LMFDB - Embedded newform 349.2.a.b.1.3

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			1.3
Root			$-1.99653$ 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)

$f(q)$	$=$	$q-1.99653 q^{2} +1.39055 q^{3} +1.98612 q^{4} -2.55061 q^{5} -2.77626 q^{6} -4.72921 q^{7} +0.0277164 q^{8} -1.06638 q^{9} +O(q^{10})$	\(q-1.99653 q^{2} +1.39055 q^{3} +1.98612 q^{4} -2.55061 q^{5} -2.77626 q^{6} -4.72921 q^{7} +0.0277164 q^{8} -1.06638 q^{9} +5.09235 q^{10} +6.31177 q^{11} +2.76179 q^{12} +4.90047 q^{13} +9.44199 q^{14} -3.54673 q^{15} -4.02757 q^{16} +5.32868 q^{17} +2.12906 q^{18} +5.28386 q^{19} -5.06581 q^{20} -6.57618 q^{21} -12.6016 q^{22} +2.28692 q^{23} +0.0385409 q^{24} +1.50560 q^{25} -9.78391 q^{26} -5.65449 q^{27} -9.39276 q^{28} +0.490308 q^{29} +7.08115 q^{30} +2.67489 q^{31} +7.98572 q^{32} +8.77681 q^{33} -10.6389 q^{34} +12.0624 q^{35} -2.11796 q^{36} -0.735772 q^{37} -10.5494 q^{38} +6.81432 q^{39} -0.0706936 q^{40} +4.70299 q^{41} +13.1295 q^{42} -10.4612 q^{43} +12.5359 q^{44} +2.71993 q^{45} -4.56590 q^{46} +3.20066 q^{47} -5.60052 q^{48} +15.3654 q^{49} -3.00596 q^{50} +7.40978 q^{51} +9.73291 q^{52} +0.220569 q^{53} +11.2893 q^{54} -16.0989 q^{55} -0.131077 q^{56} +7.34744 q^{57} -0.978912 q^{58} +8.86152 q^{59} -7.04423 q^{60} -3.78465 q^{61} -5.34049 q^{62} +5.04315 q^{63} -7.88856 q^{64} -12.4992 q^{65} -17.5231 q^{66} -1.29300 q^{67} +10.5834 q^{68} +3.18007 q^{69} -24.0828 q^{70} +0.475339 q^{71} -0.0295563 q^{72} -9.82860 q^{73} +1.46899 q^{74} +2.09360 q^{75} +10.4944 q^{76} -29.8497 q^{77} -13.6050 q^{78} +4.32881 q^{79} +10.2728 q^{80} -4.66367 q^{81} -9.38965 q^{82} +11.1595 q^{83} -13.0611 q^{84} -13.5914 q^{85} +20.8860 q^{86} +0.681795 q^{87} +0.174940 q^{88} +9.95000 q^{89} -5.43040 q^{90} -23.1753 q^{91} +4.54209 q^{92} +3.71956 q^{93} -6.39021 q^{94} -13.4770 q^{95} +11.1045 q^{96} +11.6004 q^{97} -30.6775 q^{98} -6.73077 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.99653	−1.41176	−0.705879	−	0.708333i	$-0.749448\pi$
$2$	−1.99653	−1.41176	−0.705879	+	0.708333i	$0.749448\pi$
$3$	1.39055	0.802832	0.401416	−	0.915896i	$-0.368518\pi$
$3$	1.39055	0.802832	0.401416	+	0.915896i	$0.368518\pi$
$4$	1.98612	0.993059
$5$	−2.55061	−1.14067	−0.570333	−	0.821413i	$-0.693186\pi$
$5$	−2.55061	−1.14067	−0.570333	+	0.821413i	$0.693186\pi$
$6$	−2.77626	−1.13340
$7$	−4.72921	−1.78747	−0.893736	−	0.448593i	$-0.851925\pi$
$7$	−4.72921	−1.78747	−0.893736	+	0.448593i	$0.851925\pi$
$8$	0.0277164	0.00979922
$9$	−1.06638	−0.355461
$10$	5.09235	1.61034
$11$	6.31177	1.90307	0.951536	−	0.307538i	$-0.0995051\pi$
$11$	6.31177	1.90307	0.951536	+	0.307538i	$0.0995051\pi$
$12$	2.76179	0.797259
$13$	4.90047	1.35915	0.679573	−	0.733608i	$-0.262165\pi$
$13$	4.90047	1.35915	0.679573	+	0.733608i	$0.262165\pi$
$14$	9.44199	2.52348
$15$	−3.54673	−0.915763
$16$	−4.02757	−1.00689
$17$	5.32868	1.29240	0.646198	−	0.763170i	$-0.276358\pi$
$17$	5.32868	1.29240	0.646198	+	0.763170i	$0.276358\pi$
$18$	2.12906	0.501825
$19$	5.28386	1.21220	0.606100	−	0.795388i	$-0.292733\pi$
$19$	5.28386	1.21220	0.606100	+	0.795388i	$0.292733\pi$
$20$	−5.06581	−1.13275
$21$	−6.57618	−1.43504
$22$	−12.6016	−2.68668
$23$	2.28692	0.476856	0.238428	−	0.971160i	$-0.423368\pi$
$23$	2.28692	0.476856	0.238428	+	0.971160i	$0.423368\pi$
$24$	0.0385409	0.00786713
$25$	1.50560	0.301119
$26$	−9.78391	−1.91878
$27$	−5.65449	−1.08821
$28$	−9.39276	−1.77507
$29$	0.490308	0.0910479	0.0455239	−	0.998963i	$-0.485504\pi$
$29$	0.490308	0.0910479	0.0455239	+	0.998963i	$0.485504\pi$
$30$	7.08115	1.29284
$31$	2.67489	0.480425	0.240212	−	0.970720i	$-0.422783\pi$
$31$	2.67489	0.480425	0.240212	+	0.970720i	$0.422783\pi$
$32$	7.98572	1.41169
$33$	8.77681	1.52785
$34$	−10.6389	−1.82455
$35$	12.0624	2.03891
$36$	−2.11796	−0.352994
$37$	−0.735772	−0.120960	−0.0604800	−	0.998169i	$-0.519263\pi$
$37$	−0.735772	−0.120960	−0.0604800	+	0.998169i	$0.519263\pi$
$38$	−10.5494	−1.71133
$39$	6.81432	1.09116
$40$	−0.0706936	−0.0111776
$41$	4.70299	0.734484	0.367242	−	0.930125i	$-0.380302\pi$
$41$	4.70299	0.734484	0.367242	+	0.930125i	$0.380302\pi$
$42$	13.1295	2.02593
$43$	−10.4612	−1.59531	−0.797656	−	0.603113i	$-0.793927\pi$
$43$	−10.4612	−1.59531	−0.797656	+	0.603113i	$0.793927\pi$
$44$	12.5359	1.88986
$45$	2.71993	0.405463
$46$	−4.56590	−0.673205
$47$	3.20066	0.466865	0.233432	−	0.972373i	$-0.425004\pi$
$47$	3.20066	0.466865	0.233432	+	0.972373i	$0.425004\pi$
$48$	−5.60052	−0.808366
$49$	15.3654	2.19506
$50$	−3.00596	−0.425108
$51$	7.40978	1.03758
$52$	9.73291	1.34971
$53$	0.220569	0.0302974	0.0151487	−	0.999885i	$-0.495178\pi$
$53$	0.220569	0.0302974	0.0151487	+	0.999885i	$0.495178\pi$
$54$	11.2893	1.53628
$55$	−16.0989	−2.17077
$56$	−0.131077	−0.0175158
$57$	7.34744	0.973193
$58$	−0.978912	−0.128537
$59$	8.86152	1.15367	0.576836	−	0.816860i	$-0.304287\pi$
$59$	8.86152	1.15367	0.576836	+	0.816860i	$0.304287\pi$
$60$	−7.04423	−0.909407
$61$	−3.78465	−0.484575	−0.242287	−	0.970205i	$-0.577898\pi$
$61$	−3.78465	−0.484575	−0.242287	+	0.970205i	$0.577898\pi$
$62$	−5.34049	−0.678243
$63$	5.04315	0.635377
$64$	−7.88856	−0.986070
$65$	−12.4992	−1.55033
$66$	−17.5231	−2.15695
$67$	−1.29300	−0.157965	−0.0789824	−	0.996876i	$-0.525167\pi$
$67$	−1.29300	−0.157965	−0.0789824	+	0.996876i	$0.525167\pi$
$68$	10.5834	1.28342
$69$	3.18007	0.382835
$70$	−24.0828	−2.87845
$71$	0.475339	0.0564124	0.0282062	−	0.999602i	$-0.491020\pi$
$71$	0.475339	0.0564124	0.0282062	+	0.999602i	$0.491020\pi$
$72$	−0.0295563	−0.00348324
$73$	−9.82860	−1.15035	−0.575175	−	0.818030i	$-0.695066\pi$
$73$	−9.82860	−1.15035	−0.575175	+	0.818030i	$0.695066\pi$
$74$	1.46899	0.170766
$75$	2.09360	0.241748
$76$	10.4944	1.20379
$77$	−29.8497	−3.40169
$78$	−13.6050	−1.54046
$79$	4.32881	0.487029	0.243515	−	0.969897i	$-0.421700\pi$
$79$	4.32881	0.487029	0.243515	+	0.969897i	$0.421700\pi$
$80$	10.2728	1.14853
$81$	−4.66367	−0.518186
$82$	−9.38965	−1.03691
$83$	11.1595	1.22492	0.612459	−	0.790502i	$-0.290180\pi$
$83$	11.1595	1.22492	0.612459	+	0.790502i	$0.290180\pi$
$84$	−13.0611	−1.42508
$85$	−13.5914	−1.47419
$86$	20.8860	2.25219
$87$	0.681795	0.0730961
$88$	0.174940	0.0186486
$89$	9.95000	1.05470	0.527349	−	0.849649i	$-0.323186\pi$
$89$	9.95000	1.05470	0.527349	+	0.849649i	$0.323186\pi$
$90$	−5.43040	−0.572415
$91$	−23.1753	−2.42944
$92$	4.54209	0.473546
$93$	3.71956	0.385700
$94$	−6.39021	−0.659100
$95$	−13.4770	−1.38272
$96$	11.1045	1.13335
$97$	11.6004	1.17784	0.588920	−	0.808191i	$-0.299553\pi$
$97$	11.6004	1.17784	0.588920	+	0.808191i	$0.299553\pi$
$98$	−30.6775	−3.09889
$99$	−6.73077	−0.676468
$100$	2.99029	0.299029
$101$	0.562600	0.0559807	0.0279904	−	0.999608i	$-0.491089\pi$
$101$	0.562600	0.0559807	0.0279904	+	0.999608i	$0.491089\pi$
$102$	−14.7938	−1.46481
$103$	3.20563	0.315860	0.157930	−	0.987450i	$-0.449518\pi$
$103$	3.20563	0.315860	0.157930	+	0.987450i	$0.449518\pi$
$104$	0.135823	0.0133186
$105$	16.7732	1.63690
$106$	−0.440371	−0.0427726
$107$	−9.52322	−0.920645	−0.460322	−	0.887752i	$-0.652266\pi$
$107$	−9.52322	−0.920645	−0.460322	+	0.887752i	$0.652266\pi$
$108$	−11.2305	−1.08065
$109$	4.87094	0.466552	0.233276	−	0.972411i	$-0.425055\pi$
$109$	4.87094	0.466552	0.233276	+	0.972411i	$0.425055\pi$
$110$	32.1418	3.06460
$111$	−1.02312	−0.0971106
$112$	19.0472	1.79979
$113$	1.27340	0.119791	0.0598956	−	0.998205i	$-0.480923\pi$
$113$	1.27340	0.119791	0.0598956	+	0.998205i	$0.480923\pi$
$114$	−14.6694	−1.37391
$115$	−5.83303	−0.543933
$116$	0.973809	0.0904159
$117$	−5.22578	−0.483123
$118$	−17.6923	−1.62870
$119$	−25.2005	−2.31012
$120$	−0.0983027	−0.00897377
$121$	28.8385	2.62168
$122$	7.55615	0.684102
$123$	6.53972	0.589667
$124$	5.31265	0.477090
$125$	8.91285	0.797189
$126$	−10.0688	−0.896999
$127$	−4.97595	−0.441545	−0.220772	−	0.975325i	$-0.570858\pi$
$127$	−4.97595	−0.441545	−0.220772	+	0.975325i	$0.570858\pi$
$128$	−0.221726	−0.0195980
$129$	−14.5467	−1.28077
$130$	24.9549	2.18869
$131$	−13.4927	−1.17886	−0.589430	−	0.807820i	$-0.700648\pi$
$131$	−13.4927	−1.17886	−0.589430	+	0.807820i	$0.700648\pi$
$132$	17.4318	1.51724
$133$	−24.9885	−2.16677
$134$	2.58151	0.223008
$135$	14.4224	1.24128
$136$	0.147692	0.0126645
$137$	−17.5030	−1.49538	−0.747692	−	0.664046i	$-0.768838\pi$
$137$	−17.5030	−1.49538	−0.747692	+	0.664046i	$0.768838\pi$
$138$	−6.34908	−0.540470
$139$	12.6042	1.06907	0.534535	−	0.845146i	$-0.320487\pi$
$139$	12.6042	1.06907	0.534535	+	0.845146i	$0.320487\pi$
$140$	23.9573	2.02476
$141$	4.45067	0.374814
$142$	−0.949028	−0.0796406
$143$	30.9306	2.58655
$144$	4.29494	0.357911
$145$	−1.25058	−0.103855
$146$	19.6231	1.62402
$147$	21.3663	1.76226
$148$	−1.46133	−0.120120
$149$	−1.46465	−0.119989	−0.0599943	−	0.998199i	$-0.519108\pi$
$149$	−1.46465	−0.119989	−0.0599943	+	0.998199i	$0.519108\pi$
$150$	−4.17993	−0.341290
$151$	−3.80030	−0.309264	−0.154632	−	0.987972i	$-0.549419\pi$
$151$	−3.80030	−0.309264	−0.154632	+	0.987972i	$0.549419\pi$
$152$	0.146449	0.0118786
$153$	−5.68242	−0.459397
$154$	59.5957	4.80236
$155$	−6.82260	−0.548004
$156$	13.5340	1.08359
$157$	2.06641	0.164918	0.0824588	−	0.996594i	$-0.473723\pi$
$157$	2.06641	0.164918	0.0824588	+	0.996594i	$0.473723\pi$
$158$	−8.64258	−0.687567
$159$	0.306711	0.0243238
$160$	−20.3684	−1.61027
$161$	−10.8153	−0.852367
$162$	9.31115	0.731553
$163$	22.0942	1.73055	0.865276	−	0.501296i	$-0.167143\pi$
$163$	22.0942	1.73055	0.865276	+	0.501296i	$0.167143\pi$
$164$	9.34070	0.729386
$165$	−22.3862	−1.74276
$166$	−22.2803	−1.72929
$167$	−7.12201	−0.551118	−0.275559	−	0.961284i	$-0.588863\pi$
$167$	−7.12201	−0.551118	−0.275559	+	0.961284i	$0.588863\pi$
$168$	−0.182268	−0.0140623
$169$	11.0146	0.847276
$170$	27.1355	2.08120
$171$	−5.63462	−0.430890
$172$	−20.7771	−1.58424
$173$	−16.9851	−1.29135	−0.645676	−	0.763611i	$-0.723424\pi$
$173$	−16.9851	−1.29135	−0.645676	+	0.763611i	$0.723424\pi$
$174$	−1.36122	−0.103194
$175$	−7.12028	−0.538243
$176$	−25.4211	−1.91619
$177$	12.3223	0.926204
$178$	−19.8654	−1.48898
$179$	11.3064	0.845077	0.422539	−	0.906345i	$-0.361139\pi$
$179$	11.3064	0.845077	0.422539	+	0.906345i	$0.361139\pi$
$180$	5.40209	0.402648
$181$	−26.4744	−1.96783	−0.983915	−	0.178639i	$-0.942831\pi$
$181$	−26.4744	−1.96783	−0.983915	+	0.178639i	$0.942831\pi$
$182$	46.2702	3.42977
$183$	−5.26272	−0.389032
$184$	0.0633852	0.00467282
$185$	1.87666	0.137975
$186$	−7.42619	−0.544515
$187$	33.6335	2.45952
$188$	6.35689	0.463624
$189$	26.7413	1.94514
$190$	26.9073	1.95206
$191$	17.7047	1.28106	0.640532	−	0.767932i	$-0.278714\pi$
$191$	17.7047	1.28106	0.640532	+	0.767932i	$0.278714\pi$
$192$	−10.9694	−0.791648
$193$	23.5467	1.69493	0.847465	−	0.530851i	$-0.178128\pi$
$193$	23.5467	1.69493	0.847465	+	0.530851i	$0.178128\pi$
$194$	−23.1605	−1.66282
$195$	−17.3807	−1.24466
$196$	30.5175	2.17982
$197$	−10.8368	−0.772092	−0.386046	−	0.922480i	$-0.626159\pi$
$197$	−10.8368	−0.772092	−0.386046	+	0.922480i	$0.626159\pi$
$198$	13.4382	0.955009
$199$	7.32930	0.519561	0.259780	−	0.965668i	$-0.416350\pi$
$199$	7.32930	0.519561	0.259780	+	0.965668i	$0.416350\pi$
$200$	0.0417297	0.00295074
$201$	−1.79797	−0.126819
$202$	−1.12324	−0.0790312
$203$	−2.31877	−0.162746
$204$	14.7167	1.03037
$205$	−11.9955	−0.837801
$206$	−6.40013	−0.445918
$207$	−2.43873	−0.169504
$208$	−19.7370	−1.36851
$209$	33.3505	2.30690
$210$	−33.4882	−2.31091
$211$	−16.2395	−1.11797	−0.558985	−	0.829178i	$-0.688809\pi$
$211$	−16.2395	−1.11797	−0.558985	+	0.829178i	$0.688809\pi$
$212$	0.438076	0.0300872
$213$	0.660981	0.0452897
$214$	19.0134	1.29973
$215$	26.6823	1.81972
$216$	−0.156722	−0.0106636
$217$	−12.6501	−0.858746
$218$	−9.72497	−0.658658
$219$	−13.6671	−0.923538
$220$	−31.9742	−2.15570
$221$	26.1130	1.75655
$222$	2.04269	0.137097
$223$	−10.0425	−0.672496	−0.336248	−	0.941774i	$-0.609158\pi$
$223$	−10.0425	−0.672496	−0.336248	+	0.941774i	$0.609158\pi$
$224$	−37.7661	−2.52336
$225$	−1.60554	−0.107036
$226$	−2.54237	−0.169116
$227$	−17.7719	−1.17956	−0.589782	−	0.807562i	$-0.700787\pi$
$227$	−17.7719	−1.17956	−0.589782	+	0.807562i	$0.700787\pi$
$228$	14.5929	0.966438
$229$	−23.3803	−1.54501	−0.772506	−	0.635008i	$-0.780997\pi$
$229$	−23.3803	−1.54501	−0.772506	+	0.635008i	$0.780997\pi$
$230$	11.6458	0.767902
$231$	−41.5074	−2.73098
$232$	0.0135896	0.000892198 0
$233$	−29.2217	−1.91438	−0.957188	−	0.289468i	$-0.906522\pi$
$233$	−29.2217	−1.91438	−0.957188	+	0.289468i	$0.906522\pi$
$234$	10.4334	0.682053
$235$	−8.16363	−0.532537
$236$	17.6000	1.14566
$237$	6.01941	0.391002
$238$	50.3134	3.26133
$239$	2.38586	0.154328	0.0771642	−	0.997018i	$-0.475413\pi$
$239$	2.38586	0.154328	0.0771642	+	0.997018i	$0.475413\pi$
$240$	14.2847	0.922075
$241$	−7.06183	−0.454892	−0.227446	−	0.973791i	$-0.573038\pi$
$241$	−7.06183	−0.454892	−0.227446	+	0.973791i	$0.573038\pi$
$242$	−57.5768	−3.70118
$243$	10.4784	0.672191
$244$	−7.51676	−0.481211
$245$	−39.1911	−2.50383
$246$	−13.0567	−0.832467
$247$	25.8934	1.64756
$248$	0.0741383	0.00470779
$249$	15.5178	0.983404
$250$	−17.7947	−1.12544
$251$	17.4010	1.09834	0.549171	−	0.835710i	$-0.314944\pi$
$251$	17.4010	1.09834	0.549171	+	0.835710i	$0.314944\pi$
$252$	10.0163	0.630967
$253$	14.4345	0.907491
$254$	9.93462	0.623354
$255$	−18.8994	−1.18353
$256$	16.2198	1.01374
$257$	−17.5466	−1.09453	−0.547264	−	0.836960i	$-0.684331\pi$
$257$	−17.5466	−1.09453	−0.547264	+	0.836960i	$0.684331\pi$
$258$	29.0429	1.80813
$259$	3.47962	0.216213
$260$	−24.8248	−1.53957
$261$	−0.522856	−0.0323640
$262$	26.9385	1.66426
$263$	26.0549	1.60661	0.803306	−	0.595567i	$-0.203072\pi$
$263$	26.0549	1.60661	0.803306	+	0.595567i	$0.203072\pi$
$264$	0.243261	0.0149717
$265$	−0.562584	−0.0345593
$266$	49.8901	3.05896
$267$	13.8359	0.846745
$268$	−2.56805	−0.156868
$269$	−7.09084	−0.432336	−0.216168	−	0.976356i	$-0.569356\pi$
$269$	−7.09084	−0.432336	−0.216168	+	0.976356i	$0.569356\pi$
$270$	−28.7947	−1.75239
$271$	−3.72961	−0.226558	−0.113279	−	0.993563i	$-0.536135\pi$
$271$	−3.72961	−0.226558	−0.113279	+	0.993563i	$0.536135\pi$
$272$	−21.4617	−1.30130
$273$	−32.2264	−1.95043
$274$	34.9452	2.11112
$275$	9.50299	0.573052
$276$	6.31598	0.380178
$277$	−4.48592	−0.269533	−0.134766	−	0.990877i	$-0.543028\pi$
$277$	−4.48592	−0.269533	−0.134766	+	0.990877i	$0.543028\pi$
$278$	−25.1645	−1.50927
$279$	−2.85246	−0.170772
$280$	0.334325	0.0199797
$281$	12.6160	0.752608	0.376304	−	0.926496i	$-0.377195\pi$
$281$	12.6160	0.752608	0.376304	+	0.926496i	$0.377195\pi$
$282$	−8.88587	−0.529146
$283$	3.45799	0.205556	0.102778	−	0.994704i	$-0.467227\pi$
$283$	3.45799	0.205556	0.102778	+	0.994704i	$0.467227\pi$
$284$	0.944080	0.0560208
$285$	−18.7404	−1.11009
$286$	−61.7539	−3.65158
$287$	−22.2414	−1.31287
$288$	−8.51584	−0.501801
$289$	11.3949	0.670286
$290$	2.49682	0.146618
$291$	16.1309	0.945607
$292$	−19.5207	−1.14237
$293$	−7.68894	−0.449193	−0.224596	−	0.974452i	$-0.572106\pi$
$293$	−7.68894	−0.449193	−0.224596	+	0.974452i	$0.572106\pi$
$294$	−42.6584	−2.48789
$295$	−22.6023	−1.31595
$296$	−0.0203929	−0.00118531
$297$	−35.6899	−2.07094
$298$	2.92421	0.169395
$299$	11.2070	0.648116
$300$	4.15814	0.240070
$301$	49.4730	2.85158
$302$	7.58741	0.436606
$303$	0.782320	0.0449431
$304$	−21.2811	−1.22056
$305$	9.65315	0.552738
$306$	11.3451	0.648556
$307$	4.23662	0.241796	0.120898	−	0.992665i	$-0.461423\pi$
$307$	4.23662	0.241796	0.120898	+	0.992665i	$0.461423\pi$
$308$	−59.2850	−3.37808
$309$	4.45758	0.253583
$310$	13.6215	0.773649
$311$	19.3277	1.09597	0.547986	−	0.836488i	$-0.315395\pi$
$311$	19.3277	1.09597	0.547986	+	0.836488i	$0.315395\pi$
$312$	0.188868	0.0106926
$313$	−22.3435	−1.26293	−0.631465	−	0.775404i	$-0.717546\pi$
$313$	−22.3435	−1.26293	−0.631465	+	0.775404i	$0.717546\pi$
$314$	−4.12564	−0.232824
$315$	−12.8631	−0.724753
$316$	8.59753	0.483649
$317$	3.79387	0.213085	0.106542	−	0.994308i	$-0.466022\pi$
$317$	3.79387	0.213085	0.106542	+	0.994308i	$0.466022\pi$
$318$	−0.612356	−0.0343392
$319$	3.09471	0.173271
$320$	20.1206	1.12478
$321$	−13.2425	−0.739123
$322$	21.5931	1.20333
$323$	28.1560	1.56664
$324$	−9.26261	−0.514589
$325$	7.37813	0.409265
$326$	−44.1117	−2.44312
$327$	6.77327	0.374562
$328$	0.130350	0.00719737
$329$	−15.1366	−0.834508
$330$	44.6946	2.46036
$331$	5.18302	0.284885	0.142442	−	0.989803i	$-0.454504\pi$
$331$	5.18302	0.284885	0.142442	+	0.989803i	$0.454504\pi$
$332$	22.1642	1.21642
$333$	0.784615	0.0429966
$334$	14.2193	0.778045
$335$	3.29793	0.180185
$336$	26.4860	1.44493
$337$	−20.6535	−1.12507	−0.562533	−	0.826775i	$-0.690173\pi$
$337$	−20.6535	−1.12507	−0.562533	+	0.826775i	$0.690173\pi$
$338$	−21.9909	−1.19615
$339$	1.77072	0.0961721
$340$	−26.9941	−1.46396
$341$	16.8833	0.914282
$342$	11.2497	0.608312
$343$	−39.5618	−2.13614
$344$	−0.289945	−0.0156328
$345$	−8.11110	−0.436687
$346$	33.9112	1.82308
$347$	16.5479	0.888340	0.444170	−	0.895942i	$-0.353499\pi$
$347$	16.5479	0.888340	0.444170	+	0.895942i	$0.353499\pi$
$348$	1.35413	0.0725887
$349$	1.00000	0.0535288
$349$	1.00000	0.0535288
$350$	14.2158	0.759868
$351$	−27.7097	−1.47903
$352$	50.4041	2.68655
$353$	−15.5069	−0.825347	−0.412673	−	0.910879i	$-0.635405\pi$
$353$	−15.5069	−0.825347	−0.412673	+	0.910879i	$0.635405\pi$
$354$	−24.6019	−1.30758
$355$	−1.21240	−0.0643477
$356$	19.7619	1.04738
$357$	−35.0424	−1.85464
$358$	−22.5735	−1.19304
$359$	−0.932618	−0.0492217	−0.0246108	−	0.999697i	$-0.507835\pi$
$359$	−0.932618	−0.0492217	−0.0246108	+	0.999697i	$0.507835\pi$
$360$	0.0753865	0.00397322
$361$	8.91916	0.469429
$362$	52.8569	2.77810
$363$	40.1012	2.10477
$364$	−46.0289	−2.41257
$365$	25.0689	1.31217
$366$	10.5072	0.549218
$367$	−2.00980	−0.104910	−0.0524552	−	0.998623i	$-0.516705\pi$
$367$	−2.00980	−0.104910	−0.0524552	+	0.998623i	$0.516705\pi$
$368$	−9.21073	−0.480143
$369$	−5.01519	−0.261081
$370$	−3.74681	−0.194787
$371$	−1.04312	−0.0541559
$372$	7.38748	0.383023
$373$	16.5404	0.856428	0.428214	−	0.903677i	$-0.359143\pi$
$373$	16.5404	0.856428	0.428214	+	0.903677i	$0.359143\pi$
$374$	−67.1501	−3.47225
$375$	12.3937	0.640009
$376$	0.0887108	0.00457491
$377$	2.40274	0.123747
$378$	−53.3896	−2.74607
$379$	16.4480	0.844877	0.422439	−	0.906392i	$-0.361174\pi$
$379$	16.4480	0.844877	0.422439	+	0.906392i	$0.361174\pi$
$380$	−26.7670	−1.37312
$381$	−6.91929	−0.354486
$382$	−35.3478	−1.80855
$383$	23.7575	1.21395	0.606977	−	0.794719i	$-0.292382\pi$
$383$	23.7575	1.21395	0.606977	+	0.794719i	$0.292382\pi$
$384$	−0.308320	−0.0157339
$385$	76.1349	3.88019
$386$	−47.0117	−2.39283
$387$	11.1556	0.567071
$388$	23.0397	1.16966
$389$	19.2030	0.973631	0.486816	−	0.873505i	$-0.338158\pi$
$389$	19.2030	0.973631	0.486816	+	0.873505i	$0.338158\pi$
$390$	34.7009	1.75715
$391$	12.1863	0.616286
$392$	0.425874	0.0215099
$393$	−18.7622	−0.946426
$394$	21.6360	1.09001
$395$	−11.0411	−0.555538
$396$	−13.3681	−0.671773
$397$	15.8140	0.793683	0.396841	−	0.917887i	$-0.370106\pi$
$397$	15.8140	0.793683	0.396841	+	0.917887i	$0.370106\pi$
$398$	−14.6331	−0.733494
$399$	−34.7476	−1.73956
$400$	−6.06390	−0.303195
$401$	−2.88848	−0.144244	−0.0721219	−	0.997396i	$-0.522977\pi$
$401$	−2.88848	−0.144244	−0.0721219	+	0.997396i	$0.522977\pi$
$402$	3.58970	0.179038
$403$	13.1082	0.652967
$404$	1.11739	0.0555922
$405$	11.8952	0.591077
$406$	4.62948	0.229757
$407$	−4.64402	−0.230196
$408$	0.205372	0.0101674
$409$	−22.4704	−1.11109	−0.555545	−	0.831487i	$-0.687490\pi$
$409$	−22.4704	−1.11109	−0.555545	+	0.831487i	$0.687490\pi$
$410$	23.9493	1.18277
$411$	−24.3387	−1.20054
$412$	6.36677	0.313668
$413$	−41.9080	−2.06216
$414$	4.86900	0.239298
$415$	−28.4636	−1.39722
$416$	39.1338	1.91869
$417$	17.5267	0.858284
$418$	−66.5852	−3.25679
$419$	12.2618	0.599027	0.299514	−	0.954092i	$-0.403176\pi$
$419$	12.2618	0.599027	0.299514	+	0.954092i	$0.403176\pi$
$420$	33.3136	1.62554
$421$	0.710908	0.0346475	0.0173238	−	0.999850i	$-0.494485\pi$
$421$	0.710908	0.0346475	0.0173238	+	0.999850i	$0.494485\pi$
$422$	32.4225	1.57830
$423$	−3.41313	−0.165952
$424$	0.00611337	0.000296891 0
$425$	8.02285	0.389165
$426$	−1.31967	−0.0639380
$427$	17.8984	0.866164
$428$	−18.9142	−0.914254
$429$	43.0105	2.07657
$430$	−53.2719	−2.56900
$431$	40.9377	1.97190	0.985951	−	0.167037i	$-0.0534198\pi$
$431$	40.9377	1.97190	0.985951	+	0.167037i	$0.0534198\pi$
$432$	22.7739	1.09571
$433$	−8.26509	−0.397195	−0.198597	−	0.980081i	$-0.563639\pi$
$433$	−8.26509	−0.397195	−0.198597	+	0.980081i	$0.563639\pi$
$434$	25.2563	1.21234
$435$	−1.73899	−0.0833783
$436$	9.67427	0.463313
$437$	12.0838	0.578045
$438$	27.2867	1.30381
$439$	−34.8778	−1.66462	−0.832312	−	0.554307i	$-0.812983\pi$
$439$	−34.8778	−1.66462	−0.832312	+	0.554307i	$0.812983\pi$
$440$	−0.446202	−0.0212719
$441$	−16.3854	−0.780258
$442$	−52.1354	−2.47983
$443$	21.1030	1.00264	0.501318	−	0.865263i	$-0.332849\pi$
$443$	21.1030	1.00264	0.501318	+	0.865263i	$0.332849\pi$
$444$	−2.03204	−0.0964365
$445$	−25.3785	−1.20306
$446$	20.0501	0.949401
$447$	−2.03666	−0.0963306
$448$	37.3066	1.76257
$449$	−17.0983	−0.806918	−0.403459	−	0.914998i	$-0.632192\pi$
$449$	−17.0983	−0.806918	−0.403459	+	0.914998i	$0.632192\pi$
$450$	3.20551	0.151109
$451$	29.6842	1.39778
$452$	2.52912	0.118960
$453$	−5.28450	−0.248287
$454$	35.4821	1.66526
$455$	59.1112	2.77117
$456$	0.203645	0.00953653
$457$	−18.1604	−0.849506	−0.424753	−	0.905309i	$-0.639639\pi$
$457$	−18.1604	−0.849506	−0.424753	+	0.905309i	$0.639639\pi$
$458$	46.6793	2.18118
$459$	−30.1310	−1.40639
$460$	−11.5851	−0.540158
$461$	−4.25988	−0.198402	−0.0992012	−	0.995067i	$-0.531629\pi$
$461$	−4.25988	−0.198402	−0.0992012	+	0.995067i	$0.531629\pi$
$462$	82.8705	3.85549
$463$	−27.3060	−1.26902	−0.634508	−	0.772916i	$-0.718797\pi$
$463$	−27.3060	−1.26902	−0.634508	+	0.772916i	$0.718797\pi$
$464$	−1.97475	−0.0916754
$465$	−9.48713	−0.439955
$466$	58.3418	2.70263
$467$	−18.6181	−0.861545	−0.430772	−	0.902461i	$-0.641759\pi$
$467$	−18.6181	−0.861545	−0.430772	+	0.902461i	$0.641759\pi$
$468$	−10.3790	−0.479770
$469$	6.11486	0.282358
$470$	16.2989	0.751813
$471$	2.87344	0.132401
$472$	0.245609	0.0113051
$473$	−66.0285	−3.03599
$474$	−12.0179	−0.552001
$475$	7.95536	0.365017
$476$	−50.0511	−2.29409
$477$	−0.235211	−0.0107696
$478$	−4.76343	−0.217874
$479$	−33.1162	−1.51312	−0.756560	−	0.653924i	$-0.773121\pi$
$479$	−33.1162	−1.51312	−0.756560	+	0.653924i	$0.773121\pi$
$480$	−28.3232	−1.29277
$481$	−3.60562	−0.164402
$482$	14.0991	0.642198
$483$	−15.0392	−0.684307
$484$	57.2767	2.60348
$485$	−29.5880	−1.34352
$486$	−20.9204	−0.948971
$487$	−31.6370	−1.43361	−0.716804	−	0.697275i	$-0.754396\pi$
$487$	−31.6370	−1.43361	−0.716804	+	0.697275i	$0.754396\pi$
$488$	−0.104897	−0.00474845
$489$	30.7230	1.38934
$490$	78.2461	3.53480
$491$	−3.58402	−0.161744	−0.0808722	−	0.996724i	$-0.525771\pi$
$491$	−3.58402	−0.161744	−0.0808722	+	0.996724i	$0.525771\pi$
$492$	12.9887	0.585574
$493$	2.61269	0.117670
$494$	−51.6968	−2.32595
$495$	17.1676	0.771624
$496$	−10.7733	−0.483736
$497$	−2.24798	−0.100836
$498$	−30.9818	−1.38833
$499$	−37.5974	−1.68309	−0.841545	−	0.540186i	$-0.818354\pi$
$499$	−37.5974	−1.68309	−0.841545	+	0.540186i	$0.818354\pi$
$500$	17.7020	0.791656
$501$	−9.90348	−0.442455
$502$	−34.7416	−1.55059
$503$	29.7359	1.32586	0.662930	−	0.748681i	$-0.269313\pi$
$503$	29.7359	1.32586	0.662930	+	0.748681i	$0.269313\pi$
$504$	0.139778	0.00622620
$505$	−1.43497	−0.0638553
$506$	−28.8189	−1.28116
$507$	15.3163	0.680220
$508$	−9.88283	−0.438480
$509$	−39.3980	−1.74628	−0.873142	−	0.487466i	$-0.837921\pi$
$509$	−39.3980	−1.74628	−0.873142	+	0.487466i	$0.837921\pi$
$510$	37.7332	1.67085
$511$	46.4815	2.05622
$512$	−31.9398	−1.41155
$513$	−29.8775	−1.31913
$514$	35.0323	1.54521
$515$	−8.17631	−0.360291
$516$	−28.8915	−1.27188
$517$	20.2019	0.888477
$518$	−6.94715	−0.305240
$519$	−23.6185	−1.03674
$520$	−0.346432	−0.0151920
$521$	8.68920	0.380681	0.190340	−	0.981718i	$-0.439041\pi$
$521$	8.68920	0.380681	0.190340	+	0.981718i	$0.439041\pi$
$522$	1.04390	0.0456901
$523$	−29.0895	−1.27200	−0.635998	−	0.771691i	$-0.719411\pi$
$523$	−29.0895	−1.27200	−0.635998	+	0.771691i	$0.719411\pi$
$524$	−26.7980	−1.17068
$525$	−9.90108	−0.432118
$526$	−52.0192	−2.26815
$527$	14.2536	0.620899
$528$	−35.3492	−1.53838
$529$	−17.7700	−0.772609
$530$	1.12321	0.0487893
$531$	−9.44978	−0.410086
$532$	−49.6300	−2.15174
$533$	23.0469	0.998270
$534$	−27.6238	−1.19540
$535$	24.2900	1.05015
$536$	−0.0358372	−0.00154793
$537$	15.7220	0.678455
$538$	14.1571	0.610354
$539$	96.9830	4.17735
$540$	28.6446	1.23267
$541$	16.3267	0.701939	0.350970	−	0.936387i	$-0.385852\pi$
$541$	16.3267	0.701939	0.350970	+	0.936387i	$0.385852\pi$
$542$	7.44626	0.319844
$543$	−36.8139	−1.57984
$544$	42.5534	1.82446
$545$	−12.4239	−0.532180
$546$	64.3408	2.75353
$547$	−37.7339	−1.61338	−0.806692	−	0.590972i	$-0.798745\pi$
$547$	−37.7339	−1.61338	−0.806692	+	0.590972i	$0.798745\pi$
$548$	−34.7631	−1.48500
$549$	4.03589	0.172247
$550$	−18.9730	−0.809010
$551$	2.59072	0.110368
$552$	0.0881399	0.00375148
$553$	−20.4718	−0.870551
$554$	8.95626	0.380515
$555$	2.60959	0.110771
$556$	25.0333	1.06165
$557$	−8.20330	−0.347585	−0.173793	−	0.984782i	$-0.555602\pi$
$557$	−8.20330	−0.347585	−0.173793	+	0.984782i	$0.555602\pi$
$558$	5.69501	0.241089
$559$	−51.2646	−2.16826
$560$	−48.5820	−2.05296
$561$	46.7688	1.97458
$562$	−25.1882	−1.06250
$563$	−12.0629	−0.508391	−0.254196	−	0.967153i	$-0.581811\pi$
$563$	−12.0629	−0.508391	−0.254196	+	0.967153i	$0.581811\pi$
$564$	8.83955	0.372212
$565$	−3.24794	−0.136642
$566$	−6.90396	−0.290195
$567$	22.0555	0.926243
$568$	0.0131747	0.000552798 0
$569$	−1.27366	−0.0533945	−0.0266973	−	0.999644i	$-0.508499\pi$
$569$	−1.27366	−0.0533945	−0.0266973	+	0.999644i	$0.508499\pi$
$570$	37.4158	1.56718
$571$	35.6400	1.49149	0.745745	−	0.666232i	$-0.232094\pi$
$571$	35.6400	1.49149	0.745745	+	0.666232i	$0.232094\pi$
$572$	61.4319	2.56860
$573$	24.6191	1.02848
$574$	44.4056	1.85345
$575$	3.44318	0.143591
$576$	8.41223	0.350510
$577$	−32.3982	−1.34875	−0.674377	−	0.738387i	$-0.735588\pi$
$577$	−32.3982	−1.34875	−0.674377	+	0.738387i	$0.735588\pi$
$578$	−22.7502	−0.946282
$579$	32.7428	1.36074
$580$	−2.48380	−0.103134
$581$	−52.7758	−2.18951
$582$	−32.2057	−1.33497
$583$	1.39218	0.0576582
$584$	−0.272413	−0.0112725
$585$	13.3289	0.551083
$586$	15.3512	0.634151
$587$	3.36715	0.138977	0.0694885	−	0.997583i	$-0.477863\pi$
$587$	3.36715	0.138977	0.0694885	+	0.997583i	$0.477863\pi$
$588$	42.4360	1.75003
$589$	14.1337	0.582371
$590$	45.1260	1.85781
$591$	−15.0691	−0.619860
$592$	2.96337	0.121794
$593$	42.6447	1.75121	0.875604	−	0.483030i	$-0.160464\pi$
$593$	42.6447	1.75121	0.875604	+	0.483030i	$0.160464\pi$
$594$	71.2558	2.92366
$595$	64.2765	2.63508
$596$	−2.90896	−0.119156
$597$	10.1917	0.417120
$598$	−22.3750	−0.914983
$599$	3.07928	0.125816	0.0629081	−	0.998019i	$-0.479963\pi$
$599$	3.07928	0.125816	0.0629081	+	0.998019i	$0.479963\pi$
$600$	0.0580271	0.00236894
$601$	7.01651	0.286209	0.143105	−	0.989708i	$-0.454291\pi$
$601$	7.01651	0.286209	0.143105	+	0.989708i	$0.454291\pi$
$602$	−98.7741	−4.02573
$603$	1.37883	0.0561504
$604$	−7.54785	−0.307118
$605$	−73.5557	−2.99046
$606$	−1.56192	−0.0634488
$607$	26.0179	1.05604	0.528018	−	0.849233i	$-0.322936\pi$
$607$	26.0179	1.05604	0.528018	+	0.849233i	$0.322936\pi$
$608$	42.1954	1.71125
$609$	−3.22435	−0.130657
$610$	−19.2728	−0.780332
$611$	15.6847	0.634537
$612$	−11.2860	−0.456208
$613$	−5.57816	−0.225300	−0.112650	−	0.993635i	$-0.535934\pi$
$613$	−5.57816	−0.225300	−0.112650	+	0.993635i	$0.535934\pi$
$614$	−8.45852	−0.341358
$615$	−16.6803	−0.672613
$616$	−0.827326	−0.0333339
$617$	13.8825	0.558889	0.279445	−	0.960162i	$-0.409850\pi$
$617$	13.8825	0.558889	0.279445	+	0.960162i	$0.409850\pi$
$618$	−8.89967	−0.357997
$619$	9.76100	0.392328	0.196164	−	0.980571i	$-0.437152\pi$
$619$	9.76100	0.392328	0.196164	+	0.980571i	$0.437152\pi$
$620$	−13.5505	−0.544200
$621$	−12.9314	−0.518918
$622$	−38.5882	−1.54725
$623$	−47.0556	−1.88524
$624$	−27.4452	−1.09869
$625$	−30.2612	−1.21045
$626$	44.6094	1.78295
$627$	46.3754	1.85206
$628$	4.10414	0.163773
$629$	−3.92069	−0.156328
$630$	25.6815	1.02318
$631$	44.0264	1.75266	0.876332	−	0.481707i	$-0.159983\pi$
$631$	44.0264	1.75266	0.876332	+	0.481707i	$0.159983\pi$
$632$	0.119979	0.00477251
$633$	−22.5817	−0.897542
$634$	−7.57455	−0.300824
$635$	12.6917	0.503655
$636$	0.609164	0.0241549
$637$	75.2977	2.98340
$638$	−6.17867	−0.244616
$639$	−0.506894	−0.0200524
$640$	0.565535	0.0223547
$641$	−29.8691	−1.17976	−0.589880	−	0.807491i	$-0.700825\pi$
$641$	−29.8691	−1.17976	−0.589880	+	0.807491i	$0.700825\pi$
$642$	26.4389	1.04346
$643$	41.5266	1.63765	0.818825	−	0.574044i	$-0.194626\pi$
$643$	41.5266	1.63765	0.818825	+	0.574044i	$0.194626\pi$
$644$	−21.4805	−0.846450
$645$	37.1029	1.46093
$646$	−56.2142	−2.21172
$647$	−0.0510650	−0.00200757	−0.00100379	−	0.999999i	$-0.500320\pi$
$647$	−0.0510650	−0.00200757	−0.00100379	+	0.999999i	$0.500320\pi$
$648$	−0.129260	−0.00507782
$649$	55.9319	2.19552
$650$	−14.7306	−0.577783
$651$	−17.5906	−0.689428
$652$	43.8817	1.71854
$653$	1.56340	0.0611805	0.0305902	−	0.999532i	$-0.490261\pi$
$653$	1.56340	0.0611805	0.0305902	+	0.999532i	$0.490261\pi$
$654$	−13.5230	−0.528791
$655$	34.4145	1.34469
$656$	−18.9416	−0.739547
$657$	10.4811	0.408905
$658$	30.2206	1.17812
$659$	−34.3683	−1.33880	−0.669399	−	0.742903i	$-0.733448\pi$
$659$	−34.3683	−1.33880	−0.669399	+	0.742903i	$0.733448\pi$
$660$	−44.4616	−1.73067
$661$	−41.8645	−1.62834	−0.814169	−	0.580627i	$-0.802807\pi$
$661$	−41.8645	−1.62834	−0.814169	+	0.580627i	$0.802807\pi$
$662$	−10.3480	−0.402188
$663$	36.3114	1.41022
$664$	0.309302	0.0120033
$665$	63.7358	2.47157
$666$	−1.56650	−0.0607008
$667$	1.12129	0.0434167
$668$	−14.1452	−0.547292
$669$	−13.9646	−0.539901
$670$	−6.58441	−0.254378
$671$	−23.8878	−0.922180
$672$	−52.5155	−2.02583
$673$	37.7733	1.45605	0.728027	−	0.685548i	$-0.240437\pi$
$673$	37.7733	1.45605	0.728027	+	0.685548i	$0.240437\pi$
$674$	41.2352	1.58832
$675$	−8.51339	−0.327680
$676$	21.8763	0.841395
$677$	−15.4200	−0.592638	−0.296319	−	0.955089i	$-0.595759\pi$
$677$	−15.4200	−0.592638	−0.296319	+	0.955089i	$0.595759\pi$
$678$	−3.53528	−0.135772
$679$	−54.8606	−2.10536
$680$	−0.376704	−0.0144459
$681$	−24.7127	−0.946992
$682$	−33.7080	−1.29074
$683$	7.20881	0.275838	0.137919	−	0.990444i	$-0.455959\pi$
$683$	7.20881	0.275838	0.137919	+	0.990444i	$0.455959\pi$
$684$	−11.1910	−0.427899
$685$	44.6433	1.70573
$686$	78.9861	3.01571
$687$	−32.5113	−1.24038
$688$	42.1331	1.60631
$689$	1.08089	0.0411786
$690$	16.1940	0.616496
$691$	6.35522	0.241764	0.120882	−	0.992667i	$-0.461428\pi$
$691$	6.35522	0.241764	0.120882	+	0.992667i	$0.461428\pi$
$692$	−33.7344	−1.28239
$693$	31.8312	1.20917
$694$	−33.0384	−1.25412
$695$	−32.1483	−1.21945
$696$	0.0188969	0.000716285 0
$697$	25.0608	0.949244
$698$	−1.99653	−0.0755696
$699$	−40.6341	−1.53692
$700$	−14.1417	−0.534507
$701$	−11.0574	−0.417631	−0.208815	−	0.977955i	$-0.566961\pi$
$701$	−11.0574	−0.417631	−0.208815	+	0.977955i	$0.566961\pi$
$702$	55.3231	2.08803
$703$	−3.88771	−0.146628
$704$	−49.7908	−1.87656
$705$	−11.3519	−0.427537
$706$	30.9599	1.16519
$707$	−2.66065	−0.100064
$708$	24.4736	0.919775
$709$	−3.39214	−0.127394	−0.0636972	−	0.997969i	$-0.520289\pi$
$709$	−3.39214	−0.127394	−0.0636972	+	0.997969i	$0.520289\pi$
$710$	2.42060	0.0908434
$711$	−4.61617	−0.173120
$712$	0.275778	0.0103352
$713$	6.11726	0.229093
$714$	69.9630	2.61830
$715$	−78.8919	−2.95039
$716$	22.4558	0.839211
$717$	3.31764	0.123900
$718$	1.86200	0.0694891
$719$	−43.3330	−1.61605	−0.808023	−	0.589151i	$-0.799462\pi$
$719$	−43.3330	−1.61605	−0.808023	+	0.589151i	$0.799462\pi$
$720$	−10.9547	−0.408257
$721$	−15.1601	−0.564592
$722$	−17.8073	−0.662720
$723$	−9.81979	−0.365202
$724$	−52.5813	−1.95417
$725$	0.738206	0.0274163
$726$	−80.0632	−2.97142
$727$	19.5690	0.725774	0.362887	−	0.931833i	$-0.381791\pi$
$727$	19.5690	0.725774	0.362887	+	0.931833i	$0.381791\pi$
$728$	−0.642337	−0.0238066
$729$	28.5617	1.05784
$730$	−50.0507	−1.85246
$731$	−55.7442	−2.06177
$732$	−10.4524	−0.386331
$733$	25.6983	0.949187	0.474593	−	0.880205i	$-0.342595\pi$
$733$	25.6983	0.949187	0.474593	+	0.880205i	$0.342595\pi$
$734$	4.01261	0.148108
$735$	−54.4970	−2.01015
$736$	18.2627	0.673172
$737$	−8.16111	−0.300619
$738$	10.0130	0.368582
$739$	−13.5746	−0.499350	−0.249675	−	0.968330i	$-0.580324\pi$
$739$	−13.5746	−0.499350	−0.249675	+	0.968330i	$0.580324\pi$
$740$	3.72728	0.137017
$741$	36.0059	1.32271
$742$	2.08261	0.0764549
$743$	−40.3090	−1.47879	−0.739396	−	0.673271i	$-0.764889\pi$
$743$	−40.3090	−1.47879	−0.739396	+	0.673271i	$0.764889\pi$
$744$	0.103093	0.00377956
$745$	3.73574	0.136867
$746$	−33.0233	−1.20907
$747$	−11.9004	−0.435411
$748$	66.8000	2.44245
$749$	45.0373	1.64563
$750$	−24.7444	−0.903537
$751$	−20.8858	−0.762134	−0.381067	−	0.924547i	$-0.624443\pi$
$751$	−20.8858	−0.762134	−0.381067	+	0.924547i	$0.624443\pi$
$752$	−12.8909	−0.470083
$753$	24.1969	0.881783
$754$	−4.79713	−0.174701
$755$	9.69308	0.352767
$756$	53.1113	1.93164
$757$	32.6730	1.18752	0.593760	−	0.804642i	$-0.297643\pi$
$757$	32.6730	1.18752	0.593760	+	0.804642i	$0.297643\pi$
$758$	−32.8389	−1.19276
$759$	20.0719	0.728562
$760$	−0.373535	−0.0135495
$761$	24.0838	0.873035	0.436518	−	0.899696i	$-0.356212\pi$
$761$	24.0838	0.873035	0.436518	+	0.899696i	$0.356212\pi$
$762$	13.8145	0.500448
$763$	−23.0357	−0.833948
$764$	35.1635	1.27217
$765$	14.4936	0.524018
$766$	−47.4326	−1.71381
$767$	43.4256	1.56801
$768$	22.5544	0.813861
$769$	−25.7918	−0.930074	−0.465037	−	0.885291i	$-0.653959\pi$
$769$	−25.7918	−0.930074	−0.465037	+	0.885291i	$0.653959\pi$
$770$	−152.005	−5.47789
$771$	−24.3994	−0.878721
$772$	46.7666	1.68317
$773$	−5.59723	−0.201318	−0.100659	−	0.994921i	$-0.532095\pi$
$773$	−5.59723	−0.201318	−0.100659	+	0.994921i	$0.532095\pi$
$774$	−22.2725	−0.800567
$775$	4.02731	0.144665
$776$	0.321521	0.0115419
$777$	4.83857	0.173583
$778$	−38.3393	−1.37453
$779$	24.8499	0.890342
$780$	−34.5200	−1.23602
$781$	3.00023	0.107357
$782$	−24.3302	−0.870047
$783$	−2.77244	−0.0990789
$784$	−61.8853	−2.21019
$785$	−5.27060	−0.188116
$786$	37.4591	1.33612
$787$	−22.3431	−0.796445	−0.398222	−	0.917289i	$-0.630373\pi$
$787$	−22.3431	−0.796445	−0.398222	+	0.917289i	$0.630373\pi$
$788$	−21.5232	−0.766733
$789$	36.2305	1.28984
$790$	22.0438	0.784284
$791$	−6.02216	−0.214123
$792$	−0.186553	−0.00662886
$793$	−18.5465	−0.658607
$794$	−31.5731	−1.12049
$795$	−0.782299	−0.0277453
$796$	14.5569	0.515954
$797$	40.4382	1.43240	0.716198	−	0.697897i	$-0.245881\pi$
$797$	40.4382	1.43240	0.716198	+	0.697897i	$0.245881\pi$
$798$	69.3745	2.45583
$799$	17.0553	0.603374
$800$	12.0233	0.425087
$801$	−10.6105	−0.374904
$802$	5.76692	0.203637
$803$	−62.0359	−2.18920
$804$	−3.57099	−0.125939
$805$	27.5856	0.972266
$806$	−26.1709	−0.921831
$807$	−9.86014	−0.347093
$808$	0.0155932	0.000548568 0
$809$	−2.68240	−0.0943083	−0.0471542	−	0.998888i	$-0.515015\pi$
$809$	−2.68240	−0.0943083	−0.0471542	+	0.998888i	$0.515015\pi$
$810$	−23.7491	−0.834458
$811$	24.6400	0.865226	0.432613	−	0.901580i	$-0.357592\pi$
$811$	24.6400	0.865226	0.432613	+	0.901580i	$0.357592\pi$
$812$	−4.60535	−0.161616
$813$	−5.18619	−0.181888
$814$	9.27192	0.324981
$815$	−56.3537	−1.97398
$816$	−29.8434	−1.04473
$817$	−55.2753	−1.93384
$818$	44.8627	1.56859
$819$	24.7138	0.863570
$820$	−23.8244	−0.831986
$821$	17.5796	0.613533	0.306766	−	0.951785i	$-0.400753\pi$
$821$	17.5796	0.613533	0.306766	+	0.951785i	$0.400753\pi$
$822$	48.5929	1.69487
$823$	39.0614	1.36160	0.680798	−	0.732471i	$-0.261633\pi$
$823$	39.0614	1.36160	0.680798	+	0.732471i	$0.261633\pi$
$824$	0.0888486	0.00309519
$825$	13.2143	0.460064
$826$	83.6704	2.91127
$827$	44.2919	1.54018	0.770091	−	0.637934i	$-0.220211\pi$
$827$	44.2919	1.54018	0.770091	+	0.637934i	$0.220211\pi$
$828$	−4.84361	−0.168327
$829$	−7.94437	−0.275919	−0.137960	−	0.990438i	$-0.544054\pi$
$829$	−7.94437	−0.275919	−0.137960	+	0.990438i	$0.544054\pi$
$830$	56.8283	1.97254
$831$	−6.23787	−0.216389
$832$	−38.6576	−1.34021
$833$	81.8774	2.83688
$834$	−34.9924	−1.21169
$835$	18.1655	0.628641
$836$	66.2381	2.29089
$837$	−15.1251	−0.522801
$838$	−24.4810	−0.845681
$839$	18.2156	0.628874	0.314437	−	0.949278i	$-0.398184\pi$
$839$	18.2156	0.628874	0.314437	+	0.949278i	$0.398184\pi$
$840$	0.464894	0.0160404
$841$	−28.7596	−0.991710
$842$	−1.41935	−0.0489139
$843$	17.5431	0.604218
$844$	−32.2535	−1.11021
$845$	−28.0939	−0.966459
$846$	6.81441	0.234284
$847$	−136.383	−4.68618
$848$	−0.888357	−0.0305063
$849$	4.80849	0.165027
$850$	−16.0178	−0.549407
$851$	−1.68265	−0.0576805
$852$	1.31279	0.0449753
$853$	−26.9654	−0.923278	−0.461639	−	0.887068i	$-0.652738\pi$
$853$	−26.9654	−0.923278	−0.461639	+	0.887068i	$0.652738\pi$
$854$	−35.7346	−1.22281
$855$	14.3717	0.491502
$856$	−0.263949	−0.00902160
$857$	−5.50240	−0.187958	−0.0939792	−	0.995574i	$-0.529959\pi$
$857$	−5.50240	−0.187958	−0.0939792	+	0.995574i	$0.529959\pi$
$858$	−85.8715	−2.93161
$859$	−25.1705	−0.858806	−0.429403	−	0.903113i	$-0.641276\pi$
$859$	−25.1705	−0.858806	−0.429403	+	0.903113i	$0.641276\pi$
$860$	52.9942	1.80709
$861$	−30.9277	−1.05401
$862$	−81.7333	−2.78385
$863$	46.2037	1.57279	0.786396	−	0.617722i	$-0.211944\pi$
$863$	46.2037	1.57279	0.786396	+	0.617722i	$0.211944\pi$
$864$	−45.1552	−1.53621
$865$	43.3223	1.47300
$866$	16.5015	0.560743
$867$	15.8451	0.538127
$868$	−25.1246	−0.852785
$869$	27.3225	0.926851
$870$	3.47194	0.117710
$871$	−6.33630	−0.214697
$872$	0.135005	0.00457184
$873$	−12.3705	−0.418676
$874$	−24.1255	−0.816059
$875$	−42.1507	−1.42495
$876$	−27.1445	−0.917127
$877$	−1.60978	−0.0543583	−0.0271792	−	0.999631i	$-0.508652\pi$
$877$	−1.60978	−0.0543583	−0.0271792	+	0.999631i	$0.508652\pi$
$878$	69.6344	2.35005
$879$	−10.6918	−0.360626
$880$	64.8393	2.18573
$881$	−16.8059	−0.566204	−0.283102	−	0.959090i	$-0.591363\pi$
$881$	−16.8059	−0.566204	−0.283102	+	0.959090i	$0.591363\pi$
$882$	32.7139	1.10154
$883$	−9.14120	−0.307626	−0.153813	−	0.988100i	$-0.549155\pi$
$883$	−9.14120	−0.307626	−0.153813	+	0.988100i	$0.549155\pi$
$884$	51.8636	1.74436
$885$	−31.4295	−1.05649
$886$	−42.1328	−1.41548
$887$	23.9446	0.803982	0.401991	−	0.915644i	$-0.368318\pi$
$887$	23.9446	0.803982	0.401991	+	0.915644i	$0.368318\pi$
$888$	−0.0283573	−0.000951608 0
$889$	23.5323	0.789249
$890$	50.6689	1.69843
$891$	−29.4361	−0.986145
$892$	−19.9456	−0.667828
$893$	16.9118	0.565933
$894$	4.06624	0.135995
$895$	−28.8381	−0.963951
$896$	1.04859	0.0350308
$897$	15.5838	0.520328
$898$	34.1372	1.13917
$899$	1.31152	0.0437416
$900$	−3.18880	−0.106293
$901$	1.17534	0.0391563
$902$	−59.2653	−1.97332
$903$	68.7944	2.28934
$904$	0.0352940	0.00117386
$905$	67.5259	2.24464
$906$	10.5506	0.350521
$907$	−58.9831	−1.95850	−0.979251	−	0.202650i	$-0.935045\pi$
$907$	−58.9831	−1.95850	−0.979251	+	0.202650i	$0.935045\pi$
$908$	−35.2972	−1.17138
$909$	−0.599947	−0.0198990
$910$	−118.017	−3.91223
$911$	23.1542	0.767132	0.383566	−	0.923513i	$-0.374696\pi$
$911$	23.1542	0.767132	0.383566	+	0.923513i	$0.374696\pi$
$912$	−29.5924	−0.979901
$913$	70.4365	2.33111
$914$	36.2577	1.19930
$915$	13.4231	0.443755
$916$	−46.4360	−1.53429
$917$	63.8096	2.10718
$918$	60.1573	1.98549
$919$	−9.49530	−0.313221	−0.156611	−	0.987660i	$-0.550057\pi$
$919$	−9.49530	−0.313221	−0.156611	+	0.987660i	$0.550057\pi$
$920$	−0.161671	−0.00533012
$921$	5.89121	0.194122
$922$	8.50496	0.280096
$923$	2.32939	0.0766726
$924$	−82.4385	−2.71203
$925$	−1.10778	−0.0364234
$926$	54.5171	1.79154
$927$	−3.41844	−0.112276
$928$	3.91546	0.128531
$929$	15.7609	0.517099	0.258549	−	0.965998i	$-0.416756\pi$
$929$	15.7609	0.517099	0.258549	+	0.965998i	$0.416756\pi$
$930$	18.9413	0.621110
$931$	81.1887	2.66085
$932$	−58.0377	−1.90109
$933$	26.8760	0.879881
$934$	37.1716	1.21629
$935$	−85.7857	−2.80549
$936$	−0.144840	−0.00473423
$937$	0.910838	0.0297558	0.0148779	−	0.999889i	$-0.495264\pi$
$937$	0.910838	0.0297558	0.0148779	+	0.999889i	$0.495264\pi$
$938$	−12.2085	−0.398621
$939$	−31.0697	−1.01392
$940$	−16.2139	−0.528840
$941$	46.3732	1.51172	0.755861	−	0.654732i	$-0.227219\pi$
$941$	46.3732	1.51172	0.755861	+	0.654732i	$0.227219\pi$
$942$	−5.73690	−0.186918
$943$	10.7554	0.350243
$944$	−35.6904	−1.16162
$945$	−68.2065	−2.21876
$946$	131.828	4.28608
$947$	−13.0557	−0.424254	−0.212127	−	0.977242i	$-0.568039\pi$
$947$	−13.0557	−0.424254	−0.212127	+	0.977242i	$0.568039\pi$
$948$	11.9552	0.388288
$949$	−48.1647	−1.56349
$950$	−15.8831	−0.515316
$951$	5.27554	0.171071
$952$	−0.698466	−0.0226374
$953$	−10.5767	−0.342612	−0.171306	−	0.985218i	$-0.554799\pi$
$953$	−10.5767	−0.342612	−0.171306	+	0.985218i	$0.554799\pi$
$954$	0.469605	0.0152040
$955$	−45.1576	−1.46127
$956$	4.73860	0.153257
$957$	4.30334	0.139107
$958$	66.1175	2.13616
$959$	82.7754	2.67296
$960$	27.9786	0.903006
$961$	−23.8450	−0.769192
$962$	7.19873	0.232096
$963$	10.1554	0.327254
$964$	−14.0256	−0.451735
$965$	−60.0584	−1.93335
$966$	30.0261	0.966075
$967$	22.0117	0.707848	0.353924	−	0.935274i	$-0.384847\pi$
$967$	22.0117	0.707848	0.353924	+	0.935274i	$0.384847\pi$
$968$	0.799299	0.0256904
$969$	39.1522	1.25775
$970$	59.0732	1.89673
$971$	−59.4556	−1.90802	−0.954011	−	0.299772i	$-0.903089\pi$
$971$	−59.4556	−1.90802	−0.954011	+	0.299772i	$0.903089\pi$
$972$	20.8114	0.667525
$973$	−59.6077	−1.91094
$974$	63.1640	2.02391
$975$	10.2596	0.328571
$976$	15.2429	0.487915
$977$	3.02562	0.0967980	0.0483990	−	0.998828i	$-0.484588\pi$
$977$	3.02562	0.0967980	0.0483990	+	0.998828i	$0.484588\pi$
$978$	−61.3393	−1.96141
$979$	62.8021	2.00717
$980$	−77.8382	−2.48645
$981$	−5.19429	−0.165841
$982$	7.15558	0.228344
$983$	14.8802	0.474604	0.237302	−	0.971436i	$-0.423737\pi$
$983$	14.8802	0.474604	0.237302	+	0.971436i	$0.423737\pi$
$984$	0.181258	0.00577828
$985$	27.6405	0.880699
$986$	−5.21631	−0.166121
$987$	−21.0481	−0.669969
$988$	51.4273	1.63612
$989$	−23.9238	−0.760733
$990$	−34.2755	−1.08935
$991$	16.4911	0.523856	0.261928	−	0.965087i	$-0.415642\pi$
$991$	16.4911	0.523856	0.261928	+	0.965087i	$0.415642\pi$
$992$	21.3609	0.678210
$993$	7.20723	0.228715
$994$	4.48815	0.142355
$995$	−18.6942	−0.592645
$996$	30.8203	0.976578
$997$	44.2805	1.40238	0.701189	−	0.712975i	$-0.252653\pi$
$997$	44.2805	1.40238	0.701189	+	0.712975i	$0.252653\pi$
$998$	75.0642	2.37612
$999$	4.16041	0.131630

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	349.2.a.b.1.3	✓	17
3.2	odd	2		3141.2.a.e.1.15		17
4.3	odd	2		5584.2.a.m.1.7		17
5.4	even	2		8725.2.a.m.1.15		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.2.a.b.1.3	✓	17	1.1	even	1	trivial
3141.2.a.e.1.15		17	3.2	odd	2
5584.2.a.m.1.7		17	4.3	odd	2
8725.2.a.m.1.15		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)

\(f(q)\)	\(=\)	\(q-1.99653 q^{2} +1.39055 q^{3} +1.98612 q^{4} -2.55061 q^{5} -2.77626 q^{6} -4.72921 q^{7} +0.0277164 q^{8} -1.06638 q^{9} +O(q^{10})\)	\(q-1.99653 q^{2} +1.39055 q^{3} +1.98612 q^{4} -2.55061 q^{5} -2.77626 q^{6} -4.72921 q^{7} +0.0277164 q^{8} -1.06638 q^{9} +5.09235 q^{10} +6.31177 q^{11} +2.76179 q^{12} +4.90047 q^{13} +9.44199 q^{14} -3.54673 q^{15} -4.02757 q^{16} +5.32868 q^{17} +2.12906 q^{18} +5.28386 q^{19} -5.06581 q^{20} -6.57618 q^{21} -12.6016 q^{22} +2.28692 q^{23} +0.0385409 q^{24} +1.50560 q^{25} -9.78391 q^{26} -5.65449 q^{27} -9.39276 q^{28} +0.490308 q^{29} +7.08115 q^{30} +2.67489 q^{31} +7.98572 q^{32} +8.77681 q^{33} -10.6389 q^{34} +12.0624 q^{35} -2.11796 q^{36} -0.735772 q^{37} -10.5494 q^{38} +6.81432 q^{39} -0.0706936 q^{40} +4.70299 q^{41} +13.1295 q^{42} -10.4612 q^{43} +12.5359 q^{44} +2.71993 q^{45} -4.56590 q^{46} +3.20066 q^{47} -5.60052 q^{48} +15.3654 q^{49} -3.00596 q^{50} +7.40978 q^{51} +9.73291 q^{52} +0.220569 q^{53} +11.2893 q^{54} -16.0989 q^{55} -0.131077 q^{56} +7.34744 q^{57} -0.978912 q^{58} +8.86152 q^{59} -7.04423 q^{60} -3.78465 q^{61} -5.34049 q^{62} +5.04315 q^{63} -7.88856 q^{64} -12.4992 q^{65} -17.5231 q^{66} -1.29300 q^{67} +10.5834 q^{68} +3.18007 q^{69} -24.0828 q^{70} +0.475339 q^{71} -0.0295563 q^{72} -9.82860 q^{73} +1.46899 q^{74} +2.09360 q^{75} +10.4944 q^{76} -29.8497 q^{77} -13.6050 q^{78} +4.32881 q^{79} +10.2728 q^{80} -4.66367 q^{81} -9.38965 q^{82} +11.1595 q^{83} -13.0611 q^{84} -13.5914 q^{85} +20.8860 q^{86} +0.681795 q^{87} +0.174940 q^{88} +9.95000 q^{89} -5.43040 q^{90} -23.1753 q^{91} +4.54209 q^{92} +3.71956 q^{93} -6.39021 q^{94} -13.4770 q^{95} +11.1045 q^{96} +11.6004 q^{97} -30.6775 q^{98} -6.73077 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 5 q^{2} + 6 q^{3} + 19 q^{4} + 5 q^{5} - 3 q^{6} + q^{7} + 9 q^{8} + 25 q^{9}+O(q^{10}) \) 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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