LMFDB - Embedded newform 6019.2.a.c.1.9

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:	$108$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
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)

$f(q)$	$=$	$q-2.56322 q^{2} -2.39331 q^{3} +4.57009 q^{4} +1.98047 q^{5} +6.13457 q^{6} +1.46442 q^{7} -6.58772 q^{8} +2.72791 q^{9} +O(q^{10})$	\(q-2.56322 q^{2} -2.39331 q^{3} +4.57009 q^{4} +1.98047 q^{5} +6.13457 q^{6} +1.46442 q^{7} -6.58772 q^{8} +2.72791 q^{9} -5.07639 q^{10} -1.05309 q^{11} -10.9376 q^{12} -1.00000 q^{13} -3.75364 q^{14} -4.73988 q^{15} +7.74558 q^{16} -4.51135 q^{17} -6.99224 q^{18} -0.322065 q^{19} +9.05095 q^{20} -3.50481 q^{21} +2.69929 q^{22} -0.436369 q^{23} +15.7664 q^{24} -1.07772 q^{25} +2.56322 q^{26} +0.651184 q^{27} +6.69255 q^{28} +1.24674 q^{29} +12.1494 q^{30} -6.86552 q^{31} -6.67818 q^{32} +2.52036 q^{33} +11.5636 q^{34} +2.90025 q^{35} +12.4668 q^{36} +8.21223 q^{37} +0.825524 q^{38} +2.39331 q^{39} -13.0468 q^{40} -7.30907 q^{41} +8.98361 q^{42} +10.9795 q^{43} -4.81270 q^{44} +5.40256 q^{45} +1.11851 q^{46} +2.66041 q^{47} -18.5375 q^{48} -4.85546 q^{49} +2.76244 q^{50} +10.7970 q^{51} -4.57009 q^{52} +6.07930 q^{53} -1.66913 q^{54} -2.08561 q^{55} -9.64721 q^{56} +0.770801 q^{57} -3.19566 q^{58} +7.73857 q^{59} -21.6617 q^{60} +9.88157 q^{61} +17.5978 q^{62} +3.99482 q^{63} +1.62649 q^{64} -1.98047 q^{65} -6.46023 q^{66} +11.0843 q^{67} -20.6173 q^{68} +1.04436 q^{69} -7.43398 q^{70} -12.4574 q^{71} -17.9707 q^{72} -3.30899 q^{73} -21.0497 q^{74} +2.57932 q^{75} -1.47187 q^{76} -1.54216 q^{77} -6.13457 q^{78} -0.210549 q^{79} +15.3399 q^{80} -9.74223 q^{81} +18.7348 q^{82} -9.57254 q^{83} -16.0173 q^{84} -8.93460 q^{85} -28.1429 q^{86} -2.98383 q^{87} +6.93743 q^{88} +18.4974 q^{89} -13.8480 q^{90} -1.46442 q^{91} -1.99425 q^{92} +16.4313 q^{93} -6.81922 q^{94} -0.637842 q^{95} +15.9829 q^{96} -1.36389 q^{97} +12.4456 q^{98} -2.87273 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9}+O(q^{10}) $ 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9	\( 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9} - q^{10} - 45 q^{11} - 6 q^{12} - 108 q^{13} - 31 q^{14} - 39 q^{15} + 73 q^{16} + 21 q^{17} - 35 q^{18} - 19 q^{19} - 79 q^{20} - 72 q^{21} - 26 q^{23} - 23 q^{24} + 92 q^{25} + 11 q^{26} + 7 q^{27} - 21 q^{28} - 94 q^{29} - 24 q^{30} - 36 q^{31} - 77 q^{32} - 32 q^{33} - 58 q^{34} - 10 q^{35} + 17 q^{36} - 54 q^{37} - 12 q^{38} - q^{39} - 4 q^{40} - 68 q^{41} - 11 q^{42} - 32 q^{43} - 151 q^{44} - 121 q^{45} - 33 q^{46} - 51 q^{47} - 27 q^{48} + 72 q^{49} - 45 q^{50} - 24 q^{51} - 95 q^{52} - 81 q^{53} - 29 q^{54} + 4 q^{55} - 68 q^{56} - 45 q^{57} - 30 q^{58} - 94 q^{59} - 108 q^{60} - 39 q^{61} - 9 q^{62} - 52 q^{63} + 31 q^{64} + 40 q^{65} - 40 q^{66} - 47 q^{67} + 24 q^{68} - 60 q^{69} - 66 q^{70} - 86 q^{71} - 91 q^{72} - 51 q^{73} - 110 q^{74} - 7 q^{75} - 51 q^{76} - 96 q^{77} + 10 q^{78} - 18 q^{79} - 136 q^{80} - 24 q^{81} - 33 q^{82} - 77 q^{83} - 113 q^{84} - 95 q^{85} - 137 q^{86} + 23 q^{87} + 19 q^{88} - 112 q^{89} - 19 q^{90} + 8 q^{91} - 111 q^{92} - 124 q^{93} - 20 q^{94} - 73 q^{95} - 77 q^{96} - 41 q^{97} - 80 q^{98} - 154 q^{99}+O(q^{100}) \) 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9 - q^10 - 45 * q^11 - 6 * q^12 - 108 * q^13 - 31 * q^14 - 39 * q^15 + 73 * q^16 + 21 * q^17 - 35 * q^18 - 19 * q^19 - 79 * q^20 - 72 * q^21 - 26 * q^23 - 23 * q^24 + 92 * q^25 + 11 * q^26 + 7 * q^27 - 21 * q^28 - 94 * q^29 - 24 * q^30 - 36 * q^31 - 77 * q^32 - 32 * q^33 - 58 * q^34 - 10 * q^35 + 17 * q^36 - 54 * q^37 - 12 * q^38 - q^39 - 4 * q^40 - 68 * q^41 - 11 * q^42 - 32 * q^43 - 151 * q^44 - 121 * q^45 - 33 * q^46 - 51 * q^47 - 27 * q^48 + 72 * q^49 - 45 * q^50 - 24 * q^51 - 95 * q^52 - 81 * q^53 - 29 * q^54 + 4 * q^55 - 68 * q^56 - 45 * q^57 - 30 * q^58 - 94 * q^59 - 108 * q^60 - 39 * q^61 - 9 * q^62 - 52 * q^63 + 31 * q^64 + 40 * q^65 - 40 * q^66 - 47 * q^67 + 24 * q^68 - 60 * q^69 - 66 * q^70 - 86 * q^71 - 91 * q^72 - 51 * q^73 - 110 * q^74 - 7 * q^75 - 51 * q^76 - 96 * q^77 + 10 * q^78 - 18 * q^79 - 136 * q^80 - 24 * q^81 - 33 * q^82 - 77 * q^83 - 113 * q^84 - 95 * q^85 - 137 * q^86 + 23 * q^87 + 19 * q^88 - 112 * q^89 - 19 * q^90 + 8 * q^91 - 111 * q^92 - 124 * q^93 - 20 * q^94 - 73 * q^95 - 77 * q^96 - 41 * q^97 - 80 * q^98 - 154 * 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 $

$2$	−2.56322	−1.81247	−0.906235	−	0.422774i	$-0.861056\pi$
$2$	−2.56322	−1.81247	−0.906235	+	0.422774i	$0.861056\pi$
$3$	−2.39331	−1.38178	−0.690888	−	0.722962i	$-0.742780\pi$
$3$	−2.39331	−1.38178	−0.690888	+	0.722962i	$0.742780\pi$
$4$	4.57009	2.28505
$5$	1.98047	0.885695	0.442847	−	0.896597i	$-0.353968\pi$
$5$	1.98047	0.885695	0.442847	+	0.896597i	$0.353968\pi$
$6$	6.13457	2.50443
$7$	1.46442	0.553500	0.276750	−	0.960942i	$-0.410743\pi$
$7$	1.46442	0.553500	0.276750	+	0.960942i	$0.410743\pi$
$8$	−6.58772	−2.32911
$9$	2.72791	0.909305
$10$	−5.07639	−1.60530
$11$	−1.05309	−0.317517	−0.158759	−	0.987317i	$-0.550749\pi$
$11$	−1.05309	−0.317517	−0.158759	+	0.987317i	$0.550749\pi$
$12$	−10.9376	−3.15742
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−3.75364	−1.00320
$15$	−4.73988	−1.22383
$16$	7.74558	1.93639
$17$	−4.51135	−1.09416	−0.547081	−	0.837080i	$-0.684261\pi$
$17$	−4.51135	−1.09416	−0.547081	+	0.837080i	$0.684261\pi$
$18$	−6.99224	−1.64809
$19$	−0.322065	−0.0738868	−0.0369434	−	0.999317i	$-0.511762\pi$
$19$	−0.322065	−0.0738868	−0.0369434	+	0.999317i	$0.511762\pi$
$20$	9.05095	2.02385
$21$	−3.50481	−0.764813
$22$	2.69929	0.575491
$23$	−0.436369	−0.0909892	−0.0454946	−	0.998965i	$-0.514486\pi$
$23$	−0.436369	−0.0909892	−0.0454946	+	0.998965i	$0.514486\pi$
$24$	15.7664	3.21831
$25$	−1.07772	−0.215545
$26$	2.56322	0.502689
$27$	0.651184	0.125320
$28$	6.69255	1.26477
$29$	1.24674	0.231514	0.115757	−	0.993278i	$-0.463071\pi$
$29$	1.24674	0.231514	0.115757	+	0.993278i	$0.463071\pi$
$30$	12.1494	2.21816
$31$	−6.86552	−1.23308	−0.616542	−	0.787322i	$-0.711467\pi$
$31$	−6.86552	−1.23308	−0.616542	+	0.787322i	$0.711467\pi$
$32$	−6.67818	−1.18055
$33$	2.52036	0.438738
$34$	11.5636	1.98314
$35$	2.90025	0.490232
$36$	12.4668	2.07780
$37$	8.21223	1.35008	0.675041	−	0.737780i	$-0.264126\pi$
$37$	8.21223	1.35008	0.675041	+	0.737780i	$0.264126\pi$
$38$	0.825524	0.133918
$39$	2.39331	0.383236
$40$	−13.0468	−2.06288
$41$	−7.30907	−1.14149	−0.570743	−	0.821129i	$-0.693345\pi$
$41$	−7.30907	−1.14149	−0.570743	+	0.821129i	$0.693345\pi$
$42$	8.98361	1.38620
$43$	10.9795	1.67436	0.837180	−	0.546928i	$-0.184203\pi$
$43$	10.9795	1.67436	0.837180	+	0.546928i	$0.184203\pi$
$44$	−4.81270	−0.725542
$45$	5.40256	0.805367
$46$	1.11851	0.164915
$47$	2.66041	0.388061	0.194031	−	0.980995i	$-0.437844\pi$
$47$	2.66041	0.388061	0.194031	+	0.980995i	$0.437844\pi$
$48$	−18.5375	−2.67566
$49$	−4.85546	−0.693638
$50$	2.76244	0.390668
$51$	10.7970	1.51189
$52$	−4.57009	−0.633758
$53$	6.07930	0.835055	0.417528	−	0.908664i	$-0.362897\pi$
$53$	6.07930	0.835055	0.417528	+	0.908664i	$0.362897\pi$
$54$	−1.66913	−0.227140
$55$	−2.08561	−0.281224
$56$	−9.64721	−1.28916
$57$	0.770801	0.102095
$58$	−3.19566	−0.419611
$59$	7.73857	1.00748	0.503738	−	0.863856i	$-0.331958\pi$
$59$	7.73857	1.00748	0.503738	+	0.863856i	$0.331958\pi$
$60$	−21.6617	−2.79651
$61$	9.88157	1.26521	0.632603	−	0.774476i	$-0.281987\pi$
$61$	9.88157	1.26521	0.632603	+	0.774476i	$0.281987\pi$
$62$	17.5978	2.23493
$63$	3.99482	0.503300
$64$	1.62649	0.203311
$65$	−1.98047	−0.245648
$66$	−6.46023	−0.795199
$67$	11.0843	1.35417	0.677084	−	0.735906i	$-0.263243\pi$
$67$	11.0843	1.35417	0.677084	+	0.735906i	$0.263243\pi$
$68$	−20.6173	−2.50021
$69$	1.04436	0.125727
$70$	−7.43398	−0.888531
$71$	−12.4574	−1.47842	−0.739212	−	0.673473i	$-0.764802\pi$
$71$	−12.4574	−1.47842	−0.739212	+	0.673473i	$0.764802\pi$
$72$	−17.9707	−2.11787
$73$	−3.30899	−0.387288	−0.193644	−	0.981072i	$-0.562031\pi$
$73$	−3.30899	−0.387288	−0.193644	+	0.981072i	$0.562031\pi$
$74$	−21.0497	−2.44698
$75$	2.57932	0.297834
$76$	−1.47187	−0.168835
$77$	−1.54216	−0.175746
$78$	−6.13457	−0.694603
$79$	−0.210549	−0.0236886	−0.0118443	−	0.999930i	$-0.503770\pi$
$79$	−0.210549	−0.0236886	−0.0118443	+	0.999930i	$0.503770\pi$
$80$	15.3399	1.71505
$81$	−9.74223	−1.08247
$82$	18.7348	2.06891
$83$	−9.57254	−1.05072	−0.525361	−	0.850879i	$-0.676070\pi$
$83$	−9.57254	−1.05072	−0.525361	+	0.850879i	$0.676070\pi$
$84$	−16.0173	−1.74763
$85$	−8.93460	−0.969094
$86$	−28.1429	−3.03473
$87$	−2.98383	−0.319900
$88$	6.93743	0.739533
$89$	18.4974	1.96072	0.980359	−	0.197220i	$-0.0631914\pi$
$89$	18.4974	1.96072	0.980359	+	0.197220i	$0.0631914\pi$
$90$	−13.8480	−1.45970
$91$	−1.46442	−0.153513
$92$	−1.99425	−0.207915
$93$	16.4313	1.70385
$94$	−6.81922	−0.703349
$95$	−0.637842	−0.0654412
$96$	15.9829	1.63125
$97$	−1.36389	−0.138482	−0.0692410	−	0.997600i	$-0.522058\pi$
$97$	−1.36389	−0.138482	−0.0692410	+	0.997600i	$0.522058\pi$
$98$	12.4456	1.25720
$99$	−2.87273	−0.288720
$100$	−4.92529	−0.492529
$101$	2.37426	0.236248	0.118124	−	0.992999i	$-0.462312\pi$
$101$	2.37426	0.236248	0.118124	+	0.992999i	$0.462312\pi$
$102$	−27.6752	−2.74025
$103$	−4.07504	−0.401525	−0.200763	−	0.979640i	$-0.564342\pi$
$103$	−4.07504	−0.401525	−0.200763	+	0.979640i	$0.564342\pi$
$104$	6.58772	0.645979
$105$	−6.94119	−0.677391
$106$	−15.5826	−1.51351
$107$	−9.50627	−0.919006	−0.459503	−	0.888176i	$-0.651972\pi$
$107$	−9.50627	−0.919006	−0.459503	+	0.888176i	$0.651972\pi$
$108$	2.97597	0.286363
$109$	−1.55811	−0.149239	−0.0746197	−	0.997212i	$-0.523774\pi$
$109$	−1.55811	−0.149239	−0.0746197	+	0.997212i	$0.523774\pi$
$110$	5.34588	0.509709
$111$	−19.6544	−1.86551
$112$	11.3428	1.07179
$113$	−16.1939	−1.52340	−0.761699	−	0.647931i	$-0.775634\pi$
$113$	−16.1939	−1.52340	−0.761699	+	0.647931i	$0.775634\pi$
$114$	−1.97573	−0.185044
$115$	−0.864218	−0.0805887
$116$	5.69771	0.529019
$117$	−2.72791	−0.252196
$118$	−19.8357	−1.82602
$119$	−6.60652	−0.605619
$120$	31.2250	2.85044
$121$	−9.89101	−0.899183
$122$	−25.3286	−2.29315
$123$	17.4928	1.57728
$124$	−31.3761	−2.81765
$125$	−12.0368	−1.07660
$126$	−10.2396	−0.912217
$127$	11.7252	1.04044	0.520221	−	0.854032i	$-0.325850\pi$
$127$	11.7252	1.04044	0.520221	+	0.854032i	$0.325850\pi$
$128$	9.18731	0.812052
$129$	−26.2773	−2.31359
$130$	5.07639	0.445229
$131$	−16.8443	−1.47169	−0.735846	−	0.677149i	$-0.763215\pi$
$131$	−16.8443	−1.47169	−0.735846	+	0.677149i	$0.763215\pi$
$132$	11.5183	1.00254
$133$	−0.471640	−0.0408964
$134$	−28.4116	−2.45439
$135$	1.28965	0.110996
$136$	29.7195	2.54842
$137$	2.46142	0.210293	0.105147	−	0.994457i	$-0.466469\pi$
$137$	2.46142	0.210293	0.105147	+	0.994457i	$0.466469\pi$
$138$	−2.67694	−0.227876
$139$	−2.43010	−0.206118	−0.103059	−	0.994675i	$-0.532863\pi$
$139$	−2.43010	−0.206118	−0.103059	+	0.994675i	$0.532863\pi$
$140$	13.2544	1.12020
$141$	−6.36718	−0.536214
$142$	31.9311	2.67960
$143$	1.05309	0.0880635
$144$	21.1293	1.76077
$145$	2.46913	0.205050
$146$	8.48166	0.701947
$147$	11.6206	0.958452
$148$	37.5307	3.08500
$149$	0.102314	0.00838193	0.00419096	−	0.999991i	$-0.498666\pi$
$149$	0.102314	0.00838193	0.00419096	+	0.999991i	$0.498666\pi$
$150$	−6.61136	−0.539816
$151$	13.5004	1.09865	0.549323	−	0.835610i	$-0.314886\pi$
$151$	13.5004	1.09865	0.549323	+	0.835610i	$0.314886\pi$
$152$	2.12167	0.172091
$153$	−12.3066	−0.994927
$154$	3.95290	0.318534
$155$	−13.5970	−1.09214
$156$	10.9376	0.875712
$157$	10.9947	0.877469	0.438735	−	0.898617i	$-0.355427\pi$
$157$	10.9947	0.877469	0.438735	+	0.898617i	$0.355427\pi$
$158$	0.539682	0.0429348
$159$	−14.5496	−1.15386
$160$	−13.2260	−1.04560
$161$	−0.639029	−0.0503625
$162$	24.9715	1.96194
$163$	−7.46943	−0.585051	−0.292525	−	0.956258i	$-0.594496\pi$
$163$	−7.46943	−0.585051	−0.292525	+	0.956258i	$0.594496\pi$
$164$	−33.4031	−2.60835
$165$	4.99150	0.388588
$166$	24.5365	1.90440
$167$	8.32006	0.643826	0.321913	−	0.946769i	$-0.395674\pi$
$167$	8.32006	0.643826	0.321913	+	0.946769i	$0.395674\pi$
$168$	23.0887	1.78133
$169$	1.00000	0.0769231
$170$	22.9014	1.75645
$171$	−0.878566	−0.0671856
$172$	50.1774	3.82599
$173$	19.4403	1.47802	0.739008	−	0.673697i	$-0.235295\pi$
$173$	19.4403	1.47802	0.739008	+	0.673697i	$0.235295\pi$
$174$	7.64820	0.579809
$175$	−1.57824	−0.119304
$176$	−8.15676	−0.614839
$177$	−18.5208	−1.39211
$178$	−47.4128	−3.55374
$179$	10.8513	0.811061	0.405530	−	0.914082i	$-0.367087\pi$
$179$	10.8513	0.811061	0.405530	+	0.914082i	$0.367087\pi$
$180$	24.6902	1.84030
$181$	−24.2764	−1.80445	−0.902224	−	0.431268i	$-0.858066\pi$
$181$	−24.2764	−1.80445	−0.902224	+	0.431268i	$0.858066\pi$
$182$	3.75364	0.278238
$183$	−23.6496	−1.74823
$184$	2.87468	0.211924
$185$	16.2641	1.19576
$186$	−42.1170	−3.08817
$187$	4.75084	0.347416
$188$	12.1583	0.886738
$189$	0.953609	0.0693649
$190$	1.63493	0.118610
$191$	−25.9256	−1.87591	−0.937957	−	0.346752i	$-0.887285\pi$
$191$	−25.9256	−1.87591	−0.937957	+	0.346752i	$0.887285\pi$
$192$	−3.89268	−0.280930
$193$	−3.71707	−0.267560	−0.133780	−	0.991011i	$-0.542712\pi$
$193$	−3.71707	−0.267560	−0.133780	+	0.991011i	$0.542712\pi$
$194$	3.49595	0.250994
$195$	4.73988	0.339430
$196$	−22.1899	−1.58500
$197$	15.3897	1.09647	0.548236	−	0.836323i	$-0.315299\pi$
$197$	15.3897	1.09647	0.548236	+	0.836323i	$0.315299\pi$
$198$	7.36343	0.523297
$199$	23.9721	1.69934	0.849670	−	0.527315i	$-0.176801\pi$
$199$	23.9721	1.69934	0.849670	+	0.527315i	$0.176801\pi$
$200$	7.09973	0.502027
$201$	−26.5282	−1.87116
$202$	−6.08575	−0.428192
$203$	1.82575	0.128143
$204$	49.3435	3.45473
$205$	−14.4754	−1.01101
$206$	10.4452	0.727753
$207$	−1.19038	−0.0827370
$208$	−7.74558	−0.537059
$209$	0.339162	0.0234603
$210$	17.7918	1.22775
$211$	0.375711	0.0258650	0.0129325	−	0.999916i	$-0.495883\pi$
$211$	0.375711	0.0258650	0.0129325	+	0.999916i	$0.495883\pi$
$212$	27.7830	1.90814
$213$	29.8144	2.04285
$214$	24.3667	1.66567
$215$	21.7446	1.48297
$216$	−4.28982	−0.291885
$217$	−10.0540	−0.682512
$218$	3.99377	0.270492
$219$	7.91942	0.535145
$220$	−9.53143	−0.642609
$221$	4.51135	0.303466
$222$	50.3785	3.38118
$223$	1.58502	0.106141	0.0530705	−	0.998591i	$-0.483099\pi$
$223$	1.58502	0.106141	0.0530705	+	0.998591i	$0.483099\pi$
$224$	−9.77968	−0.653433
$225$	−2.93994	−0.195996
$226$	41.5086	2.76111
$227$	−20.2927	−1.34687	−0.673437	−	0.739245i	$-0.735183\pi$
$227$	−20.2927	−1.34687	−0.673437	+	0.739245i	$0.735183\pi$
$228$	3.52263	0.233292
$229$	−5.18866	−0.342877	−0.171438	−	0.985195i	$-0.554841\pi$
$229$	−5.18866	−0.342877	−0.171438	+	0.985195i	$0.554841\pi$
$230$	2.21518	0.146065
$231$	3.69087	0.242841
$232$	−8.21316	−0.539220
$233$	−16.2291	−1.06320	−0.531601	−	0.846995i	$-0.678410\pi$
$233$	−16.2291	−1.06320	−0.531601	+	0.846995i	$0.678410\pi$
$234$	6.99224	0.457097
$235$	5.26888	0.343704
$236$	35.3660	2.30213
$237$	0.503907	0.0327323
$238$	16.9340	1.09767
$239$	−21.7085	−1.40421	−0.702103	−	0.712075i	$-0.747755\pi$
$239$	−21.7085	−1.40421	−0.702103	+	0.712075i	$0.747755\pi$
$240$	−36.7131	−2.36982
$241$	11.0353	0.710847	0.355423	−	0.934705i	$-0.384337\pi$
$241$	11.0353	0.710847	0.355423	+	0.934705i	$0.384337\pi$
$242$	25.3528	1.62974
$243$	21.3626	1.37041
$244$	45.1597	2.89106
$245$	−9.61612	−0.614351
$246$	−44.8380	−2.85877
$247$	0.322065	0.0204925
$248$	45.2281	2.87199
$249$	22.9100	1.45186
$250$	30.8529	1.95131
$251$	24.2143	1.52839	0.764197	−	0.644983i	$-0.223135\pi$
$251$	24.2143	1.52839	0.764197	+	0.644983i	$0.223135\pi$
$252$	18.2567	1.15006
$253$	0.459534	0.0288907
$254$	−30.0542	−1.88577
$255$	21.3832	1.33907
$256$	−26.8021	−1.67513
$257$	−17.1349	−1.06884	−0.534422	−	0.845218i	$-0.679471\pi$
$257$	−17.1349	−1.06884	−0.534422	+	0.845218i	$0.679471\pi$
$258$	67.3546	4.19331
$259$	12.0262	0.747271
$260$	−9.05095	−0.561316
$261$	3.40100	0.210516
$262$	43.1756	2.66740
$263$	18.6865	1.15226	0.576128	−	0.817360i	$-0.304563\pi$
$263$	18.6865	1.15226	0.576128	+	0.817360i	$0.304563\pi$
$264$	−16.6034	−1.02187
$265$	12.0399	0.739604
$266$	1.20892	0.0741234
$267$	−44.2699	−2.70927
$268$	50.6565	3.09434
$269$	−15.4148	−0.939859	−0.469930	−	0.882704i	$-0.655721\pi$
$269$	−15.4148	−0.939859	−0.469930	+	0.882704i	$0.655721\pi$
$270$	−3.30566	−0.201176
$271$	1.03181	0.0626781	0.0313390	−	0.999509i	$-0.490023\pi$
$271$	1.03181	0.0626781	0.0313390	+	0.999509i	$0.490023\pi$
$272$	−34.9430	−2.11873
$273$	3.50481	0.212121
$274$	−6.30916	−0.381150
$275$	1.13493	0.0684391
$276$	4.77285	0.287292
$277$	13.9223	0.836509	0.418255	−	0.908330i	$-0.362642\pi$
$277$	13.9223	0.836509	0.418255	+	0.908330i	$0.362642\pi$
$278$	6.22887	0.373583
$279$	−18.7286	−1.12125
$280$	−19.1060	−1.14180
$281$	−21.8732	−1.30485	−0.652424	−	0.757854i	$-0.726248\pi$
$281$	−21.8732	−1.30485	−0.652424	+	0.757854i	$0.726248\pi$
$282$	16.3205	0.971871
$283$	17.3719	1.03265	0.516327	−	0.856392i	$-0.327299\pi$
$283$	17.3719	1.03265	0.516327	+	0.856392i	$0.327299\pi$
$284$	−56.9316	−3.37827
$285$	1.52655	0.0904250
$286$	−2.69929	−0.159612
$287$	−10.7036	−0.631812
$288$	−18.2175	−1.07348
$289$	3.35225	0.197191
$290$	−6.32893	−0.371648
$291$	3.26420	0.191351
$292$	−15.1224	−0.884971
$293$	30.8755	1.80377	0.901884	−	0.431978i	$-0.142184\pi$
$293$	30.8755	1.80377	0.901884	+	0.431978i	$0.142184\pi$
$294$	−29.7862	−1.73717
$295$	15.3260	0.892317
$296$	−54.0998	−3.14449
$297$	−0.685753	−0.0397914
$298$	−0.262254	−0.0151920
$299$	0.436369	0.0252359
$300$	11.7877	0.680565
$301$	16.0787	0.926758
$302$	−34.6045	−1.99126
$303$	−5.68233	−0.326441
$304$	−2.49458	−0.143074
$305$	19.5702	1.12059
$306$	31.5444	1.80328
$307$	19.0131	1.08513	0.542567	−	0.840013i	$-0.317452\pi$
$307$	19.0131	1.08513	0.542567	+	0.840013i	$0.317452\pi$
$308$	−7.04784	−0.401588
$309$	9.75281	0.554818
$310$	34.8521	1.97946
$311$	−27.5211	−1.56058	−0.780290	−	0.625418i	$-0.784928\pi$
$311$	−27.5211	−1.56058	−0.780290	+	0.625418i	$0.784928\pi$
$312$	−15.7664	−0.892598
$313$	−21.8496	−1.23501	−0.617505	−	0.786567i	$-0.711856\pi$
$313$	−21.8496	−1.23501	−0.617505	+	0.786567i	$0.711856\pi$
$314$	−28.1817	−1.59039
$315$	7.91164	0.445770
$316$	−0.962227	−0.0541295
$317$	−14.4644	−0.812400	−0.406200	−	0.913784i	$-0.633146\pi$
$317$	−14.4644	−0.812400	−0.406200	+	0.913784i	$0.633146\pi$
$318$	37.2939	2.09134
$319$	−1.31292	−0.0735096
$320$	3.22122	0.180071
$321$	22.7514	1.26986
$322$	1.63797	0.0912806
$323$	1.45295	0.0808442
$324$	−44.5229	−2.47349
$325$	1.07772	0.0597813
$326$	19.1458	1.06039
$327$	3.72902	0.206215
$328$	48.1501	2.65864
$329$	3.89597	0.214792
$330$	−12.7943	−0.704304
$331$	23.9420	1.31597	0.657986	−	0.753030i	$-0.271408\pi$
$331$	23.9420	1.31597	0.657986	+	0.753030i	$0.271408\pi$
$332$	−43.7474	−2.40095
$333$	22.4023	1.22764
$334$	−21.3261	−1.16691
$335$	21.9522	1.19938
$336$	−27.1468	−1.48098
$337$	−3.02838	−0.164966	−0.0824831	−	0.996592i	$-0.526285\pi$
$337$	−3.02838	−0.164966	−0.0824831	+	0.996592i	$0.526285\pi$
$338$	−2.56322	−0.139421
$339$	38.7570	2.10499
$340$	−40.8320	−2.21443
$341$	7.22998	0.391526
$342$	2.25196	0.121772
$343$	−17.3614	−0.937429
$344$	−72.3299	−3.89977
$345$	2.06834	0.111356
$346$	−49.8296	−2.67886
$347$	−8.26574	−0.443728	−0.221864	−	0.975078i	$-0.571214\pi$
$347$	−8.26574	−0.443728	−0.221864	+	0.975078i	$0.571214\pi$
$348$	−13.6364	−0.730986
$349$	−30.5334	−1.63442	−0.817208	−	0.576342i	$-0.804479\pi$
$349$	−30.5334	−1.63442	−0.817208	+	0.576342i	$0.804479\pi$
$350$	4.04538	0.216235
$351$	−0.651184	−0.0347576
$352$	7.03270	0.374844
$353$	3.32339	0.176886	0.0884432	−	0.996081i	$-0.471811\pi$
$353$	3.32339	0.176886	0.0884432	+	0.996081i	$0.471811\pi$
$354$	47.4728	2.52315
$355$	−24.6716	−1.30943
$356$	84.5348	4.48033
$357$	15.8114	0.836830
$358$	−27.8141	−1.47002
$359$	−19.0599	−1.00594	−0.502971	−	0.864303i	$-0.667760\pi$
$359$	−19.0599	−1.00594	−0.502971	+	0.864303i	$0.667760\pi$
$360$	−35.5906	−1.87579
$361$	−18.8963	−0.994541
$362$	62.2256	3.27051
$363$	23.6722	1.24247
$364$	−6.69255	−0.350785
$365$	−6.55336	−0.343019
$366$	60.6192	3.16862
$367$	32.9275	1.71880	0.859401	−	0.511303i	$-0.170837\pi$
$367$	32.9275	1.71880	0.859401	+	0.511303i	$0.170837\pi$
$368$	−3.37993	−0.176191
$369$	−19.9385	−1.03796
$370$	−41.6885	−2.16728
$371$	8.90266	0.462203
$372$	75.0926	3.89337
$373$	−24.5068	−1.26891	−0.634456	−	0.772959i	$-0.718776\pi$
$373$	−24.5068	−1.26891	−0.634456	+	0.772959i	$0.718776\pi$
$374$	−12.1774	−0.629680
$375$	28.8077	1.48762
$376$	−17.5261	−0.903837
$377$	−1.24674	−0.0642103
$378$	−2.44431	−0.125722
$379$	−13.1778	−0.676897	−0.338449	−	0.940985i	$-0.609902\pi$
$379$	−13.1778	−0.676897	−0.338449	+	0.940985i	$0.609902\pi$
$380$	−2.91500	−0.149536
$381$	−28.0620	−1.43766
$382$	66.4531	3.40004
$383$	−33.6940	−1.72168	−0.860842	−	0.508872i	$-0.830063\pi$
$383$	−33.6940	−1.72168	−0.860842	+	0.508872i	$0.830063\pi$
$384$	−21.9881	−1.12207
$385$	−3.05422	−0.155657
$386$	9.52766	0.484945
$387$	29.9512	1.52250
$388$	−6.23310	−0.316438
$389$	−21.1426	−1.07197	−0.535987	−	0.844226i	$-0.680061\pi$
$389$	−21.1426	−1.07197	−0.535987	+	0.844226i	$0.680061\pi$
$390$	−12.1494	−0.615207
$391$	1.96861	0.0995570
$392$	31.9864	1.61556
$393$	40.3135	2.03355
$394$	−39.4473	−1.98732
$395$	−0.416986	−0.0209808
$396$	−13.1286	−0.659739
$397$	−7.22916	−0.362821	−0.181411	−	0.983407i	$-0.558066\pi$
$397$	−7.22916	−0.362821	−0.181411	+	0.983407i	$0.558066\pi$
$398$	−61.4459	−3.08000
$399$	1.12878	0.0565096
$400$	−8.34758	−0.417379
$401$	−3.15229	−0.157418	−0.0787090	−	0.996898i	$-0.525080\pi$
$401$	−3.15229	−0.157418	−0.0787090	+	0.996898i	$0.525080\pi$
$402$	67.9976	3.39141
$403$	6.86552	0.341996
$404$	10.8506	0.539837
$405$	−19.2942	−0.958738
$406$	−4.67981	−0.232255
$407$	−8.64818	−0.428675
$408$	−71.1278	−3.52135
$409$	−7.74633	−0.383031	−0.191516	−	0.981490i	$-0.561340\pi$
$409$	−7.74633	−0.383031	−0.191516	+	0.981490i	$0.561340\pi$
$410$	37.1037	1.83242
$411$	−5.89093	−0.290578
$412$	−18.6233	−0.917504
$413$	11.3325	0.557638
$414$	3.05120	0.149958
$415$	−18.9582	−0.930620
$416$	6.67818	0.327425
$417$	5.81597	0.284809
$418$	−0.869348	−0.0425212
$419$	−4.12325	−0.201434	−0.100717	−	0.994915i	$-0.532114\pi$
$419$	−4.12325	−0.201434	−0.100717	+	0.994915i	$0.532114\pi$
$420$	−31.7219	−1.54787
$421$	−3.74617	−0.182577	−0.0912885	−	0.995824i	$-0.529099\pi$
$421$	−3.74617	−0.182577	−0.0912885	+	0.995824i	$0.529099\pi$
$422$	−0.963031	−0.0468796
$423$	7.25738	0.352866
$424$	−40.0487	−1.94494
$425$	4.86198	0.235841
$426$	−76.4209	−3.70260
$427$	14.4708	0.700291
$428$	−43.4445	−2.09997
$429$	−2.52036	−0.121684
$430$	−55.7363	−2.68784
$431$	20.3700	0.981186	0.490593	−	0.871389i	$-0.336780\pi$
$431$	20.3700	0.981186	0.490593	+	0.871389i	$0.336780\pi$
$432$	5.04380	0.242670
$433$	0.407658	0.0195908	0.00979540	−	0.999952i	$-0.496882\pi$
$433$	0.407658	0.0195908	0.00979540	+	0.999952i	$0.496882\pi$
$434$	25.7707	1.23703
$435$	−5.90939	−0.283334
$436$	−7.12069	−0.341019
$437$	0.140539	0.00672291
$438$	−20.2992	−0.969934
$439$	21.9928	1.04966	0.524830	−	0.851207i	$-0.324129\pi$
$439$	21.9928	1.04966	0.524830	+	0.851207i	$0.324129\pi$
$440$	13.7394	0.655001
$441$	−13.2453	−0.630728
$442$	−11.5636	−0.550023
$443$	−3.63646	−0.172774	−0.0863868	−	0.996262i	$-0.527532\pi$
$443$	−3.63646	−0.172774	−0.0863868	+	0.996262i	$0.527532\pi$
$444$	−89.8224	−4.26278
$445$	36.6336	1.73660
$446$	−4.06276	−0.192377
$447$	−0.244870	−0.0115819
$448$	2.38187	0.112533
$449$	5.33266	0.251664	0.125832	−	0.992052i	$-0.459840\pi$
$449$	5.33266	0.251664	0.125832	+	0.992052i	$0.459840\pi$
$450$	7.53570	0.355236
$451$	7.69708	0.362441
$452$	−74.0078	−3.48104
$453$	−32.3106	−1.51808
$454$	52.0146	2.44117
$455$	−2.90025	−0.135966
$456$	−5.07782	−0.237791
$457$	−18.0640	−0.844997	−0.422498	−	0.906364i	$-0.638847\pi$
$457$	−18.0640	−0.844997	−0.422498	+	0.906364i	$0.638847\pi$
$458$	13.2997	0.621453
$459$	−2.93772	−0.137121
$460$	−3.94956	−0.184149
$461$	−17.7094	−0.824811	−0.412406	−	0.911000i	$-0.635311\pi$
$461$	−17.7094	−0.824811	−0.412406	+	0.911000i	$0.635311\pi$
$462$	−9.46051	−0.440143
$463$	−1.00000	−0.0464739
$463$	−1.00000	−0.0464739
$464$	9.65671	0.448301
$465$	32.5417	1.50909
$466$	41.5987	1.92702
$467$	22.7457	1.05255	0.526273	−	0.850316i	$-0.323589\pi$
$467$	22.7457	1.05255	0.526273	+	0.850316i	$0.323589\pi$
$468$	−12.4668	−0.576279
$469$	16.2322	0.749532
$470$	−13.5053	−0.622953
$471$	−26.3136	−1.21247
$472$	−50.9795	−2.34652
$473$	−11.5624	−0.531638
$474$	−1.29163	−0.0593263
$475$	0.347097	0.0159259
$476$	−30.1924	−1.38387
$477$	16.5838	0.759320
$478$	55.6437	2.54508
$479$	3.71595	0.169786	0.0848930	−	0.996390i	$-0.472945\pi$
$479$	3.71595	0.169786	0.0848930	+	0.996390i	$0.472945\pi$
$480$	31.6538	1.44479
$481$	−8.21223	−0.374445
$482$	−28.2859	−1.28839
$483$	1.52939	0.0695898
$484$	−45.2029	−2.05468
$485$	−2.70115	−0.122653
$486$	−54.7570	−2.48383
$487$	35.7140	1.61835	0.809177	−	0.587565i	$-0.199913\pi$
$487$	35.7140	1.61835	0.809177	+	0.587565i	$0.199913\pi$
$488$	−65.0970	−2.94680
$489$	17.8766	0.808409
$490$	24.6482	1.11349
$491$	3.51616	0.158682	0.0793411	−	0.996848i	$-0.474718\pi$
$491$	3.51616	0.158682	0.0793411	+	0.996848i	$0.474718\pi$
$492$	79.9440	3.60415
$493$	−5.62447	−0.253313
$494$	−0.825524	−0.0371421
$495$	−5.68936	−0.255718
$496$	−53.1774	−2.38774
$497$	−18.2429	−0.818308
$498$	−58.7234	−2.63146
$499$	17.8697	0.799956	0.399978	−	0.916525i	$-0.369018\pi$
$499$	17.8697	0.799956	0.399978	+	0.916525i	$0.369018\pi$
$500$	−55.0092	−2.46009
$501$	−19.9125	−0.889623
$502$	−62.0666	−2.77017
$503$	−1.99613	−0.0890030	−0.0445015	−	0.999009i	$-0.514170\pi$
$503$	−1.99613	−0.0890030	−0.0445015	+	0.999009i	$0.514170\pi$
$504$	−26.3168	−1.17224
$505$	4.70216	0.209243
$506$	−1.17789	−0.0523635
$507$	−2.39331	−0.106290
$508$	53.5852	2.37746
$509$	−29.9226	−1.32630	−0.663148	−	0.748488i	$-0.730780\pi$
$509$	−29.9226	−1.32630	−0.663148	+	0.748488i	$0.730780\pi$
$510$	−54.8100	−2.42703
$511$	−4.84576	−0.214364
$512$	50.3250	2.22407
$513$	−0.209724	−0.00925953
$514$	43.9204	1.93725
$515$	−8.07051	−0.355629
$516$	−120.090	−5.28666
$517$	−2.80164	−0.123216
$518$	−30.8257	−1.35441
$519$	−46.5265	−2.04229
$520$	13.0468	0.572140
$521$	5.65157	0.247600	0.123800	−	0.992307i	$-0.460492\pi$
$521$	5.65157	0.247600	0.123800	+	0.992307i	$0.460492\pi$
$522$	−8.71750	−0.381555
$523$	−22.8950	−1.00113	−0.500564	−	0.865700i	$-0.666874\pi$
$523$	−22.8950	−1.00113	−0.500564	+	0.865700i	$0.666874\pi$
$524$	−76.9800	−3.36289
$525$	3.77722	0.164851
$526$	−47.8975	−2.08843
$527$	30.9727	1.34919
$528$	19.5216	0.849570
$529$	−22.8096	−0.991721
$530$	−30.8609	−1.34051
$531$	21.1102	0.916103
$532$	−2.15544	−0.0934501
$533$	7.30907	0.316591
$534$	113.473	4.91048
$535$	−18.8269	−0.813959
$536$	−73.0205	−3.15400
$537$	−25.9704	−1.12070
$538$	39.5116	1.70347
$539$	5.11322	0.220242
$540$	5.89384	0.253630
$541$	23.3275	1.00293	0.501464	−	0.865178i	$-0.332795\pi$
$541$	23.3275	1.00293	0.501464	+	0.865178i	$0.332795\pi$
$542$	−2.64476	−0.113602
$543$	58.1008	2.49334
$544$	30.1276	1.29171
$545$	−3.08579	−0.132181
$546$	−8.98361	−0.384463
$547$	−26.0532	−1.11395	−0.556977	−	0.830528i	$-0.688039\pi$
$547$	−26.0532	−1.11395	−0.556977	+	0.830528i	$0.688039\pi$
$548$	11.2489	0.480530
$549$	26.9561	1.15046
$550$	−2.90909	−0.124044
$551$	−0.401531	−0.0171058
$552$	−6.87998	−0.292831
$553$	−0.308332	−0.0131116
$554$	−35.6859	−1.51615
$555$	−38.9250	−1.65227
$556$	−11.1058	−0.470990
$557$	−23.5669	−0.998562	−0.499281	−	0.866440i	$-0.666403\pi$
$557$	−23.5669	−0.998562	−0.499281	+	0.866440i	$0.666403\pi$
$558$	48.0054	2.03223
$559$	−10.9795	−0.464384
$560$	22.4641	0.949283
$561$	−11.3702	−0.480050
$562$	56.0659	2.36500
$563$	23.7893	1.00260	0.501300	−	0.865273i	$-0.332855\pi$
$563$	23.7893	1.00260	0.501300	+	0.865273i	$0.332855\pi$
$564$	−29.0986	−1.22527
$565$	−32.0717	−1.34927
$566$	−44.5280	−1.87165
$567$	−14.2667	−0.599147
$568$	82.0660	3.44341
$569$	−28.5800	−1.19814	−0.599069	−	0.800698i	$-0.704462\pi$
$569$	−28.5800	−1.19814	−0.599069	+	0.800698i	$0.704462\pi$
$570$	−3.91288	−0.163893
$571$	13.6238	0.570139	0.285069	−	0.958507i	$-0.407983\pi$
$571$	13.6238	0.570139	0.285069	+	0.958507i	$0.407983\pi$
$572$	4.81270	0.201229
$573$	62.0480	2.59209
$574$	27.4356	1.14514
$575$	0.470285	0.0196122
$576$	4.43692	0.184872
$577$	−30.6388	−1.27551	−0.637755	−	0.770239i	$-0.720137\pi$
$577$	−30.6388	−1.27551	−0.637755	+	0.770239i	$0.720137\pi$
$578$	−8.59255	−0.357403
$579$	8.89608	0.369709
$580$	11.2842	0.468550
$581$	−14.0183	−0.581575
$582$	−8.36687	−0.346818
$583$	−6.40202	−0.265145
$584$	21.7987	0.902036
$585$	−5.40256	−0.223369
$586$	−79.1408	−3.26928
$587$	−16.8905	−0.697144	−0.348572	−	0.937282i	$-0.613333\pi$
$587$	−16.8905	−0.697144	−0.348572	+	0.937282i	$0.613333\pi$
$588$	53.1073	2.19011
$589$	2.21114	0.0911086
$590$	−39.2840	−1.61730
$591$	−36.8323	−1.51508
$592$	63.6085	2.61429
$593$	−14.3521	−0.589370	−0.294685	−	0.955594i	$-0.595215\pi$
$593$	−14.3521	−0.589370	−0.294685	+	0.955594i	$0.595215\pi$
$594$	1.75774	0.0721207
$595$	−13.0840	−0.536394
$596$	0.467587	0.0191531
$597$	−57.3727	−2.34811
$598$	−1.11851	−0.0457393
$599$	43.5647	1.78001	0.890004	−	0.455953i	$-0.150702\pi$
$599$	43.5647	1.78001	0.890004	+	0.455953i	$0.150702\pi$
$600$	−16.9918	−0.693689
$601$	32.7379	1.33541	0.667703	−	0.744427i	$-0.267277\pi$
$601$	32.7379	1.33541	0.667703	+	0.744427i	$0.267277\pi$
$602$	−41.2131	−1.67972
$603$	30.2371	1.23135
$604$	61.6981	2.51046
$605$	−19.5889	−0.796402
$606$	14.5651	0.591665
$607$	37.2769	1.51302	0.756512	−	0.653979i	$-0.226902\pi$
$607$	37.2769	1.51302	0.756512	+	0.653979i	$0.226902\pi$
$608$	2.15081	0.0872268
$609$	−4.36959	−0.177065
$610$	−50.1627	−2.03103
$611$	−2.66041	−0.107629
$612$	−56.2422	−2.27346
$613$	−40.7834	−1.64723	−0.823613	−	0.567152i	$-0.808045\pi$
$613$	−40.7834	−1.64723	−0.823613	+	0.567152i	$0.808045\pi$
$614$	−48.7347	−1.96677
$615$	34.6441	1.39699
$616$	10.1593	0.409331
$617$	−14.5704	−0.586583	−0.293292	−	0.956023i	$-0.594751\pi$
$617$	−14.5704	−0.586583	−0.293292	+	0.956023i	$0.594751\pi$
$618$	−24.9986	−1.00559
$619$	−8.38533	−0.337035	−0.168517	−	0.985699i	$-0.553898\pi$
$619$	−8.38533	−0.337035	−0.168517	+	0.985699i	$0.553898\pi$
$620$	−62.1395	−2.49558
$621$	−0.284157	−0.0114028
$622$	70.5427	2.82850
$623$	27.0880	1.08526
$624$	18.5375	0.742095
$625$	−18.4499	−0.737996
$626$	56.0052	2.23842
$627$	−0.811719	−0.0324169
$628$	50.2466	2.00506
$629$	−37.0482	−1.47721
$630$	−20.2793	−0.807946
$631$	−31.8311	−1.26717	−0.633587	−	0.773671i	$-0.718418\pi$
$631$	−31.8311	−1.26717	−0.633587	+	0.773671i	$0.718418\pi$
$632$	1.38703	0.0551733
$633$	−0.899192	−0.0357397
$634$	37.0754	1.47245
$635$	23.2214	0.921514
$636$	−66.4931	−2.63662
$637$	4.85546	0.192380
$638$	3.36531	0.133234
$639$	−33.9828	−1.34434
$640$	18.1952	0.719230
$641$	−1.07310	−0.0423851	−0.0211925	−	0.999775i	$-0.506746\pi$
$641$	−1.07310	−0.0423851	−0.0211925	+	0.999775i	$0.506746\pi$
$642$	−58.3169	−2.30158
$643$	10.9677	0.432523	0.216262	−	0.976335i	$-0.430614\pi$
$643$	10.9677	0.432523	0.216262	+	0.976335i	$0.430614\pi$
$644$	−2.92042	−0.115081
$645$	−52.0416	−2.04913
$646$	−3.72422	−0.146528
$647$	−25.3715	−0.997458	−0.498729	−	0.866758i	$-0.666200\pi$
$647$	−25.3715	−0.997458	−0.498729	+	0.866758i	$0.666200\pi$
$648$	64.1790	2.52119
$649$	−8.14938	−0.319891
$650$	−2.76244	−0.108352
$651$	24.0624	0.943079
$652$	−34.1360	−1.33687
$653$	−36.5957	−1.43210	−0.716049	−	0.698050i	$-0.754051\pi$
$653$	−36.5957	−1.43210	−0.716049	+	0.698050i	$0.754051\pi$
$654$	−9.55831	−0.373759
$655$	−33.3597	−1.30347
$656$	−56.6130	−2.21037
$657$	−9.02663	−0.352163
$658$	−9.98623	−0.389304
$659$	33.5190	1.30572	0.652858	−	0.757480i	$-0.273570\pi$
$659$	33.5190	1.30572	0.652858	+	0.757480i	$0.273570\pi$
$660$	22.8116	0.887942
$661$	12.6134	0.490605	0.245303	−	0.969447i	$-0.421113\pi$
$661$	12.6134	0.490605	0.245303	+	0.969447i	$0.421113\pi$
$662$	−61.3687	−2.38516
$663$	−10.7970	−0.419322
$664$	63.0612	2.44725
$665$	−0.934070	−0.0362217
$666$	−57.4219	−2.22505
$667$	−0.544038	−0.0210652
$668$	38.0235	1.47117
$669$	−3.79345	−0.146663
$670$	−56.2684	−2.17384
$671$	−10.4061	−0.401725
$672$	23.4058	0.902897
$673$	−37.6582	−1.45162	−0.725808	−	0.687897i	$-0.758534\pi$
$673$	−37.6582	−1.45162	−0.725808	+	0.687897i	$0.758534\pi$
$674$	7.76240	0.298996
$675$	−0.701796	−0.0270121
$676$	4.57009	0.175773
$677$	20.5046	0.788056	0.394028	−	0.919098i	$-0.371081\pi$
$677$	20.5046	0.788056	0.394028	+	0.919098i	$0.371081\pi$
$678$	−99.3428	−3.81524
$679$	−1.99731	−0.0766498
$680$	58.8587	2.25713
$681$	48.5666	1.86108
$682$	−18.5320	−0.709628
$683$	−37.6491	−1.44060	−0.720300	−	0.693662i	$-0.755996\pi$
$683$	−37.6491	−1.44060	−0.720300	+	0.693662i	$0.755996\pi$
$684$	−4.01513	−0.153522
$685$	4.87478	0.186256
$686$	44.5011	1.69906
$687$	12.4181	0.473779
$688$	85.0426	3.24222
$689$	−6.07930	−0.231603
$690$	−5.30160	−0.201829
$691$	6.90301	0.262603	0.131301	−	0.991342i	$-0.458084\pi$
$691$	6.90301	0.262603	0.131301	+	0.991342i	$0.458084\pi$
$692$	88.8438	3.37734
$693$	−4.20689	−0.159807
$694$	21.1869	0.804244
$695$	−4.81274	−0.182558
$696$	19.6566	0.745082
$697$	32.9738	1.24897
$698$	78.2639	2.96233
$699$	38.8412	1.46911
$700$	−7.21272	−0.272615
$701$	24.7946	0.936478	0.468239	−	0.883602i	$-0.344889\pi$
$701$	24.7946	0.936478	0.468239	+	0.883602i	$0.344889\pi$
$702$	1.66913	0.0629972
$703$	−2.64487	−0.0997533
$704$	−1.71283	−0.0645548
$705$	−12.6100	−0.474922
$706$	−8.51858	−0.320601
$707$	3.47692	0.130763
$708$	−84.6417	−3.18103
$709$	18.8353	0.707373	0.353687	−	0.935364i	$-0.384928\pi$
$709$	18.8353	0.707373	0.353687	+	0.935364i	$0.384928\pi$
$710$	63.2387	2.37331
$711$	−0.574359	−0.0215401
$712$	−121.856	−4.56673
$713$	2.99590	0.112197
$714$	−40.5282	−1.51673
$715$	2.08561	0.0779974
$716$	49.5912	1.85331
$717$	51.9551	1.94030
$718$	48.8546	1.82324
$719$	20.3520	0.759002	0.379501	−	0.925191i	$-0.376096\pi$
$719$	20.3520	0.759002	0.379501	+	0.925191i	$0.376096\pi$
$720$	41.8460	1.55951
$721$	−5.96758	−0.222244
$722$	48.4353	1.80258
$723$	−26.4109	−0.982231
$724$	−110.945	−4.12325
$725$	−1.34364	−0.0499015
$726$	−60.6771	−2.25194
$727$	−49.0613	−1.81958	−0.909791	−	0.415067i	$-0.863758\pi$
$727$	−49.0613	−1.81958	−0.909791	+	0.415067i	$0.863758\pi$
$728$	9.64721	0.357549
$729$	−21.9005	−0.811130
$730$	16.7977	0.621711
$731$	−49.5324	−1.83202
$732$	−108.081	−3.99479
$733$	−2.27043	−0.0838601	−0.0419301	−	0.999121i	$-0.513351\pi$
$733$	−2.27043	−0.0838601	−0.0419301	+	0.999121i	$0.513351\pi$
$734$	−84.4004	−3.11528
$735$	23.0143	0.848896
$736$	2.91415	0.107417
$737$	−11.6728	−0.429972
$738$	51.1068	1.88127
$739$	−22.1241	−0.813850	−0.406925	−	0.913462i	$-0.633399\pi$
$739$	−22.1241	−0.813850	−0.406925	+	0.913462i	$0.633399\pi$
$740$	74.3285	2.73237
$741$	−0.770801	−0.0283161
$742$	−22.8195	−0.837729
$743$	−37.9916	−1.39378	−0.696888	−	0.717180i	$-0.745432\pi$
$743$	−37.9916	−1.39378	−0.696888	+	0.717180i	$0.745432\pi$
$744$	−108.245	−3.96844
$745$	0.202631	0.00742383
$746$	62.8162	2.29986
$747$	−26.1131	−0.955427
$748$	21.7118	0.793861
$749$	−13.9212	−0.508670
$750$	−73.8404	−2.69627
$751$	−43.4343	−1.58494	−0.792471	−	0.609910i	$-0.791206\pi$
$751$	−43.4343	−1.58494	−0.792471	+	0.609910i	$0.791206\pi$
$752$	20.6064	0.751439
$753$	−57.9523	−2.11190
$754$	3.19566	0.116379
$755$	26.7372	0.973066
$756$	4.35808	0.158502
$757$	−46.7084	−1.69765	−0.848823	−	0.528676i	$-0.822689\pi$
$757$	−46.7084	−1.69765	−0.848823	+	0.528676i	$0.822689\pi$
$758$	33.7776	1.22686
$759$	−1.09981	−0.0399204
$760$	4.20192	0.152420
$761$	−23.2379	−0.842373	−0.421186	−	0.906974i	$-0.638386\pi$
$761$	−23.2379	−0.842373	−0.421186	+	0.906974i	$0.638386\pi$
$762$	71.9290	2.60571
$763$	−2.28173	−0.0826040
$764$	−118.483	−4.28655
$765$	−24.3728	−0.881202
$766$	86.3652	3.12050
$767$	−7.73857	−0.279424
$768$	64.1456	2.31465
$769$	48.8205	1.76051	0.880255	−	0.474500i	$-0.157371\pi$
$769$	48.8205	1.76051	0.880255	+	0.474500i	$0.157371\pi$
$770$	7.82863	0.282124
$771$	41.0090	1.47690
$772$	−16.9874	−0.611388
$773$	−31.0947	−1.11840	−0.559199	−	0.829033i	$-0.688891\pi$
$773$	−31.0947	−1.11840	−0.559199	+	0.829033i	$0.688891\pi$
$774$	−76.7714	−2.75949
$775$	7.39913	0.265784
$776$	8.98492	0.322540
$777$	−28.7823	−1.03256
$778$	54.1932	1.94292
$779$	2.35400	0.0843407
$780$	21.6617	0.775613
$781$	13.1187	0.469425
$782$	−5.04599	−0.180444
$783$	0.811856	0.0290134
$784$	−37.6084	−1.34316
$785$	21.7746	0.777170
$786$	−103.332	−3.68575
$787$	−40.6300	−1.44830	−0.724151	−	0.689642i	$-0.757768\pi$
$787$	−40.6300	−1.44830	−0.724151	+	0.689642i	$0.757768\pi$
$788$	70.3325	2.50549
$789$	−44.7224	−1.59216
$790$	1.06883	0.0380272
$791$	−23.7148	−0.843201
$792$	18.9247	0.672461
$793$	−9.88157	−0.350905
$794$	18.5299	0.657603
$795$	−28.8151	−1.02197
$796$	109.555	3.88307
$797$	49.6548	1.75886	0.879431	−	0.476027i	$-0.157923\pi$
$797$	49.6548	1.75886	0.879431	+	0.476027i	$0.157923\pi$
$798$	−2.89331	−0.102422
$799$	−12.0020	−0.424602
$800$	7.19723	0.254460
$801$	50.4593	1.78289
$802$	8.08002	0.285315
$803$	3.48465	0.122971
$804$	−121.236	−4.27568
$805$	−1.26558	−0.0446059
$806$	−17.5978	−0.619857
$807$	36.8924	1.29868
$808$	−15.6410	−0.550247
$809$	−7.12548	−0.250518	−0.125259	−	0.992124i	$-0.539976\pi$
$809$	−7.12548	−0.250518	−0.125259	+	0.992124i	$0.539976\pi$
$810$	49.4553	1.73768
$811$	20.1584	0.707857	0.353928	−	0.935273i	$-0.384846\pi$
$811$	20.1584	0.707857	0.353928	+	0.935273i	$0.384846\pi$
$812$	8.34386	0.292812
$813$	−2.46944	−0.0866070
$814$	22.1672	0.776960
$815$	−14.7930	−0.518176
$816$	83.6293	2.92761
$817$	−3.53612	−0.123713
$818$	19.8555	0.694233
$819$	−3.99482	−0.139590
$820$	−66.1541	−2.31020
$821$	−29.2926	−1.02232	−0.511159	−	0.859486i	$-0.670784\pi$
$821$	−29.2926	−1.02232	−0.511159	+	0.859486i	$0.670784\pi$
$822$	15.0998	0.526665
$823$	52.1349	1.81731	0.908654	−	0.417550i	$-0.137111\pi$
$823$	52.1349	1.81731	0.908654	+	0.417550i	$0.137111\pi$
$824$	26.8452	0.935197
$825$	−2.71625	−0.0945676
$826$	−29.0478	−1.01070
$827$	−40.9040	−1.42237	−0.711185	−	0.703005i	$-0.751841\pi$
$827$	−40.9040	−1.42237	−0.711185	+	0.703005i	$0.751841\pi$
$828$	−5.44014	−0.189058
$829$	−12.4958	−0.433999	−0.216999	−	0.976172i	$-0.569627\pi$
$829$	−12.4958	−0.433999	−0.216999	+	0.976172i	$0.569627\pi$
$830$	48.5939	1.68672
$831$	−33.3203	−1.15587
$832$	−1.62649	−0.0563883
$833$	21.9047	0.758952
$834$	−14.9076	−0.516208
$835$	16.4777	0.570233
$836$	1.55000	0.0536080
$837$	−4.47072	−0.154531
$838$	10.5688	0.365093
$839$	45.4987	1.57079	0.785395	−	0.618995i	$-0.212460\pi$
$839$	45.4987	1.57079	0.785395	+	0.618995i	$0.212460\pi$
$840$	45.7266	1.57772
$841$	−27.4456	−0.946401
$842$	9.60225	0.330915
$843$	52.3494	1.80301
$844$	1.71704	0.0591028
$845$	1.98047	0.0681304
$846$	−18.6023	−0.639559
$847$	−14.4846	−0.497698
$848$	47.0877	1.61700
$849$	−41.5763	−1.42690
$850$	−12.4623	−0.427454
$851$	−3.58356	−0.122843
$852$	136.255	4.66801
$853$	17.0490	0.583748	0.291874	−	0.956457i	$-0.405721\pi$
$853$	17.0490	0.583748	0.291874	+	0.956457i	$0.405721\pi$
$854$	−37.0919	−1.26926
$855$	−1.73998	−0.0595060
$856$	62.6246	2.14046
$857$	12.0689	0.412265	0.206133	−	0.978524i	$-0.433912\pi$
$857$	12.0689	0.412265	0.206133	+	0.978524i	$0.433912\pi$
$858$	6.46023	0.220549
$859$	8.47756	0.289251	0.144625	−	0.989486i	$-0.453802\pi$
$859$	8.47756	0.289251	0.144625	+	0.989486i	$0.453802\pi$
$860$	99.3750	3.38866
$861$	25.6169	0.873023
$862$	−52.2127	−1.77837
$863$	25.7290	0.875824	0.437912	−	0.899018i	$-0.355718\pi$
$863$	25.7290	0.875824	0.437912	+	0.899018i	$0.355718\pi$
$864$	−4.34872	−0.147947
$865$	38.5009	1.30907
$866$	−1.04492	−0.0355077
$867$	−8.02296	−0.272474
$868$	−45.9479	−1.55957
$869$	0.221726	0.00752153
$870$	15.1471	0.513534
$871$	−11.0843	−0.375578
$872$	10.2644	0.347595
$873$	−3.72057	−0.125922
$874$	−0.360233	−0.0121851
$875$	−17.6269	−0.595899
$876$	36.1925	1.22283
$877$	−0.274544	−0.00927070	−0.00463535	−	0.999989i	$-0.501475\pi$
$877$	−0.274544	−0.00927070	−0.00463535	+	0.999989i	$0.501475\pi$
$878$	−56.3725	−1.90248
$879$	−73.8946	−2.49240
$880$	−16.1542	−0.544560
$881$	−9.70484	−0.326964	−0.163482	−	0.986546i	$-0.552273\pi$
$881$	−9.70484	−0.326964	−0.163482	+	0.986546i	$0.552273\pi$
$882$	33.9506	1.14318
$883$	29.2003	0.982670	0.491335	−	0.870971i	$-0.336509\pi$
$883$	29.2003	0.982670	0.491335	+	0.870971i	$0.336509\pi$
$884$	20.6173	0.693434
$885$	−36.6799	−1.23298
$886$	9.32105	0.313147
$887$	39.5210	1.32699	0.663493	−	0.748182i	$-0.269073\pi$
$887$	39.5210	1.32699	0.663493	+	0.748182i	$0.269073\pi$
$888$	129.477	4.34498
$889$	17.1706	0.575885
$890$	−93.8999	−3.14753
$891$	10.2594	0.343703
$892$	7.24371	0.242537
$893$	−0.856826	−0.0286726
$894$	0.627655	0.0209919
$895$	21.4906	0.718352
$896$	13.4541	0.449471
$897$	−1.04436	−0.0348703
$898$	−13.6688	−0.456133
$899$	−8.55951	−0.285476
$900$	−13.4358	−0.447859
$901$	−27.4258	−0.913686
$902$	−19.7293	−0.656914
$903$	−38.4811	−1.28057
$904$	106.681	3.54816
$905$	−48.0787	−1.59819
$906$	82.8191	2.75148
$907$	12.8140	0.425482	0.212741	−	0.977109i	$-0.431761\pi$
$907$	12.8140	0.425482	0.212741	+	0.977109i	$0.431761\pi$
$908$	−92.7395	−3.07767
$909$	6.47678	0.214821
$910$	7.43398	0.246434
$911$	−16.2102	−0.537069	−0.268534	−	0.963270i	$-0.586539\pi$
$911$	−16.2102	−0.537069	−0.268534	+	0.963270i	$0.586539\pi$
$912$	5.97029	0.197696
$913$	10.0807	0.333623
$914$	46.3019	1.53153
$915$	−46.8375	−1.54840
$916$	−23.7127	−0.783489
$917$	−24.6672	−0.814582
$918$	7.53001	0.248527
$919$	51.4103	1.69587	0.847934	−	0.530101i	$-0.177846\pi$
$919$	51.4103	1.69587	0.847934	+	0.530101i	$0.177846\pi$
$920$	5.69322	0.187700
$921$	−45.5041	−1.49941
$922$	45.3932	1.49495
$923$	12.4574	0.410041
$924$	16.8676	0.554904
$925$	−8.85050	−0.291003
$926$	2.56322	0.0842326
$927$	−11.1164	−0.365109
$928$	−8.32594	−0.273312
$929$	3.90109	0.127990	0.0639952	−	0.997950i	$-0.479616\pi$
$929$	3.90109	0.127990	0.0639952	+	0.997950i	$0.479616\pi$
$930$	−83.4116	−2.73518
$931$	1.56378	0.0512507
$932$	−74.1685	−2.42947
$933$	65.8665	2.15637
$934$	−58.3022	−1.90771
$935$	9.40891	0.307704
$936$	17.9707	0.587392
$937$	25.1619	0.822004	0.411002	−	0.911634i	$-0.365179\pi$
$937$	25.1619	0.822004	0.411002	+	0.911634i	$0.365179\pi$
$938$	−41.6066	−1.35850
$939$	52.2927	1.70651
$940$	24.0793	0.785380
$941$	8.97743	0.292656	0.146328	−	0.989236i	$-0.453255\pi$
$941$	8.97743	0.292656	0.146328	+	0.989236i	$0.453255\pi$
$942$	67.4475	2.19756
$943$	3.18945	0.103863
$944$	59.9397	1.95087
$945$	1.88860	0.0614361
$946$	29.6369	0.963579
$947$	−18.3014	−0.594715	−0.297358	−	0.954766i	$-0.596105\pi$
$947$	−18.3014	−0.594715	−0.297358	+	0.954766i	$0.596105\pi$
$948$	2.30290	0.0747949
$949$	3.30899	0.107414
$950$	−0.889686	−0.0288652
$951$	34.6177	1.12256
$952$	43.5219	1.41055
$953$	−43.4432	−1.40726	−0.703632	−	0.710565i	$-0.748440\pi$
$953$	−43.4432	−1.40726	−0.703632	+	0.710565i	$0.748440\pi$
$954$	−42.5079	−1.37624
$955$	−51.3451	−1.66149
$956$	−99.2099	−3.20868
$957$	3.14223	0.101574
$958$	−9.52479	−0.307732
$959$	3.60456	0.116397
$960$	−7.70936	−0.248818
$961$	16.1354	0.520496
$962$	21.0497	0.678671
$963$	−25.9323	−0.835656
$964$	50.4324	1.62432
$965$	−7.36156	−0.236977
$966$	−3.92017	−0.126129
$967$	23.0283	0.740541	0.370271	−	0.928924i	$-0.379265\pi$
$967$	23.0283	0.740541	0.370271	+	0.928924i	$0.379265\pi$
$968$	65.1592	2.09430
$969$	−3.47735	−0.111709
$970$	6.92363	0.222304
$971$	−35.2808	−1.13221	−0.566107	−	0.824331i	$-0.691551\pi$
$971$	−35.2808	−1.13221	−0.566107	+	0.824331i	$0.691551\pi$
$972$	97.6290	3.13145
$973$	−3.55869	−0.114086
$974$	−91.5427	−2.93322
$975$	−2.57932	−0.0826044
$976$	76.5385	2.44994
$977$	−45.9431	−1.46985	−0.734924	−	0.678149i	$-0.762782\pi$
$977$	−45.9431	−1.46985	−0.734924	+	0.678149i	$0.762782\pi$
$978$	−45.8217	−1.46522
$979$	−19.4793	−0.622562
$980$	−43.9466	−1.40382
$981$	−4.25038	−0.135704
$982$	−9.01269	−0.287607
$983$	44.1189	1.40717	0.703586	−	0.710610i	$-0.251581\pi$
$983$	44.1189	1.40717	0.703586	+	0.710610i	$0.251581\pi$
$984$	−115.238	−3.67365
$985$	30.4790	0.971140
$986$	14.4167	0.459123
$987$	−9.32425	−0.296794
$988$	1.47187	0.0468264
$989$	−4.79112	−0.152349
$990$	14.5831	0.463481
$991$	−17.9541	−0.570329	−0.285165	−	0.958479i	$-0.592048\pi$
$991$	−17.9541	−0.570329	−0.285165	+	0.958479i	$0.592048\pi$
$992$	45.8492	1.45571
$993$	−57.3006	−1.81838
$994$	46.7607	1.48316
$995$	47.4762	1.50510
$996$	104.701	3.31758
$997$	13.6148	0.431184	0.215592	−	0.976484i	$-0.430832\pi$
$997$	13.6148	0.431184	0.215592	+	0.976484i	$0.430832\pi$
$998$	−45.8039	−1.44990
$999$	5.34767	0.169193

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.c.1.9	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.c.1.9	✓	108	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)

\(f(q)\)	\(=\)	\(q-2.56322 q^{2} -2.39331 q^{3} +4.57009 q^{4} +1.98047 q^{5} +6.13457 q^{6} +1.46442 q^{7} -6.58772 q^{8} +2.72791 q^{9} +O(q^{10})\)	\(q-2.56322 q^{2} -2.39331 q^{3} +4.57009 q^{4} +1.98047 q^{5} +6.13457 q^{6} +1.46442 q^{7} -6.58772 q^{8} +2.72791 q^{9} -5.07639 q^{10} -1.05309 q^{11} -10.9376 q^{12} -1.00000 q^{13} -3.75364 q^{14} -4.73988 q^{15} +7.74558 q^{16} -4.51135 q^{17} -6.99224 q^{18} -0.322065 q^{19} +9.05095 q^{20} -3.50481 q^{21} +2.69929 q^{22} -0.436369 q^{23} +15.7664 q^{24} -1.07772 q^{25} +2.56322 q^{26} +0.651184 q^{27} +6.69255 q^{28} +1.24674 q^{29} +12.1494 q^{30} -6.86552 q^{31} -6.67818 q^{32} +2.52036 q^{33} +11.5636 q^{34} +2.90025 q^{35} +12.4668 q^{36} +8.21223 q^{37} +0.825524 q^{38} +2.39331 q^{39} -13.0468 q^{40} -7.30907 q^{41} +8.98361 q^{42} +10.9795 q^{43} -4.81270 q^{44} +5.40256 q^{45} +1.11851 q^{46} +2.66041 q^{47} -18.5375 q^{48} -4.85546 q^{49} +2.76244 q^{50} +10.7970 q^{51} -4.57009 q^{52} +6.07930 q^{53} -1.66913 q^{54} -2.08561 q^{55} -9.64721 q^{56} +0.770801 q^{57} -3.19566 q^{58} +7.73857 q^{59} -21.6617 q^{60} +9.88157 q^{61} +17.5978 q^{62} +3.99482 q^{63} +1.62649 q^{64} -1.98047 q^{65} -6.46023 q^{66} +11.0843 q^{67} -20.6173 q^{68} +1.04436 q^{69} -7.43398 q^{70} -12.4574 q^{71} -17.9707 q^{72} -3.30899 q^{73} -21.0497 q^{74} +2.57932 q^{75} -1.47187 q^{76} -1.54216 q^{77} -6.13457 q^{78} -0.210549 q^{79} +15.3399 q^{80} -9.74223 q^{81} +18.7348 q^{82} -9.57254 q^{83} -16.0173 q^{84} -8.93460 q^{85} -28.1429 q^{86} -2.98383 q^{87} +6.93743 q^{88} +18.4974 q^{89} -13.8480 q^{90} -1.46442 q^{91} -1.99425 q^{92} +16.4313 q^{93} -6.81922 q^{94} -0.637842 q^{95} +15.9829 q^{96} -1.36389 q^{97} +12.4456 q^{98} -2.87273 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9}+O(q^{10}) \) 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9	\( 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9} - q^{10} - 45 q^{11} - 6 q^{12} - 108 q^{13} - 31 q^{14} - 39 q^{15} + 73 q^{16} + 21 q^{17} - 35 q^{18} - 19 q^{19} - 79 q^{20} - 72 q^{21} - 26 q^{23} - 23 q^{24} + 92 q^{25} + 11 q^{26} + 7 q^{27} - 21 q^{28} - 94 q^{29} - 24 q^{30} - 36 q^{31} - 77 q^{32} - 32 q^{33} - 58 q^{34} - 10 q^{35} + 17 q^{36} - 54 q^{37} - 12 q^{38} - q^{39} - 4 q^{40} - 68 q^{41} - 11 q^{42} - 32 q^{43} - 151 q^{44} - 121 q^{45} - 33 q^{46} - 51 q^{47} - 27 q^{48} + 72 q^{49} - 45 q^{50} - 24 q^{51} - 95 q^{52} - 81 q^{53} - 29 q^{54} + 4 q^{55} - 68 q^{56} - 45 q^{57} - 30 q^{58} - 94 q^{59} - 108 q^{60} - 39 q^{61} - 9 q^{62} - 52 q^{63} + 31 q^{64} + 40 q^{65} - 40 q^{66} - 47 q^{67} + 24 q^{68} - 60 q^{69} - 66 q^{70} - 86 q^{71} - 91 q^{72} - 51 q^{73} - 110 q^{74} - 7 q^{75} - 51 q^{76} - 96 q^{77} + 10 q^{78} - 18 q^{79} - 136 q^{80} - 24 q^{81} - 33 q^{82} - 77 q^{83} - 113 q^{84} - 95 q^{85} - 137 q^{86} + 23 q^{87} + 19 q^{88} - 112 q^{89} - 19 q^{90} + 8 q^{91} - 111 q^{92} - 124 q^{93} - 20 q^{94} - 73 q^{95} - 77 q^{96} - 41 q^{97} - 80 q^{98} - 154 q^{99}+O(q^{100}) \) 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9 - q^10 - 45 * q^11 - 6 * q^12 - 108 * q^13 - 31 * q^14 - 39 * q^15 + 73 * q^16 + 21 * q^17 - 35 * q^18 - 19 * q^19 - 79 * q^20 - 72 * q^21 - 26 * q^23 - 23 * q^24 + 92 * q^25 + 11 * q^26 + 7 * q^27 - 21 * q^28 - 94 * q^29 - 24 * q^30 - 36 * q^31 - 77 * q^32 - 32 * q^33 - 58 * q^34 - 10 * q^35 + 17 * q^36 - 54 * q^37 - 12 * q^38 - q^39 - 4 * q^40 - 68 * q^41 - 11 * q^42 - 32 * q^43 - 151 * q^44 - 121 * q^45 - 33 * q^46 - 51 * q^47 - 27 * q^48 + 72 * q^49 - 45 * q^50 - 24 * q^51 - 95 * q^52 - 81 * q^53 - 29 * q^54 + 4 * q^55 - 68 * q^56 - 45 * q^57 - 30 * q^58 - 94 * q^59 - 108 * q^60 - 39 * q^61 - 9 * q^62 - 52 * q^63 + 31 * q^64 + 40 * q^65 - 40 * q^66 - 47 * q^67 + 24 * q^68 - 60 * q^69 - 66 * q^70 - 86 * q^71 - 91 * q^72 - 51 * q^73 - 110 * q^74 - 7 * q^75 - 51 * q^76 - 96 * q^77 + 10 * q^78 - 18 * q^79 - 136 * q^80 - 24 * q^81 - 33 * q^82 - 77 * q^83 - 113 * q^84 - 95 * q^85 - 137 * q^86 + 23 * q^87 + 19 * q^88 - 112 * q^89 - 19 * q^90 + 8 * q^91 - 111 * q^92 - 124 * q^93 - 20 * q^94 - 73 * q^95 - 77 * q^96 - 41 * q^97 - 80 * q^98 - 154 * q^99

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