LMFDB - Embedded newform 6422.2.a.bn.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6422,2,Mod(1,6422)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6422, 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("6422.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6422 = 2 \cdot 13^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6422.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:	$51.2799281781$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 4 x^{13} - 22 x^{12} + 98 x^{11} + 164 x^{10} - 912 x^{9} - 374 x^{8} + 3996 x^{7} - 817 x^{6} + \cdots + 358 $ x^14 - 4x^13 - 22x^12 + 98x^11 + 164x^10 - 912x^9 - 374x^8 + 3996x^7 - 817x^6 - 8194x^5 + 4418x^4 + 6430x^3 - 4327x^2 - 922*x + 358
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 494)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$2.66506$ of defining polynomial
Character	$\chi$	$=$	6422.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.66506 q^{3} +1.00000 q^{4} -2.40281 q^{5} +2.66506 q^{6} -0.679986 q^{7} +1.00000 q^{8} +4.10252 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.66506 q^{3} +1.00000 q^{4} -2.40281 q^{5} +2.66506 q^{6} -0.679986 q^{7} +1.00000 q^{8} +4.10252 q^{9} -2.40281 q^{10} -5.57053 q^{11} +2.66506 q^{12} -0.679986 q^{14} -6.40363 q^{15} +1.00000 q^{16} +0.0885969 q^{17} +4.10252 q^{18} +1.00000 q^{19} -2.40281 q^{20} -1.81220 q^{21} -5.57053 q^{22} +8.34453 q^{23} +2.66506 q^{24} +0.773507 q^{25} +2.93829 q^{27} -0.679986 q^{28} +8.72221 q^{29} -6.40363 q^{30} +7.96336 q^{31} +1.00000 q^{32} -14.8458 q^{33} +0.0885969 q^{34} +1.63388 q^{35} +4.10252 q^{36} +6.66156 q^{37} +1.00000 q^{38} -2.40281 q^{40} +9.81592 q^{41} -1.81220 q^{42} +8.29860 q^{43} -5.57053 q^{44} -9.85760 q^{45} +8.34453 q^{46} -6.11796 q^{47} +2.66506 q^{48} -6.53762 q^{49} +0.773507 q^{50} +0.236116 q^{51} +7.27889 q^{53} +2.93829 q^{54} +13.3849 q^{55} -0.679986 q^{56} +2.66506 q^{57} +8.72221 q^{58} -9.91003 q^{59} -6.40363 q^{60} -8.84960 q^{61} +7.96336 q^{62} -2.78966 q^{63} +1.00000 q^{64} -14.8458 q^{66} +6.42790 q^{67} +0.0885969 q^{68} +22.2387 q^{69} +1.63388 q^{70} +3.00421 q^{71} +4.10252 q^{72} +2.92701 q^{73} +6.66156 q^{74} +2.06144 q^{75} +1.00000 q^{76} +3.78789 q^{77} +3.25379 q^{79} -2.40281 q^{80} -4.47686 q^{81} +9.81592 q^{82} -0.470597 q^{83} -1.81220 q^{84} -0.212882 q^{85} +8.29860 q^{86} +23.2452 q^{87} -5.57053 q^{88} +0.714677 q^{89} -9.85760 q^{90} +8.34453 q^{92} +21.2228 q^{93} -6.11796 q^{94} -2.40281 q^{95} +2.66506 q^{96} +9.59704 q^{97} -6.53762 q^{98} -22.8533 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 14 q^{2} + 4 q^{3} + 14 q^{4} - 2 q^{5} + 4 q^{6} + 2 q^{7} + 14 q^{8} + 18 q^{9}+O(q^{10}) $ 14 * q + 14 * q^2 + 4 * q^3 + 14 * q^4 - 2 * q^5 + 4 * q^6 + 2 * q^7 + 14 * q^8 + 18 * q^9	\( 14 q + 14 q^{2} + 4 q^{3} + 14 q^{4} - 2 q^{5} + 4 q^{6} + 2 q^{7} + 14 q^{8} + 18 q^{9} - 2 q^{10} + 10 q^{11} + 4 q^{12} + 2 q^{14} - 4 q^{15} + 14 q^{16} + 2 q^{17} + 18 q^{18} + 14 q^{19} - 2 q^{20} - 18 q^{21} + 10 q^{22} + 12 q^{23} + 4 q^{24} + 44 q^{25} + 10 q^{27} + 2 q^{28} + 4 q^{29} - 4 q^{30} + 4 q^{31} + 14 q^{32} + 12 q^{33} + 2 q^{34} + 14 q^{35} + 18 q^{36} + 18 q^{37} + 14 q^{38} - 2 q^{40} + 6 q^{41} - 18 q^{42} + 28 q^{43} + 10 q^{44} + 8 q^{45} + 12 q^{46} - 20 q^{47} + 4 q^{48} + 28 q^{49} + 44 q^{50} + 10 q^{51} + 12 q^{53} + 10 q^{54} - 2 q^{55} + 2 q^{56} + 4 q^{57} + 4 q^{58} + 16 q^{59} - 4 q^{60} + 30 q^{61} + 4 q^{62} + 28 q^{63} + 14 q^{64} + 12 q^{66} + 2 q^{67} + 2 q^{68} - 42 q^{69} + 14 q^{70} + 44 q^{71} + 18 q^{72} - 36 q^{73} + 18 q^{74} + 46 q^{75} + 14 q^{76} + 68 q^{77} + 34 q^{79} - 2 q^{80} - 6 q^{81} + 6 q^{82} + 2 q^{83} - 18 q^{84} - 30 q^{85} + 28 q^{86} + 52 q^{87} + 10 q^{88} + 42 q^{89} + 8 q^{90} + 12 q^{92} - 12 q^{93} - 20 q^{94} - 2 q^{95} + 4 q^{96} + 40 q^{97} + 28 q^{98} + 12 q^{99}+O(q^{100}) \) 14 * q + 14 * q^2 + 4 * q^3 + 14 * q^4 - 2 * q^5 + 4 * q^6 + 2 * q^7 + 14 * q^8 + 18 * q^9 - 2 * q^10 + 10 * q^11 + 4 * q^12 + 2 * q^14 - 4 * q^15 + 14 * q^16 + 2 * q^17 + 18 * q^18 + 14 * q^19 - 2 * q^20 - 18 * q^21 + 10 * q^22 + 12 * q^23 + 4 * q^24 + 44 * q^25 + 10 * q^27 + 2 * q^28 + 4 * q^29 - 4 * q^30 + 4 * q^31 + 14 * q^32 + 12 * q^33 + 2 * q^34 + 14 * q^35 + 18 * q^36 + 18 * q^37 + 14 * q^38 - 2 * q^40 + 6 * q^41 - 18 * q^42 + 28 * q^43 + 10 * q^44 + 8 * q^45 + 12 * q^46 - 20 * q^47 + 4 * q^48 + 28 * q^49 + 44 * q^50 + 10 * q^51 + 12 * q^53 + 10 * q^54 - 2 * q^55 + 2 * q^56 + 4 * q^57 + 4 * q^58 + 16 * q^59 - 4 * q^60 + 30 * q^61 + 4 * q^62 + 28 * q^63 + 14 * q^64 + 12 * q^66 + 2 * q^67 + 2 * q^68 - 42 * q^69 + 14 * q^70 + 44 * q^71 + 18 * q^72 - 36 * q^73 + 18 * q^74 + 46 * q^75 + 14 * q^76 + 68 * q^77 + 34 * q^79 - 2 * q^80 - 6 * q^81 + 6 * q^82 + 2 * q^83 - 18 * q^84 - 30 * q^85 + 28 * q^86 + 52 * q^87 + 10 * q^88 + 42 * q^89 + 8 * q^90 + 12 * q^92 - 12 * q^93 - 20 * q^94 - 2 * q^95 + 4 * q^96 + 40 * q^97 + 28 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	2.66506	1.53867	0.769335	−	0.638845i	$-0.220587\pi$
$3$	2.66506	1.53867	0.769335	+	0.638845i	$0.220587\pi$
$4$	1.00000	0.500000
$5$	−2.40281	−1.07457	−0.537285	−	0.843401i	$-0.680550\pi$
$5$	−2.40281	−1.07457	−0.537285	+	0.843401i	$0.680550\pi$
$6$	2.66506	1.08800
$7$	−0.679986	−0.257011	−0.128505	−	0.991709i	$-0.541018\pi$
$7$	−0.679986	−0.257011	−0.128505	+	0.991709i	$0.541018\pi$
$8$	1.00000	0.353553
$9$	4.10252	1.36751
$10$	−2.40281	−0.759836
$11$	−5.57053	−1.67958	−0.839790	−	0.542912i	$-0.817322\pi$
$11$	−5.57053	−1.67958	−0.839790	+	0.542912i	$0.817322\pi$
$12$	2.66506	0.769335
$13$	0	0
$13$	0	0
$14$	−0.679986	−0.181734
$15$	−6.40363	−1.65341
$16$	1.00000	0.250000
$17$	0.0885969	0.0214879	0.0107439	−	0.999942i	$-0.496580\pi$
$17$	0.0885969	0.0214879	0.0107439	+	0.999942i	$0.496580\pi$
$18$	4.10252	0.966974
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−2.40281	−0.537285
$21$	−1.81220	−0.395455
$22$	−5.57053	−1.18764
$23$	8.34453	1.73996	0.869978	−	0.493091i	$-0.164133\pi$
$23$	8.34453	1.73996	0.869978	+	0.493091i	$0.164133\pi$
$24$	2.66506	0.544002
$25$	0.773507	0.154701
$26$	0	0
$27$	2.93829	0.565474
$28$	−0.679986	−0.128505
$29$	8.72221	1.61967	0.809837	−	0.586655i	$-0.199556\pi$
$29$	8.72221	1.61967	0.809837	+	0.586655i	$0.199556\pi$
$30$	−6.40363	−1.16914
$31$	7.96336	1.43026	0.715130	−	0.698991i	$-0.246367\pi$
$31$	7.96336	1.43026	0.715130	+	0.698991i	$0.246367\pi$
$32$	1.00000	0.176777
$33$	−14.8458	−2.58432
$34$	0.0885969	0.0151942
$35$	1.63388	0.276176
$36$	4.10252	0.683754
$37$	6.66156	1.09515	0.547577	−	0.836755i	$-0.315550\pi$
$37$	6.66156	1.09515	0.547577	+	0.836755i	$0.315550\pi$
$38$	1.00000	0.162221
$39$	0	0
$40$	−2.40281	−0.379918
$41$	9.81592	1.53299	0.766494	−	0.642251i	$-0.221999\pi$
$41$	9.81592	1.53299	0.766494	+	0.642251i	$0.221999\pi$
$42$	−1.81220	−0.279629
$43$	8.29860	1.26552	0.632762	−	0.774346i	$-0.281921\pi$
$43$	8.29860	1.26552	0.632762	+	0.774346i	$0.281921\pi$
$44$	−5.57053	−0.839790
$45$	−9.85760	−1.46948
$46$	8.34453	1.23033
$47$	−6.11796	−0.892396	−0.446198	−	0.894934i	$-0.647222\pi$
$47$	−6.11796	−0.892396	−0.446198	+	0.894934i	$0.647222\pi$
$48$	2.66506	0.384668
$49$	−6.53762	−0.933946
$50$	0.773507	0.109390
$51$	0.236116	0.0330628
$52$	0	0
$53$	7.27889	0.999833	0.499916	−	0.866074i	$-0.333364\pi$
$53$	7.27889	0.999833	0.499916	+	0.866074i	$0.333364\pi$
$54$	2.93829	0.399851
$55$	13.3849	1.80483
$56$	−0.679986	−0.0908670
$57$	2.66506	0.352995
$58$	8.72221	1.14528
$59$	−9.91003	−1.29018	−0.645088	−	0.764108i	$-0.723179\pi$
$59$	−9.91003	−1.29018	−0.645088	+	0.764108i	$0.723179\pi$
$60$	−6.40363	−0.826705
$61$	−8.84960	−1.13307	−0.566537	−	0.824036i	$-0.691717\pi$
$61$	−8.84960	−1.13307	−0.566537	+	0.824036i	$0.691717\pi$
$62$	7.96336	1.01135
$63$	−2.78966	−0.351464
$64$	1.00000	0.125000
$65$	0	0
$66$	−14.8458	−1.82739
$67$	6.42790	0.785293	0.392647	−	0.919689i	$-0.371560\pi$
$67$	6.42790	0.785293	0.392647	+	0.919689i	$0.371560\pi$
$68$	0.0885969	0.0107439
$69$	22.2387	2.67722
$70$	1.63388	0.195286
$71$	3.00421	0.356534	0.178267	−	0.983982i	$-0.442951\pi$
$71$	3.00421	0.356534	0.178267	+	0.983982i	$0.442951\pi$
$72$	4.10252	0.483487
$73$	2.92701	0.342580	0.171290	−	0.985221i	$-0.445206\pi$
$73$	2.92701	0.342580	0.171290	+	0.985221i	$0.445206\pi$
$74$	6.66156	0.774390
$75$	2.06144	0.238035
$76$	1.00000	0.114708
$77$	3.78789	0.431670
$78$	0	0
$79$	3.25379	0.366079	0.183040	−	0.983106i	$-0.441406\pi$
$79$	3.25379	0.366079	0.183040	+	0.983106i	$0.441406\pi$
$80$	−2.40281	−0.268643
$81$	−4.47686	−0.497429
$82$	9.81592	1.08399
$83$	−0.470597	−0.0516548	−0.0258274	−	0.999666i	$-0.508222\pi$
$83$	−0.470597	−0.0516548	−0.0258274	+	0.999666i	$0.508222\pi$
$84$	−1.81220	−0.197727
$85$	−0.212882	−0.0230903
$86$	8.29860	0.894861
$87$	23.2452	2.49214
$88$	−5.57053	−0.593821
$89$	0.714677	0.0757556	0.0378778	−	0.999282i	$-0.487940\pi$
$89$	0.714677	0.0757556	0.0378778	+	0.999282i	$0.487940\pi$
$90$	−9.85760	−1.03908
$91$	0	0
$92$	8.34453	0.869978
$93$	21.2228	2.20070
$94$	−6.11796	−0.631019
$95$	−2.40281	−0.246523
$96$	2.66506	0.272001
$97$	9.59704	0.974432	0.487216	−	0.873282i	$-0.338013\pi$
$97$	9.59704	0.974432	0.487216	+	0.873282i	$0.338013\pi$
$98$	−6.53762	−0.660399
$99$	−22.8533	−2.29684
$100$	0.773507	0.0773507
$101$	−5.46267	−0.543556	−0.271778	−	0.962360i	$-0.587612\pi$
$101$	−5.46267	−0.543556	−0.271778	+	0.962360i	$0.587612\pi$
$102$	0.236116	0.0233789
$103$	−19.2501	−1.89677	−0.948384	−	0.317124i	$-0.897283\pi$
$103$	−19.2501	−1.89677	−0.948384	+	0.317124i	$0.897283\pi$
$104$	0	0
$105$	4.35438	0.424944
$106$	7.27889	0.706989
$107$	−5.10754	−0.493765	−0.246882	−	0.969045i	$-0.579406\pi$
$107$	−5.10754	−0.493765	−0.246882	+	0.969045i	$0.579406\pi$
$108$	2.93829	0.282737
$109$	2.28431	0.218797	0.109399	−	0.993998i	$-0.465108\pi$
$109$	2.28431	0.218797	0.109399	+	0.993998i	$0.465108\pi$
$110$	13.3849	1.27620
$111$	17.7534	1.68508
$112$	−0.679986	−0.0642526
$113$	13.0383	1.22654	0.613269	−	0.789874i	$-0.289854\pi$
$113$	13.0383	1.22654	0.613269	+	0.789874i	$0.289854\pi$
$114$	2.66506	0.249605
$115$	−20.0504	−1.86970
$116$	8.72221	0.809837
$117$	0	0
$118$	−9.91003	−0.912292
$119$	−0.0602446	−0.00552262
$120$	−6.40363	−0.584569
$121$	20.0308	1.82099
$122$	−8.84960	−0.801205
$123$	26.1600	2.35877
$124$	7.96336	0.715130
$125$	10.1555	0.908333
$126$	−2.78966	−0.248523
$127$	13.3891	1.18809	0.594046	−	0.804431i	$-0.297530\pi$
$127$	13.3891	1.18809	0.594046	+	0.804431i	$0.297530\pi$
$128$	1.00000	0.0883883
$129$	22.1162	1.94723
$130$	0	0
$131$	4.40525	0.384888	0.192444	−	0.981308i	$-0.438359\pi$
$131$	4.40525	0.384888	0.192444	+	0.981308i	$0.438359\pi$
$132$	−14.8458	−1.29216
$133$	−0.679986	−0.0589623
$134$	6.42790	0.555286
$135$	−7.06016	−0.607642
$136$	0.0885969	0.00759712
$137$	5.21300	0.445377	0.222688	−	0.974890i	$-0.428517\pi$
$137$	5.21300	0.445377	0.222688	+	0.974890i	$0.428517\pi$
$138$	22.2387	1.89308
$139$	21.1936	1.79762	0.898808	−	0.438342i	$-0.144434\pi$
$139$	21.1936	1.79762	0.898808	+	0.438342i	$0.144434\pi$
$140$	1.63388	0.138088
$141$	−16.3047	−1.37310
$142$	3.00421	0.252108
$143$	0	0
$144$	4.10252	0.341877
$145$	−20.9578	−1.74045
$146$	2.92701	0.242241
$147$	−17.4231	−1.43703
$148$	6.66156	0.547577
$149$	−10.1963	−0.835314	−0.417657	−	0.908605i	$-0.637149\pi$
$149$	−10.1963	−0.835314	−0.417657	+	0.908605i	$0.637149\pi$
$150$	2.06144	0.168316
$151$	17.7428	1.44389	0.721946	−	0.691949i	$-0.243248\pi$
$151$	17.7428	1.44389	0.721946	+	0.691949i	$0.243248\pi$
$152$	1.00000	0.0811107
$153$	0.363471	0.0293849
$154$	3.78789	0.305237
$155$	−19.1344	−1.53692
$156$	0	0
$157$	−18.7354	−1.49525	−0.747624	−	0.664122i	$-0.768806\pi$
$157$	−18.7354	−1.49525	−0.747624	+	0.664122i	$0.768806\pi$
$158$	3.25379	0.258857
$159$	19.3987	1.53841
$160$	−2.40281	−0.189959
$161$	−5.67417	−0.447187
$162$	−4.47686	−0.351736
$163$	7.58834	0.594365	0.297183	−	0.954821i	$-0.403953\pi$
$163$	7.58834	0.594365	0.297183	+	0.954821i	$0.403953\pi$
$164$	9.81592	0.766494
$165$	35.6716	2.77703
$166$	−0.470597	−0.0365254
$167$	−0.227199	−0.0175812	−0.00879060	−	0.999961i	$-0.502798\pi$
$167$	−0.227199	−0.0175812	−0.00879060	+	0.999961i	$0.502798\pi$
$168$	−1.81220	−0.139814
$169$	0	0
$170$	−0.212882	−0.0163273
$171$	4.10252	0.313728
$172$	8.29860	0.632762
$173$	−21.3505	−1.62325	−0.811623	−	0.584181i	$-0.801416\pi$
$173$	−21.3505	−1.62325	−0.811623	+	0.584181i	$0.801416\pi$
$174$	23.2452	1.76221
$175$	−0.525974	−0.0397599
$176$	−5.57053	−0.419895
$177$	−26.4108	−1.98516
$178$	0.714677	0.0535673
$179$	0.910117	0.0680254	0.0340127	−	0.999421i	$-0.489171\pi$
$179$	0.910117	0.0680254	0.0340127	+	0.999421i	$0.489171\pi$
$180$	−9.85760	−0.734742
$181$	−0.388590	−0.0288837	−0.0144418	−	0.999896i	$-0.504597\pi$
$181$	−0.388590	−0.0288837	−0.0144418	+	0.999896i	$0.504597\pi$
$182$	0	0
$183$	−23.5847	−1.74343
$184$	8.34453	0.615167
$185$	−16.0065	−1.17682
$186$	21.2228	1.55613
$187$	−0.493532	−0.0360906
$188$	−6.11796	−0.446198
$189$	−1.99800	−0.145333
$190$	−2.40281	−0.174318
$191$	2.19909	0.159121	0.0795604	−	0.996830i	$-0.474648\pi$
$191$	2.19909	0.159121	0.0795604	+	0.996830i	$0.474648\pi$
$192$	2.66506	0.192334
$193$	−0.389510	−0.0280375	−0.0140188	−	0.999902i	$-0.504462\pi$
$193$	−0.389510	−0.0280375	−0.0140188	+	0.999902i	$0.504462\pi$
$194$	9.59704	0.689027
$195$	0	0
$196$	−6.53762	−0.466973
$197$	3.76396	0.268171	0.134086	−	0.990970i	$-0.457190\pi$
$197$	3.76396	0.268171	0.134086	+	0.990970i	$0.457190\pi$
$198$	−22.8533	−1.62411
$199$	−6.25241	−0.443221	−0.221611	−	0.975135i	$-0.571131\pi$
$199$	−6.25241	−0.443221	−0.221611	+	0.975135i	$0.571131\pi$
$200$	0.773507	0.0546952
$201$	17.1307	1.20831
$202$	−5.46267	−0.384352
$203$	−5.93098	−0.416273
$204$	0.236116	0.0165314
$205$	−23.5858	−1.64730
$206$	−19.2501	−1.34122
$207$	34.2337	2.37940
$208$	0	0
$209$	−5.57053	−0.385322
$210$	4.35438	0.300481
$211$	−4.31955	−0.297370	−0.148685	−	0.988885i	$-0.547504\pi$
$211$	−4.31955	−0.297370	−0.148685	+	0.988885i	$0.547504\pi$
$212$	7.27889	0.499916
$213$	8.00640	0.548589
$214$	−5.10754	−0.349144
$215$	−19.9400	−1.35990
$216$	2.93829	0.199925
$217$	−5.41497	−0.367592
$218$	2.28431	0.154713
$219$	7.80064	0.527118
$220$	13.3849	0.902413
$221$	0	0
$222$	17.7534	1.19153
$223$	0.207493	0.0138947	0.00694737	−	0.999976i	$-0.497789\pi$
$223$	0.207493	0.0138947	0.00694737	+	0.999976i	$0.497789\pi$
$224$	−0.679986	−0.0454335
$225$	3.17333	0.211555
$226$	13.0383	0.867294
$227$	−12.7628	−0.847096	−0.423548	−	0.905874i	$-0.639215\pi$
$227$	−12.7628	−0.847096	−0.423548	+	0.905874i	$0.639215\pi$
$228$	2.66506	0.176498
$229$	−3.65111	−0.241272	−0.120636	−	0.992697i	$-0.538493\pi$
$229$	−3.65111	−0.241272	−0.120636	+	0.992697i	$0.538493\pi$
$230$	−20.0504	−1.32208
$231$	10.0949	0.664198
$232$	8.72221	0.572641
$233$	−2.64461	−0.173254	−0.0866271	−	0.996241i	$-0.527609\pi$
$233$	−2.64461	−0.173254	−0.0866271	+	0.996241i	$0.527609\pi$
$234$	0	0
$235$	14.7003	0.958943
$236$	−9.91003	−0.645088
$237$	8.67152	0.563276
$238$	−0.0602446	−0.00390508
$239$	−5.15691	−0.333573	−0.166786	−	0.985993i	$-0.553339\pi$
$239$	−5.15691	−0.333573	−0.166786	+	0.985993i	$0.553339\pi$
$240$	−6.40363	−0.413353
$241$	−14.8768	−0.958297	−0.479149	−	0.877734i	$-0.659055\pi$
$241$	−14.8768	−0.958297	−0.479149	+	0.877734i	$0.659055\pi$
$242$	20.0308	1.28763
$243$	−20.7460	−1.33085
$244$	−8.84960	−0.566537
$245$	15.7087	1.00359
$246$	26.1600	1.66790
$247$	0	0
$248$	7.96336	0.505674
$249$	−1.25417	−0.0794797
$250$	10.1555	0.642288
$251$	10.5977	0.668919	0.334459	−	0.942410i	$-0.391446\pi$
$251$	10.5977	0.668919	0.334459	+	0.942410i	$0.391446\pi$
$252$	−2.78966	−0.175732
$253$	−46.4835	−2.92239
$254$	13.3891	0.840108
$255$	−0.567342	−0.0355283
$256$	1.00000	0.0625000
$257$	−10.1532	−0.633337	−0.316669	−	0.948536i	$-0.602564\pi$
$257$	−10.1532	−0.633337	−0.316669	+	0.948536i	$0.602564\pi$
$258$	22.1162	1.37690
$259$	−4.52977	−0.281466
$260$	0	0
$261$	35.7831	2.21492
$262$	4.40525	0.272157
$263$	−22.9675	−1.41623	−0.708117	−	0.706095i	$-0.750455\pi$
$263$	−22.9675	−1.41623	−0.708117	+	0.706095i	$0.750455\pi$
$264$	−14.8458	−0.913695
$265$	−17.4898	−1.07439
$266$	−0.679986	−0.0416926
$267$	1.90465	0.116563
$268$	6.42790	0.392647
$269$	13.9883	0.852884	0.426442	−	0.904515i	$-0.359767\pi$
$269$	13.9883	0.852884	0.426442	+	0.904515i	$0.359767\pi$
$270$	−7.06016	−0.429668
$271$	−30.6015	−1.85891	−0.929454	−	0.368938i	$-0.879722\pi$
$271$	−30.6015	−1.85891	−0.929454	+	0.368938i	$0.879722\pi$
$272$	0.0885969	0.00537197
$273$	0	0
$274$	5.21300	0.314929
$275$	−4.30885	−0.259833
$276$	22.2387	1.33861
$277$	0.657414	0.0395002	0.0197501	−	0.999805i	$-0.493713\pi$
$277$	0.657414	0.0395002	0.0197501	+	0.999805i	$0.493713\pi$
$278$	21.1936	1.27111
$279$	32.6699	1.95589
$280$	1.63388	0.0976429
$281$	−13.4279	−0.801042	−0.400521	−	0.916288i	$-0.631171\pi$
$281$	−13.4279	−0.801042	−0.400521	+	0.916288i	$0.631171\pi$
$282$	−16.3047	−0.970931
$283$	11.8274	0.703063	0.351531	−	0.936176i	$-0.385661\pi$
$283$	11.8274	0.703063	0.351531	+	0.936176i	$0.385661\pi$
$284$	3.00421	0.178267
$285$	−6.40363	−0.379318
$286$	0	0
$287$	−6.67469	−0.393994
$288$	4.10252	0.241744
$289$	−16.9922	−0.999538
$290$	−20.9578	−1.23069
$291$	25.5766	1.49933
$292$	2.92701	0.171290
$293$	−5.93975	−0.347004	−0.173502	−	0.984834i	$-0.555508\pi$
$293$	−5.93975	−0.347004	−0.173502	+	0.984834i	$0.555508\pi$
$294$	−17.4231	−1.01614
$295$	23.8119	1.38639
$296$	6.66156	0.387195
$297$	−16.3678	−0.949759
$298$	−10.1963	−0.590656
$299$	0	0
$300$	2.06144	0.119017
$301$	−5.64293	−0.325253
$302$	17.7428	1.02099
$303$	−14.5583	−0.836354
$304$	1.00000	0.0573539
$305$	21.2639	1.21757
$306$	0.363471	0.0207782
$307$	−2.98476	−0.170349	−0.0851746	−	0.996366i	$-0.527145\pi$
$307$	−2.98476	−0.170349	−0.0851746	+	0.996366i	$0.527145\pi$
$308$	3.78789	0.215835
$309$	−51.3026	−2.91850
$310$	−19.1344	−1.08676
$311$	16.9232	0.959624	0.479812	−	0.877371i	$-0.340705\pi$
$311$	16.9232	0.959624	0.479812	+	0.877371i	$0.340705\pi$
$312$	0	0
$313$	−6.38300	−0.360788	−0.180394	−	0.983594i	$-0.557737\pi$
$313$	−6.38300	−0.360788	−0.180394	+	0.983594i	$0.557737\pi$
$314$	−18.7354	−1.05730
$315$	6.70303	0.377673
$316$	3.25379	0.183040
$317$	−5.05240	−0.283771	−0.141886	−	0.989883i	$-0.545316\pi$
$317$	−5.05240	−0.283771	−0.141886	+	0.989883i	$0.545316\pi$
$318$	19.3987	1.08782
$319$	−48.5874	−2.72037
$320$	−2.40281	−0.134321
$321$	−13.6119	−0.759741
$322$	−5.67417	−0.316209
$323$	0.0885969	0.00492966
$324$	−4.47686	−0.248715
$325$	0	0
$326$	7.58834	0.420280
$327$	6.08781	0.336657
$328$	9.81592	0.541993
$329$	4.16013	0.229355
$330$	35.6716	1.96366
$331$	12.1193	0.666139	0.333070	−	0.942902i	$-0.391916\pi$
$331$	12.1193	0.666139	0.333070	+	0.942902i	$0.391916\pi$
$332$	−0.470597	−0.0258274
$333$	27.3292	1.49763
$334$	−0.227199	−0.0124318
$335$	−15.4450	−0.843853
$336$	−1.81220	−0.0988637
$337$	−12.4390	−0.677597	−0.338799	−	0.940859i	$-0.610021\pi$
$337$	−12.4390	−0.677597	−0.338799	+	0.940859i	$0.610021\pi$
$338$	0	0
$339$	34.7478	1.88724
$340$	−0.212882	−0.0115451
$341$	−44.3601	−2.40224
$342$	4.10252	0.221839
$343$	9.20539	0.497044
$344$	8.29860	0.447431
$345$	−53.4353	−2.87686
$346$	−21.3505	−1.14781
$347$	25.1516	1.35021	0.675104	−	0.737722i	$-0.264099\pi$
$347$	25.1516	1.35021	0.675104	+	0.737722i	$0.264099\pi$
$348$	23.2452	1.24607
$349$	−13.1872	−0.705895	−0.352948	−	0.935643i	$-0.614821\pi$
$349$	−13.1872	−0.705895	−0.352948	+	0.935643i	$0.614821\pi$
$350$	−0.525974	−0.0281145
$351$	0	0
$352$	−5.57053	−0.296910
$353$	−4.49299	−0.239138	−0.119569	−	0.992826i	$-0.538151\pi$
$353$	−4.49299	−0.239138	−0.119569	+	0.992826i	$0.538151\pi$
$354$	−26.4108	−1.40372
$355$	−7.21856	−0.383121
$356$	0.714677	0.0378778
$357$	−0.160555	−0.00849749
$358$	0.910117	0.0481012
$359$	−5.85214	−0.308864	−0.154432	−	0.988003i	$-0.549355\pi$
$359$	−5.85214	−0.308864	−0.154432	+	0.988003i	$0.549355\pi$
$360$	−9.85760	−0.519541
$361$	1.00000	0.0526316
$362$	−0.388590	−0.0204238
$363$	53.3833	2.80190
$364$	0	0
$365$	−7.03305	−0.368126
$366$	−23.5847	−1.23279
$367$	18.2839	0.954412	0.477206	−	0.878791i	$-0.341650\pi$
$367$	18.2839	0.954412	0.477206	+	0.878791i	$0.341650\pi$
$368$	8.34453	0.434989
$369$	40.2700	2.09637
$370$	−16.0065	−0.832137
$371$	−4.94955	−0.256968
$372$	21.2228	1.10035
$373$	8.26296	0.427840	0.213920	−	0.976851i	$-0.431377\pi$
$373$	8.26296	0.427840	0.213920	+	0.976851i	$0.431377\pi$
$374$	−0.493532	−0.0255199
$375$	27.0649	1.39763
$376$	−6.11796	−0.315510
$377$	0	0
$378$	−1.99800	−0.102766
$379$	32.8351	1.68663	0.843313	−	0.537423i	$-0.180602\pi$
$379$	32.8351	1.68663	0.843313	+	0.537423i	$0.180602\pi$
$380$	−2.40281	−0.123262
$381$	35.6827	1.82808
$382$	2.19909	0.112515
$383$	−23.6057	−1.20619	−0.603097	−	0.797668i	$-0.706067\pi$
$383$	−23.6057	−1.20619	−0.603097	+	0.797668i	$0.706067\pi$
$384$	2.66506	0.136001
$385$	−9.10158	−0.463859
$386$	−0.389510	−0.0198255
$387$	34.0452	1.73062
$388$	9.59704	0.487216
$389$	−31.6452	−1.60448	−0.802238	−	0.597004i	$-0.796358\pi$
$389$	−31.6452	−1.60448	−0.802238	+	0.597004i	$0.796358\pi$
$390$	0	0
$391$	0.739300	0.0373880
$392$	−6.53762	−0.330200
$393$	11.7402	0.592217
$394$	3.76396	0.189626
$395$	−7.81824	−0.393378
$396$	−22.8533	−1.14842
$397$	36.2239	1.81803	0.909014	−	0.416767i	$-0.136837\pi$
$397$	36.2239	1.81803	0.909014	+	0.416767i	$0.136837\pi$
$398$	−6.25241	−0.313405
$399$	−1.81220	−0.0907235
$400$	0.773507	0.0386753
$401$	5.43819	0.271570	0.135785	−	0.990738i	$-0.456644\pi$
$401$	5.43819	0.271570	0.135785	+	0.990738i	$0.456644\pi$
$402$	17.1307	0.854403
$403$	0	0
$404$	−5.46267	−0.271778
$405$	10.7571	0.534523
$406$	−5.93098	−0.294350
$407$	−37.1084	−1.83940
$408$	0.236116	0.0116895
$409$	31.6058	1.56281	0.781403	−	0.624027i	$-0.214505\pi$
$409$	31.6058	1.56281	0.781403	+	0.624027i	$0.214505\pi$
$410$	−23.5858	−1.16482
$411$	13.8929	0.685289
$412$	−19.2501	−0.948384
$413$	6.73868	0.331589
$414$	34.2337	1.68249
$415$	1.13076	0.0555067
$416$	0	0
$417$	56.4821	2.76594
$418$	−5.57053	−0.272464
$419$	−33.1838	−1.62113	−0.810566	−	0.585647i	$-0.800841\pi$
$419$	−33.1838	−1.62113	−0.810566	+	0.585647i	$0.800841\pi$
$420$	4.35438	0.212472
$421$	20.2497	0.986908	0.493454	−	0.869772i	$-0.335734\pi$
$421$	20.2497	0.986908	0.493454	+	0.869772i	$0.335734\pi$
$422$	−4.31955	−0.210272
$423$	−25.0991	−1.22036
$424$	7.27889	0.353494
$425$	0.0685303	0.00332421
$426$	8.00640	0.387911
$427$	6.01760	0.291212
$428$	−5.10754	−0.246882
$429$	0	0
$430$	−19.9400	−0.961591
$431$	17.2707	0.831901	0.415950	−	0.909387i	$-0.363449\pi$
$431$	17.2707	0.831901	0.415950	+	0.909387i	$0.363449\pi$
$432$	2.93829	0.141369
$433$	28.0742	1.34916	0.674579	−	0.738202i	$-0.264325\pi$
$433$	28.0742	1.34916	0.674579	+	0.738202i	$0.264325\pi$
$434$	−5.41497	−0.259927
$435$	−55.8538	−2.67798
$436$	2.28431	0.109399
$437$	8.34453	0.399173
$438$	7.80064	0.372729
$439$	7.87177	0.375699	0.187849	−	0.982198i	$-0.439848\pi$
$439$	7.87177	0.375699	0.187849	+	0.982198i	$0.439848\pi$
$440$	13.3849	0.638102
$441$	−26.8207	−1.27718
$442$	0	0
$443$	−28.3139	−1.34523	−0.672617	−	0.739991i	$-0.734830\pi$
$443$	−28.3139	−1.34523	−0.672617	+	0.739991i	$0.734830\pi$
$444$	17.7534	0.842540
$445$	−1.71723	−0.0814047
$446$	0.207493	0.00982507
$447$	−27.1737	−1.28527
$448$	−0.679986	−0.0321263
$449$	20.1897	0.952809	0.476404	−	0.879226i	$-0.341940\pi$
$449$	20.1897	0.952809	0.476404	+	0.879226i	$0.341940\pi$
$450$	3.17333	0.149592
$451$	−54.6799	−2.57478
$452$	13.0383	0.613269
$453$	47.2857	2.22168
$454$	−12.7628	−0.598987
$455$	0	0
$456$	2.66506	0.124803
$457$	−5.05880	−0.236640	−0.118320	−	0.992975i	$-0.537751\pi$
$457$	−5.05880	−0.236640	−0.118320	+	0.992975i	$0.537751\pi$
$458$	−3.65111	−0.170605
$459$	0.260323	0.0121509
$460$	−20.0504	−0.934852
$461$	−19.5003	−0.908218	−0.454109	−	0.890946i	$-0.650042\pi$
$461$	−19.5003	−0.908218	−0.454109	+	0.890946i	$0.650042\pi$
$462$	10.0949	0.469659
$463$	20.3598	0.946200	0.473100	−	0.881009i	$-0.343135\pi$
$463$	20.3598	0.946200	0.473100	+	0.881009i	$0.343135\pi$
$464$	8.72221	0.404918
$465$	−50.9944	−2.36481
$466$	−2.64461	−0.122509
$467$	−7.75858	−0.359024	−0.179512	−	0.983756i	$-0.557452\pi$
$467$	−7.75858	−0.359024	−0.179512	+	0.983756i	$0.557452\pi$
$468$	0	0
$469$	−4.37088	−0.201829
$470$	14.7003	0.678075
$471$	−49.9309	−2.30070
$472$	−9.91003	−0.456146
$473$	−46.2276	−2.12555
$474$	8.67152	0.398296
$475$	0.773507	0.0354909
$476$	−0.0602446	−0.00276131
$477$	29.8618	1.36728
$478$	−5.15691	−0.235871
$479$	−32.4532	−1.48282	−0.741412	−	0.671050i	$-0.765843\pi$
$479$	−32.4532	−1.48282	−0.741412	+	0.671050i	$0.765843\pi$
$480$	−6.40363	−0.292284
$481$	0	0
$482$	−14.8768	−0.677619
$483$	−15.1220	−0.688074
$484$	20.0308	0.910493
$485$	−23.0599	−1.04710
$486$	−20.7460	−0.941056
$487$	35.0468	1.58812	0.794062	−	0.607837i	$-0.207962\pi$
$487$	35.0468	1.58812	0.794062	+	0.607837i	$0.207962\pi$
$488$	−8.84960	−0.400602
$489$	20.2234	0.914532
$490$	15.7087	0.709645
$491$	12.7690	0.576258	0.288129	−	0.957592i	$-0.406967\pi$
$491$	12.7690	0.576258	0.288129	+	0.957592i	$0.406967\pi$
$492$	26.1600	1.17938
$493$	0.772760	0.0348034
$494$	0	0
$495$	54.9121	2.46811
$496$	7.96336	0.357565
$497$	−2.04282	−0.0916331
$498$	−1.25417	−0.0562006
$499$	−15.9490	−0.713976	−0.356988	−	0.934109i	$-0.616196\pi$
$499$	−15.9490	−0.713976	−0.356988	+	0.934109i	$0.616196\pi$
$500$	10.1555	0.454166
$501$	−0.605499	−0.0270517
$502$	10.5977	0.472997
$503$	−8.86235	−0.395153	−0.197576	−	0.980288i	$-0.563307\pi$
$503$	−8.86235	−0.395153	−0.197576	+	0.980288i	$0.563307\pi$
$504$	−2.78966	−0.124261
$505$	13.1258	0.584089
$506$	−46.4835	−2.06644
$507$	0	0
$508$	13.3891	0.594046
$509$	−33.7230	−1.49475	−0.747373	−	0.664405i	$-0.768685\pi$
$509$	−33.7230	−1.49475	−0.747373	+	0.664405i	$0.768685\pi$
$510$	−0.567342	−0.0251223
$511$	−1.99032	−0.0880467
$512$	1.00000	0.0441942
$513$	2.93829	0.129729
$514$	−10.1532	−0.447837
$515$	46.2544	2.03821
$516$	22.1162	0.973613
$517$	34.0803	1.49885
$518$	−4.52977	−0.199027
$519$	−56.9002	−2.49764
$520$	0	0
$521$	14.7802	0.647534	0.323767	−	0.946137i	$-0.395051\pi$
$521$	14.7802	0.647534	0.323767	+	0.946137i	$0.395051\pi$
$522$	35.7831	1.56618
$523$	−34.6903	−1.51690	−0.758450	−	0.651732i	$-0.774043\pi$
$523$	−34.6903	−1.51690	−0.758450	+	0.651732i	$0.774043\pi$
$524$	4.40525	0.192444
$525$	−1.40175	−0.0611774
$526$	−22.9675	−1.00143
$527$	0.705528	0.0307333
$528$	−14.8458	−0.646080
$529$	46.6313	2.02745
$530$	−17.4898	−0.759709
$531$	−40.6562	−1.76433
$532$	−0.679986	−0.0294811
$533$	0	0
$534$	1.90465	0.0824224
$535$	12.2725	0.530585
$536$	6.42790	0.277643
$537$	2.42551	0.104669
$538$	13.9883	0.603080
$539$	36.4180	1.56864
$540$	−7.06016	−0.303821
$541$	0.623989	0.0268274	0.0134137	−	0.999910i	$-0.495730\pi$
$541$	0.623989	0.0268274	0.0134137	+	0.999910i	$0.495730\pi$
$542$	−30.6015	−1.31445
$543$	−1.03561	−0.0444424
$544$	0.0885969	0.00379856
$545$	−5.48876	−0.235113
$546$	0	0
$547$	28.7039	1.22729	0.613645	−	0.789582i	$-0.289703\pi$
$547$	28.7039	1.22729	0.613645	+	0.789582i	$0.289703\pi$
$548$	5.21300	0.222688
$549$	−36.3057	−1.54949
$550$	−4.30885	−0.183730
$551$	8.72221	0.371579
$552$	22.2387	0.946540
$553$	−2.21253	−0.0940863
$554$	0.657414	0.0279308
$555$	−42.6582	−1.81074
$556$	21.1936	0.898808
$557$	6.39907	0.271138	0.135569	−	0.990768i	$-0.456714\pi$
$557$	6.39907	0.271138	0.135569	+	0.990768i	$0.456714\pi$
$558$	32.6699	1.38303
$559$	0	0
$560$	1.63388	0.0690440
$561$	−1.31529	−0.0555316
$562$	−13.4279	−0.566422
$563$	−15.3346	−0.646278	−0.323139	−	0.946352i	$-0.604738\pi$
$563$	−15.3346	−0.646278	−0.323139	+	0.946352i	$0.604738\pi$
$564$	−16.3047	−0.686552
$565$	−31.3286	−1.31800
$566$	11.8274	0.497141
$567$	3.04421	0.127845
$568$	3.00421	0.126054
$569$	29.8071	1.24958	0.624790	−	0.780793i	$-0.285185\pi$
$569$	29.8071	1.24958	0.624790	+	0.780793i	$0.285185\pi$
$570$	−6.40363	−0.268219
$571$	3.39460	0.142060	0.0710299	−	0.997474i	$-0.477371\pi$
$571$	3.39460	0.142060	0.0710299	+	0.997474i	$0.477371\pi$
$572$	0	0
$573$	5.86070	0.244834
$574$	−6.67469	−0.278596
$575$	6.45456	0.269174
$576$	4.10252	0.170939
$577$	−5.13774	−0.213887	−0.106943	−	0.994265i	$-0.534106\pi$
$577$	−5.13774	−0.213887	−0.106943	+	0.994265i	$0.534106\pi$
$578$	−16.9922	−0.706780
$579$	−1.03807	−0.0431405
$580$	−20.9578	−0.870226
$581$	0.320000	0.0132758
$582$	25.5766	1.06019
$583$	−40.5473	−1.67930
$584$	2.92701	0.121120
$585$	0	0
$586$	−5.93975	−0.245369
$587$	−7.01511	−0.289544	−0.144772	−	0.989465i	$-0.546245\pi$
$587$	−7.01511	−0.289544	−0.144772	+	0.989465i	$0.546245\pi$
$588$	−17.4231	−0.718517
$589$	7.96336	0.328124
$590$	23.8119	0.980322
$591$	10.0312	0.412627
$592$	6.66156	0.273788
$593$	43.3220	1.77902	0.889511	−	0.456915i	$-0.151046\pi$
$593$	43.3220	1.77902	0.889511	+	0.456915i	$0.151046\pi$
$594$	−16.3678	−0.671581
$595$	0.144757	0.00593444
$596$	−10.1963	−0.417657
$597$	−16.6630	−0.681972
$598$	0	0
$599$	−10.4109	−0.425379	−0.212690	−	0.977120i	$-0.568222\pi$
$599$	−10.4109	−0.425379	−0.212690	+	0.977120i	$0.568222\pi$
$600$	2.06144	0.0841579
$601$	−6.89290	−0.281167	−0.140584	−	0.990069i	$-0.544898\pi$
$601$	−6.89290	−0.281167	−0.140584	+	0.990069i	$0.544898\pi$
$602$	−5.64293	−0.229989
$603$	26.3706	1.07390
$604$	17.7428	0.721946
$605$	−48.1304	−1.95678
$606$	−14.5583	−0.591391
$607$	39.3075	1.59544	0.797721	−	0.603027i	$-0.206039\pi$
$607$	39.3075	1.59544	0.797721	+	0.603027i	$0.206039\pi$
$608$	1.00000	0.0405554
$609$	−15.8064	−0.640507
$610$	21.2639	0.860951
$611$	0	0
$612$	0.363471	0.0146924
$613$	−42.9341	−1.73409	−0.867047	−	0.498227i	$-0.833985\pi$
$613$	−42.9341	−1.73409	−0.867047	+	0.498227i	$0.833985\pi$
$614$	−2.98476	−0.120455
$615$	−62.8575	−2.53466
$616$	3.78789	0.152618
$617$	−2.76170	−0.111182	−0.0555910	−	0.998454i	$-0.517704\pi$
$617$	−2.76170	−0.111182	−0.0555910	+	0.998454i	$0.517704\pi$
$618$	−51.3026	−2.06369
$619$	33.4749	1.34547	0.672734	−	0.739884i	$-0.265120\pi$
$619$	33.4749	1.34547	0.672734	+	0.739884i	$0.265120\pi$
$620$	−19.1344	−0.768458
$621$	24.5187	0.983900
$622$	16.9232	0.678557
$623$	−0.485970	−0.0194700
$624$	0	0
$625$	−28.2692	−1.13077
$626$	−6.38300	−0.255116
$627$	−14.8458	−0.592884
$628$	−18.7354	−0.747624
$629$	0.590193	0.0235325
$630$	6.70303	0.267055
$631$	15.8359	0.630419	0.315210	−	0.949022i	$-0.397925\pi$
$631$	15.8359	0.630419	0.315210	+	0.949022i	$0.397925\pi$
$632$	3.25379	0.129429
$633$	−11.5118	−0.457555
$634$	−5.05240	−0.200656
$635$	−32.1715	−1.27669
$636$	19.3987	0.769207
$637$	0	0
$638$	−48.5874	−1.92359
$639$	12.3249	0.487564
$640$	−2.40281	−0.0949795
$641$	−20.7495	−0.819555	−0.409778	−	0.912185i	$-0.634394\pi$
$641$	−20.7495	−0.819555	−0.409778	+	0.912185i	$0.634394\pi$
$642$	−13.6119	−0.537218
$643$	−16.4785	−0.649847	−0.324923	−	0.945740i	$-0.605339\pi$
$643$	−16.4785	−0.649847	−0.324923	+	0.945740i	$0.605339\pi$
$644$	−5.67417	−0.223594
$645$	−53.1412	−2.09243
$646$	0.0885969	0.00348580
$647$	6.47097	0.254400	0.127200	−	0.991877i	$-0.459401\pi$
$647$	6.47097	0.254400	0.127200	+	0.991877i	$0.459401\pi$
$648$	−4.47686	−0.175868
$649$	55.2042	2.16695
$650$	0	0
$651$	−14.4312	−0.565603
$652$	7.58834	0.297183
$653$	44.2117	1.73014	0.865069	−	0.501653i	$-0.167274\pi$
$653$	44.2117	1.73014	0.865069	+	0.501653i	$0.167274\pi$
$654$	6.08781	0.238052
$655$	−10.5850	−0.413590
$656$	9.81592	0.383247
$657$	12.0081	0.468481
$658$	4.16013	0.162179
$659$	15.2968	0.595879	0.297940	−	0.954585i	$-0.403701\pi$
$659$	15.2968	0.595879	0.297940	+	0.954585i	$0.403701\pi$
$660$	35.6716	1.38852
$661$	17.1940	0.668771	0.334385	−	0.942436i	$-0.391471\pi$
$661$	17.1940	0.668771	0.334385	+	0.942436i	$0.391471\pi$
$662$	12.1193	0.471032
$663$	0	0
$664$	−0.470597	−0.0182627
$665$	1.63388	0.0633591
$666$	27.3292	1.05899
$667$	72.7828	2.81816
$668$	−0.227199	−0.00879060
$669$	0.552980	0.0213794
$670$	−15.4450	−0.596694
$671$	49.2970	1.90309
$672$	−1.81220	−0.0699072
$673$	−49.9087	−1.92384	−0.961920	−	0.273330i	$-0.911875\pi$
$673$	−49.9087	−1.92384	−0.961920	+	0.273330i	$0.911875\pi$
$674$	−12.4390	−0.479134
$675$	2.27279	0.0874797
$676$	0	0
$677$	−1.25153	−0.0481004	−0.0240502	−	0.999711i	$-0.507656\pi$
$677$	−1.25153	−0.0481004	−0.0240502	+	0.999711i	$0.507656\pi$
$678$	34.7478	1.33448
$679$	−6.52585	−0.250439
$680$	−0.212882	−0.00816364
$681$	−34.0135	−1.30340
$682$	−44.3601	−1.69864
$683$	−39.9124	−1.52721	−0.763603	−	0.645686i	$-0.776572\pi$
$683$	−39.9124	−1.52721	−0.763603	+	0.645686i	$0.776572\pi$
$684$	4.10252	0.156864
$685$	−12.5259	−0.478589
$686$	9.20539	0.351464
$687$	−9.73041	−0.371238
$688$	8.29860	0.316381
$689$	0	0
$690$	−53.4353	−2.03425
$691$	−44.5289	−1.69396	−0.846980	−	0.531624i	$-0.821582\pi$
$691$	−44.5289	−1.69396	−0.846980	+	0.531624i	$0.821582\pi$
$692$	−21.3505	−0.811623
$693$	15.5399	0.590312
$694$	25.1516	0.954741
$695$	−50.9242	−1.93167
$696$	23.2452	0.881106
$697$	0.869660	0.0329407
$698$	−13.1872	−0.499143
$699$	−7.04804	−0.266581
$700$	−0.525974	−0.0198799
$701$	−27.3181	−1.03179	−0.515895	−	0.856652i	$-0.672541\pi$
$701$	−27.3181	−1.03179	−0.515895	+	0.856652i	$0.672541\pi$
$702$	0	0
$703$	6.66156	0.251245
$704$	−5.57053	−0.209947
$705$	39.1772	1.47550
$706$	−4.49299	−0.169096
$707$	3.71454	0.139700
$708$	−26.4108	−0.992578
$709$	−13.4562	−0.505357	−0.252678	−	0.967550i	$-0.581311\pi$
$709$	−13.4562	−0.505357	−0.252678	+	0.967550i	$0.581311\pi$
$710$	−7.21856	−0.270908
$711$	13.3487	0.500617
$712$	0.714677	0.0267836
$713$	66.4505	2.48859
$714$	−0.160555	−0.00600863
$715$	0	0
$716$	0.910117	0.0340127
$717$	−13.7435	−0.513259
$718$	−5.85214	−0.218400
$719$	−23.3855	−0.872131	−0.436065	−	0.899915i	$-0.643628\pi$
$719$	−23.3855	−0.872131	−0.436065	+	0.899915i	$0.643628\pi$
$720$	−9.85760	−0.367371
$721$	13.0898	0.487489
$722$	1.00000	0.0372161
$723$	−39.6474	−1.47450
$724$	−0.388590	−0.0144418
$725$	6.74669	0.250566
$726$	53.3833	1.98124
$727$	−0.483658	−0.0179379	−0.00896893	−	0.999960i	$-0.502855\pi$
$727$	−0.483658	−0.0179379	−0.00896893	+	0.999960i	$0.502855\pi$
$728$	0	0
$729$	−41.8586	−1.55032
$730$	−7.03305	−0.260305
$731$	0.735230	0.0271935
$732$	−23.5847	−0.871715
$733$	−8.40607	−0.310485	−0.155243	−	0.987876i	$-0.549616\pi$
$733$	−8.40607	−0.310485	−0.155243	+	0.987876i	$0.549616\pi$
$734$	18.2839	0.674871
$735$	41.8645	1.54420
$736$	8.34453	0.307584
$737$	−35.8068	−1.31896
$738$	40.2700	1.48236
$739$	31.9691	1.17600	0.588002	−	0.808860i	$-0.299915\pi$
$739$	31.9691	1.17600	0.588002	+	0.808860i	$0.299915\pi$
$740$	−16.0065	−0.588410
$741$	0	0
$742$	−4.94955	−0.181704
$743$	−35.4426	−1.30026	−0.650131	−	0.759822i	$-0.725286\pi$
$743$	−35.4426	−1.30026	−0.650131	+	0.759822i	$0.725286\pi$
$744$	21.2228	0.778065
$745$	24.4998	0.897604
$746$	8.26296	0.302529
$747$	−1.93064	−0.0706383
$748$	−0.493532	−0.0180453
$749$	3.47306	0.126903
$750$	27.0649	0.988270
$751$	−1.59277	−0.0581210	−0.0290605	−	0.999578i	$-0.509252\pi$
$751$	−1.59277	−0.0581210	−0.0290605	+	0.999578i	$0.509252\pi$
$752$	−6.11796	−0.223099
$753$	28.2434	1.02925
$754$	0	0
$755$	−42.6327	−1.55156
$756$	−1.99800	−0.0726665
$757$	39.8019	1.44662	0.723312	−	0.690521i	$-0.242619\pi$
$757$	39.8019	1.44662	0.723312	+	0.690521i	$0.242619\pi$
$758$	32.8351	1.19262
$759$	−123.881	−4.49660
$760$	−2.40281	−0.0871592
$761$	32.2976	1.17079	0.585393	−	0.810750i	$-0.300940\pi$
$761$	32.2976	1.17079	0.585393	+	0.810750i	$0.300940\pi$
$762$	35.6827	1.29265
$763$	−1.55330	−0.0562332
$764$	2.19909	0.0795604
$765$	−0.873352	−0.0315761
$766$	−23.6057	−0.852907
$767$	0	0
$768$	2.66506	0.0961669
$769$	−9.55042	−0.344397	−0.172199	−	0.985062i	$-0.555087\pi$
$769$	−9.55042	−0.344397	−0.172199	+	0.985062i	$0.555087\pi$
$770$	−9.10158	−0.327998
$771$	−27.0588	−0.974497
$772$	−0.389510	−0.0140188
$773$	−33.7951	−1.21553	−0.607763	−	0.794118i	$-0.707933\pi$
$773$	−33.7951	−1.21553	−0.607763	+	0.794118i	$0.707933\pi$
$774$	34.0452	1.22373
$775$	6.15971	0.221263
$776$	9.59704	0.344514
$777$	−12.0721	−0.433084
$778$	−31.6452	−1.13454
$779$	9.81592	0.351692
$780$	0	0
$781$	−16.7351	−0.598828
$782$	0.739300	0.0264373
$783$	25.6284	0.915884
$784$	−6.53762	−0.233486
$785$	45.0177	1.60675
$786$	11.7402	0.418760
$787$	−32.0475	−1.14237	−0.571185	−	0.820821i	$-0.693516\pi$
$787$	−32.0475	−1.14237	−0.571185	+	0.820821i	$0.693516\pi$
$788$	3.76396	0.134086
$789$	−61.2096	−2.17912
$790$	−7.81824	−0.278160
$791$	−8.86585	−0.315233
$792$	−22.8533	−0.812055
$793$	0	0
$794$	36.2239	1.28554
$795$	−46.6113	−1.65313
$796$	−6.25241	−0.221611
$797$	41.2919	1.46263	0.731316	−	0.682038i	$-0.238906\pi$
$797$	41.2919	1.46263	0.731316	+	0.682038i	$0.238906\pi$
$798$	−1.81220	−0.0641512
$799$	−0.542032	−0.0191757
$800$	0.773507	0.0273476
$801$	2.93198	0.103596
$802$	5.43819	0.192029
$803$	−16.3050	−0.575391
$804$	17.1307	0.604154
$805$	13.6340	0.480534
$806$	0	0
$807$	37.2797	1.31231
$808$	−5.46267	−0.192176
$809$	16.6954	0.586980	0.293490	−	0.955962i	$-0.405183\pi$
$809$	16.6954	0.586980	0.293490	+	0.955962i	$0.405183\pi$
$810$	10.7571	0.377965
$811$	9.29950	0.326550	0.163275	−	0.986581i	$-0.447794\pi$
$811$	9.29950	0.326550	0.163275	+	0.986581i	$0.447794\pi$
$812$	−5.93098	−0.208137
$813$	−81.5547	−2.86025
$814$	−37.1084	−1.30065
$815$	−18.2334	−0.638687
$816$	0.236116	0.00826570
$817$	8.29860	0.290331
$818$	31.6058	1.10507
$819$	0	0
$820$	−23.5858	−0.823652
$821$	−55.2281	−1.92747	−0.963737	−	0.266855i	$-0.914016\pi$
$821$	−55.2281	−1.92747	−0.963737	+	0.266855i	$0.914016\pi$
$822$	13.8929	0.484572
$823$	−7.53367	−0.262607	−0.131304	−	0.991342i	$-0.541916\pi$
$823$	−7.53367	−0.262607	−0.131304	+	0.991342i	$0.541916\pi$
$824$	−19.2501	−0.670609
$825$	−11.4833	−0.399798
$826$	6.73868	0.234469
$827$	7.95233	0.276529	0.138265	−	0.990395i	$-0.455848\pi$
$827$	7.95233	0.276529	0.138265	+	0.990395i	$0.455848\pi$
$828$	34.2337	1.18970
$829$	−10.7228	−0.372420	−0.186210	−	0.982510i	$-0.559620\pi$
$829$	−10.7228	−0.372420	−0.186210	+	0.982510i	$0.559620\pi$
$830$	1.13076	0.0392491
$831$	1.75204	0.0607778
$832$	0	0
$833$	−0.579213	−0.0200685
$834$	56.4821	1.95582
$835$	0.545917	0.0188922
$836$	−5.57053	−0.192661
$837$	23.3987	0.808776
$838$	−33.1838	−1.14631
$839$	−0.835664	−0.0288503	−0.0144252	−	0.999896i	$-0.504592\pi$
$839$	−0.835664	−0.0288503	−0.0144252	+	0.999896i	$0.504592\pi$
$840$	4.35438	0.150240
$841$	47.0769	1.62334
$842$	20.2497	0.697849
$843$	−35.7861	−1.23254
$844$	−4.31955	−0.148685
$845$	0	0
$846$	−25.0991	−0.862924
$847$	−13.6207	−0.468013
$848$	7.27889	0.249958
$849$	31.5206	1.08178
$850$	0.0685303	0.00235057
$851$	55.5876	1.90552
$852$	8.00640	0.274295
$853$	−4.76950	−0.163305	−0.0816524	−	0.996661i	$-0.526020\pi$
$853$	−4.76950	−0.163305	−0.0816524	+	0.996661i	$0.526020\pi$
$854$	6.01760	0.205918
$855$	−9.85760	−0.337123
$856$	−5.10754	−0.174572
$857$	−21.2873	−0.727160	−0.363580	−	0.931563i	$-0.618446\pi$
$857$	−21.2873	−0.727160	−0.363580	+	0.931563i	$0.618446\pi$
$858$	0	0
$859$	−6.69797	−0.228532	−0.114266	−	0.993450i	$-0.536452\pi$
$859$	−6.69797	−0.228532	−0.114266	+	0.993450i	$0.536452\pi$
$860$	−19.9400	−0.679948
$861$	−17.7884	−0.606228
$862$	17.2707	0.588243
$863$	−44.2369	−1.50584	−0.752921	−	0.658111i	$-0.771356\pi$
$863$	−44.2369	−1.50584	−0.752921	+	0.658111i	$0.771356\pi$
$864$	2.93829	0.0999627
$865$	51.3012	1.74429
$866$	28.0742	0.953999
$867$	−45.2850	−1.53796
$868$	−5.41497	−0.183796
$869$	−18.1253	−0.614859
$870$	−55.8538	−1.89362
$871$	0	0
$872$	2.28431	0.0773564
$873$	39.3721	1.33254
$874$	8.34453	0.282258
$875$	−6.90558	−0.233451
$876$	7.80064	0.263559
$877$	14.8748	0.502285	0.251142	−	0.967950i	$-0.419194\pi$
$877$	14.8748	0.502285	0.251142	+	0.967950i	$0.419194\pi$
$878$	7.87177	0.265659
$879$	−15.8298	−0.533925
$880$	13.3849	0.451206
$881$	43.3235	1.45960	0.729802	−	0.683658i	$-0.239612\pi$
$881$	43.3235	1.45960	0.729802	+	0.683658i	$0.239612\pi$
$882$	−26.8207	−0.903101
$883$	38.5557	1.29750	0.648752	−	0.761000i	$-0.275291\pi$
$883$	38.5557	1.29750	0.648752	+	0.761000i	$0.275291\pi$
$884$	0	0
$885$	63.4602	2.13319
$886$	−28.3139	−0.951224
$887$	2.97826	0.100000	0.0500001	−	0.998749i	$-0.484078\pi$
$887$	2.97826	0.100000	0.0500001	+	0.998749i	$0.484078\pi$
$888$	17.7534	0.595766
$889$	−9.10441	−0.305352
$890$	−1.71723	−0.0575618
$891$	24.9385	0.835472
$892$	0.207493	0.00694737
$893$	−6.11796	−0.204730
$894$	−27.1737	−0.908826
$895$	−2.18684	−0.0730980
$896$	−0.679986	−0.0227167
$897$	0	0
$898$	20.1897	0.673737
$899$	69.4580	2.31656
$900$	3.17333	0.105778
$901$	0.644887	0.0214843
$902$	−54.6799	−1.82064
$903$	−15.0387	−0.500458
$904$	13.0383	0.433647
$905$	0.933709	0.0310375
$906$	47.2857	1.57096
$907$	−15.5016	−0.514721	−0.257361	−	0.966315i	$-0.582853\pi$
$907$	−15.5016	−0.514721	−0.257361	+	0.966315i	$0.582853\pi$
$908$	−12.7628	−0.423548
$909$	−22.4107	−0.743317
$910$	0	0
$911$	13.6311	0.451620	0.225810	−	0.974171i	$-0.427497\pi$
$911$	13.6311	0.451620	0.225810	+	0.974171i	$0.427497\pi$
$912$	2.66506	0.0882488
$913$	2.62148	0.0867582
$914$	−5.05880	−0.167330
$915$	56.6695	1.87344
$916$	−3.65111	−0.120636
$917$	−2.99551	−0.0989204
$918$	0.260323	0.00859195
$919$	15.5639	0.513406	0.256703	−	0.966490i	$-0.417364\pi$
$919$	15.5639	0.513406	0.256703	+	0.966490i	$0.417364\pi$
$920$	−20.0504	−0.661040
$921$	−7.95455	−0.262111
$922$	−19.5003	−0.642207
$923$	0	0
$924$	10.0949	0.332099
$925$	5.15276	0.169422
$926$	20.3598	0.669065
$927$	−78.9740	−2.59385
$928$	8.72221	0.286320
$929$	24.3345	0.798389	0.399195	−	0.916866i	$-0.369290\pi$
$929$	24.3345	0.798389	0.399195	+	0.916866i	$0.369290\pi$
$930$	−50.9944	−1.67217
$931$	−6.53762	−0.214262
$932$	−2.64461	−0.0866271
$933$	45.1012	1.47655
$934$	−7.75858	−0.253869
$935$	1.18586	0.0387819
$936$	0	0
$937$	−37.6879	−1.23121	−0.615605	−	0.788055i	$-0.711088\pi$
$937$	−37.6879	−1.23121	−0.615605	+	0.788055i	$0.711088\pi$
$938$	−4.37088	−0.142714
$939$	−17.0110	−0.555135
$940$	14.7003	0.479471
$941$	−3.05942	−0.0997341	−0.0498671	−	0.998756i	$-0.515880\pi$
$941$	−3.05942	−0.0997341	−0.0498671	+	0.998756i	$0.515880\pi$
$942$	−49.9309	−1.62684
$943$	81.9093	2.66733
$944$	−9.91003	−0.322544
$945$	4.80081	0.156170
$946$	−46.2276	−1.50299
$947$	41.3564	1.34390	0.671951	−	0.740595i	$-0.265456\pi$
$947$	41.3564	1.34390	0.671951	+	0.740595i	$0.265456\pi$
$948$	8.67152	0.281638
$949$	0	0
$950$	0.773507	0.0250959
$951$	−13.4649	−0.436630
$952$	−0.0602446	−0.00195254
$953$	−5.58101	−0.180787	−0.0903933	−	0.995906i	$-0.528812\pi$
$953$	−5.58101	−0.180787	−0.0903933	+	0.995906i	$0.528812\pi$
$954$	29.8618	0.966813
$955$	−5.28401	−0.170986
$956$	−5.15691	−0.166786
$957$	−129.488	−4.18575
$958$	−32.4532	−1.04851
$959$	−3.54477	−0.114467
$960$	−6.40363	−0.206676
$961$	32.4150	1.04565
$962$	0	0
$963$	−20.9538	−0.675227
$964$	−14.8768	−0.479149
$965$	0.935919	0.0301283
$966$	−15.1220	−0.486542
$967$	−40.2775	−1.29524	−0.647619	−	0.761964i	$-0.724235\pi$
$967$	−40.2775	−1.29524	−0.647619	+	0.761964i	$0.724235\pi$
$968$	20.0308	0.643816
$969$	0.236116	0.00758513
$970$	−23.0599	−0.740408
$971$	−54.0643	−1.73501	−0.867504	−	0.497431i	$-0.834277\pi$
$971$	−54.0643	−1.73501	−0.867504	+	0.497431i	$0.834277\pi$
$972$	−20.7460	−0.665427
$973$	−14.4113	−0.462007
$974$	35.0468	1.12297
$975$	0	0
$976$	−8.84960	−0.283269
$977$	−17.4505	−0.558292	−0.279146	−	0.960249i	$-0.590051\pi$
$977$	−17.4505	−0.558292	−0.279146	+	0.960249i	$0.590051\pi$
$978$	20.2234	0.646672
$979$	−3.98113	−0.127237
$980$	15.7087	0.501795
$981$	9.37143	0.299207
$982$	12.7690	0.407476
$983$	−27.8691	−0.888885	−0.444442	−	0.895807i	$-0.646598\pi$
$983$	−27.8691	−0.888885	−0.444442	+	0.895807i	$0.646598\pi$
$984$	26.1600	0.833949
$985$	−9.04410	−0.288169
$986$	0.772760	0.0246097
$987$	11.0870	0.352902
$988$	0	0
$989$	69.2480	2.20196
$990$	54.9121	1.74522
$991$	−15.4784	−0.491687	−0.245844	−	0.969309i	$-0.579065\pi$
$991$	−15.4784	−0.491687	−0.245844	+	0.969309i	$0.579065\pi$
$992$	7.96336	0.252837
$993$	32.2987	1.02497
$994$	−2.04282	−0.0647944
$995$	15.0234	0.476273
$996$	−1.25417	−0.0397398
$997$	26.0136	0.823859	0.411929	−	0.911216i	$-0.364855\pi$
$997$	26.0136	0.823859	0.411929	+	0.911216i	$0.364855\pi$
$998$	−15.9490	−0.504857
$999$	19.5736	0.619281

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6422.2.a.bn.1.12		14
13.2	odd	12		494.2.m.b.381.9	yes	28
13.7	odd	12		494.2.m.b.153.9	✓	28
13.12	even	2		6422.2.a.bm.1.12		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
494.2.m.b.153.9	✓	28	13.7	odd	12
494.2.m.b.381.9	yes	28	13.2	odd	12
6422.2.a.bm.1.12		14	13.12	even	2
6422.2.a.bn.1.12		14	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6422 = 2 \cdot 13^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6422.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.66506 q^{3} +1.00000 q^{4} -2.40281 q^{5} +2.66506 q^{6} -0.679986 q^{7} +1.00000 q^{8} +4.10252 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.66506 q^{3} +1.00000 q^{4} -2.40281 q^{5} +2.66506 q^{6} -0.679986 q^{7} +1.00000 q^{8} +4.10252 q^{9} -2.40281 q^{10} -5.57053 q^{11} +2.66506 q^{12} -0.679986 q^{14} -6.40363 q^{15} +1.00000 q^{16} +0.0885969 q^{17} +4.10252 q^{18} +1.00000 q^{19} -2.40281 q^{20} -1.81220 q^{21} -5.57053 q^{22} +8.34453 q^{23} +2.66506 q^{24} +0.773507 q^{25} +2.93829 q^{27} -0.679986 q^{28} +8.72221 q^{29} -6.40363 q^{30} +7.96336 q^{31} +1.00000 q^{32} -14.8458 q^{33} +0.0885969 q^{34} +1.63388 q^{35} +4.10252 q^{36} +6.66156 q^{37} +1.00000 q^{38} -2.40281 q^{40} +9.81592 q^{41} -1.81220 q^{42} +8.29860 q^{43} -5.57053 q^{44} -9.85760 q^{45} +8.34453 q^{46} -6.11796 q^{47} +2.66506 q^{48} -6.53762 q^{49} +0.773507 q^{50} +0.236116 q^{51} +7.27889 q^{53} +2.93829 q^{54} +13.3849 q^{55} -0.679986 q^{56} +2.66506 q^{57} +8.72221 q^{58} -9.91003 q^{59} -6.40363 q^{60} -8.84960 q^{61} +7.96336 q^{62} -2.78966 q^{63} +1.00000 q^{64} -14.8458 q^{66} +6.42790 q^{67} +0.0885969 q^{68} +22.2387 q^{69} +1.63388 q^{70} +3.00421 q^{71} +4.10252 q^{72} +2.92701 q^{73} +6.66156 q^{74} +2.06144 q^{75} +1.00000 q^{76} +3.78789 q^{77} +3.25379 q^{79} -2.40281 q^{80} -4.47686 q^{81} +9.81592 q^{82} -0.470597 q^{83} -1.81220 q^{84} -0.212882 q^{85} +8.29860 q^{86} +23.2452 q^{87} -5.57053 q^{88} +0.714677 q^{89} -9.85760 q^{90} +8.34453 q^{92} +21.2228 q^{93} -6.11796 q^{94} -2.40281 q^{95} +2.66506 q^{96} +9.59704 q^{97} -6.53762 q^{98} -22.8533 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 14 q^{2} + 4 q^{3} + 14 q^{4} - 2 q^{5} + 4 q^{6} + 2 q^{7} + 14 q^{8} + 18 q^{9}+O(q^{10}) \) 14 * q + 14 * q^2 + 4 * q^3 + 14 * q^4 - 2 * q^5 + 4 * q^6 + 2 * q^7 + 14 * q^8 + 18 * q^9	\( 14 q + 14 q^{2} + 4 q^{3} + 14 q^{4} - 2 q^{5} + 4 q^{6} + 2 q^{7} + 14 q^{8} + 18 q^{9} - 2 q^{10} + 10 q^{11} + 4 q^{12} + 2 q^{14} - 4 q^{15} + 14 q^{16} + 2 q^{17} + 18 q^{18} + 14 q^{19} - 2 q^{20} - 18 q^{21} + 10 q^{22} + 12 q^{23} + 4 q^{24} + 44 q^{25} + 10 q^{27} + 2 q^{28} + 4 q^{29} - 4 q^{30} + 4 q^{31} + 14 q^{32} + 12 q^{33} + 2 q^{34} + 14 q^{35} + 18 q^{36} + 18 q^{37} + 14 q^{38} - 2 q^{40} + 6 q^{41} - 18 q^{42} + 28 q^{43} + 10 q^{44} + 8 q^{45} + 12 q^{46} - 20 q^{47} + 4 q^{48} + 28 q^{49} + 44 q^{50} + 10 q^{51} + 12 q^{53} + 10 q^{54} - 2 q^{55} + 2 q^{56} + 4 q^{57} + 4 q^{58} + 16 q^{59} - 4 q^{60} + 30 q^{61} + 4 q^{62} + 28 q^{63} + 14 q^{64} + 12 q^{66} + 2 q^{67} + 2 q^{68} - 42 q^{69} + 14 q^{70} + 44 q^{71} + 18 q^{72} - 36 q^{73} + 18 q^{74} + 46 q^{75} + 14 q^{76} + 68 q^{77} + 34 q^{79} - 2 q^{80} - 6 q^{81} + 6 q^{82} + 2 q^{83} - 18 q^{84} - 30 q^{85} + 28 q^{86} + 52 q^{87} + 10 q^{88} + 42 q^{89} + 8 q^{90} + 12 q^{92} - 12 q^{93} - 20 q^{94} - 2 q^{95} + 4 q^{96} + 40 q^{97} + 28 q^{98} + 12 q^{99}+O(q^{100}) \) 14 * q + 14 * q^2 + 4 * q^3 + 14 * q^4 - 2 * q^5 + 4 * q^6 + 2 * q^7 + 14 * q^8 + 18 * q^9 - 2 * q^10 + 10 * q^11 + 4 * q^12 + 2 * q^14 - 4 * q^15 + 14 * q^16 + 2 * q^17 + 18 * q^18 + 14 * q^19 - 2 * q^20 - 18 * q^21 + 10 * q^22 + 12 * q^23 + 4 * q^24 + 44 * q^25 + 10 * q^27 + 2 * q^28 + 4 * q^29 - 4 * q^30 + 4 * q^31 + 14 * q^32 + 12 * q^33 + 2 * q^34 + 14 * q^35 + 18 * q^36 + 18 * q^37 + 14 * q^38 - 2 * q^40 + 6 * q^41 - 18 * q^42 + 28 * q^43 + 10 * q^44 + 8 * q^45 + 12 * q^46 - 20 * q^47 + 4 * q^48 + 28 * q^49 + 44 * q^50 + 10 * q^51 + 12 * q^53 + 10 * q^54 - 2 * q^55 + 2 * q^56 + 4 * q^57 + 4 * q^58 + 16 * q^59 - 4 * q^60 + 30 * q^61 + 4 * q^62 + 28 * q^63 + 14 * q^64 + 12 * q^66 + 2 * q^67 + 2 * q^68 - 42 * q^69 + 14 * q^70 + 44 * q^71 + 18 * q^72 - 36 * q^73 + 18 * q^74 + 46 * q^75 + 14 * q^76 + 68 * q^77 + 34 * q^79 - 2 * q^80 - 6 * q^81 + 6 * q^82 + 2 * q^83 - 18 * q^84 - 30 * q^85 + 28 * q^86 + 52 * q^87 + 10 * q^88 + 42 * q^89 + 8 * q^90 + 12 * q^92 - 12 * q^93 - 20 * q^94 - 2 * q^95 + 4 * q^96 + 40 * q^97 + 28 * q^98 + 12 * q^99

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