LMFDB - Embedded newform 8011.2.a.b.1.15

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			1.15
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)

$f(q)$	$=$	$q-2.61797 q^{2} +1.26070 q^{3} +4.85374 q^{4} +0.306561 q^{5} -3.30046 q^{6} -1.43849 q^{7} -7.47100 q^{8} -1.41065 q^{9} +O(q^{10})$	\(q-2.61797 q^{2} +1.26070 q^{3} +4.85374 q^{4} +0.306561 q^{5} -3.30046 q^{6} -1.43849 q^{7} -7.47100 q^{8} -1.41065 q^{9} -0.802565 q^{10} +2.14470 q^{11} +6.11909 q^{12} -3.19914 q^{13} +3.76591 q^{14} +0.386480 q^{15} +9.85133 q^{16} -3.80611 q^{17} +3.69302 q^{18} +4.63838 q^{19} +1.48797 q^{20} -1.81349 q^{21} -5.61474 q^{22} -3.20363 q^{23} -9.41866 q^{24} -4.90602 q^{25} +8.37523 q^{26} -5.56048 q^{27} -6.98204 q^{28} -3.93433 q^{29} -1.01179 q^{30} -3.98336 q^{31} -10.8484 q^{32} +2.70381 q^{33} +9.96426 q^{34} -0.440983 q^{35} -6.84691 q^{36} +3.40998 q^{37} -12.1431 q^{38} -4.03314 q^{39} -2.29031 q^{40} +8.71086 q^{41} +4.74766 q^{42} -7.51262 q^{43} +10.4098 q^{44} -0.432449 q^{45} +8.38698 q^{46} -8.65394 q^{47} +12.4195 q^{48} -4.93076 q^{49} +12.8438 q^{50} -4.79834 q^{51} -15.5278 q^{52} -1.13168 q^{53} +14.5572 q^{54} +0.657480 q^{55} +10.7469 q^{56} +5.84758 q^{57} +10.2999 q^{58} +12.0044 q^{59} +1.87587 q^{60} -1.57506 q^{61} +10.4283 q^{62} +2.02919 q^{63} +8.69818 q^{64} -0.980730 q^{65} -7.07848 q^{66} +11.9537 q^{67} -18.4739 q^{68} -4.03880 q^{69} +1.15448 q^{70} +15.1590 q^{71} +10.5389 q^{72} +0.359001 q^{73} -8.92722 q^{74} -6.18500 q^{75} +22.5135 q^{76} -3.08511 q^{77} +10.5586 q^{78} -0.646053 q^{79} +3.02003 q^{80} -2.77814 q^{81} -22.8047 q^{82} +6.65148 q^{83} -8.80223 q^{84} -1.16680 q^{85} +19.6678 q^{86} -4.95999 q^{87} -16.0230 q^{88} -8.54918 q^{89} +1.13214 q^{90} +4.60191 q^{91} -15.5496 q^{92} -5.02181 q^{93} +22.6557 q^{94} +1.42194 q^{95} -13.6766 q^{96} -12.6530 q^{97} +12.9086 q^{98} -3.02541 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.61797	−1.85118	−0.925590	−	0.378526i	$-0.876431\pi$
$2$	−2.61797	−1.85118	−0.925590	+	0.378526i	$0.876431\pi$
$3$	1.26070	0.727863	0.363932	−	0.931426i	$-0.381434\pi$
$3$	1.26070	0.727863	0.363932	+	0.931426i	$0.381434\pi$
$4$	4.85374	2.42687
$5$	0.306561	0.137098	0.0685491	−	0.997648i	$-0.478163\pi$
$5$	0.306561	0.137098	0.0685491	+	0.997648i	$0.478163\pi$
$6$	−3.30046	−1.34741
$7$	−1.43849	−0.543696	−0.271848	−	0.962340i	$-0.587635\pi$
$7$	−1.43849	−0.543696	−0.271848	+	0.962340i	$0.587635\pi$
$8$	−7.47100	−2.64140
$9$	−1.41065	−0.470215
$10$	−0.802565	−0.253793
$11$	2.14470	0.646650	0.323325	−	0.946288i	$-0.395199\pi$
$11$	2.14470	0.646650	0.323325	+	0.946288i	$0.395199\pi$
$12$	6.11909	1.76643
$13$	−3.19914	−0.887281	−0.443641	−	0.896205i	$-0.646313\pi$
$13$	−3.19914	−0.887281	−0.443641	+	0.896205i	$0.646313\pi$
$14$	3.76591	1.00648
$15$	0.386480	0.0997887
$16$	9.85133	2.46283
$17$	−3.80611	−0.923117	−0.461558	−	0.887110i	$-0.652709\pi$
$17$	−3.80611	−0.923117	−0.461558	+	0.887110i	$0.652709\pi$
$18$	3.69302	0.870454
$19$	4.63838	1.06412	0.532058	−	0.846708i	$-0.321419\pi$
$19$	4.63838	1.06412	0.532058	+	0.846708i	$0.321419\pi$
$20$	1.48797	0.332719
$21$	−1.81349	−0.395737
$22$	−5.61474	−1.19707
$23$	−3.20363	−0.668002	−0.334001	−	0.942573i	$-0.608399\pi$
$23$	−3.20363	−0.668002	−0.334001	+	0.942573i	$0.608399\pi$
$24$	−9.41866	−1.92257
$25$	−4.90602	−0.981204
$26$	8.37523	1.64252
$27$	−5.56048	−1.07012
$28$	−6.98204	−1.31948
$29$	−3.93433	−0.730586	−0.365293	−	0.930893i	$-0.619031\pi$
$29$	−3.93433	−0.730586	−0.365293	+	0.930893i	$0.619031\pi$
$30$	−1.01179	−0.184727
$31$	−3.98336	−0.715433	−0.357716	−	0.933830i	$-0.616445\pi$
$31$	−3.98336	−0.715433	−0.357716	+	0.933830i	$0.616445\pi$
$32$	−10.8484	−1.91775
$33$	2.70381	0.470673
$34$	9.96426	1.70886
$35$	−0.440983	−0.0745398
$36$	−6.84691	−1.14115
$37$	3.40998	0.560598	0.280299	−	0.959913i	$-0.409566\pi$
$37$	3.40998	0.560598	0.280299	+	0.959913i	$0.409566\pi$
$38$	−12.1431	−1.96987
$39$	−4.03314	−0.645819
$40$	−2.29031	−0.362130
$41$	8.71086	1.36041	0.680204	−	0.733023i	$-0.261891\pi$
$41$	8.71086	1.36041	0.680204	+	0.733023i	$0.261891\pi$
$42$	4.74766	0.732580
$43$	−7.51262	−1.14566	−0.572832	−	0.819673i	$-0.694155\pi$
$43$	−7.51262	−1.14566	−0.572832	+	0.819673i	$0.694155\pi$
$44$	10.4098	1.56934
$45$	−0.432449	−0.0644656
$46$	8.38698	1.23659
$47$	−8.65394	−1.26231	−0.631153	−	0.775658i	$-0.717418\pi$
$47$	−8.65394	−1.26231	−0.631153	+	0.775658i	$0.717418\pi$
$48$	12.4195	1.79260
$49$	−4.93076	−0.704394
$50$	12.8438	1.81639
$51$	−4.79834	−0.671903
$52$	−15.5278	−2.15332
$53$	−1.13168	−0.155448	−0.0777238	−	0.996975i	$-0.524765\pi$
$53$	−1.13168	−0.155448	−0.0777238	+	0.996975i	$0.524765\pi$
$54$	14.5572	1.98098
$55$	0.657480	0.0886545
$56$	10.7469	1.43612
$57$	5.84758	0.774531
$58$	10.2999	1.35245
$59$	12.0044	1.56284	0.781419	−	0.624006i	$-0.214496\pi$
$59$	12.0044	1.56284	0.781419	+	0.624006i	$0.214496\pi$
$60$	1.87587	0.242174
$61$	−1.57506	−0.201666	−0.100833	−	0.994903i	$-0.532151\pi$
$61$	−1.57506	−0.201666	−0.100833	+	0.994903i	$0.532151\pi$
$62$	10.4283	1.32440
$63$	2.02919	0.255654
$64$	8.69818	1.08727
$65$	−0.980730	−0.121645
$66$	−7.07848	−0.871301
$67$	11.9537	1.46037	0.730187	−	0.683247i	$-0.239433\pi$
$67$	11.9537	1.46037	0.730187	+	0.683247i	$0.239433\pi$
$68$	−18.4739	−2.24029
$69$	−4.03880	−0.486214
$70$	1.15448	0.137987
$71$	15.1590	1.79904	0.899522	−	0.436876i	$-0.143915\pi$
$71$	15.1590	1.79904	0.899522	+	0.436876i	$0.143915\pi$
$72$	10.5389	1.24203
$73$	0.359001	0.0420179	0.0210090	−	0.999779i	$-0.493312\pi$
$73$	0.359001	0.0420179	0.0210090	+	0.999779i	$0.493312\pi$
$74$	−8.92722	−1.03777
$75$	−6.18500	−0.714182
$76$	22.5135	2.58247
$77$	−3.08511	−0.351581
$78$	10.5586	1.19553
$79$	−0.646053	−0.0726866	−0.0363433	−	0.999339i	$-0.511571\pi$
$79$	−0.646053	−0.0726866	−0.0363433	+	0.999339i	$0.511571\pi$
$80$	3.02003	0.337650
$81$	−2.77814	−0.308682
$82$	−22.8047	−2.51836
$83$	6.65148	0.730095	0.365048	−	0.930989i	$-0.381053\pi$
$83$	6.65148	0.730095	0.365048	+	0.930989i	$0.381053\pi$
$84$	−8.80223	−0.960402
$85$	−1.16680	−0.126558
$86$	19.6678	2.12083
$87$	−4.95999	−0.531767
$88$	−16.0230	−1.70806
$89$	−8.54918	−0.906211	−0.453106	−	0.891457i	$-0.649684\pi$
$89$	−8.54918	−0.906211	−0.453106	+	0.891457i	$0.649684\pi$
$90$	1.13214	0.119338
$91$	4.60191	0.482412
$92$	−15.5496	−1.62115
$93$	−5.02181	−0.520737
$94$	22.6557	2.33676
$95$	1.42194	0.145888
$96$	−13.6766	−1.39586
$97$	−12.6530	−1.28472	−0.642360	−	0.766403i	$-0.722045\pi$
$97$	−12.6530	−1.28472	−0.642360	+	0.766403i	$0.722045\pi$
$98$	12.9086	1.30396
$99$	−3.02541	−0.304065
$100$	−23.8126	−2.38126
$101$	−6.34079	−0.630933	−0.315466	−	0.948937i	$-0.602161\pi$
$101$	−6.34079	−0.630933	−0.315466	+	0.948937i	$0.602161\pi$
$102$	12.5619	1.24381
$103$	11.5248	1.13557	0.567787	−	0.823175i	$-0.307800\pi$
$103$	11.5248	1.13557	0.567787	+	0.823175i	$0.307800\pi$
$104$	23.9008	2.34366
$105$	−0.555946	−0.0542547
$106$	2.96269	0.287762
$107$	−11.1373	−1.07668	−0.538341	−	0.842727i	$-0.680949\pi$
$107$	−11.1373	−1.07668	−0.538341	+	0.842727i	$0.680949\pi$
$108$	−26.9892	−2.59703
$109$	11.5157	1.10301	0.551503	−	0.834173i	$-0.314054\pi$
$109$	11.5157	1.10301	0.551503	+	0.834173i	$0.314054\pi$
$110$	−1.72126	−0.164116
$111$	4.29895	0.408038
$112$	−14.1710	−1.33903
$113$	2.90877	0.273634	0.136817	−	0.990596i	$-0.456313\pi$
$113$	2.90877	0.273634	0.136817	+	0.990596i	$0.456313\pi$
$114$	−15.3088	−1.43380
$115$	−0.982106	−0.0915818
$116$	−19.0962	−1.77304
$117$	4.51285	0.417213
$118$	−31.4271	−2.89310
$119$	5.47503	0.501895
$120$	−2.88739	−0.263581
$121$	−6.40028	−0.581844
$122$	4.12346	0.373321
$123$	10.9817	0.990191
$124$	−19.3342	−1.73626
$125$	−3.03680	−0.271619
$126$	−5.31236	−0.473263
$127$	11.9053	1.05642	0.528212	−	0.849113i	$-0.322863\pi$
$127$	11.9053	1.05642	0.528212	+	0.849113i	$0.322863\pi$
$128$	−1.07465	−0.0949866
$129$	−9.47113	−0.833886
$130$	2.56752	0.225186
$131$	18.0008	1.57274	0.786369	−	0.617757i	$-0.211959\pi$
$131$	18.0008	1.57274	0.786369	+	0.617757i	$0.211959\pi$
$132$	13.1236	1.14226
$133$	−6.67224	−0.578556
$134$	−31.2943	−2.70342
$135$	−1.70463	−0.146711
$136$	28.4354	2.43832
$137$	8.19044	0.699757	0.349878	−	0.936795i	$-0.386223\pi$
$137$	8.19044	0.699757	0.349878	+	0.936795i	$0.386223\pi$
$138$	10.5734	0.900070
$139$	−0.764507	−0.0648446	−0.0324223	−	0.999474i	$-0.510322\pi$
$139$	−0.764507	−0.0648446	−0.0324223	+	0.999474i	$0.510322\pi$
$140$	−2.14042	−0.180898
$141$	−10.9100	−0.918786
$142$	−39.6858	−3.33035
$143$	−6.86118	−0.573761
$144$	−13.8967	−1.15806
$145$	−1.20611	−0.100162
$146$	−0.939853	−0.0777828
$147$	−6.21619	−0.512703
$148$	16.5512	1.36050
$149$	13.4093	1.09853	0.549266	−	0.835647i	$-0.314907\pi$
$149$	13.4093	1.09853	0.549266	+	0.835647i	$0.314907\pi$
$150$	16.1921	1.32208
$151$	0.0304420	0.00247734	0.00123867	−	0.999999i	$-0.499606\pi$
$151$	0.0304420	0.00247734	0.00123867	+	0.999999i	$0.499606\pi$
$152$	−34.6533	−2.81075
$153$	5.36907	0.434064
$154$	8.07672	0.650841
$155$	−1.22114	−0.0980845
$156$	−19.5758	−1.56732
$157$	−4.61814	−0.368568	−0.184284	−	0.982873i	$-0.558997\pi$
$157$	−4.61814	−0.368568	−0.184284	+	0.982873i	$0.558997\pi$
$158$	1.69134	0.134556
$159$	−1.42670	−0.113145
$160$	−3.32570	−0.262920
$161$	4.60837	0.363190
$162$	7.27307	0.571427
$163$	−13.6220	−1.06695	−0.533477	−	0.845814i	$-0.679115\pi$
$163$	−13.6220	−1.06695	−0.533477	+	0.845814i	$0.679115\pi$
$164$	42.2803	3.30154
$165$	0.828882	0.0645284
$166$	−17.4134	−1.35154
$167$	13.6096	1.05314	0.526572	−	0.850130i	$-0.323477\pi$
$167$	13.6096	1.05314	0.526572	+	0.850130i	$0.323477\pi$
$168$	13.5486	1.04530
$169$	−2.76552	−0.212732
$170$	3.05465	0.234281
$171$	−6.54311	−0.500364
$172$	−36.4643	−2.78038
$173$	−17.8627	−1.35807	−0.679037	−	0.734104i	$-0.737602\pi$
$173$	−17.8627	−1.35807	−0.679037	+	0.734104i	$0.737602\pi$
$174$	12.9851	0.984396
$175$	7.05724	0.533477
$176$	21.1281	1.59259
$177$	15.1339	1.13753
$178$	22.3815	1.67756
$179$	−1.22572	−0.0916148	−0.0458074	−	0.998950i	$-0.514586\pi$
$179$	−1.22572	−0.0916148	−0.0458074	+	0.998950i	$0.514586\pi$
$180$	−2.09899	−0.156450
$181$	17.3486	1.28951	0.644757	−	0.764388i	$-0.276959\pi$
$181$	17.3486	1.28951	0.644757	+	0.764388i	$0.276959\pi$
$182$	−12.0477	−0.893031
$183$	−1.98568	−0.146785
$184$	23.9343	1.76446
$185$	1.04537	0.0768569
$186$	13.1469	0.963979
$187$	−8.16294	−0.596934
$188$	−42.0040	−3.06345
$189$	7.99867	0.581818
$190$	−3.72260	−0.270066
$191$	8.04609	0.582194	0.291097	−	0.956693i	$-0.405980\pi$
$191$	8.04609	0.582194	0.291097	+	0.956693i	$0.405980\pi$
$192$	10.9658	0.791385
$193$	−1.91820	−0.138075	−0.0690377	−	0.997614i	$-0.521993\pi$
$193$	−1.91820	−0.138075	−0.0690377	+	0.997614i	$0.521993\pi$
$194$	33.1252	2.37825
$195$	−1.23640	−0.0885406
$196$	−23.9326	−1.70947
$197$	3.97652	0.283315	0.141658	−	0.989916i	$-0.454757\pi$
$197$	3.97652	0.283315	0.141658	+	0.989916i	$0.454757\pi$
$198$	7.92041	0.562879
$199$	3.41021	0.241744	0.120872	−	0.992668i	$-0.461431\pi$
$199$	3.41021	0.241744	0.120872	+	0.992668i	$0.461431\pi$
$200$	36.6529	2.59175
$201$	15.0700	1.06295
$202$	16.6000	1.16797
$203$	5.65947	0.397217
$204$	−23.2899	−1.63062
$205$	2.67041	0.186509
$206$	−30.1716	−2.10215
$207$	4.51918	0.314105
$208$	−31.5158	−2.18522
$209$	9.94791	0.688111
$210$	1.45545	0.100435
$211$	11.1255	0.765911	0.382956	−	0.923767i	$-0.374906\pi$
$211$	11.1255	0.765911	0.382956	+	0.923767i	$0.374906\pi$
$212$	−5.49286	−0.377251
$213$	19.1109	1.30946
$214$	29.1570	1.99313
$215$	−2.30307	−0.157068
$216$	41.5424	2.82660
$217$	5.73001	0.388978
$218$	−30.1478	−2.04186
$219$	0.452592	0.0305833
$220$	3.19124	0.215153
$221$	12.1763	0.819064
$222$	−11.2545	−0.755353
$223$	−1.44898	−0.0970311	−0.0485155	−	0.998822i	$-0.515449\pi$
$223$	−1.44898	−0.0970311	−0.0485155	+	0.998822i	$0.515449\pi$
$224$	15.6053	1.04267
$225$	6.92066	0.461377
$226$	−7.61506	−0.506546
$227$	16.3369	1.08432	0.542158	−	0.840277i	$-0.317607\pi$
$227$	16.3369	1.08432	0.542158	+	0.840277i	$0.317607\pi$
$228$	28.3827	1.87969
$229$	0.826735	0.0546322	0.0273161	−	0.999627i	$-0.491304\pi$
$229$	0.826735	0.0546322	0.0273161	+	0.999627i	$0.491304\pi$
$230$	2.57112	0.169535
$231$	−3.88939	−0.255903
$232$	29.3933	1.92977
$233$	0.970813	0.0636000	0.0318000	−	0.999494i	$-0.489876\pi$
$233$	0.970813	0.0636000	0.0318000	+	0.999494i	$0.489876\pi$
$234$	−11.8145	−0.772337
$235$	−2.65296	−0.173060
$236$	58.2662	3.79281
$237$	−0.814476	−0.0529059
$238$	−14.3334	−0.929099
$239$	−15.8436	−1.02484	−0.512418	−	0.858736i	$-0.671250\pi$
$239$	−15.8436	−1.02484	−0.512418	+	0.858736i	$0.671250\pi$
$240$	3.80734	0.245763
$241$	−2.58060	−0.166231	−0.0831155	−	0.996540i	$-0.526487\pi$
$241$	−2.58060	−0.166231	−0.0831155	+	0.996540i	$0.526487\pi$
$242$	16.7557	1.07710
$243$	13.1791	0.845437
$244$	−7.64495	−0.489418
$245$	−1.51158	−0.0965711
$246$	−28.7498	−1.83302
$247$	−14.8388	−0.944171
$248$	29.7597	1.88974
$249$	8.38550	0.531409
$250$	7.95023	0.502817
$251$	16.7979	1.06028	0.530138	−	0.847911i	$-0.322140\pi$
$251$	16.7979	1.06028	0.530138	+	0.847911i	$0.322140\pi$
$252$	9.84918	0.620440
$253$	−6.87080	−0.431964
$254$	−31.1676	−1.95563
$255$	−1.47098	−0.0921166
$256$	−14.5830	−0.911435
$257$	16.7370	1.04402	0.522011	−	0.852939i	$-0.325182\pi$
$257$	16.7370	1.04402	0.522011	+	0.852939i	$0.325182\pi$
$258$	24.7951	1.54367
$259$	−4.90521	−0.304795
$260$	−4.76021	−0.295216
$261$	5.54994	0.343533
$262$	−47.1255	−2.91142
$263$	20.7574	1.27996	0.639978	−	0.768394i	$-0.278944\pi$
$263$	20.7574	1.27996	0.639978	+	0.768394i	$0.278944\pi$
$264$	−20.2002	−1.24323
$265$	−0.346927	−0.0213116
$266$	17.4677	1.07101
$267$	−10.7779	−0.659598
$268$	58.0201	3.54414
$269$	17.4002	1.06091	0.530455	−	0.847713i	$-0.322021\pi$
$269$	17.4002	1.06091	0.530455	+	0.847713i	$0.322021\pi$
$270$	4.46265	0.271588
$271$	7.29446	0.443107	0.221553	−	0.975148i	$-0.428887\pi$
$271$	7.29446	0.443107	0.221553	+	0.975148i	$0.428887\pi$
$272$	−37.4952	−2.27348
$273$	5.80161	0.351130
$274$	−21.4423	−1.29538
$275$	−10.5219	−0.634496
$276$	−19.6033	−1.17998
$277$	29.7651	1.78841	0.894206	−	0.447655i	$-0.147741\pi$
$277$	29.7651	1.78841	0.894206	+	0.447655i	$0.147741\pi$
$278$	2.00145	0.120039
$279$	5.61911	0.336407
$280$	3.29458	0.196889
$281$	8.47562	0.505613	0.252806	−	0.967517i	$-0.418646\pi$
$281$	8.47562	0.505613	0.252806	+	0.967517i	$0.418646\pi$
$282$	28.5620	1.70084
$283$	−1.62463	−0.0965742	−0.0482871	−	0.998833i	$-0.515376\pi$
$283$	−1.62463	−0.0965742	−0.0482871	+	0.998833i	$0.515376\pi$
$284$	73.5779	4.36605
$285$	1.79264	0.106187
$286$	17.9623	1.06213
$287$	−12.5304	−0.739649
$288$	15.3033	0.901756
$289$	−2.51355	−0.147856
$290$	3.15755	0.185418
$291$	−15.9516	−0.935101
$292$	1.74250	0.101972
$293$	−7.82481	−0.457130	−0.228565	−	0.973529i	$-0.573403\pi$
$293$	−7.82481	−0.457130	−0.228565	+	0.973529i	$0.573403\pi$
$294$	16.2738	0.949105
$295$	3.68007	0.214262
$296$	−25.4760	−1.48076
$297$	−11.9255	−0.691990
$298$	−35.1051	−2.03358
$299$	10.2488	0.592706
$300$	−30.0204	−1.73323
$301$	10.8068	0.622893
$302$	−0.0796962	−0.00458600
$303$	−7.99381	−0.459233
$304$	45.6942	2.62074
$305$	−0.482853	−0.0276481
$306$	−14.0560	−0.803530
$307$	−8.32610	−0.475195	−0.237598	−	0.971364i	$-0.576360\pi$
$307$	−8.32610	−0.475195	−0.237598	+	0.971364i	$0.576360\pi$
$308$	−14.9743	−0.853243
$309$	14.5293	0.826543
$310$	3.19691	0.181572
$311$	−17.8404	−1.01164	−0.505819	−	0.862640i	$-0.668810\pi$
$311$	−17.8404	−1.01164	−0.505819	+	0.862640i	$0.668810\pi$
$312$	30.1316	1.70586
$313$	−10.4731	−0.591973	−0.295986	−	0.955192i	$-0.595648\pi$
$313$	−10.4731	−0.591973	−0.295986	+	0.955192i	$0.595648\pi$
$314$	12.0901	0.682285
$315$	0.622071	0.0350497
$316$	−3.13577	−0.176401
$317$	11.8069	0.663143	0.331572	−	0.943430i	$-0.392421\pi$
$317$	11.8069	0.663143	0.331572	+	0.943430i	$0.392421\pi$
$318$	3.73505	0.209451
$319$	−8.43793	−0.472434
$320$	2.66652	0.149063
$321$	−14.0407	−0.783677
$322$	−12.0645	−0.672331
$323$	−17.6542	−0.982304
$324$	−13.4844	−0.749132
$325$	15.6950	0.870604
$326$	35.6618	1.97513
$327$	14.5178	0.802838
$328$	−65.0788	−3.59338
$329$	12.4486	0.686312
$330$	−2.16998	−0.119454
$331$	−8.82622	−0.485133	−0.242566	−	0.970135i	$-0.577989\pi$
$331$	−8.82622	−0.485133	−0.242566	+	0.970135i	$0.577989\pi$
$332$	32.2846	1.77185
$333$	−4.81028	−0.263602
$334$	−35.6295	−1.94956
$335$	3.66453	0.200215
$336$	−17.8653	−0.974633
$337$	−18.2774	−0.995633	−0.497817	−	0.867282i	$-0.665865\pi$
$337$	−18.2774	−0.995633	−0.497817	+	0.867282i	$0.665865\pi$
$338$	7.24002	0.393805
$339$	3.66708	0.199168
$340$	−5.66336	−0.307139
$341$	−8.54310	−0.462635
$342$	17.1296	0.926264
$343$	17.1622	0.926673
$344$	56.1268	3.02615
$345$	−1.23814	−0.0666590
$346$	46.7638	2.51404
$347$	12.1185	0.650555	0.325278	−	0.945619i	$-0.394542\pi$
$347$	12.1185	0.650555	0.325278	+	0.945619i	$0.394542\pi$
$348$	−24.0745	−1.29053
$349$	31.0920	1.66432	0.832158	−	0.554539i	$-0.187105\pi$
$349$	31.0920	1.66432	0.832158	+	0.554539i	$0.187105\pi$
$350$	−18.4756	−0.987563
$351$	17.7888	0.949493
$352$	−23.2666	−1.24011
$353$	5.14565	0.273876	0.136938	−	0.990580i	$-0.456274\pi$
$353$	5.14565	0.273876	0.136938	+	0.990580i	$0.456274\pi$
$354$	−39.6200	−2.10578
$355$	4.64716	0.246645
$356$	−41.4955	−2.19926
$357$	6.90235	0.365311
$358$	3.20890	0.169596
$359$	13.6632	0.721116	0.360558	−	0.932737i	$-0.382586\pi$
$359$	13.6632	0.721116	0.360558	+	0.932737i	$0.382586\pi$
$360$	3.23082	0.170279
$361$	2.51455	0.132345
$362$	−45.4181	−2.38712
$363$	−8.06881	−0.423502
$364$	22.3365	1.17075
$365$	0.110056	0.00576058
$366$	5.19843	0.271726
$367$	−24.2666	−1.26670	−0.633352	−	0.773864i	$-0.718322\pi$
$367$	−24.2666	−1.26670	−0.633352	+	0.773864i	$0.718322\pi$
$368$	−31.5600	−1.64518
$369$	−12.2879	−0.639685
$370$	−2.73673	−0.142276
$371$	1.62790	0.0845163
$372$	−24.3746	−1.26376
$373$	−4.97493	−0.257592	−0.128796	−	0.991671i	$-0.541111\pi$
$373$	−4.97493	−0.257592	−0.128796	+	0.991671i	$0.541111\pi$
$374$	21.3703	1.10503
$375$	−3.82848	−0.197702
$376$	64.6535	3.33425
$377$	12.5865	0.648235
$378$	−20.9403	−1.07705
$379$	−10.7244	−0.550876	−0.275438	−	0.961319i	$-0.588823\pi$
$379$	−10.7244	−0.550876	−0.275438	+	0.961319i	$0.588823\pi$
$380$	6.90175	0.354052
$381$	15.0090	0.768932
$382$	−21.0644	−1.07775
$383$	0.642144	0.0328120	0.0164060	−	0.999865i	$-0.494778\pi$
$383$	0.642144	0.0328120	0.0164060	+	0.999865i	$0.494778\pi$
$384$	−1.35481	−0.0691373
$385$	−0.945775	−0.0482011
$386$	5.02179	0.255602
$387$	10.5976	0.538709
$388$	−61.4145	−3.11785
$389$	−18.7104	−0.948654	−0.474327	−	0.880349i	$-0.657309\pi$
$389$	−18.7104	−0.948654	−0.474327	+	0.880349i	$0.657309\pi$
$390$	3.23686	0.163905
$391$	12.1933	0.616644
$392$	36.8377	1.86058
$393$	22.6935	1.14474
$394$	−10.4104	−0.524468
$395$	−0.198054	−0.00996520
$396$	−14.6845	−0.737926
$397$	−11.6015	−0.582261	−0.291130	−	0.956683i	$-0.594031\pi$
$397$	−11.6015	−0.582261	−0.291130	+	0.956683i	$0.594031\pi$
$398$	−8.92782	−0.447511
$399$	−8.41166	−0.421110
$400$	−48.3308	−2.41654
$401$	17.3902	0.868427	0.434213	−	0.900810i	$-0.357026\pi$
$401$	17.3902	0.868427	0.434213	+	0.900810i	$0.357026\pi$
$402$	−39.4526	−1.96772
$403$	12.7433	0.634790
$404$	−30.7766	−1.53119
$405$	−0.851669	−0.0423198
$406$	−14.8163	−0.735320
$407$	7.31338	0.362511
$408$	35.8484	1.77476
$409$	−2.54231	−0.125709	−0.0628545	−	0.998023i	$-0.520020\pi$
$409$	−2.54231	−0.125709	−0.0628545	+	0.998023i	$0.520020\pi$
$410$	−6.99104	−0.345263
$411$	10.3257	0.509327
$412$	55.9385	2.75589
$413$	−17.2681	−0.849710
$414$	−11.8311	−0.581465
$415$	2.03908	0.100095
$416$	34.7056	1.70158
$417$	−0.963810	−0.0471980
$418$	−26.0433	−1.27382
$419$	11.2979	0.551938	0.275969	−	0.961166i	$-0.411001\pi$
$419$	11.2979	0.551938	0.275969	+	0.961166i	$0.411001\pi$
$420$	−2.69842	−0.131669
$421$	−19.4419	−0.947539	−0.473769	−	0.880649i	$-0.657107\pi$
$421$	−19.4419	−0.947539	−0.473769	+	0.880649i	$0.657107\pi$
$422$	−29.1262	−1.41784
$423$	12.2076	0.593556
$424$	8.45474	0.410599
$425$	18.6728	0.905766
$426$	−50.0317	−2.42404
$427$	2.26571	0.109645
$428$	−54.0575	−2.61297
$429$	−8.64986	−0.417619
$430$	6.02937	0.290762
$431$	30.5031	1.46928	0.734641	−	0.678456i	$-0.237350\pi$
$431$	30.5031	1.46928	0.734641	+	0.678456i	$0.237350\pi$
$432$	−54.7781	−2.63551
$433$	−33.2187	−1.59639	−0.798194	−	0.602400i	$-0.794211\pi$
$433$	−33.2187	−1.59639	−0.798194	+	0.602400i	$0.794211\pi$
$434$	−15.0010	−0.720069
$435$	−1.52054	−0.0729042
$436$	55.8944	2.67685
$437$	−14.8596	−0.710832
$438$	−1.18487	−0.0566152
$439$	11.2379	0.536357	0.268179	−	0.963369i	$-0.413578\pi$
$439$	11.2379	0.536357	0.268179	+	0.963369i	$0.413578\pi$
$440$	−4.91203	−0.234172
$441$	6.95556	0.331217
$442$	−31.8770	−1.51624
$443$	20.1855	0.959042	0.479521	−	0.877530i	$-0.340810\pi$
$443$	20.1855	0.959042	0.479521	+	0.877530i	$0.340810\pi$
$444$	20.8660	0.990257
$445$	−2.62084	−0.124240
$446$	3.79339	0.179622
$447$	16.9051	0.799582
$448$	−12.5122	−0.591146
$449$	−16.3341	−0.770854	−0.385427	−	0.922738i	$-0.625946\pi$
$449$	−16.3341	−0.770854	−0.385427	+	0.922738i	$0.625946\pi$
$450$	−18.1180	−0.854093
$451$	18.6822	0.879708
$452$	14.1184	0.664075
$453$	0.0383781	0.00180316
$454$	−42.7693	−2.00726
$455$	1.41077	0.0661377
$456$	−43.6873	−2.04584
$457$	−12.7483	−0.596341	−0.298170	−	0.954513i	$-0.596376\pi$
$457$	−12.7483	−0.596341	−0.298170	+	0.954513i	$0.596376\pi$
$458$	−2.16436	−0.101134
$459$	21.1638	0.987841
$460$	−4.76689	−0.222257
$461$	−17.1503	−0.798771	−0.399386	−	0.916783i	$-0.630777\pi$
$461$	−17.1503	−0.798771	−0.399386	+	0.916783i	$0.630777\pi$
$462$	10.1823	0.473723
$463$	−14.9112	−0.692983	−0.346492	−	0.938053i	$-0.612627\pi$
$463$	−14.9112	−0.692983	−0.346492	+	0.938053i	$0.612627\pi$
$464$	−38.7583	−1.79931
$465$	−1.53949	−0.0713921
$466$	−2.54155	−0.117735
$467$	−26.0415	−1.20506	−0.602528	−	0.798098i	$-0.705840\pi$
$467$	−26.0415	−1.20506	−0.602528	+	0.798098i	$0.705840\pi$
$468$	21.9042	1.01252
$469$	−17.1952	−0.794001
$470$	6.94535	0.320365
$471$	−5.82207	−0.268267
$472$	−89.6848	−4.12808
$473$	−16.1123	−0.740844
$474$	2.13227	0.0979384
$475$	−22.7560	−1.04412
$476$	26.5744	1.21803
$477$	1.59639	0.0730938
$478$	41.4779	1.89716
$479$	20.8625	0.953232	0.476616	−	0.879112i	$-0.341863\pi$
$479$	20.8625	0.953232	0.476616	+	0.879112i	$0.341863\pi$
$480$	−4.19270	−0.191370
$481$	−10.9090	−0.497408
$482$	6.75591	0.307723
$483$	5.80975	0.264353
$484$	−31.0653	−1.41206
$485$	−3.87892	−0.176133
$486$	−34.5023	−1.56506
$487$	28.6657	1.29897	0.649483	−	0.760376i	$-0.274985\pi$
$487$	28.6657	1.29897	0.649483	+	0.760376i	$0.274985\pi$
$488$	11.7673	0.532680
$489$	−17.1732	−0.776597
$490$	3.95726	0.178771
$491$	−29.8768	−1.34832	−0.674161	−	0.738585i	$-0.735494\pi$
$491$	−29.8768	−1.34832	−0.674161	+	0.738585i	$0.735494\pi$
$492$	53.3026	2.40307
$493$	14.9745	0.674416
$494$	38.8475	1.74783
$495$	−0.927471	−0.0416867
$496$	−39.2414	−1.76199
$497$	−21.8060	−0.978133
$498$	−21.9529	−0.983735
$499$	15.9901	0.715814	0.357907	−	0.933757i	$-0.383491\pi$
$499$	15.9901	0.715814	0.357907	+	0.933757i	$0.383491\pi$
$500$	−14.7398	−0.659185
$501$	17.1576	0.766545
$502$	−43.9764	−1.96276
$503$	−9.27556	−0.413577	−0.206788	−	0.978386i	$-0.566301\pi$
$503$	−9.27556	−0.413577	−0.206788	+	0.978386i	$0.566301\pi$
$504$	−15.1601	−0.675285
$505$	−1.94384	−0.0864997
$506$	17.9875	0.799643
$507$	−3.48647	−0.154840
$508$	57.7852	2.56380
$509$	−18.3968	−0.815425	−0.407713	−	0.913110i	$-0.633673\pi$
$509$	−18.3968	−0.815425	−0.407713	+	0.913110i	$0.633673\pi$
$510$	3.85098	0.170524
$511$	−0.516418	−0.0228450
$512$	40.3270	1.78222
$513$	−25.7916	−1.13873
$514$	−43.8168	−1.93267
$515$	3.53306	0.155685
$516$	−45.9704	−2.02373
$517$	−18.5601	−0.816271
$518$	12.8417	0.564231
$519$	−22.5194	−0.988492
$520$	7.32703	0.321312
$521$	−3.85217	−0.168766	−0.0843832	−	0.996433i	$-0.526892\pi$
$521$	−3.85217	−0.168766	−0.0843832	+	0.996433i	$0.526892\pi$
$522$	−14.5296	−0.635941
$523$	2.26358	0.0989795	0.0494898	−	0.998775i	$-0.484240\pi$
$523$	2.26358	0.0989795	0.0494898	+	0.998775i	$0.484240\pi$
$524$	87.3713	3.81683
$525$	8.89703	0.388298
$526$	−54.3421	−2.36943
$527$	15.1611	0.660428
$528$	26.6361	1.15919
$529$	−12.7368	−0.553773
$530$	0.908243	0.0394516
$531$	−16.9339	−0.734871
$532$	−32.3853	−1.40408
$533$	−27.8673	−1.20706
$534$	28.2162	1.22103
$535$	−3.41425	−0.147611
$536$	−89.3059	−3.85743
$537$	−1.54526	−0.0666830
$538$	−45.5532	−1.96394
$539$	−10.5750	−0.455497
$540$	−8.27381	−0.356048
$541$	−5.51425	−0.237076	−0.118538	−	0.992949i	$-0.537821\pi$
$541$	−5.51425	−0.237076	−0.118538	+	0.992949i	$0.537821\pi$
$542$	−19.0966	−0.820271
$543$	21.8713	0.938589
$544$	41.2903	1.77031
$545$	3.53027	0.151220
$546$	−15.1884	−0.650005
$547$	22.7586	0.973085	0.486543	−	0.873657i	$-0.338258\pi$
$547$	22.7586	0.973085	0.486543	+	0.873657i	$0.338258\pi$
$548$	39.7543	1.69822
$549$	2.22186	0.0948265
$550$	27.5460	1.17457
$551$	−18.2489	−0.777429
$552$	30.1738	1.28428
$553$	0.929337	0.0395194
$554$	−77.9240	−3.31068
$555$	1.31789	0.0559413
$556$	−3.71072	−0.157370
$557$	39.7440	1.68401	0.842003	−	0.539472i	$-0.181376\pi$
$557$	39.7440	1.68401	0.842003	+	0.539472i	$0.181376\pi$
$558$	−14.7106	−0.622751
$559$	24.0339	1.01653
$560$	−4.34427	−0.183579
$561$	−10.2910	−0.434486
$562$	−22.1889	−0.935981
$563$	1.77435	0.0747800	0.0373900	−	0.999301i	$-0.488096\pi$
$563$	1.77435	0.0747800	0.0373900	+	0.999301i	$0.488096\pi$
$564$	−52.9542	−2.22978
$565$	0.891715	0.0375147
$566$	4.25323	0.178776
$567$	3.99631	0.167829
$568$	−113.253	−4.75199
$569$	28.0634	1.17648	0.588240	−	0.808687i	$-0.299821\pi$
$569$	28.0634	1.17648	0.588240	+	0.808687i	$0.299821\pi$
$570$	−4.69307	−0.196571
$571$	−9.34358	−0.391017	−0.195508	−	0.980702i	$-0.562636\pi$
$571$	−9.34358	−0.391017	−0.195508	+	0.980702i	$0.562636\pi$
$572$	−33.3024	−1.39244
$573$	10.1437	0.423758
$574$	32.8043	1.36922
$575$	15.7171	0.655446
$576$	−12.2700	−0.511252
$577$	−2.10749	−0.0877361	−0.0438681	−	0.999037i	$-0.513968\pi$
$577$	−2.10749	−0.0877361	−0.0438681	+	0.999037i	$0.513968\pi$
$578$	6.58038	0.273708
$579$	−2.41827	−0.100500
$580$	−5.85414	−0.243080
$581$	−9.56806	−0.396950
$582$	41.7608	1.73104
$583$	−2.42710	−0.100520
$584$	−2.68210	−0.110986
$585$	1.38346	0.0571991
$586$	20.4851	0.846231
$587$	−32.0162	−1.32145	−0.660726	−	0.750628i	$-0.729751\pi$
$587$	−32.0162	−1.32145	−0.660726	+	0.750628i	$0.729751\pi$
$588$	−30.1718	−1.24426
$589$	−18.4763	−0.761304
$590$	−9.63431	−0.396638
$591$	5.01318	0.206215
$592$	33.5929	1.38066
$593$	21.4455	0.880663	0.440331	−	0.897835i	$-0.354861\pi$
$593$	21.4455	0.880663	0.440331	+	0.897835i	$0.354861\pi$
$594$	31.2207	1.28100
$595$	1.67843	0.0688089
$596$	65.0853	2.66600
$597$	4.29924	0.175956
$598$	−26.8311	−1.09721
$599$	−12.0350	−0.491737	−0.245869	−	0.969303i	$-0.579073\pi$
$599$	−12.0350	−0.491737	−0.245869	+	0.969303i	$0.579073\pi$
$600$	46.2081	1.88644
$601$	−43.5498	−1.77643	−0.888216	−	0.459426i	$-0.848055\pi$
$601$	−43.5498	−1.77643	−0.888216	+	0.459426i	$0.848055\pi$
$602$	−28.2918	−1.15309
$603$	−16.8624	−0.686691
$604$	0.147758	0.00601218
$605$	−1.96207	−0.0797697
$606$	20.9275	0.850123
$607$	45.0782	1.82967	0.914833	−	0.403831i	$-0.132322\pi$
$607$	45.0782	1.82967	0.914833	+	0.403831i	$0.132322\pi$
$608$	−50.3191	−2.04071
$609$	7.13487	0.289120
$610$	1.26409	0.0511816
$611$	27.6851	1.12002
$612$	26.0601	1.05342
$613$	0.144746	0.00584622	0.00292311	−	0.999996i	$-0.499070\pi$
$613$	0.144746	0.00584622	0.00292311	+	0.999996i	$0.499070\pi$
$614$	21.7974	0.879673
$615$	3.36657	0.135753
$616$	23.0489	0.928666
$617$	30.2069	1.21608	0.608041	−	0.793905i	$-0.291955\pi$
$617$	30.2069	1.21608	0.608041	+	0.793905i	$0.291955\pi$
$618$	−38.0372	−1.53008
$619$	−46.1879	−1.85645	−0.928224	−	0.372021i	$-0.878665\pi$
$619$	−46.1879	−1.85645	−0.928224	+	0.372021i	$0.878665\pi$
$620$	−5.92711	−0.238038
$621$	17.8137	0.714839
$622$	46.7056	1.87273
$623$	12.2979	0.492704
$624$	−39.7318	−1.59054
$625$	23.5991	0.943966
$626$	27.4181	1.09585
$627$	12.5413	0.500851
$628$	−22.4153	−0.894466
$629$	−12.9788	−0.517497
$630$	−1.62856	−0.0648834
$631$	−7.18123	−0.285880	−0.142940	−	0.989731i	$-0.545656\pi$
$631$	−7.18123	−0.285880	−0.142940	+	0.989731i	$0.545656\pi$
$632$	4.82666	0.191994
$633$	14.0259	0.557478
$634$	−30.9101	−1.22760
$635$	3.64970	0.144834
$636$	−6.92483	−0.274587
$637$	15.7742	0.624996
$638$	22.0902	0.874560
$639$	−21.3840	−0.845938
$640$	−0.329446	−0.0130225
$641$	−9.07665	−0.358506	−0.179253	−	0.983803i	$-0.557368\pi$
$641$	−9.07665	−0.358506	−0.179253	+	0.983803i	$0.557368\pi$
$642$	36.7581	1.45073
$643$	27.2560	1.07487	0.537435	−	0.843305i	$-0.319393\pi$
$643$	27.2560	1.07487	0.537435	+	0.843305i	$0.319393\pi$
$644$	22.3678	0.881416
$645$	−2.90348	−0.114324
$646$	46.2180	1.81842
$647$	2.28574	0.0898618	0.0449309	−	0.998990i	$-0.485693\pi$
$647$	2.28574	0.0898618	0.0449309	+	0.998990i	$0.485693\pi$
$648$	20.7555	0.815352
$649$	25.7458	1.01061
$650$	−41.0891	−1.61165
$651$	7.22380	0.283123
$652$	−66.1175	−2.58936
$653$	18.7175	0.732474	0.366237	−	0.930522i	$-0.380646\pi$
$653$	18.7175	0.732474	0.366237	+	0.930522i	$0.380646\pi$
$654$	−38.0072	−1.48620
$655$	5.51834	0.215619
$656$	85.8136	3.35046
$657$	−0.506424	−0.0197575
$658$	−32.5899	−1.27049
$659$	32.8968	1.28148	0.640740	−	0.767758i	$-0.278628\pi$
$659$	32.8968	1.28148	0.640740	+	0.767758i	$0.278628\pi$
$660$	4.02318	0.156602
$661$	14.8430	0.577327	0.288663	−	0.957431i	$-0.406789\pi$
$661$	14.8430	0.577327	0.288663	+	0.957431i	$0.406789\pi$
$662$	23.1067	0.898069
$663$	15.3506	0.596167
$664$	−49.6932	−1.92847
$665$	−2.04545	−0.0793190
$666$	12.5931	0.487974
$667$	12.6041	0.488033
$668$	66.0576	2.55585
$669$	−1.82673	−0.0706253
$670$	−9.59361	−0.370634
$671$	−3.37803	−0.130407
$672$	19.6736	0.758924
$673$	−40.3923	−1.55701	−0.778505	−	0.627639i	$-0.784021\pi$
$673$	−40.3923	−1.55701	−0.778505	+	0.627639i	$0.784021\pi$
$674$	47.8496	1.84310
$675$	27.2798	1.05000
$676$	−13.4231	−0.516273
$677$	−41.2475	−1.58527	−0.792635	−	0.609697i	$-0.791291\pi$
$677$	−41.2475	−1.58527	−0.792635	+	0.609697i	$0.791291\pi$
$678$	−9.60028	−0.368696
$679$	18.2012	0.698498
$680$	8.71718	0.334289
$681$	20.5958	0.789233
$682$	22.3655	0.856421
$683$	12.1394	0.464499	0.232250	−	0.972656i	$-0.425391\pi$
$683$	12.1394	0.464499	0.232250	+	0.972656i	$0.425391\pi$
$684$	−31.7586	−1.21432
$685$	2.51087	0.0959353
$686$	−44.9301	−1.71544
$687$	1.04226	0.0397647
$688$	−74.0093	−2.82158
$689$	3.62039	0.137926
$690$	3.24140	0.123398
$691$	1.24102	0.0472105	0.0236052	−	0.999721i	$-0.492486\pi$
$691$	1.24102	0.0472105	0.0236052	+	0.999721i	$0.492486\pi$
$692$	−86.7008	−3.29587
$693$	4.35200	0.165319
$694$	−31.7258	−1.20430
$695$	−0.234368	−0.00889007
$696$	37.0561	1.40461
$697$	−33.1545	−1.25582
$698$	−81.3977	−3.08095
$699$	1.22390	0.0462921
$700$	34.2540	1.29468
$701$	−25.3081	−0.955874	−0.477937	−	0.878394i	$-0.658615\pi$
$701$	−25.3081	−0.955874	−0.477937	+	0.878394i	$0.658615\pi$
$702$	−46.5703	−1.75768
$703$	15.8168	0.596541
$704$	18.6549	0.703085
$705$	−3.34457	−0.125964
$706$	−13.4711	−0.506993
$707$	9.12114	0.343036
$708$	73.4560	2.76064
$709$	8.94358	0.335883	0.167942	−	0.985797i	$-0.446288\pi$
$709$	8.94358	0.335883	0.167942	+	0.985797i	$0.446288\pi$
$710$	−12.1661	−0.456585
$711$	0.911352	0.0341784
$712$	63.8709	2.39366
$713$	12.7612	0.477910
$714$	−18.0701	−0.676257
$715$	−2.10337	−0.0786615
$716$	−5.94934	−0.222337
$717$	−19.9739	−0.745940
$718$	−35.7698	−1.33492
$719$	26.5539	0.990292	0.495146	−	0.868810i	$-0.335115\pi$
$719$	26.5539	0.990292	0.495146	+	0.868810i	$0.335115\pi$
$720$	−4.26019	−0.158768
$721$	−16.5783	−0.617408
$722$	−6.58299	−0.244994
$723$	−3.25335	−0.120993
$724$	84.2058	3.12948
$725$	19.3019	0.716854
$726$	21.1239	0.783980
$727$	−10.9201	−0.405005	−0.202503	−	0.979282i	$-0.564907\pi$
$727$	−10.9201	−0.405005	−0.202503	+	0.979282i	$0.564907\pi$
$728$	−34.3809	−1.27424
$729$	24.9492	0.924045
$730$	−0.288122	−0.0106639
$731$	28.5938	1.05758
$732$	−9.63796	−0.356229
$733$	−10.7268	−0.396204	−0.198102	−	0.980181i	$-0.563478\pi$
$733$	−10.7268	−0.396204	−0.198102	+	0.980181i	$0.563478\pi$
$734$	63.5290	2.34490
$735$	−1.90564	−0.0702906
$736$	34.7543	1.28106
$737$	25.6370	0.944352
$738$	32.1694	1.18417
$739$	−12.2472	−0.450520	−0.225260	−	0.974299i	$-0.572323\pi$
$739$	−12.2472	−0.450520	−0.225260	+	0.974299i	$0.572323\pi$
$740$	5.07394	0.186522
$741$	−18.7072	−0.687227
$742$	−4.26178	−0.156455
$743$	17.5079	0.642303	0.321151	−	0.947028i	$-0.395930\pi$
$743$	17.5079	0.642303	0.321151	+	0.947028i	$0.395930\pi$
$744$	37.5179	1.37547
$745$	4.11077	0.150607
$746$	13.0242	0.476850
$747$	−9.38289	−0.343302
$748$	−39.6208	−1.44868
$749$	16.0208	0.585388
$750$	10.0228	0.365982
$751$	51.1566	1.86673	0.933366	−	0.358927i	$-0.116857\pi$
$751$	51.1566	1.86673	0.933366	+	0.358927i	$0.116857\pi$
$752$	−85.2528	−3.10885
$753$	21.1771	0.771736
$754$	−32.9509	−1.20000
$755$	0.00933233	0.000339638 0
$756$	38.8235	1.41200
$757$	1.70821	0.0620860	0.0310430	−	0.999518i	$-0.490117\pi$
$757$	1.70821	0.0620860	0.0310430	+	0.999518i	$0.490117\pi$
$758$	28.0761	1.01977
$759$	−8.66199	−0.314410
$760$	−10.6233	−0.385349
$761$	−30.4614	−1.10422	−0.552112	−	0.833770i	$-0.686178\pi$
$761$	−30.4614	−1.10422	−0.552112	+	0.833770i	$0.686178\pi$
$762$	−39.2929	−1.42343
$763$	−16.5652	−0.599701
$764$	39.0536	1.41291
$765$	1.64595	0.0595093
$766$	−1.68111	−0.0607410
$767$	−38.4037	−1.38668
$768$	−18.3847	−0.663400
$769$	21.1952	0.764318	0.382159	−	0.924097i	$-0.375181\pi$
$769$	21.1952	0.764318	0.382159	+	0.924097i	$0.375181\pi$
$770$	2.47601	0.0892290
$771$	21.1002	0.759905
$772$	−9.31047	−0.335091
$773$	1.45276	0.0522520	0.0261260	−	0.999659i	$-0.491683\pi$
$773$	1.45276	0.0522520	0.0261260	+	0.999659i	$0.491683\pi$
$774$	−27.7443	−0.997247
$775$	19.5424	0.701986
$776$	94.5308	3.39346
$777$	−6.18398	−0.221849
$778$	48.9831	1.75613
$779$	40.4043	1.44763
$780$	−6.00118	−0.214877
$781$	32.5115	1.16335
$782$	−31.9217	−1.14152
$783$	21.8768	0.781811
$784$	−48.5745	−1.73480
$785$	−1.41574	−0.0505299
$786$	−59.4109	−2.11912
$787$	37.5672	1.33913	0.669563	−	0.742755i	$-0.266481\pi$
$787$	37.5672	1.33913	0.669563	+	0.742755i	$0.266481\pi$
$788$	19.3010	0.687569
$789$	26.1687	0.931632
$790$	0.518499	0.0184474
$791$	−4.18423	−0.148774
$792$	22.6028	0.803156
$793$	5.03885	0.178935
$794$	30.3722	1.07787
$795$	−0.437370	−0.0155119
$796$	16.5523	0.586680
$797$	32.1631	1.13927	0.569637	−	0.821896i	$-0.307084\pi$
$797$	32.1631	1.13927	0.569637	+	0.821896i	$0.307084\pi$
$798$	22.0214	0.779551
$799$	32.9378	1.16526
$800$	53.2227	1.88171
$801$	12.0599	0.426114
$802$	−45.5270	−1.60761
$803$	0.769949	0.0271709
$804$	73.1457	2.57965
$805$	1.41274	0.0497927
$806$	−33.3616	−1.17511
$807$	21.9364	0.772198
$808$	47.3721	1.66654
$809$	−29.5131	−1.03762	−0.518812	−	0.854888i	$-0.673625\pi$
$809$	−29.5131	−1.03762	−0.518812	+	0.854888i	$0.673625\pi$
$810$	2.22964	0.0783415
$811$	51.2879	1.80096	0.900481	−	0.434896i	$-0.143215\pi$
$811$	51.2879	1.80096	0.900481	+	0.434896i	$0.143215\pi$
$812$	27.4696	0.963994
$813$	9.19610	0.322521
$814$	−19.1462	−0.671073
$815$	−4.17596	−0.146277
$816$	−47.2701	−1.65478
$817$	−34.8464	−1.21912
$818$	6.65567	0.232710
$819$	−6.49167	−0.226837
$820$	12.9615	0.452634
$821$	−34.2790	−1.19634	−0.598172	−	0.801367i	$-0.704106\pi$
$821$	−34.2790	−1.19634	−0.598172	+	0.801367i	$0.704106\pi$
$822$	−27.0322	−0.942857
$823$	−4.33258	−0.151024	−0.0755122	−	0.997145i	$-0.524059\pi$
$823$	−4.33258	−0.151024	−0.0755122	+	0.997145i	$0.524059\pi$
$824$	−86.1019	−2.99950
$825$	−13.2649	−0.461826
$826$	45.2074	1.57297
$827$	27.7728	0.965755	0.482877	−	0.875688i	$-0.339592\pi$
$827$	27.7728	0.965755	0.482877	+	0.875688i	$0.339592\pi$
$828$	21.9349	0.762292
$829$	15.3857	0.534368	0.267184	−	0.963646i	$-0.413907\pi$
$829$	15.3857	0.534368	0.267184	+	0.963646i	$0.413907\pi$
$830$	−5.33825	−0.185293
$831$	37.5248	1.30172
$832$	−27.8267	−0.964716
$833$	18.7670	0.650238
$834$	2.52322	0.0873720
$835$	4.17218	0.144384
$836$	48.2846	1.66996
$837$	22.1494	0.765596
$838$	−29.5775	−1.02174
$839$	12.0889	0.417357	0.208678	−	0.977984i	$-0.433084\pi$
$839$	12.0889	0.417357	0.208678	+	0.977984i	$0.433084\pi$
$840$	4.15347	0.143308
$841$	−13.5211	−0.466244
$842$	50.8981	1.75407
$843$	10.6852	0.368017
$844$	54.0003	1.85877
$845$	−0.847798	−0.0291651
$846$	−31.9592	−1.09878
$847$	9.20671	0.316346
$848$	−11.1485	−0.382841
$849$	−2.04816	−0.0702928
$850$	−48.8849	−1.67674
$851$	−10.9243	−0.374480
$852$	92.7594	3.17788
$853$	−11.8908	−0.407132	−0.203566	−	0.979061i	$-0.565253\pi$
$853$	−11.8908	−0.407132	−0.203566	+	0.979061i	$0.565253\pi$
$854$	−5.93154	−0.202973
$855$	−2.00586	−0.0685990
$856$	83.2066	2.84394
$857$	24.0313	0.820894	0.410447	−	0.911884i	$-0.365373\pi$
$857$	24.0313	0.820894	0.410447	+	0.911884i	$0.365373\pi$
$858$	22.6450	0.773089
$859$	−44.1456	−1.50623	−0.753114	−	0.657890i	$-0.771449\pi$
$859$	−44.1456	−1.50623	−0.753114	+	0.657890i	$0.771449\pi$
$860$	−11.1785	−0.381185
$861$	−15.7971	−0.538363
$862$	−79.8561	−2.71991
$863$	8.85583	0.301456	0.150728	−	0.988575i	$-0.451838\pi$
$863$	8.85583	0.301456	0.150728	+	0.988575i	$0.451838\pi$
$864$	60.3226	2.05221
$865$	−5.47599	−0.186189
$866$	86.9654	2.95520
$867$	−3.16882	−0.107619
$868$	27.8120	0.944000
$869$	−1.38559	−0.0470028
$870$	3.98071	0.134959
$871$	−38.2415	−1.29576
$872$	−86.0339	−2.91348
$873$	17.8489	0.604095
$874$	38.9020	1.31588
$875$	4.36839	0.147678
$876$	2.19676	0.0742218
$877$	30.1102	1.01675	0.508374	−	0.861137i	$-0.330247\pi$
$877$	30.1102	1.01675	0.508374	+	0.861137i	$0.330247\pi$
$878$	−29.4205	−0.992894
$879$	−9.86471	−0.332728
$880$	6.47705	0.218341
$881$	−41.8158	−1.40881	−0.704405	−	0.709798i	$-0.748786\pi$
$881$	−41.8158	−1.40881	−0.704405	+	0.709798i	$0.748786\pi$
$882$	−18.2094	−0.613142
$883$	−47.6824	−1.60464	−0.802321	−	0.596893i	$-0.796402\pi$
$883$	−47.6824	−1.60464	−0.802321	+	0.596893i	$0.796402\pi$
$884$	59.1004	1.98776
$885$	4.63946	0.155954
$886$	−52.8450	−1.77536
$887$	44.2469	1.48566	0.742832	−	0.669477i	$-0.233482\pi$
$887$	44.2469	1.48566	0.742832	+	0.669477i	$0.233482\pi$
$888$	−32.1175	−1.07779
$889$	−17.1256	−0.574374
$890$	6.86128	0.229990
$891$	−5.95827	−0.199609
$892$	−7.03299	−0.235482
$893$	−40.1402	−1.34324
$894$	−44.2568	−1.48017
$895$	−0.375758	−0.0125602
$896$	1.54587	0.0516439
$897$	12.9207	0.431409
$898$	42.7621	1.42699
$899$	15.6718	0.522685
$900$	33.5911	1.11970
$901$	4.30728	0.143496
$902$	−48.9092	−1.62850
$903$	13.6241	0.453381
$904$	−21.7314	−0.722776
$905$	5.31841	0.176790
$906$	−0.100473	−0.00333798
$907$	−6.89056	−0.228797	−0.114399	−	0.993435i	$-0.536494\pi$
$907$	−6.89056	−0.228797	−0.114399	+	0.993435i	$0.536494\pi$
$908$	79.2949	2.63149
$909$	8.94462	0.296674
$910$	−3.69334	−0.122433
$911$	38.0127	1.25942	0.629708	−	0.776832i	$-0.283175\pi$
$911$	38.0127	1.25942	0.629708	+	0.776832i	$0.283175\pi$
$912$	57.6065	1.90754
$913$	14.2654	0.472116
$914$	33.3746	1.10393
$915$	−0.608730	−0.0201240
$916$	4.01276	0.132585
$917$	−25.8939	−0.855092
$918$	−55.4061	−1.82867
$919$	55.0205	1.81496	0.907480	−	0.420095i	$-0.138003\pi$
$919$	55.0205	1.81496	0.907480	+	0.420095i	$0.138003\pi$
$920$	7.33731	0.241904
$921$	−10.4967	−0.345877
$922$	44.8990	1.47867
$923$	−48.4958	−1.59626
$924$	−18.8781	−0.621044
$925$	−16.7294	−0.550061
$926$	39.0371	1.28284
$927$	−16.2574	−0.533965
$928$	42.6813	1.40108
$929$	37.1759	1.21970	0.609852	−	0.792516i	$-0.291229\pi$
$929$	37.1759	1.21970	0.609852	+	0.792516i	$0.291229\pi$
$930$	4.03033	0.132160
$931$	−22.8707	−0.749558
$932$	4.71207	0.154349
$933$	−22.4914	−0.736334
$934$	68.1757	2.23078
$935$	−2.50244	−0.0818385
$936$	−33.7155	−1.10203
$937$	−7.38376	−0.241217	−0.120608	−	0.992700i	$-0.538485\pi$
$937$	−7.38376	−0.241217	−0.120608	+	0.992700i	$0.538485\pi$
$938$	45.0164	1.46984
$939$	−13.2034	−0.430875
$940$	−12.8768	−0.419994
$941$	−24.9506	−0.813365	−0.406683	−	0.913570i	$-0.633314\pi$
$941$	−24.9506	−0.813365	−0.406683	+	0.913570i	$0.633314\pi$
$942$	15.2420	0.496610
$943$	−27.9063	−0.908755
$944$	118.259	3.84901
$945$	2.45208	0.0797661
$946$	42.1814	1.37144
$947$	31.9341	1.03772	0.518859	−	0.854860i	$-0.326357\pi$
$947$	31.9341	1.03772	0.518859	+	0.854860i	$0.326357\pi$
$948$	−3.95326	−0.128396
$949$	−1.14850	−0.0372817
$950$	59.5744	1.93285
$951$	14.8850	0.482678
$952$	−40.9039	−1.32570
$953$	−39.8078	−1.28950	−0.644750	−	0.764394i	$-0.723039\pi$
$953$	−39.8078	−1.28950	−0.644750	+	0.764394i	$0.723039\pi$
$954$	−4.17930	−0.135310
$955$	2.46661	0.0798177
$956$	−76.9006	−2.48714
$957$	−10.6377	−0.343867
$958$	−54.6173	−1.76460
$959$	−11.7818	−0.380455
$960$	3.36167	0.108497
$961$	−15.1328	−0.488156
$962$	28.5594	0.920792
$963$	15.7108	0.506272
$964$	−12.5256	−0.403421
$965$	−0.588046	−0.0189299
$966$	−15.2097	−0.489365
$967$	−26.9510	−0.866686	−0.433343	−	0.901229i	$-0.642666\pi$
$967$	−26.9510	−0.866686	−0.433343	+	0.901229i	$0.642666\pi$
$968$	47.8165	1.53688
$969$	−22.2565	−0.714983
$970$	10.1549	0.326054
$971$	−22.4582	−0.720719	−0.360359	−	0.932814i	$-0.617346\pi$
$971$	−22.4582	−0.720719	−0.360359	+	0.932814i	$0.617346\pi$
$972$	63.9678	2.05177
$973$	1.09973	0.0352558
$974$	−75.0457	−2.40462
$975$	19.7867	0.633681
$976$	−15.5165	−0.496670
$977$	19.9005	0.636674	0.318337	−	0.947978i	$-0.396876\pi$
$977$	19.9005	0.636674	0.318337	+	0.947978i	$0.396876\pi$
$978$	44.9587	1.43762
$979$	−18.3354	−0.586002
$980$	−7.33680	−0.234366
$981$	−16.2446	−0.518650
$982$	78.2164	2.49599
$983$	12.7730	0.407397	0.203698	−	0.979034i	$-0.434704\pi$
$983$	12.7730	0.407397	0.203698	+	0.979034i	$0.434704\pi$
$984$	−82.0446	−2.61549
$985$	1.21904	0.0388420
$986$	−39.2026	−1.24847
$987$	15.6939	0.499541
$988$	−72.0238	−2.29138
$989$	24.0676	0.765306
$990$	2.42809	0.0771696
$991$	57.5291	1.82747	0.913736	−	0.406307i	$-0.133184\pi$
$991$	57.5291	1.82747	0.913736	+	0.406307i	$0.133184\pi$
$992$	43.2132	1.37202
$993$	−11.1272	−0.353110
$994$	57.0874	1.81070
$995$	1.04544	0.0331426
$996$	40.7010	1.28966
$997$	19.0551	0.603481	0.301741	−	0.953390i	$-0.402432\pi$
$997$	19.0551	0.603481	0.301741	+	0.953390i	$0.402432\pi$
$998$	−41.8614	−1.32510
$999$	−18.9612	−0.599904

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8011.2.a.b.1.15	✓	358

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8011.2.a.b.1.15	✓	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)

\(f(q)\)	\(=\)	\(q-2.61797 q^{2} +1.26070 q^{3} +4.85374 q^{4} +0.306561 q^{5} -3.30046 q^{6} -1.43849 q^{7} -7.47100 q^{8} -1.41065 q^{9} +O(q^{10})\)	\(q-2.61797 q^{2} +1.26070 q^{3} +4.85374 q^{4} +0.306561 q^{5} -3.30046 q^{6} -1.43849 q^{7} -7.47100 q^{8} -1.41065 q^{9} -0.802565 q^{10} +2.14470 q^{11} +6.11909 q^{12} -3.19914 q^{13} +3.76591 q^{14} +0.386480 q^{15} +9.85133 q^{16} -3.80611 q^{17} +3.69302 q^{18} +4.63838 q^{19} +1.48797 q^{20} -1.81349 q^{21} -5.61474 q^{22} -3.20363 q^{23} -9.41866 q^{24} -4.90602 q^{25} +8.37523 q^{26} -5.56048 q^{27} -6.98204 q^{28} -3.93433 q^{29} -1.01179 q^{30} -3.98336 q^{31} -10.8484 q^{32} +2.70381 q^{33} +9.96426 q^{34} -0.440983 q^{35} -6.84691 q^{36} +3.40998 q^{37} -12.1431 q^{38} -4.03314 q^{39} -2.29031 q^{40} +8.71086 q^{41} +4.74766 q^{42} -7.51262 q^{43} +10.4098 q^{44} -0.432449 q^{45} +8.38698 q^{46} -8.65394 q^{47} +12.4195 q^{48} -4.93076 q^{49} +12.8438 q^{50} -4.79834 q^{51} -15.5278 q^{52} -1.13168 q^{53} +14.5572 q^{54} +0.657480 q^{55} +10.7469 q^{56} +5.84758 q^{57} +10.2999 q^{58} +12.0044 q^{59} +1.87587 q^{60} -1.57506 q^{61} +10.4283 q^{62} +2.02919 q^{63} +8.69818 q^{64} -0.980730 q^{65} -7.07848 q^{66} +11.9537 q^{67} -18.4739 q^{68} -4.03880 q^{69} +1.15448 q^{70} +15.1590 q^{71} +10.5389 q^{72} +0.359001 q^{73} -8.92722 q^{74} -6.18500 q^{75} +22.5135 q^{76} -3.08511 q^{77} +10.5586 q^{78} -0.646053 q^{79} +3.02003 q^{80} -2.77814 q^{81} -22.8047 q^{82} +6.65148 q^{83} -8.80223 q^{84} -1.16680 q^{85} +19.6678 q^{86} -4.95999 q^{87} -16.0230 q^{88} -8.54918 q^{89} +1.13214 q^{90} +4.60191 q^{91} -15.5496 q^{92} -5.02181 q^{93} +22.6557 q^{94} +1.42194 q^{95} -13.6766 q^{96} -12.6530 q^{97} +12.9086 q^{98} -3.02541 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 358 q + 33 q^{2} + 11 q^{3} + 391 q^{4} + 76 q^{5} + 32 q^{6} + 19 q^{7} + 99 q^{8} + 451 q^{9}+O(q^{10}) \) 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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