LMFDB - Embedded newform 5054.2.a.ba.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5054,2,Mod(1,5054)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5054, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("5054.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5054 = 2 \cdot 7 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5054.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:	$40.3563931816$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.48952000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 13x^{4} + 44x^{2} + 36x + 4 $ x^6 - x^5 - 13x^4 + 44x^2 + 36*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-2.25033$ of defining polynomial
Character	$\chi$	$=$	5054.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.63229 q^{3} +1.00000 q^{4} -2.92353 q^{5} -1.63229 q^{6} -1.00000 q^{7} -1.00000 q^{8} -0.335615 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.63229 q^{3} +1.00000 q^{4} -2.92353 q^{5} -1.63229 q^{6} -1.00000 q^{7} -1.00000 q^{8} -0.335615 q^{9} +2.92353 q^{10} +2.43913 q^{11} +1.63229 q^{12} +5.49430 q^{13} +1.00000 q^{14} -4.77206 q^{15} +1.00000 q^{16} +5.99495 q^{17} +0.335615 q^{18} -2.92353 q^{20} -1.63229 q^{21} -2.43913 q^{22} +2.84308 q^{23} -1.63229 q^{24} +3.54701 q^{25} -5.49430 q^{26} -5.44471 q^{27} -1.00000 q^{28} -4.56463 q^{29} +4.77206 q^{30} -7.26972 q^{31} -1.00000 q^{32} +3.98138 q^{33} -5.99495 q^{34} +2.92353 q^{35} -0.335615 q^{36} +0.110567 q^{37} +8.96831 q^{39} +2.92353 q^{40} +4.66775 q^{41} +1.63229 q^{42} +3.94660 q^{43} +2.43913 q^{44} +0.981180 q^{45} -2.84308 q^{46} -11.9233 q^{47} +1.63229 q^{48} +1.00000 q^{49} -3.54701 q^{50} +9.78553 q^{51} +5.49430 q^{52} +12.6324 q^{53} +5.44471 q^{54} -7.13087 q^{55} +1.00000 q^{56} +4.56463 q^{58} +3.29471 q^{59} -4.77206 q^{60} -3.12659 q^{61} +7.26972 q^{62} +0.335615 q^{63} +1.00000 q^{64} -16.0627 q^{65} -3.98138 q^{66} -6.71720 q^{67} +5.99495 q^{68} +4.64075 q^{69} -2.92353 q^{70} -12.8533 q^{71} +0.335615 q^{72} +13.5286 q^{73} -0.110567 q^{74} +5.78976 q^{75} -2.43913 q^{77} -8.96831 q^{78} +2.86348 q^{79} -2.92353 q^{80} -7.88052 q^{81} -4.66775 q^{82} -5.61368 q^{83} -1.63229 q^{84} -17.5264 q^{85} -3.94660 q^{86} -7.45083 q^{87} -2.43913 q^{88} +16.1053 q^{89} -0.981180 q^{90} -5.49430 q^{91} +2.84308 q^{92} -11.8663 q^{93} +11.9233 q^{94} -1.63229 q^{96} +8.58809 q^{97} -1.00000 q^{98} -0.818610 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 2 q^{3} + 6 q^{4} - 5 q^{5} - 2 q^{6} - 6 q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 + 2 * q^3 + 6 * q^4 - 5 * q^5 - 2 * q^6 - 6 * q^7 - 6 * q^8 + 12 * q^9	\( 6 q - 6 q^{2} + 2 q^{3} + 6 q^{4} - 5 q^{5} - 2 q^{6} - 6 q^{7} - 6 q^{8} + 12 q^{9} + 5 q^{10} - 4 q^{11} + 2 q^{12} + 23 q^{13} + 6 q^{14} - 6 q^{15} + 6 q^{16} - 3 q^{17} - 12 q^{18} - 5 q^{20} - 2 q^{21} + 4 q^{22} - 4 q^{23} - 2 q^{24} + 13 q^{25} - 23 q^{26} - 4 q^{27} - 6 q^{28} + 5 q^{29} + 6 q^{30} + 12 q^{31} - 6 q^{32} + 10 q^{33} + 3 q^{34} + 5 q^{35} + 12 q^{36} + q^{37} + 4 q^{39} + 5 q^{40} + 19 q^{41} + 2 q^{42} - 2 q^{43} - 4 q^{44} - 55 q^{45} + 4 q^{46} - 12 q^{47} + 2 q^{48} + 6 q^{49} - 13 q^{50} + 44 q^{51} + 23 q^{52} - 11 q^{53} + 4 q^{54} + 28 q^{55} + 6 q^{56} - 5 q^{58} - 4 q^{59} - 6 q^{60} - q^{61} - 12 q^{62} - 12 q^{63} + 6 q^{64} - 24 q^{65} - 10 q^{66} - 14 q^{67} - 3 q^{68} + 10 q^{69} - 5 q^{70} - 8 q^{71} - 12 q^{72} + 5 q^{73} - q^{74} + 56 q^{75} + 4 q^{77} - 4 q^{78} + 30 q^{79} - 5 q^{80} + 30 q^{81} - 19 q^{82} - 12 q^{83} - 2 q^{84} - 16 q^{85} + 2 q^{86} - 14 q^{87} + 4 q^{88} + 11 q^{89} + 55 q^{90} - 23 q^{91} - 4 q^{92} + 10 q^{93} + 12 q^{94} - 2 q^{96} + 25 q^{97} - 6 q^{98} - 50 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 2 * q^3 + 6 * q^4 - 5 * q^5 - 2 * q^6 - 6 * q^7 - 6 * q^8 + 12 * q^9 + 5 * q^10 - 4 * q^11 + 2 * q^12 + 23 * q^13 + 6 * q^14 - 6 * q^15 + 6 * q^16 - 3 * q^17 - 12 * q^18 - 5 * q^20 - 2 * q^21 + 4 * q^22 - 4 * q^23 - 2 * q^24 + 13 * q^25 - 23 * q^26 - 4 * q^27 - 6 * q^28 + 5 * q^29 + 6 * q^30 + 12 * q^31 - 6 * q^32 + 10 * q^33 + 3 * q^34 + 5 * q^35 + 12 * q^36 + q^37 + 4 * q^39 + 5 * q^40 + 19 * q^41 + 2 * q^42 - 2 * q^43 - 4 * q^44 - 55 * q^45 + 4 * q^46 - 12 * q^47 + 2 * q^48 + 6 * q^49 - 13 * q^50 + 44 * q^51 + 23 * q^52 - 11 * q^53 + 4 * q^54 + 28 * q^55 + 6 * q^56 - 5 * q^58 - 4 * q^59 - 6 * q^60 - q^61 - 12 * q^62 - 12 * q^63 + 6 * q^64 - 24 * q^65 - 10 * q^66 - 14 * q^67 - 3 * q^68 + 10 * q^69 - 5 * q^70 - 8 * q^71 - 12 * q^72 + 5 * q^73 - q^74 + 56 * q^75 + 4 * q^77 - 4 * q^78 + 30 * q^79 - 5 * q^80 + 30 * q^81 - 19 * q^82 - 12 * q^83 - 2 * q^84 - 16 * q^85 + 2 * q^86 - 14 * q^87 + 4 * q^88 + 11 * q^89 + 55 * q^90 - 23 * q^91 - 4 * q^92 + 10 * q^93 + 12 * q^94 - 2 * q^96 + 25 * q^97 - 6 * q^98 - 50 * 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
$3$	1.63229	0.942406	0.471203	−	0.882025i	$-0.343820\pi$
$3$	1.63229	0.942406	0.471203	+	0.882025i	$0.343820\pi$
$4$	1.00000	0.500000
$5$	−2.92353	−1.30744	−0.653720	−	0.756736i	$-0.726793\pi$
$5$	−2.92353	−1.30744	−0.653720	+	0.756736i	$0.726793\pi$
$6$	−1.63229	−0.666381
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	−0.335615	−0.111872
$10$	2.92353	0.924500
$11$	2.43913	0.735426	0.367713	−	0.929939i	$-0.380141\pi$
$11$	2.43913	0.735426	0.367713	+	0.929939i	$0.380141\pi$
$12$	1.63229	0.471203
$13$	5.49430	1.52384	0.761922	−	0.647669i	$-0.224256\pi$
$13$	5.49430	1.52384	0.761922	+	0.647669i	$0.224256\pi$
$14$	1.00000	0.267261
$15$	−4.77206	−1.23214
$16$	1.00000	0.250000
$17$	5.99495	1.45399	0.726995	−	0.686643i	$-0.240916\pi$
$17$	5.99495	1.45399	0.726995	+	0.686643i	$0.240916\pi$
$18$	0.335615	0.0791053
$19$	0	0
$19$	0	0
$20$	−2.92353	−0.653720
$21$	−1.63229	−0.356196
$22$	−2.43913	−0.520025
$23$	2.84308	0.592824	0.296412	−	0.955060i	$-0.404210\pi$
$23$	2.84308	0.592824	0.296412	+	0.955060i	$0.404210\pi$
$24$	−1.63229	−0.333191
$25$	3.54701	0.709402
$26$	−5.49430	−1.07752
$27$	−5.44471	−1.04783
$28$	−1.00000	−0.188982
$29$	−4.56463	−0.847631	−0.423816	−	0.905748i	$-0.639310\pi$
$29$	−4.56463	−0.847631	−0.423816	+	0.905748i	$0.639310\pi$
$30$	4.77206	0.871254
$31$	−7.26972	−1.30568	−0.652840	−	0.757496i	$-0.726423\pi$
$31$	−7.26972	−1.30568	−0.652840	+	0.757496i	$0.726423\pi$
$32$	−1.00000	−0.176777
$33$	3.98138	0.693070
$34$	−5.99495	−1.02813
$35$	2.92353	0.494166
$36$	−0.335615	−0.0559359
$37$	0.110567	0.0181771	0.00908854	−	0.999959i	$-0.497107\pi$
$37$	0.110567	0.0181771	0.00908854	+	0.999959i	$0.497107\pi$
$38$	0	0
$39$	8.96831	1.43608
$40$	2.92353	0.462250
$41$	4.66775	0.728980	0.364490	−	0.931207i	$-0.381243\pi$
$41$	4.66775	0.728980	0.364490	+	0.931207i	$0.381243\pi$
$42$	1.63229	0.251868
$43$	3.94660	0.601851	0.300925	−	0.953648i	$-0.402704\pi$
$43$	3.94660	0.601851	0.300925	+	0.953648i	$0.402704\pi$
$44$	2.43913	0.367713
$45$	0.981180	0.146266
$46$	−2.84308	−0.419190
$47$	−11.9233	−1.73920	−0.869598	−	0.493761i	$-0.835622\pi$
$47$	−11.9233	−1.73920	−0.869598	+	0.493761i	$0.835622\pi$
$48$	1.63229	0.235601
$49$	1.00000	0.142857
$50$	−3.54701	−0.501623
$51$	9.78553	1.37025
$52$	5.49430	0.761922
$53$	12.6324	1.73519	0.867595	−	0.497271i	$-0.165664\pi$
$53$	12.6324	1.73519	0.867595	+	0.497271i	$0.165664\pi$
$54$	5.44471	0.740931
$55$	−7.13087	−0.961526
$56$	1.00000	0.133631
$57$	0	0
$58$	4.56463	0.599366
$59$	3.29471	0.428935	0.214467	−	0.976731i	$-0.431198\pi$
$59$	3.29471	0.428935	0.214467	+	0.976731i	$0.431198\pi$
$60$	−4.77206	−0.616070
$61$	−3.12659	−0.400319	−0.200160	−	0.979763i	$-0.564146\pi$
$61$	−3.12659	−0.400319	−0.200160	+	0.979763i	$0.564146\pi$
$62$	7.26972	0.923255
$63$	0.335615	0.0422835
$64$	1.00000	0.125000
$65$	−16.0627	−1.99234
$66$	−3.98138	−0.490074
$67$	−6.71720	−0.820636	−0.410318	−	0.911942i	$-0.634582\pi$
$67$	−6.71720	−0.820636	−0.410318	+	0.911942i	$0.634582\pi$
$68$	5.99495	0.726995
$69$	4.64075	0.558680
$70$	−2.92353	−0.349428
$71$	−12.8533	−1.52540	−0.762702	−	0.646751i	$-0.776127\pi$
$71$	−12.8533	−1.52540	−0.762702	+	0.646751i	$0.776127\pi$
$72$	0.335615	0.0395526
$73$	13.5286	1.58340	0.791702	−	0.610907i	$-0.209195\pi$
$73$	13.5286	1.58340	0.791702	+	0.610907i	$0.209195\pi$
$74$	−0.110567	−0.0128531
$75$	5.78976	0.668544
$76$	0	0
$77$	−2.43913	−0.277965
$78$	−8.96831	−1.01546
$79$	2.86348	0.322167	0.161083	−	0.986941i	$-0.448501\pi$
$79$	2.86348	0.322167	0.161083	+	0.986941i	$0.448501\pi$
$80$	−2.92353	−0.326860
$81$	−7.88052	−0.875613
$82$	−4.66775	−0.515467
$83$	−5.61368	−0.616181	−0.308091	−	0.951357i	$-0.599690\pi$
$83$	−5.61368	−0.616181	−0.308091	+	0.951357i	$0.599690\pi$
$84$	−1.63229	−0.178098
$85$	−17.5264	−1.90101
$86$	−3.94660	−0.425573
$87$	−7.45083	−0.798812
$88$	−2.43913	−0.260012
$89$	16.1053	1.70716	0.853580	−	0.520962i	$-0.174427\pi$
$89$	16.1053	1.70716	0.853580	+	0.520962i	$0.174427\pi$
$90$	−0.981180	−0.103425
$91$	−5.49430	−0.575959
$92$	2.84308	0.296412
$93$	−11.8663	−1.23048
$94$	11.9233	1.22980
$95$	0	0
$96$	−1.63229	−0.166595
$97$	8.58809	0.871989	0.435994	−	0.899949i	$-0.356397\pi$
$97$	8.58809	0.871989	0.435994	+	0.899949i	$0.356397\pi$
$98$	−1.00000	−0.101015
$99$	−0.818610	−0.0822734
$100$	3.54701	0.354701
$101$	−8.89241	−0.884828	−0.442414	−	0.896811i	$-0.645878\pi$
$101$	−8.89241	−0.884828	−0.442414	+	0.896811i	$0.645878\pi$
$102$	−9.78553	−0.968912
$103$	8.46794	0.834371	0.417186	−	0.908821i	$-0.363017\pi$
$103$	8.46794	0.834371	0.417186	+	0.908821i	$0.363017\pi$
$104$	−5.49430	−0.538760
$105$	4.77206	0.465705
$106$	−12.6324	−1.22697
$107$	1.76973	0.171086	0.0855430	−	0.996334i	$-0.472737\pi$
$107$	1.76973	0.171086	0.0855430	+	0.996334i	$0.472737\pi$
$108$	−5.44471	−0.523917
$109$	15.8075	1.51409	0.757043	−	0.653366i	$-0.226644\pi$
$109$	15.8075	1.51409	0.757043	+	0.653366i	$0.226644\pi$
$110$	7.13087	0.679902
$111$	0.180478	0.0171302
$112$	−1.00000	−0.0944911
$113$	−1.57811	−0.148456	−0.0742280	−	0.997241i	$-0.523649\pi$
$113$	−1.57811	−0.148456	−0.0742280	+	0.997241i	$0.523649\pi$
$114$	0	0
$115$	−8.31183	−0.775082
$116$	−4.56463	−0.423816
$117$	−1.84397	−0.170475
$118$	−3.29471	−0.303303
$119$	−5.99495	−0.549557
$120$	4.77206	0.435627
$121$	−5.05063	−0.459148
$122$	3.12659	0.283068
$123$	7.61914	0.686995
$124$	−7.26972	−0.652840
$125$	4.24786	0.379940
$126$	−0.335615	−0.0298990
$127$	5.14621	0.456652	0.228326	−	0.973585i	$-0.426675\pi$
$127$	5.14621	0.456652	0.228326	+	0.973585i	$0.426675\pi$
$128$	−1.00000	−0.0883883
$129$	6.44201	0.567188
$130$	16.0627	1.40879
$131$	−11.3017	−0.987431	−0.493715	−	0.869624i	$-0.664362\pi$
$131$	−11.3017	−0.987431	−0.493715	+	0.869624i	$0.664362\pi$
$132$	3.98138	0.346535
$133$	0	0
$134$	6.71720	0.580277
$135$	15.9177	1.36998
$136$	−5.99495	−0.514063
$137$	11.1466	0.952317	0.476159	−	0.879359i	$-0.342029\pi$
$137$	11.1466	0.952317	0.476159	+	0.879359i	$0.342029\pi$
$138$	−4.64075	−0.395047
$139$	−2.15135	−0.182475	−0.0912374	−	0.995829i	$-0.529082\pi$
$139$	−2.15135	−0.182475	−0.0912374	+	0.995829i	$0.529082\pi$
$140$	2.92353	0.247083
$141$	−19.4624	−1.63903
$142$	12.8533	1.07862
$143$	13.4013	1.12067
$144$	−0.335615	−0.0279679
$145$	13.3448	1.10823
$146$	−13.5286	−1.11964
$147$	1.63229	0.134629
$148$	0.110567	0.00908854
$149$	−10.4265	−0.854170	−0.427085	−	0.904211i	$-0.640460\pi$
$149$	−10.4265	−0.854170	−0.427085	+	0.904211i	$0.640460\pi$
$150$	−5.78976	−0.472732
$151$	12.7692	1.03914	0.519572	−	0.854427i	$-0.326091\pi$
$151$	12.7692	1.03914	0.519572	+	0.854427i	$0.326091\pi$
$152$	0	0
$153$	−2.01200	−0.162660
$154$	2.43913	0.196551
$155$	21.2532	1.70710
$156$	8.96831	0.718040
$157$	23.0774	1.84178	0.920890	−	0.389822i	$-0.127463\pi$
$157$	23.0774	1.84178	0.920890	+	0.389822i	$0.127463\pi$
$158$	−2.86348	−0.227806
$159$	20.6198	1.63525
$160$	2.92353	0.231125
$161$	−2.84308	−0.224066
$162$	7.88052	0.619152
$163$	21.1754	1.65859	0.829293	−	0.558814i	$-0.188743\pi$
$163$	21.1754	1.65859	0.829293	+	0.558814i	$0.188743\pi$
$164$	4.66775	0.364490
$165$	−11.6397	−0.906148
$166$	5.61368	0.435706
$167$	−21.6652	−1.67650	−0.838251	−	0.545285i	$-0.816422\pi$
$167$	−21.6652	−1.67650	−0.838251	+	0.545285i	$0.816422\pi$
$168$	1.63229	0.125934
$169$	17.1873	1.32210
$170$	17.5264	1.34421
$171$	0	0
$172$	3.94660	0.300925
$173$	16.5214	1.25610	0.628049	−	0.778173i	$-0.283854\pi$
$173$	16.5214	1.25610	0.628049	+	0.778173i	$0.283854\pi$
$174$	7.45083	0.564846
$175$	−3.54701	−0.268129
$176$	2.43913	0.183857
$177$	5.37794	0.404231
$178$	−16.1053	−1.20714
$179$	−17.4874	−1.30707	−0.653536	−	0.756895i	$-0.726715\pi$
$179$	−17.4874	−1.30707	−0.653536	+	0.756895i	$0.726715\pi$
$180$	0.981180	0.0731328
$181$	17.2953	1.28555	0.642774	−	0.766056i	$-0.277783\pi$
$181$	17.2953	1.28555	0.642774	+	0.766056i	$0.277783\pi$
$182$	5.49430	0.407264
$183$	−5.10352	−0.377263
$184$	−2.84308	−0.209595
$185$	−0.323245	−0.0237654
$186$	11.8663	0.870081
$187$	14.6225	1.06930
$188$	−11.9233	−0.869598
$189$	5.44471	0.396044
$190$	0	0
$191$	20.4665	1.48091	0.740453	−	0.672108i	$-0.234611\pi$
$191$	20.4665	1.48091	0.740453	+	0.672108i	$0.234611\pi$
$192$	1.63229	0.117801
$193$	6.18941	0.445523	0.222762	−	0.974873i	$-0.428493\pi$
$193$	6.18941	0.445523	0.222762	+	0.974873i	$0.428493\pi$
$194$	−8.58809	−0.616589
$195$	−26.2191	−1.87759
$196$	1.00000	0.0714286
$197$	−7.80572	−0.556135	−0.278067	−	0.960562i	$-0.589694\pi$
$197$	−7.80572	−0.556135	−0.278067	+	0.960562i	$0.589694\pi$
$198$	0.818610	0.0581761
$199$	−0.998499	−0.0707817	−0.0353908	−	0.999374i	$-0.511268\pi$
$199$	−0.998499	−0.0707817	−0.0353908	+	0.999374i	$0.511268\pi$
$200$	−3.54701	−0.250811
$201$	−10.9644	−0.773372
$202$	8.89241	0.625668
$203$	4.56463	0.320375
$204$	9.78553	0.685124
$205$	−13.6463	−0.953099
$206$	−8.46794	−0.589989
$207$	−0.954182	−0.0663202
$208$	5.49430	0.380961
$209$	0	0
$210$	−4.77206	−0.329303
$211$	27.5891	1.89931	0.949655	−	0.313299i	$-0.101434\pi$
$211$	27.5891	1.89931	0.949655	+	0.313299i	$0.101434\pi$
$212$	12.6324	0.867595
$213$	−20.9803	−1.43755
$214$	−1.76973	−0.120976
$215$	−11.5380	−0.786884
$216$	5.44471	0.370465
$217$	7.26972	0.493501
$218$	−15.8075	−1.07062
$219$	22.0827	1.49221
$220$	−7.13087	−0.480763
$221$	32.9381	2.21565
$222$	−0.180478	−0.0121129
$223$	8.74005	0.585277	0.292638	−	0.956223i	$-0.405467\pi$
$223$	8.74005	0.585277	0.292638	+	0.956223i	$0.405467\pi$
$224$	1.00000	0.0668153
$225$	−1.19043	−0.0793620
$226$	1.57811	0.104974
$227$	4.33659	0.287830	0.143915	−	0.989590i	$-0.454031\pi$
$227$	4.33659	0.287830	0.143915	+	0.989590i	$0.454031\pi$
$228$	0	0
$229$	11.1985	0.740020	0.370010	−	0.929028i	$-0.379354\pi$
$229$	11.1985	0.740020	0.370010	+	0.929028i	$0.379354\pi$
$230$	8.31183	0.548066
$231$	−3.98138	−0.261956
$232$	4.56463	0.299683
$233$	16.2883	1.06708	0.533542	−	0.845774i	$-0.320861\pi$
$233$	16.2883	1.06708	0.533542	+	0.845774i	$0.320861\pi$
$234$	1.84397	0.120544
$235$	34.8582	2.27390
$236$	3.29471	0.214467
$237$	4.67404	0.303612
$238$	5.99495	0.388595
$239$	−11.9722	−0.774415	−0.387208	−	0.921993i	$-0.626560\pi$
$239$	−11.9722	−0.774415	−0.387208	+	0.921993i	$0.626560\pi$
$240$	−4.77206	−0.308035
$241$	−9.48175	−0.610773	−0.305387	−	0.952228i	$-0.598786\pi$
$241$	−9.48175	−0.610773	−0.305387	+	0.952228i	$0.598786\pi$
$242$	5.05063	0.324667
$243$	3.47079	0.222652
$244$	−3.12659	−0.200160
$245$	−2.92353	−0.186777
$246$	−7.61914	−0.485779
$247$	0	0
$248$	7.26972	0.461628
$249$	−9.16317	−0.580693
$250$	−4.24786	−0.268658
$251$	−7.35559	−0.464280	−0.232140	−	0.972682i	$-0.574573\pi$
$251$	−7.35559	−0.464280	−0.232140	+	0.972682i	$0.574573\pi$
$252$	0.335615	0.0211418
$253$	6.93466	0.435978
$254$	−5.14621	−0.322902
$255$	−28.6083	−1.79152
$256$	1.00000	0.0625000
$257$	3.27043	0.204004	0.102002	−	0.994784i	$-0.467475\pi$
$257$	3.27043	0.204004	0.102002	+	0.994784i	$0.467475\pi$
$258$	−6.44201	−0.401062
$259$	−0.110567	−0.00687029
$260$	−16.0627	−0.996168
$261$	1.53196	0.0948260
$262$	11.3017	0.698219
$263$	0.794703	0.0490035	0.0245018	−	0.999700i	$-0.492200\pi$
$263$	0.794703	0.0490035	0.0245018	+	0.999700i	$0.492200\pi$
$264$	−3.98138	−0.245037
$265$	−36.9311	−2.26866
$266$	0	0
$267$	26.2886	1.60884
$268$	−6.71720	−0.410318
$269$	23.3513	1.42375	0.711876	−	0.702306i	$-0.247846\pi$
$269$	23.3513	1.42375	0.711876	+	0.702306i	$0.247846\pi$
$270$	−15.9177	−0.968723
$271$	−10.9568	−0.665576	−0.332788	−	0.943002i	$-0.607989\pi$
$271$	−10.9568	−0.665576	−0.332788	+	0.943002i	$0.607989\pi$
$272$	5.99495	0.363497
$273$	−8.96831	−0.542787
$274$	−11.1466	−0.673390
$275$	8.65162	0.521713
$276$	4.64075	0.279340
$277$	−21.6198	−1.29901	−0.649503	−	0.760359i	$-0.725023\pi$
$277$	−21.6198	−1.29901	−0.649503	+	0.760359i	$0.725023\pi$
$278$	2.15135	0.129029
$279$	2.43983	0.146069
$280$	−2.92353	−0.174714
$281$	22.0614	1.31607	0.658037	−	0.752986i	$-0.271387\pi$
$281$	22.0614	1.31607	0.658037	+	0.752986i	$0.271387\pi$
$282$	19.4624	1.15897
$283$	−11.8267	−0.703026	−0.351513	−	0.936183i	$-0.614333\pi$
$283$	−11.8267	−0.703026	−0.351513	+	0.936183i	$0.614333\pi$
$284$	−12.8533	−0.762702
$285$	0	0
$286$	−13.4013	−0.792437
$287$	−4.66775	−0.275529
$288$	0.335615	0.0197763
$289$	18.9395	1.11409
$290$	−13.3448	−0.783635
$291$	14.0183	0.821767
$292$	13.5286	0.791702
$293$	−1.52456	−0.0890656	−0.0445328	−	0.999008i	$-0.514180\pi$
$293$	−1.52456	−0.0890656	−0.0445328	+	0.999008i	$0.514180\pi$
$294$	−1.63229	−0.0951973
$295$	−9.63218	−0.560807
$296$	−0.110567	−0.00642657
$297$	−13.2804	−0.770605
$298$	10.4265	0.603989
$299$	15.6207	0.903371
$300$	5.78976	0.334272
$301$	−3.94660	−0.227478
$302$	−12.7692	−0.734786
$303$	−14.5150	−0.833867
$304$	0	0
$305$	9.14067	0.523393
$306$	2.01200	0.115018
$307$	23.6725	1.35106	0.675532	−	0.737331i	$-0.263914\pi$
$307$	23.6725	1.35106	0.675532	+	0.737331i	$0.263914\pi$
$308$	−2.43913	−0.138983
$309$	13.8222	0.786316
$310$	−21.2532	−1.20710
$311$	−22.6201	−1.28267	−0.641335	−	0.767261i	$-0.721619\pi$
$311$	−22.6201	−1.28267	−0.641335	+	0.767261i	$0.721619\pi$
$312$	−8.96831	−0.507731
$313$	19.7631	1.11707	0.558537	−	0.829479i	$-0.311363\pi$
$313$	19.7631	1.11707	0.558537	+	0.829479i	$0.311363\pi$
$314$	−23.0774	−1.30234
$315$	−0.981180	−0.0552832
$316$	2.86348	0.161083
$317$	−18.6720	−1.04873	−0.524363	−	0.851495i	$-0.675697\pi$
$317$	−18.6720	−1.04873	−0.524363	+	0.851495i	$0.675697\pi$
$318$	−20.6198	−1.15630
$319$	−11.1338	−0.623370
$320$	−2.92353	−0.163430
$321$	2.88872	0.161232
$322$	2.84308	0.158439
$323$	0	0
$324$	−7.88052	−0.437806
$325$	19.4883	1.08102
$326$	−21.1754	−1.17280
$327$	25.8025	1.42688
$328$	−4.66775	−0.257733
$329$	11.9233	0.657354
$330$	11.6397	0.640743
$331$	18.4670	1.01504	0.507518	−	0.861641i	$-0.330563\pi$
$331$	18.4670	1.01504	0.507518	+	0.861641i	$0.330563\pi$
$332$	−5.61368	−0.308091
$333$	−0.0371079	−0.00203350
$334$	21.6652	1.18547
$335$	19.6379	1.07293
$336$	−1.63229	−0.0890490
$337$	11.8115	0.643414	0.321707	−	0.946839i	$-0.395743\pi$
$337$	11.8115	0.643414	0.321707	+	0.946839i	$0.395743\pi$
$338$	−17.1873	−0.934866
$339$	−2.57594	−0.139906
$340$	−17.5264	−0.950503
$341$	−17.7318	−0.960232
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	−3.94660	−0.212786
$345$	−13.5673	−0.730441
$346$	−16.5214	−0.888196
$347$	36.7602	1.97339	0.986697	−	0.162572i	$-0.0519789\pi$
$347$	36.7602	1.97339	0.986697	+	0.162572i	$0.0519789\pi$
$348$	−7.45083	−0.399406
$349$	−25.3499	−1.35695	−0.678474	−	0.734625i	$-0.737358\pi$
$349$	−25.3499	−1.35695	−0.678474	+	0.734625i	$0.737358\pi$
$350$	3.54701	0.189596
$351$	−29.9148	−1.59674
$352$	−2.43913	−0.130006
$353$	−22.8734	−1.21743	−0.608715	−	0.793389i	$-0.708315\pi$
$353$	−22.8734	−1.21743	−0.608715	+	0.793389i	$0.708315\pi$
$354$	−5.37794	−0.285834
$355$	37.5769	1.99437
$356$	16.1053	0.853580
$357$	−9.78553	−0.517905
$358$	17.4874	0.924240
$359$	−29.8313	−1.57443	−0.787217	−	0.616676i	$-0.788479\pi$
$359$	−29.8313	−1.57443	−0.787217	+	0.616676i	$0.788479\pi$
$360$	−0.981180	−0.0517127
$361$	0	0
$362$	−17.2953	−0.909020
$363$	−8.24411	−0.432704
$364$	−5.49430	−0.287979
$365$	−39.5513	−2.07021
$366$	5.10352	0.266765
$367$	31.6699	1.65316	0.826579	−	0.562821i	$-0.190284\pi$
$367$	31.6699	1.65316	0.826579	+	0.562821i	$0.190284\pi$
$368$	2.84308	0.148206
$369$	−1.56657	−0.0815523
$370$	0.323245	0.0168047
$371$	−12.6324	−0.655840
$372$	−11.8663	−0.615240
$373$	23.2366	1.20315	0.601573	−	0.798818i	$-0.294541\pi$
$373$	23.2366	1.20315	0.601573	+	0.798818i	$0.294541\pi$
$374$	−14.6225	−0.756111
$375$	6.93376	0.358058
$376$	11.9233	0.614898
$377$	−25.0795	−1.29166
$378$	−5.44471	−0.280045
$379$	0.393594	0.0202176	0.0101088	−	0.999949i	$-0.496782\pi$
$379$	0.393594	0.0202176	0.0101088	+	0.999949i	$0.496782\pi$
$380$	0	0
$381$	8.40012	0.430351
$382$	−20.4665	−1.04716
$383$	23.1814	1.18452	0.592258	−	0.805748i	$-0.298237\pi$
$383$	23.1814	1.18452	0.592258	+	0.805748i	$0.298237\pi$
$384$	−1.63229	−0.0832977
$385$	7.13087	0.363423
$386$	−6.18941	−0.315033
$387$	−1.32454	−0.0673301
$388$	8.58809	0.435994
$389$	20.7545	1.05230	0.526149	−	0.850393i	$-0.323636\pi$
$389$	20.7545	1.05230	0.526149	+	0.850393i	$0.323636\pi$
$390$	26.2191	1.32766
$391$	17.0441	0.861960
$392$	−1.00000	−0.0505076
$393$	−18.4476	−0.930560
$394$	7.80572	0.393247
$395$	−8.37146	−0.421214
$396$	−0.818610	−0.0411367
$397$	17.4752	0.877055	0.438527	−	0.898718i	$-0.355500\pi$
$397$	17.4752	0.877055	0.438527	+	0.898718i	$0.355500\pi$
$398$	0.998499	0.0500502
$399$	0	0
$400$	3.54701	0.177350
$401$	−8.74372	−0.436640	−0.218320	−	0.975877i	$-0.570058\pi$
$401$	−8.74372	−0.436640	−0.218320	+	0.975877i	$0.570058\pi$
$402$	10.9644	0.546857
$403$	−39.9420	−1.98965
$404$	−8.89241	−0.442414
$405$	23.0389	1.14481
$406$	−4.56463	−0.226539
$407$	0.269687	0.0133679
$408$	−9.78553	−0.484456
$409$	−11.2869	−0.558101	−0.279051	−	0.960276i	$-0.590020\pi$
$409$	−11.2869	−0.558101	−0.279051	+	0.960276i	$0.590020\pi$
$410$	13.6463	0.673942
$411$	18.1945	0.897469
$412$	8.46794	0.417186
$413$	−3.29471	−0.162122
$414$	0.954182	0.0468955
$415$	16.4117	0.805620
$416$	−5.49430	−0.269380
$417$	−3.51163	−0.171965
$418$	0	0
$419$	−15.2367	−0.744359	−0.372180	−	0.928161i	$-0.621389\pi$
$419$	−15.2367	−0.744359	−0.372180	+	0.928161i	$0.621389\pi$
$420$	4.77206	0.232852
$421$	−10.6586	−0.519467	−0.259734	−	0.965680i	$-0.583635\pi$
$421$	−10.6586	−0.519467	−0.259734	+	0.965680i	$0.583635\pi$
$422$	−27.5891	−1.34301
$423$	4.00165	0.194567
$424$	−12.6324	−0.613483
$425$	21.2641	1.03146
$426$	20.9803	1.01650
$427$	3.12659	0.151306
$428$	1.76973	0.0855430
$429$	21.8749	1.05613
$430$	11.5380	0.556411
$431$	−8.92527	−0.429915	−0.214957	−	0.976623i	$-0.568961\pi$
$431$	−8.92527	−0.429915	−0.214957	+	0.976623i	$0.568961\pi$
$432$	−5.44471	−0.261959
$433$	−15.2025	−0.730587	−0.365294	−	0.930892i	$-0.619031\pi$
$433$	−15.2025	−0.730587	−0.365294	+	0.930892i	$0.619031\pi$
$434$	−7.26972	−0.348958
$435$	21.7827	1.04440
$436$	15.8075	0.757043
$437$	0	0
$438$	−22.0827	−1.05515
$439$	−17.5128	−0.835841	−0.417920	−	0.908484i	$-0.637241\pi$
$439$	−17.5128	−0.835841	−0.417920	+	0.908484i	$0.637241\pi$
$440$	7.13087	0.339951
$441$	−0.335615	−0.0159817
$442$	−32.9381	−1.56670
$443$	−29.3468	−1.39431	−0.697153	−	0.716922i	$-0.745550\pi$
$443$	−29.3468	−1.39431	−0.697153	+	0.716922i	$0.745550\pi$
$444$	0.180478	0.00856509
$445$	−47.0843	−2.23201
$446$	−8.74005	−0.413853
$447$	−17.0191	−0.804975
$448$	−1.00000	−0.0472456
$449$	−27.6526	−1.30501	−0.652504	−	0.757785i	$-0.726282\pi$
$449$	−27.6526	−1.30501	−0.652504	+	0.757785i	$0.726282\pi$
$450$	1.19043	0.0561174
$451$	11.3853	0.536111
$452$	−1.57811	−0.0742280
$453$	20.8431	0.979295
$454$	−4.33659	−0.203526
$455$	16.0627	0.753032
$456$	0	0
$457$	−6.75513	−0.315992	−0.157996	−	0.987440i	$-0.550503\pi$
$457$	−6.75513	−0.315992	−0.157996	+	0.987440i	$0.550503\pi$
$458$	−11.1985	−0.523273
$459$	−32.6408	−1.52354
$460$	−8.31183	−0.387541
$461$	−7.93946	−0.369778	−0.184889	−	0.982759i	$-0.559192\pi$
$461$	−7.93946	−0.369778	−0.184889	+	0.982759i	$0.559192\pi$
$462$	3.98138	0.185231
$463$	−0.0999421	−0.00464470	−0.00232235	−	0.999997i	$-0.500739\pi$
$463$	−0.0999421	−0.00464470	−0.00232235	+	0.999997i	$0.500739\pi$
$464$	−4.56463	−0.211908
$465$	34.6915	1.60878
$466$	−16.2883	−0.754542
$467$	31.4677	1.45615	0.728076	−	0.685496i	$-0.240415\pi$
$467$	31.4677	1.45615	0.728076	+	0.685496i	$0.240415\pi$
$468$	−1.84397	−0.0852375
$469$	6.71720	0.310171
$470$	−34.8582	−1.60789
$471$	37.6692	1.73570
$472$	−3.29471	−0.151651
$473$	9.62628	0.442617
$474$	−4.67404	−0.214686
$475$	0	0
$476$	−5.99495	−0.274778
$477$	−4.23962	−0.194119
$478$	11.9722	0.547594
$479$	3.72891	0.170378	0.0851892	−	0.996365i	$-0.472851\pi$
$479$	3.72891	0.170378	0.0851892	+	0.996365i	$0.472851\pi$
$480$	4.77206	0.217814
$481$	0.607487	0.0276990
$482$	9.48175	0.431882
$483$	−4.64075	−0.211161
$484$	−5.05063	−0.229574
$485$	−25.1075	−1.14007
$486$	−3.47079	−0.157438
$487$	13.7074	0.621140	0.310570	−	0.950550i	$-0.399480\pi$
$487$	13.7074	0.621140	0.310570	+	0.950550i	$0.399480\pi$
$488$	3.12659	0.141534
$489$	34.5645	1.56306
$490$	2.92353	0.132071
$491$	−16.5816	−0.748315	−0.374158	−	0.927365i	$-0.622068\pi$
$491$	−16.5816	−0.748315	−0.374158	+	0.927365i	$0.622068\pi$
$492$	7.61914	0.343498
$493$	−27.3648	−1.23245
$494$	0	0
$495$	2.39323	0.107568
$496$	−7.26972	−0.326420
$497$	12.8533	0.576548
$498$	9.16317	0.410612
$499$	−14.2656	−0.638616	−0.319308	−	0.947651i	$-0.603450\pi$
$499$	−14.2656	−0.638616	−0.319308	+	0.947651i	$0.603450\pi$
$500$	4.24786	0.189970
$501$	−35.3639	−1.57994
$502$	7.35559	0.328296
$503$	4.79821	0.213942	0.106971	−	0.994262i	$-0.465885\pi$
$503$	4.79821	0.213942	0.106971	+	0.994262i	$0.465885\pi$
$504$	−0.335615	−0.0149495
$505$	25.9972	1.15686
$506$	−6.93466	−0.308283
$507$	28.0547	1.24595
$508$	5.14621	0.228326
$509$	−38.4818	−1.70568	−0.852838	−	0.522176i	$-0.825120\pi$
$509$	−38.4818	−1.70568	−0.852838	+	0.522176i	$0.825120\pi$
$510$	28.6083	1.26679
$511$	−13.5286	−0.598471
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−3.27043	−0.144253
$515$	−24.7563	−1.09089
$516$	6.44201	0.283594
$517$	−29.0826	−1.27905
$518$	0.110567	0.00485803
$519$	26.9678	1.18375
$520$	16.0627	0.704397
$521$	31.4752	1.37896	0.689478	−	0.724307i	$-0.257840\pi$
$521$	31.4752	1.37896	0.689478	+	0.724307i	$0.257840\pi$
$522$	−1.53196	−0.0670521
$523$	29.4539	1.28793	0.643966	−	0.765054i	$-0.277288\pi$
$523$	29.4539	1.28793	0.643966	+	0.765054i	$0.277288\pi$
$524$	−11.3017	−0.493715
$525$	−5.78976	−0.252686
$526$	−0.794703	−0.0346507
$527$	−43.5816	−1.89845
$528$	3.98138	0.173267
$529$	−14.9169	−0.648560
$530$	36.9311	1.60418
$531$	−1.10576	−0.0479857
$532$	0	0
$533$	25.6460	1.11085
$534$	−26.2886	−1.13762
$535$	−5.17385	−0.223685
$536$	6.71720	0.290139
$537$	−28.5446	−1.23179
$538$	−23.3513	−1.00674
$539$	2.43913	0.105061
$540$	15.9177	0.684991
$541$	−28.4303	−1.22231	−0.611157	−	0.791509i	$-0.709296\pi$
$541$	−28.4303	−1.22231	−0.611157	+	0.791509i	$0.709296\pi$
$542$	10.9568	0.470633
$543$	28.2310	1.21151
$544$	−5.99495	−0.257032
$545$	−46.2137	−1.97958
$546$	8.96831	0.383808
$547$	6.22509	0.266166	0.133083	−	0.991105i	$-0.457512\pi$
$547$	6.22509	0.266166	0.133083	+	0.991105i	$0.457512\pi$
$548$	11.1466	0.476159
$549$	1.04933	0.0447844
$550$	−8.65162	−0.368906
$551$	0	0
$552$	−4.64075	−0.197523
$553$	−2.86348	−0.121768
$554$	21.6198	0.918536
$555$	−0.527631	−0.0223967
$556$	−2.15135	−0.0912374
$557$	−26.7237	−1.13232	−0.566160	−	0.824295i	$-0.691572\pi$
$557$	−26.7237	−1.13232	−0.566160	+	0.824295i	$0.691572\pi$
$558$	−2.43983	−0.103286
$559$	21.6838	0.917127
$560$	2.92353	0.123542
$561$	23.8682	1.00772
$562$	−22.0614	−0.930605
$563$	−20.5056	−0.864207	−0.432103	−	0.901824i	$-0.642228\pi$
$563$	−20.5056	−0.864207	−0.432103	+	0.901824i	$0.642228\pi$
$564$	−19.4624	−0.819514
$565$	4.61364	0.194097
$566$	11.8267	0.497115
$567$	7.88052	0.330951
$568$	12.8533	0.539311
$569$	7.02200	0.294378	0.147189	−	0.989108i	$-0.452978\pi$
$569$	7.02200	0.294378	0.147189	+	0.989108i	$0.452978\pi$
$570$	0	0
$571$	−18.7535	−0.784809	−0.392404	−	0.919793i	$-0.628357\pi$
$571$	−18.7535	−0.784809	−0.392404	+	0.919793i	$0.628357\pi$
$572$	13.4013	0.560337
$573$	33.4074	1.39561
$574$	4.66775	0.194828
$575$	10.0844	0.420550
$576$	−0.335615	−0.0139840
$577$	−17.4231	−0.725333	−0.362666	−	0.931919i	$-0.618134\pi$
$577$	−17.4231	−0.725333	−0.362666	+	0.931919i	$0.618134\pi$
$578$	−18.9395	−0.787778
$579$	10.1029	0.419864
$580$	13.3448	0.554114
$581$	5.61368	0.232895
$582$	−14.0183	−0.581077
$583$	30.8121	1.27610
$584$	−13.5286	−0.559818
$585$	5.39089	0.222886
$586$	1.52456	0.0629789
$587$	6.74187	0.278267	0.139133	−	0.990274i	$-0.455568\pi$
$587$	6.74187	0.278267	0.139133	+	0.990274i	$0.455568\pi$
$588$	1.63229	0.0673147
$589$	0	0
$590$	9.63218	0.396550
$591$	−12.7412	−0.524104
$592$	0.110567	0.00454427
$593$	17.5849	0.722127	0.361063	−	0.932541i	$-0.382414\pi$
$593$	17.5849	0.722127	0.361063	+	0.932541i	$0.382414\pi$
$594$	13.2804	0.544900
$595$	17.5264	0.718513
$596$	−10.4265	−0.427085
$597$	−1.62984	−0.0667051
$598$	−15.6207	−0.638780
$599$	39.5876	1.61750	0.808752	−	0.588149i	$-0.200143\pi$
$599$	39.5876	1.61750	0.808752	+	0.588149i	$0.200143\pi$
$600$	−5.78976	−0.236366
$601$	−24.1762	−0.986167	−0.493083	−	0.869982i	$-0.664130\pi$
$601$	−24.1762	−0.986167	−0.493083	+	0.869982i	$0.664130\pi$
$602$	3.94660	0.160851
$603$	2.25439	0.0918060
$604$	12.7692	0.519572
$605$	14.7656	0.600309
$606$	14.5150	0.589633
$607$	−24.8942	−1.01042	−0.505211	−	0.862996i	$-0.668585\pi$
$607$	−24.8942	−1.01042	−0.505211	+	0.862996i	$0.668585\pi$
$608$	0	0
$609$	7.45083	0.301923
$610$	−9.14067	−0.370095
$611$	−65.5103	−2.65026
$612$	−2.01200	−0.0813302
$613$	45.1814	1.82486	0.912430	−	0.409233i	$-0.134204\pi$
$613$	45.1814	1.82486	0.912430	+	0.409233i	$0.134204\pi$
$614$	−23.6725	−0.955346
$615$	−22.2748	−0.898205
$616$	2.43913	0.0982755
$617$	−6.05480	−0.243757	−0.121879	−	0.992545i	$-0.538892\pi$
$617$	−6.05480	−0.243757	−0.121879	+	0.992545i	$0.538892\pi$
$618$	−13.8222	−0.556009
$619$	9.19274	0.369487	0.184744	−	0.982787i	$-0.440855\pi$
$619$	9.19274	0.369487	0.184744	+	0.982787i	$0.440855\pi$
$620$	21.2532	0.853550
$621$	−15.4797	−0.621181
$622$	22.6201	0.906984
$623$	−16.1053	−0.645246
$624$	8.96831	0.359020
$625$	−30.1538	−1.20615
$626$	−19.7631	−0.789891
$627$	0	0
$628$	23.0774	0.920890
$629$	0.662843	0.0264293
$630$	0.981180	0.0390911
$631$	23.9342	0.952806	0.476403	−	0.879227i	$-0.341940\pi$
$631$	23.9342	0.952806	0.476403	+	0.879227i	$0.341940\pi$
$632$	−2.86348	−0.113903
$633$	45.0335	1.78992
$634$	18.6720	0.741562
$635$	−15.0451	−0.597045
$636$	20.6198	0.817627
$637$	5.49430	0.217692
$638$	11.1338	0.440789
$639$	4.31375	0.170649
$640$	2.92353	0.115563
$641$	−21.0418	−0.831101	−0.415550	−	0.909570i	$-0.636411\pi$
$641$	−21.0418	−0.831101	−0.415550	+	0.909570i	$0.636411\pi$
$642$	−2.88872	−0.114009
$643$	2.10672	0.0830808	0.0415404	−	0.999137i	$-0.486773\pi$
$643$	2.10672	0.0830808	0.0415404	+	0.999137i	$0.486773\pi$
$644$	−2.84308	−0.112033
$645$	−18.8334	−0.741564
$646$	0	0
$647$	5.83134	0.229253	0.114627	−	0.993409i	$-0.463433\pi$
$647$	5.83134	0.229253	0.114627	+	0.993409i	$0.463433\pi$
$648$	7.88052	0.309576
$649$	8.03624	0.315450
$650$	−19.4883	−0.764395
$651$	11.8663	0.465078
$652$	21.1754	0.829293
$653$	−17.7807	−0.695812	−0.347906	−	0.937529i	$-0.613107\pi$
$653$	−17.7807	−0.695812	−0.347906	+	0.937529i	$0.613107\pi$
$654$	−25.8025	−1.00896
$655$	33.0407	1.29101
$656$	4.66775	0.182245
$657$	−4.54041	−0.177138
$658$	−11.9233	−0.464820
$659$	28.2934	1.10215	0.551077	−	0.834455i	$-0.314217\pi$
$659$	28.2934	1.10215	0.551077	+	0.834455i	$0.314217\pi$
$660$	−11.6397	−0.453074
$661$	16.5905	0.645298	0.322649	−	0.946519i	$-0.395427\pi$
$661$	16.5905	0.645298	0.322649	+	0.946519i	$0.395427\pi$
$662$	−18.4670	−0.717738
$663$	53.7646	2.08804
$664$	5.61368	0.217853
$665$	0	0
$666$	0.0371079	0.00143790
$667$	−12.9776	−0.502496
$668$	−21.6652	−0.838251
$669$	14.2663	0.551568
$670$	−19.6379	−0.758678
$671$	−7.62617	−0.294405
$672$	1.63229	0.0629671
$673$	15.2872	0.589279	0.294640	−	0.955608i	$-0.404800\pi$
$673$	15.2872	0.589279	0.294640	+	0.955608i	$0.404800\pi$
$674$	−11.8115	−0.454963
$675$	−19.3124	−0.743335
$676$	17.1873	0.661050
$677$	22.7878	0.875806	0.437903	−	0.899022i	$-0.355721\pi$
$677$	22.7878	0.875806	0.437903	+	0.899022i	$0.355721\pi$
$678$	2.57594	0.0989283
$679$	−8.58809	−0.329581
$680$	17.5264	0.672107
$681$	7.07860	0.271252
$682$	17.7318	0.678986
$683$	6.49073	0.248361	0.124180	−	0.992260i	$-0.460370\pi$
$683$	6.49073	0.248361	0.124180	+	0.992260i	$0.460370\pi$
$684$	0	0
$685$	−32.5873	−1.24510
$686$	1.00000	0.0381802
$687$	18.2793	0.697399
$688$	3.94660	0.150463
$689$	69.4060	2.64416
$690$	13.5673	0.516500
$691$	34.0045	1.29359	0.646796	−	0.762663i	$-0.276109\pi$
$691$	34.0045	1.29359	0.646796	+	0.762663i	$0.276109\pi$
$692$	16.5214	0.628049
$693$	0.818610	0.0310964
$694$	−36.7602	−1.39540
$695$	6.28951	0.238575
$696$	7.45083	0.282423
$697$	27.9830	1.05993
$698$	25.3499	0.959507
$699$	26.5873	1.00563
$700$	−3.54701	−0.134064
$701$	40.2705	1.52100	0.760498	−	0.649340i	$-0.224955\pi$
$701$	40.2705	1.52100	0.760498	+	0.649340i	$0.224955\pi$
$702$	29.9148	1.12906
$703$	0	0
$704$	2.43913	0.0919283
$705$	56.8988	2.14293
$706$	22.8734	0.860853
$707$	8.89241	0.334434
$708$	5.37794	0.202115
$709$	36.9887	1.38914	0.694570	−	0.719425i	$-0.255595\pi$
$709$	36.9887	1.38914	0.694570	+	0.719425i	$0.255595\pi$
$710$	−37.5769	−1.41024
$711$	−0.961027	−0.0360413
$712$	−16.1053	−0.603572
$713$	−20.6684	−0.774038
$714$	9.78553	0.366214
$715$	−39.1791	−1.46522
$716$	−17.4874	−0.653536
$717$	−19.5421	−0.729813
$718$	29.8313	1.11329
$719$	−3.55013	−0.132397	−0.0661987	−	0.997806i	$-0.521087\pi$
$719$	−3.55013	−0.132397	−0.0661987	+	0.997806i	$0.521087\pi$
$720$	0.981180	0.0365664
$721$	−8.46794	−0.315363
$722$	0	0
$723$	−15.4770	−0.575596
$724$	17.2953	0.642774
$725$	−16.1908	−0.601311
$726$	8.24411	0.305968
$727$	−16.8789	−0.626004	−0.313002	−	0.949753i	$-0.601335\pi$
$727$	−16.8789	−0.626004	−0.313002	+	0.949753i	$0.601335\pi$
$728$	5.49430	0.203632
$729$	29.3069	1.08544
$730$	39.5513	1.46386
$731$	23.6597	0.875085
$732$	−5.10352	−0.188631
$733$	−41.0112	−1.51479	−0.757393	−	0.652960i	$-0.773527\pi$
$733$	−41.0112	−1.51479	−0.757393	+	0.652960i	$0.773527\pi$
$734$	−31.6699	−1.16896
$735$	−4.77206	−0.176020
$736$	−2.84308	−0.104797
$737$	−16.3841	−0.603517
$738$	1.56657	0.0576662
$739$	−1.86865	−0.0687396	−0.0343698	−	0.999409i	$-0.510942\pi$
$739$	−1.86865	−0.0687396	−0.0343698	+	0.999409i	$0.510942\pi$
$740$	−0.323245	−0.0118827
$741$	0	0
$742$	12.6324	0.463749
$743$	14.6771	0.538451	0.269226	−	0.963077i	$-0.413232\pi$
$743$	14.6771	0.538451	0.269226	+	0.963077i	$0.413232\pi$
$744$	11.8663	0.435040
$745$	30.4821	1.11678
$746$	−23.2366	−0.850753
$747$	1.88404	0.0689332
$748$	14.6225	0.534651
$749$	−1.76973	−0.0646644
$750$	−6.93376	−0.253185
$751$	19.2150	0.701164	0.350582	−	0.936532i	$-0.385984\pi$
$751$	19.2150	0.701164	0.350582	+	0.936532i	$0.385984\pi$
$752$	−11.9233	−0.434799
$753$	−12.0065	−0.437541
$754$	25.0795	0.913340
$755$	−37.3311	−1.35862
$756$	5.44471	0.198022
$757$	−49.6720	−1.80536	−0.902679	−	0.430314i	$-0.858403\pi$
$757$	−49.6720	−1.80536	−0.902679	+	0.430314i	$0.858403\pi$
$758$	−0.393594	−0.0142960
$759$	11.3194	0.410868
$760$	0	0
$761$	51.2605	1.85819	0.929097	−	0.369837i	$-0.120586\pi$
$761$	51.2605	1.85819	0.929097	+	0.369837i	$0.120586\pi$
$762$	−8.40012	−0.304304
$763$	−15.8075	−0.572270
$764$	20.4665	0.740453
$765$	5.88213	0.212669
$766$	−23.1814	−0.837579
$767$	18.1021	0.653630
$768$	1.63229	0.0589003
$769$	−1.80109	−0.0649491	−0.0324745	−	0.999473i	$-0.510339\pi$
$769$	−1.80109	−0.0649491	−0.0324745	+	0.999473i	$0.510339\pi$
$770$	−7.13087	−0.256979
$771$	5.33831	0.192255
$772$	6.18941	0.222762
$773$	13.7651	0.495096	0.247548	−	0.968876i	$-0.420375\pi$
$773$	13.7651	0.495096	0.247548	+	0.968876i	$0.420375\pi$
$774$	1.32454	0.0476096
$775$	−25.7858	−0.926251
$776$	−8.58809	−0.308295
$777$	−0.180478	−0.00647460
$778$	−20.7545	−0.744087
$779$	0	0
$780$	−26.2191	−0.938794
$781$	−31.3508	−1.12182
$782$	−17.0441	−0.609497
$783$	24.8531	0.888177
$784$	1.00000	0.0357143
$785$	−67.4675	−2.40802
$786$	18.4476	0.658006
$787$	31.2963	1.11559	0.557797	−	0.829977i	$-0.311647\pi$
$787$	31.2963	1.11559	0.557797	+	0.829977i	$0.311647\pi$
$788$	−7.80572	−0.278067
$789$	1.29719	0.0461812
$790$	8.37146	0.297843
$791$	1.57811	0.0561111
$792$	0.818610	0.0290880
$793$	−17.1784	−0.610024
$794$	−17.4752	−0.620171
$795$	−60.2824	−2.13800
$796$	−0.998499	−0.0353908
$797$	−28.6145	−1.01358	−0.506789	−	0.862070i	$-0.669168\pi$
$797$	−28.6145	−1.01358	−0.506789	+	0.862070i	$0.669168\pi$
$798$	0	0
$799$	−71.4798	−2.52877
$800$	−3.54701	−0.125406
$801$	−5.40519	−0.190983
$802$	8.74372	0.308751
$803$	32.9981	1.16448
$804$	−10.9644	−0.386686
$805$	8.31183	0.292953
$806$	39.9420	1.40690
$807$	38.1161	1.34175
$808$	8.89241	0.312834
$809$	−1.37261	−0.0482584	−0.0241292	−	0.999709i	$-0.507681\pi$
$809$	−1.37261	−0.0482584	−0.0241292	+	0.999709i	$0.507681\pi$
$810$	−23.0389	−0.809504
$811$	29.7882	1.04601	0.523003	−	0.852331i	$-0.324812\pi$
$811$	29.7882	1.04601	0.523003	+	0.852331i	$0.324812\pi$
$812$	4.56463	0.160187
$813$	−17.8847	−0.627243
$814$	−0.269687	−0.00945253
$815$	−61.9069	−2.16850
$816$	9.78553	0.342562
$817$	0	0
$818$	11.2869	0.394637
$819$	1.84397	0.0644335
$820$	−13.6463	−0.476549
$821$	−9.52205	−0.332322	−0.166161	−	0.986099i	$-0.553137\pi$
$821$	−9.52205	−0.332322	−0.166161	+	0.986099i	$0.553137\pi$
$822$	−18.1945	−0.634606
$823$	−37.9195	−1.32179	−0.660896	−	0.750478i	$-0.729823\pi$
$823$	−37.9195	−1.32179	−0.660896	+	0.750478i	$0.729823\pi$
$824$	−8.46794	−0.294995
$825$	14.1220	0.491665
$826$	3.29471	0.114638
$827$	24.8024	0.862465	0.431233	−	0.902241i	$-0.358079\pi$
$827$	24.8024	0.862465	0.431233	+	0.902241i	$0.358079\pi$
$828$	−0.954182	−0.0331601
$829$	13.3104	0.462290	0.231145	−	0.972919i	$-0.425753\pi$
$829$	13.3104	0.462290	0.231145	+	0.972919i	$0.425753\pi$
$830$	−16.4117	−0.569660
$831$	−35.2898	−1.22419
$832$	5.49430	0.190480
$833$	5.99495	0.207713
$834$	3.51163	0.121598
$835$	63.3387	2.19193
$836$	0	0
$837$	39.5815	1.36814
$838$	15.2367	0.526341
$839$	10.7346	0.370599	0.185299	−	0.982682i	$-0.440674\pi$
$839$	10.7346	0.370599	0.185299	+	0.982682i	$0.440674\pi$
$840$	−4.77206	−0.164652
$841$	−8.16411	−0.281521
$842$	10.6586	0.367319
$843$	36.0107	1.24028
$844$	27.5891	0.949655
$845$	−50.2475	−1.72857
$846$	−4.00165	−0.137579
$847$	5.05063	0.173542
$848$	12.6324	0.433798
$849$	−19.3047	−0.662536
$850$	−21.2641	−0.729354
$851$	0.314351	0.0107758
$852$	−20.9803	−0.718774
$853$	−39.8073	−1.36298	−0.681488	−	0.731830i	$-0.738667\pi$
$853$	−39.8073	−1.36298	−0.681488	+	0.731830i	$0.738667\pi$
$854$	−3.12659	−0.106990
$855$	0	0
$856$	−1.76973	−0.0604880
$857$	−30.4214	−1.03917	−0.519587	−	0.854418i	$-0.673914\pi$
$857$	−30.4214	−1.03917	−0.519587	+	0.854418i	$0.673914\pi$
$858$	−21.8749	−0.746797
$859$	23.1498	0.789862	0.394931	−	0.918711i	$-0.370769\pi$
$859$	23.1498	0.789862	0.394931	+	0.918711i	$0.370769\pi$
$860$	−11.5380	−0.393442
$861$	−7.61914	−0.259660
$862$	8.92527	0.303996
$863$	−48.6103	−1.65471	−0.827357	−	0.561676i	$-0.810157\pi$
$863$	−48.6103	−1.65471	−0.827357	+	0.561676i	$0.810157\pi$
$864$	5.44471	0.185233
$865$	−48.3008	−1.64228
$866$	15.2025	0.516603
$867$	30.9148	1.04992
$868$	7.26972	0.246750
$869$	6.98441	0.236930
$870$	−21.7827	−0.738502
$871$	−36.9063	−1.25052
$872$	−15.8075	−0.535310
$873$	−2.88229	−0.0975509
$874$	0	0
$875$	−4.24786	−0.143604
$876$	22.0827	0.746105
$877$	−38.3631	−1.29543	−0.647716	−	0.761882i	$-0.724275\pi$
$877$	−38.3631	−1.29543	−0.647716	+	0.761882i	$0.724275\pi$
$878$	17.5128	0.591029
$879$	−2.48853	−0.0839359
$880$	−7.13087	−0.240382
$881$	32.8410	1.10644	0.553221	−	0.833035i	$-0.313399\pi$
$881$	32.8410	1.10644	0.553221	+	0.833035i	$0.313399\pi$
$882$	0.335615	0.0113008
$883$	−50.3248	−1.69356	−0.846781	−	0.531941i	$-0.821463\pi$
$883$	−50.3248	−1.69356	−0.846781	+	0.531941i	$0.821463\pi$
$884$	32.9381	1.10783
$885$	−15.7225	−0.528508
$886$	29.3468	0.985924
$887$	39.7140	1.33347	0.666733	−	0.745297i	$-0.267692\pi$
$887$	39.7140	1.33347	0.666733	+	0.745297i	$0.267692\pi$
$888$	−0.180478	−0.00605643
$889$	−5.14621	−0.172598
$890$	47.0843	1.57827
$891$	−19.2216	−0.643949
$892$	8.74005	0.292638
$893$	0	0
$894$	17.0191	0.569203
$895$	51.1250	1.70892
$896$	1.00000	0.0334077
$897$	25.4976	0.851342
$898$	27.6526	0.922780
$899$	33.1836	1.10674
$900$	−1.19043	−0.0396810
$901$	75.7305	2.52295
$902$	−11.3853	−0.379088
$903$	−6.44201	−0.214377
$904$	1.57811	0.0524871
$905$	−50.5632	−1.68078
$906$	−20.8431	−0.692466
$907$	−37.2174	−1.23578	−0.617891	−	0.786263i	$-0.712013\pi$
$907$	−37.2174	−1.23578	−0.617891	+	0.786263i	$0.712013\pi$
$908$	4.33659	0.143915
$909$	2.98443	0.0989873
$910$	−16.0627	−0.532474
$911$	38.5674	1.27779	0.638897	−	0.769293i	$-0.279391\pi$
$911$	38.5674	1.27779	0.638897	+	0.769293i	$0.279391\pi$
$912$	0	0
$913$	−13.6925	−0.453156
$914$	6.75513	0.223440
$915$	14.9203	0.493249
$916$	11.1985	0.370010
$917$	11.3017	0.373214
$918$	32.6408	1.07731
$919$	−3.05442	−0.100756	−0.0503780	−	0.998730i	$-0.516043\pi$
$919$	−3.05442	−0.100756	−0.0503780	+	0.998730i	$0.516043\pi$
$920$	8.31183	0.274033
$921$	38.6406	1.27325
$922$	7.93946	0.261472
$923$	−70.6197	−2.32448
$924$	−3.98138	−0.130978
$925$	0.392181	0.0128948
$926$	0.0999421	0.00328430
$927$	−2.84197	−0.0933425
$928$	4.56463	0.149841
$929$	57.8845	1.89913	0.949564	−	0.313573i	$-0.101526\pi$
$929$	57.8845	1.89913	0.949564	+	0.313573i	$0.101526\pi$
$930$	−34.6915	−1.13758
$931$	0	0
$932$	16.2883	0.533542
$933$	−36.9227	−1.20879
$934$	−31.4677	−1.02966
$935$	−42.7492	−1.39805
$936$	1.84397	0.0602720
$937$	31.3722	1.02489	0.512443	−	0.858721i	$-0.328741\pi$
$937$	31.3722	1.02489	0.512443	+	0.858721i	$0.328741\pi$
$938$	−6.71720	−0.219324
$939$	32.2591	1.05274
$940$	34.8582	1.13695
$941$	5.98133	0.194986	0.0974929	−	0.995236i	$-0.468918\pi$
$941$	5.98133	0.194986	0.0974929	+	0.995236i	$0.468918\pi$
$942$	−37.6692	−1.22733
$943$	13.2708	0.432157
$944$	3.29471	0.107234
$945$	−15.9177	−0.517804
$946$	−9.62628	−0.312977
$947$	−4.47352	−0.145370	−0.0726849	−	0.997355i	$-0.523157\pi$
$947$	−4.47352	−0.145370	−0.0726849	+	0.997355i	$0.523157\pi$
$948$	4.67404	0.151806
$949$	74.3302	2.41286
$950$	0	0
$951$	−30.4783	−0.988326
$952$	5.99495	0.194298
$953$	−52.7157	−1.70763	−0.853815	−	0.520577i	$-0.825717\pi$
$953$	−52.7157	−1.70763	−0.853815	+	0.520577i	$0.825717\pi$
$954$	4.23962	0.137263
$955$	−59.8344	−1.93620
$956$	−11.9722	−0.387208
$957$	−18.1736	−0.587468
$958$	−3.72891	−0.120476
$959$	−11.1466	−0.359942
$960$	−4.77206	−0.154017
$961$	21.8488	0.704801
$962$	−0.607487	−0.0195862
$963$	−0.593947	−0.0191397
$964$	−9.48175	−0.305387
$965$	−18.0949	−0.582496
$966$	4.64075	0.149314
$967$	−53.3381	−1.71524	−0.857618	−	0.514287i	$-0.828057\pi$
$967$	−53.3381	−1.71524	−0.857618	+	0.514287i	$0.828057\pi$
$968$	5.05063	0.162333
$969$	0	0
$970$	25.1075	0.806154
$971$	−43.1341	−1.38424	−0.692120	−	0.721782i	$-0.743323\pi$
$971$	−43.1341	−1.38424	−0.692120	+	0.721782i	$0.743323\pi$
$972$	3.47079	0.111326
$973$	2.15135	0.0689690
$974$	−13.7074	−0.439213
$975$	31.8107	1.01876
$976$	−3.12659	−0.100080
$977$	−14.0398	−0.449173	−0.224586	−	0.974454i	$-0.572103\pi$
$977$	−14.0398	−0.449173	−0.224586	+	0.974454i	$0.572103\pi$
$978$	−34.5645	−1.10525
$979$	39.2830	1.25549
$980$	−2.92353	−0.0933886
$981$	−5.30524	−0.169383
$982$	16.5816	0.529139
$983$	3.27410	0.104427	0.0522137	−	0.998636i	$-0.483372\pi$
$983$	3.27410	0.104427	0.0522137	+	0.998636i	$0.483372\pi$
$984$	−7.61914	−0.242889
$985$	22.8202	0.727113
$986$	27.3648	0.871472
$987$	19.4624	0.619494
$988$	0	0
$989$	11.2205	0.356791
$990$	−2.39323	−0.0760618
$991$	34.1681	1.08539	0.542693	−	0.839931i	$-0.317405\pi$
$991$	34.1681	1.08539	0.542693	+	0.839931i	$0.317405\pi$
$992$	7.26972	0.230814
$993$	30.1435	0.956575
$994$	−12.8533	−0.407681
$995$	2.91914	0.0925429
$996$	−9.16317	−0.290346
$997$	33.6101	1.06444	0.532221	−	0.846606i	$-0.321358\pi$
$997$	33.6101	1.06444	0.532221	+	0.846606i	$0.321358\pi$
$998$	14.2656	0.451570
$999$	−0.602004	−0.0190466

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.ba.1.4	✓	6
19.18	odd	2		5054.2.a.bd.1.3	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5054.2.a.ba.1.4	✓	6	1.1	even	1	trivial
5054.2.a.bd.1.3	yes	6	19.18	odd	2

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:	\( N \)	\(=\)	\( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5054.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.63229 q^{3} +1.00000 q^{4} -2.92353 q^{5} -1.63229 q^{6} -1.00000 q^{7} -1.00000 q^{8} -0.335615 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.63229 q^{3} +1.00000 q^{4} -2.92353 q^{5} -1.63229 q^{6} -1.00000 q^{7} -1.00000 q^{8} -0.335615 q^{9} +2.92353 q^{10} +2.43913 q^{11} +1.63229 q^{12} +5.49430 q^{13} +1.00000 q^{14} -4.77206 q^{15} +1.00000 q^{16} +5.99495 q^{17} +0.335615 q^{18} -2.92353 q^{20} -1.63229 q^{21} -2.43913 q^{22} +2.84308 q^{23} -1.63229 q^{24} +3.54701 q^{25} -5.49430 q^{26} -5.44471 q^{27} -1.00000 q^{28} -4.56463 q^{29} +4.77206 q^{30} -7.26972 q^{31} -1.00000 q^{32} +3.98138 q^{33} -5.99495 q^{34} +2.92353 q^{35} -0.335615 q^{36} +0.110567 q^{37} +8.96831 q^{39} +2.92353 q^{40} +4.66775 q^{41} +1.63229 q^{42} +3.94660 q^{43} +2.43913 q^{44} +0.981180 q^{45} -2.84308 q^{46} -11.9233 q^{47} +1.63229 q^{48} +1.00000 q^{49} -3.54701 q^{50} +9.78553 q^{51} +5.49430 q^{52} +12.6324 q^{53} +5.44471 q^{54} -7.13087 q^{55} +1.00000 q^{56} +4.56463 q^{58} +3.29471 q^{59} -4.77206 q^{60} -3.12659 q^{61} +7.26972 q^{62} +0.335615 q^{63} +1.00000 q^{64} -16.0627 q^{65} -3.98138 q^{66} -6.71720 q^{67} +5.99495 q^{68} +4.64075 q^{69} -2.92353 q^{70} -12.8533 q^{71} +0.335615 q^{72} +13.5286 q^{73} -0.110567 q^{74} +5.78976 q^{75} -2.43913 q^{77} -8.96831 q^{78} +2.86348 q^{79} -2.92353 q^{80} -7.88052 q^{81} -4.66775 q^{82} -5.61368 q^{83} -1.63229 q^{84} -17.5264 q^{85} -3.94660 q^{86} -7.45083 q^{87} -2.43913 q^{88} +16.1053 q^{89} -0.981180 q^{90} -5.49430 q^{91} +2.84308 q^{92} -11.8663 q^{93} +11.9233 q^{94} -1.63229 q^{96} +8.58809 q^{97} -1.00000 q^{98} -0.818610 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 2 q^{3} + 6 q^{4} - 5 q^{5} - 2 q^{6} - 6 q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 + 2 * q^3 + 6 * q^4 - 5 * q^5 - 2 * q^6 - 6 * q^7 - 6 * q^8 + 12 * q^9	\( 6 q - 6 q^{2} + 2 q^{3} + 6 q^{4} - 5 q^{5} - 2 q^{6} - 6 q^{7} - 6 q^{8} + 12 q^{9} + 5 q^{10} - 4 q^{11} + 2 q^{12} + 23 q^{13} + 6 q^{14} - 6 q^{15} + 6 q^{16} - 3 q^{17} - 12 q^{18} - 5 q^{20} - 2 q^{21} + 4 q^{22} - 4 q^{23} - 2 q^{24} + 13 q^{25} - 23 q^{26} - 4 q^{27} - 6 q^{28} + 5 q^{29} + 6 q^{30} + 12 q^{31} - 6 q^{32} + 10 q^{33} + 3 q^{34} + 5 q^{35} + 12 q^{36} + q^{37} + 4 q^{39} + 5 q^{40} + 19 q^{41} + 2 q^{42} - 2 q^{43} - 4 q^{44} - 55 q^{45} + 4 q^{46} - 12 q^{47} + 2 q^{48} + 6 q^{49} - 13 q^{50} + 44 q^{51} + 23 q^{52} - 11 q^{53} + 4 q^{54} + 28 q^{55} + 6 q^{56} - 5 q^{58} - 4 q^{59} - 6 q^{60} - q^{61} - 12 q^{62} - 12 q^{63} + 6 q^{64} - 24 q^{65} - 10 q^{66} - 14 q^{67} - 3 q^{68} + 10 q^{69} - 5 q^{70} - 8 q^{71} - 12 q^{72} + 5 q^{73} - q^{74} + 56 q^{75} + 4 q^{77} - 4 q^{78} + 30 q^{79} - 5 q^{80} + 30 q^{81} - 19 q^{82} - 12 q^{83} - 2 q^{84} - 16 q^{85} + 2 q^{86} - 14 q^{87} + 4 q^{88} + 11 q^{89} + 55 q^{90} - 23 q^{91} - 4 q^{92} + 10 q^{93} + 12 q^{94} - 2 q^{96} + 25 q^{97} - 6 q^{98} - 50 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 2 * q^3 + 6 * q^4 - 5 * q^5 - 2 * q^6 - 6 * q^7 - 6 * q^8 + 12 * q^9 + 5 * q^10 - 4 * q^11 + 2 * q^12 + 23 * q^13 + 6 * q^14 - 6 * q^15 + 6 * q^16 - 3 * q^17 - 12 * q^18 - 5 * q^20 - 2 * q^21 + 4 * q^22 - 4 * q^23 - 2 * q^24 + 13 * q^25 - 23 * q^26 - 4 * q^27 - 6 * q^28 + 5 * q^29 + 6 * q^30 + 12 * q^31 - 6 * q^32 + 10 * q^33 + 3 * q^34 + 5 * q^35 + 12 * q^36 + q^37 + 4 * q^39 + 5 * q^40 + 19 * q^41 + 2 * q^42 - 2 * q^43 - 4 * q^44 - 55 * q^45 + 4 * q^46 - 12 * q^47 + 2 * q^48 + 6 * q^49 - 13 * q^50 + 44 * q^51 + 23 * q^52 - 11 * q^53 + 4 * q^54 + 28 * q^55 + 6 * q^56 - 5 * q^58 - 4 * q^59 - 6 * q^60 - q^61 - 12 * q^62 - 12 * q^63 + 6 * q^64 - 24 * q^65 - 10 * q^66 - 14 * q^67 - 3 * q^68 + 10 * q^69 - 5 * q^70 - 8 * q^71 - 12 * q^72 + 5 * q^73 - q^74 + 56 * q^75 + 4 * q^77 - 4 * q^78 + 30 * q^79 - 5 * q^80 + 30 * q^81 - 19 * q^82 - 12 * q^83 - 2 * q^84 - 16 * q^85 + 2 * q^86 - 14 * q^87 + 4 * q^88 + 11 * q^89 + 55 * q^90 - 23 * q^91 - 4 * q^92 + 10 * q^93 + 12 * q^94 - 2 * q^96 + 25 * q^97 - 6 * q^98 - 50 * q^99

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