LMFDB - Embedded newform 9251.2.a.ba.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9251,2,Mod(1,9251)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9251, 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("9251.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9251 = 11 \cdot 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9251.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:	$73.8696069099$
Analytic rank:	$1$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	9251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.667928 q^{2} +2.16237 q^{3} -1.55387 q^{4} +3.76965 q^{5} -1.44431 q^{6} -2.15374 q^{7} +2.37373 q^{8} +1.67584 q^{9} +O(q^{10})$	\(q-0.667928 q^{2} +2.16237 q^{3} -1.55387 q^{4} +3.76965 q^{5} -1.44431 q^{6} -2.15374 q^{7} +2.37373 q^{8} +1.67584 q^{9} -2.51785 q^{10} +1.00000 q^{11} -3.36005 q^{12} -3.37185 q^{13} +1.43854 q^{14} +8.15137 q^{15} +1.52226 q^{16} +6.32910 q^{17} -1.11934 q^{18} -3.38499 q^{19} -5.85755 q^{20} -4.65717 q^{21} -0.667928 q^{22} -2.58688 q^{23} +5.13289 q^{24} +9.21023 q^{25} +2.25216 q^{26} -2.86331 q^{27} +3.34663 q^{28} -5.44453 q^{30} -7.71384 q^{31} -5.76422 q^{32} +2.16237 q^{33} -4.22738 q^{34} -8.11882 q^{35} -2.60405 q^{36} -11.5612 q^{37} +2.26093 q^{38} -7.29120 q^{39} +8.94813 q^{40} +4.34917 q^{41} +3.11066 q^{42} -3.26849 q^{43} -1.55387 q^{44} +6.31734 q^{45} +1.72785 q^{46} -7.48624 q^{47} +3.29169 q^{48} -2.36142 q^{49} -6.15177 q^{50} +13.6859 q^{51} +5.23943 q^{52} -5.54688 q^{53} +1.91249 q^{54} +3.76965 q^{55} -5.11239 q^{56} -7.31961 q^{57} +3.76002 q^{59} -12.6662 q^{60} -10.1387 q^{61} +5.15229 q^{62} -3.60933 q^{63} +0.805564 q^{64} -12.7107 q^{65} -1.44431 q^{66} -10.6196 q^{67} -9.83461 q^{68} -5.59379 q^{69} +5.42279 q^{70} -2.13508 q^{71} +3.97800 q^{72} -12.9504 q^{73} +7.72204 q^{74} +19.9159 q^{75} +5.25985 q^{76} -2.15374 q^{77} +4.87000 q^{78} +11.2820 q^{79} +5.73839 q^{80} -11.2191 q^{81} -2.90493 q^{82} +5.82198 q^{83} +7.23665 q^{84} +23.8585 q^{85} +2.18311 q^{86} +2.37373 q^{88} +9.99923 q^{89} -4.21953 q^{90} +7.26209 q^{91} +4.01968 q^{92} -16.6802 q^{93} +5.00027 q^{94} -12.7602 q^{95} -12.4644 q^{96} -6.92880 q^{97} +1.57726 q^{98} +1.67584 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 5 q^{3} + 28 q^{4} - 12 q^{5} - 8 q^{6} - 15 q^{7} - 3 q^{8} + 25 q^{9}+O(q^{10}) $ 40 * q - 5 * q^3 + 28 * q^4 - 12 * q^5 - 8 * q^6 - 15 * q^7 - 3 * q^8 + 25 * q^9	\( 40 q - 5 q^{3} + 28 q^{4} - 12 q^{5} - 8 q^{6} - 15 q^{7} - 3 q^{8} + 25 q^{9} - 25 q^{10} + 40 q^{11} - 17 q^{12} - 35 q^{13} + 3 q^{14} + 15 q^{15} - 6 q^{17} + 24 q^{18} + 2 q^{19} - 6 q^{20} - 5 q^{21} + 8 q^{23} - 18 q^{24} + 20 q^{25} - 20 q^{26} + q^{27} - 50 q^{28} - 5 q^{30} - 12 q^{31} - 6 q^{32} - 5 q^{33} - 26 q^{34} - 28 q^{35} - 22 q^{36} - 17 q^{37} - 12 q^{38} - 30 q^{39} + 30 q^{40} + 9 q^{41} - 34 q^{42} + 6 q^{43} + 28 q^{44} - 89 q^{45} - 7 q^{46} - 8 q^{47} + 33 q^{48} + q^{49} + 17 q^{50} - 52 q^{51} - 65 q^{52} - 51 q^{53} + 5 q^{54} - 12 q^{55} - 4 q^{56} - 49 q^{57} - 56 q^{59} + 15 q^{60} - 39 q^{61} + 53 q^{63} - 13 q^{64} - 13 q^{65} - 8 q^{66} - 68 q^{67} - 107 q^{68} - 31 q^{69} + 51 q^{70} - 47 q^{71} + 71 q^{72} + 19 q^{73} - 54 q^{74} - 22 q^{75} + 54 q^{76} - 15 q^{77} + 28 q^{78} + 10 q^{79} + 10 q^{80} - 4 q^{81} + 34 q^{82} - 40 q^{83} + 11 q^{84} + 26 q^{85} - 46 q^{86} - 3 q^{88} + 29 q^{89} - 100 q^{90} - 50 q^{91} + 76 q^{92} - 73 q^{93} - 116 q^{94} + 5 q^{95} + 13 q^{96} - 22 q^{97} + 102 q^{98} + 25 q^{99}+O(q^{100}) \) 40 * q - 5 * q^3 + 28 * q^4 - 12 * q^5 - 8 * q^6 - 15 * q^7 - 3 * q^8 + 25 * q^9 - 25 * q^10 + 40 * q^11 - 17 * q^12 - 35 * q^13 + 3 * q^14 + 15 * q^15 - 6 * q^17 + 24 * q^18 + 2 * q^19 - 6 * q^20 - 5 * q^21 + 8 * q^23 - 18 * q^24 + 20 * q^25 - 20 * q^26 + q^27 - 50 * q^28 - 5 * q^30 - 12 * q^31 - 6 * q^32 - 5 * q^33 - 26 * q^34 - 28 * q^35 - 22 * q^36 - 17 * q^37 - 12 * q^38 - 30 * q^39 + 30 * q^40 + 9 * q^41 - 34 * q^42 + 6 * q^43 + 28 * q^44 - 89 * q^45 - 7 * q^46 - 8 * q^47 + 33 * q^48 + q^49 + 17 * q^50 - 52 * q^51 - 65 * q^52 - 51 * q^53 + 5 * q^54 - 12 * q^55 - 4 * q^56 - 49 * q^57 - 56 * q^59 + 15 * q^60 - 39 * q^61 + 53 * q^63 - 13 * q^64 - 13 * q^65 - 8 * q^66 - 68 * q^67 - 107 * q^68 - 31 * q^69 + 51 * q^70 - 47 * q^71 + 71 * q^72 + 19 * q^73 - 54 * q^74 - 22 * q^75 + 54 * q^76 - 15 * q^77 + 28 * q^78 + 10 * q^79 + 10 * q^80 - 4 * q^81 + 34 * q^82 - 40 * q^83 + 11 * q^84 + 26 * q^85 - 46 * q^86 - 3 * q^88 + 29 * q^89 - 100 * q^90 - 50 * q^91 + 76 * q^92 - 73 * q^93 - 116 * q^94 + 5 * q^95 + 13 * q^96 - 22 * q^97 + 102 * q^98 + 25 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.667928	−0.472297	−0.236148	−	0.971717i	$-0.575885\pi$
$2$	−0.667928	−0.472297	−0.236148	+	0.971717i	$0.575885\pi$
$3$	2.16237	1.24844	0.624222	−	0.781247i	$-0.285416\pi$
$3$	2.16237	1.24844	0.624222	+	0.781247i	$0.285416\pi$
$4$	−1.55387	−0.776936
$5$	3.76965	1.68584	0.842918	−	0.538041i	$-0.180836\pi$
$5$	3.76965	1.68584	0.842918	+	0.538041i	$0.180836\pi$
$6$	−1.44431	−0.589636
$7$	−2.15374	−0.814036	−0.407018	−	0.913420i	$-0.633431\pi$
$7$	−2.15374	−0.814036	−0.407018	+	0.913420i	$0.633431\pi$
$8$	2.37373	0.839241
$9$	1.67584	0.558615
$10$	−2.51785	−0.796215
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−3.36005	−0.969962
$13$	−3.37185	−0.935184	−0.467592	−	0.883944i	$-0.654878\pi$
$13$	−3.37185	−0.935184	−0.467592	+	0.883944i	$0.654878\pi$
$14$	1.43854	0.384466
$15$	8.15137	2.10467
$16$	1.52226	0.380565
$17$	6.32910	1.53503	0.767516	−	0.641030i	$-0.221492\pi$
$17$	6.32910	1.53503	0.767516	+	0.641030i	$0.221492\pi$
$18$	−1.11934	−0.263832
$19$	−3.38499	−0.776571	−0.388285	−	0.921539i	$-0.626933\pi$
$19$	−3.38499	−0.776571	−0.388285	+	0.921539i	$0.626933\pi$
$20$	−5.85755	−1.30979
$21$	−4.65717	−1.01628
$22$	−0.667928	−0.142403
$23$	−2.58688	−0.539402	−0.269701	−	0.962944i	$-0.586925\pi$
$23$	−2.58688	−0.539402	−0.269701	+	0.962944i	$0.586925\pi$
$24$	5.13289	1.04775
$25$	9.21023	1.84205
$26$	2.25216	0.441684
$27$	−2.86331	−0.551045
$28$	3.34663	0.632454
$29$	0	0
$29$	0	0
$30$	−5.44453	−0.994030
$31$	−7.71384	−1.38545	−0.692723	−	0.721204i	$-0.743589\pi$
$31$	−7.71384	−1.38545	−0.692723	+	0.721204i	$0.743589\pi$
$32$	−5.76422	−1.01898
$33$	2.16237	0.376420
$34$	−4.22738	−0.724990
$35$	−8.11882	−1.37233
$36$	−2.60405	−0.434008
$37$	−11.5612	−1.90065	−0.950323	−	0.311264i	$-0.899248\pi$
$37$	−11.5612	−1.90065	−0.950323	+	0.311264i	$0.899248\pi$
$38$	2.26093	0.366772
$39$	−7.29120	−1.16753
$40$	8.94813	1.41482
$41$	4.34917	0.679226	0.339613	−	0.940565i	$-0.389704\pi$
$41$	4.34917	0.679226	0.339613	+	0.940565i	$0.389704\pi$
$42$	3.11066	0.479985
$43$	−3.26849	−0.498440	−0.249220	−	0.968447i	$-0.580174\pi$
$43$	−3.26849	−0.498440	−0.249220	+	0.968447i	$0.580174\pi$
$44$	−1.55387	−0.234255
$45$	6.31734	0.941733
$46$	1.72785	0.254758
$47$	−7.48624	−1.09198	−0.545990	−	0.837792i	$-0.683846\pi$
$47$	−7.48624	−1.09198	−0.545990	+	0.837792i	$0.683846\pi$
$48$	3.29169	0.475115
$49$	−2.36142	−0.337346
$50$	−6.15177	−0.869992
$51$	13.6859	1.91640
$52$	5.23943	0.726578
$53$	−5.54688	−0.761923	−0.380961	−	0.924591i	$-0.624407\pi$
$53$	−5.54688	−0.761923	−0.380961	+	0.924591i	$0.624407\pi$
$54$	1.91249	0.260257
$55$	3.76965	0.508299
$56$	−5.11239	−0.683172
$57$	−7.31961	−0.969506
$58$	0	0
$59$	3.76002	0.489513	0.244756	−	0.969585i	$-0.421292\pi$
$59$	3.76002	0.489513	0.244756	+	0.969585i	$0.421292\pi$
$60$	−12.6662	−1.63520
$61$	−10.1387	−1.29813	−0.649064	−	0.760734i	$-0.724839\pi$
$61$	−10.1387	−1.29813	−0.649064	+	0.760734i	$0.724839\pi$
$62$	5.15229	0.654341
$63$	−3.60933	−0.454732
$64$	0.805564	0.100696
$65$	−12.7107	−1.57657
$66$	−1.44431	−0.177782
$67$	−10.6196	−1.29739	−0.648695	−	0.761049i	$-0.724685\pi$
$67$	−10.6196	−1.29739	−0.648695	+	0.761049i	$0.724685\pi$
$68$	−9.83461	−1.19262
$69$	−5.59379	−0.673413
$70$	5.42279	0.648147
$71$	−2.13508	−0.253387	−0.126694	−	0.991942i	$-0.540436\pi$
$71$	−2.13508	−0.253387	−0.126694	+	0.991942i	$0.540436\pi$
$72$	3.97800	0.468812
$73$	−12.9504	−1.51572	−0.757862	−	0.652414i	$-0.773756\pi$
$73$	−12.9504	−1.51572	−0.757862	+	0.652414i	$0.773756\pi$
$74$	7.72204	0.897669
$75$	19.9159	2.29969
$76$	5.25985	0.603346
$77$	−2.15374	−0.245441
$78$	4.87000	0.551419
$79$	11.2820	1.26932	0.634661	−	0.772791i	$-0.281140\pi$
$79$	11.2820	1.26932	0.634661	+	0.772791i	$0.281140\pi$
$80$	5.73839	0.641571
$81$	−11.2191	−1.24656
$82$	−2.90493	−0.320796
$83$	5.82198	0.639045	0.319522	−	0.947579i	$-0.396478\pi$
$83$	5.82198	0.639045	0.319522	+	0.947579i	$0.396478\pi$
$84$	7.23665	0.789584
$85$	23.8585	2.58781
$86$	2.18311	0.235411
$87$	0	0
$88$	2.37373	0.253041
$89$	9.99923	1.05992	0.529958	−	0.848024i	$-0.322208\pi$
$89$	9.99923	1.05992	0.529958	+	0.848024i	$0.322208\pi$
$90$	−4.21953	−0.444777
$91$	7.26209	0.761273
$92$	4.01968	0.419081
$93$	−16.6802	−1.72965
$94$	5.00027	0.515738
$95$	−12.7602	−1.30917
$96$	−12.4644	−1.27214
$97$	−6.92880	−0.703513	−0.351756	−	0.936092i	$-0.614415\pi$
$97$	−6.92880	−0.703513	−0.351756	+	0.936092i	$0.614415\pi$
$98$	1.57726	0.159327
$99$	1.67584	0.168429
$100$	−14.3115	−1.43115
$101$	−3.29696	−0.328060	−0.164030	−	0.986455i	$-0.552449\pi$
$101$	−3.29696	−0.328060	−0.164030	+	0.986455i	$0.552449\pi$
$102$	−9.14117	−0.905111
$103$	9.84856	0.970407	0.485204	−	0.874401i	$-0.338746\pi$
$103$	9.84856	0.970407	0.485204	+	0.874401i	$0.338746\pi$
$104$	−8.00388	−0.784845
$105$	−17.5559	−1.71328
$106$	3.70492	0.359854
$107$	−2.68110	−0.259192	−0.129596	−	0.991567i	$-0.541368\pi$
$107$	−2.68110	−0.259192	−0.129596	+	0.991567i	$0.541368\pi$
$108$	4.44922	0.428127
$109$	−13.7898	−1.32083	−0.660413	−	0.750903i	$-0.729619\pi$
$109$	−13.7898	−1.32083	−0.660413	+	0.750903i	$0.729619\pi$
$110$	−2.51785	−0.240068
$111$	−24.9996	−2.37285
$112$	−3.27855	−0.309794
$113$	−2.11356	−0.198827	−0.0994136	−	0.995046i	$-0.531697\pi$
$113$	−2.11356	−0.198827	−0.0994136	+	0.995046i	$0.531697\pi$
$114$	4.88897	0.457894
$115$	−9.75162	−0.909343
$116$	0	0
$117$	−5.65070	−0.522408
$118$	−2.51142	−0.231195
$119$	−13.6312	−1.24957
$120$	19.3492	1.76633
$121$	1.00000	0.0909091
$122$	6.77192	0.613101
$123$	9.40451	0.847976
$124$	11.9863	1.07640
$125$	15.8711	1.41955
$126$	2.41077	0.214769
$127$	15.6585	1.38946	0.694732	−	0.719269i	$-0.255523\pi$
$127$	15.6585	1.38946	0.694732	+	0.719269i	$0.255523\pi$
$128$	10.9904	0.971422
$129$	−7.06768	−0.622274
$130$	8.48983	0.744608
$131$	9.64412	0.842611	0.421305	−	0.906919i	$-0.361572\pi$
$131$	9.64412	0.842611	0.421305	+	0.906919i	$0.361572\pi$
$132$	−3.36005	−0.292454
$133$	7.29038	0.632157
$134$	7.09312	0.612753
$135$	−10.7937	−0.928972
$136$	15.0236	1.28826
$137$	20.4169	1.74433	0.872165	−	0.489212i	$-0.162716\pi$
$137$	20.4169	1.74433	0.872165	+	0.489212i	$0.162716\pi$
$138$	3.73625	0.318051
$139$	−14.6037	−1.23867	−0.619335	−	0.785127i	$-0.712598\pi$
$139$	−14.6037	−1.23867	−0.619335	+	0.785127i	$0.712598\pi$
$140$	12.6156	1.06621
$141$	−16.1880	−1.36328
$142$	1.42608	0.119674
$143$	−3.37185	−0.281969
$144$	2.55107	0.212590
$145$	0	0
$146$	8.64991	0.715872
$147$	−5.10626	−0.421158
$148$	17.9646	1.47668
$149$	1.80982	0.148266	0.0741331	−	0.997248i	$-0.476381\pi$
$149$	1.80982	0.148266	0.0741331	+	0.997248i	$0.476381\pi$
$150$	−13.3024	−1.08614
$151$	13.6503	1.11084	0.555422	−	0.831569i	$-0.312557\pi$
$151$	13.6503	1.11084	0.555422	+	0.831569i	$0.312557\pi$
$152$	−8.03507	−0.651730
$153$	10.6066	0.857492
$154$	1.43854	0.115921
$155$	−29.0784	−2.33564
$156$	11.3296	0.907093
$157$	19.1223	1.52612	0.763061	−	0.646327i	$-0.223696\pi$
$157$	19.1223	1.52612	0.763061	+	0.646327i	$0.223696\pi$
$158$	−7.53555	−0.599497
$159$	−11.9944	−0.951219
$160$	−21.7291	−1.71783
$161$	5.57146	0.439092
$162$	7.49354	0.588748
$163$	−4.36511	−0.341901	−0.170951	−	0.985280i	$-0.554684\pi$
$163$	−4.36511	−0.341901	−0.170951	+	0.985280i	$0.554684\pi$
$164$	−6.75805	−0.527715
$165$	8.15137	0.634583
$166$	−3.88866	−0.301819
$167$	6.35457	0.491731	0.245866	−	0.969304i	$-0.420928\pi$
$167$	6.35457	0.491731	0.245866	+	0.969304i	$0.420928\pi$
$168$	−11.0549	−0.852903
$169$	−1.63059	−0.125430
$170$	−15.9357	−1.22222
$171$	−5.67272	−0.433804
$172$	5.07881	0.387256
$173$	21.7135	1.65085	0.825423	−	0.564515i	$-0.190937\pi$
$173$	21.7135	1.65085	0.825423	+	0.564515i	$0.190937\pi$
$174$	0	0
$175$	−19.8364	−1.49949
$176$	1.52226	0.114745
$177$	8.13055	0.611129
$178$	−6.67877	−0.500595
$179$	2.99804	0.224084	0.112042	−	0.993703i	$-0.464261\pi$
$179$	2.99804	0.224084	0.112042	+	0.993703i	$0.464261\pi$
$180$	−9.81634	−0.731667
$181$	−13.5835	−1.00965	−0.504827	−	0.863221i	$-0.668444\pi$
$181$	−13.5835	−1.00965	−0.504827	+	0.863221i	$0.668444\pi$
$182$	−4.85055	−0.359547
$183$	−21.9236	−1.62064
$184$	−6.14056	−0.452688
$185$	−43.5816	−3.20418
$186$	11.1412	0.816909
$187$	6.32910	0.462830
$188$	11.6327	0.848398
$189$	6.16682	0.448570
$190$	8.52292	0.618317
$191$	−9.64558	−0.697930	−0.348965	−	0.937136i	$-0.613467\pi$
$191$	−9.64558	−0.697930	−0.348965	+	0.937136i	$0.613467\pi$
$192$	1.74193	0.125713
$193$	−17.8328	−1.28363	−0.641817	−	0.766857i	$-0.721819\pi$
$193$	−17.8328	−1.28363	−0.641817	+	0.766857i	$0.721819\pi$
$194$	4.62794	0.332267
$195$	−27.4852	−1.96826
$196$	3.66934	0.262096
$197$	−12.4371	−0.886104	−0.443052	−	0.896496i	$-0.646104\pi$
$197$	−12.4371	−0.886104	−0.443052	+	0.896496i	$0.646104\pi$
$198$	−1.11934	−0.0795483
$199$	11.3837	0.806971	0.403486	−	0.914986i	$-0.367799\pi$
$199$	11.3837	0.806971	0.403486	+	0.914986i	$0.367799\pi$
$200$	21.8626	1.54592
$201$	−22.9635	−1.61972
$202$	2.20213	0.154942
$203$	0	0
$204$	−21.2661	−1.48892
$205$	16.3948	1.14506
$206$	−6.57813	−0.458320
$207$	−4.33521	−0.301318
$208$	−5.13285	−0.355899
$209$	−3.38499	−0.234145
$210$	11.7261	0.809176
$211$	12.5978	0.867269	0.433634	−	0.901089i	$-0.357231\pi$
$211$	12.5978	0.867269	0.433634	+	0.901089i	$0.357231\pi$
$212$	8.61914	0.591965
$213$	−4.61683	−0.316340
$214$	1.79078	0.122415
$215$	−12.3210	−0.840288
$216$	−6.79674	−0.462459
$217$	16.6136	1.12780
$218$	9.21061	0.623821
$219$	−28.0035	−1.89230
$220$	−5.85755	−0.394916
$221$	−21.3408	−1.43554
$222$	16.6979	1.12069
$223$	−15.9922	−1.07092	−0.535460	−	0.844561i	$-0.679862\pi$
$223$	−15.9922	−1.07092	−0.535460	+	0.844561i	$0.679862\pi$
$224$	12.4146	0.829487
$225$	15.4349	1.02899
$226$	1.41171	0.0939054
$227$	17.9782	1.19325	0.596627	−	0.802519i	$-0.296507\pi$
$227$	17.9782	1.19325	0.596627	+	0.802519i	$0.296507\pi$
$228$	11.3737	0.753244
$229$	23.8261	1.57447	0.787237	−	0.616651i	$-0.211511\pi$
$229$	23.8261	1.57447	0.787237	+	0.616651i	$0.211511\pi$
$230$	6.51338	0.429480
$231$	−4.65717	−0.306420
$232$	0	0
$233$	−12.2409	−0.801926	−0.400963	−	0.916094i	$-0.631324\pi$
$233$	−12.2409	−0.801926	−0.400963	+	0.916094i	$0.631324\pi$
$234$	3.77426	0.246731
$235$	−28.2205	−1.84090
$236$	−5.84259	−0.380320
$237$	24.3958	1.58468
$238$	9.10467	0.590168
$239$	−10.8874	−0.704248	−0.352124	−	0.935953i	$-0.614540\pi$
$239$	−10.8874	−0.704248	−0.352124	+	0.935953i	$0.614540\pi$
$240$	12.4085	0.800966
$241$	−12.0278	−0.774781	−0.387390	−	0.921916i	$-0.626623\pi$
$241$	−12.0278	−0.774781	−0.387390	+	0.921916i	$0.626623\pi$
$242$	−0.667928	−0.0429361
$243$	−15.6699	−1.00522
$244$	15.7542	1.00856
$245$	−8.90172	−0.568710
$246$	−6.28154	−0.400496
$247$	11.4137	0.726237
$248$	−18.3106	−1.16272
$249$	12.5893	0.797812
$250$	−10.6007	−0.670449
$251$	3.37406	0.212969	0.106485	−	0.994314i	$-0.466041\pi$
$251$	3.37406	0.212969	0.106485	+	0.994314i	$0.466041\pi$
$252$	5.60843	0.353298
$253$	−2.58688	−0.162636
$254$	−10.4587	−0.656239
$255$	51.5908	3.23074
$256$	−8.95192	−0.559495
$257$	−24.0910	−1.50276	−0.751379	−	0.659871i	$-0.770611\pi$
$257$	−24.0910	−1.50276	−0.751379	+	0.659871i	$0.770611\pi$
$258$	4.72070	0.293898
$259$	24.8997	1.54719
$260$	19.7508	1.22489
$261$	0	0
$262$	−6.44158	−0.397962
$263$	−10.1317	−0.624748	−0.312374	−	0.949959i	$-0.601124\pi$
$263$	−10.1317	−0.624748	−0.312374	+	0.949959i	$0.601124\pi$
$264$	5.13289	0.315907
$265$	−20.9098	−1.28448
$266$	−4.86945	−0.298565
$267$	21.6220	1.32325
$268$	16.5015	1.00799
$269$	−28.2592	−1.72299	−0.861495	−	0.507765i	$-0.830472\pi$
$269$	−28.2592	−1.72299	−0.861495	+	0.507765i	$0.830472\pi$
$270$	7.20940	0.438750
$271$	9.85318	0.598538	0.299269	−	0.954169i	$-0.403257\pi$
$271$	9.85318	0.598538	0.299269	+	0.954169i	$0.403257\pi$
$272$	9.63455	0.584180
$273$	15.7033	0.950408
$274$	−13.6370	−0.823841
$275$	9.21023	0.555398
$276$	8.69203	0.523199
$277$	−10.0708	−0.605094	−0.302547	−	0.953134i	$-0.597837\pi$
$277$	−10.0708	−0.605094	−0.302547	+	0.953134i	$0.597837\pi$
$278$	9.75422	0.585020
$279$	−12.9272	−0.773931
$280$	−19.2719	−1.15172
$281$	−30.6382	−1.82772	−0.913860	−	0.406029i	$-0.866913\pi$
$281$	−30.6382	−1.82772	−0.913860	+	0.406029i	$0.866913\pi$
$282$	10.8124	0.643871
$283$	29.8360	1.77356	0.886782	−	0.462188i	$-0.152935\pi$
$283$	29.8360	1.77356	0.886782	+	0.462188i	$0.152935\pi$
$284$	3.31764	0.196866
$285$	−27.5923	−1.63443
$286$	2.25216	0.133173
$287$	−9.36696	−0.552914
$288$	−9.65994	−0.569218
$289$	23.0575	1.35632
$290$	0	0
$291$	−14.9826	−0.878297
$292$	20.1232	1.17762
$293$	−8.90533	−0.520255	−0.260127	−	0.965574i	$-0.583765\pi$
$293$	−8.90533	−0.520255	−0.260127	+	0.965574i	$0.583765\pi$
$294$	3.41062	0.198911
$295$	14.1739	0.825238
$296$	−27.4431	−1.59510
$297$	−2.86331	−0.166146
$298$	−1.20883	−0.0700257
$299$	8.72258	0.504440
$300$	−30.9468	−1.78671
$301$	7.03946	0.405748
$302$	−9.11741	−0.524648
$303$	−7.12926	−0.409565
$304$	−5.15285	−0.295536
$305$	−38.2193	−2.18843
$306$	−7.08444	−0.404990
$307$	20.6798	1.18026	0.590129	−	0.807309i	$-0.299077\pi$
$307$	20.6798	1.18026	0.590129	+	0.807309i	$0.299077\pi$
$308$	3.34663	0.190692
$309$	21.2962	1.21150
$310$	19.4223	1.10311
$311$	−18.4077	−1.04381	−0.521904	−	0.853004i	$-0.674778\pi$
$311$	−18.4077	−1.04381	−0.521904	+	0.853004i	$0.674778\pi$
$312$	−17.3073	−0.979835
$313$	14.1708	0.800981	0.400490	−	0.916301i	$-0.368840\pi$
$313$	14.1708	0.800981	0.400490	+	0.916301i	$0.368840\pi$
$314$	−12.7723	−0.720782
$315$	−13.6059	−0.766605
$316$	−17.5308	−0.986182
$317$	−26.0605	−1.46370	−0.731852	−	0.681464i	$-0.761344\pi$
$317$	−26.0605	−1.46370	−0.731852	+	0.681464i	$0.761344\pi$
$318$	8.01141	0.449257
$319$	0	0
$320$	3.03669	0.169756
$321$	−5.79753	−0.323587
$322$	−3.72133	−0.207382
$323$	−21.4240	−1.19206
$324$	17.4330	0.968501
$325$	−31.0555	−1.72265
$326$	2.91558	0.161479
$327$	−29.8187	−1.64898
$328$	10.3238	0.570034
$329$	16.1234	0.888911
$330$	−5.44453	−0.299711
$331$	−12.9627	−0.712494	−0.356247	−	0.934392i	$-0.615944\pi$
$331$	−12.9627	−0.712494	−0.356247	+	0.934392i	$0.615944\pi$
$332$	−9.04661	−0.496497
$333$	−19.3747	−1.06173
$334$	−4.24440	−0.232243
$335$	−40.0321	−2.18719
$336$	−7.08944	−0.386761
$337$	7.16077	0.390072	0.195036	−	0.980796i	$-0.437518\pi$
$337$	7.16077	0.390072	0.195036	+	0.980796i	$0.437518\pi$
$338$	1.08912	0.0592403
$339$	−4.57030	−0.248225
$340$	−37.0730	−2.01057
$341$	−7.71384	−0.417728
$342$	3.78897	0.204884
$343$	20.1620	1.08865
$344$	−7.75851	−0.418311
$345$	−21.0866	−1.13526
$346$	−14.5031	−0.779689
$347$	34.6426	1.85971	0.929856	−	0.367924i	$-0.119931\pi$
$347$	34.6426	1.85971	0.929856	+	0.367924i	$0.119931\pi$
$348$	0	0
$349$	−13.5835	−0.727110	−0.363555	−	0.931573i	$-0.618437\pi$
$349$	−13.5835	−0.727110	−0.363555	+	0.931573i	$0.618437\pi$
$350$	13.2493	0.708204
$351$	9.65468	0.515329
$352$	−5.76422	−0.307234
$353$	12.4975	0.665176	0.332588	−	0.943072i	$-0.392078\pi$
$353$	12.4975	0.665176	0.332588	+	0.943072i	$0.392078\pi$
$354$	−5.43062	−0.288634
$355$	−8.04849	−0.427169
$356$	−15.5375	−0.823487
$357$	−29.4757	−1.56002
$358$	−2.00247	−0.105834
$359$	−2.39462	−0.126383	−0.0631917	−	0.998001i	$-0.520128\pi$
$359$	−2.39462	−0.126383	−0.0631917	+	0.998001i	$0.520128\pi$
$360$	14.9957	0.790341
$361$	−7.54181	−0.396938
$362$	9.07281	0.476856
$363$	2.16237	0.113495
$364$	−11.2844	−0.591461
$365$	−48.8183	−2.55526
$366$	14.6434	0.765423
$367$	1.18817	0.0620219	0.0310109	−	0.999519i	$-0.490127\pi$
$367$	1.18817	0.0620219	0.0310109	+	0.999519i	$0.490127\pi$
$368$	−3.93791	−0.205278
$369$	7.28853	0.379426
$370$	29.1094	1.51332
$371$	11.9465	0.620233
$372$	25.9189	1.34383
$373$	−16.7010	−0.864747	−0.432373	−	0.901695i	$-0.642324\pi$
$373$	−16.7010	−0.864747	−0.432373	+	0.901695i	$0.642324\pi$
$374$	−4.22738	−0.218593
$375$	34.3191	1.77223
$376$	−17.7703	−0.916434
$377$	0	0
$378$	−4.11900	−0.211858
$379$	18.0334	0.926311	0.463156	−	0.886277i	$-0.346717\pi$
$379$	18.0334	0.926311	0.463156	+	0.886277i	$0.346717\pi$
$380$	19.8278	1.01714
$381$	33.8594	1.73467
$382$	6.44256	0.329630
$383$	−0.245700	−0.0125547	−0.00627733	−	0.999980i	$-0.501998\pi$
$383$	−0.245700	−0.0125547	−0.00627733	+	0.999980i	$0.501998\pi$
$384$	23.7653	1.21277
$385$	−8.11882	−0.413773
$386$	11.9110	0.606256
$387$	−5.47748	−0.278436
$388$	10.7665	0.546584
$389$	−8.13767	−0.412596	−0.206298	−	0.978489i	$-0.566142\pi$
$389$	−8.13767	−0.412596	−0.206298	+	0.978489i	$0.566142\pi$
$390$	18.3582	0.929602
$391$	−16.3726	−0.827999
$392$	−5.60538	−0.283114
$393$	20.8542	1.05195
$394$	8.30707	0.418504
$395$	42.5291	2.13987
$396$	−2.60405	−0.130858
$397$	0.230447	0.0115658	0.00578290	−	0.999983i	$-0.498159\pi$
$397$	0.230447	0.0115658	0.00578290	+	0.999983i	$0.498159\pi$
$398$	−7.60351	−0.381130
$399$	15.7645	0.789213
$400$	14.0204	0.701019
$401$	−33.3658	−1.66621	−0.833104	−	0.553117i	$-0.813438\pi$
$401$	−33.3658	−1.66621	−0.833104	+	0.553117i	$0.813438\pi$
$402$	15.3380	0.764988
$403$	26.0099	1.29565
$404$	5.12306	0.254882
$405$	−42.2919	−2.10150
$406$	0	0
$407$	−11.5612	−0.573067
$408$	32.4865	1.60832
$409$	33.5029	1.65661	0.828306	−	0.560276i	$-0.189305\pi$
$409$	33.5029	1.65661	0.828306	+	0.560276i	$0.189305\pi$
$410$	−10.9506	−0.540810
$411$	44.1488	2.17770
$412$	−15.3034	−0.753944
$413$	−8.09809	−0.398481
$414$	2.89561	0.142311
$415$	21.9468	1.07733
$416$	19.4361	0.952935
$417$	−31.5786	−1.54641
$418$	2.26093	0.110586
$419$	5.86688	0.286616	0.143308	−	0.989678i	$-0.454226\pi$
$419$	5.86688	0.286616	0.143308	+	0.989678i	$0.454226\pi$
$420$	27.2796	1.33111
$421$	−13.7784	−0.671518	−0.335759	−	0.941948i	$-0.608993\pi$
$421$	−13.7784	−0.671518	−0.335759	+	0.941948i	$0.608993\pi$
$422$	−8.41443	−0.409608
$423$	−12.5458	−0.609996
$424$	−13.1668	−0.639437
$425$	58.2924	2.82760
$426$	3.08371	0.149406
$427$	21.8361	1.05672
$428$	4.16609	0.201375
$429$	−7.29120	−0.352022
$430$	8.22957	0.396865
$431$	−6.54137	−0.315087	−0.157543	−	0.987512i	$-0.550357\pi$
$431$	−6.54137	−0.315087	−0.157543	+	0.987512i	$0.550357\pi$
$432$	−4.35871	−0.209709
$433$	11.6752	0.561073	0.280537	−	0.959843i	$-0.409488\pi$
$433$	11.6752	0.561073	0.280537	+	0.959843i	$0.409488\pi$
$434$	−11.0967	−0.532657
$435$	0	0
$436$	21.4276	1.02620
$437$	8.75657	0.418884
$438$	18.7043	0.893726
$439$	9.85132	0.470178	0.235089	−	0.971974i	$-0.424462\pi$
$439$	9.85132	0.470178	0.235089	+	0.971974i	$0.424462\pi$
$440$	8.94813	0.426585
$441$	−3.95737	−0.188446
$442$	14.2541	0.678000
$443$	−14.2946	−0.679156	−0.339578	−	0.940578i	$-0.610284\pi$
$443$	−14.2946	−0.679156	−0.339578	+	0.940578i	$0.610284\pi$
$444$	38.8461	1.84355
$445$	37.6936	1.78685
$446$	10.6817	0.505792
$447$	3.91350	0.185102
$448$	−1.73497	−0.0819698
$449$	23.1211	1.09115	0.545575	−	0.838062i	$-0.316311\pi$
$449$	23.1211	1.09115	0.545575	+	0.838062i	$0.316311\pi$
$450$	−10.3094	−0.485990
$451$	4.34917	0.204794
$452$	3.28420	0.154476
$453$	29.5170	1.38683
$454$	−12.0081	−0.563569
$455$	27.3755	1.28338
$456$	−17.3748	−0.813649
$457$	−22.1859	−1.03781	−0.518906	−	0.854831i	$-0.673660\pi$
$457$	−22.1859	−1.03781	−0.518906	+	0.854831i	$0.673660\pi$
$458$	−15.9141	−0.743619
$459$	−18.1222	−0.845872
$460$	15.1528	0.706501
$461$	4.04619	0.188450	0.0942249	−	0.995551i	$-0.469963\pi$
$461$	4.04619	0.188450	0.0942249	+	0.995551i	$0.469963\pi$
$462$	3.11066	0.144721
$463$	−10.4475	−0.485534	−0.242767	−	0.970085i	$-0.578055\pi$
$463$	−10.4475	−0.485534	−0.242767	+	0.970085i	$0.578055\pi$
$464$	0	0
$465$	−62.8783	−2.91591
$466$	8.17602	0.378747
$467$	−2.51349	−0.116311	−0.0581553	−	0.998308i	$-0.518522\pi$
$467$	−2.51349	−0.116311	−0.0581553	+	0.998308i	$0.518522\pi$
$468$	8.78047	0.405877
$469$	22.8718	1.05612
$470$	18.8492	0.869451
$471$	41.3494	1.90528
$472$	8.92527	0.410819
$473$	−3.26849	−0.150285
$474$	−16.2947	−0.748438
$475$	−31.1766	−1.43048
$476$	21.1812	0.970837
$477$	−9.29571	−0.425621
$478$	7.27200	0.332614
$479$	42.1317	1.92505	0.962524	−	0.271197i	$-0.0874194\pi$
$479$	42.1317	1.92505	0.962524	+	0.271197i	$0.0874194\pi$
$480$	−46.9863	−2.14462
$481$	38.9826	1.77745
$482$	8.03373	0.365926
$483$	12.0475	0.548183
$484$	−1.55387	−0.0706305
$485$	−26.1191	−1.18601
$486$	10.4663	0.474763
$487$	−29.7859	−1.34973	−0.674864	−	0.737942i	$-0.735798\pi$
$487$	−29.7859	−1.34973	−0.674864	+	0.737942i	$0.735798\pi$
$488$	−24.0666	−1.08944
$489$	−9.43897	−0.426845
$490$	5.94571	0.268600
$491$	5.61197	0.253264	0.126632	−	0.991950i	$-0.459583\pi$
$491$	5.61197	0.253264	0.126632	+	0.991950i	$0.459583\pi$
$492$	−14.6134	−0.658823
$493$	0	0
$494$	−7.62354	−0.342999
$495$	6.31734	0.283943
$496$	−11.7425	−0.527253
$497$	4.59840	0.206266
$498$	−8.40873	−0.376804
$499$	−10.6575	−0.477096	−0.238548	−	0.971131i	$-0.576671\pi$
$499$	−10.6575	−0.477096	−0.238548	+	0.971131i	$0.576671\pi$
$500$	−24.6616	−1.10290
$501$	13.7409	0.613900
$502$	−2.25363	−0.100585
$503$	39.9886	1.78300	0.891501	−	0.453019i	$-0.149653\pi$
$503$	39.9886	1.78300	0.891501	+	0.453019i	$0.149653\pi$
$504$	−8.56757	−0.381630
$505$	−12.4284	−0.553056
$506$	1.72785	0.0768123
$507$	−3.52595	−0.156593
$508$	−24.3313	−1.07952
$509$	−8.66819	−0.384211	−0.192105	−	0.981374i	$-0.561532\pi$
$509$	−8.66819	−0.384211	−0.192105	+	0.981374i	$0.561532\pi$
$510$	−34.4590	−1.52587
$511$	27.8917	1.23385
$512$	−16.0015	−0.707175
$513$	9.69230	0.427926
$514$	16.0911	0.709747
$515$	37.1256	1.63595
$516$	10.9823	0.483467
$517$	−7.48624	−0.329244
$518$	−16.6312	−0.730735
$519$	46.9526	2.06099
$520$	−30.1718	−1.32312
$521$	−30.2679	−1.32606	−0.663030	−	0.748593i	$-0.730730\pi$
$521$	−30.2679	−1.32606	−0.663030	+	0.748593i	$0.730730\pi$
$522$	0	0
$523$	21.8353	0.954793	0.477396	−	0.878688i	$-0.341581\pi$
$523$	21.8353	0.954793	0.477396	+	0.878688i	$0.341581\pi$
$524$	−14.9857	−0.654655
$525$	−42.8936	−1.87203
$526$	6.76725	0.295066
$527$	−48.8216	−2.12670
$528$	3.29169	0.143253
$529$	−16.3081	−0.709046
$530$	13.9662	0.606654
$531$	6.30120	0.273449
$532$	−11.3283	−0.491145
$533$	−14.6648	−0.635201
$534$	−14.4420	−0.624965
$535$	−10.1068	−0.436955
$536$	−25.2081	−1.08882
$537$	6.48287	0.279756
$538$	18.8751	0.813763
$539$	−2.36142	−0.101714
$540$	16.7720	0.721752
$541$	9.24654	0.397540	0.198770	−	0.980046i	$-0.436305\pi$
$541$	9.24654	0.397540	0.198770	+	0.980046i	$0.436305\pi$
$542$	−6.58122	−0.282688
$543$	−29.3726	−1.26050
$544$	−36.4823	−1.56417
$545$	−51.9827	−2.22670
$546$	−10.4887	−0.448874
$547$	2.14908	0.0918882	0.0459441	−	0.998944i	$-0.485370\pi$
$547$	2.14908	0.0918882	0.0459441	+	0.998944i	$0.485370\pi$
$548$	−31.7252	−1.35523
$549$	−16.9909	−0.725153
$550$	−6.15177	−0.262312
$551$	0	0
$552$	−13.2782	−0.565156
$553$	−24.2984	−1.03327
$554$	6.72656	0.285784
$555$	−94.2395	−4.00024
$556$	22.6923	0.962367
$557$	−11.5963	−0.491350	−0.245675	−	0.969352i	$-0.579010\pi$
$557$	−11.5963	−0.491350	−0.245675	+	0.969352i	$0.579010\pi$
$558$	8.63444	0.365525
$559$	11.0209	0.466133
$560$	−12.3590	−0.522262
$561$	13.6859	0.577817
$562$	20.4641	0.863226
$563$	10.1657	0.428432	0.214216	−	0.976786i	$-0.431280\pi$
$563$	10.1657	0.428432	0.214216	+	0.976786i	$0.431280\pi$
$564$	25.1541	1.05918
$565$	−7.96738	−0.335190
$566$	−19.9283	−0.837648
$567$	24.1629	1.01475
$568$	−5.06810	−0.212653
$569$	−18.1567	−0.761169	−0.380585	−	0.924746i	$-0.624277\pi$
$569$	−18.1567	−0.761169	−0.380585	+	0.924746i	$0.624277\pi$
$570$	18.4297	0.771935
$571$	−5.30273	−0.221912	−0.110956	−	0.993825i	$-0.535391\pi$
$571$	−5.30273	−0.221912	−0.110956	+	0.993825i	$0.535391\pi$
$572$	5.23943	0.219072
$573$	−20.8573	−0.871327
$574$	6.25646	0.261139
$575$	−23.8257	−0.993602
$576$	1.35000	0.0562500
$577$	43.6476	1.81707	0.908536	−	0.417806i	$-0.137201\pi$
$577$	43.6476	1.81707	0.908536	+	0.417806i	$0.137201\pi$
$578$	−15.4008	−0.640587
$579$	−38.5612	−1.60255
$580$	0	0
$581$	−12.5390	−0.520205
$582$	10.0073	0.414817
$583$	−5.54688	−0.229728
$584$	−30.7407	−1.27206
$585$	−21.3012	−0.880694
$586$	5.94812	0.245715
$587$	39.5189	1.63112	0.815559	−	0.578673i	$-0.196429\pi$
$587$	39.5189	1.63112	0.815559	+	0.578673i	$0.196429\pi$
$588$	7.93448	0.327212
$589$	26.1113	1.07590
$590$	−9.46717	−0.389757
$591$	−26.8935	−1.10625
$592$	−17.5991	−0.723320
$593$	−15.7975	−0.648727	−0.324363	−	0.945933i	$-0.605150\pi$
$593$	−15.7975	−0.648727	−0.324363	+	0.945933i	$0.605150\pi$
$594$	1.91249	0.0784703
$595$	−51.3848	−2.10657
$596$	−2.81223	−0.115193
$597$	24.6158	1.00746
$598$	−5.82606	−0.238245
$599$	26.9199	1.09992	0.549959	−	0.835192i	$-0.314643\pi$
$599$	26.9199	1.09992	0.549959	+	0.835192i	$0.314643\pi$
$600$	47.2750	1.93000
$601$	−0.413065	−0.0168493	−0.00842465	−	0.999965i	$-0.502682\pi$
$601$	−0.413065	−0.0168493	−0.00842465	+	0.999965i	$0.502682\pi$
$602$	−4.70185	−0.191633
$603$	−17.7968	−0.724741
$604$	−21.2108	−0.863055
$605$	3.76965	0.153258
$606$	4.76183	0.193436
$607$	7.01514	0.284736	0.142368	−	0.989814i	$-0.454528\pi$
$607$	7.01514	0.284736	0.142368	+	0.989814i	$0.454528\pi$
$608$	19.5119	0.791311
$609$	0	0
$610$	25.5278	1.03359
$611$	25.2425	1.02120
$612$	−16.4813	−0.666216
$613$	−22.7534	−0.919000	−0.459500	−	0.888178i	$-0.651971\pi$
$613$	−22.7534	−0.919000	−0.459500	+	0.888178i	$0.651971\pi$
$614$	−13.8126	−0.557432
$615$	35.4517	1.42955
$616$	−5.11239	−0.205984
$617$	−4.17075	−0.167908	−0.0839541	−	0.996470i	$-0.526755\pi$
$617$	−4.17075	−0.167908	−0.0839541	+	0.996470i	$0.526755\pi$
$618$	−14.2243	−0.572187
$619$	−33.2773	−1.33753	−0.668764	−	0.743474i	$-0.733177\pi$
$619$	−33.2773	−1.33753	−0.668764	+	0.743474i	$0.733177\pi$
$620$	45.1842	1.81464
$621$	7.40705	0.297235
$622$	12.2951	0.492987
$623$	−21.5357	−0.862810
$624$	−11.0991	−0.444320
$625$	13.7771	0.551086
$626$	−9.46507	−0.378300
$627$	−7.31961	−0.292317
$628$	−29.7135	−1.18570
$629$	−73.1719	−2.91755
$630$	9.08775	0.362065
$631$	−15.3536	−0.611217	−0.305609	−	0.952157i	$-0.598860\pi$
$631$	−15.3536	−0.611217	−0.305609	+	0.952157i	$0.598860\pi$
$632$	26.7804	1.06527
$633$	27.2411	1.08274
$634$	17.4065	0.691302
$635$	59.0269	2.34241
$636$	18.6378	0.739036
$637$	7.96237	0.315480
$638$	0	0
$639$	−3.57806	−0.141546
$640$	41.4299	1.63766
$641$	13.9556	0.551214	0.275607	−	0.961270i	$-0.411121\pi$
$641$	13.9556	0.551214	0.275607	+	0.961270i	$0.411121\pi$
$642$	3.87234	0.152829
$643$	32.0349	1.26333	0.631666	−	0.775240i	$-0.282371\pi$
$643$	32.0349	1.26333	0.631666	+	0.775240i	$0.282371\pi$
$644$	−8.65733	−0.341147
$645$	−26.6426	−1.04905
$646$	14.3097	0.563006
$647$	6.02886	0.237019	0.118509	−	0.992953i	$-0.462188\pi$
$647$	6.02886	0.237019	0.118509	+	0.992953i	$0.462188\pi$
$648$	−26.6311	−1.04617
$649$	3.76002	0.147594
$650$	20.7429	0.813603
$651$	35.9247	1.40800
$652$	6.78282	0.265636
$653$	−23.6984	−0.927390	−0.463695	−	0.885995i	$-0.653477\pi$
$653$	−23.6984	−0.927390	−0.463695	+	0.885995i	$0.653477\pi$
$654$	19.9167	0.778807
$655$	36.3549	1.42050
$656$	6.62057	0.258490
$657$	−21.7028	−0.846706
$658$	−10.7693	−0.419829
$659$	38.0568	1.48248	0.741242	−	0.671238i	$-0.234237\pi$
$659$	38.0568	1.48248	0.741242	+	0.671238i	$0.234237\pi$
$660$	−12.6662	−0.493031
$661$	−14.6662	−0.570449	−0.285225	−	0.958461i	$-0.592068\pi$
$661$	−14.6662	−0.570449	−0.285225	+	0.958461i	$0.592068\pi$
$662$	8.65815	0.336509
$663$	−46.1467	−1.79219
$664$	13.8198	0.536313
$665$	27.4822	1.06571
$666$	12.9409	0.501451
$667$	0	0
$668$	−9.87419	−0.382044
$669$	−34.5811	−1.33698
$670$	26.7386	1.03300
$671$	−10.1387	−0.391400
$672$	26.8450	1.03557
$673$	8.71794	0.336052	0.168026	−	0.985783i	$-0.446261\pi$
$673$	8.71794	0.336052	0.168026	+	0.985783i	$0.446261\pi$
$674$	−4.78288	−0.184230
$675$	−26.3718	−1.01505
$676$	2.53374	0.0974514
$677$	−19.9128	−0.765310	−0.382655	−	0.923891i	$-0.624990\pi$
$677$	−19.9128	−0.765310	−0.382655	+	0.923891i	$0.624990\pi$
$678$	3.05263	0.117236
$679$	14.9228	0.572685
$680$	56.6336	2.17180
$681$	38.8755	1.48971
$682$	5.15229	0.197291
$683$	−12.3402	−0.472183	−0.236091	−	0.971731i	$-0.575866\pi$
$683$	−12.3402	−0.472183	−0.236091	+	0.971731i	$0.575866\pi$
$684$	8.81469	0.337038
$685$	76.9643	2.94066
$686$	−13.4668	−0.514164
$687$	51.5209	1.96564
$688$	−4.97549	−0.189689
$689$	18.7033	0.712538
$690$	14.0843	0.536182
$691$	−20.2436	−0.770102	−0.385051	−	0.922895i	$-0.625816\pi$
$691$	−20.2436	−0.770102	−0.385051	+	0.922895i	$0.625816\pi$
$692$	−33.7400	−1.28260
$693$	−3.60933	−0.137107
$694$	−23.1388	−0.878336
$695$	−55.0508	−2.08820
$696$	0	0
$697$	27.5263	1.04263
$698$	9.07283	0.343412
$699$	−26.4693	−1.00116
$700$	30.8232	1.16501
$701$	18.0590	0.682077	0.341039	−	0.940049i	$-0.389221\pi$
$701$	18.0590	0.682077	0.341039	+	0.940049i	$0.389221\pi$
$702$	−6.44863	−0.243388
$703$	39.1345	1.47599
$704$	0.805564	0.0303608
$705$	−61.0231	−2.29826
$706$	−8.34744	−0.314160
$707$	7.10079	0.267053
$708$	−12.6338	−0.474808
$709$	5.18588	0.194760	0.0973799	−	0.995247i	$-0.468954\pi$
$709$	5.18588	0.194760	0.0973799	+	0.995247i	$0.468954\pi$
$710$	5.37581	0.201751
$711$	18.9068	0.709062
$712$	23.7355	0.889525
$713$	19.9548	0.747312
$714$	19.6877	0.736792
$715$	−12.7107	−0.475353
$716$	−4.65857	−0.174099
$717$	−23.5426	−0.879214
$718$	1.59944	0.0596904
$719$	14.4223	0.537862	0.268931	−	0.963159i	$-0.413330\pi$
$719$	14.4223	0.537862	0.268931	+	0.963159i	$0.413330\pi$
$720$	9.61664	0.358391
$721$	−21.2112	−0.789946
$722$	5.03739	0.187472
$723$	−26.0086	−0.967271
$724$	21.1070	0.784436
$725$	0	0
$726$	−1.44431	−0.0536033
$727$	−43.3141	−1.60643	−0.803216	−	0.595688i	$-0.796880\pi$
$727$	−43.3141	−1.60643	−0.803216	+	0.595688i	$0.796880\pi$
$728$	17.2382	0.638892
$729$	−0.226796	−0.00839985
$730$	32.6071	1.20684
$731$	−20.6866	−0.765121
$732$	34.0665	1.25913
$733$	29.7058	1.09721	0.548605	−	0.836082i	$-0.315159\pi$
$733$	29.7058	1.09721	0.548605	+	0.836082i	$0.315159\pi$
$734$	−0.793611	−0.0292927
$735$	−19.2488	−0.710003
$736$	14.9114	0.549640
$737$	−10.6196	−0.391178
$738$	−4.86821	−0.179201
$739$	3.71924	0.136814	0.0684072	−	0.997657i	$-0.478208\pi$
$739$	3.71924	0.136814	0.0684072	+	0.997657i	$0.478208\pi$
$740$	67.7202	2.48944
$741$	24.6807	0.906667
$742$	−7.97942	−0.292934
$743$	−35.5654	−1.30477	−0.652384	−	0.757889i	$-0.726231\pi$
$743$	−35.5654	−1.30477	−0.652384	+	0.757889i	$0.726231\pi$
$744$	−39.5942	−1.45160
$745$	6.82238	0.249953
$746$	11.1551	0.408417
$747$	9.75673	0.356980
$748$	−9.83461	−0.359589
$749$	5.77438	0.210991
$750$	−22.9227	−0.837019
$751$	−36.8493	−1.34465	−0.672324	−	0.740257i	$-0.734704\pi$
$751$	−36.8493	−1.34465	−0.672324	+	0.740257i	$0.734704\pi$
$752$	−11.3960	−0.415570
$753$	7.29598	0.265880
$754$	0	0
$755$	51.4567	1.87270
$756$	−9.58245	−0.348510
$757$	−44.6796	−1.62391	−0.811955	−	0.583721i	$-0.801596\pi$
$757$	−44.6796	−1.62391	−0.811955	+	0.583721i	$0.801596\pi$
$758$	−12.0450	−0.437494
$759$	−5.59379	−0.203042
$760$	−30.2894	−1.09871
$761$	9.46541	0.343121	0.171560	−	0.985174i	$-0.445119\pi$
$761$	9.46541	0.343121	0.171560	+	0.985174i	$0.445119\pi$
$762$	−22.6157	−0.819279
$763$	29.6996	1.07520
$764$	14.9880	0.542247
$765$	39.9831	1.44559
$766$	0.164110	0.00592952
$767$	−12.6782	−0.457784
$768$	−19.3574	−0.698499
$769$	42.4894	1.53221	0.766103	−	0.642718i	$-0.222193\pi$
$769$	42.4894	1.53221	0.766103	+	0.642718i	$0.222193\pi$
$770$	5.42279	0.195424
$771$	−52.0937	−1.87611
$772$	27.7099	0.997302
$773$	13.2459	0.476423	0.238211	−	0.971213i	$-0.423439\pi$
$773$	13.2459	0.476423	0.238211	+	0.971213i	$0.423439\pi$
$774$	3.65856	0.131504
$775$	−71.0462	−2.55205
$776$	−16.4471	−0.590417
$777$	53.8424	1.93159
$778$	5.43538	0.194868
$779$	−14.7219	−0.527467
$780$	42.7085	1.52921
$781$	−2.13508	−0.0763991
$782$	10.9357	0.391061
$783$	0	0
$784$	−3.59470	−0.128382
$785$	72.0841	2.57279
$786$	−13.9291	−0.496834
$787$	−2.38662	−0.0850737	−0.0425368	−	0.999095i	$-0.513544\pi$
$787$	−2.38662	−0.0850737	−0.0425368	+	0.999095i	$0.513544\pi$
$788$	19.3256	0.688446
$789$	−21.9085	−0.779963
$790$	−28.4064	−1.01065
$791$	4.55205	0.161852
$792$	3.97800	0.141352
$793$	34.1862	1.21399
$794$	−0.153922	−0.00546249
$795$	−45.2147	−1.60360
$796$	−17.6889	−0.626965
$797$	−52.5373	−1.86097	−0.930483	−	0.366334i	$-0.880613\pi$
$797$	−52.5373	−1.86097	−0.930483	+	0.366334i	$0.880613\pi$
$798$	−10.5296	−0.372742
$799$	−47.3811	−1.67622
$800$	−53.0898	−1.87701
$801$	16.7572	0.592085
$802$	22.2859	0.786944
$803$	−12.9504	−0.457008
$804$	35.6823	1.25842
$805$	21.0024	0.740238
$806$	−17.3728	−0.611930
$807$	−61.1067	−2.15106
$808$	−7.82611	−0.275321
$809$	−4.87007	−0.171223	−0.0856113	−	0.996329i	$-0.527284\pi$
$809$	−4.87007	−0.171223	−0.0856113	+	0.996329i	$0.527284\pi$
$810$	28.2480	0.992533
$811$	−35.0190	−1.22968	−0.614842	−	0.788650i	$-0.710780\pi$
$811$	−35.0190	−1.22968	−0.614842	+	0.788650i	$0.710780\pi$
$812$	0	0
$813$	21.3062	0.747242
$814$	7.72204	0.270657
$815$	−16.4549	−0.576390
$816$	20.8335	0.729317
$817$	11.0638	0.387074
$818$	−22.3775	−0.782412
$819$	12.1701	0.425259
$820$	−25.4755	−0.889641
$821$	−18.1120	−0.632115	−0.316057	−	0.948740i	$-0.602359\pi$
$821$	−18.1120	−0.632115	−0.316057	+	0.948740i	$0.602359\pi$
$822$	−29.4882	−1.02852
$823$	−20.0003	−0.697167	−0.348583	−	0.937278i	$-0.613337\pi$
$823$	−20.0003	−0.697167	−0.348583	+	0.937278i	$0.613337\pi$
$824$	23.3778	0.814405
$825$	19.9159	0.693383
$826$	5.40894	0.188201
$827$	−1.11452	−0.0387558	−0.0193779	−	0.999812i	$-0.506169\pi$
$827$	−1.11452	−0.0387558	−0.0193779	+	0.999812i	$0.506169\pi$
$828$	6.73636	0.234105
$829$	2.19371	0.0761907	0.0380954	−	0.999274i	$-0.487871\pi$
$829$	2.19371	0.0761907	0.0380954	+	0.999274i	$0.487871\pi$
$830$	−14.6589	−0.508817
$831$	−21.7768	−0.755427
$832$	−2.71625	−0.0941689
$833$	−14.9457	−0.517837
$834$	21.0922	0.730365
$835$	23.9545	0.828979
$836$	5.25985	0.181916
$837$	22.0871	0.763443
$838$	−3.91865	−0.135368
$839$	−8.10912	−0.279958	−0.139979	−	0.990154i	$-0.544704\pi$
$839$	−8.10912	−0.279958	−0.139979	+	0.990154i	$0.544704\pi$
$840$	−41.6730	−1.43785
$841$	0	0
$842$	9.20298	0.317156
$843$	−66.2511	−2.28181
$844$	−19.5754	−0.673812
$845$	−6.14676	−0.211455
$846$	8.37967	0.288099
$847$	−2.15374	−0.0740033
$848$	−8.44381	−0.289962
$849$	64.5164	2.21420
$850$	−38.9352	−1.33547
$851$	29.9074	1.02521
$852$	7.17396	0.245776
$853$	−23.1488	−0.792601	−0.396301	−	0.918121i	$-0.629706\pi$
$853$	−23.1488	−0.792601	−0.396301	+	0.918121i	$0.629706\pi$
$854$	−14.5849	−0.499086
$855$	−21.3842	−0.731323
$856$	−6.36421	−0.217524
$857$	24.0422	0.821266	0.410633	−	0.911801i	$-0.365308\pi$
$857$	24.0422	0.821266	0.410633	+	0.911801i	$0.365308\pi$
$858$	4.87000	0.166259
$859$	−13.2242	−0.451204	−0.225602	−	0.974220i	$-0.572435\pi$
$859$	−13.2242	−0.451204	−0.225602	+	0.974220i	$0.572435\pi$
$860$	19.1453	0.652850
$861$	−20.2548	−0.690283
$862$	4.36917	0.148814
$863$	50.0110	1.70239	0.851197	−	0.524846i	$-0.175877\pi$
$863$	50.0110	1.70239	0.851197	+	0.524846i	$0.175877\pi$
$864$	16.5048	0.561504
$865$	81.8522	2.78306
$866$	−7.79818	−0.264993
$867$	49.8589	1.69330
$868$	−25.8154	−0.876231
$869$	11.2820	0.382715
$870$	0	0
$871$	35.8077	1.21330
$872$	−32.7333	−1.10849
$873$	−11.6116	−0.392993
$874$	−5.84876	−0.197837
$875$	−34.1821	−1.15557
$876$	43.5138	1.47020
$877$	−11.2030	−0.378299	−0.189150	−	0.981948i	$-0.560573\pi$
$877$	−11.2030	−0.378299	−0.189150	+	0.981948i	$0.560573\pi$
$878$	−6.57997	−0.222063
$879$	−19.2566	−0.649509
$880$	5.73839	0.193441
$881$	15.2677	0.514380	0.257190	−	0.966361i	$-0.417203\pi$
$881$	15.2677	0.514380	0.257190	+	0.966361i	$0.417203\pi$
$882$	2.64324	0.0890026
$883$	34.3592	1.15628	0.578140	−	0.815937i	$-0.303779\pi$
$883$	34.3592	1.15628	0.578140	+	0.815937i	$0.303779\pi$
$884$	33.1609	1.11532
$885$	30.6493	1.03026
$886$	9.54775	0.320763
$887$	59.1396	1.98571	0.992857	−	0.119307i	$-0.0380674\pi$
$887$	59.1396	1.98571	0.992857	+	0.119307i	$0.0380674\pi$
$888$	−59.3422	−1.99139
$889$	−33.7242	−1.13107
$890$	−25.1766	−0.843921
$891$	−11.2191	−0.375853
$892$	24.8499	0.832036
$893$	25.3409	0.848000
$894$	−2.61394	−0.0874232
$895$	11.3015	0.377769
$896$	−23.6704	−0.790773
$897$	18.8615	0.629766
$898$	−15.4432	−0.515347
$899$	0	0
$900$	−23.9839	−0.799462
$901$	−35.1068	−1.16958
$902$	−2.90493	−0.0967236
$903$	15.2219	0.506554
$904$	−5.01703	−0.166864
$905$	−51.2050	−1.70211
$906$	−19.7152	−0.654994
$907$	54.1367	1.79758	0.898790	−	0.438378i	$-0.144447\pi$
$907$	54.1367	1.79758	0.898790	+	0.438378i	$0.144447\pi$
$908$	−27.9358	−0.927081
$909$	−5.52520	−0.183259
$910$	−18.2849	−0.606137
$911$	−25.0253	−0.829124	−0.414562	−	0.910021i	$-0.636065\pi$
$911$	−25.0253	−0.829124	−0.414562	+	0.910021i	$0.636065\pi$
$912$	−11.1424	−0.368961
$913$	5.82198	0.192679
$914$	14.8186	0.490155
$915$	−82.6443	−2.73214
$916$	−37.0227	−1.22327
$917$	−20.7709	−0.685915
$918$	12.1043	0.399502
$919$	34.0562	1.12341	0.561705	−	0.827338i	$-0.310146\pi$
$919$	34.0562	1.12341	0.561705	+	0.827338i	$0.310146\pi$
$920$	−23.1477	−0.763158
$921$	44.7174	1.47349
$922$	−2.70256	−0.0890042
$923$	7.19918	0.236964
$924$	7.23665	0.238068
$925$	−106.481	−3.50108
$926$	6.97815	0.229316
$927$	16.5046	0.542084
$928$	0	0
$929$	8.79728	0.288629	0.144315	−	0.989532i	$-0.453902\pi$
$929$	8.79728	0.288629	0.144315	+	0.989532i	$0.453902\pi$
$930$	41.9982	1.37718
$931$	7.99339	0.261973
$932$	19.0207	0.623045
$933$	−39.8044	−1.30314
$934$	1.67883	0.0549331
$935$	23.8585	0.780255
$936$	−13.4133	−0.438426
$937$	−50.3743	−1.64566	−0.822828	−	0.568291i	$-0.807605\pi$
$937$	−50.3743	−1.64566	−0.822828	+	0.568291i	$0.807605\pi$
$938$	−15.2767	−0.498803
$939$	30.6425	0.999980
$940$	43.8510	1.43026
$941$	4.33231	0.141229	0.0706146	−	0.997504i	$-0.477504\pi$
$941$	4.33231	0.141229	0.0706146	+	0.997504i	$0.477504\pi$
$942$	−27.6184	−0.899857
$943$	−11.2508	−0.366376
$944$	5.72373	0.186292
$945$	23.2467	0.756216
$946$	2.18311	0.0709792
$947$	21.6094	0.702212	0.351106	−	0.936336i	$-0.385806\pi$
$947$	21.6094	0.702212	0.351106	+	0.936336i	$0.385806\pi$
$948$	−37.9080	−1.23119
$949$	43.6667	1.41748
$950$	20.8237	0.675610
$951$	−56.3524	−1.82735
$952$	−32.3568	−1.04869
$953$	−5.54254	−0.179541	−0.0897703	−	0.995962i	$-0.528613\pi$
$953$	−5.54254	−0.179541	−0.0897703	+	0.995962i	$0.528613\pi$
$954$	6.20887	0.201020
$955$	−36.3604	−1.17660
$956$	16.9176	0.547155
$957$	0	0
$958$	−28.1410	−0.909194
$959$	−43.9725	−1.41995
$960$	6.56645	0.211931
$961$	28.5033	0.919461
$962$	−26.0376	−0.839486
$963$	−4.49311	−0.144788
$964$	18.6897	0.601955
$965$	−67.2234	−2.16400
$966$	−8.04690	−0.258905
$967$	6.25781	0.201238	0.100619	−	0.994925i	$-0.467918\pi$
$967$	6.25781	0.201238	0.100619	+	0.994925i	$0.467918\pi$
$968$	2.37373	0.0762946
$969$	−46.3265	−1.48822
$970$	17.4457	0.560147
$971$	24.2474	0.778137	0.389069	−	0.921209i	$-0.372797\pi$
$971$	24.2474	0.778137	0.389069	+	0.921209i	$0.372797\pi$
$972$	24.3490	0.780993
$973$	31.4525	1.00832
$974$	19.8949	0.637472
$975$	−67.1536	−2.15064
$976$	−15.4338	−0.494023
$977$	−31.1770	−0.997442	−0.498721	−	0.866763i	$-0.666197\pi$
$977$	−31.1770	−0.997442	−0.498721	+	0.866763i	$0.666197\pi$
$978$	6.30456	0.201598
$979$	9.99923	0.319577
$980$	13.8321	0.441851
$981$	−23.1096	−0.737833
$982$	−3.74839	−0.119616
$983$	−57.1303	−1.82217	−0.911087	−	0.412214i	$-0.864756\pi$
$983$	−57.1303	−1.82217	−0.911087	+	0.412214i	$0.864756\pi$
$984$	22.3238	0.711656
$985$	−46.8833	−1.49383
$986$	0	0
$987$	34.8647	1.10976
$988$	−17.7354	−0.564240
$989$	8.45518	0.268859
$990$	−4.21953	−0.134105
$991$	−1.42863	−0.0453820	−0.0226910	−	0.999743i	$-0.507223\pi$
$991$	−1.42863	−0.0453820	−0.0226910	+	0.999743i	$0.507223\pi$
$992$	44.4643	1.41174
$993$	−28.0301	−0.889510
$994$	−3.07140	−0.0974188
$995$	42.9126	1.36042
$996$	−19.5621	−0.619849
$997$	38.4742	1.21849	0.609244	−	0.792983i	$-0.291473\pi$
$997$	38.4742	1.21849	0.609244	+	0.792983i	$0.291473\pi$
$998$	7.11846	0.225331
$999$	33.1033	1.04734

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9251.2.a.ba.1.16	✓	40
29.28	even	2		9251.2.a.bb.1.25	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9251.2.a.ba.1.16	✓	40	1.1	even	1	trivial
9251.2.a.bb.1.25	yes	40	29.28	even	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:	\( N \)	\(=\)	\( 9251 = 11 \cdot 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9251.a (trivial)

\(f(q)\)	\(=\)	\(q-0.667928 q^{2} +2.16237 q^{3} -1.55387 q^{4} +3.76965 q^{5} -1.44431 q^{6} -2.15374 q^{7} +2.37373 q^{8} +1.67584 q^{9} +O(q^{10})\)	\(q-0.667928 q^{2} +2.16237 q^{3} -1.55387 q^{4} +3.76965 q^{5} -1.44431 q^{6} -2.15374 q^{7} +2.37373 q^{8} +1.67584 q^{9} -2.51785 q^{10} +1.00000 q^{11} -3.36005 q^{12} -3.37185 q^{13} +1.43854 q^{14} +8.15137 q^{15} +1.52226 q^{16} +6.32910 q^{17} -1.11934 q^{18} -3.38499 q^{19} -5.85755 q^{20} -4.65717 q^{21} -0.667928 q^{22} -2.58688 q^{23} +5.13289 q^{24} +9.21023 q^{25} +2.25216 q^{26} -2.86331 q^{27} +3.34663 q^{28} -5.44453 q^{30} -7.71384 q^{31} -5.76422 q^{32} +2.16237 q^{33} -4.22738 q^{34} -8.11882 q^{35} -2.60405 q^{36} -11.5612 q^{37} +2.26093 q^{38} -7.29120 q^{39} +8.94813 q^{40} +4.34917 q^{41} +3.11066 q^{42} -3.26849 q^{43} -1.55387 q^{44} +6.31734 q^{45} +1.72785 q^{46} -7.48624 q^{47} +3.29169 q^{48} -2.36142 q^{49} -6.15177 q^{50} +13.6859 q^{51} +5.23943 q^{52} -5.54688 q^{53} +1.91249 q^{54} +3.76965 q^{55} -5.11239 q^{56} -7.31961 q^{57} +3.76002 q^{59} -12.6662 q^{60} -10.1387 q^{61} +5.15229 q^{62} -3.60933 q^{63} +0.805564 q^{64} -12.7107 q^{65} -1.44431 q^{66} -10.6196 q^{67} -9.83461 q^{68} -5.59379 q^{69} +5.42279 q^{70} -2.13508 q^{71} +3.97800 q^{72} -12.9504 q^{73} +7.72204 q^{74} +19.9159 q^{75} +5.25985 q^{76} -2.15374 q^{77} +4.87000 q^{78} +11.2820 q^{79} +5.73839 q^{80} -11.2191 q^{81} -2.90493 q^{82} +5.82198 q^{83} +7.23665 q^{84} +23.8585 q^{85} +2.18311 q^{86} +2.37373 q^{88} +9.99923 q^{89} -4.21953 q^{90} +7.26209 q^{91} +4.01968 q^{92} -16.6802 q^{93} +5.00027 q^{94} -12.7602 q^{95} -12.4644 q^{96} -6.92880 q^{97} +1.57726 q^{98} +1.67584 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 5 q^{3} + 28 q^{4} - 12 q^{5} - 8 q^{6} - 15 q^{7} - 3 q^{8} + 25 q^{9}+O(q^{10}) \) 40 * q - 5 * q^3 + 28 * q^4 - 12 * q^5 - 8 * q^6 - 15 * q^7 - 3 * q^8 + 25 * q^9	\( 40 q - 5 q^{3} + 28 q^{4} - 12 q^{5} - 8 q^{6} - 15 q^{7} - 3 q^{8} + 25 q^{9} - 25 q^{10} + 40 q^{11} - 17 q^{12} - 35 q^{13} + 3 q^{14} + 15 q^{15} - 6 q^{17} + 24 q^{18} + 2 q^{19} - 6 q^{20} - 5 q^{21} + 8 q^{23} - 18 q^{24} + 20 q^{25} - 20 q^{26} + q^{27} - 50 q^{28} - 5 q^{30} - 12 q^{31} - 6 q^{32} - 5 q^{33} - 26 q^{34} - 28 q^{35} - 22 q^{36} - 17 q^{37} - 12 q^{38} - 30 q^{39} + 30 q^{40} + 9 q^{41} - 34 q^{42} + 6 q^{43} + 28 q^{44} - 89 q^{45} - 7 q^{46} - 8 q^{47} + 33 q^{48} + q^{49} + 17 q^{50} - 52 q^{51} - 65 q^{52} - 51 q^{53} + 5 q^{54} - 12 q^{55} - 4 q^{56} - 49 q^{57} - 56 q^{59} + 15 q^{60} - 39 q^{61} + 53 q^{63} - 13 q^{64} - 13 q^{65} - 8 q^{66} - 68 q^{67} - 107 q^{68} - 31 q^{69} + 51 q^{70} - 47 q^{71} + 71 q^{72} + 19 q^{73} - 54 q^{74} - 22 q^{75} + 54 q^{76} - 15 q^{77} + 28 q^{78} + 10 q^{79} + 10 q^{80} - 4 q^{81} + 34 q^{82} - 40 q^{83} + 11 q^{84} + 26 q^{85} - 46 q^{86} - 3 q^{88} + 29 q^{89} - 100 q^{90} - 50 q^{91} + 76 q^{92} - 73 q^{93} - 116 q^{94} + 5 q^{95} + 13 q^{96} - 22 q^{97} + 102 q^{98} + 25 q^{99}+O(q^{100}) \) 40 * q - 5 * q^3 + 28 * q^4 - 12 * q^5 - 8 * q^6 - 15 * q^7 - 3 * q^8 + 25 * q^9 - 25 * q^10 + 40 * q^11 - 17 * q^12 - 35 * q^13 + 3 * q^14 + 15 * q^15 - 6 * q^17 + 24 * q^18 + 2 * q^19 - 6 * q^20 - 5 * q^21 + 8 * q^23 - 18 * q^24 + 20 * q^25 - 20 * q^26 + q^27 - 50 * q^28 - 5 * q^30 - 12 * q^31 - 6 * q^32 - 5 * q^33 - 26 * q^34 - 28 * q^35 - 22 * q^36 - 17 * q^37 - 12 * q^38 - 30 * q^39 + 30 * q^40 + 9 * q^41 - 34 * q^42 + 6 * q^43 + 28 * q^44 - 89 * q^45 - 7 * q^46 - 8 * q^47 + 33 * q^48 + q^49 + 17 * q^50 - 52 * q^51 - 65 * q^52 - 51 * q^53 + 5 * q^54 - 12 * q^55 - 4 * q^56 - 49 * q^57 - 56 * q^59 + 15 * q^60 - 39 * q^61 + 53 * q^63 - 13 * q^64 - 13 * q^65 - 8 * q^66 - 68 * q^67 - 107 * q^68 - 31 * q^69 + 51 * q^70 - 47 * q^71 + 71 * q^72 + 19 * q^73 - 54 * q^74 - 22 * q^75 + 54 * q^76 - 15 * q^77 + 28 * q^78 + 10 * q^79 + 10 * q^80 - 4 * q^81 + 34 * q^82 - 40 * q^83 + 11 * q^84 + 26 * q^85 - 46 * q^86 - 3 * q^88 + 29 * q^89 - 100 * q^90 - 50 * q^91 + 76 * q^92 - 73 * q^93 - 116 * q^94 + 5 * q^95 + 13 * q^96 - 22 * q^97 + 102 * q^98 + 25 * q^99

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