LMFDB - Embedded newform 3381.2.a.y.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3381,2,Mod(1,3381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3381, 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("3381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3381 = 3 \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3381.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:	$26.9974209234$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.3176240.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 9x^{3} + 7x^{2} + 19x - 9 $ x^5 - x^4 - 9x^3 + 7x^2 + 19*x - 9
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			1.5
Root			$2.48738$ of defining polynomial
Character	$\chi$	$=$	3381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.48738 q^{2} -1.00000 q^{3} +4.18706 q^{4} -2.95267 q^{5} -2.48738 q^{6} +5.44006 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.48738 q^{2} -1.00000 q^{3} +4.18706 q^{4} -2.95267 q^{5} -2.48738 q^{6} +5.44006 q^{8} +1.00000 q^{9} -7.34443 q^{10} -0.300319 q^{11} -4.18706 q^{12} -3.25299 q^{13} +2.95267 q^{15} +5.15736 q^{16} +2.43560 q^{17} +2.48738 q^{18} +0.970302 q^{19} -12.3630 q^{20} -0.747007 q^{22} +1.00000 q^{23} -5.44006 q^{24} +3.71829 q^{25} -8.09143 q^{26} -1.00000 q^{27} -6.80972 q^{29} +7.34443 q^{30} -2.23439 q^{31} +1.94822 q^{32} +0.300319 q^{33} +6.05825 q^{34} +4.18706 q^{36} -11.4797 q^{37} +2.41351 q^{38} +3.25299 q^{39} -16.0627 q^{40} -0.769093 q^{41} -7.25299 q^{43} -1.25745 q^{44} -2.95267 q^{45} +2.48738 q^{46} +4.88011 q^{47} -5.15736 q^{48} +9.24880 q^{50} -2.43560 q^{51} -13.6205 q^{52} -3.72623 q^{53} -2.48738 q^{54} +0.886743 q^{55} -0.970302 q^{57} -16.9384 q^{58} -8.22329 q^{59} +12.3630 q^{60} +7.13658 q^{61} -5.55777 q^{62} -5.46877 q^{64} +9.60503 q^{65} +0.747007 q^{66} -1.47846 q^{67} +10.1980 q^{68} -1.00000 q^{69} -1.85704 q^{71} +5.44006 q^{72} -13.9574 q^{73} -28.5544 q^{74} -3.71829 q^{75} +4.06271 q^{76} +8.09143 q^{78} +13.1428 q^{79} -15.2280 q^{80} +1.00000 q^{81} -1.91303 q^{82} -9.41036 q^{83} -7.19152 q^{85} -18.0410 q^{86} +6.80972 q^{87} -1.63375 q^{88} -7.19701 q^{89} -7.34443 q^{90} +4.18706 q^{92} +2.23439 q^{93} +12.1387 q^{94} -2.86498 q^{95} -1.94822 q^{96} -1.43908 q^{97} -0.300319 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + q^{2} - 5 q^{3} + 9 q^{4} - 2 q^{5} - q^{6} + 3 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + q^2 - 5 * q^3 + 9 * q^4 - 2 * q^5 - q^6 + 3 * q^8 + 5 * q^9	$ 5 q + q^{2} - 5 q^{3} + 9 q^{4} - 2 q^{5} - q^{6} + 3 q^{8} + 5 q^{9} - 2 q^{11} - 9 q^{12} - 4 q^{13} + 2 q^{15} + q^{16} - 2 q^{17} + q^{18} - 8 q^{19} - 12 q^{20} - 16 q^{22} + 5 q^{23} - 3 q^{24} + 5 q^{25} - 16 q^{26} - 5 q^{27} + 4 q^{29} - 12 q^{31} + 7 q^{32} + 2 q^{33} - 10 q^{34} + 9 q^{36} - 6 q^{37} + 8 q^{38} + 4 q^{39} - 30 q^{40} - 6 q^{41} - 24 q^{43} + 16 q^{44} - 2 q^{45} + q^{46} - 24 q^{47} - q^{48} - 3 q^{50} + 2 q^{51} + 4 q^{52} + 2 q^{53} - q^{54} - 8 q^{55} + 8 q^{57} + 4 q^{58} - 16 q^{59} + 12 q^{60} - 22 q^{61} - 6 q^{62} - 29 q^{64} + 22 q^{65} + 16 q^{66} - 16 q^{67} - 14 q^{68} - 5 q^{69} + 16 q^{71} + 3 q^{72} + 8 q^{74} - 5 q^{75} - 30 q^{76} + 16 q^{78} + 12 q^{79} + 6 q^{80} + 5 q^{81} - 24 q^{82} - 10 q^{83} - 14 q^{85} - 20 q^{86} - 4 q^{87} - 8 q^{88} + 16 q^{89} + 9 q^{92} + 12 q^{93} + 32 q^{94} + 18 q^{95} - 7 q^{96} + 4 q^{97} - 2 q^{99}+O(q^{100}) $ 5 * q + q^2 - 5 * q^3 + 9 * q^4 - 2 * q^5 - q^6 + 3 * q^8 + 5 * q^9 - 2 * q^11 - 9 * q^12 - 4 * q^13 + 2 * q^15 + q^16 - 2 * q^17 + q^18 - 8 * q^19 - 12 * q^20 - 16 * q^22 + 5 * q^23 - 3 * q^24 + 5 * q^25 - 16 * q^26 - 5 * q^27 + 4 * q^29 - 12 * q^31 + 7 * q^32 + 2 * q^33 - 10 * q^34 + 9 * q^36 - 6 * q^37 + 8 * q^38 + 4 * q^39 - 30 * q^40 - 6 * q^41 - 24 * q^43 + 16 * q^44 - 2 * q^45 + q^46 - 24 * q^47 - q^48 - 3 * q^50 + 2 * q^51 + 4 * q^52 + 2 * q^53 - q^54 - 8 * q^55 + 8 * q^57 + 4 * q^58 - 16 * q^59 + 12 * q^60 - 22 * q^61 - 6 * q^62 - 29 * q^64 + 22 * q^65 + 16 * q^66 - 16 * q^67 - 14 * q^68 - 5 * q^69 + 16 * q^71 + 3 * q^72 + 8 * q^74 - 5 * q^75 - 30 * q^76 + 16 * q^78 + 12 * q^79 + 6 * q^80 + 5 * q^81 - 24 * q^82 - 10 * q^83 - 14 * q^85 - 20 * q^86 - 4 * q^87 - 8 * q^88 + 16 * q^89 + 9 * q^92 + 12 * q^93 + 32 * q^94 + 18 * q^95 - 7 * q^96 + 4 * 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 $

$2$	2.48738	1.75884	0.879422	−	0.476043i	$-0.157929\pi$
$2$	2.48738	1.75884	0.879422	+	0.476043i	$0.157929\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.18706	2.09353
$5$	−2.95267	−1.32048	−0.660238	−	0.751056i	$-0.729545\pi$
$5$	−2.95267	−1.32048	−0.660238	+	0.751056i	$0.729545\pi$
$6$	−2.48738	−1.01547
$7$	0	0
$7$	0	0
$8$	5.44006	1.92335
$9$	1.00000	0.333333
$10$	−7.34443	−2.32251
$11$	−0.300319	−0.0905495	−0.0452747	−	0.998975i	$-0.514416\pi$
$11$	−0.300319	−0.0905495	−0.0452747	+	0.998975i	$0.514416\pi$
$12$	−4.18706	−1.20870
$13$	−3.25299	−0.902218	−0.451109	−	0.892469i	$-0.648971\pi$
$13$	−3.25299	−0.902218	−0.451109	+	0.892469i	$0.648971\pi$
$14$	0	0
$15$	2.95267	0.762377
$16$	5.15736	1.28934
$17$	2.43560	0.590719	0.295359	−	0.955386i	$-0.404561\pi$
$17$	2.43560	0.590719	0.295359	+	0.955386i	$0.404561\pi$
$18$	2.48738	0.586281
$19$	0.970302	0.222602	0.111301	−	0.993787i	$-0.464498\pi$
$19$	0.970302	0.222602	0.111301	+	0.993787i	$0.464498\pi$
$20$	−12.3630	−2.76446
$21$	0	0
$22$	−0.747007	−0.159262
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−5.44006	−1.11045
$25$	3.71829	0.743657
$26$	−8.09143	−1.58686
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−6.80972	−1.26453	−0.632267	−	0.774751i	$-0.717875\pi$
$29$	−6.80972	−1.26453	−0.632267	+	0.774751i	$0.717875\pi$
$30$	7.34443	1.34090
$31$	−2.23439	−0.401308	−0.200654	−	0.979662i	$-0.564307\pi$
$31$	−2.23439	−0.401308	−0.200654	+	0.979662i	$0.564307\pi$
$32$	1.94822	0.344399
$33$	0.300319	0.0522788
$34$	6.05825	1.03898
$35$	0	0
$36$	4.18706	0.697844
$37$	−11.4797	−1.88725	−0.943626	−	0.331014i	$-0.892609\pi$
$37$	−11.4797	−1.88725	−0.943626	+	0.331014i	$0.892609\pi$
$38$	2.41351	0.391523
$39$	3.25299	0.520896
$40$	−16.0627	−2.53974
$41$	−0.769093	−0.120112	−0.0600561	−	0.998195i	$-0.519128\pi$
$41$	−0.769093	−0.120112	−0.0600561	+	0.998195i	$0.519128\pi$
$42$	0	0
$43$	−7.25299	−1.10607	−0.553036	−	0.833158i	$-0.686531\pi$
$43$	−7.25299	−1.10607	−0.553036	+	0.833158i	$0.686531\pi$
$44$	−1.25745	−0.189568
$45$	−2.95267	−0.440159
$46$	2.48738	0.366744
$47$	4.88011	0.711837	0.355919	−	0.934517i	$-0.384168\pi$
$47$	4.88011	0.711837	0.355919	+	0.934517i	$0.384168\pi$
$48$	−5.15736	−0.744401
$49$	0	0
$50$	9.24880	1.30798
$51$	−2.43560	−0.341052
$52$	−13.6205	−1.88882
$53$	−3.72623	−0.511837	−0.255918	−	0.966698i	$-0.582378\pi$
$53$	−3.72623	−0.511837	−0.255918	+	0.966698i	$0.582378\pi$
$54$	−2.48738	−0.338490
$55$	0.886743	0.119568
$56$	0	0
$57$	−0.970302	−0.128520
$58$	−16.9384	−2.22412
$59$	−8.22329	−1.07058	−0.535291	−	0.844668i	$-0.679798\pi$
$59$	−8.22329	−1.07058	−0.535291	+	0.844668i	$0.679798\pi$
$60$	12.3630	1.59606
$61$	7.13658	0.913746	0.456873	−	0.889532i	$-0.348969\pi$
$61$	7.13658	0.913746	0.456873	+	0.889532i	$0.348969\pi$
$62$	−5.55777	−0.705838
$63$	0	0
$64$	−5.46877	−0.683597
$65$	9.60503	1.19136
$66$	0.747007	0.0919502
$67$	−1.47846	−0.180623	−0.0903114	−	0.995914i	$-0.528786\pi$
$67$	−1.47846	−0.180623	−0.0903114	+	0.995914i	$0.528786\pi$
$68$	10.1980	1.23669
$69$	−1.00000	−0.120386
$70$	0	0
$71$	−1.85704	−0.220391	−0.110195	−	0.993910i	$-0.535148\pi$
$71$	−1.85704	−0.220391	−0.110195	+	0.993910i	$0.535148\pi$
$72$	5.44006	0.641117
$73$	−13.9574	−1.63359	−0.816795	−	0.576928i	$-0.804251\pi$
$73$	−13.9574	−1.63359	−0.816795	+	0.576928i	$0.804251\pi$
$74$	−28.5544	−3.31938
$75$	−3.71829	−0.429351
$76$	4.06271	0.466025
$77$	0	0
$78$	8.09143	0.916174
$79$	13.1428	1.47868	0.739340	−	0.673333i	$-0.235138\pi$
$79$	13.1428	1.47868	0.739340	+	0.673333i	$0.235138\pi$
$80$	−15.2280	−1.70254
$81$	1.00000	0.111111
$82$	−1.91303	−0.211259
$83$	−9.41036	−1.03292	−0.516460	−	0.856311i	$-0.672751\pi$
$83$	−9.41036	−1.03292	−0.516460	+	0.856311i	$0.672751\pi$
$84$	0	0
$85$	−7.19152	−0.780030
$86$	−18.0410	−1.94541
$87$	6.80972	0.730079
$88$	−1.63375	−0.174158
$89$	−7.19701	−0.762882	−0.381441	−	0.924393i	$-0.624572\pi$
$89$	−7.19701	−0.762882	−0.381441	+	0.924393i	$0.624572\pi$
$90$	−7.34443	−0.774170
$91$	0	0
$92$	4.18706	0.436531
$93$	2.23439	0.231695
$94$	12.1387	1.25201
$95$	−2.86498	−0.293941
$96$	−1.94822	−0.198839
$97$	−1.43908	−0.146116	−0.0730580	−	0.997328i	$-0.523276\pi$
$97$	−1.43908	−0.146116	−0.0730580	+	0.997328i	$0.523276\pi$
$98$	0	0
$99$	−0.300319	−0.0301832
$100$	15.5687	1.55687
$101$	−13.5633	−1.34959	−0.674797	−	0.738003i	$-0.735769\pi$
$101$	−13.5633	−1.34959	−0.674797	+	0.738003i	$0.735769\pi$
$102$	−6.05825	−0.599856
$103$	13.3489	1.31530	0.657652	−	0.753322i	$-0.271550\pi$
$103$	13.3489	1.31530	0.657652	+	0.753322i	$0.271550\pi$
$104$	−17.6965	−1.73528
$105$	0	0
$106$	−9.26855	−0.900241
$107$	1.98237	0.191643	0.0958216	−	0.995399i	$-0.469452\pi$
$107$	1.98237	0.191643	0.0958216	+	0.995399i	$0.469452\pi$
$108$	−4.18706	−0.402900
$109$	11.6702	1.11781	0.558903	−	0.829233i	$-0.311222\pi$
$109$	11.6702	1.11781	0.558903	+	0.829233i	$0.311222\pi$
$110$	2.20567	0.210302
$111$	11.4797	1.08961
$112$	0	0
$113$	10.6921	1.00583	0.502913	−	0.864337i	$-0.332262\pi$
$113$	10.6921	1.00583	0.502913	+	0.864337i	$0.332262\pi$
$114$	−2.41351	−0.226046
$115$	−2.95267	−0.275338
$116$	−28.5127	−2.64734
$117$	−3.25299	−0.300739
$118$	−20.4545	−1.88299
$119$	0	0
$120$	16.0627	1.46632
$121$	−10.9098	−0.991801
$122$	17.7514	1.60714
$123$	0.769093	0.0693468
$124$	−9.35552	−0.840150
$125$	3.78448	0.338494
$126$	0	0
$127$	−13.9706	−1.23969	−0.619844	−	0.784725i	$-0.712804\pi$
$127$	−13.9706	−1.23969	−0.619844	+	0.784725i	$0.712804\pi$
$128$	−17.4994	−1.54674
$129$	7.25299	0.638590
$130$	23.8914	2.09541
$131$	16.4257	1.43512	0.717562	−	0.696495i	$-0.245258\pi$
$131$	16.4257	1.43512	0.717562	+	0.696495i	$0.245258\pi$
$132$	1.25745	0.109447
$133$	0	0
$134$	−3.67750	−0.317687
$135$	2.95267	0.254126
$136$	13.2498	1.13616
$137$	−1.27508	−0.108937	−0.0544687	−	0.998515i	$-0.517347\pi$
$137$	−1.27508	−0.108937	−0.0544687	+	0.998515i	$0.517347\pi$
$138$	−2.48738	−0.211740
$139$	−21.3333	−1.80947	−0.904735	−	0.425975i	$-0.859931\pi$
$139$	−21.3333	−1.80947	−0.904735	+	0.425975i	$0.859931\pi$
$140$	0	0
$141$	−4.88011	−0.410979
$142$	−4.61918	−0.387633
$143$	0.976935	0.0816954
$144$	5.15736	0.429780
$145$	20.1069	1.66979
$146$	−34.7174	−2.87323
$147$	0	0
$148$	−48.0662	−3.95102
$149$	−7.51600	−0.615735	−0.307867	−	0.951429i	$-0.599615\pi$
$149$	−7.51600	−0.615735	−0.307867	+	0.951429i	$0.599615\pi$
$150$	−9.24880	−0.755161
$151$	−9.43657	−0.767938	−0.383969	−	0.923346i	$-0.625443\pi$
$151$	−9.43657	−0.767938	−0.383969	+	0.923346i	$0.625443\pi$
$152$	5.27849	0.428142
$153$	2.43560	0.196906
$154$	0	0
$155$	6.59742	0.529917
$156$	13.6205	1.09051
$157$	17.9495	1.43253	0.716264	−	0.697830i	$-0.245851\pi$
$157$	17.9495	1.43253	0.716264	+	0.697830i	$0.245851\pi$
$158$	32.6911	2.60077
$159$	3.72623	0.295509
$160$	−5.75245	−0.454771
$161$	0	0
$162$	2.48738	0.195427
$163$	20.9781	1.64313	0.821565	−	0.570115i	$-0.193101\pi$
$163$	20.9781	1.64313	0.821565	+	0.570115i	$0.193101\pi$
$164$	−3.22024	−0.251459
$165$	−0.886743	−0.0690329
$166$	−23.4071	−1.81675
$167$	6.34436	0.490941	0.245471	−	0.969404i	$-0.421058\pi$
$167$	6.34436	0.490941	0.245471	+	0.969404i	$0.421058\pi$
$168$	0	0
$169$	−2.41803	−0.186003
$170$	−17.8881	−1.37195
$171$	0.970302	0.0742008
$172$	−30.3687	−2.31559
$173$	15.8915	1.20821	0.604103	−	0.796906i	$-0.293532\pi$
$173$	15.8915	1.20821	0.604103	+	0.796906i	$0.293532\pi$
$174$	16.9384	1.28409
$175$	0	0
$176$	−1.54885	−0.116749
$177$	8.22329	0.618101
$178$	−17.9017	−1.34179
$179$	−1.01207	−0.0756458	−0.0378229	−	0.999284i	$-0.512042\pi$
$179$	−1.01207	−0.0756458	−0.0378229	+	0.999284i	$0.512042\pi$
$180$	−12.3630	−0.921486
$181$	−25.7627	−1.91493	−0.957464	−	0.288553i	$-0.906826\pi$
$181$	−25.7627	−1.91493	−0.957464	+	0.288553i	$0.906826\pi$
$182$	0	0
$183$	−7.13658	−0.527551
$184$	5.44006	0.401046
$185$	33.8958	2.49207
$186$	5.55777	0.407516
$187$	−0.731455	−0.0534893
$188$	20.4333	1.49025
$189$	0	0
$190$	−7.12631	−0.516997
$191$	16.6819	1.20706	0.603530	−	0.797341i	$-0.293761\pi$
$191$	16.6819	1.20706	0.603530	+	0.797341i	$0.293761\pi$
$192$	5.46877	0.394675
$193$	19.9431	1.43553	0.717767	−	0.696283i	$-0.245164\pi$
$193$	19.9431	1.43553	0.717767	+	0.696283i	$0.245164\pi$
$194$	−3.57953	−0.256995
$195$	−9.60503	−0.687831
$196$	0	0
$197$	12.9265	0.920972	0.460486	−	0.887667i	$-0.347675\pi$
$197$	12.9265	0.920972	0.460486	+	0.887667i	$0.347675\pi$
$198$	−0.747007	−0.0530875
$199$	16.9076	1.19855	0.599273	−	0.800545i	$-0.295456\pi$
$199$	16.9076	1.19855	0.599273	+	0.800545i	$0.295456\pi$
$200$	20.2277	1.43031
$201$	1.47846	0.104283
$202$	−33.7370	−2.37373
$203$	0	0
$204$	−10.1980	−0.714002
$205$	2.27088	0.158605
$206$	33.2038	2.31342
$207$	1.00000	0.0695048
$208$	−16.7769	−1.16327
$209$	−0.291400	−0.0201565
$210$	0	0
$211$	2.49957	0.172077	0.0860387	−	0.996292i	$-0.472579\pi$
$211$	2.49957	0.172077	0.0860387	+	0.996292i	$0.472579\pi$
$212$	−15.6019	−1.07155
$213$	1.85704	0.127243
$214$	4.93092	0.337070
$215$	21.4157	1.46054
$216$	−5.44006	−0.370149
$217$	0	0
$218$	29.0283	1.96605
$219$	13.9574	0.943153
$220$	3.71285	0.250320
$221$	−7.92298	−0.532957
$222$	28.5544	1.91645
$223$	−10.4994	−0.703089	−0.351544	−	0.936171i	$-0.614343\pi$
$223$	−10.4994	−0.703089	−0.351544	+	0.936171i	$0.614343\pi$
$224$	0	0
$225$	3.71829	0.247886
$226$	26.5952	1.76909
$227$	14.8428	0.985151	0.492576	−	0.870270i	$-0.336055\pi$
$227$	14.8428	0.985151	0.492576	+	0.870270i	$0.336055\pi$
$228$	−4.06271	−0.269060
$229$	−14.6129	−0.965646	−0.482823	−	0.875718i	$-0.660389\pi$
$229$	−14.6129	−0.965646	−0.482823	+	0.875718i	$0.660389\pi$
$230$	−7.34443	−0.484277
$231$	0	0
$232$	−37.0452	−2.43214
$233$	−0.213346	−0.0139768	−0.00698838	−	0.999976i	$-0.502224\pi$
$233$	−0.213346	−0.0139768	−0.00698838	+	0.999976i	$0.502224\pi$
$234$	−8.09143	−0.528953
$235$	−14.4094	−0.939964
$236$	−34.4314	−2.24130
$237$	−13.1428	−0.853716
$238$	0	0
$239$	29.9652	1.93829	0.969143	−	0.246500i	$-0.0792804\pi$
$239$	29.9652	1.93829	0.969143	+	0.246500i	$0.0792804\pi$
$240$	15.2280	0.982964
$241$	−2.98553	−0.192315	−0.0961573	−	0.995366i	$-0.530655\pi$
$241$	−2.98553	−0.192315	−0.0961573	+	0.995366i	$0.530655\pi$
$242$	−27.1368	−1.74442
$243$	−1.00000	−0.0641500
$244$	29.8813	1.91296
$245$	0	0
$246$	1.91303	0.121970
$247$	−3.15638	−0.200836
$248$	−12.1552	−0.771855
$249$	9.41036	0.596357
$250$	9.41344	0.595358
$251$	−11.4083	−0.720084	−0.360042	−	0.932936i	$-0.617238\pi$
$251$	−11.4083	−0.720084	−0.360042	+	0.932936i	$0.617238\pi$
$252$	0	0
$253$	−0.300319	−0.0188809
$254$	−34.7501	−2.18042
$255$	7.19152	0.450351
$256$	−32.5900	−2.03688
$257$	11.6175	0.724679	0.362339	−	0.932046i	$-0.381978\pi$
$257$	11.6175	0.724679	0.362339	+	0.932046i	$0.381978\pi$
$258$	18.0410	1.12318
$259$	0	0
$260$	40.2169	2.49414
$261$	−6.80972	−0.421511
$262$	40.8571	2.52416
$263$	−9.55259	−0.589038	−0.294519	−	0.955646i	$-0.595159\pi$
$263$	−9.55259	−0.589038	−0.294519	+	0.955646i	$0.595159\pi$
$264$	1.63375	0.100550
$265$	11.0023	0.675868
$266$	0	0
$267$	7.19701	0.440450
$268$	−6.19041	−0.378139
$269$	2.59193	0.158033	0.0790164	−	0.996873i	$-0.474822\pi$
$269$	2.59193	0.158033	0.0790164	+	0.996873i	$0.474822\pi$
$270$	7.34443	0.446967
$271$	−15.9415	−0.968378	−0.484189	−	0.874963i	$-0.660885\pi$
$271$	−15.9415	−0.968378	−0.484189	+	0.874963i	$0.660885\pi$
$272$	12.5613	0.761638
$273$	0	0
$274$	−3.17161	−0.191604
$275$	−1.11667	−0.0673378
$276$	−4.18706	−0.252032
$277$	−16.7120	−1.00413	−0.502063	−	0.864831i	$-0.667425\pi$
$277$	−16.7120	−1.00413	−0.502063	+	0.864831i	$0.667425\pi$
$278$	−53.0641	−3.18257
$279$	−2.23439	−0.133769
$280$	0	0
$281$	−3.19918	−0.190847	−0.0954237	−	0.995437i	$-0.530421\pi$
$281$	−3.19918	−0.190847	−0.0954237	+	0.995437i	$0.530421\pi$
$282$	−12.1387	−0.722849
$283$	−7.62027	−0.452978	−0.226489	−	0.974014i	$-0.572725\pi$
$283$	−7.62027	−0.452978	−0.226489	+	0.974014i	$0.572725\pi$
$284$	−7.77556	−0.461395
$285$	2.86498	0.169707
$286$	2.43001	0.143689
$287$	0	0
$288$	1.94822	0.114800
$289$	−11.0679	−0.651051
$290$	50.0135	2.93689
$291$	1.43908	0.0843601
$292$	−58.4405	−3.41997
$293$	18.0882	1.05672	0.528362	−	0.849019i	$-0.322806\pi$
$293$	18.0882	1.05672	0.528362	+	0.849019i	$0.322806\pi$
$294$	0	0
$295$	24.2807	1.41368
$296$	−62.4502	−3.62984
$297$	0.300319	0.0174263
$298$	−18.6952	−1.08298
$299$	−3.25299	−0.188125
$300$	−15.5687	−0.898859
$301$	0	0
$302$	−23.4724	−1.35068
$303$	13.5633	0.779189
$304$	5.00420	0.287010
$305$	−21.0720	−1.20658
$306$	6.05825	0.346327
$307$	−23.4867	−1.34045	−0.670227	−	0.742156i	$-0.733803\pi$
$307$	−23.4867	−1.34045	−0.670227	+	0.742156i	$0.733803\pi$
$308$	0	0
$309$	−13.3489	−0.759392
$310$	16.4103	0.932042
$311$	−1.53578	−0.0870863	−0.0435431	−	0.999052i	$-0.513865\pi$
$311$	−1.53578	−0.0870863	−0.0435431	+	0.999052i	$0.513865\pi$
$312$	17.6965	1.00186
$313$	32.8316	1.85575	0.927876	−	0.372890i	$-0.121633\pi$
$313$	32.8316	1.85575	0.927876	+	0.372890i	$0.121633\pi$
$314$	44.6473	2.51959
$315$	0	0
$316$	55.0297	3.09566
$317$	28.1192	1.57933	0.789666	−	0.613537i	$-0.210254\pi$
$317$	28.1192	1.57933	0.789666	+	0.613537i	$0.210254\pi$
$318$	9.26855	0.519754
$319$	2.04509	0.114503
$320$	16.1475	0.902673
$321$	−1.98237	−0.110645
$322$	0	0
$323$	2.36326	0.131495
$324$	4.18706	0.232615
$325$	−12.0956	−0.670941
$326$	52.1805	2.89001
$327$	−11.6702	−0.645366
$328$	−4.18391	−0.231018
$329$	0	0
$330$	−2.20567	−0.121418
$331$	−11.1354	−0.612059	−0.306030	−	0.952022i	$-0.599001\pi$
$331$	−11.1354	−0.612059	−0.306030	+	0.952022i	$0.599001\pi$
$332$	−39.4017	−2.16245
$333$	−11.4797	−0.629084
$334$	15.7808	0.863489
$335$	4.36542	0.238508
$336$	0	0
$337$	−24.1703	−1.31664	−0.658320	−	0.752738i	$-0.728733\pi$
$337$	−24.1703	−1.31664	−0.658320	+	0.752738i	$0.728733\pi$
$338$	−6.01457	−0.327150
$339$	−10.6921	−0.580713
$340$	−30.1113	−1.63302
$341$	0.671028	0.0363382
$342$	2.41351	0.130508
$343$	0	0
$344$	−39.4567	−2.12736
$345$	2.95267	0.158967
$346$	39.5281	2.12504
$347$	−5.21214	−0.279802	−0.139901	−	0.990165i	$-0.544678\pi$
$347$	−5.21214	−0.279802	−0.139901	+	0.990165i	$0.544678\pi$
$348$	28.5127	1.52844
$349$	−18.4178	−0.985884	−0.492942	−	0.870062i	$-0.664079\pi$
$349$	−18.4178	−0.985884	−0.492942	+	0.870062i	$0.664079\pi$
$350$	0	0
$351$	3.25299	0.173632
$352$	−0.585085	−0.0311852
$353$	−24.6832	−1.31376	−0.656878	−	0.753997i	$-0.728123\pi$
$353$	−24.6832	−1.31376	−0.656878	+	0.753997i	$0.728123\pi$
$354$	20.4545	1.08714
$355$	5.48325	0.291021
$356$	−30.1343	−1.59712
$357$	0	0
$358$	−2.51741	−0.133049
$359$	−10.8991	−0.575231	−0.287616	−	0.957746i	$-0.592863\pi$
$359$	−10.8991	−0.575231	−0.287616	+	0.957746i	$0.592863\pi$
$360$	−16.0627	−0.846579
$361$	−18.0585	−0.950448
$362$	−64.0817	−3.36806
$363$	10.9098	0.572616
$364$	0	0
$365$	41.2116	2.15712
$366$	−17.7514	−0.927881
$367$	−5.32575	−0.278002	−0.139001	−	0.990292i	$-0.544389\pi$
$367$	−5.32575	−0.278002	−0.139001	+	0.990292i	$0.544389\pi$
$368$	5.15736	0.268846
$369$	−0.769093	−0.0400374
$370$	84.3118	4.38316
$371$	0	0
$372$	9.35552	0.485061
$373$	−34.9189	−1.80803	−0.904016	−	0.427499i	$-0.859395\pi$
$373$	−34.9189	−1.80803	−0.904016	+	0.427499i	$0.859395\pi$
$374$	−1.81941	−0.0940793
$375$	−3.78448	−0.195430
$376$	26.5481	1.36911
$377$	22.1520	1.14088
$378$	0	0
$379$	15.0871	0.774973	0.387487	−	0.921875i	$-0.373343\pi$
$379$	15.0871	0.774973	0.387487	+	0.921875i	$0.373343\pi$
$380$	−11.9959	−0.615375
$381$	13.9706	0.715734
$382$	41.4942	2.12303
$383$	14.6206	0.747075	0.373538	−	0.927615i	$-0.378145\pi$
$383$	14.6206	0.747075	0.373538	+	0.927615i	$0.378145\pi$
$384$	17.4994	0.893010
$385$	0	0
$386$	49.6060	2.52488
$387$	−7.25299	−0.368690
$388$	−6.02550	−0.305898
$389$	25.4138	1.28853	0.644265	−	0.764803i	$-0.277164\pi$
$389$	25.4138	1.28853	0.644265	+	0.764803i	$0.277164\pi$
$390$	−23.8914	−1.20979
$391$	2.43560	0.123173
$392$	0	0
$393$	−16.4257	−0.828569
$394$	32.1530	1.61985
$395$	−38.8064	−1.95256
$396$	−1.25745	−0.0631894
$397$	5.28687	0.265341	0.132670	−	0.991160i	$-0.457645\pi$
$397$	5.28687	0.265341	0.132670	+	0.991160i	$0.457645\pi$
$398$	42.0556	2.10805
$399$	0	0
$400$	19.1766	0.958828
$401$	−25.9881	−1.29778	−0.648891	−	0.760881i	$-0.724767\pi$
$401$	−25.9881	−1.29778	−0.648891	+	0.760881i	$0.724767\pi$
$402$	3.67750	0.183417
$403$	7.26845	0.362067
$404$	−56.7902	−2.82542
$405$	−2.95267	−0.146720
$406$	0	0
$407$	3.44757	0.170890
$408$	−13.2498	−0.655962
$409$	10.2564	0.507145	0.253573	−	0.967316i	$-0.418394\pi$
$409$	10.2564	0.507145	0.253573	+	0.967316i	$0.418394\pi$
$410$	5.64855	0.278962
$411$	1.27508	0.0628950
$412$	55.8926	2.75363
$413$	0	0
$414$	2.48738	0.122248
$415$	27.7857	1.36395
$416$	−6.33753	−0.310723
$417$	21.3333	1.04470
$418$	−0.724822	−0.0354522
$419$	21.9805	1.07382	0.536910	−	0.843640i	$-0.319592\pi$
$419$	21.9805	1.07382	0.536910	+	0.843640i	$0.319592\pi$
$420$	0	0
$421$	−3.99928	−0.194913	−0.0974566	−	0.995240i	$-0.531071\pi$
$421$	−3.99928	−0.194913	−0.0974566	+	0.995240i	$0.531071\pi$
$422$	6.21738	0.302657
$423$	4.88011	0.237279
$424$	−20.2709	−0.984441
$425$	9.05624	0.439292
$426$	4.61918	0.223800
$427$	0	0
$428$	8.30032	0.401211
$429$	−0.976935	−0.0471668
$430$	53.2691	2.56886
$431$	13.9146	0.670242	0.335121	−	0.942175i	$-0.391223\pi$
$431$	13.9146	0.670242	0.335121	+	0.942175i	$0.391223\pi$
$432$	−5.15736	−0.248134
$433$	31.8706	1.53160	0.765802	−	0.643076i	$-0.222342\pi$
$433$	31.8706	1.53160	0.765802	+	0.643076i	$0.222342\pi$
$434$	0	0
$435$	−20.1069	−0.964051
$436$	48.8640	2.34016
$437$	0.970302	0.0464158
$438$	34.7174	1.65886
$439$	−5.19608	−0.247995	−0.123998	−	0.992283i	$-0.539572\pi$
$439$	−5.19608	−0.247995	−0.123998	+	0.992283i	$0.539572\pi$
$440$	4.82393	0.229972
$441$	0	0
$442$	−19.7075	−0.937388
$443$	20.9375	0.994773	0.497386	−	0.867529i	$-0.334293\pi$
$443$	20.9375	0.994773	0.497386	+	0.867529i	$0.334293\pi$
$444$	48.0662	2.28112
$445$	21.2504	1.00737
$446$	−26.1159	−1.23662
$447$	7.51600	0.355495
$448$	0	0
$449$	11.1881	0.527999	0.264000	−	0.964523i	$-0.414958\pi$
$449$	11.1881	0.527999	0.264000	+	0.964523i	$0.414958\pi$
$450$	9.24880	0.435992
$451$	0.230973	0.0108761
$452$	44.7684	2.10573
$453$	9.43657	0.443369
$454$	36.9197	1.73273
$455$	0	0
$456$	−5.27849	−0.247188
$457$	−7.26283	−0.339741	−0.169870	−	0.985466i	$-0.554335\pi$
$457$	−7.26283	−0.339741	−0.169870	+	0.985466i	$0.554335\pi$
$458$	−36.3478	−1.69842
$459$	−2.43560	−0.113684
$460$	−12.3630	−0.576429
$461$	−3.54389	−0.165055	−0.0825276	−	0.996589i	$-0.526299\pi$
$461$	−3.54389	−0.165055	−0.0825276	+	0.996589i	$0.526299\pi$
$462$	0	0
$463$	20.2770	0.942351	0.471175	−	0.882040i	$-0.343830\pi$
$463$	20.2770	0.942351	0.471175	+	0.882040i	$0.343830\pi$
$464$	−35.1202	−1.63041
$465$	−6.59742	−0.305948
$466$	−0.530673	−0.0245829
$467$	−34.4891	−1.59596	−0.797982	−	0.602681i	$-0.794099\pi$
$467$	−34.4891	−1.59596	−0.797982	+	0.602681i	$0.794099\pi$
$468$	−13.6205	−0.629607
$469$	0	0
$470$	−35.8416	−1.65325
$471$	−17.9495	−0.827070
$472$	−44.7352	−2.05910
$473$	2.17821	0.100154
$474$	−32.6911	−1.50155
$475$	3.60786	0.165540
$476$	0	0
$477$	−3.72623	−0.170612
$478$	74.5348	3.40914
$479$	38.2627	1.74827	0.874134	−	0.485685i	$-0.161430\pi$
$479$	38.2627	1.74827	0.874134	+	0.485685i	$0.161430\pi$
$480$	5.75245	0.262562
$481$	37.3434	1.70271
$482$	−7.42614	−0.338251
$483$	0	0
$484$	−45.6800	−2.07637
$485$	4.24912	0.192943
$486$	−2.48738	−0.112830
$487$	14.7815	0.669815	0.334907	−	0.942251i	$-0.391295\pi$
$487$	14.7815	0.669815	0.334907	+	0.942251i	$0.391295\pi$
$488$	38.8234	1.75745
$489$	−20.9781	−0.948661
$490$	0	0
$491$	−30.4865	−1.37584	−0.687918	−	0.725788i	$-0.741475\pi$
$491$	−30.4865	−1.37584	−0.687918	+	0.725788i	$0.741475\pi$
$492$	3.22024	0.145180
$493$	−16.5857	−0.746983
$494$	−7.85113	−0.353239
$495$	0.886743	0.0398561
$496$	−11.5235	−0.517423
$497$	0	0
$498$	23.4071	1.04890
$499$	−4.15750	−0.186115	−0.0930575	−	0.995661i	$-0.529664\pi$
$499$	−4.15750	−0.186115	−0.0930575	+	0.995661i	$0.529664\pi$
$500$	15.8459	0.708648
$501$	−6.34436	−0.283445
$502$	−28.3767	−1.26652
$503$	−22.3829	−0.998006	−0.499003	−	0.866600i	$-0.666300\pi$
$503$	−22.3829	−0.998006	−0.499003	+	0.866600i	$0.666300\pi$
$504$	0	0
$505$	40.0479	1.78211
$506$	−0.747007	−0.0332085
$507$	2.41803	0.107389
$508$	−58.4956	−2.59532
$509$	27.1135	1.20178	0.600891	−	0.799331i	$-0.294812\pi$
$509$	27.1135	1.20178	0.600891	+	0.799331i	$0.294812\pi$
$510$	17.8881	0.792096
$511$	0	0
$512$	−46.0650	−2.03581
$513$	−0.970302	−0.0428399
$514$	28.8971	1.27460
$515$	−39.4149	−1.73683
$516$	30.3687	1.33691
$517$	−1.46559	−0.0644565
$518$	0	0
$519$	−15.8915	−0.697558
$520$	52.2519	2.29140
$521$	2.99695	0.131299	0.0656493	−	0.997843i	$-0.479088\pi$
$521$	2.99695	0.131299	0.0656493	+	0.997843i	$0.479088\pi$
$522$	−16.9384	−0.741372
$523$	−33.6062	−1.46950	−0.734748	−	0.678341i	$-0.762699\pi$
$523$	−33.6062	−1.46950	−0.734748	+	0.678341i	$0.762699\pi$
$524$	68.7756	3.00448
$525$	0	0
$526$	−23.7609	−1.03603
$527$	−5.44206	−0.237060
$528$	1.54885	0.0674051
$529$	1.00000	0.0434783
$530$	27.3670	1.18875
$531$	−8.22329	−0.356861
$532$	0	0
$533$	2.50185	0.108367
$534$	17.9017	0.774682
$535$	−5.85330	−0.253060
$536$	−8.04291	−0.347401
$537$	1.01207	0.0436741
$538$	6.44711	0.277955
$539$	0	0
$540$	12.3630	0.532020
$541$	31.4917	1.35394	0.676968	−	0.736013i	$-0.263294\pi$
$541$	31.4917	1.35394	0.676968	+	0.736013i	$0.263294\pi$
$542$	−39.6526	−1.70323
$543$	25.7627	1.10558
$544$	4.74506	0.203443
$545$	−34.4584	−1.47604
$546$	0	0
$547$	−8.47222	−0.362246	−0.181123	−	0.983460i	$-0.557973\pi$
$547$	−8.47222	−0.362246	−0.181123	+	0.983460i	$0.557973\pi$
$548$	−5.33884	−0.228064
$549$	7.13658	0.304582
$550$	−2.77759	−0.118437
$551$	−6.60748	−0.281488
$552$	−5.44006	−0.231544
$553$	0	0
$554$	−41.5691	−1.76610
$555$	−33.8958	−1.43880
$556$	−89.3240	−3.78818
$557$	28.7102	1.21649	0.608245	−	0.793750i	$-0.291874\pi$
$557$	28.7102	1.21649	0.608245	+	0.793750i	$0.291874\pi$
$558$	−5.55777	−0.235279
$559$	23.5939	0.997917
$560$	0	0
$561$	0.731455	0.0308820
$562$	−7.95759	−0.335671
$563$	−23.6370	−0.996179	−0.498090	−	0.867125i	$-0.665965\pi$
$563$	−23.6370	−0.996179	−0.498090	+	0.867125i	$0.665965\pi$
$564$	−20.4333	−0.860398
$565$	−31.5702	−1.32817
$566$	−18.9545	−0.796718
$567$	0	0
$568$	−10.1024	−0.423888
$569$	4.79873	0.201173	0.100587	−	0.994928i	$-0.467928\pi$
$569$	4.79873	0.201173	0.100587	+	0.994928i	$0.467928\pi$
$570$	7.12631	0.298488
$571$	−9.96566	−0.417050	−0.208525	−	0.978017i	$-0.566866\pi$
$571$	−9.96566	−0.417050	−0.208525	+	0.978017i	$0.566866\pi$
$572$	4.09049	0.171032
$573$	−16.6819	−0.696896
$574$	0	0
$575$	3.71829	0.155063
$576$	−5.46877	−0.227866
$577$	−18.7896	−0.782222	−0.391111	−	0.920344i	$-0.627909\pi$
$577$	−18.7896	−0.782222	−0.391111	+	0.920344i	$0.627909\pi$
$578$	−27.5300	−1.14510
$579$	−19.9431	−0.828806
$580$	84.1888	3.49575
$581$	0	0
$582$	3.57953	0.148376
$583$	1.11906	0.0463465
$584$	−75.9290	−3.14196
$585$	9.60503	0.397119
$586$	44.9923	1.85861
$587$	−20.0795	−0.828770	−0.414385	−	0.910102i	$-0.636003\pi$
$587$	−20.0795	−0.828770	−0.414385	+	0.910102i	$0.636003\pi$
$588$	0	0
$589$	−2.16803	−0.0893321
$590$	60.3954	2.48644
$591$	−12.9265	−0.531723
$592$	−59.2050	−2.43331
$593$	28.1319	1.15524	0.577619	−	0.816307i	$-0.303982\pi$
$593$	28.1319	1.15524	0.577619	+	0.816307i	$0.303982\pi$
$594$	0.747007	0.0306501
$595$	0	0
$596$	−31.4700	−1.28906
$597$	−16.9076	−0.691981
$598$	−8.09143	−0.330883
$599$	10.4708	0.427823	0.213912	−	0.976853i	$-0.431380\pi$
$599$	10.4708	0.427823	0.213912	+	0.976853i	$0.431380\pi$
$600$	−20.2277	−0.825792
$601$	−42.6206	−1.73853	−0.869266	−	0.494345i	$-0.835408\pi$
$601$	−42.6206	−1.73853	−0.869266	+	0.494345i	$0.835408\pi$
$602$	0	0
$603$	−1.47846	−0.0602076
$604$	−39.5115	−1.60770
$605$	32.2131	1.30965
$606$	33.7370	1.37047
$607$	31.1435	1.26408	0.632038	−	0.774937i	$-0.282219\pi$
$607$	31.1435	1.26408	0.632038	+	0.774937i	$0.282219\pi$
$608$	1.89036	0.0766641
$609$	0	0
$610$	−52.4141	−2.12219
$611$	−15.8750	−0.642232
$612$	10.1980	0.412229
$613$	7.83177	0.316322	0.158161	−	0.987413i	$-0.449443\pi$
$613$	7.83177	0.316322	0.158161	+	0.987413i	$0.449443\pi$
$614$	−58.4203	−2.35765
$615$	−2.27088	−0.0915708
$616$	0	0
$617$	−17.6638	−0.711119	−0.355559	−	0.934654i	$-0.615710\pi$
$617$	−17.6638	−0.711119	−0.355559	+	0.934654i	$0.615710\pi$
$618$	−33.2038	−1.33565
$619$	11.6514	0.468308	0.234154	−	0.972200i	$-0.424768\pi$
$619$	11.6514	0.468308	0.234154	+	0.972200i	$0.424768\pi$
$620$	27.6238	1.10940
$621$	−1.00000	−0.0401286
$622$	−3.82008	−0.153171
$623$	0	0
$624$	16.7769	0.671612
$625$	−29.7658	−1.19063
$626$	81.6647	3.26398
$627$	0.291400	0.0116374
$628$	75.1558	2.99904
$629$	−27.9599	−1.11483
$630$	0	0
$631$	31.6865	1.26142	0.630710	−	0.776019i	$-0.282764\pi$
$631$	31.6865	1.26142	0.630710	+	0.776019i	$0.282764\pi$
$632$	71.4975	2.84402
$633$	−2.49957	−0.0993489
$634$	69.9432	2.77780
$635$	41.2505	1.63698
$636$	15.6019	0.618657
$637$	0	0
$638$	5.08691	0.201393
$639$	−1.85704	−0.0734636
$640$	51.6699	2.04243
$641$	18.8852	0.745920	0.372960	−	0.927847i	$-0.378343\pi$
$641$	18.8852	0.745920	0.372960	+	0.927847i	$0.378343\pi$
$642$	−4.93092	−0.194608
$643$	−21.1214	−0.832945	−0.416473	−	0.909148i	$-0.636734\pi$
$643$	−21.1214	−0.832945	−0.416473	+	0.909148i	$0.636734\pi$
$644$	0	0
$645$	−21.4157	−0.843244
$646$	5.87833	0.231280
$647$	−39.7268	−1.56182	−0.780910	−	0.624644i	$-0.785244\pi$
$647$	−39.7268	−1.56182	−0.780910	+	0.624644i	$0.785244\pi$
$648$	5.44006	0.213706
$649$	2.46961	0.0969406
$650$	−30.0863	−1.18008
$651$	0	0
$652$	87.8365	3.43994
$653$	−37.5537	−1.46959	−0.734795	−	0.678289i	$-0.762722\pi$
$653$	−37.5537	−1.46959	−0.734795	+	0.678289i	$0.762722\pi$
$654$	−29.0283	−1.13510
$655$	−48.4999	−1.89505
$656$	−3.96649	−0.154866
$657$	−13.9574	−0.544530
$658$	0	0
$659$	4.58394	0.178565	0.0892825	−	0.996006i	$-0.471543\pi$
$659$	4.58394	0.178565	0.0892825	+	0.996006i	$0.471543\pi$
$660$	−3.71285	−0.144522
$661$	17.2566	0.671204	0.335602	−	0.942004i	$-0.391060\pi$
$661$	17.2566	0.671204	0.335602	+	0.942004i	$0.391060\pi$
$662$	−27.6981	−1.07652
$663$	7.92298	0.307703
$664$	−51.1929	−1.98667
$665$	0	0
$666$	−28.5544	−1.10646
$667$	−6.80972	−0.263673
$668$	26.5642	1.02780
$669$	10.4994	0.405928
$670$	10.8585	0.419499
$671$	−2.14325	−0.0827392
$672$	0	0
$673$	−40.0814	−1.54502	−0.772512	−	0.635001i	$-0.781000\pi$
$673$	−40.0814	−1.54502	−0.772512	+	0.635001i	$0.781000\pi$
$674$	−60.1208	−2.31577
$675$	−3.71829	−0.143117
$676$	−10.1245	−0.389402
$677$	13.0756	0.502537	0.251269	−	0.967917i	$-0.419152\pi$
$677$	13.0756	0.502537	0.251269	+	0.967917i	$0.419152\pi$
$678$	−26.5952	−1.02138
$679$	0	0
$680$	−39.1223	−1.50027
$681$	−14.8428	−0.568777
$682$	1.66910	0.0639132
$683$	−44.2949	−1.69490	−0.847449	−	0.530877i	$-0.821863\pi$
$683$	−44.2949	−1.69490	−0.847449	+	0.530877i	$0.821863\pi$
$684$	4.06271	0.155342
$685$	3.76490	0.143849
$686$	0	0
$687$	14.6129	0.557516
$688$	−37.4063	−1.42610
$689$	12.1214	0.461788
$690$	7.34443	0.279597
$691$	−25.3978	−0.966178	−0.483089	−	0.875571i	$-0.660485\pi$
$691$	−25.3978	−0.966178	−0.483089	+	0.875571i	$0.660485\pi$
$692$	66.5385	2.52942
$693$	0	0
$694$	−12.9646	−0.492128
$695$	62.9904	2.38936
$696$	37.0452	1.40420
$697$	−1.87320	−0.0709525
$698$	−45.8122	−1.73402
$699$	0.213346	0.00806949
$700$	0	0
$701$	−14.6871	−0.554723	−0.277361	−	0.960766i	$-0.589460\pi$
$701$	−14.6871	−0.554723	−0.277361	+	0.960766i	$0.589460\pi$
$702$	8.09143	0.305391
$703$	−11.1388	−0.420107
$704$	1.64237	0.0618993
$705$	14.4094	0.542689
$706$	−61.3966	−2.31069
$707$	0	0
$708$	34.4314	1.29401
$709$	−37.4448	−1.40627	−0.703134	−	0.711057i	$-0.748217\pi$
$709$	−37.4448	−1.40627	−0.703134	+	0.711057i	$0.748217\pi$
$710$	13.6389	0.511860
$711$	13.1428	0.492893
$712$	−39.1521	−1.46729
$713$	−2.23439	−0.0836785
$714$	0	0
$715$	−2.88457	−0.107877
$716$	−4.23761	−0.158367
$717$	−29.9652	−1.11907
$718$	−27.1102	−1.01174
$719$	−44.6748	−1.66609	−0.833044	−	0.553207i	$-0.813404\pi$
$719$	−44.6748	−1.66609	−0.833044	+	0.553207i	$0.813404\pi$
$720$	−15.2280	−0.567515
$721$	0	0
$722$	−44.9184	−1.67169
$723$	2.98553	0.111033
$724$	−107.870	−4.00896
$725$	−25.3205	−0.940380
$726$	27.1368	1.00714
$727$	22.8807	0.848596	0.424298	−	0.905523i	$-0.360521\pi$
$727$	22.8807	0.848596	0.424298	+	0.905523i	$0.360521\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	102.509	3.79403
$731$	−17.6654	−0.653377
$732$	−29.8813	−1.10445
$733$	39.3772	1.45443	0.727215	−	0.686410i	$-0.240814\pi$
$733$	39.3772	1.45443	0.727215	+	0.686410i	$0.240814\pi$
$734$	−13.2472	−0.488962
$735$	0	0
$736$	1.94822	0.0718122
$737$	0.444010	0.0163553
$738$	−1.91303	−0.0704195
$739$	15.1725	0.558131	0.279065	−	0.960272i	$-0.409975\pi$
$739$	15.1725	0.558131	0.279065	+	0.960272i	$0.409975\pi$
$740$	141.924	5.21723
$741$	3.15638	0.115953
$742$	0	0
$743$	27.0790	0.993433	0.496717	−	0.867913i	$-0.334539\pi$
$743$	27.0790	0.993433	0.496717	+	0.867913i	$0.334539\pi$
$744$	12.1552	0.445631
$745$	22.1923	0.813063
$746$	−86.8566	−3.18004
$747$	−9.41036	−0.344307
$748$	−3.06265	−0.111981
$749$	0	0
$750$	−9.41344	−0.343730
$751$	−48.2179	−1.75950	−0.879748	−	0.475441i	$-0.842289\pi$
$751$	−48.2179	−1.75950	−0.879748	+	0.475441i	$0.842289\pi$
$752$	25.1685	0.917801
$753$	11.4083	0.415741
$754$	55.1004	2.00664
$755$	27.8631	1.01404
$756$	0	0
$757$	6.99103	0.254093	0.127047	−	0.991897i	$-0.459450\pi$
$757$	6.99103	0.254093	0.127047	+	0.991897i	$0.459450\pi$
$758$	37.5274	1.36306
$759$	0.300319	0.0109009
$760$	−15.5857	−0.565352
$761$	−19.9052	−0.721564	−0.360782	−	0.932650i	$-0.617490\pi$
$761$	−19.9052	−0.721564	−0.360782	+	0.932650i	$0.617490\pi$
$762$	34.7501	1.25886
$763$	0	0
$764$	69.8481	2.52702
$765$	−7.19152	−0.260010
$766$	36.3669	1.31399
$767$	26.7503	0.965898
$768$	32.5900	1.17599
$769$	−21.4940	−0.775094	−0.387547	−	0.921850i	$-0.626678\pi$
$769$	−21.4940	−0.775094	−0.387547	+	0.921850i	$0.626678\pi$
$770$	0	0
$771$	−11.6175	−0.418393
$772$	83.5029	3.00534
$773$	32.5346	1.17019	0.585093	−	0.810966i	$-0.301058\pi$
$773$	32.5346	1.17019	0.585093	+	0.810966i	$0.301058\pi$
$774$	−18.0410	−0.648469
$775$	−8.30809	−0.298436
$776$	−7.82865	−0.281032
$777$	0	0
$778$	63.2137	2.26632
$779$	−0.746252	−0.0267373
$780$	−40.2169	−1.43999
$781$	0.557705	0.0199563
$782$	6.05825	0.216643
$783$	6.80972	0.243360
$784$	0	0
$785$	−52.9991	−1.89162
$786$	−40.8571	−1.45732
$787$	16.5555	0.590140	0.295070	−	0.955476i	$-0.404657\pi$
$787$	16.5555	0.590140	0.295070	+	0.955476i	$0.404657\pi$
$788$	54.1239	1.92808
$789$	9.55259	0.340081
$790$	−96.5262	−3.43425
$791$	0	0
$792$	−1.63375	−0.0580528
$793$	−23.2153	−0.824398
$794$	13.1505	0.466693
$795$	−11.0023	−0.390213
$796$	70.7930	2.50919
$797$	−7.58157	−0.268553	−0.134277	−	0.990944i	$-0.542871\pi$
$797$	−7.58157	−0.268553	−0.134277	+	0.990944i	$0.542871\pi$
$798$	0	0
$799$	11.8860	0.420496
$800$	7.24402	0.256115
$801$	−7.19701	−0.254294
$802$	−64.6422	−2.28260
$803$	4.19167	0.147921
$804$	6.19041	0.218319
$805$	0	0
$806$	18.0794	0.636819
$807$	−2.59193	−0.0912402
$808$	−73.7849	−2.59574
$809$	−18.6361	−0.655209	−0.327605	−	0.944815i	$-0.606241\pi$
$809$	−18.6361	−0.655209	−0.327605	+	0.944815i	$0.606241\pi$
$810$	−7.34443	−0.258057
$811$	5.52322	0.193946	0.0969732	−	0.995287i	$-0.469084\pi$
$811$	5.52322	0.193946	0.0969732	+	0.995287i	$0.469084\pi$
$812$	0	0
$813$	15.9415	0.559093
$814$	8.57542	0.300568
$815$	−61.9414	−2.16971
$816$	−12.5613	−0.439732
$817$	−7.03759	−0.246214
$818$	25.5115	0.891989
$819$	0	0
$820$	9.50832	0.332045
$821$	−10.4312	−0.364053	−0.182026	−	0.983294i	$-0.558266\pi$
$821$	−10.4312	−0.364053	−0.182026	+	0.983294i	$0.558266\pi$
$822$	3.17161	0.110623
$823$	19.1718	0.668288	0.334144	−	0.942522i	$-0.391553\pi$
$823$	19.1718	0.668288	0.334144	+	0.942522i	$0.391553\pi$
$824$	72.6187	2.52979
$825$	1.11667	0.0388775
$826$	0	0
$827$	14.1133	0.490767	0.245384	−	0.969426i	$-0.421086\pi$
$827$	14.1133	0.490767	0.245384	+	0.969426i	$0.421086\pi$
$828$	4.18706	0.145510
$829$	30.6262	1.06369	0.531846	−	0.846841i	$-0.321498\pi$
$829$	30.6262	1.06369	0.531846	+	0.846841i	$0.321498\pi$
$830$	69.1137	2.39897
$831$	16.7120	0.579732
$832$	17.7899	0.616753
$833$	0	0
$834$	53.0641	1.83746
$835$	−18.7328	−0.648276
$836$	−1.22011	−0.0421983
$837$	2.23439	0.0772317
$838$	54.6739	1.88868
$839$	−4.35888	−0.150485	−0.0752426	−	0.997165i	$-0.523973\pi$
$839$	−4.35888	−0.150485	−0.0752426	+	0.997165i	$0.523973\pi$
$840$	0	0
$841$	17.3723	0.599044
$842$	−9.94774	−0.342822
$843$	3.19918	0.110186
$844$	10.4658	0.360249
$845$	7.13967	0.245612
$846$	12.1387	0.417337
$847$	0	0
$848$	−19.2175	−0.659932
$849$	7.62027	0.261527
$850$	22.5263	0.772647
$851$	−11.4797	−0.393519
$852$	7.77556	0.266386
$853$	45.4480	1.55611	0.778055	−	0.628197i	$-0.216207\pi$
$853$	45.4480	1.55611	0.778055	+	0.628197i	$0.216207\pi$
$854$	0	0
$855$	−2.86498	−0.0979804
$856$	10.7842	0.368597
$857$	−23.1141	−0.789563	−0.394781	−	0.918775i	$-0.629180\pi$
$857$	−23.1141	−0.789563	−0.394781	+	0.918775i	$0.629180\pi$
$858$	−2.43001	−0.0829591
$859$	8.90579	0.303862	0.151931	−	0.988391i	$-0.451451\pi$
$859$	8.90579	0.303862	0.151931	+	0.988391i	$0.451451\pi$
$860$	89.6690	3.05769
$861$	0	0
$862$	34.6109	1.17885
$863$	26.9221	0.916440	0.458220	−	0.888839i	$-0.348487\pi$
$863$	26.9221	0.916440	0.458220	+	0.888839i	$0.348487\pi$
$864$	−1.94822	−0.0662796
$865$	−46.9223	−1.59541
$866$	79.2744	2.69385
$867$	11.0679	0.375885
$868$	0	0
$869$	−3.94703	−0.133894
$870$	−50.0135	−1.69562
$871$	4.80943	0.162961
$872$	63.4868	2.14993
$873$	−1.43908	−0.0487053
$874$	2.41351	0.0816382
$875$	0	0
$876$	58.4405	1.97452
$877$	18.9481	0.639832	0.319916	−	0.947446i	$-0.396345\pi$
$877$	18.9481	0.639832	0.319916	+	0.947446i	$0.396345\pi$
$878$	−12.9246	−0.436185
$879$	−18.0882	−0.610100
$880$	4.57326	0.154164
$881$	−8.51644	−0.286926	−0.143463	−	0.989656i	$-0.545824\pi$
$881$	−8.51644	−0.286926	−0.143463	+	0.989656i	$0.545824\pi$
$882$	0	0
$883$	3.58752	0.120730	0.0603648	−	0.998176i	$-0.480774\pi$
$883$	3.58752	0.120730	0.0603648	+	0.998176i	$0.480774\pi$
$884$	−33.1740	−1.11576
$885$	−24.2807	−0.816187
$886$	52.0797	1.74965
$887$	0.640317	0.0214997	0.0107499	−	0.999942i	$-0.496578\pi$
$887$	0.640317	0.0214997	0.0107499	+	0.999942i	$0.496578\pi$
$888$	62.4502	2.09569
$889$	0	0
$890$	52.8579	1.77180
$891$	−0.300319	−0.0100611
$892$	−43.9614	−1.47194
$893$	4.73518	0.158457
$894$	18.6952	0.625260
$895$	2.98832	0.0998884
$896$	0	0
$897$	3.25299	0.108614
$898$	27.8291	0.928668
$899$	15.2156	0.507467
$900$	15.5687	0.518957
$901$	−9.07558	−0.302352
$902$	0.574518	0.0191294
$903$	0	0
$904$	58.1654	1.93455
$905$	76.0689	2.52862
$906$	23.4724	0.779817
$907$	−32.5276	−1.08006	−0.540031	−	0.841645i	$-0.681588\pi$
$907$	−32.5276	−1.08006	−0.540031	+	0.841645i	$0.681588\pi$
$908$	62.1477	2.06244
$909$	−13.5633	−0.449865
$910$	0	0
$911$	−4.68006	−0.155057	−0.0775287	−	0.996990i	$-0.524703\pi$
$911$	−4.68006	−0.155057	−0.0775287	+	0.996990i	$0.524703\pi$
$912$	−5.00420	−0.165706
$913$	2.82611	0.0935304
$914$	−18.0654	−0.597551
$915$	21.0720	0.696619
$916$	−61.1850	−2.02161
$917$	0	0
$918$	−6.05825	−0.199952
$919$	−27.2884	−0.900163	−0.450081	−	0.892988i	$-0.648605\pi$
$919$	−27.2884	−0.900163	−0.450081	+	0.892988i	$0.648605\pi$
$920$	−16.0627	−0.529572
$921$	23.4867	0.773912
$922$	−8.81499	−0.290306
$923$	6.04095	0.198840
$924$	0	0
$925$	−42.6848	−1.40347
$926$	50.4365	1.65745
$927$	13.3489	0.438435
$928$	−13.2668	−0.435504
$929$	−23.9973	−0.787326	−0.393663	−	0.919255i	$-0.628792\pi$
$929$	−23.9973	−0.787326	−0.393663	+	0.919255i	$0.628792\pi$
$930$	−16.4103	−0.538115
$931$	0	0
$932$	−0.893293	−0.0292608
$933$	1.53578	0.0502793
$934$	−85.7875	−2.80705
$935$	2.15975	0.0706313
$936$	−17.6965	−0.578427
$937$	−46.8035	−1.52900	−0.764502	−	0.644621i	$-0.777015\pi$
$937$	−46.8035	−1.52900	−0.764502	+	0.644621i	$0.777015\pi$
$938$	0	0
$939$	−32.8316	−1.07142
$940$	−60.3330	−1.96784
$941$	11.4806	0.374257	0.187129	−	0.982335i	$-0.440082\pi$
$941$	11.4806	0.374257	0.187129	+	0.982335i	$0.440082\pi$
$942$	−44.6473	−1.45469
$943$	−0.769093	−0.0250451
$944$	−42.4105	−1.38034
$945$	0	0
$946$	5.41803	0.176156
$947$	24.2980	0.789578	0.394789	−	0.918772i	$-0.370818\pi$
$947$	24.2980	0.789578	0.394789	+	0.918772i	$0.370818\pi$
$948$	−55.0297	−1.78728
$949$	45.4033	1.47385
$950$	8.97412	0.291159
$951$	−28.1192	−0.911828
$952$	0	0
$953$	47.1931	1.52873	0.764367	−	0.644781i	$-0.223052\pi$
$953$	47.1931	1.52873	0.764367	+	0.644781i	$0.223052\pi$
$954$	−9.26855	−0.300080
$955$	−49.2562	−1.59389
$956$	125.466	4.05786
$957$	−2.04509	−0.0661082
$958$	95.1739	3.07493
$959$	0	0
$960$	−16.1475	−0.521159
$961$	−26.0075	−0.838952
$962$	92.8872	2.99480
$963$	1.98237	0.0638811
$964$	−12.5006	−0.402617
$965$	−58.8854	−1.89559
$966$	0	0
$967$	−7.83288	−0.251889	−0.125944	−	0.992037i	$-0.540196\pi$
$967$	−7.83288	−0.251889	−0.125944	+	0.992037i	$0.540196\pi$
$968$	−59.3500	−1.90758
$969$	−2.36326	−0.0759189
$970$	10.5692	0.339356
$971$	51.5362	1.65388	0.826938	−	0.562293i	$-0.190081\pi$
$971$	51.5362	1.65388	0.826938	+	0.562293i	$0.190081\pi$
$972$	−4.18706	−0.134300
$973$	0	0
$974$	36.7673	1.17810
$975$	12.0956	0.387368
$976$	36.8060	1.17813
$977$	9.62152	0.307820	0.153910	−	0.988085i	$-0.450813\pi$
$977$	9.62152	0.307820	0.153910	+	0.988085i	$0.450813\pi$
$978$	−52.1805	−1.66855
$979$	2.16140	0.0690785
$980$	0	0
$981$	11.6702	0.372602
$982$	−75.8315	−2.41988
$983$	−55.3155	−1.76429	−0.882145	−	0.470977i	$-0.843901\pi$
$983$	−55.3155	−1.76429	−0.882145	+	0.470977i	$0.843901\pi$
$984$	4.18391	0.133378
$985$	−38.1676	−1.21612
$986$	−41.2550	−1.31383
$987$	0	0
$988$	−13.2160	−0.420456
$989$	−7.25299	−0.230632
$990$	2.20567	0.0701007
$991$	−14.9911	−0.476207	−0.238103	−	0.971240i	$-0.576526\pi$
$991$	−14.9911	−0.476207	−0.238103	+	0.971240i	$0.576526\pi$
$992$	−4.35307	−0.138210
$993$	11.1354	0.353373
$994$	0	0
$995$	−49.9225	−1.58265
$996$	39.4017	1.24849
$997$	−55.5793	−1.76021	−0.880107	−	0.474775i	$-0.842529\pi$
$997$	−55.5793	−1.76021	−0.880107	+	0.474775i	$0.842529\pi$
$998$	−10.3413	−0.327347
$999$	11.4797	0.363202

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3381.2.a.y.1.5	✓	5
7.6	odd	2		3381.2.a.z.1.5	yes	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3381.2.a.y.1.5	✓	5	1.1	even	1	trivial
3381.2.a.z.1.5	yes	5	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3381 = 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3381.a (trivial)

\(f(q)\)	\(=\)	\(q+2.48738 q^{2} -1.00000 q^{3} +4.18706 q^{4} -2.95267 q^{5} -2.48738 q^{6} +5.44006 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.48738 q^{2} -1.00000 q^{3} +4.18706 q^{4} -2.95267 q^{5} -2.48738 q^{6} +5.44006 q^{8} +1.00000 q^{9} -7.34443 q^{10} -0.300319 q^{11} -4.18706 q^{12} -3.25299 q^{13} +2.95267 q^{15} +5.15736 q^{16} +2.43560 q^{17} +2.48738 q^{18} +0.970302 q^{19} -12.3630 q^{20} -0.747007 q^{22} +1.00000 q^{23} -5.44006 q^{24} +3.71829 q^{25} -8.09143 q^{26} -1.00000 q^{27} -6.80972 q^{29} +7.34443 q^{30} -2.23439 q^{31} +1.94822 q^{32} +0.300319 q^{33} +6.05825 q^{34} +4.18706 q^{36} -11.4797 q^{37} +2.41351 q^{38} +3.25299 q^{39} -16.0627 q^{40} -0.769093 q^{41} -7.25299 q^{43} -1.25745 q^{44} -2.95267 q^{45} +2.48738 q^{46} +4.88011 q^{47} -5.15736 q^{48} +9.24880 q^{50} -2.43560 q^{51} -13.6205 q^{52} -3.72623 q^{53} -2.48738 q^{54} +0.886743 q^{55} -0.970302 q^{57} -16.9384 q^{58} -8.22329 q^{59} +12.3630 q^{60} +7.13658 q^{61} -5.55777 q^{62} -5.46877 q^{64} +9.60503 q^{65} +0.747007 q^{66} -1.47846 q^{67} +10.1980 q^{68} -1.00000 q^{69} -1.85704 q^{71} +5.44006 q^{72} -13.9574 q^{73} -28.5544 q^{74} -3.71829 q^{75} +4.06271 q^{76} +8.09143 q^{78} +13.1428 q^{79} -15.2280 q^{80} +1.00000 q^{81} -1.91303 q^{82} -9.41036 q^{83} -7.19152 q^{85} -18.0410 q^{86} +6.80972 q^{87} -1.63375 q^{88} -7.19701 q^{89} -7.34443 q^{90} +4.18706 q^{92} +2.23439 q^{93} +12.1387 q^{94} -2.86498 q^{95} -1.94822 q^{96} -1.43908 q^{97} -0.300319 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + q^{2} - 5 q^{3} + 9 q^{4} - 2 q^{5} - q^{6} + 3 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + q^2 - 5 * q^3 + 9 * q^4 - 2 * q^5 - q^6 + 3 * q^8 + 5 * q^9	\( 5 q + q^{2} - 5 q^{3} + 9 q^{4} - 2 q^{5} - q^{6} + 3 q^{8} + 5 q^{9} - 2 q^{11} - 9 q^{12} - 4 q^{13} + 2 q^{15} + q^{16} - 2 q^{17} + q^{18} - 8 q^{19} - 12 q^{20} - 16 q^{22} + 5 q^{23} - 3 q^{24} + 5 q^{25} - 16 q^{26} - 5 q^{27} + 4 q^{29} - 12 q^{31} + 7 q^{32} + 2 q^{33} - 10 q^{34} + 9 q^{36} - 6 q^{37} + 8 q^{38} + 4 q^{39} - 30 q^{40} - 6 q^{41} - 24 q^{43} + 16 q^{44} - 2 q^{45} + q^{46} - 24 q^{47} - q^{48} - 3 q^{50} + 2 q^{51} + 4 q^{52} + 2 q^{53} - q^{54} - 8 q^{55} + 8 q^{57} + 4 q^{58} - 16 q^{59} + 12 q^{60} - 22 q^{61} - 6 q^{62} - 29 q^{64} + 22 q^{65} + 16 q^{66} - 16 q^{67} - 14 q^{68} - 5 q^{69} + 16 q^{71} + 3 q^{72} + 8 q^{74} - 5 q^{75} - 30 q^{76} + 16 q^{78} + 12 q^{79} + 6 q^{80} + 5 q^{81} - 24 q^{82} - 10 q^{83} - 14 q^{85} - 20 q^{86} - 4 q^{87} - 8 q^{88} + 16 q^{89} + 9 q^{92} + 12 q^{93} + 32 q^{94} + 18 q^{95} - 7 q^{96} + 4 q^{97} - 2 q^{99}+O(q^{100}) \) 5 * q + q^2 - 5 * q^3 + 9 * q^4 - 2 * q^5 - q^6 + 3 * q^8 + 5 * q^9 - 2 * q^11 - 9 * q^12 - 4 * q^13 + 2 * q^15 + q^16 - 2 * q^17 + q^18 - 8 * q^19 - 12 * q^20 - 16 * q^22 + 5 * q^23 - 3 * q^24 + 5 * q^25 - 16 * q^26 - 5 * q^27 + 4 * q^29 - 12 * q^31 + 7 * q^32 + 2 * q^33 - 10 * q^34 + 9 * q^36 - 6 * q^37 + 8 * q^38 + 4 * q^39 - 30 * q^40 - 6 * q^41 - 24 * q^43 + 16 * q^44 - 2 * q^45 + q^46 - 24 * q^47 - q^48 - 3 * q^50 + 2 * q^51 + 4 * q^52 + 2 * q^53 - q^54 - 8 * q^55 + 8 * q^57 + 4 * q^58 - 16 * q^59 + 12 * q^60 - 22 * q^61 - 6 * q^62 - 29 * q^64 + 22 * q^65 + 16 * q^66 - 16 * q^67 - 14 * q^68 - 5 * q^69 + 16 * q^71 + 3 * q^72 + 8 * q^74 - 5 * q^75 - 30 * q^76 + 16 * q^78 + 12 * q^79 + 6 * q^80 + 5 * q^81 - 24 * q^82 - 10 * q^83 - 14 * q^85 - 20 * q^86 - 4 * q^87 - 8 * q^88 + 16 * q^89 + 9 * q^92 + 12 * q^93 + 32 * q^94 + 18 * q^95 - 7 * q^96 + 4 * q^97 - 2 * q^99

Introduction

L-functions

Modular forms

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Database

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