LMFDB - Embedded newform 9251.2.a.m.1.2

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:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 4x^{5} + 15x^{4} + x^{3} - 14x^{2} + 1 $ x^7 - 3x^6 - 4x^5 + 15x^4 + x^3 - 14x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 319)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.07719$ of defining polynomial
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)

$f(q)$	$=$	$q-2.07719 q^{2} -2.68771 q^{3} +2.31473 q^{4} -2.92190 q^{5} +5.58288 q^{6} +0.102367 q^{7} -0.653749 q^{8} +4.22376 q^{9} +O(q^{10})$	\(q-2.07719 q^{2} -2.68771 q^{3} +2.31473 q^{4} -2.92190 q^{5} +5.58288 q^{6} +0.102367 q^{7} -0.653749 q^{8} +4.22376 q^{9} +6.06936 q^{10} -1.00000 q^{11} -6.22131 q^{12} -3.37025 q^{13} -0.212636 q^{14} +7.85322 q^{15} -3.27149 q^{16} -0.441389 q^{17} -8.77357 q^{18} -3.10306 q^{19} -6.76341 q^{20} -0.275132 q^{21} +2.07719 q^{22} +1.33656 q^{23} +1.75709 q^{24} +3.53752 q^{25} +7.00065 q^{26} -3.28912 q^{27} +0.236951 q^{28} -16.3126 q^{30} +2.16523 q^{31} +8.10302 q^{32} +2.68771 q^{33} +0.916849 q^{34} -0.299106 q^{35} +9.77686 q^{36} +12.0423 q^{37} +6.44565 q^{38} +9.05823 q^{39} +1.91019 q^{40} -8.03540 q^{41} +0.571502 q^{42} -7.18807 q^{43} -2.31473 q^{44} -12.3414 q^{45} -2.77630 q^{46} -10.5596 q^{47} +8.79281 q^{48} -6.98952 q^{49} -7.34811 q^{50} +1.18632 q^{51} -7.80120 q^{52} -4.18807 q^{53} +6.83213 q^{54} +2.92190 q^{55} -0.0669223 q^{56} +8.34012 q^{57} +14.6375 q^{59} +18.1781 q^{60} -6.93654 q^{61} -4.49761 q^{62} +0.432374 q^{63} -10.2885 q^{64} +9.84754 q^{65} -5.58288 q^{66} -0.191591 q^{67} -1.02169 q^{68} -3.59229 q^{69} +0.621301 q^{70} +13.1036 q^{71} -2.76128 q^{72} +4.28144 q^{73} -25.0142 q^{74} -9.50782 q^{75} -7.18274 q^{76} -0.102367 q^{77} -18.8157 q^{78} -2.69814 q^{79} +9.55899 q^{80} -3.83111 q^{81} +16.6911 q^{82} -4.25122 q^{83} -0.636856 q^{84} +1.28970 q^{85} +14.9310 q^{86} +0.653749 q^{88} -1.30233 q^{89} +25.6355 q^{90} -0.345002 q^{91} +3.09378 q^{92} -5.81951 q^{93} +21.9342 q^{94} +9.06685 q^{95} -21.7785 q^{96} -4.21264 q^{97} +14.5186 q^{98} -4.22376 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 3 q^{2} + 3 q^{4} + 4 q^{5} + q^{7} - 6 q^{8} + 13 q^{9}+O(q^{10}) $ 7 * q - 3 * q^2 + 3 * q^4 + 4 * q^5 + q^7 - 6 * q^8 + 13 * q^9	\( 7 q - 3 q^{2} + 3 q^{4} + 4 q^{5} + q^{7} - 6 q^{8} + 13 q^{9} - 3 q^{10} - 7 q^{11} - 7 q^{12} + 14 q^{14} + 12 q^{15} - q^{16} - 18 q^{17} - 10 q^{18} - 10 q^{19} + 17 q^{20} - 14 q^{21} + 3 q^{22} + 4 q^{23} + 9 q^{25} - 3 q^{26} + 9 q^{27} + 2 q^{28} - 31 q^{30} + 13 q^{31} + 5 q^{32} - 15 q^{34} - 4 q^{35} - 19 q^{36} + 5 q^{37} - 10 q^{38} - q^{39} - 8 q^{40} - 31 q^{41} + 20 q^{42} - 9 q^{43} - 3 q^{44} - 17 q^{45} + 14 q^{46} + 7 q^{47} + 41 q^{48} + 2 q^{49} - 34 q^{50} + 7 q^{51} - 35 q^{52} + 12 q^{53} + 4 q^{54} - 4 q^{55} + 13 q^{56} - 2 q^{57} + 12 q^{59} + 44 q^{60} - 15 q^{61} - 3 q^{62} - 51 q^{63} - 22 q^{64} - 9 q^{65} - 25 q^{67} + 6 q^{68} + 8 q^{69} + 48 q^{70} + 4 q^{71} - 7 q^{72} - 7 q^{73} - 38 q^{74} + 13 q^{75} - 14 q^{76} - q^{77} - 25 q^{78} - 11 q^{79} + 2 q^{80} + 23 q^{81} - 8 q^{82} + 36 q^{83} - 5 q^{84} + 5 q^{85} + 48 q^{86} + 6 q^{88} - 26 q^{89} + 13 q^{90} - 38 q^{91} - 19 q^{92} - 49 q^{93} + 8 q^{94} - 22 q^{95} - 39 q^{96} - 14 q^{97} + 41 q^{98} - 13 q^{99}+O(q^{100}) \) 7 * q - 3 * q^2 + 3 * q^4 + 4 * q^5 + q^7 - 6 * q^8 + 13 * q^9 - 3 * q^10 - 7 * q^11 - 7 * q^12 + 14 * q^14 + 12 * q^15 - q^16 - 18 * q^17 - 10 * q^18 - 10 * q^19 + 17 * q^20 - 14 * q^21 + 3 * q^22 + 4 * q^23 + 9 * q^25 - 3 * q^26 + 9 * q^27 + 2 * q^28 - 31 * q^30 + 13 * q^31 + 5 * q^32 - 15 * q^34 - 4 * q^35 - 19 * q^36 + 5 * q^37 - 10 * q^38 - q^39 - 8 * q^40 - 31 * q^41 + 20 * q^42 - 9 * q^43 - 3 * q^44 - 17 * q^45 + 14 * q^46 + 7 * q^47 + 41 * q^48 + 2 * q^49 - 34 * q^50 + 7 * q^51 - 35 * q^52 + 12 * q^53 + 4 * q^54 - 4 * q^55 + 13 * q^56 - 2 * q^57 + 12 * q^59 + 44 * q^60 - 15 * q^61 - 3 * q^62 - 51 * q^63 - 22 * q^64 - 9 * q^65 - 25 * q^67 + 6 * q^68 + 8 * q^69 + 48 * q^70 + 4 * q^71 - 7 * q^72 - 7 * q^73 - 38 * q^74 + 13 * q^75 - 14 * q^76 - q^77 - 25 * q^78 - 11 * q^79 + 2 * q^80 + 23 * q^81 - 8 * q^82 + 36 * q^83 - 5 * q^84 + 5 * q^85 + 48 * q^86 + 6 * q^88 - 26 * q^89 + 13 * q^90 - 38 * q^91 - 19 * q^92 - 49 * q^93 + 8 * q^94 - 22 * q^95 - 39 * q^96 - 14 * q^97 + 41 * q^98 - 13 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.07719	−1.46880	−0.734398	−	0.678719i	$-0.762536\pi$
$2$	−2.07719	−1.46880	−0.734398	+	0.678719i	$0.762536\pi$
$3$	−2.68771	−1.55175	−0.775874	−	0.630888i	$-0.782691\pi$
$3$	−2.68771	−1.55175	−0.775874	+	0.630888i	$0.782691\pi$
$4$	2.31473	1.15736
$5$	−2.92190	−1.30672	−0.653358	−	0.757049i	$-0.726640\pi$
$5$	−2.92190	−1.30672	−0.653358	+	0.757049i	$0.726640\pi$
$6$	5.58288	2.27920
$7$	0.102367	0.0386911	0.0193455	−	0.999813i	$-0.493842\pi$
$7$	0.102367	0.0386911	0.0193455	+	0.999813i	$0.493842\pi$
$8$	−0.653749	−0.231135
$9$	4.22376	1.40792
$10$	6.06936	1.91930
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−6.22131	−1.79594
$13$	−3.37025	−0.934738	−0.467369	−	0.884062i	$-0.654798\pi$
$13$	−3.37025	−0.934738	−0.467369	+	0.884062i	$0.654798\pi$
$14$	−0.212636	−0.0568293
$15$	7.85322	2.02769
$16$	−3.27149	−0.817873
$17$	−0.441389	−0.107052	−0.0535262	−	0.998566i	$-0.517046\pi$
$17$	−0.441389	−0.107052	−0.0535262	+	0.998566i	$0.517046\pi$
$18$	−8.77357	−2.06795
$19$	−3.10306	−0.711891	−0.355946	−	0.934507i	$-0.615841\pi$
$19$	−3.10306	−0.711891	−0.355946	+	0.934507i	$0.615841\pi$
$20$	−6.76341	−1.51234
$21$	−0.275132	−0.0600388
$22$	2.07719	0.442859
$23$	1.33656	0.278693	0.139346	−	0.990244i	$-0.455500\pi$
$23$	1.33656	0.278693	0.139346	+	0.990244i	$0.455500\pi$
$24$	1.75709	0.358664
$25$	3.53752	0.707504
$26$	7.00065	1.37294
$27$	−3.28912	−0.632991
$28$	0.236951	0.0447796
$29$	0	0
$29$	0	0
$30$	−16.3126	−2.97827
$31$	2.16523	0.388887	0.194444	−	0.980914i	$-0.437710\pi$
$31$	2.16523	0.388887	0.194444	+	0.980914i	$0.437710\pi$
$32$	8.10302	1.43242
$33$	2.68771	0.467870
$34$	0.916849	0.157238
$35$	−0.299106	−0.0505582
$36$	9.77686	1.62948
$37$	12.0423	1.97974	0.989872	−	0.141966i	$-0.0453423\pi$
$37$	12.0423	1.97974	0.989872	+	0.141966i	$0.0453423\pi$
$38$	6.44565	1.04562
$39$	9.05823	1.45048
$40$	1.91019	0.302028
$41$	−8.03540	−1.25492	−0.627459	−	0.778649i	$-0.715905\pi$
$41$	−8.03540	−1.25492	−0.627459	+	0.778649i	$0.715905\pi$
$42$	0.571502	0.0881847
$43$	−7.18807	−1.09617	−0.548085	−	0.836423i	$-0.684643\pi$
$43$	−7.18807	−1.09617	−0.548085	+	0.836423i	$0.684643\pi$
$44$	−2.31473	−0.348958
$45$	−12.3414	−1.83975
$46$	−2.77630	−0.409343
$47$	−10.5596	−1.54027	−0.770135	−	0.637881i	$-0.779811\pi$
$47$	−10.5596	−1.54027	−0.770135	+	0.637881i	$0.779811\pi$
$48$	8.79281	1.26913
$49$	−6.98952	−0.998503
$50$	−7.34811	−1.03918
$51$	1.18632	0.166118
$52$	−7.80120	−1.08183
$53$	−4.18807	−0.575275	−0.287638	−	0.957739i	$-0.592870\pi$
$53$	−4.18807	−0.575275	−0.287638	+	0.957739i	$0.592870\pi$
$54$	6.83213	0.929735
$55$	2.92190	0.393989
$56$	−0.0669223	−0.00894287
$57$	8.34012	1.10468
$58$	0	0
$59$	14.6375	1.90563	0.952817	−	0.303544i	$-0.0981699\pi$
$59$	14.6375	1.90563	0.952817	+	0.303544i	$0.0981699\pi$
$60$	18.1781	2.34678
$61$	−6.93654	−0.888133	−0.444066	−	0.895994i	$-0.646465\pi$
$61$	−6.93654	−0.888133	−0.444066	+	0.895994i	$0.646465\pi$
$62$	−4.49761	−0.571197
$63$	0.432374	0.0544740
$64$	−10.2885	−1.28607
$65$	9.84754	1.22144
$66$	−5.58288	−0.687205
$67$	−0.191591	−0.0234066	−0.0117033	−	0.999932i	$-0.503725\pi$
$67$	−0.191591	−0.0234066	−0.0117033	+	0.999932i	$0.503725\pi$
$68$	−1.02169	−0.123899
$69$	−3.59229	−0.432461
$70$	0.621301	0.0742597
$71$	13.1036	1.55511	0.777555	−	0.628815i	$-0.216460\pi$
$71$	13.1036	1.55511	0.777555	+	0.628815i	$0.216460\pi$
$72$	−2.76128	−0.325420
$73$	4.28144	0.501104	0.250552	−	0.968103i	$-0.419388\pi$
$73$	4.28144	0.501104	0.250552	+	0.968103i	$0.419388\pi$
$74$	−25.0142	−2.90784
$75$	−9.50782	−1.09787
$76$	−7.18274	−0.823917
$77$	−0.102367	−0.0116658
$78$	−18.8157	−2.13046
$79$	−2.69814	−0.303564	−0.151782	−	0.988414i	$-0.548501\pi$
$79$	−2.69814	−0.303564	−0.151782	+	0.988414i	$0.548501\pi$
$80$	9.55899	1.06873
$81$	−3.83111	−0.425679
$82$	16.6911	1.84322
$83$	−4.25122	−0.466632	−0.233316	−	0.972401i	$-0.574958\pi$
$83$	−4.25122	−0.466632	−0.233316	+	0.972401i	$0.574958\pi$
$84$	−0.636856	−0.0694867
$85$	1.28970	0.139887
$86$	14.9310	1.61005
$87$	0	0
$88$	0.653749	0.0696899
$89$	−1.30233	−0.138047	−0.0690235	−	0.997615i	$-0.521988\pi$
$89$	−1.30233	−0.138047	−0.0690235	+	0.997615i	$0.521988\pi$
$90$	25.6355	2.70222
$91$	−0.345002	−0.0361660
$92$	3.09378	0.322549
$93$	−5.81951	−0.603455
$94$	21.9342	2.26234
$95$	9.06685	0.930239
$96$	−21.7785	−2.22276
$97$	−4.21264	−0.427728	−0.213864	−	0.976863i	$-0.568605\pi$
$97$	−4.21264	−0.427728	−0.213864	+	0.976863i	$0.568605\pi$
$98$	14.5186	1.46660
$99$	−4.22376	−0.424504
$100$	8.18840	0.818840
$101$	−1.34210	−0.133544	−0.0667720	−	0.997768i	$-0.521270\pi$
$101$	−1.34210	−0.133544	−0.0667720	+	0.997768i	$0.521270\pi$
$102$	−2.46422	−0.243994
$103$	−6.97324	−0.687094	−0.343547	−	0.939135i	$-0.611629\pi$
$103$	−6.97324	−0.687094	−0.343547	+	0.939135i	$0.611629\pi$
$104$	2.20330	0.216051
$105$	0.803910	0.0784536
$106$	8.69942	0.844962
$107$	−8.87163	−0.857653	−0.428826	−	0.903387i	$-0.641073\pi$
$107$	−8.87163	−0.857653	−0.428826	+	0.903387i	$0.641073\pi$
$108$	−7.61341	−0.732601
$109$	−6.30698	−0.604099	−0.302050	−	0.953292i	$-0.597671\pi$
$109$	−6.30698	−0.604099	−0.302050	+	0.953292i	$0.597671\pi$
$110$	−6.06936	−0.578690
$111$	−32.3662	−3.07206
$112$	−0.334893	−0.0316444
$113$	20.4375	1.92260	0.961300	−	0.275504i	$-0.0888446\pi$
$113$	20.4375	1.92260	0.961300	+	0.275504i	$0.0888446\pi$
$114$	−17.3240	−1.62254
$115$	−3.90531	−0.364172
$116$	0	0
$117$	−14.2351	−1.31604
$118$	−30.4048	−2.79899
$119$	−0.0451836	−0.00414197
$120$	−5.13403	−0.468671
$121$	1.00000	0.0909091
$122$	14.4085	1.30449
$123$	21.5968	1.94732
$124$	5.01193	0.450084
$125$	4.27322	0.382209
$126$	−0.898123	−0.0800112
$127$	−19.7878	−1.75588	−0.877942	−	0.478766i	$-0.841084\pi$
$127$	−19.7878	−1.75588	−0.877942	+	0.478766i	$0.841084\pi$
$128$	5.16524	0.456547
$129$	19.3194	1.70098
$130$	−20.4552	−1.79404
$131$	−14.2171	−1.24216	−0.621078	−	0.783749i	$-0.713305\pi$
$131$	−14.2171	−1.24216	−0.621078	+	0.783749i	$0.713305\pi$
$132$	6.22131	0.541495
$133$	−0.317651	−0.0275438
$134$	0.397972	0.0343795
$135$	9.61048	0.827139
$136$	0.288557	0.0247436
$137$	10.4719	0.894676	0.447338	−	0.894365i	$-0.352372\pi$
$137$	10.4719	0.894676	0.447338	+	0.894365i	$0.352372\pi$
$138$	7.46188	0.635198
$139$	−20.4433	−1.73398	−0.866989	−	0.498327i	$-0.833948\pi$
$139$	−20.4433	−1.73398	−0.866989	+	0.498327i	$0.833948\pi$
$140$	−0.692349	−0.0585142
$141$	28.3810	2.39011
$142$	−27.2187	−2.28414
$143$	3.37025	0.281834
$144$	−13.8180	−1.15150
$145$	0	0
$146$	−8.89337	−0.736020
$147$	18.7858	1.54942
$148$	27.8747	2.29128
$149$	−2.40880	−0.197336	−0.0986681	−	0.995120i	$-0.531458\pi$
$149$	−2.40880	−0.197336	−0.0986681	+	0.995120i	$0.531458\pi$
$150$	19.7496	1.61255
$151$	14.7071	1.19685	0.598423	−	0.801180i	$-0.295794\pi$
$151$	14.7071	1.19685	0.598423	+	0.801180i	$0.295794\pi$
$152$	2.02862	0.164543
$153$	−1.86432	−0.150721
$154$	0.212636	0.0171347
$155$	−6.32660	−0.508165
$156$	20.9673	1.67873
$157$	15.4501	1.23305	0.616524	−	0.787336i	$-0.288540\pi$
$157$	15.4501	1.23305	0.616524	+	0.787336i	$0.288540\pi$
$158$	5.60456	0.445874
$159$	11.2563	0.892682
$160$	−23.6762	−1.87177
$161$	0.136820	0.0107829
$162$	7.95795	0.625236
$163$	16.9933	1.33102	0.665508	−	0.746391i	$-0.268215\pi$
$163$	16.9933	1.33102	0.665508	+	0.746391i	$0.268215\pi$
$164$	−18.5998	−1.45240
$165$	−7.85322	−0.611372
$166$	8.83059	0.685387
$167$	12.6835	0.981481	0.490741	−	0.871306i	$-0.336726\pi$
$167$	12.6835	0.981481	0.490741	+	0.871306i	$0.336726\pi$
$168$	0.179867	0.0138771
$169$	−1.64144	−0.126265
$170$	−2.67895	−0.205466
$171$	−13.1066	−1.00229
$172$	−16.6384	−1.26867
$173$	−15.5261	−1.18043	−0.590213	−	0.807248i	$-0.700956\pi$
$173$	−15.5261	−1.18043	−0.590213	+	0.807248i	$0.700956\pi$
$174$	0	0
$175$	0.362125	0.0273741
$176$	3.27149	0.246598
$177$	−39.3412	−2.95706
$178$	2.70519	0.202763
$179$	−10.2247	−0.764231	−0.382115	−	0.924115i	$-0.624804\pi$
$179$	−10.2247	−0.764231	−0.382115	+	0.924115i	$0.624804\pi$
$180$	−28.5670	−2.12926
$181$	3.66408	0.272349	0.136175	−	0.990685i	$-0.456519\pi$
$181$	3.66408	0.272349	0.136175	+	0.990685i	$0.456519\pi$
$182$	0.716635	0.0531205
$183$	18.6434	1.37816
$184$	−0.873778	−0.0644158
$185$	−35.1865	−2.58696
$186$	12.0882	0.886353
$187$	0.441389	0.0322775
$188$	−24.4425	−1.78265
$189$	−0.336697	−0.0244911
$190$	−18.8336	−1.36633
$191$	24.8774	1.80007	0.900034	−	0.435819i	$-0.143541\pi$
$191$	24.8774	1.80007	0.900034	+	0.435819i	$0.143541\pi$
$192$	27.6526	1.99565
$193$	0.0315942	0.00227420	0.00113710	−	0.999999i	$-0.499638\pi$
$193$	0.0315942	0.00227420	0.00113710	+	0.999999i	$0.499638\pi$
$194$	8.75045	0.628246
$195$	−26.4673	−1.89536
$196$	−16.1788	−1.15563
$197$	20.6855	1.47378	0.736891	−	0.676011i	$-0.236293\pi$
$197$	20.6855	1.47378	0.736891	+	0.676011i	$0.236293\pi$
$198$	8.77357	0.623510
$199$	−2.62121	−0.185813	−0.0929064	−	0.995675i	$-0.529616\pi$
$199$	−2.62121	−0.185813	−0.0929064	+	0.995675i	$0.529616\pi$
$200$	−2.31265	−0.163529
$201$	0.514941	0.0363211
$202$	2.78780	0.196149
$203$	0	0
$204$	2.74601	0.192259
$205$	23.4787	1.63982
$206$	14.4848	1.00920
$207$	5.64533	0.392378
$208$	11.0257	0.764497
$209$	3.10306	0.214643
$210$	−1.66987	−0.115232
$211$	−11.3863	−0.783863	−0.391932	−	0.919994i	$-0.628193\pi$
$211$	−11.3863	−0.783863	−0.391932	+	0.919994i	$0.628193\pi$
$212$	−9.69423	−0.665802
$213$	−35.2186	−2.41314
$214$	18.4281	1.25972
$215$	21.0028	1.43238
$216$	2.15026	0.146306
$217$	0.221648	0.0150465
$218$	13.1008	0.887299
$219$	−11.5072	−0.777588
$220$	6.76341	0.455989
$221$	1.48759	0.100066
$222$	67.2308	4.51223
$223$	19.8692	1.33054	0.665271	−	0.746602i	$-0.268316\pi$
$223$	19.8692	1.33054	0.665271	+	0.746602i	$0.268316\pi$
$224$	0.829481	0.0554220
$225$	14.9417	0.996110
$226$	−42.4527	−2.82391
$227$	6.61886	0.439309	0.219654	−	0.975578i	$-0.429507\pi$
$227$	6.61886	0.439309	0.219654	+	0.975578i	$0.429507\pi$
$228$	19.3051	1.27851
$229$	1.27330	0.0841418	0.0420709	−	0.999115i	$-0.486604\pi$
$229$	1.27330	0.0841418	0.0420709	+	0.999115i	$0.486604\pi$
$230$	8.11209	0.534895
$231$	0.275132	0.0181024
$232$	0	0
$233$	21.5656	1.41281	0.706405	−	0.707807i	$-0.250316\pi$
$233$	21.5656	1.41281	0.706405	+	0.707807i	$0.250316\pi$
$234$	29.5691	1.93299
$235$	30.8540	2.01269
$236$	33.8817	2.20551
$237$	7.25181	0.471055
$238$	0.0938550	0.00608372
$239$	−3.40480	−0.220238	−0.110119	−	0.993918i	$-0.535123\pi$
$239$	−3.40480	−0.220238	−0.110119	+	0.993918i	$0.535123\pi$
$240$	−25.6917	−1.65839
$241$	11.8780	0.765130	0.382565	−	0.923929i	$-0.375041\pi$
$241$	11.8780	0.765130	0.382565	+	0.923929i	$0.375041\pi$
$242$	−2.07719	−0.133527
$243$	20.1643	1.29354
$244$	−16.0562	−1.02789
$245$	20.4227	1.30476
$246$	−44.8607	−2.86021
$247$	10.4581	0.665432
$248$	−1.41552	−0.0898856
$249$	11.4260	0.724094
$250$	−8.87630	−0.561387
$251$	5.46766	0.345115	0.172558	−	0.984999i	$-0.444797\pi$
$251$	5.46766	0.345115	0.172558	+	0.984999i	$0.444797\pi$
$252$	1.00083	0.0630462
$253$	−1.33656	−0.0840291
$254$	41.1031	2.57904
$255$	−3.46632	−0.217070
$256$	9.84788	0.615493
$257$	14.8169	0.924254	0.462127	−	0.886814i	$-0.347086\pi$
$257$	14.8169	0.924254	0.462127	+	0.886814i	$0.347086\pi$
$258$	−40.1301	−2.49839
$259$	1.23273	0.0765984
$260$	22.7944	1.41365
$261$	0	0
$262$	29.5317	1.82447
$263$	25.8643	1.59486	0.797430	−	0.603412i	$-0.206192\pi$
$263$	25.8643	1.59486	0.797430	+	0.603412i	$0.206192\pi$
$264$	−1.75709	−0.108141
$265$	12.2371	0.751721
$266$	0.659822	0.0404563
$267$	3.50029	0.214214
$268$	−0.443481	−0.0270899
$269$	17.3100	1.05541	0.527705	−	0.849428i	$-0.323053\pi$
$269$	17.3100	1.05541	0.527705	+	0.849428i	$0.323053\pi$
$270$	−19.9628	−1.21490
$271$	29.1012	1.76777	0.883887	−	0.467700i	$-0.154917\pi$
$271$	29.1012	1.76777	0.883887	+	0.467700i	$0.154917\pi$
$272$	1.44400	0.0875553
$273$	0.927263	0.0561205
$274$	−21.7522	−1.31410
$275$	−3.53752	−0.213321
$276$	−8.31518	−0.500515
$277$	−11.2686	−0.677065	−0.338532	−	0.940955i	$-0.609930\pi$
$277$	−11.2686	−0.677065	−0.338532	+	0.940955i	$0.609930\pi$
$278$	42.4647	2.54686
$279$	9.14543	0.547523
$280$	0.195540	0.0116858
$281$	26.6642	1.59065	0.795326	−	0.606182i	$-0.207300\pi$
$281$	26.6642	1.59065	0.795326	+	0.606182i	$0.207300\pi$
$282$	−58.9528	−3.51059
$283$	1.04668	0.0622185	0.0311092	−	0.999516i	$-0.490096\pi$
$283$	1.04668	0.0622185	0.0311092	+	0.999516i	$0.490096\pi$
$284$	30.3312	1.79983
$285$	−24.3690	−1.44350
$286$	−7.00065	−0.413957
$287$	−0.822559	−0.0485541
$288$	34.2252	2.01674
$289$	−16.8052	−0.988540
$290$	0	0
$291$	11.3223	0.663727
$292$	9.91036	0.579960
$293$	−31.2675	−1.82667	−0.913334	−	0.407211i	$-0.866501\pi$
$293$	−31.2675	−1.82667	−0.913334	+	0.407211i	$0.866501\pi$
$294$	−39.0217	−2.27579
$295$	−42.7692	−2.49012
$296$	−7.87265	−0.457588
$297$	3.28912	0.190854
$298$	5.00353	0.289847
$299$	−4.50455	−0.260505
$300$	−22.0080	−1.27063
$301$	−0.735820	−0.0424120
$302$	−30.5494	−1.75792
$303$	3.60717	0.207227
$304$	10.1516	0.582236
$305$	20.2679	1.16054
$306$	3.87255	0.221379
$307$	19.8183	1.13109	0.565544	−	0.824718i	$-0.308666\pi$
$307$	19.8183	1.13109	0.565544	+	0.824718i	$0.308666\pi$
$308$	−0.236951	−0.0135016
$309$	18.7420	1.06620
$310$	13.1416	0.746391
$311$	−12.1648	−0.689801	−0.344901	−	0.938639i	$-0.612087\pi$
$311$	−12.1648	−0.689801	−0.344901	+	0.938639i	$0.612087\pi$
$312$	−5.92181	−0.335257
$313$	−5.39482	−0.304933	−0.152467	−	0.988309i	$-0.548722\pi$
$313$	−5.39482	−0.304933	−0.152467	+	0.988309i	$0.548722\pi$
$314$	−32.0927	−1.81110
$315$	−1.26335	−0.0711819
$316$	−6.24546	−0.351334
$317$	25.1883	1.41472	0.707359	−	0.706855i	$-0.249887\pi$
$317$	25.1883	1.41472	0.707359	+	0.706855i	$0.249887\pi$
$318$	−23.3815	−1.31117
$319$	0	0
$320$	30.0621	1.68052
$321$	23.8443	1.33086
$322$	−0.284201	−0.0158379
$323$	1.36966	0.0762097
$324$	−8.86798	−0.492665
$325$	−11.9223	−0.661331
$326$	−35.2983	−1.95499
$327$	16.9513	0.937409
$328$	5.25313	0.290056
$329$	−1.08095	−0.0595947
$330$	16.3126	0.897981
$331$	−21.0153	−1.15511	−0.577553	−	0.816353i	$-0.695992\pi$
$331$	−21.0153	−1.15511	−0.577553	+	0.816353i	$0.695992\pi$
$332$	−9.84040	−0.540062
$333$	50.8639	2.78732
$334$	−26.3461	−1.44160
$335$	0.559811	0.0305857
$336$	0.900093	0.0491041
$337$	−2.26303	−0.123275	−0.0616376	−	0.998099i	$-0.519632\pi$
$337$	−2.26303	−0.123275	−0.0616376	+	0.998099i	$0.519632\pi$
$338$	3.40959	0.185457
$339$	−54.9300	−2.98339
$340$	2.98529	0.161900
$341$	−2.16523	−0.117254
$342$	27.2249	1.47216
$343$	−1.43206	−0.0773242
$344$	4.69919	0.253363
$345$	10.4963	0.565104
$346$	32.2506	1.73381
$347$	16.1631	0.867682	0.433841	−	0.900989i	$-0.357158\pi$
$347$	16.1631	0.867682	0.433841	+	0.900989i	$0.357158\pi$
$348$	0	0
$349$	−18.2356	−0.976131	−0.488066	−	0.872807i	$-0.662297\pi$
$349$	−18.2356	−0.976131	−0.488066	+	0.872807i	$0.662297\pi$
$350$	−0.752204	−0.0402070
$351$	11.0851	0.591681
$352$	−8.10302	−0.431892
$353$	3.72703	0.198370	0.0991848	−	0.995069i	$-0.468376\pi$
$353$	3.72703	0.198370	0.0991848	+	0.995069i	$0.468376\pi$
$354$	81.7192	4.34333
$355$	−38.2874	−2.03209
$356$	−3.01454	−0.159771
$357$	0.121440	0.00642730
$358$	21.2387	1.12250
$359$	31.6024	1.66791	0.833955	−	0.551833i	$-0.186071\pi$
$359$	31.6024	1.66791	0.833955	+	0.551833i	$0.186071\pi$
$360$	8.06820	0.425231
$361$	−9.37101	−0.493211
$362$	−7.61101	−0.400026
$363$	−2.68771	−0.141068
$364$	−0.798585	−0.0418572
$365$	−12.5099	−0.654801
$366$	−38.7259	−2.02423
$367$	−2.88197	−0.150438	−0.0752189	−	0.997167i	$-0.523966\pi$
$367$	−2.88197	−0.150438	−0.0752189	+	0.997167i	$0.523966\pi$
$368$	−4.37256	−0.227935
$369$	−33.9396	−1.76683
$370$	73.0890	3.79972
$371$	−0.428719	−0.0222580
$372$	−13.4706	−0.698417
$373$	14.0908	0.729592	0.364796	−	0.931088i	$-0.381139\pi$
$373$	14.0908	0.729592	0.364796	+	0.931088i	$0.381139\pi$
$374$	−0.916849	−0.0474091
$375$	−11.4852	−0.593091
$376$	6.90330	0.356011
$377$	0	0
$378$	0.699384	0.0359724
$379$	17.4628	0.897002	0.448501	−	0.893782i	$-0.351958\pi$
$379$	17.4628	0.897002	0.448501	+	0.893782i	$0.351958\pi$
$380$	20.9873	1.07662
$381$	53.1838	2.72469
$382$	−51.6752	−2.64393
$383$	3.71283	0.189717	0.0948583	−	0.995491i	$-0.469760\pi$
$383$	3.71283	0.189717	0.0948583	+	0.995491i	$0.469760\pi$
$384$	−13.8826	−0.708445
$385$	0.299106	0.0152439
$386$	−0.0656273	−0.00334034
$387$	−30.3607	−1.54332
$388$	−9.75110	−0.495037
$389$	−27.9614	−1.41770	−0.708850	−	0.705359i	$-0.750786\pi$
$389$	−27.9614	−1.41770	−0.708850	+	0.705359i	$0.750786\pi$
$390$	54.9776	2.78390
$391$	−0.589945	−0.0298348
$392$	4.56939	0.230789
$393$	38.2114	1.92751
$394$	−42.9678	−2.16469
$395$	7.88371	0.396672
$396$	−9.77686	−0.491306
$397$	0.111762	0.00560916	0.00280458	−	0.999996i	$-0.499107\pi$
$397$	0.111762	0.00560916	0.00280458	+	0.999996i	$0.499107\pi$
$398$	5.44476	0.272921
$399$	0.853752	0.0427411
$400$	−11.5730	−0.578649
$401$	24.8729	1.24209	0.621046	−	0.783774i	$-0.286708\pi$
$401$	24.8729	1.24209	0.621046	+	0.783774i	$0.286708\pi$
$402$	−1.06963	−0.0533483
$403$	−7.29737	−0.363508
$404$	−3.10660	−0.154559
$405$	11.1941	0.556241
$406$	0	0
$407$	−12.0423	−0.596915
$408$	−0.775558	−0.0383958
$409$	6.76997	0.334754	0.167377	−	0.985893i	$-0.446470\pi$
$409$	6.76997	0.334754	0.167377	+	0.985893i	$0.446470\pi$
$410$	−48.7697	−2.40856
$411$	−28.1454	−1.38831
$412$	−16.1412	−0.795218
$413$	1.49839	0.0737310
$414$	−11.7264	−0.576323
$415$	12.4216	0.609754
$416$	−27.3092	−1.33894
$417$	54.9456	2.69070
$418$	−6.44565	−0.315267
$419$	−29.6568	−1.44883	−0.724415	−	0.689364i	$-0.757890\pi$
$419$	−29.6568	−1.44883	−0.724415	+	0.689364i	$0.757890\pi$
$420$	1.86083	0.0907993
$421$	10.5302	0.513210	0.256605	−	0.966516i	$-0.417396\pi$
$421$	10.5302	0.513210	0.256605	+	0.966516i	$0.417396\pi$
$422$	23.6515	1.15134
$423$	−44.6011	−2.16858
$424$	2.73794	0.132966
$425$	−1.56142	−0.0757401
$426$	73.1558	3.54441
$427$	−0.710072	−0.0343628
$428$	−20.5354	−0.992616
$429$	−9.05823	−0.437336
$430$	−43.6269	−2.10388
$431$	−24.7801	−1.19361	−0.596807	−	0.802384i	$-0.703564\pi$
$431$	−24.7801	−1.19361	−0.596807	+	0.802384i	$0.703564\pi$
$432$	10.7603	0.517706
$433$	5.22891	0.251285	0.125643	−	0.992076i	$-0.459901\pi$
$433$	5.22891	0.251285	0.125643	+	0.992076i	$0.459901\pi$
$434$	−0.460406	−0.0221002
$435$	0	0
$436$	−14.5989	−0.699162
$437$	−4.14744	−0.198399
$438$	23.9028	1.14212
$439$	18.8153	0.898003	0.449002	−	0.893531i	$-0.351780\pi$
$439$	18.8153	0.898003	0.449002	+	0.893531i	$0.351780\pi$
$440$	−1.91019	−0.0910648
$441$	−29.5221	−1.40581
$442$	−3.09001	−0.146977
$443$	6.00611	0.285359	0.142679	−	0.989769i	$-0.454428\pi$
$443$	6.00611	0.285359	0.142679	+	0.989769i	$0.454428\pi$
$444$	−74.9189	−3.55549
$445$	3.80529	0.180388
$446$	−41.2722	−1.95430
$447$	6.47414	0.306216
$448$	−1.05321	−0.0497593
$449$	14.0684	0.663929	0.331965	−	0.943292i	$-0.392289\pi$
$449$	14.0684	0.663929	0.331965	+	0.943292i	$0.392289\pi$
$450$	−31.0367	−1.46308
$451$	8.03540	0.378372
$452$	47.3073	2.22515
$453$	−39.5283	−1.85720
$454$	−13.7486	−0.645256
$455$	1.00806	0.0472587
$456$	−5.45234	−0.255329
$457$	−17.3243	−0.810398	−0.405199	−	0.914229i	$-0.632798\pi$
$457$	−17.3243	−0.810398	−0.405199	+	0.914229i	$0.632798\pi$
$458$	−2.64488	−0.123587
$459$	1.45178	0.0677633
$460$	−9.03974	−0.421480
$461$	−38.7943	−1.80683	−0.903414	−	0.428769i	$-0.858948\pi$
$461$	−38.7943	−1.80683	−0.903414	+	0.428769i	$0.858948\pi$
$462$	−0.571502	−0.0265887
$463$	−2.70103	−0.125527	−0.0627636	−	0.998028i	$-0.519991\pi$
$463$	−2.70103	−0.125527	−0.0627636	+	0.998028i	$0.519991\pi$
$464$	0	0
$465$	17.0041	0.788544
$466$	−44.7959	−2.07513
$467$	−16.6418	−0.770089	−0.385044	−	0.922898i	$-0.625814\pi$
$467$	−16.6418	−0.770089	−0.385044	+	0.922898i	$0.625814\pi$
$468$	−32.9504	−1.52313
$469$	−0.0196126	−0.000905626 0
$470$	−64.0897	−2.95624
$471$	−41.5252	−1.91338
$472$	−9.56923	−0.440459
$473$	7.18807	0.330508
$474$	−15.0634	−0.691885
$475$	−10.9771	−0.503666
$476$	−0.104588	−0.00479377
$477$	−17.6894	−0.809942
$478$	7.07243	0.323485
$479$	−22.3381	−1.02065	−0.510327	−	0.859980i	$-0.670476\pi$
$479$	−22.3381	−1.02065	−0.510327	+	0.859980i	$0.670476\pi$
$480$	63.6348	2.90452
$481$	−40.5855	−1.85054
$482$	−24.6729	−1.12382
$483$	−0.367732	−0.0167324
$484$	2.31473	0.105215
$485$	12.3089	0.558919
$486$	−41.8850	−1.89994
$487$	25.4241	1.15208	0.576039	−	0.817422i	$-0.304598\pi$
$487$	25.4241	1.15208	0.576039	+	0.817422i	$0.304598\pi$
$488$	4.53476	0.205279
$489$	−45.6729	−2.06540
$490$	−42.4219	−1.91643
$491$	5.18539	0.234013	0.117007	−	0.993131i	$-0.462670\pi$
$491$	5.18539	0.234013	0.117007	+	0.993131i	$0.462670\pi$
$492$	49.9907	2.25375
$493$	0	0
$494$	−21.7234	−0.977384
$495$	12.3414	0.554706
$496$	−7.08354	−0.318061
$497$	1.34137	0.0601689
$498$	−23.7340	−1.06355
$499$	14.1841	0.634967	0.317484	−	0.948264i	$-0.397162\pi$
$499$	14.1841	0.634967	0.317484	+	0.948264i	$0.397162\pi$
$500$	9.89134	0.442354
$501$	−34.0896	−1.52301
$502$	−11.3574	−0.506904
$503$	−0.502656	−0.0224123	−0.0112062	−	0.999937i	$-0.503567\pi$
$503$	−0.502656	−0.0224123	−0.0112062	+	0.999937i	$0.503567\pi$
$504$	−0.282664	−0.0125909
$505$	3.92149	0.174504
$506$	2.77630	0.123422
$507$	4.41171	0.195931
$508$	−45.8034	−2.03220
$509$	20.5067	0.908942	0.454471	−	0.890762i	$-0.349828\pi$
$509$	20.5067	0.908942	0.454471	+	0.890762i	$0.349828\pi$
$510$	7.20022	0.318831
$511$	0.438277	0.0193883
$512$	−30.7864	−1.36058
$513$	10.2063	0.450621
$514$	−30.7776	−1.35754
$515$	20.3752	0.897836
$516$	44.7192	1.96865
$517$	10.5596	0.464409
$518$	−2.56063	−0.112507
$519$	41.7295	1.83172
$520$	−6.43782	−0.282317
$521$	17.5095	0.767107	0.383553	−	0.923519i	$-0.374700\pi$
$521$	17.5095	0.767107	0.383553	+	0.923519i	$0.374700\pi$
$522$	0	0
$523$	24.5021	1.07140	0.535701	−	0.844408i	$-0.320047\pi$
$523$	24.5021	1.07140	0.535701	+	0.844408i	$0.320047\pi$
$524$	−32.9087	−1.43763
$525$	−0.973286	−0.0424777
$526$	−53.7251	−2.34252
$527$	−0.955710	−0.0416314
$528$	−8.79281	−0.382658
$529$	−21.2136	−0.922330
$530$	−25.4189	−1.10412
$531$	61.8252	2.68298
$532$	−0.735275	−0.0318782
$533$	27.0813	1.17302
$534$	−7.27077	−0.314637
$535$	25.9220	1.12071
$536$	0.125253	0.00541009
$537$	27.4810	1.18589
$538$	−35.9562	−1.55018
$539$	6.98952	0.301060
$540$	22.2457	0.957300
$541$	31.2056	1.34163	0.670816	−	0.741624i	$-0.265944\pi$
$541$	31.2056	1.34163	0.670816	+	0.741624i	$0.265944\pi$
$542$	−60.4489	−2.59650
$543$	−9.84798	−0.422617
$544$	−3.57658	−0.153345
$545$	18.4284	0.789385
$546$	−1.92610	−0.0824296
$547$	45.5297	1.94671	0.973354	−	0.229306i	$-0.0736456\pi$
$547$	45.5297	1.94671	0.973354	+	0.229306i	$0.0736456\pi$
$548$	24.2396	1.03547
$549$	−29.2983	−1.25042
$550$	7.34811	0.313325
$551$	0	0
$552$	2.34846	0.0999570
$553$	−0.276200	−0.0117452
$554$	23.4071	0.994471
$555$	94.5709	4.01431
$556$	−47.3207	−2.00684
$557$	−38.7840	−1.64333	−0.821666	−	0.569970i	$-0.806955\pi$
$557$	−38.7840	−1.64333	−0.821666	+	0.569970i	$0.806955\pi$
$558$	−18.9968	−0.804200
$559$	24.2256	1.02463
$560$	0.978524	0.0413502
$561$	−1.18632	−0.0500866
$562$	−55.3866	−2.33634
$563$	34.9260	1.47196	0.735978	−	0.677006i	$-0.236723\pi$
$563$	34.9260	1.47196	0.735978	+	0.677006i	$0.236723\pi$
$564$	65.6942	2.76623
$565$	−59.7165	−2.51229
$566$	−2.17415	−0.0913863
$567$	−0.392179	−0.0164700
$568$	−8.56646	−0.359441
$569$	−11.4247	−0.478949	−0.239475	−	0.970903i	$-0.576975\pi$
$569$	−11.4247	−0.478949	−0.239475	+	0.970903i	$0.576975\pi$
$570$	50.6191	2.12020
$571$	7.59778	0.317957	0.158979	−	0.987282i	$-0.449180\pi$
$571$	7.59778	0.317957	0.158979	+	0.987282i	$0.449180\pi$
$572$	7.80120	0.326185
$573$	−66.8633	−2.79325
$574$	1.70861	0.0713161
$575$	4.72813	0.197176
$576$	−43.4564	−1.81068
$577$	−33.2456	−1.38403	−0.692015	−	0.721883i	$-0.743277\pi$
$577$	−33.2456	−1.38403	−0.692015	+	0.721883i	$0.743277\pi$
$578$	34.9076	1.45196
$579$	−0.0849160	−0.00352899
$580$	0	0
$581$	−0.435184	−0.0180545
$582$	−23.5186	−0.974879
$583$	4.18807	0.173452
$584$	−2.79899	−0.115823
$585$	41.5937	1.71969
$586$	64.9486	2.68300
$587$	23.9416	0.988176	0.494088	−	0.869412i	$-0.335502\pi$
$587$	23.9416	0.988176	0.494088	+	0.869412i	$0.335502\pi$
$588$	43.4840	1.79325
$589$	−6.71885	−0.276845
$590$	88.8399	3.65748
$591$	−55.5966	−2.28694
$592$	−39.3963	−1.61918
$593$	7.56424	0.310626	0.155313	−	0.987865i	$-0.450361\pi$
$593$	7.56424	0.310626	0.155313	+	0.987865i	$0.450361\pi$
$594$	−6.83213	−0.280326
$595$	0.132022	0.00541238
$596$	−5.57571	−0.228390
$597$	7.04505	0.288335
$598$	9.35682	0.382629
$599$	−42.8878	−1.75235	−0.876175	−	0.481994i	$-0.839913\pi$
$599$	−42.8878	−1.75235	−0.876175	+	0.481994i	$0.839913\pi$
$600$	6.21573	0.253756
$601$	16.4274	0.670087	0.335044	−	0.942203i	$-0.391249\pi$
$601$	16.4274	0.670087	0.335044	+	0.942203i	$0.391249\pi$
$602$	1.52844	0.0622946
$603$	−0.809236	−0.0329546
$604$	34.0429	1.38519
$605$	−2.92190	−0.118792
$606$	−7.49279	−0.304374
$607$	14.1277	0.573425	0.286713	−	0.958017i	$-0.407437\pi$
$607$	14.1277	0.573425	0.286713	+	0.958017i	$0.407437\pi$
$608$	−25.1442	−1.01973
$609$	0	0
$610$	−42.1003	−1.70459
$611$	35.5883	1.43975
$612$	−4.31540	−0.174440
$613$	6.84005	0.276267	0.138134	−	0.990414i	$-0.455890\pi$
$613$	6.84005	0.276267	0.138134	+	0.990414i	$0.455890\pi$
$614$	−41.1664	−1.66134
$615$	−63.1037	−2.54459
$616$	0.0669223	0.00269638
$617$	39.5495	1.59220	0.796102	−	0.605163i	$-0.206892\pi$
$617$	39.5495	1.59220	0.796102	+	0.605163i	$0.206892\pi$
$618$	−38.9308	−1.56603
$619$	8.37548	0.336639	0.168320	−	0.985732i	$-0.446166\pi$
$619$	8.37548	0.336639	0.168320	+	0.985732i	$0.446166\pi$
$620$	−14.6444	−0.588132
$621$	−4.39612	−0.176410
$622$	25.2686	1.01318
$623$	−0.133316	−0.00534118
$624$	−29.6339	−1.18631
$625$	−30.1735	−1.20694
$626$	11.2061	0.447885
$627$	−8.34012	−0.333072
$628$	35.7627	1.42709
$629$	−5.31534	−0.211936
$630$	2.62423	0.104552
$631$	13.1885	0.525025	0.262513	−	0.964929i	$-0.415449\pi$
$631$	13.1885	0.525025	0.262513	+	0.964929i	$0.415449\pi$
$632$	1.76391	0.0701644
$633$	30.6030	1.21636
$634$	−52.3210	−2.07793
$635$	57.8181	2.29444
$636$	26.0552	1.03316
$637$	23.5564	0.933339
$638$	0	0
$639$	55.3465	2.18947
$640$	−15.0923	−0.596577
$641$	−32.0227	−1.26482	−0.632411	−	0.774633i	$-0.717935\pi$
$641$	−32.0227	−1.26482	−0.632411	+	0.774633i	$0.717935\pi$
$642$	−49.5293	−1.95476
$643$	−17.5343	−0.691486	−0.345743	−	0.938329i	$-0.612373\pi$
$643$	−17.5343	−0.691486	−0.345743	+	0.938329i	$0.612373\pi$
$644$	0.316701	0.0124798
$645$	−56.4495	−2.22269
$646$	−2.84504	−0.111937
$647$	−0.254429	−0.0100026	−0.00500132	−	0.999987i	$-0.501592\pi$
$647$	−0.254429	−0.0100026	−0.00500132	+	0.999987i	$0.501592\pi$
$648$	2.50459	0.0983894
$649$	−14.6375	−0.574571
$650$	24.7649	0.971361
$651$	−0.595725	−0.0233483
$652$	39.3348	1.54047
$653$	12.4598	0.487589	0.243795	−	0.969827i	$-0.421608\pi$
$653$	12.4598	0.487589	0.243795	+	0.969827i	$0.421608\pi$
$654$	−35.2111	−1.37686
$655$	41.5410	1.62314
$656$	26.2877	1.02636
$657$	18.0838	0.705515
$658$	2.24534	0.0875324
$659$	−36.8005	−1.43355	−0.716773	−	0.697307i	$-0.754381\pi$
$659$	−36.8005	−1.43355	−0.716773	+	0.697307i	$0.754381\pi$
$660$	−18.1781	−0.707580
$661$	3.95929	0.153998	0.0769992	−	0.997031i	$-0.475466\pi$
$661$	3.95929	0.153998	0.0769992	+	0.997031i	$0.475466\pi$
$662$	43.6529	1.69662
$663$	−3.99820	−0.155277
$664$	2.77923	0.107855
$665$	0.928145	0.0359919
$666$	−105.654	−4.09401
$667$	0	0
$668$	29.3589	1.13593
$669$	−53.4026	−2.06467
$670$	−1.16284	−0.0449242
$671$	6.93654	0.267782
$672$	−2.22940	−0.0860010
$673$	−26.3528	−1.01582	−0.507912	−	0.861409i	$-0.669583\pi$
$673$	−26.3528	−1.01582	−0.507912	+	0.861409i	$0.669583\pi$
$674$	4.70075	0.181066
$675$	−11.6353	−0.447844
$676$	−3.79949	−0.146134
$677$	40.7489	1.56611	0.783054	−	0.621954i	$-0.213661\pi$
$677$	40.7489	1.56611	0.783054	+	0.621954i	$0.213661\pi$
$678$	114.100	4.38199
$679$	−0.431235	−0.0165493
$680$	−0.843137	−0.0323328
$681$	−17.7895	−0.681697
$682$	4.49761	0.172222
$683$	−21.1125	−0.807849	−0.403925	−	0.914792i	$-0.632354\pi$
$683$	−21.1125	−0.807849	−0.403925	+	0.914792i	$0.632354\pi$
$684$	−30.3382	−1.16001
$685$	−30.5979	−1.16909
$686$	2.97467	0.113574
$687$	−3.42225	−0.130567
$688$	23.5157	0.896528
$689$	14.1148	0.537732
$690$	−21.8029	−0.830022
$691$	−9.13515	−0.347517	−0.173759	−	0.984788i	$-0.555591\pi$
$691$	−9.13515	−0.347517	−0.173759	+	0.984788i	$0.555591\pi$
$692$	−35.9386	−1.36618
$693$	−0.432374	−0.0164245
$694$	−33.5739	−1.27445
$695$	59.7334	2.26582
$696$	0	0
$697$	3.54673	0.134342
$698$	37.8789	1.43374
$699$	−57.9621	−2.19233
$700$	0.838221	0.0316818
$701$	11.1939	0.422788	0.211394	−	0.977401i	$-0.432200\pi$
$701$	11.1939	0.422788	0.211394	+	0.977401i	$0.432200\pi$
$702$	−23.0260	−0.869059
$703$	−37.3680	−1.40936
$704$	10.2885	0.387764
$705$	−82.9265	−3.12319
$706$	−7.74175	−0.291365
$707$	−0.137387	−0.00516696
$708$	−91.0641	−3.42240
$709$	−52.0408	−1.95443	−0.977217	−	0.212241i	$-0.931924\pi$
$709$	−52.0408	−1.95443	−0.977217	+	0.212241i	$0.931924\pi$
$710$	79.5304	2.98472
$711$	−11.3963	−0.427395
$712$	0.851399	0.0319075
$713$	2.89397	0.108380
$714$	−0.252255	−0.00944040
$715$	−9.84754	−0.368277
$716$	−23.6674	−0.884493
$717$	9.15111	0.341754
$718$	−65.6442	−2.44982
$719$	10.8225	0.403610	0.201805	−	0.979426i	$-0.435319\pi$
$719$	10.8225	0.403610	0.201805	+	0.979426i	$0.435319\pi$
$720$	40.3749	1.50468
$721$	−0.713830	−0.0265844
$722$	19.4654	0.724427
$723$	−31.9246	−1.18729
$724$	8.48136	0.315207
$725$	0	0
$726$	5.58288	0.207200
$727$	−22.7370	−0.843270	−0.421635	−	0.906766i	$-0.638544\pi$
$727$	−22.7370	−0.843270	−0.421635	+	0.906766i	$0.638544\pi$
$728$	0.225545	0.00835924
$729$	−42.7022	−1.58156
$730$	25.9856	0.961769
$731$	3.17273	0.117348
$732$	43.1543	1.59503
$733$	−15.7802	−0.582854	−0.291427	−	0.956593i	$-0.594130\pi$
$733$	−15.7802	−0.582854	−0.291427	+	0.956593i	$0.594130\pi$
$734$	5.98641	0.220963
$735$	−54.8902	−2.02466
$736$	10.8302	0.399207
$737$	0.191591	0.00705735
$738$	70.4991	2.59511
$739$	−44.4058	−1.63350	−0.816748	−	0.576995i	$-0.804225\pi$
$739$	−44.4058	−1.63350	−0.816748	+	0.576995i	$0.804225\pi$
$740$	−81.4471	−2.99405
$741$	−28.1082	−1.03258
$742$	0.890533	0.0326925
$743$	33.6702	1.23524	0.617619	−	0.786477i	$-0.288097\pi$
$743$	33.6702	1.23524	0.617619	+	0.786477i	$0.288097\pi$
$744$	3.80450	0.139480
$745$	7.03827	0.257862
$746$	−29.2692	−1.07162
$747$	−17.9561	−0.656980
$748$	1.02169	0.0373569
$749$	−0.908161	−0.0331835
$750$	23.8569	0.871130
$751$	−34.1093	−1.24467	−0.622334	−	0.782752i	$-0.713815\pi$
$751$	−34.1093	−1.24467	−0.622334	+	0.782752i	$0.713815\pi$
$752$	34.5455	1.25975
$753$	−14.6955	−0.535532
$754$	0	0
$755$	−42.9727	−1.56394
$756$	−0.779361	−0.0283451
$757$	−29.3227	−1.06575	−0.532876	−	0.846193i	$-0.678889\pi$
$757$	−29.3227	−1.06575	−0.532876	+	0.846193i	$0.678889\pi$
$758$	−36.2735	−1.31751
$759$	3.59229	0.130392
$760$	−5.92744	−0.215011
$761$	28.3155	1.02644	0.513218	−	0.858258i	$-0.328453\pi$
$761$	28.3155	1.02644	0.513218	+	0.858258i	$0.328453\pi$
$762$	−110.473	−4.00202
$763$	−0.645626	−0.0233732
$764$	57.5845	2.08333
$765$	5.44737	0.196950
$766$	−7.71226	−0.278655
$767$	−49.3318	−1.78127
$768$	−26.4682	−0.955090
$769$	−45.7495	−1.64977	−0.824885	−	0.565301i	$-0.808760\pi$
$769$	−45.7495	−1.64977	−0.824885	+	0.565301i	$0.808760\pi$
$770$	−0.621301	−0.0223901
$771$	−39.8235	−1.43421
$772$	0.0731320	0.00263208
$773$	−12.9086	−0.464290	−0.232145	−	0.972681i	$-0.574574\pi$
$773$	−12.9086	−0.464290	−0.232145	+	0.972681i	$0.574574\pi$
$774$	63.0650	2.26682
$775$	7.65956	0.275140
$776$	2.75401	0.0988631
$777$	−3.31323	−0.118861
$778$	58.0813	2.08231
$779$	24.9343	0.893365
$780$	−61.2645	−2.19362
$781$	−13.1036	−0.468883
$782$	1.22543	0.0438212
$783$	0	0
$784$	22.8662	0.816649
$785$	−45.1436	−1.61124
$786$	−79.3725	−2.83112
$787$	32.7783	1.16842	0.584210	−	0.811602i	$-0.301404\pi$
$787$	32.7783	1.16842	0.584210	+	0.811602i	$0.301404\pi$
$788$	47.8814	1.70570
$789$	−69.5156	−2.47482
$790$	−16.3760	−0.582631
$791$	2.09213	0.0743874
$792$	2.76128	0.0981179
$793$	23.3778	0.830171
$794$	−0.232151	−0.00823871
$795$	−32.8898	−1.16648
$796$	−6.06739	−0.215053
$797$	−0.601158	−0.0212941	−0.0106471	−	0.999943i	$-0.503389\pi$
$797$	−0.601158	−0.0212941	−0.0106471	+	0.999943i	$0.503389\pi$
$798$	−1.77341	−0.0627779
$799$	4.66087	0.164890
$800$	28.6646	1.01345
$801$	−5.50074	−0.194359
$802$	−51.6657	−1.82438
$803$	−4.28144	−0.151089
$804$	1.19195	0.0420367
$805$	−0.399775	−0.0140902
$806$	15.1580	0.533919
$807$	−46.5242	−1.63773
$808$	0.877397	0.0308667
$809$	21.7480	0.764617	0.382309	−	0.924035i	$-0.375129\pi$
$809$	21.7480	0.764617	0.382309	+	0.924035i	$0.375129\pi$
$810$	−23.2524	−0.817005
$811$	−28.7751	−1.01043	−0.505215	−	0.862993i	$-0.668587\pi$
$811$	−28.7751	−1.01043	−0.505215	+	0.862993i	$0.668587\pi$
$812$	0	0
$813$	−78.2156	−2.74314
$814$	25.0142	0.876747
$815$	−49.6527	−1.73926
$816$	−3.88105	−0.135864
$817$	22.3050	0.780353
$818$	−14.0625	−0.491685
$819$	−1.45721	−0.0509189
$820$	54.3467	1.89787
$821$	5.67515	0.198064	0.0990321	−	0.995084i	$-0.468425\pi$
$821$	5.67515	0.198064	0.0990321	+	0.995084i	$0.468425\pi$
$822$	58.4635	2.03915
$823$	−20.2861	−0.707130	−0.353565	−	0.935410i	$-0.615031\pi$
$823$	−20.2861	−0.707130	−0.353565	+	0.935410i	$0.615031\pi$
$824$	4.55875	0.158812
$825$	9.50782	0.331020
$826$	−3.11245	−0.108296
$827$	1.63861	0.0569802	0.0284901	−	0.999594i	$-0.490930\pi$
$827$	1.63861	0.0569802	0.0284901	+	0.999594i	$0.490930\pi$
$828$	13.0674	0.454124
$829$	−14.8148	−0.514541	−0.257270	−	0.966339i	$-0.582823\pi$
$829$	−14.8148	−0.514541	−0.257270	+	0.966339i	$0.582823\pi$
$830$	−25.8021	−0.895605
$831$	30.2867	1.05063
$832$	34.6749	1.20214
$833$	3.08510	0.106892
$834$	−114.133	−3.95209
$835$	−37.0601	−1.28252
$836$	7.18274	0.248420
$837$	−7.12171	−0.246162
$838$	61.6029	2.12804
$839$	42.1240	1.45428	0.727140	−	0.686489i	$-0.240849\pi$
$839$	42.1240	1.45428	0.727140	+	0.686489i	$0.240849\pi$
$840$	−0.525555	−0.0181334
$841$	0	0
$842$	−21.8732	−0.753801
$843$	−71.6655	−2.46829
$844$	−26.3561	−0.907215
$845$	4.79613	0.164992
$846$	92.6450	3.18520
$847$	0.102367	0.00351737
$848$	13.7012	0.470502
$849$	−2.81316	−0.0965474
$850$	3.24337	0.111247
$851$	16.0953	0.551741
$852$	−81.5215	−2.79288
$853$	−39.4648	−1.35125	−0.675625	−	0.737246i	$-0.736126\pi$
$853$	−39.4648	−1.35125	−0.675625	+	0.737246i	$0.736126\pi$
$854$	1.47496	0.0504720
$855$	38.2962	1.30970
$856$	5.79982	0.198234
$857$	11.5836	0.395689	0.197845	−	0.980233i	$-0.436606\pi$
$857$	11.5836	0.395689	0.197845	+	0.980233i	$0.436606\pi$
$858$	18.8157	0.642357
$859$	−20.7946	−0.709504	−0.354752	−	0.934960i	$-0.615435\pi$
$859$	−20.7946	−0.709504	−0.354752	+	0.934960i	$0.615435\pi$
$860$	48.6158	1.65779
$861$	2.21080	0.0753437
$862$	51.4730	1.75318
$863$	24.8040	0.844339	0.422170	−	0.906517i	$-0.361269\pi$
$863$	24.8040	0.844339	0.422170	+	0.906517i	$0.361269\pi$
$864$	−26.6518	−0.906712
$865$	45.3657	1.54248
$866$	−10.8614	−0.369087
$867$	45.1674	1.53396
$868$	0.513055	0.0174142
$869$	2.69814	0.0915281
$870$	0	0
$871$	0.645709	0.0218790
$872$	4.12318	0.139629
$873$	−17.7932	−0.602208
$874$	8.61503	0.291408
$875$	0.437436	0.0147881
$876$	−26.6361	−0.899952
$877$	−24.6070	−0.830921	−0.415460	−	0.909611i	$-0.636380\pi$
$877$	−24.6070	−0.830921	−0.415460	+	0.909611i	$0.636380\pi$
$878$	−39.0829	−1.31898
$879$	84.0379	2.83453
$880$	−9.55899	−0.322233
$881$	−22.4382	−0.755963	−0.377981	−	0.925813i	$-0.623382\pi$
$881$	−22.4382	−0.755963	−0.377981	+	0.925813i	$0.623382\pi$
$882$	61.3230	2.06485
$883$	−25.7923	−0.867979	−0.433990	−	0.900918i	$-0.642895\pi$
$883$	−25.7923	−0.867979	−0.433990	+	0.900918i	$0.642895\pi$
$884$	3.44336	0.115813
$885$	114.951	3.86404
$886$	−12.4758	−0.419134
$887$	8.10631	0.272183	0.136092	−	0.990696i	$-0.456546\pi$
$887$	8.10631	0.272183	0.136092	+	0.990696i	$0.456546\pi$
$888$	21.1594	0.710062
$889$	−2.02562	−0.0679370
$890$	−7.90432	−0.264953
$891$	3.83111	0.128347
$892$	45.9918	1.53992
$893$	32.7669	1.09650
$894$	−13.4480	−0.449769
$895$	29.8756	0.998632
$896$	0.528749	0.0176643
$897$	12.1069	0.404238
$898$	−29.2228	−0.975177
$899$	0	0
$900$	34.5859	1.15286
$901$	1.84857	0.0615846
$902$	−16.6911	−0.555752
$903$	1.97767	0.0658127
$904$	−13.3610	−0.444381
$905$	−10.7061	−0.355883
$906$	82.1079	2.72785
$907$	8.07311	0.268063	0.134032	−	0.990977i	$-0.457208\pi$
$907$	8.07311	0.268063	0.134032	+	0.990977i	$0.457208\pi$
$908$	15.3208	0.508440
$909$	−5.66871	−0.188019
$910$	−2.09394	−0.0694134
$911$	19.5899	0.649043	0.324522	−	0.945878i	$-0.394797\pi$
$911$	19.5899	0.649043	0.324522	+	0.945878i	$0.394797\pi$
$912$	−27.2846	−0.903484
$913$	4.25122	0.140695
$914$	35.9859	1.19031
$915$	−54.4741	−1.80086
$916$	2.94733	0.0973827
$917$	−1.45536	−0.0480603
$918$	−3.01562	−0.0995304
$919$	21.9209	0.723102	0.361551	−	0.932352i	$-0.382247\pi$
$919$	21.9209	0.723102	0.361551	+	0.932352i	$0.382247\pi$
$920$	2.55310	0.0841731
$921$	−53.2657	−1.75516
$922$	80.5831	2.65386
$923$	−44.1623	−1.45362
$924$	0.636856	0.0209510
$925$	42.5999	1.40068
$926$	5.61055	0.184374
$927$	−29.4533	−0.967375
$928$	0	0
$929$	30.0041	0.984403	0.492202	−	0.870481i	$-0.336192\pi$
$929$	30.0041	0.984403	0.492202	+	0.870481i	$0.336192\pi$
$930$	−35.3207	−1.15821
$931$	21.6889	0.710825
$932$	49.9185	1.63514
$933$	32.6953	1.07040
$934$	34.5681	1.13110
$935$	−1.28970	−0.0421775
$936$	9.30620	0.304183
$937$	−34.2777	−1.11980	−0.559901	−	0.828559i	$-0.689161\pi$
$937$	−34.2777	−1.11980	−0.559901	+	0.828559i	$0.689161\pi$
$938$	0.0407391	0.00133018
$939$	14.4997	0.473179
$940$	71.4186	2.32942
$941$	5.16529	0.168384	0.0841918	−	0.996450i	$-0.473169\pi$
$941$	5.16529	0.168384	0.0841918	+	0.996450i	$0.473169\pi$
$942$	86.2558	2.81037
$943$	−10.7398	−0.349737
$944$	−47.8863	−1.55857
$945$	0.983796	0.0320029
$946$	−14.9310	−0.485448
$947$	21.5238	0.699428	0.349714	−	0.936857i	$-0.386279\pi$
$947$	21.5238	0.699428	0.349714	+	0.936857i	$0.386279\pi$
$948$	16.7860	0.545183
$949$	−14.4295	−0.468401
$950$	22.8016	0.739783
$951$	−67.6988	−2.19528
$952$	0.0295387	0.000957356 0
$953$	16.9499	0.549063	0.274531	−	0.961578i	$-0.411477\pi$
$953$	16.9499	0.549063	0.274531	+	0.961578i	$0.411477\pi$
$954$	36.7443	1.18964
$955$	−72.6895	−2.35218
$956$	−7.88119	−0.254896
$957$	0	0
$958$	46.4005	1.49913
$959$	1.07198	0.0346160
$960$	−80.7981	−2.60775
$961$	−26.3118	−0.848767
$962$	84.3040	2.71807
$963$	−37.4717	−1.20751
$964$	27.4944	0.885533
$965$	−0.0923153	−0.00297174
$966$	0.763850	0.0245765
$967$	−25.2590	−0.812275	−0.406138	−	0.913812i	$-0.633125\pi$
$967$	−25.2590	−0.812275	−0.406138	+	0.913812i	$0.633125\pi$
$968$	−0.653749	−0.0210123
$969$	−3.68123	−0.118258
$970$	−25.5680	−0.820939
$971$	−50.8988	−1.63342	−0.816710	−	0.577048i	$-0.804204\pi$
$971$	−50.8988	−1.63342	−0.816710	+	0.577048i	$0.804204\pi$
$972$	46.6747	1.49709
$973$	−2.09272	−0.0670895
$974$	−52.8108	−1.69217
$975$	32.0437	1.02622
$976$	22.6928	0.726380
$977$	19.9719	0.638959	0.319480	−	0.947593i	$-0.396492\pi$
$977$	19.9719	0.638959	0.319480	+	0.947593i	$0.396492\pi$
$978$	94.8715	3.03365
$979$	1.30233	0.0416227
$980$	47.2730	1.51008
$981$	−26.6392	−0.850524
$982$	−10.7710	−0.343718
$983$	10.3207	0.329181	0.164590	−	0.986362i	$-0.447370\pi$
$983$	10.3207	0.329181	0.164590	+	0.986362i	$0.447370\pi$
$984$	−14.1189	−0.450094
$985$	−60.4411	−1.92581
$986$	0	0
$987$	2.90527	0.0924759
$988$	24.2076	0.770146
$989$	−9.60731	−0.305495
$990$	−25.6355	−0.814750
$991$	1.50195	0.0477110	0.0238555	−	0.999715i	$-0.492406\pi$
$991$	1.50195	0.0477110	0.0238555	+	0.999715i	$0.492406\pi$
$992$	17.5449	0.557052
$993$	56.4830	1.79243
$994$	−2.78629	−0.0883758
$995$	7.65893	0.242804
$996$	26.4481	0.838041
$997$	24.5802	0.778462	0.389231	−	0.921140i	$-0.372741\pi$
$997$	24.5802	0.778462	0.389231	+	0.921140i	$0.372741\pi$
$998$	−29.4631	−0.932638
$999$	−39.6086	−1.25316

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9251.2.a.m.1.2		7
29.28	even	2		319.2.a.d.1.6	✓	7
87.86	odd	2		2871.2.a.m.1.2		7
116.115	odd	2		5104.2.a.x.1.2		7
145.144	even	2		7975.2.a.j.1.2		7
319.318	odd	2		3509.2.a.m.1.2		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
319.2.a.d.1.6	✓	7	29.28	even	2
2871.2.a.m.1.2		7	87.86	odd	2
3509.2.a.m.1.2		7	319.318	odd	2
5104.2.a.x.1.2		7	116.115	odd	2
7975.2.a.j.1.2		7	145.144	even	2
9251.2.a.m.1.2		7	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 9251 = 11 \cdot 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9251.a (trivial)

\(f(q)\)	\(=\)	\(q-2.07719 q^{2} -2.68771 q^{3} +2.31473 q^{4} -2.92190 q^{5} +5.58288 q^{6} +0.102367 q^{7} -0.653749 q^{8} +4.22376 q^{9} +O(q^{10})\)	\(q-2.07719 q^{2} -2.68771 q^{3} +2.31473 q^{4} -2.92190 q^{5} +5.58288 q^{6} +0.102367 q^{7} -0.653749 q^{8} +4.22376 q^{9} +6.06936 q^{10} -1.00000 q^{11} -6.22131 q^{12} -3.37025 q^{13} -0.212636 q^{14} +7.85322 q^{15} -3.27149 q^{16} -0.441389 q^{17} -8.77357 q^{18} -3.10306 q^{19} -6.76341 q^{20} -0.275132 q^{21} +2.07719 q^{22} +1.33656 q^{23} +1.75709 q^{24} +3.53752 q^{25} +7.00065 q^{26} -3.28912 q^{27} +0.236951 q^{28} -16.3126 q^{30} +2.16523 q^{31} +8.10302 q^{32} +2.68771 q^{33} +0.916849 q^{34} -0.299106 q^{35} +9.77686 q^{36} +12.0423 q^{37} +6.44565 q^{38} +9.05823 q^{39} +1.91019 q^{40} -8.03540 q^{41} +0.571502 q^{42} -7.18807 q^{43} -2.31473 q^{44} -12.3414 q^{45} -2.77630 q^{46} -10.5596 q^{47} +8.79281 q^{48} -6.98952 q^{49} -7.34811 q^{50} +1.18632 q^{51} -7.80120 q^{52} -4.18807 q^{53} +6.83213 q^{54} +2.92190 q^{55} -0.0669223 q^{56} +8.34012 q^{57} +14.6375 q^{59} +18.1781 q^{60} -6.93654 q^{61} -4.49761 q^{62} +0.432374 q^{63} -10.2885 q^{64} +9.84754 q^{65} -5.58288 q^{66} -0.191591 q^{67} -1.02169 q^{68} -3.59229 q^{69} +0.621301 q^{70} +13.1036 q^{71} -2.76128 q^{72} +4.28144 q^{73} -25.0142 q^{74} -9.50782 q^{75} -7.18274 q^{76} -0.102367 q^{77} -18.8157 q^{78} -2.69814 q^{79} +9.55899 q^{80} -3.83111 q^{81} +16.6911 q^{82} -4.25122 q^{83} -0.636856 q^{84} +1.28970 q^{85} +14.9310 q^{86} +0.653749 q^{88} -1.30233 q^{89} +25.6355 q^{90} -0.345002 q^{91} +3.09378 q^{92} -5.81951 q^{93} +21.9342 q^{94} +9.06685 q^{95} -21.7785 q^{96} -4.21264 q^{97} +14.5186 q^{98} -4.22376 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 3 q^{2} + 3 q^{4} + 4 q^{5} + q^{7} - 6 q^{8} + 13 q^{9}+O(q^{10}) \) 7 * q - 3 * q^2 + 3 * q^4 + 4 * q^5 + q^7 - 6 * q^8 + 13 * q^9	\( 7 q - 3 q^{2} + 3 q^{4} + 4 q^{5} + q^{7} - 6 q^{8} + 13 q^{9} - 3 q^{10} - 7 q^{11} - 7 q^{12} + 14 q^{14} + 12 q^{15} - q^{16} - 18 q^{17} - 10 q^{18} - 10 q^{19} + 17 q^{20} - 14 q^{21} + 3 q^{22} + 4 q^{23} + 9 q^{25} - 3 q^{26} + 9 q^{27} + 2 q^{28} - 31 q^{30} + 13 q^{31} + 5 q^{32} - 15 q^{34} - 4 q^{35} - 19 q^{36} + 5 q^{37} - 10 q^{38} - q^{39} - 8 q^{40} - 31 q^{41} + 20 q^{42} - 9 q^{43} - 3 q^{44} - 17 q^{45} + 14 q^{46} + 7 q^{47} + 41 q^{48} + 2 q^{49} - 34 q^{50} + 7 q^{51} - 35 q^{52} + 12 q^{53} + 4 q^{54} - 4 q^{55} + 13 q^{56} - 2 q^{57} + 12 q^{59} + 44 q^{60} - 15 q^{61} - 3 q^{62} - 51 q^{63} - 22 q^{64} - 9 q^{65} - 25 q^{67} + 6 q^{68} + 8 q^{69} + 48 q^{70} + 4 q^{71} - 7 q^{72} - 7 q^{73} - 38 q^{74} + 13 q^{75} - 14 q^{76} - q^{77} - 25 q^{78} - 11 q^{79} + 2 q^{80} + 23 q^{81} - 8 q^{82} + 36 q^{83} - 5 q^{84} + 5 q^{85} + 48 q^{86} + 6 q^{88} - 26 q^{89} + 13 q^{90} - 38 q^{91} - 19 q^{92} - 49 q^{93} + 8 q^{94} - 22 q^{95} - 39 q^{96} - 14 q^{97} + 41 q^{98} - 13 q^{99}+O(q^{100}) \) 7 * q - 3 * q^2 + 3 * q^4 + 4 * q^5 + q^7 - 6 * q^8 + 13 * q^9 - 3 * q^10 - 7 * q^11 - 7 * q^12 + 14 * q^14 + 12 * q^15 - q^16 - 18 * q^17 - 10 * q^18 - 10 * q^19 + 17 * q^20 - 14 * q^21 + 3 * q^22 + 4 * q^23 + 9 * q^25 - 3 * q^26 + 9 * q^27 + 2 * q^28 - 31 * q^30 + 13 * q^31 + 5 * q^32 - 15 * q^34 - 4 * q^35 - 19 * q^36 + 5 * q^37 - 10 * q^38 - q^39 - 8 * q^40 - 31 * q^41 + 20 * q^42 - 9 * q^43 - 3 * q^44 - 17 * q^45 + 14 * q^46 + 7 * q^47 + 41 * q^48 + 2 * q^49 - 34 * q^50 + 7 * q^51 - 35 * q^52 + 12 * q^53 + 4 * q^54 - 4 * q^55 + 13 * q^56 - 2 * q^57 + 12 * q^59 + 44 * q^60 - 15 * q^61 - 3 * q^62 - 51 * q^63 - 22 * q^64 - 9 * q^65 - 25 * q^67 + 6 * q^68 + 8 * q^69 + 48 * q^70 + 4 * q^71 - 7 * q^72 - 7 * q^73 - 38 * q^74 + 13 * q^75 - 14 * q^76 - q^77 - 25 * q^78 - 11 * q^79 + 2 * q^80 + 23 * q^81 - 8 * q^82 + 36 * q^83 - 5 * q^84 + 5 * q^85 + 48 * q^86 + 6 * q^88 - 26 * q^89 + 13 * q^90 - 38 * q^91 - 19 * q^92 - 49 * q^93 + 8 * q^94 - 22 * q^95 - 39 * q^96 - 14 * q^97 + 41 * q^98 - 13 * q^99

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