LMFDB - Embedded newform 1849.2.a.o.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,2,Mod(1,1849)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1849.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:	$14.7643393337$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 5 x^{17} - 15 x^{16} + 106 x^{15} + 47 x^{14} - 897 x^{13} + 364 x^{12} + 3855 x^{11} + \cdots - 27 $ x^18 - 5x^17 - 15x^16 + 106x^15 + 47x^14 - 897x^13 + 364x^12 + 3855x^11 - 3223x^10 - 8851x^9 + 9909x^8 + 10400x^7 - 14483x^6 - 5118x^5 + 9945x^4 - 27x^3 - 2493x^2 + 513*x - 27
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$1.69598$ of defining polynomial
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.69598 q^{2} +1.71311 q^{3} +0.876333 q^{4} -0.385406 q^{5} +2.90540 q^{6} +3.49171 q^{7} -1.90571 q^{8} -0.0652397 q^{9} +O(q^{10})$	\(q+1.69598 q^{2} +1.71311 q^{3} +0.876333 q^{4} -0.385406 q^{5} +2.90540 q^{6} +3.49171 q^{7} -1.90571 q^{8} -0.0652397 q^{9} -0.653640 q^{10} +4.33570 q^{11} +1.50126 q^{12} -1.27835 q^{13} +5.92185 q^{14} -0.660245 q^{15} -4.98471 q^{16} +0.562744 q^{17} -0.110645 q^{18} +7.63085 q^{19} -0.337744 q^{20} +5.98170 q^{21} +7.35324 q^{22} +7.41258 q^{23} -3.26470 q^{24} -4.85146 q^{25} -2.16806 q^{26} -5.25111 q^{27} +3.05990 q^{28} -3.41307 q^{29} -1.11976 q^{30} +0.978183 q^{31} -4.64252 q^{32} +7.42755 q^{33} +0.954400 q^{34} -1.34573 q^{35} -0.0571717 q^{36} -4.39598 q^{37} +12.9417 q^{38} -2.18997 q^{39} +0.734474 q^{40} +4.85149 q^{41} +10.1448 q^{42} +3.79952 q^{44} +0.0251438 q^{45} +12.5716 q^{46} -4.37114 q^{47} -8.53937 q^{48} +5.19204 q^{49} -8.22796 q^{50} +0.964045 q^{51} -1.12026 q^{52} +9.67103 q^{53} -8.90575 q^{54} -1.67101 q^{55} -6.65419 q^{56} +13.0725 q^{57} -5.78848 q^{58} -4.68688 q^{59} -0.578595 q^{60} +5.41010 q^{61} +1.65897 q^{62} -0.227798 q^{63} +2.09582 q^{64} +0.492686 q^{65} +12.5969 q^{66} +13.1200 q^{67} +0.493151 q^{68} +12.6986 q^{69} -2.28232 q^{70} -7.63193 q^{71} +0.124328 q^{72} -2.07620 q^{73} -7.45548 q^{74} -8.31111 q^{75} +6.68716 q^{76} +15.1390 q^{77} -3.71413 q^{78} -8.28468 q^{79} +1.92114 q^{80} -8.80002 q^{81} +8.22801 q^{82} -11.6495 q^{83} +5.24196 q^{84} -0.216885 q^{85} -5.84697 q^{87} -8.26260 q^{88} -2.72786 q^{89} +0.0426432 q^{90} -4.46364 q^{91} +6.49589 q^{92} +1.67574 q^{93} -7.41335 q^{94} -2.94098 q^{95} -7.95316 q^{96} -0.490296 q^{97} +8.80557 q^{98} -0.282860 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 5 q^{2} + 5 q^{3} + 19 q^{4} + 11 q^{5} + 4 q^{6} + 6 q^{7} + 12 q^{8} + 15 q^{9}+O(q^{10}) $ 18 * q + 5 * q^2 + 5 * q^3 + 19 * q^4 + 11 * q^5 + 4 * q^6 + 6 * q^7 + 12 * q^8 + 15 * q^9	\( 18 q + 5 q^{2} + 5 q^{3} + 19 q^{4} + 11 q^{5} + 4 q^{6} + 6 q^{7} + 12 q^{8} + 15 q^{9} - 7 q^{10} - 2 q^{11} + 16 q^{12} - 7 q^{13} - 4 q^{14} + 3 q^{15} + 9 q^{16} - 11 q^{17} + 25 q^{18} + 31 q^{19} + 25 q^{20} + 19 q^{22} - 11 q^{23} + 18 q^{24} + 9 q^{25} + 27 q^{26} + 23 q^{27} + 20 q^{28} + 37 q^{29} - 17 q^{30} - 12 q^{31} + 39 q^{32} + 38 q^{33} + 14 q^{34} + 16 q^{35} + 47 q^{36} - 19 q^{37} + 56 q^{38} + 46 q^{39} + 6 q^{40} - 7 q^{41} - q^{42} + 7 q^{44} + 23 q^{45} - 47 q^{46} - q^{47} + 15 q^{48} - 6 q^{49} - 3 q^{50} + 38 q^{51} + 15 q^{52} + 3 q^{53} - 67 q^{54} + 28 q^{55} - 81 q^{56} + 46 q^{57} + 34 q^{58} + 17 q^{59} - 83 q^{60} + 28 q^{61} + 33 q^{62} + 26 q^{63} + 10 q^{64} + 16 q^{65} - 72 q^{66} + 18 q^{67} + 53 q^{68} + 7 q^{69} - 34 q^{70} + 86 q^{71} - 2 q^{72} - 27 q^{73} - 79 q^{74} + 31 q^{75} + 59 q^{76} + 43 q^{77} + 91 q^{78} + 17 q^{79} + 8 q^{80} - 10 q^{81} + 13 q^{82} - 12 q^{83} - 32 q^{84} + 28 q^{85} - 43 q^{87} - 23 q^{88} + 51 q^{89} + 10 q^{90} - 20 q^{91} + 18 q^{92} - 30 q^{93} - 15 q^{94} - q^{95} - 20 q^{96} - 19 q^{97} - 5 q^{98} + 38 q^{99}+O(q^{100}) \) 18 * q + 5 * q^2 + 5 * q^3 + 19 * q^4 + 11 * q^5 + 4 * q^6 + 6 * q^7 + 12 * q^8 + 15 * q^9 - 7 * q^10 - 2 * q^11 + 16 * q^12 - 7 * q^13 - 4 * q^14 + 3 * q^15 + 9 * q^16 - 11 * q^17 + 25 * q^18 + 31 * q^19 + 25 * q^20 + 19 * q^22 - 11 * q^23 + 18 * q^24 + 9 * q^25 + 27 * q^26 + 23 * q^27 + 20 * q^28 + 37 * q^29 - 17 * q^30 - 12 * q^31 + 39 * q^32 + 38 * q^33 + 14 * q^34 + 16 * q^35 + 47 * q^36 - 19 * q^37 + 56 * q^38 + 46 * q^39 + 6 * q^40 - 7 * q^41 - q^42 + 7 * q^44 + 23 * q^45 - 47 * q^46 - q^47 + 15 * q^48 - 6 * q^49 - 3 * q^50 + 38 * q^51 + 15 * q^52 + 3 * q^53 - 67 * q^54 + 28 * q^55 - 81 * q^56 + 46 * q^57 + 34 * q^58 + 17 * q^59 - 83 * q^60 + 28 * q^61 + 33 * q^62 + 26 * q^63 + 10 * q^64 + 16 * q^65 - 72 * q^66 + 18 * q^67 + 53 * q^68 + 7 * q^69 - 34 * q^70 + 86 * q^71 - 2 * q^72 - 27 * q^73 - 79 * q^74 + 31 * q^75 + 59 * q^76 + 43 * q^77 + 91 * q^78 + 17 * q^79 + 8 * q^80 - 10 * q^81 + 13 * q^82 - 12 * q^83 - 32 * q^84 + 28 * q^85 - 43 * q^87 - 23 * q^88 + 51 * q^89 + 10 * q^90 - 20 * q^91 + 18 * q^92 - 30 * q^93 - 15 * q^94 - q^95 - 20 * q^96 - 19 * q^97 - 5 * q^98 + 38 * 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 $

$2$	1.69598	1.19924	0.599618	−	0.800286i	$-0.295319\pi$
$2$	1.69598	1.19924	0.599618	+	0.800286i	$0.295319\pi$
$3$	1.71311	0.989067	0.494533	−	0.869159i	$-0.335339\pi$
$3$	1.71311	0.989067	0.494533	+	0.869159i	$0.335339\pi$
$4$	0.876333	0.438166
$5$	−0.385406	−0.172359	−0.0861795	−	0.996280i	$-0.527466\pi$
$5$	−0.385406	−0.172359	−0.0861795	+	0.996280i	$0.527466\pi$
$6$	2.90540	1.18612
$7$	3.49171	1.31974	0.659871	−	0.751379i	$-0.270611\pi$
$7$	3.49171	1.31974	0.659871	+	0.751379i	$0.270611\pi$
$8$	−1.90571	−0.673771
$9$	−0.0652397	−0.0217466
$10$	−0.653640	−0.206699
$11$	4.33570	1.30726	0.653631	−	0.756813i	$-0.273245\pi$
$11$	4.33570	1.30726	0.653631	+	0.756813i	$0.273245\pi$
$12$	1.50126	0.433376
$13$	−1.27835	−0.354551	−0.177276	−	0.984161i	$-0.556728\pi$
$13$	−1.27835	−0.354551	−0.177276	+	0.984161i	$0.556728\pi$
$14$	5.92185	1.58268
$15$	−0.660245	−0.170475
$16$	−4.98471	−1.24618
$17$	0.562744	0.136486	0.0682428	−	0.997669i	$-0.478261\pi$
$17$	0.562744	0.136486	0.0682428	+	0.997669i	$0.478261\pi$
$18$	−0.110645	−0.0260792
$19$	7.63085	1.75064	0.875318	−	0.483548i	$-0.160652\pi$
$19$	7.63085	1.75064	0.875318	+	0.483548i	$0.160652\pi$
$20$	−0.337744	−0.0755219
$21$	5.98170	1.30531
$22$	7.35324	1.56772
$23$	7.41258	1.54563	0.772815	−	0.634632i	$-0.218848\pi$
$23$	7.41258	1.54563	0.772815	+	0.634632i	$0.218848\pi$
$24$	−3.26470	−0.666405
$25$	−4.85146	−0.970292
$26$	−2.16806	−0.425191
$27$	−5.25111	−1.01058
$28$	3.05990	0.578267
$29$	−3.41307	−0.633790	−0.316895	−	0.948461i	$-0.602640\pi$
$29$	−3.41307	−0.633790	−0.316895	+	0.948461i	$0.602640\pi$
$30$	−1.11976	−0.204439
$31$	0.978183	0.175687	0.0878434	−	0.996134i	$-0.472002\pi$
$31$	0.978183	0.175687	0.0878434	+	0.996134i	$0.472002\pi$
$32$	−4.64252	−0.820689
$33$	7.42755	1.29297
$34$	0.954400	0.163678
$35$	−1.34573	−0.227470
$36$	−0.0571717	−0.00952861
$37$	−4.39598	−0.722695	−0.361348	−	0.932431i	$-0.617683\pi$
$37$	−4.39598	−0.722695	−0.361348	+	0.932431i	$0.617683\pi$
$38$	12.9417	2.09943
$39$	−2.18997	−0.350675
$40$	0.734474	0.116130
$41$	4.85149	0.757676	0.378838	−	0.925463i	$-0.376324\pi$
$41$	4.85149	0.757676	0.378838	+	0.925463i	$0.376324\pi$
$42$	10.1448	1.56538
$43$	0	0
$43$	0	0
$44$	3.79952	0.572799
$45$	0.0251438	0.00374821
$46$	12.5716	1.85357
$47$	−4.37114	−0.637597	−0.318798	−	0.947823i	$-0.603279\pi$
$47$	−4.37114	−0.637597	−0.318798	+	0.947823i	$0.603279\pi$
$48$	−8.53937	−1.23255
$49$	5.19204	0.741720
$50$	−8.22796	−1.16361
$51$	0.964045	0.134993
$52$	−1.12026	−0.155353
$53$	9.67103	1.32842	0.664209	−	0.747547i	$-0.268768\pi$
$53$	9.67103	1.32842	0.664209	+	0.747547i	$0.268768\pi$
$54$	−8.90575	−1.21192
$55$	−1.67101	−0.225319
$56$	−6.65419	−0.889204
$57$	13.0725	1.73150
$58$	−5.78848	−0.760064
$59$	−4.68688	−0.610180	−0.305090	−	0.952324i	$-0.598686\pi$
$59$	−4.68688	−0.610180	−0.305090	+	0.952324i	$0.598686\pi$
$60$	−0.578595	−0.0746962
$61$	5.41010	0.692692	0.346346	−	0.938107i	$-0.387422\pi$
$61$	5.41010	0.692692	0.346346	+	0.938107i	$0.387422\pi$
$62$	1.65897	0.210690
$63$	−0.227798	−0.0286999
$64$	2.09582	0.261978
$65$	0.492686	0.0611101
$66$	12.5969	1.55058
$67$	13.1200	1.60286	0.801431	−	0.598087i	$-0.204072\pi$
$67$	13.1200	1.60286	0.801431	+	0.598087i	$0.204072\pi$
$68$	0.493151	0.0598034
$69$	12.6986	1.52873
$70$	−2.28232	−0.272790
$71$	−7.63193	−0.905744	−0.452872	−	0.891576i	$-0.649601\pi$
$71$	−7.63193	−0.905744	−0.452872	+	0.891576i	$0.649601\pi$
$72$	0.124328	0.0146522
$73$	−2.07620	−0.243001	−0.121501	−	0.992591i	$-0.538771\pi$
$73$	−2.07620	−0.243001	−0.121501	+	0.992591i	$0.538771\pi$
$74$	−7.45548	−0.866682
$75$	−8.31111	−0.959684
$76$	6.68716	0.767070
$77$	15.1390	1.72525
$78$	−3.71413	−0.420542
$79$	−8.28468	−0.932099	−0.466049	−	0.884759i	$-0.654323\pi$
$79$	−8.28468	−0.932099	−0.466049	+	0.884759i	$0.654323\pi$
$80$	1.92114	0.214790
$81$	−8.80002	−0.977781
$82$	8.22801	0.908632
$83$	−11.6495	−1.27870	−0.639349	−	0.768917i	$-0.720796\pi$
$83$	−11.6495	−1.27870	−0.639349	+	0.768917i	$0.720796\pi$
$84$	5.24196	0.571945
$85$	−0.216885	−0.0235245
$86$	0	0
$87$	−5.84697	−0.626861
$88$	−8.26260	−0.880796
$89$	−2.72786	−0.289153	−0.144576	−	0.989494i	$-0.546182\pi$
$89$	−2.72786	−0.289153	−0.144576	+	0.989494i	$0.546182\pi$
$90$	0.0426432	0.00449499
$91$	−4.46364	−0.467917
$92$	6.49589	0.677243
$93$	1.67574	0.173766
$94$	−7.41335	−0.764629
$95$	−2.94098	−0.301738
$96$	−7.95316	−0.811716
$97$	−0.490296	−0.0497820	−0.0248910	−	0.999690i	$-0.507924\pi$
$97$	−0.490296	−0.0497820	−0.0248910	+	0.999690i	$0.507924\pi$
$98$	8.80557	0.889497
$99$	−0.282860	−0.0284285
$100$	−4.25149	−0.425149
$101$	2.20226	0.219134	0.109567	−	0.993979i	$-0.465054\pi$
$101$	2.20226	0.219134	0.109567	+	0.993979i	$0.465054\pi$
$102$	1.63500	0.161889
$103$	−5.11795	−0.504287	−0.252143	−	0.967690i	$-0.581135\pi$
$103$	−5.11795	−0.504287	−0.252143	+	0.967690i	$0.581135\pi$
$104$	2.43617	0.238887
$105$	−2.30539	−0.224983
$106$	16.4018	1.59309
$107$	−10.2750	−0.993323	−0.496661	−	0.867944i	$-0.665441\pi$
$107$	−10.2750	−0.993323	−0.496661	+	0.867944i	$0.665441\pi$
$108$	−4.60172	−0.442800
$109$	−1.12391	−0.107651	−0.0538253	−	0.998550i	$-0.517141\pi$
$109$	−1.12391	−0.107651	−0.0538253	+	0.998550i	$0.517141\pi$
$110$	−2.83399	−0.270210
$111$	−7.53082	−0.714794
$112$	−17.4052	−1.64463
$113$	−15.9715	−1.50247	−0.751236	−	0.660034i	$-0.770542\pi$
$113$	−15.9715	−1.50247	−0.751236	+	0.660034i	$0.770542\pi$
$114$	22.1707	2.07647
$115$	−2.85686	−0.266403
$116$	−2.99098	−0.277706
$117$	0.0833994	0.00771027
$118$	−7.94883	−0.731749
$119$	1.96494	0.180126
$120$	1.25824	0.114861
$121$	7.79829	0.708936
$122$	9.17539	0.830701
$123$	8.31116	0.749392
$124$	0.857213	0.0769800
$125$	3.79682	0.339598
$126$	−0.386340	−0.0344179
$127$	−3.36699	−0.298772	−0.149386	−	0.988779i	$-0.547730\pi$
$127$	−3.36699	−0.298772	−0.149386	+	0.988779i	$0.547730\pi$
$128$	12.8395	1.13486
$129$	0	0
$130$	0.835583	0.0732855
$131$	1.53820	0.134393	0.0671965	−	0.997740i	$-0.478595\pi$
$131$	1.53820	0.134393	0.0671965	+	0.997740i	$0.478595\pi$
$132$	6.50900	0.566536
$133$	26.6447	2.31039
$134$	22.2512	1.92221
$135$	2.02381	0.174182
$136$	−1.07243	−0.0919600
$137$	3.18726	0.272306	0.136153	−	0.990688i	$-0.456526\pi$
$137$	3.18726	0.272306	0.136153	+	0.990688i	$0.456526\pi$
$138$	21.5365	1.83331
$139$	−20.0762	−1.70284	−0.851421	−	0.524483i	$-0.824259\pi$
$139$	−20.0762	−1.70284	−0.851421	+	0.524483i	$0.824259\pi$
$140$	−1.17931	−0.0996695
$141$	−7.48827	−0.630626
$142$	−12.9436	−1.08620
$143$	−5.54256	−0.463492
$144$	0.325201	0.0271000
$145$	1.31542	0.109239
$146$	−3.52119	−0.291416
$147$	8.89456	0.733611
$148$	−3.85234	−0.316661
$149$	12.6418	1.03566	0.517830	−	0.855484i	$-0.326740\pi$
$149$	12.6418	1.03566	0.517830	+	0.855484i	$0.326740\pi$
$150$	−14.0954	−1.15089
$151$	−1.00556	−0.0818314	−0.0409157	−	0.999163i	$-0.513028\pi$
$151$	−1.00556	−0.0818314	−0.0409157	+	0.999163i	$0.513028\pi$
$152$	−14.5422	−1.17953
$153$	−0.0367132	−0.00296809
$154$	25.6754	2.06898
$155$	−0.376998	−0.0302812
$156$	−1.91914	−0.153654
$157$	−4.76336	−0.380158	−0.190079	−	0.981769i	$-0.560874\pi$
$157$	−4.76336	−0.380158	−0.190079	+	0.981769i	$0.560874\pi$
$158$	−14.0506	−1.11781
$159$	16.5676	1.31389
$160$	1.78926	0.141453
$161$	25.8826	2.03983
$162$	−14.9246	−1.17259
$163$	9.49710	0.743871	0.371935	−	0.928259i	$-0.378694\pi$
$163$	9.49710	0.743871	0.371935	+	0.928259i	$0.378694\pi$
$164$	4.25152	0.331988
$165$	−2.86263	−0.222855
$166$	−19.7572	−1.53346
$167$	−22.6314	−1.75127	−0.875634	−	0.482975i	$-0.839556\pi$
$167$	−22.6314	−1.75127	−0.875634	+	0.482975i	$0.839556\pi$
$168$	−11.3994	−0.879482
$169$	−11.3658	−0.874293
$170$	−0.367832	−0.0282114
$171$	−0.497834	−0.0380703
$172$	0	0
$173$	9.30235	0.707245	0.353622	−	0.935388i	$-0.384950\pi$
$173$	9.30235	0.707245	0.353622	+	0.935388i	$0.384950\pi$
$174$	−9.91632	−0.751754
$175$	−16.9399	−1.28054
$176$	−21.6122	−1.62908
$177$	−8.02916	−0.603509
$178$	−4.62639	−0.346763
$179$	−7.22963	−0.540368	−0.270184	−	0.962809i	$-0.587084\pi$
$179$	−7.22963	−0.540368	−0.270184	+	0.962809i	$0.587084\pi$
$180$	0.0220343	0.00164234
$181$	−18.7996	−1.39736	−0.698681	−	0.715434i	$-0.746229\pi$
$181$	−18.7996	−1.39736	−0.698681	+	0.715434i	$0.746229\pi$
$182$	−7.57022	−0.561142
$183$	9.26812	0.685119
$184$	−14.1262	−1.04140
$185$	1.69424	0.124563
$186$	2.84201	0.208386
$187$	2.43989	0.178422
$188$	−3.83058	−0.279374
$189$	−18.3353	−1.33370
$190$	−4.98783	−0.361855
$191$	7.03254	0.508856	0.254428	−	0.967092i	$-0.418113\pi$
$191$	7.03254	0.508856	0.254428	+	0.967092i	$0.418113\pi$
$192$	3.59038	0.259113
$193$	−4.11668	−0.296325	−0.148163	−	0.988963i	$-0.547336\pi$
$193$	−4.11668	−0.296325	−0.148163	+	0.988963i	$0.547336\pi$
$194$	−0.831530	−0.0597004
$195$	0.844027	0.0604420
$196$	4.54996	0.324997
$197$	1.80406	0.128534	0.0642669	−	0.997933i	$-0.479529\pi$
$197$	1.80406	0.128534	0.0642669	+	0.997933i	$0.479529\pi$
$198$	−0.479723	−0.0340924
$199$	22.7677	1.61396	0.806981	−	0.590578i	$-0.201100\pi$
$199$	22.7677	1.61396	0.806981	+	0.590578i	$0.201100\pi$
$200$	9.24549	0.653755
$201$	22.4760	1.58534
$202$	3.73499	0.262793
$203$	−11.9174	−0.836440
$204$	0.844824	0.0591495
$205$	−1.86980	−0.130592
$206$	−8.67992	−0.604759
$207$	−0.483594	−0.0336121
$208$	6.37222	0.441834
$209$	33.0851	2.28854
$210$	−3.90988	−0.269807
$211$	7.88645	0.542926	0.271463	−	0.962449i	$-0.412493\pi$
$211$	7.88645	0.542926	0.271463	+	0.962449i	$0.412493\pi$
$212$	8.47504	0.582068
$213$	−13.0744	−0.895841
$214$	−17.4262	−1.19123
$215$	0	0
$216$	10.0071	0.680897
$217$	3.41553	0.231861
$218$	−1.90612	−0.129098
$219$	−3.55677	−0.240345
$220$	−1.46436	−0.0987270
$221$	−0.719386	−0.0483911
$222$	−12.7721	−0.857206
$223$	−8.61045	−0.576598	−0.288299	−	0.957540i	$-0.593090\pi$
$223$	−8.61045	−0.576598	−0.288299	+	0.957540i	$0.593090\pi$
$224$	−16.2103	−1.08310
$225$	0.316508	0.0211005
$226$	−27.0873	−1.80182
$227$	8.14778	0.540787	0.270393	−	0.962750i	$-0.412846\pi$
$227$	8.14778	0.540787	0.270393	+	0.962750i	$0.412846\pi$
$228$	11.4559	0.758684
$229$	−24.7774	−1.63734	−0.818669	−	0.574266i	$-0.805288\pi$
$229$	−24.7774	−1.63734	−0.818669	+	0.574266i	$0.805288\pi$
$230$	−4.84516	−0.319480
$231$	25.9348	1.70639
$232$	6.50432	0.427030
$233$	−8.62179	−0.564832	−0.282416	−	0.959292i	$-0.591136\pi$
$233$	−8.62179	−0.564832	−0.282416	+	0.959292i	$0.591136\pi$
$234$	0.141443	0.00924644
$235$	1.68467	0.109896
$236$	−4.10727	−0.267360
$237$	−14.1926	−0.921908
$238$	3.33249	0.216013
$239$	3.36616	0.217739	0.108869	−	0.994056i	$-0.465277\pi$
$239$	3.36616	0.217739	0.108869	+	0.994056i	$0.465277\pi$
$240$	3.29113	0.212441
$241$	27.0162	1.74027	0.870134	−	0.492816i	$-0.164032\pi$
$241$	27.0162	1.74027	0.870134	+	0.492816i	$0.164032\pi$
$242$	13.2257	0.850181
$243$	0.677869	0.0434853
$244$	4.74105	0.303514
$245$	−2.00105	−0.127842
$246$	14.0955	0.898698
$247$	−9.75492	−0.620691
$248$	−1.86413	−0.118373
$249$	−19.9569	−1.26472
$250$	6.43931	0.407258
$251$	−10.7657	−0.679526	−0.339763	−	0.940511i	$-0.610347\pi$
$251$	−10.7657	−0.679526	−0.339763	+	0.940511i	$0.610347\pi$
$252$	−0.199627	−0.0125753
$253$	32.1387	2.02054
$254$	−5.71034	−0.358298
$255$	−0.371549	−0.0232673
$256$	17.5838	1.09899
$257$	−12.7546	−0.795610	−0.397805	−	0.917470i	$-0.630228\pi$
$257$	−12.7546	−0.795610	−0.397805	+	0.917470i	$0.630228\pi$
$258$	0	0
$259$	−15.3495	−0.953772
$260$	0.431757	0.0267764
$261$	0.222667	0.0137828
$262$	2.60875	0.161169
$263$	14.8333	0.914660	0.457330	−	0.889297i	$-0.348806\pi$
$263$	14.8333	0.914660	0.457330	+	0.889297i	$0.348806\pi$
$264$	−14.1548	−0.871166
$265$	−3.72728	−0.228965
$266$	45.1888	2.77070
$267$	−4.67314	−0.285992
$268$	11.4975	0.702320
$269$	10.7088	0.652928	0.326464	−	0.945210i	$-0.394143\pi$
$269$	10.7088	0.652928	0.326464	+	0.945210i	$0.394143\pi$
$270$	3.43233	0.208885
$271$	14.4895	0.880173	0.440087	−	0.897955i	$-0.354948\pi$
$271$	14.4895	0.880173	0.440087	+	0.897955i	$0.354948\pi$
$272$	−2.80511	−0.170085
$273$	−7.64673	−0.462801
$274$	5.40551	0.326559
$275$	−21.0345	−1.26843
$276$	11.1282	0.669839
$277$	−20.4174	−1.22677	−0.613383	−	0.789786i	$-0.710192\pi$
$277$	−20.4174	−1.22677	−0.613383	+	0.789786i	$0.710192\pi$
$278$	−34.0488	−2.04211
$279$	−0.0638163	−0.00382058
$280$	2.56457	0.153262
$281$	−7.25146	−0.432586	−0.216293	−	0.976329i	$-0.569397\pi$
$281$	−7.25146	−0.432586	−0.216293	+	0.976329i	$0.569397\pi$
$282$	−12.6999	−0.756269
$283$	−30.4795	−1.81182	−0.905909	−	0.423472i	$-0.860811\pi$
$283$	−30.4795	−1.81182	−0.905909	+	0.423472i	$0.860811\pi$
$284$	−6.68811	−0.396866
$285$	−5.03823	−0.298439
$286$	−9.40004	−0.555836
$287$	16.9400	0.999937
$288$	0.302876	0.0178471
$289$	−16.6833	−0.981372
$290$	2.23092	0.131004
$291$	−0.839933	−0.0492377
$292$	−1.81945	−0.106475
$293$	25.6862	1.50060	0.750302	−	0.661095i	$-0.229908\pi$
$293$	25.6862	1.50060	0.750302	+	0.661095i	$0.229908\pi$
$294$	15.0850	0.879772
$295$	1.80635	0.105170
$296$	8.37748	0.486931
$297$	−22.7672	−1.32109
$298$	21.4402	1.24200
$299$	−9.47590	−0.548005
$300$	−7.28330	−0.420501
$301$	0	0
$302$	−1.70541	−0.0981352
$303$	3.77273	0.216738
$304$	−38.0375	−2.18160
$305$	−2.08509	−0.119392
$306$	−0.0622648	−0.00355944
$307$	15.8498	0.904597	0.452298	−	0.891867i	$-0.350604\pi$
$307$	15.8498	0.904597	0.452298	+	0.891867i	$0.350604\pi$
$308$	13.2668	0.755947
$309$	−8.76764	−0.498773
$310$	−0.639379	−0.0363143
$311$	27.0156	1.53192	0.765958	−	0.642891i	$-0.222265\pi$
$311$	27.0156	1.53192	0.765958	+	0.642891i	$0.222265\pi$
$312$	4.17344	0.236275
$313$	−19.2734	−1.08940	−0.544699	−	0.838631i	$-0.683356\pi$
$313$	−19.2734	−1.08940	−0.544699	+	0.838631i	$0.683356\pi$
$314$	−8.07854	−0.455899
$315$	0.0877948	0.00494668
$316$	−7.26013	−0.408414
$317$	−12.8617	−0.722383	−0.361192	−	0.932492i	$-0.617630\pi$
$317$	−12.8617	−0.722383	−0.361192	+	0.932492i	$0.617630\pi$
$318$	28.0982	1.57567
$319$	−14.7980	−0.828531
$320$	−0.807743	−0.0451542
$321$	−17.6023	−0.982463
$322$	43.8962	2.44624
$323$	4.29421	0.238936
$324$	−7.71175	−0.428431
$325$	6.20188	0.344019
$326$	16.1069	0.892076
$327$	−1.92538	−0.106474
$328$	−9.24555	−0.510500
$329$	−15.2628	−0.841464
$330$	−4.85494	−0.267256
$331$	2.54475	0.139872	0.0699360	−	0.997551i	$-0.477720\pi$
$331$	2.54475	0.139872	0.0699360	+	0.997551i	$0.477720\pi$
$332$	−10.2088	−0.560282
$333$	0.286792	0.0157161
$334$	−38.3823	−2.10018
$335$	−5.05653	−0.276268
$336$	−29.8170	−1.62665
$337$	0.737478	0.0401730	0.0200865	−	0.999798i	$-0.493606\pi$
$337$	0.737478	0.0401730	0.0200865	+	0.999798i	$0.493606\pi$
$338$	−19.2761	−1.04848
$339$	−27.3610	−1.48604
$340$	−0.190064	−0.0103076
$341$	4.24111	0.229669
$342$	−0.844314	−0.0456553
$343$	−6.31287	−0.340863
$344$	0	0
$345$	−4.89412	−0.263491
$346$	15.7766	0.848153
$347$	5.24239	0.281426	0.140713	−	0.990050i	$-0.455060\pi$
$347$	5.24239	0.281426	0.140713	+	0.990050i	$0.455060\pi$
$348$	−5.12389	−0.274669
$349$	−9.97384	−0.533888	−0.266944	−	0.963712i	$-0.586014\pi$
$349$	−9.97384	−0.533888	−0.266944	+	0.963712i	$0.586014\pi$
$350$	−28.7297	−1.53566
$351$	6.71277	0.358301
$352$	−20.1286	−1.07286
$353$	25.0510	1.33333	0.666664	−	0.745358i	$-0.267722\pi$
$353$	25.0510	1.33333	0.666664	+	0.745358i	$0.267722\pi$
$354$	−13.6173	−0.723749
$355$	2.94140	0.156113
$356$	−2.39052	−0.126697
$357$	3.36617	0.178156
$358$	−12.2613	−0.648028
$359$	13.7616	0.726310	0.363155	−	0.931729i	$-0.381700\pi$
$359$	13.7616	0.726310	0.363155	+	0.931729i	$0.381700\pi$
$360$	−0.0479168	−0.00252544
$361$	39.2298	2.06473
$362$	−31.8836	−1.67577
$363$	13.3594	0.701185
$364$	−3.91163	−0.205025
$365$	0.800182	0.0418835
$366$	15.7185	0.821619
$367$	−27.4826	−1.43458	−0.717291	−	0.696774i	$-0.754618\pi$
$367$	−27.4826	−1.43458	−0.717291	+	0.696774i	$0.754618\pi$
$368$	−36.9495	−1.92613
$369$	−0.316510	−0.0164768
$370$	2.87339	0.149380
$371$	33.7684	1.75317
$372$	1.46850	0.0761384
$373$	−15.7151	−0.813695	−0.406848	−	0.913496i	$-0.633372\pi$
$373$	−15.7151	−0.813695	−0.406848	+	0.913496i	$0.633372\pi$
$374$	4.13799	0.213971
$375$	6.50438	0.335885
$376$	8.33014	0.429594
$377$	4.36310	0.224711
$378$	−31.0963	−1.59942
$379$	−25.7329	−1.32181	−0.660906	−	0.750469i	$-0.729828\pi$
$379$	−25.7329	−1.32181	−0.660906	+	0.750469i	$0.729828\pi$
$380$	−2.57727	−0.132211
$381$	−5.76804	−0.295506
$382$	11.9270	0.610239
$383$	18.0457	0.922093	0.461047	−	0.887376i	$-0.347474\pi$
$383$	18.0457	0.922093	0.461047	+	0.887376i	$0.347474\pi$
$384$	21.9955	1.12245
$385$	−5.83467	−0.297362
$386$	−6.98179	−0.355364
$387$	0	0
$388$	−0.429662	−0.0218128
$389$	25.3006	1.28279	0.641397	−	0.767209i	$-0.278355\pi$
$389$	25.3006	1.28279	0.641397	+	0.767209i	$0.278355\pi$
$390$	1.43145	0.0724842
$391$	4.17139	0.210956
$392$	−9.89453	−0.499749
$393$	2.63511	0.132924
$394$	3.05964	0.154142
$395$	3.19297	0.160656
$396$	−0.247879	−0.0124564
$397$	2.64315	0.132656	0.0663278	−	0.997798i	$-0.478872\pi$
$397$	2.64315	0.132656	0.0663278	+	0.997798i	$0.478872\pi$
$398$	38.6135	1.93552
$399$	45.6454	2.28513
$400$	24.1831	1.20916
$401$	29.4091	1.46862	0.734310	−	0.678814i	$-0.237506\pi$
$401$	29.4091	1.46862	0.734310	+	0.678814i	$0.237506\pi$
$402$	38.1188	1.90119
$403$	−1.25046	−0.0622900
$404$	1.92992	0.0960170
$405$	3.39159	0.168529
$406$	−20.2117	−1.00309
$407$	−19.0597	−0.944752
$408$	−1.83719	−0.0909546
$409$	0.379146	0.0187476	0.00937379	−	0.999956i	$-0.497016\pi$
$409$	0.379146	0.0187476	0.00937379	+	0.999956i	$0.497016\pi$
$410$	−3.17113	−0.156611
$411$	5.46014	0.269329
$412$	−4.48503	−0.220962
$413$	−16.3652	−0.805280
$414$	−0.820164	−0.0403088
$415$	4.48979	0.220395
$416$	5.93478	0.290976
$417$	−34.3928	−1.68422
$418$	56.1115	2.74450
$419$	−16.5380	−0.807933	−0.403966	−	0.914774i	$-0.632369\pi$
$419$	−16.5380	−0.807933	−0.403966	+	0.914774i	$0.632369\pi$
$420$	−2.02028	−0.0985798
$421$	9.16877	0.446859	0.223429	−	0.974720i	$-0.428275\pi$
$421$	9.16877	0.446859	0.223429	+	0.974720i	$0.428275\pi$
$422$	13.3752	0.651096
$423$	0.285172	0.0138655
$424$	−18.4302	−0.895050
$425$	−2.73013	−0.132431
$426$	−22.1738	−1.07432
$427$	18.8905	0.914175
$428$	−9.00433	−0.435241
$429$	−9.49503	−0.458425
$430$	0	0
$431$	9.52715	0.458907	0.229453	−	0.973320i	$-0.426306\pi$
$431$	9.52715	0.458907	0.229453	+	0.973320i	$0.426306\pi$
$432$	26.1752	1.25936
$433$	28.8184	1.38492	0.692462	−	0.721455i	$-0.256526\pi$
$433$	28.8184	1.38492	0.692462	+	0.721455i	$0.256526\pi$
$434$	5.79266	0.278056
$435$	2.25346	0.108045
$436$	−0.984915	−0.0471689
$437$	56.5642	2.70583
$438$	−6.03220	−0.288230
$439$	−6.73072	−0.321240	−0.160620	−	0.987016i	$-0.551349\pi$
$439$	−6.73072	−0.321240	−0.160620	+	0.987016i	$0.551349\pi$
$440$	3.18446	0.151813
$441$	−0.338727	−0.0161299
$442$	−1.22006	−0.0580324
$443$	3.32364	0.157911	0.0789554	−	0.996878i	$-0.474842\pi$
$443$	3.32364	0.157911	0.0789554	+	0.996878i	$0.474842\pi$
$444$	−6.59951	−0.313199
$445$	1.05134	0.0498381
$446$	−14.6031	−0.691477
$447$	21.6569	1.02434
$448$	7.31800	0.345743
$449$	4.28899	0.202410	0.101205	−	0.994866i	$-0.467730\pi$
$449$	4.28899	0.202410	0.101205	+	0.994866i	$0.467730\pi$
$450$	0.536789	0.0253045
$451$	21.0346	0.990481
$452$	−13.9963	−0.658333
$453$	−1.72264	−0.0809368
$454$	13.8184	0.648531
$455$	1.72032	0.0806497
$456$	−24.9124	−1.16663
$457$	2.21317	0.103528	0.0517638	−	0.998659i	$-0.483516\pi$
$457$	2.21317	0.103528	0.0517638	+	0.998659i	$0.483516\pi$
$458$	−42.0219	−1.96355
$459$	−2.95503	−0.137929
$460$	−2.50356	−0.116729
$461$	15.2417	0.709875	0.354937	−	0.934890i	$-0.384502\pi$
$461$	15.2417	0.709875	0.354937	+	0.934890i	$0.384502\pi$
$462$	43.9849	2.04636
$463$	10.7503	0.499607	0.249804	−	0.968296i	$-0.419634\pi$
$463$	10.7503	0.499607	0.249804	+	0.968296i	$0.419634\pi$
$464$	17.0131	0.789815
$465$	−0.645840	−0.0299501
$466$	−14.6223	−0.677367
$467$	14.8278	0.686150	0.343075	−	0.939308i	$-0.388532\pi$
$467$	14.8278	0.686150	0.343075	+	0.939308i	$0.388532\pi$
$468$	0.0730856	0.00337838
$469$	45.8112	2.11536
$470$	2.85715	0.131791
$471$	−8.16018	−0.376001
$472$	8.93184	0.411121
$473$	0	0
$474$	−24.0703	−1.10559
$475$	−37.0208	−1.69863
$476$	1.72194	0.0789250
$477$	−0.630935	−0.0288885
$478$	5.70893	0.261120
$479$	−34.3183	−1.56804	−0.784022	−	0.620733i	$-0.786835\pi$
$479$	−34.3183	−1.56804	−0.784022	+	0.620733i	$0.786835\pi$
$480$	3.06520	0.139907
$481$	5.61962	0.256233
$482$	45.8188	2.08699
$483$	44.3398	2.01753
$484$	6.83390	0.310632
$485$	0.188963	0.00858038
$486$	1.14965	0.0521492
$487$	−6.50198	−0.294633	−0.147317	−	0.989089i	$-0.547064\pi$
$487$	−6.50198	−0.294633	−0.147317	+	0.989089i	$0.547064\pi$
$488$	−10.3101	−0.466716
$489$	16.2696	0.735738
$490$	−3.39372	−0.153313
$491$	8.14924	0.367770	0.183885	−	0.982948i	$-0.441133\pi$
$491$	8.14924	0.367770	0.183885	+	0.982948i	$0.441133\pi$
$492$	7.28334	0.328358
$493$	−1.92068	−0.0865032
$494$	−16.5441	−0.744354
$495$	0.109016	0.00489990
$496$	−4.87595	−0.218937
$497$	−26.6485	−1.19535
$498$	−33.8464	−1.51669
$499$	−7.89326	−0.353351	−0.176676	−	0.984269i	$-0.556534\pi$
$499$	−7.89326	−0.353351	−0.176676	+	0.984269i	$0.556534\pi$
$500$	3.32728	0.148800
$501$	−38.7701	−1.73212
$502$	−18.2584	−0.814911
$503$	−24.4913	−1.09201	−0.546007	−	0.837781i	$-0.683853\pi$
$503$	−24.4913	−1.09201	−0.546007	+	0.837781i	$0.683853\pi$
$504$	0.434117	0.0193371
$505$	−0.848767	−0.0377696
$506$	54.5065	2.42311
$507$	−19.4709	−0.864735
$508$	−2.95061	−0.130912
$509$	30.3112	1.34352	0.671760	−	0.740769i	$-0.265539\pi$
$509$	30.3112	1.34352	0.671760	+	0.740769i	$0.265539\pi$
$510$	−0.630138	−0.0279030
$511$	−7.24950	−0.320699
$512$	4.14275	0.183085
$513$	−40.0704	−1.76915
$514$	−21.6315	−0.954124
$515$	1.97249	0.0869184
$516$	0	0
$517$	−18.9520	−0.833507
$518$	−26.0324	−1.14380
$519$	15.9360	0.699513
$520$	−0.938917	−0.0411742
$521$	−12.5768	−0.551000	−0.275500	−	0.961301i	$-0.588843\pi$
$521$	−12.5768	−0.551000	−0.275500	+	0.961301i	$0.588843\pi$
$522$	0.377638	0.0165288
$523$	36.1603	1.58118	0.790589	−	0.612347i	$-0.209775\pi$
$523$	36.1603	1.58118	0.790589	+	0.612347i	$0.209775\pi$
$524$	1.34797	0.0588865
$525$	−29.0200	−1.26654
$526$	25.1569	1.09689
$527$	0.550467	0.0239787
$528$	−37.0242	−1.61127
$529$	31.9463	1.38897
$530$	−6.32137	−0.274583
$531$	0.305770	0.0132693
$532$	23.3496	1.01233
$533$	−6.20192	−0.268635
$534$	−7.92553	−0.342971
$535$	3.96006	0.171208
$536$	−25.0029	−1.07996
$537$	−12.3852	−0.534460
$538$	18.1619	0.783015
$539$	22.5111	0.969623
$540$	1.77353	0.0763206
$541$	−4.44255	−0.191000	−0.0955001	−	0.995429i	$-0.530445\pi$
$541$	−4.44255	−0.191000	−0.0955001	+	0.995429i	$0.530445\pi$
$542$	24.5738	1.05554
$543$	−32.2058	−1.38208
$544$	−2.61255	−0.112012
$545$	0.433160	0.0185546
$546$	−12.9687	−0.555007
$547$	0.987831	0.0422366	0.0211183	−	0.999777i	$-0.493277\pi$
$547$	0.987831	0.0422366	0.0211183	+	0.999777i	$0.493277\pi$
$548$	2.79310	0.119315
$549$	−0.352953	−0.0150637
$550$	−35.6740	−1.52114
$551$	−26.0446	−1.10954
$552$	−24.1999	−1.03001
$553$	−28.9277	−1.23013
$554$	−34.6275	−1.47118
$555$	2.90243	0.123201
$556$	−17.5934	−0.746128
$557$	9.43919	0.399951	0.199976	−	0.979801i	$-0.435914\pi$
$557$	9.43919	0.399951	0.199976	+	0.979801i	$0.435914\pi$
$558$	−0.108231	−0.00458178
$559$	0	0
$560$	6.70806	0.283467
$561$	4.17981	0.176472
$562$	−12.2983	−0.518772
$563$	−27.5755	−1.16217	−0.581084	−	0.813844i	$-0.697371\pi$
$563$	−27.5755	−1.16217	−0.581084	+	0.813844i	$0.697371\pi$
$564$	−6.56222	−0.276319
$565$	6.15552	0.258965
$566$	−51.6925	−2.17280
$567$	−30.7271	−1.29042
$568$	14.5443	0.610264
$569$	−20.2737	−0.849918	−0.424959	−	0.905213i	$-0.639711\pi$
$569$	−20.2737	−0.849918	−0.424959	+	0.905213i	$0.639711\pi$
$570$	−8.54472	−0.357899
$571$	17.9510	0.751227	0.375613	−	0.926776i	$-0.377432\pi$
$571$	17.9510	0.751227	0.375613	+	0.926776i	$0.377432\pi$
$572$	−4.85712	−0.203087
$573$	12.0475	0.503293
$574$	28.7298	1.19916
$575$	−35.9618	−1.49971
$576$	−0.136731	−0.00569711
$577$	−1.04615	−0.0435516	−0.0217758	−	0.999763i	$-0.506932\pi$
$577$	−1.04615	−0.0435516	−0.0217758	+	0.999763i	$0.506932\pi$
$578$	−28.2945	−1.17690
$579$	−7.05234	−0.293085
$580$	1.15274	0.0478651
$581$	−40.6766	−1.68755
$582$	−1.42451	−0.0590477
$583$	41.9307	1.73659
$584$	3.95665	0.163727
$585$	−0.0321427	−0.00132894
$586$	43.5632	1.79958
$587$	16.5466	0.682951	0.341476	−	0.939891i	$-0.389073\pi$
$587$	16.5466	0.682951	0.341476	+	0.939891i	$0.389073\pi$
$588$	7.79459	0.321444
$589$	7.46436	0.307564
$590$	3.06353	0.126124
$591$	3.09056	0.127129
$592$	21.9127	0.900606
$593$	10.0815	0.413996	0.206998	−	0.978341i	$-0.433631\pi$
$593$	10.0815	0.413996	0.206998	+	0.978341i	$0.433631\pi$
$594$	−38.6126	−1.58430
$595$	−0.757300	−0.0310463
$596$	11.0785	0.453791
$597$	39.0037	1.59632
$598$	−16.0709	−0.657187
$599$	34.0034	1.38934	0.694670	−	0.719329i	$-0.255551\pi$
$599$	34.0034	1.38934	0.694670	+	0.719329i	$0.255551\pi$
$600$	15.8386	0.646607
$601$	27.2454	1.11136	0.555681	−	0.831396i	$-0.312458\pi$
$601$	27.2454	1.11136	0.555681	+	0.831396i	$0.312458\pi$
$602$	0	0
$603$	−0.855944	−0.0348567
$604$	−0.881206	−0.0358558
$605$	−3.00551	−0.122191
$606$	6.39846	0.259920
$607$	23.8921	0.969750	0.484875	−	0.874583i	$-0.338865\pi$
$607$	23.8921	0.969750	0.484875	+	0.874583i	$0.338865\pi$
$608$	−35.4263	−1.43673
$609$	−20.4159	−0.827295
$610$	−3.53626	−0.143179
$611$	5.58787	0.226061
$612$	−0.0321730	−0.00130052
$613$	−33.4726	−1.35195	−0.675973	−	0.736926i	$-0.736277\pi$
$613$	−33.4726	−1.35195	−0.675973	+	0.736926i	$0.736277\pi$
$614$	26.8809	1.08482
$615$	−3.20318	−0.129165
$616$	−28.8506	−1.16242
$617$	−15.7750	−0.635078	−0.317539	−	0.948245i	$-0.602856\pi$
$617$	−15.7750	−0.635078	−0.317539	+	0.948245i	$0.602856\pi$
$618$	−14.8697	−0.598147
$619$	19.3970	0.779631	0.389816	−	0.920893i	$-0.372539\pi$
$619$	19.3970	0.779631	0.389816	+	0.920893i	$0.372539\pi$
$620$	−0.330376	−0.0132682
$621$	−38.9242	−1.56198
$622$	45.8178	1.83713
$623$	−9.52491	−0.381607
$624$	10.9163	0.437003
$625$	22.7940	0.911760
$626$	−32.6873	−1.30645
$627$	56.6785	2.26352
$628$	−4.17429	−0.166572
$629$	−2.47381	−0.0986374
$630$	0.148898	0.00593223
$631$	1.59224	0.0633860	0.0316930	−	0.999498i	$-0.489910\pi$
$631$	1.59224	0.0633860	0.0316930	+	0.999498i	$0.489910\pi$
$632$	15.7882	0.628021
$633$	13.5104	0.536990
$634$	−21.8131	−0.866308
$635$	1.29766	0.0514961
$636$	14.5187	0.575704
$637$	−6.63726	−0.262978
$638$	−25.0971	−0.993603
$639$	0.497905	0.0196968
$640$	−4.94842	−0.195604
$641$	6.81759	0.269279	0.134639	−	0.990895i	$-0.457012\pi$
$641$	6.81759	0.269279	0.134639	+	0.990895i	$0.457012\pi$
$642$	−29.8530	−1.17820
$643$	17.2334	0.679617	0.339809	−	0.940495i	$-0.389638\pi$
$643$	17.2334	0.679617	0.339809	+	0.940495i	$0.389638\pi$
$644$	22.6817	0.893786
$645$	0	0
$646$	7.28288	0.286541
$647$	−13.4834	−0.530086	−0.265043	−	0.964237i	$-0.585386\pi$
$647$	−13.4834	−0.530086	−0.265043	+	0.964237i	$0.585386\pi$
$648$	16.7703	0.658800
$649$	−20.3209	−0.797665
$650$	10.5182	0.412559
$651$	5.85119	0.229326
$652$	8.32262	0.325939
$653$	38.4173	1.50338	0.751692	−	0.659514i	$-0.229238\pi$
$653$	38.4173	1.50338	0.751692	+	0.659514i	$0.229238\pi$
$654$	−3.26539	−0.127687
$655$	−0.592832	−0.0231639
$656$	−24.1833	−0.944198
$657$	0.135451	0.00528444
$658$	−25.8853	−1.00911
$659$	−7.11871	−0.277306	−0.138653	−	0.990341i	$-0.544277\pi$
$659$	−7.11871	−0.277306	−0.138653	+	0.990341i	$0.544277\pi$
$660$	−2.50861	−0.0976476
$661$	22.3871	0.870757	0.435378	−	0.900248i	$-0.356615\pi$
$661$	22.3871	0.870757	0.435378	+	0.900248i	$0.356615\pi$
$662$	4.31583	0.167740
$663$	−1.23239	−0.0478621
$664$	22.2006	0.861549
$665$	−10.2690	−0.398216
$666$	0.486393	0.0188473
$667$	−25.2996	−0.979605
$668$	−19.8326	−0.767347
$669$	−14.7507	−0.570294
$670$	−8.57575	−0.331310
$671$	23.4566	0.905531
$672$	−27.7701	−1.07126
$673$	−1.98173	−0.0763901	−0.0381950	−	0.999270i	$-0.512161\pi$
$673$	−1.98173	−0.0763901	−0.0381950	+	0.999270i	$0.512161\pi$
$674$	1.25074	0.0481769
$675$	25.4755	0.980554
$676$	−9.96023	−0.383086
$677$	6.78651	0.260827	0.130413	−	0.991460i	$-0.458370\pi$
$677$	6.78651	0.260827	0.130413	+	0.991460i	$0.458370\pi$
$678$	−46.4036	−1.78212
$679$	−1.71197	−0.0656994
$680$	0.413321	0.0158501
$681$	13.9581	0.534874
$682$	7.19281	0.275427
$683$	10.3447	0.395828	0.197914	−	0.980219i	$-0.436583\pi$
$683$	10.3447	0.395828	0.197914	+	0.980219i	$0.436583\pi$
$684$	−0.436268	−0.0166811
$685$	−1.22839	−0.0469344
$686$	−10.7065	−0.408775
$687$	−42.4465	−1.61944
$688$	0	0
$689$	−12.3630	−0.470993
$690$	−8.30031	−0.315987
$691$	11.1645	0.424719	0.212359	−	0.977192i	$-0.431885\pi$
$691$	11.1645	0.424719	0.212359	+	0.977192i	$0.431885\pi$
$692$	8.15196	0.309891
$693$	−0.987664	−0.0375182
$694$	8.89097	0.337497
$695$	7.73750	0.293500
$696$	11.1426	0.422361
$697$	2.73015	0.103412
$698$	−16.9154	−0.640257
$699$	−14.7701	−0.558657
$700$	−14.8450	−0.561088
$701$	−46.5107	−1.75668	−0.878342	−	0.478032i	$-0.841350\pi$
$701$	−46.5107	−1.75668	−0.878342	+	0.478032i	$0.841350\pi$
$702$	11.3847	0.429688
$703$	−33.5451	−1.26518
$704$	9.08685	0.342473
$705$	2.88603	0.108694
$706$	42.4858	1.59897
$707$	7.68967	0.289200
$708$	−7.03621	−0.264437
$709$	7.23588	0.271749	0.135875	−	0.990726i	$-0.456616\pi$
$709$	7.23588	0.271749	0.135875	+	0.990726i	$0.456616\pi$
$710$	4.98854	0.187216
$711$	0.540489	0.0202699
$712$	5.19852	0.194823
$713$	7.25085	0.271547
$714$	5.70894	0.213652
$715$	2.13614	0.0798870
$716$	−6.33556	−0.236771
$717$	5.76662	0.215358
$718$	23.3394	0.871017
$719$	−36.4059	−1.35771	−0.678856	−	0.734271i	$-0.737524\pi$
$719$	−36.4059	−1.35771	−0.678856	+	0.734271i	$0.737524\pi$
$720$	−0.125334	−0.00467094
$721$	−17.8704	−0.665529
$722$	66.5328	2.47609
$723$	46.2819	1.72124
$724$	−16.4747	−0.612277
$725$	16.5584	0.614962
$726$	22.6572	0.840886
$727$	−42.3271	−1.56982	−0.784912	−	0.619607i	$-0.787292\pi$
$727$	−42.3271	−1.56982	−0.784912	+	0.619607i	$0.787292\pi$
$728$	8.50641	0.315269
$729$	27.5613	1.02079
$730$	1.35709	0.0502281
$731$	0	0
$732$	8.12195	0.300196
$733$	18.3593	0.678118	0.339059	−	0.940765i	$-0.389891\pi$
$733$	18.3593	0.678118	0.339059	+	0.940765i	$0.389891\pi$
$734$	−46.6099	−1.72040
$735$	−3.42802	−0.126444
$736$	−34.4130	−1.26848
$737$	56.8843	2.09536
$738$	−0.536793	−0.0197596
$739$	−31.2767	−1.15053	−0.575266	−	0.817966i	$-0.695101\pi$
$739$	−31.2767	−1.15053	−0.575266	+	0.817966i	$0.695101\pi$
$740$	1.48472	0.0545793
$741$	−16.7113	−0.613905
$742$	57.2704	2.10246
$743$	−23.9703	−0.879385	−0.439692	−	0.898148i	$-0.644913\pi$
$743$	−23.9703	−0.879385	−0.439692	+	0.898148i	$0.644913\pi$
$744$	−3.19348	−0.117078
$745$	−4.87225	−0.178505
$746$	−26.6524	−0.975812
$747$	0.760009	0.0278073
$748$	2.13816	0.0781787
$749$	−35.8774	−1.31093
$750$	11.0313	0.402805
$751$	51.0277	1.86203	0.931013	−	0.364986i	$-0.118926\pi$
$751$	51.0277	1.86203	0.931013	+	0.364986i	$0.118926\pi$
$752$	21.7889	0.794558
$753$	−18.4429	−0.672096
$754$	7.39972	0.269482
$755$	0.387550	0.0141044
$756$	−16.0679	−0.584382
$757$	−22.5555	−0.819794	−0.409897	−	0.912132i	$-0.634435\pi$
$757$	−22.5555	−0.819794	−0.409897	+	0.912132i	$0.634435\pi$
$758$	−43.6424	−1.58516
$759$	55.0573	1.99845
$760$	5.60466	0.203302
$761$	−36.0892	−1.30823	−0.654117	−	0.756393i	$-0.726960\pi$
$761$	−36.0892	−1.30823	−0.654117	+	0.756393i	$0.726960\pi$
$762$	−9.78246	−0.354381
$763$	−3.92435	−0.142071
$764$	6.16284	0.222964
$765$	0.0141495	0.000511577 0
$766$	30.6051	1.10581
$767$	5.99149	0.216340
$768$	30.1231	1.08697
$769$	−25.6553	−0.925155	−0.462578	−	0.886579i	$-0.653075\pi$
$769$	−25.6553	−0.925155	−0.462578	+	0.886579i	$0.653075\pi$
$770$	−9.89546	−0.356608
$771$	−21.8501	−0.786912
$772$	−3.60758	−0.129840
$773$	30.1582	1.08472	0.542358	−	0.840148i	$-0.317532\pi$
$773$	30.1582	1.08472	0.542358	+	0.840148i	$0.317532\pi$
$774$	0	0
$775$	−4.74562	−0.170468
$776$	0.934363	0.0335417
$777$	−26.2954	−0.943344
$778$	42.9093	1.53837
$779$	37.0210	1.32641
$780$	0.739648	0.0264837
$781$	−33.0898	−1.18405
$782$	7.07457	0.252986
$783$	17.9224	0.640493
$784$	−25.8808	−0.924314
$785$	1.83583	0.0655236
$786$	4.46908	0.159407
$787$	20.7557	0.739861	0.369931	−	0.929059i	$-0.379381\pi$
$787$	20.7557	0.739861	0.369931	+	0.929059i	$0.379381\pi$
$788$	1.58096	0.0563192
$789$	25.4111	0.904660
$790$	5.41519	0.192664
$791$	−55.7678	−1.98288
$792$	0.539049	0.0191543
$793$	−6.91602	−0.245595
$794$	4.48271	0.159085
$795$	−6.38525	−0.226462
$796$	19.9521	0.707184
$797$	16.8285	0.596096	0.298048	−	0.954551i	$-0.403664\pi$
$797$	16.8285	0.596096	0.298048	+	0.954551i	$0.403664\pi$
$798$	77.4135	2.74041
$799$	−2.45984	−0.0870227
$800$	22.5230	0.796308
$801$	0.177965	0.00628808
$802$	49.8771	1.76122
$803$	−9.00180	−0.317667
$804$	19.6965	0.694642
$805$	−9.97531	−0.351584
$806$	−2.12075	−0.0747004
$807$	18.3454	0.645789
$808$	−4.19688	−0.147646
$809$	34.0594	1.19747	0.598733	−	0.800949i	$-0.295671\pi$
$809$	34.0594	1.19747	0.598733	+	0.800949i	$0.295671\pi$
$810$	5.75205	0.202106
$811$	−13.3965	−0.470413	−0.235207	−	0.971945i	$-0.575577\pi$
$811$	−13.3965	−0.470413	−0.235207	+	0.971945i	$0.575577\pi$
$812$	−10.4436	−0.366500
$813$	24.8221	0.870550
$814$	−32.3247	−1.13298
$815$	−3.66025	−0.128213
$816$	−4.80548	−0.168226
$817$	0	0
$818$	0.643023	0.0224828
$819$	0.291206	0.0101756
$820$	−1.63856	−0.0572211
$821$	13.1343	0.458392	0.229196	−	0.973380i	$-0.426390\pi$
$821$	13.1343	0.458392	0.229196	+	0.973380i	$0.426390\pi$
$822$	9.26026	0.322989
$823$	19.2202	0.669974	0.334987	−	0.942223i	$-0.391268\pi$
$823$	19.2202	0.669974	0.334987	+	0.942223i	$0.391268\pi$
$824$	9.75334	0.339774
$825$	−36.0345	−1.25456
$826$	−27.7550	−0.965720
$827$	−32.8869	−1.14359	−0.571795	−	0.820397i	$-0.693753\pi$
$827$	−32.8869	−1.14359	−0.571795	+	0.820397i	$0.693753\pi$
$828$	−0.423789	−0.0147277
$829$	11.9149	0.413822	0.206911	−	0.978360i	$-0.433659\pi$
$829$	11.9149	0.413822	0.206911	+	0.978360i	$0.433659\pi$
$830$	7.61457	0.264306
$831$	−34.9774	−1.21335
$832$	−2.67920	−0.0928845
$833$	2.92179	0.101234
$834$	−58.3294	−2.01978
$835$	8.72228	0.301847
$836$	28.9935	1.00276
$837$	−5.13654	−0.177545
$838$	−28.0480	−0.968902
$839$	53.4766	1.84622	0.923109	−	0.384538i	$-0.125639\pi$
$839$	53.4766	1.84622	0.923109	+	0.384538i	$0.125639\pi$
$840$	4.39340	0.151587
$841$	−17.3510	−0.598310
$842$	15.5500	0.535889
$843$	−12.4226	−0.427856
$844$	6.91115	0.237892
$845$	4.38046	0.150692
$846$	0.483645	0.0166280
$847$	27.2294	0.935613
$848$	−48.2073	−1.65544
$849$	−52.2149	−1.79201
$850$	−4.63024	−0.158816
$851$	−32.5856	−1.11702
$852$	−11.4575	−0.392528
$853$	28.9075	0.989772	0.494886	−	0.868958i	$-0.335210\pi$
$853$	28.9075	0.989772	0.494886	+	0.868958i	$0.335210\pi$
$854$	32.0378	1.09631
$855$	0.191868	0.00656176
$856$	19.5812	0.669272
$857$	38.0369	1.29931	0.649657	−	0.760227i	$-0.274912\pi$
$857$	38.0369	1.29931	0.649657	+	0.760227i	$0.274912\pi$
$858$	−16.1033	−0.549759
$859$	−38.9400	−1.32861	−0.664307	−	0.747460i	$-0.731273\pi$
$859$	−38.9400	−1.32861	−0.664307	+	0.747460i	$0.731273\pi$
$860$	0	0
$861$	29.0202	0.989005
$862$	16.1578	0.550337
$863$	47.7573	1.62568	0.812839	−	0.582489i	$-0.197921\pi$
$863$	47.7573	1.62568	0.812839	+	0.582489i	$0.197921\pi$
$864$	24.3783	0.829368
$865$	−3.58519	−0.121900
$866$	48.8753	1.66085
$867$	−28.5804	−0.970642
$868$	2.99314	0.101594
$869$	−35.9199	−1.21850
$870$	3.82181	0.129572
$871$	−16.7720	−0.568297
$872$	2.14184	0.0725319
$873$	0.0319867	0.00108259
$874$	95.9316	3.24493
$875$	13.2574	0.448181
$876$	−3.11692	−0.105311
$877$	−34.6549	−1.17021	−0.585107	−	0.810956i	$-0.698947\pi$
$877$	−34.6549	−1.17021	−0.585107	+	0.810956i	$0.698947\pi$
$878$	−11.4151	−0.385242
$879$	44.0034	1.48420
$880$	8.32948	0.280787
$881$	−52.3900	−1.76506	−0.882532	−	0.470253i	$-0.844163\pi$
$881$	−52.3900	−1.76506	−0.882532	+	0.470253i	$0.844163\pi$
$882$	−0.574473	−0.0193435
$883$	−28.9075	−0.972814	−0.486407	−	0.873732i	$-0.661693\pi$
$883$	−28.9075	−0.972814	−0.486407	+	0.873732i	$0.661693\pi$
$884$	−0.630422	−0.0212034
$885$	3.09449	0.104020
$886$	5.63681	0.189372
$887$	45.5226	1.52850	0.764250	−	0.644920i	$-0.223109\pi$
$887$	45.5226	1.52850	0.764250	+	0.644920i	$0.223109\pi$
$888$	14.3516	0.481607
$889$	−11.7566	−0.394302
$890$	1.78304	0.0597677
$891$	−38.1543	−1.27822
$892$	−7.54562	−0.252646
$893$	−33.3555	−1.11620
$894$	36.7296	1.22842
$895$	2.78635	0.0931373
$896$	44.8318	1.49772
$897$	−16.2333	−0.542014
$898$	7.27402	0.242737
$899$	−3.33860	−0.111349
$900$	0.277366	0.00924554
$901$	5.44232	0.181310
$902$	35.6742	1.18782
$903$	0	0
$904$	30.4371	1.01232
$905$	7.24548	0.240848
$906$	−2.92156	−0.0970623
$907$	21.9204	0.727856	0.363928	−	0.931427i	$-0.381435\pi$
$907$	21.9204	0.727856	0.363928	+	0.931427i	$0.381435\pi$
$908$	7.14016	0.236955
$909$	−0.143675	−0.00476540
$910$	2.91761	0.0967179
$911$	44.9281	1.48854	0.744268	−	0.667881i	$-0.232799\pi$
$911$	44.9281	1.48854	0.744268	+	0.667881i	$0.232799\pi$
$912$	−65.1626	−2.15775
$913$	−50.5087	−1.67159
$914$	3.75348	0.124154
$915$	−3.57199	−0.118086
$916$	−21.7133	−0.717426
$917$	5.37094	0.177364
$918$	−5.01166	−0.165409
$919$	−35.1017	−1.15790	−0.578949	−	0.815363i	$-0.696537\pi$
$919$	−35.1017	−1.15790	−0.578949	+	0.815363i	$0.696537\pi$
$920$	5.44434	0.179495
$921$	27.1525	0.894707
$922$	25.8495	0.851307
$923$	9.75631	0.321133
$924$	22.7276	0.747682
$925$	21.3269	0.701226
$926$	18.2322	0.599147
$927$	0.333893	0.0109665
$928$	15.8452	0.520145
$929$	−8.73266	−0.286509	−0.143255	−	0.989686i	$-0.545757\pi$
$929$	−8.73266	−0.286509	−0.143255	+	0.989686i	$0.545757\pi$
$930$	−1.09533	−0.0359173
$931$	39.6197	1.29848
$932$	−7.55556	−0.247490
$933$	46.2809	1.51517
$934$	25.1476	0.822855
$935$	−0.940349	−0.0307527
$936$	−0.158935	−0.00519496
$937$	28.8980	0.944056	0.472028	−	0.881584i	$-0.343522\pi$
$937$	28.8980	0.944056	0.472028	+	0.881584i	$0.343522\pi$
$938$	77.6947	2.53682
$939$	−33.0176	−1.07749
$940$	1.47633	0.0481525
$941$	−3.17576	−0.103527	−0.0517635	−	0.998659i	$-0.516484\pi$
$941$	−3.17576	−0.103527	−0.0517635	+	0.998659i	$0.516484\pi$
$942$	−13.8395	−0.450914
$943$	35.9621	1.17109
$944$	23.3627	0.760392
$945$	7.06656	0.229875
$946$	0	0
$947$	47.5288	1.54448	0.772239	−	0.635332i	$-0.219137\pi$
$947$	47.5288	1.54448	0.772239	+	0.635332i	$0.219137\pi$
$948$	−12.4374	−0.403949
$949$	2.65412	0.0861565
$950$	−62.7863	−2.03706
$951$	−22.0335	−0.714485
$952$	−3.74461	−0.121363
$953$	−40.6532	−1.31689	−0.658443	−	0.752631i	$-0.728785\pi$
$953$	−40.6532	−1.31689	−0.658443	+	0.752631i	$0.728785\pi$
$954$	−1.07005	−0.0346441
$955$	−2.71038	−0.0877060
$956$	2.94988	0.0954059
$957$	−25.3507	−0.819472
$958$	−58.2031	−1.88046
$959$	11.1290	0.359374
$960$	−1.38376	−0.0446605
$961$	−30.0432	−0.969134
$962$	9.53074	0.307283
$963$	0.670338	0.0216013
$964$	23.6752	0.762527
$965$	1.58660	0.0510743
$966$	75.1992	2.41950
$967$	−7.55318	−0.242894	−0.121447	−	0.992598i	$-0.538753\pi$
$967$	−7.55318	−0.242894	−0.121447	+	0.992598i	$0.538753\pi$
$968$	−14.8613	−0.477660
$969$	7.35648	0.236324
$970$	0.320477	0.0102899
$971$	−20.9356	−0.671856	−0.335928	−	0.941888i	$-0.609050\pi$
$971$	−20.9356	−0.671856	−0.335928	+	0.941888i	$0.609050\pi$
$972$	0.594039	0.0190538
$973$	−70.1003	−2.24731
$974$	−11.0272	−0.353334
$975$	10.6245	0.340257
$976$	−26.9678	−0.863217
$977$	24.5346	0.784931	0.392465	−	0.919767i	$-0.371622\pi$
$977$	24.5346	0.784931	0.392465	+	0.919767i	$0.371622\pi$
$978$	27.5929	0.882323
$979$	−11.8272	−0.377999
$980$	−1.75358	−0.0560161
$981$	0.0733232	0.00234103
$982$	13.8209	0.441043
$983$	−1.96322	−0.0626170	−0.0313085	−	0.999510i	$-0.509967\pi$
$983$	−1.96322	−0.0626170	−0.0313085	+	0.999510i	$0.509967\pi$
$984$	−15.8387	−0.504919
$985$	−0.695296	−0.0221540
$986$	−3.25743	−0.103738
$987$	−26.1469	−0.832264
$988$	−8.54856	−0.271966
$989$	0	0
$990$	0.184888	0.00587614
$991$	−16.5007	−0.524161	−0.262080	−	0.965046i	$-0.584409\pi$
$991$	−16.5007	−0.524161	−0.262080	+	0.965046i	$0.584409\pi$
$992$	−4.54123	−0.144184
$993$	4.35945	0.138343
$994$	−45.1952	−1.43350
$995$	−8.77483	−0.278181
$996$	−17.4889	−0.554157
$997$	33.2320	1.05247	0.526235	−	0.850339i	$-0.323603\pi$
$997$	33.2320	1.05247	0.526235	+	0.850339i	$0.323603\pi$
$998$	−13.3868	−0.423751
$999$	23.0838	0.730338

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.2.a.o.1.13		18
43.19	odd	42		43.2.g.a.17.3	✓	36
43.34	odd	42		43.2.g.a.38.3	yes	36
43.42	odd	2		1849.2.a.n.1.6		18
129.62	even	42		387.2.y.c.361.1		36
129.77	even	42		387.2.y.c.253.1		36
172.19	even	42		688.2.bg.c.17.3		36
172.163	even	42		688.2.bg.c.81.3		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.g.a.17.3	✓	36	43.19	odd	42
43.2.g.a.38.3	yes	36	43.34	odd	42
387.2.y.c.253.1		36	129.77	even	42
387.2.y.c.361.1		36	129.62	even	42
688.2.bg.c.17.3		36	172.19	even	42
688.2.bg.c.81.3		36	172.163	even	42
1849.2.a.n.1.6		18	43.42	odd	2
1849.2.a.o.1.13		18	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q+1.69598 q^{2} +1.71311 q^{3} +0.876333 q^{4} -0.385406 q^{5} +2.90540 q^{6} +3.49171 q^{7} -1.90571 q^{8} -0.0652397 q^{9} +O(q^{10})\)	\(q+1.69598 q^{2} +1.71311 q^{3} +0.876333 q^{4} -0.385406 q^{5} +2.90540 q^{6} +3.49171 q^{7} -1.90571 q^{8} -0.0652397 q^{9} -0.653640 q^{10} +4.33570 q^{11} +1.50126 q^{12} -1.27835 q^{13} +5.92185 q^{14} -0.660245 q^{15} -4.98471 q^{16} +0.562744 q^{17} -0.110645 q^{18} +7.63085 q^{19} -0.337744 q^{20} +5.98170 q^{21} +7.35324 q^{22} +7.41258 q^{23} -3.26470 q^{24} -4.85146 q^{25} -2.16806 q^{26} -5.25111 q^{27} +3.05990 q^{28} -3.41307 q^{29} -1.11976 q^{30} +0.978183 q^{31} -4.64252 q^{32} +7.42755 q^{33} +0.954400 q^{34} -1.34573 q^{35} -0.0571717 q^{36} -4.39598 q^{37} +12.9417 q^{38} -2.18997 q^{39} +0.734474 q^{40} +4.85149 q^{41} +10.1448 q^{42} +3.79952 q^{44} +0.0251438 q^{45} +12.5716 q^{46} -4.37114 q^{47} -8.53937 q^{48} +5.19204 q^{49} -8.22796 q^{50} +0.964045 q^{51} -1.12026 q^{52} +9.67103 q^{53} -8.90575 q^{54} -1.67101 q^{55} -6.65419 q^{56} +13.0725 q^{57} -5.78848 q^{58} -4.68688 q^{59} -0.578595 q^{60} +5.41010 q^{61} +1.65897 q^{62} -0.227798 q^{63} +2.09582 q^{64} +0.492686 q^{65} +12.5969 q^{66} +13.1200 q^{67} +0.493151 q^{68} +12.6986 q^{69} -2.28232 q^{70} -7.63193 q^{71} +0.124328 q^{72} -2.07620 q^{73} -7.45548 q^{74} -8.31111 q^{75} +6.68716 q^{76} +15.1390 q^{77} -3.71413 q^{78} -8.28468 q^{79} +1.92114 q^{80} -8.80002 q^{81} +8.22801 q^{82} -11.6495 q^{83} +5.24196 q^{84} -0.216885 q^{85} -5.84697 q^{87} -8.26260 q^{88} -2.72786 q^{89} +0.0426432 q^{90} -4.46364 q^{91} +6.49589 q^{92} +1.67574 q^{93} -7.41335 q^{94} -2.94098 q^{95} -7.95316 q^{96} -0.490296 q^{97} +8.80557 q^{98} -0.282860 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 5 q^{2} + 5 q^{3} + 19 q^{4} + 11 q^{5} + 4 q^{6} + 6 q^{7} + 12 q^{8} + 15 q^{9}+O(q^{10}) \) 18 * q + 5 * q^2 + 5 * q^3 + 19 * q^4 + 11 * q^5 + 4 * q^6 + 6 * q^7 + 12 * q^8 + 15 * q^9	\( 18 q + 5 q^{2} + 5 q^{3} + 19 q^{4} + 11 q^{5} + 4 q^{6} + 6 q^{7} + 12 q^{8} + 15 q^{9} - 7 q^{10} - 2 q^{11} + 16 q^{12} - 7 q^{13} - 4 q^{14} + 3 q^{15} + 9 q^{16} - 11 q^{17} + 25 q^{18} + 31 q^{19} + 25 q^{20} + 19 q^{22} - 11 q^{23} + 18 q^{24} + 9 q^{25} + 27 q^{26} + 23 q^{27} + 20 q^{28} + 37 q^{29} - 17 q^{30} - 12 q^{31} + 39 q^{32} + 38 q^{33} + 14 q^{34} + 16 q^{35} + 47 q^{36} - 19 q^{37} + 56 q^{38} + 46 q^{39} + 6 q^{40} - 7 q^{41} - q^{42} + 7 q^{44} + 23 q^{45} - 47 q^{46} - q^{47} + 15 q^{48} - 6 q^{49} - 3 q^{50} + 38 q^{51} + 15 q^{52} + 3 q^{53} - 67 q^{54} + 28 q^{55} - 81 q^{56} + 46 q^{57} + 34 q^{58} + 17 q^{59} - 83 q^{60} + 28 q^{61} + 33 q^{62} + 26 q^{63} + 10 q^{64} + 16 q^{65} - 72 q^{66} + 18 q^{67} + 53 q^{68} + 7 q^{69} - 34 q^{70} + 86 q^{71} - 2 q^{72} - 27 q^{73} - 79 q^{74} + 31 q^{75} + 59 q^{76} + 43 q^{77} + 91 q^{78} + 17 q^{79} + 8 q^{80} - 10 q^{81} + 13 q^{82} - 12 q^{83} - 32 q^{84} + 28 q^{85} - 43 q^{87} - 23 q^{88} + 51 q^{89} + 10 q^{90} - 20 q^{91} + 18 q^{92} - 30 q^{93} - 15 q^{94} - q^{95} - 20 q^{96} - 19 q^{97} - 5 q^{98} + 38 q^{99}+O(q^{100}) \) 18 * q + 5 * q^2 + 5 * q^3 + 19 * q^4 + 11 * q^5 + 4 * q^6 + 6 * q^7 + 12 * q^8 + 15 * q^9 - 7 * q^10 - 2 * q^11 + 16 * q^12 - 7 * q^13 - 4 * q^14 + 3 * q^15 + 9 * q^16 - 11 * q^17 + 25 * q^18 + 31 * q^19 + 25 * q^20 + 19 * q^22 - 11 * q^23 + 18 * q^24 + 9 * q^25 + 27 * q^26 + 23 * q^27 + 20 * q^28 + 37 * q^29 - 17 * q^30 - 12 * q^31 + 39 * q^32 + 38 * q^33 + 14 * q^34 + 16 * q^35 + 47 * q^36 - 19 * q^37 + 56 * q^38 + 46 * q^39 + 6 * q^40 - 7 * q^41 - q^42 + 7 * q^44 + 23 * q^45 - 47 * q^46 - q^47 + 15 * q^48 - 6 * q^49 - 3 * q^50 + 38 * q^51 + 15 * q^52 + 3 * q^53 - 67 * q^54 + 28 * q^55 - 81 * q^56 + 46 * q^57 + 34 * q^58 + 17 * q^59 - 83 * q^60 + 28 * q^61 + 33 * q^62 + 26 * q^63 + 10 * q^64 + 16 * q^65 - 72 * q^66 + 18 * q^67 + 53 * q^68 + 7 * q^69 - 34 * q^70 + 86 * q^71 - 2 * q^72 - 27 * q^73 - 79 * q^74 + 31 * q^75 + 59 * q^76 + 43 * q^77 + 91 * q^78 + 17 * q^79 + 8 * q^80 - 10 * q^81 + 13 * q^82 - 12 * q^83 - 32 * q^84 + 28 * q^85 - 43 * q^87 - 23 * q^88 + 51 * q^89 + 10 * q^90 - 20 * q^91 + 18 * q^92 - 30 * q^93 - 15 * q^94 - q^95 - 20 * q^96 - 19 * q^97 - 5 * q^98 + 38 * q^99

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