LMFDB - Embedded newform 287.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(1,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, 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("287.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.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:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.24698$ of defining polynomial
Character	$\chi$	$=$	287.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.246980 q^{2} +3.24698 q^{3} -1.93900 q^{4} +0.890084 q^{5} -0.801938 q^{6} -1.00000 q^{7} +0.972853 q^{8} +7.54288 q^{9} +O(q^{10})$	\(q-0.246980 q^{2} +3.24698 q^{3} -1.93900 q^{4} +0.890084 q^{5} -0.801938 q^{6} -1.00000 q^{7} +0.972853 q^{8} +7.54288 q^{9} -0.219833 q^{10} +1.60388 q^{11} -6.29590 q^{12} -2.29590 q^{13} +0.246980 q^{14} +2.89008 q^{15} +3.63773 q^{16} +7.43296 q^{17} -1.86294 q^{18} -0.841166 q^{19} -1.72587 q^{20} -3.24698 q^{21} -0.396125 q^{22} -8.85086 q^{23} +3.15883 q^{24} -4.20775 q^{25} +0.567040 q^{26} +14.7506 q^{27} +1.93900 q^{28} -5.20775 q^{29} -0.713792 q^{30} -8.81163 q^{31} -2.84415 q^{32} +5.20775 q^{33} -1.83579 q^{34} -0.890084 q^{35} -14.6256 q^{36} +5.40581 q^{37} +0.207751 q^{38} -7.45473 q^{39} +0.865921 q^{40} +1.00000 q^{41} +0.801938 q^{42} +0.170915 q^{43} -3.10992 q^{44} +6.71379 q^{45} +2.18598 q^{46} +5.80194 q^{47} +11.8116 q^{48} +1.00000 q^{49} +1.03923 q^{50} +24.1347 q^{51} +4.45175 q^{52} -9.60388 q^{53} -3.64310 q^{54} +1.42758 q^{55} -0.972853 q^{56} -2.73125 q^{57} +1.28621 q^{58} -8.37196 q^{59} -5.60388 q^{60} +8.31767 q^{61} +2.17629 q^{62} -7.54288 q^{63} -6.57301 q^{64} -2.04354 q^{65} -1.28621 q^{66} -5.90217 q^{67} -14.4125 q^{68} -28.7385 q^{69} +0.219833 q^{70} -0.219833 q^{71} +7.33811 q^{72} -6.98792 q^{73} -1.33513 q^{74} -13.6625 q^{75} +1.63102 q^{76} -1.60388 q^{77} +1.84117 q^{78} +12.9879 q^{79} +3.23788 q^{80} +25.2664 q^{81} -0.246980 q^{82} -7.42758 q^{83} +6.29590 q^{84} +6.61596 q^{85} -0.0422126 q^{86} -16.9095 q^{87} +1.56033 q^{88} +6.33944 q^{89} -1.65817 q^{90} +2.29590 q^{91} +17.1618 q^{92} -28.6112 q^{93} -1.43296 q^{94} -0.748709 q^{95} -9.23490 q^{96} +1.86294 q^{97} -0.246980 q^{98} +12.0978 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 4 q^{2} + 5 q^{3} + 4 q^{4} + 2 q^{5} + 2 q^{6} - 3 q^{7} + 9 q^{8} + 4 q^{9}+O(q^{10}) $ 3 * q + 4 * q^2 + 5 * q^3 + 4 * q^4 + 2 * q^5 + 2 * q^6 - 3 * q^7 + 9 * q^8 + 4 * q^9	\( 3 q + 4 q^{2} + 5 q^{3} + 4 q^{4} + 2 q^{5} + 2 q^{6} - 3 q^{7} + 9 q^{8} + 4 q^{9} - 2 q^{10} - 4 q^{11} - 5 q^{12} + 7 q^{13} - 4 q^{14} + 8 q^{15} + 18 q^{16} + 3 q^{17} - 11 q^{18} - 11 q^{19} - 16 q^{20} - 5 q^{21} - 10 q^{22} - 13 q^{23} + q^{24} + 5 q^{25} + 21 q^{26} + 8 q^{27} - 4 q^{28} + 2 q^{29} + 6 q^{30} + 27 q^{32} - 2 q^{33} - 17 q^{34} - 2 q^{35} - 32 q^{36} + 3 q^{37} - 17 q^{38} - 36 q^{40} + 3 q^{41} - 2 q^{42} + 11 q^{43} - 10 q^{44} + 12 q^{45} - 8 q^{46} + 13 q^{47} + 9 q^{48} + 3 q^{49} + 16 q^{50} + 26 q^{51} + 35 q^{52} - 20 q^{53} - 15 q^{54} - 12 q^{55} - 9 q^{56} - 16 q^{57} + 12 q^{58} + 4 q^{59} - 8 q^{60} + 8 q^{61} + 14 q^{62} - 4 q^{63} + 49 q^{64} - 12 q^{66} - 36 q^{67} - 52 q^{68} - 31 q^{69} + 2 q^{70} - 2 q^{71} - 23 q^{72} - 2 q^{73} - 3 q^{74} - q^{75} - 10 q^{76} + 4 q^{77} + 14 q^{78} + 20 q^{79} - 58 q^{80} + 27 q^{81} + 4 q^{82} - 6 q^{83} + 5 q^{84} + 30 q^{85} + 31 q^{86} - 6 q^{87} + 2 q^{88} - q^{89} + 16 q^{90} - 7 q^{91} - q^{92} - 14 q^{93} + 15 q^{94} - 26 q^{95} - 4 q^{96} + 11 q^{97} + 4 q^{98} + 18 q^{99}+O(q^{100}) \) 3 * q + 4 * q^2 + 5 * q^3 + 4 * q^4 + 2 * q^5 + 2 * q^6 - 3 * q^7 + 9 * q^8 + 4 * q^9 - 2 * q^10 - 4 * q^11 - 5 * q^12 + 7 * q^13 - 4 * q^14 + 8 * q^15 + 18 * q^16 + 3 * q^17 - 11 * q^18 - 11 * q^19 - 16 * q^20 - 5 * q^21 - 10 * q^22 - 13 * q^23 + q^24 + 5 * q^25 + 21 * q^26 + 8 * q^27 - 4 * q^28 + 2 * q^29 + 6 * q^30 + 27 * q^32 - 2 * q^33 - 17 * q^34 - 2 * q^35 - 32 * q^36 + 3 * q^37 - 17 * q^38 - 36 * q^40 + 3 * q^41 - 2 * q^42 + 11 * q^43 - 10 * q^44 + 12 * q^45 - 8 * q^46 + 13 * q^47 + 9 * q^48 + 3 * q^49 + 16 * q^50 + 26 * q^51 + 35 * q^52 - 20 * q^53 - 15 * q^54 - 12 * q^55 - 9 * q^56 - 16 * q^57 + 12 * q^58 + 4 * q^59 - 8 * q^60 + 8 * q^61 + 14 * q^62 - 4 * q^63 + 49 * q^64 - 12 * q^66 - 36 * q^67 - 52 * q^68 - 31 * q^69 + 2 * q^70 - 2 * q^71 - 23 * q^72 - 2 * q^73 - 3 * q^74 - q^75 - 10 * q^76 + 4 * q^77 + 14 * q^78 + 20 * q^79 - 58 * q^80 + 27 * q^81 + 4 * q^82 - 6 * q^83 + 5 * q^84 + 30 * q^85 + 31 * q^86 - 6 * q^87 + 2 * q^88 - q^89 + 16 * q^90 - 7 * q^91 - q^92 - 14 * q^93 + 15 * q^94 - 26 * q^95 - 4 * q^96 + 11 * q^97 + 4 * q^98 + 18 * 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 $

$2$	−0.246980	−0.174641	−0.0873205	−	0.996180i	$-0.527830\pi$
$2$	−0.246980	−0.174641	−0.0873205	+	0.996180i	$0.527830\pi$
$3$	3.24698	1.87464	0.937322	−	0.348464i	$-0.113297\pi$
$3$	3.24698	1.87464	0.937322	+	0.348464i	$0.113297\pi$
$4$	−1.93900	−0.969501
$5$	0.890084	0.398058	0.199029	−	0.979994i	$-0.436221\pi$
$5$	0.890084	0.398058	0.199029	+	0.979994i	$0.436221\pi$
$6$	−0.801938	−0.327390
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0.972853	0.343955
$9$	7.54288	2.51429
$10$	−0.219833	−0.0695171
$11$	1.60388	0.483587	0.241793	−	0.970328i	$-0.422264\pi$
$11$	1.60388	0.483587	0.241793	+	0.970328i	$0.422264\pi$
$12$	−6.29590	−1.81747
$13$	−2.29590	−0.636767	−0.318384	−	0.947962i	$-0.603140\pi$
$13$	−2.29590	−0.636767	−0.318384	+	0.947962i	$0.603140\pi$
$14$	0.246980	0.0660081
$15$	2.89008	0.746216
$16$	3.63773	0.909432
$17$	7.43296	1.80276	0.901379	−	0.433031i	$-0.142556\pi$
$17$	7.43296	1.80276	0.901379	+	0.433031i	$0.142556\pi$
$18$	−1.86294	−0.439098
$19$	−0.841166	−0.192977	−0.0964884	−	0.995334i	$-0.530761\pi$
$19$	−0.841166	−0.192977	−0.0964884	+	0.995334i	$0.530761\pi$
$20$	−1.72587	−0.385917
$21$	−3.24698	−0.708549
$22$	−0.396125	−0.0844540
$23$	−8.85086	−1.84553	−0.922765	−	0.385362i	$-0.874077\pi$
$23$	−8.85086	−1.84553	−0.922765	+	0.385362i	$0.874077\pi$
$24$	3.15883	0.644794
$25$	−4.20775	−0.841550
$26$	0.567040	0.111206
$27$	14.7506	2.83876
$28$	1.93900	0.366437
$29$	−5.20775	−0.967055	−0.483528	−	0.875329i	$-0.660645\pi$
$29$	−5.20775	−0.967055	−0.483528	+	0.875329i	$0.660645\pi$
$30$	−0.713792	−0.130320
$31$	−8.81163	−1.58261	−0.791307	−	0.611418i	$-0.790599\pi$
$31$	−8.81163	−1.58261	−0.791307	+	0.611418i	$0.790599\pi$
$32$	−2.84415	−0.502779
$33$	5.20775	0.906553
$34$	−1.83579	−0.314835
$35$	−0.890084	−0.150452
$36$	−14.6256	−2.43761
$37$	5.40581	0.888710	0.444355	−	0.895851i	$-0.353433\pi$
$37$	5.40581	0.888710	0.444355	+	0.895851i	$0.353433\pi$
$38$	0.207751	0.0337017
$39$	−7.45473	−1.19371
$40$	0.865921	0.136914
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0.801938	0.123742
$43$	0.170915	0.0260643	0.0130322	−	0.999915i	$-0.495852\pi$
$43$	0.170915	0.0260643	0.0130322	+	0.999915i	$0.495852\pi$
$44$	−3.10992	−0.468838
$45$	6.71379	1.00083
$46$	2.18598	0.322305
$47$	5.80194	0.846300	0.423150	−	0.906060i	$-0.360924\pi$
$47$	5.80194	0.846300	0.423150	+	0.906060i	$0.360924\pi$
$48$	11.8116	1.70486
$49$	1.00000	0.142857
$50$	1.03923	0.146969
$51$	24.1347	3.37953
$52$	4.45175	0.617346
$53$	−9.60388	−1.31919	−0.659597	−	0.751620i	$-0.729273\pi$
$53$	−9.60388	−1.31919	−0.659597	+	0.751620i	$0.729273\pi$
$54$	−3.64310	−0.495764
$55$	1.42758	0.192495
$56$	−0.972853	−0.130003
$57$	−2.73125	−0.361763
$58$	1.28621	0.168887
$59$	−8.37196	−1.08994	−0.544968	−	0.838457i	$-0.683458\pi$
$59$	−8.37196	−1.08994	−0.544968	+	0.838457i	$0.683458\pi$
$60$	−5.60388	−0.723457
$61$	8.31767	1.06497	0.532484	−	0.846440i	$-0.321259\pi$
$61$	8.31767	1.06497	0.532484	+	0.846440i	$0.321259\pi$
$62$	2.17629	0.276389
$63$	−7.54288	−0.950313
$64$	−6.57301	−0.821626
$65$	−2.04354	−0.253470
$66$	−1.28621	−0.158321
$67$	−5.90217	−0.721064	−0.360532	−	0.932747i	$-0.617405\pi$
$67$	−5.90217	−0.721064	−0.360532	+	0.932747i	$0.617405\pi$
$68$	−14.4125	−1.74777
$69$	−28.7385	−3.45971
$70$	0.219833	0.0262750
$71$	−0.219833	−0.0260893	−0.0130447	−	0.999915i	$-0.504152\pi$
$71$	−0.219833	−0.0260893	−0.0130447	+	0.999915i	$0.504152\pi$
$72$	7.33811	0.864804
$73$	−6.98792	−0.817874	−0.408937	−	0.912563i	$-0.634100\pi$
$73$	−6.98792	−0.817874	−0.408937	+	0.912563i	$0.634100\pi$
$74$	−1.33513	−0.155205
$75$	−13.6625	−1.57761
$76$	1.63102	0.187091
$77$	−1.60388	−0.182779
$78$	1.84117	0.208471
$79$	12.9879	1.46125	0.730627	−	0.682776i	$-0.239228\pi$
$79$	12.9879	1.46125	0.730627	+	0.682776i	$0.239228\pi$
$80$	3.23788	0.362006
$81$	25.2664	2.80737
$82$	−0.246980	−0.0272743
$83$	−7.42758	−0.815283	−0.407642	−	0.913142i	$-0.633649\pi$
$83$	−7.42758	−0.815283	−0.407642	+	0.913142i	$0.633649\pi$
$84$	6.29590	0.686939
$85$	6.61596	0.717601
$86$	−0.0422126	−0.00455190
$87$	−16.9095	−1.81288
$88$	1.56033	0.166332
$89$	6.33944	0.671979	0.335990	−	0.941866i	$-0.390929\pi$
$89$	6.33944	0.671979	0.335990	+	0.941866i	$0.390929\pi$
$90$	−1.65817	−0.174786
$91$	2.29590	0.240675
$92$	17.1618	1.78924
$93$	−28.6112	−2.96684
$94$	−1.43296	−0.147799
$95$	−0.748709	−0.0768159
$96$	−9.23490	−0.942533
$97$	1.86294	0.189153	0.0945763	−	0.995518i	$-0.469850\pi$
$97$	1.86294	0.189153	0.0945763	+	0.995518i	$0.469850\pi$
$98$	−0.246980	−0.0249487
$99$	12.0978	1.21588
$100$	8.15883	0.815883
$101$	−5.78448	−0.575577	−0.287789	−	0.957694i	$-0.592920\pi$
$101$	−5.78448	−0.575577	−0.287789	+	0.957694i	$0.592920\pi$
$102$	−5.96077	−0.590204
$103$	8.27413	0.815274	0.407637	−	0.913144i	$-0.366353\pi$
$103$	8.27413	0.815274	0.407637	+	0.913144i	$0.366353\pi$
$104$	−2.23357	−0.219020
$105$	−2.89008	−0.282043
$106$	2.37196	0.230385
$107$	1.15883	0.112029	0.0560143	−	0.998430i	$-0.482161\pi$
$107$	1.15883	0.112029	0.0560143	+	0.998430i	$0.482161\pi$
$108$	−28.6015	−2.75218
$109$	2.67025	0.255764	0.127882	−	0.991789i	$-0.459182\pi$
$109$	2.67025	0.255764	0.127882	+	0.991789i	$0.459182\pi$
$110$	−0.352584	−0.0336176
$111$	17.5526	1.66602
$112$	−3.63773	−0.343733
$113$	0.972853	0.0915183	0.0457592	−	0.998953i	$-0.485429\pi$
$113$	0.972853	0.0915183	0.0457592	+	0.998953i	$0.485429\pi$
$114$	0.674563	0.0631786
$115$	−7.87800	−0.734627
$116$	10.0978	0.937560
$117$	−17.3177	−1.60102
$118$	2.06770	0.190348
$119$	−7.43296	−0.681378
$120$	2.81163	0.256665
$121$	−8.42758	−0.766144
$122$	−2.05429	−0.185987
$123$	3.24698	0.292770
$124$	17.0858	1.53435
$125$	−8.19567	−0.733043
$126$	1.86294	0.165964
$127$	12.4722	1.10673	0.553364	−	0.832940i	$-0.313344\pi$
$127$	12.4722	1.10673	0.553364	+	0.832940i	$0.313344\pi$
$128$	7.31170	0.646269
$129$	0.554958	0.0488613
$130$	0.504713	0.0442662
$131$	2.27413	0.198691	0.0993457	−	0.995053i	$-0.468325\pi$
$131$	2.27413	0.198691	0.0993457	+	0.995053i	$0.468325\pi$
$132$	−10.0978	−0.878904
$133$	0.841166	0.0729384
$134$	1.45771	0.125927
$135$	13.1293	1.12999
$136$	7.23118	0.620068
$137$	−9.60388	−0.820514	−0.410257	−	0.911970i	$-0.634561\pi$
$137$	−9.60388	−0.820514	−0.410257	+	0.911970i	$0.634561\pi$
$138$	7.09783	0.604208
$139$	12.0543	1.02243	0.511216	−	0.859452i	$-0.329195\pi$
$139$	12.0543	1.02243	0.511216	+	0.859452i	$0.329195\pi$
$140$	1.72587	0.145863
$141$	18.8388	1.58651
$142$	0.0542942	0.00455626
$143$	−3.68233	−0.307932
$144$	27.4389	2.28658
$145$	−4.63533	−0.384944
$146$	1.72587	0.142834
$147$	3.24698	0.267806
$148$	−10.4819	−0.861605
$149$	6.53750	0.535573	0.267786	−	0.963478i	$-0.413708\pi$
$149$	6.53750	0.535573	0.267786	+	0.963478i	$0.413708\pi$
$150$	3.37435	0.275515
$151$	14.7681	1.20181	0.600905	−	0.799321i	$-0.294807\pi$
$151$	14.7681	1.20181	0.600905	+	0.799321i	$0.294807\pi$
$152$	−0.818331	−0.0663754
$153$	56.0659	4.53266
$154$	0.396125	0.0319206
$155$	−7.84309	−0.629972
$156$	14.4547	1.15730
$157$	22.2881	1.77879	0.889393	−	0.457143i	$-0.151127\pi$
$157$	22.2881	1.77879	0.889393	+	0.457143i	$0.151127\pi$
$158$	−3.20775	−0.255195
$159$	−31.1836	−2.47302
$160$	−2.53153	−0.200135
$161$	8.85086	0.697545
$162$	−6.24027	−0.490282
$163$	−0.576728	−0.0451729	−0.0225864	−	0.999745i	$-0.507190\pi$
$163$	−0.576728	−0.0451729	−0.0225864	+	0.999745i	$0.507190\pi$
$164$	−1.93900	−0.151411
$165$	4.63533	0.360860
$166$	1.83446	0.142382
$167$	−10.1709	−0.787049	−0.393525	−	0.919314i	$-0.628744\pi$
$167$	−10.1709	−0.787049	−0.393525	+	0.919314i	$0.628744\pi$
$168$	−3.15883	−0.243709
$169$	−7.72886	−0.594527
$170$	−1.63401	−0.125323
$171$	−6.34481	−0.485200
$172$	−0.331405	−0.0252694
$173$	8.37196	0.636508	0.318254	−	0.948005i	$-0.396903\pi$
$173$	8.37196	0.636508	0.318254	+	0.948005i	$0.396903\pi$
$174$	4.17629	0.316604
$175$	4.20775	0.318076
$176$	5.83446	0.439789
$177$	−27.1836	−2.04324
$178$	−1.56571	−0.117355
$179$	−1.06638	−0.0797047	−0.0398523	−	0.999206i	$-0.512689\pi$
$179$	−1.06638	−0.0797047	−0.0398523	+	0.999206i	$0.512689\pi$
$180$	−13.0180	−0.970308
$181$	5.07069	0.376901	0.188451	−	0.982083i	$-0.439653\pi$
$181$	5.07069	0.376901	0.188451	+	0.982083i	$0.439653\pi$
$182$	−0.567040	−0.0420318
$183$	27.0073	1.99644
$184$	−8.61058	−0.634780
$185$	4.81163	0.353758
$186$	7.06638	0.518132
$187$	11.9215	0.871790
$188$	−11.2500	−0.820488
$189$	−14.7506	−1.07295
$190$	0.184916	0.0134152
$191$	−1.82371	−0.131959	−0.0659794	−	0.997821i	$-0.521017\pi$
$191$	−1.82371	−0.131959	−0.0659794	+	0.997821i	$0.521017\pi$
$192$	−21.3424	−1.54026
$193$	22.0978	1.59064	0.795318	−	0.606192i	$-0.207304\pi$
$193$	22.0978	1.59064	0.795318	+	0.606192i	$0.207304\pi$
$194$	−0.460107	−0.0330338
$195$	−6.63533	−0.475166
$196$	−1.93900	−0.138500
$197$	22.0683	1.57230	0.786150	−	0.618035i	$-0.212071\pi$
$197$	22.0683	1.57230	0.786150	+	0.618035i	$0.212071\pi$
$198$	−2.98792	−0.212342
$199$	−4.37435	−0.310090	−0.155045	−	0.987907i	$-0.549552\pi$
$199$	−4.37435	−0.310090	−0.155045	+	0.987907i	$0.549552\pi$
$200$	−4.09352	−0.289456
$201$	−19.1642	−1.35174
$202$	1.42865	0.100519
$203$	5.20775	0.365512
$204$	−46.7972	−3.27646
$205$	0.890084	0.0621661
$206$	−2.04354	−0.142380
$207$	−66.7609	−4.64020
$208$	−8.35185	−0.579096
$209$	−1.34913	−0.0933210
$210$	0.713792	0.0492563
$211$	7.43834	0.512076	0.256038	−	0.966667i	$-0.417583\pi$
$211$	7.43834	0.512076	0.256038	+	0.966667i	$0.417583\pi$
$212$	18.6219	1.27896
$213$	−0.713792	−0.0489082
$214$	−0.286208	−0.0195648
$215$	0.152129	0.0103751
$216$	14.3502	0.976407
$217$	8.81163	0.598172
$218$	−0.659498	−0.0446668
$219$	−22.6896	−1.53322
$220$	−2.76809	−0.186624
$221$	−17.0653	−1.14794
$222$	−4.33513	−0.290955
$223$	−23.7017	−1.58718	−0.793592	−	0.608450i	$-0.791791\pi$
$223$	−23.7017	−1.58718	−0.793592	+	0.608450i	$0.791791\pi$
$224$	2.84415	0.190033
$225$	−31.7385	−2.11590
$226$	−0.240275	−0.0159828
$227$	−9.78017	−0.649133	−0.324566	−	0.945863i	$-0.605218\pi$
$227$	−9.78017	−0.649133	−0.324566	+	0.945863i	$0.605218\pi$
$228$	5.29590	0.350729
$229$	21.1793	1.39957	0.699783	−	0.714356i	$-0.253280\pi$
$229$	21.1793	1.39957	0.699783	+	0.714356i	$0.253280\pi$
$230$	1.94571	0.128296
$231$	−5.20775	−0.342645
$232$	−5.06638	−0.332624
$233$	13.4276	0.879670	0.439835	−	0.898079i	$-0.355037\pi$
$233$	13.4276	0.879670	0.439835	+	0.898079i	$0.355037\pi$
$234$	4.27711	0.279603
$235$	5.16421	0.336876
$236$	16.2332	1.05669
$237$	42.1715	2.73933
$238$	1.83579	0.118997
$239$	−8.05429	−0.520989	−0.260494	−	0.965475i	$-0.583886\pi$
$239$	−8.05429	−0.520989	−0.260494	+	0.965475i	$0.583886\pi$
$240$	10.5133	0.678633
$241$	−22.1280	−1.42539	−0.712694	−	0.701475i	$-0.752525\pi$
$241$	−22.1280	−1.42539	−0.712694	+	0.701475i	$0.752525\pi$
$242$	2.08144	0.133800
$243$	37.7875	2.42407
$244$	−16.1280	−1.03249
$245$	0.890084	0.0568654
$246$	−0.801938	−0.0511297
$247$	1.93123	0.122881
$248$	−8.57242	−0.544349
$249$	−24.1172	−1.52837
$250$	2.02416	0.128019
$251$	−12.7138	−0.802487	−0.401244	−	0.915971i	$-0.631422\pi$
$251$	−12.7138	−0.802487	−0.401244	+	0.915971i	$0.631422\pi$
$252$	14.6256	0.921329
$253$	−14.1957	−0.892474
$254$	−3.08038	−0.193280
$255$	21.4819	1.34525
$256$	11.3402	0.708761
$257$	−21.1008	−1.31623	−0.658116	−	0.752916i	$-0.728647\pi$
$257$	−21.1008	−1.31623	−0.658116	+	0.752916i	$0.728647\pi$
$258$	−0.137063	−0.00853319
$259$	−5.40581	−0.335901
$260$	3.96243	0.245739
$261$	−39.2814	−2.43146
$262$	−0.561663	−0.0346997
$263$	6.93362	0.427546	0.213773	−	0.976883i	$-0.431425\pi$
$263$	6.93362	0.427546	0.213773	+	0.976883i	$0.431425\pi$
$264$	5.06638	0.311814
$265$	−8.54825	−0.525115
$266$	−0.207751	−0.0127380
$267$	20.5840	1.25972
$268$	11.4443	0.699072
$269$	19.1400	1.16699	0.583495	−	0.812117i	$-0.301685\pi$
$269$	19.1400	1.16699	0.583495	+	0.812117i	$0.301685\pi$
$270$	−3.24267	−0.197342
$271$	−28.3177	−1.72018	−0.860088	−	0.510146i	$-0.829591\pi$
$271$	−28.3177	−1.72018	−0.860088	+	0.510146i	$0.829591\pi$
$272$	27.0391	1.63949
$273$	7.45473	0.451181
$274$	2.37196	0.143295
$275$	−6.74871	−0.406962
$276$	55.7241	3.35419
$277$	0.533188	0.0320362	0.0160181	−	0.999872i	$-0.494901\pi$
$277$	0.533188	0.0320362	0.0160181	+	0.999872i	$0.494901\pi$
$278$	−2.97716	−0.178558
$279$	−66.4650	−3.97916
$280$	−0.865921	−0.0517487
$281$	30.7090	1.83195	0.915973	−	0.401240i	$-0.131421\pi$
$281$	30.7090	1.83195	0.915973	+	0.401240i	$0.131421\pi$
$282$	−4.65279	−0.277070
$283$	−1.97584	−0.117451	−0.0587257	−	0.998274i	$-0.518704\pi$
$283$	−1.97584	−0.117451	−0.0587257	+	0.998274i	$0.518704\pi$
$284$	0.426256	0.0252936
$285$	−2.43104	−0.144002
$286$	0.909461	0.0537776
$287$	−1.00000	−0.0590281
$288$	−21.4531	−1.26413
$289$	38.2489	2.24994
$290$	1.14483	0.0672269
$291$	6.04892	0.354594
$292$	13.5496	0.792929
$293$	−11.4276	−0.667607	−0.333803	−	0.942643i	$-0.608332\pi$
$293$	−11.4276	−0.667607	−0.333803	+	0.942643i	$0.608332\pi$
$294$	−0.801938	−0.0467700
$295$	−7.45175	−0.433857
$296$	5.25906	0.305677
$297$	23.6582	1.37279
$298$	−1.61463	−0.0935330
$299$	20.3207	1.17517
$300$	26.4916	1.52949
$301$	−0.170915	−0.00985139
$302$	−3.64742	−0.209885
$303$	−18.7821	−1.07900
$304$	−3.05993	−0.175499
$305$	7.40342	0.423919
$306$	−13.8471	−0.791588
$307$	−20.8116	−1.18778	−0.593891	−	0.804545i	$-0.702409\pi$
$307$	−20.8116	−1.18778	−0.593891	+	0.804545i	$0.702409\pi$
$308$	3.10992	0.177204
$309$	26.8659	1.52835
$310$	1.93708	0.110019
$311$	−2.07308	−0.117554	−0.0587768	−	0.998271i	$-0.518720\pi$
$311$	−2.07308	−0.117554	−0.0587768	+	0.998271i	$0.518720\pi$
$312$	−7.25236	−0.410584
$313$	−11.0804	−0.626300	−0.313150	−	0.949704i	$-0.601384\pi$
$313$	−11.0804	−0.626300	−0.313150	+	0.949704i	$0.601384\pi$
$314$	−5.50471	−0.310649
$315$	−6.71379	−0.378279
$316$	−25.1836	−1.41669
$317$	−10.3418	−0.580855	−0.290428	−	0.956897i	$-0.593798\pi$
$317$	−10.3418	−0.580855	−0.290428	+	0.956897i	$0.593798\pi$
$318$	7.70171	0.431890
$319$	−8.35258	−0.467655
$320$	−5.85053	−0.327054
$321$	3.76271	0.210014
$322$	−2.18598	−0.121820
$323$	−6.25236	−0.347890
$324$	−48.9915	−2.72175
$325$	9.66056	0.535872
$326$	0.142440	0.00788903
$327$	8.67025	0.479466
$328$	0.972853	0.0537168
$329$	−5.80194	−0.319871
$330$	−1.14483	−0.0630210
$331$	20.8310	1.14498	0.572488	−	0.819913i	$-0.305978\pi$
$331$	20.8310	1.14498	0.572488	+	0.819913i	$0.305978\pi$
$332$	14.4021	0.790418
$333$	40.7754	2.23448
$334$	2.51201	0.137451
$335$	−5.25342	−0.287025
$336$	−11.8116	−0.644377
$337$	33.9608	1.84996	0.924981	−	0.380014i	$-0.124081\pi$
$337$	33.9608	1.84996	0.924981	+	0.380014i	$0.124081\pi$
$338$	1.90887	0.103829
$339$	3.15883	0.171564
$340$	−12.8283	−0.695715
$341$	−14.1328	−0.765331
$342$	1.56704	0.0847358
$343$	−1.00000	−0.0539949
$344$	0.166275	0.00896497
$345$	−25.5797	−1.37717
$346$	−2.06770	−0.111160
$347$	−24.0978	−1.29364	−0.646820	−	0.762643i	$-0.723901\pi$
$347$	−24.0978	−1.29364	−0.646820	+	0.762643i	$0.723901\pi$
$348$	32.7875	1.75759
$349$	4.11721	0.220389	0.110195	−	0.993910i	$-0.464853\pi$
$349$	4.11721	0.220389	0.110195	+	0.993910i	$0.464853\pi$
$350$	−1.03923	−0.0555491
$351$	−33.8659	−1.80763
$352$	−4.56166	−0.243137
$353$	33.6775	1.79247	0.896237	−	0.443575i	$-0.146290\pi$
$353$	33.6775	1.79247	0.896237	+	0.443575i	$0.146290\pi$
$354$	6.71379	0.356834
$355$	−0.195669	−0.0103851
$356$	−12.2922	−0.651484
$357$	−24.1347	−1.27734
$358$	0.263373	0.0139197
$359$	−2.33944	−0.123471	−0.0617354	−	0.998093i	$-0.519663\pi$
$359$	−2.33944	−0.123471	−0.0617354	+	0.998093i	$0.519663\pi$
$360$	6.53153	0.344242
$361$	−18.2924	−0.962760
$362$	−1.25236	−0.0658224
$363$	−27.3642	−1.43625
$364$	−4.45175	−0.233335
$365$	−6.21983	−0.325561
$366$	−6.67025	−0.348660
$367$	−8.32842	−0.434740	−0.217370	−	0.976089i	$-0.569748\pi$
$367$	−8.32842	−0.434740	−0.217370	+	0.976089i	$0.569748\pi$
$368$	−32.1970	−1.67838
$369$	7.54288	0.392666
$370$	−1.18837	−0.0617806
$371$	9.60388	0.498608
$372$	55.4771	2.87635
$373$	4.10321	0.212456	0.106228	−	0.994342i	$-0.466123\pi$
$373$	4.10321	0.212456	0.106228	+	0.994342i	$0.466123\pi$
$374$	−2.94438	−0.152250
$375$	−26.6112	−1.37419
$376$	5.64443	0.291089
$377$	11.9565	0.615789
$378$	3.64310	0.187381
$379$	−37.2422	−1.91300	−0.956501	−	0.291727i	$-0.905770\pi$
$379$	−37.2422	−1.91300	−0.956501	+	0.291727i	$0.905770\pi$
$380$	1.45175	0.0744730
$381$	40.4969	2.07472
$382$	0.450419	0.0230454
$383$	−11.1685	−0.570685	−0.285342	−	0.958426i	$-0.592107\pi$
$383$	−11.1685	−0.570685	−0.285342	+	0.958426i	$0.592107\pi$
$384$	23.7409	1.21152
$385$	−1.42758	−0.0727564
$386$	−5.45771	−0.277790
$387$	1.28919	0.0655333
$388$	−3.61224	−0.183384
$389$	12.6136	0.639533	0.319767	−	0.947496i	$-0.396396\pi$
$389$	12.6136	0.639533	0.319767	+	0.947496i	$0.396396\pi$
$390$	1.63879	0.0829835
$391$	−65.7881	−3.32704
$392$	0.972853	0.0491365
$393$	7.38404	0.372476
$394$	−5.45042	−0.274588
$395$	11.5603	0.581664
$396$	−23.4577	−1.17879
$397$	15.8672	0.796354	0.398177	−	0.917309i	$-0.369643\pi$
$397$	15.8672	0.796354	0.398177	+	0.917309i	$0.369643\pi$
$398$	1.08038	0.0541544
$399$	2.73125	0.136734
$400$	−15.3067	−0.765333
$401$	−2.19806	−0.109766	−0.0548830	−	0.998493i	$-0.517479\pi$
$401$	−2.19806	−0.109766	−0.0548830	+	0.998493i	$0.517479\pi$
$402$	4.73317	0.236069
$403$	20.2306	1.00776
$404$	11.2161	0.558022
$405$	22.4892	1.11750
$406$	−1.28621	−0.0638334
$407$	8.67025	0.429768
$408$	23.4795	1.16241
$409$	−10.2306	−0.505870	−0.252935	−	0.967483i	$-0.581396\pi$
$409$	−10.2306	−0.505870	−0.252935	+	0.967483i	$0.581396\pi$
$410$	−0.219833	−0.0108568
$411$	−31.1836	−1.53817
$412$	−16.0435	−0.790409
$413$	8.37196	0.411957
$414$	16.4886	0.810370
$415$	−6.61117	−0.324530
$416$	6.52988	0.320154
$417$	39.1400	1.91670
$418$	0.333207	0.0162977
$419$	−3.48188	−0.170101	−0.0850504	−	0.996377i	$-0.527105\pi$
$419$	−3.48188	−0.170101	−0.0850504	+	0.996377i	$0.527105\pi$
$420$	5.60388	0.273441
$421$	−37.0810	−1.80722	−0.903608	−	0.428361i	$-0.859091\pi$
$421$	−37.0810	−1.80722	−0.903608	+	0.428361i	$0.859091\pi$
$422$	−1.83712	−0.0894295
$423$	43.7633	2.12784
$424$	−9.34316	−0.453744
$425$	−31.2760	−1.51711
$426$	0.176292	0.00854138
$427$	−8.31767	−0.402520
$428$	−2.24698	−0.108612
$429$	−11.9565	−0.577263
$430$	−0.0375727	−0.00181192
$431$	23.5603	1.13486	0.567431	−	0.823421i	$-0.307937\pi$
$431$	23.5603	1.13486	0.567431	+	0.823421i	$0.307937\pi$
$432$	53.6588	2.58166
$433$	26.3284	1.26526	0.632632	−	0.774453i	$-0.281975\pi$
$433$	26.3284	1.26526	0.632632	+	0.774453i	$0.281975\pi$
$434$	−2.17629	−0.104465
$435$	−15.0508	−0.721632
$436$	−5.17762	−0.247963
$437$	7.44504	0.356145
$438$	5.60388	0.267764
$439$	14.2107	0.678241	0.339121	−	0.940743i	$-0.389870\pi$
$439$	14.2107	0.678241	0.339121	+	0.940743i	$0.389870\pi$
$440$	1.38883	0.0662098
$441$	7.54288	0.359185
$442$	4.21478	0.200477
$443$	22.5786	1.07274	0.536372	−	0.843982i	$-0.319794\pi$
$443$	22.5786	1.07274	0.536372	+	0.843982i	$0.319794\pi$
$444$	−34.0344	−1.61520
$445$	5.64263	0.267486
$446$	5.85384	0.277187
$447$	21.2271	1.00401
$448$	6.57301	0.310545
$449$	−34.6262	−1.63411	−0.817057	−	0.576558i	$-0.804396\pi$
$449$	−34.6262	−1.63411	−0.817057	+	0.576558i	$0.804396\pi$
$450$	7.83877	0.369523
$451$	1.60388	0.0755235
$452$	−1.88636	−0.0887270
$453$	47.9517	2.25297
$454$	2.41550	0.113365
$455$	2.04354	0.0958027
$456$	−2.65710	−0.124430
$457$	20.7767	0.971893	0.485947	−	0.873988i	$-0.338475\pi$
$457$	20.7767	0.971893	0.485947	+	0.873988i	$0.338475\pi$
$458$	−5.23085	−0.244422
$459$	109.641	5.11760
$460$	15.2755	0.712222
$461$	−20.6112	−0.959958	−0.479979	−	0.877280i	$-0.659356\pi$
$461$	−20.6112	−0.959958	−0.479979	+	0.877280i	$0.659356\pi$
$462$	1.28621	0.0598398
$463$	2.73795	0.127244	0.0636218	−	0.997974i	$-0.479735\pi$
$463$	2.73795	0.127244	0.0636218	+	0.997974i	$0.479735\pi$
$464$	−18.9444	−0.879471
$465$	−25.4663	−1.18097
$466$	−3.31634	−0.153626
$467$	30.0194	1.38913	0.694566	−	0.719429i	$-0.255597\pi$
$467$	30.0194	1.38913	0.694566	+	0.719429i	$0.255597\pi$
$468$	33.5790	1.55219
$469$	5.90217	0.272537
$470$	−1.27545	−0.0588323
$471$	72.3691	3.33459
$472$	−8.14469	−0.374890
$473$	0.274127	0.0126044
$474$	−10.4155	−0.478400
$475$	3.53942	0.162400
$476$	14.4125	0.660597
$477$	−72.4408	−3.31684
$478$	1.98925	0.0909860
$479$	−13.1927	−0.602789	−0.301395	−	0.953500i	$-0.597452\pi$
$479$	−13.1927	−0.602789	−0.301395	+	0.953500i	$0.597452\pi$
$480$	−8.21983	−0.375182
$481$	−12.4112	−0.565902
$482$	5.46516	0.248931
$483$	28.7385	1.30765
$484$	16.3411	0.742777
$485$	1.65817	0.0752936
$486$	−9.33273	−0.423341
$487$	1.31575	0.0596222	0.0298111	−	0.999556i	$-0.490509\pi$
$487$	1.31575	0.0596222	0.0298111	+	0.999556i	$0.490509\pi$
$488$	8.09187	0.366302
$489$	−1.87263	−0.0846830
$490$	−0.219833	−0.00993102
$491$	30.9439	1.39648	0.698239	−	0.715864i	$-0.253967\pi$
$491$	30.9439	1.39648	0.698239	+	0.715864i	$0.253967\pi$
$492$	−6.29590	−0.283841
$493$	−38.7090	−1.74337
$494$	−0.476975	−0.0214601
$495$	10.7681	0.483989
$496$	−32.0543	−1.43928
$497$	0.219833	0.00986084
$498$	5.95646	0.266915
$499$	−27.4228	−1.22761	−0.613807	−	0.789457i	$-0.710363\pi$
$499$	−27.4228	−1.22761	−0.613807	+	0.789457i	$0.710363\pi$
$500$	15.8914	0.710686
$501$	−33.0248	−1.47544
$502$	3.14005	0.140147
$503$	3.16852	0.141277	0.0706387	−	0.997502i	$-0.477496\pi$
$503$	3.16852	0.141277	0.0706387	+	0.997502i	$0.477496\pi$
$504$	−7.33811	−0.326865
$505$	−5.14867	−0.229113
$506$	3.50604	0.155863
$507$	−25.0954	−1.11453
$508$	−24.1836	−1.07297
$509$	−18.0084	−0.798207	−0.399103	−	0.916906i	$-0.630679\pi$
$509$	−18.0084	−0.798207	−0.399103	+	0.916906i	$0.630679\pi$
$510$	−5.30559	−0.234935
$511$	6.98792	0.309127
$512$	−17.4242	−0.770048
$513$	−12.4077	−0.547815
$514$	5.21147	0.229868
$515$	7.36467	0.324526
$516$	−1.07606	−0.0473711
$517$	9.30559	0.409259
$518$	1.33513	0.0586621
$519$	27.1836	1.19323
$520$	−1.98806	−0.0871824
$521$	−40.2234	−1.76222	−0.881110	−	0.472912i	$-0.843203\pi$
$521$	−40.2234	−1.76222	−0.881110	+	0.472912i	$0.843203\pi$
$522$	9.70171	0.424632
$523$	−13.1400	−0.574574	−0.287287	−	0.957845i	$-0.592753\pi$
$523$	−13.1400	−0.574574	−0.287287	+	0.957845i	$0.592753\pi$
$524$	−4.40953	−0.192631
$525$	13.6625	0.596280
$526$	−1.71246	−0.0746670
$527$	−65.4965	−2.85307
$528$	18.9444	0.824448
$529$	55.3376	2.40598
$530$	2.11124	0.0917066
$531$	−63.1487	−2.74042
$532$	−1.63102	−0.0707138
$533$	−2.29590	−0.0994463
$534$	−5.08383	−0.219999
$535$	1.03146	0.0445939
$536$	−5.74194	−0.248014
$537$	−3.46250	−0.149418
$538$	−4.72720	−0.203804
$539$	1.60388	0.0690838
$540$	−25.4577	−1.09553
$541$	−8.20105	−0.352591	−0.176295	−	0.984337i	$-0.556411\pi$
$541$	−8.20105	−0.352591	−0.176295	+	0.984337i	$0.556411\pi$
$542$	6.99389	0.300413
$543$	16.4644	0.706556
$544$	−21.1405	−0.906390
$545$	2.37675	0.101809
$546$	−1.84117	−0.0787946
$547$	15.6280	0.668207	0.334103	−	0.942536i	$-0.391567\pi$
$547$	15.6280	0.668207	0.334103	+	0.942536i	$0.391567\pi$
$548$	18.6219	0.795489
$549$	62.7391	2.67764
$550$	1.66679	0.0710723
$551$	4.38059	0.186619
$552$	−27.9584	−1.18999
$553$	−12.9879	−0.552302
$554$	−0.131687	−0.00559482
$555$	15.6233	0.663170
$556$	−23.3733	−0.991248
$557$	−18.5133	−0.784435	−0.392218	−	0.919872i	$-0.628292\pi$
$557$	−18.5133	−0.784435	−0.392218	+	0.919872i	$0.628292\pi$
$558$	16.4155	0.694924
$559$	−0.392404	−0.0165969
$560$	−3.23788	−0.136825
$561$	38.7090	1.63430
$562$	−7.58450	−0.319933
$563$	−22.3502	−0.941948	−0.470974	−	0.882147i	$-0.656097\pi$
$563$	−22.3502	−0.941948	−0.470974	+	0.882147i	$0.656097\pi$
$564$	−36.5284	−1.53812
$565$	0.865921	0.0364296
$566$	0.487991	0.0205118
$567$	−25.2664	−1.06109
$568$	−0.213865	−0.00897356
$569$	−40.7385	−1.70785	−0.853924	−	0.520397i	$-0.825784\pi$
$569$	−40.7385	−1.70785	−0.853924	+	0.520397i	$0.825784\pi$
$570$	0.600418	0.0251487
$571$	−11.1400	−0.466196	−0.233098	−	0.972453i	$-0.574886\pi$
$571$	−11.1400	−0.466196	−0.233098	+	0.972453i	$0.574886\pi$
$572$	7.14005	0.298540
$573$	−5.92154	−0.247376
$574$	0.246980	0.0103087
$575$	37.2422	1.55311
$576$	−49.5794	−2.06581
$577$	4.43535	0.184646	0.0923231	−	0.995729i	$-0.470571\pi$
$577$	4.43535	0.184646	0.0923231	+	0.995729i	$0.470571\pi$
$578$	−9.44670	−0.392931
$579$	71.7512	2.98188
$580$	8.98792	0.373203
$581$	7.42758	0.308148
$582$	−1.49396	−0.0619266
$583$	−15.4034	−0.637944
$584$	−6.79822	−0.281312
$585$	−15.4142	−0.637298
$586$	2.82238	0.116591
$587$	29.6238	1.22271	0.611353	−	0.791358i	$-0.290625\pi$
$587$	29.6238	1.22271	0.611353	+	0.791358i	$0.290625\pi$
$588$	−6.29590	−0.259638
$589$	7.41204	0.305408
$590$	1.84043	0.0757693
$591$	71.6553	2.94751
$592$	19.6649	0.808221
$593$	13.5907	0.558104	0.279052	−	0.960276i	$-0.409980\pi$
$593$	13.5907	0.558104	0.279052	+	0.960276i	$0.409980\pi$
$594$	−5.84309	−0.239745
$595$	−6.61596	−0.271228
$596$	−12.6762	−0.519238
$597$	−14.2034	−0.581308
$598$	−5.01879	−0.205233
$599$	−13.0640	−0.533780	−0.266890	−	0.963727i	$-0.585996\pi$
$599$	−13.0640	−0.533780	−0.266890	+	0.963727i	$0.585996\pi$
$600$	−13.2916	−0.542627
$601$	23.5308	0.959841	0.479921	−	0.877312i	$-0.340665\pi$
$601$	23.5308	0.959841	0.479921	+	0.877312i	$0.340665\pi$
$602$	0.0422126	0.00172046
$603$	−44.5193	−1.81297
$604$	−28.6353	−1.16516
$605$	−7.50125	−0.304969
$606$	4.63879	0.188438
$607$	0.352584	0.0143109	0.00715547	−	0.999974i	$-0.497722\pi$
$607$	0.352584	0.0143109	0.00715547	+	0.999974i	$0.497722\pi$
$608$	2.39240	0.0970248
$609$	16.9095	0.685206
$610$	−1.82849	−0.0740336
$611$	−13.3207	−0.538896
$612$	−108.712	−4.39442
$613$	38.9487	1.57312	0.786561	−	0.617512i	$-0.211859\pi$
$613$	38.9487	1.57312	0.786561	+	0.617512i	$0.211859\pi$
$614$	5.14005	0.207435
$615$	2.89008	0.116539
$616$	−1.56033	−0.0628677
$617$	−8.09246	−0.325790	−0.162895	−	0.986643i	$-0.552083\pi$
$617$	−8.09246	−0.325790	−0.162895	+	0.986643i	$0.552083\pi$
$618$	−6.63533	−0.266912
$619$	−30.4155	−1.22250	−0.611251	−	0.791437i	$-0.709333\pi$
$619$	−30.4155	−1.22250	−0.611251	+	0.791437i	$0.709333\pi$
$620$	15.2078	0.610758
$621$	−130.556	−5.23902
$622$	0.512009	0.0205297
$623$	−6.33944	−0.253984
$624$	−27.1183	−1.08560
$625$	13.7439	0.549757
$626$	2.73663	0.109378
$627$	−4.38059	−0.174944
$628$	−43.2167	−1.72453
$629$	40.1812	1.60213
$630$	1.65817	0.0660631
$631$	31.4795	1.25318	0.626589	−	0.779350i	$-0.284450\pi$
$631$	31.4795	1.25318	0.626589	+	0.779350i	$0.284450\pi$
$632$	12.6353	0.502607
$633$	24.1521	0.959961
$634$	2.55422	0.101441
$635$	11.1013	0.440541
$636$	60.4650	2.39759
$637$	−2.29590	−0.0909667
$638$	2.06292	0.0816717
$639$	−1.65817	−0.0655962
$640$	6.50802	0.257252
$641$	26.0495	1.02889	0.514447	−	0.857522i	$-0.327997\pi$
$641$	26.0495	1.02889	0.514447	+	0.857522i	$0.327997\pi$
$642$	−0.929312	−0.0366770
$643$	−15.5821	−0.614498	−0.307249	−	0.951629i	$-0.599408\pi$
$643$	−15.5821	−0.614498	−0.307249	+	0.951629i	$0.599408\pi$
$644$	−17.1618	−0.676270
$645$	0.493959	0.0194496
$646$	1.54420	0.0607559
$647$	5.94571	0.233750	0.116875	−	0.993147i	$-0.462712\pi$
$647$	5.94571	0.233750	0.116875	+	0.993147i	$0.462712\pi$
$648$	24.5804	0.965611
$649$	−13.4276	−0.527079
$650$	−2.38596	−0.0935851
$651$	28.6112	1.12136
$652$	1.11828	0.0437951
$653$	15.0556	0.589172	0.294586	−	0.955625i	$-0.404818\pi$
$653$	15.0556	0.589172	0.294586	+	0.955625i	$0.404818\pi$
$654$	−2.14138	−0.0837344
$655$	2.02416	0.0790906
$656$	3.63773	0.142029
$657$	−52.7090	−2.05637
$658$	1.43296	0.0558626
$659$	12.4069	0.483303	0.241652	−	0.970363i	$-0.422311\pi$
$659$	12.4069	0.483303	0.241652	+	0.970363i	$0.422311\pi$
$660$	−8.98792	−0.349854
$661$	13.3297	0.518467	0.259234	−	0.965815i	$-0.416530\pi$
$661$	13.3297	0.518467	0.259234	+	0.965815i	$0.416530\pi$
$662$	−5.14483	−0.199960
$663$	−55.4107	−2.15197
$664$	−7.22595	−0.280421
$665$	0.748709	0.0290337
$666$	−10.0707	−0.390231
$667$	46.0930	1.78473
$668$	19.7214	0.763044
$669$	−76.9590	−2.97541
$670$	1.29749	0.0501263
$671$	13.3405	0.515004
$672$	9.23490	0.356244
$673$	24.0543	0.927225	0.463612	−	0.886038i	$-0.346553\pi$
$673$	24.0543	0.927225	0.463612	+	0.886038i	$0.346553\pi$
$674$	−8.38762	−0.323079
$675$	−62.0670	−2.38896
$676$	14.9863	0.576395
$677$	−47.2707	−1.81676	−0.908380	−	0.418146i	$-0.862680\pi$
$677$	−47.2707	−1.81676	−0.908380	+	0.418146i	$0.862680\pi$
$678$	−0.780167	−0.0299622
$679$	−1.86294	−0.0714929
$680$	6.43635	0.246823
$681$	−31.7560	−1.21689
$682$	3.49050	0.133658
$683$	−0.646088	−0.0247219	−0.0123609	−	0.999924i	$-0.503935\pi$
$683$	−0.646088	−0.0247219	−0.0123609	+	0.999924i	$0.503935\pi$
$684$	12.3026	0.470402
$685$	−8.54825	−0.326612
$686$	0.246980	0.00942973
$687$	68.7687	2.62369
$688$	0.621743	0.0237037
$689$	22.0495	0.840019
$690$	6.31767	0.240509
$691$	18.9420	0.720587	0.360294	−	0.932839i	$-0.382677\pi$
$691$	18.9420	0.720587	0.360294	+	0.932839i	$0.382677\pi$
$692$	−16.2332	−0.617095
$693$	−12.0978	−0.459559
$694$	5.95167	0.225922
$695$	10.7293	0.406987
$696$	−16.4504	−0.623552
$697$	7.43296	0.281543
$698$	−1.01687	−0.0384890
$699$	43.5991	1.64907
$700$	−8.15883	−0.308375
$701$	−16.6571	−0.629130	−0.314565	−	0.949236i	$-0.601859\pi$
$701$	−16.6571	−0.629130	−0.314565	+	0.949236i	$0.601859\pi$
$702$	8.36419	0.315686
$703$	−4.54719	−0.171500
$704$	−10.5423	−0.397327
$705$	16.7681	0.631523
$706$	−8.31767	−0.313040
$707$	5.78448	0.217548
$708$	52.7090	1.98093
$709$	−1.83446	−0.0688947	−0.0344473	−	0.999407i	$-0.510967\pi$
$709$	−1.83446	−0.0688947	−0.0344473	+	0.999407i	$0.510967\pi$
$710$	0.0483263	0.00181366
$711$	97.9663	3.67402
$712$	6.16734	0.231131
$713$	77.9904	2.92076
$714$	5.96077	0.223076
$715$	−3.27758	−0.122575
$716$	2.06770	0.0772737
$717$	−26.1521	−0.976669
$718$	0.577793	0.0215631
$719$	−15.6689	−0.584352	−0.292176	−	0.956365i	$-0.594379\pi$
$719$	−15.6689	−0.584352	−0.292176	+	0.956365i	$0.594379\pi$
$720$	24.4229	0.910189
$721$	−8.27413	−0.308145
$722$	4.51786	0.168137
$723$	−71.8491	−2.67210
$724$	−9.83207	−0.365406
$725$	21.9129	0.813825
$726$	6.75840	0.250828
$727$	−4.92825	−0.182779	−0.0913893	−	0.995815i	$-0.529131\pi$
$727$	−4.92825	−0.182779	−0.0913893	+	0.995815i	$0.529131\pi$
$728$	2.23357	0.0827816
$729$	46.8961	1.73689
$730$	1.53617	0.0568563
$731$	1.27041	0.0469877
$732$	−52.3672	−1.93555
$733$	42.1473	1.55675	0.778374	−	0.627801i	$-0.216045\pi$
$733$	42.1473	1.55675	0.778374	+	0.627801i	$0.216045\pi$
$734$	2.05695	0.0759234
$735$	2.89008	0.106602
$736$	25.1732	0.927895
$737$	−9.46634	−0.348697
$738$	−1.86294	−0.0685756
$739$	−28.4674	−1.04719	−0.523595	−	0.851967i	$-0.675410\pi$
$739$	−28.4674	−1.04719	−0.523595	+	0.851967i	$0.675410\pi$
$740$	−9.32975	−0.342968
$741$	6.27067	0.230359
$742$	−2.37196	−0.0870774
$743$	29.8157	1.09383	0.546916	−	0.837188i	$-0.315802\pi$
$743$	29.8157	1.09383	0.546916	+	0.837188i	$0.315802\pi$
$744$	−27.8345	−1.02046
$745$	5.81892	0.213189
$746$	−1.01341	−0.0371036
$747$	−56.0253	−2.04986
$748$	−23.1159	−0.845200
$749$	−1.15883	−0.0423429
$750$	6.57242	0.239991
$751$	20.9444	0.764271	0.382136	−	0.924106i	$-0.375189\pi$
$751$	20.9444	0.764271	0.382136	+	0.924106i	$0.375189\pi$
$752$	21.1059	0.769652
$753$	−41.2814	−1.50438
$754$	−2.95300	−0.107542
$755$	13.1448	0.478389
$756$	28.6015	1.04023
$757$	−25.4082	−0.923477	−0.461738	−	0.887016i	$-0.652774\pi$
$757$	−25.4082	−0.923477	−0.461738	+	0.887016i	$0.652774\pi$
$758$	9.19806	0.334089
$759$	−46.0930	−1.67307
$760$	−0.728383	−0.0264212
$761$	−30.5918	−1.10895	−0.554476	−	0.832200i	$-0.687081\pi$
$761$	−30.5918	−1.10895	−0.554476	+	0.832200i	$0.687081\pi$
$762$	−10.0019	−0.362331
$763$	−2.67025	−0.0966696
$764$	3.53617	0.127934
$765$	49.9033	1.80426
$766$	2.75840	0.0996649
$767$	19.2212	0.694036
$768$	36.8213	1.32867
$769$	7.21850	0.260306	0.130153	−	0.991494i	$-0.458453\pi$
$769$	7.21850	0.260306	0.130153	+	0.991494i	$0.458453\pi$
$770$	0.352584	0.0127062
$771$	−68.5139	−2.46747
$772$	−42.8477	−1.54212
$773$	36.1554	1.30042	0.650209	−	0.759755i	$-0.274681\pi$
$773$	36.1554	1.30042	0.650209	+	0.759755i	$0.274681\pi$
$774$	−0.318404	−0.0114448
$775$	37.0771	1.33185
$776$	1.81236	0.0650601
$777$	−17.5526	−0.629695
$778$	−3.11529	−0.111689
$779$	−0.841166	−0.0301379
$780$	12.8659	0.460674
$781$	−0.352584	−0.0126164
$782$	16.2483	0.581038
$783$	−76.8176	−2.74524
$784$	3.63773	0.129919
$785$	19.8383	0.708059
$786$	−1.82371	−0.0650495
$787$	−53.1138	−1.89330	−0.946650	−	0.322262i	$-0.895557\pi$
$787$	−53.1138	−1.89330	−0.946650	+	0.322262i	$0.895557\pi$
$788$	−42.7904	−1.52435
$789$	22.5133	0.801496
$790$	−2.85517	−0.101582
$791$	−0.972853	−0.0345907
$792$	11.7694	0.418208
$793$	−19.0965	−0.678137
$794$	−3.91889	−0.139076
$795$	−27.7560	−0.984404
$796$	8.48188	0.300632
$797$	−27.2379	−0.964815	−0.482408	−	0.875947i	$-0.660238\pi$
$797$	−27.2379	−0.964815	−0.482408	+	0.875947i	$0.660238\pi$
$798$	−0.674563	−0.0238793
$799$	43.1256	1.52567
$800$	11.9675	0.423114
$801$	47.8176	1.68955
$802$	0.542877	0.0191696
$803$	−11.2078	−0.395513
$804$	37.1594	1.31051
$805$	7.87800	0.277663
$806$	−4.99654	−0.175996
$807$	62.1473	2.18769
$808$	−5.62745	−0.197973
$809$	−25.3357	−0.890756	−0.445378	−	0.895343i	$-0.646931\pi$
$809$	−25.3357	−0.890756	−0.445378	+	0.895343i	$0.646931\pi$
$810$	−5.55437	−0.195161
$811$	8.74392	0.307041	0.153520	−	0.988145i	$-0.450939\pi$
$811$	8.74392	0.307041	0.153520	+	0.988145i	$0.450939\pi$
$812$	−10.0978	−0.354365
$813$	−91.9469	−3.22472
$814$	−2.14138	−0.0750552
$815$	−0.513337	−0.0179814
$816$	87.7954	3.07345
$817$	−0.143768	−0.00502981
$818$	2.52675	0.0883456
$819$	17.3177	0.605128
$820$	−1.72587	−0.0602701
$821$	42.5682	1.48564	0.742821	−	0.669491i	$-0.233488\pi$
$821$	42.5682	1.48564	0.742821	+	0.669491i	$0.233488\pi$
$822$	7.70171	0.268628
$823$	11.9108	0.415184	0.207592	−	0.978215i	$-0.433437\pi$
$823$	11.9108	0.415184	0.207592	+	0.978215i	$0.433437\pi$
$824$	8.04951	0.280418
$825$	−21.9129	−0.762910
$826$	−2.06770	−0.0719446
$827$	−30.1038	−1.04681	−0.523406	−	0.852083i	$-0.675339\pi$
$827$	−30.1038	−1.04681	−0.523406	+	0.852083i	$0.675339\pi$
$828$	129.449	4.49868
$829$	−30.0194	−1.04262	−0.521308	−	0.853369i	$-0.674556\pi$
$829$	−30.0194	−1.04262	−0.521308	+	0.853369i	$0.674556\pi$
$830$	1.63282	0.0566762
$831$	1.73125	0.0600564
$832$	15.0909	0.523184
$833$	7.43296	0.257537
$834$	−9.66679	−0.334734
$835$	−9.05297	−0.313291
$836$	2.61596	0.0904748
$837$	−129.977	−4.49266
$838$	0.859953	0.0297066
$839$	−42.6590	−1.47275	−0.736377	−	0.676572i	$-0.763465\pi$
$839$	−42.6590	−1.47275	−0.736377	+	0.676572i	$0.763465\pi$
$840$	−2.81163	−0.0970103
$841$	−1.87933	−0.0648045
$842$	9.15824	0.315614
$843$	99.7115	3.43425
$844$	−14.4229	−0.496458
$845$	−6.87933	−0.236656
$846$	−10.8086	−0.371609
$847$	8.42758	0.289575
$848$	−34.9363	−1.19972
$849$	−6.41550	−0.220179
$850$	7.72455	0.264950
$851$	−47.8461	−1.64014
$852$	1.38404	0.0474165
$853$	2.00000	0.0684787	0.0342393	−	0.999414i	$-0.489099\pi$
$853$	2.00000	0.0684787	0.0342393	+	0.999414i	$0.489099\pi$
$854$	2.05429	0.0702965
$855$	−5.64742	−0.193138
$856$	1.12737	0.0385329
$857$	−28.4456	−0.971684	−0.485842	−	0.874047i	$-0.661487\pi$
$857$	−28.4456	−0.971684	−0.485842	+	0.874047i	$0.661487\pi$
$858$	2.95300	0.100814
$859$	33.2164	1.13333	0.566664	−	0.823949i	$-0.308234\pi$
$859$	33.2164	1.13333	0.566664	+	0.823949i	$0.308234\pi$
$860$	−0.294978	−0.0100587
$861$	−3.24698	−0.110657
$862$	−5.81892	−0.198193
$863$	−2.17151	−0.0739189	−0.0369595	−	0.999317i	$-0.511767\pi$
$863$	−2.17151	−0.0739189	−0.0369595	+	0.999317i	$0.511767\pi$
$864$	−41.9530	−1.42727
$865$	7.45175	0.253367
$866$	−6.50258	−0.220967
$867$	124.193	4.21783
$868$	−17.0858	−0.579928
$869$	20.8310	0.706643
$870$	3.71725	0.126027
$871$	13.5508	0.459150
$872$	2.59776	0.0879713
$873$	14.0519	0.475585
$874$	−1.83877	−0.0621974
$875$	8.19567	0.277064
$876$	43.9952	1.48646
$877$	21.4728	0.725084	0.362542	−	0.931967i	$-0.381909\pi$
$877$	21.4728	0.725084	0.362542	+	0.931967i	$0.381909\pi$
$878$	−3.50976	−0.118449
$879$	−37.1051	−1.25152
$880$	5.19316	0.175061
$881$	23.8189	0.802480	0.401240	−	0.915973i	$-0.368579\pi$
$881$	23.8189	0.802480	0.401240	+	0.915973i	$0.368579\pi$
$882$	−1.86294	−0.0627283
$883$	−14.0349	−0.472313	−0.236156	−	0.971715i	$-0.575888\pi$
$883$	−14.0349	−0.472313	−0.236156	+	0.971715i	$0.575888\pi$
$884$	33.0897	1.11293
$885$	−24.1957	−0.813329
$886$	−5.57647	−0.187345
$887$	10.8382	0.363911	0.181955	−	0.983307i	$-0.441757\pi$
$887$	10.8382	0.363911	0.181955	+	0.983307i	$0.441757\pi$
$888$	17.0761	0.573035
$889$	−12.4722	−0.418304
$890$	−1.39361	−0.0467141
$891$	40.5241	1.35761
$892$	45.9576	1.53878
$893$	−4.88040	−0.163316
$894$	−5.24267	−0.175341
$895$	−0.949164	−0.0317270
$896$	−7.31170	−0.244267
$897$	65.9807	2.20303
$898$	8.55197	0.285383
$899$	45.8888	1.53048
$900$	61.5411	2.05137
$901$	−71.3852	−2.37819
$902$	−0.396125	−0.0131895
$903$	−0.554958	−0.0184679
$904$	0.946443	0.0314782
$905$	4.51334	0.150028
$906$	−11.8431	−0.393460
$907$	41.3682	1.37361	0.686805	−	0.726842i	$-0.259013\pi$
$907$	41.3682	1.37361	0.686805	+	0.726842i	$0.259013\pi$
$908$	18.9638	0.629334
$909$	−43.6316	−1.44717
$910$	−0.504713	−0.0167311
$911$	−23.9377	−0.793090	−0.396545	−	0.918015i	$-0.629791\pi$
$911$	−23.9377	−0.793090	−0.396545	+	0.918015i	$0.629791\pi$
$912$	−9.93554	−0.328999
$913$	−11.9129	−0.394260
$914$	−5.13142	−0.169732
$915$	24.0388	0.794697
$916$	−41.0666	−1.35688
$917$	−2.27413	−0.0750983
$918$	−27.0790	−0.893742
$919$	−25.0315	−0.825712	−0.412856	−	0.910796i	$-0.635469\pi$
$919$	−25.0315	−0.825712	−0.412856	+	0.910796i	$0.635469\pi$
$920$	−7.66414	−0.252679
$921$	−67.5749	−2.22667
$922$	5.09054	0.167648
$923$	0.504713	0.0166128
$924$	10.0978	0.332194
$925$	−22.7463	−0.747894
$926$	−0.676219	−0.0222219
$927$	62.4107	2.04984
$928$	14.8116	0.486215
$929$	−21.7362	−0.713140	−0.356570	−	0.934269i	$-0.616054\pi$
$929$	−21.7362	−0.713140	−0.356570	+	0.934269i	$0.616054\pi$
$930$	6.28967	0.206246
$931$	−0.841166	−0.0275681
$932$	−26.0361	−0.852841
$933$	−6.73125	−0.220371
$934$	−7.41417	−0.242599
$935$	10.6112	0.347022
$936$	−16.8475	−0.550679
$937$	31.4359	1.02697	0.513484	−	0.858099i	$-0.328355\pi$
$937$	31.4359	1.02697	0.513484	+	0.858099i	$0.328355\pi$
$938$	−1.45771	−0.0475961
$939$	−35.9778	−1.17409
$940$	−10.0134	−0.326601
$941$	−34.6461	−1.12943	−0.564715	−	0.825286i	$-0.691014\pi$
$941$	−34.6461	−1.12943	−0.564715	+	0.825286i	$0.691014\pi$
$942$	−17.8737	−0.582356
$943$	−8.85086	−0.288223
$944$	−30.4549	−0.991223
$945$	−13.1293	−0.427096
$946$	−0.0677037	−0.00220124
$947$	40.1672	1.30526	0.652629	−	0.757677i	$-0.273666\pi$
$947$	40.1672	1.30526	0.652629	+	0.757677i	$0.273666\pi$
$948$	−81.7706	−2.65579
$949$	16.0435	0.520795
$950$	−0.874164	−0.0283616
$951$	−33.5797	−1.08890
$952$	−7.23118	−0.234364
$953$	−7.29457	−0.236294	−0.118147	−	0.992996i	$-0.537695\pi$
$953$	−7.29457	−0.236294	−0.118147	+	0.992996i	$0.537695\pi$
$954$	17.8914	0.579256
$955$	−1.62325	−0.0525272
$956$	15.6173	0.505099
$957$	−27.1207	−0.876687
$958$	3.25832	0.105272
$959$	9.60388	0.310125
$960$	−18.9965	−0.613111
$961$	46.6448	1.50467
$962$	3.06531	0.0988296
$963$	8.74094	0.281673
$964$	42.9061	1.38191
$965$	19.6689	0.633165
$966$	−7.09783	−0.228369
$967$	−47.1138	−1.51508	−0.757538	−	0.652791i	$-0.773598\pi$
$967$	−47.1138	−1.51508	−0.757538	+	0.652791i	$0.773598\pi$
$968$	−8.19880	−0.263519
$969$	−20.3013	−0.652171
$970$	−0.409534	−0.0131493
$971$	24.1575	0.775251	0.387626	−	0.921817i	$-0.373295\pi$
$971$	24.1575	0.775251	0.387626	+	0.921817i	$0.373295\pi$
$972$	−73.2699	−2.35013
$973$	−12.0543	−0.386443
$974$	−0.324963	−0.0104125
$975$	31.3676	1.00457
$976$	30.2574	0.968516
$977$	12.8116	0.409880	0.204940	−	0.978775i	$-0.434300\pi$
$977$	12.8116	0.409880	0.204940	+	0.978775i	$0.434300\pi$
$978$	0.462500	0.0147891
$979$	10.1677	0.324960
$980$	−1.72587	−0.0551310
$981$	20.1414	0.643065
$982$	−7.64251	−0.243882
$983$	−7.07979	−0.225810	−0.112905	−	0.993606i	$-0.536016\pi$
$983$	−7.07979	−0.225810	−0.112905	+	0.993606i	$0.536016\pi$
$984$	3.15883	0.100700
$985$	19.6426	0.625866
$986$	9.56033	0.304463
$987$	−18.8388	−0.599645
$988$	−3.74466	−0.119133
$989$	−1.51275	−0.0481025
$990$	−2.65950	−0.0845244
$991$	18.2500	0.579729	0.289865	−	0.957068i	$-0.406390\pi$
$991$	18.2500	0.579729	0.289865	+	0.957068i	$0.406390\pi$
$992$	25.0616	0.795706
$993$	67.6378	2.14642
$994$	−0.0542942	−0.00172211
$995$	−3.89354	−0.123434
$996$	46.7633	1.48175
$997$	44.4956	1.40919	0.704595	−	0.709610i	$-0.251129\pi$
$997$	44.4956	1.40919	0.704595	+	0.709610i	$0.251129\pi$
$998$	6.77287	0.214392
$999$	79.7391	2.52283

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.a.d.1.1	✓	3
3.2	odd	2		2583.2.a.l.1.3		3
4.3	odd	2		4592.2.a.r.1.1		3
5.4	even	2		7175.2.a.i.1.3		3
7.6	odd	2		2009.2.a.k.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.a.d.1.1	✓	3	1.1	even	1	trivial
2009.2.a.k.1.1		3	7.6	odd	2
2583.2.a.l.1.3		3	3.2	odd	2
4592.2.a.r.1.1		3	4.3	odd	2
7175.2.a.i.1.3		3	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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.a (trivial)

\(f(q)\)	\(=\)	\(q-0.246980 q^{2} +3.24698 q^{3} -1.93900 q^{4} +0.890084 q^{5} -0.801938 q^{6} -1.00000 q^{7} +0.972853 q^{8} +7.54288 q^{9} +O(q^{10})\)	\(q-0.246980 q^{2} +3.24698 q^{3} -1.93900 q^{4} +0.890084 q^{5} -0.801938 q^{6} -1.00000 q^{7} +0.972853 q^{8} +7.54288 q^{9} -0.219833 q^{10} +1.60388 q^{11} -6.29590 q^{12} -2.29590 q^{13} +0.246980 q^{14} +2.89008 q^{15} +3.63773 q^{16} +7.43296 q^{17} -1.86294 q^{18} -0.841166 q^{19} -1.72587 q^{20} -3.24698 q^{21} -0.396125 q^{22} -8.85086 q^{23} +3.15883 q^{24} -4.20775 q^{25} +0.567040 q^{26} +14.7506 q^{27} +1.93900 q^{28} -5.20775 q^{29} -0.713792 q^{30} -8.81163 q^{31} -2.84415 q^{32} +5.20775 q^{33} -1.83579 q^{34} -0.890084 q^{35} -14.6256 q^{36} +5.40581 q^{37} +0.207751 q^{38} -7.45473 q^{39} +0.865921 q^{40} +1.00000 q^{41} +0.801938 q^{42} +0.170915 q^{43} -3.10992 q^{44} +6.71379 q^{45} +2.18598 q^{46} +5.80194 q^{47} +11.8116 q^{48} +1.00000 q^{49} +1.03923 q^{50} +24.1347 q^{51} +4.45175 q^{52} -9.60388 q^{53} -3.64310 q^{54} +1.42758 q^{55} -0.972853 q^{56} -2.73125 q^{57} +1.28621 q^{58} -8.37196 q^{59} -5.60388 q^{60} +8.31767 q^{61} +2.17629 q^{62} -7.54288 q^{63} -6.57301 q^{64} -2.04354 q^{65} -1.28621 q^{66} -5.90217 q^{67} -14.4125 q^{68} -28.7385 q^{69} +0.219833 q^{70} -0.219833 q^{71} +7.33811 q^{72} -6.98792 q^{73} -1.33513 q^{74} -13.6625 q^{75} +1.63102 q^{76} -1.60388 q^{77} +1.84117 q^{78} +12.9879 q^{79} +3.23788 q^{80} +25.2664 q^{81} -0.246980 q^{82} -7.42758 q^{83} +6.29590 q^{84} +6.61596 q^{85} -0.0422126 q^{86} -16.9095 q^{87} +1.56033 q^{88} +6.33944 q^{89} -1.65817 q^{90} +2.29590 q^{91} +17.1618 q^{92} -28.6112 q^{93} -1.43296 q^{94} -0.748709 q^{95} -9.23490 q^{96} +1.86294 q^{97} -0.246980 q^{98} +12.0978 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 4 q^{2} + 5 q^{3} + 4 q^{4} + 2 q^{5} + 2 q^{6} - 3 q^{7} + 9 q^{8} + 4 q^{9}+O(q^{10}) \) 3 * q + 4 * q^2 + 5 * q^3 + 4 * q^4 + 2 * q^5 + 2 * q^6 - 3 * q^7 + 9 * q^8 + 4 * q^9	\( 3 q + 4 q^{2} + 5 q^{3} + 4 q^{4} + 2 q^{5} + 2 q^{6} - 3 q^{7} + 9 q^{8} + 4 q^{9} - 2 q^{10} - 4 q^{11} - 5 q^{12} + 7 q^{13} - 4 q^{14} + 8 q^{15} + 18 q^{16} + 3 q^{17} - 11 q^{18} - 11 q^{19} - 16 q^{20} - 5 q^{21} - 10 q^{22} - 13 q^{23} + q^{24} + 5 q^{25} + 21 q^{26} + 8 q^{27} - 4 q^{28} + 2 q^{29} + 6 q^{30} + 27 q^{32} - 2 q^{33} - 17 q^{34} - 2 q^{35} - 32 q^{36} + 3 q^{37} - 17 q^{38} - 36 q^{40} + 3 q^{41} - 2 q^{42} + 11 q^{43} - 10 q^{44} + 12 q^{45} - 8 q^{46} + 13 q^{47} + 9 q^{48} + 3 q^{49} + 16 q^{50} + 26 q^{51} + 35 q^{52} - 20 q^{53} - 15 q^{54} - 12 q^{55} - 9 q^{56} - 16 q^{57} + 12 q^{58} + 4 q^{59} - 8 q^{60} + 8 q^{61} + 14 q^{62} - 4 q^{63} + 49 q^{64} - 12 q^{66} - 36 q^{67} - 52 q^{68} - 31 q^{69} + 2 q^{70} - 2 q^{71} - 23 q^{72} - 2 q^{73} - 3 q^{74} - q^{75} - 10 q^{76} + 4 q^{77} + 14 q^{78} + 20 q^{79} - 58 q^{80} + 27 q^{81} + 4 q^{82} - 6 q^{83} + 5 q^{84} + 30 q^{85} + 31 q^{86} - 6 q^{87} + 2 q^{88} - q^{89} + 16 q^{90} - 7 q^{91} - q^{92} - 14 q^{93} + 15 q^{94} - 26 q^{95} - 4 q^{96} + 11 q^{97} + 4 q^{98} + 18 q^{99}+O(q^{100}) \) 3 * q + 4 * q^2 + 5 * q^3 + 4 * q^4 + 2 * q^5 + 2 * q^6 - 3 * q^7 + 9 * q^8 + 4 * q^9 - 2 * q^10 - 4 * q^11 - 5 * q^12 + 7 * q^13 - 4 * q^14 + 8 * q^15 + 18 * q^16 + 3 * q^17 - 11 * q^18 - 11 * q^19 - 16 * q^20 - 5 * q^21 - 10 * q^22 - 13 * q^23 + q^24 + 5 * q^25 + 21 * q^26 + 8 * q^27 - 4 * q^28 + 2 * q^29 + 6 * q^30 + 27 * q^32 - 2 * q^33 - 17 * q^34 - 2 * q^35 - 32 * q^36 + 3 * q^37 - 17 * q^38 - 36 * q^40 + 3 * q^41 - 2 * q^42 + 11 * q^43 - 10 * q^44 + 12 * q^45 - 8 * q^46 + 13 * q^47 + 9 * q^48 + 3 * q^49 + 16 * q^50 + 26 * q^51 + 35 * q^52 - 20 * q^53 - 15 * q^54 - 12 * q^55 - 9 * q^56 - 16 * q^57 + 12 * q^58 + 4 * q^59 - 8 * q^60 + 8 * q^61 + 14 * q^62 - 4 * q^63 + 49 * q^64 - 12 * q^66 - 36 * q^67 - 52 * q^68 - 31 * q^69 + 2 * q^70 - 2 * q^71 - 23 * q^72 - 2 * q^73 - 3 * q^74 - q^75 - 10 * q^76 + 4 * q^77 + 14 * q^78 + 20 * q^79 - 58 * q^80 + 27 * q^81 + 4 * q^82 - 6 * q^83 + 5 * q^84 + 30 * q^85 + 31 * q^86 - 6 * q^87 + 2 * q^88 - q^89 + 16 * q^90 - 7 * q^91 - q^92 - 14 * q^93 + 15 * q^94 - 26 * q^95 - 4 * q^96 + 11 * q^97 + 4 * q^98 + 18 * q^99

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