LMFDB - Embedded newform 221.2.a.g.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [221,2,Mod(1,221)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(221, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("221.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 221 = 13 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	221.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:	$1.76469388467$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.28134208.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 9x^{4} + 6x^{3} + 23x^{2} - 7x - 11 $ x^6 - x^5 - 9x^4 + 6x^3 + 23x^2 - 7x - 11
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.37245$ of defining polynomial
Character	$\chi$	$=$	221.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.301567 q^{2} +2.62851 q^{3} -1.90906 q^{4} +0.792671 q^{5} -0.792671 q^{6} +0.519592 q^{7} +1.17884 q^{8} +3.90906 q^{9} +O(q^{10})$	\(q-0.301567 q^{2} +2.62851 q^{3} -1.90906 q^{4} +0.792671 q^{5} -0.792671 q^{6} +0.519592 q^{7} +1.17884 q^{8} +3.90906 q^{9} -0.239043 q^{10} +2.90906 q^{11} -5.01797 q^{12} +1.00000 q^{13} -0.156692 q^{14} +2.08354 q^{15} +3.46262 q^{16} -1.00000 q^{17} -1.17884 q^{18} -4.16607 q^{19} -1.51325 q^{20} +1.36575 q^{21} -0.877275 q^{22} -2.16589 q^{23} +3.09859 q^{24} -4.37167 q^{25} -0.301567 q^{26} +2.38947 q^{27} -0.991931 q^{28} -4.38947 q^{29} -0.628327 q^{30} +1.17448 q^{31} -3.40189 q^{32} +7.64648 q^{33} +0.301567 q^{34} +0.411865 q^{35} -7.46262 q^{36} +4.46435 q^{37} +1.25635 q^{38} +2.62851 q^{39} +0.934433 q^{40} +6.85381 q^{41} -0.411865 q^{42} +1.84331 q^{43} -5.55356 q^{44} +3.09859 q^{45} +0.653161 q^{46} -9.38206 q^{47} +9.10152 q^{48} -6.73002 q^{49} +1.31835 q^{50} -2.62851 q^{51} -1.90906 q^{52} -12.3228 q^{53} -0.720583 q^{54} +2.30592 q^{55} +0.612516 q^{56} -10.9506 q^{57} +1.32372 q^{58} -4.01684 q^{59} -3.97760 q^{60} -0.548951 q^{61} -0.354185 q^{62} +2.03111 q^{63} -5.89933 q^{64} +0.792671 q^{65} -2.30592 q^{66} +11.7611 q^{67} +1.90906 q^{68} -5.69307 q^{69} -0.124205 q^{70} -5.59406 q^{71} +4.60816 q^{72} +13.6224 q^{73} -1.34630 q^{74} -11.4910 q^{75} +7.95328 q^{76} +1.51152 q^{77} -0.792671 q^{78} -3.34909 q^{79} +2.74471 q^{80} -5.44644 q^{81} -2.06688 q^{82} -2.31185 q^{83} -2.60730 q^{84} -0.792671 q^{85} -0.555880 q^{86} -11.5377 q^{87} +3.42932 q^{88} +2.00972 q^{89} -0.934433 q^{90} +0.519592 q^{91} +4.13481 q^{92} +3.08714 q^{93} +2.82932 q^{94} -3.30232 q^{95} -8.94190 q^{96} +12.5884 q^{97} +2.02955 q^{98} +11.3717 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} + q^{3} + 7 q^{4} - 2 q^{5} + 2 q^{6} + 7 q^{7} + 6 q^{8} + 5 q^{9}+O(q^{10}) $ 6 * q + q^2 + q^3 + 7 * q^4 - 2 * q^5 + 2 * q^6 + 7 * q^7 + 6 * q^8 + 5 * q^9	\( 6 q + q^{2} + q^{3} + 7 q^{4} - 2 q^{5} + 2 q^{6} + 7 q^{7} + 6 q^{8} + 5 q^{9} - 9 q^{10} - q^{11} + 7 q^{12} + 6 q^{13} - 2 q^{14} + 3 q^{15} + 9 q^{16} - 6 q^{17} - 6 q^{18} + 23 q^{19} - 3 q^{20} + 5 q^{21} - 7 q^{22} - 10 q^{23} - q^{24} + 4 q^{25} + q^{26} - 8 q^{27} - 7 q^{28} - 4 q^{29} - 34 q^{30} + 16 q^{31} + 13 q^{32} - 6 q^{33} - q^{34} + 9 q^{35} - 33 q^{36} + 4 q^{37} + 7 q^{38} + q^{39} - 22 q^{40} - 4 q^{41} - 9 q^{42} + 10 q^{43} - 40 q^{44} - q^{45} + 20 q^{46} - 6 q^{47} + 8 q^{48} + 21 q^{49} - 16 q^{50} - q^{51} + 7 q^{52} - 27 q^{53} - 5 q^{54} + q^{55} - 51 q^{56} - 36 q^{57} + 3 q^{58} + 10 q^{59} + 5 q^{60} + 11 q^{61} - 25 q^{62} + 21 q^{63} - 8 q^{64} - 2 q^{65} - q^{66} + 18 q^{67} - 7 q^{68} - 18 q^{69} - 54 q^{70} - 17 q^{72} + 12 q^{73} + 13 q^{74} + 54 q^{76} + 14 q^{77} + 2 q^{78} - 6 q^{79} + 35 q^{80} - 26 q^{81} + 8 q^{82} + 26 q^{83} + 44 q^{84} + 2 q^{85} + 9 q^{86} + 9 q^{87} - 23 q^{88} + 21 q^{89} + 22 q^{90} + 7 q^{91} + 10 q^{92} + q^{93} + 44 q^{94} - 15 q^{95} - 33 q^{96} + 3 q^{97} + 38 q^{98} + 38 q^{99}+O(q^{100}) \) 6 * q + q^2 + q^3 + 7 * q^4 - 2 * q^5 + 2 * q^6 + 7 * q^7 + 6 * q^8 + 5 * q^9 - 9 * q^10 - q^11 + 7 * q^12 + 6 * q^13 - 2 * q^14 + 3 * q^15 + 9 * q^16 - 6 * q^17 - 6 * q^18 + 23 * q^19 - 3 * q^20 + 5 * q^21 - 7 * q^22 - 10 * q^23 - q^24 + 4 * q^25 + q^26 - 8 * q^27 - 7 * q^28 - 4 * q^29 - 34 * q^30 + 16 * q^31 + 13 * q^32 - 6 * q^33 - q^34 + 9 * q^35 - 33 * q^36 + 4 * q^37 + 7 * q^38 + q^39 - 22 * q^40 - 4 * q^41 - 9 * q^42 + 10 * q^43 - 40 * q^44 - q^45 + 20 * q^46 - 6 * q^47 + 8 * q^48 + 21 * q^49 - 16 * q^50 - q^51 + 7 * q^52 - 27 * q^53 - 5 * q^54 + q^55 - 51 * q^56 - 36 * q^57 + 3 * q^58 + 10 * q^59 + 5 * q^60 + 11 * q^61 - 25 * q^62 + 21 * q^63 - 8 * q^64 - 2 * q^65 - q^66 + 18 * q^67 - 7 * q^68 - 18 * q^69 - 54 * q^70 - 17 * q^72 + 12 * q^73 + 13 * q^74 + 54 * q^76 + 14 * q^77 + 2 * q^78 - 6 * q^79 + 35 * q^80 - 26 * q^81 + 8 * q^82 + 26 * q^83 + 44 * q^84 + 2 * q^85 + 9 * q^86 + 9 * q^87 - 23 * q^88 + 21 * q^89 + 22 * q^90 + 7 * q^91 + 10 * q^92 + q^93 + 44 * q^94 - 15 * q^95 - 33 * q^96 + 3 * q^97 + 38 * q^98 + 38 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.301567	−0.213240	−0.106620	−	0.994300i	$-0.534003\pi$
$2$	−0.301567	−0.213240	−0.106620	+	0.994300i	$0.534003\pi$
$3$	2.62851	1.51757	0.758785	−	0.651341i	$-0.225793\pi$
$3$	2.62851	1.51757	0.758785	+	0.651341i	$0.225793\pi$
$4$	−1.90906	−0.954529
$5$	0.792671	0.354493	0.177247	−	0.984166i	$-0.443281\pi$
$5$	0.792671	0.354493	0.177247	+	0.984166i	$0.443281\pi$
$6$	−0.792671	−0.323606
$7$	0.519592	0.196387	0.0981936	−	0.995167i	$-0.468694\pi$
$7$	0.519592	0.196387	0.0981936	+	0.995167i	$0.468694\pi$
$8$	1.17884	0.416783
$9$	3.90906	1.30302
$10$	−0.239043	−0.0755920
$11$	2.90906	0.877114	0.438557	−	0.898703i	$-0.355490\pi$
$11$	2.90906	0.877114	0.438557	+	0.898703i	$0.355490\pi$
$12$	−5.01797	−1.44856
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−0.156692	−0.0418776
$15$	2.08354	0.537968
$16$	3.46262	0.865654
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.17884	−0.277856
$19$	−4.16607	−0.955763	−0.477882	−	0.878424i	$-0.658595\pi$
$19$	−4.16607	−0.955763	−0.477882	+	0.878424i	$0.658595\pi$
$20$	−1.51325	−0.338374
$21$	1.36575	0.298031
$22$	−0.877275	−0.187036
$23$	−2.16589	−0.451620	−0.225810	−	0.974171i	$-0.572503\pi$
$23$	−2.16589	−0.451620	−0.225810	+	0.974171i	$0.572503\pi$
$24$	3.09859	0.632498
$25$	−4.37167	−0.874335
$26$	−0.301567	−0.0591421
$27$	2.38947	0.459853
$28$	−0.991931	−0.187457
$29$	−4.38947	−0.815103	−0.407552	−	0.913182i	$-0.633617\pi$
$29$	−4.38947	−0.815103	−0.407552	+	0.913182i	$0.633617\pi$
$30$	−0.628327	−0.114716
$31$	1.17448	0.210944	0.105472	−	0.994422i	$-0.466365\pi$
$31$	1.17448	0.210944	0.105472	+	0.994422i	$0.466365\pi$
$32$	−3.40189	−0.601375
$33$	7.64648	1.33108
$34$	0.301567	0.0517183
$35$	0.411865	0.0696179
$36$	−7.46262	−1.24377
$37$	4.46435	0.733934	0.366967	−	0.930234i	$-0.380396\pi$
$37$	4.46435	0.733934	0.366967	+	0.930234i	$0.380396\pi$
$38$	1.25635	0.203807
$39$	2.62851	0.420898
$40$	0.934433	0.147747
$41$	6.85381	1.07039	0.535193	−	0.844730i	$-0.320239\pi$
$41$	6.85381	1.07039	0.535193	+	0.844730i	$0.320239\pi$
$42$	−0.411865	−0.0635522
$43$	1.84331	0.281102	0.140551	−	0.990073i	$-0.455113\pi$
$43$	1.84331	0.281102	0.140551	+	0.990073i	$0.455113\pi$
$44$	−5.55356	−0.837230
$45$	3.09859	0.461911
$46$	0.653161	0.0963033
$47$	−9.38206	−1.36851	−0.684257	−	0.729241i	$-0.739874\pi$
$47$	−9.38206	−1.36851	−0.684257	+	0.729241i	$0.739874\pi$
$48$	9.10152	1.31369
$49$	−6.73002	−0.961432
$50$	1.31835	0.186443
$51$	−2.62851	−0.368065
$52$	−1.90906	−0.264739
$53$	−12.3228	−1.69266	−0.846331	−	0.532657i	$-0.821194\pi$
$53$	−12.3228	−1.69266	−0.846331	+	0.532657i	$0.821194\pi$
$54$	−0.720583	−0.0980589
$55$	2.30592	0.310931
$56$	0.612516	0.0818510
$57$	−10.9506	−1.45044
$58$	1.32372	0.173812
$59$	−4.01684	−0.522948	−0.261474	−	0.965210i	$-0.584209\pi$
$59$	−4.01684	−0.522948	−0.261474	+	0.965210i	$0.584209\pi$
$60$	−3.97760	−0.513506
$61$	−0.548951	−0.0702860	−0.0351430	−	0.999382i	$-0.511189\pi$
$61$	−0.548951	−0.0702860	−0.0351430	+	0.999382i	$0.511189\pi$
$62$	−0.354185	−0.0449816
$63$	2.03111	0.255896
$64$	−5.89933	−0.737417
$65$	0.792671	0.0983187
$66$	−2.30592	−0.283840
$67$	11.7611	1.43685	0.718426	−	0.695603i	$-0.244863\pi$
$67$	11.7611	1.43685	0.718426	+	0.695603i	$0.244863\pi$
$68$	1.90906	0.231507
$69$	−5.69307	−0.685365
$70$	−0.124205	−0.0148453
$71$	−5.59406	−0.663892	−0.331946	−	0.943298i	$-0.607705\pi$
$71$	−5.59406	−0.663892	−0.331946	+	0.943298i	$0.607705\pi$
$72$	4.60816	0.543077
$73$	13.6224	1.59438	0.797188	−	0.603731i	$-0.206320\pi$
$73$	13.6224	1.59438	0.797188	+	0.603731i	$0.206320\pi$
$74$	−1.34630	−0.156504
$75$	−11.4910	−1.32686
$76$	7.95328	0.912303
$77$	1.51152	0.172254
$78$	−0.792671	−0.0897523
$79$	−3.34909	−0.376802	−0.188401	−	0.982092i	$-0.560331\pi$
$79$	−3.34909	−0.376802	−0.188401	+	0.982092i	$0.560331\pi$
$80$	2.74471	0.306868
$81$	−5.44644	−0.605160
$82$	−2.06688	−0.228249
$83$	−2.31185	−0.253758	−0.126879	−	0.991918i	$-0.540496\pi$
$83$	−2.31185	−0.253758	−0.126879	+	0.991918i	$0.540496\pi$
$84$	−2.60730	−0.284480
$85$	−0.792671	−0.0859772
$86$	−0.555880	−0.0599421
$87$	−11.5377	−1.23698
$88$	3.42932	0.365566
$89$	2.00972	0.213030	0.106515	−	0.994311i	$-0.466031\pi$
$89$	2.00972	0.213030	0.106515	+	0.994311i	$0.466031\pi$
$90$	−0.934433	−0.0984979
$91$	0.519592	0.0544680
$92$	4.13481	0.431084
$93$	3.08714	0.320122
$94$	2.82932	0.291822
$95$	−3.30232	−0.338811
$96$	−8.94190	−0.912629
$97$	12.5884	1.27816	0.639078	−	0.769142i	$-0.279316\pi$
$97$	12.5884	1.27816	0.639078	+	0.769142i	$0.279316\pi$
$98$	2.02955	0.205016
$99$	11.3717	1.14290
$100$	8.34578	0.834578
$101$	−5.37167	−0.534501	−0.267251	−	0.963627i	$-0.586115\pi$
$101$	−5.37167	−0.534501	−0.267251	+	0.963627i	$0.586115\pi$
$102$	0.792671	0.0784861
$103$	12.0463	1.18696	0.593481	−	0.804848i	$-0.297753\pi$
$103$	12.0463	1.18696	0.593481	+	0.804848i	$0.297753\pi$
$104$	1.17884	0.115595
$105$	1.08259	0.105650
$106$	3.71614	0.360943
$107$	9.23581	0.892859	0.446430	−	0.894819i	$-0.352695\pi$
$107$	9.23581	0.892859	0.446430	+	0.894819i	$0.352695\pi$
$108$	−4.56163	−0.438943
$109$	1.68034	0.160947	0.0804735	−	0.996757i	$-0.474357\pi$
$109$	1.68034	0.160947	0.0804735	+	0.996757i	$0.474357\pi$
$110$	−0.695390	−0.0663028
$111$	11.7346	1.11380
$112$	1.79915	0.170003
$113$	12.4513	1.17132	0.585659	−	0.810558i	$-0.300836\pi$
$113$	12.4513	1.17132	0.585659	+	0.810558i	$0.300836\pi$
$114$	3.30232	0.309291
$115$	−1.71684	−0.160096
$116$	8.37974	0.778040
$117$	3.90906	0.361392
$118$	1.21135	0.111513
$119$	−0.519592	−0.0476309
$120$	2.45616	0.224216
$121$	−2.53738	−0.230671
$122$	0.165545	0.0149878
$123$	18.0153	1.62439
$124$	−2.24216	−0.201352
$125$	−7.42865	−0.664439
$126$	−0.612516	−0.0545673
$127$	3.23116	0.286719	0.143359	−	0.989671i	$-0.454210\pi$
$127$	3.23116	0.286719	0.143359	+	0.989671i	$0.454210\pi$
$128$	8.58283	0.758622
$129$	4.84515	0.426592
$130$	−0.239043	−0.0209655
$131$	−0.555358	−0.0485219	−0.0242609	−	0.999706i	$-0.507723\pi$
$131$	−0.555358	−0.0485219	−0.0242609	+	0.999706i	$0.507723\pi$
$132$	−14.5976	−1.27056
$133$	−2.16466	−0.187700
$134$	−3.54677	−0.306394
$135$	1.89406	0.163015
$136$	−1.17884	−0.101085
$137$	−7.82784	−0.668777	−0.334389	−	0.942435i	$-0.608530\pi$
$137$	−7.82784	−0.668777	−0.334389	+	0.942435i	$0.608530\pi$
$138$	1.71684	0.146147
$139$	18.1176	1.53672	0.768359	−	0.640019i	$-0.221074\pi$
$139$	18.1176	1.53672	0.768359	+	0.640019i	$0.221074\pi$
$140$	−0.786274	−0.0664523
$141$	−24.6608	−2.07682
$142$	1.68698	0.141568
$143$	2.90906	0.243268
$144$	13.5356	1.12796
$145$	−3.47940	−0.288948
$146$	−4.10805	−0.339984
$147$	−17.6899	−1.45904
$148$	−8.52269	−0.700561
$149$	17.5126	1.43468	0.717342	−	0.696721i	$-0.245358\pi$
$149$	17.5126	1.43468	0.717342	+	0.696721i	$0.245358\pi$
$150$	3.46530	0.282940
$151$	23.3974	1.90405	0.952025	−	0.306019i	$-0.0989971\pi$
$151$	23.3974	1.90405	0.952025	+	0.306019i	$0.0989971\pi$
$152$	−4.91114	−0.398346
$153$	−3.90906	−0.316029
$154$	−0.455825	−0.0367314
$155$	0.930979	0.0747780
$156$	−5.01797	−0.401759
$157$	−21.2591	−1.69666	−0.848329	−	0.529470i	$-0.822391\pi$
$157$	−21.2591	−1.69666	−0.848329	+	0.529470i	$0.822391\pi$
$158$	1.00997	0.0803492
$159$	−32.3905	−2.56873
$160$	−2.69658	−0.213183
$161$	−1.12538	−0.0886924
$162$	1.64247	0.129044
$163$	−2.71678	−0.212795	−0.106397	−	0.994324i	$-0.533932\pi$
$163$	−2.71678	−0.212795	−0.106397	+	0.994324i	$0.533932\pi$
$164$	−13.0843	−1.02171
$165$	6.06114	0.471859
$166$	0.697176	0.0541113
$167$	−15.3119	−1.18487	−0.592436	−	0.805617i	$-0.701834\pi$
$167$	−15.3119	−1.18487	−0.592436	+	0.805617i	$0.701834\pi$
$168$	1.61000	0.124215
$169$	1.00000	0.0769231
$170$	0.239043	0.0183338
$171$	−16.2854	−1.24538
$172$	−3.51898	−0.268320
$173$	−19.5601	−1.48713	−0.743565	−	0.668663i	$-0.766867\pi$
$173$	−19.5601	−1.48713	−0.743565	+	0.668663i	$0.766867\pi$
$174$	3.47940	0.263773
$175$	−2.27149	−0.171708
$176$	10.0729	0.759277
$177$	−10.5583	−0.793611
$178$	−0.606065	−0.0454265
$179$	18.2790	1.36623	0.683117	−	0.730309i	$-0.260624\pi$
$179$	18.2790	1.36623	0.683117	+	0.730309i	$0.260624\pi$
$180$	−5.91540	−0.440908
$181$	5.58255	0.414947	0.207474	−	0.978241i	$-0.433476\pi$
$181$	5.58255	0.414947	0.207474	+	0.978241i	$0.433476\pi$
$182$	−0.156692	−0.0116148
$183$	−1.44292	−0.106664
$184$	−2.55324	−0.188228
$185$	3.53876	0.260175
$186$	−0.930979	−0.0682627
$187$	−2.90906	−0.212731
$188$	17.9109	1.30629
$189$	1.24155	0.0903093
$190$	0.995871	0.0722481
$191$	−9.02196	−0.652806	−0.326403	−	0.945231i	$-0.605837\pi$
$191$	−9.02196	−0.652806	−0.326403	+	0.945231i	$0.605837\pi$
$192$	−15.5065	−1.11908
$193$	−5.92858	−0.426749	−0.213374	−	0.976971i	$-0.568445\pi$
$193$	−5.92858	−0.426749	−0.213374	+	0.976971i	$0.568445\pi$
$194$	−3.79624	−0.272554
$195$	2.08354	0.149205
$196$	12.8480	0.917715
$197$	−18.1075	−1.29011	−0.645053	−	0.764138i	$-0.723165\pi$
$197$	−18.1075	−1.29011	−0.645053	+	0.764138i	$0.723165\pi$
$198$	−3.42932	−0.243711
$199$	4.91949	0.348734	0.174367	−	0.984681i	$-0.444212\pi$
$199$	4.91949	0.348734	0.174367	+	0.984681i	$0.444212\pi$
$200$	−5.15351	−0.364408
$201$	30.9143	2.18052
$202$	1.61992	0.113977
$203$	−2.28073	−0.160076
$204$	5.01797	0.351328
$205$	5.43282	0.379444
$206$	−3.63277	−0.253107
$207$	−8.46660	−0.588469
$208$	3.46262	0.240089
$209$	−12.1194	−0.838313
$210$	−0.326473	−0.0225288
$211$	10.1407	0.698115	0.349057	−	0.937101i	$-0.386502\pi$
$211$	10.1407	0.698115	0.349057	+	0.937101i	$0.386502\pi$
$212$	23.5249	1.61569
$213$	−14.7040	−1.00750
$214$	−2.78521	−0.190393
$215$	1.46114	0.0996487
$216$	2.81680	0.191659
$217$	0.610252	0.0414266
$218$	−0.506733	−0.0343203
$219$	35.8065	2.41958
$220$	−4.40214	−0.296792
$221$	−1.00000	−0.0672673
$222$	−3.53876	−0.237506
$223$	12.8238	0.858743	0.429371	−	0.903128i	$-0.358735\pi$
$223$	12.8238	0.858743	0.429371	+	0.903128i	$0.358735\pi$
$224$	−1.76760	−0.118102
$225$	−17.0891	−1.13927
$226$	−3.75489	−0.249772
$227$	9.59990	0.637168	0.318584	−	0.947895i	$-0.396793\pi$
$227$	9.59990	0.637168	0.318584	+	0.947895i	$0.396793\pi$
$228$	20.9053	1.38448
$229$	−24.4739	−1.61728	−0.808640	−	0.588303i	$-0.799796\pi$
$229$	−24.4739	−1.61728	−0.808640	+	0.588303i	$0.799796\pi$
$230$	0.517742	0.0341389
$231$	3.97305	0.261408
$232$	−5.17448	−0.339722
$233$	24.2241	1.58697	0.793486	−	0.608588i	$-0.208264\pi$
$233$	24.2241	1.58697	0.793486	+	0.608588i	$0.208264\pi$
$234$	−1.17884	−0.0770633
$235$	−7.43689	−0.485129
$236$	7.66838	0.499169
$237$	−8.80312	−0.571824
$238$	0.156692	0.0101568
$239$	20.9735	1.35666	0.678332	−	0.734756i	$-0.262703\pi$
$239$	20.9735	1.35666	0.678332	+	0.734756i	$0.262703\pi$
$240$	7.21450	0.465694
$241$	−25.3068	−1.63016	−0.815079	−	0.579350i	$-0.803306\pi$
$241$	−25.3068	−1.63016	−0.815079	+	0.579350i	$0.803306\pi$
$242$	0.765190	0.0491883
$243$	−21.4844	−1.37823
$244$	1.04798	0.0670900
$245$	−5.33469	−0.340821
$246$	−5.43282	−0.346384
$247$	−4.16607	−0.265081
$248$	1.38453	0.0879178
$249$	−6.07671	−0.385096
$250$	2.24023	0.141685
$251$	21.5150	1.35801	0.679007	−	0.734132i	$-0.262411\pi$
$251$	21.5150	1.35801	0.679007	+	0.734132i	$0.262411\pi$
$252$	−3.87752	−0.244260
$253$	−6.30071	−0.396122
$254$	−0.974409	−0.0611399
$255$	−2.08354	−0.130476
$256$	9.21037	0.575648
$257$	−2.02556	−0.126351	−0.0631754	−	0.998002i	$-0.520123\pi$
$257$	−2.02556	−0.126351	−0.0631754	+	0.998002i	$0.520123\pi$
$258$	−1.46114	−0.0909664
$259$	2.31964	0.144135
$260$	−1.51325	−0.0938480
$261$	−17.1587	−1.06210
$262$	0.167478	0.0103468
$263$	−12.6626	−0.780809	−0.390405	−	0.920643i	$-0.627665\pi$
$263$	−12.6626	−0.780809	−0.390405	+	0.920643i	$0.627665\pi$
$264$	9.01399	0.554773
$265$	−9.76789	−0.600037
$266$	0.652789	0.0400251
$267$	5.28257	0.323288
$268$	−22.4527	−1.37152
$269$	4.81840	0.293783	0.146891	−	0.989153i	$-0.453073\pi$
$269$	4.81840	0.293783	0.146891	+	0.989153i	$0.453073\pi$
$270$	−0.571185	−0.0347612
$271$	5.76144	0.349983	0.174991	−	0.984570i	$-0.444010\pi$
$271$	5.76144	0.349983	0.174991	+	0.984570i	$0.444010\pi$
$272$	−3.46262	−0.209952
$273$	1.36575	0.0826591
$274$	2.36061	0.142610
$275$	−12.7174	−0.766891
$276$	10.8684	0.654200
$277$	−0.445963	−0.0267953	−0.0133977	−	0.999910i	$-0.504265\pi$
$277$	−0.445963	−0.0267953	−0.0133977	+	0.999910i	$0.504265\pi$
$278$	−5.46367	−0.327689
$279$	4.59112	0.274863
$280$	0.485524	0.0290156
$281$	−17.2730	−1.03042	−0.515210	−	0.857064i	$-0.672286\pi$
$281$	−17.2730	−1.03042	−0.515210	+	0.857064i	$0.672286\pi$
$282$	7.43689	0.442860
$283$	−21.5692	−1.28215	−0.641077	−	0.767476i	$-0.721512\pi$
$283$	−21.5692	−1.28215	−0.641077	+	0.767476i	$0.721512\pi$
$284$	10.6794	0.633704
$285$	−8.68019	−0.514170
$286$	−0.877275	−0.0518743
$287$	3.56119	0.210210
$288$	−13.2982	−0.783604
$289$	1.00000	0.0588235
$290$	1.04927	0.0616153
$291$	33.0887	1.93969
$292$	−26.0059	−1.52188
$293$	−3.41879	−0.199728	−0.0998639	−	0.995001i	$-0.531841\pi$
$293$	−3.41879	−0.199728	−0.0998639	+	0.995001i	$0.531841\pi$
$294$	5.33469	0.311126
$295$	−3.18403	−0.185382
$296$	5.26276	0.305892
$297$	6.95109	0.403343
$298$	−5.28120	−0.305932
$299$	−2.16589	−0.125257
$300$	21.9369	1.26653
$301$	0.957768	0.0552048
$302$	−7.05587	−0.406019
$303$	−14.1195	−0.811143
$304$	−14.4255	−0.827360
$305$	−0.435137	−0.0249159
$306$	1.17884	0.0673899
$307$	25.3012	1.44401	0.722007	−	0.691886i	$-0.243220\pi$
$307$	25.3012	1.44401	0.722007	+	0.691886i	$0.243220\pi$
$308$	−2.88558	−0.164421
$309$	31.6639	1.80130
$310$	−0.280752	−0.0159457
$311$	28.2726	1.60319	0.801595	−	0.597867i	$-0.203985\pi$
$311$	28.2726	1.60319	0.801595	+	0.597867i	$0.203985\pi$
$312$	3.09859	0.175423
$313$	−29.5305	−1.66916	−0.834582	−	0.550884i	$-0.814291\pi$
$313$	−29.5305	−1.66916	−0.834582	+	0.550884i	$0.814291\pi$
$314$	6.41102	0.361795
$315$	1.61000	0.0907135
$316$	6.39361	0.359669
$317$	−34.6807	−1.94786	−0.973930	−	0.226848i	$-0.927158\pi$
$317$	−34.6807	−1.94786	−0.973930	+	0.226848i	$0.927158\pi$
$318$	9.76789	0.547756
$319$	−12.7692	−0.714938
$320$	−4.67623	−0.261409
$321$	24.2764	1.35498
$322$	0.339377	0.0189128
$323$	4.16607	0.231807
$324$	10.3976	0.577643
$325$	−4.37167	−0.242497
$326$	0.819291	0.0453763
$327$	4.41678	0.244248
$328$	8.07956	0.446119
$329$	−4.87485	−0.268759
$330$	−1.82784	−0.100619
$331$	−34.3851	−1.88997	−0.944987	−	0.327107i	$-0.893926\pi$
$331$	−34.3851	−1.88997	−0.944987	+	0.327107i	$0.893926\pi$
$332$	4.41345	0.242219
$333$	17.4514	0.956330
$334$	4.61757	0.252662
$335$	9.32271	0.509354
$336$	4.72907	0.257992
$337$	23.9307	1.30359	0.651793	−	0.758397i	$-0.274017\pi$
$337$	23.9307	1.30359	0.651793	+	0.758397i	$0.274017\pi$
$338$	−0.301567	−0.0164031
$339$	32.7283	1.77756
$340$	1.51325	0.0820677
$341$	3.41664	0.185021
$342$	4.91114	0.265564
$343$	−7.13401	−0.385200
$344$	2.17297	0.117159
$345$	−4.51273	−0.242957
$346$	5.89869	0.317115
$347$	−6.95161	−0.373182	−0.186591	−	0.982438i	$-0.559744\pi$
$347$	−6.95161	−0.373182	−0.186591	+	0.982438i	$0.559744\pi$
$348$	22.0262	1.18073
$349$	32.3434	1.73130	0.865652	−	0.500646i	$-0.166904\pi$
$349$	32.3434	1.73130	0.865652	+	0.500646i	$0.166904\pi$
$350$	0.685005	0.0366150
$351$	2.38947	0.127540
$352$	−9.89630	−0.527475
$353$	28.5522	1.51968	0.759841	−	0.650109i	$-0.225277\pi$
$353$	28.5522	1.51968	0.759841	+	0.650109i	$0.225277\pi$
$354$	3.18403	0.169229
$355$	−4.43424	−0.235345
$356$	−3.83668	−0.203343
$357$	−1.36575	−0.0722833
$358$	−5.51233	−0.291336
$359$	10.6546	0.562326	0.281163	−	0.959660i	$-0.409280\pi$
$359$	10.6546	0.562326	0.281163	+	0.959660i	$0.409280\pi$
$360$	3.65275	0.192517
$361$	−1.64382	−0.0865169
$362$	−1.68351	−0.0884833
$363$	−6.66954	−0.350060
$364$	−0.991931	−0.0519913
$365$	10.7980	0.565195
$366$	0.435137	0.0227450
$367$	30.7661	1.60598	0.802989	−	0.595994i	$-0.203242\pi$
$367$	30.7661	1.60598	0.802989	+	0.595994i	$0.203242\pi$
$368$	−7.49965	−0.390947
$369$	26.7919	1.39473
$370$	−1.06717	−0.0554796
$371$	−6.40281	−0.332417
$372$	−5.89353	−0.305565
$373$	4.59135	0.237731	0.118866	−	0.992910i	$-0.462074\pi$
$373$	4.59135	0.237731	0.118866	+	0.992910i	$0.462074\pi$
$374$	0.877275	0.0453628
$375$	−19.5263	−1.00833
$376$	−11.0600	−0.570374
$377$	−4.38947	−0.226069
$378$	−0.374409	−0.0192575
$379$	5.44535	0.279709	0.139855	−	0.990172i	$-0.455337\pi$
$379$	5.44535	0.279709	0.139855	+	0.990172i	$0.455337\pi$
$380$	6.30433	0.323405
$381$	8.49312	0.435116
$382$	2.72072	0.139204
$383$	−13.7016	−0.700117	−0.350058	−	0.936728i	$-0.613838\pi$
$383$	−13.7016	−0.700117	−0.350058	+	0.936728i	$0.613838\pi$
$384$	22.5600	1.15126
$385$	1.19814	0.0610629
$386$	1.78786	0.0909998
$387$	7.20560	0.366281
$388$	−24.0320	−1.22004
$389$	−24.9817	−1.26662	−0.633311	−	0.773897i	$-0.718305\pi$
$389$	−24.9817	−1.26662	−0.633311	+	0.773897i	$0.718305\pi$
$390$	−0.628327	−0.0318166
$391$	2.16589	0.109534
$392$	−7.93363	−0.400709
$393$	−1.45976	−0.0736354
$394$	5.46062	0.275102
$395$	−2.65473	−0.133574
$396$	−21.7092	−1.09093
$397$	3.54176	0.177756	0.0888780	−	0.996043i	$-0.471672\pi$
$397$	3.54176	0.177756	0.0888780	+	0.996043i	$0.471672\pi$
$398$	−1.48355	−0.0743639
$399$	−5.68982	−0.284848
$400$	−15.1374	−0.756871
$401$	−28.1841	−1.40745	−0.703724	−	0.710474i	$-0.748481\pi$
$401$	−28.1841	−1.40745	−0.703724	+	0.710474i	$0.748481\pi$
$402$	−9.32271	−0.464974
$403$	1.17448	0.0585052
$404$	10.2548	0.510197
$405$	−4.31723	−0.214525
$406$	0.687792	0.0341346
$407$	12.9870	0.643744
$408$	−3.09859	−0.153403
$409$	−22.6445	−1.11970	−0.559849	−	0.828595i	$-0.689141\pi$
$409$	−22.6445	−1.11970	−0.559849	+	0.828595i	$0.689141\pi$
$410$	−1.63836	−0.0809126
$411$	−20.5755	−1.01492
$412$	−22.9972	−1.13299
$413$	−2.08712	−0.102700
$414$	2.55324	0.125485
$415$	−1.83253	−0.0899555
$416$	−3.40189	−0.166791
$417$	47.6224	2.33208
$418$	3.65479	0.178762
$419$	6.16414	0.301138	0.150569	−	0.988600i	$-0.451889\pi$
$419$	6.16414	0.301138	0.150569	+	0.988600i	$0.451889\pi$
$420$	−2.06673	−0.100846
$421$	11.3636	0.553829	0.276915	−	0.960895i	$-0.410688\pi$
$421$	11.3636	0.553829	0.276915	+	0.960895i	$0.410688\pi$
$422$	−3.05810	−0.148866
$423$	−36.6750	−1.78320
$424$	−14.5266	−0.705473
$425$	4.37167	0.212057
$426$	4.43424	0.214840
$427$	−0.285230	−0.0138033
$428$	−17.6317	−0.852260
$429$	7.64648	0.369176
$430$	−0.440630	−0.0212491
$431$	2.35318	0.113349	0.0566743	−	0.998393i	$-0.481950\pi$
$431$	2.35318	0.113349	0.0566743	+	0.998393i	$0.481950\pi$
$432$	8.27380	0.398073
$433$	−1.83217	−0.0880484	−0.0440242	−	0.999030i	$-0.514018\pi$
$433$	−1.83217	−0.0880484	−0.0440242	+	0.999030i	$0.514018\pi$
$434$	−0.184032	−0.00883381
$435$	−9.14563	−0.438500
$436$	−3.20786	−0.153629
$437$	9.02327	0.431642
$438$	−10.7980	−0.515950
$439$	−11.0770	−0.528676	−0.264338	−	0.964430i	$-0.585153\pi$
$439$	−11.0770	−0.528676	−0.264338	+	0.964430i	$0.585153\pi$
$440$	2.71832	0.129591
$441$	−26.3081	−1.25276
$442$	0.301567	0.0143441
$443$	−33.0939	−1.57234	−0.786168	−	0.618013i	$-0.787938\pi$
$443$	−33.0939	−1.57234	−0.786168	+	0.618013i	$0.787938\pi$
$444$	−22.4020	−1.06315
$445$	1.59305	0.0755177
$446$	−3.86722	−0.183118
$447$	46.0319	2.17723
$448$	−3.06525	−0.144819
$449$	23.8928	1.12757	0.563786	−	0.825921i	$-0.309344\pi$
$449$	23.8928	1.12757	0.563786	+	0.825921i	$0.309344\pi$
$450$	5.15351	0.242939
$451$	19.9381	0.938850
$452$	−23.7702	−1.11806
$453$	61.5002	2.88953
$454$	−2.89501	−0.135870
$455$	0.411865	0.0193085
$456$	−12.9090	−0.604518
$457$	3.88289	0.181634	0.0908170	−	0.995868i	$-0.471052\pi$
$457$	3.88289	0.181634	0.0908170	+	0.995868i	$0.471052\pi$
$458$	7.38051	0.344869
$459$	−2.38947	−0.111531
$460$	3.27755	0.152816
$461$	−12.7192	−0.592394	−0.296197	−	0.955127i	$-0.595718\pi$
$461$	−12.7192	−0.592394	−0.296197	+	0.955127i	$0.595718\pi$
$462$	−1.19814	−0.0557425
$463$	11.4030	0.529941	0.264971	−	0.964256i	$-0.414638\pi$
$463$	11.4030	0.529941	0.264971	+	0.964256i	$0.414638\pi$
$464$	−15.1990	−0.705597
$465$	2.44709	0.113481
$466$	−7.30518	−0.338406
$467$	−12.1805	−0.563648	−0.281824	−	0.959466i	$-0.590939\pi$
$467$	−12.1805	−0.563648	−0.281824	+	0.959466i	$0.590939\pi$
$468$	−7.46262	−0.344960
$469$	6.11099	0.282179
$470$	2.24272	0.103449
$471$	−55.8796	−2.57480
$472$	−4.73522	−0.217956
$473$	5.36229	0.246558
$474$	2.65473	0.121936
$475$	18.2127	0.835657
$476$	0.991931	0.0454651
$477$	−48.1704	−2.20557
$478$	−6.32491	−0.289295
$479$	25.8162	1.17957	0.589787	−	0.807559i	$-0.299212\pi$
$479$	25.8162	1.17957	0.589787	+	0.807559i	$0.299212\pi$
$480$	−7.08798	−0.323521
$481$	4.46435	0.203557
$482$	7.63170	0.347614
$483$	−2.95807	−0.134597
$484$	4.84401	0.220182
$485$	9.97844	0.453098
$486$	6.47898	0.293893
$487$	−15.8984	−0.720425	−0.360212	−	0.932870i	$-0.617296\pi$
$487$	−15.8984	−0.720425	−0.360212	+	0.932870i	$0.617296\pi$
$488$	−0.647126	−0.0292940
$489$	−7.14108	−0.322931
$490$	1.60877	0.0726766
$491$	15.9982	0.721991	0.360995	−	0.932568i	$-0.382437\pi$
$491$	15.9982	0.721991	0.360995	+	0.932568i	$0.382437\pi$
$492$	−34.3923	−1.55052
$493$	4.38947	0.197692
$494$	1.25635	0.0565258
$495$	9.01399	0.405149
$496$	4.06679	0.182604
$497$	−2.90663	−0.130380
$498$	1.83253	0.0821177
$499$	9.15142	0.409674	0.204837	−	0.978796i	$-0.434334\pi$
$499$	9.15142	0.409674	0.204837	+	0.978796i	$0.434334\pi$
$500$	14.1817	0.634226
$501$	−40.2475	−1.79813
$502$	−6.48820	−0.289583
$503$	−28.0587	−1.25108	−0.625538	−	0.780194i	$-0.715121\pi$
$503$	−28.0587	−1.25108	−0.625538	+	0.780194i	$0.715121\pi$
$504$	2.39436	0.106653
$505$	−4.25797	−0.189477
$506$	1.90008	0.0844690
$507$	2.62851	0.116736
$508$	−6.16846	−0.273681
$509$	28.8738	1.27981	0.639903	−	0.768455i	$-0.278974\pi$
$509$	28.8738	1.27981	0.639903	+	0.768455i	$0.278974\pi$
$510$	0.628327	0.0278228
$511$	7.07806	0.313115
$512$	−19.9432	−0.881373
$513$	−9.95469	−0.439510
$514$	0.610841	0.0269430
$515$	9.54878	0.420769
$516$	−9.24967	−0.407194
$517$	−27.2930	−1.20034
$518$	−0.699526	−0.0307354
$519$	−51.4140	−2.25682
$520$	0.934433	0.0409776
$521$	12.5970	0.551882	0.275941	−	0.961175i	$-0.411010\pi$
$521$	12.5970	0.551882	0.275941	+	0.961175i	$0.411010\pi$
$522$	5.17448	0.226481
$523$	6.65716	0.291097	0.145549	−	0.989351i	$-0.453505\pi$
$523$	6.65716	0.291097	0.145549	+	0.989351i	$0.453505\pi$
$524$	1.06021	0.0463155
$525$	−5.97062	−0.260579
$526$	3.81862	0.166500
$527$	−1.17448	−0.0511613
$528$	26.4768	1.15226
$529$	−18.3089	−0.796040
$530$	2.94567	0.127952
$531$	−15.7021	−0.681412
$532$	4.13246	0.179165
$533$	6.85381	0.296872
$534$	−1.59305	−0.0689379
$535$	7.32095	0.316512
$536$	13.8645	0.598856
$537$	48.0464	2.07336
$538$	−1.45307	−0.0626462
$539$	−19.5780	−0.843285
$540$	−3.61587	−0.155602
$541$	28.9363	1.24407	0.622034	−	0.782991i	$-0.286307\pi$
$541$	28.9363	1.24407	0.622034	+	0.782991i	$0.286307\pi$
$542$	−1.73746	−0.0746303
$543$	14.6738	0.629712
$544$	3.40189	0.145855
$545$	1.33195	0.0570546
$546$	−0.411865	−0.0176262
$547$	34.2571	1.46473	0.732364	−	0.680914i	$-0.238417\pi$
$547$	34.2571	1.46473	0.732364	+	0.680914i	$0.238417\pi$
$548$	14.9438	0.638367
$549$	−2.14588	−0.0915840
$550$	3.83516	0.163532
$551$	18.2868	0.779046
$552$	−6.71122	−0.285649
$553$	−1.74016	−0.0739992
$554$	0.134488	0.00571383
$555$	9.30165	0.394833
$556$	−34.5876	−1.46684
$557$	38.4162	1.62775	0.813874	−	0.581042i	$-0.197355\pi$
$557$	38.4162	1.62775	0.813874	+	0.581042i	$0.197355\pi$
$558$	−1.38453	−0.0586118
$559$	1.84331	0.0779636
$560$	1.42613	0.0602650
$561$	−7.64648	−0.322835
$562$	5.20896	0.219727
$563$	40.0488	1.68786	0.843928	−	0.536456i	$-0.180237\pi$
$563$	40.0488	1.68786	0.843928	+	0.536456i	$0.180237\pi$
$564$	47.0790	1.98238
$565$	9.86976	0.415224
$566$	6.50455	0.273406
$567$	−2.82993	−0.118846
$568$	−6.59451	−0.276699
$569$	12.4612	0.522401	0.261201	−	0.965285i	$-0.415882\pi$
$569$	12.4612	0.522401	0.261201	+	0.965285i	$0.415882\pi$
$570$	2.61766	0.109642
$571$	−8.66499	−0.362618	−0.181309	−	0.983426i	$-0.558033\pi$
$571$	−8.66499	−0.362618	−0.181309	+	0.983426i	$0.558033\pi$
$572$	−5.55356	−0.232206
$573$	−23.7143	−0.990679
$574$	−1.07393	−0.0448252
$575$	9.46858	0.394867
$576$	−23.0608	−0.960868
$577$	−25.4123	−1.05793	−0.528964	−	0.848644i	$-0.677419\pi$
$577$	−25.4123	−1.05793	−0.528964	+	0.848644i	$0.677419\pi$
$578$	−0.301567	−0.0125435
$579$	−15.5833	−0.647621
$580$	6.64238	0.275810
$581$	−1.20122	−0.0498349
$582$	−9.97844	−0.413620
$583$	−35.8476	−1.48466
$584$	16.0586	0.664509
$585$	3.09859	0.128111
$586$	1.03099	0.0425899
$587$	−24.9726	−1.03073	−0.515364	−	0.856971i	$-0.672343\pi$
$587$	−24.9726	−1.03073	−0.515364	+	0.856971i	$0.672343\pi$
$588$	33.7711	1.39270
$589$	−4.89299	−0.201612
$590$	0.960198	0.0395307
$591$	−47.5957	−1.95783
$592$	15.4583	0.635333
$593$	−35.3802	−1.45289	−0.726445	−	0.687224i	$-0.758829\pi$
$593$	−35.3802	−1.45289	−0.726445	+	0.687224i	$0.758829\pi$
$594$	−2.09622	−0.0860089
$595$	−0.411865	−0.0168848
$596$	−33.4325	−1.36945
$597$	12.9309	0.529228
$598$	0.653161	0.0267097
$599$	−26.6743	−1.08988	−0.544942	−	0.838474i	$-0.683448\pi$
$599$	−26.6743	−1.08988	−0.544942	+	0.838474i	$0.683448\pi$
$600$	−13.5460	−0.553015
$601$	32.9492	1.34402	0.672012	−	0.740540i	$-0.265430\pi$
$601$	32.9492	1.34402	0.672012	+	0.740540i	$0.265430\pi$
$602$	−0.288831	−0.0117719
$603$	45.9750	1.87225
$604$	−44.6669	−1.81747
$605$	−2.01131	−0.0817714
$606$	4.25797	0.172968
$607$	−39.2161	−1.59173	−0.795865	−	0.605474i	$-0.792984\pi$
$607$	−39.2161	−1.59173	−0.795865	+	0.605474i	$0.792984\pi$
$608$	14.1725	0.574772
$609$	−5.99492	−0.242926
$610$	0.131223	0.00531306
$611$	−9.38206	−0.379558
$612$	7.46262	0.301658
$613$	43.7946	1.76885	0.884424	−	0.466684i	$-0.154552\pi$
$613$	43.7946	1.76885	0.884424	+	0.466684i	$0.154552\pi$
$614$	−7.62999	−0.307921
$615$	14.2802	0.575833
$616$	1.78185	0.0717926
$617$	24.2054	0.974474	0.487237	−	0.873270i	$-0.338005\pi$
$617$	24.2054	0.974474	0.487237	+	0.873270i	$0.338005\pi$
$618$	−9.54878	−0.384108
$619$	35.1257	1.41182	0.705910	−	0.708302i	$-0.250538\pi$
$619$	35.1257	1.41182	0.705910	+	0.708302i	$0.250538\pi$
$620$	−1.77729	−0.0713778
$621$	−5.17533	−0.207679
$622$	−8.52606	−0.341864
$623$	1.04424	0.0418364
$624$	9.10152	0.364352
$625$	15.9699	0.638796
$626$	8.90542	0.355932
$627$	−31.8558	−1.27220
$628$	40.5848	1.61951
$629$	−4.46435	−0.178005
$630$	−0.485524	−0.0193437
$631$	−26.7154	−1.06352	−0.531761	−	0.846894i	$-0.678470\pi$
$631$	−26.7154	−1.06352	−0.531761	+	0.846894i	$0.678470\pi$
$632$	−3.94805	−0.157045
$633$	26.6549	1.05944
$634$	10.4585	0.415361
$635$	2.56124	0.101640
$636$	61.8353	2.45193
$637$	−6.73002	−0.266653
$638$	3.85077	0.152453
$639$	−21.8675	−0.865064
$640$	6.80335	0.268926
$641$	−25.9752	−1.02596	−0.512979	−	0.858401i	$-0.671458\pi$
$641$	−25.9752	−1.02596	−0.512979	+	0.858401i	$0.671458\pi$
$642$	−7.32095	−0.288935
$643$	−18.8467	−0.743240	−0.371620	−	0.928385i	$-0.621198\pi$
$643$	−18.8467	−0.743240	−0.371620	+	0.928385i	$0.621198\pi$
$644$	2.14842	0.0846595
$645$	3.84061	0.151224
$646$	−1.25635	−0.0494304
$647$	−7.79836	−0.306585	−0.153293	−	0.988181i	$-0.548988\pi$
$647$	−7.79836	−0.306585	−0.153293	+	0.988181i	$0.548988\pi$
$648$	−6.42049	−0.252221
$649$	−11.6852	−0.458685
$650$	1.31835	0.0517100
$651$	1.60405	0.0628678
$652$	5.18649	0.203119
$653$	−17.3230	−0.677902	−0.338951	−	0.940804i	$-0.610072\pi$
$653$	−17.3230	−0.677902	−0.338951	+	0.940804i	$0.610072\pi$
$654$	−1.33195	−0.0520835
$655$	−0.440216	−0.0172007
$656$	23.7321	0.926584
$657$	53.2506	2.07750
$658$	1.47009	0.0573101
$659$	19.0325	0.741401	0.370701	−	0.928752i	$-0.379118\pi$
$659$	19.0325	0.741401	0.370701	+	0.928752i	$0.379118\pi$
$660$	−11.5711	−0.450403
$661$	21.9959	0.855540	0.427770	−	0.903888i	$-0.359299\pi$
$661$	21.9959	0.855540	0.427770	+	0.903888i	$0.359299\pi$
$662$	10.3694	0.403018
$663$	−2.62851	−0.102083
$664$	−2.72530	−0.105762
$665$	−1.71586	−0.0665382
$666$	−5.26276	−0.203928
$667$	9.50711	0.368117
$668$	29.2314	1.13100
$669$	33.7074	1.30320
$670$	−2.81142	−0.108615
$671$	−1.59693	−0.0616488
$672$	−4.64614	−0.179229
$673$	−16.7076	−0.644032	−0.322016	−	0.946734i	$-0.604361\pi$
$673$	−16.7076	−0.644032	−0.322016	+	0.946734i	$0.604361\pi$
$674$	−7.21669	−0.277977
$675$	−10.4460	−0.402065
$676$	−1.90906	−0.0734253
$677$	−11.9976	−0.461105	−0.230552	−	0.973060i	$-0.574053\pi$
$677$	−11.9976	−0.461105	−0.230552	+	0.973060i	$0.574053\pi$
$678$	−9.86976	−0.379046
$679$	6.54082	0.251014
$680$	−0.934433	−0.0358339
$681$	25.2334	0.966947
$682$	−1.03034	−0.0394539
$683$	−31.9597	−1.22290	−0.611451	−	0.791282i	$-0.709414\pi$
$683$	−31.9597	−1.22290	−0.611451	+	0.791282i	$0.709414\pi$
$684$	31.0898	1.18875
$685$	−6.20490	−0.237077
$686$	2.15138	0.0821401
$687$	−64.3299	−2.45434
$688$	6.38267	0.243337
$689$	−12.3228	−0.469460
$690$	1.36089	0.0518081
$691$	22.0953	0.840546	0.420273	−	0.907398i	$-0.361934\pi$
$691$	22.0953	0.840546	0.420273	+	0.907398i	$0.361934\pi$
$692$	37.3414	1.41951
$693$	5.90863	0.224450
$694$	2.09638	0.0795773
$695$	14.3613	0.544756
$696$	−13.6012	−0.515551
$697$	−6.85381	−0.259607
$698$	−9.75370	−0.369183
$699$	63.6732	2.40834
$700$	4.33640	0.163900
$701$	45.9236	1.73451	0.867256	−	0.497863i	$-0.165882\pi$
$701$	45.9236	1.73451	0.867256	+	0.497863i	$0.165882\pi$
$702$	−0.720583	−0.0271967
$703$	−18.5988	−0.701467
$704$	−17.1615	−0.646798
$705$	−19.5479	−0.736217
$706$	−8.61041	−0.324057
$707$	−2.79108	−0.104969
$708$	20.1564	0.757524
$709$	−52.0600	−1.95516	−0.977578	−	0.210575i	$-0.932466\pi$
$709$	−52.0600	−1.95516	−0.977578	+	0.210575i	$0.932466\pi$
$710$	1.33722	0.0501850
$711$	−13.0918	−0.490981
$712$	2.36914	0.0887875
$713$	−2.54381	−0.0952663
$714$	0.411865	0.0154137
$715$	2.30592	0.0862367
$716$	−34.8956	−1.30411
$717$	55.1291	2.05883
$718$	−3.21306	−0.119910
$719$	16.7262	0.623781	0.311890	−	0.950118i	$-0.399038\pi$
$719$	16.7262	0.623781	0.311890	+	0.950118i	$0.399038\pi$
$720$	10.7292	0.399855
$721$	6.25918	0.233104
$722$	0.495722	0.0184488
$723$	−66.5193	−2.47388
$724$	−10.6574	−0.396079
$725$	19.1893	0.712673
$726$	2.01131	0.0746467
$727$	−30.3497	−1.12561	−0.562804	−	0.826590i	$-0.690277\pi$
$727$	−30.3497	−1.12561	−0.562804	+	0.826590i	$0.690277\pi$
$728$	0.612516	0.0227014
$729$	−40.1326	−1.48639
$730$	−3.25633	−0.120522
$731$	−1.84331	−0.0681772
$732$	2.75462	0.101814
$733$	19.0800	0.704738	0.352369	−	0.935861i	$-0.385376\pi$
$733$	19.0800	0.704738	0.352369	+	0.935861i	$0.385376\pi$
$734$	−9.27803	−0.342458
$735$	−14.0223	−0.517220
$736$	7.36813	0.271593
$737$	34.2138	1.26028
$738$	−8.07956	−0.297413
$739$	23.6616	0.870407	0.435203	−	0.900332i	$-0.356677\pi$
$739$	23.6616	0.870407	0.435203	+	0.900332i	$0.356677\pi$
$740$	−6.75569	−0.248344
$741$	−10.9506	−0.402279
$742$	1.93087	0.0708846
$743$	−21.2932	−0.781172	−0.390586	−	0.920566i	$-0.627728\pi$
$743$	−21.2932	−0.781172	−0.390586	+	0.920566i	$0.627728\pi$
$744$	3.63925	0.133421
$745$	13.8817	0.508586
$746$	−1.38460	−0.0506937
$747$	−9.03714	−0.330652
$748$	5.55356	0.203058
$749$	4.79885	0.175346
$750$	5.88847	0.215017
$751$	36.9916	1.34984	0.674921	−	0.737890i	$-0.264178\pi$
$751$	36.9916	1.34984	0.674921	+	0.737890i	$0.264178\pi$
$752$	−32.4865	−1.18466
$753$	56.5523	2.06088
$754$	1.32372	0.0482069
$755$	18.5464	0.674973
$756$	−2.37018	−0.0862028
$757$	8.17425	0.297098	0.148549	−	0.988905i	$-0.452540\pi$
$757$	8.17425	0.297098	0.148549	+	0.988905i	$0.452540\pi$
$758$	−1.64214	−0.0596451
$759$	−16.5615	−0.601143
$760$	−3.89292	−0.141211
$761$	4.61076	0.167140	0.0835700	−	0.996502i	$-0.473368\pi$
$761$	4.61076	0.167140	0.0835700	+	0.996502i	$0.473368\pi$
$762$	−2.56124	−0.0927840
$763$	0.873089	0.0316080
$764$	17.2234	0.623122
$765$	−3.09859	−0.112030
$766$	4.13193	0.149293
$767$	−4.01684	−0.145040
$768$	24.2095	0.873587
$769$	−2.88794	−0.104142	−0.0520708	−	0.998643i	$-0.516582\pi$
$769$	−2.88794	−0.104142	−0.0520708	+	0.998643i	$0.516582\pi$
$770$	−0.361319	−0.0130210
$771$	−5.32419	−0.191746
$772$	11.3180	0.407344
$773$	9.36385	0.336794	0.168397	−	0.985719i	$-0.446141\pi$
$773$	9.36385	0.336794	0.168397	+	0.985719i	$0.446141\pi$
$774$	−2.17297	−0.0781057
$775$	−5.13446	−0.184435
$776$	14.8397	0.532715
$777$	6.09719	0.218735
$778$	7.53365	0.270094
$779$	−28.5535	−1.02304
$780$	−3.97760	−0.142421
$781$	−16.2734	−0.582309
$782$	−0.653161	−0.0233570
$783$	−10.4885	−0.374828
$784$	−23.3035	−0.832267
$785$	−16.8514	−0.601453
$786$	0.440216	0.0157020
$787$	45.6682	1.62790	0.813948	−	0.580937i	$-0.197314\pi$
$787$	45.6682	1.62790	0.813948	+	0.580937i	$0.197314\pi$
$788$	34.5683	1.23144
$789$	−33.2838	−1.18493
$790$	0.800577	0.0284832
$791$	6.46958	0.230032
$792$	13.4054	0.476340
$793$	−0.548951	−0.0194938
$794$	−1.06808	−0.0379047
$795$	−25.6750	−0.910598
$796$	−9.39159	−0.332876
$797$	−4.61369	−0.163425	−0.0817127	−	0.996656i	$-0.526039\pi$
$797$	−4.61369	−0.163425	−0.0817127	+	0.996656i	$0.526039\pi$
$798$	1.71586	0.0607408
$799$	9.38206	0.331914
$800$	14.8720	0.525803
$801$	7.85612	0.277582
$802$	8.49939	0.300124
$803$	39.6282	1.39845
$804$	−59.0171	−2.08137
$805$	−0.892056	−0.0314408
$806$	−0.354185	−0.0124756
$807$	12.6652	0.445836
$808$	−6.33235	−0.222771
$809$	−10.3148	−0.362650	−0.181325	−	0.983423i	$-0.558039\pi$
$809$	−10.3148	−0.362650	−0.181325	+	0.983423i	$0.558039\pi$
$810$	1.30193	0.0457453
$811$	17.7710	0.624025	0.312013	−	0.950078i	$-0.398997\pi$
$811$	17.7710	0.624025	0.312013	+	0.950078i	$0.398997\pi$
$812$	4.35405	0.152797
$813$	15.1440	0.531123
$814$	−3.91646	−0.137272
$815$	−2.15351	−0.0754343
$816$	−9.10152	−0.318617
$817$	−7.67936	−0.268667
$818$	6.82882	0.238764
$819$	2.03111	0.0709729
$820$	−10.3716	−0.362190
$821$	−40.1933	−1.40275	−0.701377	−	0.712790i	$-0.747431\pi$
$821$	−40.1933	−1.40275	−0.701377	+	0.712790i	$0.747431\pi$
$822$	6.20490	0.216421
$823$	−38.5083	−1.34231	−0.671157	−	0.741315i	$-0.734203\pi$
$823$	−38.5083	−1.34231	−0.671157	+	0.741315i	$0.734203\pi$
$824$	14.2007	0.494706
$825$	−33.4279	−1.16381
$826$	0.629405	0.0218998
$827$	−44.6381	−1.55222	−0.776109	−	0.630598i	$-0.782810\pi$
$827$	−44.6381	−1.55222	−0.776109	+	0.630598i	$0.782810\pi$
$828$	16.1632	0.561711
$829$	−7.29204	−0.253263	−0.126632	−	0.991950i	$-0.540417\pi$
$829$	−7.29204	−0.253263	−0.126632	+	0.991950i	$0.540417\pi$
$830$	0.552631	0.0191821
$831$	−1.17222	−0.0406638
$832$	−5.89933	−0.204523
$833$	6.73002	0.233182
$834$	−14.3613	−0.497292
$835$	−12.1373	−0.420029
$836$	23.1365	0.800194
$837$	2.80639	0.0970030
$838$	−1.85890	−0.0642146
$839$	−12.5000	−0.431547	−0.215774	−	0.976443i	$-0.569227\pi$
$839$	−12.5000	−0.431547	−0.215774	+	0.976443i	$0.569227\pi$
$840$	1.27620	0.0440332
$841$	−9.73259	−0.335607
$842$	−3.42689	−0.118098
$843$	−45.4022	−1.56373
$844$	−19.3592	−0.666370
$845$	0.792671	0.0272687
$846$	11.0600	0.380249
$847$	−1.31840	−0.0453009
$848$	−42.6690	−1.46526
$849$	−56.6948	−1.94576
$850$	−1.31835	−0.0452191
$851$	−9.66930	−0.331459
$852$	28.0708	0.961691
$853$	−26.1387	−0.894970	−0.447485	−	0.894291i	$-0.647680\pi$
$853$	−26.1387	−0.894970	−0.447485	+	0.894291i	$0.647680\pi$
$854$	0.0860160	0.00294341
$855$	−12.9090	−0.441478
$856$	10.8876	0.372129
$857$	6.85700	0.234231	0.117115	−	0.993118i	$-0.462635\pi$
$857$	6.85700	0.234231	0.117115	+	0.993118i	$0.462635\pi$
$858$	−2.30592	−0.0787230
$859$	49.1004	1.67528	0.837642	−	0.546220i	$-0.183934\pi$
$859$	49.1004	1.67528	0.837642	+	0.546220i	$0.183934\pi$
$860$	−2.78939	−0.0951175
$861$	9.36061	0.319009
$862$	−0.709640	−0.0241704
$863$	18.0088	0.613027	0.306514	−	0.951866i	$-0.400838\pi$
$863$	18.0088	0.613027	0.306514	+	0.951866i	$0.400838\pi$
$864$	−8.12870	−0.276544
$865$	−15.5048	−0.527177
$866$	0.552521	0.0187754
$867$	2.62851	0.0892688
$868$	−1.16501	−0.0395429
$869$	−9.74270	−0.330498
$870$	2.75802	0.0935056
$871$	11.7611	0.398511
$872$	1.98085	0.0670801
$873$	49.2087	1.66546
$874$	−2.72112	−0.0920432
$875$	−3.85987	−0.130487
$876$	−68.3566	−2.30956
$877$	−1.09058	−0.0368264	−0.0184132	−	0.999830i	$-0.505861\pi$
$877$	−1.09058	−0.0368264	−0.0184132	+	0.999830i	$0.505861\pi$
$878$	3.34045	0.112735
$879$	−8.98631	−0.303101
$880$	7.98453	0.269158
$881$	−44.5730	−1.50170	−0.750852	−	0.660471i	$-0.770357\pi$
$881$	−44.5730	−1.50170	−0.750852	+	0.660471i	$0.770357\pi$
$882$	7.93363	0.267139
$883$	−5.83736	−0.196443	−0.0982214	−	0.995165i	$-0.531315\pi$
$883$	−5.83736	−0.196443	−0.0982214	+	0.995165i	$0.531315\pi$
$884$	1.90906	0.0642086
$885$	−8.36926	−0.281329
$886$	9.98000	0.335285
$887$	−34.4008	−1.15507	−0.577533	−	0.816368i	$-0.695984\pi$
$887$	−34.4008	−1.15507	−0.577533	+	0.816368i	$0.695984\pi$
$888$	13.8332	0.464212
$889$	1.67888	0.0563079
$890$	−0.480410	−0.0161034
$891$	−15.8440	−0.530794
$892$	−24.4813	−0.819694
$893$	39.0864	1.30798
$894$	−13.8817	−0.464273
$895$	14.4892	0.484321
$896$	4.45957	0.148984
$897$	−5.69307	−0.190086
$898$	−7.20528	−0.240443
$899$	−5.15536	−0.171941
$900$	32.6241	1.08747
$901$	12.3228	0.410531
$902$	−6.01268	−0.200200
$903$	2.51750	0.0837772
$904$	14.6781	0.488186
$905$	4.42512	0.147096
$906$	−18.5464	−0.616163
$907$	11.8364	0.393020	0.196510	−	0.980502i	$-0.437039\pi$
$907$	11.8364	0.393020	0.196510	+	0.980502i	$0.437039\pi$
$908$	−18.3268	−0.608195
$909$	−20.9982	−0.696466
$910$	−0.124205	−0.00411735
$911$	−6.55788	−0.217272	−0.108636	−	0.994082i	$-0.534648\pi$
$911$	−6.55788	−0.217272	−0.108636	+	0.994082i	$0.534648\pi$
$912$	−37.9176	−1.25558
$913$	−6.72529	−0.222575
$914$	−1.17095	−0.0387316
$915$	−1.14376	−0.0378116
$916$	46.7221	1.54374
$917$	−0.288560	−0.00952908
$918$	0.720583	0.0237828
$919$	−43.1171	−1.42230	−0.711150	−	0.703040i	$-0.751825\pi$
$919$	−43.1171	−1.42230	−0.711150	+	0.703040i	$0.751825\pi$
$920$	−2.02388	−0.0667254
$921$	66.5044	2.19139
$922$	3.83570	0.126322
$923$	−5.59406	−0.184131
$924$	−7.58478	−0.249521
$925$	−19.5167	−0.641704
$926$	−3.43876	−0.113005
$927$	47.0898	1.54663
$928$	14.9325	0.490183
$929$	−2.64916	−0.0869162	−0.0434581	−	0.999055i	$-0.513838\pi$
$929$	−2.64916	−0.0869162	−0.0434581	+	0.999055i	$0.513838\pi$
$930$	−0.737959	−0.0241986
$931$	28.0378	0.918901
$932$	−46.2452	−1.51481
$933$	74.3147	2.43295
$934$	3.67324	0.120192
$935$	−2.30592	−0.0754118
$936$	4.60816	0.150622
$937$	17.4947	0.571527	0.285764	−	0.958300i	$-0.407753\pi$
$937$	17.4947	0.571527	0.285764	+	0.958300i	$0.407753\pi$
$938$	−1.84287	−0.0601719
$939$	−77.6212	−2.53307
$940$	14.1974	0.463070
$941$	16.8686	0.549901	0.274950	−	0.961458i	$-0.411339\pi$
$941$	16.8686	0.549901	0.274950	+	0.961458i	$0.411339\pi$
$942$	16.8514	0.549049
$943$	−14.8446	−0.483407
$944$	−13.9088	−0.452692
$945$	0.984138	0.0320140
$946$	−1.61709	−0.0525761
$947$	−4.43747	−0.144199	−0.0720993	−	0.997397i	$-0.522970\pi$
$947$	−4.43747	−0.144199	−0.0720993	+	0.997397i	$0.522970\pi$
$948$	16.8057	0.545822
$949$	13.6224	0.442200
$950$	−5.49235	−0.178195
$951$	−91.1584	−2.95601
$952$	−0.612516	−0.0198518
$953$	22.6220	0.732798	0.366399	−	0.930458i	$-0.380591\pi$
$953$	22.6220	0.732798	0.366399	+	0.930458i	$0.380591\pi$
$954$	14.5266	0.470316
$955$	−7.15144	−0.231415
$956$	−40.0397	−1.29497
$957$	−33.5640	−1.08497
$958$	−7.78532	−0.251532
$959$	−4.06728	−0.131339
$960$	−12.2915	−0.396707
$961$	−29.6206	−0.955503
$962$	−1.34630	−0.0434064
$963$	36.1033	1.16341
$964$	48.3122	1.55603
$965$	−4.69941	−0.151279
$966$	0.892056	0.0287014
$967$	19.9189	0.640549	0.320275	−	0.947325i	$-0.396225\pi$
$967$	19.9189	0.640549	0.320275	+	0.947325i	$0.396225\pi$
$968$	−2.99117	−0.0961400
$969$	10.9506	0.351783
$970$	−3.00917	−0.0966185
$971$	17.4305	0.559373	0.279686	−	0.960091i	$-0.409770\pi$
$971$	17.4305	0.559373	0.279686	+	0.960091i	$0.409770\pi$
$972$	41.0150	1.31556
$973$	9.41378	0.301792
$974$	4.79442	0.153623
$975$	−11.4910	−0.368006
$976$	−1.90081	−0.0608433
$977$	−31.9242	−1.02135	−0.510673	−	0.859775i	$-0.670604\pi$
$977$	−31.9242	−1.02135	−0.510673	+	0.859775i	$0.670604\pi$
$978$	2.15351	0.0688617
$979$	5.84640	0.186852
$980$	10.1842	0.325323
$981$	6.56853	0.209717
$982$	−4.82454	−0.153957
$983$	−25.7807	−0.822278	−0.411139	−	0.911573i	$-0.634869\pi$
$983$	−25.7807	−0.822278	−0.411139	+	0.911573i	$0.634869\pi$
$984$	21.2372	0.677017
$985$	−14.3533	−0.457334
$986$	−1.32372	−0.0421557
$987$	−12.8136	−0.407861
$988$	7.95328	0.253027
$989$	−3.99241	−0.126951
$990$	−2.71832	−0.0863938
$991$	16.2633	0.516620	0.258310	−	0.966062i	$-0.416834\pi$
$991$	16.2633	0.516620	0.258310	+	0.966062i	$0.416834\pi$
$992$	−3.99547	−0.126856
$993$	−90.3815	−2.86817
$994$	0.876542	0.0278022
$995$	3.89954	0.123624
$996$	11.6008	0.367585
$997$	48.0580	1.52201	0.761006	−	0.648745i	$-0.224706\pi$
$997$	48.0580	1.52201	0.761006	+	0.648745i	$0.224706\pi$
$998$	−2.75976	−0.0873587
$999$	10.6674	0.337502

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	221.2.a.g.1.3	✓	6
3.2	odd	2		1989.2.a.p.1.4		6
4.3	odd	2		3536.2.a.bh.1.1		6
5.4	even	2		5525.2.a.bb.1.4		6
13.12	even	2		2873.2.a.n.1.4		6
17.16	even	2		3757.2.a.w.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
221.2.a.g.1.3	✓	6	1.1	even	1	trivial
1989.2.a.p.1.4		6	3.2	odd	2
2873.2.a.n.1.4		6	13.12	even	2
3536.2.a.bh.1.1		6	4.3	odd	2
3757.2.a.w.1.3		6	17.16	even	2
5525.2.a.bb.1.4		6	5.4	even	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:	\( N \)	\(=\)	\( 221 = 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	221.a (trivial)

\(f(q)\)	\(=\)	\(q-0.301567 q^{2} +2.62851 q^{3} -1.90906 q^{4} +0.792671 q^{5} -0.792671 q^{6} +0.519592 q^{7} +1.17884 q^{8} +3.90906 q^{9} +O(q^{10})\)	\(q-0.301567 q^{2} +2.62851 q^{3} -1.90906 q^{4} +0.792671 q^{5} -0.792671 q^{6} +0.519592 q^{7} +1.17884 q^{8} +3.90906 q^{9} -0.239043 q^{10} +2.90906 q^{11} -5.01797 q^{12} +1.00000 q^{13} -0.156692 q^{14} +2.08354 q^{15} +3.46262 q^{16} -1.00000 q^{17} -1.17884 q^{18} -4.16607 q^{19} -1.51325 q^{20} +1.36575 q^{21} -0.877275 q^{22} -2.16589 q^{23} +3.09859 q^{24} -4.37167 q^{25} -0.301567 q^{26} +2.38947 q^{27} -0.991931 q^{28} -4.38947 q^{29} -0.628327 q^{30} +1.17448 q^{31} -3.40189 q^{32} +7.64648 q^{33} +0.301567 q^{34} +0.411865 q^{35} -7.46262 q^{36} +4.46435 q^{37} +1.25635 q^{38} +2.62851 q^{39} +0.934433 q^{40} +6.85381 q^{41} -0.411865 q^{42} +1.84331 q^{43} -5.55356 q^{44} +3.09859 q^{45} +0.653161 q^{46} -9.38206 q^{47} +9.10152 q^{48} -6.73002 q^{49} +1.31835 q^{50} -2.62851 q^{51} -1.90906 q^{52} -12.3228 q^{53} -0.720583 q^{54} +2.30592 q^{55} +0.612516 q^{56} -10.9506 q^{57} +1.32372 q^{58} -4.01684 q^{59} -3.97760 q^{60} -0.548951 q^{61} -0.354185 q^{62} +2.03111 q^{63} -5.89933 q^{64} +0.792671 q^{65} -2.30592 q^{66} +11.7611 q^{67} +1.90906 q^{68} -5.69307 q^{69} -0.124205 q^{70} -5.59406 q^{71} +4.60816 q^{72} +13.6224 q^{73} -1.34630 q^{74} -11.4910 q^{75} +7.95328 q^{76} +1.51152 q^{77} -0.792671 q^{78} -3.34909 q^{79} +2.74471 q^{80} -5.44644 q^{81} -2.06688 q^{82} -2.31185 q^{83} -2.60730 q^{84} -0.792671 q^{85} -0.555880 q^{86} -11.5377 q^{87} +3.42932 q^{88} +2.00972 q^{89} -0.934433 q^{90} +0.519592 q^{91} +4.13481 q^{92} +3.08714 q^{93} +2.82932 q^{94} -3.30232 q^{95} -8.94190 q^{96} +12.5884 q^{97} +2.02955 q^{98} +11.3717 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} + q^{3} + 7 q^{4} - 2 q^{5} + 2 q^{6} + 7 q^{7} + 6 q^{8} + 5 q^{9}+O(q^{10}) \) 6 * q + q^2 + q^3 + 7 * q^4 - 2 * q^5 + 2 * q^6 + 7 * q^7 + 6 * q^8 + 5 * q^9	\( 6 q + q^{2} + q^{3} + 7 q^{4} - 2 q^{5} + 2 q^{6} + 7 q^{7} + 6 q^{8} + 5 q^{9} - 9 q^{10} - q^{11} + 7 q^{12} + 6 q^{13} - 2 q^{14} + 3 q^{15} + 9 q^{16} - 6 q^{17} - 6 q^{18} + 23 q^{19} - 3 q^{20} + 5 q^{21} - 7 q^{22} - 10 q^{23} - q^{24} + 4 q^{25} + q^{26} - 8 q^{27} - 7 q^{28} - 4 q^{29} - 34 q^{30} + 16 q^{31} + 13 q^{32} - 6 q^{33} - q^{34} + 9 q^{35} - 33 q^{36} + 4 q^{37} + 7 q^{38} + q^{39} - 22 q^{40} - 4 q^{41} - 9 q^{42} + 10 q^{43} - 40 q^{44} - q^{45} + 20 q^{46} - 6 q^{47} + 8 q^{48} + 21 q^{49} - 16 q^{50} - q^{51} + 7 q^{52} - 27 q^{53} - 5 q^{54} + q^{55} - 51 q^{56} - 36 q^{57} + 3 q^{58} + 10 q^{59} + 5 q^{60} + 11 q^{61} - 25 q^{62} + 21 q^{63} - 8 q^{64} - 2 q^{65} - q^{66} + 18 q^{67} - 7 q^{68} - 18 q^{69} - 54 q^{70} - 17 q^{72} + 12 q^{73} + 13 q^{74} + 54 q^{76} + 14 q^{77} + 2 q^{78} - 6 q^{79} + 35 q^{80} - 26 q^{81} + 8 q^{82} + 26 q^{83} + 44 q^{84} + 2 q^{85} + 9 q^{86} + 9 q^{87} - 23 q^{88} + 21 q^{89} + 22 q^{90} + 7 q^{91} + 10 q^{92} + q^{93} + 44 q^{94} - 15 q^{95} - 33 q^{96} + 3 q^{97} + 38 q^{98} + 38 q^{99}+O(q^{100}) \) 6 * q + q^2 + q^3 + 7 * q^4 - 2 * q^5 + 2 * q^6 + 7 * q^7 + 6 * q^8 + 5 * q^9 - 9 * q^10 - q^11 + 7 * q^12 + 6 * q^13 - 2 * q^14 + 3 * q^15 + 9 * q^16 - 6 * q^17 - 6 * q^18 + 23 * q^19 - 3 * q^20 + 5 * q^21 - 7 * q^22 - 10 * q^23 - q^24 + 4 * q^25 + q^26 - 8 * q^27 - 7 * q^28 - 4 * q^29 - 34 * q^30 + 16 * q^31 + 13 * q^32 - 6 * q^33 - q^34 + 9 * q^35 - 33 * q^36 + 4 * q^37 + 7 * q^38 + q^39 - 22 * q^40 - 4 * q^41 - 9 * q^42 + 10 * q^43 - 40 * q^44 - q^45 + 20 * q^46 - 6 * q^47 + 8 * q^48 + 21 * q^49 - 16 * q^50 - q^51 + 7 * q^52 - 27 * q^53 - 5 * q^54 + q^55 - 51 * q^56 - 36 * q^57 + 3 * q^58 + 10 * q^59 + 5 * q^60 + 11 * q^61 - 25 * q^62 + 21 * q^63 - 8 * q^64 - 2 * q^65 - q^66 + 18 * q^67 - 7 * q^68 - 18 * q^69 - 54 * q^70 - 17 * q^72 + 12 * q^73 + 13 * q^74 + 54 * q^76 + 14 * q^77 + 2 * q^78 - 6 * q^79 + 35 * q^80 - 26 * q^81 + 8 * q^82 + 26 * q^83 + 44 * q^84 + 2 * q^85 + 9 * q^86 + 9 * q^87 - 23 * q^88 + 21 * q^89 + 22 * q^90 + 7 * q^91 + 10 * q^92 + q^93 + 44 * q^94 - 15 * q^95 - 33 * q^96 + 3 * q^97 + 38 * q^98 + 38 * q^99

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