LMFDB - Embedded newform 8011.2.a.b.1.9

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:	$0$
Dimension:	$358$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
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)

$f(q)$	$=$	$q-2.67959 q^{2} -1.76320 q^{3} +5.18019 q^{4} -3.93630 q^{5} +4.72465 q^{6} -2.55729 q^{7} -8.52159 q^{8} +0.108876 q^{9} +O(q^{10})$	\(q-2.67959 q^{2} -1.76320 q^{3} +5.18019 q^{4} -3.93630 q^{5} +4.72465 q^{6} -2.55729 q^{7} -8.52159 q^{8} +0.108876 q^{9} +10.5477 q^{10} +1.40777 q^{11} -9.13371 q^{12} -2.73241 q^{13} +6.85247 q^{14} +6.94049 q^{15} +12.4740 q^{16} -1.27752 q^{17} -0.291742 q^{18} -3.42030 q^{19} -20.3908 q^{20} +4.50901 q^{21} -3.77225 q^{22} +5.50852 q^{23} +15.0253 q^{24} +10.4945 q^{25} +7.32174 q^{26} +5.09763 q^{27} -13.2472 q^{28} +4.57184 q^{29} -18.5976 q^{30} -6.23935 q^{31} -16.3819 q^{32} -2.48218 q^{33} +3.42322 q^{34} +10.0662 q^{35} +0.563996 q^{36} -3.97944 q^{37} +9.16500 q^{38} +4.81779 q^{39} +33.5435 q^{40} +9.88896 q^{41} -12.0823 q^{42} +0.0738129 q^{43} +7.29252 q^{44} -0.428567 q^{45} -14.7606 q^{46} -3.58950 q^{47} -21.9941 q^{48} -0.460288 q^{49} -28.1208 q^{50} +2.25252 q^{51} -14.1544 q^{52} -0.0891657 q^{53} -13.6595 q^{54} -5.54141 q^{55} +21.7921 q^{56} +6.03068 q^{57} -12.2507 q^{58} -0.736911 q^{59} +35.9530 q^{60} +12.7896 q^{61} +16.7189 q^{62} -0.278426 q^{63} +18.9488 q^{64} +10.7556 q^{65} +6.65123 q^{66} -0.110608 q^{67} -6.61778 q^{68} -9.71263 q^{69} -26.9734 q^{70} -10.3081 q^{71} -0.927793 q^{72} -5.98043 q^{73} +10.6632 q^{74} -18.5038 q^{75} -17.7178 q^{76} -3.60008 q^{77} -12.9097 q^{78} -1.36862 q^{79} -49.1013 q^{80} -9.31477 q^{81} -26.4983 q^{82} -2.90034 q^{83} +23.3575 q^{84} +5.02870 q^{85} -0.197788 q^{86} -8.06108 q^{87} -11.9965 q^{88} +18.5008 q^{89} +1.14838 q^{90} +6.98756 q^{91} +28.5352 q^{92} +11.0012 q^{93} +9.61838 q^{94} +13.4633 q^{95} +28.8846 q^{96} -13.4129 q^{97} +1.23338 q^{98} +0.153272 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 358 q + 33 q^{2} + 11 q^{3} + 391 q^{4} + 76 q^{5} + 32 q^{6} + 19 q^{7} + 99 q^{8} + 451 q^{9}+O(q^{10}) $ 358 * q + 33 * q^2 + 11 * q^3 + 391 * q^4 + 76 * q^5 + 32 * q^6 + 19 * q^7 + 99 * q^8 + 451 * q^9	\( 358 q + 33 q^{2} + 11 q^{3} + 391 q^{4} + 76 q^{5} + 32 q^{6} + 19 q^{7} + 99 q^{8} + 451 q^{9} + 21 q^{10} + 70 q^{11} + 20 q^{12} + 53 q^{13} + 69 q^{14} + 28 q^{15} + 449 q^{16} + 88 q^{17} + 86 q^{18} + 44 q^{19} + 136 q^{20} + 125 q^{21} + 17 q^{22} + 104 q^{23} + 84 q^{24} + 444 q^{25} + 100 q^{26} + 32 q^{27} + 46 q^{28} + 373 q^{29} + 99 q^{30} + 30 q^{31} + 221 q^{32} + 56 q^{33} + 26 q^{34} + 164 q^{35} + 599 q^{36} + 81 q^{37} + 66 q^{38} + 143 q^{39} + 42 q^{40} + 182 q^{41} + 32 q^{42} + 40 q^{43} + 184 q^{44} + 198 q^{45} + 54 q^{46} + 66 q^{47} + 5 q^{48} + 479 q^{49} + 184 q^{50} + 123 q^{51} + 64 q^{52} + 221 q^{53} + 67 q^{54} + 38 q^{55} + 174 q^{56} + 84 q^{57} + 44 q^{58} + 127 q^{59} + 29 q^{60} + 174 q^{61} + 86 q^{62} + 48 q^{63} + 549 q^{64} + 202 q^{65} + 32 q^{66} + 29 q^{67} + 172 q^{68} + 249 q^{69} + 12 q^{70} + 185 q^{71} + 218 q^{72} + 57 q^{73} + 272 q^{74} + 24 q^{75} + 84 q^{76} + 384 q^{77} + 12 q^{78} + 93 q^{79} + 215 q^{80} + 702 q^{81} + 48 q^{82} + 121 q^{83} + 179 q^{84} + 177 q^{85} + 209 q^{86} + 91 q^{87} + 36 q^{88} + 186 q^{89} + 66 q^{90} + 32 q^{91} + 272 q^{92} + 220 q^{93} + 60 q^{94} + 170 q^{95} + 162 q^{96} + 22 q^{97} + 196 q^{98} + 152 q^{99}+O(q^{100}) \) 358 * q + 33 * q^2 + 11 * q^3 + 391 * q^4 + 76 * q^5 + 32 * q^6 + 19 * q^7 + 99 * q^8 + 451 * q^9 + 21 * q^10 + 70 * q^11 + 20 * q^12 + 53 * q^13 + 69 * q^14 + 28 * q^15 + 449 * q^16 + 88 * q^17 + 86 * q^18 + 44 * q^19 + 136 * q^20 + 125 * q^21 + 17 * q^22 + 104 * q^23 + 84 * q^24 + 444 * q^25 + 100 * q^26 + 32 * q^27 + 46 * q^28 + 373 * q^29 + 99 * q^30 + 30 * q^31 + 221 * q^32 + 56 * q^33 + 26 * q^34 + 164 * q^35 + 599 * q^36 + 81 * q^37 + 66 * q^38 + 143 * q^39 + 42 * q^40 + 182 * q^41 + 32 * q^42 + 40 * q^43 + 184 * q^44 + 198 * q^45 + 54 * q^46 + 66 * q^47 + 5 * q^48 + 479 * q^49 + 184 * q^50 + 123 * q^51 + 64 * q^52 + 221 * q^53 + 67 * q^54 + 38 * q^55 + 174 * q^56 + 84 * q^57 + 44 * q^58 + 127 * q^59 + 29 * q^60 + 174 * q^61 + 86 * q^62 + 48 * q^63 + 549 * q^64 + 202 * q^65 + 32 * q^66 + 29 * q^67 + 172 * q^68 + 249 * q^69 + 12 * q^70 + 185 * q^71 + 218 * q^72 + 57 * q^73 + 272 * q^74 + 24 * q^75 + 84 * q^76 + 384 * q^77 + 12 * q^78 + 93 * q^79 + 215 * q^80 + 702 * q^81 + 48 * q^82 + 121 * q^83 + 179 * q^84 + 177 * q^85 + 209 * q^86 + 91 * q^87 + 36 * q^88 + 186 * q^89 + 66 * q^90 + 32 * q^91 + 272 * q^92 + 220 * q^93 + 60 * q^94 + 170 * q^95 + 162 * q^96 + 22 * q^97 + 196 * q^98 + 152 * 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 $

$2$	−2.67959	−1.89475	−0.947377	−	0.320119i	$-0.896277\pi$
$2$	−2.67959	−1.89475	−0.947377	+	0.320119i	$0.896277\pi$
$3$	−1.76320	−1.01798	−0.508992	−	0.860771i	$-0.669982\pi$
$3$	−1.76320	−1.01798	−0.508992	+	0.860771i	$0.669982\pi$
$4$	5.18019	2.59009
$5$	−3.93630	−1.76037	−0.880184	−	0.474633i	$-0.842581\pi$
$5$	−3.93630	−1.76037	−0.880184	+	0.474633i	$0.842581\pi$
$6$	4.72465	1.92883
$7$	−2.55729	−0.966563	−0.483282	−	0.875465i	$-0.660555\pi$
$7$	−2.55729	−0.966563	−0.483282	+	0.875465i	$0.660555\pi$
$8$	−8.52159	−3.01284
$9$	0.108876	0.0362919
$10$	10.5477	3.33546
$11$	1.40777	0.424459	0.212230	−	0.977220i	$-0.431928\pi$
$11$	1.40777	0.424459	0.212230	+	0.977220i	$0.431928\pi$
$12$	−9.13371	−2.63667
$13$	−2.73241	−0.757835	−0.378917	−	0.925430i	$-0.623704\pi$
$13$	−2.73241	−0.757835	−0.378917	+	0.925430i	$0.623704\pi$
$14$	6.85247	1.83140
$15$	6.94049	1.79203
$16$	12.4740	3.11849
$17$	−1.27752	−0.309844	−0.154922	−	0.987927i	$-0.549513\pi$
$17$	−1.27752	−0.309844	−0.154922	+	0.987927i	$0.549513\pi$
$18$	−0.291742	−0.0687642
$19$	−3.42030	−0.784672	−0.392336	−	0.919822i	$-0.628333\pi$
$19$	−3.42030	−0.784672	−0.392336	+	0.919822i	$0.628333\pi$
$20$	−20.3908	−4.55952
$21$	4.50901	0.983946
$22$	−3.77225	−0.804246
$23$	5.50852	1.14861	0.574303	−	0.818643i	$-0.305273\pi$
$23$	5.50852	1.14861	0.574303	+	0.818643i	$0.305273\pi$
$24$	15.0253	3.06702
$25$	10.4945	2.09889
$26$	7.32174	1.43591
$27$	5.09763	0.981040
$28$	−13.2472	−2.50349
$29$	4.57184	0.848970	0.424485	−	0.905435i	$-0.360455\pi$
$29$	4.57184	0.848970	0.424485	+	0.905435i	$0.360455\pi$
$30$	−18.5976	−3.39545
$31$	−6.23935	−1.12062	−0.560310	−	0.828283i	$-0.689318\pi$
$31$	−6.23935	−1.12062	−0.560310	+	0.828283i	$0.689318\pi$
$32$	−16.3819	−2.89594
$33$	−2.48218	−0.432093
$34$	3.42322	0.587078
$35$	10.0662	1.70151
$36$	0.563996	0.0939993
$37$	−3.97944	−0.654215	−0.327108	−	0.944987i	$-0.606074\pi$
$37$	−3.97944	−0.654215	−0.327108	+	0.944987i	$0.606074\pi$
$38$	9.16500	1.48676
$39$	4.81779	0.771464
$40$	33.5435	5.30370
$41$	9.88896	1.54440	0.772198	−	0.635382i	$-0.219157\pi$
$41$	9.88896	1.54440	0.772198	+	0.635382i	$0.219157\pi$
$42$	−12.0823	−1.86434
$43$	0.0738129	0.0112564	0.00562818	−	0.999984i	$-0.498208\pi$
$43$	0.0738129	0.0112564	0.00562818	+	0.999984i	$0.498208\pi$
$44$	7.29252	1.09939
$45$	−0.428567	−0.0638870
$46$	−14.7606	−2.17633
$47$	−3.58950	−0.523583	−0.261791	−	0.965125i	$-0.584313\pi$
$47$	−3.58950	−0.523583	−0.261791	+	0.965125i	$0.584313\pi$
$48$	−21.9941	−3.17458
$49$	−0.460288	−0.0657554
$50$	−28.1208	−3.97689
$51$	2.25252	0.315416
$52$	−14.1544	−1.96286
$53$	−0.0891657	−0.0122479	−0.00612393	−	0.999981i	$-0.501949\pi$
$53$	−0.0891657	−0.0122479	−0.00612393	+	0.999981i	$0.501949\pi$
$54$	−13.6595	−1.85883
$55$	−5.54141	−0.747204
$56$	21.7921	2.91210
$57$	6.03068	0.798783
$58$	−12.2507	−1.60859
$59$	−0.736911	−0.0959376	−0.0479688	−	0.998849i	$-0.515275\pi$
$59$	−0.736911	−0.0959376	−0.0479688	+	0.998849i	$0.515275\pi$
$60$	35.9530	4.64152
$61$	12.7896	1.63754	0.818770	−	0.574122i	$-0.194657\pi$
$61$	12.7896	1.63754	0.818770	+	0.574122i	$0.194657\pi$
$62$	16.7189	2.12330
$63$	−0.278426	−0.0350784
$64$	18.9488	2.36860
$65$	10.7556	1.33407
$66$	6.65123	0.818710
$67$	−0.110608	−0.0135129	−0.00675646	−	0.999977i	$-0.502151\pi$
$67$	−0.110608	−0.0135129	−0.00675646	+	0.999977i	$0.502151\pi$
$68$	−6.61778	−0.802524
$69$	−9.71263	−1.16926
$70$	−26.9734	−3.22394
$71$	−10.3081	−1.22334	−0.611672	−	0.791111i	$-0.709503\pi$
$71$	−10.3081	−1.22334	−0.611672	+	0.791111i	$0.709503\pi$
$72$	−0.927793	−0.109341
$73$	−5.98043	−0.699956	−0.349978	−	0.936758i	$-0.613811\pi$
$73$	−5.98043	−0.699956	−0.349978	+	0.936758i	$0.613811\pi$
$74$	10.6632	1.23958
$75$	−18.5038	−2.13664
$76$	−17.7178	−2.03237
$77$	−3.60008	−0.410267
$78$	−12.9097	−1.46173
$79$	−1.36862	−0.153982	−0.0769911	−	0.997032i	$-0.524531\pi$
$79$	−1.36862	−0.153982	−0.0769911	+	0.997032i	$0.524531\pi$
$80$	−49.1013	−5.48969
$81$	−9.31477	−1.03497
$82$	−26.4983	−2.92625
$83$	−2.90034	−0.318353	−0.159177	−	0.987250i	$-0.550884\pi$
$83$	−2.90034	−0.318353	−0.159177	+	0.987250i	$0.550884\pi$
$84$	23.3575	2.54851
$85$	5.02870	0.545439
$86$	−0.197788	−0.0213280
$87$	−8.06108	−0.864238
$88$	−11.9965	−1.27883
$89$	18.5008	1.96108	0.980541	−	0.196317i	$-0.0628981\pi$
$89$	18.5008	1.96108	0.980541	+	0.196317i	$0.0628981\pi$
$90$	1.14838	0.121050
$91$	6.98756	0.732495
$92$	28.5352	2.97500
$93$	11.0012	1.14077
$94$	9.61838	0.992061
$95$	13.4633	1.38131
$96$	28.8846	2.94802
$97$	−13.4129	−1.36187	−0.680936	−	0.732343i	$-0.738427\pi$
$97$	−13.4129	−1.36187	−0.680936	+	0.732343i	$0.738427\pi$
$98$	1.23338	0.124590
$99$	0.153272	0.0154044
$100$	54.3633	5.43633
$101$	−0.619098	−0.0616025	−0.0308013	−	0.999526i	$-0.509806\pi$
$101$	−0.619098	−0.0616025	−0.0308013	+	0.999526i	$0.509806\pi$
$102$	−6.03583	−0.597636
$103$	−5.13500	−0.505967	−0.252983	−	0.967471i	$-0.581412\pi$
$103$	−5.13500	−0.505967	−0.252983	+	0.967471i	$0.581412\pi$
$104$	23.2845	2.28323
$105$	−17.7488	−1.73211
$106$	0.238927	0.0232067
$107$	−3.57501	−0.345609	−0.172805	−	0.984956i	$-0.555283\pi$
$107$	−3.57501	−0.345609	−0.172805	+	0.984956i	$0.555283\pi$
$108$	26.4067	2.54099
$109$	−2.41004	−0.230840	−0.115420	−	0.993317i	$-0.536821\pi$
$109$	−2.41004	−0.230840	−0.115420	+	0.993317i	$0.536821\pi$
$110$	14.8487	1.41577
$111$	7.01654	0.665981
$112$	−31.8995	−3.01422
$113$	−14.3872	−1.35343	−0.676716	−	0.736244i	$-0.736598\pi$
$113$	−14.3872	−1.35343	−0.676716	+	0.736244i	$0.736598\pi$
$114$	−16.1597	−1.51350
$115$	−21.6832	−2.02197
$116$	23.6830	2.19891
$117$	−0.297493	−0.0275032
$118$	1.97462	0.181778
$119$	3.26698	0.299483
$120$	−59.1440	−5.39908
$121$	−9.01818	−0.819834
$122$	−34.2708	−3.10273
$123$	−17.4362	−1.57217
$124$	−32.3210	−2.90251
$125$	−21.6279	−1.93445
$126$	0.746067	0.0664649
$127$	8.49452	0.753767	0.376883	−	0.926261i	$-0.376996\pi$
$127$	8.49452	0.753767	0.376883	+	0.926261i	$0.376996\pi$
$128$	−18.0112	−1.59198
$129$	−0.130147	−0.0114588
$130$	−28.8206	−2.52773
$131$	4.17126	0.364445	0.182222	−	0.983257i	$-0.441671\pi$
$131$	4.17126	0.364445	0.182222	+	0.983257i	$0.441671\pi$
$132$	−12.8582	−1.11916
$133$	8.74670	0.758435
$134$	0.296384	0.0256037
$135$	−20.0658	−1.72699
$136$	10.8865	0.933509
$137$	3.18442	0.272064	0.136032	−	0.990704i	$-0.456565\pi$
$137$	3.18442	0.272064	0.136032	+	0.990704i	$0.456565\pi$
$138$	26.0258	2.21547
$139$	−22.1332	−1.87731	−0.938656	−	0.344856i	$-0.887928\pi$
$139$	−22.1332	−1.87731	−0.938656	+	0.344856i	$0.887928\pi$
$140$	52.1451	4.40706
$141$	6.32901	0.532999
$142$	27.6214	2.31794
$143$	−3.84661	−0.321670
$144$	1.35811	0.113176
$145$	−17.9961	−1.49450
$146$	16.0251	1.32624
$147$	0.811579	0.0669379
$148$	−20.6142	−1.69448
$149$	0.910743	0.0746110	0.0373055	−	0.999304i	$-0.488123\pi$
$149$	0.910743	0.0746110	0.0373055	+	0.999304i	$0.488123\pi$
$150$	49.5827	4.04841
$151$	3.94541	0.321073	0.160536	−	0.987030i	$-0.448678\pi$
$151$	3.94541	0.321073	0.160536	+	0.987030i	$0.448678\pi$
$152$	29.1464	2.36409
$153$	−0.139091	−0.0112448
$154$	9.64672	0.777355
$155$	24.5599	1.97270
$156$	24.9571	1.99816
$157$	−16.8836	−1.34746	−0.673729	−	0.738979i	$-0.735308\pi$
$157$	−16.8836	−1.34746	−0.673729	+	0.738979i	$0.735308\pi$
$158$	3.66735	0.291759
$159$	0.157217	0.0124681
$160$	64.4842	5.09792
$161$	−14.0869	−1.11020
$162$	24.9597	1.96102
$163$	6.60610	0.517430	0.258715	−	0.965954i	$-0.416701\pi$
$163$	6.60610	0.517430	0.258715	+	0.965954i	$0.416701\pi$
$164$	51.2267	4.00013
$165$	9.77062	0.760642
$166$	7.77170	0.603201
$167$	−5.52442	−0.427493	−0.213746	−	0.976889i	$-0.568567\pi$
$167$	−5.52442	−0.427493	−0.213746	+	0.976889i	$0.568567\pi$
$168$	−38.4239	−2.96447
$169$	−5.53392	−0.425686
$170$	−13.4748	−1.03347
$171$	−0.372388	−0.0284772
$172$	0.382365	0.0291550
$173$	−22.9879	−1.74774	−0.873868	−	0.486163i	$-0.838396\pi$
$173$	−22.9879	−1.74774	−0.873868	+	0.486163i	$0.838396\pi$
$174$	21.6004	1.63752
$175$	−26.8373	−2.02871
$176$	17.5605	1.32367
$177$	1.29932	0.0976630
$178$	−49.5745	−3.71577
$179$	−4.90666	−0.366741	−0.183371	−	0.983044i	$-0.558701\pi$
$179$	−4.90666	−0.366741	−0.183371	+	0.983044i	$0.558701\pi$
$180$	−2.22006	−0.165473
$181$	19.4443	1.44528	0.722642	−	0.691223i	$-0.242928\pi$
$181$	19.4443	1.44528	0.722642	+	0.691223i	$0.242928\pi$
$182$	−18.7238	−1.38790
$183$	−22.5506	−1.66699
$184$	−46.9414	−3.46057
$185$	15.6643	1.15166
$186$	−29.4787	−2.16149
$187$	−1.79845	−0.131516
$188$	−18.5943	−1.35613
$189$	−13.0361	−0.948237
$190$	−36.0762	−2.61724
$191$	11.9773	0.866643	0.433322	−	0.901239i	$-0.357341\pi$
$191$	11.9773	0.866643	0.433322	+	0.901239i	$0.357341\pi$
$192$	−33.4106	−2.41120
$193$	−14.5795	−1.04946	−0.524728	−	0.851270i	$-0.675833\pi$
$193$	−14.5795	−1.04946	−0.524728	+	0.851270i	$0.675833\pi$
$194$	35.9410	2.58041
$195$	−18.9643	−1.35806
$196$	−2.38438	−0.170313
$197$	−5.12730	−0.365305	−0.182653	−	0.983178i	$-0.558468\pi$
$197$	−5.12730	−0.365305	−0.182653	+	0.983178i	$0.558468\pi$
$198$	−0.410706	−0.0291876
$199$	17.9179	1.27016	0.635082	−	0.772445i	$-0.280966\pi$
$199$	17.9179	1.27016	0.635082	+	0.772445i	$0.280966\pi$
$200$	−89.4295	−6.32362
$201$	0.195024	0.0137559
$202$	1.65893	0.116722
$203$	−11.6915	−0.820583
$204$	11.6685	0.816957
$205$	−38.9259	−2.71870
$206$	13.7597	0.958683
$207$	0.599744	0.0416851
$208$	−34.0840	−2.36330
$209$	−4.81501	−0.333061
$210$	47.5595	3.28192
$211$	3.05004	0.209974	0.104987	−	0.994474i	$-0.466520\pi$
$211$	3.05004	0.209974	0.104987	+	0.994474i	$0.466520\pi$
$212$	−0.461895	−0.0317231
$213$	18.1752	1.24535
$214$	9.57955	0.654845
$215$	−0.290550	−0.0198153
$216$	−43.4399	−2.95571
$217$	15.9558	1.08315
$218$	6.45790	0.437384
$219$	10.5447	0.712544
$220$	−28.7056	−1.93533
$221$	3.49071	0.234810
$222$	−18.8014	−1.26187
$223$	−15.8701	−1.06274	−0.531370	−	0.847140i	$-0.678323\pi$
$223$	−15.8701	−1.06274	−0.531370	+	0.847140i	$0.678323\pi$
$224$	41.8933	2.79911
$225$	1.14259	0.0761727
$226$	38.5517	2.56442
$227$	3.30990	0.219686	0.109843	−	0.993949i	$-0.464965\pi$
$227$	3.30990	0.219686	0.109843	+	0.993949i	$0.464965\pi$
$228$	31.2401	2.06892
$229$	17.7221	1.17111	0.585554	−	0.810634i	$-0.300877\pi$
$229$	17.7221	1.17111	0.585554	+	0.810634i	$0.300877\pi$
$230$	58.1020	3.83114
$231$	6.34765	0.417645
$232$	−38.9594	−2.55781
$233$	14.4415	0.946096	0.473048	−	0.881037i	$-0.343154\pi$
$233$	14.4415	0.946096	0.473048	+	0.881037i	$0.343154\pi$
$234$	0.797158	0.0521119
$235$	14.1294	0.921698
$236$	−3.81734	−0.248487
$237$	2.41316	0.156751
$238$	−8.75416	−0.567448
$239$	−11.9333	−0.771898	−0.385949	−	0.922520i	$-0.626126\pi$
$239$	−11.9333	−0.771898	−0.385949	+	0.922520i	$0.626126\pi$
$240$	86.5754	5.58842
$241$	−5.94809	−0.383150	−0.191575	−	0.981478i	$-0.561360\pi$
$241$	−5.94809	−0.383150	−0.191575	+	0.981478i	$0.561360\pi$
$242$	24.1650	1.55338
$243$	1.13092	0.0725483
$244$	66.2525	4.24138
$245$	1.81183	0.115754
$246$	46.7219	2.97888
$247$	9.34568	0.594652
$248$	53.1692	3.37625
$249$	5.11387	0.324078
$250$	57.9537	3.66531
$251$	−9.09108	−0.573824	−0.286912	−	0.957957i	$-0.592629\pi$
$251$	−9.09108	−0.573824	−0.286912	+	0.957957i	$0.592629\pi$
$252$	−1.44230	−0.0908563
$253$	7.75474	0.487537
$254$	−22.7618	−1.42820
$255$	−8.86660	−0.555248
$256$	10.3650	0.647810
$257$	7.43202	0.463597	0.231798	−	0.972764i	$-0.425539\pi$
$257$	7.43202	0.463597	0.231798	+	0.972764i	$0.425539\pi$
$258$	0.348740	0.0217116
$259$	10.1766	0.632341
$260$	55.7160	3.45536
$261$	0.497762	0.0308107
$262$	−11.1773	−0.690533
$263$	31.0762	1.91624	0.958121	−	0.286365i	$-0.0924470\pi$
$263$	31.0762	1.91624	0.958121	+	0.286365i	$0.0924470\pi$
$264$	21.1522	1.30183
$265$	0.350983	0.0215607
$266$	−23.4375	−1.43705
$267$	−32.6206	−1.99635
$268$	−0.572970	−0.0349997
$269$	−3.47735	−0.212018	−0.106009	−	0.994365i	$-0.533807\pi$
$269$	−3.47735	−0.212018	−0.106009	+	0.994365i	$0.533807\pi$
$270$	53.7681	3.27222
$271$	−13.6748	−0.830683	−0.415342	−	0.909665i	$-0.636338\pi$
$271$	−13.6748	−0.830683	−0.415342	+	0.909665i	$0.636338\pi$
$272$	−15.9357	−0.966245
$273$	−12.3205	−0.745669
$274$	−8.53294	−0.515494
$275$	14.7738	0.890894
$276$	−50.3133	−3.02850
$277$	−10.8085	−0.649419	−0.324709	−	0.945814i	$-0.605267\pi$
$277$	−10.8085	−0.649419	−0.324709	+	0.945814i	$0.605267\pi$
$278$	59.3078	3.55704
$279$	−0.679313	−0.0406694
$280$	−85.7804	−5.12636
$281$	−11.1885	−0.667449	−0.333724	−	0.942671i	$-0.608305\pi$
$281$	−11.1885	−0.667449	−0.333724	+	0.942671i	$0.608305\pi$
$282$	−16.9591	−1.00990
$283$	−26.1812	−1.55631	−0.778156	−	0.628071i	$-0.783845\pi$
$283$	−26.1812	−1.55631	−0.778156	+	0.628071i	$0.783845\pi$
$284$	−53.3978	−3.16858
$285$	−23.7386	−1.40615
$286$	10.3073	0.609486
$287$	−25.2889	−1.49276
$288$	−1.78359	−0.105099
$289$	−15.3679	−0.903997
$290$	48.2223	2.83171
$291$	23.6496	1.38636
$292$	−30.9797	−1.81295
$293$	−4.87985	−0.285084	−0.142542	−	0.989789i	$-0.545528\pi$
$293$	−4.87985	−0.285084	−0.142542	+	0.989789i	$0.545528\pi$
$294$	−2.17470	−0.126831
$295$	2.90070	0.168885
$296$	33.9111	1.97104
$297$	7.17630	0.416411
$298$	−2.44042	−0.141370
$299$	−15.0516	−0.870454
$300$	−95.8534	−5.53410
$301$	−0.188761	−0.0108800
$302$	−10.5721	−0.608354
$303$	1.09159	0.0627104
$304$	−42.6648	−2.44699
$305$	−50.3437	−2.88267
$306$	0.372705	0.0213061
$307$	14.8391	0.846914	0.423457	−	0.905916i	$-0.360817\pi$
$307$	14.8391	0.846914	0.423457	+	0.905916i	$0.360817\pi$
$308$	−18.6491	−1.06263
$309$	9.05404	0.515066
$310$	−65.8105	−3.73779
$311$	−3.82519	−0.216907	−0.108453	−	0.994102i	$-0.534590\pi$
$311$	−3.82519	−0.216907	−0.108453	+	0.994102i	$0.534590\pi$
$312$	−41.0553	−2.32430
$313$	14.6682	0.829094	0.414547	−	0.910028i	$-0.363940\pi$
$313$	14.6682	0.829094	0.414547	+	0.910028i	$0.363940\pi$
$314$	45.2411	2.55310
$315$	1.09597	0.0617508
$316$	−7.08973	−0.398829
$317$	30.7893	1.72930	0.864649	−	0.502377i	$-0.167541\pi$
$317$	30.7893	1.72930	0.864649	+	0.502377i	$0.167541\pi$
$318$	−0.421277	−0.0236240
$319$	6.43611	0.360353
$320$	−74.5883	−4.16961
$321$	6.30346	0.351825
$322$	37.7470	2.10356
$323$	4.36950	0.243125
$324$	−48.2523	−2.68068
$325$	−28.6752	−1.59061
$326$	−17.7016	−0.980402
$327$	4.24938	0.234991
$328$	−84.2697	−4.65301
$329$	9.17938	0.506076
$330$	−26.1812	−1.44123
$331$	−21.9532	−1.20666	−0.603329	−	0.797492i	$-0.706159\pi$
$331$	−21.9532	−1.20666	−0.603329	+	0.797492i	$0.706159\pi$
$332$	−15.0243	−0.824565
$333$	−0.433263	−0.0237427
$334$	14.8032	0.809994
$335$	0.435386	0.0237877
$336$	56.2452	3.06843
$337$	−27.1026	−1.47637	−0.738185	−	0.674598i	$-0.764317\pi$
$337$	−27.1026	−1.47637	−0.738185	+	0.674598i	$0.764317\pi$
$338$	14.8286	0.806571
$339$	25.3675	1.37777
$340$	26.0496	1.41274
$341$	−8.78358	−0.475657
$342$	0.997845	0.0539573
$343$	19.0781	1.03012
$344$	−0.629003	−0.0339136
$345$	38.2318	2.05833
$346$	61.5980	3.31153
$347$	−16.9744	−0.911236	−0.455618	−	0.890175i	$-0.650582\pi$
$347$	−16.9744	−0.911236	−0.455618	+	0.890175i	$0.650582\pi$
$348$	−41.7579	−2.23846
$349$	−28.2467	−1.51201	−0.756005	−	0.654565i	$-0.772852\pi$
$349$	−28.2467	−1.51201	−0.756005	+	0.654565i	$0.772852\pi$
$350$	71.9130	3.84391
$351$	−13.9288	−0.743466
$352$	−23.0620	−1.22921
$353$	−16.2422	−0.864486	−0.432243	−	0.901757i	$-0.642278\pi$
$353$	−16.2422	−0.864486	−0.432243	+	0.901757i	$0.642278\pi$
$354$	−3.48165	−0.185047
$355$	40.5757	2.15353
$356$	95.8376	5.07938
$357$	−5.76034	−0.304869
$358$	13.1478	0.694884
$359$	−31.8933	−1.68326	−0.841631	−	0.540053i	$-0.818404\pi$
$359$	−31.8933	−1.68326	−0.841631	+	0.540053i	$0.818404\pi$
$360$	3.65207	0.192481
$361$	−7.30152	−0.384291
$362$	−52.1027	−2.73846
$363$	15.9009	0.834578
$364$	36.1969	1.89723
$365$	23.5408	1.23218
$366$	60.4263	3.15853
$367$	−1.84572	−0.0963458	−0.0481729	−	0.998839i	$-0.515340\pi$
$367$	−1.84572	−0.0963458	−0.0481729	+	0.998839i	$0.515340\pi$
$368$	68.7132	3.58192
$369$	1.07667	0.0560490
$370$	−41.9737	−2.18211
$371$	0.228022	0.0118383
$372$	56.9884	2.95471
$373$	6.89626	0.357075	0.178537	−	0.983933i	$-0.442863\pi$
$373$	6.89626	0.357075	0.178537	+	0.983933i	$0.442863\pi$
$374$	4.81911	0.249190
$375$	38.1342	1.96924
$376$	30.5883	1.57747
$377$	−12.4922	−0.643379
$378$	34.9314	1.79668
$379$	−13.2930	−0.682817	−0.341408	−	0.939915i	$-0.610904\pi$
$379$	−13.2930	−0.682817	−0.341408	+	0.939915i	$0.610904\pi$
$380$	69.7427	3.57772
$381$	−14.9775	−0.767323
$382$	−32.0941	−1.64208
$383$	−3.78187	−0.193245	−0.0966223	−	0.995321i	$-0.530804\pi$
$383$	−3.78187	−0.193245	−0.0966223	+	0.995321i	$0.530804\pi$
$384$	31.7574	1.62061
$385$	14.1710	0.722220
$386$	39.0671	1.98846
$387$	0.00803642	0.000408514 0
$388$	−69.4813	−3.52738
$389$	−6.19540	−0.314119	−0.157060	−	0.987589i	$-0.550202\pi$
$389$	−6.19540	−0.314119	−0.157060	+	0.987589i	$0.550202\pi$
$390$	50.8164	2.57319
$391$	−7.03724	−0.355888
$392$	3.92238	0.198110
$393$	−7.35477	−0.370999
$394$	13.7391	0.692164
$395$	5.38732	0.271065
$396$	0.793978	0.0398989
$397$	−1.44165	−0.0723543	−0.0361771	−	0.999345i	$-0.511518\pi$
$397$	−1.44165	−0.0723543	−0.0361771	+	0.999345i	$0.511518\pi$
$398$	−48.0125	−2.40665
$399$	−15.4222	−0.772075
$400$	130.908	6.54538
$401$	15.7940	0.788716	0.394358	−	0.918957i	$-0.370967\pi$
$401$	15.7940	0.788716	0.394358	+	0.918957i	$0.370967\pi$
$402$	−0.522584	−0.0260641
$403$	17.0485	0.849245
$404$	−3.20704	−0.159556
$405$	36.6657	1.82194
$406$	31.3284	1.55480
$407$	−5.60214	−0.277688
$408$	−19.1951	−0.950297
$409$	−0.0784059	−0.00387692	−0.00193846	−	0.999998i	$-0.500617\pi$
$409$	−0.0784059	−0.00387692	−0.00193846	+	0.999998i	$0.500617\pi$
$410$	104.305	5.15128
$411$	−5.61478	−0.276957
$412$	−26.6003	−1.31050
$413$	1.88449	0.0927298
$414$	−1.60707	−0.0789830
$415$	11.4166	0.560418
$416$	44.7622	2.19465
$417$	39.0252	1.91107
$418$	12.9022	0.631069
$419$	−10.3094	−0.503648	−0.251824	−	0.967773i	$-0.581030\pi$
$419$	−10.3094	−0.503648	−0.251824	+	0.967773i	$0.581030\pi$
$420$	−91.9422	−4.48632
$421$	10.5306	0.513228	0.256614	−	0.966514i	$-0.417393\pi$
$421$	10.5306	0.513228	0.256614	+	0.966514i	$0.417393\pi$
$422$	−8.17285	−0.397848
$423$	−0.390809	−0.0190018
$424$	0.759834	0.0369008
$425$	−13.4069	−0.650328
$426$	−48.7021	−2.35962
$427$	−32.7066	−1.58279
$428$	−18.5192	−0.895161
$429$	6.78235	0.327455
$430$	0.778553	0.0375452
$431$	−8.94280	−0.430759	−0.215380	−	0.976530i	$-0.569099\pi$
$431$	−8.94280	−0.430759	−0.215380	+	0.976530i	$0.569099\pi$
$432$	63.5877	3.05937
$433$	−26.0613	−1.25243	−0.626213	−	0.779652i	$-0.715396\pi$
$433$	−26.0613	−1.25243	−0.626213	+	0.779652i	$0.715396\pi$
$434$	−42.7550	−2.05230
$435$	31.7308	1.52138
$436$	−12.4844	−0.597896
$437$	−18.8408	−0.901279
$438$	−28.2554	−1.35010
$439$	19.8924	0.949410	0.474705	−	0.880145i	$-0.342555\pi$
$439$	19.8924	0.949410	0.474705	+	0.880145i	$0.342555\pi$
$440$	47.2217	2.25120
$441$	−0.0501141	−0.00238638
$442$	−9.35365	−0.444908
$443$	14.2506	0.677066	0.338533	−	0.940954i	$-0.390069\pi$
$443$	14.2506	0.677066	0.338533	+	0.940954i	$0.390069\pi$
$444$	36.3470	1.72495
$445$	−72.8247	−3.45222
$446$	42.5253	2.01363
$447$	−1.60582	−0.0759528
$448$	−48.4576	−2.28941
$449$	−2.89085	−0.136428	−0.0682139	−	0.997671i	$-0.521730\pi$
$449$	−2.89085	−0.136428	−0.0682139	+	0.997671i	$0.521730\pi$
$450$	−3.06167	−0.144329
$451$	13.9214	0.655533
$452$	−74.5283	−3.50552
$453$	−6.95655	−0.326847
$454$	−8.86917	−0.416251
$455$	−27.5051	−1.28946
$456$	−51.3910	−2.40660
$457$	−39.7598	−1.85989	−0.929943	−	0.367703i	$-0.880144\pi$
$457$	−39.7598	−1.85989	−0.929943	+	0.367703i	$0.880144\pi$
$458$	−47.4878	−2.21896
$459$	−6.51232	−0.303969
$460$	−112.323	−5.23709
$461$	15.5939	0.726281	0.363140	−	0.931734i	$-0.381705\pi$
$461$	15.5939	0.726281	0.363140	+	0.931734i	$0.381705\pi$
$462$	−17.0091	−0.791335
$463$	17.3940	0.808366	0.404183	−	0.914678i	$-0.367556\pi$
$463$	17.3940	0.808366	0.404183	+	0.914678i	$0.367556\pi$
$464$	57.0291	2.64751
$465$	−43.3041	−2.00818
$466$	−38.6973	−1.79262
$467$	29.8479	1.38120	0.690598	−	0.723239i	$-0.257347\pi$
$467$	29.8479	1.38120	0.690598	+	0.723239i	$0.257347\pi$
$468$	−1.54107	−0.0712360
$469$	0.282856	0.0130611
$470$	−37.8608	−1.74639
$471$	29.7692	1.37169
$472$	6.27965	0.289045
$473$	0.103912	0.00477787
$474$	−6.46627	−0.297006
$475$	−35.8942	−1.64694
$476$	16.9236	0.775690
$477$	−0.00970797	−0.000444497 0
$478$	31.9762	1.46256
$479$	−17.3541	−0.792928	−0.396464	−	0.918050i	$-0.629763\pi$
$479$	−17.3541	−0.792928	−0.396464	+	0.918050i	$0.629763\pi$
$480$	−113.698	−5.18960
$481$	10.8735	0.495787
$482$	15.9384	0.725975
$483$	24.8380	1.13017
$484$	−46.7159	−2.12345
$485$	52.7972	2.39740
$486$	−3.03039	−0.137461
$487$	−24.5512	−1.11252	−0.556260	−	0.831008i	$-0.687764\pi$
$487$	−24.5512	−1.11252	−0.556260	+	0.831008i	$0.687764\pi$
$488$	−108.988	−4.93364
$489$	−11.6479	−0.526735
$490$	−4.85496	−0.219325
$491$	28.7218	1.29620	0.648098	−	0.761557i	$-0.275565\pi$
$491$	28.7218	1.29620	0.648098	+	0.761557i	$0.275565\pi$
$492$	−90.3229	−4.07207
$493$	−5.84061	−0.263048
$494$	−25.0426	−1.12672
$495$	−0.603324	−0.0271174
$496$	−77.8295	−3.49465
$497$	26.3607	1.18244
$498$	−13.7031	−0.614049
$499$	2.55228	0.114256	0.0571279	−	0.998367i	$-0.481806\pi$
$499$	2.55228	0.114256	0.0571279	+	0.998367i	$0.481806\pi$
$500$	−112.036	−5.01042
$501$	9.74067	0.435181
$502$	24.3604	1.08726
$503$	−25.6503	−1.14369	−0.571845	−	0.820362i	$-0.693772\pi$
$503$	−25.6503	−1.14369	−0.571845	+	0.820362i	$0.693772\pi$
$504$	2.37263	0.105685
$505$	2.43696	0.108443
$506$	−20.7795	−0.923762
$507$	9.75741	0.433342
$508$	44.0032	1.95233
$509$	−34.4210	−1.52568	−0.762841	−	0.646586i	$-0.776196\pi$
$509$	−34.4210	−1.52568	−0.762841	+	0.646586i	$0.776196\pi$
$510$	23.7588	1.05206
$511$	15.2937	0.676552
$512$	8.24862	0.364541
$513$	−17.4354	−0.769794
$514$	−19.9147	−0.878402
$515$	20.2129	0.890687
$516$	−0.674186	−0.0296794
$517$	−5.05320	−0.222239
$518$	−27.2690	−1.19813
$519$	40.5322	1.77917
$520$	−91.6548	−4.01933
$521$	4.67049	0.204618	0.102309	−	0.994753i	$-0.467377\pi$
$521$	4.67049	0.204618	0.102309	+	0.994753i	$0.467377\pi$
$522$	−1.33380	−0.0583787
$523$	−12.3436	−0.539747	−0.269874	−	0.962896i	$-0.586982\pi$
$523$	−12.3436	−0.539747	−0.269874	+	0.962896i	$0.586982\pi$
$524$	21.6079	0.943946
$525$	47.3196	2.06520
$526$	−83.2714	−3.63081
$527$	7.97088	0.347217
$528$	−30.9627	−1.34748
$529$	7.34383	0.319297
$530$	−0.940490	−0.0408523
$531$	−0.0802316	−0.00348175
$532$	45.3095	1.96442
$533$	−27.0207	−1.17040
$534$	87.4098	3.78259
$535$	14.0723	0.608399
$536$	0.942556	0.0407122
$537$	8.65143	0.373337
$538$	9.31786	0.401721
$539$	−0.647980	−0.0279105
$540$	−103.945	−4.47307
$541$	−20.7266	−0.891105	−0.445552	−	0.895256i	$-0.646993\pi$
$541$	−20.7266	−0.891105	−0.445552	+	0.895256i	$0.646993\pi$
$542$	36.6428	1.57394
$543$	−34.2842	−1.47128
$544$	20.9282	0.897289
$545$	9.48663	0.406362
$546$	33.0138	1.41286
$547$	25.1093	1.07360	0.536798	−	0.843711i	$-0.319634\pi$
$547$	25.1093	1.07360	0.536798	+	0.843711i	$0.319634\pi$
$548$	16.4959	0.704671
$549$	1.39247	0.0594293
$550$	−39.5877	−1.68803
$551$	−15.6371	−0.666163
$552$	82.7671	3.52280
$553$	3.49996	0.148834
$554$	28.9623	1.23049
$555$	−27.6192	−1.17237
$556$	−114.654	−4.86241
$557$	9.08336	0.384874	0.192437	−	0.981309i	$-0.438361\pi$
$557$	9.08336	0.384874	0.192437	+	0.981309i	$0.438361\pi$
$558$	1.82028	0.0770585
$559$	−0.201687	−0.00853046
$560$	125.566	5.30614
$561$	3.17103	0.133881
$562$	29.9805	1.26465
$563$	−26.3365	−1.10995	−0.554976	−	0.831866i	$-0.687273\pi$
$563$	−26.3365	−1.10995	−0.554976	+	0.831866i	$0.687273\pi$
$564$	32.7855	1.38052
$565$	56.6323	2.38254
$566$	70.1549	2.94883
$567$	23.8205	1.00037
$568$	87.8413	3.68574
$569$	−11.2263	−0.470632	−0.235316	−	0.971919i	$-0.575613\pi$
$569$	−11.2263	−0.470632	−0.235316	+	0.971919i	$0.575613\pi$
$570$	63.6096	2.66431
$571$	20.4743	0.856823	0.428412	−	0.903584i	$-0.359073\pi$
$571$	20.4743	0.856823	0.428412	+	0.903584i	$0.359073\pi$
$572$	−19.9262	−0.833156
$573$	−21.1183	−0.882229
$574$	67.7638	2.82841
$575$	57.8090	2.41080
$576$	2.06306	0.0859610
$577$	−25.8342	−1.07549	−0.537746	−	0.843107i	$-0.680724\pi$
$577$	−25.8342	−1.07549	−0.537746	+	0.843107i	$0.680724\pi$
$578$	41.1798	1.71285
$579$	25.7066	1.06833
$580$	−93.2234	−3.87089
$581$	7.41699	0.307708
$582$	−63.3712	−2.62682
$583$	−0.125525	−0.00519871
$584$	50.9628	2.10885
$585$	1.17102	0.0484158
$586$	13.0760	0.540164
$587$	−28.0740	−1.15874	−0.579368	−	0.815066i	$-0.696701\pi$
$587$	−28.0740	−1.15874	−0.579368	+	0.815066i	$0.696701\pi$
$588$	4.20413	0.173376
$589$	21.3405	0.879319
$590$	−7.77269	−0.319996
$591$	9.04046	0.371875
$592$	−49.6394	−2.04017
$593$	−26.2442	−1.07772	−0.538859	−	0.842396i	$-0.681145\pi$
$593$	−26.2442	−1.07772	−0.538859	+	0.842396i	$0.681145\pi$
$594$	−19.2295	−0.788997
$595$	−12.8598	−0.527201
$596$	4.71782	0.193250
$597$	−31.5928	−1.29301
$598$	40.3320	1.64930
$599$	22.7241	0.928482	0.464241	−	0.885709i	$-0.346327\pi$
$599$	22.7241	0.928482	0.464241	+	0.885709i	$0.346327\pi$
$600$	157.682	6.43735
$601$	4.57880	0.186773	0.0933866	−	0.995630i	$-0.470231\pi$
$601$	4.57880	0.186773	0.0933866	+	0.995630i	$0.470231\pi$
$602$	0.505801	0.0206149
$603$	−0.0120425	−0.000490409 0
$604$	20.4380	0.831609
$605$	35.4983	1.44321
$606$	−2.92502	−0.118821
$607$	26.3845	1.07091	0.535457	−	0.844562i	$-0.320139\pi$
$607$	26.3845	1.07091	0.535457	+	0.844562i	$0.320139\pi$
$608$	56.0311	2.27236
$609$	20.6145	0.835341
$610$	134.900	5.46195
$611$	9.80800	0.396789
$612$	−0.720515	−0.0291251
$613$	−5.30786	−0.214383	−0.107191	−	0.994238i	$-0.534186\pi$
$613$	−5.30786	−0.214383	−0.107191	+	0.994238i	$0.534186\pi$
$614$	−39.7627	−1.60469
$615$	68.6342	2.76760
$616$	30.6784	1.23607
$617$	46.1306	1.85715	0.928575	−	0.371145i	$-0.121035\pi$
$617$	46.1306	1.85715	0.928575	+	0.371145i	$0.121035\pi$
$618$	−24.2611	−0.975924
$619$	−32.5442	−1.30806	−0.654030	−	0.756468i	$-0.726923\pi$
$619$	−32.5442	−1.30806	−0.654030	+	0.756468i	$0.726923\pi$
$620$	127.225	5.10949
$621$	28.0804	1.12683
$622$	10.2499	0.410985
$623$	−47.3118	−1.89551
$624$	60.0970	2.40581
$625$	32.6614	1.30646
$626$	−39.3046	−1.57093
$627$	8.48982	0.339051
$628$	−87.4602	−3.49004
$629$	5.08380	0.202704
$630$	−2.93674	−0.117003
$631$	47.0883	1.87455	0.937277	−	0.348585i	$-0.113338\pi$
$631$	47.0883	1.87455	0.937277	+	0.348585i	$0.113338\pi$
$632$	11.6629	0.463924
$633$	−5.37783	−0.213750
$634$	−82.5025	−3.27659
$635$	−33.4370	−1.32691
$636$	0.814414	0.0322936
$637$	1.25770	0.0498317
$638$	−17.2461	−0.682781
$639$	−1.12230	−0.0443974
$640$	70.8976	2.80247
$641$	−20.9382	−0.827008	−0.413504	−	0.910502i	$-0.635695\pi$
$641$	−20.9382	−0.827008	−0.413504	+	0.910502i	$0.635695\pi$
$642$	−16.8907	−0.666622
$643$	−1.46300	−0.0576951	−0.0288475	−	0.999584i	$-0.509184\pi$
$643$	−1.46300	−0.0576951	−0.0288475	+	0.999584i	$0.509184\pi$
$644$	−72.9726	−2.87553
$645$	0.512297	0.0201717
$646$	−11.7085	−0.460663
$647$	−45.5453	−1.79057	−0.895285	−	0.445495i	$-0.853028\pi$
$647$	−45.5453	−1.79057	−0.895285	+	0.445495i	$0.853028\pi$
$648$	79.3767	3.11821
$649$	−1.03740	−0.0407216
$650$	76.8377	3.01382
$651$	−28.1333	−1.10263
$652$	34.2208	1.34019
$653$	−1.62927	−0.0637583	−0.0318792	−	0.999492i	$-0.510149\pi$
$653$	−1.62927	−0.0637583	−0.0318792	+	0.999492i	$0.510149\pi$
$654$	−11.3866	−0.445250
$655$	−16.4193	−0.641557
$656$	123.355	4.81619
$657$	−0.651122	−0.0254027
$658$	−24.5970	−0.958889
$659$	9.01689	0.351248	0.175624	−	0.984457i	$-0.443806\pi$
$659$	9.01689	0.351248	0.175624	+	0.984457i	$0.443806\pi$
$660$	50.6137	1.97013
$661$	−40.8048	−1.58712	−0.793561	−	0.608491i	$-0.791775\pi$
$661$	−40.8048	−1.58712	−0.793561	+	0.608491i	$0.791775\pi$
$662$	58.8256	2.28632
$663$	−6.15482	−0.239033
$664$	24.7155	0.959146
$665$	−34.4296	−1.33512
$666$	1.16097	0.0449866
$667$	25.1841	0.975133
$668$	−28.6176	−1.10725
$669$	27.9822	1.08185
$670$	−1.16666	−0.0450718
$671$	18.0048	0.695069
$672$	−73.8662	−2.84945
$673$	−25.9461	−1.00015	−0.500075	−	0.865982i	$-0.666694\pi$
$673$	−25.9461	−1.00015	−0.500075	+	0.865982i	$0.666694\pi$
$674$	72.6237	2.79736
$675$	53.4969	2.05910
$676$	−28.6668	−1.10257
$677$	−25.9626	−0.997825	−0.498912	−	0.866652i	$-0.666267\pi$
$677$	−25.9626	−0.997825	−0.498912	+	0.866652i	$0.666267\pi$
$678$	−67.9744	−2.61054
$679$	34.3006	1.31634
$680$	−42.8525	−1.64332
$681$	−5.83602	−0.223637
$682$	23.5364	0.901254
$683$	6.35212	0.243057	0.121529	−	0.992588i	$-0.461220\pi$
$683$	6.35212	0.243057	0.121529	+	0.992588i	$0.461220\pi$
$684$	−1.92904	−0.0737586
$685$	−12.5348	−0.478932
$686$	−51.1214	−1.95182
$687$	−31.2476	−1.19217
$688$	0.920740	0.0351029
$689$	0.243637	0.00928185
$690$	−102.446	−3.90004
$691$	32.8473	1.24957	0.624785	−	0.780797i	$-0.285187\pi$
$691$	32.8473	1.24957	0.624785	+	0.780797i	$0.285187\pi$
$692$	−119.082	−4.52680
$693$	−0.391960	−0.0148893
$694$	45.4845	1.72657
$695$	87.1228	3.30476
$696$	68.6932	2.60381
$697$	−12.6333	−0.478521
$698$	75.6895	2.86489
$699$	−25.4633	−0.963110
$700$	−139.022	−5.25456
$701$	39.1416	1.47836	0.739179	−	0.673509i	$-0.235214\pi$
$701$	39.1416	1.47836	0.739179	+	0.673509i	$0.235214\pi$
$702$	37.3235	1.40869
$703$	13.6109	0.513344
$704$	26.6756	1.00538
$705$	−24.9129	−0.938274
$706$	43.5225	1.63799
$707$	1.58321	0.0595428
$708$	6.73073	0.252956
$709$	32.2835	1.21243	0.606217	−	0.795299i	$-0.292686\pi$
$709$	32.2835	1.21243	0.606217	+	0.795299i	$0.292686\pi$
$710$	−108.726	−4.08042
$711$	−0.149010	−0.00558830
$712$	−157.656	−5.90842
$713$	−34.3696	−1.28715
$714$	15.4353	0.577653
$715$	15.1414	0.566257
$716$	−25.4174	−0.949894
$717$	21.0407	0.785780
$718$	85.4608	3.18937
$719$	−4.01496	−0.149733	−0.0748664	−	0.997194i	$-0.523853\pi$
$719$	−4.01496	−0.149733	−0.0748664	+	0.997194i	$0.523853\pi$
$720$	−5.34593	−0.199231
$721$	13.1317	0.489049
$722$	19.5651	0.728136
$723$	10.4877	0.390041
$724$	100.725	3.74342
$725$	47.9790	1.78190
$726$	−42.6077	−1.58132
$727$	3.12013	0.115719	0.0578597	−	0.998325i	$-0.481572\pi$
$727$	3.12013	0.115719	0.0578597	+	0.998325i	$0.481572\pi$
$728$	−59.5451	−2.20689
$729$	25.9503	0.961122
$730$	−63.0795	−2.33468
$731$	−0.0942973	−0.00348771
$732$	−116.816	−4.31766
$733$	50.5369	1.86662	0.933311	−	0.359068i	$-0.116905\pi$
$733$	50.5369	1.86662	0.933311	+	0.359068i	$0.116905\pi$
$734$	4.94577	0.182552
$735$	−3.19462	−0.117835
$736$	−90.2402	−3.32630
$737$	−0.155711	−0.00573568
$738$	−2.88502	−0.106199
$739$	−0.672270	−0.0247299	−0.0123649	−	0.999924i	$-0.503936\pi$
$739$	−0.672270	−0.0247299	−0.0123649	+	0.999924i	$0.503936\pi$
$740$	81.1438	2.98291
$741$	−16.4783	−0.605346
$742$	−0.611005	−0.0224307
$743$	−35.7447	−1.31135	−0.655673	−	0.755045i	$-0.727615\pi$
$743$	−35.7447	−1.31135	−0.655673	+	0.755045i	$0.727615\pi$
$744$	−93.7479	−3.43697
$745$	−3.58496	−0.131343
$746$	−18.4791	−0.676569
$747$	−0.315776	−0.0115536
$748$	−9.31633	−0.340639
$749$	9.14233	0.334053
$750$	−102.184	−3.73123
$751$	12.4924	0.455855	0.227928	−	0.973678i	$-0.426805\pi$
$751$	12.4924	0.455855	0.227928	+	0.973678i	$0.426805\pi$
$752$	−44.7754	−1.63279
$753$	16.0294	0.584144
$754$	33.4738	1.21905
$755$	−15.5303	−0.565206
$756$	−67.5295	−2.45602
$757$	33.7346	1.22610	0.613052	−	0.790042i	$-0.289941\pi$
$757$	33.7346	1.22610	0.613052	+	0.790042i	$0.289941\pi$
$758$	35.6198	1.29377
$759$	−13.6732	−0.496305
$760$	−114.729	−4.16166
$761$	9.11708	0.330494	0.165247	−	0.986252i	$-0.447158\pi$
$761$	9.11708	0.330494	0.165247	+	0.986252i	$0.447158\pi$
$762$	40.1336	1.45389
$763$	6.16315	0.223121
$764$	62.0444	2.24469
$765$	0.547502	0.0197950
$766$	10.1339	0.366151
$767$	2.01354	0.0727049
$768$	−18.2755	−0.659460
$769$	14.6084	0.526792	0.263396	−	0.964688i	$-0.415157\pi$
$769$	14.6084	0.526792	0.263396	+	0.964688i	$0.415157\pi$
$770$	−37.9724	−1.36843
$771$	−13.1041	−0.471934
$772$	−75.5246	−2.71819
$773$	−22.8709	−0.822608	−0.411304	−	0.911498i	$-0.634927\pi$
$773$	−22.8709	−0.822608	−0.411304	+	0.911498i	$0.634927\pi$
$774$	−0.0215343	−0.000774034 0
$775$	−65.4786	−2.35206
$776$	114.299	4.10310
$777$	−17.9433	−0.643713
$778$	16.6011	0.595179
$779$	−33.8232	−1.21184
$780$	−98.2385	−3.51750
$781$	−14.5114	−0.519260
$782$	18.8569	0.674321
$783$	23.3056	0.832873
$784$	−5.74162	−0.205058
$785$	66.4589	2.37202
$786$	19.7077	0.702952
$787$	−41.3364	−1.47348	−0.736742	−	0.676174i	$-0.763637\pi$
$787$	−41.3364	−1.47348	−0.736742	+	0.676174i	$0.763637\pi$
$788$	−26.5604	−0.946175
$789$	−54.7936	−1.95070
$790$	−14.4358	−0.513602
$791$	36.7922	1.30818
$792$	−1.30612	−0.0464110
$793$	−34.9464	−1.24098
$794$	3.86302	0.137094
$795$	−0.618853	−0.0219485
$796$	92.8179	3.28984
$797$	8.82065	0.312444	0.156222	−	0.987722i	$-0.450069\pi$
$797$	8.82065	0.312444	0.156222	+	0.987722i	$0.450069\pi$
$798$	41.3251	1.46289
$799$	4.58565	0.162229
$800$	−171.919	−6.07827
$801$	2.01429	0.0711713
$802$	−42.3215	−1.49442
$803$	−8.41908	−0.297103
$804$	1.01026	0.0356292
$805$	55.4502	1.95436
$806$	−45.6829	−1.60911
$807$	6.13126	0.215831
$808$	5.27570	0.185598
$809$	22.8529	0.803464	0.401732	−	0.915757i	$-0.368408\pi$
$809$	22.8529	0.803464	0.401732	+	0.915757i	$0.368408\pi$
$810$	−98.2491	−3.45212
$811$	7.26827	0.255223	0.127612	−	0.991824i	$-0.459269\pi$
$811$	7.26827	0.255223	0.127612	+	0.991824i	$0.459269\pi$
$812$	−60.5642	−2.12539
$813$	24.1114	0.845623
$814$	15.0114	0.526150
$815$	−26.0036	−0.910866
$816$	28.0979	0.983623
$817$	−0.252463	−0.00883255
$818$	0.210095	0.00734582
$819$	0.760775	0.0265836
$820$	−201.644	−7.04170
$821$	55.1608	1.92512	0.962562	−	0.271062i	$-0.0873750\pi$
$821$	55.1608	1.92512	0.962562	+	0.271062i	$0.0873750\pi$
$822$	15.0453	0.524765
$823$	−7.46788	−0.260314	−0.130157	−	0.991493i	$-0.541548\pi$
$823$	−7.46788	−0.260314	−0.130157	+	0.991493i	$0.541548\pi$
$824$	43.7584	1.52440
$825$	−26.0492	−0.906916
$826$	−5.04966	−0.175700
$827$	−44.0972	−1.53341	−0.766706	−	0.641999i	$-0.778105\pi$
$827$	−44.0972	−1.53341	−0.766706	+	0.641999i	$0.778105\pi$
$828$	3.10679	0.107968
$829$	32.3580	1.12384	0.561920	−	0.827192i	$-0.310063\pi$
$829$	32.3580	1.12384	0.561920	+	0.827192i	$0.310063\pi$
$830$	−30.5918	−1.06186
$831$	19.0575	0.661098
$832$	−51.7760	−1.79501
$833$	0.588026	0.0203739
$834$	−104.571	−3.62101
$835$	21.7458	0.752544
$836$	−24.9426	−0.862659
$837$	−31.8059	−1.09937
$838$	27.6250	0.954290
$839$	37.1210	1.28156	0.640780	−	0.767725i	$-0.278611\pi$
$839$	37.1210	1.28156	0.640780	+	0.767725i	$0.278611\pi$
$840$	151.248	5.21856
$841$	−8.09825	−0.279250
$842$	−28.2175	−0.972441
$843$	19.7275	0.679452
$844$	15.7998	0.543851
$845$	21.7832	0.749364
$846$	1.04721	0.0360037
$847$	23.0621	0.792422
$848$	−1.11225	−0.0381948
$849$	46.1627	1.58430
$850$	35.9249	1.23221
$851$	−21.9208	−0.751436
$852$	94.1510	3.22556
$853$	23.5796	0.807352	0.403676	−	0.914902i	$-0.367732\pi$
$853$	23.5796	0.807352	0.403676	+	0.914902i	$0.367732\pi$
$854$	87.6403	2.99899
$855$	1.46583	0.0501303
$856$	30.4648	1.04127
$857$	6.10651	0.208595	0.104297	−	0.994546i	$-0.466741\pi$
$857$	6.10651	0.208595	0.104297	+	0.994546i	$0.466741\pi$
$858$	−18.1739	−0.620447
$859$	34.5877	1.18012	0.590059	−	0.807360i	$-0.299105\pi$
$859$	34.5877	1.18012	0.590059	+	0.807360i	$0.299105\pi$
$860$	−1.50510	−0.0513236
$861$	44.5894	1.51960
$862$	23.9630	0.816183
$863$	23.1648	0.788541	0.394270	−	0.918995i	$-0.370997\pi$
$863$	23.1648	0.788541	0.394270	+	0.918995i	$0.370997\pi$
$864$	−83.5090	−2.84103
$865$	90.4872	3.07666
$866$	69.8335	2.37304
$867$	27.0968	0.920255
$868$	82.6540	2.80546
$869$	−1.92671	−0.0653592
$870$	−85.0255	−2.88263
$871$	0.302227	0.0102406
$872$	20.5373	0.695482
$873$	−1.46034	−0.0494249
$874$	50.4856	1.70770
$875$	55.3086	1.86977
$876$	54.6235	1.84556
$877$	49.6852	1.67775	0.838875	−	0.544324i	$-0.183214\pi$
$877$	49.6852	1.67775	0.838875	+	0.544324i	$0.183214\pi$
$878$	−53.3033	−1.79890
$879$	8.60415	0.290211
$880$	−69.1234	−2.33015
$881$	−25.9924	−0.875705	−0.437853	−	0.899047i	$-0.644261\pi$
$881$	−25.9924	−0.875705	−0.437853	+	0.899047i	$0.644261\pi$
$882$	0.134285	0.00452161
$883$	52.3121	1.76044	0.880221	−	0.474564i	$-0.157394\pi$
$883$	52.3121	1.76044	0.880221	+	0.474564i	$0.157394\pi$
$884$	18.0825	0.608181
$885$	−5.11452	−0.171923
$886$	−38.1857	−1.28287
$887$	27.1327	0.911027	0.455514	−	0.890229i	$-0.349456\pi$
$887$	27.1327	0.911027	0.455514	+	0.890229i	$0.349456\pi$
$888$	−59.7921	−2.00649
$889$	−21.7229	−0.728563
$890$	195.140	6.54111
$891$	−13.1131	−0.439305
$892$	−82.2101	−2.75260
$893$	12.2772	0.410840
$894$	4.30294	0.143912
$895$	19.3141	0.645599
$896$	46.0598	1.53875
$897$	26.5389	0.886109
$898$	7.74629	0.258497
$899$	−28.5253	−0.951373
$900$	5.91883	0.197294
$901$	0.113911	0.00379492
$902$	−37.3036	−1.24207
$903$	0.332823	0.0110757
$904$	122.602	4.07767
$905$	−76.5386	−2.54423
$906$	18.6407	0.619295
$907$	37.8100	1.25546	0.627730	−	0.778431i	$-0.283984\pi$
$907$	37.8100	1.25546	0.627730	+	0.778431i	$0.283984\pi$
$908$	17.1459	0.569007
$909$	−0.0674046	−0.00223567
$910$	73.7024	2.44321
$911$	−15.3308	−0.507932	−0.253966	−	0.967213i	$-0.581735\pi$
$911$	−15.3308	−0.507932	−0.253966	+	0.967213i	$0.581735\pi$
$912$	75.2266	2.49100
$913$	−4.08301	−0.135128
$914$	106.540	3.52403
$915$	88.7660	2.93451
$916$	91.8037	3.03328
$917$	−10.6671	−0.352259
$918$	17.4503	0.575946
$919$	−31.3384	−1.03376	−0.516879	−	0.856059i	$-0.672906\pi$
$919$	−31.3384	−1.03376	−0.516879	+	0.856059i	$0.672906\pi$
$920$	184.775	6.09187
$921$	−26.1644	−0.862145
$922$	−41.7852	−1.37612
$923$	28.1659	0.927093
$924$	32.8820	1.08174
$925$	−41.7620	−1.37313
$926$	−46.6087	−1.53166
$927$	−0.559076	−0.0183625
$928$	−74.8956	−2.45857
$929$	40.4213	1.32618	0.663090	−	0.748540i	$-0.269245\pi$
$929$	40.4213	1.32618	0.663090	+	0.748540i	$0.269245\pi$
$930$	116.037	3.80501
$931$	1.57432	0.0515964
$932$	74.8098	2.45048
$933$	6.74458	0.220808
$934$	−79.9800	−2.61703
$935$	7.07926	0.231516
$936$	2.53511	0.0828628
$937$	−46.1999	−1.50928	−0.754642	−	0.656136i	$-0.772190\pi$
$937$	−46.1999	−1.50928	−0.754642	+	0.656136i	$0.772190\pi$
$938$	−0.757938	−0.0247476
$939$	−25.8629	−0.844005
$940$	73.1927	2.38728
$941$	30.4574	0.992883	0.496441	−	0.868070i	$-0.334640\pi$
$941$	30.4574	0.992883	0.496441	+	0.868070i	$0.334640\pi$
$942$	−79.7691	−2.59902
$943$	54.4736	1.77390
$944$	−9.19221	−0.299181
$945$	51.3140	1.66925
$946$	−0.278441	−0.00905288
$947$	−50.7411	−1.64886	−0.824431	−	0.565962i	$-0.808505\pi$
$947$	−50.7411	−1.64886	−0.824431	+	0.565962i	$0.808505\pi$
$948$	12.5006	0.406001
$949$	16.3410	0.530451
$950$	96.1818	3.12055
$951$	−54.2876	−1.76040
$952$	−27.8399	−0.902295
$953$	57.9225	1.87629	0.938147	−	0.346238i	$-0.112541\pi$
$953$	57.9225	1.87629	0.938147	+	0.346238i	$0.112541\pi$
$954$	0.0260133	0.000842213 0
$955$	−47.1461	−1.52561
$956$	−61.8165	−1.99929
$957$	−11.3482	−0.366834
$958$	46.5017	1.50240
$959$	−8.14348	−0.262967
$960$	131.514	4.24460
$961$	7.92946	0.255789
$962$	−29.1364	−0.939395
$963$	−0.389231	−0.0125428
$964$	−30.8122	−0.992395
$965$	57.3893	1.84743
$966$	−66.5555	−2.14139
$967$	34.0320	1.09440	0.547198	−	0.837003i	$-0.315695\pi$
$967$	34.0320	1.09440	0.547198	+	0.837003i	$0.315695\pi$
$968$	76.8492	2.47003
$969$	−7.70430	−0.247498
$970$	−141.475	−4.54248
$971$	−29.1470	−0.935372	−0.467686	−	0.883895i	$-0.654912\pi$
$971$	−29.1470	−0.935372	−0.467686	+	0.883895i	$0.654912\pi$
$972$	5.85836	0.187907
$973$	56.6009	1.81454
$974$	65.7870	2.10795
$975$	50.5601	1.61922
$976$	159.537	5.10666
$977$	−23.4948	−0.751666	−0.375833	−	0.926687i	$-0.622643\pi$
$977$	−23.4948	−0.751666	−0.375833	+	0.926687i	$0.622643\pi$
$978$	31.2115	0.998034
$979$	26.0449	0.832399
$980$	9.38562	0.299813
$981$	−0.262394	−0.00837760
$982$	−76.9625	−2.45597
$983$	8.10480	0.258503	0.129251	−	0.991612i	$-0.458743\pi$
$983$	8.10480	0.258503	0.129251	+	0.991612i	$0.458743\pi$
$984$	148.584	4.73670
$985$	20.1826	0.643071
$986$	15.6504	0.498411
$987$	−16.1851	−0.515177
$988$	48.4124	1.54020
$989$	0.406600	0.0129291
$990$	1.61666	0.0513808
$991$	−21.9803	−0.698229	−0.349114	−	0.937080i	$-0.613518\pi$
$991$	−21.9803	−0.698229	−0.349114	+	0.937080i	$0.613518\pi$
$992$	102.212	3.24525
$993$	38.7079	1.22836
$994$	−70.6358	−2.24043
$995$	−70.5301	−2.23595
$996$	26.4908	0.839394
$997$	12.2064	0.386579	0.193290	−	0.981142i	$-0.438084\pi$
$997$	12.2064	0.386579	0.193290	+	0.981142i	$0.438084\pi$
$998$	−6.83906	−0.216487
$999$	−20.2857	−0.641811

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8011.2.a.b.1.9	✓	358

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8011.2.a.b.1.9	✓	358	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)

\(f(q)\)	\(=\)	\(q-2.67959 q^{2} -1.76320 q^{3} +5.18019 q^{4} -3.93630 q^{5} +4.72465 q^{6} -2.55729 q^{7} -8.52159 q^{8} +0.108876 q^{9} +O(q^{10})\)	\(q-2.67959 q^{2} -1.76320 q^{3} +5.18019 q^{4} -3.93630 q^{5} +4.72465 q^{6} -2.55729 q^{7} -8.52159 q^{8} +0.108876 q^{9} +10.5477 q^{10} +1.40777 q^{11} -9.13371 q^{12} -2.73241 q^{13} +6.85247 q^{14} +6.94049 q^{15} +12.4740 q^{16} -1.27752 q^{17} -0.291742 q^{18} -3.42030 q^{19} -20.3908 q^{20} +4.50901 q^{21} -3.77225 q^{22} +5.50852 q^{23} +15.0253 q^{24} +10.4945 q^{25} +7.32174 q^{26} +5.09763 q^{27} -13.2472 q^{28} +4.57184 q^{29} -18.5976 q^{30} -6.23935 q^{31} -16.3819 q^{32} -2.48218 q^{33} +3.42322 q^{34} +10.0662 q^{35} +0.563996 q^{36} -3.97944 q^{37} +9.16500 q^{38} +4.81779 q^{39} +33.5435 q^{40} +9.88896 q^{41} -12.0823 q^{42} +0.0738129 q^{43} +7.29252 q^{44} -0.428567 q^{45} -14.7606 q^{46} -3.58950 q^{47} -21.9941 q^{48} -0.460288 q^{49} -28.1208 q^{50} +2.25252 q^{51} -14.1544 q^{52} -0.0891657 q^{53} -13.6595 q^{54} -5.54141 q^{55} +21.7921 q^{56} +6.03068 q^{57} -12.2507 q^{58} -0.736911 q^{59} +35.9530 q^{60} +12.7896 q^{61} +16.7189 q^{62} -0.278426 q^{63} +18.9488 q^{64} +10.7556 q^{65} +6.65123 q^{66} -0.110608 q^{67} -6.61778 q^{68} -9.71263 q^{69} -26.9734 q^{70} -10.3081 q^{71} -0.927793 q^{72} -5.98043 q^{73} +10.6632 q^{74} -18.5038 q^{75} -17.7178 q^{76} -3.60008 q^{77} -12.9097 q^{78} -1.36862 q^{79} -49.1013 q^{80} -9.31477 q^{81} -26.4983 q^{82} -2.90034 q^{83} +23.3575 q^{84} +5.02870 q^{85} -0.197788 q^{86} -8.06108 q^{87} -11.9965 q^{88} +18.5008 q^{89} +1.14838 q^{90} +6.98756 q^{91} +28.5352 q^{92} +11.0012 q^{93} +9.61838 q^{94} +13.4633 q^{95} +28.8846 q^{96} -13.4129 q^{97} +1.23338 q^{98} +0.153272 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 358 q + 33 q^{2} + 11 q^{3} + 391 q^{4} + 76 q^{5} + 32 q^{6} + 19 q^{7} + 99 q^{8} + 451 q^{9}+O(q^{10}) \) 358 * q + 33 * q^2 + 11 * q^3 + 391 * q^4 + 76 * q^5 + 32 * q^6 + 19 * q^7 + 99 * q^8 + 451 * q^9	\( 358 q + 33 q^{2} + 11 q^{3} + 391 q^{4} + 76 q^{5} + 32 q^{6} + 19 q^{7} + 99 q^{8} + 451 q^{9} + 21 q^{10} + 70 q^{11} + 20 q^{12} + 53 q^{13} + 69 q^{14} + 28 q^{15} + 449 q^{16} + 88 q^{17} + 86 q^{18} + 44 q^{19} + 136 q^{20} + 125 q^{21} + 17 q^{22} + 104 q^{23} + 84 q^{24} + 444 q^{25} + 100 q^{26} + 32 q^{27} + 46 q^{28} + 373 q^{29} + 99 q^{30} + 30 q^{31} + 221 q^{32} + 56 q^{33} + 26 q^{34} + 164 q^{35} + 599 q^{36} + 81 q^{37} + 66 q^{38} + 143 q^{39} + 42 q^{40} + 182 q^{41} + 32 q^{42} + 40 q^{43} + 184 q^{44} + 198 q^{45} + 54 q^{46} + 66 q^{47} + 5 q^{48} + 479 q^{49} + 184 q^{50} + 123 q^{51} + 64 q^{52} + 221 q^{53} + 67 q^{54} + 38 q^{55} + 174 q^{56} + 84 q^{57} + 44 q^{58} + 127 q^{59} + 29 q^{60} + 174 q^{61} + 86 q^{62} + 48 q^{63} + 549 q^{64} + 202 q^{65} + 32 q^{66} + 29 q^{67} + 172 q^{68} + 249 q^{69} + 12 q^{70} + 185 q^{71} + 218 q^{72} + 57 q^{73} + 272 q^{74} + 24 q^{75} + 84 q^{76} + 384 q^{77} + 12 q^{78} + 93 q^{79} + 215 q^{80} + 702 q^{81} + 48 q^{82} + 121 q^{83} + 179 q^{84} + 177 q^{85} + 209 q^{86} + 91 q^{87} + 36 q^{88} + 186 q^{89} + 66 q^{90} + 32 q^{91} + 272 q^{92} + 220 q^{93} + 60 q^{94} + 170 q^{95} + 162 q^{96} + 22 q^{97} + 196 q^{98} + 152 q^{99}+O(q^{100}) \) 358 * q + 33 * q^2 + 11 * q^3 + 391 * q^4 + 76 * q^5 + 32 * q^6 + 19 * q^7 + 99 * q^8 + 451 * q^9 + 21 * q^10 + 70 * q^11 + 20 * q^12 + 53 * q^13 + 69 * q^14 + 28 * q^15 + 449 * q^16 + 88 * q^17 + 86 * q^18 + 44 * q^19 + 136 * q^20 + 125 * q^21 + 17 * q^22 + 104 * q^23 + 84 * q^24 + 444 * q^25 + 100 * q^26 + 32 * q^27 + 46 * q^28 + 373 * q^29 + 99 * q^30 + 30 * q^31 + 221 * q^32 + 56 * q^33 + 26 * q^34 + 164 * q^35 + 599 * q^36 + 81 * q^37 + 66 * q^38 + 143 * q^39 + 42 * q^40 + 182 * q^41 + 32 * q^42 + 40 * q^43 + 184 * q^44 + 198 * q^45 + 54 * q^46 + 66 * q^47 + 5 * q^48 + 479 * q^49 + 184 * q^50 + 123 * q^51 + 64 * q^52 + 221 * q^53 + 67 * q^54 + 38 * q^55 + 174 * q^56 + 84 * q^57 + 44 * q^58 + 127 * q^59 + 29 * q^60 + 174 * q^61 + 86 * q^62 + 48 * q^63 + 549 * q^64 + 202 * q^65 + 32 * q^66 + 29 * q^67 + 172 * q^68 + 249 * q^69 + 12 * q^70 + 185 * q^71 + 218 * q^72 + 57 * q^73 + 272 * q^74 + 24 * q^75 + 84 * q^76 + 384 * q^77 + 12 * q^78 + 93 * q^79 + 215 * q^80 + 702 * q^81 + 48 * q^82 + 121 * q^83 + 179 * q^84 + 177 * q^85 + 209 * q^86 + 91 * q^87 + 36 * q^88 + 186 * q^89 + 66 * q^90 + 32 * q^91 + 272 * q^92 + 220 * q^93 + 60 * q^94 + 170 * q^95 + 162 * q^96 + 22 * q^97 + 196 * q^98 + 152 * q^99

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