LMFDB - Embedded newform 5054.2.a.bm.1.2

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:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 24 x^{10} + 68 x^{9} + 213 x^{8} - 555 x^{7} - 814 x^{6} + 1911 x^{5} + 1005 x^{4} + \cdots + 1 $ x^12 - 3x^11 - 24x^10 + 68x^9 + 213x^8 - 555x^7 - 814x^6 + 1911x^5 + 1005x^4 - 2326x^3 + 570x^2 + 105*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
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			1.2
Root			$-2.59018$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.59018 q^{3} +1.00000 q^{4} +3.85497 q^{5} -2.59018 q^{6} +1.00000 q^{7} +1.00000 q^{8} +3.70904 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.59018 q^{3} +1.00000 q^{4} +3.85497 q^{5} -2.59018 q^{6} +1.00000 q^{7} +1.00000 q^{8} +3.70904 q^{9} +3.85497 q^{10} +5.26154 q^{11} -2.59018 q^{12} -2.42924 q^{13} +1.00000 q^{14} -9.98506 q^{15} +1.00000 q^{16} -3.44274 q^{17} +3.70904 q^{18} +3.85497 q^{20} -2.59018 q^{21} +5.26154 q^{22} -5.54344 q^{23} -2.59018 q^{24} +9.86076 q^{25} -2.42924 q^{26} -1.83655 q^{27} +1.00000 q^{28} +9.13075 q^{29} -9.98506 q^{30} +6.65254 q^{31} +1.00000 q^{32} -13.6283 q^{33} -3.44274 q^{34} +3.85497 q^{35} +3.70904 q^{36} -0.133845 q^{37} +6.29218 q^{39} +3.85497 q^{40} -6.10171 q^{41} -2.59018 q^{42} +9.10961 q^{43} +5.26154 q^{44} +14.2982 q^{45} -5.54344 q^{46} +2.28429 q^{47} -2.59018 q^{48} +1.00000 q^{49} +9.86076 q^{50} +8.91732 q^{51} -2.42924 q^{52} -5.31740 q^{53} -1.83655 q^{54} +20.2830 q^{55} +1.00000 q^{56} +9.13075 q^{58} -6.81470 q^{59} -9.98506 q^{60} -1.44924 q^{61} +6.65254 q^{62} +3.70904 q^{63} +1.00000 q^{64} -9.36464 q^{65} -13.6283 q^{66} +5.82537 q^{67} -3.44274 q^{68} +14.3585 q^{69} +3.85497 q^{70} +8.66200 q^{71} +3.70904 q^{72} +9.83354 q^{73} -0.133845 q^{74} -25.5412 q^{75} +5.26154 q^{77} +6.29218 q^{78} +0.632146 q^{79} +3.85497 q^{80} -6.37014 q^{81} -6.10171 q^{82} -5.21626 q^{83} -2.59018 q^{84} -13.2716 q^{85} +9.10961 q^{86} -23.6503 q^{87} +5.26154 q^{88} -2.58645 q^{89} +14.2982 q^{90} -2.42924 q^{91} -5.54344 q^{92} -17.2313 q^{93} +2.28429 q^{94} -2.59018 q^{96} +1.58507 q^{97} +1.00000 q^{98} +19.5153 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 3 q^{3} + 12 q^{4} + 3 q^{5} + 3 q^{6} + 12 q^{7} + 12 q^{8} + 21 q^{9}+O(q^{10}) $ 12 * q + 12 * q^2 + 3 * q^3 + 12 * q^4 + 3 * q^5 + 3 * q^6 + 12 * q^7 + 12 * q^8 + 21 * q^9	\( 12 q + 12 q^{2} + 3 q^{3} + 12 q^{4} + 3 q^{5} + 3 q^{6} + 12 q^{7} + 12 q^{8} + 21 q^{9} + 3 q^{10} + 3 q^{11} + 3 q^{12} - 6 q^{13} + 12 q^{14} - 6 q^{15} + 12 q^{16} + 3 q^{17} + 21 q^{18} + 3 q^{20} + 3 q^{21} + 3 q^{22} + 12 q^{23} + 3 q^{24} + 33 q^{25} - 6 q^{26} + 21 q^{27} + 12 q^{28} + 6 q^{29} - 6 q^{30} + 3 q^{31} + 12 q^{32} - 6 q^{33} + 3 q^{34} + 3 q^{35} + 21 q^{36} + 27 q^{37} + 27 q^{39} + 3 q^{40} - 27 q^{41} + 3 q^{42} + 30 q^{43} + 3 q^{44} + 30 q^{45} + 12 q^{46} + 21 q^{47} + 3 q^{48} + 12 q^{49} + 33 q^{50} + 3 q^{51} - 6 q^{52} + 6 q^{53} + 21 q^{54} + 48 q^{55} + 12 q^{56} + 6 q^{58} - 27 q^{59} - 6 q^{60} + 18 q^{61} + 3 q^{62} + 21 q^{63} + 12 q^{64} - 9 q^{65} - 6 q^{66} + 9 q^{67} + 3 q^{68} + 18 q^{69} + 3 q^{70} + 27 q^{71} + 21 q^{72} - 9 q^{73} + 27 q^{74} + 33 q^{75} + 3 q^{77} + 27 q^{78} - 12 q^{79} + 3 q^{80} + 24 q^{81} - 27 q^{82} + 9 q^{83} + 3 q^{84} + 78 q^{85} + 30 q^{86} - 45 q^{87} + 3 q^{88} - 24 q^{89} + 30 q^{90} - 6 q^{91} + 12 q^{92} + 3 q^{93} + 21 q^{94} + 3 q^{96} - 18 q^{97} + 12 q^{98} + 48 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 3 * q^3 + 12 * q^4 + 3 * q^5 + 3 * q^6 + 12 * q^7 + 12 * q^8 + 21 * q^9 + 3 * q^10 + 3 * q^11 + 3 * q^12 - 6 * q^13 + 12 * q^14 - 6 * q^15 + 12 * q^16 + 3 * q^17 + 21 * q^18 + 3 * q^20 + 3 * q^21 + 3 * q^22 + 12 * q^23 + 3 * q^24 + 33 * q^25 - 6 * q^26 + 21 * q^27 + 12 * q^28 + 6 * q^29 - 6 * q^30 + 3 * q^31 + 12 * q^32 - 6 * q^33 + 3 * q^34 + 3 * q^35 + 21 * q^36 + 27 * q^37 + 27 * q^39 + 3 * q^40 - 27 * q^41 + 3 * q^42 + 30 * q^43 + 3 * q^44 + 30 * q^45 + 12 * q^46 + 21 * q^47 + 3 * q^48 + 12 * q^49 + 33 * q^50 + 3 * q^51 - 6 * q^52 + 6 * q^53 + 21 * q^54 + 48 * q^55 + 12 * q^56 + 6 * q^58 - 27 * q^59 - 6 * q^60 + 18 * q^61 + 3 * q^62 + 21 * q^63 + 12 * q^64 - 9 * q^65 - 6 * q^66 + 9 * q^67 + 3 * q^68 + 18 * q^69 + 3 * q^70 + 27 * q^71 + 21 * q^72 - 9 * q^73 + 27 * q^74 + 33 * q^75 + 3 * q^77 + 27 * q^78 - 12 * q^79 + 3 * q^80 + 24 * q^81 - 27 * q^82 + 9 * q^83 + 3 * q^84 + 78 * q^85 + 30 * q^86 - 45 * q^87 + 3 * q^88 - 24 * q^89 + 30 * q^90 - 6 * q^91 + 12 * q^92 + 3 * q^93 + 21 * q^94 + 3 * q^96 - 18 * q^97 + 12 * q^98 + 48 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.59018	−1.49544	−0.747721	−	0.664013i	$-0.768852\pi$
$3$	−2.59018	−1.49544	−0.747721	+	0.664013i	$0.768852\pi$
$4$	1.00000	0.500000
$5$	3.85497	1.72399	0.861996	−	0.506914i	$-0.169214\pi$
$5$	3.85497	1.72399	0.861996	+	0.506914i	$0.169214\pi$
$6$	−2.59018	−1.05744
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	3.70904	1.23635
$10$	3.85497	1.21905
$11$	5.26154	1.58641	0.793207	−	0.608953i	$-0.208410\pi$
$11$	5.26154	1.58641	0.793207	+	0.608953i	$0.208410\pi$
$12$	−2.59018	−0.747721
$13$	−2.42924	−0.673750	−0.336875	−	0.941549i	$-0.609370\pi$
$13$	−2.42924	−0.673750	−0.336875	+	0.941549i	$0.609370\pi$
$14$	1.00000	0.267261
$15$	−9.98506	−2.57813
$16$	1.00000	0.250000
$17$	−3.44274	−0.834987	−0.417494	−	0.908680i	$-0.637091\pi$
$17$	−3.44274	−0.834987	−0.417494	+	0.908680i	$0.637091\pi$
$18$	3.70904	0.874229
$19$	0	0
$19$	0	0
$20$	3.85497	0.861996
$21$	−2.59018	−0.565224
$22$	5.26154	1.12176
$23$	−5.54344	−1.15589	−0.577943	−	0.816077i	$-0.696145\pi$
$23$	−5.54344	−1.15589	−0.577943	+	0.816077i	$0.696145\pi$
$24$	−2.59018	−0.528719
$25$	9.86076	1.97215
$26$	−2.42924	−0.476413
$27$	−1.83655	−0.353443
$28$	1.00000	0.188982
$29$	9.13075	1.69554	0.847769	−	0.530365i	$-0.177945\pi$
$29$	9.13075	1.69554	0.847769	+	0.530365i	$0.177945\pi$
$30$	−9.98506	−1.82301
$31$	6.65254	1.19483	0.597416	−	0.801932i	$-0.296194\pi$
$31$	6.65254	1.19483	0.597416	+	0.801932i	$0.296194\pi$
$32$	1.00000	0.176777
$33$	−13.6283	−2.37239
$34$	−3.44274	−0.590425
$35$	3.85497	0.651608
$36$	3.70904	0.618174
$37$	−0.133845	−0.0220039	−0.0110020	−	0.999939i	$-0.503502\pi$
$37$	−0.133845	−0.0220039	−0.0110020	+	0.999939i	$0.503502\pi$
$38$	0	0
$39$	6.29218	1.00755
$40$	3.85497	0.609524
$41$	−6.10171	−0.952926	−0.476463	−	0.879194i	$-0.658081\pi$
$41$	−6.10171	−0.952926	−0.476463	+	0.879194i	$0.658081\pi$
$42$	−2.59018	−0.399674
$43$	9.10961	1.38920	0.694601	−	0.719395i	$-0.255581\pi$
$43$	9.10961	1.38920	0.694601	+	0.719395i	$0.255581\pi$
$44$	5.26154	0.793207
$45$	14.2982	2.13145
$46$	−5.54344	−0.817335
$47$	2.28429	0.333198	0.166599	−	0.986025i	$-0.446721\pi$
$47$	2.28429	0.333198	0.166599	+	0.986025i	$0.446721\pi$
$48$	−2.59018	−0.373861
$49$	1.00000	0.142857
$50$	9.86076	1.39452
$51$	8.91732	1.24867
$52$	−2.42924	−0.336875
$53$	−5.31740	−0.730402	−0.365201	−	0.930929i	$-0.619000\pi$
$53$	−5.31740	−0.730402	−0.365201	+	0.930929i	$0.619000\pi$
$54$	−1.83655	−0.249922
$55$	20.2830	2.73497
$56$	1.00000	0.133631
$57$	0	0
$58$	9.13075	1.19893
$59$	−6.81470	−0.887198	−0.443599	−	0.896225i	$-0.646299\pi$
$59$	−6.81470	−0.887198	−0.443599	+	0.896225i	$0.646299\pi$
$60$	−9.98506	−1.28907
$61$	−1.44924	−0.185556	−0.0927779	−	0.995687i	$-0.529575\pi$
$61$	−1.44924	−0.185556	−0.0927779	+	0.995687i	$0.529575\pi$
$62$	6.65254	0.844873
$63$	3.70904	0.467295
$64$	1.00000	0.125000
$65$	−9.36464	−1.16154
$66$	−13.6283	−1.67753
$67$	5.82537	0.711682	0.355841	−	0.934547i	$-0.384195\pi$
$67$	5.82537	0.711682	0.355841	+	0.934547i	$0.384195\pi$
$68$	−3.44274	−0.417494
$69$	14.3585	1.72856
$70$	3.85497	0.460756
$71$	8.66200	1.02799	0.513995	−	0.857793i	$-0.328165\pi$
$71$	8.66200	1.02799	0.513995	+	0.857793i	$0.328165\pi$
$72$	3.70904	0.437115
$73$	9.83354	1.15093	0.575464	−	0.817827i	$-0.304821\pi$
$73$	9.83354	1.15093	0.575464	+	0.817827i	$0.304821\pi$
$74$	−0.133845	−0.0155591
$75$	−25.5412	−2.94924
$76$	0	0
$77$	5.26154	0.599608
$78$	6.29218	0.712449
$79$	0.632146	0.0711220	0.0355610	−	0.999368i	$-0.488678\pi$
$79$	0.632146	0.0711220	0.0355610	+	0.999368i	$0.488678\pi$
$80$	3.85497	0.430998
$81$	−6.37014	−0.707793
$82$	−6.10171	−0.673821
$83$	−5.21626	−0.572559	−0.286279	−	0.958146i	$-0.592419\pi$
$83$	−5.21626	−0.572559	−0.286279	+	0.958146i	$0.592419\pi$
$84$	−2.59018	−0.282612
$85$	−13.2716	−1.43951
$86$	9.10961	0.982314
$87$	−23.6503	−2.53558
$88$	5.26154	0.560882
$89$	−2.58645	−0.274163	−0.137082	−	0.990560i	$-0.543772\pi$
$89$	−2.58645	−0.274163	−0.137082	+	0.990560i	$0.543772\pi$
$90$	14.2982	1.50717
$91$	−2.42924	−0.254654
$92$	−5.54344	−0.577943
$93$	−17.2313	−1.78680
$94$	2.28429	0.235607
$95$	0	0
$96$	−2.59018	−0.264359
$97$	1.58507	0.160939	0.0804697	−	0.996757i	$-0.474358\pi$
$97$	1.58507	0.160939	0.0804697	+	0.996757i	$0.474358\pi$
$98$	1.00000	0.101015
$99$	19.5153	1.96136
$100$	9.86076	0.986076
$101$	−11.9532	−1.18939	−0.594693	−	0.803953i	$-0.702726\pi$
$101$	−11.9532	−1.18939	−0.594693	+	0.803953i	$0.702726\pi$
$102$	8.91732	0.882946
$103$	12.2367	1.20572	0.602859	−	0.797848i	$-0.294028\pi$
$103$	12.2367	1.20572	0.602859	+	0.797848i	$0.294028\pi$
$104$	−2.42924	−0.238207
$105$	−9.98506	−0.974442
$106$	−5.31740	−0.516472
$107$	−6.13537	−0.593128	−0.296564	−	0.955013i	$-0.595841\pi$
$107$	−6.13537	−0.593128	−0.296564	+	0.955013i	$0.595841\pi$
$108$	−1.83655	−0.176722
$109$	−15.0996	−1.44628	−0.723140	−	0.690701i	$-0.757302\pi$
$109$	−15.0996	−1.44628	−0.723140	+	0.690701i	$0.757302\pi$
$110$	20.2830	1.93391
$111$	0.346682	0.0329056
$112$	1.00000	0.0944911
$113$	0.664656	0.0625256	0.0312628	−	0.999511i	$-0.490047\pi$
$113$	0.664656	0.0625256	0.0312628	+	0.999511i	$0.490047\pi$
$114$	0	0
$115$	−21.3698	−1.99274
$116$	9.13075	0.847769
$117$	−9.01016	−0.832989
$118$	−6.81470	−0.627344
$119$	−3.44274	−0.315595
$120$	−9.98506	−0.911507
$121$	16.6838	1.51671
$122$	−1.44924	−0.131208
$123$	15.8045	1.42505
$124$	6.65254	0.597416
$125$	18.7381	1.67598
$126$	3.70904	0.330428
$127$	−20.3966	−1.80990	−0.904952	−	0.425513i	$-0.860094\pi$
$127$	−20.3966	−1.80990	−0.904952	+	0.425513i	$0.860094\pi$
$128$	1.00000	0.0883883
$129$	−23.5955	−2.07747
$130$	−9.36464	−0.821333
$131$	7.30369	0.638126	0.319063	−	0.947733i	$-0.396632\pi$
$131$	7.30369	0.638126	0.319063	+	0.947733i	$0.396632\pi$
$132$	−13.6283	−1.18619
$133$	0	0
$134$	5.82537	0.503235
$135$	−7.07982	−0.609334
$136$	−3.44274	−0.295213
$137$	4.75134	0.405935	0.202967	−	0.979186i	$-0.434941\pi$
$137$	4.75134	0.405935	0.202967	+	0.979186i	$0.434941\pi$
$138$	14.3585	1.22228
$139$	−1.38913	−0.117825	−0.0589124	−	0.998263i	$-0.518763\pi$
$139$	−1.38913	−0.117825	−0.0589124	+	0.998263i	$0.518763\pi$
$140$	3.85497	0.325804
$141$	−5.91673	−0.498278
$142$	8.66200	0.726899
$143$	−12.7815	−1.06885
$144$	3.70904	0.309087
$145$	35.1987	2.92310
$146$	9.83354	0.813829
$147$	−2.59018	−0.213635
$148$	−0.133845	−0.0110020
$149$	0.0788590	0.00646038	0.00323019	−	0.999995i	$-0.498972\pi$
$149$	0.0788590	0.00646038	0.00323019	+	0.999995i	$0.498972\pi$
$150$	−25.5412	−2.08543
$151$	22.7246	1.84930	0.924650	−	0.380818i	$-0.124358\pi$
$151$	22.7246	1.84930	0.924650	+	0.380818i	$0.124358\pi$
$152$	0	0
$153$	−12.7693	−1.03233
$154$	5.26154	0.423987
$155$	25.6453	2.05988
$156$	6.29218	0.503777
$157$	−20.1279	−1.60638	−0.803192	−	0.595720i	$-0.796867\pi$
$157$	−20.1279	−1.60638	−0.803192	+	0.595720i	$0.796867\pi$
$158$	0.632146	0.0502908
$159$	13.7730	1.09227
$160$	3.85497	0.304762
$161$	−5.54344	−0.436884
$162$	−6.37014	−0.500485
$163$	9.55162	0.748141	0.374070	−	0.927400i	$-0.377962\pi$
$163$	9.55162	0.748141	0.374070	+	0.927400i	$0.377962\pi$
$164$	−6.10171	−0.476463
$165$	−52.5368	−4.08998
$166$	−5.21626	−0.404860
$167$	2.50415	0.193777	0.0968884	−	0.995295i	$-0.469111\pi$
$167$	2.50415	0.193777	0.0968884	+	0.995295i	$0.469111\pi$
$168$	−2.59018	−0.199837
$169$	−7.09879	−0.546061
$170$	−13.2716	−1.01789
$171$	0	0
$172$	9.10961	0.694601
$173$	2.54024	0.193131	0.0965655	−	0.995327i	$-0.469214\pi$
$173$	2.54024	0.193131	0.0965655	+	0.995327i	$0.469214\pi$
$174$	−23.6503	−1.79293
$175$	9.86076	0.745403
$176$	5.26154	0.396603
$177$	17.6513	1.32675
$178$	−2.58645	−0.193863
$179$	24.1642	1.80611	0.903057	−	0.429520i	$-0.141317\pi$
$179$	24.1642	1.80611	0.903057	+	0.429520i	$0.141317\pi$
$180$	14.2982	1.06573
$181$	8.17918	0.607954	0.303977	−	0.952679i	$-0.401685\pi$
$181$	8.17918	0.607954	0.303977	+	0.952679i	$0.401685\pi$
$182$	−2.42924	−0.180067
$183$	3.75379	0.277488
$184$	−5.54344	−0.408668
$185$	−0.515966	−0.0379346
$186$	−17.2313	−1.26346
$187$	−18.1141	−1.32463
$188$	2.28429	0.166599
$189$	−1.83655	−0.133589
$190$	0	0
$191$	9.30589	0.673350	0.336675	−	0.941621i	$-0.390698\pi$
$191$	9.30589	0.673350	0.336675	+	0.941621i	$0.390698\pi$
$192$	−2.59018	−0.186930
$193$	−2.84390	−0.204709	−0.102354	−	0.994748i	$-0.532638\pi$
$193$	−2.84390	−0.204709	−0.102354	+	0.994748i	$0.532638\pi$
$194$	1.58507	0.113801
$195$	24.2561	1.73702
$196$	1.00000	0.0714286
$197$	−13.3152	−0.948666	−0.474333	−	0.880345i	$-0.657311\pi$
$197$	−13.3152	−0.948666	−0.474333	+	0.880345i	$0.657311\pi$
$198$	19.5153	1.38689
$199$	4.89238	0.346811	0.173406	−	0.984850i	$-0.444523\pi$
$199$	4.89238	0.346811	0.173406	+	0.984850i	$0.444523\pi$
$200$	9.86076	0.697261
$201$	−15.0888	−1.06428
$202$	−11.9532	−0.841023
$203$	9.13075	0.640853
$204$	8.91732	0.624337
$205$	−23.5219	−1.64284
$206$	12.2367	0.852572
$207$	−20.5608	−1.42908
$208$	−2.42924	−0.168438
$209$	0	0
$210$	−9.98506	−0.689035
$211$	−1.11001	−0.0764162	−0.0382081	−	0.999270i	$-0.512165\pi$
$211$	−1.11001	−0.0764162	−0.0382081	+	0.999270i	$0.512165\pi$
$212$	−5.31740	−0.365201
$213$	−22.4361	−1.53730
$214$	−6.13537	−0.419405
$215$	35.1172	2.39498
$216$	−1.83655	−0.124961
$217$	6.65254	0.451604
$218$	−15.0996	−1.02267
$219$	−25.4707	−1.72115
$220$	20.2830	1.36748
$221$	8.36325	0.562573
$222$	0.346682	0.0232678
$223$	8.47642	0.567623	0.283812	−	0.958880i	$-0.408401\pi$
$223$	8.47642	0.567623	0.283812	+	0.958880i	$0.408401\pi$
$224$	1.00000	0.0668153
$225$	36.5740	2.43826
$226$	0.664656	0.0442123
$227$	−15.9103	−1.05601	−0.528003	−	0.849243i	$-0.677059\pi$
$227$	−15.9103	−1.05601	−0.528003	+	0.849243i	$0.677059\pi$
$228$	0	0
$229$	−15.4908	−1.02366	−0.511831	−	0.859086i	$-0.671033\pi$
$229$	−15.4908	−1.02366	−0.511831	+	0.859086i	$0.671033\pi$
$230$	−21.3698	−1.40908
$231$	−13.6283	−0.896679
$232$	9.13075	0.599463
$233$	16.4647	1.07864	0.539321	−	0.842100i	$-0.318681\pi$
$233$	16.4647	1.07864	0.539321	+	0.842100i	$0.318681\pi$
$234$	−9.01016	−0.589012
$235$	8.80586	0.574431
$236$	−6.81470	−0.443599
$237$	−1.63737	−0.106359
$238$	−3.44274	−0.223160
$239$	13.5299	0.875174	0.437587	−	0.899176i	$-0.355833\pi$
$239$	13.5299	0.875174	0.437587	+	0.899176i	$0.355833\pi$
$240$	−9.98506	−0.644533
$241$	7.36721	0.474564	0.237282	−	0.971441i	$-0.423743\pi$
$241$	7.36721	0.474564	0.237282	+	0.971441i	$0.423743\pi$
$242$	16.6838	1.07247
$243$	22.0094	1.41191
$244$	−1.44924	−0.0927779
$245$	3.85497	0.246285
$246$	15.8045	1.00766
$247$	0	0
$248$	6.65254	0.422437
$249$	13.5111	0.856228
$250$	18.7381	1.18510
$251$	−6.78791	−0.428449	−0.214225	−	0.976784i	$-0.568722\pi$
$251$	−6.78791	−0.428449	−0.214225	+	0.976784i	$0.568722\pi$
$252$	3.70904	0.233648
$253$	−29.1670	−1.83371
$254$	−20.3966	−1.27980
$255$	34.3760	2.15271
$256$	1.00000	0.0625000
$257$	−0.876680	−0.0546858	−0.0273429	−	0.999626i	$-0.508705\pi$
$257$	−0.876680	−0.0546858	−0.0273429	+	0.999626i	$0.508705\pi$
$258$	−23.5955	−1.46899
$259$	−0.133845	−0.00831670
$260$	−9.36464	−0.580770
$261$	33.8663	2.09627
$262$	7.30369	0.451223
$263$	−12.2648	−0.756280	−0.378140	−	0.925749i	$-0.623436\pi$
$263$	−12.2648	−0.756280	−0.378140	+	0.925749i	$0.623436\pi$
$264$	−13.6283	−0.838766
$265$	−20.4984	−1.25921
$266$	0	0
$267$	6.69938	0.409996
$268$	5.82537	0.355841
$269$	23.0604	1.40602	0.703010	−	0.711180i	$-0.251839\pi$
$269$	23.0604	1.40602	0.703010	+	0.711180i	$0.251839\pi$
$270$	−7.07982	−0.430864
$271$	7.05003	0.428259	0.214129	−	0.976805i	$-0.431309\pi$
$271$	7.05003	0.428259	0.214129	+	0.976805i	$0.431309\pi$
$272$	−3.44274	−0.208747
$273$	6.29218	0.380820
$274$	4.75134	0.287039
$275$	51.8827	3.12865
$276$	14.3585	0.864281
$277$	−7.26044	−0.436237	−0.218119	−	0.975922i	$-0.569992\pi$
$277$	−7.26044	−0.436237	−0.218119	+	0.975922i	$0.569992\pi$
$278$	−1.38913	−0.0833147
$279$	24.6745	1.47723
$280$	3.85497	0.230378
$281$	−4.00948	−0.239185	−0.119593	−	0.992823i	$-0.538159\pi$
$281$	−4.00948	−0.239185	−0.119593	+	0.992823i	$0.538159\pi$
$282$	−5.91673	−0.352336
$283$	13.3577	0.794035	0.397018	−	0.917811i	$-0.370045\pi$
$283$	13.3577	0.794035	0.397018	+	0.917811i	$0.370045\pi$
$284$	8.66200	0.513995
$285$	0	0
$286$	−12.7815	−0.755789
$287$	−6.10171	−0.360172
$288$	3.70904	0.218557
$289$	−5.14754	−0.302797
$290$	35.1987	2.06694
$291$	−4.10562	−0.240676
$292$	9.83354	0.575464
$293$	11.3498	0.663060	0.331530	−	0.943445i	$-0.392435\pi$
$293$	11.3498	0.663060	0.331530	+	0.943445i	$0.392435\pi$
$294$	−2.59018	−0.151062
$295$	−26.2704	−1.52952
$296$	−0.133845	−0.00777956
$297$	−9.66305	−0.560707
$298$	0.0788590	0.00456818
$299$	13.4663	0.778779
$300$	−25.5412	−1.47462
$301$	9.10961	0.525069
$302$	22.7246	1.30765
$303$	30.9609	1.77866
$304$	0	0
$305$	−5.58676	−0.319897
$306$	−12.7693	−0.729970
$307$	−14.9605	−0.853839	−0.426919	−	0.904290i	$-0.640401\pi$
$307$	−14.9605	−0.853839	−0.426919	+	0.904290i	$0.640401\pi$
$308$	5.26154	0.299804
$309$	−31.6953	−1.80308
$310$	25.6453	1.45656
$311$	−23.4236	−1.32823	−0.664117	−	0.747629i	$-0.731192\pi$
$311$	−23.4236	−1.32823	−0.664117	+	0.747629i	$0.731192\pi$
$312$	6.29218	0.356224
$313$	13.6994	0.774335	0.387168	−	0.922009i	$-0.373453\pi$
$313$	13.6994	0.774335	0.387168	+	0.922009i	$0.373453\pi$
$314$	−20.1279	−1.13589
$315$	14.2982	0.805614
$316$	0.632146	0.0355610
$317$	−0.754813	−0.0423945	−0.0211972	−	0.999775i	$-0.506748\pi$
$317$	−0.754813	−0.0423945	−0.0211972	+	0.999775i	$0.506748\pi$
$318$	13.7730	0.772354
$319$	48.0418	2.68982
$320$	3.85497	0.215499
$321$	15.8917	0.886989
$322$	−5.54344	−0.308924
$323$	0	0
$324$	−6.37014	−0.353897
$325$	−23.9542	−1.32874
$326$	9.55162	0.529015
$327$	39.1107	2.16283
$328$	−6.10171	−0.336910
$329$	2.28429	0.125937
$330$	−52.5368	−2.89205
$331$	26.1190	1.43563	0.717816	−	0.696233i	$-0.245142\pi$
$331$	26.1190	1.43563	0.717816	+	0.696233i	$0.245142\pi$
$332$	−5.21626	−0.286279
$333$	−0.496435	−0.0272045
$334$	2.50415	0.137021
$335$	22.4566	1.22693
$336$	−2.59018	−0.141306
$337$	16.9598	0.923860	0.461930	−	0.886916i	$-0.347157\pi$
$337$	16.9598	0.923860	0.461930	+	0.886916i	$0.347157\pi$
$338$	−7.09879	−0.386123
$339$	−1.72158	−0.0935034
$340$	−13.2716	−0.719756
$341$	35.0026	1.89550
$342$	0	0
$343$	1.00000	0.0539949
$344$	9.10961	0.491157
$345$	55.3516	2.98003
$346$	2.54024	0.136564
$347$	−25.9705	−1.39417	−0.697084	−	0.716989i	$-0.745520\pi$
$347$	−25.9705	−1.39417	−0.697084	+	0.716989i	$0.745520\pi$
$348$	−23.6503	−1.26779
$349$	28.3067	1.51522	0.757611	−	0.652707i	$-0.226367\pi$
$349$	28.3067	1.51522	0.757611	+	0.652707i	$0.226367\pi$
$350$	9.86076	0.527080
$351$	4.46141	0.238133
$352$	5.26154	0.280441
$353$	−14.5191	−0.772774	−0.386387	−	0.922337i	$-0.626277\pi$
$353$	−14.5191	−0.772774	−0.386387	+	0.922337i	$0.626277\pi$
$354$	17.6513	0.938156
$355$	33.3917	1.77225
$356$	−2.58645	−0.137082
$357$	8.91732	0.471955
$358$	24.1642	1.27712
$359$	31.0871	1.64071	0.820357	−	0.571852i	$-0.193775\pi$
$359$	31.0871	1.64071	0.820357	+	0.571852i	$0.193775\pi$
$360$	14.2982	0.753583
$361$	0	0
$362$	8.17918	0.429888
$363$	−43.2140	−2.26815
$364$	−2.42924	−0.127327
$365$	37.9079	1.98419
$366$	3.75379	0.196214
$367$	−34.4540	−1.79849	−0.899243	−	0.437450i	$-0.855882\pi$
$367$	−34.4540	−1.79849	−0.899243	+	0.437450i	$0.855882\pi$
$368$	−5.54344	−0.288972
$369$	−22.6315	−1.17815
$370$	−0.515966	−0.0268238
$371$	−5.31740	−0.276066
$372$	−17.2313	−0.893401
$373$	22.3117	1.15526	0.577628	−	0.816300i	$-0.303978\pi$
$373$	22.3117	1.15526	0.577628	+	0.816300i	$0.303978\pi$
$374$	−18.1141	−0.936658
$375$	−48.5350	−2.50633
$376$	2.28429	0.117803
$377$	−22.1808	−1.14237
$378$	−1.83655	−0.0944617
$379$	−10.5330	−0.541043	−0.270521	−	0.962714i	$-0.587196\pi$
$379$	−10.5330	−0.541043	−0.270521	+	0.962714i	$0.587196\pi$
$380$	0	0
$381$	52.8309	2.70661
$382$	9.30589	0.476131
$383$	9.54782	0.487871	0.243935	−	0.969792i	$-0.421562\pi$
$383$	9.54782	0.487871	0.243935	+	0.969792i	$0.421562\pi$
$384$	−2.59018	−0.132180
$385$	20.2830	1.03372
$386$	−2.84390	−0.144751
$387$	33.7879	1.71754
$388$	1.58507	0.0804697
$389$	24.6556	1.25009	0.625044	−	0.780590i	$-0.285081\pi$
$389$	24.6556	1.25009	0.625044	+	0.780590i	$0.285081\pi$
$390$	24.2561	1.22826
$391$	19.0846	0.965150
$392$	1.00000	0.0505076
$393$	−18.9179	−0.954281
$394$	−13.3152	−0.670808
$395$	2.43690	0.122614
$396$	19.5153	0.980679
$397$	−26.8591	−1.34802	−0.674011	−	0.738722i	$-0.735430\pi$
$397$	−26.8591	−1.34802	−0.674011	+	0.738722i	$0.735430\pi$
$398$	4.89238	0.245233
$399$	0	0
$400$	9.86076	0.493038
$401$	−16.3538	−0.816668	−0.408334	−	0.912833i	$-0.633890\pi$
$401$	−16.3538	−0.816668	−0.408334	+	0.912833i	$0.633890\pi$
$402$	−15.0888	−0.752559
$403$	−16.1606	−0.805018
$404$	−11.9532	−0.594693
$405$	−24.5567	−1.22023
$406$	9.13075	0.453152
$407$	−0.704228	−0.0349073
$408$	8.91732	0.441473
$409$	−22.6251	−1.11874	−0.559369	−	0.828919i	$-0.688957\pi$
$409$	−22.6251	−1.11874	−0.559369	+	0.828919i	$0.688957\pi$
$410$	−23.5219	−1.16166
$411$	−12.3068	−0.607052
$412$	12.2367	0.602859
$413$	−6.81470	−0.335329
$414$	−20.5608	−1.01051
$415$	−20.1085	−0.987087
$416$	−2.42924	−0.119103
$417$	3.59811	0.176200
$418$	0	0
$419$	26.9109	1.31468	0.657342	−	0.753593i	$-0.271681\pi$
$419$	26.9109	1.31468	0.657342	+	0.753593i	$0.271681\pi$
$420$	−9.98506	−0.487221
$421$	−27.3720	−1.33403	−0.667016	−	0.745043i	$-0.732429\pi$
$421$	−27.3720	−1.33403	−0.667016	+	0.745043i	$0.732429\pi$
$422$	−1.11001	−0.0540344
$423$	8.47253	0.411948
$424$	−5.31740	−0.258236
$425$	−33.9480	−1.64672
$426$	−22.4361	−1.08703
$427$	−1.44924	−0.0701335
$428$	−6.13537	−0.296564
$429$	33.1065	1.59840
$430$	35.1172	1.69350
$431$	−0.123924	−0.00596922	−0.00298461	−	0.999996i	$-0.500950\pi$
$431$	−0.123924	−0.00596922	−0.00298461	+	0.999996i	$0.500950\pi$
$432$	−1.83655	−0.0883608
$433$	10.1248	0.486569	0.243284	−	0.969955i	$-0.421775\pi$
$433$	10.1248	0.486569	0.243284	+	0.969955i	$0.421775\pi$
$434$	6.65254	0.319332
$435$	−91.1711	−4.37132
$436$	−15.0996	−0.723140
$437$	0	0
$438$	−25.4707	−1.21703
$439$	−4.61529	−0.220276	−0.110138	−	0.993916i	$-0.535129\pi$
$439$	−4.61529	−0.220276	−0.110138	+	0.993916i	$0.535129\pi$
$440$	20.2830	0.966956
$441$	3.70904	0.176621
$442$	8.36325	0.397799
$443$	−39.7691	−1.88949	−0.944744	−	0.327808i	$-0.893690\pi$
$443$	−39.7691	−1.88949	−0.944744	+	0.327808i	$0.893690\pi$
$444$	0.346682	0.0164528
$445$	−9.97069	−0.472656
$446$	8.47642	0.401370
$447$	−0.204259	−0.00966112
$448$	1.00000	0.0472456
$449$	−17.9749	−0.848288	−0.424144	−	0.905595i	$-0.639425\pi$
$449$	−17.9749	−0.848288	−0.424144	+	0.905595i	$0.639425\pi$
$450$	36.5740	1.72411
$451$	−32.1044	−1.51174
$452$	0.664656	0.0312628
$453$	−58.8608	−2.76552
$454$	−15.9103	−0.746709
$455$	−9.36464	−0.439021
$456$	0	0
$457$	16.1400	0.754996	0.377498	−	0.926010i	$-0.376785\pi$
$457$	16.1400	0.754996	0.377498	+	0.926010i	$0.376785\pi$
$458$	−15.4908	−0.723839
$459$	6.32275	0.295121
$460$	−21.3698	−0.996370
$461$	41.9269	1.95273	0.976366	−	0.216125i	$-0.0693418\pi$
$461$	41.9269	1.95273	0.976366	+	0.216125i	$0.0693418\pi$
$462$	−13.6283	−0.634048
$463$	21.3569	0.992539	0.496270	−	0.868168i	$-0.334703\pi$
$463$	21.3569	0.992539	0.496270	+	0.868168i	$0.334703\pi$
$464$	9.13075	0.423885
$465$	−66.4260	−3.08043
$466$	16.4647	0.762715
$467$	−29.3462	−1.35798	−0.678991	−	0.734147i	$-0.737582\pi$
$467$	−29.3462	−1.35798	−0.678991	+	0.734147i	$0.737582\pi$
$468$	−9.01016	−0.416495
$469$	5.82537	0.268990
$470$	8.80586	0.406184
$471$	52.1350	2.40226
$472$	−6.81470	−0.313672
$473$	47.9305	2.20385
$474$	−1.63737	−0.0752070
$475$	0	0
$476$	−3.44274	−0.157798
$477$	−19.7225	−0.903030
$478$	13.5299	0.618841
$479$	31.4867	1.43867	0.719333	−	0.694666i	$-0.244448\pi$
$479$	31.4867	1.43867	0.719333	+	0.694666i	$0.244448\pi$
$480$	−9.98506	−0.455754
$481$	0.325141	0.0148251
$482$	7.36721	0.335567
$483$	14.3585	0.653335
$484$	16.6838	0.758353
$485$	6.11039	0.277458
$486$	22.0094	0.998369
$487$	−13.8409	−0.627190	−0.313595	−	0.949557i	$-0.601533\pi$
$487$	−13.8409	−0.627190	−0.313595	+	0.949557i	$0.601533\pi$
$488$	−1.44924	−0.0656039
$489$	−24.7404	−1.11880
$490$	3.85497	0.174150
$491$	−26.2987	−1.18684	−0.593422	−	0.804892i	$-0.702223\pi$
$491$	−26.2987	−1.18684	−0.593422	+	0.804892i	$0.702223\pi$
$492$	15.8045	0.712523
$493$	−31.4348	−1.41575
$494$	0	0
$495$	75.2306	3.38137
$496$	6.65254	0.298708
$497$	8.66200	0.388544
$498$	13.5111	0.605445
$499$	−7.72963	−0.346026	−0.173013	−	0.984920i	$-0.555350\pi$
$499$	−7.72963	−0.346026	−0.173013	+	0.984920i	$0.555350\pi$
$500$	18.7381	0.837991
$501$	−6.48620	−0.289782
$502$	−6.78791	−0.302959
$503$	−30.9042	−1.37795	−0.688974	−	0.724786i	$-0.741939\pi$
$503$	−30.9042	−1.37795	−0.688974	+	0.724786i	$0.741939\pi$
$504$	3.70904	0.165214
$505$	−46.0791	−2.05049
$506$	−29.1670	−1.29663
$507$	18.3871	0.816602
$508$	−20.3966	−0.904952
$509$	−19.4917	−0.863953	−0.431976	−	0.901885i	$-0.642184\pi$
$509$	−19.4917	−0.863953	−0.431976	+	0.901885i	$0.642184\pi$
$510$	34.3760	1.52219
$511$	9.83354	0.435010
$512$	1.00000	0.0441942
$513$	0	0
$514$	−0.876680	−0.0386687
$515$	47.1721	2.07865
$516$	−23.5955	−1.03874
$517$	12.0189	0.528590
$518$	−0.133845	−0.00588079
$519$	−6.57969	−0.288816
$520$	−9.36464	−0.410667
$521$	−7.57763	−0.331982	−0.165991	−	0.986127i	$-0.553082\pi$
$521$	−7.57763	−0.331982	−0.165991	+	0.986127i	$0.553082\pi$
$522$	33.8663	1.48229
$523$	−23.6027	−1.03207	−0.516037	−	0.856566i	$-0.672593\pi$
$523$	−23.6027	−1.03207	−0.516037	+	0.856566i	$0.672593\pi$
$524$	7.30369	0.319063
$525$	−25.5412	−1.11471
$526$	−12.2648	−0.534770
$527$	−22.9030	−0.997669
$528$	−13.6283	−0.593097
$529$	7.72970	0.336074
$530$	−20.4984	−0.890394
$531$	−25.2760	−1.09688
$532$	0	0
$533$	14.8225	0.642034
$534$	6.69938	0.289911
$535$	−23.6516	−1.02255
$536$	5.82537	0.251617
$537$	−62.5896	−2.70094
$538$	23.0604	0.994206
$539$	5.26154	0.226630
$540$	−7.07982	−0.304667
$541$	6.91102	0.297128	0.148564	−	0.988903i	$-0.452535\pi$
$541$	6.91102	0.297128	0.148564	+	0.988903i	$0.452535\pi$
$542$	7.05003	0.302825
$543$	−21.1856	−0.909160
$544$	−3.44274	−0.147606
$545$	−58.2085	−2.49338
$546$	6.29218	0.269280
$547$	8.55630	0.365841	0.182920	−	0.983128i	$-0.441445\pi$
$547$	8.55630	0.365841	0.182920	+	0.983128i	$0.441445\pi$
$548$	4.75134	0.202967
$549$	−5.37528	−0.229411
$550$	51.8827	2.21229
$551$	0	0
$552$	14.3585	0.611139
$553$	0.632146	0.0268816
$554$	−7.26044	−0.308466
$555$	1.33645	0.0567290
$556$	−1.38913	−0.0589124
$557$	20.3153	0.860788	0.430394	−	0.902641i	$-0.358375\pi$
$557$	20.3153	0.860788	0.430394	+	0.902641i	$0.358375\pi$
$558$	24.6745	1.04456
$559$	−22.1294	−0.935976
$560$	3.85497	0.162902
$561$	46.9188	1.98091
$562$	−4.00948	−0.169130
$563$	12.8562	0.541822	0.270911	−	0.962604i	$-0.412675\pi$
$563$	12.8562	0.541822	0.270911	+	0.962604i	$0.412675\pi$
$564$	−5.91673	−0.249139
$565$	2.56223	0.107794
$566$	13.3577	0.561468
$567$	−6.37014	−0.267521
$568$	8.66200	0.363449
$569$	41.6674	1.74679	0.873395	−	0.487013i	$-0.161914\pi$
$569$	41.6674	1.74679	0.873395	+	0.487013i	$0.161914\pi$
$570$	0	0
$571$	−17.0664	−0.714207	−0.357104	−	0.934065i	$-0.616236\pi$
$571$	−17.0664	−0.714207	−0.357104	+	0.934065i	$0.616236\pi$
$572$	−12.7815	−0.534423
$573$	−24.1039	−1.00696
$574$	−6.10171	−0.254680
$575$	−54.6625	−2.27958
$576$	3.70904	0.154543
$577$	−35.3060	−1.46981	−0.734903	−	0.678172i	$-0.762773\pi$
$577$	−35.3060	−1.46981	−0.734903	+	0.678172i	$0.762773\pi$
$578$	−5.14754	−0.214109
$579$	7.36623	0.306130
$580$	35.1987	1.46155
$581$	−5.21626	−0.216407
$582$	−4.10562	−0.170183
$583$	−27.9777	−1.15872
$584$	9.83354	0.406915
$585$	−34.7338	−1.43607
$586$	11.3498	0.468854
$587$	11.9624	0.493743	0.246871	−	0.969048i	$-0.420597\pi$
$587$	11.9624	0.493743	0.246871	+	0.969048i	$0.420597\pi$
$588$	−2.59018	−0.106817
$589$	0	0
$590$	−26.2704	−1.08154
$591$	34.4887	1.41868
$592$	−0.133845	−0.00550098
$593$	0.0763758	0.00313638	0.00156819	−	0.999999i	$-0.499501\pi$
$593$	0.0763758	0.00313638	0.00156819	+	0.999999i	$0.499501\pi$
$594$	−9.66305	−0.396480
$595$	−13.2716	−0.544084
$596$	0.0788590	0.00323019
$597$	−12.6721	−0.518636
$598$	13.4663	0.550680
$599$	3.65710	0.149425	0.0747126	−	0.997205i	$-0.476196\pi$
$599$	3.65710	0.149425	0.0747126	+	0.997205i	$0.476196\pi$
$600$	−25.5412	−1.04271
$601$	−47.6454	−1.94349	−0.971747	−	0.236024i	$-0.924156\pi$
$601$	−47.6454	−1.94349	−0.971747	+	0.236024i	$0.924156\pi$
$602$	9.10961	0.371280
$603$	21.6065	0.879885
$604$	22.7246	0.924650
$605$	64.3154	2.61479
$606$	30.9609	1.25770
$607$	−2.55177	−0.103573	−0.0517865	−	0.998658i	$-0.516492\pi$
$607$	−2.55177	−0.103573	−0.0517865	+	0.998658i	$0.516492\pi$
$608$	0	0
$609$	−23.6503	−0.958359
$610$	−5.58676	−0.226201
$611$	−5.54909	−0.224492
$612$	−12.7693	−0.516167
$613$	8.11179	0.327632	0.163816	−	0.986491i	$-0.447620\pi$
$613$	8.11179	0.327632	0.163816	+	0.986491i	$0.447620\pi$
$614$	−14.9605	−0.603755
$615$	60.9259	2.45677
$616$	5.26154	0.211993
$617$	3.51434	0.141482	0.0707411	−	0.997495i	$-0.477464\pi$
$617$	3.51434	0.141482	0.0707411	+	0.997495i	$0.477464\pi$
$618$	−31.6953	−1.27497
$619$	1.47148	0.0591438	0.0295719	−	0.999563i	$-0.490586\pi$
$619$	1.47148	0.0591438	0.0295719	+	0.999563i	$0.490586\pi$
$620$	25.6453	1.02994
$621$	10.1808	0.408540
$622$	−23.4236	−0.939203
$623$	−2.58645	−0.103624
$624$	6.29218	0.251889
$625$	22.9308	0.917230
$626$	13.6994	0.547538
$627$	0	0
$628$	−20.1279	−0.803192
$629$	0.460792	0.0183730
$630$	14.2982	0.569655
$631$	−15.9826	−0.636259	−0.318129	−	0.948047i	$-0.603055\pi$
$631$	−15.9826	−0.636259	−0.318129	+	0.948047i	$0.603055\pi$
$632$	0.632146	0.0251454
$633$	2.87513	0.114276
$634$	−0.754813	−0.0299774
$635$	−78.6282	−3.12026
$636$	13.7730	0.546137
$637$	−2.42924	−0.0962500
$638$	48.0418	1.90199
$639$	32.1277	1.27095
$640$	3.85497	0.152381
$641$	−13.6192	−0.537925	−0.268963	−	0.963151i	$-0.586681\pi$
$641$	−13.6192	−0.537925	−0.268963	+	0.963151i	$0.586681\pi$
$642$	15.8917	0.627196
$643$	13.3215	0.525349	0.262674	−	0.964885i	$-0.415396\pi$
$643$	13.3215	0.525349	0.262674	+	0.964885i	$0.415396\pi$
$644$	−5.54344	−0.218442
$645$	−90.9600	−3.58155
$646$	0	0
$647$	−46.5654	−1.83068	−0.915338	−	0.402686i	$-0.868077\pi$
$647$	−46.5654	−1.83068	−0.915338	+	0.402686i	$0.868077\pi$
$648$	−6.37014	−0.250243
$649$	−35.8558	−1.40746
$650$	−23.9542	−0.939559
$651$	−17.2313	−0.675347
$652$	9.55162	0.374070
$653$	−8.65255	−0.338601	−0.169300	−	0.985565i	$-0.554151\pi$
$653$	−8.65255	−0.338601	−0.169300	+	0.985565i	$0.554151\pi$
$654$	39.1107	1.52935
$655$	28.1555	1.10012
$656$	−6.10171	−0.238232
$657$	36.4730	1.42295
$658$	2.28429	0.0890509
$659$	46.8035	1.82321	0.911603	−	0.411072i	$-0.134846\pi$
$659$	46.8035	1.82321	0.911603	+	0.411072i	$0.134846\pi$
$660$	−52.5368	−2.04499
$661$	−39.7454	−1.54592	−0.772959	−	0.634456i	$-0.781224\pi$
$661$	−39.7454	−1.54592	−0.772959	+	0.634456i	$0.781224\pi$
$662$	26.1190	1.01515
$663$	−21.6623	−0.841295
$664$	−5.21626	−0.202430
$665$	0	0
$666$	−0.496435	−0.0192365
$667$	−50.6158	−1.95985
$668$	2.50415	0.0968884
$669$	−21.9555	−0.848847
$670$	22.4566	0.867573
$671$	−7.62522	−0.294368
$672$	−2.59018	−0.0999184
$673$	29.7783	1.14787	0.573934	−	0.818902i	$-0.305417\pi$
$673$	29.7783	1.14787	0.573934	+	0.818902i	$0.305417\pi$
$674$	16.9598	0.653268
$675$	−18.1097	−0.697044
$676$	−7.09879	−0.273030
$677$	8.51839	0.327388	0.163694	−	0.986511i	$-0.447659\pi$
$677$	8.51839	0.327388	0.163694	+	0.986511i	$0.447659\pi$
$678$	−1.72158	−0.0661169
$679$	1.58507	0.0608294
$680$	−13.2716	−0.508944
$681$	41.2106	1.57919
$682$	35.0026	1.34032
$683$	−3.66707	−0.140317	−0.0701583	−	0.997536i	$-0.522350\pi$
$683$	−3.66707	−0.140317	−0.0701583	+	0.997536i	$0.522350\pi$
$684$	0	0
$685$	18.3163	0.699829
$686$	1.00000	0.0381802
$687$	40.1241	1.53083
$688$	9.10961	0.347301
$689$	12.9173	0.492108
$690$	55.3516	2.10720
$691$	14.7839	0.562408	0.281204	−	0.959648i	$-0.409266\pi$
$691$	14.7839	0.562408	0.281204	+	0.959648i	$0.409266\pi$
$692$	2.54024	0.0965655
$693$	19.5153	0.741323
$694$	−25.9705	−0.985826
$695$	−5.35506	−0.203129
$696$	−23.6503	−0.896463
$697$	21.0066	0.795681
$698$	28.3067	1.07142
$699$	−42.6467	−1.61305
$700$	9.86076	0.372702
$701$	−6.43598	−0.243083	−0.121542	−	0.992586i	$-0.538784\pi$
$701$	−6.43598	−0.243083	−0.121542	+	0.992586i	$0.538784\pi$
$702$	4.46141	0.168385
$703$	0	0
$704$	5.26154	0.198302
$705$	−22.8088	−0.859029
$706$	−14.5191	−0.546433
$707$	−11.9532	−0.449546
$708$	17.6513	0.663377
$709$	27.1462	1.01950	0.509749	−	0.860323i	$-0.329738\pi$
$709$	27.1462	1.01950	0.509749	+	0.860323i	$0.329738\pi$
$710$	33.3917	1.25317
$711$	2.34466	0.0879314
$712$	−2.58645	−0.0969314
$713$	−36.8779	−1.38109
$714$	8.91732	0.333722
$715$	−49.2724	−1.84268
$716$	24.1642	0.903057
$717$	−35.0448	−1.30877
$718$	31.0871	1.16016
$719$	4.00423	0.149333	0.0746663	−	0.997209i	$-0.476211\pi$
$719$	4.00423	0.149333	0.0746663	+	0.997209i	$0.476211\pi$
$720$	14.2982	0.532863
$721$	12.2367	0.455719
$722$	0	0
$723$	−19.0824	−0.709683
$724$	8.17918	0.303977
$725$	90.0361	3.34386
$726$	−43.2140	−1.60382
$727$	24.8798	0.922741	0.461370	−	0.887208i	$-0.347358\pi$
$727$	24.8798	0.922741	0.461370	+	0.887208i	$0.347358\pi$
$728$	−2.42924	−0.0900337
$729$	−37.8981	−1.40363
$730$	37.9079	1.40304
$731$	−31.3620	−1.15997
$732$	3.75379	0.138744
$733$	20.1589	0.744587	0.372294	−	0.928115i	$-0.378571\pi$
$733$	20.1589	0.744587	0.372294	+	0.928115i	$0.378571\pi$
$734$	−34.4540	−1.27172
$735$	−9.98506	−0.368305
$736$	−5.54344	−0.204334
$737$	30.6504	1.12902
$738$	−22.6315	−0.833076
$739$	40.3315	1.48362	0.741809	−	0.670611i	$-0.233968\pi$
$739$	40.3315	1.48362	0.741809	+	0.670611i	$0.233968\pi$
$740$	−0.515966	−0.0189673
$741$	0	0
$742$	−5.31740	−0.195208
$743$	29.2525	1.07317	0.536584	−	0.843847i	$-0.319714\pi$
$743$	29.2525	1.07317	0.536584	+	0.843847i	$0.319714\pi$
$744$	−17.2313	−0.631730
$745$	0.303999	0.0111376
$746$	22.3117	0.816889
$747$	−19.3473	−0.707881
$748$	−18.1141	−0.662317
$749$	−6.13537	−0.224181
$750$	−48.5350	−1.77225
$751$	5.92477	0.216198	0.108099	−	0.994140i	$-0.465524\pi$
$751$	5.92477	0.216198	0.108099	+	0.994140i	$0.465524\pi$
$752$	2.28429	0.0832995
$753$	17.5819	0.640721
$754$	−22.1808	−0.807777
$755$	87.6025	3.18818
$756$	−1.83655	−0.0667945
$757$	−38.6449	−1.40457	−0.702286	−	0.711895i	$-0.747837\pi$
$757$	−38.6449	−1.40457	−0.702286	+	0.711895i	$0.747837\pi$
$758$	−10.5330	−0.382575
$759$	75.5478	2.74221
$760$	0	0
$761$	−14.0315	−0.508641	−0.254320	−	0.967120i	$-0.581852\pi$
$761$	−14.0315	−0.508641	−0.254320	+	0.967120i	$0.581852\pi$
$762$	52.8309	1.91386
$763$	−15.0996	−0.546642
$764$	9.30589	0.336675
$765$	−49.2251	−1.77974
$766$	9.54782	0.344977
$767$	16.5545	0.597750
$768$	−2.59018	−0.0934651
$769$	−54.1340	−1.95212	−0.976060	−	0.217500i	$-0.930210\pi$
$769$	−54.1340	−1.95212	−0.976060	+	0.217500i	$0.930210\pi$
$770$	20.2830	0.730950
$771$	2.27076	0.0817795
$772$	−2.84390	−0.102354
$773$	−28.1833	−1.01368	−0.506842	−	0.862039i	$-0.669187\pi$
$773$	−28.1833	−1.01368	−0.506842	+	0.862039i	$0.669187\pi$
$774$	33.7879	1.21448
$775$	65.5991	2.35639
$776$	1.58507	0.0569007
$777$	0.346682	0.0124371
$778$	24.6556	0.883945
$779$	0	0
$780$	24.2561	0.868508
$781$	45.5754	1.63082
$782$	19.0846	0.682464
$783$	−16.7690	−0.599277
$784$	1.00000	0.0357143
$785$	−77.5925	−2.76940
$786$	−18.9179	−0.674778
$787$	−34.1495	−1.21730	−0.608649	−	0.793440i	$-0.708288\pi$
$787$	−34.1495	−1.21730	−0.608649	+	0.793440i	$0.708288\pi$
$788$	−13.3152	−0.474333
$789$	31.7680	1.13097
$790$	2.43690	0.0867010
$791$	0.664656	0.0236325
$792$	19.5153	0.693445
$793$	3.52055	0.125018
$794$	−26.8591	−0.953195
$795$	53.0946	1.88307
$796$	4.89238	0.173406
$797$	−45.7572	−1.62080	−0.810401	−	0.585875i	$-0.800751\pi$
$797$	−45.7572	−1.62080	−0.810401	+	0.585875i	$0.800751\pi$
$798$	0	0
$799$	−7.86422	−0.278216
$800$	9.86076	0.348630
$801$	−9.59326	−0.338961
$802$	−16.3538	−0.577471
$803$	51.7395	1.82585
$804$	−15.0888	−0.532139
$805$	−21.3698	−0.753185
$806$	−16.1606	−0.569234
$807$	−59.7307	−2.10262
$808$	−11.9532	−0.420512
$809$	−53.7413	−1.88944	−0.944722	−	0.327874i	$-0.893668\pi$
$809$	−53.7413	−1.88944	−0.944722	+	0.327874i	$0.893668\pi$
$810$	−24.5567	−0.862833
$811$	30.2394	1.06185	0.530925	−	0.847419i	$-0.321845\pi$
$811$	30.2394	1.06185	0.530925	+	0.847419i	$0.321845\pi$
$812$	9.13075	0.320427
$813$	−18.2608	−0.640436
$814$	−0.704228	−0.0246832
$815$	36.8212	1.28979
$816$	8.91732	0.312169
$817$	0	0
$818$	−22.6251	−0.791067
$819$	−9.01016	−0.314840
$820$	−23.5219	−0.821419
$821$	−14.7489	−0.514739	−0.257369	−	0.966313i	$-0.582856\pi$
$821$	−14.7489	−0.514739	−0.257369	+	0.966313i	$0.582856\pi$
$822$	−12.3068	−0.429250
$823$	34.8498	1.21479	0.607394	−	0.794401i	$-0.292215\pi$
$823$	34.8498	1.21479	0.607394	+	0.794401i	$0.292215\pi$
$824$	12.2367	0.426286
$825$	−134.386	−4.67871
$826$	−6.81470	−0.237114
$827$	16.2642	0.565563	0.282782	−	0.959184i	$-0.408743\pi$
$827$	16.2642	0.565563	0.282782	+	0.959184i	$0.408743\pi$
$828$	−20.5608	−0.714539
$829$	−4.90354	−0.170307	−0.0851534	−	0.996368i	$-0.527138\pi$
$829$	−4.90354	−0.170307	−0.0851534	+	0.996368i	$0.527138\pi$
$830$	−20.1085	−0.697976
$831$	18.8058	0.652368
$832$	−2.42924	−0.0842188
$833$	−3.44274	−0.119284
$834$	3.59811	0.124592
$835$	9.65340	0.334070
$836$	0	0
$837$	−12.2177	−0.422305
$838$	26.9109	0.929621
$839$	−20.0232	−0.691279	−0.345639	−	0.938367i	$-0.612338\pi$
$839$	−20.0232	−0.691279	−0.345639	+	0.938367i	$0.612338\pi$
$840$	−9.98506	−0.344517
$841$	54.3706	1.87485
$842$	−27.3720	−0.943303
$843$	10.3853	0.357688
$844$	−1.11001	−0.0382081
$845$	−27.3656	−0.941404
$846$	8.47253	0.291292
$847$	16.6838	0.573261
$848$	−5.31740	−0.182600
$849$	−34.5990	−1.18743
$850$	−33.9480	−1.16441
$851$	0.741959	0.0254340
$852$	−22.4361	−0.768650
$853$	−0.699222	−0.0239409	−0.0119704	−	0.999928i	$-0.503810\pi$
$853$	−0.699222	−0.0239409	−0.0119704	+	0.999928i	$0.503810\pi$
$854$	−1.44924	−0.0495919
$855$	0	0
$856$	−6.13537	−0.209703
$857$	−20.9127	−0.714364	−0.357182	−	0.934035i	$-0.616262\pi$
$857$	−20.9127	−0.714364	−0.357182	+	0.934035i	$0.616262\pi$
$858$	33.1065	1.13024
$859$	33.3721	1.13864	0.569321	−	0.822115i	$-0.307206\pi$
$859$	33.3721	1.13864	0.569321	+	0.822115i	$0.307206\pi$
$860$	35.1172	1.19749
$861$	15.8045	0.538617
$862$	−0.123924	−0.00422087
$863$	−4.56830	−0.155507	−0.0777534	−	0.996973i	$-0.524775\pi$
$863$	−4.56830	−0.155507	−0.0777534	+	0.996973i	$0.524775\pi$
$864$	−1.83655	−0.0624805
$865$	9.79254	0.332957
$866$	10.1248	0.344056
$867$	13.3331	0.452815
$868$	6.65254	0.225802
$869$	3.32606	0.112829
$870$	−91.1711	−3.09099
$871$	−14.1512	−0.479496
$872$	−15.0996	−0.511337
$873$	5.87909	0.198977
$874$	0	0
$875$	18.7381	0.633462
$876$	−25.4707	−0.860574
$877$	2.59212	0.0875296	0.0437648	−	0.999042i	$-0.486065\pi$
$877$	2.59212	0.0875296	0.0437648	+	0.999042i	$0.486065\pi$
$878$	−4.61529	−0.155758
$879$	−29.3979	−0.991568
$880$	20.2830	0.683741
$881$	−38.7299	−1.30484	−0.652422	−	0.757856i	$-0.726247\pi$
$881$	−38.7299	−1.30484	−0.652422	+	0.757856i	$0.726247\pi$
$882$	3.70904	0.124890
$883$	18.3195	0.616499	0.308249	−	0.951306i	$-0.400257\pi$
$883$	18.3195	0.616499	0.308249	+	0.951306i	$0.400257\pi$
$884$	8.36325	0.281286
$885$	68.0452	2.28731
$886$	−39.7691	−1.33607
$887$	2.11705	0.0710835	0.0355418	−	0.999368i	$-0.488684\pi$
$887$	2.11705	0.0710835	0.0355418	+	0.999368i	$0.488684\pi$
$888$	0.346682	0.0116339
$889$	−20.3966	−0.684080
$890$	−9.97069	−0.334218
$891$	−33.5167	−1.12285
$892$	8.47642	0.283812
$893$	0	0
$894$	−0.204259	−0.00683145
$895$	93.1520	3.11373
$896$	1.00000	0.0334077
$897$	−34.8803	−1.16462
$898$	−17.9749	−0.599830
$899$	60.7427	2.02588
$900$	36.5740	1.21913
$901$	18.3064	0.609876
$902$	−32.1044	−1.06896
$903$	−23.5955	−0.785210
$904$	0.664656	0.0221061
$905$	31.5305	1.04811
$906$	−58.8608	−1.95552
$907$	10.3828	0.344756	0.172378	−	0.985031i	$-0.444855\pi$
$907$	10.3828	0.344756	0.172378	+	0.985031i	$0.444855\pi$
$908$	−15.9103	−0.528003
$909$	−44.3348	−1.47049
$910$	−9.36464	−0.310435
$911$	−22.2452	−0.737018	−0.368509	−	0.929624i	$-0.620132\pi$
$911$	−22.2452	−0.737018	−0.368509	+	0.929624i	$0.620132\pi$
$912$	0	0
$913$	−27.4455	−0.908315
$914$	16.1400	0.533863
$915$	14.4707	0.478387
$916$	−15.4908	−0.511831
$917$	7.30369	0.241189
$918$	6.32275	0.208682
$919$	11.4486	0.377656	0.188828	−	0.982010i	$-0.439531\pi$
$919$	11.4486	0.377656	0.188828	+	0.982010i	$0.439531\pi$
$920$	−21.3698	−0.704540
$921$	38.7503	1.27687
$922$	41.9269	1.38079
$923$	−21.0421	−0.692609
$924$	−13.6283	−0.448339
$925$	−1.31981	−0.0433951
$926$	21.3569	0.701831
$927$	45.3864	1.49069
$928$	9.13075	0.299732
$929$	56.3022	1.84721	0.923607	−	0.383340i	$-0.125226\pi$
$929$	56.3022	1.84721	0.923607	+	0.383340i	$0.125226\pi$
$930$	−66.4260	−2.17819
$931$	0	0
$932$	16.4647	0.539321
$933$	60.6715	1.98630
$934$	−29.3462	−0.960238
$935$	−69.8292	−2.28366
$936$	−9.01016	−0.294506
$937$	9.33040	0.304811	0.152405	−	0.988318i	$-0.451298\pi$
$937$	9.33040	0.304811	0.152405	+	0.988318i	$0.451298\pi$
$938$	5.82537	0.190205
$939$	−35.4839	−1.15797
$940$	8.80586	0.287216
$941$	15.6759	0.511021	0.255511	−	0.966806i	$-0.417756\pi$
$941$	15.6759	0.511021	0.255511	+	0.966806i	$0.417756\pi$
$942$	52.1350	1.69865
$943$	33.8244	1.10147
$944$	−6.81470	−0.221799
$945$	−7.07982	−0.230307
$946$	47.9305	1.55836
$947$	−31.0354	−1.00851	−0.504257	−	0.863554i	$-0.668233\pi$
$947$	−31.0354	−1.00851	−0.504257	+	0.863554i	$0.668233\pi$
$948$	−1.63737	−0.0531794
$949$	−23.8880	−0.775438
$950$	0	0
$951$	1.95510	0.0633985
$952$	−3.44274	−0.111580
$953$	−11.4148	−0.369762	−0.184881	−	0.982761i	$-0.559190\pi$
$953$	−11.4148	−0.369762	−0.184881	+	0.982761i	$0.559190\pi$
$954$	−19.7225	−0.638539
$955$	35.8739	1.16085
$956$	13.5299	0.437587
$957$	−124.437	−4.02248
$958$	31.4867	1.01729
$959$	4.75134	0.153429
$960$	−9.98506	−0.322266
$961$	13.2563	0.427622
$962$	0.325141	0.0104830
$963$	−22.7563	−0.733313
$964$	7.36721	0.237282
$965$	−10.9631	−0.352916
$966$	14.3585	0.461978
$967$	21.1594	0.680441	0.340220	−	0.940346i	$-0.389498\pi$
$967$	21.1594	0.680441	0.340220	+	0.940346i	$0.389498\pi$
$968$	16.6838	0.536237
$969$	0	0
$970$	6.11039	0.196193
$971$	22.8181	0.732268	0.366134	−	0.930562i	$-0.380681\pi$
$971$	22.8181	0.732268	0.366134	+	0.930562i	$0.380681\pi$
$972$	22.0094	0.705953
$973$	−1.38913	−0.0445336
$974$	−13.8409	−0.443490
$975$	62.0456	1.98705
$976$	−1.44924	−0.0463890
$977$	−49.5476	−1.58517	−0.792584	−	0.609762i	$-0.791265\pi$
$977$	−49.5476	−1.58517	−0.792584	+	0.609762i	$0.791265\pi$
$978$	−24.7404	−0.791112
$979$	−13.6087	−0.434937
$980$	3.85497	0.123142
$981$	−56.0051	−1.78810
$982$	−26.2987	−0.839225
$983$	19.4485	0.620310	0.310155	−	0.950686i	$-0.399619\pi$
$983$	19.4485	0.620310	0.310155	+	0.950686i	$0.399619\pi$
$984$	15.8045	0.503830
$985$	−51.3295	−1.63549
$986$	−31.4348	−1.00109
$987$	−5.91673	−0.188332
$988$	0	0
$989$	−50.4986	−1.60576
$990$	75.2306	2.39099
$991$	−39.7070	−1.26134	−0.630668	−	0.776053i	$-0.717219\pi$
$991$	−39.7070	−1.26134	−0.630668	+	0.776053i	$0.717219\pi$
$992$	6.65254	0.211218
$993$	−67.6530	−2.14690
$994$	8.66200	0.274742
$995$	18.8599	0.597900
$996$	13.5111	0.428114
$997$	25.7391	0.815167	0.407583	−	0.913168i	$-0.366372\pi$
$997$	25.7391	0.815167	0.407583	+	0.913168i	$0.366372\pi$
$998$	−7.72963	−0.244677
$999$	0.245812	0.00777714

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.bm.1.2		12
19.3	odd	18		266.2.u.d.85.4	✓	24
19.13	odd	18		266.2.u.d.169.4	yes	24
19.18	odd	2		5054.2.a.bl.1.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
266.2.u.d.85.4	✓	24	19.3	odd	18
266.2.u.d.169.4	yes	24	19.13	odd	18
5054.2.a.bl.1.11		12	19.18	odd	2
5054.2.a.bm.1.2		12	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.59018 q^{3} +1.00000 q^{4} +3.85497 q^{5} -2.59018 q^{6} +1.00000 q^{7} +1.00000 q^{8} +3.70904 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.59018 q^{3} +1.00000 q^{4} +3.85497 q^{5} -2.59018 q^{6} +1.00000 q^{7} +1.00000 q^{8} +3.70904 q^{9} +3.85497 q^{10} +5.26154 q^{11} -2.59018 q^{12} -2.42924 q^{13} +1.00000 q^{14} -9.98506 q^{15} +1.00000 q^{16} -3.44274 q^{17} +3.70904 q^{18} +3.85497 q^{20} -2.59018 q^{21} +5.26154 q^{22} -5.54344 q^{23} -2.59018 q^{24} +9.86076 q^{25} -2.42924 q^{26} -1.83655 q^{27} +1.00000 q^{28} +9.13075 q^{29} -9.98506 q^{30} +6.65254 q^{31} +1.00000 q^{32} -13.6283 q^{33} -3.44274 q^{34} +3.85497 q^{35} +3.70904 q^{36} -0.133845 q^{37} +6.29218 q^{39} +3.85497 q^{40} -6.10171 q^{41} -2.59018 q^{42} +9.10961 q^{43} +5.26154 q^{44} +14.2982 q^{45} -5.54344 q^{46} +2.28429 q^{47} -2.59018 q^{48} +1.00000 q^{49} +9.86076 q^{50} +8.91732 q^{51} -2.42924 q^{52} -5.31740 q^{53} -1.83655 q^{54} +20.2830 q^{55} +1.00000 q^{56} +9.13075 q^{58} -6.81470 q^{59} -9.98506 q^{60} -1.44924 q^{61} +6.65254 q^{62} +3.70904 q^{63} +1.00000 q^{64} -9.36464 q^{65} -13.6283 q^{66} +5.82537 q^{67} -3.44274 q^{68} +14.3585 q^{69} +3.85497 q^{70} +8.66200 q^{71} +3.70904 q^{72} +9.83354 q^{73} -0.133845 q^{74} -25.5412 q^{75} +5.26154 q^{77} +6.29218 q^{78} +0.632146 q^{79} +3.85497 q^{80} -6.37014 q^{81} -6.10171 q^{82} -5.21626 q^{83} -2.59018 q^{84} -13.2716 q^{85} +9.10961 q^{86} -23.6503 q^{87} +5.26154 q^{88} -2.58645 q^{89} +14.2982 q^{90} -2.42924 q^{91} -5.54344 q^{92} -17.2313 q^{93} +2.28429 q^{94} -2.59018 q^{96} +1.58507 q^{97} +1.00000 q^{98} +19.5153 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 3 q^{3} + 12 q^{4} + 3 q^{5} + 3 q^{6} + 12 q^{7} + 12 q^{8} + 21 q^{9}+O(q^{10}) \) 12 * q + 12 * q^2 + 3 * q^3 + 12 * q^4 + 3 * q^5 + 3 * q^6 + 12 * q^7 + 12 * q^8 + 21 * q^9	\( 12 q + 12 q^{2} + 3 q^{3} + 12 q^{4} + 3 q^{5} + 3 q^{6} + 12 q^{7} + 12 q^{8} + 21 q^{9} + 3 q^{10} + 3 q^{11} + 3 q^{12} - 6 q^{13} + 12 q^{14} - 6 q^{15} + 12 q^{16} + 3 q^{17} + 21 q^{18} + 3 q^{20} + 3 q^{21} + 3 q^{22} + 12 q^{23} + 3 q^{24} + 33 q^{25} - 6 q^{26} + 21 q^{27} + 12 q^{28} + 6 q^{29} - 6 q^{30} + 3 q^{31} + 12 q^{32} - 6 q^{33} + 3 q^{34} + 3 q^{35} + 21 q^{36} + 27 q^{37} + 27 q^{39} + 3 q^{40} - 27 q^{41} + 3 q^{42} + 30 q^{43} + 3 q^{44} + 30 q^{45} + 12 q^{46} + 21 q^{47} + 3 q^{48} + 12 q^{49} + 33 q^{50} + 3 q^{51} - 6 q^{52} + 6 q^{53} + 21 q^{54} + 48 q^{55} + 12 q^{56} + 6 q^{58} - 27 q^{59} - 6 q^{60} + 18 q^{61} + 3 q^{62} + 21 q^{63} + 12 q^{64} - 9 q^{65} - 6 q^{66} + 9 q^{67} + 3 q^{68} + 18 q^{69} + 3 q^{70} + 27 q^{71} + 21 q^{72} - 9 q^{73} + 27 q^{74} + 33 q^{75} + 3 q^{77} + 27 q^{78} - 12 q^{79} + 3 q^{80} + 24 q^{81} - 27 q^{82} + 9 q^{83} + 3 q^{84} + 78 q^{85} + 30 q^{86} - 45 q^{87} + 3 q^{88} - 24 q^{89} + 30 q^{90} - 6 q^{91} + 12 q^{92} + 3 q^{93} + 21 q^{94} + 3 q^{96} - 18 q^{97} + 12 q^{98} + 48 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 3 * q^3 + 12 * q^4 + 3 * q^5 + 3 * q^6 + 12 * q^7 + 12 * q^8 + 21 * q^9 + 3 * q^10 + 3 * q^11 + 3 * q^12 - 6 * q^13 + 12 * q^14 - 6 * q^15 + 12 * q^16 + 3 * q^17 + 21 * q^18 + 3 * q^20 + 3 * q^21 + 3 * q^22 + 12 * q^23 + 3 * q^24 + 33 * q^25 - 6 * q^26 + 21 * q^27 + 12 * q^28 + 6 * q^29 - 6 * q^30 + 3 * q^31 + 12 * q^32 - 6 * q^33 + 3 * q^34 + 3 * q^35 + 21 * q^36 + 27 * q^37 + 27 * q^39 + 3 * q^40 - 27 * q^41 + 3 * q^42 + 30 * q^43 + 3 * q^44 + 30 * q^45 + 12 * q^46 + 21 * q^47 + 3 * q^48 + 12 * q^49 + 33 * q^50 + 3 * q^51 - 6 * q^52 + 6 * q^53 + 21 * q^54 + 48 * q^55 + 12 * q^56 + 6 * q^58 - 27 * q^59 - 6 * q^60 + 18 * q^61 + 3 * q^62 + 21 * q^63 + 12 * q^64 - 9 * q^65 - 6 * q^66 + 9 * q^67 + 3 * q^68 + 18 * q^69 + 3 * q^70 + 27 * q^71 + 21 * q^72 - 9 * q^73 + 27 * q^74 + 33 * q^75 + 3 * q^77 + 27 * q^78 - 12 * q^79 + 3 * q^80 + 24 * q^81 - 27 * q^82 + 9 * q^83 + 3 * q^84 + 78 * q^85 + 30 * q^86 - 45 * q^87 + 3 * q^88 - 24 * q^89 + 30 * q^90 - 6 * q^91 + 12 * q^92 + 3 * q^93 + 21 * q^94 + 3 * q^96 - 18 * q^97 + 12 * q^98 + 48 * q^99

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