LMFDB - Embedded newform 3971.2.a.i.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3971,2,Mod(1,3971)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3971, 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("3971.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3971 = 11 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3971.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:	$31.7085946427$
Analytic rank:	$0$
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} - x^{6} - 14x^{5} + 10x^{4} + 59x^{3} - 27x^{2} - 66x + 30 $ x^7 - x^6 - 14x^5 + 10x^4 + 59x^3 - 27x^2 - 66*x + 30
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 209)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$1.19313$ of defining polynomial
Character	$\chi$	$=$	3971.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.19313 q^{2} -3.16232 q^{3} -0.576442 q^{4} +1.08235 q^{5} -3.77306 q^{6} -1.30958 q^{7} -3.07403 q^{8} +7.00029 q^{9} +O(q^{10})$	\(q+1.19313 q^{2} -3.16232 q^{3} -0.576442 q^{4} +1.08235 q^{5} -3.77306 q^{6} -1.30958 q^{7} -3.07403 q^{8} +7.00029 q^{9} +1.29138 q^{10} -1.00000 q^{11} +1.82290 q^{12} -2.53997 q^{13} -1.56249 q^{14} -3.42273 q^{15} -2.51483 q^{16} -5.43892 q^{17} +8.35226 q^{18} -0.623909 q^{20} +4.14130 q^{21} -1.19313 q^{22} +3.87095 q^{23} +9.72108 q^{24} -3.82853 q^{25} -3.03052 q^{26} -12.6502 q^{27} +0.754894 q^{28} +2.41412 q^{29} -4.08376 q^{30} -3.03647 q^{31} +3.14754 q^{32} +3.16232 q^{33} -6.48934 q^{34} -1.41741 q^{35} -4.03526 q^{36} -6.85067 q^{37} +8.03222 q^{39} -3.32716 q^{40} +6.11344 q^{41} +4.94111 q^{42} -2.95329 q^{43} +0.576442 q^{44} +7.57673 q^{45} +4.61854 q^{46} -12.0923 q^{47} +7.95271 q^{48} -5.28501 q^{49} -4.56793 q^{50} +17.1996 q^{51} +1.46415 q^{52} +0.992927 q^{53} -15.0933 q^{54} -1.08235 q^{55} +4.02567 q^{56} +2.88036 q^{58} +14.2251 q^{59} +1.97300 q^{60} -5.82518 q^{61} -3.62290 q^{62} -9.16741 q^{63} +8.78508 q^{64} -2.74913 q^{65} +3.77306 q^{66} -8.79718 q^{67} +3.13522 q^{68} -12.2412 q^{69} -1.69116 q^{70} +2.44975 q^{71} -21.5191 q^{72} +5.84063 q^{73} -8.17374 q^{74} +12.1070 q^{75} +1.30958 q^{77} +9.58348 q^{78} -17.0397 q^{79} -2.72192 q^{80} +19.0032 q^{81} +7.29413 q^{82} -7.01303 q^{83} -2.38722 q^{84} -5.88679 q^{85} -3.52366 q^{86} -7.63422 q^{87} +3.07403 q^{88} +9.13103 q^{89} +9.04003 q^{90} +3.32629 q^{91} -2.23138 q^{92} +9.60229 q^{93} -14.4277 q^{94} -9.95354 q^{96} +14.7950 q^{97} -6.30570 q^{98} -7.00029 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + q^{2} - 2 q^{3} + 15 q^{4} + 2 q^{5} - 2 q^{6} + 10 q^{7} + 9 q^{8} + 11 q^{9}+O(q^{10}) $ 7 * q + q^2 - 2 * q^3 + 15 * q^4 + 2 * q^5 - 2 * q^6 + 10 * q^7 + 9 * q^8 + 11 * q^9	\( 7 q + q^{2} - 2 q^{3} + 15 q^{4} + 2 q^{5} - 2 q^{6} + 10 q^{7} + 9 q^{8} + 11 q^{9} + 6 q^{10} - 7 q^{11} + 16 q^{12} + 4 q^{13} - 6 q^{14} - 12 q^{15} + 27 q^{16} + 2 q^{17} - 9 q^{18} - 4 q^{20} + 14 q^{21} - q^{22} + 10 q^{23} - 2 q^{24} + 9 q^{25} - 8 q^{26} + 4 q^{27} + 26 q^{28} + 18 q^{29} - 42 q^{30} - 24 q^{31} + 49 q^{32} + 2 q^{33} + 6 q^{34} + 8 q^{35} + 29 q^{36} + 24 q^{39} + 2 q^{40} + 12 q^{41} - 44 q^{42} + 2 q^{43} - 15 q^{44} - 4 q^{45} + 4 q^{46} + 8 q^{47} + 72 q^{48} + 17 q^{49} + 33 q^{50} + 24 q^{51} + 60 q^{52} - 2 q^{53} - 52 q^{54} - 2 q^{55} - 26 q^{56} - 8 q^{58} + 10 q^{59} - 42 q^{60} + 14 q^{61} + 14 q^{62} + 55 q^{64} + 14 q^{65} + 2 q^{66} - 8 q^{67} - 18 q^{68} + 6 q^{69} + 66 q^{70} - 10 q^{71} - 53 q^{72} - 6 q^{73} + 26 q^{74} - 26 q^{75} - 10 q^{77} - 22 q^{78} - 52 q^{79} - 12 q^{80} - q^{81} + 24 q^{82} - 10 q^{83} + 6 q^{84} - 12 q^{85} - 8 q^{86} + 6 q^{87} - 9 q^{88} - 20 q^{90} - 12 q^{91} + 2 q^{93} - 24 q^{94} + 6 q^{96} + 24 q^{97} - 19 q^{98} - 11 q^{99}+O(q^{100}) \) 7 * q + q^2 - 2 * q^3 + 15 * q^4 + 2 * q^5 - 2 * q^6 + 10 * q^7 + 9 * q^8 + 11 * q^9 + 6 * q^10 - 7 * q^11 + 16 * q^12 + 4 * q^13 - 6 * q^14 - 12 * q^15 + 27 * q^16 + 2 * q^17 - 9 * q^18 - 4 * q^20 + 14 * q^21 - q^22 + 10 * q^23 - 2 * q^24 + 9 * q^25 - 8 * q^26 + 4 * q^27 + 26 * q^28 + 18 * q^29 - 42 * q^30 - 24 * q^31 + 49 * q^32 + 2 * q^33 + 6 * q^34 + 8 * q^35 + 29 * q^36 + 24 * q^39 + 2 * q^40 + 12 * q^41 - 44 * q^42 + 2 * q^43 - 15 * q^44 - 4 * q^45 + 4 * q^46 + 8 * q^47 + 72 * q^48 + 17 * q^49 + 33 * q^50 + 24 * q^51 + 60 * q^52 - 2 * q^53 - 52 * q^54 - 2 * q^55 - 26 * q^56 - 8 * q^58 + 10 * q^59 - 42 * q^60 + 14 * q^61 + 14 * q^62 + 55 * q^64 + 14 * q^65 + 2 * q^66 - 8 * q^67 - 18 * q^68 + 6 * q^69 + 66 * q^70 - 10 * q^71 - 53 * q^72 - 6 * q^73 + 26 * q^74 - 26 * q^75 - 10 * q^77 - 22 * q^78 - 52 * q^79 - 12 * q^80 - q^81 + 24 * q^82 - 10 * q^83 + 6 * q^84 - 12 * q^85 - 8 * q^86 + 6 * q^87 - 9 * q^88 - 20 * q^90 - 12 * q^91 + 2 * q^93 - 24 * q^94 + 6 * q^96 + 24 * q^97 - 19 * q^98 - 11 * 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 $

$2$	1.19313	0.843670	0.421835	−	0.906673i	$-0.361386\pi$
$2$	1.19313	0.843670	0.421835	+	0.906673i	$0.361386\pi$
$3$	−3.16232	−1.82577	−0.912884	−	0.408218i	$-0.866150\pi$
$3$	−3.16232	−1.82577	−0.912884	+	0.408218i	$0.866150\pi$
$4$	−0.576442	−0.288221
$5$	1.08235	0.484040	0.242020	−	0.970271i	$-0.422190\pi$
$5$	1.08235	0.484040	0.242020	+	0.970271i	$0.422190\pi$
$6$	−3.77306	−1.54035
$7$	−1.30958	−0.494973	−0.247487	−	0.968891i	$-0.579605\pi$
$7$	−1.30958	−0.494973	−0.247487	+	0.968891i	$0.579605\pi$
$8$	−3.07403	−1.08683
$9$	7.00029	2.33343
$10$	1.29138	0.408370
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.82290	0.526225
$13$	−2.53997	−0.704462	−0.352231	−	0.935913i	$-0.614577\pi$
$13$	−2.53997	−0.704462	−0.352231	+	0.935913i	$0.614577\pi$
$14$	−1.56249	−0.417594
$15$	−3.42273	−0.883744
$16$	−2.51483	−0.628708
$17$	−5.43892	−1.31913	−0.659566	−	0.751646i	$-0.729260\pi$
$17$	−5.43892	−1.31913	−0.659566	+	0.751646i	$0.729260\pi$
$18$	8.35226	1.96865
$19$	0	0
$19$	0	0
$20$	−0.623909	−0.139510
$21$	4.14130	0.903706
$22$	−1.19313	−0.254376
$23$	3.87095	0.807148	0.403574	−	0.914947i	$-0.367768\pi$
$23$	3.87095	0.807148	0.403574	+	0.914947i	$0.367768\pi$
$24$	9.72108	1.98431
$25$	−3.82853	−0.765706
$26$	−3.03052	−0.594334
$27$	−12.6502	−2.43454
$28$	0.754894	0.142662
$29$	2.41412	0.448290	0.224145	−	0.974556i	$-0.428041\pi$
$29$	2.41412	0.448290	0.224145	+	0.974556i	$0.428041\pi$
$30$	−4.08376	−0.745588
$31$	−3.03647	−0.545366	−0.272683	−	0.962104i	$-0.587911\pi$
$31$	−3.03647	−0.545366	−0.272683	+	0.962104i	$0.587911\pi$
$32$	3.14754	0.556412
$33$	3.16232	0.550490
$34$	−6.48934	−1.11291
$35$	−1.41741	−0.239587
$36$	−4.03526	−0.672544
$37$	−6.85067	−1.12624	−0.563122	−	0.826374i	$-0.690400\pi$
$37$	−6.85067	−1.12624	−0.563122	+	0.826374i	$0.690400\pi$
$38$	0	0
$39$	8.03222	1.28618
$40$	−3.32716	−0.526070
$41$	6.11344	0.954759	0.477380	−	0.878697i	$-0.341587\pi$
$41$	6.11344	0.954759	0.477380	+	0.878697i	$0.341587\pi$
$42$	4.94111	0.762430
$43$	−2.95329	−0.450373	−0.225186	−	0.974316i	$-0.572299\pi$
$43$	−2.95329	−0.450373	−0.225186	+	0.974316i	$0.572299\pi$
$44$	0.576442	0.0869019
$45$	7.57673	1.12947
$46$	4.61854	0.680966
$47$	−12.0923	−1.76385	−0.881925	−	0.471391i	$-0.843752\pi$
$47$	−12.0923	−1.76385	−0.881925	+	0.471391i	$0.843752\pi$
$48$	7.95271	1.14787
$49$	−5.28501	−0.755002
$50$	−4.56793	−0.646003
$51$	17.1996	2.40843
$52$	1.46415	0.203041
$53$	0.992927	0.136389	0.0681945	−	0.997672i	$-0.478276\pi$
$53$	0.992927	0.136389	0.0681945	+	0.997672i	$0.478276\pi$
$54$	−15.0933	−2.05394
$55$	−1.08235	−0.145943
$56$	4.02567	0.537953
$57$	0	0
$58$	2.88036	0.378209
$59$	14.2251	1.85195	0.925977	−	0.377580i	$-0.123244\pi$
$59$	14.2251	1.85195	0.925977	+	0.377580i	$0.123244\pi$
$60$	1.97300	0.254714
$61$	−5.82518	−0.745838	−0.372919	−	0.927864i	$-0.621643\pi$
$61$	−5.82518	−0.745838	−0.372919	+	0.927864i	$0.621643\pi$
$62$	−3.62290	−0.460109
$63$	−9.16741	−1.15499
$64$	8.78508	1.09814
$65$	−2.74913	−0.340988
$66$	3.77306	0.464432
$67$	−8.79718	−1.07475	−0.537373	−	0.843345i	$-0.680583\pi$
$67$	−8.79718	−1.07475	−0.537373	+	0.843345i	$0.680583\pi$
$68$	3.13522	0.380202
$69$	−12.2412	−1.47367
$70$	−1.69116	−0.202132
$71$	2.44975	0.290732	0.145366	−	0.989378i	$-0.453564\pi$
$71$	2.44975	0.290732	0.145366	+	0.989378i	$0.453564\pi$
$72$	−21.5191	−2.53605
$73$	5.84063	0.683594	0.341797	−	0.939774i	$-0.388965\pi$
$73$	5.84063	0.683594	0.341797	+	0.939774i	$0.388965\pi$
$74$	−8.17374	−0.950178
$75$	12.1070	1.39800
$76$	0	0
$77$	1.30958	0.149240
$78$	9.58348	1.08512
$79$	−17.0397	−1.91711	−0.958557	−	0.284902i	$-0.908039\pi$
$79$	−17.0397	−1.91711	−0.958557	+	0.284902i	$0.908039\pi$
$80$	−2.72192	−0.304319
$81$	19.0032	2.11147
$82$	7.29413	0.805502
$83$	−7.01303	−0.769780	−0.384890	−	0.922963i	$-0.625761\pi$
$83$	−7.01303	−0.769780	−0.384890	+	0.922963i	$0.625761\pi$
$84$	−2.38722	−0.260467
$85$	−5.88679	−0.638512
$86$	−3.52366	−0.379966
$87$	−7.63422	−0.818475
$88$	3.07403	0.327693
$89$	9.13103	0.967887	0.483944	−	0.875099i	$-0.339204\pi$
$89$	9.13103	0.967887	0.483944	+	0.875099i	$0.339204\pi$
$90$	9.04003	0.952902
$91$	3.32629	0.348690
$92$	−2.23138	−0.232637
$93$	9.60229	0.995712
$94$	−14.4277	−1.48811
$95$	0	0
$96$	−9.95354	−1.01588
$97$	14.7950	1.50220	0.751100	−	0.660188i	$-0.229524\pi$
$97$	14.7950	1.50220	0.751100	+	0.660188i	$0.229524\pi$
$98$	−6.30570	−0.636972
$99$	−7.00029	−0.703556
$100$	2.20692	0.220692
$101$	19.0516	1.89570	0.947852	−	0.318711i	$-0.103250\pi$
$101$	19.0516	1.89570	0.947852	+	0.318711i	$0.103250\pi$
$102$	20.5214	2.03192
$103$	−10.4722	−1.03186	−0.515928	−	0.856632i	$-0.672553\pi$
$103$	−10.4722	−1.03186	−0.515928	+	0.856632i	$0.672553\pi$
$104$	7.80795	0.765633
$105$	4.48232	0.437430
$106$	1.18469	0.115067
$107$	−14.4916	−1.40095	−0.700477	−	0.713675i	$-0.747029\pi$
$107$	−14.4916	−1.40095	−0.700477	+	0.713675i	$0.747029\pi$
$108$	7.29212	0.701684
$109$	6.39919	0.612931	0.306465	−	0.951882i	$-0.400854\pi$
$109$	6.39919	0.612931	0.306465	+	0.951882i	$0.400854\pi$
$110$	−1.29138	−0.123128
$111$	21.6640	2.05626
$112$	3.29336	0.311193
$113$	2.91702	0.274410	0.137205	−	0.990543i	$-0.456188\pi$
$113$	2.91702	0.274410	0.137205	+	0.990543i	$0.456188\pi$
$114$	0	0
$115$	4.18970	0.390692
$116$	−1.39160	−0.129207
$117$	−17.7806	−1.64381
$118$	16.9724	1.56244
$119$	7.12268	0.652935
$120$	10.5216	0.960483
$121$	1.00000	0.0909091
$122$	−6.95020	−0.629241
$123$	−19.3327	−1.74317
$124$	1.75035	0.157186
$125$	−9.55552	−0.854671
$126$	−10.9379	−0.974426
$127$	12.1995	1.08253	0.541267	−	0.840851i	$-0.317945\pi$
$127$	12.1995	1.08253	0.541267	+	0.840851i	$0.317945\pi$
$128$	4.18666	0.370052
$129$	9.33926	0.822276
$130$	−3.28007	−0.287681
$131$	18.7468	1.63792	0.818959	−	0.573852i	$-0.194551\pi$
$131$	18.7468	1.63792	0.818959	+	0.573852i	$0.194551\pi$
$132$	−1.82290	−0.158663
$133$	0	0
$134$	−10.4962	−0.906731
$135$	−13.6919	−1.17841
$136$	16.7194	1.43368
$137$	16.8291	1.43781	0.718904	−	0.695109i	$-0.244644\pi$
$137$	16.8291	1.43781	0.718904	+	0.695109i	$0.244644\pi$
$138$	−14.6053	−1.24329
$139$	12.5906	1.06792	0.533959	−	0.845511i	$-0.320704\pi$
$139$	12.5906	1.06792	0.533959	+	0.845511i	$0.320704\pi$
$140$	0.817056	0.0690539
$141$	38.2399	3.22038
$142$	2.92287	0.245282
$143$	2.53997	0.212403
$144$	−17.6045	−1.46705
$145$	2.61291	0.216990
$146$	6.96862	0.576727
$147$	16.7129	1.37846
$148$	3.94902	0.324607
$149$	6.22689	0.510126	0.255063	−	0.966924i	$-0.417904\pi$
$149$	6.22689	0.510126	0.255063	+	0.966924i	$0.417904\pi$
$150$	14.4453	1.17945
$151$	−6.14114	−0.499759	−0.249879	−	0.968277i	$-0.580391\pi$
$151$	−6.14114	−0.499759	−0.249879	+	0.968277i	$0.580391\pi$
$152$	0	0
$153$	−38.0740	−3.07810
$154$	1.56249	0.125909
$155$	−3.28651	−0.263979
$156$	−4.63011	−0.370705
$157$	19.7489	1.57613	0.788065	−	0.615592i	$-0.211083\pi$
$157$	19.7489	1.57613	0.788065	+	0.615592i	$0.211083\pi$
$158$	−20.3305	−1.61741
$159$	−3.13996	−0.249015
$160$	3.40672	0.269325
$161$	−5.06930	−0.399517
$162$	22.6733	1.78138
$163$	−5.70383	−0.446759	−0.223379	−	0.974732i	$-0.571709\pi$
$163$	−5.70383	−0.446759	−0.223379	+	0.974732i	$0.571709\pi$
$164$	−3.52405	−0.275182
$165$	3.42273	0.266459
$166$	−8.36745	−0.649440
$167$	10.1612	0.786294	0.393147	−	0.919476i	$-0.371386\pi$
$167$	10.1612	0.786294	0.393147	+	0.919476i	$0.371386\pi$
$168$	−12.7305	−0.982178
$169$	−6.54853	−0.503733
$170$	−7.02371	−0.538694
$171$	0	0
$172$	1.70240	0.129807
$173$	−2.22385	−0.169076	−0.0845382	−	0.996420i	$-0.526942\pi$
$173$	−2.22385	−0.169076	−0.0845382	+	0.996420i	$0.526942\pi$
$174$	−9.10862	−0.690522
$175$	5.01375	0.379004
$176$	2.51483	0.189562
$177$	−44.9845	−3.38124
$178$	10.8945	0.816577
$179$	−12.0997	−0.904376	−0.452188	−	0.891923i	$-0.649356\pi$
$179$	−12.0997	−0.904376	−0.452188	+	0.891923i	$0.649356\pi$
$180$	−4.36755	−0.325538
$181$	0.359088	0.0266908	0.0133454	−	0.999911i	$-0.495752\pi$
$181$	0.359088	0.0266908	0.0133454	+	0.999911i	$0.495752\pi$
$182$	3.96869	0.294179
$183$	18.4211	1.36173
$184$	−11.8994	−0.877235
$185$	−7.41479	−0.545147
$186$	11.4568	0.840052
$187$	5.43892	0.397733
$188$	6.97053	0.508378
$189$	16.5664	1.20503
$190$	0	0
$191$	21.3246	1.54299	0.771496	−	0.636235i	$-0.219509\pi$
$191$	21.3246	1.54299	0.771496	+	0.636235i	$0.219509\pi$
$192$	−27.7813	−2.00494
$193$	14.5451	1.04698	0.523491	−	0.852031i	$-0.324630\pi$
$193$	14.5451	1.04698	0.523491	+	0.852031i	$0.324630\pi$
$194$	17.6523	1.26736
$195$	8.69364	0.622564
$196$	3.04650	0.217607
$197$	−4.71318	−0.335800	−0.167900	−	0.985804i	$-0.553699\pi$
$197$	−4.71318	−0.335800	−0.167900	+	0.985804i	$0.553699\pi$
$198$	−8.35226	−0.593569
$199$	−1.77204	−0.125616	−0.0628081	−	0.998026i	$-0.520006\pi$
$199$	−1.77204	−0.125616	−0.0628081	+	0.998026i	$0.520006\pi$
$200$	11.7690	0.832194
$201$	27.8195	1.96224
$202$	22.7310	1.59935
$203$	−3.16147	−0.221892
$204$	−9.91459	−0.694160
$205$	6.61686	0.462141
$206$	−12.4947	−0.870546
$207$	27.0977	1.88342
$208$	6.38761	0.442901
$209$	0	0
$210$	5.34799	0.369046
$211$	−17.8069	−1.22588	−0.612940	−	0.790129i	$-0.710013\pi$
$211$	−17.8069	−1.22588	−0.612940	+	0.790129i	$0.710013\pi$
$212$	−0.572365	−0.0393102
$213$	−7.74692	−0.530810
$214$	−17.2903	−1.18194
$215$	−3.19648	−0.217998
$216$	38.8871	2.64593
$217$	3.97648	0.269941
$218$	7.63506	0.517111
$219$	−18.4700	−1.24808
$220$	0.623909	0.0420640
$221$	13.8147	0.929279
$222$	25.8480	1.73481
$223$	9.69081	0.648945	0.324472	−	0.945895i	$-0.394813\pi$
$223$	9.69081	0.648945	0.324472	+	0.945895i	$0.394813\pi$
$224$	−4.12194	−0.275409
$225$	−26.8008	−1.78672
$226$	3.48038	0.231511
$227$	6.02204	0.399697	0.199848	−	0.979827i	$-0.435955\pi$
$227$	6.02204	0.399697	0.199848	+	0.979827i	$0.435955\pi$
$228$	0	0
$229$	21.7503	1.43730	0.718649	−	0.695373i	$-0.244761\pi$
$229$	21.7503	1.43730	0.718649	+	0.695373i	$0.244761\pi$
$230$	4.99885	0.329615
$231$	−4.14130	−0.272478
$232$	−7.42107	−0.487217
$233$	−15.6866	−1.02766	−0.513831	−	0.857891i	$-0.671774\pi$
$233$	−15.6866	−1.02766	−0.513831	+	0.857891i	$0.671774\pi$
$234$	−21.2145	−1.38684
$235$	−13.0881	−0.853773
$236$	−8.19996	−0.533772
$237$	53.8850	3.50021
$238$	8.49828	0.550862
$239$	21.8841	1.41556	0.707782	−	0.706430i	$-0.249696\pi$
$239$	21.8841	1.41556	0.707782	+	0.706430i	$0.249696\pi$
$240$	8.60758	0.555617
$241$	−5.98510	−0.385534	−0.192767	−	0.981245i	$-0.561746\pi$
$241$	−5.98510	−0.385534	−0.192767	+	0.981245i	$0.561746\pi$
$242$	1.19313	0.0766973
$243$	−22.1437	−1.42052
$244$	3.35788	0.214966
$245$	−5.72021	−0.365451
$246$	−23.0664	−1.47066
$247$	0	0
$248$	9.33419	0.592722
$249$	22.1775	1.40544
$250$	−11.4010	−0.721061
$251$	−6.63439	−0.418759	−0.209379	−	0.977834i	$-0.567144\pi$
$251$	−6.63439	−0.418759	−0.209379	+	0.977834i	$0.567144\pi$
$252$	5.28448	0.332891
$253$	−3.87095	−0.243364
$254$	14.5556	0.913302
$255$	18.6159	1.16578
$256$	−12.5749	−0.785933
$257$	9.31591	0.581111	0.290555	−	0.956858i	$-0.406160\pi$
$257$	9.31591	0.581111	0.290555	+	0.956858i	$0.406160\pi$
$258$	11.1429	0.693730
$259$	8.97148	0.557460
$260$	1.58471	0.0982798
$261$	16.8995	1.04605
$262$	22.3674	1.38186
$263$	−9.25004	−0.570382	−0.285191	−	0.958471i	$-0.592057\pi$
$263$	−9.25004	−0.570382	−0.285191	+	0.958471i	$0.592057\pi$
$264$	−9.72108	−0.598291
$265$	1.07469	0.0660177
$266$	0	0
$267$	−28.8753	−1.76714
$268$	5.07106	0.309764
$269$	17.0076	1.03697	0.518486	−	0.855086i	$-0.326496\pi$
$269$	17.0076	1.03697	0.518486	+	0.855086i	$0.326496\pi$
$270$	−16.3362	−0.994191
$271$	7.43527	0.451660	0.225830	−	0.974167i	$-0.427491\pi$
$271$	7.43527	0.451660	0.225830	+	0.974167i	$0.427491\pi$
$272$	13.6780	0.829349
$273$	−10.5188	−0.636627
$274$	20.0793	1.21304
$275$	3.82853	0.230869
$276$	7.05633	0.424741
$277$	2.31338	0.138998	0.0694989	−	0.997582i	$-0.477860\pi$
$277$	2.31338	0.138998	0.0694989	+	0.997582i	$0.477860\pi$
$278$	15.0222	0.900970
$279$	−21.2562	−1.27257
$280$	4.35717	0.260391
$281$	5.20248	0.310354	0.155177	−	0.987887i	$-0.450405\pi$
$281$	5.20248	0.310354	0.155177	+	0.987887i	$0.450405\pi$
$282$	45.6251	2.71694
$283$	26.7125	1.58789	0.793947	−	0.607987i	$-0.208023\pi$
$283$	26.7125	1.58789	0.793947	+	0.607987i	$0.208023\pi$
$284$	−1.41214	−0.0837952
$285$	0	0
$286$	3.03052	0.179198
$287$	−8.00602	−0.472580
$288$	22.0337	1.29835
$289$	12.5819	0.740110
$290$	3.11754	0.183068
$291$	−46.7864	−2.74267
$292$	−3.36678	−0.197026
$293$	0.937617	0.0547762	0.0273881	−	0.999625i	$-0.491281\pi$
$293$	0.937617	0.0547762	0.0273881	+	0.999625i	$0.491281\pi$
$294$	19.9407	1.16296
$295$	15.3965	0.896419
$296$	21.0592	1.22404
$297$	12.6502	0.734040
$298$	7.42948	0.430378
$299$	−9.83210	−0.568605
$300$	−6.97901	−0.402933
$301$	3.86756	0.222922
$302$	−7.32717	−0.421631
$303$	−60.2473	−3.46112
$304$	0	0
$305$	−6.30486	−0.361015
$306$	−45.4273	−2.59690
$307$	4.83167	0.275758	0.137879	−	0.990449i	$-0.455971\pi$
$307$	4.83167	0.275758	0.137879	+	0.990449i	$0.455971\pi$
$308$	−0.754894	−0.0430141
$309$	33.1165	1.88393
$310$	−3.92123	−0.222711
$311$	−14.3916	−0.816071	−0.408036	−	0.912966i	$-0.633786\pi$
$311$	−14.3916	−0.816071	−0.408036	+	0.912966i	$0.633786\pi$
$312$	−24.6913	−1.39787
$313$	−29.3478	−1.65884	−0.829418	−	0.558628i	$-0.811328\pi$
$313$	−29.3478	−1.65884	−0.829418	+	0.558628i	$0.811328\pi$
$314$	23.5629	1.32973
$315$	−9.92231	−0.559059
$316$	9.82238	0.552552
$317$	16.4027	0.921267	0.460633	−	0.887590i	$-0.347622\pi$
$317$	16.4027	0.921267	0.460633	+	0.887590i	$0.347622\pi$
$318$	−3.74638	−0.210086
$319$	−2.41412	−0.135165
$320$	9.50849	0.531541
$321$	45.8271	2.55782
$322$	−6.04833	−0.337060
$323$	0	0
$324$	−10.9543	−0.608569
$325$	9.72436	0.539411
$326$	−6.80541	−0.376917
$327$	−20.2363	−1.11907
$328$	−18.7929	−1.03766
$329$	15.8358	0.873058
$330$	4.08376	0.224803
$331$	−14.1995	−0.780477	−0.390239	−	0.920714i	$-0.627608\pi$
$331$	−14.1995	−0.780477	−0.390239	+	0.920714i	$0.627608\pi$
$332$	4.04260	0.221867
$333$	−47.9567	−2.62801
$334$	12.1236	0.663372
$335$	−9.52159	−0.520220
$336$	−10.4147	−0.568167
$337$	22.1449	1.20631	0.603154	−	0.797624i	$-0.293910\pi$
$337$	22.1449	1.20631	0.603154	+	0.797624i	$0.293910\pi$
$338$	−7.81325	−0.424985
$339$	−9.22456	−0.501009
$340$	3.39339	0.184033
$341$	3.03647	0.164434
$342$	0	0
$343$	16.0882	0.868679
$344$	9.07850	0.489480
$345$	−13.2492	−0.713312
$346$	−2.65334	−0.142645
$347$	−19.1475	−1.02789	−0.513946	−	0.857823i	$-0.671817\pi$
$347$	−19.1475	−1.02789	−0.513946	+	0.857823i	$0.671817\pi$
$348$	4.40069	0.235902
$349$	−16.0709	−0.860255	−0.430127	−	0.902768i	$-0.641531\pi$
$349$	−16.0709	−0.860255	−0.430127	+	0.902768i	$0.641531\pi$
$350$	5.98205	0.319754
$351$	32.1312	1.71504
$352$	−3.14754	−0.167764
$353$	10.9142	0.580902	0.290451	−	0.956890i	$-0.406195\pi$
$353$	10.9142	0.580902	0.290451	+	0.956890i	$0.406195\pi$
$354$	−53.6723	−2.85265
$355$	2.65148	0.140726
$356$	−5.26351	−0.278965
$357$	−22.5242	−1.19211
$358$	−14.4365	−0.762995
$359$	−35.4105	−1.86889	−0.934446	−	0.356104i	$-0.884105\pi$
$359$	−35.4105	−1.86889	−0.934446	+	0.356104i	$0.884105\pi$
$360$	−23.2911	−1.22755
$361$	0	0
$362$	0.428438	0.0225182
$363$	−3.16232	−0.165979
$364$	−1.91741	−0.100500
$365$	6.32158	0.330886
$366$	21.9788	1.14885
$367$	−23.3384	−1.21825	−0.609127	−	0.793073i	$-0.708480\pi$
$367$	−23.3384	−1.21825	−0.609127	+	0.793073i	$0.708480\pi$
$368$	−9.73477	−0.507460
$369$	42.7959	2.22786
$370$	−8.84681	−0.459924
$371$	−1.30031	−0.0675089
$372$	−5.53517	−0.286985
$373$	17.1972	0.890440	0.445220	−	0.895421i	$-0.353126\pi$
$373$	17.1972	0.890440	0.445220	+	0.895421i	$0.353126\pi$
$374$	6.48934	0.335556
$375$	30.2176	1.56043
$376$	37.1722	1.91701
$377$	−6.13180	−0.315804
$378$	19.7659	1.01665
$379$	−25.2353	−1.29625	−0.648125	−	0.761534i	$-0.724447\pi$
$379$	−25.2353	−1.29625	−0.648125	+	0.761534i	$0.724447\pi$
$380$	0	0
$381$	−38.5789	−1.97646
$382$	25.4430	1.30178
$383$	−29.6247	−1.51375	−0.756877	−	0.653558i	$-0.773276\pi$
$383$	−29.6247	−1.51375	−0.756877	+	0.653558i	$0.773276\pi$
$384$	−13.2396	−0.675630
$385$	1.41741	0.0722381
$386$	17.3542	0.883307
$387$	−20.6739	−1.05091
$388$	−8.52843	−0.432966
$389$	7.70975	0.390900	0.195450	−	0.980714i	$-0.437383\pi$
$389$	7.70975	0.390900	0.195450	+	0.980714i	$0.437383\pi$
$390$	10.3726	0.525239
$391$	−21.0538	−1.06474
$392$	16.2463	0.820561
$393$	−59.2836	−2.99046
$394$	−5.62344	−0.283305
$395$	−18.4428	−0.927959
$396$	4.03526	0.202780
$397$	8.26973	0.415046	0.207523	−	0.978230i	$-0.433460\pi$
$397$	8.26973	0.415046	0.207523	+	0.978230i	$0.433460\pi$
$398$	−2.11427	−0.105979
$399$	0	0
$400$	9.62810	0.481405
$401$	−1.98297	−0.0990247	−0.0495123	−	0.998774i	$-0.515767\pi$
$401$	−1.98297	−0.0990247	−0.0495123	+	0.998774i	$0.515767\pi$
$402$	33.1923	1.65548
$403$	7.71255	0.384189
$404$	−10.9821	−0.546382
$405$	20.5680	1.02203
$406$	−3.77204	−0.187203
$407$	6.85067	0.339575
$408$	−52.8722	−2.61756
$409$	−25.8761	−1.27949	−0.639746	−	0.768586i	$-0.720960\pi$
$409$	−25.8761	−1.27949	−0.639746	+	0.768586i	$0.720960\pi$
$410$	7.89477	0.389895
$411$	−53.2191	−2.62510
$412$	6.03661	0.297402
$413$	−18.6289	−0.916667
$414$	32.3311	1.58899
$415$	−7.59052	−0.372604
$416$	−7.99467	−0.391971
$417$	−39.8154	−1.94977
$418$	0	0
$419$	36.2262	1.76977	0.884883	−	0.465813i	$-0.154238\pi$
$419$	36.2262	1.76977	0.884883	+	0.465813i	$0.154238\pi$
$420$	−2.58380	−0.126076
$421$	5.91248	0.288156	0.144078	−	0.989566i	$-0.453978\pi$
$421$	5.91248	0.288156	0.144078	+	0.989566i	$0.453978\pi$
$422$	−21.2460	−1.03424
$423$	−84.6499	−4.11582
$424$	−3.05229	−0.148232
$425$	20.8231	1.01007
$426$	−9.24308	−0.447828
$427$	7.62852	0.369170
$428$	8.35356	0.403784
$429$	−8.03222	−0.387799
$430$	−3.81382	−0.183919
$431$	11.1886	0.538935	0.269468	−	0.963009i	$-0.413152\pi$
$431$	11.1886	0.538935	0.269468	+	0.963009i	$0.413152\pi$
$432$	31.8132	1.53061
$433$	−13.3903	−0.643497	−0.321748	−	0.946825i	$-0.604271\pi$
$433$	−13.3903	−0.643497	−0.321748	+	0.946825i	$0.604271\pi$
$434$	4.74446	0.227741
$435$	−8.26287	−0.396174
$436$	−3.68876	−0.176660
$437$	0	0
$438$	−22.0370	−1.05297
$439$	−23.6338	−1.12798	−0.563989	−	0.825782i	$-0.690734\pi$
$439$	−23.6338	−1.12798	−0.563989	+	0.825782i	$0.690734\pi$
$440$	3.32716	0.158616
$441$	−36.9966	−1.76174
$442$	16.4828	0.784005
$443$	−25.6914	−1.22063	−0.610317	−	0.792158i	$-0.708958\pi$
$443$	−25.6914	−1.22063	−0.610317	+	0.792158i	$0.708958\pi$
$444$	−12.4881	−0.592657
$445$	9.88293	0.468496
$446$	11.5624	0.547495
$447$	−19.6914	−0.931373
$448$	−11.5047	−0.543547
$449$	9.72223	0.458820	0.229410	−	0.973330i	$-0.426320\pi$
$449$	9.72223	0.458820	0.229410	+	0.973330i	$0.426320\pi$
$450$	−31.9768	−1.50740
$451$	−6.11344	−0.287871
$452$	−1.68149	−0.0790907
$453$	19.4203	0.912444
$454$	7.18507	0.337212
$455$	3.60019	0.168780
$456$	0	0
$457$	−2.04841	−0.0958207	−0.0479103	−	0.998852i	$-0.515256\pi$
$457$	−2.04841	−0.0958207	−0.0479103	+	0.998852i	$0.515256\pi$
$458$	25.9509	1.21261
$459$	68.8036	3.21148
$460$	−2.41512	−0.112606
$461$	−22.8905	−1.06612	−0.533059	−	0.846078i	$-0.678958\pi$
$461$	−22.8905	−1.06612	−0.533059	+	0.846078i	$0.678958\pi$
$462$	−4.94111	−0.229881
$463$	34.9486	1.62420	0.812098	−	0.583520i	$-0.198325\pi$
$463$	34.9486	1.62420	0.812098	+	0.583520i	$0.198325\pi$
$464$	−6.07110	−0.281844
$465$	10.3930	0.481964
$466$	−18.7161	−0.867008
$467$	13.7353	0.635595	0.317797	−	0.948159i	$-0.397057\pi$
$467$	13.7353	0.635595	0.317797	+	0.948159i	$0.397057\pi$
$468$	10.2495	0.473782
$469$	11.5206	0.531971
$470$	−15.6158	−0.720302
$471$	−62.4523	−2.87765
$472$	−43.7284	−2.01276
$473$	2.95329	0.135792
$474$	64.2918	2.95302
$475$	0	0
$476$	−4.10581	−0.188190
$477$	6.95078	0.318254
$478$	26.1106	1.19427
$479$	3.13630	0.143301	0.0716506	−	0.997430i	$-0.477173\pi$
$479$	3.13630	0.143301	0.0716506	+	0.997430i	$0.477173\pi$
$480$	−10.7732	−0.491726
$481$	17.4005	0.793396
$482$	−7.14100	−0.325264
$483$	16.0308	0.729425
$484$	−0.576442	−0.0262019
$485$	16.0133	0.727124
$486$	−26.4203	−1.19845
$487$	−21.2263	−0.961854	−0.480927	−	0.876761i	$-0.659700\pi$
$487$	−21.2263	−0.961854	−0.480927	+	0.876761i	$0.659700\pi$
$488$	17.9068	0.810602
$489$	18.0374	0.815678
$490$	−6.82495	−0.308320
$491$	28.5840	1.28998	0.644988	−	0.764193i	$-0.276862\pi$
$491$	28.5840	1.28998	0.644988	+	0.764193i	$0.276862\pi$
$492$	11.1442	0.502418
$493$	−13.1302	−0.591354
$494$	0	0
$495$	−7.57673	−0.340549
$496$	7.63620	0.342876
$497$	−3.20814	−0.143905
$498$	26.4606	1.18573
$499$	−20.1316	−0.901212	−0.450606	−	0.892723i	$-0.648792\pi$
$499$	−20.1316	−0.901212	−0.450606	+	0.892723i	$0.648792\pi$
$500$	5.50820	0.246334
$501$	−32.1329	−1.43559
$502$	−7.91568	−0.353294
$503$	−6.37170	−0.284100	−0.142050	−	0.989859i	$-0.545369\pi$
$503$	−6.37170	−0.284100	−0.142050	+	0.989859i	$0.545369\pi$
$504$	28.1809	1.25528
$505$	20.6204	0.917596
$506$	−4.61854	−0.205319
$507$	20.7086	0.919700
$508$	−7.03233	−0.312009
$509$	9.83799	0.436061	0.218031	−	0.975942i	$-0.430037\pi$
$509$	9.83799	0.436061	0.218031	+	0.975942i	$0.430037\pi$
$510$	22.2112	0.983530
$511$	−7.64874	−0.338360
$512$	−23.3769	−1.03312
$513$	0	0
$514$	11.1151	0.490266
$515$	−11.3345	−0.499459
$516$	−5.38354	−0.236997
$517$	12.0923	0.531820
$518$	10.7041	0.470313
$519$	7.03254	0.308694
$520$	8.45090	0.370597
$521$	−21.1840	−0.928088	−0.464044	−	0.885812i	$-0.653602\pi$
$521$	−21.1840	−0.928088	−0.464044	+	0.885812i	$0.653602\pi$
$522$	20.1633	0.882525
$523$	−22.1326	−0.967790	−0.483895	−	0.875126i	$-0.660778\pi$
$523$	−22.1326	−0.967790	−0.483895	+	0.875126i	$0.660778\pi$
$524$	−10.8065	−0.472083
$525$	−15.8551	−0.691973
$526$	−11.0365	−0.481214
$527$	16.5151	0.719410
$528$	−7.95271	−0.346097
$529$	−8.01578	−0.348512
$530$	1.28224	0.0556971
$531$	99.5800	4.32141
$532$	0	0
$533$	−15.5280	−0.672592
$534$	−34.4519	−1.49088
$535$	−15.6849	−0.678117
$536$	27.0428	1.16807
$537$	38.2633	1.65118
$538$	20.2923	0.874862
$539$	5.28501	0.227642
$540$	7.89259	0.339643
$541$	−1.83412	−0.0788551	−0.0394275	−	0.999222i	$-0.512553\pi$
$541$	−1.83412	−0.0788551	−0.0394275	+	0.999222i	$0.512553\pi$
$542$	8.87124	0.381052
$543$	−1.13555	−0.0487312
$544$	−17.1192	−0.733981
$545$	6.92613	0.296683
$546$	−12.5503	−0.537103
$547$	20.2583	0.866181	0.433091	−	0.901350i	$-0.357423\pi$
$547$	20.2583	0.866181	0.433091	+	0.901350i	$0.357423\pi$
$548$	−9.70101	−0.414406
$549$	−40.7780	−1.74036
$550$	4.56793	0.194777
$551$	0	0
$552$	37.6298	1.60163
$553$	22.3147	0.948920
$554$	2.76017	0.117268
$555$	23.4480	0.995311
$556$	−7.25773	−0.307796
$557$	15.1944	0.643805	0.321903	−	0.946773i	$-0.395678\pi$
$557$	15.1944	0.643805	0.321903	+	0.946773i	$0.395678\pi$
$558$	−25.3614	−1.07363
$559$	7.50128	0.317270
$560$	3.56455	0.150630
$561$	−17.1996	−0.726169
$562$	6.20723	0.261836
$563$	22.4513	0.946210	0.473105	−	0.881006i	$-0.343133\pi$
$563$	22.4513	0.946210	0.473105	+	0.881006i	$0.343133\pi$
$564$	−22.0431	−0.928181
$565$	3.15722	0.132825
$566$	31.8715	1.33966
$567$	−24.8861	−1.04512
$568$	−7.53062	−0.315978
$569$	7.54832	0.316442	0.158221	−	0.987404i	$-0.449424\pi$
$569$	7.54832	0.316442	0.158221	+	0.987404i	$0.449424\pi$
$570$	0	0
$571$	−0.101602	−0.00425192	−0.00212596	−	0.999998i	$-0.500677\pi$
$571$	−0.101602	−0.00425192	−0.00212596	+	0.999998i	$0.500677\pi$
$572$	−1.46415	−0.0612191
$573$	−67.4352	−2.81715
$574$	−9.55221	−0.398702
$575$	−14.8200	−0.618038
$576$	61.4981	2.56242
$577$	−27.8194	−1.15814	−0.579068	−	0.815279i	$-0.696584\pi$
$577$	−27.8194	−1.15814	−0.579068	+	0.815279i	$0.696584\pi$
$578$	15.0118	0.624409
$579$	−45.9964	−1.91155
$580$	−1.50619	−0.0625412
$581$	9.18409	0.381020
$582$	−55.8223	−2.31391
$583$	−0.992927	−0.0411228
$584$	−17.9543	−0.742952
$585$	−19.2447	−0.795671
$586$	1.11870	0.0462130
$587$	15.7385	0.649596	0.324798	−	0.945783i	$-0.394704\pi$
$587$	15.7385	0.649596	0.324798	+	0.945783i	$0.394704\pi$
$588$	−9.63403	−0.397301
$589$	0	0
$590$	18.3700	0.756282
$591$	14.9046	0.613094
$592$	17.2283	0.708078
$593$	33.1616	1.36178	0.680892	−	0.732384i	$-0.261592\pi$
$593$	33.1616	1.36178	0.680892	+	0.732384i	$0.261592\pi$
$594$	15.0933	0.619288
$595$	7.70920	0.316046
$596$	−3.58944	−0.147029
$597$	5.60375	0.229346
$598$	−11.7310	−0.479715
$599$	5.80115	0.237029	0.118514	−	0.992952i	$-0.462187\pi$
$599$	5.80115	0.237029	0.118514	+	0.992952i	$0.462187\pi$
$600$	−37.2174	−1.51939
$601$	21.7148	0.885766	0.442883	−	0.896580i	$-0.353956\pi$
$601$	21.7148	0.885766	0.442883	+	0.896580i	$0.353956\pi$
$602$	4.61450	0.188073
$603$	−61.5828	−2.50785
$604$	3.54001	0.144041
$605$	1.08235	0.0440036
$606$	−71.8828	−2.92004
$607$	30.3992	1.23386	0.616932	−	0.787016i	$-0.288375\pi$
$607$	30.3992	1.23386	0.616932	+	0.787016i	$0.288375\pi$
$608$	0	0
$609$	9.99759	0.405123
$610$	−7.52251	−0.304578
$611$	30.7142	1.24256
$612$	21.9475	0.887174
$613$	8.70645	0.351650	0.175825	−	0.984421i	$-0.443741\pi$
$613$	8.70645	0.351650	0.175825	+	0.984421i	$0.443741\pi$
$614$	5.76481	0.232649
$615$	−20.9246	−0.843763
$616$	−4.02567	−0.162199
$617$	−14.9292	−0.601026	−0.300513	−	0.953778i	$-0.597158\pi$
$617$	−14.9292	−0.601026	−0.300513	+	0.953778i	$0.597158\pi$
$618$	39.5122	1.58941
$619$	−16.5120	−0.663673	−0.331836	−	0.943337i	$-0.607668\pi$
$619$	−16.5120	−0.663673	−0.331836	+	0.943337i	$0.607668\pi$
$620$	1.89448	0.0760842
$621$	−48.9683	−1.96503
$622$	−17.1710	−0.688495
$623$	−11.9578	−0.479078
$624$	−20.1997	−0.808634
$625$	8.80027	0.352011
$626$	−35.0157	−1.39951
$627$	0	0
$628$	−11.3841	−0.454274
$629$	37.2603	1.48566
$630$	−11.8386	−0.471661
$631$	33.1047	1.31788	0.658938	−	0.752197i	$-0.271006\pi$
$631$	33.1047	1.31788	0.658938	+	0.752197i	$0.271006\pi$
$632$	52.3805	2.08358
$633$	56.3113	2.23817
$634$	19.5705	0.777245
$635$	13.2041	0.523989
$636$	1.81000	0.0717713
$637$	13.4238	0.531870
$638$	−2.88036	−0.114034
$639$	17.1490	0.678404
$640$	4.53142	0.179120
$641$	−9.80138	−0.387131	−0.193566	−	0.981087i	$-0.562005\pi$
$641$	−9.80138	−0.387131	−0.193566	+	0.981087i	$0.562005\pi$
$642$	54.6776	2.15795
$643$	−14.1775	−0.559106	−0.279553	−	0.960130i	$-0.590186\pi$
$643$	−14.1775	−0.559106	−0.279553	+	0.960130i	$0.590186\pi$
$644$	2.92216	0.115149
$645$	10.1083	0.398014
$646$	0	0
$647$	2.89498	0.113813	0.0569067	−	0.998379i	$-0.481876\pi$
$647$	2.89498	0.113813	0.0569067	+	0.998379i	$0.481876\pi$
$648$	−58.4164	−2.29481
$649$	−14.2251	−0.558385
$650$	11.6024	0.455085
$651$	−12.5749	−0.492850
$652$	3.28793	0.128765
$653$	14.5415	0.569054	0.284527	−	0.958668i	$-0.408164\pi$
$653$	14.5415	0.569054	0.284527	+	0.958668i	$0.408164\pi$
$654$	−24.1445	−0.944126
$655$	20.2906	0.792817
$656$	−15.3743	−0.600265
$657$	40.8861	1.59512
$658$	18.8942	0.736573
$659$	−23.8625	−0.929550	−0.464775	−	0.885429i	$-0.653865\pi$
$659$	−23.8625	−0.929550	−0.464775	+	0.885429i	$0.653865\pi$
$660$	−1.97300	−0.0767991
$661$	5.72037	0.222497	0.111248	−	0.993793i	$-0.464515\pi$
$661$	5.72037	0.222497	0.111248	+	0.993793i	$0.464515\pi$
$662$	−16.9419	−0.658465
$663$	−43.6866	−1.69665
$664$	21.5582	0.836622
$665$	0	0
$666$	−57.2186	−2.21717
$667$	9.34492	0.361837
$668$	−5.85732	−0.226626
$669$	−30.6455	−1.18482
$670$	−11.3605	−0.438894
$671$	5.82518	0.224879
$672$	13.0349	0.502833
$673$	−17.0169	−0.655954	−0.327977	−	0.944686i	$-0.606367\pi$
$673$	−17.0169	−0.655954	−0.327977	+	0.944686i	$0.606367\pi$
$674$	26.4217	1.01773
$675$	48.4317	1.86414
$676$	3.77485	0.145186
$677$	−30.2237	−1.16159	−0.580796	−	0.814049i	$-0.697259\pi$
$677$	−30.2237	−1.16159	−0.580796	+	0.814049i	$0.697259\pi$
$678$	−11.0061	−0.422686
$679$	−19.3751	−0.743549
$680$	18.0962	0.693956
$681$	−19.0436	−0.729753
$682$	3.62290	0.138728
$683$	30.7218	1.17554	0.587768	−	0.809029i	$-0.300007\pi$
$683$	30.7218	1.17554	0.587768	+	0.809029i	$0.300007\pi$
$684$	0	0
$685$	18.2149	0.695956
$686$	19.1952	0.732878
$687$	−68.7814	−2.62417
$688$	7.42703	0.283153
$689$	−2.52201	−0.0960809
$690$	−15.8080	−0.601800
$691$	−29.7093	−1.13020	−0.565098	−	0.825024i	$-0.691162\pi$
$691$	−29.7093	−1.13020	−0.565098	+	0.825024i	$0.691162\pi$
$692$	1.28192	0.0487314
$693$	9.16741	0.348241
$694$	−22.8454	−0.867201
$695$	13.6273	0.516914
$696$	23.4678	0.889546
$697$	−33.2505	−1.25945
$698$	−19.1747	−0.725771
$699$	49.6061	1.87627
$700$	−2.89013	−0.109237
$701$	9.54914	0.360666	0.180333	−	0.983606i	$-0.442282\pi$
$701$	9.54914	0.360666	0.180333	+	0.983606i	$0.442282\pi$
$702$	38.3367	1.44693
$703$	0	0
$704$	−8.78508	−0.331100
$705$	41.3888	1.55879
$706$	13.0220	0.490090
$707$	−24.9495	−0.938322
$708$	25.9309	0.974544
$709$	42.6564	1.60200	0.800998	−	0.598667i	$-0.204303\pi$
$709$	42.6564	1.60200	0.800998	+	0.598667i	$0.204303\pi$
$710$	3.16356	0.118726
$711$	−119.283	−4.47345
$712$	−28.0691	−1.05193
$713$	−11.7540	−0.440191
$714$	−26.8743	−1.00575
$715$	2.74913	0.102812
$716$	6.97479	0.260660
$717$	−69.2046	−2.58449
$718$	−42.2493	−1.57673
$719$	−16.7679	−0.625335	−0.312668	−	0.949863i	$-0.601223\pi$
$719$	−16.7679	−0.625335	−0.312668	+	0.949863i	$0.601223\pi$
$720$	−19.0542	−0.710108
$721$	13.7141	0.510741
$722$	0	0
$723$	18.9268	0.703896
$724$	−0.206993	−0.00769285
$725$	−9.24252	−0.343259
$726$	−3.77306	−0.140031
$727$	21.4858	0.796864	0.398432	−	0.917198i	$-0.369554\pi$
$727$	21.4858	0.796864	0.398432	+	0.917198i	$0.369554\pi$
$728$	−10.2251	−0.378968
$729$	13.0158	0.482066
$730$	7.54246	0.279159
$731$	16.0627	0.594101
$732$	−10.6187	−0.392478
$733$	−34.1734	−1.26222	−0.631111	−	0.775692i	$-0.717401\pi$
$733$	−34.1734	−1.26222	−0.631111	+	0.775692i	$0.717401\pi$
$734$	−27.8457	−1.02780
$735$	18.0892	0.667228
$736$	12.1840	0.449106
$737$	8.79718	0.324048
$738$	51.0610	1.87958
$739$	−11.5412	−0.424548	−0.212274	−	0.977210i	$-0.568087\pi$
$739$	−11.5412	−0.424548	−0.212274	+	0.977210i	$0.568087\pi$
$740$	4.27420	0.157123
$741$	0	0
$742$	−1.55144	−0.0569552
$743$	−24.7316	−0.907313	−0.453657	−	0.891177i	$-0.649881\pi$
$743$	−24.7316	−0.907313	−0.453657	+	0.891177i	$0.649881\pi$
$744$	−29.5177	−1.08217
$745$	6.73964	0.246921
$746$	20.5185	0.751237
$747$	−49.0932	−1.79623
$748$	−3.13522	−0.114635
$749$	18.9778	0.693435
$750$	36.0536	1.31649
$751$	−46.2026	−1.68596	−0.842978	−	0.537949i	$-0.819199\pi$
$751$	−46.2026	−1.68596	−0.842978	+	0.537949i	$0.819199\pi$
$752$	30.4102	1.10895
$753$	20.9801	0.764557
$754$	−7.31603	−0.266434
$755$	−6.64683	−0.241903
$756$	−9.54958	−0.347315
$757$	−43.9301	−1.59667	−0.798333	−	0.602216i	$-0.794285\pi$
$757$	−43.9301	−1.59667	−0.798333	+	0.602216i	$0.794285\pi$
$758$	−30.1090	−1.09361
$759$	12.2412	0.444327
$760$	0	0
$761$	−32.1299	−1.16471	−0.582355	−	0.812935i	$-0.697869\pi$
$761$	−32.1299	−1.16471	−0.582355	+	0.812935i	$0.697869\pi$
$762$	−46.0296	−1.66748
$763$	−8.38022	−0.303384
$764$	−12.2924	−0.444723
$765$	−41.2093	−1.48992
$766$	−35.3461	−1.27711
$767$	−36.1315	−1.30463
$768$	39.7660	1.43493
$769$	27.7514	1.00074	0.500371	−	0.865811i	$-0.333197\pi$
$769$	27.7514	1.00074	0.500371	+	0.865811i	$0.333197\pi$
$770$	1.69116	0.0609451
$771$	−29.4599	−1.06097
$772$	−8.38442	−0.301762
$773$	39.5999	1.42431	0.712154	−	0.702023i	$-0.247720\pi$
$773$	39.5999	1.42431	0.712154	+	0.702023i	$0.247720\pi$
$774$	−24.6666	−0.886624
$775$	11.6252	0.417590
$776$	−45.4801	−1.63264
$777$	−28.3707	−1.01779
$778$	9.19873	0.329790
$779$	0	0
$780$	−5.01138	−0.179436
$781$	−2.44975	−0.0876591
$782$	−25.1199	−0.898285
$783$	−30.5391	−1.09138
$784$	13.2909	0.474675
$785$	21.3751	0.762910
$786$	−70.7330	−2.52296
$787$	26.9286	0.959902	0.479951	−	0.877295i	$-0.340654\pi$
$787$	26.9286	0.959902	0.479951	+	0.877295i	$0.340654\pi$
$788$	2.71688	0.0967847
$789$	29.2516	1.04139
$790$	−22.0047	−0.782891
$791$	−3.82006	−0.135826
$792$	21.5191	0.764648
$793$	14.7958	0.525415
$794$	9.86685	0.350162
$795$	−3.39852	−0.120533
$796$	1.02148	0.0362052
$797$	−18.3883	−0.651348	−0.325674	−	0.945482i	$-0.605591\pi$
$797$	−18.3883	−0.651348	−0.325674	+	0.945482i	$0.605591\pi$
$798$	0	0
$799$	65.7693	2.32675
$800$	−12.0504	−0.426048
$801$	63.9199	2.25850
$802$	−2.36594	−0.0835442
$803$	−5.84063	−0.206111
$804$	−16.0363	−0.565558
$805$	−5.48673	−0.193382
$806$	9.20207	0.324129
$807$	−53.7835	−1.89327
$808$	−58.5651	−2.06031
$809$	47.5038	1.67014	0.835072	−	0.550141i	$-0.185426\pi$
$809$	47.5038	1.67014	0.835072	+	0.550141i	$0.185426\pi$
$810$	24.5403	0.862260
$811$	39.8438	1.39910	0.699552	−	0.714582i	$-0.253383\pi$
$811$	39.8438	1.39910	0.699552	+	0.714582i	$0.253383\pi$
$812$	1.82240	0.0639539
$813$	−23.5127	−0.824627
$814$	8.17374	0.286489
$815$	−6.17352	−0.216249
$816$	−43.2542	−1.51420
$817$	0	0
$818$	−30.8736	−1.07947
$819$	23.2850	0.813643
$820$	−3.81423	−0.133199
$821$	−39.8464	−1.39065	−0.695325	−	0.718695i	$-0.744740\pi$
$821$	−39.8464	−1.39065	−0.695325	+	0.718695i	$0.744740\pi$
$822$	−63.4973	−2.21472
$823$	−24.5258	−0.854917	−0.427459	−	0.904035i	$-0.640591\pi$
$823$	−24.5258	−0.854917	−0.427459	+	0.904035i	$0.640591\pi$
$824$	32.1918	1.12146
$825$	−12.1070	−0.421513
$826$	−22.2267	−0.773365
$827$	38.5836	1.34168	0.670841	−	0.741601i	$-0.265933\pi$
$827$	38.5836	1.34168	0.670841	+	0.741601i	$0.265933\pi$
$828$	−15.6203	−0.542842
$829$	5.07772	0.176357	0.0881783	−	0.996105i	$-0.471895\pi$
$829$	5.07772	0.176357	0.0881783	+	0.996105i	$0.471895\pi$
$830$	−9.05647	−0.314355
$831$	−7.31567	−0.253778
$832$	−22.3139	−0.773595
$833$	28.7448	0.995947
$834$	−47.5050	−1.64496
$835$	10.9979	0.380597
$836$	0	0
$837$	38.4120	1.32771
$838$	43.2226	1.49310
$839$	44.8328	1.54780	0.773900	−	0.633308i	$-0.218303\pi$
$839$	44.8328	1.54780	0.773900	+	0.633308i	$0.218303\pi$
$840$	−13.7788	−0.475413
$841$	−23.1720	−0.799036
$842$	7.05435	0.243109
$843$	−16.4519	−0.566635
$844$	10.2647	0.353325
$845$	−7.08777	−0.243827
$846$	−100.998	−3.47239
$847$	−1.30958	−0.0449976
$848$	−2.49704	−0.0857488
$849$	−84.4736	−2.89913
$850$	24.8446	0.852163
$851$	−26.5186	−0.909045
$852$	4.46565	0.152991
$853$	−23.4081	−0.801477	−0.400738	−	0.916193i	$-0.631246\pi$
$853$	−23.4081	−0.801477	−0.400738	+	0.916193i	$0.631246\pi$
$854$	9.10181	0.311457
$855$	0	0
$856$	44.5476	1.52260
$857$	12.1302	0.414359	0.207180	−	0.978303i	$-0.433572\pi$
$857$	12.1302	0.414359	0.207180	+	0.978303i	$0.433572\pi$
$858$	−9.58348	−0.327175
$859$	−4.25984	−0.145344	−0.0726720	−	0.997356i	$-0.523153\pi$
$859$	−4.25984	−0.145344	−0.0726720	+	0.997356i	$0.523153\pi$
$860$	1.84259	0.0628317
$861$	25.3176	0.862822
$862$	13.3494	0.454684
$863$	−19.0125	−0.647194	−0.323597	−	0.946195i	$-0.604892\pi$
$863$	−19.0125	−0.647194	−0.323597	+	0.946195i	$0.604892\pi$
$864$	−39.8171	−1.35460
$865$	−2.40698	−0.0818397
$866$	−15.9764	−0.542899
$867$	−39.7880	−1.35127
$868$	−2.29221	−0.0778028
$869$	17.0397	0.578031
$870$	−9.85867	−0.334240
$871$	22.3446	0.757118
$872$	−19.6713	−0.666154
$873$	103.569	3.50528
$874$	0	0
$875$	12.5137	0.423039
$876$	10.6469	0.359724
$877$	2.17273	0.0733678	0.0366839	−	0.999327i	$-0.488321\pi$
$877$	2.17273	0.0733678	0.0366839	+	0.999327i	$0.488321\pi$
$878$	−28.1981	−0.951641
$879$	−2.96505	−0.100009
$880$	2.72192	0.0917558
$881$	21.5283	0.725305	0.362653	−	0.931924i	$-0.381871\pi$
$881$	21.5283	0.725305	0.362653	+	0.931924i	$0.381871\pi$
$882$	−44.1418	−1.48633
$883$	−5.14254	−0.173060	−0.0865302	−	0.996249i	$-0.527578\pi$
$883$	−5.14254	−0.173060	−0.0865302	+	0.996249i	$0.527578\pi$
$884$	−7.96339	−0.267838
$885$	−48.6887	−1.63665
$886$	−30.6531	−1.02981
$887$	42.8806	1.43979	0.719895	−	0.694083i	$-0.244190\pi$
$887$	42.8806	1.43979	0.719895	+	0.694083i	$0.244190\pi$
$888$	−66.5959	−2.23481
$889$	−15.9762	−0.535825
$890$	11.7916	0.395256
$891$	−19.0032	−0.636632
$892$	−5.58619	−0.187039
$893$	0	0
$894$	−23.4944	−0.785771
$895$	−13.0961	−0.437754
$896$	−5.48275	−0.183166
$897$	31.0923	1.03814
$898$	11.5999	0.387093
$899$	−7.33039	−0.244482
$900$	15.4491	0.514971
$901$	−5.40045	−0.179915
$902$	−7.29413	−0.242868
$903$	−12.2305	−0.407005
$904$	−8.96700	−0.298238
$905$	0.388657	0.0129194
$906$	23.1709	0.769801
$907$	28.3695	0.941992	0.470996	−	0.882135i	$-0.343895\pi$
$907$	28.3695	0.941992	0.470996	+	0.882135i	$0.343895\pi$
$908$	−3.47135	−0.115201
$909$	133.367	4.42349
$910$	4.29550	0.142394
$911$	−40.0237	−1.32604	−0.663022	−	0.748600i	$-0.730727\pi$
$911$	−40.0237	−1.32604	−0.663022	+	0.748600i	$0.730727\pi$
$912$	0	0
$913$	7.01303	0.232097
$914$	−2.44402	−0.0808410
$915$	19.9380	0.659130
$916$	−12.5378	−0.414259
$917$	−24.5504	−0.810726
$918$	82.0916	2.70943
$919$	51.0340	1.68345	0.841727	−	0.539903i	$-0.181539\pi$
$919$	51.0340	1.68345	0.841727	+	0.539903i	$0.181539\pi$
$920$	−12.8793	−0.424617
$921$	−15.2793	−0.503470
$922$	−27.3113	−0.899451
$923$	−6.22231	−0.204810
$924$	2.38722	0.0785338
$925$	26.2280	0.862371
$926$	41.6981	1.37029
$927$	−73.3084	−2.40776
$928$	7.59853	0.249434
$929$	30.7910	1.01022	0.505110	−	0.863055i	$-0.331452\pi$
$929$	30.7910	1.01022	0.505110	+	0.863055i	$0.331452\pi$
$930$	12.4002	0.406618
$931$	0	0
$932$	9.04241	0.296194
$933$	45.5108	1.48996
$934$	16.3880	0.536232
$935$	5.88679	0.192519
$936$	54.6580	1.78655
$937$	25.9052	0.846287	0.423143	−	0.906063i	$-0.360927\pi$
$937$	25.9052	0.846287	0.423143	+	0.906063i	$0.360927\pi$
$938$	13.7455	0.448808
$939$	92.8073	3.02865
$940$	7.54452	0.246075
$941$	31.0254	1.01140	0.505699	−	0.862710i	$-0.331235\pi$
$941$	31.0254	1.01140	0.505699	+	0.862710i	$0.331235\pi$
$942$	−74.5137	−2.42779
$943$	23.6648	0.770632
$944$	−35.7738	−1.16434
$945$	17.9306	0.583282
$946$	3.52366	0.114564
$947$	32.3742	1.05202	0.526009	−	0.850479i	$-0.323688\pi$
$947$	32.3742	1.05202	0.526009	+	0.850479i	$0.323688\pi$
$948$	−31.0616	−1.00883
$949$	−14.8350	−0.481566
$950$	0	0
$951$	−51.8706	−1.68202
$952$	−21.8953	−0.709632
$953$	−3.88933	−0.125988	−0.0629938	−	0.998014i	$-0.520065\pi$
$953$	−3.88933	−0.125988	−0.0629938	+	0.998014i	$0.520065\pi$
$954$	8.29318	0.268502
$955$	23.0805	0.746869
$956$	−12.6149	−0.407996
$957$	7.63422	0.246779
$958$	3.74201	0.120899
$959$	−22.0390	−0.711676
$960$	−30.0689	−0.970471
$961$	−21.7799	−0.702576
$962$	20.7611	0.669364
$963$	−101.445	−3.26903
$964$	3.45006	0.111119
$965$	15.7429	0.506780
$966$	19.1268	0.615394
$967$	15.6679	0.503846	0.251923	−	0.967747i	$-0.418937\pi$
$967$	15.6679	0.503846	0.251923	+	0.967747i	$0.418937\pi$
$968$	−3.07403	−0.0988030
$969$	0	0
$970$	19.1059	0.613453
$971$	−25.6584	−0.823417	−0.411708	−	0.911316i	$-0.635068\pi$
$971$	−25.6584	−0.823417	−0.411708	+	0.911316i	$0.635068\pi$
$972$	12.7645	0.409423
$973$	−16.4883	−0.528590
$974$	−25.3257	−0.811487
$975$	−30.7516	−0.984839
$976$	14.6493	0.468914
$977$	−44.6708	−1.42914	−0.714572	−	0.699562i	$-0.753379\pi$
$977$	−44.6708	−1.42914	−0.714572	+	0.699562i	$0.753379\pi$
$978$	21.5209	0.688163
$979$	−9.13103	−0.291829
$980$	3.29737	0.105331
$981$	44.7962	1.43023
$982$	34.1044	1.08831
$983$	−48.0898	−1.53383	−0.766913	−	0.641751i	$-0.778208\pi$
$983$	−48.0898	−1.53383	−0.766913	+	0.641751i	$0.778208\pi$
$984$	59.4292	1.89453
$985$	−5.10129	−0.162541
$986$	−15.6660	−0.498908
$987$	−50.0780	−1.59400
$988$	0	0
$989$	−11.4320	−0.363517
$990$	−9.04003	−0.287311
$991$	57.3200	1.82083	0.910415	−	0.413697i	$-0.135763\pi$
$991$	57.3200	1.82083	0.910415	+	0.413697i	$0.135763\pi$
$992$	−9.55740	−0.303448
$993$	44.9035	1.42497
$994$	−3.82773	−0.121408
$995$	−1.91795	−0.0608032
$996$	−12.7840	−0.405077
$997$	14.1271	0.447411	0.223705	−	0.974657i	$-0.428185\pi$
$997$	14.1271	0.447411	0.223705	+	0.974657i	$0.428185\pi$
$998$	−24.0196	−0.760326
$999$	86.6625	2.74188

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3971.2.a.i.1.5		7
19.18	odd	2		209.2.a.d.1.3	✓	7
57.56	even	2		1881.2.a.p.1.5		7
76.75	even	2		3344.2.a.ba.1.1		7
95.94	odd	2		5225.2.a.n.1.5		7
209.208	even	2		2299.2.a.q.1.5		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
209.2.a.d.1.3	✓	7	19.18	odd	2
1881.2.a.p.1.5		7	57.56	even	2
2299.2.a.q.1.5		7	209.208	even	2
3344.2.a.ba.1.1		7	76.75	even	2
3971.2.a.i.1.5		7	1.1	even	1	trivial
5225.2.a.n.1.5		7	95.94	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3971 = 11 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3971.a (trivial)

\(f(q)\)	\(=\)	\(q+1.19313 q^{2} -3.16232 q^{3} -0.576442 q^{4} +1.08235 q^{5} -3.77306 q^{6} -1.30958 q^{7} -3.07403 q^{8} +7.00029 q^{9} +O(q^{10})\)	\(q+1.19313 q^{2} -3.16232 q^{3} -0.576442 q^{4} +1.08235 q^{5} -3.77306 q^{6} -1.30958 q^{7} -3.07403 q^{8} +7.00029 q^{9} +1.29138 q^{10} -1.00000 q^{11} +1.82290 q^{12} -2.53997 q^{13} -1.56249 q^{14} -3.42273 q^{15} -2.51483 q^{16} -5.43892 q^{17} +8.35226 q^{18} -0.623909 q^{20} +4.14130 q^{21} -1.19313 q^{22} +3.87095 q^{23} +9.72108 q^{24} -3.82853 q^{25} -3.03052 q^{26} -12.6502 q^{27} +0.754894 q^{28} +2.41412 q^{29} -4.08376 q^{30} -3.03647 q^{31} +3.14754 q^{32} +3.16232 q^{33} -6.48934 q^{34} -1.41741 q^{35} -4.03526 q^{36} -6.85067 q^{37} +8.03222 q^{39} -3.32716 q^{40} +6.11344 q^{41} +4.94111 q^{42} -2.95329 q^{43} +0.576442 q^{44} +7.57673 q^{45} +4.61854 q^{46} -12.0923 q^{47} +7.95271 q^{48} -5.28501 q^{49} -4.56793 q^{50} +17.1996 q^{51} +1.46415 q^{52} +0.992927 q^{53} -15.0933 q^{54} -1.08235 q^{55} +4.02567 q^{56} +2.88036 q^{58} +14.2251 q^{59} +1.97300 q^{60} -5.82518 q^{61} -3.62290 q^{62} -9.16741 q^{63} +8.78508 q^{64} -2.74913 q^{65} +3.77306 q^{66} -8.79718 q^{67} +3.13522 q^{68} -12.2412 q^{69} -1.69116 q^{70} +2.44975 q^{71} -21.5191 q^{72} +5.84063 q^{73} -8.17374 q^{74} +12.1070 q^{75} +1.30958 q^{77} +9.58348 q^{78} -17.0397 q^{79} -2.72192 q^{80} +19.0032 q^{81} +7.29413 q^{82} -7.01303 q^{83} -2.38722 q^{84} -5.88679 q^{85} -3.52366 q^{86} -7.63422 q^{87} +3.07403 q^{88} +9.13103 q^{89} +9.04003 q^{90} +3.32629 q^{91} -2.23138 q^{92} +9.60229 q^{93} -14.4277 q^{94} -9.95354 q^{96} +14.7950 q^{97} -6.30570 q^{98} -7.00029 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + q^{2} - 2 q^{3} + 15 q^{4} + 2 q^{5} - 2 q^{6} + 10 q^{7} + 9 q^{8} + 11 q^{9}+O(q^{10}) \) 7 * q + q^2 - 2 * q^3 + 15 * q^4 + 2 * q^5 - 2 * q^6 + 10 * q^7 + 9 * q^8 + 11 * q^9	\( 7 q + q^{2} - 2 q^{3} + 15 q^{4} + 2 q^{5} - 2 q^{6} + 10 q^{7} + 9 q^{8} + 11 q^{9} + 6 q^{10} - 7 q^{11} + 16 q^{12} + 4 q^{13} - 6 q^{14} - 12 q^{15} + 27 q^{16} + 2 q^{17} - 9 q^{18} - 4 q^{20} + 14 q^{21} - q^{22} + 10 q^{23} - 2 q^{24} + 9 q^{25} - 8 q^{26} + 4 q^{27} + 26 q^{28} + 18 q^{29} - 42 q^{30} - 24 q^{31} + 49 q^{32} + 2 q^{33} + 6 q^{34} + 8 q^{35} + 29 q^{36} + 24 q^{39} + 2 q^{40} + 12 q^{41} - 44 q^{42} + 2 q^{43} - 15 q^{44} - 4 q^{45} + 4 q^{46} + 8 q^{47} + 72 q^{48} + 17 q^{49} + 33 q^{50} + 24 q^{51} + 60 q^{52} - 2 q^{53} - 52 q^{54} - 2 q^{55} - 26 q^{56} - 8 q^{58} + 10 q^{59} - 42 q^{60} + 14 q^{61} + 14 q^{62} + 55 q^{64} + 14 q^{65} + 2 q^{66} - 8 q^{67} - 18 q^{68} + 6 q^{69} + 66 q^{70} - 10 q^{71} - 53 q^{72} - 6 q^{73} + 26 q^{74} - 26 q^{75} - 10 q^{77} - 22 q^{78} - 52 q^{79} - 12 q^{80} - q^{81} + 24 q^{82} - 10 q^{83} + 6 q^{84} - 12 q^{85} - 8 q^{86} + 6 q^{87} - 9 q^{88} - 20 q^{90} - 12 q^{91} + 2 q^{93} - 24 q^{94} + 6 q^{96} + 24 q^{97} - 19 q^{98} - 11 q^{99}+O(q^{100}) \) 7 * q + q^2 - 2 * q^3 + 15 * q^4 + 2 * q^5 - 2 * q^6 + 10 * q^7 + 9 * q^8 + 11 * q^9 + 6 * q^10 - 7 * q^11 + 16 * q^12 + 4 * q^13 - 6 * q^14 - 12 * q^15 + 27 * q^16 + 2 * q^17 - 9 * q^18 - 4 * q^20 + 14 * q^21 - q^22 + 10 * q^23 - 2 * q^24 + 9 * q^25 - 8 * q^26 + 4 * q^27 + 26 * q^28 + 18 * q^29 - 42 * q^30 - 24 * q^31 + 49 * q^32 + 2 * q^33 + 6 * q^34 + 8 * q^35 + 29 * q^36 + 24 * q^39 + 2 * q^40 + 12 * q^41 - 44 * q^42 + 2 * q^43 - 15 * q^44 - 4 * q^45 + 4 * q^46 + 8 * q^47 + 72 * q^48 + 17 * q^49 + 33 * q^50 + 24 * q^51 + 60 * q^52 - 2 * q^53 - 52 * q^54 - 2 * q^55 - 26 * q^56 - 8 * q^58 + 10 * q^59 - 42 * q^60 + 14 * q^61 + 14 * q^62 + 55 * q^64 + 14 * q^65 + 2 * q^66 - 8 * q^67 - 18 * q^68 + 6 * q^69 + 66 * q^70 - 10 * q^71 - 53 * q^72 - 6 * q^73 + 26 * q^74 - 26 * q^75 - 10 * q^77 - 22 * q^78 - 52 * q^79 - 12 * q^80 - q^81 + 24 * q^82 - 10 * q^83 + 6 * q^84 - 12 * q^85 - 8 * q^86 + 6 * q^87 - 9 * q^88 - 20 * q^90 - 12 * q^91 + 2 * q^93 - 24 * q^94 + 6 * q^96 + 24 * q^97 - 19 * q^98 - 11 * q^99

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