LMFDB - Embedded newform 4011.2.a.l.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4011,2,Mod(1,4011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4011, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4011 = 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4011.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.0279962507$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	4011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.53559 q^{2} -1.00000 q^{3} +0.358037 q^{4} -0.986091 q^{5} +1.53559 q^{6} +1.00000 q^{7} +2.52138 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.53559 q^{2} -1.00000 q^{3} +0.358037 q^{4} -0.986091 q^{5} +1.53559 q^{6} +1.00000 q^{7} +2.52138 q^{8} +1.00000 q^{9} +1.51423 q^{10} +1.24869 q^{11} -0.358037 q^{12} -4.81512 q^{13} -1.53559 q^{14} +0.986091 q^{15} -4.58788 q^{16} +0.345448 q^{17} -1.53559 q^{18} +7.09931 q^{19} -0.353058 q^{20} -1.00000 q^{21} -1.91748 q^{22} -0.730182 q^{23} -2.52138 q^{24} -4.02762 q^{25} +7.39405 q^{26} -1.00000 q^{27} +0.358037 q^{28} +2.84885 q^{29} -1.51423 q^{30} +9.79868 q^{31} +2.00235 q^{32} -1.24869 q^{33} -0.530467 q^{34} -0.986091 q^{35} +0.358037 q^{36} +1.25696 q^{37} -10.9016 q^{38} +4.81512 q^{39} -2.48631 q^{40} -3.50549 q^{41} +1.53559 q^{42} +1.04941 q^{43} +0.447079 q^{44} -0.986091 q^{45} +1.12126 q^{46} -2.87345 q^{47} +4.58788 q^{48} +1.00000 q^{49} +6.18478 q^{50} -0.345448 q^{51} -1.72399 q^{52} -4.76759 q^{53} +1.53559 q^{54} -1.23132 q^{55} +2.52138 q^{56} -7.09931 q^{57} -4.37467 q^{58} +9.01123 q^{59} +0.353058 q^{60} -2.97243 q^{61} -15.0468 q^{62} +1.00000 q^{63} +6.10098 q^{64} +4.74814 q^{65} +1.91748 q^{66} -4.84325 q^{67} +0.123683 q^{68} +0.730182 q^{69} +1.51423 q^{70} +10.1948 q^{71} +2.52138 q^{72} +4.22971 q^{73} -1.93017 q^{74} +4.02762 q^{75} +2.54182 q^{76} +1.24869 q^{77} -7.39405 q^{78} -4.18910 q^{79} +4.52407 q^{80} +1.00000 q^{81} +5.38299 q^{82} -7.63061 q^{83} -0.358037 q^{84} -0.340644 q^{85} -1.61146 q^{86} -2.84885 q^{87} +3.14843 q^{88} -11.6137 q^{89} +1.51423 q^{90} -4.81512 q^{91} -0.261433 q^{92} -9.79868 q^{93} +4.41244 q^{94} -7.00056 q^{95} -2.00235 q^{96} +1.49408 q^{97} -1.53559 q^{98} +1.24869 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 6 q^{2} - 28 q^{3} + 34 q^{4} + 8 q^{5} + 6 q^{6} + 28 q^{7} - 15 q^{8} + 28 q^{9}+O(q^{10}) $ 28 * q - 6 * q^2 - 28 * q^3 + 34 * q^4 + 8 * q^5 + 6 * q^6 + 28 * q^7 - 15 * q^8 + 28 * q^9	\( 28 q - 6 q^{2} - 28 q^{3} + 34 q^{4} + 8 q^{5} + 6 q^{6} + 28 q^{7} - 15 q^{8} + 28 q^{9} + 4 q^{10} - 8 q^{11} - 34 q^{12} + 26 q^{13} - 6 q^{14} - 8 q^{15} + 62 q^{16} + 9 q^{17} - 6 q^{18} + 25 q^{19} + 20 q^{20} - 28 q^{21} + 3 q^{22} - 30 q^{23} + 15 q^{24} + 42 q^{25} + 25 q^{26} - 28 q^{27} + 34 q^{28} - 5 q^{29} - 4 q^{30} + 18 q^{31} - 26 q^{32} + 8 q^{33} + 30 q^{34} + 8 q^{35} + 34 q^{36} + 36 q^{37} - 2 q^{38} - 26 q^{39} + 28 q^{40} + 21 q^{41} + 6 q^{42} + 8 q^{43} - 20 q^{44} + 8 q^{45} + 24 q^{46} + 6 q^{47} - 62 q^{48} + 28 q^{49} - 48 q^{50} - 9 q^{51} + 54 q^{52} - 12 q^{53} + 6 q^{54} + 15 q^{55} - 15 q^{56} - 25 q^{57} + 19 q^{58} + 33 q^{59} - 20 q^{60} + 48 q^{61} + 28 q^{63} + 75 q^{64} + 21 q^{65} - 3 q^{66} + 27 q^{67} + 19 q^{68} + 30 q^{69} + 4 q^{70} - 45 q^{71} - 15 q^{72} + 61 q^{73} - 31 q^{74} - 42 q^{75} + 63 q^{76} - 8 q^{77} - 25 q^{78} + 35 q^{79} + 84 q^{80} + 28 q^{81} + 11 q^{82} + 43 q^{83} - 34 q^{84} + 43 q^{85} - q^{86} + 5 q^{87} - 27 q^{88} + 25 q^{89} + 4 q^{90} + 26 q^{91} - 102 q^{92} - 18 q^{93} + 55 q^{94} - 43 q^{95} + 26 q^{96} + 40 q^{97} - 6 q^{98} - 8 q^{99}+O(q^{100}) \) 28 * q - 6 * q^2 - 28 * q^3 + 34 * q^4 + 8 * q^5 + 6 * q^6 + 28 * q^7 - 15 * q^8 + 28 * q^9 + 4 * q^10 - 8 * q^11 - 34 * q^12 + 26 * q^13 - 6 * q^14 - 8 * q^15 + 62 * q^16 + 9 * q^17 - 6 * q^18 + 25 * q^19 + 20 * q^20 - 28 * q^21 + 3 * q^22 - 30 * q^23 + 15 * q^24 + 42 * q^25 + 25 * q^26 - 28 * q^27 + 34 * q^28 - 5 * q^29 - 4 * q^30 + 18 * q^31 - 26 * q^32 + 8 * q^33 + 30 * q^34 + 8 * q^35 + 34 * q^36 + 36 * q^37 - 2 * q^38 - 26 * q^39 + 28 * q^40 + 21 * q^41 + 6 * q^42 + 8 * q^43 - 20 * q^44 + 8 * q^45 + 24 * q^46 + 6 * q^47 - 62 * q^48 + 28 * q^49 - 48 * q^50 - 9 * q^51 + 54 * q^52 - 12 * q^53 + 6 * q^54 + 15 * q^55 - 15 * q^56 - 25 * q^57 + 19 * q^58 + 33 * q^59 - 20 * q^60 + 48 * q^61 + 28 * q^63 + 75 * q^64 + 21 * q^65 - 3 * q^66 + 27 * q^67 + 19 * q^68 + 30 * q^69 + 4 * q^70 - 45 * q^71 - 15 * q^72 + 61 * q^73 - 31 * q^74 - 42 * q^75 + 63 * q^76 - 8 * q^77 - 25 * q^78 + 35 * q^79 + 84 * q^80 + 28 * q^81 + 11 * q^82 + 43 * q^83 - 34 * q^84 + 43 * q^85 - q^86 + 5 * q^87 - 27 * q^88 + 25 * q^89 + 4 * q^90 + 26 * q^91 - 102 * q^92 - 18 * q^93 + 55 * q^94 - 43 * q^95 + 26 * q^96 + 40 * q^97 - 6 * q^98 - 8 * 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 $

$2$	−1.53559	−1.08583	−0.542913	−	0.839789i	$-0.682679\pi$
$2$	−1.53559	−1.08583	−0.542913	+	0.839789i	$0.682679\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.358037	0.179019
$5$	−0.986091	−0.440993	−0.220497	−	0.975388i	$-0.570768\pi$
$5$	−0.986091	−0.440993	−0.220497	+	0.975388i	$0.570768\pi$
$6$	1.53559	0.626902
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	2.52138	0.891443
$9$	1.00000	0.333333
$10$	1.51423	0.478842
$11$	1.24869	0.376495	0.188248	−	0.982122i	$-0.439719\pi$
$11$	1.24869	0.376495	0.188248	+	0.982122i	$0.439719\pi$
$12$	−0.358037	−0.103357
$13$	−4.81512	−1.33547	−0.667737	−	0.744398i	$-0.732737\pi$
$13$	−4.81512	−1.33547	−0.667737	+	0.744398i	$0.732737\pi$
$14$	−1.53559	−0.410404
$15$	0.986091	0.254608
$16$	−4.58788	−1.14697
$17$	0.345448	0.0837836	0.0418918	−	0.999122i	$-0.486662\pi$
$17$	0.345448	0.0837836	0.0418918	+	0.999122i	$0.486662\pi$
$18$	−1.53559	−0.361942
$19$	7.09931	1.62869	0.814346	−	0.580379i	$-0.197096\pi$
$19$	7.09931	1.62869	0.814346	+	0.580379i	$0.197096\pi$
$20$	−0.353058	−0.0789461
$21$	−1.00000	−0.218218
$22$	−1.91748	−0.408808
$23$	−0.730182	−0.152254	−0.0761268	−	0.997098i	$-0.524255\pi$
$23$	−0.730182	−0.152254	−0.0761268	+	0.997098i	$0.524255\pi$
$24$	−2.52138	−0.514675
$25$	−4.02762	−0.805525
$26$	7.39405	1.45009
$27$	−1.00000	−0.192450
$28$	0.358037	0.0676627
$29$	2.84885	0.529018	0.264509	−	0.964383i	$-0.414790\pi$
$29$	2.84885	0.529018	0.264509	+	0.964383i	$0.414790\pi$
$30$	−1.51423	−0.276460
$31$	9.79868	1.75989	0.879947	−	0.475071i	$-0.157578\pi$
$31$	9.79868	1.75989	0.879947	+	0.475071i	$0.157578\pi$
$32$	2.00235	0.353968
$33$	−1.24869	−0.217370
$34$	−0.530467	−0.0909744
$35$	−0.986091	−0.166680
$36$	0.358037	0.0596729
$37$	1.25696	0.206642	0.103321	−	0.994648i	$-0.467053\pi$
$37$	1.25696	0.206642	0.103321	+	0.994648i	$0.467053\pi$
$38$	−10.9016	−1.76848
$39$	4.81512	0.771036
$40$	−2.48631	−0.393120
$41$	−3.50549	−0.547465	−0.273732	−	0.961806i	$-0.588258\pi$
$41$	−3.50549	−0.547465	−0.273732	+	0.961806i	$0.588258\pi$
$42$	1.53559	0.236947
$43$	1.04941	0.160033	0.0800167	−	0.996794i	$-0.474503\pi$
$43$	1.04941	0.160033	0.0800167	+	0.996794i	$0.474503\pi$
$44$	0.447079	0.0673997
$45$	−0.986091	−0.146998
$46$	1.12126	0.165321
$47$	−2.87345	−0.419136	−0.209568	−	0.977794i	$-0.567206\pi$
$47$	−2.87345	−0.419136	−0.209568	+	0.977794i	$0.567206\pi$
$48$	4.58788	0.662204
$49$	1.00000	0.142857
$50$	6.18478	0.874660
$51$	−0.345448	−0.0483725
$52$	−1.72399	−0.239075
$53$	−4.76759	−0.654879	−0.327440	−	0.944872i	$-0.606186\pi$
$53$	−4.76759	−0.654879	−0.327440	+	0.944872i	$0.606186\pi$
$54$	1.53559	0.208967
$55$	−1.23132	−0.166032
$56$	2.52138	0.336934
$57$	−7.09931	−0.940326
$58$	−4.37467	−0.574422
$59$	9.01123	1.17316	0.586581	−	0.809890i	$-0.300474\pi$
$59$	9.01123	1.17316	0.586581	+	0.809890i	$0.300474\pi$
$60$	0.353058	0.0455795
$61$	−2.97243	−0.380580	−0.190290	−	0.981728i	$-0.560943\pi$
$61$	−2.97243	−0.380580	−0.190290	+	0.981728i	$0.560943\pi$
$62$	−15.0468	−1.91094
$63$	1.00000	0.125988
$64$	6.10098	0.762623
$65$	4.74814	0.588935
$66$	1.91748	0.236026
$67$	−4.84325	−0.591697	−0.295849	−	0.955235i	$-0.595602\pi$
$67$	−4.84325	−0.591697	−0.295849	+	0.955235i	$0.595602\pi$
$68$	0.123683	0.0149988
$69$	0.730182	0.0879036
$70$	1.51423	0.180985
$71$	10.1948	1.20990	0.604951	−	0.796262i	$-0.293193\pi$
$71$	10.1948	1.20990	0.604951	+	0.796262i	$0.293193\pi$
$72$	2.52138	0.297148
$73$	4.22971	0.495050	0.247525	−	0.968882i	$-0.420383\pi$
$73$	4.22971	0.495050	0.247525	+	0.968882i	$0.420383\pi$
$74$	−1.93017	−0.224378
$75$	4.02762	0.465070
$76$	2.54182	0.291566
$77$	1.24869	0.142302
$78$	−7.39405	−0.837211
$79$	−4.18910	−0.471310	−0.235655	−	0.971837i	$-0.575724\pi$
$79$	−4.18910	−0.471310	−0.235655	+	0.971837i	$0.575724\pi$
$80$	4.52407	0.505807
$81$	1.00000	0.111111
$82$	5.38299	0.594452
$83$	−7.63061	−0.837569	−0.418784	−	0.908086i	$-0.637544\pi$
$83$	−7.63061	−0.837569	−0.418784	+	0.908086i	$0.637544\pi$
$84$	−0.358037	−0.0390651
$85$	−0.340644	−0.0369480
$86$	−1.61146	−0.173769
$87$	−2.84885	−0.305429
$88$	3.14843	0.335624
$89$	−11.6137	−1.23105	−0.615523	−	0.788119i	$-0.711055\pi$
$89$	−11.6137	−1.23105	−0.615523	+	0.788119i	$0.711055\pi$
$90$	1.51423	0.159614
$91$	−4.81512	−0.504761
$92$	−0.261433	−0.0272562
$93$	−9.79868	−1.01608
$94$	4.41244	0.455108
$95$	−7.00056	−0.718243
$96$	−2.00235	−0.204364
$97$	1.49408	0.151701	0.0758504	−	0.997119i	$-0.475833\pi$
$97$	1.49408	0.151701	0.0758504	+	0.997119i	$0.475833\pi$
$98$	−1.53559	−0.155118
$99$	1.24869	0.125498
$100$	−1.44204	−0.144204
$101$	−6.35004	−0.631853	−0.315926	−	0.948784i	$-0.602315\pi$
$101$	−6.35004	−0.631853	−0.315926	+	0.948784i	$0.602315\pi$
$102$	0.530467	0.0525241
$103$	3.22672	0.317938	0.158969	−	0.987284i	$-0.449183\pi$
$103$	3.22672	0.317938	0.158969	+	0.987284i	$0.449183\pi$
$104$	−12.1407	−1.19050
$105$	0.986091	0.0962326
$106$	7.32107	0.711085
$107$	7.58567	0.733334	0.366667	−	0.930352i	$-0.380499\pi$
$107$	7.58567	0.733334	0.366667	+	0.930352i	$0.380499\pi$
$108$	−0.358037	−0.0344522
$109$	8.42288	0.806765	0.403383	−	0.915031i	$-0.367834\pi$
$109$	8.42288	0.806765	0.403383	+	0.915031i	$0.367834\pi$
$110$	1.89081	0.180282
$111$	−1.25696	−0.119305
$112$	−4.58788	−0.433514
$113$	−6.13475	−0.577109	−0.288554	−	0.957463i	$-0.593175\pi$
$113$	−6.13475	−0.577109	−0.288554	+	0.957463i	$0.593175\pi$
$114$	10.9016	1.02103
$115$	0.720026	0.0671428
$116$	1.02000	0.0947042
$117$	−4.81512	−0.445158
$118$	−13.8376	−1.27385
$119$	0.345448	0.0316672
$120$	2.48631	0.226968
$121$	−9.44077	−0.858251
$122$	4.56443	0.413244
$123$	3.50549	0.316079
$124$	3.50829	0.315054
$125$	8.90206	0.796224
$126$	−1.53559	−0.136801
$127$	−8.88845	−0.788722	−0.394361	−	0.918956i	$-0.629034\pi$
$127$	−8.88845	−0.788722	−0.394361	+	0.918956i	$0.629034\pi$
$128$	−13.3733	−1.18204
$129$	−1.04941	−0.0923954
$130$	−7.29120	−0.639481
$131$	−21.4744	−1.87623	−0.938114	−	0.346326i	$-0.887429\pi$
$131$	−21.4744	−1.87623	−0.938114	+	0.346326i	$0.887429\pi$
$132$	−0.447079	−0.0389132
$133$	7.09931	0.615588
$134$	7.43725	0.642480
$135$	0.986091	0.0848692
$136$	0.871007	0.0746883
$137$	−21.9201	−1.87276	−0.936382	−	0.350983i	$-0.885847\pi$
$137$	−21.9201	−1.87276	−0.936382	+	0.350983i	$0.885847\pi$
$138$	−1.12126	−0.0954480
$139$	13.1399	1.11451	0.557256	−	0.830341i	$-0.311854\pi$
$139$	13.1399	1.11451	0.557256	+	0.830341i	$0.311854\pi$
$140$	−0.353058	−0.0298388
$141$	2.87345	0.241988
$142$	−15.6551	−1.31374
$143$	−6.01260	−0.502799
$144$	−4.58788	−0.382324
$145$	−2.80923	−0.233294
$146$	−6.49510	−0.537538
$147$	−1.00000	−0.0824786
$148$	0.450037	0.0369928
$149$	−12.3302	−1.01013	−0.505065	−	0.863081i	$-0.668531\pi$
$149$	−12.3302	−1.01013	−0.505065	+	0.863081i	$0.668531\pi$
$150$	−6.18478	−0.504985
$151$	17.1950	1.39931	0.699653	−	0.714483i	$-0.253338\pi$
$151$	17.1950	1.39931	0.699653	+	0.714483i	$0.253338\pi$
$152$	17.9001	1.45189
$153$	0.345448	0.0279279
$154$	−1.91748	−0.154515
$155$	−9.66239	−0.776102
$156$	1.72399	0.138030
$157$	12.7799	1.01995	0.509975	−	0.860189i	$-0.329655\pi$
$157$	12.7799	1.01995	0.509975	+	0.860189i	$0.329655\pi$
$158$	6.43274	0.511761
$159$	4.76759	0.378095
$160$	−1.97450	−0.156098
$161$	−0.730182	−0.0575464
$162$	−1.53559	−0.120647
$163$	9.09051	0.712023	0.356012	−	0.934481i	$-0.384136\pi$
$163$	9.09051	0.712023	0.356012	+	0.934481i	$0.384136\pi$
$164$	−1.25510	−0.0980065
$165$	1.23132	0.0958585
$166$	11.7175	0.909454
$167$	5.76656	0.446230	0.223115	−	0.974792i	$-0.428377\pi$
$167$	5.76656	0.446230	0.223115	+	0.974792i	$0.428377\pi$
$168$	−2.52138	−0.194529
$169$	10.1854	0.783489
$170$	0.523089	0.0401191
$171$	7.09931	0.542898
$172$	0.375728	0.0286490
$173$	−16.8681	−1.28246	−0.641228	−	0.767351i	$-0.721575\pi$
$173$	−16.8681	−1.28246	−0.641228	+	0.767351i	$0.721575\pi$
$174$	4.37467	0.331643
$175$	−4.02762	−0.304460
$176$	−5.72886	−0.431829
$177$	−9.01123	−0.677326
$178$	17.8338	1.33670
$179$	19.9777	1.49320	0.746601	−	0.665272i	$-0.231685\pi$
$179$	19.9777	1.49320	0.746601	+	0.665272i	$0.231685\pi$
$180$	−0.353058	−0.0263154
$181$	−3.71989	−0.276497	−0.138249	−	0.990398i	$-0.544147\pi$
$181$	−3.71989	−0.276497	−0.138249	+	0.990398i	$0.544147\pi$
$182$	7.39405	0.548083
$183$	2.97243	0.219728
$184$	−1.84107	−0.135725
$185$	−1.23947	−0.0911279
$186$	15.0468	1.10328
$187$	0.431359	0.0315441
$188$	−1.02880	−0.0750331
$189$	−1.00000	−0.0727393
$190$	10.7500	0.779887
$191$	−1.00000	−0.0723575
$191$	−1.00000	−0.0723575
$192$	−6.10098	−0.440301
$193$	12.8944	0.928163	0.464081	−	0.885793i	$-0.346385\pi$
$193$	12.8944	0.928163	0.464081	+	0.885793i	$0.346385\pi$
$194$	−2.29429	−0.164721
$195$	−4.74814	−0.340022
$196$	0.358037	0.0255741
$197$	−18.7218	−1.33388	−0.666938	−	0.745113i	$-0.732395\pi$
$197$	−18.7218	−1.33388	−0.666938	+	0.745113i	$0.732395\pi$
$198$	−1.91748	−0.136269
$199$	14.5871	1.03405	0.517027	−	0.855969i	$-0.327039\pi$
$199$	14.5871	1.03405	0.517027	+	0.855969i	$0.327039\pi$
$200$	−10.1552	−0.718080
$201$	4.84325	0.341617
$202$	9.75106	0.686082
$203$	2.84885	0.199950
$204$	−0.123683	−0.00865958
$205$	3.45673	0.241428
$206$	−4.95492	−0.345226
$207$	−0.730182	−0.0507512
$208$	22.0912	1.53175
$209$	8.86485	0.613195
$210$	−1.51423	−0.104492
$211$	19.8876	1.36912	0.684559	−	0.728957i	$-0.259995\pi$
$211$	19.8876	1.36912	0.684559	+	0.728957i	$0.259995\pi$
$212$	−1.70698	−0.117236
$213$	−10.1948	−0.698538
$214$	−11.6485	−0.796273
$215$	−1.03481	−0.0705737
$216$	−2.52138	−0.171558
$217$	9.79868	0.665178
$218$	−12.9341	−0.876007
$219$	−4.22971	−0.285817
$220$	−0.440860	−0.0297228
$221$	−1.66337	−0.111891
$222$	1.93017	0.129545
$223$	5.32041	0.356281	0.178140	−	0.984005i	$-0.442992\pi$
$223$	5.32041	0.356281	0.178140	+	0.984005i	$0.442992\pi$
$224$	2.00235	0.133787
$225$	−4.02762	−0.268508
$226$	9.42046	0.626640
$227$	−7.46092	−0.495198	−0.247599	−	0.968863i	$-0.579642\pi$
$227$	−7.46092	−0.495198	−0.247599	+	0.968863i	$0.579642\pi$
$228$	−2.54182	−0.168336
$229$	−3.69419	−0.244119	−0.122059	−	0.992523i	$-0.538950\pi$
$229$	−3.69419	−0.244119	−0.122059	+	0.992523i	$0.538950\pi$
$230$	−1.10567	−0.0729054
$231$	−1.24869	−0.0821580
$232$	7.18304	0.471590
$233$	18.4046	1.20572	0.602862	−	0.797846i	$-0.294027\pi$
$233$	18.4046	1.20572	0.602862	+	0.797846i	$0.294027\pi$
$234$	7.39405	0.483364
$235$	2.83348	0.184836
$236$	3.22636	0.210018
$237$	4.18910	0.272111
$238$	−0.530467	−0.0343851
$239$	6.93765	0.448759	0.224379	−	0.974502i	$-0.427964\pi$
$239$	6.93765	0.448759	0.224379	+	0.974502i	$0.427964\pi$
$240$	−4.52407	−0.292028
$241$	18.0371	1.16187	0.580934	−	0.813950i	$-0.302687\pi$
$241$	18.0371	1.16187	0.580934	+	0.813950i	$0.302687\pi$
$242$	14.4971	0.931912
$243$	−1.00000	−0.0641500
$244$	−1.06424	−0.0681310
$245$	−0.986091	−0.0629991
$246$	−5.38299	−0.343207
$247$	−34.1840	−2.17508
$248$	24.7062	1.56885
$249$	7.63061	0.483570
$250$	−13.6699	−0.864561
$251$	28.7000	1.81153	0.905765	−	0.423780i	$-0.139297\pi$
$251$	28.7000	1.81153	0.905765	+	0.423780i	$0.139297\pi$
$252$	0.358037	0.0225542
$253$	−0.911773	−0.0573227
$254$	13.6490	0.856415
$255$	0.340644	0.0213319
$256$	8.33395	0.520872
$257$	17.0309	1.06236	0.531180	−	0.847259i	$-0.321749\pi$
$257$	17.0309	1.06236	0.531180	+	0.847259i	$0.321749\pi$
$258$	1.61146	0.100325
$259$	1.25696	0.0781035
$260$	1.70001	0.105430
$261$	2.84885	0.176339
$262$	32.9759	2.03726
$263$	−3.79249	−0.233855	−0.116927	−	0.993140i	$-0.537305\pi$
$263$	−3.79249	−0.233855	−0.116927	+	0.993140i	$0.537305\pi$
$264$	−3.14843	−0.193773
$265$	4.70128	0.288797
$266$	−10.9016	−0.668422
$267$	11.6137	0.710745
$268$	−1.73406	−0.105925
$269$	25.2081	1.53696	0.768481	−	0.639872i	$-0.221013\pi$
$269$	25.2081	1.53696	0.768481	+	0.639872i	$0.221013\pi$
$270$	−1.51423	−0.0921532
$271$	2.62373	0.159380	0.0796900	−	0.996820i	$-0.474607\pi$
$271$	2.62373	0.159380	0.0796900	+	0.996820i	$0.474607\pi$
$272$	−1.58488	−0.0960973
$273$	4.81512	0.291424
$274$	33.6603	2.03350
$275$	−5.02927	−0.303276
$276$	0.261433	0.0157364
$277$	5.81992	0.349685	0.174842	−	0.984596i	$-0.444058\pi$
$277$	5.81992	0.349685	0.174842	+	0.984596i	$0.444058\pi$
$278$	−20.1775	−1.21017
$279$	9.79868	0.586632
$280$	−2.48631	−0.148586
$281$	−15.2326	−0.908702	−0.454351	−	0.890823i	$-0.650129\pi$
$281$	−15.2326	−0.908702	−0.454351	+	0.890823i	$0.650129\pi$
$282$	−4.41244	−0.262757
$283$	10.0896	0.599767	0.299884	−	0.953976i	$-0.403052\pi$
$283$	10.0896	0.599767	0.299884	+	0.953976i	$0.403052\pi$
$284$	3.65013	0.216595
$285$	7.00056	0.414678
$286$	9.23289	0.545952
$287$	−3.50549	−0.206922
$288$	2.00235	0.117989
$289$	−16.8807	−0.992980
$290$	4.31382	0.253316
$291$	−1.49408	−0.0875845
$292$	1.51439	0.0886232
$293$	7.95291	0.464614	0.232307	−	0.972643i	$-0.425373\pi$
$293$	7.95291	0.464614	0.232307	+	0.972643i	$0.425373\pi$
$294$	1.53559	0.0895574
$295$	−8.88589	−0.517357
$296$	3.16927	0.184210
$297$	−1.24869	−0.0724565
$298$	18.9341	1.09683
$299$	3.51591	0.203330
$300$	1.44204	0.0832562
$301$	1.04941	0.0604870
$302$	−26.4044	−1.51940
$303$	6.35004	0.364800
$304$	−32.5708	−1.86806
$305$	2.93109	0.167833
$306$	−0.530467	−0.0303248
$307$	16.2787	0.929073	0.464537	−	0.885554i	$-0.346221\pi$
$307$	16.2787	0.929073	0.464537	+	0.885554i	$0.346221\pi$
$308$	0.447079	0.0254747
$309$	−3.22672	−0.183562
$310$	14.8375	0.842712
$311$	14.4507	0.819424	0.409712	−	0.912215i	$-0.365629\pi$
$311$	14.4507	0.819424	0.409712	+	0.912215i	$0.365629\pi$
$312$	12.1407	0.687335
$313$	−8.31737	−0.470126	−0.235063	−	0.971980i	$-0.575530\pi$
$313$	−8.31737	−0.470126	−0.235063	+	0.971980i	$0.575530\pi$
$314$	−19.6247	−1.10749
$315$	−0.986091	−0.0555599
$316$	−1.49985	−0.0843734
$317$	14.8776	0.835612	0.417806	−	0.908536i	$-0.362799\pi$
$317$	14.8776	0.835612	0.417806	+	0.908536i	$0.362799\pi$
$318$	−7.32107	−0.410545
$319$	3.55734	0.199173
$320$	−6.01613	−0.336312
$321$	−7.58567	−0.423391
$322$	1.12126	0.0624854
$323$	2.45244	0.136458
$324$	0.358037	0.0198910
$325$	19.3935	1.07576
$326$	−13.9593	−0.773134
$327$	−8.42288	−0.465786
$328$	−8.83867	−0.488034
$329$	−2.87345	−0.158418
$330$	−1.89081	−0.104086
$331$	−28.2820	−1.55452	−0.777259	−	0.629181i	$-0.783390\pi$
$331$	−28.2820	−1.55452	−0.777259	+	0.629181i	$0.783390\pi$
$332$	−2.73205	−0.149940
$333$	1.25696	0.0688808
$334$	−8.85507	−0.484528
$335$	4.77589	0.260935
$336$	4.58788	0.250290
$337$	−14.4707	−0.788270	−0.394135	−	0.919053i	$-0.628956\pi$
$337$	−14.4707	−0.788270	−0.394135	+	0.919053i	$0.628956\pi$
$338$	−15.6405	−0.850733
$339$	6.13475	0.333194
$340$	−0.121963	−0.00661438
$341$	12.2355	0.662592
$342$	−10.9016	−0.589492
$343$	1.00000	0.0539949
$344$	2.64596	0.142661
$345$	−0.720026	−0.0387649
$346$	25.9024	1.39252
$347$	21.4550	1.15176	0.575882	−	0.817533i	$-0.304659\pi$
$347$	21.4550	1.15176	0.575882	+	0.817533i	$0.304659\pi$
$348$	−1.02000	−0.0546775
$349$	11.5110	0.616171	0.308085	−	0.951359i	$-0.400312\pi$
$349$	11.5110	0.616171	0.308085	+	0.951359i	$0.400312\pi$
$350$	6.18478	0.330590
$351$	4.81512	0.257012
$352$	2.50032	0.133267
$353$	21.2106	1.12892	0.564462	−	0.825459i	$-0.309084\pi$
$353$	21.2106	1.12892	0.564462	+	0.825459i	$0.309084\pi$
$354$	13.8376	0.735458
$355$	−10.0530	−0.533559
$356$	−4.15813	−0.220380
$357$	−0.345448	−0.0182831
$358$	−30.6775	−1.62136
$359$	−5.74396	−0.303154	−0.151577	−	0.988445i	$-0.548435\pi$
$359$	−5.74396	−0.303154	−0.151577	+	0.988445i	$0.548435\pi$
$360$	−2.48631	−0.131040
$361$	31.4002	1.65264
$362$	5.71223	0.300228
$363$	9.44077	0.495512
$364$	−1.72399	−0.0903617
$365$	−4.17088	−0.218314
$366$	−4.56443	−0.238587
$367$	28.0138	1.46231	0.731154	−	0.682212i	$-0.238982\pi$
$367$	28.0138	1.46231	0.731154	+	0.682212i	$0.238982\pi$
$368$	3.34999	0.174630
$369$	−3.50549	−0.182488
$370$	1.90332	0.0989491
$371$	−4.76759	−0.247521
$372$	−3.50829	−0.181897
$373$	14.5412	0.752917	0.376458	−	0.926434i	$-0.377142\pi$
$373$	14.5412	0.752917	0.376458	+	0.926434i	$0.377142\pi$
$374$	−0.662391	−0.0342514
$375$	−8.90206	−0.459700
$376$	−7.24506	−0.373635
$377$	−13.7176	−0.706490
$378$	1.53559	0.0789822
$379$	−0.412014	−0.0211638	−0.0105819	−	0.999944i	$-0.503368\pi$
$379$	−0.412014	−0.0211638	−0.0105819	+	0.999944i	$0.503368\pi$
$380$	−2.50646	−0.128579
$381$	8.88845	0.455369
$382$	1.53559	0.0785676
$383$	11.8125	0.603591	0.301795	−	0.953373i	$-0.402414\pi$
$383$	11.8125	0.603591	0.301795	+	0.953373i	$0.402414\pi$
$384$	13.3733	0.682454
$385$	−1.23132	−0.0627541
$386$	−19.8006	−1.00782
$387$	1.04941	0.0533445
$388$	0.534937	0.0271573
$389$	−13.2173	−0.670146	−0.335073	−	0.942192i	$-0.608761\pi$
$389$	−13.2173	−0.670146	−0.335073	+	0.942192i	$0.608761\pi$
$390$	7.29120	0.369204
$391$	−0.252240	−0.0127563
$392$	2.52138	0.127349
$393$	21.4744	1.08324
$394$	28.7491	1.44836
$395$	4.13083	0.207845
$396$	0.447079	0.0224666
$397$	15.0139	0.753528	0.376764	−	0.926309i	$-0.377037\pi$
$397$	15.0139	0.753528	0.376764	+	0.926309i	$0.377037\pi$
$398$	−22.3998	−1.12280
$399$	−7.09931	−0.355410
$400$	18.4783	0.923914
$401$	−3.23731	−0.161664	−0.0808318	−	0.996728i	$-0.525758\pi$
$401$	−3.23731	−0.161664	−0.0808318	+	0.996728i	$0.525758\pi$
$402$	−7.43725	−0.370936
$403$	−47.1818	−2.35029
$404$	−2.27355	−0.113113
$405$	−0.986091	−0.0489993
$406$	−4.37467	−0.217111
$407$	1.56955	0.0777998
$408$	−0.871007	−0.0431213
$409$	29.7744	1.47225	0.736124	−	0.676847i	$-0.236654\pi$
$409$	29.7744	1.47225	0.736124	+	0.676847i	$0.236654\pi$
$410$	−5.30812	−0.262149
$411$	21.9201	1.08124
$412$	1.15529	0.0569169
$413$	9.01123	0.443414
$414$	1.12126	0.0551070
$415$	7.52448	0.369362
$416$	−9.64153	−0.472715
$417$	−13.1399	−0.643463
$418$	−13.6128	−0.665823
$419$	20.4836	1.00069	0.500344	−	0.865826i	$-0.333207\pi$
$419$	20.4836	1.00069	0.500344	+	0.865826i	$0.333207\pi$
$420$	0.353058	0.0172274
$421$	27.5652	1.34344	0.671722	−	0.740803i	$-0.265555\pi$
$421$	27.5652	1.34344	0.671722	+	0.740803i	$0.265555\pi$
$422$	−30.5392	−1.48662
$423$	−2.87345	−0.139712
$424$	−12.0209	−0.583788
$425$	−1.39134	−0.0674897
$426$	15.6551	0.758491
$427$	−2.97243	−0.143846
$428$	2.71595	0.131281
$429$	6.01260	0.290291
$430$	1.58905	0.0766308
$431$	−16.6351	−0.801284	−0.400642	−	0.916235i	$-0.631213\pi$
$431$	−16.6351	−0.801284	−0.400642	+	0.916235i	$0.631213\pi$
$432$	4.58788	0.220735
$433$	22.7574	1.09365	0.546826	−	0.837246i	$-0.315836\pi$
$433$	22.7574	1.09365	0.546826	+	0.837246i	$0.315836\pi$
$434$	−15.0468	−0.722267
$435$	2.80923	0.134692
$436$	3.01571	0.144426
$437$	−5.18379	−0.247974
$438$	6.49510	0.310348
$439$	−27.0839	−1.29264	−0.646321	−	0.763065i	$-0.723693\pi$
$439$	−27.0839	−1.29264	−0.646321	+	0.763065i	$0.723693\pi$
$440$	−3.10464	−0.148008
$441$	1.00000	0.0476190
$442$	2.55426	0.121494
$443$	−5.91590	−0.281073	−0.140536	−	0.990076i	$-0.544883\pi$
$443$	−5.91590	−0.281073	−0.140536	+	0.990076i	$0.544883\pi$
$444$	−0.450037	−0.0213578
$445$	11.4521	0.542883
$446$	−8.16996	−0.386859
$447$	12.3302	0.583199
$448$	6.10098	0.288244
$449$	−20.7081	−0.977275	−0.488638	−	0.872487i	$-0.662506\pi$
$449$	−20.7081	−0.977275	−0.488638	+	0.872487i	$0.662506\pi$
$450$	6.18478	0.291553
$451$	−4.37727	−0.206118
$452$	−2.19647	−0.103313
$453$	−17.1950	−0.807889
$454$	11.4569	0.537699
$455$	4.74814	0.222596
$456$	−17.9001	−0.838247
$457$	28.4701	1.33178	0.665888	−	0.746051i	$-0.268053\pi$
$457$	28.4701	1.33178	0.665888	+	0.746051i	$0.268053\pi$
$458$	5.67276	0.265071
$459$	−0.345448	−0.0161242
$460$	0.257796	0.0120198
$461$	−31.9453	−1.48784	−0.743921	−	0.668267i	$-0.767036\pi$
$461$	−31.9453	−1.48784	−0.743921	+	0.668267i	$0.767036\pi$
$462$	1.91748	0.0892093
$463$	−16.4531	−0.764639	−0.382319	−	0.924030i	$-0.624875\pi$
$463$	−16.4531	−0.764639	−0.382319	+	0.924030i	$0.624875\pi$
$464$	−13.0702	−0.606769
$465$	9.66239	0.448083
$466$	−28.2619	−1.30921
$467$	−12.8762	−0.595838	−0.297919	−	0.954591i	$-0.596292\pi$
$467$	−12.8762	−0.595838	−0.297919	+	0.954591i	$0.596292\pi$
$468$	−1.72399	−0.0796916
$469$	−4.84325	−0.223641
$470$	−4.35107	−0.200700
$471$	−12.7799	−0.588868
$472$	22.7208	1.04581
$473$	1.31039	0.0602518
$474$	−6.43274	−0.295465
$475$	−28.5933	−1.31195
$476$	0.123683	0.00566902
$477$	−4.76759	−0.218293
$478$	−10.6534	−0.487274
$479$	11.2150	0.512427	0.256213	−	0.966620i	$-0.417525\pi$
$479$	11.2150	0.512427	0.256213	+	0.966620i	$0.417525\pi$
$480$	1.97450	0.0901230
$481$	−6.05239	−0.275965
$482$	−27.6975	−1.26159
$483$	0.730182	0.0332244
$484$	−3.38015	−0.153643
$485$	−1.47330	−0.0668991
$486$	1.53559	0.0696558
$487$	13.6003	0.616288	0.308144	−	0.951340i	$-0.400292\pi$
$487$	13.6003	0.616288	0.308144	+	0.951340i	$0.400292\pi$
$488$	−7.49463	−0.339266
$489$	−9.09051	−0.411087
$490$	1.51423	0.0684060
$491$	1.69617	0.0765471	0.0382736	−	0.999267i	$-0.487814\pi$
$491$	1.69617	0.0765471	0.0382736	+	0.999267i	$0.487814\pi$
$492$	1.25510	0.0565841
$493$	0.984131	0.0443230
$494$	52.4926	2.36175
$495$	−1.23132	−0.0553439
$496$	−44.9552	−2.01855
$497$	10.1948	0.457300
$498$	−11.7175	−0.525074
$499$	−35.2688	−1.57885	−0.789425	−	0.613847i	$-0.789621\pi$
$499$	−35.2688	−1.57885	−0.789425	+	0.613847i	$0.789621\pi$
$500$	3.18727	0.142539
$501$	−5.76656	−0.257631
$502$	−44.0715	−1.96701
$503$	−0.604103	−0.0269356	−0.0134678	−	0.999909i	$-0.504287\pi$
$503$	−0.604103	−0.0269356	−0.0134678	+	0.999909i	$0.504287\pi$
$504$	2.52138	0.112311
$505$	6.26172	0.278643
$506$	1.40011	0.0622425
$507$	−10.1854	−0.452347
$508$	−3.18240	−0.141196
$509$	23.1242	1.02496	0.512481	−	0.858698i	$-0.328726\pi$
$509$	23.1242	1.02496	0.512481	+	0.858698i	$0.328726\pi$
$510$	−0.523089	−0.0231628
$511$	4.22971	0.187111
$512$	13.9491	0.616468
$513$	−7.09931	−0.313442
$514$	−26.1525	−1.15354
$515$	−3.18184	−0.140209
$516$	−0.375728	−0.0165405
$517$	−3.58805	−0.157802
$518$	−1.93017	−0.0848068
$519$	16.8681	0.740426
$520$	11.9719	0.525002
$521$	−24.8599	−1.08913	−0.544567	−	0.838717i	$-0.683306\pi$
$521$	−24.8599	−1.08913	−0.544567	+	0.838717i	$0.683306\pi$
$522$	−4.37467	−0.191474
$523$	41.5929	1.81873	0.909365	−	0.415999i	$-0.136568\pi$
$523$	41.5929	1.81873	0.909365	+	0.415999i	$0.136568\pi$
$524$	−7.68865	−0.335880
$525$	4.02762	0.175780
$526$	5.82371	0.253926
$527$	3.38494	0.147450
$528$	5.72886	0.249317
$529$	−22.4668	−0.976819
$530$	−7.21924	−0.313584
$531$	9.01123	0.391054
$532$	2.54182	0.110202
$533$	16.8793	0.731125
$534$	−17.8338	−0.771745
$535$	−7.48016	−0.323395
$536$	−12.2117	−0.527464
$537$	−19.9777	−0.862100
$538$	−38.7092	−1.66887
$539$	1.24869	0.0537850
$540$	0.353058	0.0151932
$541$	13.4275	0.577295	0.288647	−	0.957436i	$-0.406795\pi$
$541$	13.4275	0.577295	0.288647	+	0.957436i	$0.406795\pi$
$542$	−4.02897	−0.173059
$543$	3.71989	0.159636
$544$	0.691708	0.0296567
$545$	−8.30572	−0.355778
$546$	−7.39405	−0.316436
$547$	−0.316161	−0.0135181	−0.00675904	−	0.999977i	$-0.502151\pi$
$547$	−0.316161	−0.0135181	−0.00675904	+	0.999977i	$0.502151\pi$
$548$	−7.84823	−0.335260
$549$	−2.97243	−0.126860
$550$	7.72289	0.329305
$551$	20.2249	0.861608
$552$	1.84107	0.0783611
$553$	−4.18910	−0.178139
$554$	−8.93701	−0.379697
$555$	1.23947	0.0526127
$556$	4.70457	0.199518
$557$	21.9542	0.930230	0.465115	−	0.885250i	$-0.346013\pi$
$557$	21.9542	0.930230	0.465115	+	0.885250i	$0.346013\pi$
$558$	−15.0468	−0.636980
$559$	−5.05303	−0.213720
$560$	4.52407	0.191177
$561$	−0.431359	−0.0182120
$562$	23.3911	0.986693
$563$	17.3249	0.730157	0.365078	−	0.930977i	$-0.381042\pi$
$563$	17.3249	0.730157	0.365078	+	0.930977i	$0.381042\pi$
$564$	1.02880	0.0433204
$565$	6.04942	0.254501
$566$	−15.4936	−0.651243
$567$	1.00000	0.0419961
$568$	25.7050	1.07856
$569$	−20.6265	−0.864710	−0.432355	−	0.901704i	$-0.642317\pi$
$569$	−20.6265	−0.864710	−0.432355	+	0.901704i	$0.642317\pi$
$570$	−10.7500	−0.450268
$571$	37.2066	1.55705	0.778524	−	0.627614i	$-0.215969\pi$
$571$	37.2066	1.55705	0.778524	+	0.627614i	$0.215969\pi$
$572$	−2.15274	−0.0900104
$573$	1.00000	0.0417756
$574$	5.38299	0.224682
$575$	2.94090	0.122644
$576$	6.10098	0.254208
$577$	−40.9324	−1.70404	−0.852019	−	0.523511i	$-0.824622\pi$
$577$	−40.9324	−1.70404	−0.852019	+	0.523511i	$0.824622\pi$
$578$	25.9218	1.07820
$579$	−12.8944	−0.535875
$580$	−1.00581	−0.0417639
$581$	−7.63061	−0.316571
$582$	2.29429	0.0951016
$583$	−5.95326	−0.246559
$584$	10.6647	0.441309
$585$	4.74814	0.196312
$586$	−12.2124	−0.504490
$587$	−32.6074	−1.34585	−0.672925	−	0.739711i	$-0.734962\pi$
$587$	−32.6074	−1.34585	−0.672925	+	0.739711i	$0.734962\pi$
$588$	−0.358037	−0.0147652
$589$	69.5638	2.86633
$590$	13.6451	0.561760
$591$	18.7218	0.770114
$592$	−5.76677	−0.237013
$593$	−4.35695	−0.178919	−0.0894593	−	0.995990i	$-0.528514\pi$
$593$	−4.35695	−0.178919	−0.0894593	+	0.995990i	$0.528514\pi$
$594$	1.91748	0.0786752
$595$	−0.340644	−0.0139650
$596$	−4.41467	−0.180832
$597$	−14.5871	−0.597011
$598$	−5.39900	−0.220782
$599$	−29.0560	−1.18720	−0.593599	−	0.804761i	$-0.702293\pi$
$599$	−29.0560	−1.18720	−0.593599	+	0.804761i	$0.702293\pi$
$600$	10.1552	0.414583
$601$	26.4978	1.08087	0.540435	−	0.841386i	$-0.318260\pi$
$601$	26.4978	1.08087	0.540435	+	0.841386i	$0.318260\pi$
$602$	−1.61146	−0.0656783
$603$	−4.84325	−0.197232
$604$	6.15644	0.250502
$605$	9.30946	0.378483
$606$	−9.75106	−0.396110
$607$	34.8926	1.41625	0.708124	−	0.706088i	$-0.249542\pi$
$607$	34.8926	1.41625	0.708124	+	0.706088i	$0.249542\pi$
$608$	14.2153	0.576505
$609$	−2.84885	−0.115441
$610$	−4.50095	−0.182238
$611$	13.8360	0.559744
$612$	0.123683	0.00499961
$613$	20.6494	0.834021	0.417010	−	0.908902i	$-0.363078\pi$
$613$	20.6494	0.834021	0.417010	+	0.908902i	$0.363078\pi$
$614$	−24.9974	−1.00881
$615$	−3.45673	−0.139389
$616$	3.14843	0.126854
$617$	44.6905	1.79917	0.899587	−	0.436742i	$-0.143868\pi$
$617$	44.6905	1.79917	0.899587	+	0.436742i	$0.143868\pi$
$618$	4.95492	0.199316
$619$	27.5143	1.10589	0.552946	−	0.833217i	$-0.313503\pi$
$619$	27.5143	1.10589	0.552946	+	0.833217i	$0.313503\pi$
$620$	−3.45950	−0.138937
$621$	0.730182	0.0293012
$622$	−22.1904	−0.889752
$623$	−11.6137	−0.465292
$624$	−22.0912	−0.884356
$625$	11.3599	0.454395
$626$	12.7721	0.510475
$627$	−8.86485	−0.354028
$628$	4.57569	0.182590
$629$	0.434214	0.0173132
$630$	1.51423	0.0603284
$631$	−13.4814	−0.536686	−0.268343	−	0.963323i	$-0.586476\pi$
$631$	−13.4814	−0.536686	−0.268343	+	0.963323i	$0.586476\pi$
$632$	−10.5623	−0.420146
$633$	−19.8876	−0.790461
$634$	−22.8460	−0.907329
$635$	8.76482	0.347821
$636$	1.70698	0.0676860
$637$	−4.81512	−0.190782
$638$	−5.46262	−0.216267
$639$	10.1948	0.403301
$640$	13.1873	0.521274
$641$	22.5323	0.889971	0.444985	−	0.895538i	$-0.353209\pi$
$641$	22.5323	0.889971	0.444985	+	0.895538i	$0.353209\pi$
$642$	11.6485	0.459729
$643$	−16.9680	−0.669152	−0.334576	−	0.942369i	$-0.608593\pi$
$643$	−16.9680	−0.669152	−0.334576	+	0.942369i	$0.608593\pi$
$644$	−0.261433	−0.0103019
$645$	1.03481	0.0407457
$646$	−3.76595	−0.148169
$647$	−10.4743	−0.411788	−0.205894	−	0.978574i	$-0.566010\pi$
$647$	−10.4743	−0.411788	−0.205894	+	0.978574i	$0.566010\pi$
$648$	2.52138	0.0990492
$649$	11.2523	0.441690
$650$	−29.7804	−1.16809
$651$	−9.79868	−0.384041
$652$	3.25474	0.127466
$653$	24.5112	0.959197	0.479598	−	0.877488i	$-0.340782\pi$
$653$	24.5112	0.959197	0.479598	+	0.877488i	$0.340782\pi$
$654$	12.9341	0.505763
$655$	21.1757	0.827404
$656$	16.0828	0.627926
$657$	4.22971	0.165017
$658$	4.41244	0.172015
$659$	17.4899	0.681308	0.340654	−	0.940189i	$-0.389352\pi$
$659$	17.4899	0.681308	0.340654	+	0.940189i	$0.389352\pi$
$660$	0.440860	0.0171605
$661$	−40.4288	−1.57250	−0.786248	−	0.617911i	$-0.787979\pi$
$661$	−40.4288	−1.57250	−0.786248	+	0.617911i	$0.787979\pi$
$662$	43.4295	1.68794
$663$	1.66337	0.0646001
$664$	−19.2397	−0.746645
$665$	−7.00056	−0.271470
$666$	−1.93017	−0.0747926
$667$	−2.08018	−0.0805449
$668$	2.06464	0.0798835
$669$	−5.32041	−0.205699
$670$	−7.33380	−0.283330
$671$	−3.71165	−0.143287
$672$	−2.00235	−0.0772422
$673$	0.251642	0.00970009	0.00485004	−	0.999988i	$-0.498456\pi$
$673$	0.251642	0.00970009	0.00485004	+	0.999988i	$0.498456\pi$
$674$	22.2211	0.855924
$675$	4.02762	0.155023
$676$	3.64674	0.140259
$677$	29.9406	1.15071	0.575355	−	0.817904i	$-0.304864\pi$
$677$	29.9406	1.15071	0.575355	+	0.817904i	$0.304864\pi$
$678$	−9.42046	−0.361791
$679$	1.49408	0.0573375
$680$	−0.858893	−0.0329370
$681$	7.46092	0.285903
$682$	−18.7888	−0.719460
$683$	19.2504	0.736595	0.368298	−	0.929708i	$-0.379941\pi$
$683$	19.2504	0.736595	0.368298	+	0.929708i	$0.379941\pi$
$684$	2.54182	0.0971888
$685$	21.6153	0.825876
$686$	−1.53559	−0.0586291
$687$	3.69419	0.140942
$688$	−4.81457	−0.183554
$689$	22.9565	0.874574
$690$	1.10567	0.0420920
$691$	40.6468	1.54628	0.773139	−	0.634237i	$-0.218686\pi$
$691$	40.6468	1.54628	0.773139	+	0.634237i	$0.218686\pi$
$692$	−6.03940	−0.229584
$693$	1.24869	0.0474339
$694$	−32.9461	−1.25062
$695$	−12.9571	−0.491492
$696$	−7.18304	−0.272272
$697$	−1.21096	−0.0458686
$698$	−17.6762	−0.669054
$699$	−18.4046	−0.696125
$700$	−1.44204	−0.0545040
$701$	14.4863	0.547139	0.273570	−	0.961852i	$-0.411796\pi$
$701$	14.4863	0.547139	0.273570	+	0.961852i	$0.411796\pi$
$702$	−7.39405	−0.279070
$703$	8.92352	0.336557
$704$	7.61826	0.287124
$705$	−2.83348	−0.106715
$706$	−32.5707	−1.22582
$707$	−6.35004	−0.238818
$708$	−3.22636	−0.121254
$709$	−10.8375	−0.407013	−0.203506	−	0.979074i	$-0.565234\pi$
$709$	−10.8375	−0.407013	−0.203506	+	0.979074i	$0.565234\pi$
$710$	15.4373	0.579353
$711$	−4.18910	−0.157103
$712$	−29.2825	−1.09741
$713$	−7.15482	−0.267950
$714$	0.530467	0.0198522
$715$	5.92897	0.221731
$716$	7.15275	0.267311
$717$	−6.93765	−0.259091
$718$	8.82036	0.329173
$719$	44.2203	1.64914	0.824569	−	0.565761i	$-0.191417\pi$
$719$	44.2203	1.64914	0.824569	+	0.565761i	$0.191417\pi$
$720$	4.52407	0.168602
$721$	3.22672	0.120169
$722$	−48.2178	−1.79448
$723$	−18.0371	−0.670805
$724$	−1.33186	−0.0494982
$725$	−11.4741	−0.426137
$726$	−14.4971	−0.538040
$727$	−20.6049	−0.764195	−0.382097	−	0.924122i	$-0.624798\pi$
$727$	−20.6049	−0.764195	−0.382097	+	0.924122i	$0.624798\pi$
$728$	−12.1407	−0.449966
$729$	1.00000	0.0370370
$730$	6.40476	0.237051
$731$	0.362517	0.0134082
$732$	1.06424	0.0393355
$733$	−25.4015	−0.938225	−0.469113	−	0.883138i	$-0.655426\pi$
$733$	−25.4015	−0.938225	−0.469113	+	0.883138i	$0.655426\pi$
$734$	−43.0177	−1.58781
$735$	0.986091	0.0363725
$736$	−1.46208	−0.0538929
$737$	−6.04773	−0.222771
$738$	5.38299	0.198151
$739$	−27.6575	−1.01740	−0.508700	−	0.860944i	$-0.669874\pi$
$739$	−27.6575	−1.01740	−0.508700	+	0.860944i	$0.669874\pi$
$740$	−0.443778	−0.0163136
$741$	34.1840	1.25578
$742$	7.32107	0.268765
$743$	24.8101	0.910194	0.455097	−	0.890442i	$-0.349605\pi$
$743$	24.8101	0.910194	0.455097	+	0.890442i	$0.349605\pi$
$744$	−24.7062	−0.905774
$745$	12.1587	0.445461
$746$	−22.3294	−0.817537
$747$	−7.63061	−0.279190
$748$	0.154443	0.00564698
$749$	7.58567	0.277174
$750$	13.6699	0.499155
$751$	−8.42648	−0.307487	−0.153743	−	0.988111i	$-0.549133\pi$
$751$	−8.42648	−0.307487	−0.153743	+	0.988111i	$0.549133\pi$
$752$	13.1830	0.480736
$753$	−28.7000	−1.04589
$754$	21.0645	0.767125
$755$	−16.9558	−0.617084
$756$	−0.358037	−0.0130217
$757$	35.1929	1.27911	0.639555	−	0.768746i	$-0.279119\pi$
$757$	35.1929	1.27911	0.639555	+	0.768746i	$0.279119\pi$
$758$	0.632685	0.0229802
$759$	0.911773	0.0330953
$760$	−17.6511	−0.640272
$761$	17.0110	0.616650	0.308325	−	0.951281i	$-0.400232\pi$
$761$	17.0110	0.616650	0.308325	+	0.951281i	$0.400232\pi$
$762$	−13.6490	−0.494452
$763$	8.42288	0.304929
$764$	−0.358037	−0.0129533
$765$	−0.340644	−0.0123160
$766$	−18.1392	−0.655395
$767$	−43.3901	−1.56673
$768$	−8.33395	−0.300725
$769$	9.68475	0.349241	0.174620	−	0.984636i	$-0.444130\pi$
$769$	9.68475	0.349241	0.174620	+	0.984636i	$0.444130\pi$
$770$	1.89081	0.0681401
$771$	−17.0309	−0.613353
$772$	4.61670	0.166159
$773$	35.8957	1.29108	0.645539	−	0.763728i	$-0.276633\pi$
$773$	35.8957	1.29108	0.645539	+	0.763728i	$0.276633\pi$
$774$	−1.61146	−0.0579228
$775$	−39.4654	−1.41764
$776$	3.76715	0.135233
$777$	−1.25696	−0.0450931
$778$	20.2964	0.727662
$779$	−24.8865	−0.891652
$780$	−1.70001	−0.0608702
$781$	12.7302	0.455522
$782$	0.387338	0.0138512
$783$	−2.84885	−0.101810
$784$	−4.58788	−0.163853
$785$	−12.6022	−0.449791
$786$	−32.9759	−1.17621
$787$	−52.2397	−1.86214	−0.931072	−	0.364834i	$-0.881126\pi$
$787$	−52.2397	−1.86214	−0.931072	+	0.364834i	$0.881126\pi$
$788$	−6.70312	−0.238789
$789$	3.79249	0.135016
$790$	−6.34327	−0.225683
$791$	−6.13475	−0.218127
$792$	3.14843	0.111875
$793$	14.3126	0.508255
$794$	−23.0553	−0.818200
$795$	−4.70128	−0.166737
$796$	5.22274	0.185115
$797$	14.4831	0.513019	0.256509	−	0.966542i	$-0.417428\pi$
$797$	14.4831	0.513019	0.256509	+	0.966542i	$0.417428\pi$
$798$	10.9016	0.385913
$799$	−0.992628	−0.0351167
$800$	−8.06470	−0.285130
$801$	−11.6137	−0.410349
$802$	4.97118	0.175539
$803$	5.28161	0.186384
$804$	1.73406	0.0611557
$805$	0.720026	0.0253776
$806$	72.4519	2.55201
$807$	−25.2081	−0.887366
$808$	−16.0109	−0.563261
$809$	−25.0959	−0.882326	−0.441163	−	0.897427i	$-0.645434\pi$
$809$	−25.0959	−0.882326	−0.441163	+	0.897427i	$0.645434\pi$
$810$	1.51423	0.0532047
$811$	0.620850	0.0218010	0.0109005	−	0.999941i	$-0.496530\pi$
$811$	0.620850	0.0218010	0.0109005	+	0.999941i	$0.496530\pi$
$812$	1.02000	0.0357948
$813$	−2.62373	−0.0920181
$814$	−2.41019	−0.0844771
$815$	−8.96407	−0.313998
$816$	1.58488	0.0554818
$817$	7.45008	0.260645
$818$	−45.7212	−1.59860
$819$	−4.81512	−0.168254
$820$	1.23764	0.0432202
$821$	−6.82130	−0.238065	−0.119032	−	0.992890i	$-0.537979\pi$
$821$	−6.82130	−0.238065	−0.119032	+	0.992890i	$0.537979\pi$
$822$	−33.6603	−1.17404
$823$	16.2413	0.566137	0.283068	−	0.959100i	$-0.408648\pi$
$823$	16.2413	0.566137	0.283068	+	0.959100i	$0.408648\pi$
$824$	8.13580	0.283424
$825$	5.02927	0.175097
$826$	−13.8376	−0.481470
$827$	−38.5968	−1.34214	−0.671071	−	0.741393i	$-0.734165\pi$
$827$	−38.5968	−1.34214	−0.671071	+	0.741393i	$0.734165\pi$
$828$	−0.261433	−0.00908541
$829$	26.5357	0.921624	0.460812	−	0.887498i	$-0.347558\pi$
$829$	26.5357	0.921624	0.460812	+	0.887498i	$0.347558\pi$
$830$	−11.5545	−0.401063
$831$	−5.81992	−0.201891
$832$	−29.3770	−1.01846
$833$	0.345448	0.0119691
$834$	20.1775	0.698690
$835$	−5.68635	−0.196784
$836$	3.17395	0.109773
$837$	−9.79868	−0.338692
$838$	−31.4544	−1.08657
$839$	21.0993	0.728430	0.364215	−	0.931315i	$-0.381337\pi$
$839$	21.0993	0.728430	0.364215	+	0.931315i	$0.381337\pi$
$840$	2.48631	0.0857859
$841$	−20.8840	−0.720140
$842$	−42.3288	−1.45875
$843$	15.2326	0.524639
$844$	7.12050	0.245098
$845$	−10.0437	−0.345513
$846$	4.41244	0.151703
$847$	−9.44077	−0.324389
$848$	21.8732	0.751128
$849$	−10.0896	−0.346276
$850$	2.13652	0.0732821
$851$	−0.917807	−0.0314620
$852$	−3.65013	−0.125051
$853$	15.0635	0.515764	0.257882	−	0.966176i	$-0.416975\pi$
$853$	15.0635	0.515764	0.257882	+	0.966176i	$0.416975\pi$
$854$	4.56443	0.156192
$855$	−7.00056	−0.239414
$856$	19.1264	0.653726
$857$	−43.1333	−1.47341	−0.736703	−	0.676216i	$-0.763619\pi$
$857$	−43.1333	−1.47341	−0.736703	+	0.676216i	$0.763619\pi$
$858$	−9.23289	−0.315206
$859$	−1.25350	−0.0427689	−0.0213844	−	0.999771i	$-0.506807\pi$
$859$	−1.25350	−0.0427689	−0.0213844	+	0.999771i	$0.506807\pi$
$860$	−0.370502	−0.0126340
$861$	3.50549	0.119467
$862$	25.5447	0.870055
$863$	−32.5981	−1.10965	−0.554827	−	0.831966i	$-0.687215\pi$
$863$	−32.5981	−1.10965	−0.554827	+	0.831966i	$0.687215\pi$
$864$	−2.00235	−0.0681212
$865$	16.6335	0.565554
$866$	−34.9461	−1.18752
$867$	16.8807	0.573297
$868$	3.50829	0.119079
$869$	−5.23090	−0.177446
$870$	−4.31382	−0.146252
$871$	23.3208	0.790196
$872$	21.2373	0.719185
$873$	1.49408	0.0505670
$874$	7.96017	0.269257
$875$	8.90206	0.300945
$876$	−1.51439	−0.0511666
$877$	−28.0531	−0.947284	−0.473642	−	0.880717i	$-0.657061\pi$
$877$	−28.0531	−0.947284	−0.473642	+	0.880717i	$0.657061\pi$
$878$	41.5897	1.40359
$879$	−7.95291	−0.268245
$880$	5.64918	0.190434
$881$	5.00380	0.168582	0.0842912	−	0.996441i	$-0.473137\pi$
$881$	5.00380	0.168582	0.0842912	+	0.996441i	$0.473137\pi$
$882$	−1.53559	−0.0517060
$883$	−19.0623	−0.641496	−0.320748	−	0.947165i	$-0.603934\pi$
$883$	−19.0623	−0.641496	−0.320748	+	0.947165i	$0.603934\pi$
$884$	−0.595550	−0.0200305
$885$	8.88589	0.298696
$886$	9.08439	0.305196
$887$	−54.9202	−1.84404	−0.922019	−	0.387143i	$-0.873462\pi$
$887$	−54.9202	−1.84404	−0.922019	+	0.387143i	$0.873462\pi$
$888$	−3.16927	−0.106354
$889$	−8.88845	−0.298109
$890$	−17.5858	−0.589477
$891$	1.24869	0.0418328
$892$	1.90490	0.0637809
$893$	−20.3995	−0.682643
$894$	−18.9341	−0.633252
$895$	−19.6998	−0.658492
$896$	−13.3733	−0.446771
$897$	−3.51591	−0.117393
$898$	31.7991	1.06115
$899$	27.9150	0.931017
$900$	−1.44204	−0.0480680
$901$	−1.64696	−0.0548681
$902$	6.72170	0.223808
$903$	−1.04941	−0.0349222
$904$	−15.4681	−0.514460
$905$	3.66815	0.121934
$906$	26.4044	0.877228
$907$	−36.9504	−1.22692	−0.613460	−	0.789726i	$-0.710223\pi$
$907$	−36.9504	−1.22692	−0.613460	+	0.789726i	$0.710223\pi$
$908$	−2.67129	−0.0886498
$909$	−6.35004	−0.210618
$910$	−7.29120	−0.241701
$911$	−7.72935	−0.256085	−0.128042	−	0.991769i	$-0.540869\pi$
$911$	−7.72935	−0.256085	−0.128042	+	0.991769i	$0.540869\pi$
$912$	32.5708	1.07853
$913$	−9.52829	−0.315340
$914$	−43.7185	−1.44608
$915$	−2.93109	−0.0968987
$916$	−1.32266	−0.0437018
$917$	−21.4744	−0.709148
$918$	0.530467	0.0175080
$919$	−44.9891	−1.48405	−0.742027	−	0.670370i	$-0.766135\pi$
$919$	−44.9891	−1.48405	−0.742027	+	0.670370i	$0.766135\pi$
$920$	1.81546	0.0598540
$921$	−16.2787	−0.536401
$922$	49.0549	1.61554
$923$	−49.0893	−1.61579
$924$	−0.447079	−0.0147078
$925$	−5.06255	−0.166456
$926$	25.2652	0.830265
$927$	3.22672	0.105979
$928$	5.70439	0.187256
$929$	−0.0136893	−0.000449132 0	−0.000224566	−	1.00000i	$-0.500071\pi$
$929$	−0.0136893	−0.000449132 0	−0.000224566		1.00000i	$0.500071\pi$
$930$	−14.8375	−0.486540
$931$	7.09931	0.232670
$932$	6.58952	0.215847
$933$	−14.4507	−0.473095
$934$	19.7725	0.646976
$935$	−0.425359	−0.0139107
$936$	−12.1407	−0.396833
$937$	−59.3107	−1.93760	−0.968799	−	0.247848i	$-0.920276\pi$
$937$	−59.3107	−1.93760	−0.968799	+	0.247848i	$0.920276\pi$
$938$	7.43725	0.242835
$939$	8.31737	0.271427
$940$	1.01449	0.0330891
$941$	4.91932	0.160365	0.0801826	−	0.996780i	$-0.474450\pi$
$941$	4.91932	0.160365	0.0801826	+	0.996780i	$0.474450\pi$
$942$	19.6247	0.639409
$943$	2.55964	0.0833534
$944$	−41.3425	−1.34558
$945$	0.986091	0.0320775
$946$	−2.01222	−0.0654230
$947$	13.1239	0.426468	0.213234	−	0.977001i	$-0.431600\pi$
$947$	13.1239	0.426468	0.213234	+	0.977001i	$0.431600\pi$
$948$	1.49985	0.0487130
$949$	−20.3665	−0.661126
$950$	43.9077	1.42455
$951$	−14.8776	−0.482441
$952$	0.871007	0.0282295
$953$	−48.3977	−1.56776	−0.783878	−	0.620915i	$-0.786761\pi$
$953$	−48.3977	−1.56776	−0.783878	+	0.620915i	$0.786761\pi$
$954$	7.32107	0.237028
$955$	0.986091	0.0319092
$956$	2.48394	0.0803363
$957$	−3.55734	−0.114992
$958$	−17.2217	−0.556406
$959$	−21.9201	−0.707838
$960$	6.01613	0.194170
$961$	65.0141	2.09723
$962$	9.29399	0.299650
$963$	7.58567	0.244445
$964$	6.45794	0.207996
$965$	−12.7151	−0.409314
$966$	−1.12126	−0.0360760
$967$	22.7773	0.732467	0.366234	−	0.930523i	$-0.380647\pi$
$967$	22.7773	0.732467	0.366234	+	0.930523i	$0.380647\pi$
$968$	−23.8038	−0.765082
$969$	−2.45244	−0.0787839
$970$	2.26238	0.0726408
$971$	21.8747	0.701993	0.350997	−	0.936377i	$-0.385843\pi$
$971$	21.8747	0.701993	0.350997	+	0.936377i	$0.385843\pi$
$972$	−0.358037	−0.0114841
$973$	13.1399	0.421246
$974$	−20.8845	−0.669182
$975$	−19.3935	−0.621089
$976$	13.6372	0.436515
$977$	−51.7978	−1.65716	−0.828578	−	0.559873i	$-0.810850\pi$
$977$	−51.7978	−1.65716	−0.828578	+	0.559873i	$0.810850\pi$
$978$	13.9593	0.446369
$979$	−14.5019	−0.463483
$980$	−0.353058	−0.0112780
$981$	8.42288	0.268922
$982$	−2.60462	−0.0831169
$983$	31.1911	0.994841	0.497421	−	0.867509i	$-0.334281\pi$
$983$	31.1911	0.994841	0.497421	+	0.867509i	$0.334281\pi$
$984$	8.83867	0.281766
$985$	18.4614	0.588230
$986$	−1.51122	−0.0481271
$987$	2.87345	0.0914629
$988$	−12.2391	−0.389379
$989$	−0.766260	−0.0243657
$990$	1.89081	0.0600939
$991$	32.4156	1.02972	0.514858	−	0.857276i	$-0.327845\pi$
$991$	32.4156	1.02972	0.514858	+	0.857276i	$0.327845\pi$
$992$	19.6204	0.622947
$993$	28.2820	0.897501
$994$	−15.6551	−0.496549
$995$	−14.3842	−0.456011
$996$	2.73205	0.0865682
$997$	18.6087	0.589342	0.294671	−	0.955599i	$-0.404790\pi$
$997$	18.6087	0.589342	0.294671	+	0.955599i	$0.404790\pi$
$998$	54.1585	1.71436
$999$	−1.25696	−0.0397683

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.l.1.10	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.l.1.10	✓	28	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:	\( N \)	\(=\)	\( 4011 = 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4011.a (trivial)

\(f(q)\)	\(=\)	\(q-1.53559 q^{2} -1.00000 q^{3} +0.358037 q^{4} -0.986091 q^{5} +1.53559 q^{6} +1.00000 q^{7} +2.52138 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.53559 q^{2} -1.00000 q^{3} +0.358037 q^{4} -0.986091 q^{5} +1.53559 q^{6} +1.00000 q^{7} +2.52138 q^{8} +1.00000 q^{9} +1.51423 q^{10} +1.24869 q^{11} -0.358037 q^{12} -4.81512 q^{13} -1.53559 q^{14} +0.986091 q^{15} -4.58788 q^{16} +0.345448 q^{17} -1.53559 q^{18} +7.09931 q^{19} -0.353058 q^{20} -1.00000 q^{21} -1.91748 q^{22} -0.730182 q^{23} -2.52138 q^{24} -4.02762 q^{25} +7.39405 q^{26} -1.00000 q^{27} +0.358037 q^{28} +2.84885 q^{29} -1.51423 q^{30} +9.79868 q^{31} +2.00235 q^{32} -1.24869 q^{33} -0.530467 q^{34} -0.986091 q^{35} +0.358037 q^{36} +1.25696 q^{37} -10.9016 q^{38} +4.81512 q^{39} -2.48631 q^{40} -3.50549 q^{41} +1.53559 q^{42} +1.04941 q^{43} +0.447079 q^{44} -0.986091 q^{45} +1.12126 q^{46} -2.87345 q^{47} +4.58788 q^{48} +1.00000 q^{49} +6.18478 q^{50} -0.345448 q^{51} -1.72399 q^{52} -4.76759 q^{53} +1.53559 q^{54} -1.23132 q^{55} +2.52138 q^{56} -7.09931 q^{57} -4.37467 q^{58} +9.01123 q^{59} +0.353058 q^{60} -2.97243 q^{61} -15.0468 q^{62} +1.00000 q^{63} +6.10098 q^{64} +4.74814 q^{65} +1.91748 q^{66} -4.84325 q^{67} +0.123683 q^{68} +0.730182 q^{69} +1.51423 q^{70} +10.1948 q^{71} +2.52138 q^{72} +4.22971 q^{73} -1.93017 q^{74} +4.02762 q^{75} +2.54182 q^{76} +1.24869 q^{77} -7.39405 q^{78} -4.18910 q^{79} +4.52407 q^{80} +1.00000 q^{81} +5.38299 q^{82} -7.63061 q^{83} -0.358037 q^{84} -0.340644 q^{85} -1.61146 q^{86} -2.84885 q^{87} +3.14843 q^{88} -11.6137 q^{89} +1.51423 q^{90} -4.81512 q^{91} -0.261433 q^{92} -9.79868 q^{93} +4.41244 q^{94} -7.00056 q^{95} -2.00235 q^{96} +1.49408 q^{97} -1.53559 q^{98} +1.24869 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 6 q^{2} - 28 q^{3} + 34 q^{4} + 8 q^{5} + 6 q^{6} + 28 q^{7} - 15 q^{8} + 28 q^{9}+O(q^{10}) \) 28 * q - 6 * q^2 - 28 * q^3 + 34 * q^4 + 8 * q^5 + 6 * q^6 + 28 * q^7 - 15 * q^8 + 28 * q^9	\( 28 q - 6 q^{2} - 28 q^{3} + 34 q^{4} + 8 q^{5} + 6 q^{6} + 28 q^{7} - 15 q^{8} + 28 q^{9} + 4 q^{10} - 8 q^{11} - 34 q^{12} + 26 q^{13} - 6 q^{14} - 8 q^{15} + 62 q^{16} + 9 q^{17} - 6 q^{18} + 25 q^{19} + 20 q^{20} - 28 q^{21} + 3 q^{22} - 30 q^{23} + 15 q^{24} + 42 q^{25} + 25 q^{26} - 28 q^{27} + 34 q^{28} - 5 q^{29} - 4 q^{30} + 18 q^{31} - 26 q^{32} + 8 q^{33} + 30 q^{34} + 8 q^{35} + 34 q^{36} + 36 q^{37} - 2 q^{38} - 26 q^{39} + 28 q^{40} + 21 q^{41} + 6 q^{42} + 8 q^{43} - 20 q^{44} + 8 q^{45} + 24 q^{46} + 6 q^{47} - 62 q^{48} + 28 q^{49} - 48 q^{50} - 9 q^{51} + 54 q^{52} - 12 q^{53} + 6 q^{54} + 15 q^{55} - 15 q^{56} - 25 q^{57} + 19 q^{58} + 33 q^{59} - 20 q^{60} + 48 q^{61} + 28 q^{63} + 75 q^{64} + 21 q^{65} - 3 q^{66} + 27 q^{67} + 19 q^{68} + 30 q^{69} + 4 q^{70} - 45 q^{71} - 15 q^{72} + 61 q^{73} - 31 q^{74} - 42 q^{75} + 63 q^{76} - 8 q^{77} - 25 q^{78} + 35 q^{79} + 84 q^{80} + 28 q^{81} + 11 q^{82} + 43 q^{83} - 34 q^{84} + 43 q^{85} - q^{86} + 5 q^{87} - 27 q^{88} + 25 q^{89} + 4 q^{90} + 26 q^{91} - 102 q^{92} - 18 q^{93} + 55 q^{94} - 43 q^{95} + 26 q^{96} + 40 q^{97} - 6 q^{98} - 8 q^{99}+O(q^{100}) \) 28 * q - 6 * q^2 - 28 * q^3 + 34 * q^4 + 8 * q^5 + 6 * q^6 + 28 * q^7 - 15 * q^8 + 28 * q^9 + 4 * q^10 - 8 * q^11 - 34 * q^12 + 26 * q^13 - 6 * q^14 - 8 * q^15 + 62 * q^16 + 9 * q^17 - 6 * q^18 + 25 * q^19 + 20 * q^20 - 28 * q^21 + 3 * q^22 - 30 * q^23 + 15 * q^24 + 42 * q^25 + 25 * q^26 - 28 * q^27 + 34 * q^28 - 5 * q^29 - 4 * q^30 + 18 * q^31 - 26 * q^32 + 8 * q^33 + 30 * q^34 + 8 * q^35 + 34 * q^36 + 36 * q^37 - 2 * q^38 - 26 * q^39 + 28 * q^40 + 21 * q^41 + 6 * q^42 + 8 * q^43 - 20 * q^44 + 8 * q^45 + 24 * q^46 + 6 * q^47 - 62 * q^48 + 28 * q^49 - 48 * q^50 - 9 * q^51 + 54 * q^52 - 12 * q^53 + 6 * q^54 + 15 * q^55 - 15 * q^56 - 25 * q^57 + 19 * q^58 + 33 * q^59 - 20 * q^60 + 48 * q^61 + 28 * q^63 + 75 * q^64 + 21 * q^65 - 3 * q^66 + 27 * q^67 + 19 * q^68 + 30 * q^69 + 4 * q^70 - 45 * q^71 - 15 * q^72 + 61 * q^73 - 31 * q^74 - 42 * q^75 + 63 * q^76 - 8 * q^77 - 25 * q^78 + 35 * q^79 + 84 * q^80 + 28 * q^81 + 11 * q^82 + 43 * q^83 - 34 * q^84 + 43 * q^85 - q^86 + 5 * q^87 - 27 * q^88 + 25 * q^89 + 4 * q^90 + 26 * q^91 - 102 * q^92 - 18 * q^93 + 55 * q^94 - 43 * q^95 + 26 * q^96 + 40 * q^97 - 6 * q^98 - 8 * q^99

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