LMFDB - Embedded newform 4033.2.a.d.1.5

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			1.5
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)

$f(q)$	$=$	$q-2.66315 q^{2} +1.52081 q^{3} +5.09239 q^{4} +1.90830 q^{5} -4.05016 q^{6} -2.83326 q^{7} -8.23552 q^{8} -0.687131 q^{9} +O(q^{10})$	\(q-2.66315 q^{2} +1.52081 q^{3} +5.09239 q^{4} +1.90830 q^{5} -4.05016 q^{6} -2.83326 q^{7} -8.23552 q^{8} -0.687131 q^{9} -5.08211 q^{10} +5.75810 q^{11} +7.74457 q^{12} -5.75389 q^{13} +7.54541 q^{14} +2.90217 q^{15} +11.7477 q^{16} +3.64029 q^{17} +1.82994 q^{18} +3.29429 q^{19} +9.71784 q^{20} -4.30886 q^{21} -15.3347 q^{22} -8.81520 q^{23} -12.5247 q^{24} -1.35837 q^{25} +15.3235 q^{26} -5.60743 q^{27} -14.4281 q^{28} +8.25297 q^{29} -7.72893 q^{30} -4.72730 q^{31} -14.8149 q^{32} +8.75699 q^{33} -9.69467 q^{34} -5.40672 q^{35} -3.49914 q^{36} -1.00000 q^{37} -8.77320 q^{38} -8.75059 q^{39} -15.7159 q^{40} -8.22487 q^{41} +11.4752 q^{42} +4.70090 q^{43} +29.3225 q^{44} -1.31125 q^{45} +23.4762 q^{46} -8.06805 q^{47} +17.8660 q^{48} +1.02737 q^{49} +3.61756 q^{50} +5.53620 q^{51} -29.3011 q^{52} +5.50423 q^{53} +14.9335 q^{54} +10.9882 q^{55} +23.3334 q^{56} +5.01000 q^{57} -21.9789 q^{58} +1.01395 q^{59} +14.7790 q^{60} -6.58289 q^{61} +12.5895 q^{62} +1.94682 q^{63} +15.9589 q^{64} -10.9802 q^{65} -23.3212 q^{66} +9.17431 q^{67} +18.5378 q^{68} -13.4063 q^{69} +14.3989 q^{70} +1.49410 q^{71} +5.65888 q^{72} +8.25195 q^{73} +2.66315 q^{74} -2.06583 q^{75} +16.7758 q^{76} -16.3142 q^{77} +23.3042 q^{78} -11.6914 q^{79} +22.4182 q^{80} -6.46646 q^{81} +21.9041 q^{82} -3.02745 q^{83} -21.9424 q^{84} +6.94679 q^{85} -12.5192 q^{86} +12.5512 q^{87} -47.4210 q^{88} -2.08727 q^{89} +3.49207 q^{90} +16.3023 q^{91} -44.8905 q^{92} -7.18933 q^{93} +21.4865 q^{94} +6.28651 q^{95} -22.5306 q^{96} -12.6361 q^{97} -2.73604 q^{98} -3.95657 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.66315	−1.88313	−0.941567	−	0.336825i	$-0.890647\pi$
$2$	−2.66315	−1.88313	−0.941567	+	0.336825i	$0.890647\pi$
$3$	1.52081	0.878041	0.439021	−	0.898477i	$-0.355326\pi$
$3$	1.52081	0.878041	0.439021	+	0.898477i	$0.355326\pi$
$4$	5.09239	2.54620
$5$	1.90830	0.853420	0.426710	−	0.904389i	$-0.359673\pi$
$5$	1.90830	0.853420	0.426710	+	0.904389i	$0.359673\pi$
$6$	−4.05016	−1.65347
$7$	−2.83326	−1.07087	−0.535436	−	0.844576i	$-0.679853\pi$
$7$	−2.83326	−1.07087	−0.535436	+	0.844576i	$0.679853\pi$
$8$	−8.23552	−2.91170
$9$	−0.687131	−0.229044
$10$	−5.08211	−1.60710
$11$	5.75810	1.73613	0.868067	−	0.496448i	$-0.165363\pi$
$11$	5.75810	1.73613	0.868067	+	0.496448i	$0.165363\pi$
$12$	7.74457	2.23567
$13$	−5.75389	−1.59584	−0.797921	−	0.602762i	$-0.794067\pi$
$13$	−5.75389	−1.59584	−0.797921	+	0.602762i	$0.794067\pi$
$14$	7.54541	2.01660
$15$	2.90217	0.749338
$16$	11.7477	2.93692
$17$	3.64029	0.882901	0.441451	−	0.897286i	$-0.354464\pi$
$17$	3.64029	0.882901	0.441451	+	0.897286i	$0.354464\pi$
$18$	1.82994	0.431320
$19$	3.29429	0.755762	0.377881	−	0.925854i	$-0.376653\pi$
$19$	3.29429	0.755762	0.377881	+	0.925854i	$0.376653\pi$
$20$	9.71784	2.17297
$21$	−4.30886	−0.940270
$22$	−15.3347	−3.26937
$23$	−8.81520	−1.83810	−0.919048	−	0.394146i	$-0.871041\pi$
$23$	−8.81520	−1.83810	−0.919048	+	0.394146i	$0.871041\pi$
$24$	−12.5247	−2.55659
$25$	−1.35837	−0.271675
$26$	15.3235	3.00519
$27$	−5.60743	−1.07915
$28$	−14.4281	−2.72665
$29$	8.25297	1.53254	0.766269	−	0.642520i	$-0.222111\pi$
$29$	8.25297	1.53254	0.766269	+	0.642520i	$0.222111\pi$
$30$	−7.72893	−1.41110
$31$	−4.72730	−0.849048	−0.424524	−	0.905417i	$-0.639559\pi$
$31$	−4.72730	−0.849048	−0.424524	+	0.905417i	$0.639559\pi$
$32$	−14.8149	−2.61892
$33$	8.75699	1.52440
$34$	−9.69467	−1.66262
$35$	−5.40672	−0.913903
$36$	−3.49914	−0.583190
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−8.77320	−1.42320
$39$	−8.75059	−1.40122
$40$	−15.7159	−2.48490
$41$	−8.22487	−1.28451	−0.642255	−	0.766491i	$-0.722001\pi$
$41$	−8.22487	−1.28451	−0.642255	+	0.766491i	$0.722001\pi$
$42$	11.4752	1.77065
$43$	4.70090	0.716881	0.358440	−	0.933553i	$-0.383309\pi$
$43$	4.70090	0.716881	0.358440	+	0.933553i	$0.383309\pi$
$44$	29.3225	4.42054
$45$	−1.31125	−0.195470
$46$	23.4762	3.46138
$47$	−8.06805	−1.17685	−0.588423	−	0.808553i	$-0.700251\pi$
$47$	−8.06805	−1.17685	−0.588423	+	0.808553i	$0.700251\pi$
$48$	17.8660	2.57874
$49$	1.02737	0.146767
$50$	3.61756	0.511600
$51$	5.53620	0.775224
$52$	−29.3011	−4.06333
$53$	5.50423	0.756063	0.378032	−	0.925793i	$-0.376601\pi$
$53$	5.50423	0.756063	0.378032	+	0.925793i	$0.376601\pi$
$54$	14.9335	2.03219
$55$	10.9882	1.48165
$56$	23.3334	3.11805
$57$	5.01000	0.663590
$58$	−21.9789	−2.88598
$59$	1.01395	0.132005	0.0660026	−	0.997819i	$-0.478975\pi$
$59$	1.01395	0.132005	0.0660026	+	0.997819i	$0.478975\pi$
$60$	14.7790	1.90796
$61$	−6.58289	−0.842852	−0.421426	−	0.906863i	$-0.638470\pi$
$61$	−6.58289	−0.842852	−0.421426	+	0.906863i	$0.638470\pi$
$62$	12.5895	1.59887
$63$	1.94682	0.245276
$64$	15.9589	1.99486
$65$	−10.9802	−1.36192
$66$	−23.3212	−2.87064
$67$	9.17431	1.12082	0.560410	−	0.828215i	$-0.310643\pi$
$67$	9.17431	1.12082	0.560410	+	0.828215i	$0.310643\pi$
$68$	18.5378	2.24804
$69$	−13.4063	−1.61392
$70$	14.3989	1.72100
$71$	1.49410	0.177317	0.0886583	−	0.996062i	$-0.471742\pi$
$71$	1.49410	0.177317	0.0886583	+	0.996062i	$0.471742\pi$
$72$	5.65888	0.666905
$73$	8.25195	0.965818	0.482909	−	0.875671i	$-0.339580\pi$
$73$	8.25195	0.965818	0.482909	+	0.875671i	$0.339580\pi$
$74$	2.66315	0.309585
$75$	−2.06583	−0.238542
$76$	16.7758	1.92432
$77$	−16.3142	−1.85918
$78$	23.3042	2.63868
$79$	−11.6914	−1.31539	−0.657693	−	0.753286i	$-0.728468\pi$
$79$	−11.6914	−1.31539	−0.657693	+	0.753286i	$0.728468\pi$
$80$	22.4182	2.50643
$81$	−6.46646	−0.718495
$82$	21.9041	2.41890
$83$	−3.02745	−0.332306	−0.166153	−	0.986100i	$-0.553135\pi$
$83$	−3.02745	−0.332306	−0.166153	+	0.986100i	$0.553135\pi$
$84$	−21.9424	−2.39411
$85$	6.94679	0.753485
$86$	−12.5192	−1.34998
$87$	12.5512	1.34563
$88$	−47.4210	−5.05509
$89$	−2.08727	−0.221250	−0.110625	−	0.993862i	$-0.535285\pi$
$89$	−2.08727	−0.221250	−0.110625	+	0.993862i	$0.535285\pi$
$90$	3.49207	0.368097
$91$	16.3023	1.70894
$92$	−44.8905	−4.68015
$93$	−7.18933	−0.745499
$94$	21.4865	2.21616
$95$	6.28651	0.644982
$96$	−22.5306	−2.29952
$97$	−12.6361	−1.28300	−0.641500	−	0.767123i	$-0.721687\pi$
$97$	−12.6361	−1.28300	−0.641500	+	0.767123i	$0.721687\pi$
$98$	−2.73604	−0.276382
$99$	−3.95657	−0.397650
$100$	−6.91737	−0.691737
$101$	4.57400	0.455130	0.227565	−	0.973763i	$-0.426924\pi$
$101$	4.57400	0.455130	0.227565	+	0.973763i	$0.426924\pi$
$102$	−14.7438	−1.45985
$103$	−11.1248	−1.09615	−0.548077	−	0.836428i	$-0.684640\pi$
$103$	−11.1248	−1.09615	−0.548077	+	0.836428i	$0.684640\pi$
$104$	47.3863	4.64661
$105$	−8.22261	−0.802445
$106$	−14.6586	−1.42377
$107$	7.82188	0.756169	0.378085	−	0.925771i	$-0.376583\pi$
$107$	7.82188	0.756169	0.378085	+	0.925771i	$0.376583\pi$
$108$	−28.5553	−2.74773
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	−29.2633	−2.79015
$111$	−1.52081	−0.144349
$112$	−33.2842	−3.14507
$113$	−13.2684	−1.24819	−0.624094	−	0.781349i	$-0.714532\pi$
$113$	−13.2684	−1.24819	−0.624094	+	0.781349i	$0.714532\pi$
$114$	−13.3424	−1.24963
$115$	−16.8221	−1.56867
$116$	42.0274	3.90214
$117$	3.95368	0.365517
$118$	−2.70031	−0.248584
$119$	−10.3139	−0.945474
$120$	−23.9009	−2.18184
$121$	22.1557	2.01416
$122$	17.5312	1.58720
$123$	−12.5085	−1.12785
$124$	−24.0733	−2.16184
$125$	−12.1337	−1.08527
$126$	−5.18469	−0.461888
$127$	−14.3285	−1.27145	−0.635724	−	0.771916i	$-0.719298\pi$
$127$	−14.3285	−1.27145	−0.635724	+	0.771916i	$0.719298\pi$
$128$	−12.8713	−1.13767
$129$	7.14919	0.629451
$130$	29.2419	2.56469
$131$	11.2001	0.978561	0.489280	−	0.872127i	$-0.337259\pi$
$131$	11.2001	0.978561	0.489280	+	0.872127i	$0.337259\pi$
$132$	44.5940	3.88141
$133$	−9.33358	−0.809324
$134$	−24.4326	−2.11066
$135$	−10.7007	−0.920969
$136$	−29.9797	−2.57074
$137$	−19.1308	−1.63445	−0.817227	−	0.576316i	$-0.804490\pi$
$137$	−19.1308	−1.63445	−0.817227	+	0.576316i	$0.804490\pi$
$138$	35.7029	3.03924
$139$	−4.18201	−0.354713	−0.177357	−	0.984147i	$-0.556755\pi$
$139$	−4.18201	−0.354713	−0.177357	+	0.984147i	$0.556755\pi$
$140$	−27.5332	−2.32698
$141$	−12.2700	−1.03332
$142$	−3.97901	−0.333911
$143$	−33.1315	−2.77060
$144$	−8.07219	−0.672683
$145$	15.7492	1.30790
$146$	−21.9762	−1.81876
$147$	1.56243	0.128867
$148$	−5.09239	−0.418592
$149$	−20.3468	−1.66687	−0.833436	−	0.552616i	$-0.813630\pi$
$149$	−20.3468	−1.66687	−0.833436	+	0.552616i	$0.813630\pi$
$150$	5.50163	0.449206
$151$	15.7402	1.28092	0.640461	−	0.767991i	$-0.278743\pi$
$151$	15.7402	1.28092	0.640461	+	0.767991i	$0.278743\pi$
$152$	−27.1302	−2.20055
$153$	−2.50136	−0.202223
$154$	43.4473	3.50108
$155$	−9.02113	−0.724594
$156$	−44.5614	−3.56777
$157$	11.7702	0.939366	0.469683	−	0.882835i	$-0.344368\pi$
$157$	11.7702	0.939366	0.469683	+	0.882835i	$0.344368\pi$
$158$	31.1360	2.47705
$159$	8.37089	0.663855
$160$	−28.2712	−2.23504
$161$	24.9758	1.96837
$162$	17.2212	1.35302
$163$	−10.9306	−0.856151	−0.428075	−	0.903743i	$-0.640808\pi$
$163$	−10.9306	−0.856151	−0.428075	+	0.903743i	$0.640808\pi$
$164$	−41.8843	−3.27061
$165$	16.7110	1.30095
$166$	8.06257	0.625777
$167$	−21.3050	−1.64863	−0.824316	−	0.566130i	$-0.808440\pi$
$167$	−21.3050	−1.64863	−0.824316	+	0.566130i	$0.808440\pi$
$168$	35.4857	2.73778
$169$	20.1073	1.54671
$170$	−18.5004	−1.41891
$171$	−2.26361	−0.173102
$172$	23.9388	1.82532
$173$	−2.83316	−0.215401	−0.107701	−	0.994183i	$-0.534349\pi$
$173$	−2.83316	−0.215401	−0.107701	+	0.994183i	$0.534349\pi$
$174$	−33.4258	−2.53401
$175$	3.84863	0.290929
$176$	67.6444	5.09889
$177$	1.54203	0.115906
$178$	5.55872	0.416644
$179$	−11.3486	−0.848232	−0.424116	−	0.905608i	$-0.639415\pi$
$179$	−11.3486	−0.848232	−0.424116	+	0.905608i	$0.639415\pi$
$180$	−6.67742	−0.497706
$181$	−2.17518	−0.161680	−0.0808401	−	0.996727i	$-0.525760\pi$
$181$	−2.17518	−0.161680	−0.0808401	+	0.996727i	$0.525760\pi$
$182$	−43.4155	−3.21817
$183$	−10.0113	−0.740059
$184$	72.5978	5.35198
$185$	−1.90830	−0.140301
$186$	19.1463	1.40388
$187$	20.9612	1.53283
$188$	−41.0857	−2.99648
$189$	15.8873	1.15563
$190$	−16.7419	−1.21459
$191$	5.11864	0.370372	0.185186	−	0.982704i	$-0.440711\pi$
$191$	5.11864	0.370372	0.185186	+	0.982704i	$0.440711\pi$
$192$	24.2705	1.75157
$193$	12.6350	0.909486	0.454743	−	0.890623i	$-0.349731\pi$
$193$	12.6350	0.909486	0.454743	+	0.890623i	$0.349731\pi$
$194$	33.6518	2.41606
$195$	−16.6988	−1.19582
$196$	5.23176	0.373697
$197$	24.2001	1.72419	0.862094	−	0.506748i	$-0.169153\pi$
$197$	24.2001	1.72419	0.862094	+	0.506748i	$0.169153\pi$
$198$	10.5370	0.748829
$199$	14.6004	1.03500	0.517499	−	0.855684i	$-0.326863\pi$
$199$	14.6004	1.03500	0.517499	+	0.855684i	$0.326863\pi$
$200$	11.1869	0.791034
$201$	13.9524	0.984127
$202$	−12.1813	−0.857070
$203$	−23.3828	−1.64115
$204$	28.1925	1.97387
$205$	−15.6956	−1.09623
$206$	29.6269	2.06421
$207$	6.05719	0.421004
$208$	−67.5949	−4.68686
$209$	18.9689	1.31210
$210$	21.8981	1.51111
$211$	−22.0729	−1.51956	−0.759779	−	0.650181i	$-0.774693\pi$
$211$	−22.0729	−1.51956	−0.759779	+	0.650181i	$0.774693\pi$
$212$	28.0297	1.92509
$213$	2.27224	0.155691
$214$	−20.8309	−1.42397
$215$	8.97075	0.611800
$216$	46.1801	3.14216
$217$	13.3937	0.909222
$218$	2.66315	0.180372
$219$	12.5497	0.848028
$220$	55.9563	3.77257
$221$	−20.9459	−1.40897
$222$	4.05016	0.271829
$223$	−4.55927	−0.305311	−0.152656	−	0.988279i	$-0.548783\pi$
$223$	−4.55927	−0.305311	−0.152656	+	0.988279i	$0.548783\pi$
$224$	41.9743	2.80453
$225$	0.933380	0.0622254
$226$	35.3359	2.35051
$227$	−13.5291	−0.897959	−0.448980	−	0.893542i	$-0.648212\pi$
$227$	−13.5291	−0.897959	−0.448980	+	0.893542i	$0.648212\pi$
$228$	25.5129	1.68963
$229$	17.6423	1.16584	0.582919	−	0.812530i	$-0.301910\pi$
$229$	17.6423	1.16584	0.582919	+	0.812530i	$0.301910\pi$
$230$	44.7998	2.95401
$231$	−24.8108	−1.63243
$232$	−67.9675	−4.46229
$233$	14.8513	0.972942	0.486471	−	0.873697i	$-0.338284\pi$
$233$	14.8513	0.972942	0.486471	+	0.873697i	$0.338284\pi$
$234$	−10.5293	−0.688319
$235$	−15.3963	−1.00434
$236$	5.16344	0.336111
$237$	−17.7804	−1.15496
$238$	27.4675	1.78046
$239$	0.431188	0.0278912	0.0139456	−	0.999903i	$-0.495561\pi$
$239$	0.431188	0.0278912	0.0139456	+	0.999903i	$0.495561\pi$
$240$	34.0938	2.20075
$241$	−0.533625	−0.0343738	−0.0171869	−	0.999852i	$-0.505471\pi$
$241$	−0.533625	−0.0343738	−0.0171869	+	0.999852i	$0.505471\pi$
$242$	−59.0042	−3.79293
$243$	6.98803	0.448282
$244$	−33.5227	−2.14607
$245$	1.96053	0.125254
$246$	33.3120	2.12390
$247$	−18.9550	−1.20608
$248$	38.9318	2.47217
$249$	−4.60418	−0.291778
$250$	32.3140	2.04371
$251$	−3.74928	−0.236652	−0.118326	−	0.992975i	$-0.537753\pi$
$251$	−3.74928	−0.236652	−0.118326	+	0.992975i	$0.537753\pi$
$252$	9.91398	0.624522
$253$	−50.7588	−3.19118
$254$	38.1590	2.39431
$255$	10.5648	0.661591
$256$	2.36040	0.147525
$257$	−13.7054	−0.854917	−0.427459	−	0.904035i	$-0.640591\pi$
$257$	−13.7054	−0.854917	−0.427459	+	0.904035i	$0.640591\pi$
$258$	−19.0394	−1.18534
$259$	2.83326	0.176050
$260$	−55.9154	−3.46772
$261$	−5.67087	−0.351018
$262$	−29.8277	−1.84276
$263$	4.91308	0.302954	0.151477	−	0.988461i	$-0.451597\pi$
$263$	4.91308	0.302954	0.151477	+	0.988461i	$0.451597\pi$
$264$	−72.1184	−4.43858
$265$	10.5037	0.645239
$266$	24.8568	1.52407
$267$	−3.17434	−0.194267
$268$	46.7192	2.85383
$269$	−24.9090	−1.51873	−0.759363	−	0.650667i	$-0.774489\pi$
$269$	−24.9090	−1.51873	−0.759363	+	0.650667i	$0.774489\pi$
$270$	28.4976	1.73431
$271$	19.9588	1.21241	0.606205	−	0.795308i	$-0.292691\pi$
$271$	19.9588	1.21241	0.606205	+	0.795308i	$0.292691\pi$
$272$	42.7650	2.59301
$273$	24.7927	1.50052
$274$	50.9482	3.07790
$275$	−7.82166	−0.471664
$276$	−68.2700	−4.10937
$277$	−7.27225	−0.436947	−0.218474	−	0.975843i	$-0.570108\pi$
$277$	−7.27225	−0.436947	−0.218474	+	0.975843i	$0.570108\pi$
$278$	11.1373	0.667973
$279$	3.24827	0.194469
$280$	44.5272	2.66101
$281$	−16.4327	−0.980293	−0.490147	−	0.871640i	$-0.663057\pi$
$281$	−16.4327	−0.980293	−0.490147	+	0.871640i	$0.663057\pi$
$282$	32.6769	1.94588
$283$	−1.52497	−0.0906503	−0.0453251	−	0.998972i	$-0.514432\pi$
$283$	−1.52497	−0.0906503	−0.0453251	+	0.998972i	$0.514432\pi$
$284$	7.60853	0.451483
$285$	9.56060	0.566321
$286$	88.2343	5.21740
$287$	23.3032	1.37555
$288$	10.1797	0.599847
$289$	−3.74826	−0.220486
$290$	−41.9425	−2.46295
$291$	−19.2171	−1.12653
$292$	42.0222	2.45916
$293$	−10.1968	−0.595706	−0.297853	−	0.954612i	$-0.596270\pi$
$293$	−10.1968	−0.595706	−0.297853	+	0.954612i	$0.596270\pi$
$294$	−4.16100	−0.242675
$295$	1.93493	0.112656
$296$	8.23552	0.478680
$297$	−32.2882	−1.87355
$298$	54.1866	3.13895
$299$	50.7217	2.93331
$300$	−10.5200	−0.607374
$301$	−13.3189	−0.767687
$302$	−41.9187	−2.41215
$303$	6.95619	0.399623
$304$	38.7003	2.21961
$305$	−12.5622	−0.719307
$306$	6.66150	0.380813
$307$	24.9669	1.42494	0.712468	−	0.701704i	$-0.247577\pi$
$307$	24.9669	1.42494	0.712468	+	0.701704i	$0.247577\pi$
$308$	−83.0784	−4.73383
$309$	−16.9187	−0.962469
$310$	24.0247	1.36451
$311$	−29.8480	−1.69252	−0.846262	−	0.532767i	$-0.821152\pi$
$311$	−29.8480	−1.69252	−0.846262	+	0.532767i	$0.821152\pi$
$312$	72.0657	4.07991
$313$	−17.2799	−0.976716	−0.488358	−	0.872643i	$-0.662404\pi$
$313$	−17.2799	−0.976716	−0.488358	+	0.872643i	$0.662404\pi$
$314$	−31.3459	−1.76895
$315$	3.71513	0.209324
$316$	−59.5373	−3.34923
$317$	−3.26515	−0.183389	−0.0916946	−	0.995787i	$-0.529228\pi$
$317$	−3.26515	−0.183389	−0.0916946	+	0.995787i	$0.529228\pi$
$318$	−22.2930	−1.25013
$319$	47.5215	2.66069
$320$	30.4544	1.70245
$321$	11.8956	0.663948
$322$	−66.5143	−3.70670
$323$	11.9922	0.667263
$324$	−32.9298	−1.82943
$325$	7.81594	0.433550
$326$	29.1099	1.61225
$327$	−1.52081	−0.0841011
$328$	67.7361	3.74010
$329$	22.8589	1.26025
$330$	−44.5040	−2.44986
$331$	16.6989	0.917854	0.458927	−	0.888474i	$-0.348234\pi$
$331$	16.6989	0.917854	0.458927	+	0.888474i	$0.348234\pi$
$332$	−15.4170	−0.846116
$333$	0.687131	0.0376545
$334$	56.7386	3.10460
$335$	17.5074	0.956531
$336$	−50.6191	−2.76150
$337$	3.01315	0.164137	0.0820685	−	0.996627i	$-0.473847\pi$
$337$	3.01315	0.164137	0.0820685	+	0.996627i	$0.473847\pi$
$338$	−53.5488	−2.91267
$339$	−20.1788	−1.09596
$340$	35.3758	1.91852
$341$	−27.2203	−1.47406
$342$	6.02834	0.325975
$343$	16.9220	0.913703
$344$	−38.7144	−2.08734
$345$	−25.5832	−1.37735
$346$	7.54516	0.405630
$347$	17.9732	0.964850	0.482425	−	0.875937i	$-0.339756\pi$
$347$	17.9732	0.964850	0.482425	+	0.875937i	$0.339756\pi$
$348$	63.9157	3.42624
$349$	10.3890	0.556112	0.278056	−	0.960565i	$-0.410310\pi$
$349$	10.3890	0.556112	0.278056	+	0.960565i	$0.410310\pi$
$350$	−10.2495	−0.547858
$351$	32.2646	1.72215
$352$	−85.3054	−4.54680
$353$	−10.8775	−0.578948	−0.289474	−	0.957186i	$-0.593480\pi$
$353$	−10.8775	−0.578948	−0.289474	+	0.957186i	$0.593480\pi$
$354$	−4.10666	−0.218267
$355$	2.85119	0.151326
$356$	−10.6292	−0.563346
$357$	−15.6855	−0.830165
$358$	30.2230	1.59734
$359$	5.63415	0.297359	0.148679	−	0.988885i	$-0.452498\pi$
$359$	5.63415	0.297359	0.148679	+	0.988885i	$0.452498\pi$
$360$	10.7989	0.569150
$361$	−8.14765	−0.428824
$362$	5.79285	0.304465
$363$	33.6947	1.76851
$364$	83.0176	4.35130
$365$	15.7472	0.824248
$366$	26.6617	1.39363
$367$	−17.1351	−0.894444	−0.447222	−	0.894423i	$-0.647587\pi$
$367$	−17.1351	−0.894444	−0.447222	+	0.894423i	$0.647587\pi$
$368$	−103.558	−5.39834
$369$	5.65156	0.294209
$370$	5.08211	0.264206
$371$	−15.5949	−0.809647
$372$	−36.6109	−1.89819
$373$	22.0572	1.14208	0.571039	−	0.820923i	$-0.306541\pi$
$373$	22.0572	1.14208	0.571039	+	0.820923i	$0.306541\pi$
$374$	−55.8229	−2.88653
$375$	−18.4531	−0.952914
$376$	66.4446	3.42662
$377$	−47.4867	−2.44569
$378$	−42.3104	−2.17621
$379$	−3.63517	−0.186726	−0.0933631	−	0.995632i	$-0.529762\pi$
$379$	−3.63517	−0.186726	−0.0933631	+	0.995632i	$0.529762\pi$
$380$	32.0134	1.64225
$381$	−21.7910	−1.11638
$382$	−13.6317	−0.697460
$383$	−25.5162	−1.30382	−0.651909	−	0.758297i	$-0.726032\pi$
$383$	−25.5162	−1.30382	−0.651909	+	0.758297i	$0.726032\pi$
$384$	−19.5748	−0.998921
$385$	−31.1325	−1.58666
$386$	−33.6489	−1.71269
$387$	−3.23013	−0.164197
$388$	−64.3479	−3.26677
$389$	−4.22127	−0.214027	−0.107013	−	0.994258i	$-0.534129\pi$
$389$	−4.22127	−0.214027	−0.107013	+	0.994258i	$0.534129\pi$
$390$	44.4715	2.25190
$391$	−32.0899	−1.62286
$392$	−8.46091	−0.427341
$393$	17.0333	0.859217
$394$	−64.4487	−3.24688
$395$	−22.3108	−1.12258
$396$	−20.1484	−1.01250
$397$	−15.3456	−0.770171	−0.385086	−	0.922881i	$-0.625828\pi$
$397$	−15.3456	−0.770171	−0.385086	+	0.922881i	$0.625828\pi$
$398$	−38.8832	−1.94904
$399$	−14.1946	−0.710620
$400$	−15.9577	−0.797887
$401$	22.0609	1.10167	0.550833	−	0.834615i	$-0.314310\pi$
$401$	22.0609	1.10167	0.550833	+	0.834615i	$0.314310\pi$
$402$	−37.1574	−1.85324
$403$	27.2004	1.35495
$404$	23.2926	1.15885
$405$	−12.3400	−0.613178
$406$	62.2721	3.09051
$407$	−5.75810	−0.285419
$408$	−45.5935	−2.25722
$409$	−8.89558	−0.439858	−0.219929	−	0.975516i	$-0.570583\pi$
$409$	−8.89558	−0.439858	−0.219929	+	0.975516i	$0.570583\pi$
$410$	41.7997	2.06434
$411$	−29.0943	−1.43512
$412$	−56.6516	−2.79102
$413$	−2.87279	−0.141361
$414$	−16.1312	−0.792807
$415$	−5.77730	−0.283596
$416$	85.2431	4.17938
$417$	−6.36005	−0.311453
$418$	−50.5170	−2.47087
$419$	−15.8380	−0.773735	−0.386867	−	0.922135i	$-0.626443\pi$
$419$	−15.8380	−0.773735	−0.386867	+	0.922135i	$0.626443\pi$
$420$	−41.8728	−2.04318
$421$	−8.13430	−0.396442	−0.198221	−	0.980157i	$-0.563516\pi$
$421$	−8.13430	−0.396442	−0.198221	+	0.980157i	$0.563516\pi$
$422$	58.7834	2.86153
$423$	5.54381	0.269549
$424$	−45.3302	−2.20143
$425$	−4.94488	−0.239862
$426$	−6.05133	−0.293188
$427$	18.6510	0.902587
$428$	39.8321	1.92536
$429$	−50.3868	−2.43270
$430$	−23.8905	−1.15210
$431$	−36.1977	−1.74358	−0.871790	−	0.489880i	$-0.837041\pi$
$431$	−36.1977	−1.74358	−0.871790	+	0.489880i	$0.837041\pi$
$432$	−65.8743	−3.16938
$433$	24.8649	1.19493	0.597464	−	0.801895i	$-0.296175\pi$
$433$	24.8649	1.19493	0.597464	+	0.801895i	$0.296175\pi$
$434$	−35.6694	−1.71219
$435$	23.9515	1.14839
$436$	−5.09239	−0.243881
$437$	−29.0398	−1.38916
$438$	−33.4217	−1.59695
$439$	15.9773	0.762557	0.381278	−	0.924460i	$-0.375484\pi$
$439$	15.9773	0.762557	0.381278	+	0.924460i	$0.375484\pi$
$440$	−90.4937	−4.31412
$441$	−0.705936	−0.0336160
$442$	55.7821	2.65328
$443$	33.2803	1.58119	0.790596	−	0.612338i	$-0.209771\pi$
$443$	33.2803	1.58119	0.790596	+	0.612338i	$0.209771\pi$
$444$	−7.74457	−0.367541
$445$	−3.98314	−0.188819
$446$	12.1420	0.574943
$447$	−30.9436	−1.46358
$448$	−45.2157	−2.13624
$449$	12.6454	0.596772	0.298386	−	0.954445i	$-0.403552\pi$
$449$	12.6454	0.596772	0.298386	+	0.954445i	$0.403552\pi$
$450$	−2.48574	−0.117179
$451$	−47.3597	−2.23008
$452$	−67.5681	−3.17813
$453$	23.9379	1.12470
$454$	36.0301	1.69098
$455$	31.1097	1.45845
$456$	−41.2599	−1.93217
$457$	−24.7432	−1.15744	−0.578719	−	0.815527i	$-0.696447\pi$
$457$	−24.7432	−1.15744	−0.578719	+	0.815527i	$0.696447\pi$
$458$	−46.9843	−2.19543
$459$	−20.4127	−0.952784
$460$	−85.6647	−3.99414
$461$	−27.1233	−1.26326	−0.631629	−	0.775271i	$-0.717614\pi$
$461$	−27.1233	−1.26326	−0.631629	+	0.775271i	$0.717614\pi$
$462$	66.0751	3.07409
$463$	27.2321	1.26558	0.632792	−	0.774322i	$-0.281909\pi$
$463$	27.2321	1.26558	0.632792	+	0.774322i	$0.281909\pi$
$464$	96.9533	4.50094
$465$	−13.7194	−0.636224
$466$	−39.5513	−1.83218
$467$	24.5842	1.13762	0.568812	−	0.822468i	$-0.307403\pi$
$467$	24.5842	1.13762	0.568812	+	0.822468i	$0.307403\pi$
$468$	20.1337	0.930679
$469$	−25.9932	−1.20026
$470$	41.0027	1.89132
$471$	17.9003	0.824802
$472$	−8.35042	−0.384359
$473$	27.0683	1.24460
$474$	47.3521	2.17495
$475$	−4.47488	−0.205321
$476$	−52.5225	−2.40736
$477$	−3.78212	−0.173171
$478$	−1.14832	−0.0525230
$479$	−27.9236	−1.27586	−0.637931	−	0.770093i	$-0.720210\pi$
$479$	−27.9236	−1.27586	−0.637931	+	0.770093i	$0.720210\pi$
$480$	−42.9953	−1.96246
$481$	5.75389	0.262355
$482$	1.42113	0.0647305
$483$	37.9834	1.72831
$484$	112.826	5.12844
$485$	−24.1135	−1.09494
$486$	−18.6102	−0.844176
$487$	18.2310	0.826126	0.413063	−	0.910702i	$-0.364459\pi$
$487$	18.2310	0.826126	0.413063	+	0.910702i	$0.364459\pi$
$488$	54.2135	2.45413
$489$	−16.6234	−0.751735
$490$	−5.22120	−0.235870
$491$	1.54878	0.0698956	0.0349478	−	0.999389i	$-0.488874\pi$
$491$	1.54878	0.0698956	0.0349478	+	0.999389i	$0.488874\pi$
$492$	−63.6981	−2.87173
$493$	30.0432	1.35308
$494$	50.4801	2.27121
$495$	−7.55034	−0.339363
$496$	−55.5348	−2.49359
$497$	−4.23317	−0.189883
$498$	12.2616	0.549458
$499$	−33.1204	−1.48267	−0.741336	−	0.671134i	$-0.765807\pi$
$499$	−33.1204	−1.48267	−0.741336	+	0.671134i	$0.765807\pi$
$500$	−61.7896	−2.76332
$501$	−32.4009	−1.44757
$502$	9.98491	0.445648
$503$	−17.1074	−0.762782	−0.381391	−	0.924414i	$-0.624555\pi$
$503$	−17.1074	−0.762782	−0.381391	+	0.924414i	$0.624555\pi$
$504$	−16.0331	−0.714170
$505$	8.72858	0.388417
$506$	135.179	6.00942
$507$	30.5794	1.35808
$508$	−72.9663	−3.23736
$509$	−1.12345	−0.0497962	−0.0248981	−	0.999690i	$-0.507926\pi$
$509$	−1.12345	−0.0497962	−0.0248981	+	0.999690i	$0.507926\pi$
$510$	−28.1356	−1.24587
$511$	−23.3799	−1.03427
$512$	19.4564	0.859860
$513$	−18.4725	−0.815581
$514$	36.4995	1.60992
$515$	−21.2294	−0.935480
$516$	36.4065	1.60271
$517$	−46.4567	−2.04316
$518$	−7.54541	−0.331526
$519$	−4.30871	−0.189131
$520$	90.4275	3.96551
$521$	−17.0720	−0.747940	−0.373970	−	0.927441i	$-0.622004\pi$
$521$	−17.0720	−0.747940	−0.373970	+	0.927441i	$0.622004\pi$
$522$	15.1024	0.661014
$523$	−23.4283	−1.02445	−0.512224	−	0.858852i	$-0.671178\pi$
$523$	−23.4283	−1.02445	−0.512224	+	0.858852i	$0.671178\pi$
$524$	57.0355	2.49161
$525$	5.85304	0.255448
$526$	−13.0843	−0.570503
$527$	−17.2088	−0.749625
$528$	102.874	4.47703
$529$	54.7077	2.37860
$530$	−27.9731	−1.21507
$531$	−0.696717	−0.0302350
$532$	−47.5303	−2.06070
$533$	47.3250	2.04987
$534$	8.45377	0.365830
$535$	14.9265	0.645330
$536$	−75.5553	−3.26349
$537$	−17.2590	−0.744783
$538$	66.3364	2.85997
$539$	5.91569	0.254807
$540$	−54.4921	−2.34497
$541$	18.1283	0.779398	0.389699	−	0.920942i	$-0.372579\pi$
$541$	18.1283	0.779398	0.389699	+	0.920942i	$0.372579\pi$
$542$	−53.1533	−2.28313
$543$	−3.30805	−0.141962
$544$	−53.9304	−2.31225
$545$	−1.90830	−0.0817428
$546$	−66.0268	−2.82569
$547$	35.7185	1.52721	0.763606	−	0.645682i	$-0.223427\pi$
$547$	35.7185	1.52721	0.763606	+	0.645682i	$0.223427\pi$
$548$	−97.4215	−4.16164
$549$	4.52330	0.193050
$550$	20.8303	0.888206
$551$	27.1877	1.15823
$552$	110.408	4.69926
$553$	33.1248	1.40861
$554$	19.3671	0.822831
$555$	−2.90217	−0.123190
$556$	−21.2964	−0.903170
$557$	41.7699	1.76985	0.884924	−	0.465735i	$-0.154210\pi$
$557$	41.7699	1.76985	0.884924	+	0.465735i	$0.154210\pi$
$558$	−8.65065	−0.366211
$559$	−27.0485	−1.14403
$560$	−63.5165	−2.68406
$561$	31.8780	1.34589
$562$	43.7628	1.84602
$563$	10.5338	0.443945	0.221973	−	0.975053i	$-0.428750\pi$
$563$	10.5338	0.443945	0.221973	+	0.975053i	$0.428750\pi$
$564$	−62.4836	−2.63104
$565$	−25.3202	−1.06523
$566$	4.06124	0.170707
$567$	18.3212	0.769417
$568$	−12.3047	−0.516292
$569$	1.77931	0.0745925	0.0372963	−	0.999304i	$-0.488125\pi$
$569$	1.77931	0.0745925	0.0372963	+	0.999304i	$0.488125\pi$
$570$	−25.4614	−1.06646
$571$	−47.2598	−1.97776	−0.988880	−	0.148713i	$-0.952487\pi$
$571$	−47.2598	−1.97776	−0.988880	+	0.148713i	$0.952487\pi$
$572$	−168.719	−7.05448
$573$	7.78449	0.325202
$574$	−62.0601	−2.59034
$575$	11.9743	0.499364
$576$	−10.9658	−0.456910
$577$	23.5199	0.979146	0.489573	−	0.871962i	$-0.337153\pi$
$577$	23.5199	0.979146	0.489573	+	0.871962i	$0.337153\pi$
$578$	9.98219	0.415204
$579$	19.2154	0.798566
$580$	80.2010	3.33017
$581$	8.57756	0.355857
$582$	51.1781	2.12140
$583$	31.6939	1.31263
$584$	−67.9591	−2.81217
$585$	7.54482	0.311940
$586$	27.1558	1.12179
$587$	17.7788	0.733810	0.366905	−	0.930258i	$-0.380417\pi$
$587$	17.7788	0.733810	0.366905	+	0.930258i	$0.380417\pi$
$588$	7.95653	0.328122
$589$	−15.5731	−0.641678
$590$	−5.15301	−0.212146
$591$	36.8039	1.51391
$592$	−11.7477	−0.482827
$593$	−0.568642	−0.0233513	−0.0116757	−	0.999932i	$-0.503717\pi$
$593$	−0.568642	−0.0233513	−0.0116757	+	0.999932i	$0.503717\pi$
$594$	85.9884	3.52815
$595$	−19.6821	−0.806886
$596$	−103.614	−4.24419
$597$	22.2045	0.908771
$598$	−135.080	−5.52382
$599$	1.98833	0.0812411	0.0406206	−	0.999175i	$-0.487067\pi$
$599$	1.98833	0.0812411	0.0406206	+	0.999175i	$0.487067\pi$
$600$	17.0132	0.694561
$601$	−11.0555	−0.450964	−0.225482	−	0.974247i	$-0.572396\pi$
$601$	−11.0555	−0.450964	−0.225482	+	0.974247i	$0.572396\pi$
$602$	35.4702	1.44566
$603$	−6.30395	−0.256717
$604$	80.1554	3.26148
$605$	42.2799	1.71892
$606$	−18.5254	−0.752543
$607$	−16.8242	−0.682871	−0.341436	−	0.939905i	$-0.610913\pi$
$607$	−16.8242	−0.682871	−0.341436	+	0.939905i	$0.610913\pi$
$608$	−48.8044	−1.97928
$609$	−35.5609	−1.44100
$610$	33.4550	1.35455
$611$	46.4227	1.87806
$612$	−12.7379	−0.514899
$613$	8.00862	0.323465	0.161733	−	0.986835i	$-0.448292\pi$
$613$	8.00862	0.323465	0.161733	+	0.986835i	$0.448292\pi$
$614$	−66.4907	−2.68335
$615$	−23.8700	−0.962531
$616$	134.356	5.41336
$617$	20.1860	0.812659	0.406330	−	0.913727i	$-0.366808\pi$
$617$	20.1860	0.812659	0.406330	+	0.913727i	$0.366808\pi$
$618$	45.0570	1.81246
$619$	22.0187	0.885004	0.442502	−	0.896767i	$-0.354091\pi$
$619$	22.0187	0.885004	0.442502	+	0.896767i	$0.354091\pi$
$620$	−45.9391	−1.84496
$621$	49.4306	1.98358
$622$	79.4898	3.18725
$623$	5.91378	0.236930
$624$	−102.799	−4.11526
$625$	−16.3630	−0.654518
$626$	46.0190	1.83929
$627$	28.8481	1.15208
$628$	59.9386	2.39181
$629$	−3.64029	−0.145148
$630$	−9.89396	−0.394185
$631$	−44.6918	−1.77915	−0.889576	−	0.456788i	$-0.849000\pi$
$631$	−44.6918	−1.77915	−0.889576	+	0.456788i	$0.849000\pi$
$632$	96.2849	3.83001
$633$	−33.5687	−1.33423
$634$	8.69560	0.345346
$635$	−27.3431	−1.08508
$636$	42.6279	1.69031
$637$	−5.91136	−0.234217
$638$	−126.557	−5.01044
$639$	−1.02664	−0.0406132
$640$	−24.5623	−0.970909
$641$	−34.4436	−1.36044	−0.680220	−	0.733008i	$-0.738116\pi$
$641$	−34.4436	−1.36044	−0.680220	+	0.733008i	$0.738116\pi$
$642$	−31.6798	−1.25030
$643$	3.99052	0.157371	0.0786855	−	0.996899i	$-0.474928\pi$
$643$	3.99052	0.157371	0.0786855	+	0.996899i	$0.474928\pi$
$644$	127.186	5.01185
$645$	13.6428	0.537186
$646$	−31.9370	−1.25655
$647$	−10.2354	−0.402394	−0.201197	−	0.979551i	$-0.564483\pi$
$647$	−10.2354	−0.402394	−0.201197	+	0.979551i	$0.564483\pi$
$648$	53.2547	2.09204
$649$	5.83844	0.229179
$650$	−20.8150	−0.816433
$651$	20.3693	0.798334
$652$	−55.6629	−2.17993
$653$	−36.1716	−1.41550	−0.707751	−	0.706462i	$-0.750290\pi$
$653$	−36.1716	−1.41550	−0.707751	+	0.706462i	$0.750290\pi$
$654$	4.05016	0.158374
$655$	21.3733	0.835123
$656$	−96.6232	−3.77250
$657$	−5.67017	−0.221214
$658$	−60.8768	−2.37322
$659$	21.7418	0.846939	0.423470	−	0.905910i	$-0.360812\pi$
$659$	21.7418	0.846939	0.423470	+	0.905910i	$0.360812\pi$
$660$	85.0990	3.31247
$661$	22.5901	0.878653	0.439327	−	0.898327i	$-0.355217\pi$
$661$	22.5901	0.878653	0.439327	+	0.898327i	$0.355217\pi$
$662$	−44.4717	−1.72844
$663$	−31.8547	−1.23713
$664$	24.9326	0.967574
$665$	−17.8113	−0.690693
$666$	−1.82994	−0.0709086
$667$	−72.7516	−2.81695
$668$	−108.494	−4.19774
$669$	−6.93380	−0.268076
$670$	−46.6249	−1.80128
$671$	−37.9049	−1.46330
$672$	63.8351	2.46249
$673$	−11.8697	−0.457544	−0.228772	−	0.973480i	$-0.573471\pi$
$673$	−11.8697	−0.457544	−0.228772	+	0.973480i	$0.573471\pi$
$674$	−8.02449	−0.309092
$675$	7.61699	0.293178
$676$	102.394	3.93824
$677$	−10.5098	−0.403925	−0.201962	−	0.979393i	$-0.564732\pi$
$677$	−10.5098	−0.403925	−0.201962	+	0.979393i	$0.564732\pi$
$678$	53.7392	2.06384
$679$	35.8013	1.37393
$680$	−57.2104	−2.19392
$681$	−20.5752	−0.788445
$682$	72.4918	2.77585
$683$	−20.1156	−0.769703	−0.384852	−	0.922978i	$-0.625747\pi$
$683$	−20.1156	−0.769703	−0.384852	+	0.922978i	$0.625747\pi$
$684$	−11.5272	−0.440753
$685$	−36.5074	−1.39487
$686$	−45.0660	−1.72063
$687$	26.8307	1.02365
$688$	55.2247	2.10542
$689$	−31.6707	−1.20656
$690$	68.1321	2.59374
$691$	35.6081	1.35460	0.677298	−	0.735709i	$-0.263151\pi$
$691$	35.6081	1.35460	0.677298	+	0.735709i	$0.263151\pi$
$692$	−14.4276	−0.548455
$693$	11.2100	0.425832
$694$	−47.8653	−1.81694
$695$	−7.98054	−0.302719
$696$	−103.366	−3.91807
$697$	−29.9410	−1.13409
$698$	−27.6676	−1.04723
$699$	22.5861	0.854283
$700$	19.5987	0.740762
$701$	−21.9323	−0.828373	−0.414186	−	0.910192i	$-0.635934\pi$
$701$	−21.9323	−0.828373	−0.414186	+	0.910192i	$0.635934\pi$
$702$	−85.9255	−3.24305
$703$	−3.29429	−0.124247
$704$	91.8929	3.46334
$705$	−23.4149	−0.881856
$706$	28.9683	1.09024
$707$	−12.9593	−0.487386
$708$	7.85262	0.295120
$709$	30.0018	1.12674	0.563371	−	0.826204i	$-0.309504\pi$
$709$	30.0018	1.12674	0.563371	+	0.826204i	$0.309504\pi$
$710$	−7.59316	−0.284966
$711$	8.03353	0.301281
$712$	17.1897	0.644213
$713$	41.6721	1.56063
$714$	41.7729	1.56331
$715$	−63.2250	−2.36448
$716$	−57.7914	−2.15977
$717$	0.655756	0.0244897
$718$	−15.0046	−0.559967
$719$	44.7603	1.66928	0.834639	−	0.550798i	$-0.185676\pi$
$719$	44.7603	1.66928	0.834639	+	0.550798i	$0.185676\pi$
$720$	−15.4042	−0.574081
$721$	31.5193	1.17384
$722$	21.6985	0.807533
$723$	−0.811543	−0.0301816
$724$	−11.0769	−0.411669
$725$	−11.2106	−0.416352
$726$	−89.7343	−3.33035
$727$	−43.8411	−1.62598	−0.812988	−	0.582281i	$-0.802161\pi$
$727$	−43.8411	−1.62598	−0.812988	+	0.582281i	$0.802161\pi$
$728$	−134.258	−4.97592
$729$	30.0269	1.11211
$730$	−41.9373	−1.55217
$731$	17.1127	0.632935
$732$	−50.9817	−1.88434
$733$	−28.7311	−1.06121	−0.530603	−	0.847620i	$-0.678034\pi$
$733$	−28.7311	−1.06121	−0.530603	+	0.847620i	$0.678034\pi$
$734$	45.6334	1.68436
$735$	2.98160	0.109978
$736$	130.596	4.81383
$737$	52.8266	1.94589
$738$	−15.0510	−0.554034
$739$	−52.3300	−1.92499	−0.962495	−	0.271300i	$-0.912546\pi$
$739$	−52.3300	−1.92499	−0.962495	+	0.271300i	$0.912546\pi$
$740$	−9.71784	−0.357235
$741$	−28.8270	−1.05899
$742$	41.5316	1.52467
$743$	6.84981	0.251295	0.125648	−	0.992075i	$-0.459899\pi$
$743$	6.84981	0.251295	0.125648	+	0.992075i	$0.459899\pi$
$744$	59.2079	2.17067
$745$	−38.8278	−1.42254
$746$	−58.7417	−2.15069
$747$	2.08025	0.0761125
$748$	106.743	3.90290
$749$	−22.1614	−0.809761
$750$	49.1435	1.79447
$751$	−24.5586	−0.896157	−0.448078	−	0.893994i	$-0.647891\pi$
$751$	−24.5586	−0.896157	−0.448078	+	0.893994i	$0.647891\pi$
$752$	−94.7809	−3.45631
$753$	−5.70195	−0.207790
$754$	126.464	4.60556
$755$	30.0371	1.09316
$756$	80.9045	2.94247
$757$	−14.1443	−0.514082	−0.257041	−	0.966401i	$-0.582747\pi$
$757$	−14.1443	−0.514082	−0.257041	+	0.966401i	$0.582747\pi$
$758$	9.68102	0.351631
$759$	−77.1946	−2.80199
$760$	−51.7727	−1.87799
$761$	17.3055	0.627325	0.313662	−	0.949535i	$-0.398444\pi$
$761$	17.3055	0.627325	0.313662	+	0.949535i	$0.398444\pi$
$762$	58.0327	2.10230
$763$	2.83326	0.102571
$764$	26.0661	0.943039
$765$	−4.77335	−0.172581
$766$	67.9537	2.45527
$767$	−5.83417	−0.210660
$768$	3.58972	0.129533
$769$	25.4240	0.916812	0.458406	−	0.888743i	$-0.348421\pi$
$769$	25.4240	0.916812	0.458406	+	0.888743i	$0.348421\pi$
$770$	82.9106	2.98789
$771$	−20.8433	−0.750653
$772$	64.3423	2.31573
$773$	31.3428	1.12732	0.563660	−	0.826007i	$-0.309393\pi$
$773$	31.3428	1.12732	0.563660	+	0.826007i	$0.309393\pi$
$774$	8.60234	0.309205
$775$	6.42144	0.230665
$776$	104.065	3.73570
$777$	4.30886	0.154579
$778$	11.2419	0.403041
$779$	−27.0951	−0.970783
$780$	−85.0368	−3.04481
$781$	8.60316	0.307845
$782$	85.4604	3.05606
$783$	−46.2780	−1.65384
$784$	12.0692	0.431043
$785$	22.4612	0.801673
$786$	−45.3623	−1.61802
$787$	−9.60509	−0.342385	−0.171192	−	0.985238i	$-0.554762\pi$
$787$	−9.60509	−0.342385	−0.171192	+	0.985238i	$0.554762\pi$
$788$	123.237	4.39012
$789$	7.47188	0.266006
$790$	59.4170	2.11396
$791$	37.5929	1.33665
$792$	32.5844	1.15784
$793$	37.8772	1.34506
$794$	40.8676	1.45034
$795$	15.9742	0.566547
$796$	74.3512	2.63531
$797$	6.23595	0.220889	0.110444	−	0.993882i	$-0.464773\pi$
$797$	6.23595	0.220889	0.110444	+	0.993882i	$0.464773\pi$
$798$	37.8025	1.33819
$799$	−29.3701	−1.03904
$800$	20.1241	0.711495
$801$	1.43423	0.0506759
$802$	−58.7515	−2.07459
$803$	47.5156	1.67679
$804$	71.0511	2.50578
$805$	47.6614	1.67984
$806$	−72.4388	−2.55155
$807$	−37.8818	−1.33350
$808$	−37.6692	−1.32520
$809$	34.1747	1.20152	0.600759	−	0.799430i	$-0.294865\pi$
$809$	34.1747	1.20152	0.600759	+	0.799430i	$0.294865\pi$
$810$	32.8633	1.15470
$811$	16.4495	0.577620	0.288810	−	0.957386i	$-0.406740\pi$
$811$	16.4495	0.577620	0.288810	+	0.957386i	$0.406740\pi$
$812$	−119.075	−4.17870
$813$	30.3536	1.06455
$814$	15.3347	0.537482
$815$	−20.8589	−0.730656
$816$	65.0376	2.27677
$817$	15.4861	0.541791
$818$	23.6903	0.828312
$819$	−11.2018	−0.391422
$820$	−79.9280	−2.79121
$821$	−32.7513	−1.14303	−0.571515	−	0.820592i	$-0.693644\pi$
$821$	−32.7513	−1.14303	−0.571515	+	0.820592i	$0.693644\pi$
$822$	77.4827	2.70252
$823$	−3.80651	−0.132687	−0.0663434	−	0.997797i	$-0.521133\pi$
$823$	−3.80651	−0.132687	−0.0663434	+	0.997797i	$0.521133\pi$
$824$	91.6181	3.19167
$825$	−11.8953	−0.414140
$826$	7.65068	0.266201
$827$	45.8443	1.59416	0.797081	−	0.603872i	$-0.206376\pi$
$827$	45.8443	1.59416	0.797081	+	0.603872i	$0.206376\pi$
$828$	30.8456	1.07196
$829$	−14.4902	−0.503265	−0.251633	−	0.967823i	$-0.580968\pi$
$829$	−14.4902	−0.503265	−0.251633	+	0.967823i	$0.580968\pi$
$830$	15.3858	0.534050
$831$	−11.0597	−0.383658
$832$	−91.8257	−3.18348
$833$	3.73992	0.129581
$834$	16.9378	0.586508
$835$	−40.6565	−1.40698
$836$	96.5969	3.34087
$837$	26.5080	0.916251
$838$	42.1789	1.45705
$839$	−5.23388	−0.180694	−0.0903468	−	0.995910i	$-0.528798\pi$
$839$	−5.23388	−0.180694	−0.0903468	+	0.995910i	$0.528798\pi$
$840$	67.7175	2.33648
$841$	39.1115	1.34867
$842$	21.6629	0.746553
$843$	−24.9911	−0.860738
$844$	−112.404	−3.86909
$845$	38.3708	1.32000
$846$	−14.7640	−0.507597
$847$	−62.7730	−2.15691
$848$	64.6619	2.22050
$849$	−2.31920	−0.0795947
$850$	13.1690	0.451692
$851$	8.81520	0.302181
$852$	11.5711	0.396421
$853$	−26.0613	−0.892321	−0.446161	−	0.894953i	$-0.647209\pi$
$853$	−26.0613	−0.892321	−0.446161	+	0.894953i	$0.647209\pi$
$854$	−49.6706	−1.69969
$855$	−4.31965	−0.147729
$856$	−64.4172	−2.20174
$857$	42.7655	1.46084	0.730421	−	0.682997i	$-0.239324\pi$
$857$	42.7655	1.46084	0.730421	+	0.682997i	$0.239324\pi$
$858$	134.188	4.58110
$859$	−44.0380	−1.50256	−0.751279	−	0.659985i	$-0.770563\pi$
$859$	−44.0380	−1.50256	−0.751279	+	0.659985i	$0.770563\pi$
$860$	45.6826	1.55776
$861$	35.4398	1.20779
$862$	96.4000	3.28340
$863$	−33.5392	−1.14169	−0.570844	−	0.821059i	$-0.693384\pi$
$863$	−33.5392	−1.14169	−0.570844	+	0.821059i	$0.693384\pi$
$864$	83.0733	2.82621
$865$	−5.40654	−0.183828
$866$	−66.2190	−2.25021
$867$	−5.70039	−0.193596
$868$	68.2058	2.31506
$869$	−67.3203	−2.28369
$870$	−63.7867	−2.16257
$871$	−52.7880	−1.78865
$872$	8.23552	0.278890
$873$	8.68264	0.293863
$874$	77.3375	2.61598
$875$	34.3780	1.16219
$876$	63.9078	2.15924
$877$	33.4114	1.12822	0.564111	−	0.825699i	$-0.309219\pi$
$877$	33.4114	1.12822	0.564111	+	0.825699i	$0.309219\pi$
$878$	−42.5501	−1.43600
$879$	−15.5075	−0.523054
$880$	129.086	4.35149
$881$	31.5381	1.06255	0.531273	−	0.847201i	$-0.321714\pi$
$881$	31.5381	1.06255	0.531273	+	0.847201i	$0.321714\pi$
$882$	1.88002	0.0633035
$883$	−28.4668	−0.957984	−0.478992	−	0.877819i	$-0.658998\pi$
$883$	−28.4668	−0.957984	−0.478992	+	0.877819i	$0.658998\pi$
$884$	−106.665	−3.58752
$885$	2.94266	0.0989165
$886$	−88.6305	−2.97760
$887$	−3.30601	−0.111005	−0.0555025	−	0.998459i	$-0.517676\pi$
$887$	−3.30601	−0.111005	−0.0555025	+	0.998459i	$0.517676\pi$
$888$	12.5247	0.420301
$889$	40.5964	1.36156
$890$	10.6077	0.355572
$891$	−37.2345	−1.24740
$892$	−23.2176	−0.777383
$893$	−26.5785	−0.889416
$894$	82.4076	2.75612
$895$	−21.6565	−0.723898
$896$	36.4676	1.21830
$897$	77.1382	2.57557
$898$	−33.6766	−1.12380
$899$	−39.0143	−1.30120
$900$	4.75314	0.158438
$901$	20.0370	0.667529
$902$	126.126	4.19954
$903$	−20.2555	−0.674061
$904$	109.272	3.63435
$905$	−4.15091	−0.137981
$906$	−63.7504	−2.11797
$907$	46.6008	1.54735	0.773677	−	0.633581i	$-0.218416\pi$
$907$	46.6008	1.54735	0.773677	+	0.633581i	$0.218416\pi$
$908$	−68.8956	−2.28638
$909$	−3.14293	−0.104245
$910$	−82.8500	−2.74645
$911$	−2.14302	−0.0710013	−0.0355007	−	0.999370i	$-0.511303\pi$
$911$	−2.14302	−0.0710013	−0.0355007	+	0.999370i	$0.511303\pi$
$912$	58.8558	1.94891
$913$	−17.4324	−0.576927
$914$	65.8950	2.17961
$915$	−19.1047	−0.631581
$916$	89.8418	2.96845
$917$	−31.7329	−1.04791
$918$	54.3622	1.79422
$919$	−21.3235	−0.703397	−0.351699	−	0.936113i	$-0.614396\pi$
$919$	−21.3235	−0.703397	−0.351699	+	0.936113i	$0.614396\pi$
$920$	138.539	4.56748
$921$	37.9700	1.25115
$922$	72.2336	2.37889
$923$	−8.59687	−0.282969
$924$	−126.347	−4.15650
$925$	1.35837	0.0446631
$926$	−72.5234	−2.38327
$927$	7.64416	0.251067
$928$	−122.267	−4.01360
$929$	−22.6739	−0.743906	−0.371953	−	0.928252i	$-0.621312\pi$
$929$	−22.6739	−0.743906	−0.371953	+	0.928252i	$0.621312\pi$
$930$	36.5370	1.19809
$931$	3.38445	0.110921
$932$	75.6287	2.47730
$933$	−45.3932	−1.48611
$934$	−65.4716	−2.14230
$935$	40.0003	1.30815
$936$	−32.5606	−1.06428
$937$	−53.2629	−1.74002	−0.870012	−	0.493031i	$-0.835889\pi$
$937$	−53.2629	−1.74002	−0.870012	+	0.493031i	$0.835889\pi$
$938$	69.2240	2.26024
$939$	−26.2794	−0.857597
$940$	−78.4040	−2.55726
$941$	−16.7386	−0.545662	−0.272831	−	0.962062i	$-0.587960\pi$
$941$	−16.7386	−0.545662	−0.272831	+	0.962062i	$0.587960\pi$
$942$	−47.6713	−1.55321
$943$	72.5039	2.36105
$944$	11.9116	0.387689
$945$	30.3178	0.986240
$946$	−72.0870	−2.34375
$947$	49.5960	1.61165	0.805826	−	0.592152i	$-0.201722\pi$
$947$	49.5960	1.61165	0.805826	+	0.592152i	$0.201722\pi$
$948$	−90.5450	−2.94076
$949$	−47.4808	−1.54129
$950$	11.9173	0.386648
$951$	−4.96568	−0.161023
$952$	84.9404	2.75293
$953$	−31.5258	−1.02122	−0.510610	−	0.859812i	$-0.670580\pi$
$953$	−31.5258	−1.02122	−0.510610	+	0.859812i	$0.670580\pi$
$954$	10.0724	0.326105
$955$	9.76792	0.316083
$956$	2.19578	0.0710166
$957$	72.2712	2.33620
$958$	74.3649	2.40262
$959$	54.2025	1.75029
$960$	46.3154	1.49482
$961$	−8.65264	−0.279118
$962$	−15.3235	−0.494050
$963$	−5.37465	−0.173196
$964$	−2.71743	−0.0875225
$965$	24.1114	0.776174
$966$	−101.156	−3.25463
$967$	−7.84754	−0.252360	−0.126180	−	0.992007i	$-0.540272\pi$
$967$	−7.84754	−0.252360	−0.126180	+	0.992007i	$0.540272\pi$
$968$	−182.464	−5.86462
$969$	18.2379	0.585885
$970$	64.2179	2.06191
$971$	−39.9194	−1.28107	−0.640537	−	0.767927i	$-0.721288\pi$
$971$	−39.9194	−1.28107	−0.640537	+	0.767927i	$0.721288\pi$
$972$	35.5858	1.14141
$973$	11.8487	0.379853
$974$	−48.5520	−1.55571
$975$	11.8866	0.380675
$976$	−77.3337	−2.47539
$977$	−18.3445	−0.586893	−0.293446	−	0.955976i	$-0.594802\pi$
$977$	−18.3445	−0.586893	−0.293446	+	0.955976i	$0.594802\pi$
$978$	44.2706	1.41562
$979$	−12.0187	−0.384120
$980$	9.98380	0.318921
$981$	0.687131	0.0219384
$982$	−4.12465	−0.131623
$983$	−6.75594	−0.215481	−0.107740	−	0.994179i	$-0.534362\pi$
$983$	−6.75594	−0.215481	−0.107740	+	0.994179i	$0.534362\pi$
$984$	103.014	3.28396
$985$	46.1812	1.47146
$986$	−80.0098	−2.54803
$987$	34.7641	1.10655
$988$	−96.5263	−3.07091
$989$	−41.4394	−1.31770
$990$	20.1077	0.639065
$991$	−3.59126	−0.114080	−0.0570401	−	0.998372i	$-0.518166\pi$
$991$	−3.59126	−0.114080	−0.0570401	+	0.998372i	$0.518166\pi$
$992$	70.0342	2.22359
$993$	25.3959	0.805913
$994$	11.2736	0.357576
$995$	27.8621	0.883288
$996$	−23.4463	−0.742925
$997$	−4.54488	−0.143938	−0.0719689	−	0.997407i	$-0.522928\pi$
$997$	−4.54488	−0.143938	−0.0719689	+	0.997407i	$0.522928\pi$
$998$	88.2047	2.79207
$999$	5.60743	0.177411

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.d.1.5	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.d.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-2.66315 q^{2} +1.52081 q^{3} +5.09239 q^{4} +1.90830 q^{5} -4.05016 q^{6} -2.83326 q^{7} -8.23552 q^{8} -0.687131 q^{9} +O(q^{10})\)	\(q-2.66315 q^{2} +1.52081 q^{3} +5.09239 q^{4} +1.90830 q^{5} -4.05016 q^{6} -2.83326 q^{7} -8.23552 q^{8} -0.687131 q^{9} -5.08211 q^{10} +5.75810 q^{11} +7.74457 q^{12} -5.75389 q^{13} +7.54541 q^{14} +2.90217 q^{15} +11.7477 q^{16} +3.64029 q^{17} +1.82994 q^{18} +3.29429 q^{19} +9.71784 q^{20} -4.30886 q^{21} -15.3347 q^{22} -8.81520 q^{23} -12.5247 q^{24} -1.35837 q^{25} +15.3235 q^{26} -5.60743 q^{27} -14.4281 q^{28} +8.25297 q^{29} -7.72893 q^{30} -4.72730 q^{31} -14.8149 q^{32} +8.75699 q^{33} -9.69467 q^{34} -5.40672 q^{35} -3.49914 q^{36} -1.00000 q^{37} -8.77320 q^{38} -8.75059 q^{39} -15.7159 q^{40} -8.22487 q^{41} +11.4752 q^{42} +4.70090 q^{43} +29.3225 q^{44} -1.31125 q^{45} +23.4762 q^{46} -8.06805 q^{47} +17.8660 q^{48} +1.02737 q^{49} +3.61756 q^{50} +5.53620 q^{51} -29.3011 q^{52} +5.50423 q^{53} +14.9335 q^{54} +10.9882 q^{55} +23.3334 q^{56} +5.01000 q^{57} -21.9789 q^{58} +1.01395 q^{59} +14.7790 q^{60} -6.58289 q^{61} +12.5895 q^{62} +1.94682 q^{63} +15.9589 q^{64} -10.9802 q^{65} -23.3212 q^{66} +9.17431 q^{67} +18.5378 q^{68} -13.4063 q^{69} +14.3989 q^{70} +1.49410 q^{71} +5.65888 q^{72} +8.25195 q^{73} +2.66315 q^{74} -2.06583 q^{75} +16.7758 q^{76} -16.3142 q^{77} +23.3042 q^{78} -11.6914 q^{79} +22.4182 q^{80} -6.46646 q^{81} +21.9041 q^{82} -3.02745 q^{83} -21.9424 q^{84} +6.94679 q^{85} -12.5192 q^{86} +12.5512 q^{87} -47.4210 q^{88} -2.08727 q^{89} +3.49207 q^{90} +16.3023 q^{91} -44.8905 q^{92} -7.18933 q^{93} +21.4865 q^{94} +6.28651 q^{95} -22.5306 q^{96} -12.6361 q^{97} -2.73604 q^{98} -3.95657 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) \) 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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