LMFDB - Embedded newform 6010.2.a.f.1.19

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			1.19
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)

$f(q)$	$=$	$q+1.00000 q^{2} +2.04538 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.04538 q^{6} -3.30792 q^{7} +1.00000 q^{8} +1.18360 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.04538 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.04538 q^{6} -3.30792 q^{7} +1.00000 q^{8} +1.18360 q^{9} -1.00000 q^{10} +4.06133 q^{11} +2.04538 q^{12} -6.07115 q^{13} -3.30792 q^{14} -2.04538 q^{15} +1.00000 q^{16} -4.71049 q^{17} +1.18360 q^{18} +2.60935 q^{19} -1.00000 q^{20} -6.76596 q^{21} +4.06133 q^{22} +5.83278 q^{23} +2.04538 q^{24} +1.00000 q^{25} -6.07115 q^{26} -3.71524 q^{27} -3.30792 q^{28} +3.86918 q^{29} -2.04538 q^{30} -4.92192 q^{31} +1.00000 q^{32} +8.30697 q^{33} -4.71049 q^{34} +3.30792 q^{35} +1.18360 q^{36} -10.2521 q^{37} +2.60935 q^{38} -12.4178 q^{39} -1.00000 q^{40} -9.93922 q^{41} -6.76596 q^{42} +1.76828 q^{43} +4.06133 q^{44} -1.18360 q^{45} +5.83278 q^{46} -1.67624 q^{47} +2.04538 q^{48} +3.94231 q^{49} +1.00000 q^{50} -9.63476 q^{51} -6.07115 q^{52} +7.93129 q^{53} -3.71524 q^{54} -4.06133 q^{55} -3.30792 q^{56} +5.33712 q^{57} +3.86918 q^{58} -6.94933 q^{59} -2.04538 q^{60} -8.73728 q^{61} -4.92192 q^{62} -3.91524 q^{63} +1.00000 q^{64} +6.07115 q^{65} +8.30697 q^{66} +3.39962 q^{67} -4.71049 q^{68} +11.9303 q^{69} +3.30792 q^{70} -0.143889 q^{71} +1.18360 q^{72} +1.02274 q^{73} -10.2521 q^{74} +2.04538 q^{75} +2.60935 q^{76} -13.4345 q^{77} -12.4178 q^{78} -15.0469 q^{79} -1.00000 q^{80} -11.1499 q^{81} -9.93922 q^{82} -11.9502 q^{83} -6.76596 q^{84} +4.71049 q^{85} +1.76828 q^{86} +7.91397 q^{87} +4.06133 q^{88} +11.4603 q^{89} -1.18360 q^{90} +20.0828 q^{91} +5.83278 q^{92} -10.0672 q^{93} -1.67624 q^{94} -2.60935 q^{95} +2.04538 q^{96} +2.24497 q^{97} +3.94231 q^{98} +4.80697 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	2.04538	1.18090	0.590452	−	0.807073i	$-0.298950\pi$
$3$	2.04538	1.18090	0.590452	+	0.807073i	$0.298950\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.04538	0.835025
$7$	−3.30792	−1.25027	−0.625137	−	0.780515i	$-0.714957\pi$
$7$	−3.30792	−1.25027	−0.625137	+	0.780515i	$0.714957\pi$
$8$	1.00000	0.353553
$9$	1.18360	0.394532
$10$	−1.00000	−0.316228
$11$	4.06133	1.22454	0.612268	−	0.790650i	$-0.290257\pi$
$11$	4.06133	1.22454	0.612268	+	0.790650i	$0.290257\pi$
$12$	2.04538	0.590452
$13$	−6.07115	−1.68383	−0.841916	−	0.539608i	$-0.818572\pi$
$13$	−6.07115	−1.68383	−0.841916	+	0.539608i	$0.818572\pi$
$14$	−3.30792	−0.884078
$15$	−2.04538	−0.528116
$16$	1.00000	0.250000
$17$	−4.71049	−1.14246	−0.571231	−	0.820789i	$-0.693534\pi$
$17$	−4.71049	−1.14246	−0.571231	+	0.820789i	$0.693534\pi$
$18$	1.18360	0.278977
$19$	2.60935	0.598626	0.299313	−	0.954155i	$-0.403243\pi$
$19$	2.60935	0.598626	0.299313	+	0.954155i	$0.403243\pi$
$20$	−1.00000	−0.223607
$21$	−6.76596	−1.47645
$22$	4.06133	0.865878
$23$	5.83278	1.21622	0.608109	−	0.793853i	$-0.291928\pi$
$23$	5.83278	1.21622	0.608109	+	0.793853i	$0.291928\pi$
$24$	2.04538	0.417512
$25$	1.00000	0.200000
$26$	−6.07115	−1.19065
$27$	−3.71524	−0.714999
$28$	−3.30792	−0.625137
$29$	3.86918	0.718489	0.359245	−	0.933243i	$-0.383034\pi$
$29$	3.86918	0.718489	0.359245	+	0.933243i	$0.383034\pi$
$30$	−2.04538	−0.373434
$31$	−4.92192	−0.884004	−0.442002	−	0.897014i	$-0.645732\pi$
$31$	−4.92192	−0.884004	−0.442002	+	0.897014i	$0.645732\pi$
$32$	1.00000	0.176777
$33$	8.30697	1.44606
$34$	−4.71049	−0.807842
$35$	3.30792	0.559140
$36$	1.18360	0.197266
$37$	−10.2521	−1.68544	−0.842720	−	0.538352i	$-0.819047\pi$
$37$	−10.2521	−1.68544	−0.842720	+	0.538352i	$0.819047\pi$
$38$	2.60935	0.423292
$39$	−12.4178	−1.98844
$40$	−1.00000	−0.158114
$41$	−9.93922	−1.55224	−0.776122	−	0.630582i	$-0.782816\pi$
$41$	−9.93922	−1.55224	−0.776122	+	0.630582i	$0.782816\pi$
$42$	−6.76596	−1.04401
$43$	1.76828	0.269660	0.134830	−	0.990869i	$-0.456951\pi$
$43$	1.76828	0.269660	0.134830	+	0.990869i	$0.456951\pi$
$44$	4.06133	0.612268
$45$	−1.18360	−0.176440
$46$	5.83278	0.859996
$47$	−1.67624	−0.244505	−0.122253	−	0.992499i	$-0.539012\pi$
$47$	−1.67624	−0.244505	−0.122253	+	0.992499i	$0.539012\pi$
$48$	2.04538	0.295226
$49$	3.94231	0.563187
$50$	1.00000	0.141421
$51$	−9.63476	−1.34914
$52$	−6.07115	−0.841916
$53$	7.93129	1.08945	0.544724	−	0.838616i	$-0.316635\pi$
$53$	7.93129	1.08945	0.544724	+	0.838616i	$0.316635\pi$
$54$	−3.71524	−0.505580
$55$	−4.06133	−0.547629
$56$	−3.30792	−0.442039
$57$	5.33712	0.706919
$58$	3.86918	0.508049
$59$	−6.94933	−0.904726	−0.452363	−	0.891834i	$-0.649419\pi$
$59$	−6.94933	−0.904726	−0.452363	+	0.891834i	$0.649419\pi$
$60$	−2.04538	−0.264058
$61$	−8.73728	−1.11869	−0.559347	−	0.828933i	$-0.688948\pi$
$61$	−8.73728	−1.11869	−0.559347	+	0.828933i	$0.688948\pi$
$62$	−4.92192	−0.625085
$63$	−3.91524	−0.493274
$64$	1.00000	0.125000
$65$	6.07115	0.753033
$66$	8.30697	1.02252
$67$	3.39962	0.415330	0.207665	−	0.978200i	$-0.433414\pi$
$67$	3.39962	0.415330	0.207665	+	0.978200i	$0.433414\pi$
$68$	−4.71049	−0.571231
$69$	11.9303	1.43624
$70$	3.30792	0.395372
$71$	−0.143889	−0.0170765	−0.00853825	−	0.999964i	$-0.502718\pi$
$71$	−0.143889	−0.0170765	−0.00853825	+	0.999964i	$0.502718\pi$
$72$	1.18360	0.139488
$73$	1.02274	0.119703	0.0598513	−	0.998207i	$-0.480937\pi$
$73$	1.02274	0.119703	0.0598513	+	0.998207i	$0.480937\pi$
$74$	−10.2521	−1.19179
$75$	2.04538	0.236181
$76$	2.60935	0.299313
$77$	−13.4345	−1.53101
$78$	−12.4178	−1.40604
$79$	−15.0469	−1.69291	−0.846456	−	0.532459i	$-0.821268\pi$
$79$	−15.0469	−1.69291	−0.846456	+	0.532459i	$0.821268\pi$
$80$	−1.00000	−0.111803
$81$	−11.1499	−1.23888
$82$	−9.93922	−1.09760
$83$	−11.9502	−1.31171	−0.655853	−	0.754888i	$-0.727691\pi$
$83$	−11.9502	−1.31171	−0.655853	+	0.754888i	$0.727691\pi$
$84$	−6.76596	−0.738227
$85$	4.71049	0.510924
$86$	1.76828	0.190678
$87$	7.91397	0.848467
$88$	4.06133	0.432939
$89$	11.4603	1.21479	0.607395	−	0.794400i	$-0.292215\pi$
$89$	11.4603	1.21479	0.607395	+	0.794400i	$0.292215\pi$
$90$	−1.18360	−0.124762
$91$	20.0828	2.10525
$92$	5.83278	0.608109
$93$	−10.0672	−1.04392
$94$	−1.67624	−0.172891
$95$	−2.60935	−0.267714
$96$	2.04538	0.208756
$97$	2.24497	0.227942	0.113971	−	0.993484i	$-0.463643\pi$
$97$	2.24497	0.227942	0.113971	+	0.993484i	$0.463643\pi$
$98$	3.94231	0.398234
$99$	4.80697	0.483119
$100$	1.00000	0.100000
$101$	−2.81048	−0.279653	−0.139827	−	0.990176i	$-0.544655\pi$
$101$	−2.81048	−0.279653	−0.139827	+	0.990176i	$0.544655\pi$
$102$	−9.63476	−0.953984
$103$	−10.0751	−0.992733	−0.496367	−	0.868113i	$-0.665333\pi$
$103$	−10.0751	−0.992733	−0.496367	+	0.868113i	$0.665333\pi$
$104$	−6.07115	−0.595325
$105$	6.76596	0.660290
$106$	7.93129	0.770355
$107$	−4.37524	−0.422970	−0.211485	−	0.977381i	$-0.567830\pi$
$107$	−4.37524	−0.422970	−0.211485	+	0.977381i	$0.567830\pi$
$108$	−3.71524	−0.357499
$109$	−14.6574	−1.40392	−0.701961	−	0.712215i	$-0.747692\pi$
$109$	−14.6574	−1.40392	−0.701961	+	0.712215i	$0.747692\pi$
$110$	−4.06133	−0.387232
$111$	−20.9696	−1.99034
$112$	−3.30792	−0.312569
$113$	9.75062	0.917262	0.458631	−	0.888627i	$-0.348340\pi$
$113$	9.75062	0.917262	0.458631	+	0.888627i	$0.348340\pi$
$114$	5.33712	0.499867
$115$	−5.83278	−0.543909
$116$	3.86918	0.359245
$117$	−7.18579	−0.664327
$118$	−6.94933	−0.639738
$119$	15.5819	1.42839
$120$	−2.04538	−0.186717
$121$	5.49437	0.499488
$122$	−8.73728	−0.791037
$123$	−20.3295	−1.83305
$124$	−4.92192	−0.442002
$125$	−1.00000	−0.0894427
$126$	−3.91524	−0.348797
$127$	−12.4406	−1.10393	−0.551964	−	0.833868i	$-0.686121\pi$
$127$	−12.4406	−1.10393	−0.551964	+	0.833868i	$0.686121\pi$
$128$	1.00000	0.0883883
$129$	3.61681	0.318442
$130$	6.07115	0.532475
$131$	10.8064	0.944160	0.472080	−	0.881556i	$-0.343503\pi$
$131$	10.8064	0.944160	0.472080	+	0.881556i	$0.343503\pi$
$132$	8.30697	0.723029
$133$	−8.63151	−0.748447
$134$	3.39962	0.293683
$135$	3.71524	0.319757
$136$	−4.71049	−0.403921
$137$	8.41721	0.719131	0.359565	−	0.933120i	$-0.382925\pi$
$137$	8.41721	0.719131	0.359565	+	0.933120i	$0.382925\pi$
$138$	11.9303	1.01557
$139$	−5.56936	−0.472387	−0.236193	−	0.971706i	$-0.575900\pi$
$139$	−5.56936	−0.472387	−0.236193	+	0.971706i	$0.575900\pi$
$140$	3.30792	0.279570
$141$	−3.42856	−0.288737
$142$	−0.143889	−0.0120749
$143$	−24.6569	−2.06191
$144$	1.18360	0.0986331
$145$	−3.86918	−0.321318
$146$	1.02274	0.0846425
$147$	8.06354	0.665070
$148$	−10.2521	−0.842720
$149$	14.1128	1.15617	0.578085	−	0.815977i	$-0.303800\pi$
$149$	14.1128	1.15617	0.578085	+	0.815977i	$0.303800\pi$
$150$	2.04538	0.167005
$151$	−2.01490	−0.163970	−0.0819850	−	0.996634i	$-0.526126\pi$
$151$	−2.01490	−0.163970	−0.0819850	+	0.996634i	$0.526126\pi$
$152$	2.60935	0.211646
$153$	−5.57532	−0.450738
$154$	−13.4345	−1.08259
$155$	4.92192	0.395338
$156$	−12.4178	−0.994222
$157$	−7.09423	−0.566181	−0.283091	−	0.959093i	$-0.591360\pi$
$157$	−7.09423	−0.566181	−0.283091	+	0.959093i	$0.591360\pi$
$158$	−15.0469	−1.19707
$159$	16.2225	1.28653
$160$	−1.00000	−0.0790569
$161$	−19.2943	−1.52061
$162$	−11.1499	−0.876018
$163$	0.187498	0.0146859	0.00734297	−	0.999973i	$-0.497663\pi$
$163$	0.187498	0.0146859	0.00734297	+	0.999973i	$0.497663\pi$
$164$	−9.93922	−0.776122
$165$	−8.30697	−0.646697
$166$	−11.9502	−0.927517
$167$	−3.94345	−0.305154	−0.152577	−	0.988292i	$-0.548757\pi$
$167$	−3.94345	−0.305154	−0.152577	+	0.988292i	$0.548757\pi$
$168$	−6.76596	−0.522005
$169$	23.8588	1.83529
$170$	4.71049	0.361278
$171$	3.08842	0.236177
$172$	1.76828	0.134830
$173$	−7.20008	−0.547412	−0.273706	−	0.961813i	$-0.588249\pi$
$173$	−7.20008	−0.547412	−0.273706	+	0.961813i	$0.588249\pi$
$174$	7.91397	0.599956
$175$	−3.30792	−0.250055
$176$	4.06133	0.306134
$177$	−14.2141	−1.06839
$178$	11.4603	0.858986
$179$	13.3026	0.994280	0.497140	−	0.867670i	$-0.334384\pi$
$179$	13.3026	0.994280	0.497140	+	0.867670i	$0.334384\pi$
$180$	−1.18360	−0.0882201
$181$	11.9466	0.887988	0.443994	−	0.896030i	$-0.353561\pi$
$181$	11.9466	0.887988	0.443994	+	0.896030i	$0.353561\pi$
$182$	20.0828	1.48864
$183$	−17.8711	−1.32107
$184$	5.83278	0.429998
$185$	10.2521	0.753752
$186$	−10.0672	−0.738165
$187$	−19.1308	−1.39899
$188$	−1.67624	−0.122253
$189$	12.2897	0.893945
$190$	−2.60935	−0.189302
$191$	−16.1153	−1.16606	−0.583031	−	0.812450i	$-0.698133\pi$
$191$	−16.1153	−1.16606	−0.583031	+	0.812450i	$0.698133\pi$
$192$	2.04538	0.147613
$193$	−9.72787	−0.700228	−0.350114	−	0.936707i	$-0.613857\pi$
$193$	−9.72787	−0.700228	−0.350114	+	0.936707i	$0.613857\pi$
$194$	2.24497	0.161179
$195$	12.4178	0.889259
$196$	3.94231	0.281594
$197$	26.9822	1.92240	0.961201	−	0.275849i	$-0.0889590\pi$
$197$	26.9822	1.92240	0.961201	+	0.275849i	$0.0889590\pi$
$198$	4.80697	0.341617
$199$	−13.9515	−0.988997	−0.494498	−	0.869179i	$-0.664648\pi$
$199$	−13.9515	−0.988997	−0.494498	+	0.869179i	$0.664648\pi$
$200$	1.00000	0.0707107
$201$	6.95354	0.490465
$202$	−2.81048	−0.197745
$203$	−12.7989	−0.898309
$204$	−9.63476	−0.674568
$205$	9.93922	0.694185
$206$	−10.0751	−0.701969
$207$	6.90366	0.479838
$208$	−6.07115	−0.420958
$209$	10.5974	0.733039
$210$	6.76596	0.466896
$211$	−1.07780	−0.0741986	−0.0370993	−	0.999312i	$-0.511812\pi$
$211$	−1.07780	−0.0741986	−0.0370993	+	0.999312i	$0.511812\pi$
$212$	7.93129	0.544724
$213$	−0.294309	−0.0201657
$214$	−4.37524	−0.299085
$215$	−1.76828	−0.120595
$216$	−3.71524	−0.252790
$217$	16.2813	1.10525
$218$	−14.6574	−0.992723
$219$	2.09190	0.141357
$220$	−4.06133	−0.273815
$221$	28.5981	1.92371
$222$	−20.9696	−1.40738
$223$	−7.22898	−0.484088	−0.242044	−	0.970265i	$-0.577818\pi$
$223$	−7.22898	−0.484088	−0.242044	+	0.970265i	$0.577818\pi$
$224$	−3.30792	−0.221019
$225$	1.18360	0.0789065
$226$	9.75062	0.648602
$227$	6.75638	0.448437	0.224218	−	0.974539i	$-0.428017\pi$
$227$	6.75638	0.448437	0.224218	+	0.974539i	$0.428017\pi$
$228$	5.33712	0.353460
$229$	17.8385	1.17880	0.589402	−	0.807840i	$-0.299363\pi$
$229$	17.8385	1.17880	0.589402	+	0.807840i	$0.299363\pi$
$230$	−5.83278	−0.384602
$231$	−27.4788	−1.80797
$232$	3.86918	0.254024
$233$	24.7812	1.62347	0.811734	−	0.584027i	$-0.198524\pi$
$233$	24.7812	1.62347	0.811734	+	0.584027i	$0.198524\pi$
$234$	−7.18579	−0.469750
$235$	1.67624	0.109346
$236$	−6.94933	−0.452363
$237$	−30.7768	−1.99916
$238$	15.5819	1.01003
$239$	12.4199	0.803373	0.401687	−	0.915777i	$-0.368424\pi$
$239$	12.4199	0.803373	0.401687	+	0.915777i	$0.368424\pi$
$240$	−2.04538	−0.132029
$241$	5.43812	0.350300	0.175150	−	0.984542i	$-0.443959\pi$
$241$	5.43812	0.350300	0.175150	+	0.984542i	$0.443959\pi$
$242$	5.49437	0.353192
$243$	−11.6601	−0.747995
$244$	−8.73728	−0.559347
$245$	−3.94231	−0.251865
$246$	−20.3295	−1.29616
$247$	−15.8417	−1.00799
$248$	−4.92192	−0.312542
$249$	−24.4428	−1.54900
$250$	−1.00000	−0.0632456
$251$	25.5531	1.61290	0.806450	−	0.591303i	$-0.201386\pi$
$251$	25.5531	1.61290	0.806450	+	0.591303i	$0.201386\pi$
$252$	−3.91524	−0.246637
$253$	23.6888	1.48930
$254$	−12.4406	−0.780595
$255$	9.63476	0.603352
$256$	1.00000	0.0625000
$257$	7.68159	0.479164	0.239582	−	0.970876i	$-0.422990\pi$
$257$	7.68159	0.479164	0.239582	+	0.970876i	$0.422990\pi$
$258$	3.61681	0.225172
$259$	33.9132	2.10726
$260$	6.07115	0.376516
$261$	4.57956	0.283467
$262$	10.8064	0.667622
$263$	−15.7890	−0.973592	−0.486796	−	0.873516i	$-0.661835\pi$
$263$	−15.7890	−0.973592	−0.486796	+	0.873516i	$0.661835\pi$
$264$	8.30697	0.511259
$265$	−7.93129	−0.487216
$266$	−8.63151	−0.529232
$267$	23.4407	1.43455
$268$	3.39962	0.207665
$269$	8.69032	0.529858	0.264929	−	0.964268i	$-0.414651\pi$
$269$	8.69032	0.529858	0.264929	+	0.964268i	$0.414651\pi$
$270$	3.71524	0.226102
$271$	9.90231	0.601523	0.300761	−	0.953699i	$-0.402759\pi$
$271$	9.90231	0.601523	0.300761	+	0.953699i	$0.402759\pi$
$272$	−4.71049	−0.285615
$273$	41.0771	2.48610
$274$	8.41721	0.508502
$275$	4.06133	0.244907
$276$	11.9303	0.718118
$277$	−23.1920	−1.39347	−0.696735	−	0.717329i	$-0.745365\pi$
$277$	−23.1920	−1.39347	−0.696735	+	0.717329i	$0.745365\pi$
$278$	−5.56936	−0.334028
$279$	−5.82557	−0.348768
$280$	3.30792	0.197686
$281$	−13.3082	−0.793898	−0.396949	−	0.917841i	$-0.629931\pi$
$281$	−13.3082	−0.793898	−0.396949	+	0.917841i	$0.629931\pi$
$282$	−3.42856	−0.204168
$283$	−33.2656	−1.97744	−0.988719	−	0.149784i	$-0.952142\pi$
$283$	−33.2656	−1.97744	−0.988719	+	0.149784i	$0.952142\pi$
$284$	−0.143889	−0.00853825
$285$	−5.33712	−0.316144
$286$	−24.6569	−1.45799
$287$	32.8781	1.94073
$288$	1.18360	0.0697441
$289$	5.18872	0.305219
$290$	−3.86918	−0.227206
$291$	4.59182	0.269178
$292$	1.02274	0.0598513
$293$	−23.5738	−1.37720	−0.688598	−	0.725144i	$-0.741773\pi$
$293$	−23.5738	−1.37720	−0.688598	+	0.725144i	$0.741773\pi$
$294$	8.06354	0.470275
$295$	6.94933	0.404606
$296$	−10.2521	−0.595893
$297$	−15.0888	−0.875542
$298$	14.1128	0.817535
$299$	−35.4117	−2.04791
$300$	2.04538	0.118090
$301$	−5.84931	−0.337149
$302$	−2.01490	−0.115944
$303$	−5.74851	−0.330244
$304$	2.60935	0.149656
$305$	8.73728	0.500295
$306$	−5.57532	−0.318720
$307$	−28.7561	−1.64120	−0.820600	−	0.571503i	$-0.806360\pi$
$307$	−28.7561	−1.64120	−0.820600	+	0.571503i	$0.806360\pi$
$308$	−13.4345	−0.765503
$309$	−20.6075	−1.17232
$310$	4.92192	0.279546
$311$	29.5877	1.67777	0.838883	−	0.544311i	$-0.183209\pi$
$311$	29.5877	1.67777	0.838883	+	0.544311i	$0.183209\pi$
$312$	−12.4178	−0.703021
$313$	−2.54113	−0.143633	−0.0718165	−	0.997418i	$-0.522880\pi$
$313$	−2.54113	−0.143633	−0.0718165	+	0.997418i	$0.522880\pi$
$314$	−7.09423	−0.400351
$315$	3.91524	0.220599
$316$	−15.0469	−0.846456
$317$	3.68916	0.207204	0.103602	−	0.994619i	$-0.466963\pi$
$317$	3.68916	0.207204	0.103602	+	0.994619i	$0.466963\pi$
$318$	16.2225	0.909715
$319$	15.7140	0.879816
$320$	−1.00000	−0.0559017
$321$	−8.94904	−0.499487
$322$	−19.2943	−1.07523
$323$	−12.2913	−0.683907
$324$	−11.1499	−0.619438
$325$	−6.07115	−0.336767
$326$	0.187498	0.0103845
$327$	−29.9800	−1.65790
$328$	−9.93922	−0.548801
$329$	5.54487	0.305699
$330$	−8.30697	−0.457284
$331$	0.613000	0.0336935	0.0168468	−	0.999858i	$-0.494637\pi$
$331$	0.613000	0.0336935	0.0168468	+	0.999858i	$0.494637\pi$
$332$	−11.9502	−0.655853
$333$	−12.1344	−0.664961
$334$	−3.94345	−0.215776
$335$	−3.39962	−0.185741
$336$	−6.76596	−0.369113
$337$	−8.67799	−0.472720	−0.236360	−	0.971666i	$-0.575954\pi$
$337$	−8.67799	−0.472720	−0.236360	+	0.971666i	$0.575954\pi$
$338$	23.8588	1.29775
$339$	19.9438	1.08320
$340$	4.71049	0.255462
$341$	−19.9895	−1.08249
$342$	3.08842	0.167003
$343$	10.1146	0.546136
$344$	1.76828	0.0953391
$345$	−11.9303	−0.642304
$346$	−7.20008	−0.387079
$347$	1.24392	0.0667771	0.0333886	−	0.999442i	$-0.489370\pi$
$347$	1.24392	0.0667771	0.0333886	+	0.999442i	$0.489370\pi$
$348$	7.91397	0.424233
$349$	24.2745	1.29939	0.649693	−	0.760197i	$-0.274898\pi$
$349$	24.2745	1.29939	0.649693	+	0.760197i	$0.274898\pi$
$350$	−3.30792	−0.176816
$351$	22.5558	1.20394
$352$	4.06133	0.216469
$353$	15.6851	0.834834	0.417417	−	0.908715i	$-0.362935\pi$
$353$	15.6851	0.834834	0.417417	+	0.908715i	$0.362935\pi$
$354$	−14.2141	−0.755469
$355$	0.143889	0.00763685
$356$	11.4603	0.607395
$357$	31.8710	1.68679
$358$	13.3026	0.703062
$359$	−17.7131	−0.934863	−0.467432	−	0.884029i	$-0.654821\pi$
$359$	−17.7131	−0.934863	−0.467432	+	0.884029i	$0.654821\pi$
$360$	−1.18360	−0.0623810
$361$	−12.1913	−0.641647
$362$	11.9466	0.627902
$363$	11.2381	0.589847
$364$	20.0828	1.05263
$365$	−1.02274	−0.0535326
$366$	−17.8711	−0.934138
$367$	35.4320	1.84953	0.924767	−	0.380534i	$-0.124260\pi$
$367$	35.4320	1.84953	0.924767	+	0.380534i	$0.124260\pi$
$368$	5.83278	0.304055
$369$	−11.7640	−0.612411
$370$	10.2521	0.532983
$371$	−26.2361	−1.36211
$372$	−10.0672	−0.521961
$373$	−10.7490	−0.556561	−0.278281	−	0.960500i	$-0.589764\pi$
$373$	−10.7490	−0.556561	−0.278281	+	0.960500i	$0.589764\pi$
$374$	−19.1308	−0.989232
$375$	−2.04538	−0.105623
$376$	−1.67624	−0.0864456
$377$	−23.4904	−1.20982
$378$	12.2897	0.632114
$379$	25.7635	1.32338	0.661690	−	0.749778i	$-0.269840\pi$
$379$	25.7635	1.32338	0.661690	+	0.749778i	$0.269840\pi$
$380$	−2.60935	−0.133857
$381$	−25.4459	−1.30363
$382$	−16.1153	−0.824530
$383$	23.0728	1.17897	0.589483	−	0.807781i	$-0.299331\pi$
$383$	23.0728	1.17897	0.589483	+	0.807781i	$0.299331\pi$
$384$	2.04538	0.104378
$385$	13.4345	0.684687
$386$	−9.72787	−0.495136
$387$	2.09293	0.106389
$388$	2.24497	0.113971
$389$	−1.16036	−0.0588325	−0.0294162	−	0.999567i	$-0.509365\pi$
$389$	−1.16036	−0.0588325	−0.0294162	+	0.999567i	$0.509365\pi$
$390$	12.4178	0.628801
$391$	−27.4752	−1.38948
$392$	3.94231	0.199117
$393$	22.1033	1.11496
$394$	26.9822	1.35934
$395$	15.0469	0.757093
$396$	4.80697	0.241560
$397$	−13.1303	−0.658989	−0.329494	−	0.944158i	$-0.606878\pi$
$397$	−13.1303	−0.658989	−0.329494	+	0.944158i	$0.606878\pi$
$398$	−13.9515	−0.699326
$399$	−17.6548	−0.883844
$400$	1.00000	0.0500000
$401$	13.5568	0.676995	0.338498	−	0.940967i	$-0.390081\pi$
$401$	13.5568	0.676995	0.338498	+	0.940967i	$0.390081\pi$
$402$	6.95354	0.346811
$403$	29.8817	1.48851
$404$	−2.81048	−0.139827
$405$	11.1499	0.554042
$406$	−12.7989	−0.635201
$407$	−41.6373	−2.06388
$408$	−9.63476	−0.476992
$409$	19.5527	0.966819	0.483410	−	0.875394i	$-0.339398\pi$
$409$	19.5527	0.966819	0.483410	+	0.875394i	$0.339398\pi$
$410$	9.93922	0.490863
$411$	17.2164	0.849224
$412$	−10.0751	−0.496367
$413$	22.9878	1.13116
$414$	6.90366	0.339296
$415$	11.9502	0.586613
$416$	−6.07115	−0.297662
$417$	−11.3915	−0.557843
$418$	10.5974	0.518337
$419$	−3.22002	−0.157308	−0.0786541	−	0.996902i	$-0.525062\pi$
$419$	−3.22002	−0.157308	−0.0786541	+	0.996902i	$0.525062\pi$
$420$	6.76596	0.330145
$421$	17.1218	0.834463	0.417232	−	0.908800i	$-0.363000\pi$
$421$	17.1218	0.834463	0.417232	+	0.908800i	$0.363000\pi$
$422$	−1.07780	−0.0524664
$423$	−1.98400	−0.0964652
$424$	7.93129	0.385178
$425$	−4.71049	−0.228492
$426$	−0.294309	−0.0142593
$427$	28.9022	1.39868
$428$	−4.37524	−0.211485
$429$	−50.4328	−2.43492
$430$	−1.76828	−0.0852739
$431$	8.72805	0.420415	0.210208	−	0.977657i	$-0.432586\pi$
$431$	8.72805	0.420415	0.210208	+	0.977657i	$0.432586\pi$
$432$	−3.71524	−0.178750
$433$	−28.4409	−1.36678	−0.683392	−	0.730052i	$-0.739496\pi$
$433$	−28.4409	−1.36678	−0.683392	+	0.730052i	$0.739496\pi$
$434$	16.2813	0.781528
$435$	−7.91397	−0.379446
$436$	−14.6574	−0.701961
$437$	15.2198	0.728060
$438$	2.09190	0.0999546
$439$	−0.268678	−0.0128233	−0.00641165	−	0.999979i	$-0.502041\pi$
$439$	−0.268678	−0.0128233	−0.00641165	+	0.999979i	$0.502041\pi$
$440$	−4.06133	−0.193616
$441$	4.66611	0.222196
$442$	28.5981	1.36027
$443$	6.16055	0.292696	0.146348	−	0.989233i	$-0.453248\pi$
$443$	6.16055	0.292696	0.146348	+	0.989233i	$0.453248\pi$
$444$	−20.9696	−0.995171
$445$	−11.4603	−0.543270
$446$	−7.22898	−0.342302
$447$	28.8662	1.36532
$448$	−3.30792	−0.156284
$449$	13.0684	0.616738	0.308369	−	0.951267i	$-0.400217\pi$
$449$	13.0684	0.616738	0.308369	+	0.951267i	$0.400217\pi$
$450$	1.18360	0.0557953
$451$	−40.3664	−1.90078
$452$	9.75062	0.458631
$453$	−4.12124	−0.193633
$454$	6.75638	0.317093
$455$	−20.0828	−0.941498
$456$	5.33712	0.249934
$457$	−26.8160	−1.25440	−0.627199	−	0.778859i	$-0.715799\pi$
$457$	−26.8160	−1.25440	−0.627199	+	0.778859i	$0.715799\pi$
$458$	17.8385	0.833540
$459$	17.5006	0.816859
$460$	−5.83278	−0.271955
$461$	−38.5181	−1.79397	−0.896984	−	0.442063i	$-0.854247\pi$
$461$	−38.5181	−1.79397	−0.896984	+	0.442063i	$0.854247\pi$
$462$	−27.4788	−1.27843
$463$	2.90319	0.134923	0.0674615	−	0.997722i	$-0.478510\pi$
$463$	2.90319	0.134923	0.0674615	+	0.997722i	$0.478510\pi$
$464$	3.86918	0.179622
$465$	10.0672	0.466856
$466$	24.7812	1.14797
$467$	−31.5922	−1.46191	−0.730956	−	0.682425i	$-0.760925\pi$
$467$	−31.5922	−1.46191	−0.730956	+	0.682425i	$0.760925\pi$
$468$	−7.18579	−0.332163
$469$	−11.2457	−0.519277
$470$	1.67624	0.0773193
$471$	−14.5104	−0.668605
$472$	−6.94933	−0.319869
$473$	7.18155	0.330208
$474$	−30.7768	−1.41362
$475$	2.60935	0.119725
$476$	15.5819	0.714196
$477$	9.38746	0.429822
$478$	12.4199	0.568071
$479$	30.3929	1.38869	0.694343	−	0.719644i	$-0.255695\pi$
$479$	30.3929	1.38869	0.694343	+	0.719644i	$0.255695\pi$
$480$	−2.04538	−0.0933586
$481$	62.2422	2.83800
$482$	5.43812	0.247699
$483$	−39.4644	−1.79569
$484$	5.49437	0.249744
$485$	−2.24497	−0.101939
$486$	−11.6601	−0.528912
$487$	−18.7972	−0.851782	−0.425891	−	0.904774i	$-0.640039\pi$
$487$	−18.7972	−0.851782	−0.425891	+	0.904774i	$0.640039\pi$
$488$	−8.73728	−0.395518
$489$	0.383505	0.0173427
$490$	−3.94231	−0.178095
$491$	18.3670	0.828892	0.414446	−	0.910074i	$-0.363975\pi$
$491$	18.3670	0.828892	0.414446	+	0.910074i	$0.363975\pi$
$492$	−20.3295	−0.916525
$493$	−18.2258	−0.820847
$494$	−15.8417	−0.712754
$495$	−4.80697	−0.216057
$496$	−4.92192	−0.221001
$497$	0.475973	0.0213503
$498$	−24.4428	−1.09531
$499$	37.7917	1.69179	0.845894	−	0.533351i	$-0.179068\pi$
$499$	37.7917	1.69179	0.845894	+	0.533351i	$0.179068\pi$
$500$	−1.00000	−0.0447214
$501$	−8.06588	−0.360357
$502$	25.5531	1.14049
$503$	27.4526	1.22405	0.612026	−	0.790837i	$-0.290355\pi$
$503$	27.4526	1.22405	0.612026	+	0.790837i	$0.290355\pi$
$504$	−3.91524	−0.174399
$505$	2.81048	0.125065
$506$	23.6888	1.05310
$507$	48.8004	2.16730
$508$	−12.4406	−0.551964
$509$	−25.3665	−1.12435	−0.562176	−	0.827018i	$-0.690036\pi$
$509$	−25.3665	−1.12435	−0.562176	+	0.827018i	$0.690036\pi$
$510$	9.63476	0.426634
$511$	−3.38314	−0.149661
$512$	1.00000	0.0441942
$513$	−9.69437	−0.428017
$514$	7.68159	0.338820
$515$	10.0751	0.443964
$516$	3.61681	0.159221
$517$	−6.80777	−0.299405
$518$	33.9132	1.49006
$519$	−14.7269	−0.646440
$520$	6.07115	0.266237
$521$	−7.15280	−0.313370	−0.156685	−	0.987649i	$-0.550081\pi$
$521$	−7.15280	−0.313370	−0.156685	+	0.987649i	$0.550081\pi$
$522$	4.57956	0.200442
$523$	−18.8622	−0.824786	−0.412393	−	0.911006i	$-0.635307\pi$
$523$	−18.8622	−0.824786	−0.412393	+	0.911006i	$0.635307\pi$
$524$	10.8064	0.472080
$525$	−6.76596	−0.295291
$526$	−15.7890	−0.688434
$527$	23.1847	1.00994
$528$	8.30697	0.361515
$529$	11.0213	0.479187
$530$	−7.93129	−0.344513
$531$	−8.22521	−0.356944
$532$	−8.63151	−0.374224
$533$	60.3424	2.61372
$534$	23.4407	1.01438
$535$	4.37524	0.189158
$536$	3.39962	0.146841
$537$	27.2088	1.17415
$538$	8.69032	0.374666
$539$	16.0110	0.689643
$540$	3.71524	0.159879
$541$	37.5527	1.61452	0.807259	−	0.590197i	$-0.200950\pi$
$541$	37.5527	1.61452	0.807259	+	0.590197i	$0.200950\pi$
$542$	9.90231	0.425341
$543$	24.4355	1.04863
$544$	−4.71049	−0.201961
$545$	14.6574	0.627853
$546$	41.0771	1.75794
$547$	−2.97857	−0.127354	−0.0636772	−	0.997971i	$-0.520283\pi$
$547$	−2.97857	−0.127354	−0.0636772	+	0.997971i	$0.520283\pi$
$548$	8.41721	0.359565
$549$	−10.3414	−0.441361
$550$	4.06133	0.173176
$551$	10.0961	0.430106
$552$	11.9303	0.507786
$553$	49.7740	2.11661
$554$	−23.1920	−0.985332
$555$	20.9696	0.890108
$556$	−5.56936	−0.236193
$557$	18.2480	0.773195	0.386597	−	0.922249i	$-0.373650\pi$
$557$	18.2480	0.773195	0.386597	+	0.922249i	$0.373650\pi$
$558$	−5.82557	−0.246616
$559$	−10.7355	−0.454062
$560$	3.30792	0.139785
$561$	−39.1299	−1.65207
$562$	−13.3082	−0.561371
$563$	13.0878	0.551586	0.275793	−	0.961217i	$-0.411060\pi$
$563$	13.0878	0.551586	0.275793	+	0.961217i	$0.411060\pi$
$564$	−3.42856	−0.144368
$565$	−9.75062	−0.410212
$566$	−33.2656	−1.39826
$567$	36.8829	1.54894
$568$	−0.143889	−0.00603746
$569$	−8.31818	−0.348716	−0.174358	−	0.984682i	$-0.555785\pi$
$569$	−8.31818	−0.348716	−0.174358	+	0.984682i	$0.555785\pi$
$570$	−5.33712	−0.223548
$571$	11.2622	0.471308	0.235654	−	0.971837i	$-0.424277\pi$
$571$	11.2622	0.471308	0.235654	+	0.971837i	$0.424277\pi$
$572$	−24.6569	−1.03096
$573$	−32.9620	−1.37701
$574$	32.8781	1.37231
$575$	5.83278	0.243244
$576$	1.18360	0.0493165
$577$	8.75792	0.364597	0.182299	−	0.983243i	$-0.441646\pi$
$577$	8.75792	0.364597	0.182299	+	0.983243i	$0.441646\pi$
$578$	5.18872	0.215822
$579$	−19.8972	−0.826901
$580$	−3.86918	−0.160659
$581$	39.5303	1.63999
$582$	4.59182	0.190337
$583$	32.2116	1.33407
$584$	1.02274	0.0423213
$585$	7.18579	0.297096
$586$	−23.5738	−0.973824
$587$	−6.96020	−0.287278	−0.143639	−	0.989630i	$-0.545880\pi$
$587$	−6.96020	−0.287278	−0.143639	+	0.989630i	$0.545880\pi$
$588$	8.06354	0.332535
$589$	−12.8430	−0.529187
$590$	6.94933	0.286100
$591$	55.1890	2.27017
$592$	−10.2521	−0.421360
$593$	26.0184	1.06845	0.534225	−	0.845343i	$-0.320604\pi$
$593$	26.0184	1.06845	0.534225	+	0.845343i	$0.320604\pi$
$594$	−15.0888	−0.619101
$595$	−15.5819	−0.638796
$596$	14.1128	0.578085
$597$	−28.5362	−1.16791
$598$	−35.4117	−1.44809
$599$	12.3161	0.503221	0.251611	−	0.967829i	$-0.419040\pi$
$599$	12.3161	0.503221	0.251611	+	0.967829i	$0.419040\pi$
$600$	2.04538	0.0835025
$601$	1.00000	0.0407909
$601$	1.00000	0.0407909
$602$	−5.84931	−0.238400
$603$	4.02379	0.163861
$604$	−2.01490	−0.0819850
$605$	−5.49437	−0.223378
$606$	−5.74851	−0.233517
$607$	−5.01038	−0.203365	−0.101683	−	0.994817i	$-0.532423\pi$
$607$	−5.01038	−0.203365	−0.101683	+	0.994817i	$0.532423\pi$
$608$	2.60935	0.105823
$609$	−26.1787	−1.06082
$610$	8.73728	0.353762
$611$	10.1767	0.411706
$612$	−5.57532	−0.225369
$613$	10.7318	0.433452	0.216726	−	0.976232i	$-0.430462\pi$
$613$	10.7318	0.433452	0.216726	+	0.976232i	$0.430462\pi$
$614$	−28.7561	−1.16050
$615$	20.3295	0.819765
$616$	−13.4345	−0.541293
$617$	31.0384	1.24956	0.624780	−	0.780801i	$-0.285189\pi$
$617$	31.0384	1.24956	0.624780	+	0.780801i	$0.285189\pi$
$618$	−20.6075	−0.828957
$619$	−3.42380	−0.137614	−0.0688070	−	0.997630i	$-0.521919\pi$
$619$	−3.42380	−0.137614	−0.0688070	+	0.997630i	$0.521919\pi$
$620$	4.92192	0.197669
$621$	−21.6702	−0.869595
$622$	29.5877	1.18636
$623$	−37.9097	−1.51882
$624$	−12.4178	−0.497111
$625$	1.00000	0.0400000
$626$	−2.54113	−0.101564
$627$	21.6758	0.865648
$628$	−7.09423	−0.283091
$629$	48.2926	1.92555
$630$	3.91524	0.155987
$631$	−10.3520	−0.412107	−0.206053	−	0.978541i	$-0.566062\pi$
$631$	−10.3520	−0.412107	−0.206053	+	0.978541i	$0.566062\pi$
$632$	−15.0469	−0.598535
$633$	−2.20451	−0.0876214
$634$	3.68916	0.146515
$635$	12.4406	0.493692
$636$	16.2225	0.643266
$637$	−23.9343	−0.948313
$638$	15.7140	0.622124
$639$	−0.170307	−0.00673723
$640$	−1.00000	−0.0395285
$641$	−41.5619	−1.64160	−0.820798	−	0.571218i	$-0.806471\pi$
$641$	−41.5619	−1.64160	−0.820798	+	0.571218i	$0.806471\pi$
$642$	−8.94904	−0.353191
$643$	−8.97570	−0.353967	−0.176984	−	0.984214i	$-0.556634\pi$
$643$	−8.97570	−0.353967	−0.176984	+	0.984214i	$0.556634\pi$
$644$	−19.2943	−0.760304
$645$	−3.61681	−0.142412
$646$	−12.2913	−0.483595
$647$	8.04086	0.316119	0.158059	−	0.987430i	$-0.449476\pi$
$647$	8.04086	0.316119	0.158059	+	0.987430i	$0.449476\pi$
$648$	−11.1499	−0.438009
$649$	−28.2235	−1.10787
$650$	−6.07115	−0.238130
$651$	33.3015	1.30519
$652$	0.187498	0.00734297
$653$	−39.4783	−1.54491	−0.772453	−	0.635071i	$-0.780971\pi$
$653$	−39.4783	−1.54491	−0.772453	+	0.635071i	$0.780971\pi$
$654$	−29.9800	−1.17231
$655$	−10.8064	−0.422241
$656$	−9.93922	−0.388061
$657$	1.21051	0.0472266
$658$	5.54487	0.216162
$659$	31.3469	1.22110	0.610551	−	0.791977i	$-0.290948\pi$
$659$	31.3469	1.22110	0.610551	+	0.791977i	$0.290948\pi$
$660$	−8.30697	−0.323348
$661$	−2.47857	−0.0964053	−0.0482027	−	0.998838i	$-0.515349\pi$
$661$	−2.47857	−0.0964053	−0.0482027	+	0.998838i	$0.515349\pi$
$662$	0.613000	0.0238249
$663$	58.4940	2.27172
$664$	−11.9502	−0.463758
$665$	8.63151	0.334716
$666$	−12.1344	−0.470198
$667$	22.5681	0.873840
$668$	−3.94345	−0.152577
$669$	−14.7860	−0.571661
$670$	−3.39962	−0.131339
$671$	−35.4850	−1.36988
$672$	−6.76596	−0.261003
$673$	−6.01472	−0.231850	−0.115925	−	0.993258i	$-0.536983\pi$
$673$	−6.01472	−0.231850	−0.115925	+	0.993258i	$0.536983\pi$
$674$	−8.67799	−0.334264
$675$	−3.71524	−0.143000
$676$	23.8588	0.917646
$677$	−0.756301	−0.0290670	−0.0145335	−	0.999894i	$-0.504626\pi$
$677$	−0.756301	−0.0290670	−0.0145335	+	0.999894i	$0.504626\pi$
$678$	19.9438	0.765936
$679$	−7.42617	−0.284990
$680$	4.71049	0.180639
$681$	13.8194	0.529560
$682$	−19.9895	−0.765439
$683$	19.1705	0.733539	0.366769	−	0.930312i	$-0.380464\pi$
$683$	19.1705	0.733539	0.366769	+	0.930312i	$0.380464\pi$
$684$	3.08842	0.118089
$685$	−8.41721	−0.321605
$686$	10.1146	0.386176
$687$	36.4867	1.39205
$688$	1.76828	0.0674149
$689$	−48.1520	−1.83445
$690$	−11.9303	−0.454178
$691$	−11.0368	−0.419860	−0.209930	−	0.977716i	$-0.567324\pi$
$691$	−11.0368	−0.419860	−0.209930	+	0.977716i	$0.567324\pi$
$692$	−7.20008	−0.273706
$693$	−15.9011	−0.604032
$694$	1.24392	0.0472186
$695$	5.56936	0.211258
$696$	7.91397	0.299978
$697$	46.8186	1.77338
$698$	24.2745	0.918804
$699$	50.6870	1.91716
$700$	−3.30792	−0.125027
$701$	5.29708	0.200068	0.100034	−	0.994984i	$-0.468105\pi$
$701$	5.29708	0.200068	0.100034	+	0.994984i	$0.468105\pi$
$702$	22.5558	0.851313
$703$	−26.7514	−1.00895
$704$	4.06133	0.153067
$705$	3.42856	0.129127
$706$	15.6851	0.590317
$707$	9.29684	0.349644
$708$	−14.2141	−0.534197
$709$	−9.13462	−0.343058	−0.171529	−	0.985179i	$-0.554871\pi$
$709$	−9.13462	−0.343058	−0.171529	+	0.985179i	$0.554871\pi$
$710$	0.143889	0.00540007
$711$	−17.8095	−0.667908
$712$	11.4603	0.429493
$713$	−28.7085	−1.07514
$714$	31.8710	1.19274
$715$	24.6569	0.922116
$716$	13.3026	0.497140
$717$	25.4034	0.948706
$718$	−17.7131	−0.661048
$719$	−35.7740	−1.33414	−0.667072	−	0.744993i	$-0.732453\pi$
$719$	−35.7740	−1.33414	−0.667072	+	0.744993i	$0.732453\pi$
$720$	−1.18360	−0.0441101
$721$	33.3277	1.24119
$722$	−12.1913	−0.453713
$723$	11.1230	0.413670
$724$	11.9466	0.443994
$725$	3.86918	0.143698
$726$	11.2381	0.417085
$727$	−29.2533	−1.08495	−0.542473	−	0.840073i	$-0.682512\pi$
$727$	−29.2533	−1.08495	−0.542473	+	0.840073i	$0.682512\pi$
$728$	20.0828	0.744320
$729$	9.60032	0.355567
$730$	−1.02274	−0.0378533
$731$	−8.32945	−0.308076
$732$	−17.8711	−0.660535
$733$	−28.1013	−1.03795	−0.518974	−	0.854790i	$-0.673686\pi$
$733$	−28.1013	−1.03795	−0.518974	+	0.854790i	$0.673686\pi$
$734$	35.4320	1.30782
$735$	−8.06354	−0.297428
$736$	5.83278	0.214999
$737$	13.8070	0.508587
$738$	−11.7640	−0.433040
$739$	−3.92651	−0.144439	−0.0722194	−	0.997389i	$-0.523008\pi$
$739$	−3.92651	−0.144439	−0.0722194	+	0.997389i	$0.523008\pi$
$740$	10.2521	0.376876
$741$	−32.4025	−1.19033
$742$	−26.2361	−0.963156
$743$	−17.5157	−0.642587	−0.321294	−	0.946980i	$-0.604118\pi$
$743$	−17.5157	−0.642587	−0.321294	+	0.946980i	$0.604118\pi$
$744$	−10.0672	−0.369082
$745$	−14.1128	−0.517055
$746$	−10.7490	−0.393548
$747$	−14.1442	−0.517511
$748$	−19.1308	−0.699493
$749$	14.4729	0.528829
$750$	−2.04538	−0.0746869
$751$	−41.0654	−1.49850	−0.749249	−	0.662288i	$-0.769586\pi$
$751$	−41.0654	−1.49850	−0.749249	+	0.662288i	$0.769586\pi$
$752$	−1.67624	−0.0611263
$753$	52.2660	1.90468
$754$	−23.4904	−0.855469
$755$	2.01490	0.0733296
$756$	12.2897	0.446972
$757$	−38.0939	−1.38455	−0.692274	−	0.721635i	$-0.743391\pi$
$757$	−38.0939	−1.38455	−0.692274	+	0.721635i	$0.743391\pi$
$758$	25.7635	0.935771
$759$	48.4527	1.75872
$760$	−2.60935	−0.0946511
$761$	26.7521	0.969763	0.484882	−	0.874580i	$-0.338863\pi$
$761$	26.7521	0.969763	0.484882	+	0.874580i	$0.338863\pi$
$762$	−25.4459	−0.921807
$763$	48.4854	1.75529
$764$	−16.1153	−0.583031
$765$	5.57532	0.201576
$766$	23.0728	0.833655
$767$	42.1904	1.52341
$768$	2.04538	0.0738065
$769$	−31.5190	−1.13661	−0.568303	−	0.822820i	$-0.692400\pi$
$769$	−31.5190	−1.13661	−0.568303	+	0.822820i	$0.692400\pi$
$770$	13.4345	0.484147
$771$	15.7118	0.565847
$772$	−9.72787	−0.350114
$773$	−41.8523	−1.50532	−0.752661	−	0.658409i	$-0.771230\pi$
$773$	−41.8523	−1.50532	−0.752661	+	0.658409i	$0.771230\pi$
$774$	2.09293	0.0752287
$775$	−4.92192	−0.176801
$776$	2.24497	0.0805897
$777$	69.3655	2.48847
$778$	−1.16036	−0.0416009
$779$	−25.9349	−0.929214
$780$	12.4178	0.444629
$781$	−0.584381	−0.0209108
$782$	−27.4752	−0.982513
$783$	−14.3750	−0.513719
$784$	3.94231	0.140797
$785$	7.09423	0.253204
$786$	22.1033	0.788397
$787$	−15.3152	−0.545926	−0.272963	−	0.962024i	$-0.588004\pi$
$787$	−15.3152	−0.545926	−0.272963	+	0.962024i	$0.588004\pi$
$788$	26.9822	0.961201
$789$	−32.2946	−1.14972
$790$	15.0469	0.535346
$791$	−32.2543	−1.14683
$792$	4.80697	0.170808
$793$	53.0453	1.88369
$794$	−13.1303	−0.465975
$795$	−16.2225	−0.575354
$796$	−13.9515	−0.494498
$797$	42.2404	1.49623	0.748115	−	0.663569i	$-0.230959\pi$
$797$	42.2404	1.49623	0.748115	+	0.663569i	$0.230959\pi$
$798$	−17.6548	−0.624972
$799$	7.89593	0.279338
$800$	1.00000	0.0353553
$801$	13.5644	0.479274
$802$	13.5568	0.478708
$803$	4.15368	0.146580
$804$	6.95354	0.245232
$805$	19.2943	0.680036
$806$	29.8817	1.05254
$807$	17.7750	0.625711
$808$	−2.81048	−0.0988724
$809$	−15.5694	−0.547390	−0.273695	−	0.961817i	$-0.588246\pi$
$809$	−15.5694	−0.547390	−0.273695	+	0.961817i	$0.588246\pi$
$810$	11.1499	0.391767
$811$	−0.429510	−0.0150821	−0.00754106	−	0.999972i	$-0.502400\pi$
$811$	−0.429510	−0.0150821	−0.00754106	+	0.999972i	$0.502400\pi$
$812$	−12.7989	−0.449155
$813$	20.2540	0.710340
$814$	−41.6373	−1.45938
$815$	−0.187498	−0.00656776
$816$	−9.63476	−0.337284
$817$	4.61405	0.161425
$818$	19.5527	0.683644
$819$	23.7700	0.830591
$820$	9.93922	0.347092
$821$	40.2226	1.40378	0.701890	−	0.712285i	$-0.252340\pi$
$821$	40.2226	1.40378	0.701890	+	0.712285i	$0.252340\pi$
$822$	17.2164	0.600492
$823$	25.7737	0.898415	0.449208	−	0.893427i	$-0.351706\pi$
$823$	25.7737	0.898415	0.449208	+	0.893427i	$0.351706\pi$
$824$	−10.0751	−0.350984
$825$	8.30697	0.289212
$826$	22.9878	0.799848
$827$	20.0648	0.697722	0.348861	−	0.937174i	$-0.386568\pi$
$827$	20.0648	0.697722	0.348861	+	0.937174i	$0.386568\pi$
$828$	6.90366	0.239919
$829$	−17.9692	−0.624095	−0.312048	−	0.950066i	$-0.601015\pi$
$829$	−17.9692	−0.624095	−0.312048	+	0.950066i	$0.601015\pi$
$830$	11.9502	0.414798
$831$	−47.4365	−1.64555
$832$	−6.07115	−0.210479
$833$	−18.5702	−0.643420
$834$	−11.3915	−0.394455
$835$	3.94345	0.136469
$836$	10.5974	0.366520
$837$	18.2861	0.632061
$838$	−3.22002	−0.111234
$839$	−5.27029	−0.181951	−0.0909753	−	0.995853i	$-0.528998\pi$
$839$	−5.27029	−0.181951	−0.0909753	+	0.995853i	$0.528998\pi$
$840$	6.76596	0.233448
$841$	−14.0294	−0.483773
$842$	17.1218	0.590055
$843$	−27.2203	−0.937517
$844$	−1.07780	−0.0370993
$845$	−23.8588	−0.820768
$846$	−1.98400	−0.0682112
$847$	−18.1749	−0.624498
$848$	7.93129	0.272362
$849$	−68.0410	−2.33516
$850$	−4.71049	−0.161568
$851$	−59.7984	−2.04986
$852$	−0.294309	−0.0100829
$853$	−18.3181	−0.627198	−0.313599	−	0.949555i	$-0.601535\pi$
$853$	−18.3181	−0.627198	−0.313599	+	0.949555i	$0.601535\pi$
$854$	28.9022	0.989013
$855$	−3.08842	−0.105622
$856$	−4.37524	−0.149543
$857$	−27.7623	−0.948342	−0.474171	−	0.880433i	$-0.657252\pi$
$857$	−27.7623	−0.948342	−0.474171	+	0.880433i	$0.657252\pi$
$858$	−50.4328	−1.72175
$859$	31.1211	1.06184	0.530919	−	0.847423i	$-0.321847\pi$
$859$	31.1211	1.06184	0.530919	+	0.847423i	$0.321847\pi$
$860$	−1.76828	−0.0602977
$861$	67.2483	2.29182
$862$	8.72805	0.297278
$863$	−38.5723	−1.31302	−0.656508	−	0.754319i	$-0.727967\pi$
$863$	−38.5723	−1.31302	−0.656508	+	0.754319i	$0.727967\pi$
$864$	−3.71524	−0.126395
$865$	7.20008	0.244810
$866$	−28.4409	−0.966462
$867$	10.6129	0.360434
$868$	16.2813	0.552624
$869$	−61.1105	−2.07303
$870$	−7.91397	−0.268309
$871$	−20.6396	−0.699347
$872$	−14.6574	−0.496361
$873$	2.65714	0.0899305
$874$	15.2198	0.514816
$875$	3.30792	0.111828
$876$	2.09190	0.0706786
$877$	−50.4851	−1.70476	−0.852380	−	0.522923i	$-0.824842\pi$
$877$	−50.4851	−1.70476	−0.852380	+	0.522923i	$0.824842\pi$
$878$	−0.268678	−0.00906744
$879$	−48.2174	−1.62633
$880$	−4.06133	−0.136907
$881$	−15.2440	−0.513585	−0.256792	−	0.966467i	$-0.582666\pi$
$881$	−15.2440	−0.513585	−0.256792	+	0.966467i	$0.582666\pi$
$882$	4.66611	0.157116
$883$	−29.4058	−0.989585	−0.494793	−	0.869011i	$-0.664756\pi$
$883$	−29.4058	−0.989585	−0.494793	+	0.869011i	$0.664756\pi$
$884$	28.5981	0.961857
$885$	14.2141	0.477800
$886$	6.16055	0.206968
$887$	−45.8342	−1.53896	−0.769481	−	0.638669i	$-0.779485\pi$
$887$	−45.8342	−1.53896	−0.769481	+	0.638669i	$0.779485\pi$
$888$	−20.9696	−0.703692
$889$	41.1526	1.38021
$890$	−11.4603	−0.384150
$891$	−45.2833	−1.51705
$892$	−7.22898	−0.242044
$893$	−4.37391	−0.146367
$894$	28.8662	0.965430
$895$	−13.3026	−0.444655
$896$	−3.30792	−0.110510
$897$	−72.4304	−2.41838
$898$	13.0684	0.436100
$899$	−19.0438	−0.635147
$900$	1.18360	0.0394532
$901$	−37.3603	−1.24465
$902$	−40.3664	−1.34405
$903$	−11.9641	−0.398140
$904$	9.75062	0.324301
$905$	−11.9466	−0.397120
$906$	−4.12124	−0.136919
$907$	−28.4569	−0.944894	−0.472447	−	0.881359i	$-0.656629\pi$
$907$	−28.4569	−0.944894	−0.472447	+	0.881359i	$0.656629\pi$
$908$	6.75638	0.224218
$909$	−3.32648	−0.110332
$910$	−20.0828	−0.665740
$911$	−27.5531	−0.912875	−0.456438	−	0.889755i	$-0.650875\pi$
$911$	−27.5531	−0.912875	−0.456438	+	0.889755i	$0.650875\pi$
$912$	5.33712	0.176730
$913$	−48.5337	−1.60623
$914$	−26.8160	−0.886993
$915$	17.8711	0.590800
$916$	17.8385	0.589402
$917$	−35.7467	−1.18046
$918$	17.5006	0.577606
$919$	18.1633	0.599152	0.299576	−	0.954072i	$-0.403155\pi$
$919$	18.1633	0.599152	0.299576	+	0.954072i	$0.403155\pi$
$920$	−5.83278	−0.192301
$921$	−58.8173	−1.93810
$922$	−38.5181	−1.26853
$923$	0.873572	0.0287540
$924$	−27.4788	−0.903985
$925$	−10.2521	−0.337088
$926$	2.90319	0.0954049
$927$	−11.9249	−0.391665
$928$	3.86918	0.127012
$929$	19.8755	0.652095	0.326048	−	0.945353i	$-0.394283\pi$
$929$	19.8755	0.652095	0.326048	+	0.945353i	$0.394283\pi$
$930$	10.0672	0.330117
$931$	10.2869	0.337139
$932$	24.7812	0.811734
$933$	60.5183	1.98128
$934$	−31.5922	−1.03373
$935$	19.1308	0.625645
$936$	−7.18579	−0.234875
$937$	52.6961	1.72151	0.860754	−	0.509021i	$-0.169993\pi$
$937$	52.6961	1.72151	0.860754	+	0.509021i	$0.169993\pi$
$938$	−11.2457	−0.367184
$939$	−5.19758	−0.169617
$940$	1.67624	0.0546730
$941$	43.4955	1.41791	0.708957	−	0.705252i	$-0.249166\pi$
$941$	43.4955	1.41791	0.708957	+	0.705252i	$0.249166\pi$
$942$	−14.5104	−0.472775
$943$	−57.9733	−1.88787
$944$	−6.94933	−0.226182
$945$	−12.2897	−0.399784
$946$	7.18155	0.233492
$947$	−37.0660	−1.20448	−0.602241	−	0.798314i	$-0.705725\pi$
$947$	−37.0660	−1.20448	−0.602241	+	0.798314i	$0.705725\pi$
$948$	−30.7768	−0.999582
$949$	−6.20920	−0.201559
$950$	2.60935	0.0846585
$951$	7.54576	0.244688
$952$	15.5819	0.505013
$953$	−48.7904	−1.58047	−0.790237	−	0.612801i	$-0.790043\pi$
$953$	−48.7904	−1.58047	−0.790237	+	0.612801i	$0.790043\pi$
$954$	9.38746	0.303930
$955$	16.1153	0.521479
$956$	12.4199	0.401687
$957$	32.1412	1.03898
$958$	30.3929	0.981949
$959$	−27.8434	−0.899111
$960$	−2.04538	−0.0660145
$961$	−6.77467	−0.218538
$962$	62.2422	2.00677
$963$	−5.17852	−0.166875
$964$	5.43812	0.175150
$965$	9.72787	0.313151
$966$	−39.4644	−1.26974
$967$	−3.46991	−0.111585	−0.0557923	−	0.998442i	$-0.517768\pi$
$967$	−3.46991	−0.111585	−0.0557923	+	0.998442i	$0.517768\pi$
$968$	5.49437	0.176596
$969$	−25.1405	−0.807628
$970$	−2.24497	−0.0720816
$971$	−35.1086	−1.12669	−0.563345	−	0.826222i	$-0.690486\pi$
$971$	−35.1086	−1.12669	−0.563345	+	0.826222i	$0.690486\pi$
$972$	−11.6601	−0.373997
$973$	18.4230	0.590614
$974$	−18.7972	−0.602301
$975$	−12.4178	−0.397689
$976$	−8.73728	−0.279674
$977$	51.7209	1.65470	0.827349	−	0.561688i	$-0.189848\pi$
$977$	51.7209	1.65470	0.827349	+	0.561688i	$0.189848\pi$
$978$	0.383505	0.0122631
$979$	46.5440	1.48755
$980$	−3.94231	−0.125933
$981$	−17.3484	−0.553893
$982$	18.3670	0.586115
$983$	−54.0903	−1.72521	−0.862607	−	0.505875i	$-0.831170\pi$
$983$	−54.0903	−1.72521	−0.862607	+	0.505875i	$0.831170\pi$
$984$	−20.3295	−0.648081
$985$	−26.9822	−0.859724
$986$	−18.2258	−0.580426
$987$	11.3414	0.361001
$988$	−15.8417	−0.503993
$989$	10.3140	0.327965
$990$	−4.80697	−0.152776
$991$	17.1224	0.543912	0.271956	−	0.962310i	$-0.412330\pi$
$991$	17.1224	0.543912	0.271956	+	0.962310i	$0.412330\pi$
$992$	−4.92192	−0.156271
$993$	1.25382	0.0397888
$994$	0.475973	0.0150970
$995$	13.9515	0.442293
$996$	−24.4428	−0.774499
$997$	−10.8425	−0.343386	−0.171693	−	0.985151i	$-0.554924\pi$
$997$	−10.8425	−0.343386	−0.171693	+	0.985151i	$0.554924\pi$
$998$	37.7917	1.19627
$999$	38.0892	1.20509

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.f.1.19	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.f.1.19	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.04538 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.04538 q^{6} -3.30792 q^{7} +1.00000 q^{8} +1.18360 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.04538 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.04538 q^{6} -3.30792 q^{7} +1.00000 q^{8} +1.18360 q^{9} -1.00000 q^{10} +4.06133 q^{11} +2.04538 q^{12} -6.07115 q^{13} -3.30792 q^{14} -2.04538 q^{15} +1.00000 q^{16} -4.71049 q^{17} +1.18360 q^{18} +2.60935 q^{19} -1.00000 q^{20} -6.76596 q^{21} +4.06133 q^{22} +5.83278 q^{23} +2.04538 q^{24} +1.00000 q^{25} -6.07115 q^{26} -3.71524 q^{27} -3.30792 q^{28} +3.86918 q^{29} -2.04538 q^{30} -4.92192 q^{31} +1.00000 q^{32} +8.30697 q^{33} -4.71049 q^{34} +3.30792 q^{35} +1.18360 q^{36} -10.2521 q^{37} +2.60935 q^{38} -12.4178 q^{39} -1.00000 q^{40} -9.93922 q^{41} -6.76596 q^{42} +1.76828 q^{43} +4.06133 q^{44} -1.18360 q^{45} +5.83278 q^{46} -1.67624 q^{47} +2.04538 q^{48} +3.94231 q^{49} +1.00000 q^{50} -9.63476 q^{51} -6.07115 q^{52} +7.93129 q^{53} -3.71524 q^{54} -4.06133 q^{55} -3.30792 q^{56} +5.33712 q^{57} +3.86918 q^{58} -6.94933 q^{59} -2.04538 q^{60} -8.73728 q^{61} -4.92192 q^{62} -3.91524 q^{63} +1.00000 q^{64} +6.07115 q^{65} +8.30697 q^{66} +3.39962 q^{67} -4.71049 q^{68} +11.9303 q^{69} +3.30792 q^{70} -0.143889 q^{71} +1.18360 q^{72} +1.02274 q^{73} -10.2521 q^{74} +2.04538 q^{75} +2.60935 q^{76} -13.4345 q^{77} -12.4178 q^{78} -15.0469 q^{79} -1.00000 q^{80} -11.1499 q^{81} -9.93922 q^{82} -11.9502 q^{83} -6.76596 q^{84} +4.71049 q^{85} +1.76828 q^{86} +7.91397 q^{87} +4.06133 q^{88} +11.4603 q^{89} -1.18360 q^{90} +20.0828 q^{91} +5.83278 q^{92} -10.0672 q^{93} -1.67624 q^{94} -2.60935 q^{95} +2.04538 q^{96} +2.24497 q^{97} +3.94231 q^{98} +4.80697 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9}+O(q^{10}) \) 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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