LMFDB - Embedded newform 4018.2.a.bn.1.4

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:	$6$
Coefficient field:	6.6.52046292.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 10x^{4} + 9x^{3} + 24x^{2} - 18x + 1 $ x^6 - x^5 - 10x^4 + 9x^3 + 24x^2 - 18x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 574)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$2.28320$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +0.486321 q^{3} +1.00000 q^{4} -0.616311 q^{5} -0.486321 q^{6} -1.00000 q^{8} -2.76349 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.486321 q^{3} +1.00000 q^{4} -0.616311 q^{5} -0.486321 q^{6} -1.00000 q^{8} -2.76349 q^{9} +0.616311 q^{10} -1.68048 q^{11} +0.486321 q^{12} -5.11251 q^{13} -0.299725 q^{15} +1.00000 q^{16} +4.37980 q^{17} +2.76349 q^{18} +7.65697 q^{19} -0.616311 q^{20} +1.68048 q^{22} +2.40331 q^{23} -0.486321 q^{24} -4.62016 q^{25} +5.11251 q^{26} -2.80291 q^{27} +4.00988 q^{29} +0.299725 q^{30} -4.02347 q^{31} -1.00000 q^{32} -0.817254 q^{33} -4.37980 q^{34} -2.76349 q^{36} +4.15268 q^{37} -7.65697 q^{38} -2.48632 q^{39} +0.616311 q^{40} -1.00000 q^{41} -9.35336 q^{43} -1.68048 q^{44} +1.70317 q^{45} -2.40331 q^{46} -2.90939 q^{47} +0.486321 q^{48} +4.62016 q^{50} +2.12999 q^{51} -5.11251 q^{52} -5.83023 q^{53} +2.80291 q^{54} +1.03570 q^{55} +3.72375 q^{57} -4.00988 q^{58} -11.3459 q^{59} -0.299725 q^{60} +1.07916 q^{61} +4.02347 q^{62} +1.00000 q^{64} +3.15090 q^{65} +0.817254 q^{66} +12.6312 q^{67} +4.37980 q^{68} +1.16878 q^{69} +6.87059 q^{71} +2.76349 q^{72} +4.58524 q^{73} -4.15268 q^{74} -2.24688 q^{75} +7.65697 q^{76} +2.48632 q^{78} +9.49284 q^{79} -0.616311 q^{80} +6.92736 q^{81} +1.00000 q^{82} -4.98021 q^{83} -2.69932 q^{85} +9.35336 q^{86} +1.95009 q^{87} +1.68048 q^{88} +2.21593 q^{89} -1.70317 q^{90} +2.40331 q^{92} -1.95670 q^{93} +2.90939 q^{94} -4.71908 q^{95} -0.486321 q^{96} +15.8435 q^{97} +4.64400 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - q^{3} + 6 q^{4} + q^{6} - 6 q^{8} + 5 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 - q^3 + 6 * q^4 + q^6 - 6 * q^8 + 5 * q^9	$ 6 q - 6 q^{2} - q^{3} + 6 q^{4} + q^{6} - 6 q^{8} + 5 q^{9} + q^{11} - q^{12} - 4 q^{13} + 2 q^{15} + 6 q^{16} + q^{17} - 5 q^{18} + 3 q^{19} - q^{22} + 21 q^{23} + q^{24} + 4 q^{26} - 13 q^{27} + 5 q^{29} - 2 q^{30} - 3 q^{31} - 6 q^{32} + 19 q^{33} - q^{34} + 5 q^{36} - 2 q^{37} - 3 q^{38} - 11 q^{39} - 6 q^{41} + 12 q^{43} + q^{44} - 28 q^{45} - 21 q^{46} + 18 q^{47} - q^{48} + 13 q^{51} - 4 q^{52} + 14 q^{53} + 13 q^{54} + 7 q^{55} + 5 q^{57} - 5 q^{58} - 16 q^{59} + 2 q^{60} + 20 q^{61} + 3 q^{62} + 6 q^{64} + 18 q^{65} - 19 q^{66} - 13 q^{67} + q^{68} - 15 q^{69} + 11 q^{71} - 5 q^{72} - q^{73} + 2 q^{74} + 23 q^{75} + 3 q^{76} + 11 q^{78} + 19 q^{79} - 6 q^{81} + 6 q^{82} - 15 q^{83} - 2 q^{85} - 12 q^{86} - 10 q^{87} - q^{88} + 14 q^{89} + 28 q^{90} + 21 q^{92} + 35 q^{93} - 18 q^{94} + 24 q^{95} + q^{96} - q^{97} + 10 q^{99}+O(q^{100}) $ 6 * q - 6 * q^2 - q^3 + 6 * q^4 + q^6 - 6 * q^8 + 5 * q^9 + q^11 - q^12 - 4 * q^13 + 2 * q^15 + 6 * q^16 + q^17 - 5 * q^18 + 3 * q^19 - q^22 + 21 * q^23 + q^24 + 4 * q^26 - 13 * q^27 + 5 * q^29 - 2 * q^30 - 3 * q^31 - 6 * q^32 + 19 * q^33 - q^34 + 5 * q^36 - 2 * q^37 - 3 * q^38 - 11 * q^39 - 6 * q^41 + 12 * q^43 + q^44 - 28 * q^45 - 21 * q^46 + 18 * q^47 - q^48 + 13 * q^51 - 4 * q^52 + 14 * q^53 + 13 * q^54 + 7 * q^55 + 5 * q^57 - 5 * q^58 - 16 * q^59 + 2 * q^60 + 20 * q^61 + 3 * q^62 + 6 * q^64 + 18 * q^65 - 19 * q^66 - 13 * q^67 + q^68 - 15 * q^69 + 11 * q^71 - 5 * q^72 - q^73 + 2 * q^74 + 23 * q^75 + 3 * q^76 + 11 * q^78 + 19 * q^79 - 6 * q^81 + 6 * q^82 - 15 * q^83 - 2 * q^85 - 12 * q^86 - 10 * q^87 - q^88 + 14 * q^89 + 28 * q^90 + 21 * q^92 + 35 * q^93 - 18 * q^94 + 24 * q^95 + q^96 - q^97 + 10 * 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
$3$	0.486321	0.280778	0.140389	−	0.990096i	$-0.455165\pi$
$3$	0.486321	0.280778	0.140389	+	0.990096i	$0.455165\pi$
$4$	1.00000	0.500000
$5$	−0.616311	−0.275623	−0.137811	−	0.990458i	$-0.544007\pi$
$5$	−0.616311	−0.275623	−0.137811	+	0.990458i	$0.544007\pi$
$6$	−0.486321	−0.198540
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	−2.76349	−0.921164
$10$	0.616311	0.194895
$11$	−1.68048	−0.506684	−0.253342	−	0.967377i	$-0.581530\pi$
$11$	−1.68048	−0.506684	−0.253342	+	0.967377i	$0.581530\pi$
$12$	0.486321	0.140389
$13$	−5.11251	−1.41796	−0.708978	−	0.705231i	$-0.750843\pi$
$13$	−5.11251	−1.41796	−0.708978	+	0.705231i	$0.750843\pi$
$14$	0	0
$15$	−0.299725	−0.0773887
$16$	1.00000	0.250000
$17$	4.37980	1.06226	0.531129	−	0.847291i	$-0.321768\pi$
$17$	4.37980	1.06226	0.531129	+	0.847291i	$0.321768\pi$
$18$	2.76349	0.651361
$19$	7.65697	1.75663	0.878315	−	0.478082i	$-0.158668\pi$
$19$	7.65697	1.75663	0.878315	+	0.478082i	$0.158668\pi$
$20$	−0.616311	−0.137811
$21$	0	0
$22$	1.68048	0.358280
$23$	2.40331	0.501125	0.250563	−	0.968100i	$-0.419384\pi$
$23$	2.40331	0.501125	0.250563	+	0.968100i	$0.419384\pi$
$24$	−0.486321	−0.0992699
$25$	−4.62016	−0.924032
$26$	5.11251	1.00265
$27$	−2.80291	−0.539420
$28$	0	0
$29$	4.00988	0.744616	0.372308	−	0.928109i	$-0.378567\pi$
$29$	4.00988	0.744616	0.372308	+	0.928109i	$0.378567\pi$
$30$	0.299725	0.0547220
$31$	−4.02347	−0.722637	−0.361318	−	0.932442i	$-0.617673\pi$
$31$	−4.02347	−0.722637	−0.361318	+	0.932442i	$0.617673\pi$
$32$	−1.00000	−0.176777
$33$	−0.817254	−0.142266
$34$	−4.37980	−0.751130
$35$	0	0
$36$	−2.76349	−0.460582
$37$	4.15268	0.682696	0.341348	−	0.939937i	$-0.389117\pi$
$37$	4.15268	0.682696	0.341348	+	0.939937i	$0.389117\pi$
$38$	−7.65697	−1.24213
$39$	−2.48632	−0.398130
$40$	0.616311	0.0974473
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	−9.35336	−1.42637	−0.713187	−	0.700974i	$-0.752749\pi$
$43$	−9.35336	−1.42637	−0.713187	+	0.700974i	$0.752749\pi$
$44$	−1.68048	−0.253342
$45$	1.70317	0.253894
$46$	−2.40331	−0.354349
$47$	−2.90939	−0.424378	−0.212189	−	0.977229i	$-0.568059\pi$
$47$	−2.90939	−0.424378	−0.212189	+	0.977229i	$0.568059\pi$
$48$	0.486321	0.0701944
$49$	0	0
$50$	4.62016	0.653389
$51$	2.12999	0.298258
$52$	−5.11251	−0.708978
$53$	−5.83023	−0.800844	−0.400422	−	0.916331i	$-0.631136\pi$
$53$	−5.83023	−0.800844	−0.400422	+	0.916331i	$0.631136\pi$
$54$	2.80291	0.381427
$55$	1.03570	0.139654
$56$	0	0
$57$	3.72375	0.493222
$58$	−4.00988	−0.526523
$59$	−11.3459	−1.47711	−0.738554	−	0.674194i	$-0.764491\pi$
$59$	−11.3459	−1.47711	−0.738554	+	0.674194i	$0.764491\pi$
$60$	−0.299725	−0.0386943
$61$	1.07916	0.138172	0.0690861	−	0.997611i	$-0.477992\pi$
$61$	1.07916	0.138172	0.0690861	+	0.997611i	$0.477992\pi$
$62$	4.02347	0.510981
$63$	0	0
$64$	1.00000	0.125000
$65$	3.15090	0.390821
$66$	0.817254	0.100597
$67$	12.6312	1.54315	0.771575	−	0.636138i	$-0.219469\pi$
$67$	12.6312	1.54315	0.771575	+	0.636138i	$0.219469\pi$
$68$	4.37980	0.531129
$69$	1.16878	0.140705
$70$	0	0
$71$	6.87059	0.815389	0.407695	−	0.913118i	$-0.366333\pi$
$71$	6.87059	0.815389	0.407695	+	0.913118i	$0.366333\pi$
$72$	2.76349	0.325681
$73$	4.58524	0.536661	0.268331	−	0.963327i	$-0.413528\pi$
$73$	4.58524	0.536661	0.268331	+	0.963327i	$0.413528\pi$
$74$	−4.15268	−0.482739
$75$	−2.24688	−0.259447
$76$	7.65697	0.878315
$77$	0	0
$78$	2.48632	0.281520
$79$	9.49284	1.06803	0.534014	−	0.845476i	$-0.320683\pi$
$79$	9.49284	1.06803	0.534014	+	0.845476i	$0.320683\pi$
$80$	−0.616311	−0.0689057
$81$	6.92736	0.769707
$82$	1.00000	0.110432
$83$	−4.98021	−0.546649	−0.273324	−	0.961922i	$-0.588123\pi$
$83$	−4.98021	−0.546649	−0.273324	+	0.961922i	$0.588123\pi$
$84$	0	0
$85$	−2.69932	−0.292782
$86$	9.35336	1.00860
$87$	1.95009	0.209071
$88$	1.68048	0.179140
$89$	2.21593	0.234888	0.117444	−	0.993079i	$-0.462530\pi$
$89$	2.21593	0.234888	0.117444	+	0.993079i	$0.462530\pi$
$90$	−1.70317	−0.179530
$91$	0	0
$92$	2.40331	0.250563
$93$	−1.95670	−0.202900
$94$	2.90939	0.300081
$95$	−4.71908	−0.484167
$96$	−0.486321	−0.0496349
$97$	15.8435	1.60867	0.804334	−	0.594178i	$-0.202523\pi$
$97$	15.8435	1.60867	0.804334	+	0.594178i	$0.202523\pi$
$98$	0	0
$99$	4.64400	0.466739
$100$	−4.62016	−0.462016
$101$	−2.90010	−0.288571	−0.144286	−	0.989536i	$-0.546088\pi$
$101$	−2.90010	−0.288571	−0.144286	+	0.989536i	$0.546088\pi$
$102$	−2.12999	−0.210900
$103$	9.44397	0.930542	0.465271	−	0.885168i	$-0.345957\pi$
$103$	9.44397	0.930542	0.465271	+	0.885168i	$0.345957\pi$
$104$	5.11251	0.501323
$105$	0	0
$106$	5.83023	0.566282
$107$	19.1366	1.85001	0.925005	−	0.379955i	$-0.124061\pi$
$107$	19.1366	1.85001	0.925005	+	0.379955i	$0.124061\pi$
$108$	−2.80291	−0.269710
$109$	5.33986	0.511466	0.255733	−	0.966748i	$-0.417683\pi$
$109$	5.33986	0.511466	0.255733	+	0.966748i	$0.417683\pi$
$110$	−1.03570	−0.0987501
$111$	2.01953	0.191686
$112$	0	0
$113$	7.95104	0.747971	0.373986	−	0.927435i	$-0.377991\pi$
$113$	7.95104	0.747971	0.373986	+	0.927435i	$0.377991\pi$
$114$	−3.72375	−0.348761
$115$	−1.48119	−0.138121
$116$	4.00988	0.372308
$117$	14.1284	1.30617
$118$	11.3459	1.04447
$119$	0	0
$120$	0.299725	0.0273610
$121$	−8.17598	−0.743271
$122$	−1.07916	−0.0977026
$123$	−0.486321	−0.0438501
$124$	−4.02347	−0.361318
$125$	5.92901	0.530307
$126$	0	0
$127$	−12.2391	−1.08605	−0.543023	−	0.839718i	$-0.682720\pi$
$127$	−12.2391	−1.08605	−0.543023	+	0.839718i	$0.682720\pi$
$128$	−1.00000	−0.0883883
$129$	−4.54874	−0.400494
$130$	−3.15090	−0.276352
$131$	−1.23803	−0.108167	−0.0540837	−	0.998536i	$-0.517224\pi$
$131$	−1.23803	−0.108167	−0.0540837	+	0.998536i	$0.517224\pi$
$132$	−0.817254	−0.0711328
$133$	0	0
$134$	−12.6312	−1.09117
$135$	1.72746	0.148676
$136$	−4.37980	−0.375565
$137$	15.5136	1.32542	0.662708	−	0.748878i	$-0.269407\pi$
$137$	15.5136	1.32542	0.662708	+	0.748878i	$0.269407\pi$
$138$	−1.16878	−0.0994932
$139$	−17.9970	−1.52649	−0.763243	−	0.646112i	$-0.776394\pi$
$139$	−17.9970	−1.52649	−0.763243	+	0.646112i	$0.776394\pi$
$140$	0	0
$141$	−1.41490	−0.119156
$142$	−6.87059	−0.576567
$143$	8.59148	0.718456
$144$	−2.76349	−0.230291
$145$	−2.47133	−0.205233
$146$	−4.58524	−0.379477
$147$	0	0
$148$	4.15268	0.341348
$149$	14.4679	1.18526	0.592628	−	0.805476i	$-0.298091\pi$
$149$	14.4679	1.18526	0.592628	+	0.805476i	$0.298091\pi$
$150$	2.24688	0.183457
$151$	2.14126	0.174253	0.0871265	−	0.996197i	$-0.472232\pi$
$151$	2.14126	0.174253	0.0871265	+	0.996197i	$0.472232\pi$
$152$	−7.65697	−0.621063
$153$	−12.1035	−0.978514
$154$	0	0
$155$	2.47971	0.199175
$156$	−2.48632	−0.199065
$157$	5.37832	0.429236	0.214618	−	0.976698i	$-0.431149\pi$
$157$	5.37832	0.429236	0.214618	+	0.976698i	$0.431149\pi$
$158$	−9.49284	−0.755210
$159$	−2.83536	−0.224859
$160$	0.616311	0.0487237
$161$	0	0
$162$	−6.92736	−0.544265
$163$	8.44420	0.661400	0.330700	−	0.943736i	$-0.392715\pi$
$163$	8.44420	0.661400	0.330700	+	0.943736i	$0.392715\pi$
$164$	−1.00000	−0.0780869
$165$	0.503682	0.0392116
$166$	4.98021	0.386539
$167$	13.3726	1.03481	0.517403	−	0.855742i	$-0.326899\pi$
$167$	13.3726	1.03481	0.517403	+	0.855742i	$0.326899\pi$
$168$	0	0
$169$	13.1378	1.01060
$170$	2.69932	0.207028
$171$	−21.1600	−1.61814
$172$	−9.35336	−0.713187
$173$	3.71068	0.282118	0.141059	−	0.990001i	$-0.454949\pi$
$173$	3.71068	0.282118	0.141059	+	0.990001i	$0.454949\pi$
$174$	−1.95009	−0.147836
$175$	0	0
$176$	−1.68048	−0.126671
$177$	−5.51774	−0.414739
$178$	−2.21593	−0.166091
$179$	−6.02645	−0.450438	−0.225219	−	0.974308i	$-0.572310\pi$
$179$	−6.02645	−0.450438	−0.225219	+	0.974308i	$0.572310\pi$
$180$	1.70317	0.126947
$181$	11.8265	0.879053	0.439527	−	0.898230i	$-0.355146\pi$
$181$	11.8265	0.879053	0.439527	+	0.898230i	$0.355146\pi$
$182$	0	0
$183$	0.524818	0.0387957
$184$	−2.40331	−0.177174
$185$	−2.55934	−0.188167
$186$	1.95670	0.143472
$187$	−7.36018	−0.538230
$188$	−2.90939	−0.212189
$189$	0	0
$190$	4.71908	0.342358
$191$	7.52434	0.544442	0.272221	−	0.962235i	$-0.412242\pi$
$191$	7.52434	0.544442	0.272221	+	0.962235i	$0.412242\pi$
$192$	0.486321	0.0350972
$193$	1.71959	0.123778	0.0618892	−	0.998083i	$-0.480287\pi$
$193$	1.71959	0.123778	0.0618892	+	0.998083i	$0.480287\pi$
$194$	−15.8435	−1.13750
$195$	1.53235	0.109734
$196$	0	0
$197$	17.3709	1.23763	0.618813	−	0.785538i	$-0.287614\pi$
$197$	17.3709	1.23763	0.618813	+	0.785538i	$0.287614\pi$
$198$	−4.64400	−0.330035
$199$	−20.0315	−1.41999	−0.709997	−	0.704204i	$-0.751304\pi$
$199$	−20.0315	−1.41999	−0.709997	+	0.704204i	$0.751304\pi$
$200$	4.62016	0.326695
$201$	6.14283	0.433282
$202$	2.90010	0.204051
$203$	0	0
$204$	2.12999	0.149129
$205$	0.616311	0.0430450
$206$	−9.44397	−0.657993
$207$	−6.64153	−0.461618
$208$	−5.11251	−0.354489
$209$	−12.8674	−0.890057
$210$	0	0
$211$	−3.19398	−0.219883	−0.109941	−	0.993938i	$-0.535066\pi$
$211$	−3.19398	−0.219883	−0.109941	+	0.993938i	$0.535066\pi$
$212$	−5.83023	−0.400422
$213$	3.34131	0.228943
$214$	−19.1366	−1.30815
$215$	5.76458	0.393141
$216$	2.80291	0.190714
$217$	0	0
$218$	−5.33986	−0.361661
$219$	2.22990	0.150682
$220$	1.03570	0.0698269
$221$	−22.3918	−1.50623
$222$	−2.01953	−0.135542
$223$	−3.67068	−0.245807	−0.122903	−	0.992419i	$-0.539221\pi$
$223$	−3.67068	−0.245807	−0.122903	+	0.992419i	$0.539221\pi$
$224$	0	0
$225$	12.7678	0.851185
$226$	−7.95104	−0.528895
$227$	9.06526	0.601682	0.300841	−	0.953674i	$-0.402733\pi$
$227$	9.06526	0.601682	0.300841	+	0.953674i	$0.402733\pi$
$228$	3.72375	0.246611
$229$	17.0097	1.12403	0.562017	−	0.827126i	$-0.310026\pi$
$229$	17.0097	1.12403	0.562017	+	0.827126i	$0.310026\pi$
$230$	1.48119	0.0976666
$231$	0	0
$232$	−4.00988	−0.263261
$233$	4.83435	0.316709	0.158354	−	0.987382i	$-0.449381\pi$
$233$	4.83435	0.316709	0.158354	+	0.987382i	$0.449381\pi$
$234$	−14.1284	−0.923601
$235$	1.79309	0.116968
$236$	−11.3459	−0.738554
$237$	4.61657	0.299878
$238$	0	0
$239$	9.41859	0.609238	0.304619	−	0.952474i	$-0.401471\pi$
$239$	9.41859	0.609238	0.304619	+	0.952474i	$0.401471\pi$
$240$	−0.299725	−0.0193472
$241$	−27.3729	−1.76324	−0.881620	−	0.471959i	$-0.843547\pi$
$241$	−27.3729	−1.76324	−0.881620	+	0.471959i	$0.843547\pi$
$242$	8.17598	0.525572
$243$	11.7776	0.755536
$244$	1.07916	0.0690861
$245$	0	0
$246$	0.486321	0.0310067
$247$	−39.1464	−2.49082
$248$	4.02347	0.255491
$249$	−2.42198	−0.153487
$250$	−5.92901	−0.374984
$251$	27.5767	1.74062	0.870311	−	0.492502i	$-0.163917\pi$
$251$	27.5767	1.74062	0.870311	+	0.492502i	$0.163917\pi$
$252$	0	0
$253$	−4.03872	−0.253912
$254$	12.2391	0.767950
$255$	−1.31274	−0.0822067
$256$	1.00000	0.0625000
$257$	4.82258	0.300824	0.150412	−	0.988623i	$-0.451940\pi$
$257$	4.82258	0.300824	0.150412	+	0.988623i	$0.451940\pi$
$258$	4.54874	0.283192
$259$	0	0
$260$	3.15090	0.195410
$261$	−11.0813	−0.685913
$262$	1.23803	0.0764859
$263$	26.6507	1.64336	0.821678	−	0.569952i	$-0.193038\pi$
$263$	26.6507	1.64336	0.821678	+	0.569952i	$0.193038\pi$
$264$	0.817254	0.0502985
$265$	3.59323	0.220731
$266$	0	0
$267$	1.07765	0.0659514
$268$	12.6312	0.771575
$269$	20.9088	1.27483	0.637416	−	0.770519i	$-0.280003\pi$
$269$	20.9088	1.27483	0.637416	+	0.770519i	$0.280003\pi$
$270$	−1.72746	−0.105130
$271$	21.0168	1.27668	0.638341	−	0.769754i	$-0.279621\pi$
$271$	21.0168	1.27668	0.638341	+	0.769754i	$0.279621\pi$
$272$	4.37980	0.265565
$273$	0	0
$274$	−15.5136	−0.937211
$275$	7.76410	0.468193
$276$	1.16878	0.0703523
$277$	−0.898457	−0.0539830	−0.0269915	−	0.999636i	$-0.508593\pi$
$277$	−0.898457	−0.0539830	−0.0269915	+	0.999636i	$0.508593\pi$
$278$	17.9970	1.07939
$279$	11.1188	0.665667
$280$	0	0
$281$	30.0786	1.79434	0.897171	−	0.441684i	$-0.145619\pi$
$281$	30.0786	1.79434	0.897171	+	0.441684i	$0.145619\pi$
$282$	1.41490	0.0842559
$283$	−19.6019	−1.16521	−0.582605	−	0.812755i	$-0.697967\pi$
$283$	−19.6019	−1.16521	−0.582605	+	0.812755i	$0.697967\pi$
$284$	6.87059	0.407695
$285$	−2.29499	−0.135943
$286$	−8.59148	−0.508025
$287$	0	0
$288$	2.76349	0.162840
$289$	2.18267	0.128393
$290$	2.47133	0.145122
$291$	7.70504	0.451678
$292$	4.58524	0.268331
$293$	−25.7367	−1.50356	−0.751778	−	0.659417i	$-0.770803\pi$
$293$	−25.7367	−1.50356	−0.751778	+	0.659417i	$0.770803\pi$
$294$	0	0
$295$	6.99259	0.407125
$296$	−4.15268	−0.241370
$297$	4.71024	0.273316
$298$	−14.4679	−0.838102
$299$	−12.2870	−0.710573
$300$	−2.24688	−0.129724
$301$	0	0
$302$	−2.14126	−0.123216
$303$	−1.41038	−0.0810243
$304$	7.65697	0.439158
$305$	−0.665098	−0.0380834
$306$	12.1035	0.691914
$307$	−17.4198	−0.994199	−0.497100	−	0.867694i	$-0.665602\pi$
$307$	−17.4198	−0.994199	−0.497100	+	0.867694i	$0.665602\pi$
$308$	0	0
$309$	4.59280	0.261275
$310$	−2.47971	−0.140838
$311$	23.0089	1.30471	0.652357	−	0.757912i	$-0.273780\pi$
$311$	23.0089	1.30471	0.652357	+	0.757912i	$0.273780\pi$
$312$	2.48632	0.140760
$313$	−7.66554	−0.433282	−0.216641	−	0.976251i	$-0.569510\pi$
$313$	−7.66554	−0.433282	−0.216641	+	0.976251i	$0.569510\pi$
$314$	−5.37832	−0.303516
$315$	0	0
$316$	9.49284	0.534014
$317$	−4.13124	−0.232033	−0.116017	−	0.993247i	$-0.537013\pi$
$317$	−4.13124	−0.232033	−0.116017	+	0.993247i	$0.537013\pi$
$318$	2.83536	0.158999
$319$	−6.73853	−0.377285
$320$	−0.616311	−0.0344528
$321$	9.30655	0.519441
$322$	0	0
$323$	33.5360	1.86599
$324$	6.92736	0.384854
$325$	23.6206	1.31024
$326$	−8.44420	−0.467681
$327$	2.59688	0.143608
$328$	1.00000	0.0552158
$329$	0	0
$330$	−0.503682	−0.0277268
$331$	−3.92192	−0.215568	−0.107784	−	0.994174i	$-0.534376\pi$
$331$	−3.92192	−0.215568	−0.107784	+	0.994174i	$0.534376\pi$
$332$	−4.98021	−0.273324
$333$	−11.4759	−0.628875
$334$	−13.3726	−0.731719
$335$	−7.78476	−0.425327
$336$	0	0
$337$	−32.3835	−1.76404	−0.882021	−	0.471210i	$-0.843818\pi$
$337$	−32.3835	−1.76404	−0.882021	+	0.471210i	$0.843818\pi$
$338$	−13.1378	−0.714600
$339$	3.86676	0.210013
$340$	−2.69932	−0.146391
$341$	6.76137	0.366149
$342$	21.1600	1.14420
$343$	0	0
$344$	9.35336	0.504300
$345$	−0.720332	−0.0387814
$346$	−3.71068	−0.199488
$347$	24.2908	1.30400	0.651999	−	0.758219i	$-0.273930\pi$
$347$	24.2908	1.30400	0.651999	+	0.758219i	$0.273930\pi$
$348$	1.95009	0.104536
$349$	−15.8847	−0.850287	−0.425143	−	0.905126i	$-0.639776\pi$
$349$	−15.8847	−0.850287	−0.425143	+	0.905126i	$0.639776\pi$
$350$	0	0
$351$	14.3299	0.764873
$352$	1.68048	0.0895700
$353$	−23.3079	−1.24056	−0.620278	−	0.784382i	$-0.712980\pi$
$353$	−23.3079	−1.24056	−0.620278	+	0.784382i	$0.712980\pi$
$354$	5.51774	0.293265
$355$	−4.23442	−0.224740
$356$	2.21593	0.117444
$357$	0	0
$358$	6.02645	0.318508
$359$	30.9375	1.63282	0.816408	−	0.577475i	$-0.195962\pi$
$359$	30.9375	1.63282	0.816408	+	0.577475i	$0.195962\pi$
$360$	−1.70317	−0.0897650
$361$	39.6292	2.08575
$362$	−11.8265	−0.621584
$363$	−3.97615	−0.208694
$364$	0	0
$365$	−2.82593	−0.147916
$366$	−0.524818	−0.0274327
$367$	−19.0487	−0.994334	−0.497167	−	0.867655i	$-0.665626\pi$
$367$	−19.0487	−0.994334	−0.497167	+	0.867655i	$0.665626\pi$
$368$	2.40331	0.125281
$369$	2.76349	0.143862
$370$	2.55934	0.133054
$371$	0	0
$372$	−1.95670	−0.101450
$373$	16.8532	0.872625	0.436312	−	0.899795i	$-0.356284\pi$
$373$	16.8532	0.872625	0.436312	+	0.899795i	$0.356284\pi$
$374$	7.36018	0.380586
$375$	2.88340	0.148898
$376$	2.90939	0.150040
$377$	−20.5005	−1.05583
$378$	0	0
$379$	26.6798	1.37045	0.685224	−	0.728332i	$-0.259704\pi$
$379$	26.6798	1.37045	0.685224	+	0.728332i	$0.259704\pi$
$380$	−4.71908	−0.242084
$381$	−5.95214	−0.304937
$382$	−7.52434	−0.384979
$383$	−30.6768	−1.56751	−0.783755	−	0.621071i	$-0.786698\pi$
$383$	−30.6768	−1.56751	−0.783755	+	0.621071i	$0.786698\pi$
$384$	−0.486321	−0.0248175
$385$	0	0
$386$	−1.71959	−0.0875246
$387$	25.8479	1.31392
$388$	15.8435	0.804334
$389$	15.5832	0.790100	0.395050	−	0.918660i	$-0.370727\pi$
$389$	15.5832	0.790100	0.395050	+	0.918660i	$0.370727\pi$
$390$	−1.53235	−0.0775934
$391$	10.5260	0.532324
$392$	0	0
$393$	−0.602081	−0.0303710
$394$	−17.3709	−0.875134
$395$	−5.85054	−0.294373
$396$	4.64400	0.233370
$397$	6.00501	0.301383	0.150691	−	0.988581i	$-0.451850\pi$
$397$	6.00501	0.301383	0.150691	+	0.988581i	$0.451850\pi$
$398$	20.0315	1.00409
$399$	0	0
$400$	−4.62016	−0.231008
$401$	9.75645	0.487214	0.243607	−	0.969874i	$-0.421669\pi$
$401$	9.75645	0.487214	0.243607	+	0.969874i	$0.421669\pi$
$402$	−6.14283	−0.306377
$403$	20.5700	1.02467
$404$	−2.90010	−0.144286
$405$	−4.26941	−0.212149
$406$	0	0
$407$	−6.97850	−0.345911
$408$	−2.12999	−0.105450
$409$	2.43844	0.120573	0.0602866	−	0.998181i	$-0.480799\pi$
$409$	2.43844	0.120573	0.0602866	+	0.998181i	$0.480799\pi$
$410$	−0.616311	−0.0304374
$411$	7.54459	0.372147
$412$	9.44397	0.465271
$413$	0	0
$414$	6.64153	0.326413
$415$	3.06936	0.150669
$416$	5.11251	0.250661
$417$	−8.75232	−0.428603
$418$	12.8674	0.629365
$419$	−4.49210	−0.219453	−0.109727	−	0.993962i	$-0.534998\pi$
$419$	−4.49210	−0.219453	−0.109727	+	0.993962i	$0.534998\pi$
$420$	0	0
$421$	−38.1666	−1.86013	−0.930064	−	0.367398i	$-0.880249\pi$
$421$	−38.1666	−1.86013	−0.930064	+	0.367398i	$0.880249\pi$
$422$	3.19398	0.155481
$423$	8.04007	0.390922
$424$	5.83023	0.283141
$425$	−20.2354	−0.981561
$426$	−3.34131	−0.161887
$427$	0	0
$428$	19.1366	0.925005
$429$	4.17822	0.201726
$430$	−5.76458	−0.277993
$431$	−31.1582	−1.50084	−0.750420	−	0.660962i	$-0.770149\pi$
$431$	−31.1582	−1.50084	−0.750420	+	0.660962i	$0.770149\pi$
$432$	−2.80291	−0.134855
$433$	−11.5301	−0.554101	−0.277051	−	0.960855i	$-0.589357\pi$
$433$	−11.5301	−0.554101	−0.277051	+	0.960855i	$0.589357\pi$
$434$	0	0
$435$	−1.20186	−0.0576248
$436$	5.33986	0.255733
$437$	18.4021	0.880291
$438$	−2.22990	−0.106549
$439$	−27.9140	−1.33226	−0.666131	−	0.745835i	$-0.732051\pi$
$439$	−27.9140	−1.33226	−0.666131	+	0.745835i	$0.732051\pi$
$440$	−1.03570	−0.0493750
$441$	0	0
$442$	22.3918	1.06507
$443$	12.6944	0.603130	0.301565	−	0.953446i	$-0.402491\pi$
$443$	12.6944	0.603130	0.301565	+	0.953446i	$0.402491\pi$
$444$	2.01953	0.0958429
$445$	−1.36570	−0.0647405
$446$	3.67068	0.173812
$447$	7.03604	0.332793
$448$	0	0
$449$	−38.5081	−1.81731	−0.908656	−	0.417546i	$-0.862890\pi$
$449$	−38.5081	−1.81731	−0.908656	+	0.417546i	$0.862890\pi$
$450$	−12.7678	−0.601879
$451$	1.68048	0.0791308
$452$	7.95104	0.373986
$453$	1.04134	0.0489264
$454$	−9.06526	−0.425454
$455$	0	0
$456$	−3.72375	−0.174380
$457$	−5.36824	−0.251116	−0.125558	−	0.992086i	$-0.540072\pi$
$457$	−5.36824	−0.251116	−0.125558	+	0.992086i	$0.540072\pi$
$458$	−17.0097	−0.794812
$459$	−12.2762	−0.573003
$460$	−1.48119	−0.0690607
$461$	−29.6642	−1.38160	−0.690799	−	0.723047i	$-0.742741\pi$
$461$	−29.6642	−1.38160	−0.690799	+	0.723047i	$0.742741\pi$
$462$	0	0
$463$	26.0446	1.21039	0.605197	−	0.796076i	$-0.293094\pi$
$463$	26.0446	1.21039	0.605197	+	0.796076i	$0.293094\pi$
$464$	4.00988	0.186154
$465$	1.20594	0.0559239
$466$	−4.83435	−0.223947
$467$	10.5096	0.486326	0.243163	−	0.969985i	$-0.421815\pi$
$467$	10.5096	0.486326	0.243163	+	0.969985i	$0.421815\pi$
$468$	14.1284	0.653085
$469$	0	0
$470$	−1.79309	−0.0827090
$471$	2.61559	0.120520
$472$	11.3459	0.522237
$473$	15.7182	0.722722
$474$	−4.61657	−0.212046
$475$	−35.3764	−1.62318
$476$	0	0
$477$	16.1118	0.737708
$478$	−9.41859	−0.430796
$479$	10.6171	0.485106	0.242553	−	0.970138i	$-0.422015\pi$
$479$	10.6171	0.485106	0.242553	+	0.970138i	$0.422015\pi$
$480$	0.299725	0.0136805
$481$	−21.2306	−0.968033
$482$	27.3729	1.24680
$483$	0	0
$484$	−8.17598	−0.371635
$485$	−9.76454	−0.443385
$486$	−11.7776	−0.534245
$487$	0.350326	0.0158748	0.00793739	−	0.999968i	$-0.497473\pi$
$487$	0.350326	0.0158748	0.00793739	+	0.999968i	$0.497473\pi$
$488$	−1.07916	−0.0488513
$489$	4.10659	0.185706
$490$	0	0
$491$	−29.9266	−1.35057	−0.675285	−	0.737557i	$-0.735979\pi$
$491$	−29.9266	−1.35057	−0.675285	+	0.737557i	$0.735979\pi$
$492$	−0.486321	−0.0219250
$493$	17.5625	0.790974
$494$	39.1464	1.76128
$495$	−2.86215	−0.128644
$496$	−4.02347	−0.180659
$497$	0	0
$498$	2.42198	0.108531
$499$	34.4378	1.54165	0.770823	−	0.637049i	$-0.219845\pi$
$499$	34.4378	1.54165	0.770823	+	0.637049i	$0.219845\pi$
$500$	5.92901	0.265153
$501$	6.50340	0.290550
$502$	−27.5767	−1.23081
$503$	12.7817	0.569907	0.284953	−	0.958541i	$-0.408022\pi$
$503$	12.7817	0.569907	0.284953	+	0.958541i	$0.408022\pi$
$504$	0	0
$505$	1.78737	0.0795368
$506$	4.03872	0.179543
$507$	6.38917	0.283753
$508$	−12.2391	−0.543023
$509$	−36.6635	−1.62508	−0.812541	−	0.582905i	$-0.801916\pi$
$509$	−36.6635	−1.62508	−0.812541	+	0.582905i	$0.801916\pi$
$510$	1.31274	0.0581289
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−21.4618	−0.947561
$514$	−4.82258	−0.212715
$515$	−5.82043	−0.256479
$516$	−4.54874	−0.200247
$517$	4.88918	0.215026
$518$	0	0
$519$	1.80458	0.0792124
$520$	−3.15090	−0.138176
$521$	−3.36045	−0.147224	−0.0736119	−	0.997287i	$-0.523453\pi$
$521$	−3.36045	−0.147224	−0.0736119	+	0.997287i	$0.523453\pi$
$522$	11.0813	0.485014
$523$	−23.7576	−1.03885	−0.519423	−	0.854517i	$-0.673853\pi$
$523$	−23.7576	−1.03885	−0.519423	+	0.854517i	$0.673853\pi$
$524$	−1.23803	−0.0540837
$525$	0	0
$526$	−26.6507	−1.16203
$527$	−17.6220	−0.767627
$528$	−0.817254	−0.0355664
$529$	−17.2241	−0.748874
$530$	−3.59323	−0.156080
$531$	31.3543	1.36066
$532$	0	0
$533$	5.11251	0.221447
$534$	−1.07765	−0.0466346
$535$	−11.7941	−0.509905
$536$	−12.6312	−0.545586
$537$	−2.93079	−0.126473
$538$	−20.9088	−0.901443
$539$	0	0
$540$	1.72746	0.0743381
$541$	−4.33577	−0.186409	−0.0932047	−	0.995647i	$-0.529711\pi$
$541$	−4.33577	−0.186409	−0.0932047	+	0.995647i	$0.529711\pi$
$542$	−21.0168	−0.902751
$543$	5.75145	0.246818
$544$	−4.37980	−0.187783
$545$	−3.29101	−0.140971
$546$	0	0
$547$	25.3371	1.08334	0.541669	−	0.840592i	$-0.317793\pi$
$547$	25.3371	1.08334	0.541669	+	0.840592i	$0.317793\pi$
$548$	15.5136	0.662708
$549$	−2.98225	−0.127279
$550$	−7.76410	−0.331062
$551$	30.7035	1.30801
$552$	−1.16878	−0.0497466
$553$	0	0
$554$	0.898457	0.0381718
$555$	−1.24466	−0.0528329
$556$	−17.9970	−0.763243
$557$	33.5582	1.42191	0.710953	−	0.703239i	$-0.248264\pi$
$557$	33.5582	1.42191	0.710953	+	0.703239i	$0.248264\pi$
$558$	−11.1188	−0.470698
$559$	47.8192	2.02254
$560$	0	0
$561$	−3.57941	−0.151123
$562$	−30.0786	−1.26879
$563$	−8.07654	−0.340385	−0.170193	−	0.985411i	$-0.554439\pi$
$563$	−8.07654	−0.340385	−0.170193	+	0.985411i	$0.554439\pi$
$564$	−1.41490	−0.0595779
$565$	−4.90031	−0.206158
$566$	19.6019	0.823928
$567$	0	0
$568$	−6.87059	−0.288284
$569$	23.4628	0.983611	0.491806	−	0.870705i	$-0.336337\pi$
$569$	23.4628	0.983611	0.491806	+	0.870705i	$0.336337\pi$
$570$	2.29499	0.0961264
$571$	5.05564	0.211572	0.105786	−	0.994389i	$-0.466264\pi$
$571$	5.05564	0.211572	0.105786	+	0.994389i	$0.466264\pi$
$572$	8.59148	0.359228
$573$	3.65924	0.152867
$574$	0	0
$575$	−11.1037	−0.463056
$576$	−2.76349	−0.115145
$577$	15.0464	0.626389	0.313195	−	0.949689i	$-0.398601\pi$
$577$	15.0464	0.626389	0.313195	+	0.949689i	$0.398601\pi$
$578$	−2.18267	−0.0907873
$579$	0.836270	0.0347542
$580$	−2.47133	−0.102616
$581$	0	0
$582$	−7.70504	−0.319384
$583$	9.79760	0.405775
$584$	−4.58524	−0.189738
$585$	−8.70748	−0.360010
$586$	25.7367	1.06317
$587$	−9.33886	−0.385456	−0.192728	−	0.981252i	$-0.561734\pi$
$587$	−9.33886	−0.385456	−0.192728	+	0.981252i	$0.561734\pi$
$588$	0	0
$589$	−30.8076	−1.26941
$590$	−6.99259	−0.287881
$591$	8.44784	0.347498
$592$	4.15268	0.170674
$593$	47.9053	1.96723	0.983617	−	0.180273i	$-0.0576982\pi$
$593$	47.9053	1.96723	0.983617	+	0.180273i	$0.0576982\pi$
$594$	−4.71024	−0.193263
$595$	0	0
$596$	14.4679	0.592628
$597$	−9.74173	−0.398703
$598$	12.2870	0.502451
$599$	26.2578	1.07287	0.536433	−	0.843943i	$-0.319772\pi$
$599$	26.2578	1.07287	0.536433	+	0.843943i	$0.319772\pi$
$600$	2.24688	0.0917285
$601$	34.5798	1.41054	0.705269	−	0.708939i	$-0.250826\pi$
$601$	34.5798	1.41054	0.705269	+	0.708939i	$0.250826\pi$
$602$	0	0
$603$	−34.9063	−1.42149
$604$	2.14126	0.0871265
$605$	5.03895	0.204862
$606$	1.41038	0.0572928
$607$	8.02107	0.325565	0.162783	−	0.986662i	$-0.447953\pi$
$607$	8.02107	0.325565	0.162783	+	0.986662i	$0.447953\pi$
$608$	−7.65697	−0.310531
$609$	0	0
$610$	0.665098	0.0269290
$611$	14.8743	0.601749
$612$	−12.1035	−0.489257
$613$	−2.25023	−0.0908861	−0.0454430	−	0.998967i	$-0.514470\pi$
$613$	−2.25023	−0.0908861	−0.0454430	+	0.998967i	$0.514470\pi$
$614$	17.4198	0.703005
$615$	0.299725	0.0120861
$616$	0	0
$617$	−38.9683	−1.56880	−0.784402	−	0.620252i	$-0.787030\pi$
$617$	−38.9683	−1.56880	−0.784402	+	0.620252i	$0.787030\pi$
$618$	−4.59280	−0.184750
$619$	−15.9889	−0.642649	−0.321324	−	0.946969i	$-0.604128\pi$
$619$	−15.9889	−0.642649	−0.321324	+	0.946969i	$0.604128\pi$
$620$	2.47971	0.0995876
$621$	−6.73626	−0.270317
$622$	−23.0089	−0.922572
$623$	0	0
$624$	−2.48632	−0.0995325
$625$	19.4467	0.777868
$626$	7.66554	0.306376
$627$	−6.25769	−0.249908
$628$	5.37832	0.214618
$629$	18.1879	0.725200
$630$	0	0
$631$	9.44784	0.376113	0.188056	−	0.982158i	$-0.439781\pi$
$631$	9.44784	0.376113	0.188056	+	0.982158i	$0.439781\pi$
$632$	−9.49284	−0.377605
$633$	−1.55330	−0.0617382
$634$	4.13124	0.164072
$635$	7.54310	0.299339
$636$	−2.83536	−0.112429
$637$	0	0
$638$	6.73853	0.266781
$639$	−18.9868	−0.751107
$640$	0.616311	0.0243618
$641$	12.8091	0.505928	0.252964	−	0.967476i	$-0.418595\pi$
$641$	12.8091	0.505928	0.252964	+	0.967476i	$0.418595\pi$
$642$	−9.30655	−0.367300
$643$	−12.3360	−0.486486	−0.243243	−	0.969965i	$-0.578211\pi$
$643$	−12.3360	−0.486486	−0.243243	+	0.969965i	$0.578211\pi$
$644$	0	0
$645$	2.80344	0.110385
$646$	−33.5360	−1.31946
$647$	49.7158	1.95453	0.977265	−	0.212022i	$-0.0680048\pi$
$647$	49.7158	1.95453	0.977265	+	0.212022i	$0.0680048\pi$
$648$	−6.92736	−0.272133
$649$	19.0666	0.748428
$650$	−23.6206	−0.926477
$651$	0	0
$652$	8.44420	0.330700
$653$	45.3400	1.77429	0.887145	−	0.461491i	$-0.152685\pi$
$653$	45.3400	1.77429	0.887145	+	0.461491i	$0.152685\pi$
$654$	−2.59688	−0.101546
$655$	0.763013	0.0298134
$656$	−1.00000	−0.0390434
$657$	−12.6713	−0.494353
$658$	0	0
$659$	2.23227	0.0869570	0.0434785	−	0.999054i	$-0.486156\pi$
$659$	2.23227	0.0869570	0.0434785	+	0.999054i	$0.486156\pi$
$660$	0.503682	0.0196058
$661$	44.1283	1.71639	0.858195	−	0.513323i	$-0.171586\pi$
$661$	44.1283	1.71639	0.858195	+	0.513323i	$0.171586\pi$
$662$	3.92192	0.152430
$663$	−10.8896	−0.422917
$664$	4.98021	0.193270
$665$	0	0
$666$	11.4759	0.444682
$667$	9.63699	0.373146
$668$	13.3726	0.517403
$669$	−1.78513	−0.0690170
$670$	7.78476	0.300752
$671$	−1.81351	−0.0700097
$672$	0	0
$673$	−27.0400	−1.04231	−0.521157	−	0.853461i	$-0.674499\pi$
$673$	−27.0400	−1.04231	−0.521157	+	0.853461i	$0.674499\pi$
$674$	32.3835	1.24737
$675$	12.9499	0.498441
$676$	13.1378	0.505299
$677$	−11.5874	−0.445342	−0.222671	−	0.974894i	$-0.571478\pi$
$677$	−11.5874	−0.445342	−0.222671	+	0.974894i	$0.571478\pi$
$678$	−3.86676	−0.148502
$679$	0	0
$680$	2.69932	0.103514
$681$	4.40863	0.168939
$682$	−6.76137	−0.258906
$683$	−42.0044	−1.60725	−0.803627	−	0.595134i	$-0.797099\pi$
$683$	−42.0044	−1.60725	−0.803627	+	0.595134i	$0.797099\pi$
$684$	−21.1600	−0.809072
$685$	−9.56121	−0.365315
$686$	0	0
$687$	8.27218	0.315603
$688$	−9.35336	−0.356594
$689$	29.8071	1.13556
$690$	0.720332	0.0274226
$691$	2.00125	0.0761311	0.0380655	−	0.999275i	$-0.487880\pi$
$691$	2.00125	0.0761311	0.0380655	+	0.999275i	$0.487880\pi$
$692$	3.71068	0.141059
$693$	0	0
$694$	−24.2908	−0.922066
$695$	11.0917	0.420734
$696$	−1.95009	−0.0739179
$697$	−4.37980	−0.165897
$698$	15.8847	0.601244
$699$	2.35104	0.0889247
$700$	0	0
$701$	−44.6984	−1.68823	−0.844117	−	0.536159i	$-0.819875\pi$
$701$	−44.6984	−1.68823	−0.844117	+	0.536159i	$0.819875\pi$
$702$	−14.3299	−0.540847
$703$	31.7969	1.19924
$704$	−1.68048	−0.0633356
$705$	0.872016	0.0328420
$706$	23.3079	0.877205
$707$	0	0
$708$	−5.51774	−0.207369
$709$	−13.1363	−0.493343	−0.246671	−	0.969099i	$-0.579337\pi$
$709$	−13.1363	−0.493343	−0.246671	+	0.969099i	$0.579337\pi$
$710$	4.23442	0.158915
$711$	−26.2334	−0.983829
$712$	−2.21593	−0.0830455
$713$	−9.66966	−0.362131
$714$	0	0
$715$	−5.29503	−0.198023
$716$	−6.02645	−0.225219
$717$	4.58046	0.171060
$718$	−30.9375	−1.15458
$719$	14.1812	0.528868	0.264434	−	0.964404i	$-0.414815\pi$
$719$	14.1812	0.528868	0.264434	+	0.964404i	$0.414815\pi$
$720$	1.70317	0.0634734
$721$	0	0
$722$	−39.6292	−1.47485
$723$	−13.3120	−0.495078
$724$	11.8265	0.439527
$725$	−18.5263	−0.688049
$726$	3.97615	0.147569
$727$	19.8678	0.736857	0.368428	−	0.929656i	$-0.379896\pi$
$727$	19.8678	0.736857	0.368428	+	0.929656i	$0.379896\pi$
$728$	0	0
$729$	−15.0544	−0.557569
$730$	2.82593	0.104592
$731$	−40.9659	−1.51518
$732$	0.524818	0.0193978
$733$	−4.39927	−0.162491	−0.0812453	−	0.996694i	$-0.525890\pi$
$733$	−4.39927	−0.162491	−0.0812453	+	0.996694i	$0.525890\pi$
$734$	19.0487	0.703101
$735$	0	0
$736$	−2.40331	−0.0885872
$737$	−21.2266	−0.781890
$738$	−2.76349	−0.101726
$739$	−49.6085	−1.82488	−0.912440	−	0.409211i	$-0.865804\pi$
$739$	−49.6085	−1.82488	−0.912440	+	0.409211i	$0.865804\pi$
$740$	−2.55934	−0.0940833
$741$	−19.0377	−0.699367
$742$	0	0
$743$	37.2462	1.36643	0.683215	−	0.730217i	$-0.260581\pi$
$743$	37.2462	1.36643	0.683215	+	0.730217i	$0.260581\pi$
$744$	1.95670	0.0717361
$745$	−8.91672	−0.326683
$746$	−16.8532	−0.617039
$747$	13.7628	0.503553
$748$	−7.36018	−0.269115
$749$	0	0
$750$	−2.88340	−0.105287
$751$	−44.0789	−1.60846	−0.804230	−	0.594318i	$-0.797422\pi$
$751$	−44.0789	−1.60846	−0.804230	+	0.594318i	$0.797422\pi$
$752$	−2.90939	−0.106094
$753$	13.4111	0.488728
$754$	20.5005	0.746586
$755$	−1.31968	−0.0480281
$756$	0	0
$757$	49.7382	1.80777	0.903883	−	0.427779i	$-0.140704\pi$
$757$	49.7382	1.80777	0.903883	+	0.427779i	$0.140704\pi$
$758$	−26.6798	−0.969053
$759$	−1.96412	−0.0712929
$760$	4.71908	0.171179
$761$	9.17555	0.332614	0.166307	−	0.986074i	$-0.446816\pi$
$761$	9.17555	0.332614	0.166307	+	0.986074i	$0.446816\pi$
$762$	5.95214	0.215623
$763$	0	0
$764$	7.52434	0.272221
$765$	7.45955	0.269701
$766$	30.6768	1.10840
$767$	58.0060	2.09447
$768$	0.486321	0.0175486
$769$	−6.52990	−0.235474	−0.117737	−	0.993045i	$-0.537564\pi$
$769$	−6.52990	−0.235474	−0.117737	+	0.993045i	$0.537564\pi$
$770$	0	0
$771$	2.34532	0.0844647
$772$	1.71959	0.0618892
$773$	3.57177	0.128468	0.0642338	−	0.997935i	$-0.479540\pi$
$773$	3.57177	0.128468	0.0642338	+	0.997935i	$0.479540\pi$
$774$	−25.8479	−0.929085
$775$	18.5891	0.667740
$776$	−15.8435	−0.568750
$777$	0	0
$778$	−15.5832	−0.558685
$779$	−7.65697	−0.274340
$780$	1.53235	0.0548668
$781$	−11.5459	−0.413145
$782$	−10.5260	−0.376410
$783$	−11.2393	−0.401660
$784$	0	0
$785$	−3.31472	−0.118307
$786$	0.602081	0.0214755
$787$	10.3998	0.370714	0.185357	−	0.982671i	$-0.440656\pi$
$787$	10.3998	0.370714	0.185357	+	0.982671i	$0.440656\pi$
$788$	17.3709	0.618813
$789$	12.9608	0.461417
$790$	5.85054	0.208153
$791$	0	0
$792$	−4.64400	−0.165017
$793$	−5.51722	−0.195922
$794$	−6.00501	−0.213110
$795$	1.74747	0.0619762
$796$	−20.0315	−0.709997
$797$	−18.3777	−0.650971	−0.325485	−	0.945547i	$-0.605528\pi$
$797$	−18.3777	−0.650971	−0.325485	+	0.945547i	$0.605528\pi$
$798$	0	0
$799$	−12.7425	−0.450799
$800$	4.62016	0.163347
$801$	−6.12371	−0.216371
$802$	−9.75645	−0.344512
$803$	−7.70541	−0.271918
$804$	6.14283	0.216641
$805$	0	0
$806$	−20.5700	−0.724549
$807$	10.1684	0.357944
$808$	2.90010	0.102025
$809$	9.73379	0.342222	0.171111	−	0.985252i	$-0.445264\pi$
$809$	9.73379	0.342222	0.171111	+	0.985252i	$0.445264\pi$
$810$	4.26941	0.150012
$811$	−31.2917	−1.09880	−0.549401	−	0.835559i	$-0.685144\pi$
$811$	−31.2917	−1.09880	−0.549401	+	0.835559i	$0.685144\pi$
$812$	0	0
$813$	10.2209	0.358464
$814$	6.97850	0.244596
$815$	−5.20425	−0.182297
$816$	2.12999	0.0745646
$817$	−71.6185	−2.50561
$818$	−2.43844	−0.0852581
$819$	0	0
$820$	0.616311	0.0215225
$821$	−37.2984	−1.30172	−0.650861	−	0.759197i	$-0.725592\pi$
$821$	−37.2984	−1.30172	−0.650861	+	0.759197i	$0.725592\pi$
$822$	−7.54459	−0.263148
$823$	4.25887	0.148455	0.0742274	−	0.997241i	$-0.476351\pi$
$823$	4.25887	0.148455	0.0742274	+	0.997241i	$0.476351\pi$
$824$	−9.44397	−0.328996
$825$	3.77584	0.131458
$826$	0	0
$827$	−7.45576	−0.259262	−0.129631	−	0.991562i	$-0.541379\pi$
$827$	−7.45576	−0.259262	−0.129631	+	0.991562i	$0.541379\pi$
$828$	−6.64153	−0.230809
$829$	49.3494	1.71397	0.856987	−	0.515338i	$-0.172334\pi$
$829$	49.3494	1.71397	0.856987	+	0.515338i	$0.172334\pi$
$830$	−3.06936	−0.106539
$831$	−0.436938	−0.0151572
$832$	−5.11251	−0.177244
$833$	0	0
$834$	8.75232	0.303068
$835$	−8.24171	−0.285216
$836$	−12.8674	−0.445029
$837$	11.2774	0.389805
$838$	4.49210	0.155177
$839$	−33.1222	−1.14351	−0.571753	−	0.820426i	$-0.693736\pi$
$839$	−33.1222	−1.14351	−0.571753	+	0.820426i	$0.693736\pi$
$840$	0	0
$841$	−12.9209	−0.445547
$842$	38.1666	1.31531
$843$	14.6279	0.503811
$844$	−3.19398	−0.109941
$845$	−8.09695	−0.278543
$846$	−8.04007	−0.276423
$847$	0	0
$848$	−5.83023	−0.200211
$849$	−9.53280	−0.327165
$850$	20.2354	0.694068
$851$	9.98018	0.342116
$852$	3.34131	0.114472
$853$	−18.9524	−0.648917	−0.324458	−	0.945900i	$-0.605182\pi$
$853$	−18.9524	−0.648917	−0.324458	+	0.945900i	$0.605182\pi$
$854$	0	0
$855$	13.0411	0.445997
$856$	−19.1366	−0.654077
$857$	−0.0245596	−0.000838940 0	−0.000419470	−	1.00000i	$-0.500134\pi$
$857$	−0.0245596	−0.000838940 0	−0.000419470		1.00000i	$0.500134\pi$
$858$	−4.17822	−0.142642
$859$	−4.64751	−0.158571	−0.0792855	−	0.996852i	$-0.525264\pi$
$859$	−4.64751	−0.158571	−0.0792855	+	0.996852i	$0.525264\pi$
$860$	5.76458	0.196571
$861$	0	0
$862$	31.1582	1.06125
$863$	1.51904	0.0517088	0.0258544	−	0.999666i	$-0.491769\pi$
$863$	1.51904	0.0517088	0.0258544	+	0.999666i	$0.491769\pi$
$864$	2.80291	0.0953568
$865$	−2.28694	−0.0777581
$866$	11.5301	0.391809
$867$	1.06148	0.0360497
$868$	0	0
$869$	−15.9526	−0.541153
$870$	1.20186	0.0407469
$871$	−64.5773	−2.18812
$872$	−5.33986	−0.180830
$873$	−43.7835	−1.48185
$874$	−18.4021	−0.622460
$875$	0	0
$876$	2.22990	0.0753412
$877$	−37.1405	−1.25415	−0.627073	−	0.778961i	$-0.715747\pi$
$877$	−37.1405	−1.25415	−0.627073	+	0.778961i	$0.715747\pi$
$878$	27.9140	0.942051
$879$	−12.5163	−0.422165
$880$	1.03570	0.0349134
$881$	−27.1593	−0.915021	−0.457511	−	0.889204i	$-0.651259\pi$
$881$	−27.1593	−0.915021	−0.457511	+	0.889204i	$0.651259\pi$
$882$	0	0
$883$	−22.3915	−0.753534	−0.376767	−	0.926308i	$-0.622964\pi$
$883$	−22.3915	−0.753534	−0.376767	+	0.926308i	$0.622964\pi$
$884$	−22.3918	−0.753117
$885$	3.40065	0.114311
$886$	−12.6944	−0.426477
$887$	16.7315	0.561788	0.280894	−	0.959739i	$-0.409369\pi$
$887$	16.7315	0.561788	0.280894	+	0.959739i	$0.409369\pi$
$888$	−2.01953	−0.0677711
$889$	0	0
$890$	1.36570	0.0457785
$891$	−11.6413	−0.389999
$892$	−3.67068	−0.122903
$893$	−22.2771	−0.745475
$894$	−7.03604	−0.235320
$895$	3.71417	0.124151
$896$	0	0
$897$	−5.97540	−0.199513
$898$	38.5081	1.28503
$899$	−16.1336	−0.538087
$900$	12.7678	0.425593
$901$	−25.5353	−0.850703
$902$	−1.68048	−0.0559539
$903$	0	0
$904$	−7.95104	−0.264448
$905$	−7.28877	−0.242287
$906$	−1.04134	−0.0345962
$907$	10.7326	0.356370	0.178185	−	0.983997i	$-0.442977\pi$
$907$	10.7326	0.356370	0.178185	+	0.983997i	$0.442977\pi$
$908$	9.06526	0.300841
$909$	8.01441	0.265821
$910$	0	0
$911$	−3.97142	−0.131579	−0.0657896	−	0.997834i	$-0.520957\pi$
$911$	−3.97142	−0.131579	−0.0657896	+	0.997834i	$0.520957\pi$
$912$	3.72375	0.123306
$913$	8.36915	0.276978
$914$	5.36824	0.177566
$915$	−0.323451	−0.0106930
$916$	17.0097	0.562017
$917$	0	0
$918$	12.2762	0.405174
$919$	−41.5804	−1.37161	−0.685805	−	0.727785i	$-0.740550\pi$
$919$	−41.5804	−1.37161	−0.685805	+	0.727785i	$0.740550\pi$
$920$	1.48119	0.0488333
$921$	−8.47160	−0.279149
$922$	29.6642	0.976938
$923$	−35.1260	−1.15619
$924$	0	0
$925$	−19.1860	−0.630833
$926$	−26.0446	−0.855878
$927$	−26.0983	−0.857182
$928$	−4.00988	−0.131631
$929$	45.6831	1.49881	0.749406	−	0.662111i	$-0.230339\pi$
$929$	45.6831	1.49881	0.749406	+	0.662111i	$0.230339\pi$
$930$	−1.20594	−0.0395442
$931$	0	0
$932$	4.83435	0.158354
$933$	11.1897	0.366334
$934$	−10.5096	−0.343885
$935$	4.53616	0.148348
$936$	−14.1284	−0.461801
$937$	−6.29104	−0.205519	−0.102760	−	0.994706i	$-0.532767\pi$
$937$	−6.29104	−0.205519	−0.102760	+	0.994706i	$0.532767\pi$
$938$	0	0
$939$	−3.72791	−0.121656
$940$	1.79309	0.0584841
$941$	−31.8867	−1.03948	−0.519739	−	0.854325i	$-0.673971\pi$
$941$	−31.8867	−1.03948	−0.519739	+	0.854325i	$0.673971\pi$
$942$	−2.61559	−0.0852205
$943$	−2.40331	−0.0782626
$944$	−11.3459	−0.369277
$945$	0	0
$946$	−15.7182	−0.511041
$947$	−15.3656	−0.499316	−0.249658	−	0.968334i	$-0.580318\pi$
$947$	−15.3656	−0.499316	−0.249658	+	0.968334i	$0.580318\pi$
$948$	4.61657	0.149939
$949$	−23.4421	−0.760962
$950$	35.3764	1.14776
$951$	−2.00911	−0.0651498
$952$	0	0
$953$	25.8172	0.836301	0.418150	−	0.908378i	$-0.362679\pi$
$953$	25.8172	0.836301	0.418150	+	0.908378i	$0.362679\pi$
$954$	−16.1118	−0.521638
$955$	−4.63733	−0.150061
$956$	9.41859	0.304619
$957$	−3.27709	−0.105933
$958$	−10.6171	−0.343021
$959$	0	0
$960$	−0.299725	−0.00967358
$961$	−14.8117	−0.477796
$962$	21.2306	0.684502
$963$	−52.8840	−1.70416
$964$	−27.3729	−0.881620
$965$	−1.05980	−0.0341161
$966$	0	0
$967$	18.6448	0.599577	0.299789	−	0.954006i	$-0.403084\pi$
$967$	18.6448	0.599577	0.299789	+	0.954006i	$0.403084\pi$
$968$	8.17598	0.262786
$969$	16.3093	0.523929
$970$	9.76454	0.313521
$971$	11.2870	0.362218	0.181109	−	0.983463i	$-0.442031\pi$
$971$	11.2870	0.362218	0.181109	+	0.983463i	$0.442031\pi$
$972$	11.7776	0.377768
$973$	0	0
$974$	−0.350326	−0.0112252
$975$	11.4872	0.367885
$976$	1.07916	0.0345431
$977$	−35.5003	−1.13575	−0.567877	−	0.823113i	$-0.692235\pi$
$977$	−35.5003	−1.13575	−0.567877	+	0.823113i	$0.692235\pi$
$978$	−4.10659	−0.131314
$979$	−3.72383	−0.119014
$980$	0	0
$981$	−14.7567	−0.471144
$982$	29.9266	0.954997
$983$	11.7626	0.375169	0.187585	−	0.982248i	$-0.439934\pi$
$983$	11.7626	0.375169	0.187585	+	0.982248i	$0.439934\pi$
$984$	0.486321	0.0155033
$985$	−10.7059	−0.341118
$986$	−17.5625	−0.559303
$987$	0	0
$988$	−39.1464	−1.24541
$989$	−22.4790	−0.714792
$990$	2.86215	0.0909650
$991$	31.6807	1.00637	0.503185	−	0.864179i	$-0.332162\pi$
$991$	31.6807	1.00637	0.503185	+	0.864179i	$0.332162\pi$
$992$	4.02347	0.127745
$993$	−1.90731	−0.0605267
$994$	0	0
$995$	12.3456	0.391383
$996$	−2.42198	−0.0767433
$997$	6.98898	0.221343	0.110672	−	0.993857i	$-0.464700\pi$
$997$	6.98898	0.221343	0.110672	+	0.993857i	$0.464700\pi$
$998$	−34.4378	−1.09011
$999$	−11.6396	−0.368260

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4018.2.a.bn.1.4		6
7.3	odd	6		574.2.e.g.247.4	yes	12
7.5	odd	6		574.2.e.g.165.4	✓	12
7.6	odd	2		4018.2.a.bo.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.e.g.165.4	✓	12	7.5	odd	6
574.2.e.g.247.4	yes	12	7.3	odd	6
4018.2.a.bn.1.4		6	1.1	even	1	trivial
4018.2.a.bo.1.3		6	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:	\( N \)	\(=\)	\( 4018 = 2 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.486321 q^{3} +1.00000 q^{4} -0.616311 q^{5} -0.486321 q^{6} -1.00000 q^{8} -2.76349 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.486321 q^{3} +1.00000 q^{4} -0.616311 q^{5} -0.486321 q^{6} -1.00000 q^{8} -2.76349 q^{9} +0.616311 q^{10} -1.68048 q^{11} +0.486321 q^{12} -5.11251 q^{13} -0.299725 q^{15} +1.00000 q^{16} +4.37980 q^{17} +2.76349 q^{18} +7.65697 q^{19} -0.616311 q^{20} +1.68048 q^{22} +2.40331 q^{23} -0.486321 q^{24} -4.62016 q^{25} +5.11251 q^{26} -2.80291 q^{27} +4.00988 q^{29} +0.299725 q^{30} -4.02347 q^{31} -1.00000 q^{32} -0.817254 q^{33} -4.37980 q^{34} -2.76349 q^{36} +4.15268 q^{37} -7.65697 q^{38} -2.48632 q^{39} +0.616311 q^{40} -1.00000 q^{41} -9.35336 q^{43} -1.68048 q^{44} +1.70317 q^{45} -2.40331 q^{46} -2.90939 q^{47} +0.486321 q^{48} +4.62016 q^{50} +2.12999 q^{51} -5.11251 q^{52} -5.83023 q^{53} +2.80291 q^{54} +1.03570 q^{55} +3.72375 q^{57} -4.00988 q^{58} -11.3459 q^{59} -0.299725 q^{60} +1.07916 q^{61} +4.02347 q^{62} +1.00000 q^{64} +3.15090 q^{65} +0.817254 q^{66} +12.6312 q^{67} +4.37980 q^{68} +1.16878 q^{69} +6.87059 q^{71} +2.76349 q^{72} +4.58524 q^{73} -4.15268 q^{74} -2.24688 q^{75} +7.65697 q^{76} +2.48632 q^{78} +9.49284 q^{79} -0.616311 q^{80} +6.92736 q^{81} +1.00000 q^{82} -4.98021 q^{83} -2.69932 q^{85} +9.35336 q^{86} +1.95009 q^{87} +1.68048 q^{88} +2.21593 q^{89} -1.70317 q^{90} +2.40331 q^{92} -1.95670 q^{93} +2.90939 q^{94} -4.71908 q^{95} -0.486321 q^{96} +15.8435 q^{97} +4.64400 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - q^{3} + 6 q^{4} + q^{6} - 6 q^{8} + 5 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 - q^3 + 6 * q^4 + q^6 - 6 * q^8 + 5 * q^9	\( 6 q - 6 q^{2} - q^{3} + 6 q^{4} + q^{6} - 6 q^{8} + 5 q^{9} + q^{11} - q^{12} - 4 q^{13} + 2 q^{15} + 6 q^{16} + q^{17} - 5 q^{18} + 3 q^{19} - q^{22} + 21 q^{23} + q^{24} + 4 q^{26} - 13 q^{27} + 5 q^{29} - 2 q^{30} - 3 q^{31} - 6 q^{32} + 19 q^{33} - q^{34} + 5 q^{36} - 2 q^{37} - 3 q^{38} - 11 q^{39} - 6 q^{41} + 12 q^{43} + q^{44} - 28 q^{45} - 21 q^{46} + 18 q^{47} - q^{48} + 13 q^{51} - 4 q^{52} + 14 q^{53} + 13 q^{54} + 7 q^{55} + 5 q^{57} - 5 q^{58} - 16 q^{59} + 2 q^{60} + 20 q^{61} + 3 q^{62} + 6 q^{64} + 18 q^{65} - 19 q^{66} - 13 q^{67} + q^{68} - 15 q^{69} + 11 q^{71} - 5 q^{72} - q^{73} + 2 q^{74} + 23 q^{75} + 3 q^{76} + 11 q^{78} + 19 q^{79} - 6 q^{81} + 6 q^{82} - 15 q^{83} - 2 q^{85} - 12 q^{86} - 10 q^{87} - q^{88} + 14 q^{89} + 28 q^{90} + 21 q^{92} + 35 q^{93} - 18 q^{94} + 24 q^{95} + q^{96} - q^{97} + 10 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - q^3 + 6 * q^4 + q^6 - 6 * q^8 + 5 * q^9 + q^11 - q^12 - 4 * q^13 + 2 * q^15 + 6 * q^16 + q^17 - 5 * q^18 + 3 * q^19 - q^22 + 21 * q^23 + q^24 + 4 * q^26 - 13 * q^27 + 5 * q^29 - 2 * q^30 - 3 * q^31 - 6 * q^32 + 19 * q^33 - q^34 + 5 * q^36 - 2 * q^37 - 3 * q^38 - 11 * q^39 - 6 * q^41 + 12 * q^43 + q^44 - 28 * q^45 - 21 * q^46 + 18 * q^47 - q^48 + 13 * q^51 - 4 * q^52 + 14 * q^53 + 13 * q^54 + 7 * q^55 + 5 * q^57 - 5 * q^58 - 16 * q^59 + 2 * q^60 + 20 * q^61 + 3 * q^62 + 6 * q^64 + 18 * q^65 - 19 * q^66 - 13 * q^67 + q^68 - 15 * q^69 + 11 * q^71 - 5 * q^72 - q^73 + 2 * q^74 + 23 * q^75 + 3 * q^76 + 11 * q^78 + 19 * q^79 - 6 * q^81 + 6 * q^82 - 15 * q^83 - 2 * q^85 - 12 * q^86 - 10 * q^87 - q^88 + 14 * q^89 + 28 * q^90 + 21 * q^92 + 35 * q^93 - 18 * q^94 + 24 * q^95 + q^96 - q^97 + 10 * q^99

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