LMFDB - Embedded newform 4018.2.a.bs.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4018,2,Mod(1,4018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4018, 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("4018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4018 = 2 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4018.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:	$32.0838915322$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 17x^{8} + 36x^{7} + 75x^{6} - 174x^{5} - 69x^{4} + 260x^{3} - 104x^{2} - 24x + 14 $ x^10 - 2x^9 - 17x^8 + 36x^7 + 75x^6 - 174x^5 - 69x^4 + 260x^3 - 104x^2 - 24*x + 14
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$2.39018$ of defining polynomial
Character	$\chi$	$=$	4018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.25734 q^{3} +1.00000 q^{4} -3.63252 q^{5} -2.25734 q^{6} -1.00000 q^{8} +2.09559 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.25734 q^{3} +1.00000 q^{4} -3.63252 q^{5} -2.25734 q^{6} -1.00000 q^{8} +2.09559 q^{9} +3.63252 q^{10} -3.11243 q^{11} +2.25734 q^{12} -0.434391 q^{13} -8.19983 q^{15} +1.00000 q^{16} +7.12850 q^{17} -2.09559 q^{18} -5.46927 q^{19} -3.63252 q^{20} +3.11243 q^{22} -0.862698 q^{23} -2.25734 q^{24} +8.19519 q^{25} +0.434391 q^{26} -2.04157 q^{27} +6.85331 q^{29} +8.19983 q^{30} -0.633510 q^{31} -1.00000 q^{32} -7.02581 q^{33} -7.12850 q^{34} +2.09559 q^{36} -1.02633 q^{37} +5.46927 q^{38} -0.980568 q^{39} +3.63252 q^{40} +1.00000 q^{41} -10.9826 q^{43} -3.11243 q^{44} -7.61225 q^{45} +0.862698 q^{46} +9.41043 q^{47} +2.25734 q^{48} -8.19519 q^{50} +16.0915 q^{51} -0.434391 q^{52} -2.28202 q^{53} +2.04157 q^{54} +11.3060 q^{55} -12.3460 q^{57} -6.85331 q^{58} +12.3540 q^{59} -8.19983 q^{60} -1.00190 q^{61} +0.633510 q^{62} +1.00000 q^{64} +1.57793 q^{65} +7.02581 q^{66} +7.10066 q^{67} +7.12850 q^{68} -1.94740 q^{69} -7.03964 q^{71} -2.09559 q^{72} -5.88752 q^{73} +1.02633 q^{74} +18.4993 q^{75} -5.46927 q^{76} +0.980568 q^{78} +16.0891 q^{79} -3.63252 q^{80} -10.8953 q^{81} -1.00000 q^{82} +13.8718 q^{83} -25.8944 q^{85} +10.9826 q^{86} +15.4702 q^{87} +3.11243 q^{88} -2.60445 q^{89} +7.61225 q^{90} -0.862698 q^{92} -1.43005 q^{93} -9.41043 q^{94} +19.8672 q^{95} -2.25734 q^{96} -5.15118 q^{97} -6.52236 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 4 q^{5} - 4 q^{6} - 10 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 4 * q^5 - 4 * q^6 - 10 * q^8 + 10 * q^9	$ 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 4 q^{5} - 4 q^{6} - 10 q^{8} + 10 q^{9} - 4 q^{10} + 4 q^{11} + 4 q^{12} + 4 q^{13} + 4 q^{15} + 10 q^{16} + 20 q^{17} - 10 q^{18} + 4 q^{20} - 4 q^{22} + 4 q^{23} - 4 q^{24} + 6 q^{25} - 4 q^{26} + 16 q^{27} - 4 q^{29} - 4 q^{30} - 4 q^{31} - 10 q^{32} + 36 q^{33} - 20 q^{34} + 10 q^{36} - 16 q^{37} + 20 q^{39} - 4 q^{40} + 10 q^{41} - 8 q^{43} + 4 q^{44} + 4 q^{45} - 4 q^{46} + 24 q^{47} + 4 q^{48} - 6 q^{50} + 20 q^{51} + 4 q^{52} - 4 q^{53} - 16 q^{54} + 20 q^{55} - 4 q^{57} + 4 q^{58} + 4 q^{60} + 4 q^{62} + 10 q^{64} - 12 q^{65} - 36 q^{66} + 8 q^{67} + 20 q^{68} + 4 q^{71} - 10 q^{72} - 24 q^{73} + 16 q^{74} + 48 q^{75} - 20 q^{78} + 24 q^{79} + 4 q^{80} - 18 q^{81} - 10 q^{82} + 48 q^{83} + 8 q^{85} + 8 q^{86} + 4 q^{87} - 4 q^{88} + 20 q^{89} - 4 q^{90} + 4 q^{92} + 4 q^{93} - 24 q^{94} - 4 q^{95} - 4 q^{96} + 4 q^{97} + 32 q^{99}+O(q^{100}) $ 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 4 * q^5 - 4 * q^6 - 10 * q^8 + 10 * q^9 - 4 * q^10 + 4 * q^11 + 4 * q^12 + 4 * q^13 + 4 * q^15 + 10 * q^16 + 20 * q^17 - 10 * q^18 + 4 * q^20 - 4 * q^22 + 4 * q^23 - 4 * q^24 + 6 * q^25 - 4 * q^26 + 16 * q^27 - 4 * q^29 - 4 * q^30 - 4 * q^31 - 10 * q^32 + 36 * q^33 - 20 * q^34 + 10 * q^36 - 16 * q^37 + 20 * q^39 - 4 * q^40 + 10 * q^41 - 8 * q^43 + 4 * q^44 + 4 * q^45 - 4 * q^46 + 24 * q^47 + 4 * q^48 - 6 * q^50 + 20 * q^51 + 4 * q^52 - 4 * q^53 - 16 * q^54 + 20 * q^55 - 4 * q^57 + 4 * q^58 + 4 * q^60 + 4 * q^62 + 10 * q^64 - 12 * q^65 - 36 * q^66 + 8 * q^67 + 20 * q^68 + 4 * q^71 - 10 * q^72 - 24 * q^73 + 16 * q^74 + 48 * q^75 - 20 * q^78 + 24 * q^79 + 4 * q^80 - 18 * q^81 - 10 * q^82 + 48 * q^83 + 8 * q^85 + 8 * q^86 + 4 * q^87 - 4 * q^88 + 20 * q^89 - 4 * q^90 + 4 * q^92 + 4 * q^93 - 24 * q^94 - 4 * q^95 - 4 * q^96 + 4 * q^97 + 32 * 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
$3$	2.25734	1.30328	0.651638	−	0.758530i	$-0.274082\pi$
$3$	2.25734	1.30328	0.651638	+	0.758530i	$0.274082\pi$
$4$	1.00000	0.500000
$5$	−3.63252	−1.62451	−0.812256	−	0.583301i	$-0.801761\pi$
$5$	−3.63252	−1.62451	−0.812256	+	0.583301i	$0.801761\pi$
$6$	−2.25734	−0.921555
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	2.09559	0.698529
$10$	3.63252	1.14870
$11$	−3.11243	−0.938432	−0.469216	−	0.883083i	$-0.655463\pi$
$11$	−3.11243	−0.938432	−0.469216	+	0.883083i	$0.655463\pi$
$12$	2.25734	0.651638
$13$	−0.434391	−0.120478	−0.0602392	−	0.998184i	$-0.519186\pi$
$13$	−0.434391	−0.120478	−0.0602392	+	0.998184i	$0.519186\pi$
$14$	0	0
$15$	−8.19983	−2.11719
$16$	1.00000	0.250000
$17$	7.12850	1.72892	0.864458	−	0.502705i	$-0.167662\pi$
$17$	7.12850	1.72892	0.864458	+	0.502705i	$0.167662\pi$
$18$	−2.09559	−0.493934
$19$	−5.46927	−1.25474	−0.627369	−	0.778722i	$-0.715868\pi$
$19$	−5.46927	−1.25474	−0.627369	+	0.778722i	$0.715868\pi$
$20$	−3.63252	−0.812256
$21$	0	0
$22$	3.11243	0.663572
$23$	−0.862698	−0.179885	−0.0899425	−	0.995947i	$-0.528668\pi$
$23$	−0.862698	−0.179885	−0.0899425	+	0.995947i	$0.528668\pi$
$24$	−2.25734	−0.460778
$25$	8.19519	1.63904
$26$	0.434391	0.0851910
$27$	−2.04157	−0.392901
$28$	0	0
$29$	6.85331	1.27263	0.636314	−	0.771430i	$-0.280458\pi$
$29$	6.85331	1.27263	0.636314	+	0.771430i	$0.280458\pi$
$30$	8.19983	1.49708
$31$	−0.633510	−0.113782	−0.0568908	−	0.998380i	$-0.518119\pi$
$31$	−0.633510	−0.113782	−0.0568908	+	0.998380i	$0.518119\pi$
$32$	−1.00000	−0.176777
$33$	−7.02581	−1.22304
$34$	−7.12850	−1.22253
$35$	0	0
$36$	2.09559	0.349264
$37$	−1.02633	−0.168728	−0.0843638	−	0.996435i	$-0.526886\pi$
$37$	−1.02633	−0.168728	−0.0843638	+	0.996435i	$0.526886\pi$
$38$	5.46927	0.887233
$39$	−0.980568	−0.157016
$40$	3.63252	0.574352
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−10.9826	−1.67483	−0.837415	−	0.546568i	$-0.815934\pi$
$43$	−10.9826	−1.67483	−0.837415	+	0.546568i	$0.815934\pi$
$44$	−3.11243	−0.469216
$45$	−7.61225	−1.13477
$46$	0.862698	0.127198
$47$	9.41043	1.37265	0.686327	−	0.727294i	$-0.259222\pi$
$47$	9.41043	1.37265	0.686327	+	0.727294i	$0.259222\pi$
$48$	2.25734	0.325819
$49$	0	0
$50$	−8.19519	−1.15897
$51$	16.0915	2.25326
$52$	−0.434391	−0.0602392
$53$	−2.28202	−0.313460	−0.156730	−	0.987641i	$-0.550095\pi$
$53$	−2.28202	−0.313460	−0.156730	+	0.987641i	$0.550095\pi$
$54$	2.04157	0.277823
$55$	11.3060	1.52449
$56$	0	0
$57$	−12.3460	−1.63527
$58$	−6.85331	−0.899883
$59$	12.3540	1.60835	0.804177	−	0.594389i	$-0.202606\pi$
$59$	12.3540	1.60835	0.804177	+	0.594389i	$0.202606\pi$
$60$	−8.19983	−1.05859
$61$	−1.00190	−0.128280	−0.0641400	−	0.997941i	$-0.520430\pi$
$61$	−1.00190	−0.128280	−0.0641400	+	0.997941i	$0.520430\pi$
$62$	0.633510	0.0804558
$63$	0	0
$64$	1.00000	0.125000
$65$	1.57793	0.195718
$66$	7.02581	0.864817
$67$	7.10066	0.867483	0.433742	−	0.901037i	$-0.357193\pi$
$67$	7.10066	0.867483	0.433742	+	0.901037i	$0.357193\pi$
$68$	7.12850	0.864458
$69$	−1.94740	−0.234440
$70$	0	0
$71$	−7.03964	−0.835452	−0.417726	−	0.908573i	$-0.637173\pi$
$71$	−7.03964	−0.835452	−0.417726	+	0.908573i	$0.637173\pi$
$72$	−2.09559	−0.246967
$73$	−5.88752	−0.689082	−0.344541	−	0.938771i	$-0.611966\pi$
$73$	−5.88752	−0.689082	−0.344541	+	0.938771i	$0.611966\pi$
$74$	1.02633	0.119309
$75$	18.4993	2.13612
$76$	−5.46927	−0.627369
$77$	0	0
$78$	0.980568	0.111027
$79$	16.0891	1.81017	0.905084	−	0.425233i	$-0.139808\pi$
$79$	16.0891	1.81017	0.905084	+	0.425233i	$0.139808\pi$
$80$	−3.63252	−0.406128
$81$	−10.8953	−1.21059
$82$	−1.00000	−0.110432
$83$	13.8718	1.52263	0.761314	−	0.648384i	$-0.224555\pi$
$83$	13.8718	1.52263	0.761314	+	0.648384i	$0.224555\pi$
$84$	0	0
$85$	−25.8944	−2.80864
$86$	10.9826	1.18428
$87$	15.4702	1.65858
$88$	3.11243	0.331786
$89$	−2.60445	−0.276071	−0.138035	−	0.990427i	$-0.544079\pi$
$89$	−2.60445	−0.276071	−0.138035	+	0.990427i	$0.544079\pi$
$90$	7.61225	0.802402
$91$	0	0
$92$	−0.862698	−0.0899425
$93$	−1.43005	−0.148289
$94$	−9.41043	−0.970612
$95$	19.8672	2.03834
$96$	−2.25734	−0.230389
$97$	−5.15118	−0.523023	−0.261512	−	0.965200i	$-0.584221\pi$
$97$	−5.15118	−0.523023	−0.261512	+	0.965200i	$0.584221\pi$
$98$	0	0
$99$	−6.52236	−0.655522
$100$	8.19519	0.819519
$101$	−1.11200	−0.110648	−0.0553242	−	0.998468i	$-0.517619\pi$
$101$	−1.11200	−0.110648	−0.0553242	+	0.998468i	$0.517619\pi$
$102$	−16.0915	−1.59329
$103$	11.7778	1.16050	0.580251	−	0.814438i	$-0.302954\pi$
$103$	11.7778	1.16050	0.580251	+	0.814438i	$0.302954\pi$
$104$	0.434391	0.0425955
$105$	0	0
$106$	2.28202	0.221650
$107$	−5.12239	−0.495201	−0.247600	−	0.968862i	$-0.579642\pi$
$107$	−5.12239	−0.495201	−0.247600	+	0.968862i	$0.579642\pi$
$108$	−2.04157	−0.196450
$109$	9.33805	0.894423	0.447211	−	0.894428i	$-0.352417\pi$
$109$	9.33805	0.894423	0.447211	+	0.894428i	$0.352417\pi$
$110$	−11.3060	−1.07798
$111$	−2.31678	−0.219899
$112$	0	0
$113$	12.5090	1.17675	0.588373	−	0.808589i	$-0.299769\pi$
$113$	12.5090	1.17675	0.588373	+	0.808589i	$0.299769\pi$
$114$	12.3460	1.15631
$115$	3.13377	0.292225
$116$	6.85331	0.636314
$117$	−0.910303	−0.0841575
$118$	−12.3540	−1.13728
$119$	0	0
$120$	8.19983	0.748539
$121$	−1.31279	−0.119345
$122$	1.00190	0.0907077
$123$	2.25734	0.203538
$124$	−0.633510	−0.0568908
$125$	−11.6066	−1.03812
$126$	0	0
$127$	10.3464	0.918091	0.459046	−	0.888413i	$-0.348191\pi$
$127$	10.3464	0.918091	0.459046	+	0.888413i	$0.348191\pi$
$128$	−1.00000	−0.0883883
$129$	−24.7915	−2.18277
$130$	−1.57793	−0.138394
$131$	0.235872	0.0206082	0.0103041	−	0.999947i	$-0.496720\pi$
$131$	0.235872	0.0206082	0.0103041	+	0.999947i	$0.496720\pi$
$132$	−7.02581	−0.611518
$133$	0	0
$134$	−7.10066	−0.613403
$135$	7.41605	0.638272
$136$	−7.12850	−0.611264
$137$	18.1191	1.54802	0.774009	−	0.633174i	$-0.218248\pi$
$137$	18.1191	1.54802	0.774009	+	0.633174i	$0.218248\pi$
$138$	1.94740	0.165774
$139$	9.81982	0.832907	0.416453	−	0.909157i	$-0.363273\pi$
$139$	9.81982	0.832907	0.416453	+	0.909157i	$0.363273\pi$
$140$	0	0
$141$	21.2426	1.78895
$142$	7.03964	0.590754
$143$	1.35201	0.113061
$144$	2.09559	0.174632
$145$	−24.8948	−2.06740
$146$	5.88752	0.487255
$147$	0	0
$148$	−1.02633	−0.0843638
$149$	−1.73638	−0.142250	−0.0711249	−	0.997467i	$-0.522659\pi$
$149$	−1.73638	−0.142250	−0.0711249	+	0.997467i	$0.522659\pi$
$150$	−18.4993	−1.51046
$151$	−10.4782	−0.852703	−0.426351	−	0.904558i	$-0.640201\pi$
$151$	−10.4782	−0.852703	−0.426351	+	0.904558i	$0.640201\pi$
$152$	5.46927	0.443617
$153$	14.9384	1.20770
$154$	0	0
$155$	2.30124	0.184840
$156$	−0.980568	−0.0785082
$157$	15.6582	1.24966	0.624828	−	0.780762i	$-0.285169\pi$
$157$	15.6582	1.24966	0.624828	+	0.780762i	$0.285169\pi$
$158$	−16.0891	−1.27998
$159$	−5.15131	−0.408525
$160$	3.63252	0.287176
$161$	0	0
$162$	10.8953	0.856014
$163$	−20.4574	−1.60235	−0.801173	−	0.598432i	$-0.795791\pi$
$163$	−20.4574	−1.60235	−0.801173	+	0.598432i	$0.795791\pi$
$164$	1.00000	0.0780869
$165$	25.5214	1.98684
$166$	−13.8718	−1.07666
$167$	17.9698	1.39054	0.695272	−	0.718747i	$-0.255284\pi$
$167$	17.9698	1.39054	0.695272	+	0.718747i	$0.255284\pi$
$168$	0	0
$169$	−12.8113	−0.985485
$170$	25.8944	1.98601
$171$	−11.4613	−0.876470
$172$	−10.9826	−0.837415
$173$	19.6269	1.49221	0.746103	−	0.665830i	$-0.231922\pi$
$173$	19.6269	1.49221	0.746103	+	0.665830i	$0.231922\pi$
$174$	−15.4702	−1.17280
$175$	0	0
$176$	−3.11243	−0.234608
$177$	27.8872	2.09613
$178$	2.60445	0.195212
$179$	−3.47301	−0.259585	−0.129792	−	0.991541i	$-0.541431\pi$
$179$	−3.47301	−0.259585	−0.129792	+	0.991541i	$0.541431\pi$
$180$	−7.61225	−0.567384
$181$	21.5319	1.60045	0.800227	−	0.599697i	$-0.204712\pi$
$181$	21.5319	1.60045	0.800227	+	0.599697i	$0.204712\pi$
$182$	0	0
$183$	−2.26163	−0.167184
$184$	0.862698	0.0635990
$185$	3.72816	0.274100
$186$	1.43005	0.104856
$187$	−22.1870	−1.62247
$188$	9.41043	0.686327
$189$	0	0
$190$	−19.8672	−1.44132
$191$	19.3411	1.39947	0.699737	−	0.714400i	$-0.253300\pi$
$191$	19.3411	1.39947	0.699737	+	0.714400i	$0.253300\pi$
$192$	2.25734	0.162910
$193$	−3.03964	−0.218798	−0.109399	−	0.993998i	$-0.534893\pi$
$193$	−3.03964	−0.218798	−0.109399	+	0.993998i	$0.534893\pi$
$194$	5.15118	0.369833
$195$	3.56193	0.255075
$196$	0	0
$197$	10.9058	0.777009	0.388505	−	0.921447i	$-0.372992\pi$
$197$	10.9058	0.777009	0.388505	+	0.921447i	$0.372992\pi$
$198$	6.52236	0.463524
$199$	−4.29145	−0.304213	−0.152107	−	0.988364i	$-0.548606\pi$
$199$	−4.29145	−0.304213	−0.152107	+	0.988364i	$0.548606\pi$
$200$	−8.19519	−0.579487
$201$	16.0286	1.13057
$202$	1.11200	0.0782403
$203$	0	0
$204$	16.0915	1.12663
$205$	−3.63252	−0.253706
$206$	−11.7778	−0.820599
$207$	−1.80786	−0.125655
$208$	−0.434391	−0.0301196
$209$	17.0227	1.17749
$210$	0	0
$211$	13.0265	0.896780	0.448390	−	0.893838i	$-0.351998\pi$
$211$	13.0265	0.896780	0.448390	+	0.893838i	$0.351998\pi$
$212$	−2.28202	−0.156730
$213$	−15.8909	−1.08882
$214$	5.12239	0.350160
$215$	39.8945	2.72078
$216$	2.04157	0.138911
$217$	0	0
$218$	−9.33805	−0.632452
$219$	−13.2901	−0.898065
$220$	11.3060	0.762247
$221$	−3.09656	−0.208297
$222$	2.31678	0.155492
$223$	−2.02733	−0.135760	−0.0678801	−	0.997693i	$-0.521624\pi$
$223$	−2.02733	−0.135760	−0.0678801	+	0.997693i	$0.521624\pi$
$224$	0	0
$225$	17.1737	1.14491
$226$	−12.5090	−0.832086
$227$	5.10558	0.338869	0.169435	−	0.985541i	$-0.445806\pi$
$227$	5.10558	0.338869	0.169435	+	0.985541i	$0.445806\pi$
$228$	−12.3460	−0.817635
$229$	6.55291	0.433028	0.216514	−	0.976279i	$-0.430531\pi$
$229$	6.55291	0.433028	0.216514	+	0.976279i	$0.430531\pi$
$230$	−3.13377	−0.206635
$231$	0	0
$232$	−6.85331	−0.449942
$233$	3.10069	0.203133	0.101567	−	0.994829i	$-0.467614\pi$
$233$	3.10069	0.203133	0.101567	+	0.994829i	$0.467614\pi$
$234$	0.910303	0.0595084
$235$	−34.1836	−2.22989
$236$	12.3540	0.804177
$237$	36.3186	2.35915
$238$	0	0
$239$	11.1555	0.721588	0.360794	−	0.932646i	$-0.382506\pi$
$239$	11.1555	0.721588	0.360794	+	0.932646i	$0.382506\pi$
$240$	−8.19983	−0.529297
$241$	19.9402	1.28446	0.642232	−	0.766510i	$-0.278009\pi$
$241$	19.9402	1.28446	0.642232	+	0.766510i	$0.278009\pi$
$242$	1.31279	0.0843895
$243$	−18.4696	−1.18483
$244$	−1.00190	−0.0641400
$245$	0	0
$246$	−2.25734	−0.143923
$247$	2.37580	0.151169
$248$	0.633510	0.0402279
$249$	31.3134	1.98440
$250$	11.6066	0.734065
$251$	17.7411	1.11981	0.559903	−	0.828558i	$-0.310838\pi$
$251$	17.7411	1.11981	0.559903	+	0.828558i	$0.310838\pi$
$252$	0	0
$253$	2.68509	0.168810
$254$	−10.3464	−0.649189
$255$	−58.4525	−3.66044
$256$	1.00000	0.0625000
$257$	−20.4943	−1.27840	−0.639199	−	0.769041i	$-0.720734\pi$
$257$	−20.4943	−1.27840	−0.639199	+	0.769041i	$0.720734\pi$
$258$	24.7915	1.54345
$259$	0	0
$260$	1.57793	0.0978592
$261$	14.3617	0.888967
$262$	−0.235872	−0.0145722
$263$	−1.42588	−0.0879236	−0.0439618	−	0.999033i	$-0.513998\pi$
$263$	−1.42588	−0.0879236	−0.0439618	+	0.999033i	$0.513998\pi$
$264$	7.02581	0.432409
$265$	8.28950	0.509220
$266$	0	0
$267$	−5.87912	−0.359797
$268$	7.10066	0.433742
$269$	−3.82345	−0.233120	−0.116560	−	0.993184i	$-0.537187\pi$
$269$	−3.82345	−0.233120	−0.116560	+	0.993184i	$0.537187\pi$
$270$	−7.41605	−0.451326
$271$	16.7744	1.01897	0.509487	−	0.860479i	$-0.329835\pi$
$271$	16.7744	1.01897	0.509487	+	0.860479i	$0.329835\pi$
$272$	7.12850	0.432229
$273$	0	0
$274$	−18.1191	−1.09461
$275$	−25.5069	−1.53813
$276$	−1.94740	−0.117220
$277$	−15.5181	−0.932394	−0.466197	−	0.884681i	$-0.654376\pi$
$277$	−15.5181	−0.932394	−0.466197	+	0.884681i	$0.654376\pi$
$278$	−9.81982	−0.588954
$279$	−1.32757	−0.0794797
$280$	0	0
$281$	−29.7018	−1.77186	−0.885929	−	0.463821i	$-0.846478\pi$
$281$	−29.7018	−1.77186	−0.885929	+	0.463821i	$0.846478\pi$
$282$	−21.2426	−1.26498
$283$	−8.53456	−0.507327	−0.253663	−	0.967293i	$-0.581636\pi$
$283$	−8.53456	−0.507327	−0.253663	+	0.967293i	$0.581636\pi$
$284$	−7.03964	−0.417726
$285$	44.8471	2.65651
$286$	−1.35201	−0.0799460
$287$	0	0
$288$	−2.09559	−0.123484
$289$	33.8156	1.98915
$290$	24.8948	1.46187
$291$	−11.6280	−0.681644
$292$	−5.88752	−0.344541
$293$	−20.6173	−1.20448	−0.602238	−	0.798317i	$-0.705724\pi$
$293$	−20.6173	−1.20448	−0.602238	+	0.798317i	$0.705724\pi$
$294$	0	0
$295$	−44.8762	−2.61279
$296$	1.02633	0.0596543
$297$	6.35424	0.368711
$298$	1.73638	0.100586
$299$	0.374748	0.0216722
$300$	18.4993	1.06806
$301$	0	0
$302$	10.4782	0.602952
$303$	−2.51017	−0.144205
$304$	−5.46927	−0.313684
$305$	3.63942	0.208392
$306$	−14.9384	−0.853971
$307$	−15.6938	−0.895693	−0.447847	−	0.894110i	$-0.647809\pi$
$307$	−15.6938	−0.895693	−0.447847	+	0.894110i	$0.647809\pi$
$308$	0	0
$309$	26.5865	1.51246
$310$	−2.30124	−0.130701
$311$	10.6080	0.601526	0.300763	−	0.953699i	$-0.402759\pi$
$311$	10.6080	0.601526	0.300763	+	0.953699i	$0.402759\pi$
$312$	0.980568	0.0555137
$313$	−35.1388	−1.98617	−0.993083	−	0.117418i	$-0.962538\pi$
$313$	−35.1388	−1.98617	−0.993083	+	0.117418i	$0.962538\pi$
$314$	−15.6582	−0.883641
$315$	0	0
$316$	16.0891	0.905084
$317$	−13.9182	−0.781725	−0.390863	−	0.920449i	$-0.627823\pi$
$317$	−13.9182	−0.781725	−0.390863	+	0.920449i	$0.627823\pi$
$318$	5.15131	0.288871
$319$	−21.3304	−1.19427
$320$	−3.63252	−0.203064
$321$	−11.5630	−0.645383
$322$	0	0
$323$	−38.9877	−2.16934
$324$	−10.8953	−0.605293
$325$	−3.55991	−0.197469
$326$	20.4574	1.13303
$327$	21.0791	1.16568
$328$	−1.00000	−0.0552158
$329$	0	0
$330$	−25.5214	−1.40491
$331$	−13.0095	−0.715065	−0.357532	−	0.933901i	$-0.616382\pi$
$331$	−13.0095	−0.715065	−0.357532	+	0.933901i	$0.616382\pi$
$332$	13.8718	0.761314
$333$	−2.15076	−0.117861
$334$	−17.9698	−0.983263
$335$	−25.7933	−1.40924
$336$	0	0
$337$	−11.3755	−0.619662	−0.309831	−	0.950792i	$-0.600273\pi$
$337$	−11.3755	−0.619662	−0.309831	+	0.950792i	$0.600273\pi$
$338$	12.8113	0.696843
$339$	28.2370	1.53363
$340$	−25.8944	−1.40432
$341$	1.97175	0.106776
$342$	11.4613	0.619758
$343$	0	0
$344$	10.9826	0.592142
$345$	7.07398	0.380850
$346$	−19.6269	−1.05515
$347$	−24.9908	−1.34158	−0.670790	−	0.741648i	$-0.734045\pi$
$347$	−24.9908	−1.34158	−0.670790	+	0.741648i	$0.734045\pi$
$348$	15.4702	0.829292
$349$	−33.9797	−1.81889	−0.909446	−	0.415822i	$-0.863494\pi$
$349$	−33.9797	−1.81889	−0.909446	+	0.415822i	$0.863494\pi$
$350$	0	0
$351$	0.886840	0.0473360
$352$	3.11243	0.165893
$353$	3.75329	0.199767	0.0998837	−	0.994999i	$-0.468153\pi$
$353$	3.75329	0.199767	0.0998837	+	0.994999i	$0.468153\pi$
$354$	−27.8872	−1.48219
$355$	25.5716	1.35720
$356$	−2.60445	−0.138035
$357$	0	0
$358$	3.47301	0.183554
$359$	3.63343	0.191765	0.0958824	−	0.995393i	$-0.469433\pi$
$359$	3.63343	0.191765	0.0958824	+	0.995393i	$0.469433\pi$
$360$	7.61225	0.401201
$361$	10.9130	0.574366
$362$	−21.5319	−1.13169
$363$	−2.96342	−0.155539
$364$	0	0
$365$	21.3865	1.11942
$366$	2.26163	0.118217
$367$	31.4196	1.64009	0.820046	−	0.572298i	$-0.193948\pi$
$367$	31.4196	1.64009	0.820046	+	0.572298i	$0.193948\pi$
$368$	−0.862698	−0.0449713
$369$	2.09559	0.109092
$370$	−3.72816	−0.193818
$371$	0	0
$372$	−1.43005	−0.0741445
$373$	−34.6608	−1.79467	−0.897333	−	0.441354i	$-0.854498\pi$
$373$	−34.6608	−1.79467	−0.897333	+	0.441354i	$0.854498\pi$
$374$	22.1870	1.14726
$375$	−26.2000	−1.35296
$376$	−9.41043	−0.485306
$377$	−2.97701	−0.153324
$378$	0	0
$379$	31.9925	1.64335	0.821673	−	0.569960i	$-0.193041\pi$
$379$	31.9925	1.64335	0.821673	+	0.569960i	$0.193041\pi$
$380$	19.8672	1.01917
$381$	23.3553	1.19653
$382$	−19.3411	−0.989578
$383$	18.1201	0.925892	0.462946	−	0.886386i	$-0.346792\pi$
$383$	18.1201	0.925892	0.462946	+	0.886386i	$0.346792\pi$
$384$	−2.25734	−0.115194
$385$	0	0
$386$	3.03964	0.154714
$387$	−23.0150	−1.16992
$388$	−5.15118	−0.261512
$389$	−2.11618	−0.107295	−0.0536473	−	0.998560i	$-0.517085\pi$
$389$	−2.11618	−0.107295	−0.0536473	+	0.998560i	$0.517085\pi$
$390$	−3.56193	−0.180365
$391$	−6.14975	−0.311006
$392$	0	0
$393$	0.532442	0.0268582
$394$	−10.9058	−0.549429
$395$	−58.4440	−2.94064
$396$	−6.52236	−0.327761
$397$	−33.1057	−1.66153	−0.830763	−	0.556627i	$-0.812095\pi$
$397$	−33.1057	−1.66153	−0.830763	+	0.556627i	$0.812095\pi$
$398$	4.29145	0.215111
$399$	0	0
$400$	8.19519	0.409759
$401$	−16.1609	−0.807035	−0.403518	−	0.914972i	$-0.632213\pi$
$401$	−16.1609	−0.807035	−0.403518	+	0.914972i	$0.632213\pi$
$402$	−16.0286	−0.799434
$403$	0.275191	0.0137082
$404$	−1.11200	−0.0553242
$405$	39.5773	1.96661
$406$	0	0
$407$	3.19438	0.158340
$408$	−16.0915	−0.796646
$409$	21.2525	1.05087	0.525434	−	0.850834i	$-0.323903\pi$
$409$	21.2525	1.05087	0.525434	+	0.850834i	$0.323903\pi$
$410$	3.63252	0.179397
$411$	40.9010	2.01750
$412$	11.7778	0.580251
$413$	0	0
$414$	1.80786	0.0888514
$415$	−50.3896	−2.47353
$416$	0.434391	0.0212978
$417$	22.1667	1.08551
$418$	−17.0227	−0.832608
$419$	10.0585	0.491390	0.245695	−	0.969347i	$-0.420984\pi$
$419$	10.0585	0.491390	0.245695	+	0.969347i	$0.420984\pi$
$420$	0	0
$421$	0.197707	0.00963564	0.00481782	−	0.999988i	$-0.498466\pi$
$421$	0.197707	0.00963564	0.00481782	+	0.999988i	$0.498466\pi$
$422$	−13.0265	−0.634119
$423$	19.7204	0.958837
$424$	2.28202	0.110825
$425$	58.4194	2.83376
$426$	15.8909	0.769915
$427$	0	0
$428$	−5.12239	−0.247600
$429$	3.05195	0.147349
$430$	−39.8945	−1.92388
$431$	20.2740	0.976563	0.488281	−	0.872686i	$-0.337624\pi$
$431$	20.2740	0.976563	0.488281	+	0.872686i	$0.337624\pi$
$432$	−2.04157	−0.0982251
$433$	22.7396	1.09280	0.546399	−	0.837525i	$-0.315998\pi$
$433$	22.7396	1.09280	0.546399	+	0.837525i	$0.315998\pi$
$434$	0	0
$435$	−56.1960	−2.69439
$436$	9.33805	0.447211
$437$	4.71833	0.225708
$438$	13.2901	0.635028
$439$	8.41152	0.401460	0.200730	−	0.979647i	$-0.435669\pi$
$439$	8.41152	0.401460	0.200730	+	0.979647i	$0.435669\pi$
$440$	−11.3060	−0.538990
$441$	0	0
$442$	3.09656	0.147288
$443$	−9.84909	−0.467944	−0.233972	−	0.972243i	$-0.575172\pi$
$443$	−9.84909	−0.467944	−0.233972	+	0.972243i	$0.575172\pi$
$444$	−2.31678	−0.109949
$445$	9.46070	0.448480
$446$	2.02733	0.0959969
$447$	−3.91960	−0.185391
$448$	0	0
$449$	13.2475	0.625186	0.312593	−	0.949887i	$-0.398802\pi$
$449$	13.2475	0.625186	0.312593	+	0.949887i	$0.398802\pi$
$450$	−17.1737	−0.809577
$451$	−3.11243	−0.146559
$452$	12.5090	0.588373
$453$	−23.6528	−1.11131
$454$	−5.10558	−0.239617
$455$	0	0
$456$	12.3460	0.578155
$457$	−1.23130	−0.0575978	−0.0287989	−	0.999585i	$-0.509168\pi$
$457$	−1.23130	−0.0575978	−0.0287989	+	0.999585i	$0.509168\pi$
$458$	−6.55291	−0.306197
$459$	−14.5533	−0.679292
$460$	3.13377	0.146113
$461$	−4.76640	−0.221994	−0.110997	−	0.993821i	$-0.535404\pi$
$461$	−4.76640	−0.221994	−0.110997	+	0.993821i	$0.535404\pi$
$462$	0	0
$463$	−29.3345	−1.36329	−0.681645	−	0.731683i	$-0.738735\pi$
$463$	−29.3345	−1.36329	−0.681645	+	0.731683i	$0.738735\pi$
$464$	6.85331	0.318157
$465$	5.19467	0.240897
$466$	−3.10069	−0.143637
$467$	20.1358	0.931775	0.465887	−	0.884844i	$-0.345735\pi$
$467$	20.1358	0.931775	0.465887	+	0.884844i	$0.345735\pi$
$468$	−0.910303	−0.0420788
$469$	0	0
$470$	34.1836	1.57677
$471$	35.3458	1.62865
$472$	−12.3540	−0.568639
$473$	34.1825	1.57171
$474$	−36.3186	−1.66817
$475$	−44.8217	−2.05656
$476$	0	0
$477$	−4.78218	−0.218961
$478$	−11.1555	−0.510240
$479$	0.688922	0.0314777	0.0157388	−	0.999876i	$-0.494990\pi$
$479$	0.688922	0.0314777	0.0157388	+	0.999876i	$0.494990\pi$
$480$	8.19983	0.374269
$481$	0.445828	0.0203280
$482$	−19.9402	−0.908253
$483$	0	0
$484$	−1.31279	−0.0596724
$485$	18.7118	0.849657
$486$	18.4696	0.837800
$487$	−16.5406	−0.749527	−0.374764	−	0.927120i	$-0.622276\pi$
$487$	−16.5406	−0.749527	−0.374764	+	0.927120i	$0.622276\pi$
$488$	1.00190	0.0453538
$489$	−46.1793	−2.08830
$490$	0	0
$491$	14.0168	0.632570	0.316285	−	0.948664i	$-0.397564\pi$
$491$	14.0168	0.632570	0.316285	+	0.948664i	$0.397564\pi$
$492$	2.25734	0.101769
$493$	48.8538	2.20027
$494$	−2.37580	−0.106892
$495$	23.6926	1.06490
$496$	−0.633510	−0.0284454
$497$	0	0
$498$	−31.3134	−1.40319
$499$	15.3030	0.685057	0.342528	−	0.939507i	$-0.388717\pi$
$499$	15.3030	0.685057	0.342528	+	0.939507i	$0.388717\pi$
$500$	−11.6066	−0.519062
$501$	40.5639	1.81226
$502$	−17.7411	−0.791823
$503$	15.4136	0.687258	0.343629	−	0.939105i	$-0.388344\pi$
$503$	15.4136	0.687258	0.343629	+	0.939105i	$0.388344\pi$
$504$	0	0
$505$	4.03937	0.179750
$506$	−2.68509	−0.119367
$507$	−28.9195	−1.28436
$508$	10.3464	0.459046
$509$	42.8969	1.90137	0.950685	−	0.310157i	$-0.100382\pi$
$509$	42.8969	1.90137	0.950685	+	0.310157i	$0.100382\pi$
$510$	58.4525	2.58832
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	11.1659	0.492987
$514$	20.4943	0.903964
$515$	−42.7831	−1.88525
$516$	−24.7915	−1.09138
$517$	−29.2893	−1.28814
$518$	0	0
$519$	44.3046	1.94476
$520$	−1.57793	−0.0691969
$521$	−25.3014	−1.10847	−0.554236	−	0.832359i	$-0.686990\pi$
$521$	−25.3014	−1.10847	−0.554236	+	0.832359i	$0.686990\pi$
$522$	−14.3617	−0.628594
$523$	36.4509	1.59389	0.796944	−	0.604053i	$-0.206449\pi$
$523$	36.4509	1.59389	0.796944	+	0.604053i	$0.206449\pi$
$524$	0.235872	0.0103041
$525$	0	0
$526$	1.42588	0.0621713
$527$	−4.51598	−0.196719
$528$	−7.02581	−0.305759
$529$	−22.2558	−0.967641
$530$	−8.28950	−0.360073
$531$	25.8889	1.12348
$532$	0	0
$533$	−0.434391	−0.0188155
$534$	5.87912	0.254415
$535$	18.6072	0.804459
$536$	−7.10066	−0.306702
$537$	−7.83976	−0.338310
$538$	3.82345	0.164841
$539$	0	0
$540$	7.41605	0.319136
$541$	−14.2212	−0.611417	−0.305709	−	0.952125i	$-0.598893\pi$
$541$	−14.2212	−0.611417	−0.305709	+	0.952125i	$0.598893\pi$
$542$	−16.7744	−0.720523
$543$	48.6049	2.08583
$544$	−7.12850	−0.305632
$545$	−33.9206	−1.45300
$546$	0	0
$547$	5.91315	0.252828	0.126414	−	0.991978i	$-0.459653\pi$
$547$	5.91315	0.252828	0.126414	+	0.991978i	$0.459653\pi$
$548$	18.1191	0.774009
$549$	−2.09956	−0.0896072
$550$	25.5069	1.08762
$551$	−37.4826	−1.59681
$552$	1.94740	0.0828870
$553$	0	0
$554$	15.5181	0.659302
$555$	8.41574	0.357228
$556$	9.81982	0.416453
$557$	−29.5831	−1.25348	−0.626738	−	0.779230i	$-0.715610\pi$
$557$	−29.5831	−1.25348	−0.626738	+	0.779230i	$0.715610\pi$
$558$	1.32757	0.0562007
$559$	4.77074	0.201781
$560$	0	0
$561$	−50.0835	−2.11453
$562$	29.7018	1.25289
$563$	29.2583	1.23309	0.616546	−	0.787319i	$-0.288532\pi$
$563$	29.2583	1.23309	0.616546	+	0.787319i	$0.288532\pi$
$564$	21.2426	0.894473
$565$	−45.4391	−1.91164
$566$	8.53456	0.358734
$567$	0	0
$568$	7.03964	0.295377
$569$	−14.9069	−0.624930	−0.312465	−	0.949929i	$-0.601155\pi$
$569$	−14.9069	−0.624930	−0.312465	+	0.949929i	$0.601155\pi$
$570$	−44.8471	−1.87844
$571$	−11.5148	−0.481879	−0.240939	−	0.970540i	$-0.577456\pi$
$571$	−11.5148	−0.481879	−0.240939	+	0.970540i	$0.577456\pi$
$572$	1.35201	0.0565304
$573$	43.6595	1.82390
$574$	0	0
$575$	−7.06998	−0.294838
$576$	2.09559	0.0873161
$577$	32.1974	1.34040	0.670198	−	0.742182i	$-0.266209\pi$
$577$	32.1974	1.34040	0.670198	+	0.742182i	$0.266209\pi$
$578$	−33.8156	−1.40654
$579$	−6.86150	−0.285154
$580$	−24.8948	−1.03370
$581$	0	0
$582$	11.6280	0.481995
$583$	7.10264	0.294161
$584$	5.88752	0.243627
$585$	3.30669	0.136715
$586$	20.6173	0.851693
$587$	−28.5265	−1.17742	−0.588708	−	0.808346i	$-0.700363\pi$
$587$	−28.5265	−1.17742	−0.588708	+	0.808346i	$0.700363\pi$
$588$	0	0
$589$	3.46484	0.142766
$590$	44.8762	1.84752
$591$	24.6182	1.01266
$592$	−1.02633	−0.0421819
$593$	40.9773	1.68273	0.841367	−	0.540464i	$-0.181751\pi$
$593$	40.9773	1.68273	0.841367	+	0.540464i	$0.181751\pi$
$594$	−6.35424	−0.260718
$595$	0	0
$596$	−1.73638	−0.0711249
$597$	−9.68727	−0.396474
$598$	−0.374748	−0.0153246
$599$	−36.9240	−1.50867	−0.754337	−	0.656488i	$-0.772041\pi$
$599$	−36.9240	−1.50867	−0.754337	+	0.656488i	$0.772041\pi$
$600$	−18.4993	−0.755232
$601$	41.4424	1.69047	0.845234	−	0.534396i	$-0.179461\pi$
$601$	41.4424	1.69047	0.845234	+	0.534396i	$0.179461\pi$
$602$	0	0
$603$	14.8800	0.605962
$604$	−10.4782	−0.426351
$605$	4.76874	0.193877
$606$	2.51017	0.101969
$607$	−1.80553	−0.0732843	−0.0366421	−	0.999328i	$-0.511666\pi$
$607$	−1.80553	−0.0732843	−0.0366421	+	0.999328i	$0.511666\pi$
$608$	5.46927	0.221808
$609$	0	0
$610$	−3.63942	−0.147356
$611$	−4.08781	−0.165375
$612$	14.9384	0.603849
$613$	9.10891	0.367905	0.183953	−	0.982935i	$-0.441111\pi$
$613$	9.10891	0.367905	0.183953	+	0.982935i	$0.441111\pi$
$614$	15.6938	0.633351
$615$	−8.19983	−0.330649
$616$	0	0
$617$	−10.6193	−0.427516	−0.213758	−	0.976887i	$-0.568570\pi$
$617$	−10.6193	−0.427516	−0.213758	+	0.976887i	$0.568570\pi$
$618$	−26.5865	−1.06947
$619$	29.0125	1.16611	0.583055	−	0.812433i	$-0.301857\pi$
$619$	29.0125	1.16611	0.583055	+	0.812433i	$0.301857\pi$
$620$	2.30124	0.0924198
$621$	1.76126	0.0706769
$622$	−10.6080	−0.425343
$623$	0	0
$624$	−0.980568	−0.0392541
$625$	1.18519	0.0474075
$626$	35.1388	1.40443
$627$	38.4261	1.53459
$628$	15.6582	0.624828
$629$	−7.31620	−0.291716
$630$	0	0
$631$	26.8061	1.06713	0.533566	−	0.845758i	$-0.320851\pi$
$631$	26.8061	1.06713	0.533566	+	0.845758i	$0.320851\pi$
$632$	−16.0891	−0.639991
$633$	29.4052	1.16875
$634$	13.9182	0.552763
$635$	−37.5834	−1.49145
$636$	−5.15131	−0.204263
$637$	0	0
$638$	21.3304	0.844480
$639$	−14.7522	−0.583587
$640$	3.63252	0.143588
$641$	−13.7133	−0.541642	−0.270821	−	0.962630i	$-0.587295\pi$
$641$	−13.7133	−0.541642	−0.270821	+	0.962630i	$0.587295\pi$
$642$	11.5630	0.456355
$643$	−20.4995	−0.808420	−0.404210	−	0.914666i	$-0.632454\pi$
$643$	−20.4995	−0.808420	−0.404210	+	0.914666i	$0.632454\pi$
$644$	0	0
$645$	90.0554	3.54593
$646$	38.9877	1.53395
$647$	34.4908	1.35597	0.677987	−	0.735074i	$-0.262852\pi$
$647$	34.4908	1.35597	0.677987	+	0.735074i	$0.262852\pi$
$648$	10.8953	0.428007
$649$	−38.4510	−1.50933
$650$	3.55991	0.139631
$651$	0	0
$652$	−20.4574	−0.801173
$653$	46.6964	1.82737	0.913685	−	0.406423i	$-0.133224\pi$
$653$	46.6964	1.82737	0.913685	+	0.406423i	$0.133224\pi$
$654$	−21.0791	−0.824260
$655$	−0.856808	−0.0334782
$656$	1.00000	0.0390434
$657$	−12.3378	−0.481344
$658$	0	0
$659$	−40.1318	−1.56331	−0.781657	−	0.623708i	$-0.785625\pi$
$659$	−40.1318	−1.56331	−0.781657	+	0.623708i	$0.785625\pi$
$660$	25.5214	0.993418
$661$	−18.1597	−0.706330	−0.353165	−	0.935561i	$-0.614895\pi$
$661$	−18.1597	−0.706330	−0.353165	+	0.935561i	$0.614895\pi$
$662$	13.0095	0.505627
$663$	−6.98998	−0.271468
$664$	−13.8718	−0.538330
$665$	0	0
$666$	2.15076	0.0833404
$667$	−5.91234	−0.228927
$668$	17.9698	0.695272
$669$	−4.57638	−0.176933
$670$	25.7933	0.996481
$671$	3.11834	0.120382
$672$	0	0
$673$	1.96827	0.0758712	0.0379356	−	0.999280i	$-0.487922\pi$
$673$	1.96827	0.0758712	0.0379356	+	0.999280i	$0.487922\pi$
$674$	11.3755	0.438167
$675$	−16.7311	−0.643979
$676$	−12.8113	−0.492742
$677$	−33.7129	−1.29569	−0.647847	−	0.761771i	$-0.724330\pi$
$677$	−33.7129	−1.29569	−0.647847	+	0.761771i	$0.724330\pi$
$678$	−28.2370	−1.08444
$679$	0	0
$680$	25.8944	0.993006
$681$	11.5250	0.441640
$682$	−1.97175	−0.0755023
$683$	13.4605	0.515052	0.257526	−	0.966271i	$-0.417093\pi$
$683$	13.4605	0.515052	0.257526	+	0.966271i	$0.417093\pi$
$684$	−11.4613	−0.438235
$685$	−65.8179	−2.51477
$686$	0	0
$687$	14.7921	0.564355
$688$	−10.9826	−0.418707
$689$	0.991290	0.0377652
$690$	−7.07398	−0.269302
$691$	−29.9749	−1.14030	−0.570149	−	0.821542i	$-0.693114\pi$
$691$	−29.9749	−1.14030	−0.570149	+	0.821542i	$0.693114\pi$
$692$	19.6269	0.746103
$693$	0	0
$694$	24.9908	0.948640
$695$	−35.6707	−1.35307
$696$	−15.4702	−0.586398
$697$	7.12850	0.270011
$698$	33.9797	1.28615
$699$	6.99932	0.264739
$700$	0	0
$701$	40.1977	1.51825	0.759123	−	0.650947i	$-0.225628\pi$
$701$	40.1977	1.51825	0.759123	+	0.650947i	$0.225628\pi$
$702$	−0.886840	−0.0334716
$703$	5.61328	0.211709
$704$	−3.11243	−0.117304
$705$	−77.1640	−2.90616
$706$	−3.75329	−0.141257
$707$	0	0
$708$	27.8872	1.04807
$709$	−9.54621	−0.358515	−0.179258	−	0.983802i	$-0.557370\pi$
$709$	−9.54621	−0.358515	−0.179258	+	0.983802i	$0.557370\pi$
$710$	−25.5716	−0.959686
$711$	33.7161	1.26445
$712$	2.60445	0.0976058
$713$	0.546528	0.0204676
$714$	0	0
$715$	−4.91120	−0.183668
$716$	−3.47301	−0.129792
$717$	25.1817	0.940428
$718$	−3.63343	−0.135598
$719$	−6.02470	−0.224684	−0.112342	−	0.993670i	$-0.535835\pi$
$719$	−6.02470	−0.224684	−0.112342	+	0.993670i	$0.535835\pi$
$720$	−7.61225	−0.283692
$721$	0	0
$722$	−10.9130	−0.406138
$723$	45.0119	1.67401
$724$	21.5319	0.800227
$725$	56.1642	2.08588
$726$	2.96342	0.109983
$727$	17.1527	0.636160	0.318080	−	0.948064i	$-0.396962\pi$
$727$	17.1527	0.636160	0.318080	+	0.948064i	$0.396962\pi$
$728$	0	0
$729$	−9.00642	−0.333571
$730$	−21.3865	−0.791551
$731$	−78.2895	−2.89564
$732$	−2.26163	−0.0835921
$733$	−47.6983	−1.76178	−0.880889	−	0.473323i	$-0.843054\pi$
$733$	−47.6983	−1.76178	−0.880889	+	0.473323i	$0.843054\pi$
$734$	−31.4196	−1.15972
$735$	0	0
$736$	0.862698	0.0317995
$737$	−22.1003	−0.814075
$738$	−2.09559	−0.0771396
$739$	42.7868	1.57394	0.786969	−	0.616992i	$-0.211649\pi$
$739$	42.7868	1.57394	0.786969	+	0.616992i	$0.211649\pi$
$740$	3.72816	0.137050
$741$	5.36299	0.197014
$742$	0	0
$743$	7.07467	0.259545	0.129772	−	0.991544i	$-0.458575\pi$
$743$	7.07467	0.259545	0.129772	+	0.991544i	$0.458575\pi$
$744$	1.43005	0.0524281
$745$	6.30743	0.231086
$746$	34.6608	1.26902
$747$	29.0695	1.06360
$748$	−22.1870	−0.811235
$749$	0	0
$750$	26.2000	0.956689
$751$	45.1753	1.64847	0.824234	−	0.566249i	$-0.191606\pi$
$751$	45.1753	1.64847	0.824234	+	0.566249i	$0.191606\pi$
$752$	9.41043	0.343163
$753$	40.0476	1.45942
$754$	2.97701	0.108416
$755$	38.0622	1.38523
$756$	0	0
$757$	29.6030	1.07594	0.537969	−	0.842964i	$-0.319192\pi$
$757$	29.6030	1.07594	0.537969	+	0.842964i	$0.319192\pi$
$758$	−31.9925	−1.16202
$759$	6.06115	0.220006
$760$	−19.8672	−0.720660
$761$	11.7635	0.426426	0.213213	−	0.977006i	$-0.431607\pi$
$761$	11.7635	0.426426	0.213213	+	0.977006i	$0.431607\pi$
$762$	−23.3553	−0.846072
$763$	0	0
$764$	19.3411	0.699737
$765$	−54.2640	−1.96192
$766$	−18.1201	−0.654704
$767$	−5.36647	−0.193772
$768$	2.25734	0.0814548
$769$	4.14683	0.149538	0.0747692	−	0.997201i	$-0.476178\pi$
$769$	4.14683	0.149538	0.0747692	+	0.997201i	$0.476178\pi$
$770$	0	0
$771$	−46.2626	−1.66611
$772$	−3.03964	−0.109399
$773$	52.9045	1.90284	0.951421	−	0.307893i	$-0.0996240\pi$
$773$	52.9045	1.90284	0.951421	+	0.307893i	$0.0996240\pi$
$774$	23.0150	0.827256
$775$	−5.19173	−0.186492
$776$	5.15118	0.184917
$777$	0	0
$778$	2.11618	0.0758687
$779$	−5.46927	−0.195957
$780$	3.56193	0.127538
$781$	21.9104	0.784015
$782$	6.14975	0.219915
$783$	−13.9915	−0.500016
$784$	0	0
$785$	−56.8785	−2.03008
$786$	−0.532442	−0.0189916
$787$	−50.8803	−1.81369	−0.906844	−	0.421467i	$-0.861515\pi$
$787$	−50.8803	−1.81369	−0.906844	+	0.421467i	$0.861515\pi$
$788$	10.9058	0.388505
$789$	−3.21870	−0.114589
$790$	58.4440	2.07935
$791$	0	0
$792$	6.52236	0.231762
$793$	0.435216	0.0154550
$794$	33.1057	1.17488
$795$	18.7122	0.663654
$796$	−4.29145	−0.152107
$797$	−47.6565	−1.68808	−0.844040	−	0.536280i	$-0.819829\pi$
$797$	−47.6565	−1.68808	−0.844040	+	0.536280i	$0.819829\pi$
$798$	0	0
$799$	67.0823	2.37320
$800$	−8.19519	−0.289744
$801$	−5.45784	−0.192843
$802$	16.1609	0.570660
$803$	18.3245	0.646657
$804$	16.0286	0.565285
$805$	0	0
$806$	−0.275191	−0.00969318
$807$	−8.63083	−0.303820
$808$	1.11200	0.0391201
$809$	20.6226	0.725051	0.362525	−	0.931974i	$-0.381915\pi$
$809$	20.6226	0.725051	0.362525	+	0.931974i	$0.381915\pi$
$810$	−39.5773	−1.39060
$811$	−5.83804	−0.205001	−0.102501	−	0.994733i	$-0.532684\pi$
$811$	−5.83804	−0.205001	−0.102501	+	0.994733i	$0.532684\pi$
$812$	0	0
$813$	37.8656	1.32800
$814$	−3.19438	−0.111963
$815$	74.3119	2.60303
$816$	16.0915	0.563314
$817$	60.0668	2.10147
$818$	−21.2525	−0.743076
$819$	0	0
$820$	−3.63252	−0.126853
$821$	−19.4797	−0.679845	−0.339923	−	0.940453i	$-0.610401\pi$
$821$	−19.4797	−0.679845	−0.339923	+	0.940453i	$0.610401\pi$
$822$	−40.9010	−1.42658
$823$	33.7026	1.17480	0.587400	−	0.809297i	$-0.300152\pi$
$823$	33.7026	1.17480	0.587400	+	0.809297i	$0.300152\pi$
$824$	−11.7778	−0.410300
$825$	−57.5778	−2.00460
$826$	0	0
$827$	−36.5462	−1.27084	−0.635419	−	0.772168i	$-0.719173\pi$
$827$	−36.5462	−1.27084	−0.635419	+	0.772168i	$0.719173\pi$
$828$	−1.80786	−0.0628274
$829$	−32.9024	−1.14275	−0.571374	−	0.820690i	$-0.693589\pi$
$829$	−32.9024	−1.14275	−0.571374	+	0.820690i	$0.693589\pi$
$830$	50.3896	1.74905
$831$	−35.0297	−1.21517
$832$	−0.434391	−0.0150598
$833$	0	0
$834$	−22.1667	−0.767570
$835$	−65.2756	−2.25895
$836$	17.0227	0.588743
$837$	1.29335	0.0447049
$838$	−10.0585	−0.347465
$839$	2.44474	0.0844019	0.0422009	−	0.999109i	$-0.486563\pi$
$839$	2.44474	0.0844019	0.0422009	+	0.999109i	$0.486563\pi$
$840$	0	0
$841$	17.9678	0.619581
$842$	−0.197707	−0.00681343
$843$	−67.0470	−2.30922
$844$	13.0265	0.448390
$845$	46.5373	1.60093
$846$	−19.7204	−0.678000
$847$	0	0
$848$	−2.28202	−0.0783650
$849$	−19.2654	−0.661187
$850$	−58.4194	−2.00377
$851$	0.885414	0.0303516
$852$	−15.8909	−0.544412
$853$	−40.5712	−1.38913	−0.694566	−	0.719429i	$-0.744403\pi$
$853$	−40.5712	−1.38913	−0.694566	+	0.719429i	$0.744403\pi$
$854$	0	0
$855$	41.6335	1.42384
$856$	5.12239	0.175080
$857$	44.7617	1.52903	0.764516	−	0.644605i	$-0.222978\pi$
$857$	44.7617	1.52903	0.764516	+	0.644605i	$0.222978\pi$
$858$	−3.05195	−0.104192
$859$	−48.0959	−1.64101	−0.820506	−	0.571638i	$-0.806308\pi$
$859$	−48.0959	−1.64101	−0.820506	+	0.571638i	$0.806308\pi$
$860$	39.8945	1.36039
$861$	0	0
$862$	−20.2740	−0.690534
$863$	−12.8003	−0.435729	−0.217864	−	0.975979i	$-0.569909\pi$
$863$	−12.8003	−0.435729	−0.217864	+	0.975979i	$0.569909\pi$
$864$	2.04157	0.0694557
$865$	−71.2951	−2.42411
$866$	−22.7396	−0.772724
$867$	76.3333	2.59241
$868$	0	0
$869$	−50.0762	−1.69872
$870$	56.1960	1.90522
$871$	−3.08446	−0.104513
$872$	−9.33805	−0.316226
$873$	−10.7947	−0.365347
$874$	−4.71833	−0.159600
$875$	0	0
$876$	−13.2901	−0.449032
$877$	−44.1894	−1.49217	−0.746086	−	0.665850i	$-0.768069\pi$
$877$	−44.1894	−1.49217	−0.746086	+	0.665850i	$0.768069\pi$
$878$	−8.41152	−0.283875
$879$	−46.5403	−1.56976
$880$	11.3060	0.381124
$881$	−3.85006	−0.129712	−0.0648560	−	0.997895i	$-0.520659\pi$
$881$	−3.85006	−0.129712	−0.0648560	+	0.997895i	$0.520659\pi$
$882$	0	0
$883$	47.4790	1.59779	0.798897	−	0.601468i	$-0.205417\pi$
$883$	47.4790	1.59779	0.798897	+	0.601468i	$0.205417\pi$
$884$	−3.09656	−0.104148
$885$	−101.301	−3.40519
$886$	9.84909	0.330887
$887$	−53.9318	−1.81085	−0.905427	−	0.424502i	$-0.860449\pi$
$887$	−53.9318	−1.81085	−0.905427	+	0.424502i	$0.860449\pi$
$888$	2.31678	0.0777460
$889$	0	0
$890$	−9.46070	−0.317123
$891$	33.9108	1.13605
$892$	−2.02733	−0.0678801
$893$	−51.4682	−1.72232
$894$	3.91960	0.131091
$895$	12.6158	0.421698
$896$	0	0
$897$	0.845934	0.0282449
$898$	−13.2475	−0.442073
$899$	−4.34164	−0.144802
$900$	17.1737	0.572457
$901$	−16.2674	−0.541946
$902$	3.11243	0.103633
$903$	0	0
$904$	−12.5090	−0.416043
$905$	−78.2151	−2.59996
$906$	23.6528	0.785813
$907$	−6.27570	−0.208381	−0.104191	−	0.994557i	$-0.533225\pi$
$907$	−6.27570	−0.208381	−0.104191	+	0.994557i	$0.533225\pi$
$908$	5.10558	0.169435
$909$	−2.33030	−0.0772911
$910$	0	0
$911$	−5.98470	−0.198282	−0.0991410	−	0.995073i	$-0.531609\pi$
$911$	−5.98470	−0.198282	−0.0991410	+	0.995073i	$0.531609\pi$
$912$	−12.3460	−0.408817
$913$	−43.1750	−1.42888
$914$	1.23130	0.0407278
$915$	8.21540	0.271593
$916$	6.55291	0.216514
$917$	0	0
$918$	14.5533	0.480332
$919$	26.1266	0.861836	0.430918	−	0.902391i	$-0.358190\pi$
$919$	26.1266	0.861836	0.430918	+	0.902391i	$0.358190\pi$
$920$	−3.13377	−0.103317
$921$	−35.4263	−1.16734
$922$	4.76640	0.156973
$923$	3.05796	0.100654
$924$	0	0
$925$	−8.41097	−0.276551
$926$	29.3345	0.963992
$927$	24.6814	0.810644
$928$	−6.85331	−0.224971
$929$	−19.1207	−0.627331	−0.313666	−	0.949534i	$-0.601557\pi$
$929$	−19.1207	−0.627331	−0.313666	+	0.949534i	$0.601557\pi$
$930$	−5.19467	−0.170340
$931$	0	0
$932$	3.10069	0.101567
$933$	23.9459	0.783954
$934$	−20.1358	−0.658864
$935$	80.5945	2.63572
$936$	0.910303	0.0297542
$937$	17.2892	0.564813	0.282406	−	0.959295i	$-0.408867\pi$
$937$	17.2892	0.564813	0.282406	+	0.959295i	$0.408867\pi$
$938$	0	0
$939$	−79.3203	−2.58852
$940$	−34.1836	−1.11495
$941$	30.7510	1.00245	0.501227	−	0.865316i	$-0.332882\pi$
$941$	30.7510	1.00245	0.501227	+	0.865316i	$0.332882\pi$
$942$	−35.3458	−1.15163
$943$	−0.862698	−0.0280933
$944$	12.3540	0.402089
$945$	0	0
$946$	−34.1825	−1.11137
$947$	−46.2262	−1.50215	−0.751076	−	0.660216i	$-0.770465\pi$
$947$	−46.2262	−1.50215	−0.751076	+	0.660216i	$0.770465\pi$
$948$	36.3186	1.17957
$949$	2.55749	0.0830195
$950$	44.8217	1.45421
$951$	−31.4182	−1.01880
$952$	0	0
$953$	−53.5802	−1.73563	−0.867817	−	0.496884i	$-0.834478\pi$
$953$	−53.5802	−1.73563	−0.867817	+	0.496884i	$0.834478\pi$
$954$	4.78218	0.154829
$955$	−70.2570	−2.27346
$956$	11.1555	0.360794
$957$	−48.1500	−1.55647
$958$	−0.688922	−0.0222581
$959$	0	0
$960$	−8.19983	−0.264648
$961$	−30.5987	−0.987054
$962$	−0.445828	−0.0143741
$963$	−10.7344	−0.345912
$964$	19.9402	0.642232
$965$	11.0415	0.355440
$966$	0	0
$967$	−38.0641	−1.22406	−0.612029	−	0.790835i	$-0.709646\pi$
$967$	−38.0641	−1.22406	−0.612029	+	0.790835i	$0.709646\pi$
$968$	1.31279	0.0421947
$969$	−88.0086	−2.82724
$970$	−18.7118	−0.600799
$971$	−9.62591	−0.308910	−0.154455	−	0.988000i	$-0.549362\pi$
$971$	−9.62591	−0.308910	−0.154455	+	0.988000i	$0.549362\pi$
$972$	−18.4696	−0.592414
$973$	0	0
$974$	16.5406	0.529996
$975$	−8.03594	−0.257356
$976$	−1.00190	−0.0320700
$977$	2.60900	0.0834693	0.0417347	−	0.999129i	$-0.486712\pi$
$977$	2.60900	0.0834693	0.0417347	+	0.999129i	$0.486712\pi$
$978$	46.1793	1.47665
$979$	8.10615	0.259074
$980$	0	0
$981$	19.5687	0.624780
$982$	−14.0168	−0.447294
$983$	−9.84756	−0.314088	−0.157044	−	0.987592i	$-0.550197\pi$
$983$	−9.84756	−0.314088	−0.157044	+	0.987592i	$0.550197\pi$
$984$	−2.25734	−0.0719614
$985$	−39.6157	−1.26226
$986$	−48.8538	−1.55582
$987$	0	0
$988$	2.37580	0.0755843
$989$	9.47467	0.301277
$990$	−23.6926	−0.753000
$991$	30.8781	0.980876	0.490438	−	0.871476i	$-0.336837\pi$
$991$	30.8781	0.980876	0.490438	+	0.871476i	$0.336837\pi$
$992$	0.633510	0.0201139
$993$	−29.3668	−0.931927
$994$	0	0
$995$	15.5888	0.494198
$996$	31.3134	0.992202
$997$	50.1887	1.58949	0.794746	−	0.606942i	$-0.207604\pi$
$997$	50.1887	1.58949	0.794746	+	0.606942i	$0.207604\pi$
$998$	−15.3030	−0.484408
$999$	2.09533	0.0662932

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4018.2.a.bs.1.8	yes	10
7.6	odd	2		4018.2.a.br.1.3	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4018.2.a.br.1.3	✓	10	7.6	odd	2
4018.2.a.bs.1.8	yes	10	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:	\( N \)	\(=\)	\( 4018 = 2 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.25734 q^{3} +1.00000 q^{4} -3.63252 q^{5} -2.25734 q^{6} -1.00000 q^{8} +2.09559 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.25734 q^{3} +1.00000 q^{4} -3.63252 q^{5} -2.25734 q^{6} -1.00000 q^{8} +2.09559 q^{9} +3.63252 q^{10} -3.11243 q^{11} +2.25734 q^{12} -0.434391 q^{13} -8.19983 q^{15} +1.00000 q^{16} +7.12850 q^{17} -2.09559 q^{18} -5.46927 q^{19} -3.63252 q^{20} +3.11243 q^{22} -0.862698 q^{23} -2.25734 q^{24} +8.19519 q^{25} +0.434391 q^{26} -2.04157 q^{27} +6.85331 q^{29} +8.19983 q^{30} -0.633510 q^{31} -1.00000 q^{32} -7.02581 q^{33} -7.12850 q^{34} +2.09559 q^{36} -1.02633 q^{37} +5.46927 q^{38} -0.980568 q^{39} +3.63252 q^{40} +1.00000 q^{41} -10.9826 q^{43} -3.11243 q^{44} -7.61225 q^{45} +0.862698 q^{46} +9.41043 q^{47} +2.25734 q^{48} -8.19519 q^{50} +16.0915 q^{51} -0.434391 q^{52} -2.28202 q^{53} +2.04157 q^{54} +11.3060 q^{55} -12.3460 q^{57} -6.85331 q^{58} +12.3540 q^{59} -8.19983 q^{60} -1.00190 q^{61} +0.633510 q^{62} +1.00000 q^{64} +1.57793 q^{65} +7.02581 q^{66} +7.10066 q^{67} +7.12850 q^{68} -1.94740 q^{69} -7.03964 q^{71} -2.09559 q^{72} -5.88752 q^{73} +1.02633 q^{74} +18.4993 q^{75} -5.46927 q^{76} +0.980568 q^{78} +16.0891 q^{79} -3.63252 q^{80} -10.8953 q^{81} -1.00000 q^{82} +13.8718 q^{83} -25.8944 q^{85} +10.9826 q^{86} +15.4702 q^{87} +3.11243 q^{88} -2.60445 q^{89} +7.61225 q^{90} -0.862698 q^{92} -1.43005 q^{93} -9.41043 q^{94} +19.8672 q^{95} -2.25734 q^{96} -5.15118 q^{97} -6.52236 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 4 q^{5} - 4 q^{6} - 10 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 4 * q^5 - 4 * q^6 - 10 * q^8 + 10 * q^9	\( 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 4 q^{5} - 4 q^{6} - 10 q^{8} + 10 q^{9} - 4 q^{10} + 4 q^{11} + 4 q^{12} + 4 q^{13} + 4 q^{15} + 10 q^{16} + 20 q^{17} - 10 q^{18} + 4 q^{20} - 4 q^{22} + 4 q^{23} - 4 q^{24} + 6 q^{25} - 4 q^{26} + 16 q^{27} - 4 q^{29} - 4 q^{30} - 4 q^{31} - 10 q^{32} + 36 q^{33} - 20 q^{34} + 10 q^{36} - 16 q^{37} + 20 q^{39} - 4 q^{40} + 10 q^{41} - 8 q^{43} + 4 q^{44} + 4 q^{45} - 4 q^{46} + 24 q^{47} + 4 q^{48} - 6 q^{50} + 20 q^{51} + 4 q^{52} - 4 q^{53} - 16 q^{54} + 20 q^{55} - 4 q^{57} + 4 q^{58} + 4 q^{60} + 4 q^{62} + 10 q^{64} - 12 q^{65} - 36 q^{66} + 8 q^{67} + 20 q^{68} + 4 q^{71} - 10 q^{72} - 24 q^{73} + 16 q^{74} + 48 q^{75} - 20 q^{78} + 24 q^{79} + 4 q^{80} - 18 q^{81} - 10 q^{82} + 48 q^{83} + 8 q^{85} + 8 q^{86} + 4 q^{87} - 4 q^{88} + 20 q^{89} - 4 q^{90} + 4 q^{92} + 4 q^{93} - 24 q^{94} - 4 q^{95} - 4 q^{96} + 4 q^{97} + 32 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 4 * q^5 - 4 * q^6 - 10 * q^8 + 10 * q^9 - 4 * q^10 + 4 * q^11 + 4 * q^12 + 4 * q^13 + 4 * q^15 + 10 * q^16 + 20 * q^17 - 10 * q^18 + 4 * q^20 - 4 * q^22 + 4 * q^23 - 4 * q^24 + 6 * q^25 - 4 * q^26 + 16 * q^27 - 4 * q^29 - 4 * q^30 - 4 * q^31 - 10 * q^32 + 36 * q^33 - 20 * q^34 + 10 * q^36 - 16 * q^37 + 20 * q^39 - 4 * q^40 + 10 * q^41 - 8 * q^43 + 4 * q^44 + 4 * q^45 - 4 * q^46 + 24 * q^47 + 4 * q^48 - 6 * q^50 + 20 * q^51 + 4 * q^52 - 4 * q^53 - 16 * q^54 + 20 * q^55 - 4 * q^57 + 4 * q^58 + 4 * q^60 + 4 * q^62 + 10 * q^64 - 12 * q^65 - 36 * q^66 + 8 * q^67 + 20 * q^68 + 4 * q^71 - 10 * q^72 - 24 * q^73 + 16 * q^74 + 48 * q^75 - 20 * q^78 + 24 * q^79 + 4 * q^80 - 18 * q^81 - 10 * q^82 + 48 * q^83 + 8 * q^85 + 8 * q^86 + 4 * q^87 - 4 * q^88 + 20 * q^89 - 4 * q^90 + 4 * q^92 + 4 * q^93 - 24 * q^94 - 4 * q^95 - 4 * q^96 + 4 * q^97 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more