LMFDB - Embedded newform 4033.2.a.d.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4033,2,Mod(1,4033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4033, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4033 = 37 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4033.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:	$32.2036671352$
Analytic rank:	$1$
Dimension:	$79$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	4033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.06826 q^{2} +0.566483 q^{3} +2.27770 q^{4} +0.827262 q^{5} -1.17163 q^{6} +0.908209 q^{7} -0.574346 q^{8} -2.67910 q^{9} +O(q^{10})$	\(q-2.06826 q^{2} +0.566483 q^{3} +2.27770 q^{4} +0.827262 q^{5} -1.17163 q^{6} +0.908209 q^{7} -0.574346 q^{8} -2.67910 q^{9} -1.71099 q^{10} +3.66274 q^{11} +1.29028 q^{12} -3.44386 q^{13} -1.87841 q^{14} +0.468630 q^{15} -3.36749 q^{16} +5.13833 q^{17} +5.54107 q^{18} -1.92001 q^{19} +1.88425 q^{20} +0.514485 q^{21} -7.57550 q^{22} +4.20861 q^{23} -0.325357 q^{24} -4.31564 q^{25} +7.12280 q^{26} -3.21711 q^{27} +2.06862 q^{28} -6.65775 q^{29} -0.969249 q^{30} -4.64372 q^{31} +8.11354 q^{32} +2.07488 q^{33} -10.6274 q^{34} +0.751327 q^{35} -6.10217 q^{36} -1.00000 q^{37} +3.97108 q^{38} -1.95089 q^{39} -0.475134 q^{40} -1.85570 q^{41} -1.06409 q^{42} +3.74176 q^{43} +8.34261 q^{44} -2.21632 q^{45} -8.70450 q^{46} +8.96463 q^{47} -1.90763 q^{48} -6.17516 q^{49} +8.92586 q^{50} +2.91078 q^{51} -7.84407 q^{52} -8.79679 q^{53} +6.65383 q^{54} +3.03005 q^{55} -0.521626 q^{56} -1.08765 q^{57} +13.7700 q^{58} -3.28335 q^{59} +1.06740 q^{60} -3.51226 q^{61} +9.60442 q^{62} -2.43318 q^{63} -10.0459 q^{64} -2.84898 q^{65} -4.29140 q^{66} +4.69107 q^{67} +11.7035 q^{68} +2.38411 q^{69} -1.55394 q^{70} -4.16845 q^{71} +1.53873 q^{72} -7.60926 q^{73} +2.06826 q^{74} -2.44474 q^{75} -4.37320 q^{76} +3.32654 q^{77} +4.03495 q^{78} +4.34396 q^{79} -2.78580 q^{80} +6.21485 q^{81} +3.83807 q^{82} -3.77274 q^{83} +1.17184 q^{84} +4.25074 q^{85} -7.73892 q^{86} -3.77151 q^{87} -2.10368 q^{88} -8.21640 q^{89} +4.58391 q^{90} -3.12775 q^{91} +9.58594 q^{92} -2.63059 q^{93} -18.5412 q^{94} -1.58835 q^{95} +4.59619 q^{96} -11.2358 q^{97} +12.7718 q^{98} -9.81284 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) $ 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + 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 $

$2$	−2.06826	−1.46248	−0.731240	−	0.682120i	$-0.761058\pi$
$2$	−2.06826	−1.46248	−0.731240	+	0.682120i	$0.761058\pi$
$3$	0.566483	0.327059	0.163530	−	0.986538i	$-0.447712\pi$
$3$	0.566483	0.327059	0.163530	+	0.986538i	$0.447712\pi$
$4$	2.27770	1.13885
$5$	0.827262	0.369963	0.184981	−	0.982742i	$-0.440777\pi$
$5$	0.827262	0.369963	0.184981	+	0.982742i	$0.440777\pi$
$6$	−1.17163	−0.478318
$7$	0.908209	0.343271	0.171635	−	0.985161i	$-0.445095\pi$
$7$	0.908209	0.343271	0.171635	+	0.985161i	$0.445095\pi$
$8$	−0.574346	−0.203062
$9$	−2.67910	−0.893032
$10$	−1.71099	−0.541063
$11$	3.66274	1.10436	0.552179	−	0.833725i	$-0.313796\pi$
$11$	3.66274	1.10436	0.552179	+	0.833725i	$0.313796\pi$
$12$	1.29028	0.372471
$13$	−3.44386	−0.955156	−0.477578	−	0.878589i	$-0.658485\pi$
$13$	−3.44386	−0.955156	−0.477578	+	0.878589i	$0.658485\pi$
$14$	−1.87841	−0.502027
$15$	0.468630	0.121000
$16$	−3.36749	−0.841874
$17$	5.13833	1.24623	0.623114	−	0.782131i	$-0.285867\pi$
$17$	5.13833	1.24623	0.623114	+	0.782131i	$0.285867\pi$
$18$	5.54107	1.30604
$19$	−1.92001	−0.440481	−0.220240	−	0.975446i	$-0.570684\pi$
$19$	−1.92001	−0.440481	−0.220240	+	0.975446i	$0.570684\pi$
$20$	1.88425	0.421331
$21$	0.514485	0.112270
$22$	−7.57550	−1.61510
$23$	4.20861	0.877556	0.438778	−	0.898595i	$-0.355411\pi$
$23$	4.20861	0.877556	0.438778	+	0.898595i	$0.355411\pi$
$24$	−0.325357	−0.0664133
$25$	−4.31564	−0.863127
$26$	7.12280	1.39690
$27$	−3.21711	−0.619134
$28$	2.06862	0.390933
$29$	−6.65775	−1.23631	−0.618157	−	0.786055i	$-0.712120\pi$
$29$	−6.65775	−1.23631	−0.618157	+	0.786055i	$0.712120\pi$
$30$	−0.969249	−0.176960
$31$	−4.64372	−0.834037	−0.417019	−	0.908898i	$-0.636925\pi$
$31$	−4.64372	−0.834037	−0.417019	+	0.908898i	$0.636925\pi$
$32$	8.11354	1.43429
$33$	2.07488	0.361191
$34$	−10.6274	−1.82258
$35$	0.751327	0.126997
$36$	−6.10217	−1.01703
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	3.97108	0.644194
$39$	−1.95089	−0.312393
$40$	−0.475134	−0.0751253
$41$	−1.85570	−0.289812	−0.144906	−	0.989445i	$-0.546288\pi$
$41$	−1.85570	−0.289812	−0.144906	+	0.989445i	$0.546288\pi$
$42$	−1.06409	−0.164193
$43$	3.74176	0.570612	0.285306	−	0.958436i	$-0.407905\pi$
$43$	3.74176	0.570612	0.285306	+	0.958436i	$0.407905\pi$
$44$	8.34261	1.25770
$45$	−2.21632	−0.330389
$46$	−8.70450	−1.28341
$47$	8.96463	1.30763	0.653813	−	0.756656i	$-0.273168\pi$
$47$	8.96463	1.30763	0.653813	+	0.756656i	$0.273168\pi$
$48$	−1.90763	−0.275343
$49$	−6.17516	−0.882165
$50$	8.92586	1.26231
$51$	2.91078	0.407590
$52$	−7.84407	−1.08778
$53$	−8.79679	−1.20833	−0.604166	−	0.796859i	$-0.706494\pi$
$53$	−8.79679	−1.20833	−0.604166	+	0.796859i	$0.706494\pi$
$54$	6.65383	0.905471
$55$	3.03005	0.408572
$56$	−0.521626	−0.0697052
$57$	−1.08765	−0.144063
$58$	13.7700	1.80808
$59$	−3.28335	−0.427456	−0.213728	−	0.976893i	$-0.568561\pi$
$59$	−3.28335	−0.427456	−0.213728	+	0.976893i	$0.568561\pi$
$60$	1.06740	0.137800
$61$	−3.51226	−0.449699	−0.224850	−	0.974393i	$-0.572189\pi$
$61$	−3.51226	−0.449699	−0.224850	+	0.974393i	$0.572189\pi$
$62$	9.60442	1.21976
$63$	−2.43318	−0.306552
$64$	−10.0459	−1.25574
$65$	−2.84898	−0.353372
$66$	−4.29140	−0.528234
$67$	4.69107	0.573106	0.286553	−	0.958064i	$-0.407491\pi$
$67$	4.69107	0.573106	0.286553	+	0.958064i	$0.407491\pi$
$68$	11.7035	1.41926
$69$	2.38411	0.287013
$70$	−1.55394	−0.185731
$71$	−4.16845	−0.494704	−0.247352	−	0.968926i	$-0.579560\pi$
$71$	−4.16845	−0.494704	−0.247352	+	0.968926i	$0.579560\pi$
$72$	1.53873	0.181341
$73$	−7.60926	−0.890596	−0.445298	−	0.895382i	$-0.646902\pi$
$73$	−7.60926	−0.890596	−0.445298	+	0.895382i	$0.646902\pi$
$74$	2.06826	0.240430
$75$	−2.44474	−0.282294
$76$	−4.37320	−0.501640
$77$	3.32654	0.379094
$78$	4.03495	0.456868
$79$	4.34396	0.488734	0.244367	−	0.969683i	$-0.421420\pi$
$79$	4.34396	0.488734	0.244367	+	0.969683i	$0.421420\pi$
$80$	−2.78580	−0.311462
$81$	6.21485	0.690539
$82$	3.83807	0.423844
$83$	−3.77274	−0.414112	−0.207056	−	0.978329i	$-0.566388\pi$
$83$	−3.77274	−0.414112	−0.207056	+	0.978329i	$0.566388\pi$
$84$	1.17184	0.127858
$85$	4.25074	0.461058
$86$	−7.73892	−0.834509
$87$	−3.77151	−0.404348
$88$	−2.10368	−0.224253
$89$	−8.21640	−0.870937	−0.435468	−	0.900204i	$-0.643417\pi$
$89$	−8.21640	−0.870937	−0.435468	+	0.900204i	$0.643417\pi$
$90$	4.58391	0.483187
$91$	−3.12775	−0.327877
$92$	9.58594	0.999403
$93$	−2.63059	−0.272780
$94$	−18.5412	−1.91238
$95$	−1.58835	−0.162962
$96$	4.59619	0.469096
$97$	−11.2358	−1.14083	−0.570413	−	0.821358i	$-0.693217\pi$
$97$	−11.2358	−1.14083	−0.570413	+	0.821358i	$0.693217\pi$
$98$	12.7718	1.29015
$99$	−9.81284	−0.986228
$100$	−9.82971	−0.982971
$101$	−11.9020	−1.18429	−0.592145	−	0.805832i	$-0.701719\pi$
$101$	−11.9020	−1.18429	−0.592145	+	0.805832i	$0.701719\pi$
$102$	−6.02024	−0.596093
$103$	10.6958	1.05389	0.526945	−	0.849900i	$-0.323338\pi$
$103$	10.6958	1.05389	0.526945	+	0.849900i	$0.323338\pi$
$104$	1.97797	0.193956
$105$	0.425614	0.0415357
$106$	18.1940	1.76716
$107$	2.00346	0.193682	0.0968408	−	0.995300i	$-0.469126\pi$
$107$	2.00346	0.193682	0.0968408	+	0.995300i	$0.469126\pi$
$108$	−7.32761	−0.705099
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	−6.26693	−0.597528
$111$	−0.566483	−0.0537682
$112$	−3.05839	−0.288991
$113$	−11.6445	−1.09542	−0.547712	−	0.836667i	$-0.684501\pi$
$113$	−11.6445	−1.09542	−0.547712	+	0.836667i	$0.684501\pi$
$114$	2.24955	0.210690
$115$	3.48163	0.324663
$116$	−15.1643	−1.40797
$117$	9.22644	0.852985
$118$	6.79082	0.625146
$119$	4.66668	0.427794
$120$	−0.269156	−0.0245704
$121$	2.41569	0.219608
$122$	7.26427	0.657676
$123$	−1.05122	−0.0947857
$124$	−10.5770	−0.949842
$125$	−7.70647	−0.689288
$126$	5.03245	0.448326
$127$	5.98802	0.531351	0.265675	−	0.964063i	$-0.414405\pi$
$127$	5.98802	0.531351	0.265675	+	0.964063i	$0.414405\pi$
$128$	4.55047	0.402209
$129$	2.11964	0.186624
$130$	5.89242	0.516800
$131$	−8.91813	−0.779181	−0.389590	−	0.920988i	$-0.627383\pi$
$131$	−8.91813	−0.779181	−0.389590	+	0.920988i	$0.627383\pi$
$132$	4.72595	0.411341
$133$	−1.74377	−0.151204
$134$	−9.70236	−0.838156
$135$	−2.66140	−0.229057
$136$	−2.95118	−0.253061
$137$	21.6555	1.85015	0.925075	−	0.379784i	$-0.124002\pi$
$137$	21.6555	1.85015	0.925075	+	0.379784i	$0.124002\pi$
$138$	−4.93096	−0.419751
$139$	1.87524	0.159056	0.0795279	−	0.996833i	$-0.474659\pi$
$139$	1.87524	0.159056	0.0795279	+	0.996833i	$0.474659\pi$
$140$	1.71129	0.144631
$141$	5.07832	0.427671
$142$	8.62144	0.723495
$143$	−12.6140	−1.05483
$144$	9.02184	0.751820
$145$	−5.50771	−0.457390
$146$	15.7379	1.30248
$147$	−3.49812	−0.288520
$148$	−2.27770	−0.187225
$149$	2.68685	0.220116	0.110058	−	0.993925i	$-0.464896\pi$
$149$	2.68685	0.220116	0.110058	+	0.993925i	$0.464896\pi$
$150$	5.05635	0.412849
$151$	−4.50649	−0.366733	−0.183367	−	0.983045i	$-0.558700\pi$
$151$	−4.50649	−0.366733	−0.183367	+	0.983045i	$0.558700\pi$
$152$	1.10275	0.0894448
$153$	−13.7661	−1.11292
$154$	−6.88014	−0.554418
$155$	−3.84158	−0.308563
$156$	−4.44354	−0.355768
$157$	−0.685829	−0.0547351	−0.0273676	−	0.999625i	$-0.508712\pi$
$157$	−0.685829	−0.0547351	−0.0273676	+	0.999625i	$0.508712\pi$
$158$	−8.98444	−0.714764
$159$	−4.98323	−0.395196
$160$	6.71203	0.530632
$161$	3.82230	0.301240
$162$	−12.8539	−1.00990
$163$	14.1208	1.10603	0.553014	−	0.833172i	$-0.313478\pi$
$163$	14.1208	1.10603	0.553014	+	0.833172i	$0.313478\pi$
$164$	−4.22672	−0.330052
$165$	1.71647	0.133627
$166$	7.80300	0.605630
$167$	−11.2878	−0.873473	−0.436736	−	0.899590i	$-0.643866\pi$
$167$	−11.2878	−0.873473	−0.436736	+	0.899590i	$0.643866\pi$
$168$	−0.295492	−0.0227977
$169$	−1.13981	−0.0876778
$170$	−8.79164	−0.674288
$171$	5.14389	0.393363
$172$	8.52258	0.649841
$173$	−19.2251	−1.46166	−0.730828	−	0.682561i	$-0.760866\pi$
$173$	−19.2251	−1.46166	−0.730828	+	0.682561i	$0.760866\pi$
$174$	7.80045	0.591351
$175$	−3.91950	−0.296286
$176$	−12.3343	−0.929731
$177$	−1.85996	−0.139803
$178$	16.9936	1.27373
$179$	12.7294	0.951444	0.475722	−	0.879596i	$-0.342187\pi$
$179$	12.7294	0.951444	0.475722	+	0.879596i	$0.342187\pi$
$180$	−5.04809	−0.376262
$181$	23.5062	1.74720	0.873599	−	0.486646i	$-0.161780\pi$
$181$	23.5062	1.74720	0.873599	+	0.486646i	$0.161780\pi$
$182$	6.46899	0.479514
$183$	−1.98964	−0.147078
$184$	−2.41720	−0.178198
$185$	−0.827262	−0.0608215
$186$	5.44075	0.398935
$187$	18.8204	1.37628
$188$	20.4187	1.48919
$189$	−2.92181	−0.212531
$190$	3.28512	0.238328
$191$	20.7342	1.50027	0.750137	−	0.661282i	$-0.229988\pi$
$191$	20.7342	1.50027	0.750137	+	0.661282i	$0.229988\pi$
$192$	−5.69085	−0.410701
$193$	−2.48917	−0.179175	−0.0895873	−	0.995979i	$-0.528555\pi$
$193$	−2.48917	−0.179175	−0.0895873	+	0.995979i	$0.528555\pi$
$194$	23.2386	1.66844
$195$	−1.61390	−0.115574
$196$	−14.0651	−1.00465
$197$	1.81073	0.129009	0.0645044	−	0.997917i	$-0.479453\pi$
$197$	1.81073	0.129009	0.0645044	+	0.997917i	$0.479453\pi$
$198$	20.2955	1.44234
$199$	−21.5718	−1.52919	−0.764593	−	0.644514i	$-0.777060\pi$
$199$	−21.5718	−1.52919	−0.764593	+	0.644514i	$0.777060\pi$
$200$	2.47867	0.175268
$201$	2.65742	0.187440
$202$	24.6163	1.73200
$203$	−6.04663	−0.424390
$204$	6.62986	0.464183
$205$	−1.53515	−0.107220
$206$	−22.1217	−1.54129
$207$	−11.2753	−0.783686
$208$	11.5972	0.804120
$209$	−7.03251	−0.486449
$210$	−0.880281	−0.0607451
$211$	10.2421	0.705093	0.352546	−	0.935794i	$-0.385316\pi$
$211$	10.2421	0.705093	0.352546	+	0.935794i	$0.385316\pi$
$212$	−20.0364	−1.37611
$213$	−2.36136	−0.161798
$214$	−4.14367	−0.283255
$215$	3.09541	0.211105
$216$	1.84774	0.125722
$217$	−4.21747	−0.286301
$218$	2.06826	0.140080
$219$	−4.31052	−0.291278
$220$	6.90153	0.465301
$221$	−17.6957	−1.19034
$222$	1.17163	0.0786350
$223$	−3.85467	−0.258128	−0.129064	−	0.991636i	$-0.541197\pi$
$223$	−3.85467	−0.258128	−0.129064	+	0.991636i	$0.541197\pi$
$224$	7.36879	0.492348
$225$	11.5620	0.770801
$226$	24.0839	1.60204
$227$	−25.9936	−1.72526	−0.862629	−	0.505837i	$-0.831184\pi$
$227$	−25.9936	−1.72526	−0.862629	+	0.505837i	$0.831184\pi$
$228$	−2.47735	−0.164066
$229$	−4.19456	−0.277184	−0.138592	−	0.990350i	$-0.544258\pi$
$229$	−4.19456	−0.277184	−0.138592	+	0.990350i	$0.544258\pi$
$230$	−7.20090	−0.474814
$231$	1.88443	0.123986
$232$	3.82385	0.251048
$233$	−17.3657	−1.13766	−0.568832	−	0.822454i	$-0.692605\pi$
$233$	−17.3657	−1.13766	−0.568832	+	0.822454i	$0.692605\pi$
$234$	−19.0827	−1.24747
$235$	7.41610	0.483773
$236$	−7.47847	−0.486807
$237$	2.46078	0.159845
$238$	−9.65190	−0.625640
$239$	13.5667	0.877558	0.438779	−	0.898595i	$-0.355411\pi$
$239$	13.5667	0.877558	0.438779	+	0.898595i	$0.355411\pi$
$240$	−1.57811	−0.101867
$241$	1.00763	0.0649071	0.0324535	−	0.999473i	$-0.489668\pi$
$241$	1.00763	0.0649071	0.0324535	+	0.999473i	$0.489668\pi$
$242$	−4.99628	−0.321173
$243$	13.1720	0.844981
$244$	−7.99987	−0.512139
$245$	−5.10847	−0.326368
$246$	2.17420	0.138622
$247$	6.61225	0.420728
$248$	2.66710	0.169361
$249$	−2.13719	−0.135439
$250$	15.9390	1.00807
$251$	11.2271	0.708648	0.354324	−	0.935123i	$-0.384711\pi$
$251$	11.2271	0.708648	0.354324	+	0.935123i	$0.384711\pi$
$252$	−5.54204	−0.349116
$253$	15.4151	0.969137
$254$	−12.3848	−0.777090
$255$	2.40798	0.150793
$256$	10.6803	0.667517
$257$	4.44146	0.277051	0.138525	−	0.990359i	$-0.455764\pi$
$257$	4.44146	0.277051	0.138525	+	0.990359i	$0.455764\pi$
$258$	−4.38397	−0.272934
$259$	−0.908209	−0.0564334
$260$	−6.48910	−0.402437
$261$	17.8368	1.10407
$262$	18.4450	1.13954
$263$	−10.9128	−0.672913	−0.336456	−	0.941699i	$-0.609228\pi$
$263$	−10.9128	−0.672913	−0.336456	+	0.941699i	$0.609228\pi$
$264$	−1.19170	−0.0733441
$265$	−7.27725	−0.447038
$266$	3.60657	0.221133
$267$	−4.65445	−0.284848
$268$	10.6848	0.652680
$269$	16.0528	0.978757	0.489378	−	0.872072i	$-0.337224\pi$
$269$	16.0528	0.978757	0.489378	+	0.872072i	$0.337224\pi$
$270$	5.50446	0.334991
$271$	−3.96112	−0.240621	−0.120310	−	0.992736i	$-0.538389\pi$
$271$	−3.96112	−0.240621	−0.120310	+	0.992736i	$0.538389\pi$
$272$	−17.3033	−1.04917
$273$	−1.77182	−0.107235
$274$	−44.7891	−2.70581
$275$	−15.8071	−0.953202
$276$	5.43027	0.326864
$277$	2.73817	0.164521	0.0822603	−	0.996611i	$-0.473786\pi$
$277$	2.73817	0.164521	0.0822603	+	0.996611i	$0.473786\pi$
$278$	−3.87848	−0.232616
$279$	12.4410	0.744822
$280$	−0.431521	−0.0257883
$281$	−6.28063	−0.374671	−0.187336	−	0.982296i	$-0.559985\pi$
$281$	−6.28063	−0.374671	−0.187336	+	0.982296i	$0.559985\pi$
$282$	−10.5033	−0.625461
$283$	−20.5295	−1.22035	−0.610177	−	0.792265i	$-0.708902\pi$
$283$	−20.5295	−1.22035	−0.610177	+	0.792265i	$0.708902\pi$
$284$	−9.49446	−0.563393
$285$	−0.899775	−0.0532981
$286$	26.0890	1.54267
$287$	−1.68537	−0.0994840
$288$	−21.7370	−1.28086
$289$	9.40242	0.553083
$290$	11.3914	0.668924
$291$	−6.36491	−0.373118
$292$	−17.3316	−1.01425
$293$	−12.7213	−0.743184	−0.371592	−	0.928396i	$-0.621188\pi$
$293$	−12.7213	−0.743184	−0.371592	+	0.928396i	$0.621188\pi$
$294$	7.23503	0.421955
$295$	−2.71619	−0.158143
$296$	0.574346	0.0333832
$297$	−11.7835	−0.683746
$298$	−5.55711	−0.321915
$299$	−14.4939	−0.838203
$300$	−5.56837	−0.321490
$301$	3.39830	0.195875
$302$	9.32059	0.536340
$303$	−6.74227	−0.387333
$304$	6.46563	0.370829
$305$	−2.90556	−0.166372
$306$	28.4718	1.62763
$307$	24.5729	1.40245	0.701224	−	0.712941i	$-0.252637\pi$
$307$	24.5729	1.40245	0.701224	+	0.712941i	$0.252637\pi$
$308$	7.57684	0.431730
$309$	6.05900	0.344684
$310$	7.94538	0.451267
$311$	−27.0646	−1.53469	−0.767347	−	0.641232i	$-0.778424\pi$
$311$	−27.0646	−1.53469	−0.767347	+	0.641232i	$0.778424\pi$
$312$	1.12049	0.0634350
$313$	3.08938	0.174622	0.0873109	−	0.996181i	$-0.472173\pi$
$313$	3.08938	0.174622	0.0873109	+	0.996181i	$0.472173\pi$
$314$	1.41847	0.0800490
$315$	−2.01288	−0.113413
$316$	9.89422	0.556594
$317$	−17.3550	−0.974757	−0.487378	−	0.873191i	$-0.662047\pi$
$317$	−17.3550	−0.974757	−0.487378	+	0.873191i	$0.662047\pi$
$318$	10.3066	0.577967
$319$	−24.3856	−1.36533
$320$	−8.31061	−0.464577
$321$	1.13493	0.0633454
$322$	−7.90551	−0.440557
$323$	−9.86565	−0.548939
$324$	14.1555	0.786418
$325$	14.8625	0.824421
$326$	−29.2055	−1.61754
$327$	−0.566483	−0.0313266
$328$	1.06581	0.0588497
$329$	8.14176	0.448870
$330$	−3.55011	−0.195427
$331$	−23.2287	−1.27677	−0.638383	−	0.769719i	$-0.720396\pi$
$331$	−23.2287	−1.27677	−0.638383	+	0.769719i	$0.720396\pi$
$332$	−8.59314	−0.471610
$333$	2.67910	0.146814
$334$	23.3460	1.27744
$335$	3.88075	0.212028
$336$	−1.73253	−0.0945171
$337$	−2.48202	−0.135204	−0.0676021	−	0.997712i	$-0.521535\pi$
$337$	−2.48202	−0.135204	−0.0676021	+	0.997712i	$0.521535\pi$
$338$	2.35742	0.128227
$339$	−6.59643	−0.358269
$340$	9.68190	0.525075
$341$	−17.0088	−0.921077
$342$	−10.6389	−0.575286
$343$	−11.9658	−0.646092
$344$	−2.14906	−0.115870
$345$	1.97228	0.106184
$346$	39.7625	2.13764
$347$	26.6694	1.43169	0.715845	−	0.698259i	$-0.246041\pi$
$347$	26.6694	1.43169	0.715845	+	0.698259i	$0.246041\pi$
$348$	−8.59034	−0.460491
$349$	−11.2802	−0.603817	−0.301909	−	0.953337i	$-0.597624\pi$
$349$	−11.2802	−0.603817	−0.301909	+	0.953337i	$0.597624\pi$
$350$	8.10654	0.433313
$351$	11.0793	0.591369
$352$	29.7178	1.58397
$353$	15.5913	0.829839	0.414920	−	0.909858i	$-0.363810\pi$
$353$	15.5913	0.829839	0.414920	+	0.909858i	$0.363810\pi$
$354$	3.84689	0.204460
$355$	−3.44840	−0.183022
$356$	−18.7145	−0.991864
$357$	2.64360	0.139914
$358$	−26.3278	−1.39147
$359$	19.9836	1.05470	0.527348	−	0.849650i	$-0.323187\pi$
$359$	19.9836	1.05470	0.527348	+	0.849650i	$0.323187\pi$
$360$	1.27293	0.0670893
$361$	−15.3136	−0.805977
$362$	−48.6168	−2.55524
$363$	1.36845	0.0718250
$364$	−7.12406	−0.373402
$365$	−6.29485	−0.329488
$366$	4.11509	0.215099
$367$	−20.4708	−1.06856	−0.534282	−	0.845306i	$-0.679418\pi$
$367$	−20.4708	−1.06856	−0.534282	+	0.845306i	$0.679418\pi$
$368$	−14.1725	−0.738792
$369$	4.97160	0.258811
$370$	1.71099	0.0889503
$371$	−7.98932	−0.414785
$372$	−5.99169	−0.310655
$373$	−0.516857	−0.0267618	−0.0133809	−	0.999910i	$-0.504259\pi$
$373$	−0.516857	−0.0267618	−0.0133809	+	0.999910i	$0.504259\pi$
$374$	−38.9254	−2.01279
$375$	−4.36559	−0.225438
$376$	−5.14880	−0.265529
$377$	22.9284	1.18087
$378$	6.04307	0.310822
$379$	13.5502	0.696025	0.348013	−	0.937490i	$-0.386857\pi$
$379$	13.5502	0.696025	0.348013	+	0.937490i	$0.386857\pi$
$380$	−3.61778	−0.185588
$381$	3.39211	0.173783
$382$	−42.8837	−2.19412
$383$	6.13999	0.313739	0.156869	−	0.987619i	$-0.449860\pi$
$383$	6.13999	0.313739	0.156869	+	0.987619i	$0.449860\pi$
$384$	2.57777	0.131546
$385$	2.75192	0.140251
$386$	5.14826	0.262039
$387$	−10.0245	−0.509575
$388$	−25.5918	−1.29923
$389$	−21.7974	−1.10517	−0.552586	−	0.833456i	$-0.686359\pi$
$389$	−21.7974	−1.10517	−0.552586	+	0.833456i	$0.686359\pi$
$390$	3.33796	0.169024
$391$	21.6252	1.09364
$392$	3.54667	0.179134
$393$	−5.05197	−0.254838
$394$	−3.74505	−0.188673
$395$	3.59360	0.180813
$396$	−22.3507	−1.12316
$397$	−1.29433	−0.0649607	−0.0324804	−	0.999472i	$-0.510341\pi$
$397$	−1.29433	−0.0649607	−0.0324804	+	0.999472i	$0.510341\pi$
$398$	44.6161	2.23640
$399$	−0.987818	−0.0494527
$400$	14.5329	0.726644
$401$	−26.3691	−1.31681	−0.658404	−	0.752665i	$-0.728768\pi$
$401$	−26.3691	−1.31681	−0.658404	+	0.752665i	$0.728768\pi$
$402$	−5.49622	−0.274127
$403$	15.9923	0.796636
$404$	−27.1090	−1.34873
$405$	5.14131	0.255474
$406$	12.5060	0.620662
$407$	−3.66274	−0.181555
$408$	−1.67179	−0.0827661
$409$	−5.89273	−0.291377	−0.145688	−	0.989331i	$-0.546540\pi$
$409$	−5.89273	−0.291377	−0.145688	+	0.989331i	$0.546540\pi$
$410$	3.17509	0.156807
$411$	12.2675	0.605109
$412$	24.3618	1.20022
$413$	−2.98197	−0.146733
$414$	23.3202	1.14613
$415$	−3.12104	−0.153206
$416$	−27.9419	−1.36997
$417$	1.06229	0.0520207
$418$	14.5450	0.711422
$419$	−10.6981	−0.522638	−0.261319	−	0.965253i	$-0.584157\pi$
$419$	−10.6981	−0.522638	−0.261319	+	0.965253i	$0.584157\pi$
$420$	0.969420	0.0473028
$421$	21.9973	1.07209	0.536043	−	0.844191i	$-0.319919\pi$
$421$	21.9973	1.07209	0.536043	+	0.844191i	$0.319919\pi$
$422$	−21.1832	−1.03118
$423$	−24.0171	−1.16775
$424$	5.05240	0.245366
$425$	−22.1752	−1.07565
$426$	4.88390	0.236626
$427$	−3.18987	−0.154369
$428$	4.56327	0.220574
$429$	−7.14561	−0.344993
$430$	−6.40212	−0.308737
$431$	−15.2122	−0.732747	−0.366373	−	0.930468i	$-0.619401\pi$
$431$	−15.2122	−0.732747	−0.366373	+	0.930468i	$0.619401\pi$
$432$	10.8336	0.521233
$433$	−30.9661	−1.48813	−0.744067	−	0.668105i	$-0.767106\pi$
$433$	−30.9661	−1.48813	−0.744067	+	0.668105i	$0.767106\pi$
$434$	8.72283	0.418709
$435$	−3.12002	−0.149594
$436$	−2.27770	−0.109082
$437$	−8.08058	−0.386547
$438$	8.91527	0.425988
$439$	12.5976	0.601250	0.300625	−	0.953742i	$-0.402805\pi$
$439$	12.5976	0.601250	0.300625	+	0.953742i	$0.402805\pi$
$440$	−1.74030	−0.0829653
$441$	16.5438	0.787802
$442$	36.5993	1.74085
$443$	21.1345	1.00413	0.502065	−	0.864830i	$-0.332574\pi$
$443$	21.1345	1.00413	0.502065	+	0.864830i	$0.332574\pi$
$444$	−1.29028	−0.0612338
$445$	−6.79712	−0.322214
$446$	7.97246	0.377507
$447$	1.52206	0.0719908
$448$	−9.12380	−0.431059
$449$	−33.2923	−1.57116	−0.785580	−	0.618760i	$-0.787635\pi$
$449$	−33.2923	−1.57116	−0.785580	+	0.618760i	$0.787635\pi$
$450$	−23.9132	−1.12728
$451$	−6.79696	−0.320056
$452$	−26.5227	−1.24752
$453$	−2.55285	−0.119944
$454$	53.7616	2.52315
$455$	−2.58747	−0.121302
$456$	0.624690	0.0292538
$457$	−21.1726	−0.990411	−0.495205	−	0.868776i	$-0.664907\pi$
$457$	−21.1726	−0.990411	−0.495205	+	0.868776i	$0.664907\pi$
$458$	8.67543	0.405376
$459$	−16.5306	−0.771582
$460$	7.93008	0.369742
$461$	−34.6730	−1.61488	−0.807440	−	0.589949i	$-0.799148\pi$
$461$	−34.6730	−1.61488	−0.807440	+	0.589949i	$0.799148\pi$
$462$	−3.89749	−0.181327
$463$	−30.7884	−1.43086	−0.715428	−	0.698686i	$-0.753768\pi$
$463$	−30.7884	−1.43086	−0.715428	+	0.698686i	$0.753768\pi$
$464$	22.4199	1.04082
$465$	−2.17619	−0.100918
$466$	35.9167	1.66381
$467$	−18.8646	−0.872951	−0.436476	−	0.899716i	$-0.643773\pi$
$467$	−18.8646	−0.872951	−0.436476	+	0.899716i	$0.643773\pi$
$468$	21.0150	0.971420
$469$	4.26048	0.196731
$470$	−15.3384	−0.707509
$471$	−0.388511	−0.0179016
$472$	1.88578	0.0868000
$473$	13.7051	0.630161
$474$	−5.08954	−0.233770
$475$	8.28607	0.380191
$476$	10.6293	0.487192
$477$	23.5674	1.07908
$478$	−28.0595	−1.28341
$479$	15.4620	0.706476	0.353238	−	0.935533i	$-0.385081\pi$
$479$	15.4620	0.706476	0.353238	+	0.935533i	$0.385081\pi$
$480$	3.80225	0.173548
$481$	3.44386	0.157027
$482$	−2.08404	−0.0949253
$483$	2.16527	0.0985232
$484$	5.50221	0.250100
$485$	−9.29498	−0.422063
$486$	−27.2430	−1.23577
$487$	−38.3096	−1.73597	−0.867987	−	0.496586i	$-0.834587\pi$
$487$	−38.3096	−1.73597	−0.867987	+	0.496586i	$0.834587\pi$
$488$	2.01725	0.0913168
$489$	7.99921	0.361737
$490$	10.5656	0.477307
$491$	14.2844	0.644645	0.322323	−	0.946630i	$-0.395536\pi$
$491$	14.2844	0.644645	0.322323	+	0.946630i	$0.395536\pi$
$492$	−2.39437	−0.107946
$493$	−34.2097	−1.54073
$494$	−13.6759	−0.615306
$495$	−8.11779	−0.364868
$496$	15.6377	0.702154
$497$	−3.78583	−0.169818
$498$	4.42027	0.198077
$499$	20.8113	0.931642	0.465821	−	0.884879i	$-0.345759\pi$
$499$	20.8113	0.931642	0.465821	+	0.884879i	$0.345759\pi$
$500$	−17.5530	−0.784994
$501$	−6.39433	−0.285677
$502$	−23.2206	−1.03638
$503$	39.5125	1.76178	0.880888	−	0.473325i	$-0.156946\pi$
$503$	39.5125	1.76178	0.880888	+	0.473325i	$0.156946\pi$
$504$	1.39749	0.0622490
$505$	−9.84605	−0.438143
$506$	−31.8824	−1.41734
$507$	−0.645684	−0.0286758
$508$	13.6389	0.605128
$509$	−23.0736	−1.02272	−0.511361	−	0.859366i	$-0.670858\pi$
$509$	−23.0736	−1.02272	−0.511361	+	0.859366i	$0.670858\pi$
$510$	−4.98032	−0.220532
$511$	−6.91080	−0.305716
$512$	−31.1905	−1.37844
$513$	6.17689	0.272717
$514$	−9.18609	−0.405181
$515$	8.84824	0.389900
$516$	4.82790	0.212536
$517$	32.8352	1.44409
$518$	1.87841	0.0825327
$519$	−10.8907	−0.478049
$520$	1.63630	0.0717564
$521$	−6.98837	−0.306166	−0.153083	−	0.988213i	$-0.548920\pi$
$521$	−6.98837	−0.306166	−0.153083	+	0.988213i	$0.548920\pi$
$522$	−36.8910	−1.61468
$523$	−9.60392	−0.419950	−0.209975	−	0.977707i	$-0.567338\pi$
$523$	−9.60392	−0.419950	−0.209975	+	0.977707i	$0.567338\pi$
$524$	−20.3128	−0.887368
$525$	−2.22033	−0.0969033
$526$	22.5705	0.984121
$527$	−23.8610	−1.03940
$528$	−6.98716	−0.304077
$529$	−5.28758	−0.229895
$530$	15.0512	0.653784
$531$	8.79642	0.381732
$532$	−3.97178	−0.172199
$533$	6.39078	0.276815
$534$	9.62662	0.416584
$535$	1.65738	0.0716550
$536$	−2.69430	−0.116376
$537$	7.21102	0.311179
$538$	−33.2014	−1.43141
$539$	−22.6180	−0.974227
$540$	−6.06185	−0.260861
$541$	−35.3986	−1.52191	−0.760953	−	0.648807i	$-0.775268\pi$
$541$	−35.3986	−1.52191	−0.760953	+	0.648807i	$0.775268\pi$
$542$	8.19263	0.351903
$543$	13.3158	0.571438
$544$	41.6900	1.78745
$545$	−0.827262	−0.0354360
$546$	3.66458	0.156829
$547$	−1.38663	−0.0592880	−0.0296440	−	0.999561i	$-0.509437\pi$
$547$	−1.38663	−0.0592880	−0.0296440	+	0.999561i	$0.509437\pi$
$548$	49.3245	2.10704
$549$	9.40970	0.401596
$550$	32.6931	1.39404
$551$	12.7830	0.544572
$552$	−1.36930	−0.0582814
$553$	3.94523	0.167768
$554$	−5.66324	−0.240608
$555$	−0.468630	−0.0198922
$556$	4.27122	0.181140
$557$	35.6545	1.51073	0.755366	−	0.655303i	$-0.227459\pi$
$557$	35.6545	1.51073	0.755366	+	0.655303i	$0.227459\pi$
$558$	−25.7312	−1.08929
$559$	−12.8861	−0.545024
$560$	−2.53009	−0.106916
$561$	10.6614	0.450126
$562$	12.9900	0.547949
$563$	−17.9662	−0.757184	−0.378592	−	0.925564i	$-0.623592\pi$
$563$	−17.9662	−0.757184	−0.378592	+	0.925564i	$0.623592\pi$
$564$	11.5669	0.487053
$565$	−9.63308	−0.405267
$566$	42.4604	1.78474
$567$	5.64438	0.237042
$568$	2.39413	0.100456
$569$	−42.4547	−1.77979	−0.889897	−	0.456161i	$-0.849224\pi$
$569$	−42.4547	−1.77979	−0.889897	+	0.456161i	$0.849224\pi$
$570$	1.86097	0.0779474
$571$	23.1152	0.967340	0.483670	−	0.875251i	$-0.339304\pi$
$571$	23.1152	0.967340	0.483670	+	0.875251i	$0.339304\pi$
$572$	−28.7308	−1.20130
$573$	11.7456	0.490679
$574$	3.48577	0.145493
$575$	−18.1628	−0.757443
$576$	26.9140	1.12142
$577$	−21.5015	−0.895120	−0.447560	−	0.894254i	$-0.647707\pi$
$577$	−21.5015	−0.895120	−0.447560	+	0.894254i	$0.647707\pi$
$578$	−19.4466	−0.808873
$579$	−1.41008	−0.0586007
$580$	−12.5449	−0.520898
$581$	−3.42643	−0.142152
$582$	13.1643	0.545677
$583$	−32.2204	−1.33443
$584$	4.37034	0.180846
$585$	7.63268	0.315573
$586$	26.3109	1.08689
$587$	−19.1595	−0.790796	−0.395398	−	0.918510i	$-0.629393\pi$
$587$	−19.1595	−0.790796	−0.395398	+	0.918510i	$0.629393\pi$
$588$	−7.96766	−0.328581
$589$	8.91600	0.367377
$590$	5.61779	0.231281
$591$	1.02575	0.0421935
$592$	3.36749	0.138403
$593$	−20.7519	−0.852179	−0.426089	−	0.904681i	$-0.640109\pi$
$593$	−20.7519	−0.852179	−0.426089	+	0.904681i	$0.640109\pi$
$594$	24.3713	0.999965
$595$	3.86057	0.158268
$596$	6.11983	0.250678
$597$	−12.2201	−0.500134
$598$	29.9771	1.22585
$599$	30.5677	1.24896	0.624480	−	0.781041i	$-0.285311\pi$
$599$	30.5677	1.24896	0.624480	+	0.781041i	$0.285311\pi$
$600$	1.40412	0.0573231
$601$	−0.554696	−0.0226265	−0.0113133	−	0.999936i	$-0.503601\pi$
$601$	−0.554696	−0.0226265	−0.0113133	+	0.999936i	$0.503601\pi$
$602$	−7.02856	−0.286463
$603$	−12.5678	−0.511802
$604$	−10.2644	−0.417653
$605$	1.99841	0.0812469
$606$	13.9448	0.566467
$607$	0.103356	0.00419510	0.00209755	−	0.999998i	$-0.499332\pi$
$607$	0.103356	0.00419510	0.00209755	+	0.999998i	$0.499332\pi$
$608$	−15.5781	−0.631775
$609$	−3.42532	−0.138801
$610$	6.00946	0.243316
$611$	−30.8730	−1.24899
$612$	−31.3549	−1.26745
$613$	−36.2794	−1.46531	−0.732656	−	0.680599i	$-0.761720\pi$
$613$	−36.2794	−1.46531	−0.732656	+	0.680599i	$0.761720\pi$
$614$	−50.8231	−2.05105
$615$	−0.869638	−0.0350672
$616$	−1.91058	−0.0769796
$617$	32.8406	1.32211	0.661056	−	0.750336i	$-0.270108\pi$
$617$	32.8406	1.32211	0.661056	+	0.750336i	$0.270108\pi$
$618$	−12.5316	−0.504094
$619$	−1.58179	−0.0635776	−0.0317888	−	0.999495i	$-0.510120\pi$
$619$	−1.58179	−0.0635776	−0.0317888	+	0.999495i	$0.510120\pi$
$620$	−8.74994	−0.351406
$621$	−13.5396	−0.543325
$622$	55.9767	2.24446
$623$	−7.46221	−0.298967
$624$	6.56962	0.262995
$625$	15.2029	0.608116
$626$	−6.38963	−0.255381
$627$	−3.98380	−0.159098
$628$	−1.56211	−0.0623349
$629$	−5.13833	−0.204879
$630$	4.16315	0.165864
$631$	−23.0889	−0.919156	−0.459578	−	0.888137i	$-0.651999\pi$
$631$	−23.0889	−0.919156	−0.459578	+	0.888137i	$0.651999\pi$
$632$	−2.49494	−0.0992432
$633$	5.80196	0.230607
$634$	35.8947	1.42556
$635$	4.95366	0.196580
$636$	−11.3503	−0.450068
$637$	21.2664	0.842605
$638$	50.4358	1.99677
$639$	11.1677	0.441787
$640$	3.76444	0.148802
$641$	23.0963	0.912249	0.456124	−	0.889916i	$-0.349237\pi$
$641$	23.0963	0.912249	0.456124	+	0.889916i	$0.349237\pi$
$642$	−2.34732	−0.0926413
$643$	10.9299	0.431032	0.215516	−	0.976500i	$-0.430857\pi$
$643$	10.9299	0.431032	0.215516	+	0.976500i	$0.430857\pi$
$644$	8.70604	0.343066
$645$	1.75350	0.0690440
$646$	20.4047	0.802813
$647$	−36.9697	−1.45343	−0.726714	−	0.686940i	$-0.758954\pi$
$647$	−36.9697	−1.45343	−0.726714	+	0.686940i	$0.758954\pi$
$648$	−3.56947	−0.140222
$649$	−12.0261	−0.472065
$650$	−30.7394	−1.20570
$651$	−2.38913	−0.0936373
$652$	32.1629	1.25960
$653$	−10.1742	−0.398146	−0.199073	−	0.979985i	$-0.563793\pi$
$653$	−10.1742	−0.398146	−0.199073	+	0.979985i	$0.563793\pi$
$654$	1.17163	0.0458145
$655$	−7.37763	−0.288268
$656$	6.24907	0.243985
$657$	20.3859	0.795331
$658$	−16.8393	−0.656463
$659$	4.76037	0.185438	0.0927188	−	0.995692i	$-0.470444\pi$
$659$	4.76037	0.185438	0.0927188	+	0.995692i	$0.470444\pi$
$660$	3.90960	0.152181
$661$	−24.3994	−0.949028	−0.474514	−	0.880248i	$-0.657376\pi$
$661$	−24.3994	−0.949028	−0.474514	+	0.880248i	$0.657376\pi$
$662$	48.0430	1.86724
$663$	−10.0243	−0.389312
$664$	2.16685	0.0840903
$665$	−1.44256	−0.0559399
$666$	−5.54107	−0.214712
$667$	−28.0199	−1.08493
$668$	−25.7101	−0.994752
$669$	−2.18361	−0.0844231
$670$	−8.02639	−0.310087
$671$	−12.8645	−0.496630
$672$	4.17430	0.161027
$673$	13.9063	0.536048	0.268024	−	0.963412i	$-0.413629\pi$
$673$	13.9063	0.536048	0.268024	+	0.963412i	$0.413629\pi$
$674$	5.13346	0.197733
$675$	13.8839	0.534391
$676$	−2.59614	−0.0998516
$677$	−23.2190	−0.892377	−0.446189	−	0.894939i	$-0.647219\pi$
$677$	−23.2190	−0.892377	−0.446189	+	0.894939i	$0.647219\pi$
$678$	13.6431	0.523961
$679$	−10.2045	−0.391612
$680$	−2.44140	−0.0936233
$681$	−14.7250	−0.564262
$682$	35.1785	1.34706
$683$	−6.20677	−0.237495	−0.118748	−	0.992924i	$-0.537888\pi$
$683$	−6.20677	−0.237495	−0.118748	+	0.992924i	$0.537888\pi$
$684$	11.7162	0.447981
$685$	17.9147	0.684487
$686$	24.7484	0.944897
$687$	−2.37615	−0.0906556
$688$	−12.6003	−0.480384
$689$	30.2949	1.15414
$690$	−4.07919	−0.155292
$691$	38.4674	1.46337	0.731685	−	0.681643i	$-0.238734\pi$
$691$	38.4674	1.46337	0.731685	+	0.681643i	$0.238734\pi$
$692$	−43.7889	−1.66460
$693$	−8.91212	−0.338543
$694$	−55.1593	−2.09382
$695$	1.55131	0.0588447
$696$	2.16615	0.0821076
$697$	−9.53520	−0.361172
$698$	23.3305	0.883071
$699$	−9.83737	−0.372084
$700$	−8.92743	−0.337425
$701$	−40.5402	−1.53118	−0.765591	−	0.643328i	$-0.777553\pi$
$701$	−40.5402	−1.53118	−0.765591	+	0.643328i	$0.777553\pi$
$702$	−22.9149	−0.864866
$703$	1.92001	0.0724146
$704$	−36.7956	−1.38679
$705$	4.20110	0.158223
$706$	−32.2468	−1.21362
$707$	−10.8095	−0.406532
$708$	−4.23643	−0.159215
$709$	−39.5545	−1.48550	−0.742751	−	0.669568i	$-0.766479\pi$
$709$	−39.5545	−1.48550	−0.742751	+	0.669568i	$0.766479\pi$
$710$	7.13219	0.267666
$711$	−11.6379	−0.436455
$712$	4.71905	0.176854
$713$	−19.5436	−0.731915
$714$	−5.46764	−0.204621
$715$	−10.4351	−0.390250
$716$	28.9938	1.08355
$717$	7.68532	0.287014
$718$	−41.3313	−1.54247
$719$	20.2663	0.755806	0.377903	−	0.925845i	$-0.376645\pi$
$719$	20.2663	0.755806	0.377903	+	0.925845i	$0.376645\pi$
$720$	7.46343	0.278146
$721$	9.71403	0.361769
$722$	31.6724	1.17872
$723$	0.570805	0.0212285
$724$	53.5399	1.98979
$725$	28.7324	1.06710
$726$	−2.83031	−0.105043
$727$	47.5678	1.76419	0.882095	−	0.471071i	$-0.156132\pi$
$727$	47.5678	1.76419	0.882095	+	0.471071i	$0.156132\pi$
$728$	1.79641	0.0665793
$729$	−11.1829	−0.414180
$730$	13.0194	0.481869
$731$	19.2264	0.711113
$732$	−4.53179	−0.167500
$733$	−7.55288	−0.278972	−0.139486	−	0.990224i	$-0.544545\pi$
$733$	−7.55288	−0.278972	−0.139486	+	0.990224i	$0.544545\pi$
$734$	42.3388	1.56275
$735$	−2.89387	−0.106742
$736$	34.1468	1.25867
$737$	17.1822	0.632914
$738$	−10.2826	−0.378506
$739$	40.8664	1.50330	0.751648	−	0.659565i	$-0.229259\pi$
$739$	40.8664	1.50330	0.751648	+	0.659565i	$0.229259\pi$
$740$	−1.88425	−0.0692664
$741$	3.74573	0.137603
$742$	16.5240	0.606615
$743$	−22.5862	−0.828607	−0.414304	−	0.910139i	$-0.635975\pi$
$743$	−22.5862	−0.828607	−0.414304	+	0.910139i	$0.635975\pi$
$744$	1.51087	0.0553912
$745$	2.22273	0.0814346
$746$	1.06899	0.0391386
$747$	10.1075	0.369815
$748$	42.8671	1.56738
$749$	1.81956	0.0664852
$750$	9.02917	0.329699
$751$	−23.7528	−0.866752	−0.433376	−	0.901213i	$-0.642678\pi$
$751$	−23.7528	−0.866752	−0.433376	+	0.901213i	$0.642678\pi$
$752$	−30.1884	−1.10086
$753$	6.35997	0.231770
$754$	−47.4218	−1.72700
$755$	−3.72805	−0.135678
$756$	−6.65500	−0.242040
$757$	−6.05143	−0.219943	−0.109972	−	0.993935i	$-0.535076\pi$
$757$	−6.05143	−0.219943	−0.109972	+	0.993935i	$0.535076\pi$
$758$	−28.0252	−1.01792
$759$	8.73238	0.316965
$760$	0.912263	0.0330913
$761$	22.3581	0.810480	0.405240	−	0.914210i	$-0.367188\pi$
$761$	22.3581	0.810480	0.405240	+	0.914210i	$0.367188\pi$
$762$	−7.01577	−0.254155
$763$	−0.908209	−0.0328794
$764$	47.2262	1.70858
$765$	−11.3882	−0.411740
$766$	−12.6991	−0.458837
$767$	11.3074	0.408287
$768$	6.05020	0.218318
$769$	5.19037	0.187169	0.0935847	−	0.995611i	$-0.470167\pi$
$769$	5.19037	0.187169	0.0935847	+	0.995611i	$0.470167\pi$
$770$	−5.69168	−0.205114
$771$	2.51601	0.0906120
$772$	−5.66958	−0.204053
$773$	35.8599	1.28979	0.644895	−	0.764271i	$-0.276901\pi$
$773$	35.8599	1.28979	0.644895	+	0.764271i	$0.276901\pi$
$774$	20.7333	0.745244
$775$	20.0406	0.719881
$776$	6.45325	0.231658
$777$	−0.514485	−0.0184571
$778$	45.0827	1.61629
$779$	3.56297	0.127657
$780$	−3.67597	−0.131621
$781$	−15.2680	−0.546331
$782$	−44.7266	−1.59942
$783$	21.4187	0.765444
$784$	20.7948	0.742672
$785$	−0.567360	−0.0202500
$786$	10.4488	0.372696
$787$	29.5628	1.05380	0.526900	−	0.849927i	$-0.323354\pi$
$787$	29.5628	1.05380	0.526900	+	0.849927i	$0.323354\pi$
$788$	4.12428	0.146921
$789$	−6.18193	−0.220082
$790$	−7.43249	−0.264436
$791$	−10.5757	−0.376027
$792$	5.63596	0.200265
$793$	12.0958	0.429533
$794$	2.67702	0.0950037
$795$	−4.12244	−0.146208
$796$	−49.1340	−1.74151
$797$	26.7360	0.947036	0.473518	−	0.880784i	$-0.342984\pi$
$797$	26.7360	0.947036	0.473518	+	0.880784i	$0.342984\pi$
$798$	2.04306	0.0723236
$799$	46.0632	1.62960
$800$	−35.0151	−1.23797
$801$	22.0125	0.777774
$802$	54.5380	1.92581
$803$	−27.8708	−0.983538
$804$	6.05278	0.213465
$805$	3.16204	0.111447
$806$	−33.0763	−1.16506
$807$	9.09365	0.320112
$808$	6.83584	0.240484
$809$	54.7136	1.92363	0.961814	−	0.273705i	$-0.0882493\pi$
$809$	54.7136	1.92363	0.961814	+	0.273705i	$0.0882493\pi$
$810$	−10.6336	−0.373625
$811$	33.9340	1.19159	0.595793	−	0.803138i	$-0.296838\pi$
$811$	33.9340	1.19159	0.595793	+	0.803138i	$0.296838\pi$
$812$	−13.7724	−0.483316
$813$	−2.24391	−0.0786973
$814$	7.57550	0.265521
$815$	11.6816	0.409189
$816$	−9.80203	−0.343140
$817$	−7.18421	−0.251344
$818$	12.1877	0.426133
$819$	8.37954	0.292805
$820$	−3.49661	−0.122107
$821$	54.2457	1.89319	0.946594	−	0.322429i	$-0.104499\pi$
$821$	54.2457	1.89319	0.946594	+	0.322429i	$0.104499\pi$
$822$	−25.3723	−0.884960
$823$	−2.57690	−0.0898249	−0.0449125	−	0.998991i	$-0.514301\pi$
$823$	−2.57690	−0.0898249	−0.0449125	+	0.998991i	$0.514301\pi$
$824$	−6.14309	−0.214005
$825$	−8.95445	−0.311754
$826$	6.16749	0.214594
$827$	16.2438	0.564852	0.282426	−	0.959289i	$-0.408861\pi$
$827$	16.2438	0.564852	0.282426	+	0.959289i	$0.408861\pi$
$828$	−25.6817	−0.892499
$829$	20.6824	0.718331	0.359166	−	0.933274i	$-0.383061\pi$
$829$	20.6824	0.718331	0.359166	+	0.933274i	$0.383061\pi$
$830$	6.45512	0.224061
$831$	1.55113	0.0538080
$832$	34.5968	1.19943
$833$	−31.7300	−1.09938
$834$	−2.19709	−0.0760792
$835$	−9.33793	−0.323153
$836$	−16.0179	−0.553991
$837$	14.9394	0.516381
$838$	22.1265	0.764347
$839$	6.46322	0.223135	0.111568	−	0.993757i	$-0.464413\pi$
$839$	6.46322	0.223135	0.111568	+	0.993757i	$0.464413\pi$
$840$	−0.244450	−0.00843432
$841$	15.3257	0.528471
$842$	−45.4962	−1.56790
$843$	−3.55787	−0.122540
$844$	23.3283	0.802993
$845$	−0.942923	−0.0324375
$846$	49.6736	1.70781
$847$	2.19395	0.0753851
$848$	29.6231	1.01726
$849$	−11.6296	−0.399128
$850$	45.8640	1.57312
$851$	−4.20861	−0.144269
$852$	−5.37846	−0.184263
$853$	35.1204	1.20250	0.601250	−	0.799061i	$-0.294670\pi$
$853$	35.1204	1.20250	0.601250	+	0.799061i	$0.294670\pi$
$854$	6.59748	0.225761
$855$	4.25535	0.145530
$856$	−1.15068	−0.0393293
$857$	7.26892	0.248302	0.124151	−	0.992263i	$-0.460379\pi$
$857$	7.26892	0.248302	0.124151	+	0.992263i	$0.460379\pi$
$858$	14.7790	0.504546
$859$	9.27986	0.316625	0.158312	−	0.987389i	$-0.449395\pi$
$859$	9.27986	0.316625	0.158312	+	0.987389i	$0.449395\pi$
$860$	7.05041	0.240417
$861$	−0.954732	−0.0325372
$862$	31.4628	1.07163
$863$	−3.01742	−0.102714	−0.0513571	−	0.998680i	$-0.516355\pi$
$863$	−3.01742	−0.102714	−0.0513571	+	0.998680i	$0.516355\pi$
$864$	−26.1022	−0.888015
$865$	−15.9042	−0.540759
$866$	64.0459	2.17637
$867$	5.32631	0.180891
$868$	−9.60612	−0.326053
$869$	15.9108	0.539738
$870$	6.45302	0.218778
$871$	−16.1554	−0.547405
$872$	0.574346	0.0194498
$873$	30.1019	1.01879
$874$	16.7127	0.565317
$875$	−6.99909	−0.236612
$876$	−9.81805	−0.331721
$877$	−4.78980	−0.161740	−0.0808700	−	0.996725i	$-0.525770\pi$
$877$	−4.78980	−0.161740	−0.0808700	+	0.996725i	$0.525770\pi$
$878$	−26.0551	−0.879316
$879$	−7.20638	−0.243065
$880$	−10.2037	−0.343966
$881$	23.3558	0.786876	0.393438	−	0.919351i	$-0.371286\pi$
$881$	23.3558	0.786876	0.393438	+	0.919351i	$0.371286\pi$
$882$	−34.2169	−1.15214
$883$	24.7528	0.832999	0.416500	−	0.909136i	$-0.363257\pi$
$883$	24.7528	0.832999	0.416500	+	0.909136i	$0.363257\pi$
$884$	−40.3054	−1.35562
$885$	−1.53868	−0.0517221
$886$	−43.7116	−1.46852
$887$	14.9511	0.502010	0.251005	−	0.967986i	$-0.419239\pi$
$887$	14.9511	0.502010	0.251005	+	0.967986i	$0.419239\pi$
$888$	0.325357	0.0109183
$889$	5.43837	0.182397
$890$	14.0582	0.471232
$891$	22.7634	0.762602
$892$	−8.77976	−0.293968
$893$	−17.2122	−0.575984
$894$	−3.14801	−0.105285
$895$	10.5306	0.351999
$896$	4.13278	0.138067
$897$	−8.21054	−0.274142
$898$	68.8570	2.29779
$899$	30.9168	1.03113
$900$	26.3347	0.877824
$901$	−45.2008	−1.50586
$902$	14.0579	0.468076
$903$	1.92508	0.0640626
$904$	6.68798	0.222439
$905$	19.4458	0.646399
$906$	5.27996	0.175415
$907$	−17.9615	−0.596401	−0.298201	−	0.954503i	$-0.596386\pi$
$907$	−17.9615	−0.596401	−0.298201	+	0.954503i	$0.596386\pi$
$908$	−59.2056	−1.96481
$909$	31.8865	1.05761
$910$	5.35155	0.177402
$911$	13.2807	0.440009	0.220004	−	0.975499i	$-0.429393\pi$
$911$	13.2807	0.440009	0.220004	+	0.975499i	$0.429393\pi$
$912$	3.66267	0.121283
$913$	−13.8186	−0.457328
$914$	43.7904	1.44846
$915$	−1.64595	−0.0544135
$916$	−9.55392	−0.315670
$917$	−8.09953	−0.267470
$918$	34.1895	1.12842
$919$	10.9126	0.359974	0.179987	−	0.983669i	$-0.442394\pi$
$919$	10.9126	0.359974	0.179987	+	0.983669i	$0.442394\pi$
$920$	−1.99966	−0.0659267
$921$	13.9201	0.458684
$922$	71.7126	2.36173
$923$	14.3556	0.472520
$924$	4.29215	0.141201
$925$	4.31564	0.141897
$926$	63.6783	2.09260
$927$	−28.6551	−0.941157
$928$	−54.0180	−1.77323
$929$	−13.2692	−0.435347	−0.217674	−	0.976022i	$-0.569847\pi$
$929$	−13.2692	−0.435347	−0.217674	+	0.976022i	$0.569847\pi$
$930$	4.50092	0.147591
$931$	11.8564	0.388577
$932$	−39.5537	−1.29563
$933$	−15.3317	−0.501936
$934$	39.0170	1.27667
$935$	15.5694	0.509173
$936$	−5.29917	−0.173209
$937$	10.4383	0.341005	0.170502	−	0.985357i	$-0.445461\pi$
$937$	10.4383	0.341005	0.170502	+	0.985357i	$0.445461\pi$
$938$	−8.81177	−0.287714
$939$	1.75008	0.0571117
$940$	16.8916	0.550944
$941$	−28.5359	−0.930244	−0.465122	−	0.885247i	$-0.653990\pi$
$941$	−28.5359	−0.930244	−0.465122	+	0.885247i	$0.653990\pi$
$942$	0.803541	0.0261808
$943$	−7.80993	−0.254326
$944$	11.0567	0.359864
$945$	−2.41710	−0.0786284
$946$	−28.3457	−0.921598
$947$	5.82379	0.189248	0.0946238	−	0.995513i	$-0.469835\pi$
$947$	5.82379	0.189248	0.0946238	+	0.995513i	$0.469835\pi$
$948$	5.60491	0.182039
$949$	26.2052	0.850658
$950$	−17.1377	−0.556022
$951$	−9.83135	−0.318803
$952$	−2.68029	−0.0868685
$953$	−10.2662	−0.332556	−0.166278	−	0.986079i	$-0.553175\pi$
$953$	−10.2662	−0.332556	−0.166278	+	0.986079i	$0.553175\pi$
$954$	−48.7436	−1.57813
$955$	17.1526	0.555046
$956$	30.9009	0.999405
$957$	−13.8141	−0.446545
$958$	−31.9794	−1.03321
$959$	19.6677	0.635103
$960$	−4.70782	−0.151944
$961$	−9.43583	−0.304382
$962$	−7.12280	−0.229648
$963$	−5.36746	−0.172964
$964$	2.29507	0.0739193
$965$	−2.05920	−0.0662880
$966$	−4.47834	−0.144088
$967$	24.3180	0.782013	0.391006	−	0.920388i	$-0.372127\pi$
$967$	24.3180	0.782013	0.391006	+	0.920388i	$0.372127\pi$
$968$	−1.38744	−0.0445941
$969$	−5.58873	−0.179536
$970$	19.2244	0.617259
$971$	3.96068	0.127104	0.0635521	−	0.997979i	$-0.479757\pi$
$971$	3.96068	0.127104	0.0635521	+	0.997979i	$0.479757\pi$
$972$	30.0017	0.962305
$973$	1.70311	0.0545992
$974$	79.2342	2.53883
$975$	8.41934	0.269635
$976$	11.8275	0.378590
$977$	−15.4809	−0.495279	−0.247639	−	0.968852i	$-0.579655\pi$
$977$	−15.4809	−0.495279	−0.247639	+	0.968852i	$0.579655\pi$
$978$	−16.5444	−0.529033
$979$	−30.0946	−0.961827
$980$	−11.6355	−0.371684
$981$	2.67910	0.0855370
$982$	−29.5438	−0.942781
$983$	−53.6476	−1.71109	−0.855546	−	0.517727i	$-0.826778\pi$
$983$	−53.6476	−1.71109	−0.855546	+	0.517727i	$0.826778\pi$
$984$	0.603766	0.0192474
$985$	1.49794	0.0477285
$986$	70.7545	2.25328
$987$	4.61217	0.146807
$988$	15.0607	0.479145
$989$	15.7476	0.500745
$990$	16.7897	0.533612
$991$	44.8371	1.42430	0.712149	−	0.702029i	$-0.247722\pi$
$991$	44.8371	1.42430	0.712149	+	0.702029i	$0.247722\pi$
$992$	−37.6771	−1.19625
$993$	−13.1587	−0.417578
$994$	7.83007	0.248355
$995$	−17.8455	−0.565742
$996$	−4.86787	−0.154244
$997$	27.6398	0.875360	0.437680	−	0.899131i	$-0.355800\pi$
$997$	27.6398	0.875360	0.437680	+	0.899131i	$0.355800\pi$
$998$	−43.0432	−1.36251
$999$	3.21711	0.101785

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.d.1.16	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.d.1.16	✓	79	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4033 = 37 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.06826 q^{2} +0.566483 q^{3} +2.27770 q^{4} +0.827262 q^{5} -1.17163 q^{6} +0.908209 q^{7} -0.574346 q^{8} -2.67910 q^{9} +O(q^{10})\)	\(q-2.06826 q^{2} +0.566483 q^{3} +2.27770 q^{4} +0.827262 q^{5} -1.17163 q^{6} +0.908209 q^{7} -0.574346 q^{8} -2.67910 q^{9} -1.71099 q^{10} +3.66274 q^{11} +1.29028 q^{12} -3.44386 q^{13} -1.87841 q^{14} +0.468630 q^{15} -3.36749 q^{16} +5.13833 q^{17} +5.54107 q^{18} -1.92001 q^{19} +1.88425 q^{20} +0.514485 q^{21} -7.57550 q^{22} +4.20861 q^{23} -0.325357 q^{24} -4.31564 q^{25} +7.12280 q^{26} -3.21711 q^{27} +2.06862 q^{28} -6.65775 q^{29} -0.969249 q^{30} -4.64372 q^{31} +8.11354 q^{32} +2.07488 q^{33} -10.6274 q^{34} +0.751327 q^{35} -6.10217 q^{36} -1.00000 q^{37} +3.97108 q^{38} -1.95089 q^{39} -0.475134 q^{40} -1.85570 q^{41} -1.06409 q^{42} +3.74176 q^{43} +8.34261 q^{44} -2.21632 q^{45} -8.70450 q^{46} +8.96463 q^{47} -1.90763 q^{48} -6.17516 q^{49} +8.92586 q^{50} +2.91078 q^{51} -7.84407 q^{52} -8.79679 q^{53} +6.65383 q^{54} +3.03005 q^{55} -0.521626 q^{56} -1.08765 q^{57} +13.7700 q^{58} -3.28335 q^{59} +1.06740 q^{60} -3.51226 q^{61} +9.60442 q^{62} -2.43318 q^{63} -10.0459 q^{64} -2.84898 q^{65} -4.29140 q^{66} +4.69107 q^{67} +11.7035 q^{68} +2.38411 q^{69} -1.55394 q^{70} -4.16845 q^{71} +1.53873 q^{72} -7.60926 q^{73} +2.06826 q^{74} -2.44474 q^{75} -4.37320 q^{76} +3.32654 q^{77} +4.03495 q^{78} +4.34396 q^{79} -2.78580 q^{80} +6.21485 q^{81} +3.83807 q^{82} -3.77274 q^{83} +1.17184 q^{84} +4.25074 q^{85} -7.73892 q^{86} -3.77151 q^{87} -2.10368 q^{88} -8.21640 q^{89} +4.58391 q^{90} -3.12775 q^{91} +9.58594 q^{92} -2.63059 q^{93} -18.5412 q^{94} -1.58835 q^{95} +4.59619 q^{96} -11.2358 q^{97} +12.7718 q^{98} -9.81284 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + q^99

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