LMFDB - Embedded newform 6022.2.a.e.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6022,2,Mod(1,6022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6022, 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("6022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6022 = 2 \cdot 3011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6022.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:	$48.0859120972$
Analytic rank:	$0$
Dimension:	$68$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	6022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.47177 q^{3} +1.00000 q^{4} +0.895866 q^{5} -1.47177 q^{6} +0.963361 q^{7} +1.00000 q^{8} -0.833884 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.47177 q^{3} +1.00000 q^{4} +0.895866 q^{5} -1.47177 q^{6} +0.963361 q^{7} +1.00000 q^{8} -0.833884 q^{9} +0.895866 q^{10} +2.48480 q^{11} -1.47177 q^{12} +3.79944 q^{13} +0.963361 q^{14} -1.31851 q^{15} +1.00000 q^{16} +6.99139 q^{17} -0.833884 q^{18} +3.74638 q^{19} +0.895866 q^{20} -1.41785 q^{21} +2.48480 q^{22} +3.06818 q^{23} -1.47177 q^{24} -4.19742 q^{25} +3.79944 q^{26} +5.64261 q^{27} +0.963361 q^{28} +6.35635 q^{29} -1.31851 q^{30} -6.11287 q^{31} +1.00000 q^{32} -3.65706 q^{33} +6.99139 q^{34} +0.863043 q^{35} -0.833884 q^{36} -0.425037 q^{37} +3.74638 q^{38} -5.59191 q^{39} +0.895866 q^{40} -2.34842 q^{41} -1.41785 q^{42} +5.39533 q^{43} +2.48480 q^{44} -0.747048 q^{45} +3.06818 q^{46} -8.05260 q^{47} -1.47177 q^{48} -6.07194 q^{49} -4.19742 q^{50} -10.2897 q^{51} +3.79944 q^{52} -8.92347 q^{53} +5.64261 q^{54} +2.22605 q^{55} +0.963361 q^{56} -5.51382 q^{57} +6.35635 q^{58} -4.89359 q^{59} -1.31851 q^{60} +13.7505 q^{61} -6.11287 q^{62} -0.803331 q^{63} +1.00000 q^{64} +3.40379 q^{65} -3.65706 q^{66} -10.8601 q^{67} +6.99139 q^{68} -4.51567 q^{69} +0.863043 q^{70} +4.08880 q^{71} -0.833884 q^{72} -12.9226 q^{73} -0.425037 q^{74} +6.17766 q^{75} +3.74638 q^{76} +2.39376 q^{77} -5.59191 q^{78} +8.96690 q^{79} +0.895866 q^{80} -5.80299 q^{81} -2.34842 q^{82} +8.85861 q^{83} -1.41785 q^{84} +6.26335 q^{85} +5.39533 q^{86} -9.35511 q^{87} +2.48480 q^{88} -16.2042 q^{89} -0.747048 q^{90} +3.66023 q^{91} +3.06818 q^{92} +8.99675 q^{93} -8.05260 q^{94} +3.35625 q^{95} -1.47177 q^{96} +13.7086 q^{97} -6.07194 q^{98} -2.07203 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 68 q^{2} + 25 q^{3} + 68 q^{4} + 20 q^{5} + 25 q^{6} + 29 q^{7} + 68 q^{8} + 87 q^{9}+O(q^{10}) $ 68 * q + 68 * q^2 + 25 * q^3 + 68 * q^4 + 20 * q^5 + 25 * q^6 + 29 * q^7 + 68 * q^8 + 87 * q^9	\( 68 q + 68 q^{2} + 25 q^{3} + 68 q^{4} + 20 q^{5} + 25 q^{6} + 29 q^{7} + 68 q^{8} + 87 q^{9} + 20 q^{10} + 46 q^{11} + 25 q^{12} + 30 q^{13} + 29 q^{14} + 13 q^{15} + 68 q^{16} + 73 q^{17} + 87 q^{18} + 56 q^{19} + 20 q^{20} - 5 q^{21} + 46 q^{22} + 63 q^{23} + 25 q^{24} + 88 q^{25} + 30 q^{26} + 67 q^{27} + 29 q^{28} + 43 q^{29} + 13 q^{30} + 68 q^{31} + 68 q^{32} + 26 q^{33} + 73 q^{34} + 50 q^{35} + 87 q^{36} + 8 q^{37} + 56 q^{38} + 6 q^{39} + 20 q^{40} + 64 q^{41} - 5 q^{42} + 52 q^{43} + 46 q^{44} + 7 q^{45} + 63 q^{46} + 94 q^{47} + 25 q^{48} + 91 q^{49} + 88 q^{50} + 20 q^{51} + 30 q^{52} + 38 q^{53} + 67 q^{54} + 37 q^{55} + 29 q^{56} + 4 q^{57} + 43 q^{58} + 84 q^{59} + 13 q^{60} + 26 q^{61} + 68 q^{62} + 22 q^{63} + 68 q^{64} - 20 q^{65} + 26 q^{66} + 54 q^{67} + 73 q^{68} - 11 q^{69} + 50 q^{70} + 46 q^{71} + 87 q^{72} + 62 q^{73} + 8 q^{74} + 54 q^{75} + 56 q^{76} + 67 q^{77} + 6 q^{78} + 67 q^{79} + 20 q^{80} + 120 q^{81} + 64 q^{82} + 130 q^{83} - 5 q^{84} - 24 q^{85} + 52 q^{86} + 72 q^{87} + 46 q^{88} + 61 q^{89} + 7 q^{90} + 43 q^{91} + 63 q^{92} + 40 q^{93} + 94 q^{94} + 55 q^{95} + 25 q^{96} + 41 q^{97} + 91 q^{98} + 106 q^{99}+O(q^{100}) \) 68 * q + 68 * q^2 + 25 * q^3 + 68 * q^4 + 20 * q^5 + 25 * q^6 + 29 * q^7 + 68 * q^8 + 87 * q^9 + 20 * q^10 + 46 * q^11 + 25 * q^12 + 30 * q^13 + 29 * q^14 + 13 * q^15 + 68 * q^16 + 73 * q^17 + 87 * q^18 + 56 * q^19 + 20 * q^20 - 5 * q^21 + 46 * q^22 + 63 * q^23 + 25 * q^24 + 88 * q^25 + 30 * q^26 + 67 * q^27 + 29 * q^28 + 43 * q^29 + 13 * q^30 + 68 * q^31 + 68 * q^32 + 26 * q^33 + 73 * q^34 + 50 * q^35 + 87 * q^36 + 8 * q^37 + 56 * q^38 + 6 * q^39 + 20 * q^40 + 64 * q^41 - 5 * q^42 + 52 * q^43 + 46 * q^44 + 7 * q^45 + 63 * q^46 + 94 * q^47 + 25 * q^48 + 91 * q^49 + 88 * q^50 + 20 * q^51 + 30 * q^52 + 38 * q^53 + 67 * q^54 + 37 * q^55 + 29 * q^56 + 4 * q^57 + 43 * q^58 + 84 * q^59 + 13 * q^60 + 26 * q^61 + 68 * q^62 + 22 * q^63 + 68 * q^64 - 20 * q^65 + 26 * q^66 + 54 * q^67 + 73 * q^68 - 11 * q^69 + 50 * q^70 + 46 * q^71 + 87 * q^72 + 62 * q^73 + 8 * q^74 + 54 * q^75 + 56 * q^76 + 67 * q^77 + 6 * q^78 + 67 * q^79 + 20 * q^80 + 120 * q^81 + 64 * q^82 + 130 * q^83 - 5 * q^84 - 24 * q^85 + 52 * q^86 + 72 * q^87 + 46 * q^88 + 61 * q^89 + 7 * q^90 + 43 * q^91 + 63 * q^92 + 40 * q^93 + 94 * q^94 + 55 * q^95 + 25 * q^96 + 41 * q^97 + 91 * q^98 + 106 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.47177	−0.849729	−0.424864	−	0.905257i	$-0.639678\pi$
$3$	−1.47177	−0.849729	−0.424864	+	0.905257i	$0.639678\pi$
$4$	1.00000	0.500000
$5$	0.895866	0.400643	0.200322	−	0.979730i	$-0.435801\pi$
$5$	0.895866	0.400643	0.200322	+	0.979730i	$0.435801\pi$
$6$	−1.47177	−0.600849
$7$	0.963361	0.364116	0.182058	−	0.983288i	$-0.441724\pi$
$7$	0.963361	0.364116	0.182058	+	0.983288i	$0.441724\pi$
$8$	1.00000	0.353553
$9$	−0.833884	−0.277961
$10$	0.895866	0.283298
$11$	2.48480	0.749194	0.374597	−	0.927188i	$-0.377781\pi$
$11$	2.48480	0.749194	0.374597	+	0.927188i	$0.377781\pi$
$12$	−1.47177	−0.424864
$13$	3.79944	1.05378	0.526888	−	0.849935i	$-0.323359\pi$
$13$	3.79944	1.05378	0.526888	+	0.849935i	$0.323359\pi$
$14$	0.963361	0.257469
$15$	−1.31851	−0.340438
$16$	1.00000	0.250000
$17$	6.99139	1.69566	0.847831	−	0.530267i	$-0.177908\pi$
$17$	6.99139	1.69566	0.847831	+	0.530267i	$0.177908\pi$
$18$	−0.833884	−0.196548
$19$	3.74638	0.859478	0.429739	−	0.902953i	$-0.358606\pi$
$19$	3.74638	0.859478	0.429739	+	0.902953i	$0.358606\pi$
$20$	0.895866	0.200322
$21$	−1.41785	−0.309400
$22$	2.48480	0.529760
$23$	3.06818	0.639760	0.319880	−	0.947458i	$-0.396357\pi$
$23$	3.06818	0.639760	0.319880	+	0.947458i	$0.396357\pi$
$24$	−1.47177	−0.300424
$25$	−4.19742	−0.839485
$26$	3.79944	0.745131
$27$	5.64261	1.08592
$28$	0.963361	0.182058
$29$	6.35635	1.18034	0.590172	−	0.807277i	$-0.299060\pi$
$29$	6.35635	1.18034	0.590172	+	0.807277i	$0.299060\pi$
$30$	−1.31851	−0.240726
$31$	−6.11287	−1.09790	−0.548952	−	0.835854i	$-0.684973\pi$
$31$	−6.11287	−1.09790	−0.548952	+	0.835854i	$0.684973\pi$
$32$	1.00000	0.176777
$33$	−3.65706	−0.636612
$34$	6.99139	1.19901
$35$	0.863043	0.145881
$36$	−0.833884	−0.138981
$37$	−0.425037	−0.0698756	−0.0349378	−	0.999389i	$-0.511123\pi$
$37$	−0.425037	−0.0698756	−0.0349378	+	0.999389i	$0.511123\pi$
$38$	3.74638	0.607742
$39$	−5.59191	−0.895423
$40$	0.895866	0.141649
$41$	−2.34842	−0.366761	−0.183380	−	0.983042i	$-0.558704\pi$
$41$	−2.34842	−0.366761	−0.183380	+	0.983042i	$0.558704\pi$
$42$	−1.41785	−0.218779
$43$	5.39533	0.822780	0.411390	−	0.911459i	$-0.365043\pi$
$43$	5.39533	0.822780	0.411390	+	0.911459i	$0.365043\pi$
$44$	2.48480	0.374597
$45$	−0.747048	−0.111363
$46$	3.06818	0.452379
$47$	−8.05260	−1.17459	−0.587296	−	0.809372i	$-0.699808\pi$
$47$	−8.05260	−1.17459	−0.587296	+	0.809372i	$0.699808\pi$
$48$	−1.47177	−0.212432
$49$	−6.07194	−0.867419
$50$	−4.19742	−0.593605
$51$	−10.2897	−1.44085
$52$	3.79944	0.526888
$53$	−8.92347	−1.22573	−0.612866	−	0.790187i	$-0.709984\pi$
$53$	−8.92347	−1.22573	−0.612866	+	0.790187i	$0.709984\pi$
$54$	5.64261	0.767862
$55$	2.22605	0.300160
$56$	0.963361	0.128735
$57$	−5.51382	−0.730323
$58$	6.35635	0.834630
$59$	−4.89359	−0.637091	−0.318545	−	0.947908i	$-0.603194\pi$
$59$	−4.89359	−0.637091	−0.318545	+	0.947908i	$0.603194\pi$
$60$	−1.31851	−0.170219
$61$	13.7505	1.76057	0.880284	−	0.474448i	$-0.157352\pi$
$61$	13.7505	1.76057	0.880284	+	0.474448i	$0.157352\pi$
$62$	−6.11287	−0.776335
$63$	−0.803331	−0.101210
$64$	1.00000	0.125000
$65$	3.40379	0.422188
$66$	−3.65706	−0.450153
$67$	−10.8601	−1.32678	−0.663389	−	0.748275i	$-0.730882\pi$
$67$	−10.8601	−1.32678	−0.663389	+	0.748275i	$0.730882\pi$
$68$	6.99139	0.847831
$69$	−4.51567	−0.543623
$70$	0.863043	0.103153
$71$	4.08880	0.485251	0.242626	−	0.970120i	$-0.421991\pi$
$71$	4.08880	0.485251	0.242626	+	0.970120i	$0.421991\pi$
$72$	−0.833884	−0.0982741
$73$	−12.9226	−1.51248	−0.756238	−	0.654296i	$-0.772965\pi$
$73$	−12.9226	−1.51248	−0.756238	+	0.654296i	$0.772965\pi$
$74$	−0.425037	−0.0494095
$75$	6.17766	0.713334
$76$	3.74638	0.429739
$77$	2.39376	0.272794
$78$	−5.59191	−0.633160
$79$	8.96690	1.00886	0.504428	−	0.863454i	$-0.331704\pi$
$79$	8.96690	1.00886	0.504428	+	0.863454i	$0.331704\pi$
$80$	0.895866	0.100161
$81$	−5.80299	−0.644776
$82$	−2.34842	−0.259339
$83$	8.85861	0.972358	0.486179	−	0.873859i	$-0.338390\pi$
$83$	8.85861	0.972358	0.486179	+	0.873859i	$0.338390\pi$
$84$	−1.41785	−0.154700
$85$	6.26335	0.679356
$86$	5.39533	0.581793
$87$	−9.35511	−1.00297
$88$	2.48480	0.264880
$89$	−16.2042	−1.71764	−0.858820	−	0.512278i	$-0.828802\pi$
$89$	−16.2042	−1.71764	−0.858820	+	0.512278i	$0.828802\pi$
$90$	−0.747048	−0.0787458
$91$	3.66023	0.383697
$92$	3.06818	0.319880
$93$	8.99675	0.932920
$94$	−8.05260	−0.830562
$95$	3.35625	0.344344
$96$	−1.47177	−0.150212
$97$	13.7086	1.39190	0.695949	−	0.718091i	$-0.254984\pi$
$97$	13.7086	1.39190	0.695949	+	0.718091i	$0.254984\pi$
$98$	−6.07194	−0.613358
$99$	−2.07203	−0.208247
$100$	−4.19742	−0.419742
$101$	7.88550	0.784637	0.392318	−	0.919830i	$-0.371673\pi$
$101$	7.88550	0.784637	0.392318	+	0.919830i	$0.371673\pi$
$102$	−10.2897	−1.01884
$103$	−0.471938	−0.0465015	−0.0232507	−	0.999730i	$-0.507402\pi$
$103$	−0.471938	−0.0465015	−0.0232507	+	0.999730i	$0.507402\pi$
$104$	3.79944	0.372566
$105$	−1.27020	−0.123959
$106$	−8.92347	−0.866724
$107$	12.8928	1.24639	0.623195	−	0.782066i	$-0.285834\pi$
$107$	12.8928	1.24639	0.623195	+	0.782066i	$0.285834\pi$
$108$	5.64261	0.542960
$109$	15.4167	1.47666	0.738328	−	0.674442i	$-0.235616\pi$
$109$	15.4167	1.47666	0.738328	+	0.674442i	$0.235616\pi$
$110$	2.22605	0.212245
$111$	0.625558	0.0593753
$112$	0.963361	0.0910291
$113$	−12.5222	−1.17799	−0.588997	−	0.808136i	$-0.700477\pi$
$113$	−12.5222	−1.17799	−0.588997	+	0.808136i	$0.700477\pi$
$114$	−5.51382	−0.516416
$115$	2.74868	0.256316
$116$	6.35635	0.590172
$117$	−3.16829	−0.292909
$118$	−4.89359	−0.450491
$119$	6.73523	0.617418
$120$	−1.31851	−0.120363
$121$	−4.82578	−0.438708
$122$	13.7505	1.24491
$123$	3.45634	0.311647
$124$	−6.11287	−0.548952
$125$	−8.23966	−0.736978
$126$	−0.803331	−0.0715664
$127$	16.0890	1.42767	0.713835	−	0.700314i	$-0.246956\pi$
$127$	16.0890	1.42767	0.713835	+	0.700314i	$0.246956\pi$
$128$	1.00000	0.0883883
$129$	−7.94070	−0.699140
$130$	3.40379	0.298532
$131$	20.6993	1.80851	0.904253	−	0.426998i	$-0.140429\pi$
$131$	20.6993	1.80851	0.904253	+	0.426998i	$0.140429\pi$
$132$	−3.65706	−0.318306
$133$	3.60911	0.312950
$134$	−10.8601	−0.938173
$135$	5.05502	0.435067
$136$	6.99139	0.599507
$137$	−2.78019	−0.237528	−0.118764	−	0.992923i	$-0.537893\pi$
$137$	−2.78019	−0.237528	−0.118764	+	0.992923i	$0.537893\pi$
$138$	−4.51567	−0.384399
$139$	6.76320	0.573647	0.286823	−	0.957983i	$-0.407401\pi$
$139$	6.76320	0.573647	0.286823	+	0.957983i	$0.407401\pi$
$140$	0.863043	0.0729404
$141$	11.8516	0.998085
$142$	4.08880	0.343125
$143$	9.44084	0.789482
$144$	−0.833884	−0.0694903
$145$	5.69444	0.472897
$146$	−12.9226	−1.06948
$147$	8.93651	0.737071
$148$	−0.425037	−0.0349378
$149$	9.00129	0.737414	0.368707	−	0.929546i	$-0.379801\pi$
$149$	9.00129	0.737414	0.368707	+	0.929546i	$0.379801\pi$
$150$	6.17766	0.504404
$151$	−12.4796	−1.01558	−0.507790	−	0.861481i	$-0.669537\pi$
$151$	−12.4796	−1.01558	−0.507790	+	0.861481i	$0.669537\pi$
$152$	3.74638	0.303871
$153$	−5.83001	−0.471328
$154$	2.39376	0.192894
$155$	−5.47631	−0.439868
$156$	−5.59191	−0.447711
$157$	−15.0763	−1.20322	−0.601610	−	0.798790i	$-0.705474\pi$
$157$	−15.0763	−1.20322	−0.601610	+	0.798790i	$0.705474\pi$
$158$	8.96690	0.713368
$159$	13.1333	1.04154
$160$	0.895866	0.0708244
$161$	2.95577	0.232947
$162$	−5.80299	−0.455926
$163$	24.7803	1.94094	0.970471	−	0.241217i	$-0.0775464\pi$
$163$	24.7803	1.94094	0.970471	+	0.241217i	$0.0775464\pi$
$164$	−2.34842	−0.183380
$165$	−3.27623	−0.255054
$166$	8.85861	0.687561
$167$	−20.9978	−1.62486	−0.812431	−	0.583058i	$-0.801856\pi$
$167$	−20.9978	−1.62486	−0.812431	+	0.583058i	$0.801856\pi$
$168$	−1.41785	−0.109389
$169$	1.43574	0.110442
$170$	6.26335	0.480377
$171$	−3.12404	−0.238901
$172$	5.39533	0.411390
$173$	−5.74180	−0.436541	−0.218270	−	0.975888i	$-0.570041\pi$
$173$	−5.74180	−0.436541	−0.218270	+	0.975888i	$0.570041\pi$
$174$	−9.35511	−0.709209
$175$	−4.04364	−0.305670
$176$	2.48480	0.187299
$177$	7.20225	0.541354
$178$	−16.2042	−1.21455
$179$	−14.5702	−1.08902	−0.544512	−	0.838753i	$-0.683285\pi$
$179$	−14.5702	−1.08902	−0.544512	+	0.838753i	$0.683285\pi$
$180$	−0.747048	−0.0556817
$181$	9.09078	0.675713	0.337856	−	0.941198i	$-0.390298\pi$
$181$	9.09078	0.675713	0.337856	+	0.941198i	$0.390298\pi$
$182$	3.66023	0.271315
$183$	−20.2376	−1.49600
$184$	3.06818	0.226189
$185$	−0.380776	−0.0279952
$186$	8.99675	0.659674
$187$	17.3722	1.27038
$188$	−8.05260	−0.587296
$189$	5.43587	0.395401
$190$	3.35625	0.243488
$191$	−23.0580	−1.66842	−0.834211	−	0.551446i	$-0.814076\pi$
$191$	−23.0580	−1.66842	−0.834211	+	0.551446i	$0.814076\pi$
$192$	−1.47177	−0.106216
$193$	7.78236	0.560187	0.280093	−	0.959973i	$-0.409635\pi$
$193$	7.78236	0.560187	0.280093	+	0.959973i	$0.409635\pi$
$194$	13.7086	0.984221
$195$	−5.00961	−0.358745
$196$	−6.07194	−0.433710
$197$	26.3072	1.87431	0.937155	−	0.348915i	$-0.113450\pi$
$197$	26.3072	1.87431	0.937155	+	0.348915i	$0.113450\pi$
$198$	−2.07203	−0.147253
$199$	3.66484	0.259794	0.129897	−	0.991528i	$-0.458535\pi$
$199$	3.66484	0.259794	0.129897	+	0.991528i	$0.458535\pi$
$200$	−4.19742	−0.296803
$201$	15.9837	1.12740
$202$	7.88550	0.554822
$203$	6.12346	0.429783
$204$	−10.2897	−0.720426
$205$	−2.10387	−0.146940
$206$	−0.471938	−0.0328815
$207$	−2.55851	−0.177828
$208$	3.79944	0.263444
$209$	9.30898	0.643916
$210$	−1.27020	−0.0876523
$211$	−16.8228	−1.15813	−0.579066	−	0.815280i	$-0.696583\pi$
$211$	−16.8228	−1.15813	−0.579066	+	0.815280i	$0.696583\pi$
$212$	−8.92347	−0.612866
$213$	−6.01779	−0.412332
$214$	12.8928	0.881331
$215$	4.83349	0.329641
$216$	5.64261	0.383931
$217$	−5.88890	−0.399765
$218$	15.4167	1.04415
$219$	19.0191	1.28519
$220$	2.22605	0.150080
$221$	26.5634	1.78685
$222$	0.625558	0.0419847
$223$	19.9636	1.33686	0.668430	−	0.743775i	$-0.266967\pi$
$223$	19.9636	1.33686	0.668430	+	0.743775i	$0.266967\pi$
$224$	0.963361	0.0643673
$225$	3.50016	0.233344
$226$	−12.5222	−0.832967
$227$	−27.2474	−1.80847	−0.904237	−	0.427031i	$-0.859560\pi$
$227$	−27.2474	−1.80847	−0.904237	+	0.427031i	$0.859560\pi$
$228$	−5.51382	−0.365161
$229$	20.2868	1.34059	0.670296	−	0.742094i	$-0.266167\pi$
$229$	20.2868	1.34059	0.670296	+	0.742094i	$0.266167\pi$
$230$	2.74868	0.181243
$231$	−3.52307	−0.231801
$232$	6.35635	0.417315
$233$	10.1920	0.667702	0.333851	−	0.942626i	$-0.391652\pi$
$233$	10.1920	0.667702	0.333851	+	0.942626i	$0.391652\pi$
$234$	−3.16829	−0.207118
$235$	−7.21405	−0.470593
$236$	−4.89359	−0.318545
$237$	−13.1972	−0.857253
$238$	6.73523	0.436580
$239$	16.2416	1.05058	0.525292	−	0.850922i	$-0.323956\pi$
$239$	16.2416	1.05058	0.525292	+	0.850922i	$0.323956\pi$
$240$	−1.31851	−0.0851096
$241$	−21.1599	−1.36303	−0.681514	−	0.731805i	$-0.738678\pi$
$241$	−21.1599	−1.36303	−0.681514	+	0.731805i	$0.738678\pi$
$242$	−4.82578	−0.310213
$243$	−8.38714	−0.538035
$244$	13.7505	0.880284
$245$	−5.43964	−0.347526
$246$	3.45634	0.220368
$247$	14.2341	0.905696
$248$	−6.11287	−0.388167
$249$	−13.0379	−0.826241
$250$	−8.23966	−0.521122
$251$	−0.958567	−0.0605042	−0.0302521	−	0.999542i	$-0.509631\pi$
$251$	−0.958567	−0.0605042	−0.0302521	+	0.999542i	$0.509631\pi$
$252$	−0.803331	−0.0506051
$253$	7.62381	0.479305
$254$	16.0890	1.00952
$255$	−9.21823	−0.577268
$256$	1.00000	0.0625000
$257$	−7.33395	−0.457479	−0.228740	−	0.973488i	$-0.573460\pi$
$257$	−7.33395	−0.457479	−0.228740	+	0.973488i	$0.573460\pi$
$258$	−7.94070	−0.494366
$259$	−0.409464	−0.0254429
$260$	3.40379	0.211094
$261$	−5.30046	−0.328090
$262$	20.6993	1.27881
$263$	−0.0210270	−0.00129658	−0.000648289	−	1.00000i	$-0.500206\pi$
$263$	−0.0210270	−0.00129658	−0.000648289		1.00000i	$0.500206\pi$
$264$	−3.65706	−0.225076
$265$	−7.99423	−0.491082
$266$	3.60911	0.221289
$267$	23.8489	1.45953
$268$	−10.8601	−0.663389
$269$	−22.5315	−1.37377	−0.686886	−	0.726765i	$-0.741023\pi$
$269$	−22.5315	−1.37377	−0.686886	+	0.726765i	$0.741023\pi$
$270$	5.05502	0.307639
$271$	22.3277	1.35631	0.678157	−	0.734917i	$-0.262779\pi$
$271$	22.3277	1.35631	0.678157	+	0.734917i	$0.262779\pi$
$272$	6.99139	0.423915
$273$	−5.38703	−0.326038
$274$	−2.78019	−0.167957
$275$	−10.4297	−0.628937
$276$	−4.51567	−0.271811
$277$	1.85021	0.111168	0.0555841	−	0.998454i	$-0.482298\pi$
$277$	1.85021	0.111168	0.0555841	+	0.998454i	$0.482298\pi$
$278$	6.76320	0.405630
$279$	5.09742	0.305175
$280$	0.863043	0.0515767
$281$	0.314425	0.0187570	0.00937851	−	0.999956i	$-0.497015\pi$
$281$	0.314425	0.0187570	0.00937851	+	0.999956i	$0.497015\pi$
$282$	11.8516	0.705753
$283$	15.8013	0.939292	0.469646	−	0.882855i	$-0.344382\pi$
$283$	15.8013	0.939292	0.469646	+	0.882855i	$0.344382\pi$
$284$	4.08880	0.242626
$285$	−4.93964	−0.292599
$286$	9.44084	0.558248
$287$	−2.26237	−0.133544
$288$	−0.833884	−0.0491371
$289$	31.8795	1.87527
$290$	5.69444	0.334389
$291$	−20.1760	−1.18274
$292$	−12.9226	−0.756238
$293$	−15.3307	−0.895627	−0.447814	−	0.894127i	$-0.647797\pi$
$293$	−15.3307	−0.895627	−0.447814	+	0.894127i	$0.647797\pi$
$294$	8.93651	0.521188
$295$	−4.38400	−0.255246
$296$	−0.425037	−0.0247048
$297$	14.0207	0.813565
$298$	9.00129	0.521430
$299$	11.6574	0.674163
$300$	6.17766	0.356667
$301$	5.19765	0.299588
$302$	−12.4796	−0.718123
$303$	−11.6057	−0.666728
$304$	3.74638	0.214869
$305$	12.3186	0.705360
$306$	−5.83001	−0.333279
$307$	2.81481	0.160650	0.0803248	−	0.996769i	$-0.474404\pi$
$307$	2.81481	0.160650	0.0803248	+	0.996769i	$0.474404\pi$
$308$	2.39376	0.136397
$309$	0.694586	0.0395136
$310$	−5.47631	−0.311034
$311$	16.8302	0.954354	0.477177	−	0.878807i	$-0.341660\pi$
$311$	16.8302	0.954354	0.477177	+	0.878807i	$0.341660\pi$
$312$	−5.59191	−0.316580
$313$	−1.23413	−0.0697573	−0.0348787	−	0.999392i	$-0.511104\pi$
$313$	−1.23413	−0.0697573	−0.0348787	+	0.999392i	$0.511104\pi$
$314$	−15.0763	−0.850804
$315$	−0.719677	−0.0405492
$316$	8.96690	0.504428
$317$	−3.18979	−0.179156	−0.0895782	−	0.995980i	$-0.528552\pi$
$317$	−3.18979	−0.179156	−0.0895782	+	0.995980i	$0.528552\pi$
$318$	13.1333	0.736480
$319$	15.7942	0.884308
$320$	0.895866	0.0500804
$321$	−18.9752	−1.05909
$322$	2.95577	0.164718
$323$	26.1924	1.45738
$324$	−5.80299	−0.322388
$325$	−15.9479	−0.884628
$326$	24.7803	1.37245
$327$	−22.6899	−1.25476
$328$	−2.34842	−0.129670
$329$	−7.75756	−0.427688
$330$	−3.27623	−0.180351
$331$	−24.9166	−1.36954	−0.684770	−	0.728759i	$-0.740098\pi$
$331$	−24.9166	−1.36954	−0.684770	+	0.728759i	$0.740098\pi$
$332$	8.85861	0.486179
$333$	0.354431	0.0194227
$334$	−20.9978	−1.14895
$335$	−9.72923	−0.531565
$336$	−1.41785	−0.0773500
$337$	4.56285	0.248554	0.124277	−	0.992248i	$-0.460339\pi$
$337$	4.56285	0.248554	0.124277	+	0.992248i	$0.460339\pi$
$338$	1.43574	0.0780942
$339$	18.4299	1.00097
$340$	6.26335	0.339678
$341$	−15.1892	−0.822543
$342$	−3.12404	−0.168929
$343$	−12.5930	−0.679958
$344$	5.39533	0.290897
$345$	−4.04543	−0.217799
$346$	−5.74180	−0.308681
$347$	18.6663	1.00206	0.501029	−	0.865430i	$-0.332955\pi$
$347$	18.6663	1.00206	0.501029	+	0.865430i	$0.332955\pi$
$348$	−9.35511	−0.501486
$349$	−12.8490	−0.687791	−0.343895	−	0.939008i	$-0.611747\pi$
$349$	−12.8490	−0.687791	−0.343895	+	0.939008i	$0.611747\pi$
$350$	−4.04364	−0.216141
$351$	21.4387	1.14432
$352$	2.48480	0.132440
$353$	19.9775	1.06329	0.531646	−	0.846966i	$-0.321574\pi$
$353$	19.9775	1.06329	0.531646	+	0.846966i	$0.321574\pi$
$354$	7.20225	0.382795
$355$	3.66302	0.194413
$356$	−16.2042	−0.858820
$357$	−9.91274	−0.524638
$358$	−14.5702	−0.770057
$359$	20.7410	1.09467	0.547333	−	0.836915i	$-0.315643\pi$
$359$	20.7410	1.09467	0.547333	+	0.836915i	$0.315643\pi$
$360$	−0.747048	−0.0393729
$361$	−4.96467	−0.261298
$362$	9.09078	0.477801
$363$	7.10246	0.372782
$364$	3.66023	0.191848
$365$	−11.5769	−0.605964
$366$	−20.2376	−1.05784
$367$	−23.5453	−1.22905	−0.614527	−	0.788896i	$-0.710653\pi$
$367$	−23.5453	−1.22905	−0.614527	+	0.788896i	$0.710653\pi$
$368$	3.06818	0.159940
$369$	1.95831	0.101945
$370$	−0.380776	−0.0197956
$371$	−8.59652	−0.446309
$372$	8.99675	0.466460
$373$	2.17423	0.112577	0.0562886	−	0.998415i	$-0.482073\pi$
$373$	2.17423	0.112577	0.0562886	+	0.998415i	$0.482073\pi$
$374$	17.3722	0.898294
$375$	12.1269	0.626231
$376$	−8.05260	−0.415281
$377$	24.1506	1.24382
$378$	5.43587	0.279591
$379$	18.7428	0.962752	0.481376	−	0.876514i	$-0.340137\pi$
$379$	18.7428	0.962752	0.481376	+	0.876514i	$0.340137\pi$
$380$	3.35625	0.172172
$381$	−23.6794	−1.21313
$382$	−23.0580	−1.17975
$383$	−16.2416	−0.829907	−0.414953	−	0.909843i	$-0.636202\pi$
$383$	−16.2416	−0.829907	−0.414953	+	0.909843i	$0.636202\pi$
$384$	−1.47177	−0.0751061
$385$	2.14449	0.109293
$386$	7.78236	0.396112
$387$	−4.49908	−0.228701
$388$	13.7086	0.695949
$389$	−26.7912	−1.35837	−0.679183	−	0.733969i	$-0.737666\pi$
$389$	−26.7912	−1.35837	−0.679183	+	0.733969i	$0.737666\pi$
$390$	−5.00961	−0.253671
$391$	21.4509	1.08482
$392$	−6.07194	−0.306679
$393$	−30.4647	−1.53674
$394$	26.3072	1.32534
$395$	8.03314	0.404191
$396$	−2.07203	−0.104123
$397$	19.4652	0.976931	0.488466	−	0.872583i	$-0.337557\pi$
$397$	19.4652	0.976931	0.488466	+	0.872583i	$0.337557\pi$
$398$	3.66484	0.183702
$399$	−5.31180	−0.265922
$400$	−4.19742	−0.209871
$401$	27.6320	1.37987	0.689937	−	0.723869i	$-0.257638\pi$
$401$	27.6320	1.37987	0.689937	+	0.723869i	$0.257638\pi$
$402$	15.9837	0.797193
$403$	−23.2255	−1.15694
$404$	7.88550	0.392318
$405$	−5.19870	−0.258325
$406$	6.12346	0.303902
$407$	−1.05613	−0.0523504
$408$	−10.2897	−0.509418
$409$	0.157325	0.00777924	0.00388962	−	0.999992i	$-0.498762\pi$
$409$	0.157325	0.00777924	0.00388962	+	0.999992i	$0.498762\pi$
$410$	−2.10387	−0.103903
$411$	4.09181	0.201834
$412$	−0.471938	−0.0232507
$413$	−4.71429	−0.231975
$414$	−2.55851	−0.125744
$415$	7.93612	0.389569
$416$	3.79944	0.186283
$417$	−9.95389	−0.487444
$418$	9.30898	0.455317
$419$	13.8923	0.678682	0.339341	−	0.940663i	$-0.389796\pi$
$419$	13.8923	0.678682	0.339341	+	0.940663i	$0.389796\pi$
$420$	−1.27020	−0.0619796
$421$	−24.8237	−1.20983	−0.604916	−	0.796289i	$-0.706793\pi$
$421$	−24.8237	−1.20983	−0.604916	+	0.796289i	$0.706793\pi$
$422$	−16.8228	−0.818924
$423$	6.71493	0.326491
$424$	−8.92347	−0.433362
$425$	−29.3458	−1.42348
$426$	−6.01779	−0.291563
$427$	13.2467	0.641051
$428$	12.8928	0.623195
$429$	−13.8948	−0.670846
$430$	4.83349	0.233092
$431$	15.1780	0.731099	0.365550	−	0.930792i	$-0.380881\pi$
$431$	15.1780	0.731099	0.365550	+	0.930792i	$0.380881\pi$
$432$	5.64261	0.271480
$433$	−7.79208	−0.374463	−0.187232	−	0.982316i	$-0.559952\pi$
$433$	−7.79208	−0.374463	−0.187232	+	0.982316i	$0.559952\pi$
$434$	−5.88890	−0.282676
$435$	−8.38092	−0.401834
$436$	15.4167	0.738328
$437$	11.4946	0.549859
$438$	19.0191	0.908770
$439$	15.0078	0.716281	0.358140	−	0.933668i	$-0.383411\pi$
$439$	15.0078	0.716281	0.358140	+	0.933668i	$0.383411\pi$
$440$	2.22605	0.106123
$441$	5.06329	0.241109
$442$	26.5634	1.26349
$443$	−8.87573	−0.421699	−0.210849	−	0.977519i	$-0.567623\pi$
$443$	−8.87573	−0.421699	−0.210849	+	0.977519i	$0.567623\pi$
$444$	0.625558	0.0296877
$445$	−14.5168	−0.688161
$446$	19.9636	0.945303
$447$	−13.2479	−0.626602
$448$	0.963361	0.0455145
$449$	7.81987	0.369042	0.184521	−	0.982829i	$-0.440927\pi$
$449$	7.81987	0.369042	0.184521	+	0.982829i	$0.440927\pi$
$450$	3.50016	0.164999
$451$	−5.83534	−0.274775
$452$	−12.5222	−0.588997
$453$	18.3672	0.862967
$454$	−27.2474	−1.27878
$455$	3.27908	0.153726
$456$	−5.51382	−0.258208
$457$	−29.3227	−1.37166	−0.685828	−	0.727764i	$-0.740560\pi$
$457$	−29.3227	−1.37166	−0.685828	+	0.727764i	$0.740560\pi$
$458$	20.2868	0.947942
$459$	39.4497	1.84135
$460$	2.74868	0.128158
$461$	−26.7843	−1.24747	−0.623736	−	0.781635i	$-0.714386\pi$
$461$	−26.7843	−1.24747	−0.623736	+	0.781635i	$0.714386\pi$
$462$	−3.52307	−0.163908
$463$	−33.7092	−1.56660	−0.783300	−	0.621644i	$-0.786465\pi$
$463$	−33.7092	−1.56660	−0.783300	+	0.621644i	$0.786465\pi$
$464$	6.35635	0.295086
$465$	8.05989	0.373768
$466$	10.1920	0.472136
$467$	24.2440	1.12188	0.560940	−	0.827856i	$-0.310440\pi$
$467$	24.2440	1.12188	0.560940	+	0.827856i	$0.310440\pi$
$468$	−3.16829	−0.146454
$469$	−10.4622	−0.483101
$470$	−7.21405	−0.332759
$471$	22.1889	1.02241
$472$	−4.89359	−0.225246
$473$	13.4063	0.616422
$474$	−13.1972	−0.606170
$475$	−15.7251	−0.721518
$476$	6.73523	0.308709
$477$	7.44113	0.340706
$478$	16.2416	0.742875
$479$	19.8986	0.909189	0.454594	−	0.890699i	$-0.349784\pi$
$479$	19.8986	0.909189	0.454594	+	0.890699i	$0.349784\pi$
$480$	−1.31851	−0.0601815
$481$	−1.61490	−0.0736332
$482$	−21.1599	−0.963807
$483$	−4.35022	−0.197942
$484$	−4.82578	−0.219354
$485$	12.2811	0.557655
$486$	−8.38714	−0.380448
$487$	−13.8223	−0.626349	−0.313175	−	0.949696i	$-0.601393\pi$
$487$	−13.8223	−0.626349	−0.313175	+	0.949696i	$0.601393\pi$
$488$	13.7505	0.622455
$489$	−36.4710	−1.64927
$490$	−5.43964	−0.245738
$491$	−14.9292	−0.673743	−0.336872	−	0.941551i	$-0.609369\pi$
$491$	−14.9292	−0.673743	−0.336872	+	0.941551i	$0.609369\pi$
$492$	3.45634	0.155824
$493$	44.4397	2.00146
$494$	14.2341	0.640424
$495$	−1.85626	−0.0834328
$496$	−6.11287	−0.274476
$497$	3.93899	0.176688
$498$	−13.0379	−0.584241
$499$	26.6956	1.19506	0.597529	−	0.801848i	$-0.296149\pi$
$499$	26.6956	1.19506	0.597529	+	0.801848i	$0.296149\pi$
$500$	−8.23966	−0.368489
$501$	30.9041	1.38069
$502$	−0.958567	−0.0427829
$503$	−19.4572	−0.867556	−0.433778	−	0.901020i	$-0.642820\pi$
$503$	−19.4572	−0.867556	−0.433778	+	0.901020i	$0.642820\pi$
$504$	−0.803331	−0.0357832
$505$	7.06435	0.314360
$506$	7.62381	0.338920
$507$	−2.11309	−0.0938456
$508$	16.0890	0.713835
$509$	26.5420	1.17645	0.588226	−	0.808697i	$-0.299827\pi$
$509$	26.5420	1.17645	0.588226	+	0.808697i	$0.299827\pi$
$510$	−9.21823	−0.408190
$511$	−12.4491	−0.550717
$512$	1.00000	0.0441942
$513$	21.1393	0.933324
$514$	−7.33395	−0.323487
$515$	−0.422793	−0.0186305
$516$	−7.94070	−0.349570
$517$	−20.0091	−0.879998
$518$	−0.409464	−0.0179908
$519$	8.45062	0.370941
$520$	3.40379	0.149266
$521$	11.7810	0.516136	0.258068	−	0.966127i	$-0.416914\pi$
$521$	11.7810	0.516136	0.258068	+	0.966127i	$0.416914\pi$
$522$	−5.30046	−0.231995
$523$	−29.0346	−1.26960	−0.634798	−	0.772678i	$-0.718917\pi$
$523$	−29.0346	−1.26960	−0.634798	+	0.772678i	$0.718917\pi$
$524$	20.6993	0.904253
$525$	5.95131	0.259737
$526$	−0.0210270	−0.000916819 0
$527$	−42.7374	−1.86167
$528$	−3.65706	−0.159153
$529$	−13.5863	−0.590707
$530$	−7.99423	−0.347247
$531$	4.08068	0.177086
$532$	3.60911	0.156475
$533$	−8.92267	−0.386484
$534$	23.8489	1.03204
$535$	11.5502	0.499358
$536$	−10.8601	−0.469087
$537$	21.4440	0.925376
$538$	−22.5315	−0.971404
$539$	−15.0875	−0.649866
$540$	5.05502	0.217533
$541$	4.01431	0.172589	0.0862943	−	0.996270i	$-0.472497\pi$
$541$	4.01431	0.172589	0.0862943	+	0.996270i	$0.472497\pi$
$542$	22.3277	0.959059
$543$	−13.3796	−0.574172
$544$	6.99139	0.299753
$545$	13.8113	0.591612
$546$	−5.38703	−0.230544
$547$	−39.8425	−1.70354	−0.851771	−	0.523914i	$-0.824471\pi$
$547$	−39.8425	−1.70354	−0.851771	+	0.523914i	$0.824471\pi$
$548$	−2.78019	−0.118764
$549$	−11.4663	−0.489369
$550$	−10.4297	−0.444726
$551$	23.8133	1.01448
$552$	−4.51567	−0.192200
$553$	8.63837	0.367341
$554$	1.85021	0.0786079
$555$	0.560416	0.0237883
$556$	6.76320	0.286823
$557$	7.21936	0.305894	0.152947	−	0.988234i	$-0.451124\pi$
$557$	7.21936	0.305894	0.152947	+	0.988234i	$0.451124\pi$
$558$	5.09742	0.215791
$559$	20.4992	0.867025
$560$	0.863043	0.0364702
$561$	−25.5679	−1.07948
$562$	0.314425	0.0132632
$563$	35.8439	1.51064	0.755320	−	0.655356i	$-0.227481\pi$
$563$	35.8439	1.51064	0.755320	+	0.655356i	$0.227481\pi$
$564$	11.8516	0.499042
$565$	−11.2182	−0.471955
$566$	15.8013	0.664180
$567$	−5.59037	−0.234774
$568$	4.08880	0.171562
$569$	−12.0533	−0.505300	−0.252650	−	0.967558i	$-0.581302\pi$
$569$	−12.0533	−0.505300	−0.252650	+	0.967558i	$0.581302\pi$
$570$	−4.93964	−0.206899
$571$	6.02786	0.252258	0.126129	−	0.992014i	$-0.459745\pi$
$571$	6.02786	0.252258	0.126129	+	0.992014i	$0.459745\pi$
$572$	9.44084	0.394741
$573$	33.9362	1.41771
$574$	−2.26237	−0.0944296
$575$	−12.8785	−0.537069
$576$	−0.833884	−0.0347451
$577$	−45.5906	−1.89796	−0.948982	−	0.315331i	$-0.897884\pi$
$577$	−45.5906	−1.89796	−0.948982	+	0.315331i	$0.897884\pi$
$578$	31.8795	1.32601
$579$	−11.4539	−0.476007
$580$	5.69444	0.236449
$581$	8.53404	0.354052
$582$	−20.1760	−0.836320
$583$	−22.1730	−0.918312
$584$	−12.9226	−0.534741
$585$	−2.83836	−0.117352
$586$	−15.3307	−0.633304
$587$	2.77463	0.114521	0.0572607	−	0.998359i	$-0.481763\pi$
$587$	2.77463	0.114521	0.0572607	+	0.998359i	$0.481763\pi$
$588$	8.93651	0.368536
$589$	−22.9011	−0.943623
$590$	−4.38400	−0.180486
$591$	−38.7182	−1.59265
$592$	−0.425037	−0.0174689
$593$	27.5366	1.13079	0.565396	−	0.824819i	$-0.308723\pi$
$593$	27.5366	1.13079	0.565396	+	0.824819i	$0.308723\pi$
$594$	14.0207	0.575278
$595$	6.03387	0.247364
$596$	9.00129	0.368707
$597$	−5.39381	−0.220754
$598$	11.6574	0.476705
$599$	3.74910	0.153184	0.0765921	−	0.997063i	$-0.475596\pi$
$599$	3.74910	0.153184	0.0765921	+	0.997063i	$0.475596\pi$
$600$	6.17766	0.252202
$601$	−12.8246	−0.523125	−0.261563	−	0.965186i	$-0.584238\pi$
$601$	−12.8246	−0.523125	−0.261563	+	0.965186i	$0.584238\pi$
$602$	5.19765	0.211840
$603$	9.05609	0.368793
$604$	−12.4796	−0.507790
$605$	−4.32326	−0.175765
$606$	−11.6057	−0.471448
$607$	−0.0848447	−0.00344374	−0.00172187	−	0.999999i	$-0.500548\pi$
$607$	−0.0848447	−0.00344374	−0.00172187	+	0.999999i	$0.500548\pi$
$608$	3.74638	0.151936
$609$	−9.01235	−0.365199
$610$	12.3186	0.498765
$611$	−30.5954	−1.23776
$612$	−5.83001	−0.235664
$613$	−15.4629	−0.624541	−0.312271	−	0.949993i	$-0.601090\pi$
$613$	−15.4629	−0.624541	−0.312271	+	0.949993i	$0.601090\pi$
$614$	2.81481	0.113596
$615$	3.09641	0.124859
$616$	2.39376	0.0964472
$617$	−10.5080	−0.423034	−0.211517	−	0.977374i	$-0.567840\pi$
$617$	−10.5080	−0.423034	−0.211517	+	0.977374i	$0.567840\pi$
$618$	0.694586	0.0279404
$619$	47.5176	1.90989	0.954947	−	0.296776i	$-0.0959115\pi$
$619$	47.5176	1.90989	0.954947	+	0.296776i	$0.0959115\pi$
$620$	−5.47631	−0.219934
$621$	17.3125	0.694728
$622$	16.8302	0.674830
$623$	−15.6105	−0.625420
$624$	−5.59191	−0.223856
$625$	13.6055	0.544220
$626$	−1.23413	−0.0493259
$627$	−13.7007	−0.547154
$628$	−15.0763	−0.601610
$629$	−2.97160	−0.118485
$630$	−0.719677	−0.0286726
$631$	−36.7924	−1.46468	−0.732341	−	0.680938i	$-0.761572\pi$
$631$	−36.7924	−1.46468	−0.732341	+	0.680938i	$0.761572\pi$
$632$	8.96690	0.356684
$633$	24.7594	0.984099
$634$	−3.18979	−0.126683
$635$	14.4136	0.571987
$636$	13.1333	0.520770
$637$	−23.0700	−0.914065
$638$	15.7942	0.625300
$639$	−3.40958	−0.134881
$640$	0.895866	0.0354122
$641$	16.1280	0.637016	0.318508	−	0.947920i	$-0.396818\pi$
$641$	16.1280	0.637016	0.318508	+	0.947920i	$0.396818\pi$
$642$	−18.9752	−0.748892
$643$	−6.62303	−0.261187	−0.130593	−	0.991436i	$-0.541688\pi$
$643$	−6.62303	−0.261187	−0.130593	+	0.991436i	$0.541688\pi$
$644$	2.95577	0.116474
$645$	−7.11380	−0.280106
$646$	26.1924	1.03053
$647$	40.6348	1.59752	0.798759	−	0.601651i	$-0.205490\pi$
$647$	40.6348	1.59752	0.798759	+	0.601651i	$0.205490\pi$
$648$	−5.80299	−0.227963
$649$	−12.1596	−0.477305
$650$	−15.9479	−0.625527
$651$	8.66712	0.339691
$652$	24.7803	0.970471
$653$	−26.7342	−1.04619	−0.523094	−	0.852275i	$-0.675222\pi$
$653$	−26.7342	−1.04619	−0.523094	+	0.852275i	$0.675222\pi$
$654$	−22.6899	−0.887247
$655$	18.5438	0.724566
$656$	−2.34842	−0.0916902
$657$	10.7759	0.420410
$658$	−7.75756	−0.302421
$659$	−0.680610	−0.0265128	−0.0132564	−	0.999912i	$-0.504220\pi$
$659$	−0.680610	−0.0265128	−0.0132564	+	0.999912i	$0.504220\pi$
$660$	−3.27623	−0.127527
$661$	−21.6148	−0.840716	−0.420358	−	0.907358i	$-0.638096\pi$
$661$	−21.6148	−0.840716	−0.420358	+	0.907358i	$0.638096\pi$
$662$	−24.9166	−0.968412
$663$	−39.0953	−1.51833
$664$	8.85861	0.343781
$665$	3.23328	0.125381
$666$	0.354431	0.0137339
$667$	19.5024	0.755137
$668$	−20.9978	−0.812431
$669$	−29.3819	−1.13597
$670$	−9.72923	−0.375873
$671$	34.1671	1.31901
$672$	−1.41785	−0.0546947
$673$	−33.0886	−1.27547	−0.637737	−	0.770254i	$-0.720129\pi$
$673$	−33.0886	−1.27547	−0.637737	+	0.770254i	$0.720129\pi$
$674$	4.56285	0.175754
$675$	−23.6844	−0.911614
$676$	1.43574	0.0552209
$677$	−8.76818	−0.336989	−0.168494	−	0.985703i	$-0.553890\pi$
$677$	−8.76818	−0.336989	−0.168494	+	0.985703i	$0.553890\pi$
$678$	18.4299	0.707796
$679$	13.2063	0.506813
$680$	6.26335	0.240188
$681$	40.1020	1.53671
$682$	−15.1892	−0.581626
$683$	50.0229	1.91407	0.957037	−	0.289965i	$-0.0936435\pi$
$683$	50.0229	1.91407	0.957037	+	0.289965i	$0.0936435\pi$
$684$	−3.12404	−0.119451
$685$	−2.49068	−0.0951639
$686$	−12.5930	−0.480803
$687$	−29.8576	−1.13914
$688$	5.39533	0.205695
$689$	−33.9042	−1.29165
$690$	−4.04543	−0.154007
$691$	4.47576	0.170266	0.0851330	−	0.996370i	$-0.472868\pi$
$691$	4.47576	0.170266	0.0851330	+	0.996370i	$0.472868\pi$
$692$	−5.74180	−0.218270
$693$	−1.99611	−0.0758261
$694$	18.6663	0.708562
$695$	6.05892	0.229828
$696$	−9.35511	−0.354604
$697$	−16.4187	−0.621902
$698$	−12.8490	−0.486342
$699$	−15.0003	−0.567365
$700$	−4.04364	−0.152835
$701$	17.6607	0.667034	0.333517	−	0.942744i	$-0.391765\pi$
$701$	17.6607	0.667034	0.333517	+	0.942744i	$0.391765\pi$
$702$	21.4387	0.809153
$703$	−1.59235	−0.0600565
$704$	2.48480	0.0936493
$705$	10.6174	0.399876
$706$	19.9775	0.751861
$707$	7.59659	0.285699
$708$	7.20225	0.270677
$709$	19.6934	0.739599	0.369800	−	0.929112i	$-0.379426\pi$
$709$	19.6934	0.739599	0.369800	+	0.929112i	$0.379426\pi$
$710$	3.66302	0.137471
$711$	−7.47735	−0.280423
$712$	−16.2042	−0.607277
$713$	−18.7554	−0.702395
$714$	−9.91274	−0.370975
$715$	8.45772	0.316301
$716$	−14.5702	−0.544512
$717$	−23.9040	−0.892711
$718$	20.7410	0.774046
$719$	18.3641	0.684867	0.342433	−	0.939542i	$-0.388749\pi$
$719$	18.3641	0.684867	0.342433	+	0.939542i	$0.388749\pi$
$720$	−0.747048	−0.0278408
$721$	−0.454647	−0.0169319
$722$	−4.96467	−0.184766
$723$	31.1426	1.15820
$724$	9.09078	0.337856
$725$	−26.6803	−0.990881
$726$	7.10246	0.263597
$727$	7.54459	0.279813	0.139907	−	0.990165i	$-0.455320\pi$
$727$	7.54459	0.279813	0.139907	+	0.990165i	$0.455320\pi$
$728$	3.66023	0.135657
$729$	29.7529	1.10196
$730$	−11.5769	−0.428481
$731$	37.7208	1.39516
$732$	−20.2376	−0.748002
$733$	7.22125	0.266723	0.133361	−	0.991067i	$-0.457423\pi$
$733$	7.22125	0.266723	0.133361	+	0.991067i	$0.457423\pi$
$734$	−23.5453	−0.869072
$735$	8.00592	0.295303
$736$	3.06818	0.113095
$737$	−26.9852	−0.994014
$738$	1.95831	0.0720862
$739$	−8.27929	−0.304558	−0.152279	−	0.988338i	$-0.548661\pi$
$739$	−8.27929	−0.304558	−0.152279	+	0.988338i	$0.548661\pi$
$740$	−0.380776	−0.0139976
$741$	−20.9494	−0.769596
$742$	−8.59652	−0.315588
$743$	−5.46420	−0.200462	−0.100231	−	0.994964i	$-0.531958\pi$
$743$	−5.46420	−0.200462	−0.100231	+	0.994964i	$0.531958\pi$
$744$	8.99675	0.329837
$745$	8.06395	0.295440
$746$	2.17423	0.0796042
$747$	−7.38705	−0.270278
$748$	17.3722	0.635190
$749$	12.4204	0.453831
$750$	12.1269	0.442812
$751$	49.6341	1.81117	0.905586	−	0.424162i	$-0.139431\pi$
$751$	49.6341	1.81117	0.905586	+	0.424162i	$0.139431\pi$
$752$	−8.05260	−0.293648
$753$	1.41079	0.0514122
$754$	24.1506	0.879512
$755$	−11.1801	−0.406885
$756$	5.43587	0.197701
$757$	9.78965	0.355811	0.177905	−	0.984048i	$-0.443068\pi$
$757$	9.78965	0.355811	0.177905	+	0.984048i	$0.443068\pi$
$758$	18.7428	0.680769
$759$	−11.2205	−0.407279
$760$	3.35625	0.121744
$761$	−34.0740	−1.23518	−0.617590	−	0.786500i	$-0.711891\pi$
$761$	−34.0740	−1.23518	−0.617590	+	0.786500i	$0.711891\pi$
$762$	−23.6794	−0.857814
$763$	14.8519	0.537674
$764$	−23.0580	−0.834211
$765$	−5.22290	−0.188834
$766$	−16.2416	−0.586833
$767$	−18.5929	−0.671350
$768$	−1.47177	−0.0531080
$769$	−47.2272	−1.70306	−0.851528	−	0.524310i	$-0.824323\pi$
$769$	−47.2272	−1.70306	−0.851528	+	0.524310i	$0.824323\pi$
$770$	2.14449	0.0772819
$771$	10.7939	0.388733
$772$	7.78236	0.280093
$773$	−34.0564	−1.22492	−0.612462	−	0.790500i	$-0.709821\pi$
$773$	−34.0564	−1.22492	−0.612462	+	0.790500i	$0.709821\pi$
$774$	−4.49908	−0.161716
$775$	25.6583	0.921673
$776$	13.7086	0.492110
$777$	0.602638	0.0216195
$778$	−26.7912	−0.960510
$779$	−8.79805	−0.315223
$780$	−5.00961	−0.179373
$781$	10.1598	0.363548
$782$	21.4509	0.767081
$783$	35.8664	1.28176
$784$	−6.07194	−0.216855
$785$	−13.5063	−0.482062
$786$	−30.4647	−1.08664
$787$	−23.5163	−0.838265	−0.419133	−	0.907925i	$-0.637666\pi$
$787$	−23.5163	−0.838265	−0.419133	+	0.907925i	$0.637666\pi$
$788$	26.3072	0.937155
$789$	0.0309469	0.00110174
$790$	8.03314	0.285806
$791$	−12.0634	−0.428927
$792$	−2.07203	−0.0736264
$793$	52.2441	1.85524
$794$	19.4652	0.690795
$795$	11.7657	0.417286
$796$	3.66484	0.129897
$797$	5.08261	0.180035	0.0900177	−	0.995940i	$-0.471308\pi$
$797$	5.08261	0.180035	0.0900177	+	0.995940i	$0.471308\pi$
$798$	−5.31180	−0.188036
$799$	−56.2989	−1.99171
$800$	−4.19742	−0.148401
$801$	13.5124	0.477437
$802$	27.6320	0.975719
$803$	−32.1101	−1.13314
$804$	15.9837	0.563700
$805$	2.64797	0.0933287
$806$	−23.2255	−0.818082
$807$	33.1613	1.16733
$808$	7.88550	0.277411
$809$	36.9984	1.30079	0.650397	−	0.759595i	$-0.274603\pi$
$809$	36.9984	1.30079	0.650397	+	0.759595i	$0.274603\pi$
$810$	−5.19870	−0.182664
$811$	−3.30175	−0.115940	−0.0579701	−	0.998318i	$-0.518463\pi$
$811$	−3.30175	−0.115940	−0.0579701	+	0.998318i	$0.518463\pi$
$812$	6.12346	0.214891
$813$	−32.8614	−1.15250
$814$	−1.05613	−0.0370173
$815$	22.1998	0.777626
$816$	−10.2897	−0.360213
$817$	20.2129	0.707161
$818$	0.157325	0.00550076
$819$	−3.05221	−0.106653
$820$	−2.10387	−0.0734702
$821$	−24.3530	−0.849927	−0.424963	−	0.905210i	$-0.639713\pi$
$821$	−24.3530	−0.849927	−0.424963	+	0.905210i	$0.639713\pi$
$822$	4.09181	0.142718
$823$	−49.1309	−1.71259	−0.856297	−	0.516484i	$-0.827241\pi$
$823$	−49.1309	−1.71259	−0.856297	+	0.516484i	$0.827241\pi$
$824$	−0.471938	−0.0164407
$825$	15.3502	0.534426
$826$	−4.71429	−0.164031
$827$	33.6440	1.16992	0.584958	−	0.811063i	$-0.301111\pi$
$827$	33.6440	1.16992	0.584958	+	0.811063i	$0.301111\pi$
$828$	−2.55851	−0.0889142
$829$	1.82687	0.0634497	0.0317248	−	0.999497i	$-0.489900\pi$
$829$	1.82687	0.0634497	0.0317248	+	0.999497i	$0.489900\pi$
$830$	7.93612	0.275467
$831$	−2.72309	−0.0944629
$832$	3.79944	0.131722
$833$	−42.4513	−1.47085
$834$	−9.95389	−0.344675
$835$	−18.8112	−0.650990
$836$	9.30898	0.321958
$837$	−34.4925	−1.19224
$838$	13.8923	0.479901
$839$	−5.79176	−0.199954	−0.0999768	−	0.994990i	$-0.531877\pi$
$839$	−5.79176	−0.199954	−0.0999768	+	0.994990i	$0.531877\pi$
$840$	−1.27020	−0.0438262
$841$	11.4032	0.393214
$842$	−24.8237	−0.855481
$843$	−0.462762	−0.0159384
$844$	−16.8228	−0.579066
$845$	1.28623	0.0442478
$846$	6.71493	0.230864
$847$	−4.64897	−0.159741
$848$	−8.92347	−0.306433
$849$	−23.2560	−0.798144
$850$	−29.3458	−1.00655
$851$	−1.30409	−0.0447036
$852$	−6.01779	−0.206166
$853$	0.783308	0.0268199	0.0134100	−	0.999910i	$-0.495731\pi$
$853$	0.783308	0.0268199	0.0134100	+	0.999910i	$0.495731\pi$
$854$	13.2467	0.453292
$855$	−2.79872	−0.0957143
$856$	12.8928	0.440665
$857$	−26.7787	−0.914744	−0.457372	−	0.889275i	$-0.651209\pi$
$857$	−26.7787	−0.914744	−0.457372	+	0.889275i	$0.651209\pi$
$858$	−13.8948	−0.474360
$859$	15.8583	0.541078	0.270539	−	0.962709i	$-0.412798\pi$
$859$	15.8583	0.541078	0.270539	+	0.962709i	$0.412798\pi$
$860$	4.83349	0.164821
$861$	3.32970	0.113476
$862$	15.1780	0.516965
$863$	−10.3793	−0.353316	−0.176658	−	0.984272i	$-0.556529\pi$
$863$	−10.3793	−0.353316	−0.176658	+	0.984272i	$0.556529\pi$
$864$	5.64261	0.191965
$865$	−5.14388	−0.174897
$866$	−7.79208	−0.264786
$867$	−46.9195	−1.59347
$868$	−5.88890	−0.199882
$869$	22.2809	0.755829
$870$	−8.38092	−0.284140
$871$	−41.2624	−1.39812
$872$	15.4167	0.522076
$873$	−11.4314	−0.386894
$874$	11.4946	0.388809
$875$	−7.93777	−0.268346
$876$	19.0191	0.642597
$877$	9.84633	0.332487	0.166244	−	0.986085i	$-0.446836\pi$
$877$	9.84633	0.332487	0.166244	+	0.986085i	$0.446836\pi$
$878$	15.0078	0.506487
$879$	22.5633	0.761040
$880$	2.22605	0.0750400
$881$	−9.50675	−0.320291	−0.160145	−	0.987093i	$-0.551196\pi$
$881$	−9.50675	−0.320291	−0.160145	+	0.987093i	$0.551196\pi$
$882$	5.06329	0.170490
$883$	20.0947	0.676239	0.338119	−	0.941103i	$-0.390209\pi$
$883$	20.0947	0.676239	0.338119	+	0.941103i	$0.390209\pi$
$884$	26.5634	0.893423
$885$	6.45225	0.216890
$886$	−8.87573	−0.298186
$887$	−35.0787	−1.17783	−0.588914	−	0.808196i	$-0.700444\pi$
$887$	−35.0787	−1.17783	−0.588914	+	0.808196i	$0.700444\pi$
$888$	0.625558	0.0209923
$889$	15.4995	0.519838
$890$	−14.5168	−0.486603
$891$	−14.4192	−0.483063
$892$	19.9636	0.668430
$893$	−30.1681	−1.00954
$894$	−13.2479	−0.443074
$895$	−13.0529	−0.436311
$896$	0.963361	0.0321836
$897$	−17.1570	−0.572856
$898$	7.81987	0.260952
$899$	−38.8555	−1.29590
$900$	3.50016	0.116672
$901$	−62.3875	−2.07843
$902$	−5.83534	−0.194295
$903$	−7.64976	−0.254568
$904$	−12.5222	−0.416483
$905$	8.14412	0.270720
$906$	18.3672	0.610210
$907$	17.4063	0.577967	0.288983	−	0.957334i	$-0.406683\pi$
$907$	17.4063	0.577967	0.288983	+	0.957334i	$0.406683\pi$
$908$	−27.2474	−0.904237
$909$	−6.57559	−0.218099
$910$	3.27908	0.108700
$911$	23.2071	0.768887	0.384443	−	0.923149i	$-0.374393\pi$
$911$	23.2071	0.768887	0.384443	+	0.923149i	$0.374393\pi$
$912$	−5.51382	−0.182581
$913$	22.0118	0.728486
$914$	−29.3227	−0.969907
$915$	−18.1302	−0.599365
$916$	20.2868	0.670296
$917$	19.9409	0.658506
$918$	39.4497	1.30203
$919$	−46.6918	−1.54022	−0.770111	−	0.637910i	$-0.779799\pi$
$919$	−46.6918	−1.54022	−0.770111	+	0.637910i	$0.779799\pi$
$920$	2.74868	0.0906213
$921$	−4.14276	−0.136509
$922$	−26.7843	−0.882095
$923$	15.5352	0.511346
$924$	−3.52307	−0.115900
$925$	1.78406	0.0586595
$926$	−33.7092	−1.10775
$927$	0.393542	0.0129256
$928$	6.35635	0.208657
$929$	−20.4278	−0.670215	−0.335108	−	0.942180i	$-0.608773\pi$
$929$	−20.4278	−0.670215	−0.335108	+	0.942180i	$0.608773\pi$
$930$	8.05989	0.264294
$931$	−22.7478	−0.745527
$932$	10.1920	0.333851
$933$	−24.7703	−0.810942
$934$	24.2440	0.793289
$935$	15.5632	0.508969
$936$	−3.16829	−0.103559
$937$	34.0097	1.11105	0.555524	−	0.831500i	$-0.312518\pi$
$937$	34.0097	1.11105	0.555524	+	0.831500i	$0.312518\pi$
$938$	−10.4622	−0.341604
$939$	1.81636	0.0592748
$940$	−7.21405	−0.235296
$941$	10.0552	0.327789	0.163894	−	0.986478i	$-0.447594\pi$
$941$	10.0552	0.327789	0.163894	+	0.986478i	$0.447594\pi$
$942$	22.1889	0.722953
$943$	−7.20537	−0.234639
$944$	−4.89359	−0.159273
$945$	4.86981	0.158415
$946$	13.4063	0.435876
$947$	−47.1248	−1.53135	−0.765676	−	0.643227i	$-0.777595\pi$
$947$	−47.1248	−1.53135	−0.765676	+	0.643227i	$0.777595\pi$
$948$	−13.1972	−0.428627
$949$	−49.0987	−1.59381
$950$	−15.7251	−0.510191
$951$	4.69465	0.152234
$952$	6.73523	0.218290
$953$	19.7001	0.638148	0.319074	−	0.947730i	$-0.396628\pi$
$953$	19.7001	0.638148	0.319074	+	0.947730i	$0.396628\pi$
$954$	7.44113	0.240916
$955$	−20.6569	−0.668442
$956$	16.2416	0.525292
$957$	−23.2455	−0.751422
$958$	19.8986	0.642893
$959$	−2.67833	−0.0864877
$960$	−1.31851	−0.0425548
$961$	6.36715	0.205392
$962$	−1.61490	−0.0520665
$963$	−10.7511	−0.346448
$964$	−21.1599	−0.681514
$965$	6.97196	0.224435
$966$	−4.35022	−0.139966
$967$	26.7147	0.859085	0.429543	−	0.903047i	$-0.358675\pi$
$967$	26.7147	0.859085	0.429543	+	0.903047i	$0.358675\pi$
$968$	−4.82578	−0.155107
$969$	−38.5492	−1.23838
$970$	12.2811	0.394322
$971$	14.4709	0.464394	0.232197	−	0.972669i	$-0.425409\pi$
$971$	14.4709	0.464394	0.232197	+	0.972669i	$0.425409\pi$
$972$	−8.38714	−0.269018
$973$	6.51540	0.208874
$974$	−13.8223	−0.442896
$975$	23.4716	0.751694
$976$	13.7505	0.440142
$977$	−33.7261	−1.07899	−0.539496	−	0.841988i	$-0.681385\pi$
$977$	−33.7261	−1.07899	−0.539496	+	0.841988i	$0.681385\pi$
$978$	−36.4710	−1.16621
$979$	−40.2641	−1.28685
$980$	−5.43964	−0.173763
$981$	−12.8558	−0.410453
$982$	−14.9292	−0.476408
$983$	3.87756	0.123675	0.0618375	−	0.998086i	$-0.480304\pi$
$983$	3.87756	0.123675	0.0618375	+	0.998086i	$0.480304\pi$
$984$	3.45634	0.110184
$985$	23.5677	0.750930
$986$	44.4397	1.41525
$987$	11.4174	0.363419
$988$	14.2341	0.452848
$989$	16.5538	0.526382
$990$	−1.85626	−0.0589959
$991$	−29.7227	−0.944174	−0.472087	−	0.881552i	$-0.656499\pi$
$991$	−29.7227	−0.944174	−0.472087	+	0.881552i	$0.656499\pi$
$992$	−6.11287	−0.194084
$993$	36.6716	1.16374
$994$	3.93899	0.124937
$995$	3.28321	0.104085
$996$	−13.0379	−0.413120
$997$	36.2062	1.14666	0.573331	−	0.819324i	$-0.305651\pi$
$997$	36.2062	1.14666	0.573331	+	0.819324i	$0.305651\pi$
$998$	26.6956	0.845033
$999$	−2.39832	−0.0758794

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6022.2.a.e.1.15	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6022.2.a.e.1.15	✓	68	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:	\( N \)	\(=\)	\( 6022 = 2 \cdot 3011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.47177 q^{3} +1.00000 q^{4} +0.895866 q^{5} -1.47177 q^{6} +0.963361 q^{7} +1.00000 q^{8} -0.833884 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.47177 q^{3} +1.00000 q^{4} +0.895866 q^{5} -1.47177 q^{6} +0.963361 q^{7} +1.00000 q^{8} -0.833884 q^{9} +0.895866 q^{10} +2.48480 q^{11} -1.47177 q^{12} +3.79944 q^{13} +0.963361 q^{14} -1.31851 q^{15} +1.00000 q^{16} +6.99139 q^{17} -0.833884 q^{18} +3.74638 q^{19} +0.895866 q^{20} -1.41785 q^{21} +2.48480 q^{22} +3.06818 q^{23} -1.47177 q^{24} -4.19742 q^{25} +3.79944 q^{26} +5.64261 q^{27} +0.963361 q^{28} +6.35635 q^{29} -1.31851 q^{30} -6.11287 q^{31} +1.00000 q^{32} -3.65706 q^{33} +6.99139 q^{34} +0.863043 q^{35} -0.833884 q^{36} -0.425037 q^{37} +3.74638 q^{38} -5.59191 q^{39} +0.895866 q^{40} -2.34842 q^{41} -1.41785 q^{42} +5.39533 q^{43} +2.48480 q^{44} -0.747048 q^{45} +3.06818 q^{46} -8.05260 q^{47} -1.47177 q^{48} -6.07194 q^{49} -4.19742 q^{50} -10.2897 q^{51} +3.79944 q^{52} -8.92347 q^{53} +5.64261 q^{54} +2.22605 q^{55} +0.963361 q^{56} -5.51382 q^{57} +6.35635 q^{58} -4.89359 q^{59} -1.31851 q^{60} +13.7505 q^{61} -6.11287 q^{62} -0.803331 q^{63} +1.00000 q^{64} +3.40379 q^{65} -3.65706 q^{66} -10.8601 q^{67} +6.99139 q^{68} -4.51567 q^{69} +0.863043 q^{70} +4.08880 q^{71} -0.833884 q^{72} -12.9226 q^{73} -0.425037 q^{74} +6.17766 q^{75} +3.74638 q^{76} +2.39376 q^{77} -5.59191 q^{78} +8.96690 q^{79} +0.895866 q^{80} -5.80299 q^{81} -2.34842 q^{82} +8.85861 q^{83} -1.41785 q^{84} +6.26335 q^{85} +5.39533 q^{86} -9.35511 q^{87} +2.48480 q^{88} -16.2042 q^{89} -0.747048 q^{90} +3.66023 q^{91} +3.06818 q^{92} +8.99675 q^{93} -8.05260 q^{94} +3.35625 q^{95} -1.47177 q^{96} +13.7086 q^{97} -6.07194 q^{98} -2.07203 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 68 q^{2} + 25 q^{3} + 68 q^{4} + 20 q^{5} + 25 q^{6} + 29 q^{7} + 68 q^{8} + 87 q^{9}+O(q^{10}) \) 68 * q + 68 * q^2 + 25 * q^3 + 68 * q^4 + 20 * q^5 + 25 * q^6 + 29 * q^7 + 68 * q^8 + 87 * q^9	\( 68 q + 68 q^{2} + 25 q^{3} + 68 q^{4} + 20 q^{5} + 25 q^{6} + 29 q^{7} + 68 q^{8} + 87 q^{9} + 20 q^{10} + 46 q^{11} + 25 q^{12} + 30 q^{13} + 29 q^{14} + 13 q^{15} + 68 q^{16} + 73 q^{17} + 87 q^{18} + 56 q^{19} + 20 q^{20} - 5 q^{21} + 46 q^{22} + 63 q^{23} + 25 q^{24} + 88 q^{25} + 30 q^{26} + 67 q^{27} + 29 q^{28} + 43 q^{29} + 13 q^{30} + 68 q^{31} + 68 q^{32} + 26 q^{33} + 73 q^{34} + 50 q^{35} + 87 q^{36} + 8 q^{37} + 56 q^{38} + 6 q^{39} + 20 q^{40} + 64 q^{41} - 5 q^{42} + 52 q^{43} + 46 q^{44} + 7 q^{45} + 63 q^{46} + 94 q^{47} + 25 q^{48} + 91 q^{49} + 88 q^{50} + 20 q^{51} + 30 q^{52} + 38 q^{53} + 67 q^{54} + 37 q^{55} + 29 q^{56} + 4 q^{57} + 43 q^{58} + 84 q^{59} + 13 q^{60} + 26 q^{61} + 68 q^{62} + 22 q^{63} + 68 q^{64} - 20 q^{65} + 26 q^{66} + 54 q^{67} + 73 q^{68} - 11 q^{69} + 50 q^{70} + 46 q^{71} + 87 q^{72} + 62 q^{73} + 8 q^{74} + 54 q^{75} + 56 q^{76} + 67 q^{77} + 6 q^{78} + 67 q^{79} + 20 q^{80} + 120 q^{81} + 64 q^{82} + 130 q^{83} - 5 q^{84} - 24 q^{85} + 52 q^{86} + 72 q^{87} + 46 q^{88} + 61 q^{89} + 7 q^{90} + 43 q^{91} + 63 q^{92} + 40 q^{93} + 94 q^{94} + 55 q^{95} + 25 q^{96} + 41 q^{97} + 91 q^{98} + 106 q^{99}+O(q^{100}) \) 68 * q + 68 * q^2 + 25 * q^3 + 68 * q^4 + 20 * q^5 + 25 * q^6 + 29 * q^7 + 68 * q^8 + 87 * q^9 + 20 * q^10 + 46 * q^11 + 25 * q^12 + 30 * q^13 + 29 * q^14 + 13 * q^15 + 68 * q^16 + 73 * q^17 + 87 * q^18 + 56 * q^19 + 20 * q^20 - 5 * q^21 + 46 * q^22 + 63 * q^23 + 25 * q^24 + 88 * q^25 + 30 * q^26 + 67 * q^27 + 29 * q^28 + 43 * q^29 + 13 * q^30 + 68 * q^31 + 68 * q^32 + 26 * q^33 + 73 * q^34 + 50 * q^35 + 87 * q^36 + 8 * q^37 + 56 * q^38 + 6 * q^39 + 20 * q^40 + 64 * q^41 - 5 * q^42 + 52 * q^43 + 46 * q^44 + 7 * q^45 + 63 * q^46 + 94 * q^47 + 25 * q^48 + 91 * q^49 + 88 * q^50 + 20 * q^51 + 30 * q^52 + 38 * q^53 + 67 * q^54 + 37 * q^55 + 29 * q^56 + 4 * q^57 + 43 * q^58 + 84 * q^59 + 13 * q^60 + 26 * q^61 + 68 * q^62 + 22 * q^63 + 68 * q^64 - 20 * q^65 + 26 * q^66 + 54 * q^67 + 73 * q^68 - 11 * q^69 + 50 * q^70 + 46 * q^71 + 87 * q^72 + 62 * q^73 + 8 * q^74 + 54 * q^75 + 56 * q^76 + 67 * q^77 + 6 * q^78 + 67 * q^79 + 20 * q^80 + 120 * q^81 + 64 * q^82 + 130 * q^83 - 5 * q^84 - 24 * q^85 + 52 * q^86 + 72 * q^87 + 46 * q^88 + 61 * q^89 + 7 * q^90 + 43 * q^91 + 63 * q^92 + 40 * q^93 + 94 * q^94 + 55 * q^95 + 25 * q^96 + 41 * q^97 + 91 * q^98 + 106 * q^99

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