LMFDB - Embedded newform 4021.2.a.b.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4021,2,Mod(1,4021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4021, 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("4021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4021 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4021.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.1078466528$
Analytic rank:	$1$
Dimension:	$151$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	4021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.38084 q^{2} +2.66837 q^{3} +3.66838 q^{4} -4.16670 q^{5} -6.35294 q^{6} +0.560262 q^{7} -3.97213 q^{8} +4.12018 q^{9} +O(q^{10})$	\(q-2.38084 q^{2} +2.66837 q^{3} +3.66838 q^{4} -4.16670 q^{5} -6.35294 q^{6} +0.560262 q^{7} -3.97213 q^{8} +4.12018 q^{9} +9.92023 q^{10} -1.82936 q^{11} +9.78858 q^{12} +1.30969 q^{13} -1.33389 q^{14} -11.1183 q^{15} +2.12024 q^{16} -4.02107 q^{17} -9.80948 q^{18} +5.81746 q^{19} -15.2850 q^{20} +1.49498 q^{21} +4.35541 q^{22} -5.24785 q^{23} -10.5991 q^{24} +12.3614 q^{25} -3.11816 q^{26} +2.98906 q^{27} +2.05525 q^{28} +3.27096 q^{29} +26.4708 q^{30} +2.14223 q^{31} +2.89633 q^{32} -4.88141 q^{33} +9.57351 q^{34} -2.33444 q^{35} +15.1144 q^{36} +2.43535 q^{37} -13.8504 q^{38} +3.49474 q^{39} +16.5507 q^{40} -4.46905 q^{41} -3.55931 q^{42} +1.06332 q^{43} -6.71079 q^{44} -17.1676 q^{45} +12.4943 q^{46} +8.35299 q^{47} +5.65757 q^{48} -6.68611 q^{49} -29.4305 q^{50} -10.7297 q^{51} +4.80444 q^{52} -0.265567 q^{53} -7.11647 q^{54} +7.62241 q^{55} -2.22543 q^{56} +15.5231 q^{57} -7.78761 q^{58} -10.8592 q^{59} -40.7861 q^{60} -0.768975 q^{61} -5.10030 q^{62} +2.30838 q^{63} -11.1362 q^{64} -5.45709 q^{65} +11.6218 q^{66} -3.01625 q^{67} -14.7508 q^{68} -14.0032 q^{69} +5.55792 q^{70} +9.16272 q^{71} -16.3659 q^{72} -6.34436 q^{73} -5.79817 q^{74} +32.9848 q^{75} +21.3406 q^{76} -1.02492 q^{77} -8.32039 q^{78} -10.4576 q^{79} -8.83440 q^{80} -4.38463 q^{81} +10.6401 q^{82} +3.79116 q^{83} +5.48416 q^{84} +16.7546 q^{85} -2.53158 q^{86} +8.72812 q^{87} +7.26647 q^{88} +9.92127 q^{89} +40.8732 q^{90} +0.733770 q^{91} -19.2511 q^{92} +5.71626 q^{93} -19.8871 q^{94} -24.2396 q^{95} +7.72847 q^{96} +0.579578 q^{97} +15.9185 q^{98} -7.53731 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 151 q - 16 q^{2} - 29 q^{3} + 120 q^{4} - 27 q^{5} - 18 q^{6} - 18 q^{7} - 48 q^{8} + 98 q^{9}+O(q^{10}) $ 151 * q - 16 * q^2 - 29 * q^3 + 120 * q^4 - 27 * q^5 - 18 * q^6 - 18 * q^7 - 48 * q^8 + 98 * q^9	\( 151 q - 16 q^{2} - 29 q^{3} + 120 q^{4} - 27 q^{5} - 18 q^{6} - 18 q^{7} - 48 q^{8} + 98 q^{9} - 7 q^{10} - 126 q^{11} - 47 q^{12} - 10 q^{13} - 58 q^{14} - 50 q^{15} + 74 q^{16} - 39 q^{17} - 47 q^{18} - 48 q^{19} - 64 q^{20} - 50 q^{21} - 7 q^{22} - 91 q^{23} - 44 q^{24} + 102 q^{25} - 94 q^{26} - 92 q^{27} - 27 q^{28} - 79 q^{29} - 12 q^{30} - 33 q^{31} - 102 q^{32} - 7 q^{33} - 17 q^{34} - 183 q^{35} - 6 q^{36} - 24 q^{37} - 77 q^{38} - 81 q^{39} - 37 q^{40} - 62 q^{41} + 4 q^{42} - 74 q^{43} - 209 q^{44} - 35 q^{45} - 37 q^{46} - 127 q^{47} - 59 q^{48} + 75 q^{49} - 79 q^{50} - 138 q^{51} - 12 q^{52} - 104 q^{53} - 43 q^{54} - 49 q^{55} - 167 q^{56} - 19 q^{57} - 32 q^{58} - 207 q^{59} - 94 q^{60} - 57 q^{61} - 69 q^{62} - 49 q^{63} - 4 q^{64} - 78 q^{65} - 51 q^{66} - 92 q^{67} - 80 q^{68} - 84 q^{69} + 5 q^{70} - 217 q^{71} - 79 q^{72} + 2 q^{73} - 113 q^{74} - 173 q^{75} - 70 q^{76} - 85 q^{77} - 46 q^{78} - 70 q^{79} - 95 q^{80} - 49 q^{81} - 12 q^{82} - 109 q^{83} - 114 q^{84} - 25 q^{85} - 136 q^{86} - 60 q^{87} - 2 q^{88} - 144 q^{89} - 55 q^{90} - 62 q^{91} - 175 q^{92} - 42 q^{93} - 15 q^{94} - 189 q^{95} - 64 q^{96} - 24 q^{97} - 37 q^{98} - 293 q^{99}+O(q^{100}) \) 151 * q - 16 * q^2 - 29 * q^3 + 120 * q^4 - 27 * q^5 - 18 * q^6 - 18 * q^7 - 48 * q^8 + 98 * q^9 - 7 * q^10 - 126 * q^11 - 47 * q^12 - 10 * q^13 - 58 * q^14 - 50 * q^15 + 74 * q^16 - 39 * q^17 - 47 * q^18 - 48 * q^19 - 64 * q^20 - 50 * q^21 - 7 * q^22 - 91 * q^23 - 44 * q^24 + 102 * q^25 - 94 * q^26 - 92 * q^27 - 27 * q^28 - 79 * q^29 - 12 * q^30 - 33 * q^31 - 102 * q^32 - 7 * q^33 - 17 * q^34 - 183 * q^35 - 6 * q^36 - 24 * q^37 - 77 * q^38 - 81 * q^39 - 37 * q^40 - 62 * q^41 + 4 * q^42 - 74 * q^43 - 209 * q^44 - 35 * q^45 - 37 * q^46 - 127 * q^47 - 59 * q^48 + 75 * q^49 - 79 * q^50 - 138 * q^51 - 12 * q^52 - 104 * q^53 - 43 * q^54 - 49 * q^55 - 167 * q^56 - 19 * q^57 - 32 * q^58 - 207 * q^59 - 94 * q^60 - 57 * q^61 - 69 * q^62 - 49 * q^63 - 4 * q^64 - 78 * q^65 - 51 * q^66 - 92 * q^67 - 80 * q^68 - 84 * q^69 + 5 * q^70 - 217 * q^71 - 79 * q^72 + 2 * q^73 - 113 * q^74 - 173 * q^75 - 70 * q^76 - 85 * q^77 - 46 * q^78 - 70 * q^79 - 95 * q^80 - 49 * q^81 - 12 * q^82 - 109 * q^83 - 114 * q^84 - 25 * q^85 - 136 * q^86 - 60 * q^87 - 2 * q^88 - 144 * q^89 - 55 * q^90 - 62 * q^91 - 175 * q^92 - 42 * q^93 - 15 * q^94 - 189 * q^95 - 64 * q^96 - 24 * q^97 - 37 * q^98 - 293 * 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 $

$2$	−2.38084	−1.68350	−0.841752	−	0.539864i	$-0.818476\pi$
$2$	−2.38084	−1.68350	−0.841752	+	0.539864i	$0.818476\pi$
$3$	2.66837	1.54058	0.770291	−	0.637692i	$-0.220111\pi$
$3$	2.66837	1.54058	0.770291	+	0.637692i	$0.220111\pi$
$4$	3.66838	1.83419
$5$	−4.16670	−1.86341	−0.931703	−	0.363221i	$-0.881677\pi$
$5$	−4.16670	−1.86341	−0.931703	+	0.363221i	$0.881677\pi$
$6$	−6.35294	−2.59358
$7$	0.560262	0.211759	0.105879	−	0.994379i	$-0.466234\pi$
$7$	0.560262	0.211759	0.105879	+	0.994379i	$0.466234\pi$
$8$	−3.97213	−1.40436
$9$	4.12018	1.37339
$10$	9.92023	3.13705
$11$	−1.82936	−0.551574	−0.275787	−	0.961219i	$-0.588938\pi$
$11$	−1.82936	−0.551574	−0.275787	+	0.961219i	$0.588938\pi$
$12$	9.78858	2.82572
$13$	1.30969	0.363243	0.181622	−	0.983369i	$-0.441865\pi$
$13$	1.30969	0.363243	0.181622	+	0.983369i	$0.441865\pi$
$14$	−1.33389	−0.356497
$15$	−11.1183	−2.87073
$16$	2.12024	0.530059
$17$	−4.02107	−0.975254	−0.487627	−	0.873052i	$-0.662137\pi$
$17$	−4.02107	−0.975254	−0.487627	+	0.873052i	$0.662137\pi$
$18$	−9.80948	−2.31212
$19$	5.81746	1.33462	0.667308	−	0.744781i	$-0.267446\pi$
$19$	5.81746	1.33462	0.667308	+	0.744781i	$0.267446\pi$
$20$	−15.2850	−3.41784
$21$	1.49498	0.326232
$22$	4.35541	0.928577
$23$	−5.24785	−1.09425	−0.547126	−	0.837050i	$-0.684278\pi$
$23$	−5.24785	−1.09425	−0.547126	+	0.837050i	$0.684278\pi$
$24$	−10.5991	−2.16353
$25$	12.3614	2.47228
$26$	−3.11816	−0.611521
$27$	2.98906	0.575246
$28$	2.05525	0.388406
$29$	3.27096	0.607402	0.303701	−	0.952767i	$-0.401778\pi$
$29$	3.27096	0.607402	0.303701	+	0.952767i	$0.401778\pi$
$30$	26.4708	4.83289
$31$	2.14223	0.384756	0.192378	−	0.981321i	$-0.438380\pi$
$31$	2.14223	0.384756	0.192378	+	0.981321i	$0.438380\pi$
$32$	2.89633	0.512003
$33$	−4.88141	−0.849745
$34$	9.57351	1.64184
$35$	−2.33444	−0.394593
$36$	15.1144	2.51907
$37$	2.43535	0.400369	0.200184	−	0.979758i	$-0.435846\pi$
$37$	2.43535	0.400369	0.200184	+	0.979758i	$0.435846\pi$
$38$	−13.8504	−2.24683
$39$	3.49474	0.559606
$40$	16.5507	2.61689
$41$	−4.46905	−0.697948	−0.348974	−	0.937132i	$-0.613470\pi$
$41$	−4.46905	−0.697948	−0.348974	+	0.937132i	$0.613470\pi$
$42$	−3.55931	−0.549213
$43$	1.06332	0.162154	0.0810772	−	0.996708i	$-0.474164\pi$
$43$	1.06332	0.162154	0.0810772	+	0.996708i	$0.474164\pi$
$44$	−6.71079	−1.01169
$45$	−17.1676	−2.55919
$46$	12.4943	1.84218
$47$	8.35299	1.21841	0.609205	−	0.793013i	$-0.291489\pi$
$47$	8.35299	1.21841	0.609205	+	0.793013i	$0.291489\pi$
$48$	5.65757	0.816600
$49$	−6.68611	−0.955158
$50$	−29.4305	−4.16210
$51$	−10.7297	−1.50246
$52$	4.80444	0.666256
$53$	−0.265567	−0.0364784	−0.0182392	−	0.999834i	$-0.505806\pi$
$53$	−0.265567	−0.0364784	−0.0182392	+	0.999834i	$0.505806\pi$
$54$	−7.11647	−0.968429
$55$	7.62241	1.02781
$56$	−2.22543	−0.297386
$57$	15.5231	2.05609
$58$	−7.78761	−1.02256
$59$	−10.8592	−1.41375	−0.706875	−	0.707338i	$-0.749896\pi$
$59$	−10.8592	−1.41375	−0.706875	+	0.707338i	$0.749896\pi$
$60$	−40.7861	−5.26546
$61$	−0.768975	−0.0984571	−0.0492286	−	0.998788i	$-0.515676\pi$
$61$	−0.768975	−0.0984571	−0.0492286	+	0.998788i	$0.515676\pi$
$62$	−5.10030	−0.647739
$63$	2.30838	0.290829
$64$	−11.1362	−1.39202
$65$	−5.45709	−0.676869
$66$	11.6218	1.43055
$67$	−3.01625	−0.368493	−0.184247	−	0.982880i	$-0.558984\pi$
$67$	−3.01625	−0.368493	−0.184247	+	0.982880i	$0.558984\pi$
$68$	−14.7508	−1.78880
$69$	−14.0032	−1.68579
$70$	5.55792	0.664299
$71$	9.16272	1.08741	0.543707	−	0.839275i	$-0.317020\pi$
$71$	9.16272	1.08741	0.543707	+	0.839275i	$0.317020\pi$
$72$	−16.3659	−1.92874
$73$	−6.34436	−0.742551	−0.371275	−	0.928523i	$-0.621079\pi$
$73$	−6.34436	−0.742551	−0.371275	+	0.928523i	$0.621079\pi$
$74$	−5.79817	−0.674023
$75$	32.9848	3.80875
$76$	21.3406	2.44794
$77$	−1.02492	−0.116801
$78$	−8.32039	−0.942099
$79$	−10.4576	−1.17657	−0.588284	−	0.808654i	$-0.700196\pi$
$79$	−10.4576	−1.17657	−0.588284	+	0.808654i	$0.700196\pi$
$80$	−8.83440	−0.987715
$81$	−4.38463	−0.487182
$82$	10.6401	1.17500
$83$	3.79116	0.416134	0.208067	−	0.978115i	$-0.433283\pi$
$83$	3.79116	0.416134	0.208067	+	0.978115i	$0.433283\pi$
$84$	5.48416	0.598371
$85$	16.7546	1.81729
$86$	−2.53158	−0.272988
$87$	8.72812	0.935752
$88$	7.26647	0.774608
$89$	9.92127	1.05165	0.525826	−	0.850592i	$-0.323756\pi$
$89$	9.92127	1.05165	0.525826	+	0.850592i	$0.323756\pi$
$90$	40.8732	4.30841
$91$	0.733770	0.0769200
$92$	−19.2511	−2.00706
$93$	5.71626	0.592749
$94$	−19.8871	−2.05120
$95$	−24.2396	−2.48693
$96$	7.72847	0.788783
$97$	0.579578	0.0588472	0.0294236	−	0.999567i	$-0.490633\pi$
$97$	0.579578	0.0588472	0.0294236	+	0.999567i	$0.490633\pi$
$98$	15.9185	1.60801
$99$	−7.53731	−0.757528
$100$	45.3463	4.53463
$101$	6.41810	0.638625	0.319312	−	0.947650i	$-0.396548\pi$
$101$	6.41810	0.638625	0.319312	+	0.947650i	$0.396548\pi$
$102$	25.5457	2.52940
$103$	−0.374609	−0.0369114	−0.0184557	−	0.999830i	$-0.505875\pi$
$103$	−0.374609	−0.0369114	−0.0184557	+	0.999830i	$0.505875\pi$
$104$	−5.20227	−0.510124
$105$	−6.22915	−0.607903
$106$	0.632271	0.0614115
$107$	−6.37575	−0.616367	−0.308184	−	0.951327i	$-0.599721\pi$
$107$	−6.37575	−0.616367	−0.308184	+	0.951327i	$0.599721\pi$
$108$	10.9650	1.05511
$109$	4.75260	0.455216	0.227608	−	0.973753i	$-0.426910\pi$
$109$	4.75260	0.455216	0.227608	+	0.973753i	$0.426910\pi$
$110$	−18.1477	−1.73032
$111$	6.49841	0.616801
$112$	1.18789	0.112245
$113$	9.30981	0.875794	0.437897	−	0.899025i	$-0.355724\pi$
$113$	9.30981	0.875794	0.437897	+	0.899025i	$0.355724\pi$
$114$	−36.9580	−3.46143
$115$	21.8662	2.03904
$116$	11.9991	1.11409
$117$	5.39617	0.498876
$118$	25.8540	2.38006
$119$	−2.25285	−0.206519
$120$	44.1633	4.03154
$121$	−7.65343	−0.695766
$122$	1.83080	0.165753
$123$	−11.9251	−1.07525
$124$	7.85852	0.705716
$125$	−30.6728	−2.74346
$126$	−5.49587	−0.489611
$127$	−18.9546	−1.68195	−0.840973	−	0.541077i	$-0.818017\pi$
$127$	−18.9546	−1.68195	−0.840973	+	0.541077i	$0.818017\pi$
$128$	20.7207	1.83147
$129$	2.83732	0.249812
$130$	12.9924	1.13951
$131$	−12.6620	−1.10628	−0.553141	−	0.833088i	$-0.686571\pi$
$131$	−12.6620	−1.10628	−0.553141	+	0.833088i	$0.686571\pi$
$132$	−17.9069	−1.55859
$133$	3.25930	0.282617
$134$	7.18118	0.620360
$135$	−12.4545	−1.07192
$136$	15.9722	1.36961
$137$	−8.16415	−0.697510	−0.348755	−	0.937214i	$-0.613395\pi$
$137$	−8.16415	−0.697510	−0.348755	+	0.937214i	$0.613395\pi$
$138$	33.3393	2.83803
$139$	−15.2059	−1.28974	−0.644872	−	0.764291i	$-0.723089\pi$
$139$	−15.2059	−1.28974	−0.644872	+	0.764291i	$0.723089\pi$
$140$	−8.56362	−0.723758
$141$	22.2889	1.87706
$142$	−21.8149	−1.83067
$143$	−2.39590	−0.200355
$144$	8.73577	0.727980
$145$	−13.6291	−1.13184
$146$	15.1049	1.25009
$147$	−17.8410	−1.47150
$148$	8.93378	0.734352
$149$	0.612543	0.0501815	0.0250907	−	0.999685i	$-0.492013\pi$
$149$	0.612543	0.0501815	0.0250907	+	0.999685i	$0.492013\pi$
$150$	−78.5313	−6.41206
$151$	−18.2245	−1.48309	−0.741544	−	0.670904i	$-0.765906\pi$
$151$	−18.2245	−1.48309	−0.741544	+	0.670904i	$0.765906\pi$
$152$	−23.1077	−1.87428
$153$	−16.5676	−1.33941
$154$	2.44017	0.196635
$155$	−8.92605	−0.716957
$156$	12.8200	1.02642
$157$	−9.04275	−0.721690	−0.360845	−	0.932626i	$-0.617512\pi$
$157$	−9.04275	−0.721690	−0.360845	+	0.932626i	$0.617512\pi$
$158$	24.8977	1.98076
$159$	−0.708629	−0.0561980
$160$	−12.0681	−0.954070
$161$	−2.94017	−0.231718
$162$	10.4391	0.820172
$163$	−2.49413	−0.195356	−0.0976779	−	0.995218i	$-0.531141\pi$
$163$	−2.49413	−0.195356	−0.0976779	+	0.995218i	$0.531141\pi$
$164$	−16.3942	−1.28017
$165$	20.3394	1.58342
$166$	−9.02613	−0.700564
$167$	11.6705	0.903093	0.451546	−	0.892248i	$-0.350873\pi$
$167$	11.6705	0.903093	0.451546	+	0.892248i	$0.350873\pi$
$168$	−5.93827	−0.458148
$169$	−11.2847	−0.868055
$170$	−39.8900	−3.05942
$171$	23.9690	1.83296
$172$	3.90065	0.297422
$173$	−24.1908	−1.83919	−0.919596	−	0.392865i	$-0.871484\pi$
$173$	−24.1908	−1.83919	−0.919596	+	0.392865i	$0.871484\pi$
$174$	−20.7802	−1.57534
$175$	6.92562	0.523528
$176$	−3.87868	−0.292367
$177$	−28.9764	−2.17800
$178$	−23.6209	−1.77046
$179$	9.08790	0.679262	0.339631	−	0.940559i	$-0.389698\pi$
$179$	9.08790	0.679262	0.339631	+	0.940559i	$0.389698\pi$
$180$	−62.9772	−4.69404
$181$	18.4354	1.37029	0.685145	−	0.728407i	$-0.259739\pi$
$181$	18.4354	1.37029	0.685145	+	0.728407i	$0.259739\pi$
$182$	−1.74698	−0.129495
$183$	−2.05191	−0.151681
$184$	20.8451	1.53672
$185$	−10.1474	−0.746050
$186$	−13.6095	−0.997896
$187$	7.35600	0.537924
$188$	30.6419	2.23479
$189$	1.67466	0.121813
$190$	57.7106	4.18676
$191$	1.25751	0.0909900	0.0454950	−	0.998965i	$-0.485513\pi$
$191$	1.25751	0.0909900	0.0454950	+	0.998965i	$0.485513\pi$
$192$	−29.7154	−2.14452
$193$	−6.05436	−0.435802	−0.217901	−	0.975971i	$-0.569921\pi$
$193$	−6.05436	−0.435802	−0.217901	+	0.975971i	$0.569921\pi$
$194$	−1.37988	−0.0990695
$195$	−14.5615	−1.04277
$196$	−24.5272	−1.75194
$197$	20.5739	1.46583	0.732915	−	0.680320i	$-0.238159\pi$
$197$	20.5739	1.46583	0.732915	+	0.680320i	$0.238159\pi$
$198$	17.9451	1.27530
$199$	−13.8188	−0.979591	−0.489795	−	0.871837i	$-0.662928\pi$
$199$	−13.8188	−0.979591	−0.489795	+	0.871837i	$0.662928\pi$
$200$	−49.1011	−3.47197
$201$	−8.04845	−0.567694
$202$	−15.2804	−1.07513
$203$	1.83259	0.128623
$204$	−39.3606	−2.75579
$205$	18.6212	1.30056
$206$	0.891883	0.0621404
$207$	−21.6221	−1.50284
$208$	2.77686	0.192540
$209$	−10.6422	−0.736140
$210$	14.8306	1.02341
$211$	−12.0222	−0.827645	−0.413823	−	0.910358i	$-0.635807\pi$
$211$	−12.0222	−0.827645	−0.413823	+	0.910358i	$0.635807\pi$
$212$	−0.974199	−0.0669082
$213$	24.4495	1.67525
$214$	15.1796	1.03766
$215$	−4.43053	−0.302160
$216$	−11.8730	−0.807852
$217$	1.20021	0.0814756
$218$	−11.3151	−0.766359
$219$	−16.9291	−1.14396
$220$	27.9619	1.88519
$221$	−5.26636	−0.354254
$222$	−15.4716	−1.03839
$223$	24.7176	1.65521	0.827606	−	0.561309i	$-0.189702\pi$
$223$	24.7176	1.65521	0.827606	+	0.561309i	$0.189702\pi$
$224$	1.62270	0.108421
$225$	50.9313	3.39542
$226$	−22.1651	−1.47440
$227$	−24.0240	−1.59453	−0.797266	−	0.603629i	$-0.793721\pi$
$227$	−24.0240	−1.59453	−0.797266	+	0.603629i	$0.793721\pi$
$228$	56.9447	3.77125
$229$	−21.7159	−1.43503	−0.717514	−	0.696544i	$-0.754720\pi$
$229$	−21.7159	−1.43503	−0.717514	+	0.696544i	$0.754720\pi$
$230$	−52.0599	−3.43273
$231$	−2.73487	−0.179941
$232$	−12.9927	−0.853011
$233$	9.74286	0.638276	0.319138	−	0.947708i	$-0.396607\pi$
$233$	9.74286	0.638276	0.319138	+	0.947708i	$0.396607\pi$
$234$	−12.8474	−0.839860
$235$	−34.8044	−2.27039
$236$	−39.8357	−2.59308
$237$	−27.9046	−1.81260
$238$	5.36367	0.347675
$239$	−12.8171	−0.829068	−0.414534	−	0.910034i	$-0.636055\pi$
$239$	−12.8171	−0.829068	−0.414534	+	0.910034i	$0.636055\pi$
$240$	−23.5734	−1.52166
$241$	−12.3571	−0.795988	−0.397994	−	0.917388i	$-0.630293\pi$
$241$	−12.3571	−0.795988	−0.397994	+	0.917388i	$0.630293\pi$
$242$	18.2216	1.17133
$243$	−20.6670	−1.32579
$244$	−2.82089	−0.180589
$245$	27.8590	1.77985
$246$	28.3916	1.81018
$247$	7.61908	0.484790
$248$	−8.50923	−0.540337
$249$	10.1162	0.641089
$250$	73.0269	4.61863
$251$	16.8649	1.06450	0.532252	−	0.846586i	$-0.321346\pi$
$251$	16.8649	1.06450	0.532252	+	0.846586i	$0.321346\pi$
$252$	8.46801	0.533435
$253$	9.60022	0.603561
$254$	45.1277	2.83156
$255$	44.7075	2.79969
$256$	−27.0603	−1.69127
$257$	−3.47728	−0.216907	−0.108453	−	0.994102i	$-0.534590\pi$
$257$	−3.47728	−0.216907	−0.108453	+	0.994102i	$0.534590\pi$
$258$	−6.75520	−0.420560
$259$	1.36443	0.0847817
$260$	−20.0187	−1.24151
$261$	13.4769	0.834202
$262$	30.1461	1.86243
$263$	−23.8585	−1.47118	−0.735590	−	0.677427i	$-0.763095\pi$
$263$	−23.8585	−1.47118	−0.735590	+	0.677427i	$0.763095\pi$
$264$	19.3896	1.19335
$265$	1.10654	0.0679740
$266$	−7.75986	−0.475787
$267$	26.4736	1.62016
$268$	−11.0647	−0.675886
$269$	−29.1615	−1.77801	−0.889005	−	0.457898i	$-0.848603\pi$
$269$	−29.1615	−1.77801	−0.889005	+	0.457898i	$0.848603\pi$
$270$	29.6522	1.80458
$271$	6.14253	0.373132	0.186566	−	0.982442i	$-0.440264\pi$
$271$	6.14253	0.373132	0.186566	+	0.982442i	$0.440264\pi$
$272$	−8.52563	−0.516942
$273$	1.95797	0.118502
$274$	19.4375	1.17426
$275$	−22.6135	−1.36365
$276$	−51.3690	−3.09205
$277$	24.7645	1.48796	0.743979	−	0.668204i	$-0.232936\pi$
$277$	24.7645	1.48796	0.743979	+	0.668204i	$0.232936\pi$
$278$	36.2026	2.17129
$279$	8.82640	0.528422
$280$	9.27272	0.554151
$281$	30.0022	1.78978	0.894890	−	0.446286i	$-0.147254\pi$
$281$	30.0022	1.78978	0.894890	+	0.446286i	$0.147254\pi$
$282$	−53.0661	−3.16004
$283$	−7.65221	−0.454877	−0.227438	−	0.973792i	$-0.573035\pi$
$283$	−7.65221	−0.454877	−0.227438	+	0.973792i	$0.573035\pi$
$284$	33.6123	1.99452
$285$	−64.6802	−3.83133
$286$	5.70425	0.337299
$287$	−2.50384	−0.147797
$288$	11.9334	0.703183
$289$	−0.830968	−0.0488804
$290$	32.4487	1.90545
$291$	1.54653	0.0906590
$292$	−23.2735	−1.36198
$293$	20.0380	1.17063	0.585315	−	0.810806i	$-0.300971\pi$
$293$	20.0380	1.17063	0.585315	+	0.810806i	$0.300971\pi$
$294$	42.4765	2.47728
$295$	45.2471	2.63439
$296$	−9.67353	−0.562262
$297$	−5.46808	−0.317290
$298$	−1.45836	−0.0844808
$299$	−6.87306	−0.397479
$300$	121.001	6.98597
$301$	0.595736	0.0343377
$302$	43.3895	2.49679
$303$	17.1258	0.983854
$304$	12.3344	0.707426
$305$	3.20409	0.183466
$306$	39.4446	2.25490
$307$	3.32726	0.189897	0.0949485	−	0.995482i	$-0.469731\pi$
$307$	3.32726	0.189897	0.0949485	+	0.995482i	$0.469731\pi$
$308$	−3.75980	−0.214234
$309$	−0.999595	−0.0568650
$310$	21.2514	1.20700
$311$	−5.46479	−0.309880	−0.154940	−	0.987924i	$-0.549518\pi$
$311$	−5.46479	−0.309880	−0.154940	+	0.987924i	$0.549518\pi$
$312$	−13.8816	−0.785888
$313$	2.18662	0.123595	0.0617976	−	0.998089i	$-0.480317\pi$
$313$	2.18662	0.123595	0.0617976	+	0.998089i	$0.480317\pi$
$314$	21.5293	1.21497
$315$	−9.61834	−0.541932
$316$	−38.3623	−2.15805
$317$	−6.15646	−0.345781	−0.172891	−	0.984941i	$-0.555311\pi$
$317$	−6.15646	−0.345781	−0.172891	+	0.984941i	$0.555311\pi$
$318$	1.68713	0.0946096
$319$	−5.98377	−0.335027
$320$	46.4010	2.59390
$321$	−17.0129	−0.949565
$322$	7.00006	0.390098
$323$	−23.3924	−1.30159
$324$	−16.0845	−0.893583
$325$	16.1896	0.898039
$326$	5.93812	0.328882
$327$	12.6817	0.701298
$328$	17.7517	0.980171
$329$	4.67986	0.258009
$330$	−48.4247	−2.66569
$331$	−20.5437	−1.12919	−0.564593	−	0.825370i	$-0.690967\pi$
$331$	−20.5437	−1.12919	−0.564593	+	0.825370i	$0.690967\pi$
$332$	13.9074	0.763268
$333$	10.0341	0.549865
$334$	−27.7856	−1.52036
$335$	12.5678	0.686652
$336$	3.16972	0.172922
$337$	−15.1554	−0.825566	−0.412783	−	0.910829i	$-0.635443\pi$
$337$	−15.1554	−0.825566	−0.412783	+	0.910829i	$0.635443\pi$
$338$	26.8670	1.46137
$339$	24.8420	1.34923
$340$	61.4623	3.33326
$341$	−3.91892	−0.212222
$342$	−57.0663	−3.08579
$343$	−7.66780	−0.414022
$344$	−4.22364	−0.227723
$345$	58.3471	3.14130
$346$	57.5943	3.09629
$347$	−2.73738	−0.146950	−0.0734751	−	0.997297i	$-0.523409\pi$
$347$	−2.73738	−0.146950	−0.0734751	+	0.997297i	$0.523409\pi$
$348$	32.0180	1.71635
$349$	−28.3742	−1.51884	−0.759418	−	0.650603i	$-0.774516\pi$
$349$	−28.3742	−1.51884	−0.759418	+	0.650603i	$0.774516\pi$
$350$	−16.4888	−0.881362
$351$	3.91475	0.208954
$352$	−5.29844	−0.282408
$353$	−12.8986	−0.686524	−0.343262	−	0.939240i	$-0.611532\pi$
$353$	−12.8986	−0.686524	−0.343262	+	0.939240i	$0.611532\pi$
$354$	68.9880	3.66667
$355$	−38.1783	−2.02630
$356$	36.3950	1.92893
$357$	−6.01144	−0.318159
$358$	−21.6368	−1.14354
$359$	−6.66198	−0.351606	−0.175803	−	0.984425i	$-0.556252\pi$
$359$	−6.66198	−0.351606	−0.175803	+	0.984425i	$0.556252\pi$
$360$	68.1919	3.59403
$361$	14.8428	0.781203
$362$	−43.8916	−2.30689
$363$	−20.4222	−1.07189
$364$	2.69174	0.141086
$365$	26.4350	1.38367
$366$	4.88525	0.255356
$367$	−4.38158	−0.228717	−0.114358	−	0.993440i	$-0.536481\pi$
$367$	−4.38158	−0.228717	−0.114358	+	0.993440i	$0.536481\pi$
$368$	−11.1267	−0.580018
$369$	−18.4133	−0.958559
$370$	24.1592	1.25598
$371$	−0.148787	−0.00772463
$372$	20.9694	1.08721
$373$	34.2259	1.77215	0.886075	−	0.463542i	$-0.153422\pi$
$373$	34.2259	1.77215	0.886075	+	0.463542i	$0.153422\pi$
$374$	−17.5134	−0.905598
$375$	−81.8463	−4.22652
$376$	−33.1792	−1.71109
$377$	4.28394	0.220634
$378$	−3.98708	−0.205073
$379$	−20.3815	−1.04693	−0.523465	−	0.852047i	$-0.675361\pi$
$379$	−20.3815	−1.04693	−0.523465	+	0.852047i	$0.675361\pi$
$380$	−88.9201	−4.56150
$381$	−50.5777	−2.59118
$382$	−2.99392	−0.153182
$383$	−5.13673	−0.262475	−0.131237	−	0.991351i	$-0.541895\pi$
$383$	−5.13673	−0.262475	−0.131237	+	0.991351i	$0.541895\pi$
$384$	55.2904	2.82153
$385$	4.27054	0.217647
$386$	14.4144	0.733675
$387$	4.38106	0.222702
$388$	2.12611	0.107937
$389$	6.09040	0.308796	0.154398	−	0.988009i	$-0.450656\pi$
$389$	6.09040	0.308796	0.154398	+	0.988009i	$0.450656\pi$
$390$	34.6686	1.75551
$391$	21.1020	1.06717
$392$	26.5581	1.34139
$393$	−33.7868	−1.70432
$394$	−48.9831	−2.46773
$395$	43.5736	2.19242
$396$	−27.6497	−1.38945
$397$	23.4678	1.17782	0.588908	−	0.808200i	$-0.299558\pi$
$397$	23.4678	1.17782	0.588908	+	0.808200i	$0.299558\pi$
$398$	32.9003	1.64915
$399$	8.69701	0.435395
$400$	26.2091	1.31046
$401$	14.1673	0.707481	0.353741	−	0.935344i	$-0.384910\pi$
$401$	14.1673	0.707481	0.353741	+	0.935344i	$0.384910\pi$
$402$	19.1620	0.955715
$403$	2.80566	0.139760
$404$	23.5440	1.17136
$405$	18.2695	0.907817
$406$	−4.36310	−0.216537
$407$	−4.45514	−0.220833
$408$	42.6198	2.10999
$409$	−8.44876	−0.417764	−0.208882	−	0.977941i	$-0.566982\pi$
$409$	−8.44876	−0.417764	−0.208882	+	0.977941i	$0.566982\pi$
$410$	−44.3340	−2.18950
$411$	−21.7849	−1.07457
$412$	−1.37421	−0.0677024
$413$	−6.08400	−0.299374
$414$	51.4787	2.53004
$415$	−15.7966	−0.775427
$416$	3.79330	0.185982
$417$	−40.5748	−1.98696
$418$	25.3374	1.23929
$419$	8.55376	0.417879	0.208939	−	0.977929i	$-0.432999\pi$
$419$	8.55376	0.417879	0.208939	+	0.977929i	$0.432999\pi$
$420$	−22.8509	−1.11501
$421$	−14.5625	−0.709734	−0.354867	−	0.934917i	$-0.615474\pi$
$421$	−14.5625	−0.709734	−0.354867	+	0.934917i	$0.615474\pi$
$422$	28.6230	1.39334
$423$	34.4159	1.67336
$424$	1.05487	0.0512288
$425$	−49.7061	−2.41110
$426$	−58.2102	−2.82030
$427$	−0.430827	−0.0208492
$428$	−23.3887	−1.13053
$429$	−6.39314	−0.308664
$430$	10.5484	0.508687
$431$	−16.3159	−0.785909	−0.392955	−	0.919558i	$-0.628547\pi$
$431$	−16.3159	−0.785909	−0.392955	+	0.919558i	$0.628547\pi$
$432$	6.33752	0.304914
$433$	−8.60560	−0.413559	−0.206779	−	0.978388i	$-0.566298\pi$
$433$	−8.60560	−0.413559	−0.206779	+	0.978388i	$0.566298\pi$
$434$	−2.85750	−0.137165
$435$	−36.3675	−1.74369
$436$	17.4343	0.834952
$437$	−30.5292	−1.46041
$438$	40.3053	1.92586
$439$	34.5914	1.65096	0.825480	−	0.564432i	$-0.190905\pi$
$439$	34.5914	1.65096	0.825480	+	0.564432i	$0.190905\pi$
$440$	−30.2772	−1.44341
$441$	−27.5480	−1.31181
$442$	12.5383	0.596388
$443$	−18.8616	−0.896140	−0.448070	−	0.893998i	$-0.647889\pi$
$443$	−18.8616	−0.896140	−0.448070	+	0.893998i	$0.647889\pi$
$444$	23.8386	1.13133
$445$	−41.3390	−1.95966
$446$	−58.8485	−2.78656
$447$	1.63449	0.0773087
$448$	−6.23916	−0.294773
$449$	−25.4699	−1.20200	−0.601000	−	0.799249i	$-0.705231\pi$
$449$	−25.4699	−1.20200	−0.601000	+	0.799249i	$0.705231\pi$
$450$	−121.259	−5.71620
$451$	8.17552	0.384970
$452$	34.1519	1.60637
$453$	−48.6297	−2.28482
$454$	57.1973	2.68440
$455$	−3.05740	−0.143333
$456$	−61.6599	−2.88749
$457$	−19.4634	−0.910461	−0.455231	−	0.890374i	$-0.650443\pi$
$457$	−19.4634	−0.910461	−0.455231	+	0.890374i	$0.650443\pi$
$458$	51.7020	2.41588
$459$	−12.0192	−0.561010
$460$	80.2136	3.73998
$461$	16.2206	0.755471	0.377735	−	0.925914i	$-0.376703\pi$
$461$	16.2206	0.755471	0.377735	+	0.925914i	$0.376703\pi$
$462$	6.51127	0.302932
$463$	5.87666	0.273112	0.136556	−	0.990632i	$-0.456397\pi$
$463$	5.87666	0.273112	0.136556	+	0.990632i	$0.456397\pi$
$464$	6.93520	0.321959
$465$	−23.8180	−1.10453
$466$	−23.1962	−1.07454
$467$	−37.2094	−1.72184	−0.860922	−	0.508737i	$-0.830113\pi$
$467$	−37.2094	−1.72184	−0.860922	+	0.508737i	$0.830113\pi$
$468$	19.7952	0.915033
$469$	−1.68989	−0.0780317
$470$	82.8636	3.82222
$471$	−24.1294	−1.11182
$472$	43.1343	1.98541
$473$	−1.94519	−0.0894401
$474$	66.4363	3.05152
$475$	71.9120	3.29955
$476$	−8.26431	−0.378794
$477$	−1.09418	−0.0500992
$478$	30.5153	1.39574
$479$	21.9563	1.00321	0.501605	−	0.865097i	$-0.332743\pi$
$479$	21.9563	1.00321	0.501605	+	0.865097i	$0.332743\pi$
$480$	−32.2022	−1.46982
$481$	3.18956	0.145431
$482$	29.4201	1.34005
$483$	−7.84545	−0.356980
$484$	−28.0757	−1.27617
$485$	−2.41493	−0.109656
$486$	49.2047	2.23197
$487$	29.3037	1.32788	0.663939	−	0.747787i	$-0.268884\pi$
$487$	29.3037	1.32788	0.663939	+	0.747787i	$0.268884\pi$
$488$	3.05447	0.138269
$489$	−6.65527	−0.300962
$490$	−66.3277	−2.99638
$491$	6.45589	0.291350	0.145675	−	0.989332i	$-0.453465\pi$
$491$	6.45589	0.291350	0.145675	+	0.989332i	$0.453465\pi$
$492$	−43.7456	−1.97221
$493$	−13.1528	−0.592371
$494$	−18.1398	−0.816147
$495$	31.4057	1.41158
$496$	4.54204	0.203944
$497$	5.13352	0.230270
$498$	−24.0850	−1.07928
$499$	0.103492	0.00463294	0.00231647	−	0.999997i	$-0.499263\pi$
$499$	0.103492	0.00463294	0.00231647	+	0.999997i	$0.499263\pi$
$500$	−112.519	−5.03202
$501$	31.1413	1.39129
$502$	−40.1526	−1.79210
$503$	−0.466966	−0.0208210	−0.0104105	−	0.999946i	$-0.503314\pi$
$503$	−0.466966	−0.0208210	−0.0104105	+	0.999946i	$0.503314\pi$
$504$	−9.16919	−0.408428
$505$	−26.7423	−1.19002
$506$	−22.8565	−1.01610
$507$	−30.1117	−1.33731
$508$	−69.5325	−3.08501
$509$	−4.45931	−0.197656	−0.0988278	−	0.995105i	$-0.531509\pi$
$509$	−4.45931	−0.197656	−0.0988278	+	0.995105i	$0.531509\pi$
$510$	−106.441	−4.71329
$511$	−3.55450	−0.157242
$512$	22.9846	1.01579
$513$	17.3888	0.767732
$514$	8.27883	0.365164
$515$	1.56089	0.0687808
$516$	10.4084	0.458203
$517$	−15.2807	−0.672043
$518$	−3.24849	−0.142730
$519$	−64.5499	−2.83343
$520$	21.6763	0.950568
$521$	−26.6586	−1.16793	−0.583967	−	0.811777i	$-0.698500\pi$
$521$	−26.6586	−1.16793	−0.583967	+	0.811777i	$0.698500\pi$
$522$	−32.0864	−1.40438
$523$	−27.7048	−1.21145	−0.605724	−	0.795675i	$-0.707116\pi$
$523$	−27.7048	−1.21145	−0.605724	+	0.795675i	$0.707116\pi$
$524$	−46.4489	−2.02913
$525$	18.4801	0.806538
$526$	56.8032	2.47674
$527$	−8.61408	−0.375235
$528$	−10.3497	−0.450415
$529$	4.53992	0.197388
$530$	−2.63448	−0.114435
$531$	−44.7420	−1.94164
$532$	11.9563	0.518373
$533$	−5.85308	−0.253525
$534$	−63.0293	−2.72754
$535$	26.5659	1.14854
$536$	11.9809	0.517497
$537$	24.2499	1.04646
$538$	69.4288	2.99329
$539$	12.2313	0.526840
$540$	−45.6879	−1.96610
$541$	10.1376	0.435849	0.217925	−	0.975966i	$-0.430071\pi$
$541$	10.1376	0.435849	0.217925	+	0.975966i	$0.430071\pi$
$542$	−14.6243	−0.628169
$543$	49.1923	2.11104
$544$	−11.6463	−0.499333
$545$	−19.8027	−0.848252
$546$	−4.66160	−0.199498
$547$	15.4358	0.659987	0.329993	−	0.943983i	$-0.392953\pi$
$547$	15.4358	0.659987	0.329993	+	0.943983i	$0.392953\pi$
$548$	−29.9492	−1.27937
$549$	−3.16832	−0.135221
$550$	53.8390	2.29570
$551$	19.0287	0.810649
$552$	55.6225	2.36745
$553$	−5.85897	−0.249149
$554$	−58.9603	−2.50498
$555$	−27.0769	−1.14935
$556$	−55.7808	−2.36563
$557$	−27.9681	−1.18505	−0.592524	−	0.805553i	$-0.701869\pi$
$557$	−27.9681	−1.18505	−0.592524	+	0.805553i	$0.701869\pi$
$558$	−21.0142	−0.889602
$559$	1.39262	0.0589015
$560$	−4.94957	−0.209158
$561$	19.6285	0.828717
$562$	−71.4303	−3.01310
$563$	19.6267	0.827168	0.413584	−	0.910466i	$-0.364277\pi$
$563$	19.6267	0.827168	0.413584	+	0.910466i	$0.364277\pi$
$564$	81.7639	3.44288
$565$	−38.7912	−1.63196
$566$	18.2187	0.765787
$567$	−2.45654	−0.103165
$568$	−36.3955	−1.52712
$569$	22.1947	0.930451	0.465226	−	0.885192i	$-0.345973\pi$
$569$	22.1947	0.930451	0.465226	+	0.885192i	$0.345973\pi$
$570$	153.993	6.45006
$571$	25.8293	1.08092	0.540462	−	0.841368i	$-0.318249\pi$
$571$	25.8293	1.08092	0.540462	+	0.841368i	$0.318249\pi$
$572$	−8.78907	−0.367489
$573$	3.35549	0.140178
$574$	5.96122	0.248817
$575$	−64.8708	−2.70530
$576$	−45.8830	−1.91179
$577$	−5.64704	−0.235089	−0.117545	−	0.993068i	$-0.537502\pi$
$577$	−5.64704	−0.235089	−0.117545	+	0.993068i	$0.537502\pi$
$578$	1.97840	0.0822905
$579$	−16.1553	−0.671389
$580$	−49.9967	−2.07600
$581$	2.12404	0.0881201
$582$	−3.68202	−0.152625
$583$	0.485818	0.0201205
$584$	25.2006	1.04281
$585$	−22.4842	−0.929609
$586$	−47.7071	−1.97076
$587$	−19.0641	−0.786860	−0.393430	−	0.919355i	$-0.628712\pi$
$587$	−19.0641	−0.786860	−0.393430	+	0.919355i	$0.628712\pi$
$588$	−65.4475	−2.69901
$589$	12.4624	0.513502
$590$	−107.726	−4.43501
$591$	54.8988	2.25823
$592$	5.16352	0.212219
$593$	−10.2334	−0.420237	−0.210119	−	0.977676i	$-0.567385\pi$
$593$	−10.2334	−0.420237	−0.210119	+	0.977676i	$0.567385\pi$
$594$	13.0186	0.534160
$595$	9.38697	0.384828
$596$	2.24704	0.0920423
$597$	−36.8737	−1.50914
$598$	16.3636	0.669159
$599$	23.7118	0.968838	0.484419	−	0.874836i	$-0.339031\pi$
$599$	23.7118	0.968838	0.484419	+	0.874836i	$0.339031\pi$
$600$	−131.020	−5.34886
$601$	45.2643	1.84637	0.923184	−	0.384359i	$-0.125577\pi$
$601$	45.2643	1.84637	0.923184	+	0.384359i	$0.125577\pi$
$602$	−1.41835	−0.0578076
$603$	−12.4275	−0.506086
$604$	−66.8543	−2.72026
$605$	31.8896	1.29650
$606$	−40.7738	−1.65632
$607$	−15.0406	−0.610479	−0.305240	−	0.952276i	$-0.598737\pi$
$607$	−15.0406	−0.610479	−0.305240	+	0.952276i	$0.598737\pi$
$608$	16.8493	0.683328
$609$	4.89003	0.198154
$610$	−7.62841	−0.308865
$611$	10.9398	0.442579
$612$	−60.7761	−2.45673
$613$	−34.0823	−1.37657	−0.688286	−	0.725440i	$-0.741636\pi$
$613$	−34.0823	−1.37657	−0.688286	+	0.725440i	$0.741636\pi$
$614$	−7.92167	−0.319692
$615$	49.6882	2.00362
$616$	4.07112	0.164030
$617$	−48.4114	−1.94897	−0.974484	−	0.224455i	$-0.927940\pi$
$617$	−48.4114	−1.94897	−0.974484	+	0.224455i	$0.927940\pi$
$618$	2.37987	0.0957325
$619$	0.00242124	9.73180e−5 0	4.86590e−5	−	1.00000i	$-0.499985\pi$
$619$	0.00242124	9.73180e−5 0	4.86590e−5		1.00000i	$0.499985\pi$
$620$	−32.7441	−1.31504
$621$	−15.6862	−0.629464
$622$	13.0108	0.521684
$623$	5.55851	0.222697
$624$	7.40967	0.296624
$625$	65.9974	2.63990
$626$	−5.20598	−0.208073
$627$	−28.3974	−1.13408
$628$	−33.1722	−1.32372
$629$	−9.79272	−0.390461
$630$	22.8997	0.912345
$631$	22.2712	0.886604	0.443302	−	0.896372i	$-0.353807\pi$
$631$	22.2712	0.886604	0.443302	+	0.896372i	$0.353807\pi$
$632$	41.5388	1.65233
$633$	−32.0797	−1.27506
$634$	14.6575	0.582125
$635$	78.9780	3.13415
$636$	−2.59952	−0.103078
$637$	−8.75674	−0.346955
$638$	14.2464	0.564019
$639$	37.7521	1.49345
$640$	−86.3370	−3.41277
$641$	−13.0279	−0.514571	−0.257286	−	0.966335i	$-0.582828\pi$
$641$	−13.0279	−0.514571	−0.257286	+	0.966335i	$0.582828\pi$
$642$	40.5048	1.59860
$643$	32.5917	1.28529	0.642645	−	0.766164i	$-0.277837\pi$
$643$	32.5917	1.28529	0.642645	+	0.766164i	$0.277837\pi$
$644$	−10.7856	−0.425014
$645$	−11.8223	−0.465502
$646$	55.6935	2.19123
$647$	−12.9421	−0.508808	−0.254404	−	0.967098i	$-0.581879\pi$
$647$	−12.9421	−0.508808	−0.254404	+	0.967098i	$0.581879\pi$
$648$	17.4163	0.684179
$649$	19.8655	0.779787
$650$	−38.5448	−1.51185
$651$	3.20260	0.125520
$652$	−9.14943	−0.358319
$653$	−42.2076	−1.65171	−0.825856	−	0.563881i	$-0.809308\pi$
$653$	−42.2076	−1.65171	−0.825856	+	0.563881i	$0.809308\pi$
$654$	−30.1930	−1.18064
$655$	52.7587	2.06145
$656$	−9.47544	−0.369954
$657$	−26.1399	−1.01982
$658$	−11.1420	−0.434360
$659$	14.3099	0.557435	0.278718	−	0.960373i	$-0.410091\pi$
$659$	14.3099	0.557435	0.278718	+	0.960373i	$0.410091\pi$
$660$	74.6126	2.90429
$661$	−36.1449	−1.40587	−0.702937	−	0.711253i	$-0.748128\pi$
$661$	−36.1449	−1.40587	−0.702937	+	0.711253i	$0.748128\pi$
$662$	48.9113	1.90099
$663$	−14.0526	−0.545758
$664$	−15.0590	−0.584402
$665$	−13.5805	−0.526630
$666$	−23.8895	−0.925700
$667$	−17.1655	−0.664651
$668$	42.8119	1.65644
$669$	65.9556	2.54999
$670$	−29.9219	−1.15598
$671$	1.40673	0.0543064
$672$	4.32996	0.167032
$673$	−24.2053	−0.933044	−0.466522	−	0.884509i	$-0.654493\pi$
$673$	−24.2053	−0.933044	−0.466522	+	0.884509i	$0.654493\pi$
$674$	36.0825	1.38984
$675$	36.9490	1.42217
$676$	−41.3966	−1.59218
$677$	−9.22875	−0.354690	−0.177345	−	0.984149i	$-0.556751\pi$
$677$	−9.22875	−0.354690	−0.177345	+	0.984149i	$0.556751\pi$
$678$	−59.1447	−2.27144
$679$	0.324715	0.0124614
$680$	−66.5515	−2.55214
$681$	−64.1050	−2.45651
$682$	9.33031	0.357276
$683$	18.8516	0.721337	0.360668	−	0.932694i	$-0.382549\pi$
$683$	18.8516	0.721337	0.360668	+	0.932694i	$0.382549\pi$
$684$	87.9274	3.36199
$685$	34.0176	1.29974
$686$	18.2558	0.697008
$687$	−57.9461	−2.21078
$688$	2.25448	0.0859514
$689$	−0.347810	−0.0132505
$690$	−138.915	−5.28840
$691$	7.54841	0.287155	0.143578	−	0.989639i	$-0.454139\pi$
$691$	7.54841	0.287155	0.143578	+	0.989639i	$0.454139\pi$
$692$	−88.7410	−3.37343
$693$	−4.22287	−0.160413
$694$	6.51725	0.247391
$695$	63.3583	2.40332
$696$	−34.6692	−1.31413
$697$	17.9704	0.680677
$698$	67.5543	2.55697
$699$	25.9975	0.983317
$700$	25.4058	0.960249
$701$	−6.22755	−0.235211	−0.117606	−	0.993060i	$-0.537522\pi$
$701$	−6.22755	−0.235211	−0.117606	+	0.993060i	$0.537522\pi$
$702$	−9.32038	−0.351775
$703$	14.1675	0.534339
$704$	20.3721	0.767801
$705$	−92.8710	−3.49773
$706$	30.7095	1.15577
$707$	3.59581	0.135234
$708$	−106.296	−3.99486
$709$	19.5869	0.735601	0.367801	−	0.929905i	$-0.380111\pi$
$709$	19.5869	0.735601	0.367801	+	0.929905i	$0.380111\pi$
$710$	90.8963	3.41128
$711$	−43.0871	−1.61589
$712$	−39.4086	−1.47690
$713$	−11.2421	−0.421021
$714$	14.3122	0.535622
$715$	9.98301	0.373343
$716$	33.3379	1.24589
$717$	−34.2007	−1.27725
$718$	15.8611	0.591930
$719$	−44.1287	−1.64572	−0.822861	−	0.568242i	$-0.807624\pi$
$719$	−44.1287	−1.64572	−0.822861	+	0.568242i	$0.807624\pi$
$720$	−36.3993	−1.35652
$721$	−0.209879	−0.00781631
$722$	−35.3384	−1.31516
$723$	−32.9731	−1.22628
$724$	67.6279	2.51337
$725$	40.4336	1.50167
$726$	48.6218	1.80452
$727$	2.08144	0.0771962	0.0385981	−	0.999255i	$-0.487711\pi$
$727$	2.08144	0.0771962	0.0385981	+	0.999255i	$0.487711\pi$
$728$	−2.91463	−0.108023
$729$	−41.9933	−1.55531
$730$	−62.9375	−2.32942
$731$	−4.27568	−0.158142
$732$	−7.52717	−0.278212
$733$	30.1434	1.11337	0.556687	−	0.830723i	$-0.312072\pi$
$733$	30.1434	1.11337	0.556687	+	0.830723i	$0.312072\pi$
$734$	10.4318	0.385046
$735$	74.3381	2.74200
$736$	−15.1995	−0.560261
$737$	5.51781	0.203251
$738$	43.8391	1.61374
$739$	−30.5553	−1.12399	−0.561997	−	0.827139i	$-0.689967\pi$
$739$	−30.5553	−1.12399	−0.561997	+	0.827139i	$0.689967\pi$
$740$	−37.2244	−1.36840
$741$	20.3305	0.746859
$742$	0.354237	0.0130044
$743$	8.32637	0.305465	0.152733	−	0.988268i	$-0.451193\pi$
$743$	8.32637	0.305465	0.152733	+	0.988268i	$0.451193\pi$
$744$	−22.7058	−0.832433
$745$	−2.55228	−0.0935085
$746$	−81.4862	−2.98342
$747$	15.6203	0.571516
$748$	26.9846	0.986654
$749$	−3.57209	−0.130521
$750$	194.863	7.11538
$751$	10.6928	0.390186	0.195093	−	0.980785i	$-0.437499\pi$
$751$	10.6928	0.390186	0.195093	+	0.980785i	$0.437499\pi$
$752$	17.7103	0.645829
$753$	45.0018	1.63996
$754$	−10.1994	−0.371439
$755$	75.9361	2.76360
$756$	6.14327	0.223429
$757$	−6.33427	−0.230223	−0.115111	−	0.993353i	$-0.536723\pi$
$757$	−6.33427	−0.230223	−0.115111	+	0.993353i	$0.536723\pi$
$758$	48.5251	1.76251
$759$	25.6169	0.929835
$760$	96.2830	3.49255
$761$	−52.2078	−1.89253	−0.946266	−	0.323389i	$-0.895178\pi$
$761$	−52.2078	−1.89253	−0.946266	+	0.323389i	$0.895178\pi$
$762$	120.417	4.36226
$763$	2.66270	0.0963961
$764$	4.61301	0.166893
$765$	69.0321	2.49586
$766$	12.2297	0.441877
$767$	−14.2222	−0.513535
$768$	−72.2067	−2.60553
$769$	28.9390	1.04357	0.521784	−	0.853077i	$-0.325267\pi$
$769$	28.9390	1.04357	0.521784	+	0.853077i	$0.325267\pi$
$770$	−10.1675	−0.366410
$771$	−9.27866	−0.334163
$772$	−22.2097	−0.799344
$773$	1.28957	0.0463825	0.0231913	−	0.999731i	$-0.492617\pi$
$773$	1.28957	0.0463825	0.0231913	+	0.999731i	$0.492617\pi$
$774$	−10.4306	−0.374920
$775$	26.4810	0.951226
$776$	−2.30216	−0.0826427
$777$	3.64081	0.130613
$778$	−14.5003	−0.519859
$779$	−25.9985	−0.931494
$780$	−53.4172	−1.91264
$781$	−16.7619	−0.599789
$782$	−50.2404	−1.79659
$783$	9.77710	0.349405
$784$	−14.1761	−0.506290
$785$	37.6785	1.34480
$786$	80.4408	2.86923
$787$	22.6115	0.806014	0.403007	−	0.915197i	$-0.367965\pi$
$787$	22.6115	0.806014	0.403007	+	0.915197i	$0.367965\pi$
$788$	75.4729	2.68861
$789$	−63.6633	−2.26647
$790$	−103.742	−3.69096
$791$	5.21593	0.185457
$792$	29.9392	1.06384
$793$	−1.00712	−0.0357639
$794$	−55.8730	−1.98286
$795$	2.95265	0.104720
$796$	−50.6927	−1.79675
$797$	37.0376	1.31194	0.655969	−	0.754787i	$-0.272260\pi$
$797$	37.0376	1.31194	0.655969	+	0.754787i	$0.272260\pi$
$798$	−20.7061	−0.732990
$799$	−33.5880	−1.18826
$800$	35.8027	1.26582
$801$	40.8775	1.44433
$802$	−33.7300	−1.19105
$803$	11.6061	0.409571
$804$	−29.5248	−1.04126
$805$	12.2508	0.431784
$806$	−6.67982	−0.235287
$807$	−77.8137	−2.73917
$808$	−25.4935	−0.896859
$809$	−2.77415	−0.0975338	−0.0487669	−	0.998810i	$-0.515529\pi$
$809$	−2.77415	−0.0975338	−0.0487669	+	0.998810i	$0.515529\pi$
$810$	−43.4966	−1.52831
$811$	49.0223	1.72141	0.860703	−	0.509108i	$-0.170025\pi$
$811$	49.0223	1.72141	0.860703	+	0.509108i	$0.170025\pi$
$812$	6.72264	0.235918
$813$	16.3905	0.574840
$814$	10.6069	0.371773
$815$	10.3923	0.364027
$816$	−22.7495	−0.796392
$817$	6.18581	0.216414
$818$	20.1151	0.703308
$819$	3.02327	0.105641
$820$	68.3096	2.38547
$821$	27.2442	0.950830	0.475415	−	0.879762i	$-0.342298\pi$
$821$	27.2442	0.950830	0.475415	+	0.879762i	$0.342298\pi$
$822$	51.8664	1.80905
$823$	18.5906	0.648026	0.324013	−	0.946053i	$-0.394968\pi$
$823$	18.5906	0.648026	0.324013	+	0.946053i	$0.394968\pi$
$824$	1.48800	0.0518368
$825$	−60.3411	−2.10081
$826$	14.4850	0.503998
$827$	53.7216	1.86808	0.934041	−	0.357165i	$-0.116257\pi$
$827$	53.7216	1.86808	0.934041	+	0.357165i	$0.116257\pi$
$828$	−79.3180	−2.75649
$829$	−8.10921	−0.281645	−0.140822	−	0.990035i	$-0.544975\pi$
$829$	−8.10921	−0.281645	−0.140822	+	0.990035i	$0.544975\pi$
$830$	37.6092	1.30543
$831$	66.0809	2.29232
$832$	−14.5849	−0.505641
$833$	26.8853	0.931521
$834$	96.6019	3.34505
$835$	−48.6276	−1.68283
$836$	−39.0398	−1.35022
$837$	6.40327	0.221329
$838$	−20.3651	−0.703501
$839$	−15.4939	−0.534909	−0.267455	−	0.963570i	$-0.586183\pi$
$839$	−15.4939	−0.534909	−0.267455	+	0.963570i	$0.586183\pi$
$840$	24.7430	0.853715
$841$	−18.3008	−0.631063
$842$	34.6710	1.19484
$843$	80.0569	2.75731
$844$	−44.1021	−1.51806
$845$	47.0200	1.61754
$846$	−81.9385	−2.81711
$847$	−4.28792	−0.147335
$848$	−0.563064	−0.0193357
$849$	−20.4189	−0.700775
$850$	118.342	4.05910
$851$	−12.7803	−0.438105
$852$	89.6900	3.07273
$853$	45.4994	1.55787	0.778935	−	0.627105i	$-0.215760\pi$
$853$	45.4994	1.55787	0.778935	+	0.627105i	$0.215760\pi$
$854$	1.02573	0.0350997
$855$	−99.8717	−3.41554
$856$	25.3253	0.865602
$857$	33.7720	1.15363	0.576814	−	0.816875i	$-0.304296\pi$
$857$	33.7720	1.15363	0.576814	+	0.816875i	$0.304296\pi$
$858$	15.2210	0.519637
$859$	−43.6086	−1.48791	−0.743953	−	0.668232i	$-0.767051\pi$
$859$	−43.6086	−1.48791	−0.743953	+	0.668232i	$0.767051\pi$
$860$	−16.2528	−0.554218
$861$	−6.68116	−0.227693
$862$	38.8455	1.32308
$863$	−17.7026	−0.602603	−0.301302	−	0.953529i	$-0.597421\pi$
$863$	−17.7026	−0.602603	−0.301302	+	0.953529i	$0.597421\pi$
$864$	8.65731	0.294528
$865$	100.796	3.42716
$866$	20.4885	0.696228
$867$	−2.21733	−0.0753044
$868$	4.40283	0.149442
$869$	19.1307	0.648964
$870$	86.5850	2.93550
$871$	−3.95035	−0.133853
$872$	−18.8779	−0.639288
$873$	2.38797	0.0808204
$874$	72.6849	2.45860
$875$	−17.1848	−0.580952
$876$	−62.1022	−2.09824
$877$	−52.7771	−1.78215	−0.891077	−	0.453852i	$-0.850050\pi$
$877$	−52.7771	−1.78215	−0.891077	+	0.453852i	$0.850050\pi$
$878$	−82.3565	−2.77940
$879$	53.4686	1.80345
$880$	16.1613	0.544798
$881$	31.5553	1.06313	0.531563	−	0.847019i	$-0.321605\pi$
$881$	31.5553	1.06313	0.531563	+	0.847019i	$0.321605\pi$
$882$	65.5872	2.20844
$883$	−20.2880	−0.682747	−0.341373	−	0.939928i	$-0.610892\pi$
$883$	−20.2880	−0.682747	−0.341373	+	0.939928i	$0.610892\pi$
$884$	−19.3190	−0.649769
$885$	120.736	4.05850
$886$	44.9063	1.50866
$887$	−19.2722	−0.647098	−0.323549	−	0.946211i	$-0.604876\pi$
$887$	−19.2722	−0.647098	−0.323549	+	0.946211i	$0.604876\pi$
$888$	−25.8125	−0.866212
$889$	−10.6195	−0.356167
$890$	98.4213	3.29909
$891$	8.02109	0.268717
$892$	90.6734	3.03597
$893$	48.5932	1.62611
$894$	−3.89145	−0.130150
$895$	−37.8666	−1.26574
$896$	11.6090	0.387830
$897$	−18.3399	−0.612350
$898$	60.6397	2.02357
$899$	7.00715	0.233702
$900$	186.835	6.22784
$901$	1.06786	0.0355757
$902$	−19.4646	−0.648099
$903$	1.58964	0.0529000
$904$	−36.9798	−1.22993
$905$	−76.8147	−2.55341
$906$	115.779	3.84651
$907$	40.3930	1.34123	0.670613	−	0.741807i	$-0.266031\pi$
$907$	40.3930	1.34123	0.670613	+	0.741807i	$0.266031\pi$
$908$	−88.1292	−2.92467
$909$	26.4437	0.877084
$910$	7.27917	0.241302
$911$	−57.1724	−1.89421	−0.947103	−	0.320928i	$-0.896005\pi$
$911$	−57.1724	−1.89421	−0.947103	+	0.320928i	$0.896005\pi$
$912$	32.9127	1.08985
$913$	−6.93541	−0.229529
$914$	46.3392	1.53277
$915$	8.54969	0.282644
$916$	−79.6622	−2.63211
$917$	−7.09402	−0.234265
$918$	28.6158	0.944463
$919$	29.8217	0.983726	0.491863	−	0.870673i	$-0.336316\pi$
$919$	29.8217	0.983726	0.491863	+	0.870673i	$0.336316\pi$
$920$	−86.8555	−2.86354
$921$	8.87836	0.292552
$922$	−38.6187	−1.27184
$923$	12.0003	0.394996
$924$	−10.0325	−0.330046
$925$	30.1043	0.989825
$926$	−13.9914	−0.459785
$927$	−1.54346	−0.0506939
$928$	9.47377	0.310992
$929$	23.3100	0.764775	0.382388	−	0.924002i	$-0.375102\pi$
$929$	23.3100	0.764775	0.382388	+	0.924002i	$0.375102\pi$
$930$	56.7067	1.85949
$931$	−38.8962	−1.27477
$932$	35.7405	1.17072
$933$	−14.5821	−0.477395
$934$	88.5894	2.89873
$935$	−30.6503	−1.00237
$936$	−21.4343	−0.700602
$937$	26.2774	0.858446	0.429223	−	0.903198i	$-0.358787\pi$
$937$	26.2774	0.858446	0.429223	+	0.903198i	$0.358787\pi$
$938$	4.02334	0.131367
$939$	5.83471	0.190409
$940$	−127.676	−4.16433
$941$	25.9370	0.845523	0.422761	−	0.906241i	$-0.361061\pi$
$941$	25.9370	0.845523	0.422761	+	0.906241i	$0.361061\pi$
$942$	57.4481	1.87176
$943$	23.4529	0.763732
$944$	−23.0241	−0.749371
$945$	−6.97780	−0.226988
$946$	4.63119	0.150573
$947$	52.6402	1.71058	0.855289	−	0.518151i	$-0.173380\pi$
$947$	52.6402	1.71058	0.855289	+	0.518151i	$0.173380\pi$
$948$	−102.365	−3.32465
$949$	−8.30915	−0.269726
$950$	−171.211	−5.55481
$951$	−16.4277	−0.532705
$952$	8.94863	0.290027
$953$	−3.42258	−0.110868	−0.0554341	−	0.998462i	$-0.517654\pi$
$953$	−3.42258	−0.110868	−0.0554341	+	0.998462i	$0.517654\pi$
$954$	2.60507	0.0843423
$955$	−5.23966	−0.169551
$956$	−47.0179	−1.52067
$957$	−15.9669	−0.516136
$958$	−52.2744	−1.68891
$959$	−4.57406	−0.147704
$960$	123.815	3.99611
$961$	−26.4108	−0.851963
$962$	−7.59381	−0.244834
$963$	−26.2693	−0.846516
$964$	−45.3303	−1.45999
$965$	25.2267	0.812077
$966$	18.6787	0.600978
$967$	38.2377	1.22964	0.614821	−	0.788667i	$-0.289228\pi$
$967$	38.2377	1.22964	0.614821	+	0.788667i	$0.289228\pi$
$968$	30.4004	0.977107
$969$	−62.4196	−2.00521
$970$	5.74955	0.184607
$971$	−18.4539	−0.592213	−0.296106	−	0.955155i	$-0.595688\pi$
$971$	−18.4539	−0.592213	−0.296106	+	0.955155i	$0.595688\pi$
$972$	−75.8144	−2.43175
$973$	−8.51926	−0.273115
$974$	−69.7673	−2.23549
$975$	43.1999	1.38350
$976$	−1.63041	−0.0521881
$977$	−45.7969	−1.46517	−0.732587	−	0.680673i	$-0.761687\pi$
$977$	−45.7969	−1.46517	−0.732587	+	0.680673i	$0.761687\pi$
$978$	15.8451	0.506670
$979$	−18.1496	−0.580064
$980$	102.197	3.26458
$981$	19.5816	0.625191
$982$	−15.3704	−0.490490
$983$	14.4013	0.459331	0.229665	−	0.973270i	$-0.426237\pi$
$983$	14.4013	0.459331	0.229665	+	0.973270i	$0.426237\pi$
$984$	47.3679	1.51003
$985$	−85.7254	−2.73144
$986$	31.3146	0.997259
$987$	12.4876	0.397484
$988$	27.9496	0.889197
$989$	−5.58013	−0.177438
$990$	−74.7719	−2.37641
$991$	19.6799	0.625152	0.312576	−	0.949893i	$-0.398808\pi$
$991$	19.6799	0.625152	0.312576	+	0.949893i	$0.398808\pi$
$992$	6.20461	0.196997
$993$	−54.8182	−1.73960
$994$	−12.2221	−0.387660
$995$	57.5789	1.82537
$996$	37.1101	1.17588
$997$	−6.83553	−0.216484	−0.108242	−	0.994125i	$-0.534522\pi$
$997$	−6.83553	−0.216484	−0.108242	+	0.994125i	$0.534522\pi$
$998$	−0.246398	−0.00779958
$999$	7.27941	0.230310

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4021.2.a.b.1.15	✓	151

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4021.2.a.b.1.15	✓	151	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:	\( N \)	\(=\)	\( 4021 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.38084 q^{2} +2.66837 q^{3} +3.66838 q^{4} -4.16670 q^{5} -6.35294 q^{6} +0.560262 q^{7} -3.97213 q^{8} +4.12018 q^{9} +O(q^{10})\)	\(q-2.38084 q^{2} +2.66837 q^{3} +3.66838 q^{4} -4.16670 q^{5} -6.35294 q^{6} +0.560262 q^{7} -3.97213 q^{8} +4.12018 q^{9} +9.92023 q^{10} -1.82936 q^{11} +9.78858 q^{12} +1.30969 q^{13} -1.33389 q^{14} -11.1183 q^{15} +2.12024 q^{16} -4.02107 q^{17} -9.80948 q^{18} +5.81746 q^{19} -15.2850 q^{20} +1.49498 q^{21} +4.35541 q^{22} -5.24785 q^{23} -10.5991 q^{24} +12.3614 q^{25} -3.11816 q^{26} +2.98906 q^{27} +2.05525 q^{28} +3.27096 q^{29} +26.4708 q^{30} +2.14223 q^{31} +2.89633 q^{32} -4.88141 q^{33} +9.57351 q^{34} -2.33444 q^{35} +15.1144 q^{36} +2.43535 q^{37} -13.8504 q^{38} +3.49474 q^{39} +16.5507 q^{40} -4.46905 q^{41} -3.55931 q^{42} +1.06332 q^{43} -6.71079 q^{44} -17.1676 q^{45} +12.4943 q^{46} +8.35299 q^{47} +5.65757 q^{48} -6.68611 q^{49} -29.4305 q^{50} -10.7297 q^{51} +4.80444 q^{52} -0.265567 q^{53} -7.11647 q^{54} +7.62241 q^{55} -2.22543 q^{56} +15.5231 q^{57} -7.78761 q^{58} -10.8592 q^{59} -40.7861 q^{60} -0.768975 q^{61} -5.10030 q^{62} +2.30838 q^{63} -11.1362 q^{64} -5.45709 q^{65} +11.6218 q^{66} -3.01625 q^{67} -14.7508 q^{68} -14.0032 q^{69} +5.55792 q^{70} +9.16272 q^{71} -16.3659 q^{72} -6.34436 q^{73} -5.79817 q^{74} +32.9848 q^{75} +21.3406 q^{76} -1.02492 q^{77} -8.32039 q^{78} -10.4576 q^{79} -8.83440 q^{80} -4.38463 q^{81} +10.6401 q^{82} +3.79116 q^{83} +5.48416 q^{84} +16.7546 q^{85} -2.53158 q^{86} +8.72812 q^{87} +7.26647 q^{88} +9.92127 q^{89} +40.8732 q^{90} +0.733770 q^{91} -19.2511 q^{92} +5.71626 q^{93} -19.8871 q^{94} -24.2396 q^{95} +7.72847 q^{96} +0.579578 q^{97} +15.9185 q^{98} -7.53731 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 151 q - 16 q^{2} - 29 q^{3} + 120 q^{4} - 27 q^{5} - 18 q^{6} - 18 q^{7} - 48 q^{8} + 98 q^{9}+O(q^{10}) \) 151 * q - 16 * q^2 - 29 * q^3 + 120 * q^4 - 27 * q^5 - 18 * q^6 - 18 * q^7 - 48 * q^8 + 98 * q^9	\( 151 q - 16 q^{2} - 29 q^{3} + 120 q^{4} - 27 q^{5} - 18 q^{6} - 18 q^{7} - 48 q^{8} + 98 q^{9} - 7 q^{10} - 126 q^{11} - 47 q^{12} - 10 q^{13} - 58 q^{14} - 50 q^{15} + 74 q^{16} - 39 q^{17} - 47 q^{18} - 48 q^{19} - 64 q^{20} - 50 q^{21} - 7 q^{22} - 91 q^{23} - 44 q^{24} + 102 q^{25} - 94 q^{26} - 92 q^{27} - 27 q^{28} - 79 q^{29} - 12 q^{30} - 33 q^{31} - 102 q^{32} - 7 q^{33} - 17 q^{34} - 183 q^{35} - 6 q^{36} - 24 q^{37} - 77 q^{38} - 81 q^{39} - 37 q^{40} - 62 q^{41} + 4 q^{42} - 74 q^{43} - 209 q^{44} - 35 q^{45} - 37 q^{46} - 127 q^{47} - 59 q^{48} + 75 q^{49} - 79 q^{50} - 138 q^{51} - 12 q^{52} - 104 q^{53} - 43 q^{54} - 49 q^{55} - 167 q^{56} - 19 q^{57} - 32 q^{58} - 207 q^{59} - 94 q^{60} - 57 q^{61} - 69 q^{62} - 49 q^{63} - 4 q^{64} - 78 q^{65} - 51 q^{66} - 92 q^{67} - 80 q^{68} - 84 q^{69} + 5 q^{70} - 217 q^{71} - 79 q^{72} + 2 q^{73} - 113 q^{74} - 173 q^{75} - 70 q^{76} - 85 q^{77} - 46 q^{78} - 70 q^{79} - 95 q^{80} - 49 q^{81} - 12 q^{82} - 109 q^{83} - 114 q^{84} - 25 q^{85} - 136 q^{86} - 60 q^{87} - 2 q^{88} - 144 q^{89} - 55 q^{90} - 62 q^{91} - 175 q^{92} - 42 q^{93} - 15 q^{94} - 189 q^{95} - 64 q^{96} - 24 q^{97} - 37 q^{98} - 293 q^{99}+O(q^{100}) \) 151 * q - 16 * q^2 - 29 * q^3 + 120 * q^4 - 27 * q^5 - 18 * q^6 - 18 * q^7 - 48 * q^8 + 98 * q^9 - 7 * q^10 - 126 * q^11 - 47 * q^12 - 10 * q^13 - 58 * q^14 - 50 * q^15 + 74 * q^16 - 39 * q^17 - 47 * q^18 - 48 * q^19 - 64 * q^20 - 50 * q^21 - 7 * q^22 - 91 * q^23 - 44 * q^24 + 102 * q^25 - 94 * q^26 - 92 * q^27 - 27 * q^28 - 79 * q^29 - 12 * q^30 - 33 * q^31 - 102 * q^32 - 7 * q^33 - 17 * q^34 - 183 * q^35 - 6 * q^36 - 24 * q^37 - 77 * q^38 - 81 * q^39 - 37 * q^40 - 62 * q^41 + 4 * q^42 - 74 * q^43 - 209 * q^44 - 35 * q^45 - 37 * q^46 - 127 * q^47 - 59 * q^48 + 75 * q^49 - 79 * q^50 - 138 * q^51 - 12 * q^52 - 104 * q^53 - 43 * q^54 - 49 * q^55 - 167 * q^56 - 19 * q^57 - 32 * q^58 - 207 * q^59 - 94 * q^60 - 57 * q^61 - 69 * q^62 - 49 * q^63 - 4 * q^64 - 78 * q^65 - 51 * q^66 - 92 * q^67 - 80 * q^68 - 84 * q^69 + 5 * q^70 - 217 * q^71 - 79 * q^72 + 2 * q^73 - 113 * q^74 - 173 * q^75 - 70 * q^76 - 85 * q^77 - 46 * q^78 - 70 * q^79 - 95 * q^80 - 49 * q^81 - 12 * q^82 - 109 * q^83 - 114 * q^84 - 25 * q^85 - 136 * q^86 - 60 * q^87 - 2 * q^88 - 144 * q^89 - 55 * q^90 - 62 * q^91 - 175 * q^92 - 42 * q^93 - 15 * q^94 - 189 * q^95 - 64 * q^96 - 24 * q^97 - 37 * q^98 - 293 * q^99

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