LMFDB - Embedded newform 3381.2.a.z.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:	$0$
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	$-0.270455\pi$
$5$	2.95267	1.32048	0.660238	+	0.751056i	$0.270455\pi$
$6$	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	$-0.351029\pi$
$13$	3.25299	0.902218	0.451109	+	0.892469i	$0.351029\pi$
$14$	0	0
$15$	2.95267	0.762377
$16$	5.15736	1.28934
$17$	−2.43560	−0.590719	−0.295359	−	0.955386i	$-0.595439\pi$
$17$	−2.43560	−0.590719	−0.295359	+	0.955386i	$0.595439\pi$
$18$	2.48738	0.586281
$19$	−0.970302	−0.222602	−0.111301	−	0.993787i	$-0.535502\pi$
$19$	−0.970302	−0.222602	−0.111301	+	0.993787i	$0.535502\pi$
$20$	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	$-0.435693\pi$
$31$	2.23439	0.401308	0.200654	+	0.979662i	$0.435693\pi$
$32$	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	$-0.480872\pi$
$41$	0.769093	0.120112	0.0600561	+	0.998195i	$0.480872\pi$
$42$	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	$-0.615832\pi$
$47$	−4.88011	−0.711837	−0.355919	+	0.934517i	$0.615832\pi$
$48$	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	$-0.320202\pi$
$59$	8.22329	1.07058	0.535291	+	0.844668i	$0.320202\pi$
$60$	12.3630	1.59606
$61$	−7.13658	−0.913746	−0.456873	−	0.889532i	$-0.651031\pi$
$61$	−7.13658	−0.913746	−0.456873	+	0.889532i	$0.651031\pi$
$62$	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	$-0.195749\pi$
$73$	13.9574	1.63359	0.816795	+	0.576928i	$0.195749\pi$
$74$	−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	$-0.327249\pi$
$83$	9.41036	1.03292	0.516460	+	0.856311i	$0.327249\pi$
$84$	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	$-0.375428\pi$
$89$	7.19701	0.762882	0.381441	+	0.924393i	$0.375428\pi$
$90$	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	$-0.476724\pi$
$97$	1.43908	0.146116	0.0730580	+	0.997328i	$0.476724\pi$
$98$	0	0
$99$	−0.300319	−0.0301832
$100$	15.5687	1.55687
$101$	13.5633	1.34959	0.674797	−	0.738003i	$-0.264231\pi$
$101$	13.5633	1.34959	0.674797	+	0.738003i	$0.264231\pi$
$102$	−6.05825	−0.599856
$103$	−13.3489	−1.31530	−0.657652	−	0.753322i	$-0.728450\pi$
$103$	−13.3489	−1.31530	−0.657652	+	0.753322i	$0.728450\pi$
$104$	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	$-0.754742\pi$
$131$	−16.4257	−1.43512	−0.717562	+	0.696495i	$0.754742\pi$
$132$	−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	$-0.140069\pi$
$139$	21.3333	1.80947	0.904735	+	0.425975i	$0.140069\pi$
$140$	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	$-0.754149\pi$
$157$	−17.9495	−1.43253	−0.716264	+	0.697830i	$0.754149\pi$
$158$	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	$-0.578942\pi$
$167$	−6.34436	−0.490941	−0.245471	+	0.969404i	$0.578942\pi$
$168$	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	$-0.706468\pi$
$173$	−15.8915	−1.20821	−0.604103	+	0.796906i	$0.706468\pi$
$174$	−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	$-0.0931740\pi$
$181$	25.7627	1.91493	0.957464	+	0.288553i	$0.0931740\pi$
$182$	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	$-0.704544\pi$
$199$	−16.9076	−1.19855	−0.599273	+	0.800545i	$0.704544\pi$
$200$	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	$-0.385657\pi$
$223$	10.4994	0.703089	0.351544	+	0.936171i	$0.385657\pi$
$224$	0	0
$225$	3.71829	0.247886
$226$	26.5952	1.76909
$227$	−14.8428	−0.985151	−0.492576	−	0.870270i	$-0.663945\pi$
$227$	−14.8428	−0.985151	−0.492576	+	0.870270i	$0.663945\pi$
$228$	−4.06271	−0.269060
$229$	14.6129	0.965646	0.482823	−	0.875718i	$-0.339611\pi$
$229$	14.6129	0.965646	0.482823	+	0.875718i	$0.339611\pi$
$230$	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	$-0.469345\pi$
$241$	2.98553	0.192315	0.0961573	+	0.995366i	$0.469345\pi$
$242$	−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	$-0.382762\pi$
$251$	11.4083	0.720084	0.360042	+	0.932936i	$0.382762\pi$
$252$	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	$-0.618022\pi$
$257$	−11.6175	−0.724679	−0.362339	+	0.932046i	$0.618022\pi$
$258$	−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	$-0.525178\pi$
$269$	−2.59193	−0.158033	−0.0790164	+	0.996873i	$0.525178\pi$
$270$	7.34443	0.446967
$271$	15.9415	0.968378	0.484189	−	0.874963i	$-0.339115\pi$
$271$	15.9415	0.968378	0.484189	+	0.874963i	$0.339115\pi$
$272$	−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	$-0.427275\pi$
$283$	7.62027	0.452978	0.226489	+	0.974014i	$0.427275\pi$
$284$	−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	$-0.677194\pi$
$293$	−18.0882	−1.05672	−0.528362	+	0.849019i	$0.677194\pi$
$294$	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	$-0.266197\pi$
$307$	23.4867	1.34045	0.670227	+	0.742156i	$0.266197\pi$
$308$	0	0
$309$	−13.3489	−0.759392
$310$	16.4103	0.932042
$311$	1.53578	0.0870863	0.0435431	−	0.999052i	$-0.486135\pi$
$311$	1.53578	0.0870863	0.0435431	+	0.999052i	$0.486135\pi$
$312$	17.6965	1.00186
$313$	−32.8316	−1.85575	−0.927876	−	0.372890i	$-0.878367\pi$
$313$	−32.8316	−1.85575	−0.927876	+	0.372890i	$0.878367\pi$
$314$	−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	$-0.335921\pi$
$349$	18.4178	0.985884	0.492942	+	0.870062i	$0.335921\pi$
$350$	0	0
$351$	3.25299	0.173632
$352$	−0.585085	−0.0311852
$353$	24.6832	1.31376	0.656878	−	0.753997i	$-0.271877\pi$
$353$	24.6832	1.31376	0.656878	+	0.753997i	$0.271877\pi$
$354$	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	$-0.455611\pi$
$367$	5.32575	0.278002	0.139001	+	0.990292i	$0.455611\pi$
$368$	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	$-0.621855\pi$
$383$	−14.6206	−0.747075	−0.373538	+	0.927615i	$0.621855\pi$
$384$	−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	$-0.542355\pi$
$397$	−5.28687	−0.265341	−0.132670	+	0.991160i	$0.542355\pi$
$398$	−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	$-0.581606\pi$
$409$	−10.2564	−0.507145	−0.253573	+	0.967316i	$0.581606\pi$
$410$	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	$-0.680408\pi$
$419$	−21.9805	−1.07382	−0.536910	+	0.843640i	$0.680408\pi$
$420$	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	$-0.777658\pi$
$433$	−31.8706	−1.53160	−0.765802	+	0.643076i	$0.777658\pi$
$434$	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	$-0.460428\pi$
$439$	5.19608	0.247995	0.123998	+	0.992283i	$0.460428\pi$
$440$	−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	$-0.473701\pi$
$461$	3.54389	0.165055	0.0825276	+	0.996589i	$0.473701\pi$
$462$	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	$-0.205901\pi$
$467$	34.4891	1.59596	0.797982	+	0.602681i	$0.205901\pi$
$468$	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	$-0.838570\pi$
$479$	−38.2627	−1.74827	−0.874134	+	0.485685i	$0.838570\pi$
$480$	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	$-0.333700\pi$
$503$	22.3829	0.998006	0.499003	+	0.866600i	$0.333700\pi$
$504$	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	$-0.705188\pi$
$509$	−27.1135	−1.20178	−0.600891	+	0.799331i	$0.705188\pi$
$510$	−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	$-0.520912\pi$
$521$	−2.99695	−0.131299	−0.0656493	+	0.997843i	$0.520912\pi$
$522$	−16.9384	−0.741372
$523$	33.6062	1.46950	0.734748	−	0.678341i	$-0.237301\pi$
$523$	33.6062	1.46950	0.734748	+	0.678341i	$0.237301\pi$
$524$	−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	$-0.334035\pi$
$563$	23.6370	0.996179	0.498090	+	0.867125i	$0.334035\pi$
$564$	−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	$-0.372091\pi$
$577$	18.7896	0.782222	0.391111	+	0.920344i	$0.372091\pi$
$578$	−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	$-0.363997\pi$
$587$	20.0795	0.828770	0.414385	+	0.910102i	$0.363997\pi$
$588$	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	$-0.696018\pi$
$593$	−28.1319	−1.15524	−0.577619	+	0.816307i	$0.696018\pi$
$594$	−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	$-0.164592\pi$
$601$	42.6206	1.73853	0.869266	+	0.494345i	$0.164592\pi$
$602$	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	$-0.717781\pi$
$607$	−31.1435	−1.26408	−0.632038	+	0.774937i	$0.717781\pi$
$608$	−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	$-0.575232\pi$
$619$	−11.6514	−0.468308	−0.234154	+	0.972200i	$0.575232\pi$
$620$	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	$-0.363266\pi$
$643$	21.1214	0.832945	0.416473	+	0.909148i	$0.363266\pi$
$644$	0	0
$645$	−21.4157	−0.843244
$646$	5.87833	0.231280
$647$	39.7268	1.56182	0.780910	−	0.624644i	$-0.214756\pi$
$647$	39.7268	1.56182	0.780910	+	0.624644i	$0.214756\pi$
$648$	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	$-0.608940\pi$
$661$	−17.2566	−0.671204	−0.335602	+	0.942004i	$0.608940\pi$
$662$	−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	$-0.580848\pi$
$677$	−13.0756	−0.502537	−0.251269	+	0.967917i	$0.580848\pi$
$678$	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	$-0.339515\pi$
$691$	25.3978	0.966178	0.483089	+	0.875571i	$0.339515\pi$
$692$	−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	$-0.186596\pi$
$719$	44.6748	1.66609	0.833044	+	0.553207i	$0.186596\pi$
$720$	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	$-0.639479\pi$
$727$	−22.8807	−0.848596	−0.424298	+	0.905523i	$0.639479\pi$
$728$	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	$-0.759186\pi$
$733$	−39.3772	−1.45443	−0.727215	+	0.686410i	$0.759186\pi$
$734$	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	$-0.382510\pi$
$761$	19.9052	0.721564	0.360782	+	0.932650i	$0.382510\pi$
$762$	−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	$-0.373322\pi$
$769$	21.4940	0.775094	0.387547	+	0.921850i	$0.373322\pi$
$770$	0	0
$771$	−11.6175	−0.418393
$772$	83.5029	3.00534
$773$	−32.5346	−1.17019	−0.585093	−	0.810966i	$-0.698942\pi$
$773$	−32.5346	−1.17019	−0.585093	+	0.810966i	$0.698942\pi$
$774$	−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	$-0.595343\pi$
$787$	−16.5555	−0.590140	−0.295070	+	0.955476i	$0.595343\pi$
$788$	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	$-0.457129\pi$
$797$	7.58157	0.268553	0.134277	+	0.990944i	$0.457129\pi$
$798$	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	$-0.530916\pi$
$811$	−5.52322	−0.193946	−0.0969732	+	0.995287i	$0.530916\pi$
$812$	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	$-0.678502\pi$
$829$	−30.6262	−1.06369	−0.531846	+	0.846841i	$0.678502\pi$
$830$	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	$-0.476027\pi$
$839$	4.35888	0.150485	0.0752426	+	0.997165i	$0.476027\pi$
$840$	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	$-0.783793\pi$
$853$	−45.4480	−1.55611	−0.778055	+	0.628197i	$0.783793\pi$
$854$	0	0
$855$	−2.86498	−0.0979804
$856$	10.7842	0.368597
$857$	23.1141	0.789563	0.394781	−	0.918775i	$-0.370820\pi$
$857$	23.1141	0.789563	0.394781	+	0.918775i	$0.370820\pi$
$858$	−2.43001	−0.0829591
$859$	−8.90579	−0.303862	−0.151931	−	0.988391i	$-0.548549\pi$
$859$	−8.90579	−0.303862	−0.151931	+	0.988391i	$0.548549\pi$
$860$	−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	$-0.454176\pi$
$881$	8.51644	0.286926	0.143463	+	0.989656i	$0.454176\pi$
$882$	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	$-0.503422\pi$
$887$	−0.640317	−0.0214997	−0.0107499	+	0.999942i	$0.503422\pi$
$888$	−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	$-0.371208\pi$
$929$	23.9973	0.787326	0.393663	+	0.919255i	$0.371208\pi$
$930$	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	$-0.222985\pi$
$937$	46.8035	1.52900	0.764502	+	0.644621i	$0.222985\pi$
$938$	0	0
$939$	−32.8316	−1.07142
$940$	−60.3330	−1.96784
$941$	−11.4806	−0.374257	−0.187129	−	0.982335i	$-0.559918\pi$
$941$	−11.4806	−0.374257	−0.187129	+	0.982335i	$0.559918\pi$
$942$	−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	$-0.809919\pi$
$971$	−51.5362	−1.65388	−0.826938	+	0.562293i	$0.809919\pi$
$972$	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	$-0.156099\pi$
$983$	55.3155	1.76429	0.882145	+	0.470977i	$0.156099\pi$
$984$	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	$-0.157471\pi$
$997$	55.5793	1.76021	0.880107	+	0.474775i	$0.157471\pi$
$998$	−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.z.1.5	yes	5
7.6	odd	2		3381.2.a.y.1.5	✓	5

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3381 = 3 \cdot 7^{2} \cdot 23 \)
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

Varieties

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Database

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