LMFDB - Embedded newform 1001.2.a.k.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1001,2,Mod(1,1001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1001, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1001 = 7 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1001.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:	$7.99302524233$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.81509.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 5x^{3} + 3x^{2} + 5x - 2 $ x^5 - x^4 - 5x^3 + 3x^2 + 5*x - 2
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			1.3
Root			$-1.71377$ of defining polynomial
Character	$\chi$	$=$	1001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.483735 q^{2} -0.0630088 q^{3} -1.76600 q^{4} +0.713765 q^{5} -0.0304796 q^{6} +1.00000 q^{7} -1.82175 q^{8} -2.99603 q^{9} +O(q^{10})$	\(q+0.483735 q^{2} -0.0630088 q^{3} -1.76600 q^{4} +0.713765 q^{5} -0.0304796 q^{6} +1.00000 q^{7} -1.82175 q^{8} -2.99603 q^{9} +0.345273 q^{10} +1.00000 q^{11} +0.111274 q^{12} -1.00000 q^{13} +0.483735 q^{14} -0.0449735 q^{15} +2.65076 q^{16} +0.237291 q^{17} -1.44929 q^{18} -1.65473 q^{19} -1.26051 q^{20} -0.0630088 q^{21} +0.483735 q^{22} -2.01971 q^{23} +0.114786 q^{24} -4.49054 q^{25} -0.483735 q^{26} +0.377803 q^{27} -1.76600 q^{28} -8.65154 q^{29} -0.0217553 q^{30} -2.07897 q^{31} +4.92576 q^{32} -0.0630088 q^{33} +0.114786 q^{34} +0.713765 q^{35} +5.29099 q^{36} -8.06751 q^{37} -0.800450 q^{38} +0.0630088 q^{39} -1.30030 q^{40} -9.06028 q^{41} -0.0304796 q^{42} +0.765543 q^{43} -1.76600 q^{44} -2.13846 q^{45} -0.977003 q^{46} -1.16184 q^{47} -0.167021 q^{48} +1.00000 q^{49} -2.17223 q^{50} -0.0149514 q^{51} +1.76600 q^{52} +1.40828 q^{53} +0.182757 q^{54} +0.713765 q^{55} -1.82175 q^{56} +0.104262 q^{57} -4.18506 q^{58} +8.96099 q^{59} +0.0794232 q^{60} +7.64949 q^{61} -1.00567 q^{62} -2.99603 q^{63} -2.91875 q^{64} -0.713765 q^{65} -0.0304796 q^{66} -9.51308 q^{67} -0.419056 q^{68} +0.127259 q^{69} +0.345273 q^{70} +5.62006 q^{71} +5.45801 q^{72} +3.82604 q^{73} -3.90254 q^{74} +0.282944 q^{75} +2.92225 q^{76} +1.00000 q^{77} +0.0304796 q^{78} -6.85076 q^{79} +1.89202 q^{80} +8.96428 q^{81} -4.38278 q^{82} -16.6596 q^{83} +0.111274 q^{84} +0.169370 q^{85} +0.370320 q^{86} +0.545123 q^{87} -1.82175 q^{88} -12.2638 q^{89} -1.03445 q^{90} -1.00000 q^{91} +3.56680 q^{92} +0.130993 q^{93} -0.562022 q^{94} -1.18109 q^{95} -0.310366 q^{96} +5.97028 q^{97} +0.483735 q^{98} -2.99603 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 4 q^{3} + 2 q^{4} - 6 q^{5} + q^{6} + 5 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 5 * q - 4 * q^3 + 2 * q^4 - 6 * q^5 + q^6 + 5 * q^7 - 3 * q^8 + 3 * q^9	$ 5 q - 4 q^{3} + 2 q^{4} - 6 q^{5} + q^{6} + 5 q^{7} - 3 q^{8} + 3 q^{9} - 3 q^{10} + 5 q^{11} - 15 q^{12} - 5 q^{13} - 7 q^{17} + 12 q^{18} - 13 q^{19} + 2 q^{20} - 4 q^{21} - 4 q^{23} - 9 q^{24} - 7 q^{25} + 2 q^{27} + 2 q^{28} + 7 q^{29} - 15 q^{31} + 4 q^{32} - 4 q^{33} - 9 q^{34} - 6 q^{35} + 17 q^{36} - 3 q^{37} - 10 q^{38} + 4 q^{39} - 2 q^{40} - 6 q^{41} + q^{42} - 19 q^{43} + 2 q^{44} - 13 q^{45} - 30 q^{46} + q^{47} + 10 q^{48} + 5 q^{49} + 7 q^{50} - 13 q^{51} - 2 q^{52} + 6 q^{53} - 34 q^{54} - 6 q^{55} - 3 q^{56} + 8 q^{57} - 14 q^{58} + 4 q^{59} + 17 q^{60} - 18 q^{61} - 10 q^{62} + 3 q^{63} - 17 q^{64} + 6 q^{65} + q^{66} + 5 q^{67} - 6 q^{68} - 17 q^{69} - 3 q^{70} - 9 q^{71} + 7 q^{72} - 18 q^{73} + q^{74} + 30 q^{75} - 12 q^{76} + 5 q^{77} - q^{78} - 27 q^{79} + 6 q^{80} - 15 q^{81} - 28 q^{82} + 2 q^{83} - 15 q^{84} + 17 q^{85} - 22 q^{86} + 13 q^{87} - 3 q^{88} - 34 q^{89} - 22 q^{90} - 5 q^{91} + 32 q^{92} + 14 q^{93} + 32 q^{94} + 19 q^{95} + 32 q^{96} - 3 q^{97} + 3 q^{99}+O(q^{100}) $ 5 * q - 4 * q^3 + 2 * q^4 - 6 * q^5 + q^6 + 5 * q^7 - 3 * q^8 + 3 * q^9 - 3 * q^10 + 5 * q^11 - 15 * q^12 - 5 * q^13 - 7 * q^17 + 12 * q^18 - 13 * q^19 + 2 * q^20 - 4 * q^21 - 4 * q^23 - 9 * q^24 - 7 * q^25 + 2 * q^27 + 2 * q^28 + 7 * q^29 - 15 * q^31 + 4 * q^32 - 4 * q^33 - 9 * q^34 - 6 * q^35 + 17 * q^36 - 3 * q^37 - 10 * q^38 + 4 * q^39 - 2 * q^40 - 6 * q^41 + q^42 - 19 * q^43 + 2 * q^44 - 13 * q^45 - 30 * q^46 + q^47 + 10 * q^48 + 5 * q^49 + 7 * q^50 - 13 * q^51 - 2 * q^52 + 6 * q^53 - 34 * q^54 - 6 * q^55 - 3 * q^56 + 8 * q^57 - 14 * q^58 + 4 * q^59 + 17 * q^60 - 18 * q^61 - 10 * q^62 + 3 * q^63 - 17 * q^64 + 6 * q^65 + q^66 + 5 * q^67 - 6 * q^68 - 17 * q^69 - 3 * q^70 - 9 * q^71 + 7 * q^72 - 18 * q^73 + q^74 + 30 * q^75 - 12 * q^76 + 5 * q^77 - q^78 - 27 * q^79 + 6 * q^80 - 15 * q^81 - 28 * q^82 + 2 * q^83 - 15 * q^84 + 17 * q^85 - 22 * q^86 + 13 * q^87 - 3 * q^88 - 34 * q^89 - 22 * q^90 - 5 * q^91 + 32 * q^92 + 14 * q^93 + 32 * q^94 + 19 * q^95 + 32 * q^96 - 3 * q^97 + 3 * 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 $

$2$	0.483735	0.342053	0.171026	−	0.985266i	$-0.445292\pi$
$2$	0.483735	0.342053	0.171026	+	0.985266i	$0.445292\pi$
$3$	−0.0630088	−0.0363782	−0.0181891	−	0.999835i	$-0.505790\pi$
$3$	−0.0630088	−0.0363782	−0.0181891	+	0.999835i	$0.505790\pi$
$4$	−1.76600	−0.883000
$5$	0.713765	0.319206	0.159603	−	0.987181i	$-0.448979\pi$
$5$	0.713765	0.319206	0.159603	+	0.987181i	$0.448979\pi$
$6$	−0.0304796	−0.0124432
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.82175	−0.644085
$9$	−2.99603	−0.998677
$10$	0.345273	0.109185
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.111274	0.0321219
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0.483735	0.129284
$15$	−0.0449735	−0.0116121
$16$	2.65076	0.662689
$17$	0.237291	0.0575516	0.0287758	−	0.999586i	$-0.490839\pi$
$17$	0.237291	0.0575516	0.0287758	+	0.999586i	$0.490839\pi$
$18$	−1.44929	−0.341600
$19$	−1.65473	−0.379620	−0.189810	−	0.981821i	$-0.560787\pi$
$19$	−1.65473	−0.379620	−0.189810	+	0.981821i	$0.560787\pi$
$20$	−1.26051	−0.281858
$21$	−0.0630088	−0.0137496
$22$	0.483735	0.103133
$23$	−2.01971	−0.421138	−0.210569	−	0.977579i	$-0.567532\pi$
$23$	−2.01971	−0.421138	−0.210569	+	0.977579i	$0.567532\pi$
$24$	0.114786	0.0234306
$25$	−4.49054	−0.898108
$26$	−0.483735	−0.0948683
$27$	0.377803	0.0727082
$28$	−1.76600	−0.333743
$29$	−8.65154	−1.60655	−0.803275	−	0.595608i	$-0.796911\pi$
$29$	−8.65154	−1.60655	−0.803275	+	0.595608i	$0.796911\pi$
$30$	−0.0217553	−0.00397195
$31$	−2.07897	−0.373393	−0.186697	−	0.982418i	$-0.559778\pi$
$31$	−2.07897	−0.373393	−0.186697	+	0.982418i	$0.559778\pi$
$32$	4.92576	0.870760
$33$	−0.0630088	−0.0109684
$34$	0.114786	0.0196857
$35$	0.713765	0.120648
$36$	5.29099	0.881832
$37$	−8.06751	−1.32629	−0.663145	−	0.748491i	$-0.730779\pi$
$37$	−8.06751	−1.32629	−0.663145	+	0.748491i	$0.730779\pi$
$38$	−0.800450	−0.129850
$39$	0.0630088	0.0100895
$40$	−1.30030	−0.205595
$41$	−9.06028	−1.41498	−0.707489	−	0.706724i	$-0.750172\pi$
$41$	−9.06028	−1.41498	−0.707489	+	0.706724i	$0.750172\pi$
$42$	−0.0304796	−0.00470310
$43$	0.765543	0.116744	0.0583721	−	0.998295i	$-0.481409\pi$
$43$	0.765543	0.116744	0.0583721	+	0.998295i	$0.481409\pi$
$44$	−1.76600	−0.266235
$45$	−2.13846	−0.318783
$46$	−0.977003	−0.144051
$47$	−1.16184	−0.169472	−0.0847358	−	0.996403i	$-0.527005\pi$
$47$	−1.16184	−0.169472	−0.0847358	+	0.996403i	$0.527005\pi$
$48$	−0.167021	−0.0241074
$49$	1.00000	0.142857
$50$	−2.17223	−0.307200
$51$	−0.0149514	−0.00209362
$52$	1.76600	0.244900
$53$	1.40828	0.193442	0.0967212	−	0.995312i	$-0.469164\pi$
$53$	1.40828	0.193442	0.0967212	+	0.995312i	$0.469164\pi$
$54$	0.182757	0.0248700
$55$	0.713765	0.0962441
$56$	−1.82175	−0.243441
$57$	0.104262	0.0138099
$58$	−4.18506	−0.549525
$59$	8.96099	1.16662	0.583311	−	0.812249i	$-0.301757\pi$
$59$	8.96099	1.16662	0.583311	+	0.812249i	$0.301757\pi$
$60$	0.0794232	0.0102535
$61$	7.64949	0.979417	0.489708	−	0.871886i	$-0.337103\pi$
$61$	7.64949	0.979417	0.489708	+	0.871886i	$0.337103\pi$
$62$	−1.00567	−0.127720
$63$	−2.99603	−0.377464
$64$	−2.91875	−0.364844
$65$	−0.713765	−0.0885317
$66$	−0.0304796	−0.00375178
$67$	−9.51308	−1.16221	−0.581104	−	0.813829i	$-0.697379\pi$
$67$	−9.51308	−1.16221	−0.581104	+	0.813829i	$0.697379\pi$
$68$	−0.419056	−0.0508180
$69$	0.127259	0.0153202
$70$	0.345273	0.0412681
$71$	5.62006	0.666978	0.333489	−	0.942754i	$-0.391774\pi$
$71$	5.62006	0.666978	0.333489	+	0.942754i	$0.391774\pi$
$72$	5.45801	0.643233
$73$	3.82604	0.447805	0.223902	−	0.974612i	$-0.428120\pi$
$73$	3.82604	0.447805	0.223902	+	0.974612i	$0.428120\pi$
$74$	−3.90254	−0.453661
$75$	0.282944	0.0326715
$76$	2.92225	0.335205
$77$	1.00000	0.113961
$78$	0.0304796	0.00345113
$79$	−6.85076	−0.770771	−0.385386	−	0.922756i	$-0.625932\pi$
$79$	−6.85076	−0.770771	−0.385386	+	0.922756i	$0.625932\pi$
$80$	1.89202	0.211534
$81$	8.96428	0.996032
$82$	−4.38278	−0.483997
$83$	−16.6596	−1.82862	−0.914312	−	0.405011i	$-0.867268\pi$
$83$	−16.6596	−1.82862	−0.914312	+	0.405011i	$0.867268\pi$
$84$	0.111274	0.0121409
$85$	0.169370	0.0183708
$86$	0.370320	0.0399326
$87$	0.545123	0.0584433
$88$	−1.82175	−0.194199
$89$	−12.2638	−1.29996	−0.649980	−	0.759951i	$-0.725223\pi$
$89$	−12.2638	−1.29996	−0.649980	+	0.759951i	$0.725223\pi$
$90$	−1.03445	−0.109041
$91$	−1.00000	−0.104828
$92$	3.56680	0.371865
$93$	0.130993	0.0135834
$94$	−0.562022	−0.0579682
$95$	−1.18109	−0.121177
$96$	−0.310366	−0.0316766
$97$	5.97028	0.606190	0.303095	−	0.952960i	$-0.401980\pi$
$97$	5.97028	0.606190	0.303095	+	0.952960i	$0.401980\pi$
$98$	0.483735	0.0488647
$99$	−2.99603	−0.301112
$100$	7.93029	0.793029
$101$	1.30594	0.129946	0.0649730	−	0.997887i	$-0.479304\pi$
$101$	1.30594	0.129946	0.0649730	+	0.997887i	$0.479304\pi$
$102$	−0.00723254	−0.000716128 0
$103$	−11.0803	−1.09178	−0.545889	−	0.837858i	$-0.683808\pi$
$103$	−11.0803	−1.09178	−0.545889	+	0.837858i	$0.683808\pi$
$104$	1.82175	0.178637
$105$	−0.0449735	−0.00438896
$106$	0.681236	0.0661675
$107$	−6.30786	−0.609804	−0.304902	−	0.952384i	$-0.598624\pi$
$107$	−6.30786	−0.609804	−0.304902	+	0.952384i	$0.598624\pi$
$108$	−0.667200	−0.0642013
$109$	3.55196	0.340216	0.170108	−	0.985425i	$-0.445588\pi$
$109$	3.55196	0.340216	0.170108	+	0.985425i	$0.445588\pi$
$110$	0.345273	0.0329205
$111$	0.508324	0.0482480
$112$	2.65076	0.250473
$113$	7.14818	0.672444	0.336222	−	0.941783i	$-0.390851\pi$
$113$	7.14818	0.672444	0.336222	+	0.941783i	$0.390851\pi$
$114$	0.0504354	0.00472371
$115$	−1.44160	−0.134429
$116$	15.2786	1.41858
$117$	2.99603	0.276983
$118$	4.33475	0.399046
$119$	0.237291	0.0217524
$120$	0.0819304	0.00747918
$121$	1.00000	0.0909091
$122$	3.70033	0.335012
$123$	0.570877	0.0514743
$124$	3.67145	0.329706
$125$	−6.77402	−0.605886
$126$	−1.44929	−0.129113
$127$	6.70107	0.594624	0.297312	−	0.954780i	$-0.403910\pi$
$127$	6.70107	0.594624	0.297312	+	0.954780i	$0.403910\pi$
$128$	−11.2634	−0.995555
$129$	−0.0482359	−0.00424694
$130$	−0.345273	−0.0302825
$131$	19.8938	1.73813	0.869064	−	0.494699i	$-0.164722\pi$
$131$	19.8938	1.73813	0.869064	+	0.494699i	$0.164722\pi$
$132$	0.111274	0.00968512
$133$	−1.65473	−0.143483
$134$	−4.60181	−0.397536
$135$	0.269662	0.0232088
$136$	−0.432285	−0.0370681
$137$	18.0673	1.54359	0.771796	−	0.635870i	$-0.219358\pi$
$137$	18.0673	1.54359	0.771796	+	0.635870i	$0.219358\pi$
$138$	0.0615598	0.00524032
$139$	−17.3966	−1.47556	−0.737781	−	0.675040i	$-0.764126\pi$
$139$	−17.3966	−1.47556	−0.737781	+	0.675040i	$0.764126\pi$
$140$	−1.26051	−0.106532
$141$	0.0732060	0.00616506
$142$	2.71862	0.228142
$143$	−1.00000	−0.0836242
$144$	−7.94175	−0.661812
$145$	−6.17517	−0.512820
$146$	1.85079	0.153173
$147$	−0.0630088	−0.00519688
$148$	14.2472	1.17111
$149$	−10.8617	−0.889825	−0.444912	−	0.895574i	$-0.646765\pi$
$149$	−10.8617	−0.889825	−0.444912	+	0.895574i	$0.646765\pi$
$150$	0.136870	0.0111754
$151$	14.9041	1.21288	0.606438	−	0.795130i	$-0.292598\pi$
$151$	14.9041	1.21288	0.606438	+	0.795130i	$0.292598\pi$
$152$	3.01449	0.244508
$153$	−0.710931	−0.0574754
$154$	0.483735	0.0389805
$155$	−1.48389	−0.119189
$156$	−0.111274	−0.00890902
$157$	20.6382	1.64711	0.823554	−	0.567238i	$-0.191988\pi$
$157$	20.6382	1.64711	0.823554	+	0.567238i	$0.191988\pi$
$158$	−3.31396	−0.263644
$159$	−0.0887342	−0.00703708
$160$	3.51584	0.277951
$161$	−2.01971	−0.159175
$162$	4.33634	0.340695
$163$	13.1554	1.03041	0.515207	−	0.857066i	$-0.327715\pi$
$163$	13.1554	1.03041	0.515207	+	0.857066i	$0.327715\pi$
$164$	16.0005	1.24943
$165$	−0.0449735	−0.00350118
$166$	−8.05882	−0.625486
$167$	2.40438	0.186056	0.0930281	−	0.995663i	$-0.470345\pi$
$167$	2.40438	0.186056	0.0930281	+	0.995663i	$0.470345\pi$
$168$	0.114786	0.00885594
$169$	1.00000	0.0769231
$170$	0.0819304	0.00628377
$171$	4.95761	0.379118
$172$	−1.35195	−0.103085
$173$	15.0388	1.14338	0.571690	−	0.820470i	$-0.306288\pi$
$173$	15.0388	1.14338	0.571690	+	0.820470i	$0.306288\pi$
$174$	0.263695	0.0199907
$175$	−4.49054	−0.339453
$176$	2.65076	0.199808
$177$	−0.564622	−0.0424396
$178$	−5.93243	−0.444655
$179$	18.6307	1.39253	0.696264	−	0.717786i	$-0.254844\pi$
$179$	18.6307	1.39253	0.696264	+	0.717786i	$0.254844\pi$
$180$	3.77652	0.281485
$181$	−8.40927	−0.625056	−0.312528	−	0.949908i	$-0.601176\pi$
$181$	−8.40927	−0.625056	−0.312528	+	0.949908i	$0.601176\pi$
$182$	−0.483735	−0.0358569
$183$	−0.481985	−0.0356294
$184$	3.67939	0.271249
$185$	−5.75831	−0.423359
$186$	0.0633660	0.00464622
$187$	0.237291	0.0173524
$188$	2.05181	0.149643
$189$	0.377803	0.0274811
$190$	−0.571333	−0.0414489
$191$	−11.0060	−0.796368	−0.398184	−	0.917306i	$-0.630359\pi$
$191$	−11.0060	−0.796368	−0.398184	+	0.917306i	$0.630359\pi$
$192$	0.183907	0.0132723
$193$	16.4895	1.18694	0.593468	−	0.804857i	$-0.297758\pi$
$193$	16.4895	1.18694	0.593468	+	0.804857i	$0.297758\pi$
$194$	2.88803	0.207349
$195$	0.0449735	0.00322062
$196$	−1.76600	−0.126143
$197$	−7.79167	−0.555134	−0.277567	−	0.960706i	$-0.589528\pi$
$197$	−7.79167	−0.555134	−0.277567	+	0.960706i	$0.589528\pi$
$198$	−1.44929	−0.102996
$199$	0.540046	0.0382828	0.0191414	−	0.999817i	$-0.493907\pi$
$199$	0.540046	0.0382828	0.0191414	+	0.999817i	$0.493907\pi$
$200$	8.18063	0.578458
$201$	0.599408	0.0422790
$202$	0.631730	0.0444483
$203$	−8.65154	−0.607219
$204$	0.0264042	0.00184867
$205$	−6.46691	−0.451669
$206$	−5.35995	−0.373445
$207$	6.05110	0.420580
$208$	−2.65076	−0.183797
$209$	−1.65473	−0.114460
$210$	−0.0217553	−0.00150126
$211$	25.4605	1.75277	0.876385	−	0.481611i	$-0.159948\pi$
$211$	25.4605	1.75277	0.876385	+	0.481611i	$0.159948\pi$
$212$	−2.48703	−0.170810
$213$	−0.354113	−0.0242634
$214$	−3.05133	−0.208585
$215$	0.546418	0.0372654
$216$	−0.688261	−0.0468302
$217$	−2.07897	−0.141129
$218$	1.71821	0.116372
$219$	−0.241074	−0.0162903
$220$	−1.26051	−0.0849835
$221$	−0.237291	−0.0159619
$222$	0.245894	0.0165034
$223$	−25.6873	−1.72015	−0.860075	−	0.510167i	$-0.829584\pi$
$223$	−25.6873	−1.72015	−0.860075	+	0.510167i	$0.829584\pi$
$224$	4.92576	0.329116
$225$	13.4538	0.896919
$226$	3.45783	0.230011
$227$	−23.6059	−1.56678	−0.783388	−	0.621533i	$-0.786510\pi$
$227$	−23.6059	−1.56678	−0.783388	+	0.621533i	$0.786510\pi$
$228$	−0.184127	−0.0121941
$229$	−20.2410	−1.33756	−0.668780	−	0.743460i	$-0.733183\pi$
$229$	−20.2410	−1.33756	−0.668780	+	0.743460i	$0.733183\pi$
$230$	−0.697351	−0.0459820
$231$	−0.0630088	−0.00414568
$232$	15.7609	1.03476
$233$	−8.87431	−0.581375	−0.290688	−	0.956818i	$-0.593884\pi$
$233$	−8.87431	−0.581375	−0.290688	+	0.956818i	$0.593884\pi$
$234$	1.44929	0.0947428
$235$	−0.829280	−0.0540962
$236$	−15.8251	−1.03013
$237$	0.431659	0.0280392
$238$	0.114786	0.00744048
$239$	19.5489	1.26451	0.632257	−	0.774759i	$-0.282129\pi$
$239$	19.5489	1.26451	0.632257	+	0.774759i	$0.282129\pi$
$240$	−0.119214	−0.00769522
$241$	−6.46413	−0.416392	−0.208196	−	0.978087i	$-0.566759\pi$
$241$	−6.46413	−0.416392	−0.208196	+	0.978087i	$0.566759\pi$
$242$	0.483735	0.0310957
$243$	−1.69824	−0.108942
$244$	−13.5090	−0.864825
$245$	0.713765	0.0456008
$246$	0.276154	0.0176069
$247$	1.65473	0.105288
$248$	3.78735	0.240497
$249$	1.04970	0.0665220
$250$	−3.27683	−0.207245
$251$	−9.95546	−0.628383	−0.314191	−	0.949360i	$-0.601733\pi$
$251$	−9.95546	−0.628383	−0.314191	+	0.949360i	$0.601733\pi$
$252$	5.29099	0.333301
$253$	−2.01971	−0.126978
$254$	3.24155	0.203393
$255$	−0.0106718	−0.000668295 0
$256$	0.388981	0.0243113
$257$	2.38326	0.148664	0.0743320	−	0.997234i	$-0.476318\pi$
$257$	2.38326	0.148664	0.0743320	+	0.997234i	$0.476318\pi$
$258$	−0.0233334	−0.00145268
$259$	−8.06751	−0.501291
$260$	1.26051	0.0781735
$261$	25.9203	1.60442
$262$	9.62333	0.594531
$263$	7.36950	0.454423	0.227211	−	0.973845i	$-0.427039\pi$
$263$	7.36950	0.454423	0.227211	+	0.973845i	$0.427039\pi$
$264$	0.114786	0.00706460
$265$	1.00518	0.0617479
$266$	−0.800450	−0.0490787
$267$	0.772727	0.0472902
$268$	16.8001	1.02623
$269$	21.7186	1.32421	0.662104	−	0.749412i	$-0.269664\pi$
$269$	21.7186	1.32421	0.662104	+	0.749412i	$0.269664\pi$
$270$	0.130445	0.00793865
$271$	−13.0778	−0.794417	−0.397208	−	0.917728i	$-0.630021\pi$
$271$	−13.0778	−0.794417	−0.397208	+	0.917728i	$0.630021\pi$
$272$	0.629001	0.0381388
$273$	0.0630088	0.00381347
$274$	8.73979	0.527990
$275$	−4.49054	−0.270790
$276$	−0.224740	−0.0135277
$277$	−20.6094	−1.23830	−0.619149	−	0.785274i	$-0.712522\pi$
$277$	−20.6094	−1.23830	−0.619149	+	0.785274i	$0.712522\pi$
$278$	−8.41536	−0.504720
$279$	6.22864	0.372899
$280$	−1.30030	−0.0777078
$281$	11.7026	0.698118	0.349059	−	0.937101i	$-0.386501\pi$
$281$	11.7026	0.698118	0.349059	+	0.937101i	$0.386501\pi$
$282$	0.0354124	0.00210877
$283$	−14.8207	−0.880999	−0.440500	−	0.897753i	$-0.645199\pi$
$283$	−14.8207	−0.880999	−0.440500	+	0.897753i	$0.645199\pi$
$284$	−9.92502	−0.588941
$285$	0.0744188	0.00440819
$286$	−0.483735	−0.0286039
$287$	−9.06028	−0.534811
$288$	−14.7577	−0.869607
$289$	−16.9437	−0.996688
$290$	−2.98715	−0.175411
$291$	−0.376180	−0.0220521
$292$	−6.75679	−0.395411
$293$	0.457552	0.0267305	0.0133653	−	0.999911i	$-0.495746\pi$
$293$	0.457552	0.0267305	0.0133653	+	0.999911i	$0.495746\pi$
$294$	−0.0304796	−0.00177761
$295$	6.39605	0.372392
$296$	14.6970	0.854244
$297$	0.377803	0.0219223
$298$	−5.25419	−0.304367
$299$	2.01971	0.116803
$300$	−0.499678	−0.0288489
$301$	0.765543	0.0441251
$302$	7.20963	0.414868
$303$	−0.0822858	−0.00472719
$304$	−4.38628	−0.251570
$305$	5.45994	0.312635
$306$	−0.343903	−0.0196596
$307$	−10.2583	−0.585474	−0.292737	−	0.956193i	$-0.594566\pi$
$307$	−10.2583	−0.585474	−0.292737	+	0.956193i	$0.594566\pi$
$308$	−1.76600	−0.100627
$309$	0.698159	0.0397169
$310$	−0.717812	−0.0407690
$311$	−6.90816	−0.391726	−0.195863	−	0.980631i	$-0.562751\pi$
$311$	−6.90816	−0.391726	−0.195863	+	0.980631i	$0.562751\pi$
$312$	−0.114786	−0.00649849
$313$	−11.3818	−0.643340	−0.321670	−	0.946852i	$-0.604244\pi$
$313$	−11.3818	−0.643340	−0.321670	+	0.946852i	$0.604244\pi$
$314$	9.98343	0.563397
$315$	−2.13846	−0.120489
$316$	12.0984	0.680591
$317$	13.4399	0.754859	0.377430	−	0.926038i	$-0.376808\pi$
$317$	13.4399	0.754859	0.377430	+	0.926038i	$0.376808\pi$
$318$	−0.0429239	−0.00240705
$319$	−8.65154	−0.484393
$320$	−2.08330	−0.116460
$321$	0.397451	0.0221835
$322$	−0.977003	−0.0544463
$323$	−0.392652	−0.0218477
$324$	−15.8309	−0.879496
$325$	4.49054	0.249090
$326$	6.36375	0.352456
$327$	−0.223805	−0.0123764
$328$	16.5055	0.911366
$329$	−1.16184	−0.0640542
$330$	−0.0217553	−0.00119759
$331$	−18.7127	−1.02854	−0.514272	−	0.857627i	$-0.671938\pi$
$331$	−18.7127	−1.02854	−0.514272	+	0.857627i	$0.671938\pi$
$332$	29.4208	1.61468
$333$	24.1705	1.32454
$334$	1.16308	0.0636410
$335$	−6.79010	−0.370983
$336$	−0.167021	−0.00911174
$337$	−7.55076	−0.411316	−0.205658	−	0.978624i	$-0.565933\pi$
$337$	−7.55076	−0.411316	−0.205658	+	0.978624i	$0.565933\pi$
$338$	0.483735	0.0263117
$339$	−0.450398	−0.0244623
$340$	−0.299108	−0.0162214
$341$	−2.07897	−0.112582
$342$	2.39817	0.129678
$343$	1.00000	0.0539949
$344$	−1.39463	−0.0751932
$345$	0.0908332	0.00489030
$346$	7.27481	0.391096
$347$	−1.78803	−0.0959867	−0.0479934	−	0.998848i	$-0.515283\pi$
$347$	−1.78803	−0.0959867	−0.0479934	+	0.998848i	$0.515283\pi$
$348$	−0.962688	−0.0516055
$349$	30.9421	1.65629	0.828147	−	0.560511i	$-0.189395\pi$
$349$	30.9421	1.65629	0.828147	+	0.560511i	$0.189395\pi$
$350$	−2.17223	−0.116111
$351$	−0.377803	−0.0201656
$352$	4.92576	0.262544
$353$	−22.1385	−1.17831	−0.589156	−	0.808019i	$-0.700540\pi$
$353$	−22.1385	−1.17831	−0.589156	+	0.808019i	$0.700540\pi$
$354$	−0.273127	−0.0145166
$355$	4.01140	0.212903
$356$	21.6579	1.14786
$357$	−0.0149514	−0.000791314 0
$358$	9.01235	0.476318
$359$	11.8794	0.626972	0.313486	−	0.949593i	$-0.398503\pi$
$359$	11.8794	0.626972	0.313486	+	0.949593i	$0.398503\pi$
$360$	3.89574	0.205323
$361$	−16.2619	−0.855888
$362$	−4.06786	−0.213802
$363$	−0.0630088	−0.00330710
$364$	1.76600	0.0925636
$365$	2.73090	0.142942
$366$	−0.233153	−0.0121871
$367$	−3.71425	−0.193882	−0.0969410	−	0.995290i	$-0.530906\pi$
$367$	−3.71425	−0.193882	−0.0969410	+	0.995290i	$0.530906\pi$
$368$	−5.35375	−0.279083
$369$	27.1449	1.41311
$370$	−2.78550	−0.144811
$371$	1.40828	0.0731144
$372$	−0.231334	−0.0119941
$373$	28.6885	1.48544	0.742718	−	0.669604i	$-0.233536\pi$
$373$	28.6885	1.48544	0.742718	+	0.669604i	$0.233536\pi$
$374$	0.114786	0.00593545
$375$	0.426823	0.0220410
$376$	2.11658	0.109154
$377$	8.65154	0.445577
$378$	0.182757	0.00939998
$379$	−1.98078	−0.101746	−0.0508729	−	0.998705i	$-0.516200\pi$
$379$	−1.98078	−0.101746	−0.0508729	+	0.998705i	$0.516200\pi$
$380$	2.08580	0.106999
$381$	−0.422226	−0.0216313
$382$	−5.32400	−0.272400
$383$	−16.4190	−0.838971	−0.419486	−	0.907762i	$-0.637790\pi$
$383$	−16.4190	−0.838971	−0.419486	+	0.907762i	$0.637790\pi$
$384$	0.709695	0.0362165
$385$	0.713765	0.0363768
$386$	7.97653	0.405995
$387$	−2.29359	−0.116590
$388$	−10.5435	−0.535265
$389$	−26.4578	−1.34146	−0.670732	−	0.741700i	$-0.734020\pi$
$389$	−26.4578	−1.34146	−0.670732	+	0.741700i	$0.734020\pi$
$390$	0.0217553	0.00110162
$391$	−0.479258	−0.0242371
$392$	−1.82175	−0.0920121
$393$	−1.25348	−0.0632299
$394$	−3.76911	−0.189885
$395$	−4.88984	−0.246034
$396$	5.29099	0.265882
$397$	−13.9125	−0.698247	−0.349123	−	0.937077i	$-0.613521\pi$
$397$	−13.9125	−0.698247	−0.349123	+	0.937077i	$0.613521\pi$
$398$	0.261239	0.0130947
$399$	0.104262	0.00521965
$400$	−11.9033	−0.595166
$401$	18.8372	0.940683	0.470341	−	0.882485i	$-0.344131\pi$
$401$	18.8372	0.940683	0.470341	+	0.882485i	$0.344131\pi$
$402$	0.289955	0.0144616
$403$	2.07897	0.103561
$404$	−2.30629	−0.114742
$405$	6.39839	0.317939
$406$	−4.18506	−0.207701
$407$	−8.06751	−0.399892
$408$	0.0272377	0.00134847
$409$	19.6393	0.971099	0.485550	−	0.874209i	$-0.338620\pi$
$409$	19.6393	0.971099	0.485550	+	0.874209i	$0.338620\pi$
$410$	−3.12827	−0.154494
$411$	−1.13840	−0.0561531
$412$	19.5679	0.964040
$413$	8.96099	0.440942
$414$	2.92713	0.143861
$415$	−11.8910	−0.583707
$416$	−4.92576	−0.241505
$417$	1.09614	0.0536782
$418$	−0.800450	−0.0391513
$419$	−23.9624	−1.17064	−0.585320	−	0.810802i	$-0.699031\pi$
$419$	−23.9624	−1.17064	−0.585320	+	0.810802i	$0.699031\pi$
$420$	0.0794232	0.00387546
$421$	−1.23600	−0.0602390	−0.0301195	−	0.999546i	$-0.509589\pi$
$421$	−1.23600	−0.0602390	−0.0301195	+	0.999546i	$0.509589\pi$
$422$	12.3161	0.599540
$423$	3.48090	0.169247
$424$	−2.56553	−0.124593
$425$	−1.06557	−0.0516875
$426$	−0.171297	−0.00829937
$427$	7.64949	0.370185
$428$	11.1397	0.538457
$429$	0.0630088	0.00304209
$430$	0.264322	0.0127467
$431$	−4.83512	−0.232899	−0.116450	−	0.993197i	$-0.537151\pi$
$431$	−4.83512	−0.232899	−0.116450	+	0.993197i	$0.537151\pi$
$432$	1.00146	0.0481829
$433$	−32.8100	−1.57675	−0.788374	−	0.615196i	$-0.789077\pi$
$433$	−32.8100	−1.57675	−0.788374	+	0.615196i	$0.789077\pi$
$434$	−1.00567	−0.0482737
$435$	0.389090	0.0186554
$436$	−6.27275	−0.300410
$437$	3.34206	0.159872
$438$	−0.116616	−0.00557214
$439$	−27.4190	−1.30864	−0.654318	−	0.756219i	$-0.727044\pi$
$439$	−27.4190	−1.30864	−0.654318	+	0.756219i	$0.727044\pi$
$440$	−1.30030	−0.0619894
$441$	−2.99603	−0.142668
$442$	−0.114786	−0.00545982
$443$	−32.1044	−1.52533	−0.762664	−	0.646795i	$-0.776109\pi$
$443$	−32.1044	−1.52533	−0.762664	+	0.646795i	$0.776109\pi$
$444$	−0.897701	−0.0426030
$445$	−8.75347	−0.414954
$446$	−12.4259	−0.588382
$447$	0.684382	0.0323702
$448$	−2.91875	−0.137898
$449$	38.7172	1.82718	0.913589	−	0.406639i	$-0.133299\pi$
$449$	38.7172	1.82718	0.913589	+	0.406639i	$0.133299\pi$
$450$	6.50807	0.306794
$451$	−9.06028	−0.426632
$452$	−12.6237	−0.593768
$453$	−0.939088	−0.0441222
$454$	−11.4190	−0.535920
$455$	−0.713765	−0.0334618
$456$	−0.189940	−0.00889474
$457$	−26.6436	−1.24634	−0.623168	−	0.782088i	$-0.714155\pi$
$457$	−26.6436	−1.24634	−0.623168	+	0.782088i	$0.714155\pi$
$458$	−9.79127	−0.457516
$459$	0.0896493	0.00418447
$460$	2.54586	0.118701
$461$	32.7891	1.52714	0.763571	−	0.645723i	$-0.223444\pi$
$461$	32.7891	1.52714	0.763571	+	0.645723i	$0.223444\pi$
$462$	−0.0304796	−0.00141804
$463$	−17.5077	−0.813650	−0.406825	−	0.913506i	$-0.633364\pi$
$463$	−17.5077	−0.813650	−0.406825	+	0.913506i	$0.633364\pi$
$464$	−22.9331	−1.06464
$465$	0.0934984	0.00433588
$466$	−4.29282	−0.198861
$467$	13.9359	0.644874	0.322437	−	0.946591i	$-0.395498\pi$
$467$	13.9359	0.644874	0.322437	+	0.946591i	$0.395498\pi$
$468$	−5.29099	−0.244576
$469$	−9.51308	−0.439273
$470$	−0.401152	−0.0185038
$471$	−1.30039	−0.0599187
$472$	−16.3247	−0.751404
$473$	0.765543	0.0351997
$474$	0.208808	0.00959089
$475$	7.43061	0.340940
$476$	−0.419056	−0.0192074
$477$	−4.21926	−0.193186
$478$	9.45649	0.432530
$479$	9.94844	0.454556	0.227278	−	0.973830i	$-0.427017\pi$
$479$	9.94844	0.454556	0.227278	+	0.973830i	$0.427017\pi$
$480$	−0.221529	−0.0101114
$481$	8.06751	0.367847
$482$	−3.12693	−0.142428
$483$	0.127259	0.00579050
$484$	−1.76600	−0.0802727
$485$	4.26138	0.193499
$486$	−0.821497	−0.0372639
$487$	6.12497	0.277549	0.138775	−	0.990324i	$-0.455684\pi$
$487$	6.12497	0.277549	0.138775	+	0.990324i	$0.455684\pi$
$488$	−13.9354	−0.630828
$489$	−0.828909	−0.0374845
$490$	0.345273	0.0155979
$491$	−3.53589	−0.159573	−0.0797863	−	0.996812i	$-0.525424\pi$
$491$	−3.53589	−0.159573	−0.0797863	+	0.996812i	$0.525424\pi$
$492$	−1.00817	−0.0454518
$493$	−2.05293	−0.0924595
$494$	0.800450	0.0360139
$495$	−2.13846	−0.0961167
$496$	−5.51083	−0.247444
$497$	5.62006	0.252094
$498$	0.507776	0.0227540
$499$	−11.4774	−0.513800	−0.256900	−	0.966438i	$-0.582701\pi$
$499$	−11.4774	−0.513800	−0.256900	+	0.966438i	$0.582701\pi$
$500$	11.9629	0.534998
$501$	−0.151497	−0.00676838
$502$	−4.81581	−0.214940
$503$	−9.61415	−0.428674	−0.214337	−	0.976760i	$-0.568759\pi$
$503$	−9.61415	−0.428674	−0.214337	+	0.976760i	$0.568759\pi$
$504$	5.45801	0.243119
$505$	0.932135	0.0414795
$506$	−0.977003	−0.0434331
$507$	−0.0630088	−0.00279832
$508$	−11.8341	−0.525053
$509$	−21.8421	−0.968133	−0.484066	−	0.875031i	$-0.660841\pi$
$509$	−21.8421	−0.968133	−0.484066	+	0.875031i	$0.660841\pi$
$510$	−0.00516233	−0.000228592 0
$511$	3.82604	0.169254
$512$	22.7150	1.00387
$513$	−0.625160	−0.0276015
$514$	1.15287	0.0508509
$515$	−7.90876	−0.348502
$516$	0.0851846	0.00375004
$517$	−1.16184	−0.0510976
$518$	−3.90254	−0.171468
$519$	−0.947578	−0.0415941
$520$	1.30030	0.0570219
$521$	26.6730	1.16857	0.584283	−	0.811550i	$-0.301376\pi$
$521$	26.6730	1.16857	0.584283	+	0.811550i	$0.301376\pi$
$522$	12.5386	0.548798
$523$	−32.4129	−1.41732	−0.708658	−	0.705552i	$-0.750699\pi$
$523$	−32.4129	−1.41732	−0.708658	+	0.705552i	$0.750699\pi$
$524$	−35.1324	−1.53477
$525$	0.282944	0.0123487
$526$	3.56489	0.155436
$527$	−0.493320	−0.0214894
$528$	−0.167021	−0.00726866
$529$	−18.9208	−0.822643
$530$	0.486243	0.0211210
$531$	−26.8474	−1.16508
$532$	2.92225	0.126695
$533$	9.06028	0.392444
$534$	0.373796	0.0161757
$535$	−4.50233	−0.194653
$536$	17.3304	0.748560
$537$	−1.17390	−0.0506576
$538$	10.5061	0.452949
$539$	1.00000	0.0430730
$540$	−0.476224	−0.0204934
$541$	−6.24356	−0.268432	−0.134216	−	0.990952i	$-0.542852\pi$
$541$	−6.24356	−0.268432	−0.134216	+	0.990952i	$0.542852\pi$
$542$	−6.32617	−0.271732
$543$	0.529858	0.0227384
$544$	1.16884	0.0501136
$545$	2.53526	0.108599
$546$	0.0304796	0.00130441
$547$	−3.51217	−0.150169	−0.0750847	−	0.997177i	$-0.523923\pi$
$547$	−3.51217	−0.150169	−0.0750847	+	0.997177i	$0.523923\pi$
$548$	−31.9068	−1.36299
$549$	−22.9181	−0.978121
$550$	−2.17223	−0.0926243
$551$	14.3159	0.609879
$552$	−0.231834	−0.00986752
$553$	−6.85076	−0.291324
$554$	−9.96949	−0.423563
$555$	0.362824	0.0154010
$556$	30.7224	1.30292
$557$	28.0108	1.18686	0.593428	−	0.804887i	$-0.297774\pi$
$557$	28.0108	1.18686	0.593428	+	0.804887i	$0.297774\pi$
$558$	3.01302	0.127551
$559$	−0.765543	−0.0323790
$560$	1.89202	0.0799523
$561$	−0.0149514	−0.000631250 0
$562$	5.66096	0.238793
$563$	34.1698	1.44008	0.720042	−	0.693930i	$-0.244122\pi$
$563$	34.1698	1.44008	0.720042	+	0.693930i	$0.244122\pi$
$564$	−0.129282	−0.00544375
$565$	5.10212	0.214648
$566$	−7.16930	−0.301348
$567$	8.96428	0.376465
$568$	−10.2383	−0.429590
$569$	20.1906	0.846435	0.423217	−	0.906028i	$-0.360901\pi$
$569$	20.1906	0.846435	0.423217	+	0.906028i	$0.360901\pi$
$570$	0.0359990	0.00150783
$571$	−39.0244	−1.63312	−0.816561	−	0.577260i	$-0.804122\pi$
$571$	−39.0244	−1.63312	−0.816561	+	0.577260i	$0.804122\pi$
$572$	1.76600	0.0738402
$573$	0.693476	0.0289704
$574$	−4.38278	−0.182934
$575$	9.06957	0.378227
$576$	8.74466	0.364361
$577$	−13.3047	−0.553881	−0.276940	−	0.960887i	$-0.589320\pi$
$577$	−13.3047	−0.553881	−0.276940	+	0.960887i	$0.589320\pi$
$578$	−8.19626	−0.340920
$579$	−1.03898	−0.0431786
$580$	10.9053	0.452820
$581$	−16.6596	−0.691155
$582$	−0.181972	−0.00754296
$583$	1.40828	0.0583251
$584$	−6.97009	−0.288424
$585$	2.13846	0.0884145
$586$	0.221334	0.00914324
$587$	30.7888	1.27079	0.635395	−	0.772187i	$-0.280837\pi$
$587$	30.7888	1.27079	0.635395	+	0.772187i	$0.280837\pi$
$588$	0.111274	0.00458884
$589$	3.44012	0.141748
$590$	3.09399	0.127378
$591$	0.490944	0.0201947
$592$	−21.3850	−0.878919
$593$	23.4197	0.961733	0.480867	−	0.876794i	$-0.340322\pi$
$593$	23.4197	0.961733	0.480867	+	0.876794i	$0.340322\pi$
$594$	0.182757	0.00749859
$595$	0.169370	0.00694350
$596$	19.1818	0.785715
$597$	−0.0340276	−0.00139266
$598$	0.977003	0.0399526
$599$	13.5931	0.555401	0.277700	−	0.960668i	$-0.410428\pi$
$599$	13.5931	0.555401	0.277700	+	0.960668i	$0.410428\pi$
$600$	−0.515452	−0.0210432
$601$	−23.6374	−0.964189	−0.482095	−	0.876119i	$-0.660124\pi$
$601$	−23.6374	−0.964189	−0.482095	+	0.876119i	$0.660124\pi$
$602$	0.370320	0.0150931
$603$	28.5015	1.16067
$604$	−26.3206	−1.07097
$605$	0.713765	0.0290187
$606$	−0.0398045	−0.00161695
$607$	5.59933	0.227270	0.113635	−	0.993523i	$-0.463751\pi$
$607$	5.59933	0.227270	0.113635	+	0.993523i	$0.463751\pi$
$608$	−8.15079	−0.330558
$609$	0.545123	0.0220895
$610$	2.64117	0.106938
$611$	1.16184	0.0470029
$612$	1.25551	0.0507508
$613$	9.31434	0.376203	0.188101	−	0.982150i	$-0.439767\pi$
$613$	9.31434	0.376203	0.188101	+	0.982150i	$0.439767\pi$
$614$	−4.96232	−0.200263
$615$	0.407472	0.0164309
$616$	−1.82175	−0.0734003
$617$	1.61618	0.0650649	0.0325325	−	0.999471i	$-0.489643\pi$
$617$	1.61618	0.0650649	0.0325325	+	0.999471i	$0.489643\pi$
$618$	0.337724	0.0135853
$619$	−28.8923	−1.16128	−0.580640	−	0.814161i	$-0.697197\pi$
$619$	−28.8923	−1.16128	−0.580640	+	0.814161i	$0.697197\pi$
$620$	2.62056	0.105244
$621$	−0.763050	−0.0306202
$622$	−3.34172	−0.133991
$623$	−12.2638	−0.491339
$624$	0.167021	0.00668619
$625$	17.6176	0.704706
$626$	−5.50580	−0.220056
$627$	0.104262	0.00416384
$628$	−36.4471	−1.45440
$629$	−1.91435	−0.0763301
$630$	−1.03445	−0.0412135
$631$	−26.5071	−1.05523	−0.527615	−	0.849484i	$-0.676913\pi$
$631$	−26.5071	−1.05523	−0.527615	+	0.849484i	$0.676913\pi$
$632$	12.4804	0.496442
$633$	−1.60423	−0.0637626
$634$	6.50135	0.258201
$635$	4.78299	0.189807
$636$	0.156705	0.00621374
$637$	−1.00000	−0.0396214
$638$	−4.18506	−0.165688
$639$	−16.8379	−0.666095
$640$	−8.03944	−0.317787
$641$	−22.9892	−0.908019	−0.454009	−	0.890997i	$-0.650007\pi$
$641$	−22.9892	−0.908019	−0.454009	+	0.890997i	$0.650007\pi$
$642$	0.192261	0.00758794
$643$	2.46510	0.0972142	0.0486071	−	0.998818i	$-0.484522\pi$
$643$	2.46510	0.0972142	0.0486071	+	0.998818i	$0.484522\pi$
$644$	3.56680	0.140552
$645$	−0.0344291	−0.00135565
$646$	−0.189940	−0.00747308
$647$	12.1166	0.476351	0.238176	−	0.971222i	$-0.423451\pi$
$647$	12.1166	0.476351	0.238176	+	0.971222i	$0.423451\pi$
$648$	−16.3307	−0.641529
$649$	8.96099	0.351750
$650$	2.17223	0.0852020
$651$	0.130993	0.00513403
$652$	−23.2325	−0.909855
$653$	10.4033	0.407114	0.203557	−	0.979063i	$-0.434750\pi$
$653$	10.4033	0.407114	0.203557	+	0.979063i	$0.434750\pi$
$654$	−0.108262	−0.00423339
$655$	14.1995	0.554820
$656$	−24.0166	−0.937691
$657$	−11.4629	−0.447212
$658$	−0.562022	−0.0219099
$659$	−43.5112	−1.69495	−0.847477	−	0.530832i	$-0.821879\pi$
$659$	−43.5112	−1.69495	−0.847477	+	0.530832i	$0.821879\pi$
$660$	0.0794232	0.00309154
$661$	−33.6698	−1.30961	−0.654803	−	0.755800i	$-0.727248\pi$
$661$	−33.6698	−1.30961	−0.654803	+	0.755800i	$0.727248\pi$
$662$	−9.05201	−0.351816
$663$	0.0149514	0.000580666 0
$664$	30.3495	1.17779
$665$	−1.18109	−0.0458006
$666$	11.6921	0.453061
$667$	17.4736	0.676579
$668$	−4.24613	−0.164288
$669$	1.61853	0.0625759
$670$	−3.28461	−0.126896
$671$	7.64949	0.295305
$672$	−0.310366	−0.0119726
$673$	17.7012	0.682330	0.341165	−	0.940003i	$-0.389178\pi$
$673$	17.7012	0.682330	0.341165	+	0.940003i	$0.389178\pi$
$674$	−3.65257	−0.140692
$675$	−1.69654	−0.0652998
$676$	−1.76600	−0.0679231
$677$	8.94806	0.343902	0.171951	−	0.985105i	$-0.444993\pi$
$677$	8.94806	0.343902	0.171951	+	0.985105i	$0.444993\pi$
$678$	−0.217874	−0.00836738
$679$	5.97028	0.229118
$680$	−0.308550	−0.0118323
$681$	1.48738	0.0569964
$682$	−1.00567	−0.0385091
$683$	39.4494	1.50949	0.754744	−	0.656019i	$-0.227761\pi$
$683$	39.4494	1.50949	0.754744	+	0.656019i	$0.227761\pi$
$684$	−8.75514	−0.334761
$685$	12.8958	0.492723
$686$	0.483735	0.0184691
$687$	1.27536	0.0486580
$688$	2.02927	0.0773651
$689$	−1.40828	−0.0536513
$690$	0.0439392	0.00167274
$691$	−45.0645	−1.71434	−0.857168	−	0.515037i	$-0.827778\pi$
$691$	−45.0645	−1.71434	−0.857168	+	0.515037i	$0.827778\pi$
$692$	−26.5586	−1.00961
$693$	−2.99603	−0.113810
$694$	−0.864935	−0.0328325
$695$	−12.4171	−0.471008
$696$	−0.993077	−0.0376425
$697$	−2.14992	−0.0814342
$698$	14.9678	0.566540
$699$	0.559160	0.0211494
$700$	7.93029	0.299737
$701$	−21.1881	−0.800264	−0.400132	−	0.916457i	$-0.631036\pi$
$701$	−21.1881	−0.800264	−0.400132	+	0.916457i	$0.631036\pi$
$702$	−0.182757	−0.00689770
$703$	13.3495	0.503487
$704$	−2.91875	−0.110004
$705$	0.0522519	0.00196792
$706$	−10.7092	−0.403045
$707$	1.30594	0.0491149
$708$	0.997122	0.0374741
$709$	14.8760	0.558678	0.279339	−	0.960193i	$-0.409885\pi$
$709$	14.8760	0.558678	0.279339	+	0.960193i	$0.409885\pi$
$710$	1.94046	0.0728240
$711$	20.5251	0.769751
$712$	22.3415	0.837285
$713$	4.19890	0.157250
$714$	−0.00723254	−0.000270671 0
$715$	−0.713765	−0.0266933
$716$	−32.9019	−1.22960
$717$	−1.23175	−0.0460007
$718$	5.74650	0.214457
$719$	17.7795	0.663064	0.331532	−	0.943444i	$-0.392435\pi$
$719$	17.7795	0.663064	0.331532	+	0.943444i	$0.392435\pi$
$720$	−5.66854	−0.211254
$721$	−11.0803	−0.412653
$722$	−7.86645	−0.292759
$723$	0.407297	0.0151476
$724$	14.8508	0.551925
$725$	38.8501	1.44286
$726$	−0.0304796	−0.00113120
$727$	−47.8176	−1.77346	−0.886728	−	0.462292i	$-0.847027\pi$
$727$	−47.8176	−1.77346	−0.886728	+	0.462292i	$0.847027\pi$
$728$	1.82175	0.0675185
$729$	−26.7859	−0.992069
$730$	1.32103	0.0488936
$731$	0.181656	0.00671881
$732$	0.851186	0.0314607
$733$	37.0290	1.36770	0.683849	−	0.729623i	$-0.260305\pi$
$733$	37.0290	1.36770	0.683849	+	0.729623i	$0.260305\pi$
$734$	−1.79671	−0.0663179
$735$	−0.0449735	−0.00165887
$736$	−9.94858	−0.366710
$737$	−9.51308	−0.350419
$738$	13.1309	0.483356
$739$	14.5186	0.534075	0.267037	−	0.963686i	$-0.413955\pi$
$739$	14.5186	0.534075	0.267037	+	0.963686i	$0.413955\pi$
$740$	10.1692	0.373826
$741$	−0.104262	−0.00383017
$742$	0.681236	0.0250090
$743$	−21.1228	−0.774920	−0.387460	−	0.921887i	$-0.626647\pi$
$743$	−21.1228	−0.774920	−0.387460	+	0.921887i	$0.626647\pi$
$744$	−0.238636	−0.00874884
$745$	−7.75270	−0.284037
$746$	13.8777	0.508097
$747$	49.9125	1.82620
$748$	−0.419056	−0.0153222
$749$	−6.30786	−0.230484
$750$	0.206469	0.00753919
$751$	34.0000	1.24068	0.620339	−	0.784333i	$-0.286995\pi$
$751$	34.0000	1.24068	0.620339	+	0.784333i	$0.286995\pi$
$752$	−3.07975	−0.112307
$753$	0.627281	0.0228594
$754$	4.18506	0.152411
$755$	10.6380	0.387157
$756$	−0.667200	−0.0242658
$757$	−31.9422	−1.16096	−0.580480	−	0.814275i	$-0.697135\pi$
$757$	−31.9422	−1.16096	−0.580480	+	0.814275i	$0.697135\pi$
$758$	−0.958174	−0.0348024
$759$	0.127259	0.00461922
$760$	2.15164	0.0780482
$761$	−3.03538	−0.110033	−0.0550163	−	0.998485i	$-0.517521\pi$
$761$	−3.03538	−0.110033	−0.0550163	+	0.998485i	$0.517521\pi$
$762$	−0.204246	−0.00739905
$763$	3.55196	0.128589
$764$	19.4366	0.703193
$765$	−0.507438	−0.0183465
$766$	−7.94245	−0.286972
$767$	−8.96099	−0.323563
$768$	−0.0245093	−0.000884402 0
$769$	30.1630	1.08771	0.543853	−	0.839181i	$-0.316965\pi$
$769$	30.1630	1.08771	0.543853	+	0.839181i	$0.316965\pi$
$770$	0.345273	0.0124428
$771$	−0.150167	−0.00540812
$772$	−29.1204	−1.04807
$773$	27.9500	1.00529	0.502647	−	0.864492i	$-0.332360\pi$
$773$	27.9500	1.00529	0.502647	+	0.864492i	$0.332360\pi$
$774$	−1.10949	−0.0398798
$775$	9.33568	0.335347
$776$	−10.8763	−0.390438
$777$	0.508324	0.0182360
$778$	−12.7986	−0.458851
$779$	14.9923	0.537154
$780$	−0.0794232	−0.00284381
$781$	5.62006	0.201101
$782$	−0.231834	−0.00829037
$783$	−3.26858	−0.116809
$784$	2.65076	0.0946699
$785$	14.7308	0.525766
$786$	−0.606355	−0.0216280
$787$	41.3438	1.47375	0.736873	−	0.676031i	$-0.236301\pi$
$787$	41.3438	1.47375	0.736873	+	0.676031i	$0.236301\pi$
$788$	13.7601	0.490183
$789$	−0.464343	−0.0165311
$790$	−2.36539	−0.0841567
$791$	7.14818	0.254160
$792$	5.45801	0.193942
$793$	−7.64949	−0.271641
$794$	−6.72995	−0.238837
$795$	−0.0633354	−0.00224627
$796$	−0.953721	−0.0338037
$797$	6.47018	0.229186	0.114593	−	0.993413i	$-0.463444\pi$
$797$	6.47018	0.229186	0.114593	+	0.993413i	$0.463444\pi$
$798$	0.0504354	0.00178539
$799$	−0.275694	−0.00975335
$800$	−22.1193	−0.782036
$801$	36.7427	1.29824
$802$	9.11220	0.321763
$803$	3.82604	0.135018
$804$	−1.05855	−0.0373323
$805$	−1.44160	−0.0508096
$806$	1.00567	0.0354232
$807$	−1.36846	−0.0481722
$808$	−2.37909	−0.0836962
$809$	19.0040	0.668146	0.334073	−	0.942547i	$-0.391577\pi$
$809$	19.0040	0.668146	0.334073	+	0.942547i	$0.391577\pi$
$810$	3.09513	0.108752
$811$	21.7025	0.762079	0.381040	−	0.924559i	$-0.375566\pi$
$811$	21.7025	0.762079	0.381040	+	0.924559i	$0.375566\pi$
$812$	15.2786	0.536174
$813$	0.824014	0.0288994
$814$	−3.90254	−0.136784
$815$	9.38989	0.328914
$816$	−0.0396326	−0.00138742
$817$	−1.26676	−0.0443184
$818$	9.50021	0.332167
$819$	2.99603	0.104690
$820$	11.4206	0.398824
$821$	5.20191	0.181548	0.0907740	−	0.995872i	$-0.471066\pi$
$821$	5.20191	0.181548	0.0907740	+	0.995872i	$0.471066\pi$
$822$	−0.550684	−0.0192073
$823$	−40.0518	−1.39612	−0.698058	−	0.716041i	$-0.745952\pi$
$823$	−40.0518	−1.39612	−0.698058	+	0.716041i	$0.745952\pi$
$824$	20.1856	0.703198
$825$	0.282944	0.00985083
$826$	4.33475	0.150825
$827$	22.8615	0.794974	0.397487	−	0.917608i	$-0.369882\pi$
$827$	22.8615	0.794974	0.397487	+	0.917608i	$0.369882\pi$
$828$	−10.6862	−0.371373
$829$	−37.6252	−1.30678	−0.653388	−	0.757023i	$-0.726653\pi$
$829$	−37.6252	−1.30678	−0.653388	+	0.757023i	$0.726653\pi$
$830$	−5.75210	−0.199658
$831$	1.29857	0.0450470
$832$	2.91875	0.101189
$833$	0.237291	0.00822165
$834$	0.530242	0.0183608
$835$	1.71616	0.0593902
$836$	2.92225	0.101068
$837$	−0.785439	−0.0271487
$838$	−11.5915	−0.400421
$839$	−53.2267	−1.83759	−0.918796	−	0.394734i	$-0.870837\pi$
$839$	−53.2267	−1.83759	−0.918796	+	0.394734i	$0.870837\pi$
$840$	0.0819304	0.00282687
$841$	45.8492	1.58101
$842$	−0.597897	−0.0206049
$843$	−0.737366	−0.0253962
$844$	−44.9632	−1.54770
$845$	0.713765	0.0245543
$846$	1.68384	0.0578915
$847$	1.00000	0.0343604
$848$	3.73301	0.128192
$849$	0.933835	0.0320491
$850$	−0.515452	−0.0176798
$851$	16.2940	0.558551
$852$	0.625364	0.0214246
$853$	−18.0410	−0.617711	−0.308855	−	0.951109i	$-0.599946\pi$
$853$	−18.0410	−0.617711	−0.308855	+	0.951109i	$0.599946\pi$
$854$	3.70033	0.126623
$855$	3.53857	0.121017
$856$	11.4913	0.392765
$857$	19.9943	0.682992	0.341496	−	0.939883i	$-0.389066\pi$
$857$	19.9943	0.682992	0.341496	+	0.939883i	$0.389066\pi$
$858$	0.0304796	0.00104056
$859$	2.51580	0.0858381	0.0429191	−	0.999079i	$-0.486334\pi$
$859$	2.51580	0.0858381	0.0429191	+	0.999079i	$0.486334\pi$
$860$	−0.964974	−0.0329053
$861$	0.570877	0.0194555
$862$	−2.33892	−0.0796639
$863$	0.173141	0.00589379	0.00294690	−	0.999996i	$-0.499062\pi$
$863$	0.173141	0.00589379	0.00294690	+	0.999996i	$0.499062\pi$
$864$	1.86097	0.0633113
$865$	10.7342	0.364973
$866$	−15.8714	−0.539331
$867$	1.06760	0.0362577
$868$	3.67145	0.124617
$869$	−6.85076	−0.232396
$870$	0.188217	0.00638114
$871$	9.51308	0.322338
$872$	−6.47077	−0.219128
$873$	−17.8871	−0.605387
$874$	1.61667	0.0546848
$875$	−6.77402	−0.229004
$876$	0.425738	0.0143843
$877$	31.8163	1.07436	0.537181	−	0.843467i	$-0.319489\pi$
$877$	31.8163	1.07436	0.537181	+	0.843467i	$0.319489\pi$
$878$	−13.2635	−0.447623
$879$	−0.0288298	−0.000972406 0
$880$	1.89202	0.0637799
$881$	−18.8015	−0.633440	−0.316720	−	0.948519i	$-0.602582\pi$
$881$	−18.8015	−0.633440	−0.316720	+	0.948519i	$0.602582\pi$
$882$	−1.44929	−0.0488000
$883$	22.7854	0.766790	0.383395	−	0.923585i	$-0.374755\pi$
$883$	22.7854	0.766790	0.383395	+	0.923585i	$0.374755\pi$
$884$	0.419056	0.0140944
$885$	−0.403007	−0.0135469
$886$	−15.5300	−0.521742
$887$	−2.92925	−0.0983545	−0.0491773	−	0.998790i	$-0.515660\pi$
$887$	−2.92925	−0.0983545	−0.0491773	+	0.998790i	$0.515660\pi$
$888$	−0.926039	−0.0310758
$889$	6.70107	0.224747
$890$	−4.23437	−0.141936
$891$	8.96428	0.300315
$892$	45.3638	1.51889
$893$	1.92252	0.0643348
$894$	0.331060	0.0110723
$895$	13.2980	0.444502
$896$	−11.2634	−0.376284
$897$	−0.127259	−0.00424906
$898$	18.7289	0.624991
$899$	17.9863	0.599875
$900$	−23.7594	−0.791980
$901$	0.334173	0.0111329
$902$	−4.38278	−0.145931
$903$	−0.0482359	−0.00160519
$904$	−13.0222	−0.433111
$905$	−6.00225	−0.199521
$906$	−0.454270	−0.0150921
$907$	24.1841	0.803021	0.401510	−	0.915854i	$-0.368485\pi$
$907$	24.1841	0.803021	0.401510	+	0.915854i	$0.368485\pi$
$908$	41.6879	1.38346
$909$	−3.91264	−0.129774
$910$	−0.345273	−0.0114457
$911$	5.35497	0.177418	0.0887090	−	0.996058i	$-0.471726\pi$
$911$	5.35497	0.177418	0.0887090	+	0.996058i	$0.471726\pi$
$912$	0.276374	0.00915166
$913$	−16.6596	−0.551351
$914$	−12.8885	−0.426313
$915$	−0.344024	−0.0113731
$916$	35.7455	1.18107
$917$	19.8938	0.656951
$918$	0.0433665	0.00143131
$919$	−5.18148	−0.170921	−0.0854606	−	0.996342i	$-0.527236\pi$
$919$	−5.18148	−0.170921	−0.0854606	+	0.996342i	$0.527236\pi$
$920$	2.62622	0.0865840
$921$	0.646365	0.0212985
$922$	15.8613	0.522363
$923$	−5.62006	−0.184986
$924$	0.111274	0.00366063
$925$	36.2275	1.19115
$926$	−8.46908	−0.278311
$927$	33.1970	1.09033
$928$	−42.6154	−1.39892
$929$	−30.3372	−0.995332	−0.497666	−	0.867369i	$-0.665809\pi$
$929$	−30.3372	−0.995332	−0.497666	+	0.867369i	$0.665809\pi$
$930$	0.0452285	0.00148310
$931$	−1.65473	−0.0542315
$932$	15.6720	0.513354
$933$	0.435275	0.0142503
$934$	6.74127	0.220581
$935$	0.169370	0.00553900
$936$	−5.45801	−0.178401
$937$	31.5306	1.03006	0.515029	−	0.857173i	$-0.327781\pi$
$937$	31.5306	1.03006	0.515029	+	0.857173i	$0.327781\pi$
$938$	−4.60181	−0.150255
$939$	0.717157	0.0234035
$940$	1.46451	0.0477670
$941$	−18.9904	−0.619071	−0.309535	−	0.950888i	$-0.600174\pi$
$941$	−18.9904	−0.619071	−0.309535	+	0.950888i	$0.600174\pi$
$942$	−0.629044	−0.0204954
$943$	18.2991	0.595901
$944$	23.7534	0.773108
$945$	0.269662	0.00877212
$946$	0.370320	0.0120401
$947$	−36.7461	−1.19409	−0.597044	−	0.802208i	$-0.703658\pi$
$947$	−36.7461	−1.19409	−0.597044	+	0.802208i	$0.703658\pi$
$948$	−0.762309	−0.0247586
$949$	−3.82604	−0.124199
$950$	3.59445	0.116619
$951$	−0.846831	−0.0274604
$952$	−0.432285	−0.0140104
$953$	1.51138	0.0489584	0.0244792	−	0.999700i	$-0.492207\pi$
$953$	1.51138	0.0489584	0.0244792	+	0.999700i	$0.492207\pi$
$954$	−2.04100	−0.0660799
$955$	−7.85571	−0.254205
$956$	−34.5234	−1.11657
$957$	0.545123	0.0176213
$958$	4.81241	0.155482
$959$	18.0673	0.583423
$960$	0.131266	0.00423660
$961$	−26.6779	−0.860577
$962$	3.90254	0.125823
$963$	18.8985	0.608997
$964$	11.4157	0.367674
$965$	11.7696	0.378877
$966$	0.0615598	0.00198065
$967$	5.06877	0.163001	0.0815004	−	0.996673i	$-0.474029\pi$
$967$	5.06877	0.163001	0.0815004	+	0.996673i	$0.474029\pi$
$968$	−1.82175	−0.0585532
$969$	0.0247405	0.000794781 0
$970$	2.06138	0.0661869
$971$	−21.7018	−0.696443	−0.348222	−	0.937412i	$-0.613214\pi$
$971$	−21.7018	−0.696443	−0.348222	+	0.937412i	$0.613214\pi$
$972$	2.99909	0.0961958
$973$	−17.3966	−0.557710
$974$	2.96287	0.0949364
$975$	−0.282944	−0.00906145
$976$	20.2769	0.649049
$977$	34.1792	1.09349	0.546744	−	0.837300i	$-0.315867\pi$
$977$	34.1792	1.09349	0.546744	+	0.837300i	$0.315867\pi$
$978$	−0.400972	−0.0128217
$979$	−12.2638	−0.391953
$980$	−1.26051	−0.0402655
$981$	−10.6418	−0.339765
$982$	−1.71044	−0.0545822
$983$	20.6351	0.658157	0.329078	−	0.944303i	$-0.393262\pi$
$983$	20.6351	0.658157	0.329078	+	0.944303i	$0.393262\pi$
$984$	−1.03999	−0.0331538
$985$	−5.56142	−0.177202
$986$	−0.993077	−0.0316260
$987$	0.0732060	0.00233017
$988$	−2.92225	−0.0929691
$989$	−1.54617	−0.0491654
$990$	−1.03445	−0.0328770
$991$	−49.1594	−1.56160	−0.780799	−	0.624782i	$-0.785188\pi$
$991$	−49.1594	−1.56160	−0.780799	+	0.624782i	$0.785188\pi$
$992$	−10.2405	−0.325136
$993$	1.17907	0.0374166
$994$	2.71862	0.0862294
$995$	0.385466	0.0122201
$996$	−1.85377	−0.0587389
$997$	−44.6767	−1.41493	−0.707463	−	0.706750i	$-0.750160\pi$
$997$	−44.6767	−1.41493	−0.707463	+	0.706750i	$0.750160\pi$
$998$	−5.55203	−0.175747
$999$	−3.04793	−0.0964322

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1001.2.a.k.1.3	✓	5
3.2	odd	2		9009.2.a.z.1.3		5
7.6	odd	2		7007.2.a.q.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1001.2.a.k.1.3	✓	5	1.1	even	1	trivial
7007.2.a.q.1.3		5	7.6	odd	2
9009.2.a.z.1.3		5	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1001 = 7 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1001.a (trivial)

\(f(q)\)	\(=\)	\(q+0.483735 q^{2} -0.0630088 q^{3} -1.76600 q^{4} +0.713765 q^{5} -0.0304796 q^{6} +1.00000 q^{7} -1.82175 q^{8} -2.99603 q^{9} +O(q^{10})\)	\(q+0.483735 q^{2} -0.0630088 q^{3} -1.76600 q^{4} +0.713765 q^{5} -0.0304796 q^{6} +1.00000 q^{7} -1.82175 q^{8} -2.99603 q^{9} +0.345273 q^{10} +1.00000 q^{11} +0.111274 q^{12} -1.00000 q^{13} +0.483735 q^{14} -0.0449735 q^{15} +2.65076 q^{16} +0.237291 q^{17} -1.44929 q^{18} -1.65473 q^{19} -1.26051 q^{20} -0.0630088 q^{21} +0.483735 q^{22} -2.01971 q^{23} +0.114786 q^{24} -4.49054 q^{25} -0.483735 q^{26} +0.377803 q^{27} -1.76600 q^{28} -8.65154 q^{29} -0.0217553 q^{30} -2.07897 q^{31} +4.92576 q^{32} -0.0630088 q^{33} +0.114786 q^{34} +0.713765 q^{35} +5.29099 q^{36} -8.06751 q^{37} -0.800450 q^{38} +0.0630088 q^{39} -1.30030 q^{40} -9.06028 q^{41} -0.0304796 q^{42} +0.765543 q^{43} -1.76600 q^{44} -2.13846 q^{45} -0.977003 q^{46} -1.16184 q^{47} -0.167021 q^{48} +1.00000 q^{49} -2.17223 q^{50} -0.0149514 q^{51} +1.76600 q^{52} +1.40828 q^{53} +0.182757 q^{54} +0.713765 q^{55} -1.82175 q^{56} +0.104262 q^{57} -4.18506 q^{58} +8.96099 q^{59} +0.0794232 q^{60} +7.64949 q^{61} -1.00567 q^{62} -2.99603 q^{63} -2.91875 q^{64} -0.713765 q^{65} -0.0304796 q^{66} -9.51308 q^{67} -0.419056 q^{68} +0.127259 q^{69} +0.345273 q^{70} +5.62006 q^{71} +5.45801 q^{72} +3.82604 q^{73} -3.90254 q^{74} +0.282944 q^{75} +2.92225 q^{76} +1.00000 q^{77} +0.0304796 q^{78} -6.85076 q^{79} +1.89202 q^{80} +8.96428 q^{81} -4.38278 q^{82} -16.6596 q^{83} +0.111274 q^{84} +0.169370 q^{85} +0.370320 q^{86} +0.545123 q^{87} -1.82175 q^{88} -12.2638 q^{89} -1.03445 q^{90} -1.00000 q^{91} +3.56680 q^{92} +0.130993 q^{93} -0.562022 q^{94} -1.18109 q^{95} -0.310366 q^{96} +5.97028 q^{97} +0.483735 q^{98} -2.99603 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 4 q^{3} + 2 q^{4} - 6 q^{5} + q^{6} + 5 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 5 * q - 4 * q^3 + 2 * q^4 - 6 * q^5 + q^6 + 5 * q^7 - 3 * q^8 + 3 * q^9	\( 5 q - 4 q^{3} + 2 q^{4} - 6 q^{5} + q^{6} + 5 q^{7} - 3 q^{8} + 3 q^{9} - 3 q^{10} + 5 q^{11} - 15 q^{12} - 5 q^{13} - 7 q^{17} + 12 q^{18} - 13 q^{19} + 2 q^{20} - 4 q^{21} - 4 q^{23} - 9 q^{24} - 7 q^{25} + 2 q^{27} + 2 q^{28} + 7 q^{29} - 15 q^{31} + 4 q^{32} - 4 q^{33} - 9 q^{34} - 6 q^{35} + 17 q^{36} - 3 q^{37} - 10 q^{38} + 4 q^{39} - 2 q^{40} - 6 q^{41} + q^{42} - 19 q^{43} + 2 q^{44} - 13 q^{45} - 30 q^{46} + q^{47} + 10 q^{48} + 5 q^{49} + 7 q^{50} - 13 q^{51} - 2 q^{52} + 6 q^{53} - 34 q^{54} - 6 q^{55} - 3 q^{56} + 8 q^{57} - 14 q^{58} + 4 q^{59} + 17 q^{60} - 18 q^{61} - 10 q^{62} + 3 q^{63} - 17 q^{64} + 6 q^{65} + q^{66} + 5 q^{67} - 6 q^{68} - 17 q^{69} - 3 q^{70} - 9 q^{71} + 7 q^{72} - 18 q^{73} + q^{74} + 30 q^{75} - 12 q^{76} + 5 q^{77} - q^{78} - 27 q^{79} + 6 q^{80} - 15 q^{81} - 28 q^{82} + 2 q^{83} - 15 q^{84} + 17 q^{85} - 22 q^{86} + 13 q^{87} - 3 q^{88} - 34 q^{89} - 22 q^{90} - 5 q^{91} + 32 q^{92} + 14 q^{93} + 32 q^{94} + 19 q^{95} + 32 q^{96} - 3 q^{97} + 3 q^{99}+O(q^{100}) \) 5 * q - 4 * q^3 + 2 * q^4 - 6 * q^5 + q^6 + 5 * q^7 - 3 * q^8 + 3 * q^9 - 3 * q^10 + 5 * q^11 - 15 * q^12 - 5 * q^13 - 7 * q^17 + 12 * q^18 - 13 * q^19 + 2 * q^20 - 4 * q^21 - 4 * q^23 - 9 * q^24 - 7 * q^25 + 2 * q^27 + 2 * q^28 + 7 * q^29 - 15 * q^31 + 4 * q^32 - 4 * q^33 - 9 * q^34 - 6 * q^35 + 17 * q^36 - 3 * q^37 - 10 * q^38 + 4 * q^39 - 2 * q^40 - 6 * q^41 + q^42 - 19 * q^43 + 2 * q^44 - 13 * q^45 - 30 * q^46 + q^47 + 10 * q^48 + 5 * q^49 + 7 * q^50 - 13 * q^51 - 2 * q^52 + 6 * q^53 - 34 * q^54 - 6 * q^55 - 3 * q^56 + 8 * q^57 - 14 * q^58 + 4 * q^59 + 17 * q^60 - 18 * q^61 - 10 * q^62 + 3 * q^63 - 17 * q^64 + 6 * q^65 + q^66 + 5 * q^67 - 6 * q^68 - 17 * q^69 - 3 * q^70 - 9 * q^71 + 7 * q^72 - 18 * q^73 + q^74 + 30 * q^75 - 12 * q^76 + 5 * q^77 - q^78 - 27 * q^79 + 6 * q^80 - 15 * q^81 - 28 * q^82 + 2 * q^83 - 15 * q^84 + 17 * q^85 - 22 * q^86 + 13 * q^87 - 3 * q^88 - 34 * q^89 - 22 * q^90 - 5 * q^91 + 32 * q^92 + 14 * q^93 + 32 * q^94 + 19 * q^95 + 32 * q^96 - 3 * q^97 + 3 * q^99

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