LMFDB - Embedded newform 619.2.a.a.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [619,2,Mod(1,619)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(619, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("619.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 619 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	619.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:	$4.94273988512$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	619.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.15106 q^{2} -1.36322 q^{3} -0.675056 q^{4} +1.59267 q^{5} -1.56915 q^{6} -0.851998 q^{7} -3.07916 q^{8} -1.14163 q^{9} +O(q^{10})$	\(q+1.15106 q^{2} -1.36322 q^{3} -0.675056 q^{4} +1.59267 q^{5} -1.56915 q^{6} -0.851998 q^{7} -3.07916 q^{8} -1.14163 q^{9} +1.83326 q^{10} +1.08090 q^{11} +0.920250 q^{12} -2.54334 q^{13} -0.980702 q^{14} -2.17116 q^{15} -2.19419 q^{16} -4.35075 q^{17} -1.31409 q^{18} +3.04936 q^{19} -1.07514 q^{20} +1.16146 q^{21} +1.24418 q^{22} -8.02788 q^{23} +4.19757 q^{24} -2.46341 q^{25} -2.92754 q^{26} +5.64595 q^{27} +0.575146 q^{28} -3.38559 q^{29} -2.49913 q^{30} -8.63415 q^{31} +3.63267 q^{32} -1.47350 q^{33} -5.00799 q^{34} -1.35695 q^{35} +0.770666 q^{36} +3.31978 q^{37} +3.51001 q^{38} +3.46713 q^{39} -4.90407 q^{40} -1.72398 q^{41} +1.33691 q^{42} +5.51725 q^{43} -0.729667 q^{44} -1.81824 q^{45} -9.24059 q^{46} -4.16926 q^{47} +2.99116 q^{48} -6.27410 q^{49} -2.83554 q^{50} +5.93103 q^{51} +1.71690 q^{52} +13.7689 q^{53} +6.49884 q^{54} +1.72151 q^{55} +2.62343 q^{56} -4.15695 q^{57} -3.89702 q^{58} +14.1133 q^{59} +1.46565 q^{60} -13.1783 q^{61} -9.93844 q^{62} +0.972667 q^{63} +8.56980 q^{64} -4.05069 q^{65} -1.69609 q^{66} +8.16779 q^{67} +2.93700 q^{68} +10.9438 q^{69} -1.56193 q^{70} -7.09081 q^{71} +3.51526 q^{72} -4.14533 q^{73} +3.82127 q^{74} +3.35817 q^{75} -2.05849 q^{76} -0.920923 q^{77} +3.99088 q^{78} -9.96423 q^{79} -3.49461 q^{80} -4.27178 q^{81} -1.98441 q^{82} -9.01183 q^{83} -0.784051 q^{84} -6.92930 q^{85} +6.35069 q^{86} +4.61530 q^{87} -3.32826 q^{88} +3.43030 q^{89} -2.09291 q^{90} +2.16692 q^{91} +5.41927 q^{92} +11.7702 q^{93} -4.79908 q^{94} +4.85662 q^{95} -4.95212 q^{96} +12.9453 q^{97} -7.22188 q^{98} -1.23399 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q - 9 q^{2} - 5 q^{3} + 15 q^{4} - 21 q^{5} - 6 q^{6} - 4 q^{7} - 21 q^{8} + 6 q^{9}+O(q^{10}) $ 21 * q - 9 * q^2 - 5 * q^3 + 15 * q^4 - 21 * q^5 - 6 * q^6 - 4 * q^7 - 21 * q^8 + 6 * q^9	\( 21 q - 9 q^{2} - 5 q^{3} + 15 q^{4} - 21 q^{5} - 6 q^{6} - 4 q^{7} - 21 q^{8} + 6 q^{9} + q^{10} - 27 q^{11} - 8 q^{12} - 11 q^{13} - 19 q^{14} - 10 q^{15} + 11 q^{16} - 14 q^{17} - 14 q^{18} - 15 q^{19} - 25 q^{20} - 42 q^{21} + 12 q^{22} - 14 q^{23} - 8 q^{24} + 16 q^{25} - 11 q^{26} - 5 q^{27} + q^{28} - 78 q^{29} + q^{30} - 8 q^{31} - 41 q^{32} - 6 q^{33} + 7 q^{34} - 3 q^{35} - q^{36} - 23 q^{37} + 21 q^{38} - 4 q^{39} + 12 q^{40} - 59 q^{41} + 39 q^{42} + 2 q^{43} - 50 q^{44} - 36 q^{45} - 15 q^{46} - 12 q^{47} + 10 q^{48} + 17 q^{49} - 23 q^{50} - 8 q^{51} + 18 q^{52} - 36 q^{53} - 4 q^{54} + 23 q^{55} - 28 q^{56} - 24 q^{57} + 46 q^{58} - 17 q^{59} + 8 q^{60} - 22 q^{61} + 42 q^{62} - 6 q^{63} + 49 q^{64} - 53 q^{65} + 29 q^{66} + 15 q^{67} - 16 q^{68} - 30 q^{69} + 44 q^{70} - 56 q^{71} + 12 q^{72} - 2 q^{73} - 12 q^{74} + 2 q^{75} - 4 q^{76} - 47 q^{77} + 36 q^{78} + 5 q^{79} + 15 q^{80} - 19 q^{81} + 47 q^{82} - q^{83} - 20 q^{84} - 29 q^{85} - 23 q^{86} + 44 q^{87} + 61 q^{88} - 12 q^{89} + 91 q^{90} + 5 q^{91} + 35 q^{92} - 15 q^{93} + 34 q^{94} - 17 q^{95} + 14 q^{96} + 21 q^{97} + 24 q^{98} - 38 q^{99}+O(q^{100}) \) 21 * q - 9 * q^2 - 5 * q^3 + 15 * q^4 - 21 * q^5 - 6 * q^6 - 4 * q^7 - 21 * q^8 + 6 * q^9 + q^10 - 27 * q^11 - 8 * q^12 - 11 * q^13 - 19 * q^14 - 10 * q^15 + 11 * q^16 - 14 * q^17 - 14 * q^18 - 15 * q^19 - 25 * q^20 - 42 * q^21 + 12 * q^22 - 14 * q^23 - 8 * q^24 + 16 * q^25 - 11 * q^26 - 5 * q^27 + q^28 - 78 * q^29 + q^30 - 8 * q^31 - 41 * q^32 - 6 * q^33 + 7 * q^34 - 3 * q^35 - q^36 - 23 * q^37 + 21 * q^38 - 4 * q^39 + 12 * q^40 - 59 * q^41 + 39 * q^42 + 2 * q^43 - 50 * q^44 - 36 * q^45 - 15 * q^46 - 12 * q^47 + 10 * q^48 + 17 * q^49 - 23 * q^50 - 8 * q^51 + 18 * q^52 - 36 * q^53 - 4 * q^54 + 23 * q^55 - 28 * q^56 - 24 * q^57 + 46 * q^58 - 17 * q^59 + 8 * q^60 - 22 * q^61 + 42 * q^62 - 6 * q^63 + 49 * q^64 - 53 * q^65 + 29 * q^66 + 15 * q^67 - 16 * q^68 - 30 * q^69 + 44 * q^70 - 56 * q^71 + 12 * q^72 - 2 * q^73 - 12 * q^74 + 2 * q^75 - 4 * q^76 - 47 * q^77 + 36 * q^78 + 5 * q^79 + 15 * q^80 - 19 * q^81 + 47 * q^82 - q^83 - 20 * q^84 - 29 * q^85 - 23 * q^86 + 44 * q^87 + 61 * q^88 - 12 * q^89 + 91 * q^90 + 5 * q^91 + 35 * q^92 - 15 * q^93 + 34 * q^94 - 17 * q^95 + 14 * q^96 + 21 * q^97 + 24 * q^98 - 38 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.15106	0.813924	0.406962	−	0.913445i	$-0.366588\pi$
$2$	1.15106	0.813924	0.406962	+	0.913445i	$0.366588\pi$
$3$	−1.36322	−0.787055	−0.393528	−	0.919313i	$-0.628745\pi$
$3$	−1.36322	−0.787055	−0.393528	+	0.919313i	$0.628745\pi$
$4$	−0.675056	−0.337528
$5$	1.59267	0.712263	0.356131	−	0.934436i	$-0.384096\pi$
$5$	1.59267	0.712263	0.356131	+	0.934436i	$0.384096\pi$
$6$	−1.56915	−0.640603
$7$	−0.851998	−0.322025	−0.161012	−	0.986952i	$-0.551476\pi$
$7$	−0.851998	−0.322025	−0.161012	+	0.986952i	$0.551476\pi$
$8$	−3.07916	−1.08865
$9$	−1.14163	−0.380544
$10$	1.83326	0.579727
$11$	1.08090	0.325903	0.162952	−	0.986634i	$-0.447899\pi$
$11$	1.08090	0.325903	0.162952	+	0.986634i	$0.447899\pi$
$12$	0.920250	0.265653
$13$	−2.54334	−0.705395	−0.352698	−	0.935737i	$-0.614736\pi$
$13$	−2.54334	−0.705395	−0.352698	+	0.935737i	$0.614736\pi$
$14$	−0.980702	−0.262104
$15$	−2.17116	−0.560590
$16$	−2.19419	−0.548547
$17$	−4.35075	−1.05521	−0.527606	−	0.849489i	$-0.676910\pi$
$17$	−4.35075	−1.05521	−0.527606	+	0.849489i	$0.676910\pi$
$18$	−1.31409	−0.309734
$19$	3.04936	0.699572	0.349786	−	0.936830i	$-0.386254\pi$
$19$	3.04936	0.699572	0.349786	+	0.936830i	$0.386254\pi$
$20$	−1.07514	−0.240409
$21$	1.16146	0.253451
$22$	1.24418	0.265260
$23$	−8.02788	−1.67393	−0.836965	−	0.547257i	$-0.815672\pi$
$23$	−8.02788	−1.67393	−0.836965	+	0.547257i	$0.815672\pi$
$24$	4.19757	0.856825
$25$	−2.46341	−0.492682
$26$	−2.92754	−0.574138
$27$	5.64595	1.08656
$28$	0.575146	0.108692
$29$	−3.38559	−0.628687	−0.314344	−	0.949309i	$-0.601784\pi$
$29$	−3.38559	−0.628687	−0.314344	+	0.949309i	$0.601784\pi$
$30$	−2.49913	−0.456278
$31$	−8.63415	−1.55074	−0.775369	−	0.631508i	$-0.782436\pi$
$31$	−8.63415	−1.55074	−0.775369	+	0.631508i	$0.782436\pi$
$32$	3.63267	0.642171
$33$	−1.47350	−0.256504
$34$	−5.00799	−0.858863
$35$	−1.35695	−0.229366
$36$	0.770666	0.128444
$37$	3.31978	0.545768	0.272884	−	0.962047i	$-0.412022\pi$
$37$	3.31978	0.545768	0.272884	+	0.962047i	$0.412022\pi$
$38$	3.51001	0.569398
$39$	3.46713	0.555185
$40$	−4.90407	−0.775402
$41$	−1.72398	−0.269240	−0.134620	−	0.990897i	$-0.542981\pi$
$41$	−1.72398	−0.269240	−0.134620	+	0.990897i	$0.542981\pi$
$42$	1.33691	0.206290
$43$	5.51725	0.841372	0.420686	−	0.907206i	$-0.361789\pi$
$43$	5.51725	0.841372	0.420686	+	0.907206i	$0.361789\pi$
$44$	−0.729667	−0.110001
$45$	−1.81824	−0.271047
$46$	−9.24059	−1.36245
$47$	−4.16926	−0.608149	−0.304075	−	0.952648i	$-0.598347\pi$
$47$	−4.16926	−0.608149	−0.304075	+	0.952648i	$0.598347\pi$
$48$	2.99116	0.431737
$49$	−6.27410	−0.896300
$50$	−2.83554	−0.401006
$51$	5.93103	0.830511
$52$	1.71690	0.238091
$53$	13.7689	1.89130	0.945651	−	0.325183i	$-0.105426\pi$
$53$	13.7689	1.89130	0.945651	+	0.325183i	$0.105426\pi$
$54$	6.49884	0.884381
$55$	1.72151	0.232129
$56$	2.62343	0.350571
$57$	−4.15695	−0.550602
$58$	−3.89702	−0.511704
$59$	14.1133	1.83740	0.918699	−	0.394959i	$-0.129241\pi$
$59$	14.1133	1.83740	0.918699	+	0.394959i	$0.129241\pi$
$60$	1.46565	0.189215
$61$	−13.1783	−1.68731	−0.843655	−	0.536886i	$-0.819601\pi$
$61$	−13.1783	−1.68731	−0.843655	+	0.536886i	$0.819601\pi$
$62$	−9.93844	−1.26218
$63$	0.972667	0.122545
$64$	8.56980	1.07122
$65$	−4.05069	−0.502427
$66$	−1.69609	−0.208775
$67$	8.16779	0.997854	0.498927	−	0.866644i	$-0.333728\pi$
$67$	8.16779	0.997854	0.498927	+	0.866644i	$0.333728\pi$
$68$	2.93700	0.356164
$69$	10.9438	1.31747
$70$	−1.56193	−0.186687
$71$	−7.09081	−0.841524	−0.420762	−	0.907171i	$-0.638237\pi$
$71$	−7.09081	−0.841524	−0.420762	+	0.907171i	$0.638237\pi$
$72$	3.51526	0.414278
$73$	−4.14533	−0.485174	−0.242587	−	0.970130i	$-0.577996\pi$
$73$	−4.14533	−0.485174	−0.242587	+	0.970130i	$0.577996\pi$
$74$	3.82127	0.444214
$75$	3.35817	0.387768
$76$	−2.05849	−0.236125
$77$	−0.920923	−0.104949
$78$	3.99088	0.451878
$79$	−9.96423	−1.12106	−0.560532	−	0.828133i	$-0.689403\pi$
$79$	−9.96423	−1.12106	−0.560532	+	0.828133i	$0.689403\pi$
$80$	−3.49461	−0.390709
$81$	−4.27178	−0.474642
$82$	−1.98441	−0.219141
$83$	−9.01183	−0.989177	−0.494589	−	0.869127i	$-0.664681\pi$
$83$	−9.01183	−0.989177	−0.494589	+	0.869127i	$0.664681\pi$
$84$	−0.784051	−0.0855469
$85$	−6.92930	−0.751588
$86$	6.35069	0.684813
$87$	4.61530	0.494812
$88$	−3.32826	−0.354793
$89$	3.43030	0.363611	0.181806	−	0.983334i	$-0.441806\pi$
$89$	3.43030	0.363611	0.181806	+	0.983334i	$0.441806\pi$
$90$	−2.09291	−0.220612
$91$	2.16692	0.227155
$92$	5.41927	0.564998
$93$	11.7702	1.22052
$94$	−4.79908	−0.494987
$95$	4.85662	0.498279
$96$	−4.95212	−0.505424
$97$	12.9453	1.31440	0.657199	−	0.753718i	$-0.271741\pi$
$97$	12.9453	1.31440	0.657199	+	0.753718i	$0.271741\pi$
$98$	−7.22188	−0.729520
$99$	−1.23399	−0.124020
$100$	1.66294	0.166294
$101$	−4.00851	−0.398862	−0.199431	−	0.979912i	$-0.563909\pi$
$101$	−4.00851	−0.398862	−0.199431	+	0.979912i	$0.563909\pi$
$102$	6.82699	0.675972
$103$	17.7717	1.75110	0.875549	−	0.483130i	$-0.160500\pi$
$103$	17.7717	1.75110	0.875549	+	0.483130i	$0.160500\pi$
$104$	7.83134	0.767926
$105$	1.84982	0.180524
$106$	15.8488	1.53938
$107$	9.77338	0.944828	0.472414	−	0.881377i	$-0.343383\pi$
$107$	9.77338	0.944828	0.472414	+	0.881377i	$0.343383\pi$
$108$	−3.81134	−0.366746
$109$	−0.344516	−0.0329986	−0.0164993	−	0.999864i	$-0.505252\pi$
$109$	−0.344516	−0.0329986	−0.0164993	+	0.999864i	$0.505252\pi$
$110$	1.98157	0.188935
$111$	−4.52559	−0.429550
$112$	1.86944	0.176646
$113$	6.33528	0.595973	0.297987	−	0.954570i	$-0.403685\pi$
$113$	6.33528	0.595973	0.297987	+	0.954570i	$0.403685\pi$
$114$	−4.78491	−0.448148
$115$	−12.7857	−1.19228
$116$	2.28546	0.212200
$117$	2.90356	0.268434
$118$	16.2453	1.49550
$119$	3.70683	0.339805
$120$	6.68533	0.610284
$121$	−9.83166	−0.893787
$122$	−15.1691	−1.37334
$123$	2.35016	0.211907
$124$	5.82853	0.523418
$125$	−11.8867	−1.06318
$126$	1.11960	0.0997420
$127$	14.2903	1.26806	0.634030	−	0.773309i	$-0.281400\pi$
$127$	14.2903	1.26806	0.634030	+	0.773309i	$0.281400\pi$
$128$	2.59904	0.229725
$129$	−7.52122	−0.662206
$130$	−4.66260	−0.408937
$131$	10.5933	0.925538	0.462769	−	0.886479i	$-0.346856\pi$
$131$	10.5933	0.925538	0.462769	+	0.886479i	$0.346856\pi$
$132$	0.994697	0.0865772
$133$	−2.59805	−0.225279
$134$	9.40163	0.812177
$135$	8.99213	0.773919
$136$	13.3966	1.14875
$137$	3.04025	0.259746	0.129873	−	0.991531i	$-0.458543\pi$
$137$	3.04025	0.259746	0.129873	+	0.991531i	$0.458543\pi$
$138$	12.5970	1.07232
$139$	15.6143	1.32439	0.662195	−	0.749331i	$-0.269625\pi$
$139$	15.6143	1.32439	0.662195	+	0.749331i	$0.269625\pi$
$140$	0.916017	0.0774175
$141$	5.68362	0.478647
$142$	−8.16196	−0.684937
$143$	−2.74909	−0.229891
$144$	2.50495	0.208746
$145$	−5.39211	−0.447791
$146$	−4.77153	−0.394895
$147$	8.55298	0.705438
$148$	−2.24104	−0.184212
$149$	−21.2825	−1.74353	−0.871767	−	0.489921i	$-0.837026\pi$
$149$	−21.2825	−1.74353	−0.871767	+	0.489921i	$0.837026\pi$
$150$	3.86546	0.315614
$151$	−4.10427	−0.334001	−0.167001	−	0.985957i	$-0.553408\pi$
$151$	−4.10427	−0.334001	−0.167001	+	0.985957i	$0.553408\pi$
$152$	−9.38946	−0.761586
$153$	4.96696	0.401555
$154$	−1.06004	−0.0854204
$155$	−13.7513	−1.10453
$156$	−2.34051	−0.187391
$157$	−21.5377	−1.71890	−0.859449	−	0.511221i	$-0.829193\pi$
$157$	−21.5377	−1.71890	−0.859449	+	0.511221i	$0.829193\pi$
$158$	−11.4695	−0.912460
$159$	−18.7700	−1.48856
$160$	5.78563	0.457394
$161$	6.83974	0.539047
$162$	−4.91709	−0.386323
$163$	−1.78732	−0.139994	−0.0699968	−	0.997547i	$-0.522299\pi$
$163$	−1.78732	−0.139994	−0.0699968	+	0.997547i	$0.522299\pi$
$164$	1.16378	0.0908762
$165$	−2.34680	−0.182698
$166$	−10.3732	−0.805115
$167$	19.6555	1.52099	0.760493	−	0.649346i	$-0.224957\pi$
$167$	19.6555	1.52099	0.760493	+	0.649346i	$0.224957\pi$
$168$	−3.57632	−0.275919
$169$	−6.53143	−0.502417
$170$	−7.97606	−0.611736
$171$	−3.48125	−0.266218
$172$	−3.72445	−0.283987
$173$	−19.1753	−1.45787	−0.728937	−	0.684581i	$-0.759985\pi$
$173$	−19.1753	−1.45787	−0.728937	+	0.684581i	$0.759985\pi$
$174$	5.31249	0.402739
$175$	2.09882	0.158656
$176$	−2.37169	−0.178773
$177$	−19.2396	−1.44613
$178$	3.94849	0.295952
$179$	−6.02849	−0.450590	−0.225295	−	0.974291i	$-0.572335\pi$
$179$	−6.02849	−0.450590	−0.225295	+	0.974291i	$0.572335\pi$
$180$	1.22741	0.0914860
$181$	3.13702	0.233173	0.116587	−	0.993181i	$-0.462805\pi$
$181$	3.13702	0.233173	0.116587	+	0.993181i	$0.462805\pi$
$182$	2.49426	0.184887
$183$	17.9649	1.32801
$184$	24.7191	1.82232
$185$	5.28730	0.388730
$186$	13.5483	0.993408
$187$	−4.70272	−0.343897
$188$	2.81449	0.205267
$189$	−4.81034	−0.349901
$190$	5.59027	0.405561
$191$	−12.8520	−0.929939	−0.464969	−	0.885327i	$-0.653935\pi$
$191$	−12.8520	−0.929939	−0.464969	+	0.885327i	$0.653935\pi$
$192$	−11.6825	−0.843113
$193$	−21.2128	−1.52693	−0.763466	−	0.645848i	$-0.776504\pi$
$193$	−21.2128	−1.52693	−0.763466	+	0.645848i	$0.776504\pi$
$194$	14.9009	1.06982
$195$	5.52199	0.395438
$196$	4.23537	0.302526
$197$	−25.0964	−1.78805	−0.894024	−	0.448019i	$-0.852130\pi$
$197$	−25.0964	−1.78805	−0.894024	+	0.448019i	$0.852130\pi$
$198$	−1.42040	−0.100943
$199$	−4.46333	−0.316397	−0.158199	−	0.987407i	$-0.550569\pi$
$199$	−4.46333	−0.316397	−0.158199	+	0.987407i	$0.550569\pi$
$200$	7.58522	0.536356
$201$	−11.1345	−0.785366
$202$	−4.61405	−0.324643
$203$	2.88451	0.202453
$204$	−4.00378	−0.280321
$205$	−2.74573	−0.191770
$206$	20.4563	1.42526
$207$	9.16489	0.637004
$208$	5.58056	0.386942
$209$	3.29605	0.227993
$210$	2.12926	0.146933
$211$	−16.2368	−1.11779	−0.558895	−	0.829239i	$-0.688774\pi$
$211$	−16.2368	−1.11779	−0.558895	+	0.829239i	$0.688774\pi$
$212$	−9.29477	−0.638368
$213$	9.66633	0.662326
$214$	11.2498	0.769018
$215$	8.78714	0.599278
$216$	−17.3848	−1.18288
$217$	7.35627	0.499376
$218$	−0.396559	−0.0268584
$219$	5.65099	0.381859
$220$	−1.16212	−0.0783499
$221$	11.0654	0.744342
$222$	−5.20923	−0.349621
$223$	−10.4101	−0.697109	−0.348554	−	0.937289i	$-0.613327\pi$
$223$	−10.4101	−0.697109	−0.348554	+	0.937289i	$0.613327\pi$
$224$	−3.09502	−0.206795
$225$	2.81231	0.187487
$226$	7.29230	0.485077
$227$	−13.2086	−0.876686	−0.438343	−	0.898808i	$-0.644434\pi$
$227$	−13.2086	−0.876686	−0.438343	+	0.898808i	$0.644434\pi$
$228$	2.80618	0.185843
$229$	6.09263	0.402612	0.201306	−	0.979528i	$-0.435481\pi$
$229$	6.09263	0.402612	0.201306	+	0.979528i	$0.435481\pi$
$230$	−14.7172	−0.970423
$231$	1.25542	0.0826006
$232$	10.4247	0.684418
$233$	−22.9685	−1.50471	−0.752357	−	0.658756i	$-0.771083\pi$
$233$	−22.9685	−1.50471	−0.752357	+	0.658756i	$0.771083\pi$
$234$	3.34217	0.218485
$235$	−6.64025	−0.433162
$236$	−9.52728	−0.620173
$237$	13.5834	0.882339
$238$	4.26679	0.276575
$239$	28.1939	1.82371	0.911856	−	0.410510i	$-0.134649\pi$
$239$	28.1939	1.82371	0.911856	+	0.410510i	$0.134649\pi$
$240$	4.76392	0.307510
$241$	11.6101	0.747870	0.373935	−	0.927455i	$-0.378008\pi$
$241$	11.6101	0.747870	0.373935	+	0.927455i	$0.378008\pi$
$242$	−11.3168	−0.727475
$243$	−11.1145	−0.712995
$244$	8.89610	0.569514
$245$	−9.99255	−0.638401
$246$	2.70518	0.172476
$247$	−7.75556	−0.493475
$248$	26.5859	1.68821
$249$	12.2851	0.778537
$250$	−13.6824	−0.865349
$251$	−13.4646	−0.849879	−0.424939	−	0.905222i	$-0.639705\pi$
$251$	−13.4646	−0.849879	−0.424939	+	0.905222i	$0.639705\pi$
$252$	−0.656605	−0.0413622
$253$	−8.67733	−0.545539
$254$	16.4490	1.03210
$255$	9.44616	0.591542
$256$	−14.1479	−0.884246
$257$	−21.7520	−1.35685	−0.678426	−	0.734669i	$-0.737338\pi$
$257$	−21.7520	−1.35685	−0.678426	+	0.734669i	$0.737338\pi$
$258$	−8.65739	−0.538985
$259$	−2.82844	−0.175751
$260$	2.73445	0.169583
$261$	3.86509	0.239243
$262$	12.1935	0.753317
$263$	−8.03681	−0.495571	−0.247786	−	0.968815i	$-0.579703\pi$
$263$	−8.03681	−0.495571	−0.247786	+	0.968815i	$0.579703\pi$
$264$	4.53714	0.279242
$265$	21.9293	1.34710
$266$	−2.99052	−0.183360
$267$	−4.67626	−0.286182
$268$	−5.51371	−0.336804
$269$	−2.91061	−0.177463	−0.0887315	−	0.996056i	$-0.528281\pi$
$269$	−2.91061	−0.177463	−0.0887315	+	0.996056i	$0.528281\pi$
$270$	10.3505	0.629911
$271$	−12.9628	−0.787433	−0.393716	−	0.919232i	$-0.628811\pi$
$271$	−12.9628	−0.787433	−0.393716	+	0.919232i	$0.628811\pi$
$272$	9.54637	0.578833
$273$	−2.95399	−0.178783
$274$	3.49952	0.211414
$275$	−2.66270	−0.160567
$276$	−7.38766	−0.444685
$277$	13.4731	0.809521	0.404761	−	0.914423i	$-0.367355\pi$
$277$	13.4731	0.809521	0.404761	+	0.914423i	$0.367355\pi$
$278$	17.9731	1.07795
$279$	9.85702	0.590124
$280$	4.17826	0.249699
$281$	1.62962	0.0972151	0.0486075	−	0.998818i	$-0.484522\pi$
$281$	1.62962	0.0972151	0.0486075	+	0.998818i	$0.484522\pi$
$282$	6.54220	0.389582
$283$	16.0932	0.956641	0.478320	−	0.878185i	$-0.341246\pi$
$283$	16.0932	0.956641	0.478320	+	0.878185i	$0.341246\pi$
$284$	4.78669	0.284038
$285$	−6.62064	−0.392173
$286$	−3.16438	−0.187113
$287$	1.46883	0.0867021
$288$	−4.14717	−0.244374
$289$	1.92905	0.113474
$290$	−6.20666	−0.364467
$291$	−17.6473	−1.03450
$292$	2.79833	0.163760
$293$	13.9880	0.817187	0.408594	−	0.912716i	$-0.366019\pi$
$293$	13.9880	0.817187	0.408594	+	0.912716i	$0.366019\pi$
$294$	9.84501	0.574173
$295$	22.4778	1.30871
$296$	−10.2221	−0.594148
$297$	6.10270	0.354115
$298$	−24.4975	−1.41910
$299$	20.4176	1.18078
$300$	−2.26695	−0.130883
$301$	−4.70068	−0.270943
$302$	−4.72427	−0.271851
$303$	5.46448	0.313926
$304$	−6.69087	−0.383748
$305$	−20.9887	−1.20181
$306$	5.71728	0.326835
$307$	9.39266	0.536068	0.268034	−	0.963410i	$-0.413626\pi$
$307$	9.39266	0.536068	0.268034	+	0.963410i	$0.413626\pi$
$308$	0.621675	0.0354232
$309$	−24.2267	−1.37821
$310$	−15.8286	−0.899006
$311$	−19.7628	−1.12065	−0.560324	−	0.828274i	$-0.689323\pi$
$311$	−19.7628	−1.12065	−0.560324	+	0.828274i	$0.689323\pi$
$312$	−10.6758	−0.604400
$313$	−16.1056	−0.910343	−0.455171	−	0.890404i	$-0.650422\pi$
$313$	−16.1056	−0.910343	−0.455171	+	0.890404i	$0.650422\pi$
$314$	−24.7913	−1.39905
$315$	1.54914	0.0872839
$316$	6.72642	0.378390
$317$	11.8481	0.665456	0.332728	−	0.943023i	$-0.392031\pi$
$317$	11.8481	0.665456	0.332728	+	0.943023i	$0.392031\pi$
$318$	−21.6055	−1.21157
$319$	−3.65947	−0.204891
$320$	13.6488	0.762993
$321$	−13.3233	−0.743632
$322$	7.87296	0.438743
$323$	−13.2670	−0.738197
$324$	2.88369	0.160205
$325$	6.26529	0.347536
$326$	−2.05732	−0.113944
$327$	0.469651	0.0259718
$328$	5.30840	0.293107
$329$	3.55220	0.195839
$330$	−2.70131	−0.148702
$331$	23.0289	1.26579	0.632893	−	0.774240i	$-0.281867\pi$
$331$	23.0289	1.26579	0.632893	+	0.774240i	$0.281867\pi$
$332$	6.08349	0.333875
$333$	−3.78997	−0.207689
$334$	22.6247	1.23797
$335$	13.0086	0.710734
$336$	−2.54846	−0.139030
$337$	4.08862	0.222721	0.111361	−	0.993780i	$-0.464479\pi$
$337$	4.08862	0.222721	0.111361	+	0.993780i	$0.464479\pi$
$338$	−7.51808	−0.408929
$339$	−8.63638	−0.469064
$340$	4.67767	0.253682
$341$	−9.33264	−0.505391
$342$	−4.00713	−0.216681
$343$	11.3095	0.610656
$344$	−16.9885	−0.915956
$345$	17.4298	0.938388
$346$	−22.0720	−1.18660
$347$	0.543123	0.0291564	0.0145782	−	0.999894i	$-0.495359\pi$
$347$	0.543123	0.0291564	0.0145782	+	0.999894i	$0.495359\pi$
$348$	−3.11558	−0.167013
$349$	16.4585	0.881001	0.440501	−	0.897752i	$-0.354801\pi$
$349$	16.4585	0.881001	0.440501	+	0.897752i	$0.354801\pi$
$350$	2.41587	0.129134
$351$	−14.3596	−0.766458
$352$	3.92654	0.209285
$353$	22.5325	1.19928	0.599642	−	0.800268i	$-0.295310\pi$
$353$	22.5325	1.19928	0.599642	+	0.800268i	$0.295310\pi$
$354$	−22.1459	−1.17704
$355$	−11.2933	−0.599386
$356$	−2.31565	−0.122729
$357$	−5.05323	−0.267445
$358$	−6.93916	−0.366746
$359$	−35.6840	−1.88333	−0.941664	−	0.336556i	$-0.890738\pi$
$359$	−35.6840	−1.88333	−0.941664	+	0.336556i	$0.890738\pi$
$360$	5.59864	0.295074
$361$	−9.70139	−0.510599
$362$	3.61091	0.189785
$363$	13.4027	0.703460
$364$	−1.46279	−0.0766711
$365$	−6.60213	−0.345571
$366$	20.6788	1.08090
$367$	28.5005	1.48772	0.743858	−	0.668338i	$-0.232994\pi$
$367$	28.5005	1.48772	0.743858	+	0.668338i	$0.232994\pi$
$368$	17.6147	0.918228
$369$	1.96815	0.102458
$370$	6.08601	0.316397
$371$	−11.7311	−0.609046
$372$	−7.94557	−0.411959
$373$	27.9614	1.44779	0.723894	−	0.689911i	$-0.242350\pi$
$373$	27.9614	1.44779	0.723894	+	0.689911i	$0.242350\pi$
$374$	−5.41313	−0.279906
$375$	16.2042	0.836783
$376$	12.8378	0.662059
$377$	8.61069	0.443473
$378$	−5.53700	−0.284793
$379$	−4.06657	−0.208886	−0.104443	−	0.994531i	$-0.533306\pi$
$379$	−4.06657	−0.208886	−0.104443	+	0.994531i	$0.533306\pi$
$380$	−3.27849	−0.168183
$381$	−19.4808	−0.998033
$382$	−14.7935	−0.756899
$383$	−24.6822	−1.26120	−0.630601	−	0.776107i	$-0.717191\pi$
$383$	−24.6822	−1.26120	−0.630601	+	0.776107i	$0.717191\pi$
$384$	−3.54306	−0.180806
$385$	−1.46672	−0.0747512
$386$	−24.4173	−1.24281
$387$	−6.29866	−0.320179
$388$	−8.73881	−0.443646
$389$	−24.5512	−1.24479	−0.622396	−	0.782702i	$-0.713841\pi$
$389$	−24.5512	−1.24479	−0.622396	+	0.782702i	$0.713841\pi$
$390$	6.35615	0.321856
$391$	34.9273	1.76635
$392$	19.3189	0.975753
$393$	−14.4409	−0.728450
$394$	−28.8876	−1.45533
$395$	−15.8697	−0.798492
$396$	0.833011	0.0418604
$397$	31.5852	1.58522	0.792609	−	0.609731i	$-0.208722\pi$
$397$	31.5852	1.58522	0.792609	+	0.609731i	$0.208722\pi$
$398$	−5.13757	−0.257523
$399$	3.54171	0.177307
$400$	5.40518	0.270259
$401$	−18.5745	−0.927567	−0.463784	−	0.885949i	$-0.653508\pi$
$401$	−18.5745	−0.927567	−0.463784	+	0.885949i	$0.653508\pi$
$402$	−12.8165	−0.639228
$403$	21.9596	1.09388
$404$	2.70597	0.134627
$405$	−6.80353	−0.338070
$406$	3.32025	0.164781
$407$	3.58834	0.177868
$408$	−18.2626	−0.904132
$409$	14.9730	0.740369	0.370184	−	0.928958i	$-0.379295\pi$
$409$	14.9730	0.740369	0.370184	+	0.928958i	$0.379295\pi$
$410$	−3.16050	−0.156086
$411$	−4.14453	−0.204435
$412$	−11.9969	−0.591045
$413$	−12.0245	−0.591687
$414$	10.5494	0.518472
$415$	−14.3529	−0.704554
$416$	−9.23910	−0.452984
$417$	−21.2858	−1.04237
$418$	3.79396	0.185569
$419$	4.70844	0.230022	0.115011	−	0.993364i	$-0.463310\pi$
$419$	4.70844	0.230022	0.115011	+	0.993364i	$0.463310\pi$
$420$	−1.24873	−0.0609319
$421$	22.3840	1.09093	0.545466	−	0.838133i	$-0.316353\pi$
$421$	22.3840	1.09093	0.545466	+	0.838133i	$0.316353\pi$
$422$	−18.6896	−0.909796
$423$	4.75976	0.231428
$424$	−42.3966	−2.05896
$425$	10.7177	0.519884
$426$	11.1265	0.539083
$427$	11.2279	0.543356
$428$	−6.59758	−0.318906
$429$	3.74762	0.180937
$430$	10.1145	0.487766
$431$	−26.7037	−1.28627	−0.643136	−	0.765752i	$-0.722367\pi$
$431$	−26.7037	−1.28627	−0.643136	+	0.765752i	$0.722367\pi$
$432$	−12.3883	−0.596031
$433$	26.7308	1.28460	0.642299	−	0.766454i	$-0.277981\pi$
$433$	26.7308	1.28460	0.642299	+	0.766454i	$0.277981\pi$
$434$	8.46753	0.406454
$435$	7.35063	0.352436
$436$	0.232568	0.0111380
$437$	−24.4799	−1.17103
$438$	6.50464	0.310804
$439$	−34.5230	−1.64769	−0.823847	−	0.566812i	$-0.808177\pi$
$439$	−34.5230	−1.64769	−0.823847	+	0.566812i	$0.808177\pi$
$440$	−5.30080	−0.252706
$441$	7.16271	0.341082
$442$	12.7370	0.605838
$443$	−26.5125	−1.25965	−0.629823	−	0.776739i	$-0.716873\pi$
$443$	−26.5125	−1.25965	−0.629823	+	0.776739i	$0.716873\pi$
$444$	3.05503	0.144985
$445$	5.46333	0.258987
$446$	−11.9826	−0.567393
$447$	29.0128	1.37226
$448$	−7.30145	−0.344961
$449$	16.0473	0.757317	0.378658	−	0.925536i	$-0.376386\pi$
$449$	16.0473	0.757317	0.378658	+	0.925536i	$0.376386\pi$
$450$	3.23714	0.152600
$451$	−1.86345	−0.0877463
$452$	−4.27667	−0.201158
$453$	5.59503	0.262877
$454$	−15.2039	−0.713555
$455$	3.45118	0.161794
$456$	12.7999	0.599410
$457$	−33.5050	−1.56730	−0.783649	−	0.621203i	$-0.786644\pi$
$457$	−33.5050	−1.56730	−0.783649	+	0.621203i	$0.786644\pi$
$458$	7.01300	0.327696
$459$	−24.5642	−1.14656
$460$	8.63110	0.402427
$461$	−10.2073	−0.475400	−0.237700	−	0.971339i	$-0.576394\pi$
$461$	−10.2073	−0.475400	−0.237700	+	0.971339i	$0.576394\pi$
$462$	1.44507	0.0672306
$463$	9.26172	0.430429	0.215214	−	0.976567i	$-0.430955\pi$
$463$	9.26172	0.430429	0.215214	+	0.976567i	$0.430955\pi$
$464$	7.42861	0.344864
$465$	18.7461	0.869329
$466$	−26.4381	−1.22472
$467$	20.0558	0.928072	0.464036	−	0.885816i	$-0.346401\pi$
$467$	20.0558	0.928072	0.464036	+	0.885816i	$0.346401\pi$
$468$	−1.96006	−0.0906040
$469$	−6.95893	−0.321334
$470$	−7.64334	−0.352561
$471$	29.3607	1.35287
$472$	−43.4571	−2.00027
$473$	5.96358	0.274206
$474$	15.6354	0.718157
$475$	−7.51183	−0.344666
$476$	−2.50232	−0.114694
$477$	−15.7190	−0.719724
$478$	32.4529	1.48436
$479$	17.6880	0.808183	0.404092	−	0.914718i	$-0.367588\pi$
$479$	17.6880	0.808183	0.404092	+	0.914718i	$0.367588\pi$
$480$	−7.88708	−0.359994
$481$	−8.44332	−0.384982
$482$	13.3639	0.608709
$483$	−9.32406	−0.424260
$484$	6.63692	0.301678
$485$	20.6176	0.936196
$486$	−12.7935	−0.580323
$487$	−11.1878	−0.506966	−0.253483	−	0.967340i	$-0.581576\pi$
$487$	−11.1878	−0.506966	−0.253483	+	0.967340i	$0.581576\pi$
$488$	40.5781	1.83688
$489$	2.43651	0.110183
$490$	−11.5021	−0.519610
$491$	−0.0519945	−0.00234648	−0.00117324	−	0.999999i	$-0.500373\pi$
$491$	−0.0519945	−0.00234648	−0.00117324	+	0.999999i	$0.500373\pi$
$492$	−1.58649	−0.0715246
$493$	14.7298	0.663399
$494$	−8.92713	−0.401651
$495$	−1.96533	−0.0883351
$496$	18.9449	0.850653
$497$	6.04135	0.270992
$498$	14.1409	0.633670
$499$	7.86927	0.352277	0.176139	−	0.984365i	$-0.443639\pi$
$499$	7.86927	0.352277	0.176139	+	0.984365i	$0.443639\pi$
$500$	8.02421	0.358854
$501$	−26.7947	−1.19710
$502$	−15.4986	−0.691736
$503$	29.3701	1.30955	0.654774	−	0.755825i	$-0.272764\pi$
$503$	29.3701	1.30955	0.654774	+	0.755825i	$0.272764\pi$
$504$	−2.99499	−0.133408
$505$	−6.38423	−0.284094
$506$	−9.98814	−0.444027
$507$	8.90377	0.395430
$508$	−9.64676	−0.428006
$509$	36.6163	1.62299	0.811495	−	0.584359i	$-0.198654\pi$
$509$	36.6163	1.62299	0.811495	+	0.584359i	$0.198654\pi$
$510$	10.8731	0.481470
$511$	3.53181	0.156238
$512$	−21.4832	−0.949434
$513$	17.2166	0.760130
$514$	−25.0379	−1.10437
$515$	28.3044	1.24724
$516$	5.07724	0.223513
$517$	−4.50655	−0.198198
$518$	−3.25571	−0.143048
$519$	26.1402	1.14743
$520$	12.4727	0.546965
$521$	−14.0906	−0.617320	−0.308660	−	0.951172i	$-0.599881\pi$
$521$	−14.0906	−0.617320	−0.308660	+	0.951172i	$0.599881\pi$
$522$	4.44896	0.194726
$523$	−29.3014	−1.28126	−0.640630	−	0.767850i	$-0.721327\pi$
$523$	−29.3014	−1.28126	−0.640630	+	0.767850i	$0.721327\pi$
$524$	−7.15105	−0.312395
$525$	−2.86115	−0.124871
$526$	−9.25087	−0.403357
$527$	37.5650	1.63636
$528$	3.23314	0.140704
$529$	41.4469	1.80204
$530$	25.2419	1.09644
$531$	−16.1122	−0.699210
$532$	1.75383	0.0760381
$533$	4.38467	0.189921
$534$	−5.38266	−0.232931
$535$	15.5657	0.672966
$536$	−25.1499	−1.08631
$537$	8.21815	0.354640
$538$	−3.35029	−0.144441
$539$	−6.78167	−0.292107
$540$	−6.07019	−0.261219
$541$	40.6826	1.74908	0.874541	−	0.484952i	$-0.161163\pi$
$541$	40.6826	1.74908	0.874541	+	0.484952i	$0.161163\pi$
$542$	−14.9210	−0.640910
$543$	−4.27645	−0.183520
$544$	−15.8048	−0.677627
$545$	−0.548699	−0.0235037
$546$	−3.40022	−0.145516
$547$	−23.4107	−1.00097	−0.500485	−	0.865745i	$-0.666845\pi$
$547$	−23.4107	−1.00097	−0.500485	+	0.865745i	$0.666845\pi$
$548$	−2.05234	−0.0876717
$549$	15.0448	0.642095
$550$	−3.06493	−0.130689
$551$	−10.3239	−0.439812
$552$	−33.6976	−1.43426
$553$	8.48950	0.361010
$554$	15.5084	0.658889
$555$	−7.20776	−0.305952
$556$	−10.5406	−0.447019
$557$	−2.04505	−0.0866515	−0.0433257	−	0.999061i	$-0.513795\pi$
$557$	−2.04505	−0.0866515	−0.0433257	+	0.999061i	$0.513795\pi$
$558$	11.3460	0.480316
$559$	−14.0322	−0.593500
$560$	2.97740	0.125818
$561$	6.41085	0.270666
$562$	1.87580	0.0791257
$563$	−14.0868	−0.593687	−0.296844	−	0.954926i	$-0.595934\pi$
$563$	−14.0868	−0.593687	−0.296844	+	0.954926i	$0.595934\pi$
$564$	−3.83676	−0.161557
$565$	10.0900	0.424489
$566$	18.5243	0.778633
$567$	3.63955	0.152847
$568$	21.8337	0.916122
$569$	−11.6173	−0.487024	−0.243512	−	0.969898i	$-0.578299\pi$
$569$	−11.6173	−0.487024	−0.243512	+	0.969898i	$0.578299\pi$
$570$	−7.62077	−0.319199
$571$	22.4366	0.938941	0.469471	−	0.882948i	$-0.344445\pi$
$571$	22.4366	0.938941	0.469471	+	0.882948i	$0.344445\pi$
$572$	1.85579	0.0775945
$573$	17.5201	0.731913
$574$	1.69071	0.0705689
$575$	19.7760	0.824715
$576$	−9.78355	−0.407648
$577$	9.26123	0.385550	0.192775	−	0.981243i	$-0.438251\pi$
$577$	9.26123	0.385550	0.192775	+	0.981243i	$0.438251\pi$
$578$	2.22046	0.0923589
$579$	28.9177	1.20178
$580$	3.63998	0.151142
$581$	7.67806	0.318540
$582$	−20.3131	−0.842007
$583$	14.8828	0.616382
$584$	12.7641	0.528183
$585$	4.62440	0.191195
$586$	16.1011	0.665128
$587$	−16.7208	−0.690142	−0.345071	−	0.938577i	$-0.612145\pi$
$587$	−16.7208	−0.690142	−0.345071	+	0.938577i	$0.612145\pi$
$588$	−5.77374	−0.238105
$589$	−26.3286	−1.08485
$590$	25.8734	1.06519
$591$	34.2120	1.40729
$592$	−7.28422	−0.299379
$593$	33.3731	1.37047	0.685234	−	0.728323i	$-0.259700\pi$
$593$	33.3731	1.37047	0.685234	+	0.728323i	$0.259700\pi$
$594$	7.02459	0.288222
$595$	5.90375	0.242030
$596$	14.3669	0.588492
$597$	6.08450	0.249022
$598$	23.5020	0.961067
$599$	−24.3588	−0.995274	−0.497637	−	0.867385i	$-0.665799\pi$
$599$	−24.3588	−0.995274	−0.497637	+	0.867385i	$0.665799\pi$
$600$	−10.3403	−0.422142
$601$	−16.3293	−0.666087	−0.333044	−	0.942911i	$-0.608076\pi$
$601$	−16.3293	−0.666087	−0.333044	+	0.942911i	$0.608076\pi$
$602$	−5.41077	−0.220527
$603$	−9.32460	−0.379727
$604$	2.77062	0.112735
$605$	−15.6586	−0.636611
$606$	6.28996	0.255512
$607$	8.99696	0.365175	0.182588	−	0.983190i	$-0.441553\pi$
$607$	8.99696	0.365175	0.182588	+	0.983190i	$0.441553\pi$
$608$	11.0773	0.449244
$609$	−3.93222	−0.159342
$610$	−24.1593	−0.978180
$611$	10.6038	0.428986
$612$	−3.35298	−0.135536
$613$	−28.0121	−1.13140	−0.565699	−	0.824612i	$-0.691394\pi$
$613$	−28.0121	−1.13140	−0.565699	+	0.824612i	$0.691394\pi$
$614$	10.8115	0.436318
$615$	3.74303	0.150933
$616$	2.83567	0.114252
$617$	−2.98288	−0.120086	−0.0600431	−	0.998196i	$-0.519124\pi$
$617$	−2.98288	−0.120086	−0.0600431	+	0.998196i	$0.519124\pi$
$618$	−27.8865	−1.12176
$619$	−1.00000	−0.0401934
$619$	−1.00000	−0.0401934
$620$	9.28292	0.372811
$621$	−45.3251	−1.81883
$622$	−22.7482	−0.912122
$623$	−2.92261	−0.117092
$624$	−7.60753	−0.304545
$625$	−6.61455	−0.264582
$626$	−18.5386	−0.740950
$627$	−4.49324	−0.179443
$628$	14.5392	0.580177
$629$	−14.4435	−0.575902
$630$	1.78315	0.0710425
$631$	19.8643	0.790787	0.395393	−	0.918512i	$-0.370608\pi$
$631$	19.8643	0.790787	0.395393	+	0.918512i	$0.370608\pi$
$632$	30.6814	1.22044
$633$	22.1344	0.879762
$634$	13.6379	0.541631
$635$	22.7597	0.903191
$636$	12.6708	0.502431
$637$	15.9572	0.632246
$638$	−4.21228	−0.166766
$639$	8.09509	0.320237
$640$	4.13940	0.163624
$641$	−24.9475	−0.985367	−0.492684	−	0.870209i	$-0.663984\pi$
$641$	−24.9475	−0.985367	−0.492684	+	0.870209i	$0.663984\pi$
$642$	−15.3359	−0.605260
$643$	8.94441	0.352733	0.176366	−	0.984325i	$-0.443566\pi$
$643$	8.94441	0.352733	0.176366	+	0.984325i	$0.443566\pi$
$644$	−4.61721	−0.181943
$645$	−11.9788	−0.471665
$646$	−15.2712	−0.600836
$647$	16.6359	0.654024	0.327012	−	0.945020i	$-0.393958\pi$
$647$	16.6359	0.654024	0.327012	+	0.945020i	$0.393958\pi$
$648$	13.1535	0.516718
$649$	15.2551	0.598814
$650$	7.21174	0.282868
$651$	−10.0282	−0.393037
$652$	1.20654	0.0472518
$653$	−28.3232	−1.10837	−0.554186	−	0.832393i	$-0.686970\pi$
$653$	−28.3232	−1.10837	−0.554186	+	0.832393i	$0.686970\pi$
$654$	0.540597	0.0211390
$655$	16.8715	0.659226
$656$	3.78273	0.147691
$657$	4.73244	0.184630
$658$	4.08880	0.159398
$659$	9.31752	0.362959	0.181480	−	0.983395i	$-0.441911\pi$
$659$	9.31752	0.362959	0.181480	+	0.983395i	$0.441911\pi$
$660$	1.58422	0.0616657
$661$	14.4740	0.562972	0.281486	−	0.959565i	$-0.409173\pi$
$661$	14.4740	0.562972	0.281486	+	0.959565i	$0.409173\pi$
$662$	26.5077	1.03025
$663$	−15.0846	−0.585838
$664$	27.7488	1.07686
$665$	−4.13783	−0.160458
$666$	−4.36249	−0.169043
$667$	27.1791	1.05238
$668$	−13.2686	−0.513376
$669$	14.1912	0.548663
$670$	14.9737	0.578483
$671$	−14.2444	−0.549900
$672$	4.21920	0.162759
$673$	−9.42102	−0.363154	−0.181577	−	0.983377i	$-0.558120\pi$
$673$	−9.42102	−0.363154	−0.181577	+	0.983377i	$0.558120\pi$
$674$	4.70626	0.181278
$675$	−13.9083	−0.535331
$676$	4.40908	0.169580
$677$	13.5484	0.520708	0.260354	−	0.965513i	$-0.416161\pi$
$677$	13.5484	0.520708	0.260354	+	0.965513i	$0.416161\pi$
$678$	−9.94101	−0.381782
$679$	−11.0294	−0.423268
$680$	21.3364	0.818214
$681$	18.0062	0.690000
$682$	−10.7424	−0.411350
$683$	−1.70765	−0.0653415	−0.0326708	−	0.999466i	$-0.510401\pi$
$683$	−1.70765	−0.0653415	−0.0326708	+	0.999466i	$0.510401\pi$
$684$	2.35004	0.0898560
$685$	4.84211	0.185008
$686$	13.0179	0.497027
$687$	−8.30559	−0.316878
$688$	−12.1059	−0.461532
$689$	−35.0190	−1.33412
$690$	20.0628	0.763776
$691$	−28.9677	−1.10198	−0.550991	−	0.834511i	$-0.685750\pi$
$691$	−28.9677	−1.10198	−0.550991	+	0.834511i	$0.685750\pi$
$692$	12.9444	0.492073
$693$	1.05135	0.0399377
$694$	0.625168	0.0237311
$695$	24.8684	0.943314
$696$	−14.2112	−0.538675
$697$	7.50061	0.284106
$698$	18.9447	0.717068
$699$	31.3111	1.18429
$700$	−1.41682	−0.0535508
$701$	−23.9253	−0.903647	−0.451824	−	0.892107i	$-0.649226\pi$
$701$	−23.9253	−0.903647	−0.451824	+	0.892107i	$0.649226\pi$
$702$	−16.5288	−0.623838
$703$	10.1232	0.381804
$704$	9.26308	0.349116
$705$	9.05212	0.340922
$706$	25.9363	0.976126
$707$	3.41524	0.128443
$708$	12.9878	0.488111
$709$	−10.6824	−0.401186	−0.200593	−	0.979675i	$-0.564287\pi$
$709$	−10.6824	−0.401186	−0.200593	+	0.979675i	$0.564287\pi$
$710$	−12.9993	−0.487855
$711$	11.3755	0.426614
$712$	−10.5624	−0.395844
$713$	69.3139	2.59583
$714$	−5.81658	−0.217680
$715$	−4.37839	−0.163742
$716$	4.06957	0.152087
$717$	−38.4345	−1.43536
$718$	−41.0744	−1.53288
$719$	−9.10690	−0.339630	−0.169815	−	0.985476i	$-0.554317\pi$
$719$	−9.10690	−0.339630	−0.169815	+	0.985476i	$0.554317\pi$
$720$	3.98956	0.148682
$721$	−15.1414	−0.563897
$722$	−11.1669	−0.415589
$723$	−15.8271	−0.588615
$724$	−2.11767	−0.0787025
$725$	8.34009	0.309743
$726$	15.4274	0.572563
$727$	−29.4304	−1.09151	−0.545756	−	0.837944i	$-0.683758\pi$
$727$	−29.4304	−1.09151	−0.545756	+	0.837944i	$0.683758\pi$
$728$	−6.67228	−0.247291
$729$	27.9668	1.03581
$730$	−7.59946	−0.281269
$731$	−24.0042	−0.887826
$732$	−12.1273	−0.448239
$733$	16.7223	0.617652	0.308826	−	0.951118i	$-0.400064\pi$
$733$	16.7223	0.617652	0.308826	+	0.951118i	$0.400064\pi$
$734$	32.8059	1.21089
$735$	13.6220	0.502457
$736$	−29.1626	−1.07495
$737$	8.82855	0.325204
$738$	2.26546	0.0833928
$739$	34.3353	1.26305	0.631523	−	0.775357i	$-0.282430\pi$
$739$	34.3353	1.26305	0.631523	+	0.775357i	$0.282430\pi$
$740$	−3.56923	−0.131207
$741$	10.5725	0.388392
$742$	−13.5032	−0.495717
$743$	−53.1137	−1.94855	−0.974277	−	0.225353i	$-0.927646\pi$
$743$	−53.1137	−1.94855	−0.974277	+	0.225353i	$0.927646\pi$
$744$	−36.2424	−1.32871
$745$	−33.8960	−1.24185
$746$	32.1853	1.17839
$747$	10.2882	0.376425
$748$	3.17460	0.116075
$749$	−8.32690	−0.304258
$750$	18.6521	0.681077
$751$	11.4910	0.419314	0.209657	−	0.977775i	$-0.432765\pi$
$751$	11.4910	0.419314	0.209657	+	0.977775i	$0.432765\pi$
$752$	9.14814	0.333598
$753$	18.3552	0.668901
$754$	9.91144	0.360953
$755$	−6.53674	−0.237896
$756$	3.24725	0.118101
$757$	12.8556	0.467246	0.233623	−	0.972327i	$-0.424942\pi$
$757$	12.8556	0.467246	0.233623	+	0.972327i	$0.424942\pi$
$758$	−4.68087	−0.170017
$759$	11.8291	0.429369
$760$	−14.9543	−0.542449
$761$	43.9066	1.59161	0.795807	−	0.605550i	$-0.207047\pi$
$761$	43.9066	1.59161	0.795807	+	0.605550i	$0.207047\pi$
$762$	−22.4236	−0.812323
$763$	0.293527	0.0106264
$764$	8.67583	0.313880
$765$	7.91071	0.286012
$766$	−28.4107	−1.02652
$767$	−35.8949	−1.29609
$768$	19.2868	0.695951
$769$	−14.6123	−0.526932	−0.263466	−	0.964669i	$-0.584866\pi$
$769$	−14.6123	−0.526932	−0.263466	+	0.964669i	$0.584866\pi$
$770$	−1.68829	−0.0608418
$771$	29.6528	1.06792
$772$	14.3198	0.515382
$773$	−43.5176	−1.56522	−0.782609	−	0.622513i	$-0.786112\pi$
$773$	−43.5176	−1.56522	−0.782609	+	0.622513i	$0.786112\pi$
$774$	−7.25015	−0.260601
$775$	21.2695	0.764021
$776$	−39.8606	−1.43091
$777$	3.85579	0.138326
$778$	−28.2599	−1.01317
$779$	−5.25704	−0.188353
$780$	−3.72765	−0.133471
$781$	−7.66445	−0.274255
$782$	40.2035	1.43768
$783$	−19.1149	−0.683109
$784$	13.7665	0.491662
$785$	−34.3025	−1.22431
$786$	−16.6224	−0.592902
$787$	35.0844	1.25062	0.625311	−	0.780376i	$-0.284972\pi$
$787$	35.0844	1.25062	0.625311	+	0.780376i	$0.284972\pi$
$788$	16.9415	0.603516
$789$	10.9559	0.390042
$790$	−18.2670	−0.649911
$791$	−5.39764	−0.191918
$792$	3.79964	0.135014
$793$	33.5169	1.19022
$794$	36.3566	1.29025
$795$	−29.8944	−1.06025
$796$	3.01300	0.106793
$797$	3.38936	0.120057	0.0600287	−	0.998197i	$-0.480881\pi$
$797$	3.38936	0.120057	0.0600287	+	0.998197i	$0.480881\pi$
$798$	4.07673	0.144315
$799$	18.1394	0.641727
$800$	−8.94875	−0.316386
$801$	−3.91614	−0.138370
$802$	−21.3804	−0.754969
$803$	−4.48068	−0.158120
$804$	7.51640	0.265083
$805$	10.8934	0.383943
$806$	25.2768	0.890338
$807$	3.96780	0.139673
$808$	12.3428	0.434219
$809$	−14.9922	−0.527096	−0.263548	−	0.964646i	$-0.584893\pi$
$809$	−14.9922	−0.527096	−0.263548	+	0.964646i	$0.584893\pi$
$810$	−7.83128	−0.275163
$811$	−9.61690	−0.337695	−0.168847	−	0.985642i	$-0.554005\pi$
$811$	−9.61690	−0.337695	−0.168847	+	0.985642i	$0.554005\pi$
$812$	−1.94721	−0.0683336
$813$	17.6711	0.619753
$814$	4.13041	0.144771
$815$	−2.84661	−0.0997122
$816$	−13.0138	−0.455574
$817$	16.8241	0.588600
$818$	17.2349	0.602604
$819$	−2.47382	−0.0864424
$820$	1.85352	0.0647277
$821$	18.5312	0.646744	0.323372	−	0.946272i	$-0.395183\pi$
$821$	18.5312	0.646744	0.323372	+	0.946272i	$0.395183\pi$
$822$	−4.77061	−0.166394
$823$	37.1617	1.29537	0.647687	−	0.761906i	$-0.275736\pi$
$823$	37.1617	1.29537	0.647687	+	0.761906i	$0.275736\pi$
$824$	−54.7218	−1.90633
$825$	3.62984	0.126375
$826$	−13.8410	−0.481588
$827$	−0.100148	−0.00348248	−0.00174124	−	0.999998i	$-0.500554\pi$
$827$	−0.100148	−0.00348248	−0.00174124	+	0.999998i	$0.500554\pi$
$828$	−6.18681	−0.215007
$829$	−26.1015	−0.906541	−0.453271	−	0.891373i	$-0.649743\pi$
$829$	−26.1015	−0.906541	−0.453271	+	0.891373i	$0.649743\pi$
$830$	−16.5210	−0.573453
$831$	−18.3668	−0.637138
$832$	−21.7959	−0.755637
$833$	27.2971	0.945787
$834$	−24.5012	−0.848409
$835$	31.3046	1.08334
$836$	−2.22502	−0.0769539
$837$	−48.7480	−1.68498
$838$	5.41971	0.187221
$839$	2.19371	0.0757352	0.0378676	−	0.999283i	$-0.487943\pi$
$839$	2.19371	0.0757352	0.0378676	+	0.999283i	$0.487943\pi$
$840$	−5.69588	−0.196527
$841$	−17.5378	−0.604752
$842$	25.7654	0.887935
$843$	−2.22153	−0.0765136
$844$	10.9608	0.377285
$845$	−10.4024	−0.357853
$846$	5.47878	0.188364
$847$	8.37655	0.287822
$848$	−30.2115	−1.03747
$849$	−21.9385	−0.752929
$850$	12.3367	0.423146
$851$	−26.6508	−0.913578
$852$	−6.52532	−0.223554
$853$	26.4161	0.904470	0.452235	−	0.891899i	$-0.350627\pi$
$853$	26.4161	0.904470	0.452235	+	0.891899i	$0.350627\pi$
$854$	12.9240	0.442250
$855$	−5.54447	−0.189617
$856$	−30.0938	−1.02858
$857$	7.62212	0.260367	0.130183	−	0.991490i	$-0.458443\pi$
$857$	7.62212	0.260367	0.130183	+	0.991490i	$0.458443\pi$
$858$	4.31374	0.147269
$859$	−47.7428	−1.62896	−0.814482	−	0.580189i	$-0.802979\pi$
$859$	−47.7428	−1.62896	−0.814482	+	0.580189i	$0.802979\pi$
$860$	−5.93181	−0.202273
$861$	−2.00233	−0.0682393
$862$	−30.7376	−1.04693
$863$	−48.1822	−1.64014	−0.820071	−	0.572261i	$-0.806066\pi$
$863$	−48.1822	−1.64014	−0.820071	+	0.572261i	$0.806066\pi$
$864$	20.5099	0.697760
$865$	−30.5399	−1.03839
$866$	30.7688	1.04557
$867$	−2.62972	−0.0893101
$868$	−4.96590	−0.168554
$869$	−10.7703	−0.365358
$870$	8.46104	0.286856
$871$	−20.7735	−0.703882
$872$	1.06082	0.0359238
$873$	−14.7788	−0.500186
$874$	−28.1779	−0.953132
$875$	10.1275	0.342371
$876$	−3.81474	−0.128888
$877$	14.4130	0.486694	0.243347	−	0.969939i	$-0.421755\pi$
$877$	14.4130	0.486694	0.243347	+	0.969939i	$0.421755\pi$
$878$	−39.7381	−1.34110
$879$	−19.0687	−0.643172
$880$	−3.77732	−0.127333
$881$	−28.6611	−0.965617	−0.482808	−	0.875726i	$-0.660383\pi$
$881$	−28.6611	−0.965617	−0.482808	+	0.875726i	$0.660383\pi$
$882$	8.24473	0.277614
$883$	39.7230	1.33679	0.668393	−	0.743808i	$-0.266983\pi$
$883$	39.7230	1.33679	0.668393	+	0.743808i	$0.266983\pi$
$884$	−7.46979	−0.251236
$885$	−30.6422	−1.03003
$886$	−30.5175	−1.02526
$887$	−39.3481	−1.32118	−0.660590	−	0.750747i	$-0.729694\pi$
$887$	−39.3481	−1.32118	−0.660590	+	0.750747i	$0.729694\pi$
$888$	13.9350	0.467628
$889$	−12.1753	−0.408347
$890$	6.28864	0.210796
$891$	−4.61736	−0.154687
$892$	7.02737	0.235294
$893$	−12.7136	−0.425444
$894$	33.3955	1.11691
$895$	−9.60138	−0.320939
$896$	−2.21437	−0.0739770
$897$	−27.8337	−0.929341
$898$	18.4714	0.616398
$899$	29.2316	0.974930
$900$	−1.89847	−0.0632822
$901$	−59.9050	−1.99573
$902$	−2.14494	−0.0714188
$903$	6.40806	0.213247
$904$	−19.5073	−0.648804
$905$	4.99624	0.166080
$906$	6.44022	0.213962
$907$	−19.0940	−0.634007	−0.317004	−	0.948424i	$-0.602677\pi$
$907$	−19.0940	−0.634007	−0.317004	+	0.948424i	$0.602677\pi$
$908$	8.91655	0.295906
$909$	4.57624	0.151784
$910$	3.97252	0.131688
$911$	−8.15769	−0.270276	−0.135138	−	0.990827i	$-0.543148\pi$
$911$	−8.15769	−0.270276	−0.135138	+	0.990827i	$0.543148\pi$
$912$	9.12113	0.302031
$913$	−9.74088	−0.322376
$914$	−38.5664	−1.27566
$915$	28.6122	0.945889
$916$	−4.11287	−0.135893
$917$	−9.02544	−0.298046
$918$	−28.2749	−0.933210
$919$	7.27092	0.239846	0.119923	−	0.992783i	$-0.461735\pi$
$919$	7.27092	0.239846	0.119923	+	0.992783i	$0.461735\pi$
$920$	39.3693	1.29797
$921$	−12.8043	−0.421915
$922$	−11.7492	−0.386939
$923$	18.0343	0.593607
$924$	−0.847479	−0.0278800
$925$	−8.17798	−0.268890
$926$	10.6608	0.350336
$927$	−20.2887	−0.666370
$928$	−12.2987	−0.403725
$929$	10.6022	0.347848	0.173924	−	0.984759i	$-0.444355\pi$
$929$	10.6022	0.347848	0.173924	+	0.984759i	$0.444355\pi$
$930$	21.5779	0.707567
$931$	−19.1320	−0.627026
$932$	15.5050	0.507883
$933$	26.9411	0.882012
$934$	23.0855	0.755380
$935$	−7.48987	−0.244945
$936$	−8.94050	−0.292229
$937$	4.72972	0.154513	0.0772567	−	0.997011i	$-0.475384\pi$
$937$	4.72972	0.154513	0.0772567	+	0.997011i	$0.475384\pi$
$938$	−8.01017	−0.261541
$939$	21.9555	0.716490
$940$	4.48254	0.146204
$941$	−7.43449	−0.242358	−0.121179	−	0.992631i	$-0.538667\pi$
$941$	−7.43449	−0.242358	−0.121179	+	0.992631i	$0.538667\pi$
$942$	33.7960	1.10113
$943$	13.8399	0.450689
$944$	−30.9673	−1.00790
$945$	−7.66127	−0.249221
$946$	6.86445	0.223183
$947$	−5.69941	−0.185206	−0.0926029	−	0.995703i	$-0.529519\pi$
$947$	−5.69941	−0.185206	−0.0926029	+	0.995703i	$0.529519\pi$
$948$	−9.16958	−0.297814
$949$	10.5430	0.342240
$950$	−8.64658	−0.280532
$951$	−16.1516	−0.523751
$952$	−11.4139	−0.369927
$953$	−24.2043	−0.784054	−0.392027	−	0.919954i	$-0.628226\pi$
$953$	−24.2043	−0.784054	−0.392027	+	0.919954i	$0.628226\pi$
$954$	−18.0935	−0.585800
$955$	−20.4690	−0.662360
$956$	−19.0325	−0.615554
$957$	4.98867	0.161261
$958$	20.3599	0.657800
$959$	−2.59029	−0.0836448
$960$	−18.6064	−0.600518
$961$	43.5485	1.40479
$962$	−9.71879	−0.313346
$963$	−11.1576	−0.359549
$964$	−7.83745	−0.252427
$965$	−33.7849	−1.08758
$966$	−10.7326	−0.345315
$967$	−41.6132	−1.33819	−0.669094	−	0.743177i	$-0.733318\pi$
$967$	−41.6132	−1.33819	−0.669094	+	0.743177i	$0.733318\pi$
$968$	30.2732	0.973018
$969$	18.0859	0.581002
$970$	23.7321	0.761992
$971$	42.4863	1.36345	0.681725	−	0.731608i	$-0.261230\pi$
$971$	42.4863	1.36345	0.681725	+	0.731608i	$0.261230\pi$
$972$	7.50290	0.240656
$973$	−13.3034	−0.426487
$974$	−12.8778	−0.412632
$975$	−8.54097	−0.273530
$976$	28.9157	0.925568
$977$	−40.5282	−1.29661	−0.648306	−	0.761380i	$-0.724522\pi$
$977$	−40.5282	−1.29661	−0.648306	+	0.761380i	$0.724522\pi$
$978$	2.80457	0.0896804
$979$	3.70781	0.118502
$980$	6.74554	0.215478
$981$	0.393310	0.0125574
$982$	−0.0598489	−0.00190985
$983$	−25.2576	−0.805591	−0.402796	−	0.915290i	$-0.631961\pi$
$983$	−25.2576	−0.805591	−0.402796	+	0.915290i	$0.631961\pi$
$984$	−7.23652	−0.230692
$985$	−39.9703	−1.27356
$986$	16.9550	0.539956
$987$	−4.84243	−0.154136
$988$	5.23544	0.166562
$989$	−44.2918	−1.40840
$990$	−2.26222	−0.0718981
$991$	−35.9068	−1.14062	−0.570308	−	0.821431i	$-0.693176\pi$
$991$	−35.9068	−1.14062	−0.570308	+	0.821431i	$0.693176\pi$
$992$	−31.3650	−0.995839
$993$	−31.3935	−0.996243
$994$	6.95397	0.220567
$995$	−7.10860	−0.225358
$996$	−8.29314	−0.262778
$997$	−22.4791	−0.711919	−0.355960	−	0.934501i	$-0.615846\pi$
$997$	−22.4791	−0.711919	−0.355960	+	0.934501i	$0.615846\pi$
$998$	9.05802	0.286727
$999$	18.7433	0.593012

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	619.2.a.a.1.16	✓	21
3.2	odd	2		5571.2.a.e.1.6		21
4.3	odd	2		9904.2.a.j.1.14		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
619.2.a.a.1.16	✓	21	1.1	even	1	trivial
5571.2.a.e.1.6		21	3.2	odd	2
9904.2.a.j.1.14		21	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 619 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	619.a (trivial)

\(f(q)\)	\(=\)	\(q+1.15106 q^{2} -1.36322 q^{3} -0.675056 q^{4} +1.59267 q^{5} -1.56915 q^{6} -0.851998 q^{7} -3.07916 q^{8} -1.14163 q^{9} +O(q^{10})\)	\(q+1.15106 q^{2} -1.36322 q^{3} -0.675056 q^{4} +1.59267 q^{5} -1.56915 q^{6} -0.851998 q^{7} -3.07916 q^{8} -1.14163 q^{9} +1.83326 q^{10} +1.08090 q^{11} +0.920250 q^{12} -2.54334 q^{13} -0.980702 q^{14} -2.17116 q^{15} -2.19419 q^{16} -4.35075 q^{17} -1.31409 q^{18} +3.04936 q^{19} -1.07514 q^{20} +1.16146 q^{21} +1.24418 q^{22} -8.02788 q^{23} +4.19757 q^{24} -2.46341 q^{25} -2.92754 q^{26} +5.64595 q^{27} +0.575146 q^{28} -3.38559 q^{29} -2.49913 q^{30} -8.63415 q^{31} +3.63267 q^{32} -1.47350 q^{33} -5.00799 q^{34} -1.35695 q^{35} +0.770666 q^{36} +3.31978 q^{37} +3.51001 q^{38} +3.46713 q^{39} -4.90407 q^{40} -1.72398 q^{41} +1.33691 q^{42} +5.51725 q^{43} -0.729667 q^{44} -1.81824 q^{45} -9.24059 q^{46} -4.16926 q^{47} +2.99116 q^{48} -6.27410 q^{49} -2.83554 q^{50} +5.93103 q^{51} +1.71690 q^{52} +13.7689 q^{53} +6.49884 q^{54} +1.72151 q^{55} +2.62343 q^{56} -4.15695 q^{57} -3.89702 q^{58} +14.1133 q^{59} +1.46565 q^{60} -13.1783 q^{61} -9.93844 q^{62} +0.972667 q^{63} +8.56980 q^{64} -4.05069 q^{65} -1.69609 q^{66} +8.16779 q^{67} +2.93700 q^{68} +10.9438 q^{69} -1.56193 q^{70} -7.09081 q^{71} +3.51526 q^{72} -4.14533 q^{73} +3.82127 q^{74} +3.35817 q^{75} -2.05849 q^{76} -0.920923 q^{77} +3.99088 q^{78} -9.96423 q^{79} -3.49461 q^{80} -4.27178 q^{81} -1.98441 q^{82} -9.01183 q^{83} -0.784051 q^{84} -6.92930 q^{85} +6.35069 q^{86} +4.61530 q^{87} -3.32826 q^{88} +3.43030 q^{89} -2.09291 q^{90} +2.16692 q^{91} +5.41927 q^{92} +11.7702 q^{93} -4.79908 q^{94} +4.85662 q^{95} -4.95212 q^{96} +12.9453 q^{97} -7.22188 q^{98} -1.23399 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - 9 q^{2} - 5 q^{3} + 15 q^{4} - 21 q^{5} - 6 q^{6} - 4 q^{7} - 21 q^{8} + 6 q^{9}+O(q^{10}) \) 21 * q - 9 * q^2 - 5 * q^3 + 15 * q^4 - 21 * q^5 - 6 * q^6 - 4 * q^7 - 21 * q^8 + 6 * q^9	\( 21 q - 9 q^{2} - 5 q^{3} + 15 q^{4} - 21 q^{5} - 6 q^{6} - 4 q^{7} - 21 q^{8} + 6 q^{9} + q^{10} - 27 q^{11} - 8 q^{12} - 11 q^{13} - 19 q^{14} - 10 q^{15} + 11 q^{16} - 14 q^{17} - 14 q^{18} - 15 q^{19} - 25 q^{20} - 42 q^{21} + 12 q^{22} - 14 q^{23} - 8 q^{24} + 16 q^{25} - 11 q^{26} - 5 q^{27} + q^{28} - 78 q^{29} + q^{30} - 8 q^{31} - 41 q^{32} - 6 q^{33} + 7 q^{34} - 3 q^{35} - q^{36} - 23 q^{37} + 21 q^{38} - 4 q^{39} + 12 q^{40} - 59 q^{41} + 39 q^{42} + 2 q^{43} - 50 q^{44} - 36 q^{45} - 15 q^{46} - 12 q^{47} + 10 q^{48} + 17 q^{49} - 23 q^{50} - 8 q^{51} + 18 q^{52} - 36 q^{53} - 4 q^{54} + 23 q^{55} - 28 q^{56} - 24 q^{57} + 46 q^{58} - 17 q^{59} + 8 q^{60} - 22 q^{61} + 42 q^{62} - 6 q^{63} + 49 q^{64} - 53 q^{65} + 29 q^{66} + 15 q^{67} - 16 q^{68} - 30 q^{69} + 44 q^{70} - 56 q^{71} + 12 q^{72} - 2 q^{73} - 12 q^{74} + 2 q^{75} - 4 q^{76} - 47 q^{77} + 36 q^{78} + 5 q^{79} + 15 q^{80} - 19 q^{81} + 47 q^{82} - q^{83} - 20 q^{84} - 29 q^{85} - 23 q^{86} + 44 q^{87} + 61 q^{88} - 12 q^{89} + 91 q^{90} + 5 q^{91} + 35 q^{92} - 15 q^{93} + 34 q^{94} - 17 q^{95} + 14 q^{96} + 21 q^{97} + 24 q^{98} - 38 q^{99}+O(q^{100}) \) 21 * q - 9 * q^2 - 5 * q^3 + 15 * q^4 - 21 * q^5 - 6 * q^6 - 4 * q^7 - 21 * q^8 + 6 * q^9 + q^10 - 27 * q^11 - 8 * q^12 - 11 * q^13 - 19 * q^14 - 10 * q^15 + 11 * q^16 - 14 * q^17 - 14 * q^18 - 15 * q^19 - 25 * q^20 - 42 * q^21 + 12 * q^22 - 14 * q^23 - 8 * q^24 + 16 * q^25 - 11 * q^26 - 5 * q^27 + q^28 - 78 * q^29 + q^30 - 8 * q^31 - 41 * q^32 - 6 * q^33 + 7 * q^34 - 3 * q^35 - q^36 - 23 * q^37 + 21 * q^38 - 4 * q^39 + 12 * q^40 - 59 * q^41 + 39 * q^42 + 2 * q^43 - 50 * q^44 - 36 * q^45 - 15 * q^46 - 12 * q^47 + 10 * q^48 + 17 * q^49 - 23 * q^50 - 8 * q^51 + 18 * q^52 - 36 * q^53 - 4 * q^54 + 23 * q^55 - 28 * q^56 - 24 * q^57 + 46 * q^58 - 17 * q^59 + 8 * q^60 - 22 * q^61 + 42 * q^62 - 6 * q^63 + 49 * q^64 - 53 * q^65 + 29 * q^66 + 15 * q^67 - 16 * q^68 - 30 * q^69 + 44 * q^70 - 56 * q^71 + 12 * q^72 - 2 * q^73 - 12 * q^74 + 2 * q^75 - 4 * q^76 - 47 * q^77 + 36 * q^78 + 5 * q^79 + 15 * q^80 - 19 * q^81 + 47 * q^82 - q^83 - 20 * q^84 - 29 * q^85 - 23 * q^86 + 44 * q^87 + 61 * q^88 - 12 * q^89 + 91 * q^90 + 5 * q^91 + 35 * q^92 - 15 * q^93 + 34 * q^94 - 17 * q^95 + 14 * q^96 + 21 * q^97 + 24 * q^98 - 38 * q^99

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