LMFDB - Embedded newform 731.2.a.c.1.1

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			1.1
Root			$-2.08764$ 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)

$f(q)$	$=$	$q-2.35826 q^{2} +1.68213 q^{3} +3.56138 q^{4} +0.252087 q^{5} -3.96689 q^{6} -3.41152 q^{7} -3.68213 q^{8} -0.170443 q^{9} +O(q^{10})$	\(q-2.35826 q^{2} +1.68213 q^{3} +3.56138 q^{4} +0.252087 q^{5} -3.96689 q^{6} -3.41152 q^{7} -3.68213 q^{8} -0.170443 q^{9} -0.594485 q^{10} +0.120752 q^{11} +5.99069 q^{12} +3.34724 q^{13} +8.04523 q^{14} +0.424042 q^{15} +1.56065 q^{16} -1.00000 q^{17} +0.401948 q^{18} -8.40679 q^{19} +0.897775 q^{20} -5.73861 q^{21} -0.284764 q^{22} +0.438192 q^{23} -6.19381 q^{24} -4.93645 q^{25} -7.89366 q^{26} -5.33309 q^{27} -12.1497 q^{28} -4.34330 q^{29} -1.00000 q^{30} +7.74481 q^{31} +3.68384 q^{32} +0.203120 q^{33} +2.35826 q^{34} -0.859997 q^{35} -0.607011 q^{36} -8.36238 q^{37} +19.8254 q^{38} +5.63049 q^{39} -0.928215 q^{40} +5.90598 q^{41} +13.5331 q^{42} -1.00000 q^{43} +0.430042 q^{44} -0.0429663 q^{45} -1.03337 q^{46} +1.29175 q^{47} +2.62522 q^{48} +4.63844 q^{49} +11.6414 q^{50} -1.68213 q^{51} +11.9208 q^{52} -4.96574 q^{53} +12.5768 q^{54} +0.0304399 q^{55} +12.5616 q^{56} -14.1413 q^{57} +10.2426 q^{58} -4.88594 q^{59} +1.51017 q^{60} -12.9060 q^{61} -18.2643 q^{62} +0.581468 q^{63} -11.8087 q^{64} +0.843795 q^{65} -0.479009 q^{66} +6.34642 q^{67} -3.56138 q^{68} +0.737096 q^{69} +2.02809 q^{70} +11.5338 q^{71} +0.627593 q^{72} -10.1106 q^{73} +19.7206 q^{74} -8.30375 q^{75} -29.9398 q^{76} -0.411946 q^{77} -13.2782 q^{78} -11.3081 q^{79} +0.393419 q^{80} -8.45962 q^{81} -13.9278 q^{82} +13.3634 q^{83} -20.4373 q^{84} -0.252087 q^{85} +2.35826 q^{86} -7.30599 q^{87} -0.444623 q^{88} +8.52517 q^{89} +0.101326 q^{90} -11.4192 q^{91} +1.56057 q^{92} +13.0278 q^{93} -3.04627 q^{94} -2.11924 q^{95} +6.19669 q^{96} -6.27714 q^{97} -10.9386 q^{98} -0.0205813 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.35826	−1.66754	−0.833770	−	0.552112i	$-0.813822\pi$
$2$	−2.35826	−1.66754	−0.833770	+	0.552112i	$0.813822\pi$
$3$	1.68213	0.971177	0.485589	−	0.874187i	$-0.338605\pi$
$3$	1.68213	0.971177	0.485589	+	0.874187i	$0.338605\pi$
$4$	3.56138	1.78069
$5$	0.252087	0.112737	0.0563683	−	0.998410i	$-0.482048\pi$
$5$	0.252087	0.112737	0.0563683	+	0.998410i	$0.482048\pi$
$6$	−3.96689	−1.61948
$7$	−3.41152	−1.28943	−0.644716	−	0.764422i	$-0.723024\pi$
$7$	−3.41152	−1.28943	−0.644716	+	0.764422i	$0.723024\pi$
$8$	−3.68213	−1.30183
$9$	−0.170443	−0.0568143
$10$	−0.594485	−0.187993
$11$	0.120752	0.0364080	0.0182040	−	0.999834i	$-0.494205\pi$
$11$	0.120752	0.0364080	0.0182040	+	0.999834i	$0.494205\pi$
$12$	5.99069	1.72936
$13$	3.34724	0.928358	0.464179	−	0.885741i	$-0.346349\pi$
$13$	3.34724	0.928358	0.464179	+	0.885741i	$0.346349\pi$
$14$	8.04523	2.15018
$15$	0.424042	0.109487
$16$	1.56065	0.390163
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	0.401948	0.0947401
$19$	−8.40679	−1.92865	−0.964325	−	0.264720i	$-0.914720\pi$
$19$	−8.40679	−1.92865	−0.964325	+	0.264720i	$0.914720\pi$
$20$	0.897775	0.200749
$21$	−5.73861	−1.25227
$22$	−0.284764	−0.0607118
$23$	0.438192	0.0913694	0.0456847	−	0.998956i	$-0.485453\pi$
$23$	0.438192	0.0913694	0.0456847	+	0.998956i	$0.485453\pi$
$24$	−6.19381	−1.26431
$25$	−4.93645	−0.987290
$26$	−7.89366	−1.54807
$27$	−5.33309	−1.02635
$28$	−12.1497	−2.29608
$29$	−4.34330	−0.806530	−0.403265	−	0.915083i	$-0.632125\pi$
$29$	−4.34330	−0.806530	−0.403265	+	0.915083i	$0.632125\pi$
$30$	−1.00000	−0.182574
$31$	7.74481	1.39101	0.695505	−	0.718521i	$-0.255181\pi$
$31$	7.74481	1.39101	0.695505	+	0.718521i	$0.255181\pi$
$32$	3.68384	0.651217
$33$	0.203120	0.0353586
$34$	2.35826	0.404438
$35$	−0.859997	−0.145366
$36$	−0.607011	−0.101169
$37$	−8.36238	−1.37477	−0.687383	−	0.726295i	$-0.741241\pi$
$37$	−8.36238	−1.37477	−0.687383	+	0.726295i	$0.741241\pi$
$38$	19.8254	3.21610
$39$	5.63049	0.901601
$40$	−0.928215	−0.146764
$41$	5.90598	0.922359	0.461180	−	0.887307i	$-0.347426\pi$
$41$	5.90598	0.922359	0.461180	+	0.887307i	$0.347426\pi$
$42$	13.5331	2.08820
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	0.430042	0.0648313
$45$	−0.0429663	−0.00640504
$46$	−1.03337	−0.152362
$47$	1.29175	0.188421	0.0942104	−	0.995552i	$-0.469967\pi$
$47$	1.29175	0.188421	0.0942104	+	0.995552i	$0.469967\pi$
$48$	2.62522	0.378918
$49$	4.63844	0.662634
$50$	11.6414	1.64635
$51$	−1.68213	−0.235545
$52$	11.9208	1.65312
$53$	−4.96574	−0.682096	−0.341048	−	0.940046i	$-0.610782\pi$
$53$	−4.96574	−0.682096	−0.341048	+	0.940046i	$0.610782\pi$
$54$	12.5768	1.71149
$55$	0.0304399	0.00410451
$56$	12.5616	1.67862
$57$	−14.1413	−1.87306
$58$	10.2426	1.34492
$59$	−4.88594	−0.636095	−0.318048	−	0.948075i	$-0.603027\pi$
$59$	−4.88594	−0.636095	−0.318048	+	0.948075i	$0.603027\pi$
$60$	1.51017	0.194963
$61$	−12.9060	−1.65244	−0.826219	−	0.563349i	$-0.809513\pi$
$61$	−12.9060	−1.65244	−0.826219	+	0.563349i	$0.809513\pi$
$62$	−18.2643	−2.31956
$63$	0.581468	0.0732581
$64$	−11.8087	−1.47609
$65$	0.843795	0.104660
$66$	−0.479009	−0.0589619
$67$	6.34642	0.775339	0.387670	−	0.921798i	$-0.373280\pi$
$67$	6.34642	0.775339	0.387670	+	0.921798i	$0.373280\pi$
$68$	−3.56138	−0.431880
$69$	0.737096	0.0887359
$70$	2.02809	0.242404
$71$	11.5338	1.36881	0.684407	−	0.729100i	$-0.260061\pi$
$71$	11.5338	1.36881	0.684407	+	0.729100i	$0.260061\pi$
$72$	0.627593	0.0739625
$73$	−10.1106	−1.18335	−0.591677	−	0.806175i	$-0.701534\pi$
$73$	−10.1106	−1.18335	−0.591677	+	0.806175i	$0.701534\pi$
$74$	19.7206	2.29248
$75$	−8.30375	−0.958834
$76$	−29.9398	−3.43433
$77$	−0.411946	−0.0469456
$78$	−13.2782	−1.50345
$79$	−11.3081	−1.27226	−0.636132	−	0.771580i	$-0.719467\pi$
$79$	−11.3081	−1.27226	−0.636132	+	0.771580i	$0.719467\pi$
$80$	0.393419	0.0439856
$81$	−8.45962	−0.939958
$82$	−13.9278	−1.53807
$83$	13.3634	1.46682	0.733412	−	0.679785i	$-0.237927\pi$
$83$	13.3634	1.46682	0.733412	+	0.679785i	$0.237927\pi$
$84$	−20.4373	−2.22990
$85$	−0.252087	−0.0273426
$86$	2.35826	0.254297
$87$	−7.30599	−0.783284
$88$	−0.444623	−0.0473970
$89$	8.52517	0.903666	0.451833	−	0.892102i	$-0.350770\pi$
$89$	8.52517	0.903666	0.451833	+	0.892102i	$0.350770\pi$
$90$	0.101326	0.0106807
$91$	−11.4192	−1.19705
$92$	1.56057	0.162700
$93$	13.0278	1.35092
$94$	−3.04627	−0.314199
$95$	−2.11924	−0.217429
$96$	6.19669	0.632447
$97$	−6.27714	−0.637347	−0.318674	−	0.947865i	$-0.603237\pi$
$97$	−6.27714	−0.637347	−0.318674	+	0.947865i	$0.603237\pi$
$98$	−10.9386	−1.10497
$99$	−0.0205813	−0.00206849
$100$	−17.5806	−1.75806
$101$	−19.3506	−1.92546	−0.962730	−	0.270465i	$-0.912823\pi$
$101$	−19.3506	−1.92546	−0.962730	+	0.270465i	$0.912823\pi$
$102$	3.96689	0.392781
$103$	1.40525	0.138464	0.0692318	−	0.997601i	$-0.477945\pi$
$103$	1.40525	0.138464	0.0692318	+	0.997601i	$0.477945\pi$
$104$	−12.3250	−1.20856
$105$	−1.44663	−0.141176
$106$	11.7105	1.13742
$107$	−16.2108	−1.56716	−0.783579	−	0.621292i	$-0.786608\pi$
$107$	−16.2108	−1.56716	−0.783579	+	0.621292i	$0.786608\pi$
$108$	−18.9932	−1.82762
$109$	−1.93419	−0.185262	−0.0926308	−	0.995701i	$-0.529528\pi$
$109$	−1.93419	−0.185262	−0.0926308	+	0.995701i	$0.529528\pi$
$110$	−0.0717850	−0.00684443
$111$	−14.0666	−1.33514
$112$	−5.32419	−0.503089
$113$	18.6189	1.75152	0.875758	−	0.482751i	$-0.160362\pi$
$113$	18.6189	1.75152	0.875758	+	0.482751i	$0.160362\pi$
$114$	33.3488	3.12341
$115$	0.110462	0.0103007
$116$	−15.4681	−1.43618
$117$	−0.570514	−0.0527440
$118$	11.5223	1.06071
$119$	3.41152	0.312733
$120$	−1.56138	−0.142534
$121$	−10.9854	−0.998674
$122$	30.4356	2.75551
$123$	9.93462	0.895775
$124$	27.5822	2.47696
$125$	−2.50485	−0.224040
$126$	−1.37125	−0.122161
$127$	15.4119	1.36759	0.683794	−	0.729675i	$-0.260329\pi$
$127$	15.4119	1.36759	0.683794	+	0.729675i	$0.260329\pi$
$128$	20.4804	1.81023
$129$	−1.68213	−0.148103
$130$	−1.98989	−0.174524
$131$	−9.67701	−0.845484	−0.422742	−	0.906250i	$-0.638932\pi$
$131$	−9.67701	−0.845484	−0.422742	+	0.906250i	$0.638932\pi$
$132$	0.723386	0.0629627
$133$	28.6799	2.48686
$134$	−14.9665	−1.29291
$135$	−1.34440	−0.115708
$136$	3.68213	0.315740
$137$	7.35811	0.628646	0.314323	−	0.949316i	$-0.398223\pi$
$137$	7.35811	0.628646	0.314323	+	0.949316i	$0.398223\pi$
$138$	−1.73826	−0.147971
$139$	2.42368	0.205574	0.102787	−	0.994703i	$-0.467224\pi$
$139$	2.42368	0.205574	0.102787	+	0.994703i	$0.467224\pi$
$140$	−3.06277	−0.258852
$141$	2.17289	0.182990
$142$	−27.1998	−2.28255
$143$	0.404185	0.0337997
$144$	−0.266002	−0.0221668
$145$	−1.09489	−0.0909254
$146$	23.8433	1.97329
$147$	7.80245	0.643535
$148$	−29.7816	−2.44803
$149$	−23.0185	−1.88575	−0.942876	−	0.333145i	$-0.891890\pi$
$149$	−23.0185	−1.88575	−0.942876	+	0.333145i	$0.891890\pi$
$150$	19.5824	1.59889
$151$	−5.02639	−0.409041	−0.204521	−	0.978862i	$-0.565564\pi$
$151$	−5.02639	−0.409041	−0.204521	+	0.978862i	$0.565564\pi$
$152$	30.9549	2.51077
$153$	0.170443	0.0137795
$154$	0.971475	0.0782837
$155$	1.95236	0.156818
$156$	20.0523	1.60547
$157$	−5.37370	−0.428868	−0.214434	−	0.976739i	$-0.568791\pi$
$157$	−5.37370	−0.428868	−0.214434	+	0.976739i	$0.568791\pi$
$158$	26.6675	2.12155
$159$	−8.35301	−0.662437
$160$	0.928646	0.0734159
$161$	−1.49490	−0.117815
$162$	19.9500	1.56742
$163$	8.85550	0.693616	0.346808	−	0.937936i	$-0.387266\pi$
$163$	8.85550	0.693616	0.346808	+	0.937936i	$0.387266\pi$
$164$	21.0334	1.64243
$165$	0.0512038	0.00398621
$166$	−31.5143	−2.44599
$167$	6.72205	0.520168	0.260084	−	0.965586i	$-0.416250\pi$
$167$	6.72205	0.520168	0.260084	+	0.965586i	$0.416250\pi$
$168$	21.1303	1.63024
$169$	−1.79596	−0.138151
$170$	0.594485	0.0455949
$171$	1.43288	0.109575
$172$	−3.56138	−0.271552
$173$	11.0675	0.841446	0.420723	−	0.907189i	$-0.361776\pi$
$173$	11.0675	0.841446	0.420723	+	0.907189i	$0.361776\pi$
$174$	17.2294	1.30616
$175$	16.8408	1.27304
$176$	0.188451	0.0142051
$177$	−8.21878	−0.617762
$178$	−20.1045	−1.50690
$179$	11.5790	0.865455	0.432728	−	0.901525i	$-0.357551\pi$
$179$	11.5790	0.865455	0.432728	+	0.901525i	$0.357551\pi$
$180$	−0.153019	−0.0114054
$181$	−7.43861	−0.552908	−0.276454	−	0.961027i	$-0.589159\pi$
$181$	−7.43861	−0.552908	−0.276454	+	0.961027i	$0.589159\pi$
$182$	26.9293	1.99614
$183$	−21.7095	−1.60481
$184$	−1.61348	−0.118947
$185$	−2.10804	−0.154986
$186$	−30.7228	−2.25271
$187$	−0.120752	−0.00883024
$188$	4.60040	0.335519
$189$	18.1939	1.32341
$190$	4.99771	0.362572
$191$	−5.57474	−0.403374	−0.201687	−	0.979450i	$-0.564642\pi$
$191$	−5.57474	−0.403374	−0.201687	+	0.979450i	$0.564642\pi$
$192$	−19.8638	−1.43355
$193$	22.1403	1.59369	0.796846	−	0.604183i	$-0.206500\pi$
$193$	22.1403	1.59369	0.796846	+	0.604183i	$0.206500\pi$
$194$	14.8031	1.06280
$195$	1.41937	0.101643
$196$	16.5192	1.17994
$197$	9.02222	0.642806	0.321403	−	0.946942i	$-0.395846\pi$
$197$	9.02222	0.642806	0.321403	+	0.946942i	$0.395846\pi$
$198$	0.0485359	0.00344930
$199$	−1.63539	−0.115930	−0.0579649	−	0.998319i	$-0.518461\pi$
$199$	−1.63539	−0.115930	−0.0579649	+	0.998319i	$0.518461\pi$
$200$	18.1767	1.28528
$201$	10.6755	0.752992
$202$	45.6338	3.21078
$203$	14.8172	1.03997
$204$	−5.99069	−0.419433
$205$	1.48882	0.103984
$206$	−3.31395	−0.230894
$207$	−0.0746867	−0.00519109
$208$	5.22388	0.362211
$209$	−1.01513	−0.0702183
$210$	3.41152	0.235417
$211$	14.4367	0.993864	0.496932	−	0.867789i	$-0.334460\pi$
$211$	14.4367	0.993864	0.496932	+	0.867789i	$0.334460\pi$
$212$	−17.6849	−1.21460
$213$	19.4014	1.32936
$214$	38.2293	2.61330
$215$	−0.252087	−0.0171922
$216$	19.6371	1.33614
$217$	−26.4216	−1.79361
$218$	4.56131	0.308931
$219$	−17.0073	−1.14925
$220$	0.108408	0.00730886
$221$	−3.34724	−0.225160
$222$	33.1727	2.22640
$223$	12.9197	0.865165	0.432583	−	0.901594i	$-0.357602\pi$
$223$	12.9197	0.865165	0.432583	+	0.901594i	$0.357602\pi$
$224$	−12.5675	−0.839699
$225$	0.841383	0.0560922
$226$	−43.9081	−2.92072
$227$	−17.1004	−1.13500	−0.567498	−	0.823375i	$-0.692088\pi$
$227$	−17.1004	−1.13500	−0.567498	+	0.823375i	$0.692088\pi$
$228$	−50.3625	−3.33534
$229$	27.8932	1.84323	0.921617	−	0.388100i	$-0.126869\pi$
$229$	27.8932	1.84323	0.921617	+	0.388100i	$0.126869\pi$
$230$	−0.260499	−0.0171768
$231$	−0.692947	−0.0455925
$232$	15.9926	1.04996
$233$	11.5099	0.754036	0.377018	−	0.926206i	$-0.376949\pi$
$233$	11.5099	0.754036	0.377018	+	0.926206i	$0.376949\pi$
$234$	1.34542	0.0879527
$235$	0.325632	0.0212419
$236$	−17.4007	−1.13269
$237$	−19.0217	−1.23559
$238$	−8.04523	−0.521495
$239$	−20.1863	−1.30574	−0.652871	−	0.757469i	$-0.726436\pi$
$239$	−20.1863	−1.30574	−0.652871	+	0.757469i	$0.726436\pi$
$240$	0.661782	0.0427179
$241$	−4.99186	−0.321554	−0.160777	−	0.986991i	$-0.551400\pi$
$241$	−4.99186	−0.321554	−0.160777	+	0.986991i	$0.551400\pi$
$242$	25.9064	1.66533
$243$	1.76911	0.113488
$244$	−45.9630	−2.94248
$245$	1.16929	0.0747030
$246$	−23.4284	−1.49374
$247$	−28.1396	−1.79048
$248$	−28.5174	−1.81086
$249$	22.4790	1.42455
$250$	5.90707	0.373596
$251$	15.8937	1.00320	0.501602	−	0.865099i	$-0.332744\pi$
$251$	15.8937	1.00320	0.501602	+	0.865099i	$0.332744\pi$
$252$	2.07083	0.130450
$253$	0.0529124	0.00332658
$254$	−36.3453	−2.28051
$255$	−0.424042	−0.0265545
$256$	−24.6805	−1.54253
$257$	4.98203	0.310770	0.155385	−	0.987854i	$-0.450338\pi$
$257$	4.98203	0.310770	0.155385	+	0.987854i	$0.450338\pi$
$258$	3.96689	0.246968
$259$	28.5284	1.77267
$260$	3.00507	0.186367
$261$	0.740284	0.0458224
$262$	22.8209	1.40988
$263$	0.361153	0.0222696	0.0111348	−	0.999938i	$-0.496456\pi$
$263$	0.361153	0.0222696	0.0111348	+	0.999938i	$0.496456\pi$
$264$	−0.747913	−0.0460309
$265$	−1.25180	−0.0768972
$266$	−67.6346	−4.14694
$267$	14.3404	0.877620
$268$	22.6020	1.38064
$269$	14.4925	0.883621	0.441811	−	0.897108i	$-0.354336\pi$
$269$	14.4925	0.883621	0.441811	+	0.897108i	$0.354336\pi$
$270$	3.17044	0.192947
$271$	7.85002	0.476855	0.238427	−	0.971160i	$-0.423368\pi$
$271$	7.85002	0.476855	0.238427	+	0.971160i	$0.423368\pi$
$272$	−1.56065	−0.0946285
$273$	−19.2085	−1.16255
$274$	−17.3523	−1.04829
$275$	−0.596085	−0.0359453
$276$	2.62508	0.158011
$277$	1.83631	0.110333	0.0551667	−	0.998477i	$-0.482431\pi$
$277$	1.83631	0.110333	0.0551667	+	0.998477i	$0.482431\pi$
$278$	−5.71567	−0.342803
$279$	−1.32005	−0.0790292
$280$	3.16662	0.189242
$281$	13.0247	0.776987	0.388493	−	0.921451i	$-0.372996\pi$
$281$	13.0247	0.776987	0.388493	+	0.921451i	$0.372996\pi$
$282$	−5.12422	−0.305143
$283$	−9.08423	−0.540001	−0.270001	−	0.962860i	$-0.587024\pi$
$283$	−9.08423	−0.540001	−0.270001	+	0.962860i	$0.587024\pi$
$284$	41.0763	2.43743
$285$	−3.56483	−0.211162
$286$	−0.953173	−0.0563623
$287$	−20.1483	−1.18932
$288$	−0.627884	−0.0369984
$289$	1.00000	0.0588235
$290$	2.58202	0.151622
$291$	−10.5590	−0.618977
$292$	−36.0076	−2.10718
$293$	−20.5237	−1.19901	−0.599503	−	0.800372i	$-0.704635\pi$
$293$	−20.5237	−1.19901	−0.599503	+	0.800372i	$0.704635\pi$
$294$	−18.4002	−1.07312
$295$	−1.23168	−0.0717112
$296$	30.7914	1.78971
$297$	−0.643980	−0.0373675
$298$	54.2836	3.14457
$299$	1.46674	0.0848235
$300$	−29.5728	−1.70739
$301$	3.41152	0.196636
$302$	11.8535	0.682093
$303$	−32.5503	−1.86996
$304$	−13.1201	−0.752488
$305$	−3.25342	−0.186290
$306$	−0.401948	−0.0229778
$307$	21.1819	1.20891	0.604456	−	0.796638i	$-0.293390\pi$
$307$	21.1819	1.20891	0.604456	+	0.796638i	$0.293390\pi$
$308$	−1.46710	−0.0835955
$309$	2.36382	0.134473
$310$	−4.60417	−0.261500
$311$	−2.94814	−0.167173	−0.0835867	−	0.996501i	$-0.526638\pi$
$311$	−2.94814	−0.167173	−0.0835867	+	0.996501i	$0.526638\pi$
$312$	−20.7322	−1.17373
$313$	−23.0727	−1.30414	−0.652072	−	0.758157i	$-0.726100\pi$
$313$	−23.0727	−1.30414	−0.652072	+	0.758157i	$0.726100\pi$
$314$	12.6726	0.715154
$315$	0.146580	0.00825887
$316$	−40.2725	−2.26550
$317$	15.3858	0.864155	0.432077	−	0.901837i	$-0.357781\pi$
$317$	15.3858	0.864155	0.432077	+	0.901837i	$0.357781\pi$
$318$	19.6985	1.10464
$319$	−0.524460	−0.0293641
$320$	−2.97682	−0.166410
$321$	−27.2687	−1.52199
$322$	3.52536	0.196460
$323$	8.40679	0.467766
$324$	−30.1279	−1.67377
$325$	−16.5235	−0.916559
$326$	−20.8835	−1.15663
$327$	−3.25355	−0.179922
$328$	−21.7466	−1.20075
$329$	−4.40682	−0.242956
$330$	−0.120752	−0.00664716
$331$	−10.4726	−0.575626	−0.287813	−	0.957687i	$-0.592928\pi$
$331$	−10.4726	−0.575626	−0.287813	+	0.957687i	$0.592928\pi$
$332$	47.5921	2.61196
$333$	1.42531	0.0781064
$334$	−15.8523	−0.867400
$335$	1.59985	0.0874090
$336$	−8.95597	−0.488588
$337$	−19.2658	−1.04947	−0.524737	−	0.851264i	$-0.675836\pi$
$337$	−19.2658	−1.04947	−0.524737	+	0.851264i	$0.675836\pi$
$338$	4.23534	0.230372
$339$	31.3193	1.70103
$340$	−0.897775	−0.0486887
$341$	0.935199	0.0506439
$342$	−3.37909	−0.182721
$343$	8.05651	0.435010
$344$	3.68213	0.198527
$345$	0.185812	0.0100038
$346$	−26.1000	−1.40314
$347$	28.0162	1.50399	0.751995	−	0.659169i	$-0.229092\pi$
$347$	28.0162	1.50399	0.751995	+	0.659169i	$0.229092\pi$
$348$	−26.0194	−1.39478
$349$	−18.1695	−0.972589	−0.486294	−	0.873795i	$-0.661652\pi$
$349$	−18.1695	−0.972589	−0.486294	+	0.873795i	$0.661652\pi$
$350$	−39.7149	−2.12285
$351$	−17.8512	−0.952824
$352$	0.444830	0.0237095
$353$	−10.2567	−0.545907	−0.272954	−	0.962027i	$-0.588001\pi$
$353$	−10.2567	−0.545907	−0.272954	+	0.962027i	$0.588001\pi$
$354$	19.3820	1.03014
$355$	2.90753	0.154315
$356$	30.3613	1.60915
$357$	5.73861	0.303719
$358$	−27.3063	−1.44318
$359$	−18.6942	−0.986641	−0.493320	−	0.869848i	$-0.664217\pi$
$359$	−18.6942	−0.986641	−0.493320	+	0.869848i	$0.664217\pi$
$360$	0.158208	0.00833827
$361$	51.6742	2.71969
$362$	17.5422	0.921996
$363$	−18.4789	−0.969890
$364$	−40.6680	−2.13158
$365$	−2.54874	−0.133407
$366$	51.1965	2.67609
$367$	15.8306	0.826349	0.413174	−	0.910652i	$-0.364420\pi$
$367$	15.8306	0.826349	0.413174	+	0.910652i	$0.364420\pi$
$368$	0.683866	0.0356490
$369$	−1.00663	−0.0524032
$370$	4.97131	0.258446
$371$	16.9407	0.879517
$372$	46.3968	2.40556
$373$	14.1309	0.731671	0.365836	−	0.930679i	$-0.380783\pi$
$373$	14.1309	0.731671	0.365836	+	0.930679i	$0.380783\pi$
$374$	0.284764	0.0147248
$375$	−4.21347	−0.217583
$376$	−4.75638	−0.245292
$377$	−14.5381	−0.748749
$378$	−42.9060	−2.20684
$379$	19.9764	1.02612	0.513060	−	0.858353i	$-0.328512\pi$
$379$	19.9764	1.02612	0.513060	+	0.858353i	$0.328512\pi$
$380$	−7.54741	−0.387174
$381$	25.9249	1.32817
$382$	13.1467	0.672642
$383$	5.17491	0.264425	0.132213	−	0.991221i	$-0.457792\pi$
$383$	5.17491	0.264425	0.132213	+	0.991221i	$0.457792\pi$
$384$	34.4506	1.75805
$385$	−0.103846	−0.00529249
$386$	−52.2125	−2.65754
$387$	0.170443	0.00866410
$388$	−22.3553	−1.13492
$389$	−10.7768	−0.546408	−0.273204	−	0.961956i	$-0.588083\pi$
$389$	−10.7768	−0.546408	−0.273204	+	0.961956i	$0.588083\pi$
$390$	−3.34724	−0.169494
$391$	−0.438192	−0.0221603
$392$	−17.0793	−0.862636
$393$	−16.2780	−0.821115
$394$	−21.2767	−1.07191
$395$	−2.85063	−0.143431
$396$	−0.0732976	−0.00368334
$397$	−15.3644	−0.771117	−0.385558	−	0.922683i	$-0.625991\pi$
$397$	−15.3644	−0.771117	−0.385558	+	0.922683i	$0.625991\pi$
$398$	3.85667	0.193318
$399$	48.2433	2.41519
$400$	−7.70409	−0.385204
$401$	9.16323	0.457590	0.228795	−	0.973475i	$-0.426521\pi$
$401$	9.16323	0.457590	0.228795	+	0.973475i	$0.426521\pi$
$402$	−25.1756	−1.25564
$403$	25.9238	1.29136
$404$	−68.9149	−3.42864
$405$	−2.13256	−0.105968
$406$	−34.9428	−1.73418
$407$	−1.00977	−0.0500525
$408$	6.19381	0.306640
$409$	−11.1488	−0.551271	−0.275635	−	0.961262i	$-0.588888\pi$
$409$	−11.1488	−0.551271	−0.275635	+	0.961262i	$0.588888\pi$
$410$	−3.51102	−0.173397
$411$	12.3773	0.610527
$412$	5.00464	0.246561
$413$	16.6685	0.820202
$414$	0.176131	0.00865634
$415$	3.36873	0.165365
$416$	12.3307	0.604562
$417$	4.07695	0.199649
$418$	2.39395	0.117092
$419$	−20.6208	−1.00739	−0.503696	−	0.863881i	$-0.668027\pi$
$419$	−20.6208	−1.00739	−0.503696	+	0.863881i	$0.668027\pi$
$420$	−5.15198	−0.251391
$421$	−27.0578	−1.31872	−0.659359	−	0.751829i	$-0.729172\pi$
$421$	−27.0578	−1.31872	−0.659359	+	0.751829i	$0.729172\pi$
$422$	−34.0455	−1.65731
$423$	−0.220169	−0.0107050
$424$	18.2845	0.887973
$425$	4.93645	0.239453
$426$	−45.7535	−2.21676
$427$	44.0289	2.13071
$428$	−57.7328	−2.79062
$429$	0.679892	0.0328255
$430$	0.594485	0.0286686
$431$	3.83029	0.184499	0.0922493	−	0.995736i	$-0.470594\pi$
$431$	3.83029	0.184499	0.0922493	+	0.995736i	$0.470594\pi$
$432$	−8.32311	−0.400446
$433$	−5.46875	−0.262811	−0.131406	−	0.991329i	$-0.541949\pi$
$433$	−5.46875	−0.262811	−0.131406	+	0.991329i	$0.541949\pi$
$434$	62.3088	2.99092
$435$	−1.84174	−0.0883047
$436$	−6.88837	−0.329893
$437$	−3.68379	−0.176220
$438$	40.1076	1.91641
$439$	17.1856	0.820222	0.410111	−	0.912036i	$-0.365490\pi$
$439$	17.1856	0.820222	0.410111	+	0.912036i	$0.365490\pi$
$440$	−0.112084	−0.00534337
$441$	−0.790589	−0.0376471
$442$	7.89366	0.375463
$443$	−2.32735	−0.110576	−0.0552880	−	0.998470i	$-0.517608\pi$
$443$	−2.32735	−0.110576	−0.0552880	+	0.998470i	$0.517608\pi$
$444$	−50.0965	−2.37747
$445$	2.14908	0.101876
$446$	−30.4679	−1.44270
$447$	−38.7201	−1.83140
$448$	40.2857	1.90332
$449$	11.2166	0.529346	0.264673	−	0.964338i	$-0.414736\pi$
$449$	11.2166	0.529346	0.264673	+	0.964338i	$0.414736\pi$
$450$	−1.98420	−0.0935360
$451$	0.713157	0.0335813
$452$	66.3088	3.11890
$453$	−8.45503	−0.397252
$454$	40.3272	1.89265
$455$	−2.87862	−0.134952
$456$	52.0701	2.43841
$457$	31.7186	1.48373	0.741867	−	0.670547i	$-0.233941\pi$
$457$	31.7186	1.48373	0.741867	+	0.670547i	$0.233941\pi$
$458$	−65.7793	−3.07367
$459$	5.33309	0.248927
$460$	0.393398	0.0183423
$461$	−25.9508	−1.20865	−0.604326	−	0.796738i	$-0.706557\pi$
$461$	−25.9508	−1.20865	−0.604326	+	0.796738i	$0.706557\pi$
$462$	1.63415	0.0760274
$463$	−20.8000	−0.966660	−0.483330	−	0.875438i	$-0.660573\pi$
$463$	−20.8000	−0.966660	−0.483330	+	0.875438i	$0.660573\pi$
$464$	−6.77838	−0.314678
$465$	3.28413	0.152298
$466$	−27.1432	−1.25739
$467$	17.6282	0.815737	0.407868	−	0.913041i	$-0.366272\pi$
$467$	17.6282	0.815737	0.407868	+	0.913041i	$0.366272\pi$
$468$	−2.03181	−0.0939207
$469$	−21.6509	−0.999747
$470$	−0.767925	−0.0354217
$471$	−9.03925	−0.416507
$472$	17.9907	0.828088
$473$	−0.120752	−0.00555217
$474$	44.8581	2.06040
$475$	41.4997	1.90414
$476$	12.1497	0.556880
$477$	0.846374	0.0387528
$478$	47.6044	2.17738
$479$	−26.4045	−1.20645	−0.603227	−	0.797569i	$-0.706119\pi$
$479$	−26.4045	−1.20645	−0.603227	+	0.797569i	$0.706119\pi$
$480$	1.56210	0.0712999
$481$	−27.9909	−1.27628
$482$	11.7721	0.536204
$483$	−2.51461	−0.114419
$484$	−39.1232	−1.77833
$485$	−1.58238	−0.0718523
$486$	−4.17201	−0.189246
$487$	−40.2114	−1.82215	−0.911076	−	0.412239i	$-0.864747\pi$
$487$	−40.2114	−1.82215	−0.911076	+	0.412239i	$0.864747\pi$
$488$	47.5214	2.15119
$489$	14.8961	0.673624
$490$	−2.75748	−0.124570
$491$	−23.6521	−1.06740	−0.533702	−	0.845673i	$-0.679199\pi$
$491$	−23.6521	−1.06740	−0.533702	+	0.845673i	$0.679199\pi$
$492$	35.3809	1.59510
$493$	4.34330	0.195612
$494$	66.3604	2.98569
$495$	−0.00518826	−0.000233195 0
$496$	12.0870	0.542721
$497$	−39.3479	−1.76499
$498$	−53.0112	−2.37549
$499$	5.80912	0.260052	0.130026	−	0.991511i	$-0.458494\pi$
$499$	5.80912	0.260052	0.130026	+	0.991511i	$0.458494\pi$
$500$	−8.92070	−0.398946
$501$	11.3073	0.505175
$502$	−37.4815	−1.67288
$503$	−7.51699	−0.335166	−0.167583	−	0.985858i	$-0.553596\pi$
$503$	−7.51699	−0.335166	−0.167583	+	0.985858i	$0.553596\pi$
$504$	−2.14104	−0.0953696
$505$	−4.87803	−0.217070
$506$	−0.124781	−0.00554720
$507$	−3.02104	−0.134169
$508$	54.8877	2.43525
$509$	−4.08998	−0.181285	−0.0906426	−	0.995883i	$-0.528892\pi$
$509$	−4.08998	−0.181285	−0.0906426	+	0.995883i	$0.528892\pi$
$510$	1.00000	0.0442807
$511$	34.4924	1.52585
$512$	17.2422	0.762006
$513$	44.8342	1.97948
$514$	−11.7489	−0.518222
$515$	0.354245	0.0156099
$516$	−5.99069	−0.263726
$517$	0.155981	0.00686002
$518$	−67.2773	−2.95599
$519$	18.6170	0.817194
$520$	−3.10696	−0.136249
$521$	43.5895	1.90969	0.954844	−	0.297106i	$-0.0960216\pi$
$521$	43.5895	1.90969	0.954844	+	0.297106i	$0.0960216\pi$
$522$	−1.74578	−0.0764107
$523$	10.6045	0.463702	0.231851	−	0.972751i	$-0.425522\pi$
$523$	10.6045	0.463702	0.231851	+	0.972751i	$0.425522\pi$
$524$	−34.4635	−1.50554
$525$	28.3284	1.23635
$526$	−0.851691	−0.0371355
$527$	−7.74481	−0.337369
$528$	0.317000	0.0137956
$529$	−22.8080	−0.991652
$530$	2.95206	0.128229
$531$	0.832774	0.0361393
$532$	102.140	4.42833
$533$	19.7688	0.856280
$534$	−33.8184	−1.46347
$535$	−4.08653	−0.176676
$536$	−23.3683	−1.00936
$537$	19.4774	0.840511
$538$	−34.1770	−1.47347
$539$	0.560099	0.0241252
$540$	−4.78792	−0.206039
$541$	−36.4433	−1.56682	−0.783409	−	0.621506i	$-0.786521\pi$
$541$	−36.4433	−1.56682	−0.783409	+	0.621506i	$0.786521\pi$
$542$	−18.5124	−0.795175
$543$	−12.5127	−0.536972
$544$	−3.68384	−0.157943
$545$	−0.487583	−0.0208857
$546$	45.2986	1.93860
$547$	−4.31868	−0.184653	−0.0923267	−	0.995729i	$-0.529430\pi$
$547$	−4.31868	−0.184653	−0.0923267	+	0.995729i	$0.529430\pi$
$548$	26.2050	1.11942
$549$	2.19973	0.0938821
$550$	1.40572	0.0599402
$551$	36.5132	1.55551
$552$	−2.71408	−0.115519
$553$	38.5778	1.64050
$554$	−4.33050	−0.183985
$555$	−3.54600	−0.150519
$556$	8.63165	0.366064
$557$	10.0168	0.424424	0.212212	−	0.977224i	$-0.431933\pi$
$557$	10.0168	0.424424	0.212212	+	0.977224i	$0.431933\pi$
$558$	3.11301	0.131784
$559$	−3.34724	−0.141573
$560$	−1.34216	−0.0567165
$561$	−0.203120	−0.00857573
$562$	−30.7155	−1.29566
$563$	−33.3798	−1.40679	−0.703395	−	0.710799i	$-0.748334\pi$
$563$	−33.3798	−1.40679	−0.703395	+	0.710799i	$0.748334\pi$
$564$	7.73847	0.325848
$565$	4.69357	0.197460
$566$	21.4229	0.900474
$567$	28.8601	1.21201
$568$	−42.4691	−1.78196
$569$	40.5491	1.69991	0.849953	−	0.526859i	$-0.176630\pi$
$569$	40.5491	1.69991	0.849953	+	0.526859i	$0.176630\pi$
$570$	8.40679	0.352122
$571$	−17.2176	−0.720534	−0.360267	−	0.932849i	$-0.617314\pi$
$571$	−17.2176	−0.720534	−0.360267	+	0.932849i	$0.617314\pi$
$572$	1.43946	0.0601867
$573$	−9.37743	−0.391748
$574$	47.5150	1.98324
$575$	−2.16311	−0.0902081
$576$	2.01272	0.0838632
$577$	3.69189	0.153695	0.0768477	−	0.997043i	$-0.475514\pi$
$577$	3.69189	0.153695	0.0768477	+	0.997043i	$0.475514\pi$
$578$	−2.35826	−0.0980906
$579$	37.2428	1.54776
$580$	−3.89930	−0.161910
$581$	−45.5894	−1.89137
$582$	24.9007	1.03217
$583$	−0.599621	−0.0248338
$584$	37.2284	1.54052
$585$	−0.143819	−0.00594618
$586$	48.4001	1.99939
$587$	0.209448	0.00864484	0.00432242	−	0.999991i	$-0.498624\pi$
$587$	0.209448	0.00864484	0.00432242	+	0.999991i	$0.498624\pi$
$588$	27.7875	1.14594
$589$	−65.1091	−2.68277
$590$	2.90462	0.119581
$591$	15.1765	0.624279
$592$	−13.0508	−0.536383
$593$	−45.8332	−1.88215	−0.941073	−	0.338204i	$-0.890181\pi$
$593$	−45.8332	−1.88215	−0.941073	+	0.338204i	$0.890181\pi$
$594$	1.51867	0.0623118
$595$	0.859997	0.0352564
$596$	−81.9777	−3.35794
$597$	−2.75094	−0.112588
$598$	−3.45894	−0.141447
$599$	−23.5892	−0.963830	−0.481915	−	0.876218i	$-0.660059\pi$
$599$	−23.5892	−0.963830	−0.481915	+	0.876218i	$0.660059\pi$
$600$	30.5755	1.24824
$601$	19.5597	0.797857	0.398928	−	0.916982i	$-0.369382\pi$
$601$	19.5597	0.797857	0.398928	+	0.916982i	$0.369382\pi$
$602$	−8.04523	−0.327899
$603$	−1.08170	−0.0440503
$604$	−17.9009	−0.728375
$605$	−2.76928	−0.112587
$606$	76.7619	3.11824
$607$	35.6132	1.44550	0.722748	−	0.691111i	$-0.242879\pi$
$607$	35.6132	1.44550	0.722748	+	0.691111i	$0.242879\pi$
$608$	−30.9693	−1.25597
$609$	24.9245	1.00999
$610$	7.67239	0.310646
$611$	4.32379	0.174922
$612$	0.607011	0.0245370
$613$	2.61160	0.105482	0.0527408	−	0.998608i	$-0.483204\pi$
$613$	2.61160	0.105482	0.0527408	+	0.998608i	$0.483204\pi$
$614$	−49.9523	−2.01591
$615$	2.50438	0.100986
$616$	1.51684	0.0611152
$617$	−25.7789	−1.03782	−0.518911	−	0.854829i	$-0.673662\pi$
$617$	−25.7789	−1.03782	−0.518911	+	0.854829i	$0.673662\pi$
$618$	−5.57449	−0.224239
$619$	17.8472	0.717338	0.358669	−	0.933465i	$-0.383231\pi$
$619$	17.8472	0.717338	0.358669	+	0.933465i	$0.383231\pi$
$620$	6.95310	0.279243
$621$	−2.33692	−0.0937774
$622$	6.95246	0.278768
$623$	−29.0838	−1.16522
$624$	8.78725	0.351771
$625$	24.0508	0.962033
$626$	54.4113	2.17471
$627$	−1.70759	−0.0681944
$628$	−19.1378	−0.763680
$629$	8.36238	0.333430
$630$	−0.345674	−0.0137720
$631$	3.33820	0.132892	0.0664458	−	0.997790i	$-0.478834\pi$
$631$	3.33820	0.132892	0.0664458	+	0.997790i	$0.478834\pi$
$632$	41.6380	1.65627
$633$	24.2844	0.965219
$634$	−36.2838	−1.44101
$635$	3.88514	0.154177
$636$	−29.7482	−1.17959
$637$	15.5260	0.615162
$638$	1.23681	0.0489659
$639$	−1.96586	−0.0777682
$640$	5.16283	0.204079
$641$	−13.9216	−0.549869	−0.274935	−	0.961463i	$-0.588656\pi$
$641$	−13.9216	−0.549869	−0.274935	+	0.961463i	$0.588656\pi$
$642$	64.3066	2.53798
$643$	−5.61656	−0.221496	−0.110748	−	0.993849i	$-0.535325\pi$
$643$	−5.61656	−0.221496	−0.110748	+	0.993849i	$0.535325\pi$
$644$	−5.32390	−0.209791
$645$	−0.424042	−0.0166966
$646$	−19.8254	−0.780019
$647$	−12.8755	−0.506190	−0.253095	−	0.967441i	$-0.581448\pi$
$647$	−12.8755	−0.506190	−0.253095	+	0.967441i	$0.581448\pi$
$648$	31.1494	1.22366
$649$	−0.589986	−0.0231590
$650$	38.9667	1.52840
$651$	−44.4445	−1.74192
$652$	31.5378	1.23511
$653$	−49.8385	−1.95033	−0.975166	−	0.221477i	$-0.928912\pi$
$653$	−49.8385	−1.95033	−0.975166	+	0.221477i	$0.928912\pi$
$654$	7.67271	0.300027
$655$	−2.43944	−0.0953169
$656$	9.21718	0.359871
$657$	1.72328	0.0672314
$658$	10.3924	0.405138
$659$	27.6176	1.07583	0.537914	−	0.843000i	$-0.319212\pi$
$659$	27.6176	1.07583	0.537914	+	0.843000i	$0.319212\pi$
$660$	0.182356	0.00709820
$661$	2.49646	0.0971010	0.0485505	−	0.998821i	$-0.484540\pi$
$661$	2.49646	0.0971010	0.0485505	+	0.998821i	$0.484540\pi$
$662$	24.6971	0.959878
$663$	−5.63049	−0.218670
$664$	−49.2057	−1.90955
$665$	7.22982	0.280360
$666$	−3.36124	−0.130245
$667$	−1.90320	−0.0736922
$668$	23.9397	0.926256
$669$	21.7325	0.840229
$670$	−3.77285	−0.145758
$671$	−1.55842	−0.0601620
$672$	−21.1401	−0.815497
$673$	−46.0809	−1.77629	−0.888143	−	0.459566i	$-0.848005\pi$
$673$	−46.0809	−1.77629	−0.888143	+	0.459566i	$0.848005\pi$
$674$	45.4337	1.75004
$675$	26.3266	1.01331
$676$	−6.39610	−0.246004
$677$	−13.9244	−0.535158	−0.267579	−	0.963536i	$-0.586224\pi$
$677$	−13.9244	−0.535158	−0.267579	+	0.963536i	$0.586224\pi$
$678$	−73.8590	−2.83654
$679$	21.4146	0.821816
$680$	0.928215	0.0355954
$681$	−28.7651	−1.10228
$682$	−2.20544	−0.0844507
$683$	−13.3748	−0.511771	−0.255885	−	0.966707i	$-0.582367\pi$
$683$	−13.3748	−0.511771	−0.255885	+	0.966707i	$0.582367\pi$
$684$	5.10302	0.195119
$685$	1.85488	0.0708713
$686$	−18.9993	−0.725397
$687$	46.9199	1.79011
$688$	−1.56065	−0.0594993
$689$	−16.6215	−0.633230
$690$	−0.438192	−0.0166817
$691$	−13.5757	−0.516442	−0.258221	−	0.966086i	$-0.583136\pi$
$691$	−13.5757	−0.516442	−0.258221	+	0.966086i	$0.583136\pi$
$692$	39.4155	1.49835
$693$	0.0702133	0.00266718
$694$	−66.0694	−2.50796
$695$	0.610978	0.0231757
$696$	26.9016	1.01970
$697$	−5.90598	−0.223705
$698$	42.8483	1.62183
$699$	19.3611	0.732303
$700$	59.9764	2.26689
$701$	2.05978	0.0777969	0.0388984	−	0.999243i	$-0.487615\pi$
$701$	2.05978	0.0777969	0.0388984	+	0.999243i	$0.487615\pi$
$702$	42.0976	1.58887
$703$	70.3008	2.65144
$704$	−1.42593	−0.0537416
$705$	0.547755	0.0206297
$706$	24.1879	0.910322
$707$	66.0150	2.48275
$708$	−29.2702	−1.10004
$709$	−19.3260	−0.725802	−0.362901	−	0.931828i	$-0.618214\pi$
$709$	−19.3260	−0.725802	−0.362901	+	0.931828i	$0.618214\pi$
$710$	−6.85669	−0.257327
$711$	1.92739	0.0722827
$712$	−31.3908	−1.17642
$713$	3.39372	0.127096
$714$	−13.5331	−0.506464
$715$	0.101890	0.00381046
$716$	41.2372	1.54111
$717$	−33.9559	−1.26811
$718$	44.0857	1.64526
$719$	−30.9365	−1.15374	−0.576869	−	0.816837i	$-0.695726\pi$
$719$	−30.9365	−1.15374	−0.576869	+	0.816837i	$0.695726\pi$
$720$	−0.0670555	−0.00249901
$721$	−4.79404	−0.178539
$722$	−121.861	−4.53520
$723$	−8.39695	−0.312286
$724$	−26.4917	−0.984556
$725$	21.4405	0.796279
$726$	43.5780	1.61733
$727$	−30.6157	−1.13547	−0.567737	−	0.823210i	$-0.692181\pi$
$727$	−30.6157	−1.13547	−0.567737	+	0.823210i	$0.692181\pi$
$728$	42.0469	1.55836
$729$	28.3547	1.05018
$730$	6.01058	0.222462
$731$	1.00000	0.0369863
$732$	−77.3156	−2.85767
$733$	9.54484	0.352547	0.176273	−	0.984341i	$-0.443596\pi$
$733$	9.54484	0.352547	0.176273	+	0.984341i	$0.443596\pi$
$734$	−37.3325	−1.37797
$735$	1.96689	0.0725499
$736$	1.61423	0.0595013
$737$	0.766341	0.0282285
$738$	2.37390	0.0873844
$739$	32.6005	1.19923	0.599614	−	0.800289i	$-0.295321\pi$
$739$	32.6005	1.19923	0.599614	+	0.800289i	$0.295321\pi$
$740$	−7.50753	−0.275982
$741$	−47.3344	−1.73887
$742$	−39.9505	−1.46663
$743$	14.1350	0.518562	0.259281	−	0.965802i	$-0.416514\pi$
$743$	14.1350	0.518562	0.259281	+	0.965802i	$0.416514\pi$
$744$	−47.9699	−1.75866
$745$	−5.80266	−0.212593
$746$	−33.3243	−1.22009
$747$	−2.27770	−0.0833365
$748$	−0.430042	−0.0157239
$749$	55.3034	2.02074
$750$	9.93645	0.362828
$751$	−30.7397	−1.12171	−0.560854	−	0.827915i	$-0.689527\pi$
$751$	−30.7397	−1.12171	−0.560854	+	0.827915i	$0.689527\pi$
$752$	2.01597	0.0735148
$753$	26.7353	0.974288
$754$	34.2845	1.24857
$755$	−1.26708	−0.0461139
$756$	64.7954	2.35659
$757$	−52.8011	−1.91909	−0.959544	−	0.281557i	$-0.909149\pi$
$757$	−52.8011	−1.91909	−0.959544	+	0.281557i	$0.909149\pi$
$758$	−47.1095	−1.71109
$759$	0.0890055	0.00323070
$760$	7.80331	0.283056
$761$	−18.1300	−0.657211	−0.328606	−	0.944467i	$-0.606579\pi$
$761$	−18.1300	−0.657211	−0.328606	+	0.944467i	$0.606579\pi$
$762$	−61.1375	−2.21478
$763$	6.59851	0.238882
$764$	−19.8537	−0.718283
$765$	0.0429663	0.00155345
$766$	−12.2038	−0.440940
$767$	−16.3544	−0.590524
$768$	−41.5158	−1.49807
$769$	14.9904	0.540567	0.270283	−	0.962781i	$-0.412883\pi$
$769$	14.9904	0.540567	0.270283	+	0.962781i	$0.412883\pi$
$770$	0.244896	0.00882543
$771$	8.38041	0.301813
$772$	78.8499	2.83787
$773$	−54.9568	−1.97666	−0.988329	−	0.152332i	$-0.951322\pi$
$773$	−54.9568	−1.97666	−0.988329	+	0.152332i	$0.951322\pi$
$774$	−0.401948	−0.0144477
$775$	−38.2319	−1.37333
$776$	23.1132	0.829717
$777$	47.9884	1.72157
$778$	25.4146	0.911157
$779$	−49.6504	−1.77891
$780$	5.05492	0.180995
$781$	1.39273	0.0498358
$782$	1.03337	0.0369532
$783$	23.1632	0.827786
$784$	7.23899	0.258535
$785$	−1.35464	−0.0483490
$786$	38.3876	1.36924
$787$	−2.55479	−0.0910684	−0.0455342	−	0.998963i	$-0.514499\pi$
$787$	−2.55479	−0.0910684	−0.0455342	+	0.998963i	$0.514499\pi$
$788$	32.1315	1.14464
$789$	0.607506	0.0216278
$790$	6.72251	0.239176
$791$	−63.5186	−2.25846
$792$	0.0757829	0.00269283
$793$	−43.1994	−1.53405
$794$	36.2332	1.28587
$795$	−2.10568	−0.0746808
$796$	−5.82424	−0.206435
$797$	9.28439	0.328870	0.164435	−	0.986388i	$-0.447420\pi$
$797$	9.28439	0.328870	0.164435	+	0.986388i	$0.447420\pi$
$798$	−113.770	−4.02742
$799$	−1.29175	−0.0456988
$800$	−18.1851	−0.642940
$801$	−1.45305	−0.0513412
$802$	−21.6093	−0.763050
$803$	−1.22087	−0.0430835
$804$	38.0195	1.34084
$805$	−0.376844	−0.0132820
$806$	−61.1349	−2.15339
$807$	24.3782	0.858153
$808$	71.2515	2.50662
$809$	−49.4945	−1.74013	−0.870067	−	0.492934i	$-0.835924\pi$
$809$	−49.4945	−1.74013	−0.870067	+	0.492934i	$0.835924\pi$
$810$	5.02912	0.176705
$811$	−7.79500	−0.273720	−0.136860	−	0.990590i	$-0.543701\pi$
$811$	−7.79500	−0.273720	−0.136860	+	0.990590i	$0.543701\pi$
$812$	52.7697	1.85185
$813$	13.2047	0.463111
$814$	2.38130	0.0834645
$815$	2.23235	0.0781959
$816$	−2.62522	−0.0919010
$817$	8.40679	0.294116
$818$	26.2916	0.919266
$819$	1.94632	0.0680098
$820$	5.30224	0.185162
$821$	13.7637	0.480357	0.240179	−	0.970729i	$-0.422794\pi$
$821$	13.7637	0.480357	0.240179	+	0.970729i	$0.422794\pi$
$822$	−29.1888	−1.01808
$823$	13.8886	0.484126	0.242063	−	0.970260i	$-0.422176\pi$
$823$	13.8886	0.484126	0.242063	+	0.970260i	$0.422176\pi$
$824$	−5.17432	−0.180256
$825$	−1.00269	−0.0349092
$826$	−39.3085	−1.36772
$827$	39.7097	1.38084	0.690421	−	0.723408i	$-0.257425\pi$
$827$	39.7097	1.38084	0.690421	+	0.723408i	$0.257425\pi$
$828$	−0.265988	−0.00924371
$829$	−55.3677	−1.92300	−0.961500	−	0.274804i	$-0.911387\pi$
$829$	−55.3677	−1.92300	−0.961500	+	0.274804i	$0.911387\pi$
$830$	−7.94434	−0.275752
$831$	3.08892	0.107153
$832$	−39.5267	−1.37034
$833$	−4.63844	−0.160712
$834$	−9.61450	−0.332923
$835$	1.69454	0.0586419
$836$	−3.61528	−0.125037
$837$	−41.3038	−1.42767
$838$	48.6292	1.67987
$839$	−10.8918	−0.376028	−0.188014	−	0.982166i	$-0.560205\pi$
$839$	−10.8918	−0.376028	−0.188014	+	0.982166i	$0.560205\pi$
$840$	5.32666	0.183787
$841$	−10.1358	−0.349509
$842$	63.8093	2.19901
$843$	21.9092	0.754592
$844$	51.4146	1.76976
$845$	−0.452738	−0.0155747
$846$	0.519216	0.0178510
$847$	37.4769	1.28772
$848$	−7.74979	−0.266129
$849$	−15.2808	−0.524437
$850$	−11.6414	−0.399298
$851$	−3.66433	−0.125612
$852$	69.0957	2.36718
$853$	−32.6496	−1.11790	−0.558950	−	0.829201i	$-0.688796\pi$
$853$	−32.6496	−1.11790	−0.558950	+	0.829201i	$0.688796\pi$
$854$	−103.831	−3.55304
$855$	0.361209	0.0123531
$856$	59.6903	2.04017
$857$	32.8424	1.12188	0.560938	−	0.827858i	$-0.310441\pi$
$857$	32.8424	1.12188	0.560938	+	0.827858i	$0.310441\pi$
$858$	−1.60336	−0.0547378
$859$	−38.5322	−1.31470	−0.657351	−	0.753585i	$-0.728323\pi$
$859$	−38.5322	−1.31470	−0.657351	+	0.753585i	$0.728323\pi$
$860$	−0.897775	−0.0306139
$861$	−33.8921	−1.15504
$862$	−9.03281	−0.307659
$863$	−3.59644	−0.122424	−0.0612121	−	0.998125i	$-0.519497\pi$
$863$	−3.59644	−0.122424	−0.0612121	+	0.998125i	$0.519497\pi$
$864$	−19.6462	−0.668379
$865$	2.78997	0.0948617
$866$	12.8967	0.438248
$867$	1.68213	0.0571281
$868$	−94.0971	−3.19386
$869$	−1.36548	−0.0463206
$870$	4.34330	0.147252
$871$	21.2430	0.719792
$872$	7.12193	0.241179
$873$	1.06989	0.0362104
$874$	8.68733	0.293853
$875$	8.54532	0.288885
$876$	−60.5694	−2.04645
$877$	−20.5421	−0.693658	−0.346829	−	0.937928i	$-0.612742\pi$
$877$	−20.5421	−0.693658	−0.346829	+	0.937928i	$0.612742\pi$
$878$	−40.5280	−1.36775
$879$	−34.5235	−1.16445
$880$	0.0475061	0.00160143
$881$	−4.49143	−0.151320	−0.0756601	−	0.997134i	$-0.524106\pi$
$881$	−4.49143	−0.151320	−0.0756601	+	0.997134i	$0.524106\pi$
$882$	1.86441	0.0627780
$883$	15.9912	0.538145	0.269073	−	0.963120i	$-0.413283\pi$
$883$	15.9912	0.538145	0.269073	+	0.963120i	$0.413283\pi$
$884$	−11.9208	−0.400940
$885$	−2.07184	−0.0696443
$886$	5.48850	0.184390
$887$	53.9426	1.81122	0.905608	−	0.424115i	$-0.139415\pi$
$887$	53.9426	1.81122	0.905608	+	0.424115i	$0.139415\pi$
$888$	51.7950	1.73813
$889$	−52.5780	−1.76341
$890$	−5.06808	−0.169883
$891$	−1.02151	−0.0342220
$892$	46.0118	1.54059
$893$	−10.8595	−0.363398
$894$	91.3120	3.05393
$895$	2.91891	0.0975684
$896$	−69.8691	−2.33416
$897$	2.46724	0.0823787
$898$	−26.4517	−0.882705
$899$	−33.6380	−1.12189
$900$	2.99648	0.0998827
$901$	4.96574	0.165433
$902$	−1.68181	−0.0559981
$903$	5.73861	0.190969
$904$	−68.5571	−2.28017
$905$	−1.87517	−0.0623329
$906$	19.9391	0.662433
$907$	18.8282	0.625179	0.312589	−	0.949888i	$-0.398804\pi$
$907$	18.8282	0.625179	0.312589	+	0.949888i	$0.398804\pi$
$908$	−60.9011	−2.02107
$909$	3.29818	0.109394
$910$	6.78852	0.225037
$911$	34.2713	1.13546	0.567730	−	0.823215i	$-0.307822\pi$
$911$	34.2713	1.13546	0.567730	+	0.823215i	$0.307822\pi$
$912$	−22.0697	−0.730800
$913$	1.61365	0.0534041
$914$	−74.8006	−2.47418
$915$	−5.47267	−0.180921
$916$	99.3382	3.28223
$917$	33.0133	1.09019
$918$	−12.5768	−0.415096
$919$	−13.6058	−0.448815	−0.224407	−	0.974495i	$-0.572045\pi$
$919$	−13.6058	−0.448815	−0.224407	+	0.974495i	$0.572045\pi$
$920$	−0.406737	−0.0134097
$921$	35.6306	1.17407
$922$	61.1988	2.01547
$923$	38.6066	1.27075
$924$	−2.46784	−0.0811861
$925$	41.2805	1.35729
$926$	49.0519	1.61194
$927$	−0.239515	−0.00786672
$928$	−16.0000	−0.525226
$929$	28.8100	0.945224	0.472612	−	0.881271i	$-0.343311\pi$
$929$	28.8100	0.945224	0.472612	+	0.881271i	$0.343311\pi$
$930$	−7.74481	−0.253962
$931$	−38.9944	−1.27799
$932$	40.9910	1.34270
$933$	−4.95914	−0.162355
$934$	−41.5719	−1.36027
$935$	−0.0304399	−0.000995490 0
$936$	2.10070	0.0686637
$937$	−44.8103	−1.46389	−0.731945	−	0.681364i	$-0.761387\pi$
$937$	−44.8103	−1.46389	−0.731945	+	0.681364i	$0.761387\pi$
$938$	51.0584	1.66712
$939$	−38.8112	−1.26656
$940$	1.15970	0.0378252
$941$	−15.2691	−0.497760	−0.248880	−	0.968534i	$-0.580062\pi$
$941$	−15.2691	−0.497760	−0.248880	+	0.968534i	$0.580062\pi$
$942$	21.3169	0.694541
$943$	2.58795	0.0842754
$944$	−7.62526	−0.248181
$945$	4.58644	0.149197
$946$	0.284764	0.00925846
$947$	−1.13590	−0.0369118	−0.0184559	−	0.999830i	$-0.505875\pi$
$947$	−1.13590	−0.0369118	−0.0184559	+	0.999830i	$0.505875\pi$
$948$	−67.7435	−2.20021
$949$	−33.8426	−1.09858
$950$	−97.8670	−3.17523
$951$	25.8810	0.839248
$952$	−12.5616	−0.407125
$953$	16.6629	0.539764	0.269882	−	0.962893i	$-0.413015\pi$
$953$	16.6629	0.539764	0.269882	+	0.962893i	$0.413015\pi$
$954$	−1.99597	−0.0646219
$955$	−1.40532	−0.0454750
$956$	−71.8910	−2.32512
$957$	−0.882210	−0.0285178
$958$	62.2687	2.01181
$959$	−25.1023	−0.810596
$960$	−5.00740	−0.161613
$961$	28.9822	0.934908
$962$	66.0098	2.12824
$963$	2.76302	0.0890370
$964$	−17.7779	−0.572587
$965$	5.58126	0.179667
$966$	5.93011	0.190798
$967$	−26.7181	−0.859197	−0.429599	−	0.903020i	$-0.641345\pi$
$967$	−26.7181	−0.859197	−0.429599	+	0.903020i	$0.641345\pi$
$968$	40.4497	1.30010
$969$	14.1413	0.454284
$970$	3.73167	0.119817
$971$	44.7350	1.43561	0.717807	−	0.696242i	$-0.245146\pi$
$971$	44.7350	1.43561	0.717807	+	0.696242i	$0.245146\pi$
$972$	6.30046	0.202087
$973$	−8.26844	−0.265074
$974$	94.8288	3.03851
$975$	−27.7947	−0.890142
$976$	−20.1417	−0.644720
$977$	−16.1109	−0.515435	−0.257717	−	0.966220i	$-0.582970\pi$
$977$	−16.1109	−0.515435	−0.257717	+	0.966220i	$0.582970\pi$
$978$	−35.1288	−1.12330
$979$	1.02943	0.0329007
$980$	4.16427	0.133023
$981$	0.329668	0.0105255
$982$	55.7777	1.77994
$983$	−47.2877	−1.50824	−0.754122	−	0.656735i	$-0.771937\pi$
$983$	−47.2877	−1.50824	−0.754122	+	0.656735i	$0.771937\pi$
$984$	−36.5806	−1.16615
$985$	2.27438	0.0724677
$986$	−10.2426	−0.326191
$987$	−7.41284	−0.235953
$988$	−100.216	−3.18828
$989$	−0.438192	−0.0139337
$990$	0.0122352	0.000388862 0
$991$	29.9314	0.950803	0.475402	−	0.879769i	$-0.342303\pi$
$991$	29.9314	0.950803	0.475402	+	0.879769i	$0.342303\pi$
$992$	28.5306	0.905849
$993$	−17.6162	−0.559035
$994$	92.7924	2.94320
$995$	−0.412260	−0.0130695
$996$	80.0560	2.53667
$997$	51.3858	1.62740	0.813702	−	0.581282i	$-0.197449\pi$
$997$	51.3858	1.62740	0.813702	+	0.581282i	$0.197449\pi$
$998$	−13.6994	−0.433647
$999$	44.5973	1.41100

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.a.c.1.1	✓	6
3.2	odd	2		6579.2.a.j.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.a.c.1.1	✓	6	1.1	even	1	trivial
6579.2.a.j.1.6		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)

\(f(q)\)	\(=\)	\(q-2.35826 q^{2} +1.68213 q^{3} +3.56138 q^{4} +0.252087 q^{5} -3.96689 q^{6} -3.41152 q^{7} -3.68213 q^{8} -0.170443 q^{9} +O(q^{10})\)	\(q-2.35826 q^{2} +1.68213 q^{3} +3.56138 q^{4} +0.252087 q^{5} -3.96689 q^{6} -3.41152 q^{7} -3.68213 q^{8} -0.170443 q^{9} -0.594485 q^{10} +0.120752 q^{11} +5.99069 q^{12} +3.34724 q^{13} +8.04523 q^{14} +0.424042 q^{15} +1.56065 q^{16} -1.00000 q^{17} +0.401948 q^{18} -8.40679 q^{19} +0.897775 q^{20} -5.73861 q^{21} -0.284764 q^{22} +0.438192 q^{23} -6.19381 q^{24} -4.93645 q^{25} -7.89366 q^{26} -5.33309 q^{27} -12.1497 q^{28} -4.34330 q^{29} -1.00000 q^{30} +7.74481 q^{31} +3.68384 q^{32} +0.203120 q^{33} +2.35826 q^{34} -0.859997 q^{35} -0.607011 q^{36} -8.36238 q^{37} +19.8254 q^{38} +5.63049 q^{39} -0.928215 q^{40} +5.90598 q^{41} +13.5331 q^{42} -1.00000 q^{43} +0.430042 q^{44} -0.0429663 q^{45} -1.03337 q^{46} +1.29175 q^{47} +2.62522 q^{48} +4.63844 q^{49} +11.6414 q^{50} -1.68213 q^{51} +11.9208 q^{52} -4.96574 q^{53} +12.5768 q^{54} +0.0304399 q^{55} +12.5616 q^{56} -14.1413 q^{57} +10.2426 q^{58} -4.88594 q^{59} +1.51017 q^{60} -12.9060 q^{61} -18.2643 q^{62} +0.581468 q^{63} -11.8087 q^{64} +0.843795 q^{65} -0.479009 q^{66} +6.34642 q^{67} -3.56138 q^{68} +0.737096 q^{69} +2.02809 q^{70} +11.5338 q^{71} +0.627593 q^{72} -10.1106 q^{73} +19.7206 q^{74} -8.30375 q^{75} -29.9398 q^{76} -0.411946 q^{77} -13.2782 q^{78} -11.3081 q^{79} +0.393419 q^{80} -8.45962 q^{81} -13.9278 q^{82} +13.3634 q^{83} -20.4373 q^{84} -0.252087 q^{85} +2.35826 q^{86} -7.30599 q^{87} -0.444623 q^{88} +8.52517 q^{89} +0.101326 q^{90} -11.4192 q^{91} +1.56057 q^{92} +13.0278 q^{93} -3.04627 q^{94} -2.11924 q^{95} +6.19669 q^{96} -6.27714 q^{97} -10.9386 q^{98} -0.0205813 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} - 3 q^{3} + 5 q^{4} + 3 q^{5} - 7 q^{6} - 7 q^{7} - 9 q^{8} - 3 q^{9}+O(q^{10}) \) 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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