8 + 12 * q^9	\( 12 q + 3 q^{2} + 12 q^{3} + 19 q^{4} + 4 q^{5} + 3 q^{6} + 12 q^{8} + 12 q^{9} - 2 q^{10} + 2 q^{11} + 19 q^{12} - 9 q^{13} + 4 q^{15} + 33 q^{16} + 5 q^{17} + 3 q^{18} - 7 q^{19} + 15 q^{20} + 24 q^{22} + q^{23} + 12 q^{24} + 30 q^{25} - 3 q^{26} + 12 q^{27} + 11 q^{29} - 2 q^{30} - 13 q^{31} + 22 q^{32} + 2 q^{33} - 8 q^{34} + 19 q^{36} + 7 q^{37} + 4 q^{38} - 9 q^{39} + 20 q^{40} + 21 q^{43} + 23 q^{44} + 4 q^{45} - 7 q^{46} + 18 q^{47} + 33 q^{48} + 52 q^{50} + 5 q^{51} - 23 q^{52} + 15 q^{53} + 3 q^{54} - 20 q^{55} - 7 q^{57} + 27 q^{58} + 12 q^{59} + 15 q^{60} - 30 q^{61} - q^{62} + 88 q^{64} + q^{65} + 24 q^{66} + 19 q^{67} + 25 q^{68} + q^{69} + 18 q^{71} + 12 q^{72} - 19 q^{73} + 3 q^{74} + 30 q^{75} - 62 q^{76} - 3 q^{78} + 16 q^{79} + 47 q^{80} + 12 q^{81} - 19 q^{82} + 37 q^{83} + 48 q^{85} - 8 q^{86} + 11 q^{87} + 46 q^{88} - 23 q^{89} - 2 q^{90} + 19 q^{92} - 13 q^{93} - 13 q^{94} + 20 q^{95} + 22 q^{96} - 9 q^{97} + 2 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + 12 * q^3 + 19 * q^4 + 4 * q^5 + 3 * q^6 + 12 * q^8 + 12 * q^9 - 2 * q^10 + 2 * q^11 + 19 * q^12 - 9 * q^13 + 4 * q^15 + 33 * q^16 + 5 * q^17 + 3 * q^18 - 7 * q^19 + 15 * q^20 + 24 * q^22 + q^23 + 12 * q^24 + 30 * q^25 - 3 * q^26 + 12 * q^27 + 11 * q^29 - 2 * q^30 - 13 * q^31 + 22 * q^32 + 2 * q^33 - 8 * q^34 + 19 * q^36 + 7 * q^37 + 4 * q^38 - 9 * q^39 + 20 * q^40 + 21 * q^43 + 23 * q^44 + 4 * q^45 - 7 * q^46 + 18 * q^47 + 33 * q^48 + 52 * q^50 + 5 * q^51 - 23 * q^52 + 15 * q^53 + 3 * q^54 - 20 * q^55 - 7 * q^57 + 27 * q^58 + 12 * q^59 + 15 * q^60 - 30 * q^61 - q^62 + 88 * q^64 + q^65 + 24 * q^66 + 19 * q^67 + 25 * q^68 + q^69 + 18 * q^71 + 12 * q^72 - 19 * q^73 + 3 * q^74 + 30 * q^75 - 62 * q^76 - 3 * q^78 + 16 * q^79 + 47 * q^80 + 12 * q^81 - 19 * q^82 + 37 * q^83 + 48 * q^85 - 8 * q^86 + 11 * q^87 + 46 * q^88 - 23 * q^89 - 2 * q^90 + 19 * q^92 - 13 * q^93 - 13 * q^94 + 20 * q^95 + 22 * q^96 - 9 * q^97 + 2 * q^99

Introduction

L-functions

Modular forms

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Database

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