LMFDB - Embedded newform 8018.2.a.f.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$1$
Dimension:	$34$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.350444 q^{3} +1.00000 q^{4} -0.178230 q^{5} +0.350444 q^{6} -3.90849 q^{7} -1.00000 q^{8} -2.87719 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.350444 q^{3} +1.00000 q^{4} -0.178230 q^{5} +0.350444 q^{6} -3.90849 q^{7} -1.00000 q^{8} -2.87719 q^{9} +0.178230 q^{10} -1.52727 q^{11} -0.350444 q^{12} -0.315173 q^{13} +3.90849 q^{14} +0.0624595 q^{15} +1.00000 q^{16} +6.70888 q^{17} +2.87719 q^{18} -1.00000 q^{19} -0.178230 q^{20} +1.36971 q^{21} +1.52727 q^{22} -3.64189 q^{23} +0.350444 q^{24} -4.96823 q^{25} +0.315173 q^{26} +2.05962 q^{27} -3.90849 q^{28} +7.13883 q^{29} -0.0624595 q^{30} +7.92567 q^{31} -1.00000 q^{32} +0.535221 q^{33} -6.70888 q^{34} +0.696609 q^{35} -2.87719 q^{36} +7.58524 q^{37} +1.00000 q^{38} +0.110451 q^{39} +0.178230 q^{40} -5.82883 q^{41} -1.36971 q^{42} -4.70286 q^{43} -1.52727 q^{44} +0.512800 q^{45} +3.64189 q^{46} -1.67658 q^{47} -0.350444 q^{48} +8.27632 q^{49} +4.96823 q^{50} -2.35108 q^{51} -0.315173 q^{52} +3.11276 q^{53} -2.05962 q^{54} +0.272204 q^{55} +3.90849 q^{56} +0.350444 q^{57} -7.13883 q^{58} -13.1462 q^{59} +0.0624595 q^{60} +3.19516 q^{61} -7.92567 q^{62} +11.2455 q^{63} +1.00000 q^{64} +0.0561732 q^{65} -0.535221 q^{66} +2.05631 q^{67} +6.70888 q^{68} +1.27628 q^{69} -0.696609 q^{70} +5.71954 q^{71} +2.87719 q^{72} +5.78654 q^{73} -7.58524 q^{74} +1.74109 q^{75} -1.00000 q^{76} +5.96931 q^{77} -0.110451 q^{78} -5.62658 q^{79} -0.178230 q^{80} +7.90979 q^{81} +5.82883 q^{82} +5.96257 q^{83} +1.36971 q^{84} -1.19572 q^{85} +4.70286 q^{86} -2.50176 q^{87} +1.52727 q^{88} +6.61534 q^{89} -0.512800 q^{90} +1.23185 q^{91} -3.64189 q^{92} -2.77750 q^{93} +1.67658 q^{94} +0.178230 q^{95} +0.350444 q^{96} +5.63552 q^{97} -8.27632 q^{98} +4.39423 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * q^98 - 28 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−0.350444	−0.202329	−0.101164	−	0.994870i	$-0.532257\pi$
$3$	−0.350444	−0.202329	−0.101164	+	0.994870i	$0.532257\pi$
$4$	1.00000	0.500000
$5$	−0.178230	−0.0797067	−0.0398534	−	0.999206i	$-0.512689\pi$
$5$	−0.178230	−0.0797067	−0.0398534	+	0.999206i	$0.512689\pi$
$6$	0.350444	0.143068
$7$	−3.90849	−1.47727	−0.738636	−	0.674105i	$-0.764530\pi$
$7$	−3.90849	−1.47727	−0.738636	+	0.674105i	$0.764530\pi$
$8$	−1.00000	−0.353553
$9$	−2.87719	−0.959063
$10$	0.178230	0.0563612
$11$	−1.52727	−0.460488	−0.230244	−	0.973133i	$-0.573952\pi$
$11$	−1.52727	−0.460488	−0.230244	+	0.973133i	$0.573952\pi$
$12$	−0.350444	−0.101164
$13$	−0.315173	−0.0874134	−0.0437067	−	0.999044i	$-0.513917\pi$
$13$	−0.315173	−0.0874134	−0.0437067	+	0.999044i	$0.513917\pi$
$14$	3.90849	1.04459
$15$	0.0624595	0.0161270
$16$	1.00000	0.250000
$17$	6.70888	1.62714	0.813571	−	0.581466i	$-0.197520\pi$
$17$	6.70888	1.62714	0.813571	+	0.581466i	$0.197520\pi$
$18$	2.87719	0.678160
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−0.178230	−0.0398534
$21$	1.36971	0.298895
$22$	1.52727	0.325614
$23$	−3.64189	−0.759387	−0.379693	−	0.925112i	$-0.623971\pi$
$23$	−3.64189	−0.759387	−0.379693	+	0.925112i	$0.623971\pi$
$24$	0.350444	0.0715340
$25$	−4.96823	−0.993647
$26$	0.315173	0.0618106
$27$	2.05962	0.396375
$28$	−3.90849	−0.738636
$29$	7.13883	1.32565	0.662824	−	0.748775i	$-0.269358\pi$
$29$	7.13883	1.32565	0.662824	+	0.748775i	$0.269358\pi$
$30$	−0.0624595	−0.0114035
$31$	7.92567	1.42349	0.711746	−	0.702436i	$-0.247905\pi$
$31$	7.92567	1.42349	0.711746	+	0.702436i	$0.247905\pi$
$32$	−1.00000	−0.176777
$33$	0.535221	0.0931700
$34$	−6.70888	−1.15056
$35$	0.696609	0.117748
$36$	−2.87719	−0.479532
$37$	7.58524	1.24701	0.623503	−	0.781821i	$-0.285709\pi$
$37$	7.58524	1.24701	0.623503	+	0.781821i	$0.285709\pi$
$38$	1.00000	0.162221
$39$	0.110451	0.0176862
$40$	0.178230	0.0281806
$41$	−5.82883	−0.910310	−0.455155	−	0.890412i	$-0.650416\pi$
$41$	−5.82883	−0.910310	−0.455155	+	0.890412i	$0.650416\pi$
$42$	−1.36971	−0.211350
$43$	−4.70286	−0.717180	−0.358590	−	0.933495i	$-0.616742\pi$
$43$	−4.70286	−0.717180	−0.358590	+	0.933495i	$0.616742\pi$
$44$	−1.52727	−0.230244
$45$	0.512800	0.0764438
$46$	3.64189	0.536968
$47$	−1.67658	−0.244555	−0.122277	−	0.992496i	$-0.539020\pi$
$47$	−1.67658	−0.244555	−0.122277	+	0.992496i	$0.539020\pi$
$48$	−0.350444	−0.0505822
$49$	8.27632	1.18233
$50$	4.96823	0.702614
$51$	−2.35108	−0.329218
$52$	−0.315173	−0.0437067
$53$	3.11276	0.427570	0.213785	−	0.976881i	$-0.431421\pi$
$53$	3.11276	0.427570	0.213785	+	0.976881i	$0.431421\pi$
$54$	−2.05962	−0.280279
$55$	0.272204	0.0367040
$56$	3.90849	0.522294
$57$	0.350444	0.0464174
$58$	−7.13883	−0.937375
$59$	−13.1462	−1.71149	−0.855746	−	0.517397i	$-0.826901\pi$
$59$	−13.1462	−1.71149	−0.855746	+	0.517397i	$0.826901\pi$
$60$	0.0624595	0.00806348
$61$	3.19516	0.409098	0.204549	−	0.978856i	$-0.434427\pi$
$61$	3.19516	0.409098	0.204549	+	0.978856i	$0.434427\pi$
$62$	−7.92567	−1.00656
$63$	11.2455	1.41680
$64$	1.00000	0.125000
$65$	0.0561732	0.00696743
$66$	−0.535221	−0.0658811
$67$	2.05631	0.251218	0.125609	−	0.992080i	$-0.459912\pi$
$67$	2.05631	0.251218	0.125609	+	0.992080i	$0.459912\pi$
$68$	6.70888	0.813571
$69$	1.27628	0.153646
$70$	−0.696609	−0.0832607
$71$	5.71954	0.678785	0.339393	−	0.940645i	$-0.389779\pi$
$71$	5.71954	0.678785	0.339393	+	0.940645i	$0.389779\pi$
$72$	2.87719	0.339080
$73$	5.78654	0.677263	0.338631	−	0.940919i	$-0.390036\pi$
$73$	5.78654	0.677263	0.338631	+	0.940919i	$0.390036\pi$
$74$	−7.58524	−0.881766
$75$	1.74109	0.201043
$76$	−1.00000	−0.114708
$77$	5.96931	0.680266
$78$	−0.110451	−0.0125061
$79$	−5.62658	−0.633040	−0.316520	−	0.948586i	$-0.602514\pi$
$79$	−5.62658	−0.633040	−0.316520	+	0.948586i	$0.602514\pi$
$80$	−0.178230	−0.0199267
$81$	7.90979	0.878865
$82$	5.82883	0.643686
$83$	5.96257	0.654478	0.327239	−	0.944942i	$-0.393882\pi$
$83$	5.96257	0.654478	0.327239	+	0.944942i	$0.393882\pi$
$84$	1.36971	0.149447
$85$	−1.19572	−0.129694
$86$	4.70286	0.507123
$87$	−2.50176	−0.268217
$88$	1.52727	0.162807
$89$	6.61534	0.701225	0.350613	−	0.936521i	$-0.385973\pi$
$89$	6.61534	0.701225	0.350613	+	0.936521i	$0.385973\pi$
$90$	−0.512800	−0.0540539
$91$	1.23185	0.129133
$92$	−3.64189	−0.379693
$93$	−2.77750	−0.288014
$94$	1.67658	0.172926
$95$	0.178230	0.0182860
$96$	0.350444	0.0357670
$97$	5.63552	0.572201	0.286100	−	0.958200i	$-0.407641\pi$
$97$	5.63552	0.572201	0.286100	+	0.958200i	$0.407641\pi$
$98$	−8.27632	−0.836034
$99$	4.39423	0.441637
$100$	−4.96823	−0.496823
$101$	3.83173	0.381272	0.190636	−	0.981661i	$-0.438945\pi$
$101$	3.83173	0.381272	0.190636	+	0.981661i	$0.438945\pi$
$102$	2.35108	0.232792
$103$	−1.12275	−0.110628	−0.0553138	−	0.998469i	$-0.517616\pi$
$103$	−1.12275	−0.110628	−0.0553138	+	0.998469i	$0.517616\pi$
$104$	0.315173	0.0309053
$105$	−0.244122	−0.0238239
$106$	−3.11276	−0.302338
$107$	−0.421369	−0.0407353	−0.0203677	−	0.999793i	$-0.506484\pi$
$107$	−0.421369	−0.0407353	−0.0203677	+	0.999793i	$0.506484\pi$
$108$	2.05962	0.198187
$109$	19.8217	1.89857	0.949287	−	0.314411i	$-0.101807\pi$
$109$	19.8217	1.89857	0.949287	+	0.314411i	$0.101807\pi$
$110$	−0.272204	−0.0259536
$111$	−2.65820	−0.252305
$112$	−3.90849	−0.369318
$113$	3.23659	0.304472	0.152236	−	0.988344i	$-0.451353\pi$
$113$	3.23659	0.304472	0.152236	+	0.988344i	$0.451353\pi$
$114$	−0.350444	−0.0328221
$115$	0.649093	0.0605282
$116$	7.13883	0.662824
$117$	0.906814	0.0838350
$118$	13.1462	1.21021
$119$	−26.2216	−2.40373
$120$	−0.0624595	−0.00570174
$121$	−8.66746	−0.787951
$122$	−3.19516	−0.289276
$123$	2.04268	0.184182
$124$	7.92567	0.711746
$125$	1.77663	0.158907
$126$	−11.2455	−1.00183
$127$	−2.71343	−0.240778	−0.120389	−	0.992727i	$-0.538414\pi$
$127$	−2.71343	−0.240778	−0.120389	+	0.992727i	$0.538414\pi$
$128$	−1.00000	−0.0883883
$129$	1.64809	0.145106
$130$	−0.0561732	−0.00492672
$131$	−5.20115	−0.454427	−0.227213	−	0.973845i	$-0.572961\pi$
$131$	−5.20115	−0.454427	−0.227213	+	0.973845i	$0.572961\pi$
$132$	0.535221	0.0465850
$133$	3.90849	0.338909
$134$	−2.05631	−0.177638
$135$	−0.367086	−0.0315937
$136$	−6.70888	−0.575282
$137$	−10.8685	−0.928556	−0.464278	−	0.885690i	$-0.653686\pi$
$137$	−10.8685	−0.928556	−0.464278	+	0.885690i	$0.653686\pi$
$138$	−1.27628	−0.108644
$139$	0.716808	0.0607989	0.0303994	−	0.999538i	$-0.490322\pi$
$139$	0.716808	0.0607989	0.0303994	+	0.999538i	$0.490322\pi$
$140$	0.696609	0.0588742
$141$	0.587547	0.0494804
$142$	−5.71954	−0.479973
$143$	0.481354	0.0402528
$144$	−2.87719	−0.239766
$145$	−1.27235	−0.105663
$146$	−5.78654	−0.478897
$147$	−2.90038	−0.239220
$148$	7.58524	0.623503
$149$	−12.5612	−1.02905	−0.514527	−	0.857474i	$-0.672032\pi$
$149$	−12.5612	−1.02905	−0.514527	+	0.857474i	$0.672032\pi$
$150$	−1.74109	−0.142159
$151$	10.0366	0.816768	0.408384	−	0.912810i	$-0.366092\pi$
$151$	10.0366	0.816768	0.408384	+	0.912810i	$0.366092\pi$
$152$	1.00000	0.0811107
$153$	−19.3027	−1.56053
$154$	−5.96931	−0.481021
$155$	−1.41259	−0.113462
$156$	0.110451	0.00884312
$157$	−10.5317	−0.840524	−0.420262	−	0.907403i	$-0.638062\pi$
$157$	−10.5317	−0.840524	−0.420262	+	0.907403i	$0.638062\pi$
$158$	5.62658	0.447627
$159$	−1.09085	−0.0865098
$160$	0.178230	0.0140903
$161$	14.2343	1.12182
$162$	−7.90979	−0.621451
$163$	−2.70092	−0.211552	−0.105776	−	0.994390i	$-0.533733\pi$
$163$	−2.70092	−0.211552	−0.105776	+	0.994390i	$0.533733\pi$
$164$	−5.82883	−0.455155
$165$	−0.0953922	−0.00742627
$166$	−5.96257	−0.462786
$167$	13.5906	1.05167	0.525836	−	0.850586i	$-0.323752\pi$
$167$	13.5906	1.05167	0.525836	+	0.850586i	$0.323752\pi$
$168$	−1.36971	−0.105675
$169$	−12.9007	−0.992359
$170$	1.19572	0.0917076
$171$	2.87719	0.220024
$172$	−4.70286	−0.358590
$173$	18.5724	1.41204	0.706018	−	0.708194i	$-0.250490\pi$
$173$	18.5724	1.41204	0.706018	+	0.708194i	$0.250490\pi$
$174$	2.50176	0.189658
$175$	19.4183	1.46789
$176$	−1.52727	−0.115122
$177$	4.60701	0.346284
$178$	−6.61534	−0.495841
$179$	12.9704	0.969452	0.484726	−	0.874666i	$-0.338919\pi$
$179$	12.9704	0.969452	0.484726	+	0.874666i	$0.338919\pi$
$180$	0.512800	0.0382219
$181$	−9.98409	−0.742112	−0.371056	−	0.928611i	$-0.621004\pi$
$181$	−9.98409	−0.742112	−0.371056	+	0.928611i	$0.621004\pi$
$182$	−1.23185	−0.0913110
$183$	−1.11972	−0.0827723
$184$	3.64189	0.268484
$185$	−1.35191	−0.0993947
$186$	2.77750	0.203656
$187$	−10.2462	−0.749279
$188$	−1.67658	−0.122277
$189$	−8.05003	−0.585553
$190$	−0.178230	−0.0129301
$191$	−0.371920	−0.0269112	−0.0134556	−	0.999909i	$-0.504283\pi$
$191$	−0.371920	−0.0269112	−0.0134556	+	0.999909i	$0.504283\pi$
$192$	−0.350444	−0.0252911
$193$	3.37266	0.242770	0.121385	−	0.992606i	$-0.461267\pi$
$193$	3.37266	0.242770	0.121385	+	0.992606i	$0.461267\pi$
$194$	−5.63552	−0.404607
$195$	−0.0196856	−0.00140971
$196$	8.27632	0.591166
$197$	−26.2737	−1.87193	−0.935963	−	0.352099i	$-0.885468\pi$
$197$	−26.2737	−1.87193	−0.935963	+	0.352099i	$0.885468\pi$
$198$	−4.39423	−0.312285
$199$	−6.26480	−0.444100	−0.222050	−	0.975035i	$-0.571275\pi$
$199$	−6.26480	−0.444100	−0.222050	+	0.975035i	$0.571275\pi$
$200$	4.96823	0.351307
$201$	−0.720620	−0.0508286
$202$	−3.83173	−0.269600
$203$	−27.9021	−1.95834
$204$	−2.35108	−0.164609
$205$	1.03887	0.0725578
$206$	1.12275	0.0782255
$207$	10.4784	0.728300
$208$	−0.315173	−0.0218533
$209$	1.52727	0.105643
$210$	0.244122	0.0168460
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	3.11276	0.213785
$213$	−2.00438	−0.137338
$214$	0.421369	0.0288042
$215$	0.838189	0.0571640
$216$	−2.05962	−0.140140
$217$	−30.9774	−2.10289
$218$	−19.8217	−1.34249
$219$	−2.02786	−0.137030
$220$	0.272204	0.0183520
$221$	−2.11446	−0.142234
$222$	2.65820	0.178407
$223$	6.21424	0.416136	0.208068	−	0.978114i	$-0.433282\pi$
$223$	6.21424	0.416136	0.208068	+	0.978114i	$0.433282\pi$
$224$	3.90849	0.261147
$225$	14.2945	0.952970
$226$	−3.23659	−0.215294
$227$	−17.2456	−1.14463	−0.572314	−	0.820034i	$-0.693954\pi$
$227$	−17.2456	−1.14463	−0.572314	+	0.820034i	$0.693954\pi$
$228$	0.350444	0.0232087
$229$	−0.785104	−0.0518811	−0.0259406	−	0.999663i	$-0.508258\pi$
$229$	−0.785104	−0.0518811	−0.0259406	+	0.999663i	$0.508258\pi$
$230$	−0.649093	−0.0427999
$231$	−2.09191	−0.137637
$232$	−7.13883	−0.468687
$233$	−11.8271	−0.774821	−0.387411	−	0.921907i	$-0.626630\pi$
$233$	−11.8271	−0.774821	−0.387411	+	0.921907i	$0.626630\pi$
$234$	−0.906814	−0.0592803
$235$	0.298817	0.0194926
$236$	−13.1462	−0.855746
$237$	1.97180	0.128082
$238$	26.2216	1.69969
$239$	−5.54195	−0.358479	−0.179239	−	0.983805i	$-0.557364\pi$
$239$	−5.54195	−0.358479	−0.179239	+	0.983805i	$0.557364\pi$
$240$	0.0624595	0.00403174
$241$	16.5329	1.06498	0.532489	−	0.846437i	$-0.321257\pi$
$241$	16.5329	1.06498	0.532489	+	0.846437i	$0.321257\pi$
$242$	8.66746	0.557165
$243$	−8.95081	−0.574195
$244$	3.19516	0.204549
$245$	−1.47509	−0.0942397
$246$	−2.04268	−0.130236
$247$	0.315173	0.0200540
$248$	−7.92567	−0.503281
$249$	−2.08955	−0.132420
$250$	−1.77663	−0.112364
$251$	−3.08097	−0.194469	−0.0972344	−	0.995262i	$-0.531000\pi$
$251$	−3.08097	−0.194469	−0.0972344	+	0.995262i	$0.531000\pi$
$252$	11.2455	0.708398
$253$	5.56214	0.349688
$254$	2.71343	0.170256
$255$	0.419033	0.0262409
$256$	1.00000	0.0625000
$257$	0.207315	0.0129320	0.00646598	−	0.999979i	$-0.497942\pi$
$257$	0.207315	0.0129320	0.00646598	+	0.999979i	$0.497942\pi$
$258$	−1.64809	−0.102605
$259$	−29.6468	−1.84217
$260$	0.0561732	0.00348372
$261$	−20.5398	−1.27138
$262$	5.20115	0.321328
$263$	−13.4049	−0.826583	−0.413291	−	0.910599i	$-0.635621\pi$
$263$	−13.4049	−0.826583	−0.413291	+	0.910599i	$0.635621\pi$
$264$	−0.535221	−0.0329406
$265$	−0.554786	−0.0340802
$266$	−3.90849	−0.239645
$267$	−2.31831	−0.141878
$268$	2.05631	0.125609
$269$	−11.2749	−0.687441	−0.343721	−	0.939072i	$-0.611687\pi$
$269$	−11.2749	−0.687441	−0.343721	+	0.939072i	$0.611687\pi$
$270$	0.367086	0.0223401
$271$	−23.7771	−1.44435	−0.722177	−	0.691708i	$-0.756859\pi$
$271$	−23.7771	−1.44435	−0.722177	+	0.691708i	$0.756859\pi$
$272$	6.70888	0.406786
$273$	−0.431695	−0.0261274
$274$	10.8685	0.656588
$275$	7.58781	0.457562
$276$	1.27628	0.0768229
$277$	−3.22032	−0.193490	−0.0967451	−	0.995309i	$-0.530843\pi$
$277$	−3.22032	−0.193490	−0.0967451	+	0.995309i	$0.530843\pi$
$278$	−0.716808	−0.0429913
$279$	−22.8037	−1.36522
$280$	−0.696609	−0.0416304
$281$	−24.0598	−1.43529	−0.717643	−	0.696411i	$-0.754779\pi$
$281$	−24.0598	−1.43529	−0.717643	+	0.696411i	$0.754779\pi$
$282$	−0.587547	−0.0349879
$283$	−17.9884	−1.06930	−0.534649	−	0.845074i	$-0.679556\pi$
$283$	−17.9884	−1.06930	−0.534649	+	0.845074i	$0.679556\pi$
$284$	5.71954	0.339393
$285$	−0.0624595	−0.00369978
$286$	−0.481354	−0.0284630
$287$	22.7819	1.34478
$288$	2.87719	0.169540
$289$	28.0090	1.64759
$290$	1.27235	0.0747151
$291$	−1.97493	−0.115773
$292$	5.78654	0.338631
$293$	−6.08806	−0.355668	−0.177834	−	0.984060i	$-0.556909\pi$
$293$	−6.08806	−0.355668	−0.177834	+	0.984060i	$0.556909\pi$
$294$	2.90038	0.169154
$295$	2.34304	0.136417
$296$	−7.58524	−0.440883
$297$	−3.14559	−0.182526
$298$	12.5612	0.727651
$299$	1.14783	0.0663806
$300$	1.74109	0.100522
$301$	18.3811	1.05947
$302$	−10.0366	−0.577542
$303$	−1.34281	−0.0771422
$304$	−1.00000	−0.0573539
$305$	−0.569471	−0.0326078
$306$	19.3027	1.10346
$307$	−22.8889	−1.30634	−0.653169	−	0.757213i	$-0.726561\pi$
$307$	−22.8889	−1.30634	−0.653169	+	0.757213i	$0.726561\pi$
$308$	5.96931	0.340133
$309$	0.393460	0.0223831
$310$	1.41259	0.0802297
$311$	6.32785	0.358819	0.179410	−	0.983774i	$-0.442581\pi$
$311$	6.32785	0.358819	0.179410	+	0.983774i	$0.442581\pi$
$312$	−0.110451	−0.00625303
$313$	8.71500	0.492601	0.246301	−	0.969194i	$-0.420785\pi$
$313$	8.71500	0.492601	0.246301	+	0.969194i	$0.420785\pi$
$314$	10.5317	0.594340
$315$	−2.00428	−0.112928
$316$	−5.62658	−0.316520
$317$	−18.9379	−1.06366	−0.531830	−	0.846851i	$-0.678496\pi$
$317$	−18.9379	−1.06366	−0.531830	+	0.846851i	$0.678496\pi$
$318$	1.09085	0.0611717
$319$	−10.9029	−0.610445
$320$	−0.178230	−0.00996334
$321$	0.147666	0.00824192
$322$	−14.2343	−0.793247
$323$	−6.70888	−0.373292
$324$	7.90979	0.439433
$325$	1.56586	0.0868580
$326$	2.70092	0.149590
$327$	−6.94639	−0.384136
$328$	5.82883	0.321843
$329$	6.55291	0.361273
$330$	0.0953922	0.00525117
$331$	−15.3285	−0.842530	−0.421265	−	0.906938i	$-0.638414\pi$
$331$	−15.3285	−0.842530	−0.421265	+	0.906938i	$0.638414\pi$
$332$	5.96257	0.327239
$333$	−21.8242	−1.19596
$334$	−13.5906	−0.743645
$335$	−0.366495	−0.0200237
$336$	1.36971	0.0747236
$337$	3.20160	0.174402	0.0872010	−	0.996191i	$-0.472208\pi$
$337$	3.20160	0.174402	0.0872010	+	0.996191i	$0.472208\pi$
$338$	12.9007	0.701704
$339$	−1.13424	−0.0616035
$340$	−1.19572	−0.0648471
$341$	−12.1046	−0.655501
$342$	−2.87719	−0.155581
$343$	−4.98848	−0.269353
$344$	4.70286	0.253561
$345$	−0.227471	−0.0122466
$346$	−18.5724	−0.998460
$347$	−7.73645	−0.415315	−0.207657	−	0.978202i	$-0.566584\pi$
$347$	−7.73645	−0.415315	−0.207657	+	0.978202i	$0.566584\pi$
$348$	−2.50176	−0.134108
$349$	18.1960	0.974009	0.487004	−	0.873400i	$-0.338090\pi$
$349$	18.1960	0.974009	0.487004	+	0.873400i	$0.338090\pi$
$350$	−19.4183	−1.03795
$351$	−0.649139	−0.0346485
$352$	1.52727	0.0814035
$353$	−11.8165	−0.628927	−0.314463	−	0.949270i	$-0.601825\pi$
$353$	−11.8165	−0.628927	−0.314463	+	0.949270i	$0.601825\pi$
$354$	−4.60701	−0.244860
$355$	−1.01939	−0.0541037
$356$	6.61534	0.350613
$357$	9.18920	0.486344
$358$	−12.9704	−0.685506
$359$	−4.87578	−0.257334	−0.128667	−	0.991688i	$-0.541070\pi$
$359$	−4.87578	−0.257334	−0.128667	+	0.991688i	$0.541070\pi$
$360$	−0.512800	−0.0270270
$361$	1.00000	0.0526316
$362$	9.98409	0.524752
$363$	3.03746	0.159425
$364$	1.23185	0.0645667
$365$	−1.03133	−0.0539824
$366$	1.11972	0.0585288
$367$	−20.7486	−1.08307	−0.541534	−	0.840679i	$-0.682156\pi$
$367$	−20.7486	−1.08307	−0.541534	+	0.840679i	$0.682156\pi$
$368$	−3.64189	−0.189847
$369$	16.7706	0.873045
$370$	1.35191	0.0702827
$371$	−12.1662	−0.631638
$372$	−2.77750	−0.144007
$373$	3.88759	0.201292	0.100646	−	0.994922i	$-0.467909\pi$
$373$	3.88759	0.201292	0.100646	+	0.994922i	$0.467909\pi$
$374$	10.2462	0.529820
$375$	−0.622610	−0.0321515
$376$	1.67658	0.0864631
$377$	−2.24997	−0.115879
$378$	8.05003	0.414049
$379$	2.86778	0.147308	0.0736540	−	0.997284i	$-0.476534\pi$
$379$	2.86778	0.147308	0.0736540	+	0.997284i	$0.476534\pi$
$380$	0.178230	0.00914299
$381$	0.950905	0.0487163
$382$	0.371920	0.0190291
$383$	10.3522	0.528975	0.264487	−	0.964389i	$-0.414797\pi$
$383$	10.3522	0.528975	0.264487	+	0.964389i	$0.414797\pi$
$384$	0.350444	0.0178835
$385$	−1.06391	−0.0542217
$386$	−3.37266	−0.171664
$387$	13.5310	0.687821
$388$	5.63552	0.286100
$389$	16.1807	0.820394	0.410197	−	0.911997i	$-0.365460\pi$
$389$	16.1807	0.820394	0.410197	+	0.911997i	$0.365460\pi$
$390$	0.0196856	0.000996817 0
$391$	−24.4330	−1.23563
$392$	−8.27632	−0.418017
$393$	1.82271	0.0919436
$394$	26.2737	1.32365
$395$	1.00282	0.0504575
$396$	4.39423	0.220819
$397$	7.66033	0.384461	0.192230	−	0.981350i	$-0.438428\pi$
$397$	7.66033	0.384461	0.192230	+	0.981350i	$0.438428\pi$
$398$	6.26480	0.314026
$399$	−1.36971	−0.0685711
$400$	−4.96823	−0.248412
$401$	36.2291	1.80920	0.904598	−	0.426266i	$-0.140171\pi$
$401$	36.2291	1.80920	0.904598	+	0.426266i	$0.140171\pi$
$402$	0.720620	0.0359412
$403$	−2.49796	−0.124432
$404$	3.83173	0.190636
$405$	−1.40976	−0.0700514
$406$	27.9021	1.38476
$407$	−11.5847	−0.574231
$408$	2.35108	0.116396
$409$	−6.16561	−0.304870	−0.152435	−	0.988314i	$-0.548711\pi$
$409$	−6.16561	−0.304870	−0.152435	+	0.988314i	$0.548711\pi$
$410$	−1.03887	−0.0513061
$411$	3.80879	0.187874
$412$	−1.12275	−0.0553138
$413$	51.3819	2.52834
$414$	−10.4784	−0.514986
$415$	−1.06271	−0.0521663
$416$	0.315173	0.0154527
$417$	−0.251201	−0.0123014
$418$	−1.52727	−0.0747010
$419$	22.0812	1.07874	0.539369	−	0.842070i	$-0.318663\pi$
$419$	22.0812	1.07874	0.539369	+	0.842070i	$0.318663\pi$
$420$	−0.244122	−0.0119120
$421$	−5.97402	−0.291156	−0.145578	−	0.989347i	$-0.546504\pi$
$421$	−5.97402	−0.291156	−0.145578	+	0.989347i	$0.546504\pi$
$422$	1.00000	0.0486792
$423$	4.82384	0.234543
$424$	−3.11276	−0.151169
$425$	−33.3313	−1.61680
$426$	2.00438	0.0971124
$427$	−12.4882	−0.604349
$428$	−0.421369	−0.0203677
$429$	−0.168687	−0.00814430
$430$	−0.838189	−0.0404211
$431$	30.4508	1.46676	0.733382	−	0.679817i	$-0.237941\pi$
$431$	30.4508	1.46676	0.733382	+	0.679817i	$0.237941\pi$
$432$	2.05962	0.0990937
$433$	−13.8536	−0.665759	−0.332880	−	0.942969i	$-0.608020\pi$
$433$	−13.8536	−0.665759	−0.332880	+	0.942969i	$0.608020\pi$
$434$	30.9774	1.48696
$435$	0.445888	0.0213787
$436$	19.8217	0.949287
$437$	3.64189	0.174215
$438$	2.02786	0.0968947
$439$	2.92118	0.139420	0.0697102	−	0.997567i	$-0.477793\pi$
$439$	2.92118	0.139420	0.0697102	+	0.997567i	$0.477793\pi$
$440$	−0.272204	−0.0129768
$441$	−23.8125	−1.13393
$442$	2.11446	0.100575
$443$	26.4299	1.25572	0.627861	−	0.778325i	$-0.283930\pi$
$443$	26.4299	1.25572	0.627861	+	0.778325i	$0.283930\pi$
$444$	−2.65820	−0.126153
$445$	−1.17905	−0.0558924
$446$	−6.21424	−0.294253
$447$	4.40199	0.208207
$448$	−3.90849	−0.184659
$449$	14.6511	0.691429	0.345715	−	0.938340i	$-0.387637\pi$
$449$	14.6511	0.691429	0.345715	+	0.938340i	$0.387637\pi$
$450$	−14.2945	−0.673852
$451$	8.90217	0.419187
$452$	3.23659	0.152236
$453$	−3.51727	−0.165256
$454$	17.2456	0.809375
$455$	−0.219553	−0.0102928
$456$	−0.350444	−0.0164110
$457$	−38.6663	−1.80873	−0.904367	−	0.426755i	$-0.859657\pi$
$457$	−38.6663	−1.80873	−0.904367	+	0.426755i	$0.859657\pi$
$458$	0.785104	0.0366855
$459$	13.8178	0.644958
$460$	0.649093	0.0302641
$461$	15.1128	0.703875	0.351937	−	0.936024i	$-0.385523\pi$
$461$	15.1128	0.703875	0.351937	+	0.936024i	$0.385523\pi$
$462$	2.09191	0.0973243
$463$	−15.5067	−0.720658	−0.360329	−	0.932825i	$-0.617336\pi$
$463$	−15.5067	−0.720658	−0.360329	+	0.932825i	$0.617336\pi$
$464$	7.13883	0.331412
$465$	0.495033	0.0229566
$466$	11.8271	0.547881
$467$	−32.0065	−1.48108	−0.740542	−	0.672010i	$-0.765431\pi$
$467$	−32.0065	−1.48108	−0.740542	+	0.672010i	$0.765431\pi$
$468$	0.906814	0.0419175
$469$	−8.03706	−0.371117
$470$	−0.298817	−0.0137834
$471$	3.69078	0.170062
$472$	13.1462	0.605103
$473$	7.18252	0.330253
$474$	−1.97180	−0.0905677
$475$	4.96823	0.227958
$476$	−26.2216	−1.20187
$477$	−8.95600	−0.410067
$478$	5.54195	0.253483
$479$	4.50579	0.205875	0.102937	−	0.994688i	$-0.467176\pi$
$479$	4.50579	0.205875	0.102937	+	0.994688i	$0.467176\pi$
$480$	−0.0624595	−0.00285087
$481$	−2.39067	−0.109005
$482$	−16.5329	−0.753053
$483$	−4.98832	−0.226977
$484$	−8.66746	−0.393975
$485$	−1.00442	−0.0456082
$486$	8.95081	0.406017
$487$	−3.49804	−0.158511	−0.0792557	−	0.996854i	$-0.525254\pi$
$487$	−3.49804	−0.158511	−0.0792557	+	0.996854i	$0.525254\pi$
$488$	−3.19516	−0.144638
$489$	0.946519	0.0428031
$490$	1.47509	0.0666376
$491$	−19.9387	−0.899821	−0.449910	−	0.893074i	$-0.648544\pi$
$491$	−19.9387	−0.899821	−0.449910	+	0.893074i	$0.648544\pi$
$492$	2.04268	0.0920910
$493$	47.8936	2.15702
$494$	−0.315173	−0.0141803
$495$	−0.783182	−0.0352014
$496$	7.92567	0.355873
$497$	−22.3548	−1.00275
$498$	2.08955	0.0936348
$499$	−3.53741	−0.158356	−0.0791782	−	0.996860i	$-0.525230\pi$
$499$	−3.53741	−0.158356	−0.0791782	+	0.996860i	$0.525230\pi$
$500$	1.77663	0.0794535
$501$	−4.76274	−0.212784
$502$	3.08097	0.137510
$503$	−14.5430	−0.648442	−0.324221	−	0.945981i	$-0.605102\pi$
$503$	−14.5430	−0.648442	−0.324221	+	0.945981i	$0.605102\pi$
$504$	−11.2455	−0.500913
$505$	−0.682928	−0.0303899
$506$	−5.56214	−0.247267
$507$	4.52096	0.200783
$508$	−2.71343	−0.120389
$509$	−16.2845	−0.721796	−0.360898	−	0.932605i	$-0.617530\pi$
$509$	−16.2845	−0.721796	−0.360898	+	0.932605i	$0.617530\pi$
$510$	−0.419033	−0.0185551
$511$	−22.6166	−1.00050
$512$	−1.00000	−0.0441942
$513$	−2.05962	−0.0909346
$514$	−0.207315	−0.00914427
$515$	0.200107	0.00881776
$516$	1.64809	0.0725530
$517$	2.56059	0.112614
$518$	29.6468	1.30261
$519$	−6.50859	−0.285695
$520$	−0.0561732	−0.00246336
$521$	39.4238	1.72719	0.863593	−	0.504189i	$-0.168209\pi$
$521$	39.4238	1.72719	0.863593	+	0.504189i	$0.168209\pi$
$522$	20.5398	0.899002
$523$	1.49680	0.0654503	0.0327251	−	0.999464i	$-0.489581\pi$
$523$	1.49680	0.0654503	0.0327251	+	0.999464i	$0.489581\pi$
$524$	−5.20115	−0.227213
$525$	−6.80502	−0.296996
$526$	13.4049	0.584482
$527$	53.1724	2.31623
$528$	0.535221	0.0232925
$529$	−9.73663	−0.423332
$530$	0.554786	0.0240984
$531$	37.8241	1.64143
$532$	3.90849	0.169455
$533$	1.83709	0.0795733
$534$	2.31831	0.100323
$535$	0.0751005	0.00324688
$536$	−2.05631	−0.0888189
$537$	−4.54539	−0.196148
$538$	11.2749	0.486094
$539$	−12.6401	−0.544449
$540$	−0.367086	−0.0157969
$541$	−0.0467454	−0.00200974	−0.00100487	−	0.999999i	$-0.500320\pi$
$541$	−0.0467454	−0.00200974	−0.00100487	+	0.999999i	$0.500320\pi$
$542$	23.7771	1.02131
$543$	3.49886	0.150151
$544$	−6.70888	−0.287641
$545$	−3.53281	−0.151329
$546$	0.431695	0.0184749
$547$	19.6108	0.838498	0.419249	−	0.907871i	$-0.362294\pi$
$547$	19.6108	0.838498	0.419249	+	0.907871i	$0.362294\pi$
$548$	−10.8685	−0.464278
$549$	−9.19307	−0.392351
$550$	−7.58781	−0.323545
$551$	−7.13883	−0.304125
$552$	−1.27628	−0.0543220
$553$	21.9914	0.935171
$554$	3.22032	0.136818
$555$	0.473770	0.0201104
$556$	0.716808	0.0303994
$557$	21.6090	0.915602	0.457801	−	0.889055i	$-0.348637\pi$
$557$	21.6090	0.915602	0.457801	+	0.889055i	$0.348637\pi$
$558$	22.8037	0.965356
$559$	1.48222	0.0626911
$560$	0.696609	0.0294371
$561$	3.59073	0.151601
$562$	24.0598	1.01490
$563$	−33.0227	−1.39174	−0.695870	−	0.718168i	$-0.744981\pi$
$563$	−33.0227	−1.39174	−0.695870	+	0.718168i	$0.744981\pi$
$564$	0.587547	0.0247402
$565$	−0.576855	−0.0242685
$566$	17.9884	0.756108
$567$	−30.9153	−1.29832
$568$	−5.71954	−0.239987
$569$	−28.6710	−1.20195	−0.600975	−	0.799268i	$-0.705221\pi$
$569$	−28.6710	−1.20195	−0.600975	+	0.799268i	$0.705221\pi$
$570$	0.0624595	0.00261614
$571$	16.0721	0.672595	0.336298	−	0.941756i	$-0.390825\pi$
$571$	16.0721	0.672595	0.336298	+	0.941756i	$0.390825\pi$
$572$	0.481354	0.0201264
$573$	0.130337	0.00544490
$574$	−22.7819	−0.950900
$575$	18.0938	0.754562
$576$	−2.87719	−0.119883
$577$	−24.4920	−1.01962	−0.509808	−	0.860288i	$-0.670284\pi$
$577$	−24.4920	−1.01962	−0.509808	+	0.860288i	$0.670284\pi$
$578$	−28.0090	−1.16502
$579$	−1.18193	−0.0491193
$580$	−1.27235	−0.0528315
$581$	−23.3047	−0.966841
$582$	1.97493	0.0818636
$583$	−4.75401	−0.196891
$584$	−5.78654	−0.239449
$585$	−0.161621	−0.00668221
$586$	6.08806	0.251496
$587$	1.70612	0.0704190	0.0352095	−	0.999380i	$-0.488790\pi$
$587$	1.70612	0.0704190	0.0352095	+	0.999380i	$0.488790\pi$
$588$	−2.90038	−0.119610
$589$	−7.92567	−0.326572
$590$	−2.34304	−0.0964616
$591$	9.20746	0.378744
$592$	7.58524	0.311751
$593$	−18.4026	−0.755705	−0.377852	−	0.925866i	$-0.623337\pi$
$593$	−18.4026	−0.755705	−0.377852	+	0.925866i	$0.623337\pi$
$594$	3.14559	0.129065
$595$	4.67347	0.191593
$596$	−12.5612	−0.514527
$597$	2.19546	0.0898542
$598$	−1.14783	−0.0469382
$599$	36.7569	1.50185	0.750923	−	0.660390i	$-0.229609\pi$
$599$	36.7569	1.50185	0.750923	+	0.660390i	$0.229609\pi$
$600$	−1.74109	−0.0710796
$601$	14.5290	0.592649	0.296324	−	0.955087i	$-0.404239\pi$
$601$	14.5290	0.592649	0.296324	+	0.955087i	$0.404239\pi$
$602$	−18.3811	−0.749158
$603$	−5.91638	−0.240934
$604$	10.0366	0.408384
$605$	1.54480	0.0628050
$606$	1.34281	0.0545478
$607$	−17.9592	−0.728942	−0.364471	−	0.931215i	$-0.618750\pi$
$607$	−17.9592	−0.728942	−0.364471	+	0.931215i	$0.618750\pi$
$608$	1.00000	0.0405554
$609$	9.77811	0.396229
$610$	0.569471	0.0230572
$611$	0.528414	0.0213773
$612$	−19.3027	−0.780266
$613$	−14.1782	−0.572652	−0.286326	−	0.958132i	$-0.592434\pi$
$613$	−14.1782	−0.572652	−0.286326	+	0.958132i	$0.592434\pi$
$614$	22.8889	0.923720
$615$	−0.364065	−0.0146805
$616$	−5.96931	−0.240510
$617$	31.1767	1.25513	0.627563	−	0.778565i	$-0.284052\pi$
$617$	31.1767	1.25513	0.627563	+	0.778565i	$0.284052\pi$
$618$	−0.393460	−0.0158273
$619$	−4.33432	−0.174211	−0.0871056	−	0.996199i	$-0.527762\pi$
$619$	−4.33432	−0.174211	−0.0871056	+	0.996199i	$0.527762\pi$
$620$	−1.41259	−0.0567310
$621$	−7.50093	−0.301002
$622$	−6.32785	−0.253724
$623$	−25.8560	−1.03590
$624$	0.110451	0.00442156
$625$	24.5245	0.980981
$626$	−8.71500	−0.348322
$627$	−0.535221	−0.0213747
$628$	−10.5317	−0.420262
$629$	50.8884	2.02905
$630$	2.00428	0.0798523
$631$	−35.6623	−1.41969	−0.709847	−	0.704356i	$-0.751236\pi$
$631$	−35.6623	−1.41969	−0.709847	+	0.704356i	$0.751236\pi$
$632$	5.62658	0.223813
$633$	0.350444	0.0139289
$634$	18.9379	0.752122
$635$	0.483614	0.0191916
$636$	−1.09085	−0.0432549
$637$	−2.60848	−0.103352
$638$	10.9029	0.431650
$639$	−16.4562	−0.650998
$640$	0.178230	0.00704514
$641$	−22.6249	−0.893628	−0.446814	−	0.894627i	$-0.647442\pi$
$641$	−22.6249	−0.893628	−0.446814	+	0.894627i	$0.647442\pi$
$642$	−0.147666	−0.00582792
$643$	9.33857	0.368277	0.184139	−	0.982900i	$-0.441050\pi$
$643$	9.33857	0.368277	0.184139	+	0.982900i	$0.441050\pi$
$644$	14.2343	0.560910
$645$	−0.293738	−0.0115659
$646$	6.70888	0.263957
$647$	15.8243	0.622118	0.311059	−	0.950391i	$-0.399316\pi$
$647$	15.8243	0.622118	0.311059	+	0.950391i	$0.399316\pi$
$648$	−7.90979	−0.310726
$649$	20.0778	0.788121
$650$	−1.56586	−0.0614179
$651$	10.8558	0.425474
$652$	−2.70092	−0.105776
$653$	−5.01270	−0.196162	−0.0980811	−	0.995178i	$-0.531270\pi$
$653$	−5.01270	−0.196162	−0.0980811	+	0.995178i	$0.531270\pi$
$654$	6.94639	0.271625
$655$	0.926999	0.0362209
$656$	−5.82883	−0.227578
$657$	−16.6490	−0.649538
$658$	−6.55291	−0.255459
$659$	−20.6192	−0.803211	−0.401606	−	0.915813i	$-0.631548\pi$
$659$	−20.6192	−0.803211	−0.401606	+	0.915813i	$0.631548\pi$
$660$	−0.0953922	−0.00371314
$661$	−23.0752	−0.897521	−0.448761	−	0.893652i	$-0.648134\pi$
$661$	−23.0752	−0.897521	−0.448761	+	0.893652i	$0.648134\pi$
$662$	15.3285	0.595759
$663$	0.740999	0.0287780
$664$	−5.96257	−0.231393
$665$	−0.696609	−0.0270133
$666$	21.8242	0.845669
$667$	−25.9989	−1.00668
$668$	13.5906	0.525836
$669$	−2.17774	−0.0841963
$670$	0.366495	0.0141589
$671$	−4.87985	−0.188385
$672$	−1.36971	−0.0528376
$673$	−32.8708	−1.26708	−0.633538	−	0.773712i	$-0.718398\pi$
$673$	−32.8708	−1.26708	−0.633538	+	0.773712i	$0.718398\pi$
$674$	−3.20160	−0.123321
$675$	−10.2327	−0.393857
$676$	−12.9007	−0.496179
$677$	−27.6238	−1.06167	−0.530835	−	0.847475i	$-0.678121\pi$
$677$	−27.6238	−1.06167	−0.530835	+	0.847475i	$0.678121\pi$
$678$	1.13424	0.0435603
$679$	−22.0264	−0.845296
$680$	1.19572	0.0458538
$681$	6.04360	0.231591
$682$	12.1046	0.463509
$683$	28.4349	1.08803	0.544016	−	0.839075i	$-0.316903\pi$
$683$	28.4349	1.08803	0.544016	+	0.839075i	$0.316903\pi$
$684$	2.87719	0.110012
$685$	1.93708	0.0740121
$686$	4.98848	0.190461
$687$	0.275135	0.0104970
$688$	−4.70286	−0.179295
$689$	−0.981059	−0.0373754
$690$	0.227471	0.00865966
$691$	8.57183	0.326088	0.163044	−	0.986619i	$-0.447869\pi$
$691$	8.57183	0.326088	0.163044	+	0.986619i	$0.447869\pi$
$692$	18.5724	0.706018
$693$	−17.1748	−0.652418
$694$	7.73645	0.293672
$695$	−0.127756	−0.00484608
$696$	2.50176	0.0948290
$697$	−39.1049	−1.48120
$698$	−18.1960	−0.688728
$699$	4.14475	0.156769
$700$	19.4183	0.733943
$701$	23.0686	0.871288	0.435644	−	0.900119i	$-0.356521\pi$
$701$	23.0686	0.871288	0.435644	+	0.900119i	$0.356521\pi$
$702$	0.649139	0.0245002
$703$	−7.58524	−0.286083
$704$	−1.52727	−0.0575610
$705$	−0.104718	−0.00394392
$706$	11.8165	0.444718
$707$	−14.9763	−0.563242
$708$	4.60701	0.173142
$709$	−17.6685	−0.663554	−0.331777	−	0.943358i	$-0.607648\pi$
$709$	−17.6685	−0.663554	−0.331777	+	0.943358i	$0.607648\pi$
$710$	1.01939	0.0382571
$711$	16.1887	0.607125
$712$	−6.61534	−0.247921
$713$	−28.8644	−1.08098
$714$	−9.18920	−0.343897
$715$	−0.0857915	−0.00320842
$716$	12.9704	0.484726
$717$	1.94214	0.0725306
$718$	4.87578	0.181963
$719$	−39.2821	−1.46498	−0.732488	−	0.680779i	$-0.761641\pi$
$719$	−39.2821	−1.46498	−0.732488	+	0.680779i	$0.761641\pi$
$720$	0.512800	0.0191109
$721$	4.38825	0.163427
$722$	−1.00000	−0.0372161
$723$	−5.79385	−0.215476
$724$	−9.98409	−0.371056
$725$	−35.4674	−1.31723
$726$	−3.03746	−0.112731
$727$	26.8301	0.995072	0.497536	−	0.867443i	$-0.334238\pi$
$727$	26.8301	0.995072	0.497536	+	0.867443i	$0.334238\pi$
$728$	−1.23185	−0.0456555
$729$	−20.5926	−0.762689
$730$	1.03133	0.0381713
$731$	−31.5509	−1.16695
$732$	−1.11972	−0.0413861
$733$	−19.3579	−0.715002	−0.357501	−	0.933913i	$-0.616371\pi$
$733$	−19.3579	−0.715002	−0.357501	+	0.933913i	$0.616371\pi$
$734$	20.7486	0.765844
$735$	0.516934	0.0190674
$736$	3.64189	0.134242
$737$	−3.14053	−0.115683
$738$	−16.7706	−0.617336
$739$	5.60953	0.206350	0.103175	−	0.994663i	$-0.467100\pi$
$739$	5.60953	0.206350	0.103175	+	0.994663i	$0.467100\pi$
$740$	−1.35191	−0.0496973
$741$	−0.110451	−0.00405750
$742$	12.1662	0.446635
$743$	−31.1987	−1.14457	−0.572285	−	0.820055i	$-0.693943\pi$
$743$	−31.1987	−1.14457	−0.572285	+	0.820055i	$0.693943\pi$
$744$	2.77750	0.101828
$745$	2.23878	0.0820225
$746$	−3.88759	−0.142335
$747$	−17.1555	−0.627685
$748$	−10.2462	−0.374640
$749$	1.64692	0.0601771
$750$	0.622610	0.0227345
$751$	1.29229	0.0471564	0.0235782	−	0.999722i	$-0.492494\pi$
$751$	1.29229	0.0471564	0.0235782	+	0.999722i	$0.492494\pi$
$752$	−1.67658	−0.0611386
$753$	1.07970	0.0393466
$754$	2.24997	0.0819391
$755$	−1.78882	−0.0651019
$756$	−8.05003	−0.292777
$757$	−28.4963	−1.03572	−0.517858	−	0.855467i	$-0.673270\pi$
$757$	−28.4963	−1.03572	−0.517858	+	0.855467i	$0.673270\pi$
$758$	−2.86778	−0.104163
$759$	−1.94922	−0.0707520
$760$	−0.178230	−0.00646507
$761$	34.8944	1.26492	0.632460	−	0.774593i	$-0.282045\pi$
$761$	34.8944	1.26492	0.632460	+	0.774593i	$0.282045\pi$
$762$	−0.950905	−0.0344477
$763$	−77.4729	−2.80471
$764$	−0.371920	−0.0134556
$765$	3.44032	0.124385
$766$	−10.3522	−0.374042
$767$	4.14334	0.149607
$768$	−0.350444	−0.0126455
$769$	−23.3590	−0.842346	−0.421173	−	0.906980i	$-0.638382\pi$
$769$	−23.3590	−0.842346	−0.421173	+	0.906980i	$0.638382\pi$
$770$	1.06391	0.0383406
$771$	−0.0726522	−0.00261651
$772$	3.37266	0.121385
$773$	29.8991	1.07540	0.537698	−	0.843137i	$-0.319294\pi$
$773$	29.8991	1.07540	0.537698	+	0.843137i	$0.319294\pi$
$774$	−13.5310	−0.486363
$775$	−39.3766	−1.41445
$776$	−5.63552	−0.202303
$777$	10.3896	0.372723
$778$	−16.1807	−0.580106
$779$	5.82883	0.208839
$780$	−0.0196856	−0.000704856 0
$781$	−8.73526	−0.312572
$782$	24.4330	0.873722
$783$	14.7033	0.525454
$784$	8.27632	0.295583
$785$	1.87707	0.0669954
$786$	−1.82271	−0.0650140
$787$	−41.2586	−1.47071	−0.735356	−	0.677681i	$-0.762985\pi$
$787$	−41.2586	−1.47071	−0.735356	+	0.677681i	$0.762985\pi$
$788$	−26.2737	−0.935963
$789$	4.69767	0.167242
$790$	−1.00282	−0.0356788
$791$	−12.6502	−0.449788
$792$	−4.39423	−0.156142
$793$	−1.00703	−0.0357606
$794$	−7.66033	−0.271855
$795$	0.194421	0.00689541
$796$	−6.26480	−0.222050
$797$	−25.2412	−0.894088	−0.447044	−	0.894512i	$-0.647523\pi$
$797$	−25.2412	−0.894088	−0.447044	+	0.894512i	$0.647523\pi$
$798$	1.36971	0.0484871
$799$	−11.2480	−0.397925
$800$	4.96823	0.175654
$801$	−19.0336	−0.672519
$802$	−36.2291	−1.27929
$803$	−8.83758	−0.311871
$804$	−0.720620	−0.0254143
$805$	−2.53698	−0.0894166
$806$	2.49796	0.0879870
$807$	3.95121	0.139089
$808$	−3.83173	−0.134800
$809$	1.69656	0.0596478	0.0298239	−	0.999555i	$-0.490505\pi$
$809$	1.69656	0.0596478	0.0298239	+	0.999555i	$0.490505\pi$
$810$	1.40976	0.0495339
$811$	−23.1413	−0.812600	−0.406300	−	0.913740i	$-0.633181\pi$
$811$	−23.1413	−0.812600	−0.406300	+	0.913740i	$0.633181\pi$
$812$	−27.9021	−0.979171
$813$	8.33253	0.292235
$814$	11.5847	0.406043
$815$	0.481383	0.0168621
$816$	−2.35108	−0.0823044
$817$	4.70286	0.164532
$818$	6.16561	0.215575
$819$	−3.54428	−0.123847
$820$	1.03887	0.0362789
$821$	37.2451	1.29986	0.649931	−	0.759993i	$-0.274798\pi$
$821$	37.2451	1.29986	0.649931	+	0.759993i	$0.274798\pi$
$822$	−3.80879	−0.132847
$823$	−18.5852	−0.647839	−0.323919	−	0.946085i	$-0.605001\pi$
$823$	−18.5852	−0.647839	−0.323919	+	0.946085i	$0.605001\pi$
$824$	1.12275	0.0391127
$825$	−2.65910	−0.0925780
$826$	−51.3819	−1.78780
$827$	11.8046	0.410486	0.205243	−	0.978711i	$-0.434201\pi$
$827$	11.8046	0.410486	0.205243	+	0.978711i	$0.434201\pi$
$828$	10.4784	0.364150
$829$	−14.2287	−0.494182	−0.247091	−	0.968992i	$-0.579475\pi$
$829$	−14.2287	−0.494182	−0.247091	+	0.968992i	$0.579475\pi$
$830$	1.06271	0.0368871
$831$	1.12854	0.0391486
$832$	−0.315173	−0.0109267
$833$	55.5248	1.92382
$834$	0.251201	0.00869838
$835$	−2.42225	−0.0838254
$836$	1.52727	0.0528216
$837$	16.3239	0.564237
$838$	−22.0812	−0.762783
$839$	−33.7128	−1.16390	−0.581948	−	0.813226i	$-0.697709\pi$
$839$	−33.7128	−1.16390	−0.581948	+	0.813226i	$0.697709\pi$
$840$	0.244122	0.00842302
$841$	21.9630	0.757343
$842$	5.97402	0.205878
$843$	8.43160	0.290400
$844$	−1.00000	−0.0344214
$845$	2.29928	0.0790977
$846$	−4.82384	−0.165847
$847$	33.8767	1.16402
$848$	3.11276	0.106893
$849$	6.30391	0.216350
$850$	33.3313	1.14325
$851$	−27.6246	−0.946959
$852$	−2.00438	−0.0686689
$853$	5.09969	0.174610	0.0873050	−	0.996182i	$-0.472175\pi$
$853$	5.09969	0.174610	0.0873050	+	0.996182i	$0.472175\pi$
$854$	12.4882	0.427339
$855$	−0.512800	−0.0175374
$856$	0.421369	0.0144021
$857$	12.5681	0.429318	0.214659	−	0.976689i	$-0.431136\pi$
$857$	12.5681	0.429318	0.214659	+	0.976689i	$0.431136\pi$
$858$	0.168687	0.00575889
$859$	−36.7667	−1.25447	−0.627233	−	0.778832i	$-0.715812\pi$
$859$	−36.7667	−1.25447	−0.627233	+	0.778832i	$0.715812\pi$
$860$	0.838189	0.0285820
$861$	−7.98379	−0.272087
$862$	−30.4508	−1.03716
$863$	−3.51129	−0.119526	−0.0597629	−	0.998213i	$-0.519034\pi$
$863$	−3.51129	−0.119526	−0.0597629	+	0.998213i	$0.519034\pi$
$864$	−2.05962	−0.0700698
$865$	−3.31016	−0.112549
$866$	13.8536	0.470763
$867$	−9.81560	−0.333355
$868$	−30.9774	−1.05144
$869$	8.59328	0.291507
$870$	−0.445888	−0.0151170
$871$	−0.648093	−0.0219598
$872$	−19.8217	−0.671247
$873$	−16.2145	−0.548776
$874$	−3.64189	−0.123189
$875$	−6.94396	−0.234749
$876$	−2.02786	−0.0685149
$877$	−26.0693	−0.880297	−0.440149	−	0.897925i	$-0.645074\pi$
$877$	−26.0693	−0.880297	−0.440149	+	0.897925i	$0.645074\pi$
$878$	−2.92118	−0.0985852
$879$	2.13352	0.0719620
$880$	0.272204	0.00917600
$881$	−3.66429	−0.123453	−0.0617266	−	0.998093i	$-0.519661\pi$
$881$	−3.66429	−0.123453	−0.0617266	+	0.998093i	$0.519661\pi$
$882$	23.8125	0.801810
$883$	−50.1886	−1.68898	−0.844490	−	0.535571i	$-0.820096\pi$
$883$	−50.1886	−1.68898	−0.844490	+	0.535571i	$0.820096\pi$
$884$	−2.11446	−0.0711170
$885$	−0.821105	−0.0276012
$886$	−26.4299	−0.887930
$887$	2.58173	0.0866861	0.0433431	−	0.999060i	$-0.486199\pi$
$887$	2.58173	0.0866861	0.0433431	+	0.999060i	$0.486199\pi$
$888$	2.65820	0.0892033
$889$	10.6054	0.355695
$890$	1.17905	0.0395219
$891$	−12.0803	−0.404707
$892$	6.21424	0.208068
$893$	1.67658	0.0561047
$894$	−4.40199	−0.147225
$895$	−2.31171	−0.0772718
$896$	3.90849	0.130574
$897$	−0.402249	−0.0134307
$898$	−14.6511	−0.488914
$899$	56.5801	1.88705
$900$	14.2945	0.476485
$901$	20.8831	0.695718
$902$	−8.90217	−0.296410
$903$	−6.44154	−0.214361
$904$	−3.23659	−0.107647
$905$	1.77946	0.0591513
$906$	3.51727	0.116853
$907$	57.4999	1.90925	0.954626	−	0.297808i	$-0.0962555\pi$
$907$	57.4999	1.90925	0.954626	+	0.297808i	$0.0962555\pi$
$908$	−17.2456	−0.572314
$909$	−11.0246	−0.365664
$910$	0.219553	0.00727810
$911$	0.499116	0.0165365	0.00826823	−	0.999966i	$-0.497368\pi$
$911$	0.499116	0.0165365	0.00826823	+	0.999966i	$0.497368\pi$
$912$	0.350444	0.0116044
$913$	−9.10644	−0.301379
$914$	38.6663	1.27897
$915$	0.199568	0.00659750
$916$	−0.785104	−0.0259406
$917$	20.3287	0.671312
$918$	−13.8178	−0.456054
$919$	4.17123	0.137596	0.0687981	−	0.997631i	$-0.478084\pi$
$919$	4.17123	0.137596	0.0687981	+	0.997631i	$0.478084\pi$
$920$	−0.649093	−0.0214000
$921$	8.02126	0.264310
$922$	−15.1128	−0.497714
$923$	−1.80265	−0.0593349
$924$	−2.09191	−0.0688187
$925$	−37.6852	−1.23908
$926$	15.5067	0.509582
$927$	3.23036	0.106099
$928$	−7.13883	−0.234344
$929$	−11.3410	−0.372085	−0.186042	−	0.982542i	$-0.559566\pi$
$929$	−11.3410	−0.372085	−0.186042	+	0.982542i	$0.559566\pi$
$930$	−0.495033	−0.0162328
$931$	−8.27632	−0.271245
$932$	−11.8271	−0.387411
$933$	−2.21756	−0.0725995
$934$	32.0065	1.04728
$935$	1.82618	0.0597226
$936$	−0.906814	−0.0296401
$937$	31.2345	1.02039	0.510194	−	0.860059i	$-0.329574\pi$
$937$	31.2345	1.02039	0.510194	+	0.860059i	$0.329574\pi$
$938$	8.03706	0.262419
$939$	−3.05412	−0.0996674
$940$	0.298817	0.00974632
$941$	−8.50659	−0.277307	−0.138653	−	0.990341i	$-0.544277\pi$
$941$	−8.50659	−0.277307	−0.138653	+	0.990341i	$0.544277\pi$
$942$	−3.69078	−0.120252
$943$	21.2280	0.691277
$944$	−13.1462	−0.427873
$945$	1.43475	0.0466725
$946$	−7.18252	−0.233524
$947$	21.4703	0.697691	0.348846	−	0.937180i	$-0.386574\pi$
$947$	21.4703	0.697691	0.348846	+	0.937180i	$0.386574\pi$
$948$	1.97180	0.0640411
$949$	−1.82376	−0.0592019
$950$	−4.96823	−0.161191
$951$	6.63668	0.215209
$952$	26.2216	0.849847
$953$	−25.9185	−0.839582	−0.419791	−	0.907621i	$-0.637897\pi$
$953$	−25.9185	−0.839582	−0.419791	+	0.907621i	$0.637897\pi$
$954$	8.95600	0.289961
$955$	0.0662871	0.00214500
$956$	−5.54195	−0.179239
$957$	3.82085	0.123511
$958$	−4.50579	−0.145575
$959$	42.4793	1.37173
$960$	0.0624595	0.00201587
$961$	31.8163	1.02633
$962$	2.39067	0.0770782
$963$	1.21236	0.0390677
$964$	16.5329	0.532489
$965$	−0.601108	−0.0193504
$966$	4.98832	0.160497
$967$	31.6303	1.01716	0.508580	−	0.861015i	$-0.330171\pi$
$967$	31.6303	1.01716	0.508580	+	0.861015i	$0.330171\pi$
$968$	8.66746	0.278583
$969$	2.35108	0.0755277
$970$	1.00442	0.0322499
$971$	47.7418	1.53211	0.766053	−	0.642777i	$-0.222218\pi$
$971$	47.7418	1.53211	0.766053	+	0.642777i	$0.222218\pi$
$972$	−8.95081	−0.287097
$973$	−2.80164	−0.0898165
$974$	3.49804	0.112085
$975$	−0.548744	−0.0175739
$976$	3.19516	0.102274
$977$	43.2744	1.38447	0.692236	−	0.721671i	$-0.256626\pi$
$977$	43.2744	1.38447	0.692236	+	0.721671i	$0.256626\pi$
$978$	−0.946519	−0.0302663
$979$	−10.1034	−0.322906
$980$	−1.47509	−0.0471199
$981$	−57.0308	−1.82085
$982$	19.9387	0.636269
$983$	12.5169	0.399228	0.199614	−	0.979875i	$-0.436031\pi$
$983$	12.5169	0.399228	0.199614	+	0.979875i	$0.436031\pi$
$984$	−2.04268	−0.0651181
$985$	4.68276	0.149205
$986$	−47.8936	−1.52524
$987$	−2.29643	−0.0730960
$988$	0.315173	0.0100270
$989$	17.1273	0.544617
$990$	0.783182	0.0248912
$991$	−3.47662	−0.110439	−0.0552193	−	0.998474i	$-0.517586\pi$
$991$	−3.47662	−0.110439	−0.0552193	+	0.998474i	$0.517586\pi$
$992$	−7.92567	−0.251640
$993$	5.37177	0.170468
$994$	22.3548	0.709051
$995$	1.11657	0.0353977
$996$	−2.08955	−0.0662098
$997$	−34.8244	−1.10290	−0.551450	−	0.834208i	$-0.685925\pi$
$997$	−34.8244	−1.10290	−0.551450	+	0.834208i	$0.685925\pi$
$998$	3.53741	0.111975
$999$	15.6227	0.494282

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.f.1.19	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.f.1.19	✓	34	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.350444 q^{3} +1.00000 q^{4} -0.178230 q^{5} +0.350444 q^{6} -3.90849 q^{7} -1.00000 q^{8} -2.87719 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.350444 q^{3} +1.00000 q^{4} -0.178230 q^{5} +0.350444 q^{6} -3.90849 q^{7} -1.00000 q^{8} -2.87719 q^{9} +0.178230 q^{10} -1.52727 q^{11} -0.350444 q^{12} -0.315173 q^{13} +3.90849 q^{14} +0.0624595 q^{15} +1.00000 q^{16} +6.70888 q^{17} +2.87719 q^{18} -1.00000 q^{19} -0.178230 q^{20} +1.36971 q^{21} +1.52727 q^{22} -3.64189 q^{23} +0.350444 q^{24} -4.96823 q^{25} +0.315173 q^{26} +2.05962 q^{27} -3.90849 q^{28} +7.13883 q^{29} -0.0624595 q^{30} +7.92567 q^{31} -1.00000 q^{32} +0.535221 q^{33} -6.70888 q^{34} +0.696609 q^{35} -2.87719 q^{36} +7.58524 q^{37} +1.00000 q^{38} +0.110451 q^{39} +0.178230 q^{40} -5.82883 q^{41} -1.36971 q^{42} -4.70286 q^{43} -1.52727 q^{44} +0.512800 q^{45} +3.64189 q^{46} -1.67658 q^{47} -0.350444 q^{48} +8.27632 q^{49} +4.96823 q^{50} -2.35108 q^{51} -0.315173 q^{52} +3.11276 q^{53} -2.05962 q^{54} +0.272204 q^{55} +3.90849 q^{56} +0.350444 q^{57} -7.13883 q^{58} -13.1462 q^{59} +0.0624595 q^{60} +3.19516 q^{61} -7.92567 q^{62} +11.2455 q^{63} +1.00000 q^{64} +0.0561732 q^{65} -0.535221 q^{66} +2.05631 q^{67} +6.70888 q^{68} +1.27628 q^{69} -0.696609 q^{70} +5.71954 q^{71} +2.87719 q^{72} +5.78654 q^{73} -7.58524 q^{74} +1.74109 q^{75} -1.00000 q^{76} +5.96931 q^{77} -0.110451 q^{78} -5.62658 q^{79} -0.178230 q^{80} +7.90979 q^{81} +5.82883 q^{82} +5.96257 q^{83} +1.36971 q^{84} -1.19572 q^{85} +4.70286 q^{86} -2.50176 q^{87} +1.52727 q^{88} +6.61534 q^{89} -0.512800 q^{90} +1.23185 q^{91} -3.64189 q^{92} -2.77750 q^{93} +1.67658 q^{94} +0.178230 q^{95} +0.350444 q^{96} +5.63552 q^{97} -8.27632 q^{98} +4.39423 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * q^98 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more