LMFDB - Embedded newform 4021.2.a.c.1.5

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:	$0$
Dimension:	$182$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
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)

$f(q)$	$=$	$q-2.67927 q^{2} -1.86893 q^{3} +5.17851 q^{4} +2.00029 q^{5} +5.00738 q^{6} -3.62338 q^{7} -8.51610 q^{8} +0.492900 q^{9} +O(q^{10})$	\(q-2.67927 q^{2} -1.86893 q^{3} +5.17851 q^{4} +2.00029 q^{5} +5.00738 q^{6} -3.62338 q^{7} -8.51610 q^{8} +0.492900 q^{9} -5.35934 q^{10} -1.87787 q^{11} -9.67827 q^{12} -4.88407 q^{13} +9.70802 q^{14} -3.73841 q^{15} +12.4599 q^{16} -0.587355 q^{17} -1.32061 q^{18} +5.62756 q^{19} +10.3585 q^{20} +6.77184 q^{21} +5.03133 q^{22} -6.53045 q^{23} +15.9160 q^{24} -0.998820 q^{25} +13.0858 q^{26} +4.68559 q^{27} -18.7637 q^{28} -3.87307 q^{29} +10.0162 q^{30} -7.11176 q^{31} -16.3514 q^{32} +3.50961 q^{33} +1.57368 q^{34} -7.24782 q^{35} +2.55249 q^{36} -11.3721 q^{37} -15.0778 q^{38} +9.12799 q^{39} -17.0347 q^{40} -5.59157 q^{41} -18.1436 q^{42} +0.0296753 q^{43} -9.72458 q^{44} +0.985945 q^{45} +17.4969 q^{46} -1.45792 q^{47} -23.2868 q^{48} +6.12886 q^{49} +2.67611 q^{50} +1.09772 q^{51} -25.2922 q^{52} -4.63412 q^{53} -12.5540 q^{54} -3.75630 q^{55} +30.8570 q^{56} -10.5175 q^{57} +10.3770 q^{58} +10.3349 q^{59} -19.3594 q^{60} +2.41090 q^{61} +19.0543 q^{62} -1.78596 q^{63} +18.8900 q^{64} -9.76958 q^{65} -9.40321 q^{66} -11.3596 q^{67} -3.04162 q^{68} +12.2050 q^{69} +19.4189 q^{70} +3.11786 q^{71} -4.19758 q^{72} +3.05105 q^{73} +30.4690 q^{74} +1.86673 q^{75} +29.1424 q^{76} +6.80424 q^{77} -24.4564 q^{78} -12.6854 q^{79} +24.9236 q^{80} -10.2357 q^{81} +14.9814 q^{82} +4.03080 q^{83} +35.0680 q^{84} -1.17488 q^{85} -0.0795084 q^{86} +7.23851 q^{87} +15.9921 q^{88} -10.0924 q^{89} -2.64162 q^{90} +17.6968 q^{91} -33.8180 q^{92} +13.2914 q^{93} +3.90618 q^{94} +11.2568 q^{95} +30.5596 q^{96} +15.4464 q^{97} -16.4209 q^{98} -0.925603 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 182 q + 18 q^{2} + 28 q^{3} + 208 q^{4} + 22 q^{5} + 18 q^{6} + 14 q^{7} + 54 q^{8} + 238 q^{9}+O(q^{10}) $ 182 * q + 18 * q^2 + 28 * q^3 + 208 * q^4 + 22 * q^5 + 18 * q^6 + 14 * q^7 + 54 * q^8 + 238 * q^9	\( 182 q + 18 q^{2} + 28 q^{3} + 208 q^{4} + 22 q^{5} + 18 q^{6} + 14 q^{7} + 54 q^{8} + 238 q^{9} + 7 q^{10} + 138 q^{11} + 47 q^{12} + 5 q^{13} + 72 q^{14} + 41 q^{15} + 256 q^{16} + 29 q^{17} + 35 q^{18} + 48 q^{19} + 56 q^{20} + 22 q^{21} + 19 q^{22} + 91 q^{23} + 46 q^{24} + 230 q^{25} + 88 q^{26} + 103 q^{27} + 15 q^{28} + 75 q^{29} + 18 q^{30} + 43 q^{31} + 116 q^{32} + 15 q^{33} + 13 q^{34} + 185 q^{35} + 364 q^{36} + 15 q^{37} + 53 q^{38} + 80 q^{39} - 13 q^{40} + 68 q^{41} + 32 q^{42} + 82 q^{43} + 259 q^{44} + 37 q^{45} + 13 q^{46} + 121 q^{47} + 53 q^{48} + 244 q^{49} + 93 q^{50} + 144 q^{51} - 16 q^{52} + 101 q^{53} + 47 q^{54} + 49 q^{55} + 199 q^{56} + 3 q^{57} + 4 q^{58} + 254 q^{59} + 24 q^{60} + 8 q^{61} + 37 q^{62} + 19 q^{63} + 326 q^{64} + 65 q^{65} + 41 q^{66} + 91 q^{67} + 50 q^{68} + 50 q^{69} + 5 q^{70} + 212 q^{71} + 77 q^{72} + 5 q^{73} + 101 q^{74} + 127 q^{75} + 22 q^{76} + 87 q^{77} - 20 q^{78} + 86 q^{79} + 71 q^{80} + 358 q^{81} - 20 q^{82} + 139 q^{83} - 30 q^{84} + 25 q^{85} + 82 q^{86} + 36 q^{87} - 8 q^{88} + 100 q^{89} - 87 q^{90} + 74 q^{91} + 171 q^{92} + 50 q^{93} - 13 q^{94} + 217 q^{95} + 42 q^{96} + 20 q^{97} + 47 q^{98} + 389 q^{99}+O(q^{100}) \) 182 * q + 18 * q^2 + 28 * q^3 + 208 * q^4 + 22 * q^5 + 18 * q^6 + 14 * q^7 + 54 * q^8 + 238 * q^9 + 7 * q^10 + 138 * q^11 + 47 * q^12 + 5 * q^13 + 72 * q^14 + 41 * q^15 + 256 * q^16 + 29 * q^17 + 35 * q^18 + 48 * q^19 + 56 * q^20 + 22 * q^21 + 19 * q^22 + 91 * q^23 + 46 * q^24 + 230 * q^25 + 88 * q^26 + 103 * q^27 + 15 * q^28 + 75 * q^29 + 18 * q^30 + 43 * q^31 + 116 * q^32 + 15 * q^33 + 13 * q^34 + 185 * q^35 + 364 * q^36 + 15 * q^37 + 53 * q^38 + 80 * q^39 - 13 * q^40 + 68 * q^41 + 32 * q^42 + 82 * q^43 + 259 * q^44 + 37 * q^45 + 13 * q^46 + 121 * q^47 + 53 * q^48 + 244 * q^49 + 93 * q^50 + 144 * q^51 - 16 * q^52 + 101 * q^53 + 47 * q^54 + 49 * q^55 + 199 * q^56 + 3 * q^57 + 4 * q^58 + 254 * q^59 + 24 * q^60 + 8 * q^61 + 37 * q^62 + 19 * q^63 + 326 * q^64 + 65 * q^65 + 41 * q^66 + 91 * q^67 + 50 * q^68 + 50 * q^69 + 5 * q^70 + 212 * q^71 + 77 * q^72 + 5 * q^73 + 101 * q^74 + 127 * q^75 + 22 * q^76 + 87 * q^77 - 20 * q^78 + 86 * q^79 + 71 * q^80 + 358 * q^81 - 20 * q^82 + 139 * q^83 - 30 * q^84 + 25 * q^85 + 82 * q^86 + 36 * q^87 - 8 * q^88 + 100 * q^89 - 87 * q^90 + 74 * q^91 + 171 * q^92 + 50 * q^93 - 13 * q^94 + 217 * q^95 + 42 * q^96 + 20 * q^97 + 47 * q^98 + 389 * 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 $

$2$	−2.67927	−1.89453	−0.947266	−	0.320447i	$-0.896167\pi$
$2$	−2.67927	−1.89453	−0.947266	+	0.320447i	$0.896167\pi$
$3$	−1.86893	−1.07903	−0.539514	−	0.841977i	$-0.681392\pi$
$3$	−1.86893	−1.07903	−0.539514	+	0.841977i	$0.681392\pi$
$4$	5.17851	2.58926
$5$	2.00029	0.894559	0.447280	−	0.894394i	$-0.352393\pi$
$5$	2.00029	0.894559	0.447280	+	0.894394i	$0.352393\pi$
$6$	5.00738	2.04425
$7$	−3.62338	−1.36951	−0.684754	−	0.728774i	$-0.740090\pi$
$7$	−3.62338	−1.36951	−0.684754	+	0.728774i	$0.740090\pi$
$8$	−8.51610	−3.01090
$9$	0.492900	0.164300
$10$	−5.35934	−1.69477
$11$	−1.87787	−0.566200	−0.283100	−	0.959090i	$-0.591363\pi$
$11$	−1.87787	−0.566200	−0.283100	+	0.959090i	$0.591363\pi$
$12$	−9.67827	−2.79388
$13$	−4.88407	−1.35460	−0.677299	−	0.735708i	$-0.736849\pi$
$13$	−4.88407	−1.35460	−0.677299	+	0.735708i	$0.736849\pi$
$14$	9.70802	2.59458
$15$	−3.73841	−0.965254
$16$	12.4599	3.11499
$17$	−0.587355	−0.142454	−0.0712272	−	0.997460i	$-0.522692\pi$
$17$	−0.587355	−0.142454	−0.0712272	+	0.997460i	$0.522692\pi$
$18$	−1.32061	−0.311272
$19$	5.62756	1.29105	0.645526	−	0.763739i	$-0.276638\pi$
$19$	5.62756	1.29105	0.645526	+	0.763739i	$0.276638\pi$
$20$	10.3585	2.31624
$21$	6.77184	1.47774
$22$	5.03133	1.07268
$23$	−6.53045	−1.36169	−0.680846	−	0.732426i	$-0.738388\pi$
$23$	−6.53045	−1.36169	−0.680846	+	0.732426i	$0.738388\pi$
$24$	15.9160	3.24884
$25$	−0.998820	−0.199764
$26$	13.0858	2.56633
$27$	4.68559	0.901743
$28$	−18.7637	−3.54601
$29$	−3.87307	−0.719212	−0.359606	−	0.933104i	$-0.617089\pi$
$29$	−3.87307	−0.719212	−0.359606	+	0.933104i	$0.617089\pi$
$30$	10.0162	1.82870
$31$	−7.11176	−1.27731	−0.638655	−	0.769494i	$-0.720509\pi$
$31$	−7.11176	−1.27731	−0.638655	+	0.769494i	$0.720509\pi$
$32$	−16.3514	−2.89055
$33$	3.50961	0.610945
$34$	1.57368	0.269885
$35$	−7.24782	−1.22511
$36$	2.55249	0.425415
$37$	−11.3721	−1.86956	−0.934782	−	0.355223i	$-0.884405\pi$
$37$	−11.3721	−1.86956	−0.934782	+	0.355223i	$0.884405\pi$
$38$	−15.0778	−2.44594
$39$	9.12799	1.46165
$40$	−17.0347	−2.69342
$41$	−5.59157	−0.873257	−0.436629	−	0.899642i	$-0.643828\pi$
$41$	−5.59157	−0.873257	−0.436629	+	0.899642i	$0.643828\pi$
$42$	−18.1436	−2.79962
$43$	0.0296753	0.00452545	0.00226272	−	0.999997i	$-0.499280\pi$
$43$	0.0296753	0.00452545	0.00226272	+	0.999997i	$0.499280\pi$
$44$	−9.72458	−1.46603
$45$	0.985945	0.146976
$46$	17.4969	2.57977
$47$	−1.45792	−0.212660	−0.106330	−	0.994331i	$-0.533910\pi$
$47$	−1.45792	−0.212660	−0.106330	+	0.994331i	$0.533910\pi$
$48$	−23.2868	−3.36116
$49$	6.12886	0.875552
$50$	2.67611	0.378460
$51$	1.09772	0.153712
$52$	−25.2922	−3.50740
$53$	−4.63412	−0.636546	−0.318273	−	0.947999i	$-0.603103\pi$
$53$	−4.63412	−0.636546	−0.318273	+	0.947999i	$0.603103\pi$
$54$	−12.5540	−1.70838
$55$	−3.75630	−0.506499
$56$	30.8570	4.12345
$57$	−10.5175	−1.39308
$58$	10.3770	1.36257
$59$	10.3349	1.34549	0.672743	−	0.739876i	$-0.265116\pi$
$59$	10.3349	1.34549	0.672743	+	0.739876i	$0.265116\pi$
$60$	−19.3594	−2.49929
$61$	2.41090	0.308684	0.154342	−	0.988017i	$-0.450674\pi$
$61$	2.41090	0.308684	0.154342	+	0.988017i	$0.450674\pi$
$62$	19.0543	2.41990
$63$	−1.78596	−0.225010
$64$	18.8900	2.36125
$65$	−9.76958	−1.21177
$66$	−9.40321	−1.15745
$67$	−11.3596	−1.38780	−0.693901	−	0.720071i	$-0.744109\pi$
$67$	−11.3596	−1.38780	−0.693901	+	0.720071i	$0.744109\pi$
$68$	−3.04162	−0.368851
$69$	12.2050	1.46930
$70$	19.4189	2.32100
$71$	3.11786	0.370022	0.185011	−	0.982736i	$-0.440768\pi$
$71$	3.11786	0.370022	0.185011	+	0.982736i	$0.440768\pi$
$72$	−4.19758	−0.494690
$73$	3.05105	0.357099	0.178549	−	0.983931i	$-0.442860\pi$
$73$	3.05105	0.357099	0.178549	+	0.983931i	$0.442860\pi$
$74$	30.4690	3.54195
$75$	1.86673	0.215551
$76$	29.1424	3.34286
$77$	6.80424	0.775415
$78$	−24.4564	−2.76914
$79$	−12.6854	−1.42722	−0.713612	−	0.700541i	$-0.752942\pi$
$79$	−12.6854	−1.42722	−0.713612	+	0.700541i	$0.752942\pi$
$80$	24.9236	2.78654
$81$	−10.2357	−1.13731
$82$	14.9814	1.65441
$83$	4.03080	0.442437	0.221219	−	0.975224i	$-0.428997\pi$
$83$	4.03080	0.442437	0.221219	+	0.975224i	$0.428997\pi$
$84$	35.0680	3.82624
$85$	−1.17488	−0.127434
$86$	−0.0795084	−0.00857361
$87$	7.23851	0.776049
$88$	15.9921	1.70477
$89$	−10.0924	−1.06979	−0.534894	−	0.844919i	$-0.679648\pi$
$89$	−10.0924	−1.06979	−0.534894	+	0.844919i	$0.679648\pi$
$90$	−2.64162	−0.278451
$91$	17.6968	1.85513
$92$	−33.8180	−3.52577
$93$	13.2914	1.37825
$94$	3.90618	0.402891
$95$	11.2568	1.15492
$96$	30.5596	3.11898
$97$	15.4464	1.56834	0.784172	−	0.620544i	$-0.213088\pi$
$97$	15.4464	1.56834	0.784172	+	0.620544i	$0.213088\pi$
$98$	−16.4209	−1.65876
$99$	−0.925603	−0.0930266
$100$	−5.17240	−0.517240
$101$	−18.6272	−1.85348	−0.926739	−	0.375707i	$-0.877400\pi$
$101$	−18.6272	−1.85348	−0.926739	+	0.375707i	$0.877400\pi$
$102$	−2.94111	−0.291213
$103$	3.10230	0.305678	0.152839	−	0.988251i	$-0.451158\pi$
$103$	3.10230	0.305678	0.152839	+	0.988251i	$0.451158\pi$
$104$	41.5932	4.07855
$105$	13.5457	1.32192
$106$	12.4161	1.20596
$107$	−1.82225	−0.176164	−0.0880819	−	0.996113i	$-0.528074\pi$
$107$	−1.82225	−0.176164	−0.0880819	+	0.996113i	$0.528074\pi$
$108$	24.2644	2.33484
$109$	−1.24146	−0.118911	−0.0594553	−	0.998231i	$-0.518936\pi$
$109$	−1.24146	−0.118911	−0.0594553	+	0.998231i	$0.518936\pi$
$110$	10.0641	0.959579
$111$	21.2537	2.01731
$112$	−45.1471	−4.26600
$113$	−0.126540	−0.0119039	−0.00595195	−	0.999982i	$-0.501895\pi$
$113$	−0.126540	−0.0119039	−0.00595195	+	0.999982i	$0.501895\pi$
$114$	28.1793	2.63924
$115$	−13.0628	−1.21811
$116$	−20.0568	−1.86222
$117$	−2.40736	−0.222560
$118$	−27.6900	−2.54907
$119$	2.12821	0.195092
$120$	31.8367	2.90628
$121$	−7.47360	−0.679418
$122$	−6.45947	−0.584813
$123$	10.4503	0.942268
$124$	−36.8283	−3.30728
$125$	−11.9994	−1.07326
$126$	4.78508	0.426289
$127$	2.16002	0.191670	0.0958352	−	0.995397i	$-0.469448\pi$
$127$	2.16002	0.191670	0.0958352	+	0.995397i	$0.469448\pi$
$128$	−17.9087	−1.58292
$129$	−0.0554611	−0.00488308
$130$	26.1754	2.29573
$131$	10.2735	0.897601	0.448801	−	0.893632i	$-0.351851\pi$
$131$	10.2735	0.897601	0.448801	+	0.893632i	$0.351851\pi$
$132$	18.1746	1.58189
$133$	−20.3908	−1.76811
$134$	30.4356	2.62924
$135$	9.37257	0.806663
$136$	5.00197	0.428915
$137$	9.43649	0.806214	0.403107	−	0.915153i	$-0.367930\pi$
$137$	9.43649	0.806214	0.403107	+	0.915153i	$0.367930\pi$
$138$	−32.7004	−2.78364
$139$	−16.9138	−1.43461	−0.717306	−	0.696758i	$-0.754625\pi$
$139$	−16.9138	−1.43461	−0.717306	+	0.696758i	$0.754625\pi$
$140$	−37.5329	−3.17211
$141$	2.72476	0.229466
$142$	−8.35360	−0.701019
$143$	9.17165	0.766972
$144$	6.14151	0.511792
$145$	−7.74729	−0.643378
$146$	−8.17461	−0.676535
$147$	−11.4544	−0.944745
$148$	−58.8906	−4.84078
$149$	5.18012	0.424372	0.212186	−	0.977229i	$-0.431942\pi$
$149$	5.18012	0.424372	0.212186	+	0.977229i	$0.431942\pi$
$150$	−5.00147	−0.408368
$151$	−3.09162	−0.251593	−0.125796	−	0.992056i	$-0.540149\pi$
$151$	−3.09162	−0.251593	−0.125796	+	0.992056i	$0.540149\pi$
$152$	−47.9249	−3.88722
$153$	−0.289507	−0.0234053
$154$	−18.2304	−1.46905
$155$	−14.2256	−1.14263
$156$	47.2694	3.78458
$157$	−5.81529	−0.464111	−0.232055	−	0.972703i	$-0.574545\pi$
$157$	−5.81529	−0.464111	−0.232055	+	0.972703i	$0.574545\pi$
$158$	33.9878	2.70392
$159$	8.66086	0.686851
$160$	−32.7076	−2.58577
$161$	23.6623	1.86485
$162$	27.4244	2.15466
$163$	−13.1872	−1.03290	−0.516452	−	0.856316i	$-0.672748\pi$
$163$	−13.1872	−1.03290	−0.516452	+	0.856316i	$0.672748\pi$
$164$	−28.9560	−2.26109
$165$	7.02026	0.546526
$166$	−10.7996	−0.838212
$167$	−18.0612	−1.39761	−0.698807	−	0.715310i	$-0.746285\pi$
$167$	−18.0612	−1.39761	−0.698807	+	0.715310i	$0.746285\pi$
$168$	−57.6697	−4.44931
$169$	10.8541	0.834934
$170$	3.14783	0.241428
$171$	2.77383	0.212120
$172$	0.153674	0.0117175
$173$	0.382080	0.0290490	0.0145245	−	0.999895i	$-0.495377\pi$
$173$	0.382080	0.0290490	0.0145245	+	0.999895i	$0.495377\pi$
$174$	−19.3939	−1.47025
$175$	3.61910	0.273578
$176$	−23.3982	−1.76370
$177$	−19.3152	−1.45182
$178$	27.0402	2.02675
$179$	23.4232	1.75073	0.875365	−	0.483463i	$-0.160621\pi$
$179$	23.4232	1.75073	0.875365	+	0.483463i	$0.160621\pi$
$180$	5.10573	0.380558
$181$	−19.7230	−1.46600	−0.732999	−	0.680229i	$-0.761880\pi$
$181$	−19.7230	−1.46600	−0.732999	+	0.680229i	$0.761880\pi$
$182$	−47.4147	−3.51461
$183$	−4.50581	−0.333079
$184$	55.6139	4.09991
$185$	−22.7476	−1.67243
$186$	−35.6112	−2.61114
$187$	1.10298	0.0806576
$188$	−7.54987	−0.550631
$189$	−16.9777	−1.23494
$190$	−30.1600	−2.18804
$191$	7.36200	0.532695	0.266348	−	0.963877i	$-0.414183\pi$
$191$	7.36200	0.532695	0.266348	+	0.963877i	$0.414183\pi$
$192$	−35.3041	−2.54786
$193$	−4.03725	−0.290607	−0.145304	−	0.989387i	$-0.546416\pi$
$193$	−4.03725	−0.290607	−0.145304	+	0.989387i	$0.546416\pi$
$194$	−41.3851	−2.97128
$195$	18.2587	1.30753
$196$	31.7384	2.26703
$197$	−4.55106	−0.324250	−0.162125	−	0.986770i	$-0.551835\pi$
$197$	−4.55106	−0.324250	−0.162125	+	0.986770i	$0.551835\pi$
$198$	2.47994	0.176242
$199$	26.8975	1.90671	0.953356	−	0.301847i	$-0.0976033\pi$
$199$	26.8975	1.90671	0.953356	+	0.301847i	$0.0976033\pi$
$200$	8.50605	0.601469
$201$	21.2304	1.49748
$202$	49.9074	3.51147
$203$	14.0336	0.984966
$204$	5.68458	0.398000
$205$	−11.1848	−0.781180
$206$	−8.31190	−0.579118
$207$	−3.21886	−0.223726
$208$	−60.8552	−4.21955
$209$	−10.5678	−0.730993
$210$	−36.2926	−2.50443
$211$	−24.5458	−1.68980	−0.844902	−	0.534921i	$-0.820341\pi$
$211$	−24.5458	−1.68980	−0.844902	+	0.534921i	$0.820341\pi$
$212$	−23.9979	−1.64818
$213$	−5.82706	−0.399264
$214$	4.88232	0.333748
$215$	0.0593594	0.00404828
$216$	−39.9030	−2.71505
$217$	25.7686	1.74929
$218$	3.32622	0.225280
$219$	−5.70220	−0.385319
$220$	−19.4520	−1.31145
$221$	2.86868	0.192968
$222$	−56.9444	−3.82186
$223$	4.04128	0.270624	0.135312	−	0.990803i	$-0.456796\pi$
$223$	4.04128	0.270624	0.135312	+	0.990803i	$0.456796\pi$
$224$	59.2473	3.95863
$225$	−0.492318	−0.0328212
$226$	0.339036	0.0225523
$227$	16.6801	1.10710	0.553550	−	0.832816i	$-0.313273\pi$
$227$	16.6801	1.10710	0.553550	+	0.832816i	$0.313273\pi$
$228$	−54.4651	−3.60704
$229$	4.06118	0.268370	0.134185	−	0.990956i	$-0.457158\pi$
$229$	4.06118	0.268370	0.134185	+	0.990956i	$0.457158\pi$
$230$	34.9989	2.30776
$231$	−12.7166	−0.836694
$232$	32.9835	2.16547
$233$	−4.86987	−0.319036	−0.159518	−	0.987195i	$-0.550994\pi$
$233$	−4.86987	−0.319036	−0.159518	+	0.987195i	$0.550994\pi$
$234$	6.44997	0.421648
$235$	−2.91628	−0.190237
$236$	53.5193	3.48381
$237$	23.7082	1.54001
$238$	−5.70205	−0.369609
$239$	14.9536	0.967269	0.483635	−	0.875270i	$-0.339316\pi$
$239$	14.9536	0.967269	0.483635	+	0.875270i	$0.339316\pi$
$240$	−46.5804	−3.00675
$241$	−25.2320	−1.62534	−0.812669	−	0.582725i	$-0.801986\pi$
$241$	−25.2320	−1.62534	−0.812669	+	0.582725i	$0.801986\pi$
$242$	20.0238	1.28718
$243$	5.07312	0.325441
$244$	12.4849	0.799263
$245$	12.2595	0.783233
$246$	−27.9991	−1.78516
$247$	−27.4854	−1.74885
$248$	60.5644	3.84585
$249$	−7.53328	−0.477402
$250$	32.1497	2.03333
$251$	17.9223	1.13125	0.565623	−	0.824664i	$-0.308636\pi$
$251$	17.9223	1.13125	0.565623	+	0.824664i	$0.308636\pi$
$252$	−9.24862	−0.582609
$253$	12.2633	0.770990
$254$	−5.78727	−0.363126
$255$	2.19577	0.137505
$256$	10.2024	0.637647
$257$	23.8109	1.48528	0.742640	−	0.669691i	$-0.233573\pi$
$257$	23.8109	1.48528	0.742640	+	0.669691i	$0.233573\pi$
$258$	0.148596	0.00925116
$259$	41.2054	2.56038
$260$	−50.5919	−3.13757
$261$	−1.90904	−0.118166
$262$	−27.5256	−1.70053
$263$	−21.3279	−1.31514	−0.657568	−	0.753395i	$-0.728415\pi$
$263$	−21.3279	−1.31514	−0.657568	+	0.753395i	$0.728415\pi$
$264$	−29.8882	−1.83949
$265$	−9.26962	−0.569428
$266$	54.6325	3.34973
$267$	18.8619	1.15433
$268$	−58.8260	−3.59337
$269$	−6.49615	−0.396077	−0.198039	−	0.980194i	$-0.563457\pi$
$269$	−6.49615	−0.396077	−0.198039	+	0.980194i	$0.563457\pi$
$270$	−25.1117	−1.52825
$271$	−4.26636	−0.259163	−0.129581	−	0.991569i	$-0.541363\pi$
$271$	−4.26636	−0.259163	−0.129581	+	0.991569i	$0.541363\pi$
$272$	−7.31841	−0.443744
$273$	−33.0741	−2.00174
$274$	−25.2829	−1.52740
$275$	1.87566	0.113106
$276$	63.2035	3.80440
$277$	−3.54748	−0.213147	−0.106574	−	0.994305i	$-0.533988\pi$
$277$	−3.54748	−0.213147	−0.106574	+	0.994305i	$0.533988\pi$
$278$	45.3168	2.71792
$279$	−3.50538	−0.209862
$280$	61.7232	3.68867
$281$	8.79885	0.524896	0.262448	−	0.964946i	$-0.415470\pi$
$281$	8.79885	0.524896	0.262448	+	0.964946i	$0.415470\pi$
$282$	−7.30037	−0.434731
$283$	−8.86187	−0.526784	−0.263392	−	0.964689i	$-0.584841\pi$
$283$	−8.86187	−0.526784	−0.263392	+	0.964689i	$0.584841\pi$
$284$	16.1459	0.958081
$285$	−21.0381	−1.24619
$286$	−24.5734	−1.45305
$287$	20.2604	1.19593
$288$	−8.05961	−0.474917
$289$	−16.6550	−0.979707
$290$	20.7571	1.21890
$291$	−28.8682	−1.69229
$292$	15.7999	0.924620
$293$	−9.10801	−0.532096	−0.266048	−	0.963960i	$-0.585718\pi$
$293$	−9.10801	−0.532096	−0.266048	+	0.963960i	$0.585718\pi$
$294$	30.6895	1.78985
$295$	20.6728	1.20362
$296$	96.8460	5.62906
$297$	−8.79894	−0.510567
$298$	−13.8790	−0.803986
$299$	31.8952	1.84454
$300$	9.66686	0.558116
$301$	−0.107525	−0.00619763
$302$	8.28331	0.476651
$303$	34.8130	1.99995
$304$	70.1191	4.02161
$305$	4.82252	0.276137
$306$	0.775669	0.0443420
$307$	9.38279	0.535504	0.267752	−	0.963488i	$-0.413719\pi$
$307$	9.38279	0.535504	0.267752	+	0.963488i	$0.413719\pi$
$308$	35.2358	2.00775
$309$	−5.79798	−0.329835
$310$	38.1143	2.16475
$311$	−18.5348	−1.05101	−0.525506	−	0.850790i	$-0.676124\pi$
$311$	−18.5348	−1.05101	−0.525506	+	0.850790i	$0.676124\pi$
$312$	−77.7348	−4.40087
$313$	18.4660	1.04376	0.521881	−	0.853018i	$-0.325231\pi$
$313$	18.4660	1.04376	0.521881	+	0.853018i	$0.325231\pi$
$314$	15.5808	0.879274
$315$	−3.57245	−0.201285
$316$	−65.6917	−3.69545
$317$	0.232033	0.0130323	0.00651613	−	0.999979i	$-0.497926\pi$
$317$	0.232033	0.0130323	0.00651613	+	0.999979i	$0.497926\pi$
$318$	−23.2048	−1.30126
$319$	7.27314	0.407217
$320$	37.7856	2.11228
$321$	3.40566	0.190086
$322$	−63.3977	−3.53302
$323$	−3.30537	−0.183916
$324$	−53.0059	−2.94477
$325$	4.87831	0.270600
$326$	35.3322	1.95687
$327$	2.32021	0.128308
$328$	47.6184	2.62929
$329$	5.28261	0.291240
$330$	−18.8092	−1.03541
$331$	−18.4653	−1.01494	−0.507471	−	0.861669i	$-0.669420\pi$
$331$	−18.4653	−1.01494	−0.507471	+	0.861669i	$0.669420\pi$
$332$	20.8735	1.14558
$333$	−5.60531	−0.307169
$334$	48.3908	2.64783
$335$	−22.7226	−1.24147
$336$	84.3768	4.60313
$337$	−27.9305	−1.52147	−0.760737	−	0.649060i	$-0.775162\pi$
$337$	−27.9305	−1.52147	−0.760737	+	0.649060i	$0.775162\pi$
$338$	−29.0812	−1.58181
$339$	0.236495	0.0128446
$340$	−6.08414	−0.329959
$341$	13.3550	0.723212
$342$	−7.43184	−0.401868
$343$	3.15645	0.170432
$344$	−0.252718	−0.0136256
$345$	24.4135	1.31438
$346$	−1.02370	−0.0550343
$347$	−14.0612	−0.754846	−0.377423	−	0.926041i	$-0.623190\pi$
$347$	−14.0612	−0.754846	−0.377423	+	0.926041i	$0.623190\pi$
$348$	37.4847	2.00939
$349$	−9.92527	−0.531287	−0.265644	−	0.964071i	$-0.585584\pi$
$349$	−9.92527	−0.531287	−0.265644	+	0.964071i	$0.585584\pi$
$350$	−9.69657	−0.518303
$351$	−22.8848	−1.22150
$352$	30.7058	1.63663
$353$	20.4160	1.08663	0.543316	−	0.839528i	$-0.317169\pi$
$353$	20.4160	1.08663	0.543316	+	0.839528i	$0.317169\pi$
$354$	51.7506	2.75052
$355$	6.23664	0.331006
$356$	−52.2634	−2.76995
$357$	−3.97747	−0.210510
$358$	−62.7571	−3.31682
$359$	−27.7789	−1.46611	−0.733057	−	0.680168i	$-0.761907\pi$
$359$	−27.7789	−1.46611	−0.733057	+	0.680168i	$0.761907\pi$
$360$	−8.39641	−0.442530
$361$	12.6695	0.666814
$362$	52.8433	2.77738
$363$	13.9676	0.733111
$364$	91.6432	4.80341
$365$	6.10300	0.319446
$366$	12.0723	0.631029
$367$	26.0672	1.36070	0.680348	−	0.732890i	$-0.261829\pi$
$367$	26.0672	1.36070	0.680348	+	0.732890i	$0.261829\pi$
$368$	−81.3690	−4.24165
$369$	−2.75609	−0.143476
$370$	60.9470	3.16848
$371$	16.7912	0.871755
$372$	68.8295	3.56864
$373$	−35.3812	−1.83197	−0.915985	−	0.401213i	$-0.868589\pi$
$373$	−35.3812	−1.83197	−0.915985	+	0.401213i	$0.868589\pi$
$374$	−2.95518	−0.152809
$375$	22.4261	1.15808
$376$	12.4158	0.640297
$377$	18.9164	0.974242
$378$	45.4879	2.33964
$379$	−20.5597	−1.05608	−0.528039	−	0.849220i	$-0.677073\pi$
$379$	−20.5597	−1.05608	−0.528039	+	0.849220i	$0.677073\pi$
$380$	58.2934	2.99039
$381$	−4.03692	−0.206818
$382$	−19.7248	−1.00921
$383$	14.2122	0.726210	0.363105	−	0.931748i	$-0.381717\pi$
$383$	14.2122	0.726210	0.363105	+	0.931748i	$0.381717\pi$
$384$	33.4702	1.70802
$385$	13.6105	0.693654
$386$	10.8169	0.550565
$387$	0.0146270	0.000743531 0
$388$	79.9893	4.06084
$389$	19.6155	0.994545	0.497273	−	0.867594i	$-0.334335\pi$
$389$	19.6155	0.994545	0.497273	+	0.867594i	$0.334335\pi$
$390$	−48.9200	−2.47716
$391$	3.83569	0.193979
$392$	−52.1940	−2.63620
$393$	−19.2005	−0.968536
$394$	12.1935	0.614301
$395$	−25.3746	−1.27674
$396$	−4.79324	−0.240869
$397$	−0.00424827	−0.000213214 0	−0.000106607	−	1.00000i	$-0.500034\pi$
$397$	−0.00424827	−0.000213214 0	−0.000106607		1.00000i	$0.500034\pi$
$398$	−72.0657	−3.61233
$399$	38.1090	1.90783
$400$	−12.4452	−0.622262
$401$	−23.8323	−1.19013	−0.595065	−	0.803678i	$-0.702874\pi$
$401$	−23.8323	−1.19013	−0.595065	+	0.803678i	$0.702874\pi$
$402$	−56.8820	−2.83702
$403$	34.7343	1.73024
$404$	−96.4612	−4.79913
$405$	−20.4745	−1.01739
$406$	−37.5999	−1.86605
$407$	21.3554	1.05855
$408$	−9.34833	−0.462811
$409$	31.2481	1.54512	0.772560	−	0.634942i	$-0.218976\pi$
$409$	31.2481	1.54512	0.772560	+	0.634942i	$0.218976\pi$
$410$	29.9671	1.47997
$411$	−17.6361	−0.869927
$412$	16.0653	0.791479
$413$	−37.4472	−1.84265
$414$	8.62420	0.423856
$415$	8.06278	0.395786
$416$	79.8614	3.91553
$417$	31.6108	1.54799
$418$	28.3141	1.38489
$419$	29.7669	1.45421	0.727104	−	0.686527i	$-0.240866\pi$
$419$	29.7669	1.45421	0.727104	+	0.686527i	$0.240866\pi$
$420$	70.1464	3.42279
$421$	−5.37432	−0.261928	−0.130964	−	0.991387i	$-0.541807\pi$
$421$	−5.37432	−0.261928	−0.130964	+	0.991387i	$0.541807\pi$
$422$	65.7650	3.20139
$423$	−0.718610	−0.0349400
$424$	39.4647	1.91657
$425$	0.586662	0.0284573
$426$	15.6123	0.756418
$427$	−8.73561	−0.422746
$428$	−9.43656	−0.456133
$429$	−17.1412	−0.827584
$430$	−0.159040	−0.00766960
$431$	12.6338	0.608549	0.304275	−	0.952584i	$-0.401586\pi$
$431$	12.6338	0.608549	0.304275	+	0.952584i	$0.401586\pi$
$432$	58.3823	2.80892
$433$	8.59574	0.413085	0.206542	−	0.978438i	$-0.433779\pi$
$433$	8.59574	0.413085	0.206542	+	0.978438i	$0.433779\pi$
$434$	−69.0411	−3.31408
$435$	14.4791	0.694222
$436$	−6.42893	−0.307890
$437$	−36.7505	−1.75802
$438$	15.2778	0.730000
$439$	5.24892	0.250517	0.125259	−	0.992124i	$-0.460024\pi$
$439$	5.24892	0.250517	0.125259	+	0.992124i	$0.460024\pi$
$440$	31.9890	1.52502
$441$	3.02092	0.143853
$442$	−7.68598	−0.365585
$443$	37.0486	1.76023	0.880116	−	0.474758i	$-0.157465\pi$
$443$	37.0486	1.76023	0.880116	+	0.474758i	$0.157465\pi$
$444$	110.062	5.22333
$445$	−20.1877	−0.956989
$446$	−10.8277	−0.512706
$447$	−9.68128	−0.457909
$448$	−68.4457	−3.23376
$449$	−2.49058	−0.117538	−0.0587688	−	0.998272i	$-0.518717\pi$
$449$	−2.49058	−0.117538	−0.0587688	+	0.998272i	$0.518717\pi$
$450$	1.31906	0.0621809
$451$	10.5003	0.494438
$452$	−0.655290	−0.0308222
$453$	5.77803	0.271475
$454$	−44.6907	−2.09744
$455$	35.3989	1.65952
$456$	89.5683	4.19442
$457$	−10.2042	−0.477334	−0.238667	−	0.971101i	$-0.576710\pi$
$457$	−10.2042	−0.477334	−0.238667	+	0.971101i	$0.576710\pi$
$458$	−10.8810	−0.508436
$459$	−2.75211	−0.128457
$460$	−67.6460	−3.15401
$461$	−29.3628	−1.36756	−0.683781	−	0.729687i	$-0.739666\pi$
$461$	−29.3628	−1.36756	−0.683781	+	0.729687i	$0.739666\pi$
$462$	34.0714	1.58514
$463$	−9.88539	−0.459413	−0.229707	−	0.973260i	$-0.573777\pi$
$463$	−9.88539	−0.459413	−0.229707	+	0.973260i	$0.573777\pi$
$464$	−48.2583	−2.24034
$465$	26.5867	1.23293
$466$	13.0477	0.604423
$467$	28.0488	1.29794	0.648971	−	0.760813i	$-0.275200\pi$
$467$	28.0488	1.29794	0.648971	+	0.760813i	$0.275200\pi$
$468$	−12.4665	−0.576265
$469$	41.1603	1.90061
$470$	7.81350	0.360410
$471$	10.8684	0.500788
$472$	−88.0129	−4.05112
$473$	−0.0557265	−0.00256231
$474$	−63.5208	−2.91761
$475$	−5.62092	−0.257906
$476$	11.0209	0.505144
$477$	−2.28416	−0.104584
$478$	−40.0649	−1.83252
$479$	27.9775	1.27833	0.639163	−	0.769071i	$-0.279281\pi$
$479$	27.9775	1.27833	0.639163	+	0.769071i	$0.279281\pi$
$480$	61.1283	2.79011
$481$	55.5422	2.53250
$482$	67.6036	3.07926
$483$	−44.2231	−2.01222
$484$	−38.7021	−1.75919
$485$	30.8973	1.40298
$486$	−13.5923	−0.616558
$487$	−6.27452	−0.284326	−0.142163	−	0.989843i	$-0.545406\pi$
$487$	−6.27452	−0.284326	−0.142163	+	0.989843i	$0.545406\pi$
$488$	−20.5315	−0.929417
$489$	24.6460	1.11453
$490$	−32.8467	−1.48386
$491$	16.9798	0.766287	0.383144	−	0.923689i	$-0.374841\pi$
$491$	16.9798	0.766287	0.383144	+	0.923689i	$0.374841\pi$
$492$	54.1168	2.43977
$493$	2.27487	0.102455
$494$	73.6409	3.31326
$495$	−1.85148	−0.0832178
$496$	−88.6121	−3.97880
$497$	−11.2972	−0.506748
$498$	20.1837	0.904454
$499$	−15.4713	−0.692589	−0.346294	−	0.938126i	$-0.612560\pi$
$499$	−15.4713	−0.692589	−0.346294	+	0.938126i	$0.612560\pi$
$500$	−62.1391	−2.77894
$501$	33.7550	1.50806
$502$	−48.0188	−2.14318
$503$	17.5641	0.783143	0.391571	−	0.920148i	$-0.371932\pi$
$503$	17.5641	0.783143	0.391571	+	0.920148i	$0.371932\pi$
$504$	15.2094	0.677482
$505$	−37.2599	−1.65805
$506$	−32.8569	−1.46067
$507$	−20.2856	−0.900916
$508$	11.1857	0.496283
$509$	−16.5237	−0.732402	−0.366201	−	0.930536i	$-0.619342\pi$
$509$	−16.5237	−0.732402	−0.366201	+	0.930536i	$0.619342\pi$
$510$	−5.88308	−0.260507
$511$	−11.0551	−0.489050
$512$	8.48257	0.374880
$513$	26.3685	1.16420
$514$	−63.7958	−2.81391
$515$	6.20551	0.273447
$516$	−0.287206	−0.0126435
$517$	2.73779	0.120408
$518$	−110.401	−4.85073
$519$	−0.714081	−0.0313447
$520$	83.1987	3.64851
$521$	29.6938	1.30091	0.650455	−	0.759545i	$-0.274578\pi$
$521$	29.6938	1.30091	0.650455	+	0.759545i	$0.274578\pi$
$522$	5.11484	0.223870
$523$	33.7815	1.47716	0.738580	−	0.674165i	$-0.235497\pi$
$523$	33.7815	1.47716	0.738580	+	0.674165i	$0.235497\pi$
$524$	53.2015	2.32412
$525$	−6.76385	−0.295199
$526$	57.1434	2.49157
$527$	4.17712	0.181958
$528$	43.7296	1.90308
$529$	19.6468	0.854207
$530$	24.8358	1.07880
$531$	5.09406	0.221063
$532$	−105.594	−4.57808
$533$	27.3096	1.18291
$534$	−50.5362	−2.18692
$535$	−3.64504	−0.157589
$536$	96.7399	4.17853
$537$	−43.7763	−1.88909
$538$	17.4050	0.750381
$539$	−11.5092	−0.495737
$540$	48.5360	2.08866
$541$	44.3331	1.90603	0.953015	−	0.302923i	$-0.0979625\pi$
$541$	44.3331	1.90603	0.953015	+	0.302923i	$0.0979625\pi$
$542$	11.4307	0.490992
$543$	36.8609	1.58185
$544$	9.60408	0.411771
$545$	−2.48329	−0.106373
$546$	88.6147	3.79236
$547$	19.8706	0.849608	0.424804	−	0.905285i	$-0.360343\pi$
$547$	19.8706	0.849608	0.424804	+	0.905285i	$0.360343\pi$
$548$	48.8670	2.08749
$549$	1.18833	0.0507169
$550$	−5.02540	−0.214284
$551$	−21.7960	−0.928540
$552$	−103.939	−4.42392
$553$	45.9642	1.95459
$554$	9.50466	0.403814
$555$	42.5136	1.80460
$556$	−87.5884	−3.71458
$557$	−32.5157	−1.37773	−0.688867	−	0.724888i	$-0.741891\pi$
$557$	−32.5157	−1.37773	−0.688867	+	0.724888i	$0.741891\pi$
$558$	9.39188	0.397590
$559$	−0.144936	−0.00613016
$560$	−90.3075	−3.81619
$561$	−2.06139	−0.0870318
$562$	−23.5745	−0.994432
$563$	−20.2360	−0.852848	−0.426424	−	0.904523i	$-0.640227\pi$
$563$	−20.2360	−0.852848	−0.426424	+	0.904523i	$0.640227\pi$
$564$	14.1102	0.594146
$565$	−0.253118	−0.0106487
$566$	23.7434	0.998009
$567$	37.0880	1.55755
$568$	−26.5520	−1.11410
$569$	1.25394	0.0525680	0.0262840	−	0.999655i	$-0.491633\pi$
$569$	1.25394	0.0525680	0.0262840	+	0.999655i	$0.491633\pi$
$570$	56.3670	2.36095
$571$	−18.9751	−0.794082	−0.397041	−	0.917801i	$-0.629963\pi$
$571$	−18.9751	−0.794082	−0.397041	+	0.917801i	$0.629963\pi$
$572$	47.4955	1.98589
$573$	−13.7591	−0.574793
$574$	−54.2831	−2.26573
$575$	6.52274	0.272017
$576$	9.31089	0.387954
$577$	25.8602	1.07657	0.538287	−	0.842761i	$-0.319072\pi$
$577$	25.8602	1.07657	0.538287	+	0.842761i	$0.319072\pi$
$578$	44.6234	1.85609
$579$	7.54533	0.313573
$580$	−40.1194	−1.66587
$581$	−14.6051	−0.605922
$582$	77.3459	3.20609
$583$	8.70229	0.360412
$584$	−25.9831	−1.07519
$585$	−4.81543	−0.199093
$586$	24.4029	1.00807
$587$	43.0848	1.77830	0.889150	−	0.457615i	$-0.151296\pi$
$587$	43.0848	1.77830	0.889150	+	0.457615i	$0.151296\pi$
$588$	−59.3168	−2.44618
$589$	−40.0219	−1.64907
$590$	−55.3881	−2.28029
$591$	8.50561	0.349874
$592$	−141.696	−5.82366
$593$	−14.8971	−0.611752	−0.305876	−	0.952071i	$-0.598949\pi$
$593$	−14.8971	−0.611752	−0.305876	+	0.952071i	$0.598949\pi$
$594$	23.5748	0.967285
$595$	4.25704	0.174522
$596$	26.8253	1.09881
$597$	−50.2695	−2.05739
$598$	−85.4559	−3.49455
$599$	22.5246	0.920330	0.460165	−	0.887833i	$-0.347790\pi$
$599$	22.5246	0.920330	0.460165	+	0.887833i	$0.347790\pi$
$600$	−15.8972	−0.649001
$601$	15.2290	0.621204	0.310602	−	0.950540i	$-0.399469\pi$
$601$	15.2290	0.621204	0.310602	+	0.950540i	$0.399469\pi$
$602$	0.288089	0.0117416
$603$	−5.59917	−0.228016
$604$	−16.0100	−0.651438
$605$	−14.9494	−0.607780
$606$	−93.2735	−3.78898
$607$	−2.61900	−0.106302	−0.0531510	−	0.998586i	$-0.516926\pi$
$607$	−2.61900	−0.106302	−0.0531510	+	0.998586i	$0.516926\pi$
$608$	−92.0186	−3.73185
$609$	−26.2278	−1.06281
$610$	−12.9208	−0.523150
$611$	7.12060	0.288069
$612$	−1.49921	−0.0606022
$613$	−35.8298	−1.44715	−0.723576	−	0.690245i	$-0.757503\pi$
$613$	−35.8298	−1.44715	−0.723576	+	0.690245i	$0.757503\pi$
$614$	−25.1391	−1.01453
$615$	20.9036	0.842915
$616$	−57.9456	−2.33469
$617$	−33.9023	−1.36486	−0.682428	−	0.730953i	$-0.739076\pi$
$617$	−33.9023	−1.36486	−0.682428	+	0.730953i	$0.739076\pi$
$618$	15.5344	0.624884
$619$	−26.7132	−1.07369	−0.536847	−	0.843679i	$-0.680385\pi$
$619$	−26.7132	−1.07369	−0.536847	+	0.843679i	$0.680385\pi$
$620$	−73.6675	−2.95856
$621$	−30.5990	−1.22790
$622$	49.6598	1.99118
$623$	36.5684	1.46508
$624$	113.734	4.55301
$625$	−19.0083	−0.760330
$626$	−49.4756	−1.97744
$627$	19.7506	0.788761
$628$	−30.1146	−1.20170
$629$	6.67946	0.266327
$630$	9.57158	0.381341
$631$	−12.0774	−0.480793	−0.240396	−	0.970675i	$-0.577277\pi$
$631$	−12.0774	−0.480793	−0.240396	+	0.970675i	$0.577277\pi$
$632$	108.031	4.29722
$633$	45.8744	1.82335
$634$	−0.621680	−0.0246900
$635$	4.32067	0.171460
$636$	44.8503	1.77843
$637$	−29.9338	−1.18602
$638$	−19.4867	−0.771487
$639$	1.53679	0.0607946
$640$	−35.8227	−1.41602
$641$	22.7510	0.898609	0.449305	−	0.893379i	$-0.351672\pi$
$641$	22.7510	0.898609	0.449305	+	0.893379i	$0.351672\pi$
$642$	−9.12471	−0.360123
$643$	32.1497	1.26786	0.633930	−	0.773390i	$-0.281441\pi$
$643$	32.1497	1.26786	0.633930	+	0.773390i	$0.281441\pi$
$644$	122.535	4.82857
$645$	−0.110939	−0.00436820
$646$	8.85601	0.348435
$647$	20.6103	0.810274	0.405137	−	0.914256i	$-0.367224\pi$
$647$	20.6103	0.810274	0.405137	+	0.914256i	$0.367224\pi$
$648$	87.1687	3.42431
$649$	−19.4076	−0.761814
$650$	−13.0703	−0.512660
$651$	−48.1597	−1.88753
$652$	−68.2903	−2.67445
$653$	−9.52244	−0.372642	−0.186321	−	0.982489i	$-0.559656\pi$
$653$	−9.52244	−0.372642	−0.186321	+	0.982489i	$0.559656\pi$
$654$	−6.21647	−0.243083
$655$	20.5501	0.802957
$656$	−69.6707	−2.72018
$657$	1.50386	0.0586713
$658$	−14.1536	−0.551763
$659$	−28.0343	−1.09206	−0.546030	−	0.837765i	$-0.683862\pi$
$659$	−28.0343	−1.09206	−0.546030	+	0.837765i	$0.683862\pi$
$660$	36.3545	1.41510
$661$	0.597726	0.0232488	0.0116244	−	0.999932i	$-0.496300\pi$
$661$	0.597726	0.0232488	0.0116244	+	0.999932i	$0.496300\pi$
$662$	49.4735	1.92284
$663$	−5.36136	−0.208218
$664$	−34.3267	−1.33213
$665$	−40.7876	−1.58167
$666$	15.0182	0.581942
$667$	25.2929	0.979345
$668$	−93.5299	−3.61878
$669$	−7.55287	−0.292011
$670$	60.8802	2.35201
$671$	−4.52737	−0.174777
$672$	−110.729	−4.27147
$673$	4.32470	0.166705	0.0833525	−	0.996520i	$-0.473437\pi$
$673$	4.32470	0.166705	0.0833525	+	0.996520i	$0.473437\pi$
$674$	74.8336	2.88248
$675$	−4.68007	−0.180136
$676$	56.2083	2.16186
$677$	43.7274	1.68058	0.840290	−	0.542138i	$-0.182385\pi$
$677$	43.7274	1.68058	0.840290	+	0.542138i	$0.182385\pi$
$678$	−0.633634	−0.0243346
$679$	−55.9681	−2.14786
$680$	10.0054	0.383690
$681$	−31.1740	−1.19459
$682$	−35.7816	−1.37015
$683$	−18.7284	−0.716621	−0.358310	−	0.933603i	$-0.616647\pi$
$683$	−18.7284	−0.716621	−0.358310	+	0.933603i	$0.616647\pi$
$684$	14.3643	0.549232
$685$	18.8758	0.721206
$686$	−8.45700	−0.322890
$687$	−7.59006	−0.289579
$688$	0.369753	0.0140967
$689$	22.6334	0.862263
$690$	−65.4105	−2.49013
$691$	38.5300	1.46575	0.732875	−	0.680364i	$-0.238178\pi$
$691$	38.5300	1.46575	0.732875	+	0.680364i	$0.238178\pi$
$692$	1.97860	0.0752153
$693$	3.35381	0.127401
$694$	37.6739	1.43008
$695$	−33.8326	−1.28335
$696$	−61.6438	−2.33660
$697$	3.28424	0.124399
$698$	26.5925	1.00654
$699$	9.10144	0.344248
$700$	18.7416	0.708364
$701$	38.9007	1.46926	0.734630	−	0.678468i	$-0.237356\pi$
$701$	38.9007	1.46926	0.734630	+	0.678468i	$0.237356\pi$
$702$	61.3146	2.31417
$703$	−63.9973	−2.41370
$704$	−35.4730	−1.33694
$705$	5.45032	0.205271
$706$	−54.7000	−2.05866
$707$	67.4934	2.53835
$708$	−100.024	−3.75912
$709$	−31.7570	−1.19266	−0.596330	−	0.802739i	$-0.703375\pi$
$709$	−31.7570	−1.19266	−0.596330	+	0.802739i	$0.703375\pi$
$710$	−16.7097	−0.627103
$711$	−6.25265	−0.234493
$712$	85.9475	3.22102
$713$	46.4430	1.73930
$714$	10.6567	0.398818
$715$	18.3460	0.686102
$716$	121.297	4.53309
$717$	−27.9473	−1.04371
$718$	74.4272	2.77760
$719$	−30.3241	−1.13090	−0.565449	−	0.824783i	$-0.691297\pi$
$719$	−30.3241	−1.13090	−0.565449	+	0.824783i	$0.691297\pi$
$720$	12.2848	0.457828
$721$	−11.2408	−0.418629
$722$	−33.9450	−1.26330
$723$	47.1569	1.75379
$724$	−102.136	−3.79584
$725$	3.86851	0.143673
$726$	−37.4231	−1.38890
$727$	29.3809	1.08968	0.544838	−	0.838541i	$-0.316591\pi$
$727$	29.3809	1.08968	0.544838	+	0.838541i	$0.316591\pi$
$728$	−150.708	−5.58561
$729$	21.2259	0.786146
$730$	−16.3516	−0.605201
$731$	−0.0174299	−0.000644670 0
$732$	−23.3334	−0.862426
$733$	−35.4615	−1.30980	−0.654901	−	0.755715i	$-0.727290\pi$
$733$	−35.4615	−1.30980	−0.654901	+	0.755715i	$0.727290\pi$
$734$	−69.8411	−2.57788
$735$	−22.9122	−0.845130
$736$	106.782	3.93604
$737$	21.3320	0.785773
$738$	7.38431	0.271820
$739$	36.6541	1.34834	0.674172	−	0.738574i	$-0.264501\pi$
$739$	36.6541	1.34834	0.674172	+	0.738574i	$0.264501\pi$
$740$	−117.799	−4.33036
$741$	51.3683	1.88706
$742$	−44.9882	−1.65157
$743$	23.0991	0.847424	0.423712	−	0.905797i	$-0.360727\pi$
$743$	23.0991	0.847424	0.423712	+	0.905797i	$0.360727\pi$
$744$	−113.191	−4.14977
$745$	10.3618	0.379626
$746$	94.7960	3.47073
$747$	1.98678	0.0726924
$748$	5.71177	0.208843
$749$	6.60271	0.241258
$750$	−60.0856	−2.19401
$751$	−34.9817	−1.27650	−0.638250	−	0.769829i	$-0.720341\pi$
$751$	−34.9817	−1.27650	−0.638250	+	0.769829i	$0.720341\pi$
$752$	−18.1656	−0.662433
$753$	−33.4956	−1.22065
$754$	−50.6821	−1.84573
$755$	−6.18416	−0.225065
$756$	−87.9191	−3.19759
$757$	−27.1362	−0.986280	−0.493140	−	0.869950i	$-0.664151\pi$
$757$	−27.1362	−0.986280	−0.493140	+	0.869950i	$0.664151\pi$
$758$	55.0850	2.00078
$759$	−22.9193	−0.831919
$760$	−95.8639	−3.47735
$761$	9.64973	0.349802	0.174901	−	0.984586i	$-0.444039\pi$
$761$	9.64973	0.349802	0.174901	+	0.984586i	$0.444039\pi$
$762$	10.8160	0.391823
$763$	4.49829	0.162849
$764$	38.1242	1.37928
$765$	−0.579099	−0.0209374
$766$	−38.0784	−1.37583
$767$	−50.4763	−1.82259
$768$	−19.0675	−0.688038
$769$	31.0577	1.11997	0.559984	−	0.828503i	$-0.310807\pi$
$769$	31.0577	1.11997	0.559984	+	0.828503i	$0.310807\pi$
$770$	−36.4662	−1.31415
$771$	−44.5008	−1.60266
$772$	−20.9069	−0.752456
$773$	5.48032	0.197113	0.0985567	−	0.995131i	$-0.468577\pi$
$773$	5.48032	0.197113	0.0985567	+	0.995131i	$0.468577\pi$
$774$	−0.0391897	−0.00140864
$775$	7.10337	0.255160
$776$	−131.543	−4.72212
$777$	−77.0101	−2.76272
$778$	−52.5553	−1.88420
$779$	−31.4669	−1.12742
$780$	94.5527	3.38553
$781$	−5.85494	−0.209506
$782$	−10.2769	−0.367500
$783$	−18.1477	−0.648544
$784$	76.3653	2.72733
$785$	−11.6323	−0.415175
$786$	51.4434	1.83492
$787$	−50.5572	−1.80217	−0.901084	−	0.433644i	$-0.857227\pi$
$787$	−50.5572	−1.80217	−0.901084	+	0.433644i	$0.857227\pi$
$788$	−23.5677	−0.839565
$789$	39.8604	1.41907
$790$	67.9856	2.41882
$791$	0.458503	0.0163025
$792$	7.88252	0.280093
$793$	−11.7750	−0.418143
$794$	0.0113823	0.000403942 0
$795$	17.3243	0.614428
$796$	139.289	4.93696
$797$	45.2923	1.60434	0.802168	−	0.597099i	$-0.203680\pi$
$797$	45.2923	1.60434	0.802168	+	0.597099i	$0.203680\pi$
$798$	−102.104	−3.61445
$799$	0.856318	0.0302944
$800$	16.3321	0.577428
$801$	−4.97452	−0.175766
$802$	63.8534	2.25474
$803$	−5.72948	−0.202189
$804$	109.942	3.87735
$805$	47.3315	1.66822
$806$	−93.0627	−3.27800
$807$	12.1408	0.427378
$808$	158.631	5.58063
$809$	14.6332	0.514474	0.257237	−	0.966348i	$-0.417188\pi$
$809$	14.6332	0.514474	0.257237	+	0.966348i	$0.417188\pi$
$810$	54.8568	1.92747
$811$	2.80532	0.0985081	0.0492541	−	0.998786i	$-0.484316\pi$
$811$	2.80532	0.0985081	0.0492541	+	0.998786i	$0.484316\pi$
$812$	72.6732	2.55033
$813$	7.97352	0.279644
$814$	−57.2169	−2.00545
$815$	−26.3784	−0.923994
$816$	13.6776	0.478811
$817$	0.167000	0.00584258
$818$	−83.7222	−2.92728
$819$	8.72277	0.304798
$820$	−57.9206	−2.02267
$821$	−15.4956	−0.540799	−0.270399	−	0.962748i	$-0.587156\pi$
$821$	−15.4956	−0.540799	−0.270399	+	0.962748i	$0.587156\pi$
$822$	47.2521	1.64810
$823$	39.5566	1.37886	0.689429	−	0.724354i	$-0.257862\pi$
$823$	39.5566	1.37886	0.689429	+	0.724354i	$0.257862\pi$
$824$	−26.4195	−0.920366
$825$	−3.50547	−0.122045
$826$	100.331	3.49097
$827$	7.45951	0.259393	0.129696	−	0.991554i	$-0.458600\pi$
$827$	7.45951	0.259393	0.129696	+	0.991554i	$0.458600\pi$
$828$	−16.6689	−0.579284
$829$	35.9454	1.24843	0.624217	−	0.781251i	$-0.285418\pi$
$829$	35.9454	1.24843	0.624217	+	0.781251i	$0.285418\pi$
$830$	−21.6024	−0.749830
$831$	6.62999	0.229992
$832$	−92.2602	−3.19855
$833$	−3.59982	−0.124726
$834$	−84.6939	−2.93271
$835$	−36.1276	−1.25025
$836$	−54.7257	−1.89273
$837$	−33.3228	−1.15180
$838$	−79.7537	−2.75505
$839$	−29.4243	−1.01584	−0.507919	−	0.861405i	$-0.669585\pi$
$839$	−29.4243	−1.01584	−0.507919	+	0.861405i	$0.669585\pi$
$840$	−115.356	−3.98017
$841$	−13.9993	−0.482734
$842$	14.3993	0.496232
$843$	−16.4444	−0.566377
$844$	−127.111	−4.37533
$845$	21.7115	0.746897
$846$	1.92535	0.0661950
$847$	27.0797	0.930469
$848$	−57.7409	−1.98283
$849$	16.5622	0.568414
$850$	−1.57183	−0.0539132
$851$	74.2650	2.54577
$852$	−30.1755	−1.03380
$853$	17.4065	0.595987	0.297993	−	0.954568i	$-0.403683\pi$
$853$	17.4065	0.595987	0.297993	+	0.954568i	$0.403683\pi$
$854$	23.4051	0.800906
$855$	5.54847	0.189754
$856$	15.5185	0.530411
$857$	10.4550	0.357135	0.178567	−	0.983928i	$-0.442854\pi$
$857$	10.4550	0.357135	0.178567	+	0.983928i	$0.442854\pi$
$858$	45.9259	1.56789
$859$	−11.4006	−0.388983	−0.194492	−	0.980904i	$-0.562306\pi$
$859$	−11.4006	−0.388983	−0.194492	+	0.980904i	$0.562306\pi$
$860$	0.307393	0.0104820
$861$	−37.8652	−1.29044
$862$	−33.8494	−1.15292
$863$	17.9911	0.612424	0.306212	−	0.951963i	$-0.400938\pi$
$863$	17.9911	0.612424	0.306212	+	0.951963i	$0.400938\pi$
$864$	−76.6161	−2.60653
$865$	0.764273	0.0259860
$866$	−23.0303	−0.782603
$867$	31.1271	1.05713
$868$	133.443	4.52935
$869$	23.8216	0.808094
$870$	−38.7936	−1.31523
$871$	55.4813	1.87991
$872$	10.5724	0.358027
$873$	7.61353	0.257679
$874$	98.4647	3.33062
$875$	43.4784	1.46984
$876$	−29.5289	−0.997690
$877$	−6.94506	−0.234518	−0.117259	−	0.993101i	$-0.537411\pi$
$877$	−6.94506	−0.234518	−0.117259	+	0.993101i	$0.537411\pi$
$878$	−14.0633	−0.474613
$879$	17.0222	0.574146
$880$	−46.8033	−1.57774
$881$	27.4833	0.925937	0.462969	−	0.886375i	$-0.346784\pi$
$881$	27.4833	0.925937	0.462969	+	0.886375i	$0.346784\pi$
$882$	−8.09386	−0.272535
$883$	56.0752	1.88708	0.943541	−	0.331257i	$-0.107473\pi$
$883$	56.0752	1.88708	0.943541	+	0.331257i	$0.107473\pi$
$884$	14.8555	0.499644
$885$	−38.6360	−1.29874
$886$	−99.2634	−3.33482
$887$	−31.5172	−1.05824	−0.529122	−	0.848546i	$-0.677478\pi$
$887$	−31.5172	−1.05824	−0.529122	+	0.848546i	$0.677478\pi$
$888$	−180.998	−6.07391
$889$	−7.82655	−0.262494
$890$	54.0884	1.81305
$891$	19.2214	0.643942
$892$	20.9278	0.700715
$893$	−8.20456	−0.274555
$894$	25.9388	0.867523
$895$	46.8532	1.56613
$896$	64.8901	2.16783
$897$	−59.6098	−1.99031
$898$	6.67294	0.222679
$899$	27.5444	0.918656
$900$	−2.54948	−0.0849825
$901$	2.72187	0.0906788
$902$	−28.1331	−0.936729
$903$	0.200957	0.00668742
$904$	1.07763	0.0358414
$905$	−39.4518	−1.31142
$906$	−15.4809	−0.514319
$907$	−45.9547	−1.52590	−0.762951	−	0.646457i	$-0.776250\pi$
$907$	−45.9547	−1.52590	−0.762951	+	0.646457i	$0.776250\pi$
$908$	86.3783	2.86657
$909$	−9.18135	−0.304526
$910$	−94.8433	−3.14402
$911$	2.13095	0.0706017	0.0353008	−	0.999377i	$-0.488761\pi$
$911$	2.13095	0.0706017	0.0353008	+	0.999377i	$0.488761\pi$
$912$	−131.048	−4.33942
$913$	−7.56932	−0.250508
$914$	27.3399	0.904325
$915$	−9.01295	−0.297959
$916$	21.0308	0.694879
$917$	−37.2248	−1.22927
$918$	7.37365	0.243367
$919$	0.242088	0.00798573	0.00399287	−	0.999992i	$-0.498729\pi$
$919$	0.242088	0.00798573	0.00399287	+	0.999992i	$0.498729\pi$
$920$	111.244	3.66762
$921$	−17.5358	−0.577823
$922$	78.6710	2.59089
$923$	−15.2278	−0.501231
$924$	−65.8533	−2.16641
$925$	11.3587	0.373471
$926$	26.4857	0.870373
$927$	1.52912	0.0502229
$928$	63.3302	2.07892
$929$	22.4497	0.736551	0.368275	−	0.929717i	$-0.379948\pi$
$929$	22.4497	0.736551	0.368275	+	0.929717i	$0.379948\pi$
$930$	−71.2330	−2.33582
$931$	34.4906	1.13038
$932$	−25.2187	−0.826064
$933$	34.6402	1.13407
$934$	−75.1503	−2.45899
$935$	2.20628	0.0721530
$936$	20.5013	0.670106
$937$	1.09712	0.0358415	0.0179207	−	0.999839i	$-0.494295\pi$
$937$	1.09712	0.0358415	0.0179207	+	0.999839i	$0.494295\pi$
$938$	−110.280	−3.60076
$939$	−34.5117	−1.12625
$940$	−15.1020	−0.492572
$941$	19.9801	0.651334	0.325667	−	0.945485i	$-0.394411\pi$
$941$	19.9801	0.651334	0.325667	+	0.945485i	$0.394411\pi$
$942$	−29.1194	−0.948760
$943$	36.5155	1.18911
$944$	128.772	4.19117
$945$	−33.9604	−1.10473
$946$	0.149306	0.00485437
$947$	−18.5167	−0.601713	−0.300857	−	0.953669i	$-0.597273\pi$
$947$	−18.5167	−0.601713	−0.300857	+	0.953669i	$0.597273\pi$
$948$	122.773	3.98749
$949$	−14.9016	−0.483725
$950$	15.0600	0.488611
$951$	−0.433653	−0.0140622
$952$	−18.1240	−0.587403
$953$	−38.1266	−1.23504	−0.617520	−	0.786555i	$-0.711863\pi$
$953$	−38.1266	−1.23504	−0.617520	+	0.786555i	$0.711863\pi$
$954$	6.11989	0.198139
$955$	14.7262	0.476528
$956$	77.4375	2.50451
$957$	−13.5930	−0.439399
$958$	−74.9595	−2.42183
$959$	−34.1920	−1.10412
$960$	−70.6187	−2.27921
$961$	19.5771	0.631519
$962$	−148.813	−4.79791
$963$	−0.898188	−0.0289437
$964$	−130.664	−4.20842
$965$	−8.07568	−0.259965
$966$	118.486	3.81222
$967$	−52.8968	−1.70105	−0.850523	−	0.525938i	$-0.823714\pi$
$967$	−52.8968	−1.70105	−0.850523	+	0.525938i	$0.823714\pi$
$968$	63.6459	2.04566
$969$	6.17751	0.198450
$970$	−82.7825	−2.65798
$971$	−55.7271	−1.78837	−0.894184	−	0.447699i	$-0.852243\pi$
$971$	−55.7271	−1.78837	−0.894184	+	0.447699i	$0.852243\pi$
$972$	26.2712	0.842649
$973$	61.2852	1.96471
$974$	16.8112	0.538664
$975$	−9.11722	−0.291985
$976$	30.0397	0.961548
$977$	−35.4185	−1.13314	−0.566569	−	0.824015i	$-0.691729\pi$
$977$	−35.4185	−1.13314	−0.566569	+	0.824015i	$0.691729\pi$
$978$	−66.0335	−2.11152
$979$	18.9522	0.605713
$980$	63.4861	2.02799
$981$	−0.611917	−0.0195370
$982$	−45.4935	−1.45176
$983$	−41.5279	−1.32453	−0.662267	−	0.749268i	$-0.730406\pi$
$983$	−41.5279	−1.32453	−0.662267	+	0.749268i	$0.730406\pi$
$984$	−88.9955	−2.83707
$985$	−9.10346	−0.290060
$986$	−6.09500	−0.194104
$987$	−9.87282	−0.314255
$988$	−142.333	−4.52823
$989$	−0.193793	−0.00616227
$990$	4.96062	0.157659
$991$	32.3587	1.02791	0.513954	−	0.857818i	$-0.328180\pi$
$991$	32.3587	1.02791	0.513954	+	0.857818i	$0.328180\pi$
$992$	116.287	3.69212
$993$	34.5103	1.09515
$994$	30.2682	0.960051
$995$	53.8029	1.70567
$996$	−39.0111	−1.23612
$997$	−45.0739	−1.42750	−0.713752	−	0.700399i	$-0.753006\pi$
$997$	−45.0739	−1.42750	−0.713752	+	0.700399i	$0.753006\pi$
$998$	41.4518	1.31213
$999$	−53.2851	−1.68587

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4021.2.a.c.1.5	✓	182

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4021.2.a.c.1.5	✓	182	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)

\(f(q)\)	\(=\)	\(q-2.67927 q^{2} -1.86893 q^{3} +5.17851 q^{4} +2.00029 q^{5} +5.00738 q^{6} -3.62338 q^{7} -8.51610 q^{8} +0.492900 q^{9} +O(q^{10})\)	\(q-2.67927 q^{2} -1.86893 q^{3} +5.17851 q^{4} +2.00029 q^{5} +5.00738 q^{6} -3.62338 q^{7} -8.51610 q^{8} +0.492900 q^{9} -5.35934 q^{10} -1.87787 q^{11} -9.67827 q^{12} -4.88407 q^{13} +9.70802 q^{14} -3.73841 q^{15} +12.4599 q^{16} -0.587355 q^{17} -1.32061 q^{18} +5.62756 q^{19} +10.3585 q^{20} +6.77184 q^{21} +5.03133 q^{22} -6.53045 q^{23} +15.9160 q^{24} -0.998820 q^{25} +13.0858 q^{26} +4.68559 q^{27} -18.7637 q^{28} -3.87307 q^{29} +10.0162 q^{30} -7.11176 q^{31} -16.3514 q^{32} +3.50961 q^{33} +1.57368 q^{34} -7.24782 q^{35} +2.55249 q^{36} -11.3721 q^{37} -15.0778 q^{38} +9.12799 q^{39} -17.0347 q^{40} -5.59157 q^{41} -18.1436 q^{42} +0.0296753 q^{43} -9.72458 q^{44} +0.985945 q^{45} +17.4969 q^{46} -1.45792 q^{47} -23.2868 q^{48} +6.12886 q^{49} +2.67611 q^{50} +1.09772 q^{51} -25.2922 q^{52} -4.63412 q^{53} -12.5540 q^{54} -3.75630 q^{55} +30.8570 q^{56} -10.5175 q^{57} +10.3770 q^{58} +10.3349 q^{59} -19.3594 q^{60} +2.41090 q^{61} +19.0543 q^{62} -1.78596 q^{63} +18.8900 q^{64} -9.76958 q^{65} -9.40321 q^{66} -11.3596 q^{67} -3.04162 q^{68} +12.2050 q^{69} +19.4189 q^{70} +3.11786 q^{71} -4.19758 q^{72} +3.05105 q^{73} +30.4690 q^{74} +1.86673 q^{75} +29.1424 q^{76} +6.80424 q^{77} -24.4564 q^{78} -12.6854 q^{79} +24.9236 q^{80} -10.2357 q^{81} +14.9814 q^{82} +4.03080 q^{83} +35.0680 q^{84} -1.17488 q^{85} -0.0795084 q^{86} +7.23851 q^{87} +15.9921 q^{88} -10.0924 q^{89} -2.64162 q^{90} +17.6968 q^{91} -33.8180 q^{92} +13.2914 q^{93} +3.90618 q^{94} +11.2568 q^{95} +30.5596 q^{96} +15.4464 q^{97} -16.4209 q^{98} -0.925603 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 182 q + 18 q^{2} + 28 q^{3} + 208 q^{4} + 22 q^{5} + 18 q^{6} + 14 q^{7} + 54 q^{8} + 238 q^{9}+O(q^{10}) \) 182 * q + 18 * q^2 + 28 * q^3 + 208 * q^4 + 22 * q^5 + 18 * q^6 + 14 * q^7 + 54 * q^8 + 238 * q^9	\( 182 q + 18 q^{2} + 28 q^{3} + 208 q^{4} + 22 q^{5} + 18 q^{6} + 14 q^{7} + 54 q^{8} + 238 q^{9} + 7 q^{10} + 138 q^{11} + 47 q^{12} + 5 q^{13} + 72 q^{14} + 41 q^{15} + 256 q^{16} + 29 q^{17} + 35 q^{18} + 48 q^{19} + 56 q^{20} + 22 q^{21} + 19 q^{22} + 91 q^{23} + 46 q^{24} + 230 q^{25} + 88 q^{26} + 103 q^{27} + 15 q^{28} + 75 q^{29} + 18 q^{30} + 43 q^{31} + 116 q^{32} + 15 q^{33} + 13 q^{34} + 185 q^{35} + 364 q^{36} + 15 q^{37} + 53 q^{38} + 80 q^{39} - 13 q^{40} + 68 q^{41} + 32 q^{42} + 82 q^{43} + 259 q^{44} + 37 q^{45} + 13 q^{46} + 121 q^{47} + 53 q^{48} + 244 q^{49} + 93 q^{50} + 144 q^{51} - 16 q^{52} + 101 q^{53} + 47 q^{54} + 49 q^{55} + 199 q^{56} + 3 q^{57} + 4 q^{58} + 254 q^{59} + 24 q^{60} + 8 q^{61} + 37 q^{62} + 19 q^{63} + 326 q^{64} + 65 q^{65} + 41 q^{66} + 91 q^{67} + 50 q^{68} + 50 q^{69} + 5 q^{70} + 212 q^{71} + 77 q^{72} + 5 q^{73} + 101 q^{74} + 127 q^{75} + 22 q^{76} + 87 q^{77} - 20 q^{78} + 86 q^{79} + 71 q^{80} + 358 q^{81} - 20 q^{82} + 139 q^{83} - 30 q^{84} + 25 q^{85} + 82 q^{86} + 36 q^{87} - 8 q^{88} + 100 q^{89} - 87 q^{90} + 74 q^{91} + 171 q^{92} + 50 q^{93} - 13 q^{94} + 217 q^{95} + 42 q^{96} + 20 q^{97} + 47 q^{98} + 389 q^{99}+O(q^{100}) \) 182 * q + 18 * q^2 + 28 * q^3 + 208 * q^4 + 22 * q^5 + 18 * q^6 + 14 * q^7 + 54 * q^8 + 238 * q^9 + 7 * q^10 + 138 * q^11 + 47 * q^12 + 5 * q^13 + 72 * q^14 + 41 * q^15 + 256 * q^16 + 29 * q^17 + 35 * q^18 + 48 * q^19 + 56 * q^20 + 22 * q^21 + 19 * q^22 + 91 * q^23 + 46 * q^24 + 230 * q^25 + 88 * q^26 + 103 * q^27 + 15 * q^28 + 75 * q^29 + 18 * q^30 + 43 * q^31 + 116 * q^32 + 15 * q^33 + 13 * q^34 + 185 * q^35 + 364 * q^36 + 15 * q^37 + 53 * q^38 + 80 * q^39 - 13 * q^40 + 68 * q^41 + 32 * q^42 + 82 * q^43 + 259 * q^44 + 37 * q^45 + 13 * q^46 + 121 * q^47 + 53 * q^48 + 244 * q^49 + 93 * q^50 + 144 * q^51 - 16 * q^52 + 101 * q^53 + 47 * q^54 + 49 * q^55 + 199 * q^56 + 3 * q^57 + 4 * q^58 + 254 * q^59 + 24 * q^60 + 8 * q^61 + 37 * q^62 + 19 * q^63 + 326 * q^64 + 65 * q^65 + 41 * q^66 + 91 * q^67 + 50 * q^68 + 50 * q^69 + 5 * q^70 + 212 * q^71 + 77 * q^72 + 5 * q^73 + 101 * q^74 + 127 * q^75 + 22 * q^76 + 87 * q^77 - 20 * q^78 + 86 * q^79 + 71 * q^80 + 358 * q^81 - 20 * q^82 + 139 * q^83 - 30 * q^84 + 25 * q^85 + 82 * q^86 + 36 * q^87 - 8 * q^88 + 100 * q^89 - 87 * q^90 + 74 * q^91 + 171 * q^92 + 50 * q^93 - 13 * q^94 + 217 * q^95 + 42 * q^96 + 20 * q^97 + 47 * q^98 + 389 * q^99

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