LMFDB - Embedded newform 1334.2.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1334,2,Mod(1,1334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1334, 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("1334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1334 = 2 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1334.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:	$10.6520436296$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.179024.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 8x^{3} + 6x - 2 $ x^5 - 8x^3 + 6x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.65344$ of defining polynomial
Character	$\chi$	$=$	1334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.07856 q^{3} +1.00000 q^{4} +0.116361 q^{5} -3.07856 q^{6} -1.89971 q^{7} +1.00000 q^{8} +6.47756 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.07856 q^{3} +1.00000 q^{4} +0.116361 q^{5} -3.07856 q^{6} -1.89971 q^{7} +1.00000 q^{8} +6.47756 q^{9} +0.116361 q^{10} -0.612678 q^{11} -3.07856 q^{12} +0.224534 q^{13} -1.89971 q^{14} -0.358226 q^{15} +1.00000 q^{16} +5.05244 q^{17} +6.47756 q^{18} -3.64526 q^{19} +0.116361 q^{20} +5.84837 q^{21} -0.612678 q^{22} -1.00000 q^{23} -3.07856 q^{24} -4.98646 q^{25} +0.224534 q^{26} -10.7059 q^{27} -1.89971 q^{28} +1.00000 q^{29} -0.358226 q^{30} -1.46292 q^{31} +1.00000 q^{32} +1.88617 q^{33} +5.05244 q^{34} -0.221052 q^{35} +6.47756 q^{36} +3.49489 q^{37} -3.64526 q^{38} -0.691242 q^{39} +0.116361 q^{40} -10.7350 q^{41} +5.84837 q^{42} +5.00253 q^{43} -0.612678 q^{44} +0.753737 q^{45} -1.00000 q^{46} -10.8141 q^{47} -3.07856 q^{48} -3.39111 q^{49} -4.98646 q^{50} -15.5543 q^{51} +0.224534 q^{52} -10.4306 q^{53} -10.7059 q^{54} -0.0712920 q^{55} -1.89971 q^{56} +11.2222 q^{57} +1.00000 q^{58} -10.6860 q^{59} -0.358226 q^{60} +4.68558 q^{61} -1.46292 q^{62} -12.3055 q^{63} +1.00000 q^{64} +0.0261271 q^{65} +1.88617 q^{66} +7.56557 q^{67} +5.05244 q^{68} +3.07856 q^{69} -0.221052 q^{70} -4.99099 q^{71} +6.47756 q^{72} +3.92396 q^{73} +3.49489 q^{74} +15.3511 q^{75} -3.64526 q^{76} +1.16391 q^{77} -0.691242 q^{78} -15.5725 q^{79} +0.116361 q^{80} +13.5261 q^{81} -10.7350 q^{82} -6.02426 q^{83} +5.84837 q^{84} +0.587908 q^{85} +5.00253 q^{86} -3.07856 q^{87} -0.612678 q^{88} -11.1941 q^{89} +0.753737 q^{90} -0.426548 q^{91} -1.00000 q^{92} +4.50368 q^{93} -10.8141 q^{94} -0.424167 q^{95} -3.07856 q^{96} -11.6637 q^{97} -3.39111 q^{98} -3.96865 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{2} - 3 q^{3} + 5 q^{4} - 5 q^{5} - 3 q^{6} - 6 q^{7} + 5 q^{8} + 2 q^{9}+O(q^{10}) $ 5 * q + 5 * q^2 - 3 * q^3 + 5 * q^4 - 5 * q^5 - 3 * q^6 - 6 * q^7 + 5 * q^8 + 2 * q^9	\( 5 q + 5 q^{2} - 3 q^{3} + 5 q^{4} - 5 q^{5} - 3 q^{6} - 6 q^{7} + 5 q^{8} + 2 q^{9} - 5 q^{10} - 9 q^{11} - 3 q^{12} - 5 q^{13} - 6 q^{14} - 3 q^{15} + 5 q^{16} - 6 q^{17} + 2 q^{18} - 10 q^{19} - 5 q^{20} - 2 q^{21} - 9 q^{22} - 5 q^{23} - 3 q^{24} - 4 q^{25} - 5 q^{26} - 9 q^{27} - 6 q^{28} + 5 q^{29} - 3 q^{30} - 15 q^{31} + 5 q^{32} - 15 q^{33} - 6 q^{34} - 2 q^{35} + 2 q^{36} - 10 q^{38} + 3 q^{39} - 5 q^{40} - 2 q^{41} - 2 q^{42} - 5 q^{43} - 9 q^{44} - 6 q^{45} - 5 q^{46} - 9 q^{47} - 3 q^{48} - 3 q^{49} - 4 q^{50} - 2 q^{51} - 5 q^{52} + 3 q^{53} - 9 q^{54} - 3 q^{55} - 6 q^{56} - 2 q^{57} + 5 q^{58} - 26 q^{59} - 3 q^{60} - 8 q^{61} - 15 q^{62} - 6 q^{63} + 5 q^{64} + 19 q^{65} - 15 q^{66} + 12 q^{67} - 6 q^{68} + 3 q^{69} - 2 q^{70} - 12 q^{71} + 2 q^{72} + 2 q^{73} + 24 q^{75} - 10 q^{76} + 36 q^{77} + 3 q^{78} - 25 q^{79} - 5 q^{80} + 9 q^{81} - 2 q^{82} - 16 q^{83} - 2 q^{84} + 4 q^{85} - 5 q^{86} - 3 q^{87} - 9 q^{88} - 20 q^{89} - 6 q^{90} - 32 q^{91} - 5 q^{92} + 11 q^{93} - 9 q^{94} + 20 q^{95} - 3 q^{96} - 4 q^{97} - 3 q^{98} + 20 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 - 3 * q^3 + 5 * q^4 - 5 * q^5 - 3 * q^6 - 6 * q^7 + 5 * q^8 + 2 * q^9 - 5 * q^10 - 9 * q^11 - 3 * q^12 - 5 * q^13 - 6 * q^14 - 3 * q^15 + 5 * q^16 - 6 * q^17 + 2 * q^18 - 10 * q^19 - 5 * q^20 - 2 * q^21 - 9 * q^22 - 5 * q^23 - 3 * q^24 - 4 * q^25 - 5 * q^26 - 9 * q^27 - 6 * q^28 + 5 * q^29 - 3 * q^30 - 15 * q^31 + 5 * q^32 - 15 * q^33 - 6 * q^34 - 2 * q^35 + 2 * q^36 - 10 * q^38 + 3 * q^39 - 5 * q^40 - 2 * q^41 - 2 * q^42 - 5 * q^43 - 9 * q^44 - 6 * q^45 - 5 * q^46 - 9 * q^47 - 3 * q^48 - 3 * q^49 - 4 * q^50 - 2 * q^51 - 5 * q^52 + 3 * q^53 - 9 * q^54 - 3 * q^55 - 6 * q^56 - 2 * q^57 + 5 * q^58 - 26 * q^59 - 3 * q^60 - 8 * q^61 - 15 * q^62 - 6 * q^63 + 5 * q^64 + 19 * q^65 - 15 * q^66 + 12 * q^67 - 6 * q^68 + 3 * q^69 - 2 * q^70 - 12 * q^71 + 2 * q^72 + 2 * q^73 + 24 * q^75 - 10 * q^76 + 36 * q^77 + 3 * q^78 - 25 * q^79 - 5 * q^80 + 9 * q^81 - 2 * q^82 - 16 * q^83 - 2 * q^84 + 4 * q^85 - 5 * q^86 - 3 * q^87 - 9 * q^88 - 20 * q^89 - 6 * q^90 - 32 * q^91 - 5 * q^92 + 11 * q^93 - 9 * q^94 + 20 * q^95 - 3 * q^96 - 4 * q^97 - 3 * q^98 + 20 * 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
$3$	−3.07856	−1.77741	−0.888705	−	0.458480i	$-0.848394\pi$
$3$	−3.07856	−1.77741	−0.888705	+	0.458480i	$0.848394\pi$
$4$	1.00000	0.500000
$5$	0.116361	0.0520384	0.0260192	−	0.999661i	$-0.491717\pi$
$5$	0.116361	0.0520384	0.0260192	+	0.999661i	$0.491717\pi$
$6$	−3.07856	−1.25682
$7$	−1.89971	−0.718022	−0.359011	−	0.933333i	$-0.616886\pi$
$7$	−1.89971	−0.718022	−0.359011	+	0.933333i	$0.616886\pi$
$8$	1.00000	0.353553
$9$	6.47756	2.15919
$10$	0.116361	0.0367967
$11$	−0.612678	−0.184729	−0.0923646	−	0.995725i	$-0.529443\pi$
$11$	−0.612678	−0.184729	−0.0923646	+	0.995725i	$0.529443\pi$
$12$	−3.07856	−0.888705
$13$	0.224534	0.0622745	0.0311372	−	0.999515i	$-0.490087\pi$
$13$	0.224534	0.0622745	0.0311372	+	0.999515i	$0.490087\pi$
$14$	−1.89971	−0.507718
$15$	−0.358226	−0.0924935
$16$	1.00000	0.250000
$17$	5.05244	1.22540	0.612698	−	0.790317i	$-0.290084\pi$
$17$	5.05244	1.22540	0.612698	+	0.790317i	$0.290084\pi$
$18$	6.47756	1.52677
$19$	−3.64526	−0.836279	−0.418139	−	0.908383i	$-0.637318\pi$
$19$	−3.64526	−0.836279	−0.418139	+	0.908383i	$0.637318\pi$
$20$	0.116361	0.0260192
$21$	5.84837	1.27622
$22$	−0.612678	−0.130623
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−3.07856	−0.628409
$25$	−4.98646	−0.997292
$26$	0.224534	0.0440347
$27$	−10.7059	−2.06035
$28$	−1.89971	−0.359011
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−0.358226	−0.0654028
$31$	−1.46292	−0.262748	−0.131374	−	0.991333i	$-0.541939\pi$
$31$	−1.46292	−0.262748	−0.131374	+	0.991333i	$0.541939\pi$
$32$	1.00000	0.176777
$33$	1.88617	0.328340
$34$	5.05244	0.866486
$35$	−0.221052	−0.0373647
$36$	6.47756	1.07959
$37$	3.49489	0.574556	0.287278	−	0.957847i	$-0.407250\pi$
$37$	3.49489	0.574556	0.287278	+	0.957847i	$0.407250\pi$
$38$	−3.64526	−0.591339
$39$	−0.691242	−0.110687
$40$	0.116361	0.0183983
$41$	−10.7350	−1.67652	−0.838261	−	0.545269i	$-0.816427\pi$
$41$	−10.7350	−1.67652	−0.838261	+	0.545269i	$0.816427\pi$
$42$	5.84837	0.902423
$43$	5.00253	0.762878	0.381439	−	0.924394i	$-0.375429\pi$
$43$	5.00253	0.762878	0.381439	+	0.924394i	$0.375429\pi$
$44$	−0.612678	−0.0923646
$45$	0.753737	0.112361
$46$	−1.00000	−0.147442
$47$	−10.8141	−1.57739	−0.788696	−	0.614783i	$-0.789243\pi$
$47$	−10.8141	−1.57739	−0.788696	+	0.614783i	$0.789243\pi$
$48$	−3.07856	−0.444352
$49$	−3.39111	−0.484445
$50$	−4.98646	−0.705192
$51$	−15.5543	−2.17803
$52$	0.224534	0.0311372
$53$	−10.4306	−1.43276	−0.716378	−	0.697713i	$-0.754201\pi$
$53$	−10.4306	−1.43276	−0.716378	+	0.697713i	$0.754201\pi$
$54$	−10.7059	−1.45689
$55$	−0.0712920	−0.00961301
$56$	−1.89971	−0.253859
$57$	11.2222	1.48641
$58$	1.00000	0.131306
$59$	−10.6860	−1.39120	−0.695601	−	0.718429i	$-0.744862\pi$
$59$	−10.6860	−1.39120	−0.695601	+	0.718429i	$0.744862\pi$
$60$	−0.358226	−0.0462468
$61$	4.68558	0.599927	0.299964	−	0.953951i	$-0.403025\pi$
$61$	4.68558	0.599927	0.299964	+	0.953951i	$0.403025\pi$
$62$	−1.46292	−0.185791
$63$	−12.3055	−1.55034
$64$	1.00000	0.125000
$65$	0.0261271	0.00324066
$66$	1.88617	0.232171
$67$	7.56557	0.924282	0.462141	−	0.886807i	$-0.347081\pi$
$67$	7.56557	0.924282	0.462141	+	0.886807i	$0.347081\pi$
$68$	5.05244	0.612698
$69$	3.07856	0.370616
$70$	−0.221052	−0.0264208
$71$	−4.99099	−0.592322	−0.296161	−	0.955138i	$-0.595706\pi$
$71$	−4.99099	−0.592322	−0.296161	+	0.955138i	$0.595706\pi$
$72$	6.47756	0.763387
$73$	3.92396	0.459265	0.229633	−	0.973277i	$-0.426248\pi$
$73$	3.92396	0.459265	0.229633	+	0.973277i	$0.426248\pi$
$74$	3.49489	0.406272
$75$	15.3511	1.77260
$76$	−3.64526	−0.418139
$77$	1.16391	0.132640
$78$	−0.691242	−0.0782677
$79$	−15.5725	−1.75204	−0.876021	−	0.482272i	$-0.839812\pi$
$79$	−15.5725	−1.75204	−0.876021	+	0.482272i	$0.839812\pi$
$80$	0.116361	0.0130096
$81$	13.5261	1.50290
$82$	−10.7350	−1.18548
$83$	−6.02426	−0.661248	−0.330624	−	0.943763i	$-0.607259\pi$
$83$	−6.02426	−0.661248	−0.330624	+	0.943763i	$0.607259\pi$
$84$	5.84837	0.638109
$85$	0.587908	0.0637676
$86$	5.00253	0.539437
$87$	−3.07856	−0.330057
$88$	−0.612678	−0.0653116
$89$	−11.1941	−1.18657	−0.593286	−	0.804992i	$-0.702170\pi$
$89$	−11.1941	−1.18657	−0.593286	+	0.804992i	$0.702170\pi$
$90$	0.753737	0.0794509
$91$	−0.426548	−0.0447144
$92$	−1.00000	−0.104257
$93$	4.50368	0.467010
$94$	−10.8141	−1.11538
$95$	−0.424167	−0.0435186
$96$	−3.07856	−0.314205
$97$	−11.6637	−1.18427	−0.592134	−	0.805840i	$-0.701714\pi$
$97$	−11.6637	−1.18427	−0.592134	+	0.805840i	$0.701714\pi$
$98$	−3.39111	−0.342554
$99$	−3.96865	−0.398865
$100$	−4.98646	−0.498646
$101$	8.61155	0.856881	0.428440	−	0.903570i	$-0.359063\pi$
$101$	8.61155	0.856881	0.428440	+	0.903570i	$0.359063\pi$
$102$	−15.5543	−1.54010
$103$	−16.0761	−1.58402	−0.792012	−	0.610506i	$-0.790966\pi$
$103$	−16.0761	−1.58402	−0.792012	+	0.610506i	$0.790966\pi$
$104$	0.224534	0.0220173
$105$	0.680524	0.0664124
$106$	−10.4306	−1.01311
$107$	12.3899	1.19777	0.598886	−	0.800834i	$-0.295610\pi$
$107$	12.3899	1.19777	0.598886	+	0.800834i	$0.295610\pi$
$108$	−10.7059	−1.03017
$109$	8.17904	0.783410	0.391705	−	0.920091i	$-0.371885\pi$
$109$	8.17904	0.783410	0.391705	+	0.920091i	$0.371885\pi$
$110$	−0.0712920	−0.00679742
$111$	−10.7592	−1.02122
$112$	−1.89971	−0.179505
$113$	8.30667	0.781426	0.390713	−	0.920513i	$-0.372228\pi$
$113$	8.30667	0.781426	0.390713	+	0.920513i	$0.372228\pi$
$114$	11.2222	1.05105
$115$	−0.116361	−0.0108508
$116$	1.00000	0.0928477
$117$	1.45443	0.134462
$118$	−10.6860	−0.983728
$119$	−9.59815	−0.879861
$120$	−0.358226	−0.0327014
$121$	−10.6246	−0.965875
$122$	4.68558	0.424213
$123$	33.0483	2.97987
$124$	−1.46292	−0.131374
$125$	−1.16204	−0.103936
$126$	−12.3055	−1.09626
$127$	13.5292	1.20052	0.600260	−	0.799805i	$-0.295064\pi$
$127$	13.5292	1.20052	0.600260	+	0.799805i	$0.295064\pi$
$128$	1.00000	0.0883883
$129$	−15.4006	−1.35595
$130$	0.0261271	0.00229149
$131$	22.6367	1.97778	0.988890	−	0.148646i	$-0.0474915\pi$
$131$	22.6367	1.97778	0.988890	+	0.148646i	$0.0474915\pi$
$132$	1.88617	0.164170
$133$	6.92492	0.600466
$134$	7.56557	0.653566
$135$	−1.24575	−0.107217
$136$	5.05244	0.433243
$137$	5.61862	0.480031	0.240015	−	0.970769i	$-0.422848\pi$
$137$	5.61862	0.480031	0.240015	+	0.970769i	$0.422848\pi$
$138$	3.07856	0.262065
$139$	−6.54480	−0.555122	−0.277561	−	0.960708i	$-0.589526\pi$
$139$	−6.54480	−0.555122	−0.277561	+	0.960708i	$0.589526\pi$
$140$	−0.221052	−0.0186823
$141$	33.2918	2.80367
$142$	−4.99099	−0.418835
$143$	−0.137567	−0.0115039
$144$	6.47756	0.539796
$145$	0.116361	0.00966328
$146$	3.92396	0.324750
$147$	10.4398	0.861057
$148$	3.49489	0.287278
$149$	−16.0249	−1.31281	−0.656406	−	0.754408i	$-0.727924\pi$
$149$	−16.0249	−1.31281	−0.656406	+	0.754408i	$0.727924\pi$
$150$	15.3511	1.25342
$151$	−7.60733	−0.619075	−0.309538	−	0.950887i	$-0.600174\pi$
$151$	−7.60733	−0.619075	−0.309538	+	0.950887i	$0.600174\pi$
$152$	−3.64526	−0.295669
$153$	32.7274	2.64586
$154$	1.16391	0.0937904
$155$	−0.170227	−0.0136730
$156$	−0.691242	−0.0553436
$157$	−5.31886	−0.424491	−0.212245	−	0.977216i	$-0.568078\pi$
$157$	−5.31886	−0.424491	−0.212245	+	0.977216i	$0.568078\pi$
$158$	−15.5725	−1.23888
$159$	32.1113	2.54659
$160$	0.116361	0.00919917
$161$	1.89971	0.149718
$162$	13.5261	1.06271
$163$	−7.15557	−0.560467	−0.280234	−	0.959932i	$-0.590412\pi$
$163$	−7.15557	−0.560467	−0.280234	+	0.959932i	$0.590412\pi$
$164$	−10.7350	−0.838261
$165$	0.219477	0.0170863
$166$	−6.02426	−0.467573
$167$	13.6801	1.05860	0.529298	−	0.848436i	$-0.322456\pi$
$167$	13.6801	1.05860	0.529298	+	0.848436i	$0.322456\pi$
$168$	5.84837	0.451212
$169$	−12.9496	−0.996122
$170$	0.587908	0.0450905
$171$	−23.6123	−1.80568
$172$	5.00253	0.381439
$173$	9.78366	0.743838	0.371919	−	0.928265i	$-0.378700\pi$
$173$	9.78366	0.743838	0.371919	+	0.928265i	$0.378700\pi$
$174$	−3.07856	−0.233385
$175$	9.47281	0.716077
$176$	−0.612678	−0.0461823
$177$	32.8976	2.47274
$178$	−11.1941	−0.839034
$179$	−4.23681	−0.316674	−0.158337	−	0.987385i	$-0.550613\pi$
$179$	−4.23681	−0.316674	−0.158337	+	0.987385i	$0.550613\pi$
$180$	0.753737	0.0561803
$181$	0.776074	0.0576851	0.0288425	−	0.999584i	$-0.490818\pi$
$181$	0.776074	0.0576851	0.0288425	+	0.999584i	$0.490818\pi$
$182$	−0.426548	−0.0316179
$183$	−14.4249	−1.06632
$184$	−1.00000	−0.0737210
$185$	0.406670	0.0298990
$186$	4.50368	0.330226
$187$	−3.09551	−0.226366
$188$	−10.8141	−0.788696
$189$	20.3380	1.47937
$190$	−0.424167	−0.0307723
$191$	2.63754	0.190846	0.0954229	−	0.995437i	$-0.469580\pi$
$191$	2.63754	0.190846	0.0954229	+	0.995437i	$0.469580\pi$
$192$	−3.07856	−0.222176
$193$	1.08631	0.0781944	0.0390972	−	0.999235i	$-0.487552\pi$
$193$	1.08631	0.0781944	0.0390972	+	0.999235i	$0.487552\pi$
$194$	−11.6637	−0.837404
$195$	−0.0804338	−0.00575999
$196$	−3.39111	−0.242222
$197$	−3.15055	−0.224467	−0.112234	−	0.993682i	$-0.535801\pi$
$197$	−3.15055	−0.224467	−0.112234	+	0.993682i	$0.535801\pi$
$198$	−3.96865	−0.282040
$199$	4.43269	0.314225	0.157113	−	0.987581i	$-0.449781\pi$
$199$	4.43269	0.314225	0.157113	+	0.987581i	$0.449781\pi$
$200$	−4.98646	−0.352596
$201$	−23.2911	−1.64283
$202$	8.61155	0.605906
$203$	−1.89971	−0.133333
$204$	−15.5543	−1.08902
$205$	−1.24914	−0.0872435
$206$	−16.0761	−1.12007
$207$	−6.47756	−0.450221
$208$	0.224534	0.0155686
$209$	2.23337	0.154485
$210$	0.680524	0.0469606
$211$	13.3543	0.919349	0.459675	−	0.888087i	$-0.347966\pi$
$211$	13.3543	0.919349	0.459675	+	0.888087i	$0.347966\pi$
$212$	−10.4306	−0.716378
$213$	15.3651	1.05280
$214$	12.3899	0.846953
$215$	0.582101	0.0396990
$216$	−10.7059	−0.728443
$217$	2.77911	0.188659
$218$	8.17904	0.553954
$219$	−12.0802	−0.816303
$220$	−0.0712920	−0.00480651
$221$	1.13444	0.0763109
$222$	−10.7592	−0.722113
$223$	7.90399	0.529290	0.264645	−	0.964346i	$-0.414745\pi$
$223$	7.90399	0.529290	0.264645	+	0.964346i	$0.414745\pi$
$224$	−1.89971	−0.126930
$225$	−32.3001	−2.15334
$226$	8.30667	0.552552
$227$	−11.0082	−0.730639	−0.365320	−	0.930882i	$-0.619040\pi$
$227$	−11.0082	−0.730639	−0.365320	+	0.930882i	$0.619040\pi$
$228$	11.2222	0.743205
$229$	−3.98406	−0.263274	−0.131637	−	0.991298i	$-0.542023\pi$
$229$	−3.98406	−0.263274	−0.131637	+	0.991298i	$0.542023\pi$
$230$	−0.116361	−0.00767264
$231$	−3.58316	−0.235755
$232$	1.00000	0.0656532
$233$	14.4294	0.945298	0.472649	−	0.881251i	$-0.343298\pi$
$233$	14.4294	0.945298	0.472649	+	0.881251i	$0.343298\pi$
$234$	1.45443	0.0950791
$235$	−1.25834	−0.0820849
$236$	−10.6860	−0.695601
$237$	47.9409	3.11410
$238$	−9.59815	−0.622156
$239$	17.9961	1.16407	0.582034	−	0.813164i	$-0.302257\pi$
$239$	17.9961	1.16407	0.582034	+	0.813164i	$0.302257\pi$
$240$	−0.358226	−0.0231234
$241$	−8.92523	−0.574924	−0.287462	−	0.957792i	$-0.592812\pi$
$241$	−8.92523	−0.574924	−0.287462	+	0.957792i	$0.592812\pi$
$242$	−10.6246	−0.682977
$243$	−9.52323	−0.610916
$244$	4.68558	0.299964
$245$	−0.394595	−0.0252097
$246$	33.0483	2.10708
$247$	−0.818483	−0.0520788
$248$	−1.46292	−0.0928953
$249$	18.5461	1.17531
$250$	−1.16204	−0.0734937
$251$	−9.67702	−0.610808	−0.305404	−	0.952223i	$-0.598792\pi$
$251$	−9.67702	−0.610808	−0.305404	+	0.952223i	$0.598792\pi$
$252$	−12.3055	−0.775171
$253$	0.612678	0.0385187
$254$	13.5292	0.848896
$255$	−1.80991	−0.113341
$256$	1.00000	0.0625000
$257$	−0.0260315	−0.00162380	−0.000811900	−	1.00000i	$-0.500258\pi$
$257$	−0.0260315	−0.00162380	−0.000811900		1.00000i	$0.500258\pi$
$258$	−15.4006	−0.958800
$259$	−6.63926	−0.412544
$260$	0.0261271	0.00162033
$261$	6.47756	0.400951
$262$	22.6367	1.39850
$263$	4.08958	0.252174	0.126087	−	0.992019i	$-0.459758\pi$
$263$	4.08958	0.252174	0.126087	+	0.992019i	$0.459758\pi$
$264$	1.88617	0.116086
$265$	−1.21372	−0.0745583
$266$	6.92492	0.424594
$267$	34.4618	2.10903
$268$	7.56557	0.462141
$269$	8.84771	0.539454	0.269727	−	0.962937i	$-0.413066\pi$
$269$	8.84771	0.539454	0.269727	+	0.962937i	$0.413066\pi$
$270$	−1.24575	−0.0758140
$271$	−7.33080	−0.445314	−0.222657	−	0.974897i	$-0.571473\pi$
$271$	−7.33080	−0.445314	−0.222657	+	0.974897i	$0.571473\pi$
$272$	5.05244	0.306349
$273$	1.31316	0.0794758
$274$	5.61862	0.339433
$275$	3.05509	0.184229
$276$	3.07856	0.185308
$277$	15.0387	0.903590	0.451795	−	0.892122i	$-0.350784\pi$
$277$	15.0387	0.903590	0.451795	+	0.892122i	$0.350784\pi$
$278$	−6.54480	−0.392531
$279$	−9.47613	−0.567321
$280$	−0.221052	−0.0132104
$281$	2.24194	0.133743	0.0668713	−	0.997762i	$-0.478698\pi$
$281$	2.24194	0.133743	0.0668713	+	0.997762i	$0.478698\pi$
$282$	33.2918	1.98250
$283$	−27.8267	−1.65412	−0.827062	−	0.562111i	$-0.809989\pi$
$283$	−27.8267	−1.65412	−0.827062	+	0.562111i	$0.809989\pi$
$284$	−4.99099	−0.296161
$285$	1.30582	0.0773504
$286$	−0.137567	−0.00813450
$287$	20.3933	1.20378
$288$	6.47756	0.381694
$289$	8.52712	0.501595
$290$	0.116361	0.00683297
$291$	35.9074	2.10493
$292$	3.92396	0.229633
$293$	−16.2758	−0.950843	−0.475421	−	0.879758i	$-0.657704\pi$
$293$	−16.2758	−0.950843	−0.475421	+	0.879758i	$0.657704\pi$
$294$	10.4398	0.608859
$295$	−1.24344	−0.0723959
$296$	3.49489	0.203136
$297$	6.55925	0.380606
$298$	−16.0249	−0.928298
$299$	−0.224534	−0.0129851
$300$	15.3511	0.886298
$301$	−9.50334	−0.547763
$302$	−7.60733	−0.437752
$303$	−26.5112	−1.52303
$304$	−3.64526	−0.209070
$305$	0.545221	0.0312192
$306$	32.7274	1.87090
$307$	21.1418	1.20663	0.603314	−	0.797504i	$-0.293847\pi$
$307$	21.1418	1.20663	0.603314	+	0.797504i	$0.293847\pi$
$308$	1.16391	0.0663198
$309$	49.4913	2.81546
$310$	−0.170227	−0.00966824
$311$	11.7359	0.665484	0.332742	−	0.943018i	$-0.392026\pi$
$311$	11.7359	0.665484	0.332742	+	0.943018i	$0.392026\pi$
$312$	−0.691242	−0.0391338
$313$	−7.73627	−0.437280	−0.218640	−	0.975806i	$-0.570162\pi$
$313$	−7.73627	−0.437280	−0.218640	+	0.975806i	$0.570162\pi$
$314$	−5.31886	−0.300160
$315$	−1.43188	−0.0806773
$316$	−15.5725	−0.876021
$317$	−7.79285	−0.437690	−0.218845	−	0.975760i	$-0.570229\pi$
$317$	−7.79285	−0.437690	−0.218845	+	0.975760i	$0.570229\pi$
$318$	32.1113	1.80071
$319$	−0.612678	−0.0343034
$320$	0.116361	0.00650480
$321$	−38.1429	−2.12893
$322$	1.89971	0.105867
$323$	−18.4174	−1.02477
$324$	13.5261	0.751448
$325$	−1.11963	−0.0621058
$326$	−7.15557	−0.396310
$327$	−25.1797	−1.39244
$328$	−10.7350	−0.592740
$329$	20.5435	1.13260
$330$	0.219477	0.0120818
$331$	−34.4089	−1.89129	−0.945643	−	0.325206i	$-0.894566\pi$
$331$	−34.4089	−1.89129	−0.945643	+	0.325206i	$0.894566\pi$
$332$	−6.02426	−0.330624
$333$	22.6383	1.24057
$334$	13.6801	0.748540
$335$	0.880340	0.0480981
$336$	5.84837	0.319055
$337$	27.9695	1.52359	0.761797	−	0.647815i	$-0.224317\pi$
$337$	27.9695	1.52359	0.761797	+	0.647815i	$0.224317\pi$
$338$	−12.9496	−0.704365
$339$	−25.5726	−1.38891
$340$	0.587908	0.0318838
$341$	0.896296	0.0485372
$342$	−23.6123	−1.27681
$343$	19.7401	1.06586
$344$	5.00253	0.269718
$345$	0.358226	0.0192862
$346$	9.78366	0.525973
$347$	16.4766	0.884512	0.442256	−	0.896889i	$-0.354178\pi$
$347$	16.4766	0.884512	0.442256	+	0.896889i	$0.354178\pi$
$348$	−3.07856	−0.165028
$349$	15.4647	0.827808	0.413904	−	0.910320i	$-0.364165\pi$
$349$	15.4647	0.827808	0.413904	+	0.910320i	$0.364165\pi$
$350$	9.47281	0.506343
$351$	−2.40383	−0.128307
$352$	−0.612678	−0.0326558
$353$	14.9355	0.794935	0.397467	−	0.917616i	$-0.369889\pi$
$353$	14.9355	0.794935	0.397467	+	0.917616i	$0.369889\pi$
$354$	32.8976	1.74849
$355$	−0.580758	−0.0308235
$356$	−11.1941	−0.593286
$357$	29.5485	1.56387
$358$	−4.23681	−0.223922
$359$	5.82739	0.307558	0.153779	−	0.988105i	$-0.450856\pi$
$359$	5.82739	0.307558	0.153779	+	0.988105i	$0.450856\pi$
$360$	0.753737	0.0397254
$361$	−5.71211	−0.300638
$362$	0.776074	0.0407895
$363$	32.7086	1.71676
$364$	−0.426548	−0.0223572
$365$	0.456598	0.0238994
$366$	−14.4249	−0.754000
$367$	−6.87668	−0.358960	−0.179480	−	0.983762i	$-0.557441\pi$
$367$	−6.87668	−0.358960	−0.179480	+	0.983762i	$0.557441\pi$
$368$	−1.00000	−0.0521286
$369$	−69.5364	−3.61992
$370$	0.406670	0.0211418
$371$	19.8151	1.02875
$372$	4.50368	0.233505
$373$	−12.7121	−0.658209	−0.329104	−	0.944294i	$-0.606747\pi$
$373$	−12.7121	−0.658209	−0.329104	+	0.944294i	$0.606747\pi$
$374$	−3.09551	−0.160065
$375$	3.57741	0.184737
$376$	−10.8141	−0.557692
$377$	0.224534	0.0115641
$378$	20.3380	1.04608
$379$	27.0953	1.39179	0.695895	−	0.718143i	$-0.255008\pi$
$379$	27.0953	1.39179	0.695895	+	0.718143i	$0.255008\pi$
$380$	−0.424167	−0.0217593
$381$	−41.6504	−2.13382
$382$	2.63754	0.134948
$383$	−6.00622	−0.306904	−0.153452	−	0.988156i	$-0.549039\pi$
$383$	−6.00622	−0.306904	−0.153452	+	0.988156i	$0.549039\pi$
$384$	−3.07856	−0.157102
$385$	0.135434	0.00690235
$386$	1.08631	0.0552918
$387$	32.4042	1.64720
$388$	−11.6637	−0.592134
$389$	27.1232	1.37520	0.687600	−	0.726090i	$-0.258664\pi$
$389$	27.1232	1.37520	0.687600	+	0.726090i	$0.258664\pi$
$390$	−0.0804338	−0.00407292
$391$	−5.05244	−0.255513
$392$	−3.39111	−0.171277
$393$	−69.6886	−3.51533
$394$	−3.15055	−0.158722
$395$	−1.81204	−0.0911735
$396$	−3.96865	−0.199432
$397$	−25.6974	−1.28971	−0.644857	−	0.764303i	$-0.723083\pi$
$397$	−25.6974	−1.28971	−0.644857	+	0.764303i	$0.723083\pi$
$398$	4.43269	0.222191
$399$	−21.3188	−1.06727
$400$	−4.98646	−0.249323
$401$	−25.9167	−1.29422	−0.647108	−	0.762398i	$-0.724022\pi$
$401$	−25.9167	−1.29422	−0.647108	+	0.762398i	$0.724022\pi$
$402$	−23.2911	−1.16165
$403$	−0.328474	−0.0163625
$404$	8.61155	0.428440
$405$	1.57391	0.0782083
$406$	−1.89971	−0.0942809
$407$	−2.14124	−0.106137
$408$	−15.5543	−0.770050
$409$	−23.7719	−1.17544	−0.587722	−	0.809063i	$-0.699975\pi$
$409$	−23.7719	−1.17544	−0.587722	+	0.809063i	$0.699975\pi$
$410$	−1.24914	−0.0616905
$411$	−17.2973	−0.853211
$412$	−16.0761	−0.792012
$413$	20.3003	0.998913
$414$	−6.47756	−0.318355
$415$	−0.700991	−0.0344103
$416$	0.224534	0.0110087
$417$	20.1486	0.986680
$418$	2.23337	0.109238
$419$	−31.5920	−1.54337	−0.771686	−	0.636004i	$-0.780586\pi$
$419$	−31.5920	−1.54337	−0.771686	+	0.636004i	$0.780586\pi$
$420$	0.680524	0.0332062
$421$	−5.51394	−0.268733	−0.134367	−	0.990932i	$-0.542900\pi$
$421$	−5.51394	−0.268733	−0.134367	+	0.990932i	$0.542900\pi$
$422$	13.3543	0.650078
$423$	−70.0486	−3.40588
$424$	−10.4306	−0.506556
$425$	−25.1938	−1.22208
$426$	15.3651	0.744441
$427$	−8.90123	−0.430761
$428$	12.3899	0.598886
$429$	0.423508	0.0204472
$430$	0.582101	0.0280714
$431$	−19.6993	−0.948880	−0.474440	−	0.880288i	$-0.657349\pi$
$431$	−19.6993	−0.948880	−0.474440	+	0.880288i	$0.657349\pi$
$432$	−10.7059	−0.515087
$433$	−35.1321	−1.68834	−0.844170	−	0.536076i	$-0.819906\pi$
$433$	−35.1321	−1.68834	−0.844170	+	0.536076i	$0.819906\pi$
$434$	2.77911	0.133402
$435$	−0.358226	−0.0171756
$436$	8.17904	0.391705
$437$	3.64526	0.174376
$438$	−12.0802	−0.577213
$439$	−10.0842	−0.481292	−0.240646	−	0.970613i	$-0.577359\pi$
$439$	−10.0842	−0.481292	−0.240646	+	0.970613i	$0.577359\pi$
$440$	−0.0712920	−0.00339871
$441$	−21.9661	−1.04601
$442$	1.13444	0.0539599
$443$	−15.3316	−0.728426	−0.364213	−	0.931316i	$-0.618662\pi$
$443$	−15.3316	−0.728426	−0.364213	+	0.931316i	$0.618662\pi$
$444$	−10.7592	−0.510611
$445$	−1.30256	−0.0617473
$446$	7.90399	0.374265
$447$	49.3337	2.33341
$448$	−1.89971	−0.0897527
$449$	21.6408	1.02129	0.510647	−	0.859791i	$-0.329406\pi$
$449$	21.6408	1.02129	0.510647	+	0.859791i	$0.329406\pi$
$450$	−32.3001	−1.52264
$451$	6.57708	0.309703
$452$	8.30667	0.390713
$453$	23.4196	1.10035
$454$	−11.0082	−0.516640
$455$	−0.0496338	−0.00232687
$456$	11.2222	0.525525
$457$	−3.36036	−0.157191	−0.0785954	−	0.996907i	$-0.525044\pi$
$457$	−3.36036	−0.157191	−0.0785954	+	0.996907i	$0.525044\pi$
$458$	−3.98406	−0.186163
$459$	−54.0908	−2.52474
$460$	−0.116361	−0.00542538
$461$	39.9839	1.86224	0.931118	−	0.364719i	$-0.118835\pi$
$461$	39.9839	1.86224	0.931118	+	0.364719i	$0.118835\pi$
$462$	−3.58316	−0.166704
$463$	−19.4691	−0.904805	−0.452402	−	0.891814i	$-0.649433\pi$
$463$	−19.4691	−0.904805	−0.452402	+	0.891814i	$0.649433\pi$
$464$	1.00000	0.0464238
$465$	0.524055	0.0243025
$466$	14.4294	0.668427
$467$	4.56418	0.211205	0.105603	−	0.994408i	$-0.466323\pi$
$467$	4.56418	0.211205	0.105603	+	0.994408i	$0.466323\pi$
$468$	1.45443	0.0672311
$469$	−14.3724	−0.663654
$470$	−1.25834	−0.0580428
$471$	16.3744	0.754494
$472$	−10.6860	−0.491864
$473$	−3.06494	−0.140926
$474$	47.9409	2.20200
$475$	18.1769	0.834014
$476$	−9.59815	−0.439930
$477$	−67.5649	−3.09359
$478$	17.9961	0.823121
$479$	−40.0775	−1.83119	−0.915594	−	0.402104i	$-0.868279\pi$
$479$	−40.0775	−1.83119	−0.915594	+	0.402104i	$0.868279\pi$
$480$	−0.358226	−0.0163507
$481$	0.784720	0.0357802
$482$	−8.92523	−0.406533
$483$	−5.84837	−0.266110
$484$	−10.6246	−0.482938
$485$	−1.35720	−0.0616274
$486$	−9.52323	−0.431983
$487$	7.30951	0.331225	0.165613	−	0.986191i	$-0.447040\pi$
$487$	7.30951	0.331225	0.165613	+	0.986191i	$0.447040\pi$
$488$	4.68558	0.212106
$489$	22.0289	0.996180
$490$	−0.394595	−0.0178260
$491$	12.4974	0.563999	0.281999	−	0.959415i	$-0.409002\pi$
$491$	12.4974	0.563999	0.281999	+	0.959415i	$0.409002\pi$
$492$	33.0483	1.48993
$493$	5.05244	0.227550
$494$	−0.818483	−0.0368253
$495$	−0.461798	−0.0207563
$496$	−1.46292	−0.0656869
$497$	9.48142	0.425300
$498$	18.5461	0.831069
$499$	−31.7563	−1.42161	−0.710804	−	0.703390i	$-0.751669\pi$
$499$	−31.7563	−1.42161	−0.710804	+	0.703390i	$0.751669\pi$
$500$	−1.16204	−0.0519679
$501$	−42.1150	−1.88156
$502$	−9.67702	−0.431907
$503$	34.8351	1.55322	0.776611	−	0.629981i	$-0.216937\pi$
$503$	34.8351	1.55322	0.776611	+	0.629981i	$0.216937\pi$
$504$	−12.3055	−0.548129
$505$	1.00205	0.0445907
$506$	0.612678	0.0272368
$507$	39.8661	1.77052
$508$	13.5292	0.600260
$509$	−32.8038	−1.45400	−0.727002	−	0.686635i	$-0.759087\pi$
$509$	−32.8038	−1.45400	−0.727002	+	0.686635i	$0.759087\pi$
$510$	−1.80991	−0.0801443
$511$	−7.45438	−0.329762
$512$	1.00000	0.0441942
$513$	39.0257	1.72303
$514$	−0.0260315	−0.00114820
$515$	−1.87064	−0.0824300
$516$	−15.4006	−0.677974
$517$	6.62553	0.291390
$518$	−6.63926	−0.291712
$519$	−30.1196	−1.32210
$520$	0.0261271	0.00114575
$521$	−11.8703	−0.520048	−0.260024	−	0.965602i	$-0.583731\pi$
$521$	−11.8703	−0.520048	−0.260024	+	0.965602i	$0.583731\pi$
$522$	6.47756	0.283515
$523$	−21.8759	−0.956567	−0.478284	−	0.878205i	$-0.658741\pi$
$523$	−21.8759	−0.956567	−0.478284	+	0.878205i	$0.658741\pi$
$524$	22.6367	0.988890
$525$	−29.1627	−1.27276
$526$	4.08958	0.178314
$527$	−7.39130	−0.321970
$528$	1.88617	0.0820849
$529$	1.00000	0.0434783
$530$	−1.21372	−0.0527207
$531$	−69.2193	−3.00386
$532$	6.92492	0.300233
$533$	−2.41037	−0.104405
$534$	34.4618	1.49131
$535$	1.44170	0.0623301
$536$	7.56557	0.326783
$537$	13.0433	0.562860
$538$	8.84771	0.381452
$539$	2.07766	0.0894911
$540$	−1.24575	−0.0536086
$541$	−8.38552	−0.360522	−0.180261	−	0.983619i	$-0.557694\pi$
$541$	−8.38552	−0.360522	−0.180261	+	0.983619i	$0.557694\pi$
$542$	−7.33080	−0.314885
$543$	−2.38919	−0.102530
$544$	5.05244	0.216621
$545$	0.951724	0.0407674
$546$	1.31316	0.0561979
$547$	23.7319	1.01470	0.507352	−	0.861739i	$-0.330624\pi$
$547$	23.7319	1.01470	0.507352	+	0.861739i	$0.330624\pi$
$548$	5.61862	0.240015
$549$	30.3511	1.29535
$550$	3.05509	0.130270
$551$	−3.64526	−0.155293
$552$	3.07856	0.131032
$553$	29.5832	1.25800
$554$	15.0387	0.638935
$555$	−1.25196	−0.0531427
$556$	−6.54480	−0.277561
$557$	14.4913	0.614015	0.307007	−	0.951707i	$-0.400672\pi$
$557$	14.4913	0.614015	0.307007	+	0.951707i	$0.400672\pi$
$558$	−9.47613	−0.401156
$559$	1.12324	0.0475078
$560$	−0.221052	−0.00934117
$561$	9.52974	0.402346
$562$	2.24194	0.0945703
$563$	−5.52354	−0.232790	−0.116395	−	0.993203i	$-0.537134\pi$
$563$	−5.52354	−0.232790	−0.116395	+	0.993203i	$0.537134\pi$
$564$	33.2918	1.40184
$565$	0.966576	0.0406642
$566$	−27.8267	−1.16964
$567$	−25.6956	−1.07911
$568$	−4.99099	−0.209417
$569$	34.6160	1.45118	0.725589	−	0.688129i	$-0.241568\pi$
$569$	34.6160	1.45118	0.725589	+	0.688129i	$0.241568\pi$
$570$	1.30582	0.0546950
$571$	−20.1960	−0.845175	−0.422587	−	0.906322i	$-0.638878\pi$
$571$	−20.1960	−0.845175	−0.422587	+	0.906322i	$0.638878\pi$
$572$	−0.137567	−0.00575196
$573$	−8.11984	−0.339211
$574$	20.3933	0.851200
$575$	4.98646	0.207950
$576$	6.47756	0.269898
$577$	12.8383	0.534467	0.267233	−	0.963632i	$-0.413891\pi$
$577$	12.8383	0.534467	0.267233	+	0.963632i	$0.413891\pi$
$578$	8.52712	0.354681
$579$	−3.34428	−0.138984
$580$	0.116361	0.00483164
$581$	11.4443	0.474791
$582$	35.9074	1.48841
$583$	6.39061	0.264672
$584$	3.92396	0.162375
$585$	0.169239	0.00699719
$586$	−16.2758	−0.672347
$587$	1.50160	0.0619777	0.0309888	−	0.999520i	$-0.490134\pi$
$587$	1.50160	0.0619777	0.0309888	+	0.999520i	$0.490134\pi$
$588$	10.4398	0.430528
$589$	5.33271	0.219730
$590$	−1.24344	−0.0511916
$591$	9.69917	0.398971
$592$	3.49489	0.143639
$593$	47.3946	1.94626	0.973132	−	0.230248i	$-0.0739536\pi$
$593$	47.3946	1.94626	0.973132	+	0.230248i	$0.0739536\pi$
$594$	6.55925	0.269129
$595$	−1.11685	−0.0457865
$596$	−16.0249	−0.656406
$597$	−13.6463	−0.558507
$598$	−0.224534	−0.00918187
$599$	1.05357	0.0430476	0.0215238	−	0.999768i	$-0.493148\pi$
$599$	1.05357	0.0430476	0.0215238	+	0.999768i	$0.493148\pi$
$600$	15.3511	0.626708
$601$	−36.5947	−1.49273	−0.746365	−	0.665536i	$-0.768203\pi$
$601$	−36.5947	−1.49273	−0.746365	+	0.665536i	$0.768203\pi$
$602$	−9.50334	−0.387327
$603$	49.0064	1.99570
$604$	−7.60733	−0.309538
$605$	−1.23630	−0.0502626
$606$	−26.5112	−1.07694
$607$	2.20036	0.0893098	0.0446549	−	0.999002i	$-0.485781\pi$
$607$	2.20036	0.0893098	0.0446549	+	0.999002i	$0.485781\pi$
$608$	−3.64526	−0.147835
$609$	5.84837	0.236988
$610$	0.545221	0.0220753
$611$	−2.42812	−0.0982312
$612$	32.7274	1.32293
$613$	−27.3470	−1.10454	−0.552268	−	0.833666i	$-0.686238\pi$
$613$	−27.3470	−1.10454	−0.552268	+	0.833666i	$0.686238\pi$
$614$	21.1418	0.853214
$615$	3.84555	0.155067
$616$	1.16391	0.0468952
$617$	6.60741	0.266004	0.133002	−	0.991116i	$-0.457538\pi$
$617$	6.60741	0.266004	0.133002	+	0.991116i	$0.457538\pi$
$618$	49.4913	1.99083
$619$	13.3113	0.535026	0.267513	−	0.963554i	$-0.413798\pi$
$619$	13.3113	0.535026	0.267513	+	0.963554i	$0.413798\pi$
$620$	−0.170227	−0.00683648
$621$	10.7059	0.429612
$622$	11.7359	0.470568
$623$	21.2655	0.851985
$624$	−0.691242	−0.0276718
$625$	24.7971	0.991883
$626$	−7.73627	−0.309204
$627$	−6.87556	−0.274583
$628$	−5.31886	−0.212245
$629$	17.6577	0.704059
$630$	−1.43188	−0.0570475
$631$	−18.1126	−0.721051	−0.360525	−	0.932749i	$-0.617403\pi$
$631$	−18.1126	−0.721051	−0.360525	+	0.932749i	$0.617403\pi$
$632$	−15.5725	−0.619441
$633$	−41.1121	−1.63406
$634$	−7.79285	−0.309494
$635$	1.57427	0.0624731
$636$	32.1113	1.27330
$637$	−0.761419	−0.0301685
$638$	−0.612678	−0.0242561
$639$	−32.3294	−1.27893
$640$	0.116361	0.00459959
$641$	−33.6010	−1.32716	−0.663580	−	0.748105i	$-0.730964\pi$
$641$	−33.6010	−1.32716	−0.663580	+	0.748105i	$0.730964\pi$
$642$	−38.1429	−1.50538
$643$	23.0758	0.910022	0.455011	−	0.890486i	$-0.349635\pi$
$643$	23.0758	0.910022	0.455011	+	0.890486i	$0.349635\pi$
$644$	1.89971	0.0748589
$645$	−1.79204	−0.0705613
$646$	−18.4174	−0.724624
$647$	−7.27557	−0.286032	−0.143016	−	0.989720i	$-0.545680\pi$
$647$	−7.27557	−0.286032	−0.143016	+	0.989720i	$0.545680\pi$
$648$	13.5261	0.531354
$649$	6.54709	0.256996
$650$	−1.11963	−0.0439155
$651$	−8.55568	−0.335324
$652$	−7.15557	−0.280234
$653$	12.6982	0.496918	0.248459	−	0.968642i	$-0.420076\pi$
$653$	12.6982	0.496918	0.248459	+	0.968642i	$0.420076\pi$
$654$	−25.1797	−0.984604
$655$	2.63404	0.102921
$656$	−10.7350	−0.419130
$657$	25.4177	0.991639
$658$	20.5435	0.800870
$659$	41.3604	1.61117	0.805585	−	0.592480i	$-0.201851\pi$
$659$	41.3604	1.61117	0.805585	+	0.592480i	$0.201851\pi$
$660$	0.219477	0.00854313
$661$	−0.276414	−0.0107513	−0.00537563	−	0.999986i	$-0.501711\pi$
$661$	−0.276414	−0.0107513	−0.00537563	+	0.999986i	$0.501711\pi$
$662$	−34.4089	−1.33734
$663$	−3.49245	−0.135636
$664$	−6.02426	−0.233787
$665$	0.805793	0.0312473
$666$	22.6383	0.877218
$667$	−1.00000	−0.0387202
$668$	13.6801	0.529298
$669$	−24.3329	−0.940766
$670$	0.880340	0.0340105
$671$	−2.87075	−0.110824
$672$	5.84837	0.225606
$673$	20.4628	0.788783	0.394392	−	0.918943i	$-0.370955\pi$
$673$	20.4628	0.788783	0.394392	+	0.918943i	$0.370955\pi$
$674$	27.9695	1.07734
$675$	53.3844	2.05477
$676$	−12.9496	−0.498061
$677$	−19.2133	−0.738428	−0.369214	−	0.929344i	$-0.620373\pi$
$677$	−19.2133	−0.738428	−0.369214	+	0.929344i	$0.620373\pi$
$678$	−25.5726	−0.982111
$679$	22.1576	0.850330
$680$	0.587908	0.0225453
$681$	33.8894	1.29865
$682$	0.896296	0.0343210
$683$	−23.9672	−0.917080	−0.458540	−	0.888674i	$-0.651627\pi$
$683$	−23.9672	−0.917080	−0.458540	+	0.888674i	$0.651627\pi$
$684$	−23.6123	−0.902841
$685$	0.653790	0.0249800
$686$	19.7401	0.753679
$687$	12.2652	0.467946
$688$	5.00253	0.190720
$689$	−2.34203	−0.0892241
$690$	0.358226	0.0136374
$691$	30.2622	1.15123	0.575614	−	0.817721i	$-0.304763\pi$
$691$	30.2622	1.15123	0.575614	+	0.817721i	$0.304763\pi$
$692$	9.78366	0.371919
$693$	7.53928	0.286394
$694$	16.4766	0.625445
$695$	−0.761561	−0.0288877
$696$	−3.07856	−0.116693
$697$	−54.2378	−2.05440
$698$	15.4647	0.585349
$699$	−44.4217	−1.68018
$700$	9.47281	0.358039
$701$	−8.04768	−0.303957	−0.151978	−	0.988384i	$-0.548564\pi$
$701$	−8.04768	−0.303957	−0.151978	+	0.988384i	$0.548564\pi$
$702$	−2.40383	−0.0907268
$703$	−12.7398	−0.480489
$704$	−0.612678	−0.0230912
$705$	3.87387	0.145899
$706$	14.9355	0.562104
$707$	−16.3594	−0.615259
$708$	32.8976	1.23637
$709$	39.1065	1.46868	0.734338	−	0.678784i	$-0.237493\pi$
$709$	39.1065	1.46868	0.734338	+	0.678784i	$0.237493\pi$
$710$	−0.580758	−0.0217955
$711$	−100.872	−3.78299
$712$	−11.1941	−0.419517
$713$	1.46292	0.0547867
$714$	29.5485	1.10583
$715$	−0.0160075	−0.000598645 0
$716$	−4.23681	−0.158337
$717$	−55.4020	−2.06903
$718$	5.82739	0.217476
$719$	24.2075	0.902789	0.451395	−	0.892324i	$-0.350927\pi$
$719$	24.2075	0.902789	0.451395	+	0.892324i	$0.350927\pi$
$720$	0.753737	0.0280901
$721$	30.5399	1.13736
$722$	−5.71211	−0.212583
$723$	27.4769	1.02188
$724$	0.776074	0.0288425
$725$	−4.98646	−0.185192
$726$	32.7086	1.21393
$727$	−11.3618	−0.421386	−0.210693	−	0.977552i	$-0.567572\pi$
$727$	−11.3618	−0.421386	−0.210693	+	0.977552i	$0.567572\pi$
$728$	−0.426548	−0.0158089
$729$	−11.2603	−0.417049
$730$	0.456598	0.0168994
$731$	25.2750	0.934828
$732$	−14.4249	−0.533158
$733$	35.8091	1.32264	0.661320	−	0.750103i	$-0.269996\pi$
$733$	35.8091	1.32264	0.661320	+	0.750103i	$0.269996\pi$
$734$	−6.87668	−0.253823
$735$	1.21478	0.0448080
$736$	−1.00000	−0.0368605
$737$	−4.63526	−0.170742
$738$	−69.5364	−2.55967
$739$	17.5636	0.646086	0.323043	−	0.946384i	$-0.395294\pi$
$739$	17.5636	0.646086	0.323043	+	0.946384i	$0.395294\pi$
$740$	0.406670	0.0149495
$741$	2.51975	0.0925654
$742$	19.8151	0.727436
$743$	34.6011	1.26939	0.634695	−	0.772763i	$-0.281126\pi$
$743$	34.6011	1.26939	0.634695	+	0.772763i	$0.281126\pi$
$744$	4.50368	0.165113
$745$	−1.86468	−0.0683166
$746$	−12.7121	−0.465424
$747$	−39.0225	−1.42776
$748$	−3.09551	−0.113183
$749$	−23.5371	−0.860026
$750$	3.57741	0.130628
$751$	−18.2640	−0.666463	−0.333232	−	0.942845i	$-0.608139\pi$
$751$	−18.2640	−0.666463	−0.333232	+	0.942845i	$0.608139\pi$
$752$	−10.8141	−0.394348
$753$	29.7913	1.08566
$754$	0.224534	0.00817704
$755$	−0.885199	−0.0322157
$756$	20.3380	0.739687
$757$	−8.86370	−0.322156	−0.161078	−	0.986942i	$-0.551497\pi$
$757$	−8.86370	−0.322156	−0.161078	+	0.986942i	$0.551497\pi$
$758$	27.0953	0.984144
$759$	−1.88617	−0.0684635
$760$	−0.424167	−0.0153861
$761$	−13.4577	−0.487841	−0.243921	−	0.969795i	$-0.578434\pi$
$761$	−13.4577	−0.487841	−0.243921	+	0.969795i	$0.578434\pi$
$762$	−41.6504	−1.50884
$763$	−15.5378	−0.562505
$764$	2.63754	0.0954229
$765$	3.80821	0.137686
$766$	−6.00622	−0.217014
$767$	−2.39937	−0.0866363
$768$	−3.07856	−0.111088
$769$	−20.4384	−0.737028	−0.368514	−	0.929622i	$-0.620133\pi$
$769$	−20.4384	−0.737028	−0.368514	+	0.929622i	$0.620133\pi$
$770$	0.135434	0.00488070
$771$	0.0801396	0.00288616
$772$	1.08631	0.0390972
$773$	−3.43676	−0.123612	−0.0618058	−	0.998088i	$-0.519686\pi$
$773$	−3.43676	−0.123612	−0.0618058	+	0.998088i	$0.519686\pi$
$774$	32.4042	1.16474
$775$	7.29478	0.262036
$776$	−11.6637	−0.418702
$777$	20.4394	0.733259
$778$	27.1232	0.972413
$779$	39.1317	1.40204
$780$	−0.0804338	−0.00287999
$781$	3.05787	0.109419
$782$	−5.05244	−0.180675
$783$	−10.7059	−0.382597
$784$	−3.39111	−0.121111
$785$	−0.618909	−0.0220898
$786$	−69.6886	−2.48571
$787$	18.3854	0.655369	0.327684	−	0.944787i	$-0.393732\pi$
$787$	18.3854	0.655369	0.327684	+	0.944787i	$0.393732\pi$
$788$	−3.15055	−0.112234
$789$	−12.5900	−0.448217
$790$	−1.81204	−0.0644694
$791$	−15.7802	−0.561081
$792$	−3.96865	−0.141020
$793$	1.05207	0.0373601
$794$	−25.6974	−0.911965
$795$	3.73652	0.132521
$796$	4.43269	0.157113
$797$	−13.9574	−0.494398	−0.247199	−	0.968965i	$-0.579510\pi$
$797$	−13.9574	−0.494398	−0.247199	+	0.968965i	$0.579510\pi$
$798$	−21.3188	−0.754677
$799$	−54.6373	−1.93293
$800$	−4.98646	−0.176298
$801$	−72.5104	−2.56203
$802$	−25.9167	−0.915149
$803$	−2.40412	−0.0848397
$804$	−23.2911	−0.821414
$805$	0.221052	0.00779108
$806$	−0.328474	−0.0115700
$807$	−27.2382	−0.958832
$808$	8.61155	0.302953
$809$	10.8362	0.380979	0.190489	−	0.981689i	$-0.438993\pi$
$809$	10.8362	0.380979	0.190489	+	0.981689i	$0.438993\pi$
$810$	1.57391	0.0553016
$811$	−9.70130	−0.340659	−0.170329	−	0.985387i	$-0.554483\pi$
$811$	−9.70130	−0.340659	−0.170329	+	0.985387i	$0.554483\pi$
$812$	−1.89971	−0.0666666
$813$	22.5683	0.791506
$814$	−2.14124	−0.0750504
$815$	−0.832632	−0.0291658
$816$	−15.5543	−0.544508
$817$	−18.2355	−0.637979
$818$	−23.7719	−0.831165
$819$	−2.76299	−0.0965467
$820$	−1.24914	−0.0436217
$821$	50.8025	1.77302	0.886509	−	0.462711i	$-0.153123\pi$
$821$	50.8025	1.77302	0.886509	+	0.462711i	$0.153123\pi$
$822$	−17.2973	−0.603312
$823$	30.5966	1.06653	0.533266	−	0.845948i	$-0.320965\pi$
$823$	30.5966	1.06653	0.533266	+	0.845948i	$0.320965\pi$
$824$	−16.0761	−0.560037
$825$	−9.40530	−0.327450
$826$	20.3003	0.706338
$827$	24.5351	0.853169	0.426584	−	0.904448i	$-0.359717\pi$
$827$	24.5351	0.853169	0.426584	+	0.904448i	$0.359717\pi$
$828$	−6.47756	−0.225111
$829$	4.08505	0.141880	0.0709399	−	0.997481i	$-0.477400\pi$
$829$	4.08505	0.141880	0.0709399	+	0.997481i	$0.477400\pi$
$830$	−0.700991	−0.0243317
$831$	−46.2977	−1.60605
$832$	0.224534	0.00778431
$833$	−17.1334	−0.593637
$834$	20.1486	0.697688
$835$	1.59183	0.0550876
$836$	2.23337	0.0772426
$837$	15.6618	0.541352
$838$	−31.5920	−1.09133
$839$	51.9457	1.79337	0.896683	−	0.442673i	$-0.145970\pi$
$839$	51.9457	1.79337	0.896683	+	0.442673i	$0.145970\pi$
$840$	0.680524	0.0234803
$841$	1.00000	0.0344828
$842$	−5.51394	−0.190023
$843$	−6.90194	−0.237715
$844$	13.3543	0.459675
$845$	−1.50683	−0.0518366
$846$	−70.0486	−2.40832
$847$	20.1837	0.693519
$848$	−10.4306	−0.358189
$849$	85.6661	2.94005
$850$	−25.1938	−0.864139
$851$	−3.49489	−0.119803
$852$	15.3651	0.526399
$853$	−49.2961	−1.68787	−0.843933	−	0.536449i	$-0.819766\pi$
$853$	−49.2961	−1.68787	−0.843933	+	0.536449i	$0.819766\pi$
$854$	−8.90123	−0.304594
$855$	−2.74757	−0.0939647
$856$	12.3899	0.423476
$857$	24.2677	0.828969	0.414484	−	0.910056i	$-0.363962\pi$
$857$	24.2677	0.828969	0.414484	+	0.910056i	$0.363962\pi$
$858$	0.423508	0.0144583
$859$	28.7638	0.981408	0.490704	−	0.871326i	$-0.336740\pi$
$859$	28.7638	0.981408	0.490704	+	0.871326i	$0.336740\pi$
$860$	0.582101	0.0198495
$861$	−62.7821	−2.13961
$862$	−19.6993	−0.670960
$863$	−26.2164	−0.892417	−0.446208	−	0.894929i	$-0.647226\pi$
$863$	−26.2164	−0.892417	−0.446208	+	0.894929i	$0.647226\pi$
$864$	−10.7059	−0.364221
$865$	1.13844	0.0387081
$866$	−35.1321	−1.19384
$867$	−26.2513	−0.891540
$868$	2.77911	0.0943293
$869$	9.54092	0.323654
$870$	−0.358226	−0.0121450
$871$	1.69873	0.0575592
$872$	8.17904	0.276977
$873$	−75.5522	−2.55705
$874$	3.64526	0.123303
$875$	2.20753	0.0746282
$876$	−12.0802	−0.408151
$877$	48.5140	1.63820	0.819100	−	0.573650i	$-0.194473\pi$
$877$	48.5140	1.63820	0.819100	+	0.573650i	$0.194473\pi$
$878$	−10.0842	−0.340325
$879$	50.1061	1.69004
$880$	−0.0712920	−0.00240325
$881$	41.6287	1.40251	0.701253	−	0.712912i	$-0.252624\pi$
$881$	41.6287	1.40251	0.701253	+	0.712912i	$0.252624\pi$
$882$	−21.9661	−0.739638
$883$	47.8916	1.61168	0.805840	−	0.592134i	$-0.201714\pi$
$883$	47.8916	1.61168	0.805840	+	0.592134i	$0.201714\pi$
$884$	1.13444	0.0381554
$885$	3.82801	0.128677
$886$	−15.3316	−0.515075
$887$	−57.4252	−1.92815	−0.964074	−	0.265634i	$-0.914419\pi$
$887$	−57.4252	−1.92815	−0.964074	+	0.265634i	$0.914419\pi$
$888$	−10.7592	−0.361056
$889$	−25.7015	−0.861999
$890$	−1.30256	−0.0436619
$891$	−8.28712	−0.277629
$892$	7.90399	0.264645
$893$	39.4200	1.31914
$894$	49.3337	1.64997
$895$	−0.493001	−0.0164792
$896$	−1.89971	−0.0634648
$897$	0.691242	0.0230799
$898$	21.6408	0.722164
$899$	−1.46292	−0.0487910
$900$	−32.3001	−1.07667
$901$	−52.7000	−1.75569
$902$	6.57708	0.218993
$903$	29.2566	0.973600
$904$	8.30667	0.276276
$905$	0.0903050	0.00300184
$906$	23.4196	0.778065
$907$	29.4865	0.979082	0.489541	−	0.871980i	$-0.337164\pi$
$907$	29.4865	0.979082	0.489541	+	0.871980i	$0.337164\pi$
$908$	−11.0082	−0.365320
$909$	55.7818	1.85016
$910$	−0.0496338	−0.00164534
$911$	47.9473	1.58857	0.794283	−	0.607548i	$-0.207847\pi$
$911$	47.9473	1.58857	0.794283	+	0.607548i	$0.207847\pi$
$912$	11.2222	0.371603
$913$	3.69093	0.122152
$914$	−3.36036	−0.111151
$915$	−1.67850	−0.0554894
$916$	−3.98406	−0.131637
$917$	−43.0032	−1.42009
$918$	−54.0908	−1.78526
$919$	41.0585	1.35440	0.677198	−	0.735801i	$-0.263194\pi$
$919$	41.0585	1.35440	0.677198	+	0.735801i	$0.263194\pi$
$920$	−0.116361	−0.00383632
$921$	−65.0864	−2.14467
$922$	39.9839	1.31680
$923$	−1.12065	−0.0368865
$924$	−3.58316	−0.117877
$925$	−17.4271	−0.573000
$926$	−19.4691	−0.639793
$927$	−104.134	−3.42020
$928$	1.00000	0.0328266
$929$	33.7838	1.10841	0.554206	−	0.832380i	$-0.313022\pi$
$929$	33.7838	1.10841	0.554206	+	0.832380i	$0.313022\pi$
$930$	0.524055	0.0171844
$931$	12.3615	0.405131
$932$	14.4294	0.472649
$933$	−36.1298	−1.18284
$934$	4.56418	0.149345
$935$	−0.360198	−0.0117797
$936$	1.45443	0.0475395
$937$	−39.8826	−1.30291	−0.651454	−	0.758688i	$-0.725841\pi$
$937$	−39.8826	−1.30291	−0.651454	+	0.758688i	$0.725841\pi$
$938$	−14.3724	−0.469275
$939$	23.8166	0.777226
$940$	−1.25834	−0.0410425
$941$	43.4879	1.41766	0.708832	−	0.705377i	$-0.249222\pi$
$941$	43.4879	1.41766	0.708832	+	0.705377i	$0.249222\pi$
$942$	16.3744	0.533508
$943$	10.7350	0.349579
$944$	−10.6860	−0.347800
$945$	2.36656	0.0769843
$946$	−3.06494	−0.0996497
$947$	9.88067	0.321079	0.160539	−	0.987029i	$-0.448677\pi$
$947$	9.88067	0.321079	0.160539	+	0.987029i	$0.448677\pi$
$948$	47.9409	1.55705
$949$	0.881063	0.0286005
$950$	18.1769	0.589737
$951$	23.9908	0.777954
$952$	−9.59815	−0.311078
$953$	2.74094	0.0887876	0.0443938	−	0.999014i	$-0.485864\pi$
$953$	2.74094	0.0887876	0.0443938	+	0.999014i	$0.485864\pi$
$954$	−67.5649	−2.18749
$955$	0.306908	0.00993131
$956$	17.9961	0.582034
$957$	1.88617	0.0609711
$958$	−40.0775	−1.29485
$959$	−10.6737	−0.344673
$960$	−0.358226	−0.0115617
$961$	−28.8599	−0.930964
$962$	0.784720	0.0253004
$963$	80.2560	2.58621
$964$	−8.92523	−0.287462
$965$	0.126405	0.00406911
$966$	−5.84837	−0.188168
$967$	11.0754	0.356161	0.178081	−	0.984016i	$-0.443011\pi$
$967$	11.0754	0.356161	0.178081	+	0.984016i	$0.443011\pi$
$968$	−10.6246	−0.341488
$969$	56.6992	1.82144
$970$	−1.35720	−0.0435771
$971$	19.2072	0.616387	0.308194	−	0.951324i	$-0.400276\pi$
$971$	19.2072	0.616387	0.308194	+	0.951324i	$0.400276\pi$
$972$	−9.52323	−0.305458
$973$	12.4332	0.398590
$974$	7.30951	0.234212
$975$	3.44685	0.110388
$976$	4.68558	0.149982
$977$	−26.2799	−0.840768	−0.420384	−	0.907346i	$-0.638105\pi$
$977$	−26.2799	−0.840768	−0.420384	+	0.907346i	$0.638105\pi$
$978$	22.0289	0.704406
$979$	6.85838	0.219195
$980$	−0.394595	−0.0126049
$981$	52.9802	1.69153
$982$	12.4974	0.398807
$983$	−46.3498	−1.47833	−0.739164	−	0.673526i	$-0.764779\pi$
$983$	−46.3498	−1.47833	−0.739164	+	0.673526i	$0.764779\pi$
$984$	33.0483	1.05354
$985$	−0.366602	−0.0116809
$986$	5.05244	0.160902
$987$	−63.2446	−2.01310
$988$	−0.818483	−0.0260394
$989$	−5.00253	−0.159071
$990$	−0.461798	−0.0146769
$991$	−57.6878	−1.83251	−0.916257	−	0.400591i	$-0.868805\pi$
$991$	−57.6878	−1.83251	−0.916257	+	0.400591i	$0.868805\pi$
$992$	−1.46292	−0.0464477
$993$	105.930	3.36159
$994$	9.48142	0.300732
$995$	0.515794	0.0163518
$996$	18.5461	0.587654
$997$	−29.4583	−0.932955	−0.466477	−	0.884533i	$-0.654477\pi$
$997$	−29.4583	−0.932955	−0.466477	+	0.884533i	$0.654477\pi$
$998$	−31.7563	−1.00523
$999$	−37.4159	−1.18379

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1334.2.a.h.1.1	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1334.2.a.h.1.1	✓	5	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:	\( N \)	\(=\)	\( 1334 = 2 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1334.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.07856 q^{3} +1.00000 q^{4} +0.116361 q^{5} -3.07856 q^{6} -1.89971 q^{7} +1.00000 q^{8} +6.47756 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.07856 q^{3} +1.00000 q^{4} +0.116361 q^{5} -3.07856 q^{6} -1.89971 q^{7} +1.00000 q^{8} +6.47756 q^{9} +0.116361 q^{10} -0.612678 q^{11} -3.07856 q^{12} +0.224534 q^{13} -1.89971 q^{14} -0.358226 q^{15} +1.00000 q^{16} +5.05244 q^{17} +6.47756 q^{18} -3.64526 q^{19} +0.116361 q^{20} +5.84837 q^{21} -0.612678 q^{22} -1.00000 q^{23} -3.07856 q^{24} -4.98646 q^{25} +0.224534 q^{26} -10.7059 q^{27} -1.89971 q^{28} +1.00000 q^{29} -0.358226 q^{30} -1.46292 q^{31} +1.00000 q^{32} +1.88617 q^{33} +5.05244 q^{34} -0.221052 q^{35} +6.47756 q^{36} +3.49489 q^{37} -3.64526 q^{38} -0.691242 q^{39} +0.116361 q^{40} -10.7350 q^{41} +5.84837 q^{42} +5.00253 q^{43} -0.612678 q^{44} +0.753737 q^{45} -1.00000 q^{46} -10.8141 q^{47} -3.07856 q^{48} -3.39111 q^{49} -4.98646 q^{50} -15.5543 q^{51} +0.224534 q^{52} -10.4306 q^{53} -10.7059 q^{54} -0.0712920 q^{55} -1.89971 q^{56} +11.2222 q^{57} +1.00000 q^{58} -10.6860 q^{59} -0.358226 q^{60} +4.68558 q^{61} -1.46292 q^{62} -12.3055 q^{63} +1.00000 q^{64} +0.0261271 q^{65} +1.88617 q^{66} +7.56557 q^{67} +5.05244 q^{68} +3.07856 q^{69} -0.221052 q^{70} -4.99099 q^{71} +6.47756 q^{72} +3.92396 q^{73} +3.49489 q^{74} +15.3511 q^{75} -3.64526 q^{76} +1.16391 q^{77} -0.691242 q^{78} -15.5725 q^{79} +0.116361 q^{80} +13.5261 q^{81} -10.7350 q^{82} -6.02426 q^{83} +5.84837 q^{84} +0.587908 q^{85} +5.00253 q^{86} -3.07856 q^{87} -0.612678 q^{88} -11.1941 q^{89} +0.753737 q^{90} -0.426548 q^{91} -1.00000 q^{92} +4.50368 q^{93} -10.8141 q^{94} -0.424167 q^{95} -3.07856 q^{96} -11.6637 q^{97} -3.39111 q^{98} -3.96865 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} - 3 q^{3} + 5 q^{4} - 5 q^{5} - 3 q^{6} - 6 q^{7} + 5 q^{8} + 2 q^{9}+O(q^{10}) \) 5 * q + 5 * q^2 - 3 * q^3 + 5 * q^4 - 5 * q^5 - 3 * q^6 - 6 * q^7 + 5 * q^8 + 2 * q^9	\( 5 q + 5 q^{2} - 3 q^{3} + 5 q^{4} - 5 q^{5} - 3 q^{6} - 6 q^{7} + 5 q^{8} + 2 q^{9} - 5 q^{10} - 9 q^{11} - 3 q^{12} - 5 q^{13} - 6 q^{14} - 3 q^{15} + 5 q^{16} - 6 q^{17} + 2 q^{18} - 10 q^{19} - 5 q^{20} - 2 q^{21} - 9 q^{22} - 5 q^{23} - 3 q^{24} - 4 q^{25} - 5 q^{26} - 9 q^{27} - 6 q^{28} + 5 q^{29} - 3 q^{30} - 15 q^{31} + 5 q^{32} - 15 q^{33} - 6 q^{34} - 2 q^{35} + 2 q^{36} - 10 q^{38} + 3 q^{39} - 5 q^{40} - 2 q^{41} - 2 q^{42} - 5 q^{43} - 9 q^{44} - 6 q^{45} - 5 q^{46} - 9 q^{47} - 3 q^{48} - 3 q^{49} - 4 q^{50} - 2 q^{51} - 5 q^{52} + 3 q^{53} - 9 q^{54} - 3 q^{55} - 6 q^{56} - 2 q^{57} + 5 q^{58} - 26 q^{59} - 3 q^{60} - 8 q^{61} - 15 q^{62} - 6 q^{63} + 5 q^{64} + 19 q^{65} - 15 q^{66} + 12 q^{67} - 6 q^{68} + 3 q^{69} - 2 q^{70} - 12 q^{71} + 2 q^{72} + 2 q^{73} + 24 q^{75} - 10 q^{76} + 36 q^{77} + 3 q^{78} - 25 q^{79} - 5 q^{80} + 9 q^{81} - 2 q^{82} - 16 q^{83} - 2 q^{84} + 4 q^{85} - 5 q^{86} - 3 q^{87} - 9 q^{88} - 20 q^{89} - 6 q^{90} - 32 q^{91} - 5 q^{92} + 11 q^{93} - 9 q^{94} + 20 q^{95} - 3 q^{96} - 4 q^{97} - 3 q^{98} + 20 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 - 3 * q^3 + 5 * q^4 - 5 * q^5 - 3 * q^6 - 6 * q^7 + 5 * q^8 + 2 * q^9 - 5 * q^10 - 9 * q^11 - 3 * q^12 - 5 * q^13 - 6 * q^14 - 3 * q^15 + 5 * q^16 - 6 * q^17 + 2 * q^18 - 10 * q^19 - 5 * q^20 - 2 * q^21 - 9 * q^22 - 5 * q^23 - 3 * q^24 - 4 * q^25 - 5 * q^26 - 9 * q^27 - 6 * q^28 + 5 * q^29 - 3 * q^30 - 15 * q^31 + 5 * q^32 - 15 * q^33 - 6 * q^34 - 2 * q^35 + 2 * q^36 - 10 * q^38 + 3 * q^39 - 5 * q^40 - 2 * q^41 - 2 * q^42 - 5 * q^43 - 9 * q^44 - 6 * q^45 - 5 * q^46 - 9 * q^47 - 3 * q^48 - 3 * q^49 - 4 * q^50 - 2 * q^51 - 5 * q^52 + 3 * q^53 - 9 * q^54 - 3 * q^55 - 6 * q^56 - 2 * q^57 + 5 * q^58 - 26 * q^59 - 3 * q^60 - 8 * q^61 - 15 * q^62 - 6 * q^63 + 5 * q^64 + 19 * q^65 - 15 * q^66 + 12 * q^67 - 6 * q^68 + 3 * q^69 - 2 * q^70 - 12 * q^71 + 2 * q^72 + 2 * q^73 + 24 * q^75 - 10 * q^76 + 36 * q^77 + 3 * q^78 - 25 * q^79 - 5 * q^80 + 9 * q^81 - 2 * q^82 - 16 * q^83 - 2 * q^84 + 4 * q^85 - 5 * q^86 - 3 * q^87 - 9 * q^88 - 20 * q^89 - 6 * q^90 - 32 * q^91 - 5 * q^92 + 11 * q^93 - 9 * q^94 + 20 * q^95 - 3 * q^96 - 4 * q^97 - 3 * q^98 + 20 * q^99

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