LMFDB - Embedded newform 2667.2.a.j.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2667,2,Mod(1,2667)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2667, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2667.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2667 = 3 \cdot 7 \cdot 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2667.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:	$21.2961022191$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	7.7.118870813.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 9x^{5} - 3x^{4} + 20x^{3} + 7x^{2} - 13x - 4 $ x^7 - 9x^5 - 3x^4 + 20x^3 + 7x^2 - 13*x - 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.20244$ of defining polynomial
Character	$\chi$	$=$	2667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.24280 q^{2} +1.00000 q^{3} -0.455452 q^{4} -3.33400 q^{5} -1.24280 q^{6} +1.00000 q^{7} +3.05163 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.24280 q^{2} +1.00000 q^{3} -0.455452 q^{4} -3.33400 q^{5} -1.24280 q^{6} +1.00000 q^{7} +3.05163 q^{8} +1.00000 q^{9} +4.14349 q^{10} +2.90717 q^{11} -0.455452 q^{12} -4.59254 q^{13} -1.24280 q^{14} -3.33400 q^{15} -2.88166 q^{16} -5.29249 q^{17} -1.24280 q^{18} +1.86822 q^{19} +1.51848 q^{20} +1.00000 q^{21} -3.61302 q^{22} +5.03184 q^{23} +3.05163 q^{24} +6.11557 q^{25} +5.70761 q^{26} +1.00000 q^{27} -0.455452 q^{28} +3.69938 q^{29} +4.14349 q^{30} +0.968597 q^{31} -2.52194 q^{32} +2.90717 q^{33} +6.57750 q^{34} -3.33400 q^{35} -0.455452 q^{36} -10.5381 q^{37} -2.32183 q^{38} -4.59254 q^{39} -10.1741 q^{40} +11.5606 q^{41} -1.24280 q^{42} +2.54868 q^{43} -1.32408 q^{44} -3.33400 q^{45} -6.25356 q^{46} +7.34702 q^{47} -2.88166 q^{48} +1.00000 q^{49} -7.60043 q^{50} -5.29249 q^{51} +2.09168 q^{52} -11.2837 q^{53} -1.24280 q^{54} -9.69250 q^{55} +3.05163 q^{56} +1.86822 q^{57} -4.59758 q^{58} -13.3410 q^{59} +1.51848 q^{60} +0.666722 q^{61} -1.20377 q^{62} +1.00000 q^{63} +8.89758 q^{64} +15.3116 q^{65} -3.61302 q^{66} -14.0335 q^{67} +2.41048 q^{68} +5.03184 q^{69} +4.14349 q^{70} +9.88541 q^{71} +3.05163 q^{72} -2.57222 q^{73} +13.0968 q^{74} +6.11557 q^{75} -0.850887 q^{76} +2.90717 q^{77} +5.70761 q^{78} +14.5706 q^{79} +9.60746 q^{80} +1.00000 q^{81} -14.3675 q^{82} +0.493442 q^{83} -0.455452 q^{84} +17.6452 q^{85} -3.16749 q^{86} +3.69938 q^{87} +8.87160 q^{88} +12.1652 q^{89} +4.14349 q^{90} -4.59254 q^{91} -2.29176 q^{92} +0.968597 q^{93} -9.13087 q^{94} -6.22866 q^{95} -2.52194 q^{96} -14.7006 q^{97} -1.24280 q^{98} +2.90717 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 2 q^{2} + 7 q^{3} + 4 q^{4} - 8 q^{5} - 2 q^{6} + 7 q^{7} - 9 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - 2 * q^2 + 7 * q^3 + 4 * q^4 - 8 * q^5 - 2 * q^6 + 7 * q^7 - 9 * q^8 + 7 * q^9	\( 7 q - 2 q^{2} + 7 q^{3} + 4 q^{4} - 8 q^{5} - 2 q^{6} + 7 q^{7} - 9 q^{8} + 7 q^{9} - 3 q^{11} + 4 q^{12} - 23 q^{13} - 2 q^{14} - 8 q^{15} + 2 q^{16} + 3 q^{17} - 2 q^{18} - 9 q^{19} - 9 q^{20} + 7 q^{21} - 19 q^{22} + 12 q^{23} - 9 q^{24} + 3 q^{25} + 18 q^{26} + 7 q^{27} + 4 q^{28} - 9 q^{29} - 33 q^{31} + 10 q^{32} - 3 q^{33} - 2 q^{34} - 8 q^{35} + 4 q^{36} - 33 q^{37} - 3 q^{38} - 23 q^{39} - 9 q^{40} - 3 q^{41} - 2 q^{42} - 9 q^{43} + 2 q^{44} - 8 q^{45} - 32 q^{46} + 11 q^{47} + 2 q^{48} + 7 q^{49} + 29 q^{50} + 3 q^{51} - 21 q^{52} + q^{53} - 2 q^{54} - 16 q^{55} - 9 q^{56} - 9 q^{57} - 5 q^{58} - 30 q^{59} - 9 q^{60} - 19 q^{61} + 3 q^{62} + 7 q^{63} - 21 q^{64} + 14 q^{65} - 19 q^{66} - 30 q^{67} + 24 q^{68} + 12 q^{69} + 8 q^{71} - 9 q^{72} - 20 q^{73} - 9 q^{74} + 3 q^{75} - 42 q^{76} - 3 q^{77} + 18 q^{78} + 8 q^{79} + 12 q^{80} + 7 q^{81} + 10 q^{82} - 34 q^{83} + 4 q^{84} - 28 q^{85} + 24 q^{86} - 9 q^{87} - q^{88} - 12 q^{89} - 23 q^{91} + 60 q^{92} - 33 q^{93} - 3 q^{94} + 12 q^{95} + 10 q^{96} + 7 q^{97} - 2 q^{98} - 3 q^{99}+O(q^{100}) \) 7 * q - 2 * q^2 + 7 * q^3 + 4 * q^4 - 8 * q^5 - 2 * q^6 + 7 * q^7 - 9 * q^8 + 7 * q^9 - 3 * q^11 + 4 * q^12 - 23 * q^13 - 2 * q^14 - 8 * q^15 + 2 * q^16 + 3 * q^17 - 2 * q^18 - 9 * q^19 - 9 * q^20 + 7 * q^21 - 19 * q^22 + 12 * q^23 - 9 * q^24 + 3 * q^25 + 18 * q^26 + 7 * q^27 + 4 * q^28 - 9 * q^29 - 33 * q^31 + 10 * q^32 - 3 * q^33 - 2 * q^34 - 8 * q^35 + 4 * q^36 - 33 * q^37 - 3 * q^38 - 23 * q^39 - 9 * q^40 - 3 * q^41 - 2 * q^42 - 9 * q^43 + 2 * q^44 - 8 * q^45 - 32 * q^46 + 11 * q^47 + 2 * q^48 + 7 * q^49 + 29 * q^50 + 3 * q^51 - 21 * q^52 + q^53 - 2 * q^54 - 16 * q^55 - 9 * q^56 - 9 * q^57 - 5 * q^58 - 30 * q^59 - 9 * q^60 - 19 * q^61 + 3 * q^62 + 7 * q^63 - 21 * q^64 + 14 * q^65 - 19 * q^66 - 30 * q^67 + 24 * q^68 + 12 * q^69 + 8 * q^71 - 9 * q^72 - 20 * q^73 - 9 * q^74 + 3 * q^75 - 42 * q^76 - 3 * q^77 + 18 * q^78 + 8 * q^79 + 12 * q^80 + 7 * q^81 + 10 * q^82 - 34 * q^83 + 4 * q^84 - 28 * q^85 + 24 * q^86 - 9 * q^87 - q^88 - 12 * q^89 - 23 * q^91 + 60 * q^92 - 33 * q^93 - 3 * q^94 + 12 * q^95 + 10 * q^96 + 7 * q^97 - 2 * q^98 - 3 * 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 $

$2$	−1.24280	−0.878791	−0.439396	−	0.898294i	$-0.644807\pi$
$2$	−1.24280	−0.878791	−0.439396	+	0.898294i	$0.644807\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.455452	−0.227726
$5$	−3.33400	−1.49101	−0.745506	−	0.666499i	$-0.767792\pi$
$5$	−3.33400	−1.49101	−0.745506	+	0.666499i	$0.767792\pi$
$6$	−1.24280	−0.507370
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	3.05163	1.07891
$9$	1.00000	0.333333
$10$	4.14349	1.31029
$11$	2.90717	0.876544	0.438272	−	0.898842i	$-0.355591\pi$
$11$	2.90717	0.876544	0.438272	+	0.898842i	$0.355591\pi$
$12$	−0.455452	−0.131478
$13$	−4.59254	−1.27374	−0.636871	−	0.770970i	$-0.719772\pi$
$13$	−4.59254	−1.27374	−0.636871	+	0.770970i	$0.719772\pi$
$14$	−1.24280	−0.332152
$15$	−3.33400	−0.860836
$16$	−2.88166	−0.720415
$17$	−5.29249	−1.28362	−0.641809	−	0.766865i	$-0.721816\pi$
$17$	−5.29249	−1.28362	−0.641809	+	0.766865i	$0.721816\pi$
$18$	−1.24280	−0.292930
$19$	1.86822	0.428600	0.214300	−	0.976768i	$-0.431253\pi$
$19$	1.86822	0.428600	0.214300	+	0.976768i	$0.431253\pi$
$20$	1.51848	0.339542
$21$	1.00000	0.218218
$22$	−3.61302	−0.770299
$23$	5.03184	1.04921	0.524606	−	0.851345i	$-0.324213\pi$
$23$	5.03184	1.04921	0.524606	+	0.851345i	$0.324213\pi$
$24$	3.05163	0.622912
$25$	6.11557	1.22311
$26$	5.70761	1.11935
$27$	1.00000	0.192450
$28$	−0.455452	−0.0860724
$29$	3.69938	0.686957	0.343478	−	0.939161i	$-0.388395\pi$
$29$	3.69938	0.686957	0.343478	+	0.939161i	$0.388395\pi$
$30$	4.14349	0.756495
$31$	0.968597	0.173965	0.0869826	−	0.996210i	$-0.472278\pi$
$31$	0.968597	0.173965	0.0869826	+	0.996210i	$0.472278\pi$
$32$	−2.52194	−0.445821
$33$	2.90717	0.506073
$34$	6.57750	1.12803
$35$	−3.33400	−0.563549
$36$	−0.455452	−0.0759087
$37$	−10.5381	−1.73246	−0.866230	−	0.499645i	$-0.833464\pi$
$37$	−10.5381	−1.73246	−0.866230	+	0.499645i	$0.833464\pi$
$38$	−2.32183	−0.376650
$39$	−4.59254	−0.735395
$40$	−10.1741	−1.60867
$41$	11.5606	1.80546	0.902731	−	0.430205i	$-0.141559\pi$
$41$	11.5606	1.80546	0.902731	+	0.430205i	$0.141559\pi$
$42$	−1.24280	−0.191768
$43$	2.54868	0.388670	0.194335	−	0.980935i	$-0.437745\pi$
$43$	2.54868	0.388670	0.194335	+	0.980935i	$0.437745\pi$
$44$	−1.32408	−0.199612
$45$	−3.33400	−0.497004
$46$	−6.25356	−0.922038
$47$	7.34702	1.07167	0.535837	−	0.844322i	$-0.319996\pi$
$47$	7.34702	1.07167	0.535837	+	0.844322i	$0.319996\pi$
$48$	−2.88166	−0.415932
$49$	1.00000	0.142857
$50$	−7.60043	−1.07486
$51$	−5.29249	−0.741097
$52$	2.09168	0.290064
$53$	−11.2837	−1.54993	−0.774966	−	0.632003i	$-0.782233\pi$
$53$	−11.2837	−1.54993	−0.774966	+	0.632003i	$0.782233\pi$
$54$	−1.24280	−0.169123
$55$	−9.69250	−1.30694
$56$	3.05163	0.407791
$57$	1.86822	0.247452
$58$	−4.59758	−0.603691
$59$	−13.3410	−1.73685	−0.868425	−	0.495820i	$-0.834868\pi$
$59$	−13.3410	−1.73685	−0.868425	+	0.495820i	$0.834868\pi$
$60$	1.51848	0.196035
$61$	0.666722	0.0853651	0.0426825	−	0.999089i	$-0.486410\pi$
$61$	0.666722	0.0853651	0.0426825	+	0.999089i	$0.486410\pi$
$62$	−1.20377	−0.152879
$63$	1.00000	0.125988
$64$	8.89758	1.11220
$65$	15.3116	1.89916
$66$	−3.61302	−0.444732
$67$	−14.0335	−1.71447	−0.857233	−	0.514929i	$-0.827818\pi$
$67$	−14.0335	−1.71447	−0.857233	+	0.514929i	$0.827818\pi$
$68$	2.41048	0.292313
$69$	5.03184	0.605763
$70$	4.14349	0.495242
$71$	9.88541	1.17318	0.586591	−	0.809883i	$-0.300470\pi$
$71$	9.88541	1.17318	0.586591	+	0.809883i	$0.300470\pi$
$72$	3.05163	0.359638
$73$	−2.57222	−0.301056	−0.150528	−	0.988606i	$-0.548097\pi$
$73$	−2.57222	−0.301056	−0.150528	+	0.988606i	$0.548097\pi$
$74$	13.0968	1.52247
$75$	6.11557	0.706166
$76$	−0.850887	−0.0976034
$77$	2.90717	0.331302
$78$	5.70761	0.646259
$79$	14.5706	1.63932	0.819661	−	0.572849i	$-0.194162\pi$
$79$	14.5706	1.63932	0.819661	+	0.572849i	$0.194162\pi$
$80$	9.60746	1.07415
$81$	1.00000	0.111111
$82$	−14.3675	−1.58662
$83$	0.493442	0.0541623	0.0270811	−	0.999633i	$-0.491379\pi$
$83$	0.493442	0.0541623	0.0270811	+	0.999633i	$0.491379\pi$
$84$	−0.455452	−0.0496939
$85$	17.6452	1.91389
$86$	−3.16749	−0.341560
$87$	3.69938	0.396615
$88$	8.87160	0.945716
$89$	12.1652	1.28951	0.644754	−	0.764390i	$-0.276960\pi$
$89$	12.1652	1.28951	0.644754	+	0.764390i	$0.276960\pi$
$90$	4.14349	0.436763
$91$	−4.59254	−0.481429
$92$	−2.29176	−0.238933
$93$	0.968597	0.100439
$94$	−9.13087	−0.941777
$95$	−6.22866	−0.639047
$96$	−2.52194	−0.257395
$97$	−14.7006	−1.49262	−0.746312	−	0.665596i	$-0.768177\pi$
$97$	−14.7006	−1.49262	−0.746312	+	0.665596i	$0.768177\pi$
$98$	−1.24280	−0.125542
$99$	2.90717	0.292181
$100$	−2.78535	−0.278535
$101$	−7.69701	−0.765881	−0.382941	−	0.923773i	$-0.625089\pi$
$101$	−7.69701	−0.765881	−0.382941	+	0.923773i	$0.625089\pi$
$102$	6.57750	0.651269
$103$	−18.0952	−1.78297	−0.891486	−	0.453048i	$-0.850337\pi$
$103$	−18.0952	−1.78297	−0.891486	+	0.453048i	$0.850337\pi$
$104$	−14.0148	−1.37426
$105$	−3.33400	−0.325365
$106$	14.0233	1.36207
$107$	−2.30658	−0.222986	−0.111493	−	0.993765i	$-0.535563\pi$
$107$	−2.30658	−0.222986	−0.111493	+	0.993765i	$0.535563\pi$
$108$	−0.455452	−0.0438259
$109$	−0.892079	−0.0854457	−0.0427228	−	0.999087i	$-0.513603\pi$
$109$	−0.892079	−0.0854457	−0.0427228	+	0.999087i	$0.513603\pi$
$110$	12.0458	1.14852
$111$	−10.5381	−1.00024
$112$	−2.88166	−0.272291
$113$	4.35699	0.409872	0.204936	−	0.978775i	$-0.434301\pi$
$113$	4.35699	0.409872	0.204936	+	0.978775i	$0.434301\pi$
$114$	−2.32183	−0.217459
$115$	−16.7762	−1.56439
$116$	−1.68489	−0.156438
$117$	−4.59254	−0.424581
$118$	16.5802	1.52633
$119$	−5.29249	−0.485162
$120$	−10.1741	−0.928769
$121$	−2.54838	−0.231671
$122$	−0.828601	−0.0750181
$123$	11.5606	1.04238
$124$	−0.441150	−0.0396164
$125$	−3.71933	−0.332667
$126$	−1.24280	−0.110717
$127$	−1.00000	−0.0887357
$127$	−1.00000	−0.0887357
$128$	−6.01402	−0.531569
$129$	2.54868	0.224399
$130$	−19.0292	−1.66897
$131$	8.71812	0.761706	0.380853	−	0.924636i	$-0.375630\pi$
$131$	8.71812	0.761706	0.380853	+	0.924636i	$0.375630\pi$
$132$	−1.32408	−0.115246
$133$	1.86822	0.161996
$134$	17.4408	1.50666
$135$	−3.33400	−0.286945
$136$	−16.1507	−1.38491
$137$	−4.66285	−0.398374	−0.199187	−	0.979962i	$-0.563830\pi$
$137$	−4.66285	−0.398374	−0.199187	+	0.979962i	$0.563830\pi$
$138$	−6.25356	−0.532339
$139$	−19.7441	−1.67467	−0.837334	−	0.546691i	$-0.815887\pi$
$139$	−19.7441	−1.67467	−0.837334	+	0.546691i	$0.815887\pi$
$140$	1.51848	0.128335
$141$	7.34702	0.618731
$142$	−12.2856	−1.03098
$143$	−13.3513	−1.11649
$144$	−2.88166	−0.240138
$145$	−12.3337	−1.02426
$146$	3.19675	0.264565
$147$	1.00000	0.0824786
$148$	4.79962	0.394526
$149$	−5.49864	−0.450467	−0.225233	−	0.974305i	$-0.572314\pi$
$149$	−5.49864	−0.450467	−0.225233	+	0.974305i	$0.572314\pi$
$150$	−7.60043	−0.620572
$151$	−11.8169	−0.961645	−0.480822	−	0.876818i	$-0.659662\pi$
$151$	−11.8169	−0.961645	−0.480822	+	0.876818i	$0.659662\pi$
$152$	5.70113	0.462423
$153$	−5.29249	−0.427873
$154$	−3.61302	−0.291146
$155$	−3.22931	−0.259384
$156$	2.09168	0.167469
$157$	3.77762	0.301487	0.150744	−	0.988573i	$-0.451833\pi$
$157$	3.77762	0.301487	0.150744	+	0.988573i	$0.451833\pi$
$158$	−18.1083	−1.44062
$159$	−11.2837	−0.894854
$160$	8.40817	0.664724
$161$	5.03184	0.396565
$162$	−1.24280	−0.0976435
$163$	−20.0111	−1.56739	−0.783694	−	0.621147i	$-0.786667\pi$
$163$	−20.0111	−1.56739	−0.783694	+	0.621147i	$0.786667\pi$
$164$	−5.26530	−0.411151
$165$	−9.69250	−0.754560
$166$	−0.613249	−0.0475973
$167$	−16.4295	−1.27135	−0.635675	−	0.771957i	$-0.719278\pi$
$167$	−16.4295	−1.27135	−0.635675	+	0.771957i	$0.719278\pi$
$168$	3.05163	0.235439
$169$	8.09145	0.622419
$170$	−21.9294	−1.68191
$171$	1.86822	0.142867
$172$	−1.16080	−0.0885103
$173$	−16.2436	−1.23498	−0.617489	−	0.786580i	$-0.711850\pi$
$173$	−16.2436	−1.23498	−0.617489	+	0.786580i	$0.711850\pi$
$174$	−4.59758	−0.348541
$175$	6.11557	0.462294
$176$	−8.37746	−0.631475
$177$	−13.3410	−1.00277
$178$	−15.1189	−1.13321
$179$	−4.00381	−0.299259	−0.149630	−	0.988742i	$-0.547808\pi$
$179$	−4.00381	−0.299259	−0.149630	+	0.988742i	$0.547808\pi$
$180$	1.51848	0.113181
$181$	−24.4061	−1.81409	−0.907044	−	0.421035i	$-0.861667\pi$
$181$	−24.4061	−1.81409	−0.907044	+	0.421035i	$0.861667\pi$
$182$	5.70761	0.423076
$183$	0.666722	0.0492855
$184$	15.3553	1.13201
$185$	35.1342	2.58312
$186$	−1.20377	−0.0882648
$187$	−15.3862	−1.12515
$188$	−3.34622	−0.244048
$189$	1.00000	0.0727393
$190$	7.74097	0.561589
$191$	−22.5671	−1.63290	−0.816450	−	0.577416i	$-0.804061\pi$
$191$	−22.5671	−1.63290	−0.816450	+	0.577416i	$0.804061\pi$
$192$	8.89758	0.642128
$193$	20.7333	1.49242	0.746208	−	0.665713i	$-0.231873\pi$
$193$	20.7333	1.49242	0.746208	+	0.665713i	$0.231873\pi$
$194$	18.2699	1.31170
$195$	15.3116	1.09648
$196$	−0.455452	−0.0325323
$197$	−3.77768	−0.269148	−0.134574	−	0.990904i	$-0.542967\pi$
$197$	−3.77768	−0.269148	−0.134574	+	0.990904i	$0.542967\pi$
$198$	−3.61302	−0.256766
$199$	−9.73569	−0.690145	−0.345072	−	0.938576i	$-0.612146\pi$
$199$	−9.73569	−0.690145	−0.345072	+	0.938576i	$0.612146\pi$
$200$	18.6625	1.31964
$201$	−14.0335	−0.989847
$202$	9.56583	0.673050
$203$	3.69938	0.259645
$204$	2.41048	0.168767
$205$	−38.5431	−2.69196
$206$	22.4887	1.56686
$207$	5.03184	0.349737
$208$	13.2341	0.917623
$209$	5.43124	0.375687
$210$	4.14349	0.285928
$211$	4.66669	0.321268	0.160634	−	0.987014i	$-0.448646\pi$
$211$	4.66669	0.321268	0.160634	+	0.987014i	$0.448646\pi$
$212$	5.13918	0.352960
$213$	9.88541	0.677337
$214$	2.86662	0.195958
$215$	−8.49730	−0.579511
$216$	3.05163	0.207637
$217$	0.968597	0.0657527
$218$	1.10867	0.0750889
$219$	−2.57222	−0.173815
$220$	4.41447	0.297624
$221$	24.3060	1.63500
$222$	13.0968	0.878999
$223$	5.37863	0.360180	0.180090	−	0.983650i	$-0.442361\pi$
$223$	5.37863	0.360180	0.180090	+	0.983650i	$0.442361\pi$
$224$	−2.52194	−0.168504
$225$	6.11557	0.407705
$226$	−5.41486	−0.360191
$227$	−11.5084	−0.763837	−0.381918	−	0.924196i	$-0.624736\pi$
$227$	−11.5084	−0.763837	−0.381918	+	0.924196i	$0.624736\pi$
$228$	−0.850887	−0.0563514
$229$	−1.87862	−0.124142	−0.0620712	−	0.998072i	$-0.519771\pi$
$229$	−1.87862	−0.124142	−0.0620712	+	0.998072i	$0.519771\pi$
$230$	20.8494	1.37477
$231$	2.90717	0.191278
$232$	11.2891	0.741168
$233$	13.5663	0.888755	0.444378	−	0.895840i	$-0.353425\pi$
$233$	13.5663	0.888755	0.444378	+	0.895840i	$0.353425\pi$
$234$	5.70761	0.373118
$235$	−24.4950	−1.59788
$236$	6.07619	0.395526
$237$	14.5706	0.946463
$238$	6.57750	0.426356
$239$	22.4619	1.45294	0.726468	−	0.687200i	$-0.241160\pi$
$239$	22.4619	1.45294	0.726468	+	0.687200i	$0.241160\pi$
$240$	9.60746	0.620159
$241$	12.0289	0.774848	0.387424	−	0.921902i	$-0.373365\pi$
$241$	12.0289	0.774848	0.387424	+	0.921902i	$0.373365\pi$
$242$	3.16712	0.203590
$243$	1.00000	0.0641500
$244$	−0.303660	−0.0194399
$245$	−3.33400	−0.213002
$246$	−14.3675	−0.916038
$247$	−8.57990	−0.545926
$248$	2.95580	0.187694
$249$	0.493442	0.0312706
$250$	4.62237	0.292345
$251$	5.27452	0.332924	0.166462	−	0.986048i	$-0.446766\pi$
$251$	5.27452	0.332924	0.166462	+	0.986048i	$0.446766\pi$
$252$	−0.455452	−0.0286908
$253$	14.6284	0.919680
$254$	1.24280	0.0779801
$255$	17.6452	1.10498
$256$	−10.3210	−0.645060
$257$	−28.6479	−1.78701	−0.893504	−	0.449055i	$-0.851761\pi$
$257$	−28.6479	−1.78701	−0.893504	+	0.449055i	$0.851761\pi$
$258$	−3.16749	−0.197199
$259$	−10.5381	−0.654808
$260$	−6.97368	−0.432489
$261$	3.69938	0.228986
$262$	−10.8349	−0.669380
$263$	−6.33902	−0.390881	−0.195440	−	0.980716i	$-0.562614\pi$
$263$	−6.33902	−0.390881	−0.195440	+	0.980716i	$0.562614\pi$
$264$	8.87160	0.546010
$265$	37.6198	2.31097
$266$	−2.32183	−0.142360
$267$	12.1652	0.744497
$268$	6.39159	0.390429
$269$	1.26346	0.0770348	0.0385174	−	0.999258i	$-0.487736\pi$
$269$	1.26346	0.0770348	0.0385174	+	0.999258i	$0.487736\pi$
$270$	4.14349	0.252165
$271$	−5.15641	−0.313230	−0.156615	−	0.987660i	$-0.550058\pi$
$271$	−5.15641	−0.313230	−0.156615	+	0.987660i	$0.550058\pi$
$272$	15.2512	0.924737
$273$	−4.59254	−0.277953
$274$	5.79498	0.350087
$275$	17.7790	1.07211
$276$	−2.29176	−0.137948
$277$	2.77471	0.166716	0.0833580	−	0.996520i	$-0.473435\pi$
$277$	2.77471	0.166716	0.0833580	+	0.996520i	$0.473435\pi$
$278$	24.5379	1.47168
$279$	0.968597	0.0579884
$280$	−10.1741	−0.608022
$281$	5.01385	0.299101	0.149551	−	0.988754i	$-0.452217\pi$
$281$	5.01385	0.299101	0.149551	+	0.988754i	$0.452217\pi$
$282$	−9.13087	−0.543735
$283$	−8.84064	−0.525521	−0.262761	−	0.964861i	$-0.584633\pi$
$283$	−8.84064	−0.525521	−0.262761	+	0.964861i	$0.584633\pi$
$284$	−4.50233	−0.267164
$285$	−6.22866	−0.368954
$286$	16.5930	0.981162
$287$	11.5606	0.682401
$288$	−2.52194	−0.148607
$289$	11.0105	0.647674
$290$	15.3283	0.900111
$291$	−14.7006	−0.861767
$292$	1.17152	0.0685583
$293$	−16.5617	−0.967545	−0.483772	−	0.875194i	$-0.660734\pi$
$293$	−16.5617	−0.967545	−0.483772	+	0.875194i	$0.660734\pi$
$294$	−1.24280	−0.0724815
$295$	44.4789	2.58966
$296$	−32.1585	−1.86918
$297$	2.90717	0.168691
$298$	6.83371	0.395866
$299$	−23.1089	−1.33643
$300$	−2.78535	−0.160812
$301$	2.54868	0.146903
$302$	14.6860	0.845085
$303$	−7.69701	−0.442182
$304$	−5.38358	−0.308770
$305$	−2.22285	−0.127280
$306$	6.57750	0.376011
$307$	−23.4209	−1.33670	−0.668352	−	0.743845i	$-0.733000\pi$
$307$	−23.4209	−1.33670	−0.668352	+	0.743845i	$0.733000\pi$
$308$	−1.32408	−0.0754462
$309$	−18.0952	−1.02940
$310$	4.01338	0.227944
$311$	−19.5726	−1.10986	−0.554929	−	0.831898i	$-0.687255\pi$
$311$	−19.5726	−1.10986	−0.554929	+	0.831898i	$0.687255\pi$
$312$	−14.0148	−0.793429
$313$	5.10217	0.288392	0.144196	−	0.989549i	$-0.453940\pi$
$313$	5.10217	0.288392	0.144196	+	0.989549i	$0.453940\pi$
$314$	−4.69483	−0.264944
$315$	−3.33400	−0.187850
$316$	−6.63622	−0.373316
$317$	−19.6691	−1.10472	−0.552362	−	0.833604i	$-0.686273\pi$
$317$	−19.6691	−1.10472	−0.552362	+	0.833604i	$0.686273\pi$
$318$	14.0233	0.786390
$319$	10.7547	0.602148
$320$	−29.6646	−1.65830
$321$	−2.30658	−0.128741
$322$	−6.25356	−0.348497
$323$	−9.88756	−0.550158
$324$	−0.455452	−0.0253029
$325$	−28.0860	−1.55793
$326$	24.8697	1.37741
$327$	−0.892079	−0.0493321
$328$	35.2787	1.94794
$329$	7.34702	0.405055
$330$	12.0458	0.663101
$331$	15.1305	0.831648	0.415824	−	0.909445i	$-0.363493\pi$
$331$	15.1305	0.831648	0.415824	+	0.909445i	$0.363493\pi$
$332$	−0.224739	−0.0123342
$333$	−10.5381	−0.577487
$334$	20.4185	1.11725
$335$	46.7877	2.55629
$336$	−2.88166	−0.157207
$337$	−7.21235	−0.392882	−0.196441	−	0.980516i	$-0.562938\pi$
$337$	−7.21235	−0.392882	−0.196441	+	0.980516i	$0.562938\pi$
$338$	−10.0560	−0.546977
$339$	4.35699	0.236639
$340$	−8.03654	−0.435842
$341$	2.81587	0.152488
$342$	−2.32183	−0.125550
$343$	1.00000	0.0539949
$344$	7.77763	0.419342
$345$	−16.7762	−0.903199
$346$	20.1875	1.08529
$347$	28.7813	1.54506	0.772531	−	0.634977i	$-0.218990\pi$
$347$	28.7813	1.54506	0.772531	+	0.634977i	$0.218990\pi$
$348$	−1.68489	−0.0903195
$349$	−28.8201	−1.54270	−0.771352	−	0.636409i	$-0.780419\pi$
$349$	−28.8201	−1.54270	−0.771352	+	0.636409i	$0.780419\pi$
$350$	−7.60043	−0.406260
$351$	−4.59254	−0.245132
$352$	−7.33171	−0.390782
$353$	26.6489	1.41838	0.709188	−	0.705019i	$-0.249062\pi$
$353$	26.6489	1.41838	0.709188	+	0.705019i	$0.249062\pi$
$354$	16.5802	0.881226
$355$	−32.9580	−1.74923
$356$	−5.54066	−0.293655
$357$	−5.29249	−0.280108
$358$	4.97593	0.262986
$359$	−14.4278	−0.761469	−0.380734	−	0.924684i	$-0.624329\pi$
$359$	−14.4278	−0.761469	−0.380734	+	0.924684i	$0.624329\pi$
$360$	−10.1741	−0.536225
$361$	−15.5097	−0.816302
$362$	30.3318	1.59421
$363$	−2.54838	−0.133755
$364$	2.09168	0.109634
$365$	8.57580	0.448878
$366$	−0.828601	−0.0433117
$367$	−8.35795	−0.436282	−0.218141	−	0.975917i	$-0.569999\pi$
$367$	−8.35795	−0.436282	−0.218141	+	0.975917i	$0.569999\pi$
$368$	−14.5000	−0.755867
$369$	11.5606	0.601821
$370$	−43.6647	−2.27002
$371$	−11.2837	−0.585819
$372$	−0.441150	−0.0228726
$373$	30.3153	1.56966	0.784832	−	0.619708i	$-0.212749\pi$
$373$	30.3153	1.56966	0.784832	+	0.619708i	$0.212749\pi$
$374$	19.1219	0.988769
$375$	−3.71933	−0.192065
$376$	22.4204	1.15624
$377$	−16.9895	−0.875006
$378$	−1.24280	−0.0639226
$379$	2.57847	0.132447	0.0662235	−	0.997805i	$-0.478905\pi$
$379$	2.57847	0.132447	0.0662235	+	0.997805i	$0.478905\pi$
$380$	2.83686	0.145528
$381$	−1.00000	−0.0512316
$382$	28.0464	1.43498
$383$	−14.6277	−0.747438	−0.373719	−	0.927542i	$-0.621918\pi$
$383$	−14.6277	−0.747438	−0.373719	+	0.927542i	$0.621918\pi$
$384$	−6.01402	−0.306901
$385$	−9.69250	−0.493976
$386$	−25.7673	−1.31152
$387$	2.54868	0.129557
$388$	6.69544	0.339909
$389$	19.5586	0.991663	0.495831	−	0.868419i	$-0.334863\pi$
$389$	19.5586	0.991663	0.495831	+	0.868419i	$0.334863\pi$
$390$	−19.0292	−0.963580
$391$	−26.6310	−1.34679
$392$	3.05163	0.154131
$393$	8.71812	0.439771
$394$	4.69489	0.236525
$395$	−48.5784	−2.44425
$396$	−1.32408	−0.0665373
$397$	−8.35455	−0.419303	−0.209651	−	0.977776i	$-0.567233\pi$
$397$	−8.35455	−0.419303	−0.209651	+	0.977776i	$0.567233\pi$
$398$	12.0995	0.606493
$399$	1.86822	0.0935282
$400$	−17.6230	−0.881150
$401$	7.25894	0.362494	0.181247	−	0.983438i	$-0.441987\pi$
$401$	7.25894	0.362494	0.181247	+	0.983438i	$0.441987\pi$
$402$	17.4408	0.869869
$403$	−4.44832	−0.221587
$404$	3.50562	0.174411
$405$	−3.33400	−0.165668
$406$	−4.59758	−0.228174
$407$	−30.6361	−1.51858
$408$	−16.1507	−0.799581
$409$	8.46320	0.418478	0.209239	−	0.977864i	$-0.432901\pi$
$409$	8.46320	0.418478	0.209239	+	0.977864i	$0.432901\pi$
$410$	47.9013	2.36567
$411$	−4.66285	−0.230001
$412$	8.24150	0.406029
$413$	−13.3410	−0.656468
$414$	−6.25356	−0.307346
$415$	−1.64514	−0.0807566
$416$	11.5821	0.567861
$417$	−19.7441	−0.966870
$418$	−6.74994	−0.330150
$419$	26.7971	1.30912	0.654561	−	0.756009i	$-0.272854\pi$
$419$	26.7971	1.30912	0.654561	+	0.756009i	$0.272854\pi$
$420$	1.51848	0.0740942
$421$	14.1261	0.688463	0.344231	−	0.938885i	$-0.388140\pi$
$421$	14.1261	0.688463	0.344231	+	0.938885i	$0.388140\pi$
$422$	−5.79976	−0.282328
$423$	7.34702	0.357225
$424$	−34.4336	−1.67225
$425$	−32.3666	−1.57001
$426$	−12.2856	−0.595238
$427$	0.666722	0.0322650
$428$	1.05054	0.0507797
$429$	−13.3513	−0.644606
$430$	10.5604	0.509269
$431$	−16.6128	−0.800211	−0.400105	−	0.916469i	$-0.631026\pi$
$431$	−16.6128	−0.800211	−0.400105	+	0.916469i	$0.631026\pi$
$432$	−2.88166	−0.138644
$433$	24.5878	1.18161	0.590807	−	0.806813i	$-0.298810\pi$
$433$	24.5878	1.18161	0.590807	+	0.806813i	$0.298810\pi$
$434$	−1.20377	−0.0577829
$435$	−12.3337	−0.591357
$436$	0.406300	0.0194582
$437$	9.40061	0.449692
$438$	3.19675	0.152747
$439$	−38.1271	−1.81971	−0.909853	−	0.414930i	$-0.863806\pi$
$439$	−38.1271	−1.81971	−0.909853	+	0.414930i	$0.863806\pi$
$440$	−29.5780	−1.41007
$441$	1.00000	0.0476190
$442$	−30.2074	−1.43682
$443$	22.7120	1.07908	0.539541	−	0.841959i	$-0.318598\pi$
$443$	22.7120	1.07908	0.539541	+	0.841959i	$0.318598\pi$
$444$	4.79962	0.227780
$445$	−40.5588	−1.92267
$446$	−6.68455	−0.316523
$447$	−5.49864	−0.260077
$448$	8.89758	0.420371
$449$	−29.0754	−1.37215	−0.686075	−	0.727531i	$-0.740668\pi$
$449$	−29.0754	−1.37215	−0.686075	+	0.727531i	$0.740668\pi$
$450$	−7.60043	−0.358287
$451$	33.6086	1.58257
$452$	−1.98440	−0.0933385
$453$	−11.8169	−0.555206
$454$	14.3026	0.671253
$455$	15.3116	0.717817
$456$	5.70113	0.266980
$457$	25.5196	1.19376	0.596879	−	0.802332i	$-0.296407\pi$
$457$	25.5196	1.19376	0.596879	+	0.802332i	$0.296407\pi$
$458$	2.33474	0.109095
$459$	−5.29249	−0.247032
$460$	7.64075	0.356252
$461$	−10.8134	−0.503631	−0.251815	−	0.967775i	$-0.581028\pi$
$461$	−10.8134	−0.503631	−0.251815	+	0.967775i	$0.581028\pi$
$462$	−3.61302	−0.168093
$463$	5.98793	0.278283	0.139141	−	0.990273i	$-0.455566\pi$
$463$	5.98793	0.278283	0.139141	+	0.990273i	$0.455566\pi$
$464$	−10.6603	−0.494894
$465$	−3.22931	−0.149755
$466$	−16.8601	−0.781030
$467$	41.9564	1.94151	0.970755	−	0.240074i	$-0.0771717\pi$
$467$	41.9564	1.94151	0.970755	+	0.240074i	$0.0771717\pi$
$468$	2.09168	0.0966881
$469$	−14.0335	−0.648007
$470$	30.4423	1.40420
$471$	3.77762	0.174064
$472$	−40.7118	−1.87391
$473$	7.40943	0.340686
$474$	−18.1083	−0.831743
$475$	11.4253	0.524227
$476$	2.41048	0.110484
$477$	−11.2837	−0.516644
$478$	−27.9156	−1.27683
$479$	−9.65088	−0.440960	−0.220480	−	0.975392i	$-0.570762\pi$
$479$	−9.65088	−0.440960	−0.220480	+	0.975392i	$0.570762\pi$
$480$	8.40817	0.383779
$481$	48.3969	2.20671
$482$	−14.9495	−0.680930
$483$	5.03184	0.228957
$484$	1.16067	0.0527575
$485$	49.0120	2.22552
$486$	−1.24280	−0.0563745
$487$	−17.7189	−0.802920	−0.401460	−	0.915877i	$-0.631497\pi$
$487$	−17.7189	−0.802920	−0.401460	+	0.915877i	$0.631497\pi$
$488$	2.03459	0.0921016
$489$	−20.0111	−0.904932
$490$	4.14349	0.187184
$491$	−4.97599	−0.224563	−0.112282	−	0.993676i	$-0.535816\pi$
$491$	−4.97599	−0.224563	−0.112282	+	0.993676i	$0.535816\pi$
$492$	−5.26530	−0.237378
$493$	−19.5789	−0.881790
$494$	10.6631	0.479755
$495$	−9.69250	−0.435646
$496$	−2.79117	−0.125327
$497$	9.88541	0.443421
$498$	−0.613249	−0.0274803
$499$	44.0654	1.97264	0.986318	−	0.164851i	$-0.0527143\pi$
$499$	44.0654	1.97264	0.986318	+	0.164851i	$0.0527143\pi$
$500$	1.69398	0.0757569
$501$	−16.4295	−0.734014
$502$	−6.55516	−0.292571
$503$	5.31840	0.237136	0.118568	−	0.992946i	$-0.462170\pi$
$503$	5.31840	0.237136	0.118568	+	0.992946i	$0.462170\pi$
$504$	3.05163	0.135930
$505$	25.6619	1.14194
$506$	−18.1802	−0.808207
$507$	8.09145	0.359354
$508$	0.455452	0.0202074
$509$	10.4607	0.463661	0.231830	−	0.972756i	$-0.425529\pi$
$509$	10.4607	0.463661	0.231830	+	0.972756i	$0.425529\pi$
$510$	−21.9294	−0.971050
$511$	−2.57222	−0.113788
$512$	24.8549	1.09844
$513$	1.86822	0.0824841
$514$	35.6036	1.57041
$515$	60.3294	2.65843
$516$	−1.16080	−0.0511014
$517$	21.3590	0.939369
$518$	13.0968	0.575440
$519$	−16.2436	−0.713015
$520$	46.7252	2.04904
$521$	35.6052	1.55989	0.779947	−	0.625846i	$-0.215246\pi$
$521$	35.6052	1.55989	0.779947	+	0.625846i	$0.215246\pi$
$522$	−4.59758	−0.201230
$523$	23.5608	1.03024	0.515120	−	0.857118i	$-0.327747\pi$
$523$	23.5608	1.03024	0.515120	+	0.857118i	$0.327747\pi$
$524$	−3.97069	−0.173460
$525$	6.11557	0.266906
$526$	7.87813	0.343503
$527$	−5.12629	−0.223305
$528$	−8.37746	−0.364582
$529$	2.31943	0.100845
$530$	−46.7538	−2.03086
$531$	−13.3410	−0.578950
$532$	−0.850887	−0.0368906
$533$	−53.0926	−2.29969
$534$	−15.1189	−0.654258
$535$	7.69015	0.332474
$536$	−42.8251	−1.84976
$537$	−4.00381	−0.172777
$538$	−1.57023	−0.0676975
$539$	2.90717	0.125221
$540$	1.51848	0.0653449
$541$	7.71667	0.331765	0.165883	−	0.986145i	$-0.446953\pi$
$541$	7.71667	0.331765	0.165883	+	0.986145i	$0.446953\pi$
$542$	6.40838	0.275264
$543$	−24.4061	−1.04736
$544$	13.3474	0.572263
$545$	2.97419	0.127400
$546$	5.70761	0.244263
$547$	−15.9737	−0.682987	−0.341494	−	0.939884i	$-0.610933\pi$
$547$	−15.9737	−0.682987	−0.341494	+	0.939884i	$0.610933\pi$
$548$	2.12370	0.0907201
$549$	0.666722	0.0284550
$550$	−22.0957	−0.942164
$551$	6.91126	0.294430
$552$	15.3553	0.653566
$553$	14.5706	0.619605
$554$	−3.44840	−0.146509
$555$	35.1342	1.49136
$556$	8.99247	0.381366
$557$	0.464136	0.0196661	0.00983304	−	0.999952i	$-0.496870\pi$
$557$	0.464136	0.0196661	0.00983304	+	0.999952i	$0.496870\pi$
$558$	−1.20377	−0.0509597
$559$	−11.7049	−0.495065
$560$	9.60746	0.405989
$561$	−15.3862	−0.649604
$562$	−6.23121	−0.262848
$563$	35.9885	1.51673	0.758367	−	0.651828i	$-0.225998\pi$
$563$	35.9885	1.51673	0.758367	+	0.651828i	$0.225998\pi$
$564$	−3.34622	−0.140901
$565$	−14.5262	−0.611123
$566$	10.9871	0.461824
$567$	1.00000	0.0419961
$568$	30.1666	1.26576
$569$	−11.1032	−0.465469	−0.232735	−	0.972540i	$-0.574767\pi$
$569$	−11.1032	−0.465469	−0.232735	+	0.972540i	$0.574767\pi$
$570$	7.74097	0.324234
$571$	10.2214	0.427753	0.213877	−	0.976861i	$-0.431391\pi$
$571$	10.2214	0.427753	0.213877	+	0.976861i	$0.431391\pi$
$572$	6.08088	0.254254
$573$	−22.5671	−0.942755
$574$	−14.3675	−0.599688
$575$	30.7726	1.28331
$576$	8.89758	0.370733
$577$	10.4490	0.434999	0.217500	−	0.976060i	$-0.430210\pi$
$577$	10.4490	0.434999	0.217500	+	0.976060i	$0.430210\pi$
$578$	−13.6838	−0.569170
$579$	20.7333	0.861646
$580$	5.61742	0.233251
$581$	0.493442	0.0204714
$582$	18.2699	0.757313
$583$	−32.8035	−1.35858
$584$	−7.84948	−0.324814
$585$	15.3116	0.633055
$586$	20.5829	0.850270
$587$	37.8825	1.56358	0.781789	−	0.623543i	$-0.214307\pi$
$587$	37.8825	1.56358	0.781789	+	0.623543i	$0.214307\pi$
$588$	−0.455452	−0.0187825
$589$	1.80956	0.0745615
$590$	−55.2783	−2.27577
$591$	−3.77768	−0.155393
$592$	30.3673	1.24809
$593$	−43.2711	−1.77693	−0.888466	−	0.458942i	$-0.848228\pi$
$593$	−43.2711	−1.77693	−0.888466	+	0.458942i	$0.848228\pi$
$594$	−3.61302	−0.148244
$595$	17.6452	0.723382
$596$	2.50437	0.102583
$597$	−9.73569	−0.398455
$598$	28.7198	1.17444
$599$	−28.8279	−1.17787	−0.588937	−	0.808179i	$-0.700453\pi$
$599$	−28.8279	−1.17787	−0.588937	+	0.808179i	$0.700453\pi$
$600$	18.6625	0.761893
$601$	29.8137	1.21612	0.608062	−	0.793889i	$-0.291947\pi$
$601$	29.8137	1.21612	0.608062	+	0.793889i	$0.291947\pi$
$602$	−3.16749	−0.129097
$603$	−14.0335	−0.571489
$604$	5.38203	0.218992
$605$	8.49630	0.345424
$606$	9.56583	0.388585
$607$	−15.0035	−0.608974	−0.304487	−	0.952516i	$-0.598485\pi$
$607$	−15.0035	−0.608974	−0.304487	+	0.952516i	$0.598485\pi$
$608$	−4.71156	−0.191079
$609$	3.69938	0.149906
$610$	2.76256	0.111853
$611$	−33.7415	−1.36504
$612$	2.41048	0.0974378
$613$	−5.68365	−0.229561	−0.114780	−	0.993391i	$-0.536616\pi$
$613$	−5.68365	−0.229561	−0.114780	+	0.993391i	$0.536616\pi$
$614$	29.1075	1.17468
$615$	−38.5431	−1.55421
$616$	8.87160	0.357447
$617$	13.5363	0.544952	0.272476	−	0.962163i	$-0.412158\pi$
$617$	13.5363	0.544952	0.272476	+	0.962163i	$0.412158\pi$
$618$	22.4887	0.904627
$619$	−27.0321	−1.08651	−0.543256	−	0.839567i	$-0.682809\pi$
$619$	−27.0321	−1.08651	−0.543256	+	0.839567i	$0.682809\pi$
$620$	1.47079	0.0590685
$621$	5.03184	0.201921
$622$	24.3247	0.975334
$623$	12.1652	0.487388
$624$	13.2341	0.529790
$625$	−18.1776	−0.727105
$626$	−6.34097	−0.253436
$627$	5.43124	0.216903
$628$	−1.72053	−0.0686565
$629$	55.7730	2.22382
$630$	4.14349	0.165081
$631$	2.75817	0.109801	0.0549004	−	0.998492i	$-0.482516\pi$
$631$	2.75817	0.109801	0.0549004	+	0.998492i	$0.482516\pi$
$632$	44.4641	1.76869
$633$	4.66669	0.185484
$634$	24.4447	0.970822
$635$	3.33400	0.132306
$636$	5.13918	0.203782
$637$	−4.59254	−0.181963
$638$	−13.3659	−0.529162
$639$	9.88541	0.391061
$640$	20.0507	0.792575
$641$	−10.2155	−0.403489	−0.201744	−	0.979438i	$-0.564661\pi$
$641$	−10.2155	−0.403489	−0.201744	+	0.979438i	$0.564661\pi$
$642$	2.86662	0.113136
$643$	−25.3762	−1.00074	−0.500370	−	0.865812i	$-0.666803\pi$
$643$	−25.3762	−1.00074	−0.500370	+	0.865812i	$0.666803\pi$
$644$	−2.29176	−0.0903081
$645$	−8.49730	−0.334581
$646$	12.2882	0.483474
$647$	−22.1567	−0.871068	−0.435534	−	0.900172i	$-0.643440\pi$
$647$	−22.1567	−0.871068	−0.435534	+	0.900172i	$0.643440\pi$
$648$	3.05163	0.119879
$649$	−38.7845	−1.52243
$650$	34.9053	1.36910
$651$	0.968597	0.0379623
$652$	9.11409	0.356935
$653$	−9.65817	−0.377954	−0.188977	−	0.981982i	$-0.560517\pi$
$653$	−9.65817	−0.377954	−0.188977	+	0.981982i	$0.560517\pi$
$654$	1.10867	0.0433526
$655$	−29.0662	−1.13571
$656$	−33.3137	−1.30068
$657$	−2.57222	−0.100352
$658$	−9.13087	−0.355958
$659$	−14.6717	−0.571527	−0.285764	−	0.958300i	$-0.592247\pi$
$659$	−14.6717	−0.571527	−0.285764	+	0.958300i	$0.592247\pi$
$660$	4.41447	0.171833
$661$	33.3172	1.29589	0.647945	−	0.761687i	$-0.275629\pi$
$661$	33.3172	1.29589	0.647945	+	0.761687i	$0.275629\pi$
$662$	−18.8042	−0.730845
$663$	24.3060	0.943967
$664$	1.50580	0.0584365
$665$	−6.22866	−0.241537
$666$	13.0968	0.507490
$667$	18.6147	0.720763
$668$	7.48283	0.289519
$669$	5.37863	0.207950
$670$	−58.1477	−2.24644
$671$	1.93827	0.0748262
$672$	−2.52194	−0.0972861
$673$	1.32670	0.0511404	0.0255702	−	0.999673i	$-0.491860\pi$
$673$	1.32670	0.0511404	0.0255702	+	0.999673i	$0.491860\pi$
$674$	8.96350	0.345261
$675$	6.11557	0.235389
$676$	−3.68527	−0.141741
$677$	11.9106	0.457761	0.228881	−	0.973454i	$-0.426493\pi$
$677$	11.9106	0.457761	0.228881	+	0.973454i	$0.426493\pi$
$678$	−5.41486	−0.207957
$679$	−14.7006	−0.564159
$680$	53.8466	2.06492
$681$	−11.5084	−0.441001
$682$	−3.49956	−0.134005
$683$	−6.04534	−0.231318	−0.115659	−	0.993289i	$-0.536898\pi$
$683$	−6.04534	−0.231318	−0.115659	+	0.993289i	$0.536898\pi$
$684$	−0.850887	−0.0325345
$685$	15.5459	0.593980
$686$	−1.24280	−0.0474503
$687$	−1.87862	−0.0716737
$688$	−7.34442	−0.280003
$689$	51.8208	1.97421
$690$	20.8494	0.793723
$691$	−26.4623	−1.00667	−0.503336	−	0.864090i	$-0.667894\pi$
$691$	−26.4623	−1.00667	−0.503336	+	0.864090i	$0.667894\pi$
$692$	7.39818	0.281237
$693$	2.90717	0.110434
$694$	−35.7694	−1.35779
$695$	65.8267	2.49695
$696$	11.2891	0.427913
$697$	−61.1844	−2.31752
$698$	35.8176	1.35571
$699$	13.5663	0.513123
$700$	−2.78535	−0.105276
$701$	27.8873	1.05329	0.526645	−	0.850085i	$-0.323450\pi$
$701$	27.8873	1.05329	0.526645	+	0.850085i	$0.323450\pi$
$702$	5.70761	0.215420
$703$	−19.6876	−0.742532
$704$	25.8668	0.974890
$705$	−24.4950	−0.922535
$706$	−33.1192	−1.24646
$707$	−7.69701	−0.289476
$708$	6.07619	0.228357
$709$	−21.7892	−0.818312	−0.409156	−	0.912465i	$-0.634177\pi$
$709$	−21.7892	−0.818312	−0.409156	+	0.912465i	$0.634177\pi$
$710$	40.9601	1.53721
$711$	14.5706	0.546440
$712$	37.1237	1.39127
$713$	4.87383	0.182526
$714$	6.57750	0.246157
$715$	44.5132	1.66470
$716$	1.82355	0.0681491
$717$	22.4619	0.838853
$718$	17.9308	0.669172
$719$	0.503768	0.0187874	0.00939368	−	0.999956i	$-0.497010\pi$
$719$	0.503768	0.0187874	0.00939368	+	0.999956i	$0.497010\pi$
$720$	9.60746	0.358049
$721$	−18.0952	−0.673900
$722$	19.2755	0.717359
$723$	12.0289	0.447359
$724$	11.1158	0.413115
$725$	22.6238	0.840227
$726$	3.16712	0.117543
$727$	23.4153	0.868427	0.434213	−	0.900810i	$-0.357026\pi$
$727$	23.4153	0.868427	0.434213	+	0.900810i	$0.357026\pi$
$728$	−14.0148	−0.519421
$729$	1.00000	0.0370370
$730$	−10.6580	−0.394470
$731$	−13.4889	−0.498903
$732$	−0.303660	−0.0112236
$733$	52.3311	1.93289	0.966446	−	0.256871i	$-0.0826915\pi$
$733$	52.3311	1.93289	0.966446	+	0.256871i	$0.0826915\pi$
$734$	10.3872	0.383400
$735$	−3.33400	−0.122977
$736$	−12.6900	−0.467760
$737$	−40.7978	−1.50280
$738$	−14.3675	−0.528875
$739$	−11.4312	−0.420504	−0.210252	−	0.977647i	$-0.567429\pi$
$739$	−11.4312	−0.420504	−0.210252	+	0.977647i	$0.567429\pi$
$740$	−16.0020	−0.588243
$741$	−8.57990	−0.315190
$742$	14.0233	0.514813
$743$	33.8238	1.24087	0.620437	−	0.784256i	$-0.286955\pi$
$743$	33.8238	1.24087	0.620437	+	0.784256i	$0.286955\pi$
$744$	2.95580	0.108365
$745$	18.3325	0.671651
$746$	−37.6758	−1.37941
$747$	0.493442	0.0180541
$748$	7.00766	0.256225
$749$	−2.30658	−0.0842807
$750$	4.62237	0.168785
$751$	−50.0895	−1.82779	−0.913896	−	0.405949i	$-0.866941\pi$
$751$	−50.0895	−1.82779	−0.913896	+	0.405949i	$0.866941\pi$
$752$	−21.1716	−0.772049
$753$	5.27452	0.192214
$754$	21.1146	0.768947
$755$	39.3975	1.43382
$756$	−0.455452	−0.0165646
$757$	16.9391	0.615663	0.307831	−	0.951441i	$-0.400397\pi$
$757$	16.9391	0.615663	0.307831	+	0.951441i	$0.400397\pi$
$758$	−3.20451	−0.116393
$759$	14.6284	0.530977
$760$	−19.0076	−0.689478
$761$	−32.7577	−1.18747	−0.593734	−	0.804662i	$-0.702347\pi$
$761$	−32.7577	−1.18747	−0.593734	+	0.804662i	$0.702347\pi$
$762$	1.24280	0.0450218
$763$	−0.892079	−0.0322954
$764$	10.2783	0.371854
$765$	17.6452	0.637963
$766$	18.1792	0.656842
$767$	61.2691	2.21230
$768$	−10.3210	−0.372426
$769$	47.6458	1.71815	0.859075	−	0.511850i	$-0.171040\pi$
$769$	47.6458	1.71815	0.859075	+	0.511850i	$0.171040\pi$
$770$	12.0458	0.434101
$771$	−28.6479	−1.03173
$772$	−9.44303	−0.339862
$773$	−47.1769	−1.69683	−0.848417	−	0.529328i	$-0.822444\pi$
$773$	−47.1769	−1.69683	−0.848417	+	0.529328i	$0.822444\pi$
$774$	−3.16749	−0.113853
$775$	5.92353	0.212779
$776$	−44.8609	−1.61041
$777$	−10.5381	−0.378054
$778$	−24.3075	−0.871464
$779$	21.5978	0.773821
$780$	−6.97368	−0.249698
$781$	28.7385	1.02835
$782$	33.0969	1.18354
$783$	3.69938	0.132205
$784$	−2.88166	−0.102916
$785$	−12.5946	−0.449521
$786$	−10.8349	−0.386467
$787$	−15.6611	−0.558257	−0.279129	−	0.960254i	$-0.590046\pi$
$787$	−15.6611	−0.558257	−0.279129	+	0.960254i	$0.590046\pi$
$788$	1.72055	0.0612921
$789$	−6.33902	−0.225675
$790$	60.3732	2.14798
$791$	4.35699	0.154917
$792$	8.87160	0.315239
$793$	−3.06195	−0.108733
$794$	10.3830	0.368479
$795$	37.6198	1.33424
$796$	4.43414	0.157164
$797$	−2.11085	−0.0747702	−0.0373851	−	0.999301i	$-0.511903\pi$
$797$	−2.11085	−0.0747702	−0.0373851	+	0.999301i	$0.511903\pi$
$798$	−2.32183	−0.0821917
$799$	−38.8841	−1.37562
$800$	−15.4231	−0.545290
$801$	12.1652	0.429836
$802$	−9.02139	−0.318556
$803$	−7.47788	−0.263889
$804$	6.39159	0.225414
$805$	−16.7762	−0.591282
$806$	5.52837	0.194729
$807$	1.26346	0.0444761
$808$	−23.4884	−0.826321
$809$	−10.8674	−0.382079	−0.191039	−	0.981582i	$-0.561186\pi$
$809$	−10.8674	−0.382079	−0.191039	+	0.981582i	$0.561186\pi$
$810$	4.14349	0.145588
$811$	−46.4996	−1.63282	−0.816411	−	0.577472i	$-0.804039\pi$
$811$	−46.4996	−1.63282	−0.816411	+	0.577472i	$0.804039\pi$
$812$	−1.68489	−0.0591280
$813$	−5.15641	−0.180843
$814$	38.0746	1.33451
$815$	66.7170	2.33699
$816$	15.2512	0.533897
$817$	4.76150	0.166584
$818$	−10.5181	−0.367755
$819$	−4.59254	−0.160476
$820$	17.5545	0.613031
$821$	−26.4225	−0.922152	−0.461076	−	0.887361i	$-0.652536\pi$
$821$	−26.4225	−0.922152	−0.461076	+	0.887361i	$0.652536\pi$
$822$	5.79498	0.202123
$823$	−26.4500	−0.921989	−0.460995	−	0.887403i	$-0.652507\pi$
$823$	−26.4500	−0.921989	−0.460995	+	0.887403i	$0.652507\pi$
$824$	−55.2199	−1.92368
$825$	17.7790	0.618985
$826$	16.5802	0.576898
$827$	31.2695	1.08735	0.543673	−	0.839297i	$-0.317033\pi$
$827$	31.2695	1.08735	0.543673	+	0.839297i	$0.317033\pi$
$828$	−2.29176	−0.0796443
$829$	−52.6203	−1.82758	−0.913790	−	0.406187i	$-0.866858\pi$
$829$	−52.6203	−1.82758	−0.913790	+	0.406187i	$0.866858\pi$
$830$	2.04457	0.0709682
$831$	2.77471	0.0962536
$832$	−40.8625	−1.41665
$833$	−5.29249	−0.183374
$834$	24.5379	0.849677
$835$	54.7758	1.89560
$836$	−2.47367	−0.0855537
$837$	0.968597	0.0334796
$838$	−33.3033	−1.15044
$839$	−29.2755	−1.01070	−0.505352	−	0.862913i	$-0.668637\pi$
$839$	−29.2755	−1.01070	−0.505352	+	0.862913i	$0.668637\pi$
$840$	−10.1741	−0.351042
$841$	−15.3146	−0.528090
$842$	−17.5559	−0.605015
$843$	5.01385	0.172686
$844$	−2.12546	−0.0731612
$845$	−26.9769	−0.928034
$846$	−9.13087	−0.313926
$847$	−2.54838	−0.0875633
$848$	32.5157	1.11659
$849$	−8.84064	−0.303410
$850$	40.2252	1.37971
$851$	−53.0263	−1.81772
$852$	−4.50233	−0.154247
$853$	−22.4780	−0.769631	−0.384816	−	0.922994i	$-0.625735\pi$
$853$	−22.4780	−0.769631	−0.384816	+	0.922994i	$0.625735\pi$
$854$	−0.828601	−0.0283542
$855$	−6.22866	−0.213016
$856$	−7.03884	−0.240583
$857$	−35.5634	−1.21482	−0.607412	−	0.794387i	$-0.707792\pi$
$857$	−35.5634	−1.21482	−0.607412	+	0.794387i	$0.707792\pi$
$858$	16.5930	0.566474
$859$	38.2979	1.30671	0.653354	−	0.757053i	$-0.273361\pi$
$859$	38.2979	1.30671	0.653354	+	0.757053i	$0.273361\pi$
$860$	3.87011	0.131970
$861$	11.5606	0.393984
$862$	20.6464	0.703218
$863$	47.7198	1.62440	0.812201	−	0.583378i	$-0.198270\pi$
$863$	47.7198	1.62440	0.812201	+	0.583378i	$0.198270\pi$
$864$	−2.52194	−0.0857983
$865$	54.1562	1.84137
$866$	−30.5577	−1.03839
$867$	11.0105	0.373935
$868$	−0.441150	−0.0149736
$869$	42.3592	1.43694
$870$	15.3283	0.519679
$871$	64.4495	2.18379
$872$	−2.72230	−0.0921886
$873$	−14.7006	−0.497541
$874$	−11.6831	−0.395185
$875$	−3.71933	−0.125736
$876$	1.17152	0.0395821
$877$	−20.9916	−0.708837	−0.354418	−	0.935087i	$-0.615321\pi$
$877$	−20.9916	−0.708837	−0.354418	+	0.935087i	$0.615321\pi$
$878$	47.3843	1.59914
$879$	−16.5617	−0.558612
$880$	27.9305	0.941536
$881$	−47.8891	−1.61343	−0.806713	−	0.590943i	$-0.798756\pi$
$881$	−47.8891	−1.61343	−0.806713	+	0.590943i	$0.798756\pi$
$882$	−1.24280	−0.0418472
$883$	10.1634	0.342026	0.171013	−	0.985269i	$-0.445296\pi$
$883$	10.1634	0.342026	0.171013	+	0.985269i	$0.445296\pi$
$884$	−11.0702	−0.372332
$885$	44.4789	1.49514
$886$	−28.2265	−0.948287
$887$	−49.2135	−1.65243	−0.826213	−	0.563357i	$-0.809510\pi$
$887$	−49.2135	−1.65243	−0.826213	+	0.563357i	$0.809510\pi$
$888$	−32.1585	−1.07917
$889$	−1.00000	−0.0335389
$890$	50.4064	1.68963
$891$	2.90717	0.0973938
$892$	−2.44971	−0.0820223
$893$	13.7259	0.459319
$894$	6.83371	0.228553
$895$	13.3487	0.446199
$896$	−6.01402	−0.200914
$897$	−23.1089	−0.771585
$898$	36.1348	1.20583
$899$	3.58320	0.119507
$900$	−2.78535	−0.0928451
$901$	59.7188	1.98952
$902$	−41.7687	−1.39075
$903$	2.54868	0.0848147
$904$	13.2959	0.442216
$905$	81.3699	2.70483
$906$	14.6860	0.487910
$907$	50.4233	1.67428	0.837139	−	0.546991i	$-0.184227\pi$
$907$	50.4233	1.67428	0.837139	+	0.546991i	$0.184227\pi$
$908$	5.24151	0.173946
$909$	−7.69701	−0.255294
$910$	−19.0292	−0.630811
$911$	19.4045	0.642899	0.321449	−	0.946927i	$-0.395830\pi$
$911$	19.4045	0.642899	0.321449	+	0.946927i	$0.395830\pi$
$912$	−5.38358	−0.178268
$913$	1.43452	0.0474756
$914$	−31.7157	−1.04906
$915$	−2.22285	−0.0734853
$916$	0.855620	0.0282705
$917$	8.71812	0.287898
$918$	6.57750	0.217090
$919$	−38.9767	−1.28572	−0.642861	−	0.765983i	$-0.722253\pi$
$919$	−38.9767	−1.28572	−0.642861	+	0.765983i	$0.722253\pi$
$920$	−51.1947	−1.68784
$921$	−23.4209	−0.771746
$922$	13.4389	0.442586
$923$	−45.3992	−1.49433
$924$	−1.32408	−0.0435589
$925$	−64.4468	−2.11900
$926$	−7.44179	−0.244552
$927$	−18.0952	−0.594324
$928$	−9.32962	−0.306260
$929$	−2.48794	−0.0816266	−0.0408133	−	0.999167i	$-0.512995\pi$
$929$	−2.48794	−0.0816266	−0.0408133	+	0.999167i	$0.512995\pi$
$930$	4.01338	0.131604
$931$	1.86822	0.0612286
$932$	−6.17878	−0.202393
$933$	−19.5726	−0.640777
$934$	−52.1433	−1.70618
$935$	51.2975	1.67761
$936$	−14.0148	−0.458086
$937$	42.9656	1.40362	0.701812	−	0.712362i	$-0.252375\pi$
$937$	42.9656	1.40362	0.701812	+	0.712362i	$0.252375\pi$
$938$	17.4408	0.569463
$939$	5.10217	0.166503
$940$	11.1563	0.363878
$941$	49.3601	1.60909	0.804547	−	0.593889i	$-0.202408\pi$
$941$	49.3601	1.60909	0.804547	+	0.593889i	$0.202408\pi$
$942$	−4.69483	−0.152966
$943$	58.1711	1.89431
$944$	38.4442	1.25125
$945$	−3.33400	−0.108455
$946$	−9.20843	−0.299392
$947$	−7.03435	−0.228586	−0.114293	−	0.993447i	$-0.536460\pi$
$947$	−7.03435	−0.228586	−0.114293	+	0.993447i	$0.536460\pi$
$948$	−6.63622	−0.215534
$949$	11.8130	0.383468
$950$	−14.1993	−0.460686
$951$	−19.6691	−0.637813
$952$	−16.1507	−0.523448
$953$	12.7667	0.413553	0.206777	−	0.978388i	$-0.433703\pi$
$953$	12.7667	0.413553	0.206777	+	0.978388i	$0.433703\pi$
$954$	14.0233	0.454022
$955$	75.2389	2.43467
$956$	−10.2303	−0.330872
$957$	10.7547	0.347650
$958$	11.9941	0.387512
$959$	−4.66285	−0.150571
$960$	−29.6646	−0.957420
$961$	−30.0618	−0.969736
$962$	−60.1476	−1.93924
$963$	−2.30658	−0.0743286
$964$	−5.47858	−0.176453
$965$	−69.1249	−2.22521
$966$	−6.25356	−0.201205
$967$	53.8825	1.73274	0.866372	−	0.499400i	$-0.166446\pi$
$967$	53.8825	1.73274	0.866372	+	0.499400i	$0.166446\pi$
$968$	−7.77671	−0.249953
$969$	−9.88756	−0.317634
$970$	−60.9120	−1.95577
$971$	−55.2100	−1.77177	−0.885887	−	0.463901i	$-0.846449\pi$
$971$	−55.2100	−1.77177	−0.885887	+	0.463901i	$0.846449\pi$
$972$	−0.455452	−0.0146086
$973$	−19.7441	−0.632965
$974$	22.0210	0.705599
$975$	−28.0860	−0.899473
$976$	−1.92127	−0.0614982
$977$	−38.3352	−1.22645	−0.613226	−	0.789908i	$-0.710128\pi$
$977$	−38.3352	−1.22645	−0.613226	+	0.789908i	$0.710128\pi$
$978$	24.8697	0.795246
$979$	35.3662	1.13031
$980$	1.51848	0.0485060
$981$	−0.892079	−0.0284819
$982$	6.18415	0.197344
$983$	−19.8976	−0.634635	−0.317317	−	0.948319i	$-0.602782\pi$
$983$	−19.8976	−0.634635	−0.317317	+	0.948319i	$0.602782\pi$
$984$	35.2787	1.12464
$985$	12.5948	0.401303
$986$	24.3326	0.774909
$987$	7.34702	0.233858
$988$	3.90774	0.124322
$989$	12.8245	0.407797
$990$	12.0458	0.382842
$991$	5.55649	0.176508	0.0882538	−	0.996098i	$-0.471871\pi$
$991$	5.55649	0.176508	0.0882538	+	0.996098i	$0.471871\pi$
$992$	−2.44275	−0.0775573
$993$	15.1305	0.480152
$994$	−12.2856	−0.389675
$995$	32.4588	1.02901
$996$	−0.224739	−0.00712114
$997$	4.32640	0.137019	0.0685093	−	0.997650i	$-0.478176\pi$
$997$	4.32640	0.137019	0.0685093	+	0.997650i	$0.478176\pi$
$998$	−54.7644	−1.73354
$999$	−10.5381	−0.333412

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2667.2.a.j.1.3	✓	7
3.2	odd	2		8001.2.a.l.1.5		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2667.2.a.j.1.3	✓	7	1.1	even	1	trivial
8001.2.a.l.1.5		7	3.2	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:	\( N \)	\(=\)	\( 2667 = 3 \cdot 7 \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2667.a (trivial)

\(f(q)\)	\(=\)	\(q-1.24280 q^{2} +1.00000 q^{3} -0.455452 q^{4} -3.33400 q^{5} -1.24280 q^{6} +1.00000 q^{7} +3.05163 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.24280 q^{2} +1.00000 q^{3} -0.455452 q^{4} -3.33400 q^{5} -1.24280 q^{6} +1.00000 q^{7} +3.05163 q^{8} +1.00000 q^{9} +4.14349 q^{10} +2.90717 q^{11} -0.455452 q^{12} -4.59254 q^{13} -1.24280 q^{14} -3.33400 q^{15} -2.88166 q^{16} -5.29249 q^{17} -1.24280 q^{18} +1.86822 q^{19} +1.51848 q^{20} +1.00000 q^{21} -3.61302 q^{22} +5.03184 q^{23} +3.05163 q^{24} +6.11557 q^{25} +5.70761 q^{26} +1.00000 q^{27} -0.455452 q^{28} +3.69938 q^{29} +4.14349 q^{30} +0.968597 q^{31} -2.52194 q^{32} +2.90717 q^{33} +6.57750 q^{34} -3.33400 q^{35} -0.455452 q^{36} -10.5381 q^{37} -2.32183 q^{38} -4.59254 q^{39} -10.1741 q^{40} +11.5606 q^{41} -1.24280 q^{42} +2.54868 q^{43} -1.32408 q^{44} -3.33400 q^{45} -6.25356 q^{46} +7.34702 q^{47} -2.88166 q^{48} +1.00000 q^{49} -7.60043 q^{50} -5.29249 q^{51} +2.09168 q^{52} -11.2837 q^{53} -1.24280 q^{54} -9.69250 q^{55} +3.05163 q^{56} +1.86822 q^{57} -4.59758 q^{58} -13.3410 q^{59} +1.51848 q^{60} +0.666722 q^{61} -1.20377 q^{62} +1.00000 q^{63} +8.89758 q^{64} +15.3116 q^{65} -3.61302 q^{66} -14.0335 q^{67} +2.41048 q^{68} +5.03184 q^{69} +4.14349 q^{70} +9.88541 q^{71} +3.05163 q^{72} -2.57222 q^{73} +13.0968 q^{74} +6.11557 q^{75} -0.850887 q^{76} +2.90717 q^{77} +5.70761 q^{78} +14.5706 q^{79} +9.60746 q^{80} +1.00000 q^{81} -14.3675 q^{82} +0.493442 q^{83} -0.455452 q^{84} +17.6452 q^{85} -3.16749 q^{86} +3.69938 q^{87} +8.87160 q^{88} +12.1652 q^{89} +4.14349 q^{90} -4.59254 q^{91} -2.29176 q^{92} +0.968597 q^{93} -9.13087 q^{94} -6.22866 q^{95} -2.52194 q^{96} -14.7006 q^{97} -1.24280 q^{98} +2.90717 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 2 q^{2} + 7 q^{3} + 4 q^{4} - 8 q^{5} - 2 q^{6} + 7 q^{7} - 9 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - 2 * q^2 + 7 * q^3 + 4 * q^4 - 8 * q^5 - 2 * q^6 + 7 * q^7 - 9 * q^8 + 7 * q^9	\( 7 q - 2 q^{2} + 7 q^{3} + 4 q^{4} - 8 q^{5} - 2 q^{6} + 7 q^{7} - 9 q^{8} + 7 q^{9} - 3 q^{11} + 4 q^{12} - 23 q^{13} - 2 q^{14} - 8 q^{15} + 2 q^{16} + 3 q^{17} - 2 q^{18} - 9 q^{19} - 9 q^{20} + 7 q^{21} - 19 q^{22} + 12 q^{23} - 9 q^{24} + 3 q^{25} + 18 q^{26} + 7 q^{27} + 4 q^{28} - 9 q^{29} - 33 q^{31} + 10 q^{32} - 3 q^{33} - 2 q^{34} - 8 q^{35} + 4 q^{36} - 33 q^{37} - 3 q^{38} - 23 q^{39} - 9 q^{40} - 3 q^{41} - 2 q^{42} - 9 q^{43} + 2 q^{44} - 8 q^{45} - 32 q^{46} + 11 q^{47} + 2 q^{48} + 7 q^{49} + 29 q^{50} + 3 q^{51} - 21 q^{52} + q^{53} - 2 q^{54} - 16 q^{55} - 9 q^{56} - 9 q^{57} - 5 q^{58} - 30 q^{59} - 9 q^{60} - 19 q^{61} + 3 q^{62} + 7 q^{63} - 21 q^{64} + 14 q^{65} - 19 q^{66} - 30 q^{67} + 24 q^{68} + 12 q^{69} + 8 q^{71} - 9 q^{72} - 20 q^{73} - 9 q^{74} + 3 q^{75} - 42 q^{76} - 3 q^{77} + 18 q^{78} + 8 q^{79} + 12 q^{80} + 7 q^{81} + 10 q^{82} - 34 q^{83} + 4 q^{84} - 28 q^{85} + 24 q^{86} - 9 q^{87} - q^{88} - 12 q^{89} - 23 q^{91} + 60 q^{92} - 33 q^{93} - 3 q^{94} + 12 q^{95} + 10 q^{96} + 7 q^{97} - 2 q^{98} - 3 q^{99}+O(q^{100}) \) 7 * q - 2 * q^2 + 7 * q^3 + 4 * q^4 - 8 * q^5 - 2 * q^6 + 7 * q^7 - 9 * q^8 + 7 * q^9 - 3 * q^11 + 4 * q^12 - 23 * q^13 - 2 * q^14 - 8 * q^15 + 2 * q^16 + 3 * q^17 - 2 * q^18 - 9 * q^19 - 9 * q^20 + 7 * q^21 - 19 * q^22 + 12 * q^23 - 9 * q^24 + 3 * q^25 + 18 * q^26 + 7 * q^27 + 4 * q^28 - 9 * q^29 - 33 * q^31 + 10 * q^32 - 3 * q^33 - 2 * q^34 - 8 * q^35 + 4 * q^36 - 33 * q^37 - 3 * q^38 - 23 * q^39 - 9 * q^40 - 3 * q^41 - 2 * q^42 - 9 * q^43 + 2 * q^44 - 8 * q^45 - 32 * q^46 + 11 * q^47 + 2 * q^48 + 7 * q^49 + 29 * q^50 + 3 * q^51 - 21 * q^52 + q^53 - 2 * q^54 - 16 * q^55 - 9 * q^56 - 9 * q^57 - 5 * q^58 - 30 * q^59 - 9 * q^60 - 19 * q^61 + 3 * q^62 + 7 * q^63 - 21 * q^64 + 14 * q^65 - 19 * q^66 - 30 * q^67 + 24 * q^68 + 12 * q^69 + 8 * q^71 - 9 * q^72 - 20 * q^73 - 9 * q^74 + 3 * q^75 - 42 * q^76 - 3 * q^77 + 18 * q^78 + 8 * q^79 + 12 * q^80 + 7 * q^81 + 10 * q^82 - 34 * q^83 + 4 * q^84 - 28 * q^85 + 24 * q^86 - 9 * q^87 - q^88 - 12 * q^89 - 23 * q^91 + 60 * q^92 - 33 * q^93 - 3 * q^94 + 12 * q^95 + 10 * q^96 + 7 * q^97 - 2 * q^98 - 3 * q^99

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