LMFDB - Embedded newform 41.2.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [41,2,Mod(1,41)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(41, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("41.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	41.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:	$0.327386648287$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.311108$ of defining polynomial
Character	$\chi$	$=$	41.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.90321 q^{2} -2.21432 q^{3} +1.62222 q^{4} -2.90321 q^{5} -4.21432 q^{6} +4.21432 q^{7} -0.719004 q^{8} +1.90321 q^{9} +O(q^{10})$	\(q+1.90321 q^{2} -2.21432 q^{3} +1.62222 q^{4} -2.90321 q^{5} -4.21432 q^{6} +4.21432 q^{7} -0.719004 q^{8} +1.90321 q^{9} -5.52543 q^{10} +2.83654 q^{11} -3.59210 q^{12} -0.622216 q^{13} +8.02074 q^{14} +6.42864 q^{15} -4.61285 q^{16} -2.00000 q^{17} +3.62222 q^{18} -0.836535 q^{19} -4.70964 q^{20} -9.33185 q^{21} +5.39853 q^{22} -3.05086 q^{23} +1.59210 q^{24} +3.42864 q^{25} -1.18421 q^{26} +2.42864 q^{27} +6.83654 q^{28} +2.42864 q^{29} +12.2351 q^{30} +9.80642 q^{31} -7.34122 q^{32} -6.28100 q^{33} -3.80642 q^{34} -12.2351 q^{35} +3.08742 q^{36} -8.70964 q^{37} -1.59210 q^{38} +1.37778 q^{39} +2.08742 q^{40} +1.00000 q^{41} -17.7605 q^{42} -1.37778 q^{43} +4.60147 q^{44} -5.52543 q^{45} -5.80642 q^{46} -6.77631 q^{47} +10.2143 q^{48} +10.7605 q^{49} +6.52543 q^{50} +4.42864 q^{51} -1.00937 q^{52} +6.42864 q^{53} +4.62222 q^{54} -8.23506 q^{55} -3.03011 q^{56} +1.85236 q^{57} +4.62222 q^{58} -7.05086 q^{59} +10.4286 q^{60} +5.18421 q^{61} +18.6637 q^{62} +8.02074 q^{63} -4.74620 q^{64} +1.80642 q^{65} -11.9541 q^{66} -2.83654 q^{67} -3.24443 q^{68} +6.75557 q^{69} -23.2859 q^{70} +8.96989 q^{71} -1.36842 q^{72} +1.39207 q^{73} -16.5763 q^{74} -7.59210 q^{75} -1.35704 q^{76} +11.9541 q^{77} +2.62222 q^{78} +8.40790 q^{79} +13.3921 q^{80} -11.0874 q^{81} +1.90321 q^{82} +8.85728 q^{83} -15.1383 q^{84} +5.80642 q^{85} -2.62222 q^{86} -5.37778 q^{87} -2.03948 q^{88} -6.29529 q^{89} -10.5161 q^{90} -2.62222 q^{91} -4.94914 q^{92} -21.7146 q^{93} -12.8968 q^{94} +2.42864 q^{95} +16.2558 q^{96} -6.85728 q^{97} +20.4795 q^{98} +5.39853 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - q^{2} + 5 q^{4} - 2 q^{5} - 6 q^{6} + 6 q^{7} - 9 q^{8} - q^{9}+O(q^{10}) $ 3 * q - q^2 + 5 * q^4 - 2 * q^5 - 6 * q^6 + 6 * q^7 - 9 * q^8 - q^9	\( 3 q - q^{2} + 5 q^{4} - 2 q^{5} - 6 q^{6} + 6 q^{7} - 9 q^{8} - q^{9} - 10 q^{10} + 2 q^{11} - 4 q^{12} - 2 q^{13} + 4 q^{14} + 6 q^{15} + 13 q^{16} - 6 q^{17} + 11 q^{18} + 4 q^{19} + 6 q^{20} - 8 q^{21} - 4 q^{22} + 4 q^{23} - 2 q^{24} - 3 q^{25} + 10 q^{26} - 6 q^{27} + 14 q^{28} - 6 q^{29} + 10 q^{30} + 16 q^{31} - 29 q^{32} - 12 q^{33} + 2 q^{34} - 10 q^{35} - 11 q^{36} - 6 q^{37} + 2 q^{38} + 4 q^{39} - 14 q^{40} + 3 q^{41} - 20 q^{42} - 4 q^{43} + 34 q^{44} - 10 q^{45} - 4 q^{46} + 24 q^{48} - q^{49} + 13 q^{50} - 30 q^{52} + 6 q^{53} + 14 q^{54} + 2 q^{55} - 16 q^{56} + 12 q^{57} + 14 q^{58} - 8 q^{59} + 18 q^{60} + 2 q^{61} + 16 q^{62} + 4 q^{63} + 13 q^{64} - 8 q^{65} - 16 q^{66} - 2 q^{67} - 10 q^{68} + 20 q^{69} - 30 q^{70} + 20 q^{71} + 23 q^{72} - 2 q^{73} - 30 q^{74} - 16 q^{75} - 24 q^{76} + 16 q^{77} + 8 q^{78} + 32 q^{79} + 34 q^{80} - 13 q^{81} - q^{82} - 12 q^{84} + 4 q^{85} - 8 q^{86} - 16 q^{87} - 40 q^{88} - 6 q^{89} + 2 q^{90} - 8 q^{91} - 28 q^{92} - 12 q^{93} - 46 q^{94} - 6 q^{95} + 2 q^{96} + 6 q^{97} + 35 q^{98} - 4 q^{99}+O(q^{100}) \) 3 * q - q^2 + 5 * q^4 - 2 * q^5 - 6 * q^6 + 6 * q^7 - 9 * q^8 - q^9 - 10 * q^10 + 2 * q^11 - 4 * q^12 - 2 * q^13 + 4 * q^14 + 6 * q^15 + 13 * q^16 - 6 * q^17 + 11 * q^18 + 4 * q^19 + 6 * q^20 - 8 * q^21 - 4 * q^22 + 4 * q^23 - 2 * q^24 - 3 * q^25 + 10 * q^26 - 6 * q^27 + 14 * q^28 - 6 * q^29 + 10 * q^30 + 16 * q^31 - 29 * q^32 - 12 * q^33 + 2 * q^34 - 10 * q^35 - 11 * q^36 - 6 * q^37 + 2 * q^38 + 4 * q^39 - 14 * q^40 + 3 * q^41 - 20 * q^42 - 4 * q^43 + 34 * q^44 - 10 * q^45 - 4 * q^46 + 24 * q^48 - q^49 + 13 * q^50 - 30 * q^52 + 6 * q^53 + 14 * q^54 + 2 * q^55 - 16 * q^56 + 12 * q^57 + 14 * q^58 - 8 * q^59 + 18 * q^60 + 2 * q^61 + 16 * q^62 + 4 * q^63 + 13 * q^64 - 8 * q^65 - 16 * q^66 - 2 * q^67 - 10 * q^68 + 20 * q^69 - 30 * q^70 + 20 * q^71 + 23 * q^72 - 2 * q^73 - 30 * q^74 - 16 * q^75 - 24 * q^76 + 16 * q^77 + 8 * q^78 + 32 * q^79 + 34 * q^80 - 13 * q^81 - q^82 - 12 * q^84 + 4 * q^85 - 8 * q^86 - 16 * q^87 - 40 * q^88 - 6 * q^89 + 2 * q^90 - 8 * q^91 - 28 * q^92 - 12 * q^93 - 46 * q^94 - 6 * q^95 + 2 * q^96 + 6 * q^97 + 35 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.90321	1.34577	0.672887	−	0.739745i	$-0.265054\pi$
$2$	1.90321	1.34577	0.672887	+	0.739745i	$0.265054\pi$
$3$	−2.21432	−1.27844	−0.639219	−	0.769025i	$-0.720742\pi$
$3$	−2.21432	−1.27844	−0.639219	+	0.769025i	$0.720742\pi$
$4$	1.62222	0.811108
$5$	−2.90321	−1.29836	−0.649178	−	0.760637i	$-0.724887\pi$
$5$	−2.90321	−1.29836	−0.649178	+	0.760637i	$0.724887\pi$
$6$	−4.21432	−1.72049
$7$	4.21432	1.59286	0.796432	−	0.604729i	$-0.206718\pi$
$7$	4.21432	1.59286	0.796432	+	0.604729i	$0.206718\pi$
$8$	−0.719004	−0.254206
$9$	1.90321	0.634404
$10$	−5.52543	−1.74729
$11$	2.83654	0.855248	0.427624	−	0.903957i	$-0.359351\pi$
$11$	2.83654	0.855248	0.427624	+	0.903957i	$0.359351\pi$
$12$	−3.59210	−1.03695
$13$	−0.622216	−0.172572	−0.0862858	−	0.996270i	$-0.527500\pi$
$13$	−0.622216	−0.172572	−0.0862858	+	0.996270i	$0.527500\pi$
$14$	8.02074	2.14363
$15$	6.42864	1.65987
$16$	−4.61285	−1.15321
$17$	−2.00000	−0.485071	−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000	−0.485071	−0.242536	+	0.970143i	$0.577979\pi$
$18$	3.62222	0.853764
$19$	−0.836535	−0.191914	−0.0959572	−	0.995385i	$-0.530591\pi$
$19$	−0.836535	−0.191914	−0.0959572	+	0.995385i	$0.530591\pi$
$20$	−4.70964	−1.05311
$21$	−9.33185	−2.03638
$22$	5.39853	1.15097
$23$	−3.05086	−0.636147	−0.318074	−	0.948066i	$-0.603036\pi$
$23$	−3.05086	−0.636147	−0.318074	+	0.948066i	$0.603036\pi$
$24$	1.59210	0.324987
$25$	3.42864	0.685728
$26$	−1.18421	−0.232242
$27$	2.42864	0.467392
$28$	6.83654	1.29198
$29$	2.42864	0.450987	0.225494	−	0.974245i	$-0.427601\pi$
$29$	2.42864	0.450987	0.225494	+	0.974245i	$0.427601\pi$
$30$	12.2351	2.23381
$31$	9.80642	1.76129	0.880643	−	0.473781i	$-0.157111\pi$
$31$	9.80642	1.76129	0.880643	+	0.473781i	$0.157111\pi$
$32$	−7.34122	−1.29776
$33$	−6.28100	−1.09338
$34$	−3.80642	−0.652796
$35$	−12.2351	−2.06810
$36$	3.08742	0.514570
$37$	−8.70964	−1.43186	−0.715928	−	0.698174i	$-0.753996\pi$
$37$	−8.70964	−1.43186	−0.715928	+	0.698174i	$0.753996\pi$
$38$	−1.59210	−0.258273
$39$	1.37778	0.220622
$40$	2.08742	0.330050
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	−17.7605	−2.74050
$43$	−1.37778	−0.210110	−0.105055	−	0.994466i	$-0.533502\pi$
$43$	−1.37778	−0.210110	−0.105055	+	0.994466i	$0.533502\pi$
$44$	4.60147	0.693698
$45$	−5.52543	−0.823682
$46$	−5.80642	−0.856110
$47$	−6.77631	−0.988427	−0.494213	−	0.869341i	$-0.664544\pi$
$47$	−6.77631	−0.988427	−0.494213	+	0.869341i	$0.664544\pi$
$48$	10.2143	1.47431
$49$	10.7605	1.53721
$50$	6.52543	0.922835
$51$	4.42864	0.620134
$52$	−1.00937	−0.139974
$53$	6.42864	0.883042	0.441521	−	0.897251i	$-0.354439\pi$
$53$	6.42864	0.883042	0.441521	+	0.897251i	$0.354439\pi$
$54$	4.62222	0.629004
$55$	−8.23506	−1.11042
$56$	−3.03011	−0.404916
$57$	1.85236	0.245351
$58$	4.62222	0.606927
$59$	−7.05086	−0.917943	−0.458972	−	0.888451i	$-0.651782\pi$
$59$	−7.05086	−0.917943	−0.458972	+	0.888451i	$0.651782\pi$
$60$	10.4286	1.34633
$61$	5.18421	0.663770	0.331885	−	0.943320i	$-0.392315\pi$
$61$	5.18421	0.663770	0.331885	+	0.943320i	$0.392315\pi$
$62$	18.6637	2.37029
$63$	8.02074	1.01052
$64$	−4.74620	−0.593275
$65$	1.80642	0.224059
$66$	−11.9541	−1.47144
$67$	−2.83654	−0.346538	−0.173269	−	0.984875i	$-0.555433\pi$
$67$	−2.83654	−0.346538	−0.173269	+	0.984875i	$0.555433\pi$
$68$	−3.24443	−0.393445
$69$	6.75557	0.813275
$70$	−23.2859	−2.78320
$71$	8.96989	1.06453	0.532265	−	0.846578i	$-0.321341\pi$
$71$	8.96989	1.06453	0.532265	+	0.846578i	$0.321341\pi$
$72$	−1.36842	−0.161269
$73$	1.39207	0.162930	0.0814650	−	0.996676i	$-0.474040\pi$
$73$	1.39207	0.162930	0.0814650	+	0.996676i	$0.474040\pi$
$74$	−16.5763	−1.92695
$75$	−7.59210	−0.876661
$76$	−1.35704	−0.155663
$77$	11.9541	1.36229
$78$	2.62222	0.296907
$79$	8.40790	0.945962	0.472981	−	0.881073i	$-0.343178\pi$
$79$	8.40790	0.945962	0.472981	+	0.881073i	$0.343178\pi$
$80$	13.3921	1.49728
$81$	−11.0874	−1.23194
$82$	1.90321	0.210175
$83$	8.85728	0.972213	0.486106	−	0.873900i	$-0.338417\pi$
$83$	8.85728	0.972213	0.486106	+	0.873900i	$0.338417\pi$
$84$	−15.1383	−1.65172
$85$	5.80642	0.629795
$86$	−2.62222	−0.282761
$87$	−5.37778	−0.576559
$88$	−2.03948	−0.217409
$89$	−6.29529	−0.667299	−0.333650	−	0.942697i	$-0.608280\pi$
$89$	−6.29529	−0.667299	−0.333650	+	0.942697i	$0.608280\pi$
$90$	−10.5161	−1.10849
$91$	−2.62222	−0.274883
$92$	−4.94914	−0.515984
$93$	−21.7146	−2.25169
$94$	−12.8968	−1.33020
$95$	2.42864	0.249173
$96$	16.2558	1.65910
$97$	−6.85728	−0.696251	−0.348126	−	0.937448i	$-0.613182\pi$
$97$	−6.85728	−0.696251	−0.348126	+	0.937448i	$0.613182\pi$
$98$	20.4795	2.06874
$99$	5.39853	0.542572
$100$	5.56199	0.556199
$101$	5.86665	0.583753	0.291877	−	0.956456i	$-0.405720\pi$
$101$	5.86665	0.583753	0.291877	+	0.956456i	$0.405720\pi$
$102$	8.42864	0.834560
$103$	−14.7971	−1.45800	−0.728999	−	0.684515i	$-0.760014\pi$
$103$	−14.7971	−1.45800	−0.728999	+	0.684515i	$0.760014\pi$
$104$	0.447375	0.0438688
$105$	27.0923	2.64394
$106$	12.2351	1.18837
$107$	3.61285	0.349267	0.174634	−	0.984633i	$-0.444126\pi$
$107$	3.61285	0.349267	0.174634	+	0.984633i	$0.444126\pi$
$108$	3.93978	0.379105
$109$	−10.9906	−1.05271	−0.526356	−	0.850264i	$-0.676442\pi$
$109$	−10.9906	−1.05271	−0.526356	+	0.850264i	$0.676442\pi$
$110$	−15.6731	−1.49437
$111$	19.2859	1.83054
$112$	−19.4400	−1.83691
$113$	−9.00492	−0.847112	−0.423556	−	0.905870i	$-0.639218\pi$
$113$	−9.00492	−0.847112	−0.423556	+	0.905870i	$0.639218\pi$
$114$	3.52543	0.330187
$115$	8.85728	0.825946
$116$	3.93978	0.365799
$117$	−1.18421	−0.109480
$118$	−13.4193	−1.23534
$119$	−8.42864	−0.772652
$120$	−4.62222	−0.421949
$121$	−2.95407	−0.268552
$122$	9.86665	0.893284
$123$	−2.21432	−0.199658
$124$	15.9081	1.42859
$125$	4.56199	0.408037
$126$	15.2652	1.35993
$127$	0.949145	0.0842230	0.0421115	−	0.999113i	$-0.486592\pi$
$127$	0.949145	0.0842230	0.0421115	+	0.999113i	$0.486592\pi$
$128$	5.64941	0.499342
$129$	3.05086	0.268613
$130$	3.43801	0.301533
$131$	−11.1842	−0.977169	−0.488584	−	0.872517i	$-0.662487\pi$
$131$	−11.1842	−0.977169	−0.488584	+	0.872517i	$0.662487\pi$
$132$	−10.1891	−0.886850
$133$	−3.52543	−0.305693
$134$	−5.39853	−0.466362
$135$	−7.05086	−0.606841
$136$	1.43801	0.123308
$137$	−11.7146	−1.00084	−0.500421	−	0.865782i	$-0.666821\pi$
$137$	−11.7146	−1.00084	−0.500421	+	0.865782i	$0.666821\pi$
$138$	12.8573	1.09448
$139$	18.2766	1.55020	0.775098	−	0.631841i	$-0.217700\pi$
$139$	18.2766	1.55020	0.775098	+	0.631841i	$0.217700\pi$
$140$	−19.8479	−1.67745
$141$	15.0049	1.26364
$142$	17.0716	1.43262
$143$	−1.76494	−0.147591
$144$	−8.77923	−0.731602
$145$	−7.05086	−0.585542
$146$	2.64941	0.219267
$147$	−23.8272	−1.96523
$148$	−14.1289	−1.16139
$149$	16.5303	1.35422	0.677110	−	0.735882i	$-0.263232\pi$
$149$	16.5303	1.35422	0.677110	+	0.735882i	$0.263232\pi$
$150$	−14.4494	−1.17979
$151$	2.60147	0.211705	0.105852	−	0.994382i	$-0.466243\pi$
$151$	2.60147	0.211705	0.105852	+	0.994382i	$0.466243\pi$
$152$	0.601472	0.0487858
$153$	−3.80642	−0.307731
$154$	22.7511	1.83334
$155$	−28.4701	−2.28678
$156$	2.23506	0.178948
$157$	13.0923	1.04488	0.522441	−	0.852675i	$-0.325021\pi$
$157$	13.0923	1.04488	0.522441	+	0.852675i	$0.325021\pi$
$158$	16.0020	1.27305
$159$	−14.2351	−1.12891
$160$	21.3131	1.68495
$161$	−12.8573	−1.01330
$162$	−21.1017	−1.65791
$163$	−5.24443	−0.410776	−0.205388	−	0.978681i	$-0.565846\pi$
$163$	−5.24443	−0.410776	−0.205388	+	0.978681i	$0.565846\pi$
$164$	1.62222	0.126674
$165$	18.2351	1.41960
$166$	16.8573	1.30838
$167$	2.02074	0.156370	0.0781849	−	0.996939i	$-0.475088\pi$
$167$	2.02074	0.156370	0.0781849	+	0.996939i	$0.475088\pi$
$168$	6.70964	0.517660
$169$	−12.6128	−0.970219
$170$	11.0509	0.847562
$171$	−1.59210	−0.121751
$172$	−2.23506	−0.170422
$173$	−1.14272	−0.0868795	−0.0434397	−	0.999056i	$-0.513832\pi$
$173$	−1.14272	−0.0868795	−0.0434397	+	0.999056i	$0.513832\pi$
$174$	−10.2351	−0.775918
$175$	14.4494	1.09227
$176$	−13.0845	−0.986282
$177$	15.6128	1.17353
$178$	−11.9813	−0.898034
$179$	−15.0114	−1.12200	−0.561001	−	0.827815i	$-0.689584\pi$
$179$	−15.0114	−1.12200	−0.561001	+	0.827815i	$0.689584\pi$
$180$	−8.96343	−0.668095
$181$	−24.5303	−1.82333	−0.911663	−	0.410938i	$-0.865201\pi$
$181$	−24.5303	−1.82333	−0.911663	+	0.410938i	$0.865201\pi$
$182$	−4.99063	−0.369930
$183$	−11.4795	−0.848589
$184$	2.19358	0.161713
$185$	25.2859	1.85906
$186$	−41.3274	−3.03027
$187$	−5.67307	−0.414856
$188$	−10.9926	−0.801721
$189$	10.2351	0.744491
$190$	4.62222	0.335331
$191$	24.8178	1.79575	0.897876	−	0.440247i	$-0.145109\pi$
$191$	24.8178	1.79575	0.897876	+	0.440247i	$0.145109\pi$
$192$	10.5096	0.758465
$193$	−13.0509	−0.939421	−0.469711	−	0.882820i	$-0.655642\pi$
$193$	−13.0509	−0.939421	−0.469711	+	0.882820i	$0.655642\pi$
$194$	−13.0509	−0.936997
$195$	−4.00000	−0.286446
$196$	17.4558	1.24685
$197$	21.1842	1.50931	0.754656	−	0.656120i	$-0.227804\pi$
$197$	21.1842	1.50931	0.754656	+	0.656120i	$0.227804\pi$
$198$	10.2745	0.730180
$199$	26.4494	1.87495	0.937474	−	0.348057i	$-0.113158\pi$
$199$	26.4494	1.87495	0.937474	+	0.348057i	$0.113158\pi$
$200$	−2.46520	−0.174316
$201$	6.28100	0.443027
$202$	11.1655	0.785600
$203$	10.2351	0.718361
$204$	7.18421	0.502995
$205$	−2.90321	−0.202769
$206$	−28.1619	−1.96213
$207$	−5.80642	−0.403574
$208$	2.87019	0.199012
$209$	−2.37286	−0.164134
$210$	51.5625	3.55815
$211$	−12.2558	−0.843725	−0.421862	−	0.906660i	$-0.638623\pi$
$211$	−12.2558	−0.843725	−0.421862	+	0.906660i	$0.638623\pi$
$212$	10.4286	0.716242
$213$	−19.8622	−1.36094
$214$	6.87601	0.470035
$215$	4.00000	0.272798
$216$	−1.74620	−0.118814
$217$	41.3274	2.80549
$218$	−20.9175	−1.41671
$219$	−3.08250	−0.208296
$220$	−13.3590	−0.900667
$221$	1.24443	0.0837095
$222$	36.7052	2.46349
$223$	−11.6128	−0.777654	−0.388827	−	0.921311i	$-0.627120\pi$
$223$	−11.6128	−0.777654	−0.388827	+	0.921311i	$0.627120\pi$
$224$	−30.9382	−2.06715
$225$	6.52543	0.435029
$226$	−17.1383	−1.14002
$227$	4.96989	0.329863	0.164932	−	0.986305i	$-0.447260\pi$
$227$	4.96989	0.329863	0.164932	+	0.986305i	$0.447260\pi$
$228$	3.00492	0.199006
$229$	15.8479	1.04726	0.523630	−	0.851946i	$-0.324578\pi$
$229$	15.8479	1.04726	0.523630	+	0.851946i	$0.324578\pi$
$230$	16.8573	1.11154
$231$	−26.4701	−1.74161
$232$	−1.74620	−0.114644
$233$	17.3461	1.13638	0.568192	−	0.822896i	$-0.307643\pi$
$233$	17.3461	1.13638	0.568192	+	0.822896i	$0.307643\pi$
$234$	−2.25380	−0.147335
$235$	19.6731	1.28333
$236$	−11.4380	−0.744551
$237$	−18.6178	−1.20935
$238$	−16.0415	−1.03982
$239$	−5.69381	−0.368302	−0.184151	−	0.982898i	$-0.558954\pi$
$239$	−5.69381	−0.368302	−0.184151	+	0.982898i	$0.558954\pi$
$240$	−29.6543	−1.91418
$241$	−20.1432	−1.29754	−0.648769	−	0.760986i	$-0.724716\pi$
$241$	−20.1432	−1.29754	−0.648769	+	0.760986i	$0.724716\pi$
$242$	−5.62222	−0.361410
$243$	17.2652	1.10756
$244$	8.40990	0.538389
$245$	−31.2400	−1.99585
$246$	−4.21432	−0.268695
$247$	0.520505	0.0331190
$248$	−7.05086	−0.447730
$249$	−19.6128	−1.24291
$250$	8.68244	0.549126
$251$	−4.81579	−0.303970	−0.151985	−	0.988383i	$-0.548567\pi$
$251$	−4.81579	−0.303970	−0.151985	+	0.988383i	$0.548567\pi$
$252$	13.0114	0.819640
$253$	−8.65386	−0.544063
$254$	1.80642	0.113345
$255$	−12.8573	−0.805154
$256$	20.2444	1.26528
$257$	−1.31756	−0.0821872	−0.0410936	−	0.999155i	$-0.513084\pi$
$257$	−1.31756	−0.0821872	−0.0410936	+	0.999155i	$0.513084\pi$
$258$	5.80642	0.361492
$259$	−36.7052	−2.28075
$260$	2.93041	0.181736
$261$	4.62222	0.286108
$262$	−21.2859	−1.31505
$263$	30.8464	1.90207	0.951035	−	0.309084i	$-0.100023\pi$
$263$	30.8464	1.90207	0.951035	+	0.309084i	$0.100023\pi$
$264$	4.51606	0.277944
$265$	−18.6637	−1.14650
$266$	−6.70964	−0.411394
$267$	13.9398	0.853100
$268$	−4.60147	−0.281080
$269$	−0.917502	−0.0559411	−0.0279705	−	0.999609i	$-0.508904\pi$
$269$	−0.917502	−0.0559411	−0.0279705	+	0.999609i	$0.508904\pi$
$270$	−13.4193	−0.816671
$271$	−5.80642	−0.352715	−0.176358	−	0.984326i	$-0.556431\pi$
$271$	−5.80642	−0.352715	−0.176358	+	0.984326i	$0.556431\pi$
$272$	9.22570	0.559390
$273$	5.80642	0.351421
$274$	−22.2953	−1.34691
$275$	9.72546	0.586467
$276$	10.9590	0.659654
$277$	10.2494	0.615824	0.307912	−	0.951415i	$-0.400370\pi$
$277$	10.2494	0.615824	0.307912	+	0.951415i	$0.400370\pi$
$278$	34.7841	2.08621
$279$	18.6637	1.11737
$280$	8.79706	0.525725
$281$	12.7556	0.760933	0.380467	−	0.924795i	$-0.375763\pi$
$281$	12.7556	0.760933	0.380467	+	0.924795i	$0.375763\pi$
$282$	28.5575	1.70058
$283$	20.7654	1.23438	0.617188	−	0.786816i	$-0.288272\pi$
$283$	20.7654	1.23438	0.617188	+	0.786816i	$0.288272\pi$
$284$	14.5511	0.863449
$285$	−5.37778	−0.318552
$286$	−3.35905	−0.198625
$287$	4.21432	0.248763
$288$	−13.9719	−0.823302
$289$	−13.0000	−0.764706
$290$	−13.4193	−0.788007
$291$	15.1842	0.890114
$292$	2.25824	0.132154
$293$	18.6953	1.09219	0.546097	−	0.837722i	$-0.316113\pi$
$293$	18.6953	1.09219	0.546097	+	0.837722i	$0.316113\pi$
$294$	−45.3481	−2.64476
$295$	20.4701	1.19182
$296$	6.26226	0.363986
$297$	6.88892	0.399736
$298$	31.4608	1.82247
$299$	1.89829	0.109781
$300$	−12.3160	−0.711066
$301$	−5.80642	−0.334677
$302$	4.95115	0.284907
$303$	−12.9906	−0.746292
$304$	3.85881	0.221318
$305$	−15.0509	−0.861809
$306$	−7.24443	−0.414137
$307$	−8.81579	−0.503144	−0.251572	−	0.967839i	$-0.580947\pi$
$307$	−8.81579	−0.503144	−0.251572	+	0.967839i	$0.580947\pi$
$308$	19.3921	1.10497
$309$	32.7654	1.86396
$310$	−54.1847	−3.07748
$311$	−7.56046	−0.428714	−0.214357	−	0.976755i	$-0.568766\pi$
$311$	−7.56046	−0.428714	−0.214357	+	0.976755i	$0.568766\pi$
$312$	−0.990632	−0.0560835
$313$	−6.68244	−0.377714	−0.188857	−	0.982005i	$-0.560478\pi$
$313$	−6.68244	−0.377714	−0.188857	+	0.982005i	$0.560478\pi$
$314$	24.9175	1.40618
$315$	−23.2859	−1.31201
$316$	13.6394	0.767277
$317$	−22.9906	−1.29128	−0.645641	−	0.763641i	$-0.723410\pi$
$317$	−22.9906	−1.29128	−0.645641	+	0.763641i	$0.723410\pi$
$318$	−27.0923	−1.51926
$319$	6.88892	0.385706
$320$	13.7792	0.770282
$321$	−8.00000	−0.446516
$322$	−24.4701	−1.36367
$323$	1.67307	0.0930921
$324$	−17.9862	−0.999233
$325$	−2.13335	−0.118337
$326$	−9.98126	−0.552811
$327$	24.3368	1.34583
$328$	−0.719004	−0.0397003
$329$	−28.5575	−1.57443
$330$	34.7052	1.91046
$331$	8.37625	0.460401	0.230200	−	0.973143i	$-0.426062\pi$
$331$	8.37625	0.460401	0.230200	+	0.973143i	$0.426062\pi$
$332$	14.3684	0.788569
$333$	−16.5763	−0.908375
$334$	3.84590	0.210438
$335$	8.23506	0.449930
$336$	43.0464	2.34837
$337$	7.37334	0.401651	0.200826	−	0.979627i	$-0.435638\pi$
$337$	7.37334	0.401651	0.200826	+	0.979627i	$0.435638\pi$
$338$	−24.0049	−1.30570
$339$	19.9398	1.08298
$340$	9.41927	0.510832
$341$	27.8163	1.50634
$342$	−3.03011	−0.163850
$343$	15.8479	0.855707
$344$	0.990632	0.0534113
$345$	−19.6128	−1.05592
$346$	−2.17484	−0.116920
$347$	10.5096	0.564185	0.282093	−	0.959387i	$-0.408971\pi$
$347$	10.5096	0.564185	0.282093	+	0.959387i	$0.408971\pi$
$348$	−8.72393	−0.467652
$349$	−18.9032	−1.01187	−0.505933	−	0.862573i	$-0.668852\pi$
$349$	−18.9032	−1.01187	−0.505933	+	0.862573i	$0.668852\pi$
$350$	27.5002	1.46995
$351$	−1.51114	−0.0806586
$352$	−20.8236	−1.10990
$353$	−18.2494	−0.971315	−0.485658	−	0.874149i	$-0.661420\pi$
$353$	−18.2494	−0.971315	−0.485658	+	0.874149i	$0.661420\pi$
$354$	29.7146	1.57931
$355$	−26.0415	−1.38214
$356$	−10.2123	−0.541251
$357$	18.6637	0.987788
$358$	−28.5698	−1.50996
$359$	−17.1240	−0.903769	−0.451885	−	0.892076i	$-0.649248\pi$
$359$	−17.1240	−0.903769	−0.451885	+	0.892076i	$0.649248\pi$
$360$	3.97280	0.209385
$361$	−18.3002	−0.963169
$362$	−46.6865	−2.45379
$363$	6.54125	0.343327
$364$	−4.25380	−0.222960
$365$	−4.04149	−0.211541
$366$	−21.8479	−1.14201
$367$	12.3368	0.643974	0.321987	−	0.946744i	$-0.395649\pi$
$367$	12.3368	0.643974	0.321987	+	0.946744i	$0.395649\pi$
$368$	14.0731	0.733613
$369$	1.90321	0.0990773
$370$	48.1245	2.50187
$371$	27.0923	1.40656
$372$	−35.2257	−1.82637
$373$	−35.7146	−1.84923	−0.924615	−	0.380903i	$-0.875613\pi$
$373$	−35.7146	−1.84923	−0.924615	+	0.380903i	$0.875613\pi$
$374$	−10.7971	−0.558302
$375$	−10.1017	−0.521650
$376$	4.87219	0.251264
$377$	−1.51114	−0.0778275
$378$	19.4795	1.00192
$379$	11.4380	0.587531	0.293765	−	0.955878i	$-0.405092\pi$
$379$	11.4380	0.587531	0.293765	+	0.955878i	$0.405092\pi$
$380$	3.93978	0.202106
$381$	−2.10171	−0.107674
$382$	47.2335	2.41668
$383$	8.25581	0.421852	0.210926	−	0.977502i	$-0.432352\pi$
$383$	8.25581	0.421852	0.210926	+	0.977502i	$0.432352\pi$
$384$	−12.5096	−0.638378
$385$	−34.7052	−1.76874
$386$	−24.8385	−1.26425
$387$	−2.62222	−0.133295
$388$	−11.1240	−0.564735
$389$	−26.0830	−1.32246	−0.661230	−	0.750184i	$-0.729965\pi$
$389$	−26.0830	−1.32246	−0.661230	+	0.750184i	$0.729965\pi$
$390$	−7.61285	−0.385492
$391$	6.10171	0.308577
$392$	−7.73683	−0.390769
$393$	24.7654	1.24925
$394$	40.3180	2.03119
$395$	−24.4099	−1.22820
$396$	8.75758	0.440085
$397$	−1.47949	−0.0742537	−0.0371269	−	0.999311i	$-0.511821\pi$
$397$	−1.47949	−0.0742537	−0.0371269	+	0.999311i	$0.511821\pi$
$398$	50.3388	2.52326
$399$	7.80642	0.390810
$400$	−15.8158	−0.790790
$401$	26.9862	1.34763	0.673813	−	0.738902i	$-0.264655\pi$
$401$	26.9862	1.34763	0.673813	+	0.738902i	$0.264655\pi$
$402$	11.9541	0.596215
$403$	−6.10171	−0.303948
$404$	9.51697	0.473487
$405$	32.1891	1.59949
$406$	19.4795	0.966751
$407$	−24.7052	−1.22459
$408$	−3.18421	−0.157642
$409$	26.4242	1.30659	0.653296	−	0.757102i	$-0.273386\pi$
$409$	26.4242	1.30659	0.653296	+	0.757102i	$0.273386\pi$
$410$	−5.52543	−0.272881
$411$	25.9398	1.27951
$412$	−24.0040	−1.18259
$413$	−29.7146	−1.46216
$414$	−11.0509	−0.543120
$415$	−25.7146	−1.26228
$416$	4.56782	0.223956
$417$	−40.4701	−1.98183
$418$	−4.51606	−0.220888
$419$	−37.0736	−1.81116	−0.905582	−	0.424171i	$-0.860566\pi$
$419$	−37.0736	−1.81116	−0.905582	+	0.424171i	$0.860566\pi$
$420$	43.9496	2.14452
$421$	20.7971	1.01359	0.506793	−	0.862068i	$-0.330831\pi$
$421$	20.7971	1.01359	0.506793	+	0.862068i	$0.330831\pi$
$422$	−23.3254	−1.13546
$423$	−12.8968	−0.627062
$424$	−4.62222	−0.224475
$425$	−6.85728	−0.332627
$426$	−37.8020	−1.83151
$427$	21.8479	1.05729
$428$	5.86082	0.283293
$429$	3.90813	0.188686
$430$	7.61285	0.367124
$431$	−21.5812	−1.03953	−0.519765	−	0.854309i	$-0.673981\pi$
$431$	−21.5812	−1.03953	−0.519765	+	0.854309i	$0.673981\pi$
$432$	−11.2029	−0.539002
$433$	36.3051	1.74471	0.872357	−	0.488870i	$-0.162591\pi$
$433$	36.3051	1.74471	0.872357	+	0.488870i	$0.162591\pi$
$434$	78.6548	3.77555
$435$	15.6128	0.748579
$436$	−17.8292	−0.853863
$437$	2.55215	0.122086
$438$	−5.86665	−0.280319
$439$	−21.0212	−1.00329	−0.501644	−	0.865074i	$-0.667271\pi$
$439$	−21.0212	−1.00329	−0.501644	+	0.865074i	$0.667271\pi$
$440$	5.92104	0.282275
$441$	20.4795	0.975214
$442$	2.36842	0.112654
$443$	22.3269	1.06078	0.530392	−	0.847752i	$-0.322045\pi$
$443$	22.3269	1.06078	0.530392	+	0.847752i	$0.322045\pi$
$444$	31.2859	1.48476
$445$	18.2766	0.866392
$446$	−22.1017	−1.04655
$447$	−36.6035	−1.73129
$448$	−20.0020	−0.945006
$449$	11.6731	0.550886	0.275443	−	0.961317i	$-0.411175\pi$
$449$	11.6731	0.550886	0.275443	+	0.961317i	$0.411175\pi$
$450$	12.4193	0.585450
$451$	2.83654	0.133567
$452$	−14.6079	−0.687099
$453$	−5.76049	−0.270651
$454$	9.45875	0.443921
$455$	7.61285	0.356896
$456$	−1.33185	−0.0623697
$457$	12.1017	0.566094	0.283047	−	0.959106i	$-0.408655\pi$
$457$	12.1017	0.566094	0.283047	+	0.959106i	$0.408655\pi$
$458$	30.1619	1.40937
$459$	−4.85728	−0.226718
$460$	14.3684	0.669931
$461$	−10.6079	−0.494060	−0.247030	−	0.969008i	$-0.579455\pi$
$461$	−10.6079	−0.494060	−0.247030	+	0.969008i	$0.579455\pi$
$462$	−50.3783	−2.34381
$463$	−25.8687	−1.20222	−0.601109	−	0.799167i	$-0.705274\pi$
$463$	−25.8687	−1.20222	−0.601109	+	0.799167i	$0.705274\pi$
$464$	−11.2029	−0.520084
$465$	63.0420	2.92350
$466$	33.0134	1.52932
$467$	−14.1936	−0.656800	−0.328400	−	0.944539i	$-0.606509\pi$
$467$	−14.1936	−0.656800	−0.328400	+	0.944539i	$0.606509\pi$
$468$	−1.92104	−0.0888002
$469$	−11.9541	−0.551988
$470$	37.4420	1.72707
$471$	−28.9906	−1.33582
$472$	5.06959	0.233347
$473$	−3.90813	−0.179696
$474$	−35.4336	−1.62752
$475$	−2.86818	−0.131601
$476$	−13.6731	−0.626704
$477$	12.2351	0.560205
$478$	−10.8365	−0.495652
$479$	10.3160	0.471351	0.235676	−	0.971832i	$-0.424270\pi$
$479$	10.3160	0.471351	0.235676	+	0.971832i	$0.424270\pi$
$480$	−47.1941	−2.15410
$481$	5.41927	0.247098
$482$	−38.3368	−1.74619
$483$	28.4701	1.29544
$484$	−4.79213	−0.217824
$485$	19.9081	0.903982
$486$	32.8593	1.49053
$487$	42.8800	1.94308	0.971540	−	0.236876i	$-0.0761236\pi$
$487$	42.8800	1.94308	0.971540	+	0.236876i	$0.0761236\pi$
$488$	−3.72746	−0.168734
$489$	11.6128	0.525151
$490$	−59.4563	−2.68596
$491$	19.5210	0.880970	0.440485	−	0.897760i	$-0.354807\pi$
$491$	19.5210	0.880970	0.440485	+	0.897760i	$0.354807\pi$
$492$	−3.59210	−0.161945
$493$	−4.85728	−0.218761
$494$	0.990632	0.0445706
$495$	−15.6731	−0.704452
$496$	−45.2355	−2.03114
$497$	37.8020	1.69565
$498$	−37.3274	−1.67268
$499$	13.7857	0.617132	0.308566	−	0.951203i	$-0.400151\pi$
$499$	13.7857	0.617132	0.308566	+	0.951203i	$0.400151\pi$
$500$	7.40054	0.330962
$501$	−4.47457	−0.199909
$502$	−9.16547	−0.409075
$503$	−15.3254	−0.683326	−0.341663	−	0.939823i	$-0.610990\pi$
$503$	−15.3254	−0.683326	−0.341663	+	0.939823i	$0.610990\pi$
$504$	−5.76694	−0.256880
$505$	−17.0321	−0.757919
$506$	−16.4701	−0.732186
$507$	27.9289	1.24037
$508$	1.53972	0.0683139
$509$	−34.3368	−1.52195	−0.760975	−	0.648781i	$-0.775279\pi$
$509$	−34.3368	−1.52195	−0.760975	+	0.648781i	$0.775279\pi$
$510$	−24.4701	−1.08356
$511$	5.86665	0.259525
$512$	27.2306	1.20343
$513$	−2.03164	−0.0896992
$514$	−2.50760	−0.110605
$515$	42.9590	1.89300
$516$	4.94914	0.217874
$517$	−19.2212	−0.845350
$518$	−69.8578	−3.06937
$519$	2.53035	0.111070
$520$	−1.29883	−0.0569573
$521$	−36.2766	−1.58930	−0.794652	−	0.607065i	$-0.792347\pi$
$521$	−36.2766	−1.58930	−0.794652	+	0.607065i	$0.792347\pi$
$522$	8.79706	0.385037
$523$	7.02227	0.307063	0.153531	−	0.988144i	$-0.450935\pi$
$523$	7.02227	0.307063	0.153531	+	0.988144i	$0.450935\pi$
$524$	−18.1432	−0.792589
$525$	−31.9956	−1.39640
$526$	58.7072	2.55976
$527$	−19.6128	−0.854349
$528$	28.9733	1.26090
$529$	−13.6923	−0.595317
$530$	−35.5210	−1.54293
$531$	−13.4193	−0.582347
$532$	−5.71900	−0.247950
$533$	−0.622216	−0.0269512
$534$	26.5303	1.14808
$535$	−10.4889	−0.453473
$536$	2.03948	0.0880921
$537$	33.2400	1.43441
$538$	−1.74620	−0.0752841
$539$	30.5225	1.31470
$540$	−11.4380	−0.492213
$541$	25.8336	1.11067	0.555337	−	0.831625i	$-0.312589\pi$
$541$	25.8336	1.11067	0.555337	+	0.831625i	$0.312589\pi$
$542$	−11.0509	−0.474675
$543$	54.3180	2.33101
$544$	14.6824	0.629504
$545$	31.9081	1.36679
$546$	11.0509	0.472933
$547$	−42.5511	−1.81935	−0.909677	−	0.415317i	$-0.863671\pi$
$547$	−42.5511	−1.81935	−0.909677	+	0.415317i	$0.863671\pi$
$548$	−19.0035	−0.811791
$549$	9.86665	0.421098
$550$	18.5096	0.789252
$551$	−2.03164	−0.0865509
$552$	−4.85728	−0.206740
$553$	35.4336	1.50679
$554$	19.5067	0.828760
$555$	−55.9911	−2.37669
$556$	29.6485	1.25738
$557$	−30.0415	−1.27290	−0.636449	−	0.771319i	$-0.719598\pi$
$557$	−30.0415	−1.27290	−0.636449	+	0.771319i	$0.719598\pi$
$558$	35.5210	1.50372
$559$	0.857279	0.0362590
$560$	56.4385	2.38496
$561$	12.5620	0.530368
$562$	24.2766	1.02404
$563$	3.61084	0.152179	0.0760894	−	0.997101i	$-0.475757\pi$
$563$	3.61084	0.152179	0.0760894	+	0.997101i	$0.475757\pi$
$564$	24.3412	1.02495
$565$	26.1432	1.09985
$566$	39.5210	1.66119
$567$	−46.7259	−1.96230
$568$	−6.44938	−0.270610
$569$	−5.95407	−0.249607	−0.124804	−	0.992181i	$-0.539830\pi$
$569$	−5.95407	−0.249607	−0.124804	+	0.992181i	$0.539830\pi$
$570$	−10.2351	−0.428700
$571$	−8.24290	−0.344955	−0.172477	−	0.985013i	$-0.555177\pi$
$571$	−8.24290	−0.344955	−0.172477	+	0.985013i	$0.555177\pi$
$572$	−2.86311	−0.119713
$573$	−54.9545	−2.29576
$574$	8.02074	0.334779
$575$	−10.4603	−0.436224
$576$	−9.03303	−0.376376
$577$	−33.2257	−1.38320	−0.691602	−	0.722279i	$-0.743095\pi$
$577$	−33.2257	−1.38320	−0.691602	+	0.722279i	$0.743095\pi$
$578$	−24.7418	−1.02912
$579$	28.8988	1.20099
$580$	−11.4380	−0.474937
$581$	37.3274	1.54860
$582$	28.8988	1.19789
$583$	18.2351	0.755219
$584$	−1.00091	−0.0414178
$585$	3.43801	0.142144
$586$	35.5812	1.46985
$587$	−8.21432	−0.339041	−0.169521	−	0.985527i	$-0.554222\pi$
$587$	−8.21432	−0.339041	−0.169521	+	0.985527i	$0.554222\pi$
$588$	−38.6528	−1.59401
$589$	−8.20342	−0.338016
$590$	38.9590	1.60392
$591$	−46.9086	−1.92956
$592$	40.1762	1.65123
$593$	18.6450	0.765657	0.382829	−	0.923819i	$-0.374950\pi$
$593$	18.6450	0.765657	0.382829	+	0.923819i	$0.374950\pi$
$594$	13.1111	0.537954
$595$	24.4701	1.00318
$596$	26.8158	1.09842
$597$	−58.5674	−2.39700
$598$	3.61285	0.147740
$599$	−0.358572	−0.0146509	−0.00732543	−	0.999973i	$-0.502332\pi$
$599$	−0.358572	−0.0146509	−0.00732543	+	0.999973i	$0.502332\pi$
$600$	5.45875	0.222853
$601$	−9.22570	−0.376324	−0.188162	−	0.982138i	$-0.560253\pi$
$601$	−9.22570	−0.376324	−0.188162	+	0.982138i	$0.560253\pi$
$602$	−11.0509	−0.450399
$603$	−5.39853	−0.219845
$604$	4.22015	0.171715
$605$	8.57628	0.348675
$606$	−24.7239	−1.00434
$607$	−44.2163	−1.79469	−0.897343	−	0.441334i	$-0.854505\pi$
$607$	−44.2163	−1.79469	−0.897343	+	0.441334i	$0.854505\pi$
$608$	6.14119	0.249058
$609$	−22.6637	−0.918380
$610$	−28.6450	−1.15980
$611$	4.21633	0.170574
$612$	−6.17484	−0.249603
$613$	−4.61777	−0.186510	−0.0932550	−	0.995642i	$-0.529727\pi$
$613$	−4.61777	−0.186510	−0.0932550	+	0.995642i	$0.529727\pi$
$614$	−16.7783	−0.677118
$615$	6.42864	0.259228
$616$	−8.59502	−0.346303
$617$	22.3872	0.901273	0.450636	−	0.892708i	$-0.351197\pi$
$617$	22.3872	0.901273	0.450636	+	0.892708i	$0.351197\pi$
$618$	62.3595	2.50847
$619$	9.92687	0.398995	0.199497	−	0.979898i	$-0.436069\pi$
$619$	9.92687	0.398995	0.199497	+	0.979898i	$0.436069\pi$
$620$	−46.1847	−1.85482
$621$	−7.40943	−0.297330
$622$	−14.3892	−0.576953
$623$	−26.5303	−1.06292
$624$	−6.35551	−0.254424
$625$	−30.3876	−1.21551
$626$	−12.7181	−0.508317
$627$	5.25428	0.209836
$628$	21.2386	0.847513
$629$	17.4193	0.694552
$630$	−44.3180	−1.76567
$631$	26.1017	1.03909	0.519546	−	0.854442i	$-0.326101\pi$
$631$	26.1017	1.03909	0.519546	+	0.854442i	$0.326101\pi$
$632$	−6.04531	−0.240469
$633$	27.1383	1.07865
$634$	−43.7560	−1.73777
$635$	−2.75557	−0.109351
$636$	−23.0923	−0.915671
$637$	−6.69535	−0.265279
$638$	13.1111	0.519073
$639$	17.0716	0.675342
$640$	−16.4014	−0.648324
$641$	−5.05086	−0.199497	−0.0997484	−	0.995013i	$-0.531804\pi$
$641$	−5.05086	−0.199497	−0.0997484	+	0.995013i	$0.531804\pi$
$642$	−15.2257	−0.600910
$643$	13.1131	0.517130	0.258565	−	0.965994i	$-0.416750\pi$
$643$	13.1131	0.517130	0.258565	+	0.965994i	$0.416750\pi$
$644$	−20.8573	−0.821892
$645$	−8.85728	−0.348755
$646$	3.18421	0.125281
$647$	−25.9398	−1.01980	−0.509899	−	0.860234i	$-0.670317\pi$
$647$	−25.9398	−1.01980	−0.509899	+	0.860234i	$0.670317\pi$
$648$	7.97190	0.313166
$649$	−20.0000	−0.785069
$650$	−4.06022	−0.159255
$651$	−91.5121	−3.58664
$652$	−8.50760	−0.333183
$653$	24.7052	0.966789	0.483394	−	0.875403i	$-0.339404\pi$
$653$	24.7052	0.966789	0.483394	+	0.875403i	$0.339404\pi$
$654$	46.3180	1.81118
$655$	32.4701	1.26871
$656$	−4.61285	−0.180101
$657$	2.64941	0.103363
$658$	−54.3511	−2.11883
$659$	35.0845	1.36670	0.683349	−	0.730092i	$-0.260523\pi$
$659$	35.0845	1.36670	0.683349	+	0.730092i	$0.260523\pi$
$660$	29.5812	1.15145
$661$	41.7703	1.62468	0.812339	−	0.583186i	$-0.198194\pi$
$661$	41.7703	1.62468	0.812339	+	0.583186i	$0.198194\pi$
$662$	15.9418	0.619595
$663$	−2.75557	−0.107017
$664$	−6.36842	−0.247142
$665$	10.2351	0.396899
$666$	−31.5482	−1.22247
$667$	−7.40943	−0.286894
$668$	3.27808	0.126833
$669$	25.7146	0.994182
$670$	15.6731	0.605504
$671$	14.7052	0.567688
$672$	68.5072	2.64272
$673$	30.7654	1.18592	0.592960	−	0.805232i	$-0.297959\pi$
$673$	30.7654	1.18592	0.592960	+	0.805232i	$0.297959\pi$
$674$	14.0330	0.540532
$675$	8.32693	0.320504
$676$	−20.4608	−0.786952
$677$	32.5892	1.25250	0.626252	−	0.779621i	$-0.284588\pi$
$677$	32.5892	1.25250	0.626252	+	0.779621i	$0.284588\pi$
$678$	37.9496	1.45745
$679$	−28.8988	−1.10903
$680$	−4.17484	−0.160098
$681$	−11.0049	−0.421710
$682$	52.9403	2.02719
$683$	−29.5734	−1.13159	−0.565797	−	0.824545i	$-0.691431\pi$
$683$	−29.5734	−1.13159	−0.565797	+	0.824545i	$0.691431\pi$
$684$	−2.58274	−0.0987534
$685$	34.0098	1.29945
$686$	30.1619	1.15159
$687$	−35.0923	−1.33886
$688$	6.35551	0.242302
$689$	−4.00000	−0.152388
$690$	−37.3274	−1.42103
$691$	25.7353	0.979017	0.489509	−	0.871999i	$-0.337176\pi$
$691$	25.7353	0.979017	0.489509	+	0.871999i	$0.337176\pi$
$692$	−1.85374	−0.0704686
$693$	22.7511	0.864244
$694$	20.0020	0.759266
$695$	−53.0607	−2.01271
$696$	3.86665	0.146565
$697$	−2.00000	−0.0757554
$698$	−35.9768	−1.36174
$699$	−38.4099	−1.45280
$700$	23.4400	0.885949
$701$	−14.9951	−0.566356	−0.283178	−	0.959067i	$-0.591389\pi$
$701$	−14.9951	−0.566356	−0.283178	+	0.959067i	$0.591389\pi$
$702$	−2.87601	−0.108548
$703$	7.28592	0.274794
$704$	−13.4628	−0.507397
$705$	−43.5625	−1.64066
$706$	−34.7324	−1.30717
$707$	24.7239	0.929839
$708$	25.3274	0.951862
$709$	−6.60348	−0.247999	−0.123999	−	0.992282i	$-0.539572\pi$
$709$	−6.60348	−0.247999	−0.123999	+	0.992282i	$0.539572\pi$
$710$	−49.5625	−1.86005
$711$	16.0020	0.600122
$712$	4.52633	0.169632
$713$	−29.9180	−1.12044
$714$	35.5210	1.32934
$715$	5.12399	0.191626
$716$	−24.3517	−0.910065
$717$	12.6079	0.470852
$718$	−32.5906	−1.21627
$719$	−15.1002	−0.563142	−0.281571	−	0.959540i	$-0.590855\pi$
$719$	−15.1002	−0.563142	−0.281571	+	0.959540i	$0.590855\pi$
$720$	25.4880	0.949880
$721$	−62.3595	−2.32239
$722$	−34.8292	−1.29621
$723$	44.6035	1.65882
$724$	−39.7935	−1.47891
$725$	8.32693	0.309254
$726$	12.4494	0.462040
$727$	15.0430	0.557915	0.278957	−	0.960303i	$-0.410011\pi$
$727$	15.0430	0.557915	0.278957	+	0.960303i	$0.410011\pi$
$728$	1.88538	0.0698769
$729$	−4.96836	−0.184013
$730$	−7.69181	−0.284687
$731$	2.75557	0.101918
$732$	−18.6222	−0.688297
$733$	43.8765	1.62062	0.810308	−	0.586005i	$-0.199300\pi$
$733$	43.8765	1.62062	0.810308	+	0.586005i	$0.199300\pi$
$734$	23.4795	0.866644
$735$	69.1753	2.55157
$736$	22.3970	0.825564
$737$	−8.04593	−0.296376
$738$	3.62222	0.133336
$739$	15.1427	0.557034	0.278517	−	0.960431i	$-0.410157\pi$
$739$	15.1427	0.557034	0.278517	+	0.960431i	$0.410157\pi$
$740$	41.0192	1.50790
$741$	−1.15257	−0.0423405
$742$	51.5625	1.89292
$743$	−9.46965	−0.347408	−0.173704	−	0.984798i	$-0.555574\pi$
$743$	−9.46965	−0.347408	−0.173704	+	0.984798i	$0.555574\pi$
$744$	15.6128	0.572395
$745$	−47.9911	−1.75826
$746$	−67.9724	−2.48865
$747$	16.8573	0.616776
$748$	−9.20294	−0.336493
$749$	15.2257	0.556335
$750$	−19.2257	−0.702023
$751$	5.55062	0.202545	0.101272	−	0.994859i	$-0.467709\pi$
$751$	5.55062	0.202545	0.101272	+	0.994859i	$0.467709\pi$
$752$	31.2581	1.13987
$753$	10.6637	0.388607
$754$	−2.87601	−0.104738
$755$	−7.55262	−0.274868
$756$	16.6035	0.603863
$757$	−7.70165	−0.279921	−0.139961	−	0.990157i	$-0.544698\pi$
$757$	−7.70165	−0.279921	−0.139961	+	0.990157i	$0.544698\pi$
$758$	21.7690	0.790684
$759$	19.1624	0.695551
$760$	−1.74620	−0.0633414
$761$	22.8113	0.826911	0.413455	−	0.910524i	$-0.364322\pi$
$761$	22.8113	0.826911	0.413455	+	0.910524i	$0.364322\pi$
$762$	−4.00000	−0.144905
$763$	−46.3180	−1.67683
$764$	40.2598	1.45655
$765$	11.0509	0.399545
$766$	15.7126	0.567718
$767$	4.38715	0.158411
$768$	−44.8276	−1.61758
$769$	27.1240	0.978116	0.489058	−	0.872251i	$-0.337341\pi$
$769$	27.1240	0.978116	0.489058	+	0.872251i	$0.337341\pi$
$770$	−66.0513	−2.38032
$771$	2.91750	0.105071
$772$	−21.1713	−0.761972
$773$	−10.6953	−0.384685	−0.192342	−	0.981328i	$-0.561608\pi$
$773$	−10.6953	−0.384685	−0.192342	+	0.981328i	$0.561608\pi$
$774$	−4.99063	−0.179385
$775$	33.6227	1.20776
$776$	4.93041	0.176991
$777$	81.2770	2.91580
$778$	−49.6414	−1.77973
$779$	−0.836535	−0.0299720
$780$	−6.48886	−0.232339
$781$	25.4434	0.910437
$782$	11.6128	0.415275
$783$	5.89829	0.210788
$784$	−49.6365	−1.77273
$785$	−38.0098	−1.35663
$786$	47.1338	1.68121
$787$	−30.7971	−1.09780	−0.548898	−	0.835889i	$-0.684953\pi$
$787$	−30.7971	−1.09780	−0.548898	+	0.835889i	$0.684953\pi$
$788$	34.3654	1.22422
$789$	−68.3037	−2.43168
$790$	−46.4572	−1.65287
$791$	−37.9496	−1.34933
$792$	−3.88156	−0.137925
$793$	−3.22570	−0.114548
$794$	−2.81579	−0.0999287
$795$	41.3274	1.46573
$796$	42.9066	1.52078
$797$	−10.0415	−0.355688	−0.177844	−	0.984059i	$-0.556912\pi$
$797$	−10.0415	−0.355688	−0.177844	+	0.984059i	$0.556912\pi$
$798$	14.8573	0.525942
$799$	13.5526	0.479457
$800$	−25.1704	−0.889908
$801$	−11.9813	−0.423337
$802$	51.3604	1.81360
$803$	3.94867	0.139345
$804$	10.1891	0.359343
$805$	37.3274	1.31562
$806$	−11.6128	−0.409045
$807$	2.03164	0.0715172
$808$	−4.21814	−0.148394
$809$	−25.1427	−0.883971	−0.441985	−	0.897022i	$-0.645726\pi$
$809$	−25.1427	−0.883971	−0.441985	+	0.897022i	$0.645726\pi$
$810$	61.2627	2.15255
$811$	−25.2859	−0.887909	−0.443954	−	0.896049i	$-0.646425\pi$
$811$	−25.2859	−0.887909	−0.443954	+	0.896049i	$0.646425\pi$
$812$	16.6035	0.582668
$813$	12.8573	0.450924
$814$	−47.0192	−1.64802
$815$	15.2257	0.533333
$816$	−20.4286	−0.715145
$817$	1.15257	0.0403232
$818$	50.2908	1.75838
$819$	−4.99063	−0.174387
$820$	−4.70964	−0.164468
$821$	16.2306	0.566452	0.283226	−	0.959053i	$-0.408595\pi$
$821$	16.2306	0.566452	0.283226	+	0.959053i	$0.408595\pi$
$822$	49.3689	1.72194
$823$	−3.20495	−0.111718	−0.0558588	−	0.998439i	$-0.517790\pi$
$823$	−3.20495	−0.111718	−0.0558588	+	0.998439i	$0.517790\pi$
$824$	10.6391	0.370632
$825$	−21.5353	−0.749762
$826$	−56.5531	−1.96773
$827$	17.6840	0.614932	0.307466	−	0.951559i	$-0.400519\pi$
$827$	17.6840	0.614932	0.307466	+	0.951559i	$0.400519\pi$
$828$	−9.41927	−0.327342
$829$	−52.4340	−1.82111	−0.910555	−	0.413389i	$-0.864345\pi$
$829$	−52.4340	−1.82111	−0.910555	+	0.413389i	$0.864345\pi$
$830$	−48.9403	−1.69874
$831$	−22.6953	−0.787293
$832$	2.95316	0.102382
$833$	−21.5210	−0.745658
$834$	−77.0232	−2.66710
$835$	−5.86665	−0.203024
$836$	−3.84929	−0.133131
$837$	23.8163	0.823211
$838$	−70.5589	−2.43742
$839$	20.9097	0.721882	0.360941	−	0.932589i	$-0.382456\pi$
$839$	20.9097	0.721882	0.360941	+	0.932589i	$0.382456\pi$
$840$	−19.4795	−0.672106
$841$	−23.1017	−0.796611
$842$	39.5812	1.36406
$843$	−28.2449	−0.972806
$844$	−19.8816	−0.684352
$845$	36.6178	1.25969
$846$	−24.5453	−0.843884
$847$	−12.4494	−0.427766
$848$	−29.6543	−1.01833
$849$	−45.9813	−1.57807
$850$	−13.0509	−0.447641
$851$	26.5718	0.910871
$852$	−32.2208	−1.10387
$853$	9.93671	0.340227	0.170113	−	0.985425i	$-0.445587\pi$
$853$	9.93671	0.340227	0.170113	+	0.985425i	$0.445587\pi$
$854$	41.5812	1.42288
$855$	4.62222	0.158076
$856$	−2.59765	−0.0887859
$857$	40.6464	1.38845	0.694226	−	0.719757i	$-0.255747\pi$
$857$	40.6464	1.38845	0.694226	+	0.719757i	$0.255747\pi$
$858$	7.43801	0.253929
$859$	15.7748	0.538229	0.269114	−	0.963108i	$-0.413269\pi$
$859$	15.7748	0.538229	0.269114	+	0.963108i	$0.413269\pi$
$860$	6.48886	0.221268
$861$	−9.33185	−0.318029
$862$	−41.0736	−1.39897
$863$	1.49823	0.0510004	0.0255002	−	0.999675i	$-0.491882\pi$
$863$	1.49823	0.0510004	0.0255002	+	0.999675i	$0.491882\pi$
$864$	−17.8292	−0.606561
$865$	3.31756	0.112800
$866$	69.0964	2.34799
$867$	28.7862	0.977629
$868$	67.0420	2.27555
$869$	23.8493	0.809032
$870$	29.7146	1.00742
$871$	1.76494	0.0598026
$872$	7.90231	0.267606
$873$	−13.0509	−0.441705
$874$	4.85728	0.164300
$875$	19.2257	0.649947
$876$	−5.00048	−0.168950
$877$	33.9210	1.14543	0.572716	−	0.819754i	$-0.305890\pi$
$877$	33.9210	1.14543	0.572716	+	0.819754i	$0.305890\pi$
$878$	−40.0078	−1.35020
$879$	−41.3975	−1.39630
$880$	37.9871	1.28054
$881$	−34.5531	−1.16412	−0.582062	−	0.813145i	$-0.697754\pi$
$881$	−34.5531	−1.16412	−0.582062	+	0.813145i	$0.697754\pi$
$882$	38.9768	1.31242
$883$	−44.5038	−1.49767	−0.748836	−	0.662756i	$-0.769387\pi$
$883$	−44.5038	−1.49767	−0.748836	+	0.662756i	$0.769387\pi$
$884$	2.01874	0.0678974
$885$	−45.3274	−1.52366
$886$	42.4929	1.42758
$887$	−8.89676	−0.298724	−0.149362	−	0.988783i	$-0.547722\pi$
$887$	−8.89676	−0.298724	−0.149362	+	0.988783i	$0.547722\pi$
$888$	−13.8666	−0.465334
$889$	4.00000	0.134156
$890$	34.7841	1.16597
$891$	−31.4499	−1.05361
$892$	−18.8385	−0.630761
$893$	5.66862	0.189693
$894$	−69.6642	−2.32992
$895$	43.5812	1.45676
$896$	23.8084	0.795384
$897$	−4.20342	−0.140348
$898$	22.2163	0.741368
$899$	23.8163	0.794317
$900$	10.5857	0.352855
$901$	−12.8573	−0.428338
$902$	5.39853	0.179751
$903$	12.8573	0.427863
$904$	6.47457	0.215341
$905$	71.2168	2.36733
$906$	−10.9634	−0.364236
$907$	−28.2449	−0.937857	−0.468928	−	0.883236i	$-0.655360\pi$
$907$	−28.2449	−0.937857	−0.468928	+	0.883236i	$0.655360\pi$
$908$	8.06223	0.267555
$909$	11.1655	0.370335
$910$	14.4889	0.480301
$911$	32.9906	1.09303	0.546514	−	0.837450i	$-0.315954\pi$
$911$	32.9906	1.09303	0.546514	+	0.837450i	$0.315954\pi$
$912$	−8.54464	−0.282941
$913$	25.1240	0.831483
$914$	23.0321	0.761835
$915$	33.3274	1.10177
$916$	25.7087	0.849440
$917$	−47.1338	−1.55650
$918$	−9.24443	−0.305112
$919$	36.3763	1.19994	0.599971	−	0.800022i	$-0.295179\pi$
$919$	36.3763	1.19994	0.599971	+	0.800022i	$0.295179\pi$
$920$	−6.36842	−0.209960
$921$	19.5210	0.643238
$922$	−20.1891	−0.664894
$923$	−5.58120	−0.183708
$924$	−42.9403	−1.41263
$925$	−29.8622	−0.981863
$926$	−49.2335	−1.61791
$927$	−28.1619	−0.924959
$928$	−17.8292	−0.585271
$929$	13.1338	0.430907	0.215453	−	0.976514i	$-0.430877\pi$
$929$	13.1338	0.430907	0.215453	+	0.976514i	$0.430877\pi$
$930$	119.982	3.93437
$931$	−9.00153	−0.295013
$932$	28.1392	0.921730
$933$	16.7413	0.548085
$934$	−27.0134	−0.883905
$935$	16.4701	0.538631
$936$	0.851450	0.0278305
$937$	6.56199	0.214371	0.107185	−	0.994239i	$-0.465816\pi$
$937$	6.56199	0.214371	0.107185	+	0.994239i	$0.465816\pi$
$938$	−22.7511	−0.742850
$939$	14.7971	0.482884
$940$	31.9140	1.04092
$941$	−26.6735	−0.869533	−0.434766	−	0.900543i	$-0.643169\pi$
$941$	−26.6735	−0.869533	−0.434766	+	0.900543i	$0.643169\pi$
$942$	−55.1753	−1.79771
$943$	−3.05086	−0.0993495
$944$	32.5245	1.05858
$945$	−29.7146	−0.966615
$946$	−7.43801	−0.241830
$947$	−47.7244	−1.55083	−0.775417	−	0.631449i	$-0.782460\pi$
$947$	−47.7244	−1.55083	−0.775417	+	0.631449i	$0.782460\pi$
$948$	−30.2020	−0.980917
$949$	−0.866170	−0.0281171
$950$	−5.45875	−0.177105
$951$	50.9086	1.65082
$952$	6.06022	0.196413
$953$	−47.6400	−1.54321	−0.771606	−	0.636101i	$-0.780546\pi$
$953$	−47.6400	−1.54321	−0.771606	+	0.636101i	$0.780546\pi$
$954$	23.2859	0.753909
$955$	−72.0513	−2.33153
$956$	−9.23659	−0.298733
$957$	−15.2543	−0.493101
$958$	19.6336	0.634333
$959$	−49.3689	−1.59420
$960$	−30.5116	−0.984758
$961$	65.1659	2.10213
$962$	10.3140	0.332537
$963$	6.87601	0.221576
$964$	−32.6766	−1.05244
$965$	37.8894	1.21970
$966$	54.1847	1.74336
$967$	44.1639	1.42022	0.710108	−	0.704092i	$-0.248646\pi$
$967$	44.1639	1.42022	0.710108	+	0.704092i	$0.248646\pi$
$968$	2.12399	0.0682675
$969$	−3.70471	−0.119013
$970$	37.8894	1.21656
$971$	−17.0903	−0.548455	−0.274227	−	0.961665i	$-0.588422\pi$
$971$	−17.0903	−0.548455	−0.274227	+	0.961665i	$0.588422\pi$
$972$	28.0078	0.898352
$973$	77.0232	2.46925
$974$	81.6098	2.61495
$975$	4.72393	0.151287
$976$	−23.9140	−0.765467
$977$	−15.4193	−0.493306	−0.246653	−	0.969104i	$-0.579331\pi$
$977$	−15.4193	−0.493306	−0.246653	+	0.969104i	$0.579331\pi$
$978$	22.1017	0.706735
$979$	−17.8568	−0.570706
$980$	−50.6780	−1.61885
$981$	−20.9175	−0.667844
$982$	37.1526	1.18559
$983$	19.8252	0.632324	0.316162	−	0.948705i	$-0.397606\pi$
$983$	19.8252	0.632324	0.316162	+	0.948705i	$0.397606\pi$
$984$	1.59210	0.0507544
$985$	−61.5022	−1.95962
$986$	−9.24443	−0.294403
$987$	63.2355	2.01281
$988$	0.844372	0.0268631
$989$	4.20342	0.133661
$990$	−29.8292	−0.948033
$991$	10.0109	0.318007	0.159003	−	0.987278i	$-0.449172\pi$
$991$	10.0109	0.318007	0.159003	+	0.987278i	$0.449172\pi$
$992$	−71.9911	−2.28572
$993$	−18.5477	−0.588594
$994$	71.9452	2.28196
$995$	−76.7882	−2.43435
$996$	−31.8163	−1.00814
$997$	−11.8765	−0.376132	−0.188066	−	0.982156i	$-0.560222\pi$
$997$	−11.8765	−0.376132	−0.188066	+	0.982156i	$0.560222\pi$
$998$	26.2371	0.830520
$999$	−21.1526	−0.669238

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	41.2.a.a.1.3	✓	3
3.2	odd	2		369.2.a.f.1.1		3
4.3	odd	2		656.2.a.f.1.3		3
5.2	odd	4		1025.2.b.h.124.5		6
5.3	odd	4		1025.2.b.h.124.2		6
5.4	even	2		1025.2.a.j.1.1		3
7.6	odd	2		2009.2.a.g.1.3		3
8.3	odd	2		2624.2.a.q.1.1		3
8.5	even	2		2624.2.a.r.1.3		3
11.10	odd	2		4961.2.a.d.1.1		3
12.11	even	2		5904.2.a.bk.1.3		3
13.12	even	2		6929.2.a.b.1.1		3
15.14	odd	2		9225.2.a.bv.1.3		3
41.40	even	2		1681.2.a.d.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
41.2.a.a.1.3	✓	3	1.1	even	1	trivial
369.2.a.f.1.1		3	3.2	odd	2
656.2.a.f.1.3		3	4.3	odd	2
1025.2.a.j.1.1		3	5.4	even	2
1025.2.b.h.124.2		6	5.3	odd	4
1025.2.b.h.124.5		6	5.2	odd	4
1681.2.a.d.1.3		3	41.40	even	2
2009.2.a.g.1.3		3	7.6	odd	2
2624.2.a.q.1.1		3	8.3	odd	2
2624.2.a.r.1.3		3	8.5	even	2
4961.2.a.d.1.1		3	11.10	odd	2
5904.2.a.bk.1.3		3	12.11	even	2
6929.2.a.b.1.1		3	13.12	even	2
9225.2.a.bv.1.3		3	15.14	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:	\( N \)	\(=\)	\( 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	41.a (trivial)

\(f(q)\)	\(=\)	\(q+1.90321 q^{2} -2.21432 q^{3} +1.62222 q^{4} -2.90321 q^{5} -4.21432 q^{6} +4.21432 q^{7} -0.719004 q^{8} +1.90321 q^{9} +O(q^{10})\)	\(q+1.90321 q^{2} -2.21432 q^{3} +1.62222 q^{4} -2.90321 q^{5} -4.21432 q^{6} +4.21432 q^{7} -0.719004 q^{8} +1.90321 q^{9} -5.52543 q^{10} +2.83654 q^{11} -3.59210 q^{12} -0.622216 q^{13} +8.02074 q^{14} +6.42864 q^{15} -4.61285 q^{16} -2.00000 q^{17} +3.62222 q^{18} -0.836535 q^{19} -4.70964 q^{20} -9.33185 q^{21} +5.39853 q^{22} -3.05086 q^{23} +1.59210 q^{24} +3.42864 q^{25} -1.18421 q^{26} +2.42864 q^{27} +6.83654 q^{28} +2.42864 q^{29} +12.2351 q^{30} +9.80642 q^{31} -7.34122 q^{32} -6.28100 q^{33} -3.80642 q^{34} -12.2351 q^{35} +3.08742 q^{36} -8.70964 q^{37} -1.59210 q^{38} +1.37778 q^{39} +2.08742 q^{40} +1.00000 q^{41} -17.7605 q^{42} -1.37778 q^{43} +4.60147 q^{44} -5.52543 q^{45} -5.80642 q^{46} -6.77631 q^{47} +10.2143 q^{48} +10.7605 q^{49} +6.52543 q^{50} +4.42864 q^{51} -1.00937 q^{52} +6.42864 q^{53} +4.62222 q^{54} -8.23506 q^{55} -3.03011 q^{56} +1.85236 q^{57} +4.62222 q^{58} -7.05086 q^{59} +10.4286 q^{60} +5.18421 q^{61} +18.6637 q^{62} +8.02074 q^{63} -4.74620 q^{64} +1.80642 q^{65} -11.9541 q^{66} -2.83654 q^{67} -3.24443 q^{68} +6.75557 q^{69} -23.2859 q^{70} +8.96989 q^{71} -1.36842 q^{72} +1.39207 q^{73} -16.5763 q^{74} -7.59210 q^{75} -1.35704 q^{76} +11.9541 q^{77} +2.62222 q^{78} +8.40790 q^{79} +13.3921 q^{80} -11.0874 q^{81} +1.90321 q^{82} +8.85728 q^{83} -15.1383 q^{84} +5.80642 q^{85} -2.62222 q^{86} -5.37778 q^{87} -2.03948 q^{88} -6.29529 q^{89} -10.5161 q^{90} -2.62222 q^{91} -4.94914 q^{92} -21.7146 q^{93} -12.8968 q^{94} +2.42864 q^{95} +16.2558 q^{96} -6.85728 q^{97} +20.4795 q^{98} +5.39853 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{2} + 5 q^{4} - 2 q^{5} - 6 q^{6} + 6 q^{7} - 9 q^{8} - q^{9}+O(q^{10}) \) 3 * q - q^2 + 5 * q^4 - 2 * q^5 - 6 * q^6 + 6 * q^7 - 9 * q^8 - q^9	\( 3 q - q^{2} + 5 q^{4} - 2 q^{5} - 6 q^{6} + 6 q^{7} - 9 q^{8} - q^{9} - 10 q^{10} + 2 q^{11} - 4 q^{12} - 2 q^{13} + 4 q^{14} + 6 q^{15} + 13 q^{16} - 6 q^{17} + 11 q^{18} + 4 q^{19} + 6 q^{20} - 8 q^{21} - 4 q^{22} + 4 q^{23} - 2 q^{24} - 3 q^{25} + 10 q^{26} - 6 q^{27} + 14 q^{28} - 6 q^{29} + 10 q^{30} + 16 q^{31} - 29 q^{32} - 12 q^{33} + 2 q^{34} - 10 q^{35} - 11 q^{36} - 6 q^{37} + 2 q^{38} + 4 q^{39} - 14 q^{40} + 3 q^{41} - 20 q^{42} - 4 q^{43} + 34 q^{44} - 10 q^{45} - 4 q^{46} + 24 q^{48} - q^{49} + 13 q^{50} - 30 q^{52} + 6 q^{53} + 14 q^{54} + 2 q^{55} - 16 q^{56} + 12 q^{57} + 14 q^{58} - 8 q^{59} + 18 q^{60} + 2 q^{61} + 16 q^{62} + 4 q^{63} + 13 q^{64} - 8 q^{65} - 16 q^{66} - 2 q^{67} - 10 q^{68} + 20 q^{69} - 30 q^{70} + 20 q^{71} + 23 q^{72} - 2 q^{73} - 30 q^{74} - 16 q^{75} - 24 q^{76} + 16 q^{77} + 8 q^{78} + 32 q^{79} + 34 q^{80} - 13 q^{81} - q^{82} - 12 q^{84} + 4 q^{85} - 8 q^{86} - 16 q^{87} - 40 q^{88} - 6 q^{89} + 2 q^{90} - 8 q^{91} - 28 q^{92} - 12 q^{93} - 46 q^{94} - 6 q^{95} + 2 q^{96} + 6 q^{97} + 35 q^{98} - 4 q^{99}+O(q^{100}) \) 3 * q - q^2 + 5 * q^4 - 2 * q^5 - 6 * q^6 + 6 * q^7 - 9 * q^8 - q^9 - 10 * q^10 + 2 * q^11 - 4 * q^12 - 2 * q^13 + 4 * q^14 + 6 * q^15 + 13 * q^16 - 6 * q^17 + 11 * q^18 + 4 * q^19 + 6 * q^20 - 8 * q^21 - 4 * q^22 + 4 * q^23 - 2 * q^24 - 3 * q^25 + 10 * q^26 - 6 * q^27 + 14 * q^28 - 6 * q^29 + 10 * q^30 + 16 * q^31 - 29 * q^32 - 12 * q^33 + 2 * q^34 - 10 * q^35 - 11 * q^36 - 6 * q^37 + 2 * q^38 + 4 * q^39 - 14 * q^40 + 3 * q^41 - 20 * q^42 - 4 * q^43 + 34 * q^44 - 10 * q^45 - 4 * q^46 + 24 * q^48 - q^49 + 13 * q^50 - 30 * q^52 + 6 * q^53 + 14 * q^54 + 2 * q^55 - 16 * q^56 + 12 * q^57 + 14 * q^58 - 8 * q^59 + 18 * q^60 + 2 * q^61 + 16 * q^62 + 4 * q^63 + 13 * q^64 - 8 * q^65 - 16 * q^66 - 2 * q^67 - 10 * q^68 + 20 * q^69 - 30 * q^70 + 20 * q^71 + 23 * q^72 - 2 * q^73 - 30 * q^74 - 16 * q^75 - 24 * q^76 + 16 * q^77 + 8 * q^78 + 32 * q^79 + 34 * q^80 - 13 * q^81 - q^82 - 12 * q^84 + 4 * q^85 - 8 * q^86 - 16 * q^87 - 40 * q^88 - 6 * q^89 + 2 * q^90 - 8 * q^91 - 28 * q^92 - 12 * q^93 - 46 * q^94 - 6 * q^95 + 2 * q^96 + 6 * q^97 + 35 * q^98 - 4 * q^99

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