LMFDB - Embedded newform 349.2.a.b.1.11

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:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 5 x^{16} - 14 x^{15} + 102 x^{14} + 26 x^{13} - 792 x^{12} + 474 x^{11} + 2887 x^{10} + \cdots - 4 $ x^17 - 5x^16 - 14x^15 + 102x^14 + 26x^13 - 792x^12 + 474x^11 + 2887x^10 - 3021x^9 - 4835x^8 + 6673x^7 + 2880x^6 - 5373x^5 - 164x^4 + 1075x^3 + 75x^2 - 41x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$1.36177$ 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)

$f(q)$	$=$	$q+1.36177 q^{2} +1.04922 q^{3} -0.145589 q^{4} +0.274763 q^{5} +1.42880 q^{6} +2.68858 q^{7} -2.92179 q^{8} -1.89913 q^{9} +O(q^{10})$	\(q+1.36177 q^{2} +1.04922 q^{3} -0.145589 q^{4} +0.274763 q^{5} +1.42880 q^{6} +2.68858 q^{7} -2.92179 q^{8} -1.89913 q^{9} +0.374163 q^{10} +5.28720 q^{11} -0.152755 q^{12} +6.33845 q^{13} +3.66123 q^{14} +0.288287 q^{15} -3.68763 q^{16} +0.934812 q^{17} -2.58617 q^{18} -5.23477 q^{19} -0.0400023 q^{20} +2.82092 q^{21} +7.19994 q^{22} -2.37431 q^{23} -3.06561 q^{24} -4.92451 q^{25} +8.63150 q^{26} -5.14028 q^{27} -0.391427 q^{28} -7.66603 q^{29} +0.392581 q^{30} -7.87329 q^{31} +0.821896 q^{32} +5.54745 q^{33} +1.27300 q^{34} +0.738723 q^{35} +0.276492 q^{36} +1.86711 q^{37} -7.12853 q^{38} +6.65045 q^{39} -0.802800 q^{40} +3.78927 q^{41} +3.84144 q^{42} -1.55926 q^{43} -0.769756 q^{44} -0.521810 q^{45} -3.23325 q^{46} +10.8803 q^{47} -3.86914 q^{48} +0.228483 q^{49} -6.70603 q^{50} +0.980826 q^{51} -0.922807 q^{52} +0.455656 q^{53} -6.99987 q^{54} +1.45273 q^{55} -7.85549 q^{56} -5.49244 q^{57} -10.4393 q^{58} -8.40335 q^{59} -0.0419714 q^{60} +2.95888 q^{61} -10.7216 q^{62} -5.10597 q^{63} +8.49448 q^{64} +1.74157 q^{65} +7.55434 q^{66} -14.0701 q^{67} -0.136098 q^{68} -2.49118 q^{69} +1.00597 q^{70} +0.382686 q^{71} +5.54887 q^{72} +14.0913 q^{73} +2.54257 q^{74} -5.16691 q^{75} +0.762122 q^{76} +14.2151 q^{77} +9.05637 q^{78} +1.88003 q^{79} -1.01322 q^{80} +0.304088 q^{81} +5.16011 q^{82} +10.6449 q^{83} -0.410695 q^{84} +0.256851 q^{85} -2.12336 q^{86} -8.04337 q^{87} -15.4481 q^{88} +1.85083 q^{89} -0.710584 q^{90} +17.0415 q^{91} +0.345672 q^{92} -8.26084 q^{93} +14.8164 q^{94} -1.43832 q^{95} +0.862352 q^{96} -12.0427 q^{97} +0.311140 q^{98} -10.0411 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 5 q^{2} + 6 q^{3} + 19 q^{4} + 5 q^{5} - 3 q^{6} + q^{7} + 9 q^{8} + 25 q^{9}+O(q^{10}) $ 17 * q + 5 * q^2 + 6 * q^3 + 19 * q^4 + 5 * q^5 - 3 * q^6 + q^7 + 9 * q^8 + 25 * q^9	\( 17 q + 5 q^{2} + 6 q^{3} + 19 q^{4} + 5 q^{5} - 3 q^{6} + q^{7} + 9 q^{8} + 25 q^{9} - 6 q^{10} + 39 q^{11} + 4 q^{12} - 6 q^{13} + 11 q^{14} + 12 q^{15} + 23 q^{16} + q^{17} + 7 q^{19} + 8 q^{20} - 3 q^{21} - q^{22} + 8 q^{23} - 21 q^{24} + 14 q^{25} + q^{26} + 9 q^{27} - 23 q^{28} + 9 q^{29} - 27 q^{30} - 2 q^{31} + 23 q^{32} - 5 q^{33} - 12 q^{34} + 16 q^{35} + 10 q^{36} - 7 q^{37} - 8 q^{38} - 39 q^{40} + 3 q^{41} - 30 q^{42} + q^{43} + 56 q^{44} - 21 q^{45} - q^{46} + 16 q^{47} - 31 q^{48} + 6 q^{49} - 5 q^{50} + 29 q^{51} - 37 q^{52} + 27 q^{53} - 36 q^{54} - 16 q^{55} + 14 q^{56} - 21 q^{57} - 44 q^{58} + 74 q^{59} - 27 q^{60} - 30 q^{61} - 18 q^{62} - 9 q^{63} - 17 q^{64} - 3 q^{65} - 66 q^{66} + 9 q^{67} - 51 q^{68} - 23 q^{69} - 77 q^{70} + 70 q^{71} - 55 q^{72} - 38 q^{73} + 26 q^{74} + 22 q^{75} - 50 q^{76} - 38 q^{77} - 75 q^{78} + 7 q^{79} - 28 q^{80} + 5 q^{81} - 56 q^{82} + 47 q^{83} - 69 q^{84} - 49 q^{85} + 17 q^{86} - 37 q^{87} - 30 q^{88} + 23 q^{89} - 64 q^{90} + 6 q^{91} + 17 q^{92} - 31 q^{93} - 40 q^{94} - 11 q^{95} - 49 q^{96} - 14 q^{97} + 5 q^{98} + 79 q^{99}+O(q^{100}) \) 17 * q + 5 * q^2 + 6 * q^3 + 19 * q^4 + 5 * q^5 - 3 * q^6 + q^7 + 9 * q^8 + 25 * q^9 - 6 * q^10 + 39 * q^11 + 4 * q^12 - 6 * q^13 + 11 * q^14 + 12 * q^15 + 23 * q^16 + q^17 + 7 * q^19 + 8 * q^20 - 3 * q^21 - q^22 + 8 * q^23 - 21 * q^24 + 14 * q^25 + q^26 + 9 * q^27 - 23 * q^28 + 9 * q^29 - 27 * q^30 - 2 * q^31 + 23 * q^32 - 5 * q^33 - 12 * q^34 + 16 * q^35 + 10 * q^36 - 7 * q^37 - 8 * q^38 - 39 * q^40 + 3 * q^41 - 30 * q^42 + q^43 + 56 * q^44 - 21 * q^45 - q^46 + 16 * q^47 - 31 * q^48 + 6 * q^49 - 5 * q^50 + 29 * q^51 - 37 * q^52 + 27 * q^53 - 36 * q^54 - 16 * q^55 + 14 * q^56 - 21 * q^57 - 44 * q^58 + 74 * q^59 - 27 * q^60 - 30 * q^61 - 18 * q^62 - 9 * q^63 - 17 * q^64 - 3 * q^65 - 66 * q^66 + 9 * q^67 - 51 * q^68 - 23 * q^69 - 77 * q^70 + 70 * q^71 - 55 * q^72 - 38 * q^73 + 26 * q^74 + 22 * q^75 - 50 * q^76 - 38 * q^77 - 75 * q^78 + 7 * q^79 - 28 * q^80 + 5 * q^81 - 56 * q^82 + 47 * q^83 - 69 * q^84 - 49 * q^85 + 17 * q^86 - 37 * q^87 - 30 * q^88 + 23 * q^89 - 64 * q^90 + 6 * q^91 + 17 * q^92 - 31 * q^93 - 40 * q^94 - 11 * q^95 - 49 * q^96 - 14 * q^97 + 5 * q^98 + 79 * 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 $

$2$	1.36177	0.962915	0.481458	−	0.876469i	$-0.340108\pi$
$2$	1.36177	0.962915	0.481458	+	0.876469i	$0.340108\pi$
$3$	1.04922	0.605769	0.302885	−	0.953027i	$-0.402050\pi$
$3$	1.04922	0.605769	0.302885	+	0.953027i	$0.402050\pi$
$4$	−0.145589	−0.0727943
$5$	0.274763	0.122878	0.0614388	−	0.998111i	$-0.480431\pi$
$5$	0.274763	0.122878	0.0614388	+	0.998111i	$0.480431\pi$
$6$	1.42880	0.583305
$7$	2.68858	1.01619	0.508095	−	0.861301i	$-0.330350\pi$
$7$	2.68858	1.01619	0.508095	+	0.861301i	$0.330350\pi$
$8$	−2.92179	−1.03301
$9$	−1.89913	−0.633043
$10$	0.374163	0.118321
$11$	5.28720	1.59415	0.797075	−	0.603880i	$-0.206379\pi$
$11$	5.28720	1.59415	0.797075	+	0.603880i	$0.206379\pi$
$12$	−0.152755	−0.0440966
$13$	6.33845	1.75797	0.878985	−	0.476849i	$-0.158221\pi$
$13$	6.33845	1.75797	0.878985	+	0.476849i	$0.158221\pi$
$14$	3.66123	0.978504
$15$	0.288287	0.0744355
$16$	−3.68763	−0.921907
$17$	0.934812	0.226725	0.113363	−	0.993554i	$-0.463838\pi$
$17$	0.934812	0.226725	0.113363	+	0.993554i	$0.463838\pi$
$18$	−2.58617	−0.609567
$19$	−5.23477	−1.20094	−0.600469	−	0.799648i	$-0.705019\pi$
$19$	−5.23477	−1.20094	−0.600469	+	0.799648i	$0.705019\pi$
$20$	−0.0400023	−0.00894479
$21$	2.82092	0.615576
$22$	7.19994	1.53503
$23$	−2.37431	−0.495077	−0.247539	−	0.968878i	$-0.579622\pi$
$23$	−2.37431	−0.495077	−0.247539	+	0.968878i	$0.579622\pi$
$24$	−3.06561	−0.625766
$25$	−4.92451	−0.984901
$26$	8.63150	1.69278
$27$	−5.14028	−0.989248
$28$	−0.391427	−0.0739728
$29$	−7.66603	−1.42355	−0.711773	−	0.702410i	$-0.752107\pi$
$29$	−7.66603	−1.42355	−0.711773	+	0.702410i	$0.752107\pi$
$30$	0.392581	0.0716751
$31$	−7.87329	−1.41408	−0.707042	−	0.707171i	$-0.749971\pi$
$31$	−7.87329	−1.41408	−0.707042	+	0.707171i	$0.749971\pi$
$32$	0.821896	0.145292
$33$	5.54745	0.965688
$34$	1.27300	0.218317
$35$	0.738723	0.124867
$36$	0.276492	0.0460820
$37$	1.86711	0.306950	0.153475	−	0.988152i	$-0.450953\pi$
$37$	1.86711	0.306950	0.153475	+	0.988152i	$0.450953\pi$
$38$	−7.12853	−1.15640
$39$	6.65045	1.06492
$40$	−0.802800	−0.126934
$41$	3.78927	0.591785	0.295892	−	0.955221i	$-0.404383\pi$
$41$	3.78927	0.591785	0.295892	+	0.955221i	$0.404383\pi$
$42$	3.84144	0.592748
$43$	−1.55926	−0.237785	−0.118893	−	0.992907i	$-0.537934\pi$
$43$	−1.55926	−0.237785	−0.118893	+	0.992907i	$0.537934\pi$
$44$	−0.769756	−0.116045
$45$	−0.521810	−0.0777869
$46$	−3.23325	−0.476717
$47$	10.8803	1.58705	0.793526	−	0.608536i	$-0.208243\pi$
$47$	10.8803	1.58705	0.793526	+	0.608536i	$0.208243\pi$
$48$	−3.86914	−0.558463
$49$	0.228483	0.0326404
$50$	−6.70603	−0.948376
$51$	0.980826	0.137343
$52$	−0.922807	−0.127970
$53$	0.455656	0.0625892	0.0312946	−	0.999510i	$-0.490037\pi$
$53$	0.455656	0.0625892	0.0312946	+	0.999510i	$0.490037\pi$
$54$	−6.99987	−0.952562
$55$	1.45273	0.195886
$56$	−7.85549	−1.04973
$57$	−5.49244	−0.727491
$58$	−10.4393	−1.37075
$59$	−8.40335	−1.09402	−0.547012	−	0.837125i	$-0.684235\pi$
$59$	−8.40335	−1.09402	−0.547012	+	0.837125i	$0.684235\pi$
$60$	−0.0419714	−0.00541848
$61$	2.95888	0.378846	0.189423	−	0.981896i	$-0.439338\pi$
$61$	2.95888	0.378846	0.189423	+	0.981896i	$0.439338\pi$
$62$	−10.7216	−1.36164
$63$	−5.10597	−0.643292
$64$	8.49448	1.06181
$65$	1.74157	0.216015
$66$	7.55434	0.929875
$67$	−14.0701	−1.71893	−0.859466	−	0.511193i	$-0.829204\pi$
$67$	−14.0701	−1.71893	−0.859466	+	0.511193i	$0.829204\pi$
$68$	−0.136098	−0.0165043
$69$	−2.49118	−0.299902
$70$	1.00597	0.120236
$71$	0.382686	0.0454165	0.0227082	−	0.999742i	$-0.492771\pi$
$71$	0.382686	0.0454165	0.0227082	+	0.999742i	$0.492771\pi$
$72$	5.54887	0.653940
$73$	14.0913	1.64926	0.824629	−	0.565674i	$-0.191384\pi$
$73$	14.0913	1.64926	0.824629	+	0.565674i	$0.191384\pi$
$74$	2.54257	0.295567
$75$	−5.16691	−0.596623
$76$	0.762122	0.0874214
$77$	14.2151	1.61996
$78$	9.05637	1.02543
$79$	1.88003	0.211520	0.105760	−	0.994392i	$-0.466273\pi$
$79$	1.88003	0.211520	0.105760	+	0.994392i	$0.466273\pi$
$80$	−1.01322	−0.113282
$81$	0.304088	0.0337875
$82$	5.16011	0.569839
$83$	10.6449	1.16843	0.584215	−	0.811599i	$-0.301403\pi$
$83$	10.6449	1.16843	0.584215	+	0.811599i	$0.301403\pi$
$84$	−0.410695	−0.0448105
$85$	0.256851	0.0278594
$86$	−2.12336	−0.228967
$87$	−8.04337	−0.862340
$88$	−15.4481	−1.64677
$89$	1.85083	0.196188	0.0980941	−	0.995177i	$-0.468725\pi$
$89$	1.85083	0.196188	0.0980941	+	0.995177i	$0.468725\pi$
$90$	−0.710584	−0.0749022
$91$	17.0415	1.78643
$92$	0.345672	0.0360388
$93$	−8.26084	−0.856609
$94$	14.8164	1.52820
$95$	−1.43832	−0.147568
$96$	0.862352	0.0880134
$97$	−12.0427	−1.22275	−0.611374	−	0.791342i	$-0.709383\pi$
$97$	−12.0427	−1.22275	−0.611374	+	0.791342i	$0.709383\pi$
$98$	0.311140	0.0314299
$99$	−10.0411	−1.00917
$100$	0.716952	0.0716952
$101$	−14.1700	−1.40997	−0.704983	−	0.709224i	$-0.749045\pi$
$101$	−14.1700	−1.40997	−0.704983	+	0.709224i	$0.749045\pi$
$102$	1.33566	0.132250
$103$	13.1663	1.29731	0.648657	−	0.761081i	$-0.275331\pi$
$103$	13.1663	1.29731	0.648657	+	0.761081i	$0.275331\pi$
$104$	−18.5197	−1.81600
$105$	0.775085	0.0756406
$106$	0.620498	0.0602681
$107$	18.1119	1.75095	0.875474	−	0.483265i	$-0.160549\pi$
$107$	18.1119	1.75095	0.875474	+	0.483265i	$0.160549\pi$
$108$	0.748367	0.0720116
$109$	−6.76552	−0.648019	−0.324009	−	0.946054i	$-0.605031\pi$
$109$	−6.76552	−0.648019	−0.324009	+	0.946054i	$0.605031\pi$
$110$	1.97828	0.188621
$111$	1.95901	0.185941
$112$	−9.91449	−0.936832
$113$	−8.31571	−0.782276	−0.391138	−	0.920332i	$-0.627918\pi$
$113$	−8.31571	−0.782276	−0.391138	+	0.920332i	$0.627918\pi$
$114$	−7.47942	−0.700512
$115$	−0.652371	−0.0608339
$116$	1.11609	0.103626
$117$	−12.0375	−1.11287
$118$	−11.4434	−1.05345
$119$	2.51332	0.230396
$120$	−0.842316	−0.0768926
$121$	16.9545	1.54132
$122$	4.02931	0.364796
$123$	3.97579	0.358485
$124$	1.14626	0.102937
$125$	−2.72688	−0.243900
$126$	−6.95315	−0.619436
$127$	14.6071	1.29617	0.648084	−	0.761569i	$-0.275570\pi$
$127$	14.6071	1.29617	0.648084	+	0.761569i	$0.275570\pi$
$128$	9.92372	0.877142
$129$	−1.63602	−0.144043
$130$	2.37162	0.208004
$131$	−3.82628	−0.334304	−0.167152	−	0.985931i	$-0.553457\pi$
$131$	−3.82628	−0.334304	−0.167152	+	0.985931i	$0.553457\pi$
$132$	−0.807646	−0.0702966
$133$	−14.0741	−1.22038
$134$	−19.1602	−1.65519
$135$	−1.41236	−0.121556
$136$	−2.73133	−0.234209
$137$	−7.04244	−0.601676	−0.300838	−	0.953675i	$-0.597266\pi$
$137$	−7.04244	−0.601676	−0.300838	+	0.953675i	$0.597266\pi$
$138$	−3.39240	−0.288781
$139$	−0.538395	−0.0456660	−0.0228330	−	0.999739i	$-0.507269\pi$
$139$	−0.538395	−0.0456660	−0.0228330	+	0.999739i	$0.507269\pi$
$140$	−0.107550	−0.00908960
$141$	11.4158	0.961388
$142$	0.521129	0.0437322
$143$	33.5127	2.80247
$144$	7.00328	0.583607
$145$	−2.10634	−0.174922
$146$	19.1890	1.58810
$147$	0.239729	0.0197725
$148$	−0.271830	−0.0223442
$149$	−5.64293	−0.462286	−0.231143	−	0.972920i	$-0.574247\pi$
$149$	−5.64293	−0.462286	−0.231143	+	0.972920i	$0.574247\pi$
$150$	−7.03613	−0.574497
$151$	−19.0494	−1.55022	−0.775111	−	0.631826i	$-0.782306\pi$
$151$	−19.0494	−1.55022	−0.775111	+	0.631826i	$0.782306\pi$
$152$	15.2949	1.24058
$153$	−1.77533	−0.143527
$154$	19.3576	1.55988
$155$	−2.16329	−0.173759
$156$	−0.968230	−0.0775205
$157$	−10.8221	−0.863697	−0.431848	−	0.901946i	$-0.642138\pi$
$157$	−10.8221	−0.863697	−0.431848	+	0.901946i	$0.642138\pi$
$158$	2.56016	0.203676
$159$	0.478085	0.0379146
$160$	0.225826	0.0178531
$161$	−6.38352	−0.503092
$162$	0.414097	0.0325345
$163$	−15.3815	−1.20477	−0.602386	−	0.798205i	$-0.705783\pi$
$163$	−15.3815	−1.20477	−0.602386	+	0.798205i	$0.705783\pi$
$164$	−0.551675	−0.0430786
$165$	1.52423	0.118661
$166$	14.4959	1.12510
$167$	20.7478	1.60551	0.802757	−	0.596307i	$-0.203366\pi$
$167$	20.7478	1.60551	0.802757	+	0.596307i	$0.203366\pi$
$168$	−8.24216	−0.635896
$169$	27.1760	2.09046
$170$	0.349772	0.0268263
$171$	9.94150	0.760246
$172$	0.227011	0.0173094
$173$	18.4408	1.40203	0.701013	−	0.713149i	$-0.252732\pi$
$173$	18.4408	1.40203	0.701013	+	0.713149i	$0.252732\pi$
$174$	−10.9532	−0.830361
$175$	−13.2399	−1.00085
$176$	−19.4972	−1.46966
$177$	−8.81699	−0.662726
$178$	2.52041	0.188913
$179$	17.8950	1.33754	0.668769	−	0.743470i	$-0.266821\pi$
$179$	17.8950	1.33754	0.668769	+	0.743470i	$0.266821\pi$
$180$	0.0759697	0.00566244
$181$	0.823442	0.0612059	0.0306030	−	0.999532i	$-0.490257\pi$
$181$	0.823442	0.0612059	0.0306030	+	0.999532i	$0.490257\pi$
$182$	23.2065	1.72018
$183$	3.10453	0.229493
$184$	6.93723	0.511419
$185$	0.513011	0.0377174
$186$	−11.2493	−0.824842
$187$	4.94254	0.361434
$188$	−1.58405	−0.115528
$189$	−13.8201	−1.00526
$190$	−1.95866	−0.142096
$191$	5.47511	0.396165	0.198082	−	0.980185i	$-0.436529\pi$
$191$	5.47511	0.396165	0.198082	+	0.980185i	$0.436529\pi$
$192$	8.91261	0.643212
$193$	8.27439	0.595603	0.297802	−	0.954628i	$-0.403747\pi$
$193$	8.27439	0.595603	0.297802	+	0.954628i	$0.403747\pi$
$194$	−16.3993	−1.17740
$195$	1.82730	0.130855
$196$	−0.0332645	−0.00237603
$197$	16.9655	1.20874	0.604371	−	0.796703i	$-0.293424\pi$
$197$	16.9655	1.20874	0.604371	+	0.796703i	$0.293424\pi$
$198$	−13.6736	−0.971742
$199$	−9.36474	−0.663849	−0.331925	−	0.943306i	$-0.607698\pi$
$199$	−9.36474	−0.663849	−0.331925	+	0.943306i	$0.607698\pi$
$200$	14.3884	1.01741
$201$	−14.7626	−1.04128
$202$	−19.2962	−1.35768
$203$	−20.6108	−1.44659
$204$	−0.142797	−0.00999780
$205$	1.04115	0.0727171
$206$	17.9294	1.24920
$207$	4.50912	0.313405
$208$	−23.3738	−1.62068
$209$	−27.6773	−1.91448
$210$	1.05549	0.0728354
$211$	12.7517	0.877866	0.438933	−	0.898520i	$-0.355356\pi$
$211$	12.7517	0.877866	0.438933	+	0.898520i	$0.355356\pi$
$212$	−0.0663384	−0.00455614
$213$	0.401523	0.0275119
$214$	24.6643	1.68601
$215$	−0.428428	−0.0292185
$216$	15.0188	1.02190
$217$	−21.1680	−1.43698
$218$	−9.21306	−0.623987
$219$	14.7849	0.999070
$220$	−0.211500	−0.0142594
$221$	5.92526	0.398576
$222$	2.66772	0.179046
$223$	5.91716	0.396242	0.198121	−	0.980178i	$-0.436516\pi$
$223$	5.91716	0.396242	0.198121	+	0.980178i	$0.436516\pi$
$224$	2.20974	0.147644
$225$	9.35228	0.623485
$226$	−11.3241	−0.753265
$227$	16.9952	1.12801	0.564007	−	0.825770i	$-0.309259\pi$
$227$	16.9952	1.12801	0.564007	+	0.825770i	$0.309259\pi$
$228$	0.799636	0.0529572
$229$	−19.1543	−1.26575	−0.632876	−	0.774253i	$-0.718126\pi$
$229$	−19.1543	−1.26575	−0.632876	+	0.774253i	$0.718126\pi$
$230$	−0.888378	−0.0585779
$231$	14.9148	0.981321
$232$	22.3985	1.47054
$233$	6.00196	0.393202	0.196601	−	0.980484i	$-0.437010\pi$
$233$	6.00196	0.393202	0.196601	+	0.980484i	$0.437010\pi$
$234$	−16.3923	−1.07160
$235$	2.98950	0.195013
$236$	1.22343	0.0796387
$237$	1.97257	0.128132
$238$	3.42256	0.221851
$239$	−2.00841	−0.129913	−0.0649567	−	0.997888i	$-0.520691\pi$
$239$	−2.00841	−0.129913	−0.0649567	+	0.997888i	$0.520691\pi$
$240$	−1.06310	−0.0686226
$241$	−24.5708	−1.58275	−0.791373	−	0.611333i	$-0.790633\pi$
$241$	−24.5708	−1.58275	−0.791373	+	0.611333i	$0.790633\pi$
$242$	23.0881	1.48416
$243$	15.7399	1.00972
$244$	−0.430779	−0.0275778
$245$	0.0627785	0.00401077
$246$	5.41411	0.345191
$247$	−33.1803	−2.11121
$248$	23.0041	1.46076
$249$	11.1689	0.707799
$250$	−3.71338	−0.234855
$251$	2.31139	0.145894	0.0729470	−	0.997336i	$-0.476760\pi$
$251$	2.31139	0.145894	0.0729470	+	0.997336i	$0.476760\pi$
$252$	0.743371	0.0468280
$253$	−12.5534	−0.789227
$254$	19.8914	1.24810
$255$	0.269494	0.0168764
$256$	−3.47516	−0.217198
$257$	−19.4573	−1.21371	−0.606856	−	0.794812i	$-0.707569\pi$
$257$	−19.4573	−1.21371	−0.606856	+	0.794812i	$0.707569\pi$
$258$	−2.22787	−0.138701
$259$	5.01987	0.311920
$260$	−0.253553	−0.0157247
$261$	14.5588	0.901166
$262$	−5.21050	−0.321906
$263$	−1.51446	−0.0933854	−0.0466927	−	0.998909i	$-0.514868\pi$
$263$	−1.51446	−0.0933854	−0.0466927	+	0.998909i	$0.514868\pi$
$264$	−16.2085	−0.997565
$265$	0.125197	0.00769081
$266$	−19.1657	−1.17512
$267$	1.94194	0.118845
$268$	2.04844	0.125128
$269$	11.6375	0.709550	0.354775	−	0.934952i	$-0.384557\pi$
$269$	11.6375	0.709550	0.354775	+	0.934952i	$0.384557\pi$
$270$	−1.92330	−0.117049
$271$	−32.4179	−1.96925	−0.984623	−	0.174695i	$-0.944106\pi$
$271$	−32.4179	−1.96925	−0.984623	+	0.174695i	$0.944106\pi$
$272$	−3.44724	−0.209019
$273$	17.8803	1.08216
$274$	−9.59017	−0.579363
$275$	−26.0368	−1.57008
$276$	0.362687	0.0218312
$277$	2.05127	0.123249	0.0616244	−	0.998099i	$-0.480372\pi$
$277$	2.05127	0.123249	0.0616244	+	0.998099i	$0.480372\pi$
$278$	−0.733169	−0.0439725
$279$	14.9524	0.895177
$280$	−2.15840	−0.128989
$281$	31.4275	1.87481	0.937403	−	0.348247i	$-0.113223\pi$
$281$	31.4275	1.87481	0.937403	+	0.348247i	$0.113223\pi$
$282$	15.5457	0.925735
$283$	30.7186	1.82603	0.913017	−	0.407923i	$-0.133747\pi$
$283$	30.7186	1.82603	0.913017	+	0.407923i	$0.133747\pi$
$284$	−0.0557147	−0.00330606
$285$	−1.50912	−0.0893924
$286$	45.6365	2.69854
$287$	10.1878	0.601365
$288$	−1.56089	−0.0919762
$289$	−16.1261	−0.948596
$290$	−2.86834	−0.168435
$291$	−12.6354	−0.740703
$292$	−2.05153	−0.120057
$293$	−8.49208	−0.496113	−0.248056	−	0.968746i	$-0.579792\pi$
$293$	−8.49208	−0.496113	−0.248056	+	0.968746i	$0.579792\pi$
$294$	0.326456	0.0190393
$295$	−2.30893	−0.134431
$296$	−5.45530	−0.317083
$297$	−27.1777	−1.57701
$298$	−7.68435	−0.445143
$299$	−15.0494	−0.870331
$300$	0.752243	0.0434308
$301$	−4.19221	−0.241635
$302$	−25.9409	−1.49273
$303$	−14.8675	−0.854114
$304$	19.3039	1.10715
$305$	0.812990	0.0465517
$306$	−2.41759	−0.138204
$307$	18.1935	1.03836	0.519180	−	0.854665i	$-0.326237\pi$
$307$	18.1935	1.03836	0.519180	+	0.854665i	$0.326237\pi$
$308$	−2.06955	−0.117924
$309$	13.8144	0.785873
$310$	−2.94589	−0.167316
$311$	−21.8772	−1.24054	−0.620272	−	0.784387i	$-0.712978\pi$
$311$	−21.8772	−1.24054	−0.620272	+	0.784387i	$0.712978\pi$
$312$	−19.4312	−1.10008
$313$	−20.8446	−1.17821	−0.589105	−	0.808057i	$-0.700519\pi$
$313$	−20.8446	−1.17821	−0.589105	+	0.808057i	$0.700519\pi$
$314$	−14.7372	−0.831667
$315$	−1.40293	−0.0790462
$316$	−0.273711	−0.0153974
$317$	6.67182	0.374727	0.187363	−	0.982291i	$-0.440006\pi$
$317$	6.67182	0.374727	0.187363	+	0.982291i	$0.440006\pi$
$318$	0.651041	0.0365086
$319$	−40.5318	−2.26935
$320$	2.33397	0.130473
$321$	19.0035	1.06067
$322$	−8.69287	−0.484435
$323$	−4.89352	−0.272283
$324$	−0.0442717	−0.00245954
$325$	−31.2137	−1.73143
$326$	−20.9460	−1.16009
$327$	−7.09854	−0.392550
$328$	−11.0715	−0.611320
$329$	29.2526	1.61275
$330$	2.07565	0.114261
$331$	14.9192	0.820035	0.410017	−	0.912078i	$-0.365523\pi$
$331$	14.9192	0.820035	0.410017	+	0.912078i	$0.365523\pi$
$332$	−1.54978	−0.0850550
$333$	−3.54588	−0.194313
$334$	28.2537	1.54597
$335$	−3.86593	−0.211218
$336$	−10.4025	−0.567504
$337$	18.2072	0.991809	0.495905	−	0.868377i	$-0.334837\pi$
$337$	18.2072	0.991809	0.495905	+	0.868377i	$0.334837\pi$
$338$	37.0074	2.01294
$339$	−8.72503	−0.473879
$340$	−0.0373946	−0.00202801
$341$	−41.6277	−2.25426
$342$	13.5380	0.732052
$343$	−18.2058	−0.983020
$344$	4.55585	0.245635
$345$	−0.684483	−0.0368513
$346$	25.1120	1.35003
$347$	5.35699	0.287578	0.143789	−	0.989608i	$-0.454071\pi$
$347$	5.35699	0.287578	0.143789	+	0.989608i	$0.454071\pi$
$348$	1.17102	0.0627735
$349$	1.00000	0.0535288
$349$	1.00000	0.0535288
$350$	−18.0297	−0.963730
$351$	−32.5814	−1.73907
$352$	4.34553	0.231617
$353$	15.3056	0.814635	0.407318	−	0.913287i	$-0.366464\pi$
$353$	15.3056	0.814635	0.407318	+	0.913287i	$0.366464\pi$
$354$	−12.0067	−0.638149
$355$	0.105148	0.00558067
$356$	−0.269461	−0.0142814
$357$	2.63703	0.139567
$358$	24.3689	1.28794
$359$	33.7746	1.78256	0.891278	−	0.453456i	$-0.149809\pi$
$359$	33.7746	1.78256	0.891278	+	0.453456i	$0.149809\pi$
$360$	1.52462	0.0803546
$361$	8.40277	0.442251
$362$	1.12134	0.0589361
$363$	17.7890	0.933683
$364$	−2.48104	−0.130042
$365$	3.87176	0.202657
$366$	4.22764	0.220982
$367$	10.0801	0.526176	0.263088	−	0.964772i	$-0.415259\pi$
$367$	10.0801	0.526176	0.263088	+	0.964772i	$0.415259\pi$
$368$	8.75555	0.456415
$369$	−7.19632	−0.374626
$370$	0.698602	0.0363186
$371$	1.22507	0.0636025
$372$	1.20268	0.0623563
$373$	−13.9977	−0.724771	−0.362386	−	0.932028i	$-0.618038\pi$
$373$	−13.9977	−0.724771	−0.362386	+	0.932028i	$0.618038\pi$
$374$	6.73059	0.348030
$375$	−2.86111	−0.147747
$376$	−31.7899	−1.63944
$377$	−48.5908	−2.50255
$378$	−18.8197	−0.967983
$379$	17.5615	0.902073	0.451037	−	0.892505i	$-0.351054\pi$
$379$	17.5615	0.902073	0.451037	+	0.892505i	$0.351054\pi$
$380$	0.209403	0.0107421
$381$	15.3261	0.785179
$382$	7.45582	0.381473
$383$	−28.2600	−1.44402	−0.722008	−	0.691885i	$-0.756781\pi$
$383$	−28.2600	−1.44402	−0.722008	+	0.691885i	$0.756781\pi$
$384$	10.4122	0.531345
$385$	3.90577	0.199057
$386$	11.2678	0.573515
$387$	2.96125	0.150529
$388$	1.75328	0.0890091
$389$	−30.8180	−1.56253	−0.781267	−	0.624197i	$-0.785426\pi$
$389$	−30.8180	−1.56253	−0.781267	+	0.624197i	$0.785426\pi$
$390$	2.48835	0.126003
$391$	−2.21953	−0.112246
$392$	−0.667579	−0.0337178
$393$	−4.01462	−0.202511
$394$	23.1031	1.16392
$395$	0.516562	0.0259910
$396$	1.46187	0.0734616
$397$	−14.2282	−0.714093	−0.357047	−	0.934087i	$-0.616216\pi$
$397$	−14.2282	−0.714093	−0.357047	+	0.934087i	$0.616216\pi$
$398$	−12.7526	−0.639230
$399$	−14.7669	−0.739269
$400$	18.1597	0.907987
$401$	11.7797	0.588250	0.294125	−	0.955767i	$-0.404972\pi$
$401$	11.7797	0.588250	0.294125	+	0.955767i	$0.404972\pi$
$402$	−20.1033	−1.00266
$403$	−49.9045	−2.48592
$404$	2.06299	0.102638
$405$	0.0835520	0.00415173
$406$	−28.0671	−1.39294
$407$	9.87177	0.489325
$408$	−2.86577	−0.141877
$409$	1.76812	0.0874277	0.0437138	−	0.999044i	$-0.486081\pi$
$409$	1.76812	0.0874277	0.0437138	+	0.999044i	$0.486081\pi$
$410$	1.41781	0.0700204
$411$	−7.38909	−0.364477
$412$	−1.91686	−0.0944371
$413$	−22.5931	−1.11173
$414$	6.14037	0.301783
$415$	2.92482	0.143574
$416$	5.20955	0.255419
$417$	−0.564896	−0.0276631
$418$	−37.6900	−1.84348
$419$	14.4021	0.703589	0.351794	−	0.936077i	$-0.385572\pi$
$419$	14.4021	0.703589	0.351794	+	0.936077i	$0.385572\pi$
$420$	−0.112844	−0.00550620
$421$	5.79931	0.282641	0.141321	−	0.989964i	$-0.454865\pi$
$421$	5.79931	0.282641	0.141321	+	0.989964i	$0.454865\pi$
$422$	17.3649	0.845311
$423$	−20.6631	−1.00467
$424$	−1.33133	−0.0646553
$425$	−4.60348	−0.223302
$426$	0.546781	0.0264916
$427$	7.95520	0.384979
$428$	−2.63689	−0.127459
$429$	35.1623	1.69765
$430$	−0.583419	−0.0281350
$431$	12.7866	0.615908	0.307954	−	0.951401i	$-0.400356\pi$
$431$	12.7866	0.615908	0.307954	+	0.951401i	$0.400356\pi$
$432$	18.9554	0.911994
$433$	−17.9281	−0.861571	−0.430786	−	0.902454i	$-0.641764\pi$
$433$	−17.9281	−0.861571	−0.430786	+	0.902454i	$0.641764\pi$
$434$	−28.8259	−1.38369
$435$	−2.21002	−0.105962
$436$	0.984982	0.0471721
$437$	12.4289	0.594557
$438$	20.1336	0.962020
$439$	6.43613	0.307180	0.153590	−	0.988135i	$-0.450917\pi$
$439$	6.43613	0.307180	0.153590	+	0.988135i	$0.450917\pi$
$440$	−4.24456	−0.202352
$441$	−0.433918	−0.0206628
$442$	8.06883	0.383795
$443$	39.2497	1.86481	0.932405	−	0.361416i	$-0.117707\pi$
$443$	39.2497	1.86481	0.932405	+	0.361416i	$0.117707\pi$
$444$	−0.285210	−0.0135355
$445$	0.508541	0.0241071
$446$	8.05779	0.381547
$447$	−5.92069	−0.280039
$448$	22.8381	1.07900
$449$	−5.33568	−0.251806	−0.125903	−	0.992043i	$-0.540183\pi$
$449$	−5.33568	−0.251806	−0.125903	+	0.992043i	$0.540183\pi$
$450$	12.7356	0.600363
$451$	20.0346	0.943394
$452$	1.21067	0.0569452
$453$	−19.9871	−0.939077
$454$	23.1436	1.08618
$455$	4.68236	0.219512
$456$	16.0478	0.751506
$457$	−12.8095	−0.599205	−0.299603	−	0.954064i	$-0.596854\pi$
$457$	−12.8095	−0.599205	−0.299603	+	0.954064i	$0.596854\pi$
$458$	−26.0837	−1.21881
$459$	−4.80519	−0.224287
$460$	0.0949778	0.00442836
$461$	−6.16450	−0.287109	−0.143555	−	0.989642i	$-0.545853\pi$
$461$	−6.16450	−0.287109	−0.143555	+	0.989642i	$0.545853\pi$
$462$	20.3105	0.944929
$463$	−20.0736	−0.932897	−0.466449	−	0.884548i	$-0.654467\pi$
$463$	−20.0736	−0.932897	−0.466449	+	0.884548i	$0.654467\pi$
$464$	28.2694	1.31238
$465$	−2.26977	−0.105258
$466$	8.17328	0.378620
$467$	−0.209683	−0.00970299	−0.00485149	−	0.999988i	$-0.501544\pi$
$467$	−0.209683	−0.00970299	−0.00485149	+	0.999988i	$0.501544\pi$
$468$	1.75253	0.0810107
$469$	−37.8285	−1.74676
$470$	4.07100	0.187781
$471$	−11.3548	−0.523201
$472$	24.5529	1.13014
$473$	−8.24414	−0.379066
$474$	2.68618	0.123380
$475$	25.7786	1.18280
$476$	−0.365911	−0.0167715
$477$	−0.865351	−0.0396217
$478$	−2.73499	−0.125096
$479$	8.03905	0.367314	0.183657	−	0.982990i	$-0.441206\pi$
$479$	8.03905	0.367314	0.183657	+	0.982990i	$0.441206\pi$
$480$	0.236942	0.0108149
$481$	11.8346	0.539610
$482$	−33.4598	−1.52405
$483$	−6.69774	−0.304758
$484$	−2.46838	−0.112199
$485$	−3.30888	−0.150248
$486$	21.4341	0.972270
$487$	8.58410	0.388983	0.194491	−	0.980904i	$-0.437694\pi$
$487$	8.58410	0.388983	0.194491	+	0.980904i	$0.437694\pi$
$488$	−8.64524	−0.391352
$489$	−16.1386	−0.729814
$490$	0.0854898	0.00386203
$491$	4.65183	0.209934	0.104967	−	0.994476i	$-0.466526\pi$
$491$	4.65183	0.209934	0.104967	+	0.994476i	$0.466526\pi$
$492$	−0.578830	−0.0260957
$493$	−7.16629	−0.322754
$494$	−45.1839	−2.03292
$495$	−2.75892	−0.124004
$496$	29.0337	1.30365
$497$	1.02888	0.0461517
$498$	15.2094	0.681550
$499$	17.1529	0.767870	0.383935	−	0.923360i	$-0.374569\pi$
$499$	17.1529	0.767870	0.383935	+	0.923360i	$0.374569\pi$
$500$	0.397003	0.0177545
$501$	21.7691	0.972571
$502$	3.14758	0.140483
$503$	−8.84851	−0.394536	−0.197268	−	0.980350i	$-0.563207\pi$
$503$	−8.84851	−0.394536	−0.197268	+	0.980350i	$0.563207\pi$
$504$	14.9186	0.664527
$505$	−3.89338	−0.173253
$506$	−17.0949	−0.759959
$507$	28.5137	1.26634
$508$	−2.12662	−0.0943537
$509$	−4.58842	−0.203378	−0.101689	−	0.994816i	$-0.532425\pi$
$509$	−4.58842	−0.203378	−0.101689	+	0.994816i	$0.532425\pi$
$510$	0.366989	0.0162505
$511$	37.8856	1.67596
$512$	−24.5798	−1.08628
$513$	26.9082	1.18802
$514$	−26.4963	−1.16870
$515$	3.61761	0.159411
$516$	0.238185	0.0104855
$517$	57.5262	2.53000
$518$	6.83590	0.300352
$519$	19.3485	0.849304
$520$	−5.08851	−0.223146
$521$	1.49371	0.0654406	0.0327203	−	0.999465i	$-0.489583\pi$
$521$	1.49371	0.0654406	0.0327203	+	0.999465i	$0.489583\pi$
$522$	19.8257	0.867747
$523$	−10.7786	−0.471314	−0.235657	−	0.971836i	$-0.575724\pi$
$523$	−10.7786	−0.471314	−0.235657	+	0.971836i	$0.575724\pi$
$524$	0.557063	0.0243354
$525$	−13.8917	−0.606282
$526$	−2.06234	−0.0899222
$527$	−7.36004	−0.320608
$528$	−20.4569	−0.890274
$529$	−17.3627	−0.754899
$530$	0.170490	0.00740560
$531$	15.9591	0.692564
$532$	2.04903	0.0888367
$533$	24.0181	1.04034
$534$	2.64447	0.114437
$535$	4.97649	0.215152
$536$	41.1098	1.77567
$537$	18.7759	0.810240
$538$	15.8476	0.683236
$539$	1.20803	0.0520337
$540$	0.205623	0.00884862
$541$	−0.518112	−0.0222754	−0.0111377	−	0.999938i	$-0.503545\pi$
$541$	−0.518112	−0.0222754	−0.0111377	+	0.999938i	$0.503545\pi$
$542$	−44.1456	−1.89622
$543$	0.863974	0.0370767
$544$	0.768318	0.0329413
$545$	−1.85891	−0.0796270
$546$	24.3488	1.04203
$547$	−4.12110	−0.176205	−0.0881027	−	0.996111i	$-0.528080\pi$
$547$	−4.12110	−0.176205	−0.0881027	+	0.996111i	$0.528080\pi$
$548$	1.02530	0.0437986
$549$	−5.61930	−0.239826
$550$	−35.4561	−1.51185
$551$	40.1299	1.70959
$552$	7.27871	0.309802
$553$	5.05461	0.214944
$554$	2.79335	0.118678
$555$	0.538264	0.0228480
$556$	0.0783842	0.00332423
$557$	20.8863	0.884980	0.442490	−	0.896773i	$-0.354095\pi$
$557$	20.8863	0.884980	0.442490	+	0.896773i	$0.354095\pi$
$558$	20.3617	0.861979
$559$	−9.88332	−0.418020
$560$	−2.72413	−0.115116
$561$	5.18582	0.218946
$562$	42.7969	1.80528
$563$	−1.23261	−0.0519485	−0.0259742	−	0.999663i	$-0.508269\pi$
$563$	−1.23261	−0.0519485	−0.0259742	+	0.999663i	$0.508269\pi$
$564$	−1.66202	−0.0699836
$565$	−2.28485	−0.0961242
$566$	41.8316	1.75831
$567$	0.817565	0.0343345
$568$	−1.11813	−0.0469156
$569$	−33.8183	−1.41774	−0.708868	−	0.705342i	$-0.750794\pi$
$569$	−33.8183	−1.41774	−0.708868	+	0.705342i	$0.750794\pi$
$570$	−2.05507	−0.0860773
$571$	11.2206	0.469566	0.234783	−	0.972048i	$-0.424562\pi$
$571$	11.2206	0.469566	0.234783	+	0.972048i	$0.424562\pi$
$572$	−4.87906	−0.204004
$573$	5.74461	0.239985
$574$	13.8734	0.579064
$575$	11.6923	0.487602
$576$	−16.1321	−0.672172
$577$	9.36075	0.389693	0.194847	−	0.980834i	$-0.437579\pi$
$577$	9.36075	0.389693	0.194847	+	0.980834i	$0.437579\pi$
$578$	−21.9600	−0.913417
$579$	8.68168	0.360798
$580$	0.306659	0.0127333
$581$	28.6197	1.18735
$582$	−17.2065	−0.713234
$583$	2.40915	0.0997766
$584$	−41.1718	−1.70370
$585$	−3.30747	−0.136747
$586$	−11.5642	−0.477715
$587$	−30.4583	−1.25715	−0.628575	−	0.777749i	$-0.716362\pi$
$587$	−30.4583	−1.25715	−0.628575	+	0.777749i	$0.716362\pi$
$588$	−0.0349019	−0.00143933
$589$	41.2148	1.69823
$590$	−3.14422	−0.129446
$591$	17.8006	0.732219
$592$	−6.88519	−0.282980
$593$	−6.20667	−0.254877	−0.127439	−	0.991846i	$-0.540676\pi$
$593$	−6.20667	−0.254877	−0.127439	+	0.991846i	$0.540676\pi$
$594$	−37.0097	−1.51853
$595$	0.690566	0.0283105
$596$	0.821546	0.0336518
$597$	−9.82571	−0.402139
$598$	−20.4938	−0.838055
$599$	−32.4226	−1.32475	−0.662375	−	0.749172i	$-0.730451\pi$
$599$	−32.4226	−1.32475	−0.662375	+	0.749172i	$0.730451\pi$
$600$	15.0966	0.616317
$601$	13.4509	0.548673	0.274337	−	0.961634i	$-0.411542\pi$
$601$	13.4509	0.548673	0.274337	+	0.961634i	$0.411542\pi$
$602$	−5.70882	−0.232674
$603$	26.7209	1.08816
$604$	2.77338	0.112847
$605$	4.65846	0.189393
$606$	−20.2461	−0.822440
$607$	13.5215	0.548820	0.274410	−	0.961613i	$-0.411518\pi$
$607$	13.5215	0.548820	0.274410	+	0.961613i	$0.411518\pi$
$608$	−4.30243	−0.174487
$609$	−21.6253	−0.876301
$610$	1.10710	0.0448253
$611$	68.9642	2.78999
$612$	0.258468	0.0104479
$613$	−38.8059	−1.56736	−0.783678	−	0.621167i	$-0.786659\pi$
$613$	−38.8059	−1.56736	−0.783678	+	0.621167i	$0.786659\pi$
$614$	24.7754	0.999853
$615$	1.09240	0.0440498
$616$	−41.5335	−1.67343
$617$	25.3389	1.02011	0.510054	−	0.860143i	$-0.329626\pi$
$617$	25.3389	1.02011	0.510054	+	0.860143i	$0.329626\pi$
$618$	18.8120	0.756729
$619$	17.8397	0.717039	0.358519	−	0.933522i	$-0.383282\pi$
$619$	17.8397	0.717039	0.358519	+	0.933522i	$0.383282\pi$
$620$	0.314950	0.0126487
$621$	12.2046	0.489754
$622$	−29.7917	−1.19454
$623$	4.97612	0.199364
$624$	−24.5244	−0.981761
$625$	23.8733	0.954931
$626$	−28.3856	−1.13452
$627$	−29.0396	−1.15973
$628$	1.57557	0.0628722
$629$	1.74539	0.0695934
$630$	−1.91047	−0.0761148
$631$	0.667175	0.0265598	0.0132799	−	0.999912i	$-0.495773\pi$
$631$	0.667175	0.0265598	0.0132799	+	0.999912i	$0.495773\pi$
$632$	−5.49305	−0.218502
$633$	13.3794	0.531785
$634$	9.08547	0.360830
$635$	4.01348	0.159270
$636$	−0.0696038	−0.00275997
$637$	1.44823	0.0573808
$638$	−55.1949	−2.18519
$639$	−0.726770	−0.0287506
$640$	2.72667	0.107781
$641$	21.3419	0.842954	0.421477	−	0.906839i	$-0.361512\pi$
$641$	21.3419	0.842954	0.421477	+	0.906839i	$0.361512\pi$
$642$	25.8783	1.02134
$643$	−35.6804	−1.40710	−0.703550	−	0.710646i	$-0.748403\pi$
$643$	−35.6804	−1.40710	−0.703550	+	0.710646i	$0.748403\pi$
$644$	0.929368	0.0366222
$645$	−0.449516	−0.0176997
$646$	−6.66384	−0.262185
$647$	−21.8361	−0.858466	−0.429233	−	0.903194i	$-0.641216\pi$
$647$	−21.8361	−0.858466	−0.429233	+	0.903194i	$0.641216\pi$
$648$	−0.888482	−0.0349029
$649$	−44.4302	−1.74404
$650$	−42.5059	−1.66722
$651$	−22.2100	−0.870477
$652$	2.23937	0.0877006
$653$	−15.5468	−0.608394	−0.304197	−	0.952609i	$-0.598388\pi$
$653$	−15.5468	−0.608394	−0.304197	+	0.952609i	$0.598388\pi$
$654$	−9.66656	−0.377992
$655$	−1.05132	−0.0410784
$656$	−13.9734	−0.545570
$657$	−26.7612	−1.04405
$658$	39.8352	1.55294
$659$	10.8768	0.423700	0.211850	−	0.977302i	$-0.432051\pi$
$659$	10.8768	0.423700	0.211850	+	0.977302i	$0.432051\pi$
$660$	−0.221911	−0.00863788
$661$	−14.5282	−0.565080	−0.282540	−	0.959256i	$-0.591177\pi$
$661$	−14.5282	−0.565080	−0.282540	+	0.959256i	$0.591177\pi$
$662$	20.3165	0.789624
$663$	6.21692	0.241445
$664$	−31.1022	−1.20700
$665$	−3.86704	−0.149957
$666$	−4.82866	−0.187107
$667$	18.2015	0.704765
$668$	−3.02064	−0.116872
$669$	6.20842	0.240031
$670$	−5.26450	−0.203385
$671$	15.6442	0.603937
$672$	2.31851	0.0894383
$673$	43.9745	1.69509	0.847547	−	0.530720i	$-0.178079\pi$
$673$	43.9745	1.69509	0.847547	+	0.530720i	$0.178079\pi$
$674$	24.7940	0.955028
$675$	25.3133	0.974311
$676$	−3.95652	−0.152174
$677$	10.1472	0.389988	0.194994	−	0.980804i	$-0.437531\pi$
$677$	10.1472	0.389988	0.194994	+	0.980804i	$0.437531\pi$
$678$	−11.8815	−0.456305
$679$	−32.3777	−1.24254
$680$	−0.750467	−0.0287791
$681$	17.8318	0.683316
$682$	−56.6872	−2.17066
$683$	−28.7221	−1.09902	−0.549509	−	0.835488i	$-0.685185\pi$
$683$	−28.7221	−1.09902	−0.549509	+	0.835488i	$0.685185\pi$
$684$	−1.44737	−0.0553416
$685$	−1.93500	−0.0739326
$686$	−24.7921	−0.946565
$687$	−20.0971	−0.766754
$688$	5.74998	0.219216
$689$	2.88816	0.110030
$690$	−0.932106	−0.0354847
$691$	10.1161	0.384836	0.192418	−	0.981313i	$-0.438367\pi$
$691$	10.1161	0.384836	0.192418	+	0.981313i	$0.438367\pi$
$692$	−2.68476	−0.102059
$693$	−26.9963	−1.02550
$694$	7.29498	0.276914
$695$	−0.147931	−0.00561134
$696$	23.5011	0.890806
$697$	3.54226	0.134172
$698$	1.36177	0.0515437
$699$	6.29740	0.238190
$700$	1.92759	0.0728559
$701$	12.5417	0.473692	0.236846	−	0.971547i	$-0.423886\pi$
$701$	12.5417	0.473692	0.236846	+	0.971547i	$0.423886\pi$
$702$	−44.3683	−1.67458
$703$	−9.77387	−0.368628
$704$	44.9120	1.69269
$705$	3.13665	0.118133
$706$	20.8427	0.784425
$707$	−38.0972	−1.43279
$708$	1.28365	0.0482427
$709$	−45.0992	−1.69374	−0.846868	−	0.531804i	$-0.821514\pi$
$709$	−45.0992	−1.69374	−0.846868	+	0.531804i	$0.821514\pi$
$710$	0.143187	0.00537371
$711$	−3.57042	−0.133901
$712$	−5.40776	−0.202664
$713$	18.6936	0.700081
$714$	3.59103	0.134391
$715$	9.20803	0.344361
$716$	−2.60531	−0.0973652
$717$	−2.10727	−0.0786976
$718$	45.9932	1.71645
$719$	8.05107	0.300254	0.150127	−	0.988667i	$-0.452032\pi$
$719$	8.05107	0.300254	0.150127	+	0.988667i	$0.452032\pi$
$720$	1.92424	0.0717123
$721$	35.3987	1.31832
$722$	11.4426	0.425850
$723$	−25.7803	−0.958779
$724$	−0.119884	−0.00445544
$725$	37.7514	1.40205
$726$	24.2245	0.899057
$727$	−35.7126	−1.32451	−0.662254	−	0.749279i	$-0.730400\pi$
$727$	−35.7126	−1.32451	−0.662254	+	0.749279i	$0.730400\pi$
$728$	−49.7916	−1.84540
$729$	15.6024	0.577867
$730$	5.27243	0.195141
$731$	−1.45762	−0.0539119
$732$	−0.451984	−0.0167058
$733$	−38.7538	−1.43140	−0.715701	−	0.698407i	$-0.753893\pi$
$733$	−38.7538	−1.43140	−0.715701	+	0.698407i	$0.753893\pi$
$734$	13.7267	0.506663
$735$	0.0658687	0.00242960
$736$	−1.95143	−0.0719307
$737$	−74.3913	−2.74024
$738$	−9.79972	−0.360733
$739$	15.9197	0.585617	0.292808	−	0.956171i	$-0.405410\pi$
$739$	15.9197	0.585617	0.292808	+	0.956171i	$0.405410\pi$
$740$	−0.0746886	−0.00274561
$741$	−34.8136	−1.27891
$742$	1.66826	0.0612438
$743$	−1.85088	−0.0679021	−0.0339510	−	0.999423i	$-0.510809\pi$
$743$	−1.85088	−0.0679021	−0.0339510	+	0.999423i	$0.510809\pi$
$744$	24.1365	0.884886
$745$	−1.55047	−0.0568047
$746$	−19.0616	−0.697893
$747$	−20.2161	−0.739667
$748$	−0.719577	−0.0263103
$749$	48.6955	1.77929
$750$	−3.89617	−0.142268
$751$	33.7927	1.23311	0.616557	−	0.787311i	$-0.288527\pi$
$751$	33.7927	1.23311	0.616557	+	0.787311i	$0.288527\pi$
$752$	−40.1224	−1.46311
$753$	2.42517	0.0883781
$754$	−66.1693	−2.40974
$755$	−5.23408	−0.190488
$756$	2.01205	0.0731774
$757$	12.8536	0.467171	0.233586	−	0.972336i	$-0.424954\pi$
$757$	12.8536	0.467171	0.233586	+	0.972336i	$0.424954\pi$
$758$	23.9147	0.868620
$759$	−13.1714	−0.478090
$760$	4.20247	0.152440
$761$	−51.6843	−1.87356	−0.936778	−	0.349925i	$-0.886207\pi$
$761$	−51.6843	−1.87356	−0.936778	+	0.349925i	$0.886207\pi$
$762$	20.8706	0.756061
$763$	−18.1897	−0.658510
$764$	−0.797113	−0.0288385
$765$	−0.487794	−0.0176362
$766$	−38.4835	−1.39047
$767$	−53.2642	−1.92326
$768$	−3.64622	−0.131572
$769$	2.85556	0.102974	0.0514871	−	0.998674i	$-0.483604\pi$
$769$	2.85556	0.102974	0.0514871	+	0.998674i	$0.483604\pi$
$770$	5.31876	0.191675
$771$	−20.4150	−0.735229
$772$	−1.20466	−0.0433565
$773$	0.230496	0.00829038	0.00414519	−	0.999991i	$-0.498681\pi$
$773$	0.230496	0.00829038	0.00414519	+	0.999991i	$0.498681\pi$
$774$	4.03253	0.144946
$775$	38.7720	1.39273
$776$	35.1862	1.26311
$777$	5.26697	0.188951
$778$	−41.9669	−1.50459
$779$	−19.8360	−0.710697
$780$	−0.266034	−0.00952553
$781$	2.02334	0.0724007
$782$	−3.02248	−0.108084
$783$	39.4055	1.40824
$784$	−0.842559	−0.0300914
$785$	−2.97351	−0.106129
$786$	−5.46698	−0.195001
$787$	6.94161	0.247442	0.123721	−	0.992317i	$-0.460517\pi$
$787$	6.94161	0.247442	0.123721	+	0.992317i	$0.460517\pi$
$788$	−2.46999	−0.0879896
$789$	−1.58900	−0.0565700
$790$	0.703437	0.0250272
$791$	−22.3575	−0.794940
$792$	29.3380	1.04248
$793$	18.7547	0.666000
$794$	−19.3755	−0.687611
$795$	0.131360	0.00465886
$796$	1.36340	0.0483244
$797$	31.0384	1.09944	0.549718	−	0.835350i	$-0.314735\pi$
$797$	31.0384	1.09944	0.549718	+	0.835350i	$0.314735\pi$
$798$	−20.1091	−0.711853
$799$	10.1710	0.359825
$800$	−4.04743	−0.143098
$801$	−3.51498	−0.124196
$802$	16.0412	0.566435
$803$	74.5034	2.62917
$804$	2.14927	0.0757990
$805$	−1.75395	−0.0618187
$806$	−67.9583	−2.39373
$807$	12.2103	0.429824
$808$	41.4018	1.45651
$809$	24.3560	0.856311	0.428156	−	0.903705i	$-0.359164\pi$
$809$	24.3560	0.856311	0.428156	+	0.903705i	$0.359164\pi$
$810$	0.113778	0.00399777
$811$	−10.4118	−0.365609	−0.182804	−	0.983149i	$-0.558517\pi$
$811$	−10.4118	−0.365609	−0.182804	+	0.983149i	$0.558517\pi$
$812$	3.00069	0.105304
$813$	−34.0136	−1.19291
$814$	13.4431	0.471179
$815$	−4.22627	−0.148040
$816$	−3.61692	−0.126618
$817$	8.16238	0.285566
$818$	2.40776	0.0841854
$819$	−32.3640	−1.13089
$820$	−0.151580	−0.00529339
$821$	−32.5693	−1.13668	−0.568338	−	0.822795i	$-0.692413\pi$
$821$	−32.5693	−1.13668	−0.568338	+	0.822795i	$0.692413\pi$
$822$	−10.0622	−0.350961
$823$	25.0969	0.874822	0.437411	−	0.899262i	$-0.355895\pi$
$823$	25.0969	0.874822	0.437411	+	0.899262i	$0.355895\pi$
$824$	−38.4692	−1.34014
$825$	−27.3185	−0.951107
$826$	−30.7666	−1.07051
$827$	−35.0843	−1.22000	−0.610000	−	0.792401i	$-0.708831\pi$
$827$	−35.0843	−1.22000	−0.610000	+	0.792401i	$0.708831\pi$
$828$	−0.656476	−0.0228141
$829$	18.6148	0.646519	0.323260	−	0.946310i	$-0.395221\pi$
$829$	18.6148	0.646519	0.323260	+	0.946310i	$0.395221\pi$
$830$	3.98293	0.138249
$831$	2.15224	0.0746604
$832$	53.8419	1.86663
$833$	0.213588	0.00740039
$834$	−0.769258	−0.0266372
$835$	5.70072	0.197282
$836$	4.02949	0.139363
$837$	40.4709	1.39888
$838$	19.6123	0.677496
$839$	−29.7765	−1.02800	−0.514000	−	0.857790i	$-0.671837\pi$
$839$	−29.7765	−1.02800	−0.514000	+	0.857790i	$0.671837\pi$
$840$	−2.26464	−0.0781374
$841$	29.7680	1.02648
$842$	7.89731	0.272159
$843$	32.9744	1.13570
$844$	−1.85651	−0.0639037
$845$	7.46695	0.256871
$846$	−28.1383	−0.967415
$847$	45.5836	1.56627
$848$	−1.68029	−0.0577014
$849$	32.2307	1.10615
$850$	−6.26888	−0.215021
$851$	−4.43308	−0.151964
$852$	−0.0584572	−0.00200271
$853$	2.89238	0.0990333	0.0495167	−	0.998773i	$-0.484232\pi$
$853$	2.89238	0.0990333	0.0495167	+	0.998773i	$0.484232\pi$
$854$	10.8331	0.370702
$855$	2.73155	0.0934172
$856$	−52.9194	−1.80875
$857$	32.9889	1.12688	0.563439	−	0.826157i	$-0.309478\pi$
$857$	32.9889	1.12688	0.563439	+	0.826157i	$0.309478\pi$
$858$	47.8829	1.63469
$859$	22.1747	0.756591	0.378295	−	0.925685i	$-0.376510\pi$
$859$	22.1747	0.756591	0.378295	+	0.925685i	$0.376510\pi$
$860$	0.0623742	0.00212694
$861$	10.6893	0.364289
$862$	17.4124	0.593068
$863$	−12.8414	−0.437128	−0.218564	−	0.975823i	$-0.570137\pi$
$863$	−12.8414	−0.437128	−0.218564	+	0.975823i	$0.570137\pi$
$864$	−4.22478	−0.143730
$865$	5.06683	0.172278
$866$	−24.4140	−0.829620
$867$	−16.9199	−0.574630
$868$	3.08182	0.104604
$869$	9.94009	0.337194
$870$	−3.00953	−0.102033
$871$	−89.1824	−3.02183
$872$	19.7674	0.669410
$873$	22.8706	0.774052
$874$	16.9253	0.572508
$875$	−7.33146	−0.247848
$876$	−2.15251	−0.0727266
$877$	41.2240	1.39204	0.696018	−	0.718024i	$-0.254953\pi$
$877$	41.2240	1.39204	0.696018	+	0.718024i	$0.254953\pi$
$878$	8.76451	0.295788
$879$	−8.91009	−0.300530
$880$	−5.35711	−0.180588
$881$	−10.7363	−0.361714	−0.180857	−	0.983509i	$-0.557887\pi$
$881$	−10.7363	−0.361714	−0.180857	+	0.983509i	$0.557887\pi$
$882$	−0.590896	−0.0198965
$883$	46.8825	1.57772	0.788861	−	0.614571i	$-0.210671\pi$
$883$	46.8825	1.57772	0.788861	+	0.614571i	$0.210671\pi$
$884$	−0.862650	−0.0290141
$885$	−2.42258	−0.0814342
$886$	53.4490	1.79565
$887$	−14.3544	−0.481975	−0.240988	−	0.970528i	$-0.577471\pi$
$887$	−14.3544	−0.481975	−0.240988	+	0.970528i	$0.577471\pi$
$888$	−5.72383	−0.192079
$889$	39.2724	1.31715
$890$	0.692514	0.0232131
$891$	1.60777	0.0538624
$892$	−0.861471	−0.0288442
$893$	−56.9557	−1.90595
$894$	−8.06260	−0.269654
$895$	4.91689	0.164354
$896$	26.6808	0.891342
$897$	−15.7902	−0.527220
$898$	−7.26596	−0.242468
$899$	60.3568	2.01301
$900$	−1.36159	−0.0453862
$901$	0.425953	0.0141905
$902$	27.2825	0.908409
$903$	−4.39857	−0.146375
$904$	24.2968	0.808099
$905$	0.226251	0.00752084
$906$	−27.2178	−0.904251
$907$	25.2827	0.839498	0.419749	−	0.907640i	$-0.362118\pi$
$907$	25.2827	0.839498	0.419749	+	0.907640i	$0.362118\pi$
$908$	−2.47431	−0.0821130
$909$	26.9106	0.892570
$910$	6.37629	0.211372
$911$	−11.7851	−0.390458	−0.195229	−	0.980758i	$-0.562545\pi$
$911$	−11.7851	−0.390458	−0.195229	+	0.980758i	$0.562545\pi$
$912$	20.2541	0.670679
$913$	56.2817	1.86265
$914$	−17.4436	−0.576984
$915$	0.853008	0.0281996
$916$	2.78865	0.0921396
$917$	−10.2873	−0.339716
$918$	−6.54356	−0.215970
$919$	44.1136	1.45517	0.727587	−	0.686015i	$-0.240642\pi$
$919$	44.1136	1.45517	0.727587	+	0.686015i	$0.240642\pi$
$920$	1.90609	0.0628420
$921$	19.0891	0.629007
$922$	−8.39462	−0.276462
$923$	2.42564	0.0798408
$924$	−2.17142	−0.0714346
$925$	−9.19458	−0.302316
$926$	−27.3355	−0.898301
$927$	−25.0045	−0.821256
$928$	−6.30067	−0.206830
$929$	0.515661	0.0169183	0.00845915	−	0.999964i	$-0.497307\pi$
$929$	0.515661	0.0169183	0.00845915	+	0.999964i	$0.497307\pi$
$930$	−3.09090	−0.101355
$931$	−1.19605	−0.0391991
$932$	−0.873818	−0.0286229
$933$	−22.9541	−0.751483
$934$	−0.285540	−0.00934316
$935$	1.35802	0.0444122
$936$	35.1712	1.14961
$937$	−18.8512	−0.615840	−0.307920	−	0.951412i	$-0.599633\pi$
$937$	−18.8512	−0.615840	−0.307920	+	0.951412i	$0.599633\pi$
$938$	−51.5137	−1.68198
$939$	−21.8707	−0.713723
$940$	−0.435237	−0.0141959
$941$	−1.88438	−0.0614291	−0.0307146	−	0.999528i	$-0.509778\pi$
$941$	−1.88438	−0.0614291	−0.0307146	+	0.999528i	$0.509778\pi$
$942$	−15.4626	−0.503798
$943$	−8.99689	−0.292979
$944$	30.9884	1.00859
$945$	−3.79724	−0.123524
$946$	−11.2266	−0.365008
$947$	−20.9256	−0.679990	−0.339995	−	0.940427i	$-0.610425\pi$
$947$	−20.9256	−0.679990	−0.339995	+	0.940427i	$0.610425\pi$
$948$	−0.287184	−0.00932729
$949$	89.3168	2.89935
$950$	35.1045	1.13894
$951$	7.00023	0.226998
$952$	−7.34340	−0.238001
$953$	−30.5495	−0.989595	−0.494798	−	0.869008i	$-0.664758\pi$
$953$	−30.5495	−0.989595	−0.494798	+	0.869008i	$0.664758\pi$
$954$	−1.17841	−0.0381523
$955$	1.50436	0.0486798
$956$	0.292402	0.00945696
$957$	−42.5269	−1.37470
$958$	10.9473	0.353692
$959$	−18.9342	−0.611417
$960$	2.44885	0.0790364
$961$	30.9887	0.999634
$962$	16.1159	0.519599
$963$	−34.3969	−1.10843
$964$	3.57723	0.115215
$965$	2.27349	0.0731863
$966$	−9.12076	−0.293456
$967$	−36.6255	−1.17780	−0.588898	−	0.808208i	$-0.700438\pi$
$967$	−36.6255	−1.17780	−0.588898	+	0.808208i	$0.700438\pi$
$968$	−49.5375	−1.59220
$969$	−5.13439	−0.164940
$970$	−4.50592	−0.144676
$971$	−19.6496	−0.630586	−0.315293	−	0.948994i	$-0.602103\pi$
$971$	−19.6496	−0.630586	−0.315293	+	0.948994i	$0.602103\pi$
$972$	−2.29155	−0.0735015
$973$	−1.44752	−0.0464053
$974$	11.6896	0.374557
$975$	−32.7502	−1.04885
$976$	−10.9112	−0.349261
$977$	−33.3201	−1.06601	−0.533003	−	0.846114i	$-0.678936\pi$
$977$	−33.3201	−1.06601	−0.533003	+	0.846114i	$0.678936\pi$
$978$	−21.9771	−0.702749
$979$	9.78574	0.312753
$980$	−0.00913984	−0.000291961 0
$981$	12.8486	0.410224
$982$	6.33472	0.202149
$983$	−28.7176	−0.915950	−0.457975	−	0.888965i	$-0.651425\pi$
$983$	−28.7176	−0.915950	−0.457975	+	0.888965i	$0.651425\pi$
$984$	−11.6164	−0.370319
$985$	4.66149	0.148527
$986$	−9.75882	−0.310784
$987$	30.6925	0.976952
$988$	4.83068	0.153684
$989$	3.70217	0.117722
$990$	−3.75700	−0.119405
$991$	−37.9143	−1.20439	−0.602194	−	0.798350i	$-0.705707\pi$
$991$	−37.9143	−1.20439	−0.602194	+	0.798350i	$0.705707\pi$
$992$	−6.47102	−0.205455
$993$	15.6536	0.496752
$994$	1.40110	0.0444402
$995$	−2.57308	−0.0815722
$996$	−1.62606	−0.0515237
$997$	−52.0573	−1.64867	−0.824335	−	0.566102i	$-0.808451\pi$
$997$	−52.0573	−1.64867	−0.824335	+	0.566102i	$0.808451\pi$
$998$	23.3583	0.739394
$999$	−9.59746	−0.303650

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	349.2.a.b.1.11	✓	17
3.2	odd	2		3141.2.a.e.1.7		17
4.3	odd	2		5584.2.a.m.1.9		17
5.4	even	2		8725.2.a.m.1.7		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.2.a.b.1.11	✓	17	1.1	even	1	trivial
3141.2.a.e.1.7		17	3.2	odd	2
5584.2.a.m.1.9		17	4.3	odd	2
8725.2.a.m.1.7		17	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)

\(f(q)\)	\(=\)	\(q+1.36177 q^{2} +1.04922 q^{3} -0.145589 q^{4} +0.274763 q^{5} +1.42880 q^{6} +2.68858 q^{7} -2.92179 q^{8} -1.89913 q^{9} +O(q^{10})\)	\(q+1.36177 q^{2} +1.04922 q^{3} -0.145589 q^{4} +0.274763 q^{5} +1.42880 q^{6} +2.68858 q^{7} -2.92179 q^{8} -1.89913 q^{9} +0.374163 q^{10} +5.28720 q^{11} -0.152755 q^{12} +6.33845 q^{13} +3.66123 q^{14} +0.288287 q^{15} -3.68763 q^{16} +0.934812 q^{17} -2.58617 q^{18} -5.23477 q^{19} -0.0400023 q^{20} +2.82092 q^{21} +7.19994 q^{22} -2.37431 q^{23} -3.06561 q^{24} -4.92451 q^{25} +8.63150 q^{26} -5.14028 q^{27} -0.391427 q^{28} -7.66603 q^{29} +0.392581 q^{30} -7.87329 q^{31} +0.821896 q^{32} +5.54745 q^{33} +1.27300 q^{34} +0.738723 q^{35} +0.276492 q^{36} +1.86711 q^{37} -7.12853 q^{38} +6.65045 q^{39} -0.802800 q^{40} +3.78927 q^{41} +3.84144 q^{42} -1.55926 q^{43} -0.769756 q^{44} -0.521810 q^{45} -3.23325 q^{46} +10.8803 q^{47} -3.86914 q^{48} +0.228483 q^{49} -6.70603 q^{50} +0.980826 q^{51} -0.922807 q^{52} +0.455656 q^{53} -6.99987 q^{54} +1.45273 q^{55} -7.85549 q^{56} -5.49244 q^{57} -10.4393 q^{58} -8.40335 q^{59} -0.0419714 q^{60} +2.95888 q^{61} -10.7216 q^{62} -5.10597 q^{63} +8.49448 q^{64} +1.74157 q^{65} +7.55434 q^{66} -14.0701 q^{67} -0.136098 q^{68} -2.49118 q^{69} +1.00597 q^{70} +0.382686 q^{71} +5.54887 q^{72} +14.0913 q^{73} +2.54257 q^{74} -5.16691 q^{75} +0.762122 q^{76} +14.2151 q^{77} +9.05637 q^{78} +1.88003 q^{79} -1.01322 q^{80} +0.304088 q^{81} +5.16011 q^{82} +10.6449 q^{83} -0.410695 q^{84} +0.256851 q^{85} -2.12336 q^{86} -8.04337 q^{87} -15.4481 q^{88} +1.85083 q^{89} -0.710584 q^{90} +17.0415 q^{91} +0.345672 q^{92} -8.26084 q^{93} +14.8164 q^{94} -1.43832 q^{95} +0.862352 q^{96} -12.0427 q^{97} +0.311140 q^{98} -10.0411 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 5 q^{2} + 6 q^{3} + 19 q^{4} + 5 q^{5} - 3 q^{6} + q^{7} + 9 q^{8} + 25 q^{9}+O(q^{10}) \) 17 * q + 5 * q^2 + 6 * q^3 + 19 * q^4 + 5 * q^5 - 3 * q^6 + q^7 + 9 * q^8 + 25 * q^9	\( 17 q + 5 q^{2} + 6 q^{3} + 19 q^{4} + 5 q^{5} - 3 q^{6} + q^{7} + 9 q^{8} + 25 q^{9} - 6 q^{10} + 39 q^{11} + 4 q^{12} - 6 q^{13} + 11 q^{14} + 12 q^{15} + 23 q^{16} + q^{17} + 7 q^{19} + 8 q^{20} - 3 q^{21} - q^{22} + 8 q^{23} - 21 q^{24} + 14 q^{25} + q^{26} + 9 q^{27} - 23 q^{28} + 9 q^{29} - 27 q^{30} - 2 q^{31} + 23 q^{32} - 5 q^{33} - 12 q^{34} + 16 q^{35} + 10 q^{36} - 7 q^{37} - 8 q^{38} - 39 q^{40} + 3 q^{41} - 30 q^{42} + q^{43} + 56 q^{44} - 21 q^{45} - q^{46} + 16 q^{47} - 31 q^{48} + 6 q^{49} - 5 q^{50} + 29 q^{51} - 37 q^{52} + 27 q^{53} - 36 q^{54} - 16 q^{55} + 14 q^{56} - 21 q^{57} - 44 q^{58} + 74 q^{59} - 27 q^{60} - 30 q^{61} - 18 q^{62} - 9 q^{63} - 17 q^{64} - 3 q^{65} - 66 q^{66} + 9 q^{67} - 51 q^{68} - 23 q^{69} - 77 q^{70} + 70 q^{71} - 55 q^{72} - 38 q^{73} + 26 q^{74} + 22 q^{75} - 50 q^{76} - 38 q^{77} - 75 q^{78} + 7 q^{79} - 28 q^{80} + 5 q^{81} - 56 q^{82} + 47 q^{83} - 69 q^{84} - 49 q^{85} + 17 q^{86} - 37 q^{87} - 30 q^{88} + 23 q^{89} - 64 q^{90} + 6 q^{91} + 17 q^{92} - 31 q^{93} - 40 q^{94} - 11 q^{95} - 49 q^{96} - 14 q^{97} + 5 q^{98} + 79 q^{99}+O(q^{100}) \) 17 * q + 5 * q^2 + 6 * q^3 + 19 * q^4 + 5 * q^5 - 3 * q^6 + q^7 + 9 * q^8 + 25 * q^9 - 6 * q^10 + 39 * q^11 + 4 * q^12 - 6 * q^13 + 11 * q^14 + 12 * q^15 + 23 * q^16 + q^17 + 7 * q^19 + 8 * q^20 - 3 * q^21 - q^22 + 8 * q^23 - 21 * q^24 + 14 * q^25 + q^26 + 9 * q^27 - 23 * q^28 + 9 * q^29 - 27 * q^30 - 2 * q^31 + 23 * q^32 - 5 * q^33 - 12 * q^34 + 16 * q^35 + 10 * q^36 - 7 * q^37 - 8 * q^38 - 39 * q^40 + 3 * q^41 - 30 * q^42 + q^43 + 56 * q^44 - 21 * q^45 - q^46 + 16 * q^47 - 31 * q^48 + 6 * q^49 - 5 * q^50 + 29 * q^51 - 37 * q^52 + 27 * q^53 - 36 * q^54 - 16 * q^55 + 14 * q^56 - 21 * q^57 - 44 * q^58 + 74 * q^59 - 27 * q^60 - 30 * q^61 - 18 * q^62 - 9 * q^63 - 17 * q^64 - 3 * q^65 - 66 * q^66 + 9 * q^67 - 51 * q^68 - 23 * q^69 - 77 * q^70 + 70 * q^71 - 55 * q^72 - 38 * q^73 + 26 * q^74 + 22 * q^75 - 50 * q^76 - 38 * q^77 - 75 * q^78 + 7 * q^79 - 28 * q^80 + 5 * q^81 - 56 * q^82 + 47 * q^83 - 69 * q^84 - 49 * q^85 + 17 * q^86 - 37 * q^87 - 30 * q^88 + 23 * q^89 - 64 * q^90 + 6 * q^91 + 17 * q^92 - 31 * q^93 - 40 * q^94 - 11 * q^95 - 49 * q^96 - 14 * q^97 + 5 * q^98 + 79 * q^99

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