LMFDB - Embedded newform 241.2.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [241,2,Mod(1,241)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(241, 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("241.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	241.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:	$1.92439468871$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 14 x^{10} + 44 x^{9} + 65 x^{8} - 219 x^{7} - 123 x^{6} + 444 x^{5} + 105 x^{4} + \cdots - 1 $ x^12 - 3x^11 - 14x^10 + 44x^9 + 65x^8 - 219x^7 - 123x^6 + 444x^5 + 105x^4 - 328x^3 - 45x^2 + 18*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.32986$ of defining polynomial
Character	$\chi$	$=$	241.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.32986 q^{2} -2.18147 q^{3} -0.231473 q^{4} -3.40432 q^{5} +2.90104 q^{6} -3.83334 q^{7} +2.96755 q^{8} +1.75880 q^{9} +O(q^{10})$	\(q-1.32986 q^{2} -2.18147 q^{3} -0.231473 q^{4} -3.40432 q^{5} +2.90104 q^{6} -3.83334 q^{7} +2.96755 q^{8} +1.75880 q^{9} +4.52727 q^{10} +4.78120 q^{11} +0.504950 q^{12} +1.75719 q^{13} +5.09781 q^{14} +7.42642 q^{15} -3.48347 q^{16} -6.01977 q^{17} -2.33895 q^{18} -4.20086 q^{19} +0.788008 q^{20} +8.36231 q^{21} -6.35832 q^{22} +4.28435 q^{23} -6.47360 q^{24} +6.58942 q^{25} -2.33681 q^{26} +2.70764 q^{27} +0.887315 q^{28} +4.96202 q^{29} -9.87609 q^{30} +4.59803 q^{31} -1.30256 q^{32} -10.4300 q^{33} +8.00545 q^{34} +13.0499 q^{35} -0.407113 q^{36} -10.0806 q^{37} +5.58655 q^{38} -3.83325 q^{39} -10.1025 q^{40} +1.12501 q^{41} -11.1207 q^{42} -9.09669 q^{43} -1.10672 q^{44} -5.98751 q^{45} -5.69758 q^{46} +7.19156 q^{47} +7.59908 q^{48} +7.69453 q^{49} -8.76300 q^{50} +13.1319 q^{51} -0.406741 q^{52} +6.07855 q^{53} -3.60079 q^{54} -16.2767 q^{55} -11.3756 q^{56} +9.16403 q^{57} -6.59879 q^{58} +1.36242 q^{59} -1.71901 q^{60} -10.9181 q^{61} -6.11473 q^{62} -6.74207 q^{63} +8.69917 q^{64} -5.98204 q^{65} +13.8705 q^{66} +9.85684 q^{67} +1.39341 q^{68} -9.34616 q^{69} -17.3546 q^{70} +11.9533 q^{71} +5.21931 q^{72} -0.162452 q^{73} +13.4057 q^{74} -14.3746 q^{75} +0.972384 q^{76} -18.3280 q^{77} +5.09768 q^{78} +14.5772 q^{79} +11.8589 q^{80} -11.1830 q^{81} -1.49611 q^{82} -5.77030 q^{83} -1.93565 q^{84} +20.4932 q^{85} +12.0973 q^{86} -10.8245 q^{87} +14.1884 q^{88} +4.73628 q^{89} +7.96255 q^{90} -6.73591 q^{91} -0.991709 q^{92} -10.0304 q^{93} -9.56377 q^{94} +14.3011 q^{95} +2.84149 q^{96} +0.439068 q^{97} -10.2326 q^{98} +8.40915 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} + q^{3} + 13 q^{4} + 6 q^{5} - q^{6} + 3 q^{7} + 9 q^{8} + 15 q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 + q^3 + 13 * q^4 + 6 * q^5 - q^6 + 3 * q^7 + 9 * q^8 + 15 * q^9	\( 12 q + 3 q^{2} + q^{3} + 13 q^{4} + 6 q^{5} - q^{6} + 3 q^{7} + 9 q^{8} + 15 q^{9} - 7 q^{10} + 22 q^{11} - 7 q^{12} - 5 q^{13} + 6 q^{14} + 13 q^{15} + 15 q^{16} - 4 q^{17} - q^{18} - 6 q^{19} + 10 q^{20} - 14 q^{21} - 12 q^{22} + 32 q^{23} - 15 q^{24} + 4 q^{25} + 8 q^{26} - 5 q^{27} - 11 q^{28} + 6 q^{29} - 19 q^{30} + 8 q^{31} + q^{32} - 24 q^{33} - 19 q^{34} + 15 q^{35} - 8 q^{36} - 8 q^{37} - 10 q^{38} + 31 q^{39} - 52 q^{40} - q^{41} - 49 q^{42} - 2 q^{43} + 42 q^{44} - 15 q^{45} - 25 q^{46} + 34 q^{47} - 49 q^{48} - 9 q^{49} - 27 q^{50} - 3 q^{51} - 41 q^{52} + 5 q^{53} - 40 q^{54} - 3 q^{55} + q^{56} - 22 q^{57} - 33 q^{58} + 26 q^{59} - 57 q^{60} - 26 q^{61} - 17 q^{62} - 4 q^{63} + 13 q^{64} - 25 q^{65} - 2 q^{66} + 6 q^{67} - 35 q^{68} - 2 q^{69} - 4 q^{70} + 94 q^{71} + 17 q^{72} - 22 q^{73} + 26 q^{74} - 20 q^{76} - 7 q^{77} + 54 q^{78} + 9 q^{79} + 19 q^{80} + 4 q^{81} + 15 q^{82} - 8 q^{83} + 2 q^{84} + 4 q^{85} + 9 q^{86} + 4 q^{87} + 6 q^{88} - 3 q^{89} + 11 q^{90} - 20 q^{91} + 36 q^{92} + 12 q^{93} + 48 q^{94} + 33 q^{95} - 23 q^{96} - 29 q^{97} + 28 q^{98} + 36 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + q^3 + 13 * q^4 + 6 * q^5 - q^6 + 3 * q^7 + 9 * q^8 + 15 * q^9 - 7 * q^10 + 22 * q^11 - 7 * q^12 - 5 * q^13 + 6 * q^14 + 13 * q^15 + 15 * q^16 - 4 * q^17 - q^18 - 6 * q^19 + 10 * q^20 - 14 * q^21 - 12 * q^22 + 32 * q^23 - 15 * q^24 + 4 * q^25 + 8 * q^26 - 5 * q^27 - 11 * q^28 + 6 * q^29 - 19 * q^30 + 8 * q^31 + q^32 - 24 * q^33 - 19 * q^34 + 15 * q^35 - 8 * q^36 - 8 * q^37 - 10 * q^38 + 31 * q^39 - 52 * q^40 - q^41 - 49 * q^42 - 2 * q^43 + 42 * q^44 - 15 * q^45 - 25 * q^46 + 34 * q^47 - 49 * q^48 - 9 * q^49 - 27 * q^50 - 3 * q^51 - 41 * q^52 + 5 * q^53 - 40 * q^54 - 3 * q^55 + q^56 - 22 * q^57 - 33 * q^58 + 26 * q^59 - 57 * q^60 - 26 * q^61 - 17 * q^62 - 4 * q^63 + 13 * q^64 - 25 * q^65 - 2 * q^66 + 6 * q^67 - 35 * q^68 - 2 * q^69 - 4 * q^70 + 94 * q^71 + 17 * q^72 - 22 * q^73 + 26 * q^74 - 20 * q^76 - 7 * q^77 + 54 * q^78 + 9 * q^79 + 19 * q^80 + 4 * q^81 + 15 * q^82 - 8 * q^83 + 2 * q^84 + 4 * q^85 + 9 * q^86 + 4 * q^87 + 6 * q^88 - 3 * q^89 + 11 * q^90 - 20 * q^91 + 36 * q^92 + 12 * q^93 + 48 * q^94 + 33 * q^95 - 23 * q^96 - 29 * q^97 + 28 * q^98 + 36 * 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 $

$2$	−1.32986	−0.940353	−0.470176	−	0.882572i	$-0.655810\pi$
$2$	−1.32986	−0.940353	−0.470176	+	0.882572i	$0.655810\pi$
$3$	−2.18147	−1.25947	−0.629735	−	0.776810i	$-0.716837\pi$
$3$	−2.18147	−1.25947	−0.629735	+	0.776810i	$0.716837\pi$
$4$	−0.231473	−0.115736
$5$	−3.40432	−1.52246	−0.761230	−	0.648482i	$-0.775404\pi$
$5$	−3.40432	−1.52246	−0.761230	+	0.648482i	$0.775404\pi$
$6$	2.90104	1.18435
$7$	−3.83334	−1.44887	−0.724434	−	0.689344i	$-0.757899\pi$
$7$	−3.83334	−1.44887	−0.724434	+	0.689344i	$0.757899\pi$
$8$	2.96755	1.04919
$9$	1.75880	0.586266
$10$	4.52727	1.43165
$11$	4.78120	1.44159	0.720793	−	0.693151i	$-0.243778\pi$
$11$	4.78120	1.44159	0.720793	+	0.693151i	$0.243778\pi$
$12$	0.504950	0.145767
$13$	1.75719	0.487356	0.243678	−	0.969856i	$-0.421646\pi$
$13$	1.75719	0.487356	0.243678	+	0.969856i	$0.421646\pi$
$14$	5.09781	1.36245
$15$	7.42642	1.91749
$16$	−3.48347	−0.870869
$17$	−6.01977	−1.46001	−0.730004	−	0.683443i	$-0.760482\pi$
$17$	−6.01977	−1.46001	−0.730004	+	0.683443i	$0.760482\pi$
$18$	−2.33895	−0.551296
$19$	−4.20086	−0.963743	−0.481871	−	0.876242i	$-0.660043\pi$
$19$	−4.20086	−0.963743	−0.481871	+	0.876242i	$0.660043\pi$
$20$	0.788008	0.176204
$21$	8.36231	1.82481
$22$	−6.35832	−1.35560
$23$	4.28435	0.893348	0.446674	−	0.894697i	$-0.352608\pi$
$23$	4.28435	0.893348	0.446674	+	0.894697i	$0.352608\pi$
$24$	−6.47360	−1.32142
$25$	6.58942	1.31788
$26$	−2.33681	−0.458287
$27$	2.70764	0.521086
$28$	0.887315	0.167687
$29$	4.96202	0.921423	0.460712	−	0.887550i	$-0.347594\pi$
$29$	4.96202	0.921423	0.460712	+	0.887550i	$0.347594\pi$
$30$	−9.87609	−1.80312
$31$	4.59803	0.825830	0.412915	−	0.910770i	$-0.364511\pi$
$31$	4.59803	0.825830	0.412915	+	0.910770i	$0.364511\pi$
$32$	−1.30256	−0.230262
$33$	−10.4300	−1.81563
$34$	8.00545	1.37292
$35$	13.0499	2.20584
$36$	−0.407113	−0.0678522
$37$	−10.0806	−1.65723	−0.828617	−	0.559816i	$-0.810872\pi$
$37$	−10.0806	−1.65723	−0.828617	+	0.559816i	$0.810872\pi$
$38$	5.58655	0.906258
$39$	−3.83325	−0.613811
$40$	−10.1025	−1.59734
$41$	1.12501	0.175698	0.0878488	−	0.996134i	$-0.472001\pi$
$41$	1.12501	0.175698	0.0878488	+	0.996134i	$0.472001\pi$
$42$	−11.1207	−1.71596
$43$	−9.09669	−1.38723	−0.693616	−	0.720345i	$-0.743984\pi$
$43$	−9.09669	−1.38723	−0.693616	+	0.720345i	$0.743984\pi$
$44$	−1.10672	−0.166844
$45$	−5.98751	−0.892566
$46$	−5.69758	−0.840062
$47$	7.19156	1.04900	0.524499	−	0.851411i	$-0.324253\pi$
$47$	7.19156	1.04900	0.524499	+	0.851411i	$0.324253\pi$
$48$	7.59908	1.09683
$49$	7.69453	1.09922
$50$	−8.76300	−1.23928
$51$	13.1319	1.83884
$52$	−0.406741	−0.0564049
$53$	6.07855	0.834953	0.417477	−	0.908688i	$-0.362915\pi$
$53$	6.07855	0.834953	0.417477	+	0.908688i	$0.362915\pi$
$54$	−3.60079	−0.490005
$55$	−16.2767	−2.19475
$56$	−11.3756	−1.52013
$57$	9.16403	1.21381
$58$	−6.59879	−0.866463
$59$	1.36242	0.177372	0.0886862	−	0.996060i	$-0.471733\pi$
$59$	1.36242	0.177372	0.0886862	+	0.996060i	$0.471733\pi$
$60$	−1.71901	−0.221924
$61$	−10.9181	−1.39791	−0.698957	−	0.715164i	$-0.746352\pi$
$61$	−10.9181	−1.39791	−0.698957	+	0.715164i	$0.746352\pi$
$62$	−6.11473	−0.776571
$63$	−6.74207	−0.849421
$64$	8.69917	1.08740
$65$	−5.98204	−0.741980
$66$	13.8705	1.70734
$67$	9.85684	1.20421	0.602103	−	0.798419i	$-0.294330\pi$
$67$	9.85684	1.20421	0.602103	+	0.798419i	$0.294330\pi$
$68$	1.39341	0.168976
$69$	−9.34616	−1.12514
$70$	−17.3546	−2.07427
$71$	11.9533	1.41859	0.709296	−	0.704911i	$-0.249013\pi$
$71$	11.9533	1.41859	0.709296	+	0.704911i	$0.249013\pi$
$72$	5.21931	0.615102
$73$	−0.162452	−0.0190135	−0.00950676	−	0.999955i	$-0.503026\pi$
$73$	−0.162452	−0.0190135	−0.00950676	+	0.999955i	$0.503026\pi$
$74$	13.4057	1.55838
$75$	−14.3746	−1.65983
$76$	0.972384	0.111540
$77$	−18.3280	−2.08867
$78$	5.09768	0.577199
$79$	14.5772	1.64006	0.820031	−	0.572319i	$-0.193956\pi$
$79$	14.5772	1.64006	0.820031	+	0.572319i	$0.193956\pi$
$80$	11.8589	1.32586
$81$	−11.1830	−1.24256
$82$	−1.49611	−0.165218
$83$	−5.77030	−0.633372	−0.316686	−	0.948530i	$-0.602570\pi$
$83$	−5.77030	−0.633372	−0.316686	+	0.948530i	$0.602570\pi$
$84$	−1.93565	−0.211196
$85$	20.4932	2.22280
$86$	12.0973	1.30449
$87$	−10.8245	−1.16051
$88$	14.1884	1.51249
$89$	4.73628	0.502044	0.251022	−	0.967981i	$-0.419233\pi$
$89$	4.73628	0.502044	0.251022	+	0.967981i	$0.419233\pi$
$90$	7.96255	0.839327
$91$	−6.73591	−0.706115
$92$	−0.991709	−0.103393
$93$	−10.0304	−1.04011
$94$	−9.56377	−0.986428
$95$	14.3011	1.46726
$96$	2.84149	0.290008
$97$	0.439068	0.0445806	0.0222903	−	0.999752i	$-0.492904\pi$
$97$	0.439068	0.0445806	0.0222903	+	0.999752i	$0.492904\pi$
$98$	−10.2326	−1.03365
$99$	8.40915	0.845152
$100$	−1.52527	−0.152527
$101$	−4.54961	−0.452703	−0.226352	−	0.974046i	$-0.572680\pi$
$101$	−4.54961	−0.452703	−0.226352	+	0.974046i	$0.572680\pi$
$102$	−17.4636	−1.72916
$103$	10.9977	1.08364	0.541819	−	0.840495i	$-0.317736\pi$
$103$	10.9977	1.08364	0.541819	+	0.840495i	$0.317736\pi$
$104$	5.21454	0.511327
$105$	−28.4680	−2.77819
$106$	−8.08362	−0.785151
$107$	0.634979	0.0613858	0.0306929	−	0.999529i	$-0.490229\pi$
$107$	0.634979	0.0613858	0.0306929	+	0.999529i	$0.490229\pi$
$108$	−0.626746	−0.0603086
$109$	5.56974	0.533484	0.266742	−	0.963768i	$-0.414053\pi$
$109$	5.56974	0.533484	0.266742	+	0.963768i	$0.414053\pi$
$110$	21.6458	2.06384
$111$	21.9904	2.08724
$112$	13.3534	1.26177
$113$	4.78347	0.449991	0.224995	−	0.974360i	$-0.427763\pi$
$113$	4.78347	0.449991	0.224995	+	0.974360i	$0.427763\pi$
$114$	−12.1869	−1.14141
$115$	−14.5853	−1.36009
$116$	−1.14857	−0.106642
$117$	3.09054	0.285720
$118$	−1.81183	−0.166793
$119$	23.0758	2.11536
$120$	22.0382	2.01181
$121$	11.8598	1.07817
$122$	14.5195	1.31453
$123$	−2.45418	−0.221286
$124$	−1.06432	−0.0955785
$125$	−5.41088	−0.483964
$126$	8.96601	0.798756
$127$	−6.09612	−0.540944	−0.270472	−	0.962728i	$-0.587180\pi$
$127$	−6.09612	−0.540944	−0.270472	+	0.962728i	$0.587180\pi$
$128$	−8.96356	−0.792274
$129$	19.8441	1.74718
$130$	7.95527	0.697723
$131$	−6.72698	−0.587739	−0.293869	−	0.955846i	$-0.594943\pi$
$131$	−6.72698	−0.587739	−0.293869	+	0.955846i	$0.594943\pi$
$132$	2.41427	0.210135
$133$	16.1033	1.39634
$134$	−13.1082	−1.13238
$135$	−9.21769	−0.793333
$136$	−17.8639	−1.53182
$137$	−9.94109	−0.849325	−0.424663	−	0.905352i	$-0.639607\pi$
$137$	−9.94109	−0.849325	−0.424663	+	0.905352i	$0.639607\pi$
$138$	12.4291	1.05803
$139$	3.28633	0.278743	0.139372	−	0.990240i	$-0.455492\pi$
$139$	3.28633	0.278743	0.139372	+	0.990240i	$0.455492\pi$
$140$	−3.02071	−0.255296
$141$	−15.6882	−1.32118
$142$	−15.8962	−1.33398
$143$	8.40146	0.702566
$144$	−6.12672	−0.510560
$145$	−16.8923	−1.40283
$146$	0.216038	0.0178794
$147$	−16.7854	−1.38443
$148$	2.33337	0.191802
$149$	9.42710	0.772298	0.386149	−	0.922436i	$-0.373805\pi$
$149$	9.42710	0.772298	0.386149	+	0.922436i	$0.373805\pi$
$150$	19.1162	1.56083
$151$	−2.34993	−0.191234	−0.0956171	−	0.995418i	$-0.530482\pi$
$151$	−2.34993	−0.191234	−0.0956171	+	0.995418i	$0.530482\pi$
$152$	−12.4662	−1.01115
$153$	−10.5875	−0.855952
$154$	24.3736	1.96408
$155$	−15.6532	−1.25729
$156$	0.887292	0.0710402
$157$	19.8666	1.58552	0.792762	−	0.609531i	$-0.208642\pi$
$157$	19.8666	1.58552	0.792762	+	0.609531i	$0.208642\pi$
$158$	−19.3856	−1.54224
$159$	−13.2602	−1.05160
$160$	4.43433	0.350565
$161$	−16.4234	−1.29434
$162$	14.8719	1.16844
$163$	−2.10105	−0.164567	−0.0822836	−	0.996609i	$-0.526221\pi$
$163$	−2.10105	−0.164567	−0.0822836	+	0.996609i	$0.526221\pi$
$164$	−0.260410	−0.0203346
$165$	35.5072	2.76423
$166$	7.67368	0.595593
$167$	21.9087	1.69535	0.847673	−	0.530518i	$-0.178003\pi$
$167$	21.9087	1.69535	0.847673	+	0.530518i	$0.178003\pi$
$168$	24.8156	1.91456
$169$	−9.91229	−0.762484
$170$	−27.2531	−2.09022
$171$	−7.38845	−0.565009
$172$	2.10564	0.160553
$173$	−5.60734	−0.426318	−0.213159	−	0.977018i	$-0.568375\pi$
$173$	−5.60734	−0.426318	−0.213159	+	0.977018i	$0.568375\pi$
$174$	14.3950	1.09128
$175$	−25.2595	−1.90944
$176$	−16.6552	−1.25543
$177$	−2.97208	−0.223395
$178$	−6.29859	−0.472099
$179$	−23.8279	−1.78098	−0.890492	−	0.454999i	$-0.849640\pi$
$179$	−23.8279	−1.78098	−0.890492	+	0.454999i	$0.849640\pi$
$180$	1.38595	0.103302
$181$	6.57832	0.488963	0.244481	−	0.969654i	$-0.421382\pi$
$181$	6.57832	0.488963	0.244481	+	0.969654i	$0.421382\pi$
$182$	8.95781	0.663997
$183$	23.8174	1.76063
$184$	12.7140	0.937288
$185$	34.3175	2.52307
$186$	13.3391	0.978069
$187$	−28.7817	−2.10473
$188$	−1.66465	−0.121407
$189$	−10.3793	−0.754985
$190$	−19.0184	−1.37974
$191$	19.1620	1.38652	0.693258	−	0.720689i	$-0.256174\pi$
$191$	19.1620	1.38652	0.693258	+	0.720689i	$0.256174\pi$
$192$	−18.9769	−1.36954
$193$	6.37070	0.458573	0.229286	−	0.973359i	$-0.426361\pi$
$193$	6.37070	0.458573	0.229286	+	0.973359i	$0.426361\pi$
$194$	−0.583899	−0.0419215
$195$	13.0496	0.934502
$196$	−1.78107	−0.127220
$197$	−12.1752	−0.867450	−0.433725	−	0.901045i	$-0.642801\pi$
$197$	−12.1752	−0.867450	−0.433725	+	0.901045i	$0.642801\pi$
$198$	−11.1830	−0.794741
$199$	−1.12984	−0.0800919	−0.0400459	−	0.999198i	$-0.512750\pi$
$199$	−1.12984	−0.0800919	−0.0400459	+	0.999198i	$0.512750\pi$
$200$	19.5544	1.38270
$201$	−21.5024	−1.51666
$202$	6.05035	0.425701
$203$	−19.0211	−1.33502
$204$	−3.03968	−0.212820
$205$	−3.82991	−0.267492
$206$	−14.6254	−1.01900
$207$	7.53529	0.523739
$208$	−6.12112	−0.424423
$209$	−20.0851	−1.38932
$210$	37.8585	2.61248
$211$	27.7361	1.90943	0.954716	−	0.297520i	$-0.0961596\pi$
$211$	27.7361	1.90943	0.954716	+	0.297520i	$0.0961596\pi$
$212$	−1.40702	−0.0966345
$213$	−26.0757	−1.78668
$214$	−0.844433	−0.0577243
$215$	30.9681	2.11201
$216$	8.03506	0.546716
$217$	−17.6258	−1.19652
$218$	−7.40697	−0.501664
$219$	0.354383	0.0239470
$220$	3.76762	0.254013
$221$	−10.5779	−0.711544
$222$	−29.2442	−1.96274
$223$	−9.10518	−0.609728	−0.304864	−	0.952396i	$-0.598611\pi$
$223$	−9.10518	−0.609728	−0.304864	+	0.952396i	$0.598611\pi$
$224$	4.99316	0.333619
$225$	11.5894	0.772629
$226$	−6.36134	−0.423150
$227$	24.1258	1.60129	0.800644	−	0.599141i	$-0.204491\pi$
$227$	24.1258	1.60129	0.800644	+	0.599141i	$0.204491\pi$
$228$	−2.12122	−0.140481
$229$	−29.6552	−1.95967	−0.979835	−	0.199809i	$-0.935968\pi$
$229$	−29.6552	−1.95967	−0.979835	+	0.199809i	$0.935968\pi$
$230$	19.3964	1.27896
$231$	39.9819	2.63061
$232$	14.7250	0.966744
$233$	−5.36189	−0.351269	−0.175635	−	0.984455i	$-0.556198\pi$
$233$	−5.36189	−0.351269	−0.175635	+	0.984455i	$0.556198\pi$
$234$	−4.10998	−0.268678
$235$	−24.4824	−1.59706
$236$	−0.315364	−0.0205284
$237$	−31.7996	−2.06561
$238$	−30.6876	−1.98918
$239$	2.14131	0.138510	0.0692549	−	0.997599i	$-0.477938\pi$
$239$	2.14131	0.138510	0.0692549	+	0.997599i	$0.477938\pi$
$240$	−25.8697	−1.66988
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	−15.7719	−1.01386
$243$	16.2725	1.04388
$244$	2.52723	0.161789
$245$	−26.1947	−1.67352
$246$	3.26371	0.208087
$247$	−7.38170	−0.469686
$248$	13.6449	0.866449
$249$	12.5877	0.797713
$250$	7.19572	0.455097
$251$	−28.1462	−1.77657	−0.888285	−	0.459293i	$-0.848103\pi$
$251$	−28.1462	−1.77657	−0.888285	+	0.459293i	$0.848103\pi$
$252$	1.56061	0.0983090
$253$	20.4843	1.28784
$254$	8.10699	0.508678
$255$	−44.7053	−2.79955
$256$	−5.47806	−0.342379
$257$	1.23067	0.0767674	0.0383837	−	0.999263i	$-0.487779\pi$
$257$	1.23067	0.0767674	0.0383837	+	0.999263i	$0.487779\pi$
$258$	−26.3899	−1.64296
$259$	38.6423	2.40111
$260$	1.38468	0.0858741
$261$	8.72718	0.540199
$262$	8.94594	0.552682
$263$	−15.0159	−0.925919	−0.462960	−	0.886379i	$-0.653213\pi$
$263$	−15.0159	−0.925919	−0.462960	+	0.886379i	$0.653213\pi$
$264$	−30.9516	−1.90494
$265$	−20.6934	−1.27118
$266$	−21.4152	−1.31305
$267$	−10.3320	−0.632310
$268$	−2.28159	−0.139370
$269$	−0.940463	−0.0573410	−0.0286705	−	0.999589i	$-0.509127\pi$
$269$	−0.940463	−0.0573410	−0.0286705	+	0.999589i	$0.509127\pi$
$270$	12.2582	0.746013
$271$	5.11230	0.310550	0.155275	−	0.987871i	$-0.450374\pi$
$271$	5.11230	0.310550	0.155275	+	0.987871i	$0.450374\pi$
$272$	20.9697	1.27148
$273$	14.6942	0.889331
$274$	13.2203	0.798665
$275$	31.5053	1.89984
$276$	2.16338	0.130220
$277$	2.39186	0.143713	0.0718565	−	0.997415i	$-0.477108\pi$
$277$	2.39186	0.143713	0.0718565	+	0.997415i	$0.477108\pi$
$278$	−4.37036	−0.262117
$279$	8.08699	0.484155
$280$	38.7263	2.31434
$281$	7.49067	0.446856	0.223428	−	0.974720i	$-0.428275\pi$
$281$	7.49067	0.446856	0.223428	+	0.974720i	$0.428275\pi$
$282$	20.8630	1.24238
$283$	−17.9408	−1.06647	−0.533235	−	0.845967i	$-0.679024\pi$
$283$	−17.9408	−1.06647	−0.533235	+	0.845967i	$0.679024\pi$
$284$	−2.76686	−0.164183
$285$	−31.1973	−1.84797
$286$	−11.1728	−0.660660
$287$	−4.31256	−0.254563
$288$	−2.29094	−0.134995
$289$	19.2376	1.13162
$290$	22.4644	1.31916
$291$	−0.957812	−0.0561479
$292$	0.0376031	0.00220056
$293$	12.6436	0.738644	0.369322	−	0.929301i	$-0.379590\pi$
$293$	12.6436	0.738644	0.369322	+	0.929301i	$0.379590\pi$
$294$	22.3222	1.30186
$295$	−4.63813	−0.270042
$296$	−29.9145	−1.73875
$297$	12.9458	0.751190
$298$	−12.5367	−0.726233
$299$	7.52840	0.435379
$300$	3.32733	0.192103
$301$	34.8708	2.00992
$302$	3.12507	0.179828
$303$	9.92483	0.570167
$304$	14.6336	0.839293
$305$	37.1686	2.12827
$306$	14.0800	0.804897
$307$	4.93084	0.281418	0.140709	−	0.990051i	$-0.455062\pi$
$307$	4.93084	0.281418	0.140709	+	0.990051i	$0.455062\pi$
$308$	4.24243	0.241735
$309$	−23.9912	−1.36481
$310$	20.8165	1.18230
$311$	33.2247	1.88400	0.942001	−	0.335609i	$-0.108942\pi$
$311$	33.2247	1.88400	0.942001	+	0.335609i	$0.108942\pi$
$312$	−11.3753	−0.644002
$313$	18.2269	1.03024	0.515122	−	0.857117i	$-0.327747\pi$
$313$	18.2269	1.03024	0.515122	+	0.857117i	$0.327747\pi$
$314$	−26.4197	−1.49095
$315$	22.9522	1.29321
$316$	−3.37422	−0.189815
$317$	15.7434	0.884235	0.442117	−	0.896957i	$-0.354227\pi$
$317$	15.7434	0.884235	0.442117	+	0.896957i	$0.354227\pi$
$318$	17.6342	0.988874
$319$	23.7244	1.32831
$320$	−29.6148	−1.65552
$321$	−1.38519	−0.0773135
$322$	21.8408	1.21714
$323$	25.2882	1.40707
$324$	2.58857	0.143809
$325$	11.5788	0.642279
$326$	2.79411	0.154751
$327$	−12.1502	−0.671908
$328$	3.33853	0.184339
$329$	−27.5677	−1.51986
$330$	−47.2195	−2.59935
$331$	−7.35834	−0.404451	−0.202225	−	0.979339i	$-0.564817\pi$
$331$	−7.35834	−0.404451	−0.202225	+	0.979339i	$0.564817\pi$
$332$	1.33567	0.0733042
$333$	−17.7297	−0.971579
$334$	−29.1355	−1.59422
$335$	−33.5559	−1.83335
$336$	−29.1299	−1.58917
$337$	−21.0122	−1.14461	−0.572303	−	0.820042i	$-0.693950\pi$
$337$	−21.0122	−1.14461	−0.572303	+	0.820042i	$0.693950\pi$
$338$	13.1820	0.717004
$339$	−10.4350	−0.566750
$340$	−4.74363	−0.257259
$341$	21.9841	1.19050
$342$	9.82561	0.531308
$343$	−2.66238	−0.143755
$344$	−26.9949	−1.45547
$345$	31.8173	1.71299
$346$	7.45697	0.400889
$347$	−0.799138	−0.0429000	−0.0214500	−	0.999770i	$-0.506828\pi$
$347$	−0.799138	−0.0429000	−0.0214500	+	0.999770i	$0.506828\pi$
$348$	2.50557	0.134313
$349$	−1.25641	−0.0672542	−0.0336271	−	0.999434i	$-0.510706\pi$
$349$	−1.25641	−0.0672542	−0.0336271	+	0.999434i	$0.510706\pi$
$350$	33.5916	1.79555
$351$	4.75784	0.253955
$352$	−6.22779	−0.331942
$353$	30.7996	1.63930	0.819649	−	0.572865i	$-0.194168\pi$
$353$	30.7996	1.63930	0.819649	+	0.572865i	$0.194168\pi$
$354$	3.95245	0.210070
$355$	−40.6928	−2.15975
$356$	−1.09632	−0.0581048
$357$	−50.3392	−2.66423
$358$	31.6878	1.67475
$359$	−14.3153	−0.755535	−0.377768	−	0.925900i	$-0.623308\pi$
$359$	−14.3153	−0.755535	−0.377768	+	0.925900i	$0.623308\pi$
$360$	−17.7682	−0.936467
$361$	−1.35280	−0.0712002
$362$	−8.74825	−0.459798
$363$	−25.8718	−1.35792
$364$	1.55918	0.0817232
$365$	0.553038	0.0289473
$366$	−31.6738	−1.65561
$367$	3.37048	0.175938	0.0879688	−	0.996123i	$-0.471962\pi$
$367$	3.37048	0.175938	0.0879688	+	0.996123i	$0.471962\pi$
$368$	−14.9244	−0.777989
$369$	1.97867	0.103005
$370$	−45.6374	−2.37258
$371$	−23.3012	−1.20974
$372$	2.32177	0.120378
$373$	5.72387	0.296371	0.148185	−	0.988960i	$-0.452657\pi$
$373$	5.72387	0.296371	0.148185	+	0.988960i	$0.452657\pi$
$374$	38.2756	1.97919
$375$	11.8037	0.609538
$376$	21.3413	1.10059
$377$	8.71920	0.449061
$378$	13.8031	0.709953
$379$	0.963739	0.0495040	0.0247520	−	0.999694i	$-0.492120\pi$
$379$	0.963739	0.0495040	0.0247520	+	0.999694i	$0.492120\pi$
$380$	−3.31031	−0.169815
$381$	13.2985	0.681302
$382$	−25.4828	−1.30382
$383$	17.5403	0.896267	0.448134	−	0.893967i	$-0.352089\pi$
$383$	17.5403	0.896267	0.448134	+	0.893967i	$0.352089\pi$
$384$	19.5537	0.997846
$385$	62.3943	3.17991
$386$	−8.47213	−0.431220
$387$	−15.9992	−0.813287
$388$	−0.101632	−0.00515960
$389$	−16.8395	−0.853796	−0.426898	−	0.904300i	$-0.640394\pi$
$389$	−16.8395	−0.853796	−0.426898	+	0.904300i	$0.640394\pi$
$390$	−17.3542	−0.878762
$391$	−25.7908	−1.30429
$392$	22.8339	1.15328
$393$	14.6747	0.740240
$394$	16.1914	0.815709
$395$	−49.6254	−2.49693
$396$	−1.94649	−0.0978148
$397$	−2.82968	−0.142017	−0.0710087	−	0.997476i	$-0.522622\pi$
$397$	−2.82968	−0.142017	−0.0710087	+	0.997476i	$0.522622\pi$
$398$	1.50252	0.0753146
$399$	−35.1289	−1.75864
$400$	−22.9541	−1.14770
$401$	−13.6028	−0.679290	−0.339645	−	0.940554i	$-0.610307\pi$
$401$	−13.6028	−0.679290	−0.339645	+	0.940554i	$0.610307\pi$
$402$	28.5951	1.42620
$403$	8.07960	0.402473
$404$	1.05311	0.0523943
$405$	38.0706	1.89174
$406$	25.2954	1.25539
$407$	−48.1971	−2.38904
$408$	38.9696	1.92928
$409$	24.6420	1.21847	0.609234	−	0.792990i	$-0.291477\pi$
$409$	24.6420	1.21847	0.609234	+	0.792990i	$0.291477\pi$
$410$	5.09324	0.251537
$411$	21.6862	1.06970
$412$	−2.54567	−0.125416
$413$	−5.22264	−0.256989
$414$	−10.0209	−0.492499
$415$	19.6439	0.964284
$416$	−2.28884	−0.112220
$417$	−7.16902	−0.351069
$418$	26.7104	1.30645
$419$	−7.82622	−0.382336	−0.191168	−	0.981557i	$-0.561228\pi$
$419$	−7.82622	−0.382336	−0.191168	+	0.981557i	$0.561228\pi$
$420$	6.58957	0.321538
$421$	21.3683	1.04143	0.520715	−	0.853731i	$-0.325666\pi$
$421$	21.3683	1.04143	0.520715	+	0.853731i	$0.325666\pi$
$422$	−36.8851	−1.79554
$423$	12.6485	0.614991
$424$	18.0384	0.876021
$425$	−39.6667	−1.92412
$426$	34.6770	1.68011
$427$	41.8527	2.02539
$428$	−0.146980	−0.00710457
$429$	−18.3275	−0.884860
$430$	−41.1832	−1.98603
$431$	33.9239	1.63406	0.817028	−	0.576598i	$-0.195620\pi$
$431$	33.9239	1.63406	0.817028	+	0.576598i	$0.195620\pi$
$432$	−9.43201	−0.453798
$433$	34.5154	1.65871	0.829353	−	0.558725i	$-0.188709\pi$
$433$	34.5154	1.65871	0.829353	+	0.558725i	$0.188709\pi$
$434$	23.4399	1.12515
$435$	36.8500	1.76682
$436$	−1.28924	−0.0617435
$437$	−17.9979	−0.860957
$438$	−0.471279	−0.0225186
$439$	2.28531	0.109072	0.0545360	−	0.998512i	$-0.482632\pi$
$439$	2.28531	0.109072	0.0545360	+	0.998512i	$0.482632\pi$
$440$	−48.3020	−2.30271
$441$	13.5331	0.644434
$442$	14.0671	0.669103
$443$	18.3736	0.872957	0.436478	−	0.899715i	$-0.356226\pi$
$443$	18.3736	0.872957	0.436478	+	0.899715i	$0.356226\pi$
$444$	−5.09018	−0.241569
$445$	−16.1238	−0.764342
$446$	12.1086	0.573360
$447$	−20.5649	−0.972687
$448$	−33.3469	−1.57549
$449$	26.0138	1.22767	0.613833	−	0.789436i	$-0.289627\pi$
$449$	26.0138	1.22767	0.613833	+	0.789436i	$0.289627\pi$
$450$	−15.4123	−0.726544
$451$	5.37891	0.253283
$452$	−1.10724	−0.0520803
$453$	5.12628	0.240854
$454$	−32.0840	−1.50578
$455$	22.9312	1.07503
$456$	27.1947	1.27351
$457$	9.10237	0.425791	0.212895	−	0.977075i	$-0.431711\pi$
$457$	9.10237	0.425791	0.212895	+	0.977075i	$0.431711\pi$
$458$	39.4372	1.84278
$459$	−16.2994	−0.760790
$460$	3.37610	0.157411
$461$	12.3824	0.576708	0.288354	−	0.957524i	$-0.406892\pi$
$461$	12.3824	0.576708	0.288354	+	0.957524i	$0.406892\pi$
$462$	−53.1703	−2.47371
$463$	25.3698	1.17904	0.589518	−	0.807755i	$-0.299318\pi$
$463$	25.3698	1.17904	0.589518	+	0.807755i	$0.299318\pi$
$464$	−17.2851	−0.802439
$465$	34.1469	1.58352
$466$	7.13057	0.330317
$467$	−21.2025	−0.981137	−0.490568	−	0.871403i	$-0.663211\pi$
$467$	−21.2025	−0.981137	−0.490568	+	0.871403i	$0.663211\pi$
$468$	−0.715375	−0.0330682
$469$	−37.7847	−1.74473
$470$	32.5582	1.50180
$471$	−43.3382	−1.99692
$472$	4.04306	0.186097
$473$	−43.4931	−1.99981
$474$	42.2891	1.94240
$475$	−27.6812	−1.27010
$476$	−5.34143	−0.244824
$477$	10.6909	0.489504
$478$	−2.84764	−0.130248
$479$	−26.5866	−1.21477	−0.607385	−	0.794407i	$-0.707782\pi$
$479$	−26.5866	−1.21477	−0.607385	+	0.794407i	$0.707782\pi$
$480$	−9.67334	−0.441526
$481$	−17.7134	−0.807663
$482$	−1.32986	−0.0605735
$483$	35.8270	1.63019
$484$	−2.74523	−0.124783
$485$	−1.49473	−0.0678721
$486$	−21.6401	−0.981615
$487$	−17.1209	−0.775822	−0.387911	−	0.921697i	$-0.626803\pi$
$487$	−17.1209	−0.775822	−0.387911	+	0.921697i	$0.626803\pi$
$488$	−32.3998	−1.46667
$489$	4.58338	0.207267
$490$	34.8352	1.57370
$491$	−5.11790	−0.230968	−0.115484	−	0.993309i	$-0.536842\pi$
$491$	−5.11790	−0.230968	−0.115484	+	0.993309i	$0.536842\pi$
$492$	0.568076	0.0256108
$493$	−29.8702	−1.34529
$494$	9.81662	0.441671
$495$	−28.6275	−1.28671
$496$	−16.0171	−0.719189
$497$	−45.8210	−2.05535
$498$	−16.7399	−0.750132
$499$	29.2980	1.31156	0.655780	−	0.754952i	$-0.272340\pi$
$499$	29.2980	1.31156	0.655780	+	0.754952i	$0.272340\pi$
$500$	1.25247	0.0560122
$501$	−47.7931	−2.13524
$502$	37.4305	1.67060
$503$	12.8905	0.574761	0.287380	−	0.957817i	$-0.407216\pi$
$503$	12.8905	0.574761	0.287380	+	0.957817i	$0.407216\pi$
$504$	−20.0074	−0.891201
$505$	15.4884	0.689223
$506$	−27.2412	−1.21102
$507$	21.6233	0.960326
$508$	1.41109	0.0626068
$509$	−11.2706	−0.499559	−0.249780	−	0.968303i	$-0.580358\pi$
$509$	−11.2706	−0.499559	−0.249780	+	0.968303i	$0.580358\pi$
$510$	59.4518	2.63257
$511$	0.622733	0.0275481
$512$	25.2122	1.11423
$513$	−11.3744	−0.502193
$514$	−1.63662	−0.0721884
$515$	−37.4398	−1.64980
$516$	−4.59338	−0.202212
$517$	34.3843	1.51222
$518$	−51.3888	−2.25789
$519$	12.2322	0.536935
$520$	−17.7520	−0.778475
$521$	41.5318	1.81954	0.909771	−	0.415110i	$-0.136257\pi$
$521$	41.5318	1.81954	0.909771	+	0.415110i	$0.136257\pi$
$522$	−11.6059	−0.507977
$523$	−8.02470	−0.350896	−0.175448	−	0.984489i	$-0.556137\pi$
$523$	−8.02470	−0.350896	−0.175448	+	0.984489i	$0.556137\pi$
$524$	1.55711	0.0680228
$525$	55.1028	2.40488
$526$	19.9690	0.870691
$527$	−27.6790	−1.20572
$528$	36.3327	1.58118
$529$	−4.64439	−0.201930
$530$	27.5193	1.19536
$531$	2.39623	0.103987
$532$	−3.72748	−0.161607
$533$	1.97686	0.0856273
$534$	13.7402	0.594595
$535$	−2.16167	−0.0934573
$536$	29.2506	1.26344
$537$	51.9799	2.24310
$538$	1.25068	0.0539208
$539$	36.7891	1.58462
$540$	2.13365	0.0918175
$541$	9.87706	0.424648	0.212324	−	0.977199i	$-0.431897\pi$
$541$	9.87706	0.424648	0.212324	+	0.977199i	$0.431897\pi$
$542$	−6.79864	−0.292027
$543$	−14.3504	−0.615834
$544$	7.84110	0.336184
$545$	−18.9612	−0.812208
$546$	−19.5412	−0.836285
$547$	19.3803	0.828641	0.414320	−	0.910131i	$-0.364019\pi$
$547$	19.3803	0.828641	0.414320	+	0.910131i	$0.364019\pi$
$548$	2.30109	0.0982978
$549$	−19.2026	−0.819549
$550$	−41.8976	−1.78652
$551$	−20.8447	−0.888015
$552$	−27.7351	−1.18049
$553$	−55.8794	−2.37623
$554$	−3.18084	−0.135141
$555$	−74.8624	−3.17773
$556$	−0.760696	−0.0322607
$557$	−18.9414	−0.802571	−0.401285	−	0.915953i	$-0.631436\pi$
$557$	−18.9414	−0.802571	−0.401285	+	0.915953i	$0.631436\pi$
$558$	−10.7546	−0.455277
$559$	−15.9846	−0.676077
$560$	−45.4592	−1.92100
$561$	62.7863	2.65084
$562$	−9.96154	−0.420202
$563$	12.0839	0.509276	0.254638	−	0.967036i	$-0.418044\pi$
$563$	12.0839	0.509276	0.254638	+	0.967036i	$0.418044\pi$
$564$	3.63138	0.152909
$565$	−16.2845	−0.685093
$566$	23.8588	1.00286
$567$	42.8684	1.80030
$568$	35.4719	1.48837
$569$	8.80054	0.368938	0.184469	−	0.982838i	$-0.440943\pi$
$569$	8.80054	0.368938	0.184469	+	0.982838i	$0.440943\pi$
$570$	41.4881	1.73774
$571$	−35.4541	−1.48371	−0.741854	−	0.670562i	$-0.766053\pi$
$571$	−35.4541	−1.48371	−0.741854	+	0.670562i	$0.766053\pi$
$572$	−1.94471	−0.0813124
$573$	−41.8014	−1.74628
$574$	5.73511	0.239379
$575$	28.2313	1.17733
$576$	15.3001	0.637503
$577$	−22.5404	−0.938368	−0.469184	−	0.883100i	$-0.655452\pi$
$577$	−22.5404	−0.938368	−0.469184	+	0.883100i	$0.655452\pi$
$578$	−25.5833	−1.06413
$579$	−13.8975	−0.577559
$580$	3.91011	0.162358
$581$	22.1195	0.917673
$582$	1.27376	0.0527989
$583$	29.0628	1.20366
$584$	−0.482082	−0.0199487
$585$	−10.5212	−0.434997
$586$	−16.8142	−0.694586
$587$	29.8831	1.23341	0.616704	−	0.787195i	$-0.288467\pi$
$587$	29.8831	1.23341	0.616704	+	0.787195i	$0.288467\pi$
$588$	3.88535	0.160229
$589$	−19.3156	−0.795887
$590$	6.16806	0.253935
$591$	26.5599	1.09253
$592$	35.1154	1.44323
$593$	30.9659	1.27162	0.635808	−	0.771847i	$-0.280667\pi$
$593$	30.9659	1.27162	0.635808	+	0.771847i	$0.280667\pi$
$594$	−17.2161	−0.706384
$595$	−78.5576	−3.22055
$596$	−2.18212	−0.0893830
$597$	2.46470	0.100873
$598$	−10.0117	−0.409410
$599$	−22.4899	−0.918912	−0.459456	−	0.888201i	$-0.651956\pi$
$599$	−22.4899	−0.918912	−0.459456	+	0.888201i	$0.651956\pi$
$600$	−42.6573	−1.74148
$601$	−22.2188	−0.906322	−0.453161	−	0.891429i	$-0.649704\pi$
$601$	−22.2188	−0.906322	−0.453161	+	0.891429i	$0.649704\pi$
$602$	−46.3732	−1.89003
$603$	17.3362	0.705984
$604$	0.543944	0.0221328
$605$	−40.3747	−1.64147
$606$	−13.1986	−0.536158
$607$	17.3047	0.702378	0.351189	−	0.936305i	$-0.385778\pi$
$607$	17.3047	0.702378	0.351189	+	0.936305i	$0.385778\pi$
$608$	5.47186	0.221913
$609$	41.4939	1.68142
$610$	−49.4290	−2.00132
$611$	12.6369	0.511235
$612$	2.45073	0.0990648
$613$	13.8909	0.561050	0.280525	−	0.959847i	$-0.409491\pi$
$613$	13.8909	0.561050	0.280525	+	0.959847i	$0.409491\pi$
$614$	−6.55732	−0.264632
$615$	8.35482	0.336899
$616$	−54.3891	−2.19140
$617$	47.6668	1.91899	0.959496	−	0.281722i	$-0.0909056\pi$
$617$	47.6668	1.91899	0.959496	+	0.281722i	$0.0909056\pi$
$618$	31.9049	1.28340
$619$	−36.3518	−1.46110	−0.730551	−	0.682858i	$-0.760737\pi$
$619$	−36.3518	−1.46110	−0.730551	+	0.682858i	$0.760737\pi$
$620$	3.62328	0.145514
$621$	11.6005	0.465511
$622$	−44.1843	−1.77163
$623$	−18.1558	−0.727396
$624$	13.3530	0.534549
$625$	−14.5267	−0.581067
$626$	−24.2392	−0.968792
$627$	43.8150	1.74980
$628$	−4.59857	−0.183503
$629$	60.6826	2.41957
$630$	−30.5232	−1.21607
$631$	−42.0906	−1.67560	−0.837801	−	0.545976i	$-0.816159\pi$
$631$	−42.0906	−1.67560	−0.837801	+	0.545976i	$0.816159\pi$
$632$	43.2585	1.72073
$633$	−60.5053	−2.40487
$634$	−20.9365	−0.831493
$635$	20.7532	0.823565
$636$	3.06937	0.121708
$637$	13.5207	0.535711
$638$	−31.5501	−1.24908
$639$	21.0234	0.831672
$640$	30.5149	1.20621
$641$	13.6204	0.537972	0.268986	−	0.963144i	$-0.413311\pi$
$641$	13.6204	0.537972	0.268986	+	0.963144i	$0.413311\pi$
$642$	1.84210	0.0727020
$643$	−15.5929	−0.614925	−0.307462	−	0.951560i	$-0.599480\pi$
$643$	−15.5929	−0.614925	−0.307462	+	0.951560i	$0.599480\pi$
$644$	3.80156	0.149803
$645$	−67.5558	−2.66001
$646$	−33.6297	−1.32314
$647$	30.8612	1.21328	0.606639	−	0.794977i	$-0.292517\pi$
$647$	30.8612	1.21328	0.606639	+	0.794977i	$0.292517\pi$
$648$	−33.1861	−1.30367
$649$	6.51402	0.255697
$650$	−15.3982	−0.603969
$651$	38.4501	1.50698
$652$	0.486336	0.0190464
$653$	41.4375	1.62157	0.810787	−	0.585342i	$-0.199040\pi$
$653$	41.4375	1.62157	0.810787	+	0.585342i	$0.199040\pi$
$654$	16.1581	0.631830
$655$	22.9008	0.894809
$656$	−3.91896	−0.153009
$657$	−0.285719	−0.0111470
$658$	36.6612	1.42920
$659$	−5.89065	−0.229467	−0.114733	−	0.993396i	$-0.536601\pi$
$659$	−5.89065	−0.229467	−0.114733	+	0.993396i	$0.536601\pi$
$660$	−8.21894	−0.319922
$661$	−12.1895	−0.474118	−0.237059	−	0.971495i	$-0.576184\pi$
$661$	−12.1895	−0.474118	−0.237059	+	0.971495i	$0.576184\pi$
$662$	9.78556	0.380327
$663$	23.0753	0.896169
$664$	−17.1236	−0.664525
$665$	−54.8209	−2.12586
$666$	23.5780	0.913627
$667$	21.2590	0.823151
$668$	−5.07127	−0.196213
$669$	19.8627	0.767935
$670$	44.6246	1.72400
$671$	−52.2014	−2.01521
$672$	−10.8924	−0.420184
$673$	−13.4033	−0.516658	−0.258329	−	0.966057i	$-0.583172\pi$
$673$	−13.4033	−0.516658	−0.258329	+	0.966057i	$0.583172\pi$
$674$	27.9432	1.07633
$675$	17.8418	0.686731
$676$	2.29443	0.0882471
$677$	−9.52226	−0.365970	−0.182985	−	0.983116i	$-0.558576\pi$
$677$	−9.52226	−0.365970	−0.182985	+	0.983116i	$0.558576\pi$
$678$	13.8771	0.532945
$679$	−1.68310	−0.0645914
$680$	60.8146	2.33213
$681$	−52.6297	−2.01677
$682$	−29.2357	−1.11949
$683$	−4.11578	−0.157486	−0.0787429	−	0.996895i	$-0.525091\pi$
$683$	−4.11578	−0.157486	−0.0787429	+	0.996895i	$0.525091\pi$
$684$	1.71023	0.0653921
$685$	33.8427	1.29306
$686$	3.54059	0.135180
$687$	64.6918	2.46815
$688$	31.6881	1.20810
$689$	10.6812	0.406920
$690$	−42.3126	−1.61081
$691$	39.0627	1.48601	0.743007	−	0.669283i	$-0.233399\pi$
$691$	39.0627	1.48601	0.743007	+	0.669283i	$0.233399\pi$
$692$	1.29795	0.0493405
$693$	−32.2352	−1.22451
$694$	1.06274	0.0403411
$695$	−11.1877	−0.424375
$696$	−32.1221	−1.21759
$697$	−6.77232	−0.256520
$698$	1.67085	0.0632427
$699$	11.6968	0.442413
$700$	5.84689	0.220992
$701$	4.81641	0.181913	0.0909566	−	0.995855i	$-0.471008\pi$
$701$	4.81641	0.181913	0.0909566	+	0.995855i	$0.471008\pi$
$702$	−6.32726	−0.238807
$703$	42.3470	1.59715
$704$	41.5924	1.56757
$705$	53.4075	2.01144
$706$	−40.9592	−1.54152
$707$	17.4402	0.655908
$708$	0.687956	0.0258550
$709$	39.1628	1.47079	0.735394	−	0.677640i	$-0.236997\pi$
$709$	39.1628	1.47079	0.735394	+	0.677640i	$0.236997\pi$
$710$	54.1157	2.03093
$711$	25.6383	0.961511
$712$	14.0551	0.526738
$713$	19.6995	0.737753
$714$	66.9441	2.50532
$715$	−28.6013	−1.06963
$716$	5.51552	0.206125
$717$	−4.67119	−0.174449
$718$	19.0374	0.710470
$719$	−32.1852	−1.20030	−0.600152	−	0.799886i	$-0.704893\pi$
$719$	−32.1852	−1.20030	−0.600152	+	0.799886i	$0.704893\pi$
$720$	20.8573	0.777307
$721$	−42.1581	−1.57005
$722$	1.79904	0.0669533
$723$	−2.18147	−0.0811296
$724$	−1.52270	−0.0565908
$725$	32.6968	1.21433
$726$	34.4059	1.27692
$727$	−1.69429	−0.0628377	−0.0314188	−	0.999506i	$-0.510003\pi$
$727$	−1.69429	−0.0628377	−0.0314188	+	0.999506i	$0.510003\pi$
$728$	−19.9891	−0.740846
$729$	−1.94876	−0.0721763
$730$	−0.735462	−0.0272207
$731$	54.7600	2.02537
$732$	−5.51307	−0.203769
$733$	18.2300	0.673340	0.336670	−	0.941623i	$-0.390699\pi$
$733$	18.2300	0.673340	0.336670	+	0.941623i	$0.390699\pi$
$734$	−4.48226	−0.165443
$735$	57.1428	2.10774
$736$	−5.58061	−0.205704
$737$	47.1275	1.73596
$738$	−2.63135	−0.0968614
$739$	−12.4675	−0.458623	−0.229312	−	0.973353i	$-0.573648\pi$
$739$	−12.4675	−0.458623	−0.229312	+	0.973353i	$0.573648\pi$
$740$	−7.94356	−0.292011
$741$	16.1029	0.591556
$742$	30.9873	1.13758
$743$	−15.6839	−0.575385	−0.287693	−	0.957723i	$-0.592888\pi$
$743$	−15.6839	−0.575385	−0.287693	+	0.957723i	$0.592888\pi$
$744$	−29.7658	−1.09127
$745$	−32.0929	−1.17579
$746$	−7.61194	−0.278693
$747$	−10.1488	−0.371324
$748$	6.66218	0.243593
$749$	−2.43409	−0.0889399
$750$	−15.6972	−0.573181
$751$	−3.58156	−0.130693	−0.0653465	−	0.997863i	$-0.520815\pi$
$751$	−3.58156	−0.130693	−0.0653465	+	0.997863i	$0.520815\pi$
$752$	−25.0516	−0.913539
$753$	61.3999	2.23754
$754$	−11.5953	−0.422276
$755$	7.99990	0.291146
$756$	2.40253	0.0873793
$757$	−15.7026	−0.570720	−0.285360	−	0.958420i	$-0.592113\pi$
$757$	−15.7026	−0.570720	−0.285360	+	0.958420i	$0.592113\pi$
$758$	−1.28164	−0.0465512
$759$	−44.6858	−1.62199
$760$	42.4391	1.53943
$761$	−36.1137	−1.30912	−0.654559	−	0.756011i	$-0.727146\pi$
$761$	−36.1137	−1.30912	−0.654559	+	0.756011i	$0.727146\pi$
$762$	−17.6851	−0.640665
$763$	−21.3507	−0.772948
$764$	−4.43549	−0.160470
$765$	36.0434	1.30315
$766$	−23.3261	−0.842807
$767$	2.39403	0.0864436
$768$	11.9502	0.431216
$769$	−50.2736	−1.81291	−0.906456	−	0.422300i	$-0.861223\pi$
$769$	−50.2736	−1.81291	−0.906456	+	0.422300i	$0.861223\pi$
$770$	−82.9757	−2.99024
$771$	−2.68467	−0.0966862
$772$	−1.47464	−0.0530736
$773$	−27.4904	−0.988762	−0.494381	−	0.869245i	$-0.664605\pi$
$773$	−27.4904	−0.988762	−0.494381	+	0.869245i	$0.664605\pi$
$774$	21.2767	0.764776
$775$	30.2983	1.08835
$776$	1.30295	0.0467733
$777$	−84.2968	−3.02413
$778$	22.3942	0.802870
$779$	−4.72602	−0.169327
$780$	−3.02063	−0.108156
$781$	57.1509	2.04502
$782$	34.2981	1.22650
$783$	13.4354	0.480141
$784$	−26.8037	−0.957275
$785$	−67.6322	−2.41390
$786$	−19.5153	−0.696087
$787$	43.4981	1.55054	0.775271	−	0.631629i	$-0.217614\pi$
$787$	43.4981	1.55054	0.775271	+	0.631629i	$0.217614\pi$
$788$	2.81824	0.100396
$789$	32.7567	1.16617
$790$	65.9949	2.34799
$791$	−18.3367	−0.651977
$792$	24.9545	0.886721
$793$	−19.1851	−0.681282
$794$	3.76307	0.133547
$795$	45.1419	1.60102
$796$	0.261526	0.00926955
$797$	38.2429	1.35463	0.677316	−	0.735692i	$-0.263143\pi$
$797$	38.2429	1.35463	0.677316	+	0.735692i	$0.263143\pi$
$798$	46.7165	1.65375
$799$	−43.2915	−1.53154
$800$	−8.58310	−0.303458
$801$	8.33015	0.294331
$802$	18.0898	0.638772
$803$	−0.776713	−0.0274096
$804$	4.97721	0.175533
$805$	55.9105	1.97058
$806$	−10.7447	−0.378467
$807$	2.05159	0.0722193
$808$	−13.5012	−0.474970
$809$	−28.3274	−0.995939	−0.497969	−	0.867195i	$-0.665921\pi$
$809$	−28.3274	−0.995939	−0.497969	+	0.867195i	$0.665921\pi$
$810$	−50.6286	−1.77891
$811$	−39.3902	−1.38318	−0.691589	−	0.722292i	$-0.743089\pi$
$811$	−39.3902	−1.38318	−0.691589	+	0.722292i	$0.743089\pi$
$812$	4.40287	0.154510
$813$	−11.1523	−0.391129
$814$	64.0954	2.24654
$815$	7.15266	0.250547
$816$	−45.7447	−1.60139
$817$	38.2139	1.33694
$818$	−32.7704	−1.14579
$819$	−11.8471	−0.413971
$820$	0.886519	0.0309586
$821$	39.6673	1.38440	0.692199	−	0.721707i	$-0.256642\pi$
$821$	39.6673	1.38440	0.692199	+	0.721707i	$0.256642\pi$
$822$	−28.8396	−1.00590
$823$	−9.49313	−0.330910	−0.165455	−	0.986217i	$-0.552909\pi$
$823$	−9.49313	−0.330910	−0.165455	+	0.986217i	$0.552909\pi$
$824$	32.6363	1.13694
$825$	−68.7277	−2.39279
$826$	6.94538	0.241661
$827$	−8.26358	−0.287353	−0.143676	−	0.989625i	$-0.545892\pi$
$827$	−8.26358	−0.287353	−0.143676	+	0.989625i	$0.545892\pi$
$828$	−1.74421	−0.0606157
$829$	−32.7576	−1.13772	−0.568860	−	0.822435i	$-0.692615\pi$
$829$	−32.7576	−1.13772	−0.568860	+	0.822435i	$0.692615\pi$
$830$	−26.1237	−0.906767
$831$	−5.21776	−0.181002
$832$	15.2861	0.529949
$833$	−46.3193	−1.60487
$834$	9.53380	0.330128
$835$	−74.5843	−2.58110
$836$	4.64916	0.160795
$837$	12.4498	0.430329
$838$	10.4078	0.359531
$839$	28.8263	0.995195	0.497597	−	0.867408i	$-0.334216\pi$
$839$	28.8263	0.995195	0.497597	+	0.867408i	$0.334216\pi$
$840$	−84.4801	−2.91484
$841$	−4.37839	−0.150979
$842$	−28.4169	−0.979311
$843$	−16.3406	−0.562801
$844$	−6.42015	−0.220991
$845$	33.7446	1.16085
$846$	−16.8207	−0.578308
$847$	−45.4629	−1.56212
$848$	−21.1745	−0.727135
$849$	39.1373	1.34319
$850$	52.7512	1.80935
$851$	−43.1886	−1.48049
$852$	6.03581	0.206783
$853$	1.74141	0.0596248	0.0298124	−	0.999556i	$-0.490509\pi$
$853$	1.74141	0.0596248	0.0298124	+	0.999556i	$0.490509\pi$
$854$	−55.6582	−1.90458
$855$	25.1527	0.860203
$856$	1.88433	0.0644051
$857$	−23.6164	−0.806720	−0.403360	−	0.915041i	$-0.632158\pi$
$857$	−23.6164	−0.806720	−0.403360	+	0.915041i	$0.632158\pi$
$858$	24.3730	0.832081
$859$	18.0458	0.615714	0.307857	−	0.951433i	$-0.400388\pi$
$859$	18.0458	0.615714	0.307857	+	0.951433i	$0.400388\pi$
$860$	−7.16827	−0.244436
$861$	9.40771	0.320614
$862$	−45.1140	−1.53659
$863$	8.06392	0.274499	0.137249	−	0.990537i	$-0.456174\pi$
$863$	8.06392	0.274499	0.137249	+	0.990537i	$0.456174\pi$
$864$	−3.52687	−0.119986
$865$	19.0892	0.649052
$866$	−45.9007	−1.55977
$867$	−41.9662	−1.42525
$868$	4.07990	0.138481
$869$	69.6964	2.36429
$870$	−49.0053	−1.66144
$871$	17.3203	0.586877
$872$	16.5285	0.559724
$873$	0.772231	0.0261361
$874$	23.9347	0.809604
$875$	20.7418	0.701200
$876$	−0.0820299	−0.00277153
$877$	−14.4702	−0.488625	−0.244312	−	0.969697i	$-0.578562\pi$
$877$	−14.4702	−0.488625	−0.244312	+	0.969697i	$0.578562\pi$
$878$	−3.03914	−0.102566
$879$	−27.5815	−0.930301
$880$	56.6996	1.91134
$881$	10.0284	0.337867	0.168933	−	0.985627i	$-0.445968\pi$
$881$	10.0284	0.337867	0.168933	+	0.985627i	$0.445968\pi$
$882$	−17.9971	−0.605995
$883$	0.730440	0.0245813	0.0122906	−	0.999924i	$-0.496088\pi$
$883$	0.730440	0.0245813	0.0122906	+	0.999924i	$0.496088\pi$
$884$	2.44849	0.0823515
$885$	10.1179	0.340110
$886$	−24.4343	−0.820887
$887$	−29.6147	−0.994366	−0.497183	−	0.867646i	$-0.665632\pi$
$887$	−29.6147	−0.994366	−0.497183	+	0.867646i	$0.665632\pi$
$888$	65.2575	2.18990
$889$	23.3685	0.783756
$890$	21.4424	0.718752
$891$	−53.4682	−1.79125
$892$	2.10760	0.0705677
$893$	−30.2107	−1.01096
$894$	27.3485	0.914669
$895$	81.1180	2.71148
$896$	34.3604	1.14790
$897$	−16.4230	−0.548346
$898$	−34.5947	−1.15444
$899$	22.8155	0.760939
$900$	−2.68264	−0.0894213
$901$	−36.5915	−1.21904
$902$	−7.15320	−0.238175
$903$	−76.0694	−2.53143
$904$	14.1952	0.472124
$905$	−22.3947	−0.744426
$906$	−6.81724	−0.226488
$907$	−3.96710	−0.131725	−0.0658627	−	0.997829i	$-0.520980\pi$
$907$	−3.96710	−0.131725	−0.0658627	+	0.997829i	$0.520980\pi$
$908$	−5.58447	−0.185327
$909$	−8.00184	−0.265404
$910$	−30.4953	−1.01091
$911$	25.8759	0.857307	0.428653	−	0.903469i	$-0.358988\pi$
$911$	25.8759	0.857307	0.428653	+	0.903469i	$0.358988\pi$
$912$	−31.9227	−1.05706
$913$	−27.5889	−0.913060
$914$	−12.1049	−0.400394
$915$	−81.0820	−2.68049
$916$	6.86437	0.226805
$917$	25.7868	0.851556
$918$	21.6759	0.715411
$919$	16.5327	0.545364	0.272682	−	0.962104i	$-0.412089\pi$
$919$	16.5327	0.545364	0.272682	+	0.962104i	$0.412089\pi$
$920$	−43.2825	−1.42698
$921$	−10.7565	−0.354437
$922$	−16.4669	−0.542309
$923$	21.0041	0.691360
$924$	−9.25471	−0.304458
$925$	−66.4250	−2.18404
$926$	−33.7383	−1.10871
$927$	19.3428	0.635300
$928$	−6.46332	−0.212169
$929$	−1.50189	−0.0492755	−0.0246378	−	0.999696i	$-0.507843\pi$
$929$	−1.50189	−0.0492755	−0.0246378	+	0.999696i	$0.507843\pi$
$930$	−45.4105	−1.48907
$931$	−32.3236	−1.05936
$932$	1.24113	0.0406546
$933$	−72.4787	−2.37285
$934$	28.1964	0.922615
$935$	97.9822	3.20436
$936$	9.17131	0.299774
$937$	−8.04782	−0.262911	−0.131455	−	0.991322i	$-0.541965\pi$
$937$	−8.04782	−0.262911	−0.131455	+	0.991322i	$0.541965\pi$
$938$	50.2483	1.64067
$939$	−39.7613	−1.29756
$940$	5.66701	0.184837
$941$	−2.66537	−0.0868887	−0.0434443	−	0.999056i	$-0.513833\pi$
$941$	−2.66537	−0.0868887	−0.0434443	+	0.999056i	$0.513833\pi$
$942$	57.6338	1.87781
$943$	4.81995	0.156959
$944$	−4.74597	−0.154468
$945$	35.3346	1.14943
$946$	57.8397	1.88053
$947$	39.0257	1.26816	0.634082	−	0.773266i	$-0.281378\pi$
$947$	39.0257	1.26816	0.634082	+	0.773266i	$0.281378\pi$
$948$	7.36075	0.239066
$949$	−0.285458	−0.00926636
$950$	36.8121	1.19434
$951$	−34.3436	−1.11367
$952$	68.4786	2.21941
$953$	−40.4838	−1.31140	−0.655700	−	0.755022i	$-0.727626\pi$
$953$	−40.4838	−1.31140	−0.655700	+	0.755022i	$0.727626\pi$
$954$	−14.2174	−0.460307
$955$	−65.2338	−2.11092
$956$	−0.495655	−0.0160306
$957$	−51.7539	−1.67297
$958$	35.3564	1.14231
$959$	38.1076	1.23056
$960$	64.6037	2.08507
$961$	−9.85816	−0.318005
$962$	23.5564	0.759489
$963$	1.11680	0.0359884
$964$	−0.231473	−0.00745524
$965$	−21.6879	−0.698159
$966$	−47.6449	−1.53295
$967$	26.3391	0.847009	0.423504	−	0.905894i	$-0.360800\pi$
$967$	26.3391	0.847009	0.423504	+	0.905894i	$0.360800\pi$
$968$	35.1946	1.13120
$969$	−55.1653	−1.77217
$970$	1.98778	0.0638238
$971$	−9.17879	−0.294561	−0.147281	−	0.989095i	$-0.547052\pi$
$971$	−9.17879	−0.294561	−0.147281	+	0.989095i	$0.547052\pi$
$972$	−3.76663	−0.120815
$973$	−12.5976	−0.403862
$974$	22.7684	0.729546
$975$	−25.2589	−0.808931
$976$	38.0328	1.21740
$977$	−27.6516	−0.884653	−0.442326	−	0.896854i	$-0.645847\pi$
$977$	−27.6516	−0.884653	−0.442326	+	0.896854i	$0.645847\pi$
$978$	−6.09525	−0.194905
$979$	22.6451	0.723740
$980$	6.06335	0.193687
$981$	9.79604	0.312763
$982$	6.80610	0.217191
$983$	−27.0845	−0.863861	−0.431930	−	0.901907i	$-0.642167\pi$
$983$	−27.0845	−0.863861	−0.431930	+	0.901907i	$0.642167\pi$
$984$	−7.28289	−0.232170
$985$	41.4485	1.32066
$986$	39.7232	1.26504
$987$	60.1381	1.91422
$988$	1.70866	0.0543598
$989$	−38.9734	−1.23928
$990$	38.0705	1.20996
$991$	−41.0027	−1.30249	−0.651246	−	0.758867i	$-0.725753\pi$
$991$	−41.0027	−1.30249	−0.651246	+	0.758867i	$0.725753\pi$
$992$	−5.98920	−0.190157
$993$	16.0520	0.509394
$994$	60.9355	1.93276
$995$	3.84632	0.121937
$996$	−2.91371	−0.0923245
$997$	−37.9223	−1.20101	−0.600505	−	0.799621i	$-0.705034\pi$
$997$	−37.9223	−1.20101	−0.600505	+	0.799621i	$0.705034\pi$
$998$	−38.9623	−1.23333
$999$	−27.2946	−0.863562

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	241.2.a.b.1.3	✓	12
3.2	odd	2		2169.2.a.h.1.10		12
4.3	odd	2		3856.2.a.n.1.10		12
5.4	even	2		6025.2.a.h.1.10		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
241.2.a.b.1.3	✓	12	1.1	even	1	trivial
2169.2.a.h.1.10		12	3.2	odd	2
3856.2.a.n.1.10		12	4.3	odd	2
6025.2.a.h.1.10		12	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:	\( N \)	\(=\)	\( 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	241.a (trivial)

\(f(q)\)	\(=\)	\(q-1.32986 q^{2} -2.18147 q^{3} -0.231473 q^{4} -3.40432 q^{5} +2.90104 q^{6} -3.83334 q^{7} +2.96755 q^{8} +1.75880 q^{9} +O(q^{10})\)	\(q-1.32986 q^{2} -2.18147 q^{3} -0.231473 q^{4} -3.40432 q^{5} +2.90104 q^{6} -3.83334 q^{7} +2.96755 q^{8} +1.75880 q^{9} +4.52727 q^{10} +4.78120 q^{11} +0.504950 q^{12} +1.75719 q^{13} +5.09781 q^{14} +7.42642 q^{15} -3.48347 q^{16} -6.01977 q^{17} -2.33895 q^{18} -4.20086 q^{19} +0.788008 q^{20} +8.36231 q^{21} -6.35832 q^{22} +4.28435 q^{23} -6.47360 q^{24} +6.58942 q^{25} -2.33681 q^{26} +2.70764 q^{27} +0.887315 q^{28} +4.96202 q^{29} -9.87609 q^{30} +4.59803 q^{31} -1.30256 q^{32} -10.4300 q^{33} +8.00545 q^{34} +13.0499 q^{35} -0.407113 q^{36} -10.0806 q^{37} +5.58655 q^{38} -3.83325 q^{39} -10.1025 q^{40} +1.12501 q^{41} -11.1207 q^{42} -9.09669 q^{43} -1.10672 q^{44} -5.98751 q^{45} -5.69758 q^{46} +7.19156 q^{47} +7.59908 q^{48} +7.69453 q^{49} -8.76300 q^{50} +13.1319 q^{51} -0.406741 q^{52} +6.07855 q^{53} -3.60079 q^{54} -16.2767 q^{55} -11.3756 q^{56} +9.16403 q^{57} -6.59879 q^{58} +1.36242 q^{59} -1.71901 q^{60} -10.9181 q^{61} -6.11473 q^{62} -6.74207 q^{63} +8.69917 q^{64} -5.98204 q^{65} +13.8705 q^{66} +9.85684 q^{67} +1.39341 q^{68} -9.34616 q^{69} -17.3546 q^{70} +11.9533 q^{71} +5.21931 q^{72} -0.162452 q^{73} +13.4057 q^{74} -14.3746 q^{75} +0.972384 q^{76} -18.3280 q^{77} +5.09768 q^{78} +14.5772 q^{79} +11.8589 q^{80} -11.1830 q^{81} -1.49611 q^{82} -5.77030 q^{83} -1.93565 q^{84} +20.4932 q^{85} +12.0973 q^{86} -10.8245 q^{87} +14.1884 q^{88} +4.73628 q^{89} +7.96255 q^{90} -6.73591 q^{91} -0.991709 q^{92} -10.0304 q^{93} -9.56377 q^{94} +14.3011 q^{95} +2.84149 q^{96} +0.439068 q^{97} -10.2326 q^{98} +8.40915 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} + q^{3} + 13 q^{4} + 6 q^{5} - q^{6} + 3 q^{7} + 9 q^{8} + 15 q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 + q^3 + 13 * q^4 + 6 * q^5 - q^6 + 3 * q^7 + 9 * q^8 + 15 * q^9	\( 12 q + 3 q^{2} + q^{3} + 13 q^{4} + 6 q^{5} - q^{6} + 3 q^{7} + 9 q^{8} + 15 q^{9} - 7 q^{10} + 22 q^{11} - 7 q^{12} - 5 q^{13} + 6 q^{14} + 13 q^{15} + 15 q^{16} - 4 q^{17} - q^{18} - 6 q^{19} + 10 q^{20} - 14 q^{21} - 12 q^{22} + 32 q^{23} - 15 q^{24} + 4 q^{25} + 8 q^{26} - 5 q^{27} - 11 q^{28} + 6 q^{29} - 19 q^{30} + 8 q^{31} + q^{32} - 24 q^{33} - 19 q^{34} + 15 q^{35} - 8 q^{36} - 8 q^{37} - 10 q^{38} + 31 q^{39} - 52 q^{40} - q^{41} - 49 q^{42} - 2 q^{43} + 42 q^{44} - 15 q^{45} - 25 q^{46} + 34 q^{47} - 49 q^{48} - 9 q^{49} - 27 q^{50} - 3 q^{51} - 41 q^{52} + 5 q^{53} - 40 q^{54} - 3 q^{55} + q^{56} - 22 q^{57} - 33 q^{58} + 26 q^{59} - 57 q^{60} - 26 q^{61} - 17 q^{62} - 4 q^{63} + 13 q^{64} - 25 q^{65} - 2 q^{66} + 6 q^{67} - 35 q^{68} - 2 q^{69} - 4 q^{70} + 94 q^{71} + 17 q^{72} - 22 q^{73} + 26 q^{74} - 20 q^{76} - 7 q^{77} + 54 q^{78} + 9 q^{79} + 19 q^{80} + 4 q^{81} + 15 q^{82} - 8 q^{83} + 2 q^{84} + 4 q^{85} + 9 q^{86} + 4 q^{87} + 6 q^{88} - 3 q^{89} + 11 q^{90} - 20 q^{91} + 36 q^{92} + 12 q^{93} + 48 q^{94} + 33 q^{95} - 23 q^{96} - 29 q^{97} + 28 q^{98} + 36 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + q^3 + 13 * q^4 + 6 * q^5 - q^6 + 3 * q^7 + 9 * q^8 + 15 * q^9 - 7 * q^10 + 22 * q^11 - 7 * q^12 - 5 * q^13 + 6 * q^14 + 13 * q^15 + 15 * q^16 - 4 * q^17 - q^18 - 6 * q^19 + 10 * q^20 - 14 * q^21 - 12 * q^22 + 32 * q^23 - 15 * q^24 + 4 * q^25 + 8 * q^26 - 5 * q^27 - 11 * q^28 + 6 * q^29 - 19 * q^30 + 8 * q^31 + q^32 - 24 * q^33 - 19 * q^34 + 15 * q^35 - 8 * q^36 - 8 * q^37 - 10 * q^38 + 31 * q^39 - 52 * q^40 - q^41 - 49 * q^42 - 2 * q^43 + 42 * q^44 - 15 * q^45 - 25 * q^46 + 34 * q^47 - 49 * q^48 - 9 * q^49 - 27 * q^50 - 3 * q^51 - 41 * q^52 + 5 * q^53 - 40 * q^54 - 3 * q^55 + q^56 - 22 * q^57 - 33 * q^58 + 26 * q^59 - 57 * q^60 - 26 * q^61 - 17 * q^62 - 4 * q^63 + 13 * q^64 - 25 * q^65 - 2 * q^66 + 6 * q^67 - 35 * q^68 - 2 * q^69 - 4 * q^70 + 94 * q^71 + 17 * q^72 - 22 * q^73 + 26 * q^74 - 20 * q^76 - 7 * q^77 + 54 * q^78 + 9 * q^79 + 19 * q^80 + 4 * q^81 + 15 * q^82 - 8 * q^83 + 2 * q^84 + 4 * q^85 + 9 * q^86 + 4 * q^87 + 6 * q^88 - 3 * q^89 + 11 * q^90 - 20 * q^91 + 36 * q^92 + 12 * q^93 + 48 * q^94 + 33 * q^95 - 23 * q^96 - 29 * q^97 + 28 * q^98 + 36 * q^99

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