LMFDB - Embedded newform 2001.2.a.j.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2001,2,Mod(1,2001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2001, 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("2001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2001 = 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2001.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:	$15.9780654445$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 9x^{5} + 10x^{4} + 19x^{3} - 20x^{2} - 5x + 1 $ x^7 - x^6 - 9x^5 + 10x^4 + 19x^3 - 20x^2 - 5*x + 1
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			1.4
Root			$-1.64802$ of defining polynomial
Character	$\chi$	$=$	2001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.865893 q^{2} +1.00000 q^{3} -1.25023 q^{4} +1.66575 q^{5} -0.865893 q^{6} -0.715958 q^{7} +2.81435 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.865893 q^{2} +1.00000 q^{3} -1.25023 q^{4} +1.66575 q^{5} -0.865893 q^{6} -0.715958 q^{7} +2.81435 q^{8} +1.00000 q^{9} -1.44236 q^{10} -0.656890 q^{11} -1.25023 q^{12} -4.37251 q^{13} +0.619943 q^{14} +1.66575 q^{15} +0.0635329 q^{16} -7.15038 q^{17} -0.865893 q^{18} +6.56857 q^{19} -2.08256 q^{20} -0.715958 q^{21} +0.568796 q^{22} -1.00000 q^{23} +2.81435 q^{24} -2.22529 q^{25} +3.78613 q^{26} +1.00000 q^{27} +0.895112 q^{28} +1.00000 q^{29} -1.44236 q^{30} +0.705852 q^{31} -5.68371 q^{32} -0.656890 q^{33} +6.19146 q^{34} -1.19260 q^{35} -1.25023 q^{36} -7.06983 q^{37} -5.68768 q^{38} -4.37251 q^{39} +4.68799 q^{40} -12.6781 q^{41} +0.619943 q^{42} -2.05769 q^{43} +0.821263 q^{44} +1.66575 q^{45} +0.865893 q^{46} +8.50359 q^{47} +0.0635329 q^{48} -6.48740 q^{49} +1.92686 q^{50} -7.15038 q^{51} +5.46665 q^{52} +3.04227 q^{53} -0.865893 q^{54} -1.09421 q^{55} -2.01496 q^{56} +6.56857 q^{57} -0.865893 q^{58} -4.81329 q^{59} -2.08256 q^{60} +2.51798 q^{61} -0.611192 q^{62} -0.715958 q^{63} +4.79442 q^{64} -7.28350 q^{65} +0.568796 q^{66} -2.81077 q^{67} +8.93961 q^{68} -1.00000 q^{69} +1.03267 q^{70} +0.253574 q^{71} +2.81435 q^{72} +13.1983 q^{73} +6.12171 q^{74} -2.22529 q^{75} -8.21222 q^{76} +0.470305 q^{77} +3.78613 q^{78} +0.611697 q^{79} +0.105830 q^{80} +1.00000 q^{81} +10.9778 q^{82} +2.06729 q^{83} +0.895112 q^{84} -11.9107 q^{85} +1.78174 q^{86} +1.00000 q^{87} -1.84872 q^{88} -12.6267 q^{89} -1.44236 q^{90} +3.13054 q^{91} +1.25023 q^{92} +0.705852 q^{93} -7.36320 q^{94} +10.9416 q^{95} -5.68371 q^{96} -16.3343 q^{97} +5.61740 q^{98} -0.656890 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - q^{2} + 7 q^{3} + 7 q^{4} - 5 q^{5} - q^{6} - 5 q^{7} + 3 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - q^2 + 7 * q^3 + 7 * q^4 - 5 * q^5 - q^6 - 5 * q^7 + 3 * q^8 + 7 * q^9	\( 7 q - q^{2} + 7 q^{3} + 7 q^{4} - 5 q^{5} - q^{6} - 5 q^{7} + 3 q^{8} + 7 q^{9} - 11 q^{10} - 12 q^{11} + 7 q^{12} - 13 q^{13} - 3 q^{14} - 5 q^{15} - 13 q^{16} - 12 q^{17} - q^{18} - 5 q^{19} - 8 q^{20} - 5 q^{21} - q^{22} - 7 q^{23} + 3 q^{24} - 4 q^{25} + 2 q^{26} + 7 q^{27} - 21 q^{28} + 7 q^{29} - 11 q^{30} - 8 q^{31} - 5 q^{32} - 12 q^{33} - 28 q^{34} + 5 q^{35} + 7 q^{36} - 24 q^{37} - 6 q^{38} - 13 q^{39} - 20 q^{40} + 9 q^{41} - 3 q^{42} - q^{43} - 23 q^{44} - 5 q^{45} + q^{46} + 27 q^{47} - 13 q^{48} - 14 q^{49} + 7 q^{50} - 12 q^{51} - 9 q^{52} - q^{53} - q^{54} - 11 q^{55} - 20 q^{56} - 5 q^{57} - q^{58} + 8 q^{59} - 8 q^{60} + q^{61} - 5 q^{63} + 3 q^{64} + 12 q^{65} - q^{66} - 16 q^{67} + 15 q^{68} - 7 q^{69} + 40 q^{70} - 13 q^{71} + 3 q^{72} - 23 q^{73} - 8 q^{74} - 4 q^{75} - 2 q^{76} + 13 q^{77} + 2 q^{78} - 44 q^{79} + 30 q^{80} + 7 q^{81} - 10 q^{82} + 21 q^{83} - 21 q^{84} + 6 q^{86} + 7 q^{87} + 21 q^{88} - 5 q^{89} - 11 q^{90} - 18 q^{91} - 7 q^{92} - 8 q^{93} + 28 q^{94} + 9 q^{95} - 5 q^{96} - 55 q^{97} + 36 q^{98} - 12 q^{99}+O(q^{100}) \) 7 * q - q^2 + 7 * q^3 + 7 * q^4 - 5 * q^5 - q^6 - 5 * q^7 + 3 * q^8 + 7 * q^9 - 11 * q^10 - 12 * q^11 + 7 * q^12 - 13 * q^13 - 3 * q^14 - 5 * q^15 - 13 * q^16 - 12 * q^17 - q^18 - 5 * q^19 - 8 * q^20 - 5 * q^21 - q^22 - 7 * q^23 + 3 * q^24 - 4 * q^25 + 2 * q^26 + 7 * q^27 - 21 * q^28 + 7 * q^29 - 11 * q^30 - 8 * q^31 - 5 * q^32 - 12 * q^33 - 28 * q^34 + 5 * q^35 + 7 * q^36 - 24 * q^37 - 6 * q^38 - 13 * q^39 - 20 * q^40 + 9 * q^41 - 3 * q^42 - q^43 - 23 * q^44 - 5 * q^45 + q^46 + 27 * q^47 - 13 * q^48 - 14 * q^49 + 7 * q^50 - 12 * q^51 - 9 * q^52 - q^53 - q^54 - 11 * q^55 - 20 * q^56 - 5 * q^57 - q^58 + 8 * q^59 - 8 * q^60 + q^61 - 5 * q^63 + 3 * q^64 + 12 * q^65 - q^66 - 16 * q^67 + 15 * q^68 - 7 * q^69 + 40 * q^70 - 13 * q^71 + 3 * q^72 - 23 * q^73 - 8 * q^74 - 4 * q^75 - 2 * q^76 + 13 * q^77 + 2 * q^78 - 44 * q^79 + 30 * q^80 + 7 * q^81 - 10 * q^82 + 21 * q^83 - 21 * q^84 + 6 * q^86 + 7 * q^87 + 21 * q^88 - 5 * q^89 - 11 * q^90 - 18 * q^91 - 7 * q^92 - 8 * q^93 + 28 * q^94 + 9 * q^95 - 5 * q^96 - 55 * q^97 + 36 * 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 $

$2$	−0.865893	−0.612279	−0.306139	−	0.951987i	$-0.599037\pi$
$2$	−0.865893	−0.612279	−0.306139	+	0.951987i	$0.599037\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.25023	−0.625115
$5$	1.66575	0.744944	0.372472	−	0.928043i	$-0.378510\pi$
$5$	1.66575	0.744944	0.372472	+	0.928043i	$0.378510\pi$
$6$	−0.865893	−0.353499
$7$	−0.715958	−0.270607	−0.135303	−	0.990804i	$-0.543201\pi$
$7$	−0.715958	−0.270607	−0.135303	+	0.990804i	$0.543201\pi$
$8$	2.81435	0.995023
$9$	1.00000	0.333333
$10$	−1.44236	−0.456114
$11$	−0.656890	−0.198060	−0.0990298	−	0.995084i	$-0.531574\pi$
$11$	−0.656890	−0.198060	−0.0990298	+	0.995084i	$0.531574\pi$
$12$	−1.25023	−0.360910
$13$	−4.37251	−1.21272	−0.606359	−	0.795191i	$-0.707370\pi$
$13$	−4.37251	−1.21272	−0.606359	+	0.795191i	$0.707370\pi$
$14$	0.619943	0.165687
$15$	1.66575	0.430094
$16$	0.0635329	0.0158832
$17$	−7.15038	−1.73422	−0.867111	−	0.498116i	$-0.834025\pi$
$17$	−7.15038	−1.73422	−0.867111	+	0.498116i	$0.834025\pi$
$18$	−0.865893	−0.204093
$19$	6.56857	1.50693	0.753467	−	0.657486i	$-0.228380\pi$
$19$	6.56857	1.50693	0.753467	+	0.657486i	$0.228380\pi$
$20$	−2.08256	−0.465676
$21$	−0.715958	−0.156235
$22$	0.568796	0.121268
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	2.81435	0.574477
$25$	−2.22529	−0.445058
$26$	3.78613	0.742521
$27$	1.00000	0.192450
$28$	0.895112	0.169160
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−1.44236	−0.263337
$31$	0.705852	0.126775	0.0633874	−	0.997989i	$-0.479810\pi$
$31$	0.705852	0.126775	0.0633874	+	0.997989i	$0.479810\pi$
$32$	−5.68371	−1.00475
$33$	−0.656890	−0.114350
$34$	6.19146	1.06183
$35$	−1.19260	−0.201587
$36$	−1.25023	−0.208372
$37$	−7.06983	−1.16227	−0.581136	−	0.813806i	$-0.697392\pi$
$37$	−7.06983	−1.16227	−0.581136	+	0.813806i	$0.697392\pi$
$38$	−5.68768	−0.922663
$39$	−4.37251	−0.700163
$40$	4.68799	0.741237
$41$	−12.6781	−1.97998	−0.989990	−	0.141139i	$-0.954924\pi$
$41$	−12.6781	−1.97998	−0.989990	+	0.141139i	$0.954924\pi$
$42$	0.619943	0.0956593
$43$	−2.05769	−0.313794	−0.156897	−	0.987615i	$-0.550149\pi$
$43$	−2.05769	−0.313794	−0.156897	+	0.987615i	$0.550149\pi$
$44$	0.821263	0.123810
$45$	1.66575	0.248315
$46$	0.865893	0.127669
$47$	8.50359	1.24038	0.620188	−	0.784453i	$-0.287056\pi$
$47$	8.50359	1.24038	0.620188	+	0.784453i	$0.287056\pi$
$48$	0.0635329	0.00917018
$49$	−6.48740	−0.926772
$50$	1.92686	0.272500
$51$	−7.15038	−1.00125
$52$	5.46665	0.758087
$53$	3.04227	0.417888	0.208944	−	0.977928i	$-0.432997\pi$
$53$	3.04227	0.417888	0.208944	+	0.977928i	$0.432997\pi$
$54$	−0.865893	−0.117833
$55$	−1.09421	−0.147543
$56$	−2.01496	−0.269260
$57$	6.56857	0.870028
$58$	−0.865893	−0.113697
$59$	−4.81329	−0.626637	−0.313318	−	0.949648i	$-0.601441\pi$
$59$	−4.81329	−0.626637	−0.313318	+	0.949648i	$0.601441\pi$
$60$	−2.08256	−0.268858
$61$	2.51798	0.322395	0.161197	−	0.986922i	$-0.448464\pi$
$61$	2.51798	0.322395	0.161197	+	0.986922i	$0.448464\pi$
$62$	−0.611192	−0.0776215
$63$	−0.715958	−0.0902022
$64$	4.79442	0.599303
$65$	−7.28350	−0.903407
$66$	0.568796	0.0700140
$67$	−2.81077	−0.343390	−0.171695	−	0.985150i	$-0.554924\pi$
$67$	−2.81077	−0.343390	−0.171695	+	0.985150i	$0.554924\pi$
$68$	8.93961	1.08409
$69$	−1.00000	−0.120386
$70$	1.03267	0.123427
$71$	0.253574	0.0300937	0.0150469	−	0.999887i	$-0.495210\pi$
$71$	0.253574	0.0300937	0.0150469	+	0.999887i	$0.495210\pi$
$72$	2.81435	0.331674
$73$	13.1983	1.54475	0.772374	−	0.635168i	$-0.219069\pi$
$73$	13.1983	1.54475	0.772374	+	0.635168i	$0.219069\pi$
$74$	6.12171	0.711635
$75$	−2.22529	−0.256954
$76$	−8.21222	−0.942006
$77$	0.470305	0.0535963
$78$	3.78613	0.428695
$79$	0.611697	0.0688213	0.0344106	−	0.999408i	$-0.489045\pi$
$79$	0.611697	0.0688213	0.0344106	+	0.999408i	$0.489045\pi$
$80$	0.105830	0.0118321
$81$	1.00000	0.111111
$82$	10.9778	1.21230
$83$	2.06729	0.226915	0.113457	−	0.993543i	$-0.463807\pi$
$83$	2.06729	0.226915	0.113457	+	0.993543i	$0.463807\pi$
$84$	0.895112	0.0976647
$85$	−11.9107	−1.29190
$86$	1.78174	0.192130
$87$	1.00000	0.107211
$88$	−1.84872	−0.197074
$89$	−12.6267	−1.33842	−0.669212	−	0.743071i	$-0.733368\pi$
$89$	−12.6267	−1.33842	−0.669212	+	0.743071i	$0.733368\pi$
$90$	−1.44236	−0.152038
$91$	3.13054	0.328169
$92$	1.25023	0.130345
$93$	0.705852	0.0731935
$94$	−7.36320	−0.759456
$95$	10.9416	1.12258
$96$	−5.68371	−0.580092
$97$	−16.3343	−1.65850	−0.829248	−	0.558881i	$-0.811231\pi$
$97$	−16.3343	−1.65850	−0.829248	+	0.558881i	$0.811231\pi$
$98$	5.61740	0.567443
$99$	−0.656890	−0.0660199
$100$	2.78212	0.278212
$101$	−0.174650	−0.0173784	−0.00868919	−	0.999962i	$-0.502766\pi$
$101$	−0.174650	−0.0173784	−0.00868919	+	0.999962i	$0.502766\pi$
$102$	6.19146	0.613046
$103$	1.40140	0.138084	0.0690419	−	0.997614i	$-0.478006\pi$
$103$	1.40140	0.138084	0.0690419	+	0.997614i	$0.478006\pi$
$104$	−12.3058	−1.20668
$105$	−1.19260	−0.116386
$106$	−2.63428	−0.255864
$107$	8.77557	0.848366	0.424183	−	0.905576i	$-0.360561\pi$
$107$	8.77557	0.848366	0.424183	+	0.905576i	$0.360561\pi$
$108$	−1.25023	−0.120303
$109$	−9.29618	−0.890413	−0.445206	−	0.895428i	$-0.646870\pi$
$109$	−9.29618	−0.890413	−0.445206	+	0.895428i	$0.646870\pi$
$110$	0.947470	0.0903377
$111$	−7.06983	−0.671038
$112$	−0.0454869	−0.00429810
$113$	11.1470	1.04862	0.524312	−	0.851527i	$-0.324323\pi$
$113$	11.1470	1.04862	0.524312	+	0.851527i	$0.324323\pi$
$114$	−5.68768	−0.532700
$115$	−1.66575	−0.155332
$116$	−1.25023	−0.116081
$117$	−4.37251	−0.404239
$118$	4.16779	0.383676
$119$	5.11937	0.469292
$120$	4.68799	0.427953
$121$	−10.5685	−0.960772
$122$	−2.18031	−0.197396
$123$	−12.6781	−1.14314
$124$	−0.882477	−0.0792488
$125$	−12.0355	−1.07649
$126$	0.619943	0.0552289
$127$	−21.2129	−1.88234	−0.941171	−	0.337932i	$-0.890273\pi$
$127$	−21.2129	−1.88234	−0.941171	+	0.337932i	$0.890273\pi$
$128$	7.21597	0.637808
$129$	−2.05769	−0.181169
$130$	6.30673	0.553137
$131$	−19.0666	−1.66586	−0.832928	−	0.553381i	$-0.813337\pi$
$131$	−19.0666	−1.66586	−0.832928	+	0.553381i	$0.813337\pi$
$132$	0.821263	0.0714818
$133$	−4.70282	−0.407786
$134$	2.43382	0.210250
$135$	1.66575	0.143365
$136$	−20.1237	−1.72559
$137$	11.5218	0.984370	0.492185	−	0.870491i	$-0.336198\pi$
$137$	11.5218	0.984370	0.492185	+	0.870491i	$0.336198\pi$
$138$	0.865893	0.0737097
$139$	0.933345	0.0791653	0.0395826	−	0.999216i	$-0.487397\pi$
$139$	0.933345	0.0791653	0.0395826	+	0.999216i	$0.487397\pi$
$140$	1.49103	0.126015
$141$	8.50359	0.716132
$142$	−0.219568	−0.0184257
$143$	2.87226	0.240190
$144$	0.0635329	0.00529440
$145$	1.66575	0.138333
$146$	−11.4283	−0.945816
$147$	−6.48740	−0.535072
$148$	8.83891	0.726554
$149$	9.85776	0.807579	0.403790	−	0.914852i	$-0.367693\pi$
$149$	9.85776	0.807579	0.403790	+	0.914852i	$0.367693\pi$
$150$	1.92686	0.157328
$151$	−14.4385	−1.17499	−0.587495	−	0.809228i	$-0.699886\pi$
$151$	−14.4385	−1.17499	−0.587495	+	0.809228i	$0.699886\pi$
$152$	18.4863	1.49943
$153$	−7.15038	−0.578074
$154$	−0.407234	−0.0328159
$155$	1.17577	0.0944402
$156$	5.46665	0.437682
$157$	−5.07449	−0.404988	−0.202494	−	0.979283i	$-0.564905\pi$
$157$	−5.07449	−0.404988	−0.202494	+	0.979283i	$0.564905\pi$
$158$	−0.529664	−0.0421378
$159$	3.04227	0.241268
$160$	−9.46762	−0.748481
$161$	0.715958	0.0564254
$162$	−0.865893	−0.0680310
$163$	−9.44012	−0.739407	−0.369704	−	0.929150i	$-0.620541\pi$
$163$	−9.44012	−0.739407	−0.369704	+	0.929150i	$0.620541\pi$
$164$	15.8505	1.23771
$165$	−1.09421	−0.0851842
$166$	−1.79005	−0.138935
$167$	20.7134	1.60285	0.801426	−	0.598094i	$-0.204075\pi$
$167$	20.7134	1.60285	0.801426	+	0.598094i	$0.204075\pi$
$168$	−2.01496	−0.155457
$169$	6.11888	0.470683
$170$	10.3134	0.791002
$171$	6.56857	0.502311
$172$	2.57258	0.196158
$173$	4.97238	0.378043	0.189022	−	0.981973i	$-0.439468\pi$
$173$	4.97238	0.378043	0.189022	+	0.981973i	$0.439468\pi$
$174$	−0.865893	−0.0656432
$175$	1.59321	0.120436
$176$	−0.0417341	−0.00314582
$177$	−4.81329	−0.361789
$178$	10.9333	0.819489
$179$	−21.5558	−1.61116	−0.805578	−	0.592490i	$-0.798145\pi$
$179$	−21.5558	−1.61116	−0.805578	+	0.592490i	$0.798145\pi$
$180$	−2.08256	−0.155225
$181$	−20.0768	−1.49230	−0.746150	−	0.665778i	$-0.768100\pi$
$181$	−20.0768	−1.49230	−0.746150	+	0.665778i	$0.768100\pi$
$182$	−2.71071	−0.200931
$183$	2.51798	0.186135
$184$	−2.81435	−0.207477
$185$	−11.7765	−0.865828
$186$	−0.611192	−0.0448148
$187$	4.69701	0.343479
$188$	−10.6314	−0.775378
$189$	−0.715958	−0.0520783
$190$	−9.47423	−0.687333
$191$	0.833088	0.0602801	0.0301401	−	0.999546i	$-0.490405\pi$
$191$	0.833088	0.0602801	0.0301401	+	0.999546i	$0.490405\pi$
$192$	4.79442	0.346008
$193$	10.9407	0.787532	0.393766	−	0.919211i	$-0.371172\pi$
$193$	10.9407	0.787532	0.393766	+	0.919211i	$0.371172\pi$
$194$	14.1437	1.01546
$195$	−7.28350	−0.521582
$196$	8.11074	0.579339
$197$	0.438846	0.0312665	0.0156332	−	0.999878i	$-0.495024\pi$
$197$	0.438846	0.0312665	0.0156332	+	0.999878i	$0.495024\pi$
$198$	0.568796	0.0404226
$199$	−5.39837	−0.382680	−0.191340	−	0.981524i	$-0.561283\pi$
$199$	−5.39837	−0.382680	−0.191340	+	0.981524i	$0.561283\pi$
$200$	−6.26275	−0.442843
$201$	−2.81077	−0.198256
$202$	0.151229	0.0106404
$203$	−0.715958	−0.0502504
$204$	8.93961	0.625898
$205$	−21.1184	−1.47497
$206$	−1.21346	−0.0845457
$207$	−1.00000	−0.0695048
$208$	−0.277798	−0.0192618
$209$	−4.31482	−0.298463
$210$	1.03267	0.0712608
$211$	−11.8593	−0.816425	−0.408212	−	0.912887i	$-0.633848\pi$
$211$	−11.8593	−0.816425	−0.408212	+	0.912887i	$0.633848\pi$
$212$	−3.80354	−0.261228
$213$	0.253574	0.0173746
$214$	−7.59870	−0.519436
$215$	−3.42759	−0.233759
$216$	2.81435	0.191492
$217$	−0.505360	−0.0343061
$218$	8.04950	0.545181
$219$	13.1983	0.891861
$220$	1.36802	0.0922316
$221$	31.2651	2.10312
$222$	6.12171	0.410862
$223$	−17.6698	−1.18325	−0.591627	−	0.806212i	$-0.701514\pi$
$223$	−17.6698	−1.18325	−0.591627	+	0.806212i	$0.701514\pi$
$224$	4.06930	0.271892
$225$	−2.22529	−0.148353
$226$	−9.65212	−0.642050
$227$	19.2183	1.27556	0.637782	−	0.770217i	$-0.279852\pi$
$227$	19.2183	1.27556	0.637782	+	0.770217i	$0.279852\pi$
$228$	−8.21222	−0.543867
$229$	0.0207973	0.00137433	0.000687163	−	1.00000i	$-0.499781\pi$
$229$	0.0207973	0.00137433	0.000687163		1.00000i	$0.499781\pi$
$230$	1.44236	0.0951062
$231$	0.470305	0.0309438
$232$	2.81435	0.184771
$233$	10.5644	0.692095	0.346048	−	0.938217i	$-0.387524\pi$
$233$	10.5644	0.692095	0.346048	+	0.938217i	$0.387524\pi$
$234$	3.78613	0.247507
$235$	14.1648	0.924011
$236$	6.01771	0.391720
$237$	0.611697	0.0397340
$238$	−4.43283	−0.287337
$239$	1.89477	0.122562	0.0612812	−	0.998121i	$-0.480481\pi$
$239$	1.89477	0.122562	0.0612812	+	0.998121i	$0.480481\pi$
$240$	0.105830	0.00683127
$241$	2.61371	0.168364	0.0841820	−	0.996450i	$-0.473172\pi$
$241$	2.61371	0.168364	0.0841820	+	0.996450i	$0.473172\pi$
$242$	9.15119	0.588260
$243$	1.00000	0.0641500
$244$	−3.14806	−0.201534
$245$	−10.8064	−0.690394
$246$	10.9778	0.699921
$247$	−28.7212	−1.82748
$248$	1.98652	0.126144
$249$	2.06729	0.131009
$250$	10.4215	0.659111
$251$	−14.8239	−0.935674	−0.467837	−	0.883815i	$-0.654967\pi$
$251$	−14.8239	−0.935674	−0.467837	+	0.883815i	$0.654967\pi$
$252$	0.895112	0.0563867
$253$	0.656890	0.0412983
$254$	18.3681	1.15252
$255$	−11.9107	−0.745878
$256$	−15.8371	−0.989819
$257$	6.92245	0.431810	0.215905	−	0.976414i	$-0.430730\pi$
$257$	6.92245	0.431810	0.215905	+	0.976414i	$0.430730\pi$
$258$	1.78174	0.110926
$259$	5.06170	0.314519
$260$	9.10604	0.564733
$261$	1.00000	0.0618984
$262$	16.5096	1.01997
$263$	−0.368207	−0.0227046	−0.0113523	−	0.999936i	$-0.503614\pi$
$263$	−0.368207	−0.0227046	−0.0113523	+	0.999936i	$0.503614\pi$
$264$	−1.84872	−0.113781
$265$	5.06766	0.311304
$266$	4.07214	0.249679
$267$	−12.6267	−0.772740
$268$	3.51410	0.214658
$269$	−7.66062	−0.467076	−0.233538	−	0.972348i	$-0.575030\pi$
$269$	−7.66062	−0.467076	−0.233538	+	0.972348i	$0.575030\pi$
$270$	−1.44236	−0.0877791
$271$	20.2402	1.22951	0.614753	−	0.788719i	$-0.289256\pi$
$271$	20.2402	1.22951	0.614753	+	0.788719i	$0.289256\pi$
$272$	−0.454284	−0.0275450
$273$	3.13054	0.189469
$274$	−9.97660	−0.602709
$275$	1.46177	0.0881480
$276$	1.25023	0.0752550
$277$	31.4385	1.88896	0.944479	−	0.328572i	$-0.106567\pi$
$277$	31.4385	1.88896	0.944479	+	0.328572i	$0.106567\pi$
$278$	−0.808176	−0.0484712
$279$	0.705852	0.0422583
$280$	−3.35641	−0.200584
$281$	−2.99818	−0.178856	−0.0894281	−	0.995993i	$-0.528504\pi$
$281$	−2.99818	−0.178856	−0.0894281	+	0.995993i	$0.528504\pi$
$282$	−7.36320	−0.438472
$283$	−25.4423	−1.51239	−0.756193	−	0.654348i	$-0.772943\pi$
$283$	−25.4423	−1.51239	−0.756193	+	0.654348i	$0.772943\pi$
$284$	−0.317026	−0.0188120
$285$	10.9416	0.648123
$286$	−2.48707	−0.147063
$287$	9.07695	0.535796
$288$	−5.68371	−0.334916
$289$	34.1279	2.00752
$290$	−1.44236	−0.0846982
$291$	−16.3343	−0.957533
$292$	−16.5009	−0.965645
$293$	−24.9329	−1.45659	−0.728297	−	0.685261i	$-0.759688\pi$
$293$	−24.9329	−1.45659	−0.728297	+	0.685261i	$0.759688\pi$
$294$	5.61740	0.327613
$295$	−8.01771	−0.466809
$296$	−19.8970	−1.15649
$297$	−0.656890	−0.0381166
$298$	−8.53577	−0.494464
$299$	4.37251	0.252869
$300$	2.78212	0.160626
$301$	1.47322	0.0849149
$302$	12.5022	0.719421
$303$	−0.174650	−0.0100334
$304$	0.417320	0.0239349
$305$	4.19432	0.240166
$306$	6.19146	0.353942
$307$	7.48358	0.427111	0.213555	−	0.976931i	$-0.431496\pi$
$307$	7.48358	0.427111	0.213555	+	0.976931i	$0.431496\pi$
$308$	−0.587990	−0.0335038
$309$	1.40140	0.0797227
$310$	−1.01809	−0.0578237
$311$	7.32248	0.415220	0.207610	−	0.978212i	$-0.433432\pi$
$311$	7.32248	0.415220	0.207610	+	0.978212i	$0.433432\pi$
$312$	−12.3058	−0.696678
$313$	32.0436	1.81121	0.905605	−	0.424122i	$-0.139417\pi$
$313$	32.0436	1.81121	0.905605	+	0.424122i	$0.139417\pi$
$314$	4.39396	0.247966
$315$	−1.19260	−0.0671956
$316$	−0.764761	−0.0430212
$317$	17.6048	0.988784	0.494392	−	0.869239i	$-0.335391\pi$
$317$	17.6048	0.988784	0.494392	+	0.869239i	$0.335391\pi$
$318$	−2.63428	−0.147723
$319$	−0.656890	−0.0367788
$320$	7.98629	0.446447
$321$	8.77557	0.489804
$322$	−0.619943	−0.0345481
$323$	−46.9677	−2.61336
$324$	−1.25023	−0.0694572
$325$	9.73011	0.539730
$326$	8.17413	0.452723
$327$	−9.29618	−0.514080
$328$	−35.6805	−1.97013
$329$	−6.08821	−0.335654
$330$	0.947470	0.0521565
$331$	−21.2917	−1.17030	−0.585148	−	0.810927i	$-0.698963\pi$
$331$	−21.2917	−1.17030	−0.585148	+	0.810927i	$0.698963\pi$
$332$	−2.58459	−0.141848
$333$	−7.06983	−0.387424
$334$	−17.9356	−0.981392
$335$	−4.68203	−0.255806
$336$	−0.0454869	−0.00248151
$337$	15.5478	0.846941	0.423470	−	0.905910i	$-0.360812\pi$
$337$	15.5478	0.846941	0.423470	+	0.905910i	$0.360812\pi$
$338$	−5.29830	−0.288189
$339$	11.1470	0.605423
$340$	14.8911	0.807585
$341$	−0.463667	−0.0251090
$342$	−5.68768	−0.307554
$343$	9.65641	0.521397
$344$	−5.79105	−0.312233
$345$	−1.66575	−0.0896808
$346$	−4.30555	−0.231468
$347$	12.8576	0.690230	0.345115	−	0.938560i	$-0.387840\pi$
$347$	12.8576	0.690230	0.345115	+	0.938560i	$0.387840\pi$
$348$	−1.25023	−0.0670193
$349$	24.0074	1.28509	0.642544	−	0.766249i	$-0.277879\pi$
$349$	24.0074	1.28509	0.642544	+	0.766249i	$0.277879\pi$
$350$	−1.37955	−0.0737402
$351$	−4.37251	−0.233388
$352$	3.73357	0.199000
$353$	−9.74926	−0.518901	−0.259450	−	0.965756i	$-0.583541\pi$
$353$	−9.74926	−0.518901	−0.259450	+	0.965756i	$0.583541\pi$
$354$	4.16779	0.221516
$355$	0.422390	0.0224181
$356$	15.7862	0.836669
$357$	5.11937	0.270946
$358$	18.6650	0.986477
$359$	−3.66746	−0.193561	−0.0967806	−	0.995306i	$-0.530855\pi$
$359$	−3.66746	−0.193561	−0.0967806	+	0.995306i	$0.530855\pi$
$360$	4.68799	0.247079
$361$	24.1461	1.27085
$362$	17.3844	0.913703
$363$	−10.5685	−0.554702
$364$	−3.91389	−0.205144
$365$	21.9851	1.15075
$366$	−2.18031	−0.113966
$367$	2.11364	0.110331	0.0551657	−	0.998477i	$-0.482431\pi$
$367$	2.11364	0.110331	0.0551657	+	0.998477i	$0.482431\pi$
$368$	−0.0635329	−0.00331188
$369$	−12.6781	−0.659993
$370$	10.1972	0.530128
$371$	−2.17814	−0.113083
$372$	−0.882477	−0.0457543
$373$	−11.8307	−0.612568	−0.306284	−	0.951940i	$-0.599086\pi$
$373$	−11.8307	−0.612568	−0.306284	+	0.951940i	$0.599086\pi$
$374$	−4.06711	−0.210305
$375$	−12.0355	−0.621510
$376$	23.9321	1.23420
$377$	−4.37251	−0.225196
$378$	0.619943	0.0318864
$379$	−12.2695	−0.630239	−0.315120	−	0.949052i	$-0.602045\pi$
$379$	−12.2695	−0.630239	−0.315120	+	0.949052i	$0.602045\pi$
$380$	−13.6795	−0.701742
$381$	−21.2129	−1.08677
$382$	−0.721365	−0.0369082
$383$	−18.8237	−0.961846	−0.480923	−	0.876763i	$-0.659698\pi$
$383$	−18.8237	−0.961846	−0.480923	+	0.876763i	$0.659698\pi$
$384$	7.21597	0.368239
$385$	0.783409	0.0399262
$386$	−9.47351	−0.482189
$387$	−2.05769	−0.104598
$388$	20.4216	1.03675
$389$	−0.609090	−0.0308821	−0.0154410	−	0.999881i	$-0.504915\pi$
$389$	−0.609090	−0.0308821	−0.0154410	+	0.999881i	$0.504915\pi$
$390$	6.30673	0.319354
$391$	7.15038	0.361610
$392$	−18.2578	−0.922160
$393$	−19.0666	−0.961783
$394$	−0.379994	−0.0191438
$395$	1.01893	0.0512680
$396$	0.821263	0.0412700
$397$	−8.50375	−0.426791	−0.213396	−	0.976966i	$-0.568452\pi$
$397$	−8.50375	−0.426791	−0.213396	+	0.976966i	$0.568452\pi$
$398$	4.67441	0.234307
$399$	−4.70282	−0.235435
$400$	−0.141379	−0.00706895
$401$	38.0500	1.90012	0.950062	−	0.312060i	$-0.101019\pi$
$401$	38.0500	1.90012	0.950062	+	0.312060i	$0.101019\pi$
$402$	2.43382	0.121388
$403$	−3.08635	−0.153742
$404$	0.218353	0.0108635
$405$	1.66575	0.0827716
$406$	0.619943	0.0307672
$407$	4.64410	0.230199
$408$	−20.1237	−0.996270
$409$	15.1451	0.748878	0.374439	−	0.927251i	$-0.377835\pi$
$409$	15.1451	0.748878	0.374439	+	0.927251i	$0.377835\pi$
$410$	18.2863	0.903096
$411$	11.5218	0.568326
$412$	−1.75207	−0.0863182
$413$	3.44611	0.169572
$414$	0.865893	0.0425563
$415$	3.44358	0.169039
$416$	24.8521	1.21848
$417$	0.933345	0.0457061
$418$	3.73618	0.182742
$419$	19.6534	0.960133	0.480067	−	0.877232i	$-0.340612\pi$
$419$	19.6534	0.960133	0.480067	+	0.877232i	$0.340612\pi$
$420$	1.49103	0.0727548
$421$	−26.7076	−1.30165	−0.650824	−	0.759228i	$-0.725577\pi$
$421$	−26.7076	−1.30165	−0.650824	+	0.759228i	$0.725577\pi$
$422$	10.2688	0.499879
$423$	8.50359	0.413459
$424$	8.56202	0.415809
$425$	15.9117	0.771829
$426$	−0.219568	−0.0106381
$427$	−1.80277	−0.0872422
$428$	−10.9715	−0.530326
$429$	2.87226	0.138674
$430$	2.96792	0.143126
$431$	−33.5313	−1.61514	−0.807572	−	0.589768i	$-0.799219\pi$
$431$	−33.5313	−1.61514	−0.807572	+	0.589768i	$0.799219\pi$
$432$	0.0635329	0.00305673
$433$	24.5137	1.17805	0.589026	−	0.808114i	$-0.299512\pi$
$433$	24.5137	1.17805	0.589026	+	0.808114i	$0.299512\pi$
$434$	0.437588	0.0210049
$435$	1.66575	0.0798664
$436$	11.6224	0.556610
$437$	−6.56857	−0.314217
$438$	−11.4283	−0.546067
$439$	13.7324	0.655410	0.327705	−	0.944780i	$-0.393725\pi$
$439$	13.7324	0.655410	0.327705	+	0.944780i	$0.393725\pi$
$440$	−3.07949	−0.146809
$441$	−6.48740	−0.308924
$442$	−27.0723	−1.28770
$443$	31.3119	1.48767	0.743837	−	0.668361i	$-0.233004\pi$
$443$	31.3119	1.48767	0.743837	+	0.668361i	$0.233004\pi$
$444$	8.83891	0.419476
$445$	−21.0328	−0.997052
$446$	15.3001	0.724481
$447$	9.85776	0.466256
$448$	−3.43260	−0.162175
$449$	8.62460	0.407020	0.203510	−	0.979073i	$-0.434765\pi$
$449$	8.62460	0.407020	0.203510	+	0.979073i	$0.434765\pi$
$450$	1.92686	0.0908332
$451$	8.32808	0.392154
$452$	−13.9363	−0.655510
$453$	−14.4385	−0.678381
$454$	−16.6410	−0.781001
$455$	5.21468	0.244468
$456$	18.4863	0.865698
$457$	−29.4709	−1.37859	−0.689295	−	0.724481i	$-0.742080\pi$
$457$	−29.4709	−1.37859	−0.689295	+	0.724481i	$0.742080\pi$
$458$	−0.0180083	−0.000841470 0
$459$	−7.15038	−0.333751
$460$	2.08256	0.0971001
$461$	40.0274	1.86426	0.932132	−	0.362120i	$-0.117947\pi$
$461$	40.0274	1.86426	0.932132	+	0.362120i	$0.117947\pi$
$462$	−0.407234	−0.0189462
$463$	−30.9773	−1.43964	−0.719819	−	0.694162i	$-0.755775\pi$
$463$	−30.9773	−1.43964	−0.719819	+	0.694162i	$0.755775\pi$
$464$	0.0635329	0.00294944
$465$	1.17577	0.0545251
$466$	−9.14762	−0.423755
$467$	32.6472	1.51073	0.755367	−	0.655302i	$-0.227459\pi$
$467$	32.6472	1.51073	0.755367	+	0.655302i	$0.227459\pi$
$468$	5.46665	0.252696
$469$	2.01239	0.0929236
$470$	−12.2652	−0.565753
$471$	−5.07449	−0.233820
$472$	−13.5463	−0.623518
$473$	1.35167	0.0621500
$474$	−0.529664	−0.0243283
$475$	−14.6170	−0.670673
$476$	−6.40039	−0.293361
$477$	3.04227	0.139296
$478$	−1.64067	−0.0750424
$479$	10.2273	0.467298	0.233649	−	0.972321i	$-0.424933\pi$
$479$	10.2273	0.467298	0.233649	+	0.972321i	$0.424933\pi$
$480$	−9.46762	−0.432136
$481$	30.9129	1.40951
$482$	−2.26319	−0.103086
$483$	0.715958	0.0325772
$484$	13.2130	0.600593
$485$	−27.2088	−1.23549
$486$	−0.865893	−0.0392777
$487$	15.4717	0.701089	0.350544	−	0.936546i	$-0.385997\pi$
$487$	15.4717	0.701089	0.350544	+	0.936546i	$0.385997\pi$
$488$	7.08649	0.320790
$489$	−9.44012	−0.426897
$490$	9.35716	0.422713
$491$	17.4990	0.789718	0.394859	−	0.918742i	$-0.370793\pi$
$491$	17.4990	0.789718	0.394859	+	0.918742i	$0.370793\pi$
$492$	15.8505	0.714595
$493$	−7.15038	−0.322037
$494$	24.8694	1.11893
$495$	−1.09421	−0.0491811
$496$	0.0448448	0.00201359
$497$	−0.181548	−0.00814356
$498$	−1.79005	−0.0802142
$499$	17.6612	0.790625	0.395312	−	0.918547i	$-0.370636\pi$
$499$	17.6612	0.790625	0.395312	+	0.918547i	$0.370636\pi$
$500$	15.0471	0.672928
$501$	20.7134	0.925407
$502$	12.8359	0.572893
$503$	20.1271	0.897424	0.448712	−	0.893677i	$-0.351883\pi$
$503$	20.1271	0.897424	0.448712	+	0.893677i	$0.351883\pi$
$504$	−2.01496	−0.0897533
$505$	−0.290923	−0.0129459
$506$	−0.568796	−0.0252861
$507$	6.11888	0.271749
$508$	26.5210	1.17668
$509$	−17.3554	−0.769266	−0.384633	−	0.923070i	$-0.625672\pi$
$509$	−17.3554	−0.769266	−0.384633	+	0.923070i	$0.625672\pi$
$510$	10.3134	0.456685
$511$	−9.44945	−0.418019
$512$	−0.718710	−0.0317628
$513$	6.56857	0.290009
$514$	−5.99410	−0.264388
$515$	2.33437	0.102865
$516$	2.57258	0.113252
$517$	−5.58592	−0.245669
$518$	−4.38289	−0.192573
$519$	4.97238	0.218263
$520$	−20.4983	−0.898911
$521$	19.9195	0.872690	0.436345	−	0.899779i	$-0.356273\pi$
$521$	19.9195	0.872690	0.436345	+	0.899779i	$0.356273\pi$
$522$	−0.865893	−0.0378991
$523$	−3.54078	−0.154827	−0.0774136	−	0.996999i	$-0.524666\pi$
$523$	−3.54078	−0.154827	−0.0774136	+	0.996999i	$0.524666\pi$
$524$	23.8376	1.04135
$525$	1.59321	0.0695336
$526$	0.318828	0.0139016
$527$	−5.04711	−0.219856
$528$	−0.0417341	−0.00181624
$529$	1.00000	0.0434783
$530$	−4.38805	−0.190605
$531$	−4.81329	−0.208879
$532$	5.87960	0.254913
$533$	55.4350	2.40116
$534$	10.9333	0.473132
$535$	14.6179	0.631985
$536$	−7.91049	−0.341681
$537$	−21.5558	−0.930202
$538$	6.63327	0.285981
$539$	4.26151	0.183556
$540$	−2.08256	−0.0896193
$541$	−34.2816	−1.47388	−0.736941	−	0.675957i	$-0.763731\pi$
$541$	−34.2816	−1.47388	−0.736941	+	0.675957i	$0.763731\pi$
$542$	−17.5259	−0.752801
$543$	−20.0768	−0.861580
$544$	40.6407	1.74246
$545$	−15.4851	−0.663308
$546$	−2.71071	−0.116008
$547$	−2.28458	−0.0976815	−0.0488407	−	0.998807i	$-0.515553\pi$
$547$	−2.28458	−0.0976815	−0.0488407	+	0.998807i	$0.515553\pi$
$548$	−14.4048	−0.615344
$549$	2.51798	0.107465
$550$	−1.26574	−0.0539712
$551$	6.56857	0.279830
$552$	−2.81435	−0.119787
$553$	−0.437949	−0.0186235
$554$	−27.2224	−1.15657
$555$	−11.7765	−0.499886
$556$	−1.16690	−0.0494874
$557$	27.4491	1.16306	0.581528	−	0.813526i	$-0.302455\pi$
$557$	27.4491	1.16306	0.581528	+	0.813526i	$0.302455\pi$
$558$	−0.611192	−0.0258738
$559$	8.99727	0.380544
$560$	−0.0757695	−0.00320185
$561$	4.69701	0.198308
$562$	2.59610	0.109510
$563$	35.1985	1.48344	0.741719	−	0.670710i	$-0.234011\pi$
$563$	35.1985	1.48344	0.741719	+	0.670710i	$0.234011\pi$
$564$	−10.6314	−0.447665
$565$	18.5681	0.781166
$566$	22.0303	0.926002
$567$	−0.715958	−0.0300674
$568$	0.713646	0.0299439
$569$	−12.8457	−0.538519	−0.269260	−	0.963068i	$-0.586779\pi$
$569$	−12.8457	−0.538519	−0.269260	+	0.963068i	$0.586779\pi$
$570$	−9.47423	−0.396832
$571$	31.0342	1.29874	0.649371	−	0.760472i	$-0.275032\pi$
$571$	31.0342	1.29874	0.649371	+	0.760472i	$0.275032\pi$
$572$	−3.59098	−0.150147
$573$	0.833088	0.0348028
$574$	−7.85967	−0.328056
$575$	2.22529	0.0928010
$576$	4.79442	0.199768
$577$	1.32689	0.0552393	0.0276197	−	0.999619i	$-0.491207\pi$
$577$	1.32689	0.0552393	0.0276197	+	0.999619i	$0.491207\pi$
$578$	−29.5511	−1.22916
$579$	10.9407	0.454682
$580$	−2.08256	−0.0864738
$581$	−1.48009	−0.0614046
$582$	14.1437	0.586277
$583$	−1.99844	−0.0827668
$584$	37.1447	1.53706
$585$	−7.28350	−0.301136
$586$	21.5892	0.891842
$587$	7.82602	0.323015	0.161507	−	0.986872i	$-0.448364\pi$
$587$	7.82602	0.323015	0.161507	+	0.986872i	$0.448364\pi$
$588$	8.11074	0.334481
$589$	4.63644	0.191041
$590$	6.94248	0.285817
$591$	0.438846	0.0180517
$592$	−0.449166	−0.0184606
$593$	−17.9167	−0.735750	−0.367875	−	0.929875i	$-0.619915\pi$
$593$	−17.9167	−0.735750	−0.367875	+	0.929875i	$0.619915\pi$
$594$	0.568796	0.0233380
$595$	8.52757	0.349596
$596$	−12.3245	−0.504830
$597$	−5.39837	−0.220940
$598$	−3.78613	−0.154826
$599$	−28.4367	−1.16189	−0.580946	−	0.813942i	$-0.697317\pi$
$599$	−28.4367	−1.16189	−0.580946	+	0.813942i	$0.697317\pi$
$600$	−6.26275	−0.255676
$601$	−2.12781	−0.0867952	−0.0433976	−	0.999058i	$-0.513818\pi$
$601$	−2.12781	−0.0867952	−0.0433976	+	0.999058i	$0.513818\pi$
$602$	−1.27565	−0.0519916
$603$	−2.81077	−0.114463
$604$	18.0515	0.734504
$605$	−17.6044	−0.715722
$606$	0.151229	0.00614324
$607$	−3.24329	−0.131641	−0.0658205	−	0.997831i	$-0.520966\pi$
$607$	−3.24329	−0.131641	−0.0658205	+	0.997831i	$0.520966\pi$
$608$	−37.3339	−1.51409
$609$	−0.715958	−0.0290121
$610$	−3.63183	−0.147049
$611$	−37.1821	−1.50423
$612$	8.93961	0.361362
$613$	4.85928	0.196264	0.0981322	−	0.995173i	$-0.468713\pi$
$613$	4.85928	0.196264	0.0981322	+	0.995173i	$0.468713\pi$
$614$	−6.47998	−0.261511
$615$	−21.1184	−0.851577
$616$	1.32360	0.0533295
$617$	18.6045	0.748989	0.374495	−	0.927229i	$-0.377816\pi$
$617$	18.6045	0.748989	0.374495	+	0.927229i	$0.377816\pi$
$618$	−1.21346	−0.0488125
$619$	−1.75731	−0.0706323	−0.0353161	−	0.999376i	$-0.511244\pi$
$619$	−1.75731	−0.0706323	−0.0353161	+	0.999376i	$0.511244\pi$
$620$	−1.46998	−0.0590359
$621$	−1.00000	−0.0401286
$622$	−6.34048	−0.254230
$623$	9.04016	0.362187
$624$	−0.277798	−0.0111208
$625$	−8.92163	−0.356865
$626$	−27.7463	−1.10897
$627$	−4.31482	−0.172318
$628$	6.34427	0.253164
$629$	50.5519	2.01564
$630$	1.03267	0.0411425
$631$	39.6157	1.57708	0.788539	−	0.614985i	$-0.210838\pi$
$631$	39.6157	1.57708	0.788539	+	0.614985i	$0.210838\pi$
$632$	1.72153	0.0684788
$633$	−11.8593	−0.471363
$634$	−15.2439	−0.605412
$635$	−35.3353	−1.40224
$636$	−3.80354	−0.150820
$637$	28.3663	1.12391
$638$	0.568796	0.0225189
$639$	0.253574	0.0100312
$640$	12.0200	0.475131
$641$	1.34325	0.0530553	0.0265276	−	0.999648i	$-0.491555\pi$
$641$	1.34325	0.0530553	0.0265276	+	0.999648i	$0.491555\pi$
$642$	−7.59870	−0.299897
$643$	0.605211	0.0238672	0.0119336	−	0.999929i	$-0.496201\pi$
$643$	0.605211	0.0238672	0.0119336	+	0.999929i	$0.496201\pi$
$644$	−0.895112	−0.0352723
$645$	−3.42759	−0.134961
$646$	40.6690	1.60010
$647$	−41.4111	−1.62804	−0.814019	−	0.580838i	$-0.802725\pi$
$647$	−41.4111	−1.62804	−0.814019	+	0.580838i	$0.802725\pi$
$648$	2.81435	0.110558
$649$	3.16180	0.124111
$650$	−8.42524	−0.330465
$651$	−0.505360	−0.0198066
$652$	11.8023	0.462214
$653$	−38.2945	−1.49858	−0.749290	−	0.662242i	$-0.769605\pi$
$653$	−38.2945	−1.49858	−0.749290	+	0.662242i	$0.769605\pi$
$654$	8.04950	0.314760
$655$	−31.7601	−1.24097
$656$	−0.805473	−0.0314484
$657$	13.1983	0.514916
$658$	5.27174	0.205514
$659$	7.30554	0.284584	0.142292	−	0.989825i	$-0.454553\pi$
$659$	7.30554	0.284584	0.142292	+	0.989825i	$0.454553\pi$
$660$	1.36802	0.0532499
$661$	−12.7358	−0.495364	−0.247682	−	0.968841i	$-0.579669\pi$
$661$	−12.7358	−0.495364	−0.247682	+	0.968841i	$0.579669\pi$
$662$	18.4363	0.716547
$663$	31.2651	1.21424
$664$	5.81808	0.225785
$665$	−7.83370	−0.303778
$666$	6.12171	0.237212
$667$	−1.00000	−0.0387202
$668$	−25.8965	−1.00197
$669$	−17.6698	−0.683152
$670$	4.05413	0.156625
$671$	−1.65404	−0.0638534
$672$	4.06930	0.156977
$673$	24.6573	0.950470	0.475235	−	0.879859i	$-0.342363\pi$
$673$	24.6573	0.950470	0.475235	+	0.879859i	$0.342363\pi$
$674$	−13.4627	−0.518564
$675$	−2.22529	−0.0856515
$676$	−7.65001	−0.294231
$677$	38.8256	1.49219	0.746095	−	0.665840i	$-0.231927\pi$
$677$	38.8256	1.49219	0.746095	+	0.665840i	$0.231927\pi$
$678$	−9.65212	−0.370688
$679$	11.6947	0.448800
$680$	−33.5209	−1.28547
$681$	19.2183	0.736448
$682$	0.401486	0.0153737
$683$	−27.9756	−1.07046	−0.535229	−	0.844707i	$-0.679775\pi$
$683$	−27.9756	−1.07046	−0.535229	+	0.844707i	$0.679775\pi$
$684$	−8.21222	−0.314002
$685$	19.1923	0.733301
$686$	−8.36142	−0.319240
$687$	0.0207973	0.000793467 0
$688$	−0.130731	−0.00498406
$689$	−13.3024	−0.506780
$690$	1.44236	0.0549096
$691$	−39.5369	−1.50405	−0.752027	−	0.659133i	$-0.770924\pi$
$691$	−39.5369	−1.50405	−0.752027	+	0.659133i	$0.770924\pi$
$692$	−6.21662	−0.236320
$693$	0.470305	0.0178654
$694$	−11.1333	−0.422613
$695$	1.55472	0.0589737
$696$	2.81435	0.106678
$697$	90.6529	3.43372
$698$	−20.7879	−0.786832
$699$	10.5644	0.399581
$700$	−1.99188	−0.0752861
$701$	12.3176	0.465229	0.232615	−	0.972569i	$-0.425272\pi$
$701$	12.3176	0.465229	0.232615	+	0.972569i	$0.425272\pi$
$702$	3.78613	0.142898
$703$	−46.4386	−1.75147
$704$	−3.14941	−0.118698
$705$	14.1648	0.533478
$706$	8.44182	0.317712
$707$	0.125042	0.00470270
$708$	6.01771	0.226159
$709$	−12.0155	−0.451253	−0.225626	−	0.974214i	$-0.572443\pi$
$709$	−12.0155	−0.451253	−0.225626	+	0.974214i	$0.572443\pi$
$710$	−0.365744	−0.0137261
$711$	0.611697	0.0229404
$712$	−35.5359	−1.33176
$713$	−0.705852	−0.0264344
$714$	−4.43283	−0.165894
$715$	4.78445	0.178928
$716$	26.9497	1.00716
$717$	1.89477	0.0707615
$718$	3.17563	0.118513
$719$	16.8456	0.628234	0.314117	−	0.949384i	$-0.398292\pi$
$719$	16.8456	0.628234	0.314117	+	0.949384i	$0.398292\pi$
$720$	0.105830	0.00394404
$721$	−1.00334	−0.0373664
$722$	−20.9079	−0.778113
$723$	2.61371	0.0972050
$724$	25.1007	0.932858
$725$	−2.22529	−0.0826452
$726$	9.15119	0.339632
$727$	9.37404	0.347664	0.173832	−	0.984775i	$-0.444385\pi$
$727$	9.37404	0.347664	0.173832	+	0.984775i	$0.444385\pi$
$728$	8.81043	0.326536
$729$	1.00000	0.0370370
$730$	−19.0367	−0.704580
$731$	14.7132	0.544189
$732$	−3.14806	−0.116356
$733$	−26.7121	−0.986634	−0.493317	−	0.869850i	$-0.664216\pi$
$733$	−26.7121	−0.986634	−0.493317	+	0.869850i	$0.664216\pi$
$734$	−1.83019	−0.0675535
$735$	−10.8064	−0.398599
$736$	5.68371	0.209504
$737$	1.84636	0.0680117
$738$	10.9778	0.404100
$739$	5.88668	0.216545	0.108273	−	0.994121i	$-0.465468\pi$
$739$	5.88668	0.216545	0.108273	+	0.994121i	$0.465468\pi$
$740$	14.7234	0.541242
$741$	−28.7212	−1.05510
$742$	1.88604	0.0692385
$743$	−16.1024	−0.590741	−0.295370	−	0.955383i	$-0.595443\pi$
$743$	−16.1024	−0.590741	−0.295370	+	0.955383i	$0.595443\pi$
$744$	1.98652	0.0728292
$745$	16.4205	0.601602
$746$	10.2441	0.375062
$747$	2.06729	0.0756383
$748$	−5.87234	−0.214714
$749$	−6.28294	−0.229573
$750$	10.4215	0.380538
$751$	−34.6373	−1.26393	−0.631967	−	0.774995i	$-0.717752\pi$
$751$	−34.6373	−1.26393	−0.631967	+	0.774995i	$0.717752\pi$
$752$	0.540258	0.0197012
$753$	−14.8239	−0.540212
$754$	3.78613	0.137883
$755$	−24.0509	−0.875302
$756$	0.895112	0.0325549
$757$	−28.2931	−1.02833	−0.514165	−	0.857691i	$-0.671898\pi$
$757$	−28.2931	−1.02833	−0.514165	+	0.857691i	$0.671898\pi$
$758$	10.6240	0.385882
$759$	0.656890	0.0238436
$760$	30.7934	1.11699
$761$	3.96877	0.143868	0.0719339	−	0.997409i	$-0.477083\pi$
$761$	3.96877	0.143868	0.0719339	+	0.997409i	$0.477083\pi$
$762$	18.3681	0.665406
$763$	6.65568	0.240952
$764$	−1.04155	−0.0376820
$765$	−11.9107	−0.430633
$766$	16.2993	0.588918
$767$	21.0462	0.759933
$768$	−15.8371	−0.571472
$769$	−7.71123	−0.278074	−0.139037	−	0.990287i	$-0.544401\pi$
$769$	−7.71123	−0.278074	−0.139037	+	0.990287i	$0.544401\pi$
$770$	−0.678348	−0.0244460
$771$	6.92245	0.249306
$772$	−13.6784	−0.492298
$773$	−47.4137	−1.70535	−0.852677	−	0.522439i	$-0.825022\pi$
$773$	−47.4137	−1.70535	−0.852677	+	0.522439i	$0.825022\pi$
$774$	1.78174	0.0640432
$775$	−1.57073	−0.0564221
$776$	−45.9704	−1.65024
$777$	5.06170	0.181587
$778$	0.527406	0.0189084
$779$	−83.2767	−2.98370
$780$	9.10604	0.326049
$781$	−0.166570	−0.00596035
$782$	−6.19146	−0.221406
$783$	1.00000	0.0357371
$784$	−0.412163	−0.0147201
$785$	−8.45281	−0.301694
$786$	16.5096	0.588879
$787$	14.3049	0.509914	0.254957	−	0.966952i	$-0.417939\pi$
$787$	14.3049	0.509914	0.254957	+	0.966952i	$0.417939\pi$
$788$	−0.548658	−0.0195451
$789$	−0.368207	−0.0131085
$790$	−0.882286	−0.0313903
$791$	−7.98079	−0.283764
$792$	−1.84872	−0.0656913
$793$	−11.0099	−0.390974
$794$	7.36334	0.261315
$795$	5.06766	0.179731
$796$	6.74920	0.239219
$797$	11.6866	0.413961	0.206981	−	0.978345i	$-0.433636\pi$
$797$	11.6866	0.413961	0.206981	+	0.978345i	$0.433636\pi$
$798$	4.07214	0.144152
$799$	−60.8039	−2.15109
$800$	12.6479	0.447171
$801$	−12.6267	−0.446141
$802$	−32.9472	−1.16341
$803$	−8.66985	−0.305952
$804$	3.51410	0.123933
$805$	1.19260	0.0420338
$806$	2.67245	0.0941330
$807$	−7.66062	−0.269666
$808$	−0.491528	−0.0172919
$809$	10.9340	0.384420	0.192210	−	0.981354i	$-0.438434\pi$
$809$	10.9340	0.384420	0.192210	+	0.981354i	$0.438434\pi$
$810$	−1.44236	−0.0506793
$811$	−15.2080	−0.534023	−0.267012	−	0.963693i	$-0.586036\pi$
$811$	−15.2080	−0.534023	−0.267012	+	0.963693i	$0.586036\pi$
$812$	0.895112	0.0314123
$813$	20.2402	0.709856
$814$	−4.02129	−0.140946
$815$	−15.7248	−0.550817
$816$	−0.454284	−0.0159031
$817$	−13.5161	−0.472867
$818$	−13.1141	−0.458522
$819$	3.13054	0.109390
$820$	26.4029	0.922028
$821$	−40.4608	−1.41209	−0.706046	−	0.708166i	$-0.749523\pi$
$821$	−40.4608	−1.41209	−0.706046	+	0.708166i	$0.749523\pi$
$822$	−9.97660	−0.347974
$823$	19.1656	0.668070	0.334035	−	0.942561i	$-0.391590\pi$
$823$	19.1656	0.668070	0.334035	+	0.942561i	$0.391590\pi$
$824$	3.94402	0.137397
$825$	1.46177	0.0508923
$826$	−2.98396	−0.103825
$827$	51.5955	1.79415	0.897076	−	0.441877i	$-0.145687\pi$
$827$	51.5955	1.79415	0.897076	+	0.441877i	$0.145687\pi$
$828$	1.25023	0.0434485
$829$	22.8118	0.792288	0.396144	−	0.918188i	$-0.370348\pi$
$829$	22.8118	0.792288	0.396144	+	0.918188i	$0.370348\pi$
$830$	−2.98177	−0.103499
$831$	31.4385	1.09059
$832$	−20.9637	−0.726785
$833$	46.3874	1.60723
$834$	−0.808176	−0.0279849
$835$	34.5033	1.19403
$836$	5.39452	0.186573
$837$	0.705852	0.0243978
$838$	−17.0178	−0.587869
$839$	−22.8445	−0.788680	−0.394340	−	0.918965i	$-0.629027\pi$
$839$	−22.8445	−0.788680	−0.394340	+	0.918965i	$0.629027\pi$
$840$	−3.35641	−0.115807
$841$	1.00000	0.0344828
$842$	23.1259	0.796972
$843$	−2.99818	−0.103263
$844$	14.8268	0.510359
$845$	10.1925	0.350633
$846$	−7.36320	−0.253152
$847$	7.56660	0.259991
$848$	0.193284	0.00663741
$849$	−25.4423	−0.873177
$850$	−13.7778	−0.472575
$851$	7.06983	0.242351
$852$	−0.317026	−0.0108611
$853$	10.6600	0.364993	0.182497	−	0.983206i	$-0.441582\pi$
$853$	10.6600	0.364993	0.182497	+	0.983206i	$0.441582\pi$
$854$	1.56101	0.0534165
$855$	10.9416	0.374194
$856$	24.6975	0.844144
$857$	29.0376	0.991904	0.495952	−	0.868350i	$-0.334819\pi$
$857$	29.0376	0.991904	0.495952	+	0.868350i	$0.334819\pi$
$858$	−2.48707	−0.0849071
$859$	38.0437	1.29804	0.649018	−	0.760773i	$-0.275180\pi$
$859$	38.0437	1.29804	0.649018	+	0.760773i	$0.275180\pi$
$860$	4.28527	0.146126
$861$	9.07695	0.309342
$862$	29.0345	0.988919
$863$	−34.2406	−1.16556	−0.582781	−	0.812629i	$-0.698036\pi$
$863$	−34.2406	−1.16556	−0.582781	+	0.812629i	$0.698036\pi$
$864$	−5.68371	−0.193364
$865$	8.28273	0.281621
$866$	−21.2262	−0.721296
$867$	34.1279	1.15904
$868$	0.631817	0.0214453
$869$	−0.401817	−0.0136307
$870$	−1.44236	−0.0489005
$871$	12.2901	0.416435
$872$	−26.1627	−0.885982
$873$	−16.3343	−0.552832
$874$	5.68768	0.192389
$875$	8.61691	0.291305
$876$	−16.5009	−0.557515
$877$	−53.2117	−1.79683	−0.898415	−	0.439148i	$-0.855281\pi$
$877$	−53.2117	−1.79683	−0.898415	+	0.439148i	$0.855281\pi$
$878$	−11.8908	−0.401294
$879$	−24.9329	−0.840965
$880$	−0.0695184	−0.00234346
$881$	−29.7942	−1.00379	−0.501896	−	0.864928i	$-0.667364\pi$
$881$	−29.7942	−1.00379	−0.501896	+	0.864928i	$0.667364\pi$
$882$	5.61740	0.189148
$883$	18.4786	0.621854	0.310927	−	0.950434i	$-0.399361\pi$
$883$	18.4786	0.621854	0.310927	+	0.950434i	$0.399361\pi$
$884$	−39.0886	−1.31469
$885$	−8.01771	−0.269512
$886$	−27.1128	−0.910871
$887$	46.6348	1.56584	0.782922	−	0.622119i	$-0.213728\pi$
$887$	46.6348	1.56584	0.782922	+	0.622119i	$0.213728\pi$
$888$	−19.8970	−0.667699
$889$	15.1875	0.509374
$890$	18.2122	0.610473
$891$	−0.656890	−0.0220066
$892$	22.0912	0.739670
$893$	55.8564	1.86916
$894$	−8.53577	−0.285479
$895$	−35.9065	−1.20022
$896$	−5.16633	−0.172595
$897$	4.37251	0.145994
$898$	−7.46798	−0.249210
$899$	0.705852	0.0235415
$900$	2.78212	0.0927374
$901$	−21.7534	−0.724711
$902$	−7.21123	−0.240108
$903$	1.47322	0.0490256
$904$	31.3716	1.04340
$905$	−33.4429	−1.11168
$906$	12.5022	0.415358
$907$	51.1950	1.69990	0.849951	−	0.526861i	$-0.176631\pi$
$907$	51.1950	1.69990	0.849951	+	0.526861i	$0.176631\pi$
$908$	−24.0273	−0.797374
$909$	−0.174650	−0.00579279
$910$	−4.51535	−0.149682
$911$	9.25114	0.306504	0.153252	−	0.988187i	$-0.451025\pi$
$911$	9.25114	0.306504	0.153252	+	0.988187i	$0.451025\pi$
$912$	0.417320	0.0138188
$913$	−1.35798	−0.0449427
$914$	25.5186	0.844081
$915$	4.19432	0.138660
$916$	−0.0260014	−0.000859111 0
$917$	13.6509	0.450792
$918$	6.19146	0.204349
$919$	42.8124	1.41225	0.706125	−	0.708087i	$-0.250441\pi$
$919$	42.8124	1.41225	0.706125	+	0.708087i	$0.250441\pi$
$920$	−4.68799	−0.154559
$921$	7.48358	0.246592
$922$	−34.6595	−1.14145
$923$	−1.10876	−0.0364952
$924$	−0.587990	−0.0193434
$925$	15.7324	0.517279
$926$	26.8230	0.881459
$927$	1.40140	0.0460279
$928$	−5.68371	−0.186577
$929$	40.4332	1.32657	0.663286	−	0.748366i	$-0.269162\pi$
$929$	40.4332	1.32657	0.663286	+	0.748366i	$0.269162\pi$
$930$	−1.01809	−0.0333845
$931$	−42.6130	−1.39658
$932$	−13.2079	−0.432639
$933$	7.32248	0.239727
$934$	−28.2690	−0.924990
$935$	7.82402	0.255873
$936$	−12.3058	−0.402227
$937$	−16.4011	−0.535802	−0.267901	−	0.963447i	$-0.586330\pi$
$937$	−16.4011	−0.535802	−0.267901	+	0.963447i	$0.586330\pi$
$938$	−1.74252	−0.0568951
$939$	32.0436	1.04570
$940$	−17.7093	−0.577613
$941$	−26.4355	−0.861772	−0.430886	−	0.902406i	$-0.641799\pi$
$941$	−26.4355	−0.861772	−0.430886	+	0.902406i	$0.641799\pi$
$942$	4.39396	0.143163
$943$	12.6781	0.412854
$944$	−0.305802	−0.00995300
$945$	−1.19260	−0.0387954
$946$	−1.17040	−0.0380531
$947$	31.4428	1.02175	0.510876	−	0.859654i	$-0.329321\pi$
$947$	31.4428	1.02175	0.510876	+	0.859654i	$0.329321\pi$
$948$	−0.764761	−0.0248383
$949$	−57.7099	−1.87334
$950$	12.6567	0.410639
$951$	17.6048	0.570875
$952$	14.4077	0.466956
$953$	−23.4157	−0.758509	−0.379254	−	0.925292i	$-0.623819\pi$
$953$	−23.4157	−0.758509	−0.379254	+	0.925292i	$0.623819\pi$
$954$	−2.63428	−0.0852881
$955$	1.38771	0.0449053
$956$	−2.36890	−0.0766156
$957$	−0.656890	−0.0212342
$958$	−8.85575	−0.286116
$959$	−8.24909	−0.266377
$960$	7.98629	0.257756
$961$	−30.5018	−0.983928
$962$	−26.7673	−0.863012
$963$	8.77557	0.282789
$964$	−3.26774	−0.105247
$965$	18.2245	0.586667
$966$	−0.619943	−0.0199463
$967$	1.40682	0.0452402	0.0226201	−	0.999744i	$-0.492799\pi$
$967$	1.40682	0.0452402	0.0226201	+	0.999744i	$0.492799\pi$
$968$	−29.7435	−0.955991
$969$	−46.9677	−1.50882
$970$	23.5599	0.756463
$971$	−41.3493	−1.32696	−0.663481	−	0.748193i	$-0.730922\pi$
$971$	−41.3493	−1.32696	−0.663481	+	0.748193i	$0.730922\pi$
$972$	−1.25023	−0.0401011
$973$	−0.668235	−0.0214226
$974$	−13.3968	−0.429262
$975$	9.73011	0.311613
$976$	0.159975	0.00512067
$977$	−16.1169	−0.515626	−0.257813	−	0.966195i	$-0.583002\pi$
$977$	−16.1169	−0.515626	−0.257813	+	0.966195i	$0.583002\pi$
$978$	8.17413	0.261380
$979$	8.29433	0.265088
$980$	13.5104	0.431575
$981$	−9.29618	−0.296804
$982$	−15.1522	−0.483527
$983$	−7.74532	−0.247037	−0.123519	−	0.992342i	$-0.539418\pi$
$983$	−7.74532	−0.247037	−0.123519	+	0.992342i	$0.539418\pi$
$984$	−35.6805	−1.13745
$985$	0.731006	0.0232918
$986$	6.19146	0.197176
$987$	−6.08821	−0.193790
$988$	35.9080	1.14239
$989$	2.05769	0.0654307
$990$	0.947470	0.0301126
$991$	−17.9134	−0.569038	−0.284519	−	0.958670i	$-0.591834\pi$
$991$	−17.9134	−0.569038	−0.284519	+	0.958670i	$0.591834\pi$
$992$	−4.01186	−0.127377
$993$	−21.2917	−0.675670
$994$	0.157201	0.00498613
$995$	−8.99231	−0.285075
$996$	−2.58459	−0.0818959
$997$	−46.5539	−1.47438	−0.737188	−	0.675687i	$-0.763847\pi$
$997$	−46.5539	−1.47438	−0.737188	+	0.675687i	$0.763847\pi$
$998$	−15.2927	−0.484083
$999$	−7.06983	−0.223679

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.j.1.4	✓	7
3.2	odd	2		6003.2.a.i.1.4		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.j.1.4	✓	7	1.1	even	1	trivial
6003.2.a.i.1.4		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:	\( N \)	\(=\)	\( 2001 = 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2001.a (trivial)

\(f(q)\)	\(=\)	\(q-0.865893 q^{2} +1.00000 q^{3} -1.25023 q^{4} +1.66575 q^{5} -0.865893 q^{6} -0.715958 q^{7} +2.81435 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.865893 q^{2} +1.00000 q^{3} -1.25023 q^{4} +1.66575 q^{5} -0.865893 q^{6} -0.715958 q^{7} +2.81435 q^{8} +1.00000 q^{9} -1.44236 q^{10} -0.656890 q^{11} -1.25023 q^{12} -4.37251 q^{13} +0.619943 q^{14} +1.66575 q^{15} +0.0635329 q^{16} -7.15038 q^{17} -0.865893 q^{18} +6.56857 q^{19} -2.08256 q^{20} -0.715958 q^{21} +0.568796 q^{22} -1.00000 q^{23} +2.81435 q^{24} -2.22529 q^{25} +3.78613 q^{26} +1.00000 q^{27} +0.895112 q^{28} +1.00000 q^{29} -1.44236 q^{30} +0.705852 q^{31} -5.68371 q^{32} -0.656890 q^{33} +6.19146 q^{34} -1.19260 q^{35} -1.25023 q^{36} -7.06983 q^{37} -5.68768 q^{38} -4.37251 q^{39} +4.68799 q^{40} -12.6781 q^{41} +0.619943 q^{42} -2.05769 q^{43} +0.821263 q^{44} +1.66575 q^{45} +0.865893 q^{46} +8.50359 q^{47} +0.0635329 q^{48} -6.48740 q^{49} +1.92686 q^{50} -7.15038 q^{51} +5.46665 q^{52} +3.04227 q^{53} -0.865893 q^{54} -1.09421 q^{55} -2.01496 q^{56} +6.56857 q^{57} -0.865893 q^{58} -4.81329 q^{59} -2.08256 q^{60} +2.51798 q^{61} -0.611192 q^{62} -0.715958 q^{63} +4.79442 q^{64} -7.28350 q^{65} +0.568796 q^{66} -2.81077 q^{67} +8.93961 q^{68} -1.00000 q^{69} +1.03267 q^{70} +0.253574 q^{71} +2.81435 q^{72} +13.1983 q^{73} +6.12171 q^{74} -2.22529 q^{75} -8.21222 q^{76} +0.470305 q^{77} +3.78613 q^{78} +0.611697 q^{79} +0.105830 q^{80} +1.00000 q^{81} +10.9778 q^{82} +2.06729 q^{83} +0.895112 q^{84} -11.9107 q^{85} +1.78174 q^{86} +1.00000 q^{87} -1.84872 q^{88} -12.6267 q^{89} -1.44236 q^{90} +3.13054 q^{91} +1.25023 q^{92} +0.705852 q^{93} -7.36320 q^{94} +10.9416 q^{95} -5.68371 q^{96} -16.3343 q^{97} +5.61740 q^{98} -0.656890 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - q^{2} + 7 q^{3} + 7 q^{4} - 5 q^{5} - q^{6} - 5 q^{7} + 3 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - q^2 + 7 * q^3 + 7 * q^4 - 5 * q^5 - q^6 - 5 * q^7 + 3 * q^8 + 7 * q^9	\( 7 q - q^{2} + 7 q^{3} + 7 q^{4} - 5 q^{5} - q^{6} - 5 q^{7} + 3 q^{8} + 7 q^{9} - 11 q^{10} - 12 q^{11} + 7 q^{12} - 13 q^{13} - 3 q^{14} - 5 q^{15} - 13 q^{16} - 12 q^{17} - q^{18} - 5 q^{19} - 8 q^{20} - 5 q^{21} - q^{22} - 7 q^{23} + 3 q^{24} - 4 q^{25} + 2 q^{26} + 7 q^{27} - 21 q^{28} + 7 q^{29} - 11 q^{30} - 8 q^{31} - 5 q^{32} - 12 q^{33} - 28 q^{34} + 5 q^{35} + 7 q^{36} - 24 q^{37} - 6 q^{38} - 13 q^{39} - 20 q^{40} + 9 q^{41} - 3 q^{42} - q^{43} - 23 q^{44} - 5 q^{45} + q^{46} + 27 q^{47} - 13 q^{48} - 14 q^{49} + 7 q^{50} - 12 q^{51} - 9 q^{52} - q^{53} - q^{54} - 11 q^{55} - 20 q^{56} - 5 q^{57} - q^{58} + 8 q^{59} - 8 q^{60} + q^{61} - 5 q^{63} + 3 q^{64} + 12 q^{65} - q^{66} - 16 q^{67} + 15 q^{68} - 7 q^{69} + 40 q^{70} - 13 q^{71} + 3 q^{72} - 23 q^{73} - 8 q^{74} - 4 q^{75} - 2 q^{76} + 13 q^{77} + 2 q^{78} - 44 q^{79} + 30 q^{80} + 7 q^{81} - 10 q^{82} + 21 q^{83} - 21 q^{84} + 6 q^{86} + 7 q^{87} + 21 q^{88} - 5 q^{89} - 11 q^{90} - 18 q^{91} - 7 q^{92} - 8 q^{93} + 28 q^{94} + 9 q^{95} - 5 q^{96} - 55 q^{97} + 36 q^{98} - 12 q^{99}+O(q^{100}) \) 7 * q - q^2 + 7 * q^3 + 7 * q^4 - 5 * q^5 - q^6 - 5 * q^7 + 3 * q^8 + 7 * q^9 - 11 * q^10 - 12 * q^11 + 7 * q^12 - 13 * q^13 - 3 * q^14 - 5 * q^15 - 13 * q^16 - 12 * q^17 - q^18 - 5 * q^19 - 8 * q^20 - 5 * q^21 - q^22 - 7 * q^23 + 3 * q^24 - 4 * q^25 + 2 * q^26 + 7 * q^27 - 21 * q^28 + 7 * q^29 - 11 * q^30 - 8 * q^31 - 5 * q^32 - 12 * q^33 - 28 * q^34 + 5 * q^35 + 7 * q^36 - 24 * q^37 - 6 * q^38 - 13 * q^39 - 20 * q^40 + 9 * q^41 - 3 * q^42 - q^43 - 23 * q^44 - 5 * q^45 + q^46 + 27 * q^47 - 13 * q^48 - 14 * q^49 + 7 * q^50 - 12 * q^51 - 9 * q^52 - q^53 - q^54 - 11 * q^55 - 20 * q^56 - 5 * q^57 - q^58 + 8 * q^59 - 8 * q^60 + q^61 - 5 * q^63 + 3 * q^64 + 12 * q^65 - q^66 - 16 * q^67 + 15 * q^68 - 7 * q^69 + 40 * q^70 - 13 * q^71 + 3 * q^72 - 23 * q^73 - 8 * q^74 - 4 * q^75 - 2 * q^76 + 13 * q^77 + 2 * q^78 - 44 * q^79 + 30 * q^80 + 7 * q^81 - 10 * q^82 + 21 * q^83 - 21 * q^84 + 6 * q^86 + 7 * q^87 + 21 * q^88 - 5 * q^89 - 11 * q^90 - 18 * q^91 - 7 * q^92 - 8 * q^93 + 28 * q^94 + 9 * q^95 - 5 * q^96 - 55 * q^97 + 36 * q^98 - 12 * q^99

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