LMFDB - Embedded newform 3381.2.a.z.1.2

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			1.2
Root			$-1.67261$ 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)

$f(q)$	$=$	$q-1.67261 q^{2} +1.00000 q^{3} +0.797614 q^{4} +3.68373 q^{5} -1.67261 q^{6} +2.01112 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.67261 q^{2} +1.00000 q^{3} +0.797614 q^{4} +3.68373 q^{5} -1.67261 q^{6} +2.01112 q^{8} +1.00000 q^{9} -6.16143 q^{10} +0.470221 q^{11} +0.797614 q^{12} +3.21351 q^{13} +3.68373 q^{15} -4.95904 q^{16} -0.599679 q^{17} -1.67261 q^{18} +5.75665 q^{19} +2.93819 q^{20} -0.786495 q^{22} +1.00000 q^{23} +2.01112 q^{24} +8.56984 q^{25} -5.37493 q^{26} +1.00000 q^{27} +1.80509 q^{29} -6.16143 q^{30} -1.88611 q^{31} +4.27229 q^{32} +0.470221 q^{33} +1.00303 q^{34} +0.797614 q^{36} +3.09153 q^{37} -9.62862 q^{38} +3.21351 q^{39} +7.40841 q^{40} -8.24245 q^{41} -7.21351 q^{43} +0.375055 q^{44} +3.68373 q^{45} -1.67261 q^{46} +1.97776 q^{47} -4.95904 q^{48} -14.3340 q^{50} -0.599679 q^{51} +2.56314 q^{52} +6.14728 q^{53} -1.67261 q^{54} +1.73217 q^{55} +5.75665 q^{57} -3.01921 q^{58} +1.45685 q^{59} +2.93819 q^{60} +12.8928 q^{61} +3.15472 q^{62} +2.77222 q^{64} +11.8377 q^{65} -0.786495 q^{66} -0.504513 q^{67} -0.478313 q^{68} +1.00000 q^{69} +7.48882 q^{71} +2.01112 q^{72} -12.0409 q^{73} -5.17091 q^{74} +8.56984 q^{75} +4.59159 q^{76} -5.37493 q^{78} +13.5125 q^{79} -18.2677 q^{80} +1.00000 q^{81} +13.7864 q^{82} -0.745535 q^{83} -2.20905 q^{85} +12.0654 q^{86} +1.80509 q^{87} +0.945670 q^{88} -14.0617 q^{89} -6.16143 q^{90} +0.797614 q^{92} -1.88611 q^{93} -3.30802 q^{94} +21.2059 q^{95} +4.27229 q^{96} -13.5289 q^{97} +0.470221 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.67261	−1.18271	−0.591356	−	0.806411i	$-0.701407\pi$
$2$	−1.67261	−1.18271	−0.591356	+	0.806411i	$0.701407\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.797614	0.398807
$5$	3.68373	1.64741	0.823706	−	0.567017i	$-0.191903\pi$
$5$	3.68373	1.64741	0.823706	+	0.567017i	$0.191903\pi$
$6$	−1.67261	−0.682839
$7$	0	0
$7$	0	0
$8$	2.01112	0.711038
$9$	1.00000	0.333333
$10$	−6.16143	−1.94841
$11$	0.470221	0.141777	0.0708885	−	0.997484i	$-0.477417\pi$
$11$	0.470221	0.141777	0.0708885	+	0.997484i	$0.477417\pi$
$12$	0.797614	0.230251
$13$	3.21351	0.891266	0.445633	−	0.895216i	$-0.352979\pi$
$13$	3.21351	0.891266	0.445633	+	0.895216i	$0.352979\pi$
$14$	0	0
$15$	3.68373	0.951134
$16$	−4.95904	−1.23976
$17$	−0.599679	−0.145444	−0.0727218	−	0.997352i	$-0.523169\pi$
$17$	−0.599679	−0.145444	−0.0727218	+	0.997352i	$0.523169\pi$
$18$	−1.67261	−0.394237
$19$	5.75665	1.32067	0.660333	−	0.750972i	$-0.270415\pi$
$19$	5.75665	1.32067	0.660333	+	0.750972i	$0.270415\pi$
$20$	2.93819	0.657000
$21$	0	0
$22$	−0.786495	−0.167681
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	2.01112	0.410518
$25$	8.56984	1.71397
$26$	−5.37493	−1.05411
$27$	1.00000	0.192450
$28$	0	0
$29$	1.80509	0.335197	0.167599	−	0.985855i	$-0.446399\pi$
$29$	1.80509	0.335197	0.167599	+	0.985855i	$0.446399\pi$
$30$	−6.16143	−1.12492
$31$	−1.88611	−0.338756	−0.169378	−	0.985551i	$-0.554176\pi$
$31$	−1.88611	−0.338756	−0.169378	+	0.985551i	$0.554176\pi$
$32$	4.27229	0.755241
$33$	0.470221	0.0818550
$34$	1.00303	0.172018
$35$	0	0
$36$	0.797614	0.132936
$37$	3.09153	0.508244	0.254122	−	0.967172i	$-0.418214\pi$
$37$	3.09153	0.508244	0.254122	+	0.967172i	$0.418214\pi$
$38$	−9.62862	−1.56197
$39$	3.21351	0.514573
$40$	7.40841	1.17137
$41$	−8.24245	−1.28725	−0.643627	−	0.765339i	$-0.722571\pi$
$41$	−8.24245	−1.28725	−0.643627	+	0.765339i	$0.722571\pi$
$42$	0	0
$43$	−7.21351	−1.10005	−0.550025	−	0.835148i	$-0.685382\pi$
$43$	−7.21351	−1.10005	−0.550025	+	0.835148i	$0.685382\pi$
$44$	0.375055	0.0565416
$45$	3.68373	0.549137
$46$	−1.67261	−0.246612
$47$	1.97776	0.288486	0.144243	−	0.989542i	$-0.453925\pi$
$47$	1.97776	0.288486	0.144243	+	0.989542i	$0.453925\pi$
$48$	−4.95904	−0.715776
$49$	0	0
$50$	−14.3340	−2.02713
$51$	−0.599679	−0.0839719
$52$	2.56314	0.355443
$53$	6.14728	0.844394	0.422197	−	0.906504i	$-0.361259\pi$
$53$	6.14728	0.844394	0.422197	+	0.906504i	$0.361259\pi$
$54$	−1.67261	−0.227613
$55$	1.73217	0.233565
$56$	0	0
$57$	5.75665	0.762487
$58$	−3.01921	−0.396442
$59$	1.45685	0.189666	0.0948329	−	0.995493i	$-0.469768\pi$
$59$	1.45685	0.189666	0.0948329	+	0.995493i	$0.469768\pi$
$60$	2.93819	0.379319
$61$	12.8928	1.65076	0.825378	−	0.564581i	$-0.190962\pi$
$61$	12.8928	1.65076	0.825378	+	0.564581i	$0.190962\pi$
$62$	3.15472	0.400650
$63$	0	0
$64$	2.77222	0.346528
$65$	11.8377	1.46828
$66$	−0.786495	−0.0968108
$67$	−0.504513	−0.0616361	−0.0308180	−	0.999525i	$-0.509811\pi$
$67$	−0.504513	−0.0616361	−0.0308180	+	0.999525i	$0.509811\pi$
$68$	−0.478313	−0.0580039
$69$	1.00000	0.120386
$70$	0	0
$71$	7.48882	0.888759	0.444380	−	0.895839i	$-0.353424\pi$
$71$	7.48882	0.888759	0.444380	+	0.895839i	$0.353424\pi$
$72$	2.01112	0.237013
$73$	−12.0409	−1.40928	−0.704639	−	0.709566i	$-0.748891\pi$
$73$	−12.0409	−1.40928	−0.704639	+	0.709566i	$0.748891\pi$
$74$	−5.17091	−0.601106
$75$	8.56984	0.989560
$76$	4.59159	0.526691
$77$	0	0
$78$	−5.37493	−0.608591
$79$	13.5125	1.52027	0.760136	−	0.649763i	$-0.225132\pi$
$79$	13.5125	1.52027	0.760136	+	0.649763i	$0.225132\pi$
$80$	−18.2677	−2.04240
$81$	1.00000	0.111111
$82$	13.7864	1.52245
$83$	−0.745535	−0.0818331	−0.0409165	−	0.999163i	$-0.513028\pi$
$83$	−0.745535	−0.0818331	−0.0409165	+	0.999163i	$0.513028\pi$
$84$	0	0
$85$	−2.20905	−0.239606
$86$	12.0654	1.30104
$87$	1.80509	0.193526
$88$	0.945670	0.100809
$89$	−14.0617	−1.49054	−0.745268	−	0.666765i	$-0.767678\pi$
$89$	−14.0617	−1.49054	−0.745268	+	0.666765i	$0.767678\pi$
$90$	−6.16143	−0.649471
$91$	0	0
$92$	0.797614	0.0831570
$93$	−1.88611	−0.195581
$94$	−3.30802	−0.341196
$95$	21.2059	2.17568
$96$	4.27229	0.436038
$97$	−13.5289	−1.37365	−0.686825	−	0.726823i	$-0.740996\pi$
$97$	−13.5289	−1.37365	−0.686825	+	0.726823i	$0.740996\pi$
$98$	0	0
$99$	0.470221	0.0472590
$100$	6.83542	0.683542
$101$	−5.11601	−0.509062	−0.254531	−	0.967065i	$-0.581921\pi$
$101$	−5.11601	−0.509062	−0.254531	+	0.967065i	$0.581921\pi$
$102$	1.00303	0.0993145
$103$	1.74999	0.172431	0.0862156	−	0.996277i	$-0.472523\pi$
$103$	1.74999	0.172431	0.0862156	+	0.996277i	$0.472523\pi$
$104$	6.46274	0.633724
$105$	0	0
$106$	−10.2820	−0.998674
$107$	9.44038	0.912636	0.456318	−	0.889817i	$-0.349168\pi$
$107$	9.44038	0.912636	0.456318	+	0.889817i	$0.349168\pi$
$108$	0.797614	0.0767504
$109$	−19.4225	−1.86034	−0.930168	−	0.367135i	$-0.880339\pi$
$109$	−19.4225	−1.86034	−0.930168	+	0.367135i	$0.880339\pi$
$110$	−2.89723	−0.276240
$111$	3.09153	0.293435
$112$	0	0
$113$	−4.31537	−0.405956	−0.202978	−	0.979183i	$-0.565062\pi$
$113$	−4.31537	−0.405956	−0.202978	+	0.979183i	$0.565062\pi$
$114$	−9.62862	−0.901803
$115$	3.68373	0.343509
$116$	1.43977	0.133679
$117$	3.21351	0.297089
$118$	−2.43674	−0.224320
$119$	0	0
$120$	7.40841	0.676292
$121$	−10.7789	−0.979899
$122$	−21.5646	−1.95237
$123$	−8.24245	−0.743196
$124$	−1.50439	−0.135098
$125$	13.1503	1.17620
$126$	0	0
$127$	17.8927	1.58772	0.793860	−	0.608101i	$-0.208068\pi$
$127$	17.8927	1.58772	0.793860	+	0.608101i	$0.208068\pi$
$128$	−13.1814	−1.16508
$129$	−7.21351	−0.635114
$130$	−19.7998	−1.73656
$131$	1.65340	0.144458	0.0722289	−	0.997388i	$-0.476989\pi$
$131$	1.65340	0.144458	0.0722289	+	0.997388i	$0.476989\pi$
$132$	0.375055	0.0326443
$133$	0	0
$134$	0.843852	0.0728977
$135$	3.68373	0.317045
$136$	−1.20603	−0.103416
$137$	7.81543	0.667718	0.333859	−	0.942623i	$-0.391649\pi$
$137$	7.81543	0.667718	0.333859	+	0.942623i	$0.391649\pi$
$138$	−1.67261	−0.142382
$139$	5.18154	0.439492	0.219746	−	0.975557i	$-0.429477\pi$
$139$	5.18154	0.439492	0.219746	+	0.975557i	$0.429477\pi$
$140$	0	0
$141$	1.97776	0.166558
$142$	−12.5259	−1.05115
$143$	1.51106	0.126361
$144$	−4.95904	−0.413253
$145$	6.64947	0.552208
$146$	20.1396	1.66677
$147$	0	0
$148$	2.46584	0.202691
$149$	15.7990	1.29430	0.647151	−	0.762362i	$-0.275960\pi$
$149$	15.7990	1.29430	0.647151	+	0.762362i	$0.275960\pi$
$150$	−14.3340	−1.17036
$151$	−19.1397	−1.55756	−0.778782	−	0.627294i	$-0.784162\pi$
$151$	−19.1397	−1.55756	−0.778782	+	0.627294i	$0.784162\pi$
$152$	11.5773	0.939044
$153$	−0.599679	−0.0484812
$154$	0	0
$155$	−6.94792	−0.558070
$156$	2.56314	0.205215
$157$	−1.30957	−0.104515	−0.0522576	−	0.998634i	$-0.516642\pi$
$157$	−1.30957	−0.104515	−0.0522576	+	0.998634i	$0.516642\pi$
$158$	−22.6011	−1.79804
$159$	6.14728	0.487511
$160$	15.7379	1.24419
$161$	0	0
$162$	−1.67261	−0.131412
$163$	−9.45011	−0.740190	−0.370095	−	0.928994i	$-0.620675\pi$
$163$	−9.45011	−0.740190	−0.370095	+	0.928994i	$0.620675\pi$
$164$	−6.57429	−0.513366
$165$	1.73217	0.134849
$166$	1.24699	0.0967849
$167$	1.79475	0.138882	0.0694410	−	0.997586i	$-0.477878\pi$
$167$	1.79475	0.138882	0.0694410	+	0.997586i	$0.477878\pi$
$168$	0	0
$169$	−2.67338	−0.205645
$170$	3.69488	0.283384
$171$	5.75665	0.440222
$172$	−5.75359	−0.438707
$173$	13.4568	1.02310	0.511549	−	0.859254i	$-0.329072\pi$
$173$	13.4568	1.02310	0.511549	+	0.859254i	$0.329072\pi$
$174$	−3.01921	−0.228886
$175$	0	0
$176$	−2.33184	−0.175769
$177$	1.45685	0.109504
$178$	23.5197	1.76287
$179$	−15.1970	−1.13588	−0.567940	−	0.823070i	$-0.692259\pi$
$179$	−15.1970	−1.13588	−0.567940	+	0.823070i	$0.692259\pi$
$180$	2.93819	0.219000
$181$	−12.6241	−0.938340	−0.469170	−	0.883108i	$-0.655447\pi$
$181$	−12.6241	−0.938340	−0.469170	+	0.883108i	$0.655447\pi$
$182$	0	0
$183$	12.8928	0.953064
$184$	2.01112	0.148262
$185$	11.3883	0.837287
$186$	3.15472	0.231316
$187$	−0.281982	−0.0206205
$188$	1.57749	0.115050
$189$	0	0
$190$	−35.4692	−2.57321
$191$	15.9343	1.15296	0.576481	−	0.817110i	$-0.304425\pi$
$191$	15.9343	1.15296	0.576481	+	0.817110i	$0.304425\pi$
$192$	2.77222	0.200068
$193$	−20.7054	−1.49041	−0.745203	−	0.666838i	$-0.767647\pi$
$193$	−20.7054	−1.49041	−0.745203	+	0.666838i	$0.767647\pi$
$194$	22.6285	1.62463
$195$	11.8377	0.847713
$196$	0	0
$197$	−6.20149	−0.441838	−0.220919	−	0.975292i	$-0.570906\pi$
$197$	−6.20149	−0.441838	−0.220919	+	0.975292i	$0.570906\pi$
$198$	−0.786495	−0.0558937
$199$	−16.3114	−1.15629	−0.578143	−	0.815936i	$-0.696222\pi$
$199$	−16.3114	−1.15629	−0.578143	+	0.815936i	$0.696222\pi$
$200$	17.2350	1.21870
$201$	−0.504513	−0.0355856
$202$	8.55708	0.602074
$203$	0	0
$204$	−0.478313	−0.0334886
$205$	−30.3629	−2.12064
$206$	−2.92704	−0.203936
$207$	1.00000	0.0695048
$208$	−15.9359	−1.10496
$209$	2.70690	0.187240
$210$	0	0
$211$	−19.0644	−1.31245	−0.656225	−	0.754566i	$-0.727848\pi$
$211$	−19.0644	−1.31245	−0.656225	+	0.754566i	$0.727848\pi$
$212$	4.90316	0.336750
$213$	7.48882	0.513125
$214$	−15.7900	−1.07939
$215$	−26.5726	−1.81223
$216$	2.01112	0.136839
$217$	0	0
$218$	32.4862	2.20024
$219$	−12.0409	−0.813647
$220$	1.38160	0.0931474
$221$	−1.92707	−0.129629
$222$	−5.17091	−0.347049
$223$	6.18141	0.413938	0.206969	−	0.978347i	$-0.433640\pi$
$223$	6.18141	0.413938	0.206969	+	0.978347i	$0.433640\pi$
$224$	0	0
$225$	8.56984	0.571323
$226$	7.21792	0.480129
$227$	14.5200	0.963727	0.481863	−	0.876246i	$-0.339960\pi$
$227$	14.5200	0.963727	0.481863	+	0.876246i	$0.339960\pi$
$228$	4.59159	0.304085
$229$	−12.2225	−0.807683	−0.403841	−	0.914829i	$-0.632325\pi$
$229$	−12.2225	−0.807683	−0.403841	+	0.914829i	$0.632325\pi$
$230$	−6.16143	−0.406272
$231$	0	0
$232$	3.63026	0.238338
$233$	−11.3162	−0.741346	−0.370673	−	0.928764i	$-0.620873\pi$
$233$	−11.3162	−0.741346	−0.370673	+	0.928764i	$0.620873\pi$
$234$	−5.37493	−0.351370
$235$	7.28553	0.475256
$236$	1.16200	0.0756401
$237$	13.5125	0.877730
$238$	0	0
$239$	−19.7343	−1.27651	−0.638254	−	0.769826i	$-0.720343\pi$
$239$	−19.7343	−1.27651	−0.638254	+	0.769826i	$0.720343\pi$
$240$	−18.2677	−1.17918
$241$	27.8145	1.79169	0.895846	−	0.444365i	$-0.146571\pi$
$241$	27.8145	1.79169	0.895846	+	0.444365i	$0.146571\pi$
$242$	18.0289	1.15894
$243$	1.00000	0.0641500
$244$	10.2835	0.658333
$245$	0	0
$246$	13.7864	0.878987
$247$	18.4990	1.17707
$248$	−3.79320	−0.240868
$249$	−0.745535	−0.0472463
$250$	−21.9953	−1.39110
$251$	9.76332	0.616255	0.308128	−	0.951345i	$-0.400298\pi$
$251$	9.76332	0.616255	0.308128	+	0.951345i	$0.400298\pi$
$252$	0	0
$253$	0.470221	0.0295625
$254$	−29.9274	−1.87781
$255$	−2.20905	−0.138336
$256$	16.5029	1.03143
$257$	28.6902	1.78964	0.894822	−	0.446423i	$-0.147302\pi$
$257$	28.6902	1.78964	0.894822	+	0.446423i	$0.147302\pi$
$258$	12.0654	0.751156
$259$	0	0
$260$	9.44189	0.585561
$261$	1.80509	0.111732
$262$	−2.76548	−0.170852
$263$	27.9327	1.72241	0.861204	−	0.508260i	$-0.169711\pi$
$263$	27.9327	1.72241	0.861204	+	0.508260i	$0.169711\pi$
$264$	0.945670	0.0582020
$265$	22.6449	1.39106
$266$	0	0
$267$	−14.0617	−0.860561
$268$	−0.402407	−0.0245809
$269$	−5.32282	−0.324538	−0.162269	−	0.986747i	$-0.551881\pi$
$269$	−5.32282	−0.324538	−0.162269	+	0.986747i	$0.551881\pi$
$270$	−6.16143	−0.374972
$271$	19.3934	1.17806	0.589032	−	0.808110i	$-0.299509\pi$
$271$	19.3934	1.17806	0.589032	+	0.808110i	$0.299509\pi$
$272$	2.97383	0.180315
$273$	0	0
$274$	−13.0722	−0.789717
$275$	4.02972	0.243001
$276$	0.797614	0.0480107
$277$	13.1785	0.791817	0.395909	−	0.918290i	$-0.370430\pi$
$277$	13.1785	0.791817	0.395909	+	0.918290i	$0.370430\pi$
$278$	−8.66668	−0.519793
$279$	−1.88611	−0.112919
$280$	0	0
$281$	12.2275	0.729433	0.364717	−	0.931119i	$-0.381166\pi$
$281$	12.2275	0.729433	0.364717	+	0.931119i	$0.381166\pi$
$282$	−3.30802	−0.196990
$283$	−4.52300	−0.268865	−0.134432	−	0.990923i	$-0.542921\pi$
$283$	−4.52300	−0.268865	−0.134432	+	0.990923i	$0.542921\pi$
$284$	5.97319	0.354443
$285$	21.2059	1.25613
$286$	−2.52741	−0.149449
$287$	0	0
$288$	4.27229	0.251747
$289$	−16.6404	−0.978846
$290$	−11.1219	−0.653103
$291$	−13.5289	−0.793077
$292$	−9.60397	−0.562030
$293$	7.38241	0.431285	0.215642	−	0.976472i	$-0.430815\pi$
$293$	7.38241	0.431285	0.215642	+	0.976472i	$0.430815\pi$
$294$	0	0
$295$	5.36664	0.312458
$296$	6.21743	0.361381
$297$	0.470221	0.0272850
$298$	−26.4255	−1.53079
$299$	3.21351	0.185842
$300$	6.83542	0.394643
$301$	0	0
$302$	32.0132	1.84215
$303$	−5.11601	−0.293907
$304$	−28.5475	−1.63731
$305$	47.4936	2.71948
$306$	1.00303	0.0573393
$307$	−17.3486	−0.990139	−0.495070	−	0.868853i	$-0.664857\pi$
$307$	−17.3486	−0.990139	−0.495070	+	0.868853i	$0.664857\pi$
$308$	0	0
$309$	1.74999	0.0995532
$310$	11.6211	0.660036
$311$	22.5267	1.27737	0.638685	−	0.769468i	$-0.279479\pi$
$311$	22.5267	1.27737	0.638685	+	0.769468i	$0.279479\pi$
$312$	6.46274	0.365881
$313$	−32.4118	−1.83202	−0.916012	−	0.401151i	$-0.868610\pi$
$313$	−32.4118	−1.83202	−0.916012	+	0.401151i	$0.868610\pi$
$314$	2.19040	0.123611
$315$	0	0
$316$	10.7777	0.606295
$317$	−9.58847	−0.538542	−0.269271	−	0.963064i	$-0.586783\pi$
$317$	−9.58847	−0.538542	−0.269271	+	0.963064i	$0.586783\pi$
$318$	−10.2820	−0.576585
$319$	0.848792	0.0475233
$320$	10.2121	0.570875
$321$	9.44038	0.526911
$322$	0	0
$323$	−3.45215	−0.192083
$324$	0.797614	0.0443119
$325$	27.5392	1.52760
$326$	15.8063	0.875431
$327$	−19.4225	−1.07407
$328$	−16.5765	−0.915286
$329$	0	0
$330$	−2.89723	−0.159487
$331$	29.4091	1.61647	0.808237	−	0.588858i	$-0.200422\pi$
$331$	29.4091	1.61647	0.808237	+	0.588858i	$0.200422\pi$
$332$	−0.594649	−0.0326356
$333$	3.09153	0.169415
$334$	−3.00191	−0.164257
$335$	−1.85849	−0.101540
$336$	0	0
$337$	−25.4350	−1.38553	−0.692766	−	0.721163i	$-0.743608\pi$
$337$	−25.4350	−1.38553	−0.692766	+	0.721163i	$0.743608\pi$
$338$	4.47152	0.243219
$339$	−4.31537	−0.234379
$340$	−1.76197	−0.0955564
$341$	−0.886889	−0.0480278
$342$	−9.62862	−0.520656
$343$	0	0
$344$	−14.5072	−0.782177
$345$	3.68373	0.198325
$346$	−22.5079	−1.21003
$347$	−1.16649	−0.0626205	−0.0313102	−	0.999510i	$-0.509968\pi$
$347$	−1.16649	−0.0626205	−0.0313102	+	0.999510i	$0.509968\pi$
$348$	1.43977	0.0771796
$349$	34.7734	1.86138	0.930689	−	0.365811i	$-0.119209\pi$
$349$	34.7734	1.86138	0.930689	+	0.365811i	$0.119209\pi$
$350$	0	0
$351$	3.21351	0.171524
$352$	2.00892	0.107076
$353$	24.6812	1.31365	0.656825	−	0.754043i	$-0.271899\pi$
$353$	24.6812	1.31365	0.656825	+	0.754043i	$0.271899\pi$
$354$	−2.43674	−0.129511
$355$	27.5868	1.46415
$356$	−11.2158	−0.594436
$357$	0	0
$358$	25.4187	1.34342
$359$	2.67117	0.140979	0.0704894	−	0.997513i	$-0.477544\pi$
$359$	2.67117	0.140979	0.0704894	+	0.997513i	$0.477544\pi$
$360$	7.40841	0.390458
$361$	14.1391	0.744161
$362$	21.1151	1.10979
$363$	−10.7789	−0.565745
$364$	0	0
$365$	−44.3553	−2.32166
$366$	−21.5646	−1.12720
$367$	−6.89437	−0.359883	−0.179942	−	0.983677i	$-0.557591\pi$
$367$	−6.89437	−0.359883	−0.179942	+	0.983677i	$0.557591\pi$
$368$	−4.95904	−0.258508
$369$	−8.24245	−0.429085
$370$	−19.0482	−0.990269
$371$	0	0
$372$	−1.50439	−0.0779990
$373$	7.87728	0.407870	0.203935	−	0.978984i	$-0.434627\pi$
$373$	7.87728	0.407870	0.203935	+	0.978984i	$0.434627\pi$
$374$	0.471645	0.0243882
$375$	13.1503	0.679079
$376$	3.97751	0.205125
$377$	5.80068	0.298750
$378$	0	0
$379$	9.66644	0.496532	0.248266	−	0.968692i	$-0.420139\pi$
$379$	9.66644	0.496532	0.248266	+	0.968692i	$0.420139\pi$
$380$	16.9142	0.867678
$381$	17.8927	0.916670
$382$	−26.6518	−1.36362
$383$	1.80354	0.0921565	0.0460783	−	0.998938i	$-0.485328\pi$
$383$	1.80354	0.0921565	0.0460783	+	0.998938i	$0.485328\pi$
$384$	−13.1814	−0.672661
$385$	0	0
$386$	34.6320	1.76272
$387$	−7.21351	−0.366683
$388$	−10.7908	−0.547821
$389$	7.49258	0.379889	0.189945	−	0.981795i	$-0.439169\pi$
$389$	7.49258	0.379889	0.189945	+	0.981795i	$0.439169\pi$
$390$	−19.7998	−1.00260
$391$	−0.599679	−0.0303271
$392$	0	0
$393$	1.65340	0.0834028
$394$	10.3726	0.522566
$395$	49.7763	2.50452
$396$	0.375055	0.0188472
$397$	−14.6621	−0.735871	−0.367936	−	0.929851i	$-0.619935\pi$
$397$	−14.6621	−0.735871	−0.367936	+	0.929851i	$0.619935\pi$
$398$	27.2826	1.36755
$399$	0	0
$400$	−42.4982	−2.12491
$401$	−18.2558	−0.911650	−0.455825	−	0.890069i	$-0.650656\pi$
$401$	−18.2558	−0.911650	−0.455825	+	0.890069i	$0.650656\pi$
$402$	0.843852	0.0420875
$403$	−6.06103	−0.301921
$404$	−4.08060	−0.203018
$405$	3.68373	0.183046
$406$	0	0
$407$	1.45370	0.0720572
$408$	−1.20603	−0.0597072
$409$	17.2581	0.853356	0.426678	−	0.904404i	$-0.359684\pi$
$409$	17.2581	0.853356	0.426678	+	0.904404i	$0.359684\pi$
$410$	50.7852	2.50810
$411$	7.81543	0.385507
$412$	1.39581	0.0687668
$413$	0	0
$414$	−1.67261	−0.0822041
$415$	−2.74635	−0.134813
$416$	13.7290	0.673120
$417$	5.18154	0.253741
$418$	−4.52758	−0.221451
$419$	6.89649	0.336915	0.168458	−	0.985709i	$-0.446121\pi$
$419$	6.89649	0.336915	0.168458	+	0.985709i	$0.446121\pi$
$420$	0	0
$421$	32.6760	1.59253	0.796266	−	0.604946i	$-0.206805\pi$
$421$	32.6760	1.59253	0.796266	+	0.604946i	$0.206805\pi$
$422$	31.8873	1.55225
$423$	1.97776	0.0961621
$424$	12.3629	0.600396
$425$	−5.13915	−0.249286
$426$	−12.5259	−0.606879
$427$	0	0
$428$	7.52978	0.363966
$429$	1.51106	0.0729545
$430$	44.4455	2.14335
$431$	−39.1679	−1.88665	−0.943325	−	0.331870i	$-0.892321\pi$
$431$	−39.1679	−1.88665	−0.943325	+	0.331870i	$0.892321\pi$
$432$	−4.95904	−0.238592
$433$	2.02386	0.0972605	0.0486303	−	0.998817i	$-0.484514\pi$
$433$	2.02386	0.0972605	0.0486303	+	0.998817i	$0.484514\pi$
$434$	0	0
$435$	6.64947	0.318818
$436$	−15.4916	−0.741915
$437$	5.75665	0.275378
$438$	20.1396	0.962309
$439$	12.9635	0.618714	0.309357	−	0.950946i	$-0.399886\pi$
$439$	12.9635	0.618714	0.309357	+	0.950946i	$0.399886\pi$
$440$	3.48359	0.166074
$441$	0	0
$442$	3.22323	0.153314
$443$	4.45555	0.211690	0.105845	−	0.994383i	$-0.466245\pi$
$443$	4.45555	0.211690	0.105845	+	0.994383i	$0.466245\pi$
$444$	2.46584	0.117024
$445$	−51.7994	−2.45553
$446$	−10.3391	−0.489569
$447$	15.7990	0.747265
$448$	0	0
$449$	13.9709	0.659329	0.329665	−	0.944098i	$-0.393064\pi$
$449$	13.9709	0.659329	0.329665	+	0.944098i	$0.393064\pi$
$450$	−14.3340	−0.675710
$451$	−3.87577	−0.182503
$452$	−3.44200	−0.161898
$453$	−19.1397	−0.899260
$454$	−24.2863	−1.13981
$455$	0	0
$456$	11.5773	0.542158
$457$	−20.9431	−0.979675	−0.489837	−	0.871814i	$-0.662944\pi$
$457$	−20.9431	−0.979675	−0.489837	+	0.871814i	$0.662944\pi$
$458$	20.4434	0.955256
$459$	−0.599679	−0.0279906
$460$	2.93819	0.136994
$461$	−29.6695	−1.38185	−0.690923	−	0.722928i	$-0.742796\pi$
$461$	−29.6695	−1.38185	−0.690923	+	0.722928i	$0.742796\pi$
$462$	0	0
$463$	39.6312	1.84182	0.920910	−	0.389776i	$-0.127447\pi$
$463$	39.6312	1.84182	0.920910	+	0.389776i	$0.127447\pi$
$464$	−8.95153	−0.415564
$465$	−6.94792	−0.322202
$466$	18.9275	0.876798
$467$	−28.1740	−1.30374	−0.651870	−	0.758331i	$-0.726015\pi$
$467$	−28.1740	−1.30374	−0.651870	+	0.758331i	$0.726015\pi$
$468$	2.56314	0.118481
$469$	0	0
$470$	−12.1858	−0.562090
$471$	−1.30957	−0.0603419
$472$	2.92990	0.134860
$473$	−3.39194	−0.155962
$474$	−22.6011	−1.03810
$475$	49.3336	2.26358
$476$	0	0
$477$	6.14728	0.281465
$478$	33.0078	1.50974
$479$	40.3717	1.84463	0.922316	−	0.386438i	$-0.126295\pi$
$479$	40.3717	1.84463	0.922316	+	0.386438i	$0.126295\pi$
$480$	15.7379	0.718335
$481$	9.93463	0.452980
$482$	−46.5228	−2.11905
$483$	0	0
$484$	−8.59740	−0.390791
$485$	−49.8367	−2.26297
$486$	−1.67261	−0.0758710
$487$	−39.2938	−1.78057	−0.890287	−	0.455401i	$-0.849496\pi$
$487$	−39.2938	−1.78057	−0.890287	+	0.455401i	$0.849496\pi$
$488$	25.9290	1.17375
$489$	−9.45011	−0.427349
$490$	0	0
$491$	19.3250	0.872124	0.436062	−	0.899917i	$-0.356373\pi$
$491$	19.3250	0.872124	0.436062	+	0.899917i	$0.356373\pi$
$492$	−6.57429	−0.296392
$493$	−1.08248	−0.0487523
$494$	−30.9416	−1.39213
$495$	1.73217	0.0778550
$496$	9.35331	0.419976
$497$	0	0
$498$	1.24699	0.0558788
$499$	16.6924	0.747254	0.373627	−	0.927579i	$-0.378114\pi$
$499$	16.6924	0.747254	0.373627	+	0.927579i	$0.378114\pi$
$500$	10.4889	0.469076
$501$	1.79475	0.0801836
$502$	−16.3302	−0.728852
$503$	−1.92491	−0.0858273	−0.0429136	−	0.999079i	$-0.513664\pi$
$503$	−1.92491	−0.0858273	−0.0429136	+	0.999079i	$0.513664\pi$
$504$	0	0
$505$	−18.8460	−0.838636
$506$	−0.786495	−0.0349640
$507$	−2.67338	−0.118729
$508$	14.2715	0.633194
$509$	−9.96280	−0.441594	−0.220797	−	0.975320i	$-0.570866\pi$
$509$	−9.96280	−0.441594	−0.220797	+	0.975320i	$0.570866\pi$
$510$	3.69488	0.163612
$511$	0	0
$512$	−1.24000	−0.0548006
$513$	5.75665	0.254162
$514$	−47.9874	−2.11663
$515$	6.44647	0.284065
$516$	−5.75359	−0.253288
$517$	0.929985	0.0409007
$518$	0	0
$519$	13.4568	0.590686
$520$	23.8070	1.04400
$521$	0.0311409	0.00136431	0.000682154	−	1.00000i	$-0.499783\pi$
$521$	0.0311409	0.00136431	0.000682154		1.00000i	$0.499783\pi$
$522$	−3.01921	−0.132147
$523$	7.89862	0.345383	0.172691	−	0.984976i	$-0.444754\pi$
$523$	7.89862	0.345383	0.172691	+	0.984976i	$0.444754\pi$
$524$	1.31877	0.0576108
$525$	0	0
$526$	−46.7205	−2.03711
$527$	1.13106	0.0492698
$528$	−2.33184	−0.101480
$529$	1.00000	0.0434783
$530$	−37.8760	−1.64523
$531$	1.45685	0.0632220
$532$	0	0
$533$	−26.4871	−1.14729
$534$	23.5197	1.01780
$535$	34.7758	1.50349
$536$	−1.01464	−0.0438256
$537$	−15.1970	−0.655800
$538$	8.90298	0.383835
$539$	0	0
$540$	2.93819	0.126440
$541$	−9.45968	−0.406703	−0.203352	−	0.979106i	$-0.565183\pi$
$541$	−9.45968	−0.406703	−0.203352	+	0.979106i	$0.565183\pi$
$542$	−32.4375	−1.39331
$543$	−12.6241	−0.541751
$544$	−2.56200	−0.109845
$545$	−71.5471	−3.06474
$546$	0	0
$547$	32.6105	1.39432	0.697162	−	0.716914i	$-0.254446\pi$
$547$	32.6105	1.39432	0.697162	+	0.716914i	$0.254446\pi$
$548$	6.23370	0.266290
$549$	12.8928	0.550252
$550$	−6.74013	−0.287400
$551$	10.3913	0.442684
$552$	2.01112	0.0855989
$553$	0	0
$554$	−22.0424	−0.936492
$555$	11.3883	0.483408
$556$	4.13287	0.175273
$557$	39.3106	1.66564	0.832822	−	0.553541i	$-0.186724\pi$
$557$	39.3106	1.66564	0.832822	+	0.553541i	$0.186724\pi$
$558$	3.15472	0.133550
$559$	−23.1806	−0.980436
$560$	0	0
$561$	−0.281982	−0.0119053
$562$	−20.4518	−0.862709
$563$	33.0618	1.39339	0.696695	−	0.717368i	$-0.254653\pi$
$563$	33.0618	1.39339	0.696695	+	0.717368i	$0.254653\pi$
$564$	1.57749	0.0664243
$565$	−15.8967	−0.668777
$566$	7.56521	0.317989
$567$	0	0
$568$	15.0609	0.631942
$569$	7.88088	0.330384	0.165192	−	0.986261i	$-0.447176\pi$
$569$	7.88088	0.330384	0.165192	+	0.986261i	$0.447176\pi$
$570$	−35.4692	−1.48564
$571$	−41.7874	−1.74875	−0.874375	−	0.485251i	$-0.838728\pi$
$571$	−41.7874	−1.74875	−0.874375	+	0.485251i	$0.838728\pi$
$572$	1.20524	0.0503936
$573$	15.9343	0.665663
$574$	0	0
$575$	8.56984	0.357387
$576$	2.77222	0.115509
$577$	−3.62802	−0.151037	−0.0755183	−	0.997144i	$-0.524061\pi$
$577$	−3.62802	−0.151037	−0.0755183	+	0.997144i	$0.524061\pi$
$578$	27.8328	1.15769
$579$	−20.7054	−0.860486
$580$	5.30371	0.220225
$581$	0	0
$582$	22.6285	0.937981
$583$	2.89058	0.119716
$584$	−24.2156	−1.00205
$585$	11.8377	0.489428
$586$	−12.3479	−0.510086
$587$	−1.11915	−0.0461923	−0.0230961	−	0.999733i	$-0.507352\pi$
$587$	−1.11915	−0.0461923	−0.0230961	+	0.999733i	$0.507352\pi$
$588$	0	0
$589$	−10.8577	−0.447384
$590$	−8.97628	−0.369548
$591$	−6.20149	−0.255095
$592$	−15.3310	−0.630100
$593$	−34.8318	−1.43037	−0.715185	−	0.698935i	$-0.753658\pi$
$593$	−34.8318	−1.43037	−0.715185	+	0.698935i	$0.753658\pi$
$594$	−0.786495	−0.0322703
$595$	0	0
$596$	12.6015	0.516176
$597$	−16.3114	−0.667582
$598$	−5.37493	−0.219797
$599$	−20.6241	−0.842678	−0.421339	−	0.906903i	$-0.638440\pi$
$599$	−20.6241	−0.842678	−0.421339	+	0.906903i	$0.638440\pi$
$600$	17.2350	0.703615
$601$	38.0160	1.55070	0.775352	−	0.631530i	$-0.217573\pi$
$601$	38.0160	1.55070	0.775352	+	0.631530i	$0.217573\pi$
$602$	0	0
$603$	−0.504513	−0.0205454
$604$	−15.2661	−0.621168
$605$	−39.7065	−1.61430
$606$	8.55708	0.347608
$607$	38.5290	1.56384	0.781921	−	0.623378i	$-0.214240\pi$
$607$	38.5290	1.56384	0.781921	+	0.623378i	$0.214240\pi$
$608$	24.5941	0.997421
$609$	0	0
$610$	−79.4381	−3.21636
$611$	6.35555	0.257118
$612$	−0.478313	−0.0193346
$613$	−29.5437	−1.19326	−0.596630	−	0.802517i	$-0.703494\pi$
$613$	−29.5437	−1.19326	−0.596630	+	0.802517i	$0.703494\pi$
$614$	29.0175	1.17105
$615$	−30.3629	−1.22435
$616$	0	0
$617$	16.5819	0.667563	0.333782	−	0.942650i	$-0.391675\pi$
$617$	16.5819	0.667563	0.333782	+	0.942650i	$0.391675\pi$
$618$	−2.92704	−0.117743
$619$	0.909573	0.0365588	0.0182794	−	0.999833i	$-0.494181\pi$
$619$	0.909573	0.0365588	0.0182794	+	0.999833i	$0.494181\pi$
$620$	−5.54176	−0.222562
$621$	1.00000	0.0401286
$622$	−37.6783	−1.51076
$623$	0	0
$624$	−15.9359	−0.637947
$625$	5.59294	0.223717
$626$	54.2122	2.16676
$627$	2.70690	0.108103
$628$	−1.04453	−0.0416814
$629$	−1.85392	−0.0739208
$630$	0	0
$631$	−10.1333	−0.403402	−0.201701	−	0.979447i	$-0.564647\pi$
$631$	−10.1333	−0.403402	−0.201701	+	0.979447i	$0.564647\pi$
$632$	27.1752	1.08097
$633$	−19.0644	−0.757743
$634$	16.0377	0.636940
$635$	65.9118	2.61563
$636$	4.90316	0.194423
$637$	0	0
$638$	−1.41970	−0.0562063
$639$	7.48882	0.296253
$640$	−48.5567	−1.91937
$641$	−25.4954	−1.00701	−0.503504	−	0.863993i	$-0.667956\pi$
$641$	−25.4954	−1.00701	−0.503504	+	0.863993i	$0.667956\pi$
$642$	−15.7900	−0.623183
$643$	−30.4640	−1.20138	−0.600691	−	0.799481i	$-0.705108\pi$
$643$	−30.4640	−1.20138	−0.600691	+	0.799481i	$0.705108\pi$
$644$	0	0
$645$	−26.5726	−1.04629
$646$	5.77408	0.227178
$647$	−20.4194	−0.802768	−0.401384	−	0.915910i	$-0.631471\pi$
$647$	−20.4194	−0.802768	−0.401384	+	0.915910i	$0.631471\pi$
$648$	2.01112	0.0790042
$649$	0.685042	0.0268902
$650$	−46.0623	−1.80671
$651$	0	0
$652$	−7.53754	−0.295193
$653$	2.79544	0.109394	0.0546970	−	0.998503i	$-0.482581\pi$
$653$	2.79544	0.109394	0.0546970	+	0.998503i	$0.482581\pi$
$654$	32.4862	1.27031
$655$	6.09066	0.237982
$656$	40.8746	1.59589
$657$	−12.0409	−0.469759
$658$	0	0
$659$	−18.5253	−0.721641	−0.360821	−	0.932635i	$-0.617503\pi$
$659$	−18.5253	−0.721641	−0.360821	+	0.932635i	$0.617503\pi$
$660$	1.38160	0.0537787
$661$	10.3177	0.401314	0.200657	−	0.979662i	$-0.435692\pi$
$661$	10.3177	0.401314	0.200657	+	0.979662i	$0.435692\pi$
$662$	−49.1899	−1.91182
$663$	−1.92707	−0.0748413
$664$	−1.49936	−0.0581864
$665$	0	0
$666$	−5.17091	−0.200369
$667$	1.80509	0.0698935
$668$	1.43152	0.0553871
$669$	6.18141	0.238987
$670$	3.10852	0.120093
$671$	6.06247	0.234039
$672$	0	0
$673$	−27.6178	−1.06459	−0.532295	−	0.846559i	$-0.678670\pi$
$673$	−27.6178	−1.06459	−0.532295	+	0.846559i	$0.678670\pi$
$674$	42.5427	1.63868
$675$	8.56984	0.329853
$676$	−2.13233	−0.0820126
$677$	−44.5481	−1.71212	−0.856062	−	0.516873i	$-0.827096\pi$
$677$	−44.5481	−1.71212	−0.856062	+	0.516873i	$0.827096\pi$
$678$	7.21792	0.277203
$679$	0	0
$680$	−4.44267	−0.170369
$681$	14.5200	0.556408
$682$	1.48342	0.0568030
$683$	−23.1646	−0.886370	−0.443185	−	0.896430i	$-0.646151\pi$
$683$	−23.1646	−0.886370	−0.443185	+	0.896430i	$0.646151\pi$
$684$	4.59159	0.175564
$685$	28.7899	1.10001
$686$	0	0
$687$	−12.2225	−0.466316
$688$	35.7721	1.36380
$689$	19.7543	0.752579
$690$	−6.16143	−0.234561
$691$	22.5838	0.859128	0.429564	−	0.903036i	$-0.358667\pi$
$691$	22.5838	0.859128	0.429564	+	0.903036i	$0.358667\pi$
$692$	10.7333	0.408019
$693$	0	0
$694$	1.95108	0.0740620
$695$	19.0874	0.724025
$696$	3.63026	0.137605
$697$	4.94282	0.187223
$698$	−58.1622	−2.20147
$699$	−11.3162	−0.428016
$700$	0	0
$701$	−49.0217	−1.85153	−0.925763	−	0.378105i	$-0.876576\pi$
$701$	−49.0217	−1.85153	−0.925763	+	0.378105i	$0.876576\pi$
$702$	−5.37493	−0.202864
$703$	17.7968	0.671221
$704$	1.30356	0.0491297
$705$	7.28553	0.274389
$706$	−41.2820	−1.55367
$707$	0	0
$708$	1.16200	0.0436708
$709$	−7.28652	−0.273651	−0.136826	−	0.990595i	$-0.543690\pi$
$709$	−7.28652	−0.273651	−0.136826	+	0.990595i	$0.543690\pi$
$710$	−46.1418	−1.73167
$711$	13.5125	0.506758
$712$	−28.2797	−1.05983
$713$	−1.88611	−0.0706355
$714$	0	0
$715$	5.56632	0.208169
$716$	−12.1214	−0.452997
$717$	−19.7343	−0.736992
$718$	−4.46781	−0.166737
$719$	−41.8331	−1.56011	−0.780056	−	0.625710i	$-0.784809\pi$
$719$	−41.8331	−1.56011	−0.780056	+	0.625710i	$0.784809\pi$
$720$	−18.2677	−0.680799
$721$	0	0
$722$	−23.6491	−0.880128
$723$	27.8145	1.03443
$724$	−10.0691	−0.374217
$725$	15.4694	0.574517
$726$	18.0289	0.669113
$727$	31.7263	1.17666	0.588332	−	0.808620i	$-0.299785\pi$
$727$	31.7263	1.17666	0.588332	+	0.808620i	$0.299785\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	74.1889	2.74586
$731$	4.32579	0.159995
$732$	10.2835	0.380089
$733$	−35.6264	−1.31589	−0.657945	−	0.753066i	$-0.728574\pi$
$733$	−35.6264	−1.31589	−0.657945	+	0.753066i	$0.728574\pi$
$734$	11.5316	0.425638
$735$	0	0
$736$	4.27229	0.157479
$737$	−0.237233	−0.00873858
$738$	13.7864	0.507483
$739$	−3.95304	−0.145415	−0.0727075	−	0.997353i	$-0.523164\pi$
$739$	−3.95304	−0.145415	−0.0727075	+	0.997353i	$0.523164\pi$
$740$	9.08349	0.333916
$741$	18.4990	0.679579
$742$	0	0
$743$	48.2627	1.77059	0.885294	−	0.465032i	$-0.153957\pi$
$743$	48.2627	1.77059	0.885294	+	0.465032i	$0.153957\pi$
$744$	−3.79320	−0.139065
$745$	58.1991	2.13225
$746$	−13.1756	−0.482393
$747$	−0.745535	−0.0272777
$748$	−0.224913	−0.00822362
$749$	0	0
$750$	−21.9953	−0.803155
$751$	−21.0917	−0.769647	−0.384823	−	0.922990i	$-0.625738\pi$
$751$	−21.0917	−0.769647	−0.384823	+	0.922990i	$0.625738\pi$
$752$	−9.80780	−0.357654
$753$	9.76332	0.355795
$754$	−9.70225	−0.353335
$755$	−70.5053	−2.56595
$756$	0	0
$757$	36.3993	1.32295	0.661477	−	0.749965i	$-0.269930\pi$
$757$	36.3993	1.32295	0.661477	+	0.749965i	$0.269930\pi$
$758$	−16.1682	−0.587254
$759$	0.470221	0.0170679
$760$	42.6477	1.54699
$761$	32.1008	1.16365	0.581827	−	0.813313i	$-0.302338\pi$
$761$	32.1008	1.16365	0.581827	+	0.813313i	$0.302338\pi$
$762$	−29.9274	−1.08416
$763$	0	0
$764$	12.7094	0.459810
$765$	−2.20905	−0.0798685
$766$	−3.01661	−0.108995
$767$	4.68160	0.169043
$768$	16.5029	0.595496
$769$	21.5730	0.777942	0.388971	−	0.921250i	$-0.372831\pi$
$769$	21.5730	0.777942	0.388971	+	0.921250i	$0.372831\pi$
$770$	0	0
$771$	28.6902	1.03325
$772$	−16.5149	−0.594384
$773$	−35.8535	−1.28956	−0.644780	−	0.764368i	$-0.723051\pi$
$773$	−35.8535	−1.28956	−0.644780	+	0.764368i	$0.723051\pi$
$774$	12.0654	0.433680
$775$	−16.1637	−0.580616
$776$	−27.2082	−0.976717
$777$	0	0
$778$	−12.5321	−0.449299
$779$	−47.4489	−1.70003
$780$	9.44189	0.338074
$781$	3.52140	0.126006
$782$	1.00303	0.0358682
$783$	1.80509	0.0645088
$784$	0	0
$785$	−4.82411	−0.172180
$786$	−2.76548	−0.0986415
$787$	−38.7636	−1.38177	−0.690887	−	0.722963i	$-0.742780\pi$
$787$	−38.7636	−1.38177	−0.690887	+	0.722963i	$0.742780\pi$
$788$	−4.94639	−0.176208
$789$	27.9327	0.994432
$790$	−83.2562	−2.96212
$791$	0	0
$792$	0.945670	0.0336029
$793$	41.4311	1.47126
$794$	24.5240	0.870324
$795$	22.6449	0.803132
$796$	−13.0102	−0.461135
$797$	43.1960	1.53008	0.765040	−	0.643982i	$-0.222719\pi$
$797$	43.1960	1.53008	0.765040	+	0.643982i	$0.222719\pi$
$798$	0	0
$799$	−1.18602	−0.0419585
$800$	36.6128	1.29446
$801$	−14.0617	−0.496845
$802$	30.5347	1.07822
$803$	−5.66187	−0.199803
$804$	−0.402407	−0.0141918
$805$	0	0
$806$	10.1377	0.357086
$807$	−5.32282	−0.187372
$808$	−10.2889	−0.361963
$809$	20.1141	0.707174	0.353587	−	0.935402i	$-0.384962\pi$
$809$	20.1141	0.707174	0.353587	+	0.935402i	$0.384962\pi$
$810$	−6.16143	−0.216490
$811$	−33.8560	−1.18885	−0.594423	−	0.804153i	$-0.702619\pi$
$811$	−33.8560	−1.18885	−0.594423	+	0.804153i	$0.702619\pi$
$812$	0	0
$813$	19.3934	0.680155
$814$	−2.43147	−0.0852229
$815$	−34.8116	−1.21940
$816$	2.97383	0.104105
$817$	−41.5257	−1.45280
$818$	−28.8660	−1.00927
$819$	0	0
$820$	−24.2179	−0.845725
$821$	23.9241	0.834958	0.417479	−	0.908687i	$-0.362914\pi$
$821$	23.9241	0.834958	0.417479	+	0.908687i	$0.362914\pi$
$822$	−13.0722	−0.455944
$823$	−18.2971	−0.637797	−0.318898	−	0.947789i	$-0.603313\pi$
$823$	−18.2971	−0.637797	−0.318898	+	0.947789i	$0.603313\pi$
$824$	3.51943	0.122605
$825$	4.02972	0.140297
$826$	0	0
$827$	−12.0135	−0.417752	−0.208876	−	0.977942i	$-0.566980\pi$
$827$	−12.0135	−0.417752	−0.208876	+	0.977942i	$0.566980\pi$
$828$	0.797614	0.0277190
$829$	−24.0882	−0.836619	−0.418309	−	0.908305i	$-0.637377\pi$
$829$	−24.0882	−0.836619	−0.418309	+	0.908305i	$0.637377\pi$
$830$	4.59356	0.159445
$831$	13.1785	0.457156
$832$	8.90856	0.308849
$833$	0	0
$834$	−8.66668	−0.300102
$835$	6.61137	0.228796
$836$	2.15906	0.0746727
$837$	−1.88611	−0.0651936
$838$	−11.5351	−0.398474
$839$	11.9559	0.412764	0.206382	−	0.978472i	$-0.433831\pi$
$839$	11.9559	0.412764	0.206382	+	0.978472i	$0.433831\pi$
$840$	0	0
$841$	−25.7416	−0.887643
$842$	−54.6542	−1.88351
$843$	12.2275	0.421138
$844$	−15.2061	−0.523414
$845$	−9.84802	−0.338782
$846$	−3.30802	−0.113732
$847$	0	0
$848$	−30.4846	−1.04685
$849$	−4.52300	−0.155229
$850$	8.59578	0.294833
$851$	3.09153	0.105976
$852$	5.97319	0.204638
$853$	−24.7705	−0.848125	−0.424063	−	0.905633i	$-0.639396\pi$
$853$	−24.7705	−0.848125	−0.424063	+	0.905633i	$0.639396\pi$
$854$	0	0
$855$	21.2059	0.725228
$856$	18.9857	0.648919
$857$	−55.0426	−1.88022	−0.940110	−	0.340871i	$-0.889278\pi$
$857$	−55.0426	−1.88022	−0.940110	+	0.340871i	$0.889278\pi$
$858$	−2.52741	−0.0862842
$859$	−51.3240	−1.75115	−0.875576	−	0.483079i	$-0.839518\pi$
$859$	−51.3240	−1.75115	−0.875576	+	0.483079i	$0.839518\pi$
$860$	−21.1947	−0.722732
$861$	0	0
$862$	65.5125	2.23136
$863$	−49.8017	−1.69527	−0.847634	−	0.530581i	$-0.821974\pi$
$863$	−49.8017	−1.69527	−0.847634	+	0.530581i	$0.821974\pi$
$864$	4.27229	0.145346
$865$	49.5710	1.68547
$866$	−3.38512	−0.115031
$867$	−16.6404	−0.565137
$868$	0	0
$869$	6.35385	0.215540
$870$	−11.1219	−0.377069
$871$	−1.62126	−0.0549341
$872$	−39.0609	−1.32277
$873$	−13.5289	−0.457883
$874$	−9.62862	−0.325693
$875$	0	0
$876$	−9.60397	−0.324488
$877$	4.40575	0.148772	0.0743858	−	0.997230i	$-0.476300\pi$
$877$	4.40575	0.148772	0.0743858	+	0.997230i	$0.476300\pi$
$878$	−21.6829	−0.731761
$879$	7.38241	0.249003
$880$	−8.58988	−0.289565
$881$	26.1576	0.881272	0.440636	−	0.897686i	$-0.354753\pi$
$881$	26.1576	0.881272	0.440636	+	0.897686i	$0.354753\pi$
$882$	0	0
$883$	−18.3108	−0.616207	−0.308104	−	0.951353i	$-0.599694\pi$
$883$	−18.3108	−0.616207	−0.308104	+	0.951353i	$0.599694\pi$
$884$	−1.53706	−0.0516969
$885$	5.36664	0.180398
$886$	−7.45239	−0.250368
$887$	−7.66660	−0.257419	−0.128710	−	0.991682i	$-0.541084\pi$
$887$	−7.66660	−0.257419	−0.128710	+	0.991682i	$0.541084\pi$
$888$	6.21743	0.208643
$889$	0	0
$890$	86.6400	2.90418
$891$	0.470221	0.0157530
$892$	4.93038	0.165081
$893$	11.3853	0.380994
$894$	−26.4255	−0.883799
$895$	−55.9817	−1.87126
$896$	0	0
$897$	3.21351	0.107296
$898$	−23.3679	−0.779796
$899$	−3.40461	−0.113550
$900$	6.83542	0.227847
$901$	−3.68640	−0.122812
$902$	6.48264	0.215848
$903$	0	0
$904$	−8.67873	−0.288650
$905$	−46.5036	−1.54583
$906$	32.0132	1.06357
$907$	−39.5578	−1.31349	−0.656747	−	0.754111i	$-0.728068\pi$
$907$	−39.5578	−1.31349	−0.656747	+	0.754111i	$0.728068\pi$
$908$	11.5814	0.384341
$909$	−5.11601	−0.169687
$910$	0	0
$911$	29.8791	0.989938	0.494969	−	0.868911i	$-0.335179\pi$
$911$	29.8791	0.989938	0.494969	+	0.868911i	$0.335179\pi$
$912$	−28.5475	−0.945301
$913$	−0.350566	−0.0116020
$914$	35.0295	1.15867
$915$	47.4936	1.57009
$916$	−9.74880	−0.322110
$917$	0	0
$918$	1.00303	0.0331048
$919$	7.43662	0.245311	0.122656	−	0.992449i	$-0.460859\pi$
$919$	7.43662	0.245311	0.122656	+	0.992449i	$0.460859\pi$
$920$	7.40841	0.244248
$921$	−17.3486	−0.571657
$922$	49.6254	1.63433
$923$	24.0654	0.792121
$924$	0	0
$925$	26.4939	0.871113
$926$	−66.2875	−2.17834
$927$	1.74999	0.0574771
$928$	7.71187	0.253155
$929$	−38.2796	−1.25591	−0.627956	−	0.778249i	$-0.716108\pi$
$929$	−38.2796	−1.25591	−0.627956	+	0.778249i	$0.716108\pi$
$930$	11.6211	0.381072
$931$	0	0
$932$	−9.02592	−0.295654
$933$	22.5267	0.737490
$934$	47.1241	1.54195
$935$	−1.03874	−0.0339705
$936$	6.46274	0.211241
$937$	−30.6658	−1.00181	−0.500904	−	0.865503i	$-0.666999\pi$
$937$	−30.6658	−1.00181	−0.500904	+	0.865503i	$0.666999\pi$
$938$	0	0
$939$	−32.4118	−1.05772
$940$	5.81104	0.189535
$941$	−13.8151	−0.450361	−0.225180	−	0.974317i	$-0.572297\pi$
$941$	−13.8151	−0.450361	−0.225180	+	0.974317i	$0.572297\pi$
$942$	2.19040	0.0713671
$943$	−8.24245	−0.268411
$944$	−7.22458	−0.235140
$945$	0	0
$946$	5.67338	0.184458
$947$	−48.3970	−1.57269	−0.786345	−	0.617787i	$-0.788029\pi$
$947$	−48.3970	−1.57269	−0.786345	+	0.617787i	$0.788029\pi$
$948$	10.7777	0.350045
$949$	−38.6934	−1.25604
$950$	−82.5157	−2.67716
$951$	−9.58847	−0.310927
$952$	0	0
$953$	−1.88970	−0.0612133	−0.0306066	−	0.999532i	$-0.509744\pi$
$953$	−1.88970	−0.0612133	−0.0306066	+	0.999532i	$0.509744\pi$
$954$	−10.2820	−0.332891
$955$	58.6975	1.89941
$956$	−15.7404	−0.509080
$957$	0.848792	0.0274376
$958$	−67.5260	−2.18167
$959$	0	0
$960$	10.2121	0.329595
$961$	−27.4426	−0.885245
$962$	−16.6167	−0.535745
$963$	9.44038	0.304212
$964$	22.1853	0.714539
$965$	−76.2730	−2.45531
$966$	0	0
$967$	−16.0490	−0.516100	−0.258050	−	0.966132i	$-0.583080\pi$
$967$	−16.0490	−0.516100	−0.258050	+	0.966132i	$0.583080\pi$
$968$	−21.6776	−0.696746
$969$	−3.45215	−0.110899
$970$	83.3572	2.67644
$971$	40.5438	1.30111	0.650556	−	0.759458i	$-0.274536\pi$
$971$	40.5438	1.30111	0.650556	+	0.759458i	$0.274536\pi$
$972$	0.797614	0.0255835
$973$	0	0
$974$	65.7231	2.10590
$975$	27.5392	0.881961
$976$	−63.9360	−2.04654
$977$	32.3363	1.03453	0.517266	−	0.855825i	$-0.326950\pi$
$977$	32.3363	1.03453	0.517266	+	0.855825i	$0.326950\pi$
$978$	15.8063	0.505430
$979$	−6.61210	−0.211324
$980$	0	0
$981$	−19.4225	−0.620112
$982$	−32.3231	−1.03147
$983$	17.9359	0.572066	0.286033	−	0.958220i	$-0.407663\pi$
$983$	17.9359	0.572066	0.286033	+	0.958220i	$0.407663\pi$
$984$	−16.5765	−0.528441
$985$	−22.8446	−0.727889
$986$	1.81056	0.0576599
$987$	0	0
$988$	14.7551	0.469422
$989$	−7.21351	−0.229376
$990$	−2.89723	−0.0920801
$991$	−19.3229	−0.613813	−0.306907	−	0.951740i	$-0.599294\pi$
$991$	−19.3229	−0.613813	−0.306907	+	0.951740i	$0.599294\pi$
$992$	−8.05801	−0.255842
$993$	29.4091	0.933271
$994$	0	0
$995$	−60.0868	−1.90488
$996$	−0.594649	−0.0188422
$997$	−14.8431	−0.470087	−0.235043	−	0.971985i	$-0.575523\pi$
$997$	−14.8431	−0.470087	−0.235043	+	0.971985i	$0.575523\pi$
$998$	−27.9198	−0.883786
$999$	3.09153	0.0978115

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3381.2.a.z.1.2	yes	5
7.6	odd	2		3381.2.a.y.1.2	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3381.2.a.y.1.2	✓	5	7.6	odd	2
3381.2.a.z.1.2	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)

\(f(q)\)	\(=\)	\(q-1.67261 q^{2} +1.00000 q^{3} +0.797614 q^{4} +3.68373 q^{5} -1.67261 q^{6} +2.01112 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.67261 q^{2} +1.00000 q^{3} +0.797614 q^{4} +3.68373 q^{5} -1.67261 q^{6} +2.01112 q^{8} +1.00000 q^{9} -6.16143 q^{10} +0.470221 q^{11} +0.797614 q^{12} +3.21351 q^{13} +3.68373 q^{15} -4.95904 q^{16} -0.599679 q^{17} -1.67261 q^{18} +5.75665 q^{19} +2.93819 q^{20} -0.786495 q^{22} +1.00000 q^{23} +2.01112 q^{24} +8.56984 q^{25} -5.37493 q^{26} +1.00000 q^{27} +1.80509 q^{29} -6.16143 q^{30} -1.88611 q^{31} +4.27229 q^{32} +0.470221 q^{33} +1.00303 q^{34} +0.797614 q^{36} +3.09153 q^{37} -9.62862 q^{38} +3.21351 q^{39} +7.40841 q^{40} -8.24245 q^{41} -7.21351 q^{43} +0.375055 q^{44} +3.68373 q^{45} -1.67261 q^{46} +1.97776 q^{47} -4.95904 q^{48} -14.3340 q^{50} -0.599679 q^{51} +2.56314 q^{52} +6.14728 q^{53} -1.67261 q^{54} +1.73217 q^{55} +5.75665 q^{57} -3.01921 q^{58} +1.45685 q^{59} +2.93819 q^{60} +12.8928 q^{61} +3.15472 q^{62} +2.77222 q^{64} +11.8377 q^{65} -0.786495 q^{66} -0.504513 q^{67} -0.478313 q^{68} +1.00000 q^{69} +7.48882 q^{71} +2.01112 q^{72} -12.0409 q^{73} -5.17091 q^{74} +8.56984 q^{75} +4.59159 q^{76} -5.37493 q^{78} +13.5125 q^{79} -18.2677 q^{80} +1.00000 q^{81} +13.7864 q^{82} -0.745535 q^{83} -2.20905 q^{85} +12.0654 q^{86} +1.80509 q^{87} +0.945670 q^{88} -14.0617 q^{89} -6.16143 q^{90} +0.797614 q^{92} -1.88611 q^{93} -3.30802 q^{94} +21.2059 q^{95} +4.27229 q^{96} -13.5289 q^{97} +0.470221 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + q^{2} + 5 q^{3} + 9 q^{4} + 2 q^{5} + q^{6} + 3 q^{8} + 5 q^{9}+O(q^{10}) \) 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

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Database

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