LMFDB - Embedded newform 9251.2.a.ba.1.30

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			1.30
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)

$f(q)$	$=$	$q+1.54958 q^{2} +0.697690 q^{3} +0.401189 q^{4} +0.276253 q^{5} +1.08112 q^{6} +3.52600 q^{7} -2.47748 q^{8} -2.51323 q^{9} +O(q^{10})$	\(q+1.54958 q^{2} +0.697690 q^{3} +0.401189 q^{4} +0.276253 q^{5} +1.08112 q^{6} +3.52600 q^{7} -2.47748 q^{8} -2.51323 q^{9} +0.428075 q^{10} +1.00000 q^{11} +0.279906 q^{12} -2.68452 q^{13} +5.46381 q^{14} +0.192739 q^{15} -4.64143 q^{16} -1.96670 q^{17} -3.89444 q^{18} +2.84622 q^{19} +0.110830 q^{20} +2.46006 q^{21} +1.54958 q^{22} +2.68222 q^{23} -1.72851 q^{24} -4.92368 q^{25} -4.15987 q^{26} -3.84653 q^{27} +1.41459 q^{28} +0.298664 q^{30} -2.53096 q^{31} -2.23728 q^{32} +0.697690 q^{33} -3.04756 q^{34} +0.974068 q^{35} -1.00828 q^{36} -8.06709 q^{37} +4.41044 q^{38} -1.87296 q^{39} -0.684411 q^{40} +5.73621 q^{41} +3.81205 q^{42} +4.46434 q^{43} +0.401189 q^{44} -0.694286 q^{45} +4.15630 q^{46} -7.81639 q^{47} -3.23828 q^{48} +5.43269 q^{49} -7.62963 q^{50} -1.37215 q^{51} -1.07700 q^{52} -7.77185 q^{53} -5.96049 q^{54} +0.276253 q^{55} -8.73560 q^{56} +1.98578 q^{57} -2.10034 q^{59} +0.0773247 q^{60} -7.14036 q^{61} -3.92192 q^{62} -8.86165 q^{63} +5.81601 q^{64} -0.741606 q^{65} +1.08112 q^{66} +3.64682 q^{67} -0.789020 q^{68} +1.87136 q^{69} +1.50939 q^{70} +1.35885 q^{71} +6.22647 q^{72} -11.3819 q^{73} -12.5006 q^{74} -3.43521 q^{75} +1.14187 q^{76} +3.52600 q^{77} -2.90230 q^{78} +4.78156 q^{79} -1.28221 q^{80} +4.85600 q^{81} +8.88870 q^{82} -1.15086 q^{83} +0.986948 q^{84} -0.543308 q^{85} +6.91784 q^{86} -2.47748 q^{88} +4.29166 q^{89} -1.07585 q^{90} -9.46562 q^{91} +1.07608 q^{92} -1.76583 q^{93} -12.1121 q^{94} +0.786277 q^{95} -1.56093 q^{96} -1.22696 q^{97} +8.41838 q^{98} -2.51323 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.54958	1.09572	0.547858	−	0.836571i	$-0.315443\pi$
$2$	1.54958	1.09572	0.547858	+	0.836571i	$0.315443\pi$
$3$	0.697690	0.402812	0.201406	−	0.979508i	$-0.435449\pi$
$3$	0.697690	0.402812	0.201406	+	0.979508i	$0.435449\pi$
$4$	0.401189	0.200594
$5$	0.276253	0.123544	0.0617720	−	0.998090i	$-0.480325\pi$
$5$	0.276253	0.123544	0.0617720	+	0.998090i	$0.480325\pi$
$6$	1.08112	0.441367
$7$	3.52600	1.33270	0.666352	−	0.745637i	$-0.267855\pi$
$7$	3.52600	1.33270	0.666352	+	0.745637i	$0.267855\pi$
$8$	−2.47748	−0.875922
$9$	−2.51323	−0.837743
$10$	0.428075	0.135369
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.279906	0.0808018
$13$	−2.68452	−0.744551	−0.372276	−	0.928122i	$-0.621422\pi$
$13$	−2.68452	−0.744551	−0.372276	+	0.928122i	$0.621422\pi$
$14$	5.46381	1.46027
$15$	0.192739	0.0497650
$16$	−4.64143	−1.16036
$17$	−1.96670	−0.476996	−0.238498	−	0.971143i	$-0.576655\pi$
$17$	−1.96670	−0.476996	−0.238498	+	0.971143i	$0.576655\pi$
$18$	−3.89444	−0.917928
$19$	2.84622	0.652968	0.326484	−	0.945203i	$-0.394136\pi$
$19$	2.84622	0.652968	0.326484	+	0.945203i	$0.394136\pi$
$20$	0.110830	0.0247822
$21$	2.46006	0.536829
$22$	1.54958	0.330371
$23$	2.68222	0.559281	0.279640	−	0.960105i	$-0.409785\pi$
$23$	2.68222	0.559281	0.279640	+	0.960105i	$0.409785\pi$
$24$	−1.72851	−0.352832
$25$	−4.92368	−0.984737
$26$	−4.15987	−0.815817
$27$	−3.84653	−0.740264
$28$	1.41459	0.267333
$29$	0	0
$29$	0	0
$30$	0.298664	0.0545283
$31$	−2.53096	−0.454574	−0.227287	−	0.973828i	$-0.572986\pi$
$31$	−2.53096	−0.454574	−0.227287	+	0.973828i	$0.572986\pi$
$32$	−2.23728	−0.395500
$33$	0.697690	0.121452
$34$	−3.04756	−0.522652
$35$	0.974068	0.164648
$36$	−1.00828	−0.168047
$37$	−8.06709	−1.32622	−0.663111	−	0.748521i	$-0.730764\pi$
$37$	−8.06709	−1.32622	−0.663111	+	0.748521i	$0.730764\pi$
$38$	4.41044	0.715468
$39$	−1.87296	−0.299914
$40$	−0.684411	−0.108215
$41$	5.73621	0.895845	0.447923	−	0.894072i	$-0.352164\pi$
$41$	5.73621	0.895845	0.447923	+	0.894072i	$0.352164\pi$
$42$	3.81205	0.588212
$43$	4.46434	0.680806	0.340403	−	0.940280i	$-0.389437\pi$
$43$	4.46434	0.680806	0.340403	+	0.940280i	$0.389437\pi$
$44$	0.401189	0.0604815
$45$	−0.694286	−0.103498
$46$	4.15630	0.612813
$47$	−7.81639	−1.14014	−0.570069	−	0.821597i	$-0.693084\pi$
$47$	−7.81639	−1.14014	−0.570069	+	0.821597i	$0.693084\pi$
$48$	−3.23828	−0.467405
$49$	5.43269	0.776099
$50$	−7.62963	−1.07899
$51$	−1.37215	−0.192140
$52$	−1.07700	−0.149353
$53$	−7.77185	−1.06755	−0.533773	−	0.845628i	$-0.679226\pi$
$53$	−7.77185	−1.06755	−0.533773	+	0.845628i	$0.679226\pi$
$54$	−5.96049	−0.811120
$55$	0.276253	0.0372499
$56$	−8.73560	−1.16734
$57$	1.98578	0.263023
$58$	0	0
$59$	−2.10034	−0.273442	−0.136721	−	0.990610i	$-0.543656\pi$
$59$	−2.10034	−0.273442	−0.136721	+	0.990610i	$0.543656\pi$
$60$	0.0773247	0.00998258
$61$	−7.14036	−0.914230	−0.457115	−	0.889408i	$-0.651117\pi$
$61$	−7.14036	−0.914230	−0.457115	+	0.889408i	$0.651117\pi$
$62$	−3.92192	−0.498085
$63$	−8.86165	−1.11646
$64$	5.81601	0.727001
$65$	−0.741606	−0.0919849
$66$	1.08112	0.133077
$67$	3.64682	0.445530	0.222765	−	0.974872i	$-0.428492\pi$
$67$	3.64682	0.445530	0.222765	+	0.974872i	$0.428492\pi$
$68$	−0.789020	−0.0956827
$69$	1.87136	0.225285
$70$	1.50939	0.180407
$71$	1.35885	0.161266	0.0806330	−	0.996744i	$-0.474306\pi$
$71$	1.35885	0.161266	0.0806330	+	0.996744i	$0.474306\pi$
$72$	6.22647	0.733797
$73$	−11.3819	−1.33215	−0.666073	−	0.745887i	$-0.732026\pi$
$73$	−11.3819	−1.33215	−0.666073	+	0.745887i	$0.732026\pi$
$74$	−12.5006	−1.45316
$75$	−3.43521	−0.396664
$76$	1.14187	0.130982
$77$	3.52600	0.401825
$78$	−2.90230	−0.328621
$79$	4.78156	0.537967	0.268984	−	0.963145i	$-0.413312\pi$
$79$	4.78156	0.537967	0.268984	+	0.963145i	$0.413312\pi$
$80$	−1.28221	−0.143355
$81$	4.85600	0.539556
$82$	8.88870	0.981592
$83$	−1.15086	−0.126323	−0.0631616	−	0.998003i	$-0.520118\pi$
$83$	−1.15086	−0.126323	−0.0631616	+	0.998003i	$0.520118\pi$
$84$	0.986948	0.107685
$85$	−0.543308	−0.0589300
$86$	6.91784	0.745970
$87$	0	0
$88$	−2.47748	−0.264100
$89$	4.29166	0.454915	0.227457	−	0.973788i	$-0.426959\pi$
$89$	4.29166	0.454915	0.227457	+	0.973788i	$0.426959\pi$
$90$	−1.07585	−0.113405
$91$	−9.46562	−0.992266
$92$	1.07608	0.112189
$93$	−1.76583	−0.183108
$94$	−12.1121	−1.24927
$95$	0.786277	0.0806704
$96$	−1.56093	−0.159312
$97$	−1.22696	−0.124579	−0.0622897	−	0.998058i	$-0.519840\pi$
$97$	−1.22696	−0.124579	−0.0622897	+	0.998058i	$0.519840\pi$
$98$	8.41838	0.850385
$99$	−2.51323	−0.252589
$100$	−1.97533	−0.197533
$101$	−11.8135	−1.17549	−0.587743	−	0.809048i	$-0.699983\pi$
$101$	−11.8135	−1.17549	−0.587743	+	0.809048i	$0.699983\pi$
$102$	−2.12625	−0.210530
$103$	−14.3958	−1.41846	−0.709231	−	0.704976i	$-0.750958\pi$
$103$	−14.3958	−1.41846	−0.709231	+	0.704976i	$0.750958\pi$
$104$	6.65084	0.652169
$105$	0.679598	0.0663220
$106$	−12.0431	−1.16973
$107$	−7.10073	−0.686454	−0.343227	−	0.939253i	$-0.611520\pi$
$107$	−7.10073	−0.686454	−0.343227	+	0.939253i	$0.611520\pi$
$108$	−1.54318	−0.148493
$109$	−11.1627	−1.06919	−0.534596	−	0.845108i	$-0.679536\pi$
$109$	−11.1627	−1.06919	−0.534596	+	0.845108i	$0.679536\pi$
$110$	0.428075	0.0408154
$111$	−5.62833	−0.534218
$112$	−16.3657	−1.54641
$113$	16.2911	1.53254	0.766269	−	0.642519i	$-0.222111\pi$
$113$	16.2911	1.53254	0.766269	+	0.642519i	$0.222111\pi$
$114$	3.07712	0.288199
$115$	0.740970	0.0690958
$116$	0	0
$117$	6.74681	0.623743
$118$	−3.25465	−0.299614
$119$	−6.93461	−0.635694
$120$	−0.477507	−0.0435902
$121$	1.00000	0.0909091
$122$	−11.0645	−1.00174
$123$	4.00210	0.360857
$124$	−1.01539	−0.0911851
$125$	−2.74145	−0.245202
$126$	−13.7318	−1.22333
$127$	5.97297	0.530016	0.265008	−	0.964246i	$-0.414625\pi$
$127$	5.97297	0.530016	0.265008	+	0.964246i	$0.414625\pi$
$128$	13.4869	1.19209
$129$	3.11473	0.274237
$130$	−1.14918	−0.100789
$131$	−15.4872	−1.35312	−0.676560	−	0.736388i	$-0.736530\pi$
$131$	−15.4872	−1.35312	−0.676560	+	0.736388i	$0.736530\pi$
$132$	0.279906	0.0243627
$133$	10.0358	0.870214
$134$	5.65103	0.488175
$135$	−1.06261	−0.0914552
$136$	4.87247	0.417811
$137$	−2.66853	−0.227988	−0.113994	−	0.993481i	$-0.536364\pi$
$137$	−2.66853	−0.227988	−0.113994	+	0.993481i	$0.536364\pi$
$138$	2.89981	0.246848
$139$	20.1621	1.71013	0.855064	−	0.518522i	$-0.173518\pi$
$139$	20.1621	1.71013	0.855064	+	0.518522i	$0.173518\pi$
$140$	0.390785	0.0330274
$141$	−5.45342	−0.459261
$142$	2.10565	0.176702
$143$	−2.68452	−0.224491
$144$	11.6650	0.972080
$145$	0	0
$146$	−17.6371	−1.45965
$147$	3.79034	0.312622
$148$	−3.23643	−0.266033
$149$	−6.42098	−0.526027	−0.263013	−	0.964792i	$-0.584716\pi$
$149$	−6.42098	−0.526027	−0.263013	+	0.964792i	$0.584716\pi$
$150$	−5.32312	−0.434631
$151$	−8.01243	−0.652042	−0.326021	−	0.945363i	$-0.605708\pi$
$151$	−8.01243	−0.652042	−0.326021	+	0.945363i	$0.605708\pi$
$152$	−7.05146	−0.571949
$153$	4.94278	0.399600
$154$	5.46381	0.440287
$155$	−0.699186	−0.0561600
$156$	−0.751412	−0.0601611
$157$	−22.9087	−1.82831	−0.914157	−	0.405360i	$-0.867146\pi$
$157$	−22.9087	−1.82831	−0.914157	+	0.405360i	$0.867146\pi$
$158$	7.40939	0.589460
$159$	−5.42234	−0.430020
$160$	−0.618056	−0.0488616
$161$	9.45750	0.745355
$162$	7.52475	0.591200
$163$	7.45658	0.584045	0.292022	−	0.956411i	$-0.405672\pi$
$163$	7.45658	0.584045	0.292022	+	0.956411i	$0.405672\pi$
$164$	2.30130	0.179702
$165$	0.192739	0.0150047
$166$	−1.78334	−0.138414
$167$	−8.77357	−0.678919	−0.339459	−	0.940621i	$-0.610244\pi$
$167$	−8.77357	−0.678919	−0.339459	+	0.940621i	$0.610244\pi$
$168$	−6.09475	−0.470220
$169$	−5.79336	−0.445643
$170$	−0.841897	−0.0645706
$171$	−7.15321	−0.547020
$172$	1.79104	0.136566
$173$	−15.8629	−1.20604	−0.603018	−	0.797728i	$-0.706035\pi$
$173$	−15.8629	−1.20604	−0.603018	+	0.797728i	$0.706035\pi$
$174$	0	0
$175$	−17.3609	−1.31236
$176$	−4.64143	−0.349861
$177$	−1.46539	−0.110145
$178$	6.65025	0.498458
$179$	−18.0853	−1.35176	−0.675878	−	0.737013i	$-0.736236\pi$
$179$	−18.0853	−1.35176	−0.675878	+	0.737013i	$0.736236\pi$
$180$	−0.278540	−0.0207611
$181$	20.4731	1.52176	0.760878	−	0.648895i	$-0.224769\pi$
$181$	20.4731	1.52176	0.760878	+	0.648895i	$0.224769\pi$
$182$	−14.6677	−1.08724
$183$	−4.98176	−0.368262
$184$	−6.64514	−0.489886
$185$	−2.22856	−0.163847
$186$	−2.73629	−0.200634
$187$	−1.96670	−0.143820
$188$	−3.13585	−0.228705
$189$	−13.5629	−0.986553
$190$	1.21840	0.0883918
$191$	26.5688	1.92245	0.961224	−	0.275770i	$-0.0889327\pi$
$191$	26.5688	1.92245	0.961224	+	0.275770i	$0.0889327\pi$
$192$	4.05777	0.292844
$193$	20.5299	1.47777	0.738887	−	0.673829i	$-0.235352\pi$
$193$	20.5299	1.47777	0.738887	+	0.673829i	$0.235352\pi$
$194$	−1.90127	−0.136504
$195$	−0.517411	−0.0370526
$196$	2.17954	0.155681
$197$	−14.4142	−1.02697	−0.513484	−	0.858099i	$-0.671645\pi$
$197$	−14.4142	−1.02697	−0.513484	+	0.858099i	$0.671645\pi$
$198$	−3.89444	−0.276766
$199$	−7.79514	−0.552583	−0.276292	−	0.961074i	$-0.589106\pi$
$199$	−7.79514	−0.552583	−0.276292	+	0.961074i	$0.589106\pi$
$200$	12.1983	0.862552
$201$	2.54435	0.179465
$202$	−18.3059	−1.28800
$203$	0	0
$204$	−0.550492	−0.0385421
$205$	1.58464	0.110676
$206$	−22.3074	−1.55423
$207$	−6.74102	−0.468533
$208$	12.4600	0.863945
$209$	2.84622	0.196877
$210$	1.05309	0.0726701
$211$	−13.7616	−0.947389	−0.473694	−	0.880689i	$-0.657080\pi$
$211$	−13.7616	−0.947389	−0.473694	+	0.880689i	$0.657080\pi$
$212$	−3.11798	−0.214144
$213$	0.948058	0.0649599
$214$	−11.0031	−0.752158
$215$	1.23329	0.0841095
$216$	9.52969	0.648414
$217$	−8.92418	−0.605813
$218$	−17.2975	−1.17153
$219$	−7.94101	−0.536604
$220$	0.110830	0.00747213
$221$	5.27965	0.355148
$222$	−8.72154	−0.585351
$223$	3.18169	0.213061	0.106531	−	0.994309i	$-0.466026\pi$
$223$	3.18169	0.213061	0.106531	+	0.994309i	$0.466026\pi$
$224$	−7.88867	−0.527084
$225$	12.3743	0.824956
$226$	25.2443	1.67923
$227$	−19.1109	−1.26843	−0.634216	−	0.773156i	$-0.718677\pi$
$227$	−19.1109	−1.26843	−0.634216	+	0.773156i	$0.718677\pi$
$228$	0.796674	0.0527610
$229$	23.1964	1.53286	0.766431	−	0.642327i	$-0.222031\pi$
$229$	23.1964	1.53286	0.766431	+	0.642327i	$0.222031\pi$
$230$	1.14819	0.0757094
$231$	2.46006	0.161860
$232$	0	0
$233$	20.7639	1.36029	0.680145	−	0.733078i	$-0.261917\pi$
$233$	20.7639	1.36029	0.680145	+	0.733078i	$0.261917\pi$
$234$	10.4547	0.683445
$235$	−2.15930	−0.140857
$236$	−0.842635	−0.0548509
$237$	3.33605	0.216700
$238$	−10.7457	−0.696541
$239$	20.9171	1.35301	0.676506	−	0.736437i	$-0.263493\pi$
$239$	20.9171	1.35301	0.676506	+	0.736437i	$0.263493\pi$
$240$	−0.894583	−0.0577451
$241$	5.71465	0.368113	0.184057	−	0.982916i	$-0.441077\pi$
$241$	5.71465	0.368113	0.184057	+	0.982916i	$0.441077\pi$
$242$	1.54958	0.0996106
$243$	14.9276	0.957604
$244$	−2.86463	−0.183389
$245$	1.50080	0.0958824
$246$	6.20156	0.395397
$247$	−7.64074	−0.486169
$248$	6.27041	0.398172
$249$	−0.802943	−0.0508845
$250$	−4.24808	−0.268672
$251$	−2.00135	−0.126324	−0.0631622	−	0.998003i	$-0.520119\pi$
$251$	−2.00135	−0.126324	−0.0631622	+	0.998003i	$0.520119\pi$
$252$	−3.55520	−0.223956
$253$	2.68222	0.168629
$254$	9.25558	0.580747
$255$	−0.379061	−0.0237377
$256$	9.26701	0.579188
$257$	29.8402	1.86138	0.930689	−	0.365811i	$-0.119208\pi$
$257$	29.8402	1.86138	0.930689	+	0.365811i	$0.119208\pi$
$258$	4.82651	0.300486
$259$	−28.4446	−1.76746
$260$	−0.297524	−0.0184517
$261$	0	0
$262$	−23.9986	−1.48264
$263$	−23.7705	−1.46575	−0.732875	−	0.680363i	$-0.761822\pi$
$263$	−23.7705	−1.46575	−0.732875	+	0.680363i	$0.761822\pi$
$264$	−1.72851	−0.106383
$265$	−2.14699	−0.131889
$266$	15.5512	0.953507
$267$	2.99425	0.183245
$268$	1.46306	0.0893709
$269$	−19.4934	−1.18853	−0.594267	−	0.804268i	$-0.702558\pi$
$269$	−19.4934	−1.18853	−0.594267	+	0.804268i	$0.702558\pi$
$270$	−1.64660	−0.100209
$271$	−9.24227	−0.561428	−0.280714	−	0.959791i	$-0.590571\pi$
$271$	−9.24227	−0.561428	−0.280714	+	0.959791i	$0.590571\pi$
$272$	9.12831	0.553485
$273$	−6.60407	−0.399696
$274$	−4.13510	−0.249810
$275$	−4.92368	−0.296909
$276$	0.750767	0.0451909
$277$	−13.9334	−0.837177	−0.418588	−	0.908176i	$-0.637475\pi$
$277$	−13.9334	−0.837177	−0.418588	+	0.908176i	$0.637475\pi$
$278$	31.2428	1.87382
$279$	6.36089	0.380816
$280$	−2.41324	−0.144218
$281$	10.2565	0.611850	0.305925	−	0.952056i	$-0.401034\pi$
$281$	10.2565	0.611850	0.305925	+	0.952056i	$0.401034\pi$
$282$	−8.45050	−0.503220
$283$	3.20477	0.190504	0.0952518	−	0.995453i	$-0.469634\pi$
$283$	3.20477	0.190504	0.0952518	+	0.995453i	$0.469634\pi$
$284$	0.545156	0.0323491
$285$	0.548578	0.0324950
$286$	−4.15987	−0.245978
$287$	20.2259	1.19390
$288$	5.62281	0.331327
$289$	−13.1321	−0.772475
$290$	0	0
$291$	−0.856041	−0.0501820
$292$	−4.56627	−0.267221
$293$	−24.1122	−1.40865	−0.704324	−	0.709879i	$-0.748750\pi$
$293$	−24.1122	−1.40865	−0.704324	+	0.709879i	$0.748750\pi$
$294$	5.87342	0.342545
$295$	−0.580226	−0.0337821
$296$	19.9861	1.16167
$297$	−3.84653	−0.223198
$298$	−9.94980	−0.576376
$299$	−7.20046	−0.416413
$300$	−1.37817	−0.0795685
$301$	15.7413	0.907313
$302$	−12.4159	−0.714453
$303$	−8.24215	−0.473499
$304$	−13.2105	−0.757676
$305$	−1.97255	−0.112948
$306$	7.65921	0.437848
$307$	12.4571	0.710962	0.355481	−	0.934683i	$-0.384317\pi$
$307$	12.4571	0.710962	0.355481	+	0.934683i	$0.384317\pi$
$308$	1.41459	0.0806039
$309$	−10.0438	−0.571373
$310$	−1.08344	−0.0615354
$311$	−23.2682	−1.31942	−0.659709	−	0.751521i	$-0.729321\pi$
$311$	−23.2682	−1.31942	−0.659709	+	0.751521i	$0.729321\pi$
$312$	4.64023	0.262701
$313$	−4.21977	−0.238516	−0.119258	−	0.992863i	$-0.538052\pi$
$313$	−4.21977	−0.238516	−0.119258	+	0.992863i	$0.538052\pi$
$314$	−35.4988	−2.00331
$315$	−2.44806	−0.137932
$316$	1.91831	0.107913
$317$	−14.3829	−0.807824	−0.403912	−	0.914798i	$-0.632350\pi$
$317$	−14.3829	−0.807824	−0.403912	+	0.914798i	$0.632350\pi$
$318$	−8.40234	−0.471180
$319$	0	0
$320$	1.60669	0.0898166
$321$	−4.95411	−0.276512
$322$	14.6551	0.816698
$323$	−5.59768	−0.311463
$324$	1.94817	0.108232
$325$	13.2177	0.733187
$326$	11.5546	0.639947
$327$	−7.78810	−0.430683
$328$	−14.2113	−0.784690
$329$	−27.5606	−1.51947
$330$	0.298664	0.0164409
$331$	−6.16974	−0.339119	−0.169560	−	0.985520i	$-0.554235\pi$
$331$	−6.16974	−0.339119	−0.169560	+	0.985520i	$0.554235\pi$
$332$	−0.461712	−0.0253397
$333$	20.2744	1.11103
$334$	−13.5953	−0.743903
$335$	1.00744	0.0550426
$336$	−11.4182	−0.622912
$337$	24.9918	1.36139	0.680694	−	0.732568i	$-0.261678\pi$
$337$	24.9918	1.36139	0.680694	+	0.732568i	$0.261678\pi$
$338$	−8.97726	−0.488299
$339$	11.3661	0.617325
$340$	−0.217969	−0.0118210
$341$	−2.53096	−0.137059
$342$	−11.0844	−0.599378
$343$	−5.52633	−0.298394
$344$	−11.0603	−0.596333
$345$	0.516967	0.0278326
$346$	−24.5808	−1.32147
$347$	−3.57510	−0.191921	−0.0959607	−	0.995385i	$-0.530592\pi$
$347$	−3.57510	−0.191921	−0.0959607	+	0.995385i	$0.530592\pi$
$348$	0	0
$349$	14.8201	0.793303	0.396651	−	0.917969i	$-0.370172\pi$
$349$	14.8201	0.793303	0.396651	+	0.917969i	$0.370172\pi$
$350$	−26.9021	−1.43798
$351$	10.3261	0.551165
$352$	−2.23728	−0.119248
$353$	−0.199558	−0.0106214	−0.00531070	−	0.999986i	$-0.501690\pi$
$353$	−0.199558	−0.0106214	−0.00531070	+	0.999986i	$0.501690\pi$
$354$	−2.27074	−0.120688
$355$	0.375387	0.0199235
$356$	1.72177	0.0912534
$357$	−4.83821	−0.256065
$358$	−28.0245	−1.48114
$359$	−19.5569	−1.03217	−0.516087	−	0.856536i	$-0.672612\pi$
$359$	−19.5569	−1.03217	−0.516087	+	0.856536i	$0.672612\pi$
$360$	1.72008	0.0906563
$361$	−10.8990	−0.573632
$362$	31.7247	1.66741
$363$	0.697690	0.0366192
$364$	−3.79750	−0.199043
$365$	−3.14427	−0.164579
$366$	−7.71962	−0.403511
$367$	21.4801	1.12125	0.560626	−	0.828069i	$-0.310561\pi$
$367$	21.4801	1.12125	0.560626	+	0.828069i	$0.310561\pi$
$368$	−12.4493	−0.648965
$369$	−14.4164	−0.750488
$370$	−3.45332	−0.179530
$371$	−27.4035	−1.42272
$372$	−0.708431	−0.0367304
$373$	−25.8364	−1.33776	−0.668880	−	0.743370i	$-0.733226\pi$
$373$	−25.8364	−1.33776	−0.668880	+	0.743370i	$0.733226\pi$
$374$	−3.04756	−0.157586
$375$	−1.91268	−0.0987704
$376$	19.3650	0.998672
$377$	0	0
$378$	−21.0167	−1.08098
$379$	30.3678	1.55989	0.779944	−	0.625849i	$-0.215248\pi$
$379$	30.3678	1.55989	0.779944	+	0.625849i	$0.215248\pi$
$380$	0.315446	0.0161820
$381$	4.16728	0.213496
$382$	41.1703	2.10646
$383$	7.90683	0.404020	0.202010	−	0.979383i	$-0.435253\pi$
$383$	7.90683	0.404020	0.202010	+	0.979383i	$0.435253\pi$
$384$	9.40969	0.480186
$385$	0.974068	0.0496431
$386$	31.8127	1.61922
$387$	−11.2199	−0.570340
$388$	−0.492244	−0.0249899
$389$	24.7669	1.25573	0.627865	−	0.778322i	$-0.283929\pi$
$389$	24.7669	1.25573	0.627865	+	0.778322i	$0.283929\pi$
$390$	−0.801768	−0.0405991
$391$	−5.27512	−0.266775
$392$	−13.4594	−0.679802
$393$	−10.8052	−0.545052
$394$	−22.3359	−1.12527
$395$	1.32092	0.0664627
$396$	−1.00828	−0.0506679
$397$	36.1336	1.81349	0.906746	−	0.421677i	$-0.138558\pi$
$397$	36.1336	1.81349	0.906746	+	0.421677i	$0.138558\pi$
$398$	−12.0792	−0.605474
$399$	7.00187	0.350532
$400$	22.8529	1.14265
$401$	−2.13871	−0.106802	−0.0534010	−	0.998573i	$-0.517006\pi$
$401$	−2.13871	−0.106802	−0.0534010	+	0.998573i	$0.517006\pi$
$402$	3.94267	0.196642
$403$	6.79442	0.338454
$404$	−4.73944	−0.235796
$405$	1.34148	0.0666589
$406$	0	0
$407$	−8.06709	−0.399871
$408$	3.39948	0.168299
$409$	−15.7488	−0.778727	−0.389363	−	0.921084i	$-0.627305\pi$
$409$	−15.7488	−0.778727	−0.389363	+	0.921084i	$0.627305\pi$
$410$	2.45553	0.121270
$411$	−1.86181	−0.0918363
$412$	−5.77544	−0.284536
$413$	−7.40582	−0.364417
$414$	−10.4457	−0.513380
$415$	−0.317928	−0.0156065
$416$	6.00603	0.294470
$417$	14.0669	0.688860
$418$	4.41044	0.215722
$419$	10.5317	0.514506	0.257253	−	0.966344i	$-0.417183\pi$
$419$	10.5317	0.514506	0.257253	+	0.966344i	$0.417183\pi$
$420$	0.272647	0.0133038
$421$	6.43433	0.313590	0.156795	−	0.987631i	$-0.449884\pi$
$421$	6.43433	0.313590	0.156795	+	0.987631i	$0.449884\pi$
$422$	−21.3247	−1.03807
$423$	19.6444	0.955143
$424$	19.2546	0.935086
$425$	9.68343	0.469715
$426$	1.46909	0.0711776
$427$	−25.1769	−1.21840
$428$	−2.84873	−0.137699
$429$	−1.87296	−0.0904275
$430$	1.91107	0.0921602
$431$	−5.64929	−0.272117	−0.136058	−	0.990701i	$-0.543443\pi$
$431$	−5.64929	−0.272117	−0.136058	+	0.990701i	$0.543443\pi$
$432$	17.8534	0.858970
$433$	32.2302	1.54889	0.774443	−	0.632643i	$-0.218030\pi$
$433$	32.2302	1.54889	0.774443	+	0.632643i	$0.218030\pi$
$434$	−13.8287	−0.663799
$435$	0	0
$436$	−4.47835	−0.214474
$437$	7.63418	0.365193
$438$	−12.3052	−0.587966
$439$	−23.3608	−1.11495	−0.557474	−	0.830194i	$-0.688230\pi$
$439$	−23.3608	−1.11495	−0.557474	+	0.830194i	$0.688230\pi$
$440$	−0.684411	−0.0326280
$441$	−13.6536	−0.650171
$442$	8.18123	0.389141
$443$	18.2902	0.868992	0.434496	−	0.900674i	$-0.356927\pi$
$443$	18.2902	0.868992	0.434496	+	0.900674i	$0.356927\pi$
$444$	−2.25802	−0.107161
$445$	1.18558	0.0562020
$446$	4.93027	0.233455
$447$	−4.47985	−0.211890
$448$	20.5073	0.968877
$449$	−22.0927	−1.04262	−0.521310	−	0.853368i	$-0.674556\pi$
$449$	−22.0927	−1.04262	−0.521310	+	0.853368i	$0.674556\pi$
$450$	19.1750	0.903918
$451$	5.73621	0.270107
$452$	6.53581	0.307419
$453$	−5.59019	−0.262650
$454$	−29.6138	−1.38984
$455$	−2.61490	−0.122589
$456$	−4.91974	−0.230388
$457$	32.1003	1.50159	0.750793	−	0.660537i	$-0.229671\pi$
$457$	32.1003	1.50159	0.750793	+	0.660537i	$0.229671\pi$
$458$	35.9446	1.67958
$459$	7.56498	0.353103
$460$	0.297269	0.0138602
$461$	−21.8188	−1.01620	−0.508101	−	0.861298i	$-0.669652\pi$
$461$	−21.8188	−1.01620	−0.508101	+	0.861298i	$0.669652\pi$
$462$	3.81205	0.177353
$463$	14.0917	0.654898	0.327449	−	0.944869i	$-0.393811\pi$
$463$	14.0917	0.654898	0.327449	+	0.944869i	$0.393811\pi$
$464$	0	0
$465$	−0.487815	−0.0226219
$466$	32.1753	1.49049
$467$	−1.56002	−0.0721892	−0.0360946	−	0.999348i	$-0.511492\pi$
$467$	−1.56002	−0.0721892	−0.0360946	+	0.999348i	$0.511492\pi$
$468$	2.70674	0.125119
$469$	12.8587	0.593760
$470$	−3.34600	−0.154340
$471$	−15.9832	−0.736466
$472$	5.20356	0.239513
$473$	4.46434	0.205271
$474$	5.16946	0.237441
$475$	−14.0139	−0.643002
$476$	−2.78209	−0.127517
$477$	19.5324	0.894328
$478$	32.4126	1.48252
$479$	−3.57295	−0.163252	−0.0816260	−	0.996663i	$-0.526011\pi$
$479$	−3.57295	−0.163252	−0.0816260	+	0.996663i	$0.526011\pi$
$480$	−0.431212	−0.0196820
$481$	21.6563	0.987440
$482$	8.85529	0.403347
$483$	6.59840	0.300238
$484$	0.401189	0.0182359
$485$	−0.338952	−0.0153910
$486$	23.1314	1.04926
$487$	−40.5580	−1.83786	−0.918929	−	0.394423i	$-0.870944\pi$
$487$	−40.5580	−1.83786	−0.918929	+	0.394423i	$0.870944\pi$
$488$	17.6901	0.800794
$489$	5.20239	0.235260
$490$	2.32560	0.105060
$491$	39.3437	1.77556	0.887779	−	0.460271i	$-0.152248\pi$
$491$	39.3437	1.77556	0.887779	+	0.460271i	$0.152248\pi$
$492$	1.60560	0.0723859
$493$	0	0
$494$	−11.8399	−0.532703
$495$	−0.694286	−0.0312059
$496$	11.7473	0.527468
$497$	4.79132	0.214920
$498$	−1.24422	−0.0557549
$499$	−21.7506	−0.973690	−0.486845	−	0.873488i	$-0.661852\pi$
$499$	−21.7506	−0.973690	−0.486845	+	0.873488i	$0.661852\pi$
$500$	−1.09984	−0.0491862
$501$	−6.12123	−0.273476
$502$	−3.10125	−0.138416
$503$	−0.460296	−0.0205236	−0.0102618	−	0.999947i	$-0.503266\pi$
$503$	−0.460296	−0.0205236	−0.0102618	+	0.999947i	$0.503266\pi$
$504$	21.9546	0.977934
$505$	−3.26351	−0.145224
$506$	4.15630	0.184770
$507$	−4.04197	−0.179510
$508$	2.39629	0.106318
$509$	−21.7892	−0.965791	−0.482895	−	0.875678i	$-0.660415\pi$
$509$	−21.7892	−0.965791	−0.482895	+	0.875678i	$0.660415\pi$
$510$	−0.587384	−0.0260098
$511$	−40.1325	−1.77536
$512$	−12.6139	−0.557461
$513$	−10.9481	−0.483369
$514$	46.2396	2.03954
$515$	−3.97688	−0.175242
$516$	1.24959	0.0550103
$517$	−7.81639	−0.343765
$518$	−44.0771	−1.93664
$519$	−11.0674	−0.485805
$520$	1.83731	0.0805716
$521$	7.85320	0.344055	0.172028	−	0.985092i	$-0.444968\pi$
$521$	7.85320	0.344055	0.172028	+	0.985092i	$0.444968\pi$
$522$	0	0
$523$	11.8452	0.517955	0.258978	−	0.965883i	$-0.416614\pi$
$523$	11.8452	0.517955	0.258978	+	0.965883i	$0.416614\pi$
$524$	−6.21328	−0.271428
$525$	−12.1125	−0.528635
$526$	−36.8342	−1.60605
$527$	4.97766	0.216830
$528$	−3.23828	−0.140928
$529$	−15.8057	−0.687205
$530$	−3.32693	−0.144513
$531$	5.27865	0.229074
$532$	4.02625	0.174560
$533$	−15.3990	−0.667003
$534$	4.63982	0.200785
$535$	−1.96160	−0.0848072
$536$	−9.03493	−0.390249
$537$	−12.6179	−0.544503
$538$	−30.2065	−1.30230
$539$	5.43269	0.234003
$540$	−0.426309	−0.0183454
$541$	5.88265	0.252915	0.126458	−	0.991972i	$-0.459639\pi$
$541$	5.88265	0.252915	0.126458	+	0.991972i	$0.459639\pi$
$542$	−14.3216	−0.615166
$543$	14.2839	0.612981
$544$	4.40008	0.188652
$545$	−3.08373	−0.132092
$546$	−10.2335	−0.437954
$547$	−24.9299	−1.06592	−0.532962	−	0.846139i	$-0.678921\pi$
$547$	−24.9299	−1.06592	−0.532962	+	0.846139i	$0.678921\pi$
$548$	−1.07059	−0.0457332
$549$	17.9454	0.765889
$550$	−7.62963	−0.325328
$551$	0	0
$552$	−4.63625	−0.197332
$553$	16.8598	0.716951
$554$	−21.5909	−0.917308
$555$	−1.55484	−0.0659994
$556$	8.08882	0.343042
$557$	2.85168	0.120830	0.0604148	−	0.998173i	$-0.480758\pi$
$557$	2.85168	0.120830	0.0604148	+	0.998173i	$0.480758\pi$
$558$	9.85669	0.417267
$559$	−11.9846	−0.506895
$560$	−4.52107	−0.191050
$561$	−1.37215	−0.0579322
$562$	15.8932	0.670414
$563$	44.4570	1.87364	0.936819	−	0.349813i	$-0.113755\pi$
$563$	44.4570	1.87364	0.936819	+	0.349813i	$0.113755\pi$
$564$	−2.18785	−0.0921252
$565$	4.50047	0.189336
$566$	4.96603	0.208738
$567$	17.1223	0.719068
$568$	−3.36653	−0.141256
$569$	6.55899	0.274967	0.137484	−	0.990504i	$-0.456099\pi$
$569$	6.55899	0.274967	0.137484	+	0.990504i	$0.456099\pi$
$570$	0.850064	0.0356053
$571$	−19.4152	−0.812499	−0.406250	−	0.913762i	$-0.633164\pi$
$571$	−19.4152	−0.812499	−0.406250	+	0.913762i	$0.633164\pi$
$572$	−1.07700	−0.0450316
$573$	18.5368	0.774384
$574$	31.3416	1.30817
$575$	−13.2064	−0.550744
$576$	−14.6170	−0.609040
$577$	25.4286	1.05861	0.529303	−	0.848433i	$-0.322454\pi$
$577$	25.4286	1.05861	0.529303	+	0.848433i	$0.322454\pi$
$578$	−20.3492	−0.846413
$579$	14.3235	0.595265
$580$	0	0
$581$	−4.05793	−0.168351
$582$	−1.32650	−0.0549852
$583$	−7.77185	−0.321877
$584$	28.1983	1.16686
$585$	1.86382	0.0770597
$586$	−37.3637	−1.54348
$587$	−13.3539	−0.551175	−0.275588	−	0.961276i	$-0.588872\pi$
$587$	−13.3539	−0.551175	−0.275588	+	0.961276i	$0.588872\pi$
$588$	1.52064	0.0627102
$589$	−7.20369	−0.296823
$590$	−0.899105	−0.0370156
$591$	−10.0566	−0.413675
$592$	37.4428	1.53889
$593$	4.79007	0.196705	0.0983524	−	0.995152i	$-0.468643\pi$
$593$	4.79007	0.196705	0.0983524	+	0.995152i	$0.468643\pi$
$594$	−5.96049	−0.244562
$595$	−1.91570	−0.0785362
$596$	−2.57602	−0.105518
$597$	−5.43860	−0.222587
$598$	−11.1577	−0.456271
$599$	−7.64483	−0.312359	−0.156180	−	0.987729i	$-0.549918\pi$
$599$	−7.64483	−0.312359	−0.156180	+	0.987729i	$0.549918\pi$
$600$	8.51066	0.347446
$601$	12.7574	0.520385	0.260192	−	0.965557i	$-0.416214\pi$
$601$	12.7574	0.520385	0.260192	+	0.965557i	$0.416214\pi$
$602$	24.3923	0.994157
$603$	−9.16529	−0.373240
$604$	−3.21450	−0.130796
$605$	0.276253	0.0112313
$606$	−12.7718	−0.518821
$607$	−11.8866	−0.482464	−0.241232	−	0.970467i	$-0.577552\pi$
$607$	−11.8866	−0.482464	−0.241232	+	0.970467i	$0.577552\pi$
$608$	−6.36781	−0.258249
$609$	0	0
$610$	−3.05661	−0.123759
$611$	20.9833	0.848891
$612$	1.98299	0.0801575
$613$	4.40816	0.178044	0.0890219	−	0.996030i	$-0.471626\pi$
$613$	4.40816	0.178044	0.0890219	+	0.996030i	$0.471626\pi$
$614$	19.3032	0.779013
$615$	1.10559	0.0445817
$616$	−8.73560	−0.351968
$617$	41.5951	1.67456	0.837278	−	0.546778i	$-0.184146\pi$
$617$	41.5951	1.67456	0.837278	+	0.546778i	$0.184146\pi$
$618$	−15.5637	−0.626063
$619$	6.74837	0.271240	0.135620	−	0.990761i	$-0.456697\pi$
$619$	6.74837	0.271240	0.135620	+	0.990761i	$0.456697\pi$
$620$	−0.280506	−0.0112654
$621$	−10.3172	−0.414015
$622$	−36.0559	−1.44571
$623$	15.1324	0.606267
$624$	8.69321	0.348007
$625$	23.8611	0.954444
$626$	−6.53887	−0.261346
$627$	1.98578	0.0793045
$628$	−9.19072	−0.366750
$629$	15.8656	0.632603
$630$	−3.79345	−0.151135
$631$	−40.6788	−1.61940	−0.809699	−	0.586845i	$-0.800370\pi$
$631$	−40.6788	−1.61940	−0.809699	+	0.586845i	$0.800370\pi$
$632$	−11.8462	−0.471217
$633$	−9.60134	−0.381619
$634$	−22.2874	−0.885146
$635$	1.65005	0.0654803
$636$	−2.17538	−0.0862596
$637$	−14.5842	−0.577846
$638$	0	0
$639$	−3.41511	−0.135099
$640$	3.72580	0.147275
$641$	5.88397	0.232403	0.116201	−	0.993226i	$-0.462928\pi$
$641$	5.88397	0.232403	0.116201	+	0.993226i	$0.462928\pi$
$642$	−7.67678	−0.302978
$643$	−40.6299	−1.60229	−0.801144	−	0.598471i	$-0.795775\pi$
$643$	−40.6299	−1.60229	−0.801144	+	0.598471i	$0.795775\pi$
$644$	3.79424	0.149514
$645$	0.860453	0.0338803
$646$	−8.67404	−0.341275
$647$	7.58417	0.298164	0.149082	−	0.988825i	$-0.452368\pi$
$647$	7.58417	0.298164	0.149082	+	0.988825i	$0.452368\pi$
$648$	−12.0306	−0.472609
$649$	−2.10034	−0.0824458
$650$	20.4819	0.803365
$651$	−6.22632	−0.244029
$652$	2.99150	0.117156
$653$	−12.8196	−0.501670	−0.250835	−	0.968030i	$-0.580705\pi$
$653$	−12.8196	−0.501670	−0.250835	+	0.968030i	$0.580705\pi$
$654$	−12.0683	−0.471906
$655$	−4.27837	−0.167170
$656$	−26.6242	−1.03950
$657$	28.6052	1.11600
$658$	−42.7073	−1.66490
$659$	−3.04495	−0.118614	−0.0593072	−	0.998240i	$-0.518889\pi$
$659$	−3.04495	−0.118614	−0.0593072	+	0.998240i	$0.518889\pi$
$660$	0.0773247	0.00300986
$661$	23.9138	0.930138	0.465069	−	0.885274i	$-0.346030\pi$
$661$	23.9138	0.930138	0.465069	+	0.885274i	$0.346030\pi$
$662$	−9.56048	−0.371579
$663$	3.68356	0.143058
$664$	2.85123	0.110649
$665$	2.77242	0.107510
$666$	31.4168	1.21738
$667$	0	0
$668$	−3.51986	−0.136187
$669$	2.21983	0.0858236
$670$	1.56111	0.0603111
$671$	−7.14036	−0.275651
$672$	−5.50385	−0.212316
$673$	−15.2179	−0.586606	−0.293303	−	0.956020i	$-0.594754\pi$
$673$	−15.2179	−0.586606	−0.293303	+	0.956020i	$0.594754\pi$
$674$	38.7267	1.49170
$675$	18.9391	0.728965
$676$	−2.32423	−0.0893936
$677$	23.8659	0.917239	0.458620	−	0.888633i	$-0.348344\pi$
$677$	23.8659	0.917239	0.458620	+	0.888633i	$0.348344\pi$
$678$	17.6127	0.676413
$679$	−4.32628	−0.166027
$680$	1.34603	0.0516181
$681$	−13.3335	−0.510939
$682$	−3.92192	−0.150178
$683$	23.7258	0.907842	0.453921	−	0.891042i	$-0.350025\pi$
$683$	23.7258	0.907842	0.453921	+	0.891042i	$0.350025\pi$
$684$	−2.86979	−0.109729
$685$	−0.737190	−0.0281666
$686$	−8.56347	−0.326955
$687$	16.1839	0.617454
$688$	−20.7209	−0.789977
$689$	20.8637	0.794842
$690$	0.801081	0.0304966
$691$	−33.2738	−1.26580	−0.632898	−	0.774235i	$-0.718135\pi$
$691$	−33.2738	−1.26580	−0.632898	+	0.774235i	$0.718135\pi$
$692$	−6.36403	−0.241924
$693$	−8.86165	−0.336626
$694$	−5.53989	−0.210291
$695$	5.56984	0.211276
$696$	0	0
$697$	−11.2814	−0.427314
$698$	22.9649	0.869235
$699$	14.4868	0.547941
$700$	−6.96501	−0.263253
$701$	36.2014	1.36731	0.683655	−	0.729806i	$-0.260389\pi$
$701$	36.2014	1.36731	0.683655	+	0.729806i	$0.260389\pi$
$702$	16.0010	0.603920
$703$	−22.9608	−0.865981
$704$	5.81601	0.219199
$705$	−1.50652	−0.0567390
$706$	−0.309230	−0.0116380
$707$	−41.6544	−1.56657
$708$	−0.587898	−0.0220946
$709$	−42.9161	−1.61175	−0.805874	−	0.592086i	$-0.798304\pi$
$709$	−42.9161	−1.61175	−0.805874	+	0.592086i	$0.798304\pi$
$710$	0.581691	0.0218305
$711$	−12.0172	−0.450678
$712$	−10.6325	−0.398470
$713$	−6.78859	−0.254235
$714$	−7.49717	−0.280575
$715$	−0.741606	−0.0277345
$716$	−7.25561	−0.271155
$717$	14.5936	0.545009
$718$	−30.3049	−1.13097
$719$	−14.3519	−0.535236	−0.267618	−	0.963525i	$-0.586236\pi$
$719$	−14.3519	−0.535236	−0.267618	+	0.963525i	$0.586236\pi$
$720$	3.22248	0.120095
$721$	−50.7597	−1.89039
$722$	−16.8889	−0.628538
$723$	3.98706	0.148280
$724$	8.21359	0.305256
$725$	0	0
$726$	1.08112	0.0401243
$727$	14.9177	0.553268	0.276634	−	0.960975i	$-0.410781\pi$
$727$	14.9177	0.553268	0.276634	+	0.960975i	$0.410781\pi$
$728$	23.4509	0.869148
$729$	−4.15319	−0.153822
$730$	−4.87229	−0.180332
$731$	−8.78004	−0.324742
$732$	−1.99863	−0.0738714
$733$	20.9551	0.773994	0.386997	−	0.922081i	$-0.373512\pi$
$733$	20.9551	0.773994	0.386997	+	0.922081i	$0.373512\pi$
$734$	33.2851	1.22857
$735$	1.04709	0.0386226
$736$	−6.00088	−0.221195
$737$	3.64682	0.134332
$738$	−22.3393	−0.822322
$739$	36.6116	1.34678	0.673390	−	0.739288i	$-0.264838\pi$
$739$	36.6116	1.34678	0.673390	+	0.739288i	$0.264838\pi$
$740$	−0.894073	−0.0328668
$741$	−5.33087	−0.195834
$742$	−42.4639	−1.55890
$743$	20.9609	0.768981	0.384490	−	0.923129i	$-0.374377\pi$
$743$	20.9609	0.768981	0.384490	+	0.923129i	$0.374377\pi$
$744$	4.37481	0.160388
$745$	−1.77381	−0.0649875
$746$	−40.0356	−1.46581
$747$	2.89237	0.105826
$748$	−0.789020	−0.0288494
$749$	−25.0372	−0.914839
$750$	−2.96385	−0.108224
$751$	17.8623	0.651803	0.325902	−	0.945404i	$-0.394332\pi$
$751$	17.8623	0.651803	0.325902	+	0.945404i	$0.394332\pi$
$752$	36.2792	1.32297
$753$	−1.39633	−0.0508849
$754$	0	0
$755$	−2.21346	−0.0805559
$756$	−5.44127	−0.197897
$757$	9.42502	0.342558	0.171279	−	0.985223i	$-0.445210\pi$
$757$	9.42502	0.342558	0.171279	+	0.985223i	$0.445210\pi$
$758$	47.0572	1.70919
$759$	1.87136	0.0679259
$760$	−1.94799	−0.0706609
$761$	−3.58110	−0.129815	−0.0649075	−	0.997891i	$-0.520675\pi$
$761$	−3.58110	−0.129815	−0.0649075	+	0.997891i	$0.520675\pi$
$762$	6.45753	0.233932
$763$	−39.3597	−1.42492
$764$	10.6591	0.385632
$765$	1.36546	0.0493682
$766$	12.2522	0.442691
$767$	5.63841	0.203591
$768$	6.46550	0.233304
$769$	−3.69922	−0.133397	−0.0666987	−	0.997773i	$-0.521247\pi$
$769$	−3.69922	−0.133397	−0.0666987	+	0.997773i	$0.521247\pi$
$770$	1.50939	0.0543948
$771$	20.8192	0.749785
$772$	8.23637	0.296433
$773$	13.7421	0.494270	0.247135	−	0.968981i	$-0.420511\pi$
$773$	13.7421	0.494270	0.247135	+	0.968981i	$0.420511\pi$
$774$	−17.3861	−0.624931
$775$	12.4617	0.447636
$776$	3.03978	0.109122
$777$	−19.8455	−0.711954
$778$	38.3782	1.37592
$779$	16.3265	0.584959
$780$	−0.207580	−0.00743254
$781$	1.35885	0.0486236
$782$	−8.17421	−0.292309
$783$	0	0
$784$	−25.2154	−0.900552
$785$	−6.32860	−0.225877
$786$	−16.7436	−0.597223
$787$	−23.0123	−0.820302	−0.410151	−	0.912018i	$-0.634524\pi$
$787$	−23.0123	−0.820302	−0.410151	+	0.912018i	$0.634524\pi$
$788$	−5.78281	−0.206004
$789$	−16.5844	−0.590422
$790$	2.04687	0.0728242
$791$	57.4425	2.04242
$792$	6.22647	0.221248
$793$	19.1684	0.680691
$794$	55.9918	1.98707
$795$	−1.49794	−0.0531264
$796$	−3.12733	−0.110845
$797$	29.6944	1.05183	0.525914	−	0.850537i	$-0.323723\pi$
$797$	29.6944	1.05183	0.525914	+	0.850537i	$0.323723\pi$
$798$	10.8499	0.384084
$799$	15.3725	0.543841
$800$	11.0157	0.389463
$801$	−10.7859	−0.381102
$802$	−3.31410	−0.117025
$803$	−11.3819	−0.401657
$804$	1.02077	0.0359996
$805$	2.61266	0.0920842
$806$	10.5285	0.370850
$807$	−13.6004	−0.478755
$808$	29.2677	1.02963
$809$	−28.8962	−1.01594	−0.507969	−	0.861375i	$-0.669604\pi$
$809$	−28.8962	−1.01594	−0.507969	+	0.861375i	$0.669604\pi$
$810$	2.07873	0.0730392
$811$	−37.9041	−1.33099	−0.665496	−	0.746402i	$-0.731780\pi$
$811$	−37.9041	−1.33099	−0.665496	+	0.746402i	$0.731780\pi$
$812$	0	0
$813$	−6.44824	−0.226150
$814$	−12.5006	−0.438145
$815$	2.05990	0.0721552
$816$	6.36873	0.222950
$817$	12.7065	0.444545
$818$	−24.4039	−0.853264
$819$	23.7893	0.831264
$820$	0.635742	0.0222011
$821$	40.8646	1.42618	0.713092	−	0.701070i	$-0.247294\pi$
$821$	40.8646	1.42618	0.713092	+	0.701070i	$0.247294\pi$
$822$	−2.88502	−0.100627
$823$	−50.2943	−1.75315	−0.876575	−	0.481266i	$-0.840177\pi$
$823$	−50.2943	−1.75315	−0.876575	+	0.481266i	$0.840177\pi$
$824$	35.6653	1.24246
$825$	−3.43521	−0.119599
$826$	−11.4759	−0.399297
$827$	27.1913	0.945534	0.472767	−	0.881187i	$-0.343255\pi$
$827$	27.1913	0.945534	0.472767	+	0.881187i	$0.343255\pi$
$828$	−2.70442	−0.0939852
$829$	−28.0962	−0.975821	−0.487911	−	0.872894i	$-0.662241\pi$
$829$	−28.0962	−0.975821	−0.487911	+	0.872894i	$0.662241\pi$
$830$	−0.492654	−0.0171003
$831$	−9.72119	−0.337224
$832$	−15.6132	−0.541289
$833$	−10.6845	−0.370196
$834$	21.7978	0.754795
$835$	−2.42372	−0.0838764
$836$	1.14187	0.0394925
$837$	9.73541	0.336505
$838$	16.3197	0.563753
$839$	−42.0123	−1.45042	−0.725212	−	0.688526i	$-0.758258\pi$
$839$	−42.0123	−1.45042	−0.725212	+	0.688526i	$0.758258\pi$
$840$	−1.68369	−0.0580929
$841$	0	0
$842$	9.97049	0.343606
$843$	7.15584	0.246460
$844$	−5.52101	−0.190041
$845$	−1.60043	−0.0550566
$846$	30.4405	1.04657
$847$	3.52600	0.121155
$848$	36.0724	1.23873
$849$	2.23594	0.0767371
$850$	15.0052	0.514675
$851$	−21.6377	−0.741730
$852$	0.380350	0.0130306
$853$	41.6448	1.42589	0.712946	−	0.701219i	$-0.247360\pi$
$853$	41.6448	1.42589	0.712946	+	0.701219i	$0.247360\pi$
$854$	−39.0136	−1.33502
$855$	−1.97609	−0.0675810
$856$	17.5919	0.601280
$857$	−50.6264	−1.72937	−0.864683	−	0.502318i	$-0.832481\pi$
$857$	−50.6264	−1.72937	−0.864683	+	0.502318i	$0.832481\pi$
$858$	−2.90230	−0.0990829
$859$	15.5949	0.532090	0.266045	−	0.963961i	$-0.414283\pi$
$859$	15.5949	0.532090	0.266045	+	0.963961i	$0.414283\pi$
$860$	0.494781	0.0168719
$861$	14.1114	0.480915
$862$	−8.75401	−0.298163
$863$	24.4168	0.831157	0.415578	−	0.909557i	$-0.363579\pi$
$863$	24.4168	0.831157	0.415578	+	0.909557i	$0.363579\pi$
$864$	8.60577	0.292774
$865$	−4.38218	−0.148999
$866$	49.9433	1.69714
$867$	−9.16212	−0.311162
$868$	−3.58028	−0.121523
$869$	4.78156	0.162203
$870$	0	0
$871$	−9.78996	−0.331720
$872$	27.6554	0.936529
$873$	3.08364	0.104365
$874$	11.8298	0.400147
$875$	−9.66635	−0.326782
$876$	−3.18585	−0.107640
$877$	−23.2206	−0.784104	−0.392052	−	0.919943i	$-0.628235\pi$
$877$	−23.2206	−0.784104	−0.392052	+	0.919943i	$0.628235\pi$
$878$	−36.1993	−1.22167
$879$	−16.8228	−0.567420
$880$	−1.28221	−0.0432232
$881$	−28.7534	−0.968728	−0.484364	−	0.874867i	$-0.660949\pi$
$881$	−28.7534	−0.968728	−0.484364	+	0.874867i	$0.660949\pi$
$882$	−21.1573	−0.712404
$883$	18.8994	0.636016	0.318008	−	0.948088i	$-0.396986\pi$
$883$	18.8994	0.636016	0.318008	+	0.948088i	$0.396986\pi$
$884$	2.11814	0.0712407
$885$	−0.404818	−0.0136078
$886$	28.3420	0.952169
$887$	−34.6579	−1.16370	−0.581850	−	0.813296i	$-0.697671\pi$
$887$	−34.6579	−1.16370	−0.581850	+	0.813296i	$0.697671\pi$
$888$	13.9441	0.467933
$889$	21.0607	0.706354
$890$	1.83715	0.0615815
$891$	4.85600	0.162682
$892$	1.27646	0.0427390
$893$	−22.2472	−0.744474
$894$	−6.94188	−0.232171
$895$	−4.99611	−0.167001
$896$	47.5549	1.58870
$897$	−5.02369	−0.167736
$898$	−34.2343	−1.14241
$899$	0	0
$900$	4.96445	0.165482
$901$	15.2849	0.509215
$902$	8.88870	0.295961
$903$	10.9825	0.365476
$904$	−40.3609	−1.34238
$905$	5.65576	0.188004
$906$	−8.66243	−0.287790
$907$	−46.2990	−1.53733	−0.768667	−	0.639649i	$-0.779080\pi$
$907$	−46.2990	−1.53733	−0.768667	+	0.639649i	$0.779080\pi$
$908$	−7.66707	−0.254441
$909$	29.6900	0.984754
$910$	−4.05200	−0.134322
$911$	34.0625	1.12854	0.564270	−	0.825590i	$-0.309158\pi$
$911$	34.0625	1.12854	0.564270	+	0.825590i	$0.309158\pi$
$912$	−9.21686	−0.305201
$913$	−1.15086	−0.0380879
$914$	49.7418	1.64531
$915$	−1.37623	−0.0454966
$916$	9.30614	0.307483
$917$	−54.6078	−1.80331
$918$	11.7225	0.386901
$919$	20.5422	0.677624	0.338812	−	0.940854i	$-0.389975\pi$
$919$	20.5422	0.677624	0.338812	+	0.940854i	$0.389975\pi$
$920$	−1.83574	−0.0605225
$921$	8.69117	0.286384
$922$	−33.8099	−1.11347
$923$	−3.64786	−0.120071
$924$	0.986948	0.0324682
$925$	39.7198	1.30598
$926$	21.8362	0.717583
$927$	36.1800	1.18831
$928$	0	0
$929$	34.4854	1.13143	0.565714	−	0.824601i	$-0.308600\pi$
$929$	34.4854	1.13143	0.565714	+	0.824601i	$0.308600\pi$
$930$	−0.755907	−0.0247872
$931$	15.4627	0.506768
$932$	8.33026	0.272867
$933$	−16.2340	−0.531477
$934$	−2.41737	−0.0790989
$935$	−0.543308	−0.0177681
$936$	−16.7151	−0.546350
$937$	−23.0703	−0.753674	−0.376837	−	0.926280i	$-0.622988\pi$
$937$	−23.0703	−0.753674	−0.376837	+	0.926280i	$0.622988\pi$
$938$	19.9255	0.650592
$939$	−2.94410	−0.0960769
$940$	−0.866288	−0.0282552
$941$	−46.1820	−1.50549	−0.752744	−	0.658313i	$-0.771270\pi$
$941$	−46.1820	−1.50549	−0.752744	+	0.658313i	$0.771270\pi$
$942$	−24.7672	−0.806958
$943$	15.3857	0.501029
$944$	9.74859	0.317290
$945$	−3.74678	−0.121883
$946$	6.91784	0.224918
$947$	−14.3713	−0.467005	−0.233503	−	0.972356i	$-0.575019\pi$
$947$	−14.3713	−0.467005	−0.233503	+	0.972356i	$0.575019\pi$
$948$	1.33839	0.0434687
$949$	30.5548	0.991851
$950$	−21.7156	−0.704548
$951$	−10.0348	−0.325401
$952$	17.1804	0.556818
$953$	22.6638	0.734154	0.367077	−	0.930191i	$-0.380359\pi$
$953$	22.6638	0.734154	0.367077	+	0.930191i	$0.380359\pi$
$954$	30.2670	0.979930
$955$	7.33969	0.237507
$956$	8.39170	0.271407
$957$	0	0
$958$	−5.53655	−0.178878
$959$	−9.40925	−0.303841
$960$	1.12097	0.0361792
$961$	−24.5942	−0.793362
$962$	33.5580	1.08195
$963$	17.8458	0.575072
$964$	2.29265	0.0738414
$965$	5.67144	0.182570
$966$	10.2247	0.328975
$967$	−39.4759	−1.26946	−0.634729	−	0.772735i	$-0.718888\pi$
$967$	−39.4759	−1.26946	−0.634729	+	0.772735i	$0.718888\pi$
$968$	−2.47748	−0.0796293
$969$	−3.90545	−0.125461
$970$	−0.525233	−0.0168642
$971$	57.4357	1.84320	0.921599	−	0.388143i	$-0.126884\pi$
$971$	57.4357	1.84320	0.921599	+	0.388143i	$0.126884\pi$
$972$	5.98877	0.192090
$973$	71.0917	2.27909
$974$	−62.8477	−2.01377
$975$	9.22187	0.295336
$976$	33.1415	1.06083
$977$	8.85648	0.283344	0.141672	−	0.989914i	$-0.454752\pi$
$977$	8.85648	0.283344	0.141672	+	0.989914i	$0.454752\pi$
$978$	8.06150	0.257778
$979$	4.29166	0.137162
$980$	0.602103	0.0192335
$981$	28.0544	0.895708
$982$	60.9661	1.94551
$983$	−1.26192	−0.0402489	−0.0201245	−	0.999797i	$-0.506406\pi$
$983$	−1.26192	−0.0402489	−0.0201245	+	0.999797i	$0.506406\pi$
$984$	−9.91512	−0.316082
$985$	−3.98196	−0.126876
$986$	0	0
$987$	−19.2288	−0.612059
$988$	−3.06538	−0.0975227
$989$	11.9743	0.380761
$990$	−1.07585	−0.0341928
$991$	31.0135	0.985175	0.492588	−	0.870263i	$-0.336051\pi$
$991$	31.0135	0.985175	0.492588	+	0.870263i	$0.336051\pi$
$992$	5.66248	0.179784
$993$	−4.30456	−0.136601
$994$	7.42451	0.235491
$995$	−2.15343	−0.0682684
$996$	−0.322132	−0.0102071
$997$	23.2073	0.734983	0.367491	−	0.930027i	$-0.380217\pi$
$997$	23.2073	0.734983	0.367491	+	0.930027i	$0.380217\pi$
$998$	−33.7042	−1.06689
$999$	31.0303	0.981755

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9251.2.a.ba.1.30	✓	40
29.28	even	2		9251.2.a.bb.1.11	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9251.2.a.ba.1.30	✓	40	1.1	even	1	trivial
9251.2.a.bb.1.11	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)

\(f(q)\)	\(=\)	\(q+1.54958 q^{2} +0.697690 q^{3} +0.401189 q^{4} +0.276253 q^{5} +1.08112 q^{6} +3.52600 q^{7} -2.47748 q^{8} -2.51323 q^{9} +O(q^{10})\)	\(q+1.54958 q^{2} +0.697690 q^{3} +0.401189 q^{4} +0.276253 q^{5} +1.08112 q^{6} +3.52600 q^{7} -2.47748 q^{8} -2.51323 q^{9} +0.428075 q^{10} +1.00000 q^{11} +0.279906 q^{12} -2.68452 q^{13} +5.46381 q^{14} +0.192739 q^{15} -4.64143 q^{16} -1.96670 q^{17} -3.89444 q^{18} +2.84622 q^{19} +0.110830 q^{20} +2.46006 q^{21} +1.54958 q^{22} +2.68222 q^{23} -1.72851 q^{24} -4.92368 q^{25} -4.15987 q^{26} -3.84653 q^{27} +1.41459 q^{28} +0.298664 q^{30} -2.53096 q^{31} -2.23728 q^{32} +0.697690 q^{33} -3.04756 q^{34} +0.974068 q^{35} -1.00828 q^{36} -8.06709 q^{37} +4.41044 q^{38} -1.87296 q^{39} -0.684411 q^{40} +5.73621 q^{41} +3.81205 q^{42} +4.46434 q^{43} +0.401189 q^{44} -0.694286 q^{45} +4.15630 q^{46} -7.81639 q^{47} -3.23828 q^{48} +5.43269 q^{49} -7.62963 q^{50} -1.37215 q^{51} -1.07700 q^{52} -7.77185 q^{53} -5.96049 q^{54} +0.276253 q^{55} -8.73560 q^{56} +1.98578 q^{57} -2.10034 q^{59} +0.0773247 q^{60} -7.14036 q^{61} -3.92192 q^{62} -8.86165 q^{63} +5.81601 q^{64} -0.741606 q^{65} +1.08112 q^{66} +3.64682 q^{67} -0.789020 q^{68} +1.87136 q^{69} +1.50939 q^{70} +1.35885 q^{71} +6.22647 q^{72} -11.3819 q^{73} -12.5006 q^{74} -3.43521 q^{75} +1.14187 q^{76} +3.52600 q^{77} -2.90230 q^{78} +4.78156 q^{79} -1.28221 q^{80} +4.85600 q^{81} +8.88870 q^{82} -1.15086 q^{83} +0.986948 q^{84} -0.543308 q^{85} +6.91784 q^{86} -2.47748 q^{88} +4.29166 q^{89} -1.07585 q^{90} -9.46562 q^{91} +1.07608 q^{92} -1.76583 q^{93} -12.1121 q^{94} +0.786277 q^{95} -1.56093 q^{96} -1.22696 q^{97} +8.41838 q^{98} -2.51323 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 5 q^{3} + 28 q^{4} - 12 q^{5} - 8 q^{6} - 15 q^{7} - 3 q^{8} + 25 q^{9}+O(q^{10}) \) 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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