LMFDB - Embedded newform 6010.2.a.f.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6010,2,Mod(1,6010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.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:	$47.9900916148$
Analytic rank:	$1$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.214164 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.214164 q^{6} -0.767476 q^{7} +1.00000 q^{8} -2.95413 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.214164 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.214164 q^{6} -0.767476 q^{7} +1.00000 q^{8} -2.95413 q^{9} -1.00000 q^{10} -2.29961 q^{11} +0.214164 q^{12} +1.53341 q^{13} -0.767476 q^{14} -0.214164 q^{15} +1.00000 q^{16} +6.58116 q^{17} -2.95413 q^{18} +0.141080 q^{19} -1.00000 q^{20} -0.164366 q^{21} -2.29961 q^{22} +4.09169 q^{23} +0.214164 q^{24} +1.00000 q^{25} +1.53341 q^{26} -1.27516 q^{27} -0.767476 q^{28} -6.75043 q^{29} -0.214164 q^{30} -6.40308 q^{31} +1.00000 q^{32} -0.492493 q^{33} +6.58116 q^{34} +0.767476 q^{35} -2.95413 q^{36} -3.89916 q^{37} +0.141080 q^{38} +0.328402 q^{39} -1.00000 q^{40} +5.23965 q^{41} -0.164366 q^{42} -6.50349 q^{43} -2.29961 q^{44} +2.95413 q^{45} +4.09169 q^{46} -2.47004 q^{47} +0.214164 q^{48} -6.41098 q^{49} +1.00000 q^{50} +1.40945 q^{51} +1.53341 q^{52} +4.85069 q^{53} -1.27516 q^{54} +2.29961 q^{55} -0.767476 q^{56} +0.0302143 q^{57} -6.75043 q^{58} +7.23892 q^{59} -0.214164 q^{60} -11.3382 q^{61} -6.40308 q^{62} +2.26723 q^{63} +1.00000 q^{64} -1.53341 q^{65} -0.492493 q^{66} +0.700037 q^{67} +6.58116 q^{68} +0.876293 q^{69} +0.767476 q^{70} -14.0221 q^{71} -2.95413 q^{72} -2.91616 q^{73} -3.89916 q^{74} +0.214164 q^{75} +0.141080 q^{76} +1.76489 q^{77} +0.328402 q^{78} +2.70377 q^{79} -1.00000 q^{80} +8.58931 q^{81} +5.23965 q^{82} +8.87666 q^{83} -0.164366 q^{84} -6.58116 q^{85} -6.50349 q^{86} -1.44570 q^{87} -2.29961 q^{88} +1.87971 q^{89} +2.95413 q^{90} -1.17686 q^{91} +4.09169 q^{92} -1.37131 q^{93} -2.47004 q^{94} -0.141080 q^{95} +0.214164 q^{96} -1.02749 q^{97} -6.41098 q^{98} +6.79335 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9}+O(q^{10}) $ 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9	\( 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9} - 22 q^{10} - 4 q^{11} - 6 q^{12} - 20 q^{13} - 12 q^{14} + 6 q^{15} + 22 q^{16} - 23 q^{17} + 12 q^{18} + q^{19} - 22 q^{20} - 8 q^{21} - 4 q^{22} - 17 q^{23} - 6 q^{24} + 22 q^{25} - 20 q^{26} - 21 q^{27} - 12 q^{28} - 13 q^{29} + 6 q^{30} - 13 q^{31} + 22 q^{32} - 21 q^{33} - 23 q^{34} + 12 q^{35} + 12 q^{36} - 16 q^{37} + q^{38} - 4 q^{39} - 22 q^{40} - 31 q^{41} - 8 q^{42} - 9 q^{43} - 4 q^{44} - 12 q^{45} - 17 q^{46} - 41 q^{47} - 6 q^{48} - 6 q^{49} + 22 q^{50} - 7 q^{51} - 20 q^{52} - 15 q^{53} - 21 q^{54} + 4 q^{55} - 12 q^{56} - 26 q^{57} - 13 q^{58} - 32 q^{59} + 6 q^{60} - 22 q^{61} - 13 q^{62} - 55 q^{63} + 22 q^{64} + 20 q^{65} - 21 q^{66} - 19 q^{67} - 23 q^{68} - 37 q^{69} + 12 q^{70} - 36 q^{71} + 12 q^{72} - 47 q^{73} - 16 q^{74} - 6 q^{75} + q^{76} - 26 q^{77} - 4 q^{78} - 10 q^{79} - 22 q^{80} - 18 q^{81} - 31 q^{82} - 48 q^{83} - 8 q^{84} + 23 q^{85} - 9 q^{86} - 50 q^{87} - 4 q^{88} - 42 q^{89} - 12 q^{90} + 25 q^{91} - 17 q^{92} - 48 q^{93} - 41 q^{94} - q^{95} - 6 q^{96} - 67 q^{97} - 6 q^{98} - 3 q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9 - 22 * q^10 - 4 * q^11 - 6 * q^12 - 20 * q^13 - 12 * q^14 + 6 * q^15 + 22 * q^16 - 23 * q^17 + 12 * q^18 + q^19 - 22 * q^20 - 8 * q^21 - 4 * q^22 - 17 * q^23 - 6 * q^24 + 22 * q^25 - 20 * q^26 - 21 * q^27 - 12 * q^28 - 13 * q^29 + 6 * q^30 - 13 * q^31 + 22 * q^32 - 21 * q^33 - 23 * q^34 + 12 * q^35 + 12 * q^36 - 16 * q^37 + q^38 - 4 * q^39 - 22 * q^40 - 31 * q^41 - 8 * q^42 - 9 * q^43 - 4 * q^44 - 12 * q^45 - 17 * q^46 - 41 * q^47 - 6 * q^48 - 6 * q^49 + 22 * q^50 - 7 * q^51 - 20 * q^52 - 15 * q^53 - 21 * q^54 + 4 * q^55 - 12 * q^56 - 26 * q^57 - 13 * q^58 - 32 * q^59 + 6 * q^60 - 22 * q^61 - 13 * q^62 - 55 * q^63 + 22 * q^64 + 20 * q^65 - 21 * q^66 - 19 * q^67 - 23 * q^68 - 37 * q^69 + 12 * q^70 - 36 * q^71 + 12 * q^72 - 47 * q^73 - 16 * q^74 - 6 * q^75 + q^76 - 26 * q^77 - 4 * q^78 - 10 * q^79 - 22 * q^80 - 18 * q^81 - 31 * q^82 - 48 * q^83 - 8 * q^84 + 23 * q^85 - 9 * q^86 - 50 * q^87 - 4 * q^88 - 42 * q^89 - 12 * q^90 + 25 * q^91 - 17 * q^92 - 48 * q^93 - 41 * q^94 - q^95 - 6 * q^96 - 67 * q^97 - 6 * q^98 - 3 * 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
$3$	0.214164	0.123648	0.0618238	−	0.998087i	$-0.480308\pi$
$3$	0.214164	0.123648	0.0618238	+	0.998087i	$0.480308\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.214164	0.0874321
$7$	−0.767476	−0.290079	−0.145039	−	0.989426i	$-0.546331\pi$
$7$	−0.767476	−0.290079	−0.145039	+	0.989426i	$0.546331\pi$
$8$	1.00000	0.353553
$9$	−2.95413	−0.984711
$10$	−1.00000	−0.316228
$11$	−2.29961	−0.693358	−0.346679	−	0.937984i	$-0.612691\pi$
$11$	−2.29961	−0.693358	−0.346679	+	0.937984i	$0.612691\pi$
$12$	0.214164	0.0618238
$13$	1.53341	0.425292	0.212646	−	0.977129i	$-0.431792\pi$
$13$	1.53341	0.425292	0.212646	+	0.977129i	$0.431792\pi$
$14$	−0.767476	−0.205117
$15$	−0.214164	−0.0552969
$16$	1.00000	0.250000
$17$	6.58116	1.59616	0.798082	−	0.602548i	$-0.205848\pi$
$17$	6.58116	1.59616	0.798082	+	0.602548i	$0.205848\pi$
$18$	−2.95413	−0.696296
$19$	0.141080	0.0323661	0.0161830	−	0.999869i	$-0.494849\pi$
$19$	0.141080	0.0323661	0.0161830	+	0.999869i	$0.494849\pi$
$20$	−1.00000	−0.223607
$21$	−0.164366	−0.0358675
$22$	−2.29961	−0.490278
$23$	4.09169	0.853176	0.426588	−	0.904446i	$-0.359715\pi$
$23$	4.09169	0.853176	0.426588	+	0.904446i	$0.359715\pi$
$24$	0.214164	0.0437160
$25$	1.00000	0.200000
$26$	1.53341	0.300727
$27$	−1.27516	−0.245405
$28$	−0.767476	−0.145039
$29$	−6.75043	−1.25352	−0.626762	−	0.779211i	$-0.715620\pi$
$29$	−6.75043	−1.25352	−0.626762	+	0.779211i	$0.715620\pi$
$30$	−0.214164	−0.0391008
$31$	−6.40308	−1.15003	−0.575013	−	0.818144i	$-0.695003\pi$
$31$	−6.40308	−1.15003	−0.575013	+	0.818144i	$0.695003\pi$
$32$	1.00000	0.176777
$33$	−0.492493	−0.0857320
$34$	6.58116	1.12866
$35$	0.767476	0.129727
$36$	−2.95413	−0.492356
$37$	−3.89916	−0.641019	−0.320509	−	0.947245i	$-0.603854\pi$
$37$	−3.89916	−0.641019	−0.320509	+	0.947245i	$0.603854\pi$
$38$	0.141080	0.0228863
$39$	0.328402	0.0525864
$40$	−1.00000	−0.158114
$41$	5.23965	0.818296	0.409148	−	0.912468i	$-0.365826\pi$
$41$	5.23965	0.818296	0.409148	+	0.912468i	$0.365826\pi$
$42$	−0.164366	−0.0253622
$43$	−6.50349	−0.991774	−0.495887	−	0.868387i	$-0.665157\pi$
$43$	−6.50349	−0.991774	−0.495887	+	0.868387i	$0.665157\pi$
$44$	−2.29961	−0.346679
$45$	2.95413	0.440376
$46$	4.09169	0.603287
$47$	−2.47004	−0.360292	−0.180146	−	0.983640i	$-0.557657\pi$
$47$	−2.47004	−0.360292	−0.180146	+	0.983640i	$0.557657\pi$
$48$	0.214164	0.0309119
$49$	−6.41098	−0.915854
$50$	1.00000	0.141421
$51$	1.40945	0.197362
$52$	1.53341	0.212646
$53$	4.85069	0.666294	0.333147	−	0.942875i	$-0.391890\pi$
$53$	4.85069	0.666294	0.333147	+	0.942875i	$0.391890\pi$
$54$	−1.27516	−0.173527
$55$	2.29961	0.310079
$56$	−0.767476	−0.102558
$57$	0.0302143	0.00400199
$58$	−6.75043	−0.886375
$59$	7.23892	0.942428	0.471214	−	0.882019i	$-0.343816\pi$
$59$	7.23892	0.942428	0.471214	+	0.882019i	$0.343816\pi$
$60$	−0.214164	−0.0276485
$61$	−11.3382	−1.45171	−0.725854	−	0.687849i	$-0.758555\pi$
$61$	−11.3382	−1.45171	−0.725854	+	0.687849i	$0.758555\pi$
$62$	−6.40308	−0.813191
$63$	2.26723	0.285644
$64$	1.00000	0.125000
$65$	−1.53341	−0.190196
$66$	−0.492493	−0.0606217
$67$	0.700037	0.0855232	0.0427616	−	0.999085i	$-0.486384\pi$
$67$	0.700037	0.0855232	0.0427616	+	0.999085i	$0.486384\pi$
$68$	6.58116	0.798082
$69$	0.876293	0.105493
$70$	0.767476	0.0917309
$71$	−14.0221	−1.66412	−0.832059	−	0.554687i	$-0.812838\pi$
$71$	−14.0221	−1.66412	−0.832059	+	0.554687i	$0.812838\pi$
$72$	−2.95413	−0.348148
$73$	−2.91616	−0.341311	−0.170655	−	0.985331i	$-0.554588\pi$
$73$	−2.91616	−0.341311	−0.170655	+	0.985331i	$0.554588\pi$
$74$	−3.89916	−0.453269
$75$	0.214164	0.0247295
$76$	0.141080	0.0161830
$77$	1.76489	0.201128
$78$	0.328402	0.0371842
$79$	2.70377	0.304197	0.152099	−	0.988365i	$-0.451397\pi$
$79$	2.70377	0.304197	0.152099	+	0.988365i	$0.451397\pi$
$80$	−1.00000	−0.111803
$81$	8.58931	0.954368
$82$	5.23965	0.578623
$83$	8.87666	0.974340	0.487170	−	0.873307i	$-0.338029\pi$
$83$	8.87666	0.974340	0.487170	+	0.873307i	$0.338029\pi$
$84$	−0.164366	−0.0179338
$85$	−6.58116	−0.713827
$86$	−6.50349	−0.701290
$87$	−1.44570	−0.154995
$88$	−2.29961	−0.245139
$89$	1.87971	0.199249	0.0996243	−	0.995025i	$-0.468236\pi$
$89$	1.87971	0.199249	0.0996243	+	0.995025i	$0.468236\pi$
$90$	2.95413	0.311393
$91$	−1.17686	−0.123368
$92$	4.09169	0.426588
$93$	−1.37131	−0.142198
$94$	−2.47004	−0.254765
$95$	−0.141080	−0.0144745
$96$	0.214164	0.0218580
$97$	−1.02749	−0.104326	−0.0521631	−	0.998639i	$-0.516612\pi$
$97$	−1.02749	−0.104326	−0.0521631	+	0.998639i	$0.516612\pi$
$98$	−6.41098	−0.647607
$99$	6.79335	0.682757
$100$	1.00000	0.100000
$101$	−17.0922	−1.70073	−0.850367	−	0.526191i	$-0.823620\pi$
$101$	−17.0922	−1.70073	−0.850367	+	0.526191i	$0.823620\pi$
$102$	1.40945	0.139556
$103$	−13.8286	−1.36257	−0.681286	−	0.732018i	$-0.738579\pi$
$103$	−13.8286	−1.36257	−0.681286	+	0.732018i	$0.738579\pi$
$104$	1.53341	0.150363
$105$	0.164366	0.0160405
$106$	4.85069	0.471141
$107$	14.7988	1.43065	0.715327	−	0.698790i	$-0.246278\pi$
$107$	14.7988	1.43065	0.715327	+	0.698790i	$0.246278\pi$
$108$	−1.27516	−0.122702
$109$	−14.4991	−1.38876	−0.694381	−	0.719607i	$-0.744322\pi$
$109$	−14.4991	−1.38876	−0.694381	+	0.719607i	$0.744322\pi$
$110$	2.29961	0.219259
$111$	−0.835061	−0.0792605
$112$	−0.767476	−0.0725197
$113$	−16.5498	−1.55688	−0.778438	−	0.627721i	$-0.783988\pi$
$113$	−16.5498	−1.55688	−0.778438	+	0.627721i	$0.783988\pi$
$114$	0.0302143	0.00282983
$115$	−4.09169	−0.381552
$116$	−6.75043	−0.626762
$117$	−4.52991	−0.418790
$118$	7.23892	0.666397
$119$	−5.05088	−0.463013
$120$	−0.214164	−0.0195504
$121$	−5.71181	−0.519255
$122$	−11.3382	−1.02651
$123$	1.12215	0.101180
$124$	−6.40308	−0.575013
$125$	−1.00000	−0.0894427
$126$	2.26723	0.201981
$127$	4.99065	0.442849	0.221424	−	0.975178i	$-0.428929\pi$
$127$	4.99065	0.442849	0.221424	+	0.975178i	$0.428929\pi$
$128$	1.00000	0.0883883
$129$	−1.39281	−0.122630
$130$	−1.53341	−0.134489
$131$	−1.33777	−0.116882	−0.0584409	−	0.998291i	$-0.518613\pi$
$131$	−1.33777	−0.116882	−0.0584409	+	0.998291i	$0.518613\pi$
$132$	−0.492493	−0.0428660
$133$	−0.108276	−0.00938870
$134$	0.700037	0.0604740
$135$	1.27516	0.109748
$136$	6.58116	0.564329
$137$	16.3638	1.39806	0.699028	−	0.715095i	$-0.253616\pi$
$137$	16.3638	1.39806	0.699028	+	0.715095i	$0.253616\pi$
$138$	0.876293	0.0745950
$139$	−2.60926	−0.221315	−0.110657	−	0.993859i	$-0.535296\pi$
$139$	−2.60926	−0.221315	−0.110657	+	0.993859i	$0.535296\pi$
$140$	0.767476	0.0648636
$141$	−0.528993	−0.0445493
$142$	−14.0221	−1.17671
$143$	−3.52625	−0.294880
$144$	−2.95413	−0.246178
$145$	6.75043	0.560593
$146$	−2.91616	−0.241343
$147$	−1.37300	−0.113243
$148$	−3.89916	−0.320509
$149$	−18.6774	−1.53012	−0.765058	−	0.643962i	$-0.777290\pi$
$149$	−18.6774	−1.53012	−0.765058	+	0.643962i	$0.777290\pi$
$150$	0.214164	0.0174864
$151$	−14.8697	−1.21008	−0.605039	−	0.796196i	$-0.706843\pi$
$151$	−14.8697	−1.21008	−0.605039	+	0.796196i	$0.706843\pi$
$152$	0.141080	0.0114431
$153$	−19.4416	−1.57176
$154$	1.76489	0.142219
$155$	6.40308	0.514307
$156$	0.328402	0.0262932
$157$	4.44606	0.354834	0.177417	−	0.984136i	$-0.443226\pi$
$157$	4.44606	0.354834	0.177417	+	0.984136i	$0.443226\pi$
$158$	2.70377	0.215100
$159$	1.03884	0.0823857
$160$	−1.00000	−0.0790569
$161$	−3.14027	−0.247488
$162$	8.58931	0.674840
$163$	15.7480	1.23348	0.616740	−	0.787167i	$-0.288453\pi$
$163$	15.7480	1.23348	0.616740	+	0.787167i	$0.288453\pi$
$164$	5.23965	0.409148
$165$	0.492493	0.0383405
$166$	8.87666	0.688962
$167$	−7.11166	−0.550317	−0.275158	−	0.961399i	$-0.588730\pi$
$167$	−7.11166	−0.550317	−0.275158	+	0.961399i	$0.588730\pi$
$168$	−0.164366	−0.0126811
$169$	−10.6486	−0.819127
$170$	−6.58116	−0.504752
$171$	−0.416770	−0.0318712
$172$	−6.50349	−0.495887
$173$	−17.4361	−1.32564	−0.662822	−	0.748777i	$-0.730641\pi$
$173$	−17.4361	−1.32564	−0.662822	+	0.748777i	$0.730641\pi$
$174$	−1.44570	−0.109598
$175$	−0.767476	−0.0580157
$176$	−2.29961	−0.173339
$177$	1.55032	0.116529
$178$	1.87971	0.140890
$179$	−16.8771	−1.26145	−0.630727	−	0.776005i	$-0.717243\pi$
$179$	−16.8771	−1.26145	−0.630727	+	0.776005i	$0.717243\pi$
$180$	2.95413	0.220188
$181$	13.9388	1.03606	0.518030	−	0.855362i	$-0.326665\pi$
$181$	13.9388	1.03606	0.518030	+	0.855362i	$0.326665\pi$
$182$	−1.17686	−0.0872345
$183$	−2.42824	−0.179500
$184$	4.09169	0.301643
$185$	3.89916	0.286672
$186$	−1.37131	−0.100549
$187$	−15.1341	−1.10671
$188$	−2.47004	−0.180146
$189$	0.978656	0.0711867
$190$	−0.141080	−0.0102350
$191$	−18.9197	−1.36898	−0.684490	−	0.729022i	$-0.739975\pi$
$191$	−18.9197	−1.36898	−0.684490	+	0.729022i	$0.739975\pi$
$192$	0.214164	0.0154560
$193$	−11.1922	−0.805630	−0.402815	−	0.915281i	$-0.631968\pi$
$193$	−11.1922	−0.805630	−0.402815	+	0.915281i	$0.631968\pi$
$194$	−1.02749	−0.0737698
$195$	−0.328402	−0.0235173
$196$	−6.41098	−0.457927
$197$	−2.77560	−0.197754	−0.0988768	−	0.995100i	$-0.531525\pi$
$197$	−2.77560	−0.197754	−0.0988768	+	0.995100i	$0.531525\pi$
$198$	6.79335	0.482782
$199$	−17.5974	−1.24744	−0.623722	−	0.781646i	$-0.714380\pi$
$199$	−17.5974	−1.24744	−0.623722	+	0.781646i	$0.714380\pi$
$200$	1.00000	0.0707107
$201$	0.149923	0.0105747
$202$	−17.0922	−1.20260
$203$	5.18079	0.363620
$204$	1.40945	0.0986810
$205$	−5.23965	−0.365953
$206$	−13.8286	−0.963483
$207$	−12.0874	−0.840132
$208$	1.53341	0.106323
$209$	−0.324429	−0.0224412
$210$	0.164366	0.0113423
$211$	−7.90218	−0.544009	−0.272004	−	0.962296i	$-0.587687\pi$
$211$	−7.90218	−0.544009	−0.272004	+	0.962296i	$0.587687\pi$
$212$	4.85069	0.333147
$213$	−3.00303	−0.205764
$214$	14.7988	1.01163
$215$	6.50349	0.443535
$216$	−1.27516	−0.0867637
$217$	4.91421	0.333598
$218$	−14.4991	−0.982003
$219$	−0.624537	−0.0422023
$220$	2.29961	0.155039
$221$	10.0916	0.678836
$222$	−0.835061	−0.0560456
$223$	20.0550	1.34299	0.671493	−	0.741011i	$-0.265653\pi$
$223$	20.0550	1.34299	0.671493	+	0.741011i	$0.265653\pi$
$224$	−0.767476	−0.0512791
$225$	−2.95413	−0.196942
$226$	−16.5498	−1.10088
$227$	3.55781	0.236140	0.118070	−	0.993005i	$-0.462329\pi$
$227$	3.55781	0.236140	0.118070	+	0.993005i	$0.462329\pi$
$228$	0.0302143	0.00200099
$229$	14.7855	0.977051	0.488526	−	0.872550i	$-0.337535\pi$
$229$	14.7855	0.977051	0.488526	+	0.872550i	$0.337535\pi$
$230$	−4.09169	−0.269798
$231$	0.377977	0.0248690
$232$	−6.75043	−0.443188
$233$	21.2368	1.39127	0.695634	−	0.718396i	$-0.255123\pi$
$233$	21.2368	1.39127	0.695634	+	0.718396i	$0.255123\pi$
$234$	−4.52991	−0.296129
$235$	2.47004	0.161127
$236$	7.23892	0.471214
$237$	0.579049	0.0376133
$238$	−5.05088	−0.327400
$239$	−26.3286	−1.70305	−0.851527	−	0.524311i	$-0.824323\pi$
$239$	−26.3286	−1.70305	−0.851527	+	0.524311i	$0.824323\pi$
$240$	−0.214164	−0.0138242
$241$	−2.69730	−0.173748	−0.0868740	−	0.996219i	$-0.527688\pi$
$241$	−2.69730	−0.173748	−0.0868740	+	0.996219i	$0.527688\pi$
$242$	−5.71181	−0.367169
$243$	5.66500	0.363410
$244$	−11.3382	−0.725854
$245$	6.41098	0.409583
$246$	1.12215	0.0715454
$247$	0.216334	0.0137650
$248$	−6.40308	−0.406596
$249$	1.90106	0.120475
$250$	−1.00000	−0.0632456
$251$	−10.9686	−0.692333	−0.346167	−	0.938173i	$-0.612517\pi$
$251$	−10.9686	−0.692333	−0.346167	+	0.938173i	$0.612517\pi$
$252$	2.26723	0.142822
$253$	−9.40928	−0.591556
$254$	4.99065	0.313141
$255$	−1.40945	−0.0882630
$256$	1.00000	0.0625000
$257$	−8.48254	−0.529126	−0.264563	−	0.964368i	$-0.585228\pi$
$257$	−8.48254	−0.529126	−0.264563	+	0.964368i	$0.585228\pi$
$258$	−1.39281	−0.0867128
$259$	2.99252	0.185946
$260$	−1.53341	−0.0950982
$261$	19.9417	1.23436
$262$	−1.33777	−0.0826479
$263$	19.0872	1.17697	0.588485	−	0.808508i	$-0.299725\pi$
$263$	19.0872	1.17697	0.588485	+	0.808508i	$0.299725\pi$
$264$	−0.492493	−0.0303109
$265$	−4.85069	−0.297976
$266$	−0.108276	−0.00663882
$267$	0.402566	0.0246366
$268$	0.700037	0.0427616
$269$	9.10594	0.555199	0.277599	−	0.960697i	$-0.410461\pi$
$269$	9.10594	0.555199	0.277599	+	0.960697i	$0.410461\pi$
$270$	1.27516	0.0776038
$271$	28.8738	1.75396	0.876980	−	0.480527i	$-0.159555\pi$
$271$	28.8738	1.75396	0.876980	+	0.480527i	$0.159555\pi$
$272$	6.58116	0.399041
$273$	−0.252041	−0.0152542
$274$	16.3638	0.988575
$275$	−2.29961	−0.138672
$276$	0.876293	0.0527466
$277$	19.7393	1.18602	0.593011	−	0.805194i	$-0.297939\pi$
$277$	19.7393	1.18602	0.593011	+	0.805194i	$0.297939\pi$
$278$	−2.60926	−0.156493
$279$	18.9155	1.13244
$280$	0.767476	0.0458655
$281$	−16.1264	−0.962022	−0.481011	−	0.876715i	$-0.659730\pi$
$281$	−16.1264	−0.962022	−0.481011	+	0.876715i	$0.659730\pi$
$282$	−0.528993	−0.0315011
$283$	12.8593	0.764404	0.382202	−	0.924079i	$-0.375166\pi$
$283$	12.8593	0.764404	0.382202	+	0.924079i	$0.375166\pi$
$284$	−14.0221	−0.832059
$285$	−0.0302143	−0.00178974
$286$	−3.52625	−0.208511
$287$	−4.02131	−0.237370
$288$	−2.95413	−0.174074
$289$	26.3116	1.54774
$290$	6.75043	0.396399
$291$	−0.220052	−0.0128997
$292$	−2.91616	−0.170655
$293$	−27.4928	−1.60615	−0.803074	−	0.595880i	$-0.796804\pi$
$293$	−27.4928	−1.60615	−0.803074	+	0.595880i	$0.796804\pi$
$294$	−1.37300	−0.0800751
$295$	−7.23892	−0.421466
$296$	−3.89916	−0.226634
$297$	2.93237	0.170153
$298$	−18.6774	−1.08196
$299$	6.27425	0.362849
$300$	0.214164	0.0123648
$301$	4.99128	0.287692
$302$	−14.8697	−0.855655
$303$	−3.66053	−0.210292
$304$	0.141080	0.00809151
$305$	11.3382	0.649224
$306$	−19.4416	−1.11140
$307$	2.52271	0.143978	0.0719892	−	0.997405i	$-0.477065\pi$
$307$	2.52271	0.143978	0.0719892	+	0.997405i	$0.477065\pi$
$308$	1.76489	0.100564
$309$	−2.96159	−0.168479
$310$	6.40308	0.363670
$311$	24.6606	1.39838	0.699188	−	0.714938i	$-0.253545\pi$
$311$	24.6606	1.39838	0.699188	+	0.714938i	$0.253545\pi$
$312$	0.328402	0.0185921
$313$	−18.4526	−1.04300	−0.521502	−	0.853250i	$-0.674628\pi$
$313$	−18.4526	−1.04300	−0.521502	+	0.853250i	$0.674628\pi$
$314$	4.44606	0.250906
$315$	−2.26723	−0.127744
$316$	2.70377	0.152099
$317$	7.87408	0.442253	0.221126	−	0.975245i	$-0.429027\pi$
$317$	7.87408	0.442253	0.221126	+	0.975245i	$0.429027\pi$
$318$	1.03884	0.0582555
$319$	15.5233	0.869140
$320$	−1.00000	−0.0559017
$321$	3.16937	0.176897
$322$	−3.14027	−0.175001
$323$	0.928472	0.0516616
$324$	8.58931	0.477184
$325$	1.53341	0.0850584
$326$	15.7480	0.872202
$327$	−3.10519	−0.171717
$328$	5.23965	0.289311
$329$	1.89569	0.104513
$330$	0.492493	0.0271108
$331$	−20.2301	−1.11195	−0.555974	−	0.831200i	$-0.687655\pi$
$331$	−20.2301	−1.11195	−0.555974	+	0.831200i	$0.687655\pi$
$332$	8.87666	0.487170
$333$	11.5187	0.631218
$334$	−7.11166	−0.389133
$335$	−0.700037	−0.0382471
$336$	−0.164366	−0.00896689
$337$	−16.6202	−0.905361	−0.452680	−	0.891673i	$-0.649532\pi$
$337$	−16.6202	−0.905361	−0.452680	+	0.891673i	$0.649532\pi$
$338$	−10.6486	−0.579210
$339$	−3.54438	−0.192504
$340$	−6.58116	−0.356913
$341$	14.7246	0.797379
$342$	−0.416770	−0.0225364
$343$	10.2926	0.555748
$344$	−6.50349	−0.350645
$345$	−0.876293	−0.0471780
$346$	−17.4361	−0.937371
$347$	−0.786632	−0.0422286	−0.0211143	−	0.999777i	$-0.506721\pi$
$347$	−0.786632	−0.0422286	−0.0211143	+	0.999777i	$0.506721\pi$
$348$	−1.44570	−0.0774976
$349$	33.0526	1.76927	0.884633	−	0.466287i	$-0.154409\pi$
$349$	33.0526	1.76927	0.884633	+	0.466287i	$0.154409\pi$
$350$	−0.767476	−0.0410233
$351$	−1.95535	−0.104369
$352$	−2.29961	−0.122569
$353$	4.78149	0.254493	0.127247	−	0.991871i	$-0.459386\pi$
$353$	4.78149	0.254493	0.127247	+	0.991871i	$0.459386\pi$
$354$	1.55032	0.0823984
$355$	14.0221	0.744216
$356$	1.87971	0.0996243
$357$	−1.08172	−0.0572505
$358$	−16.8771	−0.891983
$359$	−12.3774	−0.653256	−0.326628	−	0.945153i	$-0.605912\pi$
$359$	−12.3774	−0.653256	−0.326628	+	0.945153i	$0.605912\pi$
$360$	2.95413	0.155697
$361$	−18.9801	−0.998952
$362$	13.9388	0.732606
$363$	−1.22326	−0.0642047
$364$	−1.17686	−0.0616841
$365$	2.91616	0.152639
$366$	−2.42824	−0.126926
$367$	−0.192024	−0.0100236	−0.00501178	−	0.999987i	$-0.501595\pi$
$367$	−0.192024	−0.0100236	−0.00501178	+	0.999987i	$0.501595\pi$
$368$	4.09169	0.213294
$369$	−15.4786	−0.805786
$370$	3.89916	0.202708
$371$	−3.72279	−0.193278
$372$	−1.37131	−0.0710990
$373$	0.883516	0.0457467	0.0228734	−	0.999738i	$-0.492719\pi$
$373$	0.883516	0.0457467	0.0228734	+	0.999738i	$0.492719\pi$
$374$	−15.1341	−0.782564
$375$	−0.214164	−0.0110594
$376$	−2.47004	−0.127382
$377$	−10.3512	−0.533114
$378$	0.978656	0.0503366
$379$	20.9080	1.07397	0.536985	−	0.843592i	$-0.319563\pi$
$379$	20.9080	1.07397	0.536985	+	0.843592i	$0.319563\pi$
$380$	−0.141080	−0.00723727
$381$	1.06882	0.0547572
$382$	−18.9197	−0.968015
$383$	−10.8357	−0.553681	−0.276840	−	0.960916i	$-0.589287\pi$
$383$	−10.8357	−0.553681	−0.276840	+	0.960916i	$0.589287\pi$
$384$	0.214164	0.0109290
$385$	−1.76489	−0.0899473
$386$	−11.1922	−0.569667
$387$	19.2122	0.976611
$388$	−1.02749	−0.0521631
$389$	10.1295	0.513588	0.256794	−	0.966466i	$-0.417334\pi$
$389$	10.1295	0.513588	0.256794	+	0.966466i	$0.417334\pi$
$390$	−0.328402	−0.0166293
$391$	26.9280	1.36181
$392$	−6.41098	−0.323803
$393$	−0.286503	−0.0144522
$394$	−2.77560	−0.139833
$395$	−2.70377	−0.136041
$396$	6.79335	0.341378
$397$	39.2809	1.97145	0.985726	−	0.168358i	$-0.0538465\pi$
$397$	39.2809	1.97145	0.985726	+	0.168358i	$0.0538465\pi$
$398$	−17.5974	−0.882076
$399$	−0.0231888	−0.00116089
$400$	1.00000	0.0500000
$401$	−11.8064	−0.589582	−0.294791	−	0.955562i	$-0.595250\pi$
$401$	−11.8064	−0.589582	−0.294791	+	0.955562i	$0.595250\pi$
$402$	0.149923	0.00747747
$403$	−9.81856	−0.489097
$404$	−17.0922	−0.850367
$405$	−8.58931	−0.426806
$406$	5.18079	0.257119
$407$	8.96655	0.444455
$408$	1.40945	0.0697780
$409$	11.1008	0.548899	0.274449	−	0.961602i	$-0.411504\pi$
$409$	11.1008	0.548899	0.274449	+	0.961602i	$0.411504\pi$
$410$	−5.23965	−0.258768
$411$	3.50454	0.172866
$412$	−13.8286	−0.681286
$413$	−5.55570	−0.273378
$414$	−12.0874	−0.594063
$415$	−8.87666	−0.435738
$416$	1.53341	0.0751817
$417$	−0.558810	−0.0273651
$418$	−0.324429	−0.0158684
$419$	35.1252	1.71598	0.857990	−	0.513666i	$-0.171713\pi$
$419$	35.1252	1.71598	0.857990	+	0.513666i	$0.171713\pi$
$420$	0.164366	0.00802023
$421$	2.49017	0.121364	0.0606818	−	0.998157i	$-0.480673\pi$
$421$	2.49017	0.121364	0.0606818	+	0.998157i	$0.480673\pi$
$422$	−7.90218	−0.384672
$423$	7.29682	0.354784
$424$	4.85069	0.235570
$425$	6.58116	0.319233
$426$	−3.00303	−0.145497
$427$	8.70180	0.421110
$428$	14.7988	0.715327
$429$	−0.755195	−0.0364612
$430$	6.50349	0.313626
$431$	6.27077	0.302053	0.151026	−	0.988530i	$-0.451742\pi$
$431$	6.27077	0.302053	0.151026	+	0.988530i	$0.451742\pi$
$432$	−1.27516	−0.0613512
$433$	20.2600	0.973632	0.486816	−	0.873504i	$-0.338158\pi$
$433$	20.2600	0.973632	0.486816	+	0.873504i	$0.338158\pi$
$434$	4.91421	0.235889
$435$	1.44570	0.0693160
$436$	−14.4991	−0.694381
$437$	0.577257	0.0276139
$438$	−0.624537	−0.0298415
$439$	34.8540	1.66349	0.831745	−	0.555158i	$-0.187342\pi$
$439$	34.8540	1.66349	0.831745	+	0.555158i	$0.187342\pi$
$440$	2.29961	0.109629
$441$	18.9389	0.901852
$442$	10.0916	0.480010
$443$	−2.28872	−0.108741	−0.0543703	−	0.998521i	$-0.517315\pi$
$443$	−2.28872	−0.108741	−0.0543703	+	0.998521i	$0.517315\pi$
$444$	−0.835061	−0.0396302
$445$	−1.87971	−0.0891067
$446$	20.0550	0.949634
$447$	−4.00004	−0.189195
$448$	−0.767476	−0.0362598
$449$	−31.2025	−1.47254	−0.736269	−	0.676688i	$-0.763414\pi$
$449$	−31.2025	−1.47254	−0.736269	+	0.676688i	$0.763414\pi$
$450$	−2.95413	−0.139259
$451$	−12.0491	−0.567372
$452$	−16.5498	−0.778438
$453$	−3.18455	−0.149623
$454$	3.55781	0.166976
$455$	1.17686	0.0551719
$456$	0.0302143	0.00141492
$457$	−33.8674	−1.58425	−0.792125	−	0.610359i	$-0.791025\pi$
$457$	−33.8674	−1.58425	−0.792125	+	0.610359i	$0.791025\pi$
$458$	14.7855	0.690880
$459$	−8.39203	−0.391707
$460$	−4.09169	−0.190776
$461$	25.9766	1.20985	0.604926	−	0.796282i	$-0.293203\pi$
$461$	25.9766	1.20985	0.604926	+	0.796282i	$0.293203\pi$
$462$	0.377977	0.0175851
$463$	−31.1425	−1.44731	−0.723657	−	0.690160i	$-0.757540\pi$
$463$	−31.1425	−1.44731	−0.723657	+	0.690160i	$0.757540\pi$
$464$	−6.75043	−0.313381
$465$	1.37131	0.0635929
$466$	21.2368	0.983776
$467$	2.09776	0.0970727	0.0485364	−	0.998821i	$-0.484544\pi$
$467$	2.09776	0.0970727	0.0485364	+	0.998821i	$0.484544\pi$
$468$	−4.52991	−0.209395
$469$	−0.537262	−0.0248085
$470$	2.47004	0.113934
$471$	0.952185	0.0438744
$472$	7.23892	0.333198
$473$	14.9555	0.687654
$474$	0.579049	0.0265966
$475$	0.141080	0.00647321
$476$	−5.05088	−0.231507
$477$	−14.3296	−0.656107
$478$	−26.3286	−1.20424
$479$	−1.16273	−0.0531267	−0.0265634	−	0.999647i	$-0.508456\pi$
$479$	−1.16273	−0.0531267	−0.0265634	+	0.999647i	$0.508456\pi$
$480$	−0.214164	−0.00977521
$481$	−5.97903	−0.272620
$482$	−2.69730	−0.122858
$483$	−0.672534	−0.0306013
$484$	−5.71181	−0.259628
$485$	1.02749	0.0466561
$486$	5.66500	0.256970
$487$	10.7664	0.487872	0.243936	−	0.969791i	$-0.421561\pi$
$487$	10.7664	0.487872	0.243936	+	0.969791i	$0.421561\pi$
$488$	−11.3382	−0.513256
$489$	3.37266	0.152517
$490$	6.41098	0.289619
$491$	−34.8828	−1.57424	−0.787119	−	0.616801i	$-0.788428\pi$
$491$	−34.8828	−1.57424	−0.787119	+	0.616801i	$0.788428\pi$
$492$	1.12215	0.0505902
$493$	−44.4256	−2.00083
$494$	0.216334	0.00973335
$495$	−6.79335	−0.305338
$496$	−6.40308	−0.287507
$497$	10.7616	0.482725
$498$	1.90106	0.0851886
$499$	24.1806	1.08247	0.541236	−	0.840871i	$-0.317957\pi$
$499$	24.1806	1.08247	0.541236	+	0.840871i	$0.317957\pi$
$500$	−1.00000	−0.0447214
$501$	−1.52306	−0.0680454
$502$	−10.9686	−0.489554
$503$	−21.5096	−0.959064	−0.479532	−	0.877524i	$-0.659194\pi$
$503$	−21.5096	−0.959064	−0.479532	+	0.877524i	$0.659194\pi$
$504$	2.26723	0.100990
$505$	17.0922	0.760591
$506$	−9.40928	−0.418293
$507$	−2.28056	−0.101283
$508$	4.99065	0.221424
$509$	−32.2832	−1.43093	−0.715465	−	0.698649i	$-0.753785\pi$
$509$	−32.2832	−1.43093	−0.715465	+	0.698649i	$0.753785\pi$
$510$	−1.40945	−0.0624113
$511$	2.23808	0.0990070
$512$	1.00000	0.0441942
$513$	−0.179900	−0.00794279
$514$	−8.48254	−0.374149
$515$	13.8286	0.609360
$516$	−1.39281	−0.0613152
$517$	5.68011	0.249811
$518$	2.99252	0.131484
$519$	−3.73419	−0.163913
$520$	−1.53341	−0.0672446
$521$	22.3673	0.979931	0.489965	−	0.871742i	$-0.337009\pi$
$521$	22.3673	0.979931	0.489965	+	0.871742i	$0.337009\pi$
$522$	19.9417	0.872824
$523$	−13.5972	−0.594564	−0.297282	−	0.954790i	$-0.596080\pi$
$523$	−13.5972	−0.594564	−0.297282	+	0.954790i	$0.596080\pi$
$524$	−1.33777	−0.0584409
$525$	−0.164366	−0.00717351
$526$	19.0872	0.832243
$527$	−42.1396	−1.83563
$528$	−0.492493	−0.0214330
$529$	−6.25808	−0.272090
$530$	−4.85069	−0.210701
$531$	−21.3847	−0.928019
$532$	−0.108276	−0.00469435
$533$	8.03455	0.348015
$534$	0.402566	0.0174207
$535$	−14.7988	−0.639808
$536$	0.700037	0.0302370
$537$	−3.61447	−0.155976
$538$	9.10594	0.392585
$539$	14.7427	0.635015
$540$	1.27516	0.0548742
$541$	33.0358	1.42032	0.710161	−	0.704040i	$-0.248622\pi$
$541$	33.0358	1.42032	0.710161	+	0.704040i	$0.248622\pi$
$542$	28.8738	1.24024
$543$	2.98518	0.128106
$544$	6.58116	0.282165
$545$	14.4991	0.621073
$546$	−0.252041	−0.0107863
$547$	11.7521	0.502484	0.251242	−	0.967924i	$-0.419161\pi$
$547$	11.7521	0.502484	0.251242	+	0.967924i	$0.419161\pi$
$548$	16.3638	0.699028
$549$	33.4946	1.42951
$550$	−2.29961	−0.0980556
$551$	−0.952353	−0.0405716
$552$	0.876293	0.0372975
$553$	−2.07508	−0.0882412
$554$	19.7393	0.838644
$555$	0.835061	0.0354464
$556$	−2.60926	−0.110657
$557$	−29.0742	−1.23191	−0.615956	−	0.787780i	$-0.711230\pi$
$557$	−29.0742	−1.23191	−0.615956	+	0.787780i	$0.711230\pi$
$558$	18.9155	0.800759
$559$	−9.97254	−0.421793
$560$	0.767476	0.0324318
$561$	−3.24117	−0.136842
$562$	−16.1264	−0.680252
$563$	0.815164	0.0343550	0.0171775	−	0.999852i	$-0.494532\pi$
$563$	0.815164	0.0343550	0.0171775	+	0.999852i	$0.494532\pi$
$564$	−0.528993	−0.0222746
$565$	16.5498	0.696257
$566$	12.8593	0.540515
$567$	−6.59209	−0.276842
$568$	−14.0221	−0.588355
$569$	−19.0270	−0.797655	−0.398827	−	0.917026i	$-0.630583\pi$
$569$	−19.0270	−0.797655	−0.398827	+	0.917026i	$0.630583\pi$
$570$	−0.0302143	−0.00126554
$571$	−1.47470	−0.0617144	−0.0308572	−	0.999524i	$-0.509824\pi$
$571$	−1.47470	−0.0617144	−0.0308572	+	0.999524i	$0.509824\pi$
$572$	−3.52625	−0.147440
$573$	−4.05192	−0.169271
$574$	−4.02131	−0.167846
$575$	4.09169	0.170635
$576$	−2.95413	−0.123089
$577$	21.9902	0.915463	0.457732	−	0.889090i	$-0.348662\pi$
$577$	21.9902	0.915463	0.457732	+	0.889090i	$0.348662\pi$
$578$	26.3116	1.09442
$579$	−2.39696	−0.0996143
$580$	6.75043	0.280296
$581$	−6.81262	−0.282635
$582$	−0.220052	−0.00912146
$583$	−11.1547	−0.461980
$584$	−2.91616	−0.120672
$585$	4.52991	0.187289
$586$	−27.4928	−1.13572
$587$	15.7071	0.648303	0.324151	−	0.946005i	$-0.394921\pi$
$587$	15.7071	0.648303	0.324151	+	0.946005i	$0.394921\pi$
$588$	−1.37300	−0.0566216
$589$	−0.903348	−0.0372218
$590$	−7.23892	−0.298022
$591$	−0.594435	−0.0244518
$592$	−3.89916	−0.160255
$593$	−44.3987	−1.82324	−0.911618	−	0.411039i	$-0.865166\pi$
$593$	−44.3987	−1.82324	−0.911618	+	0.411039i	$0.865166\pi$
$594$	2.93237	0.120317
$595$	5.05088	0.207066
$596$	−18.6774	−0.765058
$597$	−3.76872	−0.154244
$598$	6.27425	0.256573
$599$	−26.5065	−1.08303	−0.541514	−	0.840692i	$-0.682149\pi$
$599$	−26.5065	−1.08303	−0.541514	+	0.840692i	$0.682149\pi$
$600$	0.214164	0.00874321
$601$	1.00000	0.0407909
$601$	1.00000	0.0407909
$602$	4.99128	0.203429
$603$	−2.06800	−0.0842156
$604$	−14.8697	−0.605039
$605$	5.71181	0.232218
$606$	−3.66053	−0.148699
$607$	10.7817	0.437615	0.218807	−	0.975768i	$-0.429783\pi$
$607$	10.7817	0.437615	0.218807	+	0.975768i	$0.429783\pi$
$608$	0.141080	0.00572156
$609$	1.10954	0.0449608
$610$	11.3382	0.459071
$611$	−3.78759	−0.153229
$612$	−19.4416	−0.785881
$613$	11.4744	0.463446	0.231723	−	0.972782i	$-0.425564\pi$
$613$	11.4744	0.463446	0.231723	+	0.972782i	$0.425564\pi$
$614$	2.52271	0.101808
$615$	−1.12215	−0.0452493
$616$	1.76489	0.0711096
$617$	−9.74877	−0.392471	−0.196235	−	0.980557i	$-0.562872\pi$
$617$	−9.74877	−0.392471	−0.196235	+	0.980557i	$0.562872\pi$
$618$	−2.96159	−0.119132
$619$	−8.38150	−0.336881	−0.168440	−	0.985712i	$-0.553873\pi$
$619$	−8.38150	−0.336881	−0.168440	+	0.985712i	$0.553873\pi$
$620$	6.40308	0.257154
$621$	−5.21756	−0.209374
$622$	24.6606	0.988801
$623$	−1.44263	−0.0577978
$624$	0.328402	0.0131466
$625$	1.00000	0.0400000
$626$	−18.4526	−0.737515
$627$	−0.0694811	−0.00277481
$628$	4.44606	0.177417
$629$	−25.6610	−1.02317
$630$	−2.26723	−0.0903285
$631$	9.22432	0.367215	0.183607	−	0.983000i	$-0.441223\pi$
$631$	9.22432	0.367215	0.183607	+	0.983000i	$0.441223\pi$
$632$	2.70377	0.107550
$633$	−1.69236	−0.0672654
$634$	7.87408	0.312720
$635$	−4.99065	−0.198048
$636$	1.03884	0.0411928
$637$	−9.83068	−0.389506
$638$	15.5233	0.614575
$639$	41.4232	1.63868
$640$	−1.00000	−0.0395285
$641$	−10.7661	−0.425237	−0.212618	−	0.977135i	$-0.568199\pi$
$641$	−10.7661	−0.425237	−0.212618	+	0.977135i	$0.568199\pi$
$642$	3.16937	0.125085
$643$	−17.0985	−0.674299	−0.337150	−	0.941451i	$-0.609463\pi$
$643$	−17.0985	−0.674299	−0.337150	+	0.941451i	$0.609463\pi$
$644$	−3.14027	−0.123744
$645$	1.39281	0.0548420
$646$	0.928472	0.0365302
$647$	−9.34614	−0.367435	−0.183717	−	0.982979i	$-0.558813\pi$
$647$	−9.34614	−0.367435	−0.183717	+	0.982979i	$0.558813\pi$
$648$	8.58931	0.337420
$649$	−16.6467	−0.653439
$650$	1.53341	0.0601454
$651$	1.05245	0.0412486
$652$	15.7480	0.616740
$653$	23.6235	0.924458	0.462229	−	0.886761i	$-0.347050\pi$
$653$	23.6235	0.924458	0.462229	+	0.886761i	$0.347050\pi$
$654$	−3.10519	−0.121422
$655$	1.33777	0.0522711
$656$	5.23965	0.204574
$657$	8.61473	0.336093
$658$	1.89569	0.0739019
$659$	33.2843	1.29657	0.648285	−	0.761397i	$-0.275486\pi$
$659$	33.2843	1.29657	0.648285	+	0.761397i	$0.275486\pi$
$660$	0.492493	0.0191703
$661$	−5.47434	−0.212927	−0.106464	−	0.994317i	$-0.533953\pi$
$661$	−5.47434	−0.212927	−0.106464	+	0.994317i	$0.533953\pi$
$662$	−20.2301	−0.786266
$663$	2.16126	0.0839365
$664$	8.87666	0.344481
$665$	0.108276	0.00419876
$666$	11.5187	0.446339
$667$	−27.6207	−1.06948
$668$	−7.11166	−0.275158
$669$	4.29507	0.166057
$670$	−0.700037	−0.0270448
$671$	26.0734	1.00655
$672$	−0.164366	−0.00634055
$673$	36.0258	1.38869	0.694346	−	0.719641i	$-0.255694\pi$
$673$	36.0258	1.38869	0.694346	+	0.719641i	$0.255694\pi$
$674$	−16.6202	−0.640187
$675$	−1.27516	−0.0490810
$676$	−10.6486	−0.409563
$677$	18.0366	0.693202	0.346601	−	0.938013i	$-0.387336\pi$
$677$	18.0366	0.693202	0.346601	+	0.938013i	$0.387336\pi$
$678$	−3.54438	−0.136121
$679$	0.788577	0.0302628
$680$	−6.58116	−0.252376
$681$	0.761954	0.0291982
$682$	14.7246	0.563832
$683$	44.3782	1.69808	0.849042	−	0.528326i	$-0.177180\pi$
$683$	44.3782	1.69808	0.849042	+	0.528326i	$0.177180\pi$
$684$	−0.416770	−0.0159356
$685$	−16.3638	−0.625229
$686$	10.2926	0.392974
$687$	3.16652	0.120810
$688$	−6.50349	−0.247943
$689$	7.43811	0.283369
$690$	−0.876293	−0.0333599
$691$	9.05744	0.344561	0.172281	−	0.985048i	$-0.444886\pi$
$691$	9.05744	0.344561	0.172281	+	0.985048i	$0.444886\pi$
$692$	−17.4361	−0.662822
$693$	−5.21373	−0.198053
$694$	−0.786632	−0.0298602
$695$	2.60926	0.0989750
$696$	−1.44570	−0.0547991
$697$	34.4830	1.30614
$698$	33.0526	1.25106
$699$	4.54816	0.172027
$700$	−0.767476	−0.0290079
$701$	15.0444	0.568217	0.284109	−	0.958792i	$-0.408302\pi$
$701$	15.0444	0.568217	0.284109	+	0.958792i	$0.408302\pi$
$702$	−1.95535	−0.0737999
$703$	−0.550096	−0.0207472
$704$	−2.29961	−0.0866697
$705$	0.528993	0.0199230
$706$	4.78149	0.179954
$707$	13.1178	0.493346
$708$	1.55032	0.0582645
$709$	−6.73810	−0.253055	−0.126527	−	0.991963i	$-0.540383\pi$
$709$	−6.73810	−0.253055	−0.126527	+	0.991963i	$0.540383\pi$
$710$	14.0221	0.526240
$711$	−7.98729	−0.299547
$712$	1.87971	0.0704450
$713$	−26.1994	−0.981175
$714$	−1.08172	−0.0404822
$715$	3.52625	0.131874
$716$	−16.8771	−0.630727
$717$	−5.63863	−0.210579
$718$	−12.3774	−0.461922
$719$	24.1823	0.901848	0.450924	−	0.892562i	$-0.351094\pi$
$719$	24.1823	0.901848	0.450924	+	0.892562i	$0.351094\pi$
$720$	2.95413	0.110094
$721$	10.6131	0.395253
$722$	−18.9801	−0.706366
$723$	−0.577664	−0.0214835
$724$	13.9388	0.518030
$725$	−6.75043	−0.250705
$726$	−1.22326	−0.0453996
$727$	−5.08549	−0.188610	−0.0943052	−	0.995543i	$-0.530063\pi$
$727$	−5.08549	−0.188610	−0.0943052	+	0.995543i	$0.530063\pi$
$728$	−1.17686	−0.0436172
$729$	−24.5547	−0.909433
$730$	2.91616	0.107932
$731$	−42.8005	−1.58303
$732$	−2.42824	−0.0897502
$733$	−39.6458	−1.46435	−0.732176	−	0.681115i	$-0.761495\pi$
$733$	−39.6458	−1.46435	−0.732176	+	0.681115i	$0.761495\pi$
$734$	−0.192024	−0.00708773
$735$	1.37300	0.0506439
$736$	4.09169	0.150822
$737$	−1.60981	−0.0592981
$738$	−15.4786	−0.569777
$739$	7.47560	0.274995	0.137497	−	0.990502i	$-0.456094\pi$
$739$	7.47560	0.274995	0.137497	+	0.990502i	$0.456094\pi$
$740$	3.89916	0.143336
$741$	0.0463310	0.00170201
$742$	−3.72279	−0.136668
$743$	−23.6404	−0.867284	−0.433642	−	0.901085i	$-0.642772\pi$
$743$	−23.6404	−0.867284	−0.433642	+	0.901085i	$0.642772\pi$
$744$	−1.37131	−0.0502746
$745$	18.6774	0.684289
$746$	0.883516	0.0323478
$747$	−26.2228	−0.959444
$748$	−15.1341	−0.553356
$749$	−11.3577	−0.415002
$750$	−0.214164	−0.00782016
$751$	36.4512	1.33012	0.665062	−	0.746788i	$-0.268405\pi$
$751$	36.4512	1.33012	0.665062	+	0.746788i	$0.268405\pi$
$752$	−2.47004	−0.0900730
$753$	−2.34908	−0.0856054
$754$	−10.3512	−0.376968
$755$	14.8697	0.541164
$756$	0.978656	0.0355934
$757$	21.3278	0.775173	0.387587	−	0.921833i	$-0.373309\pi$
$757$	21.3278	0.775173	0.387587	+	0.921833i	$0.373309\pi$
$758$	20.9080	0.759412
$759$	−2.01513	−0.0731445
$760$	−0.141080	−0.00511752
$761$	32.2041	1.16740	0.583698	−	0.811971i	$-0.301605\pi$
$761$	32.2041	1.16740	0.583698	+	0.811971i	$0.301605\pi$
$762$	1.06882	0.0387192
$763$	11.1277	0.402850
$764$	−18.9197	−0.684490
$765$	19.4416	0.702913
$766$	−10.8357	−0.391511
$767$	11.1003	0.400807
$768$	0.214164	0.00772798
$769$	3.16143	0.114004	0.0570020	−	0.998374i	$-0.481846\pi$
$769$	3.16143	0.114004	0.0570020	+	0.998374i	$0.481846\pi$
$770$	−1.76489	−0.0636023
$771$	−1.81665	−0.0654252
$772$	−11.1922	−0.402815
$773$	−27.4006	−0.985532	−0.492766	−	0.870162i	$-0.664014\pi$
$773$	−27.4006	−0.985532	−0.492766	+	0.870162i	$0.664014\pi$
$774$	19.2122	0.690568
$775$	−6.40308	−0.230005
$776$	−1.02749	−0.0368849
$777$	0.640889	0.0229918
$778$	10.1295	0.363162
$779$	0.739212	0.0264850
$780$	−0.328402	−0.0117587
$781$	32.2453	1.15383
$782$	26.9280	0.962945
$783$	8.60789	0.307621
$784$	−6.41098	−0.228964
$785$	−4.44606	−0.158687
$786$	−0.286503	−0.0102192
$787$	−14.9354	−0.532389	−0.266195	−	0.963919i	$-0.585766\pi$
$787$	−14.9354	−0.532389	−0.266195	+	0.963919i	$0.585766\pi$
$788$	−2.77560	−0.0988768
$789$	4.08780	0.145529
$790$	−2.70377	−0.0961957
$791$	12.7016	0.451617
$792$	6.79335	0.241391
$793$	−17.3861	−0.617400
$794$	39.2809	1.39403
$795$	−1.03884	−0.0368440
$796$	−17.5974	−0.623722
$797$	28.4978	1.00944	0.504722	−	0.863282i	$-0.331595\pi$
$797$	28.4978	1.00944	0.504722	+	0.863282i	$0.331595\pi$
$798$	−0.0231888	−0.000820874 0
$799$	−16.2557	−0.575085
$800$	1.00000	0.0353553
$801$	−5.55291	−0.196202
$802$	−11.8064	−0.416898
$803$	6.70602	0.236650
$804$	0.149923	0.00528737
$805$	3.14027	0.110680
$806$	−9.81856	−0.345844
$807$	1.95016	0.0686490
$808$	−17.0922	−0.601300
$809$	29.3516	1.03195	0.515974	−	0.856604i	$-0.327430\pi$
$809$	29.3516	1.03195	0.515974	+	0.856604i	$0.327430\pi$
$810$	−8.58931	−0.301798
$811$	−5.72142	−0.200906	−0.100453	−	0.994942i	$-0.532029\pi$
$811$	−5.72142	−0.200906	−0.100453	+	0.994942i	$0.532029\pi$
$812$	5.18079	0.181810
$813$	6.18373	0.216873
$814$	8.96655	0.314277
$815$	−15.7480	−0.551629
$816$	1.40945	0.0493405
$817$	−0.917515	−0.0320998
$818$	11.1008	0.388130
$819$	3.47659	0.121482
$820$	−5.23965	−0.182977
$821$	−17.9214	−0.625461	−0.312730	−	0.949842i	$-0.601244\pi$
$821$	−17.9214	−0.625461	−0.312730	+	0.949842i	$0.601244\pi$
$822$	3.50454	0.122235
$823$	−56.2934	−1.96227	−0.981133	−	0.193334i	$-0.938070\pi$
$823$	−56.2934	−1.96227	−0.981133	+	0.193334i	$0.938070\pi$
$824$	−13.8286	−0.481742
$825$	−0.492493	−0.0171464
$826$	−5.55570	−0.193308
$827$	24.1704	0.840489	0.420244	−	0.907411i	$-0.361944\pi$
$827$	24.1704	0.840489	0.420244	+	0.907411i	$0.361944\pi$
$828$	−12.0874	−0.420066
$829$	−3.94922	−0.137162	−0.0685810	−	0.997646i	$-0.521847\pi$
$829$	−3.94922	−0.137162	−0.0685810	+	0.997646i	$0.521847\pi$
$830$	−8.87666	−0.308113
$831$	4.22746	0.146649
$832$	1.53341	0.0531615
$833$	−42.1917	−1.46185
$834$	−0.558810	−0.0193500
$835$	7.11166	0.246109
$836$	−0.324429	−0.0112206
$837$	8.16495	0.282222
$838$	35.1252	1.21338
$839$	−44.8837	−1.54956	−0.774779	−	0.632232i	$-0.782139\pi$
$839$	−44.8837	−1.54956	−0.774779	+	0.632232i	$0.782139\pi$
$840$	0.164366	0.00567116
$841$	16.5683	0.571322
$842$	2.49017	0.0858171
$843$	−3.45370	−0.118952
$844$	−7.90218	−0.272004
$845$	10.6486	0.366325
$846$	7.29682	0.250870
$847$	4.38368	0.150625
$848$	4.85069	0.166573
$849$	2.75399	0.0945168
$850$	6.58116	0.225732
$851$	−15.9542	−0.546902
$852$	−3.00303	−0.102882
$853$	−49.5020	−1.69492	−0.847459	−	0.530862i	$-0.821868\pi$
$853$	−49.5020	−1.69492	−0.847459	+	0.530862i	$0.821868\pi$
$854$	8.70180	0.297770
$855$	0.416770	0.0142532
$856$	14.7988	0.505813
$857$	31.6476	1.08106	0.540531	−	0.841324i	$-0.318223\pi$
$857$	31.6476	1.08106	0.540531	+	0.841324i	$0.318223\pi$
$858$	−0.755195	−0.0257819
$859$	50.4724	1.72210	0.861048	−	0.508523i	$-0.169808\pi$
$859$	50.4724	1.72210	0.861048	+	0.508523i	$0.169808\pi$
$860$	6.50349	0.221767
$861$	−0.861220	−0.0293503
$862$	6.27077	0.213583
$863$	−8.19129	−0.278835	−0.139417	−	0.990234i	$-0.544523\pi$
$863$	−8.19129	−0.278835	−0.139417	+	0.990234i	$0.544523\pi$
$864$	−1.27516	−0.0433819
$865$	17.4361	0.592846
$866$	20.2600	0.688462
$867$	5.63500	0.191375
$868$	4.91421	0.166799
$869$	−6.21760	−0.210918
$870$	1.44570	0.0490138
$871$	1.07345	0.0363723
$872$	−14.4991	−0.491002
$873$	3.03536	0.102731
$874$	0.577257	0.0195260
$875$	0.767476	0.0259454
$876$	−0.624537	−0.0211011
$877$	10.4865	0.354103	0.177051	−	0.984202i	$-0.443344\pi$
$877$	10.4865	0.354103	0.177051	+	0.984202i	$0.443344\pi$
$878$	34.8540	1.17626
$879$	−5.88797	−0.198596
$880$	2.29961	0.0775197
$881$	−40.0200	−1.34831	−0.674154	−	0.738591i	$-0.735492\pi$
$881$	−40.0200	−1.34831	−0.674154	+	0.738591i	$0.735492\pi$
$882$	18.9389	0.637706
$883$	−10.7358	−0.361289	−0.180644	−	0.983548i	$-0.557818\pi$
$883$	−10.7358	−0.361289	−0.180644	+	0.983548i	$0.557818\pi$
$884$	10.0916	0.339418
$885$	−1.55032	−0.0521133
$886$	−2.28872	−0.0768912
$887$	−2.38783	−0.0801755	−0.0400878	−	0.999196i	$-0.512764\pi$
$887$	−2.38783	−0.0801755	−0.0400878	+	0.999196i	$0.512764\pi$
$888$	−0.835061	−0.0280228
$889$	−3.83021	−0.128461
$890$	−1.87971	−0.0630079
$891$	−19.7520	−0.661718
$892$	20.0550	0.671493
$893$	−0.348474	−0.0116612
$894$	−4.00004	−0.133781
$895$	16.8771	0.564140
$896$	−0.767476	−0.0256396
$897$	1.34372	0.0448654
$898$	−31.2025	−1.04124
$899$	43.2235	1.44159
$900$	−2.95413	−0.0984711
$901$	31.9232	1.06351
$902$	−12.0491	−0.401193
$903$	1.06895	0.0355725
$904$	−16.5498	−0.550439
$905$	−13.9388	−0.463340
$906$	−3.18455	−0.105800
$907$	52.3907	1.73961	0.869803	−	0.493400i	$-0.164246\pi$
$907$	52.3907	1.73961	0.869803	+	0.493400i	$0.164246\pi$
$908$	3.55781	0.118070
$909$	50.4925	1.67473
$910$	1.17686	0.0390124
$911$	24.8484	0.823265	0.411632	−	0.911350i	$-0.364959\pi$
$911$	24.8484	0.823265	0.411632	+	0.911350i	$0.364959\pi$
$912$	0.0302143	0.00100050
$913$	−20.4128	−0.675566
$914$	−33.8674	−1.12023
$915$	2.42824	0.0802750
$916$	14.7855	0.488526
$917$	1.02671	0.0339049
$918$	−8.39203	−0.276978
$919$	54.8563	1.80954	0.904771	−	0.425898i	$-0.140042\pi$
$919$	54.8563	1.80954	0.904771	+	0.425898i	$0.140042\pi$
$920$	−4.09169	−0.134899
$921$	0.540273	0.0178026
$922$	25.9766	0.855495
$923$	−21.5017	−0.707736
$924$	0.377977	0.0124345
$925$	−3.89916	−0.128204
$926$	−31.1425	−1.02341
$927$	40.8515	1.34174
$928$	−6.75043	−0.221594
$929$	56.4448	1.85190	0.925948	−	0.377652i	$-0.123269\pi$
$929$	56.4448	1.85190	0.925948	+	0.377652i	$0.123269\pi$
$930$	1.37131	0.0449670
$931$	−0.904463	−0.0296426
$932$	21.2368	0.695634
$933$	5.28142	0.172906
$934$	2.09776	0.0686408
$935$	15.1341	0.494937
$936$	−4.52991	−0.148065
$937$	−9.06394	−0.296106	−0.148053	−	0.988979i	$-0.547301\pi$
$937$	−9.06394	−0.296106	−0.148053	+	0.988979i	$0.547301\pi$
$938$	−0.537262	−0.0175422
$939$	−3.95189	−0.128965
$940$	2.47004	0.0805637
$941$	35.7080	1.16405	0.582024	−	0.813171i	$-0.302261\pi$
$941$	35.7080	1.16405	0.582024	+	0.813171i	$0.302261\pi$
$942$	0.952185	0.0310239
$943$	21.4390	0.698151
$944$	7.23892	0.235607
$945$	−0.978656	−0.0318357
$946$	14.9555	0.486245
$947$	−16.9251	−0.549993	−0.274997	−	0.961445i	$-0.588677\pi$
$947$	−16.9251	−0.549993	−0.274997	+	0.961445i	$0.588677\pi$
$948$	0.579049	0.0188066
$949$	−4.47168	−0.145157
$950$	0.141080	0.00457725
$951$	1.68635	0.0546835
$952$	−5.05088	−0.163700
$953$	38.5468	1.24865	0.624327	−	0.781163i	$-0.285373\pi$
$953$	38.5468	1.24865	0.624327	+	0.781163i	$0.285373\pi$
$954$	−14.3296	−0.463938
$955$	18.9197	0.612227
$956$	−26.3286	−0.851527
$957$	3.32454	0.107467
$958$	−1.16273	−0.0375663
$959$	−12.5588	−0.405546
$960$	−0.214164	−0.00691211
$961$	9.99938	0.322561
$962$	−5.97903	−0.192772
$963$	−43.7177	−1.40878
$964$	−2.69730	−0.0868740
$965$	11.1922	0.360289
$966$	−0.672534	−0.0216384
$967$	48.7445	1.56752	0.783758	−	0.621066i	$-0.213300\pi$
$967$	48.7445	1.56752	0.783758	+	0.621066i	$0.213300\pi$
$968$	−5.71181	−0.183584
$969$	0.198845	0.00638783
$970$	1.02749	0.0329908
$971$	−24.0479	−0.771734	−0.385867	−	0.922554i	$-0.626098\pi$
$971$	−24.0479	−0.771734	−0.385867	+	0.922554i	$0.626098\pi$
$972$	5.66500	0.181705
$973$	2.00255	0.0641987
$974$	10.7664	0.344977
$975$	0.328402	0.0105173
$976$	−11.3382	−0.362927
$977$	−57.9935	−1.85538	−0.927688	−	0.373357i	$-0.878207\pi$
$977$	−57.9935	−1.85538	−0.927688	+	0.373357i	$0.878207\pi$
$978$	3.37266	0.107846
$979$	−4.32259	−0.138150
$980$	6.41098	0.204791
$981$	42.8323	1.36753
$982$	−34.8828	−1.11315
$983$	−20.2487	−0.645835	−0.322917	−	0.946427i	$-0.604664\pi$
$983$	−20.2487	−0.645835	−0.322917	+	0.946427i	$0.604664\pi$
$984$	1.12215	0.0357727
$985$	2.77560	0.0884381
$986$	−44.4256	−1.41480
$987$	0.405989	0.0129228
$988$	0.216334	0.00688251
$989$	−26.6103	−0.846158
$990$	−6.79335	−0.215907
$991$	16.1450	0.512863	0.256431	−	0.966562i	$-0.417453\pi$
$991$	16.1450	0.512863	0.256431	+	0.966562i	$0.417453\pi$
$992$	−6.40308	−0.203298
$993$	−4.33256	−0.137490
$994$	10.7616	0.341338
$995$	17.5974	0.557874
$996$	1.90106	0.0602374
$997$	28.6198	0.906398	0.453199	−	0.891409i	$-0.350283\pi$
$997$	28.6198	0.906398	0.453199	+	0.891409i	$0.350283\pi$
$998$	24.1806	0.765423
$999$	4.97206	0.157309

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.f.1.13	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.f.1.13	✓	22	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:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.214164 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.214164 q^{6} -0.767476 q^{7} +1.00000 q^{8} -2.95413 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.214164 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.214164 q^{6} -0.767476 q^{7} +1.00000 q^{8} -2.95413 q^{9} -1.00000 q^{10} -2.29961 q^{11} +0.214164 q^{12} +1.53341 q^{13} -0.767476 q^{14} -0.214164 q^{15} +1.00000 q^{16} +6.58116 q^{17} -2.95413 q^{18} +0.141080 q^{19} -1.00000 q^{20} -0.164366 q^{21} -2.29961 q^{22} +4.09169 q^{23} +0.214164 q^{24} +1.00000 q^{25} +1.53341 q^{26} -1.27516 q^{27} -0.767476 q^{28} -6.75043 q^{29} -0.214164 q^{30} -6.40308 q^{31} +1.00000 q^{32} -0.492493 q^{33} +6.58116 q^{34} +0.767476 q^{35} -2.95413 q^{36} -3.89916 q^{37} +0.141080 q^{38} +0.328402 q^{39} -1.00000 q^{40} +5.23965 q^{41} -0.164366 q^{42} -6.50349 q^{43} -2.29961 q^{44} +2.95413 q^{45} +4.09169 q^{46} -2.47004 q^{47} +0.214164 q^{48} -6.41098 q^{49} +1.00000 q^{50} +1.40945 q^{51} +1.53341 q^{52} +4.85069 q^{53} -1.27516 q^{54} +2.29961 q^{55} -0.767476 q^{56} +0.0302143 q^{57} -6.75043 q^{58} +7.23892 q^{59} -0.214164 q^{60} -11.3382 q^{61} -6.40308 q^{62} +2.26723 q^{63} +1.00000 q^{64} -1.53341 q^{65} -0.492493 q^{66} +0.700037 q^{67} +6.58116 q^{68} +0.876293 q^{69} +0.767476 q^{70} -14.0221 q^{71} -2.95413 q^{72} -2.91616 q^{73} -3.89916 q^{74} +0.214164 q^{75} +0.141080 q^{76} +1.76489 q^{77} +0.328402 q^{78} +2.70377 q^{79} -1.00000 q^{80} +8.58931 q^{81} +5.23965 q^{82} +8.87666 q^{83} -0.164366 q^{84} -6.58116 q^{85} -6.50349 q^{86} -1.44570 q^{87} -2.29961 q^{88} +1.87971 q^{89} +2.95413 q^{90} -1.17686 q^{91} +4.09169 q^{92} -1.37131 q^{93} -2.47004 q^{94} -0.141080 q^{95} +0.214164 q^{96} -1.02749 q^{97} -6.41098 q^{98} +6.79335 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9}+O(q^{10}) \) 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9	\( 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9} - 22 q^{10} - 4 q^{11} - 6 q^{12} - 20 q^{13} - 12 q^{14} + 6 q^{15} + 22 q^{16} - 23 q^{17} + 12 q^{18} + q^{19} - 22 q^{20} - 8 q^{21} - 4 q^{22} - 17 q^{23} - 6 q^{24} + 22 q^{25} - 20 q^{26} - 21 q^{27} - 12 q^{28} - 13 q^{29} + 6 q^{30} - 13 q^{31} + 22 q^{32} - 21 q^{33} - 23 q^{34} + 12 q^{35} + 12 q^{36} - 16 q^{37} + q^{38} - 4 q^{39} - 22 q^{40} - 31 q^{41} - 8 q^{42} - 9 q^{43} - 4 q^{44} - 12 q^{45} - 17 q^{46} - 41 q^{47} - 6 q^{48} - 6 q^{49} + 22 q^{50} - 7 q^{51} - 20 q^{52} - 15 q^{53} - 21 q^{54} + 4 q^{55} - 12 q^{56} - 26 q^{57} - 13 q^{58} - 32 q^{59} + 6 q^{60} - 22 q^{61} - 13 q^{62} - 55 q^{63} + 22 q^{64} + 20 q^{65} - 21 q^{66} - 19 q^{67} - 23 q^{68} - 37 q^{69} + 12 q^{70} - 36 q^{71} + 12 q^{72} - 47 q^{73} - 16 q^{74} - 6 q^{75} + q^{76} - 26 q^{77} - 4 q^{78} - 10 q^{79} - 22 q^{80} - 18 q^{81} - 31 q^{82} - 48 q^{83} - 8 q^{84} + 23 q^{85} - 9 q^{86} - 50 q^{87} - 4 q^{88} - 42 q^{89} - 12 q^{90} + 25 q^{91} - 17 q^{92} - 48 q^{93} - 41 q^{94} - q^{95} - 6 q^{96} - 67 q^{97} - 6 q^{98} - 3 q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9 - 22 * q^10 - 4 * q^11 - 6 * q^12 - 20 * q^13 - 12 * q^14 + 6 * q^15 + 22 * q^16 - 23 * q^17 + 12 * q^18 + q^19 - 22 * q^20 - 8 * q^21 - 4 * q^22 - 17 * q^23 - 6 * q^24 + 22 * q^25 - 20 * q^26 - 21 * q^27 - 12 * q^28 - 13 * q^29 + 6 * q^30 - 13 * q^31 + 22 * q^32 - 21 * q^33 - 23 * q^34 + 12 * q^35 + 12 * q^36 - 16 * q^37 + q^38 - 4 * q^39 - 22 * q^40 - 31 * q^41 - 8 * q^42 - 9 * q^43 - 4 * q^44 - 12 * q^45 - 17 * q^46 - 41 * q^47 - 6 * q^48 - 6 * q^49 + 22 * q^50 - 7 * q^51 - 20 * q^52 - 15 * q^53 - 21 * q^54 + 4 * q^55 - 12 * q^56 - 26 * q^57 - 13 * q^58 - 32 * q^59 + 6 * q^60 - 22 * q^61 - 13 * q^62 - 55 * q^63 + 22 * q^64 + 20 * q^65 - 21 * q^66 - 19 * q^67 - 23 * q^68 - 37 * q^69 + 12 * q^70 - 36 * q^71 + 12 * q^72 - 47 * q^73 - 16 * q^74 - 6 * q^75 + q^76 - 26 * q^77 - 4 * q^78 - 10 * q^79 - 22 * q^80 - 18 * q^81 - 31 * q^82 - 48 * q^83 - 8 * q^84 + 23 * q^85 - 9 * q^86 - 50 * q^87 - 4 * q^88 - 42 * q^89 - 12 * q^90 + 25 * q^91 - 17 * q^92 - 48 * q^93 - 41 * q^94 - q^95 - 6 * q^96 - 67 * q^97 - 6 * q^98 - 3 * q^99

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