LMFDB - Embedded newform 731.2.a.f.1.5

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:	$0$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
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)

$f(q)$	$=$	$q-1.79843 q^{2} -0.497156 q^{3} +1.23435 q^{4} -2.09348 q^{5} +0.894100 q^{6} +2.50164 q^{7} +1.37698 q^{8} -2.75284 q^{9} +O(q^{10})$	\(q-1.79843 q^{2} -0.497156 q^{3} +1.23435 q^{4} -2.09348 q^{5} +0.894100 q^{6} +2.50164 q^{7} +1.37698 q^{8} -2.75284 q^{9} +3.76498 q^{10} -5.64455 q^{11} -0.613662 q^{12} +5.23803 q^{13} -4.49902 q^{14} +1.04079 q^{15} -4.94508 q^{16} -1.00000 q^{17} +4.95078 q^{18} +1.48152 q^{19} -2.58408 q^{20} -1.24371 q^{21} +10.1513 q^{22} -1.59633 q^{23} -0.684572 q^{24} -0.617332 q^{25} -9.42022 q^{26} +2.86006 q^{27} +3.08789 q^{28} -2.50096 q^{29} -1.87178 q^{30} -4.16303 q^{31} +6.13943 q^{32} +2.80622 q^{33} +1.79843 q^{34} -5.23714 q^{35} -3.39795 q^{36} +7.99735 q^{37} -2.66440 q^{38} -2.60412 q^{39} -2.88267 q^{40} +11.7180 q^{41} +2.23671 q^{42} +1.00000 q^{43} -6.96732 q^{44} +5.76301 q^{45} +2.87089 q^{46} +9.21620 q^{47} +2.45848 q^{48} -0.741800 q^{49} +1.11023 q^{50} +0.497156 q^{51} +6.46554 q^{52} -5.98145 q^{53} -5.14361 q^{54} +11.8168 q^{55} +3.44470 q^{56} -0.736545 q^{57} +4.49779 q^{58} +6.65907 q^{59} +1.28469 q^{60} +3.15844 q^{61} +7.48692 q^{62} -6.88660 q^{63} -1.15115 q^{64} -10.9657 q^{65} -5.04679 q^{66} +12.4800 q^{67} -1.23435 q^{68} +0.793625 q^{69} +9.41862 q^{70} -0.0484302 q^{71} -3.79059 q^{72} +8.47368 q^{73} -14.3827 q^{74} +0.306910 q^{75} +1.82870 q^{76} -14.1206 q^{77} +4.68332 q^{78} -3.03133 q^{79} +10.3524 q^{80} +6.83661 q^{81} -21.0740 q^{82} +13.6413 q^{83} -1.53516 q^{84} +2.09348 q^{85} -1.79843 q^{86} +1.24337 q^{87} -7.77241 q^{88} +8.23287 q^{89} -10.3644 q^{90} +13.1037 q^{91} -1.97042 q^{92} +2.06968 q^{93} -16.5747 q^{94} -3.10153 q^{95} -3.05225 q^{96} -16.3664 q^{97} +1.33407 q^{98} +15.5385 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 2 q^{2} - q^{3} + 32 q^{4} - 3 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 34 q^{9}+O(q^{10}) $ 21 * q + 2 * q^2 - q^3 + 32 * q^4 - 3 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 34 * q^9	\( 21 q + 2 q^{2} - q^{3} + 32 q^{4} - 3 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 34 q^{9} + 12 q^{10} + 2 q^{11} - 5 q^{12} + 26 q^{13} - 3 q^{14} + 5 q^{15} + 62 q^{16} - 21 q^{17} - 10 q^{18} + 16 q^{19} - 27 q^{20} + 36 q^{21} - 14 q^{22} - q^{23} + 15 q^{24} + 40 q^{25} - 3 q^{26} - 16 q^{27} + 25 q^{28} + 15 q^{29} + 38 q^{30} + 18 q^{31} + 14 q^{32} + 14 q^{33} - 2 q^{34} - 5 q^{35} + 73 q^{36} + 12 q^{37} + 19 q^{38} - 11 q^{39} + 41 q^{40} - 45 q^{42} + 21 q^{43} - 34 q^{44} - 18 q^{45} + 28 q^{46} - q^{47} - 36 q^{48} + 40 q^{49} + 24 q^{50} + q^{51} + 23 q^{52} + 39 q^{53} - 83 q^{54} - 2 q^{55} - 10 q^{56} + 3 q^{57} + 19 q^{58} + 4 q^{59} - 35 q^{60} + 50 q^{61} + 5 q^{62} - 37 q^{63} + 120 q^{64} - 8 q^{65} - 37 q^{66} + 16 q^{67} - 32 q^{68} + 33 q^{69} - q^{70} + q^{71} - 54 q^{72} + 15 q^{73} + 52 q^{74} + 11 q^{75} - 15 q^{76} + 13 q^{77} - 100 q^{78} + 56 q^{79} - 100 q^{80} + 97 q^{81} - 11 q^{82} + 61 q^{84} + 3 q^{85} + 2 q^{86} - 8 q^{87} - 56 q^{88} + 5 q^{89} - 69 q^{90} - 4 q^{91} - 27 q^{92} + 17 q^{93} - 47 q^{94} - 9 q^{95} + 81 q^{96} - 28 q^{97} + 18 q^{98} - 19 q^{99}+O(q^{100}) \) 21 * q + 2 * q^2 - q^3 + 32 * q^4 - 3 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 34 * q^9 + 12 * q^10 + 2 * q^11 - 5 * q^12 + 26 * q^13 - 3 * q^14 + 5 * q^15 + 62 * q^16 - 21 * q^17 - 10 * q^18 + 16 * q^19 - 27 * q^20 + 36 * q^21 - 14 * q^22 - q^23 + 15 * q^24 + 40 * q^25 - 3 * q^26 - 16 * q^27 + 25 * q^28 + 15 * q^29 + 38 * q^30 + 18 * q^31 + 14 * q^32 + 14 * q^33 - 2 * q^34 - 5 * q^35 + 73 * q^36 + 12 * q^37 + 19 * q^38 - 11 * q^39 + 41 * q^40 - 45 * q^42 + 21 * q^43 - 34 * q^44 - 18 * q^45 + 28 * q^46 - q^47 - 36 * q^48 + 40 * q^49 + 24 * q^50 + q^51 + 23 * q^52 + 39 * q^53 - 83 * q^54 - 2 * q^55 - 10 * q^56 + 3 * q^57 + 19 * q^58 + 4 * q^59 - 35 * q^60 + 50 * q^61 + 5 * q^62 - 37 * q^63 + 120 * q^64 - 8 * q^65 - 37 * q^66 + 16 * q^67 - 32 * q^68 + 33 * q^69 - q^70 + q^71 - 54 * q^72 + 15 * q^73 + 52 * q^74 + 11 * q^75 - 15 * q^76 + 13 * q^77 - 100 * q^78 + 56 * q^79 - 100 * q^80 + 97 * q^81 - 11 * q^82 + 61 * q^84 + 3 * q^85 + 2 * q^86 - 8 * q^87 - 56 * q^88 + 5 * q^89 - 69 * q^90 - 4 * q^91 - 27 * q^92 + 17 * q^93 - 47 * q^94 - 9 * q^95 + 81 * q^96 - 28 * q^97 + 18 * q^98 - 19 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.79843	−1.27168	−0.635841	−	0.771820i	$-0.719346\pi$
$2$	−1.79843	−1.27168	−0.635841	+	0.771820i	$0.719346\pi$
$3$	−0.497156	−0.287033	−0.143517	−	0.989648i	$-0.545841\pi$
$3$	−0.497156	−0.287033	−0.143517	+	0.989648i	$0.545841\pi$
$4$	1.23435	0.617173
$5$	−2.09348	−0.936234	−0.468117	−	0.883667i	$-0.655067\pi$
$5$	−2.09348	−0.936234	−0.468117	+	0.883667i	$0.655067\pi$
$6$	0.894100	0.365015
$7$	2.50164	0.945531	0.472765	−	0.881188i	$-0.343256\pi$
$7$	2.50164	0.945531	0.472765	+	0.881188i	$0.343256\pi$
$8$	1.37698	0.486834
$9$	−2.75284	−0.917612
$10$	3.76498	1.19059
$11$	−5.64455	−1.70190	−0.850948	−	0.525250i	$-0.823972\pi$
$11$	−5.64455	−1.70190	−0.850948	+	0.525250i	$0.823972\pi$
$12$	−0.613662	−0.177149
$13$	5.23803	1.45277	0.726384	−	0.687289i	$-0.241199\pi$
$13$	5.23803	1.45277	0.726384	+	0.687289i	$0.241199\pi$
$14$	−4.49902	−1.20241
$15$	1.04079	0.268730
$16$	−4.94508	−1.23627
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	4.95078	1.16691
$19$	1.48152	0.339883	0.169942	−	0.985454i	$-0.445642\pi$
$19$	1.48152	0.339883	0.169942	+	0.985454i	$0.445642\pi$
$20$	−2.58408	−0.577818
$21$	−1.24371	−0.271399
$22$	10.1513	2.16427
$23$	−1.59633	−0.332858	−0.166429	−	0.986053i	$-0.553224\pi$
$23$	−1.59633	−0.332858	−0.166429	+	0.986053i	$0.553224\pi$
$24$	−0.684572	−0.139738
$25$	−0.617332	−0.123466
$26$	−9.42022	−1.84746
$27$	2.86006	0.550418
$28$	3.08789	0.583556
$29$	−2.50096	−0.464416	−0.232208	−	0.972666i	$-0.574595\pi$
$29$	−2.50096	−0.464416	−0.232208	+	0.972666i	$0.574595\pi$
$30$	−1.87178	−0.341739
$31$	−4.16303	−0.747703	−0.373851	−	0.927489i	$-0.621963\pi$
$31$	−4.16303	−0.747703	−0.373851	+	0.927489i	$0.621963\pi$
$32$	6.13943	1.08531
$33$	2.80622	0.488501
$34$	1.79843	0.308428
$35$	−5.23714	−0.885238
$36$	−3.39795	−0.566325
$37$	7.99735	1.31476	0.657378	−	0.753561i	$-0.271666\pi$
$37$	7.99735	1.31476	0.657378	+	0.753561i	$0.271666\pi$
$38$	−2.66440	−0.432223
$39$	−2.60412	−0.416993
$40$	−2.88267	−0.455791
$41$	11.7180	1.83004	0.915022	−	0.403403i	$-0.132173\pi$
$41$	11.7180	1.83004	0.915022	+	0.403403i	$0.132173\pi$
$42$	2.23671	0.345133
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−6.96732	−1.05036
$45$	5.76301	0.859099
$46$	2.87089	0.423289
$47$	9.21620	1.34432	0.672160	−	0.740406i	$-0.265367\pi$
$47$	9.21620	1.34432	0.672160	+	0.740406i	$0.265367\pi$
$48$	2.45848	0.354851
$49$	−0.741800	−0.105971
$50$	1.11023	0.157010
$51$	0.497156	0.0696158
$52$	6.46554	0.896609
$53$	−5.98145	−0.821615	−0.410808	−	0.911722i	$-0.634753\pi$
$53$	−5.98145	−0.821615	−0.410808	+	0.911722i	$0.634753\pi$
$54$	−5.14361	−0.699956
$55$	11.8168	1.59337
$56$	3.44470	0.460317
$57$	−0.736545	−0.0975578
$58$	4.49779	0.590589
$59$	6.65907	0.866937	0.433468	−	0.901169i	$-0.357290\pi$
$59$	6.65907	0.866937	0.433468	+	0.901169i	$0.357290\pi$
$60$	1.28469	0.165853
$61$	3.15844	0.404397	0.202199	−	0.979345i	$-0.435191\pi$
$61$	3.15844	0.404397	0.202199	+	0.979345i	$0.435191\pi$
$62$	7.48692	0.950840
$63$	−6.88660	−0.867630
$64$	−1.15115	−0.143894
$65$	−10.9657	−1.36013
$66$	−5.04679	−0.621217
$67$	12.4800	1.52468	0.762339	−	0.647178i	$-0.224051\pi$
$67$	12.4800	1.52468	0.762339	+	0.647178i	$0.224051\pi$
$68$	−1.23435	−0.149686
$69$	0.793625	0.0955413
$70$	9.41862	1.12574
$71$	−0.0484302	−0.00574760	−0.00287380	−	0.999996i	$-0.500915\pi$
$71$	−0.0484302	−0.00574760	−0.00287380	+	0.999996i	$0.500915\pi$
$72$	−3.79059	−0.446725
$73$	8.47368	0.991770	0.495885	−	0.868388i	$-0.334844\pi$
$73$	8.47368	0.991770	0.495885	+	0.868388i	$0.334844\pi$
$74$	−14.3827	−1.67195
$75$	0.306910	0.0354389
$76$	1.82870	0.209767
$77$	−14.1206	−1.60920
$78$	4.68332	0.530282
$79$	−3.03133	−0.341052	−0.170526	−	0.985353i	$-0.554547\pi$
$79$	−3.03133	−0.341052	−0.170526	+	0.985353i	$0.554547\pi$
$80$	10.3524	1.15744
$81$	6.83661	0.759624
$82$	−21.0740	−2.32723
$83$	13.6413	1.49732	0.748662	−	0.662952i	$-0.230697\pi$
$83$	13.6413	1.49732	0.748662	+	0.662952i	$0.230697\pi$
$84$	−1.53516	−0.167500
$85$	2.09348	0.227070
$86$	−1.79843	−0.193930
$87$	1.24337	0.133303
$88$	−7.77241	−0.828542
$89$	8.23287	0.872683	0.436341	−	0.899781i	$-0.356274\pi$
$89$	8.23287	0.872683	0.436341	+	0.899781i	$0.356274\pi$
$90$	−10.3644	−1.09250
$91$	13.1037	1.37364
$92$	−1.97042	−0.205431
$93$	2.06968	0.214616
$94$	−16.5747	−1.70955
$95$	−3.10153	−0.318210
$96$	−3.05225	−0.311519
$97$	−16.3664	−1.66175	−0.830876	−	0.556457i	$-0.812160\pi$
$97$	−16.3664	−1.66175	−0.830876	+	0.556457i	$0.812160\pi$
$98$	1.33407	0.134762
$99$	15.5385	1.56168
$100$	−0.762001	−0.0762001
$101$	16.6813	1.65985	0.829924	−	0.557877i	$-0.188384\pi$
$101$	16.6813	1.65985	0.829924	+	0.557877i	$0.188384\pi$
$102$	−0.894100	−0.0885290
$103$	4.05591	0.399641	0.199820	−	0.979833i	$-0.435964\pi$
$103$	4.05591	0.399641	0.199820	+	0.979833i	$0.435964\pi$
$104$	7.21264	0.707257
$105$	2.60367	0.254093
$106$	10.7572	1.04483
$107$	−0.471967	−0.0456268	−0.0228134	−	0.999740i	$-0.507262\pi$
$107$	−0.471967	−0.0456268	−0.0228134	+	0.999740i	$0.507262\pi$
$108$	3.53030	0.339703
$109$	−8.89489	−0.851976	−0.425988	−	0.904729i	$-0.640073\pi$
$109$	−8.89489	−0.851976	−0.425988	+	0.904729i	$0.640073\pi$
$110$	−21.2516	−2.02626
$111$	−3.97593	−0.377379
$112$	−12.3708	−1.16893
$113$	10.8766	1.02319	0.511594	−	0.859228i	$-0.329055\pi$
$113$	10.8766	1.02319	0.511594	+	0.859228i	$0.329055\pi$
$114$	1.32462	0.124062
$115$	3.34189	0.311633
$116$	−3.08704	−0.286625
$117$	−14.4194	−1.33308
$118$	−11.9759	−1.10247
$119$	−2.50164	−0.229325
$120$	1.43314	0.130827
$121$	20.8610	1.89645
$122$	−5.68023	−0.514264
$123$	−5.82568	−0.525284
$124$	−5.13862	−0.461462
$125$	11.7598	1.05183
$126$	12.3851	1.10335
$127$	4.21379	0.373913	0.186956	−	0.982368i	$-0.440138\pi$
$127$	4.21379	0.373913	0.186956	+	0.982368i	$0.440138\pi$
$128$	−10.2086	−0.902320
$129$	−0.497156	−0.0437721
$130$	19.7211	1.72965
$131$	1.10075	0.0961726	0.0480863	−	0.998843i	$-0.484688\pi$
$131$	1.10075	0.0961726	0.0480863	+	0.998843i	$0.484688\pi$
$132$	3.46385	0.301489
$133$	3.70622	0.321370
$134$	−22.4444	−1.93890
$135$	−5.98748	−0.515320
$136$	−1.37698	−0.118075
$137$	−17.6133	−1.50480	−0.752402	−	0.658705i	$-0.771105\pi$
$137$	−17.6133	−1.50480	−0.752402	+	0.658705i	$0.771105\pi$
$138$	−1.42728	−0.121498
$139$	−11.4032	−0.967210	−0.483605	−	0.875286i	$-0.660673\pi$
$139$	−11.4032	−0.967210	−0.483605	+	0.875286i	$0.660673\pi$
$140$	−6.46444	−0.546345
$141$	−4.58189	−0.385865
$142$	0.0870982	0.00730912
$143$	−29.5663	−2.47246
$144$	13.6130	1.13442
$145$	5.23571	0.434802
$146$	−15.2393	−1.26121
$147$	0.368790	0.0304173
$148$	9.87149	0.811431
$149$	−5.72038	−0.468632	−0.234316	−	0.972161i	$-0.575285\pi$
$149$	−5.72038	−0.468632	−0.234316	+	0.972161i	$0.575285\pi$
$150$	−0.551956	−0.0450670
$151$	−8.80293	−0.716372	−0.358186	−	0.933650i	$-0.616605\pi$
$151$	−8.80293	−0.716372	−0.358186	+	0.933650i	$0.616605\pi$
$152$	2.04001	0.165467
$153$	2.75284	0.222554
$154$	25.3949	2.04638
$155$	8.71524	0.700025
$156$	−3.21438	−0.257356
$157$	11.4873	0.916788	0.458394	−	0.888749i	$-0.348425\pi$
$157$	11.4873	0.916788	0.458394	+	0.888749i	$0.348425\pi$
$158$	5.45164	0.433709
$159$	2.97371	0.235831
$160$	−12.8528	−1.01610
$161$	−3.99344	−0.314728
$162$	−12.2952	−0.965999
$163$	2.88708	0.226133	0.113067	−	0.993587i	$-0.463933\pi$
$163$	2.88708	0.226133	0.113067	+	0.993587i	$0.463933\pi$
$164$	14.4641	1.12945
$165$	−5.87478	−0.457351
$166$	−24.5329	−1.90412
$167$	−0.314363	−0.0243262	−0.0121631	−	0.999926i	$-0.503872\pi$
$167$	−0.314363	−0.0243262	−0.0121631	+	0.999926i	$0.503872\pi$
$168$	−1.71255	−0.132126
$169$	14.4370	1.11054
$170$	−3.76498	−0.288761
$171$	−4.07837	−0.311881
$172$	1.23435	0.0941179
$173$	−4.99384	−0.379675	−0.189837	−	0.981816i	$-0.560796\pi$
$173$	−4.99384	−0.379675	−0.189837	+	0.981816i	$0.560796\pi$
$174$	−2.23610	−0.169519
$175$	−1.54434	−0.116741
$176$	27.9128	2.10400
$177$	−3.31060	−0.248840
$178$	−14.8062	−1.10977
$179$	−12.7307	−0.951537	−0.475769	−	0.879570i	$-0.657830\pi$
$179$	−12.7307	−0.951537	−0.475769	+	0.879570i	$0.657830\pi$
$180$	7.11355	0.530213
$181$	5.07024	0.376868	0.188434	−	0.982086i	$-0.439659\pi$
$181$	5.07024	0.376868	0.188434	+	0.982086i	$0.439659\pi$
$182$	−23.5660	−1.74683
$183$	−1.57024	−0.116075
$184$	−2.19811	−0.162047
$185$	−16.7423	−1.23092
$186$	−3.72217	−0.272922
$187$	5.64455	0.412770
$188$	11.3760	0.829678
$189$	7.15483	0.520437
$190$	5.57788	0.404662
$191$	−18.4344	−1.33387	−0.666933	−	0.745118i	$-0.732393\pi$
$191$	−18.4344	−1.33387	−0.666933	+	0.745118i	$0.732393\pi$
$192$	0.572303	0.0413024
$193$	9.15240	0.658804	0.329402	−	0.944190i	$-0.393153\pi$
$193$	9.15240	0.658804	0.329402	+	0.944190i	$0.393153\pi$
$194$	29.4337	2.11322
$195$	5.45168	0.390403
$196$	−0.915637	−0.0654026
$197$	−4.71556	−0.335970	−0.167985	−	0.985790i	$-0.553726\pi$
$197$	−4.71556	−0.335970	−0.167985	+	0.985790i	$0.553726\pi$
$198$	−27.9449	−1.98596
$199$	−3.61721	−0.256417	−0.128209	−	0.991747i	$-0.540923\pi$
$199$	−3.61721	−0.256417	−0.128209	+	0.991747i	$0.540923\pi$
$200$	−0.850051	−0.0601077
$201$	−6.20452	−0.437633
$202$	−30.0001	−2.11080
$203$	−6.25649	−0.439120
$204$	0.613662	0.0429649
$205$	−24.5314	−1.71335
$206$	−7.29427	−0.508216
$207$	4.39444	0.305434
$208$	−25.9025	−1.79601
$209$	−8.36250	−0.578446
$210$	−4.68252	−0.323125
$211$	−10.8606	−0.747678	−0.373839	−	0.927494i	$-0.621959\pi$
$211$	−10.8606	−0.747678	−0.373839	+	0.927494i	$0.621959\pi$
$212$	−7.38317	−0.507078
$213$	0.0240774	0.00164975
$214$	0.848799	0.0580227
$215$	−2.09348	−0.142774
$216$	3.93823	0.267962
$217$	−10.4144	−0.706976
$218$	15.9968	1.08344
$219$	−4.21274	−0.284671
$220$	14.5860	0.983386
$221$	−5.23803	−0.352348
$222$	7.15043	0.479905
$223$	9.34267	0.625631	0.312816	−	0.949814i	$-0.398728\pi$
$223$	9.34267	0.625631	0.312816	+	0.949814i	$0.398728\pi$
$224$	15.3586	1.02619
$225$	1.69941	0.113294
$226$	−19.5608	−1.30117
$227$	−13.3280	−0.884612	−0.442306	−	0.896864i	$-0.645839\pi$
$227$	−13.3280	−0.884612	−0.442306	+	0.896864i	$0.645839\pi$
$228$	−0.909151	−0.0602100
$229$	15.7755	1.04247	0.521237	−	0.853412i	$-0.325471\pi$
$229$	15.7755	1.04247	0.521237	+	0.853412i	$0.325471\pi$
$230$	−6.01015	−0.396298
$231$	7.02016	0.461892
$232$	−3.44376	−0.226094
$233$	−2.39285	−0.156761	−0.0783806	−	0.996924i	$-0.524975\pi$
$233$	−2.39285	−0.156761	−0.0783806	+	0.996924i	$0.524975\pi$
$234$	25.9323	1.69525
$235$	−19.2939	−1.25860
$236$	8.21959	0.535050
$237$	1.50705	0.0978931
$238$	4.49902	0.291628
$239$	−0.339675	−0.0219717	−0.0109859	−	0.999940i	$-0.503497\pi$
$239$	−0.339675	−0.0219717	−0.0109859	+	0.999940i	$0.503497\pi$
$240$	−5.14678	−0.332223
$241$	19.1539	1.23381	0.616907	−	0.787036i	$-0.288386\pi$
$241$	19.1539	1.23381	0.616907	+	0.787036i	$0.288386\pi$
$242$	−37.5169	−2.41168
$243$	−11.9790	−0.768455
$244$	3.89861	0.249583
$245$	1.55294	0.0992140
$246$	10.4771	0.667993
$247$	7.76023	0.493772
$248$	−5.73240	−0.364007
$249$	−6.78184	−0.429782
$250$	−21.1491	−1.33759
$251$	30.0767	1.89842	0.949211	−	0.314641i	$-0.101884\pi$
$251$	30.0767	1.89842	0.949211	+	0.314641i	$0.101884\pi$
$252$	−8.50045	−0.535478
$253$	9.01057	0.566490
$254$	−7.57819	−0.475498
$255$	−1.04079	−0.0651766
$256$	20.6617	1.29136
$257$	−5.10935	−0.318713	−0.159356	−	0.987221i	$-0.550942\pi$
$257$	−5.10935	−0.318713	−0.159356	+	0.987221i	$0.550942\pi$
$258$	0.894100	0.0556642
$259$	20.0065	1.24314
$260$	−13.5355	−0.839435
$261$	6.88472	0.426154
$262$	−1.97961	−0.122301
$263$	−13.9154	−0.858062	−0.429031	−	0.903290i	$-0.641145\pi$
$263$	−13.9154	−0.858062	−0.429031	+	0.903290i	$0.641145\pi$
$264$	3.86410	0.237819
$265$	12.5221	0.769224
$266$	−6.66538	−0.408680
$267$	−4.09302	−0.250489
$268$	15.4047	0.940989
$269$	21.6312	1.31888	0.659439	−	0.751758i	$-0.270794\pi$
$269$	21.6312	1.31888	0.659439	+	0.751758i	$0.270794\pi$
$270$	10.7681	0.655323
$271$	−26.9399	−1.63648	−0.818242	−	0.574874i	$-0.805051\pi$
$271$	−26.9399	−1.63648	−0.818242	+	0.574874i	$0.805051\pi$
$272$	4.94508	0.299840
$273$	−6.51457	−0.394279
$274$	31.6762	1.91363
$275$	3.48456	0.210127
$276$	0.979608	0.0589655
$277$	−27.9307	−1.67819	−0.839096	−	0.543983i	$-0.816916\pi$
$277$	−27.9307	−1.67819	−0.839096	+	0.543983i	$0.816916\pi$
$278$	20.5079	1.22998
$279$	11.4601	0.686101
$280$	−7.21141	−0.430964
$281$	0.723655	0.0431696	0.0215848	−	0.999767i	$-0.493129\pi$
$281$	0.723655	0.0431696	0.0215848	+	0.999767i	$0.493129\pi$
$282$	8.24020	0.490697
$283$	29.9230	1.77874	0.889368	−	0.457193i	$-0.151145\pi$
$283$	29.9230	1.77874	0.889368	+	0.457193i	$0.151145\pi$
$284$	−0.0597795	−0.00354726
$285$	1.54194	0.0913369
$286$	53.1729	3.14418
$287$	29.3142	1.73036
$288$	−16.9008	−0.995891
$289$	1.00000	0.0588235
$290$	−9.41605	−0.552929
$291$	8.13664	0.476978
$292$	10.4595	0.612093
$293$	−5.45512	−0.318692	−0.159346	−	0.987223i	$-0.550938\pi$
$293$	−5.45512	−0.318692	−0.159346	+	0.987223i	$0.550938\pi$
$294$	−0.663243	−0.0386811
$295$	−13.9406	−0.811655
$296$	11.0122	0.640068
$297$	−16.1437	−0.936755
$298$	10.2877	0.595950
$299$	−8.36163	−0.483566
$300$	0.378833	0.0218719
$301$	2.50164	0.144192
$302$	15.8314	0.910997
$303$	−8.29319	−0.476431
$304$	−7.32623	−0.420188
$305$	−6.61214	−0.378610
$306$	−4.95078	−0.283017
$307$	2.13287	0.121729	0.0608646	−	0.998146i	$-0.480614\pi$
$307$	2.13287	0.121729	0.0608646	+	0.998146i	$0.480614\pi$
$308$	−17.4297	−0.993151
$309$	−2.01642	−0.114710
$310$	−15.6737	−0.890208
$311$	23.5519	1.33551	0.667754	−	0.744382i	$-0.267256\pi$
$311$	23.5519	1.33551	0.667754	+	0.744382i	$0.267256\pi$
$312$	−3.58581	−0.203006
$313$	34.9462	1.97527	0.987637	−	0.156755i	$-0.0501034\pi$
$313$	34.9462	1.97527	0.987637	+	0.156755i	$0.0501034\pi$
$314$	−20.6591	−1.16586
$315$	14.4170	0.812305
$316$	−3.74171	−0.210488
$317$	34.3477	1.92916	0.964581	−	0.263788i	$-0.0849720\pi$
$317$	34.3477	1.92916	0.964581	+	0.263788i	$0.0849720\pi$
$318$	−5.34801	−0.299902
$319$	14.1168	0.790388
$320$	2.40992	0.134719
$321$	0.234641	0.0130964
$322$	7.18192	0.400233
$323$	−1.48152	−0.0824338
$324$	8.43874	0.468819
$325$	−3.23360	−0.179368
$326$	−5.19220	−0.287569
$327$	4.42215	0.244545
$328$	16.1354	0.890929
$329$	23.0556	1.27110
$330$	10.5654	0.581604
$331$	26.1790	1.43893	0.719463	−	0.694531i	$-0.244388\pi$
$331$	26.1790	1.43893	0.719463	+	0.694531i	$0.244388\pi$
$332$	16.8380	0.924107
$333$	−22.0154	−1.20644
$334$	0.565360	0.0309351
$335$	−26.1267	−1.42745
$336$	6.15022	0.335522
$337$	2.10746	0.114801	0.0574004	−	0.998351i	$-0.481719\pi$
$337$	2.10746	0.114801	0.0574004	+	0.998351i	$0.481719\pi$
$338$	−25.9638	−1.41225
$339$	−5.40738	−0.293689
$340$	2.58408	0.140141
$341$	23.4985	1.27251
$342$	7.33466	0.396613
$343$	−19.3672	−1.04573
$344$	1.37698	0.0742415
$345$	−1.66144	−0.0894490
$346$	8.98107	0.482825
$347$	0.593055	0.0318369	0.0159184	−	0.999873i	$-0.494933\pi$
$347$	0.593055	0.0318369	0.0159184	+	0.999873i	$0.494933\pi$
$348$	1.53474	0.0822708
$349$	7.60025	0.406832	0.203416	−	0.979092i	$-0.434796\pi$
$349$	7.60025	0.406832	0.203416	+	0.979092i	$0.434796\pi$
$350$	2.77739	0.148458
$351$	14.9811	0.799630
$352$	−34.6543	−1.84708
$353$	24.0562	1.28038	0.640190	−	0.768217i	$-0.278856\pi$
$353$	24.0562	1.28038	0.640190	+	0.768217i	$0.278856\pi$
$354$	5.95387	0.316445
$355$	0.101388	0.00538110
$356$	10.1622	0.538596
$357$	1.24371	0.0658239
$358$	22.8953	1.21005
$359$	7.23513	0.381856	0.190928	−	0.981604i	$-0.438850\pi$
$359$	7.23513	0.381856	0.190928	+	0.981604i	$0.438850\pi$
$360$	7.93553	0.418239
$361$	−16.8051	−0.884479
$362$	−9.11846	−0.479256
$363$	−10.3711	−0.544344
$364$	16.1744	0.847771
$365$	−17.7395	−0.928528
$366$	2.82396	0.147611
$367$	−15.1606	−0.791376	−0.395688	−	0.918385i	$-0.629494\pi$
$367$	−15.1606	−0.791376	−0.395688	+	0.918385i	$0.629494\pi$
$368$	7.89399	0.411503
$369$	−32.2577	−1.67927
$370$	30.1098	1.56534
$371$	−14.9634	−0.776863
$372$	2.55470	0.132455
$373$	15.2875	0.791558	0.395779	−	0.918346i	$-0.370475\pi$
$373$	15.2875	0.791558	0.395779	+	0.918346i	$0.370475\pi$
$374$	−10.1513	−0.524912
$375$	−5.84645	−0.301909
$376$	12.6905	0.654461
$377$	−13.1001	−0.674689
$378$	−12.8675	−0.661830
$379$	−31.5103	−1.61857	−0.809287	−	0.587414i	$-0.800146\pi$
$379$	−31.5103	−1.61857	−0.809287	+	0.587414i	$0.800146\pi$
$380$	−3.82836	−0.196391
$381$	−2.09491	−0.107325
$382$	33.1529	1.69625
$383$	−22.0881	−1.12865	−0.564324	−	0.825553i	$-0.690863\pi$
$383$	−22.0881	−1.12865	−0.564324	+	0.825553i	$0.690863\pi$
$384$	5.07526	0.258996
$385$	29.5613	1.50658
$386$	−16.4599	−0.837789
$387$	−2.75284	−0.139935
$388$	−20.2017	−1.02559
$389$	31.9346	1.61915	0.809574	−	0.587017i	$-0.199698\pi$
$389$	31.9346	1.61915	0.809574	+	0.587017i	$0.199698\pi$
$390$	−9.80445	−0.496468
$391$	1.59633	0.0807299
$392$	−1.02144	−0.0515905
$393$	−0.547242	−0.0276047
$394$	8.48060	0.427246
$395$	6.34604	0.319304
$396$	19.1799	0.963826
$397$	3.60398	0.180878	0.0904392	−	0.995902i	$-0.471173\pi$
$397$	3.60398	0.180878	0.0904392	+	0.995902i	$0.471173\pi$
$398$	6.50529	0.326081
$399$	−1.84257	−0.0922439
$400$	3.05276	0.152638
$401$	−7.51870	−0.375466	−0.187733	−	0.982220i	$-0.560114\pi$
$401$	−7.51870	−0.375466	−0.187733	+	0.982220i	$0.560114\pi$
$402$	11.1584	0.556530
$403$	−21.8061	−1.08624
$404$	20.5904	1.02441
$405$	−14.3123	−0.711185
$406$	11.2519	0.558420
$407$	−45.1414	−2.23758
$408$	0.684572	0.0338913
$409$	−15.5434	−0.768572	−0.384286	−	0.923214i	$-0.625552\pi$
$409$	−15.5434	−0.768572	−0.384286	+	0.923214i	$0.625552\pi$
$410$	44.1180	2.17883
$411$	8.75654	0.431928
$412$	5.00640	0.246647
$413$	16.6586	0.819715
$414$	−7.90308	−0.388415
$415$	−28.5578	−1.40185
$416$	32.1585	1.57670
$417$	5.66919	0.277621
$418$	15.0394	0.735599
$419$	2.59670	0.126857	0.0634285	−	0.997986i	$-0.479797\pi$
$419$	2.59670	0.126857	0.0634285	+	0.997986i	$0.479797\pi$
$420$	3.21383	0.156819
$421$	−8.60834	−0.419545	−0.209773	−	0.977750i	$-0.567272\pi$
$421$	−8.60834	−0.419545	−0.209773	+	0.977750i	$0.567272\pi$
$422$	19.5321	0.950808
$423$	−25.3707	−1.23356
$424$	−8.23631	−0.399991
$425$	0.617332	0.0299450
$426$	−0.0433014	−0.00209796
$427$	7.90129	0.382370
$428$	−0.582571	−0.0281596
$429$	14.6991	0.709678
$430$	3.76498	0.181563
$431$	−25.9930	−1.25204	−0.626020	−	0.779807i	$-0.715317\pi$
$431$	−25.9930	−1.25204	−0.626020	+	0.779807i	$0.715317\pi$
$432$	−14.1432	−0.680466
$433$	14.5668	0.700034	0.350017	−	0.936743i	$-0.386176\pi$
$433$	14.5668	0.700034	0.350017	+	0.936743i	$0.386176\pi$
$434$	18.7296	0.899048
$435$	−2.60296	−0.124803
$436$	−10.9794	−0.525816
$437$	−2.36499	−0.113133
$438$	7.57632	0.362010
$439$	−0.593617	−0.0283318	−0.0141659	−	0.999900i	$-0.504509\pi$
$439$	−0.593617	−0.0283318	−0.0141659	+	0.999900i	$0.504509\pi$
$440$	16.2714	0.775709
$441$	2.04205	0.0972406
$442$	9.42022	0.448074
$443$	−1.64139	−0.0779847	−0.0389923	−	0.999240i	$-0.512415\pi$
$443$	−1.64139	−0.0779847	−0.0389923	+	0.999240i	$0.512415\pi$
$444$	−4.90767	−0.232908
$445$	−17.2354	−0.817035
$446$	−16.8021	−0.795603
$447$	2.84392	0.134513
$448$	−2.87977	−0.136057
$449$	−30.1055	−1.42077	−0.710384	−	0.703815i	$-0.751478\pi$
$449$	−30.1055	−1.42077	−0.710384	+	0.703815i	$0.751478\pi$
$450$	−3.05627	−0.144074
$451$	−66.1429	−3.11455
$452$	13.4255	0.631483
$453$	4.37643	0.205623
$454$	23.9695	1.12494
$455$	−27.4323	−1.28605
$456$	−1.01420	−0.0474945
$457$	25.9673	1.21470	0.607349	−	0.794435i	$-0.292233\pi$
$457$	25.9673	1.21470	0.607349	+	0.794435i	$0.292233\pi$
$458$	−28.3711	−1.32570
$459$	−2.86006	−0.133496
$460$	4.12505	0.192331
$461$	−3.82257	−0.178035	−0.0890174	−	0.996030i	$-0.528373\pi$
$461$	−3.82257	−0.178035	−0.0890174	+	0.996030i	$0.528373\pi$
$462$	−12.6253	−0.587380
$463$	3.75343	0.174437	0.0872183	−	0.996189i	$-0.472202\pi$
$463$	3.75343	0.174437	0.0872183	+	0.996189i	$0.472202\pi$
$464$	12.3674	0.574144
$465$	−4.33283	−0.200930
$466$	4.30338	0.199350
$467$	−31.2919	−1.44802	−0.724008	−	0.689791i	$-0.757702\pi$
$467$	−31.2919	−1.44802	−0.724008	+	0.689791i	$0.757702\pi$
$468$	−17.7986	−0.822739
$469$	31.2205	1.44163
$470$	34.6988	1.60054
$471$	−5.71099	−0.263148
$472$	9.16937	0.422055
$473$	−5.64455	−0.259537
$474$	−2.71031	−0.124489
$475$	−0.914588	−0.0419642
$476$	−3.08789	−0.141533
$477$	16.4660	0.753924
$478$	0.610881	0.0279410
$479$	−14.4702	−0.661162	−0.330581	−	0.943778i	$-0.607245\pi$
$479$	−14.4702	−0.661162	−0.330581	+	0.943778i	$0.607245\pi$
$480$	6.38984	0.291655
$481$	41.8904	1.91004
$482$	−34.4470	−1.56902
$483$	1.98536	0.0903372
$484$	25.7496	1.17044
$485$	34.2627	1.55579
$486$	21.5434	0.977230
$487$	−34.1864	−1.54913	−0.774567	−	0.632492i	$-0.782032\pi$
$487$	−34.1864	−1.54913	−0.774567	+	0.632492i	$0.782032\pi$
$488$	4.34910	0.196874
$489$	−1.43533	−0.0649077
$490$	−2.79286	−0.126169
$491$	22.6096	1.02036	0.510179	−	0.860068i	$-0.329579\pi$
$491$	22.6096	1.02036	0.510179	+	0.860068i	$0.329579\pi$
$492$	−7.19090	−0.324191
$493$	2.50096	0.112637
$494$	−13.9562	−0.627920
$495$	−32.5296	−1.46210
$496$	20.5865	0.924363
$497$	−0.121155	−0.00543454
$498$	12.1967	0.546545
$499$	−34.1576	−1.52910	−0.764552	−	0.644562i	$-0.777040\pi$
$499$	−34.1576	−1.52910	−0.764552	+	0.644562i	$0.777040\pi$
$500$	14.5156	0.649159
$501$	0.156288	0.00698242
$502$	−54.0907	−2.41419
$503$	−7.74357	−0.345269	−0.172634	−	0.984986i	$-0.555228\pi$
$503$	−7.74357	−0.345269	−0.172634	+	0.984986i	$0.555228\pi$
$504$	−9.48268	−0.422392
$505$	−34.9219	−1.55401
$506$	−16.2049	−0.720394
$507$	−7.17742	−0.318760
$508$	5.20127	0.230769
$509$	21.2960	0.943928	0.471964	−	0.881618i	$-0.343545\pi$
$509$	21.2960	0.943928	0.471964	+	0.881618i	$0.343545\pi$
$510$	1.87178	0.0828839
$511$	21.1981	0.937749
$512$	−16.7415	−0.739875
$513$	4.23722	0.187078
$514$	9.18880	0.405301
$515$	−8.49098	−0.374157
$516$	−0.613662	−0.0270150
$517$	−52.0213	−2.28789
$518$	−35.9802	−1.58088
$519$	2.48272	0.108979
$520$	−15.0995	−0.662158
$521$	24.9616	1.09359	0.546794	−	0.837267i	$-0.315848\pi$
$521$	24.9616	1.09359	0.546794	+	0.837267i	$0.315848\pi$
$522$	−12.3817	−0.541932
$523$	23.9697	1.04812	0.524061	−	0.851681i	$-0.324416\pi$
$523$	23.9697	1.04812	0.524061	+	0.851681i	$0.324416\pi$
$524$	1.35870	0.0593551
$525$	0.767779	0.0335086
$526$	25.0259	1.09118
$527$	4.16303	0.181345
$528$	−13.8770	−0.603919
$529$	−20.4517	−0.889206
$530$	−22.5200	−0.978208
$531$	−18.3313	−0.795511
$532$	4.57476	0.198341
$533$	61.3793	2.65863
$534$	7.36101	0.318542
$535$	0.988055	0.0427174
$536$	17.1847	0.742266
$537$	6.32914	0.273123
$538$	−38.9022	−1.67719
$539$	4.18713	0.180352
$540$	−7.39062	−0.318041
$541$	26.1512	1.12433	0.562164	−	0.827025i	$-0.309969\pi$
$541$	26.1512	1.12433	0.562164	+	0.827025i	$0.309969\pi$
$542$	48.4495	2.08108
$543$	−2.52070	−0.108174
$544$	−6.13943	−0.263226
$545$	18.6213	0.797649
$546$	11.7160	0.501398
$547$	−1.39351	−0.0595822	−0.0297911	−	0.999556i	$-0.509484\pi$
$547$	−1.39351	−0.0595822	−0.0297911	+	0.999556i	$0.509484\pi$
$548$	−21.7409	−0.928723
$549$	−8.69468	−0.371080
$550$	−6.26673	−0.267214
$551$	−3.70521	−0.157847
$552$	1.09280	0.0465128
$553$	−7.58330	−0.322475
$554$	50.2313	2.13413
$555$	8.32354	0.353315
$556$	−14.0755	−0.596936
$557$	40.2352	1.70482	0.852409	−	0.522875i	$-0.175141\pi$
$557$	40.2352	1.70482	0.852409	+	0.522875i	$0.175141\pi$
$558$	−20.6103	−0.872502
$559$	5.23803	0.221545
$560$	25.8981	1.09439
$561$	−2.80622	−0.118479
$562$	−1.30144	−0.0548980
$563$	28.7866	1.21321	0.606605	−	0.795003i	$-0.292531\pi$
$563$	28.7866	1.21321	0.606605	+	0.795003i	$0.292531\pi$
$564$	−5.65563	−0.238145
$565$	−22.7700	−0.957943
$566$	−53.8143	−2.26198
$567$	17.1027	0.718248
$568$	−0.0666872	−0.00279813
$569$	6.84877	0.287116	0.143558	−	0.989642i	$-0.454146\pi$
$569$	6.84877	0.287116	0.143558	+	0.989642i	$0.454146\pi$
$570$	−2.77308	−0.116151
$571$	42.2305	1.76729	0.883647	−	0.468155i	$-0.155081\pi$
$571$	42.2305	1.76729	0.883647	+	0.468155i	$0.155081\pi$
$572$	−36.4951	−1.52593
$573$	9.16477	0.382864
$574$	−52.7195	−2.20047
$575$	0.985466	0.0410968
$576$	3.16894	0.132039
$577$	−8.81271	−0.366878	−0.183439	−	0.983031i	$-0.558723\pi$
$577$	−8.81271	−0.366878	−0.183439	+	0.983031i	$0.558723\pi$
$578$	−1.79843	−0.0748048
$579$	−4.55017	−0.189099
$580$	6.46267	0.268348
$581$	34.1255	1.41577
$582$	−14.6332	−0.606564
$583$	33.7626	1.39830
$584$	11.6681	0.482828
$585$	30.1868	1.24807
$586$	9.81065	0.405274
$587$	24.0601	0.993068	0.496534	−	0.868017i	$-0.334606\pi$
$587$	24.0601	0.993068	0.496534	+	0.868017i	$0.334606\pi$
$588$	0.455214	0.0187727
$589$	−6.16761	−0.254132
$590$	25.0712	1.03217
$591$	2.34437	0.0964345
$592$	−39.5475	−1.62539
$593$	−15.7529	−0.646894	−0.323447	−	0.946246i	$-0.604842\pi$
$593$	−15.7529	−0.646894	−0.323447	+	0.946246i	$0.604842\pi$
$594$	29.0334	1.19125
$595$	5.23714	0.214702
$596$	−7.06092	−0.289227
$597$	1.79832	0.0736002
$598$	15.0378	0.614941
$599$	−12.4412	−0.508332	−0.254166	−	0.967161i	$-0.581801\pi$
$599$	−12.4412	−0.508332	−0.254166	+	0.967161i	$0.581801\pi$
$600$	0.422608	0.0172529
$601$	−20.8947	−0.852313	−0.426157	−	0.904649i	$-0.640133\pi$
$601$	−20.8947	−0.852313	−0.426157	+	0.904649i	$0.640133\pi$
$602$	−4.49902	−0.183366
$603$	−34.3555	−1.39906
$604$	−10.8659	−0.442125
$605$	−43.6720	−1.77552
$606$	14.9147	0.605869
$607$	−20.1345	−0.817236	−0.408618	−	0.912705i	$-0.633989\pi$
$607$	−20.1345	−0.817236	−0.408618	+	0.912705i	$0.633989\pi$
$608$	9.09567	0.368878
$609$	3.11045	0.126042
$610$	11.8915	0.481472
$611$	48.2747	1.95299
$612$	3.39795	0.137354
$613$	34.9138	1.41015	0.705077	−	0.709131i	$-0.250912\pi$
$613$	34.9138	1.41015	0.705077	+	0.709131i	$0.250912\pi$
$614$	−3.83581	−0.154801
$615$	12.1959	0.491788
$616$	−19.4438	−0.783412
$617$	−1.82593	−0.0735090	−0.0367545	−	0.999324i	$-0.511702\pi$
$617$	−1.82593	−0.0735090	−0.0367545	+	0.999324i	$0.511702\pi$
$618$	3.62639	0.145875
$619$	5.47769	0.220167	0.110083	−	0.993922i	$-0.464888\pi$
$619$	5.47769	0.220167	0.110083	+	0.993922i	$0.464888\pi$
$620$	10.7576	0.432036
$621$	−4.56560	−0.183211
$622$	−42.3565	−1.69834
$623$	20.5957	0.825149
$624$	12.8776	0.515516
$625$	−21.5322	−0.861290
$626$	−62.8482	−2.51192
$627$	4.15747	0.166033
$628$	14.1793	0.565816
$629$	−7.99735	−0.318875
$630$	−25.9279	−1.03299
$631$	−19.4226	−0.773200	−0.386600	−	0.922247i	$-0.626351\pi$
$631$	−19.4226	−0.773200	−0.386600	+	0.922247i	$0.626351\pi$
$632$	−4.17407	−0.166036
$633$	5.39944	0.214608
$634$	−61.7720	−2.45328
$635$	−8.82148	−0.350070
$636$	3.67059	0.145548
$637$	−3.88557	−0.153952
$638$	−25.3880	−1.00512
$639$	0.133320	0.00527407
$640$	21.3715	0.844782
$641$	−6.05669	−0.239225	−0.119613	−	0.992821i	$-0.538165\pi$
$641$	−6.05669	−0.239225	−0.119613	+	0.992821i	$0.538165\pi$
$642$	−0.421986	−0.0166544
$643$	−11.3041	−0.445790	−0.222895	−	0.974842i	$-0.571551\pi$
$643$	−11.3041	−0.445790	−0.222895	+	0.974842i	$0.571551\pi$
$644$	−4.92929	−0.194241
$645$	1.04079	0.0409810
$646$	2.66440	0.104830
$647$	−46.8478	−1.84178	−0.920889	−	0.389826i	$-0.872535\pi$
$647$	−46.8478	−1.84178	−0.920889	+	0.389826i	$0.872535\pi$
$648$	9.41385	0.369811
$649$	−37.5874	−1.47544
$650$	5.81540	0.228099
$651$	5.17759	0.202926
$652$	3.56365	0.139563
$653$	−7.25207	−0.283795	−0.141898	−	0.989881i	$-0.545320\pi$
$653$	−7.25207	−0.283795	−0.141898	+	0.989881i	$0.545320\pi$
$654$	−7.95292	−0.310984
$655$	−2.30439	−0.0900400
$656$	−57.9465	−2.26243
$657$	−23.3267	−0.910060
$658$	−41.4638	−1.61643
$659$	−35.3903	−1.37861	−0.689304	−	0.724472i	$-0.742084\pi$
$659$	−35.3903	−1.37861	−0.689304	+	0.724472i	$0.742084\pi$
$660$	−7.25150	−0.282264
$661$	−11.2898	−0.439122	−0.219561	−	0.975599i	$-0.570463\pi$
$661$	−11.2898	−0.439122	−0.219561	+	0.975599i	$0.570463\pi$
$662$	−47.0810	−1.82985
$663$	2.60412	0.101136
$664$	18.7837	0.728949
$665$	−7.75891	−0.300878
$666$	39.5931	1.53420
$667$	3.99236	0.154585
$668$	−0.388033	−0.0150134
$669$	−4.64476	−0.179577
$670$	46.9870	1.81527
$671$	−17.8280	−0.688242
$672$	−7.63564	−0.294551
$673$	1.13147	0.0436149	0.0218075	−	0.999762i	$-0.493058\pi$
$673$	1.13147	0.0436149	0.0218075	+	0.999762i	$0.493058\pi$
$674$	−3.79012	−0.145990
$675$	−1.76560	−0.0679581
$676$	17.8202	0.685392
$677$	−47.7499	−1.83518	−0.917590	−	0.397529i	$-0.869868\pi$
$677$	−47.7499	−1.83518	−0.917590	+	0.397529i	$0.869868\pi$
$678$	9.72479	0.373478
$679$	−40.9427	−1.57124
$680$	2.88267	0.110545
$681$	6.62611	0.253913
$682$	−42.2603	−1.61823
$683$	15.5231	0.593976	0.296988	−	0.954881i	$-0.404018\pi$
$683$	15.5231	0.593976	0.296988	+	0.954881i	$0.404018\pi$
$684$	−5.03412	−0.192484
$685$	36.8731	1.40885
$686$	34.8305	1.32984
$687$	−7.84289	−0.299225
$688$	−4.94508	−0.188529
$689$	−31.3310	−1.19362
$690$	2.98798	0.113751
$691$	−35.0004	−1.33148	−0.665739	−	0.746185i	$-0.731883\pi$
$691$	−35.0004	−1.33148	−0.665739	+	0.746185i	$0.731883\pi$
$692$	−6.16412	−0.234325
$693$	38.8718	1.47662
$694$	−1.06657	−0.0404863
$695$	23.8725	0.905535
$696$	1.71208	0.0648964
$697$	−11.7180	−0.443851
$698$	−13.6685	−0.517361
$699$	1.18962	0.0449956
$700$	−1.90625	−0.0720495
$701$	42.1605	1.59238	0.796190	−	0.605046i	$-0.206845\pi$
$701$	42.1605	1.59238	0.796190	+	0.605046i	$0.206845\pi$
$702$	−26.9424	−1.01687
$703$	11.8482	0.446864
$704$	6.49775	0.244893
$705$	9.59210	0.361259
$706$	−43.2633	−1.62823
$707$	41.7305	1.56944
$708$	−4.08642	−0.153577
$709$	−6.64975	−0.249737	−0.124868	−	0.992173i	$-0.539851\pi$
$709$	−6.64975	−0.249737	−0.124868	+	0.992173i	$0.539851\pi$
$710$	−0.182339	−0.00684304
$711$	8.34476	0.312953
$712$	11.3365	0.424852
$713$	6.64558	0.248879
$714$	−2.23671	−0.0837069
$715$	61.8966	2.31480
$716$	−15.7141	−0.587263
$717$	0.168871	0.00630662
$718$	−13.0119	−0.485599
$719$	45.7579	1.70648	0.853241	−	0.521517i	$-0.174634\pi$
$719$	45.7579	1.70648	0.853241	+	0.521517i	$0.174634\pi$
$720$	−28.4986	−1.06208
$721$	10.1464	0.377873
$722$	30.2228	1.12478
$723$	−9.52250	−0.354145
$724$	6.25842	0.232592
$725$	1.54392	0.0573398
$726$	18.6518	0.692232
$727$	6.29700	0.233543	0.116771	−	0.993159i	$-0.462746\pi$
$727$	6.29700	0.233543	0.116771	+	0.993159i	$0.462746\pi$
$728$	18.0434	0.668734
$729$	−14.5544	−0.539052
$730$	31.9032	1.18079
$731$	−1.00000	−0.0369863
$732$	−1.93822	−0.0716386
$733$	−37.3244	−1.37861	−0.689305	−	0.724471i	$-0.742084\pi$
$733$	−37.3244	−1.37861	−0.689305	+	0.724471i	$0.742084\pi$
$734$	27.2652	1.00638
$735$	−0.772056	−0.0284777
$736$	−9.80056	−0.361253
$737$	−70.4441	−2.59484
$738$	58.0132	2.13550
$739$	−47.8783	−1.76123	−0.880616	−	0.473830i	$-0.842871\pi$
$739$	−47.8783	−1.76123	−0.880616	+	0.473830i	$0.842871\pi$
$740$	−20.6658	−0.759689
$741$	−3.85805	−0.141729
$742$	26.9107	0.987922
$743$	51.7675	1.89916	0.949582	−	0.313519i	$-0.101508\pi$
$743$	51.7675	1.89916	0.949582	+	0.313519i	$0.101508\pi$
$744$	2.84989	0.104482
$745$	11.9755	0.438749
$746$	−27.4935	−1.00661
$747$	−37.5522	−1.37396
$748$	6.96732	0.254751
$749$	−1.18069	−0.0431415
$750$	10.5144	0.383932
$751$	29.4031	1.07293	0.536467	−	0.843921i	$-0.319759\pi$
$751$	29.4031	1.07293	0.536467	+	0.843921i	$0.319759\pi$
$752$	−45.5748	−1.66194
$753$	−14.9528	−0.544910
$754$	23.5596	0.857989
$755$	18.4288	0.670692
$756$	8.83153	0.321200
$757$	36.9376	1.34252	0.671259	−	0.741223i	$-0.265754\pi$
$757$	36.9376	1.34252	0.671259	+	0.741223i	$0.265754\pi$
$758$	56.6690	2.05831
$759$	−4.47966	−0.162601
$760$	−4.27073	−0.154916
$761$	−16.7344	−0.606623	−0.303311	−	0.952892i	$-0.598092\pi$
$761$	−16.7344	−0.606623	−0.303311	+	0.952892i	$0.598092\pi$
$762$	3.76754	0.136484
$763$	−22.2518	−0.805570
$764$	−22.7544	−0.823225
$765$	−5.76301	−0.208362
$766$	39.7238	1.43528
$767$	34.8804	1.25946
$768$	−10.2721	−0.370662
$769$	29.8700	1.07714	0.538570	−	0.842581i	$-0.318965\pi$
$769$	29.8700	1.07714	0.538570	+	0.842581i	$0.318965\pi$
$770$	−53.1639	−1.91589
$771$	2.54015	0.0914811
$772$	11.2972	0.406596
$773$	53.6638	1.93015	0.965076	−	0.261972i	$-0.0843727\pi$
$773$	53.6638	1.93015	0.965076	+	0.261972i	$0.0843727\pi$
$774$	4.95078	0.177952
$775$	2.56997	0.0923162
$776$	−22.5361	−0.808998
$777$	−9.94634	−0.356823
$778$	−57.4321	−2.05904
$779$	17.3604	0.622002
$780$	6.72925	0.240946
$781$	0.273367	0.00978183
$782$	−2.87089	−0.102663
$783$	−7.15288	−0.255623
$784$	3.66826	0.131009
$785$	−24.0485	−0.858328
$786$	0.984176	0.0351044
$787$	−25.9494	−0.924996	−0.462498	−	0.886620i	$-0.653047\pi$
$787$	−25.9494	−0.924996	−0.462498	+	0.886620i	$0.653047\pi$
$788$	−5.82063	−0.207351
$789$	6.91814	0.246292
$790$	−11.4129	−0.406053
$791$	27.2094	0.967455
$792$	21.3962	0.760280
$793$	16.5440	0.587495
$794$	−6.48150	−0.230020
$795$	−6.22542	−0.220793
$796$	−4.46488	−0.158254
$797$	−9.21826	−0.326528	−0.163264	−	0.986582i	$-0.552202\pi$
$797$	−9.21826	−0.326528	−0.163264	+	0.986582i	$0.552202\pi$
$798$	3.31373	0.117305
$799$	−9.21620	−0.326046
$800$	−3.79006	−0.133999
$801$	−22.6637	−0.800784
$802$	13.5218	0.477473
$803$	−47.8301	−1.68789
$804$	−7.65852	−0.270095
$805$	8.36021	0.294659
$806$	39.2167	1.38135
$807$	−10.7541	−0.378562
$808$	22.9697	0.808071
$809$	−34.5891	−1.21609	−0.608043	−	0.793904i	$-0.708045\pi$
$809$	−34.5891	−1.21609	−0.608043	+	0.793904i	$0.708045\pi$
$810$	25.7397	0.904401
$811$	6.08773	0.213769	0.106885	−	0.994271i	$-0.465912\pi$
$811$	6.08773	0.213769	0.106885	+	0.994271i	$0.465912\pi$
$812$	−7.72267	−0.271013
$813$	13.3933	0.469725
$814$	81.1837	2.84549
$815$	−6.04404	−0.211714
$816$	−2.45848	−0.0860639
$817$	1.48152	0.0518317
$818$	27.9537	0.977378
$819$	−36.0722	−1.26047
$820$	−30.2803	−1.05743
$821$	20.4524	0.713794	0.356897	−	0.934144i	$-0.383835\pi$
$821$	20.4524	0.713794	0.356897	+	0.934144i	$0.383835\pi$
$822$	−15.7480	−0.549275
$823$	31.1694	1.08650	0.543248	−	0.839572i	$-0.317194\pi$
$823$	31.1694	1.08650	0.543248	+	0.839572i	$0.317194\pi$
$824$	5.58489	0.194559
$825$	−1.73237	−0.0603134
$826$	−29.9593	−1.04242
$827$	1.47822	0.0514028	0.0257014	−	0.999670i	$-0.491818\pi$
$827$	1.47822	0.0514028	0.0257014	+	0.999670i	$0.491818\pi$
$828$	5.42425	0.188506
$829$	−4.05570	−0.140860	−0.0704301	−	0.997517i	$-0.522437\pi$
$829$	−4.05570	−0.140860	−0.0704301	+	0.997517i	$0.522437\pi$
$830$	51.3591	1.78270
$831$	13.8859	0.481697
$832$	−6.02978	−0.209045
$833$	0.741800	0.0257018
$834$	−10.1956	−0.353046
$835$	0.658114	0.0227750
$836$	−10.3222	−0.357001
$837$	−11.9065	−0.411549
$838$	−4.66997	−0.161322
$839$	−34.9312	−1.20596	−0.602979	−	0.797757i	$-0.706020\pi$
$839$	−34.9312	−1.20596	−0.602979	+	0.797757i	$0.706020\pi$
$840$	3.58520	0.123701
$841$	−22.7452	−0.784318
$842$	15.4815	0.533527
$843$	−0.359769	−0.0123911
$844$	−13.4058	−0.461446
$845$	−30.2235	−1.03972
$846$	45.6273	1.56870
$847$	52.1866	1.79315
$848$	29.5788	1.01574
$849$	−14.8764	−0.510556
$850$	−1.11023	−0.0380805
$851$	−12.7664	−0.437627
$852$	0.0297198	0.00101818
$853$	−21.6081	−0.739848	−0.369924	−	0.929062i	$-0.620616\pi$
$853$	−21.6081	−0.739848	−0.369924	+	0.929062i	$0.620616\pi$
$854$	−14.2099	−0.486253
$855$	8.53800	0.291994
$856$	−0.649887	−0.0222127
$857$	21.9295	0.749098	0.374549	−	0.927207i	$-0.377798\pi$
$857$	21.9295	0.749098	0.374549	+	0.927207i	$0.377798\pi$
$858$	−26.4352	−0.902484
$859$	−24.8551	−0.848044	−0.424022	−	0.905652i	$-0.639382\pi$
$859$	−24.8551	−0.848044	−0.424022	+	0.905652i	$0.639382\pi$
$860$	−2.58408	−0.0881164
$861$	−14.5737	−0.496672
$862$	46.7466	1.59220
$863$	−38.0356	−1.29475	−0.647373	−	0.762174i	$-0.724132\pi$
$863$	−38.0356	−1.29475	−0.647373	+	0.762174i	$0.724132\pi$
$864$	17.5591	0.597373
$865$	10.4545	0.355464
$866$	−26.1973	−0.890220
$867$	−0.497156	−0.0168843
$868$	−12.8550	−0.436326
$869$	17.1105	0.580434
$870$	4.68125	0.158709
$871$	65.3708	2.21500
$872$	−12.2481	−0.414771
$873$	45.0539	1.52484
$874$	4.25327	0.143869
$875$	29.4187	0.994535
$876$	−5.19998	−0.175691
$877$	33.5537	1.13303	0.566514	−	0.824052i	$-0.308292\pi$
$877$	33.5537	1.13303	0.566514	+	0.824052i	$0.308292\pi$
$878$	1.06758	0.0360290
$879$	2.71205	0.0914751
$880$	−58.4349	−1.96984
$881$	−29.3264	−0.988031	−0.494016	−	0.869453i	$-0.664471\pi$
$881$	−29.3264	−0.988031	−0.494016	+	0.869453i	$0.664471\pi$
$882$	−3.67249	−0.123659
$883$	−20.9967	−0.706596	−0.353298	−	0.935511i	$-0.614940\pi$
$883$	−20.9967	−0.706596	−0.353298	+	0.935511i	$0.614940\pi$
$884$	−6.46554	−0.217460
$885$	6.93067	0.232972
$886$	2.95192	0.0991717
$887$	22.2102	0.745745	0.372873	−	0.927883i	$-0.378373\pi$
$887$	22.2102	0.745745	0.372873	+	0.927883i	$0.378373\pi$
$888$	−5.47476	−0.183721
$889$	10.5414	0.353546
$890$	30.9966	1.03901
$891$	−38.5896	−1.29280
$892$	11.5321	0.386122
$893$	13.6540	0.456912
$894$	−5.11459	−0.171057
$895$	26.6515	0.890861
$896$	−25.5382	−0.853171
$897$	4.15703	0.138799
$898$	54.1426	1.80676
$899$	10.4116	0.347245
$900$	2.09766	0.0699221
$901$	5.98145	0.199271
$902$	118.953	3.96071
$903$	−1.24371	−0.0413879
$904$	14.9769	0.498123
$905$	−10.6145	−0.352836
$906$	−7.87070	−0.261486
$907$	−38.4566	−1.27693	−0.638466	−	0.769650i	$-0.720431\pi$
$907$	−38.4566	−1.27693	−0.638466	+	0.769650i	$0.720431\pi$
$908$	−16.4514	−0.545958
$909$	−45.9208	−1.52310
$910$	49.3350	1.63544
$911$	17.1386	0.567826	0.283913	−	0.958850i	$-0.408367\pi$
$911$	17.1386	0.567826	0.283913	+	0.958850i	$0.408367\pi$
$912$	3.64228	0.120608
$913$	−76.9989	−2.54829
$914$	−46.7003	−1.54471
$915$	3.28727	0.108674
$916$	19.4724	0.643387
$917$	2.75367	0.0909341
$918$	5.14361	0.169764
$919$	36.3002	1.19743	0.598717	−	0.800961i	$-0.295677\pi$
$919$	36.3002	1.19743	0.598717	+	0.800961i	$0.295677\pi$
$920$	4.60170	0.151714
$921$	−1.06037	−0.0349403
$922$	6.87462	0.226404
$923$	−0.253679	−0.00834994
$924$	8.66530	0.285067
$925$	−4.93702	−0.162328
$926$	−6.75027	−0.221828
$927$	−11.1653	−0.366715
$928$	−15.3544	−0.504034
$929$	−17.6745	−0.579881	−0.289940	−	0.957045i	$-0.593635\pi$
$929$	−17.6745	−0.579881	−0.289940	+	0.957045i	$0.593635\pi$
$930$	7.79229	0.255519
$931$	−1.09899	−0.0360179
$932$	−2.95361	−0.0967487
$933$	−11.7090	−0.383335
$934$	56.2762	1.84141
$935$	−11.8168	−0.386450
$936$	−19.8552	−0.648988
$937$	32.3910	1.05817	0.529084	−	0.848569i	$-0.322536\pi$
$937$	32.3910	1.05817	0.529084	+	0.848569i	$0.322536\pi$
$938$	−56.1479	−1.83329
$939$	−17.3737	−0.566969
$940$	−23.8154	−0.776772
$941$	44.9524	1.46541	0.732703	−	0.680548i	$-0.238258\pi$
$941$	44.9524	1.46541	0.732703	+	0.680548i	$0.238258\pi$
$942$	10.2708	0.334641
$943$	−18.7058	−0.609145
$944$	−32.9296	−1.07177
$945$	−14.9785	−0.487251
$946$	10.1513	0.330048
$947$	52.5821	1.70869	0.854344	−	0.519708i	$-0.173959\pi$
$947$	52.5821	1.70869	0.854344	+	0.519708i	$0.173959\pi$
$948$	1.86021	0.0604169
$949$	44.3854	1.44081
$950$	1.64482	0.0533650
$951$	−17.0762	−0.553733
$952$	−3.44470	−0.111643
$953$	23.8924	0.773950	0.386975	−	0.922090i	$-0.373520\pi$
$953$	23.8924	0.773950	0.386975	+	0.922090i	$0.373520\pi$
$954$	−29.6128	−0.958751
$955$	38.5921	1.24881
$956$	−0.419276	−0.0135604
$957$	−7.01824	−0.226868
$958$	26.0237	0.840788
$959$	−44.0620	−1.42284
$960$	−1.19811	−0.0386687
$961$	−13.6692	−0.440940
$962$	−75.3368	−2.42896
$963$	1.29925	0.0418677
$964$	23.6426	0.761476
$965$	−19.1604	−0.616795
$966$	−3.57054	−0.114880
$967$	40.6802	1.30819	0.654094	−	0.756413i	$-0.273050\pi$
$967$	40.6802	1.30819	0.654094	+	0.756413i	$0.273050\pi$
$968$	28.7250	0.923257
$969$	0.736545	0.0236612
$970$	−61.6190	−1.97847
$971$	−38.6541	−1.24047	−0.620235	−	0.784416i	$-0.712963\pi$
$971$	−38.6541	−1.24047	−0.620235	+	0.784416i	$0.712963\pi$
$972$	−14.7863	−0.474270
$973$	−28.5268	−0.914527
$974$	61.4818	1.97000
$975$	1.60761	0.0514846
$976$	−15.6188	−0.499944
$977$	12.2999	0.393510	0.196755	−	0.980453i	$-0.436960\pi$
$977$	12.2999	0.393510	0.196755	+	0.980453i	$0.436960\pi$
$978$	2.58133	0.0825419
$979$	−46.4709	−1.48522
$980$	1.91687	0.0612321
$981$	24.4862	0.781784
$982$	−40.6618	−1.29757
$983$	42.8547	1.36685	0.683427	−	0.730019i	$-0.260489\pi$
$983$	42.8547	1.36685	0.683427	+	0.730019i	$0.260489\pi$
$984$	−8.02181	−0.255726
$985$	9.87194	0.314546
$986$	−4.49779	−0.143239
$987$	−11.4622	−0.364847
$988$	9.57881	0.304742
$989$	−1.59633	−0.0507604
$990$	58.5022	1.85932
$991$	5.36136	0.170309	0.0851547	−	0.996368i	$-0.472862\pi$
$991$	5.36136	0.170309	0.0851547	+	0.996368i	$0.472862\pi$
$992$	−25.5586	−0.811488
$993$	−13.0150	−0.413019
$994$	0.217888	0.00691100
$995$	7.57256	0.240066
$996$	−8.37113	−0.265249
$997$	−13.8365	−0.438206	−0.219103	−	0.975702i	$-0.570313\pi$
$997$	−13.8365	−0.438206	−0.219103	+	0.975702i	$0.570313\pi$
$998$	61.4300	1.94453
$999$	22.8729	0.723666

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.a.f.1.5	✓	21
3.2	odd	2		6579.2.a.u.1.17		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.a.f.1.5	✓	21	1.1	even	1	trivial
6579.2.a.u.1.17		21	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)

\(f(q)\)	\(=\)	\(q-1.79843 q^{2} -0.497156 q^{3} +1.23435 q^{4} -2.09348 q^{5} +0.894100 q^{6} +2.50164 q^{7} +1.37698 q^{8} -2.75284 q^{9} +O(q^{10})\)	\(q-1.79843 q^{2} -0.497156 q^{3} +1.23435 q^{4} -2.09348 q^{5} +0.894100 q^{6} +2.50164 q^{7} +1.37698 q^{8} -2.75284 q^{9} +3.76498 q^{10} -5.64455 q^{11} -0.613662 q^{12} +5.23803 q^{13} -4.49902 q^{14} +1.04079 q^{15} -4.94508 q^{16} -1.00000 q^{17} +4.95078 q^{18} +1.48152 q^{19} -2.58408 q^{20} -1.24371 q^{21} +10.1513 q^{22} -1.59633 q^{23} -0.684572 q^{24} -0.617332 q^{25} -9.42022 q^{26} +2.86006 q^{27} +3.08789 q^{28} -2.50096 q^{29} -1.87178 q^{30} -4.16303 q^{31} +6.13943 q^{32} +2.80622 q^{33} +1.79843 q^{34} -5.23714 q^{35} -3.39795 q^{36} +7.99735 q^{37} -2.66440 q^{38} -2.60412 q^{39} -2.88267 q^{40} +11.7180 q^{41} +2.23671 q^{42} +1.00000 q^{43} -6.96732 q^{44} +5.76301 q^{45} +2.87089 q^{46} +9.21620 q^{47} +2.45848 q^{48} -0.741800 q^{49} +1.11023 q^{50} +0.497156 q^{51} +6.46554 q^{52} -5.98145 q^{53} -5.14361 q^{54} +11.8168 q^{55} +3.44470 q^{56} -0.736545 q^{57} +4.49779 q^{58} +6.65907 q^{59} +1.28469 q^{60} +3.15844 q^{61} +7.48692 q^{62} -6.88660 q^{63} -1.15115 q^{64} -10.9657 q^{65} -5.04679 q^{66} +12.4800 q^{67} -1.23435 q^{68} +0.793625 q^{69} +9.41862 q^{70} -0.0484302 q^{71} -3.79059 q^{72} +8.47368 q^{73} -14.3827 q^{74} +0.306910 q^{75} +1.82870 q^{76} -14.1206 q^{77} +4.68332 q^{78} -3.03133 q^{79} +10.3524 q^{80} +6.83661 q^{81} -21.0740 q^{82} +13.6413 q^{83} -1.53516 q^{84} +2.09348 q^{85} -1.79843 q^{86} +1.24337 q^{87} -7.77241 q^{88} +8.23287 q^{89} -10.3644 q^{90} +13.1037 q^{91} -1.97042 q^{92} +2.06968 q^{93} -16.5747 q^{94} -3.10153 q^{95} -3.05225 q^{96} -16.3664 q^{97} +1.33407 q^{98} +15.5385 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 2 q^{2} - q^{3} + 32 q^{4} - 3 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 34 q^{9}+O(q^{10}) \) 21 * q + 2 * q^2 - q^3 + 32 * q^4 - 3 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 34 * q^9	\( 21 q + 2 q^{2} - q^{3} + 32 q^{4} - 3 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 34 q^{9} + 12 q^{10} + 2 q^{11} - 5 q^{12} + 26 q^{13} - 3 q^{14} + 5 q^{15} + 62 q^{16} - 21 q^{17} - 10 q^{18} + 16 q^{19} - 27 q^{20} + 36 q^{21} - 14 q^{22} - q^{23} + 15 q^{24} + 40 q^{25} - 3 q^{26} - 16 q^{27} + 25 q^{28} + 15 q^{29} + 38 q^{30} + 18 q^{31} + 14 q^{32} + 14 q^{33} - 2 q^{34} - 5 q^{35} + 73 q^{36} + 12 q^{37} + 19 q^{38} - 11 q^{39} + 41 q^{40} - 45 q^{42} + 21 q^{43} - 34 q^{44} - 18 q^{45} + 28 q^{46} - q^{47} - 36 q^{48} + 40 q^{49} + 24 q^{50} + q^{51} + 23 q^{52} + 39 q^{53} - 83 q^{54} - 2 q^{55} - 10 q^{56} + 3 q^{57} + 19 q^{58} + 4 q^{59} - 35 q^{60} + 50 q^{61} + 5 q^{62} - 37 q^{63} + 120 q^{64} - 8 q^{65} - 37 q^{66} + 16 q^{67} - 32 q^{68} + 33 q^{69} - q^{70} + q^{71} - 54 q^{72} + 15 q^{73} + 52 q^{74} + 11 q^{75} - 15 q^{76} + 13 q^{77} - 100 q^{78} + 56 q^{79} - 100 q^{80} + 97 q^{81} - 11 q^{82} + 61 q^{84} + 3 q^{85} + 2 q^{86} - 8 q^{87} - 56 q^{88} + 5 q^{89} - 69 q^{90} - 4 q^{91} - 27 q^{92} + 17 q^{93} - 47 q^{94} - 9 q^{95} + 81 q^{96} - 28 q^{97} + 18 q^{98} - 19 q^{99}+O(q^{100}) \) 21 * q + 2 * q^2 - q^3 + 32 * q^4 - 3 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 34 * q^9 + 12 * q^10 + 2 * q^11 - 5 * q^12 + 26 * q^13 - 3 * q^14 + 5 * q^15 + 62 * q^16 - 21 * q^17 - 10 * q^18 + 16 * q^19 - 27 * q^20 + 36 * q^21 - 14 * q^22 - q^23 + 15 * q^24 + 40 * q^25 - 3 * q^26 - 16 * q^27 + 25 * q^28 + 15 * q^29 + 38 * q^30 + 18 * q^31 + 14 * q^32 + 14 * q^33 - 2 * q^34 - 5 * q^35 + 73 * q^36 + 12 * q^37 + 19 * q^38 - 11 * q^39 + 41 * q^40 - 45 * q^42 + 21 * q^43 - 34 * q^44 - 18 * q^45 + 28 * q^46 - q^47 - 36 * q^48 + 40 * q^49 + 24 * q^50 + q^51 + 23 * q^52 + 39 * q^53 - 83 * q^54 - 2 * q^55 - 10 * q^56 + 3 * q^57 + 19 * q^58 + 4 * q^59 - 35 * q^60 + 50 * q^61 + 5 * q^62 - 37 * q^63 + 120 * q^64 - 8 * q^65 - 37 * q^66 + 16 * q^67 - 32 * q^68 + 33 * q^69 - q^70 + q^71 - 54 * q^72 + 15 * q^73 + 52 * q^74 + 11 * q^75 - 15 * q^76 + 13 * q^77 - 100 * q^78 + 56 * q^79 - 100 * q^80 + 97 * q^81 - 11 * q^82 + 61 * q^84 + 3 * q^85 + 2 * q^86 - 8 * q^87 - 56 * q^88 + 5 * q^89 - 69 * q^90 - 4 * q^91 - 27 * q^92 + 17 * q^93 - 47 * q^94 - 9 * q^95 + 81 * q^96 - 28 * q^97 + 18 * q^98 - 19 * q^99

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