LMFDB - Embedded newform 5054.2.a.bc.1.1

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:	$1$
Dimension:	$6$
Coefficient field:	6.6.1528713.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 3x^{4} + 7x^{3} + 3x^{2} - 3x - 1 $ x^6 - 3x^5 - 3x^4 + 7x^3 + 3x^2 - 3*x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 266)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$0.768740$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.44476 q^{3} +1.00000 q^{4} -1.45177 q^{5} -2.44476 q^{6} -1.00000 q^{7} +1.00000 q^{8} +2.97685 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.44476 q^{3} +1.00000 q^{4} -1.45177 q^{5} -2.44476 q^{6} -1.00000 q^{7} +1.00000 q^{8} +2.97685 q^{9} -1.45177 q^{10} -0.0803156 q^{11} -2.44476 q^{12} +1.21350 q^{13} -1.00000 q^{14} +3.54924 q^{15} +1.00000 q^{16} -0.678975 q^{17} +2.97685 q^{18} -1.45177 q^{20} +2.44476 q^{21} -0.0803156 q^{22} +3.73241 q^{23} -2.44476 q^{24} -2.89235 q^{25} +1.21350 q^{26} +0.0566005 q^{27} -1.00000 q^{28} +0.545271 q^{29} +3.54924 q^{30} -4.53804 q^{31} +1.00000 q^{32} +0.196352 q^{33} -0.678975 q^{34} +1.45177 q^{35} +2.97685 q^{36} +4.15768 q^{37} -2.96671 q^{39} -1.45177 q^{40} -2.81225 q^{41} +2.44476 q^{42} -7.05367 q^{43} -0.0803156 q^{44} -4.32171 q^{45} +3.73241 q^{46} +2.51108 q^{47} -2.44476 q^{48} +1.00000 q^{49} -2.89235 q^{50} +1.65993 q^{51} +1.21350 q^{52} +11.4110 q^{53} +0.0566005 q^{54} +0.116600 q^{55} -1.00000 q^{56} +0.545271 q^{58} -5.91697 q^{59} +3.54924 q^{60} +7.79095 q^{61} -4.53804 q^{62} -2.97685 q^{63} +1.00000 q^{64} -1.76173 q^{65} +0.196352 q^{66} +7.30739 q^{67} -0.678975 q^{68} -9.12484 q^{69} +1.45177 q^{70} +10.6609 q^{71} +2.97685 q^{72} +1.07365 q^{73} +4.15768 q^{74} +7.07111 q^{75} +0.0803156 q^{77} -2.96671 q^{78} +15.0136 q^{79} -1.45177 q^{80} -9.06892 q^{81} -2.81225 q^{82} -15.2091 q^{83} +2.44476 q^{84} +0.985718 q^{85} -7.05367 q^{86} -1.33306 q^{87} -0.0803156 q^{88} +8.57008 q^{89} -4.32171 q^{90} -1.21350 q^{91} +3.73241 q^{92} +11.0944 q^{93} +2.51108 q^{94} -2.44476 q^{96} -6.23599 q^{97} +1.00000 q^{98} -0.239087 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} - 3 q^{3} + 6 q^{4} - 3 q^{5} - 3 q^{6} - 6 q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 - 3 * q^3 + 6 * q^4 - 3 * q^5 - 3 * q^6 - 6 * q^7 + 6 * q^8 - 3 * q^9	$ 6 q + 6 q^{2} - 3 q^{3} + 6 q^{4} - 3 q^{5} - 3 q^{6} - 6 q^{7} + 6 q^{8} - 3 q^{9} - 3 q^{10} + 3 q^{11} - 3 q^{12} - 6 q^{13} - 6 q^{14} + 6 q^{15} + 6 q^{16} - 9 q^{17} - 3 q^{18} - 3 q^{20} + 3 q^{21} + 3 q^{22} - 3 q^{24} + 3 q^{25} - 6 q^{26} - 3 q^{27} - 6 q^{28} - 6 q^{29} + 6 q^{30} - 3 q^{31} + 6 q^{32} - 6 q^{33} - 9 q^{34} + 3 q^{35} - 3 q^{36} + 3 q^{37} - 9 q^{39} - 3 q^{40} - 9 q^{41} + 3 q^{42} - 6 q^{43} + 3 q^{44} - 12 q^{45} + 9 q^{47} - 3 q^{48} + 6 q^{49} + 3 q^{50} + 27 q^{51} - 6 q^{52} - 6 q^{53} - 3 q^{54} - 24 q^{55} - 6 q^{56} - 6 q^{58} - 15 q^{59} + 6 q^{60} - 30 q^{61} - 3 q^{62} + 3 q^{63} + 6 q^{64} - 3 q^{65} - 6 q^{66} - 15 q^{67} - 9 q^{68} - 24 q^{69} + 3 q^{70} - 21 q^{71} - 3 q^{72} - 33 q^{73} + 3 q^{74} - 33 q^{75} - 3 q^{77} - 9 q^{78} + 30 q^{79} - 3 q^{80} - 18 q^{81} - 9 q^{82} - 33 q^{83} + 3 q^{84} - 18 q^{85} - 6 q^{86} + 15 q^{87} + 3 q^{88} + 12 q^{89} - 12 q^{90} + 6 q^{91} - 21 q^{93} + 9 q^{94} - 3 q^{96} + 18 q^{97} + 6 q^{98}+O(q^{100}) $ 6 * q + 6 * q^2 - 3 * q^3 + 6 * q^4 - 3 * q^5 - 3 * q^6 - 6 * q^7 + 6 * q^8 - 3 * q^9 - 3 * q^10 + 3 * q^11 - 3 * q^12 - 6 * q^13 - 6 * q^14 + 6 * q^15 + 6 * q^16 - 9 * q^17 - 3 * q^18 - 3 * q^20 + 3 * q^21 + 3 * q^22 - 3 * q^24 + 3 * q^25 - 6 * q^26 - 3 * q^27 - 6 * q^28 - 6 * q^29 + 6 * q^30 - 3 * q^31 + 6 * q^32 - 6 * q^33 - 9 * q^34 + 3 * q^35 - 3 * q^36 + 3 * q^37 - 9 * q^39 - 3 * q^40 - 9 * q^41 + 3 * q^42 - 6 * q^43 + 3 * q^44 - 12 * q^45 + 9 * q^47 - 3 * q^48 + 6 * q^49 + 3 * q^50 + 27 * q^51 - 6 * q^52 - 6 * q^53 - 3 * q^54 - 24 * q^55 - 6 * q^56 - 6 * q^58 - 15 * q^59 + 6 * q^60 - 30 * q^61 - 3 * q^62 + 3 * q^63 + 6 * q^64 - 3 * q^65 - 6 * q^66 - 15 * q^67 - 9 * q^68 - 24 * q^69 + 3 * q^70 - 21 * q^71 - 3 * q^72 - 33 * q^73 + 3 * q^74 - 33 * q^75 - 3 * q^77 - 9 * q^78 + 30 * q^79 - 3 * q^80 - 18 * q^81 - 9 * q^82 - 33 * q^83 + 3 * q^84 - 18 * q^85 - 6 * q^86 + 15 * q^87 + 3 * q^88 + 12 * q^89 - 12 * q^90 + 6 * q^91 - 21 * q^93 + 9 * q^94 - 3 * q^96 + 18 * q^97 + 6 * q^98

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
$3$	−2.44476	−1.41148	−0.705741	−	0.708470i	$-0.749386\pi$
$3$	−2.44476	−1.41148	−0.705741	+	0.708470i	$0.749386\pi$
$4$	1.00000	0.500000
$5$	−1.45177	−0.649253	−0.324626	−	0.945842i	$-0.605239\pi$
$5$	−1.45177	−0.649253	−0.324626	+	0.945842i	$0.605239\pi$
$6$	−2.44476	−0.998069
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	2.97685	0.992283
$10$	−1.45177	−0.459091
$11$	−0.0803156	−0.0242161	−0.0121080	−	0.999927i	$-0.503854\pi$
$11$	−0.0803156	−0.0242161	−0.0121080	+	0.999927i	$0.503854\pi$
$12$	−2.44476	−0.705741
$13$	1.21350	0.336564	0.168282	−	0.985739i	$-0.446178\pi$
$13$	1.21350	0.336564	0.168282	+	0.985739i	$0.446178\pi$
$14$	−1.00000	−0.267261
$15$	3.54924	0.916409
$16$	1.00000	0.250000
$17$	−0.678975	−0.164676	−0.0823378	−	0.996604i	$-0.526239\pi$
$17$	−0.678975	−0.164676	−0.0823378	+	0.996604i	$0.526239\pi$
$18$	2.97685	0.701650
$19$	0	0
$19$	0	0
$20$	−1.45177	−0.324626
$21$	2.44476	0.533490
$22$	−0.0803156	−0.0171233
$23$	3.73241	0.778261	0.389130	−	0.921183i	$-0.372776\pi$
$23$	3.73241	0.778261	0.389130	+	0.921183i	$0.372776\pi$
$24$	−2.44476	−0.499034
$25$	−2.89235	−0.578471
$26$	1.21350	0.237987
$27$	0.0566005	0.0108928
$28$	−1.00000	−0.188982
$29$	0.545271	0.101254	0.0506271	−	0.998718i	$-0.483878\pi$
$29$	0.545271	0.101254	0.0506271	+	0.998718i	$0.483878\pi$
$30$	3.54924	0.647999
$31$	−4.53804	−0.815057	−0.407528	−	0.913193i	$-0.633609\pi$
$31$	−4.53804	−0.815057	−0.407528	+	0.913193i	$0.633609\pi$
$32$	1.00000	0.176777
$33$	0.196352	0.0341806
$34$	−0.678975	−0.116443
$35$	1.45177	0.245394
$36$	2.97685	0.496141
$37$	4.15768	0.683518	0.341759	−	0.939788i	$-0.388977\pi$
$37$	4.15768	0.683518	0.341759	+	0.939788i	$0.388977\pi$
$38$	0	0
$39$	−2.96671	−0.475055
$40$	−1.45177	−0.229546
$41$	−2.81225	−0.439200	−0.219600	−	0.975590i	$-0.570475\pi$
$41$	−2.81225	−0.439200	−0.219600	+	0.975590i	$0.570475\pi$
$42$	2.44476	0.377235
$43$	−7.05367	−1.07567	−0.537837	−	0.843049i	$-0.680759\pi$
$43$	−7.05367	−1.07567	−0.537837	+	0.843049i	$0.680759\pi$
$44$	−0.0803156	−0.0121080
$45$	−4.32171	−0.644242
$46$	3.73241	0.550313
$47$	2.51108	0.366279	0.183139	−	0.983087i	$-0.441374\pi$
$47$	2.51108	0.366279	0.183139	+	0.983087i	$0.441374\pi$
$48$	−2.44476	−0.352871
$49$	1.00000	0.142857
$50$	−2.89235	−0.409041
$51$	1.65993	0.232437
$52$	1.21350	0.168282
$53$	11.4110	1.56742	0.783712	−	0.621124i	$-0.213324\pi$
$53$	11.4110	1.56742	0.783712	+	0.621124i	$0.213324\pi$
$54$	0.0566005	0.00770235
$55$	0.116600	0.0157224
$56$	−1.00000	−0.133631
$57$	0	0
$58$	0.545271	0.0715976
$59$	−5.91697	−0.770323	−0.385162	−	0.922849i	$-0.625854\pi$
$59$	−5.91697	−0.770323	−0.385162	+	0.922849i	$0.625854\pi$
$60$	3.54924	0.458204
$61$	7.79095	0.997529	0.498764	−	0.866738i	$-0.333787\pi$
$61$	7.79095	0.997529	0.498764	+	0.866738i	$0.333787\pi$
$62$	−4.53804	−0.576332
$63$	−2.97685	−0.375048
$64$	1.00000	0.125000
$65$	−1.76173	−0.218515
$66$	0.196352	0.0241693
$67$	7.30739	0.892740	0.446370	−	0.894848i	$-0.352716\pi$
$67$	7.30739	0.892740	0.446370	+	0.894848i	$0.352716\pi$
$68$	−0.678975	−0.0823378
$69$	−9.12484	−1.09850
$70$	1.45177	0.173520
$71$	10.6609	1.26521	0.632607	−	0.774473i	$-0.281985\pi$
$71$	10.6609	1.26521	0.632607	+	0.774473i	$0.281985\pi$
$72$	2.97685	0.350825
$73$	1.07365	0.125661	0.0628307	−	0.998024i	$-0.479987\pi$
$73$	1.07365	0.125661	0.0628307	+	0.998024i	$0.479987\pi$
$74$	4.15768	0.483320
$75$	7.07111	0.816501
$76$	0	0
$77$	0.0803156	0.00915281
$78$	−2.96671	−0.335914
$79$	15.0136	1.68916	0.844581	−	0.535428i	$-0.179849\pi$
$79$	15.0136	1.68916	0.844581	+	0.535428i	$0.179849\pi$
$80$	−1.45177	−0.162313
$81$	−9.06892	−1.00766
$82$	−2.81225	−0.310561
$83$	−15.2091	−1.66942	−0.834710	−	0.550690i	$-0.814365\pi$
$83$	−15.2091	−1.66942	−0.834710	+	0.550690i	$0.814365\pi$
$84$	2.44476	0.266745
$85$	0.985718	0.106916
$86$	−7.05367	−0.760617
$87$	−1.33306	−0.142919
$88$	−0.0803156	−0.00856167
$89$	8.57008	0.908427	0.454214	−	0.890893i	$-0.349920\pi$
$89$	8.57008	0.908427	0.454214	+	0.890893i	$0.349920\pi$
$90$	−4.32171	−0.455548
$91$	−1.21350	−0.127209
$92$	3.73241	0.389130
$93$	11.0944	1.15044
$94$	2.51108	0.258998
$95$	0	0
$96$	−2.44476	−0.249517
$97$	−6.23599	−0.633169	−0.316584	−	0.948564i	$-0.602536\pi$
$97$	−6.23599	−0.633169	−0.316584	+	0.948564i	$0.602536\pi$
$98$	1.00000	0.101015
$99$	−0.239087	−0.0240292
$100$	−2.89235	−0.289235
$101$	−7.15840	−0.712287	−0.356144	−	0.934431i	$-0.615909\pi$
$101$	−7.15840	−0.712287	−0.356144	+	0.934431i	$0.615909\pi$
$102$	1.65993	0.164358
$103$	−15.3473	−1.51222	−0.756108	−	0.654447i	$-0.772901\pi$
$103$	−15.3473	−1.51222	−0.756108	+	0.654447i	$0.772901\pi$
$104$	1.21350	0.118993
$105$	−3.54924	−0.346370
$106$	11.4110	1.10834
$107$	−17.6431	−1.70562	−0.852810	−	0.522222i	$-0.825103\pi$
$107$	−17.6431	−1.70562	−0.852810	+	0.522222i	$0.825103\pi$
$108$	0.0566005	0.00544639
$109$	−3.99537	−0.382687	−0.191344	−	0.981523i	$-0.561284\pi$
$109$	−3.99537	−0.382687	−0.191344	+	0.981523i	$0.561284\pi$
$110$	0.116600	0.0111174
$111$	−10.1645	−0.964773
$112$	−1.00000	−0.0944911
$113$	−12.9264	−1.21601	−0.608007	−	0.793932i	$-0.708031\pi$
$113$	−12.9264	−1.21601	−0.608007	+	0.793932i	$0.708031\pi$
$114$	0	0
$115$	−5.41861	−0.505288
$116$	0.545271	0.0506271
$117$	3.61240	0.333967
$118$	−5.91697	−0.544701
$119$	0.678975	0.0622415
$120$	3.54924	0.323999
$121$	−10.9935	−0.999414
$122$	7.79095	0.705359
$123$	6.87528	0.619923
$124$	−4.53804	−0.407528
$125$	11.4579	1.02483
$126$	−2.97685	−0.265199
$127$	7.03048	0.623855	0.311927	−	0.950106i	$-0.399025\pi$
$127$	7.03048	0.623855	0.311927	+	0.950106i	$0.399025\pi$
$128$	1.00000	0.0883883
$129$	17.2445	1.51830
$130$	−1.76173	−0.154514
$131$	−19.0888	−1.66779	−0.833897	−	0.551920i	$-0.813895\pi$
$131$	−19.0888	−1.66779	−0.833897	+	0.551920i	$0.813895\pi$
$132$	0.196352	0.0170903
$133$	0	0
$134$	7.30739	0.631263
$135$	−0.0821711	−0.00707216
$136$	−0.678975	−0.0582216
$137$	−20.9316	−1.78831	−0.894154	−	0.447759i	$-0.852222\pi$
$137$	−20.9316	−1.78831	−0.894154	+	0.447759i	$0.852222\pi$
$138$	−9.12484	−0.776758
$139$	−14.6240	−1.24039	−0.620196	−	0.784447i	$-0.712947\pi$
$139$	−14.6240	−1.24039	−0.620196	+	0.784447i	$0.712947\pi$
$140$	1.45177	0.122697
$141$	−6.13898	−0.516996
$142$	10.6609	0.894641
$143$	−0.0974630	−0.00815026
$144$	2.97685	0.248071
$145$	−0.791610	−0.0657396
$146$	1.07365	0.0888561
$147$	−2.44476	−0.201640
$148$	4.15768	0.341759
$149$	−6.34543	−0.519838	−0.259919	−	0.965630i	$-0.583696\pi$
$149$	−6.34543	−0.519838	−0.259919	+	0.965630i	$0.583696\pi$
$150$	7.07111	0.577354
$151$	15.9050	1.29433	0.647167	−	0.762348i	$-0.275954\pi$
$151$	15.9050	1.29433	0.647167	+	0.762348i	$0.275954\pi$
$152$	0	0
$153$	−2.02121	−0.163405
$154$	0.0803156	0.00647202
$155$	6.58821	0.529178
$156$	−2.96671	−0.237527
$157$	6.84675	0.546430	0.273215	−	0.961953i	$-0.411913\pi$
$157$	6.84675	0.546430	0.273215	+	0.961953i	$0.411913\pi$
$158$	15.0136	1.19442
$159$	−27.8972	−2.21239
$160$	−1.45177	−0.114773
$161$	−3.73241	−0.294155
$162$	−9.06892	−0.712522
$163$	−4.20329	−0.329227	−0.164614	−	0.986358i	$-0.552638\pi$
$163$	−4.20329	−0.329227	−0.164614	+	0.986358i	$0.552638\pi$
$164$	−2.81225	−0.219600
$165$	−0.285059	−0.0221918
$166$	−15.2091	−1.18046
$167$	−23.0950	−1.78715	−0.893573	−	0.448917i	$-0.851810\pi$
$167$	−23.0950	−1.78715	−0.893573	+	0.448917i	$0.851810\pi$
$168$	2.44476	0.188617
$169$	−11.5274	−0.886724
$170$	0.985718	0.0756011
$171$	0	0
$172$	−7.05367	−0.537837
$173$	10.5476	0.801918	0.400959	−	0.916096i	$-0.368677\pi$
$173$	10.5476	0.801918	0.400959	+	0.916096i	$0.368677\pi$
$174$	−1.33306	−0.101059
$175$	2.89235	0.218641
$176$	−0.0803156	−0.00605402
$177$	14.4656	1.08730
$178$	8.57008	0.642355
$179$	−6.66638	−0.498269	−0.249134	−	0.968469i	$-0.580146\pi$
$179$	−6.66638	−0.498269	−0.249134	+	0.968469i	$0.580146\pi$
$180$	−4.32171	−0.322121
$181$	0.766114	0.0569448	0.0284724	−	0.999595i	$-0.490936\pi$
$181$	0.766114	0.0569448	0.0284724	+	0.999595i	$0.490936\pi$
$182$	−1.21350	−0.0899506
$183$	−19.0470	−1.40799
$184$	3.73241	0.275157
$185$	−6.03600	−0.443776
$186$	11.0944	0.813483
$187$	0.0545323	0.00398780
$188$	2.51108	0.183139
$189$	−0.0566005	−0.00411708
$190$	0	0
$191$	10.9636	0.793299	0.396649	−	0.917970i	$-0.370173\pi$
$191$	10.9636	0.793299	0.396649	+	0.917970i	$0.370173\pi$
$192$	−2.44476	−0.176435
$193$	−1.65316	−0.118997	−0.0594986	−	0.998228i	$-0.518950\pi$
$193$	−1.65316	−0.118997	−0.0594986	+	0.998228i	$0.518950\pi$
$194$	−6.23599	−0.447718
$195$	4.30700	0.308430
$196$	1.00000	0.0714286
$197$	10.6032	0.755450	0.377725	−	0.925918i	$-0.376706\pi$
$197$	10.6032	0.755450	0.377725	+	0.925918i	$0.376706\pi$
$198$	−0.239087	−0.0169912
$199$	−27.7467	−1.96691	−0.983456	−	0.181149i	$-0.942018\pi$
$199$	−27.7467	−1.96691	−0.983456	+	0.181149i	$0.942018\pi$
$200$	−2.89235	−0.204520
$201$	−17.8648	−1.26009
$202$	−7.15840	−0.503663
$203$	−0.545271	−0.0382705
$204$	1.65993	0.116218
$205$	4.08275	0.285152
$206$	−15.3473	−1.06930
$207$	11.1108	0.772255
$208$	1.21350	0.0841411
$209$	0	0
$210$	−3.54924	−0.244921
$211$	−4.24827	−0.292463	−0.146231	−	0.989250i	$-0.546714\pi$
$211$	−4.24827	−0.292463	−0.146231	+	0.989250i	$0.546714\pi$
$212$	11.4110	0.783712
$213$	−26.0633	−1.78583
$214$	−17.6431	−1.20605
$215$	10.2403	0.698385
$216$	0.0566005	0.00385118
$217$	4.53804	0.308063
$218$	−3.99537	−0.270601
$219$	−2.62482	−0.177369
$220$	0.116600	0.00786118
$221$	−0.823936	−0.0554239
$222$	−10.1645	−0.682198
$223$	17.2029	1.15199	0.575996	−	0.817452i	$-0.304614\pi$
$223$	17.2029	1.15199	0.575996	+	0.817452i	$0.304614\pi$
$224$	−1.00000	−0.0668153
$225$	−8.61010	−0.574007
$226$	−12.9264	−0.859852
$227$	−1.43713	−0.0953859	−0.0476929	−	0.998862i	$-0.515187\pi$
$227$	−1.43713	−0.0953859	−0.0476929	+	0.998862i	$0.515187\pi$
$228$	0	0
$229$	1.16527	0.0770030	0.0385015	−	0.999259i	$-0.487742\pi$
$229$	1.16527	0.0770030	0.0385015	+	0.999259i	$0.487742\pi$
$230$	−5.41861	−0.357292
$231$	−0.196352	−0.0129190
$232$	0.545271	0.0357988
$233$	8.85252	0.579948	0.289974	−	0.957035i	$-0.406353\pi$
$233$	8.85252	0.579948	0.289974	+	0.957035i	$0.406353\pi$
$234$	3.61240	0.236150
$235$	−3.64552	−0.237807
$236$	−5.91697	−0.385162
$237$	−36.7046	−2.38422
$238$	0.678975	0.0440114
$239$	−1.33358	−0.0862624	−0.0431312	−	0.999069i	$-0.513733\pi$
$239$	−1.33358	−0.0862624	−0.0431312	+	0.999069i	$0.513733\pi$
$240$	3.54924	0.229102
$241$	18.6042	1.19840	0.599200	−	0.800600i	$-0.295486\pi$
$241$	18.6042	1.19840	0.599200	+	0.800600i	$0.295486\pi$
$242$	−10.9935	−0.706692
$243$	22.0015	1.41140
$244$	7.79095	0.498764
$245$	−1.45177	−0.0927504
$246$	6.87528	0.438352
$247$	0	0
$248$	−4.53804	−0.288166
$249$	37.1827	2.35636
$250$	11.4579	0.724662
$251$	−9.40659	−0.593739	−0.296869	−	0.954918i	$-0.595943\pi$
$251$	−9.40659	−0.593739	−0.296869	+	0.954918i	$0.595943\pi$
$252$	−2.97685	−0.187524
$253$	−0.299771	−0.0188464
$254$	7.03048	0.441132
$255$	−2.40984	−0.150910
$256$	1.00000	0.0625000
$257$	18.4316	1.14973	0.574866	−	0.818248i	$-0.305054\pi$
$257$	18.4316	1.14973	0.574866	+	0.818248i	$0.305054\pi$
$258$	17.2445	1.07360
$259$	−4.15768	−0.258345
$260$	−1.76173	−0.109258
$261$	1.62319	0.100473
$262$	−19.0888	−1.17931
$263$	4.58105	0.282480	0.141240	−	0.989975i	$-0.454891\pi$
$263$	4.58105	0.282480	0.141240	+	0.989975i	$0.454891\pi$
$264$	0.196352	0.0120847
$265$	−16.5662	−1.01765
$266$	0	0
$267$	−20.9518	−1.28223
$268$	7.30739	0.446370
$269$	−23.5661	−1.43685	−0.718426	−	0.695603i	$-0.755137\pi$
$269$	−23.5661	−1.43685	−0.718426	+	0.695603i	$0.755137\pi$
$270$	−0.0821711	−0.00500078
$271$	−16.3826	−0.995174	−0.497587	−	0.867414i	$-0.665780\pi$
$271$	−16.3826	−0.995174	−0.497587	+	0.867414i	$0.665780\pi$
$272$	−0.678975	−0.0411689
$273$	2.96671	0.179554
$274$	−20.9316	−1.26453
$275$	0.232301	0.0140083
$276$	−9.12484	−0.549251
$277$	−10.7610	−0.646563	−0.323282	−	0.946303i	$-0.604786\pi$
$277$	−10.7610	−0.646563	−0.323282	+	0.946303i	$0.604786\pi$
$278$	−14.6240	−0.877090
$279$	−13.5091	−0.808767
$280$	1.45177	0.0867600
$281$	5.09518	0.303953	0.151976	−	0.988384i	$-0.451436\pi$
$281$	5.09518	0.303953	0.151976	+	0.988384i	$0.451436\pi$
$282$	−6.13898	−0.365571
$283$	−17.7341	−1.05419	−0.527093	−	0.849808i	$-0.676718\pi$
$283$	−17.7341	−1.05419	−0.527093	+	0.849808i	$0.676718\pi$
$284$	10.6609	0.632607
$285$	0	0
$286$	−0.0974630	−0.00576311
$287$	2.81225	0.166002
$288$	2.97685	0.175412
$289$	−16.5390	−0.972882
$290$	−0.791610	−0.0464849
$291$	15.2455	0.893707
$292$	1.07365	0.0628307
$293$	−19.8843	−1.16165	−0.580825	−	0.814028i	$-0.697270\pi$
$293$	−19.8843	−1.16165	−0.580825	+	0.814028i	$0.697270\pi$
$294$	−2.44476	−0.142581
$295$	8.59009	0.500135
$296$	4.15768	0.241660
$297$	−0.00454591	−0.000263780 0
$298$	−6.34543	−0.367581
$299$	4.52927	0.261935
$300$	7.07111	0.408251
$301$	7.05367	0.406567
$302$	15.9050	0.915232
$303$	17.5006	1.00538
$304$	0	0
$305$	−11.3107	−0.647648
$306$	−2.02121	−0.115545
$307$	−30.3062	−1.72967	−0.864833	−	0.502059i	$-0.832576\pi$
$307$	−30.3062	−1.72967	−0.864833	+	0.502059i	$0.832576\pi$
$308$	0.0803156	0.00457641
$309$	37.5205	2.13447
$310$	6.58821	0.374185
$311$	11.6259	0.659243	0.329621	−	0.944113i	$-0.393079\pi$
$311$	11.6259	0.659243	0.329621	+	0.944113i	$0.393079\pi$
$312$	−2.96671	−0.167957
$313$	−27.5972	−1.55989	−0.779944	−	0.625849i	$-0.784752\pi$
$313$	−27.5972	−1.55989	−0.779944	+	0.625849i	$0.784752\pi$
$314$	6.84675	0.386385
$315$	4.32171	0.243501
$316$	15.0136	0.844581
$317$	4.00989	0.225218	0.112609	−	0.993639i	$-0.464079\pi$
$317$	4.00989	0.225218	0.112609	+	0.993639i	$0.464079\pi$
$318$	−27.8972	−1.56440
$319$	−0.0437938	−0.00245198
$320$	−1.45177	−0.0811566
$321$	43.1330	2.40745
$322$	−3.73241	−0.207999
$323$	0	0
$324$	−9.06892	−0.503829
$325$	−3.50987	−0.194693
$326$	−4.20329	−0.232799
$327$	9.76772	0.540156
$328$	−2.81225	−0.155281
$329$	−2.51108	−0.138440
$330$	−0.285059	−0.0156920
$331$	−9.40117	−0.516735	−0.258368	−	0.966047i	$-0.583185\pi$
$331$	−9.40117	−0.516735	−0.258368	+	0.966047i	$0.583185\pi$
$332$	−15.2091	−0.834710
$333$	12.3768	0.678243
$334$	−23.0950	−1.26370
$335$	−10.6087	−0.579614
$336$	2.44476	0.133373
$337$	7.21910	0.393249	0.196625	−	0.980479i	$-0.437002\pi$
$337$	7.21910	0.393249	0.196625	+	0.980479i	$0.437002\pi$
$338$	−11.5274	−0.627009
$339$	31.6019	1.71638
$340$	0.985718	0.0534580
$341$	0.364476	0.0197375
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	−7.05367	−0.380308
$345$	13.2472	0.713205
$346$	10.5476	0.567042
$347$	−12.9271	−0.693961	−0.346981	−	0.937872i	$-0.612793\pi$
$347$	−12.9271	−0.693961	−0.346981	+	0.937872i	$0.612793\pi$
$348$	−1.33306	−0.0714593
$349$	−1.44996	−0.0776144	−0.0388072	−	0.999247i	$-0.512356\pi$
$349$	−1.44996	−0.0776144	−0.0388072	+	0.999247i	$0.512356\pi$
$350$	2.89235	0.154603
$351$	0.0686847	0.00366612
$352$	−0.0803156	−0.00428084
$353$	22.9072	1.21923	0.609614	−	0.792698i	$-0.291324\pi$
$353$	22.9072	1.21923	0.609614	+	0.792698i	$0.291324\pi$
$354$	14.4656	0.768836
$355$	−15.4772	−0.821444
$356$	8.57008	0.454214
$357$	−1.65993	−0.0878528
$358$	−6.66638	−0.352329
$359$	2.58989	0.136689	0.0683447	−	0.997662i	$-0.478228\pi$
$359$	2.58989	0.136689	0.0683447	+	0.997662i	$0.478228\pi$
$360$	−4.32171	−0.227774
$361$	0	0
$362$	0.766114	0.0402661
$363$	26.8766	1.41065
$364$	−1.21350	−0.0636047
$365$	−1.55870	−0.0815861
$366$	−19.0470	−0.995602
$367$	−5.76764	−0.301068	−0.150534	−	0.988605i	$-0.548099\pi$
$367$	−5.76764	−0.301068	−0.150534	+	0.988605i	$0.548099\pi$
$368$	3.73241	0.194565
$369$	−8.37165	−0.435810
$370$	−6.03600	−0.313797
$371$	−11.4110	−0.592431
$372$	11.0944	0.575219
$373$	−16.0506	−0.831067	−0.415533	−	0.909578i	$-0.636405\pi$
$373$	−16.0506	−0.831067	−0.415533	+	0.909578i	$0.636405\pi$
$374$	0.0545323	0.00281980
$375$	−28.0118	−1.44652
$376$	2.51108	0.129499
$377$	0.661686	0.0340786
$378$	−0.0566005	−0.00291122
$379$	−33.7214	−1.73215	−0.866076	−	0.499912i	$-0.833366\pi$
$379$	−33.7214	−1.73215	−0.866076	+	0.499912i	$0.833366\pi$
$380$	0	0
$381$	−17.1878	−0.880560
$382$	10.9636	0.560947
$383$	−7.52222	−0.384367	−0.192184	−	0.981359i	$-0.561557\pi$
$383$	−7.52222	−0.384367	−0.192184	+	0.981359i	$0.561557\pi$
$384$	−2.44476	−0.124759
$385$	−0.116600	−0.00594249
$386$	−1.65316	−0.0841437
$387$	−20.9977	−1.06737
$388$	−6.23599	−0.316584
$389$	36.7396	1.86277	0.931387	−	0.364032i	$-0.118600\pi$
$389$	36.7396	1.86277	0.931387	+	0.364032i	$0.118600\pi$
$390$	4.30700	0.218093
$391$	−2.53421	−0.128161
$392$	1.00000	0.0505076
$393$	46.6675	2.35406
$394$	10.6032	0.534184
$395$	−21.7963	−1.09669
$396$	−0.239087	−0.0120146
$397$	8.01219	0.402120	0.201060	−	0.979579i	$-0.435561\pi$
$397$	8.01219	0.402120	0.201060	+	0.979579i	$0.435561\pi$
$398$	−27.7467	−1.39082
$399$	0	0
$400$	−2.89235	−0.144618
$401$	3.40160	0.169868	0.0849338	−	0.996387i	$-0.472932\pi$
$401$	3.40160	0.169868	0.0849338	+	0.996387i	$0.472932\pi$
$402$	−17.8648	−0.891016
$403$	−5.50692	−0.274319
$404$	−7.15840	−0.356144
$405$	13.1660	0.654225
$406$	−0.545271	−0.0270613
$407$	−0.333926	−0.0165521
$408$	1.65993	0.0821788
$409$	0.893474	0.0441795	0.0220897	−	0.999756i	$-0.492968\pi$
$409$	0.893474	0.0441795	0.0220897	+	0.999756i	$0.492968\pi$
$410$	4.08275	0.201633
$411$	51.1728	2.52417
$412$	−15.3473	−0.756108
$413$	5.91697	0.291155
$414$	11.1108	0.546066
$415$	22.0802	1.08388
$416$	1.21350	0.0594967
$417$	35.7522	1.75079
$418$	0	0
$419$	0.695750	0.0339896	0.0169948	−	0.999856i	$-0.494590\pi$
$419$	0.695750	0.0339896	0.0169948	+	0.999856i	$0.494590\pi$
$420$	−3.54924	−0.173185
$421$	−19.2146	−0.936460	−0.468230	−	0.883607i	$-0.655108\pi$
$421$	−19.2146	−0.936460	−0.468230	+	0.883607i	$0.655108\pi$
$422$	−4.24827	−0.206803
$423$	7.47510	0.363452
$424$	11.4110	0.554168
$425$	1.96384	0.0952600
$426$	−26.0633	−1.26277
$427$	−7.79095	−0.377030
$428$	−17.6431	−0.852810
$429$	0.238274	0.0115040
$430$	10.2403	0.493832
$431$	−33.7492	−1.62564	−0.812821	−	0.582514i	$-0.802069\pi$
$431$	−33.7492	−1.62564	−0.812821	+	0.582514i	$0.802069\pi$
$432$	0.0566005	0.00272319
$433$	−9.68445	−0.465405	−0.232703	−	0.972548i	$-0.574757\pi$
$433$	−9.68445	−0.465405	−0.232703	+	0.972548i	$0.574757\pi$
$434$	4.53804	0.217833
$435$	1.93529	0.0927903
$436$	−3.99537	−0.191344
$437$	0	0
$438$	−2.62482	−0.125419
$439$	17.7933	0.849229	0.424614	−	0.905374i	$-0.360410\pi$
$439$	17.7933	0.849229	0.424614	+	0.905374i	$0.360410\pi$
$440$	0.116600	0.00555869
$441$	2.97685	0.141755
$442$	−0.823936	−0.0391906
$443$	27.2850	1.29635	0.648175	−	0.761492i	$-0.275533\pi$
$443$	27.2850	1.29635	0.648175	+	0.761492i	$0.275533\pi$
$444$	−10.1645	−0.482387
$445$	−12.4418	−0.589799
$446$	17.2029	0.814581
$447$	15.5130	0.733742
$448$	−1.00000	−0.0472456
$449$	−27.4047	−1.29331	−0.646654	−	0.762783i	$-0.723832\pi$
$449$	−27.4047	−1.29331	−0.646654	+	0.762783i	$0.723832\pi$
$450$	−8.61010	−0.405884
$451$	0.225868	0.0106357
$452$	−12.9264	−0.608007
$453$	−38.8840	−1.82693
$454$	−1.43713	−0.0674480
$455$	1.76173	0.0825910
$456$	0	0
$457$	20.5647	0.961974	0.480987	−	0.876728i	$-0.340278\pi$
$457$	20.5647	0.961974	0.480987	+	0.876728i	$0.340278\pi$
$458$	1.16527	0.0544493
$459$	−0.0384303	−0.00179377
$460$	−5.41861	−0.252644
$461$	21.4404	0.998580	0.499290	−	0.866435i	$-0.333594\pi$
$461$	21.4404	0.998580	0.499290	+	0.866435i	$0.333594\pi$
$462$	−0.196352	−0.00913514
$463$	−18.8104	−0.874193	−0.437096	−	0.899415i	$-0.643993\pi$
$463$	−18.8104	−0.874193	−0.437096	+	0.899415i	$0.643993\pi$
$464$	0.545271	0.0253136
$465$	−16.1066	−0.746925
$466$	8.85252	0.410085
$467$	1.40243	0.0648965	0.0324482	−	0.999473i	$-0.489670\pi$
$467$	1.40243	0.0648965	0.0324482	+	0.999473i	$0.489670\pi$
$468$	3.61240	0.166983
$469$	−7.30739	−0.337424
$470$	−3.64552	−0.168155
$471$	−16.7387	−0.771277
$472$	−5.91697	−0.272350
$473$	0.566520	0.0260486
$474$	−36.7046	−1.68590
$475$	0	0
$476$	0.678975	0.0311208
$477$	33.9689	1.55533
$478$	−1.33358	−0.0609967
$479$	−16.7870	−0.767016	−0.383508	−	0.923538i	$-0.625284\pi$
$479$	−16.7870	−0.767016	−0.383508	+	0.923538i	$0.625284\pi$
$480$	3.54924	0.162000
$481$	5.04534	0.230048
$482$	18.6042	0.847396
$483$	9.12484	0.415194
$484$	−10.9935	−0.499707
$485$	9.05324	0.411087
$486$	22.0015	0.998009
$487$	−20.0438	−0.908273	−0.454136	−	0.890932i	$-0.650052\pi$
$487$	−20.0438	−0.908273	−0.454136	+	0.890932i	$0.650052\pi$
$488$	7.79095	0.352680
$489$	10.2760	0.464699
$490$	−1.45177	−0.0655844
$491$	−18.7810	−0.847575	−0.423787	−	0.905762i	$-0.639300\pi$
$491$	−18.7810	−0.847575	−0.423787	+	0.905762i	$0.639300\pi$
$492$	6.87528	0.309961
$493$	−0.370225	−0.0166741
$494$	0	0
$495$	0.347101	0.0156010
$496$	−4.53804	−0.203764
$497$	−10.6609	−0.478206
$498$	37.1827	1.66620
$499$	−21.2960	−0.953339	−0.476670	−	0.879083i	$-0.658156\pi$
$499$	−21.2960	−0.953339	−0.476670	+	0.879083i	$0.658156\pi$
$500$	11.4579	0.512413
$501$	56.4618	2.52253
$502$	−9.40659	−0.419837
$503$	−10.9258	−0.487156	−0.243578	−	0.969881i	$-0.578321\pi$
$503$	−10.9258	−0.487156	−0.243578	+	0.969881i	$0.578321\pi$
$504$	−2.97685	−0.132599
$505$	10.3924	0.462454
$506$	−0.299771	−0.0133264
$507$	28.1818	1.25160
$508$	7.03048	0.311927
$509$	12.7263	0.564083	0.282041	−	0.959402i	$-0.408988\pi$
$509$	12.7263	0.564083	0.282041	+	0.959402i	$0.408988\pi$
$510$	−2.40984	−0.106710
$511$	−1.07365	−0.0474956
$512$	1.00000	0.0441942
$513$	0	0
$514$	18.4316	0.812983
$515$	22.2808	0.981810
$516$	17.2445	0.759148
$517$	−0.201679	−0.00886983
$518$	−4.15768	−0.182678
$519$	−25.7863	−1.13189
$520$	−1.76173	−0.0772568
$521$	14.8992	0.652747	0.326373	−	0.945241i	$-0.394173\pi$
$521$	14.8992	0.652747	0.326373	+	0.945241i	$0.394173\pi$
$522$	1.62319	0.0710450
$523$	41.5824	1.81827	0.909135	−	0.416502i	$-0.136744\pi$
$523$	41.5824	1.81827	0.909135	+	0.416502i	$0.136744\pi$
$524$	−19.0888	−0.833897
$525$	−7.07111	−0.308609
$526$	4.58105	0.199743
$527$	3.08122	0.134220
$528$	0.196352	0.00854514
$529$	−9.06914	−0.394310
$530$	−16.5662	−0.719591
$531$	−17.6139	−0.764379
$532$	0	0
$533$	−3.41267	−0.147819
$534$	−20.9518	−0.906673
$535$	25.6137	1.10738
$536$	7.30739	0.315631
$537$	16.2977	0.703298
$538$	−23.5661	−1.01601
$539$	−0.0803156	−0.00345944
$540$	−0.0821711	−0.00353608
$541$	22.0056	0.946096	0.473048	−	0.881037i	$-0.343154\pi$
$541$	22.0056	0.946096	0.473048	+	0.881037i	$0.343154\pi$
$542$	−16.3826	−0.703694
$543$	−1.87297	−0.0803766
$544$	−0.678975	−0.0291108
$545$	5.80038	0.248461
$546$	2.96671	0.126964
$547$	−17.4038	−0.744132	−0.372066	−	0.928206i	$-0.621351\pi$
$547$	−17.4038	−0.744132	−0.372066	+	0.928206i	$0.621351\pi$
$548$	−20.9316	−0.894154
$549$	23.1925	0.989830
$550$	0.232301	0.00990536
$551$	0	0
$552$	−9.12484	−0.388379
$553$	−15.0136	−0.638443
$554$	−10.7610	−0.457189
$555$	14.7566	0.626382
$556$	−14.6240	−0.620196
$557$	37.7834	1.60093	0.800467	−	0.599377i	$-0.204585\pi$
$557$	37.7834	1.60093	0.800467	+	0.599377i	$0.204585\pi$
$558$	−13.5091	−0.571884
$559$	−8.55963	−0.362034
$560$	1.45177	0.0613486
$561$	−0.133318	−0.00562870
$562$	5.09518	0.214927
$563$	−8.31855	−0.350585	−0.175292	−	0.984516i	$-0.556087\pi$
$563$	−8.31855	−0.350585	−0.175292	+	0.984516i	$0.556087\pi$
$564$	−6.13898	−0.258498
$565$	18.7662	0.789500
$566$	−17.7341	−0.745422
$567$	9.06892	0.380859
$568$	10.6609	0.447321
$569$	42.6913	1.78971	0.894856	−	0.446356i	$-0.147278\pi$
$569$	42.6913	1.78971	0.894856	+	0.446356i	$0.147278\pi$
$570$	0	0
$571$	−3.42854	−0.143480	−0.0717400	−	0.997423i	$-0.522855\pi$
$571$	−3.42854	−0.143480	−0.0717400	+	0.997423i	$0.522855\pi$
$572$	−0.0974630	−0.00407513
$573$	−26.8034	−1.11973
$574$	2.81225	0.117381
$575$	−10.7954	−0.450201
$576$	2.97685	0.124035
$577$	22.0012	0.915922	0.457961	−	0.888972i	$-0.348580\pi$
$577$	22.0012	0.915922	0.457961	+	0.888972i	$0.348580\pi$
$578$	−16.5390	−0.687931
$579$	4.04158	0.167962
$580$	−0.791610	−0.0328698
$581$	15.2091	0.630982
$582$	15.2455	0.631946
$583$	−0.916484	−0.0379569
$584$	1.07365	0.0444280
$585$	−5.24439	−0.216829
$586$	−19.8843	−0.821411
$587$	−15.5324	−0.641092	−0.320546	−	0.947233i	$-0.603866\pi$
$587$	−15.5324	−0.641092	−0.320546	+	0.947233i	$0.603866\pi$
$588$	−2.44476	−0.100820
$589$	0	0
$590$	8.59009	0.353649
$591$	−25.9224	−1.06630
$592$	4.15768	0.170879
$593$	6.22377	0.255580	0.127790	−	0.991801i	$-0.459212\pi$
$593$	6.22377	0.255580	0.127790	+	0.991801i	$0.459212\pi$
$594$	−0.00454591	−0.000186521 0
$595$	−0.985718	−0.0404105
$596$	−6.34543	−0.259919
$597$	67.8340	2.77626
$598$	4.52927	0.185216
$599$	39.5458	1.61580	0.807899	−	0.589321i	$-0.200605\pi$
$599$	39.5458	1.61580	0.807899	+	0.589321i	$0.200605\pi$
$600$	7.07111	0.288677
$601$	12.3811	0.505035	0.252517	−	0.967592i	$-0.418741\pi$
$601$	12.3811	0.505035	0.252517	+	0.967592i	$0.418741\pi$
$602$	7.05367	0.287486
$603$	21.7530	0.885851
$604$	15.9050	0.647167
$605$	15.9601	0.648872
$606$	17.5006	0.710912
$607$	41.6461	1.69036	0.845182	−	0.534479i	$-0.179492\pi$
$607$	41.6461	1.69036	0.845182	+	0.534479i	$0.179492\pi$
$608$	0	0
$609$	1.33306	0.0540181
$610$	−11.3107	−0.457956
$611$	3.04719	0.123276
$612$	−2.02121	−0.0817024
$613$	−32.1557	−1.29876	−0.649378	−	0.760466i	$-0.724971\pi$
$613$	−32.1557	−1.29876	−0.649378	+	0.760466i	$0.724971\pi$
$614$	−30.3062	−1.22306
$615$	−9.98134	−0.402487
$616$	0.0803156	0.00323601
$617$	33.5408	1.35030	0.675151	−	0.737680i	$-0.264078\pi$
$617$	33.5408	1.35030	0.675151	+	0.737680i	$0.264078\pi$
$618$	37.5205	1.50929
$619$	−28.6867	−1.15302	−0.576508	−	0.817092i	$-0.695585\pi$
$619$	−28.6867	−1.15302	−0.576508	+	0.817092i	$0.695585\pi$
$620$	6.58821	0.264589
$621$	0.211256	0.00847742
$622$	11.6259	0.466155
$623$	−8.57008	−0.343353
$624$	−2.96671	−0.118764
$625$	−2.17251	−0.0869006
$626$	−27.5972	−1.10301
$627$	0	0
$628$	6.84675	0.273215
$629$	−2.82296	−0.112559
$630$	4.32171	0.172181
$631$	26.5521	1.05702	0.528510	−	0.848927i	$-0.322751\pi$
$631$	26.5521	1.05702	0.528510	+	0.848927i	$0.322751\pi$
$632$	15.0136	0.597209
$633$	10.3860	0.412806
$634$	4.00989	0.159253
$635$	−10.2067	−0.405039
$636$	−27.8972	−1.10620
$637$	1.21350	0.0480806
$638$	−0.0437938	−0.00173381
$639$	31.7358	1.25545
$640$	−1.45177	−0.0573864
$641$	−9.98354	−0.394326	−0.197163	−	0.980371i	$-0.563173\pi$
$641$	−9.98354	−0.394326	−0.197163	+	0.980371i	$0.563173\pi$
$642$	43.1330	1.70233
$643$	46.8588	1.84793	0.923965	−	0.382478i	$-0.124929\pi$
$643$	46.8588	1.84793	0.923965	+	0.382478i	$0.124929\pi$
$644$	−3.73241	−0.147077
$645$	−25.0351	−0.985758
$646$	0	0
$647$	−4.41063	−0.173400	−0.0866998	−	0.996234i	$-0.527632\pi$
$647$	−4.41063	−0.173400	−0.0866998	+	0.996234i	$0.527632\pi$
$648$	−9.06892	−0.356261
$649$	0.475225	0.0186542
$650$	−3.50987	−0.137668
$651$	−11.0944	−0.434825
$652$	−4.20329	−0.164614
$653$	8.42098	0.329538	0.164769	−	0.986332i	$-0.447312\pi$
$653$	8.42098	0.329538	0.164769	+	0.986332i	$0.447312\pi$
$654$	9.76772	0.381948
$655$	27.7126	1.08282
$656$	−2.81225	−0.109800
$657$	3.19610	0.124692
$658$	−2.51108	−0.0978921
$659$	0.152395	0.00593647	0.00296823	−	0.999996i	$-0.499055\pi$
$659$	0.152395	0.00593647	0.00296823	+	0.999996i	$0.499055\pi$
$660$	−0.285059	−0.0110959
$661$	−17.6039	−0.684713	−0.342357	−	0.939570i	$-0.611225\pi$
$661$	−17.6039	−0.684713	−0.342357	+	0.939570i	$0.611225\pi$
$662$	−9.40117	−0.365387
$663$	2.01432	0.0782299
$664$	−15.2091	−0.590229
$665$	0	0
$666$	12.3768	0.479590
$667$	2.03517	0.0788022
$668$	−23.0950	−0.893573
$669$	−42.0570	−1.62602
$670$	−10.6087	−0.409849
$671$	−0.625735	−0.0241562
$672$	2.44476	0.0943086
$673$	26.5514	1.02348	0.511740	−	0.859141i	$-0.329001\pi$
$673$	26.5514	1.02348	0.511740	+	0.859141i	$0.329001\pi$
$674$	7.21910	0.278069
$675$	−0.163709	−0.00630115
$676$	−11.5274	−0.443362
$677$	9.81351	0.377164	0.188582	−	0.982057i	$-0.439611\pi$
$677$	9.81351	0.377164	0.188582	+	0.982057i	$0.439611\pi$
$678$	31.6019	1.21367
$679$	6.23599	0.239315
$680$	0.985718	0.0378005
$681$	3.51344	0.134635
$682$	0.364476	0.0139565
$683$	20.6029	0.788348	0.394174	−	0.919036i	$-0.371031\pi$
$683$	20.6029	0.788348	0.394174	+	0.919036i	$0.371031\pi$
$684$	0	0
$685$	30.3880	1.16106
$686$	−1.00000	−0.0381802
$687$	−2.84880	−0.108688
$688$	−7.05367	−0.268919
$689$	13.8473	0.527539
$690$	13.2472	0.504312
$691$	−27.0878	−1.03047	−0.515234	−	0.857050i	$-0.672295\pi$
$691$	−27.0878	−1.03047	−0.515234	+	0.857050i	$0.672295\pi$
$692$	10.5476	0.400959
$693$	0.239087	0.00908218
$694$	−12.9271	−0.490705
$695$	21.2307	0.805328
$696$	−1.33306	−0.0505293
$697$	1.90945	0.0723255
$698$	−1.44996	−0.0548817
$699$	−21.6423	−0.818586
$700$	2.89235	0.109321
$701$	−39.2139	−1.48109	−0.740545	−	0.672007i	$-0.765433\pi$
$701$	−39.2139	−1.48109	−0.740545	+	0.672007i	$0.765433\pi$
$702$	0.0686847	0.00259234
$703$	0	0
$704$	−0.0803156	−0.00302701
$705$	8.91241	0.335661
$706$	22.9072	0.862124
$707$	7.15840	0.269219
$708$	14.4656	0.543649
$709$	−16.2725	−0.611128	−0.305564	−	0.952172i	$-0.598845\pi$
$709$	−16.2725	−0.611128	−0.305564	+	0.952172i	$0.598845\pi$
$710$	−15.4772	−0.580848
$711$	44.6932	1.67613
$712$	8.57008	0.321177
$713$	−16.9378	−0.634327
$714$	−1.65993	−0.0621213
$715$	0.141494	0.00529158
$716$	−6.66638	−0.249134
$717$	3.26029	0.121758
$718$	2.58989	0.0966539
$719$	−34.8345	−1.29911	−0.649553	−	0.760316i	$-0.725044\pi$
$719$	−34.8345	−1.29911	−0.649553	+	0.760316i	$0.725044\pi$
$720$	−4.32171	−0.161061
$721$	15.3473	0.571564
$722$	0	0
$723$	−45.4827	−1.69152
$724$	0.766114	0.0284724
$725$	−1.57712	−0.0585726
$726$	26.8766	0.997484
$727$	44.6663	1.65658	0.828290	−	0.560300i	$-0.189314\pi$
$727$	44.6663	1.65658	0.828290	+	0.560300i	$0.189314\pi$
$728$	−1.21350	−0.0449753
$729$	−26.5817	−0.984506
$730$	−1.55870	−0.0576901
$731$	4.78926	0.177137
$732$	−19.0470	−0.703997
$733$	−33.7641	−1.24710	−0.623552	−	0.781782i	$-0.714311\pi$
$733$	−33.7641	−1.24710	−0.623552	+	0.781782i	$0.714311\pi$
$734$	−5.76764	−0.212887
$735$	3.54924	0.130916
$736$	3.73241	0.137578
$737$	−0.586898	−0.0216187
$738$	−8.37165	−0.308165
$739$	−47.1751	−1.73537	−0.867683	−	0.497118i	$-0.834392\pi$
$739$	−47.1751	−1.73537	−0.867683	+	0.497118i	$0.834392\pi$
$740$	−6.03600	−0.221888
$741$	0	0
$742$	−11.4110	−0.418912
$743$	−45.6726	−1.67557	−0.837783	−	0.546003i	$-0.816149\pi$
$743$	−45.6726	−1.67557	−0.837783	+	0.546003i	$0.816149\pi$
$744$	11.0944	0.406741
$745$	9.21212	0.337506
$746$	−16.0506	−0.587653
$747$	−45.2753	−1.65654
$748$	0.0545323	0.00199390
$749$	17.6431	0.644663
$750$	−28.0118	−1.02285
$751$	−48.6627	−1.77573	−0.887864	−	0.460107i	$-0.847811\pi$
$751$	−48.6627	−1.77573	−0.887864	+	0.460107i	$0.847811\pi$
$752$	2.51108	0.0915696
$753$	22.9968	0.838052
$754$	0.661686	0.0240972
$755$	−23.0905	−0.840350
$756$	−0.0566005	−0.00205854
$757$	22.1569	0.805308	0.402654	−	0.915352i	$-0.368088\pi$
$757$	22.1569	0.805308	0.402654	+	0.915352i	$0.368088\pi$
$758$	−33.7214	−1.22482
$759$	0.732867	0.0266014
$760$	0	0
$761$	27.2552	0.988000	0.494000	−	0.869462i	$-0.335534\pi$
$761$	27.2552	0.988000	0.494000	+	0.869462i	$0.335534\pi$
$762$	−17.1878	−0.622650
$763$	3.99537	0.144642
$764$	10.9636	0.396649
$765$	2.93433	0.106091
$766$	−7.52222	−0.271789
$767$	−7.18024	−0.259263
$768$	−2.44476	−0.0882177
$769$	−40.0316	−1.44358	−0.721788	−	0.692115i	$-0.756679\pi$
$769$	−40.0316	−1.44358	−0.721788	+	0.692115i	$0.756679\pi$
$770$	−0.116600	−0.00420197
$771$	−45.0608	−1.62283
$772$	−1.65316	−0.0594986
$773$	20.6665	0.743322	0.371661	−	0.928368i	$-0.378788\pi$
$773$	20.6665	0.743322	0.371661	+	0.928368i	$0.378788\pi$
$774$	−20.9977	−0.754747
$775$	13.1256	0.471487
$776$	−6.23599	−0.223859
$777$	10.1645	0.364650
$778$	36.7396	1.31718
$779$	0	0
$780$	4.30700	0.154215
$781$	−0.856235	−0.0306385
$782$	−2.53421	−0.0906232
$783$	0.0308626	0.00110294
$784$	1.00000	0.0357143
$785$	−9.93993	−0.354771
$786$	46.6675	1.66457
$787$	28.4116	1.01276	0.506382	−	0.862309i	$-0.330983\pi$
$787$	28.4116	1.01276	0.506382	+	0.862309i	$0.330983\pi$
$788$	10.6032	0.377725
$789$	−11.1996	−0.398715
$790$	−21.7963	−0.775479
$791$	12.9264	0.459610
$792$	−0.239087	−0.00849560
$793$	9.45431	0.335732
$794$	8.01219	0.284342
$795$	40.5004	1.43640
$796$	−27.7467	−0.983456
$797$	6.49068	0.229912	0.114956	−	0.993371i	$-0.463327\pi$
$797$	6.49068	0.229912	0.114956	+	0.993371i	$0.463327\pi$
$798$	0	0
$799$	−1.70496	−0.0603171
$800$	−2.89235	−0.102260
$801$	25.5118	0.901416
$802$	3.40160	0.120115
$803$	−0.0862311	−0.00304303
$804$	−17.8648	−0.630044
$805$	5.41861	0.190981
$806$	−5.50692	−0.193973
$807$	57.6135	2.02809
$808$	−7.15840	−0.251832
$809$	18.8765	0.663664	0.331832	−	0.943338i	$-0.392333\pi$
$809$	18.8765	0.663664	0.331832	+	0.943338i	$0.392333\pi$
$810$	13.1660	0.462607
$811$	−18.1286	−0.636582	−0.318291	−	0.947993i	$-0.603109\pi$
$811$	−18.1286	−0.636582	−0.318291	+	0.947993i	$0.603109\pi$
$812$	−0.545271	−0.0191353
$813$	40.0516	1.40467
$814$	−0.333926	−0.0117041
$815$	6.10223	0.213752
$816$	1.65993	0.0581092
$817$	0	0
$818$	0.893474	0.0312396
$819$	−3.61240	−0.126228
$820$	4.08275	0.142576
$821$	3.10582	0.108394	0.0541969	−	0.998530i	$-0.482740\pi$
$821$	3.10582	0.108394	0.0541969	+	0.998530i	$0.482740\pi$
$822$	51.1728	1.78485
$823$	55.4431	1.93262	0.966312	−	0.257374i	$-0.0828574\pi$
$823$	55.4431	1.93262	0.966312	+	0.257374i	$0.0828574\pi$
$824$	−15.3473	−0.534649
$825$	−0.567921	−0.0197725
$826$	5.91697	0.205878
$827$	12.8250	0.445969	0.222985	−	0.974822i	$-0.428420\pi$
$827$	12.8250	0.445969	0.222985	+	0.974822i	$0.428420\pi$
$828$	11.1108	0.386127
$829$	1.83831	0.0638473	0.0319236	−	0.999490i	$-0.489837\pi$
$829$	1.83831	0.0638473	0.0319236	+	0.999490i	$0.489837\pi$
$830$	22.0802	0.766416
$831$	26.3080	0.912613
$832$	1.21350	0.0420705
$833$	−0.678975	−0.0235251
$834$	35.7522	1.23800
$835$	33.5287	1.16031
$836$	0	0
$837$	−0.256856	−0.00887823
$838$	0.695750	0.0240343
$839$	11.0848	0.382689	0.191345	−	0.981523i	$-0.438715\pi$
$839$	11.0848	0.382689	0.191345	+	0.981523i	$0.438715\pi$
$840$	−3.54924	−0.122460
$841$	−28.7027	−0.989748
$842$	−19.2146	−0.662178
$843$	−12.4565	−0.429024
$844$	−4.24827	−0.146231
$845$	16.7352	0.575708
$846$	7.47510	0.256999
$847$	10.9935	0.377743
$848$	11.4110	0.391856
$849$	43.3557	1.48796
$850$	1.96384	0.0673590
$851$	15.5181	0.531955
$852$	−26.0633	−0.892914
$853$	−30.9951	−1.06125	−0.530626	−	0.847606i	$-0.678043\pi$
$853$	−30.9951	−1.06125	−0.530626	+	0.847606i	$0.678043\pi$
$854$	−7.79095	−0.266601
$855$	0	0
$856$	−17.6431	−0.603027
$857$	−34.0592	−1.16344	−0.581720	−	0.813389i	$-0.697620\pi$
$857$	−34.0592	−1.16344	−0.581720	+	0.813389i	$0.697620\pi$
$858$	0.238274	0.00813452
$859$	45.5920	1.55558	0.777789	−	0.628525i	$-0.216341\pi$
$859$	45.5920	1.55558	0.777789	+	0.628525i	$0.216341\pi$
$860$	10.2403	0.349192
$861$	−6.87528	−0.234309
$862$	−33.7492	−1.14950
$863$	28.8245	0.981197	0.490598	−	0.871386i	$-0.336778\pi$
$863$	28.8245	0.981197	0.490598	+	0.871386i	$0.336778\pi$
$864$	0.0566005	0.00192559
$865$	−15.3127	−0.520647
$866$	−9.68445	−0.329091
$867$	40.4339	1.37321
$868$	4.53804	0.154031
$869$	−1.20583	−0.0409049
$870$	1.93529	0.0656126
$871$	8.86752	0.300464
$872$	−3.99537	−0.135300
$873$	−18.5636	−0.628283
$874$	0	0
$875$	−11.4579	−0.387348
$876$	−2.62482	−0.0886845
$877$	−57.7144	−1.94888	−0.974438	−	0.224657i	$-0.927874\pi$
$877$	−57.7144	−1.94888	−0.974438	+	0.224657i	$0.927874\pi$
$878$	17.7933	0.600495
$879$	48.6122	1.63965
$880$	0.116600	0.00393059
$881$	47.3155	1.59410	0.797051	−	0.603912i	$-0.206392\pi$
$881$	47.3155	1.59410	0.797051	+	0.603912i	$0.206392\pi$
$882$	2.97685	0.100236
$883$	−32.5517	−1.09545	−0.547727	−	0.836657i	$-0.684507\pi$
$883$	−32.5517	−1.09545	−0.547727	+	0.836657i	$0.684507\pi$
$884$	−0.823936	−0.0277120
$885$	−21.0007	−0.705931
$886$	27.2850	0.916658
$887$	−4.44519	−0.149255	−0.0746274	−	0.997211i	$-0.523777\pi$
$887$	−4.44519	−0.149255	−0.0746274	+	0.997211i	$0.523777\pi$
$888$	−10.1645	−0.341099
$889$	−7.03048	−0.235795
$890$	−12.4418	−0.417051
$891$	0.728376	0.0244015
$892$	17.2029	0.575996
$893$	0	0
$894$	15.5130	0.518834
$895$	9.67807	0.323502
$896$	−1.00000	−0.0334077
$897$	−11.0730	−0.369716
$898$	−27.4047	−0.914507
$899$	−2.47446	−0.0825280
$900$	−8.61010	−0.287003
$901$	−7.74780	−0.258117
$902$	0.225868	0.00752057
$903$	−17.2445	−0.573862
$904$	−12.9264	−0.429926
$905$	−1.11222	−0.0369716
$906$	−38.8840	−1.29183
$907$	−38.3731	−1.27416	−0.637079	−	0.770798i	$-0.719858\pi$
$907$	−38.3731	−1.27416	−0.637079	+	0.770798i	$0.719858\pi$
$908$	−1.43713	−0.0476929
$909$	−21.3095	−0.706790
$910$	1.76173	0.0584007
$911$	−55.3653	−1.83434	−0.917168	−	0.398502i	$-0.869530\pi$
$911$	−55.3653	−1.83434	−0.917168	+	0.398502i	$0.869530\pi$
$912$	0	0
$913$	1.22153	0.0404268
$914$	20.5647	0.680218
$915$	27.6519	0.914144
$916$	1.16527	0.0385015
$917$	19.0888	0.630367
$918$	−0.0384303	−0.00126839
$919$	−47.2743	−1.55943	−0.779717	−	0.626132i	$-0.784637\pi$
$919$	−47.2743	−1.55943	−0.779717	+	0.626132i	$0.784637\pi$
$920$	−5.41861	−0.178646
$921$	74.0914	2.44139
$922$	21.4404	0.706103
$923$	12.9370	0.425826
$924$	−0.196352	−0.00645952
$925$	−12.0255	−0.395395
$926$	−18.8104	−0.618148
$927$	−45.6866	−1.50054
$928$	0.545271	0.0178994
$929$	−26.8471	−0.880825	−0.440413	−	0.897796i	$-0.645168\pi$
$929$	−26.8471	−0.880825	−0.440413	+	0.897796i	$0.645168\pi$
$930$	−16.1066	−0.528156
$931$	0	0
$932$	8.85252	0.289974
$933$	−28.4225	−0.930509
$934$	1.40243	0.0458887
$935$	−0.0791685	−0.00258909
$936$	3.61240	0.118075
$937$	2.58764	0.0845346	0.0422673	−	0.999106i	$-0.486542\pi$
$937$	2.58764	0.0845346	0.0422673	+	0.999106i	$0.486542\pi$
$938$	−7.30739	−0.238595
$939$	67.4686	2.20175
$940$	−3.64552	−0.118904
$941$	−34.3990	−1.12138	−0.560688	−	0.828027i	$-0.689463\pi$
$941$	−34.3990	−1.12138	−0.560688	+	0.828027i	$0.689463\pi$
$942$	−16.7387	−0.545375
$943$	−10.4965	−0.341812
$944$	−5.91697	−0.192581
$945$	0.0821711	0.00267303
$946$	0.566520	0.0184191
$947$	48.8429	1.58718	0.793590	−	0.608453i	$-0.208209\pi$
$947$	48.8429	1.58718	0.793590	+	0.608453i	$0.208209\pi$
$948$	−36.7046	−1.19211
$949$	1.30288	0.0422932
$950$	0	0
$951$	−9.80322	−0.317891
$952$	0.678975	0.0220057
$953$	−2.96218	−0.0959546	−0.0479773	−	0.998848i	$-0.515278\pi$
$953$	−2.96218	−0.0959546	−0.0479773	+	0.998848i	$0.515278\pi$
$954$	33.9689	1.09978
$955$	−15.9167	−0.515052
$956$	−1.33358	−0.0431312
$957$	0.107065	0.00346093
$958$	−16.7870	−0.542362
$959$	20.9316	0.675917
$960$	3.54924	0.114551
$961$	−10.4062	−0.335682
$962$	5.04534	0.162668
$963$	−52.5207	−1.69246
$964$	18.6042	0.599200
$965$	2.40001	0.0772592
$966$	9.12484	0.293587
$967$	−22.8686	−0.735403	−0.367702	−	0.929944i	$-0.619855\pi$
$967$	−22.8686	−0.735403	−0.367702	+	0.929944i	$0.619855\pi$
$968$	−10.9935	−0.353346
$969$	0	0
$970$	9.05324	0.290682
$971$	−53.2435	−1.70866	−0.854332	−	0.519727i	$-0.826033\pi$
$971$	−53.2435	−1.70866	−0.854332	+	0.519727i	$0.826033\pi$
$972$	22.0015	0.705699
$973$	14.6240	0.468824
$974$	−20.0438	−0.642246
$975$	8.58079	0.274805
$976$	7.79095	0.249382
$977$	44.9506	1.43810	0.719049	−	0.694960i	$-0.244578\pi$
$977$	44.9506	1.43810	0.719049	+	0.694960i	$0.244578\pi$
$978$	10.2760	0.328591
$979$	−0.688312	−0.0219985
$980$	−1.45177	−0.0463752
$981$	−11.8936	−0.379734
$982$	−18.7810	−0.599326
$983$	42.4640	1.35439	0.677195	−	0.735803i	$-0.263195\pi$
$983$	42.4640	1.35439	0.677195	+	0.735803i	$0.263195\pi$
$984$	6.87528	0.219176
$985$	−15.3935	−0.490478
$986$	−0.370225	−0.0117904
$987$	6.13898	0.195406
$988$	0	0
$989$	−26.3272	−0.837155
$990$	0.347101	0.0110316
$991$	55.8881	1.77534	0.887671	−	0.460478i	$-0.152322\pi$
$991$	55.8881	1.77534	0.887671	+	0.460478i	$0.152322\pi$
$992$	−4.53804	−0.144083
$993$	22.9836	0.729363
$994$	−10.6609	−0.338143
$995$	40.2819	1.27702
$996$	37.1827	1.17818
$997$	3.38604	0.107237	0.0536185	−	0.998561i	$-0.482925\pi$
$997$	3.38604	0.107237	0.0536185	+	0.998561i	$0.482925\pi$
$998$	−21.2960	−0.674113
$999$	0.235327	0.00744540

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.bc.1.1		6
19.3	odd	18		266.2.u.b.85.2	✓	12
19.13	odd	18		266.2.u.b.169.2	yes	12
19.18	odd	2		5054.2.a.bb.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
266.2.u.b.85.2	✓	12	19.3	odd	18
266.2.u.b.169.2	yes	12	19.13	odd	18
5054.2.a.bb.1.6		6	19.18	odd	2
5054.2.a.bc.1.1		6	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:	\( N \)	\(=\)	\( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5054.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.44476 q^{3} +1.00000 q^{4} -1.45177 q^{5} -2.44476 q^{6} -1.00000 q^{7} +1.00000 q^{8} +2.97685 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.44476 q^{3} +1.00000 q^{4} -1.45177 q^{5} -2.44476 q^{6} -1.00000 q^{7} +1.00000 q^{8} +2.97685 q^{9} -1.45177 q^{10} -0.0803156 q^{11} -2.44476 q^{12} +1.21350 q^{13} -1.00000 q^{14} +3.54924 q^{15} +1.00000 q^{16} -0.678975 q^{17} +2.97685 q^{18} -1.45177 q^{20} +2.44476 q^{21} -0.0803156 q^{22} +3.73241 q^{23} -2.44476 q^{24} -2.89235 q^{25} +1.21350 q^{26} +0.0566005 q^{27} -1.00000 q^{28} +0.545271 q^{29} +3.54924 q^{30} -4.53804 q^{31} +1.00000 q^{32} +0.196352 q^{33} -0.678975 q^{34} +1.45177 q^{35} +2.97685 q^{36} +4.15768 q^{37} -2.96671 q^{39} -1.45177 q^{40} -2.81225 q^{41} +2.44476 q^{42} -7.05367 q^{43} -0.0803156 q^{44} -4.32171 q^{45} +3.73241 q^{46} +2.51108 q^{47} -2.44476 q^{48} +1.00000 q^{49} -2.89235 q^{50} +1.65993 q^{51} +1.21350 q^{52} +11.4110 q^{53} +0.0566005 q^{54} +0.116600 q^{55} -1.00000 q^{56} +0.545271 q^{58} -5.91697 q^{59} +3.54924 q^{60} +7.79095 q^{61} -4.53804 q^{62} -2.97685 q^{63} +1.00000 q^{64} -1.76173 q^{65} +0.196352 q^{66} +7.30739 q^{67} -0.678975 q^{68} -9.12484 q^{69} +1.45177 q^{70} +10.6609 q^{71} +2.97685 q^{72} +1.07365 q^{73} +4.15768 q^{74} +7.07111 q^{75} +0.0803156 q^{77} -2.96671 q^{78} +15.0136 q^{79} -1.45177 q^{80} -9.06892 q^{81} -2.81225 q^{82} -15.2091 q^{83} +2.44476 q^{84} +0.985718 q^{85} -7.05367 q^{86} -1.33306 q^{87} -0.0803156 q^{88} +8.57008 q^{89} -4.32171 q^{90} -1.21350 q^{91} +3.73241 q^{92} +11.0944 q^{93} +2.51108 q^{94} -2.44476 q^{96} -6.23599 q^{97} +1.00000 q^{98} -0.239087 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} - 3 q^{3} + 6 q^{4} - 3 q^{5} - 3 q^{6} - 6 q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 - 3 * q^3 + 6 * q^4 - 3 * q^5 - 3 * q^6 - 6 * q^7 + 6 * q^8 - 3 * q^9	\( 6 q + 6 q^{2} - 3 q^{3} + 6 q^{4} - 3 q^{5} - 3 q^{6} - 6 q^{7} + 6 q^{8} - 3 q^{9} - 3 q^{10} + 3 q^{11} - 3 q^{12} - 6 q^{13} - 6 q^{14} + 6 q^{15} + 6 q^{16} - 9 q^{17} - 3 q^{18} - 3 q^{20} + 3 q^{21} + 3 q^{22} - 3 q^{24} + 3 q^{25} - 6 q^{26} - 3 q^{27} - 6 q^{28} - 6 q^{29} + 6 q^{30} - 3 q^{31} + 6 q^{32} - 6 q^{33} - 9 q^{34} + 3 q^{35} - 3 q^{36} + 3 q^{37} - 9 q^{39} - 3 q^{40} - 9 q^{41} + 3 q^{42} - 6 q^{43} + 3 q^{44} - 12 q^{45} + 9 q^{47} - 3 q^{48} + 6 q^{49} + 3 q^{50} + 27 q^{51} - 6 q^{52} - 6 q^{53} - 3 q^{54} - 24 q^{55} - 6 q^{56} - 6 q^{58} - 15 q^{59} + 6 q^{60} - 30 q^{61} - 3 q^{62} + 3 q^{63} + 6 q^{64} - 3 q^{65} - 6 q^{66} - 15 q^{67} - 9 q^{68} - 24 q^{69} + 3 q^{70} - 21 q^{71} - 3 q^{72} - 33 q^{73} + 3 q^{74} - 33 q^{75} - 3 q^{77} - 9 q^{78} + 30 q^{79} - 3 q^{80} - 18 q^{81} - 9 q^{82} - 33 q^{83} + 3 q^{84} - 18 q^{85} - 6 q^{86} + 15 q^{87} + 3 q^{88} + 12 q^{89} - 12 q^{90} + 6 q^{91} - 21 q^{93} + 9 q^{94} - 3 q^{96} + 18 q^{97} + 6 q^{98}+O(q^{100}) \) 6 * q + 6 * q^2 - 3 * q^3 + 6 * q^4 - 3 * q^5 - 3 * q^6 - 6 * q^7 + 6 * q^8 - 3 * q^9 - 3 * q^10 + 3 * q^11 - 3 * q^12 - 6 * q^13 - 6 * q^14 + 6 * q^15 + 6 * q^16 - 9 * q^17 - 3 * q^18 - 3 * q^20 + 3 * q^21 + 3 * q^22 - 3 * q^24 + 3 * q^25 - 6 * q^26 - 3 * q^27 - 6 * q^28 - 6 * q^29 + 6 * q^30 - 3 * q^31 + 6 * q^32 - 6 * q^33 - 9 * q^34 + 3 * q^35 - 3 * q^36 + 3 * q^37 - 9 * q^39 - 3 * q^40 - 9 * q^41 + 3 * q^42 - 6 * q^43 + 3 * q^44 - 12 * q^45 + 9 * q^47 - 3 * q^48 + 6 * q^49 + 3 * q^50 + 27 * q^51 - 6 * q^52 - 6 * q^53 - 3 * q^54 - 24 * q^55 - 6 * q^56 - 6 * q^58 - 15 * q^59 + 6 * q^60 - 30 * q^61 - 3 * q^62 + 3 * q^63 + 6 * q^64 - 3 * q^65 - 6 * q^66 - 15 * q^67 - 9 * q^68 - 24 * q^69 + 3 * q^70 - 21 * q^71 - 3 * q^72 - 33 * q^73 + 3 * q^74 - 33 * q^75 - 3 * q^77 - 9 * q^78 + 30 * q^79 - 3 * q^80 - 18 * q^81 - 9 * q^82 - 33 * q^83 + 3 * q^84 - 18 * q^85 - 6 * q^86 + 15 * q^87 + 3 * q^88 + 12 * q^89 - 12 * q^90 + 6 * q^91 - 21 * q^93 + 9 * q^94 - 3 * q^96 + 18 * q^97 + 6 * q^98

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