LMFDB - Embedded newform 731.2.a.c.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(1,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, 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("731.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.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:	$5.83706438776$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.2460365.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 6x^{4} + 6x^{3} + 7x^{2} - 7x + 1 $ x^6 - x^5 - 6x^4 + 6x^3 + 7x^2 - 7x + 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			1.3
Root			$1.48737$ of defining polynomial
Character	$\chi$	$=$	731.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.212277 q^{2} -2.83954 q^{3} -1.95494 q^{4} -1.65901 q^{5} +0.602769 q^{6} +2.53919 q^{7} +0.839542 q^{8} +5.06300 q^{9} +O(q^{10})$	\(q-0.212277 q^{2} -2.83954 q^{3} -1.95494 q^{4} -1.65901 q^{5} +0.602769 q^{6} +2.53919 q^{7} +0.839542 q^{8} +5.06300 q^{9} +0.352169 q^{10} +1.11540 q^{11} +5.55113 q^{12} +2.39509 q^{13} -0.539012 q^{14} +4.71083 q^{15} +3.73166 q^{16} -1.00000 q^{17} -1.07476 q^{18} -5.01350 q^{19} +3.24326 q^{20} -7.21014 q^{21} -0.236773 q^{22} +3.24795 q^{23} -2.38391 q^{24} -2.24769 q^{25} -0.508423 q^{26} -5.85797 q^{27} -4.96396 q^{28} -1.28054 q^{29} -1.00000 q^{30} +0.498801 q^{31} -2.47123 q^{32} -3.16722 q^{33} +0.212277 q^{34} -4.21254 q^{35} -9.89785 q^{36} -11.9871 q^{37} +1.06425 q^{38} -6.80097 q^{39} -1.39281 q^{40} +10.5784 q^{41} +1.53055 q^{42} -1.00000 q^{43} -2.18053 q^{44} -8.39957 q^{45} -0.689465 q^{46} +0.400325 q^{47} -10.5962 q^{48} -0.552508 q^{49} +0.477132 q^{50} +2.83954 q^{51} -4.68226 q^{52} -5.37685 q^{53} +1.24351 q^{54} -1.85045 q^{55} +2.13176 q^{56} +14.2360 q^{57} +0.271830 q^{58} +5.21308 q^{59} -9.20938 q^{60} +0.0130677 q^{61} -0.105884 q^{62} +12.8559 q^{63} -6.93874 q^{64} -3.97349 q^{65} +0.672327 q^{66} -8.24406 q^{67} +1.95494 q^{68} -9.22270 q^{69} +0.894226 q^{70} -8.15605 q^{71} +4.25060 q^{72} +5.99199 q^{73} +2.54459 q^{74} +6.38240 q^{75} +9.80108 q^{76} +2.83221 q^{77} +1.44369 q^{78} -1.43914 q^{79} -6.19086 q^{80} +1.44496 q^{81} -2.24555 q^{82} -1.09306 q^{83} +14.0954 q^{84} +1.65901 q^{85} +0.212277 q^{86} +3.63616 q^{87} +0.936422 q^{88} -10.7179 q^{89} +1.78303 q^{90} +6.08160 q^{91} -6.34955 q^{92} -1.41637 q^{93} -0.0849797 q^{94} +8.31744 q^{95} +7.01716 q^{96} -6.18621 q^{97} +0.117285 q^{98} +5.64725 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} - 3 q^{3} + 5 q^{4} + 3 q^{5} - 7 q^{6} - 7 q^{7} - 9 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q - q^2 - 3 * q^3 + 5 * q^4 + 3 * q^5 - 7 * q^6 - 7 * q^7 - 9 * q^8 - 3 * q^9	\( 6 q - q^{2} - 3 q^{3} + 5 q^{4} + 3 q^{5} - 7 q^{6} - 7 q^{7} - 9 q^{8} - 3 q^{9} - 4 q^{10} + 4 q^{11} + 11 q^{12} - 10 q^{13} - 7 q^{14} + q^{15} - q^{16} - 6 q^{17} + q^{18} - 20 q^{19} + q^{20} - 8 q^{21} + 2 q^{22} - 3 q^{23} - 9 q^{24} - 7 q^{25} - 3 q^{26} - 6 q^{27} - 11 q^{28} - 15 q^{29} - 6 q^{30} + 12 q^{31} + q^{32} - 2 q^{33} + q^{34} - 9 q^{35} - 16 q^{36} - 14 q^{37} + 27 q^{38} + 5 q^{39} - 7 q^{40} - 2 q^{41} + 19 q^{42} - 6 q^{43} - 12 q^{44} - 18 q^{45} + 14 q^{46} - 11 q^{47} - 6 q^{48} + 3 q^{49} + 7 q^{50} + 3 q^{51} - 5 q^{52} + 3 q^{53} + 25 q^{54} + 6 q^{55} + 22 q^{56} + 11 q^{57} - 21 q^{58} + 2 q^{59} - q^{60} - 20 q^{61} + 3 q^{62} + 23 q^{63} - 39 q^{64} - 34 q^{65} + 7 q^{66} - 2 q^{67} - 5 q^{68} - 17 q^{69} - q^{70} + q^{71} + 21 q^{72} + 13 q^{73} + 28 q^{74} - 5 q^{75} - 29 q^{76} - 11 q^{77} - 26 q^{79} + 12 q^{80} + 2 q^{81} - 9 q^{82} + 10 q^{83} - 3 q^{84} - 3 q^{85} + q^{86} + 12 q^{87} - 6 q^{88} - 15 q^{89} + 15 q^{90} + 8 q^{91} - 9 q^{92} - 11 q^{93} - 33 q^{94} - 21 q^{95} + 25 q^{96} - 22 q^{97} - 3 q^{98} - 5 q^{99}+O(q^{100}) \) 6 * q - q^2 - 3 * q^3 + 5 * q^4 + 3 * q^5 - 7 * q^6 - 7 * q^7 - 9 * q^8 - 3 * q^9 - 4 * q^10 + 4 * q^11 + 11 * q^12 - 10 * q^13 - 7 * q^14 + q^15 - q^16 - 6 * q^17 + q^18 - 20 * q^19 + q^20 - 8 * q^21 + 2 * q^22 - 3 * q^23 - 9 * q^24 - 7 * q^25 - 3 * q^26 - 6 * q^27 - 11 * q^28 - 15 * q^29 - 6 * q^30 + 12 * q^31 + q^32 - 2 * q^33 + q^34 - 9 * q^35 - 16 * q^36 - 14 * q^37 + 27 * q^38 + 5 * q^39 - 7 * q^40 - 2 * q^41 + 19 * q^42 - 6 * q^43 - 12 * q^44 - 18 * q^45 + 14 * q^46 - 11 * q^47 - 6 * q^48 + 3 * q^49 + 7 * q^50 + 3 * q^51 - 5 * q^52 + 3 * q^53 + 25 * q^54 + 6 * q^55 + 22 * q^56 + 11 * q^57 - 21 * q^58 + 2 * q^59 - q^60 - 20 * q^61 + 3 * q^62 + 23 * q^63 - 39 * q^64 - 34 * q^65 + 7 * q^66 - 2 * q^67 - 5 * q^68 - 17 * q^69 - q^70 + q^71 + 21 * q^72 + 13 * q^73 + 28 * q^74 - 5 * q^75 - 29 * q^76 - 11 * q^77 - 26 * q^79 + 12 * q^80 + 2 * q^81 - 9 * q^82 + 10 * q^83 - 3 * q^84 - 3 * q^85 + q^86 + 12 * q^87 - 6 * q^88 - 15 * q^89 + 15 * q^90 + 8 * q^91 - 9 * q^92 - 11 * q^93 - 33 * q^94 - 21 * q^95 + 25 * q^96 - 22 * q^97 - 3 * q^98 - 5 * 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 $

$2$	−0.212277	−0.150102	−0.0750512	−	0.997180i	$-0.523912\pi$
$2$	−0.212277	−0.150102	−0.0750512	+	0.997180i	$0.523912\pi$
$3$	−2.83954	−1.63941	−0.819705	−	0.572786i	$-0.805863\pi$
$3$	−2.83954	−1.63941	−0.819705	+	0.572786i	$0.805863\pi$
$4$	−1.95494	−0.977469
$5$	−1.65901	−0.741932	−0.370966	−	0.928646i	$-0.620973\pi$
$5$	−1.65901	−0.741932	−0.370966	+	0.928646i	$0.620973\pi$
$6$	0.602769	0.246079
$7$	2.53919	0.959724	0.479862	−	0.877344i	$-0.340687\pi$
$7$	2.53919	0.959724	0.479862	+	0.877344i	$0.340687\pi$
$8$	0.839542	0.296823
$9$	5.06300	1.68767
$10$	0.352169	0.111366
$11$	1.11540	0.336305	0.168152	−	0.985761i	$-0.446220\pi$
$11$	1.11540	0.336305	0.168152	+	0.985761i	$0.446220\pi$
$12$	5.55113	1.60247
$13$	2.39509	0.664280	0.332140	−	0.943230i	$-0.392229\pi$
$13$	2.39509	0.664280	0.332140	+	0.943230i	$0.392229\pi$
$14$	−0.539012	−0.144057
$15$	4.71083	1.21633
$16$	3.73166	0.932915
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.07476	−0.253323
$19$	−5.01350	−1.15017	−0.575087	−	0.818092i	$-0.695032\pi$
$19$	−5.01350	−1.15017	−0.575087	+	0.818092i	$0.695032\pi$
$20$	3.24326	0.725216
$21$	−7.21014	−1.57338
$22$	−0.236773	−0.0504801
$23$	3.24795	0.677245	0.338622	−	0.940922i	$-0.390039\pi$
$23$	3.24795	0.677245	0.338622	+	0.940922i	$0.390039\pi$
$24$	−2.38391	−0.486615
$25$	−2.24769	−0.449537
$26$	−0.508423	−0.0997100
$27$	−5.85797	−1.12737
$28$	−4.96396	−0.938101
$29$	−1.28054	−0.237791	−0.118896	−	0.992907i	$-0.537935\pi$
$29$	−1.28054	−0.237791	−0.118896	+	0.992907i	$0.537935\pi$
$30$	−1.00000	−0.182574
$31$	0.498801	0.0895873	0.0447936	−	0.998996i	$-0.485737\pi$
$31$	0.498801	0.0895873	0.0447936	+	0.998996i	$0.485737\pi$
$32$	−2.47123	−0.436856
$33$	−3.16722	−0.551341
$34$	0.212277	0.0364052
$35$	−4.21254	−0.712050
$36$	−9.89785	−1.64964
$37$	−11.9871	−1.97067	−0.985336	−	0.170625i	$-0.945421\pi$
$37$	−11.9871	−1.97067	−0.985336	+	0.170625i	$0.945421\pi$
$38$	1.06425	0.172644
$39$	−6.80097	−1.08903
$40$	−1.39281	−0.220222
$41$	10.5784	1.65207	0.826036	−	0.563617i	$-0.190591\pi$
$41$	10.5784	1.65207	0.826036	+	0.563617i	$0.190591\pi$
$42$	1.53055	0.236168
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−2.18053	−0.328728
$45$	−8.39957	−1.25213
$46$	−0.689465	−0.101656
$47$	0.400325	0.0583934	0.0291967	−	0.999574i	$-0.490705\pi$
$47$	0.400325	0.0583934	0.0291967	+	0.999574i	$0.490705\pi$
$48$	−10.5962	−1.52943
$49$	−0.552508	−0.0789297
$50$	0.477132	0.0674766
$51$	2.83954	0.397615
$52$	−4.68226	−0.649313
$53$	−5.37685	−0.738566	−0.369283	−	0.929317i	$-0.620397\pi$
$53$	−5.37685	−0.738566	−0.369283	+	0.929317i	$0.620397\pi$
$54$	1.24351	0.169221
$55$	−1.85045	−0.249515
$56$	2.13176	0.284868
$57$	14.2360	1.88561
$58$	0.271830	0.0356930
$59$	5.21308	0.678685	0.339342	−	0.940663i	$-0.389796\pi$
$59$	5.21308	0.678685	0.339342	+	0.940663i	$0.389796\pi$
$60$	−9.20938	−1.18893
$61$	0.0130677	0.00167314	0.000836571	−	1.00000i	$-0.499734\pi$
$61$	0.0130677	0.00167314	0.000836571		1.00000i	$0.499734\pi$
$62$	−0.105884	−0.0134473
$63$	12.8559	1.61969
$64$	−6.93874	−0.867342
$65$	−3.97349	−0.492850
$66$	0.672327	0.0827577
$67$	−8.24406	−1.00717	−0.503586	−	0.863945i	$-0.667986\pi$
$67$	−8.24406	−1.00717	−0.503586	+	0.863945i	$0.667986\pi$
$68$	1.95494	0.237071
$69$	−9.22270	−1.11028
$70$	0.894226	0.106880
$71$	−8.15605	−0.967946	−0.483973	−	0.875083i	$-0.660807\pi$
$71$	−8.15605	−0.967946	−0.483973	+	0.875083i	$0.660807\pi$
$72$	4.25060	0.500938
$73$	5.99199	0.701310	0.350655	−	0.936505i	$-0.385959\pi$
$73$	5.99199	0.701310	0.350655	+	0.936505i	$0.385959\pi$
$74$	2.54459	0.295803
$75$	6.38240	0.736976
$76$	9.80108	1.12426
$77$	2.83221	0.322760
$78$	1.44369	0.163466
$79$	−1.43914	−0.161916	−0.0809579	−	0.996718i	$-0.525798\pi$
$79$	−1.43914	−0.161916	−0.0809579	+	0.996718i	$0.525798\pi$
$80$	−6.19086	−0.692160
$81$	1.44496	0.160551
$82$	−2.24555	−0.247980
$83$	−1.09306	−0.119978	−0.0599892	−	0.998199i	$-0.519107\pi$
$83$	−1.09306	−0.119978	−0.0599892	+	0.998199i	$0.519107\pi$
$84$	14.0954	1.53793
$85$	1.65901	0.179945
$86$	0.212277	0.0228904
$87$	3.63616	0.389837
$88$	0.936422	0.0998229
$89$	−10.7179	−1.13610	−0.568048	−	0.822995i	$-0.692301\pi$
$89$	−10.7179	−1.13610	−0.568048	+	0.822995i	$0.692301\pi$
$90$	1.78303	0.187948
$91$	6.08160	0.637525
$92$	−6.34955	−0.661986
$93$	−1.41637	−0.146870
$94$	−0.0849797	−0.00876499
$95$	8.31744	0.853351
$96$	7.01716	0.716186
$97$	−6.18621	−0.628115	−0.314057	−	0.949404i	$-0.601688\pi$
$97$	−6.18621	−0.628115	−0.314057	+	0.949404i	$0.601688\pi$
$98$	0.117285	0.0118475
$99$	5.64725	0.567570
$100$	4.39409	0.439409
$101$	−1.95718	−0.194747	−0.0973736	−	0.995248i	$-0.531044\pi$
$101$	−1.95718	−0.194747	−0.0973736	+	0.995248i	$0.531044\pi$
$102$	−0.602769	−0.0596830
$103$	7.26547	0.715888	0.357944	−	0.933743i	$-0.383478\pi$
$103$	7.26547	0.715888	0.357944	+	0.933743i	$0.383478\pi$
$104$	2.01078	0.197173
$105$	11.9617	1.16734
$106$	1.14138	0.110861
$107$	8.14989	0.787880	0.393940	−	0.919136i	$-0.371112\pi$
$107$	8.14989	0.787880	0.393940	+	0.919136i	$0.371112\pi$
$108$	11.4520	1.10197
$109$	−16.1863	−1.55036	−0.775181	−	0.631739i	$-0.782342\pi$
$109$	−16.1863	−1.55036	−0.775181	+	0.631739i	$0.782342\pi$
$110$	0.392809	0.0374528
$111$	34.0380	3.23074
$112$	9.47540	0.895341
$113$	4.46484	0.420017	0.210008	−	0.977700i	$-0.432651\pi$
$113$	4.46484	0.420017	0.210008	+	0.977700i	$0.432651\pi$
$114$	−3.02198	−0.283034
$115$	−5.38839	−0.502470
$116$	2.50339	0.232433
$117$	12.1264	1.12108
$118$	−1.10662	−0.101872
$119$	−2.53919	−0.232767
$120$	3.95494	0.361035
$121$	−9.75589	−0.886899
$122$	−0.00277396	−0.000251143 0
$123$	−30.0379	−2.70842
$124$	−0.975125	−0.0875688
$125$	12.0240	1.07546
$126$	−2.72901	−0.243120
$127$	−0.291837	−0.0258963	−0.0129482	−	0.999916i	$-0.504122\pi$
$127$	−0.291837	−0.0258963	−0.0129482	+	0.999916i	$0.504122\pi$
$128$	6.41539	0.567046
$129$	2.83954	0.250008
$130$	0.843479	0.0739780
$131$	0.474123	0.0414243	0.0207122	−	0.999785i	$-0.493407\pi$
$131$	0.474123	0.0414243	0.0207122	+	0.999785i	$0.493407\pi$
$132$	6.19171	0.538919
$133$	−12.7302	−1.10385
$134$	1.75002	0.151179
$135$	9.71843	0.836430
$136$	−0.839542	−0.0719901
$137$	−19.1328	−1.63463	−0.817314	−	0.576192i	$-0.804538\pi$
$137$	−19.1328	−1.63463	−0.817314	+	0.576192i	$0.804538\pi$
$138$	1.95777	0.166656
$139$	−9.70162	−0.822881	−0.411440	−	0.911437i	$-0.634974\pi$
$139$	−9.70162	−0.822881	−0.411440	+	0.911437i	$0.634974\pi$
$140$	8.23526	0.696007
$141$	−1.13674	−0.0957307
$142$	1.73134	0.145291
$143$	2.67148	0.223400
$144$	18.8934	1.57445
$145$	2.12444	0.176425
$146$	−1.27196	−0.105268
$147$	1.56887	0.129398
$148$	23.4341	1.92627
$149$	−20.2460	−1.65861	−0.829307	−	0.558793i	$-0.811265\pi$
$149$	−20.2460	−1.65861	−0.829307	+	0.558793i	$0.811265\pi$
$150$	−1.35484	−0.110622
$151$	−5.52591	−0.449692	−0.224846	−	0.974394i	$-0.572188\pi$
$151$	−5.52591	−0.449692	−0.224846	+	0.974394i	$0.572188\pi$
$152$	−4.20904	−0.341398
$153$	−5.06300	−0.409319
$154$	−0.601212	−0.0484470
$155$	−0.827516	−0.0664677
$156$	13.2955	1.06449
$157$	−8.65527	−0.690766	−0.345383	−	0.938462i	$-0.612251\pi$
$157$	−8.65527	−0.690766	−0.345383	+	0.938462i	$0.612251\pi$
$158$	0.305496	0.0243040
$159$	15.2678	1.21081
$160$	4.09979	0.324117
$161$	8.24717	0.649968
$162$	−0.306731	−0.0240991
$163$	19.2922	1.51108	0.755541	−	0.655102i	$-0.227374\pi$
$163$	19.2922	1.51108	0.755541	+	0.655102i	$0.227374\pi$
$164$	−20.6802	−1.61485
$165$	5.25444	0.409058
$166$	0.232030	0.0180091
$167$	2.26648	0.175385	0.0876926	−	0.996148i	$-0.472051\pi$
$167$	2.26648	0.175385	0.0876926	+	0.996148i	$0.472051\pi$
$168$	−6.05322	−0.467016
$169$	−7.26352	−0.558733
$170$	−0.352169	−0.0270102
$171$	−25.3833	−1.94111
$172$	1.95494	0.149063
$173$	−2.78795	−0.211964	−0.105982	−	0.994368i	$-0.533799\pi$
$173$	−2.78795	−0.211964	−0.105982	+	0.994368i	$0.533799\pi$
$174$	−0.771872	−0.0585155
$175$	−5.70730	−0.431432
$176$	4.16228	0.313744
$177$	−14.8027	−1.11264
$178$	2.27517	0.170531
$179$	−24.8463	−1.85710	−0.928549	−	0.371209i	$-0.878943\pi$
$179$	−24.8463	−1.85710	−0.928549	+	0.371209i	$0.878943\pi$
$180$	16.4206	1.22392
$181$	−1.71039	−0.127132	−0.0635662	−	0.997978i	$-0.520247\pi$
$181$	−1.71039	−0.127132	−0.0635662	+	0.997978i	$0.520247\pi$
$182$	−1.29098	−0.0956941
$183$	−0.0371062	−0.00274297
$184$	2.72679	0.201022
$185$	19.8868	1.46210
$186$	0.300662	0.0220456
$187$	−1.11540	−0.0815659
$188$	−0.782611	−0.0570778
$189$	−14.8745	−1.08196
$190$	−1.76560	−0.128090
$191$	20.5373	1.48602	0.743012	−	0.669278i	$-0.233397\pi$
$191$	20.5373	1.48602	0.743012	+	0.669278i	$0.233397\pi$
$192$	19.7028	1.42193
$193$	−13.1576	−0.947105	−0.473553	−	0.880766i	$-0.657029\pi$
$193$	−13.1576	−0.947105	−0.473553	+	0.880766i	$0.657029\pi$
$194$	1.31319	0.0942815
$195$	11.2829	0.807984
$196$	1.08012	0.0771513
$197$	15.4265	1.09909	0.549547	−	0.835463i	$-0.314800\pi$
$197$	15.4265	1.09909	0.549547	+	0.835463i	$0.314800\pi$
$198$	−1.19878	−0.0851936
$199$	9.69335	0.687144	0.343572	−	0.939126i	$-0.388363\pi$
$199$	9.69335	0.687144	0.343572	+	0.939126i	$0.388363\pi$
$200$	−1.88703	−0.133433
$201$	23.4094	1.65117
$202$	0.415465	0.0292320
$203$	−3.25155	−0.228214
$204$	−5.55113	−0.388657
$205$	−17.5497	−1.22572
$206$	−1.54229	−0.107457
$207$	16.4444	1.14296
$208$	8.93768	0.619717
$209$	−5.59204	−0.386809
$210$	−2.53919	−0.175221
$211$	−20.9824	−1.44449	−0.722244	−	0.691639i	$-0.756889\pi$
$211$	−20.9824	−1.44449	−0.722244	+	0.691639i	$0.756889\pi$
$212$	10.5114	0.721926
$213$	23.1595	1.58686
$214$	−1.73003	−0.118263
$215$	1.65901	0.113144
$216$	−4.91801	−0.334628
$217$	1.26655	0.0859791
$218$	3.43597	0.232713
$219$	−17.0145	−1.14973
$220$	3.61752	0.243893
$221$	−2.39509	−0.161111
$222$	−7.22547	−0.484942
$223$	14.4719	0.969109	0.484555	−	0.874761i	$-0.338982\pi$
$223$	14.4719	0.969109	0.484555	+	0.874761i	$0.338982\pi$
$224$	−6.27492	−0.419261
$225$	−11.3800	−0.758668
$226$	−0.947783	−0.0630456
$227$	19.4270	1.28941	0.644706	−	0.764430i	$-0.276980\pi$
$227$	19.4270	1.28941	0.644706	+	0.764430i	$0.276980\pi$
$228$	−27.8306	−1.84312
$229$	−17.1473	−1.13312	−0.566562	−	0.824019i	$-0.691727\pi$
$229$	−17.1473	−1.13312	−0.566562	+	0.824019i	$0.691727\pi$
$230$	1.14383	0.0754219
$231$	−8.04217	−0.529136
$232$	−1.07507	−0.0705818
$233$	−1.27543	−0.0835559	−0.0417780	−	0.999127i	$-0.513302\pi$
$233$	−1.27543	−0.0835559	−0.0417780	+	0.999127i	$0.513302\pi$
$234$	−2.57415	−0.168277
$235$	−0.664143	−0.0433239
$236$	−10.1912	−0.663393
$237$	4.08650	0.265446
$238$	0.539012	0.0349389
$239$	−9.91245	−0.641183	−0.320592	−	0.947218i	$-0.603882\pi$
$239$	−9.91245	−0.641183	−0.320592	+	0.947218i	$0.603882\pi$
$240$	17.5792	1.13473
$241$	−29.4709	−1.89839	−0.949193	−	0.314694i	$-0.898098\pi$
$241$	−29.4709	−1.89839	−0.949193	+	0.314694i	$0.898098\pi$
$242$	2.07095	0.133126
$243$	13.4709	0.864158
$244$	−0.0255465	−0.00163544
$245$	0.916616	0.0585604
$246$	6.37635	0.406541
$247$	−12.0078	−0.764038
$248$	0.418764	0.0265916
$249$	3.10378	0.196694
$250$	−2.55241	−0.161429
$251$	16.6596	1.05155	0.525774	−	0.850624i	$-0.323776\pi$
$251$	16.6596	1.05155	0.525774	+	0.850624i	$0.323776\pi$
$252$	−25.1325	−1.58320
$253$	3.62276	0.227761
$254$	0.0619502	0.00388710
$255$	−4.71083	−0.295004
$256$	12.5156	0.782227
$257$	−13.6655	−0.852434	−0.426217	−	0.904621i	$-0.640154\pi$
$257$	−13.6655	−0.852434	−0.426217	+	0.904621i	$0.640154\pi$
$258$	−0.602769	−0.0375268
$259$	−30.4376	−1.89130
$260$	7.76792	0.481746
$261$	−6.48339	−0.401312
$262$	−0.100645	−0.00621789
$263$	−13.8793	−0.855835	−0.427917	−	0.903818i	$-0.640753\pi$
$263$	−13.8793	−0.855835	−0.427917	+	0.903818i	$0.640753\pi$
$264$	−2.65901	−0.163651
$265$	8.92024	0.547966
$266$	2.70233	0.165691
$267$	30.4340	1.86253
$268$	16.1166	0.984480
$269$	−1.13342	−0.0691057	−0.0345528	−	0.999403i	$-0.511001\pi$
$269$	−1.13342	−0.0691057	−0.0345528	+	0.999403i	$0.511001\pi$
$270$	−2.06300	−0.125550
$271$	15.3569	0.932868	0.466434	−	0.884556i	$-0.345538\pi$
$271$	15.3569	0.932868	0.466434	+	0.884556i	$0.345538\pi$
$272$	−3.73166	−0.226265
$273$	−17.2690	−1.04517
$274$	4.06146	0.245362
$275$	−2.50706	−0.151181
$276$	18.0298	1.08527
$277$	24.7714	1.48837	0.744183	−	0.667975i	$-0.232839\pi$
$277$	24.7714	1.48837	0.744183	+	0.667975i	$0.232839\pi$
$278$	2.05943	0.123516
$279$	2.52543	0.151193
$280$	−3.53661	−0.211353
$281$	−0.0469321	−0.00279973	−0.00139987	−	0.999999i	$-0.500446\pi$
$281$	−0.0469321	−0.00279973	−0.00139987	+	0.999999i	$0.500446\pi$
$282$	0.241304	0.0143694
$283$	−16.9012	−1.00467	−0.502335	−	0.864673i	$-0.667526\pi$
$283$	−16.9012	−1.00467	−0.502335	+	0.864673i	$0.667526\pi$
$284$	15.9446	0.946137
$285$	−23.6177	−1.39899
$286$	−0.567093	−0.0335329
$287$	26.8606	1.58553
$288$	−12.5118	−0.737267
$289$	1.00000	0.0588235
$290$	−0.450969	−0.0264818
$291$	17.5660	1.02974
$292$	−11.7140	−0.685509
$293$	30.8356	1.80143	0.900717	−	0.434407i	$-0.143042\pi$
$293$	30.8356	1.80143	0.900717	+	0.434407i	$0.143042\pi$
$294$	−0.333035	−0.0194230
$295$	−8.64854	−0.503538
$296$	−10.0637	−0.584941
$297$	−6.53396	−0.379139
$298$	4.29775	0.248962
$299$	7.77915	0.449880
$300$	−12.4772	−0.720371
$301$	−2.53919	−0.146357
$302$	1.17302	0.0674999
$303$	5.55751	0.319271
$304$	−18.7087	−1.07302
$305$	−0.0216794	−0.00124136
$306$	1.07476	0.0614398
$307$	3.07155	0.175303	0.0876513	−	0.996151i	$-0.472064\pi$
$307$	3.07155	0.175303	0.0876513	+	0.996151i	$0.472064\pi$
$308$	−5.53679	−0.315488
$309$	−20.6306	−1.17363
$310$	0.175662	0.00997696
$311$	−32.2382	−1.82806	−0.914030	−	0.405646i	$-0.867047\pi$
$311$	−32.2382	−1.82806	−0.914030	+	0.405646i	$0.867047\pi$
$312$	−5.70970	−0.323248
$313$	0.706328	0.0399240	0.0199620	−	0.999801i	$-0.493645\pi$
$313$	0.706328	0.0399240	0.0199620	+	0.999801i	$0.493645\pi$
$314$	1.83731	0.103686
$315$	−21.3281	−1.20170
$316$	2.81343	0.158268
$317$	11.8604	0.666148	0.333074	−	0.942901i	$-0.391914\pi$
$317$	11.8604	0.666148	0.333074	+	0.942901i	$0.391914\pi$
$318$	−3.24100	−0.181746
$319$	−1.42831	−0.0799703
$320$	11.5114	0.643509
$321$	−23.1420	−1.29166
$322$	−1.75068	−0.0975618
$323$	5.01350	0.278958
$324$	−2.82480	−0.156934
$325$	−5.38342	−0.298618
$326$	−4.09529	−0.226817
$327$	45.9616	2.54168
$328$	8.88103	0.490373
$329$	1.01650	0.0560416
$330$	−1.11540	−0.0614006
$331$	−24.7566	−1.36075	−0.680373	−	0.732866i	$-0.738182\pi$
$331$	−24.7566	−1.36075	−0.680373	+	0.732866i	$0.738182\pi$
$332$	2.13686	0.117275
$333$	−60.6908	−3.32584
$334$	−0.481120	−0.0263257
$335$	13.6770	0.747253
$336$	−26.9058	−1.46783
$337$	13.2780	0.723296	0.361648	−	0.932315i	$-0.382214\pi$
$337$	13.2780	0.723296	0.361648	+	0.932315i	$0.382214\pi$
$338$	1.54188	0.0838671
$339$	−12.6781	−0.688580
$340$	−3.24326	−0.175891
$341$	0.556361	0.0301286
$342$	5.38829	0.291365
$343$	−19.1773	−1.03547
$344$	−0.839542	−0.0452651
$345$	15.3005	0.823754
$346$	0.591818	0.0318163
$347$	0.888881	0.0477177	0.0238588	−	0.999715i	$-0.492405\pi$
$347$	0.888881	0.0477177	0.0238588	+	0.999715i	$0.492405\pi$
$348$	−7.10847	−0.381054
$349$	26.9773	1.44406	0.722030	−	0.691862i	$-0.243209\pi$
$349$	26.9773	1.44406	0.722030	+	0.691862i	$0.243209\pi$
$350$	1.21153	0.0647589
$351$	−14.0304	−0.748887
$352$	−2.75640	−0.146917
$353$	22.5168	1.19845	0.599224	−	0.800581i	$-0.295476\pi$
$353$	22.5168	1.19845	0.599224	+	0.800581i	$0.295476\pi$
$354$	3.14228	0.167010
$355$	13.5310	0.718150
$356$	20.9529	1.11050
$357$	7.21014	0.381601
$358$	5.27429	0.278755
$359$	19.5922	1.03404	0.517018	−	0.855975i	$-0.327042\pi$
$359$	19.5922	1.03404	0.517018	+	0.855975i	$0.327042\pi$
$360$	−7.05179	−0.371662
$361$	6.13514	0.322902
$362$	0.363077	0.0190829
$363$	27.7023	1.45399
$364$	−11.8892	−0.623161
$365$	−9.94078	−0.520324
$366$	0.00787678	0.000411726 0
$367$	−8.26173	−0.431259	−0.215630	−	0.976475i	$-0.569180\pi$
$367$	−8.26173	−0.431259	−0.215630	+	0.976475i	$0.569180\pi$
$368$	12.1203	0.631812
$369$	53.5585	2.78815
$370$	−4.22150	−0.219465
$371$	−13.6528	−0.708820
$372$	2.76891	0.143561
$373$	−18.9938	−0.983462	−0.491731	−	0.870747i	$-0.663636\pi$
$373$	−18.9938	−0.983462	−0.491731	+	0.870747i	$0.663636\pi$
$374$	0.236773	0.0122432
$375$	−34.1426	−1.76312
$376$	0.336090	0.0173325
$377$	−3.06702	−0.157960
$378$	3.15751	0.162405
$379$	22.6083	1.16131	0.580654	−	0.814150i	$-0.302797\pi$
$379$	22.6083	1.16131	0.580654	+	0.814150i	$0.302797\pi$
$380$	−16.2601	−0.834125
$381$	0.828682	0.0424547
$382$	−4.35958	−0.223056
$383$	−16.3572	−0.835814	−0.417907	−	0.908490i	$-0.637236\pi$
$383$	−16.3572	−0.835814	−0.417907	+	0.908490i	$0.637236\pi$
$384$	−18.2168	−0.929621
$385$	−4.69866	−0.239466
$386$	2.79306	0.142163
$387$	−5.06300	−0.257367
$388$	12.0937	0.613963
$389$	−31.5393	−1.59911	−0.799554	−	0.600594i	$-0.794931\pi$
$389$	−31.5393	−1.59911	−0.799554	+	0.600594i	$0.794931\pi$
$390$	−2.39509	−0.121280
$391$	−3.24795	−0.164256
$392$	−0.463853	−0.0234281
$393$	−1.34629	−0.0679114
$394$	−3.27469	−0.164977
$395$	2.38755	0.120131
$396$	−11.0400	−0.554782
$397$	−22.6234	−1.13543	−0.567717	−	0.823224i	$-0.692173\pi$
$397$	−22.6234	−1.13543	−0.567717	+	0.823224i	$0.692173\pi$
$398$	−2.05767	−0.103142
$399$	36.1480	1.80966
$400$	−8.38760	−0.419380
$401$	17.2056	0.859205	0.429603	−	0.903018i	$-0.358654\pi$
$401$	17.2056	0.859205	0.429603	+	0.903018i	$0.358654\pi$
$402$	−4.96927	−0.247844
$403$	1.19468	0.0595110
$404$	3.82618	0.190359
$405$	−2.39720	−0.119118
$406$	0.690228	0.0342554
$407$	−13.3704	−0.662746
$408$	2.38391	0.118021
$409$	−0.928413	−0.0459071	−0.0229535	−	0.999737i	$-0.507307\pi$
$409$	−0.928413	−0.0459071	−0.0229535	+	0.999737i	$0.507307\pi$
$410$	3.72540	0.183984
$411$	54.3285	2.67983
$412$	−14.2036	−0.699759
$413$	13.2370	0.651350
$414$	−3.49076	−0.171562
$415$	1.81339	0.0890159
$416$	−5.91883	−0.290194
$417$	27.5482	1.34904
$418$	1.18706	0.0580610
$419$	−20.6047	−1.00660	−0.503302	−	0.864111i	$-0.667882\pi$
$419$	−20.6047	−1.00660	−0.503302	+	0.864111i	$0.667882\pi$
$420$	−23.3844	−1.14104
$421$	−25.6177	−1.24853	−0.624265	−	0.781213i	$-0.714601\pi$
$421$	−25.6177	−1.24853	−0.624265	+	0.781213i	$0.714601\pi$
$422$	4.45408	0.216821
$423$	2.02684	0.0985486
$424$	−4.51409	−0.219223
$425$	2.24769	0.109029
$426$	−4.91622	−0.238192
$427$	0.0331813	0.00160575
$428$	−15.9325	−0.770129
$429$	−7.58578	−0.366245
$430$	−0.352169	−0.0169831
$431$	31.2758	1.50650	0.753250	−	0.657734i	$-0.228485\pi$
$431$	31.2758	1.50650	0.753250	+	0.657734i	$0.228485\pi$
$432$	−21.8600	−1.05174
$433$	−30.1102	−1.44700	−0.723502	−	0.690322i	$-0.757469\pi$
$433$	−30.1102	−1.44700	−0.723502	+	0.690322i	$0.757469\pi$
$434$	−0.268859	−0.0129057
$435$	−6.03243	−0.289233
$436$	31.6431	1.51543
$437$	−16.2836	−0.778950
$438$	3.61179	0.172578
$439$	7.51969	0.358895	0.179448	−	0.983768i	$-0.442569\pi$
$439$	7.51969	0.358895	0.179448	+	0.983768i	$0.442569\pi$
$440$	−1.55353	−0.0740618
$441$	−2.79735	−0.133207
$442$	0.508423	0.0241832
$443$	−4.83603	−0.229767	−0.114883	−	0.993379i	$-0.536649\pi$
$443$	−4.83603	−0.229767	−0.114883	+	0.993379i	$0.536649\pi$
$444$	−66.5421	−3.15795
$445$	17.7811	0.842907
$446$	−3.07205	−0.145466
$447$	57.4893	2.71915
$448$	−17.6188	−0.832409
$449$	24.1377	1.13913	0.569565	−	0.821947i	$-0.307112\pi$
$449$	24.1377	1.13913	0.569565	+	0.821947i	$0.307112\pi$
$450$	2.41572	0.113878
$451$	11.7991	0.555600
$452$	−8.72849	−0.410554
$453$	15.6911	0.737230
$454$	−4.12389	−0.193544
$455$	−10.0894	−0.473000
$456$	11.9517	0.559692
$457$	−0.253686	−0.0118669	−0.00593347	−	0.999982i	$-0.501889\pi$
$457$	−0.253686	−0.0118669	−0.00593347	+	0.999982i	$0.501889\pi$
$458$	3.63997	0.170085
$459$	5.85797	0.273427
$460$	10.5340	0.491149
$461$	−24.3643	−1.13476	−0.567379	−	0.823457i	$-0.692042\pi$
$461$	−24.3643	−1.13476	−0.567379	+	0.823457i	$0.692042\pi$
$462$	1.70717	0.0794245
$463$	−3.20234	−0.148825	−0.0744127	−	0.997228i	$-0.523708\pi$
$463$	−3.20234	−0.148825	−0.0744127	+	0.997228i	$0.523708\pi$
$464$	−4.77856	−0.221839
$465$	2.34977	0.108968
$466$	0.270743	0.0125419
$467$	3.56529	0.164982	0.0824909	−	0.996592i	$-0.473712\pi$
$467$	3.56529	0.164982	0.0824909	+	0.996592i	$0.473712\pi$
$468$	−23.7063	−1.09582
$469$	−20.9332	−0.966608
$470$	0.140982	0.00650303
$471$	24.5770	1.13245
$472$	4.37660	0.201449
$473$	−1.11540	−0.0512860
$474$	−0.867469	−0.0398442
$475$	11.2688	0.517046
$476$	4.96396	0.227523
$477$	−27.2230	−1.24645
$478$	2.10418	0.0962431
$479$	−6.80763	−0.311048	−0.155524	−	0.987832i	$-0.549707\pi$
$479$	−6.80763	−0.311048	−0.155524	+	0.987832i	$0.549707\pi$
$480$	−11.6415	−0.531361
$481$	−28.7103	−1.30908
$482$	6.25599	0.284952
$483$	−23.4182	−1.06556
$484$	19.0722	0.866917
$485$	10.2630	0.466018
$486$	−2.85956	−0.129712
$487$	2.20169	0.0997679	0.0498840	−	0.998755i	$-0.484115\pi$
$487$	2.20169	0.0997679	0.0498840	+	0.998755i	$0.484115\pi$
$488$	0.0109708	0.000496627 0
$489$	−54.7810	−2.47728
$490$	−0.194576	−0.00879006
$491$	24.9880	1.12769	0.563847	−	0.825879i	$-0.309321\pi$
$491$	24.9880	1.12769	0.563847	+	0.825879i	$0.309321\pi$
$492$	58.7222	2.64740
$493$	1.28054	0.0576728
$494$	2.54898	0.114684
$495$	−9.36885	−0.421098
$496$	1.86136	0.0835774
$497$	−20.7098	−0.928961
$498$	−0.658860	−0.0295242
$499$	5.04332	0.225770	0.112885	−	0.993608i	$-0.463991\pi$
$499$	5.04332	0.225770	0.112885	+	0.993608i	$0.463991\pi$
$500$	−23.5061	−1.05123
$501$	−6.43575	−0.287528
$502$	−3.53646	−0.157840
$503$	−20.4975	−0.913938	−0.456969	−	0.889483i	$-0.651065\pi$
$503$	−20.4975	−0.913938	−0.456969	+	0.889483i	$0.651065\pi$
$504$	10.7931	0.480762
$505$	3.24699	0.144489
$506$	−0.769027	−0.0341874
$507$	20.6251	0.915992
$508$	0.570523	0.0253129
$509$	−27.7373	−1.22944	−0.614718	−	0.788747i	$-0.710730\pi$
$509$	−27.7373	−1.22944	−0.614718	+	0.788747i	$0.710730\pi$
$510$	1.00000	0.0442807
$511$	15.2148	0.673064
$512$	−15.4876	−0.684460
$513$	29.3689	1.29667
$514$	2.90088	0.127952
$515$	−12.0535	−0.531140
$516$	−5.55113	−0.244375
$517$	0.446521	0.0196380
$518$	6.46120	0.283889
$519$	7.91651	0.347496
$520$	−3.33591	−0.146289
$521$	−9.37969	−0.410932	−0.205466	−	0.978664i	$-0.565871\pi$
$521$	−9.37969	−0.410932	−0.205466	+	0.978664i	$0.565871\pi$
$522$	1.37627	0.0602379
$523$	−36.4986	−1.59597	−0.797986	−	0.602675i	$-0.794101\pi$
$523$	−36.4986	−1.59597	−0.797986	+	0.602675i	$0.794101\pi$
$524$	−0.926881	−0.0404910
$525$	16.2061	0.707293
$526$	2.94626	0.128463
$527$	−0.498801	−0.0217281
$528$	−11.8190	−0.514355
$529$	−12.4508	−0.541339
$530$	−1.89356	−0.0822510
$531$	26.3938	1.14539
$532$	24.8868	1.07898
$533$	25.3363	1.09744
$534$	−6.46043	−0.279570
$535$	−13.5208	−0.584553
$536$	−6.92124	−0.298952
$537$	70.5521	3.04455
$538$	0.240598	0.0103729
$539$	−0.616265	−0.0265444
$540$	−18.9989	−0.817584
$541$	−21.2609	−0.914075	−0.457038	−	0.889447i	$-0.651090\pi$
$541$	−21.2609	−0.914075	−0.457038	+	0.889447i	$0.651090\pi$
$542$	−3.25992	−0.140026
$543$	4.85673	0.208422
$544$	2.47123	0.105953
$545$	26.8532	1.15026
$546$	3.66580	0.156882
$547$	14.5000	0.619976	0.309988	−	0.950740i	$-0.399675\pi$
$547$	14.5000	0.619976	0.309988	+	0.950740i	$0.399675\pi$
$548$	37.4035	1.59780
$549$	0.0661615	0.00282371
$550$	0.532191	0.0226927
$551$	6.42000	0.273501
$552$	−7.74284	−0.329557
$553$	−3.65425	−0.155395
$554$	−5.25839	−0.223407
$555$	−56.4693	−2.39699
$556$	18.9661	0.804341
$557$	41.8703	1.77410	0.887052	−	0.461670i	$-0.152750\pi$
$557$	41.8703	1.77410	0.887052	+	0.461670i	$0.152750\pi$
$558$	−0.536090	−0.0226945
$559$	−2.39509	−0.101302
$560$	−15.7198	−0.664282
$561$	3.16722	0.133720
$562$	0.00996259	0.000420247 0
$563$	30.3605	1.27954	0.639772	−	0.768565i	$-0.279029\pi$
$563$	30.3605	1.27954	0.639772	+	0.768565i	$0.279029\pi$
$564$	2.22226	0.0935739
$565$	−7.40722	−0.311624
$566$	3.58773	0.150803
$567$	3.66902	0.154085
$568$	−6.84735	−0.287308
$569$	−1.79244	−0.0751431	−0.0375716	−	0.999294i	$-0.511962\pi$
$569$	−1.79244	−0.0751431	−0.0375716	+	0.999294i	$0.511962\pi$
$570$	5.01350	0.209992
$571$	18.7085	0.782926	0.391463	−	0.920194i	$-0.371969\pi$
$571$	18.7085	0.782926	0.391463	+	0.920194i	$0.371969\pi$
$572$	−5.22258	−0.218367
$573$	−58.3164	−2.43620
$574$	−5.70189	−0.237992
$575$	−7.30037	−0.304447
$576$	−35.1308	−1.46378
$577$	0.286316	0.0119195	0.00595975	−	0.999982i	$-0.498103\pi$
$577$	0.286316	0.0119195	0.00595975	+	0.999982i	$0.498103\pi$
$578$	−0.212277	−0.00882955
$579$	37.3616	1.55269
$580$	−4.15314	−0.172450
$581$	−2.77548	−0.115146
$582$	−3.72886	−0.154566
$583$	−5.99731	−0.248383
$584$	5.03053	0.208165
$585$	−20.1178	−0.831767
$586$	−6.54568	−0.270399
$587$	−23.7797	−0.981495	−0.490748	−	0.871302i	$-0.663276\pi$
$587$	−23.7797	−0.981495	−0.490748	+	0.871302i	$0.663276\pi$
$588$	−3.06704	−0.126483
$589$	−2.50074	−0.103041
$590$	1.83589	0.0755822
$591$	−43.8043	−1.80187
$592$	−44.7319	−1.83847
$593$	16.1975	0.665152	0.332576	−	0.943076i	$-0.392082\pi$
$593$	16.1975	0.665152	0.332576	+	0.943076i	$0.392082\pi$
$594$	1.38701	0.0569097
$595$	4.21254	0.172697
$596$	39.5796	1.62124
$597$	−27.5247	−1.12651
$598$	−1.65133	−0.0675281
$599$	8.90490	0.363844	0.181922	−	0.983313i	$-0.441768\pi$
$599$	8.90490	0.363844	0.181922	+	0.983313i	$0.441768\pi$
$600$	5.35829	0.218751
$601$	−5.00807	−0.204283	−0.102142	−	0.994770i	$-0.532569\pi$
$601$	−5.00807	−0.204283	−0.102142	+	0.994770i	$0.532569\pi$
$602$	0.539012	0.0219685
$603$	−41.7397	−1.69977
$604$	10.8028	0.439561
$605$	16.1851	0.658019
$606$	−1.17973	−0.0479233
$607$	35.2057	1.42895	0.714477	−	0.699659i	$-0.246665\pi$
$607$	35.2057	1.42895	0.714477	+	0.699659i	$0.246665\pi$
$608$	12.3895	0.502461
$609$	9.23290	0.374136
$610$	0.00460203	0.000186331 0
$611$	0.958816	0.0387895
$612$	9.89785	0.400097
$613$	23.4816	0.948411	0.474205	−	0.880414i	$-0.342735\pi$
$613$	23.4816	0.948411	0.474205	+	0.880414i	$0.342735\pi$
$614$	−0.652019	−0.0263134
$615$	49.8331	2.00947
$616$	2.37776	0.0958025
$617$	8.17066	0.328939	0.164469	−	0.986382i	$-0.447409\pi$
$617$	8.17066	0.328939	0.164469	+	0.986382i	$0.447409\pi$
$618$	4.37940	0.176165
$619$	19.2859	0.775166	0.387583	−	0.921835i	$-0.373310\pi$
$619$	19.2859	0.775166	0.387583	+	0.921835i	$0.373310\pi$
$620$	1.61774	0.0649701
$621$	−19.0264	−0.763504
$622$	6.84342	0.274396
$623$	−27.2148	−1.09034
$624$	−25.3789	−1.01597
$625$	−8.70948	−0.348379
$626$	−0.149937	−0.00599269
$627$	15.8788	0.634139
$628$	16.9205	0.675203
$629$	11.9871	0.477958
$630$	4.52746	0.180378
$631$	18.3501	0.730508	0.365254	−	0.930908i	$-0.380982\pi$
$631$	18.3501	0.730508	0.365254	+	0.930908i	$0.380982\pi$
$632$	−1.20822	−0.0480603
$633$	59.5804	2.36811
$634$	−2.51770	−0.0999905
$635$	0.484160	0.0192133
$636$	−29.8476	−1.18353
$637$	−1.32331	−0.0524314
$638$	0.303198	0.0120037
$639$	−41.2941	−1.63357
$640$	−10.6432	−0.420709
$641$	40.9509	1.61746	0.808732	−	0.588177i	$-0.200154\pi$
$641$	40.9509	1.61746	0.808732	+	0.588177i	$0.200154\pi$
$642$	4.91250	0.193881
$643$	−29.1707	−1.15038	−0.575191	−	0.818019i	$-0.695072\pi$
$643$	−29.1707	−1.15038	−0.575191	+	0.818019i	$0.695072\pi$
$644$	−16.1227	−0.635324
$645$	−4.71083	−0.185489
$646$	−1.06425	−0.0418723
$647$	33.5423	1.31868	0.659341	−	0.751844i	$-0.270835\pi$
$647$	33.5423	1.31868	0.659341	+	0.751844i	$0.270835\pi$
$648$	1.21310	0.0476552
$649$	5.81465	0.228245
$650$	1.14278	0.0448233
$651$	−3.59642	−0.140955
$652$	−37.7151	−1.47704
$653$	−1.36258	−0.0533218	−0.0266609	−	0.999645i	$-0.508487\pi$
$653$	−1.36258	−0.0533218	−0.0266609	+	0.999645i	$0.508487\pi$
$654$	−9.75658	−0.381512
$655$	−0.786575	−0.0307340
$656$	39.4751	1.54124
$657$	30.3374	1.18358
$658$	−0.215780	−0.00841197
$659$	−3.00400	−0.117019	−0.0585097	−	0.998287i	$-0.518635\pi$
$659$	−3.00400	−0.117019	−0.0585097	+	0.998287i	$0.518635\pi$
$660$	−10.2721	−0.399841
$661$	−45.7661	−1.78010	−0.890048	−	0.455868i	$-0.849329\pi$
$661$	−45.7661	−1.78010	−0.890048	+	0.455868i	$0.849329\pi$
$662$	5.25525	0.204251
$663$	6.80097	0.264128
$664$	−0.917666	−0.0356124
$665$	21.1196	0.818982
$666$	12.8833	0.499216
$667$	−4.15915	−0.161043
$668$	−4.43082	−0.171434
$669$	−41.0935	−1.58877
$670$	−2.90331	−0.112165
$671$	0.0145756	0.000562686 0
$672$	17.8179	0.687341
$673$	−18.0592	−0.696130	−0.348065	−	0.937470i	$-0.613161\pi$
$673$	−18.0592	−0.696130	−0.348065	+	0.937470i	$0.613161\pi$
$674$	−2.81860	−0.108568
$675$	13.1669	0.506793
$676$	14.1997	0.546144
$677$	21.1629	0.813355	0.406677	−	0.913572i	$-0.366687\pi$
$677$	21.1629	0.813355	0.406677	+	0.913572i	$0.366687\pi$
$678$	2.69127	0.103358
$679$	−15.7080	−0.602817
$680$	1.39281	0.0534118
$681$	−55.1637	−2.11388
$682$	−0.118103	−0.00452238
$683$	5.23314	0.200241	0.100120	−	0.994975i	$-0.468077\pi$
$683$	5.23314	0.200241	0.100120	+	0.994975i	$0.468077\pi$
$684$	49.6228	1.89738
$685$	31.7416	1.21278
$686$	4.07089	0.155427
$687$	48.6904	1.85766
$688$	−3.73166	−0.142268
$689$	−12.8781	−0.490615
$690$	−3.24795	−0.123647
$691$	−18.4677	−0.702543	−0.351272	−	0.936274i	$-0.614251\pi$
$691$	−18.4677	−0.702543	−0.351272	+	0.936274i	$0.614251\pi$
$692$	5.45028	0.207188
$693$	14.3395	0.544711
$694$	−0.188689	−0.00716253
$695$	16.0951	0.610522
$696$	3.05271	0.115713
$697$	−10.5784	−0.400686
$698$	−5.72665	−0.216757
$699$	3.62163	0.136982
$700$	11.1574	0.421711
$701$	−31.0116	−1.17129	−0.585645	−	0.810567i	$-0.699159\pi$
$701$	−31.0116	−1.17129	−0.585645	+	0.810567i	$0.699159\pi$
$702$	2.97833	0.112410
$703$	60.0974	2.26662
$704$	−7.73945	−0.291691
$705$	1.88586	0.0710257
$706$	−4.77980	−0.179890
$707$	−4.96967	−0.186904
$708$	28.9385	1.08757
$709$	39.7743	1.49376	0.746878	−	0.664961i	$-0.231552\pi$
$709$	39.7743	1.49376	0.746878	+	0.664961i	$0.231552\pi$
$710$	−2.87231	−0.107796
$711$	−7.28636	−0.273260
$712$	−8.99814	−0.337220
$713$	1.62008	0.0606725
$714$	−1.53055	−0.0572792
$715$	−4.43201	−0.165748
$716$	48.5730	1.81526
$717$	28.1468	1.05116
$718$	−4.15897	−0.155211
$719$	27.8343	1.03804	0.519022	−	0.854761i	$-0.326296\pi$
$719$	27.8343	1.03804	0.519022	+	0.854761i	$0.326296\pi$
$720$	−31.3443	−1.16813
$721$	18.4484	0.687055
$722$	−1.30235	−0.0484684
$723$	83.6838	3.11223
$724$	3.34371	0.124268
$725$	2.87826	0.106896
$726$	−5.88055	−0.218248
$727$	20.7165	0.768332	0.384166	−	0.923264i	$-0.374489\pi$
$727$	20.7165	0.768332	0.384166	+	0.923264i	$0.374489\pi$
$728$	5.10576	0.189232
$729$	−42.5860	−1.57726
$730$	2.11020	0.0781019
$731$	1.00000	0.0369863
$732$	0.0725403	0.00268117
$733$	33.5896	1.24066	0.620330	−	0.784341i	$-0.286999\pi$
$733$	33.5896	1.24066	0.620330	+	0.784341i	$0.286999\pi$
$734$	1.75378	0.0647330
$735$	−2.60277	−0.0960046
$736$	−8.02644	−0.295858
$737$	−9.19540	−0.338717
$738$	−11.3692	−0.418507
$739$	24.8390	0.913716	0.456858	−	0.889540i	$-0.348975\pi$
$739$	24.8390	0.913716	0.456858	+	0.889540i	$0.348975\pi$
$740$	−38.8774	−1.42916
$741$	34.0966	1.25257
$742$	2.89818	0.106396
$743$	3.14892	0.115523	0.0577614	−	0.998330i	$-0.481604\pi$
$743$	3.14892	0.115523	0.0577614	+	0.998330i	$0.481604\pi$
$744$	−1.18910	−0.0435945
$745$	33.5883	1.23058
$746$	4.03194	0.147620
$747$	−5.53414	−0.202484
$748$	2.18053	0.0797281
$749$	20.6941	0.756147
$750$	7.24769	0.264648
$751$	50.6694	1.84895	0.924476	−	0.381240i	$-0.124503\pi$
$751$	50.6694	1.84895	0.924476	+	0.381240i	$0.124503\pi$
$752$	1.49388	0.0544761
$753$	−47.3058	−1.72392
$754$	0.651058	0.0237101
$755$	9.16755	0.333641
$756$	29.0787	1.05758
$757$	−33.9812	−1.23507	−0.617534	−	0.786544i	$-0.711868\pi$
$757$	−33.9812	−1.23507	−0.617534	+	0.786544i	$0.711868\pi$
$758$	−4.79921	−0.174315
$759$	−10.2870	−0.373393
$760$	6.98284	0.253294
$761$	20.2111	0.732652	0.366326	−	0.930487i	$-0.380616\pi$
$761$	20.2111	0.732652	0.366326	+	0.930487i	$0.380616\pi$
$762$	−0.175910	−0.00637255
$763$	−41.1000	−1.48792
$764$	−40.1491	−1.45254
$765$	8.39957	0.303687
$766$	3.47225	0.125458
$767$	12.4858	0.450836
$768$	−35.5387	−1.28239
$769$	54.2117	1.95492	0.977461	−	0.211114i	$-0.0677091\pi$
$769$	54.2117	1.95492	0.977461	+	0.211114i	$0.0677091\pi$
$770$	0.997416	0.0359444
$771$	38.8039	1.39749
$772$	25.7223	0.925766
$773$	−6.03236	−0.216969	−0.108485	−	0.994098i	$-0.534600\pi$
$773$	−6.03236	−0.216969	−0.108485	+	0.994098i	$0.534600\pi$
$774$	1.07476	0.0386314
$775$	−1.12115	−0.0402728
$776$	−5.19359	−0.186439
$777$	86.4289	3.10062
$778$	6.69507	0.240030
$779$	−53.0349	−1.90017
$780$	−22.0573	−0.789779
$781$	−9.09724	−0.325525
$782$	0.689465	0.0246552
$783$	7.50139	0.268078
$784$	−2.06177	−0.0736347
$785$	14.3592	0.512501
$786$	0.285787	0.0101937
$787$	−42.1924	−1.50400	−0.751998	−	0.659165i	$-0.770910\pi$
$787$	−42.1924	−1.50400	−0.751998	+	0.659165i	$0.770910\pi$
$788$	−30.1579	−1.07433
$789$	39.4109	1.40306
$790$	−0.506821	−0.0180319
$791$	11.3371	0.403100
$792$	4.74110	0.168468
$793$	0.0312983	0.00111143
$794$	4.80242	0.170431
$795$	−25.3294	−0.898341
$796$	−18.9499	−0.671662
$797$	7.85342	0.278182	0.139091	−	0.990280i	$-0.455582\pi$
$797$	7.85342	0.278182	0.139091	+	0.990280i	$0.455582\pi$
$798$	−7.67339	−0.271635
$799$	−0.400325	−0.0141625
$800$	5.55455	0.196383
$801$	−54.2648	−1.91735
$802$	−3.65234	−0.128969
$803$	6.68345	0.235854
$804$	−45.7639	−1.61397
$805$	−13.6821	−0.482232
$806$	−0.253602	−0.00893274
$807$	3.21839	0.113293
$808$	−1.64314	−0.0578054
$809$	33.1598	1.16584	0.582919	−	0.812531i	$-0.301911\pi$
$809$	33.1598	1.16584	0.582919	+	0.812531i	$0.301911\pi$
$810$	0.508870	0.0178799
$811$	−17.7207	−0.622259	−0.311130	−	0.950367i	$-0.600707\pi$
$811$	−17.7207	−0.622259	−0.311130	+	0.950367i	$0.600707\pi$
$812$	6.35657	0.223072
$813$	−43.6067	−1.52935
$814$	2.83823	0.0994798
$815$	−32.0059	−1.12112
$816$	10.5962	0.370942
$817$	5.01350	0.175400
$818$	0.197081	0.00689076
$819$	30.7911	1.07593
$820$	34.3086	1.19811
$821$	−46.1710	−1.61138	−0.805689	−	0.592339i	$-0.798205\pi$
$821$	−46.1710	−1.61138	−0.805689	+	0.592339i	$0.798205\pi$
$822$	−11.5327	−0.402249
$823$	29.8326	1.03990	0.519949	−	0.854197i	$-0.325951\pi$
$823$	29.8326	1.03990	0.519949	+	0.854197i	$0.325951\pi$
$824$	6.09967	0.212492
$825$	7.11890	0.247848
$826$	−2.80991	−0.0977692
$827$	−32.2143	−1.12020	−0.560101	−	0.828424i	$-0.689238\pi$
$827$	−32.2143	−1.12020	−0.560101	+	0.828424i	$0.689238\pi$
$828$	−32.1477	−1.11721
$829$	29.4265	1.02203	0.511013	−	0.859573i	$-0.329270\pi$
$829$	29.4265	1.02203	0.511013	+	0.859573i	$0.329270\pi$
$830$	−0.384941	−0.0133615
$831$	−70.3393	−2.44004
$832$	−16.6189	−0.576158
$833$	0.552508	0.0191433
$834$	−5.84784	−0.202494
$835$	−3.76011	−0.130124
$836$	10.9321	0.378094
$837$	−2.92196	−0.100998
$838$	4.37389	0.151094
$839$	−35.6961	−1.23237	−0.616183	−	0.787603i	$-0.711322\pi$
$839$	−35.6961	−1.23237	−0.616183	+	0.787603i	$0.711322\pi$
$840$	10.0423	0.346494
$841$	−27.3602	−0.943455
$842$	5.43804	0.187407
$843$	0.133266	0.00458991
$844$	41.0193	1.41194
$845$	12.0503	0.414542
$846$	−0.430252	−0.0147924
$847$	−24.7721	−0.851178
$848$	−20.0646	−0.689020
$849$	47.9916	1.64707
$850$	−0.477132	−0.0163655
$851$	−38.9336	−1.33463
$852$	−45.2753	−1.55111
$853$	44.7203	1.53120	0.765598	−	0.643320i	$-0.222443\pi$
$853$	44.7203	1.53120	0.765598	+	0.643320i	$0.222443\pi$
$854$	−0.00704362	−0.000241028 0
$855$	42.1112	1.44017
$856$	6.84218	0.233861
$857$	−45.1768	−1.54321	−0.771605	−	0.636102i	$-0.780546\pi$
$857$	−45.1768	−1.54321	−0.771605	+	0.636102i	$0.780546\pi$
$858$	1.61029	0.0549742
$859$	39.5488	1.34939	0.674694	−	0.738098i	$-0.264276\pi$
$859$	39.5488	1.34939	0.674694	+	0.738098i	$0.264276\pi$
$860$	−3.24326	−0.110594
$861$	−76.2719	−2.59934
$862$	−6.63912	−0.226129
$863$	−47.9021	−1.63061	−0.815303	−	0.579034i	$-0.803430\pi$
$863$	−47.9021	−1.63061	−0.815303	+	0.579034i	$0.803430\pi$
$864$	14.4764	0.492497
$865$	4.62524	0.157263
$866$	6.39170	0.217199
$867$	−2.83954	−0.0964359
$868$	−2.47603	−0.0840419
$869$	−1.60521	−0.0544531
$870$	1.28054	0.0434145
$871$	−19.7453	−0.669044
$872$	−13.5890	−0.460183
$873$	−31.3208	−1.06005
$874$	3.45663	0.116922
$875$	30.5312	1.03214
$876$	33.2623	1.12383
$877$	33.5981	1.13453	0.567264	−	0.823536i	$-0.308002\pi$
$877$	33.5981	1.13453	0.567264	+	0.823536i	$0.308002\pi$
$878$	−1.59626	−0.0538710
$879$	−87.5589	−2.95329
$880$	−6.90527	−0.232777
$881$	5.00316	0.168561	0.0842804	−	0.996442i	$-0.473141\pi$
$881$	5.00316	0.168561	0.0842804	+	0.996442i	$0.473141\pi$
$882$	0.593812	0.0199947
$883$	−18.9288	−0.637005	−0.318503	−	0.947922i	$-0.603180\pi$
$883$	−18.9288	−0.637005	−0.318503	+	0.947922i	$0.603180\pi$
$884$	4.68226	0.157482
$885$	24.5579	0.825505
$886$	1.02658	0.0344885
$887$	22.5167	0.756037	0.378019	−	0.925798i	$-0.376606\pi$
$887$	22.5167	0.756037	0.378019	+	0.925798i	$0.376606\pi$
$888$	28.5763	0.958958
$889$	−0.741029	−0.0248533
$890$	−3.77452	−0.126522
$891$	1.61170	0.0539940
$892$	−28.2916	−0.947274
$893$	−2.00703	−0.0671626
$894$	−12.2036	−0.408151
$895$	41.2202	1.37784
$896$	16.2899	0.544208
$897$	−22.0892	−0.737538
$898$	−5.12388	−0.170986
$899$	−0.638737	−0.0213031
$900$	22.2473	0.741575
$901$	5.37685	0.179129
$902$	−2.50468	−0.0833968
$903$	7.21014	0.239938
$904$	3.74842	0.124671
$905$	2.83756	0.0943236
$906$	−3.33085	−0.110660
$907$	−19.7476	−0.655709	−0.327855	−	0.944728i	$-0.606326\pi$
$907$	−19.7476	−0.655709	−0.327855	+	0.944728i	$0.606326\pi$
$908$	−37.9785	−1.26036
$909$	−9.90922	−0.328668
$910$	2.14175	0.0709985
$911$	−45.3377	−1.50210	−0.751052	−	0.660243i	$-0.770453\pi$
$911$	−45.3377	−1.50210	−0.751052	+	0.660243i	$0.770453\pi$
$912$	53.1241	1.75911
$913$	−1.21919	−0.0403493
$914$	0.0538517	0.00178126
$915$	0.0615595	0.00203509
$916$	33.5219	1.10759
$917$	1.20389	0.0397559
$918$	−1.24351	−0.0410420
$919$	−51.7641	−1.70754	−0.853771	−	0.520649i	$-0.825690\pi$
$919$	−51.7641	−1.70754	−0.853771	+	0.520649i	$0.825690\pi$
$920$	−4.52378	−0.149144
$921$	−8.72180	−0.287393
$922$	5.17197	0.170330
$923$	−19.5345	−0.642987
$924$	15.7219	0.517214
$925$	26.9433	0.885890
$926$	0.679783	0.0223391
$927$	36.7851	1.20818
$928$	3.16452	0.103880
$929$	−55.7602	−1.82943	−0.914716	−	0.404098i	$-0.867585\pi$
$929$	−55.7602	−1.82943	−0.914716	+	0.404098i	$0.867585\pi$
$930$	−0.498801	−0.0163563
$931$	2.76999	0.0907829
$932$	2.49338	0.0816734
$933$	91.5417	2.99694
$934$	−0.756828	−0.0247642
$935$	1.85045	0.0605163
$936$	10.1806	0.332763
$937$	−3.30658	−0.108021	−0.0540106	−	0.998540i	$-0.517200\pi$
$937$	−3.30658	−0.108021	−0.0540106	+	0.998540i	$0.517200\pi$
$938$	4.44364	0.145090
$939$	−2.00565	−0.0654518
$940$	1.29836	0.0423478
$941$	−13.2953	−0.433415	−0.216708	−	0.976237i	$-0.569532\pi$
$941$	−13.2953	−0.433415	−0.216708	+	0.976237i	$0.569532\pi$
$942$	−5.21713	−0.169983
$943$	34.3582	1.11886
$944$	19.4534	0.633155
$945$	24.6770	0.802742
$946$	0.236773	0.00769815
$947$	−7.42234	−0.241194	−0.120597	−	0.992702i	$-0.538481\pi$
$947$	−7.42234	−0.241194	−0.120597	+	0.992702i	$0.538481\pi$
$948$	−7.98885	−0.259466
$949$	14.3514	0.465866
$950$	−2.39210	−0.0776099
$951$	−33.6782	−1.09209
$952$	−2.13176	−0.0690907
$953$	−13.2058	−0.427777	−0.213888	−	0.976858i	$-0.568613\pi$
$953$	−13.2058	−0.427777	−0.213888	+	0.976858i	$0.568613\pi$
$954$	5.77880	0.187096
$955$	−34.0715	−1.10253
$956$	19.3782	0.626737
$957$	4.05576	0.131104
$958$	1.44510	0.0466891
$959$	−48.5819	−1.56879
$960$	−32.6872	−1.05498
$961$	−30.7512	−0.991974
$962$	6.09453	0.196496
$963$	41.2629	1.32968
$964$	57.6138	1.85561
$965$	21.8286	0.702688
$966$	4.97114	0.159944
$967$	−16.1744	−0.520135	−0.260067	−	0.965591i	$-0.583745\pi$
$967$	−16.1744	−0.520135	−0.260067	+	0.965591i	$0.583745\pi$
$968$	−8.19048	−0.263252
$969$	−14.2360	−0.457327
$970$	−2.17860	−0.0699505
$971$	51.3760	1.64873	0.824367	−	0.566056i	$-0.191531\pi$
$971$	51.3760	1.64873	0.824367	+	0.566056i	$0.191531\pi$
$972$	−26.3348	−0.844688
$973$	−24.6343	−0.789739
$974$	−0.467367	−0.0149754
$975$	15.2864	0.489558
$976$	0.0487641	0.00156090
$977$	9.39621	0.300611	0.150306	−	0.988640i	$-0.451974\pi$
$977$	9.39621	0.300611	0.150306	+	0.988640i	$0.451974\pi$
$978$	11.6287	0.371846
$979$	−11.9547	−0.382075
$980$	−1.79193	−0.0572410
$981$	−81.9510	−2.61649
$982$	−5.30438	−0.169270
$983$	−17.8674	−0.569883	−0.284942	−	0.958545i	$-0.591974\pi$
$983$	−17.8674	−0.569883	−0.284942	+	0.958545i	$0.591974\pi$
$984$	−25.2181	−0.803922
$985$	−25.5928	−0.815453
$986$	−0.271830	−0.00865683
$987$	−2.88640	−0.0918751
$988$	23.4745	0.746823
$989$	−3.24795	−0.103279
$990$	1.98879	0.0632079
$991$	−29.1968	−0.927467	−0.463733	−	0.885975i	$-0.653490\pi$
$991$	−29.1968	−0.927467	−0.463733	+	0.885975i	$0.653490\pi$
$992$	−1.23265	−0.0391367
$993$	70.2974	2.23082
$994$	4.39621	0.139439
$995$	−16.0814	−0.509814
$996$	−6.06770	−0.192262
$997$	−40.5691	−1.28484	−0.642419	−	0.766354i	$-0.722069\pi$
$997$	−40.5691	−1.28484	−0.642419	+	0.766354i	$0.722069\pi$
$998$	−1.07058	−0.0338886
$999$	70.2203	2.22167

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.a.c.1.3	✓	6
3.2	odd	2		6579.2.a.j.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.a.c.1.3	✓	6	1.1	even	1	trivial
6579.2.a.j.1.4		6	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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.a (trivial)

\(f(q)\)	\(=\)	\(q-0.212277 q^{2} -2.83954 q^{3} -1.95494 q^{4} -1.65901 q^{5} +0.602769 q^{6} +2.53919 q^{7} +0.839542 q^{8} +5.06300 q^{9} +O(q^{10})\)	\(q-0.212277 q^{2} -2.83954 q^{3} -1.95494 q^{4} -1.65901 q^{5} +0.602769 q^{6} +2.53919 q^{7} +0.839542 q^{8} +5.06300 q^{9} +0.352169 q^{10} +1.11540 q^{11} +5.55113 q^{12} +2.39509 q^{13} -0.539012 q^{14} +4.71083 q^{15} +3.73166 q^{16} -1.00000 q^{17} -1.07476 q^{18} -5.01350 q^{19} +3.24326 q^{20} -7.21014 q^{21} -0.236773 q^{22} +3.24795 q^{23} -2.38391 q^{24} -2.24769 q^{25} -0.508423 q^{26} -5.85797 q^{27} -4.96396 q^{28} -1.28054 q^{29} -1.00000 q^{30} +0.498801 q^{31} -2.47123 q^{32} -3.16722 q^{33} +0.212277 q^{34} -4.21254 q^{35} -9.89785 q^{36} -11.9871 q^{37} +1.06425 q^{38} -6.80097 q^{39} -1.39281 q^{40} +10.5784 q^{41} +1.53055 q^{42} -1.00000 q^{43} -2.18053 q^{44} -8.39957 q^{45} -0.689465 q^{46} +0.400325 q^{47} -10.5962 q^{48} -0.552508 q^{49} +0.477132 q^{50} +2.83954 q^{51} -4.68226 q^{52} -5.37685 q^{53} +1.24351 q^{54} -1.85045 q^{55} +2.13176 q^{56} +14.2360 q^{57} +0.271830 q^{58} +5.21308 q^{59} -9.20938 q^{60} +0.0130677 q^{61} -0.105884 q^{62} +12.8559 q^{63} -6.93874 q^{64} -3.97349 q^{65} +0.672327 q^{66} -8.24406 q^{67} +1.95494 q^{68} -9.22270 q^{69} +0.894226 q^{70} -8.15605 q^{71} +4.25060 q^{72} +5.99199 q^{73} +2.54459 q^{74} +6.38240 q^{75} +9.80108 q^{76} +2.83221 q^{77} +1.44369 q^{78} -1.43914 q^{79} -6.19086 q^{80} +1.44496 q^{81} -2.24555 q^{82} -1.09306 q^{83} +14.0954 q^{84} +1.65901 q^{85} +0.212277 q^{86} +3.63616 q^{87} +0.936422 q^{88} -10.7179 q^{89} +1.78303 q^{90} +6.08160 q^{91} -6.34955 q^{92} -1.41637 q^{93} -0.0849797 q^{94} +8.31744 q^{95} +7.01716 q^{96} -6.18621 q^{97} +0.117285 q^{98} +5.64725 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} - 3 q^{3} + 5 q^{4} + 3 q^{5} - 7 q^{6} - 7 q^{7} - 9 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q - q^2 - 3 * q^3 + 5 * q^4 + 3 * q^5 - 7 * q^6 - 7 * q^7 - 9 * q^8 - 3 * q^9	\( 6 q - q^{2} - 3 q^{3} + 5 q^{4} + 3 q^{5} - 7 q^{6} - 7 q^{7} - 9 q^{8} - 3 q^{9} - 4 q^{10} + 4 q^{11} + 11 q^{12} - 10 q^{13} - 7 q^{14} + q^{15} - q^{16} - 6 q^{17} + q^{18} - 20 q^{19} + q^{20} - 8 q^{21} + 2 q^{22} - 3 q^{23} - 9 q^{24} - 7 q^{25} - 3 q^{26} - 6 q^{27} - 11 q^{28} - 15 q^{29} - 6 q^{30} + 12 q^{31} + q^{32} - 2 q^{33} + q^{34} - 9 q^{35} - 16 q^{36} - 14 q^{37} + 27 q^{38} + 5 q^{39} - 7 q^{40} - 2 q^{41} + 19 q^{42} - 6 q^{43} - 12 q^{44} - 18 q^{45} + 14 q^{46} - 11 q^{47} - 6 q^{48} + 3 q^{49} + 7 q^{50} + 3 q^{51} - 5 q^{52} + 3 q^{53} + 25 q^{54} + 6 q^{55} + 22 q^{56} + 11 q^{57} - 21 q^{58} + 2 q^{59} - q^{60} - 20 q^{61} + 3 q^{62} + 23 q^{63} - 39 q^{64} - 34 q^{65} + 7 q^{66} - 2 q^{67} - 5 q^{68} - 17 q^{69} - q^{70} + q^{71} + 21 q^{72} + 13 q^{73} + 28 q^{74} - 5 q^{75} - 29 q^{76} - 11 q^{77} - 26 q^{79} + 12 q^{80} + 2 q^{81} - 9 q^{82} + 10 q^{83} - 3 q^{84} - 3 q^{85} + q^{86} + 12 q^{87} - 6 q^{88} - 15 q^{89} + 15 q^{90} + 8 q^{91} - 9 q^{92} - 11 q^{93} - 33 q^{94} - 21 q^{95} + 25 q^{96} - 22 q^{97} - 3 q^{98} - 5 q^{99}+O(q^{100}) \) 6 * q - q^2 - 3 * q^3 + 5 * q^4 + 3 * q^5 - 7 * q^6 - 7 * q^7 - 9 * q^8 - 3 * q^9 - 4 * q^10 + 4 * q^11 + 11 * q^12 - 10 * q^13 - 7 * q^14 + q^15 - q^16 - 6 * q^17 + q^18 - 20 * q^19 + q^20 - 8 * q^21 + 2 * q^22 - 3 * q^23 - 9 * q^24 - 7 * q^25 - 3 * q^26 - 6 * q^27 - 11 * q^28 - 15 * q^29 - 6 * q^30 + 12 * q^31 + q^32 - 2 * q^33 + q^34 - 9 * q^35 - 16 * q^36 - 14 * q^37 + 27 * q^38 + 5 * q^39 - 7 * q^40 - 2 * q^41 + 19 * q^42 - 6 * q^43 - 12 * q^44 - 18 * q^45 + 14 * q^46 - 11 * q^47 - 6 * q^48 + 3 * q^49 + 7 * q^50 + 3 * q^51 - 5 * q^52 + 3 * q^53 + 25 * q^54 + 6 * q^55 + 22 * q^56 + 11 * q^57 - 21 * q^58 + 2 * q^59 - q^60 - 20 * q^61 + 3 * q^62 + 23 * q^63 - 39 * q^64 - 34 * q^65 + 7 * q^66 - 2 * q^67 - 5 * q^68 - 17 * q^69 - q^70 + q^71 + 21 * q^72 + 13 * q^73 + 28 * q^74 - 5 * q^75 - 29 * q^76 - 11 * q^77 - 26 * q^79 + 12 * q^80 + 2 * q^81 - 9 * q^82 + 10 * q^83 - 3 * q^84 - 3 * q^85 + q^86 + 12 * q^87 - 6 * q^88 - 15 * q^89 + 15 * q^90 + 8 * q^91 - 9 * q^92 - 11 * q^93 - 33 * q^94 - 21 * q^95 + 25 * q^96 - 22 * q^97 - 3 * q^98 - 5 * q^99

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