LMFDB - Embedded newform 4022.2.a.e.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4022,2,Mod(1,4022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4022, 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("4022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4022 = 2 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4022.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:	$32.1158316930$
Analytic rank:	$0$
Dimension:	$46$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	4022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.98506 q^{3} +1.00000 q^{4} +2.19729 q^{5} +2.98506 q^{6} -1.49134 q^{7} -1.00000 q^{8} +5.91056 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.98506 q^{3} +1.00000 q^{4} +2.19729 q^{5} +2.98506 q^{6} -1.49134 q^{7} -1.00000 q^{8} +5.91056 q^{9} -2.19729 q^{10} -5.19508 q^{11} -2.98506 q^{12} -3.96332 q^{13} +1.49134 q^{14} -6.55902 q^{15} +1.00000 q^{16} -7.73224 q^{17} -5.91056 q^{18} -6.65084 q^{19} +2.19729 q^{20} +4.45172 q^{21} +5.19508 q^{22} -0.635732 q^{23} +2.98506 q^{24} -0.171936 q^{25} +3.96332 q^{26} -8.68818 q^{27} -1.49134 q^{28} -9.19678 q^{29} +6.55902 q^{30} -8.69635 q^{31} -1.00000 q^{32} +15.5076 q^{33} +7.73224 q^{34} -3.27689 q^{35} +5.91056 q^{36} +5.57869 q^{37} +6.65084 q^{38} +11.8307 q^{39} -2.19729 q^{40} -4.25727 q^{41} -4.45172 q^{42} -2.99732 q^{43} -5.19508 q^{44} +12.9872 q^{45} +0.635732 q^{46} +5.57394 q^{47} -2.98506 q^{48} -4.77592 q^{49} +0.171936 q^{50} +23.0812 q^{51} -3.96332 q^{52} +5.62868 q^{53} +8.68818 q^{54} -11.4151 q^{55} +1.49134 q^{56} +19.8531 q^{57} +9.19678 q^{58} -4.65841 q^{59} -6.55902 q^{60} +14.2348 q^{61} +8.69635 q^{62} -8.81463 q^{63} +1.00000 q^{64} -8.70856 q^{65} -15.5076 q^{66} +4.18113 q^{67} -7.73224 q^{68} +1.89770 q^{69} +3.27689 q^{70} -1.00394 q^{71} -5.91056 q^{72} +10.7868 q^{73} -5.57869 q^{74} +0.513238 q^{75} -6.65084 q^{76} +7.74761 q^{77} -11.8307 q^{78} -13.3879 q^{79} +2.19729 q^{80} +8.20303 q^{81} +4.25727 q^{82} -12.0477 q^{83} +4.45172 q^{84} -16.9899 q^{85} +2.99732 q^{86} +27.4529 q^{87} +5.19508 q^{88} -3.22745 q^{89} -12.9872 q^{90} +5.91065 q^{91} -0.635732 q^{92} +25.9591 q^{93} -5.57394 q^{94} -14.6138 q^{95} +2.98506 q^{96} -4.42490 q^{97} +4.77592 q^{98} -30.7059 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 46 q^{2} + 8 q^{3} + 46 q^{4} + 14 q^{5} - 8 q^{6} + 28 q^{7} - 46 q^{8} + 58 q^{9}+O(q^{10}) $ 46 * q - 46 * q^2 + 8 * q^3 + 46 * q^4 + 14 * q^5 - 8 * q^6 + 28 * q^7 - 46 * q^8 + 58 * q^9	\( 46 q - 46 q^{2} + 8 q^{3} + 46 q^{4} + 14 q^{5} - 8 q^{6} + 28 q^{7} - 46 q^{8} + 58 q^{9} - 14 q^{10} - 6 q^{11} + 8 q^{12} + 37 q^{13} - 28 q^{14} + 9 q^{15} + 46 q^{16} + 6 q^{17} - 58 q^{18} + 18 q^{19} + 14 q^{20} + 19 q^{21} + 6 q^{22} - 4 q^{23} - 8 q^{24} + 86 q^{25} - 37 q^{26} + 32 q^{27} + 28 q^{28} + 15 q^{29} - 9 q^{30} + 18 q^{31} - 46 q^{32} + 37 q^{33} - 6 q^{34} - 2 q^{35} + 58 q^{36} + 74 q^{37} - 18 q^{38} - 3 q^{39} - 14 q^{40} - 18 q^{41} - 19 q^{42} + 25 q^{43} - 6 q^{44} + 94 q^{45} + 4 q^{46} + 18 q^{47} + 8 q^{48} + 92 q^{49} - 86 q^{50} - 10 q^{51} + 37 q^{52} + 17 q^{53} - 32 q^{54} + 37 q^{55} - 28 q^{56} + 43 q^{57} - 15 q^{58} - 24 q^{59} + 9 q^{60} + 46 q^{61} - 18 q^{62} + 80 q^{63} + 46 q^{64} + 24 q^{65} - 37 q^{66} + 61 q^{67} + 6 q^{68} + 59 q^{69} + 2 q^{70} - 8 q^{71} - 58 q^{72} + 101 q^{73} - 74 q^{74} + 34 q^{75} + 18 q^{76} + 40 q^{77} + 3 q^{78} + 9 q^{79} + 14 q^{80} + 58 q^{81} + 18 q^{82} + 18 q^{83} + 19 q^{84} + 60 q^{85} - 25 q^{86} + 20 q^{87} + 6 q^{88} - 25 q^{89} - 94 q^{90} + 51 q^{91} - 4 q^{92} + 63 q^{93} - 18 q^{94} - 31 q^{95} - 8 q^{96} + 76 q^{97} - 92 q^{98} + 21 q^{99}+O(q^{100}) \) 46 * q - 46 * q^2 + 8 * q^3 + 46 * q^4 + 14 * q^5 - 8 * q^6 + 28 * q^7 - 46 * q^8 + 58 * q^9 - 14 * q^10 - 6 * q^11 + 8 * q^12 + 37 * q^13 - 28 * q^14 + 9 * q^15 + 46 * q^16 + 6 * q^17 - 58 * q^18 + 18 * q^19 + 14 * q^20 + 19 * q^21 + 6 * q^22 - 4 * q^23 - 8 * q^24 + 86 * q^25 - 37 * q^26 + 32 * q^27 + 28 * q^28 + 15 * q^29 - 9 * q^30 + 18 * q^31 - 46 * q^32 + 37 * q^33 - 6 * q^34 - 2 * q^35 + 58 * q^36 + 74 * q^37 - 18 * q^38 - 3 * q^39 - 14 * q^40 - 18 * q^41 - 19 * q^42 + 25 * q^43 - 6 * q^44 + 94 * q^45 + 4 * q^46 + 18 * q^47 + 8 * q^48 + 92 * q^49 - 86 * q^50 - 10 * q^51 + 37 * q^52 + 17 * q^53 - 32 * q^54 + 37 * q^55 - 28 * q^56 + 43 * q^57 - 15 * q^58 - 24 * q^59 + 9 * q^60 + 46 * q^61 - 18 * q^62 + 80 * q^63 + 46 * q^64 + 24 * q^65 - 37 * q^66 + 61 * q^67 + 6 * q^68 + 59 * q^69 + 2 * q^70 - 8 * q^71 - 58 * q^72 + 101 * q^73 - 74 * q^74 + 34 * q^75 + 18 * q^76 + 40 * q^77 + 3 * q^78 + 9 * q^79 + 14 * q^80 + 58 * q^81 + 18 * q^82 + 18 * q^83 + 19 * q^84 + 60 * q^85 - 25 * q^86 + 20 * q^87 + 6 * q^88 - 25 * q^89 - 94 * q^90 + 51 * q^91 - 4 * q^92 + 63 * q^93 - 18 * q^94 - 31 * q^95 - 8 * q^96 + 76 * q^97 - 92 * q^98 + 21 * 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
$3$	−2.98506	−1.72342	−0.861711	−	0.507399i	$-0.830607\pi$
$3$	−2.98506	−1.72342	−0.861711	+	0.507399i	$0.830607\pi$
$4$	1.00000	0.500000
$5$	2.19729	0.982656	0.491328	−	0.870975i	$-0.336512\pi$
$5$	2.19729	0.982656	0.491328	+	0.870975i	$0.336512\pi$
$6$	2.98506	1.21864
$7$	−1.49134	−0.563672	−0.281836	−	0.959463i	$-0.590943\pi$
$7$	−1.49134	−0.563672	−0.281836	+	0.959463i	$0.590943\pi$
$8$	−1.00000	−0.353553
$9$	5.91056	1.97019
$10$	−2.19729	−0.694843
$11$	−5.19508	−1.56638	−0.783189	−	0.621784i	$-0.786408\pi$
$11$	−5.19508	−1.56638	−0.783189	+	0.621784i	$0.786408\pi$
$12$	−2.98506	−0.861711
$13$	−3.96332	−1.09923	−0.549614	−	0.835419i	$-0.685225\pi$
$13$	−3.96332	−1.09923	−0.549614	+	0.835419i	$0.685225\pi$
$14$	1.49134	0.398576
$15$	−6.55902	−1.69353
$16$	1.00000	0.250000
$17$	−7.73224	−1.87534	−0.937672	−	0.347523i	$-0.887023\pi$
$17$	−7.73224	−1.87534	−0.937672	+	0.347523i	$0.887023\pi$
$18$	−5.91056	−1.39313
$19$	−6.65084	−1.52581	−0.762904	−	0.646512i	$-0.776227\pi$
$19$	−6.65084	−1.52581	−0.762904	+	0.646512i	$0.776227\pi$
$20$	2.19729	0.491328
$21$	4.45172	0.971445
$22$	5.19508	1.10760
$23$	−0.635732	−0.132559	−0.0662797	−	0.997801i	$-0.521113\pi$
$23$	−0.635732	−0.132559	−0.0662797	+	0.997801i	$0.521113\pi$
$24$	2.98506	0.609322
$25$	−0.171936	−0.0343872
$26$	3.96332	0.777272
$27$	−8.68818	−1.67204
$28$	−1.49134	−0.281836
$29$	−9.19678	−1.70780	−0.853900	−	0.520438i	$-0.825769\pi$
$29$	−9.19678	−1.70780	−0.853900	+	0.520438i	$0.825769\pi$
$30$	6.55902	1.19751
$31$	−8.69635	−1.56191	−0.780955	−	0.624587i	$-0.785267\pi$
$31$	−8.69635	−1.56191	−0.780955	+	0.624587i	$0.785267\pi$
$32$	−1.00000	−0.176777
$33$	15.5076	2.69953
$34$	7.73224	1.32607
$35$	−3.27689	−0.553895
$36$	5.91056	0.985093
$37$	5.57869	0.917131	0.458565	−	0.888661i	$-0.348363\pi$
$37$	5.57869	0.917131	0.458565	+	0.888661i	$0.348363\pi$
$38$	6.65084	1.07891
$39$	11.8307	1.89444
$40$	−2.19729	−0.347421
$41$	−4.25727	−0.664874	−0.332437	−	0.943126i	$-0.607871\pi$
$41$	−4.25727	−0.664874	−0.332437	+	0.943126i	$0.607871\pi$
$42$	−4.45172	−0.686915
$43$	−2.99732	−0.457087	−0.228544	−	0.973534i	$-0.573396\pi$
$43$	−2.99732	−0.457087	−0.228544	+	0.973534i	$0.573396\pi$
$44$	−5.19508	−0.783189
$45$	12.9872	1.93602
$46$	0.635732	0.0937336
$47$	5.57394	0.813043	0.406522	−	0.913641i	$-0.366742\pi$
$47$	5.57394	0.813043	0.406522	+	0.913641i	$0.366742\pi$
$48$	−2.98506	−0.430856
$49$	−4.77592	−0.682274
$50$	0.171936	0.0243154
$51$	23.0812	3.23201
$52$	−3.96332	−0.549614
$53$	5.62868	0.773159	0.386579	−	0.922256i	$-0.373656\pi$
$53$	5.62868	0.773159	0.386579	+	0.922256i	$0.373656\pi$
$54$	8.68818	1.18231
$55$	−11.4151	−1.53921
$56$	1.49134	0.199288
$57$	19.8531	2.62961
$58$	9.19678	1.20760
$59$	−4.65841	−0.606473	−0.303237	−	0.952915i	$-0.598067\pi$
$59$	−4.65841	−0.606473	−0.303237	+	0.952915i	$0.598067\pi$
$60$	−6.55902	−0.846766
$61$	14.2348	1.82258	0.911288	−	0.411769i	$-0.135089\pi$
$61$	14.2348	1.82258	0.911288	+	0.411769i	$0.135089\pi$
$62$	8.69635	1.10444
$63$	−8.81463	−1.11054
$64$	1.00000	0.125000
$65$	−8.70856	−1.08016
$66$	−15.5076	−1.90886
$67$	4.18113	0.510807	0.255403	−	0.966835i	$-0.417792\pi$
$67$	4.18113	0.510807	0.255403	+	0.966835i	$0.417792\pi$
$68$	−7.73224	−0.937672
$69$	1.89770	0.228456
$70$	3.27689	0.391663
$71$	−1.00394	−0.119145	−0.0595726	−	0.998224i	$-0.518974\pi$
$71$	−1.00394	−0.119145	−0.0595726	+	0.998224i	$0.518974\pi$
$72$	−5.91056	−0.696566
$73$	10.7868	1.26250	0.631252	−	0.775578i	$-0.282541\pi$
$73$	10.7868	1.26250	0.631252	+	0.775578i	$0.282541\pi$
$74$	−5.57869	−0.648509
$75$	0.513238	0.0592636
$76$	−6.65084	−0.762904
$77$	7.74761	0.882923
$78$	−11.8307	−1.33957
$79$	−13.3879	−1.50626	−0.753130	−	0.657872i	$-0.771457\pi$
$79$	−13.3879	−1.50626	−0.753130	+	0.657872i	$0.771457\pi$
$80$	2.19729	0.245664
$81$	8.20303	0.911448
$82$	4.25727	0.470137
$83$	−12.0477	−1.32240	−0.661202	−	0.750208i	$-0.729954\pi$
$83$	−12.0477	−1.32240	−0.661202	+	0.750208i	$0.729954\pi$
$84$	4.45172	0.485722
$85$	−16.9899	−1.84282
$86$	2.99732	0.323209
$87$	27.4529	2.94326
$88$	5.19508	0.553798
$89$	−3.22745	−0.342109	−0.171055	−	0.985262i	$-0.554717\pi$
$89$	−3.22745	−0.342109	−0.171055	+	0.985262i	$0.554717\pi$
$90$	−12.9872	−1.36897
$91$	5.91065	0.619604
$92$	−0.635732	−0.0662797
$93$	25.9591	2.69183
$94$	−5.57394	−0.574908
$95$	−14.6138	−1.49934
$96$	2.98506	0.304661
$97$	−4.42490	−0.449280	−0.224640	−	0.974442i	$-0.572121\pi$
$97$	−4.42490	−0.449280	−0.224640	+	0.974442i	$0.572121\pi$
$98$	4.77592	0.482441
$99$	−30.7059	−3.08605
$100$	−0.171936	−0.0171936
$101$	6.94327	0.690881	0.345440	−	0.938441i	$-0.387730\pi$
$101$	6.94327	0.690881	0.345440	+	0.938441i	$0.387730\pi$
$102$	−23.0812	−2.28538
$103$	11.1259	1.09627	0.548133	−	0.836391i	$-0.315339\pi$
$103$	11.1259	1.09627	0.548133	+	0.836391i	$0.315339\pi$
$104$	3.96332	0.388636
$105$	9.78170	0.954596
$106$	−5.62868	−0.546706
$107$	5.92837	0.573117	0.286558	−	0.958063i	$-0.407489\pi$
$107$	5.92837	0.573117	0.286558	+	0.958063i	$0.407489\pi$
$108$	−8.68818	−0.836021
$109$	−13.9916	−1.34015	−0.670077	−	0.742292i	$-0.733739\pi$
$109$	−13.9916	−1.34015	−0.670077	+	0.742292i	$0.733739\pi$
$110$	11.4151	1.08839
$111$	−16.6527	−1.58060
$112$	−1.49134	−0.140918
$113$	4.96025	0.466621	0.233311	−	0.972402i	$-0.425044\pi$
$113$	4.96025	0.466621	0.233311	+	0.972402i	$0.425044\pi$
$114$	−19.8531	−1.85942
$115$	−1.39689	−0.130260
$116$	−9.19678	−0.853900
$117$	−23.4255	−2.16568
$118$	4.65841	0.428841
$119$	11.5314	1.05708
$120$	6.55902	0.598754
$121$	15.9889	1.45354
$122$	−14.2348	−1.28876
$123$	12.7082	1.14586
$124$	−8.69635	−0.780955
$125$	−11.3642	−1.01645
$126$	8.81463	0.785269
$127$	−17.3022	−1.53533	−0.767663	−	0.640854i	$-0.778580\pi$
$127$	−17.3022	−1.53533	−0.767663	+	0.640854i	$0.778580\pi$
$128$	−1.00000	−0.0883883
$129$	8.94717	0.787754
$130$	8.70856	0.763791
$131$	−4.01213	−0.350541	−0.175271	−	0.984520i	$-0.556080\pi$
$131$	−4.01213	−0.350541	−0.175271	+	0.984520i	$0.556080\pi$
$132$	15.5076	1.34976
$133$	9.91863	0.860055
$134$	−4.18113	−0.361195
$135$	−19.0904	−1.64304
$136$	7.73224	0.663034
$137$	0.918080	0.0784368	0.0392184	−	0.999231i	$-0.487513\pi$
$137$	0.918080	0.0784368	0.0392184	+	0.999231i	$0.487513\pi$
$138$	−1.89770	−0.161543
$139$	3.05430	0.259062	0.129531	−	0.991575i	$-0.458653\pi$
$139$	3.05430	0.259062	0.129531	+	0.991575i	$0.458653\pi$
$140$	−3.27689	−0.276948
$141$	−16.6385	−1.40122
$142$	1.00394	0.0842484
$143$	20.5898	1.72181
$144$	5.91056	0.492547
$145$	−20.2080	−1.67818
$146$	−10.7868	−0.892726
$147$	14.2564	1.17585
$148$	5.57869	0.458565
$149$	8.66726	0.710050	0.355025	−	0.934857i	$-0.384472\pi$
$149$	8.66726	0.710050	0.355025	+	0.934857i	$0.384472\pi$
$150$	−0.513238	−0.0419057
$151$	−5.77494	−0.469958	−0.234979	−	0.972000i	$-0.575502\pi$
$151$	−5.77494	−0.469958	−0.234979	+	0.972000i	$0.575502\pi$
$152$	6.65084	0.539454
$153$	−45.7019	−3.69478
$154$	−7.74761	−0.624321
$155$	−19.1084	−1.53482
$156$	11.8307	0.947218
$157$	−4.66468	−0.372282	−0.186141	−	0.982523i	$-0.559598\pi$
$157$	−4.66468	−0.372282	−0.186141	+	0.982523i	$0.559598\pi$
$158$	13.3879	1.06509
$159$	−16.8019	−1.33248
$160$	−2.19729	−0.173711
$161$	0.948090	0.0747200
$162$	−8.20303	−0.644491
$163$	5.81263	0.455280	0.227640	−	0.973745i	$-0.426899\pi$
$163$	5.81263	0.455280	0.227640	+	0.973745i	$0.426899\pi$
$164$	−4.25727	−0.332437
$165$	34.0747	2.65271
$166$	12.0477	0.935081
$167$	−13.6955	−1.05979	−0.529895	−	0.848063i	$-0.677769\pi$
$167$	−13.6955	−1.05979	−0.529895	+	0.848063i	$0.677769\pi$
$168$	−4.45172	−0.343458
$169$	2.70794	0.208303
$170$	16.9899	1.30307
$171$	−39.3102	−3.00612
$172$	−2.99732	−0.228544
$173$	6.79074	0.516290	0.258145	−	0.966106i	$-0.416889\pi$
$173$	6.79074	0.516290	0.258145	+	0.966106i	$0.416889\pi$
$174$	−27.4529	−2.08120
$175$	0.256414	0.0193831
$176$	−5.19508	−0.391594
$177$	13.9056	1.04521
$178$	3.22745	0.241908
$179$	−9.25120	−0.691467	−0.345734	−	0.938333i	$-0.612370\pi$
$179$	−9.25120	−0.691467	−0.345734	+	0.938333i	$0.612370\pi$
$180$	12.9872	0.968008
$181$	9.24156	0.686920	0.343460	−	0.939167i	$-0.388401\pi$
$181$	9.24156	0.686920	0.343460	+	0.939167i	$0.388401\pi$
$182$	−5.91065	−0.438126
$183$	−42.4916	−3.14107
$184$	0.635732	0.0468668
$185$	12.2580	0.901224
$186$	−25.9591	−1.90341
$187$	40.1696	2.93749
$188$	5.57394	0.406522
$189$	12.9570	0.942483
$190$	14.6138	1.06020
$191$	−23.5291	−1.70251	−0.851254	−	0.524753i	$-0.824158\pi$
$191$	−23.5291	−1.70251	−0.851254	+	0.524753i	$0.824158\pi$
$192$	−2.98506	−0.215428
$193$	−25.9546	−1.86826	−0.934128	−	0.356939i	$-0.883820\pi$
$193$	−25.9546	−1.86826	−0.934128	+	0.356939i	$0.883820\pi$
$194$	4.42490	0.317689
$195$	25.9955	1.86158
$196$	−4.77592	−0.341137
$197$	5.24253	0.373515	0.186757	−	0.982406i	$-0.440202\pi$
$197$	5.24253	0.373515	0.186757	+	0.982406i	$0.440202\pi$
$198$	30.7059	2.18217
$199$	8.62599	0.611481	0.305740	−	0.952115i	$-0.401096\pi$
$199$	8.62599	0.611481	0.305740	+	0.952115i	$0.401096\pi$
$200$	0.171936	0.0121577
$201$	−12.4809	−0.880336
$202$	−6.94327	−0.488526
$203$	13.7155	0.962638
$204$	23.0812	1.61600
$205$	−9.35444	−0.653342
$206$	−11.1259	−0.775177
$207$	−3.75753	−0.261167
$208$	−3.96332	−0.274807
$209$	34.5517	2.38999
$210$	−9.78170	−0.675001
$211$	−23.3050	−1.60438	−0.802191	−	0.597067i	$-0.796333\pi$
$211$	−23.3050	−1.60438	−0.802191	+	0.597067i	$0.796333\pi$
$212$	5.62868	0.386579
$213$	2.99680	0.205338
$214$	−5.92837	−0.405255
$215$	−6.58597	−0.449159
$216$	8.68818	0.591156
$217$	12.9692	0.880405
$218$	13.9916	0.947631
$219$	−32.1993	−2.17583
$220$	−11.4151	−0.769605
$221$	30.6454	2.06143
$222$	16.6527	1.11766
$223$	29.0978	1.94853	0.974267	−	0.225396i	$-0.0723674\pi$
$223$	29.0978	1.94853	0.974267	+	0.225396i	$0.0723674\pi$
$224$	1.49134	0.0996440
$225$	−1.01624	−0.0677491
$226$	−4.96025	−0.329951
$227$	10.7655	0.714533	0.357267	−	0.934002i	$-0.383709\pi$
$227$	10.7655	0.714533	0.357267	+	0.934002i	$0.383709\pi$
$228$	19.8531	1.31481
$229$	15.8681	1.04859	0.524297	−	0.851536i	$-0.324328\pi$
$229$	15.8681	1.04859	0.524297	+	0.851536i	$0.324328\pi$
$230$	1.39689	0.0921079
$231$	−23.1271	−1.52165
$232$	9.19678	0.603798
$233$	−11.1134	−0.728063	−0.364032	−	0.931387i	$-0.618600\pi$
$233$	−11.1134	−0.728063	−0.364032	+	0.931387i	$0.618600\pi$
$234$	23.4255	1.53137
$235$	12.2475	0.798942
$236$	−4.65841	−0.303237
$237$	39.9637	2.59592
$238$	−11.5314	−0.747467
$239$	13.0163	0.841953	0.420977	−	0.907071i	$-0.361687\pi$
$239$	13.0163	0.841953	0.420977	+	0.907071i	$0.361687\pi$
$240$	−6.55902	−0.423383
$241$	5.82107	0.374968	0.187484	−	0.982268i	$-0.439967\pi$
$241$	5.82107	0.374968	0.187484	+	0.982268i	$0.439967\pi$
$242$	−15.9889	−1.02781
$243$	1.57804	0.101231
$244$	14.2348	0.911288
$245$	−10.4941	−0.670441
$246$	−12.7082	−0.810244
$247$	26.3594	1.67721
$248$	8.69635	0.552219
$249$	35.9630	2.27906
$250$	11.3642	0.718736
$251$	−6.11522	−0.385989	−0.192995	−	0.981200i	$-0.561820\pi$
$251$	−6.11522	−0.385989	−0.192995	+	0.981200i	$0.561820\pi$
$252$	−8.81463	−0.555269
$253$	3.30268	0.207638
$254$	17.3022	1.08564
$255$	50.7159	3.17595
$256$	1.00000	0.0625000
$257$	−15.3049	−0.954693	−0.477347	−	0.878715i	$-0.658401\pi$
$257$	−15.3049	−0.954693	−0.477347	+	0.878715i	$0.658401\pi$
$258$	−8.94717	−0.557026
$259$	−8.31970	−0.516961
$260$	−8.70856	−0.540082
$261$	−54.3581	−3.36468
$262$	4.01213	0.247870
$263$	−25.0871	−1.54694	−0.773469	−	0.633834i	$-0.781480\pi$
$263$	−25.0871	−1.54694	−0.773469	+	0.633834i	$0.781480\pi$
$264$	−15.5076	−0.954428
$265$	12.3678	0.759749
$266$	−9.91863	−0.608150
$267$	9.63412	0.589599
$268$	4.18113	0.255403
$269$	3.60330	0.219697	0.109849	−	0.993948i	$-0.464963\pi$
$269$	3.60330	0.219697	0.109849	+	0.993948i	$0.464963\pi$
$270$	19.0904	1.16181
$271$	−29.0893	−1.76705	−0.883524	−	0.468386i	$-0.844836\pi$
$271$	−29.0893	−1.76705	−0.883524	+	0.468386i	$0.844836\pi$
$272$	−7.73224	−0.468836
$273$	−17.6436	−1.06784
$274$	−0.918080	−0.0554632
$275$	0.893221	0.0538633
$276$	1.89770	0.114228
$277$	−5.17148	−0.310724	−0.155362	−	0.987858i	$-0.549654\pi$
$277$	−5.17148	−0.310724	−0.155362	+	0.987858i	$0.549654\pi$
$278$	−3.05430	−0.183185
$279$	−51.4003	−3.07725
$280$	3.27689	0.195832
$281$	16.0087	0.955001	0.477500	−	0.878632i	$-0.341543\pi$
$281$	16.0087	0.955001	0.477500	+	0.878632i	$0.341543\pi$
$282$	16.6385	0.990810
$283$	22.3691	1.32971	0.664854	−	0.746973i	$-0.268494\pi$
$283$	22.3691	1.32971	0.664854	+	0.746973i	$0.268494\pi$
$284$	−1.00394	−0.0595726
$285$	43.6230	2.58400
$286$	−20.5898	−1.21750
$287$	6.34902	0.374771
$288$	−5.91056	−0.348283
$289$	42.7875	2.51691
$290$	20.2080	1.18665
$291$	13.2086	0.774299
$292$	10.7868	0.631252
$293$	28.9395	1.69066	0.845331	−	0.534243i	$-0.179403\pi$
$293$	28.9395	1.69066	0.845331	+	0.534243i	$0.179403\pi$
$294$	−14.2564	−0.831449
$295$	−10.2359	−0.595954
$296$	−5.57869	−0.324255
$297$	45.1358	2.61905
$298$	−8.66726	−0.502081
$299$	2.51961	0.145713
$300$	0.513238	0.0296318
$301$	4.47001	0.257647
$302$	5.77494	0.332310
$303$	−20.7260	−1.19068
$304$	−6.65084	−0.381452
$305$	31.2779	1.79097
$306$	45.7019	2.61260
$307$	20.9286	1.19446	0.597228	−	0.802072i	$-0.296269\pi$
$307$	20.9286	1.19446	0.597228	+	0.802072i	$0.296269\pi$
$308$	7.74761	0.441461
$309$	−33.2114	−1.88933
$310$	19.1084	1.08528
$311$	−17.9172	−1.01599	−0.507994	−	0.861360i	$-0.669613\pi$
$311$	−17.9172	−1.01599	−0.507994	+	0.861360i	$0.669613\pi$
$312$	−11.8307	−0.669784
$313$	−8.94503	−0.505603	−0.252802	−	0.967518i	$-0.581352\pi$
$313$	−8.94503	−0.505603	−0.252802	+	0.967518i	$0.581352\pi$
$314$	4.66468	0.263243
$315$	−19.3683	−1.09128
$316$	−13.3879	−0.753130
$317$	−13.8567	−0.778270	−0.389135	−	0.921181i	$-0.627226\pi$
$317$	−13.8567	−0.778270	−0.389135	+	0.921181i	$0.627226\pi$
$318$	16.8019	0.942206
$319$	47.7781	2.67506
$320$	2.19729	0.122832
$321$	−17.6965	−0.987723
$322$	−0.948090	−0.0528350
$323$	51.4259	2.86141
$324$	8.20303	0.455724
$325$	0.681437	0.0377993
$326$	−5.81263	−0.321932
$327$	41.7657	2.30965
$328$	4.25727	0.235068
$329$	−8.31262	−0.458290
$330$	−34.0747	−1.87575
$331$	−20.7676	−1.14149	−0.570744	−	0.821128i	$-0.693345\pi$
$331$	−20.7676	−1.14149	−0.570744	+	0.821128i	$0.693345\pi$
$332$	−12.0477	−0.661202
$333$	32.9732	1.80692
$334$	13.6955	0.749385
$335$	9.18714	0.501947
$336$	4.45172	0.242861
$337$	−8.79525	−0.479108	−0.239554	−	0.970883i	$-0.577001\pi$
$337$	−8.79525	−0.479108	−0.239554	+	0.970883i	$0.577001\pi$
$338$	−2.70794	−0.147292
$339$	−14.8066	−0.804186
$340$	−16.9899	−0.921409
$341$	45.1783	2.44654
$342$	39.3102	2.12565
$343$	17.5618	0.948250
$344$	2.99732	0.161605
$345$	4.16978	0.224493
$346$	−6.79074	−0.365072
$347$	10.3858	0.557541	0.278771	−	0.960358i	$-0.410073\pi$
$347$	10.3858	0.557541	0.278771	+	0.960358i	$0.410073\pi$
$348$	27.4529	1.47163
$349$	−9.85411	−0.527478	−0.263739	−	0.964594i	$-0.584956\pi$
$349$	−9.85411	−0.527478	−0.263739	+	0.964594i	$0.584956\pi$
$350$	−0.256414	−0.0137059
$351$	34.4341	1.83796
$352$	5.19508	0.276899
$353$	−21.1051	−1.12331	−0.561655	−	0.827372i	$-0.689835\pi$
$353$	−21.1051	−1.12331	−0.561655	+	0.827372i	$0.689835\pi$
$354$	−13.9056	−0.739075
$355$	−2.20593	−0.117079
$356$	−3.22745	−0.171055
$357$	−34.4218	−1.82179
$358$	9.25120	0.488941
$359$	−18.0644	−0.953402	−0.476701	−	0.879066i	$-0.658168\pi$
$359$	−18.0644	−0.953402	−0.476701	+	0.879066i	$0.658168\pi$
$360$	−12.9872	−0.684485
$361$	25.2337	1.32809
$362$	−9.24156	−0.485726
$363$	−47.7278	−2.50506
$364$	5.91065	0.309802
$365$	23.7018	1.24061
$366$	42.4916	2.22107
$367$	15.5577	0.812106	0.406053	−	0.913849i	$-0.366905\pi$
$367$	15.5577	0.812106	0.406053	+	0.913849i	$0.366905\pi$
$368$	−0.635732	−0.0331398
$369$	−25.1628	−1.30993
$370$	−12.2580	−0.637262
$371$	−8.39425	−0.435808
$372$	25.9591	1.34592
$373$	−20.2426	−1.04812	−0.524060	−	0.851681i	$-0.675583\pi$
$373$	−20.2426	−1.04812	−0.524060	+	0.851681i	$0.675583\pi$
$374$	−40.1696	−2.07712
$375$	33.9228	1.75177
$376$	−5.57394	−0.287454
$377$	36.4498	1.87726
$378$	−12.9570	−0.666436
$379$	21.7845	1.11899	0.559496	−	0.828833i	$-0.310995\pi$
$379$	21.7845	1.11899	0.559496	+	0.828833i	$0.310995\pi$
$380$	−14.6138	−0.749672
$381$	51.6482	2.64602
$382$	23.5291	1.20386
$383$	0.747847	0.0382132	0.0191066	−	0.999817i	$-0.493918\pi$
$383$	0.747847	0.0382132	0.0191066	+	0.999817i	$0.493918\pi$
$384$	2.98506	0.152330
$385$	17.0237	0.867609
$386$	25.9546	1.32106
$387$	−17.7158	−0.900547
$388$	−4.42490	−0.224640
$389$	−30.7171	−1.55742	−0.778708	−	0.627386i	$-0.784125\pi$
$389$	−30.7171	−1.55742	−0.778708	+	0.627386i	$0.784125\pi$
$390$	−25.9955	−1.31633
$391$	4.91563	0.248594
$392$	4.77592	0.241220
$393$	11.9764	0.604130
$394$	−5.24253	−0.264115
$395$	−29.4171	−1.48014
$396$	−30.7059	−1.54303
$397$	−28.8247	−1.44667	−0.723336	−	0.690496i	$-0.757392\pi$
$397$	−28.8247	−1.44667	−0.723336	+	0.690496i	$0.757392\pi$
$398$	−8.62599	−0.432382
$399$	−29.6077	−1.48224
$400$	−0.171936	−0.00859679
$401$	−24.2006	−1.20852	−0.604261	−	0.796787i	$-0.706531\pi$
$401$	−24.2006	−1.20852	−0.604261	+	0.796787i	$0.706531\pi$
$402$	12.4809	0.622492
$403$	34.4664	1.71690
$404$	6.94327	0.345440
$405$	18.0244	0.895640
$406$	−13.7155	−0.680688
$407$	−28.9818	−1.43657
$408$	−23.0812	−1.14269
$409$	−1.78369	−0.0881980	−0.0440990	−	0.999027i	$-0.514042\pi$
$409$	−1.78369	−0.0881980	−0.0440990	+	0.999027i	$0.514042\pi$
$410$	9.35444	0.461983
$411$	−2.74052	−0.135180
$412$	11.1259	0.548133
$413$	6.94725	0.341852
$414$	3.75753	0.184673
$415$	−26.4722	−1.29947
$416$	3.96332	0.194318
$417$	−9.11725	−0.446474
$418$	−34.5517	−1.68998
$419$	−29.0928	−1.42128	−0.710638	−	0.703558i	$-0.751594\pi$
$419$	−29.0928	−1.42128	−0.710638	+	0.703558i	$0.751594\pi$
$420$	9.78170	0.477298
$421$	−15.4248	−0.751758	−0.375879	−	0.926669i	$-0.622659\pi$
$421$	−15.4248	−0.751758	−0.375879	+	0.926669i	$0.622659\pi$
$422$	23.3050	1.13447
$423$	32.9451	1.60185
$424$	−5.62868	−0.273353
$425$	1.32945	0.0644877
$426$	−2.99680	−0.145196
$427$	−21.2288	−1.02733
$428$	5.92837	0.286558
$429$	−61.4617	−2.96740
$430$	6.58597	0.317604
$431$	−24.7725	−1.19325	−0.596624	−	0.802521i	$-0.703492\pi$
$431$	−24.7725	−1.19325	−0.596624	+	0.802521i	$0.703492\pi$
$432$	−8.68818	−0.418010
$433$	−8.15219	−0.391769	−0.195885	−	0.980627i	$-0.562758\pi$
$433$	−8.15219	−0.391769	−0.195885	+	0.980627i	$0.562758\pi$
$434$	−12.9692	−0.622540
$435$	60.3219	2.89221
$436$	−13.9916	−0.670077
$437$	4.22815	0.202260
$438$	32.1993	1.53854
$439$	28.1897	1.34542	0.672710	−	0.739906i	$-0.265130\pi$
$439$	28.1897	1.34542	0.672710	+	0.739906i	$0.265130\pi$
$440$	11.4151	0.544193
$441$	−28.2283	−1.34421
$442$	−30.6454	−1.45765
$443$	22.0695	1.04855	0.524276	−	0.851548i	$-0.324336\pi$
$443$	22.0695	1.04855	0.524276	+	0.851548i	$0.324336\pi$
$444$	−16.6527	−0.790302
$445$	−7.09163	−0.336176
$446$	−29.0978	−1.37782
$447$	−25.8723	−1.22372
$448$	−1.49134	−0.0704590
$449$	−12.7078	−0.599718	−0.299859	−	0.953984i	$-0.596940\pi$
$449$	−12.7078	−0.599718	−0.299859	+	0.953984i	$0.596940\pi$
$450$	1.01624	0.0479059
$451$	22.1169	1.04144
$452$	4.96025	0.233311
$453$	17.2385	0.809936
$454$	−10.7655	−0.505251
$455$	12.9874	0.608858
$456$	−19.8531	−0.929708
$457$	26.4347	1.23656	0.618281	−	0.785957i	$-0.287829\pi$
$457$	26.4347	1.23656	0.618281	+	0.785957i	$0.287829\pi$
$458$	−15.8681	−0.741467
$459$	67.1791	3.13565
$460$	−1.39689	−0.0651301
$461$	11.1970	0.521497	0.260749	−	0.965407i	$-0.416031\pi$
$461$	11.1970	0.521497	0.260749	+	0.965407i	$0.416031\pi$
$462$	23.1271	1.07597
$463$	−26.2783	−1.22126	−0.610629	−	0.791917i	$-0.709083\pi$
$463$	−26.2783	−1.22126	−0.610629	+	0.791917i	$0.709083\pi$
$464$	−9.19678	−0.426950
$465$	57.0395	2.64514
$466$	11.1134	0.514818
$467$	−11.9505	−0.553002	−0.276501	−	0.961014i	$-0.589175\pi$
$467$	−11.9505	−0.553002	−0.276501	+	0.961014i	$0.589175\pi$
$468$	−23.4255	−1.08284
$469$	−6.23547	−0.287927
$470$	−12.2475	−0.564937
$471$	13.9243	0.641600
$472$	4.65841	0.214421
$473$	15.5713	0.715971
$474$	−39.9637	−1.83559
$475$	1.14352	0.0524682
$476$	11.5314	0.528539
$477$	33.2687	1.52327
$478$	−13.0163	−0.595351
$479$	−25.1197	−1.14775	−0.573874	−	0.818943i	$-0.694560\pi$
$479$	−25.1197	−1.14775	−0.573874	+	0.818943i	$0.694560\pi$
$480$	6.55902	0.299377
$481$	−22.1101	−1.00814
$482$	−5.82107	−0.265143
$483$	−2.83010	−0.128774
$484$	15.9889	0.726768
$485$	−9.72276	−0.441488
$486$	−1.57804	−0.0715812
$487$	−35.2081	−1.59543	−0.797717	−	0.603033i	$-0.793959\pi$
$487$	−35.2081	−1.59543	−0.797717	+	0.603033i	$0.793959\pi$
$488$	−14.2348	−0.644378
$489$	−17.3510	−0.784640
$490$	10.4941	0.474073
$491$	−12.4092	−0.560019	−0.280009	−	0.959997i	$-0.590338\pi$
$491$	−12.4092	−0.560019	−0.280009	+	0.959997i	$0.590338\pi$
$492$	12.7082	0.572929
$493$	71.1117	3.20271
$494$	−26.3594	−1.18597
$495$	−67.4695	−3.03253
$496$	−8.69635	−0.390478
$497$	1.49720	0.0671588
$498$	−35.9630	−1.61154
$499$	8.93430	0.399954	0.199977	−	0.979801i	$-0.435913\pi$
$499$	8.93430	0.399954	0.199977	+	0.979801i	$0.435913\pi$
$500$	−11.3642	−0.508223
$501$	40.8819	1.82647
$502$	6.11522	0.272936
$503$	14.2829	0.636842	0.318421	−	0.947949i	$-0.396847\pi$
$503$	14.2829	0.636842	0.318421	+	0.947949i	$0.396847\pi$
$504$	8.81463	0.392635
$505$	15.2563	0.678898
$506$	−3.30268	−0.146822
$507$	−8.08335	−0.358994
$508$	−17.3022	−0.767663
$509$	23.2762	1.03170	0.515849	−	0.856679i	$-0.327477\pi$
$509$	23.2762	1.03170	0.515849	+	0.856679i	$0.327477\pi$
$510$	−50.7159	−2.24574
$511$	−16.0868	−0.711638
$512$	−1.00000	−0.0441942
$513$	57.7837	2.55121
$514$	15.3049	0.675070
$515$	24.4467	1.07725
$516$	8.94717	0.393877
$517$	−28.9571	−1.27353
$518$	8.31970	0.365546
$519$	−20.2707	−0.889787
$520$	8.70856	0.381895
$521$	41.1401	1.80238	0.901190	−	0.433424i	$-0.142695\pi$
$521$	41.1401	1.80238	0.901190	+	0.433424i	$0.142695\pi$
$522$	54.3581	2.37919
$523$	−39.3634	−1.72124	−0.860620	−	0.509247i	$-0.829924\pi$
$523$	−39.3634	−1.72124	−0.860620	+	0.509247i	$0.829924\pi$
$524$	−4.01213	−0.175271
$525$	−0.765410	−0.0334052
$526$	25.0871	1.09385
$527$	67.2422	2.92912
$528$	15.5076	0.674882
$529$	−22.5958	−0.982428
$530$	−12.3678	−0.537224
$531$	−27.5338	−1.19486
$532$	9.91863	0.430027
$533$	16.8729	0.730848
$534$	−9.63412	−0.416909
$535$	13.0263	0.563177
$536$	−4.18113	−0.180597
$537$	27.6154	1.19169
$538$	−3.60330	−0.155349
$539$	24.8113	1.06870
$540$	−19.0904	−0.821521
$541$	17.7211	0.761891	0.380945	−	0.924598i	$-0.375599\pi$
$541$	17.7211	0.761891	0.380945	+	0.924598i	$0.375599\pi$
$542$	29.0893	1.24949
$543$	−27.5866	−1.18385
$544$	7.73224	0.331517
$545$	−30.7436	−1.31691
$546$	17.6436	0.755077
$547$	30.6981	1.31255	0.656277	−	0.754520i	$-0.272130\pi$
$547$	30.6981	1.31255	0.656277	+	0.754520i	$0.272130\pi$
$548$	0.918080	0.0392184
$549$	84.1355	3.59082
$550$	−0.893221	−0.0380871
$551$	61.1663	2.60577
$552$	−1.89770	−0.0807713
$553$	19.9659	0.849036
$554$	5.17148	0.219715
$555$	−36.5907	−1.55319
$556$	3.05430	0.129531
$557$	−26.1703	−1.10887	−0.554436	−	0.832227i	$-0.687066\pi$
$557$	−26.1703	−1.10887	−0.554436	+	0.832227i	$0.687066\pi$
$558$	51.4003	2.17595
$559$	11.8794	0.502443
$560$	−3.27689	−0.138474
$561$	−119.909	−5.06255
$562$	−16.0087	−0.675288
$563$	−15.7436	−0.663514	−0.331757	−	0.943365i	$-0.607641\pi$
$563$	−15.7436	−0.663514	−0.331757	+	0.943365i	$0.607641\pi$
$564$	−16.6385	−0.700609
$565$	10.8991	0.458528
$566$	−22.3691	−0.940245
$567$	−12.2335	−0.513758
$568$	1.00394	0.0421242
$569$	18.4941	0.775312	0.387656	−	0.921804i	$-0.373285\pi$
$569$	18.4941	0.775312	0.387656	+	0.921804i	$0.373285\pi$
$570$	−43.6230	−1.82717
$571$	28.5163	1.19337	0.596686	−	0.802475i	$-0.296484\pi$
$571$	28.5163	1.19337	0.596686	+	0.802475i	$0.296484\pi$
$572$	20.5898	0.860903
$573$	70.2358	2.93414
$574$	−6.34902	−0.265003
$575$	0.109305	0.00455834
$576$	5.91056	0.246273
$577$	−5.77649	−0.240478	−0.120239	−	0.992745i	$-0.538366\pi$
$577$	−5.77649	−0.240478	−0.120239	+	0.992745i	$0.538366\pi$
$578$	−42.7875	−1.77973
$579$	77.4760	3.21979
$580$	−20.2080	−0.839090
$581$	17.9671	0.745402
$582$	−13.2086	−0.547512
$583$	−29.2415	−1.21106
$584$	−10.7868	−0.446363
$585$	−51.4724	−2.12812
$586$	−28.9395	−1.19548
$587$	−22.4228	−0.925487	−0.462743	−	0.886492i	$-0.653135\pi$
$587$	−22.4228	−0.925487	−0.462743	+	0.886492i	$0.653135\pi$
$588$	14.2564	0.587923
$589$	57.8380	2.38317
$590$	10.2359	0.421403
$591$	−15.6492	−0.643724
$592$	5.57869	0.229283
$593$	4.61283	0.189426	0.0947131	−	0.995505i	$-0.469807\pi$
$593$	4.61283	0.189426	0.0947131	+	0.995505i	$0.469807\pi$
$594$	−45.1358	−1.85195
$595$	25.3377	1.03874
$596$	8.66726	0.355025
$597$	−25.7491	−1.05384
$598$	−2.51961	−0.103035
$599$	0.481335	0.0196668	0.00983341	−	0.999952i	$-0.496870\pi$
$599$	0.481335	0.0196668	0.00983341	+	0.999952i	$0.496870\pi$
$600$	−0.513238	−0.0209529
$601$	−24.7784	−1.01073	−0.505367	−	0.862905i	$-0.668643\pi$
$601$	−24.7784	−1.01073	−0.505367	+	0.862905i	$0.668643\pi$
$602$	−4.47001	−0.182184
$603$	24.7128	1.00638
$604$	−5.77494	−0.234979
$605$	35.1322	1.42833
$606$	20.7260	0.841938
$607$	−6.01464	−0.244127	−0.122063	−	0.992522i	$-0.538951\pi$
$607$	−6.01464	−0.244127	−0.122063	+	0.992522i	$0.538951\pi$
$608$	6.65084	0.269727
$609$	−40.9415	−1.65903
$610$	−31.2779	−1.26640
$611$	−22.0913	−0.893720
$612$	−45.7019	−1.84739
$613$	−26.1371	−1.05567	−0.527834	−	0.849347i	$-0.676996\pi$
$613$	−26.1371	−1.05567	−0.527834	+	0.849347i	$0.676996\pi$
$614$	−20.9286	−0.844608
$615$	27.9235	1.12598
$616$	−7.74761	−0.312160
$617$	−25.8564	−1.04094	−0.520470	−	0.853880i	$-0.674243\pi$
$617$	−25.8564	−1.04094	−0.520470	+	0.853880i	$0.674243\pi$
$618$	33.2114	1.33596
$619$	35.9101	1.44335	0.721675	−	0.692232i	$-0.243372\pi$
$619$	35.9101	1.44335	0.721675	+	0.692232i	$0.243372\pi$
$620$	−19.1084	−0.767410
$621$	5.52336	0.221645
$622$	17.9172	0.718412
$623$	4.81321	0.192837
$624$	11.8307	0.473609
$625$	−24.1108	−0.964430
$626$	8.94503	0.357515
$627$	−103.139	−4.11896
$628$	−4.66468	−0.186141
$629$	−43.1357	−1.71993
$630$	19.3683	0.771650
$631$	7.59650	0.302412	0.151206	−	0.988502i	$-0.451684\pi$
$631$	7.59650	0.302412	0.151206	+	0.988502i	$0.451684\pi$
$632$	13.3879	0.532543
$633$	69.5667	2.76503
$634$	13.8567	0.550320
$635$	−38.0180	−1.50870
$636$	−16.8019	−0.666240
$637$	18.9285	0.749975
$638$	−47.7781	−1.89155
$639$	−5.93382	−0.234738
$640$	−2.19729	−0.0868553
$641$	−17.8123	−0.703544	−0.351772	−	0.936086i	$-0.614421\pi$
$641$	−17.8123	−0.703544	−0.351772	+	0.936086i	$0.614421\pi$
$642$	17.6965	0.698425
$643$	43.6635	1.72192	0.860959	−	0.508674i	$-0.169864\pi$
$643$	43.6635	1.72192	0.860959	+	0.508674i	$0.169864\pi$
$644$	0.948090	0.0373600
$645$	19.6595	0.774091
$646$	−51.4259	−2.02332
$647$	−7.09651	−0.278993	−0.139496	−	0.990223i	$-0.544548\pi$
$647$	−7.09651	−0.278993	−0.139496	+	0.990223i	$0.544548\pi$
$648$	−8.20303	−0.322246
$649$	24.2008	0.949965
$650$	−0.681437	−0.0267282
$651$	−38.7137	−1.51731
$652$	5.81263	0.227640
$653$	−19.4430	−0.760863	−0.380431	−	0.924809i	$-0.624224\pi$
$653$	−19.4430	−0.760863	−0.380431	+	0.924809i	$0.624224\pi$
$654$	−41.7657	−1.63317
$655$	−8.81579	−0.344461
$656$	−4.25727	−0.166218
$657$	63.7563	2.48737
$658$	8.31262	0.324060
$659$	5.16451	0.201181	0.100590	−	0.994928i	$-0.467927\pi$
$659$	5.16451	0.201181	0.100590	+	0.994928i	$0.467927\pi$
$660$	34.0747	1.32635
$661$	−2.54252	−0.0988928	−0.0494464	−	0.998777i	$-0.515746\pi$
$661$	−2.54252	−0.0988928	−0.0494464	+	0.998777i	$0.515746\pi$
$662$	20.7676	0.807154
$663$	−91.4781	−3.55272
$664$	12.0477	0.467541
$665$	21.7941	0.845138
$666$	−32.9732	−1.27768
$667$	5.84669	0.226385
$668$	−13.6955	−0.529895
$669$	−86.8586	−3.35815
$670$	−9.18714	−0.354930
$671$	−73.9509	−2.85484
$672$	−4.45172	−0.171729
$673$	−27.7270	−1.06880	−0.534399	−	0.845232i	$-0.679462\pi$
$673$	−27.7270	−1.06880	−0.534399	+	0.845232i	$0.679462\pi$
$674$	8.79525	0.338781
$675$	1.49381	0.0574968
$676$	2.70794	0.104151
$677$	−24.8978	−0.956899	−0.478449	−	0.878115i	$-0.658801\pi$
$677$	−24.8978	−0.956899	−0.478449	+	0.878115i	$0.658801\pi$
$678$	14.8066	0.568645
$679$	6.59900	0.253246
$680$	16.9899	0.651534
$681$	−32.1357	−1.23144
$682$	−45.1783	−1.72997
$683$	−37.0681	−1.41837	−0.709186	−	0.705022i	$-0.750937\pi$
$683$	−37.0681	−1.41837	−0.709186	+	0.705022i	$0.750937\pi$
$684$	−39.3102	−1.50306
$685$	2.01728	0.0770764
$686$	−17.5618	−0.670514
$687$	−47.3672	−1.80717
$688$	−2.99732	−0.114272
$689$	−22.3083	−0.849878
$690$	−4.16978	−0.158741
$691$	20.4450	0.777763	0.388882	−	0.921288i	$-0.372862\pi$
$691$	20.4450	0.777763	0.388882	+	0.921288i	$0.372862\pi$
$692$	6.79074	0.258145
$693$	45.7927	1.73952
$694$	−10.3858	−0.394241
$695$	6.71117	0.254569
$696$	−27.4529	−1.04060
$697$	32.9182	1.24687
$698$	9.85411	0.372984
$699$	33.1741	1.25476
$700$	0.256414	0.00969154
$701$	−8.18784	−0.309250	−0.154625	−	0.987973i	$-0.549417\pi$
$701$	−8.18784	−0.309250	−0.154625	+	0.987973i	$0.549417\pi$
$702$	−34.4341	−1.29963
$703$	−37.1030	−1.39936
$704$	−5.19508	−0.195797
$705$	−36.5596	−1.37691
$706$	21.1051	0.794300
$707$	−10.3547	−0.389430
$708$	13.9056	0.522605
$709$	−13.6434	−0.512390	−0.256195	−	0.966625i	$-0.582469\pi$
$709$	−13.6434	−0.512390	−0.256195	+	0.966625i	$0.582469\pi$
$710$	2.20593	0.0827872
$711$	−79.1302	−2.96761
$712$	3.22745	0.120954
$713$	5.52855	0.207046
$714$	34.4218	1.28820
$715$	45.2417	1.69194
$716$	−9.25120	−0.345734
$717$	−38.8543	−1.45104
$718$	18.0644	0.674157
$719$	42.6848	1.59188	0.795938	−	0.605378i	$-0.206978\pi$
$719$	42.6848	1.59188	0.795938	+	0.605378i	$0.206978\pi$
$720$	12.9872	0.484004
$721$	−16.5924	−0.617934
$722$	−25.2337	−0.939100
$723$	−17.3762	−0.646229
$724$	9.24156	0.343460
$725$	1.58126	0.0587264
$726$	47.7278	1.77134
$727$	−11.0638	−0.410333	−0.205166	−	0.978727i	$-0.565774\pi$
$727$	−11.0638	−0.410333	−0.205166	+	0.978727i	$0.565774\pi$
$728$	−5.91065	−0.219063
$729$	−29.3196	−1.08591
$730$	−23.7018	−0.877242
$731$	23.1760	0.857195
$732$	−42.4916	−1.57054
$733$	4.81819	0.177964	0.0889820	−	0.996033i	$-0.471639\pi$
$733$	4.81819	0.177964	0.0889820	+	0.996033i	$0.471639\pi$
$734$	−15.5577	−0.574246
$735$	31.3253	1.15545
$736$	0.635732	0.0234334
$737$	−21.7213	−0.800116
$738$	25.1628	0.926257
$739$	1.95217	0.0718117	0.0359058	−	0.999355i	$-0.488568\pi$
$739$	1.95217	0.0718117	0.0359058	+	0.999355i	$0.488568\pi$
$740$	12.2580	0.450612
$741$	−78.6844	−2.89054
$742$	8.39425	0.308163
$743$	−6.95360	−0.255103	−0.127551	−	0.991832i	$-0.540712\pi$
$743$	−6.95360	−0.255103	−0.127551	+	0.991832i	$0.540712\pi$
$744$	−25.9591	−0.951706
$745$	19.0445	0.697735
$746$	20.2426	0.741132
$747$	−71.2085	−2.60538
$748$	40.1696	1.46875
$749$	−8.84118	−0.323050
$750$	−33.9228	−1.23869
$751$	37.4489	1.36653	0.683264	−	0.730171i	$-0.260560\pi$
$751$	37.4489	1.36653	0.683264	+	0.730171i	$0.260560\pi$
$752$	5.57394	0.203261
$753$	18.2543	0.665223
$754$	−36.4498	−1.32742
$755$	−12.6892	−0.461807
$756$	12.9570	0.471241
$757$	−0.534186	−0.0194153	−0.00970767	−	0.999953i	$-0.503090\pi$
$757$	−0.534186	−0.0194153	−0.00970767	+	0.999953i	$0.503090\pi$
$758$	−21.7845	−0.791247
$759$	−9.85869	−0.357848
$760$	14.6138	0.530098
$761$	−29.9254	−1.08479	−0.542397	−	0.840122i	$-0.682483\pi$
$761$	−29.9254	−1.08479	−0.542397	+	0.840122i	$0.682483\pi$
$762$	−51.6482	−1.87102
$763$	20.8662	0.755406
$764$	−23.5291	−0.851254
$765$	−100.420	−3.63069
$766$	−0.747847	−0.0270208
$767$	18.4628	0.666652
$768$	−2.98506	−0.107714
$769$	−22.3756	−0.806885	−0.403442	−	0.915005i	$-0.632186\pi$
$769$	−22.3756	−0.806885	−0.403442	+	0.915005i	$0.632186\pi$
$770$	−17.0237	−0.613492
$771$	45.6860	1.64534
$772$	−25.9546	−0.934128
$773$	−36.7085	−1.32031	−0.660157	−	0.751128i	$-0.729510\pi$
$773$	−36.7085	−1.32031	−0.660157	+	0.751128i	$0.729510\pi$
$774$	17.7158	0.636783
$775$	1.49521	0.0537097
$776$	4.42490	0.158844
$777$	24.8348	0.890942
$778$	30.7171	1.10126
$779$	28.3144	1.01447
$780$	25.9955	0.930789
$781$	5.21553	0.186626
$782$	−4.91563	−0.175783
$783$	79.9033	2.85551
$784$	−4.77592	−0.170569
$785$	−10.2496	−0.365825
$786$	−11.9764	−0.427185
$787$	38.4786	1.37162	0.685808	−	0.727783i	$-0.259449\pi$
$787$	38.4786	1.37162	0.685808	+	0.727783i	$0.259449\pi$
$788$	5.24253	0.186757
$789$	74.8864	2.66603
$790$	29.4171	1.04661
$791$	−7.39740	−0.263021
$792$	30.7059	1.09109
$793$	−56.4170	−2.00343
$794$	28.8247	1.02295
$795$	−36.9186	−1.30937
$796$	8.62599	0.305740
$797$	−11.8824	−0.420896	−0.210448	−	0.977605i	$-0.567492\pi$
$797$	−11.8824	−0.420896	−0.210448	+	0.977605i	$0.567492\pi$
$798$	29.6077	1.04810
$799$	−43.0991	−1.52474
$800$	0.171936	0.00607885
$801$	−19.0760	−0.674019
$802$	24.2006	0.854553
$803$	−56.0386	−1.97756
$804$	−12.4809	−0.440168
$805$	2.08322	0.0734240
$806$	−34.4664	−1.21403
$807$	−10.7561	−0.378631
$808$	−6.94327	−0.244263
$809$	−5.34227	−0.187824	−0.0939121	−	0.995580i	$-0.529937\pi$
$809$	−5.34227	−0.187824	−0.0939121	+	0.995580i	$0.529937\pi$
$810$	−18.0244	−0.633313
$811$	−24.8297	−0.871889	−0.435945	−	0.899974i	$-0.643586\pi$
$811$	−24.8297	−0.871889	−0.435945	+	0.899974i	$0.643586\pi$
$812$	13.7155	0.481319
$813$	86.8331	3.04537
$814$	28.9818	1.01581
$815$	12.7720	0.447384
$816$	23.0812	0.808002
$817$	19.9347	0.697427
$818$	1.78369	0.0623654
$819$	34.9352	1.22074
$820$	−9.35444	−0.326671
$821$	20.8612	0.728061	0.364031	−	0.931387i	$-0.381400\pi$
$821$	20.8612	0.728061	0.364031	+	0.931387i	$0.381400\pi$
$822$	2.74052	0.0955866
$823$	34.3916	1.19882	0.599408	−	0.800444i	$-0.295403\pi$
$823$	34.3916	1.19882	0.599408	+	0.800444i	$0.295403\pi$
$824$	−11.1259	−0.387588
$825$	−2.66632	−0.0928292
$826$	−6.94725	−0.241726
$827$	−8.80202	−0.306076	−0.153038	−	0.988220i	$-0.548906\pi$
$827$	−8.80202	−0.306076	−0.153038	+	0.988220i	$0.548906\pi$
$828$	−3.75753	−0.130583
$829$	20.7480	0.720607	0.360304	−	0.932835i	$-0.382673\pi$
$829$	20.7480	0.720607	0.360304	+	0.932835i	$0.382673\pi$
$830$	26.4722	0.918863
$831$	15.4372	0.535509
$832$	−3.96332	−0.137404
$833$	36.9285	1.27950
$834$	9.11725	0.315705
$835$	−30.0929	−1.04141
$836$	34.5517	1.19499
$837$	75.5554	2.61158
$838$	29.0928	1.00499
$839$	−43.9094	−1.51592	−0.757961	−	0.652300i	$-0.773804\pi$
$839$	−43.9094	−1.51592	−0.757961	+	0.652300i	$0.773804\pi$
$840$	−9.78170	−0.337501
$841$	55.5808	1.91658
$842$	15.4248	0.531573
$843$	−47.7870	−1.64587
$844$	−23.3050	−0.802191
$845$	5.95011	0.204690
$846$	−32.9451	−1.13268
$847$	−23.8448	−0.819318
$848$	5.62868	0.193290
$849$	−66.7732	−2.29165
$850$	−1.32945	−0.0455997
$851$	−3.54655	−0.121574
$852$	2.99680	0.102669
$853$	16.0570	0.549783	0.274891	−	0.961475i	$-0.411358\pi$
$853$	16.0570	0.549783	0.274891	+	0.961475i	$0.411358\pi$
$854$	21.2288	0.726436
$855$	−86.3757	−2.95399
$856$	−5.92837	−0.202627
$857$	−32.0017	−1.09316	−0.546578	−	0.837408i	$-0.684070\pi$
$857$	−32.0017	−1.09316	−0.546578	+	0.837408i	$0.684070\pi$
$858$	61.4617	2.09827
$859$	1.19629	0.0408169	0.0204085	−	0.999792i	$-0.493503\pi$
$859$	1.19629	0.0408169	0.0204085	+	0.999792i	$0.493503\pi$
$860$	−6.58597	−0.224580
$861$	−18.9522	−0.645888
$862$	24.7725	0.843754
$863$	30.1828	1.02743	0.513716	−	0.857960i	$-0.328268\pi$
$863$	30.1828	1.02743	0.513716	+	0.857960i	$0.328268\pi$
$864$	8.68818	0.295578
$865$	14.9212	0.507336
$866$	8.15219	0.277023
$867$	−127.723	−4.33770
$868$	12.9692	0.440202
$869$	69.5515	2.35937
$870$	−60.3219	−2.04510
$871$	−16.5712	−0.561493
$872$	13.9916	0.473816
$873$	−26.1536	−0.885165
$874$	−4.22815	−0.143019
$875$	16.9479	0.572942
$876$	−32.1993	−1.08791
$877$	−1.31407	−0.0443730	−0.0221865	−	0.999754i	$-0.507063\pi$
$877$	−1.31407	−0.0443730	−0.0221865	+	0.999754i	$0.507063\pi$
$878$	−28.1897	−0.951355
$879$	−86.3859	−2.91373
$880$	−11.4151	−0.384802
$881$	−25.5913	−0.862194	−0.431097	−	0.902306i	$-0.641873\pi$
$881$	−25.5913	−0.862194	−0.431097	+	0.902306i	$0.641873\pi$
$882$	28.2283	0.950498
$883$	15.8676	0.533988	0.266994	−	0.963698i	$-0.413970\pi$
$883$	15.8676	0.533988	0.266994	+	0.963698i	$0.413970\pi$
$884$	30.6454	1.03072
$885$	30.5546	1.02708
$886$	−22.0695	−0.741439
$887$	46.3989	1.55792	0.778961	−	0.627072i	$-0.215747\pi$
$887$	46.3989	1.55792	0.778961	+	0.627072i	$0.215747\pi$
$888$	16.6527	0.558828
$889$	25.8035	0.865420
$890$	7.09163	0.237712
$891$	−42.6154	−1.42767
$892$	29.0978	0.974267
$893$	−37.0714	−1.24055
$894$	25.8723	0.865298
$895$	−20.3275	−0.679474
$896$	1.49134	0.0498220
$897$	−7.52119	−0.251125
$898$	12.7078	0.424064
$899$	79.9784	2.66743
$900$	−1.01624	−0.0338746
$901$	−43.5223	−1.44994
$902$	−22.1169	−0.736411
$903$	−13.3432	−0.444035
$904$	−4.96025	−0.164976
$905$	20.3064	0.675006
$906$	−17.2385	−0.572711
$907$	17.8207	0.591727	0.295863	−	0.955230i	$-0.404393\pi$
$907$	17.8207	0.591727	0.295863	+	0.955230i	$0.404393\pi$
$908$	10.7655	0.357267
$909$	41.0386	1.36116
$910$	−12.9874	−0.430527
$911$	3.59295	0.119040	0.0595199	−	0.998227i	$-0.481043\pi$
$911$	3.59295	0.119040	0.0595199	+	0.998227i	$0.481043\pi$
$912$	19.8531	0.657403
$913$	62.5887	2.07138
$914$	−26.4347	−0.874382
$915$	−93.3662	−3.08659
$916$	15.8681	0.524297
$917$	5.98342	0.197590
$918$	−67.1791	−2.21724
$919$	35.0430	1.15596	0.577981	−	0.816050i	$-0.303841\pi$
$919$	35.0430	1.15596	0.577981	+	0.816050i	$0.303841\pi$
$920$	1.39689	0.0460539
$921$	−62.4729	−2.05855
$922$	−11.1970	−0.368754
$923$	3.97892	0.130968
$924$	−23.1271	−0.760824
$925$	−0.959176	−0.0315375
$926$	26.2783	0.863560
$927$	65.7602	2.15985
$928$	9.19678	0.301899
$929$	11.8166	0.387690	0.193845	−	0.981032i	$-0.437904\pi$
$929$	11.8166	0.387690	0.193845	+	0.981032i	$0.437904\pi$
$930$	−57.0395	−1.87040
$931$	31.7639	1.04102
$932$	−11.1134	−0.364032
$933$	53.4837	1.75098
$934$	11.9505	0.391031
$935$	88.2642	2.88655
$936$	23.4255	0.765685
$937$	−43.3507	−1.41620	−0.708102	−	0.706110i	$-0.750448\pi$
$937$	−43.3507	−1.41620	−0.708102	+	0.706110i	$0.750448\pi$
$938$	6.23547	0.203595
$939$	26.7014	0.871368
$940$	12.2475	0.399471
$941$	−30.8641	−1.00614	−0.503070	−	0.864245i	$-0.667796\pi$
$941$	−30.8641	−1.00614	−0.503070	+	0.864245i	$0.667796\pi$
$942$	−13.9243	−0.453680
$943$	2.70648	0.0881352
$944$	−4.65841	−0.151618
$945$	28.4702	0.926136
$946$	−15.5713	−0.506268
$947$	−55.8555	−1.81506	−0.907529	−	0.419989i	$-0.862034\pi$
$947$	−55.8555	−1.81506	−0.907529	+	0.419989i	$0.862034\pi$
$948$	39.9637	1.29796
$949$	−42.7518	−1.38778
$950$	−1.14352	−0.0371006
$951$	41.3630	1.34129
$952$	−11.5314	−0.373734
$953$	−3.16525	−0.102532	−0.0512662	−	0.998685i	$-0.516326\pi$
$953$	−3.16525	−0.102532	−0.0512662	+	0.998685i	$0.516326\pi$
$954$	−33.2687	−1.07711
$955$	−51.7002	−1.67298
$956$	13.0163	0.420977
$957$	−142.620	−4.61026
$958$	25.1197	0.811581
$959$	−1.36916	−0.0442126
$960$	−6.55902	−0.211691
$961$	44.6265	1.43956
$962$	22.1101	0.712860
$963$	35.0400	1.12915
$964$	5.82107	0.187484
$965$	−57.0297	−1.83585
$966$	2.83010	0.0910570
$967$	51.7739	1.66494	0.832468	−	0.554074i	$-0.186927\pi$
$967$	51.7739	1.66494	0.832468	+	0.554074i	$0.186927\pi$
$968$	−15.9889	−0.513903
$969$	−153.509	−4.93142
$970$	9.72276	0.312179
$971$	−1.53206	−0.0491660	−0.0245830	−	0.999698i	$-0.507826\pi$
$971$	−1.53206	−0.0491660	−0.0245830	+	0.999698i	$0.507826\pi$
$972$	1.57804	0.0506156
$973$	−4.55498	−0.146026
$974$	35.2081	1.12814
$975$	−2.03413	−0.0651443
$976$	14.2348	0.455644
$977$	21.6749	0.693442	0.346721	−	0.937968i	$-0.387295\pi$
$977$	21.6749	0.693442	0.346721	+	0.937968i	$0.387295\pi$
$978$	17.3510	0.554825
$979$	16.7669	0.535872
$980$	−10.4941	−0.335220
$981$	−82.6982	−2.64035
$982$	12.4092	0.395993
$983$	−21.6432	−0.690311	−0.345156	−	0.938545i	$-0.612174\pi$
$983$	−21.6432	−0.690311	−0.345156	+	0.938545i	$0.612174\pi$
$984$	−12.7082	−0.405122
$985$	11.5193	0.367037
$986$	−71.1117	−2.26466
$987$	24.8136	0.789827
$988$	26.3594	0.838605
$989$	1.90549	0.0605912
$990$	67.4695	2.14432
$991$	−46.6232	−1.48103	−0.740517	−	0.672037i	$-0.765419\pi$
$991$	−46.6232	−1.48103	−0.740517	+	0.672037i	$0.765419\pi$
$992$	8.69635	0.276109
$993$	61.9923	1.96727
$994$	−1.49720	−0.0474884
$995$	18.9538	0.600875
$996$	35.9630	1.13953
$997$	1.28337	0.0406448	0.0203224	−	0.999793i	$-0.493531\pi$
$997$	1.28337	0.0406448	0.0203224	+	0.999793i	$0.493531\pi$
$998$	−8.93430	−0.282810
$999$	−48.4687	−1.53348

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4022.2.a.e.1.3	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4022.2.a.e.1.3	✓	46	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:	\( N \)	\(=\)	\( 4022 = 2 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4022.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.98506 q^{3} +1.00000 q^{4} +2.19729 q^{5} +2.98506 q^{6} -1.49134 q^{7} -1.00000 q^{8} +5.91056 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.98506 q^{3} +1.00000 q^{4} +2.19729 q^{5} +2.98506 q^{6} -1.49134 q^{7} -1.00000 q^{8} +5.91056 q^{9} -2.19729 q^{10} -5.19508 q^{11} -2.98506 q^{12} -3.96332 q^{13} +1.49134 q^{14} -6.55902 q^{15} +1.00000 q^{16} -7.73224 q^{17} -5.91056 q^{18} -6.65084 q^{19} +2.19729 q^{20} +4.45172 q^{21} +5.19508 q^{22} -0.635732 q^{23} +2.98506 q^{24} -0.171936 q^{25} +3.96332 q^{26} -8.68818 q^{27} -1.49134 q^{28} -9.19678 q^{29} +6.55902 q^{30} -8.69635 q^{31} -1.00000 q^{32} +15.5076 q^{33} +7.73224 q^{34} -3.27689 q^{35} +5.91056 q^{36} +5.57869 q^{37} +6.65084 q^{38} +11.8307 q^{39} -2.19729 q^{40} -4.25727 q^{41} -4.45172 q^{42} -2.99732 q^{43} -5.19508 q^{44} +12.9872 q^{45} +0.635732 q^{46} +5.57394 q^{47} -2.98506 q^{48} -4.77592 q^{49} +0.171936 q^{50} +23.0812 q^{51} -3.96332 q^{52} +5.62868 q^{53} +8.68818 q^{54} -11.4151 q^{55} +1.49134 q^{56} +19.8531 q^{57} +9.19678 q^{58} -4.65841 q^{59} -6.55902 q^{60} +14.2348 q^{61} +8.69635 q^{62} -8.81463 q^{63} +1.00000 q^{64} -8.70856 q^{65} -15.5076 q^{66} +4.18113 q^{67} -7.73224 q^{68} +1.89770 q^{69} +3.27689 q^{70} -1.00394 q^{71} -5.91056 q^{72} +10.7868 q^{73} -5.57869 q^{74} +0.513238 q^{75} -6.65084 q^{76} +7.74761 q^{77} -11.8307 q^{78} -13.3879 q^{79} +2.19729 q^{80} +8.20303 q^{81} +4.25727 q^{82} -12.0477 q^{83} +4.45172 q^{84} -16.9899 q^{85} +2.99732 q^{86} +27.4529 q^{87} +5.19508 q^{88} -3.22745 q^{89} -12.9872 q^{90} +5.91065 q^{91} -0.635732 q^{92} +25.9591 q^{93} -5.57394 q^{94} -14.6138 q^{95} +2.98506 q^{96} -4.42490 q^{97} +4.77592 q^{98} -30.7059 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 46 q^{2} + 8 q^{3} + 46 q^{4} + 14 q^{5} - 8 q^{6} + 28 q^{7} - 46 q^{8} + 58 q^{9}+O(q^{10}) \) 46 * q - 46 * q^2 + 8 * q^3 + 46 * q^4 + 14 * q^5 - 8 * q^6 + 28 * q^7 - 46 * q^8 + 58 * q^9	\( 46 q - 46 q^{2} + 8 q^{3} + 46 q^{4} + 14 q^{5} - 8 q^{6} + 28 q^{7} - 46 q^{8} + 58 q^{9} - 14 q^{10} - 6 q^{11} + 8 q^{12} + 37 q^{13} - 28 q^{14} + 9 q^{15} + 46 q^{16} + 6 q^{17} - 58 q^{18} + 18 q^{19} + 14 q^{20} + 19 q^{21} + 6 q^{22} - 4 q^{23} - 8 q^{24} + 86 q^{25} - 37 q^{26} + 32 q^{27} + 28 q^{28} + 15 q^{29} - 9 q^{30} + 18 q^{31} - 46 q^{32} + 37 q^{33} - 6 q^{34} - 2 q^{35} + 58 q^{36} + 74 q^{37} - 18 q^{38} - 3 q^{39} - 14 q^{40} - 18 q^{41} - 19 q^{42} + 25 q^{43} - 6 q^{44} + 94 q^{45} + 4 q^{46} + 18 q^{47} + 8 q^{48} + 92 q^{49} - 86 q^{50} - 10 q^{51} + 37 q^{52} + 17 q^{53} - 32 q^{54} + 37 q^{55} - 28 q^{56} + 43 q^{57} - 15 q^{58} - 24 q^{59} + 9 q^{60} + 46 q^{61} - 18 q^{62} + 80 q^{63} + 46 q^{64} + 24 q^{65} - 37 q^{66} + 61 q^{67} + 6 q^{68} + 59 q^{69} + 2 q^{70} - 8 q^{71} - 58 q^{72} + 101 q^{73} - 74 q^{74} + 34 q^{75} + 18 q^{76} + 40 q^{77} + 3 q^{78} + 9 q^{79} + 14 q^{80} + 58 q^{81} + 18 q^{82} + 18 q^{83} + 19 q^{84} + 60 q^{85} - 25 q^{86} + 20 q^{87} + 6 q^{88} - 25 q^{89} - 94 q^{90} + 51 q^{91} - 4 q^{92} + 63 q^{93} - 18 q^{94} - 31 q^{95} - 8 q^{96} + 76 q^{97} - 92 q^{98} + 21 q^{99}+O(q^{100}) \) 46 * q - 46 * q^2 + 8 * q^3 + 46 * q^4 + 14 * q^5 - 8 * q^6 + 28 * q^7 - 46 * q^8 + 58 * q^9 - 14 * q^10 - 6 * q^11 + 8 * q^12 + 37 * q^13 - 28 * q^14 + 9 * q^15 + 46 * q^16 + 6 * q^17 - 58 * q^18 + 18 * q^19 + 14 * q^20 + 19 * q^21 + 6 * q^22 - 4 * q^23 - 8 * q^24 + 86 * q^25 - 37 * q^26 + 32 * q^27 + 28 * q^28 + 15 * q^29 - 9 * q^30 + 18 * q^31 - 46 * q^32 + 37 * q^33 - 6 * q^34 - 2 * q^35 + 58 * q^36 + 74 * q^37 - 18 * q^38 - 3 * q^39 - 14 * q^40 - 18 * q^41 - 19 * q^42 + 25 * q^43 - 6 * q^44 + 94 * q^45 + 4 * q^46 + 18 * q^47 + 8 * q^48 + 92 * q^49 - 86 * q^50 - 10 * q^51 + 37 * q^52 + 17 * q^53 - 32 * q^54 + 37 * q^55 - 28 * q^56 + 43 * q^57 - 15 * q^58 - 24 * q^59 + 9 * q^60 + 46 * q^61 - 18 * q^62 + 80 * q^63 + 46 * q^64 + 24 * q^65 - 37 * q^66 + 61 * q^67 + 6 * q^68 + 59 * q^69 + 2 * q^70 - 8 * q^71 - 58 * q^72 + 101 * q^73 - 74 * q^74 + 34 * q^75 + 18 * q^76 + 40 * q^77 + 3 * q^78 + 9 * q^79 + 14 * q^80 + 58 * q^81 + 18 * q^82 + 18 * q^83 + 19 * q^84 + 60 * q^85 - 25 * q^86 + 20 * q^87 + 6 * q^88 - 25 * q^89 - 94 * q^90 + 51 * q^91 - 4 * q^92 + 63 * q^93 - 18 * q^94 - 31 * q^95 - 8 * q^96 + 76 * q^97 - 92 * q^98 + 21 * q^99

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