LMFDB - Embedded newform 4033.2.a.d.1.52

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			1.52
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)

$f(q)$	$=$	$q+0.800770 q^{2} -2.24038 q^{3} -1.35877 q^{4} +3.40847 q^{5} -1.79403 q^{6} -1.16728 q^{7} -2.68960 q^{8} +2.01929 q^{9} +O(q^{10})$	\(q+0.800770 q^{2} -2.24038 q^{3} -1.35877 q^{4} +3.40847 q^{5} -1.79403 q^{6} -1.16728 q^{7} -2.68960 q^{8} +2.01929 q^{9} +2.72940 q^{10} -1.94466 q^{11} +3.04415 q^{12} +6.91321 q^{13} -0.934720 q^{14} -7.63626 q^{15} +0.563786 q^{16} -3.24565 q^{17} +1.61699 q^{18} -6.93569 q^{19} -4.63132 q^{20} +2.61514 q^{21} -1.55723 q^{22} +4.54894 q^{23} +6.02572 q^{24} +6.61767 q^{25} +5.53589 q^{26} +2.19716 q^{27} +1.58606 q^{28} +1.32074 q^{29} -6.11489 q^{30} -7.67316 q^{31} +5.83066 q^{32} +4.35678 q^{33} -2.59902 q^{34} -3.97863 q^{35} -2.74375 q^{36} -1.00000 q^{37} -5.55389 q^{38} -15.4882 q^{39} -9.16742 q^{40} +2.15843 q^{41} +2.09413 q^{42} +6.01611 q^{43} +2.64235 q^{44} +6.88269 q^{45} +3.64265 q^{46} -8.65764 q^{47} -1.26309 q^{48} -5.63746 q^{49} +5.29923 q^{50} +7.27148 q^{51} -9.39345 q^{52} +5.83799 q^{53} +1.75942 q^{54} -6.62833 q^{55} +3.13951 q^{56} +15.5386 q^{57} +1.05761 q^{58} -4.00049 q^{59} +10.3759 q^{60} -2.41089 q^{61} -6.14443 q^{62} -2.35707 q^{63} +3.54145 q^{64} +23.5635 q^{65} +3.48878 q^{66} +9.32010 q^{67} +4.41009 q^{68} -10.1913 q^{69} -3.18597 q^{70} +9.04000 q^{71} -5.43108 q^{72} -8.97072 q^{73} -0.800770 q^{74} -14.8261 q^{75} +9.42399 q^{76} +2.26996 q^{77} -12.4025 q^{78} +7.69096 q^{79} +1.92165 q^{80} -10.9803 q^{81} +1.72840 q^{82} -7.05547 q^{83} -3.55337 q^{84} -11.0627 q^{85} +4.81752 q^{86} -2.95896 q^{87} +5.23037 q^{88} +0.0557557 q^{89} +5.51145 q^{90} -8.06963 q^{91} -6.18095 q^{92} +17.1908 q^{93} -6.93278 q^{94} -23.6401 q^{95} -13.0629 q^{96} -6.80793 q^{97} -4.51431 q^{98} -3.92684 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.800770	0.566230	0.283115	−	0.959086i	$-0.408632\pi$
$2$	0.800770	0.566230	0.283115	+	0.959086i	$0.408632\pi$
$3$	−2.24038	−1.29348	−0.646741	−	0.762710i	$-0.723869\pi$
$3$	−2.24038	−1.29348	−0.646741	+	0.762710i	$0.723869\pi$
$4$	−1.35877	−0.679384
$5$	3.40847	1.52431	0.762157	−	0.647392i	$-0.224140\pi$
$5$	3.40847	1.52431	0.762157	+	0.647392i	$0.224140\pi$
$6$	−1.79403	−0.732408
$7$	−1.16728	−0.441189	−0.220595	−	0.975366i	$-0.570800\pi$
$7$	−1.16728	−0.441189	−0.220595	+	0.975366i	$0.570800\pi$
$8$	−2.68960	−0.950917
$9$	2.01929	0.673097
$10$	2.72940	0.863112
$11$	−1.94466	−0.586338	−0.293169	−	0.956061i	$-0.594710\pi$
$11$	−1.94466	−0.586338	−0.293169	+	0.956061i	$0.594710\pi$
$12$	3.04415	0.878771
$13$	6.91321	1.91738	0.958690	−	0.284455i	$-0.0918125\pi$
$13$	6.91321	1.91738	0.958690	+	0.284455i	$0.0918125\pi$
$14$	−0.934720	−0.249815
$15$	−7.63626	−1.97167
$16$	0.563786	0.140946
$17$	−3.24565	−0.787186	−0.393593	−	0.919285i	$-0.628768\pi$
$17$	−3.24565	−0.787186	−0.393593	+	0.919285i	$0.628768\pi$
$18$	1.61699	0.381127
$19$	−6.93569	−1.59116	−0.795578	−	0.605851i	$-0.792833\pi$
$19$	−6.93569	−1.59116	−0.795578	+	0.605851i	$0.792833\pi$
$20$	−4.63132	−1.03559
$21$	2.61514	0.570671
$22$	−1.55723	−0.332002
$23$	4.54894	0.948519	0.474259	−	0.880385i	$-0.342716\pi$
$23$	4.54894	0.948519	0.474259	+	0.880385i	$0.342716\pi$
$24$	6.02572	1.22999
$25$	6.61767	1.32353
$26$	5.53589	1.08568
$27$	2.19716	0.422844
$28$	1.58606	0.299737
$29$	1.32074	0.245255	0.122628	−	0.992453i	$-0.460868\pi$
$29$	1.32074	0.245255	0.122628	+	0.992453i	$0.460868\pi$
$30$	−6.11489	−1.11642
$31$	−7.67316	−1.37814	−0.689070	−	0.724695i	$-0.741981\pi$
$31$	−7.67316	−1.37814	−0.689070	+	0.724695i	$0.741981\pi$
$32$	5.83066	1.03073
$33$	4.35678	0.758418
$34$	−2.59902	−0.445728
$35$	−3.97863	−0.672511
$36$	−2.74375	−0.457291
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−5.55389	−0.900960
$39$	−15.4882	−2.48010
$40$	−9.16742	−1.44950
$41$	2.15843	0.337090	0.168545	−	0.985694i	$-0.446093\pi$
$41$	2.15843	0.337090	0.168545	+	0.985694i	$0.446093\pi$
$42$	2.09413	0.323131
$43$	6.01611	0.917448	0.458724	−	0.888579i	$-0.348307\pi$
$43$	6.01611	0.917448	0.458724	+	0.888579i	$0.348307\pi$
$44$	2.64235	0.398349
$45$	6.88269	1.02601
$46$	3.64265	0.537080
$47$	−8.65764	−1.26285	−0.631424	−	0.775438i	$-0.717529\pi$
$47$	−8.65764	−1.26285	−0.631424	+	0.775438i	$0.717529\pi$
$48$	−1.26309	−0.182312
$49$	−5.63746	−0.805352
$50$	5.29923	0.749425
$51$	7.27148	1.01821
$52$	−9.39345	−1.30264
$53$	5.83799	0.801909	0.400955	−	0.916098i	$-0.368679\pi$
$53$	5.83799	0.801909	0.400955	+	0.916098i	$0.368679\pi$
$54$	1.75942	0.239427
$55$	−6.62833	−0.893764
$56$	3.13951	0.419535
$57$	15.5386	2.05813
$58$	1.05761	0.138871
$59$	−4.00049	−0.520819	−0.260409	−	0.965498i	$-0.583858\pi$
$59$	−4.00049	−0.520819	−0.260409	+	0.965498i	$0.583858\pi$
$60$	10.3759	1.33952
$61$	−2.41089	−0.308683	−0.154342	−	0.988018i	$-0.549326\pi$
$61$	−2.41089	−0.308683	−0.154342	+	0.988018i	$0.549326\pi$
$62$	−6.14443	−0.780344
$63$	−2.35707	−0.296963
$64$	3.54145	0.442681
$65$	23.5635	2.92269
$66$	3.48878	0.429439
$67$	9.32010	1.13863	0.569316	−	0.822119i	$-0.307208\pi$
$67$	9.32010	1.13863	0.569316	+	0.822119i	$0.307208\pi$
$68$	4.41009	0.534801
$69$	−10.1913	−1.22689
$70$	−3.18597	−0.380796
$71$	9.04000	1.07285	0.536425	−	0.843948i	$-0.319774\pi$
$71$	9.04000	1.07285	0.536425	+	0.843948i	$0.319774\pi$
$72$	−5.43108	−0.640059
$73$	−8.97072	−1.04994	−0.524972	−	0.851120i	$-0.675924\pi$
$73$	−8.97072	−1.04994	−0.524972	+	0.851120i	$0.675924\pi$
$74$	−0.800770	−0.0930876
$75$	−14.8261	−1.71197
$76$	9.42399	1.08101
$77$	2.26996	0.258686
$78$	−12.4025	−1.40430
$79$	7.69096	0.865300	0.432650	−	0.901562i	$-0.357579\pi$
$79$	7.69096	0.865300	0.432650	+	0.901562i	$0.357579\pi$
$80$	1.92165	0.214847
$81$	−10.9803	−1.22004
$82$	1.72840	0.190870
$83$	−7.05547	−0.774439	−0.387219	−	0.921988i	$-0.626564\pi$
$83$	−7.05547	−0.774439	−0.387219	+	0.921988i	$0.626564\pi$
$84$	−3.55337	−0.387705
$85$	−11.0627	−1.19992
$86$	4.81752	0.519486
$87$	−2.95896	−0.317234
$88$	5.23037	0.557559
$89$	0.0557557	0.00591009	0.00295505	−	0.999996i	$-0.499059\pi$
$89$	0.0557557	0.00591009	0.00295505	+	0.999996i	$0.499059\pi$
$90$	5.51145	0.580958
$91$	−8.06963	−0.845927
$92$	−6.18095	−0.644408
$93$	17.1908	1.78260
$94$	−6.93278	−0.715062
$95$	−23.6401	−2.42542
$96$	−13.0629	−1.33322
$97$	−6.80793	−0.691240	−0.345620	−	0.938375i	$-0.612331\pi$
$97$	−6.80793	−0.691240	−0.345620	+	0.938375i	$0.612331\pi$
$98$	−4.51431	−0.456014
$99$	−3.92684	−0.394662
$100$	−8.99188	−0.899188
$101$	−17.5555	−1.74684	−0.873418	−	0.486971i	$-0.838102\pi$
$101$	−17.5555	−1.74684	−0.873418	+	0.486971i	$0.838102\pi$
$102$	5.82278	0.576541
$103$	8.27153	0.815018	0.407509	−	0.913201i	$-0.366398\pi$
$103$	8.27153	0.815018	0.407509	+	0.913201i	$0.366398\pi$
$104$	−18.5938	−1.82327
$105$	8.91364	0.869882
$106$	4.67488	0.454065
$107$	−8.69797	−0.840864	−0.420432	−	0.907324i	$-0.638122\pi$
$107$	−8.69797	−0.840864	−0.420432	+	0.907324i	$0.638122\pi$
$108$	−2.98543	−0.287273
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	−5.30776	−0.506075
$111$	2.24038	0.212647
$112$	−0.658095	−0.0621841
$113$	6.13669	0.577291	0.288646	−	0.957436i	$-0.406795\pi$
$113$	6.13669	0.577291	0.288646	+	0.957436i	$0.406795\pi$
$114$	12.4428	1.16538
$115$	15.5049	1.44584
$116$	−1.79458	−0.166623
$117$	13.9598	1.29058
$118$	−3.20347	−0.294903
$119$	3.78858	0.347298
$120$	20.5385	1.87490
$121$	−7.21829	−0.656208
$122$	−1.93057	−0.174786
$123$	−4.83569	−0.436019
$124$	10.4260	0.936286
$125$	5.51379	0.493169
$126$	−1.88747	−0.168149
$127$	−13.8410	−1.22819	−0.614096	−	0.789232i	$-0.710479\pi$
$127$	−13.8410	−1.22819	−0.614096	+	0.789232i	$0.710479\pi$
$128$	−8.82544	−0.780066
$129$	−13.4784	−1.18670
$130$	18.8689	1.65491
$131$	−1.71136	−0.149523	−0.0747613	−	0.997201i	$-0.523819\pi$
$131$	−1.71136	−0.149523	−0.0747613	+	0.997201i	$0.523819\pi$
$132$	−5.91985	−0.515257
$133$	8.09587	0.702001
$134$	7.46326	0.644727
$135$	7.48895	0.644547
$136$	8.72950	0.748549
$137$	11.0628	0.945161	0.472580	−	0.881288i	$-0.343323\pi$
$137$	11.0628	0.945161	0.472580	+	0.881288i	$0.343323\pi$
$138$	−8.16091	−0.694703
$139$	−15.6276	−1.32552	−0.662758	−	0.748834i	$-0.730614\pi$
$139$	−15.6276	−1.32552	−0.662758	+	0.748834i	$0.730614\pi$
$140$	5.40604	0.456893
$141$	19.3964	1.63347
$142$	7.23896	0.607480
$143$	−13.4439	−1.12423
$144$	1.13845	0.0948706
$145$	4.50171	0.373846
$146$	−7.18348	−0.594509
$147$	12.6300	1.04171
$148$	1.35877	0.111690
$149$	−17.9718	−1.47231	−0.736153	−	0.676815i	$-0.763360\pi$
$149$	−17.9718	−1.47231	−0.736153	+	0.676815i	$0.763360\pi$
$150$	−11.8723	−0.969368
$151$	7.01982	0.571265	0.285632	−	0.958339i	$-0.407796\pi$
$151$	7.01982	0.571265	0.285632	+	0.958339i	$0.407796\pi$
$152$	18.6542	1.51306
$153$	−6.55391	−0.529852
$154$	1.81772	0.146476
$155$	−26.1537	−2.10072
$156$	21.0449	1.68494
$157$	16.1232	1.28677	0.643387	−	0.765542i	$-0.277529\pi$
$157$	16.1232	1.28677	0.643387	+	0.765542i	$0.277529\pi$
$158$	6.15869	0.489959
$159$	−13.0793	−1.03726
$160$	19.8736	1.57115
$161$	−5.30987	−0.418476
$162$	−8.79272	−0.690821
$163$	−17.5825	−1.37717	−0.688585	−	0.725156i	$-0.741768\pi$
$163$	−17.5825	−1.37717	−0.688585	+	0.725156i	$0.741768\pi$
$164$	−2.93280	−0.229013
$165$	14.8500	1.15607
$166$	−5.64981	−0.438510
$167$	−11.5581	−0.894394	−0.447197	−	0.894435i	$-0.647578\pi$
$167$	−11.5581	−0.894394	−0.447197	+	0.894435i	$0.647578\pi$
$168$	−7.03368	−0.542661
$169$	34.7925	2.67634
$170$	−8.85868	−0.679430
$171$	−14.0052	−1.07100
$172$	−8.17450	−0.623299
$173$	−4.10372	−0.312000	−0.156000	−	0.987757i	$-0.549860\pi$
$173$	−4.10372	−0.312000	−0.156000	+	0.987757i	$0.549860\pi$
$174$	−2.36944	−0.179627
$175$	−7.72466	−0.583930
$176$	−1.09637	−0.0826423
$177$	8.96260	0.673670
$178$	0.0446475	0.00334647
$179$	−23.7858	−1.77783	−0.888917	−	0.458068i	$-0.848541\pi$
$179$	−23.7858	−1.77783	−0.888917	+	0.458068i	$0.848541\pi$
$180$	−9.35198	−0.697056
$181$	8.99481	0.668579	0.334290	−	0.942470i	$-0.391504\pi$
$181$	8.99481	0.668579	0.334290	+	0.942470i	$0.391504\pi$
$182$	−6.46192	−0.478989
$183$	5.40131	0.399276
$184$	−12.2348	−0.901963
$185$	−3.40847	−0.250596
$186$	13.7658	1.00936
$187$	6.31170	0.461557
$188$	11.7637	0.857958
$189$	−2.56469	−0.186554
$190$	−18.9303	−1.37335
$191$	−5.58187	−0.403890	−0.201945	−	0.979397i	$-0.564726\pi$
$191$	−5.58187	−0.403890	−0.201945	+	0.979397i	$0.564726\pi$
$192$	−7.93417	−0.572600
$193$	4.93066	0.354917	0.177458	−	0.984128i	$-0.443212\pi$
$193$	4.93066	0.354917	0.177458	+	0.984128i	$0.443212\pi$
$194$	−5.45158	−0.391401
$195$	−52.7911	−3.78045
$196$	7.66000	0.547143
$197$	21.2541	1.51429	0.757147	−	0.653245i	$-0.226593\pi$
$197$	21.2541	1.51429	0.757147	+	0.653245i	$0.226593\pi$
$198$	−3.14449	−0.223469
$199$	−19.1565	−1.35797	−0.678984	−	0.734153i	$-0.737579\pi$
$199$	−19.1565	−1.35797	−0.678984	+	0.734153i	$0.737579\pi$
$200$	−17.7989	−1.25857
$201$	−20.8805	−1.47280
$202$	−14.0579	−0.989111
$203$	−1.54167	−0.108204
$204$	−9.88026	−0.691756
$205$	7.35693	0.513831
$206$	6.62359	0.461487
$207$	9.18562	0.638445
$208$	3.89757	0.270248
$209$	13.4876	0.932955
$210$	7.13777	0.492553
$211$	−15.9017	−1.09472	−0.547359	−	0.836898i	$-0.684367\pi$
$211$	−15.9017	−1.09472	−0.547359	+	0.836898i	$0.684367\pi$
$212$	−7.93247	−0.544804
$213$	−20.2530	−1.38771
$214$	−6.96507	−0.476122
$215$	20.5057	1.39848
$216$	−5.90948	−0.402089
$217$	8.95671	0.608021
$218$	−0.800770	−0.0542350
$219$	20.0978	1.35808
$220$	9.00636	0.607209
$221$	−22.4379	−1.50933
$222$	1.79403	0.120407
$223$	−17.1400	−1.14778	−0.573888	−	0.818933i	$-0.694566\pi$
$223$	−17.1400	−1.14778	−0.573888	+	0.818933i	$0.694566\pi$
$224$	−6.80600	−0.454745
$225$	13.3630	0.890867
$226$	4.91408	0.326880
$227$	−9.43045	−0.625921	−0.312960	−	0.949766i	$-0.601321\pi$
$227$	−9.43045	−0.625921	−0.312960	+	0.949766i	$0.601321\pi$
$228$	−21.1133	−1.39826
$229$	−20.8664	−1.37889	−0.689447	−	0.724336i	$-0.742146\pi$
$229$	−20.8664	−1.37889	−0.689447	+	0.724336i	$0.742146\pi$
$230$	12.4159	0.818678
$231$	−5.08557	−0.334606
$232$	−3.55226	−0.233218
$233$	5.27372	0.345493	0.172746	−	0.984966i	$-0.444736\pi$
$233$	5.27372	0.345493	0.172746	+	0.984966i	$0.444736\pi$
$234$	11.1786	0.730766
$235$	−29.5093	−1.92498
$236$	5.43573	0.353836
$237$	−17.2306	−1.11925
$238$	3.03378	0.196651
$239$	6.20326	0.401255	0.200628	−	0.979668i	$-0.435702\pi$
$239$	6.20326	0.401255	0.200628	+	0.979668i	$0.435702\pi$
$240$	−4.30522	−0.277901
$241$	−25.4096	−1.63678	−0.818389	−	0.574665i	$-0.805133\pi$
$241$	−25.4096	−1.63678	−0.818389	+	0.574665i	$0.805133\pi$
$242$	−5.78018	−0.371564
$243$	18.0086	1.15525
$244$	3.27584	0.209714
$245$	−19.2151	−1.22761
$246$	−3.87227	−0.246887
$247$	−47.9479	−3.05085
$248$	20.6377	1.31050
$249$	15.8069	1.00172
$250$	4.41528	0.279247
$251$	−11.9596	−0.754883	−0.377442	−	0.926033i	$-0.623196\pi$
$251$	−11.9596	−0.754883	−0.377442	+	0.926033i	$0.623196\pi$
$252$	3.20271	0.201752
$253$	−8.84615	−0.556153
$254$	−11.0835	−0.695439
$255$	24.7846	1.55207
$256$	−14.1500	−0.884377
$257$	−7.83712	−0.488866	−0.244433	−	0.969666i	$-0.578602\pi$
$257$	−7.83712	−0.488866	−0.244433	+	0.969666i	$0.578602\pi$
$258$	−10.7931	−0.671946
$259$	1.16728	0.0725311
$260$	−32.0173	−1.98563
$261$	2.66696	0.165081
$262$	−1.37041	−0.0846641
$263$	7.35076	0.453267	0.226634	−	0.973980i	$-0.427228\pi$
$263$	7.35076	0.453267	0.226634	+	0.973980i	$0.427228\pi$
$264$	−11.7180	−0.721193
$265$	19.8986	1.22236
$266$	6.48293	0.397494
$267$	−0.124914	−0.00764460
$268$	−12.6639	−0.773568
$269$	−8.58201	−0.523254	−0.261627	−	0.965169i	$-0.584259\pi$
$269$	−8.58201	−0.523254	−0.261627	+	0.965169i	$0.584259\pi$
$270$	5.99693	0.364961
$271$	−14.5721	−0.885191	−0.442596	−	0.896721i	$-0.645942\pi$
$271$	−14.5721	−0.885191	−0.442596	+	0.896721i	$0.645942\pi$
$272$	−1.82985	−0.110951
$273$	18.0790	1.09419
$274$	8.85877	0.535178
$275$	−12.8691	−0.776039
$276$	13.8477	0.833531
$277$	−2.72563	−0.163767	−0.0818835	−	0.996642i	$-0.526094\pi$
$277$	−2.72563	−0.163767	−0.0818835	+	0.996642i	$0.526094\pi$
$278$	−12.5141	−0.750546
$279$	−15.4943	−0.927622
$280$	10.7009	0.639503
$281$	28.7074	1.71254	0.856270	−	0.516529i	$-0.172776\pi$
$281$	28.7074	1.71254	0.856270	+	0.516529i	$0.172776\pi$
$282$	15.5320	0.924920
$283$	6.04031	0.359059	0.179530	−	0.983753i	$-0.442542\pi$
$283$	6.04031	0.359059	0.179530	+	0.983753i	$0.442542\pi$
$284$	−12.2833	−0.728878
$285$	52.9627	3.13724
$286$	−10.7654	−0.636574
$287$	−2.51948	−0.148720
$288$	11.7738	0.693778
$289$	−6.46575	−0.380338
$290$	3.60483	0.211683
$291$	15.2523	0.894107
$292$	12.1891	0.713315
$293$	−14.7972	−0.864462	−0.432231	−	0.901763i	$-0.642274\pi$
$293$	−14.7972	−0.864462	−0.432231	+	0.901763i	$0.642274\pi$
$294$	10.1138	0.589846
$295$	−13.6355	−0.793892
$296$	2.68960	0.156330
$297$	−4.27274	−0.247929
$298$	−14.3913	−0.833664
$299$	31.4477	1.81867
$300$	20.1452	1.16308
$301$	−7.02247	−0.404768
$302$	5.62126	0.323467
$303$	39.3309	2.25950
$304$	−3.91024	−0.224268
$305$	−8.21746	−0.470530
$306$	−5.24817	−0.300018
$307$	25.4308	1.45141	0.725707	−	0.688004i	$-0.241513\pi$
$307$	25.4308	1.45141	0.725707	+	0.688004i	$0.241513\pi$
$308$	−3.08435	−0.175747
$309$	−18.5313	−1.05421
$310$	−20.9431	−1.18949
$311$	−23.1989	−1.31549	−0.657743	−	0.753242i	$-0.728489\pi$
$311$	−23.1989	−1.31549	−0.657743	+	0.753242i	$0.728489\pi$
$312$	41.6570	2.35837
$313$	−4.82157	−0.272531	−0.136265	−	0.990672i	$-0.543510\pi$
$313$	−4.82157	−0.272531	−0.136265	+	0.990672i	$0.543510\pi$
$314$	12.9110	0.728609
$315$	−8.03401	−0.452665
$316$	−10.4502	−0.587871
$317$	−22.7817	−1.27955	−0.639773	−	0.768564i	$-0.720972\pi$
$317$	−22.7817	−1.27955	−0.639773	+	0.768564i	$0.720972\pi$
$318$	−10.4735	−0.587325
$319$	−2.56840	−0.143803
$320$	12.0709	0.674785
$321$	19.4867	1.08764
$322$	−4.25198	−0.236954
$323$	22.5108	1.25254
$324$	14.9197	0.828874
$325$	45.7494	2.53772
$326$	−14.0796	−0.779795
$327$	2.24038	0.123893
$328$	−5.80530	−0.320544
$329$	10.1059	0.557155
$330$	11.8914	0.654600
$331$	−27.9904	−1.53849	−0.769245	−	0.638954i	$-0.779367\pi$
$331$	−27.9904	−1.53849	−0.769245	+	0.638954i	$0.779367\pi$
$332$	9.58675	0.526141
$333$	−2.01929	−0.110656
$334$	−9.25539	−0.506432
$335$	31.7673	1.73563
$336$	1.47438	0.0804340
$337$	28.5245	1.55383	0.776913	−	0.629607i	$-0.216784\pi$
$337$	28.5245	1.55383	0.776913	+	0.629607i	$0.216784\pi$
$338$	27.8607	1.51542
$339$	−13.7485	−0.746716
$340$	15.0316	0.815206
$341$	14.9217	0.808056
$342$	−11.2149	−0.606433
$343$	14.7514	0.796502
$344$	−16.1809	−0.872417
$345$	−34.7369	−1.87017
$346$	−3.28614	−0.176664
$347$	−17.2567	−0.926386	−0.463193	−	0.886257i	$-0.653296\pi$
$347$	−17.2567	−0.926386	−0.463193	+	0.886257i	$0.653296\pi$
$348$	4.02054	0.215523
$349$	−5.65324	−0.302611	−0.151305	−	0.988487i	$-0.548348\pi$
$349$	−5.65324	−0.302611	−0.151305	+	0.988487i	$0.548348\pi$
$350$	−6.18567	−0.330638
$351$	15.1894	0.810751
$352$	−11.3387	−0.604353
$353$	−5.26117	−0.280024	−0.140012	−	0.990150i	$-0.544714\pi$
$353$	−5.26117	−0.280024	−0.140012	+	0.990150i	$0.544714\pi$
$354$	7.17698	0.381452
$355$	30.8126	1.63536
$356$	−0.0757591	−0.00401522
$357$	−8.48784	−0.449224
$358$	−19.0469	−1.00666
$359$	8.63803	0.455898	0.227949	−	0.973673i	$-0.426798\pi$
$359$	8.63803	0.455898	0.227949	+	0.973673i	$0.426798\pi$
$360$	−18.5117	−0.975652
$361$	29.1038	1.53178
$362$	7.20277	0.378569
$363$	16.1717	0.848793
$364$	10.9648	0.574709
$365$	−30.5765	−1.60044
$366$	4.32521	0.226082
$367$	−23.9347	−1.24938	−0.624690	−	0.780873i	$-0.714775\pi$
$367$	−23.9347	−1.24938	−0.624690	+	0.780873i	$0.714775\pi$
$368$	2.56463	0.133690
$369$	4.35849	0.226894
$370$	−2.72940	−0.141895
$371$	−6.81455	−0.353794
$372$	−23.3583	−1.21107
$373$	5.17880	0.268148	0.134074	−	0.990971i	$-0.457194\pi$
$373$	5.17880	0.268148	0.134074	+	0.990971i	$0.457194\pi$
$374$	5.05422	0.261347
$375$	−12.3530	−0.637905
$376$	23.2856	1.20086
$377$	9.13056	0.470248
$378$	−2.05373	−0.105632
$379$	34.2016	1.75682	0.878409	−	0.477909i	$-0.158605\pi$
$379$	34.2016	1.75682	0.878409	+	0.477909i	$0.158605\pi$
$380$	32.1214	1.64779
$381$	31.0091	1.58864
$382$	−4.46979	−0.228694
$383$	25.1310	1.28413	0.642067	−	0.766649i	$-0.278077\pi$
$383$	25.1310	1.28413	0.642067	+	0.766649i	$0.278077\pi$
$384$	19.7723	1.00900
$385$	7.73710	0.394319
$386$	3.94832	0.200964
$387$	12.1483	0.617531
$388$	9.25039	0.469617
$389$	−34.7161	−1.76018	−0.880088	−	0.474810i	$-0.842517\pi$
$389$	−34.7161	−1.76018	−0.880088	+	0.474810i	$0.842517\pi$
$390$	−42.2735	−2.14060
$391$	−14.7643	−0.746661
$392$	15.1625	0.765823
$393$	3.83410	0.193405
$394$	17.0197	0.857438
$395$	26.2144	1.31899
$396$	5.33566	0.268127
$397$	1.14837	0.0576350	0.0288175	−	0.999585i	$-0.490826\pi$
$397$	1.14837	0.0576350	0.0288175	+	0.999585i	$0.490826\pi$
$398$	−15.3399	−0.768921
$399$	−18.1378	−0.908026
$400$	3.73095	0.186548
$401$	−11.1839	−0.558499	−0.279249	−	0.960219i	$-0.590086\pi$
$401$	−11.1839	−0.558499	−0.279249	+	0.960219i	$0.590086\pi$
$402$	−16.7205	−0.833943
$403$	−53.0461	−2.64242
$404$	23.8538	1.18677
$405$	−37.4262	−1.85972
$406$	−1.23452	−0.0612684
$407$	1.94466	0.0963934
$408$	−19.5574	−0.968234
$409$	−4.09014	−0.202244	−0.101122	−	0.994874i	$-0.532243\pi$
$409$	−4.09014	−0.202244	−0.101122	+	0.994874i	$0.532243\pi$
$410$	5.89121	0.290946
$411$	−24.7849	−1.22255
$412$	−11.2391	−0.553710
$413$	4.66968	0.229780
$414$	7.35557	0.361507
$415$	−24.0484	−1.18049
$416$	40.3086	1.97629
$417$	35.0117	1.71453
$418$	10.8004	0.528267
$419$	19.1379	0.934946	0.467473	−	0.884007i	$-0.345164\pi$
$419$	19.1379	0.934946	0.467473	+	0.884007i	$0.345164\pi$
$420$	−12.1116	−0.590984
$421$	−27.9785	−1.36359	−0.681794	−	0.731545i	$-0.738800\pi$
$421$	−27.9785	−1.36359	−0.681794	+	0.731545i	$0.738800\pi$
$422$	−12.7336	−0.619862
$423$	−17.4823	−0.850018
$424$	−15.7018	−0.762549
$425$	−21.4787	−1.04187
$426$	−16.2180	−0.785765
$427$	2.81418	0.136188
$428$	11.8185	0.571270
$429$	30.1193	1.45417
$430$	16.4204	0.791861
$431$	29.1608	1.40462	0.702312	−	0.711869i	$-0.252151\pi$
$431$	29.1608	1.40462	0.702312	+	0.711869i	$0.252151\pi$
$432$	1.23873	0.0595983
$433$	31.0454	1.49195	0.745974	−	0.665975i	$-0.231984\pi$
$433$	31.0454	1.49195	0.745974	+	0.665975i	$0.231984\pi$
$434$	7.17226	0.344279
$435$	−10.0855	−0.483564
$436$	1.35877	0.0650732
$437$	−31.5500	−1.50924
$438$	16.0937	0.768987
$439$	−27.7701	−1.32540	−0.662698	−	0.748887i	$-0.730589\pi$
$439$	−27.7701	−1.32540	−0.662698	+	0.748887i	$0.730589\pi$
$440$	17.8275	0.849895
$441$	−11.3837	−0.542080
$442$	−17.9676	−0.854630
$443$	24.9352	1.18471	0.592354	−	0.805678i	$-0.298199\pi$
$443$	24.9352	1.18471	0.592354	+	0.805678i	$0.298199\pi$
$444$	−3.04415	−0.144469
$445$	0.190042	0.00900884
$446$	−13.7252	−0.649905
$447$	40.2636	1.90440
$448$	−4.13385	−0.195306
$449$	1.83458	0.0865793	0.0432896	−	0.999063i	$-0.486216\pi$
$449$	1.83458	0.0865793	0.0432896	+	0.999063i	$0.486216\pi$
$450$	10.7007	0.504435
$451$	−4.19741	−0.197648
$452$	−8.33834	−0.392203
$453$	−15.7270	−0.738921
$454$	−7.55162	−0.354415
$455$	−27.5051	−1.28946
$456$	−41.7925	−1.95711
$457$	−23.4494	−1.09692	−0.548459	−	0.836178i	$-0.684785\pi$
$457$	−23.4494	−1.09692	−0.548459	+	0.836178i	$0.684785\pi$
$458$	−16.7092	−0.780771
$459$	−7.13121	−0.332857
$460$	−21.0676	−0.982281
$461$	−5.25865	−0.244920	−0.122460	−	0.992473i	$-0.539078\pi$
$461$	−5.25865	−0.244920	−0.122460	+	0.992473i	$0.539078\pi$
$462$	−4.07237	−0.189464
$463$	−26.7133	−1.24147	−0.620735	−	0.784020i	$-0.713166\pi$
$463$	−26.7133	−1.24147	−0.620735	+	0.784020i	$0.713166\pi$
$464$	0.744615	0.0345679
$465$	58.5942	2.71724
$466$	4.22303	0.195628
$467$	16.8479	0.779630	0.389815	−	0.920893i	$-0.372539\pi$
$467$	16.8479	0.779630	0.389815	+	0.920893i	$0.372539\pi$
$468$	−18.9681	−0.876800
$469$	−10.8791	−0.502352
$470$	−23.6302	−1.08998
$471$	−36.1221	−1.66442
$472$	10.7597	0.495255
$473$	−11.6993	−0.537935
$474$	−13.7978	−0.633753
$475$	−45.8981	−2.10595
$476$	−5.14779	−0.235949
$477$	11.7886	0.539762
$478$	4.96738	0.227203
$479$	−6.47707	−0.295945	−0.147973	−	0.988991i	$-0.547275\pi$
$479$	−6.47707	−0.295945	−0.147973	+	0.988991i	$0.547275\pi$
$480$	−44.5245	−2.03225
$481$	−6.91321	−0.315215
$482$	−20.3473	−0.926792
$483$	11.8961	0.541292
$484$	9.80797	0.445817
$485$	−23.2046	−1.05367
$486$	14.4208	0.654139
$487$	8.31640	0.376852	0.188426	−	0.982087i	$-0.439661\pi$
$487$	8.31640	0.376852	0.188426	+	0.982087i	$0.439661\pi$
$488$	6.48434	0.293532
$489$	39.3915	1.78135
$490$	−15.3869	−0.695109
$491$	−33.5701	−1.51500	−0.757499	−	0.652836i	$-0.773579\pi$
$491$	−33.5701	−1.51500	−0.757499	+	0.652836i	$0.773579\pi$
$492$	6.57058	0.296225
$493$	−4.28666	−0.193062
$494$	−38.3952	−1.72748
$495$	−13.3845	−0.601589
$496$	−4.32602	−0.194244
$497$	−10.5522	−0.473330
$498$	12.6577	0.567205
$499$	18.1158	0.810973	0.405486	−	0.914101i	$-0.367102\pi$
$499$	18.1158	0.810973	0.405486	+	0.914101i	$0.367102\pi$
$500$	−7.49197	−0.335051
$501$	25.8945	1.15688
$502$	−9.57689	−0.427437
$503$	28.6040	1.27539	0.637696	−	0.770288i	$-0.279888\pi$
$503$	28.6040	1.27539	0.637696	+	0.770288i	$0.279888\pi$
$504$	6.33958	0.282387
$505$	−59.8374	−2.66273
$506$	−7.08373	−0.314910
$507$	−77.9482	−3.46180
$508$	18.8067	0.834414
$509$	27.4499	1.21670	0.608348	−	0.793671i	$-0.291833\pi$
$509$	27.4499	1.21670	0.608348	+	0.793671i	$0.291833\pi$
$510$	19.8468	0.878830
$511$	10.4713	0.463224
$512$	6.31996	0.279306
$513$	−15.2388	−0.672810
$514$	−6.27573	−0.276811
$515$	28.1933	1.24234
$516$	18.3140	0.806227
$517$	16.8362	0.740455
$518$	0.934720	0.0410693
$519$	9.19389	0.403567
$520$	−63.3763	−2.77923
$521$	19.4684	0.852925	0.426462	−	0.904505i	$-0.359760\pi$
$521$	19.4684	0.852925	0.426462	+	0.904505i	$0.359760\pi$
$522$	2.13562	0.0934735
$523$	40.0123	1.74962	0.874808	−	0.484470i	$-0.160988\pi$
$523$	40.0123	1.74962	0.874808	+	0.484470i	$0.160988\pi$
$524$	2.32535	0.101583
$525$	17.3062	0.755303
$526$	5.88627	0.256653
$527$	24.9044	1.08485
$528$	2.45629	0.106896
$529$	−2.30717	−0.100312
$530$	15.9342	0.692137
$531$	−8.07814	−0.350561
$532$	−11.0004	−0.476928
$533$	14.9217	0.646329
$534$	−0.100027	−0.00432860
$535$	−29.6468	−1.28174
$536$	−25.0673	−1.08274
$537$	53.2892	2.29960
$538$	−6.87221	−0.296282
$539$	10.9630	0.472208
$540$	−10.1758	−0.437895
$541$	35.7565	1.53729	0.768645	−	0.639675i	$-0.220931\pi$
$541$	35.7565	1.53729	0.768645	+	0.639675i	$0.220931\pi$
$542$	−11.6689	−0.501222
$543$	−20.1518	−0.864795
$544$	−18.9243	−0.811372
$545$	−3.40847	−0.146003
$546$	14.4771	0.619564
$547$	42.4891	1.81670	0.908352	−	0.418206i	$-0.137341\pi$
$547$	42.4891	1.81670	0.908352	+	0.418206i	$0.137341\pi$
$548$	−15.0318	−0.642127
$549$	−4.86829	−0.207774
$550$	−10.3052	−0.439416
$551$	−9.16025	−0.390240
$552$	27.4106	1.16667
$553$	−8.97748	−0.381761
$554$	−2.18260	−0.0927297
$555$	7.63626	0.324141
$556$	21.2343	0.900534
$557$	14.6803	0.622024	0.311012	−	0.950406i	$-0.399332\pi$
$557$	14.6803	0.622024	0.311012	+	0.950406i	$0.399332\pi$
$558$	−12.4074	−0.525247
$559$	41.5906	1.75910
$560$	−2.24310	−0.0947881
$561$	−14.1406	−0.597016
$562$	22.9880	0.969691
$563$	9.53610	0.401899	0.200949	−	0.979602i	$-0.435597\pi$
$563$	9.53610	0.401899	0.200949	+	0.979602i	$0.435597\pi$
$564$	−26.3552	−1.10975
$565$	20.9167	0.879974
$566$	4.83690	0.203310
$567$	12.8171	0.538268
$568$	−24.3140	−1.02019
$569$	24.0915	1.00997	0.504985	−	0.863128i	$-0.331498\pi$
$569$	24.0915	1.00997	0.504985	+	0.863128i	$0.331498\pi$
$570$	42.4109	1.77640
$571$	−7.31931	−0.306303	−0.153152	−	0.988203i	$-0.548942\pi$
$571$	−7.31931	−0.306303	−0.153152	+	0.988203i	$0.548942\pi$
$572$	18.2671	0.763785
$573$	12.5055	0.522424
$574$	−2.01753	−0.0842099
$575$	30.1034	1.25540
$576$	7.15121	0.297967
$577$	−31.4652	−1.30991	−0.654956	−	0.755667i	$-0.727313\pi$
$577$	−31.4652	−1.30991	−0.654956	+	0.755667i	$0.727313\pi$
$578$	−5.17758	−0.215359
$579$	−11.0465	−0.459079
$580$	−6.11677	−0.253985
$581$	8.23569	0.341674
$582$	12.2136	0.506270
$583$	−11.3529	−0.470190
$584$	24.1277	0.998410
$585$	47.5815	1.96725
$586$	−11.8492	−0.489484
$587$	−3.61851	−0.149352	−0.0746759	−	0.997208i	$-0.523792\pi$
$587$	−3.61851	−0.149352	−0.0746759	+	0.997208i	$0.523792\pi$
$588$	−17.1613	−0.707720
$589$	53.2186	2.19284
$590$	−10.9189	−0.449525
$591$	−47.6172	−1.95871
$592$	−0.563786	−0.0231715
$593$	18.7090	0.768288	0.384144	−	0.923273i	$-0.374497\pi$
$593$	18.7090	0.768288	0.384144	+	0.923273i	$0.374497\pi$
$594$	−3.42148	−0.140385
$595$	12.9132	0.529392
$596$	24.4195	1.00026
$597$	42.9178	1.75651
$598$	25.1824	1.02979
$599$	7.92020	0.323611	0.161805	−	0.986823i	$-0.448268\pi$
$599$	7.92020	0.323611	0.161805	+	0.986823i	$0.448268\pi$
$600$	39.8762	1.62794
$601$	0.493558	0.0201326	0.0100663	−	0.999949i	$-0.496796\pi$
$601$	0.493558	0.0201326	0.0100663	+	0.999949i	$0.496796\pi$
$602$	−5.62338	−0.229192
$603$	18.8200	0.766409
$604$	−9.53831	−0.388108
$605$	−24.6033	−1.00027
$606$	31.4950	1.27940
$607$	6.55771	0.266169	0.133085	−	0.991105i	$-0.457512\pi$
$607$	6.55771	0.266169	0.133085	+	0.991105i	$0.457512\pi$
$608$	−40.4397	−1.64004
$609$	3.45392	0.139960
$610$	−6.58029	−0.266428
$611$	−59.8521	−2.42136
$612$	8.90524	0.359973
$613$	30.8826	1.24734	0.623668	−	0.781689i	$-0.285642\pi$
$613$	30.8826	1.24734	0.623668	+	0.781689i	$0.285642\pi$
$614$	20.3642	0.821833
$615$	−16.4823	−0.664631
$616$	−6.10529	−0.245989
$617$	−15.7679	−0.634792	−0.317396	−	0.948293i	$-0.602808\pi$
$617$	−15.7679	−0.634792	−0.317396	+	0.948293i	$0.602808\pi$
$618$	−14.8393	−0.596926
$619$	−12.6044	−0.506615	−0.253307	−	0.967386i	$-0.581518\pi$
$619$	−12.6044	−0.506615	−0.253307	+	0.967386i	$0.581518\pi$
$620$	35.5369	1.42719
$621$	9.99474	0.401075
$622$	−18.5769	−0.744867
$623$	−0.0650824	−0.00260747
$624$	−8.73203	−0.349561
$625$	−14.2948	−0.571791
$626$	−3.86096	−0.154315
$627$	−30.2173	−1.20676
$628$	−21.9077	−0.874213
$629$	3.24565	0.129413
$630$	−6.43339	−0.256313
$631$	28.8285	1.14764	0.573822	−	0.818980i	$-0.305460\pi$
$631$	28.8285	1.14764	0.573822	+	0.818980i	$0.305460\pi$
$632$	−20.6856	−0.822829
$633$	35.6258	1.41600
$634$	−18.2429	−0.724517
$635$	−47.1767	−1.87215
$636$	17.7717	0.704695
$637$	−38.9730	−1.54416
$638$	−2.05669	−0.0814253
$639$	18.2544	0.722132
$640$	−30.0813	−1.18907
$641$	−10.7395	−0.424185	−0.212093	−	0.977250i	$-0.568028\pi$
$641$	−10.7395	−0.424185	−0.212093	+	0.977250i	$0.568028\pi$
$642$	15.6044	0.615856
$643$	−12.0149	−0.473822	−0.236911	−	0.971531i	$-0.576135\pi$
$643$	−12.0149	−0.473822	−0.236911	+	0.971531i	$0.576135\pi$
$644$	7.21488	0.284306
$645$	−45.9406	−1.80891
$646$	18.0260	0.709223
$647$	−15.4681	−0.608112	−0.304056	−	0.952654i	$-0.598341\pi$
$647$	−15.4681	−0.608112	−0.304056	+	0.952654i	$0.598341\pi$
$648$	29.5327	1.16015
$649$	7.77960	0.305376
$650$	36.6347	1.43693
$651$	−20.0664	−0.786464
$652$	23.8906	0.935627
$653$	16.4044	0.641955	0.320977	−	0.947087i	$-0.395989\pi$
$653$	16.4044	0.641955	0.320977	+	0.947087i	$0.395989\pi$
$654$	1.79403	0.0701520
$655$	−5.83314	−0.227919
$656$	1.21689	0.0475116
$657$	−18.1145	−0.706714
$658$	8.09248	0.315478
$659$	38.3870	1.49535	0.747673	−	0.664067i	$-0.231171\pi$
$659$	38.3870	1.49535	0.747673	+	0.664067i	$0.231171\pi$
$660$	−20.1776	−0.785414
$661$	25.1700	0.979000	0.489500	−	0.872003i	$-0.337179\pi$
$661$	25.1700	0.979000	0.489500	+	0.872003i	$0.337179\pi$
$662$	−22.4138	−0.871139
$663$	50.2693	1.95230
$664$	18.9764	0.736427
$665$	27.5945	1.07007
$666$	−1.61699	−0.0626570
$667$	6.00797	0.232629
$668$	15.7048	0.607637
$669$	38.4000	1.48463
$670$	25.4383	0.982767
$671$	4.68838	0.180993
$672$	15.2480	0.588205
$673$	−36.2463	−1.39719	−0.698597	−	0.715515i	$-0.746192\pi$
$673$	−36.2463	−1.39719	−0.698597	+	0.715515i	$0.746192\pi$
$674$	22.8415	0.879823
$675$	14.5401	0.559648
$676$	−47.2749	−1.81826
$677$	28.3573	1.08986	0.544931	−	0.838481i	$-0.316556\pi$
$677$	28.3573	1.08986	0.544931	+	0.838481i	$0.316556\pi$
$678$	−11.0094	−0.422813
$679$	7.94674	0.304968
$680$	29.7542	1.14102
$681$	21.1278	0.809618
$682$	11.9489	0.457545
$683$	−36.7314	−1.40549	−0.702745	−	0.711442i	$-0.748042\pi$
$683$	−36.7314	−1.40549	−0.702745	+	0.711442i	$0.748042\pi$
$684$	19.0298	0.727622
$685$	37.7073	1.44072
$686$	11.8125	0.451003
$687$	46.7487	1.78357
$688$	3.39180	0.129311
$689$	40.3592	1.53756
$690$	−27.8162	−1.05895
$691$	11.6910	0.444746	0.222373	−	0.974962i	$-0.428620\pi$
$691$	11.6910	0.444746	0.222373	+	0.974962i	$0.428620\pi$
$692$	5.57601	0.211968
$693$	4.58371	0.174121
$694$	−13.8186	−0.524547
$695$	−53.2662	−2.02050
$696$	7.95841	0.301663
$697$	−7.00550	−0.265352
$698$	−4.52694	−0.171347
$699$	−11.8151	−0.446889
$700$	10.4960	0.396712
$701$	−36.1079	−1.36378	−0.681889	−	0.731456i	$-0.738841\pi$
$701$	−36.1079	−1.36378	−0.681889	+	0.731456i	$0.738841\pi$
$702$	12.1632	0.459072
$703$	6.93569	0.261584
$704$	−6.88692	−0.259561
$705$	66.1120	2.48992
$706$	−4.21298	−0.158558
$707$	20.4921	0.770686
$708$	−12.1781	−0.457681
$709$	−1.38058	−0.0518486	−0.0259243	−	0.999664i	$-0.508253\pi$
$709$	−1.38058	−0.0518486	−0.0259243	+	0.999664i	$0.508253\pi$
$710$	24.6738	0.925991
$711$	15.5303	0.582431
$712$	−0.149961	−0.00562001
$713$	−34.9047	−1.30719
$714$	−6.79680	−0.254364
$715$	−45.8230	−1.71368
$716$	32.3194	1.20783
$717$	−13.8976	−0.519017
$718$	6.91708	0.258143
$719$	−1.32081	−0.0492580	−0.0246290	−	0.999697i	$-0.507840\pi$
$719$	−1.32081	−0.0492580	−0.0246290	+	0.999697i	$0.507840\pi$
$720$	3.88037	0.144613
$721$	−9.65517	−0.359577
$722$	23.3054	0.867338
$723$	56.9272	2.11714
$724$	−12.2219	−0.454222
$725$	8.74023	0.324604
$726$	12.9498	0.480612
$727$	20.5898	0.763633	0.381817	−	0.924238i	$-0.375299\pi$
$727$	20.5898	0.763633	0.381817	+	0.924238i	$0.375299\pi$
$728$	21.7041	0.804407
$729$	−7.40509	−0.274263
$730$	−24.4847	−0.906219
$731$	−19.5262	−0.722202
$732$	−7.33913	−0.271262
$733$	−21.4173	−0.791066	−0.395533	−	0.918452i	$-0.629440\pi$
$733$	−21.4173	−0.791066	−0.395533	+	0.918452i	$0.629440\pi$
$734$	−19.1662	−0.707436
$735$	43.0491	1.58789
$736$	26.5233	0.977662
$737$	−18.1245	−0.667623
$738$	3.49015	0.128474
$739$	47.5167	1.74793	0.873966	−	0.485988i	$-0.161540\pi$
$739$	47.5167	1.74793	0.873966	+	0.485988i	$0.161540\pi$
$740$	4.63132	0.170251
$741$	107.421	3.94622
$742$	−5.45688	−0.200329
$743$	9.55984	0.350716	0.175358	−	0.984505i	$-0.443892\pi$
$743$	9.55984	0.350716	0.175358	+	0.984505i	$0.443892\pi$
$744$	−46.2363	−1.69510
$745$	−61.2563	−2.24426
$746$	4.14702	0.151833
$747$	−14.2470	−0.521272
$748$	−8.57613	−0.313574
$749$	10.1529	0.370980
$750$	−9.89189	−0.361201
$751$	25.5996	0.934142	0.467071	−	0.884220i	$-0.345309\pi$
$751$	25.5996	0.934142	0.467071	+	0.884220i	$0.345309\pi$
$752$	−4.88106	−0.177994
$753$	26.7940	0.976428
$754$	7.31147	0.266268
$755$	23.9269	0.870787
$756$	3.48483	0.126742
$757$	−48.0386	−1.74599	−0.872996	−	0.487728i	$-0.837826\pi$
$757$	−48.0386	−1.74599	−0.872996	+	0.487728i	$0.837826\pi$
$758$	27.3876	0.994763
$759$	19.8187	0.719374
$760$	63.5824	2.30638
$761$	29.3142	1.06264	0.531319	−	0.847172i	$-0.321696\pi$
$761$	29.3142	1.06264	0.531319	+	0.847172i	$0.321696\pi$
$762$	24.8311	0.899538
$763$	1.16728	0.0422583
$764$	7.58446	0.274396
$765$	−22.3388	−0.807662
$766$	20.1241	0.727115
$767$	−27.6562	−0.998607
$768$	31.7014	1.14393
$769$	3.44520	0.124237	0.0621186	−	0.998069i	$-0.480214\pi$
$769$	3.44520	0.124237	0.0621186	+	0.998069i	$0.480214\pi$
$770$	6.19563	0.223275
$771$	17.5581	0.632340
$772$	−6.69962	−0.241125
$773$	23.3160	0.838617	0.419308	−	0.907844i	$-0.362273\pi$
$773$	23.3160	0.838617	0.419308	+	0.907844i	$0.362273\pi$
$774$	9.72797	0.349665
$775$	−50.7785	−1.82402
$776$	18.3106	0.657312
$777$	−2.61514	−0.0938177
$778$	−27.7996	−0.996664
$779$	−14.9702	−0.536362
$780$	71.7308	2.56837
$781$	−17.5798	−0.629053
$782$	−11.8228	−0.422781
$783$	2.90188	0.103705
$784$	−3.17832	−0.113512
$785$	54.9555	1.96145
$786$	3.07023	0.109512
$787$	−36.1577	−1.28888	−0.644441	−	0.764654i	$-0.722910\pi$
$787$	−36.1577	−1.28888	−0.644441	+	0.764654i	$0.722910\pi$
$788$	−28.8794	−1.02879
$789$	−16.4685	−0.586293
$790$	20.9917	0.746851
$791$	−7.16322	−0.254695
$792$	10.5616	0.375291
$793$	−16.6670	−0.591863
$794$	0.919579	0.0326347
$795$	−44.5804	−1.58110
$796$	26.0292	0.922581
$797$	−21.0534	−0.745750	−0.372875	−	0.927882i	$-0.621628\pi$
$797$	−21.0534	−0.745750	−0.372875	+	0.927882i	$0.621628\pi$
$798$	−14.5242	−0.514151
$799$	28.0997	0.994096
$800$	38.5854	1.36420
$801$	0.112587	0.00397807
$802$	−8.95575	−0.316239
$803$	17.4450	0.615622
$804$	28.3718	1.00060
$805$	−18.0985	−0.637890
$806$	−42.4777	−1.49621
$807$	19.2269	0.676820
$808$	47.2172	1.66110
$809$	15.5009	0.544983	0.272491	−	0.962158i	$-0.412152\pi$
$809$	15.5009	0.544983	0.272491	+	0.962158i	$0.412152\pi$
$810$	−29.9697	−1.05303
$811$	−49.1775	−1.72686	−0.863428	−	0.504472i	$-0.831687\pi$
$811$	−49.1775	−1.72686	−0.863428	+	0.504472i	$0.831687\pi$
$812$	2.09477	0.0735121
$813$	32.6470	1.14498
$814$	1.55723	0.0545808
$815$	−59.9296	−2.09924
$816$	4.09956	0.143513
$817$	−41.7259	−1.45980
$818$	−3.27526	−0.114517
$819$	−16.2949	−0.569391
$820$	−9.99637	−0.349088
$821$	−16.4071	−0.572610	−0.286305	−	0.958138i	$-0.592427\pi$
$821$	−16.4071	−0.572610	−0.286305	+	0.958138i	$0.592427\pi$
$822$	−19.8470	−0.692244
$823$	7.02011	0.244705	0.122353	−	0.992487i	$-0.460956\pi$
$823$	7.02011	0.244705	0.122353	+	0.992487i	$0.460956\pi$
$824$	−22.2471	−0.775014
$825$	28.8317	1.00379
$826$	3.73934	0.130108
$827$	44.6005	1.55091	0.775457	−	0.631401i	$-0.217520\pi$
$827$	44.6005	1.55091	0.775457	+	0.631401i	$0.217520\pi$
$828$	−12.4811	−0.433749
$829$	7.95925	0.276436	0.138218	−	0.990402i	$-0.455862\pi$
$829$	7.95925	0.276436	0.138218	+	0.990402i	$0.455862\pi$
$830$	−19.2572	−0.668427
$831$	6.10643	0.211830
$832$	24.4828	0.848787
$833$	18.2972	0.633962
$834$	28.0363	0.970818
$835$	−39.3955	−1.36334
$836$	−18.3265	−0.633835
$837$	−16.8592	−0.582738
$838$	15.3250	0.529394
$839$	9.94092	0.343199	0.171599	−	0.985167i	$-0.445107\pi$
$839$	9.94092	0.343199	0.171599	+	0.985167i	$0.445107\pi$
$840$	−23.9741	−0.827185
$841$	−27.2556	−0.939850
$842$	−22.4043	−0.772104
$843$	−64.3154	−2.21514
$844$	21.6067	0.743734
$845$	118.589	4.07959
$846$	−13.9993	−0.481306
$847$	8.42574	0.289512
$848$	3.29137	0.113026
$849$	−13.5326	−0.464437
$850$	−17.1995	−0.589937
$851$	−4.54894	−0.155936
$852$	27.5191	0.942790
$853$	−18.4987	−0.633383	−0.316692	−	0.948529i	$-0.602572\pi$
$853$	−18.4987	−0.633383	−0.316692	+	0.948529i	$0.602572\pi$
$854$	2.25351	0.0771136
$855$	−47.7362	−1.63254
$856$	23.3941	0.799592
$857$	−53.4918	−1.82725	−0.913623	−	0.406562i	$-0.866728\pi$
$857$	−53.4918	−1.82725	−0.913623	+	0.406562i	$0.866728\pi$
$858$	24.1186	0.823397
$859$	20.6718	0.705314	0.352657	−	0.935753i	$-0.385278\pi$
$859$	20.6718	0.705314	0.352657	+	0.935753i	$0.385278\pi$
$860$	−27.8625	−0.950104
$861$	5.64459	0.192367
$862$	23.3510	0.795340
$863$	56.1038	1.90980	0.954898	−	0.296935i	$-0.0959644\pi$
$863$	56.1038	1.90980	0.954898	+	0.296935i	$0.0959644\pi$
$864$	12.8109	0.435835
$865$	−13.9874	−0.475587
$866$	24.8602	0.844786
$867$	14.4857	0.491961
$868$	−12.1701	−0.413080
$869$	−14.9563	−0.507358
$870$	−8.07618	−0.273808
$871$	64.4318	2.18319
$872$	2.68960	0.0910813
$873$	−13.7472	−0.465271
$874$	−25.2643	−0.854577
$875$	−6.43613	−0.217581
$876$	−27.3083	−0.922660
$877$	−54.8826	−1.85325	−0.926626	−	0.375984i	$-0.877305\pi$
$877$	−54.8826	−1.85325	−0.926626	+	0.375984i	$0.877305\pi$
$878$	−22.2375	−0.750478
$879$	33.1513	1.11817
$880$	−3.73696	−0.125973
$881$	5.90480	0.198938	0.0994689	−	0.995041i	$-0.468286\pi$
$881$	5.90480	0.198938	0.0994689	+	0.995041i	$0.468286\pi$
$882$	−9.11570	−0.306942
$883$	−36.1794	−1.21753	−0.608766	−	0.793350i	$-0.708335\pi$
$883$	−36.1794	−1.21753	−0.608766	+	0.793350i	$0.708335\pi$
$884$	30.4878	1.02542
$885$	30.5487	1.02688
$886$	19.9674	0.670817
$887$	46.7990	1.57136	0.785678	−	0.618636i	$-0.212314\pi$
$887$	46.7990	1.57136	0.785678	+	0.618636i	$0.212314\pi$
$888$	−6.02572	−0.202210
$889$	16.1563	0.541865
$890$	0.152180	0.00510107
$891$	21.3531	0.715354
$892$	23.2892	0.779781
$893$	60.0467	2.00939
$894$	32.2419	1.07833
$895$	−81.0732	−2.70998
$896$	10.3017	0.344157
$897$	−70.4548	−2.35242
$898$	1.46908	0.0490238
$899$	−10.1343	−0.337996
$900$	−18.1572	−0.605241
$901$	−18.9481	−0.631252
$902$	−3.36116	−0.111914
$903$	15.7330	0.523561
$904$	−16.5052	−0.548956
$905$	30.6586	1.01912
$906$	−12.5937	−0.418399
$907$	−34.5102	−1.14589	−0.572947	−	0.819593i	$-0.694200\pi$
$907$	−34.5102	−1.14589	−0.572947	+	0.819593i	$0.694200\pi$
$908$	12.8138	0.425241
$909$	−35.4496	−1.17579
$910$	−22.0253	−0.730130
$911$	18.1840	0.602461	0.301231	−	0.953551i	$-0.402603\pi$
$911$	18.1840	0.602461	0.301231	+	0.953551i	$0.402603\pi$
$912$	8.76042	0.290087
$913$	13.7205	0.454083
$914$	−18.7776	−0.621107
$915$	18.4102	0.608623
$916$	28.3527	0.936798
$917$	1.99764	0.0659678
$918$	−5.71046	−0.188473
$919$	20.0528	0.661480	0.330740	−	0.943722i	$-0.392702\pi$
$919$	20.0528	0.661480	0.330740	+	0.943722i	$0.392702\pi$
$920$	−41.7020	−1.37487
$921$	−56.9746	−1.87738
$922$	−4.21096	−0.138681
$923$	62.4954	2.05706
$924$	6.91011	0.227326
$925$	−6.61767	−0.217588
$926$	−21.3912	−0.702958
$927$	16.7026	0.548586
$928$	7.70079	0.252791
$929$	−25.9146	−0.850229	−0.425115	−	0.905140i	$-0.639766\pi$
$929$	−25.9146	−0.850229	−0.425115	+	0.905140i	$0.639766\pi$
$930$	46.9205	1.53858
$931$	39.0997	1.28144
$932$	−7.16576	−0.234722
$933$	51.9742	1.70156
$934$	13.4913	0.441449
$935$	21.5132	0.703558
$936$	−37.5462	−1.22724
$937$	−19.7485	−0.645154	−0.322577	−	0.946543i	$-0.604549\pi$
$937$	−19.7485	−0.645154	−0.322577	+	0.946543i	$0.604549\pi$
$938$	−8.71169	−0.284447
$939$	10.8021	0.352514
$940$	40.0963	1.30780
$941$	40.2924	1.31350	0.656748	−	0.754110i	$-0.271932\pi$
$941$	40.2924	1.31350	0.656748	+	0.754110i	$0.271932\pi$
$942$	−28.9255	−0.942443
$943$	9.81855	0.319736
$944$	−2.25542	−0.0734076
$945$	−8.74169	−0.284367
$946$	−9.36845	−0.304595
$947$	−29.5945	−0.961692	−0.480846	−	0.876805i	$-0.659670\pi$
$947$	−29.5945	−0.961692	−0.480846	+	0.876805i	$0.659670\pi$
$948$	23.4124	0.760401
$949$	−62.0165	−2.01314
$950$	−36.7538	−1.19245
$951$	51.0396	1.65507
$952$	−10.1897	−0.330252
$953$	−32.6369	−1.05721	−0.528607	−	0.848867i	$-0.677286\pi$
$953$	−32.6369	−1.05721	−0.528607	+	0.848867i	$0.677286\pi$
$954$	9.43994	0.305629
$955$	−19.0256	−0.615655
$956$	−8.42879	−0.272607
$957$	5.75418	0.186006
$958$	−5.18664	−0.167573
$959$	−12.9134	−0.416995
$960$	−27.0434	−0.872822
$961$	27.8774	0.899270
$962$	−5.53589	−0.178484
$963$	−17.5637	−0.565983
$964$	34.5258	1.11200
$965$	16.8060	0.541005
$966$	9.52605	0.306496
$967$	−34.7715	−1.11818	−0.559088	−	0.829109i	$-0.688849\pi$
$967$	−34.7715	−1.11818	−0.559088	+	0.829109i	$0.688849\pi$
$968$	19.4143	0.623999
$969$	−50.4327	−1.62013
$970$	−18.5816	−0.596618
$971$	−35.5458	−1.14072	−0.570359	−	0.821395i	$-0.693196\pi$
$971$	−35.5458	−1.14072	−0.570359	+	0.821395i	$0.693196\pi$
$972$	−24.4695	−0.784861
$973$	18.2417	0.584803
$974$	6.65952	0.213385
$975$	−102.496	−3.28249
$976$	−1.35923	−0.0435078
$977$	−50.6507	−1.62046	−0.810230	−	0.586112i	$-0.800658\pi$
$977$	−50.6507	−1.62046	−0.810230	+	0.586112i	$0.800658\pi$
$978$	31.5435	1.00865
$979$	−0.108426	−0.00346531
$980$	26.1089	0.834018
$981$	−2.01929	−0.0644710
$982$	−26.8819	−0.857837
$983$	0.0295723	0.000943211 0	0.000471605	−	1.00000i	$-0.499850\pi$
$983$	0.0295723	0.000943211 0	0.000471605		1.00000i	$0.499850\pi$
$984$	13.0061	0.414618
$985$	72.4440	2.30826
$986$	−3.43263	−0.109317
$987$	−22.6410	−0.720670
$988$	65.1500	2.07270
$989$	27.3669	0.870217
$990$	−10.7179	−0.340638
$991$	54.9014	1.74400	0.872001	−	0.489505i	$-0.162822\pi$
$991$	54.9014	1.74400	0.872001	+	0.489505i	$0.162822\pi$
$992$	−44.7396	−1.42048
$993$	62.7090	1.99001
$994$	−8.44987	−0.268014
$995$	−65.2943	−2.06997
$996$	−21.4779	−0.680554
$997$	−16.6449	−0.527150	−0.263575	−	0.964639i	$-0.584902\pi$
$997$	−16.6449	−0.527150	−0.263575	+	0.964639i	$0.584902\pi$
$998$	14.5066	0.459197
$999$	−2.19716	−0.0695151

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.d.1.52	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.d.1.52	✓	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)

\(f(q)\)	\(=\)	\(q+0.800770 q^{2} -2.24038 q^{3} -1.35877 q^{4} +3.40847 q^{5} -1.79403 q^{6} -1.16728 q^{7} -2.68960 q^{8} +2.01929 q^{9} +O(q^{10})\)	\(q+0.800770 q^{2} -2.24038 q^{3} -1.35877 q^{4} +3.40847 q^{5} -1.79403 q^{6} -1.16728 q^{7} -2.68960 q^{8} +2.01929 q^{9} +2.72940 q^{10} -1.94466 q^{11} +3.04415 q^{12} +6.91321 q^{13} -0.934720 q^{14} -7.63626 q^{15} +0.563786 q^{16} -3.24565 q^{17} +1.61699 q^{18} -6.93569 q^{19} -4.63132 q^{20} +2.61514 q^{21} -1.55723 q^{22} +4.54894 q^{23} +6.02572 q^{24} +6.61767 q^{25} +5.53589 q^{26} +2.19716 q^{27} +1.58606 q^{28} +1.32074 q^{29} -6.11489 q^{30} -7.67316 q^{31} +5.83066 q^{32} +4.35678 q^{33} -2.59902 q^{34} -3.97863 q^{35} -2.74375 q^{36} -1.00000 q^{37} -5.55389 q^{38} -15.4882 q^{39} -9.16742 q^{40} +2.15843 q^{41} +2.09413 q^{42} +6.01611 q^{43} +2.64235 q^{44} +6.88269 q^{45} +3.64265 q^{46} -8.65764 q^{47} -1.26309 q^{48} -5.63746 q^{49} +5.29923 q^{50} +7.27148 q^{51} -9.39345 q^{52} +5.83799 q^{53} +1.75942 q^{54} -6.62833 q^{55} +3.13951 q^{56} +15.5386 q^{57} +1.05761 q^{58} -4.00049 q^{59} +10.3759 q^{60} -2.41089 q^{61} -6.14443 q^{62} -2.35707 q^{63} +3.54145 q^{64} +23.5635 q^{65} +3.48878 q^{66} +9.32010 q^{67} +4.41009 q^{68} -10.1913 q^{69} -3.18597 q^{70} +9.04000 q^{71} -5.43108 q^{72} -8.97072 q^{73} -0.800770 q^{74} -14.8261 q^{75} +9.42399 q^{76} +2.26996 q^{77} -12.4025 q^{78} +7.69096 q^{79} +1.92165 q^{80} -10.9803 q^{81} +1.72840 q^{82} -7.05547 q^{83} -3.55337 q^{84} -11.0627 q^{85} +4.81752 q^{86} -2.95896 q^{87} +5.23037 q^{88} +0.0557557 q^{89} +5.51145 q^{90} -8.06963 q^{91} -6.18095 q^{92} +17.1908 q^{93} -6.93278 q^{94} -23.6401 q^{95} -13.0629 q^{96} -6.80793 q^{97} -4.51431 q^{98} -3.92684 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) \) 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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