LMFDB - Embedded newform 4011.2.a.l.1.11

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			1.11
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)

$f(q)$	$=$	$q-0.815618 q^{2} -1.00000 q^{3} -1.33477 q^{4} +3.08846 q^{5} +0.815618 q^{6} +1.00000 q^{7} +2.71990 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.815618 q^{2} -1.00000 q^{3} -1.33477 q^{4} +3.08846 q^{5} +0.815618 q^{6} +1.00000 q^{7} +2.71990 q^{8} +1.00000 q^{9} -2.51900 q^{10} -2.21007 q^{11} +1.33477 q^{12} -5.17365 q^{13} -0.815618 q^{14} -3.08846 q^{15} +0.451138 q^{16} -6.12701 q^{17} -0.815618 q^{18} -8.62010 q^{19} -4.12237 q^{20} -1.00000 q^{21} +1.80258 q^{22} -2.41275 q^{23} -2.71990 q^{24} +4.53858 q^{25} +4.21972 q^{26} -1.00000 q^{27} -1.33477 q^{28} +9.41552 q^{29} +2.51900 q^{30} +2.92813 q^{31} -5.80775 q^{32} +2.21007 q^{33} +4.99730 q^{34} +3.08846 q^{35} -1.33477 q^{36} +2.59356 q^{37} +7.03071 q^{38} +5.17365 q^{39} +8.40029 q^{40} +3.44478 q^{41} +0.815618 q^{42} -10.1514 q^{43} +2.94993 q^{44} +3.08846 q^{45} +1.96788 q^{46} +9.11332 q^{47} -0.451138 q^{48} +1.00000 q^{49} -3.70174 q^{50} +6.12701 q^{51} +6.90562 q^{52} +0.150275 q^{53} +0.815618 q^{54} -6.82572 q^{55} +2.71990 q^{56} +8.62010 q^{57} -7.67947 q^{58} +13.8352 q^{59} +4.12237 q^{60} -2.40911 q^{61} -2.38824 q^{62} +1.00000 q^{63} +3.83463 q^{64} -15.9786 q^{65} -1.80258 q^{66} +5.03788 q^{67} +8.17814 q^{68} +2.41275 q^{69} -2.51900 q^{70} -3.26738 q^{71} +2.71990 q^{72} +13.3969 q^{73} -2.11535 q^{74} -4.53858 q^{75} +11.5058 q^{76} -2.21007 q^{77} -4.21972 q^{78} +5.33391 q^{79} +1.39332 q^{80} +1.00000 q^{81} -2.80962 q^{82} +0.273602 q^{83} +1.33477 q^{84} -18.9230 q^{85} +8.27963 q^{86} -9.41552 q^{87} -6.01117 q^{88} +7.07001 q^{89} -2.51900 q^{90} -5.17365 q^{91} +3.22046 q^{92} -2.92813 q^{93} -7.43299 q^{94} -26.6228 q^{95} +5.80775 q^{96} -13.4309 q^{97} -0.815618 q^{98} -2.21007 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.815618	−0.576729	−0.288365	−	0.957521i	$-0.593111\pi$
$2$	−0.815618	−0.576729	−0.288365	+	0.957521i	$0.593111\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.33477	−0.667384
$5$	3.08846	1.38120	0.690600	−	0.723237i	$-0.257346\pi$
$5$	3.08846	1.38120	0.690600	+	0.723237i	$0.257346\pi$
$6$	0.815618	0.332975
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	2.71990	0.961629
$9$	1.00000	0.333333
$10$	−2.51900	−0.796579
$11$	−2.21007	−0.666362	−0.333181	−	0.942863i	$-0.608122\pi$
$11$	−2.21007	−0.666362	−0.333181	+	0.942863i	$0.608122\pi$
$12$	1.33477	0.385314
$13$	−5.17365	−1.43491	−0.717456	−	0.696604i	$-0.754694\pi$
$13$	−5.17365	−1.43491	−0.717456	+	0.696604i	$0.754694\pi$
$14$	−0.815618	−0.217983
$15$	−3.08846	−0.797437
$16$	0.451138	0.112784
$17$	−6.12701	−1.48602	−0.743010	−	0.669281i	$-0.766602\pi$
$17$	−6.12701	−1.48602	−0.743010	+	0.669281i	$0.766602\pi$
$18$	−0.815618	−0.192243
$19$	−8.62010	−1.97759	−0.988793	−	0.149291i	$-0.952301\pi$
$19$	−8.62010	−1.97759	−0.988793	+	0.149291i	$0.952301\pi$
$20$	−4.12237	−0.921791
$21$	−1.00000	−0.218218
$22$	1.80258	0.384310
$23$	−2.41275	−0.503093	−0.251546	−	0.967845i	$-0.580939\pi$
$23$	−2.41275	−0.503093	−0.251546	+	0.967845i	$0.580939\pi$
$24$	−2.71990	−0.555197
$25$	4.53858	0.907715
$26$	4.21972	0.827556
$27$	−1.00000	−0.192450
$28$	−1.33477	−0.252247
$29$	9.41552	1.74842	0.874209	−	0.485550i	$-0.161381\pi$
$29$	9.41552	1.74842	0.874209	+	0.485550i	$0.161381\pi$
$30$	2.51900	0.459905
$31$	2.92813	0.525908	0.262954	−	0.964808i	$-0.415303\pi$
$31$	2.92813	0.525908	0.262954	+	0.964808i	$0.415303\pi$
$32$	−5.80775	−1.02667
$33$	2.21007	0.384724
$34$	4.99730	0.857031
$35$	3.08846	0.522045
$36$	−1.33477	−0.222461
$37$	2.59356	0.426379	0.213189	−	0.977011i	$-0.431615\pi$
$37$	2.59356	0.426379	0.213189	+	0.977011i	$0.431615\pi$
$38$	7.03071	1.14053
$39$	5.17365	0.828447
$40$	8.40029	1.32820
$41$	3.44478	0.537984	0.268992	−	0.963142i	$-0.413309\pi$
$41$	3.44478	0.537984	0.268992	+	0.963142i	$0.413309\pi$
$42$	0.815618	0.125853
$43$	−10.1514	−1.54807	−0.774034	−	0.633145i	$-0.781764\pi$
$43$	−10.1514	−1.54807	−0.774034	+	0.633145i	$0.781764\pi$
$44$	2.94993	0.444719
$45$	3.08846	0.460400
$46$	1.96788	0.290148
$47$	9.11332	1.32932	0.664658	−	0.747148i	$-0.268577\pi$
$47$	9.11332	1.32932	0.664658	+	0.747148i	$0.268577\pi$
$48$	−0.451138	−0.0651161
$49$	1.00000	0.142857
$50$	−3.70174	−0.523506
$51$	6.12701	0.857954
$52$	6.90562	0.957637
$53$	0.150275	0.0206419	0.0103210	−	0.999947i	$-0.496715\pi$
$53$	0.150275	0.0206419	0.0103210	+	0.999947i	$0.496715\pi$
$54$	0.815618	0.110992
$55$	−6.82572	−0.920380
$56$	2.71990	0.363461
$57$	8.62010	1.14176
$58$	−7.67947	−1.00836
$59$	13.8352	1.80118	0.900592	−	0.434666i	$-0.143133\pi$
$59$	13.8352	1.80118	0.900592	+	0.434666i	$0.143133\pi$
$60$	4.12237	0.532196
$61$	−2.40911	−0.308455	−0.154228	−	0.988035i	$-0.549289\pi$
$61$	−2.40911	−0.308455	−0.154228	+	0.988035i	$0.549289\pi$
$62$	−2.38824	−0.303307
$63$	1.00000	0.125988
$64$	3.83463	0.479329
$65$	−15.9786	−1.98190
$66$	−1.80258	−0.221882
$67$	5.03788	0.615475	0.307737	−	0.951471i	$-0.400428\pi$
$67$	5.03788	0.615475	0.307737	+	0.951471i	$0.400428\pi$
$68$	8.17814	0.991745
$69$	2.41275	0.290461
$70$	−2.51900	−0.301078
$71$	−3.26738	−0.387767	−0.193883	−	0.981025i	$-0.562108\pi$
$71$	−3.26738	−0.387767	−0.193883	+	0.981025i	$0.562108\pi$
$72$	2.71990	0.320543
$73$	13.3969	1.56799	0.783993	−	0.620769i	$-0.213180\pi$
$73$	13.3969	1.56799	0.783993	+	0.620769i	$0.213180\pi$
$74$	−2.11535	−0.245905
$75$	−4.53858	−0.524070
$76$	11.5058	1.31981
$77$	−2.21007	−0.251861
$78$	−4.21972	−0.477789
$79$	5.33391	0.600112	0.300056	−	0.953922i	$-0.402995\pi$
$79$	5.33391	0.600112	0.300056	+	0.953922i	$0.402995\pi$
$80$	1.39332	0.155778
$81$	1.00000	0.111111
$82$	−2.80962	−0.310271
$83$	0.273602	0.0300317	0.0150159	−	0.999887i	$-0.495220\pi$
$83$	0.273602	0.0300317	0.0150159	+	0.999887i	$0.495220\pi$
$84$	1.33477	0.145635
$85$	−18.9230	−2.05249
$86$	8.27963	0.892815
$87$	−9.41552	−1.00945
$88$	−6.01117	−0.640793
$89$	7.07001	0.749420	0.374710	−	0.927142i	$-0.377742\pi$
$89$	7.07001	0.749420	0.374710	+	0.927142i	$0.377742\pi$
$90$	−2.51900	−0.265526
$91$	−5.17365	−0.542346
$92$	3.22046	0.335756
$93$	−2.92813	−0.303633
$94$	−7.43299	−0.766655
$95$	−26.6228	−2.73144
$96$	5.80775	0.592751
$97$	−13.4309	−1.36371	−0.681853	−	0.731490i	$-0.738825\pi$
$97$	−13.4309	−1.36371	−0.681853	+	0.731490i	$0.738825\pi$
$98$	−0.815618	−0.0823899
$99$	−2.21007	−0.222121
$100$	−6.05794	−0.605794
$101$	13.8580	1.37892	0.689462	−	0.724322i	$-0.257847\pi$
$101$	13.8580	1.37892	0.689462	+	0.724322i	$0.257847\pi$
$102$	−4.99730	−0.494807
$103$	16.4319	1.61908	0.809541	−	0.587063i	$-0.199716\pi$
$103$	16.4319	1.61908	0.809541	+	0.587063i	$0.199716\pi$
$104$	−14.0718	−1.37985
$105$	−3.08846	−0.301403
$106$	−0.122567	−0.0119048
$107$	−1.80353	−0.174354	−0.0871771	−	0.996193i	$-0.527785\pi$
$107$	−1.80353	−0.174354	−0.0871771	+	0.996193i	$0.527785\pi$
$108$	1.33477	0.128438
$109$	9.28771	0.889602	0.444801	−	0.895630i	$-0.353274\pi$
$109$	9.28771	0.889602	0.444801	+	0.895630i	$0.353274\pi$
$110$	5.56718	0.530810
$111$	−2.59356	−0.246170
$112$	0.451138	0.0426285
$113$	5.65286	0.531776	0.265888	−	0.964004i	$-0.414335\pi$
$113$	5.65286	0.531776	0.265888	+	0.964004i	$0.414335\pi$
$114$	−7.03071	−0.658486
$115$	−7.45167	−0.694872
$116$	−12.5675	−1.16687
$117$	−5.17365	−0.478304
$118$	−11.2842	−1.03880
$119$	−6.12701	−0.561662
$120$	−8.40029	−0.766838
$121$	−6.11558	−0.555962
$122$	1.96492	0.177895
$123$	−3.44478	−0.310605
$124$	−3.90838	−0.350983
$125$	−1.42509	−0.127464
$126$	−0.815618	−0.0726610
$127$	−17.2578	−1.53138	−0.765690	−	0.643210i	$-0.777602\pi$
$127$	−17.2578	−1.53138	−0.765690	+	0.643210i	$0.777602\pi$
$128$	8.48790	0.750232
$129$	10.1514	0.893777
$130$	13.0324	1.14302
$131$	1.12503	0.0982947	0.0491473	−	0.998792i	$-0.484350\pi$
$131$	1.12503	0.0982947	0.0491473	+	0.998792i	$0.484350\pi$
$132$	−2.94993	−0.256759
$133$	−8.62010	−0.747457
$134$	−4.10899	−0.354962
$135$	−3.08846	−0.265812
$136$	−16.6648	−1.42900
$137$	−5.60618	−0.478968	−0.239484	−	0.970900i	$-0.576978\pi$
$137$	−5.60618	−0.478968	−0.239484	+	0.970900i	$0.576978\pi$
$138$	−1.96788	−0.167517
$139$	−8.59571	−0.729078	−0.364539	−	0.931188i	$-0.618773\pi$
$139$	−8.59571	−0.729078	−0.364539	+	0.931188i	$0.618773\pi$
$140$	−4.12237	−0.348404
$141$	−9.11332	−0.767480
$142$	2.66493	0.223636
$143$	11.4341	0.956171
$144$	0.451138	0.0375948
$145$	29.0794	2.41492
$146$	−10.9267	−0.904304
$147$	−1.00000	−0.0824786
$148$	−3.46180	−0.284558
$149$	17.8648	1.46354	0.731770	−	0.681552i	$-0.238695\pi$
$149$	17.8648	1.46354	0.731770	+	0.681552i	$0.238695\pi$
$150$	3.70174	0.302246
$151$	12.5353	1.02011	0.510053	−	0.860143i	$-0.329626\pi$
$151$	12.5353	1.02011	0.510053	+	0.860143i	$0.329626\pi$
$152$	−23.4458	−1.90170
$153$	−6.12701	−0.495340
$154$	1.80258	0.145256
$155$	9.04342	0.726385
$156$	−6.90562	−0.552892
$157$	5.49704	0.438712	0.219356	−	0.975645i	$-0.429604\pi$
$157$	5.49704	0.438712	0.219356	+	0.975645i	$0.429604\pi$
$158$	−4.35044	−0.346102
$159$	−0.150275	−0.0119176
$160$	−17.9370	−1.41804
$161$	−2.41275	−0.190151
$162$	−0.815618	−0.0640810
$163$	−1.31558	−0.103044	−0.0515220	−	0.998672i	$-0.516407\pi$
$163$	−1.31558	−0.103044	−0.0515220	+	0.998672i	$0.516407\pi$
$164$	−4.59798	−0.359042
$165$	6.82572	0.531381
$166$	−0.223155	−0.0173202
$167$	10.5490	0.816303	0.408151	−	0.912914i	$-0.366174\pi$
$167$	10.5490	0.816303	0.408151	+	0.912914i	$0.366174\pi$
$168$	−2.71990	−0.209845
$169$	13.7666	1.05897
$170$	15.4340	1.18373
$171$	−8.62010	−0.659196
$172$	13.5497	1.03315
$173$	20.8969	1.58876	0.794380	−	0.607421i	$-0.207796\pi$
$173$	20.8969	1.58876	0.794380	+	0.607421i	$0.207796\pi$
$174$	7.67947	0.582179
$175$	4.53858	0.343084
$176$	−0.997047	−0.0751553
$177$	−13.8352	−1.03991
$178$	−5.76643	−0.432212
$179$	2.47548	0.185026	0.0925131	−	0.995711i	$-0.470510\pi$
$179$	2.47548	0.185026	0.0925131	+	0.995711i	$0.470510\pi$
$180$	−4.12237	−0.307264
$181$	7.80980	0.580498	0.290249	−	0.956951i	$-0.406262\pi$
$181$	7.80980	0.580498	0.290249	+	0.956951i	$0.406262\pi$
$182$	4.21972	0.312787
$183$	2.40911	0.178087
$184$	−6.56243	−0.483788
$185$	8.01010	0.588915
$186$	2.38824	0.175114
$187$	13.5411	0.990227
$188$	−12.1642	−0.887163
$189$	−1.00000	−0.0727393
$190$	21.7141	1.57530
$191$	−1.00000	−0.0723575
$191$	−1.00000	−0.0723575
$192$	−3.83463	−0.276741
$193$	−12.5739	−0.905086	−0.452543	−	0.891743i	$-0.649483\pi$
$193$	−12.5739	−0.905086	−0.452543	+	0.891743i	$0.649483\pi$
$194$	10.9545	0.786488
$195$	15.9786	1.14425
$196$	−1.33477	−0.0953405
$197$	−5.55839	−0.396019	−0.198009	−	0.980200i	$-0.563448\pi$
$197$	−5.55839	−0.396019	−0.198009	+	0.980200i	$0.563448\pi$
$198$	1.80258	0.128103
$199$	16.6303	1.17889	0.589445	−	0.807809i	$-0.299347\pi$
$199$	16.6303	1.17889	0.589445	+	0.807809i	$0.299347\pi$
$200$	12.3445	0.872885
$201$	−5.03788	−0.355345
$202$	−11.3028	−0.795265
$203$	9.41552	0.660840
$204$	−8.17814	−0.572584
$205$	10.6391	0.743064
$206$	−13.4021	−0.933772
$207$	−2.41275	−0.167698
$208$	−2.33403	−0.161836
$209$	19.0510	1.31779
$210$	2.51900	0.173828
$211$	13.0162	0.896075	0.448037	−	0.894015i	$-0.352123\pi$
$211$	13.0162	0.896075	0.448037	+	0.894015i	$0.352123\pi$
$212$	−0.200583	−0.0137761
$213$	3.26738	0.223877
$214$	1.47099	0.100555
$215$	−31.3520	−2.13819
$216$	−2.71990	−0.185066
$217$	2.92813	0.198775
$218$	−7.57523	−0.513059
$219$	−13.3969	−0.905278
$220$	9.11074	0.614246
$221$	31.6990	2.13231
$222$	2.11535	0.141973
$223$	−14.9736	−1.00271	−0.501354	−	0.865242i	$-0.667164\pi$
$223$	−14.9736	−1.00271	−0.501354	+	0.865242i	$0.667164\pi$
$224$	−5.80775	−0.388047
$225$	4.53858	0.302572
$226$	−4.61057	−0.306691
$227$	9.60601	0.637574	0.318787	−	0.947826i	$-0.396725\pi$
$227$	9.60601	0.637574	0.318787	+	0.947826i	$0.396725\pi$
$228$	−11.5058	−0.761992
$229$	18.6758	1.23413	0.617066	−	0.786912i	$-0.288321\pi$
$229$	18.6758	1.23413	0.617066	+	0.786912i	$0.288321\pi$
$230$	6.07772	0.400753
$231$	2.21007	0.145412
$232$	25.6092	1.68133
$233$	−1.65909	−0.108691	−0.0543453	−	0.998522i	$-0.517307\pi$
$233$	−1.65909	−0.108691	−0.0543453	+	0.998522i	$0.517307\pi$
$234$	4.21972	0.275852
$235$	28.1461	1.83605
$236$	−18.4667	−1.20208
$237$	−5.33391	−0.346475
$238$	4.99730	0.323927
$239$	−17.6126	−1.13927	−0.569634	−	0.821899i	$-0.692915\pi$
$239$	−17.6126	−1.13927	−0.569634	+	0.821899i	$0.692915\pi$
$240$	−1.39332	−0.0899384
$241$	14.5689	0.938464	0.469232	−	0.883075i	$-0.344531\pi$
$241$	14.5689	0.938464	0.469232	+	0.883075i	$0.344531\pi$
$242$	4.98798	0.320639
$243$	−1.00000	−0.0641500
$244$	3.21560	0.205858
$245$	3.08846	0.197314
$246$	2.80962	0.179135
$247$	44.5974	2.83766
$248$	7.96422	0.505729
$249$	−0.273602	−0.0173388
$250$	1.16233	0.0735122
$251$	−29.7237	−1.87614	−0.938072	−	0.346440i	$-0.887391\pi$
$251$	−29.7237	−1.87614	−0.938072	+	0.346440i	$0.887391\pi$
$252$	−1.33477	−0.0840824
$253$	5.33235	0.335242
$254$	14.0758	0.883191
$255$	18.9230	1.18501
$256$	−14.5921	−0.912009
$257$	5.55434	0.346470	0.173235	−	0.984880i	$-0.444578\pi$
$257$	5.55434	0.346470	0.173235	+	0.984880i	$0.444578\pi$
$258$	−8.27963	−0.515467
$259$	2.59356	0.161156
$260$	21.3277	1.32269
$261$	9.41552	0.582806
$262$	−0.917598	−0.0566894
$263$	−30.1498	−1.85911	−0.929557	−	0.368677i	$-0.879811\pi$
$263$	−30.1498	−1.85911	−0.929557	+	0.368677i	$0.879811\pi$
$264$	6.01117	0.369962
$265$	0.464120	0.0285106
$266$	7.03071	0.431080
$267$	−7.07001	−0.432678
$268$	−6.72440	−0.410758
$269$	−4.79505	−0.292359	−0.146180	−	0.989258i	$-0.546698\pi$
$269$	−4.79505	−0.292359	−0.146180	+	0.989258i	$0.546698\pi$
$270$	2.51900	0.153302
$271$	−25.3577	−1.54037	−0.770186	−	0.637819i	$-0.779837\pi$
$271$	−25.3577	−1.54037	−0.770186	+	0.637819i	$0.779837\pi$
$272$	−2.76413	−0.167600
$273$	5.17365	0.313124
$274$	4.57250	0.276235
$275$	−10.0306	−0.604867
$276$	−3.22046	−0.193849
$277$	23.8884	1.43532	0.717658	−	0.696396i	$-0.245214\pi$
$277$	23.8884	1.43532	0.717658	+	0.696396i	$0.245214\pi$
$278$	7.01081	0.420481
$279$	2.92813	0.175303
$280$	8.40029	0.502013
$281$	18.7292	1.11729	0.558645	−	0.829407i	$-0.311321\pi$
$281$	18.7292	1.11729	0.558645	+	0.829407i	$0.311321\pi$
$282$	7.43299	0.442628
$283$	28.1140	1.67120	0.835601	−	0.549337i	$-0.185120\pi$
$283$	28.1140	1.67120	0.835601	+	0.549337i	$0.185120\pi$
$284$	4.36119	0.258789
$285$	26.6228	1.57700
$286$	−9.32589	−0.551452
$287$	3.44478	0.203339
$288$	−5.80775	−0.342225
$289$	20.5403	1.20825
$290$	−23.7177	−1.39275
$291$	13.4309	0.787335
$292$	−17.8817	−1.04645
$293$	−4.89099	−0.285735	−0.142867	−	0.989742i	$-0.545632\pi$
$293$	−4.89099	−0.285735	−0.142867	+	0.989742i	$0.545632\pi$
$294$	0.815618	0.0475678
$295$	42.7293	2.48780
$296$	7.05422	0.410018
$297$	2.21007	0.128241
$298$	−14.5708	−0.844066
$299$	12.4827	0.721894
$300$	6.05794	0.349755
$301$	−10.1514	−0.585114
$302$	−10.2240	−0.588325
$303$	−13.8580	−0.796122
$304$	−3.88885	−0.223041
$305$	−7.44044	−0.426039
$306$	4.99730	0.285677
$307$	11.4423	0.653046	0.326523	−	0.945189i	$-0.394123\pi$
$307$	11.4423	0.653046	0.326523	+	0.945189i	$0.394123\pi$
$308$	2.94993	0.168088
$309$	−16.4319	−0.934778
$310$	−7.37598	−0.418927
$311$	−22.5774	−1.28025	−0.640123	−	0.768273i	$-0.721116\pi$
$311$	−22.5774	−1.28025	−0.640123	+	0.768273i	$0.721116\pi$
$312$	14.0718	0.796658
$313$	24.0230	1.35786	0.678929	−	0.734204i	$-0.262444\pi$
$313$	24.0230	1.35786	0.678929	+	0.734204i	$0.262444\pi$
$314$	−4.48349	−0.253018
$315$	3.08846	0.174015
$316$	−7.11953	−0.400505
$317$	−29.1905	−1.63950	−0.819751	−	0.572721i	$-0.805888\pi$
$317$	−29.1905	−1.63950	−0.819751	+	0.572721i	$0.805888\pi$
$318$	0.122567	0.00687324
$319$	−20.8090	−1.16508
$320$	11.8431	0.662049
$321$	1.80353	0.100663
$322$	1.96788	0.109666
$323$	52.8155	2.93873
$324$	−1.33477	−0.0741537
$325$	−23.4810	−1.30249
$326$	1.07301	0.0594285
$327$	−9.28771	−0.513612
$328$	9.36944	0.517341
$329$	9.11332	0.502434
$330$	−5.56718	−0.306463
$331$	4.51139	0.247969	0.123984	−	0.992284i	$-0.460433\pi$
$331$	4.51139	0.247969	0.123984	+	0.992284i	$0.460433\pi$
$332$	−0.365195	−0.0200427
$333$	2.59356	0.142126
$334$	−8.60392	−0.470786
$335$	15.5593	0.850094
$336$	−0.451138	−0.0246116
$337$	−21.9203	−1.19408	−0.597038	−	0.802213i	$-0.703656\pi$
$337$	−21.9203	−1.19408	−0.597038	+	0.802213i	$0.703656\pi$
$338$	−11.2283	−0.610740
$339$	−5.65286	−0.307021
$340$	25.2578	1.36980
$341$	−6.47139	−0.350445
$342$	7.03071	0.380177
$343$	1.00000	0.0539949
$344$	−27.6106	−1.48867
$345$	7.45167	0.401185
$346$	−17.0439	−0.916284
$347$	−35.1113	−1.88487	−0.942436	−	0.334386i	$-0.891471\pi$
$347$	−35.1113	−1.88487	−0.942436	+	0.334386i	$0.891471\pi$
$348$	12.5675	0.673690
$349$	−8.23074	−0.440581	−0.220291	−	0.975434i	$-0.570701\pi$
$349$	−8.23074	−0.440581	−0.220291	+	0.975434i	$0.570701\pi$
$350$	−3.70174	−0.197867
$351$	5.17365	0.276149
$352$	12.8355	0.684137
$353$	−15.1990	−0.808961	−0.404480	−	0.914547i	$-0.632548\pi$
$353$	−15.1990	−0.808961	−0.404480	+	0.914547i	$0.632548\pi$
$354$	11.2842	0.599749
$355$	−10.0912	−0.535583
$356$	−9.43682	−0.500150
$357$	6.12701	0.324276
$358$	−2.01905	−0.106710
$359$	−11.8858	−0.627310	−0.313655	−	0.949537i	$-0.601553\pi$
$359$	−11.8858	−0.627310	−0.313655	+	0.949537i	$0.601553\pi$
$360$	8.40029	0.442734
$361$	55.3061	2.91085
$362$	−6.36982	−0.334790
$363$	6.11558	0.320985
$364$	6.90562	0.361953
$365$	41.3757	2.16570
$366$	−1.96492	−0.102708
$367$	−23.9552	−1.25045	−0.625227	−	0.780443i	$-0.714994\pi$
$367$	−23.9552	−1.25045	−0.625227	+	0.780443i	$0.714994\pi$
$368$	−1.08848	−0.0567410
$369$	3.44478	0.179328
$370$	−6.53319	−0.339644
$371$	0.150275	0.00780191
$372$	3.90838	0.202640
$373$	22.2503	1.15208	0.576039	−	0.817422i	$-0.304598\pi$
$373$	22.2503	1.15208	0.576039	+	0.817422i	$0.304598\pi$
$374$	−11.0444	−0.571093
$375$	1.42509	0.0735914
$376$	24.7873	1.27831
$377$	−48.7126	−2.50883
$378$	0.815618	0.0419509
$379$	5.20137	0.267176	0.133588	−	0.991037i	$-0.457350\pi$
$379$	5.20137	0.267176	0.133588	+	0.991037i	$0.457350\pi$
$380$	35.5353	1.82292
$381$	17.2578	0.884142
$382$	0.815618	0.0417307
$383$	32.5866	1.66510	0.832548	−	0.553953i	$-0.186881\pi$
$383$	32.5866	1.66510	0.832548	+	0.553953i	$0.186881\pi$
$384$	−8.48790	−0.433147
$385$	−6.82572	−0.347871
$386$	10.2555	0.521989
$387$	−10.1514	−0.516022
$388$	17.9272	0.910114
$389$	12.0917	0.613072	0.306536	−	0.951859i	$-0.400830\pi$
$389$	12.0917	0.613072	0.306536	+	0.951859i	$0.400830\pi$
$390$	−13.0324	−0.659923
$391$	14.7829	0.747606
$392$	2.71990	0.137376
$393$	−1.12503	−0.0567505
$394$	4.53352	0.228396
$395$	16.4736	0.828875
$396$	2.94993	0.148240
$397$	−5.47133	−0.274598	−0.137299	−	0.990530i	$-0.543842\pi$
$397$	−5.47133	−0.274598	−0.137299	+	0.990530i	$0.543842\pi$
$398$	−13.5640	−0.679900
$399$	8.62010	0.431545
$400$	2.04752	0.102376
$401$	9.74214	0.486499	0.243250	−	0.969964i	$-0.421787\pi$
$401$	9.74214	0.486499	0.243250	+	0.969964i	$0.421787\pi$
$402$	4.10899	0.204938
$403$	−15.1491	−0.754632
$404$	−18.4972	−0.920271
$405$	3.08846	0.153467
$406$	−7.67947	−0.381126
$407$	−5.73196	−0.284123
$408$	16.6648	0.825033
$409$	10.3183	0.510209	0.255104	−	0.966914i	$-0.417890\pi$
$409$	10.3183	0.510209	0.255104	+	0.966914i	$0.417890\pi$
$410$	−8.67741	−0.428547
$411$	5.60618	0.276532
$412$	−21.9327	−1.08055
$413$	13.8352	0.680784
$414$	1.96788	0.0967161
$415$	0.845009	0.0414799
$416$	30.0473	1.47319
$417$	8.59571	0.420934
$418$	−15.5384	−0.760007
$419$	−8.95289	−0.437378	−0.218689	−	0.975795i	$-0.570178\pi$
$419$	−8.95289	−0.437378	−0.218689	+	0.975795i	$0.570178\pi$
$420$	4.12237	0.201151
$421$	18.0402	0.879225	0.439613	−	0.898187i	$-0.355116\pi$
$421$	18.0402	0.879225	0.439613	+	0.898187i	$0.355116\pi$
$422$	−10.6163	−0.516792
$423$	9.11332	0.443105
$424$	0.408734	0.0198499
$425$	−27.8079	−1.34888
$426$	−2.66493	−0.129116
$427$	−2.40911	−0.116585
$428$	2.40730	0.116361
$429$	−11.4341	−0.552046
$430$	25.5713	1.23316
$431$	−25.1702	−1.21241	−0.606204	−	0.795309i	$-0.707308\pi$
$431$	−25.1702	−1.21241	−0.606204	+	0.795309i	$0.707308\pi$
$432$	−0.451138	−0.0217054
$433$	−8.62369	−0.414428	−0.207214	−	0.978296i	$-0.566440\pi$
$433$	−8.62369	−0.414428	−0.207214	+	0.978296i	$0.566440\pi$
$434$	−2.38824	−0.114639
$435$	−29.0794	−1.39425
$436$	−12.3969	−0.593706
$437$	20.7981	0.994910
$438$	10.9267	0.522100
$439$	6.65544	0.317647	0.158824	−	0.987307i	$-0.449230\pi$
$439$	6.65544	0.317647	0.158824	+	0.987307i	$0.449230\pi$
$440$	−18.5652	−0.885063
$441$	1.00000	0.0476190
$442$	−25.8543	−1.22976
$443$	33.8301	1.60732	0.803658	−	0.595092i	$-0.202884\pi$
$443$	33.8301	1.60732	0.803658	+	0.595092i	$0.202884\pi$
$444$	3.46180	0.164290
$445$	21.8354	1.03510
$446$	12.2127	0.578290
$447$	−17.8648	−0.844975
$448$	3.83463	0.181169
$449$	−29.4524	−1.38994	−0.694972	−	0.719037i	$-0.744583\pi$
$449$	−29.4524	−1.38994	−0.694972	+	0.719037i	$0.744583\pi$
$450$	−3.70174	−0.174502
$451$	−7.61322	−0.358492
$452$	−7.54525	−0.354899
$453$	−12.5353	−0.588959
$454$	−7.83484	−0.367707
$455$	−15.9786	−0.749088
$456$	23.4458	1.09795
$457$	9.24486	0.432457	0.216228	−	0.976343i	$-0.430624\pi$
$457$	9.24486	0.432457	0.216228	+	0.976343i	$0.430624\pi$
$458$	−15.2323	−0.711759
$459$	6.12701	0.285985
$460$	9.94625	0.463746
$461$	−20.3798	−0.949180	−0.474590	−	0.880207i	$-0.657404\pi$
$461$	−20.3798	−0.949180	−0.474590	+	0.880207i	$0.657404\pi$
$462$	−1.80258	−0.0838634
$463$	5.71160	0.265440	0.132720	−	0.991154i	$-0.457629\pi$
$463$	5.71160	0.265440	0.132720	+	0.991154i	$0.457629\pi$
$464$	4.24770	0.197194
$465$	−9.04342	−0.419379
$466$	1.35318	0.0626850
$467$	22.2034	1.02745	0.513725	−	0.857955i	$-0.328265\pi$
$467$	22.2034	1.02745	0.513725	+	0.857955i	$0.328265\pi$
$468$	6.90562	0.319212
$469$	5.03788	0.232628
$470$	−22.9565	−1.05890
$471$	−5.49704	−0.253290
$472$	37.6302	1.73207
$473$	22.4352	1.03157
$474$	4.35044	0.199822
$475$	−39.1230	−1.79509
$476$	8.17814	0.374844
$477$	0.150275	0.00688064
$478$	14.3652	0.657049
$479$	−0.0457816	−0.00209182	−0.00104591	−	0.999999i	$-0.500333\pi$
$479$	−0.0457816	−0.00209182	−0.00104591	+	0.999999i	$0.500333\pi$
$480$	17.9370	0.818708
$481$	−13.4182	−0.611816
$482$	−11.8826	−0.541239
$483$	2.41275	0.109784
$484$	8.16287	0.371040
$485$	−41.4809	−1.88355
$486$	0.815618	0.0369972
$487$	28.9870	1.31353	0.656764	−	0.754096i	$-0.271925\pi$
$487$	28.9870	1.31353	0.656764	+	0.754096i	$0.271925\pi$
$488$	−6.55254	−0.296619
$489$	1.31558	0.0594925
$490$	−2.51900	−0.113797
$491$	−24.6261	−1.11136	−0.555679	−	0.831397i	$-0.687542\pi$
$491$	−24.6261	−1.11136	−0.555679	+	0.831397i	$0.687542\pi$
$492$	4.59798	0.207293
$493$	−57.6890	−2.59818
$494$	−36.3744	−1.63656
$495$	−6.82572	−0.306793
$496$	1.32099	0.0593143
$497$	−3.26738	−0.146562
$498$	0.223155	0.00999981
$499$	−3.53211	−0.158119	−0.0790594	−	0.996870i	$-0.525192\pi$
$499$	−3.53211	−0.158119	−0.0790594	+	0.996870i	$0.525192\pi$
$500$	1.90217	0.0850674
$501$	−10.5490	−0.471293
$502$	24.2432	1.08203
$503$	44.3826	1.97892	0.989460	−	0.144803i	$-0.0462549\pi$
$503$	44.3826	1.97892	0.989460	+	0.144803i	$0.0462549\pi$
$504$	2.71990	0.121154
$505$	42.7999	1.90457
$506$	−4.34916	−0.193344
$507$	−13.7666	−0.611398
$508$	23.0351	1.02202
$509$	−4.97701	−0.220602	−0.110301	−	0.993898i	$-0.535182\pi$
$509$	−4.97701	−0.220602	−0.110301	+	0.993898i	$0.535182\pi$
$510$	−15.4340	−0.683427
$511$	13.3969	0.592643
$512$	−5.07419	−0.224250
$513$	8.62010	0.380587
$514$	−4.53022	−0.199820
$515$	50.7492	2.23628
$516$	−13.5497	−0.596492
$517$	−20.1411	−0.885805
$518$	−2.11535	−0.0929434
$519$	−20.8969	−0.917271
$520$	−43.4601	−1.90585
$521$	5.13135	0.224808	0.112404	−	0.993663i	$-0.464145\pi$
$521$	5.13135	0.224808	0.112404	+	0.993663i	$0.464145\pi$
$522$	−7.67947	−0.336121
$523$	21.3091	0.931783	0.465891	−	0.884842i	$-0.345734\pi$
$523$	21.3091	0.931783	0.465891	+	0.884842i	$0.345734\pi$
$524$	−1.50166	−0.0656002
$525$	−4.53858	−0.198080
$526$	24.5907	1.07221
$527$	−17.9407	−0.781510
$528$	0.997047	0.0433909
$529$	−17.1786	−0.746898
$530$	−0.378544	−0.0164429
$531$	13.8352	0.600395
$532$	11.5058	0.498841
$533$	−17.8221	−0.771960
$534$	5.76643	0.249538
$535$	−5.57014	−0.240818
$536$	13.7025	0.591858
$537$	−2.47548	−0.106825
$538$	3.91093	0.168612
$539$	−2.21007	−0.0951946
$540$	4.12237	0.177399
$541$	20.9919	0.902512	0.451256	−	0.892395i	$-0.350976\pi$
$541$	20.9919	0.902512	0.451256	+	0.892395i	$0.350976\pi$
$542$	20.6822	0.888378
$543$	−7.80980	−0.335151
$544$	35.5842	1.52566
$545$	28.6847	1.22872
$546$	−4.21972	−0.180587
$547$	−13.7486	−0.587848	−0.293924	−	0.955829i	$-0.594961\pi$
$547$	−13.7486	−0.587848	−0.293924	+	0.955829i	$0.594961\pi$
$548$	7.48295	0.319656
$549$	−2.40911	−0.102818
$550$	8.18112	0.348844
$551$	−81.1627	−3.45765
$552$	6.56243	0.279315
$553$	5.33391	0.226821
$554$	−19.4838	−0.827788
$555$	−8.01010	−0.340010
$556$	11.4733	0.486575
$557$	−28.0730	−1.18949	−0.594745	−	0.803915i	$-0.702747\pi$
$557$	−28.0730	−1.18949	−0.594745	+	0.803915i	$0.702747\pi$
$558$	−2.38824	−0.101102
$559$	52.5195	2.22134
$560$	1.39332	0.0588785
$561$	−13.5411	−0.571708
$562$	−15.2759	−0.644374
$563$	35.6802	1.50374	0.751870	−	0.659311i	$-0.229152\pi$
$563$	35.6802	1.50374	0.751870	+	0.659311i	$0.229152\pi$
$564$	12.1642	0.512204
$565$	17.4586	0.734490
$566$	−22.9303	−0.963831
$567$	1.00000	0.0419961
$568$	−8.88693	−0.372887
$569$	−41.4025	−1.73568	−0.867842	−	0.496840i	$-0.834494\pi$
$569$	−41.4025	−1.73568	−0.867842	+	0.496840i	$0.834494\pi$
$570$	−21.7141	−0.909502
$571$	−34.3203	−1.43626	−0.718131	−	0.695908i	$-0.755002\pi$
$571$	−34.3203	−1.43626	−0.718131	+	0.695908i	$0.755002\pi$
$572$	−15.2619	−0.638133
$573$	1.00000	0.0417756
$574$	−2.80962	−0.117271
$575$	−10.9504	−0.456665
$576$	3.83463	0.159776
$577$	30.5103	1.27016	0.635080	−	0.772446i	$-0.280967\pi$
$577$	30.5103	1.27016	0.635080	+	0.772446i	$0.280967\pi$
$578$	−16.7530	−0.696835
$579$	12.5739	0.522552
$580$	−38.8143	−1.61168
$581$	0.273602	0.0113509
$582$	−10.9545	−0.454079
$583$	−0.332120	−0.0137550
$584$	36.4381	1.50782
$585$	−15.9786	−0.660634
$586$	3.98918	0.164791
$587$	−1.98104	−0.0817664	−0.0408832	−	0.999164i	$-0.513017\pi$
$587$	−1.98104	−0.0817664	−0.0408832	+	0.999164i	$0.513017\pi$
$588$	1.33477	0.0550449
$589$	−25.2408	−1.04003
$590$	−34.8508	−1.43478
$591$	5.55839	0.228642
$592$	1.17005	0.0480889
$593$	−6.97837	−0.286567	−0.143284	−	0.989682i	$-0.545766\pi$
$593$	−6.97837	−0.286567	−0.143284	+	0.989682i	$0.545766\pi$
$594$	−1.80258	−0.0739606
$595$	−18.9230	−0.775769
$596$	−23.8453	−0.976742
$597$	−16.6303	−0.680632
$598$	−10.1811	−0.416337
$599$	−19.0079	−0.776642	−0.388321	−	0.921524i	$-0.626945\pi$
$599$	−19.0079	−0.776642	−0.388321	+	0.921524i	$0.626945\pi$
$600$	−12.3445	−0.503960
$601$	−6.33381	−0.258361	−0.129181	−	0.991621i	$-0.541235\pi$
$601$	−6.33381	−0.258361	−0.129181	+	0.991621i	$0.541235\pi$
$602$	8.27963	0.337452
$603$	5.03788	0.205158
$604$	−16.7317	−0.680803
$605$	−18.8877	−0.767895
$606$	11.3028	0.459147
$607$	−25.7466	−1.04502	−0.522511	−	0.852633i	$-0.675005\pi$
$607$	−25.7466	−1.04502	−0.522511	+	0.852633i	$0.675005\pi$
$608$	50.0634	2.03034
$609$	−9.41552	−0.381536
$610$	6.06856	0.245709
$611$	−47.1491	−1.90745
$612$	8.17814	0.330582
$613$	−39.3929	−1.59106	−0.795532	−	0.605912i	$-0.792808\pi$
$613$	−39.3929	−1.59106	−0.795532	+	0.605912i	$0.792808\pi$
$614$	−9.33254	−0.376631
$615$	−10.6391	−0.429008
$616$	−6.01117	−0.242197
$617$	9.31598	0.375047	0.187524	−	0.982260i	$-0.439954\pi$
$617$	9.31598	0.375047	0.187524	+	0.982260i	$0.439954\pi$
$618$	13.4021	0.539113
$619$	13.3165	0.535234	0.267617	−	0.963525i	$-0.413764\pi$
$619$	13.3165	0.535234	0.267617	+	0.963525i	$0.413764\pi$
$620$	−12.0709	−0.484777
$621$	2.41275	0.0968203
$622$	18.4145	0.738355
$623$	7.07001	0.283254
$624$	2.33403	0.0934359
$625$	−27.0942	−1.08377
$626$	−19.5936	−0.783116
$627$	−19.0510	−0.760826
$628$	−7.33727	−0.292789
$629$	−15.8908	−0.633607
$630$	−2.51900	−0.100359
$631$	17.2147	0.685306	0.342653	−	0.939462i	$-0.388674\pi$
$631$	17.2147	0.685306	0.342653	+	0.939462i	$0.388674\pi$
$632$	14.5077	0.577085
$633$	−13.0162	−0.517349
$634$	23.8083	0.945548
$635$	−53.2999	−2.11514
$636$	0.200583	0.00795362
$637$	−5.17365	−0.204987
$638$	16.9722	0.671935
$639$	−3.26738	−0.129256
$640$	26.2145	1.03622
$641$	39.4218	1.55707	0.778533	−	0.627603i	$-0.215964\pi$
$641$	39.4218	1.55707	0.778533	+	0.627603i	$0.215964\pi$
$642$	−1.47099	−0.0580555
$643$	−32.8591	−1.29584	−0.647918	−	0.761710i	$-0.724360\pi$
$643$	−32.8591	−1.29584	−0.647918	+	0.761710i	$0.724360\pi$
$644$	3.22046	0.126904
$645$	31.3520	1.23449
$646$	−43.0773	−1.69485
$647$	42.9384	1.68808	0.844042	−	0.536277i	$-0.180170\pi$
$647$	42.9384	1.68808	0.844042	+	0.536277i	$0.180170\pi$
$648$	2.71990	0.106848
$649$	−30.5767	−1.20024
$650$	19.1515	0.751185
$651$	−2.92813	−0.114763
$652$	1.75599	0.0687699
$653$	11.0599	0.432809	0.216404	−	0.976304i	$-0.430567\pi$
$653$	11.0599	0.432809	0.216404	+	0.976304i	$0.430567\pi$
$654$	7.57523	0.296215
$655$	3.47462	0.135765
$656$	1.55407	0.0606763
$657$	13.3969	0.522662
$658$	−7.43299	−0.289768
$659$	38.4822	1.49905	0.749527	−	0.661974i	$-0.230281\pi$
$659$	38.4822	1.49905	0.749527	+	0.661974i	$0.230281\pi$
$660$	−9.11074	−0.354635
$661$	−3.80613	−0.148041	−0.0740206	−	0.997257i	$-0.523583\pi$
$661$	−3.80613	−0.148041	−0.0740206	+	0.997257i	$0.523583\pi$
$662$	−3.67957	−0.143011
$663$	−31.6990	−1.23109
$664$	0.744170	0.0288794
$665$	−26.6228	−1.03239
$666$	−2.11535	−0.0819683
$667$	−22.7173	−0.879617
$668$	−14.0804	−0.544787
$669$	14.9736	0.578913
$670$	−12.6904	−0.490274
$671$	5.32431	0.205543
$672$	5.80775	0.224039
$673$	−14.0777	−0.542657	−0.271328	−	0.962487i	$-0.587463\pi$
$673$	−14.0777	−0.542657	−0.271328	+	0.962487i	$0.587463\pi$
$674$	17.8786	0.688658
$675$	−4.53858	−0.174690
$676$	−18.3753	−0.706741
$677$	−0.570595	−0.0219297	−0.0109649	−	0.999940i	$-0.503490\pi$
$677$	−0.570595	−0.0219297	−0.0109649	+	0.999940i	$0.503490\pi$
$678$	4.61057	0.177068
$679$	−13.4309	−0.515432
$680$	−51.4687	−1.97373
$681$	−9.60601	−0.368103
$682$	5.27818	0.202112
$683$	28.0388	1.07287	0.536436	−	0.843941i	$-0.319770\pi$
$683$	28.0388	1.07287	0.536436	+	0.843941i	$0.319770\pi$
$684$	11.5058	0.439936
$685$	−17.3145	−0.661551
$686$	−0.815618	−0.0311404
$687$	−18.6758	−0.712526
$688$	−4.57966	−0.174598
$689$	−0.777473	−0.0296193
$690$	−6.07772	−0.231375
$691$	22.1732	0.843509	0.421755	−	0.906710i	$-0.361414\pi$
$691$	22.1732	0.843509	0.421755	+	0.906710i	$0.361414\pi$
$692$	−27.8925	−1.06031
$693$	−2.21007	−0.0839537
$694$	28.6374	1.08706
$695$	−26.5475	−1.00700
$696$	−25.6092	−0.970716
$697$	−21.1062	−0.799455
$698$	6.71314	0.254096
$699$	1.65909	0.0627525
$700$	−6.05794	−0.228969
$701$	31.1913	1.17808	0.589040	−	0.808104i	$-0.299506\pi$
$701$	31.1913	1.17808	0.589040	+	0.808104i	$0.299506\pi$
$702$	−4.21972	−0.159263
$703$	−22.3568	−0.843201
$704$	−8.47481	−0.319406
$705$	−28.1461	−1.06004
$706$	12.3966	0.466551
$707$	13.8580	0.521184
$708$	18.4667	0.694022
$709$	−0.0265520	−0.000997181 0	−0.000498591	−	1.00000i	$-0.500159\pi$
$709$	−0.0265520	−0.000997181 0	−0.000498591		1.00000i	$0.500159\pi$
$710$	8.23053	0.308886
$711$	5.33391	0.200037
$712$	19.2297	0.720663
$713$	−7.06485	−0.264581
$714$	−4.99730	−0.187019
$715$	35.3139	1.32066
$716$	−3.30419	−0.123483
$717$	17.6126	0.657756
$718$	9.69429	0.361788
$719$	19.8088	0.738745	0.369373	−	0.929281i	$-0.379573\pi$
$719$	19.8088	0.738745	0.369373	+	0.929281i	$0.379573\pi$
$720$	1.39332	0.0519260
$721$	16.4319	0.611956
$722$	−45.1087	−1.67877
$723$	−14.5689	−0.541822
$724$	−10.4243	−0.387415
$725$	42.7330	1.58707
$726$	−4.98798	−0.185121
$727$	18.7941	0.697035	0.348517	−	0.937302i	$-0.386685\pi$
$727$	18.7941	0.697035	0.348517	+	0.937302i	$0.386685\pi$
$728$	−14.0718	−0.521535
$729$	1.00000	0.0370370
$730$	−33.7468	−1.24902
$731$	62.1975	2.30046
$732$	−3.21560	−0.118852
$733$	−19.5864	−0.723442	−0.361721	−	0.932286i	$-0.617811\pi$
$733$	−19.5864	−0.723442	−0.361721	+	0.932286i	$0.617811\pi$
$734$	19.5383	0.721173
$735$	−3.08846	−0.113920
$736$	14.0126	0.516513
$737$	−11.1341	−0.410129
$738$	−2.80962	−0.103424
$739$	43.7533	1.60949	0.804745	−	0.593620i	$-0.202302\pi$
$739$	43.7533	1.60949	0.804745	+	0.593620i	$0.202302\pi$
$740$	−10.6916	−0.393032
$741$	−44.5974	−1.63833
$742$	−0.122567	−0.00449959
$743$	−16.7472	−0.614395	−0.307197	−	0.951646i	$-0.599391\pi$
$743$	−16.7472	−0.614395	−0.307197	+	0.951646i	$0.599391\pi$
$744$	−7.96422	−0.291983
$745$	55.1746	2.02144
$746$	−18.1478	−0.664437
$747$	0.273602	0.0100106
$748$	−18.0743	−0.660861
$749$	−1.80353	−0.0658997
$750$	−1.16233	−0.0424423
$751$	−37.1491	−1.35559	−0.677795	−	0.735251i	$-0.737064\pi$
$751$	−37.1491	−1.35559	−0.677795	+	0.735251i	$0.737064\pi$
$752$	4.11136	0.149926
$753$	29.7237	1.08319
$754$	39.7309	1.44691
$755$	38.7147	1.40897
$756$	1.33477	0.0485450
$757$	43.9367	1.59691	0.798453	−	0.602058i	$-0.205652\pi$
$757$	43.9367	1.59691	0.798453	+	0.602058i	$0.205652\pi$
$758$	−4.24233	−0.154088
$759$	−5.33235	−0.193552
$760$	−72.4113	−2.62663
$761$	46.9358	1.70142	0.850711	−	0.525633i	$-0.176172\pi$
$761$	46.9358	1.70142	0.850711	+	0.525633i	$0.176172\pi$
$762$	−14.0758	−0.509911
$763$	9.28771	0.336238
$764$	1.33477	0.0482902
$765$	−18.9230	−0.684164
$766$	−26.5782	−0.960309
$767$	−71.5782	−2.58454
$768$	14.5921	0.526549
$769$	32.1474	1.15927	0.579633	−	0.814877i	$-0.303196\pi$
$769$	32.1474	1.15927	0.579633	+	0.814877i	$0.303196\pi$
$770$	5.56718	0.200627
$771$	−5.55434	−0.200035
$772$	16.7832	0.604040
$773$	47.3164	1.70185	0.850926	−	0.525285i	$-0.176041\pi$
$773$	47.3164	1.70185	0.850926	+	0.525285i	$0.176041\pi$
$774$	8.27963	0.297605
$775$	13.2896	0.477375
$776$	−36.5308	−1.31138
$777$	−2.59356	−0.0930435
$778$	−9.86219	−0.353577
$779$	−29.6944	−1.06391
$780$	−21.3277	−0.763655
$781$	7.22114	0.258393
$782$	−12.0572	−0.431166
$783$	−9.41552	−0.336483
$784$	0.451138	0.0161121
$785$	16.9774	0.605949
$786$	0.917598	0.0327296
$787$	−11.1186	−0.396334	−0.198167	−	0.980168i	$-0.563499\pi$
$787$	−11.1186	−0.396334	−0.198167	+	0.980168i	$0.563499\pi$
$788$	7.41915	0.264296
$789$	30.1498	1.07336
$790$	−13.4361	−0.478036
$791$	5.65286	0.200993
$792$	−6.01117	−0.213598
$793$	12.4639	0.442606
$794$	4.46251	0.158369
$795$	−0.464120	−0.0164606
$796$	−22.1976	−0.786772
$797$	−17.9472	−0.635724	−0.317862	−	0.948137i	$-0.602965\pi$
$797$	−17.9472	−0.635724	−0.317862	+	0.948137i	$0.602965\pi$
$798$	−7.03071	−0.248884
$799$	−55.8375	−1.97539
$800$	−26.3589	−0.931928
$801$	7.07001	0.249807
$802$	−7.94587	−0.280578
$803$	−29.6081	−1.04485
$804$	6.72440	0.237151
$805$	−7.45167	−0.262637
$806$	12.3559	0.435218
$807$	4.79505	0.168794
$808$	37.6923	1.32601
$809$	−7.57695	−0.266391	−0.133196	−	0.991090i	$-0.542524\pi$
$809$	−7.57695	−0.266391	−0.133196	+	0.991090i	$0.542524\pi$
$810$	−2.51900	−0.0885087
$811$	43.1434	1.51497	0.757485	−	0.652853i	$-0.226428\pi$
$811$	43.1434	1.51497	0.757485	+	0.652853i	$0.226428\pi$
$812$	−12.5675	−0.441034
$813$	25.3577	0.889335
$814$	4.67509	0.163862
$815$	−4.06311	−0.142324
$816$	2.76413	0.0967638
$817$	87.5057	3.06144
$818$	−8.41582	−0.294252
$819$	−5.17365	−0.180782
$820$	−14.2007	−0.495909
$821$	17.8002	0.621230	0.310615	−	0.950536i	$-0.399465\pi$
$821$	17.8002	0.621230	0.310615	+	0.950536i	$0.399465\pi$
$822$	−4.57250	−0.159484
$823$	−32.6101	−1.13672	−0.568359	−	0.822781i	$-0.692421\pi$
$823$	−32.6101	−1.13672	−0.568359	+	0.822781i	$0.692421\pi$
$824$	44.6930	1.55696
$825$	10.0306	0.349220
$826$	−11.2842	−0.392628
$827$	−13.0957	−0.455384	−0.227692	−	0.973733i	$-0.573118\pi$
$827$	−13.0957	−0.455384	−0.227692	+	0.973733i	$0.573118\pi$
$828$	3.22046	0.111919
$829$	−12.5449	−0.435702	−0.217851	−	0.975982i	$-0.569905\pi$
$829$	−12.5449	−0.435702	−0.217851	+	0.975982i	$0.569905\pi$
$830$	−0.689205	−0.0239226
$831$	−23.8884	−0.828680
$832$	−19.8390	−0.687795
$833$	−6.12701	−0.212288
$834$	−7.01081	−0.242765
$835$	32.5800	1.12748
$836$	−25.4287	−0.879471
$837$	−2.92813	−0.101211
$838$	7.30214	0.252248
$839$	−0.829511	−0.0286379	−0.0143189	−	0.999897i	$-0.504558\pi$
$839$	−0.829511	−0.0286379	−0.0143189	+	0.999897i	$0.504558\pi$
$840$	−8.40029	−0.289837
$841$	59.6520	2.05697
$842$	−14.7139	−0.507075
$843$	−18.7292	−0.645068
$844$	−17.3737	−0.598026
$845$	42.5177	1.46265
$846$	−7.43299	−0.255552
$847$	−6.11558	−0.210134
$848$	0.0677949	0.00232809
$849$	−28.1140	−0.964869
$850$	22.6806	0.777939
$851$	−6.25761	−0.214508
$852$	−4.36119	−0.149412
$853$	42.2134	1.44536	0.722680	−	0.691183i	$-0.242910\pi$
$853$	42.2134	1.44536	0.722680	+	0.691183i	$0.242910\pi$
$854$	1.96492	0.0672380
$855$	−26.6228	−0.910481
$856$	−4.90542	−0.167664
$857$	−50.8543	−1.73715	−0.868575	−	0.495557i	$-0.834964\pi$
$857$	−50.8543	−1.73715	−0.868575	+	0.495557i	$0.834964\pi$
$858$	9.32589	0.318381
$859$	−36.3072	−1.23879	−0.619393	−	0.785081i	$-0.712621\pi$
$859$	−36.3072	−1.23879	−0.619393	+	0.785081i	$0.712621\pi$
$860$	41.8477	1.42699
$861$	−3.44478	−0.117398
$862$	20.5293	0.699231
$863$	−17.3287	−0.589875	−0.294938	−	0.955517i	$-0.595299\pi$
$863$	−17.3287	−0.589875	−0.294938	+	0.955517i	$0.595299\pi$
$864$	5.80775	0.197584
$865$	64.5392	2.19440
$866$	7.03364	0.239013
$867$	−20.5403	−0.697585
$868$	−3.90838	−0.132659
$869$	−11.7883	−0.399892
$870$	23.7177	0.804106
$871$	−26.0642	−0.883152
$872$	25.2616	0.855466
$873$	−13.4309	−0.454568
$874$	−16.9633	−0.573793
$875$	−1.42509	−0.0481769
$876$	17.8817	0.604167
$877$	26.2991	0.888057	0.444028	−	0.896013i	$-0.353549\pi$
$877$	26.2991	0.888057	0.444028	+	0.896013i	$0.353549\pi$
$878$	−5.42830	−0.183196
$879$	4.89099	0.164969
$880$	−3.07934	−0.103804
$881$	12.6502	0.426195	0.213098	−	0.977031i	$-0.431645\pi$
$881$	12.6502	0.426195	0.213098	+	0.977031i	$0.431645\pi$
$882$	−0.815618	−0.0274633
$883$	−7.40443	−0.249179	−0.124589	−	0.992208i	$-0.539761\pi$
$883$	−7.40443	−0.249179	−0.124589	+	0.992208i	$0.539761\pi$
$884$	−42.3108	−1.42307
$885$	−42.7293	−1.43633
$886$	−27.5924	−0.926986
$887$	−37.7662	−1.26807	−0.634033	−	0.773306i	$-0.718602\pi$
$887$	−37.7662	−1.26807	−0.634033	+	0.773306i	$0.718602\pi$
$888$	−7.05422	−0.236724
$889$	−17.2578	−0.578807
$890$	−17.8094	−0.596972
$891$	−2.21007	−0.0740402
$892$	19.9863	0.669190
$893$	−78.5578	−2.62884
$894$	14.5708	0.487322
$895$	7.64542	0.255558
$896$	8.48790	0.283561
$897$	−12.4827	−0.416786
$898$	24.0219	0.801621
$899$	27.5699	0.919508
$900$	−6.05794	−0.201931
$901$	−0.920740	−0.0306743
$902$	6.20948	0.206753
$903$	10.1514	0.337816
$904$	15.3752	0.511371
$905$	24.1203	0.801784
$906$	10.2240	0.339670
$907$	15.8394	0.525939	0.262969	−	0.964804i	$-0.415298\pi$
$907$	15.8394	0.525939	0.262969	+	0.964804i	$0.415298\pi$
$908$	−12.8218	−0.425506
$909$	13.8580	0.459641
$910$	13.0324	0.432021
$911$	−36.0512	−1.19443	−0.597214	−	0.802082i	$-0.703726\pi$
$911$	−36.0512	−1.19443	−0.597214	+	0.802082i	$0.703726\pi$
$912$	3.88885	0.128773
$913$	−0.604681	−0.0200120
$914$	−7.54028	−0.249410
$915$	7.44044	0.245974
$916$	−24.9278	−0.823639
$917$	1.12503	0.0371519
$918$	−4.99730	−0.164936
$919$	37.1701	1.22613	0.613064	−	0.790033i	$-0.289937\pi$
$919$	37.1701	1.22613	0.613064	+	0.790033i	$0.289937\pi$
$920$	−20.2678	−0.668209
$921$	−11.4423	−0.377036
$922$	16.6221	0.547420
$923$	16.9043	0.556411
$924$	−2.94993	−0.0970457
$925$	11.7711	0.387030
$926$	−4.65848	−0.153087
$927$	16.4319	0.539694
$928$	−54.6830	−1.79506
$929$	−44.1328	−1.44795	−0.723975	−	0.689826i	$-0.757687\pi$
$929$	−44.1328	−1.44795	−0.723975	+	0.689826i	$0.757687\pi$
$930$	7.37598	0.241868
$931$	−8.62010	−0.282512
$932$	2.21450	0.0725383
$933$	22.5774	0.739150
$934$	−18.1095	−0.592560
$935$	41.8213	1.36770
$936$	−14.0718	−0.459951
$937$	32.8860	1.07434	0.537169	−	0.843475i	$-0.319494\pi$
$937$	32.8860	1.07434	0.537169	+	0.843475i	$0.319494\pi$
$938$	−4.10899	−0.134163
$939$	−24.0230	−0.783960
$940$	−37.5685	−1.22535
$941$	−47.8864	−1.56105	−0.780526	−	0.625123i	$-0.785049\pi$
$941$	−47.8864	−1.56105	−0.780526	+	0.625123i	$0.785049\pi$
$942$	4.48349	0.146080
$943$	−8.31139	−0.270656
$944$	6.24156	0.203145
$945$	−3.08846	−0.100468
$946$	−18.2986	−0.594938
$947$	39.8809	1.29595	0.647977	−	0.761660i	$-0.275615\pi$
$947$	39.8809	1.29595	0.647977	+	0.761660i	$0.275615\pi$
$948$	7.11953	0.231232
$949$	−69.3108	−2.24992
$950$	31.9094	1.03528
$951$	29.1905	0.946567
$952$	−16.6648	−0.540111
$953$	7.82106	0.253349	0.126674	−	0.991944i	$-0.459570\pi$
$953$	7.82106	0.253349	0.126674	+	0.991944i	$0.459570\pi$
$954$	−0.122567	−0.00396827
$955$	−3.08846	−0.0999402
$956$	23.5088	0.760328
$957$	20.8090	0.672659
$958$	0.0373403	0.00120641
$959$	−5.60618	−0.181033
$960$	−11.8431	−0.382234
$961$	−22.4260	−0.723420
$962$	10.9441	0.352852
$963$	−1.80353	−0.0581180
$964$	−19.4461	−0.626315
$965$	−38.8338	−1.25011
$966$	−1.96788	−0.0633155
$967$	−51.0979	−1.64320	−0.821598	−	0.570067i	$-0.806917\pi$
$967$	−51.0979	−1.64320	−0.821598	+	0.570067i	$0.806917\pi$
$968$	−16.6337	−0.534629
$969$	−52.8155	−1.69668
$970$	33.8326	1.08630
$971$	−12.0322	−0.386131	−0.193065	−	0.981186i	$-0.561843\pi$
$971$	−12.0322	−0.386131	−0.193065	+	0.981186i	$0.561843\pi$
$972$	1.33477	0.0428127
$973$	−8.59571	−0.275566
$974$	−23.6423	−0.757550
$975$	23.4810	0.751994
$976$	−1.08684	−0.0347890
$977$	3.34694	0.107078	0.0535391	−	0.998566i	$-0.482950\pi$
$977$	3.34694	0.107078	0.0535391	+	0.998566i	$0.482950\pi$
$978$	−1.07301	−0.0343110
$979$	−15.6252	−0.499385
$980$	−4.12237	−0.131684
$981$	9.28771	0.296534
$982$	20.0855	0.640953
$983$	0.132207	0.00421676	0.00210838	−	0.999998i	$-0.499329\pi$
$983$	0.132207	0.00421676	0.00210838	+	0.999998i	$0.499329\pi$
$984$	−9.36944	−0.298687
$985$	−17.1668	−0.546981
$986$	47.0522	1.49845
$987$	−9.11332	−0.290080
$988$	−59.5271	−1.89381
$989$	24.4927	0.778821
$990$	5.56718	0.176937
$991$	36.7871	1.16858	0.584290	−	0.811545i	$-0.301373\pi$
$991$	36.7871	1.16858	0.584290	+	0.811545i	$0.301373\pi$
$992$	−17.0059	−0.539937
$993$	−4.51139	−0.143165
$994$	2.66493	0.0845265
$995$	51.3619	1.62828
$996$	0.365195	0.0115717
$997$	−24.2972	−0.769499	−0.384749	−	0.923021i	$-0.625712\pi$
$997$	−24.2972	−0.769499	−0.384749	+	0.923021i	$0.625712\pi$
$998$	2.88085	0.0911917
$999$	−2.59356	−0.0820566

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.l.1.11	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.l.1.11	✓	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)

\(f(q)\)	\(=\)	\(q-0.815618 q^{2} -1.00000 q^{3} -1.33477 q^{4} +3.08846 q^{5} +0.815618 q^{6} +1.00000 q^{7} +2.71990 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.815618 q^{2} -1.00000 q^{3} -1.33477 q^{4} +3.08846 q^{5} +0.815618 q^{6} +1.00000 q^{7} +2.71990 q^{8} +1.00000 q^{9} -2.51900 q^{10} -2.21007 q^{11} +1.33477 q^{12} -5.17365 q^{13} -0.815618 q^{14} -3.08846 q^{15} +0.451138 q^{16} -6.12701 q^{17} -0.815618 q^{18} -8.62010 q^{19} -4.12237 q^{20} -1.00000 q^{21} +1.80258 q^{22} -2.41275 q^{23} -2.71990 q^{24} +4.53858 q^{25} +4.21972 q^{26} -1.00000 q^{27} -1.33477 q^{28} +9.41552 q^{29} +2.51900 q^{30} +2.92813 q^{31} -5.80775 q^{32} +2.21007 q^{33} +4.99730 q^{34} +3.08846 q^{35} -1.33477 q^{36} +2.59356 q^{37} +7.03071 q^{38} +5.17365 q^{39} +8.40029 q^{40} +3.44478 q^{41} +0.815618 q^{42} -10.1514 q^{43} +2.94993 q^{44} +3.08846 q^{45} +1.96788 q^{46} +9.11332 q^{47} -0.451138 q^{48} +1.00000 q^{49} -3.70174 q^{50} +6.12701 q^{51} +6.90562 q^{52} +0.150275 q^{53} +0.815618 q^{54} -6.82572 q^{55} +2.71990 q^{56} +8.62010 q^{57} -7.67947 q^{58} +13.8352 q^{59} +4.12237 q^{60} -2.40911 q^{61} -2.38824 q^{62} +1.00000 q^{63} +3.83463 q^{64} -15.9786 q^{65} -1.80258 q^{66} +5.03788 q^{67} +8.17814 q^{68} +2.41275 q^{69} -2.51900 q^{70} -3.26738 q^{71} +2.71990 q^{72} +13.3969 q^{73} -2.11535 q^{74} -4.53858 q^{75} +11.5058 q^{76} -2.21007 q^{77} -4.21972 q^{78} +5.33391 q^{79} +1.39332 q^{80} +1.00000 q^{81} -2.80962 q^{82} +0.273602 q^{83} +1.33477 q^{84} -18.9230 q^{85} +8.27963 q^{86} -9.41552 q^{87} -6.01117 q^{88} +7.07001 q^{89} -2.51900 q^{90} -5.17365 q^{91} +3.22046 q^{92} -2.92813 q^{93} -7.43299 q^{94} -26.6228 q^{95} +5.80775 q^{96} -13.4309 q^{97} -0.815618 q^{98} -2.21007 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 6 q^{2} - 28 q^{3} + 34 q^{4} + 8 q^{5} + 6 q^{6} + 28 q^{7} - 15 q^{8} + 28 q^{9}+O(q^{10}) \) 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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