LMFDB - Embedded newform 4034.2.a.a.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4034,2,Mod(1,4034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4034, 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("4034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4034 = 2 \cdot 2017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4034.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:	$32.2116521754$
Analytic rank:	$1$
Dimension:	$33$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	4034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.73960 q^{3} +1.00000 q^{4} -3.73363 q^{5} -2.73960 q^{6} -3.98248 q^{7} +1.00000 q^{8} +4.50543 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.73960 q^{3} +1.00000 q^{4} -3.73363 q^{5} -2.73960 q^{6} -3.98248 q^{7} +1.00000 q^{8} +4.50543 q^{9} -3.73363 q^{10} +2.12582 q^{11} -2.73960 q^{12} +0.839544 q^{13} -3.98248 q^{14} +10.2287 q^{15} +1.00000 q^{16} +2.17455 q^{17} +4.50543 q^{18} -5.54305 q^{19} -3.73363 q^{20} +10.9104 q^{21} +2.12582 q^{22} +3.87115 q^{23} -2.73960 q^{24} +8.94000 q^{25} +0.839544 q^{26} -4.12428 q^{27} -3.98248 q^{28} -0.330532 q^{29} +10.2287 q^{30} +0.561723 q^{31} +1.00000 q^{32} -5.82389 q^{33} +2.17455 q^{34} +14.8691 q^{35} +4.50543 q^{36} +3.52661 q^{37} -5.54305 q^{38} -2.30002 q^{39} -3.73363 q^{40} -3.39658 q^{41} +10.9104 q^{42} +9.88584 q^{43} +2.12582 q^{44} -16.8216 q^{45} +3.87115 q^{46} +6.13435 q^{47} -2.73960 q^{48} +8.86015 q^{49} +8.94000 q^{50} -5.95740 q^{51} +0.839544 q^{52} -13.9419 q^{53} -4.12428 q^{54} -7.93701 q^{55} -3.98248 q^{56} +15.1858 q^{57} -0.330532 q^{58} +5.52199 q^{59} +10.2287 q^{60} +0.0453785 q^{61} +0.561723 q^{62} -17.9428 q^{63} +1.00000 q^{64} -3.13455 q^{65} -5.82389 q^{66} +12.1370 q^{67} +2.17455 q^{68} -10.6054 q^{69} +14.8691 q^{70} +1.91788 q^{71} +4.50543 q^{72} -9.50955 q^{73} +3.52661 q^{74} -24.4921 q^{75} -5.54305 q^{76} -8.46602 q^{77} -2.30002 q^{78} +4.55352 q^{79} -3.73363 q^{80} -2.21739 q^{81} -3.39658 q^{82} -2.73185 q^{83} +10.9104 q^{84} -8.11896 q^{85} +9.88584 q^{86} +0.905527 q^{87} +2.12582 q^{88} +7.28215 q^{89} -16.8216 q^{90} -3.34347 q^{91} +3.87115 q^{92} -1.53890 q^{93} +6.13435 q^{94} +20.6957 q^{95} -2.73960 q^{96} -15.6773 q^{97} +8.86015 q^{98} +9.57771 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9}+O(q^{10}) $ 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9	\( 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9} - 22 q^{10} - 19 q^{11} - 14 q^{12} - 29 q^{13} - 12 q^{14} - 5 q^{15} + 33 q^{16} - 47 q^{17} + 17 q^{18} - 35 q^{19} - 22 q^{20} - 31 q^{21} - 19 q^{22} - 2 q^{23} - 14 q^{24} + 13 q^{25} - 29 q^{26} - 47 q^{27} - 12 q^{28} - 29 q^{29} - 5 q^{30} - 53 q^{31} + 33 q^{32} - 23 q^{33} - 47 q^{34} - 14 q^{35} + 17 q^{36} - 42 q^{37} - 35 q^{38} - 22 q^{40} - 42 q^{41} - 31 q^{42} - 26 q^{43} - 19 q^{44} - 55 q^{45} - 2 q^{46} - 14 q^{48} - 21 q^{49} + 13 q^{50} - 13 q^{51} - 29 q^{52} - 40 q^{53} - 47 q^{54} - 34 q^{55} - 12 q^{56} - 30 q^{57} - 29 q^{58} - 45 q^{59} - 5 q^{60} - 93 q^{61} - 53 q^{62} + 4 q^{63} + 33 q^{64} - 26 q^{65} - 23 q^{66} - 28 q^{67} - 47 q^{68} - 60 q^{69} - 14 q^{70} + 4 q^{71} + 17 q^{72} - 52 q^{73} - 42 q^{74} - 41 q^{75} - 35 q^{76} - 38 q^{77} - 38 q^{79} - 22 q^{80} + 25 q^{81} - 42 q^{82} - 42 q^{83} - 31 q^{84} - 21 q^{85} - 26 q^{86} + 12 q^{87} - 19 q^{88} - 58 q^{89} - 55 q^{90} - 79 q^{91} - 2 q^{92} + 25 q^{93} + 16 q^{95} - 14 q^{96} - 64 q^{97} - 21 q^{98} - 38 q^{99}+O(q^{100}) \) 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9 - 22 * q^10 - 19 * q^11 - 14 * q^12 - 29 * q^13 - 12 * q^14 - 5 * q^15 + 33 * q^16 - 47 * q^17 + 17 * q^18 - 35 * q^19 - 22 * q^20 - 31 * q^21 - 19 * q^22 - 2 * q^23 - 14 * q^24 + 13 * q^25 - 29 * q^26 - 47 * q^27 - 12 * q^28 - 29 * q^29 - 5 * q^30 - 53 * q^31 + 33 * q^32 - 23 * q^33 - 47 * q^34 - 14 * q^35 + 17 * q^36 - 42 * q^37 - 35 * q^38 - 22 * q^40 - 42 * q^41 - 31 * q^42 - 26 * q^43 - 19 * q^44 - 55 * q^45 - 2 * q^46 - 14 * q^48 - 21 * q^49 + 13 * q^50 - 13 * q^51 - 29 * q^52 - 40 * q^53 - 47 * q^54 - 34 * q^55 - 12 * q^56 - 30 * q^57 - 29 * q^58 - 45 * q^59 - 5 * q^60 - 93 * q^61 - 53 * q^62 + 4 * q^63 + 33 * q^64 - 26 * q^65 - 23 * q^66 - 28 * q^67 - 47 * q^68 - 60 * q^69 - 14 * q^70 + 4 * q^71 + 17 * q^72 - 52 * q^73 - 42 * q^74 - 41 * q^75 - 35 * q^76 - 38 * q^77 - 38 * q^79 - 22 * q^80 + 25 * q^81 - 42 * q^82 - 42 * q^83 - 31 * q^84 - 21 * q^85 - 26 * q^86 + 12 * q^87 - 19 * q^88 - 58 * q^89 - 55 * q^90 - 79 * q^91 - 2 * q^92 + 25 * q^93 + 16 * q^95 - 14 * q^96 - 64 * q^97 - 21 * q^98 - 38 * 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
$3$	−2.73960	−1.58171	−0.790856	−	0.612003i	$-0.790364\pi$
$3$	−2.73960	−1.58171	−0.790856	+	0.612003i	$0.790364\pi$
$4$	1.00000	0.500000
$5$	−3.73363	−1.66973	−0.834865	−	0.550454i	$-0.814455\pi$
$5$	−3.73363	−1.66973	−0.834865	+	0.550454i	$0.814455\pi$
$6$	−2.73960	−1.11844
$7$	−3.98248	−1.50524	−0.752618	−	0.658457i	$-0.771209\pi$
$7$	−3.98248	−1.50524	−0.752618	+	0.658457i	$0.771209\pi$
$8$	1.00000	0.353553
$9$	4.50543	1.50181
$10$	−3.73363	−1.18068
$11$	2.12582	0.640957	0.320479	−	0.947256i	$-0.396156\pi$
$11$	2.12582	0.640957	0.320479	+	0.947256i	$0.396156\pi$
$12$	−2.73960	−0.790856
$13$	0.839544	0.232848	0.116424	−	0.993200i	$-0.462857\pi$
$13$	0.839544	0.232848	0.116424	+	0.993200i	$0.462857\pi$
$14$	−3.98248	−1.06436
$15$	10.2287	2.64103
$16$	1.00000	0.250000
$17$	2.17455	0.527405	0.263703	−	0.964604i	$-0.415056\pi$
$17$	2.17455	0.527405	0.263703	+	0.964604i	$0.415056\pi$
$18$	4.50543	1.06194
$19$	−5.54305	−1.27166	−0.635832	−	0.771828i	$-0.719343\pi$
$19$	−5.54305	−1.27166	−0.635832	+	0.771828i	$0.719343\pi$
$20$	−3.73363	−0.834865
$21$	10.9104	2.38085
$22$	2.12582	0.453225
$23$	3.87115	0.807192	0.403596	−	0.914937i	$-0.367760\pi$
$23$	3.87115	0.807192	0.403596	+	0.914937i	$0.367760\pi$
$24$	−2.73960	−0.559219
$25$	8.94000	1.78800
$26$	0.839544	0.164648
$27$	−4.12428	−0.793718
$28$	−3.98248	−0.752618
$29$	−0.330532	−0.0613783	−0.0306891	−	0.999529i	$-0.509770\pi$
$29$	−0.330532	−0.0613783	−0.0306891	+	0.999529i	$0.509770\pi$
$30$	10.2287	1.86749
$31$	0.561723	0.100889	0.0504443	−	0.998727i	$-0.483936\pi$
$31$	0.561723	0.100889	0.0504443	+	0.998727i	$0.483936\pi$
$32$	1.00000	0.176777
$33$	−5.82389	−1.01381
$34$	2.17455	0.372932
$35$	14.8691	2.51334
$36$	4.50543	0.750905
$37$	3.52661	0.579771	0.289885	−	0.957061i	$-0.406383\pi$
$37$	3.52661	0.579771	0.289885	+	0.957061i	$0.406383\pi$
$38$	−5.54305	−0.899202
$39$	−2.30002	−0.368298
$40$	−3.73363	−0.590339
$41$	−3.39658	−0.530457	−0.265228	−	0.964186i	$-0.585447\pi$
$41$	−3.39658	−0.530457	−0.265228	+	0.964186i	$0.585447\pi$
$42$	10.9104	1.68351
$43$	9.88584	1.50758	0.753789	−	0.657117i	$-0.228224\pi$
$43$	9.88584	1.50758	0.753789	+	0.657117i	$0.228224\pi$
$44$	2.12582	0.320479
$45$	−16.8216	−2.50762
$46$	3.87115	0.570771
$47$	6.13435	0.894787	0.447393	−	0.894337i	$-0.352352\pi$
$47$	6.13435	0.894787	0.447393	+	0.894337i	$0.352352\pi$
$48$	−2.73960	−0.395428
$49$	8.86015	1.26574
$50$	8.94000	1.26431
$51$	−5.95740	−0.834202
$52$	0.839544	0.116424
$53$	−13.9419	−1.91507	−0.957536	−	0.288314i	$-0.906905\pi$
$53$	−13.9419	−1.91507	−0.957536	+	0.288314i	$0.906905\pi$
$54$	−4.12428	−0.561244
$55$	−7.93701	−1.07023
$56$	−3.98248	−0.532181
$57$	15.1858	2.01140
$58$	−0.330532	−0.0434010
$59$	5.52199	0.718902	0.359451	−	0.933164i	$-0.382964\pi$
$59$	5.52199	0.718902	0.359451	+	0.933164i	$0.382964\pi$
$60$	10.2287	1.32052
$61$	0.0453785	0.00581012	0.00290506	−	0.999996i	$-0.499075\pi$
$61$	0.0453785	0.00581012	0.00290506	+	0.999996i	$0.499075\pi$
$62$	0.561723	0.0713390
$63$	−17.9428	−2.26058
$64$	1.00000	0.125000
$65$	−3.13455	−0.388793
$66$	−5.82389	−0.716871
$67$	12.1370	1.48277	0.741384	−	0.671082i	$-0.234170\pi$
$67$	12.1370	1.48277	0.741384	+	0.671082i	$0.234170\pi$
$68$	2.17455	0.263703
$69$	−10.6054	−1.27674
$70$	14.8691	1.77720
$71$	1.91788	0.227611	0.113806	−	0.993503i	$-0.463696\pi$
$71$	1.91788	0.227611	0.113806	+	0.993503i	$0.463696\pi$
$72$	4.50543	0.530970
$73$	−9.50955	−1.11301	−0.556504	−	0.830845i	$-0.687858\pi$
$73$	−9.50955	−1.11301	−0.556504	+	0.830845i	$0.687858\pi$
$74$	3.52661	0.409960
$75$	−24.4921	−2.82810
$76$	−5.54305	−0.635832
$77$	−8.46602	−0.964792
$78$	−2.30002	−0.260426
$79$	4.55352	0.512312	0.256156	−	0.966636i	$-0.417544\pi$
$79$	4.55352	0.512312	0.256156	+	0.966636i	$0.417544\pi$
$80$	−3.73363	−0.417433
$81$	−2.21739	−0.246377
$82$	−3.39658	−0.375089
$83$	−2.73185	−0.299859	−0.149930	−	0.988697i	$-0.547905\pi$
$83$	−2.73185	−0.299859	−0.149930	+	0.988697i	$0.547905\pi$
$84$	10.9104	1.19042
$85$	−8.11896	−0.880624
$86$	9.88584	1.06602
$87$	0.905527	0.0970827
$88$	2.12582	0.226613
$89$	7.28215	0.771906	0.385953	−	0.922518i	$-0.373873\pi$
$89$	7.28215	0.771906	0.385953	+	0.922518i	$0.373873\pi$
$90$	−16.8216	−1.77315
$91$	−3.34347	−0.350491
$92$	3.87115	0.403596
$93$	−1.53890	−0.159576
$94$	6.13435	0.632710
$95$	20.6957	2.12334
$96$	−2.73960	−0.279610
$97$	−15.6773	−1.59179	−0.795895	−	0.605434i	$-0.793000\pi$
$97$	−15.6773	−1.59179	−0.795895	+	0.605434i	$0.793000\pi$
$98$	8.86015	0.895010
$99$	9.57771	0.962596
$100$	8.94000	0.894000
$101$	−14.0693	−1.39995	−0.699975	−	0.714168i	$-0.746805\pi$
$101$	−14.0693	−1.39995	−0.699975	+	0.714168i	$0.746805\pi$
$102$	−5.95740	−0.589870
$103$	−0.159603	−0.0157262	−0.00786309	−	0.999969i	$-0.502503\pi$
$103$	−0.159603	−0.0157262	−0.00786309	+	0.999969i	$0.502503\pi$
$104$	0.839544	0.0823241
$105$	−40.7355	−3.97538
$106$	−13.9419	−1.35416
$107$	−4.63295	−0.447884	−0.223942	−	0.974602i	$-0.571893\pi$
$107$	−4.63295	−0.447884	−0.223942	+	0.974602i	$0.571893\pi$
$108$	−4.12428	−0.396859
$109$	9.37781	0.898232	0.449116	−	0.893474i	$-0.351739\pi$
$109$	9.37781	0.898232	0.449116	+	0.893474i	$0.351739\pi$
$110$	−7.93701	−0.756764
$111$	−9.66151	−0.917030
$112$	−3.98248	−0.376309
$113$	6.33800	0.596228	0.298114	−	0.954530i	$-0.403642\pi$
$113$	6.33800	0.596228	0.298114	+	0.954530i	$0.403642\pi$
$114$	15.1858	1.42228
$115$	−14.4535	−1.34779
$116$	−0.330532	−0.0306891
$117$	3.78251	0.349693
$118$	5.52199	0.508341
$119$	−8.66009	−0.793869
$120$	10.2287	0.933746
$121$	−6.48091	−0.589174
$122$	0.0453785	0.00410838
$123$	9.30528	0.839029
$124$	0.561723	0.0504443
$125$	−14.7105	−1.31575
$126$	−17.9428	−1.59847
$127$	4.50906	0.400114	0.200057	−	0.979784i	$-0.435887\pi$
$127$	4.50906	0.400114	0.200057	+	0.979784i	$0.435887\pi$
$128$	1.00000	0.0883883
$129$	−27.0833	−2.38455
$130$	−3.13455	−0.274918
$131$	−13.3292	−1.16457	−0.582287	−	0.812983i	$-0.697842\pi$
$131$	−13.3292	−1.16457	−0.582287	+	0.812983i	$0.697842\pi$
$132$	−5.82389	−0.506905
$133$	22.0751	1.91415
$134$	12.1370	1.04847
$135$	15.3985	1.32530
$136$	2.17455	0.186466
$137$	−7.16582	−0.612218	−0.306109	−	0.951997i	$-0.599027\pi$
$137$	−7.16582	−0.612218	−0.306109	+	0.951997i	$0.599027\pi$
$138$	−10.6054	−0.902794
$139$	−18.8948	−1.60264	−0.801318	−	0.598239i	$-0.795867\pi$
$139$	−18.8948	−1.60264	−0.801318	+	0.598239i	$0.795867\pi$
$140$	14.8691	1.25667
$141$	−16.8057	−1.41529
$142$	1.91788	0.160945
$143$	1.78472	0.149245
$144$	4.50543	0.375452
$145$	1.23408	0.102485
$146$	−9.50955	−0.787016
$147$	−24.2733	−2.00203
$148$	3.52661	0.289885
$149$	−20.5118	−1.68039	−0.840197	−	0.542282i	$-0.817561\pi$
$149$	−20.5118	−1.68039	−0.840197	+	0.542282i	$0.817561\pi$
$150$	−24.4921	−1.99977
$151$	7.10897	0.578520	0.289260	−	0.957251i	$-0.406591\pi$
$151$	7.10897	0.578520	0.289260	+	0.957251i	$0.406591\pi$
$152$	−5.54305	−0.449601
$153$	9.79727	0.792062
$154$	−8.46602	−0.682211
$155$	−2.09727	−0.168457
$156$	−2.30002	−0.184149
$157$	10.5621	0.842951	0.421475	−	0.906840i	$-0.361512\pi$
$157$	10.5621	0.842951	0.421475	+	0.906840i	$0.361512\pi$
$158$	4.55352	0.362259
$159$	38.1954	3.02909
$160$	−3.73363	−0.295169
$161$	−15.4168	−1.21501
$162$	−2.21739	−0.174215
$163$	−17.0125	−1.33252	−0.666262	−	0.745718i	$-0.732107\pi$
$163$	−17.0125	−1.33252	−0.666262	+	0.745718i	$0.732107\pi$
$164$	−3.39658	−0.265228
$165$	21.7443	1.69279
$166$	−2.73185	−0.212032
$167$	11.8203	0.914685	0.457342	−	0.889291i	$-0.348801\pi$
$167$	11.8203	0.914685	0.457342	+	0.889291i	$0.348801\pi$
$168$	10.9104	0.841757
$169$	−12.2952	−0.945782
$170$	−8.11896	−0.622696
$171$	−24.9738	−1.90980
$172$	9.88584	0.753789
$173$	8.82219	0.670739	0.335369	−	0.942087i	$-0.391139\pi$
$173$	8.82219	0.670739	0.335369	+	0.942087i	$0.391139\pi$
$174$	0.905527	0.0686478
$175$	−35.6034	−2.69136
$176$	2.12582	0.160239
$177$	−15.1281	−1.13710
$178$	7.28215	0.545820
$179$	−12.2328	−0.914322	−0.457161	−	0.889384i	$-0.651134\pi$
$179$	−12.2328	−0.914322	−0.457161	+	0.889384i	$0.651134\pi$
$180$	−16.8216	−1.25381
$181$	6.78393	0.504245	0.252123	−	0.967695i	$-0.418871\pi$
$181$	6.78393	0.504245	0.252123	+	0.967695i	$0.418871\pi$
$182$	−3.34347	−0.247834
$183$	−0.124319	−0.00918993
$184$	3.87115	0.285385
$185$	−13.1671	−0.968061
$186$	−1.53890	−0.112838
$187$	4.62268	0.338044
$188$	6.13435	0.447393
$189$	16.4249	1.19473
$190$	20.6957	1.50142
$191$	4.56907	0.330606	0.165303	−	0.986243i	$-0.447140\pi$
$191$	4.56907	0.330606	0.165303	+	0.986243i	$0.447140\pi$
$192$	−2.73960	−0.197714
$193$	8.57590	0.617307	0.308653	−	0.951175i	$-0.400122\pi$
$193$	8.57590	0.617307	0.308653	+	0.951175i	$0.400122\pi$
$194$	−15.6773	−1.12557
$195$	8.58742	0.614958
$196$	8.86015	0.632868
$197$	−0.289575	−0.0206314	−0.0103157	−	0.999947i	$-0.503284\pi$
$197$	−0.289575	−0.0206314	−0.0103157	+	0.999947i	$0.503284\pi$
$198$	9.57771	0.680658
$199$	6.67296	0.473034	0.236517	−	0.971627i	$-0.423994\pi$
$199$	6.67296	0.473034	0.236517	+	0.971627i	$0.423994\pi$
$200$	8.94000	0.632154
$201$	−33.2505	−2.34531
$202$	−14.0693	−0.989914
$203$	1.31634	0.0923888
$204$	−5.95740	−0.417101
$205$	12.6816	0.885720
$206$	−0.159603	−0.0111201
$207$	17.4412	1.21225
$208$	0.839544	0.0582119
$209$	−11.7835	−0.815082
$210$	−40.7355	−2.81102
$211$	−12.8347	−0.883579	−0.441789	−	0.897119i	$-0.645656\pi$
$211$	−12.8347	−0.883579	−0.441789	+	0.897119i	$0.645656\pi$
$212$	−13.9419	−0.957536
$213$	−5.25424	−0.360015
$214$	−4.63295	−0.316702
$215$	−36.9101	−2.51725
$216$	−4.12428	−0.280622
$217$	−2.23705	−0.151861
$218$	9.37781	0.635146
$219$	26.0524	1.76046
$220$	−7.93701	−0.535113
$221$	1.82563	0.122805
$222$	−9.66151	−0.648438
$223$	21.9107	1.46725	0.733623	−	0.679556i	$-0.237828\pi$
$223$	21.9107	1.46725	0.733623	+	0.679556i	$0.237828\pi$
$224$	−3.98248	−0.266091
$225$	40.2786	2.68524
$226$	6.33800	0.421597
$227$	2.32514	0.154325	0.0771626	−	0.997019i	$-0.475414\pi$
$227$	2.32514	0.154325	0.0771626	+	0.997019i	$0.475414\pi$
$228$	15.1858	1.00570
$229$	−20.9266	−1.38287	−0.691436	−	0.722438i	$-0.743021\pi$
$229$	−20.9266	−1.38287	−0.691436	+	0.722438i	$0.743021\pi$
$230$	−14.4535	−0.953033
$231$	23.1935	1.52602
$232$	−0.330532	−0.0217005
$233$	−15.7997	−1.03507	−0.517536	−	0.855661i	$-0.673151\pi$
$233$	−15.7997	−1.03507	−0.517536	+	0.855661i	$0.673151\pi$
$234$	3.78251	0.247270
$235$	−22.9034	−1.49405
$236$	5.52199	0.359451
$237$	−12.4749	−0.810329
$238$	−8.66009	−0.561350
$239$	6.51347	0.421321	0.210661	−	0.977559i	$-0.432438\pi$
$239$	6.51347	0.421321	0.210661	+	0.977559i	$0.432438\pi$
$240$	10.2287	0.660258
$241$	2.02343	0.130340	0.0651702	−	0.997874i	$-0.479241\pi$
$241$	2.02343	0.130340	0.0651702	+	0.997874i	$0.479241\pi$
$242$	−6.48091	−0.416609
$243$	18.4476	1.18342
$244$	0.0453785	0.00290506
$245$	−33.0805	−2.11344
$246$	9.30528	0.593283
$247$	−4.65364	−0.296104
$248$	0.561723	0.0356695
$249$	7.48418	0.474291
$250$	−14.7105	−0.930375
$251$	−6.44830	−0.407013	−0.203507	−	0.979074i	$-0.565234\pi$
$251$	−6.44830	−0.407013	−0.203507	+	0.979074i	$0.565234\pi$
$252$	−17.9428	−1.13029
$253$	8.22936	0.517375
$254$	4.50906	0.282923
$255$	22.2427	1.39289
$256$	1.00000	0.0625000
$257$	19.7391	1.23129	0.615646	−	0.788023i	$-0.288895\pi$
$257$	19.7391	1.23129	0.615646	+	0.788023i	$0.288895\pi$
$258$	−27.0833	−1.68613
$259$	−14.0446	−0.872692
$260$	−3.13455	−0.194397
$261$	−1.48919	−0.0921785
$262$	−13.3292	−0.823479
$263$	22.1102	1.36337	0.681686	−	0.731645i	$-0.261247\pi$
$263$	22.1102	1.36337	0.681686	+	0.731645i	$0.261247\pi$
$264$	−5.82389	−0.358436
$265$	52.0540	3.19765
$266$	22.0751	1.35351
$267$	−19.9502	−1.22093
$268$	12.1370	0.741384
$269$	11.0789	0.675491	0.337745	−	0.941238i	$-0.390336\pi$
$269$	11.0789	0.675491	0.337745	+	0.941238i	$0.390336\pi$
$270$	15.3985	0.937126
$271$	14.4858	0.879947	0.439974	−	0.898011i	$-0.354988\pi$
$271$	14.4858	0.879947	0.439974	+	0.898011i	$0.354988\pi$
$272$	2.17455	0.131851
$273$	9.15978	0.554375
$274$	−7.16582	−0.432903
$275$	19.0048	1.14603
$276$	−10.6054	−0.638372
$277$	−7.76364	−0.466472	−0.233236	−	0.972420i	$-0.574931\pi$
$277$	−7.76364	−0.466472	−0.233236	+	0.972420i	$0.574931\pi$
$278$	−18.8948	−1.13323
$279$	2.53081	0.151515
$280$	14.8691	0.888599
$281$	24.8680	1.48350	0.741751	−	0.670675i	$-0.233995\pi$
$281$	24.8680	1.48350	0.741751	+	0.670675i	$0.233995\pi$
$282$	−16.8057	−1.00076
$283$	−28.3442	−1.68489	−0.842443	−	0.538785i	$-0.818883\pi$
$283$	−28.3442	−1.68489	−0.842443	+	0.538785i	$0.818883\pi$
$284$	1.91788	0.113806
$285$	−56.6981	−3.35850
$286$	1.78472	0.105532
$287$	13.5268	0.798462
$288$	4.50543	0.265485
$289$	−12.2713	−0.721844
$290$	1.23408	0.0724680
$291$	42.9497	2.51775
$292$	−9.50955	−0.556504
$293$	12.4983	0.730159	0.365079	−	0.930976i	$-0.381042\pi$
$293$	12.4983	0.730159	0.365079	+	0.930976i	$0.381042\pi$
$294$	−24.2733	−1.41565
$295$	−20.6171	−1.20037
$296$	3.52661	0.204980
$297$	−8.76746	−0.508740
$298$	−20.5118	−1.18822
$299$	3.25001	0.187953
$300$	−24.4921	−1.41405
$301$	−39.3702	−2.26926
$302$	7.10897	0.409075
$303$	38.5444	2.21432
$304$	−5.54305	−0.317916
$305$	−0.169427	−0.00970134
$306$	9.79727	0.560073
$307$	13.2011	0.753425	0.376712	−	0.926330i	$-0.377055\pi$
$307$	13.2011	0.753425	0.376712	+	0.926330i	$0.377055\pi$
$308$	−8.46602	−0.482396
$309$	0.437250	0.0248743
$310$	−2.09727	−0.119117
$311$	4.20000	0.238160	0.119080	−	0.992885i	$-0.462006\pi$
$311$	4.20000	0.238160	0.119080	+	0.992885i	$0.462006\pi$
$312$	−2.30002	−0.130213
$313$	−22.6796	−1.28192	−0.640962	−	0.767572i	$-0.721464\pi$
$313$	−22.6796	−1.28192	−0.640962	+	0.767572i	$0.721464\pi$
$314$	10.5621	0.596056
$315$	66.9917	3.77456
$316$	4.55352	0.256156
$317$	6.71686	0.377257	0.188628	−	0.982049i	$-0.439596\pi$
$317$	6.71686	0.377257	0.188628	+	0.982049i	$0.439596\pi$
$318$	38.1954	2.14189
$319$	−0.702650	−0.0393408
$320$	−3.73363	−0.208716
$321$	12.6924	0.708423
$322$	−15.4168	−0.859144
$323$	−12.0536	−0.670682
$324$	−2.21739	−0.123188
$325$	7.50553	0.416332
$326$	−17.0125	−0.942237
$327$	−25.6915	−1.42074
$328$	−3.39658	−0.187545
$329$	−24.4299	−1.34687
$330$	21.7443	1.19698
$331$	−17.1222	−0.941123	−0.470561	−	0.882367i	$-0.655949\pi$
$331$	−17.1222	−0.941123	−0.470561	+	0.882367i	$0.655949\pi$
$332$	−2.73185	−0.149930
$333$	15.8889	0.870705
$334$	11.8203	0.646780
$335$	−45.3150	−2.47582
$336$	10.9104	0.595212
$337$	−5.86185	−0.319315	−0.159658	−	0.987172i	$-0.551039\pi$
$337$	−5.86185	−0.319315	−0.159658	+	0.987172i	$0.551039\pi$
$338$	−12.2952	−0.668769
$339$	−17.3636	−0.943061
$340$	−8.11896	−0.440312
$341$	1.19412	0.0646652
$342$	−24.9738	−1.35043
$343$	−7.40800	−0.399994
$344$	9.88584	0.533009
$345$	39.5968	2.13182
$346$	8.82219	0.474284
$347$	−31.7171	−1.70267	−0.851333	−	0.524626i	$-0.824205\pi$
$347$	−31.7171	−1.70267	−0.851333	+	0.524626i	$0.824205\pi$
$348$	0.905527	0.0485413
$349$	36.9736	1.97915	0.989576	−	0.144012i	$-0.0460002\pi$
$349$	36.9736	1.97915	0.989576	+	0.144012i	$0.0460002\pi$
$350$	−35.6034	−1.90308
$351$	−3.46252	−0.184815
$352$	2.12582	0.113306
$353$	−17.5603	−0.934638	−0.467319	−	0.884089i	$-0.654780\pi$
$353$	−17.5603	−0.934638	−0.467319	+	0.884089i	$0.654780\pi$
$354$	−15.1281	−0.804048
$355$	−7.16067	−0.380049
$356$	7.28215	0.385953
$357$	23.7252	1.25567
$358$	−12.2328	−0.646523
$359$	4.28734	0.226277	0.113138	−	0.993579i	$-0.463910\pi$
$359$	4.28734	0.226277	0.113138	+	0.993579i	$0.463910\pi$
$360$	−16.8216	−0.886577
$361$	11.7254	0.617128
$362$	6.78393	0.356555
$363$	17.7551	0.931903
$364$	−3.34347	−0.175245
$365$	35.5051	1.85842
$366$	−0.124319	−0.00649826
$367$	−15.4152	−0.804666	−0.402333	−	0.915493i	$-0.631801\pi$
$367$	−15.4152	−0.804666	−0.402333	+	0.915493i	$0.631801\pi$
$368$	3.87115	0.201798
$369$	−15.3030	−0.796645
$370$	−13.1671	−0.684523
$371$	55.5235	2.88263
$372$	−1.53890	−0.0797882
$373$	−4.05390	−0.209903	−0.104951	−	0.994477i	$-0.533469\pi$
$373$	−4.05390	−0.209903	−0.104951	+	0.994477i	$0.533469\pi$
$374$	4.62268	0.239033
$375$	40.3010	2.08113
$376$	6.13435	0.316355
$377$	−0.277496	−0.0142918
$378$	16.4249	0.844804
$379$	−7.01110	−0.360136	−0.180068	−	0.983654i	$-0.557632\pi$
$379$	−7.01110	−0.360136	−0.180068	+	0.983654i	$0.557632\pi$
$380$	20.6957	1.06167
$381$	−12.3530	−0.632865
$382$	4.56907	0.233774
$383$	5.81589	0.297178	0.148589	−	0.988899i	$-0.452527\pi$
$383$	5.81589	0.297178	0.148589	+	0.988899i	$0.452527\pi$
$384$	−2.73960	−0.139805
$385$	31.6090	1.61094
$386$	8.57590	0.436502
$387$	44.5400	2.26409
$388$	−15.6773	−0.795895
$389$	−7.41222	−0.375814	−0.187907	−	0.982187i	$-0.560170\pi$
$389$	−7.41222	−0.375814	−0.187907	+	0.982187i	$0.560170\pi$
$390$	8.58742	0.434841
$391$	8.41801	0.425717
$392$	8.86015	0.447505
$393$	36.5166	1.84202
$394$	−0.289575	−0.0145886
$395$	−17.0012	−0.855422
$396$	9.57771	0.481298
$397$	15.1240	0.759050	0.379525	−	0.925181i	$-0.376087\pi$
$397$	15.1240	0.759050	0.379525	+	0.925181i	$0.376087\pi$
$398$	6.67296	0.334485
$399$	−60.4770	−3.02764
$400$	8.94000	0.447000
$401$	−7.71561	−0.385299	−0.192650	−	0.981268i	$-0.561708\pi$
$401$	−7.71561	−0.385299	−0.192650	+	0.981268i	$0.561708\pi$
$402$	−33.2505	−1.65838
$403$	0.471592	0.0234917
$404$	−14.0693	−0.699975
$405$	8.27893	0.411383
$406$	1.31634	0.0653287
$407$	7.49692	0.371608
$408$	−5.95740	−0.294935
$409$	19.5470	0.966535	0.483267	−	0.875473i	$-0.339450\pi$
$409$	19.5470	0.966535	0.483267	+	0.875473i	$0.339450\pi$
$410$	12.6816	0.626298
$411$	19.6315	0.968351
$412$	−0.159603	−0.00786309
$413$	−21.9912	−1.08212
$414$	17.4412	0.857189
$415$	10.1997	0.500684
$416$	0.839544	0.0411621
$417$	51.7643	2.53491
$418$	−11.7835	−0.576350
$419$	25.9688	1.26866	0.634330	−	0.773062i	$-0.281276\pi$
$419$	25.9688	1.26866	0.634330	+	0.773062i	$0.281276\pi$
$420$	−40.7355	−1.98769
$421$	9.93456	0.484181	0.242090	−	0.970254i	$-0.422167\pi$
$421$	9.93456	0.484181	0.242090	+	0.970254i	$0.422167\pi$
$422$	−12.8347	−0.624785
$423$	27.6379	1.34380
$424$	−13.9419	−0.677080
$425$	19.4405	0.943001
$426$	−5.25424	−0.254569
$427$	−0.180719	−0.00874560
$428$	−4.63295	−0.223942
$429$	−4.88942	−0.236063
$430$	−36.9101	−1.77996
$431$	−34.7326	−1.67301	−0.836504	−	0.547960i	$-0.815405\pi$
$431$	−34.7326	−1.67301	−0.836504	+	0.547960i	$0.815405\pi$
$432$	−4.12428	−0.198430
$433$	−11.9052	−0.572128	−0.286064	−	0.958210i	$-0.592347\pi$
$433$	−11.9052	−0.572128	−0.286064	+	0.958210i	$0.592347\pi$
$434$	−2.23705	−0.107382
$435$	−3.38090	−0.162102
$436$	9.37781	0.449116
$437$	−21.4580	−1.02648
$438$	26.0524	1.24483
$439$	2.00428	0.0956590	0.0478295	−	0.998856i	$-0.484770\pi$
$439$	2.00428	0.0956590	0.0478295	+	0.998856i	$0.484770\pi$
$440$	−7.93701	−0.378382
$441$	39.9188	1.90089
$442$	1.82563	0.0868363
$443$	32.8947	1.56287	0.781436	−	0.623985i	$-0.214487\pi$
$443$	32.8947	1.56287	0.781436	+	0.623985i	$0.214487\pi$
$444$	−9.66151	−0.458515
$445$	−27.1889	−1.28888
$446$	21.9107	1.03750
$447$	56.1943	2.65790
$448$	−3.98248	−0.188154
$449$	−13.0577	−0.616232	−0.308116	−	0.951349i	$-0.599698\pi$
$449$	−13.0577	−0.616232	−0.308116	+	0.951349i	$0.599698\pi$
$450$	40.2786	1.89875
$451$	−7.22050	−0.340000
$452$	6.33800	0.298114
$453$	−19.4758	−0.915051
$454$	2.32514	0.109124
$455$	12.4833	0.585225
$456$	15.1858	0.711139
$457$	12.6621	0.592306	0.296153	−	0.955141i	$-0.404296\pi$
$457$	12.6621	0.592306	0.296153	+	0.955141i	$0.404296\pi$
$458$	−20.9266	−0.977838
$459$	−8.96844	−0.418611
$460$	−14.4535	−0.673896
$461$	−7.17875	−0.334348	−0.167174	−	0.985927i	$-0.553464\pi$
$461$	−7.17875	−0.334348	−0.167174	+	0.985927i	$0.553464\pi$
$462$	23.1935	1.07906
$463$	10.0355	0.466390	0.233195	−	0.972430i	$-0.425082\pi$
$463$	10.0355	0.466390	0.233195	+	0.972430i	$0.425082\pi$
$464$	−0.330532	−0.0153446
$465$	5.74568	0.266450
$466$	−15.7997	−0.731907
$467$	−25.8758	−1.19739	−0.598694	−	0.800978i	$-0.704313\pi$
$467$	−25.8758	−1.19739	−0.598694	+	0.800978i	$0.704313\pi$
$468$	3.78251	0.174847
$469$	−48.3353	−2.23191
$470$	−22.9034	−1.05646
$471$	−28.9361	−1.33330
$472$	5.52199	0.254170
$473$	21.0155	0.966293
$474$	−12.4749	−0.572989
$475$	−49.5549	−2.27373
$476$	−8.66009	−0.396935
$477$	−62.8144	−2.87607
$478$	6.51347	0.297919
$479$	−7.89789	−0.360864	−0.180432	−	0.983587i	$-0.557750\pi$
$479$	−7.89789	−0.360864	−0.180432	+	0.983587i	$0.557750\pi$
$480$	10.2287	0.466873
$481$	2.96074	0.134998
$482$	2.02343	0.0921646
$483$	42.2359	1.92180
$484$	−6.48091	−0.294587
$485$	58.5333	2.65786
$486$	18.4476	0.836801
$487$	−1.74647	−0.0791402	−0.0395701	−	0.999217i	$-0.512599\pi$
$487$	−1.74647	−0.0791402	−0.0395701	+	0.999217i	$0.512599\pi$
$488$	0.0453785	0.00205419
$489$	46.6076	2.10767
$490$	−33.0805	−1.49443
$491$	21.5836	0.974053	0.487026	−	0.873387i	$-0.338082\pi$
$491$	21.5836	0.974053	0.487026	+	0.873387i	$0.338082\pi$
$492$	9.30528	0.419514
$493$	−0.718757	−0.0323712
$494$	−4.65364	−0.209377
$495$	−35.7596	−1.60728
$496$	0.561723	0.0252221
$497$	−7.63794	−0.342608
$498$	7.48418	0.335374
$499$	−40.5820	−1.81670	−0.908350	−	0.418210i	$-0.862658\pi$
$499$	−40.5820	−1.81670	−0.908350	+	0.418210i	$0.862658\pi$
$500$	−14.7105	−0.657875
$501$	−32.3830	−1.44677
$502$	−6.44830	−0.287802
$503$	−7.45192	−0.332265	−0.166132	−	0.986103i	$-0.553128\pi$
$503$	−7.45192	−0.332265	−0.166132	+	0.986103i	$0.553128\pi$
$504$	−17.9428	−0.799235
$505$	52.5296	2.33754
$506$	8.22936	0.365840
$507$	33.6839	1.49595
$508$	4.50906	0.200057
$509$	11.4255	0.506426	0.253213	−	0.967411i	$-0.418513\pi$
$509$	11.4255	0.506426	0.253213	+	0.967411i	$0.418513\pi$
$510$	22.2427	0.984924
$511$	37.8716	1.67534
$512$	1.00000	0.0441942
$513$	22.8611	1.00934
$514$	19.7391	0.870655
$515$	0.595900	0.0262585
$516$	−27.0833	−1.19228
$517$	13.0405	0.573520
$518$	−14.0446	−0.617086
$519$	−24.1693	−1.06092
$520$	−3.13455	−0.137459
$521$	17.2059	0.753805	0.376903	−	0.926253i	$-0.376989\pi$
$521$	17.2059	0.753805	0.376903	+	0.926253i	$0.376989\pi$
$522$	−1.48919	−0.0651800
$523$	−2.94815	−0.128913	−0.0644567	−	0.997921i	$-0.520531\pi$
$523$	−2.94815	−0.128913	−0.0644567	+	0.997921i	$0.520531\pi$
$524$	−13.3292	−0.582287
$525$	97.5392	4.25696
$526$	22.1102	0.964050
$527$	1.22149	0.0532091
$528$	−5.82389	−0.253452
$529$	−8.01416	−0.348442
$530$	52.0540	2.26108
$531$	24.8789	1.07965
$532$	22.0751	0.957077
$533$	−2.85158	−0.123516
$534$	−19.9502	−0.863330
$535$	17.2977	0.747846
$536$	12.1370	0.524237
$537$	33.5130	1.44619
$538$	11.0789	0.477644
$539$	18.8350	0.811282
$540$	15.3985	0.662648
$541$	−42.6716	−1.83459	−0.917297	−	0.398204i	$-0.869633\pi$
$541$	−42.6716	−1.83459	−0.917297	+	0.398204i	$0.869633\pi$
$542$	14.4858	0.622217
$543$	−18.5853	−0.797570
$544$	2.17455	0.0932329
$545$	−35.0133	−1.49980
$546$	9.15978	0.392002
$547$	−13.3823	−0.572187	−0.286093	−	0.958202i	$-0.592357\pi$
$547$	−13.3823	−0.572187	−0.286093	+	0.958202i	$0.592357\pi$
$548$	−7.16582	−0.306109
$549$	0.204450	0.00872570
$550$	19.0048	0.810367
$551$	1.83216	0.0780525
$552$	−10.6054	−0.451397
$553$	−18.1343	−0.771150
$554$	−7.76364	−0.329846
$555$	36.0725	1.53119
$556$	−18.8948	−0.801318
$557$	−43.6676	−1.85026	−0.925128	−	0.379657i	$-0.876042\pi$
$557$	−43.6676	−1.85026	−0.925128	+	0.379657i	$0.876042\pi$
$558$	2.53081	0.107138
$559$	8.29961	0.351036
$560$	14.8691	0.628335
$561$	−12.6643	−0.534688
$562$	24.8680	1.04899
$563$	42.1713	1.77731	0.888655	−	0.458577i	$-0.151641\pi$
$563$	42.1713	1.77731	0.888655	+	0.458577i	$0.151641\pi$
$564$	−16.8057	−0.707647
$565$	−23.6637	−0.995541
$566$	−28.3442	−1.19139
$567$	8.83072	0.370855
$568$	1.91788	0.0804727
$569$	−38.3309	−1.60691	−0.803457	−	0.595363i	$-0.797008\pi$
$569$	−38.3309	−1.60691	−0.803457	+	0.595363i	$0.797008\pi$
$570$	−56.6981	−2.37482
$571$	−28.1021	−1.17604	−0.588018	−	0.808848i	$-0.700092\pi$
$571$	−28.1021	−1.17604	−0.588018	+	0.808848i	$0.700092\pi$
$572$	1.78472	0.0746227
$573$	−12.5174	−0.522923
$574$	13.5268	0.564598
$575$	34.6081	1.44326
$576$	4.50543	0.187726
$577$	−8.80902	−0.366724	−0.183362	−	0.983045i	$-0.558698\pi$
$577$	−8.80902	−0.366724	−0.183362	+	0.983045i	$0.558698\pi$
$578$	−12.2713	−0.510421
$579$	−23.4946	−0.976401
$580$	1.23408	0.0512426
$581$	10.8795	0.451359
$582$	42.9497	1.78032
$583$	−29.6380	−1.22748
$584$	−9.50955	−0.393508
$585$	−14.1225	−0.583893
$586$	12.4983	0.516300
$587$	5.96009	0.245999	0.123000	−	0.992407i	$-0.460749\pi$
$587$	5.96009	0.245999	0.123000	+	0.992407i	$0.460749\pi$
$588$	−24.2733	−1.00101
$589$	−3.11366	−0.128296
$590$	−20.6171	−0.848792
$591$	0.793320	0.0326328
$592$	3.52661	0.144943
$593$	−30.6997	−1.26069	−0.630344	−	0.776316i	$-0.717086\pi$
$593$	−30.6997	−1.26069	−0.630344	+	0.776316i	$0.717086\pi$
$594$	−8.76746	−0.359733
$595$	32.3336	1.32555
$596$	−20.5118	−0.840197
$597$	−18.2813	−0.748203
$598$	3.25001	0.132903
$599$	−14.1822	−0.579469	−0.289735	−	0.957107i	$-0.593567\pi$
$599$	−14.1822	−0.579469	−0.289735	+	0.957107i	$0.593567\pi$
$600$	−24.4921	−0.999885
$601$	−17.6650	−0.720572	−0.360286	−	0.932842i	$-0.617321\pi$
$601$	−17.6650	−0.720572	−0.360286	+	0.932842i	$0.617321\pi$
$602$	−39.3702	−1.60461
$603$	54.6823	2.22683
$604$	7.10897	0.289260
$605$	24.1973	0.983761
$606$	38.5444	1.56576
$607$	6.35046	0.257757	0.128879	−	0.991660i	$-0.458862\pi$
$607$	6.35046	0.257757	0.128879	+	0.991660i	$0.458862\pi$
$608$	−5.54305	−0.224800
$609$	−3.60624	−0.146132
$610$	−0.169427	−0.00685988
$611$	5.15006	0.208349
$612$	9.79727	0.396031
$613$	25.7672	1.04073	0.520363	−	0.853945i	$-0.325796\pi$
$613$	25.7672	1.04073	0.520363	+	0.853945i	$0.325796\pi$
$614$	13.2011	0.532752
$615$	−34.7425	−1.40095
$616$	−8.46602	−0.341106
$617$	26.4712	1.06569	0.532846	−	0.846212i	$-0.321123\pi$
$617$	26.4712	1.06569	0.532846	+	0.846212i	$0.321123\pi$
$618$	0.437250	0.0175888
$619$	−20.9028	−0.840154	−0.420077	−	0.907488i	$-0.637997\pi$
$619$	−20.9028	−0.840154	−0.420077	+	0.907488i	$0.637997\pi$
$620$	−2.09727	−0.0842283
$621$	−15.9657	−0.640683
$622$	4.20000	0.168405
$623$	−29.0010	−1.16190
$624$	−2.30002	−0.0920745
$625$	10.2236	0.408946
$626$	−22.6796	−0.906457
$627$	32.2821	1.28922
$628$	10.5621	0.421475
$629$	7.66877	0.305774
$630$	66.9917	2.66901
$631$	−37.1221	−1.47781	−0.738903	−	0.673812i	$-0.764656\pi$
$631$	−37.1221	−1.47781	−0.738903	+	0.673812i	$0.764656\pi$
$632$	4.55352	0.181129
$633$	35.1621	1.39757
$634$	6.71686	0.266761
$635$	−16.8352	−0.668083
$636$	38.1954	1.51455
$637$	7.43849	0.294724
$638$	−0.702650	−0.0278182
$639$	8.64090	0.341829
$640$	−3.73363	−0.147585
$641$	−24.0036	−0.948085	−0.474042	−	0.880502i	$-0.657206\pi$
$641$	−24.0036	−0.948085	−0.474042	+	0.880502i	$0.657206\pi$
$642$	12.6924	0.500931
$643$	4.30373	0.169723	0.0848614	−	0.996393i	$-0.472955\pi$
$643$	4.30373	0.169723	0.0848614	+	0.996393i	$0.472955\pi$
$644$	−15.4168	−0.607507
$645$	101.119	3.98156
$646$	−12.0536	−0.474244
$647$	30.6467	1.20485	0.602423	−	0.798177i	$-0.294202\pi$
$647$	30.6467	1.20485	0.602423	+	0.798177i	$0.294202\pi$
$648$	−2.21739	−0.0871074
$649$	11.7387	0.460786
$650$	7.50553	0.294391
$651$	6.12864	0.240200
$652$	−17.0125	−0.666262
$653$	−33.4384	−1.30855	−0.654274	−	0.756258i	$-0.727026\pi$
$653$	−33.4384	−1.30855	−0.654274	+	0.756258i	$0.727026\pi$
$654$	−25.6915	−1.00462
$655$	49.7662	1.94453
$656$	−3.39658	−0.132614
$657$	−42.8446	−1.67153
$658$	−24.4299	−0.952378
$659$	−29.5196	−1.14992	−0.574959	−	0.818182i	$-0.694982\pi$
$659$	−29.5196	−1.14992	−0.574959	+	0.818182i	$0.694982\pi$
$660$	21.7443	0.846394
$661$	−13.3817	−0.520489	−0.260245	−	0.965543i	$-0.583803\pi$
$661$	−13.3817	−0.520489	−0.260245	+	0.965543i	$0.583803\pi$
$662$	−17.1222	−0.665474
$663$	−5.00150	−0.194242
$664$	−2.73185	−0.106016
$665$	−82.4203	−3.19612
$666$	15.8889	0.615682
$667$	−1.27954	−0.0495440
$668$	11.8203	0.457342
$669$	−60.0265	−2.32076
$670$	−45.3150	−1.75067
$671$	0.0964663	0.00372404
$672$	10.9104	0.420879
$673$	−23.7678	−0.916180	−0.458090	−	0.888906i	$-0.651466\pi$
$673$	−23.7678	−0.916180	−0.458090	+	0.888906i	$0.651466\pi$
$674$	−5.86185	−0.225790
$675$	−36.8711	−1.41917
$676$	−12.2952	−0.472891
$677$	−32.2832	−1.24074	−0.620371	−	0.784308i	$-0.713018\pi$
$677$	−32.2832	−1.24074	−0.620371	+	0.784308i	$0.713018\pi$
$678$	−17.3636	−0.666845
$679$	62.4346	2.39602
$680$	−8.11896	−0.311348
$681$	−6.36997	−0.244098
$682$	1.19412	0.0457252
$683$	48.5120	1.85626	0.928129	−	0.372258i	$-0.121416\pi$
$683$	48.5120	1.85626	0.928129	+	0.372258i	$0.121416\pi$
$684$	−24.9738	−0.954898
$685$	26.7545	1.02224
$686$	−7.40800	−0.282839
$687$	57.3307	2.18730
$688$	9.88584	0.376894
$689$	−11.7049	−0.445920
$690$	39.5968	1.50742
$691$	−47.7978	−1.81831	−0.909156	−	0.416455i	$-0.863272\pi$
$691$	−47.7978	−1.81831	−0.909156	+	0.416455i	$0.863272\pi$
$692$	8.82219	0.335369
$693$	−38.1430	−1.44893
$694$	−31.7171	−1.20397
$695$	70.5462	2.67597
$696$	0.905527	0.0343239
$697$	−7.38602	−0.279765
$698$	36.9736	1.39947
$699$	43.2849	1.63719
$700$	−35.6034	−1.34568
$701$	−36.2868	−1.37053	−0.685267	−	0.728292i	$-0.740315\pi$
$701$	−36.2868	−1.37053	−0.685267	+	0.728292i	$0.740315\pi$
$702$	−3.46252	−0.130684
$703$	−19.5482	−0.737273
$704$	2.12582	0.0801197
$705$	62.7463	2.36316
$706$	−17.5603	−0.660889
$707$	56.0308	2.10725
$708$	−15.1281	−0.568548
$709$	−12.6122	−0.473662	−0.236831	−	0.971551i	$-0.576109\pi$
$709$	−12.6122	−0.473662	−0.236831	+	0.971551i	$0.576109\pi$
$710$	−7.16067	−0.268735
$711$	20.5156	0.769395
$712$	7.28215	0.272910
$713$	2.17452	0.0814364
$714$	23.7252	0.887894
$715$	−6.66347	−0.249200
$716$	−12.2328	−0.457161
$717$	−17.8443	−0.666409
$718$	4.28734	0.160002
$719$	38.7128	1.44374	0.721872	−	0.692026i	$-0.243282\pi$
$719$	38.7128	1.44374	0.721872	+	0.692026i	$0.243282\pi$
$720$	−16.8216	−0.626905
$721$	0.635617	0.0236716
$722$	11.7254	0.436375
$723$	−5.54339	−0.206161
$724$	6.78393	0.252123
$725$	−2.95496	−0.109744
$726$	17.7551	0.658955
$727$	−39.3587	−1.45973	−0.729866	−	0.683590i	$-0.760418\pi$
$727$	−39.3587	−1.45973	−0.729866	+	0.683590i	$0.760418\pi$
$728$	−3.34347	−0.123917
$729$	−43.8870	−1.62544
$730$	35.5051	1.31410
$731$	21.4972	0.795104
$732$	−0.124319	−0.00459497
$733$	−48.0083	−1.77323	−0.886613	−	0.462512i	$-0.846948\pi$
$733$	−48.0083	−1.77323	−0.886613	+	0.462512i	$0.846948\pi$
$734$	−15.4152	−0.568985
$735$	90.6275	3.34285
$736$	3.87115	0.142693
$737$	25.8010	0.950390
$738$	−15.3030	−0.563313
$739$	35.5689	1.30842	0.654212	−	0.756312i	$-0.273001\pi$
$739$	35.5689	1.30842	0.654212	+	0.756312i	$0.273001\pi$
$740$	−13.1671	−0.484031
$741$	12.7491	0.468351
$742$	55.5235	2.03833
$743$	35.2834	1.29442	0.647211	−	0.762311i	$-0.275935\pi$
$743$	35.2834	1.29442	0.647211	+	0.762311i	$0.275935\pi$
$744$	−1.53890	−0.0564188
$745$	76.5836	2.80580
$746$	−4.05390	−0.148424
$747$	−12.3081	−0.450332
$748$	4.62268	0.169022
$749$	18.4506	0.674171
$750$	40.3010	1.47158
$751$	−34.3955	−1.25511	−0.627555	−	0.778572i	$-0.715944\pi$
$751$	−34.3955	−1.25511	−0.627555	+	0.778572i	$0.715944\pi$
$752$	6.13435	0.223697
$753$	17.6658	0.643778
$754$	−0.277496	−0.0101058
$755$	−26.5423	−0.965972
$756$	16.4249	0.597367
$757$	−14.8410	−0.539405	−0.269703	−	0.962944i	$-0.586925\pi$
$757$	−14.8410	−0.539405	−0.269703	+	0.962944i	$0.586925\pi$
$758$	−7.01110	−0.254655
$759$	−22.5452	−0.818338
$760$	20.6957	0.750712
$761$	−17.5911	−0.637678	−0.318839	−	0.947809i	$-0.603293\pi$
$761$	−17.5911	−0.637678	−0.318839	+	0.947809i	$0.603293\pi$
$762$	−12.3530	−0.447503
$763$	−37.3470	−1.35205
$764$	4.56907	0.165303
$765$	−36.5794	−1.32253
$766$	5.81589	0.210136
$767$	4.63596	0.167395
$768$	−2.73960	−0.0988569
$769$	−39.2649	−1.41593	−0.707964	−	0.706248i	$-0.750386\pi$
$769$	−39.2649	−1.41593	−0.707964	+	0.706248i	$0.750386\pi$
$770$	31.6090	1.13911
$771$	−54.0774	−1.94755
$772$	8.57590	0.308653
$773$	−34.8820	−1.25462	−0.627309	−	0.778771i	$-0.715843\pi$
$773$	−34.8820	−1.25462	−0.627309	+	0.778771i	$0.715843\pi$
$774$	44.5400	1.60096
$775$	5.02181	0.180389
$776$	−15.6773	−0.562783
$777$	38.4768	1.38035
$778$	−7.41222	−0.265741
$779$	18.8274	0.674562
$780$	8.58742	0.307479
$781$	4.07707	0.145889
$782$	8.41801	0.301027
$783$	1.36321	0.0487170
$784$	8.86015	0.316434
$785$	−39.4352	−1.40750
$786$	36.5166	1.30251
$787$	−31.9125	−1.13756	−0.568779	−	0.822490i	$-0.692584\pi$
$787$	−31.9125	−1.13756	−0.568779	+	0.822490i	$0.692584\pi$
$788$	−0.289575	−0.0103157
$789$	−60.5732	−2.15646
$790$	−17.0012	−0.604875
$791$	−25.2409	−0.897465
$792$	9.57771	0.340329
$793$	0.0380973	0.00135287
$794$	15.1240	0.536729
$795$	−142.607	−5.05776
$796$	6.67296	0.236517
$797$	19.4334	0.688367	0.344183	−	0.938902i	$-0.388156\pi$
$797$	19.4334	0.688367	0.344183	+	0.938902i	$0.388156\pi$
$798$	−60.4770	−2.14086
$799$	13.3394	0.471915
$800$	8.94000	0.316077
$801$	32.8092	1.15926
$802$	−7.71561	−0.272448
$803$	−20.2155	−0.713391
$804$	−33.2505	−1.17265
$805$	57.5606	2.02875
$806$	0.471592	0.0166111
$807$	−30.3517	−1.06843
$808$	−14.0693	−0.494957
$809$	47.7474	1.67871	0.839355	−	0.543584i	$-0.182933\pi$
$809$	47.7474	1.67871	0.839355	+	0.543584i	$0.182933\pi$
$810$	8.27893	0.290892
$811$	−52.6023	−1.84712	−0.923558	−	0.383459i	$-0.874733\pi$
$811$	−52.6023	−1.84712	−0.923558	+	0.383459i	$0.874733\pi$
$812$	1.31634	0.0461944
$813$	−39.6853	−1.39182
$814$	7.49692	0.262767
$815$	63.5185	2.22496
$816$	−5.95740	−0.208551
$817$	−54.7977	−1.91713
$818$	19.5470	0.683443
$819$	−15.0638	−0.526371
$820$	12.6816	0.442860
$821$	26.0836	0.910325	0.455162	−	0.890408i	$-0.349581\pi$
$821$	26.0836	0.910325	0.455162	+	0.890408i	$0.349581\pi$
$822$	19.6315	0.684728
$823$	14.1003	0.491507	0.245753	−	0.969332i	$-0.420965\pi$
$823$	14.1003	0.491507	0.245753	+	0.969332i	$0.420965\pi$
$824$	−0.159603	−0.00556005
$825$	−52.0656	−1.81269
$826$	−21.9912	−0.765173
$827$	20.6399	0.717721	0.358860	−	0.933391i	$-0.383165\pi$
$827$	20.6399	0.717721	0.358860	+	0.933391i	$0.383165\pi$
$828$	17.4412	0.606124
$829$	−8.63568	−0.299930	−0.149965	−	0.988691i	$-0.547916\pi$
$829$	−8.63568	−0.299930	−0.149965	+	0.988691i	$0.547916\pi$
$830$	10.1997	0.354037
$831$	21.2693	0.737824
$832$	0.839544	0.0291060
$833$	19.2668	0.667555
$834$	51.7643	1.79245
$835$	−44.1328	−1.52728
$836$	−11.7835	−0.407541
$837$	−2.31671	−0.0800771
$838$	25.9688	0.897078
$839$	29.0589	1.00322	0.501612	−	0.865093i	$-0.332740\pi$
$839$	29.0589	1.00322	0.501612	+	0.865093i	$0.332740\pi$
$840$	−40.7355	−1.40551
$841$	−28.8907	−0.996233
$842$	9.93456	0.342368
$843$	−68.1286	−2.34647
$844$	−12.8347	−0.441789
$845$	45.9056	1.57920
$846$	27.6379	0.950210
$847$	25.8101	0.886845
$848$	−13.9419	−0.478768
$849$	77.6518	2.66500
$850$	19.4405	0.666802
$851$	13.6520	0.467986
$852$	−5.25424	−0.180007
$853$	−41.0025	−1.40390	−0.701950	−	0.712226i	$-0.747687\pi$
$853$	−41.0025	−1.40390	−0.701950	+	0.712226i	$0.747687\pi$
$854$	−0.180719	−0.00618407
$855$	93.2431	3.18885
$856$	−4.63295	−0.158351
$857$	44.9037	1.53388	0.766940	−	0.641719i	$-0.221778\pi$
$857$	44.9037	1.53388	0.766940	+	0.641719i	$0.221778\pi$
$858$	−4.88942	−0.166922
$859$	−11.2076	−0.382398	−0.191199	−	0.981551i	$-0.561238\pi$
$859$	−11.2076	−0.382398	−0.191199	+	0.981551i	$0.561238\pi$
$860$	−36.9101	−1.25862
$861$	−37.0581	−1.26294
$862$	−34.7326	−1.18300
$863$	52.3415	1.78173	0.890863	−	0.454272i	$-0.150101\pi$
$863$	52.3415	1.78173	0.890863	+	0.454272i	$0.150101\pi$
$864$	−4.12428	−0.140311
$865$	−32.9388	−1.11995
$866$	−11.9052	−0.404556
$867$	33.6186	1.14175
$868$	−2.23705	−0.0759305
$869$	9.67995	0.328370
$870$	−3.38090	−0.114623
$871$	10.1895	0.345259
$872$	9.37781	0.317573
$873$	−70.6331	−2.39057
$874$	−21.4580	−0.725828
$875$	58.5844	1.98051
$876$	26.0524	0.880229
$877$	9.83860	0.332226	0.166113	−	0.986107i	$-0.446878\pi$
$877$	9.83860	0.332226	0.166113	+	0.986107i	$0.446878\pi$
$878$	2.00428	0.0676411
$879$	−34.2404	−1.15490
$880$	−7.93701	−0.267557
$881$	−28.4671	−0.959082	−0.479541	−	0.877520i	$-0.659197\pi$
$881$	−28.4671	−0.959082	−0.479541	+	0.877520i	$0.659197\pi$
$882$	39.9188	1.34413
$883$	32.8260	1.10468	0.552342	−	0.833617i	$-0.313734\pi$
$883$	32.8260	1.10468	0.552342	+	0.833617i	$0.313734\pi$
$884$	1.82563	0.0614025
$885$	56.4826	1.89864
$886$	32.8947	1.10512
$887$	14.6444	0.491711	0.245855	−	0.969307i	$-0.420931\pi$
$887$	14.6444	0.491711	0.245855	+	0.969307i	$0.420931\pi$
$888$	−9.66151	−0.324219
$889$	−17.9572	−0.602266
$890$	−27.1889	−0.911372
$891$	−4.71377	−0.157917
$892$	21.9107	0.733623
$893$	−34.0030	−1.13787
$894$	56.1943	1.87942
$895$	45.6727	1.52667
$896$	−3.98248	−0.133045
$897$	−8.90373	−0.297287
$898$	−13.0577	−0.435742
$899$	−0.185668	−0.00619236
$900$	40.2786	1.34262
$901$	−30.3174	−1.01002
$902$	−7.22050	−0.240416
$903$	107.859	3.58931
$904$	6.33800	0.210799
$905$	−25.3287	−0.841954
$906$	−19.4758	−0.647039
$907$	13.9662	0.463740	0.231870	−	0.972747i	$-0.425516\pi$
$907$	13.9662	0.463740	0.231870	+	0.972747i	$0.425516\pi$
$908$	2.32514	0.0771626
$909$	−63.3883	−2.10246
$910$	12.4833	0.413817
$911$	−15.8450	−0.524970	−0.262485	−	0.964936i	$-0.584542\pi$
$911$	−15.8450	−0.524970	−0.262485	+	0.964936i	$0.584542\pi$
$912$	15.1858	0.502851
$913$	−5.80740	−0.192197
$914$	12.6621	0.418823
$915$	0.464162	0.0153447
$916$	−20.9266	−0.691436
$917$	53.0831	1.75296
$918$	−8.96844	−0.296003
$919$	33.4352	1.10292	0.551462	−	0.834200i	$-0.314070\pi$
$919$	33.4352	1.10292	0.551462	+	0.834200i	$0.314070\pi$
$920$	−14.4535	−0.476517
$921$	−36.1657	−1.19170
$922$	−7.17875	−0.236420
$923$	1.61015	0.0529987
$924$	23.1935	0.763011
$925$	31.5279	1.03663
$926$	10.0355	0.329787
$927$	−0.719082	−0.0236177
$928$	−0.330532	−0.0108502
$929$	−1.23878	−0.0406430	−0.0203215	−	0.999793i	$-0.506469\pi$
$929$	−1.23878	−0.0406430	−0.0203215	+	0.999793i	$0.506469\pi$
$930$	5.74568	0.188408
$931$	−49.1123	−1.60959
$932$	−15.7997	−0.517536
$933$	−11.5063	−0.376700
$934$	−25.8758	−0.846681
$935$	−17.2594	−0.564443
$936$	3.78251	0.123635
$937$	13.3518	0.436184	0.218092	−	0.975928i	$-0.430017\pi$
$937$	13.3518	0.436184	0.218092	+	0.975928i	$0.430017\pi$
$938$	−48.3353	−1.57820
$939$	62.1330	2.02763
$940$	−22.9034	−0.747027
$941$	30.2376	0.985718	0.492859	−	0.870109i	$-0.335952\pi$
$941$	30.2376	0.985718	0.492859	+	0.870109i	$0.335952\pi$
$942$	−28.9361	−0.942789
$943$	−13.1487	−0.428180
$944$	5.52199	0.179726
$945$	−61.3244	−1.99488
$946$	21.0155	0.683272
$947$	6.80369	0.221090	0.110545	−	0.993871i	$-0.464740\pi$
$947$	6.80369	0.221090	0.110545	+	0.993871i	$0.464740\pi$
$948$	−12.4749	−0.405164
$949$	−7.98369	−0.259161
$950$	−49.5549	−1.60777
$951$	−18.4015	−0.596711
$952$	−8.66009	−0.280675
$953$	−22.4727	−0.727964	−0.363982	−	0.931406i	$-0.618583\pi$
$953$	−22.4727	−0.727964	−0.363982	+	0.931406i	$0.618583\pi$
$954$	−62.8144	−2.03369
$955$	−17.0592	−0.552023
$956$	6.51347	0.210661
$957$	1.92498	0.0622259
$958$	−7.89789	−0.255169
$959$	28.5377	0.921532
$960$	10.2287	0.330129
$961$	−30.6845	−0.989822
$962$	2.96074	0.0954582
$963$	−20.8734	−0.672636
$964$	2.02343	0.0651702
$965$	−32.0192	−1.03074
$966$	42.2359	1.35892
$967$	42.3103	1.36061	0.680304	−	0.732930i	$-0.261848\pi$
$967$	42.3103	1.36061	0.680304	+	0.732930i	$0.261848\pi$
$968$	−6.48091	−0.208304
$969$	33.0222	1.06082
$970$	58.5333	1.87939
$971$	−32.4841	−1.04247	−0.521233	−	0.853415i	$-0.674528\pi$
$971$	−32.4841	−1.04247	−0.521233	+	0.853415i	$0.674528\pi$
$972$	18.4476	0.591708
$973$	75.2482	2.41235
$974$	−1.74647	−0.0559605
$975$	−20.5622	−0.658517
$976$	0.0453785	0.00145253
$977$	43.9054	1.40466	0.702330	−	0.711852i	$-0.252143\pi$
$977$	43.9054	1.40466	0.702330	+	0.711852i	$0.252143\pi$
$978$	46.6076	1.49035
$979$	15.4805	0.494759
$980$	−33.0805	−1.05672
$981$	42.2511	1.34897
$982$	21.5836	0.688759
$983$	−27.4200	−0.874564	−0.437282	−	0.899325i	$-0.644059\pi$
$983$	−27.4200	−0.874564	−0.437282	+	0.899325i	$0.644059\pi$
$984$	9.30528	0.296642
$985$	1.08117	0.0344488
$986$	−0.718757	−0.0228899
$987$	66.9283	2.13035
$988$	−4.65364	−0.148052
$989$	38.2696	1.21690
$990$	−35.7596	−1.13652
$991$	−19.3984	−0.616212	−0.308106	−	0.951352i	$-0.599695\pi$
$991$	−19.3984	−0.616212	−0.308106	+	0.951352i	$0.599695\pi$
$992$	0.561723	0.0178347
$993$	46.9081	1.48858
$994$	−7.63794	−0.242261
$995$	−24.9144	−0.789839
$996$	7.48418	0.237145
$997$	−50.1456	−1.58813	−0.794064	−	0.607834i	$-0.792038\pi$
$997$	−50.1456	−1.58813	−0.794064	+	0.607834i	$0.792038\pi$
$998$	−40.5820	−1.28460
$999$	−14.5447	−0.460175

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.a.1.4	✓	33

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.a.1.4	✓	33	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:	\( N \)	\(=\)	\( 4034 = 2 \cdot 2017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.73960 q^{3} +1.00000 q^{4} -3.73363 q^{5} -2.73960 q^{6} -3.98248 q^{7} +1.00000 q^{8} +4.50543 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.73960 q^{3} +1.00000 q^{4} -3.73363 q^{5} -2.73960 q^{6} -3.98248 q^{7} +1.00000 q^{8} +4.50543 q^{9} -3.73363 q^{10} +2.12582 q^{11} -2.73960 q^{12} +0.839544 q^{13} -3.98248 q^{14} +10.2287 q^{15} +1.00000 q^{16} +2.17455 q^{17} +4.50543 q^{18} -5.54305 q^{19} -3.73363 q^{20} +10.9104 q^{21} +2.12582 q^{22} +3.87115 q^{23} -2.73960 q^{24} +8.94000 q^{25} +0.839544 q^{26} -4.12428 q^{27} -3.98248 q^{28} -0.330532 q^{29} +10.2287 q^{30} +0.561723 q^{31} +1.00000 q^{32} -5.82389 q^{33} +2.17455 q^{34} +14.8691 q^{35} +4.50543 q^{36} +3.52661 q^{37} -5.54305 q^{38} -2.30002 q^{39} -3.73363 q^{40} -3.39658 q^{41} +10.9104 q^{42} +9.88584 q^{43} +2.12582 q^{44} -16.8216 q^{45} +3.87115 q^{46} +6.13435 q^{47} -2.73960 q^{48} +8.86015 q^{49} +8.94000 q^{50} -5.95740 q^{51} +0.839544 q^{52} -13.9419 q^{53} -4.12428 q^{54} -7.93701 q^{55} -3.98248 q^{56} +15.1858 q^{57} -0.330532 q^{58} +5.52199 q^{59} +10.2287 q^{60} +0.0453785 q^{61} +0.561723 q^{62} -17.9428 q^{63} +1.00000 q^{64} -3.13455 q^{65} -5.82389 q^{66} +12.1370 q^{67} +2.17455 q^{68} -10.6054 q^{69} +14.8691 q^{70} +1.91788 q^{71} +4.50543 q^{72} -9.50955 q^{73} +3.52661 q^{74} -24.4921 q^{75} -5.54305 q^{76} -8.46602 q^{77} -2.30002 q^{78} +4.55352 q^{79} -3.73363 q^{80} -2.21739 q^{81} -3.39658 q^{82} -2.73185 q^{83} +10.9104 q^{84} -8.11896 q^{85} +9.88584 q^{86} +0.905527 q^{87} +2.12582 q^{88} +7.28215 q^{89} -16.8216 q^{90} -3.34347 q^{91} +3.87115 q^{92} -1.53890 q^{93} +6.13435 q^{94} +20.6957 q^{95} -2.73960 q^{96} -15.6773 q^{97} +8.86015 q^{98} +9.57771 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9}+O(q^{10}) \) 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9	\( 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9} - 22 q^{10} - 19 q^{11} - 14 q^{12} - 29 q^{13} - 12 q^{14} - 5 q^{15} + 33 q^{16} - 47 q^{17} + 17 q^{18} - 35 q^{19} - 22 q^{20} - 31 q^{21} - 19 q^{22} - 2 q^{23} - 14 q^{24} + 13 q^{25} - 29 q^{26} - 47 q^{27} - 12 q^{28} - 29 q^{29} - 5 q^{30} - 53 q^{31} + 33 q^{32} - 23 q^{33} - 47 q^{34} - 14 q^{35} + 17 q^{36} - 42 q^{37} - 35 q^{38} - 22 q^{40} - 42 q^{41} - 31 q^{42} - 26 q^{43} - 19 q^{44} - 55 q^{45} - 2 q^{46} - 14 q^{48} - 21 q^{49} + 13 q^{50} - 13 q^{51} - 29 q^{52} - 40 q^{53} - 47 q^{54} - 34 q^{55} - 12 q^{56} - 30 q^{57} - 29 q^{58} - 45 q^{59} - 5 q^{60} - 93 q^{61} - 53 q^{62} + 4 q^{63} + 33 q^{64} - 26 q^{65} - 23 q^{66} - 28 q^{67} - 47 q^{68} - 60 q^{69} - 14 q^{70} + 4 q^{71} + 17 q^{72} - 52 q^{73} - 42 q^{74} - 41 q^{75} - 35 q^{76} - 38 q^{77} - 38 q^{79} - 22 q^{80} + 25 q^{81} - 42 q^{82} - 42 q^{83} - 31 q^{84} - 21 q^{85} - 26 q^{86} + 12 q^{87} - 19 q^{88} - 58 q^{89} - 55 q^{90} - 79 q^{91} - 2 q^{92} + 25 q^{93} + 16 q^{95} - 14 q^{96} - 64 q^{97} - 21 q^{98} - 38 q^{99}+O(q^{100}) \) 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9 - 22 * q^10 - 19 * q^11 - 14 * q^12 - 29 * q^13 - 12 * q^14 - 5 * q^15 + 33 * q^16 - 47 * q^17 + 17 * q^18 - 35 * q^19 - 22 * q^20 - 31 * q^21 - 19 * q^22 - 2 * q^23 - 14 * q^24 + 13 * q^25 - 29 * q^26 - 47 * q^27 - 12 * q^28 - 29 * q^29 - 5 * q^30 - 53 * q^31 + 33 * q^32 - 23 * q^33 - 47 * q^34 - 14 * q^35 + 17 * q^36 - 42 * q^37 - 35 * q^38 - 22 * q^40 - 42 * q^41 - 31 * q^42 - 26 * q^43 - 19 * q^44 - 55 * q^45 - 2 * q^46 - 14 * q^48 - 21 * q^49 + 13 * q^50 - 13 * q^51 - 29 * q^52 - 40 * q^53 - 47 * q^54 - 34 * q^55 - 12 * q^56 - 30 * q^57 - 29 * q^58 - 45 * q^59 - 5 * q^60 - 93 * q^61 - 53 * q^62 + 4 * q^63 + 33 * q^64 - 26 * q^65 - 23 * q^66 - 28 * q^67 - 47 * q^68 - 60 * q^69 - 14 * q^70 + 4 * q^71 + 17 * q^72 - 52 * q^73 - 42 * q^74 - 41 * q^75 - 35 * q^76 - 38 * q^77 - 38 * q^79 - 22 * q^80 + 25 * q^81 - 42 * q^82 - 42 * q^83 - 31 * q^84 - 21 * q^85 - 26 * q^86 + 12 * q^87 - 19 * q^88 - 58 * q^89 - 55 * q^90 - 79 * q^91 - 2 * q^92 + 25 * q^93 + 16 * q^95 - 14 * q^96 - 64 * q^97 - 21 * q^98 - 38 * q^99

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