LMFDB - Embedded newform 349.2.a.a.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [349,2,Mod(1,349)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(349, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("349.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	349.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:	$2.78677903054$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 5x^{10} - x^{9} + 35x^{8} - 24x^{7} - 80x^{6} + 66x^{5} + 77x^{4} - 56x^{3} - 31x^{2} + 15x + 4 $ x^11 - 5x^10 - x^9 + 35x^8 - 24x^7 - 80x^6 + 66x^5 + 77x^4 - 56x^3 - 31x^2 + 15*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-0.216390$ of defining polynomial
Character	$\chi$	$=$	349.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.216390 q^{2} +2.05625 q^{3} -1.95318 q^{4} -4.07164 q^{5} +0.444951 q^{6} -1.74178 q^{7} -0.855428 q^{8} +1.22815 q^{9} +O(q^{10})$	\(q+0.216390 q^{2} +2.05625 q^{3} -1.95318 q^{4} -4.07164 q^{5} +0.444951 q^{6} -1.74178 q^{7} -0.855428 q^{8} +1.22815 q^{9} -0.881063 q^{10} -4.97223 q^{11} -4.01621 q^{12} +4.99907 q^{13} -0.376903 q^{14} -8.37230 q^{15} +3.72124 q^{16} +1.60294 q^{17} +0.265759 q^{18} -8.02830 q^{19} +7.95263 q^{20} -3.58152 q^{21} -1.07594 q^{22} -5.45432 q^{23} -1.75897 q^{24} +11.5783 q^{25} +1.08175 q^{26} -3.64337 q^{27} +3.40200 q^{28} +0.688298 q^{29} -1.81168 q^{30} +9.28346 q^{31} +2.51610 q^{32} -10.2241 q^{33} +0.346860 q^{34} +7.09190 q^{35} -2.39879 q^{36} -2.03861 q^{37} -1.73724 q^{38} +10.2793 q^{39} +3.48300 q^{40} +4.03811 q^{41} -0.775006 q^{42} -1.12782 q^{43} +9.71164 q^{44} -5.00057 q^{45} -1.18026 q^{46} -6.84742 q^{47} +7.65179 q^{48} -3.96621 q^{49} +2.50542 q^{50} +3.29604 q^{51} -9.76406 q^{52} +5.31954 q^{53} -0.788388 q^{54} +20.2451 q^{55} +1.48997 q^{56} -16.5082 q^{57} +0.148941 q^{58} -12.9663 q^{59} +16.3526 q^{60} -6.24017 q^{61} +2.00885 q^{62} -2.13916 q^{63} -6.89803 q^{64} -20.3544 q^{65} -2.21240 q^{66} -3.62580 q^{67} -3.13082 q^{68} -11.2154 q^{69} +1.53462 q^{70} +10.7032 q^{71} -1.05059 q^{72} -1.62229 q^{73} -0.441135 q^{74} +23.8078 q^{75} +15.6807 q^{76} +8.66052 q^{77} +2.22434 q^{78} +1.73746 q^{79} -15.1516 q^{80} -11.1761 q^{81} +0.873807 q^{82} -12.6775 q^{83} +6.99534 q^{84} -6.52660 q^{85} -0.244050 q^{86} +1.41531 q^{87} +4.25338 q^{88} +3.93359 q^{89} -1.08207 q^{90} -8.70727 q^{91} +10.6532 q^{92} +19.0891 q^{93} -1.48171 q^{94} +32.6884 q^{95} +5.17371 q^{96} -8.97460 q^{97} -0.858248 q^{98} -6.10663 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 5 q^{2} - 6 q^{3} + 5 q^{4} - 9 q^{5} - 5 q^{6} - 3 q^{7} - 15 q^{8} + 3 q^{9}+O(q^{10}) $ 11 * q - 5 * q^2 - 6 * q^3 + 5 * q^4 - 9 * q^5 - 5 * q^6 - 3 * q^7 - 15 * q^8 + 3 * q^9	\( 11 q - 5 q^{2} - 6 q^{3} + 5 q^{4} - 9 q^{5} - 5 q^{6} - 3 q^{7} - 15 q^{8} + 3 q^{9} + 2 q^{10} - 31 q^{11} - 4 q^{13} - 7 q^{14} - 12 q^{15} + 5 q^{16} - q^{17} - 17 q^{19} - 10 q^{20} - 15 q^{21} + 17 q^{22} - 24 q^{23} - 3 q^{24} + 10 q^{25} - 11 q^{26} - 15 q^{27} + 3 q^{28} - 17 q^{29} + 9 q^{30} - 10 q^{31} - 5 q^{32} + 11 q^{33} + 2 q^{34} - 28 q^{35} - 4 q^{36} - q^{37} + 2 q^{38} + 8 q^{39} + 21 q^{40} - 15 q^{41} + 30 q^{42} - 5 q^{43} - 24 q^{44} - 3 q^{45} + 23 q^{46} + 4 q^{47} + 29 q^{48} + 14 q^{49} - 3 q^{50} - 19 q^{51} + 25 q^{52} - 3 q^{53} + 28 q^{54} + 24 q^{55} + 8 q^{56} + 11 q^{57} + 8 q^{58} - 52 q^{59} + 21 q^{60} + 42 q^{62} + 35 q^{63} + 5 q^{64} - 3 q^{65} + 30 q^{66} - 23 q^{67} + 15 q^{68} + 25 q^{69} + 27 q^{70} - 30 q^{71} + 23 q^{72} + 12 q^{73} + 30 q^{74} + 34 q^{75} + 2 q^{76} + 6 q^{77} + 41 q^{78} + 11 q^{79} + 18 q^{80} + 7 q^{81} + 46 q^{82} - 13 q^{83} + 23 q^{84} + 19 q^{85} - 21 q^{86} + 35 q^{87} + 80 q^{88} - 19 q^{89} + 38 q^{90} - 30 q^{91} + q^{92} + 13 q^{93} - 2 q^{94} - 7 q^{95} + 13 q^{96} + 26 q^{97} + 35 q^{98} - 41 q^{99}+O(q^{100}) \) 11 * q - 5 * q^2 - 6 * q^3 + 5 * q^4 - 9 * q^5 - 5 * q^6 - 3 * q^7 - 15 * q^8 + 3 * q^9 + 2 * q^10 - 31 * q^11 - 4 * q^13 - 7 * q^14 - 12 * q^15 + 5 * q^16 - q^17 - 17 * q^19 - 10 * q^20 - 15 * q^21 + 17 * q^22 - 24 * q^23 - 3 * q^24 + 10 * q^25 - 11 * q^26 - 15 * q^27 + 3 * q^28 - 17 * q^29 + 9 * q^30 - 10 * q^31 - 5 * q^32 + 11 * q^33 + 2 * q^34 - 28 * q^35 - 4 * q^36 - q^37 + 2 * q^38 + 8 * q^39 + 21 * q^40 - 15 * q^41 + 30 * q^42 - 5 * q^43 - 24 * q^44 - 3 * q^45 + 23 * q^46 + 4 * q^47 + 29 * q^48 + 14 * q^49 - 3 * q^50 - 19 * q^51 + 25 * q^52 - 3 * q^53 + 28 * q^54 + 24 * q^55 + 8 * q^56 + 11 * q^57 + 8 * q^58 - 52 * q^59 + 21 * q^60 + 42 * q^62 + 35 * q^63 + 5 * q^64 - 3 * q^65 + 30 * q^66 - 23 * q^67 + 15 * q^68 + 25 * q^69 + 27 * q^70 - 30 * q^71 + 23 * q^72 + 12 * q^73 + 30 * q^74 + 34 * q^75 + 2 * q^76 + 6 * q^77 + 41 * q^78 + 11 * q^79 + 18 * q^80 + 7 * q^81 + 46 * q^82 - 13 * q^83 + 23 * q^84 + 19 * q^85 - 21 * q^86 + 35 * q^87 + 80 * q^88 - 19 * q^89 + 38 * q^90 - 30 * q^91 + q^92 + 13 * q^93 - 2 * q^94 - 7 * q^95 + 13 * q^96 + 26 * q^97 + 35 * q^98 - 41 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.216390	0.153011	0.0765054	−	0.997069i	$-0.475624\pi$
$2$	0.216390	0.153011	0.0765054	+	0.997069i	$0.475624\pi$
$3$	2.05625	1.18717	0.593587	−	0.804770i	$-0.297711\pi$
$3$	2.05625	1.18717	0.593587	+	0.804770i	$0.297711\pi$
$4$	−1.95318	−0.976588
$5$	−4.07164	−1.82089	−0.910447	−	0.413626i	$-0.864262\pi$
$5$	−4.07164	−1.82089	−0.910447	+	0.413626i	$0.864262\pi$
$6$	0.444951	0.181651
$7$	−1.74178	−0.658330	−0.329165	−	0.944272i	$-0.606767\pi$
$7$	−1.74178	−0.658330	−0.329165	+	0.944272i	$0.606767\pi$
$8$	−0.855428	−0.302439
$9$	1.22815	0.409382
$10$	−0.881063	−0.278616
$11$	−4.97223	−1.49918	−0.749592	−	0.661900i	$-0.769750\pi$
$11$	−4.97223	−1.49918	−0.749592	+	0.661900i	$0.769750\pi$
$12$	−4.01621	−1.15938
$13$	4.99907	1.38649	0.693246	−	0.720701i	$-0.256180\pi$
$13$	4.99907	1.38649	0.693246	+	0.720701i	$0.256180\pi$
$14$	−0.376903	−0.100732
$15$	−8.37230	−2.16172
$16$	3.72124	0.930311
$17$	1.60294	0.388770	0.194385	−	0.980925i	$-0.437729\pi$
$17$	1.60294	0.388770	0.194385	+	0.980925i	$0.437729\pi$
$18$	0.265759	0.0626399
$19$	−8.02830	−1.84182	−0.920909	−	0.389777i	$-0.872552\pi$
$19$	−8.02830	−1.84182	−0.920909	+	0.389777i	$0.872552\pi$
$20$	7.95263	1.77826
$21$	−3.58152	−0.781553
$22$	−1.07594	−0.229391
$23$	−5.45432	−1.13730	−0.568652	−	0.822578i	$-0.692535\pi$
$23$	−5.45432	−1.13730	−0.568652	+	0.822578i	$0.692535\pi$
$24$	−1.75897	−0.359048
$25$	11.5783	2.31565
$26$	1.08175	0.212148
$27$	−3.64337	−0.701166
$28$	3.40200	0.642917
$29$	0.688298	0.127814	0.0639068	−	0.997956i	$-0.479644\pi$
$29$	0.688298	0.127814	0.0639068	+	0.997956i	$0.479644\pi$
$30$	−1.81168	−0.330766
$31$	9.28346	1.66736	0.833680	−	0.552249i	$-0.186230\pi$
$31$	9.28346	1.66736	0.833680	+	0.552249i	$0.186230\pi$
$32$	2.51610	0.444787
$33$	−10.2241	−1.77979
$34$	0.346860	0.0594860
$35$	7.09190	1.19875
$36$	−2.39879	−0.399798
$37$	−2.03861	−0.335146	−0.167573	−	0.985860i	$-0.553593\pi$
$37$	−2.03861	−0.335146	−0.167573	+	0.985860i	$0.553593\pi$
$38$	−1.73724	−0.281818
$39$	10.2793	1.64601
$40$	3.48300	0.550710
$41$	4.03811	0.630647	0.315323	−	0.948984i	$-0.397887\pi$
$41$	4.03811	0.630647	0.315323	+	0.948984i	$0.397887\pi$
$42$	−0.775006	−0.119586
$43$	−1.12782	−0.171991	−0.0859957	−	0.996296i	$-0.527407\pi$
$43$	−1.12782	−0.171991	−0.0859957	+	0.996296i	$0.527407\pi$
$44$	9.71164	1.46408
$45$	−5.00057	−0.745442
$46$	−1.18026	−0.174020
$47$	−6.84742	−0.998799	−0.499400	−	0.866372i	$-0.666446\pi$
$47$	−6.84742	−0.998799	−0.499400	+	0.866372i	$0.666446\pi$
$48$	7.65179	1.10444
$49$	−3.96621	−0.566601
$50$	2.50542	0.354320
$51$	3.29604	0.461538
$52$	−9.76406	−1.35403
$53$	5.31954	0.730695	0.365347	−	0.930871i	$-0.380950\pi$
$53$	5.31954	0.730695	0.365347	+	0.930871i	$0.380950\pi$
$54$	−0.788388	−0.107286
$55$	20.2451	2.72985
$56$	1.48997	0.199105
$57$	−16.5082	−2.18656
$58$	0.148941	0.0195569
$59$	−12.9663	−1.68807	−0.844035	−	0.536289i	$-0.819826\pi$
$59$	−12.9663	−1.68807	−0.844035	+	0.536289i	$0.819826\pi$
$60$	16.3526	2.11111
$61$	−6.24017	−0.798972	−0.399486	−	0.916739i	$-0.630811\pi$
$61$	−6.24017	−0.798972	−0.399486	+	0.916739i	$0.630811\pi$
$62$	2.00885	0.255124
$63$	−2.13916	−0.269509
$64$	−6.89803	−0.862254
$65$	−20.3544	−2.52465
$66$	−2.21240	−0.272327
$67$	−3.62580	−0.442962	−0.221481	−	0.975165i	$-0.571089\pi$
$67$	−3.62580	−0.442962	−0.221481	+	0.975165i	$0.571089\pi$
$68$	−3.13082	−0.379668
$69$	−11.2154	−1.35018
$70$	1.53462	0.183422
$71$	10.7032	1.27023	0.635115	−	0.772417i	$-0.280953\pi$
$71$	10.7032	1.27023	0.635115	+	0.772417i	$0.280953\pi$
$72$	−1.05059	−0.123813
$73$	−1.62229	−0.189874	−0.0949371	−	0.995483i	$-0.530265\pi$
$73$	−1.62229	−0.189874	−0.0949371	+	0.995483i	$0.530265\pi$
$74$	−0.441135	−0.0512809
$75$	23.8078	2.74908
$76$	15.6807	1.79870
$77$	8.66052	0.986958
$78$	2.22434	0.251857
$79$	1.73746	0.195480	0.0977398	−	0.995212i	$-0.468839\pi$
$79$	1.73746	0.195480	0.0977398	+	0.995212i	$0.468839\pi$
$80$	−15.1516	−1.69400
$81$	−11.1761	−1.24179
$82$	0.873807	0.0964958
$83$	−12.6775	−1.39154	−0.695768	−	0.718267i	$-0.744936\pi$
$83$	−12.6775	−1.39154	−0.695768	+	0.718267i	$0.744936\pi$
$84$	6.99534	0.763255
$85$	−6.52660	−0.707909
$86$	−0.244050	−0.0263165
$87$	1.41531	0.151737
$88$	4.25338	0.453412
$89$	3.93359	0.416960	0.208480	−	0.978027i	$-0.433148\pi$
$89$	3.93359	0.416960	0.208480	+	0.978027i	$0.433148\pi$
$90$	−1.08207	−0.114061
$91$	−8.70727	−0.912770
$92$	10.6532	1.11068
$93$	19.0891	1.97945
$94$	−1.48171	−0.152827
$95$	32.6884	3.35376
$96$	5.17371	0.528040
$97$	−8.97460	−0.911233	−0.455616	−	0.890176i	$-0.650581\pi$
$97$	−8.97460	−0.911233	−0.455616	+	0.890176i	$0.650581\pi$
$98$	−0.858248	−0.0866962
$99$	−6.10663	−0.613739
$100$	−22.6144	−2.26144
$101$	1.39380	0.138688	0.0693441	−	0.997593i	$-0.477909\pi$
$101$	1.39380	0.138688	0.0693441	+	0.997593i	$0.477909\pi$
$102$	0.713230	0.0706203
$103$	10.8253	1.06664	0.533322	−	0.845912i	$-0.320943\pi$
$103$	10.8253	1.06664	0.533322	+	0.845912i	$0.320943\pi$
$104$	−4.27634	−0.419330
$105$	14.5827	1.42312
$106$	1.15110	0.111804
$107$	−1.94319	−0.187856	−0.0939278	−	0.995579i	$-0.529942\pi$
$107$	−1.94319	−0.187856	−0.0939278	+	0.995579i	$0.529942\pi$
$108$	7.11613	0.684750
$109$	11.3937	1.09131	0.545657	−	0.838008i	$-0.316280\pi$
$109$	11.3937	1.09131	0.545657	+	0.838008i	$0.316280\pi$
$110$	4.38085	0.417697
$111$	−4.19189	−0.397876
$112$	−6.48158	−0.612452
$113$	−3.45965	−0.325456	−0.162728	−	0.986671i	$-0.552029\pi$
$113$	−3.45965	−0.325456	−0.162728	+	0.986671i	$0.552029\pi$
$114$	−3.57220	−0.334567
$115$	22.2080	2.07091
$116$	−1.34437	−0.124821
$117$	6.13959	0.567605
$118$	−2.80578	−0.258293
$119$	−2.79196	−0.255939
$120$	7.16189	0.653789
$121$	13.7231	1.24755
$122$	−1.35031	−0.122251
$123$	8.30335	0.748688
$124$	−18.1322	−1.62832
$125$	−26.7843	−2.39566
$126$	−0.462893	−0.0412378
$127$	−8.38764	−0.744282	−0.372141	−	0.928176i	$-0.621376\pi$
$127$	−8.38764	−0.744282	−0.372141	+	0.928176i	$0.621376\pi$
$128$	−6.52486	−0.576721
$129$	−2.31908	−0.204184
$130$	−4.40449	−0.386300
$131$	−8.44171	−0.737556	−0.368778	−	0.929518i	$-0.620224\pi$
$131$	−8.44171	−0.737556	−0.368778	+	0.929518i	$0.620224\pi$
$132$	19.9695	1.73812
$133$	13.9835	1.21252
$134$	−0.784588	−0.0677780
$135$	14.8345	1.27675
$136$	−1.37120	−0.117579
$137$	2.09566	0.179045	0.0895224	−	0.995985i	$-0.471466\pi$
$137$	2.09566	0.179045	0.0895224	+	0.995985i	$0.471466\pi$
$138$	−2.42691	−0.206592
$139$	12.7711	1.08323	0.541614	−	0.840627i	$-0.317813\pi$
$139$	12.7711	1.08323	0.541614	+	0.840627i	$0.317813\pi$
$140$	−13.8517	−1.17068
$141$	−14.0800	−1.18575
$142$	2.31606	0.194359
$143$	−24.8565	−2.07861
$144$	4.57023	0.380853
$145$	−2.80250	−0.232735
$146$	−0.351046	−0.0290528
$147$	−8.15550	−0.672654
$148$	3.98177	0.327299
$149$	13.4123	1.09878	0.549390	−	0.835566i	$-0.314860\pi$
$149$	13.4123	1.09878	0.549390	+	0.835566i	$0.314860\pi$
$150$	5.15176	0.420640
$151$	−21.9246	−1.78420	−0.892101	−	0.451836i	$-0.850769\pi$
$151$	−21.9246	−1.78420	−0.892101	+	0.451836i	$0.850769\pi$
$152$	6.86763	0.557038
$153$	1.96865	0.159156
$154$	1.87405	0.151015
$155$	−37.7989	−3.03608
$156$	−20.0773	−1.60747
$157$	0.720852	0.0575303	0.0287651	−	0.999586i	$-0.490843\pi$
$157$	0.720852	0.0575303	0.0287651	+	0.999586i	$0.490843\pi$
$158$	0.375969	0.0299105
$159$	10.9383	0.867462
$160$	−10.2446	−0.809910
$161$	9.50021	0.748722
$162$	−2.41840	−0.190007
$163$	10.8809	0.852254	0.426127	−	0.904663i	$-0.359878\pi$
$163$	10.8809	0.852254	0.426127	+	0.904663i	$0.359878\pi$
$164$	−7.88714	−0.615882
$165$	41.6290	3.24081
$166$	−2.74328	−0.212920
$167$	−13.7314	−1.06257	−0.531283	−	0.847195i	$-0.678290\pi$
$167$	−13.7314	−1.06257	−0.531283	+	0.847195i	$0.678290\pi$
$168$	3.06373	0.236372
$169$	11.9907	0.922360
$170$	−1.41229	−0.108318
$171$	−9.85993	−0.754008
$172$	2.20284	0.167965
$173$	−7.96153	−0.605304	−0.302652	−	0.953101i	$-0.597872\pi$
$173$	−7.96153	−0.605304	−0.302652	+	0.953101i	$0.597872\pi$
$174$	0.306259	0.0232174
$175$	−20.1668	−1.52446
$176$	−18.5029	−1.39471
$177$	−26.6619	−2.00403
$178$	0.851190	0.0637994
$179$	−11.9237	−0.891221	−0.445610	−	0.895227i	$-0.647013\pi$
$179$	−11.9237	−0.891221	−0.445610	+	0.895227i	$0.647013\pi$
$180$	9.76700	0.727989
$181$	−1.04046	−0.0773369	−0.0386685	−	0.999252i	$-0.512312\pi$
$181$	−1.04046	−0.0773369	−0.0386685	+	0.999252i	$0.512312\pi$
$182$	−1.88417	−0.139664
$183$	−12.8313	−0.948519
$184$	4.66578	0.343966
$185$	8.30050	0.610265
$186$	4.13069	0.302877
$187$	−7.97018	−0.582837
$188$	13.3742	0.975415
$189$	6.34593	0.461599
$190$	7.07344	0.513161
$191$	−15.7376	−1.13874	−0.569368	−	0.822083i	$-0.692812\pi$
$191$	−15.7376	−1.13874	−0.569368	+	0.822083i	$0.692812\pi$
$192$	−14.1840	−1.02365
$193$	−15.0000	−1.07972	−0.539862	−	0.841754i	$-0.681524\pi$
$193$	−15.0000	−1.07972	−0.539862	+	0.841754i	$0.681524\pi$
$194$	−1.94201	−0.139428
$195$	−41.8537	−2.99720
$196$	7.74670	0.553336
$197$	−10.7156	−0.763452	−0.381726	−	0.924276i	$-0.624670\pi$
$197$	−10.7156	−0.763452	−0.381726	+	0.924276i	$0.624670\pi$
$198$	−1.32141	−0.0939088
$199$	26.2413	1.86019	0.930097	−	0.367313i	$-0.119722\pi$
$199$	26.2413	1.86019	0.930097	+	0.367313i	$0.119722\pi$
$200$	−9.90437	−0.700345
$201$	−7.45554	−0.525873
$202$	0.301604	0.0212208
$203$	−1.19886	−0.0841436
$204$	−6.43774	−0.450732
$205$	−16.4417	−1.14834
$206$	2.34248	0.163208
$207$	−6.69870	−0.465592
$208$	18.6028	1.28987
$209$	39.9186	2.76122
$210$	3.15555	0.217753
$211$	7.47927	0.514894	0.257447	−	0.966292i	$-0.417119\pi$
$211$	7.47927	0.514894	0.257447	+	0.966292i	$0.417119\pi$
$212$	−10.3900	−0.713588
$213$	22.0083	1.50799
$214$	−0.420488	−0.0287439
$215$	4.59209	0.313178
$216$	3.11664	0.212060
$217$	−16.1697	−1.09767
$218$	2.46547	0.166983
$219$	−3.33582	−0.225414
$220$	−39.5423	−2.66594
$221$	8.01320	0.539026
$222$	−0.907082	−0.0608794
$223$	18.2796	1.22409	0.612047	−	0.790821i	$-0.290346\pi$
$223$	18.2796	1.22409	0.612047	+	0.790821i	$0.290346\pi$
$224$	−4.38248	−0.292817
$225$	14.2198	0.947987
$226$	−0.748633	−0.0497983
$227$	12.3973	0.822840	0.411420	−	0.911446i	$-0.365033\pi$
$227$	12.3973	0.822840	0.411420	+	0.911446i	$0.365033\pi$
$228$	32.2433	2.13537
$229$	−9.26813	−0.612456	−0.306228	−	0.951958i	$-0.599067\pi$
$229$	−9.26813	−0.612456	−0.306228	+	0.951958i	$0.599067\pi$
$230$	4.80560	0.316872
$231$	17.8082	1.17169
$232$	−0.588789	−0.0386559
$233$	21.8194	1.42943	0.714717	−	0.699414i	$-0.246556\pi$
$233$	21.8194	1.42943	0.714717	+	0.699414i	$0.246556\pi$
$234$	1.32855	0.0868498
$235$	27.8803	1.81871
$236$	25.3255	1.64855
$237$	3.57265	0.232068
$238$	−0.604153	−0.0391614
$239$	6.00738	0.388585	0.194293	−	0.980944i	$-0.437759\pi$
$239$	6.00738	0.388585	0.194293	+	0.980944i	$0.437759\pi$
$240$	−31.1554	−2.01107
$241$	−7.92112	−0.510244	−0.255122	−	0.966909i	$-0.582116\pi$
$241$	−7.92112	−0.510244	−0.255122	+	0.966909i	$0.582116\pi$
$242$	2.96953	0.190889
$243$	−12.0507	−0.773053
$244$	12.1881	0.780266
$245$	16.1490	1.03172
$246$	1.79676	0.114557
$247$	−40.1340	−2.55367
$248$	−7.94133	−0.504275
$249$	−26.0680	−1.65199
$250$	−5.79587	−0.366563
$251$	13.0158	0.821549	0.410775	−	0.911737i	$-0.365258\pi$
$251$	13.0158	0.821549	0.410775	+	0.911737i	$0.365258\pi$
$252$	4.17815	0.263199
$253$	27.1201	1.70503
$254$	−1.81500	−0.113883
$255$	−13.4203	−0.840411
$256$	12.3841	0.774009
$257$	10.7042	0.667711	0.333855	−	0.942624i	$-0.391650\pi$
$257$	10.7042	0.667711	0.333855	+	0.942624i	$0.391650\pi$
$258$	−0.501826	−0.0312423
$259$	3.55081	0.220636
$260$	39.7557	2.46555
$261$	0.845331	0.0523247
$262$	−1.82670	−0.112854
$263$	−19.0698	−1.17590	−0.587948	−	0.808899i	$-0.700064\pi$
$263$	−19.0698	−1.17590	−0.587948	+	0.808899i	$0.700064\pi$
$264$	8.74600	0.538279
$265$	−21.6593	−1.33052
$266$	3.02589	0.185529
$267$	8.08843	0.495004
$268$	7.08183	0.432592
$269$	−3.25969	−0.198747	−0.0993735	−	0.995050i	$-0.531684\pi$
$269$	−3.25969	−0.198747	−0.0993735	+	0.995050i	$0.531684\pi$
$270$	3.21003	0.195356
$271$	14.8129	0.899822	0.449911	−	0.893073i	$-0.351456\pi$
$271$	14.8129	0.899822	0.449911	+	0.893073i	$0.351456\pi$
$272$	5.96493	0.361677
$273$	−17.9043	−1.08362
$274$	0.453481	0.0273958
$275$	−57.5698	−3.47159
$276$	21.9057	1.31857
$277$	−10.7684	−0.647013	−0.323507	−	0.946226i	$-0.604862\pi$
$277$	−10.7684	−0.647013	−0.323507	+	0.946226i	$0.604862\pi$
$278$	2.76353	0.165746
$279$	11.4015	0.682587
$280$	−6.06660	−0.362549
$281$	−14.1629	−0.844887	−0.422444	−	0.906389i	$-0.638828\pi$
$281$	−14.1629	−0.844887	−0.422444	+	0.906389i	$0.638828\pi$
$282$	−3.04677	−0.181432
$283$	−29.3632	−1.74546	−0.872730	−	0.488203i	$-0.837653\pi$
$283$	−29.3632	−1.74546	−0.872730	+	0.488203i	$0.837653\pi$
$284$	−20.9051	−1.24049
$285$	67.2153	3.98149
$286$	−5.37870	−0.318049
$287$	−7.03349	−0.415174
$288$	3.09014	0.182088
$289$	−14.4306	−0.848858
$290$	−0.606434	−0.0356110
$291$	−18.4540	−1.08179
$292$	3.16861	0.185429
$293$	−21.3597	−1.24785	−0.623923	−	0.781486i	$-0.714462\pi$
$293$	−21.3597	−1.24785	−0.623923	+	0.781486i	$0.714462\pi$
$294$	−1.76477	−0.102923
$295$	52.7942	3.07379
$296$	1.74388	0.101361
$297$	18.1156	1.05118
$298$	2.90229	0.168125
$299$	−27.2665	−1.57686
$300$	−46.5007	−2.68472
$301$	1.96442	0.113227
$302$	−4.74428	−0.273002
$303$	2.86599	0.164647
$304$	−29.8753	−1.71346
$305$	25.4077	1.45484
$306$	0.425995	0.0243525
$307$	9.24306	0.527530	0.263765	−	0.964587i	$-0.415036\pi$
$307$	9.24306	0.527530	0.263765	+	0.964587i	$0.415036\pi$
$308$	−16.9155	−0.963851
$309$	22.2594	1.26629
$310$	−8.17931	−0.464554
$311$	1.27569	0.0723375	0.0361688	−	0.999346i	$-0.488485\pi$
$311$	1.27569	0.0723375	0.0361688	+	0.999346i	$0.488485\pi$
$312$	−8.79321	−0.497817
$313$	16.7371	0.946037	0.473018	−	0.881053i	$-0.343164\pi$
$313$	16.7371	0.946037	0.473018	+	0.881053i	$0.343164\pi$
$314$	0.155985	0.00880275
$315$	8.70989	0.490747
$316$	−3.39357	−0.190903
$317$	−14.6883	−0.824980	−0.412490	−	0.910962i	$-0.635341\pi$
$317$	−14.6883	−0.824980	−0.412490	+	0.910962i	$0.635341\pi$
$318$	2.36693	0.132731
$319$	−3.42237	−0.191616
$320$	28.0863	1.57007
$321$	−3.99568	−0.223017
$322$	2.05575	0.114563
$323$	−12.8689	−0.716044
$324$	21.8289	1.21272
$325$	57.8805	3.21063
$326$	2.35451	0.130404
$327$	23.4282	1.29558
$328$	−3.45431	−0.190732
$329$	11.9267	0.657540
$330$	9.00810	0.495879
$331$	−23.7720	−1.30663	−0.653315	−	0.757086i	$-0.726622\pi$
$331$	−23.7720	−1.30663	−0.653315	+	0.757086i	$0.726622\pi$
$332$	24.7614	1.35896
$333$	−2.50371	−0.137203
$334$	−2.97133	−0.162584
$335$	14.7630	0.806587
$336$	−13.3277	−0.727087
$337$	32.7376	1.78333	0.891666	−	0.452694i	$-0.149537\pi$
$337$	32.7376	1.78333	0.891666	+	0.452694i	$0.149537\pi$
$338$	2.59466	0.141131
$339$	−7.11388	−0.386373
$340$	12.7476	0.691335
$341$	−46.1595	−2.49968
$342$	−2.13359	−0.115371
$343$	19.1007	1.03134
$344$	0.964771	0.0520169
$345$	45.6652	2.45853
$346$	−1.72279	−0.0926180
$347$	27.1235	1.45607	0.728034	−	0.685541i	$-0.240434\pi$
$347$	27.1235	1.45607	0.728034	+	0.685541i	$0.240434\pi$
$348$	−2.76435	−0.148185
$349$	−1.00000	−0.0535288
$349$	−1.00000	−0.0535288
$350$	−4.36389	−0.233260
$351$	−18.2134	−0.972161
$352$	−12.5106	−0.666817
$353$	2.47989	0.131991	0.0659956	−	0.997820i	$-0.478978\pi$
$353$	2.47989	0.131991	0.0659956	+	0.997820i	$0.478978\pi$
$354$	−5.76937	−0.306639
$355$	−43.5794	−2.31296
$356$	−7.68299	−0.407198
$357$	−5.74097	−0.303844
$358$	−2.58017	−0.136366
$359$	−3.23334	−0.170649	−0.0853246	−	0.996353i	$-0.527193\pi$
$359$	−3.23334	−0.170649	−0.0853246	+	0.996353i	$0.527193\pi$
$360$	4.27763	0.225451
$361$	45.4536	2.39230
$362$	−0.225146	−0.0118334
$363$	28.2180	1.48106
$364$	17.0068	0.891399
$365$	6.60537	0.345741
$366$	−2.77657	−0.145134
$367$	4.48356	0.234040	0.117020	−	0.993130i	$-0.462666\pi$
$367$	4.48356	0.234040	0.117020	+	0.993130i	$0.462666\pi$
$368$	−20.2969	−1.05805
$369$	4.95939	0.258176
$370$	1.79614	0.0933771
$371$	−9.26546	−0.481038
$372$	−37.2843	−1.93310
$373$	12.3772	0.640866	0.320433	−	0.947271i	$-0.396172\pi$
$373$	12.3772	0.640866	0.320433	+	0.947271i	$0.396172\pi$
$374$	−1.72467	−0.0891805
$375$	−55.0752	−2.84407
$376$	5.85748	0.302076
$377$	3.44085	0.177213
$378$	1.37320	0.0706296
$379$	−9.88327	−0.507669	−0.253835	−	0.967248i	$-0.581692\pi$
$379$	−9.88327	−0.507669	−0.253835	+	0.967248i	$0.581692\pi$
$380$	−63.8461	−3.27524
$381$	−17.2470	−0.883593
$382$	−3.40547	−0.174239
$383$	−10.6917	−0.546321	−0.273160	−	0.961968i	$-0.588069\pi$
$383$	−10.6917	−0.546321	−0.273160	+	0.961968i	$0.588069\pi$
$384$	−13.4167	−0.684669
$385$	−35.2625	−1.79715
$386$	−3.24585	−0.165209
$387$	−1.38513	−0.0704102
$388$	17.5290	0.889899
$389$	−1.09907	−0.0557251	−0.0278626	−	0.999612i	$-0.508870\pi$
$389$	−1.09907	−0.0557251	−0.0278626	+	0.999612i	$0.508870\pi$
$390$	−9.05672	−0.458605
$391$	−8.74294	−0.442150
$392$	3.39281	0.171363
$393$	−17.3582	−0.875607
$394$	−2.31874	−0.116816
$395$	−7.07432	−0.355948
$396$	11.9273	0.599370
$397$	4.68092	0.234929	0.117464	−	0.993077i	$-0.462523\pi$
$397$	4.68092	0.234929	0.117464	+	0.993077i	$0.462523\pi$
$398$	5.67835	0.284630
$399$	28.7536	1.43948
$400$	43.0856	2.15428
$401$	4.76420	0.237913	0.118956	−	0.992899i	$-0.462045\pi$
$401$	4.76420	0.237913	0.118956	+	0.992899i	$0.462045\pi$
$402$	−1.61330	−0.0804643
$403$	46.4087	2.31178
$404$	−2.72233	−0.135441
$405$	45.5051	2.26116
$406$	−0.259422	−0.0128749
$407$	10.1364	0.502445
$408$	−2.81952	−0.139587
$409$	−8.93747	−0.441929	−0.220965	−	0.975282i	$-0.570921\pi$
$409$	−8.93747	−0.441929	−0.220965	+	0.975282i	$0.570921\pi$
$410$	−3.55783	−0.175709
$411$	4.30920	0.212557
$412$	−21.1436	−1.04167
$413$	22.5844	1.11131
$414$	−1.44953	−0.0712407
$415$	51.6182	2.53384
$416$	12.5781	0.616694
$417$	26.2605	1.28598
$418$	8.63798	0.422497
$419$	5.24648	0.256308	0.128154	−	0.991754i	$-0.459095\pi$
$419$	5.24648	0.256308	0.128154	+	0.991754i	$0.459095\pi$
$420$	−28.4825	−1.38981
$421$	30.2690	1.47522	0.737609	−	0.675228i	$-0.235955\pi$
$421$	30.2690	1.47522	0.737609	+	0.675228i	$0.235955\pi$
$422$	1.61844	0.0787844
$423$	−8.40964	−0.408891
$424$	−4.55048	−0.220991
$425$	18.5593	0.900256
$426$	4.76238	0.230738
$427$	10.8690	0.525987
$428$	3.79540	0.183457
$429$	−51.1111	−2.46767
$430$	0.993682	0.0479196
$431$	−9.93840	−0.478716	−0.239358	−	0.970931i	$-0.576937\pi$
$431$	−9.93840	−0.478716	−0.239358	+	0.970931i	$0.576937\pi$
$432$	−13.5579	−0.652303
$433$	−41.2073	−1.98030	−0.990149	−	0.140015i	$-0.955285\pi$
$433$	−41.2073	−1.98030	−0.990149	+	0.140015i	$0.955285\pi$
$434$	−3.49897	−0.167956
$435$	−5.76263	−0.276297
$436$	−22.2538	−1.06576
$437$	43.7889	2.09471
$438$	−0.721838	−0.0344907
$439$	−11.6583	−0.556422	−0.278211	−	0.960520i	$-0.589741\pi$
$439$	−11.6583	−0.556422	−0.278211	+	0.960520i	$0.589741\pi$
$440$	−17.3183	−0.825615
$441$	−4.87109	−0.231957
$442$	1.73398	0.0824769
$443$	35.0836	1.66687	0.833437	−	0.552615i	$-0.186370\pi$
$443$	35.0836	1.66687	0.833437	+	0.552615i	$0.186370\pi$
$444$	8.18749	0.388561
$445$	−16.0162	−0.759239
$446$	3.95553	0.187300
$447$	27.5790	1.30444
$448$	12.0148	0.567648
$449$	3.94521	0.186186	0.0930931	−	0.995657i	$-0.470325\pi$
$449$	3.94521	0.186186	0.0930931	+	0.995657i	$0.470325\pi$
$450$	3.07703	0.145052
$451$	−20.0784	−0.945455
$452$	6.75729	0.317836
$453$	−45.0825	−2.11816
$454$	2.68266	0.125903
$455$	35.4529	1.66206
$456$	14.1215	0.661302
$457$	−34.6412	−1.62045	−0.810224	−	0.586121i	$-0.800654\pi$
$457$	−34.6412	−1.62045	−0.810224	+	0.586121i	$0.800654\pi$
$458$	−2.00553	−0.0937124
$459$	−5.84009	−0.272592
$460$	−43.3762	−2.02242
$461$	17.6181	0.820557	0.410279	−	0.911960i	$-0.365431\pi$
$461$	17.6181	0.820557	0.410279	+	0.911960i	$0.365431\pi$
$462$	3.85351	0.179281
$463$	−18.5662	−0.862843	−0.431422	−	0.902150i	$-0.641988\pi$
$463$	−18.5662	−0.862843	−0.431422	+	0.902150i	$0.641988\pi$
$464$	2.56132	0.118907
$465$	−77.7239	−3.60436
$466$	4.72149	0.218719
$467$	15.5760	0.720773	0.360386	−	0.932803i	$-0.382645\pi$
$467$	15.5760	0.720773	0.360386	+	0.932803i	$0.382645\pi$
$468$	−11.9917	−0.554316
$469$	6.31534	0.291615
$470$	6.03301	0.278282
$471$	1.48225	0.0682984
$472$	11.0917	0.510539
$473$	5.60779	0.257847
$474$	0.773085	0.0355090
$475$	−92.9538	−4.26501
$476$	5.45320	0.249947
$477$	6.53317	0.299134
$478$	1.29994	0.0594577
$479$	11.8237	0.540238	0.270119	−	0.962827i	$-0.412937\pi$
$479$	11.8237	0.540238	0.270119	+	0.962827i	$0.412937\pi$
$480$	−21.0655	−0.961504
$481$	−10.1912	−0.464677
$482$	−1.71405	−0.0780729
$483$	19.5348	0.888863
$484$	−26.8035	−1.21834
$485$	36.5414	1.65926
$486$	−2.60765	−0.118286
$487$	12.4027	0.562018	0.281009	−	0.959705i	$-0.409331\pi$
$487$	12.4027	0.562018	0.281009	+	0.959705i	$0.409331\pi$
$488$	5.33801	0.241641
$489$	22.3737	1.01177
$490$	3.49448	0.157864
$491$	−25.4932	−1.15049	−0.575247	−	0.817980i	$-0.695094\pi$
$491$	−25.4932	−1.15049	−0.575247	+	0.817980i	$0.695094\pi$
$492$	−16.2179	−0.731159
$493$	1.10330	0.0496901
$494$	−8.68460	−0.390739
$495$	24.8640	1.11755
$496$	34.5460	1.55116
$497$	−18.6425	−0.836231
$498$	−5.64086	−0.252773
$499$	−8.35177	−0.373877	−0.186938	−	0.982372i	$-0.559856\pi$
$499$	−8.35177	−0.373877	−0.186938	+	0.982372i	$0.559856\pi$
$500$	52.3145	2.33958
$501$	−28.2351	−1.26145
$502$	2.81649	0.125706
$503$	41.7850	1.86310	0.931550	−	0.363613i	$-0.118457\pi$
$503$	41.7850	1.86310	0.931550	+	0.363613i	$0.118457\pi$
$504$	1.82990	0.0815100
$505$	−5.67505	−0.252536
$506$	5.86852	0.260888
$507$	24.6558	1.09500
$508$	16.3825	0.726857
$509$	−38.2004	−1.69321	−0.846603	−	0.532226i	$-0.821356\pi$
$509$	−38.2004	−1.69321	−0.846603	+	0.532226i	$0.821356\pi$
$510$	−2.90402	−0.128592
$511$	2.82566	0.125000
$512$	15.7295	0.695153
$513$	29.2500	1.29142
$514$	2.31629	0.102167
$515$	−44.0766	−1.94225
$516$	4.52957	0.199403
$517$	34.0470	1.49738
$518$	0.768360	0.0337598
$519$	−16.3709	−0.718601
$520$	17.4117	0.763555
$521$	23.8013	1.04275	0.521376	−	0.853327i	$-0.325419\pi$
$521$	23.8013	1.04275	0.521376	+	0.853327i	$0.325419\pi$
$522$	0.182921	0.00800624
$523$	−0.327524	−0.0143216	−0.00716082	−	0.999974i	$-0.502279\pi$
$523$	−0.327524	−0.0143216	−0.00716082	+	0.999974i	$0.502279\pi$
$524$	16.4881	0.720288
$525$	−41.4678	−1.80980
$526$	−4.12652	−0.179925
$527$	14.8808	0.648219
$528$	−38.0465	−1.65576
$529$	6.74959	0.293460
$530$	−4.68685	−0.203584
$531$	−15.9245	−0.691066
$532$	−27.3123	−1.18414
$533$	20.1868	0.874387
$534$	1.75026	0.0757409
$535$	7.91199	0.342065
$536$	3.10161	0.133969
$537$	−24.5181	−1.05803
$538$	−0.705365	−0.0304104
$539$	19.7209	0.849439
$540$	−28.9743	−1.24686
$541$	−13.3535	−0.574113	−0.287057	−	0.957914i	$-0.592677\pi$
$541$	−13.3535	−0.574113	−0.287057	+	0.957914i	$0.592677\pi$
$542$	3.20537	0.137682
$543$	−2.13945	−0.0918124
$544$	4.03315	0.172920
$545$	−46.3909	−1.98717
$546$	−3.87431	−0.165805
$547$	−13.0057	−0.556082	−0.278041	−	0.960569i	$-0.589685\pi$
$547$	−13.0057	−0.556082	−0.278041	+	0.960569i	$0.589685\pi$
$548$	−4.09320	−0.174853
$549$	−7.66384	−0.327085
$550$	−12.4575	−0.531191
$551$	−5.52586	−0.235410
$552$	9.59398	0.408347
$553$	−3.02627	−0.128690
$554$	−2.33018	−0.0990000
$555$	17.0679	0.724490
$556$	−24.9442	−1.05787
$557$	−18.4038	−0.779793	−0.389896	−	0.920859i	$-0.627489\pi$
$557$	−18.4038	−0.779793	−0.389896	+	0.920859i	$0.627489\pi$
$558$	2.46716	0.104443
$559$	−5.63806	−0.238465
$560$	26.3907	1.11521
$561$	−16.3887	−0.691930
$562$	−3.06471	−0.129277
$563$	21.9346	0.924433	0.462217	−	0.886767i	$-0.347054\pi$
$563$	21.9346	0.924433	0.462217	+	0.886767i	$0.347054\pi$
$564$	27.5007	1.15799
$565$	14.0864	0.592621
$566$	−6.35390	−0.267074
$567$	19.4663	0.817507
$568$	−9.15578	−0.384168
$569$	−8.39151	−0.351791	−0.175895	−	0.984409i	$-0.556282\pi$
$569$	−8.39151	−0.351791	−0.175895	+	0.984409i	$0.556282\pi$
$570$	14.5447	0.609211
$571$	−20.5051	−0.858112	−0.429056	−	0.903278i	$-0.641154\pi$
$571$	−20.5051	−0.858112	−0.429056	+	0.903278i	$0.641154\pi$
$572$	48.5491	2.02994
$573$	−32.3604	−1.35188
$574$	−1.52198	−0.0635261
$575$	−63.1516	−2.63360
$576$	−8.47180	−0.352991
$577$	−9.71153	−0.404296	−0.202148	−	0.979355i	$-0.564792\pi$
$577$	−9.71153	−0.404296	−0.202148	+	0.979355i	$0.564792\pi$
$578$	−3.12263	−0.129884
$579$	−30.8437	−1.28182
$580$	5.47378	0.227286
$581$	22.0814	0.916090
$582$	−3.99326	−0.165526
$583$	−26.4500	−1.09545
$584$	1.38775	0.0574254
$585$	−24.9982	−1.03355
$586$	−4.62202	−0.190934
$587$	−18.9815	−0.783449	−0.391724	−	0.920083i	$-0.628121\pi$
$587$	−18.9815	−0.783449	−0.391724	+	0.920083i	$0.628121\pi$
$588$	15.9291	0.656906
$589$	−74.5304	−3.07097
$590$	11.4241	0.470324
$591$	−22.0338	−0.906351
$592$	−7.58617	−0.311790
$593$	9.25164	0.379919	0.189960	−	0.981792i	$-0.439164\pi$
$593$	9.25164	0.379919	0.189960	+	0.981792i	$0.439164\pi$
$594$	3.92005	0.160841
$595$	11.3679	0.466038
$596$	−26.1966	−1.07305
$597$	53.9585	2.20838
$598$	−5.90020	−0.241277
$599$	−12.9629	−0.529649	−0.264825	−	0.964297i	$-0.585314\pi$
$599$	−12.9629	−0.529649	−0.264825	+	0.964297i	$0.585314\pi$
$600$	−20.3658	−0.831431
$601$	−14.2827	−0.582603	−0.291302	−	0.956631i	$-0.594088\pi$
$601$	−14.2827	−0.582603	−0.291302	+	0.956631i	$0.594088\pi$
$602$	0.425080	0.0173250
$603$	−4.45302	−0.181341
$604$	42.8227	1.74243
$605$	−55.8754	−2.27166
$606$	0.620172	0.0251928
$607$	3.64589	0.147982	0.0739910	−	0.997259i	$-0.476426\pi$
$607$	3.64589	0.147982	0.0739910	+	0.997259i	$0.476426\pi$
$608$	−20.2000	−0.819217
$609$	−2.46515	−0.0998931
$610$	5.49798	0.222607
$611$	−34.2307	−1.38483
$612$	−3.84511	−0.155429
$613$	−3.02050	−0.121997	−0.0609985	−	0.998138i	$-0.519428\pi$
$613$	−3.02050	−0.121997	−0.0609985	+	0.998138i	$0.519428\pi$
$614$	2.00011	0.0807178
$615$	−33.8083	−1.36328
$616$	−7.40845	−0.298495
$617$	20.3614	0.819718	0.409859	−	0.912149i	$-0.365578\pi$
$617$	20.3614	0.819718	0.409859	+	0.912149i	$0.365578\pi$
$618$	4.81671	0.193757
$619$	−35.9504	−1.44497	−0.722483	−	0.691388i	$-0.756999\pi$
$619$	−35.9504	−1.44497	−0.722483	+	0.691388i	$0.756999\pi$
$620$	73.8279	2.96500
$621$	19.8721	0.797439
$622$	0.276046	0.0110684
$623$	−6.85144	−0.274497
$624$	38.2518	1.53130
$625$	51.1649	2.04660
$626$	3.62174	0.144754
$627$	82.0824	3.27805
$628$	−1.40795	−0.0561833
$629$	−3.26777	−0.130295
$630$	1.88473	0.0750896
$631$	−16.1235	−0.641865	−0.320933	−	0.947102i	$-0.603996\pi$
$631$	−16.1235	−0.641865	−0.320933	+	0.947102i	$0.603996\pi$
$632$	−1.48627	−0.0591207
$633$	15.3792	0.611269
$634$	−3.17841	−0.126231
$635$	34.1514	1.35526
$636$	−21.3644	−0.847153
$637$	−19.8274	−0.785588
$638$	−0.740568	−0.0293194
$639$	13.1450	0.520010
$640$	26.5669	1.05015
$641$	−29.9474	−1.18285	−0.591425	−	0.806360i	$-0.701434\pi$
$641$	−29.9474	−1.18285	−0.591425	+	0.806360i	$0.701434\pi$
$642$	−0.864626	−0.0341241
$643$	−4.71956	−0.186121	−0.0930606	−	0.995660i	$-0.529665\pi$
$643$	−4.71956	−0.186121	−0.0930606	+	0.995660i	$0.529665\pi$
$644$	−18.5556	−0.731192
$645$	9.44246	0.371797
$646$	−2.78470	−0.109562
$647$	−12.4813	−0.490690	−0.245345	−	0.969436i	$-0.578901\pi$
$647$	−12.4813	−0.490690	−0.245345	+	0.969436i	$0.578901\pi$
$648$	9.56034	0.375566
$649$	64.4714	2.53073
$650$	12.5248	0.491262
$651$	−33.2489	−1.30313
$652$	−21.2522	−0.832301
$653$	42.5932	1.66680	0.833400	−	0.552670i	$-0.186391\pi$
$653$	42.5932	1.66680	0.833400	+	0.552670i	$0.186391\pi$
$654$	5.06962	0.198238
$655$	34.3716	1.34301
$656$	15.0268	0.586698
$657$	−1.99241	−0.0777311
$658$	2.58082	0.100611
$659$	0.102737	0.00400208	0.00200104	−	0.999998i	$-0.499363\pi$
$659$	0.102737	0.00400208	0.00200104	+	0.999998i	$0.499363\pi$
$660$	−81.3087	−3.16494
$661$	13.3343	0.518644	0.259322	−	0.965791i	$-0.416501\pi$
$661$	13.3343	0.518644	0.259322	+	0.965791i	$0.416501\pi$
$662$	−5.14403	−0.199928
$663$	16.4771	0.639918
$664$	10.8447	0.420855
$665$	−56.9359	−2.20788
$666$	−0.541779	−0.0209935
$667$	−3.75420	−0.145363
$668$	26.8198	1.03769
$669$	37.5874	1.45321
$670$	3.19456	0.123417
$671$	31.0275	1.19781
$672$	−9.01146	−0.347624
$673$	−31.0371	−1.19639	−0.598196	−	0.801350i	$-0.704116\pi$
$673$	−31.0371	−1.19639	−0.598196	+	0.801350i	$0.704116\pi$
$674$	7.08410	0.272869
$675$	−42.1839	−1.62366
$676$	−23.4199	−0.900765
$677$	21.3068	0.818886	0.409443	−	0.912336i	$-0.365723\pi$
$677$	21.3068	0.818886	0.409443	+	0.912336i	$0.365723\pi$
$678$	−1.53937	−0.0591193
$679$	15.6318	0.599892
$680$	5.58303	0.214099
$681$	25.4920	0.976854
$682$	−9.98846	−0.382478
$683$	16.5574	0.633553	0.316776	−	0.948500i	$-0.397399\pi$
$683$	16.5574	0.633553	0.316776	+	0.948500i	$0.397399\pi$
$684$	19.2582	0.736355
$685$	−8.53280	−0.326021
$686$	4.13320	0.157806
$687$	−19.0576	−0.727091
$688$	−4.19690	−0.160005
$689$	26.5927	1.01310
$690$	9.88149	0.376182
$691$	0.465454	0.0177067	0.00885334	−	0.999961i	$-0.497182\pi$
$691$	0.465454	0.0177067	0.00885334	+	0.999961i	$0.497182\pi$
$692$	15.5503	0.591132
$693$	10.6364	0.404043
$694$	5.86926	0.222794
$695$	−51.9993	−1.97244
$696$	−1.21070	−0.0458913
$697$	6.47285	0.245177
$698$	−0.216390	−0.00819048
$699$	44.8660	1.69699
$700$	39.3892	1.48877
$701$	26.6015	1.00473	0.502363	−	0.864657i	$-0.332464\pi$
$701$	26.6015	1.00473	0.502363	+	0.864657i	$0.332464\pi$
$702$	−3.94121	−0.148751
$703$	16.3666	0.617277
$704$	34.2986	1.29268
$705$	57.3287	2.15912
$706$	0.536624	0.0201961
$707$	−2.42769	−0.0913026
$708$	52.0754	1.95711
$709$	−16.1397	−0.606141	−0.303071	−	0.952968i	$-0.598012\pi$
$709$	−16.1397	−0.606141	−0.303071	+	0.952968i	$0.598012\pi$
$710$	−9.43015	−0.353907
$711$	2.13386	0.0800259
$712$	−3.36490	−0.126105
$713$	−50.6350	−1.89629
$714$	−1.24229	−0.0464915
$715$	101.207	3.78492
$716$	23.2891	0.870355
$717$	12.3526	0.461318
$718$	−0.699663	−0.0261112
$719$	−35.2946	−1.31627	−0.658133	−	0.752902i	$-0.728654\pi$
$719$	−35.2946	−1.31627	−0.658133	+	0.752902i	$0.728654\pi$
$720$	−18.6084	−0.693493
$721$	−18.8552	−0.702204
$722$	9.83571	0.366047
$723$	−16.2878	−0.605749
$724$	2.03220	0.0755263
$725$	7.96930	0.295972
$726$	6.10609	0.226618
$727$	11.6704	0.432833	0.216416	−	0.976301i	$-0.430563\pi$
$727$	11.6704	0.432833	0.216416	+	0.976301i	$0.430563\pi$
$728$	7.44844	0.276057
$729$	8.74908	0.324040
$730$	1.42934	0.0529021
$731$	−1.80783	−0.0668651
$732$	25.0618	0.926312
$733$	−13.5048	−0.498811	−0.249405	−	0.968399i	$-0.580235\pi$
$733$	−13.5048	−0.498811	−0.249405	+	0.968399i	$0.580235\pi$
$734$	0.970198	0.0358107
$735$	33.2063	1.22483
$736$	−13.7236	−0.505858
$737$	18.0283	0.664082
$738$	1.07316	0.0395037
$739$	−32.8192	−1.20727	−0.603636	−	0.797260i	$-0.706282\pi$
$739$	−32.8192	−1.20727	−0.603636	+	0.797260i	$0.706282\pi$
$740$	−16.2123	−0.595977
$741$	−82.5254	−3.03165
$742$	−2.00495	−0.0736041
$743$	24.9593	0.915667	0.457833	−	0.889038i	$-0.348626\pi$
$743$	24.9593	0.915667	0.457833	+	0.889038i	$0.348626\pi$
$744$	−16.3293	−0.598662
$745$	−54.6101	−2.00076
$746$	2.67830	0.0980594
$747$	−15.5698	−0.569670
$748$	15.5672	0.569192
$749$	3.38461	0.123671
$750$	−11.9177	−0.435174
$751$	−18.7361	−0.683692	−0.341846	−	0.939756i	$-0.611052\pi$
$751$	−18.7361	−0.683692	−0.341846	+	0.939756i	$0.611052\pi$
$752$	−25.4809	−0.929194
$753$	26.7637	0.975322
$754$	0.744565	0.0271155
$755$	89.2693	3.24884
$756$	−12.3947	−0.450792
$757$	−4.45708	−0.161995	−0.0809977	−	0.996714i	$-0.525811\pi$
$757$	−4.45708	−0.161995	−0.0809977	+	0.996714i	$0.525811\pi$
$758$	−2.13864	−0.0776789
$759$	55.7656	2.02416
$760$	−27.9625	−1.01431
$761$	20.9665	0.760034	0.380017	−	0.924979i	$-0.375918\pi$
$761$	20.9665	0.760034	0.380017	+	0.924979i	$0.375918\pi$
$762$	−3.73209	−0.135199
$763$	−19.8452	−0.718445
$764$	30.7384	1.11207
$765$	−8.01562	−0.289805
$766$	−2.31358	−0.0835930
$767$	−64.8194	−2.34049
$768$	25.4649	0.918884
$769$	2.61038	0.0941327	0.0470663	−	0.998892i	$-0.485013\pi$
$769$	2.61038	0.0941327	0.0470663	+	0.998892i	$0.485013\pi$
$770$	−7.63046	−0.274983
$771$	22.0105	0.792689
$772$	29.2976	1.05444
$773$	15.9577	0.573957	0.286979	−	0.957937i	$-0.407349\pi$
$773$	15.9577	0.573957	0.286979	+	0.957937i	$0.407349\pi$
$774$	−0.299729	−0.0107735
$775$	107.486	3.86103
$776$	7.67712	0.275593
$777$	7.30133	0.261934
$778$	−0.237828	−0.00852655
$779$	−32.4192	−1.16154
$780$	81.7476	2.92703
$781$	−53.2185	−1.90431
$782$	−1.89189	−0.0676537
$783$	−2.50772	−0.0896186
$784$	−14.7592	−0.527116
$785$	−2.93505	−0.104756
$786$	−3.75615	−0.133977
$787$	23.1778	0.826200	0.413100	−	0.910686i	$-0.364446\pi$
$787$	23.1778	0.826200	0.413100	+	0.910686i	$0.364446\pi$
$788$	20.9294	0.745578
$789$	−39.2123	−1.39599
$790$	−1.53081	−0.0544639
$791$	6.02593	0.214258
$792$	5.22378	0.185619
$793$	−31.1950	−1.10777
$794$	1.01290	0.0359466
$795$	−44.5368	−1.57956
$796$	−51.2538	−1.81664
$797$	−39.8330	−1.41096	−0.705479	−	0.708731i	$-0.749268\pi$
$797$	−39.8330	−1.41096	−0.705479	+	0.708731i	$0.749268\pi$
$798$	6.22198	0.220256
$799$	−10.9760	−0.388303
$800$	29.1320	1.02997
$801$	4.83103	0.170696
$802$	1.03093	0.0364032
$803$	8.06638	0.284656
$804$	14.5620	0.513561
$805$	−38.6815	−1.36334
$806$	10.0424	0.353727
$807$	−6.70273	−0.235947
$808$	−1.19229	−0.0419448
$809$	−13.9008	−0.488726	−0.244363	−	0.969684i	$-0.578579\pi$
$809$	−13.9008	−0.488726	−0.244363	+	0.969684i	$0.578579\pi$
$810$	9.84684	0.345983
$811$	29.5994	1.03937	0.519687	−	0.854357i	$-0.326048\pi$
$811$	29.5994	1.03937	0.519687	+	0.854357i	$0.326048\pi$
$812$	2.34159	0.0821736
$813$	30.4590	1.06824
$814$	2.19343	0.0768795
$815$	−44.3029	−1.55186
$816$	12.2654	0.429374
$817$	9.05450	0.316777
$818$	−1.93398	−0.0676200
$819$	−10.6938	−0.373672
$820$	32.1136	1.12146
$821$	2.86522	0.0999969	0.0499985	−	0.998749i	$-0.484078\pi$
$821$	2.86522	0.0999969	0.0499985	+	0.998749i	$0.484078\pi$
$822$	0.932468	0.0325236
$823$	−2.25219	−0.0785065	−0.0392533	−	0.999229i	$-0.512498\pi$
$823$	−2.25219	−0.0785065	−0.0392533	+	0.999229i	$0.512498\pi$
$824$	−9.26023	−0.322595
$825$	−118.378	−4.12138
$826$	4.88704	0.170042
$827$	17.3577	0.603588	0.301794	−	0.953373i	$-0.402415\pi$
$827$	17.3577	0.603588	0.301794	+	0.953373i	$0.402415\pi$
$828$	13.0837	0.454692
$829$	34.7430	1.20667	0.603337	−	0.797486i	$-0.293837\pi$
$829$	34.7430	1.20667	0.603337	+	0.797486i	$0.293837\pi$
$830$	11.1697	0.387705
$831$	−22.1426	−0.768117
$832$	−34.4837	−1.19551
$833$	−6.35759	−0.220278
$834$	5.68251	0.196769
$835$	55.9092	1.93482
$836$	−77.9679	−2.69658
$837$	−33.8230	−1.16910
$838$	1.13529	0.0392178
$839$	53.1461	1.83481	0.917403	−	0.397959i	$-0.130281\pi$
$839$	53.1461	1.83481	0.917403	+	0.397959i	$0.130281\pi$
$840$	−12.4744	−0.430409
$841$	−28.5262	−0.983664
$842$	6.54990	0.225724
$843$	−29.1224	−1.00303
$844$	−14.6083	−0.502839
$845$	−48.8218	−1.67952
$846$	−1.81976	−0.0625647
$847$	−23.9025	−0.821301
$848$	19.7953	0.679774
$849$	−60.3779	−2.07217
$850$	4.01604	0.137749
$851$	11.1192	0.381162
$852$	−42.9861	−1.47268
$853$	−10.3226	−0.353439	−0.176720	−	0.984261i	$-0.556549\pi$
$853$	−10.3226	−0.353439	−0.176720	+	0.984261i	$0.556549\pi$
$854$	2.35194	0.0804818
$855$	40.1461	1.37297
$856$	1.66226	0.0568149
$857$	33.4159	1.14147	0.570733	−	0.821135i	$-0.306659\pi$
$857$	33.4159	1.14147	0.570733	+	0.821135i	$0.306659\pi$
$858$	−11.0599	−0.377580
$859$	−41.9793	−1.43232	−0.716158	−	0.697938i	$-0.754101\pi$
$859$	−41.9793	−1.43232	−0.716158	+	0.697938i	$0.754101\pi$
$860$	−8.96916	−0.305846
$861$	−14.4626	−0.492884
$862$	−2.15057	−0.0732488
$863$	−20.8109	−0.708411	−0.354205	−	0.935168i	$-0.615249\pi$
$863$	−20.8109	−0.708411	−0.354205	+	0.935168i	$0.615249\pi$
$864$	−9.16706	−0.311870
$865$	32.4165	1.10219
$866$	−8.91686	−0.303007
$867$	−29.6728	−1.00774
$868$	31.5823	1.07197
$869$	−8.63905	−0.293060
$870$	−1.24698	−0.0422765
$871$	−18.1256	−0.614164
$872$	−9.74645	−0.330056
$873$	−11.0221	−0.373043
$874$	9.47548	0.320513
$875$	46.6524	1.57714
$876$	6.51544	0.220136
$877$	12.1066	0.408812	0.204406	−	0.978886i	$-0.434474\pi$
$877$	12.1066	0.408812	0.204406	+	0.978886i	$0.434474\pi$
$878$	−2.52275	−0.0851386
$879$	−43.9208	−1.48141
$880$	75.3371	2.53961
$881$	−24.4526	−0.823828	−0.411914	−	0.911223i	$-0.635140\pi$
$881$	−24.4526	−0.823828	−0.411914	+	0.911223i	$0.635140\pi$
$882$	−1.05405	−0.0354919
$883$	−35.8815	−1.20751	−0.603755	−	0.797170i	$-0.706329\pi$
$883$	−35.8815	−1.20751	−0.603755	+	0.797170i	$0.706329\pi$
$884$	−15.6512	−0.526407
$885$	108.558	3.64913
$886$	7.59175	0.255050
$887$	38.5783	1.29533	0.647666	−	0.761925i	$-0.275745\pi$
$887$	38.5783	1.29533	0.647666	+	0.761925i	$0.275745\pi$
$888$	3.58586	0.120333
$889$	14.6094	0.489984
$890$	−3.46574	−0.116172
$891$	55.5701	1.86167
$892$	−35.7033	−1.19544
$893$	54.9732	1.83961
$894$	5.96782	0.199594
$895$	48.5491	1.62282
$896$	11.3649	0.379673
$897$	−56.0666	−1.87201
$898$	0.853705	0.0284885
$899$	6.38979	0.213111
$900$	−27.7738	−0.925793
$901$	8.52690	0.284072
$902$	−4.34477	−0.144665
$903$	4.03932	0.134420
$904$	2.95948	0.0984307
$905$	4.23639	0.140822
$906$	−9.75540	−0.324101
$907$	−49.4472	−1.64187	−0.820933	−	0.571024i	$-0.806546\pi$
$907$	−49.4472	−1.64187	−0.820933	+	0.571024i	$0.806546\pi$
$908$	−24.2142	−0.803575
$909$	1.71179	0.0567765
$910$	7.67165	0.254313
$911$	−46.3390	−1.53528	−0.767639	−	0.640882i	$-0.778569\pi$
$911$	−46.3390	−1.53528	−0.767639	+	0.640882i	$0.778569\pi$
$912$	−61.4309	−2.03418
$913$	63.0354	2.08617
$914$	−7.49601	−0.247946
$915$	52.2445	1.72715
$916$	18.1023	0.598117
$917$	14.7036	0.485555
$918$	−1.26374	−0.0417096
$919$	−17.5243	−0.578074	−0.289037	−	0.957318i	$-0.593335\pi$
$919$	−17.5243	−0.578074	−0.289037	+	0.957318i	$0.593335\pi$
$920$	−18.9974	−0.626325
$921$	19.0060	0.626269
$922$	3.81238	0.125554
$923$	53.5058	1.76117
$924$	−34.7825	−1.14426
$925$	−23.6036	−0.776081
$926$	−4.01753	−0.132024
$927$	13.2950	0.436665
$928$	1.73182	0.0568499
$929$	19.1339	0.627763	0.313882	−	0.949462i	$-0.398371\pi$
$929$	19.1339	0.627763	0.313882	+	0.949462i	$0.398371\pi$
$930$	−16.8187	−0.551506
$931$	31.8419	1.04358
$932$	−42.6170	−1.39597
$933$	2.62312	0.0858773
$934$	3.37050	0.110286
$935$	32.4517	1.06129
$936$	−5.25198	−0.171666
$937$	−24.1804	−0.789938	−0.394969	−	0.918694i	$-0.629245\pi$
$937$	−24.1804	−0.789938	−0.394969	+	0.918694i	$0.629245\pi$
$938$	1.36658	0.0446203
$939$	34.4156	1.12311
$940$	−54.4550	−1.77613
$941$	53.2529	1.73600	0.867998	−	0.496567i	$-0.165406\pi$
$941$	53.2529	1.73600	0.867998	+	0.496567i	$0.165406\pi$
$942$	0.320744	0.0104504
$943$	−22.0251	−0.717237
$944$	−48.2508	−1.57043
$945$	−25.8384	−0.840522
$946$	1.21347	0.0394533
$947$	−37.7243	−1.22588	−0.612938	−	0.790131i	$-0.710012\pi$
$947$	−37.7243	−1.22588	−0.612938	+	0.790131i	$0.710012\pi$
$948$	−6.97801	−0.226635
$949$	−8.10992	−0.263259
$950$	−20.1143	−0.652593
$951$	−30.2028	−0.979394
$952$	2.38832	0.0774060
$953$	−46.1402	−1.49463	−0.747313	−	0.664472i	$-0.768657\pi$
$953$	−46.1402	−1.49463	−0.747313	+	0.664472i	$0.768657\pi$
$954$	1.41371	0.0457707
$955$	64.0780	2.07352
$956$	−11.7335	−0.379487
$957$	−7.03724	−0.227482
$958$	2.55853	0.0826623
$959$	−3.65018	−0.117871
$960$	57.7524	1.86395
$961$	55.1827	1.78009
$962$	−2.20526	−0.0711006
$963$	−2.38653	−0.0769047
$964$	15.4713	0.498298
$965$	61.0746	1.96606
$966$	4.22713	0.136006
$967$	11.3857	0.366139	0.183069	−	0.983100i	$-0.441397\pi$
$967$	11.3857	0.366139	0.183069	+	0.983100i	$0.441397\pi$
$968$	−11.7391	−0.377309
$969$	−26.4616	−0.850069
$970$	7.90719	0.253884
$971$	−18.8792	−0.605862	−0.302931	−	0.953013i	$-0.597965\pi$
$971$	−18.8792	−0.605862	−0.302931	+	0.953013i	$0.597965\pi$
$972$	23.5371	0.754954
$973$	−22.2444	−0.713122
$974$	2.68381	0.0859949
$975$	119.017	3.81158
$976$	−23.2212	−0.743292
$977$	0.118211	0.00378191	0.00189096	−	0.999998i	$-0.499398\pi$
$977$	0.118211	0.00378191	0.00189096	+	0.999998i	$0.499398\pi$
$978$	4.84145	0.154812
$979$	−19.5587	−0.625099
$980$	−31.5418	−1.00757
$981$	13.9931	0.446765
$982$	−5.51648	−0.176038
$983$	13.2897	0.423875	0.211937	−	0.977283i	$-0.432023\pi$
$983$	13.2897	0.423875	0.211937	+	0.977283i	$0.432023\pi$
$984$	−7.10291	−0.226433
$985$	43.6299	1.39017
$986$	0.238743	0.00760313
$987$	24.5242	0.780614
$988$	78.3888	2.49388
$989$	6.15150	0.195606
$990$	5.38032	0.170998
$991$	−54.0911	−1.71826	−0.859130	−	0.511758i	$-0.828994\pi$
$991$	−54.0911	−1.71826	−0.859130	+	0.511758i	$0.828994\pi$
$992$	23.3581	0.741620
$993$	−48.8812	−1.55120
$994$	−4.03406	−0.127952
$995$	−106.845	−3.38722
$996$	50.9154	1.61332
$997$	18.9284	0.599470	0.299735	−	0.954023i	$-0.403102\pi$
$997$	18.9284	0.599470	0.299735	+	0.954023i	$0.403102\pi$
$998$	−1.80724	−0.0572072
$999$	7.42741	0.234993

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	349.2.a.a.1.7	✓	11
3.2	odd	2		3141.2.a.b.1.5		11
4.3	odd	2		5584.2.a.j.1.2		11
5.4	even	2		8725.2.a.l.1.5		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.2.a.a.1.7	✓	11	1.1	even	1	trivial
3141.2.a.b.1.5		11	3.2	odd	2
5584.2.a.j.1.2		11	4.3	odd	2
8725.2.a.l.1.5		11	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	349.a (trivial)

\(f(q)\)	\(=\)	\(q+0.216390 q^{2} +2.05625 q^{3} -1.95318 q^{4} -4.07164 q^{5} +0.444951 q^{6} -1.74178 q^{7} -0.855428 q^{8} +1.22815 q^{9} +O(q^{10})\)	\(q+0.216390 q^{2} +2.05625 q^{3} -1.95318 q^{4} -4.07164 q^{5} +0.444951 q^{6} -1.74178 q^{7} -0.855428 q^{8} +1.22815 q^{9} -0.881063 q^{10} -4.97223 q^{11} -4.01621 q^{12} +4.99907 q^{13} -0.376903 q^{14} -8.37230 q^{15} +3.72124 q^{16} +1.60294 q^{17} +0.265759 q^{18} -8.02830 q^{19} +7.95263 q^{20} -3.58152 q^{21} -1.07594 q^{22} -5.45432 q^{23} -1.75897 q^{24} +11.5783 q^{25} +1.08175 q^{26} -3.64337 q^{27} +3.40200 q^{28} +0.688298 q^{29} -1.81168 q^{30} +9.28346 q^{31} +2.51610 q^{32} -10.2241 q^{33} +0.346860 q^{34} +7.09190 q^{35} -2.39879 q^{36} -2.03861 q^{37} -1.73724 q^{38} +10.2793 q^{39} +3.48300 q^{40} +4.03811 q^{41} -0.775006 q^{42} -1.12782 q^{43} +9.71164 q^{44} -5.00057 q^{45} -1.18026 q^{46} -6.84742 q^{47} +7.65179 q^{48} -3.96621 q^{49} +2.50542 q^{50} +3.29604 q^{51} -9.76406 q^{52} +5.31954 q^{53} -0.788388 q^{54} +20.2451 q^{55} +1.48997 q^{56} -16.5082 q^{57} +0.148941 q^{58} -12.9663 q^{59} +16.3526 q^{60} -6.24017 q^{61} +2.00885 q^{62} -2.13916 q^{63} -6.89803 q^{64} -20.3544 q^{65} -2.21240 q^{66} -3.62580 q^{67} -3.13082 q^{68} -11.2154 q^{69} +1.53462 q^{70} +10.7032 q^{71} -1.05059 q^{72} -1.62229 q^{73} -0.441135 q^{74} +23.8078 q^{75} +15.6807 q^{76} +8.66052 q^{77} +2.22434 q^{78} +1.73746 q^{79} -15.1516 q^{80} -11.1761 q^{81} +0.873807 q^{82} -12.6775 q^{83} +6.99534 q^{84} -6.52660 q^{85} -0.244050 q^{86} +1.41531 q^{87} +4.25338 q^{88} +3.93359 q^{89} -1.08207 q^{90} -8.70727 q^{91} +10.6532 q^{92} +19.0891 q^{93} -1.48171 q^{94} +32.6884 q^{95} +5.17371 q^{96} -8.97460 q^{97} -0.858248 q^{98} -6.10663 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 5 q^{2} - 6 q^{3} + 5 q^{4} - 9 q^{5} - 5 q^{6} - 3 q^{7} - 15 q^{8} + 3 q^{9}+O(q^{10}) \) 11 * q - 5 * q^2 - 6 * q^3 + 5 * q^4 - 9 * q^5 - 5 * q^6 - 3 * q^7 - 15 * q^8 + 3 * q^9	\( 11 q - 5 q^{2} - 6 q^{3} + 5 q^{4} - 9 q^{5} - 5 q^{6} - 3 q^{7} - 15 q^{8} + 3 q^{9} + 2 q^{10} - 31 q^{11} - 4 q^{13} - 7 q^{14} - 12 q^{15} + 5 q^{16} - q^{17} - 17 q^{19} - 10 q^{20} - 15 q^{21} + 17 q^{22} - 24 q^{23} - 3 q^{24} + 10 q^{25} - 11 q^{26} - 15 q^{27} + 3 q^{28} - 17 q^{29} + 9 q^{30} - 10 q^{31} - 5 q^{32} + 11 q^{33} + 2 q^{34} - 28 q^{35} - 4 q^{36} - q^{37} + 2 q^{38} + 8 q^{39} + 21 q^{40} - 15 q^{41} + 30 q^{42} - 5 q^{43} - 24 q^{44} - 3 q^{45} + 23 q^{46} + 4 q^{47} + 29 q^{48} + 14 q^{49} - 3 q^{50} - 19 q^{51} + 25 q^{52} - 3 q^{53} + 28 q^{54} + 24 q^{55} + 8 q^{56} + 11 q^{57} + 8 q^{58} - 52 q^{59} + 21 q^{60} + 42 q^{62} + 35 q^{63} + 5 q^{64} - 3 q^{65} + 30 q^{66} - 23 q^{67} + 15 q^{68} + 25 q^{69} + 27 q^{70} - 30 q^{71} + 23 q^{72} + 12 q^{73} + 30 q^{74} + 34 q^{75} + 2 q^{76} + 6 q^{77} + 41 q^{78} + 11 q^{79} + 18 q^{80} + 7 q^{81} + 46 q^{82} - 13 q^{83} + 23 q^{84} + 19 q^{85} - 21 q^{86} + 35 q^{87} + 80 q^{88} - 19 q^{89} + 38 q^{90} - 30 q^{91} + q^{92} + 13 q^{93} - 2 q^{94} - 7 q^{95} + 13 q^{96} + 26 q^{97} + 35 q^{98} - 41 q^{99}+O(q^{100}) \) 11 * q - 5 * q^2 - 6 * q^3 + 5 * q^4 - 9 * q^5 - 5 * q^6 - 3 * q^7 - 15 * q^8 + 3 * q^9 + 2 * q^10 - 31 * q^11 - 4 * q^13 - 7 * q^14 - 12 * q^15 + 5 * q^16 - q^17 - 17 * q^19 - 10 * q^20 - 15 * q^21 + 17 * q^22 - 24 * q^23 - 3 * q^24 + 10 * q^25 - 11 * q^26 - 15 * q^27 + 3 * q^28 - 17 * q^29 + 9 * q^30 - 10 * q^31 - 5 * q^32 + 11 * q^33 + 2 * q^34 - 28 * q^35 - 4 * q^36 - q^37 + 2 * q^38 + 8 * q^39 + 21 * q^40 - 15 * q^41 + 30 * q^42 - 5 * q^43 - 24 * q^44 - 3 * q^45 + 23 * q^46 + 4 * q^47 + 29 * q^48 + 14 * q^49 - 3 * q^50 - 19 * q^51 + 25 * q^52 - 3 * q^53 + 28 * q^54 + 24 * q^55 + 8 * q^56 + 11 * q^57 + 8 * q^58 - 52 * q^59 + 21 * q^60 + 42 * q^62 + 35 * q^63 + 5 * q^64 - 3 * q^65 + 30 * q^66 - 23 * q^67 + 15 * q^68 + 25 * q^69 + 27 * q^70 - 30 * q^71 + 23 * q^72 + 12 * q^73 + 30 * q^74 + 34 * q^75 + 2 * q^76 + 6 * q^77 + 41 * q^78 + 11 * q^79 + 18 * q^80 + 7 * q^81 + 46 * q^82 - 13 * q^83 + 23 * q^84 + 19 * q^85 - 21 * q^86 + 35 * q^87 + 80 * q^88 - 19 * q^89 + 38 * q^90 - 30 * q^91 + q^92 + 13 * q^93 - 2 * q^94 - 7 * q^95 + 13 * q^96 + 26 * q^97 + 35 * q^98 - 41 * q^99

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