LMFDB - Embedded newform 2541.2.a.bj.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2541,2,Mod(1,2541)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2541, 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("2541.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2541 = 3 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2541.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:	$20.2899871536$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.316.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 2 $ x^3 - x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.81361$ of defining polynomial
Character	$\chi$	$=$	2541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.81361 q^{2} +1.00000 q^{3} +1.28917 q^{4} -2.10278 q^{5} -1.81361 q^{6} +1.00000 q^{7} +1.28917 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.81361 q^{2} +1.00000 q^{3} +1.28917 q^{4} -2.10278 q^{5} -1.81361 q^{6} +1.00000 q^{7} +1.28917 q^{8} +1.00000 q^{9} +3.81361 q^{10} +1.28917 q^{12} +0.186393 q^{13} -1.81361 q^{14} -2.10278 q^{15} -4.91638 q^{16} -2.10278 q^{17} -1.81361 q^{18} +4.52444 q^{19} -2.71083 q^{20} +1.00000 q^{21} -1.94610 q^{23} +1.28917 q^{24} -0.578337 q^{25} -0.338044 q^{26} +1.00000 q^{27} +1.28917 q^{28} +0.186393 q^{29} +3.81361 q^{30} +4.20555 q^{31} +6.33804 q^{32} +3.81361 q^{34} -2.10278 q^{35} +1.28917 q^{36} -1.28917 q^{37} -8.20555 q^{38} +0.186393 q^{39} -2.71083 q^{40} +8.91638 q^{41} -1.81361 q^{42} +10.9653 q^{43} -2.10278 q^{45} +3.52946 q^{46} -9.01916 q^{47} -4.91638 q^{48} +1.00000 q^{49} +1.04888 q^{50} -2.10278 q^{51} +0.240293 q^{52} -6.71083 q^{53} -1.81361 q^{54} +1.28917 q^{56} +4.52444 q^{57} -0.338044 q^{58} -4.44082 q^{59} -2.71083 q^{60} +11.3083 q^{61} -7.62721 q^{62} +1.00000 q^{63} -1.66196 q^{64} -0.391944 q^{65} -5.07306 q^{67} -2.71083 q^{68} -1.94610 q^{69} +3.81361 q^{70} +6.72999 q^{71} +1.28917 q^{72} -11.2005 q^{73} +2.33804 q^{74} -0.578337 q^{75} +5.83276 q^{76} -0.338044 q^{78} -7.45998 q^{79} +10.3380 q^{80} +1.00000 q^{81} -16.1708 q^{82} -12.1758 q^{83} +1.28917 q^{84} +4.42166 q^{85} -19.8867 q^{86} +0.186393 q^{87} +0.946101 q^{89} +3.81361 q^{90} +0.186393 q^{91} -2.50885 q^{92} +4.20555 q^{93} +16.3572 q^{94} -9.51388 q^{95} +6.33804 q^{96} +7.27358 q^{97} -1.81361 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{2} + 3 q^{3} + 3 q^{4} + q^{5} + q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + q^2 + 3 * q^3 + 3 * q^4 + q^5 + q^6 + 3 * q^7 + 3 * q^8 + 3 * q^9	$ 3 q + q^{2} + 3 q^{3} + 3 q^{4} + q^{5} + q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{9} + 5 q^{10} + 3 q^{12} + 7 q^{13} + q^{14} + q^{15} - q^{16} + q^{17} + q^{18} + 8 q^{19} - 9 q^{20} + 3 q^{21} - 2 q^{23} + 3 q^{24} + 11 q^{26} + 3 q^{27} + 3 q^{28} + 7 q^{29} + 5 q^{30} - 2 q^{31} + 7 q^{32} + 5 q^{34} + q^{35} + 3 q^{36} - 3 q^{37} - 10 q^{38} + 7 q^{39} - 9 q^{40} + 13 q^{41} + q^{42} + 8 q^{43} + q^{45} + 20 q^{46} - 6 q^{47} - q^{48} + 3 q^{49} - 8 q^{50} + q^{51} + 11 q^{52} - 21 q^{53} + q^{54} + 3 q^{56} + 8 q^{57} + 11 q^{58} + 6 q^{59} - 9 q^{60} + 12 q^{61} - 10 q^{62} + 3 q^{63} - 17 q^{64} + 7 q^{65} + 2 q^{67} - 9 q^{68} - 2 q^{69} + 5 q^{70} + 3 q^{72} - 4 q^{73} - 5 q^{74} - 10 q^{76} + 11 q^{78} + 18 q^{79} + 19 q^{80} + 3 q^{81} - 9 q^{82} - 12 q^{83} + 3 q^{84} + 15 q^{85} - 36 q^{86} + 7 q^{87} - q^{89} + 5 q^{90} + 7 q^{91} + 44 q^{92} - 2 q^{93} + 16 q^{94} + 8 q^{95} + 7 q^{96} - 25 q^{97} + q^{98}+O(q^{100}) $ 3 * q + q^2 + 3 * q^3 + 3 * q^4 + q^5 + q^6 + 3 * q^7 + 3 * q^8 + 3 * q^9 + 5 * q^10 + 3 * q^12 + 7 * q^13 + q^14 + q^15 - q^16 + q^17 + q^18 + 8 * q^19 - 9 * q^20 + 3 * q^21 - 2 * q^23 + 3 * q^24 + 11 * q^26 + 3 * q^27 + 3 * q^28 + 7 * q^29 + 5 * q^30 - 2 * q^31 + 7 * q^32 + 5 * q^34 + q^35 + 3 * q^36 - 3 * q^37 - 10 * q^38 + 7 * q^39 - 9 * q^40 + 13 * q^41 + q^42 + 8 * q^43 + q^45 + 20 * q^46 - 6 * q^47 - q^48 + 3 * q^49 - 8 * q^50 + q^51 + 11 * q^52 - 21 * q^53 + q^54 + 3 * q^56 + 8 * q^57 + 11 * q^58 + 6 * q^59 - 9 * q^60 + 12 * q^61 - 10 * q^62 + 3 * q^63 - 17 * q^64 + 7 * q^65 + 2 * q^67 - 9 * q^68 - 2 * q^69 + 5 * q^70 + 3 * q^72 - 4 * q^73 - 5 * q^74 - 10 * q^76 + 11 * q^78 + 18 * q^79 + 19 * q^80 + 3 * q^81 - 9 * q^82 - 12 * q^83 + 3 * q^84 + 15 * q^85 - 36 * q^86 + 7 * q^87 - q^89 + 5 * q^90 + 7 * q^91 + 44 * q^92 - 2 * q^93 + 16 * q^94 + 8 * q^95 + 7 * q^96 - 25 * q^97 + q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.81361	−1.28241	−0.641207	−	0.767368i	$-0.721566\pi$
$2$	−1.81361	−1.28241	−0.641207	+	0.767368i	$0.721566\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.28917	0.644584
$5$	−2.10278	−0.940390	−0.470195	−	0.882563i	$-0.655816\pi$
$5$	−2.10278	−0.940390	−0.470195	+	0.882563i	$0.655816\pi$
$6$	−1.81361	−0.740402
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.28917	0.455790
$9$	1.00000	0.333333
$10$	3.81361	1.20597
$11$	0	0
$11$	0	0
$12$	1.28917	0.372151
$13$	0.186393	0.0516963	0.0258481	−	0.999666i	$-0.491771\pi$
$13$	0.186393	0.0516963	0.0258481	+	0.999666i	$0.491771\pi$
$14$	−1.81361	−0.484707
$15$	−2.10278	−0.542934
$16$	−4.91638	−1.22910
$17$	−2.10278	−0.509998	−0.254999	−	0.966941i	$-0.582075\pi$
$17$	−2.10278	−0.509998	−0.254999	+	0.966941i	$0.582075\pi$
$18$	−1.81361	−0.427471
$19$	4.52444	1.03798	0.518989	−	0.854781i	$-0.326309\pi$
$19$	4.52444	1.03798	0.518989	+	0.854781i	$0.326309\pi$
$20$	−2.71083	−0.606160
$21$	1.00000	0.218218
$22$	0	0
$23$	−1.94610	−0.405790	−0.202895	−	0.979200i	$-0.565035\pi$
$23$	−1.94610	−0.405790	−0.202895	+	0.979200i	$0.565035\pi$
$24$	1.28917	0.263150
$25$	−0.578337	−0.115667
$26$	−0.338044	−0.0662960
$27$	1.00000	0.192450
$28$	1.28917	0.243630
$29$	0.186393	0.0346124	0.0173062	−	0.999850i	$-0.494491\pi$
$29$	0.186393	0.0346124	0.0173062	+	0.999850i	$0.494491\pi$
$30$	3.81361	0.696266
$31$	4.20555	0.755339	0.377670	−	0.925940i	$-0.376726\pi$
$31$	4.20555	0.755339	0.377670	+	0.925940i	$0.376726\pi$
$32$	6.33804	1.12042
$33$	0	0
$34$	3.81361	0.654028
$35$	−2.10278	−0.355434
$36$	1.28917	0.214861
$37$	−1.28917	−0.211938	−0.105969	−	0.994369i	$-0.533794\pi$
$37$	−1.28917	−0.211938	−0.105969	+	0.994369i	$0.533794\pi$
$38$	−8.20555	−1.33112
$39$	0.186393	0.0298468
$40$	−2.71083	−0.428620
$41$	8.91638	1.39250	0.696252	−	0.717797i	$-0.254849\pi$
$41$	8.91638	1.39250	0.696252	+	0.717797i	$0.254849\pi$
$42$	−1.81361	−0.279846
$43$	10.9653	1.67219	0.836093	−	0.548588i	$-0.184834\pi$
$43$	10.9653	1.67219	0.836093	+	0.548588i	$0.184834\pi$
$44$	0	0
$45$	−2.10278	−0.313463
$46$	3.52946	0.520391
$47$	−9.01916	−1.31558	−0.657790	−	0.753202i	$-0.728508\pi$
$47$	−9.01916	−1.31558	−0.657790	+	0.753202i	$0.728508\pi$
$48$	−4.91638	−0.709619
$49$	1.00000	0.142857
$50$	1.04888	0.148333
$51$	−2.10278	−0.294447
$52$	0.240293	0.0333226
$53$	−6.71083	−0.921804	−0.460902	−	0.887451i	$-0.652474\pi$
$53$	−6.71083	−0.921804	−0.460902	+	0.887451i	$0.652474\pi$
$54$	−1.81361	−0.246801
$55$	0	0
$56$	1.28917	0.172272
$57$	4.52444	0.599276
$58$	−0.338044	−0.0443874
$59$	−4.44082	−0.578145	−0.289073	−	0.957307i	$-0.593347\pi$
$59$	−4.44082	−0.578145	−0.289073	+	0.957307i	$0.593347\pi$
$60$	−2.71083	−0.349967
$61$	11.3083	1.44788	0.723941	−	0.689862i	$-0.242329\pi$
$61$	11.3083	1.44788	0.723941	+	0.689862i	$0.242329\pi$
$62$	−7.62721	−0.968657
$63$	1.00000	0.125988
$64$	−1.66196	−0.207744
$65$	−0.391944	−0.0486146
$66$	0	0
$67$	−5.07306	−0.619772	−0.309886	−	0.950774i	$-0.600291\pi$
$67$	−5.07306	−0.619772	−0.309886	+	0.950774i	$0.600291\pi$
$68$	−2.71083	−0.328737
$69$	−1.94610	−0.234283
$70$	3.81361	0.455813
$71$	6.72999	0.798703	0.399351	−	0.916798i	$-0.369235\pi$
$71$	6.72999	0.798703	0.399351	+	0.916798i	$0.369235\pi$
$72$	1.28917	0.151930
$73$	−11.2005	−1.31092	−0.655461	−	0.755229i	$-0.727526\pi$
$73$	−11.2005	−1.31092	−0.655461	+	0.755229i	$0.727526\pi$
$74$	2.33804	0.271792
$75$	−0.578337	−0.0667806
$76$	5.83276	0.669064
$77$	0	0
$78$	−0.338044	−0.0382760
$79$	−7.45998	−0.839313	−0.419656	−	0.907683i	$-0.637849\pi$
$79$	−7.45998	−0.839313	−0.419656	+	0.907683i	$0.637849\pi$
$80$	10.3380	1.15583
$81$	1.00000	0.111111
$82$	−16.1708	−1.78577
$83$	−12.1758	−1.33647	−0.668236	−	0.743950i	$-0.732950\pi$
$83$	−12.1758	−1.33647	−0.668236	+	0.743950i	$0.732950\pi$
$84$	1.28917	0.140660
$85$	4.42166	0.479597
$86$	−19.8867	−2.14443
$87$	0.186393	0.0199835
$88$	0	0
$89$	0.946101	0.100286	0.0501432	−	0.998742i	$-0.484032\pi$
$89$	0.946101	0.100286	0.0501432	+	0.998742i	$0.484032\pi$
$90$	3.81361	0.401989
$91$	0.186393	0.0195393
$92$	−2.50885	−0.261566
$93$	4.20555	0.436095
$94$	16.3572	1.68712
$95$	−9.51388	−0.976103
$96$	6.33804	0.646874
$97$	7.27358	0.738520	0.369260	−	0.929326i	$-0.379611\pi$
$97$	7.27358	0.738520	0.369260	+	0.929326i	$0.379611\pi$
$98$	−1.81361	−0.183202
$99$	0	0
$100$	−0.745574	−0.0745574
$101$	−15.3919	−1.53156	−0.765778	−	0.643105i	$-0.777646\pi$
$101$	−15.3919	−1.53156	−0.765778	+	0.643105i	$0.777646\pi$
$102$	3.81361	0.377603
$103$	10.5244	1.03700	0.518502	−	0.855077i	$-0.326490\pi$
$103$	10.5244	1.03700	0.518502	+	0.855077i	$0.326490\pi$
$104$	0.240293	0.0235626
$105$	−2.10278	−0.205210
$106$	12.1708	1.18213
$107$	13.5733	1.31218	0.656091	−	0.754682i	$-0.272209\pi$
$107$	13.5733	1.31218	0.656091	+	0.754682i	$0.272209\pi$
$108$	1.28917	0.124050
$109$	17.6167	1.68737	0.843685	−	0.536839i	$-0.180382\pi$
$109$	17.6167	1.68737	0.843685	+	0.536839i	$0.180382\pi$
$110$	0	0
$111$	−1.28917	−0.122362
$112$	−4.91638	−0.464554
$113$	10.5436	0.991858	0.495929	−	0.868363i	$-0.334828\pi$
$113$	10.5436	0.991858	0.495929	+	0.868363i	$0.334828\pi$
$114$	−8.20555	−0.768520
$115$	4.09221	0.381601
$116$	0.240293	0.0223106
$117$	0.186393	0.0172321
$118$	8.05390	0.741422
$119$	−2.10278	−0.192761
$120$	−2.71083	−0.247464
$121$	0	0
$122$	−20.5089	−1.85678
$123$	8.91638	0.803963
$124$	5.42166	0.486880
$125$	11.7300	1.04916
$126$	−1.81361	−0.161569
$127$	21.2091	1.88201	0.941003	−	0.338399i	$-0.109885\pi$
$127$	21.2091	1.88201	0.941003	+	0.338399i	$0.109885\pi$
$128$	−9.66196	−0.854004
$129$	10.9653	0.965437
$130$	0.710831	0.0623440
$131$	5.55918	0.485708	0.242854	−	0.970063i	$-0.421916\pi$
$131$	5.55918	0.485708	0.242854	+	0.970063i	$0.421916\pi$
$132$	0	0
$133$	4.52444	0.392319
$134$	9.20053	0.794804
$135$	−2.10278	−0.180978
$136$	−2.71083	−0.232452
$137$	22.4550	1.91846	0.959228	−	0.282633i	$-0.0912079\pi$
$137$	22.4550	1.91846	0.959228	+	0.282633i	$0.0912079\pi$
$138$	3.52946	0.300448
$139$	3.27001	0.277359	0.138679	−	0.990337i	$-0.455714\pi$
$139$	3.27001	0.277359	0.138679	+	0.990337i	$0.455714\pi$
$140$	−2.71083	−0.229107
$141$	−9.01916	−0.759550
$142$	−12.2056	−1.02427
$143$	0	0
$144$	−4.91638	−0.409698
$145$	−0.391944	−0.0325491
$146$	20.3133	1.68114
$147$	1.00000	0.0824786
$148$	−1.66196	−0.136612
$149$	−2.65693	−0.217664	−0.108832	−	0.994060i	$-0.534711\pi$
$149$	−2.65693	−0.217664	−0.108832	+	0.994060i	$0.534711\pi$
$150$	1.04888	0.0856404
$151$	−16.5330	−1.34544	−0.672720	−	0.739898i	$-0.734874\pi$
$151$	−16.5330	−1.34544	−0.672720	+	0.739898i	$0.734874\pi$
$152$	5.83276	0.473100
$153$	−2.10278	−0.169999
$154$	0	0
$155$	−8.84333	−0.710313
$156$	0.240293	0.0192388
$157$	17.1950	1.37231	0.686155	−	0.727456i	$-0.259297\pi$
$157$	17.1950	1.37231	0.686155	+	0.727456i	$0.259297\pi$
$158$	13.5295	1.07635
$159$	−6.71083	−0.532204
$160$	−13.3275	−1.05363
$161$	−1.94610	−0.153374
$162$	−1.81361	−0.142490
$163$	−4.20555	−0.329404	−0.164702	−	0.986343i	$-0.552666\pi$
$163$	−4.20555	−0.329404	−0.164702	+	0.986343i	$0.552666\pi$
$164$	11.4947	0.897587
$165$	0	0
$166$	22.0822	1.71391
$167$	0.646370	0.0500176	0.0250088	−	0.999687i	$-0.492039\pi$
$167$	0.646370	0.0500176	0.0250088	+	0.999687i	$0.492039\pi$
$168$	1.28917	0.0994615
$169$	−12.9653	−0.997327
$170$	−8.01916	−0.615041
$171$	4.52444	0.345992
$172$	14.1361	1.07786
$173$	−1.35363	−0.102915	−0.0514573	−	0.998675i	$-0.516387\pi$
$173$	−1.35363	−0.102915	−0.0514573	+	0.998675i	$0.516387\pi$
$174$	−0.338044	−0.0256271
$175$	−0.578337	−0.0437182
$176$	0	0
$177$	−4.44082	−0.333792
$178$	−1.71585	−0.128609
$179$	−13.9406	−1.04197	−0.520983	−	0.853567i	$-0.674435\pi$
$179$	−13.9406	−1.04197	−0.520983	+	0.853567i	$0.674435\pi$
$180$	−2.71083	−0.202053
$181$	1.39697	0.103836	0.0519179	−	0.998651i	$-0.483467\pi$
$181$	1.39697	0.103836	0.0519179	+	0.998651i	$0.483467\pi$
$182$	−0.338044	−0.0250575
$183$	11.3083	0.835935
$184$	−2.50885	−0.184955
$185$	2.71083	0.199304
$186$	−7.62721	−0.559254
$187$	0	0
$188$	−11.6272	−0.848002
$189$	1.00000	0.0727393
$190$	17.2544	1.25177
$191$	13.4061	0.970030	0.485015	−	0.874506i	$-0.338814\pi$
$191$	13.4061	0.970030	0.485015	+	0.874506i	$0.338814\pi$
$192$	−1.66196	−0.119941
$193$	15.0978	1.08676	0.543380	−	0.839487i	$-0.317144\pi$
$193$	15.0978	1.08676	0.543380	+	0.839487i	$0.317144\pi$
$194$	−13.1914	−0.947089
$195$	−0.391944	−0.0280677
$196$	1.28917	0.0920835
$197$	−3.96526	−0.282513	−0.141256	−	0.989973i	$-0.545114\pi$
$197$	−3.96526	−0.282513	−0.141256	+	0.989973i	$0.545114\pi$
$198$	0	0
$199$	22.5628	1.59943	0.799716	−	0.600379i	$-0.204984\pi$
$199$	22.5628	1.59943	0.799716	+	0.600379i	$0.204984\pi$
$200$	−0.745574	−0.0527200
$201$	−5.07306	−0.357826
$202$	27.9149	1.96409
$203$	0.186393	0.0130823
$204$	−2.71083	−0.189796
$205$	−18.7491	−1.30950
$206$	−19.0872	−1.32987
$207$	−1.94610	−0.135263
$208$	−0.916382	−0.0635396
$209$	0	0
$210$	3.81361	0.263164
$211$	6.18137	0.425543	0.212772	−	0.977102i	$-0.431751\pi$
$211$	6.18137	0.425543	0.212772	+	0.977102i	$0.431751\pi$
$212$	−8.65139	−0.594180
$213$	6.72999	0.461131
$214$	−24.6167	−1.68276
$215$	−23.0575	−1.57251
$216$	1.28917	0.0877168
$217$	4.20555	0.285491
$218$	−31.9497	−2.16390
$219$	−11.2005	−0.756861
$220$	0	0
$221$	−0.391944	−0.0263650
$222$	2.33804	0.156919
$223$	−11.2544	−0.753652	−0.376826	−	0.926284i	$-0.622985\pi$
$223$	−11.2544	−0.753652	−0.376826	+	0.926284i	$0.622985\pi$
$224$	6.33804	0.423478
$225$	−0.578337	−0.0385558
$226$	−19.1219	−1.27197
$227$	21.2630	1.41128	0.705638	−	0.708572i	$-0.250660\pi$
$227$	21.2630	1.41128	0.705638	+	0.708572i	$0.250660\pi$
$228$	5.83276	0.386284
$229$	−6.07306	−0.401319	−0.200659	−	0.979661i	$-0.564308\pi$
$229$	−6.07306	−0.401319	−0.200659	+	0.979661i	$0.564308\pi$
$230$	−7.42166	−0.489370
$231$	0	0
$232$	0.240293	0.0157760
$233$	1.60806	0.105347	0.0526736	−	0.998612i	$-0.483226\pi$
$233$	1.60806	0.105347	0.0526736	+	0.998612i	$0.483226\pi$
$234$	−0.338044	−0.0220987
$235$	18.9653	1.23716
$236$	−5.72496	−0.372663
$237$	−7.45998	−0.484578
$238$	3.81361	0.247199
$239$	0.578337	0.0374095	0.0187048	−	0.999825i	$-0.494046\pi$
$239$	0.578337	0.0374095	0.0187048	+	0.999825i	$0.494046\pi$
$240$	10.3380	0.667318
$241$	20.5244	1.32210	0.661048	−	0.750344i	$-0.270112\pi$
$241$	20.5244	1.32210	0.661048	+	0.750344i	$0.270112\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	14.5783	0.933282
$245$	−2.10278	−0.134341
$246$	−16.1708	−1.03101
$247$	0.843326	0.0536595
$248$	5.42166	0.344276
$249$	−12.1758	−0.771612
$250$	−21.2736	−1.34546
$251$	12.8222	0.809330	0.404665	−	0.914465i	$-0.367388\pi$
$251$	12.8222	0.809330	0.404665	+	0.914465i	$0.367388\pi$
$252$	1.28917	0.0812100
$253$	0	0
$254$	−38.4650	−2.41351
$255$	4.42166	0.276895
$256$	20.8469	1.30293
$257$	24.4444	1.52480	0.762400	−	0.647107i	$-0.224021\pi$
$257$	24.4444	1.52480	0.762400	+	0.647107i	$0.224021\pi$
$258$	−19.8867	−1.23809
$259$	−1.28917	−0.0801050
$260$	−0.505281	−0.0313362
$261$	0.186393	0.0115375
$262$	−10.0822	−0.622878
$263$	−22.7683	−1.40395	−0.701977	−	0.712200i	$-0.747699\pi$
$263$	−22.7683	−1.40395	−0.701977	+	0.712200i	$0.747699\pi$
$264$	0	0
$265$	14.1114	0.866855
$266$	−8.20555	−0.503115
$267$	0.946101	0.0579004
$268$	−6.54002	−0.399496
$269$	19.5925	1.19457	0.597287	−	0.802028i	$-0.296245\pi$
$269$	19.5925	1.19457	0.597287	+	0.802028i	$0.296245\pi$
$270$	3.81361	0.232089
$271$	10.9511	0.665233	0.332617	−	0.943062i	$-0.392068\pi$
$271$	10.9511	0.665233	0.332617	+	0.943062i	$0.392068\pi$
$272$	10.3380	0.626836
$273$	0.186393	0.0112810
$274$	−40.7244	−2.46025
$275$	0	0
$276$	−2.50885	−0.151015
$277$	9.89169	0.594334	0.297167	−	0.954826i	$-0.403958\pi$
$277$	9.89169	0.594334	0.297167	+	0.954826i	$0.403958\pi$
$278$	−5.93051	−0.355689
$279$	4.20555	0.251780
$280$	−2.71083	−0.162003
$281$	31.5960	1.88486	0.942431	−	0.334401i	$-0.108534\pi$
$281$	31.5960	1.88486	0.942431	+	0.334401i	$0.108534\pi$
$282$	16.3572	0.974057
$283$	5.52946	0.328692	0.164346	−	0.986403i	$-0.447449\pi$
$283$	5.52946	0.328692	0.164346	+	0.986403i	$0.447449\pi$
$284$	8.67609	0.514831
$285$	−9.51388	−0.563553
$286$	0	0
$287$	8.91638	0.526317
$288$	6.33804	0.373473
$289$	−12.5783	−0.739902
$290$	0.710831	0.0417415
$291$	7.27358	0.426385
$292$	−14.4394	−0.845000
$293$	8.94610	0.522637	0.261318	−	0.965253i	$-0.415843\pi$
$293$	8.94610	0.522637	0.261318	+	0.965253i	$0.415843\pi$
$294$	−1.81361	−0.105772
$295$	9.33804	0.543682
$296$	−1.66196	−0.0965992
$297$	0	0
$298$	4.81863	0.279136
$299$	−0.362741	−0.0209778
$300$	−0.745574	−0.0430457
$301$	10.9653	0.632027
$302$	29.9844	1.72541
$303$	−15.3919	−0.884244
$304$	−22.2439	−1.27577
$305$	−23.7789	−1.36157
$306$	3.81361	0.218009
$307$	−10.2494	−0.584964	−0.292482	−	0.956271i	$-0.594481\pi$
$307$	−10.2494	−0.584964	−0.292482	+	0.956271i	$0.594481\pi$
$308$	0	0
$309$	10.5244	0.598714
$310$	16.0383	0.910915
$311$	−5.82417	−0.330258	−0.165129	−	0.986272i	$-0.552804\pi$
$311$	−5.82417	−0.330258	−0.165129	+	0.986272i	$0.552804\pi$
$312$	0.240293	0.0136039
$313$	−18.8569	−1.06586	−0.532929	−	0.846160i	$-0.678909\pi$
$313$	−18.8569	−1.06586	−0.532929	+	0.846160i	$0.678909\pi$
$314$	−31.1849	−1.75987
$315$	−2.10278	−0.118478
$316$	−9.61717	−0.541008
$317$	−33.9844	−1.90875	−0.954377	−	0.298603i	$-0.903479\pi$
$317$	−33.9844	−1.90875	−0.954377	+	0.298603i	$0.903479\pi$
$318$	12.1708	0.682505
$319$	0	0
$320$	3.49472	0.195361
$321$	13.5733	0.757589
$322$	3.52946	0.196689
$323$	−9.51388	−0.529366
$324$	1.28917	0.0716205
$325$	−0.107798	−0.00597957
$326$	7.62721	0.422432
$327$	17.6167	0.974203
$328$	11.4947	0.634690
$329$	−9.01916	−0.497242
$330$	0	0
$331$	17.4741	0.960464	0.480232	−	0.877142i	$-0.340552\pi$
$331$	17.4741	0.960464	0.480232	+	0.877142i	$0.340552\pi$
$332$	−15.6967	−0.861468
$333$	−1.28917	−0.0706460
$334$	−1.17226	−0.0641432
$335$	10.6675	0.582828
$336$	−4.91638	−0.268211
$337$	19.0141	1.03577	0.517883	−	0.855452i	$-0.326720\pi$
$337$	19.0141	1.03577	0.517883	+	0.855452i	$0.326720\pi$
$338$	23.5139	1.27899
$339$	10.5436	0.572649
$340$	5.70027	0.309140
$341$	0	0
$342$	−8.20555	−0.443705
$343$	1.00000	0.0539949
$344$	14.1361	0.762166
$345$	4.09221	0.220317
$346$	2.45495	0.131979
$347$	19.8272	1.06438	0.532191	−	0.846625i	$-0.321369\pi$
$347$	19.8272	1.06438	0.532191	+	0.846625i	$0.321369\pi$
$348$	0.240293	0.0128810
$349$	10.9547	0.586391	0.293196	−	0.956052i	$-0.405281\pi$
$349$	10.9547	0.586391	0.293196	+	0.956052i	$0.405281\pi$
$350$	1.04888	0.0560648
$351$	0.186393	0.00994895
$352$	0	0
$353$	22.9164	1.21972	0.609858	−	0.792511i	$-0.291226\pi$
$353$	22.9164	1.21972	0.609858	+	0.792511i	$0.291226\pi$
$354$	8.05390	0.428060
$355$	−14.1517	−0.751092
$356$	1.21968	0.0646431
$357$	−2.10278	−0.111291
$358$	25.2827	1.33623
$359$	13.4161	0.708076	0.354038	−	0.935231i	$-0.384808\pi$
$359$	13.4161	0.708076	0.354038	+	0.935231i	$0.384808\pi$
$360$	−2.71083	−0.142873
$361$	1.47054	0.0773968
$362$	−2.53355	−0.133160
$363$	0	0
$364$	0.240293	0.0125948
$365$	23.5522	1.23278
$366$	−20.5089	−1.07201
$367$	−33.6499	−1.75651	−0.878256	−	0.478190i	$-0.841293\pi$
$367$	−33.6499	−1.75651	−0.878256	+	0.478190i	$0.841293\pi$
$368$	9.56777	0.498755
$369$	8.91638	0.464168
$370$	−4.91638	−0.255591
$371$	−6.71083	−0.348409
$372$	5.42166	0.281100
$373$	−14.4947	−0.750508	−0.375254	−	0.926922i	$-0.622445\pi$
$373$	−14.4947	−0.750508	−0.375254	+	0.926922i	$0.622445\pi$
$374$	0	0
$375$	11.7300	0.605734
$376$	−11.6272	−0.599628
$377$	0.0347425	0.00178933
$378$	−1.81361	−0.0932819
$379$	28.0524	1.44096	0.720479	−	0.693477i	$-0.243922\pi$
$379$	28.0524	1.44096	0.720479	+	0.693477i	$0.243922\pi$
$380$	−12.2650	−0.629181
$381$	21.2091	1.08658
$382$	−24.3133	−1.24398
$383$	11.7053	0.598112	0.299056	−	0.954235i	$-0.403328\pi$
$383$	11.7053	0.598112	0.299056	+	0.954235i	$0.403328\pi$
$384$	−9.66196	−0.493060
$385$	0	0
$386$	−27.3814	−1.39368
$387$	10.9653	0.557395
$388$	9.37687	0.476039
$389$	−23.1219	−1.17233	−0.586164	−	0.810192i	$-0.699363\pi$
$389$	−23.1219	−1.17233	−0.586164	+	0.810192i	$0.699363\pi$
$390$	0.710831	0.0359943
$391$	4.09221	0.206952
$392$	1.28917	0.0651128
$393$	5.55918	0.280424
$394$	7.19142	0.362298
$395$	15.6867	0.789281
$396$	0	0
$397$	17.8675	0.896744	0.448372	−	0.893847i	$-0.352004\pi$
$397$	17.8675	0.896744	0.448372	+	0.893847i	$0.352004\pi$
$398$	−40.9200	−2.05113
$399$	4.52444	0.226505
$400$	2.84333	0.142166
$401$	13.6620	0.682246	0.341123	−	0.940019i	$-0.389193\pi$
$401$	13.6620	0.682246	0.341123	+	0.940019i	$0.389193\pi$
$402$	9.20053	0.458881
$403$	0.783887	0.0390482
$404$	−19.8428	−0.987217
$405$	−2.10278	−0.104488
$406$	−0.338044	−0.0167769
$407$	0	0
$408$	−2.71083	−0.134206
$409$	12.8030	0.633070	0.316535	−	0.948581i	$-0.397481\pi$
$409$	12.8030	0.633070	0.316535	+	0.948581i	$0.397481\pi$
$410$	34.0036	1.67932
$411$	22.4550	1.10762
$412$	13.5678	0.668436
$413$	−4.44082	−0.218518
$414$	3.52946	0.173464
$415$	25.6030	1.25680
$416$	1.18137	0.0579214
$417$	3.27001	0.160133
$418$	0	0
$419$	6.91136	0.337642	0.168821	−	0.985647i	$-0.446004\pi$
$419$	6.91136	0.337642	0.168821	+	0.985647i	$0.446004\pi$
$420$	−2.71083	−0.132275
$421$	5.41110	0.263721	0.131860	−	0.991268i	$-0.457905\pi$
$421$	5.41110	0.263721	0.131860	+	0.991268i	$0.457905\pi$
$422$	−11.2106	−0.545722
$423$	−9.01916	−0.438526
$424$	−8.65139	−0.420149
$425$	1.21611	0.0589901
$426$	−12.2056	−0.591361
$427$	11.3083	0.547248
$428$	17.4983	0.845812
$429$	0	0
$430$	41.8172	2.01660
$431$	−18.4705	−0.889695	−0.444847	−	0.895606i	$-0.646742\pi$
$431$	−18.4705	−0.889695	−0.444847	+	0.895606i	$0.646742\pi$
$432$	−4.91638	−0.236540
$433$	−13.3330	−0.640744	−0.320372	−	0.947292i	$-0.603808\pi$
$433$	−13.3330	−0.640744	−0.320372	+	0.947292i	$0.603808\pi$
$434$	−7.62721	−0.366118
$435$	−0.391944	−0.0187923
$436$	22.7108	1.08765
$437$	−8.80501	−0.421201
$438$	20.3133	0.970609
$439$	9.51941	0.454337	0.227168	−	0.973855i	$-0.427053\pi$
$439$	9.51941	0.454337	0.227168	+	0.973855i	$0.427053\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	0.710831	0.0338108
$443$	−37.2005	−1.76745	−0.883725	−	0.468006i	$-0.844972\pi$
$443$	−37.2005	−1.76745	−0.883725	+	0.468006i	$0.844972\pi$
$444$	−1.66196	−0.0788729
$445$	−1.98944	−0.0943084
$446$	20.4111	0.966494
$447$	−2.65693	−0.125669
$448$	−1.66196	−0.0785200
$449$	15.7003	0.740941	0.370471	−	0.928844i	$-0.379196\pi$
$449$	15.7003	0.740941	0.370471	+	0.928844i	$0.379196\pi$
$450$	1.04888	0.0494445
$451$	0	0
$452$	13.5925	0.639336
$453$	−16.5330	−0.776790
$454$	−38.5628	−1.80984
$455$	−0.391944	−0.0183746
$456$	5.83276	0.273144
$457$	−31.7738	−1.48632	−0.743159	−	0.669115i	$-0.766673\pi$
$457$	−31.7738	−1.48632	−0.743159	+	0.669115i	$0.766673\pi$
$458$	11.0141	0.514657
$459$	−2.10278	−0.0981491
$460$	5.27555	0.245974
$461$	−9.04385	−0.421214	−0.210607	−	0.977571i	$-0.567544\pi$
$461$	−9.04385	−0.421214	−0.210607	+	0.977571i	$0.567544\pi$
$462$	0	0
$463$	−38.3799	−1.78367	−0.891833	−	0.452364i	$-0.850581\pi$
$463$	−38.3799	−1.78367	−0.891833	+	0.452364i	$0.850581\pi$
$464$	−0.916382	−0.0425419
$465$	−8.84333	−0.410099
$466$	−2.91638	−0.135099
$467$	31.1950	1.44353	0.721766	−	0.692137i	$-0.243331\pi$
$467$	31.1950	1.44353	0.721766	+	0.692137i	$0.243331\pi$
$468$	0.240293	0.0111075
$469$	−5.07306	−0.234252
$470$	−34.3955	−1.58655
$471$	17.1950	0.792303
$472$	−5.72496	−0.263513
$473$	0	0
$474$	13.5295	0.621429
$475$	−2.61665	−0.120060
$476$	−2.71083	−0.124251
$477$	−6.71083	−0.307268
$478$	−1.04888	−0.0479745
$479$	31.9391	1.45934	0.729668	−	0.683802i	$-0.239675\pi$
$479$	31.9391	1.45934	0.729668	+	0.683802i	$0.239675\pi$
$480$	−13.3275	−0.608314
$481$	−0.240293	−0.0109564
$482$	−37.2233	−1.69547
$483$	−1.94610	−0.0885507
$484$	0	0
$485$	−15.2947	−0.694497
$486$	−1.81361	−0.0822669
$487$	−26.3869	−1.19571	−0.597853	−	0.801606i	$-0.703979\pi$
$487$	−26.3869	−1.19571	−0.597853	+	0.801606i	$0.703979\pi$
$488$	14.5783	0.659930
$489$	−4.20555	−0.190182
$490$	3.81361	0.172281
$491$	−14.3572	−0.647931	−0.323966	−	0.946069i	$-0.605016\pi$
$491$	−14.3572	−0.647931	−0.323966	+	0.946069i	$0.605016\pi$
$492$	11.4947	0.518222
$493$	−0.391944	−0.0176523
$494$	−1.52946	−0.0688137
$495$	0	0
$496$	−20.6761	−0.928384
$497$	6.72999	0.301881
$498$	22.0822	0.989526
$499$	−30.3174	−1.35719	−0.678597	−	0.734510i	$-0.737412\pi$
$499$	−30.3174	−1.35719	−0.678597	+	0.734510i	$0.737412\pi$
$500$	15.1219	0.676273
$501$	0.646370	0.0288777
$502$	−23.2544	−1.03790
$503$	−12.0086	−0.535437	−0.267718	−	0.963497i	$-0.586270\pi$
$503$	−12.0086	−0.535437	−0.267718	+	0.963497i	$0.586270\pi$
$504$	1.28917	0.0574241
$505$	32.3658	1.44026
$506$	0	0
$507$	−12.9653	−0.575807
$508$	27.3421	1.21311
$509$	−9.54913	−0.423258	−0.211629	−	0.977350i	$-0.567877\pi$
$509$	−9.54913	−0.423258	−0.211629	+	0.977350i	$0.567877\pi$
$510$	−8.01916	−0.355094
$511$	−11.2005	−0.495482
$512$	−18.4842	−0.816892
$513$	4.52444	0.199759
$514$	−44.3325	−1.95542
$515$	−22.1305	−0.975187
$516$	14.1361	0.622306
$517$	0	0
$518$	2.33804	0.102728
$519$	−1.35363	−0.0594178
$520$	−0.505281	−0.0221581
$521$	−26.7542	−1.17212	−0.586061	−	0.810267i	$-0.699322\pi$
$521$	−26.7542	−1.17212	−0.586061	+	0.810267i	$0.699322\pi$
$522$	−0.338044	−0.0147958
$523$	−24.9739	−1.09203	−0.546015	−	0.837775i	$-0.683856\pi$
$523$	−24.9739	−1.09203	−0.546015	+	0.837775i	$0.683856\pi$
$524$	7.16672	0.313080
$525$	−0.578337	−0.0252407
$526$	41.2927	1.80045
$527$	−8.84333	−0.385221
$528$	0	0
$529$	−19.2127	−0.835334
$530$	−25.5925	−1.11167
$531$	−4.44082	−0.192715
$532$	5.83276	0.252882
$533$	1.66196	0.0719873
$534$	−1.71585	−0.0742523
$535$	−28.5416	−1.23396
$536$	−6.54002	−0.282486
$537$	−13.9406	−0.601580
$538$	−35.5330	−1.53194
$539$	0	0
$540$	−2.71083	−0.116656
$541$	9.03474	0.388434	0.194217	−	0.980959i	$-0.437783\pi$
$541$	9.03474	0.388434	0.194217	+	0.980959i	$0.437783\pi$
$542$	−19.8610	−0.853104
$543$	1.39697	0.0599496
$544$	−13.3275	−0.571411
$545$	−37.0439	−1.58678
$546$	−0.338044	−0.0144670
$547$	11.3522	0.485384	0.242692	−	0.970103i	$-0.421970\pi$
$547$	11.3522	0.485384	0.242692	+	0.970103i	$0.421970\pi$
$548$	28.9482	1.23661
$549$	11.3083	0.482628
$550$	0	0
$551$	0.843326	0.0359269
$552$	−2.50885	−0.106784
$553$	−7.45998	−0.317230
$554$	−17.9396	−0.762182
$555$	2.71083	0.115068
$556$	4.21560	0.178781
$557$	−16.5089	−0.699503	−0.349751	−	0.936843i	$-0.613734\pi$
$557$	−16.5089	−0.699503	−0.349751	+	0.936843i	$0.613734\pi$
$558$	−7.62721	−0.322886
$559$	2.04385	0.0864458
$560$	10.3380	0.436862
$561$	0	0
$562$	−57.3028	−2.41717
$563$	−2.51030	−0.105797	−0.0528984	−	0.998600i	$-0.516846\pi$
$563$	−2.51030	−0.105797	−0.0528984	+	0.998600i	$0.516846\pi$
$564$	−11.6272	−0.489594
$565$	−22.1708	−0.932733
$566$	−10.0283	−0.421519
$567$	1.00000	0.0419961
$568$	8.67609	0.364041
$569$	5.92498	0.248388	0.124194	−	0.992258i	$-0.460366\pi$
$569$	5.92498	0.248388	0.124194	+	0.992258i	$0.460366\pi$
$570$	17.2544	0.722708
$571$	25.7633	1.07816	0.539080	−	0.842255i	$-0.318772\pi$
$571$	25.7633	1.07816	0.539080	+	0.842255i	$0.318772\pi$
$572$	0	0
$573$	13.4061	0.560047
$574$	−16.1708	−0.674956
$575$	1.12550	0.0469367
$576$	−1.66196	−0.0692481
$577$	22.4997	0.936677	0.468338	−	0.883549i	$-0.344853\pi$
$577$	22.4997	0.936677	0.468338	+	0.883549i	$0.344853\pi$
$578$	22.8122	0.948861
$579$	15.0978	0.627441
$580$	−0.505281	−0.0209807
$581$	−12.1758	−0.505139
$582$	−13.1914	−0.546802
$583$	0	0
$584$	−14.4394	−0.597505
$585$	−0.391944	−0.0162049
$586$	−16.2247	−0.670236
$587$	−16.2736	−0.671683	−0.335841	−	0.941919i	$-0.609021\pi$
$587$	−16.2736	−0.671683	−0.335841	+	0.941919i	$0.609021\pi$
$588$	1.28917	0.0531644
$589$	19.0278	0.784025
$590$	−16.9355	−0.697225
$591$	−3.96526	−0.163109
$592$	6.33804	0.260492
$593$	36.1794	1.48571	0.742855	−	0.669452i	$-0.233471\pi$
$593$	36.1794	1.48571	0.742855	+	0.669452i	$0.233471\pi$
$594$	0	0
$595$	4.42166	0.181271
$596$	−3.42523	−0.140303
$597$	22.5628	0.923432
$598$	0.657869	0.0269022
$599$	1.69670	0.0693252	0.0346626	−	0.999399i	$-0.488964\pi$
$599$	1.69670	0.0693252	0.0346626	+	0.999399i	$0.488964\pi$
$600$	−0.745574	−0.0304379
$601$	−2.61862	−0.106816	−0.0534079	−	0.998573i	$-0.517008\pi$
$601$	−2.61862	−0.106816	−0.0534079	+	0.998573i	$0.517008\pi$
$602$	−19.8867	−0.810520
$603$	−5.07306	−0.206591
$604$	−21.3139	−0.867249
$605$	0	0
$606$	27.9149	1.13397
$607$	−37.0333	−1.50313	−0.751567	−	0.659656i	$-0.770702\pi$
$607$	−37.0333	−1.50313	−0.751567	+	0.659656i	$0.770702\pi$
$608$	28.6761	1.16297
$609$	0.186393	0.00755305
$610$	43.1255	1.74610
$611$	−1.68111	−0.0680105
$612$	−2.71083	−0.109579
$613$	18.7733	0.758247	0.379124	−	0.925346i	$-0.376225\pi$
$613$	18.7733	0.758247	0.379124	+	0.925346i	$0.376225\pi$
$614$	18.5884	0.750166
$615$	−18.7491	−0.756038
$616$	0	0
$617$	−28.3764	−1.14239	−0.571195	−	0.820815i	$-0.693520\pi$
$617$	−28.3764	−1.14239	−0.571195	+	0.820815i	$0.693520\pi$
$618$	−19.0872	−0.767799
$619$	8.09775	0.325476	0.162738	−	0.986669i	$-0.447967\pi$
$619$	8.09775	0.325476	0.162738	+	0.986669i	$0.447967\pi$
$620$	−11.4005	−0.457857
$621$	−1.94610	−0.0780943
$622$	10.5628	0.423528
$623$	0.946101	0.0379047
$624$	−0.916382	−0.0366846
$625$	−21.7738	−0.870954
$626$	34.1991	1.36687
$627$	0	0
$628$	22.1672	0.884569
$629$	2.71083	0.108088
$630$	3.81361	0.151938
$631$	−20.5925	−0.819773	−0.409887	−	0.912136i	$-0.634432\pi$
$631$	−20.5925	−0.819773	−0.409887	+	0.912136i	$0.634432\pi$
$632$	−9.61717	−0.382550
$633$	6.18137	0.245687
$634$	61.6344	2.44781
$635$	−44.5980	−1.76982
$636$	−8.65139	−0.343050
$637$	0.186393	0.00738518
$638$	0	0
$639$	6.72999	0.266234
$640$	20.3169	0.803097
$641$	16.8242	0.664515	0.332257	−	0.943189i	$-0.392190\pi$
$641$	16.8242	0.664515	0.332257	+	0.943189i	$0.392190\pi$
$642$	−24.6167	−0.971542
$643$	−27.6655	−1.09102	−0.545511	−	0.838104i	$-0.683664\pi$
$643$	−27.6655	−1.09102	−0.545511	+	0.838104i	$0.683664\pi$
$644$	−2.50885	−0.0988626
$645$	−23.0575	−0.907887
$646$	17.2544	0.678866
$647$	37.2530	1.46457	0.732283	−	0.681001i	$-0.238455\pi$
$647$	37.2530	1.46457	0.732283	+	0.681001i	$0.238455\pi$
$648$	1.28917	0.0506433
$649$	0	0
$650$	0.195504	0.00766828
$651$	4.20555	0.164829
$652$	−5.42166	−0.212329
$653$	−0.280575	−0.0109797	−0.00548987	−	0.999985i	$-0.501747\pi$
$653$	−0.280575	−0.0109797	−0.00548987	+	0.999985i	$0.501747\pi$
$654$	−31.9497	−1.24933
$655$	−11.6897	−0.456755
$656$	−43.8363	−1.71152
$657$	−11.2005	−0.436974
$658$	16.3572	0.637670
$659$	25.9250	1.00989	0.504947	−	0.863150i	$-0.331512\pi$
$659$	25.9250	1.00989	0.504947	+	0.863150i	$0.331512\pi$
$660$	0	0
$661$	30.9446	1.20361	0.601804	−	0.798644i	$-0.294449\pi$
$661$	30.9446	1.20361	0.601804	+	0.798644i	$0.294449\pi$
$662$	−31.6912	−1.23171
$663$	−0.391944	−0.0152218
$664$	−15.6967	−0.609150
$665$	−9.51388	−0.368932
$666$	2.33804	0.0905974
$667$	−0.362741	−0.0140454
$668$	0.833279	0.0322405
$669$	−11.2544	−0.435121
$670$	−19.3466	−0.747426
$671$	0	0
$672$	6.33804	0.244495
$673$	10.9653	0.422680	0.211340	−	0.977413i	$-0.432217\pi$
$673$	10.9653	0.422680	0.211340	+	0.977413i	$0.432217\pi$
$674$	−34.4842	−1.32828
$675$	−0.578337	−0.0222602
$676$	−16.7144	−0.642862
$677$	−32.4544	−1.24733	−0.623663	−	0.781694i	$-0.714356\pi$
$677$	−32.4544	−1.24733	−0.623663	+	0.781694i	$0.714356\pi$
$678$	−19.1219	−0.734373
$679$	7.27358	0.279134
$680$	5.70027	0.218595
$681$	21.2630	0.814801
$682$	0	0
$683$	17.0972	0.654208	0.327104	−	0.944988i	$-0.393927\pi$
$683$	17.0972	0.654208	0.327104	+	0.944988i	$0.393927\pi$
$684$	5.83276	0.223021
$685$	−47.2177	−1.80410
$686$	−1.81361	−0.0692438
$687$	−6.07306	−0.231702
$688$	−53.9094	−2.05528
$689$	−1.25086	−0.0476538
$690$	−7.42166	−0.282538
$691$	−22.8816	−0.870459	−0.435229	−	0.900320i	$-0.643333\pi$
$691$	−22.8816	−0.870459	−0.435229	+	0.900320i	$0.643333\pi$
$692$	−1.74506	−0.0663371
$693$	0	0
$694$	−35.9588	−1.36498
$695$	−6.87610	−0.260825
$696$	0.240293	0.00910827
$697$	−18.7491	−0.710174
$698$	−19.8675	−0.751996
$699$	1.60806	0.0608223
$700$	−0.745574	−0.0281800
$701$	−34.8414	−1.31594	−0.657970	−	0.753044i	$-0.728585\pi$
$701$	−34.8414	−1.31594	−0.657970	+	0.753044i	$0.728585\pi$
$702$	−0.338044	−0.0127587
$703$	−5.83276	−0.219987
$704$	0	0
$705$	18.9653	0.714273
$706$	−41.5613	−1.56418
$707$	−15.3919	−0.578874
$708$	−5.72496	−0.215157
$709$	−7.78746	−0.292464	−0.146232	−	0.989250i	$-0.546715\pi$
$709$	−7.78746	−0.292464	−0.146232	+	0.989250i	$0.546715\pi$
$710$	25.6655	0.963210
$711$	−7.45998	−0.279771
$712$	1.21968	0.0457096
$713$	−8.18442	−0.306509
$714$	3.81361	0.142721
$715$	0	0
$716$	−17.9717	−0.671635
$717$	0.578337	0.0215984
$718$	−24.3316	−0.908046
$719$	36.0383	1.34400	0.672001	−	0.740550i	$-0.265435\pi$
$719$	36.0383	1.34400	0.672001	+	0.740550i	$0.265435\pi$
$720$	10.3380	0.385276
$721$	10.5244	0.391951
$722$	−2.66698	−0.0992547
$723$	20.5244	0.763312
$724$	1.80093	0.0669309
$725$	−0.107798	−0.00400353
$726$	0	0
$727$	−46.6988	−1.73196	−0.865982	−	0.500076i	$-0.833305\pi$
$727$	−46.6988	−1.73196	−0.865982	+	0.500076i	$0.833305\pi$
$728$	0.240293	0.00890584
$729$	1.00000	0.0370370
$730$	−42.7144	−1.58093
$731$	−23.0575	−0.852811
$732$	14.5783	0.538831
$733$	−0.116908	−0.00431811	−0.00215906	−	0.999998i	$-0.500687\pi$
$733$	−0.116908	−0.00431811	−0.00215906	+	0.999998i	$0.500687\pi$
$734$	61.0278	2.25258
$735$	−2.10278	−0.0775620
$736$	−12.3345	−0.454655
$737$	0	0
$738$	−16.1708	−0.595256
$739$	−46.3799	−1.70611	−0.853057	−	0.521818i	$-0.825254\pi$
$739$	−46.3799	−1.70611	−0.853057	+	0.521818i	$0.825254\pi$
$740$	3.49472	0.128468
$741$	0.843326	0.0309803
$742$	12.1708	0.446804
$743$	−45.3466	−1.66361	−0.831803	−	0.555070i	$-0.812691\pi$
$743$	−45.3466	−1.66361	−0.831803	+	0.555070i	$0.812691\pi$
$744$	5.42166	0.198768
$745$	5.58693	0.204689
$746$	26.2877	0.962462
$747$	−12.1758	−0.445490
$748$	0	0
$749$	13.5733	0.495958
$750$	−21.2736	−0.776801
$751$	34.2680	1.25046	0.625229	−	0.780441i	$-0.285005\pi$
$751$	34.2680	1.25046	0.625229	+	0.780441i	$0.285005\pi$
$752$	44.3416	1.61697
$753$	12.8222	0.467267
$754$	−0.0630093	−0.00229466
$755$	34.7652	1.26524
$756$	1.28917	0.0468866
$757$	−22.0106	−0.799988	−0.399994	−	0.916518i	$-0.630988\pi$
$757$	−22.0106	−0.799988	−0.399994	+	0.916518i	$0.630988\pi$
$758$	−50.8761	−1.84790
$759$	0	0
$760$	−12.2650	−0.444898
$761$	−11.2877	−0.409179	−0.204590	−	0.978848i	$-0.565586\pi$
$761$	−11.2877	−0.409179	−0.204590	+	0.978848i	$0.565586\pi$
$762$	−38.4650	−1.39344
$763$	17.6167	0.637766
$764$	17.2827	0.625266
$765$	4.42166	0.159866
$766$	−21.2288	−0.767027
$767$	−0.827740	−0.0298880
$768$	20.8469	0.752248
$769$	−12.3864	−0.446665	−0.223333	−	0.974742i	$-0.571694\pi$
$769$	−12.3864	−0.446665	−0.223333	+	0.974742i	$0.571694\pi$
$770$	0	0
$771$	24.4444	0.880343
$772$	19.4635	0.700508
$773$	26.9013	0.967573	0.483786	−	0.875186i	$-0.339261\pi$
$773$	26.9013	0.967573	0.483786	+	0.875186i	$0.339261\pi$
$774$	−19.8867	−0.714811
$775$	−2.43223	−0.0873681
$776$	9.37687	0.336610
$777$	−1.28917	−0.0462487
$778$	41.9341	1.50341
$779$	40.3416	1.44539
$780$	−0.505281	−0.0180920
$781$	0	0
$782$	−7.42166	−0.265398
$783$	0.186393	0.00666116
$784$	−4.91638	−0.175585
$785$	−36.1572	−1.29051
$786$	−10.0822	−0.359619
$787$	−16.9583	−0.604497	−0.302248	−	0.953229i	$-0.597737\pi$
$787$	−16.9583	−0.604497	−0.302248	+	0.953229i	$0.597737\pi$
$788$	−5.11189	−0.182103
$789$	−22.7683	−0.810573
$790$	−28.4494	−1.01218
$791$	10.5436	0.374887
$792$	0	0
$793$	2.10780	0.0748501
$794$	−32.4046	−1.15000
$795$	14.1114	0.500479
$796$	29.0872	1.03097
$797$	5.99141	0.212226	0.106113	−	0.994354i	$-0.466159\pi$
$797$	5.99141	0.212226	0.106113	+	0.994354i	$0.466159\pi$
$798$	−8.20555	−0.290473
$799$	18.9653	0.670943
$800$	−3.66553	−0.129596
$801$	0.946101	0.0334288
$802$	−24.7774	−0.874921
$803$	0	0
$804$	−6.54002	−0.230649
$805$	4.09221	0.144232
$806$	−1.42166	−0.0500759
$807$	19.5925	0.689688
$808$	−19.8428	−0.698068
$809$	−30.2877	−1.06486	−0.532430	−	0.846474i	$-0.678721\pi$
$809$	−30.2877	−1.06486	−0.532430	+	0.846474i	$0.678721\pi$
$810$	3.81361	0.133996
$811$	25.2388	0.886256	0.443128	−	0.896458i	$-0.353869\pi$
$811$	25.2388	0.886256	0.443128	+	0.896458i	$0.353869\pi$
$812$	0.240293	0.00843262
$813$	10.9511	0.384073
$814$	0	0
$815$	8.84333	0.309768
$816$	10.3380	0.361904
$817$	49.6116	1.73569
$818$	−23.2197	−0.811857
$819$	0.186393	0.00651312
$820$	−24.1708	−0.844081
$821$	0.0977518	0.00341156	0.00170578	−	0.999999i	$-0.499457\pi$
$821$	0.0977518	0.00341156	0.00170578	+	0.999999i	$0.499457\pi$
$822$	−40.7244	−1.42043
$823$	38.7839	1.35192	0.675961	−	0.736938i	$-0.263729\pi$
$823$	38.7839	1.35192	0.675961	+	0.736938i	$0.263729\pi$
$824$	13.5678	0.472656
$825$	0	0
$826$	8.05390	0.280231
$827$	27.8555	0.968630	0.484315	−	0.874894i	$-0.339069\pi$
$827$	27.8555	0.968630	0.484315	+	0.874894i	$0.339069\pi$
$828$	−2.50885	−0.0871886
$829$	−40.4585	−1.40518	−0.702591	−	0.711594i	$-0.747974\pi$
$829$	−40.4585	−1.40518	−0.702591	+	0.711594i	$0.747974\pi$
$830$	−46.4338	−1.61174
$831$	9.89169	0.343139
$832$	−0.309778	−0.0107396
$833$	−2.10278	−0.0728568
$834$	−5.93051	−0.205357
$835$	−1.35917	−0.0470360
$836$	0	0
$837$	4.20555	0.145365
$838$	−12.5345	−0.432997
$839$	−53.6741	−1.85304	−0.926518	−	0.376250i	$-0.877213\pi$
$839$	−53.6741	−1.85304	−0.926518	+	0.376250i	$0.877213\pi$
$840$	−2.71083	−0.0935326
$841$	−28.9653	−0.998802
$842$	−9.81361	−0.338199
$843$	31.5960	1.08823
$844$	7.96883	0.274298
$845$	27.2630	0.937876
$846$	16.3572	0.562372
$847$	0	0
$848$	32.9930	1.13298
$849$	5.52946	0.189771
$850$	−2.20555	−0.0756497
$851$	2.50885	0.0860023
$852$	8.67609	0.297238
$853$	11.6408	0.398574	0.199287	−	0.979941i	$-0.436137\pi$
$853$	11.6408	0.398574	0.199287	+	0.979941i	$0.436137\pi$
$854$	−20.5089	−0.701798
$855$	−9.51388	−0.325368
$856$	17.4983	0.598079
$857$	−34.9497	−1.19386	−0.596929	−	0.802294i	$-0.703613\pi$
$857$	−34.9497	−1.19386	−0.596929	+	0.802294i	$0.703613\pi$
$858$	0	0
$859$	−48.1049	−1.64132	−0.820659	−	0.571418i	$-0.806393\pi$
$859$	−48.1049	−1.64132	−0.820659	+	0.571418i	$0.806393\pi$
$860$	−29.7250	−1.01361
$861$	8.91638	0.303869
$862$	33.4983	1.14096
$863$	33.4499	1.13865	0.569324	−	0.822113i	$-0.307205\pi$
$863$	33.4499	1.13865	0.569324	+	0.822113i	$0.307205\pi$
$864$	6.33804	0.215625
$865$	2.84638	0.0967798
$866$	24.1809	0.821699
$867$	−12.5783	−0.427183
$868$	5.42166	0.184023
$869$	0	0
$870$	0.710831	0.0240994
$871$	−0.945585	−0.0320399
$872$	22.7108	0.769086
$873$	7.27358	0.246173
$874$	15.9688	0.540154
$875$	11.7300	0.396546
$876$	−14.4394	−0.487861
$877$	27.7980	0.938672	0.469336	−	0.883020i	$-0.344493\pi$
$877$	27.7980	0.938672	0.469336	+	0.883020i	$0.344493\pi$
$878$	−17.2645	−0.582648
$879$	8.94610	0.301744
$880$	0	0
$881$	33.8363	1.13998	0.569988	−	0.821653i	$-0.306948\pi$
$881$	33.8363	1.13998	0.569988	+	0.821653i	$0.306948\pi$
$882$	−1.81361	−0.0610673
$883$	−37.4630	−1.26073	−0.630366	−	0.776298i	$-0.717095\pi$
$883$	−37.4630	−1.26073	−0.630366	+	0.776298i	$0.717095\pi$
$884$	−0.505281	−0.0169945
$885$	9.33804	0.313895
$886$	67.4671	2.26660
$887$	−3.48970	−0.117173	−0.0585863	−	0.998282i	$-0.518659\pi$
$887$	−3.48970	−0.117173	−0.0585863	+	0.998282i	$0.518659\pi$
$888$	−1.66196	−0.0557716
$889$	21.2091	0.711331
$890$	3.60806	0.120942
$891$	0	0
$892$	−14.5089	−0.485792
$893$	−40.8066	−1.36554
$894$	4.81863	0.161159
$895$	29.3139	0.979854
$896$	−9.66196	−0.322783
$897$	−0.362741	−0.0121116
$898$	−28.4741	−0.950193
$899$	0.783887	0.0261441
$900$	−0.745574	−0.0248525
$901$	14.1114	0.470118
$902$	0	0
$903$	10.9653	0.364901
$904$	13.5925	0.452079
$905$	−2.93751	−0.0976460
$906$	29.9844	0.996165
$907$	25.6655	0.852210	0.426105	−	0.904674i	$-0.359885\pi$
$907$	25.6655	0.852210	0.426105	+	0.904674i	$0.359885\pi$
$908$	27.4116	0.909686
$909$	−15.3919	−0.510519
$910$	0.710831	0.0235638
$911$	−14.8716	−0.492718	−0.246359	−	0.969179i	$-0.579234\pi$
$911$	−14.8716	−0.492718	−0.246359	+	0.969179i	$0.579234\pi$
$912$	−22.2439	−0.736568
$913$	0	0
$914$	57.6252	1.90607
$915$	−23.7789	−0.786105
$916$	−7.82919	−0.258684
$917$	5.55918	0.183580
$918$	3.81361	0.125868
$919$	−30.7144	−1.01317	−0.506587	−	0.862189i	$-0.669093\pi$
$919$	−30.7144	−1.01317	−0.506587	+	0.862189i	$0.669093\pi$
$920$	5.27555	0.173930
$921$	−10.2494	−0.337729
$922$	16.4020	0.540171
$923$	1.25443	0.0412899
$924$	0	0
$925$	0.745574	0.0245143
$926$	69.6061	2.28740
$927$	10.5244	0.345668
$928$	1.18137	0.0387804
$929$	−21.2111	−0.695913	−0.347957	−	0.937511i	$-0.613124\pi$
$929$	−21.2111	−0.695913	−0.347957	+	0.937511i	$0.613124\pi$
$930$	16.0383	0.525917
$931$	4.52444	0.148282
$932$	2.07306	0.0679052
$933$	−5.82417	−0.190675
$934$	−56.5754	−1.85120
$935$	0	0
$936$	0.240293	0.00785421
$937$	58.9008	1.92421	0.962103	−	0.272688i	$-0.0879126\pi$
$937$	58.9008	1.92421	0.962103	+	0.272688i	$0.0879126\pi$
$938$	9.20053	0.300408
$939$	−18.8569	−0.615373
$940$	24.4494	0.797452
$941$	50.8852	1.65881	0.829405	−	0.558647i	$-0.188680\pi$
$941$	50.8852	1.65881	0.829405	+	0.558647i	$0.188680\pi$
$942$	−31.1849	−1.01606
$943$	−17.3522	−0.565065
$944$	21.8328	0.710596
$945$	−2.10278	−0.0684033
$946$	0	0
$947$	−12.6277	−0.410346	−0.205173	−	0.978726i	$-0.565776\pi$
$947$	−12.6277	−0.410346	−0.205173	+	0.978726i	$0.565776\pi$
$948$	−9.61717	−0.312351
$949$	−2.08771	−0.0677698
$950$	4.74557	0.153967
$951$	−33.9844	−1.10202
$952$	−2.71083	−0.0878586
$953$	−44.4458	−1.43974	−0.719871	−	0.694108i	$-0.755799\pi$
$953$	−44.4458	−1.43974	−0.719871	+	0.694108i	$0.755799\pi$
$954$	12.1708	0.394044
$955$	−28.1900	−0.912206
$956$	0.745574	0.0241136
$957$	0	0
$958$	−57.9250	−1.87147
$959$	22.4550	0.725108
$960$	3.49472	0.112792
$961$	−13.3133	−0.429463
$962$	0.435796	0.0140506
$963$	13.5733	0.437394
$964$	26.4595	0.852202
$965$	−31.7472	−1.02198
$966$	3.52946	0.113559
$967$	22.7214	0.730671	0.365335	−	0.930876i	$-0.380954\pi$
$967$	22.7214	0.730671	0.365335	+	0.930876i	$0.380954\pi$
$968$	0	0
$969$	−9.51388	−0.305630
$970$	27.7386	0.890632
$971$	18.2736	0.586427	0.293214	−	0.956047i	$-0.405275\pi$
$971$	18.2736	0.586427	0.293214	+	0.956047i	$0.405275\pi$
$972$	1.28917	0.0413501
$973$	3.27001	0.104832
$974$	47.8555	1.53339
$975$	−0.107798	−0.00345231
$976$	−55.5960	−1.77959
$977$	−31.6152	−1.01146	−0.505730	−	0.862692i	$-0.668777\pi$
$977$	−31.6152	−1.01146	−0.505730	+	0.862692i	$0.668777\pi$
$978$	7.62721	0.243891
$979$	0	0
$980$	−2.71083	−0.0865943
$981$	17.6167	0.562456
$982$	26.0383	0.830916
$983$	33.8328	1.07910	0.539549	−	0.841954i	$-0.318595\pi$
$983$	33.8328	1.07910	0.539549	+	0.841954i	$0.318595\pi$
$984$	11.4947	0.366438
$985$	8.33804	0.265672
$986$	0.710831	0.0226375
$987$	−9.01916	−0.287083
$988$	1.08719	0.0345881
$989$	−21.3395	−0.678557
$990$	0	0
$991$	−2.71440	−0.0862258	−0.0431129	−	0.999070i	$-0.513728\pi$
$991$	−2.71440	−0.0862258	−0.0431129	+	0.999070i	$0.513728\pi$
$992$	26.6550	0.846296
$993$	17.4741	0.554524
$994$	−12.2056	−0.387137
$995$	−47.4444	−1.50409
$996$	−15.6967	−0.497369
$997$	−43.2197	−1.36878	−0.684391	−	0.729116i	$-0.739932\pi$
$997$	−43.2197	−1.36878	−0.684391	+	0.729116i	$0.739932\pi$
$998$	54.9839	1.74048
$999$	−1.28917	−0.0407875

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2541.2.a.bj.1.1	yes	3
3.2	odd	2		7623.2.a.ca.1.3		3
11.10	odd	2		2541.2.a.bh.1.3	✓	3
33.32	even	2		7623.2.a.cc.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2541.2.a.bh.1.3	✓	3	11.10	odd	2
2541.2.a.bj.1.1	yes	3	1.1	even	1	trivial
7623.2.a.ca.1.3		3	3.2	odd	2
7623.2.a.cc.1.1		3	33.32	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2541 = 3 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2541.a (trivial)

\(f(q)\)	\(=\)	\(q-1.81361 q^{2} +1.00000 q^{3} +1.28917 q^{4} -2.10278 q^{5} -1.81361 q^{6} +1.00000 q^{7} +1.28917 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.81361 q^{2} +1.00000 q^{3} +1.28917 q^{4} -2.10278 q^{5} -1.81361 q^{6} +1.00000 q^{7} +1.28917 q^{8} +1.00000 q^{9} +3.81361 q^{10} +1.28917 q^{12} +0.186393 q^{13} -1.81361 q^{14} -2.10278 q^{15} -4.91638 q^{16} -2.10278 q^{17} -1.81361 q^{18} +4.52444 q^{19} -2.71083 q^{20} +1.00000 q^{21} -1.94610 q^{23} +1.28917 q^{24} -0.578337 q^{25} -0.338044 q^{26} +1.00000 q^{27} +1.28917 q^{28} +0.186393 q^{29} +3.81361 q^{30} +4.20555 q^{31} +6.33804 q^{32} +3.81361 q^{34} -2.10278 q^{35} +1.28917 q^{36} -1.28917 q^{37} -8.20555 q^{38} +0.186393 q^{39} -2.71083 q^{40} +8.91638 q^{41} -1.81361 q^{42} +10.9653 q^{43} -2.10278 q^{45} +3.52946 q^{46} -9.01916 q^{47} -4.91638 q^{48} +1.00000 q^{49} +1.04888 q^{50} -2.10278 q^{51} +0.240293 q^{52} -6.71083 q^{53} -1.81361 q^{54} +1.28917 q^{56} +4.52444 q^{57} -0.338044 q^{58} -4.44082 q^{59} -2.71083 q^{60} +11.3083 q^{61} -7.62721 q^{62} +1.00000 q^{63} -1.66196 q^{64} -0.391944 q^{65} -5.07306 q^{67} -2.71083 q^{68} -1.94610 q^{69} +3.81361 q^{70} +6.72999 q^{71} +1.28917 q^{72} -11.2005 q^{73} +2.33804 q^{74} -0.578337 q^{75} +5.83276 q^{76} -0.338044 q^{78} -7.45998 q^{79} +10.3380 q^{80} +1.00000 q^{81} -16.1708 q^{82} -12.1758 q^{83} +1.28917 q^{84} +4.42166 q^{85} -19.8867 q^{86} +0.186393 q^{87} +0.946101 q^{89} +3.81361 q^{90} +0.186393 q^{91} -2.50885 q^{92} +4.20555 q^{93} +16.3572 q^{94} -9.51388 q^{95} +6.33804 q^{96} +7.27358 q^{97} -1.81361 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{2} + 3 q^{3} + 3 q^{4} + q^{5} + q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + q^2 + 3 * q^3 + 3 * q^4 + q^5 + q^6 + 3 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + q^{2} + 3 q^{3} + 3 q^{4} + q^{5} + q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{9} + 5 q^{10} + 3 q^{12} + 7 q^{13} + q^{14} + q^{15} - q^{16} + q^{17} + q^{18} + 8 q^{19} - 9 q^{20} + 3 q^{21} - 2 q^{23} + 3 q^{24} + 11 q^{26} + 3 q^{27} + 3 q^{28} + 7 q^{29} + 5 q^{30} - 2 q^{31} + 7 q^{32} + 5 q^{34} + q^{35} + 3 q^{36} - 3 q^{37} - 10 q^{38} + 7 q^{39} - 9 q^{40} + 13 q^{41} + q^{42} + 8 q^{43} + q^{45} + 20 q^{46} - 6 q^{47} - q^{48} + 3 q^{49} - 8 q^{50} + q^{51} + 11 q^{52} - 21 q^{53} + q^{54} + 3 q^{56} + 8 q^{57} + 11 q^{58} + 6 q^{59} - 9 q^{60} + 12 q^{61} - 10 q^{62} + 3 q^{63} - 17 q^{64} + 7 q^{65} + 2 q^{67} - 9 q^{68} - 2 q^{69} + 5 q^{70} + 3 q^{72} - 4 q^{73} - 5 q^{74} - 10 q^{76} + 11 q^{78} + 18 q^{79} + 19 q^{80} + 3 q^{81} - 9 q^{82} - 12 q^{83} + 3 q^{84} + 15 q^{85} - 36 q^{86} + 7 q^{87} - q^{89} + 5 q^{90} + 7 q^{91} + 44 q^{92} - 2 q^{93} + 16 q^{94} + 8 q^{95} + 7 q^{96} - 25 q^{97} + q^{98}+O(q^{100}) \) 3 * q + q^2 + 3 * q^3 + 3 * q^4 + q^5 + q^6 + 3 * q^7 + 3 * q^8 + 3 * q^9 + 5 * q^10 + 3 * q^12 + 7 * q^13 + q^14 + q^15 - q^16 + q^17 + q^18 + 8 * q^19 - 9 * q^20 + 3 * q^21 - 2 * q^23 + 3 * q^24 + 11 * q^26 + 3 * q^27 + 3 * q^28 + 7 * q^29 + 5 * q^30 - 2 * q^31 + 7 * q^32 + 5 * q^34 + q^35 + 3 * q^36 - 3 * q^37 - 10 * q^38 + 7 * q^39 - 9 * q^40 + 13 * q^41 + q^42 + 8 * q^43 + q^45 + 20 * q^46 - 6 * q^47 - q^48 + 3 * q^49 - 8 * q^50 + q^51 + 11 * q^52 - 21 * q^53 + q^54 + 3 * q^56 + 8 * q^57 + 11 * q^58 + 6 * q^59 - 9 * q^60 + 12 * q^61 - 10 * q^62 + 3 * q^63 - 17 * q^64 + 7 * q^65 + 2 * q^67 - 9 * q^68 - 2 * q^69 + 5 * q^70 + 3 * q^72 - 4 * q^73 - 5 * q^74 - 10 * q^76 + 11 * q^78 + 18 * q^79 + 19 * q^80 + 3 * q^81 - 9 * q^82 - 12 * q^83 + 3 * q^84 + 15 * q^85 - 36 * q^86 + 7 * q^87 - q^89 + 5 * q^90 + 7 * q^91 + 44 * q^92 - 2 * q^93 + 16 * q^94 + 8 * q^95 + 7 * q^96 - 25 * q^97 + q^98

Introduction

L-functions

Modular forms

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Database

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