LMFDB - Embedded newform 8007.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, 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("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$1$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.68305 q^{2} -1.00000 q^{3} +5.19875 q^{4} -0.525183 q^{5} +2.68305 q^{6} +1.96908 q^{7} -8.58242 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.68305 q^{2} -1.00000 q^{3} +5.19875 q^{4} -0.525183 q^{5} +2.68305 q^{6} +1.96908 q^{7} -8.58242 q^{8} +1.00000 q^{9} +1.40909 q^{10} +4.22427 q^{11} -5.19875 q^{12} -5.20022 q^{13} -5.28315 q^{14} +0.525183 q^{15} +12.6295 q^{16} +1.00000 q^{17} -2.68305 q^{18} -2.46399 q^{19} -2.73030 q^{20} -1.96908 q^{21} -11.3339 q^{22} -3.47936 q^{23} +8.58242 q^{24} -4.72418 q^{25} +13.9524 q^{26} -1.00000 q^{27} +10.2368 q^{28} +6.01287 q^{29} -1.40909 q^{30} -1.06983 q^{31} -16.7209 q^{32} -4.22427 q^{33} -2.68305 q^{34} -1.03413 q^{35} +5.19875 q^{36} -2.45043 q^{37} +6.61102 q^{38} +5.20022 q^{39} +4.50734 q^{40} +10.2823 q^{41} +5.28315 q^{42} -1.10840 q^{43} +21.9609 q^{44} -0.525183 q^{45} +9.33530 q^{46} +3.91359 q^{47} -12.6295 q^{48} -3.12271 q^{49} +12.6752 q^{50} -1.00000 q^{51} -27.0346 q^{52} -0.313221 q^{53} +2.68305 q^{54} -2.21852 q^{55} -16.8995 q^{56} +2.46399 q^{57} -16.1328 q^{58} +9.87145 q^{59} +2.73030 q^{60} -1.73138 q^{61} +2.87040 q^{62} +1.96908 q^{63} +19.6038 q^{64} +2.73107 q^{65} +11.3339 q^{66} -0.944877 q^{67} +5.19875 q^{68} +3.47936 q^{69} +2.77462 q^{70} -4.49834 q^{71} -8.58242 q^{72} -5.99990 q^{73} +6.57463 q^{74} +4.72418 q^{75} -12.8097 q^{76} +8.31794 q^{77} -13.9524 q^{78} +14.0311 q^{79} -6.63282 q^{80} +1.00000 q^{81} -27.5879 q^{82} -14.1379 q^{83} -10.2368 q^{84} -0.525183 q^{85} +2.97390 q^{86} -6.01287 q^{87} -36.2544 q^{88} -2.39575 q^{89} +1.40909 q^{90} -10.2397 q^{91} -18.0884 q^{92} +1.06983 q^{93} -10.5004 q^{94} +1.29405 q^{95} +16.7209 q^{96} -3.48900 q^{97} +8.37840 q^{98} +4.22427 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9}+O(q^{10}) $ 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9} + 4 q^{10} + q^{11} - 30 q^{12} - 26 q^{13} - 4 q^{14} + 3 q^{15} + 8 q^{16} + 39 q^{17} - 4 q^{18} - 14 q^{19} - 14 q^{20} + 5 q^{21} - 17 q^{22} + 2 q^{23} + 3 q^{24} - 6 q^{25} - 17 q^{26} - 39 q^{27} - 14 q^{28} - 7 q^{29} - 4 q^{30} - q^{31} - 30 q^{32} - q^{33} - 4 q^{34} + q^{35} + 30 q^{36} - 24 q^{37} - 20 q^{38} + 26 q^{39} + 12 q^{40} + q^{41} + 4 q^{42} - 41 q^{43} - 2 q^{44} - 3 q^{45} - 6 q^{46} - 9 q^{47} - 8 q^{48} - 10 q^{49} - 9 q^{50} - 39 q^{51} - 37 q^{52} - 47 q^{53} + 4 q^{54} - 39 q^{55} + 8 q^{56} + 14 q^{57} - 27 q^{58} + 41 q^{59} + 14 q^{60} - 41 q^{61} + 36 q^{62} - 5 q^{63} - 47 q^{64} - 39 q^{65} + 17 q^{66} - 36 q^{67} + 30 q^{68} - 2 q^{69} - 52 q^{70} - 2 q^{71} - 3 q^{72} - 63 q^{73} - 6 q^{74} + 6 q^{75} - 34 q^{76} - 64 q^{77} + 17 q^{78} + 20 q^{79} - 28 q^{80} + 39 q^{81} - 37 q^{82} + 45 q^{83} + 14 q^{84} - 3 q^{85} + 32 q^{86} + 7 q^{87} + 6 q^{88} - 32 q^{89} + 4 q^{90} - 11 q^{91} + 28 q^{92} + q^{93} - 44 q^{94} + 22 q^{95} + 30 q^{96} - 20 q^{97} + 63 q^{98} + q^{99}+O(q^{100}) \) 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9 + 4 * q^10 + q^11 - 30 * q^12 - 26 * q^13 - 4 * q^14 + 3 * q^15 + 8 * q^16 + 39 * q^17 - 4 * q^18 - 14 * q^19 - 14 * q^20 + 5 * q^21 - 17 * q^22 + 2 * q^23 + 3 * q^24 - 6 * q^25 - 17 * q^26 - 39 * q^27 - 14 * q^28 - 7 * q^29 - 4 * q^30 - q^31 - 30 * q^32 - q^33 - 4 * q^34 + q^35 + 30 * q^36 - 24 * q^37 - 20 * q^38 + 26 * q^39 + 12 * q^40 + q^41 + 4 * q^42 - 41 * q^43 - 2 * q^44 - 3 * q^45 - 6 * q^46 - 9 * q^47 - 8 * q^48 - 10 * q^49 - 9 * q^50 - 39 * q^51 - 37 * q^52 - 47 * q^53 + 4 * q^54 - 39 * q^55 + 8 * q^56 + 14 * q^57 - 27 * q^58 + 41 * q^59 + 14 * q^60 - 41 * q^61 + 36 * q^62 - 5 * q^63 - 47 * q^64 - 39 * q^65 + 17 * q^66 - 36 * q^67 + 30 * q^68 - 2 * q^69 - 52 * q^70 - 2 * q^71 - 3 * q^72 - 63 * q^73 - 6 * q^74 + 6 * q^75 - 34 * q^76 - 64 * q^77 + 17 * q^78 + 20 * q^79 - 28 * q^80 + 39 * q^81 - 37 * q^82 + 45 * q^83 + 14 * q^84 - 3 * q^85 + 32 * q^86 + 7 * q^87 + 6 * q^88 - 32 * q^89 + 4 * q^90 - 11 * q^91 + 28 * q^92 + q^93 - 44 * q^94 + 22 * q^95 + 30 * q^96 - 20 * q^97 + 63 * q^98 + 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 $

$2$	−2.68305	−1.89720	−0.948601	−	0.316474i	$-0.897501\pi$
$2$	−2.68305	−1.89720	−0.948601	+	0.316474i	$0.897501\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.19875	2.59938
$5$	−0.525183	−0.234869	−0.117435	−	0.993081i	$-0.537467\pi$
$5$	−0.525183	−0.234869	−0.117435	+	0.993081i	$0.537467\pi$
$6$	2.68305	1.09535
$7$	1.96908	0.744243	0.372122	−	0.928184i	$-0.378630\pi$
$7$	1.96908	0.744243	0.372122	+	0.928184i	$0.378630\pi$
$8$	−8.58242	−3.03434
$9$	1.00000	0.333333
$10$	1.40909	0.445594
$11$	4.22427	1.27367	0.636833	−	0.771002i	$-0.280244\pi$
$11$	4.22427	1.27367	0.636833	+	0.771002i	$0.280244\pi$
$12$	−5.19875	−1.50075
$13$	−5.20022	−1.44228	−0.721140	−	0.692789i	$-0.756382\pi$
$13$	−5.20022	−1.44228	−0.721140	+	0.692789i	$0.756382\pi$
$14$	−5.28315	−1.41198
$15$	0.525183	0.135602
$16$	12.6295	3.15739
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.68305	−0.632401
$19$	−2.46399	−0.565279	−0.282640	−	0.959226i	$-0.591210\pi$
$19$	−2.46399	−0.565279	−0.282640	+	0.959226i	$0.591210\pi$
$20$	−2.73030	−0.610513
$21$	−1.96908	−0.429689
$22$	−11.3339	−2.41640
$23$	−3.47936	−0.725497	−0.362749	−	0.931887i	$-0.618162\pi$
$23$	−3.47936	−0.725497	−0.362749	+	0.931887i	$0.618162\pi$
$24$	8.58242	1.75188
$25$	−4.72418	−0.944837
$26$	13.9524	2.73630
$27$	−1.00000	−0.192450
$28$	10.2368	1.93457
$29$	6.01287	1.11656	0.558281	−	0.829652i	$-0.311461\pi$
$29$	6.01287	1.11656	0.558281	+	0.829652i	$0.311461\pi$
$30$	−1.40909	−0.257264
$31$	−1.06983	−0.192147	−0.0960734	−	0.995374i	$-0.530628\pi$
$31$	−1.06983	−0.192147	−0.0960734	+	0.995374i	$0.530628\pi$
$32$	−16.7209	−2.95586
$33$	−4.22427	−0.735351
$34$	−2.68305	−0.460139
$35$	−1.03413	−0.174800
$36$	5.19875	0.866459
$37$	−2.45043	−0.402849	−0.201424	−	0.979504i	$-0.564557\pi$
$37$	−2.45043	−0.402849	−0.201424	+	0.979504i	$0.564557\pi$
$38$	6.61102	1.07245
$39$	5.20022	0.832701
$40$	4.50734	0.712673
$41$	10.2823	1.60583	0.802913	−	0.596097i	$-0.203283\pi$
$41$	10.2823	1.60583	0.802913	+	0.596097i	$0.203283\pi$
$42$	5.28315	0.815207
$43$	−1.10840	−0.169030	−0.0845150	−	0.996422i	$-0.526934\pi$
$43$	−1.10840	−0.169030	−0.0845150	+	0.996422i	$0.526934\pi$
$44$	21.9609	3.31074
$45$	−0.525183	−0.0782897
$46$	9.33530	1.37642
$47$	3.91359	0.570856	0.285428	−	0.958400i	$-0.407864\pi$
$47$	3.91359	0.570856	0.285428	+	0.958400i	$0.407864\pi$
$48$	−12.6295	−1.82292
$49$	−3.12271	−0.446102
$50$	12.6752	1.79255
$51$	−1.00000	−0.140028
$52$	−27.0346	−3.74903
$53$	−0.313221	−0.0430242	−0.0215121	−	0.999769i	$-0.506848\pi$
$53$	−0.313221	−0.0430242	−0.0215121	+	0.999769i	$0.506848\pi$
$54$	2.68305	0.365117
$55$	−2.21852	−0.299145
$56$	−16.8995	−2.25829
$57$	2.46399	0.326364
$58$	−16.1328	−2.11834
$59$	9.87145	1.28515	0.642577	−	0.766222i	$-0.277865\pi$
$59$	9.87145	1.28515	0.642577	+	0.766222i	$0.277865\pi$
$60$	2.73030	0.352480
$61$	−1.73138	−0.221680	−0.110840	−	0.993838i	$-0.535354\pi$
$61$	−1.73138	−0.221680	−0.110840	+	0.993838i	$0.535354\pi$
$62$	2.87040	0.364541
$63$	1.96908	0.248081
$64$	19.6038	2.45047
$65$	2.73107	0.338747
$66$	11.3339	1.39511
$67$	−0.944877	−0.115435	−0.0577176	−	0.998333i	$-0.518382\pi$
$67$	−0.944877	−0.115435	−0.0577176	+	0.998333i	$0.518382\pi$
$68$	5.19875	0.630442
$69$	3.47936	0.418866
$70$	2.77462	0.331630
$71$	−4.49834	−0.533855	−0.266928	−	0.963717i	$-0.586008\pi$
$71$	−4.49834	−0.533855	−0.266928	+	0.963717i	$0.586008\pi$
$72$	−8.58242	−1.01145
$73$	−5.99990	−0.702235	−0.351118	−	0.936331i	$-0.614198\pi$
$73$	−5.99990	−0.702235	−0.351118	+	0.936331i	$0.614198\pi$
$74$	6.57463	0.764286
$75$	4.72418	0.545502
$76$	−12.8097	−1.46937
$77$	8.31794	0.947917
$78$	−13.9524	−1.57980
$79$	14.0311	1.57863	0.789313	−	0.613991i	$-0.210437\pi$
$79$	14.0311	1.57863	0.789313	+	0.613991i	$0.210437\pi$
$80$	−6.63282	−0.741572
$81$	1.00000	0.111111
$82$	−27.5879	−3.04658
$83$	−14.1379	−1.55183	−0.775917	−	0.630835i	$-0.782712\pi$
$83$	−14.1379	−1.55183	−0.775917	+	0.630835i	$0.782712\pi$
$84$	−10.2368	−1.11692
$85$	−0.525183	−0.0569641
$86$	2.97390	0.320684
$87$	−6.01287	−0.644647
$88$	−36.2544	−3.86474
$89$	−2.39575	−0.253949	−0.126975	−	0.991906i	$-0.540527\pi$
$89$	−2.39575	−0.253949	−0.126975	+	0.991906i	$0.540527\pi$
$90$	1.40909	0.148531
$91$	−10.2397	−1.07341
$92$	−18.0884	−1.88584
$93$	1.06983	0.110936
$94$	−10.5004	−1.08303
$95$	1.29405	0.132767
$96$	16.7209	1.70656
$97$	−3.48900	−0.354254	−0.177127	−	0.984188i	$-0.556680\pi$
$97$	−3.48900	−0.354254	−0.177127	+	0.984188i	$0.556680\pi$
$98$	8.37840	0.846346
$99$	4.22427	0.424555
$100$	−24.5599	−2.45599
$101$	14.6229	1.45504	0.727519	−	0.686088i	$-0.240673\pi$
$101$	14.6229	1.45504	0.727519	+	0.686088i	$0.240673\pi$
$102$	2.68305	0.265661
$103$	4.78327	0.471310	0.235655	−	0.971837i	$-0.424276\pi$
$103$	4.78327	0.471310	0.235655	+	0.971837i	$0.424276\pi$
$104$	44.6304	4.37637
$105$	1.03413	0.100921
$106$	0.840387	0.0816256
$107$	−1.64236	−0.158773	−0.0793864	−	0.996844i	$-0.525296\pi$
$107$	−1.64236	−0.158773	−0.0793864	+	0.996844i	$0.525296\pi$
$108$	−5.19875	−0.500250
$109$	−7.37010	−0.705928	−0.352964	−	0.935637i	$-0.614826\pi$
$109$	−7.37010	−0.705928	−0.352964	+	0.935637i	$0.614826\pi$
$110$	5.95239	0.567538
$111$	2.45043	0.232585
$112$	24.8686	2.34986
$113$	0.795801	0.0748627	0.0374313	−	0.999299i	$-0.488082\pi$
$113$	0.795801	0.0748627	0.0374313	+	0.999299i	$0.488082\pi$
$114$	−6.61102	−0.619179
$115$	1.82730	0.170397
$116$	31.2594	2.90236
$117$	−5.20022	−0.480760
$118$	−26.4856	−2.43820
$119$	1.96908	0.180506
$120$	−4.50734	−0.411462
$121$	6.84446	0.622223
$122$	4.64537	0.420572
$123$	−10.2823	−0.927124
$124$	−5.56177	−0.499462
$125$	5.10698	0.456782
$126$	−5.28315	−0.470660
$127$	−1.68371	−0.149405	−0.0747024	−	0.997206i	$-0.523801\pi$
$127$	−1.68371	−0.149405	−0.0747024	+	0.997206i	$0.523801\pi$
$128$	−19.1562	−1.69319
$129$	1.10840	0.0975895
$130$	−7.32758	−0.642672
$131$	−7.37430	−0.644295	−0.322148	−	0.946689i	$-0.604405\pi$
$131$	−7.37430	−0.644295	−0.322148	+	0.946689i	$0.604405\pi$
$132$	−21.9609	−1.91145
$133$	−4.85181	−0.420705
$134$	2.53515	0.219004
$135$	0.525183	0.0452006
$136$	−8.58242	−0.735936
$137$	−0.569722	−0.0486747	−0.0243373	−	0.999704i	$-0.507748\pi$
$137$	−0.569722	−0.0486747	−0.0243373	+	0.999704i	$0.507748\pi$
$138$	−9.33530	−0.794674
$139$	−13.0764	−1.10913	−0.554563	−	0.832142i	$-0.687115\pi$
$139$	−13.0764	−1.10913	−0.554563	+	0.832142i	$0.687115\pi$
$140$	−5.37618	−0.454370
$141$	−3.91359	−0.329584
$142$	12.0693	1.01283
$143$	−21.9671	−1.83698
$144$	12.6295	1.05246
$145$	−3.15786	−0.262246
$146$	16.0980	1.33228
$147$	3.12271	0.257557
$148$	−12.7392	−1.04716
$149$	−21.6746	−1.77566	−0.887828	−	0.460176i	$-0.847786\pi$
$149$	−21.6746	−1.77566	−0.887828	+	0.460176i	$0.847786\pi$
$150$	−12.6752	−1.03493
$151$	8.73297	0.710679	0.355339	−	0.934737i	$-0.384365\pi$
$151$	8.73297	0.710679	0.355339	+	0.934737i	$0.384365\pi$
$152$	21.1470	1.71525
$153$	1.00000	0.0808452
$154$	−22.3174	−1.79839
$155$	0.561856	0.0451293
$156$	27.0346	2.16450
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	−37.6462	−2.99497
$159$	0.313221	0.0248400
$160$	8.78151	0.694239
$161$	−6.85115	−0.539947
$162$	−2.68305	−0.210800
$163$	17.4146	1.36402	0.682010	−	0.731343i	$-0.261106\pi$
$163$	17.4146	1.36402	0.682010	+	0.731343i	$0.261106\pi$
$164$	53.4551	4.17415
$165$	2.21852	0.172711
$166$	37.9326	2.94414
$167$	−9.92685	−0.768163	−0.384082	−	0.923299i	$-0.625482\pi$
$167$	−9.92685	−0.768163	−0.384082	+	0.923299i	$0.625482\pi$
$168$	16.8995	1.30382
$169$	14.0422	1.08017
$170$	1.40909	0.108072
$171$	−2.46399	−0.188426
$172$	−5.76232	−0.439373
$173$	13.2231	1.00534	0.502668	−	0.864479i	$-0.332352\pi$
$173$	13.2231	1.00534	0.502668	+	0.864479i	$0.332352\pi$
$174$	16.1328	1.22303
$175$	−9.30231	−0.703188
$176$	53.3506	4.02145
$177$	−9.87145	−0.741983
$178$	6.42793	0.481794
$179$	−9.29057	−0.694410	−0.347205	−	0.937789i	$-0.612869\pi$
$179$	−9.29057	−0.694410	−0.347205	+	0.937789i	$0.612869\pi$
$180$	−2.73030	−0.203504
$181$	0.364362	0.0270828	0.0135414	−	0.999908i	$-0.495690\pi$
$181$	0.364362	0.0270828	0.0135414	+	0.999908i	$0.495690\pi$
$182$	27.4735	2.03647
$183$	1.73138	0.127987
$184$	29.8613	2.20141
$185$	1.28693	0.0946167
$186$	−2.87040	−0.210468
$187$	4.22427	0.308909
$188$	20.3458	1.48387
$189$	−1.96908	−0.143230
$190$	−3.47200	−0.251885
$191$	−18.6207	−1.34735	−0.673674	−	0.739028i	$-0.735285\pi$
$191$	−18.6207	−1.34735	−0.673674	+	0.739028i	$0.735285\pi$
$192$	−19.6038	−1.41478
$193$	1.28633	0.0925923	0.0462961	−	0.998928i	$-0.485258\pi$
$193$	1.28633	0.0925923	0.0462961	+	0.998928i	$0.485258\pi$
$194$	9.36116	0.672092
$195$	−2.73107	−0.195576
$196$	−16.2342	−1.15959
$197$	−15.7333	−1.12095	−0.560475	−	0.828171i	$-0.689382\pi$
$197$	−15.7333	−1.12095	−0.560475	+	0.828171i	$0.689382\pi$
$198$	−11.3339	−0.805467
$199$	−17.8497	−1.26533	−0.632667	−	0.774424i	$-0.718040\pi$
$199$	−17.8497	−1.26533	−0.632667	+	0.774424i	$0.718040\pi$
$200$	40.5449	2.86696
$201$	0.944877	0.0666465
$202$	−39.2341	−2.76050
$203$	11.8398	0.830993
$204$	−5.19875	−0.363986
$205$	−5.40009	−0.377159
$206$	−12.8338	−0.894171
$207$	−3.47936	−0.241832
$208$	−65.6763	−4.55383
$209$	−10.4086	−0.719976
$210$	−2.77462	−0.191467
$211$	−14.8184	−1.02014	−0.510071	−	0.860132i	$-0.670381\pi$
$211$	−14.8184	−1.02014	−0.510071	+	0.860132i	$0.670381\pi$
$212$	−1.62836	−0.111836
$213$	4.49834	0.308221
$214$	4.40653	0.301224
$215$	0.582115	0.0396999
$216$	8.58242	0.583960
$217$	−2.10658	−0.143004
$218$	19.7744	1.33929
$219$	5.99990	0.405436
$220$	−11.5335	−0.777590
$221$	−5.20022	−0.349804
$222$	−6.57463	−0.441261
$223$	11.4958	0.769819	0.384909	−	0.922954i	$-0.374233\pi$
$223$	11.4958	0.769819	0.384909	+	0.922954i	$0.374233\pi$
$224$	−32.9247	−2.19988
$225$	−4.72418	−0.314946
$226$	−2.13517	−0.142030
$227$	−4.92541	−0.326911	−0.163456	−	0.986551i	$-0.552264\pi$
$227$	−4.92541	−0.326911	−0.163456	+	0.986551i	$0.552264\pi$
$228$	12.8097	0.848343
$229$	13.2873	0.878048	0.439024	−	0.898475i	$-0.355324\pi$
$229$	13.2873	0.878048	0.439024	+	0.898475i	$0.355324\pi$
$230$	−4.90274	−0.323277
$231$	−8.31794	−0.547280
$232$	−51.6049	−3.38803
$233$	8.74326	0.572790	0.286395	−	0.958112i	$-0.407543\pi$
$233$	8.74326	0.572790	0.286395	+	0.958112i	$0.407543\pi$
$234$	13.9524	0.912099
$235$	−2.05535	−0.134076
$236$	51.3192	3.34060
$237$	−14.0311	−0.911420
$238$	−5.28315	−0.342456
$239$	−1.27237	−0.0823028	−0.0411514	−	0.999153i	$-0.513103\pi$
$239$	−1.27237	−0.0823028	−0.0411514	+	0.999153i	$0.513103\pi$
$240$	6.63282	0.428147
$241$	−16.9556	−1.09221	−0.546104	−	0.837718i	$-0.683890\pi$
$241$	−16.9556	−1.09221	−0.546104	+	0.837718i	$0.683890\pi$
$242$	−18.3640	−1.18048
$243$	−1.00000	−0.0641500
$244$	−9.00101	−0.576230
$245$	1.64000	0.104776
$246$	27.5879	1.75894
$247$	12.8133	0.815291
$248$	9.18171	0.583039
$249$	14.1379	0.895952
$250$	−13.7023	−0.866608
$251$	5.43742	0.343207	0.171603	−	0.985166i	$-0.445105\pi$
$251$	5.43742	0.343207	0.171603	+	0.985166i	$0.445105\pi$
$252$	10.2368	0.644856
$253$	−14.6978	−0.924041
$254$	4.51747	0.283451
$255$	0.525183	0.0328882
$256$	12.1895	0.761847
$257$	−4.67582	−0.291669	−0.145835	−	0.989309i	$-0.546587\pi$
$257$	−4.67582	−0.291669	−0.145835	+	0.989309i	$0.546587\pi$
$258$	−2.97390	−0.185147
$259$	−4.82511	−0.299817
$260$	14.1981	0.880531
$261$	6.01287	0.372187
$262$	19.7856	1.22236
$263$	−7.20880	−0.444514	−0.222257	−	0.974988i	$-0.571342\pi$
$263$	−7.20880	−0.444514	−0.222257	+	0.974988i	$0.571342\pi$
$264$	36.2544	2.23131
$265$	0.164498	0.0101051
$266$	13.0176	0.798163
$267$	2.39575	0.146618
$268$	−4.91218	−0.300059
$269$	13.0760	0.797257	0.398629	−	0.917112i	$-0.369486\pi$
$269$	13.0760	0.797257	0.398629	+	0.917112i	$0.369486\pi$
$270$	−1.40909	−0.0857546
$271$	−32.0423	−1.94643	−0.973215	−	0.229896i	$-0.926161\pi$
$271$	−32.0423	−1.94643	−0.973215	+	0.229896i	$0.926161\pi$
$272$	12.6295	0.765778
$273$	10.2397	0.619732
$274$	1.52859	0.0923457
$275$	−19.9562	−1.20341
$276$	18.0884	1.08879
$277$	−1.69388	−0.101775	−0.0508876	−	0.998704i	$-0.516205\pi$
$277$	−1.69388	−0.101775	−0.0508876	+	0.998704i	$0.516205\pi$
$278$	35.0847	2.10424
$279$	−1.06983	−0.0640489
$280$	8.87533	0.530402
$281$	5.84064	0.348423	0.174212	−	0.984708i	$-0.444262\pi$
$281$	5.84064	0.348423	0.174212	+	0.984708i	$0.444262\pi$
$282$	10.5004	0.625287
$283$	29.7877	1.77070	0.885349	−	0.464927i	$-0.153919\pi$
$283$	29.7877	1.77070	0.885349	+	0.464927i	$0.153919\pi$
$284$	−23.3858	−1.38769
$285$	−1.29405	−0.0766528
$286$	58.9389	3.48513
$287$	20.2467	1.19512
$288$	−16.7209	−0.985286
$289$	1.00000	0.0588235
$290$	8.47269	0.497533
$291$	3.48900	0.204529
$292$	−31.1920	−1.82537
$293$	18.4116	1.07562	0.537809	−	0.843067i	$-0.319252\pi$
$293$	18.4116	1.07562	0.537809	+	0.843067i	$0.319252\pi$
$294$	−8.37840	−0.488638
$295$	−5.18432	−0.301843
$296$	21.0306	1.22238
$297$	−4.22427	−0.245117
$298$	58.1541	3.36878
$299$	18.0934	1.04637
$300$	24.5599	1.41796
$301$	−2.18254	−0.125799
$302$	−23.4310	−1.34830
$303$	−14.6229	−0.840066
$304$	−31.1191	−1.78480
$305$	0.909290	0.0520658
$306$	−2.68305	−0.153380
$307$	8.16216	0.465839	0.232920	−	0.972496i	$-0.425172\pi$
$307$	8.16216	0.465839	0.232920	+	0.972496i	$0.425172\pi$
$308$	43.2429	2.46399
$309$	−4.78327	−0.272111
$310$	−1.50749	−0.0856195
$311$	−27.3450	−1.55060	−0.775298	−	0.631596i	$-0.782400\pi$
$311$	−27.3450	−1.55060	−0.775298	+	0.631596i	$0.782400\pi$
$312$	−44.6304	−2.52670
$313$	−4.70021	−0.265671	−0.132836	−	0.991138i	$-0.542408\pi$
$313$	−4.70021	−0.265671	−0.132836	+	0.991138i	$0.542408\pi$
$314$	−2.68305	−0.151413
$315$	−1.03413	−0.0582666
$316$	72.9444	4.10345
$317$	13.4376	0.754733	0.377366	−	0.926064i	$-0.376830\pi$
$317$	13.4376	0.754733	0.377366	+	0.926064i	$0.376830\pi$
$318$	−0.840387	−0.0471266
$319$	25.4000	1.42213
$320$	−10.2956	−0.575540
$321$	1.64236	0.0916676
$322$	18.3820	1.02439
$323$	−2.46399	−0.137100
$324$	5.19875	0.288820
$325$	24.5668	1.36272
$326$	−46.7243	−2.58782
$327$	7.37010	0.407568
$328$	−88.2470	−4.87262
$329$	7.70618	0.424855
$330$	−5.95239	−0.327668
$331$	−0.300459	−0.0165147	−0.00825736	−	0.999966i	$-0.502628\pi$
$331$	−0.300459	−0.0165147	−0.00825736	+	0.999966i	$0.502628\pi$
$332$	−73.4994	−4.03380
$333$	−2.45043	−0.134283
$334$	26.6342	1.45736
$335$	0.496234	0.0271121
$336$	−24.8686	−1.35669
$337$	−4.54283	−0.247464	−0.123732	−	0.992316i	$-0.539486\pi$
$337$	−4.54283	−0.247464	−0.123732	+	0.992316i	$0.539486\pi$
$338$	−37.6760	−2.04931
$339$	−0.795801	−0.0432220
$340$	−2.73030	−0.148071
$341$	−4.51924	−0.244731
$342$	6.61102	0.357483
$343$	−19.9325	−1.07625
$344$	9.51279	0.512895
$345$	−1.82730	−0.0983787
$346$	−35.4783	−1.90733
$347$	−19.0103	−1.02053	−0.510264	−	0.860018i	$-0.670452\pi$
$347$	−19.0103	−1.02053	−0.510264	+	0.860018i	$0.670452\pi$
$348$	−31.2594	−1.67568
$349$	27.6053	1.47768	0.738838	−	0.673883i	$-0.235375\pi$
$349$	27.6053	1.47768	0.738838	+	0.673883i	$0.235375\pi$
$350$	24.9585	1.33409
$351$	5.20022	0.277567
$352$	−70.6334	−3.76477
$353$	11.1009	0.590841	0.295420	−	0.955367i	$-0.404540\pi$
$353$	11.1009	0.590841	0.295420	+	0.955367i	$0.404540\pi$
$354$	26.4856	1.40769
$355$	2.36245	0.125386
$356$	−12.4549	−0.660111
$357$	−1.96908	−0.104215
$358$	24.9271	1.31744
$359$	16.6406	0.878258	0.439129	−	0.898424i	$-0.355287\pi$
$359$	16.6406	0.878258	0.439129	+	0.898424i	$0.355287\pi$
$360$	4.50734	0.237558
$361$	−12.9287	−0.680459
$362$	−0.977601	−0.0513816
$363$	−6.84446	−0.359241
$364$	−53.2335	−2.79019
$365$	3.15105	0.164933
$366$	−4.64537	−0.242817
$367$	0.832625	0.0434627	0.0217313	−	0.999764i	$-0.493082\pi$
$367$	0.832625	0.0434627	0.0217313	+	0.999764i	$0.493082\pi$
$368$	−43.9428	−2.29068
$369$	10.2823	0.535275
$370$	−3.45289	−0.179507
$371$	−0.616758	−0.0320205
$372$	5.56177	0.288365
$373$	−30.9085	−1.60038	−0.800191	−	0.599746i	$-0.795268\pi$
$373$	−30.9085	−1.60038	−0.800191	+	0.599746i	$0.795268\pi$
$374$	−11.3339	−0.586063
$375$	−5.10698	−0.263723
$376$	−33.5880	−1.73217
$377$	−31.2682	−1.61039
$378$	5.28315	0.271736
$379$	31.0197	1.59337	0.796687	−	0.604392i	$-0.206584\pi$
$379$	31.0197	1.59337	0.796687	+	0.604392i	$0.206584\pi$
$380$	6.72744	0.345110
$381$	1.68371	0.0862588
$382$	49.9603	2.55619
$383$	−15.9414	−0.814570	−0.407285	−	0.913301i	$-0.633524\pi$
$383$	−15.9414	−0.814570	−0.407285	+	0.913301i	$0.633524\pi$
$384$	19.1562	0.977562
$385$	−4.36844	−0.222636
$386$	−3.45129	−0.175666
$387$	−1.10840	−0.0563433
$388$	−18.1384	−0.920840
$389$	17.1540	0.869740	0.434870	−	0.900493i	$-0.356794\pi$
$389$	17.1540	0.869740	0.434870	+	0.900493i	$0.356794\pi$
$390$	7.32758	0.371047
$391$	−3.47936	−0.175959
$392$	26.8004	1.35363
$393$	7.37430	0.371984
$394$	42.2132	2.12667
$395$	−7.36892	−0.370770
$396$	21.9609	1.10358
$397$	−6.37064	−0.319733	−0.159867	−	0.987139i	$-0.551106\pi$
$397$	−6.37064	−0.319733	−0.159867	+	0.987139i	$0.551106\pi$
$398$	47.8917	2.40059
$399$	4.85181	0.242894
$400$	−59.6643	−2.98321
$401$	−6.01989	−0.300619	−0.150309	−	0.988639i	$-0.548027\pi$
$401$	−6.01989	−0.300619	−0.150309	+	0.988639i	$0.548027\pi$
$402$	−2.53515	−0.126442
$403$	5.56334	0.277130
$404$	76.0211	3.78219
$405$	−0.525183	−0.0260966
$406$	−31.7669	−1.57656
$407$	−10.3513	−0.513094
$408$	8.58242	0.424893
$409$	4.65418	0.230134	0.115067	−	0.993358i	$-0.463292\pi$
$409$	4.65418	0.230134	0.115067	+	0.993358i	$0.463292\pi$
$410$	14.4887	0.715546
$411$	0.569722	0.0281023
$412$	24.8671	1.22511
$413$	19.4377	0.956467
$414$	9.33530	0.458805
$415$	7.42498	0.364478
$416$	86.9520	4.26317
$417$	13.0764	0.640355
$418$	27.9267	1.36594
$419$	−2.80762	−0.137161	−0.0685807	−	0.997646i	$-0.521847\pi$
$419$	−2.80762	−0.137161	−0.0685807	+	0.997646i	$0.521847\pi$
$420$	5.37618	0.262331
$421$	25.1136	1.22396	0.611980	−	0.790873i	$-0.290373\pi$
$421$	25.1136	1.22396	0.611980	+	0.790873i	$0.290373\pi$
$422$	39.7585	1.93542
$423$	3.91359	0.190285
$424$	2.68819	0.130550
$425$	−4.72418	−0.229157
$426$	−12.0693	−0.584759
$427$	−3.40923	−0.164984
$428$	−8.53822	−0.412711
$429$	21.9671	1.06058
$430$	−1.56184	−0.0753188
$431$	−32.3123	−1.55643	−0.778214	−	0.628000i	$-0.783874\pi$
$431$	−32.3123	−1.55643	−0.778214	+	0.628000i	$0.783874\pi$
$432$	−12.6295	−0.607639
$433$	20.3466	0.977795	0.488897	−	0.872341i	$-0.337399\pi$
$433$	20.3466	0.977795	0.488897	+	0.872341i	$0.337399\pi$
$434$	5.65206	0.271307
$435$	3.15786	0.151408
$436$	−38.3154	−1.83497
$437$	8.57313	0.410109
$438$	−16.0980	−0.769194
$439$	29.0723	1.38755	0.693773	−	0.720193i	$-0.255947\pi$
$439$	29.0723	1.38755	0.693773	+	0.720193i	$0.255947\pi$
$440$	19.0402	0.907707
$441$	−3.12271	−0.148701
$442$	13.9524	0.663650
$443$	37.7468	1.79341	0.896703	−	0.442632i	$-0.145955\pi$
$443$	37.7468	1.79341	0.896703	+	0.442632i	$0.145955\pi$
$444$	12.7392	0.604576
$445$	1.25821	0.0596449
$446$	−30.8439	−1.46050
$447$	21.6746	1.02518
$448$	38.6015	1.82375
$449$	0.730718	0.0344847	0.0172423	−	0.999851i	$-0.494511\pi$
$449$	0.730718	0.0344847	0.0172423	+	0.999851i	$0.494511\pi$
$450$	12.6752	0.597515
$451$	43.4352	2.04528
$452$	4.13717	0.194596
$453$	−8.73297	−0.410311
$454$	13.2151	0.620217
$455$	5.37769	0.252110
$456$	−21.1470	−0.990301
$457$	3.98661	0.186486	0.0932429	−	0.995643i	$-0.470277\pi$
$457$	3.98661	0.186486	0.0932429	+	0.995643i	$0.470277\pi$
$458$	−35.6504	−1.66584
$459$	−1.00000	−0.0466760
$460$	9.49970	0.442926
$461$	−4.05045	−0.188648	−0.0943241	−	0.995542i	$-0.530069\pi$
$461$	−4.05045	−0.188648	−0.0943241	+	0.995542i	$0.530069\pi$
$462$	22.3174	1.03830
$463$	−34.5064	−1.60365	−0.801824	−	0.597561i	$-0.796137\pi$
$463$	−34.5064	−1.60365	−0.801824	+	0.597561i	$0.796137\pi$
$464$	75.9398	3.52541
$465$	−0.561856	−0.0260554
$466$	−23.4586	−1.08670
$467$	13.9182	0.644060	0.322030	−	0.946730i	$-0.395635\pi$
$467$	13.9182	0.644060	0.322030	+	0.946730i	$0.395635\pi$
$468$	−27.0346	−1.24968
$469$	−1.86054	−0.0859118
$470$	5.51461	0.254370
$471$	−1.00000	−0.0460776
$472$	−84.7209	−3.89959
$473$	−4.68220	−0.215288
$474$	37.6462	1.72915
$475$	11.6404	0.534096
$476$	10.2368	0.469202
$477$	−0.313221	−0.0143414
$478$	3.41383	0.156145
$479$	−20.7831	−0.949605	−0.474802	−	0.880092i	$-0.657480\pi$
$479$	−20.7831	−0.949605	−0.474802	+	0.880092i	$0.657480\pi$
$480$	−8.78151	−0.400819
$481$	12.7428	0.581021
$482$	45.4928	2.07214
$483$	6.85115	0.311738
$484$	35.5826	1.61739
$485$	1.83236	0.0832033
$486$	2.68305	0.121706
$487$	−12.1529	−0.550699	−0.275350	−	0.961344i	$-0.588794\pi$
$487$	−12.1529	−0.550699	−0.275350	+	0.961344i	$0.588794\pi$
$488$	14.8594	0.672654
$489$	−17.4146	−0.787517
$490$	−4.40019	−0.198780
$491$	7.84423	0.354005	0.177003	−	0.984210i	$-0.443360\pi$
$491$	7.84423	0.354005	0.177003	+	0.984210i	$0.443360\pi$
$492$	−53.4551	−2.40994
$493$	6.01287	0.270806
$494$	−34.3787	−1.54677
$495$	−2.21852	−0.0997148
$496$	−13.5114	−0.606682
$497$	−8.85761	−0.397318
$498$	−37.9326	−1.69980
$499$	−25.6403	−1.14782	−0.573908	−	0.818920i	$-0.694573\pi$
$499$	−25.6403	−1.14782	−0.573908	+	0.818920i	$0.694573\pi$
$500$	26.5499	1.18735
$501$	9.92685	0.443499
$502$	−14.5889	−0.651133
$503$	20.8869	0.931302	0.465651	−	0.884968i	$-0.345820\pi$
$503$	20.8869	0.931302	0.465651	+	0.884968i	$0.345820\pi$
$504$	−16.8995	−0.752763
$505$	−7.67972	−0.341743
$506$	39.4348	1.75309
$507$	−14.0422	−0.623638
$508$	−8.75317	−0.388359
$509$	19.6975	0.873075	0.436537	−	0.899686i	$-0.356205\pi$
$509$	19.6975	0.873075	0.436537	+	0.899686i	$0.356205\pi$
$510$	−1.40909	−0.0623957
$511$	−11.8143	−0.522634
$512$	5.60731	0.247810
$513$	2.46399	0.108788
$514$	12.5454	0.553356
$515$	−2.51210	−0.110696
$516$	5.76232	0.253672
$517$	16.5321	0.727079
$518$	12.9460	0.568814
$519$	−13.2231	−0.580432
$520$	−23.4391	−1.02787
$521$	−23.2349	−1.01794	−0.508971	−	0.860784i	$-0.669974\pi$
$521$	−23.2349	−1.01794	−0.508971	+	0.860784i	$0.669974\pi$
$522$	−16.1328	−0.706114
$523$	−20.1944	−0.883040	−0.441520	−	0.897251i	$-0.645561\pi$
$523$	−20.1944	−0.883040	−0.441520	+	0.897251i	$0.645561\pi$
$524$	−38.3372	−1.67477
$525$	9.30231	0.405986
$526$	19.3416	0.843333
$527$	−1.06983	−0.0466024
$528$	−53.3506	−2.32179
$529$	−10.8940	−0.473653
$530$	−0.441357	−0.0191713
$531$	9.87145	0.428384
$532$	−25.2234	−1.09357
$533$	−53.4702	−2.31605
$534$	−6.42793	−0.278164
$535$	0.862539	0.0372908
$536$	8.10933	0.350270
$537$	9.29057	0.400918
$538$	−35.0835	−1.51256
$539$	−13.1912	−0.568185
$540$	2.73030	0.117493
$541$	−38.5884	−1.65904	−0.829522	−	0.558474i	$-0.811387\pi$
$541$	−38.5884	−1.65904	−0.829522	+	0.558474i	$0.811387\pi$
$542$	85.9710	3.69277
$543$	−0.364362	−0.0156363
$544$	−16.7209	−0.716901
$545$	3.87066	0.165801
$546$	−27.4735	−1.17576
$547$	−3.27485	−0.140022	−0.0700112	−	0.997546i	$-0.522304\pi$
$547$	−3.27485	−0.140022	−0.0700112	+	0.997546i	$0.522304\pi$
$548$	−2.96185	−0.126524
$549$	−1.73138	−0.0738934
$550$	53.5435	2.28310
$551$	−14.8157	−0.631169
$552$	−29.8613	−1.27098
$553$	27.6285	1.17488
$554$	4.54475	0.193088
$555$	−1.28693	−0.0546270
$556$	−67.9810	−2.88304
$557$	5.83397	0.247193	0.123597	−	0.992333i	$-0.460557\pi$
$557$	5.83397	0.247193	0.123597	+	0.992333i	$0.460557\pi$
$558$	2.87040	0.121514
$559$	5.76394	0.243789
$560$	−13.0606	−0.551910
$561$	−4.22427	−0.178349
$562$	−15.6707	−0.661030
$563$	−1.16962	−0.0492934	−0.0246467	−	0.999696i	$-0.507846\pi$
$563$	−1.16962	−0.0492934	−0.0246467	+	0.999696i	$0.507846\pi$
$564$	−20.3458	−0.856712
$565$	−0.417941	−0.0175829
$566$	−79.9220	−3.35937
$567$	1.96908	0.0826937
$568$	38.6067	1.61990
$569$	17.2410	0.722780	0.361390	−	0.932415i	$-0.382302\pi$
$569$	17.2410	0.722780	0.361390	+	0.932415i	$0.382302\pi$
$570$	3.47200	0.145426
$571$	36.3301	1.52037	0.760183	−	0.649709i	$-0.225109\pi$
$571$	36.3301	1.52037	0.760183	+	0.649709i	$0.225109\pi$
$572$	−114.202	−4.77501
$573$	18.6207	0.777892
$574$	−54.3229	−2.26739
$575$	16.4371	0.685476
$576$	19.6038	0.816825
$577$	−4.00989	−0.166934	−0.0834670	−	0.996511i	$-0.526599\pi$
$577$	−4.00989	−0.166934	−0.0834670	+	0.996511i	$0.526599\pi$
$578$	−2.68305	−0.111600
$579$	−1.28633	−0.0534582
$580$	−16.4169	−0.681676
$581$	−27.8386	−1.15494
$582$	−9.36116	−0.388032
$583$	−1.32313	−0.0547984
$584$	51.4937	2.13082
$585$	2.73107	0.112916
$586$	−49.3993	−2.04067
$587$	−6.14913	−0.253802	−0.126901	−	0.991915i	$-0.540503\pi$
$587$	−6.14913	−0.253802	−0.126901	+	0.991915i	$0.540503\pi$
$588$	16.2342	0.669488
$589$	2.63605	0.108617
$590$	13.9098	0.572657
$591$	15.7333	0.647181
$592$	−30.9479	−1.27195
$593$	29.8906	1.22746	0.613731	−	0.789515i	$-0.289668\pi$
$593$	29.8906	1.22746	0.613731	+	0.789515i	$0.289668\pi$
$594$	11.3339	0.465037
$595$	−1.03413	−0.0423952
$596$	−112.681	−4.61560
$597$	17.8497	0.730541
$598$	−48.5456	−1.98518
$599$	12.0840	0.493737	0.246869	−	0.969049i	$-0.420598\pi$
$599$	12.0840	0.493737	0.246869	+	0.969049i	$0.420598\pi$
$600$	−40.5449	−1.65524
$601$	−46.1564	−1.88276	−0.941378	−	0.337352i	$-0.890469\pi$
$601$	−46.1564	−1.88276	−0.941378	+	0.337352i	$0.890469\pi$
$602$	5.85586	0.238667
$603$	−0.944877	−0.0384784
$604$	45.4006	1.84732
$605$	−3.59459	−0.146141
$606$	39.2341	1.59378
$607$	31.4387	1.27606	0.638028	−	0.770013i	$-0.279750\pi$
$607$	31.4387	1.27606	0.638028	+	0.770013i	$0.279750\pi$
$608$	41.2001	1.67088
$609$	−11.8398	−0.479774
$610$	−2.43967	−0.0987794
$611$	−20.3515	−0.823334
$612$	5.19875	0.210147
$613$	−43.0077	−1.73706	−0.868532	−	0.495634i	$-0.834936\pi$
$613$	−43.0077	−1.73706	−0.868532	+	0.495634i	$0.834936\pi$
$614$	−21.8995	−0.883791
$615$	5.40009	0.217753
$616$	−71.3880	−2.87630
$617$	−26.4014	−1.06288	−0.531441	−	0.847095i	$-0.678349\pi$
$617$	−26.4014	−1.06288	−0.531441	+	0.847095i	$0.678349\pi$
$618$	12.8338	0.516250
$619$	−41.7683	−1.67881	−0.839406	−	0.543505i	$-0.817097\pi$
$619$	−41.7683	−1.67881	−0.839406	+	0.543505i	$0.817097\pi$
$620$	2.92095	0.117308
$621$	3.47936	0.139622
$622$	73.3681	2.94179
$623$	−4.71744	−0.189000
$624$	65.6763	2.62916
$625$	20.9388	0.837553
$626$	12.6109	0.504032
$627$	10.4086	0.415679
$628$	5.19875	0.207453
$629$	−2.45043	−0.0977052
$630$	2.77462	0.110543
$631$	9.06904	0.361033	0.180516	−	0.983572i	$-0.442223\pi$
$631$	9.06904	0.361033	0.180516	+	0.983572i	$0.442223\pi$
$632$	−120.421	−4.79009
$633$	14.8184	0.588979
$634$	−36.0539	−1.43188
$635$	0.884254	0.0350905
$636$	1.62836	0.0645686
$637$	16.2388	0.643404
$638$	−68.1494	−2.69806
$639$	−4.49834	−0.177952
$640$	10.0605	0.397677
$641$	7.86576	0.310679	0.155339	−	0.987861i	$-0.450353\pi$
$641$	7.86576	0.310679	0.155339	+	0.987861i	$0.450353\pi$
$642$	−4.40653	−0.173912
$643$	−19.9507	−0.786778	−0.393389	−	0.919372i	$-0.628697\pi$
$643$	−19.9507	−0.786778	−0.393389	+	0.919372i	$0.628697\pi$
$644$	−35.6175	−1.40352
$645$	−0.582115	−0.0229208
$646$	6.61102	0.260107
$647$	4.03796	0.158749	0.0793743	−	0.996845i	$-0.474708\pi$
$647$	4.03796	0.158749	0.0793743	+	0.996845i	$0.474708\pi$
$648$	−8.58242	−0.337149
$649$	41.6997	1.63685
$650$	−65.9139	−2.58535
$651$	2.10658	0.0825634
$652$	90.5344	3.54560
$653$	22.3712	0.875451	0.437726	−	0.899109i	$-0.355784\pi$
$653$	22.3712	0.875451	0.437726	+	0.899109i	$0.355784\pi$
$654$	−19.7744	−0.773239
$655$	3.87286	0.151325
$656$	129.861	5.07021
$657$	−5.99990	−0.234078
$658$	−20.6761	−0.806037
$659$	−35.1178	−1.36799	−0.683997	−	0.729484i	$-0.739760\pi$
$659$	−35.1178	−1.36799	−0.683997	+	0.729484i	$0.739760\pi$
$660$	11.5335	0.448942
$661$	−41.3855	−1.60971	−0.804855	−	0.593471i	$-0.797757\pi$
$661$	−41.3855	−1.60971	−0.804855	+	0.593471i	$0.797757\pi$
$662$	0.806146	0.0313318
$663$	5.20022	0.201960
$664$	121.337	4.70880
$665$	2.54809	0.0988106
$666$	6.57463	0.254762
$667$	−20.9209	−0.810062
$668$	−51.6073	−1.99675
$669$	−11.4958	−0.444455
$670$	−1.33142	−0.0514372
$671$	−7.31381	−0.282346
$672$	32.9247	1.27010
$673$	−21.3386	−0.822542	−0.411271	−	0.911513i	$-0.634915\pi$
$673$	−21.3386	−0.822542	−0.411271	+	0.911513i	$0.634915\pi$
$674$	12.1886	0.469489
$675$	4.72418	0.181834
$676$	73.0022	2.80778
$677$	−15.8047	−0.607423	−0.303712	−	0.952764i	$-0.598226\pi$
$677$	−15.8047	−0.607423	−0.303712	+	0.952764i	$0.598226\pi$
$678$	2.13517	0.0820008
$679$	−6.87013	−0.263651
$680$	4.50734	0.172849
$681$	4.92541	0.188742
$682$	12.1254	0.464304
$683$	−18.0900	−0.692195	−0.346097	−	0.938199i	$-0.612493\pi$
$683$	−18.0900	−0.692195	−0.346097	+	0.938199i	$0.612493\pi$
$684$	−12.8097	−0.489791
$685$	0.299209	0.0114322
$686$	53.4798	2.04187
$687$	−13.2873	−0.506941
$688$	−13.9986	−0.533693
$689$	1.62882	0.0620530
$690$	4.90274	0.186644
$691$	42.3034	1.60930	0.804649	−	0.593750i	$-0.202353\pi$
$691$	42.3034	1.60930	0.804649	+	0.593750i	$0.202353\pi$
$692$	68.7439	2.61325
$693$	8.31794	0.315972
$694$	51.0057	1.93615
$695$	6.86751	0.260500
$696$	51.6049	1.95608
$697$	10.2823	0.389470
$698$	−74.0663	−2.80345
$699$	−8.74326	−0.330700
$700$	−48.3604	−1.82785
$701$	26.8295	1.01334	0.506668	−	0.862141i	$-0.330877\pi$
$701$	26.8295	1.01334	0.506668	+	0.862141i	$0.330877\pi$
$702$	−13.9524	−0.526601
$703$	6.03786	0.227722
$704$	82.8117	3.12108
$705$	2.05535	0.0774090
$706$	−29.7842	−1.12094
$707$	28.7938	1.08290
$708$	−51.3192	−1.92870
$709$	14.4920	0.544260	0.272130	−	0.962261i	$-0.412272\pi$
$709$	14.4920	0.544260	0.272130	+	0.962261i	$0.412272\pi$
$710$	−6.33858	−0.237883
$711$	14.0311	0.526209
$712$	20.5614	0.770570
$713$	3.72232	0.139402
$714$	5.28315	0.197717
$715$	11.5368	0.431450
$716$	−48.2994	−1.80503
$717$	1.27237	0.0475175
$718$	−44.6476	−1.66623
$719$	−13.7306	−0.512065	−0.256033	−	0.966668i	$-0.582415\pi$
$719$	−13.7306	−0.512065	−0.256033	+	0.966668i	$0.582415\pi$
$720$	−6.63282	−0.247191
$721$	9.41866	0.350769
$722$	34.6884	1.29097
$723$	16.9556	0.630586
$724$	1.89423	0.0703984
$725$	−28.4059	−1.05497
$726$	18.3640	0.681552
$727$	−23.0804	−0.856004	−0.428002	−	0.903778i	$-0.640782\pi$
$727$	−23.0804	−0.856004	−0.428002	+	0.903778i	$0.640782\pi$
$728$	87.8810	3.25709
$729$	1.00000	0.0370370
$730$	−8.45442	−0.312912
$731$	−1.10840	−0.0409958
$732$	9.00101	0.332687
$733$	−35.4714	−1.31017	−0.655083	−	0.755557i	$-0.727366\pi$
$733$	−35.4714	−1.31017	−0.655083	+	0.755557i	$0.727366\pi$
$734$	−2.23397	−0.0824575
$735$	−1.64000	−0.0604922
$736$	58.1779	2.14447
$737$	−3.99142	−0.147026
$738$	−27.5879	−1.01553
$739$	−38.3900	−1.41220	−0.706099	−	0.708113i	$-0.749547\pi$
$739$	−38.3900	−1.41220	−0.706099	+	0.708113i	$0.749547\pi$
$740$	6.69041	0.245945
$741$	−12.8133	−0.470709
$742$	1.65479	0.0607493
$743$	−24.2286	−0.888862	−0.444431	−	0.895813i	$-0.646594\pi$
$743$	−24.2286	−0.888862	−0.444431	+	0.895813i	$0.646594\pi$
$744$	−9.18171	−0.336618
$745$	11.3832	0.417047
$746$	82.9290	3.03625
$747$	−14.1379	−0.517278
$748$	21.9609	0.802972
$749$	−3.23394	−0.118166
$750$	13.7023	0.500336
$751$	9.35483	0.341363	0.170681	−	0.985326i	$-0.445403\pi$
$751$	9.35483	0.341363	0.170681	+	0.985326i	$0.445403\pi$
$752$	49.4268	1.80241
$753$	−5.43742	−0.198150
$754$	83.8941	3.05524
$755$	−4.58641	−0.166916
$756$	−10.2368	−0.372308
$757$	−37.7971	−1.37376	−0.686880	−	0.726771i	$-0.741020\pi$
$757$	−37.7971	−1.37376	−0.686880	+	0.726771i	$0.741020\pi$
$758$	−83.2273	−3.02295
$759$	14.6978	0.533495
$760$	−11.1061	−0.402859
$761$	−22.2799	−0.807647	−0.403824	−	0.914837i	$-0.632319\pi$
$761$	−22.2799	−0.807647	−0.403824	+	0.914837i	$0.632319\pi$
$762$	−4.51747	−0.163651
$763$	−14.5123	−0.525382
$764$	−96.8046	−3.50227
$765$	−0.525183	−0.0189880
$766$	42.7717	1.54540
$767$	−51.3337	−1.85355
$768$	−12.1895	−0.439852
$769$	23.3314	0.841353	0.420677	−	0.907211i	$-0.361793\pi$
$769$	23.3314	0.841353	0.420677	+	0.907211i	$0.361793\pi$
$770$	11.7207	0.422386
$771$	4.67582	0.168395
$772$	6.68733	0.240682
$773$	−16.4383	−0.591243	−0.295622	−	0.955305i	$-0.595527\pi$
$773$	−16.4383	−0.591243	−0.295622	+	0.955305i	$0.595527\pi$
$774$	2.97390	0.106895
$775$	5.05406	0.181547
$776$	29.9440	1.07493
$777$	4.82511	0.173100
$778$	−46.0249	−1.65007
$779$	−25.3355	−0.907740
$780$	−14.1981	−0.508375
$781$	−19.0022	−0.679953
$782$	9.33530	0.333830
$783$	−6.01287	−0.214882
$784$	−39.4384	−1.40852
$785$	−0.525183	−0.0187446
$786$	−19.7856	−0.705729
$787$	−2.45543	−0.0875264	−0.0437632	−	0.999042i	$-0.513935\pi$
$787$	−2.45543	−0.0875264	−0.0437632	+	0.999042i	$0.513935\pi$
$788$	−81.7935	−2.91377
$789$	7.20880	0.256640
$790$	19.7712	0.703427
$791$	1.56700	0.0557160
$792$	−36.2544	−1.28825
$793$	9.00354	0.319725
$794$	17.0927	0.606599
$795$	−0.164498	−0.00583416
$796$	−92.7963	−3.28908
$797$	3.15365	0.111708	0.0558540	−	0.998439i	$-0.482212\pi$
$797$	3.15365	0.111708	0.0558540	+	0.998439i	$0.482212\pi$
$798$	−13.0176	−0.460820
$799$	3.91359	0.138453
$800$	78.9924	2.79280
$801$	−2.39575	−0.0846498
$802$	16.1517	0.570335
$803$	−25.3452	−0.894413
$804$	4.91218	0.173239
$805$	3.59811	0.126817
$806$	−14.9267	−0.525771
$807$	−13.0760	−0.460297
$808$	−125.500	−4.41508
$809$	−13.4486	−0.472829	−0.236414	−	0.971652i	$-0.575972\pi$
$809$	−13.4486	−0.472829	−0.236414	+	0.971652i	$0.575972\pi$
$810$	1.40909	0.0495105
$811$	31.0390	1.08993	0.544963	−	0.838460i	$-0.316544\pi$
$811$	31.0390	1.08993	0.544963	+	0.838460i	$0.316544\pi$
$812$	61.5524	2.16007
$813$	32.0423	1.12377
$814$	27.7730	0.973444
$815$	−9.14587	−0.320366
$816$	−12.6295	−0.442122
$817$	2.73110	0.0955491
$818$	−12.4874	−0.436611
$819$	−10.2397	−0.357802
$820$	−28.0737	−0.980378
$821$	−12.6421	−0.441211	−0.220606	−	0.975363i	$-0.570803\pi$
$821$	−12.6421	−0.441211	−0.220606	+	0.975363i	$0.570803\pi$
$822$	−1.52859	−0.0533158
$823$	13.0192	0.453819	0.226910	−	0.973916i	$-0.427138\pi$
$823$	13.0192	0.453819	0.226910	+	0.973916i	$0.427138\pi$
$824$	−41.0521	−1.43012
$825$	19.9562	0.694786
$826$	−52.1523	−1.81461
$827$	4.78001	0.166217	0.0831087	−	0.996540i	$-0.473515\pi$
$827$	4.78001	0.166217	0.0831087	+	0.996540i	$0.473515\pi$
$828$	−18.0884	−0.628614
$829$	−10.1331	−0.351936	−0.175968	−	0.984396i	$-0.556306\pi$
$829$	−10.1331	−0.351936	−0.175968	+	0.984396i	$0.556306\pi$
$830$	−19.9216	−0.691488
$831$	1.69388	0.0587599
$832$	−101.944	−3.53427
$833$	−3.12271	−0.108196
$834$	−35.0847	−1.21488
$835$	5.21342	0.180418
$836$	−54.1117	−1.87149
$837$	1.06983	0.0369787
$838$	7.53299	0.260223
$839$	14.1591	0.488827	0.244413	−	0.969671i	$-0.421405\pi$
$839$	14.1591	0.488827	0.244413	+	0.969671i	$0.421405\pi$
$840$	−8.87533	−0.306228
$841$	7.15457	0.246709
$842$	−67.3810	−2.32210
$843$	−5.84064	−0.201162
$844$	−77.0373	−2.65173
$845$	−7.37475	−0.253699
$846$	−10.5004	−0.361010
$847$	13.4773	0.463085
$848$	−3.95584	−0.135844
$849$	−29.7877	−1.02231
$850$	12.6752	0.434756
$851$	8.52595	0.292266
$852$	23.3858	0.801184
$853$	−17.4867	−0.598734	−0.299367	−	0.954138i	$-0.596775\pi$
$853$	−17.4867	−0.598734	−0.299367	+	0.954138i	$0.596775\pi$
$854$	9.14712	0.313008
$855$	1.29405	0.0442555
$856$	14.0954	0.481771
$857$	−19.5390	−0.667439	−0.333720	−	0.942672i	$-0.608304\pi$
$857$	−19.5390	−0.667439	−0.333720	+	0.942672i	$0.608304\pi$
$858$	−58.9389	−2.01214
$859$	−14.5065	−0.494955	−0.247478	−	0.968894i	$-0.579602\pi$
$859$	−14.5065	−0.494955	−0.247478	+	0.968894i	$0.579602\pi$
$860$	3.02627	0.103195
$861$	−20.2467	−0.690006
$862$	86.6954	2.95286
$863$	2.92595	0.0996007	0.0498003	−	0.998759i	$-0.484142\pi$
$863$	2.92595	0.0996007	0.0498003	+	0.998759i	$0.484142\pi$
$864$	16.7209	0.568855
$865$	−6.94457	−0.236123
$866$	−54.5909	−1.85507
$867$	−1.00000	−0.0339618
$868$	−10.9516	−0.371721
$869$	59.2713	2.01064
$870$	−8.47269	−0.287251
$871$	4.91356	0.166490
$872$	63.2533	2.14203
$873$	−3.48900	−0.118085
$874$	−23.0021	−0.778059
$875$	10.0561	0.339957
$876$	31.1920	1.05388
$877$	25.7074	0.868076	0.434038	−	0.900895i	$-0.357088\pi$
$877$	25.7074	0.868076	0.434038	+	0.900895i	$0.357088\pi$
$878$	−78.0025	−2.63246
$879$	−18.4116	−0.621009
$880$	−28.0188	−0.944515
$881$	−38.4911	−1.29680	−0.648399	−	0.761301i	$-0.724561\pi$
$881$	−38.4911	−1.29680	−0.648399	+	0.761301i	$0.724561\pi$
$882$	8.37840	0.282115
$883$	−38.6798	−1.30168	−0.650840	−	0.759215i	$-0.725583\pi$
$883$	−38.6798	−1.30168	−0.650840	+	0.759215i	$0.725583\pi$
$884$	−27.0346	−0.909274
$885$	5.18432	0.174269
$886$	−101.277	−3.40245
$887$	0.587850	0.0197381	0.00986903	−	0.999951i	$-0.496859\pi$
$887$	0.587850	0.0197381	0.00986903	+	0.999951i	$0.496859\pi$
$888$	−21.0306	−0.705742
$889$	−3.31536	−0.111193
$890$	−3.37584	−0.113158
$891$	4.22427	0.141518
$892$	59.7641	2.00105
$893$	−9.64306	−0.322693
$894$	−58.1541	−1.94497
$895$	4.87925	0.163095
$896$	−37.7202	−1.26014
$897$	−18.0934	−0.604122
$898$	−1.96055	−0.0654244
$899$	−6.43273	−0.214544
$900$	−24.5599	−0.818662
$901$	−0.313221	−0.0104349
$902$	−116.539	−3.88032
$903$	2.18254	0.0726303
$904$	−6.82990	−0.227159
$905$	−0.191357	−0.00636091
$906$	23.4310	0.778442
$907$	−2.55925	−0.0849784	−0.0424892	−	0.999097i	$-0.513529\pi$
$907$	−2.55925	−0.0849784	−0.0424892	+	0.999097i	$0.513529\pi$
$908$	−25.6060	−0.849765
$909$	14.6229	0.485012
$910$	−14.4286	−0.478304
$911$	−52.3925	−1.73584	−0.867920	−	0.496703i	$-0.834544\pi$
$911$	−52.3925	−1.73584	−0.867920	+	0.496703i	$0.834544\pi$
$912$	31.1191	1.03046
$913$	−59.7222	−1.97652
$914$	−10.6963	−0.353801
$915$	−0.909290	−0.0300602
$916$	69.0773	2.28238
$917$	−14.5206	−0.479513
$918$	2.68305	0.0885538
$919$	18.5955	0.613410	0.306705	−	0.951805i	$-0.400773\pi$
$919$	18.5955	0.613410	0.306705	+	0.951805i	$0.400773\pi$
$920$	−15.6827	−0.517043
$921$	−8.16216	−0.268952
$922$	10.8676	0.357904
$923$	23.3924	0.769969
$924$	−43.2429	−1.42259
$925$	11.5763	0.380626
$926$	92.5823	3.04244
$927$	4.78327	0.157103
$928$	−100.540	−3.30040
$929$	41.1434	1.34987	0.674936	−	0.737876i	$-0.264171\pi$
$929$	41.1434	1.34987	0.674936	+	0.737876i	$0.264171\pi$
$930$	1.50749	0.0494324
$931$	7.69435	0.252172
$932$	45.4541	1.48890
$933$	27.3450	0.895237
$934$	−37.3433	−1.22191
$935$	−2.21852	−0.0725532
$936$	44.6304	1.45879
$937$	29.5112	0.964089	0.482045	−	0.876147i	$-0.339894\pi$
$937$	29.5112	0.964089	0.482045	+	0.876147i	$0.339894\pi$
$938$	4.99192	0.162992
$939$	4.70021	0.153385
$940$	−10.6853	−0.348515
$941$	−29.4078	−0.958667	−0.479334	−	0.877633i	$-0.659122\pi$
$941$	−29.4078	−0.958667	−0.479334	+	0.877633i	$0.659122\pi$
$942$	2.68305	0.0874185
$943$	−35.7759	−1.16502
$944$	124.672	4.05772
$945$	1.03413	0.0336402
$946$	12.5626	0.408444
$947$	−39.8043	−1.29347	−0.646733	−	0.762716i	$-0.723865\pi$
$947$	−39.8043	−1.29347	−0.646733	+	0.762716i	$0.723865\pi$
$948$	−72.9444	−2.36913
$949$	31.2008	1.01282
$950$	−31.2317	−1.01329
$951$	−13.4376	−0.435745
$952$	−16.8995	−0.547716
$953$	−36.7652	−1.19094	−0.595471	−	0.803377i	$-0.703035\pi$
$953$	−36.7652	−1.19094	−0.595471	+	0.803377i	$0.703035\pi$
$954$	0.840387	0.0272085
$955$	9.77929	0.316450
$956$	−6.61474	−0.213936
$957$	−25.4000	−0.821064
$958$	55.7621	1.80159
$959$	−1.12183	−0.0362258
$960$	10.2956	0.332288
$961$	−29.8555	−0.963080
$962$	−34.1895	−1.10231
$963$	−1.64236	−0.0529243
$964$	−88.1481	−2.83906
$965$	−0.675560	−0.0217471
$966$	−18.3820	−0.591431
$967$	−52.7353	−1.69585	−0.847926	−	0.530114i	$-0.822149\pi$
$967$	−52.7353	−1.69585	−0.847926	+	0.530114i	$0.822149\pi$
$968$	−58.7420	−1.88804
$969$	2.46399	0.0791549
$970$	−4.91632	−0.157854
$971$	15.6728	0.502964	0.251482	−	0.967862i	$-0.419082\pi$
$971$	15.6728	0.502964	0.251482	+	0.967862i	$0.419082\pi$
$972$	−5.19875	−0.166750
$973$	−25.7485	−0.825460
$974$	32.6067	1.04479
$975$	−24.5668	−0.786766
$976$	−21.8665	−0.699930
$977$	−32.1780	−1.02947	−0.514733	−	0.857351i	$-0.672109\pi$
$977$	−32.1780	−1.02947	−0.514733	+	0.857351i	$0.672109\pi$
$978$	46.7243	1.49408
$979$	−10.1203	−0.323447
$980$	8.52594	0.272351
$981$	−7.37010	−0.235309
$982$	−21.0465	−0.671619
$983$	14.9410	0.476544	0.238272	−	0.971199i	$-0.423419\pi$
$983$	14.9410	0.476544	0.238272	+	0.971199i	$0.423419\pi$
$984$	88.2470	2.81321
$985$	8.26286	0.263277
$986$	−16.1328	−0.513774
$987$	−7.70618	−0.245290
$988$	66.6132	2.11925
$989$	3.85654	0.122631
$990$	5.95239	0.189179
$991$	−47.8781	−1.52090	−0.760448	−	0.649398i	$-0.775021\pi$
$991$	−47.8781	−1.52090	−0.760448	+	0.649398i	$0.775021\pi$
$992$	17.8884	0.567958
$993$	0.300459	0.00953477
$994$	23.7654	0.753793
$995$	9.37437	0.297188
$996$	73.4994	2.32892
$997$	−52.4215	−1.66021	−0.830103	−	0.557610i	$-0.811719\pi$
$997$	−52.4215	−1.66021	−0.830103	+	0.557610i	$0.811719\pi$
$998$	68.7941	2.17764
$999$	2.45043	0.0775283

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.c.1.1	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.c.1.1	✓	39	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.68305 q^{2} -1.00000 q^{3} +5.19875 q^{4} -0.525183 q^{5} +2.68305 q^{6} +1.96908 q^{7} -8.58242 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.68305 q^{2} -1.00000 q^{3} +5.19875 q^{4} -0.525183 q^{5} +2.68305 q^{6} +1.96908 q^{7} -8.58242 q^{8} +1.00000 q^{9} +1.40909 q^{10} +4.22427 q^{11} -5.19875 q^{12} -5.20022 q^{13} -5.28315 q^{14} +0.525183 q^{15} +12.6295 q^{16} +1.00000 q^{17} -2.68305 q^{18} -2.46399 q^{19} -2.73030 q^{20} -1.96908 q^{21} -11.3339 q^{22} -3.47936 q^{23} +8.58242 q^{24} -4.72418 q^{25} +13.9524 q^{26} -1.00000 q^{27} +10.2368 q^{28} +6.01287 q^{29} -1.40909 q^{30} -1.06983 q^{31} -16.7209 q^{32} -4.22427 q^{33} -2.68305 q^{34} -1.03413 q^{35} +5.19875 q^{36} -2.45043 q^{37} +6.61102 q^{38} +5.20022 q^{39} +4.50734 q^{40} +10.2823 q^{41} +5.28315 q^{42} -1.10840 q^{43} +21.9609 q^{44} -0.525183 q^{45} +9.33530 q^{46} +3.91359 q^{47} -12.6295 q^{48} -3.12271 q^{49} +12.6752 q^{50} -1.00000 q^{51} -27.0346 q^{52} -0.313221 q^{53} +2.68305 q^{54} -2.21852 q^{55} -16.8995 q^{56} +2.46399 q^{57} -16.1328 q^{58} +9.87145 q^{59} +2.73030 q^{60} -1.73138 q^{61} +2.87040 q^{62} +1.96908 q^{63} +19.6038 q^{64} +2.73107 q^{65} +11.3339 q^{66} -0.944877 q^{67} +5.19875 q^{68} +3.47936 q^{69} +2.77462 q^{70} -4.49834 q^{71} -8.58242 q^{72} -5.99990 q^{73} +6.57463 q^{74} +4.72418 q^{75} -12.8097 q^{76} +8.31794 q^{77} -13.9524 q^{78} +14.0311 q^{79} -6.63282 q^{80} +1.00000 q^{81} -27.5879 q^{82} -14.1379 q^{83} -10.2368 q^{84} -0.525183 q^{85} +2.97390 q^{86} -6.01287 q^{87} -36.2544 q^{88} -2.39575 q^{89} +1.40909 q^{90} -10.2397 q^{91} -18.0884 q^{92} +1.06983 q^{93} -10.5004 q^{94} +1.29405 q^{95} +16.7209 q^{96} -3.48900 q^{97} +8.37840 q^{98} +4.22427 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9}+O(q^{10}) \) 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9} + 4 q^{10} + q^{11} - 30 q^{12} - 26 q^{13} - 4 q^{14} + 3 q^{15} + 8 q^{16} + 39 q^{17} - 4 q^{18} - 14 q^{19} - 14 q^{20} + 5 q^{21} - 17 q^{22} + 2 q^{23} + 3 q^{24} - 6 q^{25} - 17 q^{26} - 39 q^{27} - 14 q^{28} - 7 q^{29} - 4 q^{30} - q^{31} - 30 q^{32} - q^{33} - 4 q^{34} + q^{35} + 30 q^{36} - 24 q^{37} - 20 q^{38} + 26 q^{39} + 12 q^{40} + q^{41} + 4 q^{42} - 41 q^{43} - 2 q^{44} - 3 q^{45} - 6 q^{46} - 9 q^{47} - 8 q^{48} - 10 q^{49} - 9 q^{50} - 39 q^{51} - 37 q^{52} - 47 q^{53} + 4 q^{54} - 39 q^{55} + 8 q^{56} + 14 q^{57} - 27 q^{58} + 41 q^{59} + 14 q^{60} - 41 q^{61} + 36 q^{62} - 5 q^{63} - 47 q^{64} - 39 q^{65} + 17 q^{66} - 36 q^{67} + 30 q^{68} - 2 q^{69} - 52 q^{70} - 2 q^{71} - 3 q^{72} - 63 q^{73} - 6 q^{74} + 6 q^{75} - 34 q^{76} - 64 q^{77} + 17 q^{78} + 20 q^{79} - 28 q^{80} + 39 q^{81} - 37 q^{82} + 45 q^{83} + 14 q^{84} - 3 q^{85} + 32 q^{86} + 7 q^{87} + 6 q^{88} - 32 q^{89} + 4 q^{90} - 11 q^{91} + 28 q^{92} + q^{93} - 44 q^{94} + 22 q^{95} + 30 q^{96} - 20 q^{97} + 63 q^{98} + q^{99}+O(q^{100}) \) 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9 + 4 * q^10 + q^11 - 30 * q^12 - 26 * q^13 - 4 * q^14 + 3 * q^15 + 8 * q^16 + 39 * q^17 - 4 * q^18 - 14 * q^19 - 14 * q^20 + 5 * q^21 - 17 * q^22 + 2 * q^23 + 3 * q^24 - 6 * q^25 - 17 * q^26 - 39 * q^27 - 14 * q^28 - 7 * q^29 - 4 * q^30 - q^31 - 30 * q^32 - q^33 - 4 * q^34 + q^35 + 30 * q^36 - 24 * q^37 - 20 * q^38 + 26 * q^39 + 12 * q^40 + q^41 + 4 * q^42 - 41 * q^43 - 2 * q^44 - 3 * q^45 - 6 * q^46 - 9 * q^47 - 8 * q^48 - 10 * q^49 - 9 * q^50 - 39 * q^51 - 37 * q^52 - 47 * q^53 + 4 * q^54 - 39 * q^55 + 8 * q^56 + 14 * q^57 - 27 * q^58 + 41 * q^59 + 14 * q^60 - 41 * q^61 + 36 * q^62 - 5 * q^63 - 47 * q^64 - 39 * q^65 + 17 * q^66 - 36 * q^67 + 30 * q^68 - 2 * q^69 - 52 * q^70 - 2 * q^71 - 3 * q^72 - 63 * q^73 - 6 * q^74 + 6 * q^75 - 34 * q^76 - 64 * q^77 + 17 * q^78 + 20 * q^79 - 28 * q^80 + 39 * q^81 - 37 * q^82 + 45 * q^83 + 14 * q^84 - 3 * q^85 + 32 * q^86 + 7 * q^87 + 6 * q^88 - 32 * q^89 + 4 * q^90 - 11 * q^91 + 28 * q^92 + q^93 - 44 * q^94 + 22 * q^95 + 30 * q^96 - 20 * q^97 + 63 * q^98 + q^99

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