LMFDB - Embedded newform 3610.2.a.bj.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3610,2,Mod(1,3610)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3610, 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("3610.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3610 = 2 \cdot 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3610.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:	$28.8259951297$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 24x^{7} - 6x^{6} + 183x^{5} + 78x^{4} - 455x^{3} - 168x^{2} + 228x - 8 $ x^9 - 24x^7 - 6x^6 + 183x^5 + 78x^4 - 455x^3 - 168x^2 + 228*x - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-2.31980$ of defining polynomial
Character	$\chi$	$=$	3610.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.31980 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.31980 q^{6} -4.91674 q^{7} +1.00000 q^{8} +2.38147 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.31980 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.31980 q^{6} -4.91674 q^{7} +1.00000 q^{8} +2.38147 q^{9} +1.00000 q^{10} +2.84657 q^{11} +2.31980 q^{12} +6.56179 q^{13} -4.91674 q^{14} +2.31980 q^{15} +1.00000 q^{16} -2.19123 q^{17} +2.38147 q^{18} +1.00000 q^{20} -11.4059 q^{21} +2.84657 q^{22} -2.65755 q^{23} +2.31980 q^{24} +1.00000 q^{25} +6.56179 q^{26} -1.43487 q^{27} -4.91674 q^{28} +7.60179 q^{29} +2.31980 q^{30} +5.41539 q^{31} +1.00000 q^{32} +6.60347 q^{33} -2.19123 q^{34} -4.91674 q^{35} +2.38147 q^{36} +2.06252 q^{37} +15.2220 q^{39} +1.00000 q^{40} +9.35729 q^{41} -11.4059 q^{42} +1.73409 q^{43} +2.84657 q^{44} +2.38147 q^{45} -2.65755 q^{46} -3.00499 q^{47} +2.31980 q^{48} +17.1744 q^{49} +1.00000 q^{50} -5.08321 q^{51} +6.56179 q^{52} +4.22215 q^{53} -1.43487 q^{54} +2.84657 q^{55} -4.91674 q^{56} +7.60179 q^{58} +0.964592 q^{59} +2.31980 q^{60} -7.49955 q^{61} +5.41539 q^{62} -11.7091 q^{63} +1.00000 q^{64} +6.56179 q^{65} +6.60347 q^{66} -1.91955 q^{67} -2.19123 q^{68} -6.16497 q^{69} -4.91674 q^{70} +6.16536 q^{71} +2.38147 q^{72} -3.97703 q^{73} +2.06252 q^{74} +2.31980 q^{75} -13.9959 q^{77} +15.2220 q^{78} -15.3229 q^{79} +1.00000 q^{80} -10.4730 q^{81} +9.35729 q^{82} -1.31206 q^{83} -11.4059 q^{84} -2.19123 q^{85} +1.73409 q^{86} +17.6346 q^{87} +2.84657 q^{88} +10.7763 q^{89} +2.38147 q^{90} -32.2626 q^{91} -2.65755 q^{92} +12.5626 q^{93} -3.00499 q^{94} +2.31980 q^{96} -2.05429 q^{97} +17.1744 q^{98} +6.77902 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{8} + 21 q^{9}+O(q^{10}) $ 9 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^8 + 21 * q^9	$ 9 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{8} + 21 q^{9} + 9 q^{10} + 12 q^{11} + 9 q^{13} + 9 q^{16} + 6 q^{17} + 21 q^{18} + 9 q^{20} + 6 q^{21} + 12 q^{22} + 18 q^{23} + 9 q^{25} + 9 q^{26} - 18 q^{27} - 6 q^{31} + 9 q^{32} + 6 q^{33} + 6 q^{34} + 21 q^{36} + 6 q^{37} + 24 q^{39} + 9 q^{40} + 6 q^{42} + 18 q^{43} + 12 q^{44} + 21 q^{45} + 18 q^{46} - 3 q^{47} + 39 q^{49} + 9 q^{50} - 48 q^{51} + 9 q^{52} - 18 q^{54} + 12 q^{55} + 21 q^{59} + 18 q^{61} - 6 q^{62} - 12 q^{63} + 9 q^{64} + 9 q^{65} + 6 q^{66} + 6 q^{68} - 30 q^{69} + 18 q^{71} + 21 q^{72} - 36 q^{73} + 6 q^{74} + 15 q^{77} + 24 q^{78} - 6 q^{79} + 9 q^{80} + 69 q^{81} - 6 q^{83} + 6 q^{84} + 6 q^{85} + 18 q^{86} - 24 q^{87} + 12 q^{88} - 18 q^{89} + 21 q^{90} - 60 q^{91} + 18 q^{92} - 3 q^{94} + 18 q^{97} + 39 q^{98} + 54 q^{99}+O(q^{100}) $ 9 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^8 + 21 * q^9 + 9 * q^10 + 12 * q^11 + 9 * q^13 + 9 * q^16 + 6 * q^17 + 21 * q^18 + 9 * q^20 + 6 * q^21 + 12 * q^22 + 18 * q^23 + 9 * q^25 + 9 * q^26 - 18 * q^27 - 6 * q^31 + 9 * q^32 + 6 * q^33 + 6 * q^34 + 21 * q^36 + 6 * q^37 + 24 * q^39 + 9 * q^40 + 6 * q^42 + 18 * q^43 + 12 * q^44 + 21 * q^45 + 18 * q^46 - 3 * q^47 + 39 * q^49 + 9 * q^50 - 48 * q^51 + 9 * q^52 - 18 * q^54 + 12 * q^55 + 21 * q^59 + 18 * q^61 - 6 * q^62 - 12 * q^63 + 9 * q^64 + 9 * q^65 + 6 * q^66 + 6 * q^68 - 30 * q^69 + 18 * q^71 + 21 * q^72 - 36 * q^73 + 6 * q^74 + 15 * q^77 + 24 * q^78 - 6 * q^79 + 9 * q^80 + 69 * q^81 - 6 * q^83 + 6 * q^84 + 6 * q^85 + 18 * q^86 - 24 * q^87 + 12 * q^88 - 18 * q^89 + 21 * q^90 - 60 * q^91 + 18 * q^92 - 3 * q^94 + 18 * q^97 + 39 * q^98 + 54 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	2.31980	1.33934	0.669668	−	0.742660i	$-0.266436\pi$
$3$	2.31980	1.33934	0.669668	+	0.742660i	$0.266436\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.31980	0.947054
$7$	−4.91674	−1.85835	−0.929177	−	0.369635i	$-0.879483\pi$
$7$	−4.91674	−1.85835	−0.929177	+	0.369635i	$0.879483\pi$
$8$	1.00000	0.353553
$9$	2.38147	0.793823
$10$	1.00000	0.316228
$11$	2.84657	0.858274	0.429137	−	0.903239i	$-0.358818\pi$
$11$	2.84657	0.858274	0.429137	+	0.903239i	$0.358818\pi$
$12$	2.31980	0.669668
$13$	6.56179	1.81991	0.909956	−	0.414704i	$-0.136115\pi$
$13$	6.56179	1.81991	0.909956	+	0.414704i	$0.136115\pi$
$14$	−4.91674	−1.31405
$15$	2.31980	0.598970
$16$	1.00000	0.250000
$17$	−2.19123	−0.531451	−0.265725	−	0.964049i	$-0.585611\pi$
$17$	−2.19123	−0.531451	−0.265725	+	0.964049i	$0.585611\pi$
$18$	2.38147	0.561317
$19$	0	0
$19$	0	0
$20$	1.00000	0.223607
$21$	−11.4059	−2.48896
$22$	2.84657	0.606891
$23$	−2.65755	−0.554137	−0.277068	−	0.960850i	$-0.589363\pi$
$23$	−2.65755	−0.554137	−0.277068	+	0.960850i	$0.589363\pi$
$24$	2.31980	0.473527
$25$	1.00000	0.200000
$26$	6.56179	1.28687
$27$	−1.43487	−0.276141
$28$	−4.91674	−0.929177
$29$	7.60179	1.41162	0.705808	−	0.708403i	$-0.250584\pi$
$29$	7.60179	1.41162	0.705808	+	0.708403i	$0.250584\pi$
$30$	2.31980	0.423535
$31$	5.41539	0.972632	0.486316	−	0.873783i	$-0.338340\pi$
$31$	5.41539	0.972632	0.486316	+	0.873783i	$0.338340\pi$
$32$	1.00000	0.176777
$33$	6.60347	1.14952
$34$	−2.19123	−0.375793
$35$	−4.91674	−0.831081
$36$	2.38147	0.396911
$37$	2.06252	0.339076	0.169538	−	0.985524i	$-0.445772\pi$
$37$	2.06252	0.339076	0.169538	+	0.985524i	$0.445772\pi$
$38$	0	0
$39$	15.2220	2.43748
$40$	1.00000	0.158114
$41$	9.35729	1.46136	0.730682	−	0.682718i	$-0.239202\pi$
$41$	9.35729	1.46136	0.730682	+	0.682718i	$0.239202\pi$
$42$	−11.4059	−1.75996
$43$	1.73409	0.264446	0.132223	−	0.991220i	$-0.457788\pi$
$43$	1.73409	0.264446	0.132223	+	0.991220i	$0.457788\pi$
$44$	2.84657	0.429137
$45$	2.38147	0.355008
$46$	−2.65755	−0.391834
$47$	−3.00499	−0.438323	−0.219162	−	0.975689i	$-0.570332\pi$
$47$	−3.00499	−0.438323	−0.219162	+	0.975689i	$0.570332\pi$
$48$	2.31980	0.334834
$49$	17.1744	2.45348
$50$	1.00000	0.141421
$51$	−5.08321	−0.711792
$52$	6.56179	0.909956
$53$	4.22215	0.579957	0.289978	−	0.957033i	$-0.406352\pi$
$53$	4.22215	0.579957	0.289978	+	0.957033i	$0.406352\pi$
$54$	−1.43487	−0.195261
$55$	2.84657	0.383832
$56$	−4.91674	−0.657027
$57$	0	0
$58$	7.60179	0.998163
$59$	0.964592	0.125579	0.0627896	−	0.998027i	$-0.480000\pi$
$59$	0.964592	0.125579	0.0627896	+	0.998027i	$0.480000\pi$
$60$	2.31980	0.299485
$61$	−7.49955	−0.960219	−0.480109	−	0.877209i	$-0.659403\pi$
$61$	−7.49955	−0.960219	−0.480109	+	0.877209i	$0.659403\pi$
$62$	5.41539	0.687755
$63$	−11.7091	−1.47520
$64$	1.00000	0.125000
$65$	6.56179	0.813890
$66$	6.60347	0.812832
$67$	−1.91955	−0.234510	−0.117255	−	0.993102i	$-0.537410\pi$
$67$	−1.91955	−0.234510	−0.117255	+	0.993102i	$0.537410\pi$
$68$	−2.19123	−0.265725
$69$	−6.16497	−0.742176
$70$	−4.91674	−0.587663
$71$	6.16536	0.731693	0.365847	−	0.930675i	$-0.380779\pi$
$71$	6.16536	0.731693	0.365847	+	0.930675i	$0.380779\pi$
$72$	2.38147	0.280659
$73$	−3.97703	−0.465477	−0.232738	−	0.972539i	$-0.574769\pi$
$73$	−3.97703	−0.465477	−0.232738	+	0.972539i	$0.574769\pi$
$74$	2.06252	0.239763
$75$	2.31980	0.267867
$76$	0	0
$77$	−13.9959	−1.59498
$78$	15.2220	1.72356
$79$	−15.3229	−1.72396	−0.861981	−	0.506940i	$-0.830777\pi$
$79$	−15.3229	−1.72396	−0.861981	+	0.506940i	$0.830777\pi$
$80$	1.00000	0.111803
$81$	−10.4730	−1.16367
$82$	9.35729	1.03334
$83$	−1.31206	−0.144018	−0.0720089	−	0.997404i	$-0.522941\pi$
$83$	−1.31206	−0.144018	−0.0720089	+	0.997404i	$0.522941\pi$
$84$	−11.4059	−1.24448
$85$	−2.19123	−0.237672
$86$	1.73409	0.186992
$87$	17.6346	1.89063
$88$	2.84657	0.303446
$89$	10.7763	1.14228	0.571142	−	0.820851i	$-0.306500\pi$
$89$	10.7763	1.14228	0.571142	+	0.820851i	$0.306500\pi$
$90$	2.38147	0.251029
$91$	−32.2626	−3.38204
$92$	−2.65755	−0.277068
$93$	12.5626	1.30268
$94$	−3.00499	−0.309941
$95$	0	0
$96$	2.31980	0.236764
$97$	−2.05429	−0.208582	−0.104291	−	0.994547i	$-0.533257\pi$
$97$	−2.05429	−0.208582	−0.104291	+	0.994547i	$0.533257\pi$
$98$	17.1744	1.73487
$99$	6.77902	0.681317
$100$	1.00000	0.100000
$101$	−5.00966	−0.498480	−0.249240	−	0.968442i	$-0.580181\pi$
$101$	−5.00966	−0.498480	−0.249240	+	0.968442i	$0.580181\pi$
$102$	−5.08321	−0.503313
$103$	9.03489	0.890234	0.445117	−	0.895472i	$-0.353162\pi$
$103$	9.03489	0.890234	0.445117	+	0.895472i	$0.353162\pi$
$104$	6.56179	0.643436
$105$	−11.4059	−1.11310
$106$	4.22215	0.410091
$107$	−5.96783	−0.576932	−0.288466	−	0.957490i	$-0.593145\pi$
$107$	−5.96783	−0.576932	−0.288466	+	0.957490i	$0.593145\pi$
$108$	−1.43487	−0.138070
$109$	15.8300	1.51624	0.758118	−	0.652118i	$-0.226119\pi$
$109$	15.8300	1.51624	0.758118	+	0.652118i	$0.226119\pi$
$110$	2.84657	0.271410
$111$	4.78463	0.454137
$112$	−4.91674	−0.464589
$113$	−18.2051	−1.71259	−0.856296	−	0.516485i	$-0.827240\pi$
$113$	−18.2051	−1.71259	−0.856296	+	0.516485i	$0.827240\pi$
$114$	0	0
$115$	−2.65755	−0.247817
$116$	7.60179	0.705808
$117$	15.6267	1.44469
$118$	0.964592	0.0887979
$119$	10.7737	0.987624
$120$	2.31980	0.211768
$121$	−2.89703	−0.263366
$122$	−7.49955	−0.678977
$123$	21.7070	1.95726
$124$	5.41539	0.486316
$125$	1.00000	0.0894427
$126$	−11.7091	−1.04313
$127$	−7.64954	−0.678787	−0.339394	−	0.940644i	$-0.610222\pi$
$127$	−7.64954	−0.678787	−0.339394	+	0.940644i	$0.610222\pi$
$128$	1.00000	0.0883883
$129$	4.02274	0.354182
$130$	6.56179	0.575507
$131$	−13.3148	−1.16332	−0.581659	−	0.813433i	$-0.697596\pi$
$131$	−13.3148	−1.16332	−0.581659	+	0.813433i	$0.697596\pi$
$132$	6.60347	0.574759
$133$	0	0
$134$	−1.91955	−0.165824
$135$	−1.43487	−0.123494
$136$	−2.19123	−0.187896
$137$	−7.22627	−0.617382	−0.308691	−	0.951162i	$-0.599891\pi$
$137$	−7.22627	−0.617382	−0.308691	+	0.951162i	$0.599891\pi$
$138$	−6.16497	−0.524797
$139$	−2.41177	−0.204564	−0.102282	−	0.994755i	$-0.532614\pi$
$139$	−2.41177	−0.204564	−0.102282	+	0.994755i	$0.532614\pi$
$140$	−4.91674	−0.415541
$141$	−6.97098	−0.587063
$142$	6.16536	0.517385
$143$	18.6786	1.56198
$144$	2.38147	0.198456
$145$	7.60179	0.631294
$146$	−3.97703	−0.329142
$147$	39.8411	3.28604
$148$	2.06252	0.169538
$149$	−6.97873	−0.571720	−0.285860	−	0.958271i	$-0.592279\pi$
$149$	−6.97873	−0.571720	−0.285860	+	0.958271i	$0.592279\pi$
$150$	2.31980	0.189411
$151$	5.69362	0.463340	0.231670	−	0.972794i	$-0.425581\pi$
$151$	5.69362	0.463340	0.231670	+	0.972794i	$0.425581\pi$
$152$	0	0
$153$	−5.21834	−0.421878
$154$	−13.9959	−1.12782
$155$	5.41539	0.434974
$156$	15.2220	1.21874
$157$	−5.31383	−0.424090	−0.212045	−	0.977260i	$-0.568012\pi$
$157$	−5.31383	−0.424090	−0.212045	+	0.977260i	$0.568012\pi$
$158$	−15.3229	−1.21903
$159$	9.79454	0.776758
$160$	1.00000	0.0790569
$161$	13.0665	1.02978
$162$	−10.4730	−0.822838
$163$	−4.47359	−0.350398	−0.175199	−	0.984533i	$-0.556057\pi$
$163$	−4.47359	−0.350398	−0.175199	+	0.984533i	$0.556057\pi$
$164$	9.35729	0.730682
$165$	6.60347	0.514080
$166$	−1.31206	−0.101836
$167$	−3.64877	−0.282350	−0.141175	−	0.989985i	$-0.545088\pi$
$167$	−3.64877	−0.282350	−0.141175	+	0.989985i	$0.545088\pi$
$168$	−11.4059	−0.879981
$169$	30.0571	2.31208
$170$	−2.19123	−0.168060
$171$	0	0
$172$	1.73409	0.132223
$173$	1.17631	0.0894333	0.0447167	−	0.999000i	$-0.485761\pi$
$173$	1.17631	0.0894333	0.0447167	+	0.999000i	$0.485761\pi$
$174$	17.6346	1.33688
$175$	−4.91674	−0.371671
$176$	2.84657	0.214568
$177$	2.23766	0.168193
$178$	10.7763	0.807717
$179$	−4.33057	−0.323682	−0.161841	−	0.986817i	$-0.551743\pi$
$179$	−4.33057	−0.323682	−0.161841	+	0.986817i	$0.551743\pi$
$180$	2.38147	0.177504
$181$	−1.36920	−0.101771	−0.0508857	−	0.998704i	$-0.516204\pi$
$181$	−1.36920	−0.101771	−0.0508857	+	0.998704i	$0.516204\pi$
$182$	−32.2626	−2.39147
$183$	−17.3974	−1.28606
$184$	−2.65755	−0.195917
$185$	2.06252	0.151640
$186$	12.5626	0.921135
$187$	−6.23749	−0.456130
$188$	−3.00499	−0.219162
$189$	7.05488	0.513167
$190$	0	0
$191$	13.6338	0.986505	0.493252	−	0.869886i	$-0.335808\pi$
$191$	13.6338	0.986505	0.493252	+	0.869886i	$0.335808\pi$
$192$	2.31980	0.167417
$193$	5.21947	0.375706	0.187853	−	0.982197i	$-0.439847\pi$
$193$	5.21947	0.375706	0.187853	+	0.982197i	$0.439847\pi$
$194$	−2.05429	−0.147490
$195$	15.2220	1.09007
$196$	17.1744	1.22674
$197$	2.85541	0.203440	0.101720	−	0.994813i	$-0.467565\pi$
$197$	2.85541	0.203440	0.101720	+	0.994813i	$0.467565\pi$
$198$	6.77902	0.481764
$199$	−1.46463	−0.103825	−0.0519123	−	0.998652i	$-0.516532\pi$
$199$	−1.46463	−0.103825	−0.0519123	+	0.998652i	$0.516532\pi$
$200$	1.00000	0.0707107
$201$	−4.45297	−0.314088
$202$	−5.00966	−0.352478
$203$	−37.3760	−2.62328
$204$	−5.08321	−0.355896
$205$	9.35729	0.653542
$206$	9.03489	0.629490
$207$	−6.32886	−0.439886
$208$	6.56179	0.454978
$209$	0	0
$210$	−11.4059	−0.787079
$211$	−1.31050	−0.0902188	−0.0451094	−	0.998982i	$-0.514364\pi$
$211$	−1.31050	−0.0902188	−0.0451094	+	0.998982i	$0.514364\pi$
$212$	4.22215	0.289978
$213$	14.3024	0.979984
$214$	−5.96783	−0.407952
$215$	1.73409	0.118264
$216$	−1.43487	−0.0976305
$217$	−26.6261	−1.80749
$218$	15.8300	1.07214
$219$	−9.22592	−0.623430
$220$	2.84657	0.191916
$221$	−14.3784	−0.967194
$222$	4.78463	0.321124
$223$	−28.1303	−1.88375	−0.941874	−	0.335967i	$-0.890937\pi$
$223$	−28.1303	−1.88375	−0.941874	+	0.335967i	$0.890937\pi$
$224$	−4.91674	−0.328514
$225$	2.38147	0.158765
$226$	−18.2051	−1.21099
$227$	−12.6466	−0.839382	−0.419691	−	0.907667i	$-0.637862\pi$
$227$	−12.6466	−0.839382	−0.419691	+	0.907667i	$0.637862\pi$
$228$	0	0
$229$	13.7440	0.908227	0.454113	−	0.890944i	$-0.349956\pi$
$229$	13.7440	0.908227	0.454113	+	0.890944i	$0.349956\pi$
$230$	−2.65755	−0.175233
$231$	−32.4676	−2.13621
$232$	7.60179	0.499082
$233$	24.6181	1.61279	0.806394	−	0.591379i	$-0.201416\pi$
$233$	24.6181	1.61279	0.806394	+	0.591379i	$0.201416\pi$
$234$	15.6267	1.02155
$235$	−3.00499	−0.196024
$236$	0.964592	0.0627896
$237$	−35.5461	−2.30897
$238$	10.7737	0.698356
$239$	−16.2940	−1.05397	−0.526984	−	0.849875i	$-0.676677\pi$
$239$	−16.2940	−1.05397	−0.526984	+	0.849875i	$0.676677\pi$
$240$	2.31980	0.149742
$241$	19.2548	1.24031	0.620155	−	0.784479i	$-0.287070\pi$
$241$	19.2548	1.24031	0.620155	+	0.784479i	$0.287070\pi$
$242$	−2.89703	−0.186228
$243$	−19.9907	−1.28240
$244$	−7.49955	−0.480109
$245$	17.1744	1.09723
$246$	21.7070	1.38399
$247$	0	0
$248$	5.41539	0.343877
$249$	−3.04373	−0.192888
$250$	1.00000	0.0632456
$251$	−27.7701	−1.75283	−0.876416	−	0.481555i	$-0.840072\pi$
$251$	−27.7701	−1.75283	−0.876416	+	0.481555i	$0.840072\pi$
$252$	−11.7091	−0.737602
$253$	−7.56490	−0.475601
$254$	−7.64954	−0.479975
$255$	−5.08321	−0.318323
$256$	1.00000	0.0625000
$257$	−13.0703	−0.815301	−0.407650	−	0.913138i	$-0.633652\pi$
$257$	−13.0703	−0.815301	−0.407650	+	0.913138i	$0.633652\pi$
$258$	4.02274	0.250445
$259$	−10.1409	−0.630124
$260$	6.56179	0.406945
$261$	18.1034	1.12057
$262$	−13.3148	−0.822589
$263$	15.0560	0.928392	0.464196	−	0.885733i	$-0.346343\pi$
$263$	15.0560	0.928392	0.464196	+	0.885733i	$0.346343\pi$
$264$	6.60347	0.406416
$265$	4.22215	0.259365
$266$	0	0
$267$	24.9988	1.52990
$268$	−1.91955	−0.117255
$269$	−24.4553	−1.49107	−0.745533	−	0.666468i	$-0.767805\pi$
$269$	−24.4553	−1.49107	−0.745533	+	0.666468i	$0.767805\pi$
$270$	−1.43487	−0.0873233
$271$	8.95074	0.543719	0.271859	−	0.962337i	$-0.412361\pi$
$271$	8.95074	0.543719	0.271859	+	0.962337i	$0.412361\pi$
$272$	−2.19123	−0.132863
$273$	−74.8428	−4.52969
$274$	−7.22627	−0.436555
$275$	2.84657	0.171655
$276$	−6.16497	−0.371088
$277$	−7.80141	−0.468741	−0.234371	−	0.972147i	$-0.575303\pi$
$277$	−7.80141	−0.468741	−0.234371	+	0.972147i	$0.575303\pi$
$278$	−2.41177	−0.144648
$279$	12.8966	0.772098
$280$	−4.91674	−0.293832
$281$	−18.2982	−1.09158	−0.545791	−	0.837921i	$-0.683771\pi$
$281$	−18.2982	−1.09158	−0.545791	+	0.837921i	$0.683771\pi$
$282$	−6.97098	−0.415116
$283$	7.22803	0.429662	0.214831	−	0.976651i	$-0.431080\pi$
$283$	7.22803	0.429662	0.214831	+	0.976651i	$0.431080\pi$
$284$	6.16536	0.365847
$285$	0	0
$286$	18.6786	1.10449
$287$	−46.0074	−2.71573
$288$	2.38147	0.140329
$289$	−12.1985	−0.717560
$290$	7.60179	0.446392
$291$	−4.76555	−0.279361
$292$	−3.97703	−0.232738
$293$	−11.3866	−0.665212	−0.332606	−	0.943066i	$-0.607928\pi$
$293$	−11.3866	−0.665212	−0.332606	+	0.943066i	$0.607928\pi$
$294$	39.8411	2.32358
$295$	0.964592	0.0561607
$296$	2.06252	0.119882
$297$	−4.08446	−0.237004
$298$	−6.97873	−0.404267
$299$	−17.4383	−1.00848
$300$	2.31980	0.133934
$301$	−8.52607	−0.491434
$302$	5.69362	0.327631
$303$	−11.6214	−0.667632
$304$	0	0
$305$	−7.49955	−0.429423
$306$	−5.21834	−0.298313
$307$	−4.94292	−0.282107	−0.141054	−	0.990002i	$-0.545049\pi$
$307$	−4.94292	−0.282107	−0.141054	+	0.990002i	$0.545049\pi$
$308$	−13.9959	−0.797488
$309$	20.9591	1.19232
$310$	5.41539	0.307573
$311$	24.1172	1.36756	0.683782	−	0.729687i	$-0.260334\pi$
$311$	24.1172	1.36756	0.683782	+	0.729687i	$0.260334\pi$
$312$	15.2220	0.861778
$313$	−30.9756	−1.75084	−0.875422	−	0.483359i	$-0.839416\pi$
$313$	−30.9756	−1.75084	−0.875422	+	0.483359i	$0.839416\pi$
$314$	−5.31383	−0.299877
$315$	−11.7091	−0.659731
$316$	−15.3229	−0.861981
$317$	6.91053	0.388134	0.194067	−	0.980988i	$-0.437832\pi$
$317$	6.91053	0.388134	0.194067	+	0.980988i	$0.437832\pi$
$318$	9.79454	0.549251
$319$	21.6390	1.21155
$320$	1.00000	0.0559017
$321$	−13.8442	−0.772706
$322$	13.0665	0.728166
$323$	0	0
$324$	−10.4730	−0.581834
$325$	6.56179	0.363983
$326$	−4.47359	−0.247769
$327$	36.7223	2.03075
$328$	9.35729	0.516670
$329$	14.7748	0.814560
$330$	6.60347	0.363509
$331$	−4.17886	−0.229691	−0.114845	−	0.993383i	$-0.536637\pi$
$331$	−4.17886	−0.229691	−0.114845	+	0.993383i	$0.536637\pi$
$332$	−1.31206	−0.0720089
$333$	4.91183	0.269167
$334$	−3.64877	−0.199652
$335$	−1.91955	−0.104876
$336$	−11.4059	−0.622240
$337$	−17.2012	−0.937008	−0.468504	−	0.883461i	$-0.655207\pi$
$337$	−17.2012	−0.937008	−0.468504	+	0.883461i	$0.655207\pi$
$338$	30.0571	1.63489
$339$	−42.2322	−2.29374
$340$	−2.19123	−0.118836
$341$	15.4153	0.834784
$342$	0	0
$343$	−50.0247	−2.70108
$344$	1.73409	0.0934958
$345$	−6.16497	−0.331911
$346$	1.17631	0.0632389
$347$	18.4628	0.991137	0.495568	−	0.868569i	$-0.334960\pi$
$347$	18.4628	0.991137	0.495568	+	0.868569i	$0.334960\pi$
$348$	17.6346	0.945315
$349$	24.7409	1.32435	0.662174	−	0.749350i	$-0.269634\pi$
$349$	24.7409	1.32435	0.662174	+	0.749350i	$0.269634\pi$
$350$	−4.91674	−0.262811
$351$	−9.41531	−0.502552
$352$	2.84657	0.151723
$353$	−6.40992	−0.341165	−0.170583	−	0.985343i	$-0.554565\pi$
$353$	−6.40992	−0.341165	−0.170583	+	0.985343i	$0.554565\pi$
$354$	2.23766	0.118930
$355$	6.16536	0.327223
$356$	10.7763	0.571142
$357$	24.9928	1.32276
$358$	−4.33057	−0.228878
$359$	−36.8154	−1.94304	−0.971522	−	0.236948i	$-0.923853\pi$
$359$	−36.8154	−1.94304	−0.971522	+	0.236948i	$0.923853\pi$
$360$	2.38147	0.125514
$361$	0	0
$362$	−1.36920	−0.0719633
$363$	−6.72053	−0.352736
$364$	−32.2626	−1.69102
$365$	−3.97703	−0.208167
$366$	−17.3974	−0.909379
$367$	14.6238	0.763356	0.381678	−	0.924295i	$-0.375346\pi$
$367$	14.6238	0.763356	0.381678	+	0.924295i	$0.375346\pi$
$368$	−2.65755	−0.138534
$369$	22.2841	1.16006
$370$	2.06252	0.107225
$371$	−20.7592	−1.07777
$372$	12.5626	0.651341
$373$	13.5574	0.701977	0.350989	−	0.936380i	$-0.385846\pi$
$373$	13.5574	0.701977	0.350989	+	0.936380i	$0.385846\pi$
$374$	−6.23749	−0.322533
$375$	2.31980	0.119794
$376$	−3.00499	−0.154971
$377$	49.8813	2.56902
$378$	7.05488	0.362864
$379$	−30.2899	−1.55589	−0.777944	−	0.628333i	$-0.783738\pi$
$379$	−30.2899	−1.55589	−0.777944	+	0.628333i	$0.783738\pi$
$380$	0	0
$381$	−17.7454	−0.909124
$382$	13.6338	0.697564
$383$	28.6630	1.46461	0.732305	−	0.680977i	$-0.238445\pi$
$383$	28.6630	1.46461	0.732305	+	0.680977i	$0.238445\pi$
$384$	2.31980	0.118382
$385$	−13.9959	−0.713295
$386$	5.21947	0.265664
$387$	4.12968	0.209923
$388$	−2.05429	−0.104291
$389$	17.1263	0.868337	0.434168	−	0.900832i	$-0.357042\pi$
$389$	17.1263	0.868337	0.434168	+	0.900832i	$0.357042\pi$
$390$	15.2220	0.770798
$391$	5.82329	0.294496
$392$	17.1744	0.867436
$393$	−30.8876	−1.55807
$394$	2.85541	0.143854
$395$	−15.3229	−0.770980
$396$	6.77902	0.340659
$397$	26.1050	1.31017	0.655085	−	0.755555i	$-0.272633\pi$
$397$	26.1050	1.31017	0.655085	+	0.755555i	$0.272633\pi$
$398$	−1.46463	−0.0734151
$399$	0	0
$400$	1.00000	0.0500000
$401$	9.31093	0.464966	0.232483	−	0.972600i	$-0.425315\pi$
$401$	9.31093	0.464966	0.232483	+	0.972600i	$0.425315\pi$
$402$	−4.45297	−0.222094
$403$	35.5346	1.77011
$404$	−5.00966	−0.249240
$405$	−10.4730	−0.520408
$406$	−37.3760	−1.85494
$407$	5.87111	0.291020
$408$	−5.08321	−0.251656
$409$	−14.5798	−0.720925	−0.360462	−	0.932774i	$-0.617381\pi$
$409$	−14.5798	−0.720925	−0.360462	+	0.932774i	$0.617381\pi$
$410$	9.35729	0.462124
$411$	−16.7635	−0.826882
$412$	9.03489	0.445117
$413$	−4.74265	−0.233371
$414$	−6.32886	−0.311047
$415$	−1.31206	−0.0644067
$416$	6.56179	0.321718
$417$	−5.59483	−0.273980
$418$	0	0
$419$	14.5969	0.713103	0.356552	−	0.934276i	$-0.383952\pi$
$419$	14.5969	0.713103	0.356552	+	0.934276i	$0.383952\pi$
$420$	−11.4059	−0.556549
$421$	39.2412	1.91250	0.956249	−	0.292555i	$-0.0945056\pi$
$421$	39.2412	1.91250	0.956249	+	0.292555i	$0.0945056\pi$
$422$	−1.31050	−0.0637943
$423$	−7.15630	−0.347951
$424$	4.22215	0.205046
$425$	−2.19123	−0.106290
$426$	14.3024	0.692953
$427$	36.8734	1.78443
$428$	−5.96783	−0.288466
$429$	43.3306	2.09202
$430$	1.73409	0.0836252
$431$	−21.8767	−1.05376	−0.526881	−	0.849939i	$-0.676639\pi$
$431$	−21.8767	−1.05376	−0.526881	+	0.849939i	$0.676639\pi$
$432$	−1.43487	−0.0690352
$433$	1.10168	0.0529436	0.0264718	−	0.999650i	$-0.491573\pi$
$433$	1.10168	0.0529436	0.0264718	+	0.999650i	$0.491573\pi$
$434$	−26.6261	−1.27809
$435$	17.6346	0.845515
$436$	15.8300	0.758118
$437$	0	0
$438$	−9.22592	−0.440832
$439$	4.21717	0.201275	0.100637	−	0.994923i	$-0.467912\pi$
$439$	4.21717	0.201275	0.100637	+	0.994923i	$0.467912\pi$
$440$	2.84657	0.135705
$441$	40.9002	1.94763
$442$	−14.3784	−0.683910
$443$	7.58310	0.360284	0.180142	−	0.983641i	$-0.442344\pi$
$443$	7.58310	0.360284	0.180142	+	0.983641i	$0.442344\pi$
$444$	4.78463	0.227069
$445$	10.7763	0.510845
$446$	−28.1303	−1.33201
$447$	−16.1893	−0.765726
$448$	−4.91674	−0.232294
$449$	−29.6975	−1.40151	−0.700756	−	0.713401i	$-0.747154\pi$
$449$	−29.6975	−1.40151	−0.700756	+	0.713401i	$0.747154\pi$
$450$	2.38147	0.112263
$451$	26.6362	1.25425
$452$	−18.2051	−0.856296
$453$	13.2080	0.620568
$454$	−12.6466	−0.593533
$455$	−32.2626	−1.51250
$456$	0	0
$457$	9.12576	0.426885	0.213442	−	0.976956i	$-0.431532\pi$
$457$	9.12576	0.426885	0.213442	+	0.976956i	$0.431532\pi$
$458$	13.7440	0.642213
$459$	3.14413	0.146755
$460$	−2.65755	−0.123909
$461$	−26.3855	−1.22890	−0.614449	−	0.788957i	$-0.710621\pi$
$461$	−26.3855	−1.22890	−0.614449	+	0.788957i	$0.710621\pi$
$462$	−32.4676	−1.51053
$463$	−15.7219	−0.730658	−0.365329	−	0.930878i	$-0.619044\pi$
$463$	−15.7219	−0.730658	−0.365329	+	0.930878i	$0.619044\pi$
$464$	7.60179	0.352904
$465$	12.5626	0.582577
$466$	24.6181	1.14041
$467$	−6.89932	−0.319263	−0.159631	−	0.987177i	$-0.551031\pi$
$467$	−6.89932	−0.319263	−0.159631	+	0.987177i	$0.551031\pi$
$468$	15.6267	0.722344
$469$	9.43794	0.435803
$470$	−3.00499	−0.138610
$471$	−12.3270	−0.567999
$472$	0.964592	0.0443989
$473$	4.93621	0.226967
$474$	−35.5461	−1.63269
$475$	0	0
$476$	10.7737	0.493812
$477$	10.0549	0.460383
$478$	−16.2940	−0.745268
$479$	−3.64861	−0.166709	−0.0833547	−	0.996520i	$-0.526563\pi$
$479$	−3.64861	−0.166709	−0.0833547	+	0.996520i	$0.526563\pi$
$480$	2.31980	0.105884
$481$	13.5338	0.617089
$482$	19.2548	0.877032
$483$	30.3116	1.37922
$484$	−2.89703	−0.131683
$485$	−2.05429	−0.0932806
$486$	−19.9907	−0.906796
$487$	22.5151	1.02026	0.510128	−	0.860098i	$-0.329598\pi$
$487$	22.5151	1.02026	0.510128	+	0.860098i	$0.329598\pi$
$488$	−7.49955	−0.339489
$489$	−10.3778	−0.469301
$490$	17.1744	0.775859
$491$	25.1612	1.13551	0.567753	−	0.823199i	$-0.307813\pi$
$491$	25.1612	1.13551	0.567753	+	0.823199i	$0.307813\pi$
$492$	21.7070	0.978629
$493$	−16.6573	−0.750205
$494$	0	0
$495$	6.77902	0.304694
$496$	5.41539	0.243158
$497$	−30.3135	−1.35975
$498$	−3.04373	−0.136393
$499$	31.7722	1.42232	0.711159	−	0.703032i	$-0.248171\pi$
$499$	31.7722	1.42232	0.711159	+	0.703032i	$0.248171\pi$
$500$	1.00000	0.0447214
$501$	−8.46441	−0.378162
$502$	−27.7701	−1.23944
$503$	−25.5621	−1.13976	−0.569878	−	0.821729i	$-0.693010\pi$
$503$	−25.5621	−1.13976	−0.569878	+	0.821729i	$0.693010\pi$
$504$	−11.7091	−0.521563
$505$	−5.00966	−0.222927
$506$	−7.56490	−0.336301
$507$	69.7264	3.09666
$508$	−7.64954	−0.339394
$509$	−9.88190	−0.438007	−0.219004	−	0.975724i	$-0.570281\pi$
$509$	−9.88190	−0.438007	−0.219004	+	0.975724i	$0.570281\pi$
$510$	−5.08321	−0.225088
$511$	19.5541	0.865020
$512$	1.00000	0.0441942
$513$	0	0
$514$	−13.0703	−0.576505
$515$	9.03489	0.398125
$516$	4.02274	0.177091
$517$	−8.55393	−0.376201
$518$	−10.1409	−0.445565
$519$	2.72881	0.119781
$520$	6.56179	0.287753
$521$	4.29775	0.188288	0.0941440	−	0.995559i	$-0.469989\pi$
$521$	4.29775	0.188288	0.0941440	+	0.995559i	$0.469989\pi$
$522$	18.1034	0.792365
$523$	−24.9031	−1.08893	−0.544467	−	0.838782i	$-0.683268\pi$
$523$	−24.9031	−1.08893	−0.544467	+	0.838782i	$0.683268\pi$
$524$	−13.3148	−0.581659
$525$	−11.4059	−0.497792
$526$	15.0560	0.656472
$527$	−11.8663	−0.516906
$528$	6.60347	0.287379
$529$	−15.9374	−0.692933
$530$	4.22215	0.183398
$531$	2.29714	0.0996876
$532$	0	0
$533$	61.4006	2.65955
$534$	24.9988	1.08181
$535$	−5.96783	−0.258012
$536$	−1.91955	−0.0829120
$537$	−10.0461	−0.433519
$538$	−24.4553	−1.05434
$539$	48.8880	2.10576
$540$	−1.43487	−0.0617469
$541$	−21.8913	−0.941181	−0.470590	−	0.882352i	$-0.655959\pi$
$541$	−21.8913	−0.941181	−0.470590	+	0.882352i	$0.655959\pi$
$542$	8.95074	0.384467
$543$	−3.17626	−0.136306
$544$	−2.19123	−0.0939481
$545$	15.8300	0.678081
$546$	−74.8428	−3.20298
$547$	−2.96232	−0.126660	−0.0633299	−	0.997993i	$-0.520172\pi$
$547$	−2.96232	−0.126660	−0.0633299	+	0.997993i	$0.520172\pi$
$548$	−7.22627	−0.308691
$549$	−17.8599	−0.762244
$550$	2.84657	0.121378
$551$	0	0
$552$	−6.16497	−0.262399
$553$	75.3388	3.20373
$554$	−7.80141	−0.331450
$555$	4.78463	0.203096
$556$	−2.41177	−0.102282
$557$	−30.7697	−1.30376	−0.651878	−	0.758324i	$-0.726018\pi$
$557$	−30.7697	−1.30376	−0.651878	+	0.758324i	$0.726018\pi$
$558$	12.8966	0.545955
$559$	11.3787	0.481269
$560$	−4.91674	−0.207770
$561$	−14.4697	−0.610912
$562$	−18.2982	−0.771865
$563$	35.5091	1.49653	0.748266	−	0.663399i	$-0.230887\pi$
$563$	35.5091	1.49653	0.748266	+	0.663399i	$0.230887\pi$
$564$	−6.97098	−0.293531
$565$	−18.2051	−0.765895
$566$	7.22803	0.303817
$567$	51.4931	2.16251
$568$	6.16536	0.258693
$569$	−33.0813	−1.38684	−0.693421	−	0.720533i	$-0.743897\pi$
$569$	−33.0813	−1.38684	−0.693421	+	0.720533i	$0.743897\pi$
$570$	0	0
$571$	2.29342	0.0959766	0.0479883	−	0.998848i	$-0.484719\pi$
$571$	2.29342	0.0959766	0.0479883	+	0.998848i	$0.484719\pi$
$572$	18.6786	0.780992
$573$	31.6276	1.32126
$574$	−46.0074	−1.92031
$575$	−2.65755	−0.110827
$576$	2.38147	0.0992279
$577$	−15.7036	−0.653747	−0.326874	−	0.945068i	$-0.605995\pi$
$577$	−15.7036	−0.653747	−0.326874	+	0.945068i	$0.605995\pi$
$578$	−12.1985	−0.507391
$579$	12.1081	0.503197
$580$	7.60179	0.315647
$581$	6.45109	0.267636
$582$	−4.76555	−0.197538
$583$	12.0187	0.497762
$584$	−3.97703	−0.164571
$585$	15.6267	0.646084
$586$	−11.3866	−0.470376
$587$	−26.5110	−1.09423	−0.547113	−	0.837059i	$-0.684273\pi$
$587$	−26.5110	−1.09423	−0.547113	+	0.837059i	$0.684273\pi$
$588$	39.8411	1.64302
$589$	0	0
$590$	0.964592	0.0397116
$591$	6.62398	0.272474
$592$	2.06252	0.0847691
$593$	−2.92920	−0.120288	−0.0601438	−	0.998190i	$-0.519156\pi$
$593$	−2.92920	−0.120288	−0.0601438	+	0.998190i	$0.519156\pi$
$594$	−4.08446	−0.167587
$595$	10.7737	0.441679
$596$	−6.97873	−0.285860
$597$	−3.39764	−0.139056
$598$	−17.4383	−0.713103
$599$	−37.0535	−1.51397	−0.756983	−	0.653435i	$-0.773327\pi$
$599$	−37.0535	−1.51397	−0.756983	+	0.653435i	$0.773327\pi$
$600$	2.31980	0.0947054
$601$	9.69599	0.395508	0.197754	−	0.980252i	$-0.436635\pi$
$601$	9.69599	0.395508	0.197754	+	0.980252i	$0.436635\pi$
$602$	−8.52607	−0.347497
$603$	−4.57135	−0.186160
$604$	5.69362	0.231670
$605$	−2.89703	−0.117781
$606$	−11.6214	−0.472087
$607$	38.0294	1.54357	0.771783	−	0.635886i	$-0.219365\pi$
$607$	38.0294	1.54357	0.771783	+	0.635886i	$0.219365\pi$
$608$	0	0
$609$	−86.7049	−3.51346
$610$	−7.49955	−0.303648
$611$	−19.7181	−0.797710
$612$	−5.21834	−0.210939
$613$	−22.8475	−0.922800	−0.461400	−	0.887192i	$-0.652653\pi$
$613$	−22.8475	−0.922800	−0.461400	+	0.887192i	$0.652653\pi$
$614$	−4.94292	−0.199480
$615$	21.7070	0.875312
$616$	−13.9959	−0.563909
$617$	−25.4472	−1.02447	−0.512233	−	0.858847i	$-0.671181\pi$
$617$	−25.4472	−1.02447	−0.512233	+	0.858847i	$0.671181\pi$
$618$	20.9591	0.843100
$619$	15.9156	0.639701	0.319850	−	0.947468i	$-0.396367\pi$
$619$	15.9156	0.639701	0.319850	+	0.947468i	$0.396367\pi$
$620$	5.41539	0.217487
$621$	3.81323	0.153020
$622$	24.1172	0.967013
$623$	−52.9843	−2.12277
$624$	15.2220	0.609369
$625$	1.00000	0.0400000
$626$	−30.9756	−1.23803
$627$	0	0
$628$	−5.31383	−0.212045
$629$	−4.51945	−0.180202
$630$	−11.7091	−0.466500
$631$	−19.9368	−0.793673	−0.396836	−	0.917889i	$-0.629892\pi$
$631$	−19.9368	−0.793673	−0.396836	+	0.917889i	$0.629892\pi$
$632$	−15.3229	−0.609513
$633$	−3.04011	−0.120833
$634$	6.91053	0.274452
$635$	−7.64954	−0.303563
$636$	9.79454	0.388379
$637$	112.695	4.46512
$638$	21.6390	0.856697
$639$	14.6826	0.580835
$640$	1.00000	0.0395285
$641$	−2.42799	−0.0958998	−0.0479499	−	0.998850i	$-0.515269\pi$
$641$	−2.42799	−0.0958998	−0.0479499	+	0.998850i	$0.515269\pi$
$642$	−13.8442	−0.546385
$643$	−6.69448	−0.264005	−0.132002	−	0.991249i	$-0.542141\pi$
$643$	−6.69448	−0.264005	−0.132002	+	0.991249i	$0.542141\pi$
$644$	13.0665	0.514891
$645$	4.02274	0.158395
$646$	0	0
$647$	28.2280	1.10976	0.554878	−	0.831932i	$-0.312765\pi$
$647$	28.2280	1.10976	0.554878	+	0.831932i	$0.312765\pi$
$648$	−10.4730	−0.411419
$649$	2.74578	0.107781
$650$	6.56179	0.257375
$651$	−61.7671	−2.42084
$652$	−4.47359	−0.175199
$653$	16.9827	0.664585	0.332293	−	0.943176i	$-0.392178\pi$
$653$	16.9827	0.664585	0.332293	+	0.943176i	$0.392178\pi$
$654$	36.7223	1.43596
$655$	−13.3148	−0.520251
$656$	9.35729	0.365341
$657$	−9.47118	−0.369506
$658$	14.7748	0.575981
$659$	18.3003	0.712877	0.356438	−	0.934319i	$-0.383991\pi$
$659$	18.3003	0.712877	0.356438	+	0.934319i	$0.383991\pi$
$660$	6.60347	0.257040
$661$	−5.43955	−0.211574	−0.105787	−	0.994389i	$-0.533736\pi$
$661$	−5.43955	−0.211574	−0.105787	+	0.994389i	$0.533736\pi$
$662$	−4.17886	−0.162416
$663$	−33.3550	−1.29540
$664$	−1.31206	−0.0509180
$665$	0	0
$666$	4.91183	0.190329
$667$	−20.2021	−0.782228
$668$	−3.64877	−0.141175
$669$	−65.2568	−2.52297
$670$	−1.91955	−0.0741587
$671$	−21.3480	−0.824131
$672$	−11.4059	−0.439990
$673$	29.9144	1.15311	0.576557	−	0.817057i	$-0.304396\pi$
$673$	29.9144	1.15311	0.576557	+	0.817057i	$0.304396\pi$
$674$	−17.2012	−0.662565
$675$	−1.43487	−0.0552281
$676$	30.0571	1.15604
$677$	31.4564	1.20897	0.604483	−	0.796618i	$-0.293380\pi$
$677$	31.4564	1.20897	0.604483	+	0.796618i	$0.293380\pi$
$678$	−42.2322	−1.62192
$679$	10.1004	0.387619
$680$	−2.19123	−0.0840298
$681$	−29.3375	−1.12421
$682$	15.4153	0.590282
$683$	49.8920	1.90906	0.954532	−	0.298109i	$-0.0963559\pi$
$683$	49.8920	1.90906	0.954532	+	0.298109i	$0.0963559\pi$
$684$	0	0
$685$	−7.22627	−0.276101
$686$	−50.0247	−1.90995
$687$	31.8832	1.21642
$688$	1.73409	0.0661115
$689$	27.7049	1.05547
$690$	−6.16497	−0.234697
$691$	18.7274	0.712424	0.356212	−	0.934405i	$-0.384068\pi$
$691$	18.7274	0.712424	0.356212	+	0.934405i	$0.384068\pi$
$692$	1.17631	0.0447167
$693$	−33.3307	−1.26613
$694$	18.4628	0.700839
$695$	−2.41177	−0.0914837
$696$	17.6346	0.668438
$697$	−20.5040	−0.776643
$698$	24.7409	0.936455
$699$	57.1091	2.16007
$700$	−4.91674	−0.185835
$701$	−17.9049	−0.676258	−0.338129	−	0.941100i	$-0.609794\pi$
$701$	−17.9049	−0.676258	−0.338129	+	0.941100i	$0.609794\pi$
$702$	−9.41531	−0.355358
$703$	0	0
$704$	2.84657	0.107284
$705$	−6.97098	−0.262542
$706$	−6.40992	−0.241240
$707$	24.6312	0.926352
$708$	2.23766	0.0840964
$709$	26.9792	1.01323	0.506613	−	0.862173i	$-0.330897\pi$
$709$	26.9792	1.01323	0.506613	+	0.862173i	$0.330897\pi$
$710$	6.16536	0.231382
$711$	−36.4910	−1.36852
$712$	10.7763	0.403859
$713$	−14.3916	−0.538971
$714$	24.9928	0.935333
$715$	18.6786	0.698540
$716$	−4.33057	−0.161841
$717$	−37.7987	−1.41162
$718$	−36.8154	−1.37394
$719$	42.4173	1.58190	0.790950	−	0.611881i	$-0.209587\pi$
$719$	42.4173	1.58190	0.790950	+	0.611881i	$0.209587\pi$
$720$	2.38147	0.0887521
$721$	−44.4222	−1.65437
$722$	0	0
$723$	44.6672	1.66119
$724$	−1.36920	−0.0508857
$725$	7.60179	0.282323
$726$	−6.72053	−0.249422
$727$	−43.0435	−1.59639	−0.798197	−	0.602396i	$-0.794213\pi$
$727$	−43.0435	−1.59639	−0.798197	+	0.602396i	$0.794213\pi$
$728$	−32.2626	−1.19573
$729$	−14.9553	−0.553901
$730$	−3.97703	−0.147197
$731$	−3.79978	−0.140540
$732$	−17.3974	−0.643028
$733$	−30.3958	−1.12269	−0.561347	−	0.827580i	$-0.689717\pi$
$733$	−30.3958	−1.12269	−0.561347	+	0.827580i	$0.689717\pi$
$734$	14.6238	0.539774
$735$	39.8411	1.46956
$736$	−2.65755	−0.0979584
$737$	−5.46414	−0.201274
$738$	22.2841	0.820289
$739$	−36.8924	−1.35711	−0.678554	−	0.734550i	$-0.737393\pi$
$739$	−36.8924	−1.35711	−0.678554	+	0.734550i	$0.737393\pi$
$740$	2.06252	0.0758198
$741$	0	0
$742$	−20.7592	−0.762095
$743$	−24.5709	−0.901420	−0.450710	−	0.892670i	$-0.648829\pi$
$743$	−24.5709	−0.901420	−0.450710	+	0.892670i	$0.648829\pi$
$744$	12.5626	0.460568
$745$	−6.97873	−0.255681
$746$	13.5574	0.496373
$747$	−3.12464	−0.114325
$748$	−6.23749	−0.228065
$749$	29.3423	1.07214
$750$	2.31980	0.0847071
$751$	−9.47401	−0.345712	−0.172856	−	0.984947i	$-0.555299\pi$
$751$	−9.47401	−0.345712	−0.172856	+	0.984947i	$0.555299\pi$
$752$	−3.00499	−0.109581
$753$	−64.4210	−2.34763
$754$	49.8813	1.81657
$755$	5.69362	0.207212
$756$	7.05488	0.256584
$757$	−7.07511	−0.257149	−0.128575	−	0.991700i	$-0.541040\pi$
$757$	−7.07511	−0.257149	−0.128575	+	0.991700i	$0.541040\pi$
$758$	−30.2899	−1.10018
$759$	−17.5490	−0.636990
$760$	0	0
$761$	−45.9880	−1.66706	−0.833531	−	0.552472i	$-0.813684\pi$
$761$	−45.9880	−1.66706	−0.833531	+	0.552472i	$0.813684\pi$
$762$	−17.7454	−0.642848
$763$	−77.8319	−2.81770
$764$	13.6338	0.493252
$765$	−5.21834	−0.188670
$766$	28.6630	1.03564
$767$	6.32945	0.228543
$768$	2.31980	0.0837085
$769$	−45.1430	−1.62790	−0.813948	−	0.580937i	$-0.802686\pi$
$769$	−45.1430	−1.62790	−0.813948	+	0.580937i	$0.802686\pi$
$770$	−13.9959	−0.504376
$771$	−30.3204	−1.09196
$772$	5.21947	0.187853
$773$	0.771491	0.0277486	0.0138743	−	0.999904i	$-0.495584\pi$
$773$	0.771491	0.0277486	0.0138743	+	0.999904i	$0.495584\pi$
$774$	4.12968	0.148438
$775$	5.41539	0.194526
$776$	−2.05429	−0.0737448
$777$	−23.5248	−0.843948
$778$	17.1263	0.614007
$779$	0	0
$780$	15.2220	0.545036
$781$	17.5501	0.627993
$782$	5.82329	0.208240
$783$	−10.9076	−0.389805
$784$	17.1744	0.613370
$785$	−5.31383	−0.189659
$786$	−30.8876	−1.10172
$787$	13.5272	0.482191	0.241095	−	0.970501i	$-0.422493\pi$
$787$	13.5272	0.482191	0.241095	+	0.970501i	$0.422493\pi$
$788$	2.85541	0.101720
$789$	34.9269	1.24343
$790$	−15.3229	−0.545165
$791$	89.5098	3.18260
$792$	6.77902	0.240882
$793$	−49.2105	−1.74751
$794$	26.1050	0.926430
$795$	9.79454	0.347377
$796$	−1.46463	−0.0519123
$797$	33.8026	1.19735	0.598674	−	0.800992i	$-0.295694\pi$
$797$	33.8026	1.19735	0.598674	+	0.800992i	$0.295694\pi$
$798$	0	0
$799$	6.58463	0.232947
$800$	1.00000	0.0353553
$801$	25.6634	0.906772
$802$	9.31093	0.328781
$803$	−11.3209	−0.399506
$804$	−4.45297	−0.157044
$805$	13.0665	0.460533
$806$	35.5346	1.25165
$807$	−56.7314	−1.99704
$808$	−5.00966	−0.176239
$809$	−12.9095	−0.453875	−0.226938	−	0.973909i	$-0.572871\pi$
$809$	−12.9095	−0.453875	−0.226938	+	0.973909i	$0.572871\pi$
$810$	−10.4730	−0.367984
$811$	−55.2362	−1.93961	−0.969803	−	0.243889i	$-0.921577\pi$
$811$	−55.2362	−1.93961	−0.969803	+	0.243889i	$0.921577\pi$
$812$	−37.3760	−1.31164
$813$	20.7639	0.728222
$814$	5.87111	0.205782
$815$	−4.47359	−0.156703
$816$	−5.08321	−0.177948
$817$	0	0
$818$	−14.5798	−0.509771
$819$	−76.8324	−2.68474
$820$	9.35729	0.326771
$821$	51.5462	1.79897	0.899487	−	0.436948i	$-0.143941\pi$
$821$	51.5462	1.79897	0.899487	+	0.436948i	$0.143941\pi$
$822$	−16.7635	−0.584694
$823$	−26.7834	−0.933609	−0.466805	−	0.884360i	$-0.654595\pi$
$823$	−26.7834	−0.933609	−0.466805	+	0.884360i	$0.654595\pi$
$824$	9.03489	0.314745
$825$	6.60347	0.229903
$826$	−4.74265	−0.165018
$827$	4.52302	0.157281	0.0786404	−	0.996903i	$-0.474942\pi$
$827$	4.52302	0.157281	0.0786404	+	0.996903i	$0.474942\pi$
$828$	−6.32886	−0.219943
$829$	13.1174	0.455584	0.227792	−	0.973710i	$-0.426849\pi$
$829$	13.1174	0.455584	0.227792	+	0.973710i	$0.426849\pi$
$830$	−1.31206	−0.0455424
$831$	−18.0977	−0.627802
$832$	6.56179	0.227489
$833$	−37.6329	−1.30390
$834$	−5.59483	−0.193733
$835$	−3.64877	−0.126271
$836$	0	0
$837$	−7.77037	−0.268583
$838$	14.5969	0.504240
$839$	25.1910	0.869688	0.434844	−	0.900506i	$-0.356803\pi$
$839$	25.1910	0.869688	0.434844	+	0.900506i	$0.356803\pi$
$840$	−11.4059	−0.393539
$841$	28.7871	0.992660
$842$	39.2412	1.35234
$843$	−42.4483	−1.46200
$844$	−1.31050	−0.0451094
$845$	30.0571	1.03399
$846$	−7.15630	−0.246039
$847$	14.2439	0.489428
$848$	4.22215	0.144989
$849$	16.7676	0.575462
$850$	−2.19123	−0.0751585
$851$	−5.48124	−0.187895
$852$	14.3024	0.489992
$853$	−34.0294	−1.16514	−0.582572	−	0.812779i	$-0.697953\pi$
$853$	−34.0294	−1.16514	−0.582572	+	0.812779i	$0.697953\pi$
$854$	36.8734	1.26178
$855$	0	0
$856$	−5.96783	−0.203976
$857$	1.08201	0.0369609	0.0184804	−	0.999829i	$-0.494117\pi$
$857$	1.08201	0.0369609	0.0184804	+	0.999829i	$0.494117\pi$
$858$	43.3306	1.47928
$859$	34.1318	1.16456	0.582280	−	0.812988i	$-0.302161\pi$
$859$	34.1318	1.16456	0.582280	+	0.812988i	$0.302161\pi$
$860$	1.73409	0.0591319
$861$	−106.728	−3.63728
$862$	−21.8767	−0.745122
$863$	34.3216	1.16832	0.584160	−	0.811639i	$-0.301424\pi$
$863$	34.3216	1.16832	0.584160	+	0.811639i	$0.301424\pi$
$864$	−1.43487	−0.0488152
$865$	1.17631	0.0399958
$866$	1.10168	0.0374368
$867$	−28.2981	−0.961054
$868$	−26.6261	−0.903747
$869$	−43.6178	−1.47963
$870$	17.6346	0.597870
$871$	−12.5957	−0.426789
$872$	15.8300	0.536070
$873$	−4.89223	−0.165577
$874$	0	0
$875$	−4.91674	−0.166216
$876$	−9.22592	−0.311715
$877$	−1.58533	−0.0535327	−0.0267664	−	0.999642i	$-0.508521\pi$
$877$	−1.58533	−0.0535327	−0.0267664	+	0.999642i	$0.508521\pi$
$878$	4.21717	0.142323
$879$	−26.4146	−0.890943
$880$	2.84657	0.0959579
$881$	−16.8300	−0.567018	−0.283509	−	0.958970i	$-0.591499\pi$
$881$	−16.8300	−0.567018	−0.283509	+	0.958970i	$0.591499\pi$
$882$	40.9002	1.37718
$883$	−47.8406	−1.60996	−0.804982	−	0.593300i	$-0.797825\pi$
$883$	−47.8406	−1.60996	−0.804982	+	0.593300i	$0.797825\pi$
$884$	−14.3784	−0.483597
$885$	2.23766	0.0752181
$886$	7.58310	0.254759
$887$	−30.8712	−1.03655	−0.518276	−	0.855213i	$-0.673426\pi$
$887$	−30.8712	−1.03655	−0.518276	+	0.855213i	$0.673426\pi$
$888$	4.78463	0.160562
$889$	37.6108	1.26143
$890$	10.7763	0.361222
$891$	−29.8122	−0.998746
$892$	−28.1303	−0.941874
$893$	0	0
$894$	−16.1893	−0.541450
$895$	−4.33057	−0.144755
$896$	−4.91674	−0.164257
$897$	−40.4533	−1.35069
$898$	−29.6975	−0.991018
$899$	41.1666	1.37298
$900$	2.38147	0.0793823
$901$	−9.25170	−0.308219
$902$	26.6362	0.886889
$903$	−19.7788	−0.658196
$904$	−18.2051	−0.605493
$905$	−1.36920	−0.0455136
$906$	13.2080	0.438808
$907$	22.7276	0.754656	0.377328	−	0.926080i	$-0.376843\pi$
$907$	22.7276	0.754656	0.377328	+	0.926080i	$0.376843\pi$
$908$	−12.6466	−0.419691
$909$	−11.9303	−0.395704
$910$	−32.2626	−1.06950
$911$	58.5516	1.93990	0.969950	−	0.243305i	$-0.0782316\pi$
$911$	58.5516	1.93990	0.969950	+	0.243305i	$0.0782316\pi$
$912$	0	0
$913$	−3.73489	−0.123607
$914$	9.12576	0.301853
$915$	−17.3974	−0.575142
$916$	13.7440	0.454113
$917$	65.4653	2.16186
$918$	3.14413	0.103772
$919$	9.12200	0.300907	0.150454	−	0.988617i	$-0.451927\pi$
$919$	9.12200	0.300907	0.150454	+	0.988617i	$0.451927\pi$
$920$	−2.65755	−0.0876167
$921$	−11.4666	−0.377836
$922$	−26.3855	−0.868962
$923$	40.4558	1.33162
$924$	−32.4676	−1.06811
$925$	2.06252	0.0678153
$926$	−15.7219	−0.516653
$927$	21.5163	0.706688
$928$	7.60179	0.249541
$929$	55.1704	1.81008	0.905041	−	0.425323i	$-0.139840\pi$
$929$	55.1704	1.81008	0.905041	+	0.425323i	$0.139840\pi$
$930$	12.5626	0.411944
$931$	0	0
$932$	24.6181	0.806394
$933$	55.9472	1.83163
$934$	−6.89932	−0.225753
$935$	−6.23749	−0.203988
$936$	15.6267	0.510774
$937$	46.3056	1.51274	0.756370	−	0.654144i	$-0.226971\pi$
$937$	46.3056	1.51274	0.756370	+	0.654144i	$0.226971\pi$
$938$	9.43794	0.308160
$939$	−71.8572	−2.34497
$940$	−3.00499	−0.0980121
$941$	21.9322	0.714969	0.357485	−	0.933919i	$-0.383634\pi$
$941$	21.9322	0.714969	0.357485	+	0.933919i	$0.383634\pi$
$942$	−12.3270	−0.401636
$943$	−24.8674	−0.809795
$944$	0.964592	0.0313948
$945$	7.05488	0.229495
$946$	4.93621	0.160490
$947$	14.6270	0.475315	0.237657	−	0.971349i	$-0.423620\pi$
$947$	14.6270	0.475315	0.237657	+	0.971349i	$0.423620\pi$
$948$	−35.5461	−1.15448
$949$	−26.0965	−0.847127
$950$	0	0
$951$	16.0310	0.519842
$952$	10.7737	0.349178
$953$	−7.15456	−0.231759	−0.115879	−	0.993263i	$-0.536969\pi$
$953$	−7.15456	−0.231759	−0.115879	+	0.993263i	$0.536969\pi$
$954$	10.0549	0.325540
$955$	13.6338	0.441178
$956$	−16.2940	−0.526984
$957$	50.1982	1.62268
$958$	−3.64861	−0.117881
$959$	35.5297	1.14731
$960$	2.31980	0.0748712
$961$	−1.67359	−0.0539869
$962$	13.5338	0.436348
$963$	−14.2122	−0.457981
$964$	19.2548	0.620155
$965$	5.21947	0.168021
$966$	30.3116	0.975259
$967$	−10.7856	−0.346841	−0.173420	−	0.984848i	$-0.555482\pi$
$967$	−10.7856	−0.346841	−0.173420	+	0.984848i	$0.555482\pi$
$968$	−2.89703	−0.0931141
$969$	0	0
$970$	−2.05429	−0.0659594
$971$	56.3934	1.80975	0.904874	−	0.425679i	$-0.139965\pi$
$971$	56.3934	1.80975	0.904874	+	0.425679i	$0.139965\pi$
$972$	−19.9907	−0.641201
$973$	11.8581	0.380152
$974$	22.5151	0.721430
$975$	15.2220	0.487495
$976$	−7.49955	−0.240055
$977$	−17.7247	−0.567063	−0.283532	−	0.958963i	$-0.591506\pi$
$977$	−17.7247	−0.567063	−0.283532	+	0.958963i	$0.591506\pi$
$978$	−10.3778	−0.331846
$979$	30.6755	0.980393
$980$	17.1744	0.548615
$981$	37.6986	1.20362
$982$	25.1612	0.802925
$983$	28.4112	0.906178	0.453089	−	0.891465i	$-0.350322\pi$
$983$	28.4112	0.906178	0.453089	+	0.891465i	$0.350322\pi$
$984$	21.7070	0.691995
$985$	2.85541	0.0909810
$986$	−16.6573	−0.530475
$987$	34.2745	1.09097
$988$	0	0
$989$	−4.60842	−0.146539
$990$	6.77902	0.215451
$991$	23.1887	0.736614	0.368307	−	0.929704i	$-0.379937\pi$
$991$	23.1887	0.736614	0.368307	+	0.929704i	$0.379937\pi$
$992$	5.41539	0.171939
$993$	−9.69411	−0.307633
$994$	−30.3135	−0.961485
$995$	−1.46463	−0.0464318
$996$	−3.04373	−0.0964442
$997$	30.4921	0.965694	0.482847	−	0.875705i	$-0.339603\pi$
$997$	30.4921	0.965694	0.482847	+	0.875705i	$0.339603\pi$
$998$	31.7722	1.00573
$999$	−2.95945	−0.0936328

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3610.2.a.bj.1.7		9
19.3	odd	18		190.2.k.d.161.1	yes	18
19.13	odd	18		190.2.k.d.131.1	✓	18
19.18	odd	2		3610.2.a.bi.1.3		9
95.3	even	36		950.2.u.g.199.1		36
95.13	even	36		950.2.u.g.549.6		36
95.22	even	36		950.2.u.g.199.6		36
95.32	even	36		950.2.u.g.549.1		36
95.79	odd	18		950.2.l.i.351.3		18
95.89	odd	18		950.2.l.i.701.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.d.131.1	✓	18	19.13	odd	18
190.2.k.d.161.1	yes	18	19.3	odd	18
950.2.l.i.351.3		18	95.79	odd	18
950.2.l.i.701.3		18	95.89	odd	18
950.2.u.g.199.1		36	95.3	even	36
950.2.u.g.199.6		36	95.22	even	36
950.2.u.g.549.1		36	95.32	even	36
950.2.u.g.549.6		36	95.13	even	36
3610.2.a.bi.1.3		9	19.18	odd	2
3610.2.a.bj.1.7		9	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:	\( N \)	\(=\)	\( 3610 = 2 \cdot 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3610.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.31980 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.31980 q^{6} -4.91674 q^{7} +1.00000 q^{8} +2.38147 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.31980 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.31980 q^{6} -4.91674 q^{7} +1.00000 q^{8} +2.38147 q^{9} +1.00000 q^{10} +2.84657 q^{11} +2.31980 q^{12} +6.56179 q^{13} -4.91674 q^{14} +2.31980 q^{15} +1.00000 q^{16} -2.19123 q^{17} +2.38147 q^{18} +1.00000 q^{20} -11.4059 q^{21} +2.84657 q^{22} -2.65755 q^{23} +2.31980 q^{24} +1.00000 q^{25} +6.56179 q^{26} -1.43487 q^{27} -4.91674 q^{28} +7.60179 q^{29} +2.31980 q^{30} +5.41539 q^{31} +1.00000 q^{32} +6.60347 q^{33} -2.19123 q^{34} -4.91674 q^{35} +2.38147 q^{36} +2.06252 q^{37} +15.2220 q^{39} +1.00000 q^{40} +9.35729 q^{41} -11.4059 q^{42} +1.73409 q^{43} +2.84657 q^{44} +2.38147 q^{45} -2.65755 q^{46} -3.00499 q^{47} +2.31980 q^{48} +17.1744 q^{49} +1.00000 q^{50} -5.08321 q^{51} +6.56179 q^{52} +4.22215 q^{53} -1.43487 q^{54} +2.84657 q^{55} -4.91674 q^{56} +7.60179 q^{58} +0.964592 q^{59} +2.31980 q^{60} -7.49955 q^{61} +5.41539 q^{62} -11.7091 q^{63} +1.00000 q^{64} +6.56179 q^{65} +6.60347 q^{66} -1.91955 q^{67} -2.19123 q^{68} -6.16497 q^{69} -4.91674 q^{70} +6.16536 q^{71} +2.38147 q^{72} -3.97703 q^{73} +2.06252 q^{74} +2.31980 q^{75} -13.9959 q^{77} +15.2220 q^{78} -15.3229 q^{79} +1.00000 q^{80} -10.4730 q^{81} +9.35729 q^{82} -1.31206 q^{83} -11.4059 q^{84} -2.19123 q^{85} +1.73409 q^{86} +17.6346 q^{87} +2.84657 q^{88} +10.7763 q^{89} +2.38147 q^{90} -32.2626 q^{91} -2.65755 q^{92} +12.5626 q^{93} -3.00499 q^{94} +2.31980 q^{96} -2.05429 q^{97} +17.1744 q^{98} +6.77902 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{8} + 21 q^{9}+O(q^{10}) \) 9 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^8 + 21 * q^9	\( 9 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{8} + 21 q^{9} + 9 q^{10} + 12 q^{11} + 9 q^{13} + 9 q^{16} + 6 q^{17} + 21 q^{18} + 9 q^{20} + 6 q^{21} + 12 q^{22} + 18 q^{23} + 9 q^{25} + 9 q^{26} - 18 q^{27} - 6 q^{31} + 9 q^{32} + 6 q^{33} + 6 q^{34} + 21 q^{36} + 6 q^{37} + 24 q^{39} + 9 q^{40} + 6 q^{42} + 18 q^{43} + 12 q^{44} + 21 q^{45} + 18 q^{46} - 3 q^{47} + 39 q^{49} + 9 q^{50} - 48 q^{51} + 9 q^{52} - 18 q^{54} + 12 q^{55} + 21 q^{59} + 18 q^{61} - 6 q^{62} - 12 q^{63} + 9 q^{64} + 9 q^{65} + 6 q^{66} + 6 q^{68} - 30 q^{69} + 18 q^{71} + 21 q^{72} - 36 q^{73} + 6 q^{74} + 15 q^{77} + 24 q^{78} - 6 q^{79} + 9 q^{80} + 69 q^{81} - 6 q^{83} + 6 q^{84} + 6 q^{85} + 18 q^{86} - 24 q^{87} + 12 q^{88} - 18 q^{89} + 21 q^{90} - 60 q^{91} + 18 q^{92} - 3 q^{94} + 18 q^{97} + 39 q^{98} + 54 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^8 + 21 * q^9 + 9 * q^10 + 12 * q^11 + 9 * q^13 + 9 * q^16 + 6 * q^17 + 21 * q^18 + 9 * q^20 + 6 * q^21 + 12 * q^22 + 18 * q^23 + 9 * q^25 + 9 * q^26 - 18 * q^27 - 6 * q^31 + 9 * q^32 + 6 * q^33 + 6 * q^34 + 21 * q^36 + 6 * q^37 + 24 * q^39 + 9 * q^40 + 6 * q^42 + 18 * q^43 + 12 * q^44 + 21 * q^45 + 18 * q^46 - 3 * q^47 + 39 * q^49 + 9 * q^50 - 48 * q^51 + 9 * q^52 - 18 * q^54 + 12 * q^55 + 21 * q^59 + 18 * q^61 - 6 * q^62 - 12 * q^63 + 9 * q^64 + 9 * q^65 + 6 * q^66 + 6 * q^68 - 30 * q^69 + 18 * q^71 + 21 * q^72 - 36 * q^73 + 6 * q^74 + 15 * q^77 + 24 * q^78 - 6 * q^79 + 9 * q^80 + 69 * q^81 - 6 * q^83 + 6 * q^84 + 6 * q^85 + 18 * q^86 - 24 * q^87 + 12 * q^88 - 18 * q^89 + 21 * q^90 - 60 * q^91 + 18 * q^92 - 3 * q^94 + 18 * q^97 + 39 * q^98 + 54 * q^99

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