LMFDB - Embedded newform 4021.2.a.b.1.1

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			1.1
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)

$f(q)$	$=$	$q-2.75476 q^{2} +1.58414 q^{3} +5.58872 q^{4} -2.10175 q^{5} -4.36394 q^{6} +2.25410 q^{7} -9.88608 q^{8} -0.490495 q^{9} +O(q^{10})$	\(q-2.75476 q^{2} +1.58414 q^{3} +5.58872 q^{4} -2.10175 q^{5} -4.36394 q^{6} +2.25410 q^{7} -9.88608 q^{8} -0.490495 q^{9} +5.78981 q^{10} +1.94977 q^{11} +8.85333 q^{12} -3.92401 q^{13} -6.20952 q^{14} -3.32946 q^{15} +16.0564 q^{16} +1.85363 q^{17} +1.35120 q^{18} +2.21776 q^{19} -11.7461 q^{20} +3.57082 q^{21} -5.37116 q^{22} -0.662128 q^{23} -15.6609 q^{24} -0.582661 q^{25} +10.8097 q^{26} -5.52944 q^{27} +12.5975 q^{28} -0.706007 q^{29} +9.17189 q^{30} -0.225375 q^{31} -24.4593 q^{32} +3.08872 q^{33} -5.10632 q^{34} -4.73755 q^{35} -2.74124 q^{36} +7.77252 q^{37} -6.10940 q^{38} -6.21619 q^{39} +20.7780 q^{40} -8.00692 q^{41} -9.83675 q^{42} +4.71441 q^{43} +10.8967 q^{44} +1.03090 q^{45} +1.82401 q^{46} -4.00297 q^{47} +25.4356 q^{48} -1.91903 q^{49} +1.60509 q^{50} +2.93642 q^{51} -21.9302 q^{52} +3.02515 q^{53} +15.2323 q^{54} -4.09793 q^{55} -22.2842 q^{56} +3.51324 q^{57} +1.94488 q^{58} -4.65922 q^{59} -18.6074 q^{60} +0.244526 q^{61} +0.620856 q^{62} -1.10563 q^{63} +35.2669 q^{64} +8.24728 q^{65} -8.50868 q^{66} -1.01244 q^{67} +10.3594 q^{68} -1.04890 q^{69} +13.0508 q^{70} -3.47487 q^{71} +4.84907 q^{72} -3.25162 q^{73} -21.4115 q^{74} -0.923017 q^{75} +12.3944 q^{76} +4.39498 q^{77} +17.1241 q^{78} +14.9629 q^{79} -33.7464 q^{80} -7.28793 q^{81} +22.0572 q^{82} +7.81484 q^{83} +19.9563 q^{84} -3.89587 q^{85} -12.9871 q^{86} -1.11842 q^{87} -19.2756 q^{88} -1.05559 q^{89} -2.83988 q^{90} -8.84512 q^{91} -3.70045 q^{92} -0.357027 q^{93} +11.0272 q^{94} -4.66116 q^{95} -38.7470 q^{96} +10.4961 q^{97} +5.28646 q^{98} -0.956354 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.75476	−1.94791	−0.973956	−	0.226737i	$-0.927194\pi$
$2$	−2.75476	−1.94791	−0.973956	+	0.226737i	$0.927194\pi$
$3$	1.58414	0.914605	0.457302	−	0.889311i	$-0.348816\pi$
$3$	1.58414	0.914605	0.457302	+	0.889311i	$0.348816\pi$
$4$	5.58872	2.79436
$5$	−2.10175	−0.939930	−0.469965	−	0.882685i	$-0.655733\pi$
$5$	−2.10175	−0.939930	−0.469965	+	0.882685i	$0.655733\pi$
$6$	−4.36394	−1.78157
$7$	2.25410	0.851970	0.425985	−	0.904730i	$-0.359928\pi$
$7$	2.25410	0.851970	0.425985	+	0.904730i	$0.359928\pi$
$8$	−9.88608	−3.49526
$9$	−0.490495	−0.163498
$10$	5.78981	1.83090
$11$	1.94977	0.587878	0.293939	−	0.955824i	$-0.405034\pi$
$11$	1.94977	0.587878	0.293939	+	0.955824i	$0.405034\pi$
$12$	8.85333	2.55574
$13$	−3.92401	−1.08832	−0.544162	−	0.838980i	$-0.683152\pi$
$13$	−3.92401	−1.08832	−0.544162	+	0.838980i	$0.683152\pi$
$14$	−6.20952	−1.65956
$15$	−3.32946	−0.859664
$16$	16.0564	4.01409
$17$	1.85363	0.449572	0.224786	−	0.974408i	$-0.427832\pi$
$17$	1.85363	0.449572	0.224786	+	0.974408i	$0.427832\pi$
$18$	1.35120	0.318481
$19$	2.21776	0.508788	0.254394	−	0.967101i	$-0.418124\pi$
$19$	2.21776	0.508788	0.254394	+	0.967101i	$0.418124\pi$
$20$	−11.7461	−2.62650
$21$	3.57082	0.779216
$22$	−5.37116	−1.14514
$23$	−0.662128	−0.138063	−0.0690316	−	0.997614i	$-0.521991\pi$
$23$	−0.662128	−0.138063	−0.0690316	+	0.997614i	$0.521991\pi$
$24$	−15.6609	−3.19678
$25$	−0.582661	−0.116532
$26$	10.8097	2.11996
$27$	−5.52944	−1.06414
$28$	12.5975	2.38071
$29$	−0.706007	−0.131102	−0.0655511	−	0.997849i	$-0.520881\pi$
$29$	−0.706007	−0.131102	−0.0655511	+	0.997849i	$0.520881\pi$
$30$	9.17189	1.67455
$31$	−0.225375	−0.0404786	−0.0202393	−	0.999795i	$-0.506443\pi$
$31$	−0.225375	−0.0404786	−0.0202393	+	0.999795i	$0.506443\pi$
$32$	−24.4593	−4.32384
$33$	3.08872	0.537676
$34$	−5.10632	−0.875727
$35$	−4.73755	−0.800792
$36$	−2.74124	−0.456874
$37$	7.77252	1.27779	0.638897	−	0.769292i	$-0.279391\pi$
$37$	7.77252	1.27779	0.638897	+	0.769292i	$0.279391\pi$
$38$	−6.10940	−0.991075
$39$	−6.21619	−0.995387
$40$	20.7780	3.28530
$41$	−8.00692	−1.25047	−0.625235	−	0.780436i	$-0.714997\pi$
$41$	−8.00692	−1.25047	−0.625235	+	0.780436i	$0.714997\pi$
$42$	−9.83675	−1.51784
$43$	4.71441	0.718941	0.359470	−	0.933157i	$-0.382957\pi$
$43$	4.71441	0.718941	0.359470	+	0.933157i	$0.382957\pi$
$44$	10.8967	1.64274
$45$	1.03090	0.153677
$46$	1.82401	0.268935
$47$	−4.00297	−0.583893	−0.291947	−	0.956435i	$-0.594303\pi$
$47$	−4.00297	−0.583893	−0.291947	+	0.956435i	$0.594303\pi$
$48$	25.4356	3.67131
$49$	−1.91903	−0.274147
$50$	1.60509	0.226994
$51$	2.93642	0.411181
$52$	−21.9302	−3.04117
$53$	3.02515	0.415536	0.207768	−	0.978178i	$-0.433380\pi$
$53$	3.02515	0.415536	0.207768	+	0.978178i	$0.433380\pi$
$54$	15.2323	2.07285
$55$	−4.09793	−0.552564
$56$	−22.2842	−2.97785
$57$	3.51324	0.465340
$58$	1.94488	0.255376
$59$	−4.65922	−0.606578	−0.303289	−	0.952899i	$-0.598085\pi$
$59$	−4.65922	−0.606578	−0.303289	+	0.952899i	$0.598085\pi$
$60$	−18.6074	−2.40221
$61$	0.244526	0.0313083	0.0156542	−	0.999877i	$-0.495017\pi$
$61$	0.244526	0.0313083	0.0156542	+	0.999877i	$0.495017\pi$
$62$	0.620856	0.0788488
$63$	−1.10563	−0.139296
$64$	35.2669	4.40837
$65$	8.24728	1.02295
$66$	−8.50868	−1.04735
$67$	−1.01244	−0.123690	−0.0618449	−	0.998086i	$-0.519698\pi$
$67$	−1.01244	−0.123690	−0.0618449	+	0.998086i	$0.519698\pi$
$68$	10.3594	1.25627
$69$	−1.04890	−0.126273
$70$	13.0508	1.55987
$71$	−3.47487	−0.412391	−0.206196	−	0.978511i	$-0.566108\pi$
$71$	−3.47487	−0.412391	−0.206196	+	0.978511i	$0.566108\pi$
$72$	4.84907	0.571469
$73$	−3.25162	−0.380574	−0.190287	−	0.981729i	$-0.560942\pi$
$73$	−3.25162	−0.380574	−0.190287	+	0.981729i	$0.560942\pi$
$74$	−21.4115	−2.48903
$75$	−0.923017	−0.106581
$76$	12.3944	1.42174
$77$	4.39498	0.500855
$78$	17.1241	1.93893
$79$	14.9629	1.68346	0.841728	−	0.539902i	$-0.181539\pi$
$79$	14.9629	1.68346	0.841728	+	0.539902i	$0.181539\pi$
$80$	−33.7464	−3.77296
$81$	−7.28793	−0.809770
$82$	22.0572	2.43581
$83$	7.81484	0.857791	0.428895	−	0.903354i	$-0.358903\pi$
$83$	7.81484	0.857791	0.428895	+	0.903354i	$0.358903\pi$
$84$	19.9563	2.17741
$85$	−3.89587	−0.422566
$86$	−12.9871	−1.40043
$87$	−1.11842	−0.119907
$88$	−19.2756	−2.05479
$89$	−1.05559	−0.111892	−0.0559461	−	0.998434i	$-0.517818\pi$
$89$	−1.05559	−0.111892	−0.0559461	+	0.998434i	$0.517818\pi$
$90$	−2.83988	−0.299349
$91$	−8.84512	−0.927221
$92$	−3.70045	−0.385798
$93$	−0.357027	−0.0370219
$94$	11.0272	1.13737
$95$	−4.66116	−0.478225
$96$	−38.7470	−3.95460
$97$	10.4961	1.06572	0.532859	−	0.846204i	$-0.321118\pi$
$97$	10.4961	1.06572	0.532859	+	0.846204i	$0.321118\pi$
$98$	5.28646	0.534013
$99$	−0.956354	−0.0961172
$100$	−3.25633	−0.325633
$101$	−17.4268	−1.73404	−0.867018	−	0.498277i	$-0.833966\pi$
$101$	−17.4268	−1.73404	−0.867018	+	0.498277i	$0.833966\pi$
$102$	−8.08914	−0.800944
$103$	−10.3766	−1.02243	−0.511217	−	0.859452i	$-0.670805\pi$
$103$	−10.3766	−1.02243	−0.511217	+	0.859452i	$0.670805\pi$
$104$	38.7931	3.80397
$105$	−7.50495	−0.732408
$106$	−8.33356	−0.809427
$107$	−10.1764	−0.983785	−0.491893	−	0.870656i	$-0.663695\pi$
$107$	−10.1764	−0.983785	−0.491893	+	0.870656i	$0.663695\pi$
$108$	−30.9025	−2.97359
$109$	−7.10750	−0.680775	−0.340387	−	0.940285i	$-0.610558\pi$
$109$	−7.10750	−0.680775	−0.340387	+	0.940285i	$0.610558\pi$
$110$	11.2888	1.07635
$111$	12.3128	1.16868
$112$	36.1927	3.41989
$113$	−12.1645	−1.14434	−0.572172	−	0.820134i	$-0.693899\pi$
$113$	−12.1645	−1.14434	−0.572172	+	0.820134i	$0.693899\pi$
$114$	−9.67815	−0.906442
$115$	1.39162	0.129770
$116$	−3.94568	−0.366347
$117$	1.92471	0.177939
$118$	12.8350	1.18156
$119$	4.17828	0.383022
$120$	32.9153	3.00475
$121$	−7.19839	−0.654399
$122$	−0.673611	−0.0609859
$123$	−12.6841	−1.14369
$124$	−1.25956	−0.113112
$125$	11.7333	1.04946
$126$	3.04574	0.271336
$127$	12.9800	1.15179	0.575894	−	0.817524i	$-0.304654\pi$
$127$	12.9800	1.15179	0.575894	+	0.817524i	$0.304654\pi$
$128$	−48.2334	−4.26327
$129$	7.46829	0.657546
$130$	−22.7193	−1.99261
$131$	−9.92162	−0.866856	−0.433428	−	0.901188i	$-0.642696\pi$
$131$	−9.92162	−0.866856	−0.433428	+	0.901188i	$0.642696\pi$
$132$	17.2620	1.50246
$133$	4.99905	0.433473
$134$	2.78904	0.240937
$135$	11.6215	1.00022
$136$	−18.3252	−1.57137
$137$	20.0585	1.71371	0.856856	−	0.515556i	$-0.172415\pi$
$137$	20.0585	1.71371	0.856856	+	0.515556i	$0.172415\pi$
$138$	2.88948	0.245969
$139$	−16.9261	−1.43565	−0.717826	−	0.696223i	$-0.754863\pi$
$139$	−16.9261	−1.43565	−0.717826	+	0.696223i	$0.754863\pi$
$140$	−26.4768	−2.23770
$141$	−6.34127	−0.534031
$142$	9.57244	0.803301
$143$	−7.65093	−0.639803
$144$	−7.87557	−0.656298
$145$	1.48385	0.123227
$146$	8.95745	0.741324
$147$	−3.04001	−0.250736
$148$	43.4385	3.57062
$149$	−21.3079	−1.74561	−0.872804	−	0.488071i	$-0.837701\pi$
$149$	−21.3079	−1.74561	−0.872804	+	0.488071i	$0.837701\pi$
$150$	2.54269	0.207610
$151$	−7.40871	−0.602913	−0.301456	−	0.953480i	$-0.597473\pi$
$151$	−7.40871	−0.602913	−0.301456	+	0.953480i	$0.597473\pi$
$152$	−21.9249	−1.77835
$153$	−0.909199	−0.0735044
$154$	−12.1071	−0.975621
$155$	0.473682	0.0380471
$156$	−34.7406	−2.78147
$157$	−19.1893	−1.53148	−0.765738	−	0.643153i	$-0.777626\pi$
$157$	−19.1893	−1.53148	−0.765738	+	0.643153i	$0.777626\pi$
$158$	−41.2192	−3.27922
$159$	4.79226	0.380051
$160$	51.4073	4.06410
$161$	−1.49250	−0.117626
$162$	20.0765	1.57736
$163$	−7.57651	−0.593438	−0.296719	−	0.954965i	$-0.595892\pi$
$163$	−7.57651	−0.593438	−0.296719	+	0.954965i	$0.595892\pi$
$164$	−44.7484	−3.49426
$165$	−6.49170	−0.505378
$166$	−21.5280	−1.67090
$167$	−0.545012	−0.0421743	−0.0210871	−	0.999778i	$-0.506713\pi$
$167$	−0.545012	−0.0421743	−0.0210871	+	0.999778i	$0.506713\pi$
$168$	−35.3014	−2.72356
$169$	2.39786	0.184451
$170$	10.7322	0.823122
$171$	−1.08780	−0.0831861
$172$	26.3475	2.00898
$173$	9.50712	0.722813	0.361407	−	0.932408i	$-0.382297\pi$
$173$	9.50712	0.722813	0.361407	+	0.932408i	$0.382297\pi$
$174$	3.08097	0.233568
$175$	−1.31338	−0.0992819
$176$	31.3062	2.35980
$177$	−7.38086	−0.554779
$178$	2.90790	0.217956
$179$	−0.675918	−0.0505205	−0.0252602	−	0.999681i	$-0.508041\pi$
$179$	−0.675918	−0.0505205	−0.0252602	+	0.999681i	$0.508041\pi$
$180$	5.76140	0.429429
$181$	−10.9761	−0.815848	−0.407924	−	0.913016i	$-0.633747\pi$
$181$	−10.9761	−0.815848	−0.407924	+	0.913016i	$0.633747\pi$
$182$	24.3662	1.80614
$183$	0.387364	0.0286348
$184$	6.54585	0.482566
$185$	−16.3359	−1.20104
$186$	0.983524	0.0721155
$187$	3.61417	0.264294
$188$	−22.3715	−1.63161
$189$	−12.4639	−0.906617
$190$	12.8404	0.931541
$191$	3.99182	0.288838	0.144419	−	0.989517i	$-0.453869\pi$
$191$	3.99182	0.288838	0.144419	+	0.989517i	$0.453869\pi$
$192$	55.8678	4.03191
$193$	8.26413	0.594865	0.297433	−	0.954743i	$-0.403870\pi$
$193$	8.26413	0.594865	0.297433	+	0.954743i	$0.403870\pi$
$194$	−28.9143	−2.07593
$195$	13.0649	0.935594
$196$	−10.7249	−0.766064
$197$	−12.1040	−0.862371	−0.431185	−	0.902263i	$-0.641905\pi$
$197$	−12.1040	−0.862371	−0.431185	+	0.902263i	$0.641905\pi$
$198$	2.63453	0.187228
$199$	0.810514	0.0574558	0.0287279	−	0.999587i	$-0.490854\pi$
$199$	0.810514	0.0574558	0.0287279	+	0.999587i	$0.490854\pi$
$200$	5.76023	0.407310
$201$	−1.60385	−0.113127
$202$	48.0068	3.37775
$203$	−1.59141	−0.111695
$204$	16.4108	1.14899
$205$	16.8285	1.17535
$206$	28.5850	1.99161
$207$	0.324771	0.0225731
$208$	−63.0053	−4.36863
$209$	4.32412	0.299106
$210$	20.6744	1.42667
$211$	−3.07713	−0.211838	−0.105919	−	0.994375i	$-0.533778\pi$
$211$	−3.07713	−0.211838	−0.105919	+	0.994375i	$0.533778\pi$
$212$	16.9067	1.16116
$213$	−5.50468	−0.377175
$214$	28.0334	1.91633
$215$	−9.90849	−0.675754
$216$	54.6645	3.71945
$217$	−0.508019	−0.0344866
$218$	19.5795	1.32609
$219$	−5.15103	−0.348074
$220$	−22.9022	−1.54406
$221$	−7.27368	−0.489281
$222$	−33.9188	−2.27648
$223$	−1.25069	−0.0837521	−0.0418761	−	0.999123i	$-0.513333\pi$
$223$	−1.25069	−0.0837521	−0.0418761	+	0.999123i	$0.513333\pi$
$224$	−55.1338	−3.68378
$225$	0.285792	0.0190528
$226$	33.5104	2.22908
$227$	17.4474	1.15803	0.579013	−	0.815319i	$-0.303438\pi$
$227$	17.4474	1.15803	0.579013	+	0.815319i	$0.303438\pi$
$228$	19.6345	1.30033
$229$	2.10943	0.139395	0.0696977	−	0.997568i	$-0.477797\pi$
$229$	2.10943	0.139395	0.0696977	+	0.997568i	$0.477797\pi$
$230$	−3.83360	−0.252780
$231$	6.96228	0.458084
$232$	6.97964	0.458236
$233$	−12.7769	−0.837045	−0.418523	−	0.908206i	$-0.637452\pi$
$233$	−12.7769	−0.837045	−0.418523	+	0.908206i	$0.637452\pi$
$234$	−5.30212	−0.346610
$235$	8.41323	0.548818
$236$	−26.0391	−1.69500
$237$	23.7033	1.53970
$238$	−11.5102	−0.746094
$239$	4.69844	0.303917	0.151959	−	0.988387i	$-0.451442\pi$
$239$	4.69844	0.303917	0.151959	+	0.988387i	$0.451442\pi$
$240$	−53.4591	−3.45077
$241$	8.00368	0.515563	0.257781	−	0.966203i	$-0.417009\pi$
$241$	8.00368	0.515563	0.257781	+	0.966203i	$0.417009\pi$
$242$	19.8299	1.27471
$243$	5.04321	0.323522
$244$	1.36659	0.0874868
$245$	4.03331	0.257679
$246$	34.9417	2.22780
$247$	−8.70250	−0.553727
$248$	2.22808	0.141483
$249$	12.3798	0.784539
$250$	−32.3226	−2.04426
$251$	24.1329	1.52325	0.761627	−	0.648016i	$-0.224401\pi$
$251$	24.1329	1.52325	0.761627	+	0.648016i	$0.224401\pi$
$252$	−6.17904	−0.389243
$253$	−1.29100	−0.0811644
$254$	−35.7568	−2.24358
$255$	−6.17161	−0.386481
$256$	62.3377	3.89611
$257$	−7.46681	−0.465767	−0.232883	−	0.972505i	$-0.574816\pi$
$257$	−7.46681	−0.465767	−0.232883	+	0.972505i	$0.574816\pi$
$258$	−20.5734	−1.28084
$259$	17.5201	1.08864
$260$	46.0917	2.85849
$261$	0.346293	0.0214350
$262$	27.3317	1.68856
$263$	−5.94621	−0.366659	−0.183330	−	0.983051i	$-0.558688\pi$
$263$	−5.94621	−0.366659	−0.183330	+	0.983051i	$0.558688\pi$
$264$	−30.5353	−1.87932
$265$	−6.35809	−0.390574
$266$	−13.7712	−0.844366
$267$	−1.67220	−0.102337
$268$	−5.65827	−0.345634
$269$	11.6823	0.712281	0.356141	−	0.934432i	$-0.384092\pi$
$269$	11.6823	0.712281	0.356141	+	0.934432i	$0.384092\pi$
$270$	−32.0144	−1.94834
$271$	15.8375	0.962062	0.481031	−	0.876703i	$-0.340262\pi$
$271$	15.8375	0.962062	0.481031	+	0.876703i	$0.340262\pi$
$272$	29.7626	1.80462
$273$	−14.0119	−0.848040
$274$	−55.2564	−3.33816
$275$	−1.13606	−0.0685067
$276$	−5.86203	−0.352853
$277$	−8.37907	−0.503450	−0.251725	−	0.967799i	$-0.580998\pi$
$277$	−8.37907	−0.503450	−0.251725	+	0.967799i	$0.580998\pi$
$278$	46.6273	2.79652
$279$	0.110546	0.00661819
$280$	46.8358	2.79897
$281$	−21.6480	−1.29141	−0.645705	−	0.763587i	$-0.723436\pi$
$281$	−21.6480	−1.29141	−0.645705	+	0.763587i	$0.723436\pi$
$282$	17.4687	1.04025
$283$	0.399452	0.0237450	0.0118725	−	0.999930i	$-0.496221\pi$
$283$	0.399452	0.0237450	0.0118725	+	0.999930i	$0.496221\pi$
$284$	−19.4201	−1.15237
$285$	−7.38394	−0.437387
$286$	21.0765	1.24628
$287$	−18.0484	−1.06536
$288$	11.9972	0.706941
$289$	−13.5640	−0.797885
$290$	−4.08765	−0.240035
$291$	16.6273	0.974711
$292$	−18.1724	−1.06346
$293$	−10.1754	−0.594454	−0.297227	−	0.954807i	$-0.596062\pi$
$293$	−10.1754	−0.594454	−0.297227	+	0.954807i	$0.596062\pi$
$294$	8.37451	0.488411
$295$	9.79249	0.570141
$296$	−76.8398	−4.46622
$297$	−10.7811	−0.625586
$298$	58.6981	3.40029
$299$	2.59820	0.150258
$300$	−5.15848	−0.297825
$301$	10.6268	0.612516
$302$	20.4093	1.17442
$303$	−27.6066	−1.58596
$304$	35.6091	2.04232
$305$	−0.513932	−0.0294276
$306$	2.50463	0.143180
$307$	22.0773	1.26002	0.630008	−	0.776588i	$-0.283051\pi$
$307$	22.0773	1.26002	0.630008	+	0.776588i	$0.283051\pi$
$308$	24.5623	1.39957
$309$	−16.4379	−0.935122
$310$	−1.30488	−0.0741123
$311$	−11.4692	−0.650357	−0.325179	−	0.945653i	$-0.605424\pi$
$311$	−11.4692	−0.650357	−0.325179	+	0.945653i	$0.605424\pi$
$312$	61.4537	3.47913
$313$	5.19668	0.293734	0.146867	−	0.989156i	$-0.453081\pi$
$313$	5.19668	0.293734	0.146867	+	0.989156i	$0.453081\pi$
$314$	52.8621	2.98318
$315$	2.32375	0.130928
$316$	83.6234	4.70418
$317$	−1.99594	−0.112103	−0.0560516	−	0.998428i	$-0.517851\pi$
$317$	−1.99594	−0.112103	−0.0560516	+	0.998428i	$0.517851\pi$
$318$	−13.2015	−0.740306
$319$	−1.37655	−0.0770722
$320$	−74.1221	−4.14355
$321$	−16.1208	−0.899774
$322$	4.11149	0.229125
$323$	4.11091	0.228737
$324$	−40.7302	−2.26279
$325$	2.28637	0.126825
$326$	20.8715	1.15597
$327$	−11.2593	−0.622640
$328$	79.1570	4.37071
$329$	−9.02310	−0.497460
$330$	17.8831	0.984432
$331$	−1.27496	−0.0700784	−0.0350392	−	0.999386i	$-0.511156\pi$
$331$	−1.27496	−0.0700784	−0.0350392	+	0.999386i	$0.511156\pi$
$332$	43.6750	2.39698
$333$	−3.81239	−0.208917
$334$	1.50138	0.0821518
$335$	2.12790	0.116260
$336$	57.3343	3.12784
$337$	−3.24412	−0.176719	−0.0883593	−	0.996089i	$-0.528162\pi$
$337$	−3.24412	−0.176719	−0.0883593	+	0.996089i	$0.528162\pi$
$338$	−6.60555	−0.359294
$339$	−19.2703	−1.04662
$340$	−21.7729	−1.18080
$341$	−0.439431	−0.0237965
$342$	2.99663	0.162039
$343$	−20.1044	−1.08554
$344$	−46.6070	−2.51288
$345$	2.20453	0.118688
$346$	−26.1899	−1.40798
$347$	1.25044	0.0671271	0.0335635	−	0.999437i	$-0.489314\pi$
$347$	1.25044	0.0671271	0.0335635	+	0.999437i	$0.489314\pi$
$348$	−6.25051	−0.335063
$349$	7.77303	0.416081	0.208040	−	0.978120i	$-0.433291\pi$
$349$	7.77303	0.416081	0.208040	+	0.978120i	$0.433291\pi$
$350$	3.61804	0.193392
$351$	21.6976	1.15813
$352$	−47.6901	−2.54189
$353$	−13.4663	−0.716738	−0.358369	−	0.933580i	$-0.616667\pi$
$353$	−13.4663	−0.716738	−0.358369	+	0.933580i	$0.616667\pi$
$354$	20.3325	1.08066
$355$	7.30329	0.387619
$356$	−5.89939	−0.312667
$357$	6.61899	0.350314
$358$	1.86199	0.0984094
$359$	26.0038	1.37243	0.686214	−	0.727400i	$-0.259271\pi$
$359$	26.0038	1.37243	0.686214	+	0.727400i	$0.259271\pi$
$360$	−10.1915	−0.537141
$361$	−14.0816	−0.741134
$362$	30.2366	1.58920
$363$	−11.4033	−0.598516
$364$	−49.4329	−2.59099
$365$	6.83409	0.357712
$366$	−1.06710	−0.0557780
$367$	−29.0687	−1.51738	−0.758688	−	0.651455i	$-0.774159\pi$
$367$	−29.0687	−1.51738	−0.758688	+	0.651455i	$0.774159\pi$
$368$	−10.6314	−0.554198
$369$	3.92736	0.204450
$370$	45.0015	2.33952
$371$	6.81899	0.354024
$372$	−1.99532	−0.103453
$373$	−5.10946	−0.264558	−0.132279	−	0.991213i	$-0.542229\pi$
$373$	−5.10946	−0.264558	−0.132279	+	0.991213i	$0.542229\pi$
$374$	−9.95617	−0.514821
$375$	18.5873	0.959843
$376$	39.5737	2.04086
$377$	2.77038	0.142682
$378$	34.3351	1.76601
$379$	−5.37268	−0.275976	−0.137988	−	0.990434i	$-0.544064\pi$
$379$	−5.37268	−0.275976	−0.137988	+	0.990434i	$0.544064\pi$
$380$	−26.0499	−1.33633
$381$	20.5621	1.05343
$382$	−10.9965	−0.562630
$383$	24.4970	1.25174	0.625869	−	0.779928i	$-0.284745\pi$
$383$	24.4970	1.25174	0.625869	+	0.779928i	$0.284745\pi$
$384$	−76.4085	−3.89921
$385$	−9.23714	−0.470768
$386$	−22.7657	−1.15875
$387$	−2.31240	−0.117546
$388$	58.6598	2.97800
$389$	−35.8596	−1.81815	−0.909077	−	0.416627i	$-0.863212\pi$
$389$	−35.8596	−1.81815	−0.909077	+	0.416627i	$0.863212\pi$
$390$	−35.9906	−1.82245
$391$	−1.22734	−0.0620694
$392$	18.9716	0.958213
$393$	−15.7173	−0.792830
$394$	33.3435	1.67982
$395$	−31.4482	−1.58233
$396$	−5.34480	−0.268586
$397$	9.23466	0.463474	0.231737	−	0.972778i	$-0.425559\pi$
$397$	9.23466	0.463474	0.231737	+	0.972778i	$0.425559\pi$
$398$	−2.23277	−0.111919
$399$	7.91920	0.396456
$400$	−9.35541	−0.467771
$401$	−18.6576	−0.931716	−0.465858	−	0.884859i	$-0.654254\pi$
$401$	−18.6576	−0.931716	−0.465858	+	0.884859i	$0.654254\pi$
$402$	4.41824	0.220362
$403$	0.884376	0.0440539
$404$	−97.3938	−4.84552
$405$	15.3174	0.761127
$406$	4.38396	0.217572
$407$	15.1546	0.751188
$408$	−29.0297	−1.43718
$409$	−5.67821	−0.280770	−0.140385	−	0.990097i	$-0.544834\pi$
$409$	−5.67821	−0.280770	−0.140385	+	0.990097i	$0.544834\pi$
$410$	−46.3586	−2.28949
$411$	31.7755	1.56737
$412$	−57.9917	−2.85705
$413$	−10.5023	−0.516787
$414$	−0.894666	−0.0439704
$415$	−16.4248	−0.806263
$416$	95.9787	4.70574
$417$	−26.8133	−1.31305
$418$	−11.9119	−0.582632
$419$	−6.67056	−0.325878	−0.162939	−	0.986636i	$-0.552097\pi$
$419$	−6.67056	−0.325878	−0.162939	+	0.986636i	$0.552097\pi$
$420$	−41.9431	−2.04661
$421$	−7.82208	−0.381225	−0.190612	−	0.981665i	$-0.561047\pi$
$421$	−7.82208	−0.381225	−0.190612	+	0.981665i	$0.561047\pi$
$422$	8.47677	0.412643
$423$	1.96344	0.0954656
$424$	−29.9068	−1.45240
$425$	−1.08004	−0.0523896
$426$	15.1641	0.734703
$427$	0.551186	0.0266738
$428$	−56.8728	−2.74905
$429$	−12.1202	−0.585167
$430$	27.2956	1.31631
$431$	−4.51099	−0.217287	−0.108643	−	0.994081i	$-0.534651\pi$
$431$	−4.51099	−0.217287	−0.108643	+	0.994081i	$0.534651\pi$
$432$	−88.7827	−4.27156
$433$	−37.0679	−1.78137	−0.890684	−	0.454623i	$-0.849774\pi$
$433$	−37.0679	−1.78137	−0.890684	+	0.454623i	$0.849774\pi$
$434$	1.39947	0.0671768
$435$	2.35063	0.112704
$436$	−39.7218	−1.90233
$437$	−1.46844	−0.0702449
$438$	14.1899	0.678018
$439$	24.0995	1.15020	0.575102	−	0.818082i	$-0.304962\pi$
$439$	24.0995	1.15020	0.575102	+	0.818082i	$0.304962\pi$
$440$	40.5124	1.93135
$441$	0.941273	0.0448225
$442$	20.0373	0.953076
$443$	−6.29590	−0.299127	−0.149564	−	0.988752i	$-0.547787\pi$
$443$	−6.29590	−0.299127	−0.149564	+	0.988752i	$0.547787\pi$
$444$	68.8127	3.26571
$445$	2.21858	0.105171
$446$	3.44534	0.163142
$447$	−33.7547	−1.59654
$448$	79.4952	3.75580
$449$	−6.24008	−0.294488	−0.147244	−	0.989100i	$-0.547040\pi$
$449$	−6.24008	−0.294488	−0.147244	+	0.989100i	$0.547040\pi$
$450$	−0.787290	−0.0371132
$451$	−15.6117	−0.735125
$452$	−67.9842	−3.19771
$453$	−11.7365	−0.551427
$454$	−48.0635	−2.25573
$455$	18.5902	0.871522
$456$	−34.7322	−1.62648
$457$	−36.9888	−1.73026	−0.865131	−	0.501547i	$-0.832765\pi$
$457$	−36.9888	−1.73026	−0.865131	+	0.501547i	$0.832765\pi$
$458$	−5.81099	−0.271530
$459$	−10.2496	−0.478408
$460$	7.77740	0.362623
$461$	−27.5069	−1.28112	−0.640561	−	0.767907i	$-0.721298\pi$
$461$	−27.5069	−1.28112	−0.640561	+	0.767907i	$0.721298\pi$
$462$	−19.1794	−0.892308
$463$	0.453593	0.0210802	0.0105401	−	0.999944i	$-0.496645\pi$
$463$	0.453593	0.0210802	0.0105401	+	0.999944i	$0.496645\pi$
$464$	−11.3359	−0.526256
$465$	0.750380	0.0347980
$466$	35.1974	1.63049
$467$	11.9808	0.554404	0.277202	−	0.960812i	$-0.410593\pi$
$467$	11.9808	0.554404	0.277202	+	0.960812i	$0.410593\pi$
$468$	10.7567	0.497227
$469$	−2.28215	−0.105380
$470$	−23.1765	−1.06905
$471$	−30.3986	−1.40069
$472$	46.0614	2.12015
$473$	9.19202	0.422650
$474$	−65.2970	−2.99919
$475$	−1.29220	−0.0592902
$476$	23.3512	1.07030
$477$	−1.48382	−0.0679394
$478$	−12.9431	−0.592004
$479$	26.3778	1.20523	0.602617	−	0.798031i	$-0.294125\pi$
$479$	26.3778	1.20523	0.602617	+	0.798031i	$0.294125\pi$
$480$	81.4365	3.71705
$481$	−30.4995	−1.39066
$482$	−22.0483	−1.00427
$483$	−2.36434	−0.107581
$484$	−40.2298	−1.82863
$485$	−22.0602	−1.00170
$486$	−13.8928	−0.630192
$487$	−33.1185	−1.50074	−0.750371	−	0.661017i	$-0.770125\pi$
$487$	−33.1185	−1.50074	−0.750371	+	0.661017i	$0.770125\pi$
$488$	−2.41740	−0.109431
$489$	−12.0023	−0.542761
$490$	−11.1108	−0.501935
$491$	6.44472	0.290846	0.145423	−	0.989370i	$-0.453546\pi$
$491$	6.44472	0.290846	0.145423	+	0.989370i	$0.453546\pi$
$492$	−70.8878	−3.19587
$493$	−1.30868	−0.0589399
$494$	23.9733	1.07861
$495$	2.01001	0.0903434
$496$	−3.61871	−0.162485
$497$	−7.83271	−0.351345
$498$	−34.1035	−1.52821
$499$	−28.2725	−1.26565	−0.632824	−	0.774295i	$-0.718104\pi$
$499$	−28.2725	−1.26565	−0.632824	+	0.774295i	$0.718104\pi$
$500$	65.5744	2.93257
$501$	−0.863376	−0.0385728
$502$	−66.4803	−2.96716
$503$	20.2084	0.901046	0.450523	−	0.892765i	$-0.351237\pi$
$503$	20.2084	0.901046	0.450523	+	0.892765i	$0.351237\pi$
$504$	10.9303	0.486875
$505$	36.6268	1.62987
$506$	3.55639	0.158101
$507$	3.79856	0.168700
$508$	72.5416	3.21851
$509$	−7.80824	−0.346094	−0.173047	−	0.984914i	$-0.555361\pi$
$509$	−7.80824	−0.346094	−0.173047	+	0.984914i	$0.555361\pi$
$510$	17.0013	0.752831
$511$	−7.32949	−0.324237
$512$	−75.2589	−3.32600
$513$	−12.2630	−0.541423
$514$	20.5693	0.907273
$515$	21.8089	0.961015
$516$	41.7382	1.83742
$517$	−7.80488	−0.343258
$518$	−48.2636	−2.12058
$519$	15.0606	0.661088
$520$	−81.5332	−3.57547
$521$	−3.21561	−0.140878	−0.0704392	−	0.997516i	$-0.522440\pi$
$521$	−3.21561	−0.140878	−0.0704392	+	0.997516i	$0.522440\pi$
$522$	−0.953956	−0.0417535
$523$	20.3437	0.889567	0.444784	−	0.895638i	$-0.353281\pi$
$523$	20.3437	0.889567	0.444784	+	0.895638i	$0.353281\pi$
$524$	−55.4492	−2.42231
$525$	−2.08057	−0.0908037
$526$	16.3804	0.714220
$527$	−0.417764	−0.0181981
$528$	49.5935	2.15828
$529$	−22.5616	−0.980939
$530$	17.5150	0.760805
$531$	2.28532	0.0991746
$532$	27.9383	1.21128
$533$	31.4192	1.36092
$534$	4.60652	0.199344
$535$	21.3881	0.924689
$536$	10.0091	0.432327
$537$	−1.07075	−0.0462063
$538$	−32.1819	−1.38746
$539$	−3.74166	−0.161165
$540$	64.9492	2.79497
$541$	2.48117	0.106674	0.0533368	−	0.998577i	$-0.483014\pi$
$541$	2.48117	0.106674	0.0533368	+	0.998577i	$0.483014\pi$
$542$	−43.6287	−1.87401
$543$	−17.3877	−0.746179
$544$	−45.3386	−1.94388
$545$	14.9382	0.639881
$546$	38.5995	1.65191
$547$	9.48989	0.405758	0.202879	−	0.979204i	$-0.434970\pi$
$547$	9.48989	0.405758	0.202879	+	0.979204i	$0.434970\pi$
$548$	112.101	4.78873
$549$	−0.119939	−0.00511887
$550$	3.12956	0.133445
$551$	−1.56575	−0.0667033
$552$	10.3695	0.441357
$553$	33.7279	1.43425
$554$	23.0824	0.980675
$555$	−25.8783	−1.09847
$556$	−94.5951	−4.01173
$557$	39.1678	1.65959	0.829796	−	0.558067i	$-0.188457\pi$
$557$	39.1678	1.65959	0.829796	+	0.558067i	$0.188457\pi$
$558$	−0.304527	−0.0128917
$559$	−18.4994	−0.782441
$560$	−76.0678	−3.21445
$561$	5.72535	0.241724
$562$	59.6350	2.51555
$563$	36.2205	1.52651	0.763256	−	0.646096i	$-0.223599\pi$
$563$	36.2205	1.52651	0.763256	+	0.646096i	$0.223599\pi$
$564$	−35.4396	−1.49228
$565$	25.5668	1.07560
$566$	−1.10040	−0.0462531
$567$	−16.4277	−0.689900
$568$	34.3528	1.44141
$569$	−23.1789	−0.971709	−0.485854	−	0.874040i	$-0.661491\pi$
$569$	−23.1789	−0.971709	−0.485854	+	0.874040i	$0.661491\pi$
$570$	20.3410	0.851992
$571$	−44.0770	−1.84456	−0.922282	−	0.386517i	$-0.873678\pi$
$571$	−44.0770	−1.84456	−0.922282	+	0.386517i	$0.873678\pi$
$572$	−42.7589	−1.78784
$573$	6.32360	0.264172
$574$	49.7191	2.07523
$575$	0.385796	0.0160888
$576$	−17.2983	−0.720761
$577$	−11.0652	−0.460651	−0.230325	−	0.973114i	$-0.573979\pi$
$577$	−11.0652	−0.460651	−0.230325	+	0.973114i	$0.573979\pi$
$578$	37.3657	1.55421
$579$	13.0916	0.544066
$580$	8.29281	0.344340
$581$	17.6155	0.730812
$582$	−45.8043	−1.89865
$583$	5.89835	0.244285
$584$	32.1458	1.33020
$585$	−4.04525	−0.167251
$586$	28.0309	1.15794
$587$	−7.22525	−0.298218	−0.149109	−	0.988821i	$-0.547641\pi$
$587$	−7.22525	−0.298218	−0.149109	+	0.988821i	$0.547641\pi$
$588$	−16.9898	−0.700646
$589$	−0.499828	−0.0205951
$590$	−26.9760	−1.11058
$591$	−19.1744	−0.788728
$592$	124.798	5.12918
$593$	−19.1197	−0.785154	−0.392577	−	0.919719i	$-0.628416\pi$
$593$	−19.1197	−0.785154	−0.392577	+	0.919719i	$0.628416\pi$
$594$	29.6995	1.21859
$595$	−8.78169	−0.360014
$596$	−119.084	−4.87786
$597$	1.28397	0.0525493
$598$	−7.15742	−0.292689
$599$	−9.04350	−0.369507	−0.184754	−	0.982785i	$-0.559149\pi$
$599$	−9.04350	−0.369507	−0.184754	+	0.982785i	$0.559149\pi$
$600$	9.12502	0.372527
$601$	−11.8006	−0.481356	−0.240678	−	0.970605i	$-0.577370\pi$
$601$	−11.8006	−0.481356	−0.240678	+	0.970605i	$0.577370\pi$
$602$	−29.2742	−1.19313
$603$	0.496599	0.0202231
$604$	−41.4052	−1.68476
$605$	15.1292	0.615089
$606$	76.0496	3.08931
$607$	−20.5982	−0.836054	−0.418027	−	0.908435i	$-0.637278\pi$
$607$	−20.5982	−0.836054	−0.418027	+	0.908435i	$0.637278\pi$
$608$	−54.2448	−2.19992
$609$	−2.52102	−0.102157
$610$	1.41576	0.0573225
$611$	15.7077	0.635465
$612$	−5.08126	−0.205398
$613$	1.51954	0.0613735	0.0306868	−	0.999529i	$-0.490231\pi$
$613$	1.51954	0.0613735	0.0306868	+	0.999529i	$0.490231\pi$
$614$	−60.8177	−2.45440
$615$	26.6587	1.07498
$616$	−43.4492	−1.75062
$617$	−34.1749	−1.37583	−0.687914	−	0.725792i	$-0.741473\pi$
$617$	−34.1749	−1.37583	−0.687914	+	0.725792i	$0.741473\pi$
$618$	45.2827	1.82154
$619$	10.5551	0.424246	0.212123	−	0.977243i	$-0.431962\pi$
$619$	10.5551	0.424246	0.212123	+	0.977243i	$0.431962\pi$
$620$	2.64728	0.106317
$621$	3.66119	0.146919
$622$	31.5949	1.26684
$623$	−2.37941	−0.0953289
$624$	−99.8094	−3.99557
$625$	−21.7472	−0.869888
$626$	−14.3156	−0.572168
$627$	6.85002	0.273563
$628$	−107.244	−4.27950
$629$	14.4074	0.574461
$630$	−6.40137	−0.255037
$631$	−0.429836	−0.0171115	−0.00855576	−	0.999963i	$-0.502723\pi$
$631$	−0.429836	−0.0171115	−0.00855576	+	0.999963i	$0.502723\pi$
$632$	−147.924	−5.88411
$633$	−4.87461	−0.193748
$634$	5.49835	0.218367
$635$	−27.2807	−1.08260
$636$	26.7826	1.06200
$637$	7.53028	0.298361
$638$	3.79208	0.150130
$639$	1.70441	0.0674253
$640$	101.374	4.00717
$641$	−45.8583	−1.81129	−0.905647	−	0.424033i	$-0.860614\pi$
$641$	−45.8583	−1.81129	−0.905647	+	0.424033i	$0.860614\pi$
$642$	44.4089	1.75268
$643$	19.4843	0.768385	0.384193	−	0.923253i	$-0.374480\pi$
$643$	19.4843	0.768385	0.384193	+	0.923253i	$0.374480\pi$
$644$	−8.34118	−0.328689
$645$	−15.6965	−0.618047
$646$	−11.3246	−0.445560
$647$	−38.8760	−1.52837	−0.764186	−	0.644996i	$-0.776859\pi$
$647$	−38.8760	−1.52837	−0.764186	+	0.644996i	$0.776859\pi$
$648$	72.0490	2.83035
$649$	−9.08441	−0.356594
$650$	−6.29840	−0.247044
$651$	−0.804774	−0.0315416
$652$	−42.3430	−1.65828
$653$	−18.4729	−0.722900	−0.361450	−	0.932392i	$-0.617718\pi$
$653$	−18.4729	−0.722900	−0.361450	+	0.932392i	$0.617718\pi$
$654$	31.0167	1.21285
$655$	20.8527	0.814784
$656$	−128.562	−5.01950
$657$	1.59491	0.0622232
$658$	24.8565	0.969007
$659$	3.69443	0.143915	0.0719574	−	0.997408i	$-0.477075\pi$
$659$	3.69443	0.143915	0.0719574	+	0.997408i	$0.477075\pi$
$660$	−36.2803	−1.41221
$661$	24.7906	0.964243	0.482121	−	0.876104i	$-0.339866\pi$
$661$	24.7906	0.964243	0.482121	+	0.876104i	$0.339866\pi$
$662$	3.51223	0.136507
$663$	−11.5225	−0.447499
$664$	−77.2582	−2.99820
$665$	−10.5067	−0.407434
$666$	10.5022	0.406953
$667$	0.467467	0.0181004
$668$	−3.04592	−0.117850
$669$	−1.98126	−0.0766001
$670$	−5.86186	−0.226464
$671$	0.476770	0.0184055
$672$	−87.3397	−3.36920
$673$	−4.47142	−0.172361	−0.0861803	−	0.996280i	$-0.527466\pi$
$673$	−4.47142	−0.172361	−0.0861803	+	0.996280i	$0.527466\pi$
$674$	8.93679	0.344232
$675$	3.22179	0.124007
$676$	13.4010	0.515423
$677$	46.4166	1.78394	0.891968	−	0.452099i	$-0.149325\pi$
$677$	46.4166	1.78394	0.891968	+	0.452099i	$0.149325\pi$
$678$	53.0853	2.03873
$679$	23.6593	0.907960
$680$	38.5149	1.47698
$681$	27.6392	1.05914
$682$	1.21053	0.0463535
$683$	−17.4545	−0.667879	−0.333939	−	0.942595i	$-0.608378\pi$
$683$	−17.4545	−0.667879	−0.333939	+	0.942595i	$0.608378\pi$
$684$	−6.07941	−0.232452
$685$	−42.1578	−1.61077
$686$	55.3828	2.11453
$687$	3.34164	0.127492
$688$	75.6963	2.88589
$689$	−11.8707	−0.452238
$690$	−6.07296	−0.231194
$691$	−44.5591	−1.69511	−0.847554	−	0.530709i	$-0.821926\pi$
$691$	−44.5591	−1.69511	−0.847554	+	0.530709i	$0.821926\pi$
$692$	53.1327	2.01980
$693$	−2.15572	−0.0818890
$694$	−3.44466	−0.130758
$695$	35.5743	1.34941
$696$	11.0567	0.419105
$697$	−14.8419	−0.562177
$698$	−21.4129	−0.810489
$699$	−20.2405	−0.765565
$700$	−7.34009	−0.277429
$701$	−12.4062	−0.468577	−0.234288	−	0.972167i	$-0.575276\pi$
$701$	−12.4062	−0.468577	−0.234288	+	0.972167i	$0.575276\pi$
$702$	−59.7717	−2.25594
$703$	17.2376	0.650127
$704$	68.7625	2.59158
$705$	13.3277	0.501952
$706$	37.0964	1.39614
$707$	−39.2819	−1.47735
$708$	−41.2496	−1.55025
$709$	−36.2791	−1.36249	−0.681245	−	0.732056i	$-0.738561\pi$
$709$	−36.2791	−1.36249	−0.681245	+	0.732056i	$0.738561\pi$
$710$	−20.1188	−0.755047
$711$	−7.33922	−0.275242
$712$	10.4356	0.391092
$713$	0.149227	0.00558861
$714$	−18.2337	−0.682381
$715$	16.0803	0.601370
$716$	−3.77752	−0.141172
$717$	7.44300	0.277964
$718$	−71.6343	−2.67337
$719$	3.53151	0.131703	0.0658516	−	0.997829i	$-0.479024\pi$
$719$	3.53151	0.131703	0.0658516	+	0.997829i	$0.479024\pi$
$720$	16.5525	0.616874
$721$	−23.3898	−0.871083
$722$	38.7913	1.44366
$723$	12.6790	0.471536
$724$	−61.3425	−2.27977
$725$	0.411363	0.0152776
$726$	31.4133	1.16586
$727$	18.5251	0.687058	0.343529	−	0.939142i	$-0.388378\pi$
$727$	18.5251	0.687058	0.343529	+	0.939142i	$0.388378\pi$
$728$	87.4435	3.24087
$729$	29.8529	1.10566
$730$	−18.8263	−0.696792
$731$	8.73879	0.323216
$732$	2.16487	0.0800158
$733$	1.15451	0.0426427	0.0213213	−	0.999773i	$-0.493213\pi$
$733$	1.15451	0.0426427	0.0213213	+	0.999773i	$0.493213\pi$
$734$	80.0775	2.95571
$735$	6.38933	0.235674
$736$	16.1952	0.596963
$737$	−1.97404	−0.0727145
$738$	−10.8189	−0.398250
$739$	6.62022	0.243529	0.121764	−	0.992559i	$-0.461145\pi$
$739$	6.62022	0.243529	0.121764	+	0.992559i	$0.461145\pi$
$740$	−91.2967	−3.35613
$741$	−13.7860	−0.506441
$742$	−18.7847	−0.689608
$743$	9.02942	0.331257	0.165629	−	0.986188i	$-0.447035\pi$
$743$	9.02942	0.331257	0.165629	+	0.986188i	$0.447035\pi$
$744$	3.52959	0.129401
$745$	44.7837	1.64075
$746$	14.0754	0.515336
$747$	−3.83314	−0.140247
$748$	20.1986	0.738533
$749$	−22.9385	−0.838156
$750$	−51.2035	−1.86969
$751$	50.9157	1.85794	0.928971	−	0.370153i	$-0.120695\pi$
$751$	50.9157	1.85794	0.928971	+	0.370153i	$0.120695\pi$
$752$	−64.2731	−2.34380
$753$	38.2299	1.39317
$754$	−7.63174	−0.277932
$755$	15.5712	0.566695
$756$	−69.6574	−2.53341
$757$	−0.0654002	−0.00237701	−0.00118851	−	0.999999i	$-0.500378\pi$
$757$	−0.0654002	−0.00237701	−0.00118851	+	0.999999i	$0.500378\pi$
$758$	14.8004	0.537577
$759$	−2.04512	−0.0742333
$760$	46.0806	1.67152
$761$	47.6467	1.72719	0.863596	−	0.504184i	$-0.168207\pi$
$761$	47.6467	1.72719	0.863596	+	0.504184i	$0.168207\pi$
$762$	−56.6439	−2.05199
$763$	−16.0210	−0.580000
$764$	22.3092	0.807117
$765$	1.91091	0.0690890
$766$	−67.4834	−2.43827
$767$	18.2828	0.660154
$768$	98.7518	3.56340
$769$	−25.3168	−0.912947	−0.456473	−	0.889737i	$-0.650888\pi$
$769$	−25.3168	−0.912947	−0.456473	+	0.889737i	$0.650888\pi$
$770$	25.4461	0.917016
$771$	−11.8285	−0.425993
$772$	46.1859	1.66227
$773$	−17.7503	−0.638433	−0.319217	−	0.947682i	$-0.603420\pi$
$773$	−17.7503	−0.638433	−0.319217	+	0.947682i	$0.603420\pi$
$774$	6.37010	0.228969
$775$	0.131317	0.00471706
$776$	−103.765	−3.72496
$777$	27.7543	0.995678
$778$	98.7848	3.54160
$779$	−17.7574	−0.636225
$780$	73.0158	2.61439
$781$	−6.77520	−0.242436
$782$	3.38104	0.120906
$783$	3.90382	0.139511
$784$	−30.8126	−1.10045
$785$	40.3311	1.43948
$786$	43.2973	1.54436
$787$	39.7731	1.41776	0.708879	−	0.705330i	$-0.249201\pi$
$787$	39.7731	1.41776	0.708879	+	0.705330i	$0.249201\pi$
$788$	−67.6456	−2.40978
$789$	−9.41965	−0.335348
$790$	86.6323	3.08224
$791$	−27.4201	−0.974947
$792$	9.45459	0.335954
$793$	−0.959523	−0.0340736
$794$	−25.4393	−0.902807
$795$	−10.0721	−0.357221
$796$	4.52974	0.160552
$797$	51.4986	1.82417	0.912087	−	0.409997i	$-0.134470\pi$
$797$	51.4986	1.82417	0.912087	+	0.409997i	$0.134470\pi$
$798$	−21.8155	−0.772261
$799$	−7.42004	−0.262502
$800$	14.2515	0.503866
$801$	0.517762	0.0182942
$802$	51.3973	1.81490
$803$	−6.33992	−0.223731
$804$	−8.96350	−0.316118
$805$	3.13686	0.110560
$806$	−2.43625	−0.0858131
$807$	18.5064	0.651456
$808$	172.283	6.06090
$809$	36.6592	1.28887	0.644434	−	0.764660i	$-0.277093\pi$
$809$	36.6592	1.28887	0.644434	+	0.764660i	$0.277093\pi$
$810$	−42.1958	−1.48261
$811$	16.2061	0.569074	0.284537	−	0.958665i	$-0.408160\pi$
$811$	16.2061	0.569074	0.284537	+	0.958665i	$0.408160\pi$
$812$	−8.89396	−0.312117
$813$	25.0889	0.879907
$814$	−41.7475	−1.46325
$815$	15.9239	0.557790
$816$	47.1482	1.65052
$817$	10.4554	0.365789
$818$	15.6421	0.546915
$819$	4.33849	0.151599
$820$	94.0499	3.28436
$821$	3.96186	0.138270	0.0691350	−	0.997607i	$-0.477976\pi$
$821$	3.96186	0.138270	0.0691350	+	0.997607i	$0.477976\pi$
$822$	−87.5339	−3.05310
$823$	6.21540	0.216655	0.108328	−	0.994115i	$-0.465450\pi$
$823$	6.21540	0.216655	0.108328	+	0.994115i	$0.465450\pi$
$824$	102.584	3.57367
$825$	−1.79967	−0.0626566
$826$	28.9315	1.00666
$827$	−29.2952	−1.01869	−0.509347	−	0.860561i	$-0.670113\pi$
$827$	−29.2952	−1.01869	−0.509347	+	0.860561i	$0.670113\pi$
$828$	1.81505	0.0630774
$829$	−9.97765	−0.346538	−0.173269	−	0.984875i	$-0.555433\pi$
$829$	−9.97765	−0.346538	−0.173269	+	0.984875i	$0.555433\pi$
$830$	45.2465	1.57053
$831$	−13.2736	−0.460457
$832$	−138.388	−4.79773
$833$	−3.55717	−0.123249
$834$	73.8643	2.55771
$835$	1.14548	0.0396409
$836$	24.1663	0.835809
$837$	1.24620	0.0430750
$838$	18.3758	0.634782
$839$	11.9561	0.412772	0.206386	−	0.978471i	$-0.433830\pi$
$839$	11.9561	0.412772	0.206386	+	0.978471i	$0.433830\pi$
$840$	74.1945	2.55995
$841$	−28.5016	−0.982812
$842$	21.5480	0.742592
$843$	−34.2935	−1.18113
$844$	−17.1972	−0.591953
$845$	−5.03970	−0.173371
$846$	−5.40881	−0.185959
$847$	−16.2259	−0.557528
$848$	48.5728	1.66800
$849$	0.632789	0.0217173
$850$	2.97525	0.102050
$851$	−5.14640	−0.176416
$852$	−30.7641	−1.05396
$853$	49.9164	1.70911	0.854553	−	0.519364i	$-0.173831\pi$
$853$	49.9164	1.70911	0.854553	+	0.519364i	$0.173831\pi$
$854$	−1.51839	−0.0519582
$855$	2.28628	0.0781891
$856$	100.604	3.43858
$857$	−1.79790	−0.0614151	−0.0307076	−	0.999528i	$-0.509776\pi$
$857$	−1.79790	−0.0614151	−0.0307076	+	0.999528i	$0.509776\pi$
$858$	33.3882	1.13985
$859$	14.5095	0.495058	0.247529	−	0.968881i	$-0.420381\pi$
$859$	14.5095	0.495058	0.247529	+	0.968881i	$0.420381\pi$
$860$	−55.3758	−1.88830
$861$	−28.5912	−0.974386
$862$	12.4267	0.423255
$863$	49.0226	1.66875	0.834375	−	0.551197i	$-0.185829\pi$
$863$	49.0226	1.66875	0.834375	+	0.551197i	$0.185829\pi$
$864$	135.246	4.60117
$865$	−19.9816	−0.679393
$866$	102.113	3.46995
$867$	−21.4874	−0.729749
$868$	−2.83918	−0.0963680
$869$	29.1742	0.989667
$870$	−6.47542	−0.219537
$871$	3.97284	0.134615
$872$	70.2653	2.37948
$873$	−5.14829	−0.174243
$874$	4.04520	0.136831
$875$	26.4481	0.894110
$876$	−28.7877	−0.972645
$877$	−0.662079	−0.0223568	−0.0111784	−	0.999938i	$-0.503558\pi$
$877$	−0.662079	−0.0223568	−0.0111784	+	0.999938i	$0.503558\pi$
$878$	−66.3883	−2.24050
$879$	−16.1193	−0.543691
$880$	−65.7978	−2.21804
$881$	35.5742	1.19853	0.599263	−	0.800552i	$-0.295460\pi$
$881$	35.5742	1.19853	0.599263	+	0.800552i	$0.295460\pi$
$882$	−2.59299	−0.0873104
$883$	−37.5465	−1.26354	−0.631770	−	0.775156i	$-0.717671\pi$
$883$	−37.5465	−1.26354	−0.631770	+	0.775156i	$0.717671\pi$
$884$	−40.6506	−1.36723
$885$	15.5127	0.521454
$886$	17.3437	0.582673
$887$	9.07790	0.304806	0.152403	−	0.988318i	$-0.451299\pi$
$887$	9.07790	0.304806	0.152403	+	0.988318i	$0.451299\pi$
$888$	−121.725	−4.08483
$889$	29.2582	0.981289
$890$	−6.11167	−0.204863
$891$	−14.2098	−0.476046
$892$	−6.98974	−0.234034
$893$	−8.87761	−0.297078
$894$	92.9861	3.10992
$895$	1.42061	0.0474857
$896$	−108.723	−3.63218
$897$	4.11591	0.137426
$898$	17.1899	0.573636
$899$	0.159117	0.00530684
$900$	1.59721	0.0532405
$901$	5.60752	0.186813
$902$	43.0064	1.43196
$903$	16.8343	0.560210
$904$	120.260	3.99977
$905$	23.0690	0.766840
$906$	32.3311	1.07413
$907$	−43.5644	−1.44653	−0.723266	−	0.690570i	$-0.757360\pi$
$907$	−43.5644	−1.44653	−0.723266	+	0.690570i	$0.757360\pi$
$908$	97.5087	3.23594
$909$	8.54779	0.283512
$910$	−51.2116	−1.69765
$911$	45.7729	1.51652	0.758262	−	0.651950i	$-0.226049\pi$
$911$	45.7729	1.51652	0.758262	+	0.651950i	$0.226049\pi$
$912$	56.4099	1.86792
$913$	15.2372	0.504277
$914$	101.895	3.37040
$915$	−0.814141	−0.0269147
$916$	11.7890	0.389521
$917$	−22.3643	−0.738536
$918$	28.2351	0.931898
$919$	−28.9616	−0.955354	−0.477677	−	0.878535i	$-0.658521\pi$
$919$	−28.9616	−0.955354	−0.477677	+	0.878535i	$0.658521\pi$
$920$	−13.7577	−0.453578
$921$	34.9735	1.15242
$922$	75.7749	2.49551
$923$	13.6354	0.448815
$924$	38.9102	1.28005
$925$	−4.52874	−0.148904
$926$	−1.24954	−0.0410625
$927$	5.08966	0.167166
$928$	17.2685	0.566865
$929$	37.4242	1.22785	0.613924	−	0.789365i	$-0.289590\pi$
$929$	37.4242	1.22785	0.613924	+	0.789365i	$0.289590\pi$
$930$	−2.06712	−0.0677835
$931$	−4.25593	−0.139483
$932$	−71.4067	−2.33901
$933$	−18.1688	−0.594820
$934$	−33.0042	−1.07993
$935$	−7.59606	−0.248418
$936$	−19.0278	−0.621944
$937$	−56.4941	−1.84558	−0.922791	−	0.385301i	$-0.874097\pi$
$937$	−56.4941	−1.84558	−0.922791	+	0.385301i	$0.874097\pi$
$938$	6.28679	0.205271
$939$	8.23228	0.268650
$940$	47.0192	1.53360
$941$	−25.8171	−0.841614	−0.420807	−	0.907150i	$-0.638253\pi$
$941$	−25.8171	−0.841614	−0.420807	+	0.907150i	$0.638253\pi$
$942$	83.7410	2.72843
$943$	5.30160	0.172644
$944$	−74.8101	−2.43486
$945$	26.1960	0.852156
$946$	−25.3218	−0.823284
$947$	9.17193	0.298048	0.149024	−	0.988834i	$-0.452387\pi$
$947$	9.17193	0.298048	0.149024	+	0.988834i	$0.452387\pi$
$948$	132.471	4.30247
$949$	12.7594	0.414188
$950$	3.55971	0.115492
$951$	−3.16186	−0.102530
$952$	−41.3068	−1.33876
$953$	22.2148	0.719609	0.359805	−	0.933028i	$-0.382843\pi$
$953$	22.2148	0.719609	0.359805	+	0.933028i	$0.382843\pi$
$954$	4.08757	0.132340
$955$	−8.38979	−0.271487
$956$	26.2583	0.849254
$957$	−2.18065	−0.0704906
$958$	−72.6647	−2.34769
$959$	45.2139	1.46003
$960$	−117.420	−3.78971
$961$	−30.9492	−0.998361
$962$	84.0188	2.70888
$963$	4.99145	0.160847
$964$	44.7304	1.44067
$965$	−17.3691	−0.559132
$966$	6.51319	0.209558
$967$	38.6726	1.24363	0.621814	−	0.783165i	$-0.286396\pi$
$967$	38.6726	1.24363	0.621814	+	0.783165i	$0.286396\pi$
$968$	71.1638	2.28729
$969$	6.51227	0.209204
$970$	60.7705	1.95122
$971$	56.6430	1.81776	0.908881	−	0.417056i	$-0.136938\pi$
$971$	56.6430	1.81776	0.908881	+	0.417056i	$0.136938\pi$
$972$	28.1851	0.904037
$973$	−38.1531	−1.22313
$974$	91.2336	2.92331
$975$	3.62193	0.115995
$976$	3.92620	0.125675
$977$	−11.6553	−0.372888	−0.186444	−	0.982466i	$-0.559696\pi$
$977$	−11.6553	−0.372888	−0.186444	+	0.982466i	$0.559696\pi$
$978$	33.0634	1.05725
$979$	−2.05816	−0.0657790
$980$	22.5410	0.720047
$981$	3.48620	0.111306
$982$	−17.7537	−0.566542
$983$	29.3978	0.937643	0.468822	−	0.883293i	$-0.344679\pi$
$983$	29.3978	0.937643	0.468822	+	0.883293i	$0.344679\pi$
$984$	125.396	3.99748
$985$	25.4394	0.810568
$986$	3.60510	0.114810
$987$	−14.2939	−0.454979
$988$	−48.6359	−1.54731
$989$	−3.12154	−0.0992592
$990$	−5.53711	−0.175981
$991$	36.4480	1.15781	0.578905	−	0.815395i	$-0.303480\pi$
$991$	36.4480	1.15781	0.578905	+	0.815395i	$0.303480\pi$
$992$	5.51253	0.175023
$993$	−2.01972	−0.0640940
$994$	21.5773	0.684389
$995$	−1.70349	−0.0540044
$996$	69.1874	2.19229
$997$	9.94513	0.314966	0.157483	−	0.987522i	$-0.449662\pi$
$997$	9.94513	0.314966	0.157483	+	0.987522i	$0.449662\pi$
$998$	77.8839	2.46537
$999$	−42.9777	−1.35975

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4021.2.a.b.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-2.75476 q^{2} +1.58414 q^{3} +5.58872 q^{4} -2.10175 q^{5} -4.36394 q^{6} +2.25410 q^{7} -9.88608 q^{8} -0.490495 q^{9} +O(q^{10})\)	\(q-2.75476 q^{2} +1.58414 q^{3} +5.58872 q^{4} -2.10175 q^{5} -4.36394 q^{6} +2.25410 q^{7} -9.88608 q^{8} -0.490495 q^{9} +5.78981 q^{10} +1.94977 q^{11} +8.85333 q^{12} -3.92401 q^{13} -6.20952 q^{14} -3.32946 q^{15} +16.0564 q^{16} +1.85363 q^{17} +1.35120 q^{18} +2.21776 q^{19} -11.7461 q^{20} +3.57082 q^{21} -5.37116 q^{22} -0.662128 q^{23} -15.6609 q^{24} -0.582661 q^{25} +10.8097 q^{26} -5.52944 q^{27} +12.5975 q^{28} -0.706007 q^{29} +9.17189 q^{30} -0.225375 q^{31} -24.4593 q^{32} +3.08872 q^{33} -5.10632 q^{34} -4.73755 q^{35} -2.74124 q^{36} +7.77252 q^{37} -6.10940 q^{38} -6.21619 q^{39} +20.7780 q^{40} -8.00692 q^{41} -9.83675 q^{42} +4.71441 q^{43} +10.8967 q^{44} +1.03090 q^{45} +1.82401 q^{46} -4.00297 q^{47} +25.4356 q^{48} -1.91903 q^{49} +1.60509 q^{50} +2.93642 q^{51} -21.9302 q^{52} +3.02515 q^{53} +15.2323 q^{54} -4.09793 q^{55} -22.2842 q^{56} +3.51324 q^{57} +1.94488 q^{58} -4.65922 q^{59} -18.6074 q^{60} +0.244526 q^{61} +0.620856 q^{62} -1.10563 q^{63} +35.2669 q^{64} +8.24728 q^{65} -8.50868 q^{66} -1.01244 q^{67} +10.3594 q^{68} -1.04890 q^{69} +13.0508 q^{70} -3.47487 q^{71} +4.84907 q^{72} -3.25162 q^{73} -21.4115 q^{74} -0.923017 q^{75} +12.3944 q^{76} +4.39498 q^{77} +17.1241 q^{78} +14.9629 q^{79} -33.7464 q^{80} -7.28793 q^{81} +22.0572 q^{82} +7.81484 q^{83} +19.9563 q^{84} -3.89587 q^{85} -12.9871 q^{86} -1.11842 q^{87} -19.2756 q^{88} -1.05559 q^{89} -2.83988 q^{90} -8.84512 q^{91} -3.70045 q^{92} -0.357027 q^{93} +11.0272 q^{94} -4.66116 q^{95} -38.7470 q^{96} +10.4961 q^{97} +5.28646 q^{98} -0.956354 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 151 q - 16 q^{2} - 29 q^{3} + 120 q^{4} - 27 q^{5} - 18 q^{6} - 18 q^{7} - 48 q^{8} + 98 q^{9}+O(q^{10}) \) 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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