LMFDB - Embedded newform 6019.2.a.b.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6019,2,Mod(1,6019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6019, 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("6019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6019 = 13 \cdot 463 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6019.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:	$48.0619569766$
Analytic rank:	$1$
Dimension:	$101$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	6019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.11661 q^{2} +2.26026 q^{3} +2.48003 q^{4} -0.342197 q^{5} -4.78408 q^{6} +3.30081 q^{7} -1.01604 q^{8} +2.10876 q^{9} +O(q^{10})$	\(q-2.11661 q^{2} +2.26026 q^{3} +2.48003 q^{4} -0.342197 q^{5} -4.78408 q^{6} +3.30081 q^{7} -1.01604 q^{8} +2.10876 q^{9} +0.724298 q^{10} -3.89198 q^{11} +5.60551 q^{12} +1.00000 q^{13} -6.98653 q^{14} -0.773454 q^{15} -2.80950 q^{16} -1.96389 q^{17} -4.46342 q^{18} +3.10114 q^{19} -0.848661 q^{20} +7.46068 q^{21} +8.23780 q^{22} +6.85451 q^{23} -2.29651 q^{24} -4.88290 q^{25} -2.11661 q^{26} -2.01443 q^{27} +8.18612 q^{28} -6.87652 q^{29} +1.63710 q^{30} -1.37340 q^{31} +7.97870 q^{32} -8.79687 q^{33} +4.15679 q^{34} -1.12953 q^{35} +5.22980 q^{36} -10.6478 q^{37} -6.56389 q^{38} +2.26026 q^{39} +0.347687 q^{40} -9.62648 q^{41} -15.7913 q^{42} -3.44101 q^{43} -9.65223 q^{44} -0.721613 q^{45} -14.5083 q^{46} +3.63132 q^{47} -6.35020 q^{48} +3.89535 q^{49} +10.3352 q^{50} -4.43890 q^{51} +2.48003 q^{52} -1.27811 q^{53} +4.26376 q^{54} +1.33183 q^{55} -3.35376 q^{56} +7.00937 q^{57} +14.5549 q^{58} -7.01952 q^{59} -1.91819 q^{60} -0.303475 q^{61} +2.90694 q^{62} +6.96062 q^{63} -11.2688 q^{64} -0.342197 q^{65} +18.6195 q^{66} +10.0382 q^{67} -4.87051 q^{68} +15.4930 q^{69} +2.39077 q^{70} -2.04769 q^{71} -2.14259 q^{72} +1.00986 q^{73} +22.5372 q^{74} -11.0366 q^{75} +7.69092 q^{76} -12.8467 q^{77} -4.78408 q^{78} +9.22395 q^{79} +0.961405 q^{80} -10.8794 q^{81} +20.3755 q^{82} -13.0472 q^{83} +18.5027 q^{84} +0.672038 q^{85} +7.28328 q^{86} -15.5427 q^{87} +3.95441 q^{88} -7.10671 q^{89} +1.52737 q^{90} +3.30081 q^{91} +16.9994 q^{92} -3.10423 q^{93} -7.68609 q^{94} -1.06120 q^{95} +18.0339 q^{96} -9.01630 q^{97} -8.24494 q^{98} -8.20725 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9}+O(q^{10}) $ 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9	\( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9} - 19 q^{10} - 42 q^{11} - 28 q^{12} + 101 q^{13} - 45 q^{14} - 15 q^{15} + 48 q^{16} - 83 q^{17} - 4 q^{18} - 18 q^{19} - 51 q^{20} - 50 q^{21} - 20 q^{22} - 64 q^{23} - 23 q^{24} + 46 q^{25} - 8 q^{26} - 37 q^{27} - 11 q^{28} - 117 q^{29} - 28 q^{30} - 10 q^{31} - 36 q^{32} - 20 q^{33} - 10 q^{34} - 53 q^{35} - 16 q^{36} - 27 q^{37} - 68 q^{38} - 13 q^{39} - 42 q^{40} - 60 q^{41} - 31 q^{42} - 16 q^{43} - 89 q^{44} - 56 q^{45} + 5 q^{46} - 23 q^{47} - 37 q^{48} + 48 q^{49} - 30 q^{50} - 68 q^{51} + 86 q^{52} - 189 q^{53} - 23 q^{54} + 3 q^{55} - 106 q^{56} - 25 q^{57} - 82 q^{59} + 6 q^{60} - 68 q^{61} - 57 q^{62} + 3 q^{63} - 2 q^{64} - 43 q^{65} - 40 q^{66} - 13 q^{67} - 138 q^{68} - 92 q^{69} + 18 q^{70} - 39 q^{71} - 20 q^{72} + 19 q^{73} - 88 q^{74} - 21 q^{75} - 53 q^{76} - 147 q^{77} - 10 q^{78} - 19 q^{79} - 104 q^{80} - 55 q^{81} + 27 q^{82} - 49 q^{83} - 59 q^{84} - 27 q^{85} - 99 q^{86} - 33 q^{87} - 41 q^{88} - 70 q^{89} - 49 q^{90} - q^{91} - 111 q^{92} - 84 q^{93} + 4 q^{94} - 82 q^{95} - 7 q^{96} + 25 q^{97} - 37 q^{98} - 41 q^{99}+O(q^{100}) \) 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9 - 19 * q^10 - 42 * q^11 - 28 * q^12 + 101 * q^13 - 45 * q^14 - 15 * q^15 + 48 * q^16 - 83 * q^17 - 4 * q^18 - 18 * q^19 - 51 * q^20 - 50 * q^21 - 20 * q^22 - 64 * q^23 - 23 * q^24 + 46 * q^25 - 8 * q^26 - 37 * q^27 - 11 * q^28 - 117 * q^29 - 28 * q^30 - 10 * q^31 - 36 * q^32 - 20 * q^33 - 10 * q^34 - 53 * q^35 - 16 * q^36 - 27 * q^37 - 68 * q^38 - 13 * q^39 - 42 * q^40 - 60 * q^41 - 31 * q^42 - 16 * q^43 - 89 * q^44 - 56 * q^45 + 5 * q^46 - 23 * q^47 - 37 * q^48 + 48 * q^49 - 30 * q^50 - 68 * q^51 + 86 * q^52 - 189 * q^53 - 23 * q^54 + 3 * q^55 - 106 * q^56 - 25 * q^57 - 82 * q^59 + 6 * q^60 - 68 * q^61 - 57 * q^62 + 3 * q^63 - 2 * q^64 - 43 * q^65 - 40 * q^66 - 13 * q^67 - 138 * q^68 - 92 * q^69 + 18 * q^70 - 39 * q^71 - 20 * q^72 + 19 * q^73 - 88 * q^74 - 21 * q^75 - 53 * q^76 - 147 * q^77 - 10 * q^78 - 19 * q^79 - 104 * q^80 - 55 * q^81 + 27 * q^82 - 49 * q^83 - 59 * q^84 - 27 * q^85 - 99 * q^86 - 33 * q^87 - 41 * q^88 - 70 * q^89 - 49 * q^90 - q^91 - 111 * q^92 - 84 * q^93 + 4 * q^94 - 82 * q^95 - 7 * q^96 + 25 * q^97 - 37 * q^98 - 41 * 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 $

$2$	−2.11661	−1.49667	−0.748334	−	0.663322i	$-0.769146\pi$
$2$	−2.11661	−1.49667	−0.748334	+	0.663322i	$0.769146\pi$
$3$	2.26026	1.30496	0.652480	−	0.757806i	$-0.273729\pi$
$3$	2.26026	1.30496	0.652480	+	0.757806i	$0.273729\pi$
$4$	2.48003	1.24002
$5$	−0.342197	−0.153035	−0.0765177	−	0.997068i	$-0.524380\pi$
$5$	−0.342197	−0.153035	−0.0765177	+	0.997068i	$0.524380\pi$
$6$	−4.78408	−1.95309
$7$	3.30081	1.24759	0.623795	−	0.781588i	$-0.285590\pi$
$7$	3.30081	1.24759	0.623795	+	0.781588i	$0.285590\pi$
$8$	−1.01604	−0.359225
$9$	2.10876	0.702920
$10$	0.724298	0.229043
$11$	−3.89198	−1.17348	−0.586738	−	0.809777i	$-0.699588\pi$
$11$	−3.89198	−1.17348	−0.586738	+	0.809777i	$0.699588\pi$
$12$	5.60551	1.61817
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−6.98653	−1.86723
$15$	−0.773454	−0.199705
$16$	−2.80950	−0.702376
$17$	−1.96389	−0.476313	−0.238157	−	0.971227i	$-0.576543\pi$
$17$	−1.96389	−0.476313	−0.238157	+	0.971227i	$0.576543\pi$
$18$	−4.46342	−1.05204
$19$	3.10114	0.711450	0.355725	−	0.934591i	$-0.384234\pi$
$19$	3.10114	0.711450	0.355725	+	0.934591i	$0.384234\pi$
$20$	−0.848661	−0.189766
$21$	7.46068	1.62805
$22$	8.23780	1.75630
$23$	6.85451	1.42926	0.714632	−	0.699500i	$-0.246594\pi$
$23$	6.85451	1.42926	0.714632	+	0.699500i	$0.246594\pi$
$24$	−2.29651	−0.468774
$25$	−4.88290	−0.976580
$26$	−2.11661	−0.415101
$27$	−2.01443	−0.387677
$28$	8.18612	1.54703
$29$	−6.87652	−1.27694	−0.638469	−	0.769647i	$-0.720432\pi$
$29$	−6.87652	−1.27694	−0.638469	+	0.769647i	$0.720432\pi$
$30$	1.63710	0.298892
$31$	−1.37340	−0.246669	−0.123335	−	0.992365i	$-0.539359\pi$
$31$	−1.37340	−0.246669	−0.123335	+	0.992365i	$0.539359\pi$
$32$	7.97870	1.41045
$33$	−8.79687	−1.53134
$34$	4.15679	0.712883
$35$	−1.12953	−0.190925
$36$	5.22980	0.871633
$37$	−10.6478	−1.75048	−0.875241	−	0.483687i	$-0.839297\pi$
$37$	−10.6478	−1.75048	−0.875241	+	0.483687i	$0.839297\pi$
$38$	−6.56389	−1.06480
$39$	2.26026	0.361931
$40$	0.347687	0.0549741
$41$	−9.62648	−1.50340	−0.751702	−	0.659503i	$-0.770767\pi$
$41$	−9.62648	−1.50340	−0.751702	+	0.659503i	$0.770767\pi$
$42$	−15.7913	−2.43666
$43$	−3.44101	−0.524749	−0.262375	−	0.964966i	$-0.584506\pi$
$43$	−3.44101	−0.524749	−0.262375	+	0.964966i	$0.584506\pi$
$44$	−9.65223	−1.45513
$45$	−0.721613	−0.107572
$46$	−14.5083	−2.13914
$47$	3.63132	0.529683	0.264841	−	0.964292i	$-0.414680\pi$
$47$	3.63132	0.529683	0.264841	+	0.964292i	$0.414680\pi$
$48$	−6.35020	−0.916572
$49$	3.89535	0.556479
$50$	10.3352	1.46162
$51$	−4.43890	−0.621570
$52$	2.48003	0.343919
$53$	−1.27811	−0.175562	−0.0877810	−	0.996140i	$-0.527978\pi$
$53$	−1.27811	−0.175562	−0.0877810	+	0.996140i	$0.527978\pi$
$54$	4.26376	0.580224
$55$	1.33183	0.179583
$56$	−3.35376	−0.448165
$57$	7.00937	0.928413
$58$	14.5549	1.91115
$59$	−7.01952	−0.913863	−0.456932	−	0.889502i	$-0.651052\pi$
$59$	−7.01952	−0.913863	−0.456932	+	0.889502i	$0.651052\pi$
$60$	−1.91819	−0.247637
$61$	−0.303475	−0.0388559	−0.0194280	−	0.999811i	$-0.506185\pi$
$61$	−0.303475	−0.0388559	−0.0194280	+	0.999811i	$0.506185\pi$
$62$	2.90694	0.369182
$63$	6.96062	0.876956
$64$	−11.2688	−1.40860
$65$	−0.342197	−0.0424444
$66$	18.6195	2.29191
$67$	10.0382	1.22636	0.613178	−	0.789945i	$-0.289891\pi$
$67$	10.0382	1.22636	0.613178	+	0.789945i	$0.289891\pi$
$68$	−4.87051	−0.590636
$69$	15.4930	1.86513
$70$	2.39077	0.285752
$71$	−2.04769	−0.243016	−0.121508	−	0.992590i	$-0.538773\pi$
$71$	−2.04769	−0.243016	−0.121508	+	0.992590i	$0.538773\pi$
$72$	−2.14259	−0.252506
$73$	1.00986	0.118195	0.0590975	−	0.998252i	$-0.481178\pi$
$73$	1.00986	0.118195	0.0590975	+	0.998252i	$0.481178\pi$
$74$	22.5372	2.61989
$75$	−11.0366	−1.27440
$76$	7.69092	0.882209
$77$	−12.8467	−1.46402
$78$	−4.78408	−0.541690
$79$	9.22395	1.03778	0.518888	−	0.854842i	$-0.326346\pi$
$79$	9.22395	1.03778	0.518888	+	0.854842i	$0.326346\pi$
$80$	0.961405	0.107488
$81$	−10.8794	−1.20882
$82$	20.3755	2.25010
$83$	−13.0472	−1.43211	−0.716056	−	0.698042i	$-0.754055\pi$
$83$	−13.0472	−1.43211	−0.716056	+	0.698042i	$0.754055\pi$
$84$	18.5027	2.01881
$85$	0.672038	0.0728928
$86$	7.28328	0.785376
$87$	−15.5427	−1.66635
$88$	3.95441	0.421542
$89$	−7.10671	−0.753309	−0.376655	−	0.926354i	$-0.622926\pi$
$89$	−7.10671	−0.753309	−0.376655	+	0.926354i	$0.622926\pi$
$90$	1.52737	0.160999
$91$	3.30081	0.346019
$92$	16.9994	1.77231
$93$	−3.10423	−0.321894
$94$	−7.68609	−0.792760
$95$	−1.06120	−0.108877
$96$	18.0339	1.84058
$97$	−9.01630	−0.915467	−0.457733	−	0.889090i	$-0.651339\pi$
$97$	−9.01630	−0.915467	−0.457733	+	0.889090i	$0.651339\pi$
$98$	−8.24494	−0.832865
$99$	−8.20725	−0.824860
$100$	−12.1098	−1.21098
$101$	−2.30434	−0.229290	−0.114645	−	0.993407i	$-0.536573\pi$
$101$	−2.30434	−0.229290	−0.114645	+	0.993407i	$0.536573\pi$
$102$	9.39541	0.930284
$103$	−6.84924	−0.674876	−0.337438	−	0.941348i	$-0.609560\pi$
$103$	−6.84924	−0.674876	−0.337438	+	0.941348i	$0.609560\pi$
$104$	−1.01604	−0.0996310
$105$	−2.55303	−0.249150
$106$	2.70526	0.262758
$107$	−10.8820	−1.05200	−0.525999	−	0.850485i	$-0.676308\pi$
$107$	−10.8820	−1.05200	−0.525999	+	0.850485i	$0.676308\pi$
$108$	−4.99585	−0.480726
$109$	10.1191	0.969232	0.484616	−	0.874727i	$-0.338959\pi$
$109$	10.1191	0.969232	0.484616	+	0.874727i	$0.338959\pi$
$110$	−2.81895	−0.268777
$111$	−24.0667	−2.28431
$112$	−9.27364	−0.876277
$113$	13.9394	1.31131	0.655654	−	0.755061i	$-0.272393\pi$
$113$	13.9394	1.31131	0.655654	+	0.755061i	$0.272393\pi$
$114$	−14.8361	−1.38953
$115$	−2.34560	−0.218728
$116$	−17.0540	−1.58342
$117$	2.10876	0.194955
$118$	14.8576	1.36775
$119$	−6.48243	−0.594244
$120$	0.785861	0.0717390
$121$	4.14750	0.377045
$122$	0.642337	0.0581545
$123$	−21.7583	−1.96188
$124$	−3.40607	−0.305874
$125$	3.38190	0.302487
$126$	−14.7329	−1.31251
$127$	−14.5916	−1.29480	−0.647398	−	0.762152i	$-0.724143\pi$
$127$	−14.5916	−1.29480	−0.647398	+	0.762152i	$0.724143\pi$
$128$	7.89420	0.697756
$129$	−7.77757	−0.684777
$130$	0.724298	0.0635251
$131$	−13.8694	−1.21177	−0.605887	−	0.795551i	$-0.707181\pi$
$131$	−13.8694	−1.21177	−0.605887	+	0.795551i	$0.707181\pi$
$132$	−21.8165	−1.89888
$133$	10.2363	0.887597
$134$	−21.2468	−1.83545
$135$	0.689333	0.0593283
$136$	1.99539	0.171104
$137$	11.9545	1.02134	0.510670	−	0.859777i	$-0.329398\pi$
$137$	11.9545	1.02134	0.510670	+	0.859777i	$0.329398\pi$
$138$	−32.7925	−2.79149
$139$	0.807304	0.0684746	0.0342373	−	0.999414i	$-0.489100\pi$
$139$	0.807304	0.0684746	0.0342373	+	0.999414i	$0.489100\pi$
$140$	−2.80127	−0.236750
$141$	8.20772	0.691215
$142$	4.33416	0.363715
$143$	−3.89198	−0.325464
$144$	−5.92457	−0.493714
$145$	2.35313	0.195417
$146$	−2.13748	−0.176899
$147$	8.80450	0.726183
$148$	−26.4068	−2.17063
$149$	9.25424	0.758137	0.379069	−	0.925369i	$-0.376244\pi$
$149$	9.25424	0.758137	0.379069	+	0.925369i	$0.376244\pi$
$150$	23.3602	1.90735
$151$	12.0346	0.979363	0.489682	−	0.871901i	$-0.337113\pi$
$151$	12.0346	0.979363	0.489682	+	0.871901i	$0.337113\pi$
$152$	−3.15088	−0.255570
$153$	−4.14138	−0.334810
$154$	27.1914	2.19115
$155$	0.469973	0.0377491
$156$	5.60551	0.448800
$157$	12.6433	1.00905	0.504524	−	0.863398i	$-0.331668\pi$
$157$	12.6433	1.00905	0.504524	+	0.863398i	$0.331668\pi$
$158$	−19.5235	−1.55321
$159$	−2.88886	−0.229101
$160$	−2.73029	−0.215849
$161$	22.6255	1.78314
$162$	23.0275	1.80921
$163$	0.312474	0.0244748	0.0122374	−	0.999925i	$-0.496105\pi$
$163$	0.312474	0.0244748	0.0122374	+	0.999925i	$0.496105\pi$
$164$	−23.8740	−1.86424
$165$	3.01027	0.234349
$166$	27.6158	2.14340
$167$	−24.6524	−1.90766	−0.953831	−	0.300342i	$-0.902899\pi$
$167$	−24.6524	−1.90766	−0.953831	+	0.300342i	$0.902899\pi$
$168$	−7.58036	−0.584837
$169$	1.00000	0.0769231
$170$	−1.42244	−0.109096
$171$	6.53956	0.500092
$172$	−8.53382	−0.650698
$173$	−11.8393	−0.900122	−0.450061	−	0.892998i	$-0.648598\pi$
$173$	−11.8393	−0.900122	−0.450061	+	0.892998i	$0.648598\pi$
$174$	32.8978	2.49398
$175$	−16.1175	−1.21837
$176$	10.9345	0.824221
$177$	−15.8659	−1.19255
$178$	15.0421	1.12745
$179$	−20.8280	−1.55676	−0.778378	−	0.627796i	$-0.783957\pi$
$179$	−20.8280	−1.55676	−0.778378	+	0.627796i	$0.783957\pi$
$180$	−1.78962	−0.133391
$181$	−0.262528	−0.0195136	−0.00975679	−	0.999952i	$-0.503106\pi$
$181$	−0.262528	−0.0195136	−0.00975679	+	0.999952i	$0.503106\pi$
$182$	−6.98653	−0.517876
$183$	−0.685931	−0.0507055
$184$	−6.96447	−0.513427
$185$	3.64364	0.267886
$186$	6.57044	0.481768
$187$	7.64342	0.558942
$188$	9.00580	0.656815
$189$	−6.64925	−0.483662
$190$	2.24615	0.162953
$191$	−16.6026	−1.20132	−0.600662	−	0.799503i	$-0.705096\pi$
$191$	−16.6026	−1.20132	−0.600662	+	0.799503i	$0.705096\pi$
$192$	−25.4703	−1.83816
$193$	2.79452	0.201154	0.100577	−	0.994929i	$-0.467931\pi$
$193$	2.79452	0.201154	0.100577	+	0.994929i	$0.467931\pi$
$194$	19.0840	1.37015
$195$	−0.773454	−0.0553882
$196$	9.66061	0.690043
$197$	1.15225	0.0820944	0.0410472	−	0.999157i	$-0.486931\pi$
$197$	1.15225	0.0820944	0.0410472	+	0.999157i	$0.486931\pi$
$198$	17.3715	1.23454
$199$	12.6792	0.898808	0.449404	−	0.893329i	$-0.351636\pi$
$199$	12.6792	0.898808	0.449404	+	0.893329i	$0.351636\pi$
$200$	4.96123	0.350812
$201$	22.6888	1.60035
$202$	4.87739	0.343172
$203$	−22.6981	−1.59309
$204$	−11.0086	−0.770757
$205$	3.29416	0.230074
$206$	14.4972	1.01007
$207$	14.4545	1.00466
$208$	−2.80950	−0.194804
$209$	−12.0696	−0.834869
$210$	5.40376	0.372895
$211$	8.82018	0.607206	0.303603	−	0.952799i	$-0.401810\pi$
$211$	8.82018	0.607206	0.303603	+	0.952799i	$0.401810\pi$
$212$	−3.16975	−0.217700
$213$	−4.62831	−0.317127
$214$	23.0328	1.57449
$215$	1.17751	0.0803052
$216$	2.04674	0.139263
$217$	−4.53332	−0.307742
$218$	−21.4181	−1.45062
$219$	2.28254	0.154240
$220$	3.30297	0.222686
$221$	−1.96389	−0.132106
$222$	50.9398	3.41885
$223$	22.5923	1.51289	0.756446	−	0.654056i	$-0.226934\pi$
$223$	22.5923	1.51289	0.756446	+	0.654056i	$0.226934\pi$
$224$	26.3362	1.75966
$225$	−10.2969	−0.686458
$226$	−29.5042	−1.96259
$227$	15.4532	1.02567	0.512834	−	0.858488i	$-0.328596\pi$
$227$	15.4532	1.02567	0.512834	+	0.858488i	$0.328596\pi$
$228$	17.3835	1.15125
$229$	18.8753	1.24731	0.623657	−	0.781698i	$-0.285646\pi$
$229$	18.8753	1.24731	0.623657	+	0.781698i	$0.285646\pi$
$230$	4.96471	0.327363
$231$	−29.0368	−1.91048
$232$	6.98683	0.458708
$233$	−9.78096	−0.640772	−0.320386	−	0.947287i	$-0.603813\pi$
$233$	−9.78096	−0.640772	−0.320386	+	0.947287i	$0.603813\pi$
$234$	−4.46342	−0.291783
$235$	−1.24263	−0.0810602
$236$	−17.4086	−1.13321
$237$	20.8485	1.35426
$238$	13.7208	0.889386
$239$	17.9218	1.15926	0.579631	−	0.814879i	$-0.303197\pi$
$239$	17.9218	1.15926	0.579631	+	0.814879i	$0.303197\pi$
$240$	2.17302	0.140268
$241$	10.2365	0.659390	0.329695	−	0.944088i	$-0.393054\pi$
$241$	10.2365	0.659390	0.329695	+	0.944088i	$0.393054\pi$
$242$	−8.77863	−0.564311
$243$	−18.5470	−1.18979
$244$	−0.752627	−0.0481820
$245$	−1.33298	−0.0851610
$246$	46.0538	2.93629
$247$	3.10114	0.197321
$248$	1.39543	0.0886097
$249$	−29.4900	−1.86885
$250$	−7.15817	−0.452722
$251$	−7.62367	−0.481202	−0.240601	−	0.970624i	$-0.577345\pi$
$251$	−7.62367	−0.481202	−0.240601	+	0.970624i	$0.577345\pi$
$252$	17.2626	1.08744
$253$	−26.6776	−1.67721
$254$	30.8847	1.93788
$255$	1.51898	0.0951222
$256$	5.82863	0.364289
$257$	−28.1211	−1.75415	−0.877073	−	0.480358i	$-0.840507\pi$
$257$	−28.1211	−1.75415	−0.877073	+	0.480358i	$0.840507\pi$
$258$	16.4621	1.02488
$259$	−35.1463	−2.18388
$260$	−0.848661	−0.0526317
$261$	−14.5009	−0.897586
$262$	29.3560	1.81362
$263$	−12.1821	−0.751180	−0.375590	−	0.926786i	$-0.622560\pi$
$263$	−12.1821	−0.751180	−0.375590	+	0.926786i	$0.622560\pi$
$264$	8.93798	0.550095
$265$	0.437366	0.0268672
$266$	−21.6662	−1.32844
$267$	−16.0630	−0.983038
$268$	24.8950	1.52070
$269$	6.98698	0.426003	0.213002	−	0.977052i	$-0.431676\pi$
$269$	6.98698	0.426003	0.213002	+	0.977052i	$0.431676\pi$
$270$	−1.45905	−0.0887948
$271$	15.0485	0.914129	0.457065	−	0.889433i	$-0.348901\pi$
$271$	15.0485	0.914129	0.457065	+	0.889433i	$0.348901\pi$
$272$	5.51756	0.334551
$273$	7.46068	0.451541
$274$	−25.3029	−1.52861
$275$	19.0041	1.14599
$276$	38.4230	2.31280
$277$	−19.7944	−1.18933	−0.594666	−	0.803973i	$-0.702716\pi$
$277$	−19.7944	−1.18933	−0.594666	+	0.803973i	$0.702716\pi$
$278$	−1.70875	−0.102484
$279$	−2.89617	−0.173389
$280$	1.14765	0.0685851
$281$	−9.06020	−0.540486	−0.270243	−	0.962792i	$-0.587104\pi$
$281$	−9.06020	−0.540486	−0.270243	+	0.962792i	$0.587104\pi$
$282$	−17.3725	−1.03452
$283$	−20.5867	−1.22375	−0.611875	−	0.790954i	$-0.709585\pi$
$283$	−20.5867	−1.22375	−0.611875	+	0.790954i	$0.709585\pi$
$284$	−5.07834	−0.301344
$285$	−2.39859	−0.142080
$286$	8.23780	0.487111
$287$	−31.7752	−1.87563
$288$	16.8252	0.991433
$289$	−13.1431	−0.773126
$290$	−4.98065	−0.292474
$291$	−20.3792	−1.19465
$292$	2.50448	0.146564
$293$	20.1054	1.17457	0.587284	−	0.809381i	$-0.300197\pi$
$293$	20.1054	1.17457	0.587284	+	0.809381i	$0.300197\pi$
$294$	−18.6357	−1.08686
$295$	2.40206	0.139853
$296$	10.8186	0.628817
$297$	7.84012	0.454930
$298$	−19.5876	−1.13468
$299$	6.85451	0.396407
$300$	−27.3712	−1.58027
$301$	−11.3581	−0.654672
$302$	−25.4726	−1.46578
$303$	−5.20840	−0.299215
$304$	−8.71265	−0.499705
$305$	0.103848	0.00594633
$306$	8.76567	0.501100
$307$	0.938680	0.0535733	0.0267866	−	0.999641i	$-0.491473\pi$
$307$	0.938680	0.0535733	0.0267866	+	0.999641i	$0.491473\pi$
$308$	−31.8602	−1.81540
$309$	−15.4810	−0.880686
$310$	−0.994749	−0.0564979
$311$	1.40111	0.0794498	0.0397249	−	0.999211i	$-0.487352\pi$
$311$	1.40111	0.0794498	0.0397249	+	0.999211i	$0.487352\pi$
$312$	−2.29651	−0.130015
$313$	11.9797	0.677135	0.338568	−	0.940942i	$-0.390058\pi$
$313$	11.9797	0.677135	0.338568	+	0.940942i	$0.390058\pi$
$314$	−26.7610	−1.51021
$315$	−2.38191	−0.134205
$316$	22.8757	1.28686
$317$	18.8367	1.05798	0.528988	−	0.848629i	$-0.322572\pi$
$317$	18.8367	1.05798	0.528988	+	0.848629i	$0.322572\pi$
$318$	6.11458	0.342889
$319$	26.7633	1.49846
$320$	3.85615	0.215565
$321$	−24.5960	−1.37282
$322$	−47.8892	−2.66876
$323$	−6.09029	−0.338873
$324$	−26.9813	−1.49896
$325$	−4.88290	−0.270855
$326$	−0.661385	−0.0366307
$327$	22.8717	1.26481
$328$	9.78090	0.540060
$329$	11.9863	0.660827
$330$	−6.37156	−0.350743
$331$	1.68088	0.0923895	0.0461948	−	0.998932i	$-0.485291\pi$
$331$	1.68088	0.0923895	0.0461948	+	0.998932i	$0.485291\pi$
$332$	−32.3574	−1.77584
$333$	−22.4536	−1.23045
$334$	52.1796	2.85514
$335$	−3.43503	−0.187676
$336$	−20.9608	−1.14351
$337$	18.5449	1.01020	0.505102	−	0.863060i	$-0.331455\pi$
$337$	18.5449	1.01020	0.505102	+	0.863060i	$0.331455\pi$
$338$	−2.11661	−0.115128
$339$	31.5066	1.71120
$340$	1.66668	0.0903883
$341$	5.34523	0.289460
$342$	−13.8417	−0.748472
$343$	−10.2478	−0.553332
$344$	3.49621	0.188503
$345$	−5.30165	−0.285431
$346$	25.0591	1.34718
$347$	17.7843	0.954710	0.477355	−	0.878711i	$-0.341596\pi$
$347$	17.7843	0.954710	0.477355	+	0.878711i	$0.341596\pi$
$348$	−38.5464	−2.06631
$349$	35.4336	1.89672	0.948358	−	0.317203i	$-0.102744\pi$
$349$	35.4336	1.89672	0.948358	+	0.317203i	$0.102744\pi$
$350$	34.1145	1.82350
$351$	−2.01443	−0.107522
$352$	−31.0529	−1.65513
$353$	12.6567	0.673647	0.336824	−	0.941568i	$-0.390647\pi$
$353$	12.6567	0.673647	0.336824	+	0.941568i	$0.390647\pi$
$354$	33.5819	1.78486
$355$	0.700715	0.0371901
$356$	−17.6249	−0.934116
$357$	−14.6520	−0.775464
$358$	44.0847	2.32995
$359$	2.03386	0.107343	0.0536716	−	0.998559i	$-0.482908\pi$
$359$	2.03386	0.107343	0.0536716	+	0.998559i	$0.482908\pi$
$360$	0.733188	0.0386424
$361$	−9.38295	−0.493839
$362$	0.555670	0.0292054
$363$	9.37441	0.492029
$364$	8.18612	0.429069
$365$	−0.345571	−0.0180880
$366$	1.45185	0.0758893
$367$	3.78949	0.197810	0.0989048	−	0.995097i	$-0.468466\pi$
$367$	3.78949	0.197810	0.0989048	+	0.995097i	$0.468466\pi$
$368$	−19.2578	−1.00388
$369$	−20.2999	−1.05677
$370$	−7.71216	−0.400936
$371$	−4.21880	−0.219029
$372$	−7.69859	−0.399153
$373$	−25.4360	−1.31703	−0.658513	−	0.752570i	$-0.728814\pi$
$373$	−25.4360	−1.31703	−0.658513	+	0.752570i	$0.728814\pi$
$374$	−16.1781	−0.836551
$375$	7.64397	0.394733
$376$	−3.68957	−0.190275
$377$	−6.87652	−0.354159
$378$	14.0739	0.723881
$379$	−13.9807	−0.718143	−0.359071	−	0.933310i	$-0.616907\pi$
$379$	−13.9807	−0.718143	−0.359071	+	0.933310i	$0.616907\pi$
$380$	−2.63181	−0.135009
$381$	−32.9808	−1.68966
$382$	35.1413	1.79798
$383$	2.64860	0.135337	0.0676686	−	0.997708i	$-0.478444\pi$
$383$	2.64860	0.135337	0.0676686	+	0.997708i	$0.478444\pi$
$384$	17.8429	0.910543
$385$	4.39610	0.224046
$386$	−5.91491	−0.301061
$387$	−7.25627	−0.368857
$388$	−22.3607	−1.13519
$389$	3.29777	0.167204	0.0836019	−	0.996499i	$-0.473358\pi$
$389$	3.29777	0.167204	0.0836019	+	0.996499i	$0.473358\pi$
$390$	1.63710	0.0828978
$391$	−13.4615	−0.680778
$392$	−3.95784	−0.199901
$393$	−31.3484	−1.58132
$394$	−2.43886	−0.122868
$395$	−3.15641	−0.158816
$396$	−20.3543	−1.02284
$397$	4.32246	0.216938	0.108469	−	0.994100i	$-0.465405\pi$
$397$	4.32246	0.216938	0.108469	+	0.994100i	$0.465405\pi$
$398$	−26.8370	−1.34522
$399$	23.1366	1.15828
$400$	13.7185	0.685926
$401$	−0.437858	−0.0218656	−0.0109328	−	0.999940i	$-0.503480\pi$
$401$	−0.437858	−0.0218656	−0.0109328	+	0.999940i	$0.503480\pi$
$402$	−48.0233	−2.39519
$403$	−1.37340	−0.0684138
$404$	−5.71484	−0.284324
$405$	3.72291	0.184993
$406$	48.0430	2.38433
$407$	41.4409	2.05415
$408$	4.51010	0.223283
$409$	−4.88121	−0.241361	−0.120680	−	0.992691i	$-0.538508\pi$
$409$	−4.88121	−0.241361	−0.120680	+	0.992691i	$0.538508\pi$
$410$	−6.97244	−0.344344
$411$	27.0202	1.33281
$412$	−16.9863	−0.836857
$413$	−23.1701	−1.14013
$414$	−30.5946	−1.50364
$415$	4.46471	0.219164
$416$	7.97870	0.391188
$417$	1.82471	0.0893566
$418$	25.5465	1.24952
$419$	11.3358	0.553789	0.276894	−	0.960900i	$-0.410695\pi$
$419$	11.3358	0.553789	0.276894	+	0.960900i	$0.410695\pi$
$420$	−6.33159	−0.308950
$421$	30.3629	1.47980	0.739898	−	0.672719i	$-0.234874\pi$
$421$	30.3629	1.47980	0.739898	+	0.672719i	$0.234874\pi$
$422$	−18.6689	−0.908786
$423$	7.65759	0.372325
$424$	1.29861	0.0630662
$425$	9.58948	0.465158
$426$	9.79632	0.474633
$427$	−1.00171	−0.0484763
$428$	−26.9876	−1.30449
$429$	−8.79687	−0.424717
$430$	−2.49232	−0.120190
$431$	24.5114	1.18067	0.590337	−	0.807157i	$-0.298995\pi$
$431$	24.5114	1.18067	0.590337	+	0.807157i	$0.298995\pi$
$432$	5.65955	0.272295
$433$	7.52141	0.361456	0.180728	−	0.983533i	$-0.442155\pi$
$433$	7.52141	0.361456	0.180728	+	0.983533i	$0.442155\pi$
$434$	9.59527	0.460588
$435$	5.31868	0.255011
$436$	25.0956	1.20186
$437$	21.2568	1.01685
$438$	−4.83125	−0.230846
$439$	33.0382	1.57683	0.788414	−	0.615145i	$-0.210902\pi$
$439$	33.0382	1.57683	0.788414	+	0.615145i	$0.210902\pi$
$440$	−1.35319	−0.0645108
$441$	8.21437	0.391160
$442$	4.15679	0.197718
$443$	−29.0084	−1.37823	−0.689115	−	0.724652i	$-0.742000\pi$
$443$	−29.0084	−1.37823	−0.689115	+	0.724652i	$0.742000\pi$
$444$	−59.6862	−2.83258
$445$	2.43190	0.115283
$446$	−47.8191	−2.26430
$447$	20.9170	0.989339
$448$	−37.1961	−1.75735
$449$	21.3563	1.00786	0.503932	−	0.863743i	$-0.331886\pi$
$449$	21.3563	1.00786	0.503932	+	0.863743i	$0.331886\pi$
$450$	21.7944	1.02740
$451$	37.4660	1.76421
$452$	34.5702	1.62604
$453$	27.2013	1.27803
$454$	−32.7085	−1.53508
$455$	−1.12953	−0.0529531
$456$	−7.12181	−0.333509
$457$	0.211498	0.00989344	0.00494672	−	0.999988i	$-0.498425\pi$
$457$	0.211498	0.00989344	0.00494672	+	0.999988i	$0.498425\pi$
$458$	−39.9516	−1.86682
$459$	3.95612	0.184656
$460$	−5.81716	−0.271226
$461$	−19.8517	−0.924587	−0.462294	−	0.886727i	$-0.652973\pi$
$461$	−19.8517	−0.924587	−0.462294	+	0.886727i	$0.652973\pi$
$462$	61.4596	2.85936
$463$	1.00000	0.0464739
$463$	1.00000	0.0464739
$464$	19.3196	0.896891
$465$	1.06226	0.0492611
$466$	20.7025	0.959023
$467$	−20.9078	−0.967498	−0.483749	−	0.875207i	$-0.660725\pi$
$467$	−20.9078	−0.967498	−0.483749	+	0.875207i	$0.660725\pi$
$468$	5.22980	0.241747
$469$	33.1341	1.52999
$470$	2.63016	0.121320
$471$	28.5772	1.31677
$472$	7.13212	0.328282
$473$	13.3923	0.615781
$474$	−44.1281	−2.02687
$475$	−15.1425	−0.694788
$476$	−16.0766	−0.736872
$477$	−2.69523	−0.123406
$478$	−37.9334	−1.73503
$479$	−17.9721	−0.821166	−0.410583	−	0.911823i	$-0.634675\pi$
$479$	−17.9721	−0.821166	−0.410583	+	0.911823i	$0.634675\pi$
$480$	−6.17116	−0.281674
$481$	−10.6478	−0.485496
$482$	−21.6666	−0.986888
$483$	51.1393	2.32692
$484$	10.2859	0.467542
$485$	3.08535	0.140099
$486$	39.2567	1.78072
$487$	−5.44974	−0.246951	−0.123476	−	0.992348i	$-0.539404\pi$
$487$	−5.44974	−0.246951	−0.123476	+	0.992348i	$0.539404\pi$
$488$	0.308343	0.0139580
$489$	0.706271	0.0319387
$490$	2.82140	0.127458
$491$	−39.5392	−1.78438	−0.892190	−	0.451661i	$-0.850832\pi$
$491$	−39.5392	−1.78438	−0.892190	+	0.451661i	$0.850832\pi$
$492$	−53.9613	−2.43276
$493$	13.5047	0.608223
$494$	−6.56389	−0.295324
$495$	2.80850	0.126233
$496$	3.85856	0.173255
$497$	−6.75905	−0.303185
$498$	62.4187	2.79705
$499$	−24.7973	−1.11008	−0.555040	−	0.831824i	$-0.687297\pi$
$499$	−24.7973	−1.11008	−0.555040	+	0.831824i	$0.687297\pi$
$500$	8.38723	0.375088
$501$	−55.7208	−2.48942
$502$	16.1363	0.720200
$503$	8.50426	0.379186	0.189593	−	0.981863i	$-0.439283\pi$
$503$	8.50426	0.379186	0.189593	+	0.981863i	$0.439283\pi$
$504$	−7.07228	−0.315024
$505$	0.788539	0.0350895
$506$	56.4661	2.51022
$507$	2.26026	0.100382
$508$	−36.1877	−1.60557
$509$	−0.375277	−0.0166338	−0.00831692	−	0.999965i	$-0.502647\pi$
$509$	−0.375277	−0.0166338	−0.00831692	+	0.999965i	$0.502647\pi$
$510$	−3.21508	−0.142366
$511$	3.33335	0.147459
$512$	−28.1253	−1.24298
$513$	−6.24702	−0.275813
$514$	59.5213	2.62537
$515$	2.34379	0.103280
$516$	−19.2886	−0.849135
$517$	−14.1330	−0.621570
$518$	74.3909	3.26855
$519$	−26.7598	−1.17462
$520$	0.347687	0.0152471
$521$	−28.1612	−1.23377	−0.616883	−	0.787055i	$-0.711605\pi$
$521$	−28.1612	−1.23377	−0.616883	+	0.787055i	$0.711605\pi$
$522$	30.6928	1.34339
$523$	−5.97880	−0.261435	−0.130717	−	0.991420i	$-0.541728\pi$
$523$	−5.97880	−0.261435	−0.130717	+	0.991420i	$0.541728\pi$
$524$	−34.3965	−1.50262
$525$	−36.4298	−1.58993
$526$	25.7847	1.12427
$527$	2.69720	0.117492
$528$	24.7148	1.07558
$529$	23.9843	1.04280
$530$	−0.925733	−0.0402113
$531$	−14.8025	−0.642373
$532$	25.3863	1.10063
$533$	−9.62648	−0.416969
$534$	33.9990	1.47128
$535$	3.72378	0.160993
$536$	−10.1992	−0.440537
$537$	−47.0766	−2.03150
$538$	−14.7887	−0.637586
$539$	−15.1606	−0.653015
$540$	1.70957	0.0735681
$541$	−17.1891	−0.739018	−0.369509	−	0.929227i	$-0.620474\pi$
$541$	−17.1891	−0.739018	−0.369509	+	0.929227i	$0.620474\pi$
$542$	−31.8517	−1.36815
$543$	−0.593382	−0.0254644
$544$	−15.6693	−0.671816
$545$	−3.46272	−0.148327
$546$	−15.7913	−0.675807
$547$	−18.5050	−0.791215	−0.395607	−	0.918420i	$-0.629466\pi$
$547$	−18.5050	−0.791215	−0.395607	+	0.918420i	$0.629466\pi$
$548$	29.6475	1.26648
$549$	−0.639955	−0.0273126
$550$	−40.2243	−1.71517
$551$	−21.3250	−0.908477
$552$	−15.7415	−0.670002
$553$	30.4465	1.29472
$554$	41.8971	1.78004
$555$	8.23556	0.349580
$556$	2.00214	0.0849096
$557$	−1.23721	−0.0524222	−0.0262111	−	0.999656i	$-0.508344\pi$
$557$	−1.23721	−0.0524222	−0.0262111	+	0.999656i	$0.508344\pi$
$558$	6.13005	0.259506
$559$	−3.44101	−0.145539
$560$	3.17342	0.134101
$561$	17.2761	0.729397
$562$	19.1769	0.808928
$563$	24.3300	1.02539	0.512694	−	0.858571i	$-0.328647\pi$
$563$	24.3300	1.02539	0.512694	+	0.858571i	$0.328647\pi$
$564$	20.3554	0.857118
$565$	−4.77003	−0.200677
$566$	43.5739	1.83155
$567$	−35.9109	−1.50812
$568$	2.08054	0.0872975
$569$	6.81417	0.285665	0.142832	−	0.989747i	$-0.454379\pi$
$569$	6.81417	0.285665	0.142832	+	0.989747i	$0.454379\pi$
$570$	5.07687	0.212647
$571$	−33.8300	−1.41574	−0.707870	−	0.706342i	$-0.750344\pi$
$571$	−33.8300	−1.41574	−0.707870	+	0.706342i	$0.750344\pi$
$572$	−9.65223	−0.403580
$573$	−37.5262	−1.56768
$574$	67.2556	2.80720
$575$	−33.4699	−1.39579
$576$	−23.7632	−0.990132
$577$	−46.6995	−1.94412	−0.972062	−	0.234724i	$-0.924581\pi$
$577$	−46.6995	−1.94412	−0.972062	+	0.234724i	$0.924581\pi$
$578$	27.8189	1.15711
$579$	6.31633	0.262498
$580$	5.83584	0.242320
$581$	−43.0662	−1.78669
$582$	43.1347	1.78799
$583$	4.97438	0.206018
$584$	−1.02606	−0.0424586
$585$	−0.721613	−0.0298350
$586$	−42.5552	−1.75794
$587$	−12.6550	−0.522329	−0.261164	−	0.965294i	$-0.584106\pi$
$587$	−12.6550	−0.522329	−0.261164	+	0.965294i	$0.584106\pi$
$588$	21.8354	0.900479
$589$	−4.25909	−0.175493
$590$	−5.08422	−0.209314
$591$	2.60438	0.107130
$592$	29.9149	1.22950
$593$	5.43742	0.223288	0.111644	−	0.993748i	$-0.464388\pi$
$593$	5.43742	0.223288	0.111644	+	0.993748i	$0.464388\pi$
$594$	−16.5945	−0.680879
$595$	2.21827	0.0909403
$596$	22.9508	0.940103
$597$	28.6583	1.17291
$598$	−14.5083	−0.593289
$599$	20.9513	0.856045	0.428023	−	0.903768i	$-0.359210\pi$
$599$	20.9513	0.856045	0.428023	+	0.903768i	$0.359210\pi$
$600$	11.2137	0.457795
$601$	1.24762	0.0508913	0.0254457	−	0.999676i	$-0.491900\pi$
$601$	1.24762	0.0508913	0.0254457	+	0.999676i	$0.491900\pi$
$602$	24.0407	0.979827
$603$	21.1681	0.862030
$604$	29.8462	1.21443
$605$	−1.41926	−0.0577012
$606$	11.0241	0.447825
$607$	37.1502	1.50788	0.753940	−	0.656943i	$-0.228151\pi$
$607$	37.1502	1.50788	0.753940	+	0.656943i	$0.228151\pi$
$608$	24.7430	1.00346
$609$	−51.3035	−2.07892
$610$	−0.219806	−0.00889969
$611$	3.63132	0.146908
$612$	−10.2707	−0.415170
$613$	−27.8148	−1.12343	−0.561714	−	0.827332i	$-0.689858\pi$
$613$	−27.8148	−1.12343	−0.561714	+	0.827332i	$0.689858\pi$
$614$	−1.98682	−0.0801814
$615$	7.44564	0.300237
$616$	13.0528	0.525911
$617$	3.55493	0.143116	0.0715581	−	0.997436i	$-0.477203\pi$
$617$	3.55493	0.143116	0.0715581	+	0.997436i	$0.477203\pi$
$618$	32.7673	1.31809
$619$	36.8180	1.47984	0.739920	−	0.672695i	$-0.234863\pi$
$619$	36.8180	1.47984	0.739920	+	0.672695i	$0.234863\pi$
$620$	1.16555	0.0468095
$621$	−13.8079	−0.554093
$622$	−2.96561	−0.118910
$623$	−23.4579	−0.939821
$624$	−6.35020	−0.254211
$625$	23.2572	0.930289
$626$	−25.3564	−1.01345
$627$	−27.2803	−1.08947
$628$	31.3559	1.25123
$629$	20.9110	0.833778
$630$	5.04157	0.200861
$631$	11.0136	0.438444	0.219222	−	0.975675i	$-0.429648\pi$
$631$	11.0136	0.438444	0.219222	+	0.975675i	$0.429648\pi$
$632$	−9.37191	−0.372795
$633$	19.9359	0.792380
$634$	−39.8700	−1.58344
$635$	4.99321	0.198150
$636$	−7.16446	−0.284089
$637$	3.89535	0.154340
$638$	−56.6474	−2.24269
$639$	−4.31809	−0.170821
$640$	−2.70138	−0.106781
$641$	−4.83790	−0.191085	−0.0955427	−	0.995425i	$-0.530459\pi$
$641$	−4.83790	−0.191085	−0.0955427	+	0.995425i	$0.530459\pi$
$642$	52.0601	2.05465
$643$	−21.8738	−0.862620	−0.431310	−	0.902204i	$-0.641948\pi$
$643$	−21.8738	−0.862620	−0.431310	+	0.902204i	$0.641948\pi$
$644$	56.1119	2.21112
$645$	2.66147	0.104795
$646$	12.8908	0.507180
$647$	−0.750523	−0.0295061	−0.0147531	−	0.999891i	$-0.504696\pi$
$647$	−0.750523	−0.0295061	−0.0147531	+	0.999891i	$0.504696\pi$
$648$	11.0539	0.434239
$649$	27.3198	1.07240
$650$	10.3352	0.405380
$651$	−10.2465	−0.401591
$652$	0.774945	0.0303492
$653$	23.9449	0.937037	0.468519	−	0.883454i	$-0.344788\pi$
$653$	23.9449	0.937037	0.468519	+	0.883454i	$0.344788\pi$
$654$	−48.4105	−1.89300
$655$	4.74607	0.185444
$656$	27.0456	1.05595
$657$	2.12955	0.0830817
$658$	−25.3703	−0.989038
$659$	4.54315	0.176976	0.0884880	−	0.996077i	$-0.471797\pi$
$659$	4.54315	0.176976	0.0884880	+	0.996077i	$0.471797\pi$
$660$	7.46556	0.290597
$661$	−11.0301	−0.429023	−0.214512	−	0.976721i	$-0.568816\pi$
$661$	−11.0301	−0.429023	−0.214512	+	0.976721i	$0.568816\pi$
$662$	−3.55777	−0.138276
$663$	−4.43890	−0.172392
$664$	13.2565	0.514451
$665$	−3.50282	−0.135834
$666$	47.5255	1.84157
$667$	−47.1352	−1.82508
$668$	−61.1389	−2.36553
$669$	51.0644	1.97426
$670$	7.27062	0.280888
$671$	1.18112	0.0455965
$672$	59.5265	2.29629
$673$	−26.9607	−1.03926	−0.519630	−	0.854392i	$-0.673930\pi$
$673$	−26.9607	−1.03926	−0.519630	+	0.854392i	$0.673930\pi$
$674$	−39.2522	−1.51194
$675$	9.83626	0.378598
$676$	2.48003	0.0953859
$677$	46.6414	1.79257	0.896287	−	0.443475i	$-0.146254\pi$
$677$	46.6414	1.79257	0.896287	+	0.443475i	$0.146254\pi$
$678$	−66.6872	−2.56111
$679$	−29.7611	−1.14213
$680$	−0.682819	−0.0261849
$681$	34.9283	1.33845
$682$	−11.3138	−0.433226
$683$	−37.9709	−1.45292	−0.726459	−	0.687210i	$-0.758835\pi$
$683$	−37.9709	−1.45292	−0.726459	+	0.687210i	$0.758835\pi$
$684$	16.2183	0.620123
$685$	−4.09079	−0.156301
$686$	21.6907	0.828154
$687$	42.6630	1.62770
$688$	9.66754	0.368571
$689$	−1.27811	−0.0486921
$690$	11.2215	0.427196
$691$	21.1209	0.803475	0.401738	−	0.915755i	$-0.368406\pi$
$691$	21.1209	0.803475	0.401738	+	0.915755i	$0.368406\pi$
$692$	−29.3617	−1.11617
$693$	−27.0906	−1.02909
$694$	−37.6423	−1.42888
$695$	−0.276257	−0.0104790
$696$	15.7920	0.598596
$697$	18.9054	0.716091
$698$	−74.9990	−2.83875
$699$	−22.1075	−0.836182
$700$	−39.9720	−1.51080
$701$	11.8860	0.448927	0.224464	−	0.974482i	$-0.427937\pi$
$701$	11.8860	0.448927	0.224464	+	0.974482i	$0.427937\pi$
$702$	4.26376	0.160925
$703$	−33.0202	−1.24538
$704$	43.8579	1.65296
$705$	−2.80866	−0.105780
$706$	−26.7892	−1.00823
$707$	−7.60619	−0.286060
$708$	−39.3480	−1.47879
$709$	−43.8049	−1.64513	−0.822564	−	0.568673i	$-0.807457\pi$
$709$	−43.8049	−1.64513	−0.822564	+	0.568673i	$0.807457\pi$
$710$	−1.48314	−0.0556612
$711$	19.4511	0.729473
$712$	7.22071	0.270607
$713$	−9.41396	−0.352556
$714$	31.0125	1.16061
$715$	1.33183	0.0498074
$716$	−51.6541	−1.93040
$717$	40.5078	1.51279
$718$	−4.30489	−0.160657
$719$	49.9301	1.86208	0.931039	−	0.364920i	$-0.118904\pi$
$719$	49.9301	1.86208	0.931039	+	0.364920i	$0.118904\pi$
$720$	2.02737	0.0755557
$721$	−22.6080	−0.841968
$722$	19.8600	0.739114
$723$	23.1371	0.860477
$724$	−0.651079	−0.0241972
$725$	33.5774	1.24703
$726$	−19.8419	−0.736404
$727$	1.46909	0.0544854	0.0272427	−	0.999629i	$-0.491327\pi$
$727$	1.46909	0.0544854	0.0272427	+	0.999629i	$0.491327\pi$
$728$	−3.35376	−0.124299
$729$	−9.28269	−0.343803
$730$	0.731439	0.0270718
$731$	6.75777	0.249945
$732$	−1.70113	−0.0628756
$733$	−1.10498	−0.0408135	−0.0204068	−	0.999792i	$-0.506496\pi$
$733$	−1.10498	−0.0408135	−0.0204068	+	0.999792i	$0.506496\pi$
$734$	−8.02086	−0.296055
$735$	−3.01288	−0.111132
$736$	54.6901	2.01590
$737$	−39.0683	−1.43910
$738$	42.9670	1.58164
$739$	−29.4119	−1.08194	−0.540968	−	0.841043i	$-0.681942\pi$
$739$	−29.4119	−1.08194	−0.540968	+	0.841043i	$0.681942\pi$
$740$	9.03634	0.332183
$741$	7.00937	0.257495
$742$	8.92955	0.327814
$743$	−32.8745	−1.20605	−0.603024	−	0.797723i	$-0.706038\pi$
$743$	−32.8745	−1.20605	−0.603024	+	0.797723i	$0.706038\pi$
$744$	3.15403	0.115632
$745$	−3.16678	−0.116022
$746$	53.8380	1.97115
$747$	−27.5134	−1.00666
$748$	18.9559	0.693097
$749$	−35.9193	−1.31246
$750$	−16.1793	−0.590784
$751$	−44.7603	−1.63333	−0.816663	−	0.577115i	$-0.804178\pi$
$751$	−44.7603	−1.63333	−0.816663	+	0.577115i	$0.804178\pi$
$752$	−10.2022	−0.372036
$753$	−17.2315	−0.627949
$754$	14.5549	0.530059
$755$	−4.11822	−0.149877
$756$	−16.4904	−0.599749
$757$	41.3483	1.50283	0.751415	−	0.659830i	$-0.229372\pi$
$757$	41.3483	1.50283	0.751415	+	0.659830i	$0.229372\pi$
$758$	29.5918	1.07482
$759$	−60.2983	−2.18869
$760$	1.07822	0.0391113
$761$	−16.1261	−0.584572	−0.292286	−	0.956331i	$-0.594416\pi$
$761$	−16.1261	−0.584572	−0.292286	+	0.956331i	$0.594416\pi$
$762$	69.8074	2.52886
$763$	33.4012	1.20920
$764$	−41.1751	−1.48966
$765$	1.41717	0.0512378
$766$	−5.60605	−0.202555
$767$	−7.01952	−0.253460
$768$	13.1742	0.475383
$769$	−44.0375	−1.58803	−0.794016	−	0.607897i	$-0.792013\pi$
$769$	−44.0375	−1.58803	−0.794016	+	0.607897i	$0.792013\pi$
$770$	−9.30483	−0.335323
$771$	−63.5609	−2.28909
$772$	6.93050	0.249434
$773$	−18.9230	−0.680611	−0.340306	−	0.940315i	$-0.610531\pi$
$773$	−18.9230	−0.680611	−0.340306	+	0.940315i	$0.610531\pi$
$774$	15.3587	0.552057
$775$	6.70616	0.240892
$776$	9.16093	0.328858
$777$	−79.4396	−2.84988
$778$	−6.98010	−0.250249
$779$	−29.8530	−1.06960
$780$	−1.91819	−0.0686823
$781$	7.96957	0.285174
$782$	28.4928	1.01890
$783$	13.8523	0.495040
$784$	−10.9440	−0.390858
$785$	−4.32651	−0.154420
$786$	66.3522	2.36670
$787$	−26.0689	−0.929256	−0.464628	−	0.885506i	$-0.653812\pi$
$787$	−26.0689	−0.929256	−0.464628	+	0.885506i	$0.653812\pi$
$788$	2.85762	0.101798
$789$	−27.5347	−0.980260
$790$	6.68089	0.237695
$791$	46.0113	1.63597
$792$	8.33891	0.296310
$793$	−0.303475	−0.0107767
$794$	−9.14895	−0.324684
$795$	0.988560	0.0350606
$796$	31.4449	1.11454
$797$	−10.8989	−0.386059	−0.193030	−	0.981193i	$-0.561831\pi$
$797$	−10.8989	−0.386059	−0.193030	+	0.981193i	$0.561831\pi$
$798$	−48.9711	−1.73356
$799$	−7.13152	−0.252295
$800$	−38.9592	−1.37742
$801$	−14.9863	−0.529516
$802$	0.926774	0.0327255
$803$	−3.93035	−0.138699
$804$	56.2690	1.98445
$805$	−7.74237	−0.272883
$806$	2.90694	0.102393
$807$	15.7924	0.555917
$808$	2.34130	0.0823668
$809$	5.46088	0.191994	0.0959972	−	0.995382i	$-0.469396\pi$
$809$	5.46088	0.191994	0.0959972	+	0.995382i	$0.469396\pi$
$810$	−7.87994	−0.276873
$811$	−10.9002	−0.382757	−0.191379	−	0.981516i	$-0.561296\pi$
$811$	−10.9002	−0.382757	−0.191379	+	0.981516i	$0.561296\pi$
$812$	−56.2920	−1.97546
$813$	34.0134	1.19290
$814$	−87.7141	−3.07438
$815$	−0.106928	−0.00374552
$816$	12.4711	0.436576
$817$	−10.6711	−0.373333
$818$	10.3316	0.361237
$819$	6.96062	0.243224
$820$	8.16962	0.285295
$821$	43.9330	1.53327	0.766637	−	0.642081i	$-0.221929\pi$
$821$	43.9330	1.53327	0.766637	+	0.642081i	$0.221929\pi$
$822$	−57.1911	−1.99477
$823$	−49.7320	−1.73355	−0.866774	−	0.498701i	$-0.833811\pi$
$823$	−49.7320	−1.73355	−0.866774	+	0.498701i	$0.833811\pi$
$824$	6.95911	0.242432
$825$	42.9542	1.49547
$826$	49.0420	1.70639
$827$	−16.3275	−0.567764	−0.283882	−	0.958859i	$-0.591622\pi$
$827$	−16.3275	−0.567764	−0.283882	+	0.958859i	$0.591622\pi$
$828$	35.8477	1.24579
$829$	−32.7178	−1.13634	−0.568168	−	0.822913i	$-0.692348\pi$
$829$	−32.7178	−1.13634	−0.568168	+	0.822913i	$0.692348\pi$
$830$	−9.45004	−0.328016
$831$	−44.7405	−1.55203
$832$	−11.2688	−0.390675
$833$	−7.65005	−0.265058
$834$	−3.86220	−0.133737
$835$	8.43600	0.291940
$836$	−29.9329	−1.03525
$837$	2.76661	0.0956281
$838$	−23.9934	−0.828838
$839$	12.0426	0.415757	0.207878	−	0.978155i	$-0.433344\pi$
$839$	12.0426	0.415757	0.207878	+	0.978155i	$0.433344\pi$
$840$	2.59398	0.0895008
$841$	18.2866	0.630572
$842$	−64.2663	−2.21476
$843$	−20.4784	−0.705313
$844$	21.8743	0.752946
$845$	−0.342197	−0.0117720
$846$	−16.2081	−0.557247
$847$	13.6901	0.470397
$848$	3.59085	0.123310
$849$	−46.5312	−1.59695
$850$	−20.2972	−0.696188
$851$	−72.9852	−2.50190
$852$	−11.4784	−0.393242
$853$	−0.247002	−0.00845719	−0.00422860	−	0.999991i	$-0.501346\pi$
$853$	−0.247002	−0.00845719	−0.00422860	+	0.999991i	$0.501346\pi$
$854$	2.12023	0.0725529
$855$	−2.23782	−0.0765318
$856$	11.0565	0.377904
$857$	4.40871	0.150599	0.0752993	−	0.997161i	$-0.476009\pi$
$857$	4.40871	0.150599	0.0752993	+	0.997161i	$0.476009\pi$
$858$	18.6195	0.635660
$859$	10.0574	0.343155	0.171577	−	0.985171i	$-0.445114\pi$
$859$	10.0574	0.343155	0.171577	+	0.985171i	$0.445114\pi$
$860$	2.92025	0.0995798
$861$	−71.8201	−2.44762
$862$	−51.8811	−1.76708
$863$	−13.6940	−0.466148	−0.233074	−	0.972459i	$-0.574878\pi$
$863$	−13.6940	−0.466148	−0.233074	+	0.972459i	$0.574878\pi$
$864$	−16.0725	−0.546799
$865$	4.05136	0.137751
$866$	−15.9199	−0.540980
$867$	−29.7069	−1.00890
$868$	−11.2428	−0.381605
$869$	−35.8994	−1.21780
$870$	−11.2576	−0.381667
$871$	10.0382	0.340130
$872$	−10.2814	−0.348172
$873$	−19.0132	−0.643500
$874$	−44.9923	−1.52189
$875$	11.1630	0.377379
$876$	5.66078	0.191260
$877$	−33.5193	−1.13187	−0.565934	−	0.824451i	$-0.691484\pi$
$877$	−33.5193	−1.13187	−0.565934	+	0.824451i	$0.691484\pi$
$878$	−69.9290	−2.35999
$879$	45.4433	1.53277
$880$	−3.74177	−0.126135
$881$	4.94264	0.166522	0.0832609	−	0.996528i	$-0.473467\pi$
$881$	4.94264	0.166522	0.0832609	+	0.996528i	$0.473467\pi$
$882$	−17.3866	−0.585438
$883$	−52.3753	−1.76257	−0.881285	−	0.472586i	$-0.843321\pi$
$883$	−52.3753	−1.76257	−0.881285	+	0.472586i	$0.843321\pi$
$884$	−4.87051	−0.163813
$885$	5.42927	0.182503
$886$	61.3994	2.06275
$887$	20.2647	0.680420	0.340210	−	0.940349i	$-0.389502\pi$
$887$	20.2647	0.680420	0.340210	+	0.940349i	$0.389502\pi$
$888$	24.4527	0.820580
$889$	−48.1641	−1.61537
$890$	−5.14737	−0.172540
$891$	42.3424	1.41852
$892$	56.0297	1.87601
$893$	11.2612	0.376843
$894$	−44.2730	−1.48071
$895$	7.12728	0.238239
$896$	26.0573	0.870512
$897$	15.4930	0.517295
$898$	−45.2029	−1.50844
$899$	9.44419	0.314982
$900$	−25.5366	−0.851219
$901$	2.51007	0.0836225
$902$	−79.3010	−2.64043
$903$	−25.6723	−0.854320
$904$	−14.1630	−0.471054
$905$	0.0898366	0.00298627
$906$	−57.5746	−1.91279
$907$	−19.5249	−0.648314	−0.324157	−	0.946003i	$-0.605081\pi$
$907$	−19.5249	−0.648314	−0.324157	+	0.946003i	$0.605081\pi$
$908$	38.3245	1.27184
$909$	−4.85930	−0.161173
$910$	2.39077	0.0792533
$911$	31.3014	1.03706	0.518530	−	0.855059i	$-0.326479\pi$
$911$	31.3014	1.03706	0.518530	+	0.855059i	$0.326479\pi$
$912$	−19.6928	−0.652095
$913$	50.7793	1.68055
$914$	−0.447658	−0.0148072
$915$	0.234724	0.00775973
$916$	46.8114	1.54669
$917$	−45.7802	−1.51180
$918$	−8.37356	−0.276369
$919$	−8.59077	−0.283383	−0.141692	−	0.989911i	$-0.545254\pi$
$919$	−8.59077	−0.283383	−0.141692	+	0.989911i	$0.545254\pi$
$920$	2.38322	0.0785725
$921$	2.12166	0.0699110
$922$	42.0183	1.38380
$923$	−2.04769	−0.0674006
$924$	−72.0122	−2.36903
$925$	51.9920	1.70949
$926$	−2.11661	−0.0695561
$927$	−14.4434	−0.474384
$928$	−54.8657	−1.80106
$929$	−5.86387	−0.192387	−0.0961937	−	0.995363i	$-0.530667\pi$
$929$	−5.86387	−0.192387	−0.0961937	+	0.995363i	$0.530667\pi$
$930$	−2.24839	−0.0737275
$931$	12.0800	0.395907
$932$	−24.2571	−0.794568
$933$	3.16687	0.103679
$934$	44.2536	1.44802
$935$	−2.61556	−0.0855379
$936$	−2.14259	−0.0700327
$937$	−11.8377	−0.386721	−0.193360	−	0.981128i	$-0.561939\pi$
$937$	−11.8377	−0.386721	−0.193360	+	0.981128i	$0.561939\pi$
$938$	−70.1318	−2.28989
$939$	27.0773	0.883634
$940$	−3.08176	−0.100516
$941$	15.8535	0.516809	0.258405	−	0.966037i	$-0.416803\pi$
$941$	15.8535	0.516809	0.258405	+	0.966037i	$0.416803\pi$
$942$	−60.4867	−1.97076
$943$	−65.9848	−2.14876
$944$	19.7214	0.641875
$945$	2.27536	0.0740174
$946$	−28.3464	−0.921620
$947$	4.69364	0.152523	0.0762615	−	0.997088i	$-0.475702\pi$
$947$	4.69364	0.152523	0.0762615	+	0.997088i	$0.475702\pi$
$948$	51.7049	1.67930
$949$	1.00986	0.0327814
$950$	32.0508	1.03987
$951$	42.5758	1.38062
$952$	6.58642	0.213467
$953$	15.2997	0.495604	0.247802	−	0.968811i	$-0.420292\pi$
$953$	15.2997	0.495604	0.247802	+	0.968811i	$0.420292\pi$
$954$	5.70474	0.184698
$955$	5.68138	0.183845
$956$	44.4466	1.43750
$957$	60.4919	1.95543
$958$	38.0399	1.22901
$959$	39.4594	1.27421
$960$	8.71589	0.281304
$961$	−29.1138	−0.939154
$962$	22.5372	0.726627
$963$	−22.9474	−0.739471
$964$	25.3868	0.817654
$965$	−0.956278	−0.0307837
$966$	−108.242	−3.48263
$967$	−12.2722	−0.394646	−0.197323	−	0.980338i	$-0.563225\pi$
$967$	−12.2722	−0.394646	−0.197323	+	0.980338i	$0.563225\pi$
$968$	−4.21403	−0.135444
$969$	−13.7656	−0.442216
$970$	−6.53049	−0.209681
$971$	31.2443	1.00268	0.501338	−	0.865251i	$-0.332841\pi$
$971$	31.2443	1.00268	0.501338	+	0.865251i	$0.332841\pi$
$972$	−45.9971	−1.47536
$973$	2.66476	0.0854282
$974$	11.5350	0.369604
$975$	−11.0366	−0.353454
$976$	0.852613	0.0272915
$977$	−13.3624	−0.427501	−0.213751	−	0.976888i	$-0.568568\pi$
$977$	−13.3624	−0.427501	−0.213751	+	0.976888i	$0.568568\pi$
$978$	−1.49490	−0.0478016
$979$	27.6591	0.883990
$980$	−3.30583	−0.105601
$981$	21.3387	0.681293
$982$	83.6890	2.67062
$983$	−60.1975	−1.92000	−0.960000	−	0.279998i	$-0.909666\pi$
$983$	−60.1975	−1.92000	−0.960000	+	0.279998i	$0.909666\pi$
$984$	22.1073	0.704756
$985$	−0.394297	−0.0125633
$986$	−28.5843	−0.910308
$987$	27.0921	0.862352
$988$	7.69092	0.244681
$989$	−23.5865	−0.750006
$990$	−5.94450	−0.188929
$991$	13.5603	0.430758	0.215379	−	0.976531i	$-0.430901\pi$
$991$	13.5603	0.430758	0.215379	+	0.976531i	$0.430901\pi$
$992$	−10.9579	−0.347914
$993$	3.79922	0.120565
$994$	14.3063	0.453767
$995$	−4.33880	−0.137549
$996$	−73.1361	−2.31740
$997$	−38.6359	−1.22361	−0.611806	−	0.791008i	$-0.709557\pi$
$997$	−38.6359	−1.22361	−0.611806	+	0.791008i	$0.709557\pi$
$998$	52.4862	1.66142
$999$	21.4492	0.678622

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.b.1.16	✓	101

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.b.1.16	✓	101	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:	\( N \)	\(=\)	\( 6019 = 13 \cdot 463 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.11661 q^{2} +2.26026 q^{3} +2.48003 q^{4} -0.342197 q^{5} -4.78408 q^{6} +3.30081 q^{7} -1.01604 q^{8} +2.10876 q^{9} +O(q^{10})\)	\(q-2.11661 q^{2} +2.26026 q^{3} +2.48003 q^{4} -0.342197 q^{5} -4.78408 q^{6} +3.30081 q^{7} -1.01604 q^{8} +2.10876 q^{9} +0.724298 q^{10} -3.89198 q^{11} +5.60551 q^{12} +1.00000 q^{13} -6.98653 q^{14} -0.773454 q^{15} -2.80950 q^{16} -1.96389 q^{17} -4.46342 q^{18} +3.10114 q^{19} -0.848661 q^{20} +7.46068 q^{21} +8.23780 q^{22} +6.85451 q^{23} -2.29651 q^{24} -4.88290 q^{25} -2.11661 q^{26} -2.01443 q^{27} +8.18612 q^{28} -6.87652 q^{29} +1.63710 q^{30} -1.37340 q^{31} +7.97870 q^{32} -8.79687 q^{33} +4.15679 q^{34} -1.12953 q^{35} +5.22980 q^{36} -10.6478 q^{37} -6.56389 q^{38} +2.26026 q^{39} +0.347687 q^{40} -9.62648 q^{41} -15.7913 q^{42} -3.44101 q^{43} -9.65223 q^{44} -0.721613 q^{45} -14.5083 q^{46} +3.63132 q^{47} -6.35020 q^{48} +3.89535 q^{49} +10.3352 q^{50} -4.43890 q^{51} +2.48003 q^{52} -1.27811 q^{53} +4.26376 q^{54} +1.33183 q^{55} -3.35376 q^{56} +7.00937 q^{57} +14.5549 q^{58} -7.01952 q^{59} -1.91819 q^{60} -0.303475 q^{61} +2.90694 q^{62} +6.96062 q^{63} -11.2688 q^{64} -0.342197 q^{65} +18.6195 q^{66} +10.0382 q^{67} -4.87051 q^{68} +15.4930 q^{69} +2.39077 q^{70} -2.04769 q^{71} -2.14259 q^{72} +1.00986 q^{73} +22.5372 q^{74} -11.0366 q^{75} +7.69092 q^{76} -12.8467 q^{77} -4.78408 q^{78} +9.22395 q^{79} +0.961405 q^{80} -10.8794 q^{81} +20.3755 q^{82} -13.0472 q^{83} +18.5027 q^{84} +0.672038 q^{85} +7.28328 q^{86} -15.5427 q^{87} +3.95441 q^{88} -7.10671 q^{89} +1.52737 q^{90} +3.30081 q^{91} +16.9994 q^{92} -3.10423 q^{93} -7.68609 q^{94} -1.06120 q^{95} +18.0339 q^{96} -9.01630 q^{97} -8.24494 q^{98} -8.20725 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9}+O(q^{10}) \) 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9	\( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9} - 19 q^{10} - 42 q^{11} - 28 q^{12} + 101 q^{13} - 45 q^{14} - 15 q^{15} + 48 q^{16} - 83 q^{17} - 4 q^{18} - 18 q^{19} - 51 q^{20} - 50 q^{21} - 20 q^{22} - 64 q^{23} - 23 q^{24} + 46 q^{25} - 8 q^{26} - 37 q^{27} - 11 q^{28} - 117 q^{29} - 28 q^{30} - 10 q^{31} - 36 q^{32} - 20 q^{33} - 10 q^{34} - 53 q^{35} - 16 q^{36} - 27 q^{37} - 68 q^{38} - 13 q^{39} - 42 q^{40} - 60 q^{41} - 31 q^{42} - 16 q^{43} - 89 q^{44} - 56 q^{45} + 5 q^{46} - 23 q^{47} - 37 q^{48} + 48 q^{49} - 30 q^{50} - 68 q^{51} + 86 q^{52} - 189 q^{53} - 23 q^{54} + 3 q^{55} - 106 q^{56} - 25 q^{57} - 82 q^{59} + 6 q^{60} - 68 q^{61} - 57 q^{62} + 3 q^{63} - 2 q^{64} - 43 q^{65} - 40 q^{66} - 13 q^{67} - 138 q^{68} - 92 q^{69} + 18 q^{70} - 39 q^{71} - 20 q^{72} + 19 q^{73} - 88 q^{74} - 21 q^{75} - 53 q^{76} - 147 q^{77} - 10 q^{78} - 19 q^{79} - 104 q^{80} - 55 q^{81} + 27 q^{82} - 49 q^{83} - 59 q^{84} - 27 q^{85} - 99 q^{86} - 33 q^{87} - 41 q^{88} - 70 q^{89} - 49 q^{90} - q^{91} - 111 q^{92} - 84 q^{93} + 4 q^{94} - 82 q^{95} - 7 q^{96} + 25 q^{97} - 37 q^{98} - 41 q^{99}+O(q^{100}) \) 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9 - 19 * q^10 - 42 * q^11 - 28 * q^12 + 101 * q^13 - 45 * q^14 - 15 * q^15 + 48 * q^16 - 83 * q^17 - 4 * q^18 - 18 * q^19 - 51 * q^20 - 50 * q^21 - 20 * q^22 - 64 * q^23 - 23 * q^24 + 46 * q^25 - 8 * q^26 - 37 * q^27 - 11 * q^28 - 117 * q^29 - 28 * q^30 - 10 * q^31 - 36 * q^32 - 20 * q^33 - 10 * q^34 - 53 * q^35 - 16 * q^36 - 27 * q^37 - 68 * q^38 - 13 * q^39 - 42 * q^40 - 60 * q^41 - 31 * q^42 - 16 * q^43 - 89 * q^44 - 56 * q^45 + 5 * q^46 - 23 * q^47 - 37 * q^48 + 48 * q^49 - 30 * q^50 - 68 * q^51 + 86 * q^52 - 189 * q^53 - 23 * q^54 + 3 * q^55 - 106 * q^56 - 25 * q^57 - 82 * q^59 + 6 * q^60 - 68 * q^61 - 57 * q^62 + 3 * q^63 - 2 * q^64 - 43 * q^65 - 40 * q^66 - 13 * q^67 - 138 * q^68 - 92 * q^69 + 18 * q^70 - 39 * q^71 - 20 * q^72 + 19 * q^73 - 88 * q^74 - 21 * q^75 - 53 * q^76 - 147 * q^77 - 10 * q^78 - 19 * q^79 - 104 * q^80 - 55 * q^81 + 27 * q^82 - 49 * q^83 - 59 * q^84 - 27 * q^85 - 99 * q^86 - 33 * q^87 - 41 * q^88 - 70 * q^89 - 49 * q^90 - q^91 - 111 * q^92 - 84 * q^93 + 4 * q^94 - 82 * q^95 - 7 * q^96 + 25 * q^97 - 37 * q^98 - 41 * q^99

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