LMFDB - Embedded newform 8011.2.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8011,2,Mod(1,8011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8011, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8011.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:	$63.9681570592$
Analytic rank:	$1$
Dimension:	$309$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	8011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.78702 q^{2} -1.95051 q^{3} +5.76751 q^{4} -0.484177 q^{5} +5.43612 q^{6} +0.734493 q^{7} -10.5001 q^{8} +0.804484 q^{9} +O(q^{10})$	\(q-2.78702 q^{2} -1.95051 q^{3} +5.76751 q^{4} -0.484177 q^{5} +5.43612 q^{6} +0.734493 q^{7} -10.5001 q^{8} +0.804484 q^{9} +1.34941 q^{10} -4.98227 q^{11} -11.2496 q^{12} +1.72452 q^{13} -2.04705 q^{14} +0.944392 q^{15} +17.7291 q^{16} -2.75009 q^{17} -2.24212 q^{18} +0.0586969 q^{19} -2.79250 q^{20} -1.43264 q^{21} +13.8857 q^{22} -3.48409 q^{23} +20.4806 q^{24} -4.76557 q^{25} -4.80629 q^{26} +4.28237 q^{27} +4.23620 q^{28} +3.86738 q^{29} -2.63204 q^{30} -3.22383 q^{31} -28.4113 q^{32} +9.71796 q^{33} +7.66458 q^{34} -0.355625 q^{35} +4.63987 q^{36} +0.376377 q^{37} -0.163590 q^{38} -3.36370 q^{39} +5.08393 q^{40} -8.81992 q^{41} +3.99279 q^{42} +4.12114 q^{43} -28.7353 q^{44} -0.389513 q^{45} +9.71025 q^{46} +5.16871 q^{47} -34.5808 q^{48} -6.46052 q^{49} +13.2818 q^{50} +5.36408 q^{51} +9.94621 q^{52} +0.462378 q^{53} -11.9351 q^{54} +2.41230 q^{55} -7.71228 q^{56} -0.114489 q^{57} -10.7785 q^{58} +13.1787 q^{59} +5.44679 q^{60} +6.66424 q^{61} +8.98488 q^{62} +0.590888 q^{63} +43.7246 q^{64} -0.834976 q^{65} -27.0842 q^{66} +13.6527 q^{67} -15.8612 q^{68} +6.79575 q^{69} +0.991136 q^{70} -10.3921 q^{71} -8.44719 q^{72} +16.4603 q^{73} -1.04897 q^{74} +9.29529 q^{75} +0.338535 q^{76} -3.65944 q^{77} +9.37472 q^{78} -5.93250 q^{79} -8.58405 q^{80} -10.7663 q^{81} +24.5813 q^{82} +3.80263 q^{83} -8.26274 q^{84} +1.33153 q^{85} -11.4857 q^{86} -7.54336 q^{87} +52.3145 q^{88} +9.86875 q^{89} +1.08558 q^{90} +1.26665 q^{91} -20.0945 q^{92} +6.28810 q^{93} -14.4053 q^{94} -0.0284197 q^{95} +55.4164 q^{96} -11.2478 q^{97} +18.0056 q^{98} -4.00815 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 309 q - 33 q^{2} - 15 q^{3} + 273 q^{4} - 74 q^{5} - 32 q^{6} - 19 q^{7} - 93 q^{8} + 214 q^{9}+O(q^{10}) $ 309 * q - 33 * q^2 - 15 * q^3 + 273 * q^4 - 74 * q^5 - 32 * q^6 - 19 * q^7 - 93 * q^8 + 214 * q^9	\( 309 q - 33 q^{2} - 15 q^{3} + 273 q^{4} - 74 q^{5} - 32 q^{6} - 19 q^{7} - 93 q^{8} + 214 q^{9} - 23 q^{10} - 72 q^{11} - 42 q^{12} - 57 q^{13} - 77 q^{14} - 44 q^{15} + 205 q^{16} - 86 q^{17} - 82 q^{18} - 58 q^{19} - 134 q^{20} - 123 q^{21} - 31 q^{22} - 94 q^{23} - 84 q^{24} + 225 q^{25} - 92 q^{26} - 48 q^{27} - 36 q^{28} - 345 q^{29} - 85 q^{30} - 36 q^{31} - 199 q^{32} - 56 q^{33} - 28 q^{34} - 168 q^{35} + 65 q^{36} - 79 q^{37} - 66 q^{38} - 145 q^{39} - 54 q^{40} - 176 q^{41} - 48 q^{42} - 58 q^{43} - 194 q^{44} - 192 q^{45} - 44 q^{46} - 82 q^{47} - 81 q^{48} + 186 q^{49} - 206 q^{50} - 145 q^{51} - 86 q^{52} - 223 q^{53} - 117 q^{54} - 58 q^{55} - 216 q^{56} - 124 q^{57} - 151 q^{59} - 91 q^{60} - 184 q^{61} - 124 q^{62} - 78 q^{63} + 101 q^{64} - 194 q^{65} - 112 q^{66} - 53 q^{67} - 182 q^{68} - 243 q^{69} - 193 q^{71} - 208 q^{72} - 69 q^{73} - 236 q^{74} - 62 q^{75} - 142 q^{76} - 324 q^{77} - 20 q^{78} - 91 q^{79} - 223 q^{80} - 27 q^{81} + 2 q^{82} - 117 q^{83} - 157 q^{84} - 171 q^{85} - 203 q^{86} - 69 q^{87} - 36 q^{88} - 172 q^{89} - 10 q^{90} - 84 q^{91} - 226 q^{92} - 220 q^{93} - 96 q^{94} - 166 q^{95} - 118 q^{96} - 12 q^{97} - 116 q^{98} - 154 q^{99}+O(q^{100}) \) 309 * q - 33 * q^2 - 15 * q^3 + 273 * q^4 - 74 * q^5 - 32 * q^6 - 19 * q^7 - 93 * q^8 + 214 * q^9 - 23 * q^10 - 72 * q^11 - 42 * q^12 - 57 * q^13 - 77 * q^14 - 44 * q^15 + 205 * q^16 - 86 * q^17 - 82 * q^18 - 58 * q^19 - 134 * q^20 - 123 * q^21 - 31 * q^22 - 94 * q^23 - 84 * q^24 + 225 * q^25 - 92 * q^26 - 48 * q^27 - 36 * q^28 - 345 * q^29 - 85 * q^30 - 36 * q^31 - 199 * q^32 - 56 * q^33 - 28 * q^34 - 168 * q^35 + 65 * q^36 - 79 * q^37 - 66 * q^38 - 145 * q^39 - 54 * q^40 - 176 * q^41 - 48 * q^42 - 58 * q^43 - 194 * q^44 - 192 * q^45 - 44 * q^46 - 82 * q^47 - 81 * q^48 + 186 * q^49 - 206 * q^50 - 145 * q^51 - 86 * q^52 - 223 * q^53 - 117 * q^54 - 58 * q^55 - 216 * q^56 - 124 * q^57 - 151 * q^59 - 91 * q^60 - 184 * q^61 - 124 * q^62 - 78 * q^63 + 101 * q^64 - 194 * q^65 - 112 * q^66 - 53 * q^67 - 182 * q^68 - 243 * q^69 - 193 * q^71 - 208 * q^72 - 69 * q^73 - 236 * q^74 - 62 * q^75 - 142 * q^76 - 324 * q^77 - 20 * q^78 - 91 * q^79 - 223 * q^80 - 27 * q^81 + 2 * q^82 - 117 * q^83 - 157 * q^84 - 171 * q^85 - 203 * q^86 - 69 * q^87 - 36 * q^88 - 172 * q^89 - 10 * q^90 - 84 * q^91 - 226 * q^92 - 220 * q^93 - 96 * q^94 - 166 * q^95 - 118 * q^96 - 12 * q^97 - 116 * q^98 - 154 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.78702	−1.97072	−0.985362	−	0.170474i	$-0.945470\pi$
$2$	−2.78702	−1.97072	−0.985362	+	0.170474i	$0.945470\pi$
$3$	−1.95051	−1.12613	−0.563063	−	0.826414i	$-0.690377\pi$
$3$	−1.95051	−1.12613	−0.563063	+	0.826414i	$0.690377\pi$
$4$	5.76751	2.88375
$5$	−0.484177	−0.216531	−0.108265	−	0.994122i	$-0.534530\pi$
$5$	−0.484177	−0.216531	−0.108265	+	0.994122i	$0.534530\pi$
$6$	5.43612	2.21929
$7$	0.734493	0.277612	0.138806	−	0.990320i	$-0.455673\pi$
$7$	0.734493	0.277612	0.138806	+	0.990320i	$0.455673\pi$
$8$	−10.5001	−3.71236
$9$	0.804484	0.268161
$10$	1.34941	0.426722
$11$	−4.98227	−1.50221	−0.751105	−	0.660182i	$-0.770479\pi$
$11$	−4.98227	−1.50221	−0.751105	+	0.660182i	$0.770479\pi$
$12$	−11.2496	−3.24747
$13$	1.72452	0.478297	0.239149	−	0.970983i	$-0.423132\pi$
$13$	1.72452	0.478297	0.239149	+	0.970983i	$0.423132\pi$
$14$	−2.04705	−0.547097
$15$	0.944392	0.243841
$16$	17.7291	4.43228
$17$	−2.75009	−0.666996	−0.333498	−	0.942751i	$-0.608229\pi$
$17$	−2.75009	−0.666996	−0.333498	+	0.942751i	$0.608229\pi$
$18$	−2.24212	−0.528472
$19$	0.0586969	0.0134660	0.00673299	−	0.999977i	$-0.497857\pi$
$19$	0.0586969	0.0134660	0.00673299	+	0.999977i	$0.497857\pi$
$20$	−2.79250	−0.624421
$21$	−1.43264	−0.312627
$22$	13.8857	2.96044
$23$	−3.48409	−0.726484	−0.363242	−	0.931695i	$-0.618330\pi$
$23$	−3.48409	−0.726484	−0.363242	+	0.931695i	$0.618330\pi$
$24$	20.4806	4.18059
$25$	−4.76557	−0.953114
$26$	−4.80629	−0.942592
$27$	4.28237	0.824143
$28$	4.23620	0.800566
$29$	3.86738	0.718154	0.359077	−	0.933308i	$-0.383091\pi$
$29$	3.86738	0.718154	0.359077	+	0.933308i	$0.383091\pi$
$30$	−2.63204	−0.480543
$31$	−3.22383	−0.579016	−0.289508	−	0.957176i	$-0.593492\pi$
$31$	−3.22383	−0.579016	−0.289508	+	0.957176i	$0.593492\pi$
$32$	−28.4113	−5.02245
$33$	9.71796	1.69168
$34$	7.66458	1.31446
$35$	−0.355625	−0.0601116
$36$	4.63987	0.773311
$37$	0.376377	0.0618759	0.0309380	−	0.999521i	$-0.490151\pi$
$37$	0.376377	0.0618759	0.0309380	+	0.999521i	$0.490151\pi$
$38$	−0.163590	−0.0265378
$39$	−3.36370	−0.538623
$40$	5.08393	0.803840
$41$	−8.81992	−1.37744	−0.688720	−	0.725028i	$-0.741827\pi$
$41$	−8.81992	−1.37744	−0.688720	+	0.725028i	$0.741827\pi$
$42$	3.99279	0.616101
$43$	4.12114	0.628468	0.314234	−	0.949346i	$-0.398252\pi$
$43$	4.12114	0.628468	0.314234	+	0.949346i	$0.398252\pi$
$44$	−28.7353	−4.33201
$45$	−0.389513	−0.0580651
$46$	9.71025	1.43170
$47$	5.16871	0.753933	0.376967	−	0.926227i	$-0.376967\pi$
$47$	5.16871	0.753933	0.376967	+	0.926227i	$0.376967\pi$
$48$	−34.5808	−4.99131
$49$	−6.46052	−0.922931
$50$	13.2818	1.87833
$51$	5.36408	0.751122
$52$	9.94621	1.37929
$53$	0.462378	0.0635126	0.0317563	−	0.999496i	$-0.489890\pi$
$53$	0.462378	0.0635126	0.0317563	+	0.999496i	$0.489890\pi$
$54$	−11.9351	−1.62416
$55$	2.41230	0.325275
$56$	−7.71228	−1.03060
$57$	−0.114489	−0.0151644
$58$	−10.7785	−1.41528
$59$	13.1787	1.71572	0.857861	−	0.513881i	$-0.171793\pi$
$59$	13.1787	1.71572	0.857861	+	0.513881i	$0.171793\pi$
$60$	5.44679	0.703177
$61$	6.66424	0.853268	0.426634	−	0.904424i	$-0.359699\pi$
$61$	6.66424	0.853268	0.426634	+	0.904424i	$0.359699\pi$
$62$	8.98488	1.14108
$63$	0.590888	0.0744449
$64$	43.7246	5.46558
$65$	−0.834976	−0.103566
$66$	−27.0842	−3.33383
$67$	13.6527	1.66794	0.833970	−	0.551810i	$-0.186063\pi$
$67$	13.6527	1.66794	0.833970	+	0.551810i	$0.186063\pi$
$68$	−15.8612	−1.92345
$69$	6.79575	0.818112
$70$	0.991136	0.118463
$71$	−10.3921	−1.23331	−0.616657	−	0.787232i	$-0.711513\pi$
$71$	−10.3921	−1.23331	−0.616657	+	0.787232i	$0.711513\pi$
$72$	−8.44719	−0.995511
$73$	16.4603	1.92654	0.963269	−	0.268539i	$-0.0865409\pi$
$73$	16.4603	1.92654	0.963269	+	0.268539i	$0.0865409\pi$
$74$	−1.04897	−0.121940
$75$	9.29529	1.07333
$76$	0.338535	0.0388326
$77$	−3.65944	−0.417032
$78$	9.37472	1.06148
$79$	−5.93250	−0.667459	−0.333729	−	0.942669i	$-0.608307\pi$
$79$	−5.93250	−0.667459	−0.333729	+	0.942669i	$0.608307\pi$
$80$	−8.58405	−0.959726
$81$	−10.7663	−1.19625
$82$	24.5813	2.71455
$83$	3.80263	0.417393	0.208696	−	0.977980i	$-0.433078\pi$
$83$	3.80263	0.417393	0.208696	+	0.977980i	$0.433078\pi$
$84$	−8.26274	−0.901538
$85$	1.33153	0.144425
$86$	−11.4857	−1.23854
$87$	−7.54336	−0.808733
$88$	52.3145	5.57675
$89$	9.86875	1.04609	0.523043	−	0.852307i	$-0.324797\pi$
$89$	9.86875	1.04609	0.523043	+	0.852307i	$0.324797\pi$
$90$	1.08558	0.114430
$91$	1.26665	0.132781
$92$	−20.0945	−2.09500
$93$	6.28810	0.652046
$94$	−14.4053	−1.48579
$95$	−0.0284197	−0.00291580
$96$	55.4164	5.65591
$97$	−11.2478	−1.14204	−0.571019	−	0.820937i	$-0.693452\pi$
$97$	−11.2478	−1.14204	−0.571019	+	0.820937i	$0.693452\pi$
$98$	18.0056	1.81884
$99$	−4.00815	−0.402835
$100$	−27.4855	−2.74855
$101$	2.68564	0.267231	0.133615	−	0.991033i	$-0.457341\pi$
$101$	2.68564	0.267231	0.133615	+	0.991033i	$0.457341\pi$
$102$	−14.9498	−1.48025
$103$	−5.63468	−0.555201	−0.277601	−	0.960697i	$-0.589539\pi$
$103$	−5.63468	−0.555201	−0.277601	+	0.960697i	$0.589539\pi$
$104$	−18.1078	−1.77561
$105$	0.693650	0.0676933
$106$	−1.28866	−0.125166
$107$	−5.86266	−0.566765	−0.283382	−	0.959007i	$-0.591457\pi$
$107$	−5.86266	−0.566765	−0.283382	+	0.959007i	$0.591457\pi$
$108$	24.6986	2.37663
$109$	11.6590	1.11673	0.558366	−	0.829595i	$-0.311429\pi$
$109$	11.6590	1.11673	0.558366	+	0.829595i	$0.311429\pi$
$110$	−6.72315	−0.641027
$111$	−0.734126	−0.0696801
$112$	13.0219	1.23046
$113$	17.2990	1.62735	0.813675	−	0.581320i	$-0.197463\pi$
$113$	17.2990	1.62735	0.813675	+	0.581320i	$0.197463\pi$
$114$	0.319083	0.0298849
$115$	1.68692	0.157306
$116$	22.3051	2.07098
$117$	1.38735	0.128261
$118$	−36.7294	−3.38122
$119$	−2.01993	−0.185166
$120$	−9.91625	−0.905226
$121$	13.8230	1.25664
$122$	−18.5734	−1.68156
$123$	17.2033	1.55117
$124$	−18.5934	−1.66974
$125$	4.72827	0.422909
$126$	−1.64682	−0.146710
$127$	−10.6594	−0.945865	−0.472933	−	0.881099i	$-0.656805\pi$
$127$	−10.6594	−0.945865	−0.472933	+	0.881099i	$0.656805\pi$
$128$	−65.0391	−5.74870
$129$	−8.03832	−0.707735
$130$	2.32710	0.204100
$131$	14.6068	1.27621	0.638103	−	0.769951i	$-0.279719\pi$
$131$	14.6068	1.27621	0.638103	+	0.769951i	$0.279719\pi$
$132$	56.0484	4.87839
$133$	0.0431125	0.00373833
$134$	−38.0503	−3.28705
$135$	−2.07343	−0.178452
$136$	28.8764	2.47613
$137$	2.61910	0.223765	0.111883	−	0.993721i	$-0.464312\pi$
$137$	2.61910	0.223765	0.111883	+	0.993721i	$0.464312\pi$
$138$	−18.9399	−1.61227
$139$	−17.0537	−1.44648	−0.723239	−	0.690598i	$-0.757347\pi$
$139$	−17.0537	−1.44648	−0.723239	+	0.690598i	$0.757347\pi$
$140$	−2.05107	−0.173347
$141$	−10.0816	−0.849024
$142$	28.9630	2.43052
$143$	−8.59205	−0.718503
$144$	14.2628	1.18857
$145$	−1.87250	−0.155503
$146$	−45.8754	−3.79667
$147$	12.6013	1.03934
$148$	2.17075	0.178435
$149$	−18.9904	−1.55575	−0.777877	−	0.628417i	$-0.783703\pi$
$149$	−18.9904	−1.55575	−0.777877	+	0.628417i	$0.783703\pi$
$150$	−25.9062	−2.11523
$151$	−9.90160	−0.805780	−0.402890	−	0.915248i	$-0.631994\pi$
$151$	−9.90160	−0.805780	−0.402890	+	0.915248i	$0.631994\pi$
$152$	−0.616325	−0.0499906
$153$	−2.21241	−0.178862
$154$	10.1990	0.821856
$155$	1.56090	0.125375
$156$	−19.4002	−1.55326
$157$	17.9588	1.43327	0.716633	−	0.697451i	$-0.245682\pi$
$157$	17.9588	1.43327	0.716633	+	0.697451i	$0.245682\pi$
$158$	16.5340	1.31538
$159$	−0.901873	−0.0715232
$160$	13.7561	1.08751
$161$	−2.55904	−0.201681
$162$	30.0058	2.35748
$163$	19.0641	1.49322	0.746609	−	0.665263i	$-0.231681\pi$
$163$	19.0641	1.49322	0.746609	+	0.665263i	$0.231681\pi$
$164$	−50.8689	−3.97220
$165$	−4.70522	−0.366301
$166$	−10.5980	−0.822566
$167$	−0.639074	−0.0494530	−0.0247265	−	0.999694i	$-0.507871\pi$
$167$	−0.639074	−0.0494530	−0.0247265	+	0.999694i	$0.507871\pi$
$168$	15.0429	1.16058
$169$	−10.0260	−0.771232
$170$	−3.71102	−0.284622
$171$	0.0472207	0.00361106
$172$	23.7687	1.81235
$173$	−22.1477	−1.68386	−0.841931	−	0.539585i	$-0.818581\pi$
$173$	−22.1477	−1.68386	−0.841931	+	0.539585i	$0.818581\pi$
$174$	21.0235	1.59379
$175$	−3.50028	−0.264596
$176$	−88.3313	−6.65822
$177$	−25.7052	−1.93212
$178$	−27.5044	−2.06155
$179$	−3.80938	−0.284726	−0.142363	−	0.989815i	$-0.545470\pi$
$179$	−3.80938	−0.284726	−0.142363	+	0.989815i	$0.545470\pi$
$180$	−2.24652	−0.167446
$181$	−16.7472	−1.24481	−0.622404	−	0.782696i	$-0.713844\pi$
$181$	−16.7472	−1.24481	−0.622404	+	0.782696i	$0.713844\pi$
$182$	−3.53019	−0.261675
$183$	−12.9987	−0.960888
$184$	36.5835	2.69697
$185$	−0.182233	−0.0133980
$186$	−17.5251	−1.28500
$187$	13.7017	1.00197
$188$	29.8106	2.17416
$189$	3.14537	0.228792
$190$	0.0792064	0.00574624
$191$	11.2407	0.813345	0.406673	−	0.913574i	$-0.366689\pi$
$191$	11.2407	0.813345	0.406673	+	0.913574i	$0.366689\pi$
$192$	−85.2853	−6.15493
$193$	14.1742	1.02028	0.510142	−	0.860090i	$-0.329593\pi$
$193$	14.1742	1.02028	0.510142	+	0.860090i	$0.329593\pi$
$194$	31.3478	2.25064
$195$	1.62863	0.116628
$196$	−37.2611	−2.66151
$197$	−18.0170	−1.28366	−0.641830	−	0.766847i	$-0.721824\pi$
$197$	−18.0170	−1.28366	−0.641830	+	0.766847i	$0.721824\pi$
$198$	11.1708	0.793876
$199$	9.14851	0.648520	0.324260	−	0.945968i	$-0.394885\pi$
$199$	9.14851	0.648520	0.324260	+	0.945968i	$0.394885\pi$
$200$	50.0392	3.53830
$201$	−26.6297	−1.87831
$202$	−7.48493	−0.526638
$203$	2.84056	0.199369
$204$	30.9374	2.16605
$205$	4.27040	0.298258
$206$	15.7040	1.09415
$207$	−2.80290	−0.194815
$208$	30.5743	2.11995
$209$	−0.292444	−0.0202288
$210$	−1.93322	−0.133405
$211$	19.3345	1.33104	0.665521	−	0.746379i	$-0.268209\pi$
$211$	19.3345	1.33104	0.665521	+	0.746379i	$0.268209\pi$
$212$	2.66677	0.183155
$213$	20.2698	1.38887
$214$	16.3394	1.11694
$215$	−1.99536	−0.136083
$216$	−44.9655	−3.05952
$217$	−2.36788	−0.160742
$218$	−32.4940	−2.20077
$219$	−32.1060	−2.16953
$220$	13.9130	0.938012
$221$	−4.74260	−0.319022
$222$	2.04603	0.137320
$223$	10.6613	0.713933	0.356966	−	0.934117i	$-0.383811\pi$
$223$	10.6613	0.713933	0.356966	+	0.934117i	$0.383811\pi$
$224$	−20.8679	−1.39429
$225$	−3.83382	−0.255588
$226$	−48.2127	−3.20706
$227$	−0.333700	−0.0221485	−0.0110742	−	0.999939i	$-0.503525\pi$
$227$	−0.333700	−0.0221485	−0.0110742	+	0.999939i	$0.503525\pi$
$228$	−0.660315	−0.0437304
$229$	−29.5539	−1.95298	−0.976488	−	0.215573i	$-0.930838\pi$
$229$	−29.5539	−1.95298	−0.976488	+	0.215573i	$0.930838\pi$
$230$	−4.70149	−0.310007
$231$	7.13777	0.469631
$232$	−40.6080	−2.66605
$233$	10.6073	0.694907	0.347453	−	0.937697i	$-0.387047\pi$
$233$	10.6073	0.694907	0.347453	+	0.937697i	$0.387047\pi$
$234$	−3.86658	−0.252767
$235$	−2.50257	−0.163250
$236$	76.0084	4.94772
$237$	11.5714	0.751643
$238$	5.62958	0.364912
$239$	7.35851	0.475982	0.237991	−	0.971267i	$-0.423511\pi$
$239$	7.35851	0.475982	0.237991	+	0.971267i	$0.423511\pi$
$240$	16.7433	1.08077
$241$	−15.3377	−0.987989	−0.493995	−	0.869465i	$-0.664464\pi$
$241$	−15.3377	−0.987989	−0.493995	+	0.869465i	$0.664464\pi$
$242$	−38.5251	−2.47648
$243$	8.15256	0.522987
$244$	38.4360	2.46062
$245$	3.12804	0.199843
$246$	−47.9461	−3.05693
$247$	0.101224	0.00644074
$248$	33.8506	2.14952
$249$	−7.41706	−0.470037
$250$	−13.1778	−0.833438
$251$	12.4263	0.784340	0.392170	−	0.919893i	$-0.371725\pi$
$251$	12.4263	0.784340	0.392170	+	0.919893i	$0.371725\pi$
$252$	3.40795	0.214681
$253$	17.3587	1.09133
$254$	29.7079	1.86404
$255$	−2.59717	−0.162641
$256$	93.8163	5.86352
$257$	4.59717	0.286764	0.143382	−	0.989667i	$-0.454202\pi$
$257$	4.59717	0.286764	0.143382	+	0.989667i	$0.454202\pi$
$258$	22.4030	1.39475
$259$	0.276446	0.0171775
$260$	−4.81573	−0.298659
$261$	3.11124	0.192581
$262$	−40.7096	−2.51505
$263$	−5.39262	−0.332523	−0.166262	−	0.986082i	$-0.553170\pi$
$263$	−5.39262	−0.332523	−0.166262	+	0.986082i	$0.553170\pi$
$264$	−102.040	−6.28012
$265$	−0.223873	−0.0137524
$266$	−0.120156	−0.00736721
$267$	−19.2491	−1.17802
$268$	78.7419	4.80993
$269$	−13.8449	−0.844138	−0.422069	−	0.906564i	$-0.638696\pi$
$269$	−13.8449	−0.844138	−0.422069	+	0.906564i	$0.638696\pi$
$270$	5.77870	0.351680
$271$	0.595220	0.0361571	0.0180785	−	0.999837i	$-0.494245\pi$
$271$	0.595220	0.0361571	0.0180785	+	0.999837i	$0.494245\pi$
$272$	−48.7568	−2.95631
$273$	−2.47062	−0.149528
$274$	−7.29951	−0.440979
$275$	23.7434	1.43178
$276$	39.1946	2.35924
$277$	12.6721	0.761392	0.380696	−	0.924700i	$-0.375684\pi$
$277$	12.6721	0.761392	0.380696	+	0.924700i	$0.375684\pi$
$278$	47.5291	2.85061
$279$	−2.59352	−0.155270
$280$	3.73411	0.223156
$281$	22.6496	1.35116	0.675582	−	0.737285i	$-0.263892\pi$
$281$	22.6496	1.35116	0.675582	+	0.737285i	$0.263892\pi$
$282$	28.0977	1.67319
$283$	4.24650	0.252428	0.126214	−	0.992003i	$-0.459717\pi$
$283$	4.24650	0.252428	0.126214	+	0.992003i	$0.459717\pi$
$284$	−59.9364	−3.55657
$285$	0.0554329	0.00328356
$286$	23.9462	1.41597
$287$	−6.47817	−0.382394
$288$	−22.8564	−1.34683
$289$	−9.43699	−0.555117
$290$	5.21870	0.306453
$291$	21.9389	1.28608
$292$	94.9352	5.55566
$293$	12.3899	0.723824	0.361912	−	0.932212i	$-0.382124\pi$
$293$	12.3899	0.723824	0.361912	+	0.932212i	$0.382124\pi$
$294$	−35.1201	−2.04825
$295$	−6.38084	−0.371507
$296$	−3.95201	−0.229706
$297$	−21.3359	−1.23804
$298$	52.9267	3.06596
$299$	−6.00840	−0.347475
$300$	53.6107	3.09521
$301$	3.02695	0.174471
$302$	27.5960	1.58797
$303$	−5.23835	−0.300936
$304$	1.04064	0.0596851
$305$	−3.22667	−0.184759
$306$	6.16603	0.352488
$307$	−26.0662	−1.48768	−0.743838	−	0.668360i	$-0.766997\pi$
$307$	−26.0662	−1.48768	−0.743838	+	0.668360i	$0.766997\pi$
$308$	−21.1059	−1.20262
$309$	10.9905	0.625227
$310$	−4.35028	−0.247079
$311$	−18.0752	−1.02495	−0.512474	−	0.858703i	$-0.671271\pi$
$311$	−18.0752	−1.02495	−0.512474	+	0.858703i	$0.671271\pi$
$312$	35.3193	1.99956
$313$	32.6084	1.84314	0.921569	−	0.388214i	$-0.126908\pi$
$313$	32.6084	1.84314	0.921569	+	0.388214i	$0.126908\pi$
$314$	−50.0515	−2.82457
$315$	−0.286095	−0.0161196
$316$	−34.2157	−1.92479
$317$	27.2613	1.53115	0.765575	−	0.643347i	$-0.222455\pi$
$317$	27.2613	1.53115	0.765575	+	0.643347i	$0.222455\pi$
$318$	2.51354	0.140952
$319$	−19.2683	−1.07882
$320$	−21.1705	−1.18347
$321$	11.4352	0.638249
$322$	7.13212	0.397457
$323$	−0.161422	−0.00898176
$324$	−62.0945	−3.44969
$325$	−8.21835	−0.455872
$326$	−53.1322	−2.94272
$327$	−22.7410	−1.25758
$328$	92.6103	5.11355
$329$	3.79638	0.209301
$330$	13.1136	0.721877
$331$	24.2344	1.33205	0.666023	−	0.745932i	$-0.267995\pi$
$331$	24.2344	1.33205	0.666023	+	0.745932i	$0.267995\pi$
$332$	21.9317	1.20366
$333$	0.302789	0.0165927
$334$	1.78111	0.0974582
$335$	−6.61031	−0.361160
$336$	−25.3994	−1.38565
$337$	32.2019	1.75415	0.877076	−	0.480352i	$-0.159491\pi$
$337$	32.2019	1.75415	0.877076	+	0.480352i	$0.159491\pi$
$338$	27.9428	1.51989
$339$	−33.7418	−1.83260
$340$	7.67963	0.416486
$341$	16.0620	0.869804
$342$	−0.131605	−0.00711640
$343$	−9.88666	−0.533830
$344$	−43.2726	−2.33310
$345$	−3.29035	−0.177146
$346$	61.7263	3.31843
$347$	18.8963	1.01441	0.507203	−	0.861827i	$-0.330680\pi$
$347$	18.8963	1.01441	0.507203	+	0.861827i	$0.330680\pi$
$348$	−43.5064	−2.33219
$349$	21.2840	1.13931	0.569653	−	0.821885i	$-0.307077\pi$
$349$	21.2840	1.13931	0.569653	+	0.821885i	$0.307077\pi$
$350$	9.75537	0.521446
$351$	7.38506	0.394185
$352$	141.553	7.54478
$353$	−5.03497	−0.267984	−0.133992	−	0.990982i	$-0.542780\pi$
$353$	−5.03497	−0.267984	−0.133992	+	0.990982i	$0.542780\pi$
$354$	71.6410	3.80768
$355$	5.03161	0.267050
$356$	56.9181	3.01665
$357$	3.93988	0.208521
$358$	10.6168	0.561117
$359$	7.23244	0.381714	0.190857	−	0.981618i	$-0.438873\pi$
$359$	7.23244	0.381714	0.190857	+	0.981618i	$0.438873\pi$
$360$	4.08994	0.215559
$361$	−18.9966	−0.999819
$362$	46.6748	2.45317
$363$	−26.9619	−1.41513
$364$	7.30543	0.382908
$365$	−7.96973	−0.417155
$366$	36.2276	1.89365
$367$	4.90449	0.256012	0.128006	−	0.991773i	$-0.459142\pi$
$367$	4.90449	0.256012	0.128006	+	0.991773i	$0.459142\pi$
$368$	−61.7699	−3.21998
$369$	−7.09548	−0.369376
$370$	0.507888	0.0264038
$371$	0.339614	0.0176319
$372$	36.2667	1.88034
$373$	−30.5965	−1.58423	−0.792114	−	0.610373i	$-0.791019\pi$
$373$	−30.5965	−1.58423	−0.792114	+	0.610373i	$0.791019\pi$
$374$	−38.1870	−1.97460
$375$	−9.22253	−0.476249
$376$	−54.2721	−2.79887
$377$	6.66939	0.343491
$378$	−8.76624	−0.450887
$379$	−2.26178	−0.116180	−0.0580900	−	0.998311i	$-0.518501\pi$
$379$	−2.26178	−0.116180	−0.0580900	+	0.998311i	$0.518501\pi$
$380$	−0.163911	−0.00840845
$381$	20.7912	1.06516
$382$	−31.3280	−1.60288
$383$	−18.9853	−0.970106	−0.485053	−	0.874485i	$-0.661200\pi$
$383$	−18.9853	−0.970106	−0.485053	+	0.874485i	$0.661200\pi$
$384$	126.859	6.47376
$385$	1.77182	0.0903003
$386$	−39.5039	−2.01070
$387$	3.31539	0.168531
$388$	−64.8717	−3.29336
$389$	−6.04589	−0.306539	−0.153269	−	0.988184i	$-0.548980\pi$
$389$	−6.04589	−0.306539	−0.153269	+	0.988184i	$0.548980\pi$
$390$	−4.53903	−0.229843
$391$	9.58158	0.484561
$392$	67.8364	3.42625
$393$	−28.4908	−1.43717
$394$	50.2139	2.52974
$395$	2.87238	0.144525
$396$	−23.1171	−1.16168
$397$	−39.0979	−1.96227	−0.981135	−	0.193326i	$-0.938072\pi$
$397$	−39.0979	−1.96227	−0.981135	+	0.193326i	$0.938072\pi$
$398$	−25.4971	−1.27805
$399$	−0.0840912	−0.00420983
$400$	−84.4895	−4.22447
$401$	6.04629	0.301938	0.150969	−	0.988539i	$-0.451761\pi$
$401$	6.04629	0.301938	0.150969	+	0.988539i	$0.451761\pi$
$402$	74.2175	3.70163
$403$	−5.55957	−0.276942
$404$	15.4894	0.770628
$405$	5.21278	0.259025
$406$	−7.91673	−0.392900
$407$	−1.87521	−0.0929507
$408$	−56.3236	−2.78843
$409$	0.992207	0.0490615	0.0245307	−	0.999699i	$-0.492191\pi$
$409$	0.992207	0.0490615	0.0245307	+	0.999699i	$0.492191\pi$
$410$	−11.9017	−0.587784
$411$	−5.10858	−0.251988
$412$	−32.4981	−1.60106
$413$	9.67968	0.476306
$414$	7.81174	0.383926
$415$	−1.84115	−0.0903783
$416$	−48.9959	−2.40222
$417$	33.2634	1.62892
$418$	0.815048	0.0398653
$419$	−18.4866	−0.903130	−0.451565	−	0.892238i	$-0.649134\pi$
$419$	−18.4866	−0.903130	−0.451565	+	0.892238i	$0.649134\pi$
$420$	4.00063	0.195211
$421$	−35.3957	−1.72508	−0.862541	−	0.505987i	$-0.831128\pi$
$421$	−35.3957	−1.72508	−0.862541	+	0.505987i	$0.831128\pi$
$422$	−53.8857	−2.62312
$423$	4.15814	0.202176
$424$	−4.85504	−0.235781
$425$	13.1058	0.635723
$426$	−56.4926	−2.73707
$427$	4.89484	0.236878
$428$	−33.8129	−1.63441
$429$	16.7589	0.809125
$430$	5.56113	0.268181
$431$	31.4730	1.51600	0.758000	−	0.652254i	$-0.226177\pi$
$431$	31.4730	1.51600	0.758000	+	0.652254i	$0.226177\pi$
$432$	75.9228	3.65284
$433$	−28.9071	−1.38918	−0.694592	−	0.719404i	$-0.744415\pi$
$433$	−28.9071	−1.38918	−0.694592	+	0.719404i	$0.744415\pi$
$434$	6.59934	0.316778
$435$	3.65232	0.175116
$436$	67.2435	3.22038
$437$	−0.204505	−0.00978282
$438$	89.4803	4.27554
$439$	−2.09237	−0.0998635	−0.0499318	−	0.998753i	$-0.515900\pi$
$439$	−2.09237	−0.0998635	−0.0499318	+	0.998753i	$0.515900\pi$
$440$	−25.3295	−1.20754
$441$	−5.19738	−0.247494
$442$	13.2178	0.628705
$443$	27.0453	1.28496	0.642480	−	0.766302i	$-0.277905\pi$
$443$	27.0453	1.28496	0.642480	+	0.766302i	$0.277905\pi$
$444$	−4.23408	−0.200940
$445$	−4.77822	−0.226510
$446$	−29.7133	−1.40696
$447$	37.0409	1.75198
$448$	32.1154	1.51731
$449$	8.44931	0.398748	0.199374	−	0.979923i	$-0.436109\pi$
$449$	8.44931	0.398748	0.199374	+	0.979923i	$0.436109\pi$
$450$	10.6850	0.503694
$451$	43.9432	2.06920
$452$	99.7720	4.69288
$453$	19.3131	0.907411
$454$	0.930031	0.0436485
$455$	−0.613284	−0.0287512
$456$	1.20215	0.0562957
$457$	14.5201	0.679224	0.339612	−	0.940566i	$-0.389704\pi$
$457$	14.5201	0.679224	0.339612	+	0.940566i	$0.389704\pi$
$458$	82.3674	3.84878
$459$	−11.7769	−0.549700
$460$	9.72932	0.453632
$461$	5.99287	0.279116	0.139558	−	0.990214i	$-0.455432\pi$
$461$	5.99287	0.279116	0.139558	+	0.990214i	$0.455432\pi$
$462$	−19.8932	−0.925513
$463$	21.3033	0.990048	0.495024	−	0.868879i	$-0.335159\pi$
$463$	21.3033	0.990048	0.495024	+	0.868879i	$0.335159\pi$
$464$	68.5653	3.18306
$465$	−3.04456	−0.141188
$466$	−29.5628	−1.36947
$467$	20.5007	0.948661	0.474331	−	0.880347i	$-0.342690\pi$
$467$	20.5007	0.948661	0.474331	+	0.880347i	$0.342690\pi$
$468$	8.00156	0.369872
$469$	10.0278	0.463041
$470$	6.97473	0.321720
$471$	−35.0287	−1.61404
$472$	−138.378	−6.36938
$473$	−20.5326	−0.944091
$474$	−32.2498	−1.48128
$475$	−0.279724	−0.0128346
$476$	−11.6499	−0.533974
$477$	0.371976	0.0170316
$478$	−20.5083	−0.938030
$479$	−28.6151	−1.30746	−0.653729	−	0.756729i	$-0.726796\pi$
$479$	−28.6151	−1.30746	−0.653729	+	0.756729i	$0.726796\pi$
$480$	−26.8314	−1.22468
$481$	0.649071	0.0295951
$482$	42.7466	1.94705
$483$	4.99143	0.227118
$484$	79.7243	3.62383
$485$	5.44592	0.247286
$486$	−22.7214	−1.03066
$487$	−16.7512	−0.759072	−0.379536	−	0.925177i	$-0.623916\pi$
$487$	−16.7512	−0.759072	−0.379536	+	0.925177i	$0.623916\pi$
$488$	−69.9754	−3.16764
$489$	−37.1848	−1.68155
$490$	−8.71792	−0.393835
$491$	−7.51533	−0.339162	−0.169581	−	0.985516i	$-0.554241\pi$
$491$	−7.51533	−0.339162	−0.169581	+	0.985516i	$0.554241\pi$
$492$	99.2203	4.47320
$493$	−10.6357	−0.479006
$494$	−0.282114	−0.0126929
$495$	1.94066	0.0872261
$496$	−57.1556	−2.56636
$497$	−7.63291	−0.342383
$498$	20.6715	0.926313
$499$	35.7253	1.59928	0.799642	−	0.600477i	$-0.205023\pi$
$499$	35.7253	1.59928	0.799642	+	0.600477i	$0.205023\pi$
$500$	27.2703	1.21957
$501$	1.24652	0.0556904
$502$	−34.6323	−1.54572
$503$	3.00707	0.134079	0.0670393	−	0.997750i	$-0.478645\pi$
$503$	3.00707	0.134079	0.0670393	+	0.997750i	$0.478645\pi$
$504$	−6.20440	−0.276366
$505$	−1.30032	−0.0578637
$506$	−48.3791	−2.15071
$507$	19.5558	0.868505
$508$	−61.4779	−2.72764
$509$	31.4067	1.39208	0.696039	−	0.718004i	$-0.254944\pi$
$509$	31.4067	1.39208	0.696039	+	0.718004i	$0.254944\pi$
$510$	7.23837	0.320520
$511$	12.0900	0.534831
$512$	−131.390	−5.80669
$513$	0.251362	0.0110979
$514$	−12.8124	−0.565132
$515$	2.72818	0.120218
$516$	−46.3611	−2.04093
$517$	−25.7519	−1.13257
$518$	−0.770462	−0.0338522
$519$	43.1994	1.89624
$520$	8.76736	0.384474
$521$	10.2114	0.447370	0.223685	−	0.974661i	$-0.428191\pi$
$521$	10.2114	0.447370	0.223685	+	0.974661i	$0.428191\pi$
$522$	−8.67111	−0.379524
$523$	−5.70489	−0.249457	−0.124729	−	0.992191i	$-0.539806\pi$
$523$	−5.70489	−0.249457	−0.124729	+	0.992191i	$0.539806\pi$
$524$	84.2451	3.68026
$525$	6.82733	0.297969
$526$	15.0294	0.655311
$527$	8.86582	0.386201
$528$	172.291	7.49800
$529$	−10.8611	−0.472222
$530$	0.623940	0.0271022
$531$	10.6021	0.460090
$532$	0.248652	0.0107804
$533$	−15.2102	−0.658825
$534$	53.6477	2.32156
$535$	2.83857	0.122722
$536$	−143.355	−6.19199
$537$	7.43022	0.320638
$538$	38.5860	1.66356
$539$	32.1880	1.38644
$540$	−11.9585	−0.514613
$541$	32.7187	1.40669	0.703343	−	0.710850i	$-0.251690\pi$
$541$	32.7187	1.40669	0.703343	+	0.710850i	$0.251690\pi$
$542$	−1.65889	−0.0712556
$543$	32.6655	1.40181
$544$	78.1336	3.34995
$545$	−5.64503	−0.241807
$546$	6.88567	0.294679
$547$	−14.0897	−0.602433	−0.301216	−	0.953556i	$-0.597393\pi$
$547$	−14.0897	−0.602433	−0.301216	+	0.953556i	$0.597393\pi$
$548$	15.1057	0.645284
$549$	5.36127	0.228813
$550$	−66.1733	−2.82164
$551$	0.227003	0.00967066
$552$	−71.3563	−3.03713
$553$	−4.35738	−0.185295
$554$	−35.3174	−1.50049
$555$	0.355447	0.0150879
$556$	−98.3574	−4.17128
$557$	−27.1499	−1.15038	−0.575189	−	0.818021i	$-0.695071\pi$
$557$	−27.1499	−1.15038	−0.575189	+	0.818021i	$0.695071\pi$
$558$	7.22819	0.305994
$559$	7.10701	0.300594
$560$	−6.30492	−0.266432
$561$	−26.7253	−1.12834
$562$	−63.1251	−2.66277
$563$	19.5059	0.822077	0.411038	−	0.911618i	$-0.365166\pi$
$563$	19.5059	0.822077	0.411038	+	0.911618i	$0.365166\pi$
$564$	−58.1457	−2.44838
$565$	−8.37577	−0.352371
$566$	−11.8351	−0.497466
$567$	−7.90774	−0.332094
$568$	109.118	4.57850
$569$	−7.72885	−0.324010	−0.162005	−	0.986790i	$-0.551796\pi$
$569$	−7.72885	−0.324010	−0.162005	+	0.986790i	$0.551796\pi$
$570$	−0.154493	−0.00647099
$571$	36.9888	1.54793	0.773967	−	0.633226i	$-0.218270\pi$
$571$	36.9888	1.54793	0.773967	+	0.633226i	$0.218270\pi$
$572$	−49.5547	−2.07199
$573$	−21.9250	−0.915930
$574$	18.0548	0.753594
$575$	16.6037	0.692422
$576$	35.1757	1.46566
$577$	25.9547	1.08051	0.540255	−	0.841502i	$-0.318328\pi$
$577$	25.9547	1.08051	0.540255	+	0.841502i	$0.318328\pi$
$578$	26.3011	1.09398
$579$	−27.6470	−1.14897
$580$	−10.7996	−0.448431
$581$	2.79300	0.115873
$582$	−61.1442	−2.53451
$583$	−2.30369	−0.0954092
$584$	−172.836	−7.15200
$585$	−0.671724	−0.0277724
$586$	−34.5309	−1.42646
$587$	19.8746	0.820313	0.410157	−	0.912015i	$-0.365474\pi$
$587$	19.8746	0.820313	0.410157	+	0.912015i	$0.365474\pi$
$588$	72.6781	2.99719
$589$	−0.189229	−0.00779703
$590$	17.7836	0.732137
$591$	35.1424	1.44556
$592$	6.67283	0.274252
$593$	−38.7734	−1.59223	−0.796117	−	0.605142i	$-0.793116\pi$
$593$	−38.7734	−1.59223	−0.796117	+	0.605142i	$0.793116\pi$
$594$	59.4638	2.43983
$595$	0.978002	0.0400942
$596$	−109.527	−4.48641
$597$	−17.8442	−0.730316
$598$	16.7456	0.684777
$599$	13.4875	0.551084	0.275542	−	0.961289i	$-0.411143\pi$
$599$	13.4875	0.551084	0.275542	+	0.961289i	$0.411143\pi$
$600$	−97.6018	−3.98458
$601$	−10.9517	−0.446727	−0.223364	−	0.974735i	$-0.571704\pi$
$601$	−10.9517	−0.446727	−0.223364	+	0.974735i	$0.571704\pi$
$602$	−8.43619	−0.343833
$603$	10.9834	0.447277
$604$	−57.1075	−2.32367
$605$	−6.69279	−0.272100
$606$	14.5994	0.593061
$607$	29.2113	1.18565	0.592824	−	0.805332i	$-0.298013\pi$
$607$	29.2113	1.18565	0.592824	+	0.805332i	$0.298013\pi$
$608$	−1.66765	−0.0676322
$609$	−5.54055	−0.224514
$610$	8.99282	0.364109
$611$	8.91356	0.360604
$612$	−12.7601	−0.515795
$613$	−16.9883	−0.686152	−0.343076	−	0.939308i	$-0.611469\pi$
$613$	−16.9883	−0.686152	−0.343076	+	0.939308i	$0.611469\pi$
$614$	72.6471	2.93180
$615$	−8.32946	−0.335876
$616$	38.4247	1.54817
$617$	−40.8625	−1.64506	−0.822532	−	0.568719i	$-0.807439\pi$
$617$	−40.8625	−1.64506	−0.822532	+	0.568719i	$0.807439\pi$
$618$	−30.6308	−1.23215
$619$	−18.7934	−0.755370	−0.377685	−	0.925934i	$-0.623280\pi$
$619$	−18.7934	−0.755370	−0.377685	+	0.925934i	$0.623280\pi$
$620$	9.00252	0.361550
$621$	−14.9202	−0.598726
$622$	50.3759	2.01989
$623$	7.24853	0.290406
$624$	−59.6355	−2.38733
$625$	21.5385	0.861542
$626$	−90.8806	−3.63232
$627$	0.570414	0.0227801
$628$	103.577	4.13319
$629$	−1.03507	−0.0412710
$630$	0.797353	0.0317673
$631$	−26.5207	−1.05577	−0.527886	−	0.849315i	$-0.677015\pi$
$631$	−26.5207	−1.05577	−0.527886	+	0.849315i	$0.677015\pi$
$632$	62.2921	2.47785
$633$	−37.7121	−1.49892
$634$	−75.9780	−3.01747
$635$	5.16102	0.204809
$636$	−5.20156	−0.206255
$637$	−11.1413	−0.441435
$638$	53.7013	2.12606
$639$	−8.36026	−0.330727
$640$	31.4905	1.24477
$641$	−29.0793	−1.14856	−0.574282	−	0.818657i	$-0.694719\pi$
$641$	−29.0793	−1.14856	−0.574282	+	0.818657i	$0.694719\pi$
$642$	−31.8701	−1.25781
$643$	−31.1168	−1.22713	−0.613564	−	0.789645i	$-0.710265\pi$
$643$	−31.1168	−1.22713	−0.613564	+	0.789645i	$0.710265\pi$
$644$	−14.7593	−0.581598
$645$	3.89197	0.153246
$646$	0.449887	0.0177006
$647$	34.6266	1.36131	0.680656	−	0.732604i	$-0.261695\pi$
$647$	34.6266	1.36131	0.680656	+	0.732604i	$0.261695\pi$
$648$	113.047	4.44091
$649$	−65.6599	−2.57738
$650$	22.9047	0.898398
$651$	4.61857	0.181016
$652$	109.953	4.30607
$653$	−31.6220	−1.23746	−0.618731	−	0.785603i	$-0.712353\pi$
$653$	−31.6220	−1.23746	−0.618731	+	0.785603i	$0.712353\pi$
$654$	63.3798	2.47834
$655$	−7.07230	−0.276338
$656$	−156.369	−6.10520
$657$	13.2421	0.516623
$658$	−10.5806	−0.412475
$659$	−7.34101	−0.285965	−0.142983	−	0.989725i	$-0.545669\pi$
$659$	−7.34101	−0.285965	−0.142983	+	0.989725i	$0.545669\pi$
$660$	−27.1374	−1.05632
$661$	−10.3445	−0.402353	−0.201177	−	0.979555i	$-0.564477\pi$
$661$	−10.3445	−0.402353	−0.201177	+	0.979555i	$0.564477\pi$
$662$	−67.5420	−2.62509
$663$	9.25049	0.359259
$664$	−39.9281	−1.54951
$665$	−0.0208741	−0.000809462 0
$666$	−0.843880	−0.0326997
$667$	−13.4743	−0.521727
$668$	−3.68586	−0.142610
$669$	−20.7949	−0.803979
$670$	18.4231	0.711747
$671$	−33.2030	−1.28179
$672$	40.7030	1.57015
$673$	38.9970	1.50322	0.751612	−	0.659605i	$-0.229277\pi$
$673$	38.9970	1.50322	0.751612	+	0.659605i	$0.229277\pi$
$674$	−89.7476	−3.45695
$675$	−20.4080	−0.785503
$676$	−57.8251	−2.22404
$677$	−15.1464	−0.582125	−0.291063	−	0.956704i	$-0.594009\pi$
$677$	−15.1464	−0.582125	−0.291063	+	0.956704i	$0.594009\pi$
$678$	94.0392	3.61155
$679$	−8.26142	−0.317044
$680$	−13.9813	−0.536158
$681$	0.650885	0.0249420
$682$	−44.7651	−1.71414
$683$	3.48952	0.133523	0.0667614	−	0.997769i	$-0.478733\pi$
$683$	3.48952	0.133523	0.0667614	+	0.997769i	$0.478733\pi$
$684$	0.272346	0.0104134
$685$	−1.26811	−0.0484520
$686$	27.5544	1.05203
$687$	57.6451	2.19930
$688$	73.0643	2.78555
$689$	0.797383	0.0303779
$690$	9.17029	0.349107
$691$	2.78882	0.106092	0.0530459	−	0.998592i	$-0.483107\pi$
$691$	2.78882	0.106092	0.0530459	+	0.998592i	$0.483107\pi$
$692$	−127.737	−4.85584
$693$	−2.94396	−0.111832
$694$	−52.6644	−1.99911
$695$	8.25702	0.313207
$696$	79.2063	3.00231
$697$	24.2556	0.918746
$698$	−59.3191	−2.24526
$699$	−20.6896	−0.782553
$700$	−20.1879	−0.763031
$701$	2.41503	0.0912146	0.0456073	−	0.998959i	$-0.485478\pi$
$701$	2.41503	0.0912146	0.0456073	+	0.998959i	$0.485478\pi$
$702$	−20.5823	−0.776831
$703$	0.0220921	0.000833221 0
$704$	−217.848	−8.21045
$705$	4.88129	0.183840
$706$	14.0326	0.528123
$707$	1.97258	0.0741865
$708$	−148.255	−5.57176
$709$	27.4078	1.02932	0.514661	−	0.857394i	$-0.327918\pi$
$709$	27.4078	1.02932	0.514661	+	0.857394i	$0.327918\pi$
$710$	−14.0232	−0.526282
$711$	−4.77260	−0.178986
$712$	−103.623	−3.88344
$713$	11.2321	0.420646
$714$	−10.9805	−0.410937
$715$	4.16007	0.155578
$716$	−21.9706	−0.821080
$717$	−14.3528	−0.536016
$718$	−20.1570	−0.752253
$719$	−26.9653	−1.00563	−0.502817	−	0.864393i	$-0.667703\pi$
$719$	−26.9653	−1.00563	−0.502817	+	0.864393i	$0.667703\pi$
$720$	−6.90572	−0.257361
$721$	−4.13863	−0.154131
$722$	52.9439	1.97037
$723$	29.9164	1.11260
$724$	−96.5895	−3.58972
$725$	−18.4303	−0.684483
$726$	75.1434	2.78883
$727$	−0.987754	−0.0366338	−0.0183169	−	0.999832i	$-0.505831\pi$
$727$	−0.987754	−0.0366338	−0.0183169	+	0.999832i	$0.505831\pi$
$728$	−13.3000	−0.492932
$729$	16.3971	0.607302
$730$	22.2118	0.822097
$731$	−11.3335	−0.419185
$732$	−74.9698	−2.77097
$733$	46.5455	1.71920	0.859599	−	0.510969i	$-0.170713\pi$
$733$	46.5455	1.71920	0.859599	+	0.510969i	$0.170713\pi$
$734$	−13.6689	−0.504530
$735$	−6.10126	−0.225049
$736$	98.9875	3.64873
$737$	−68.0213	−2.50560
$738$	19.7753	0.727938
$739$	−45.3851	−1.66952	−0.834759	−	0.550615i	$-0.814393\pi$
$739$	−45.3851	−1.66952	−0.834759	+	0.550615i	$0.814393\pi$
$740$	−1.05103	−0.0386366
$741$	−0.197439	−0.00725309
$742$	−0.946512	−0.0347476
$743$	−0.204287	−0.00749456	−0.00374728	−	0.999993i	$-0.501193\pi$
$743$	−0.204287	−0.00749456	−0.00374728	+	0.999993i	$0.501193\pi$
$744$	−66.0259	−2.42063
$745$	9.19472	0.336868
$746$	85.2733	3.12208
$747$	3.05915	0.111929
$748$	79.0247	2.88943
$749$	−4.30608	−0.157341
$750$	25.7034	0.938556
$751$	−38.6969	−1.41207	−0.706036	−	0.708176i	$-0.749518\pi$
$751$	−38.6969	−1.41207	−0.706036	+	0.708176i	$0.749518\pi$
$752$	91.6367	3.34165
$753$	−24.2376	−0.883266
$754$	−18.5878	−0.676926
$755$	4.79413	0.174476
$756$	18.1410	0.659781
$757$	−45.0457	−1.63721	−0.818607	−	0.574354i	$-0.805253\pi$
$757$	−45.0457	−1.63721	−0.818607	+	0.574354i	$0.805253\pi$
$758$	6.30365	0.228959
$759$	−33.8583	−1.22898
$760$	0.298411	0.0108245
$761$	−46.6461	−1.69092	−0.845459	−	0.534040i	$-0.820673\pi$
$761$	−46.6461	−1.69092	−0.845459	+	0.534040i	$0.820673\pi$
$762$	−57.9455	−2.09914
$763$	8.56347	0.310018
$764$	64.8306	2.34549
$765$	1.07120	0.0387292
$766$	52.9126	1.91181
$767$	22.7270	0.820625
$768$	−182.990	−6.60307
$769$	−34.7097	−1.25166	−0.625832	−	0.779958i	$-0.715240\pi$
$769$	−34.7097	−1.25166	−0.625832	+	0.779958i	$0.715240\pi$
$770$	−4.93811	−0.177957
$771$	−8.96682	−0.322932
$772$	81.7500	2.94225
$773$	−14.6907	−0.528388	−0.264194	−	0.964470i	$-0.585106\pi$
$773$	−14.6907	−0.528388	−0.264194	+	0.964470i	$0.585106\pi$
$774$	−9.24008	−0.332128
$775$	15.3634	0.551869
$776$	118.103	4.23966
$777$	−0.539210	−0.0193441
$778$	16.8500	0.604103
$779$	−0.517702	−0.0185486
$780$	9.39312	0.336328
$781$	51.7761	1.85270
$782$	−26.7041	−0.954937
$783$	16.5616	0.591862
$784$	−114.539	−4.09069
$785$	−8.69523	−0.310346
$786$	79.4045	2.83226
$787$	36.8062	1.31200	0.656000	−	0.754761i	$-0.272247\pi$
$787$	36.8062	1.31200	0.656000	+	0.754761i	$0.272247\pi$
$788$	−103.913	−3.70176
$789$	10.5184	0.374463
$790$	−8.00540	−0.284819
$791$	12.7060	0.451773
$792$	42.0862	1.49547
$793$	11.4926	0.408116
$794$	108.967	3.86709
$795$	0.436667	0.0154870
$796$	52.7641	1.87017
$797$	−38.6277	−1.36826	−0.684132	−	0.729358i	$-0.739819\pi$
$797$	−38.6277	−1.36826	−0.684132	+	0.729358i	$0.739819\pi$
$798$	0.234364	0.00829641
$799$	−14.2144	−0.502870
$800$	135.396	4.78697
$801$	7.93925	0.280519
$802$	−16.8512	−0.595036
$803$	−82.0099	−2.89407
$804$	−153.587	−5.41659
$805$	1.23903	0.0436701
$806$	15.4947	0.545776
$807$	27.0046	0.950606
$808$	−28.1995	−0.992057
$809$	11.5036	0.404446	0.202223	−	0.979340i	$-0.435183\pi$
$809$	11.5036	0.404446	0.202223	+	0.979340i	$0.435183\pi$
$810$	−14.5281	−0.510467
$811$	−35.9267	−1.26156	−0.630779	−	0.775963i	$-0.717264\pi$
$811$	−35.9267	−1.26156	−0.630779	+	0.775963i	$0.717264\pi$
$812$	16.3830	0.574930
$813$	−1.16098	−0.0407174
$814$	5.22625	0.183180
$815$	−9.23042	−0.323328
$816$	95.1005	3.32918
$817$	0.241898	0.00846294
$818$	−2.76531	−0.0966867
$819$	1.01900	0.0356068
$820$	24.6296	0.860102
$821$	−39.0534	−1.36297	−0.681486	−	0.731831i	$-0.738666\pi$
$821$	−39.0534	−1.36297	−0.681486	+	0.731831i	$0.738666\pi$
$822$	14.2378	0.496599
$823$	−28.9496	−1.00912	−0.504559	−	0.863377i	$-0.668345\pi$
$823$	−28.9496	−1.00912	−0.504559	+	0.863377i	$0.668345\pi$
$824$	59.1649	2.06111
$825$	−46.3116	−1.61236
$826$	−26.9775	−0.938668
$827$	40.6808	1.41461	0.707305	−	0.706909i	$-0.249911\pi$
$827$	40.6808	1.41461	0.707305	+	0.706909i	$0.249911\pi$
$828$	−16.1657	−0.561798
$829$	−11.3016	−0.392520	−0.196260	−	0.980552i	$-0.562880\pi$
$829$	−11.3016	−0.392520	−0.196260	+	0.980552i	$0.562880\pi$
$830$	5.13132	0.178111
$831$	−24.7170	−0.857424
$832$	75.4042	2.61417
$833$	17.7670	0.615591
$834$	−92.7060	−3.21015
$835$	0.309425	0.0107081
$836$	−1.68667	−0.0583347
$837$	−13.8056	−0.477192
$838$	51.5227	1.77982
$839$	15.9006	0.548951	0.274476	−	0.961594i	$-0.411496\pi$
$839$	15.9006	0.548951	0.274476	+	0.961594i	$0.411496\pi$
$840$	−7.28342	−0.251302
$841$	−14.0434	−0.484254
$842$	98.6488	3.39966
$843$	−44.1783	−1.52158
$844$	111.512	3.83840
$845$	4.85437	0.166995
$846$	−11.5888	−0.398432
$847$	10.1529	0.348858
$848$	8.19757	0.281506
$849$	−8.28283	−0.284266
$850$	−36.5261	−1.25284
$851$	−1.31133	−0.0449518
$852$	116.906	4.00515
$853$	−32.8728	−1.12554	−0.562772	−	0.826612i	$-0.690265\pi$
$853$	−32.8728	−1.12554	−0.562772	+	0.826612i	$0.690265\pi$
$854$	−13.6420	−0.466821
$855$	−0.0228632	−0.000781905 0
$856$	61.5588	2.10403
$857$	16.4603	0.562274	0.281137	−	0.959668i	$-0.409289\pi$
$857$	16.4603	0.562274	0.281137	+	0.959668i	$0.409289\pi$
$858$	−46.7074	−1.59456
$859$	−5.29088	−0.180522	−0.0902612	−	0.995918i	$-0.528770\pi$
$859$	−5.29088	−0.180522	−0.0902612	+	0.995918i	$0.528770\pi$
$860$	−11.5083	−0.392429
$861$	12.6357	0.430624
$862$	−87.7160	−2.98762
$863$	10.8266	0.368541	0.184271	−	0.982876i	$-0.441008\pi$
$863$	10.8266	0.368541	0.184271	+	0.982876i	$0.441008\pi$
$864$	−121.668	−4.13922
$865$	10.7234	0.364608
$866$	80.5647	2.73770
$867$	18.4069	0.625132
$868$	−13.6568	−0.463541
$869$	29.5573	1.00266
$870$	−10.1791	−0.345104
$871$	23.5444	0.797771
$872$	−122.421	−4.14571
$873$	−9.04865	−0.306251
$874$	0.569962	0.0192792
$875$	3.47288	0.117405
$876$	−185.172	−6.25638
$877$	−22.5454	−0.761303	−0.380652	−	0.924719i	$-0.624300\pi$
$877$	−22.5454	−0.761303	−0.380652	+	0.924719i	$0.624300\pi$
$878$	5.83150	0.196804
$879$	−24.1665	−0.815117
$880$	42.7680	1.44171
$881$	38.2801	1.28969	0.644845	−	0.764314i	$-0.276922\pi$
$881$	38.2801	1.28969	0.644845	+	0.764314i	$0.276922\pi$
$882$	14.4852	0.487743
$883$	−5.42659	−0.182619	−0.0913097	−	0.995823i	$-0.529105\pi$
$883$	−5.42659	−0.182619	−0.0913097	+	0.995823i	$0.529105\pi$
$884$	−27.3530	−0.919981
$885$	12.4459	0.418364
$886$	−75.3759	−2.53230
$887$	−13.5930	−0.456407	−0.228204	−	0.973613i	$-0.573285\pi$
$887$	−13.5930	−0.456407	−0.228204	+	0.973613i	$0.573285\pi$
$888$	7.70842	0.258678
$889$	−7.82923	−0.262584
$890$	13.3170	0.446388
$891$	53.6404	1.79702
$892$	61.4891	2.05881
$893$	0.303387	0.0101525
$894$	−103.234	−3.45266
$895$	1.84441	0.0616520
$896$	−47.7708	−1.59591
$897$	11.7194	0.391301
$898$	−23.5484	−0.785822
$899$	−12.4678	−0.415823
$900$	−22.1116	−0.737054
$901$	−1.27158	−0.0423626
$902$	−122.471	−4.07783
$903$	−5.90409	−0.196476
$904$	−181.642	−6.04131
$905$	8.10860	0.269539
$906$	−53.8262	−1.78826
$907$	4.67548	0.155247	0.0776234	−	0.996983i	$-0.475267\pi$
$907$	4.67548	0.155247	0.0776234	+	0.996983i	$0.475267\pi$
$908$	−1.92462	−0.0638707
$909$	2.16055	0.0716609
$910$	1.70924	0.0566607
$911$	−6.53089	−0.216378	−0.108189	−	0.994130i	$-0.534505\pi$
$911$	−6.53089	−0.216378	−0.108189	+	0.994130i	$0.534505\pi$
$912$	−2.02979	−0.0672130
$913$	−18.9457	−0.627012
$914$	−40.4680	−1.33856
$915$	6.29365	0.208062
$916$	−170.452	−5.63190
$917$	10.7286	0.354290
$918$	32.8226	1.08331
$919$	−1.78235	−0.0587942	−0.0293971	−	0.999568i	$-0.509359\pi$
$919$	−1.78235	−0.0587942	−0.0293971	+	0.999568i	$0.509359\pi$
$920$	−17.7129	−0.583976
$921$	50.8423	1.67531
$922$	−16.7023	−0.550060
$923$	−17.9214	−0.589890
$924$	41.1672	1.35430
$925$	−1.79365	−0.0589748
$926$	−59.3728	−1.95111
$927$	−4.53301	−0.148883
$928$	−109.877	−3.60689
$929$	−23.4277	−0.768637	−0.384318	−	0.923201i	$-0.625564\pi$
$929$	−23.4277	−0.768637	−0.384318	+	0.923201i	$0.625564\pi$
$930$	8.48525	0.278242
$931$	−0.379212	−0.0124282
$932$	61.1776	2.00394
$933$	35.2557	1.15422
$934$	−57.1361	−1.86955
$935$	−6.63406	−0.216957
$936$	−14.5674	−0.476150
$937$	−17.2687	−0.564143	−0.282072	−	0.959393i	$-0.591022\pi$
$937$	−17.2687	−0.564143	−0.282072	+	0.959393i	$0.591022\pi$
$938$	−27.9477	−0.912525
$939$	−63.6031	−2.07561
$940$	−14.4336	−0.470772
$941$	31.6672	1.03232	0.516161	−	0.856491i	$-0.327360\pi$
$941$	31.6672	1.03232	0.516161	+	0.856491i	$0.327360\pi$
$942$	97.6259	3.18083
$943$	30.7294	1.00069
$944$	233.647	7.60457
$945$	−1.52292	−0.0495406
$946$	57.2250	1.86054
$947$	46.3039	1.50467	0.752337	−	0.658779i	$-0.228927\pi$
$947$	46.3039	1.50467	0.752337	+	0.658779i	$0.228927\pi$
$948$	66.7381	2.16755
$949$	28.3863	0.921457
$950$	0.779598	0.0252935
$951$	−53.1735	−1.72427
$952$	21.2095	0.687404
$953$	−19.4511	−0.630082	−0.315041	−	0.949078i	$-0.602018\pi$
$953$	−19.4511	−0.630082	−0.315041	+	0.949078i	$0.602018\pi$
$954$	−1.03671	−0.0335646
$955$	−5.44247	−0.176114
$956$	42.4402	1.37262
$957$	37.5830	1.21489
$958$	79.7510	2.57664
$959$	1.92371	0.0621200
$960$	41.2932	1.33273
$961$	−20.6069	−0.664740
$962$	−1.80898	−0.0583237
$963$	−4.71641	−0.151984
$964$	−88.4604	−2.84912
$965$	−6.86284	−0.220923
$966$	−13.9113	−0.447587
$967$	−49.8254	−1.60228	−0.801138	−	0.598480i	$-0.795772\pi$
$967$	−49.8254	−1.60228	−0.801138	+	0.598480i	$0.795772\pi$
$968$	−145.143	−4.66509
$969$	0.314855	0.0101146
$970$	−15.1779	−0.487333
$971$	−33.3003	−1.06866	−0.534329	−	0.845276i	$-0.679436\pi$
$971$	−33.3003	−1.06866	−0.534329	+	0.845276i	$0.679436\pi$
$972$	47.0199	1.50817
$973$	−12.5258	−0.401560
$974$	46.6862	1.49592
$975$	16.0300	0.513369
$976$	118.151	3.78193
$977$	−15.4350	−0.493808	−0.246904	−	0.969040i	$-0.579413\pi$
$977$	−15.4350	−0.493808	−0.246904	+	0.969040i	$0.579413\pi$
$978$	103.635	3.31388
$979$	−49.1688	−1.57144
$980$	18.0410	0.576298
$981$	9.37949	0.299464
$982$	20.9454	0.668395
$983$	53.4526	1.70487	0.852437	−	0.522830i	$-0.175124\pi$
$983$	53.4526	1.70487	0.852437	+	0.522830i	$0.175124\pi$
$984$	−180.637	−5.75851
$985$	8.72344	0.277952
$986$	29.6418	0.943989
$987$	−7.40487	−0.235700
$988$	0.583812	0.0185735
$989$	−14.3584	−0.456572
$990$	−5.40866	−0.171899
$991$	−3.99855	−0.127018	−0.0635090	−	0.997981i	$-0.520229\pi$
$991$	−3.99855	−0.127018	−0.0635090	+	0.997981i	$0.520229\pi$
$992$	91.5930	2.90808
$993$	−47.2695	−1.50005
$994$	21.2731	0.674742
$995$	−4.42950	−0.140425
$996$	−42.7779	−1.35547
$997$	−16.5225	−0.523271	−0.261636	−	0.965167i	$-0.584262\pi$
$997$	−16.5225	−0.523271	−0.261636	+	0.965167i	$0.584262\pi$
$998$	−99.5673	−3.15175
$999$	1.61178	0.0509946

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8011.2.a.a.1.2	✓	309

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8011.2.a.a.1.2	✓	309	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:	\( N \)	\(=\)	\( 8011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8011.a (trivial)

\(f(q)\)	\(=\)	\(q-2.78702 q^{2} -1.95051 q^{3} +5.76751 q^{4} -0.484177 q^{5} +5.43612 q^{6} +0.734493 q^{7} -10.5001 q^{8} +0.804484 q^{9} +O(q^{10})\)	\(q-2.78702 q^{2} -1.95051 q^{3} +5.76751 q^{4} -0.484177 q^{5} +5.43612 q^{6} +0.734493 q^{7} -10.5001 q^{8} +0.804484 q^{9} +1.34941 q^{10} -4.98227 q^{11} -11.2496 q^{12} +1.72452 q^{13} -2.04705 q^{14} +0.944392 q^{15} +17.7291 q^{16} -2.75009 q^{17} -2.24212 q^{18} +0.0586969 q^{19} -2.79250 q^{20} -1.43264 q^{21} +13.8857 q^{22} -3.48409 q^{23} +20.4806 q^{24} -4.76557 q^{25} -4.80629 q^{26} +4.28237 q^{27} +4.23620 q^{28} +3.86738 q^{29} -2.63204 q^{30} -3.22383 q^{31} -28.4113 q^{32} +9.71796 q^{33} +7.66458 q^{34} -0.355625 q^{35} +4.63987 q^{36} +0.376377 q^{37} -0.163590 q^{38} -3.36370 q^{39} +5.08393 q^{40} -8.81992 q^{41} +3.99279 q^{42} +4.12114 q^{43} -28.7353 q^{44} -0.389513 q^{45} +9.71025 q^{46} +5.16871 q^{47} -34.5808 q^{48} -6.46052 q^{49} +13.2818 q^{50} +5.36408 q^{51} +9.94621 q^{52} +0.462378 q^{53} -11.9351 q^{54} +2.41230 q^{55} -7.71228 q^{56} -0.114489 q^{57} -10.7785 q^{58} +13.1787 q^{59} +5.44679 q^{60} +6.66424 q^{61} +8.98488 q^{62} +0.590888 q^{63} +43.7246 q^{64} -0.834976 q^{65} -27.0842 q^{66} +13.6527 q^{67} -15.8612 q^{68} +6.79575 q^{69} +0.991136 q^{70} -10.3921 q^{71} -8.44719 q^{72} +16.4603 q^{73} -1.04897 q^{74} +9.29529 q^{75} +0.338535 q^{76} -3.65944 q^{77} +9.37472 q^{78} -5.93250 q^{79} -8.58405 q^{80} -10.7663 q^{81} +24.5813 q^{82} +3.80263 q^{83} -8.26274 q^{84} +1.33153 q^{85} -11.4857 q^{86} -7.54336 q^{87} +52.3145 q^{88} +9.86875 q^{89} +1.08558 q^{90} +1.26665 q^{91} -20.0945 q^{92} +6.28810 q^{93} -14.4053 q^{94} -0.0284197 q^{95} +55.4164 q^{96} -11.2478 q^{97} +18.0056 q^{98} -4.00815 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 309 q - 33 q^{2} - 15 q^{3} + 273 q^{4} - 74 q^{5} - 32 q^{6} - 19 q^{7} - 93 q^{8} + 214 q^{9}+O(q^{10}) \) 309 * q - 33 * q^2 - 15 * q^3 + 273 * q^4 - 74 * q^5 - 32 * q^6 - 19 * q^7 - 93 * q^8 + 214 * q^9	\( 309 q - 33 q^{2} - 15 q^{3} + 273 q^{4} - 74 q^{5} - 32 q^{6} - 19 q^{7} - 93 q^{8} + 214 q^{9} - 23 q^{10} - 72 q^{11} - 42 q^{12} - 57 q^{13} - 77 q^{14} - 44 q^{15} + 205 q^{16} - 86 q^{17} - 82 q^{18} - 58 q^{19} - 134 q^{20} - 123 q^{21} - 31 q^{22} - 94 q^{23} - 84 q^{24} + 225 q^{25} - 92 q^{26} - 48 q^{27} - 36 q^{28} - 345 q^{29} - 85 q^{30} - 36 q^{31} - 199 q^{32} - 56 q^{33} - 28 q^{34} - 168 q^{35} + 65 q^{36} - 79 q^{37} - 66 q^{38} - 145 q^{39} - 54 q^{40} - 176 q^{41} - 48 q^{42} - 58 q^{43} - 194 q^{44} - 192 q^{45} - 44 q^{46} - 82 q^{47} - 81 q^{48} + 186 q^{49} - 206 q^{50} - 145 q^{51} - 86 q^{52} - 223 q^{53} - 117 q^{54} - 58 q^{55} - 216 q^{56} - 124 q^{57} - 151 q^{59} - 91 q^{60} - 184 q^{61} - 124 q^{62} - 78 q^{63} + 101 q^{64} - 194 q^{65} - 112 q^{66} - 53 q^{67} - 182 q^{68} - 243 q^{69} - 193 q^{71} - 208 q^{72} - 69 q^{73} - 236 q^{74} - 62 q^{75} - 142 q^{76} - 324 q^{77} - 20 q^{78} - 91 q^{79} - 223 q^{80} - 27 q^{81} + 2 q^{82} - 117 q^{83} - 157 q^{84} - 171 q^{85} - 203 q^{86} - 69 q^{87} - 36 q^{88} - 172 q^{89} - 10 q^{90} - 84 q^{91} - 226 q^{92} - 220 q^{93} - 96 q^{94} - 166 q^{95} - 118 q^{96} - 12 q^{97} - 116 q^{98} - 154 q^{99}+O(q^{100}) \) 309 * q - 33 * q^2 - 15 * q^3 + 273 * q^4 - 74 * q^5 - 32 * q^6 - 19 * q^7 - 93 * q^8 + 214 * q^9 - 23 * q^10 - 72 * q^11 - 42 * q^12 - 57 * q^13 - 77 * q^14 - 44 * q^15 + 205 * q^16 - 86 * q^17 - 82 * q^18 - 58 * q^19 - 134 * q^20 - 123 * q^21 - 31 * q^22 - 94 * q^23 - 84 * q^24 + 225 * q^25 - 92 * q^26 - 48 * q^27 - 36 * q^28 - 345 * q^29 - 85 * q^30 - 36 * q^31 - 199 * q^32 - 56 * q^33 - 28 * q^34 - 168 * q^35 + 65 * q^36 - 79 * q^37 - 66 * q^38 - 145 * q^39 - 54 * q^40 - 176 * q^41 - 48 * q^42 - 58 * q^43 - 194 * q^44 - 192 * q^45 - 44 * q^46 - 82 * q^47 - 81 * q^48 + 186 * q^49 - 206 * q^50 - 145 * q^51 - 86 * q^52 - 223 * q^53 - 117 * q^54 - 58 * q^55 - 216 * q^56 - 124 * q^57 - 151 * q^59 - 91 * q^60 - 184 * q^61 - 124 * q^62 - 78 * q^63 + 101 * q^64 - 194 * q^65 - 112 * q^66 - 53 * q^67 - 182 * q^68 - 243 * q^69 - 193 * q^71 - 208 * q^72 - 69 * q^73 - 236 * q^74 - 62 * q^75 - 142 * q^76 - 324 * q^77 - 20 * q^78 - 91 * q^79 - 223 * q^80 - 27 * q^81 + 2 * q^82 - 117 * q^83 - 157 * q^84 - 171 * q^85 - 203 * q^86 - 69 * q^87 - 36 * q^88 - 172 * q^89 - 10 * q^90 - 84 * q^91 - 226 * q^92 - 220 * q^93 - 96 * q^94 - 166 * q^95 - 118 * q^96 - 12 * q^97 - 116 * q^98 - 154 * q^99

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