LMFDB - Embedded newform 4022.2.a.d.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4022, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4022 = 2 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4022.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.1158316930$
Analytic rank:	$1$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	4022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.37393 q^{3} +1.00000 q^{4} +1.41638 q^{5} +2.37393 q^{6} +3.16627 q^{7} -1.00000 q^{8} +2.63555 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.37393 q^{3} +1.00000 q^{4} +1.41638 q^{5} +2.37393 q^{6} +3.16627 q^{7} -1.00000 q^{8} +2.63555 q^{9} -1.41638 q^{10} -4.44420 q^{11} -2.37393 q^{12} -2.06102 q^{13} -3.16627 q^{14} -3.36240 q^{15} +1.00000 q^{16} +2.79893 q^{17} -2.63555 q^{18} +3.09851 q^{19} +1.41638 q^{20} -7.51651 q^{21} +4.44420 q^{22} +3.32085 q^{23} +2.37393 q^{24} -2.99385 q^{25} +2.06102 q^{26} +0.865174 q^{27} +3.16627 q^{28} -2.05372 q^{29} +3.36240 q^{30} +2.77414 q^{31} -1.00000 q^{32} +10.5502 q^{33} -2.79893 q^{34} +4.48466 q^{35} +2.63555 q^{36} -7.57692 q^{37} -3.09851 q^{38} +4.89272 q^{39} -1.41638 q^{40} +1.40681 q^{41} +7.51651 q^{42} -9.29805 q^{43} -4.44420 q^{44} +3.73296 q^{45} -3.32085 q^{46} -3.62831 q^{47} -2.37393 q^{48} +3.02526 q^{49} +2.99385 q^{50} -6.64448 q^{51} -2.06102 q^{52} +0.794159 q^{53} -0.865174 q^{54} -6.29470 q^{55} -3.16627 q^{56} -7.35565 q^{57} +2.05372 q^{58} -9.14533 q^{59} -3.36240 q^{60} -1.82446 q^{61} -2.77414 q^{62} +8.34487 q^{63} +1.00000 q^{64} -2.91920 q^{65} -10.5502 q^{66} -12.9905 q^{67} +2.79893 q^{68} -7.88346 q^{69} -4.48466 q^{70} +11.9626 q^{71} -2.63555 q^{72} +1.59346 q^{73} +7.57692 q^{74} +7.10721 q^{75} +3.09851 q^{76} -14.0715 q^{77} -4.89272 q^{78} -2.45179 q^{79} +1.41638 q^{80} -9.96052 q^{81} -1.40681 q^{82} +12.3138 q^{83} -7.51651 q^{84} +3.96437 q^{85} +9.29805 q^{86} +4.87540 q^{87} +4.44420 q^{88} +3.08210 q^{89} -3.73296 q^{90} -6.52574 q^{91} +3.32085 q^{92} -6.58562 q^{93} +3.62831 q^{94} +4.38868 q^{95} +2.37393 q^{96} +14.3010 q^{97} -3.02526 q^{98} -11.7129 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q - 37 q^{2} - 5 q^{3} + 37 q^{4} - 13 q^{5} + 5 q^{6} - 22 q^{7} - 37 q^{8} + 32 q^{9}+O(q^{10}) $ 37 * q - 37 * q^2 - 5 * q^3 + 37 * q^4 - 13 * q^5 + 5 * q^6 - 22 * q^7 - 37 * q^8 + 32 * q^9	\( 37 q - 37 q^{2} - 5 q^{3} + 37 q^{4} - 13 q^{5} + 5 q^{6} - 22 q^{7} - 37 q^{8} + 32 q^{9} + 13 q^{10} + 12 q^{11} - 5 q^{12} - 36 q^{13} + 22 q^{14} - 7 q^{15} + 37 q^{16} + 4 q^{17} - 32 q^{18} - 10 q^{19} - 13 q^{20} - 11 q^{21} - 12 q^{22} - q^{23} + 5 q^{24} + 8 q^{25} + 36 q^{26} - 20 q^{27} - 22 q^{28} - 6 q^{29} + 7 q^{30} - 23 q^{31} - 37 q^{32} - 27 q^{33} - 4 q^{34} + 24 q^{35} + 32 q^{36} - 46 q^{37} + 10 q^{38} + 5 q^{39} + 13 q^{40} + 11 q^{41} + 11 q^{42} - 22 q^{43} + 12 q^{44} - 57 q^{45} + q^{46} - 18 q^{47} - 5 q^{48} - q^{49} - 8 q^{50} + 18 q^{51} - 36 q^{52} - 25 q^{53} + 20 q^{54} - 25 q^{55} + 22 q^{56} - 25 q^{57} + 6 q^{58} + 24 q^{59} - 7 q^{60} - 40 q^{61} + 23 q^{62} - 38 q^{63} + 37 q^{64} + 14 q^{65} + 27 q^{66} - 49 q^{67} + 4 q^{68} - 19 q^{69} - 24 q^{70} + 27 q^{71} - 32 q^{72} - 87 q^{73} + 46 q^{74} - 5 q^{75} - 10 q^{76} - 50 q^{77} - 5 q^{78} + 11 q^{79} - 13 q^{80} + 5 q^{81} - 11 q^{82} - 9 q^{83} - 11 q^{84} - 68 q^{85} + 22 q^{86} - 12 q^{87} - 12 q^{88} - 3 q^{89} + 57 q^{90} - 19 q^{91} - q^{92} - 69 q^{93} + 18 q^{94} + 27 q^{95} + 5 q^{96} - 98 q^{97} + q^{98} + 33 q^{99}+O(q^{100}) \) 37 * q - 37 * q^2 - 5 * q^3 + 37 * q^4 - 13 * q^5 + 5 * q^6 - 22 * q^7 - 37 * q^8 + 32 * q^9 + 13 * q^10 + 12 * q^11 - 5 * q^12 - 36 * q^13 + 22 * q^14 - 7 * q^15 + 37 * q^16 + 4 * q^17 - 32 * q^18 - 10 * q^19 - 13 * q^20 - 11 * q^21 - 12 * q^22 - q^23 + 5 * q^24 + 8 * q^25 + 36 * q^26 - 20 * q^27 - 22 * q^28 - 6 * q^29 + 7 * q^30 - 23 * q^31 - 37 * q^32 - 27 * q^33 - 4 * q^34 + 24 * q^35 + 32 * q^36 - 46 * q^37 + 10 * q^38 + 5 * q^39 + 13 * q^40 + 11 * q^41 + 11 * q^42 - 22 * q^43 + 12 * q^44 - 57 * q^45 + q^46 - 18 * q^47 - 5 * q^48 - q^49 - 8 * q^50 + 18 * q^51 - 36 * q^52 - 25 * q^53 + 20 * q^54 - 25 * q^55 + 22 * q^56 - 25 * q^57 + 6 * q^58 + 24 * q^59 - 7 * q^60 - 40 * q^61 + 23 * q^62 - 38 * q^63 + 37 * q^64 + 14 * q^65 + 27 * q^66 - 49 * q^67 + 4 * q^68 - 19 * q^69 - 24 * q^70 + 27 * q^71 - 32 * q^72 - 87 * q^73 + 46 * q^74 - 5 * q^75 - 10 * q^76 - 50 * q^77 - 5 * q^78 + 11 * q^79 - 13 * q^80 + 5 * q^81 - 11 * q^82 - 9 * q^83 - 11 * q^84 - 68 * q^85 + 22 * q^86 - 12 * q^87 - 12 * q^88 - 3 * q^89 + 57 * q^90 - 19 * q^91 - q^92 - 69 * q^93 + 18 * q^94 + 27 * q^95 + 5 * q^96 - 98 * q^97 + q^98 + 33 * 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
$3$	−2.37393	−1.37059	−0.685295	−	0.728265i	$-0.740327\pi$
$3$	−2.37393	−1.37059	−0.685295	+	0.728265i	$0.740327\pi$
$4$	1.00000	0.500000
$5$	1.41638	0.633427	0.316713	−	0.948521i	$-0.397421\pi$
$5$	1.41638	0.633427	0.316713	+	0.948521i	$0.397421\pi$
$6$	2.37393	0.969154
$7$	3.16627	1.19674	0.598369	−	0.801221i	$-0.295816\pi$
$7$	3.16627	1.19674	0.598369	+	0.801221i	$0.295816\pi$
$8$	−1.00000	−0.353553
$9$	2.63555	0.878517
$10$	−1.41638	−0.447900
$11$	−4.44420	−1.33998	−0.669989	−	0.742371i	$-0.733701\pi$
$11$	−4.44420	−1.33998	−0.669989	+	0.742371i	$0.733701\pi$
$12$	−2.37393	−0.685295
$13$	−2.06102	−0.571624	−0.285812	−	0.958286i	$-0.592263\pi$
$13$	−2.06102	−0.571624	−0.285812	+	0.958286i	$0.592263\pi$
$14$	−3.16627	−0.846221
$15$	−3.36240	−0.868168
$16$	1.00000	0.250000
$17$	2.79893	0.678841	0.339420	−	0.940635i	$-0.389769\pi$
$17$	2.79893	0.678841	0.339420	+	0.940635i	$0.389769\pi$
$18$	−2.63555	−0.621206
$19$	3.09851	0.710847	0.355423	−	0.934705i	$-0.384337\pi$
$19$	3.09851	0.710847	0.355423	+	0.934705i	$0.384337\pi$
$20$	1.41638	0.316713
$21$	−7.51651	−1.64024
$22$	4.44420	0.947507
$23$	3.32085	0.692444	0.346222	−	0.938153i	$-0.387464\pi$
$23$	3.32085	0.692444	0.346222	+	0.938153i	$0.387464\pi$
$24$	2.37393	0.484577
$25$	−2.99385	−0.598771
$26$	2.06102	0.404199
$27$	0.865174	0.166503
$28$	3.16627	0.598369
$29$	−2.05372	−0.381367	−0.190684	−	0.981652i	$-0.561070\pi$
$29$	−2.05372	−0.381367	−0.190684	+	0.981652i	$0.561070\pi$
$30$	3.36240	0.613888
$31$	2.77414	0.498250	0.249125	−	0.968471i	$-0.419857\pi$
$31$	2.77414	0.498250	0.249125	+	0.968471i	$0.419857\pi$
$32$	−1.00000	−0.176777
$33$	10.5502	1.83656
$34$	−2.79893	−0.480013
$35$	4.48466	0.758045
$36$	2.63555	0.439259
$37$	−7.57692	−1.24564	−0.622819	−	0.782366i	$-0.714013\pi$
$37$	−7.57692	−1.24564	−0.622819	+	0.782366i	$0.714013\pi$
$38$	−3.09851	−0.502645
$39$	4.89272	0.783462
$40$	−1.41638	−0.223950
$41$	1.40681	0.219706	0.109853	−	0.993948i	$-0.464962\pi$
$41$	1.40681	0.219706	0.109853	+	0.993948i	$0.464962\pi$
$42$	7.51651	1.15982
$43$	−9.29805	−1.41794	−0.708969	−	0.705239i	$-0.750840\pi$
$43$	−9.29805	−1.41794	−0.708969	+	0.705239i	$0.750840\pi$
$44$	−4.44420	−0.669989
$45$	3.73296	0.556476
$46$	−3.32085	−0.489632
$47$	−3.62831	−0.529243	−0.264622	−	0.964352i	$-0.585247\pi$
$47$	−3.62831	−0.529243	−0.264622	+	0.964352i	$0.585247\pi$
$48$	−2.37393	−0.342648
$49$	3.02526	0.432181
$50$	2.99385	0.423395
$51$	−6.64448	−0.930413
$52$	−2.06102	−0.285812
$53$	0.794159	0.109086	0.0545430	−	0.998511i	$-0.482630\pi$
$53$	0.794159	0.109086	0.0545430	+	0.998511i	$0.482630\pi$
$54$	−0.865174	−0.117735
$55$	−6.29470	−0.848777
$56$	−3.16627	−0.423111
$57$	−7.35565	−0.974280
$58$	2.05372	0.269667
$59$	−9.14533	−1.19062	−0.595310	−	0.803496i	$-0.702971\pi$
$59$	−9.14533	−1.19062	−0.595310	+	0.803496i	$0.702971\pi$
$60$	−3.36240	−0.434084
$61$	−1.82446	−0.233598	−0.116799	−	0.993156i	$-0.537263\pi$
$61$	−1.82446	−0.233598	−0.116799	+	0.993156i	$0.537263\pi$
$62$	−2.77414	−0.352316
$63$	8.34487	1.05135
$64$	1.00000	0.125000
$65$	−2.91920	−0.362082
$66$	−10.5502	−1.29864
$67$	−12.9905	−1.58704	−0.793522	−	0.608541i	$-0.791755\pi$
$67$	−12.9905	−1.58704	−0.793522	+	0.608541i	$0.791755\pi$
$68$	2.79893	0.339420
$69$	−7.88346	−0.949057
$70$	−4.48466	−0.536019
$71$	11.9626	1.41970	0.709849	−	0.704354i	$-0.248763\pi$
$71$	11.9626	1.41970	0.709849	+	0.704354i	$0.248763\pi$
$72$	−2.63555	−0.310603
$73$	1.59346	0.186500	0.0932501	−	0.995643i	$-0.470274\pi$
$73$	1.59346	0.186500	0.0932501	+	0.995643i	$0.470274\pi$
$74$	7.57692	0.880799
$75$	7.10721	0.820669
$76$	3.09851	0.355423
$77$	−14.0715	−1.60360
$78$	−4.89272	−0.553991
$79$	−2.45179	−0.275848	−0.137924	−	0.990443i	$-0.544043\pi$
$79$	−2.45179	−0.275848	−0.137924	+	0.990443i	$0.544043\pi$
$80$	1.41638	0.158357
$81$	−9.96052	−1.10672
$82$	−1.40681	−0.155356
$83$	12.3138	1.35162	0.675809	−	0.737077i	$-0.263795\pi$
$83$	12.3138	1.35162	0.675809	+	0.737077i	$0.263795\pi$
$84$	−7.51651	−0.820118
$85$	3.96437	0.429996
$86$	9.29805	1.00263
$87$	4.87540	0.522698
$88$	4.44420	0.473754
$89$	3.08210	0.326702	0.163351	−	0.986568i	$-0.447770\pi$
$89$	3.08210	0.326702	0.163351	+	0.986568i	$0.447770\pi$
$90$	−3.73296	−0.393488
$91$	−6.52574	−0.684084
$92$	3.32085	0.346222
$93$	−6.58562	−0.682897
$94$	3.62831	0.374231
$95$	4.38868	0.450269
$96$	2.37393	0.242288
$97$	14.3010	1.45205	0.726023	−	0.687671i	$-0.241367\pi$
$97$	14.3010	1.45205	0.726023	+	0.687671i	$0.241367\pi$
$98$	−3.02526	−0.305598
$99$	−11.7129	−1.17719
$100$	−2.99385	−0.299385
$101$	4.79143	0.476765	0.238382	−	0.971171i	$-0.423383\pi$
$101$	4.79143	0.476765	0.238382	+	0.971171i	$0.423383\pi$
$102$	6.64448	0.657901
$103$	2.36122	0.232658	0.116329	−	0.993211i	$-0.462887\pi$
$103$	2.36122	0.232658	0.116329	+	0.993211i	$0.462887\pi$
$104$	2.06102	0.202100
$105$	−10.6463	−1.03897
$106$	−0.794159	−0.0771355
$107$	9.64480	0.932398	0.466199	−	0.884680i	$-0.345623\pi$
$107$	9.64480	0.932398	0.466199	+	0.884680i	$0.345623\pi$
$108$	0.865174	0.0832514
$109$	−14.6103	−1.39941	−0.699707	−	0.714430i	$-0.746686\pi$
$109$	−14.6103	−1.39941	−0.699707	+	0.714430i	$0.746686\pi$
$110$	6.29470	0.600176
$111$	17.9871	1.70726
$112$	3.16627	0.299184
$113$	5.83917	0.549303	0.274651	−	0.961544i	$-0.411438\pi$
$113$	5.83917	0.549303	0.274651	+	0.961544i	$0.411438\pi$
$114$	7.35565	0.688920
$115$	4.70359	0.438612
$116$	−2.05372	−0.190684
$117$	−5.43192	−0.502182
$118$	9.14533	0.841896
$119$	8.86218	0.812394
$120$	3.36240	0.306944
$121$	8.75093	0.795539
$122$	1.82446	0.165179
$123$	−3.33966	−0.301127
$124$	2.77414	0.249125
$125$	−11.3224	−1.01270
$126$	−8.34487	−0.743420
$127$	−8.39481	−0.744919	−0.372459	−	0.928049i	$-0.621485\pi$
$127$	−8.39481	−0.744919	−0.372459	+	0.928049i	$0.621485\pi$
$128$	−1.00000	−0.0883883
$129$	22.0729	1.94341
$130$	2.91920	0.256030
$131$	−6.24893	−0.545971	−0.272986	−	0.962018i	$-0.588011\pi$
$131$	−6.24893	−0.545971	−0.272986	+	0.962018i	$0.588011\pi$
$132$	10.5502	0.918280
$133$	9.81072	0.850697
$134$	12.9905	1.12221
$135$	1.22542	0.105467
$136$	−2.79893	−0.240007
$137$	−1.77696	−0.151816	−0.0759078	−	0.997115i	$-0.524185\pi$
$137$	−1.77696	−0.151816	−0.0759078	+	0.997115i	$0.524185\pi$
$138$	7.88346	0.671085
$139$	2.82872	0.239928	0.119964	−	0.992778i	$-0.461722\pi$
$139$	2.82872	0.239928	0.119964	+	0.992778i	$0.461722\pi$
$140$	4.48466	0.379023
$141$	8.61336	0.725375
$142$	−11.9626	−1.00388
$143$	9.15959	0.765963
$144$	2.63555	0.219629
$145$	−2.90886	−0.241568
$146$	−1.59346	−0.131876
$147$	−7.18177	−0.592342
$148$	−7.57692	−0.622819
$149$	−19.3924	−1.58869	−0.794343	−	0.607470i	$-0.792185\pi$
$149$	−19.3924	−1.58869	−0.794343	+	0.607470i	$0.792185\pi$
$150$	−7.10721	−0.580301
$151$	2.69389	0.219225	0.109613	−	0.993974i	$-0.465039\pi$
$151$	2.69389	0.219225	0.109613	+	0.993974i	$0.465039\pi$
$152$	−3.09851	−0.251322
$153$	7.37673	0.596374
$154$	14.0715	1.13392
$155$	3.92925	0.315605
$156$	4.89272	0.391731
$157$	−5.91854	−0.472351	−0.236176	−	0.971710i	$-0.575894\pi$
$157$	−5.91854	−0.472351	−0.236176	+	0.971710i	$0.575894\pi$
$158$	2.45179	0.195054
$159$	−1.88528	−0.149512
$160$	−1.41638	−0.111975
$161$	10.5147	0.828674
$162$	9.96052	0.782572
$163$	−15.4816	−1.21261	−0.606307	−	0.795231i	$-0.707350\pi$
$163$	−15.4816	−1.21261	−0.606307	+	0.795231i	$0.707350\pi$
$164$	1.40681	0.109853
$165$	14.9432	1.16333
$166$	−12.3138	−0.955738
$167$	23.0706	1.78525	0.892627	−	0.450796i	$-0.148860\pi$
$167$	23.0706	1.78525	0.892627	+	0.450796i	$0.148860\pi$
$168$	7.51651	0.579911
$169$	−8.75220	−0.673246
$170$	−3.96437	−0.304053
$171$	8.16628	0.624491
$172$	−9.29805	−0.708969
$173$	−4.19988	−0.319311	−0.159656	−	0.987173i	$-0.551038\pi$
$173$	−4.19988	−0.319311	−0.159656	+	0.987173i	$0.551038\pi$
$174$	−4.87540	−0.369603
$175$	−9.47935	−0.716571
$176$	−4.44420	−0.334994
$177$	21.7104	1.63185
$178$	−3.08210	−0.231013
$179$	8.96546	0.670110	0.335055	−	0.942199i	$-0.391245\pi$
$179$	8.96546	0.670110	0.335055	+	0.942199i	$0.391245\pi$
$180$	3.73296	0.278238
$181$	−7.69334	−0.571841	−0.285921	−	0.958253i	$-0.592299\pi$
$181$	−7.69334	−0.571841	−0.285921	+	0.958253i	$0.592299\pi$
$182$	6.52574	0.483720
$183$	4.33115	0.320168
$184$	−3.32085	−0.244816
$185$	−10.7318	−0.789020
$186$	6.58562	0.482881
$187$	−12.4390	−0.909631
$188$	−3.62831	−0.264622
$189$	2.73937	0.199260
$190$	−4.38868	−0.318388
$191$	7.44623	0.538790	0.269395	−	0.963030i	$-0.413176\pi$
$191$	7.44623	0.538790	0.269395	+	0.963030i	$0.413176\pi$
$192$	−2.37393	−0.171324
$193$	−21.1416	−1.52181	−0.760903	−	0.648866i	$-0.775244\pi$
$193$	−21.1416	−1.52181	−0.760903	+	0.648866i	$0.775244\pi$
$194$	−14.3010	−1.02675
$195$	6.92997	0.496266
$196$	3.02526	0.216090
$197$	7.08373	0.504695	0.252348	−	0.967637i	$-0.418797\pi$
$197$	7.08373	0.504695	0.252348	+	0.967637i	$0.418797\pi$
$198$	11.7129	0.832402
$199$	−5.32629	−0.377571	−0.188786	−	0.982018i	$-0.560455\pi$
$199$	−5.32629	−0.377571	−0.188786	+	0.982018i	$0.560455\pi$
$200$	2.99385	0.211697
$201$	30.8386	2.17519
$202$	−4.79143	−0.337124
$203$	−6.50264	−0.456396
$204$	−6.64448	−0.465206
$205$	1.99258	0.139168
$206$	−2.36122	−0.164514
$207$	8.75226	0.608324
$208$	−2.06102	−0.142906
$209$	−13.7704	−0.952519
$210$	10.6463	0.734662
$211$	25.6308	1.76450	0.882248	−	0.470784i	$-0.156029\pi$
$211$	25.6308	1.76450	0.882248	+	0.470784i	$0.156029\pi$
$212$	0.794159	0.0545430
$213$	−28.3984	−1.94582
$214$	−9.64480	−0.659305
$215$	−13.1696	−0.898160
$216$	−0.865174	−0.0588676
$217$	8.78367	0.596275
$218$	14.6103	0.989535
$219$	−3.78276	−0.255615
$220$	−6.29470	−0.424389
$221$	−5.76866	−0.388042
$222$	−17.9871	−1.20721
$223$	−18.4835	−1.23775	−0.618874	−	0.785490i	$-0.712411\pi$
$223$	−18.4835	−1.23775	−0.618874	+	0.785490i	$0.712411\pi$
$224$	−3.16627	−0.211555
$225$	−7.89046	−0.526031
$226$	−5.83917	−0.388416
$227$	14.6988	0.975593	0.487796	−	0.872957i	$-0.337801\pi$
$227$	14.6988	0.975593	0.487796	+	0.872957i	$0.337801\pi$
$228$	−7.35565	−0.487140
$229$	11.4057	0.753710	0.376855	−	0.926272i	$-0.377005\pi$
$229$	11.4057	0.753710	0.376855	+	0.926272i	$0.377005\pi$
$230$	−4.70359	−0.310146
$231$	33.4049	2.19788
$232$	2.05372	0.134834
$233$	−16.2319	−1.06339	−0.531694	−	0.846937i	$-0.678444\pi$
$233$	−16.2319	−1.06339	−0.531694	+	0.846937i	$0.678444\pi$
$234$	5.43192	0.355096
$235$	−5.13908	−0.335237
$236$	−9.14533	−0.595310
$237$	5.82038	0.378075
$238$	−8.86218	−0.574450
$239$	−22.3615	−1.44645	−0.723223	−	0.690615i	$-0.757340\pi$
$239$	−22.3615	−1.44645	−0.723223	+	0.690615i	$0.757340\pi$
$240$	−3.36240	−0.217042
$241$	−23.9131	−1.54038	−0.770188	−	0.637817i	$-0.779838\pi$
$241$	−23.9131	−1.54038	−0.770188	+	0.637817i	$0.779838\pi$
$242$	−8.75093	−0.562531
$243$	21.0501	1.35036
$244$	−1.82446	−0.116799
$245$	4.28494	0.273755
$246$	3.33966	0.212929
$247$	−6.38609	−0.406337
$248$	−2.77414	−0.176158
$249$	−29.2322	−1.85251
$250$	11.3224	0.716090
$251$	1.86610	0.117787	0.0588935	−	0.998264i	$-0.481243\pi$
$251$	1.86610	0.117787	0.0588935	+	0.998264i	$0.481243\pi$
$252$	8.34487	0.525677
$253$	−14.7585	−0.927859
$254$	8.39481	0.526737
$255$	−9.41113	−0.589348
$256$	1.00000	0.0625000
$257$	−3.58404	−0.223566	−0.111783	−	0.993733i	$-0.535656\pi$
$257$	−3.58404	−0.223566	−0.111783	+	0.993733i	$0.535656\pi$
$258$	−22.0729	−1.37420
$259$	−23.9906	−1.49070
$260$	−2.91920	−0.181041
$261$	−5.41270	−0.335038
$262$	6.24893	0.386060
$263$	−18.3625	−1.13228	−0.566139	−	0.824310i	$-0.691564\pi$
$263$	−18.3625	−1.13228	−0.566139	+	0.824310i	$0.691564\pi$
$264$	−10.5502	−0.649322
$265$	1.12483	0.0690980
$266$	−9.81072	−0.601534
$267$	−7.31670	−0.447775
$268$	−12.9905	−0.793522
$269$	20.3637	1.24160	0.620798	−	0.783971i	$-0.286809\pi$
$269$	20.3637	1.24160	0.620798	+	0.783971i	$0.286809\pi$
$270$	−1.22542	−0.0745766
$271$	17.5673	1.06714	0.533570	−	0.845756i	$-0.320850\pi$
$271$	17.5673	1.06714	0.533570	+	0.845756i	$0.320850\pi$
$272$	2.79893	0.169710
$273$	15.4917	0.937599
$274$	1.77696	0.107350
$275$	13.3053	0.802339
$276$	−7.88346	−0.474529
$277$	−20.8347	−1.25183	−0.625917	−	0.779889i	$-0.715275\pi$
$277$	−20.8347	−1.25183	−0.625917	+	0.779889i	$0.715275\pi$
$278$	−2.82872	−0.169655
$279$	7.31139	0.437721
$280$	−4.48466	−0.268009
$281$	−8.01510	−0.478141	−0.239070	−	0.971002i	$-0.576843\pi$
$281$	−8.01510	−0.478141	−0.239070	+	0.971002i	$0.576843\pi$
$282$	−8.61336	−0.512918
$283$	−2.38474	−0.141758	−0.0708790	−	0.997485i	$-0.522580\pi$
$283$	−2.38474	−0.141758	−0.0708790	+	0.997485i	$0.522580\pi$
$284$	11.9626	0.709849
$285$	−10.4184	−0.617135
$286$	−9.15959	−0.541618
$287$	4.45433	0.262931
$288$	−2.63555	−0.155301
$289$	−9.16598	−0.539175
$290$	2.90886	0.170814
$291$	−33.9496	−1.99016
$292$	1.59346	0.0932501
$293$	−12.7712	−0.746100	−0.373050	−	0.927811i	$-0.621688\pi$
$293$	−12.7712	−0.746100	−0.373050	+	0.927811i	$0.621688\pi$
$294$	7.18177	0.418849
$295$	−12.9533	−0.754170
$296$	7.57692	0.440399
$297$	−3.84501	−0.223110
$298$	19.3924	1.12337
$299$	−6.84433	−0.395818
$300$	7.10721	0.410335
$301$	−29.4401	−1.69690
$302$	−2.69389	−0.155016
$303$	−11.3745	−0.653449
$304$	3.09851	0.177712
$305$	−2.58414	−0.147967
$306$	−7.37673	−0.421700
$307$	34.6563	1.97794	0.988971	−	0.148112i	$-0.0473197\pi$
$307$	34.6563	1.97794	0.988971	+	0.148112i	$0.0473197\pi$
$308$	−14.0715	−0.801801
$309$	−5.60538	−0.318879
$310$	−3.92925	−0.223166
$311$	−3.64803	−0.206861	−0.103430	−	0.994637i	$-0.532982\pi$
$311$	−3.64803	−0.206861	−0.103430	+	0.994637i	$0.532982\pi$
$312$	−4.89272	−0.276996
$313$	−26.1275	−1.47681	−0.738407	−	0.674356i	$-0.764421\pi$
$313$	−26.1275	−1.47681	−0.738407	+	0.674356i	$0.764421\pi$
$314$	5.91854	0.334003
$315$	11.8195	0.665956
$316$	−2.45179	−0.137924
$317$	−30.0238	−1.68630	−0.843151	−	0.537677i	$-0.819302\pi$
$317$	−30.0238	−1.68630	−0.843151	+	0.537677i	$0.819302\pi$
$318$	1.88528	0.105721
$319$	9.12717	0.511023
$320$	1.41638	0.0791783
$321$	−22.8961	−1.27793
$322$	−10.5147	−0.585961
$323$	8.67252	0.482552
$324$	−9.96052	−0.553362
$325$	6.17039	0.342272
$326$	15.4816	0.857447
$327$	34.6839	1.91802
$328$	−1.40681	−0.0776779
$329$	−11.4882	−0.633365
$330$	−14.9432	−0.822595
$331$	13.8025	0.758656	0.379328	−	0.925262i	$-0.376155\pi$
$331$	13.8025	0.758656	0.379328	+	0.925262i	$0.376155\pi$
$332$	12.3138	0.675809
$333$	−19.9694	−1.09431
$334$	−23.0706	−1.26237
$335$	−18.3996	−1.00528
$336$	−7.51651	−0.410059
$337$	−6.06005	−0.330112	−0.165056	−	0.986284i	$-0.552780\pi$
$337$	−6.06005	−0.330112	−0.165056	+	0.986284i	$0.552780\pi$
$338$	8.75220	0.476057
$339$	−13.8618	−0.752869
$340$	3.96437	0.214998
$341$	−12.3288	−0.667644
$342$	−8.16628	−0.441582
$343$	−12.5851	−0.679531
$344$	9.29805	0.501317
$345$	−11.1660	−0.601158
$346$	4.19988	0.225787
$347$	−28.5321	−1.53168	−0.765842	−	0.643029i	$-0.777677\pi$
$347$	−28.5321	−1.53168	−0.765842	+	0.643029i	$0.777677\pi$
$348$	4.87540	0.261349
$349$	−1.92898	−0.103256	−0.0516279	−	0.998666i	$-0.516441\pi$
$349$	−1.92898	−0.103256	−0.0516279	+	0.998666i	$0.516441\pi$
$350$	9.47935	0.506693
$351$	−1.78314	−0.0951770
$352$	4.44420	0.236877
$353$	−14.1267	−0.751887	−0.375943	−	0.926643i	$-0.622681\pi$
$353$	−14.1267	−0.751887	−0.375943	+	0.926643i	$0.622681\pi$
$354$	−21.7104	−1.15389
$355$	16.9436	0.899275
$356$	3.08210	0.163351
$357$	−21.0382	−1.11346
$358$	−8.96546	−0.473839
$359$	−18.6111	−0.982254	−0.491127	−	0.871088i	$-0.663415\pi$
$359$	−18.6111	−0.982254	−0.491127	+	0.871088i	$0.663415\pi$
$360$	−3.73296	−0.196744
$361$	−9.39924	−0.494697
$362$	7.69334	0.404353
$363$	−20.7741	−1.09036
$364$	−6.52574	−0.342042
$365$	2.25695	0.118134
$366$	−4.33115	−0.226393
$367$	15.2361	0.795316	0.397658	−	0.917534i	$-0.369823\pi$
$367$	15.2361	0.795316	0.397658	+	0.917534i	$0.369823\pi$
$368$	3.32085	0.173111
$369$	3.70771	0.193016
$370$	10.7318	0.557921
$371$	2.51452	0.130547
$372$	−6.58562	−0.341448
$373$	−24.8313	−1.28572	−0.642859	−	0.765985i	$-0.722252\pi$
$373$	−24.8313	−1.28572	−0.642859	+	0.765985i	$0.722252\pi$
$374$	12.4390	0.643207
$375$	26.8785	1.38800
$376$	3.62831	0.187116
$377$	4.23277	0.217999
$378$	−2.73937	−0.140898
$379$	28.0836	1.44256	0.721279	−	0.692644i	$-0.243554\pi$
$379$	28.0836	1.44256	0.721279	+	0.692644i	$0.243554\pi$
$380$	4.38868	0.225135
$381$	19.9287	1.02098
$382$	−7.44623	−0.380982
$383$	−21.3990	−1.09344	−0.546720	−	0.837316i	$-0.684124\pi$
$383$	−21.3990	−1.09344	−0.546720	+	0.837316i	$0.684124\pi$
$384$	2.37393	0.121144
$385$	−19.9307	−1.01576
$386$	21.1416	1.07608
$387$	−24.5055	−1.24568
$388$	14.3010	0.726023
$389$	9.28682	0.470861	0.235430	−	0.971891i	$-0.424350\pi$
$389$	9.28682	0.470861	0.235430	+	0.971891i	$0.424350\pi$
$390$	−6.92997	−0.350913
$391$	9.29482	0.470059
$392$	−3.02526	−0.152799
$393$	14.8345	0.748303
$394$	−7.08373	−0.356873
$395$	−3.47268	−0.174729
$396$	−11.7129	−0.588597
$397$	−38.2160	−1.91800	−0.959002	−	0.283400i	$-0.908538\pi$
$397$	−38.2160	−1.91800	−0.959002	+	0.283400i	$0.908538\pi$
$398$	5.32629	0.266983
$399$	−23.2900	−1.16596
$400$	−2.99385	−0.149693
$401$	20.3989	1.01867	0.509337	−	0.860567i	$-0.329891\pi$
$401$	20.3989	1.01867	0.509337	+	0.860567i	$0.329891\pi$
$402$	−30.8386	−1.53809
$403$	−5.71756	−0.284812
$404$	4.79143	0.238382
$405$	−14.1079	−0.701029
$406$	6.50264	0.322721
$407$	33.6734	1.66913
$408$	6.64448	0.328951
$409$	−17.0232	−0.841741	−0.420871	−	0.907121i	$-0.638275\pi$
$409$	−17.0232	−0.841741	−0.420871	+	0.907121i	$0.638275\pi$
$410$	−1.99258	−0.0984064
$411$	4.21837	0.208077
$412$	2.36122	0.116329
$413$	−28.9566	−1.42486
$414$	−8.75226	−0.430150
$415$	17.4411	0.856150
$416$	2.06102	0.101050
$417$	−6.71518	−0.328844
$418$	13.7704	0.673532
$419$	19.8428	0.969382	0.484691	−	0.874685i	$-0.338932\pi$
$419$	19.8428	0.969382	0.484691	+	0.874685i	$0.338932\pi$
$420$	−10.6463	−0.519485
$421$	4.55232	0.221867	0.110933	−	0.993828i	$-0.464616\pi$
$421$	4.55232	0.221867	0.110933	+	0.993828i	$0.464616\pi$
$422$	−25.6308	−1.24769
$423$	−9.56260	−0.464949
$424$	−0.794159	−0.0385677
$425$	−8.37960	−0.406470
$426$	28.3984	1.37591
$427$	−5.77674	−0.279556
$428$	9.64480	0.466199
$429$	−21.7442	−1.04982
$430$	13.1696	0.635095
$431$	8.09066	0.389713	0.194857	−	0.980832i	$-0.437576\pi$
$431$	8.09066	0.389713	0.194857	+	0.980832i	$0.437576\pi$
$432$	0.865174	0.0416257
$433$	−6.65044	−0.319600	−0.159800	−	0.987149i	$-0.551085\pi$
$433$	−6.65044	−0.319600	−0.159800	+	0.987149i	$0.551085\pi$
$434$	−8.78367	−0.421630
$435$	6.90544	0.331091
$436$	−14.6103	−0.699707
$437$	10.2897	0.492222
$438$	3.78276	0.180747
$439$	−10.4721	−0.499805	−0.249903	−	0.968271i	$-0.580399\pi$
$439$	−10.4721	−0.499805	−0.249903	+	0.968271i	$0.580399\pi$
$440$	6.29470	0.300088
$441$	7.97324	0.379678
$442$	5.76866	0.274387
$443$	−19.6743	−0.934755	−0.467378	−	0.884058i	$-0.654801\pi$
$443$	−19.6743	−0.934755	−0.467378	+	0.884058i	$0.654801\pi$
$444$	17.9871	0.853630
$445$	4.36544	0.206942
$446$	18.4835	0.875220
$447$	46.0362	2.17744
$448$	3.16627	0.149592
$449$	39.1663	1.84837	0.924185	−	0.381946i	$-0.124746\pi$
$449$	39.1663	1.84837	0.924185	+	0.381946i	$0.124746\pi$
$450$	7.89046	0.371960
$451$	−6.25213	−0.294401
$452$	5.83917	0.274651
$453$	−6.39510	−0.300468
$454$	−14.6988	−0.689848
$455$	−9.24296	−0.433317
$456$	7.35565	0.344460
$457$	10.3078	0.482179	0.241090	−	0.970503i	$-0.422495\pi$
$457$	10.3078	0.482179	0.241090	+	0.970503i	$0.422495\pi$
$458$	−11.4057	−0.532954
$459$	2.42156	0.113029
$460$	4.70359	0.219306
$461$	23.9079	1.11350	0.556752	−	0.830679i	$-0.312047\pi$
$461$	23.9079	1.11350	0.556752	+	0.830679i	$0.312047\pi$
$462$	−33.4049	−1.55414
$463$	−10.6920	−0.496898	−0.248449	−	0.968645i	$-0.579921\pi$
$463$	−10.6920	−0.496898	−0.248449	+	0.968645i	$0.579921\pi$
$464$	−2.05372	−0.0953418
$465$	−9.32777	−0.432565
$466$	16.2319	0.751928
$467$	−22.5874	−1.04522	−0.522610	−	0.852572i	$-0.675041\pi$
$467$	−22.5874	−1.04522	−0.522610	+	0.852572i	$0.675041\pi$
$468$	−5.43192	−0.251091
$469$	−41.1315	−1.89928
$470$	5.13908	0.237048
$471$	14.0502	0.647400
$472$	9.14533	0.420948
$473$	41.3224	1.90001
$474$	−5.82038	−0.267339
$475$	−9.27649	−0.425634
$476$	8.86218	0.406197
$477$	2.09305	0.0958340
$478$	22.3615	1.02279
$479$	−35.9701	−1.64352	−0.821758	−	0.569837i	$-0.807006\pi$
$479$	−35.9701	−1.64352	−0.821758	+	0.569837i	$0.807006\pi$
$480$	3.36240	0.153472
$481$	15.6162	0.712036
$482$	23.9131	1.08921
$483$	−24.9612	−1.13577
$484$	8.75093	0.397770
$485$	20.2557	0.919764
$486$	−21.0501	−0.954851
$487$	24.2832	1.10038	0.550189	−	0.835040i	$-0.314556\pi$
$487$	24.2832	1.10038	0.550189	+	0.835040i	$0.314556\pi$
$488$	1.82446	0.0825895
$489$	36.7523	1.66200
$490$	−4.28494	−0.193574
$491$	−18.0957	−0.816648	−0.408324	−	0.912837i	$-0.633887\pi$
$491$	−18.0957	−0.816648	−0.408324	+	0.912837i	$0.633887\pi$
$492$	−3.33966	−0.150564
$493$	−5.74824	−0.258888
$494$	6.38609	0.287324
$495$	−16.5900	−0.745666
$496$	2.77414	0.124563
$497$	37.8768	1.69901
$498$	29.2322	1.30993
$499$	30.2498	1.35417	0.677084	−	0.735905i	$-0.263243\pi$
$499$	30.2498	1.35417	0.677084	+	0.735905i	$0.263243\pi$
$500$	−11.3224	−0.506352
$501$	−54.7680	−2.44685
$502$	−1.86610	−0.0832880
$503$	18.8877	0.842160	0.421080	−	0.907023i	$-0.361651\pi$
$503$	18.8877	0.842160	0.421080	+	0.907023i	$0.361651\pi$
$504$	−8.34487	−0.371710
$505$	6.78650	0.301995
$506$	14.7585	0.656096
$507$	20.7771	0.922744
$508$	−8.39481	−0.372459
$509$	−22.7809	−1.00974	−0.504872	−	0.863194i	$-0.668460\pi$
$509$	−22.7809	−1.00974	−0.504872	+	0.863194i	$0.668460\pi$
$510$	9.41113	0.416732
$511$	5.04532	0.223192
$512$	−1.00000	−0.0441942
$513$	2.68075	0.118358
$514$	3.58404	0.158085
$515$	3.34440	0.147372
$516$	22.0729	0.971707
$517$	16.1249	0.709174
$518$	23.9906	1.05409
$519$	9.97023	0.437645
$520$	2.91920	0.128015
$521$	1.81383	0.0794653	0.0397326	−	0.999210i	$-0.487349\pi$
$521$	1.81383	0.0794653	0.0397326	+	0.999210i	$0.487349\pi$
$522$	5.41270	0.236907
$523$	7.93604	0.347019	0.173509	−	0.984832i	$-0.444489\pi$
$523$	7.93604	0.347019	0.173509	+	0.984832i	$0.444489\pi$
$524$	−6.24893	−0.272986
$525$	22.5033	0.982126
$526$	18.3625	0.800642
$527$	7.76463	0.338233
$528$	10.5502	0.459140
$529$	−11.9720	−0.520521
$530$	−1.12483	−0.0488597
$531$	−24.1030	−1.04598
$532$	9.81072	0.425349
$533$	−2.89945	−0.125589
$534$	7.31670	0.316624
$535$	13.6607	0.590605
$536$	12.9905	0.561105
$537$	−21.2834	−0.918446
$538$	−20.3637	−0.877941
$539$	−13.4449	−0.579112
$540$	1.22542	0.0527336
$541$	−2.53307	−0.108905	−0.0544526	−	0.998516i	$-0.517341\pi$
$541$	−2.53307	−0.108905	−0.0544526	+	0.998516i	$0.517341\pi$
$542$	−17.5673	−0.754582
$543$	18.2635	0.783760
$544$	−2.79893	−0.120003
$545$	−20.6938	−0.886426
$546$	−15.4917	−0.662982
$547$	−35.8652	−1.53349	−0.766743	−	0.641955i	$-0.778124\pi$
$547$	−35.8652	−1.53349	−0.766743	+	0.641955i	$0.778124\pi$
$548$	−1.77696	−0.0759078
$549$	−4.80846	−0.205220
$550$	−13.3053	−0.567340
$551$	−6.36348	−0.271094
$552$	7.88346	0.335542
$553$	−7.76303	−0.330118
$554$	20.8347	0.885181
$555$	25.4766	1.08142
$556$	2.82872	0.119964
$557$	26.0462	1.10361	0.551806	−	0.833972i	$-0.313939\pi$
$557$	26.0462	1.10361	0.551806	+	0.833972i	$0.313939\pi$
$558$	−7.31139	−0.309516
$559$	19.1635	0.810528
$560$	4.48466	0.189511
$561$	29.5294	1.24673
$562$	8.01510	0.338097
$563$	18.4888	0.779210	0.389605	−	0.920982i	$-0.372612\pi$
$563$	18.4888	0.779210	0.389605	+	0.920982i	$0.372612\pi$
$564$	8.61336	0.362688
$565$	8.27051	0.347943
$566$	2.38474	0.100238
$567$	−31.5377	−1.32446
$568$	−11.9626	−0.501939
$569$	−30.1733	−1.26493	−0.632464	−	0.774589i	$-0.717957\pi$
$569$	−30.1733	−1.26493	−0.632464	+	0.774589i	$0.717957\pi$
$570$	10.4184	0.436380
$571$	−20.6712	−0.865063	−0.432532	−	0.901619i	$-0.642380\pi$
$571$	−20.6712	−0.865063	−0.432532	+	0.901619i	$0.642380\pi$
$572$	9.15959	0.382982
$573$	−17.6768	−0.738461
$574$	−4.45433	−0.185920
$575$	−9.94213	−0.414615
$576$	2.63555	0.109815
$577$	−3.45409	−0.143795	−0.0718977	−	0.997412i	$-0.522906\pi$
$577$	−3.45409	−0.143795	−0.0718977	+	0.997412i	$0.522906\pi$
$578$	9.16598	0.381254
$579$	50.1887	2.08577
$580$	−2.90886	−0.120784
$581$	38.9889	1.61753
$582$	33.9496	1.40725
$583$	−3.52940	−0.146173
$584$	−1.59346	−0.0659378
$585$	−7.69370	−0.318095
$586$	12.7712	0.527572
$587$	−35.2812	−1.45621	−0.728106	−	0.685465i	$-0.759599\pi$
$587$	−35.2812	−1.45621	−0.728106	+	0.685465i	$0.759599\pi$
$588$	−7.18177	−0.296171
$589$	8.59570	0.354180
$590$	12.9533	0.533279
$591$	−16.8163	−0.691730
$592$	−7.57692	−0.311409
$593$	23.6069	0.969419	0.484710	−	0.874675i	$-0.338925\pi$
$593$	23.6069	0.969419	0.484710	+	0.874675i	$0.338925\pi$
$594$	3.84501	0.157763
$595$	12.5523	0.514592
$596$	−19.3924	−0.794343
$597$	12.6443	0.517495
$598$	6.84433	0.279885
$599$	−18.2746	−0.746680	−0.373340	−	0.927695i	$-0.621787\pi$
$599$	−18.2746	−0.746680	−0.373340	+	0.927695i	$0.621787\pi$
$600$	−7.10721	−0.290150
$601$	33.6960	1.37449	0.687244	−	0.726427i	$-0.258820\pi$
$601$	33.6960	1.37449	0.687244	+	0.726427i	$0.258820\pi$
$602$	29.4401	1.19989
$603$	−34.2372	−1.39425
$604$	2.69389	0.109613
$605$	12.3947	0.503916
$606$	11.3745	0.462058
$607$	30.7874	1.24962	0.624811	−	0.780776i	$-0.285176\pi$
$607$	30.7874	1.24962	0.624811	+	0.780776i	$0.285176\pi$
$608$	−3.09851	−0.125661
$609$	15.4368	0.625532
$610$	2.58414	0.104629
$611$	7.47801	0.302528
$612$	7.37673	0.298187
$613$	5.25178	0.212117	0.106059	−	0.994360i	$-0.466177\pi$
$613$	5.25178	0.212117	0.106059	+	0.994360i	$0.466177\pi$
$614$	−34.6563	−1.39862
$615$	−4.73025	−0.190742
$616$	14.0715	0.566959
$617$	−19.5456	−0.786877	−0.393439	−	0.919351i	$-0.628715\pi$
$617$	−19.5456	−0.786877	−0.393439	+	0.919351i	$0.628715\pi$
$618$	5.60538	0.225482
$619$	−7.80734	−0.313804	−0.156902	−	0.987614i	$-0.550151\pi$
$619$	−7.80734	−0.313804	−0.156902	+	0.987614i	$0.550151\pi$
$620$	3.92925	0.157802
$621$	2.87311	0.115294
$622$	3.64803	0.146273
$623$	9.75876	0.390977
$624$	4.89272	0.195866
$625$	−1.06757	−0.0427026
$626$	26.1275	1.04426
$627$	32.6900	1.30551
$628$	−5.91854	−0.236176
$629$	−21.2073	−0.845590
$630$	−11.8195	−0.470902
$631$	−18.3688	−0.731250	−0.365625	−	0.930762i	$-0.619145\pi$
$631$	−18.3688	−0.731250	−0.365625	+	0.930762i	$0.619145\pi$
$632$	2.45179	0.0975270
$633$	−60.8458	−2.41840
$634$	30.0238	1.19240
$635$	−11.8903	−0.471851
$636$	−1.88528	−0.0747561
$637$	−6.23513	−0.247045
$638$	−9.12717	−0.361348
$639$	31.5280	1.24723
$640$	−1.41638	−0.0559875
$641$	−30.0907	−1.18851	−0.594256	−	0.804276i	$-0.702554\pi$
$641$	−30.0907	−1.18851	−0.594256	+	0.804276i	$0.702554\pi$
$642$	22.8961	0.903636
$643$	−32.7097	−1.28994	−0.644972	−	0.764206i	$-0.723131\pi$
$643$	−32.7097	−1.28994	−0.644972	+	0.764206i	$0.723131\pi$
$644$	10.5147	0.414337
$645$	31.2638	1.23101
$646$	−8.67252	−0.341216
$647$	−37.2113	−1.46293	−0.731464	−	0.681880i	$-0.761163\pi$
$647$	−37.2113	−1.46293	−0.731464	+	0.681880i	$0.761163\pi$
$648$	9.96052	0.391286
$649$	40.6437	1.59540
$650$	−6.17039	−0.242023
$651$	−20.8518	−0.817248
$652$	−15.4816	−0.606307
$653$	−28.6940	−1.12288	−0.561441	−	0.827517i	$-0.689753\pi$
$653$	−28.6940	−1.12288	−0.561441	+	0.827517i	$0.689753\pi$
$654$	−34.6839	−1.35625
$655$	−8.85089	−0.345833
$656$	1.40681	0.0549265
$657$	4.19964	0.163844
$658$	11.4882	0.447857
$659$	−46.5365	−1.81280	−0.906402	−	0.422417i	$-0.861182\pi$
$659$	−46.5365	−1.81280	−0.906402	+	0.422417i	$0.861182\pi$
$660$	14.9432	0.581663
$661$	4.42030	0.171930	0.0859650	−	0.996298i	$-0.472603\pi$
$661$	4.42030	0.171930	0.0859650	+	0.996298i	$0.472603\pi$
$662$	−13.8025	−0.536451
$663$	13.6944	0.531846
$664$	−12.3138	−0.477869
$665$	13.8958	0.538854
$666$	19.9694	0.773797
$667$	−6.82010	−0.264075
$668$	23.0706	0.892627
$669$	43.8786	1.69645
$670$	18.3996	0.710838
$671$	8.10827	0.313016
$672$	7.51651	0.289956
$673$	−4.42534	−0.170584	−0.0852921	−	0.996356i	$-0.527182\pi$
$673$	−4.42534	−0.170584	−0.0852921	+	0.996356i	$0.527182\pi$
$674$	6.06005	0.233424
$675$	−2.59020	−0.0996970
$676$	−8.75220	−0.336623
$677$	−0.302682	−0.0116330	−0.00581650	−	0.999983i	$-0.501851\pi$
$677$	−0.302682	−0.0116330	−0.00581650	+	0.999983i	$0.501851\pi$
$678$	13.8618	0.532359
$679$	45.2808	1.73772
$680$	−3.96437	−0.152026
$681$	−34.8939	−1.33714
$682$	12.3288	0.472096
$683$	−11.5143	−0.440582	−0.220291	−	0.975434i	$-0.570701\pi$
$683$	−11.5143	−0.440582	−0.220291	+	0.975434i	$0.570701\pi$
$684$	8.16628	0.312246
$685$	−2.51685	−0.0961640
$686$	12.5851	0.480501
$687$	−27.0764	−1.03303
$688$	−9.29805	−0.354485
$689$	−1.63678	−0.0623562
$690$	11.1660	0.425083
$691$	4.01475	0.152728	0.0763642	−	0.997080i	$-0.475669\pi$
$691$	4.01475	0.152728	0.0763642	+	0.997080i	$0.475669\pi$
$692$	−4.19988	−0.159656
$693$	−37.0863	−1.40879
$694$	28.5321	1.08306
$695$	4.00655	0.151977
$696$	−4.87540	−0.184802
$697$	3.93756	0.149146
$698$	1.92898	0.0730129
$699$	38.5334	1.45747
$700$	−9.47935	−0.358286
$701$	−6.99361	−0.264145	−0.132073	−	0.991240i	$-0.542163\pi$
$701$	−6.99361	−0.264145	−0.132073	+	0.991240i	$0.542163\pi$
$702$	1.78314	0.0673003
$703$	−23.4772	−0.885458
$704$	−4.44420	−0.167497
$705$	12.1998	0.459472
$706$	14.1267	0.531664
$707$	15.1709	0.570562
$708$	21.7104	0.815926
$709$	6.11941	0.229819	0.114910	−	0.993376i	$-0.463342\pi$
$709$	6.11941	0.229819	0.114910	+	0.993376i	$0.463342\pi$
$710$	−16.9436	−0.635883
$711$	−6.46182	−0.242337
$712$	−3.08210	−0.115507
$713$	9.21249	0.345010
$714$	21.0382	0.787335
$715$	12.9735	0.485181
$716$	8.96546	0.335055
$717$	53.0847	1.98248
$718$	18.6111	0.694558
$719$	31.1963	1.16343	0.581714	−	0.813394i	$-0.302382\pi$
$719$	31.1963	1.16343	0.581714	+	0.813394i	$0.302382\pi$
$720$	3.73296	0.139119
$721$	7.47627	0.278431
$722$	9.39924	0.349803
$723$	56.7680	2.11122
$724$	−7.69334	−0.285921
$725$	6.14855	0.228351
$726$	20.7741	0.771000
$727$	−13.7522	−0.510040	−0.255020	−	0.966936i	$-0.582082\pi$
$727$	−13.7522	−0.510040	−0.255020	+	0.966936i	$0.582082\pi$
$728$	6.52574	0.241860
$729$	−20.0899	−0.744070
$730$	−2.25695	−0.0835334
$731$	−26.0246	−0.962555
$732$	4.33115	0.160084
$733$	−40.8649	−1.50938	−0.754690	−	0.656081i	$-0.772213\pi$
$733$	−40.8649	−1.50938	−0.754690	+	0.656081i	$0.772213\pi$
$734$	−15.2361	−0.562373
$735$	−10.1721	−0.375205
$736$	−3.32085	−0.122408
$737$	57.7325	2.12660
$738$	−3.70771	−0.136483
$739$	−12.5626	−0.462124	−0.231062	−	0.972939i	$-0.574220\pi$
$739$	−12.5626	−0.462124	−0.231062	+	0.972939i	$0.574220\pi$
$740$	−10.7318	−0.394510
$741$	15.1601	0.556922
$742$	−2.51452	−0.0923109
$743$	−24.3701	−0.894052	−0.447026	−	0.894521i	$-0.647517\pi$
$743$	−24.3701	−0.894052	−0.447026	+	0.894521i	$0.647517\pi$
$744$	6.58562	0.241440
$745$	−27.4671	−1.00632
$746$	24.8313	0.909140
$747$	32.4537	1.18742
$748$	−12.4390	−0.454816
$749$	30.5380	1.11584
$750$	−26.8785	−0.981466
$751$	23.3729	0.852888	0.426444	−	0.904514i	$-0.359766\pi$
$751$	23.3729	0.852888	0.426444	+	0.904514i	$0.359766\pi$
$752$	−3.62831	−0.132311
$753$	−4.42999	−0.161438
$754$	−4.23277	−0.154148
$755$	3.81558	0.138863
$756$	2.73937	0.0996301
$757$	−13.2576	−0.481857	−0.240929	−	0.970543i	$-0.577452\pi$
$757$	−13.2576	−0.481857	−0.240929	+	0.970543i	$0.577452\pi$
$758$	−28.0836	−1.02004
$759$	35.0357	1.27172
$760$	−4.38868	−0.159194
$761$	0.800084	0.0290030	0.0145015	−	0.999895i	$-0.495384\pi$
$761$	0.800084	0.0290030	0.0145015	+	0.999895i	$0.495384\pi$
$762$	−19.9287	−0.721941
$763$	−46.2602	−1.67473
$764$	7.44623	0.269395
$765$	10.4483	0.377759
$766$	21.3990	0.773178
$767$	18.8487	0.680587
$768$	−2.37393	−0.0856619
$769$	5.26194	0.189750	0.0948751	−	0.995489i	$-0.469755\pi$
$769$	5.26194	0.189750	0.0948751	+	0.995489i	$0.469755\pi$
$770$	19.9307	0.718253
$771$	8.50826	0.306418
$772$	−21.1416	−0.760903
$773$	−43.2707	−1.55634	−0.778170	−	0.628053i	$-0.783852\pi$
$773$	−43.2707	−1.55634	−0.778170	+	0.628053i	$0.783852\pi$
$774$	24.5055	0.880832
$775$	−8.30537	−0.298338
$776$	−14.3010	−0.513375
$777$	56.9520	2.04314
$778$	−9.28682	−0.332949
$779$	4.35900	0.156177
$780$	6.92997	0.248133
$781$	−53.1642	−1.90236
$782$	−9.29482	−0.332382
$783$	−1.77683	−0.0634987
$784$	3.02526	0.108045
$785$	−8.38294	−0.299200
$786$	−14.8345	−0.529130
$787$	−52.0113	−1.85400	−0.927001	−	0.375060i	$-0.877622\pi$
$787$	−52.0113	−1.85400	−0.927001	+	0.375060i	$0.877622\pi$
$788$	7.08373	0.252348
$789$	43.5913	1.55189
$790$	3.47268	0.123552
$791$	18.4884	0.657371
$792$	11.7129	0.416201
$793$	3.76025	0.133530
$794$	38.2160	1.35623
$795$	−2.67028	−0.0947050
$796$	−5.32629	−0.188786
$797$	18.4528	0.653633	0.326816	−	0.945088i	$-0.394024\pi$
$797$	18.4528	0.653633	0.326816	+	0.945088i	$0.394024\pi$
$798$	23.2900	0.824456
$799$	−10.1554	−0.359272
$800$	2.99385	0.105849
$801$	8.12304	0.287013
$802$	−20.3989	−0.720312
$803$	−7.08165	−0.249906
$804$	30.8386	1.08759
$805$	14.8928	0.524904
$806$	5.71756	0.201392
$807$	−48.3420	−1.70172
$808$	−4.79143	−0.168562
$809$	4.41714	0.155298	0.0776491	−	0.996981i	$-0.475259\pi$
$809$	4.41714	0.155298	0.0776491	+	0.996981i	$0.475259\pi$
$810$	14.1079	0.495702
$811$	−34.8498	−1.22374	−0.611871	−	0.790957i	$-0.709583\pi$
$811$	−34.8498	−1.22374	−0.611871	+	0.790957i	$0.709583\pi$
$812$	−6.50264	−0.228198
$813$	−41.7037	−1.46261
$814$	−33.6734	−1.18025
$815$	−21.9279	−0.768101
$816$	−6.64448	−0.232603
$817$	−28.8101	−1.00794
$818$	17.0232	0.595201
$819$	−17.1989	−0.600980
$820$	1.99258	0.0695839
$821$	39.2890	1.37120	0.685598	−	0.727980i	$-0.259541\pi$
$821$	39.2890	1.37120	0.685598	+	0.727980i	$0.259541\pi$
$822$	−4.21837	−0.147133
$823$	27.3813	0.954453	0.477226	−	0.878780i	$-0.341642\pi$
$823$	27.3813	0.954453	0.477226	+	0.878780i	$0.341642\pi$
$824$	−2.36122	−0.0822571
$825$	−31.5859	−1.09968
$826$	28.9566	1.00753
$827$	15.9293	0.553917	0.276958	−	0.960882i	$-0.410674\pi$
$827$	15.9293	0.553917	0.276958	+	0.960882i	$0.410674\pi$
$828$	8.75226	0.304162
$829$	30.7171	1.06685	0.533425	−	0.845847i	$-0.320905\pi$
$829$	30.7171	1.06685	0.533425	+	0.845847i	$0.320905\pi$
$830$	−17.4411	−0.605390
$831$	49.4601	1.71575
$832$	−2.06102	−0.0714530
$833$	8.46751	0.293382
$834$	6.71518	0.232528
$835$	32.6768	1.13083
$836$	−13.7704	−0.476259
$837$	2.40011	0.0829600
$838$	−19.8428	−0.685457
$839$	31.6241	1.09179	0.545893	−	0.837855i	$-0.316191\pi$
$839$	31.6241	1.09179	0.545893	+	0.837855i	$0.316191\pi$
$840$	10.6463	0.367331
$841$	−24.7822	−0.854559
$842$	−4.55232	−0.156883
$843$	19.0273	0.655335
$844$	25.6308	0.882248
$845$	−12.3965	−0.426452
$846$	9.56260	0.328769
$847$	27.7078	0.952052
$848$	0.794159	0.0272715
$849$	5.66120	0.194292
$850$	8.37960	0.287418
$851$	−25.1618	−0.862535
$852$	−28.3984	−0.972912
$853$	13.4862	0.461760	0.230880	−	0.972982i	$-0.425839\pi$
$853$	13.4862	0.461760	0.230880	+	0.972982i	$0.425839\pi$
$854$	5.77674	0.197676
$855$	11.5666	0.395569
$856$	−9.64480	−0.329652
$857$	−7.12007	−0.243217	−0.121608	−	0.992578i	$-0.538805\pi$
$857$	−7.12007	−0.243217	−0.121608	+	0.992578i	$0.538805\pi$
$858$	21.7442	0.742336
$859$	−2.23156	−0.0761397	−0.0380699	−	0.999275i	$-0.512121\pi$
$859$	−2.23156	−0.0761397	−0.0380699	+	0.999275i	$0.512121\pi$
$860$	−13.1696	−0.449080
$861$	−10.5743	−0.360370
$862$	−8.09066	−0.275569
$863$	−6.11691	−0.208222	−0.104111	−	0.994566i	$-0.533200\pi$
$863$	−6.11691	−0.208222	−0.104111	+	0.994566i	$0.533200\pi$
$864$	−0.865174	−0.0294338
$865$	−5.94865	−0.202260
$866$	6.65044	0.225991
$867$	21.7594	0.738988
$868$	8.78367	0.298137
$869$	10.8963	0.369630
$870$	−6.90544	−0.234116
$871$	26.7737	0.907193
$872$	14.6103	0.494767
$873$	37.6910	1.27565
$874$	−10.2897	−0.348053
$875$	−35.8497	−1.21194
$876$	−3.78276	−0.127808
$877$	−25.1912	−0.850645	−0.425323	−	0.905042i	$-0.639839\pi$
$877$	−25.1912	−0.850645	−0.425323	+	0.905042i	$0.639839\pi$
$878$	10.4721	0.353416
$879$	30.3179	1.02260
$880$	−6.29470	−0.212194
$881$	43.0782	1.45134	0.725671	−	0.688041i	$-0.241529\pi$
$881$	43.0782	1.45134	0.725671	+	0.688041i	$0.241529\pi$
$882$	−7.97324	−0.268473
$883$	47.7967	1.60849	0.804244	−	0.594300i	$-0.202571\pi$
$883$	47.7967	1.60849	0.804244	+	0.594300i	$0.202571\pi$
$884$	−5.76866	−0.194021
$885$	30.7503	1.03366
$886$	19.6743	0.660972
$887$	30.3822	1.02014	0.510068	−	0.860134i	$-0.329620\pi$
$887$	30.3822	1.02014	0.510068	+	0.860134i	$0.329620\pi$
$888$	−17.9871	−0.603607
$889$	−26.5802	−0.891472
$890$	−4.36544	−0.146330
$891$	44.2666	1.48299
$892$	−18.4835	−0.618874
$893$	−11.2423	−0.376211
$894$	−46.0362	−1.53968
$895$	12.6985	0.424465
$896$	−3.16627	−0.105778
$897$	16.2480	0.542504
$898$	−39.1663	−1.30699
$899$	−5.69732	−0.190016
$900$	−7.89046	−0.263015
$901$	2.22280	0.0740521
$902$	6.25213	0.208173
$903$	69.8888	2.32576
$904$	−5.83917	−0.194208
$905$	−10.8967	−0.362219
$906$	6.39510	0.212463
$907$	11.0060	0.365450	0.182725	−	0.983164i	$-0.441508\pi$
$907$	11.0060	0.365450	0.182725	+	0.983164i	$0.441508\pi$
$908$	14.6988	0.487796
$909$	12.6281	0.418846
$910$	9.24296	0.306401
$911$	1.41592	0.0469115	0.0234558	−	0.999725i	$-0.492533\pi$
$911$	1.41592	0.0469115	0.0234558	+	0.999725i	$0.492533\pi$
$912$	−7.35565	−0.243570
$913$	−54.7251	−1.81114
$914$	−10.3078	−0.340952
$915$	6.13457	0.202803
$916$	11.4057	0.376855
$917$	−19.7858	−0.653384
$918$	−2.42156	−0.0799235
$919$	−16.3417	−0.539061	−0.269531	−	0.962992i	$-0.586869\pi$
$919$	−16.3417	−0.539061	−0.269531	+	0.962992i	$0.586869\pi$
$920$	−4.70359	−0.155073
$921$	−82.2718	−2.71095
$922$	−23.9079	−0.787366
$923$	−24.6551	−0.811534
$924$	33.4049	1.09894
$925$	22.6842	0.745852
$926$	10.6920	0.351360
$927$	6.22313	0.204394
$928$	2.05372	0.0674168
$929$	35.1659	1.15376	0.576878	−	0.816830i	$-0.304271\pi$
$929$	35.1659	1.15376	0.576878	+	0.816830i	$0.304271\pi$
$930$	9.32777	0.305870
$931$	9.37381	0.307214
$932$	−16.2319	−0.531694
$933$	8.66017	0.283521
$934$	22.5874	0.739082
$935$	−17.6184	−0.576185
$936$	5.43192	0.177548
$937$	14.7129	0.480649	0.240325	−	0.970693i	$-0.422746\pi$
$937$	14.7129	0.480649	0.240325	+	0.970693i	$0.422746\pi$
$938$	41.1315	1.34299
$939$	62.0249	2.02411
$940$	−5.13908	−0.167618
$941$	55.0972	1.79612	0.898059	−	0.439874i	$-0.144977\pi$
$941$	55.0972	1.79612	0.898059	+	0.439874i	$0.144977\pi$
$942$	−14.0502	−0.457781
$943$	4.67179	0.152134
$944$	−9.14533	−0.297655
$945$	3.88001	0.126217
$946$	−41.3224	−1.34351
$947$	10.8074	0.351192	0.175596	−	0.984462i	$-0.443815\pi$
$947$	10.8074	0.351192	0.175596	+	0.984462i	$0.443815\pi$
$948$	5.82038	0.189037
$949$	−3.28415	−0.106608
$950$	9.27649	0.300969
$951$	71.2743	2.31123
$952$	−8.86218	−0.287225
$953$	−19.5550	−0.633449	−0.316724	−	0.948518i	$-0.602583\pi$
$953$	−19.5550	−0.633449	−0.316724	+	0.948518i	$0.602583\pi$
$954$	−2.09305	−0.0677649
$955$	10.5467	0.341284
$956$	−22.3615	−0.723223
$957$	−21.6673	−0.700403
$958$	35.9701	1.16214
$959$	−5.62632	−0.181683
$960$	−3.36240	−0.108521
$961$	−23.3041	−0.751747
$962$	−15.6162	−0.503486
$963$	25.4194	0.819127
$964$	−23.9131	−0.770188
$965$	−29.9446	−0.963952
$966$	24.9612	0.803112
$967$	−41.7434	−1.34238	−0.671189	−	0.741287i	$-0.734216\pi$
$967$	−41.7434	−1.34238	−0.671189	+	0.741287i	$0.734216\pi$
$968$	−8.75093	−0.281266
$969$	−20.5880	−0.661381
$970$	−20.2557	−0.650371
$971$	20.1226	0.645765	0.322882	−	0.946439i	$-0.395348\pi$
$971$	20.1226	0.645765	0.322882	+	0.946439i	$0.395348\pi$
$972$	21.0501	0.675182
$973$	8.95648	0.287131
$974$	−24.2832	−0.778084
$975$	−14.6481	−0.469114
$976$	−1.82446	−0.0583996
$977$	−7.04950	−0.225534	−0.112767	−	0.993621i	$-0.535971\pi$
$977$	−7.04950	−0.225534	−0.112767	+	0.993621i	$0.535971\pi$
$978$	−36.7523	−1.17521
$979$	−13.6975	−0.437773
$980$	4.28494	0.136877
$981$	−38.5062	−1.22941
$982$	18.0957	0.577457
$983$	19.8434	0.632906	0.316453	−	0.948608i	$-0.397508\pi$
$983$	19.8434	0.632906	0.316453	+	0.948608i	$0.397508\pi$
$984$	3.33966	0.106465
$985$	10.0333	0.319687
$986$	5.74824	0.183061
$987$	27.2722	0.868084
$988$	−6.38609	−0.203169
$989$	−30.8774	−0.981843
$990$	16.5900	0.527265
$991$	47.9333	1.52265	0.761325	−	0.648370i	$-0.224549\pi$
$991$	47.9333	1.52265	0.761325	+	0.648370i	$0.224549\pi$
$992$	−2.77414	−0.0880790
$993$	−32.7663	−1.03981
$994$	−37.8768	−1.20138
$995$	−7.54408	−0.239164
$996$	−29.2322	−0.926257
$997$	−21.9692	−0.695773	−0.347886	−	0.937537i	$-0.613101\pi$
$997$	−21.9692	−0.695773	−0.347886	+	0.937537i	$0.613101\pi$
$998$	−30.2498	−0.957542
$999$	−6.55535	−0.207402

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4022.2.a.d.1.6	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4022.2.a.d.1.6	✓	37	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4022 = 2 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4022.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.37393 q^{3} +1.00000 q^{4} +1.41638 q^{5} +2.37393 q^{6} +3.16627 q^{7} -1.00000 q^{8} +2.63555 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.37393 q^{3} +1.00000 q^{4} +1.41638 q^{5} +2.37393 q^{6} +3.16627 q^{7} -1.00000 q^{8} +2.63555 q^{9} -1.41638 q^{10} -4.44420 q^{11} -2.37393 q^{12} -2.06102 q^{13} -3.16627 q^{14} -3.36240 q^{15} +1.00000 q^{16} +2.79893 q^{17} -2.63555 q^{18} +3.09851 q^{19} +1.41638 q^{20} -7.51651 q^{21} +4.44420 q^{22} +3.32085 q^{23} +2.37393 q^{24} -2.99385 q^{25} +2.06102 q^{26} +0.865174 q^{27} +3.16627 q^{28} -2.05372 q^{29} +3.36240 q^{30} +2.77414 q^{31} -1.00000 q^{32} +10.5502 q^{33} -2.79893 q^{34} +4.48466 q^{35} +2.63555 q^{36} -7.57692 q^{37} -3.09851 q^{38} +4.89272 q^{39} -1.41638 q^{40} +1.40681 q^{41} +7.51651 q^{42} -9.29805 q^{43} -4.44420 q^{44} +3.73296 q^{45} -3.32085 q^{46} -3.62831 q^{47} -2.37393 q^{48} +3.02526 q^{49} +2.99385 q^{50} -6.64448 q^{51} -2.06102 q^{52} +0.794159 q^{53} -0.865174 q^{54} -6.29470 q^{55} -3.16627 q^{56} -7.35565 q^{57} +2.05372 q^{58} -9.14533 q^{59} -3.36240 q^{60} -1.82446 q^{61} -2.77414 q^{62} +8.34487 q^{63} +1.00000 q^{64} -2.91920 q^{65} -10.5502 q^{66} -12.9905 q^{67} +2.79893 q^{68} -7.88346 q^{69} -4.48466 q^{70} +11.9626 q^{71} -2.63555 q^{72} +1.59346 q^{73} +7.57692 q^{74} +7.10721 q^{75} +3.09851 q^{76} -14.0715 q^{77} -4.89272 q^{78} -2.45179 q^{79} +1.41638 q^{80} -9.96052 q^{81} -1.40681 q^{82} +12.3138 q^{83} -7.51651 q^{84} +3.96437 q^{85} +9.29805 q^{86} +4.87540 q^{87} +4.44420 q^{88} +3.08210 q^{89} -3.73296 q^{90} -6.52574 q^{91} +3.32085 q^{92} -6.58562 q^{93} +3.62831 q^{94} +4.38868 q^{95} +2.37393 q^{96} +14.3010 q^{97} -3.02526 q^{98} -11.7129 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q - 37 q^{2} - 5 q^{3} + 37 q^{4} - 13 q^{5} + 5 q^{6} - 22 q^{7} - 37 q^{8} + 32 q^{9}+O(q^{10}) \) 37 * q - 37 * q^2 - 5 * q^3 + 37 * q^4 - 13 * q^5 + 5 * q^6 - 22 * q^7 - 37 * q^8 + 32 * q^9	\( 37 q - 37 q^{2} - 5 q^{3} + 37 q^{4} - 13 q^{5} + 5 q^{6} - 22 q^{7} - 37 q^{8} + 32 q^{9} + 13 q^{10} + 12 q^{11} - 5 q^{12} - 36 q^{13} + 22 q^{14} - 7 q^{15} + 37 q^{16} + 4 q^{17} - 32 q^{18} - 10 q^{19} - 13 q^{20} - 11 q^{21} - 12 q^{22} - q^{23} + 5 q^{24} + 8 q^{25} + 36 q^{26} - 20 q^{27} - 22 q^{28} - 6 q^{29} + 7 q^{30} - 23 q^{31} - 37 q^{32} - 27 q^{33} - 4 q^{34} + 24 q^{35} + 32 q^{36} - 46 q^{37} + 10 q^{38} + 5 q^{39} + 13 q^{40} + 11 q^{41} + 11 q^{42} - 22 q^{43} + 12 q^{44} - 57 q^{45} + q^{46} - 18 q^{47} - 5 q^{48} - q^{49} - 8 q^{50} + 18 q^{51} - 36 q^{52} - 25 q^{53} + 20 q^{54} - 25 q^{55} + 22 q^{56} - 25 q^{57} + 6 q^{58} + 24 q^{59} - 7 q^{60} - 40 q^{61} + 23 q^{62} - 38 q^{63} + 37 q^{64} + 14 q^{65} + 27 q^{66} - 49 q^{67} + 4 q^{68} - 19 q^{69} - 24 q^{70} + 27 q^{71} - 32 q^{72} - 87 q^{73} + 46 q^{74} - 5 q^{75} - 10 q^{76} - 50 q^{77} - 5 q^{78} + 11 q^{79} - 13 q^{80} + 5 q^{81} - 11 q^{82} - 9 q^{83} - 11 q^{84} - 68 q^{85} + 22 q^{86} - 12 q^{87} - 12 q^{88} - 3 q^{89} + 57 q^{90} - 19 q^{91} - q^{92} - 69 q^{93} + 18 q^{94} + 27 q^{95} + 5 q^{96} - 98 q^{97} + q^{98} + 33 q^{99}+O(q^{100}) \) 37 * q - 37 * q^2 - 5 * q^3 + 37 * q^4 - 13 * q^5 + 5 * q^6 - 22 * q^7 - 37 * q^8 + 32 * q^9 + 13 * q^10 + 12 * q^11 - 5 * q^12 - 36 * q^13 + 22 * q^14 - 7 * q^15 + 37 * q^16 + 4 * q^17 - 32 * q^18 - 10 * q^19 - 13 * q^20 - 11 * q^21 - 12 * q^22 - q^23 + 5 * q^24 + 8 * q^25 + 36 * q^26 - 20 * q^27 - 22 * q^28 - 6 * q^29 + 7 * q^30 - 23 * q^31 - 37 * q^32 - 27 * q^33 - 4 * q^34 + 24 * q^35 + 32 * q^36 - 46 * q^37 + 10 * q^38 + 5 * q^39 + 13 * q^40 + 11 * q^41 + 11 * q^42 - 22 * q^43 + 12 * q^44 - 57 * q^45 + q^46 - 18 * q^47 - 5 * q^48 - q^49 - 8 * q^50 + 18 * q^51 - 36 * q^52 - 25 * q^53 + 20 * q^54 - 25 * q^55 + 22 * q^56 - 25 * q^57 + 6 * q^58 + 24 * q^59 - 7 * q^60 - 40 * q^61 + 23 * q^62 - 38 * q^63 + 37 * q^64 + 14 * q^65 + 27 * q^66 - 49 * q^67 + 4 * q^68 - 19 * q^69 - 24 * q^70 + 27 * q^71 - 32 * q^72 - 87 * q^73 + 46 * q^74 - 5 * q^75 - 10 * q^76 - 50 * q^77 - 5 * q^78 + 11 * q^79 - 13 * q^80 + 5 * q^81 - 11 * q^82 - 9 * q^83 - 11 * q^84 - 68 * q^85 + 22 * q^86 - 12 * q^87 - 12 * q^88 - 3 * q^89 + 57 * q^90 - 19 * q^91 - q^92 - 69 * q^93 + 18 * q^94 + 27 * q^95 + 5 * q^96 - 98 * q^97 + q^98 + 33 * q^99

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