LMFDB - Embedded newform 1862.2.a.o.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1862,2,Mod(1,1862)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1862, 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("1862.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1862 = 2 \cdot 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1862.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:	$14.8681448564$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.469.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 5x + 4 $ x^3 - x^2 - 5*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2.16425$ of defining polynomial
Character	$\chi$	$=$	1862.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.683969 q^{3} +1.00000 q^{4} +2.16425 q^{5} -0.683969 q^{6} -1.00000 q^{8} -2.53219 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.683969 q^{3} +1.00000 q^{4} +2.16425 q^{5} -0.683969 q^{6} -1.00000 q^{8} -2.53219 q^{9} -2.16425 q^{10} -3.64453 q^{11} +0.683969 q^{12} -4.00000 q^{13} +1.48028 q^{15} +1.00000 q^{16} +4.32850 q^{17} +2.53219 q^{18} +1.00000 q^{19} +2.16425 q^{20} +3.64453 q^{22} -1.36794 q^{23} -0.683969 q^{24} -0.316031 q^{25} +4.00000 q^{26} -3.78384 q^{27} -4.16425 q^{29} -1.48028 q^{30} -1.36794 q^{31} -1.00000 q^{32} -2.49274 q^{33} -4.32850 q^{34} -2.53219 q^{36} +0.164248 q^{37} -1.00000 q^{38} -2.73588 q^{39} -2.16425 q^{40} -11.8607 q^{41} -7.86068 q^{43} -3.64453 q^{44} -5.48028 q^{45} +1.36794 q^{46} +6.27659 q^{47} +0.683969 q^{48} +0.316031 q^{50} +2.96056 q^{51} -4.00000 q^{52} -1.64453 q^{53} +3.78384 q^{54} -7.88766 q^{55} +0.683969 q^{57} +4.16425 q^{58} -10.8212 q^{59} +1.48028 q^{60} -2.27659 q^{61} +1.36794 q^{62} +1.00000 q^{64} -8.65699 q^{65} +2.49274 q^{66} +10.3534 q^{67} +4.32850 q^{68} -0.935628 q^{69} -6.05191 q^{71} +2.53219 q^{72} -3.67150 q^{73} -0.164248 q^{74} -0.216155 q^{75} +1.00000 q^{76} +2.73588 q^{78} +12.0854 q^{79} +2.16425 q^{80} +5.00853 q^{81} +11.8607 q^{82} +6.96056 q^{83} +9.36794 q^{85} +7.86068 q^{86} -2.84822 q^{87} +3.64453 q^{88} +14.7089 q^{89} +5.48028 q^{90} -1.36794 q^{92} -0.935628 q^{93} -6.27659 q^{94} +2.16425 q^{95} -0.683969 q^{96} -14.0519 q^{97} +9.22862 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} - q^{3} + 3 q^{4} - q^{5} + q^{6} - 3 q^{8} + 6 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 - q^3 + 3 * q^4 - q^5 + q^6 - 3 * q^8 + 6 * q^9	$ 3 q - 3 q^{2} - q^{3} + 3 q^{4} - q^{5} + q^{6} - 3 q^{8} + 6 q^{9} + q^{10} + q^{11} - q^{12} - 12 q^{13} + 3 q^{16} - 2 q^{17} - 6 q^{18} + 3 q^{19} - q^{20} - q^{22} + 2 q^{23} + q^{24} - 4 q^{25} + 12 q^{26} - 28 q^{27} - 5 q^{29} + 2 q^{31} - 3 q^{32} + 15 q^{33} + 2 q^{34} + 6 q^{36} - 7 q^{37} - 3 q^{38} + 4 q^{39} + q^{40} - 7 q^{41} + 5 q^{43} + q^{44} - 12 q^{45} - 2 q^{46} + 13 q^{47} - q^{48} + 4 q^{50} - 12 q^{52} + 7 q^{53} + 28 q^{54} - 22 q^{55} - q^{57} + 5 q^{58} + 5 q^{59} - q^{61} - 2 q^{62} + 3 q^{64} + 4 q^{65} - 15 q^{66} - 20 q^{67} - 2 q^{68} - 30 q^{69} - 9 q^{71} - 6 q^{72} - 26 q^{73} + 7 q^{74} + 16 q^{75} + 3 q^{76} - 4 q^{78} + 11 q^{79} - q^{80} + 35 q^{81} + 7 q^{82} + 12 q^{83} + 22 q^{85} - 5 q^{86} + 2 q^{87} - q^{88} + 5 q^{89} + 12 q^{90} + 2 q^{92} - 30 q^{93} - 13 q^{94} - q^{95} + q^{96} - 33 q^{97} - 7 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 - q^3 + 3 * q^4 - q^5 + q^6 - 3 * q^8 + 6 * q^9 + q^10 + q^11 - q^12 - 12 * q^13 + 3 * q^16 - 2 * q^17 - 6 * q^18 + 3 * q^19 - q^20 - q^22 + 2 * q^23 + q^24 - 4 * q^25 + 12 * q^26 - 28 * q^27 - 5 * q^29 + 2 * q^31 - 3 * q^32 + 15 * q^33 + 2 * q^34 + 6 * q^36 - 7 * q^37 - 3 * q^38 + 4 * q^39 + q^40 - 7 * q^41 + 5 * q^43 + q^44 - 12 * q^45 - 2 * q^46 + 13 * q^47 - q^48 + 4 * q^50 - 12 * q^52 + 7 * q^53 + 28 * q^54 - 22 * q^55 - q^57 + 5 * q^58 + 5 * q^59 - q^61 - 2 * q^62 + 3 * q^64 + 4 * q^65 - 15 * q^66 - 20 * q^67 - 2 * q^68 - 30 * q^69 - 9 * q^71 - 6 * q^72 - 26 * q^73 + 7 * q^74 + 16 * q^75 + 3 * q^76 - 4 * q^78 + 11 * q^79 - q^80 + 35 * q^81 + 7 * q^82 + 12 * q^83 + 22 * q^85 - 5 * q^86 + 2 * q^87 - q^88 + 5 * q^89 + 12 * q^90 + 2 * q^92 - 30 * q^93 - 13 * q^94 - q^95 + q^96 - 33 * q^97 - 7 * 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
$3$	0.683969	0.394890	0.197445	−	0.980314i	$-0.436736\pi$
$3$	0.683969	0.394890	0.197445	+	0.980314i	$0.436736\pi$
$4$	1.00000	0.500000
$5$	2.16425	0.967881	0.483941	−	0.875101i	$-0.339205\pi$
$5$	2.16425	0.967881	0.483941	+	0.875101i	$0.339205\pi$
$6$	−0.683969	−0.279229
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	−2.53219	−0.844062
$10$	−2.16425	−0.684395
$11$	−3.64453	−1.09887	−0.549433	−	0.835538i	$-0.685156\pi$
$11$	−3.64453	−1.09887	−0.549433	+	0.835538i	$0.685156\pi$
$12$	0.683969	0.197445
$13$	−4.00000	−1.10940	−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000	−1.10940	−0.554700	+	0.832050i	$0.687167\pi$
$14$	0	0
$15$	1.48028	0.382206
$16$	1.00000	0.250000
$17$	4.32850	1.04981	0.524907	−	0.851159i	$-0.324100\pi$
$17$	4.32850	1.04981	0.524907	+	0.851159i	$0.324100\pi$
$18$	2.53219	0.596842
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	2.16425	0.483941
$21$	0	0
$22$	3.64453	0.777016
$23$	−1.36794	−0.285235	−0.142617	−	0.989778i	$-0.545552\pi$
$23$	−1.36794	−0.285235	−0.142617	+	0.989778i	$0.545552\pi$
$24$	−0.683969	−0.139615
$25$	−0.316031	−0.0632062
$26$	4.00000	0.784465
$27$	−3.78384	−0.728201
$28$	0	0
$29$	−4.16425	−0.773281	−0.386641	−	0.922230i	$-0.626365\pi$
$29$	−4.16425	−0.773281	−0.386641	+	0.922230i	$0.626365\pi$
$30$	−1.48028	−0.270261
$31$	−1.36794	−0.245689	−0.122844	−	0.992426i	$-0.539202\pi$
$31$	−1.36794	−0.245689	−0.122844	+	0.992426i	$0.539202\pi$
$32$	−1.00000	−0.176777
$33$	−2.49274	−0.433931
$34$	−4.32850	−0.742331
$35$	0	0
$36$	−2.53219	−0.422031
$37$	0.164248	0.0270022	0.0135011	−	0.999909i	$-0.495702\pi$
$37$	0.164248	0.0270022	0.0135011	+	0.999909i	$0.495702\pi$
$38$	−1.00000	−0.162221
$39$	−2.73588	−0.438091
$40$	−2.16425	−0.342198
$41$	−11.8607	−1.85233	−0.926164	−	0.377122i	$-0.876914\pi$
$41$	−11.8607	−1.85233	−0.926164	+	0.377122i	$0.876914\pi$
$42$	0	0
$43$	−7.86068	−1.19874	−0.599371	−	0.800471i	$-0.704583\pi$
$43$	−7.86068	−1.19874	−0.599371	+	0.800471i	$0.704583\pi$
$44$	−3.64453	−0.549433
$45$	−5.48028	−0.816952
$46$	1.36794	0.201691
$47$	6.27659	0.915535	0.457767	−	0.889072i	$-0.348649\pi$
$47$	6.27659	0.915535	0.457767	+	0.889072i	$0.348649\pi$
$48$	0.683969	0.0987224
$49$	0	0
$50$	0.316031	0.0446935
$51$	2.96056	0.414561
$52$	−4.00000	−0.554700
$53$	−1.64453	−0.225893	−0.112947	−	0.993601i	$-0.536029\pi$
$53$	−1.64453	−0.225893	−0.112947	+	0.993601i	$0.536029\pi$
$54$	3.78384	0.514916
$55$	−7.88766	−1.06357
$56$	0	0
$57$	0.683969	0.0905939
$58$	4.16425	0.546793
$59$	−10.8212	−1.40881	−0.704403	−	0.709801i	$-0.748785\pi$
$59$	−10.8212	−1.40881	−0.704403	+	0.709801i	$0.748785\pi$
$60$	1.48028	0.191103
$61$	−2.27659	−0.291487	−0.145744	−	0.989322i	$-0.546557\pi$
$61$	−2.27659	−0.291487	−0.145744	+	0.989322i	$0.546557\pi$
$62$	1.36794	0.173728
$63$	0	0
$64$	1.00000	0.125000
$65$	−8.65699	−1.07377
$66$	2.49274	0.306836
$67$	10.3534	1.26487	0.632436	−	0.774612i	$-0.282055\pi$
$67$	10.3534	1.26487	0.632436	+	0.774612i	$0.282055\pi$
$68$	4.32850	0.524907
$69$	−0.935628	−0.112636
$70$	0	0
$71$	−6.05191	−0.718229	−0.359115	−	0.933293i	$-0.616921\pi$
$71$	−6.05191	−0.718229	−0.359115	+	0.933293i	$0.616921\pi$
$72$	2.53219	0.298421
$73$	−3.67150	−0.429717	−0.214859	−	0.976645i	$-0.568929\pi$
$73$	−3.67150	−0.429717	−0.214859	+	0.976645i	$0.568929\pi$
$74$	−0.164248	−0.0190934
$75$	−0.216155	−0.0249595
$76$	1.00000	0.114708
$77$	0	0
$78$	2.73588	0.309777
$79$	12.0854	1.35971	0.679855	−	0.733347i	$-0.262043\pi$
$79$	12.0854	1.35971	0.679855	+	0.733347i	$0.262043\pi$
$80$	2.16425	0.241970
$81$	5.00853	0.556503
$82$	11.8607	1.30979
$83$	6.96056	0.764020	0.382010	−	0.924158i	$-0.375232\pi$
$83$	6.96056	0.764020	0.382010	+	0.924158i	$0.375232\pi$
$84$	0	0
$85$	9.36794	1.01610
$86$	7.86068	0.847639
$87$	−2.84822	−0.305361
$88$	3.64453	0.388508
$89$	14.7089	1.55914	0.779570	−	0.626315i	$-0.215438\pi$
$89$	14.7089	1.55914	0.779570	+	0.626315i	$0.215438\pi$
$90$	5.48028	0.577672
$91$	0	0
$92$	−1.36794	−0.142617
$93$	−0.935628	−0.0970201
$94$	−6.27659	−0.647381
$95$	2.16425	0.222047
$96$	−0.683969	−0.0698073
$97$	−14.0519	−1.42676	−0.713378	−	0.700780i	$-0.752835\pi$
$97$	−14.0519	−1.42676	−0.713378	+	0.700780i	$0.752835\pi$
$98$	0	0
$99$	9.22862	0.927511
$100$	−0.316031	−0.0316031
$101$	−1.03944	−0.103428	−0.0517142	−	0.998662i	$-0.516468\pi$
$101$	−1.03944	−0.103428	−0.0517142	+	0.998662i	$0.516468\pi$
$102$	−2.96056	−0.293139
$103$	−8.00000	−0.788263	−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000	−0.788263	−0.394132	+	0.919054i	$0.628955\pi$
$104$	4.00000	0.392232
$105$	0	0
$106$	1.64453	0.159731
$107$	6.02493	0.582452	0.291226	−	0.956654i	$-0.405937\pi$
$107$	6.02493	0.582452	0.291226	+	0.956654i	$0.405937\pi$
$108$	−3.78384	−0.364101
$109$	−17.0374	−1.63189	−0.815943	−	0.578132i	$-0.803782\pi$
$109$	−17.0374	−1.63189	−0.815943	+	0.578132i	$0.803782\pi$
$110$	7.88766	0.752059
$111$	0.112341	0.0106629
$112$	0	0
$113$	4.73588	0.445514	0.222757	−	0.974874i	$-0.428494\pi$
$113$	4.73588	0.445514	0.222757	+	0.974874i	$0.428494\pi$
$114$	−0.683969	−0.0640596
$115$	−2.96056	−0.276073
$116$	−4.16425	−0.386641
$117$	10.1287	0.936403
$118$	10.8212	0.996176
$119$	0	0
$120$	−1.48028	−0.135130
$121$	2.28258	0.207507
$122$	2.27659	0.206113
$123$	−8.11234	−0.731465
$124$	−1.36794	−0.122844
$125$	−11.5052	−1.02906
$126$	0	0
$127$	−3.31603	−0.294250	−0.147125	−	0.989118i	$-0.547002\pi$
$127$	−3.31603	−0.294250	−0.147125	+	0.989118i	$0.547002\pi$
$128$	−1.00000	−0.0883883
$129$	−5.37646	−0.473371
$130$	8.65699	0.759268
$131$	−8.32850	−0.727664	−0.363832	−	0.931465i	$-0.618532\pi$
$131$	−8.32850	−0.727664	−0.363832	+	0.931465i	$0.618532\pi$
$132$	−2.49274	−0.216966
$133$	0	0
$134$	−10.3534	−0.894400
$135$	−8.18918	−0.704812
$136$	−4.32850	−0.371165
$137$	5.53219	0.472647	0.236323	−	0.971674i	$-0.424058\pi$
$137$	5.53219	0.472647	0.236323	+	0.971674i	$0.424058\pi$
$138$	0.935628	0.0796459
$139$	−9.92112	−0.841498	−0.420749	−	0.907177i	$-0.638233\pi$
$139$	−9.92112	−0.841498	−0.420749	+	0.907177i	$0.638233\pi$
$140$	0	0
$141$	4.29299	0.361535
$142$	6.05191	0.507865
$143$	14.5781	1.21908
$144$	−2.53219	−0.211016
$145$	−9.01247	−0.748444
$146$	3.67150	0.303856
$147$	0	0
$148$	0.164248	0.0135011
$149$	14.6570	1.20075	0.600374	−	0.799720i	$-0.295018\pi$
$149$	14.6570	1.20075	0.600374	+	0.799720i	$0.295018\pi$
$150$	0.216155	0.0176490
$151$	11.3929	0.927138	0.463569	−	0.886061i	$-0.346569\pi$
$151$	11.3929	0.927138	0.463569	+	0.886061i	$0.346569\pi$
$152$	−1.00000	−0.0811107
$153$	−10.9606	−0.886109
$154$	0	0
$155$	−2.96056	−0.237798
$156$	−2.73588	−0.219045
$157$	−15.7483	−1.25685	−0.628427	−	0.777868i	$-0.716301\pi$
$157$	−15.7483	−1.25685	−0.628427	+	0.777868i	$0.716301\pi$
$158$	−12.0854	−0.961460
$159$	−1.12481	−0.0892029
$160$	−2.16425	−0.171099
$161$	0	0
$162$	−5.00853	−0.393507
$163$	−20.3015	−1.59014	−0.795069	−	0.606519i	$-0.792565\pi$
$163$	−20.3015	−1.59014	−0.795069	+	0.606519i	$0.792565\pi$
$164$	−11.8607	−0.926164
$165$	−5.39492	−0.419994
$166$	−6.96056	−0.540244
$167$	7.06437	0.546658	0.273329	−	0.961921i	$-0.411875\pi$
$167$	7.06437	0.546658	0.273329	+	0.961921i	$0.411875\pi$
$168$	0	0
$169$	3.00000	0.230769
$170$	−9.36794	−0.718488
$171$	−2.53219	−0.193641
$172$	−7.86068	−0.599371
$173$	−24.7608	−1.88253	−0.941265	−	0.337670i	$-0.890361\pi$
$173$	−24.7608	−1.88253	−0.941265	+	0.337670i	$0.890361\pi$
$174$	2.84822	0.215923
$175$	0	0
$176$	−3.64453	−0.274717
$177$	−7.40139	−0.556323
$178$	−14.7089	−1.10248
$179$	8.10381	0.605708	0.302854	−	0.953037i	$-0.402061\pi$
$179$	8.10381	0.605708	0.302854	+	0.953037i	$0.402061\pi$
$180$	−5.48028	−0.408476
$181$	1.92112	0.142795	0.0713977	−	0.997448i	$-0.477254\pi$
$181$	1.92112	0.142795	0.0713977	+	0.997448i	$0.477254\pi$
$182$	0	0
$183$	−1.55712	−0.115105
$184$	1.36794	0.100846
$185$	0.355473	0.0261349
$186$	0.935628	0.0686035
$187$	−15.7753	−1.15361
$188$	6.27659	0.457767
$189$	0	0
$190$	−2.16425	−0.157011
$191$	13.4718	0.974782	0.487391	−	0.873184i	$-0.337949\pi$
$191$	13.4718	0.974782	0.487391	+	0.873184i	$0.337949\pi$
$192$	0.683969	0.0493612
$193$	10.4323	0.750934	0.375467	−	0.926836i	$-0.377482\pi$
$193$	10.4323	0.750934	0.375467	+	0.926836i	$0.377482\pi$
$194$	14.0519	1.00887
$195$	−5.92112	−0.424020
$196$	0	0
$197$	21.2891	1.51678	0.758391	−	0.651800i	$-0.225986\pi$
$197$	21.2891	1.51678	0.758391	+	0.651800i	$0.225986\pi$
$198$	−9.22862	−0.655849
$199$	22.1103	1.56736	0.783679	−	0.621167i	$-0.213341\pi$
$199$	22.1103	1.56736	0.783679	+	0.621167i	$0.213341\pi$
$200$	0.316031	0.0223468
$201$	7.08142	0.499485
$202$	1.03944	0.0731349
$203$	0	0
$204$	2.96056	0.207280
$205$	−25.6695	−1.79283
$206$	8.00000	0.557386
$207$	3.46387	0.240756
$208$	−4.00000	−0.277350
$209$	−3.64453	−0.252097
$210$	0	0
$211$	−0.103815	−0.00714691	−0.00357345	−	0.999994i	$-0.501137\pi$
$211$	−0.103815	−0.00714691	−0.00357345	+	0.999994i	$0.501137\pi$
$212$	−1.64453	−0.112947
$213$	−4.13932	−0.283621
$214$	−6.02493	−0.411856
$215$	−17.0125	−1.16024
$216$	3.78384	0.257458
$217$	0	0
$218$	17.0374	1.15392
$219$	−2.51120	−0.169691
$220$	−7.88766	−0.531786
$221$	−17.3140	−1.16466
$222$	−0.112341	−0.00753980
$223$	7.72136	0.517061	0.258530	−	0.966003i	$-0.416762\pi$
$223$	7.72136	0.517061	0.258530	+	0.966003i	$0.416762\pi$
$224$	0	0
$225$	0.800249	0.0533499
$226$	−4.73588	−0.315026
$227$	−13.3140	−0.883680	−0.441840	−	0.897094i	$-0.645674\pi$
$227$	−13.3140	−0.883680	−0.441840	+	0.897094i	$0.645674\pi$
$228$	0.683969	0.0452970
$229$	5.55712	0.367225	0.183612	−	0.982999i	$-0.441221\pi$
$229$	5.55712	0.367225	0.183612	+	0.982999i	$0.441221\pi$
$230$	2.96056	0.195213
$231$	0	0
$232$	4.16425	0.273396
$233$	18.6300	1.22049	0.610246	−	0.792212i	$-0.291070\pi$
$233$	18.6300	1.22049	0.610246	+	0.792212i	$0.291070\pi$
$234$	−10.1287	−0.662137
$235$	13.5841	0.886129
$236$	−10.8212	−0.704403
$237$	8.26602	0.536935
$238$	0	0
$239$	−12.1038	−0.782931	−0.391465	−	0.920193i	$-0.628032\pi$
$239$	−12.1038	−0.782931	−0.391465	+	0.920193i	$0.628032\pi$
$240$	1.48028	0.0955516
$241$	−2.71742	−0.175045	−0.0875224	−	0.996163i	$-0.527895\pi$
$241$	−2.71742	−0.175045	−0.0875224	+	0.996163i	$0.527895\pi$
$242$	−2.28258	−0.146729
$243$	14.7772	0.947959
$244$	−2.27659	−0.145744
$245$	0	0
$246$	8.11234	0.517224
$247$	−4.00000	−0.254514
$248$	1.36794	0.0868642
$249$	4.76081	0.301704
$250$	11.5052	0.727653
$251$	9.26412	0.584746	0.292373	−	0.956304i	$-0.405555\pi$
$251$	9.26412	0.584746	0.292373	+	0.956304i	$0.405555\pi$
$252$	0	0
$253$	4.98549	0.313435
$254$	3.31603	0.208066
$255$	6.40738	0.401246
$256$	1.00000	0.0625000
$257$	−12.5177	−0.780831	−0.390416	−	0.920639i	$-0.627669\pi$
$257$	−12.5177	−0.780831	−0.390416	+	0.920639i	$0.627669\pi$
$258$	5.37646	0.334724
$259$	0	0
$260$	−8.65699	−0.536884
$261$	10.5447	0.652698
$262$	8.32850	0.514536
$263$	−5.92112	−0.365112	−0.182556	−	0.983195i	$-0.558437\pi$
$263$	−5.92112	−0.365112	−0.182556	+	0.983195i	$0.558437\pi$
$264$	2.49274	0.153418
$265$	−3.55916	−0.218638
$266$	0	0
$267$	10.0604	0.615689
$268$	10.3534	0.632436
$269$	−11.9460	−0.728363	−0.364182	−	0.931328i	$-0.618651\pi$
$269$	−11.9460	−0.728363	−0.364182	+	0.931328i	$0.618651\pi$
$270$	8.18918	0.498378
$271$	−21.0039	−1.27590	−0.637949	−	0.770078i	$-0.720217\pi$
$271$	−21.0039	−1.27590	−0.637949	+	0.770078i	$0.720217\pi$
$272$	4.32850	0.262454
$273$	0	0
$274$	−5.53219	−0.334212
$275$	1.15178	0.0694551
$276$	−0.935628	−0.0563182
$277$	−14.9855	−0.900391	−0.450195	−	0.892930i	$-0.648646\pi$
$277$	−14.9855	−0.900391	−0.450195	+	0.892930i	$0.648646\pi$
$278$	9.92112	0.595029
$279$	3.46387	0.207377
$280$	0	0
$281$	−27.0893	−1.61601	−0.808006	−	0.589174i	$-0.799453\pi$
$281$	−27.0893	−1.61601	−0.808006	+	0.589174i	$0.799453\pi$
$282$	−4.29299	−0.255644
$283$	33.4178	1.98648	0.993241	−	0.116071i	$-0.0370299\pi$
$283$	33.4178	1.98648	0.993241	+	0.116071i	$0.0370299\pi$
$284$	−6.05191	−0.359115
$285$	1.48028	0.0876841
$286$	−14.5781	−0.862022
$287$	0	0
$288$	2.53219	0.149211
$289$	1.73588	0.102110
$290$	9.01247	0.529230
$291$	−9.61107	−0.563411
$292$	−3.67150	−0.214859
$293$	19.0644	1.11375	0.556876	−	0.830595i	$-0.312000\pi$
$293$	19.0644	1.11375	0.556876	+	0.830595i	$0.312000\pi$
$294$	0	0
$295$	−23.4198	−1.36356
$296$	−0.164248	−0.00954672
$297$	13.7903	0.800196
$298$	−14.6570	−0.849057
$299$	5.47175	0.316440
$300$	−0.216155	−0.0124797
$301$	0	0
$302$	−11.3929	−0.655586
$303$	−0.710947	−0.0408428
$304$	1.00000	0.0573539
$305$	−4.92710	−0.282125
$306$	10.9606	0.626573
$307$	−25.8856	−1.47737	−0.738685	−	0.674051i	$-0.764553\pi$
$307$	−25.8856	−1.47737	−0.738685	+	0.674051i	$0.764553\pi$
$308$	0	0
$309$	−5.47175	−0.311277
$310$	2.96056	0.168148
$311$	31.1412	1.76586	0.882928	−	0.469508i	$-0.155569\pi$
$311$	31.1412	1.76586	0.882928	+	0.469508i	$0.155569\pi$
$312$	2.73588	0.154889
$313$	−23.2891	−1.31638	−0.658188	−	0.752854i	$-0.728677\pi$
$313$	−23.2891	−1.31638	−0.658188	+	0.752854i	$0.728677\pi$
$314$	15.7483	0.888730
$315$	0	0
$316$	12.0854	0.679855
$317$	8.38040	0.470690	0.235345	−	0.971912i	$-0.424378\pi$
$317$	8.38040	0.470690	0.235345	+	0.971912i	$0.424378\pi$
$318$	1.12481	0.0630760
$319$	15.1767	0.849733
$320$	2.16425	0.120985
$321$	4.12087	0.230004
$322$	0	0
$323$	4.32850	0.240844
$324$	5.00853	0.278251
$325$	1.26412	0.0701210
$326$	20.3015	1.12440
$327$	−11.6531	−0.644415
$328$	11.8607	0.654897
$329$	0	0
$330$	5.39492	0.296980
$331$	7.39287	0.406349	0.203174	−	0.979143i	$-0.434874\pi$
$331$	7.39287	0.406349	0.203174	+	0.979143i	$0.434874\pi$
$332$	6.96056	0.382010
$333$	−0.415906	−0.0227915
$334$	−7.06437	−0.386545
$335$	22.4074	1.22425
$336$	0	0
$337$	−32.3534	−1.76240	−0.881202	−	0.472740i	$-0.843265\pi$
$337$	−32.3534	−1.76240	−0.881202	+	0.472740i	$0.843265\pi$
$338$	−3.00000	−0.163178
$339$	3.23919	0.175929
$340$	9.36794	0.508048
$341$	4.98549	0.269979
$342$	2.53219	0.136925
$343$	0	0
$344$	7.86068	0.423820
$345$	−2.02493	−0.109019
$346$	24.7608	1.33115
$347$	25.4718	1.36740	0.683698	−	0.729765i	$-0.260371\pi$
$347$	25.4718	1.36740	0.683698	+	0.729765i	$0.260371\pi$
$348$	−2.84822	−0.152680
$349$	−20.8817	−1.11777	−0.558885	−	0.829245i	$-0.688771\pi$
$349$	−20.8817	−1.11777	−0.558885	+	0.829245i	$0.688771\pi$
$350$	0	0
$351$	15.1354	0.807867
$352$	3.64453	0.194254
$353$	−5.92112	−0.315149	−0.157575	−	0.987507i	$-0.550367\pi$
$353$	−5.92112	−0.315149	−0.157575	+	0.987507i	$0.550367\pi$
$354$	7.40139	0.393380
$355$	−13.0978	−0.695161
$356$	14.7089	0.779570
$357$	0	0
$358$	−8.10381	−0.428300
$359$	−26.9606	−1.42292	−0.711462	−	0.702725i	$-0.751967\pi$
$359$	−26.9606	−1.42292	−0.711462	+	0.702725i	$0.751967\pi$
$360$	5.48028	0.288836
$361$	1.00000	0.0526316
$362$	−1.92112	−0.100972
$363$	1.56121	0.0819423
$364$	0	0
$365$	−7.94605	−0.415915
$366$	1.55712	0.0813918
$367$	−0.301518	−0.0157391	−0.00786957	−	0.999969i	$-0.502505\pi$
$367$	−0.301518	−0.0157391	−0.00786957	+	0.999969i	$0.502505\pi$
$368$	−1.36794	−0.0713087
$369$	30.0335	1.56348
$370$	−0.355473	−0.0184802
$371$	0	0
$372$	−0.935628	−0.0485100
$373$	−8.82124	−0.456746	−0.228373	−	0.973574i	$-0.573341\pi$
$373$	−8.82124	−0.456746	−0.228373	+	0.973574i	$0.573341\pi$
$374$	15.7753	0.815722
$375$	−7.86921	−0.406364
$376$	−6.27659	−0.323690
$377$	16.6570	0.857879
$378$	0	0
$379$	11.0644	0.568339	0.284169	−	0.958774i	$-0.408282\pi$
$379$	11.0644	0.568339	0.284169	+	0.958774i	$0.408282\pi$
$380$	2.16425	0.111024
$381$	−2.26806	−0.116196
$382$	−13.4718	−0.689275
$383$	−7.51373	−0.383934	−0.191967	−	0.981401i	$-0.561487\pi$
$383$	−7.51373	−0.383934	−0.191967	+	0.981401i	$0.561487\pi$
$384$	−0.683969	−0.0349037
$385$	0	0
$386$	−10.4323	−0.530991
$387$	19.9047	1.01181
$388$	−14.0519	−0.713378
$389$	−1.01451	−0.0514378	−0.0257189	−	0.999669i	$-0.508187\pi$
$389$	−1.01451	−0.0514378	−0.0257189	+	0.999669i	$0.508187\pi$
$390$	5.92112	0.299827
$391$	−5.92112	−0.299444
$392$	0	0
$393$	−5.69643	−0.287347
$394$	−21.2891	−1.07253
$395$	26.1557	1.31604
$396$	9.22862	0.463756
$397$	−2.93358	−0.147232	−0.0736161	−	0.997287i	$-0.523454\pi$
$397$	−2.93358	−0.147232	−0.0736161	+	0.997287i	$0.523454\pi$
$398$	−22.1103	−1.10829
$399$	0	0
$400$	−0.316031	−0.0158015
$401$	16.9606	0.846970	0.423485	−	0.905903i	$-0.360807\pi$
$401$	16.9606	0.846970	0.423485	+	0.905903i	$0.360807\pi$
$402$	−7.08142	−0.353189
$403$	5.47175	0.272567
$404$	−1.03944	−0.0517142
$405$	10.8397	0.538629
$406$	0	0
$407$	−0.598606	−0.0296718
$408$	−2.96056	−0.146569
$409$	−0.787784	−0.0389534	−0.0194767	−	0.999810i	$-0.506200\pi$
$409$	−0.787784	−0.0389534	−0.0194767	+	0.999810i	$0.506200\pi$
$410$	25.6695	1.26772
$411$	3.78384	0.186643
$412$	−8.00000	−0.394132
$413$	0	0
$414$	−3.46387	−0.170240
$415$	15.0644	0.739481
$416$	4.00000	0.196116
$417$	−6.78574	−0.332299
$418$	3.64453	0.178260
$419$	20.8817	1.02014	0.510068	−	0.860134i	$-0.329620\pi$
$419$	20.8817	1.02014	0.510068	+	0.860134i	$0.329620\pi$
$420$	0	0
$421$	−5.84223	−0.284733	−0.142366	−	0.989814i	$-0.545471\pi$
$421$	−5.84223	−0.284733	−0.142366	+	0.989814i	$0.545471\pi$
$422$	0.103815	0.00505363
$423$	−15.8935	−0.772768
$424$	1.64453	0.0798653
$425$	−1.36794	−0.0663548
$426$	4.13932	0.200551
$427$	0	0
$428$	6.02493	0.291226
$429$	9.97098	0.481403
$430$	17.0125	0.820414
$431$	−28.6840	−1.38166	−0.690829	−	0.723018i	$-0.742754\pi$
$431$	−28.6840	−1.38166	−0.690829	+	0.723018i	$0.742754\pi$
$432$	−3.78384	−0.182050
$433$	−2.26806	−0.108996	−0.0544981	−	0.998514i	$-0.517356\pi$
$433$	−2.26806	−0.108996	−0.0544981	+	0.998514i	$0.517356\pi$
$434$	0	0
$435$	−6.16425	−0.295553
$436$	−17.0374	−0.815943
$437$	−1.36794	−0.0654374
$438$	2.51120	0.119990
$439$	32.6030	1.55606	0.778029	−	0.628228i	$-0.216220\pi$
$439$	32.6030	1.55606	0.778029	+	0.628228i	$0.216220\pi$
$440$	7.88766	0.376029
$441$	0	0
$442$	17.3140	0.823542
$443$	8.31004	0.394822	0.197411	−	0.980321i	$-0.436747\pi$
$443$	8.31004	0.394822	0.197411	+	0.980321i	$0.436747\pi$
$444$	0.112341	0.00533145
$445$	31.8337	1.50906
$446$	−7.72136	−0.365617
$447$	10.0249	0.474163
$448$	0	0
$449$	32.1287	1.51625	0.758125	−	0.652110i	$-0.226116\pi$
$449$	32.1287	1.51625	0.758125	+	0.652110i	$0.226116\pi$
$450$	−0.800249	−0.0377241
$451$	43.2266	2.03546
$452$	4.73588	0.222757
$453$	7.79237	0.366117
$454$	13.3140	0.624856
$455$	0	0
$456$	−0.683969	−0.0320298
$457$	13.9730	0.653630	0.326815	−	0.945088i	$-0.394025\pi$
$457$	13.9730	0.653630	0.326815	+	0.945088i	$0.394025\pi$
$458$	−5.55712	−0.259667
$459$	−16.3784	−0.764476
$460$	−2.96056	−0.138037
$461$	31.6944	1.47615	0.738077	−	0.674716i	$-0.235734\pi$
$461$	31.6944	1.47615	0.738077	+	0.674716i	$0.235734\pi$
$462$	0	0
$463$	35.1682	1.63440	0.817202	−	0.576351i	$-0.195524\pi$
$463$	35.1682	1.63440	0.817202	+	0.576351i	$0.195524\pi$
$464$	−4.16425	−0.193320
$465$	−2.02493	−0.0939039
$466$	−18.6300	−0.863019
$467$	−8.81476	−0.407899	−0.203949	−	0.978981i	$-0.565378\pi$
$467$	−8.81476	−0.407899	−0.203949	+	0.978981i	$0.565378\pi$
$468$	10.1287	0.468201
$469$	0	0
$470$	−13.5841	−0.626588
$471$	−10.7714	−0.496319
$472$	10.8212	0.498088
$473$	28.6485	1.31726
$474$	−8.26602	−0.379671
$475$	−0.316031	−0.0145005
$476$	0	0
$477$	4.16425	0.190668
$478$	12.1038	0.553616
$479$	33.9894	1.55302	0.776508	−	0.630107i	$-0.216989\pi$
$479$	33.9894	1.55302	0.776508	+	0.630107i	$0.216989\pi$
$480$	−1.48028	−0.0675652
$481$	−0.656992	−0.0299562
$482$	2.71742	0.123775
$483$	0	0
$484$	2.28258	0.103753
$485$	−30.4118	−1.38093
$486$	−14.7772	−0.670308
$487$	−15.3075	−0.693649	−0.346825	−	0.937930i	$-0.612740\pi$
$487$	−15.3075	−0.693649	−0.346825	+	0.937930i	$0.612740\pi$
$488$	2.27659	0.103056
$489$	−13.8856	−0.627929
$490$	0	0
$491$	−23.1852	−1.04634	−0.523168	−	0.852230i	$-0.675250\pi$
$491$	−23.1852	−1.04634	−0.523168	+	0.852230i	$0.675250\pi$
$492$	−8.11234	−0.365733
$493$	−18.0249	−0.811802
$494$	4.00000	0.179969
$495$	19.9730	0.897721
$496$	−1.36794	−0.0614222
$497$	0	0
$498$	−4.76081	−0.213337
$499$	−21.5032	−0.962614	−0.481307	−	0.876552i	$-0.659838\pi$
$499$	−21.5032	−0.962614	−0.481307	+	0.876552i	$0.659838\pi$
$500$	−11.5052	−0.514529
$501$	4.83181	0.215869
$502$	−9.26412	−0.413478
$503$	32.4678	1.44767	0.723834	−	0.689974i	$-0.242378\pi$
$503$	32.4678	1.44767	0.723834	+	0.689974i	$0.242378\pi$
$504$	0	0
$505$	−2.24961	−0.100106
$506$	−4.98549	−0.221632
$507$	2.05191	0.0911284
$508$	−3.31603	−0.147125
$509$	14.7359	0.653156	0.326578	−	0.945170i	$-0.394104\pi$
$509$	14.7359	0.653156	0.326578	+	0.945170i	$0.394104\pi$
$510$	−6.40738	−0.283724
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−3.78384	−0.167061
$514$	12.5177	0.552131
$515$	−17.3140	−0.762945
$516$	−5.37646	−0.236686
$517$	−22.8752	−1.00605
$518$	0	0
$519$	−16.9356	−0.743392
$520$	8.65699	0.379634
$521$	6.14580	0.269252	0.134626	−	0.990896i	$-0.457017\pi$
$521$	6.14580	0.269252	0.134626	+	0.990896i	$0.457017\pi$
$522$	−10.5447	−0.461527
$523$	5.31398	0.232364	0.116182	−	0.993228i	$-0.462934\pi$
$523$	5.31398	0.232364	0.116182	+	0.993228i	$0.462934\pi$
$524$	−8.32850	−0.363832
$525$	0	0
$526$	5.92112	0.258173
$527$	−5.92112	−0.257928
$528$	−2.49274	−0.108483
$529$	−21.1287	−0.918641
$530$	3.55916	0.154600
$531$	27.4014	1.18912
$532$	0	0
$533$	47.4427	2.05497
$534$	−10.0604	−0.435358
$535$	13.0394	0.563744
$536$	−10.3534	−0.447200
$537$	5.54276	0.239188
$538$	11.9460	0.515031
$539$	0	0
$540$	−8.18918	−0.352406
$541$	19.2102	0.825910	0.412955	−	0.910752i	$-0.364497\pi$
$541$	19.2102	0.825910	0.412955	+	0.910752i	$0.364497\pi$
$542$	21.0039	0.902196
$543$	1.31398	0.0563884
$544$	−4.32850	−0.185583
$545$	−36.8731	−1.57947
$546$	0	0
$547$	−14.7359	−0.630061	−0.315030	−	0.949082i	$-0.602015\pi$
$547$	−14.7359	−0.630061	−0.315030	+	0.949082i	$0.602015\pi$
$548$	5.53219	0.236323
$549$	5.76475	0.246033
$550$	−1.15178	−0.0491122
$551$	−4.16425	−0.177403
$552$	0.935628	0.0398230
$553$	0	0
$554$	14.9855	0.636672
$555$	0.243133	0.0103204
$556$	−9.92112	−0.420749
$557$	−20.9606	−0.888127	−0.444064	−	0.895995i	$-0.646464\pi$
$557$	−20.9606	−0.888127	−0.444064	+	0.895995i	$0.646464\pi$
$558$	−3.46387	−0.146637
$559$	31.4427	1.32989
$560$	0	0
$561$	−10.7898	−0.455547
$562$	27.0893	1.14269
$563$	−20.0768	−0.846138	−0.423069	−	0.906098i	$-0.639047\pi$
$563$	−20.0768	−0.846138	−0.423069	+	0.906098i	$0.639047\pi$
$564$	4.29299	0.180768
$565$	10.2496	0.431204
$566$	−33.4178	−1.40465
$567$	0	0
$568$	6.05191	0.253932
$569$	−36.9066	−1.54721	−0.773603	−	0.633671i	$-0.781547\pi$
$569$	−36.9066	−1.54721	−0.773603	+	0.633671i	$0.781547\pi$
$570$	−1.48028	−0.0620021
$571$	−29.0125	−1.21413	−0.607067	−	0.794651i	$-0.707654\pi$
$571$	−29.0125	−1.21413	−0.607067	+	0.794651i	$0.707654\pi$
$572$	14.5781	0.609541
$573$	9.21426	0.384931
$574$	0	0
$575$	0.432311	0.0180286
$576$	−2.53219	−0.105508
$577$	7.11833	0.296340	0.148170	−	0.988962i	$-0.452662\pi$
$577$	7.11833	0.296340	0.148170	+	0.988962i	$0.452662\pi$
$578$	−1.73588	−0.0722029
$579$	7.13538	0.296536
$580$	−9.01247	−0.374222
$581$	0	0
$582$	9.61107	0.398392
$583$	5.99352	0.248226
$584$	3.67150	0.151928
$585$	21.9211	0.906327
$586$	−19.0644	−0.787542
$587$	35.7214	1.47438	0.737189	−	0.675686i	$-0.236153\pi$
$587$	35.7214	1.47438	0.737189	+	0.675686i	$0.236153\pi$
$588$	0	0
$589$	−1.36794	−0.0563649
$590$	23.4198	0.964180
$591$	14.5611	0.598962
$592$	0.164248	0.00675055
$593$	−1.16031	−0.0476482	−0.0238241	−	0.999716i	$-0.507584\pi$
$593$	−1.16031	−0.0476482	−0.0238241	+	0.999716i	$0.507584\pi$
$594$	−13.7903	−0.565824
$595$	0	0
$596$	14.6570	0.600374
$597$	15.1228	0.618933
$598$	−5.47175	−0.223757
$599$	−20.1807	−0.824559	−0.412280	−	0.911057i	$-0.635267\pi$
$599$	−20.1807	−0.824559	−0.412280	+	0.911057i	$0.635267\pi$
$600$	0.216155	0.00882451
$601$	−32.8817	−1.34127	−0.670636	−	0.741787i	$-0.733979\pi$
$601$	−32.8817	−1.34127	−0.670636	+	0.741787i	$0.733979\pi$
$602$	0	0
$603$	−26.2168	−1.06763
$604$	11.3929	0.463569
$605$	4.94006	0.200842
$606$	0.710947	0.0288802
$607$	7.01042	0.284544	0.142272	−	0.989828i	$-0.454559\pi$
$607$	7.01042	0.284544	0.142272	+	0.989828i	$0.454559\pi$
$608$	−1.00000	−0.0405554
$609$	0	0
$610$	4.92710	0.199493
$611$	−25.1064	−1.01569
$612$	−10.9606	−0.443054
$613$	30.5361	1.23334	0.616671	−	0.787221i	$-0.288481\pi$
$613$	30.5361	1.23334	0.616671	+	0.787221i	$0.288481\pi$
$614$	25.8856	1.04466
$615$	−17.5571	−0.707971
$616$	0	0
$617$	19.2826	0.776287	0.388144	−	0.921599i	$-0.373116\pi$
$617$	19.2826	0.776287	0.388144	+	0.921599i	$0.373116\pi$
$618$	5.47175	0.220106
$619$	16.8148	0.675842	0.337921	−	0.941174i	$-0.390276\pi$
$619$	16.8148	0.675842	0.337921	+	0.941174i	$0.390276\pi$
$620$	−2.96056	−0.118899
$621$	5.17607	0.207708
$622$	−31.1412	−1.24865
$623$	0	0
$624$	−2.73588	−0.109523
$625$	−23.3200	−0.932799
$626$	23.2891	0.930818
$627$	−2.49274	−0.0995506
$628$	−15.7483	−0.628427
$629$	0.710947	0.0283473
$630$	0	0
$631$	29.8672	1.18899	0.594496	−	0.804098i	$-0.297351\pi$
$631$	29.8672	1.18899	0.594496	+	0.804098i	$0.297351\pi$
$632$	−12.0854	−0.480730
$633$	−0.0710061	−0.00282224
$634$	−8.38040	−0.332828
$635$	−7.17671	−0.284799
$636$	−1.12481	−0.0446014
$637$	0	0
$638$	−15.1767	−0.600852
$639$	15.3246	0.606230
$640$	−2.16425	−0.0855494
$641$	36.5242	1.44262	0.721309	−	0.692614i	$-0.243541\pi$
$641$	36.5242	1.44262	0.721309	+	0.692614i	$0.243541\pi$
$642$	−4.12087	−0.162638
$643$	−13.5926	−0.536041	−0.268020	−	0.963413i	$-0.586369\pi$
$643$	−13.5926	−0.536041	−0.268020	+	0.963413i	$0.586369\pi$
$644$	0	0
$645$	−11.6360	−0.458167
$646$	−4.32850	−0.170302
$647$	−12.5177	−0.492121	−0.246060	−	0.969255i	$-0.579136\pi$
$647$	−12.5177	−0.492121	−0.246060	+	0.969255i	$0.579136\pi$
$648$	−5.00853	−0.196753
$649$	39.4383	1.54809
$650$	−1.26412	−0.0495830
$651$	0	0
$652$	−20.3015	−0.795069
$653$	41.7214	1.63268	0.816342	−	0.577569i	$-0.195999\pi$
$653$	41.7214	1.63268	0.816342	+	0.577569i	$0.195999\pi$
$654$	11.6531	0.455670
$655$	−18.0249	−0.704292
$656$	−11.8607	−0.463082
$657$	9.29693	0.362708
$658$	0	0
$659$	42.0748	1.63900	0.819501	−	0.573078i	$-0.194251\pi$
$659$	42.0748	1.63900	0.819501	+	0.573078i	$0.194251\pi$
$660$	−5.39492	−0.209997
$661$	−41.8672	−1.62844	−0.814222	−	0.580554i	$-0.802836\pi$
$661$	−41.8672	−1.62844	−0.814222	+	0.580554i	$0.802836\pi$
$662$	−7.39287	−0.287332
$663$	−11.8422	−0.459914
$664$	−6.96056	−0.270122
$665$	0	0
$666$	0.415906	0.0161160
$667$	5.69643	0.220567
$668$	7.06437	0.273329
$669$	5.28117	0.204182
$670$	−22.4074	−0.865673
$671$	8.29709	0.320306
$672$	0	0
$673$	−40.5242	−1.56209	−0.781046	−	0.624474i	$-0.785313\pi$
$673$	−40.5242	−1.56209	−0.781046	+	0.624474i	$0.785313\pi$
$674$	32.3534	1.24621
$675$	1.19581	0.0460268
$676$	3.00000	0.115385
$677$	−19.7753	−0.760027	−0.380014	−	0.924981i	$-0.624081\pi$
$677$	−19.7753	−0.760027	−0.380014	+	0.924981i	$0.624081\pi$
$678$	−3.23919	−0.124400
$679$	0	0
$680$	−9.36794	−0.359244
$681$	−9.10635	−0.348956
$682$	−4.98549	−0.190904
$683$	22.7359	0.869964	0.434982	−	0.900439i	$-0.356755\pi$
$683$	22.7359	0.869964	0.434982	+	0.900439i	$0.356755\pi$
$684$	−2.53219	−0.0968206
$685$	11.9730	0.457466
$686$	0	0
$687$	3.80090	0.145013
$688$	−7.86068	−0.299686
$689$	6.57811	0.250606
$690$	2.02493	0.0770878
$691$	0.553177	0.0210438	0.0105219	−	0.999945i	$-0.496651\pi$
$691$	0.553177	0.0210438	0.0105219	+	0.999945i	$0.496651\pi$
$692$	−24.7608	−0.941265
$693$	0	0
$694$	−25.4718	−0.966895
$695$	−21.4718	−0.814470
$696$	2.84822	0.107961
$697$	−51.3389	−1.94460
$698$	20.8817	0.790383
$699$	12.7424	0.481960
$700$	0	0
$701$	45.0603	1.70190	0.850952	−	0.525244i	$-0.176026\pi$
$701$	45.0603	1.70190	0.850952	+	0.525244i	$0.176026\pi$
$702$	−15.1354	−0.571248
$703$	0.164248	0.00619473
$704$	−3.64453	−0.137358
$705$	9.29110	0.349923
$706$	5.92112	0.222844
$707$	0	0
$708$	−7.40139	−0.278161
$709$	20.6819	0.776726	0.388363	−	0.921506i	$-0.373041\pi$
$709$	20.6819	0.776726	0.388363	+	0.921506i	$0.373041\pi$
$710$	13.0978	0.491553
$711$	−30.6024	−1.14768
$712$	−14.7089	−0.551239
$713$	1.87126	0.0700791
$714$	0	0
$715$	31.5506	1.17993
$716$	8.10381	0.302854
$717$	−8.27864	−0.309171
$718$	26.9606	1.00616
$719$	−20.7069	−0.772235	−0.386118	−	0.922450i	$-0.626184\pi$
$719$	−20.7069	−0.772235	−0.386118	+	0.922450i	$0.626184\pi$
$720$	−5.48028	−0.204238
$721$	0	0
$722$	−1.00000	−0.0372161
$723$	−1.85863	−0.0691234
$724$	1.92112	0.0713977
$725$	1.31603	0.0488762
$726$	−1.56121	−0.0579420
$727$	−48.9585	−1.81577	−0.907885	−	0.419219i	$-0.862304\pi$
$727$	−48.9585	−1.81577	−0.907885	+	0.419219i	$0.862304\pi$
$728$	0	0
$729$	−4.91842	−0.182164
$730$	7.94605	0.294096
$731$	−34.0249	−1.25846
$732$	−1.55712	−0.0575527
$733$	−51.1996	−1.89110	−0.945550	−	0.325477i	$-0.894475\pi$
$733$	−51.1996	−1.89110	−0.945550	+	0.325477i	$0.894475\pi$
$734$	0.301518	0.0111293
$735$	0	0
$736$	1.36794	0.0504229
$737$	−37.7333	−1.38993
$738$	−30.0335	−1.10555
$739$	38.9251	1.43188	0.715941	−	0.698161i	$-0.245998\pi$
$739$	38.9251	1.43188	0.715941	+	0.698161i	$0.245998\pi$
$740$	0.355473	0.0130675
$741$	−2.73588	−0.100505
$742$	0	0
$743$	−28.9500	−1.06207	−0.531036	−	0.847349i	$-0.678197\pi$
$743$	−28.9500	−1.06207	−0.531036	+	0.847349i	$0.678197\pi$
$744$	0.935628	0.0343018
$745$	31.7214	1.16218
$746$	8.82124	0.322969
$747$	−17.6254	−0.644881
$748$	−15.7753	−0.576803
$749$	0	0
$750$	7.86921	0.287343
$751$	−2.77138	−0.101129	−0.0505645	−	0.998721i	$-0.516102\pi$
$751$	−2.77138	−0.101129	−0.0505645	+	0.998721i	$0.516102\pi$
$752$	6.27659	0.228884
$753$	6.33637	0.230910
$754$	−16.6570	−0.606612
$755$	24.6570	0.897360
$756$	0	0
$757$	−2.81476	−0.102304	−0.0511521	−	0.998691i	$-0.516289\pi$
$757$	−2.81476	−0.102304	−0.0511521	+	0.998691i	$0.516289\pi$
$758$	−11.0644	−0.401876
$759$	3.40992	0.123772
$760$	−2.16425	−0.0785055
$761$	26.0249	0.943403	0.471701	−	0.881758i	$-0.343640\pi$
$761$	26.0249	0.943403	0.471701	+	0.881758i	$0.343640\pi$
$762$	2.26806	0.0821632
$763$	0	0
$764$	13.4718	0.487391
$765$	−23.7214	−0.857648
$766$	7.51373	0.271482
$767$	43.2850	1.56293
$768$	0.683969	0.0246806
$769$	9.53866	0.343973	0.171987	−	0.985099i	$-0.444981\pi$
$769$	9.53866	0.343973	0.171987	+	0.985099i	$0.444981\pi$
$770$	0	0
$771$	−8.56170	−0.308342
$772$	10.4323	0.375467
$773$	−20.6570	−0.742980	−0.371490	−	0.928437i	$-0.621153\pi$
$773$	−20.6570	−0.742980	−0.371490	+	0.928437i	$0.621153\pi$
$774$	−19.9047	−0.715460
$775$	0.432311	0.0155291
$776$	14.0519	0.504434
$777$	0	0
$778$	1.01451	0.0363720
$779$	−11.8607	−0.424953
$780$	−5.92112	−0.212010
$781$	22.0563	0.789238
$782$	5.92112	0.211739
$783$	15.7569	0.563104
$784$	0	0
$785$	−34.0833	−1.21649
$786$	5.69643	0.203185
$787$	−25.8856	−0.922722	−0.461361	−	0.887212i	$-0.652639\pi$
$787$	−25.8856	−0.922722	−0.461361	+	0.887212i	$0.652639\pi$
$788$	21.2891	0.758391
$789$	−4.04986	−0.144179
$790$	−26.1557	−0.930579
$791$	0	0
$792$	−9.22862	−0.327925
$793$	9.10635	0.323376
$794$	2.93358	0.104109
$795$	−2.43436	−0.0863378
$796$	22.1103	0.783679
$797$	−30.4572	−1.07885	−0.539425	−	0.842033i	$-0.681359\pi$
$797$	−30.4572	−1.07885	−0.539425	+	0.842033i	$0.681359\pi$
$798$	0	0
$799$	27.1682	0.961141
$800$	0.316031	0.0111734
$801$	−37.2457	−1.31601
$802$	−16.9606	−0.598898
$803$	13.3809	0.472202
$804$	7.08142	0.249743
$805$	0	0
$806$	−5.47175	−0.192734
$807$	−8.17073	−0.287623
$808$	1.03944	0.0365675
$809$	16.7673	0.589506	0.294753	−	0.955573i	$-0.404763\pi$
$809$	16.7673	0.589506	0.294753	+	0.955573i	$0.404763\pi$
$810$	−10.8397	−0.380868
$811$	36.6799	1.28800	0.644002	−	0.765024i	$-0.277273\pi$
$811$	36.6799	1.28800	0.644002	+	0.765024i	$0.277273\pi$
$812$	0	0
$813$	−14.3660	−0.503839
$814$	0.598606	0.0209811
$815$	−43.9375	−1.53906
$816$	2.96056	0.103640
$817$	−7.86068	−0.275010
$818$	0.787784	0.0275442
$819$	0	0
$820$	−25.6695	−0.896416
$821$	50.2206	1.75271	0.876355	−	0.481665i	$-0.159968\pi$
$821$	50.2206	1.75271	0.876355	+	0.481665i	$0.159968\pi$
$822$	−3.78384	−0.131977
$823$	27.8422	0.970519	0.485260	−	0.874370i	$-0.338725\pi$
$823$	27.8422	0.970519	0.485260	+	0.874370i	$0.338725\pi$
$824$	8.00000	0.278693
$825$	0.787784	0.0274271
$826$	0	0
$827$	−29.0893	−1.01153	−0.505767	−	0.862670i	$-0.668790\pi$
$827$	−29.0893	−1.01153	−0.505767	+	0.862670i	$0.668790\pi$
$828$	3.46387	0.120378
$829$	−29.0893	−1.01031	−0.505157	−	0.863028i	$-0.668565\pi$
$829$	−29.0893	−1.01031	−0.505157	+	0.863028i	$0.668565\pi$
$830$	−15.0644	−0.522892
$831$	−10.2496	−0.355555
$832$	−4.00000	−0.138675
$833$	0	0
$834$	6.78574	0.234971
$835$	15.2891	0.529100
$836$	−3.64453	−0.126049
$837$	5.17607	0.178911
$838$	−20.8817	−0.721345
$839$	16.1707	0.558275	0.279138	−	0.960251i	$-0.409951\pi$
$839$	16.1707	0.558275	0.279138	+	0.960251i	$0.409951\pi$
$840$	0	0
$841$	−11.6590	−0.402036
$842$	5.84223	0.201337
$843$	−18.5282	−0.638147
$844$	−0.103815	−0.00357345
$845$	6.49274	0.223357
$846$	15.8935	0.546429
$847$	0	0
$848$	−1.64453	−0.0564733
$849$	22.8567	0.784441
$850$	1.36794	0.0469199
$851$	−0.224681	−0.00770197
$852$	−4.13932	−0.141811
$853$	−55.9775	−1.91663	−0.958316	−	0.285711i	$-0.907770\pi$
$853$	−55.9775	−1.91663	−0.958316	+	0.285711i	$0.907770\pi$
$854$	0	0
$855$	−5.48028	−0.187422
$856$	−6.02493	−0.205928
$857$	−43.1682	−1.47460	−0.737299	−	0.675567i	$-0.763899\pi$
$857$	−43.1682	−1.47460	−0.737299	+	0.675567i	$0.763899\pi$
$858$	−9.97098	−0.340403
$859$	15.4468	0.527039	0.263519	−	0.964654i	$-0.415117\pi$
$859$	15.4468	0.527039	0.263519	+	0.964654i	$0.415117\pi$
$860$	−17.0125	−0.580120
$861$	0	0
$862$	28.6840	0.976980
$863$	9.83575	0.334813	0.167406	−	0.985888i	$-0.446461\pi$
$863$	9.83575	0.334813	0.167406	+	0.985888i	$0.446461\pi$
$864$	3.78384	0.128729
$865$	−53.5885	−1.82206
$866$	2.26806	0.0770719
$867$	1.18729	0.0403223
$868$	0	0
$869$	−44.0454	−1.49414
$870$	6.16425	0.208988
$871$	−41.4137	−1.40325
$872$	17.0374	0.576959
$873$	35.5820	1.20427
$874$	1.36794	0.0462712
$875$	0	0
$876$	−2.51120	−0.0848454
$877$	13.5407	0.457237	0.228619	−	0.973516i	$-0.426579\pi$
$877$	13.5407	0.457237	0.228619	+	0.973516i	$0.426579\pi$
$878$	−32.6030	−1.10030
$879$	13.0394	0.439809
$880$	−7.88766	−0.265893
$881$	28.9684	0.975971	0.487986	−	0.872852i	$-0.337732\pi$
$881$	28.9684	0.975971	0.487986	+	0.872852i	$0.337732\pi$
$882$	0	0
$883$	57.0623	1.92030	0.960150	−	0.279485i	$-0.0901637\pi$
$883$	57.0623	1.92030	0.960150	+	0.279485i	$0.0901637\pi$
$884$	−17.3140	−0.582332
$885$	−16.0185	−0.538454
$886$	−8.31004	−0.279181
$887$	28.9855	0.973237	0.486619	−	0.873614i	$-0.338230\pi$
$887$	28.9855	0.973237	0.486619	+	0.873614i	$0.338230\pi$
$888$	−0.112341	−0.00376990
$889$	0	0
$890$	−31.8337	−1.06707
$891$	−18.2537	−0.611522
$892$	7.72136	0.258530
$893$	6.27659	0.210038
$894$	−10.0249	−0.335284
$895$	17.5387	0.586253
$896$	0	0
$897$	3.74251	0.124959
$898$	−32.1287	−1.07215
$899$	5.69643	0.189987
$900$	0.800249	0.0266750
$901$	−7.11833	−0.237146
$902$	−43.2266	−1.43929
$903$	0	0
$904$	−4.73588	−0.157513
$905$	4.15777	0.138209
$906$	−7.79237	−0.258884
$907$	5.80025	0.192594	0.0962971	−	0.995353i	$-0.469300\pi$
$907$	5.80025	0.192594	0.0962971	+	0.995353i	$0.469300\pi$
$908$	−13.3140	−0.441840
$909$	2.63206	0.0873000
$910$	0	0
$911$	−9.55712	−0.316641	−0.158321	−	0.987388i	$-0.550608\pi$
$911$	−9.55712	−0.316641	−0.158321	+	0.987388i	$0.550608\pi$
$912$	0.683969	0.0226485
$913$	−25.3679	−0.839556
$914$	−13.9730	−0.462187
$915$	−3.36999	−0.111408
$916$	5.55712	0.183612
$917$	0	0
$918$	16.3784	0.540566
$919$	56.0997	1.85056	0.925280	−	0.379286i	$-0.123830\pi$
$919$	56.0997	1.85056	0.925280	+	0.379286i	$0.123830\pi$
$920$	2.96056	0.0976067
$921$	−17.7050	−0.583398
$922$	−31.6944	−1.04380
$923$	24.2076	0.796804
$924$	0	0
$925$	−0.0519074	−0.00170671
$926$	−35.1682	−1.15570
$927$	20.2575	0.665343
$928$	4.16425	0.136698
$929$	48.0997	1.57810	0.789050	−	0.614329i	$-0.210573\pi$
$929$	48.0997	1.57810	0.789050	+	0.614329i	$0.210573\pi$
$930$	2.02493	0.0664001
$931$	0	0
$932$	18.6300	0.610246
$933$	21.2996	0.697318
$934$	8.81476	0.288428
$935$	−34.1417	−1.11655
$936$	−10.1287	−0.331068
$937$	−52.0499	−1.70039	−0.850197	−	0.526464i	$-0.823517\pi$
$937$	−52.0499	−1.70039	−0.850197	+	0.526464i	$0.823517\pi$
$938$	0	0
$939$	−15.9290	−0.519823
$940$	13.5841	0.443064
$941$	−53.3679	−1.73975	−0.869873	−	0.493277i	$-0.835799\pi$
$941$	−53.3679	−1.73975	−0.869873	+	0.493277i	$0.835799\pi$
$942$	10.7714	0.350951
$943$	16.2247	0.528348
$944$	−10.8212	−0.352201
$945$	0	0
$946$	−28.6485	−0.931442
$947$	−15.0913	−0.490403	−0.245201	−	0.969472i	$-0.578854\pi$
$947$	−15.0913	−0.490403	−0.245201	+	0.969472i	$0.578854\pi$
$948$	8.26602	0.268468
$949$	14.6860	0.476728
$950$	0.316031	0.0102534
$951$	5.73194	0.185871
$952$	0	0
$953$	40.9565	1.32671	0.663355	−	0.748305i	$-0.269132\pi$
$953$	40.9565	1.32671	0.663355	+	0.748305i	$0.269132\pi$
$954$	−4.16425	−0.134823
$955$	29.1562	0.943473
$956$	−12.1038	−0.391465
$957$	10.3804	0.335551
$958$	−33.9894	−1.09815
$959$	0	0
$960$	1.48028	0.0477758
$961$	−29.1287	−0.939637
$962$	0.656992	0.0211823
$963$	−15.2562	−0.491626
$964$	−2.71742	−0.0875224
$965$	22.5781	0.726815
$966$	0	0
$967$	−46.2995	−1.48889	−0.744445	−	0.667683i	$-0.767286\pi$
$967$	−46.2995	−1.48889	−0.744445	+	0.667683i	$0.767286\pi$
$968$	−2.28258	−0.0733647
$969$	2.96056	0.0951068
$970$	30.4118	0.976464
$971$	−3.15826	−0.101353	−0.0506767	−	0.998715i	$-0.516138\pi$
$971$	−3.15826	−0.101353	−0.0506767	+	0.998715i	$0.516138\pi$
$972$	14.7772	0.473979
$973$	0	0
$974$	15.3075	0.490484
$975$	0.864621	0.0276900
$976$	−2.27659	−0.0728718
$977$	15.5387	0.497126	0.248563	−	0.968616i	$-0.420042\pi$
$977$	15.5387	0.497126	0.248563	+	0.968616i	$0.420042\pi$
$978$	13.8856	0.444013
$979$	−53.6070	−1.71329
$980$	0	0
$981$	43.1419	1.37741
$982$	23.1852	0.739871
$983$	−41.5387	−1.32488	−0.662439	−	0.749116i	$-0.730479\pi$
$983$	−41.5387	−1.32488	−0.662439	+	0.749116i	$0.730479\pi$
$984$	8.11234	0.258612
$985$	46.0748	1.46806
$986$	18.0249	0.574031
$987$	0	0
$988$	−4.00000	−0.127257
$989$	10.7529	0.341923
$990$	−19.9730	−0.634784
$991$	−12.1807	−0.386931	−0.193466	−	0.981107i	$-0.561973\pi$
$991$	−12.1807	−0.386931	−0.193466	+	0.981107i	$0.561973\pi$
$992$	1.36794	0.0434321
$993$	5.05649	0.160463
$994$	0	0
$995$	47.8522	1.51702
$996$	4.76081	0.150852
$997$	−6.11439	−0.193645	−0.0968223	−	0.995302i	$-0.530868\pi$
$997$	−6.11439	−0.193645	−0.0968223	+	0.995302i	$0.530868\pi$
$998$	21.5032	0.680671
$999$	−0.621489	−0.0196630

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1862.2.a.o.1.2	✓	3
7.6	odd	2		1862.2.a.p.1.2	yes	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1862.2.a.o.1.2	✓	3	1.1	even	1	trivial
1862.2.a.p.1.2	yes	3	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1862 = 2 \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1862.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.683969 q^{3} +1.00000 q^{4} +2.16425 q^{5} -0.683969 q^{6} -1.00000 q^{8} -2.53219 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.683969 q^{3} +1.00000 q^{4} +2.16425 q^{5} -0.683969 q^{6} -1.00000 q^{8} -2.53219 q^{9} -2.16425 q^{10} -3.64453 q^{11} +0.683969 q^{12} -4.00000 q^{13} +1.48028 q^{15} +1.00000 q^{16} +4.32850 q^{17} +2.53219 q^{18} +1.00000 q^{19} +2.16425 q^{20} +3.64453 q^{22} -1.36794 q^{23} -0.683969 q^{24} -0.316031 q^{25} +4.00000 q^{26} -3.78384 q^{27} -4.16425 q^{29} -1.48028 q^{30} -1.36794 q^{31} -1.00000 q^{32} -2.49274 q^{33} -4.32850 q^{34} -2.53219 q^{36} +0.164248 q^{37} -1.00000 q^{38} -2.73588 q^{39} -2.16425 q^{40} -11.8607 q^{41} -7.86068 q^{43} -3.64453 q^{44} -5.48028 q^{45} +1.36794 q^{46} +6.27659 q^{47} +0.683969 q^{48} +0.316031 q^{50} +2.96056 q^{51} -4.00000 q^{52} -1.64453 q^{53} +3.78384 q^{54} -7.88766 q^{55} +0.683969 q^{57} +4.16425 q^{58} -10.8212 q^{59} +1.48028 q^{60} -2.27659 q^{61} +1.36794 q^{62} +1.00000 q^{64} -8.65699 q^{65} +2.49274 q^{66} +10.3534 q^{67} +4.32850 q^{68} -0.935628 q^{69} -6.05191 q^{71} +2.53219 q^{72} -3.67150 q^{73} -0.164248 q^{74} -0.216155 q^{75} +1.00000 q^{76} +2.73588 q^{78} +12.0854 q^{79} +2.16425 q^{80} +5.00853 q^{81} +11.8607 q^{82} +6.96056 q^{83} +9.36794 q^{85} +7.86068 q^{86} -2.84822 q^{87} +3.64453 q^{88} +14.7089 q^{89} +5.48028 q^{90} -1.36794 q^{92} -0.935628 q^{93} -6.27659 q^{94} +2.16425 q^{95} -0.683969 q^{96} -14.0519 q^{97} +9.22862 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - q^{3} + 3 q^{4} - q^{5} + q^{6} - 3 q^{8} + 6 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 - q^3 + 3 * q^4 - q^5 + q^6 - 3 * q^8 + 6 * q^9	\( 3 q - 3 q^{2} - q^{3} + 3 q^{4} - q^{5} + q^{6} - 3 q^{8} + 6 q^{9} + q^{10} + q^{11} - q^{12} - 12 q^{13} + 3 q^{16} - 2 q^{17} - 6 q^{18} + 3 q^{19} - q^{20} - q^{22} + 2 q^{23} + q^{24} - 4 q^{25} + 12 q^{26} - 28 q^{27} - 5 q^{29} + 2 q^{31} - 3 q^{32} + 15 q^{33} + 2 q^{34} + 6 q^{36} - 7 q^{37} - 3 q^{38} + 4 q^{39} + q^{40} - 7 q^{41} + 5 q^{43} + q^{44} - 12 q^{45} - 2 q^{46} + 13 q^{47} - q^{48} + 4 q^{50} - 12 q^{52} + 7 q^{53} + 28 q^{54} - 22 q^{55} - q^{57} + 5 q^{58} + 5 q^{59} - q^{61} - 2 q^{62} + 3 q^{64} + 4 q^{65} - 15 q^{66} - 20 q^{67} - 2 q^{68} - 30 q^{69} - 9 q^{71} - 6 q^{72} - 26 q^{73} + 7 q^{74} + 16 q^{75} + 3 q^{76} - 4 q^{78} + 11 q^{79} - q^{80} + 35 q^{81} + 7 q^{82} + 12 q^{83} + 22 q^{85} - 5 q^{86} + 2 q^{87} - q^{88} + 5 q^{89} + 12 q^{90} + 2 q^{92} - 30 q^{93} - 13 q^{94} - q^{95} + q^{96} - 33 q^{97} - 7 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - q^3 + 3 * q^4 - q^5 + q^6 - 3 * q^8 + 6 * q^9 + q^10 + q^11 - q^12 - 12 * q^13 + 3 * q^16 - 2 * q^17 - 6 * q^18 + 3 * q^19 - q^20 - q^22 + 2 * q^23 + q^24 - 4 * q^25 + 12 * q^26 - 28 * q^27 - 5 * q^29 + 2 * q^31 - 3 * q^32 + 15 * q^33 + 2 * q^34 + 6 * q^36 - 7 * q^37 - 3 * q^38 + 4 * q^39 + q^40 - 7 * q^41 + 5 * q^43 + q^44 - 12 * q^45 - 2 * q^46 + 13 * q^47 - q^48 + 4 * q^50 - 12 * q^52 + 7 * q^53 + 28 * q^54 - 22 * q^55 - q^57 + 5 * q^58 + 5 * q^59 - q^61 - 2 * q^62 + 3 * q^64 + 4 * q^65 - 15 * q^66 - 20 * q^67 - 2 * q^68 - 30 * q^69 - 9 * q^71 - 6 * q^72 - 26 * q^73 + 7 * q^74 + 16 * q^75 + 3 * q^76 - 4 * q^78 + 11 * q^79 - q^80 + 35 * q^81 + 7 * q^82 + 12 * q^83 + 22 * q^85 - 5 * q^86 + 2 * q^87 - q^88 + 5 * q^89 + 12 * q^90 + 2 * q^92 - 30 * q^93 - 13 * q^94 - q^95 + q^96 - 33 * q^97 - 7 * q^99

Introduction

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