LMFDB - Embedded newform 4022.2.a.d.1.14

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			1.14
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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.24109 q^{3} +1.00000 q^{4} -1.11151 q^{5} +1.24109 q^{6} +1.91739 q^{7} -1.00000 q^{8} -1.45969 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.24109 q^{3} +1.00000 q^{4} -1.11151 q^{5} +1.24109 q^{6} +1.91739 q^{7} -1.00000 q^{8} -1.45969 q^{9} +1.11151 q^{10} +3.49577 q^{11} -1.24109 q^{12} +0.165638 q^{13} -1.91739 q^{14} +1.37948 q^{15} +1.00000 q^{16} +1.61194 q^{17} +1.45969 q^{18} -0.652389 q^{19} -1.11151 q^{20} -2.37966 q^{21} -3.49577 q^{22} -8.69554 q^{23} +1.24109 q^{24} -3.76455 q^{25} -0.165638 q^{26} +5.53489 q^{27} +1.91739 q^{28} +4.71992 q^{29} -1.37948 q^{30} +2.84008 q^{31} -1.00000 q^{32} -4.33858 q^{33} -1.61194 q^{34} -2.13120 q^{35} -1.45969 q^{36} -10.3164 q^{37} +0.652389 q^{38} -0.205573 q^{39} +1.11151 q^{40} +9.20909 q^{41} +2.37966 q^{42} -4.01672 q^{43} +3.49577 q^{44} +1.62246 q^{45} +8.69554 q^{46} -0.404702 q^{47} -1.24109 q^{48} -3.32360 q^{49} +3.76455 q^{50} -2.00057 q^{51} +0.165638 q^{52} +0.182256 q^{53} -5.53489 q^{54} -3.88558 q^{55} -1.91739 q^{56} +0.809674 q^{57} -4.71992 q^{58} -4.79272 q^{59} +1.37948 q^{60} +7.80807 q^{61} -2.84008 q^{62} -2.79880 q^{63} +1.00000 q^{64} -0.184108 q^{65} +4.33858 q^{66} +2.84545 q^{67} +1.61194 q^{68} +10.7920 q^{69} +2.13120 q^{70} -12.8359 q^{71} +1.45969 q^{72} +1.04071 q^{73} +10.3164 q^{74} +4.67216 q^{75} -0.652389 q^{76} +6.70278 q^{77} +0.205573 q^{78} +12.7802 q^{79} -1.11151 q^{80} -2.49023 q^{81} -9.20909 q^{82} +0.388345 q^{83} -2.37966 q^{84} -1.79168 q^{85} +4.01672 q^{86} -5.85786 q^{87} -3.49577 q^{88} +14.6108 q^{89} -1.62246 q^{90} +0.317594 q^{91} -8.69554 q^{92} -3.52481 q^{93} +0.404702 q^{94} +0.725135 q^{95} +1.24109 q^{96} -10.4163 q^{97} +3.32360 q^{98} -5.10275 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.24109	−0.716545	−0.358272	−	0.933617i	$-0.616634\pi$
$3$	−1.24109	−0.716545	−0.358272	+	0.933617i	$0.616634\pi$
$4$	1.00000	0.500000
$5$	−1.11151	−0.497081	−0.248541	−	0.968621i	$-0.579951\pi$
$5$	−1.11151	−0.497081	−0.248541	+	0.968621i	$0.579951\pi$
$6$	1.24109	0.506674
$7$	1.91739	0.724707	0.362353	−	0.932041i	$-0.381973\pi$
$7$	1.91739	0.724707	0.362353	+	0.932041i	$0.381973\pi$
$8$	−1.00000	−0.353553
$9$	−1.45969	−0.486564
$10$	1.11151	0.351489
$11$	3.49577	1.05402	0.527008	−	0.849861i	$-0.323314\pi$
$11$	3.49577	1.05402	0.527008	+	0.849861i	$0.323314\pi$
$12$	−1.24109	−0.358272
$13$	0.165638	0.0459398	0.0229699	−	0.999736i	$-0.492688\pi$
$13$	0.165638	0.0459398	0.0229699	+	0.999736i	$0.492688\pi$
$14$	−1.91739	−0.512445
$15$	1.37948	0.356181
$16$	1.00000	0.250000
$17$	1.61194	0.390953	0.195477	−	0.980708i	$-0.437375\pi$
$17$	1.61194	0.390953	0.195477	+	0.980708i	$0.437375\pi$
$18$	1.45969	0.344052
$19$	−0.652389	−0.149668	−0.0748341	−	0.997196i	$-0.523843\pi$
$19$	−0.652389	−0.149668	−0.0748341	+	0.997196i	$0.523843\pi$
$20$	−1.11151	−0.248541
$21$	−2.37966	−0.519285
$22$	−3.49577	−0.745301
$23$	−8.69554	−1.81315	−0.906573	−	0.422049i	$-0.861311\pi$
$23$	−8.69554	−1.81315	−0.906573	+	0.422049i	$0.861311\pi$
$24$	1.24109	0.253337
$25$	−3.76455	−0.752910
$26$	−0.165638	−0.0324844
$27$	5.53489	1.06519
$28$	1.91739	0.362353
$29$	4.71992	0.876468	0.438234	−	0.898861i	$-0.355604\pi$
$29$	4.71992	0.876468	0.438234	+	0.898861i	$0.355604\pi$
$30$	−1.37948	−0.251858
$31$	2.84008	0.510094	0.255047	−	0.966929i	$-0.417909\pi$
$31$	2.84008	0.510094	0.255047	+	0.966929i	$0.417909\pi$
$32$	−1.00000	−0.176777
$33$	−4.33858	−0.755249
$34$	−1.61194	−0.276446
$35$	−2.13120	−0.360238
$36$	−1.45969	−0.243282
$37$	−10.3164	−1.69600	−0.848002	−	0.529994i	$-0.822194\pi$
$37$	−10.3164	−1.69600	−0.848002	+	0.529994i	$0.822194\pi$
$38$	0.652389	0.105831
$39$	−0.205573	−0.0329179
$40$	1.11151	0.175745
$41$	9.20909	1.43822	0.719109	−	0.694897i	$-0.244550\pi$
$41$	9.20909	1.43822	0.719109	+	0.694897i	$0.244550\pi$
$42$	2.37966	0.367190
$43$	−4.01672	−0.612544	−0.306272	−	0.951944i	$-0.599082\pi$
$43$	−4.01672	−0.612544	−0.306272	+	0.951944i	$0.599082\pi$
$44$	3.49577	0.527008
$45$	1.62246	0.241862
$46$	8.69554	1.28209
$47$	−0.404702	−0.0590318	−0.0295159	−	0.999564i	$-0.509397\pi$
$47$	−0.404702	−0.0590318	−0.0295159	+	0.999564i	$0.509397\pi$
$48$	−1.24109	−0.179136
$49$	−3.32360	−0.474800
$50$	3.76455	0.532388
$51$	−2.00057	−0.280136
$52$	0.165638	0.0229699
$53$	0.182256	0.0250347	0.0125174	−	0.999922i	$-0.496015\pi$
$53$	0.182256	0.0250347	0.0125174	+	0.999922i	$0.496015\pi$
$54$	−5.53489	−0.753203
$55$	−3.88558	−0.523931
$56$	−1.91739	−0.256223
$57$	0.809674	0.107244
$58$	−4.71992	−0.619757
$59$	−4.79272	−0.623958	−0.311979	−	0.950089i	$-0.600992\pi$
$59$	−4.79272	−0.623958	−0.311979	+	0.950089i	$0.600992\pi$
$60$	1.37948	0.178090
$61$	7.80807	0.999721	0.499861	−	0.866106i	$-0.333385\pi$
$61$	7.80807	0.999721	0.499861	+	0.866106i	$0.333385\pi$
$62$	−2.84008	−0.360691
$63$	−2.79880	−0.352616
$64$	1.00000	0.125000
$65$	−0.184108	−0.0228358
$66$	4.33858	0.534042
$67$	2.84545	0.347627	0.173814	−	0.984779i	$-0.444391\pi$
$67$	2.84545	0.347627	0.173814	+	0.984779i	$0.444391\pi$
$68$	1.61194	0.195477
$69$	10.7920	1.29920
$70$	2.13120	0.254727
$71$	−12.8359	−1.52334	−0.761671	−	0.647964i	$-0.775621\pi$
$71$	−12.8359	−1.52334	−0.761671	+	0.647964i	$0.775621\pi$
$72$	1.45969	0.172026
$73$	1.04071	0.121806	0.0609032	−	0.998144i	$-0.480602\pi$
$73$	1.04071	0.121806	0.0609032	+	0.998144i	$0.480602\pi$
$74$	10.3164	1.19926
$75$	4.67216	0.539494
$76$	−0.652389	−0.0748341
$77$	6.70278	0.763852
$78$	0.205573	0.0232765
$79$	12.7802	1.43789	0.718945	−	0.695067i	$-0.244625\pi$
$79$	12.7802	1.43789	0.718945	+	0.695067i	$0.244625\pi$
$80$	−1.11151	−0.124270
$81$	−2.49023	−0.276692
$82$	−9.20909	−1.01697
$83$	0.388345	0.0426264	0.0213132	−	0.999773i	$-0.493215\pi$
$83$	0.388345	0.0426264	0.0213132	+	0.999773i	$0.493215\pi$
$84$	−2.37966	−0.259643
$85$	−1.79168	−0.194335
$86$	4.01672	0.433134
$87$	−5.85786	−0.628029
$88$	−3.49577	−0.372651
$89$	14.6108	1.54874	0.774368	−	0.632735i	$-0.218068\pi$
$89$	14.6108	1.54874	0.774368	+	0.632735i	$0.218068\pi$
$90$	−1.62246	−0.171022
$91$	0.317594	0.0332929
$92$	−8.69554	−0.906573
$93$	−3.52481	−0.365505
$94$	0.404702	0.0417418
$95$	0.725135	0.0743973
$96$	1.24109	0.126668
$97$	−10.4163	−1.05761	−0.528806	−	0.848743i	$-0.677360\pi$
$97$	−10.4163	−1.05761	−0.528806	+	0.848743i	$0.677360\pi$
$98$	3.32360	0.335734
$99$	−5.10275	−0.512845
$100$	−3.76455	−0.376455
$101$	−6.37865	−0.634699	−0.317350	−	0.948309i	$-0.602793\pi$
$101$	−6.37865	−0.634699	−0.317350	+	0.948309i	$0.602793\pi$
$102$	2.00057	0.198086
$103$	−0.786887	−0.0775343	−0.0387671	−	0.999248i	$-0.512343\pi$
$103$	−0.786887	−0.0775343	−0.0387671	+	0.999248i	$0.512343\pi$
$104$	−0.165638	−0.0162422
$105$	2.64501	0.258127
$106$	−0.182256	−0.0177022
$107$	14.8712	1.43766	0.718828	−	0.695188i	$-0.244679\pi$
$107$	14.8712	1.43766	0.718828	+	0.695188i	$0.244679\pi$
$108$	5.53489	0.532595
$109$	−3.90365	−0.373902	−0.186951	−	0.982369i	$-0.559861\pi$
$109$	−3.90365	−0.373902	−0.186951	+	0.982369i	$0.559861\pi$
$110$	3.88558	0.370475
$111$	12.8036	1.21526
$112$	1.91739	0.181177
$113$	−4.11867	−0.387452	−0.193726	−	0.981056i	$-0.562057\pi$
$113$	−4.11867	−0.387452	−0.193726	+	0.981056i	$0.562057\pi$
$114$	−0.809674	−0.0758330
$115$	9.66516	0.901281
$116$	4.71992	0.438234
$117$	−0.241781	−0.0223526
$118$	4.79272	0.441205
$119$	3.09073	0.283327
$120$	−1.37948	−0.125929
$121$	1.22043	0.110948
$122$	−7.80807	−0.706910
$123$	−11.4293	−1.03055
$124$	2.84008	0.255047
$125$	9.74186	0.871339
$126$	2.79880	0.249337
$127$	−20.8678	−1.85171	−0.925857	−	0.377874i	$-0.876655\pi$
$127$	−20.8678	−1.85171	−0.925857	+	0.377874i	$0.876655\pi$
$128$	−1.00000	−0.0883883
$129$	4.98512	0.438916
$130$	0.184108	0.0161474
$131$	−12.1660	−1.06295	−0.531473	−	0.847075i	$-0.678361\pi$
$131$	−12.1660	−1.06295	−0.531473	+	0.847075i	$0.678361\pi$
$132$	−4.33858	−0.377625
$133$	−1.25089	−0.108466
$134$	−2.84545	−0.245810
$135$	−6.15207	−0.529486
$136$	−1.61194	−0.138223
$137$	19.4677	1.66324	0.831618	−	0.555348i	$-0.187415\pi$
$137$	19.4677	1.66324	0.831618	+	0.555348i	$0.187415\pi$
$138$	−10.7920	−0.918674
$139$	6.19099	0.525113	0.262556	−	0.964917i	$-0.415434\pi$
$139$	6.19099	0.525113	0.262556	+	0.964917i	$0.415434\pi$
$140$	−2.13120	−0.180119
$141$	0.502272	0.0422990
$142$	12.8359	1.07717
$143$	0.579034	0.0484213
$144$	−1.45969	−0.121641
$145$	−5.24623	−0.435676
$146$	−1.04071	−0.0861301
$147$	4.12489	0.340215
$148$	−10.3164	−0.848002
$149$	7.58305	0.621227	0.310614	−	0.950536i	$-0.399465\pi$
$149$	7.58305	0.621227	0.310614	+	0.950536i	$0.399465\pi$
$150$	−4.67216	−0.381480
$151$	−11.5936	−0.943473	−0.471737	−	0.881739i	$-0.656373\pi$
$151$	−11.5936	−0.943473	−0.471737	+	0.881739i	$0.656373\pi$
$152$	0.652389	0.0529157
$153$	−2.35294	−0.190224
$154$	−6.70278	−0.540125
$155$	−3.15677	−0.253558
$156$	−0.205573	−0.0164590
$157$	7.02971	0.561032	0.280516	−	0.959849i	$-0.409494\pi$
$157$	7.02971	0.561032	0.280516	+	0.959849i	$0.409494\pi$
$158$	−12.7802	−1.01674
$159$	−0.226196	−0.0179385
$160$	1.11151	0.0878724
$161$	−16.6728	−1.31400
$162$	2.49023	0.195651
$163$	−5.40127	−0.423060	−0.211530	−	0.977371i	$-0.567845\pi$
$163$	−5.40127	−0.423060	−0.211530	+	0.977371i	$0.567845\pi$
$164$	9.20909	0.719109
$165$	4.82236	0.375420
$166$	−0.388345	−0.0301414
$167$	−15.6549	−1.21141	−0.605706	−	0.795689i	$-0.707109\pi$
$167$	−15.6549	−1.21141	−0.605706	+	0.795689i	$0.707109\pi$
$168$	2.37966	0.183595
$169$	−12.9726	−0.997890
$170$	1.79168	0.137416
$171$	0.952286	0.0728231
$172$	−4.01672	−0.306272
$173$	−7.21811	−0.548782	−0.274391	−	0.961618i	$-0.588476\pi$
$173$	−7.21811	−0.548782	−0.274391	+	0.961618i	$0.588476\pi$
$174$	5.85786	0.444083
$175$	−7.21813	−0.545639
$176$	3.49577	0.263504
$177$	5.94820	0.447094
$178$	−14.6108	−1.09512
$179$	−3.65407	−0.273118	−0.136559	−	0.990632i	$-0.543604\pi$
$179$	−3.65407	−0.273118	−0.136559	+	0.990632i	$0.543604\pi$
$180$	1.62246	0.120931
$181$	−19.2639	−1.43187	−0.715937	−	0.698165i	$-0.754000\pi$
$181$	−19.2639	−1.43187	−0.715937	+	0.698165i	$0.754000\pi$
$182$	−0.317594	−0.0235416
$183$	−9.69054	−0.716345
$184$	8.69554	0.641044
$185$	11.4667	0.843051
$186$	3.52481	0.258451
$187$	5.63498	0.412071
$188$	−0.404702	−0.0295159
$189$	10.6126	0.771950
$190$	−0.725135	−0.0526068
$191$	−1.81786	−0.131536	−0.0657678	−	0.997835i	$-0.520950\pi$
$191$	−1.81786	−0.131536	−0.0657678	+	0.997835i	$0.520950\pi$
$192$	−1.24109	−0.0895681
$193$	−18.9504	−1.36408	−0.682039	−	0.731316i	$-0.738906\pi$
$193$	−18.9504	−1.36408	−0.682039	+	0.731316i	$0.738906\pi$
$194$	10.4163	0.747845
$195$	0.228495	0.0163629
$196$	−3.32360	−0.237400
$197$	−3.92513	−0.279654	−0.139827	−	0.990176i	$-0.544655\pi$
$197$	−3.92513	−0.279654	−0.139827	+	0.990176i	$0.544655\pi$
$198$	5.10275	0.362636
$199$	0.410975	0.0291332	0.0145666	−	0.999894i	$-0.495363\pi$
$199$	0.410975	0.0291332	0.0145666	+	0.999894i	$0.495363\pi$
$200$	3.76455	0.266194
$201$	−3.53147	−0.249090
$202$	6.37865	0.448800
$203$	9.04996	0.635182
$204$	−2.00057	−0.140068
$205$	−10.2360	−0.714911
$206$	0.786887	0.0548250
$207$	12.6928	0.882211
$208$	0.165638	0.0114850
$209$	−2.28060	−0.157753
$210$	−2.64501	−0.182523
$211$	−4.58156	−0.315408	−0.157704	−	0.987486i	$-0.550409\pi$
$211$	−4.58156	−0.315408	−0.157704	+	0.987486i	$0.550409\pi$
$212$	0.182256	0.0125174
$213$	15.9306	1.09154
$214$	−14.8712	−1.01658
$215$	4.46462	0.304484
$216$	−5.53489	−0.376601
$217$	5.44556	0.369669
$218$	3.90365	0.264389
$219$	−1.29162	−0.0872797
$220$	−3.88558	−0.261966
$221$	0.266999	0.0179603
$222$	−12.8036	−0.859320
$223$	11.9595	0.800868	0.400434	−	0.916326i	$-0.368859\pi$
$223$	11.9595	0.800868	0.400434	+	0.916326i	$0.368859\pi$
$224$	−1.91739	−0.128111
$225$	5.49508	0.366339
$226$	4.11867	0.273970
$227$	10.3468	0.686744	0.343372	−	0.939199i	$-0.388431\pi$
$227$	10.3468	0.686744	0.343372	+	0.939199i	$0.388431\pi$
$228$	0.809674	0.0536220
$229$	5.86781	0.387756	0.193878	−	0.981026i	$-0.437893\pi$
$229$	5.86781	0.387756	0.193878	+	0.981026i	$0.437893\pi$
$230$	−9.66516	−0.637302
$231$	−8.31876	−0.547334
$232$	−4.71992	−0.309878
$233$	11.1265	0.728920	0.364460	−	0.931219i	$-0.381254\pi$
$233$	11.1265	0.728920	0.364460	+	0.931219i	$0.381254\pi$
$234$	0.241781	0.0158057
$235$	0.449829	0.0293436
$236$	−4.79272	−0.311979
$237$	−15.8615	−1.03031
$238$	−3.09073	−0.200342
$239$	9.84832	0.637035	0.318517	−	0.947917i	$-0.396815\pi$
$239$	9.84832	0.637035	0.318517	+	0.947917i	$0.396815\pi$
$240$	1.37948	0.0890452
$241$	0.130895	0.00843172	0.00421586	−	0.999991i	$-0.498658\pi$
$241$	0.130895	0.00843172	0.00421586	+	0.999991i	$0.498658\pi$
$242$	−1.22043	−0.0784523
$243$	−13.5141	−0.866927
$244$	7.80807	0.499861
$245$	3.69420	0.236014
$246$	11.4293	0.728707
$247$	−0.108061	−0.00687573
$248$	−2.84008	−0.180346
$249$	−0.481972	−0.0305438
$250$	−9.74186	−0.616130
$251$	−26.1017	−1.64752	−0.823762	−	0.566936i	$-0.808129\pi$
$251$	−26.1017	−1.64752	−0.823762	+	0.566936i	$0.808129\pi$
$252$	−2.79880	−0.176308
$253$	−30.3977	−1.91108
$254$	20.8678	1.30936
$255$	2.22365	0.139250
$256$	1.00000	0.0625000
$257$	10.4910	0.654409	0.327204	−	0.944954i	$-0.393893\pi$
$257$	10.4910	0.654409	0.327204	+	0.944954i	$0.393893\pi$
$258$	−4.98512	−0.310360
$259$	−19.7806	−1.22911
$260$	−0.184108	−0.0114179
$261$	−6.88963	−0.426457
$262$	12.1660	0.751616
$263$	9.78237	0.603207	0.301603	−	0.953433i	$-0.402478\pi$
$263$	9.78237	0.603207	0.301603	+	0.953433i	$0.402478\pi$
$264$	4.33858	0.267021
$265$	−0.202579	−0.0124443
$266$	1.25089	0.0766968
$267$	−18.1333	−1.10974
$268$	2.84545	0.173814
$269$	−15.2855	−0.931972	−0.465986	−	0.884792i	$-0.654300\pi$
$269$	−15.2855	−0.931972	−0.465986	+	0.884792i	$0.654300\pi$
$270$	6.15207	0.374403
$271$	11.0088	0.668740	0.334370	−	0.942442i	$-0.391476\pi$
$271$	11.0088	0.668740	0.334370	+	0.942442i	$0.391476\pi$
$272$	1.61194	0.0977383
$273$	−0.394164	−0.0238559
$274$	−19.4677	−1.17609
$275$	−13.1600	−0.793579
$276$	10.7920	0.649600
$277$	−31.9794	−1.92146	−0.960729	−	0.277487i	$-0.910499\pi$
$277$	−31.9794	−1.92146	−0.960729	+	0.277487i	$0.910499\pi$
$278$	−6.19099	−0.371311
$279$	−4.14564	−0.248193
$280$	2.13120	0.127363
$281$	−17.0011	−1.01420	−0.507100	−	0.861887i	$-0.669282\pi$
$281$	−17.0011	−1.01420	−0.507100	+	0.861887i	$0.669282\pi$
$282$	−0.502272	−0.0299099
$283$	−6.08250	−0.361567	−0.180784	−	0.983523i	$-0.557863\pi$
$283$	−6.08250	−0.361567	−0.180784	+	0.983523i	$0.557863\pi$
$284$	−12.8359	−0.761671
$285$	−0.899959	−0.0533090
$286$	−0.579034	−0.0342390
$287$	17.6575	1.04229
$288$	1.45969	0.0860131
$289$	−14.4016	−0.847156
$290$	5.24623	0.308069
$291$	12.9276	0.757827
$292$	1.04071	0.0609032
$293$	−19.4461	−1.13605	−0.568027	−	0.823010i	$-0.692293\pi$
$293$	−19.4461	−1.13605	−0.568027	+	0.823010i	$0.692293\pi$
$294$	−4.12489	−0.240569
$295$	5.32714	0.310158
$296$	10.3164	0.599628
$297$	19.3487	1.12273
$298$	−7.58305	−0.439274
$299$	−1.44032	−0.0832956
$300$	4.67216	0.269747
$301$	−7.70164	−0.443915
$302$	11.5936	0.667136
$303$	7.91649	0.454791
$304$	−0.652389	−0.0374171
$305$	−8.67873	−0.496943
$306$	2.35294	0.134508
$307$	−14.5006	−0.827594	−0.413797	−	0.910369i	$-0.635798\pi$
$307$	−14.5006	−0.827594	−0.413797	+	0.910369i	$0.635798\pi$
$308$	6.70278	0.381926
$309$	0.976599	0.0555568
$310$	3.15677	0.179293
$311$	8.65490	0.490774	0.245387	−	0.969425i	$-0.421085\pi$
$311$	8.65490	0.490774	0.245387	+	0.969425i	$0.421085\pi$
$312$	0.205573	0.0116383
$313$	7.21387	0.407752	0.203876	−	0.978997i	$-0.434646\pi$
$313$	7.21387	0.407752	0.203876	+	0.978997i	$0.434646\pi$
$314$	−7.02971	−0.396710
$315$	3.11089	0.175279
$316$	12.7802	0.718945
$317$	8.21415	0.461353	0.230676	−	0.973031i	$-0.425906\pi$
$317$	8.21415	0.461353	0.230676	+	0.973031i	$0.425906\pi$
$318$	0.226196	0.0126844
$319$	16.4998	0.923811
$320$	−1.11151	−0.0621351
$321$	−18.4566	−1.03015
$322$	16.6728	0.929138
$323$	−1.05161	−0.0585133
$324$	−2.49023	−0.138346
$325$	−0.623554	−0.0345886
$326$	5.40127	0.299149
$327$	4.84479	0.267918
$328$	−9.20909	−0.508487
$329$	−0.775973	−0.0427808
$330$	−4.82236	−0.265462
$331$	15.8619	0.871849	0.435924	−	0.899983i	$-0.356422\pi$
$331$	15.8619	0.871849	0.435924	+	0.899983i	$0.356422\pi$
$332$	0.388345	0.0213132
$333$	15.0587	0.825213
$334$	15.6549	0.856598
$335$	−3.16274	−0.172799
$336$	−2.37966	−0.129821
$337$	−9.86705	−0.537492	−0.268746	−	0.963211i	$-0.586609\pi$
$337$	−9.86705	−0.537492	−0.268746	+	0.963211i	$0.586609\pi$
$338$	12.9726	0.705614
$339$	5.11165	0.277627
$340$	−1.79168	−0.0971677
$341$	9.92829	0.537647
$342$	−0.952286	−0.0514937
$343$	−19.7944	−1.06880
$344$	4.01672	0.216567
$345$	−11.9954	−0.645808
$346$	7.21811	0.388048
$347$	10.3995	0.558272	0.279136	−	0.960252i	$-0.409952\pi$
$347$	10.3995	0.558272	0.279136	+	0.960252i	$0.409952\pi$
$348$	−5.85786	−0.314014
$349$	−13.4065	−0.717634	−0.358817	−	0.933408i	$-0.616820\pi$
$349$	−13.4065	−0.717634	−0.358817	+	0.933408i	$0.616820\pi$
$350$	7.21813	0.385825
$351$	0.916790	0.0489346
$352$	−3.49577	−0.186325
$353$	−7.72435	−0.411126	−0.205563	−	0.978644i	$-0.565903\pi$
$353$	−7.72435	−0.411126	−0.205563	+	0.978644i	$0.565903\pi$
$354$	−5.94820	−0.316143
$355$	14.2672	0.757225
$356$	14.6108	0.774368
$357$	−3.83588	−0.203016
$358$	3.65407	0.193124
$359$	−2.06221	−0.108839	−0.0544195	−	0.998518i	$-0.517331\pi$
$359$	−2.06221	−0.108839	−0.0544195	+	0.998518i	$0.517331\pi$
$360$	−1.62246	−0.0855110
$361$	−18.5744	−0.977599
$362$	19.2639	1.01249
$363$	−1.51467	−0.0794994
$364$	0.317594	0.0166465
$365$	−1.15676	−0.0605476
$366$	9.69054	0.506532
$367$	−32.1627	−1.67888	−0.839439	−	0.543454i	$-0.817116\pi$
$367$	−32.1627	−1.67888	−0.839439	+	0.543454i	$0.817116\pi$
$368$	−8.69554	−0.453287
$369$	−13.4424	−0.699784
$370$	−11.4667	−0.596127
$371$	0.349456	0.0181429
$372$	−3.52481	−0.182753
$373$	−30.1847	−1.56290	−0.781451	−	0.623967i	$-0.785520\pi$
$373$	−30.1847	−1.56290	−0.781451	+	0.623967i	$0.785520\pi$
$374$	−5.63498	−0.291378
$375$	−12.0905	−0.624353
$376$	0.404702	0.0208709
$377$	0.781801	0.0402648
$378$	−10.6126	−0.545851
$379$	−14.0380	−0.721084	−0.360542	−	0.932743i	$-0.617408\pi$
$379$	−14.0380	−0.721084	−0.360542	+	0.932743i	$0.617408\pi$
$380$	0.725135	0.0371986
$381$	25.8988	1.32684
$382$	1.81786	0.0930097
$383$	−21.9724	−1.12274	−0.561368	−	0.827566i	$-0.689725\pi$
$383$	−21.9724	−1.12274	−0.561368	+	0.827566i	$0.689725\pi$
$384$	1.24109	0.0633342
$385$	−7.45018	−0.379697
$386$	18.9504	0.964548
$387$	5.86317	0.298042
$388$	−10.4163	−0.528806
$389$	−5.26340	−0.266865	−0.133432	−	0.991058i	$-0.542600\pi$
$389$	−5.26340	−0.266865	−0.133432	+	0.991058i	$0.542600\pi$
$390$	−0.228495	−0.0115703
$391$	−14.0167	−0.708855
$392$	3.32360	0.167867
$393$	15.0991	0.761648
$394$	3.92513	0.197745
$395$	−14.2053	−0.714748
$396$	−5.10275	−0.256423
$397$	−4.22663	−0.212129	−0.106064	−	0.994359i	$-0.533825\pi$
$397$	−4.22663	−0.212129	−0.106064	+	0.994359i	$0.533825\pi$
$398$	−0.410975	−0.0206003
$399$	1.55247	0.0777205
$400$	−3.76455	−0.188228
$401$	−15.3480	−0.766443	−0.383221	−	0.923657i	$-0.625185\pi$
$401$	−15.3480	−0.766443	−0.383221	+	0.923657i	$0.625185\pi$
$402$	3.53147	0.176134
$403$	0.470427	0.0234336
$404$	−6.37865	−0.317350
$405$	2.76791	0.137539
$406$	−9.04996	−0.449142
$407$	−36.0637	−1.78761
$408$	2.00057	0.0990429
$409$	−1.75952	−0.0870025	−0.0435013	−	0.999053i	$-0.513851\pi$
$409$	−1.75952	−0.0870025	−0.0435013	+	0.999053i	$0.513851\pi$
$410$	10.2360	0.505518
$411$	−24.1612	−1.19178
$412$	−0.786887	−0.0387671
$413$	−9.18953	−0.452187
$414$	−12.6928	−0.623817
$415$	−0.431649	−0.0211888
$416$	−0.165638	−0.00812109
$417$	−7.68359	−0.376267
$418$	2.28060	0.111548
$419$	31.0397	1.51639	0.758194	−	0.652029i	$-0.226082\pi$
$419$	31.0397	1.51639	0.758194	+	0.652029i	$0.226082\pi$
$420$	2.64501	0.129063
$421$	−36.6536	−1.78639	−0.893193	−	0.449674i	$-0.851540\pi$
$421$	−36.6536	−1.78639	−0.893193	+	0.449674i	$0.851540\pi$
$422$	4.58156	0.223027
$423$	0.590739	0.0287227
$424$	−0.182256	−0.00885112
$425$	−6.06824	−0.294353
$426$	−15.9306	−0.771838
$427$	14.9712	0.724505
$428$	14.8712	0.718828
$429$	−0.718635	−0.0346960
$430$	−4.46462	−0.215303
$431$	−22.7176	−1.09427	−0.547135	−	0.837045i	$-0.684281\pi$
$431$	−22.7176	−1.09427	−0.547135	+	0.837045i	$0.684281\pi$
$432$	5.53489	0.266297
$433$	−2.22512	−0.106932	−0.0534662	−	0.998570i	$-0.517027\pi$
$433$	−2.22512	−0.106932	−0.0534662	+	0.998570i	$0.517027\pi$
$434$	−5.44556	−0.261395
$435$	6.51106	0.312181
$436$	−3.90365	−0.186951
$437$	5.67287	0.271370
$438$	1.29162	0.0617161
$439$	6.28552	0.299992	0.149996	−	0.988687i	$-0.452074\pi$
$439$	6.28552	0.299992	0.149996	+	0.988687i	$0.452074\pi$
$440$	3.88558	0.185238
$441$	4.85143	0.231020
$442$	−0.266999	−0.0126999
$443$	3.65866	0.173828	0.0869142	−	0.996216i	$-0.472299\pi$
$443$	3.65866	0.173828	0.0869142	+	0.996216i	$0.472299\pi$
$444$	12.8036	0.607631
$445$	−16.2400	−0.769848
$446$	−11.9595	−0.566299
$447$	−9.41126	−0.445137
$448$	1.91739	0.0905884
$449$	4.03813	0.190571	0.0952856	−	0.995450i	$-0.469624\pi$
$449$	4.03813	0.190571	0.0952856	+	0.995450i	$0.469624\pi$
$450$	−5.49508	−0.259041
$451$	32.1929	1.51590
$452$	−4.11867	−0.193726
$453$	14.3887	0.676041
$454$	−10.3468	−0.485602
$455$	−0.353008	−0.0165493
$456$	−0.809674	−0.0379165
$457$	7.55217	0.353276	0.176638	−	0.984276i	$-0.443478\pi$
$457$	7.55217	0.353276	0.176638	+	0.984276i	$0.443478\pi$
$458$	−5.86781	−0.274185
$459$	8.92191	0.416439
$460$	9.66516	0.450640
$461$	−32.3961	−1.50884	−0.754418	−	0.656394i	$-0.772081\pi$
$461$	−32.3961	−1.50884	−0.754418	+	0.656394i	$0.772081\pi$
$462$	8.31876	0.387024
$463$	−14.4493	−0.671514	−0.335757	−	0.941949i	$-0.608992\pi$
$463$	−14.4493	−0.671514	−0.335757	+	0.941949i	$0.608992\pi$
$464$	4.71992	0.219117
$465$	3.91785	0.181686
$466$	−11.1265	−0.515424
$467$	−28.2865	−1.30894	−0.654471	−	0.756087i	$-0.727109\pi$
$467$	−28.2865	−1.30894	−0.654471	+	0.756087i	$0.727109\pi$
$468$	−0.241781	−0.0111763
$469$	5.45585	0.251928
$470$	−0.449829	−0.0207491
$471$	−8.72452	−0.402005
$472$	4.79272	0.220603
$473$	−14.0416	−0.645631
$474$	15.8615	0.728541
$475$	2.45595	0.112687
$476$	3.09073	0.141663
$477$	−0.266037	−0.0121810
$478$	−9.84832	−0.450452
$479$	2.08452	0.0952443	0.0476221	−	0.998865i	$-0.484836\pi$
$479$	2.08452	0.0952443	0.0476221	+	0.998865i	$0.484836\pi$
$480$	−1.37948	−0.0629645
$481$	−1.70879	−0.0779141
$482$	−0.130895	−0.00596213
$483$	20.6925	0.941540
$484$	1.22043	0.0554741
$485$	11.5778	0.525719
$486$	13.5141	0.613010
$487$	6.26852	0.284054	0.142027	−	0.989863i	$-0.454638\pi$
$487$	6.26852	0.284054	0.142027	+	0.989863i	$0.454638\pi$
$488$	−7.80807	−0.353455
$489$	6.70348	0.303142
$490$	−3.69420	−0.166887
$491$	−25.7108	−1.16031	−0.580157	−	0.814505i	$-0.697009\pi$
$491$	−25.7108	−1.16031	−0.580157	+	0.814505i	$0.697009\pi$
$492$	−11.4293	−0.515274
$493$	7.60824	0.342658
$494$	0.108061	0.00486188
$495$	5.67174	0.254926
$496$	2.84008	0.127524
$497$	−24.6115	−1.10398
$498$	0.481972	0.0215977
$499$	−5.73815	−0.256875	−0.128437	−	0.991718i	$-0.540996\pi$
$499$	−5.73815	−0.256875	−0.128437	+	0.991718i	$0.540996\pi$
$500$	9.74186	0.435669
$501$	19.4292	0.868031
$502$	26.1017	1.16498
$503$	−32.3556	−1.44266	−0.721332	−	0.692589i	$-0.756470\pi$
$503$	−32.3556	−1.44266	−0.721332	+	0.692589i	$0.756470\pi$
$504$	2.79880	0.124669
$505$	7.08992	0.315497
$506$	30.3977	1.35134
$507$	16.1001	0.715033
$508$	−20.8678	−0.925857
$509$	33.4225	1.48142	0.740712	−	0.671823i	$-0.234488\pi$
$509$	33.4225	1.48142	0.740712	+	0.671823i	$0.234488\pi$
$510$	−2.22365	−0.0984647
$511$	1.99546	0.0882739
$512$	−1.00000	−0.0441942
$513$	−3.61090	−0.159425
$514$	−10.4910	−0.462737
$515$	0.874631	0.0385408
$516$	4.98512	0.219458
$517$	−1.41475	−0.0622205
$518$	19.7806	0.869109
$519$	8.95833	0.393227
$520$	0.184108	0.00807368
$521$	20.7389	0.908588	0.454294	−	0.890852i	$-0.349892\pi$
$521$	20.7389	0.908588	0.454294	+	0.890852i	$0.349892\pi$
$522$	6.88963	0.301551
$523$	−29.7963	−1.30290	−0.651450	−	0.758692i	$-0.725839\pi$
$523$	−29.7963	−1.30290	−0.651450	+	0.758692i	$0.725839\pi$
$524$	−12.1660	−0.531473
$525$	8.95836	0.390975
$526$	−9.78237	−0.426532
$527$	4.57805	0.199423
$528$	−4.33858	−0.188812
$529$	52.6125	2.28750
$530$	0.202579	0.00879945
$531$	6.99588	0.303595
$532$	−1.25089	−0.0542328
$533$	1.52538	0.0660715
$534$	18.1333	0.784704
$535$	−16.5295	−0.714632
$536$	−2.84545	−0.122905
$537$	4.53504	0.195701
$538$	15.2855	0.659003
$539$	−11.6185	−0.500446
$540$	−6.15207	−0.264743
$541$	15.4754	0.665339	0.332670	−	0.943043i	$-0.392051\pi$
$541$	15.4754	0.665339	0.332670	+	0.943043i	$0.392051\pi$
$542$	−11.0088	−0.472871
$543$	23.9083	1.02600
$544$	−1.61194	−0.0691114
$545$	4.33894	0.185860
$546$	0.394164	0.0168686
$547$	24.0202	1.02703	0.513514	−	0.858081i	$-0.328344\pi$
$547$	24.0202	1.02703	0.513514	+	0.858081i	$0.328344\pi$
$548$	19.4677	0.831618
$549$	−11.3974	−0.486428
$550$	13.1600	0.561145
$551$	−3.07923	−0.131179
$552$	−10.7920	−0.459337
$553$	24.5048	1.04205
$554$	31.9794	1.35868
$555$	−14.2313	−0.604084
$556$	6.19099	0.262556
$557$	27.0498	1.14614	0.573069	−	0.819507i	$-0.305753\pi$
$557$	27.0498	1.14614	0.573069	+	0.819507i	$0.305753\pi$
$558$	4.14564	0.175499
$559$	−0.665324	−0.0281402
$560$	−2.13120	−0.0900595
$561$	−6.99353	−0.295267
$562$	17.0011	0.717147
$563$	7.06174	0.297617	0.148808	−	0.988866i	$-0.452456\pi$
$563$	7.06174	0.297617	0.148808	+	0.988866i	$0.452456\pi$
$564$	0.502272	0.0211495
$565$	4.57793	0.192595
$566$	6.08250	0.255667
$567$	−4.77476	−0.200521
$568$	12.8359	0.538583
$569$	12.9160	0.541466	0.270733	−	0.962655i	$-0.412734\pi$
$569$	12.9160	0.541466	0.270733	+	0.962655i	$0.412734\pi$
$570$	0.899959	0.0376951
$571$	34.2066	1.43150	0.715752	−	0.698355i	$-0.246084\pi$
$571$	34.2066	1.43150	0.715752	+	0.698355i	$0.246084\pi$
$572$	0.579034	0.0242106
$573$	2.25613	0.0942511
$574$	−17.6575	−0.737008
$575$	32.7348	1.36514
$576$	−1.45969	−0.0608204
$577$	−3.77777	−0.157271	−0.0786353	−	0.996903i	$-0.525056\pi$
$577$	−3.77777	−0.157271	−0.0786353	+	0.996903i	$0.525056\pi$
$578$	14.4016	0.599029
$579$	23.5191	0.977423
$580$	−5.24623	−0.217838
$581$	0.744611	0.0308917
$582$	−12.9276	−0.535864
$583$	0.637125	0.0263870
$584$	−1.04071	−0.0430650
$585$	0.268741	0.0111111
$586$	19.4461	0.803312
$587$	10.2059	0.421243	0.210621	−	0.977568i	$-0.432451\pi$
$587$	10.2059	0.421243	0.210621	+	0.977568i	$0.432451\pi$
$588$	4.12489	0.170108
$589$	−1.85284	−0.0763449
$590$	−5.32714	−0.219315
$591$	4.87144	0.200384
$592$	−10.3164	−0.424001
$593$	9.34759	0.383860	0.191930	−	0.981409i	$-0.438525\pi$
$593$	9.34759	0.383860	0.191930	+	0.981409i	$0.438525\pi$
$594$	−19.3487	−0.793887
$595$	−3.43537	−0.140836
$596$	7.58305	0.310614
$597$	−0.510057	−0.0208753
$598$	1.44032	0.0588989
$599$	33.5547	1.37101	0.685503	−	0.728070i	$-0.259582\pi$
$599$	33.5547	1.37101	0.685503	+	0.728070i	$0.259582\pi$
$600$	−4.67216	−0.190740
$601$	−21.6666	−0.883798	−0.441899	−	0.897065i	$-0.645695\pi$
$601$	−21.6666	−0.883798	−0.441899	+	0.897065i	$0.645695\pi$
$602$	7.70164	0.313895
$603$	−4.15348	−0.169143
$604$	−11.5936	−0.471737
$605$	−1.35652	−0.0551503
$606$	−7.91649	−0.321585
$607$	2.37471	0.0963863	0.0481932	−	0.998838i	$-0.484654\pi$
$607$	2.37471	0.0963863	0.0481932	+	0.998838i	$0.484654\pi$
$608$	0.652389	0.0264579
$609$	−11.2318	−0.455137
$610$	8.67873	0.351391
$611$	−0.0670342	−0.00271191
$612$	−2.35294	−0.0951118
$613$	−29.7809	−1.20284	−0.601419	−	0.798933i	$-0.705398\pi$
$613$	−29.7809	−1.20284	−0.601419	+	0.798933i	$0.705398\pi$
$614$	14.5006	0.585197
$615$	12.7038	0.512266
$616$	−6.70278	−0.270063
$617$	−49.2612	−1.98318	−0.991590	−	0.129416i	$-0.958690\pi$
$617$	−49.2612	−1.98318	−0.991590	+	0.129416i	$0.958690\pi$
$618$	−0.976599	−0.0392846
$619$	−8.76658	−0.352359	−0.176179	−	0.984358i	$-0.556374\pi$
$619$	−8.76658	−0.352359	−0.176179	+	0.984358i	$0.556374\pi$
$620$	−3.15677	−0.126779
$621$	−48.1288	−1.93134
$622$	−8.65490	−0.347030
$623$	28.0146	1.12238
$624$	−0.205573	−0.00822949
$625$	7.99461	0.319784
$626$	−7.21387	−0.288324
$627$	2.83044	0.113037
$628$	7.02971	0.280516
$629$	−16.6294	−0.663058
$630$	−3.11089	−0.123941
$631$	35.9027	1.42926	0.714632	−	0.699501i	$-0.246594\pi$
$631$	35.9027	1.42926	0.714632	+	0.699501i	$0.246594\pi$
$632$	−12.7802	−0.508371
$633$	5.68614	0.226004
$634$	−8.21415	−0.326226
$635$	23.1947	0.920452
$636$	−0.226196	−0.00896926
$637$	−0.550516	−0.0218122
$638$	−16.4998	−0.653233
$639$	18.7365	0.741203
$640$	1.11151	0.0439362
$641$	−22.0970	−0.872780	−0.436390	−	0.899758i	$-0.643743\pi$
$641$	−22.0970	−0.872780	−0.436390	+	0.899758i	$0.643743\pi$
$642$	18.4566	0.728423
$643$	18.6862	0.736912	0.368456	−	0.929645i	$-0.379887\pi$
$643$	18.6862	0.736912	0.368456	+	0.929645i	$0.379887\pi$
$644$	−16.6728	−0.657000
$645$	−5.54100	−0.218177
$646$	1.05161	0.0413751
$647$	30.7618	1.20937	0.604685	−	0.796465i	$-0.293299\pi$
$647$	30.7618	1.20937	0.604685	+	0.796465i	$0.293299\pi$
$648$	2.49023	0.0978255
$649$	−16.7542	−0.657662
$650$	0.623554	0.0244578
$651$	−6.75844	−0.264884
$652$	−5.40127	−0.211530
$653$	−10.4827	−0.410220	−0.205110	−	0.978739i	$-0.565755\pi$
$653$	−10.4827	−0.410220	−0.205110	+	0.978739i	$0.565755\pi$
$654$	−4.84479	−0.189446
$655$	13.5226	0.528370
$656$	9.20909	0.359554
$657$	−1.51912	−0.0592665
$658$	0.775973	0.0302506
$659$	−40.5931	−1.58128	−0.790641	−	0.612280i	$-0.790253\pi$
$659$	−40.5931	−1.58128	−0.790641	+	0.612280i	$0.790253\pi$
$660$	4.82236	0.187710
$661$	−3.39729	−0.132139	−0.0660697	−	0.997815i	$-0.521046\pi$
$661$	−3.39729	−0.132139	−0.0660697	+	0.997815i	$0.521046\pi$
$662$	−15.8619	−0.616490
$663$	−0.331371	−0.0128694
$664$	−0.388345	−0.0150707
$665$	1.39037	0.0539162
$666$	−15.0587	−0.583514
$667$	−41.0423	−1.58916
$668$	−15.6549	−0.605706
$669$	−14.8428	−0.573858
$670$	3.16274	0.122187
$671$	27.2952	1.05372
$672$	2.37966	0.0917975
$673$	−15.4959	−0.597324	−0.298662	−	0.954359i	$-0.596540\pi$
$673$	−15.4959	−0.597324	−0.298662	+	0.954359i	$0.596540\pi$
$674$	9.86705	0.380065
$675$	−20.8364	−0.801992
$676$	−12.9726	−0.498945
$677$	−6.28863	−0.241692	−0.120846	−	0.992671i	$-0.538561\pi$
$677$	−6.28863	−0.241692	−0.120846	+	0.992671i	$0.538561\pi$
$678$	−5.11165	−0.196312
$679$	−19.9721	−0.766459
$680$	1.79168	0.0687080
$681$	−12.8414	−0.492083
$682$	−9.92829	−0.380174
$683$	47.4114	1.81415	0.907073	−	0.420973i	$-0.138311\pi$
$683$	47.4114	1.81415	0.907073	+	0.420973i	$0.138311\pi$
$684$	0.952286	0.0364115
$685$	−21.6385	−0.826763
$686$	19.7944	0.755754
$687$	−7.28249	−0.277844
$688$	−4.01672	−0.153136
$689$	0.0301885	0.00115009
$690$	11.9954	0.456655
$691$	50.9932	1.93987	0.969937	−	0.243358i	$-0.0782489\pi$
$691$	50.9932	1.93987	0.969937	+	0.243358i	$0.0782489\pi$
$692$	−7.21811	−0.274391
$693$	−9.78398	−0.371663
$694$	−10.3995	−0.394758
$695$	−6.88133	−0.261024
$696$	5.85786	0.222042
$697$	14.8445	0.562276
$698$	13.4065	0.507444
$699$	−13.8090	−0.522304
$700$	−7.21813	−0.272820
$701$	−14.3308	−0.541265	−0.270633	−	0.962683i	$-0.587233\pi$
$701$	−14.3308	−0.541265	−0.270633	+	0.962683i	$0.587233\pi$
$702$	−0.916790	−0.0346020
$703$	6.73029	0.253838
$704$	3.49577	0.131752
$705$	−0.558279	−0.0210260
$706$	7.72435	0.290710
$707$	−12.2304	−0.459971
$708$	5.94820	0.223547
$709$	38.6440	1.45130	0.725652	−	0.688062i	$-0.241538\pi$
$709$	38.6440	1.45130	0.725652	+	0.688062i	$0.241538\pi$
$710$	−14.2672	−0.535439
$711$	−18.6552	−0.699625
$712$	−14.6108	−0.547561
$713$	−24.6961	−0.924876
$714$	3.83588	0.143554
$715$	−0.643601	−0.0240693
$716$	−3.65407	−0.136559
$717$	−12.2227	−0.456464
$718$	2.06221	0.0769609
$719$	36.0487	1.34439	0.672195	−	0.740374i	$-0.265352\pi$
$719$	36.0487	1.34439	0.672195	+	0.740374i	$0.265352\pi$
$720$	1.62246	0.0604654
$721$	−1.50877	−0.0561896
$722$	18.5744	0.691267
$723$	−0.162453	−0.00604171
$724$	−19.2639	−0.715937
$725$	−17.7684	−0.659902
$726$	1.51467	0.0562146
$727$	19.2305	0.713220	0.356610	−	0.934253i	$-0.383933\pi$
$727$	19.2305	0.713220	0.356610	+	0.934253i	$0.383933\pi$
$728$	−0.317594	−0.0117708
$729$	24.2429	0.897884
$730$	1.15676	0.0428136
$731$	−6.47472	−0.239476
$732$	−9.69054	−0.358173
$733$	−25.7189	−0.949951	−0.474976	−	0.879999i	$-0.657543\pi$
$733$	−25.7189	−0.949951	−0.474976	+	0.879999i	$0.657543\pi$
$734$	32.1627	1.18715
$735$	−4.58485	−0.169115
$736$	8.69554	0.320522
$737$	9.94705	0.366404
$738$	13.4424	0.494822
$739$	−36.7433	−1.35163	−0.675813	−	0.737073i	$-0.736207\pi$
$739$	−36.7433	−1.35163	−0.675813	+	0.737073i	$0.736207\pi$
$740$	11.4667	0.421526
$741$	0.134113	0.00492677
$742$	−0.349456	−0.0128289
$743$	6.05889	0.222279	0.111140	−	0.993805i	$-0.464550\pi$
$743$	6.05889	0.222279	0.111140	+	0.993805i	$0.464550\pi$
$744$	3.52481	0.129226
$745$	−8.42861	−0.308800
$746$	30.1847	1.10514
$747$	−0.566864	−0.0207405
$748$	5.63498	0.206035
$749$	28.5140	1.04188
$750$	12.0905	0.441484
$751$	32.3527	1.18057	0.590284	−	0.807196i	$-0.299016\pi$
$751$	32.3527	1.18057	0.590284	+	0.807196i	$0.299016\pi$
$752$	−0.404702	−0.0147580
$753$	32.3946	1.18052
$754$	−0.781801	−0.0284715
$755$	12.8864	0.468983
$756$	10.6126	0.385975
$757$	−53.7324	−1.95294	−0.976469	−	0.215657i	$-0.930811\pi$
$757$	−53.7324	−1.95294	−0.976469	+	0.215657i	$0.930811\pi$
$758$	14.0380	0.509884
$759$	37.7263	1.36938
$760$	−0.725135	−0.0263034
$761$	4.73058	0.171483	0.0857417	−	0.996317i	$-0.472674\pi$
$761$	4.73058	0.171483	0.0857417	+	0.996317i	$0.472674\pi$
$762$	−25.8988	−0.938215
$763$	−7.48484	−0.270969
$764$	−1.81786	−0.0657678
$765$	2.61531	0.0945566
$766$	21.9724	0.793895
$767$	−0.793858	−0.0286645
$768$	−1.24109	−0.0447841
$769$	−7.16900	−0.258521	−0.129260	−	0.991611i	$-0.541260\pi$
$769$	−7.16900	−0.258521	−0.129260	+	0.991611i	$0.541260\pi$
$770$	7.45018	0.268486
$771$	−13.0203	−0.468913
$772$	−18.9504	−0.682039
$773$	−9.18175	−0.330245	−0.165122	−	0.986273i	$-0.552802\pi$
$773$	−9.18175	−0.330245	−0.165122	+	0.986273i	$0.552802\pi$
$774$	−5.86317	−0.210747
$775$	−10.6916	−0.384055
$776$	10.4163	0.373922
$777$	24.5495	0.880709
$778$	5.26340	0.188702
$779$	−6.00790	−0.215256
$780$	0.228495	0.00818145
$781$	−44.8714	−1.60563
$782$	14.0167	0.501236
$783$	26.1242	0.933604
$784$	−3.32360	−0.118700
$785$	−7.81358	−0.278879
$786$	−15.0991	−0.538566
$787$	−7.99970	−0.285159	−0.142579	−	0.989783i	$-0.545540\pi$
$787$	−7.99970	−0.285159	−0.142579	+	0.989783i	$0.545540\pi$
$788$	−3.92513	−0.139827
$789$	−12.1408	−0.432225
$790$	14.2053	0.505403
$791$	−7.89712	−0.280789
$792$	5.10275	0.181318
$793$	1.29332	0.0459270
$794$	4.22663	0.149998
$795$	0.251419	0.00891690
$796$	0.410975	0.0145666
$797$	30.3326	1.07444	0.537219	−	0.843443i	$-0.319475\pi$
$797$	30.3326	1.07444	0.537219	+	0.843443i	$0.319475\pi$
$798$	−1.55247	−0.0549567
$799$	−0.652356	−0.0230787
$800$	3.76455	0.133097
$801$	−21.3272	−0.753559
$802$	15.3480	0.541957
$803$	3.63810	0.128386
$804$	−3.53147	−0.124545
$805$	18.5319	0.653164
$806$	−0.470427	−0.0165701
$807$	18.9707	0.667799
$808$	6.37865	0.224400
$809$	−2.79476	−0.0982587	−0.0491293	−	0.998792i	$-0.515645\pi$
$809$	−2.79476	−0.0982587	−0.0491293	+	0.998792i	$0.515645\pi$
$810$	−2.76791	−0.0972545
$811$	12.4251	0.436305	0.218152	−	0.975915i	$-0.429997\pi$
$811$	12.4251	0.436305	0.218152	+	0.975915i	$0.429997\pi$
$812$	9.04996	0.317591
$813$	−13.6630	−0.479182
$814$	36.0637	1.26403
$815$	6.00355	0.210295
$816$	−2.00057	−0.0700339
$817$	2.62046	0.0916784
$818$	1.75952	0.0615201
$819$	−0.463589	−0.0161991
$820$	−10.2360	−0.357456
$821$	−11.6450	−0.406412	−0.203206	−	0.979136i	$-0.565136\pi$
$821$	−11.6450	−0.406412	−0.203206	+	0.979136i	$0.565136\pi$
$822$	24.1612	0.842718
$823$	−9.64023	−0.336037	−0.168019	−	0.985784i	$-0.553737\pi$
$823$	−9.64023	−0.336037	−0.168019	+	0.985784i	$0.553737\pi$
$824$	0.786887	0.0274125
$825$	16.3328	0.568635
$826$	9.18953	0.319745
$827$	7.92434	0.275556	0.137778	−	0.990463i	$-0.456004\pi$
$827$	7.92434	0.275556	0.137778	+	0.990463i	$0.456004\pi$
$828$	12.6928	0.441105
$829$	1.57571	0.0547266	0.0273633	−	0.999626i	$-0.491289\pi$
$829$	1.57571	0.0547266	0.0273633	+	0.999626i	$0.491289\pi$
$830$	0.431649	0.0149827
$831$	39.6894	1.37681
$832$	0.165638	0.00574248
$833$	−5.35745	−0.185625
$834$	7.68359	0.266061
$835$	17.4005	0.602170
$836$	−2.28060	−0.0788763
$837$	15.7195	0.543347
$838$	−31.0397	−1.07225
$839$	52.3986	1.80900	0.904500	−	0.426474i	$-0.140244\pi$
$839$	52.3986	1.80900	0.904500	+	0.426474i	$0.140244\pi$
$840$	−2.64501	−0.0912616
$841$	−6.72231	−0.231804
$842$	36.6536	1.26317
$843$	21.0999	0.726719
$844$	−4.58156	−0.157704
$845$	14.4191	0.496032
$846$	−0.590739	−0.0203100
$847$	2.34005	0.0804050
$848$	0.182256	0.00625869
$849$	7.54894	0.259079
$850$	6.06824	0.208139
$851$	89.7066	3.07510
$852$	15.9306	0.545772
$853$	0.444809	0.0152300	0.00761498	−	0.999971i	$-0.497576\pi$
$853$	0.444809	0.0152300	0.00761498	+	0.999971i	$0.497576\pi$
$854$	−14.9712	−0.512302
$855$	−1.05847	−0.0361990
$856$	−14.8712	−0.508288
$857$	21.0346	0.718529	0.359264	−	0.933236i	$-0.383028\pi$
$857$	21.0346	0.718529	0.359264	+	0.933236i	$0.383028\pi$
$858$	0.718635	0.0245338
$859$	−38.8021	−1.32391	−0.661955	−	0.749543i	$-0.730273\pi$
$859$	−38.8021	−1.32391	−0.661955	+	0.749543i	$0.730273\pi$
$860$	4.46462	0.152242
$861$	−21.9145	−0.746845
$862$	22.7176	0.773765
$863$	−39.4435	−1.34267	−0.671335	−	0.741154i	$-0.734279\pi$
$863$	−39.4435	−1.34267	−0.671335	+	0.741154i	$0.734279\pi$
$864$	−5.53489	−0.188301
$865$	8.02298	0.272789
$866$	2.22512	0.0756126
$867$	17.8738	0.607025
$868$	5.44556	0.184834
$869$	44.6768	1.51556
$870$	−6.51106	−0.220745
$871$	0.471316	0.0159699
$872$	3.90365	0.132194
$873$	15.2045	0.514596
$874$	−5.67287	−0.191888
$875$	18.6790	0.631465
$876$	−1.29162	−0.0436399
$877$	14.1598	0.478143	0.239072	−	0.971002i	$-0.423157\pi$
$877$	14.1598	0.478143	0.239072	+	0.971002i	$0.423157\pi$
$878$	−6.28552	−0.212126
$879$	24.1344	0.814034
$880$	−3.88558	−0.130983
$881$	51.4742	1.73421	0.867105	−	0.498126i	$-0.165978\pi$
$881$	51.4742	1.73421	0.867105	+	0.498126i	$0.165978\pi$
$882$	−4.85143	−0.163356
$883$	18.7671	0.631563	0.315782	−	0.948832i	$-0.397733\pi$
$883$	18.7671	0.631563	0.315782	+	0.948832i	$0.397733\pi$
$884$	0.266999	0.00898016
$885$	−6.61147	−0.222242
$886$	−3.65866	−0.122915
$887$	20.8125	0.698817	0.349408	−	0.936971i	$-0.386383\pi$
$887$	20.8125	0.698817	0.349408	+	0.936971i	$0.386383\pi$
$888$	−12.8036	−0.429660
$889$	−40.0117	−1.34195
$890$	16.2400	0.544365
$891$	−8.70529	−0.291638
$892$	11.9595	0.400434
$893$	0.264023	0.00883519
$894$	9.41126	0.314760
$895$	4.06153	0.135762
$896$	−1.91739	−0.0640556
$897$	1.78756	0.0596851
$898$	−4.03813	−0.134754
$899$	13.4050	0.447081
$900$	5.49508	0.183169
$901$	0.293785	0.00978741
$902$	−32.1929	−1.07191
$903$	9.55844	0.318085
$904$	4.11867	0.136985
$905$	21.4120	0.711758
$906$	−14.3887	−0.478033
$907$	4.13994	0.137464	0.0687322	−	0.997635i	$-0.478105\pi$
$907$	4.13994	0.137464	0.0687322	+	0.997635i	$0.478105\pi$
$908$	10.3468	0.343372
$909$	9.31085	0.308822
$910$	0.353008	0.0117021
$911$	7.84179	0.259810	0.129905	−	0.991526i	$-0.458533\pi$
$911$	7.84179	0.259810	0.129905	+	0.991526i	$0.458533\pi$
$912$	0.809674	0.0268110
$913$	1.35757	0.0449289
$914$	−7.55217	−0.249804
$915$	10.7711	0.356082
$916$	5.86781	0.193878
$917$	−23.3270	−0.770324
$918$	−8.92191	−0.294467
$919$	38.7595	1.27856	0.639279	−	0.768975i	$-0.279233\pi$
$919$	38.7595	1.27856	0.639279	+	0.768975i	$0.279233\pi$
$920$	−9.66516	−0.318651
$921$	17.9966	0.593008
$922$	32.3961	1.06691
$923$	−2.12612	−0.0699821
$924$	−8.31876	−0.273667
$925$	38.8366	1.27694
$926$	14.4493	0.474832
$927$	1.14861	0.0377254
$928$	−4.71992	−0.154939
$929$	−19.6765	−0.645565	−0.322783	−	0.946473i	$-0.604618\pi$
$929$	−19.6765	−0.645565	−0.322783	+	0.946473i	$0.604618\pi$
$930$	−3.91785	−0.128471
$931$	2.16828	0.0710624
$932$	11.1265	0.364460
$933$	−10.7415	−0.351662
$934$	28.2865	0.925562
$935$	−6.26332	−0.204833
$936$	0.241781	0.00790285
$937$	−21.5781	−0.704927	−0.352463	−	0.935826i	$-0.614656\pi$
$937$	−21.5781	−0.704927	−0.352463	+	0.935826i	$0.614656\pi$
$938$	−5.45585	−0.178140
$939$	−8.95308	−0.292173
$940$	0.449829	0.0146718
$941$	−39.6113	−1.29129	−0.645645	−	0.763638i	$-0.723411\pi$
$941$	−39.6113	−1.29129	−0.645645	+	0.763638i	$0.723411\pi$
$942$	8.72452	0.284260
$943$	−80.0780	−2.60770
$944$	−4.79272	−0.155990
$945$	−11.7959	−0.383722
$946$	14.0416	0.456530
$947$	−17.2758	−0.561390	−0.280695	−	0.959797i	$-0.590565\pi$
$947$	−17.2758	−0.561390	−0.280695	+	0.959797i	$0.590565\pi$
$948$	−15.8615	−0.515156
$949$	0.172382	0.00559576
$950$	−2.45595	−0.0796816
$951$	−10.1945	−0.330580
$952$	−3.09073	−0.100171
$953$	4.63322	0.150085	0.0750423	−	0.997180i	$-0.476091\pi$
$953$	4.63322	0.150085	0.0750423	+	0.997180i	$0.476091\pi$
$954$	0.266037	0.00861326
$955$	2.02056	0.0653839
$956$	9.84832	0.318517
$957$	−20.4778	−0.661952
$958$	−2.08452	−0.0673479
$959$	37.3272	1.20536
$960$	1.37948	0.0445226
$961$	−22.9339	−0.739804
$962$	1.70879	0.0550936
$963$	−21.7074	−0.699511
$964$	0.130895	0.00421586
$965$	21.0635	0.678057
$966$	−20.6925	−0.665769
$967$	11.8813	0.382078	0.191039	−	0.981582i	$-0.438814\pi$
$967$	11.8813	0.382078	0.191039	+	0.981582i	$0.438814\pi$
$968$	−1.22043	−0.0392261
$969$	1.30515	0.0419274
$970$	−11.5778	−0.371740
$971$	−26.8137	−0.860492	−0.430246	−	0.902712i	$-0.641573\pi$
$971$	−26.8137	−0.860492	−0.430246	+	0.902712i	$0.641573\pi$
$972$	−13.5141	−0.433463
$973$	11.8706	0.380553
$974$	−6.26852	−0.200856
$975$	0.773888	0.0247843
$976$	7.80807	0.249930
$977$	17.0934	0.546868	0.273434	−	0.961891i	$-0.411841\pi$
$977$	17.0934	0.546868	0.273434	+	0.961891i	$0.411841\pi$
$978$	−6.70348	−0.214354
$979$	51.0759	1.63239
$980$	3.69420	0.118007
$981$	5.69812	0.181927
$982$	25.7108	0.820466
$983$	20.0980	0.641027	0.320514	−	0.947244i	$-0.396144\pi$
$983$	20.0980	0.641027	0.320514	+	0.947244i	$0.396144\pi$
$984$	11.4293	0.364354
$985$	4.36281	0.139011
$986$	−7.60824	−0.242296
$987$	0.963054	0.0306543
$988$	−0.108061	−0.00343787
$989$	34.9276	1.11063
$990$	−5.67174	−0.180260
$991$	−33.6891	−1.07017	−0.535084	−	0.844799i	$-0.679720\pi$
$991$	−33.6891	−1.07017	−0.535084	+	0.844799i	$0.679720\pi$
$992$	−2.84008	−0.0901728
$993$	−19.6861	−0.624719
$994$	24.6115	0.780630
$995$	−0.456801	−0.0144816
$996$	−0.481972	−0.0152719
$997$	28.4196	0.900057	0.450028	−	0.893014i	$-0.351414\pi$
$997$	28.4196	0.900057	0.450028	+	0.893014i	$0.351414\pi$
$998$	5.73815	0.181638
$999$	−57.1000	−1.80656

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4022.2.a.d.1.14	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4022.2.a.d.1.14	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.24109 q^{3} +1.00000 q^{4} -1.11151 q^{5} +1.24109 q^{6} +1.91739 q^{7} -1.00000 q^{8} -1.45969 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.24109 q^{3} +1.00000 q^{4} -1.11151 q^{5} +1.24109 q^{6} +1.91739 q^{7} -1.00000 q^{8} -1.45969 q^{9} +1.11151 q^{10} +3.49577 q^{11} -1.24109 q^{12} +0.165638 q^{13} -1.91739 q^{14} +1.37948 q^{15} +1.00000 q^{16} +1.61194 q^{17} +1.45969 q^{18} -0.652389 q^{19} -1.11151 q^{20} -2.37966 q^{21} -3.49577 q^{22} -8.69554 q^{23} +1.24109 q^{24} -3.76455 q^{25} -0.165638 q^{26} +5.53489 q^{27} +1.91739 q^{28} +4.71992 q^{29} -1.37948 q^{30} +2.84008 q^{31} -1.00000 q^{32} -4.33858 q^{33} -1.61194 q^{34} -2.13120 q^{35} -1.45969 q^{36} -10.3164 q^{37} +0.652389 q^{38} -0.205573 q^{39} +1.11151 q^{40} +9.20909 q^{41} +2.37966 q^{42} -4.01672 q^{43} +3.49577 q^{44} +1.62246 q^{45} +8.69554 q^{46} -0.404702 q^{47} -1.24109 q^{48} -3.32360 q^{49} +3.76455 q^{50} -2.00057 q^{51} +0.165638 q^{52} +0.182256 q^{53} -5.53489 q^{54} -3.88558 q^{55} -1.91739 q^{56} +0.809674 q^{57} -4.71992 q^{58} -4.79272 q^{59} +1.37948 q^{60} +7.80807 q^{61} -2.84008 q^{62} -2.79880 q^{63} +1.00000 q^{64} -0.184108 q^{65} +4.33858 q^{66} +2.84545 q^{67} +1.61194 q^{68} +10.7920 q^{69} +2.13120 q^{70} -12.8359 q^{71} +1.45969 q^{72} +1.04071 q^{73} +10.3164 q^{74} +4.67216 q^{75} -0.652389 q^{76} +6.70278 q^{77} +0.205573 q^{78} +12.7802 q^{79} -1.11151 q^{80} -2.49023 q^{81} -9.20909 q^{82} +0.388345 q^{83} -2.37966 q^{84} -1.79168 q^{85} +4.01672 q^{86} -5.85786 q^{87} -3.49577 q^{88} +14.6108 q^{89} -1.62246 q^{90} +0.317594 q^{91} -8.69554 q^{92} -3.52481 q^{93} +0.404702 q^{94} +0.725135 q^{95} +1.24109 q^{96} -10.4163 q^{97} +3.32360 q^{98} -5.10275 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q - 37 q^{2} - 5 q^{3} + 37 q^{4} - 13 q^{5} + 5 q^{6} - 22 q^{7} - 37 q^{8} + 32 q^{9}+O(q^{10}) \) 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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