LMFDB - Embedded newform 4029.2.a.i.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.1717269744$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.40882 q^{2} -1.00000 q^{3} -0.0152236 q^{4} -1.73169 q^{5} +1.40882 q^{6} -3.56707 q^{7} +2.83909 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.40882 q^{2} -1.00000 q^{3} -0.0152236 q^{4} -1.73169 q^{5} +1.40882 q^{6} -3.56707 q^{7} +2.83909 q^{8} +1.00000 q^{9} +2.43964 q^{10} -1.25182 q^{11} +0.0152236 q^{12} -0.386358 q^{13} +5.02536 q^{14} +1.73169 q^{15} -3.96932 q^{16} +1.00000 q^{17} -1.40882 q^{18} -5.37119 q^{19} +0.0263625 q^{20} +3.56707 q^{21} +1.76359 q^{22} +7.48686 q^{23} -2.83909 q^{24} -2.00126 q^{25} +0.544310 q^{26} -1.00000 q^{27} +0.0543036 q^{28} -5.33712 q^{29} -2.43964 q^{30} -1.07583 q^{31} -0.0861158 q^{32} +1.25182 q^{33} -1.40882 q^{34} +6.17705 q^{35} -0.0152236 q^{36} -1.63763 q^{37} +7.56705 q^{38} +0.386358 q^{39} -4.91641 q^{40} -7.12213 q^{41} -5.02536 q^{42} -0.269566 q^{43} +0.0190572 q^{44} -1.73169 q^{45} -10.5476 q^{46} -5.98037 q^{47} +3.96932 q^{48} +5.72398 q^{49} +2.81942 q^{50} -1.00000 q^{51} +0.00588176 q^{52} -5.65334 q^{53} +1.40882 q^{54} +2.16776 q^{55} -10.1272 q^{56} +5.37119 q^{57} +7.51905 q^{58} -6.73716 q^{59} -0.0263625 q^{60} -3.48968 q^{61} +1.51565 q^{62} -3.56707 q^{63} +8.05996 q^{64} +0.669052 q^{65} -1.76359 q^{66} -0.361777 q^{67} -0.0152236 q^{68} -7.48686 q^{69} -8.70235 q^{70} -1.98865 q^{71} +2.83909 q^{72} -5.29412 q^{73} +2.30713 q^{74} +2.00126 q^{75} +0.0817689 q^{76} +4.46534 q^{77} -0.544310 q^{78} -1.00000 q^{79} +6.87362 q^{80} +1.00000 q^{81} +10.0338 q^{82} -7.94738 q^{83} -0.0543036 q^{84} -1.73169 q^{85} +0.379770 q^{86} +5.33712 q^{87} -3.55404 q^{88} -10.7568 q^{89} +2.43964 q^{90} +1.37817 q^{91} -0.113977 q^{92} +1.07583 q^{93} +8.42527 q^{94} +9.30123 q^{95} +0.0861158 q^{96} +8.03370 q^{97} -8.06406 q^{98} -1.25182 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 2 q^{2} - 25 q^{3} + 26 q^{4} - 2 q^{5} + 2 q^{6} + 12 q^{7} + 25 q^{9}+O(q^{10}) $ 25 * q - 2 * q^2 - 25 * q^3 + 26 * q^4 - 2 * q^5 + 2 * q^6 + 12 * q^7 + 25 * q^9	\( 25 q - 2 q^{2} - 25 q^{3} + 26 q^{4} - 2 q^{5} + 2 q^{6} + 12 q^{7} + 25 q^{9} + 19 q^{10} + 19 q^{11} - 26 q^{12} + 4 q^{13} + 15 q^{14} + 2 q^{15} + 32 q^{16} + 25 q^{17} - 2 q^{18} + 29 q^{19} - 8 q^{20} - 12 q^{21} + 23 q^{22} + 6 q^{23} + 15 q^{25} - 8 q^{26} - 25 q^{27} + 23 q^{28} + 11 q^{29} - 19 q^{30} + 38 q^{31} - 27 q^{32} - 19 q^{33} - 2 q^{34} + 20 q^{35} + 26 q^{36} + 8 q^{37} - 25 q^{38} - 4 q^{39} + 48 q^{40} + 24 q^{41} - 15 q^{42} + 11 q^{43} + 6 q^{44} - 2 q^{45} + 25 q^{46} + 23 q^{47} - 32 q^{48} + 21 q^{49} - 21 q^{50} - 25 q^{51} + 31 q^{52} - 16 q^{53} + 2 q^{54} - 11 q^{55} + 18 q^{56} - 29 q^{57} - 5 q^{58} + 27 q^{59} + 8 q^{60} + 40 q^{61} - 34 q^{62} + 12 q^{63} + 46 q^{64} - 19 q^{65} - 23 q^{66} + 24 q^{67} + 26 q^{68} - 6 q^{69} + 17 q^{70} + 19 q^{71} + 13 q^{73} - 56 q^{74} - 15 q^{75} + 21 q^{76} - 30 q^{77} + 8 q^{78} - 25 q^{79} - 40 q^{80} + 25 q^{81} + 61 q^{82} + q^{83} - 23 q^{84} - 2 q^{85} + 62 q^{86} - 11 q^{87} - q^{88} - 10 q^{89} + 19 q^{90} + 50 q^{91} + 18 q^{92} - 38 q^{93} + 15 q^{94} + 14 q^{95} + 27 q^{96} + 19 q^{97} - 23 q^{98} + 19 q^{99}+O(q^{100}) \) 25 * q - 2 * q^2 - 25 * q^3 + 26 * q^4 - 2 * q^5 + 2 * q^6 + 12 * q^7 + 25 * q^9 + 19 * q^10 + 19 * q^11 - 26 * q^12 + 4 * q^13 + 15 * q^14 + 2 * q^15 + 32 * q^16 + 25 * q^17 - 2 * q^18 + 29 * q^19 - 8 * q^20 - 12 * q^21 + 23 * q^22 + 6 * q^23 + 15 * q^25 - 8 * q^26 - 25 * q^27 + 23 * q^28 + 11 * q^29 - 19 * q^30 + 38 * q^31 - 27 * q^32 - 19 * q^33 - 2 * q^34 + 20 * q^35 + 26 * q^36 + 8 * q^37 - 25 * q^38 - 4 * q^39 + 48 * q^40 + 24 * q^41 - 15 * q^42 + 11 * q^43 + 6 * q^44 - 2 * q^45 + 25 * q^46 + 23 * q^47 - 32 * q^48 + 21 * q^49 - 21 * q^50 - 25 * q^51 + 31 * q^52 - 16 * q^53 + 2 * q^54 - 11 * q^55 + 18 * q^56 - 29 * q^57 - 5 * q^58 + 27 * q^59 + 8 * q^60 + 40 * q^61 - 34 * q^62 + 12 * q^63 + 46 * q^64 - 19 * q^65 - 23 * q^66 + 24 * q^67 + 26 * q^68 - 6 * q^69 + 17 * q^70 + 19 * q^71 + 13 * q^73 - 56 * q^74 - 15 * q^75 + 21 * q^76 - 30 * q^77 + 8 * q^78 - 25 * q^79 - 40 * q^80 + 25 * q^81 + 61 * q^82 + q^83 - 23 * q^84 - 2 * q^85 + 62 * q^86 - 11 * q^87 - q^88 - 10 * q^89 + 19 * q^90 + 50 * q^91 + 18 * q^92 - 38 * q^93 + 15 * q^94 + 14 * q^95 + 27 * q^96 + 19 * q^97 - 23 * q^98 + 19 * 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 $

$2$	−1.40882	−0.996187	−0.498093	−	0.867123i	$-0.665966\pi$
$2$	−1.40882	−0.996187	−0.498093	+	0.867123i	$0.665966\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.0152236	−0.00761180
$5$	−1.73169	−0.774434	−0.387217	−	0.921989i	$-0.626564\pi$
$5$	−1.73169	−0.774434	−0.387217	+	0.921989i	$0.626564\pi$
$6$	1.40882	0.575149
$7$	−3.56707	−1.34823	−0.674113	−	0.738629i	$-0.735474\pi$
$7$	−3.56707	−1.34823	−0.674113	+	0.738629i	$0.735474\pi$
$8$	2.83909	1.00377
$9$	1.00000	0.333333
$10$	2.43964	0.771481
$11$	−1.25182	−0.377439	−0.188719	−	0.982031i	$-0.560434\pi$
$11$	−1.25182	−0.377439	−0.188719	+	0.982031i	$0.560434\pi$
$12$	0.0152236	0.00439467
$13$	−0.386358	−0.107157	−0.0535783	−	0.998564i	$-0.517063\pi$
$13$	−0.386358	−0.107157	−0.0535783	+	0.998564i	$0.517063\pi$
$14$	5.02536	1.34308
$15$	1.73169	0.447120
$16$	−3.96932	−0.992330
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.40882	−0.332062
$19$	−5.37119	−1.23224	−0.616118	−	0.787654i	$-0.711296\pi$
$19$	−5.37119	−1.23224	−0.616118	+	0.787654i	$0.711296\pi$
$20$	0.0263625	0.00589484
$21$	3.56707	0.778398
$22$	1.76359	0.375999
$23$	7.48686	1.56112	0.780559	−	0.625082i	$-0.214934\pi$
$23$	7.48686	1.56112	0.780559	+	0.625082i	$0.214934\pi$
$24$	−2.83909	−0.579527
$25$	−2.00126	−0.400252
$26$	0.544310	0.106748
$27$	−1.00000	−0.192450
$28$	0.0543036	0.0102624
$29$	−5.33712	−0.991079	−0.495539	−	0.868585i	$-0.665030\pi$
$29$	−5.33712	−0.991079	−0.495539	+	0.868585i	$0.665030\pi$
$30$	−2.43964	−0.445415
$31$	−1.07583	−0.193225	−0.0966124	−	0.995322i	$-0.530801\pi$
$31$	−1.07583	−0.193225	−0.0966124	+	0.995322i	$0.530801\pi$
$32$	−0.0861158	−0.0152233
$33$	1.25182	0.217914
$34$	−1.40882	−0.241611
$35$	6.17705	1.04411
$36$	−0.0152236	−0.00253727
$37$	−1.63763	−0.269225	−0.134613	−	0.990898i	$-0.542979\pi$
$37$	−1.63763	−0.269225	−0.134613	+	0.990898i	$0.542979\pi$
$38$	7.56705	1.22754
$39$	0.386358	0.0618669
$40$	−4.91641	−0.777353
$41$	−7.12213	−1.11229	−0.556145	−	0.831085i	$-0.687720\pi$
$41$	−7.12213	−1.11229	−0.556145	+	0.831085i	$0.687720\pi$
$42$	−5.02536	−0.775430
$43$	−0.269566	−0.0411084	−0.0205542	−	0.999789i	$-0.506543\pi$
$43$	−0.269566	−0.0411084	−0.0205542	+	0.999789i	$0.506543\pi$
$44$	0.0190572	0.00287299
$45$	−1.73169	−0.258145
$46$	−10.5476	−1.55517
$47$	−5.98037	−0.872327	−0.436163	−	0.899867i	$-0.643663\pi$
$47$	−5.98037	−0.872327	−0.436163	+	0.899867i	$0.643663\pi$
$48$	3.96932	0.572922
$49$	5.72398	0.817712
$50$	2.81942	0.398726
$51$	−1.00000	−0.140028
$52$	0.00588176	0.000815654 0
$53$	−5.65334	−0.776547	−0.388273	−	0.921544i	$-0.626928\pi$
$53$	−5.65334	−0.776547	−0.388273	+	0.921544i	$0.626928\pi$
$54$	1.40882	0.191716
$55$	2.16776	0.292301
$56$	−10.1272	−1.35331
$57$	5.37119	0.711432
$58$	7.51905	0.987300
$59$	−6.73716	−0.877103	−0.438552	−	0.898706i	$-0.644508\pi$
$59$	−6.73716	−0.877103	−0.438552	+	0.898706i	$0.644508\pi$
$60$	−0.0263625	−0.00340338
$61$	−3.48968	−0.446807	−0.223404	−	0.974726i	$-0.571717\pi$
$61$	−3.48968	−0.446807	−0.223404	+	0.974726i	$0.571717\pi$
$62$	1.51565	0.192488
$63$	−3.56707	−0.449408
$64$	8.05996	1.00750
$65$	0.669052	0.0829857
$66$	−1.76359	−0.217083
$67$	−0.361777	−0.0441981	−0.0220990	−	0.999756i	$-0.507035\pi$
$67$	−0.361777	−0.0441981	−0.0220990	+	0.999756i	$0.507035\pi$
$68$	−0.0152236	−0.00184613
$69$	−7.48686	−0.901312
$70$	−8.70235	−1.04013
$71$	−1.98865	−0.236009	−0.118005	−	0.993013i	$-0.537650\pi$
$71$	−1.98865	−0.236009	−0.118005	+	0.993013i	$0.537650\pi$
$72$	2.83909	0.334590
$73$	−5.29412	−0.619630	−0.309815	−	0.950797i	$-0.600267\pi$
$73$	−5.29412	−0.619630	−0.309815	+	0.950797i	$0.600267\pi$
$74$	2.30713	0.268199
$75$	2.00126	0.231086
$76$	0.0817689	0.00937953
$77$	4.46534	0.508872
$78$	−0.544310	−0.0616309
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	6.87362	0.768494
$81$	1.00000	0.111111
$82$	10.0338	1.10805
$83$	−7.94738	−0.872338	−0.436169	−	0.899865i	$-0.643665\pi$
$83$	−7.94738	−0.872338	−0.436169	+	0.899865i	$0.643665\pi$
$84$	−0.0543036	−0.00592501
$85$	−1.73169	−0.187828
$86$	0.379770	0.0409516
$87$	5.33712	0.572200
$88$	−3.55404	−0.378862
$89$	−10.7568	−1.14022	−0.570110	−	0.821568i	$-0.693100\pi$
$89$	−10.7568	−1.14022	−0.570110	+	0.821568i	$0.693100\pi$
$90$	2.43964	0.257160
$91$	1.37817	0.144471
$92$	−0.113977	−0.0118829
$93$	1.07583	0.111558
$94$	8.42527	0.869001
$95$	9.30123	0.954286
$96$	0.0861158	0.00878916
$97$	8.03370	0.815699	0.407849	−	0.913049i	$-0.366279\pi$
$97$	8.03370	0.815699	0.407849	+	0.913049i	$0.366279\pi$
$98$	−8.06406	−0.814594
$99$	−1.25182	−0.125813
$100$	0.0304664	0.00304664
$101$	−3.95470	−0.393507	−0.196754	−	0.980453i	$-0.563040\pi$
$101$	−3.95470	−0.393507	−0.196754	+	0.980453i	$0.563040\pi$
$102$	1.40882	0.139494
$103$	−6.54473	−0.644871	−0.322436	−	0.946591i	$-0.604502\pi$
$103$	−6.54473	−0.644871	−0.322436	+	0.946591i	$0.604502\pi$
$104$	−1.09691	−0.107560
$105$	−6.17705	−0.602818
$106$	7.96455	0.773585
$107$	−10.7384	−1.03812	−0.519059	−	0.854739i	$-0.673717\pi$
$107$	−10.7384	−1.03812	−0.519059	+	0.854739i	$0.673717\pi$
$108$	0.0152236	0.00146489
$109$	2.66568	0.255326	0.127663	−	0.991818i	$-0.459252\pi$
$109$	2.66568	0.255326	0.127663	+	0.991818i	$0.459252\pi$
$110$	−3.05399	−0.291187
$111$	1.63763	0.155437
$112$	14.1588	1.33788
$113$	−15.9083	−1.49652	−0.748261	−	0.663404i	$-0.769111\pi$
$113$	−15.9083	−1.49652	−0.748261	+	0.663404i	$0.769111\pi$
$114$	−7.56705	−0.708719
$115$	−12.9649	−1.20898
$116$	0.0812502	0.00754389
$117$	−0.386358	−0.0357188
$118$	9.49145	0.873759
$119$	−3.56707	−0.326993
$120$	4.91641	0.448805
$121$	−9.43294	−0.857540
$122$	4.91633	0.445103
$123$	7.12213	0.642181
$124$	0.0163780	0.00147079
$125$	12.1240	1.08440
$126$	5.02536	0.447695
$127$	−7.06406	−0.626834	−0.313417	−	0.949616i	$-0.601474\pi$
$127$	−7.06406	−0.626834	−0.313417	+	0.949616i	$0.601474\pi$
$128$	−11.1828	−0.988430
$129$	0.269566	0.0237339
$130$	−0.942574	−0.0826692
$131$	−7.33069	−0.640486	−0.320243	−	0.947336i	$-0.603764\pi$
$131$	−7.33069	−0.640486	−0.320243	+	0.947336i	$0.603764\pi$
$132$	−0.0190572	−0.00165872
$133$	19.1594	1.66133
$134$	0.509679	0.0440295
$135$	1.73169	0.149040
$136$	2.83909	0.243450
$137$	−5.22283	−0.446217	−0.223108	−	0.974794i	$-0.571620\pi$
$137$	−5.22283	−0.446217	−0.223108	+	0.974794i	$0.571620\pi$
$138$	10.5476	0.897875
$139$	19.6844	1.66960	0.834802	−	0.550550i	$-0.185582\pi$
$139$	19.6844	1.66960	0.834802	+	0.550550i	$0.185582\pi$
$140$	−0.0940369	−0.00794757
$141$	5.98037	0.503638
$142$	2.80165	0.235110
$143$	0.483652	0.0404450
$144$	−3.96932	−0.330777
$145$	9.24223	0.767525
$146$	7.45847	0.617267
$147$	−5.72398	−0.472106
$148$	0.0249307	0.00204929
$149$	12.4823	1.02259	0.511295	−	0.859405i	$-0.329166\pi$
$149$	12.4823	1.02259	0.511295	+	0.859405i	$0.329166\pi$
$150$	−2.81942	−0.230204
$151$	3.37668	0.274790	0.137395	−	0.990516i	$-0.456127\pi$
$151$	3.37668	0.274790	0.137395	+	0.990516i	$0.456127\pi$
$152$	−15.2493	−1.23688
$153$	1.00000	0.0808452
$154$	−6.29086	−0.506932
$155$	1.86300	0.149640
$156$	−0.00588176	−0.000470918 0
$157$	12.6584	1.01025	0.505125	−	0.863046i	$-0.331446\pi$
$157$	12.6584	1.01025	0.505125	+	0.863046i	$0.331446\pi$
$158$	1.40882	0.112080
$159$	5.65334	0.448339
$160$	0.149126	0.0117894
$161$	−26.7061	−2.10474
$162$	−1.40882	−0.110687
$163$	−8.13448	−0.637141	−0.318571	−	0.947899i	$-0.603203\pi$
$163$	−8.13448	−0.637141	−0.318571	+	0.947899i	$0.603203\pi$
$164$	0.108424	0.00846653
$165$	−2.16776	−0.168760
$166$	11.1964	0.869012
$167$	6.40116	0.495337	0.247668	−	0.968845i	$-0.420336\pi$
$167$	6.40116	0.495337	0.247668	+	0.968845i	$0.420336\pi$
$168$	10.1272	0.781333
$169$	−12.8507	−0.988517
$170$	2.43964	0.187112
$171$	−5.37119	−0.410745
$172$	0.00410376	0.000312909 0
$173$	−1.58073	−0.120180	−0.0600902	−	0.998193i	$-0.519139\pi$
$173$	−1.58073	−0.120180	−0.0600902	+	0.998193i	$0.519139\pi$
$174$	−7.51905	−0.570018
$175$	7.13863	0.539630
$176$	4.96889	0.374544
$177$	6.73716	0.506396
$178$	15.1544	1.13587
$179$	18.5081	1.38336	0.691681	−	0.722203i	$-0.256870\pi$
$179$	18.5081	1.38336	0.691681	+	0.722203i	$0.256870\pi$
$180$	0.0263625	0.00196495
$181$	−7.85588	−0.583923	−0.291962	−	0.956430i	$-0.594308\pi$
$181$	−7.85588	−0.583923	−0.291962	+	0.956430i	$0.594308\pi$
$182$	−1.94159	−0.143920
$183$	3.48968	0.257964
$184$	21.2559	1.56700
$185$	2.83587	0.208497
$186$	−1.51565	−0.111133
$187$	−1.25182	−0.0915423
$188$	0.0910428	0.00663998
$189$	3.56707	0.259466
$190$	−13.1038	−0.950647
$191$	−15.1024	−1.09277	−0.546385	−	0.837534i	$-0.683996\pi$
$191$	−15.1024	−1.09277	−0.546385	+	0.837534i	$0.683996\pi$
$192$	−8.05996	−0.581678
$193$	3.85717	0.277645	0.138823	−	0.990317i	$-0.455668\pi$
$193$	3.85717	0.277645	0.138823	+	0.990317i	$0.455668\pi$
$194$	−11.3180	−0.812588
$195$	−0.669052	−0.0479118
$196$	−0.0871396	−0.00622426
$197$	−0.193404	−0.0137795	−0.00688974	−	0.999976i	$-0.502193\pi$
$197$	−0.193404	−0.0137795	−0.00688974	+	0.999976i	$0.502193\pi$
$198$	1.76359	0.125333
$199$	8.29739	0.588187	0.294093	−	0.955777i	$-0.404982\pi$
$199$	8.29739	0.588187	0.294093	+	0.955777i	$0.404982\pi$
$200$	−5.68176	−0.401761
$201$	0.361777	0.0255178
$202$	5.57146	0.392007
$203$	19.0379	1.33620
$204$	0.0152236	0.00106587
$205$	12.3333	0.861395
$206$	9.22035	0.642412
$207$	7.48686	0.520373
$208$	1.53358	0.106335
$209$	6.72378	0.465094
$210$	8.70235	0.600519
$211$	−5.70394	−0.392676	−0.196338	−	0.980536i	$-0.562905\pi$
$211$	−5.70394	−0.392676	−0.196338	+	0.980536i	$0.562905\pi$
$212$	0.0860642	0.00591092
$213$	1.98865	0.136260
$214$	15.1284	1.03416
$215$	0.466803	0.0318357
$216$	−2.83909	−0.193176
$217$	3.83756	0.260510
$218$	−3.75546	−0.254352
$219$	5.29412	0.357744
$220$	−0.0330012	−0.00222494
$221$	−0.386358	−0.0259893
$222$	−2.30713	−0.154845
$223$	3.76935	0.252414	0.126207	−	0.992004i	$-0.459720\pi$
$223$	3.76935	0.252414	0.126207	+	0.992004i	$0.459720\pi$
$224$	0.307181	0.0205244
$225$	−2.00126	−0.133417
$226$	22.4119	1.49082
$227$	22.7085	1.50722	0.753608	−	0.657324i	$-0.228312\pi$
$227$	22.7085	1.50722	0.753608	+	0.657324i	$0.228312\pi$
$228$	−0.0817689	−0.00541528
$229$	13.3848	0.884492	0.442246	−	0.896894i	$-0.354182\pi$
$229$	13.3848	0.884492	0.442246	+	0.896894i	$0.354182\pi$
$230$	18.2652	1.20437
$231$	−4.46534	−0.293798
$232$	−15.1526	−0.994815
$233$	−21.8099	−1.42881	−0.714407	−	0.699730i	$-0.753303\pi$
$233$	−21.8099	−1.42881	−0.714407	+	0.699730i	$0.753303\pi$
$234$	0.544310	0.0355826
$235$	10.3561	0.675560
$236$	0.102564	0.00667633
$237$	1.00000	0.0649570
$238$	5.02536	0.325746
$239$	−4.91225	−0.317747	−0.158874	−	0.987299i	$-0.550786\pi$
$239$	−4.91225	−0.317747	−0.158874	+	0.987299i	$0.550786\pi$
$240$	−6.87362	−0.443690
$241$	−8.09964	−0.521744	−0.260872	−	0.965373i	$-0.584010\pi$
$241$	−8.09964	−0.521744	−0.260872	+	0.965373i	$0.584010\pi$
$242$	13.2893	0.854270
$243$	−1.00000	−0.0641500
$244$	0.0531254	0.00340101
$245$	−9.91214	−0.633264
$246$	−10.0338	−0.639732
$247$	2.07521	0.132042
$248$	−3.05438	−0.193953
$249$	7.94738	0.503645
$250$	−17.0805	−1.08027
$251$	17.1853	1.08473	0.542364	−	0.840143i	$-0.317529\pi$
$251$	17.1853	1.08473	0.542364	+	0.840143i	$0.317529\pi$
$252$	0.0543036	0.00342081
$253$	−9.37222	−0.589227
$254$	9.95200	0.624444
$255$	1.73169	0.108442
$256$	−0.365345	−0.0228341
$257$	4.36695	0.272403	0.136201	−	0.990681i	$-0.456511\pi$
$257$	4.36695	0.272403	0.136201	+	0.990681i	$0.456511\pi$
$258$	−0.379770	−0.0236434
$259$	5.84155	0.362976
$260$	−0.0101854	−0.000631670 0
$261$	−5.33712	−0.330360
$262$	10.3276	0.638043
$263$	−5.66396	−0.349255	−0.174627	−	0.984635i	$-0.555872\pi$
$263$	−5.66396	−0.349255	−0.174627	+	0.984635i	$0.555872\pi$
$264$	3.55404	0.218736
$265$	9.78982	0.601384
$266$	−26.9922	−1.65500
$267$	10.7568	0.658307
$268$	0.00550755	0.000336427 0
$269$	18.8787	1.15105	0.575526	−	0.817783i	$-0.304797\pi$
$269$	18.8787	1.15105	0.575526	+	0.817783i	$0.304797\pi$
$270$	−2.43964	−0.148472
$271$	−6.69421	−0.406644	−0.203322	−	0.979112i	$-0.565174\pi$
$271$	−6.69421	−0.406644	−0.203322	+	0.979112i	$0.565174\pi$
$272$	−3.96932	−0.240675
$273$	−1.37817	−0.0834105
$274$	7.35803	0.444515
$275$	2.50522	0.151071
$276$	0.113977	0.00686061
$277$	−18.3818	−1.10445	−0.552227	−	0.833694i	$-0.686222\pi$
$277$	−18.3818	−1.10445	−0.552227	+	0.833694i	$0.686222\pi$
$278$	−27.7317	−1.66324
$279$	−1.07583	−0.0644082
$280$	17.5372	1.04805
$281$	−6.38236	−0.380740	−0.190370	−	0.981712i	$-0.560969\pi$
$281$	−6.38236	−0.380740	−0.190370	+	0.981712i	$0.560969\pi$
$282$	−8.42527	−0.501718
$283$	19.6260	1.16664	0.583322	−	0.812241i	$-0.301753\pi$
$283$	19.6260	1.16664	0.583322	+	0.812241i	$0.301753\pi$
$284$	0.0302744	0.00179646
$285$	−9.30123	−0.550957
$286$	−0.681379	−0.0402908
$287$	25.4051	1.49962
$288$	−0.0861158	−0.00507442
$289$	1.00000	0.0588235
$290$	−13.0206	−0.764598
$291$	−8.03370	−0.470944
$292$	0.0805956	0.00471650
$293$	−11.0492	−0.645498	−0.322749	−	0.946485i	$-0.604607\pi$
$293$	−11.0492	−0.645498	−0.322749	+	0.946485i	$0.604607\pi$
$294$	8.06406	0.470306
$295$	11.6666	0.679259
$296$	−4.64939	−0.270240
$297$	1.25182	0.0726381
$298$	−17.5853	−1.01869
$299$	−2.89261	−0.167284
$300$	−0.0304664	−0.00175898
$301$	0.961559	0.0554234
$302$	−4.75713	−0.273742
$303$	3.95470	0.227192
$304$	21.3200	1.22279
$305$	6.04302	0.346023
$306$	−1.40882	−0.0805369
$307$	25.1560	1.43573	0.717864	−	0.696184i	$-0.245120\pi$
$307$	25.1560	1.43573	0.717864	+	0.696184i	$0.245120\pi$
$308$	−0.0679785	−0.00387343
$309$	6.54473	0.372317
$310$	−2.62463	−0.149069
$311$	11.7833	0.668171	0.334085	−	0.942543i	$-0.391573\pi$
$311$	11.7833	0.668171	0.334085	+	0.942543i	$0.391573\pi$
$312$	1.09691	0.0621001
$313$	20.7912	1.17519	0.587595	−	0.809156i	$-0.300075\pi$
$313$	20.7912	1.17519	0.587595	+	0.809156i	$0.300075\pi$
$314$	−17.8334	−1.00640
$315$	6.17705	0.348037
$316$	0.0152236	0.000856394 0
$317$	−23.9367	−1.34442	−0.672210	−	0.740361i	$-0.734655\pi$
$317$	−23.9367	−1.34442	−0.672210	+	0.740361i	$0.734655\pi$
$318$	−7.96455	−0.446630
$319$	6.68113	0.374072
$320$	−13.9573	−0.780239
$321$	10.7384	0.599357
$322$	37.6242	2.09671
$323$	−5.37119	−0.298861
$324$	−0.0152236	−0.000845755 0
$325$	0.773204	0.0428896
$326$	11.4600	0.634712
$327$	−2.66568	−0.147412
$328$	−20.2204	−1.11648
$329$	21.3324	1.17609
$330$	3.05399	0.168117
$331$	−0.678951	−0.0373185	−0.0186593	−	0.999826i	$-0.505940\pi$
$331$	−0.678951	−0.0373185	−0.0186593	+	0.999826i	$0.505940\pi$
$332$	0.120988	0.00664006
$333$	−1.63763	−0.0897417
$334$	−9.01809	−0.493448
$335$	0.626484	0.0342285
$336$	−14.1588	−0.772428
$337$	−6.88508	−0.375054	−0.187527	−	0.982259i	$-0.560047\pi$
$337$	−6.88508	−0.375054	−0.187527	+	0.982259i	$0.560047\pi$
$338$	18.1044	0.984748
$339$	15.9083	0.864018
$340$	0.0263625	0.00142971
$341$	1.34675	0.0729305
$342$	7.56705	0.409179
$343$	4.55165	0.245766
$344$	−0.765321	−0.0412633
$345$	12.9649	0.698007
$346$	2.22696	0.119722
$347$	−0.546412	−0.0293330	−0.0146665	−	0.999892i	$-0.504669\pi$
$347$	−0.546412	−0.0293330	−0.0146665	+	0.999892i	$0.504669\pi$
$348$	−0.0812502	−0.00435547
$349$	14.8312	0.793896	0.396948	−	0.917841i	$-0.370069\pi$
$349$	14.8312	0.793896	0.396948	+	0.917841i	$0.370069\pi$
$350$	−10.0571	−0.537572
$351$	0.386358	0.0206223
$352$	0.107802	0.00574585
$353$	−24.4021	−1.29879	−0.649395	−	0.760451i	$-0.724978\pi$
$353$	−24.4021	−1.29879	−0.649395	+	0.760451i	$0.724978\pi$
$354$	−9.49145	−0.504465
$355$	3.44372	0.182774
$356$	0.163758	0.00867913
$357$	3.56707	0.188789
$358$	−26.0746	−1.37809
$359$	−0.133987	−0.00707158	−0.00353579	−	0.999994i	$-0.501125\pi$
$359$	−0.133987	−0.00707158	−0.00353579	+	0.999994i	$0.501125\pi$
$360$	−4.91641	−0.259118
$361$	9.84972	0.518406
$362$	11.0675	0.581696
$363$	9.43294	0.495101
$364$	−0.0209807	−0.00109969
$365$	9.16776	0.479863
$366$	−4.91633	−0.256981
$367$	−29.1495	−1.52159	−0.760795	−	0.648993i	$-0.775191\pi$
$367$	−29.1495	−1.52159	−0.760795	+	0.648993i	$0.775191\pi$
$368$	−29.7178	−1.54915
$369$	−7.12213	−0.370763
$370$	−3.99523	−0.207702
$371$	20.1659	1.04696
$372$	−0.0163780	−0.000849160 0
$373$	20.2631	1.04918	0.524591	−	0.851355i	$-0.324218\pi$
$373$	20.2631	1.04918	0.524591	+	0.851355i	$0.324218\pi$
$374$	1.76359	0.0911933
$375$	−12.1240	−0.626080
$376$	−16.9788	−0.875615
$377$	2.06204	0.106201
$378$	−5.02536	−0.258477
$379$	22.1563	1.13809	0.569047	−	0.822305i	$-0.307312\pi$
$379$	22.1563	1.13809	0.569047	+	0.822305i	$0.307312\pi$
$380$	−0.141598	−0.00726383
$381$	7.06406	0.361903
$382$	21.2765	1.08860
$383$	−26.8753	−1.37327	−0.686633	−	0.727004i	$-0.740912\pi$
$383$	−26.8753	−1.37327	−0.686633	+	0.727004i	$0.740912\pi$
$384$	11.1828	0.570671
$385$	−7.73257	−0.394088
$386$	−5.43406	−0.276587
$387$	−0.269566	−0.0137028
$388$	−0.122302	−0.00620893
$389$	−27.8506	−1.41208	−0.706040	−	0.708171i	$-0.749520\pi$
$389$	−27.8506	−1.41208	−0.706040	+	0.708171i	$0.749520\pi$
$390$	0.942574	0.0477291
$391$	7.48686	0.378627
$392$	16.2509	0.820794
$393$	7.33069	0.369785
$394$	0.272472	0.0137269
$395$	1.73169	0.0871306
$396$	0.0190572	0.000957663 0
$397$	12.7409	0.639446	0.319723	−	0.947511i	$-0.396410\pi$
$397$	12.7409	0.639446	0.319723	+	0.947511i	$0.396410\pi$
$398$	−11.6895	−0.585944
$399$	−19.1594	−0.959171
$400$	7.94364	0.397182
$401$	5.46894	0.273106	0.136553	−	0.990633i	$-0.456398\pi$
$401$	5.46894	0.273106	0.136553	+	0.990633i	$0.456398\pi$
$402$	−0.509679	−0.0254205
$403$	0.415656	0.0207053
$404$	0.0602048	0.00299530
$405$	−1.73169	−0.0860482
$406$	−26.8210	−1.33110
$407$	2.05003	0.101616
$408$	−2.83909	−0.140556
$409$	27.7952	1.37438	0.687192	−	0.726476i	$-0.258843\pi$
$409$	27.7952	1.37438	0.687192	+	0.726476i	$0.258843\pi$
$410$	−17.3754	−0.858111
$411$	5.22283	0.257623
$412$	0.0996343	0.00490863
$413$	24.0319	1.18253
$414$	−10.5476	−0.518389
$415$	13.7624	0.675568
$416$	0.0332716	0.00163127
$417$	−19.6844	−0.963947
$418$	−9.47260	−0.463320
$419$	33.6542	1.64411	0.822057	−	0.569405i	$-0.192826\pi$
$419$	33.6542	1.64411	0.822057	+	0.569405i	$0.192826\pi$
$420$	0.0940369	0.00458853
$421$	−3.28136	−0.159924	−0.0799618	−	0.996798i	$-0.525480\pi$
$421$	−3.28136	−0.159924	−0.0799618	+	0.996798i	$0.525480\pi$
$422$	8.03584	0.391178
$423$	−5.98037	−0.290776
$424$	−16.0503	−0.779474
$425$	−2.00126	−0.0970754
$426$	−2.80165	−0.135741
$427$	12.4479	0.602397
$428$	0.163477	0.00790194
$429$	−0.483652	−0.0233509
$430$	−0.657642	−0.0317143
$431$	20.3952	0.982404	0.491202	−	0.871046i	$-0.336558\pi$
$431$	20.3952	0.982404	0.491202	+	0.871046i	$0.336558\pi$
$432$	3.96932	0.190974
$433$	−0.799388	−0.0384161	−0.0192081	−	0.999816i	$-0.506114\pi$
$433$	−0.799388	−0.0384161	−0.0192081	+	0.999816i	$0.506114\pi$
$434$	−5.40643	−0.259517
$435$	−9.24223	−0.443131
$436$	−0.0405812	−0.00194349
$437$	−40.2134	−1.92367
$438$	−7.45847	−0.356379
$439$	−0.147929	−0.00706028	−0.00353014	−	0.999994i	$-0.501124\pi$
$439$	−0.147929	−0.00706028	−0.00353014	+	0.999994i	$0.501124\pi$
$440$	6.15448	0.293403
$441$	5.72398	0.272571
$442$	0.544310	0.0258902
$443$	8.60833	0.408994	0.204497	−	0.978867i	$-0.434444\pi$
$443$	8.60833	0.408994	0.204497	+	0.978867i	$0.434444\pi$
$444$	−0.0249307	−0.00118316
$445$	18.6274	0.883026
$446$	−5.31034	−0.251452
$447$	−12.4823	−0.590392
$448$	−28.7504	−1.35833
$449$	−30.5582	−1.44213	−0.721065	−	0.692867i	$-0.756347\pi$
$449$	−30.5582	−1.44213	−0.721065	+	0.692867i	$0.756347\pi$
$450$	2.81942	0.132909
$451$	8.91564	0.419821
$452$	0.242181	0.0113912
$453$	−3.37668	−0.158650
$454$	−31.9922	−1.50147
$455$	−2.38655	−0.111883
$456$	15.2493	0.714114
$457$	−21.8588	−1.02251	−0.511257	−	0.859428i	$-0.670820\pi$
$457$	−21.8588	−1.02251	−0.511257	+	0.859428i	$0.670820\pi$
$458$	−18.8568	−0.881120
$459$	−1.00000	−0.0466760
$460$	0.197372	0.00920254
$461$	23.0723	1.07459	0.537293	−	0.843396i	$-0.319447\pi$
$461$	23.0723	1.07459	0.537293	+	0.843396i	$0.319447\pi$
$462$	6.29086	0.292677
$463$	−21.0348	−0.977572	−0.488786	−	0.872404i	$-0.662560\pi$
$463$	−21.0348	−0.977572	−0.488786	+	0.872404i	$0.662560\pi$
$464$	21.1848	0.983478
$465$	−1.86300	−0.0863946
$466$	30.7262	1.42337
$467$	−10.5793	−0.489552	−0.244776	−	0.969580i	$-0.578714\pi$
$467$	−10.5793	−0.489552	−0.244776	+	0.969580i	$0.578714\pi$
$468$	0.00588176	0.000271885 0
$469$	1.29048	0.0595890
$470$	−14.5899	−0.672984
$471$	−12.6584	−0.583269
$472$	−19.1274	−0.880410
$473$	0.337448	0.0155159
$474$	−1.40882	−0.0647093
$475$	10.7492	0.493205
$476$	0.0543036	0.00248900
$477$	−5.65334	−0.258849
$478$	6.92049	0.316536
$479$	11.7423	0.536518	0.268259	−	0.963347i	$-0.413552\pi$
$479$	11.7423	0.536518	0.268259	+	0.963347i	$0.413552\pi$
$480$	−0.149126	−0.00680662
$481$	0.632713	0.0288492
$482$	11.4109	0.519754
$483$	26.7061	1.21517
$484$	0.143603	0.00652742
$485$	−13.9119	−0.631705
$486$	1.40882	0.0639054
$487$	−26.3058	−1.19203	−0.596014	−	0.802974i	$-0.703250\pi$
$487$	−26.3058	−1.19203	−0.596014	+	0.802974i	$0.703250\pi$
$488$	−9.90750	−0.448491
$489$	8.13448	0.367854
$490$	13.9644	0.630849
$491$	41.5571	1.87545	0.937723	−	0.347385i	$-0.112930\pi$
$491$	41.5571	1.87545	0.937723	+	0.347385i	$0.112930\pi$
$492$	−0.108424	−0.00488815
$493$	−5.33712	−0.240372
$494$	−2.92359	−0.131539
$495$	2.16776	0.0974338
$496$	4.27031	0.191743
$497$	7.09366	0.318194
$498$	−11.1964	−0.501724
$499$	−2.54197	−0.113794	−0.0568970	−	0.998380i	$-0.518121\pi$
$499$	−2.54197	−0.113794	−0.0568970	+	0.998380i	$0.518121\pi$
$500$	−0.184571	−0.00825426
$501$	−6.40116	−0.285983
$502$	−24.2111	−1.08059
$503$	26.2983	1.17258	0.586292	−	0.810100i	$-0.300587\pi$
$503$	26.2983	1.17258	0.586292	+	0.810100i	$0.300587\pi$
$504$	−10.1272	−0.451103
$505$	6.84830	0.304745
$506$	13.2038	0.586980
$507$	12.8507	0.570721
$508$	0.107540	0.00477133
$509$	22.7700	1.00926	0.504632	−	0.863335i	$-0.331628\pi$
$509$	22.7700	1.00926	0.504632	+	0.863335i	$0.331628\pi$
$510$	−2.43964	−0.108029
$511$	18.8845	0.835401
$512$	22.8803	1.01118
$513$	5.37119	0.237144
$514$	−6.15224	−0.271364
$515$	11.3334	0.499410
$516$	−0.00410376	−0.000180658 0
$517$	7.48636	0.329250
$518$	−8.22970	−0.361592
$519$	1.58073	0.0693862
$520$	1.89950	0.0832985
$521$	6.49698	0.284638	0.142319	−	0.989821i	$-0.454544\pi$
$521$	6.49698	0.284638	0.142319	+	0.989821i	$0.454544\pi$
$522$	7.51905	0.329100
$523$	43.3731	1.89657	0.948287	−	0.317415i	$-0.102815\pi$
$523$	43.3731	1.89657	0.948287	+	0.317415i	$0.102815\pi$
$524$	0.111600	0.00487525
$525$	−7.13863	−0.311556
$526$	7.97950	0.347923
$527$	−1.07583	−0.0468639
$528$	−4.96889	−0.216243
$529$	33.0531	1.43709
$530$	−13.7921	−0.599091
$531$	−6.73716	−0.292368
$532$	−0.291675	−0.0126457
$533$	2.75170	0.119189
$534$	−15.1544	−0.655796
$535$	18.5955	0.803953
$536$	−1.02712	−0.0443647
$537$	−18.5081	−0.798685
$538$	−26.5966	−1.14666
$539$	−7.16541	−0.308636
$540$	−0.0263625	−0.00113446
$541$	0.0962684	0.00413890	0.00206945	−	0.999998i	$-0.499341\pi$
$541$	0.0962684	0.00413890	0.00206945	+	0.999998i	$0.499341\pi$
$542$	9.43094	0.405094
$543$	7.85588	0.337128
$544$	−0.0861158	−0.00369218
$545$	−4.61612	−0.197733
$546$	1.94159	0.0830924
$547$	26.9440	1.15204	0.576021	−	0.817435i	$-0.304604\pi$
$547$	26.9440	1.15204	0.576021	+	0.817435i	$0.304604\pi$
$548$	0.0795103	0.00339651
$549$	−3.48968	−0.148936
$550$	−3.52941	−0.150495
$551$	28.6667	1.22124
$552$	−21.2559	−0.904710
$553$	3.56707	0.151687
$554$	25.8966	1.10024
$555$	−2.83587	−0.120376
$556$	−0.299667	−0.0127087
$557$	−34.0866	−1.44430	−0.722148	−	0.691739i	$-0.756845\pi$
$557$	−34.0866	−1.44430	−0.722148	+	0.691739i	$0.756845\pi$
$558$	1.51565	0.0641626
$559$	0.104149	0.00440503
$560$	−24.5187	−1.03610
$561$	1.25182	0.0528520
$562$	8.99160	0.379288
$563$	−16.4022	−0.691271	−0.345635	−	0.938369i	$-0.612337\pi$
$563$	−16.4022	−0.691271	−0.345635	+	0.938369i	$0.612337\pi$
$564$	−0.0910428	−0.00383359
$565$	27.5481	1.15896
$566$	−27.6495	−1.16220
$567$	−3.56707	−0.149803
$568$	−5.64596	−0.236899
$569$	2.69249	0.112875	0.0564375	−	0.998406i	$-0.482026\pi$
$569$	2.69249	0.112875	0.0564375	+	0.998406i	$0.482026\pi$
$570$	13.1038	0.548856
$571$	9.34916	0.391250	0.195625	−	0.980679i	$-0.437326\pi$
$571$	9.34916	0.391250	0.195625	+	0.980679i	$0.437326\pi$
$572$	−0.00736293	−0.000307859 0
$573$	15.1024	0.630911
$574$	−35.7913	−1.49390
$575$	−14.9832	−0.624841
$576$	8.05996	0.335832
$577$	23.8244	0.991823	0.495912	−	0.868373i	$-0.334834\pi$
$577$	23.8244	0.991823	0.495912	+	0.868373i	$0.334834\pi$
$578$	−1.40882	−0.0585992
$579$	−3.85717	−0.160299
$580$	−0.140700	−0.00584225
$581$	28.3488	1.17611
$582$	11.3180	0.469148
$583$	7.07698	0.293099
$584$	−15.0305	−0.621966
$585$	0.669052	0.0276619
$586$	15.5663	0.643037
$587$	−23.8437	−0.984136	−0.492068	−	0.870557i	$-0.663759\pi$
$587$	−23.8437	−0.984136	−0.492068	+	0.870557i	$0.663759\pi$
$588$	0.0871396	0.00359358
$589$	5.77849	0.238098
$590$	−16.4362	−0.676668
$591$	0.193404	0.00795559
$592$	6.50029	0.267160
$593$	−48.5977	−1.99567	−0.997833	−	0.0657936i	$-0.979042\pi$
$593$	−48.5977	−1.99567	−0.997833	+	0.0657936i	$0.979042\pi$
$594$	−1.76359	−0.0723611
$595$	6.17705	0.253234
$596$	−0.190025	−0.00778375
$597$	−8.29739	−0.339590
$598$	4.07517	0.166646
$599$	27.5297	1.12483	0.562417	−	0.826853i	$-0.309871\pi$
$599$	27.5297	1.12483	0.562417	+	0.826853i	$0.309871\pi$
$600$	5.68176	0.231957
$601$	44.4256	1.81216	0.906079	−	0.423108i	$-0.139061\pi$
$601$	44.4256	1.81216	0.906079	+	0.423108i	$0.139061\pi$
$602$	−1.35467	−0.0552120
$603$	−0.361777	−0.0147327
$604$	−0.0514052	−0.00209165
$605$	16.3349	0.664108
$606$	−5.57146	−0.226325
$607$	35.1354	1.42610	0.713050	−	0.701113i	$-0.247313\pi$
$607$	35.1354	1.42610	0.713050	+	0.701113i	$0.247313\pi$
$608$	0.462545	0.0187587
$609$	−19.0379	−0.771454
$610$	−8.51354	−0.344703
$611$	2.31057	0.0934755
$612$	−0.0152236	−0.000615377 0
$613$	−14.7319	−0.595017	−0.297508	−	0.954719i	$-0.596156\pi$
$613$	−14.7319	−0.595017	−0.297508	+	0.954719i	$0.596156\pi$
$614$	−35.4403	−1.43025
$615$	−12.3333	−0.497327
$616$	12.6775	0.510791
$617$	6.91042	0.278203	0.139102	−	0.990278i	$-0.455579\pi$
$617$	6.91042	0.278203	0.139102	+	0.990278i	$0.455579\pi$
$618$	−9.22035	−0.370897
$619$	−7.75860	−0.311844	−0.155922	−	0.987769i	$-0.549835\pi$
$619$	−7.75860	−0.311844	−0.155922	+	0.987769i	$0.549835\pi$
$620$	−0.0283616	−0.00113903
$621$	−7.48686	−0.300437
$622$	−16.6006	−0.665623
$623$	38.3703	1.53727
$624$	−1.53358	−0.0613924
$625$	−10.9887	−0.439546
$626$	−29.2911	−1.17071
$627$	−6.72378	−0.268522
$628$	−0.192706	−0.00768983
$629$	−1.63763	−0.0652967
$630$	−8.70235	−0.346710
$631$	−16.7518	−0.666880	−0.333440	−	0.942771i	$-0.608209\pi$
$631$	−16.7518	−0.666880	−0.333440	+	0.942771i	$0.608209\pi$
$632$	−2.83909	−0.112933
$633$	5.70394	0.226711
$634$	33.7225	1.33929
$635$	12.2327	0.485442
$636$	−0.0860642	−0.00341267
$637$	−2.21151	−0.0876231
$638$	−9.41252	−0.372645
$639$	−1.98865	−0.0786698
$640$	19.3651	0.765474
$641$	−34.0461	−1.34474	−0.672370	−	0.740215i	$-0.734724\pi$
$641$	−34.0461	−1.34474	−0.672370	+	0.740215i	$0.734724\pi$
$642$	−15.1284	−0.597072
$643$	0.975622	0.0384748	0.0192374	−	0.999815i	$-0.493876\pi$
$643$	0.975622	0.0384748	0.0192374	+	0.999815i	$0.493876\pi$
$644$	0.406564	0.0160209
$645$	−0.466803	−0.0183804
$646$	7.56705	0.297722
$647$	−36.9006	−1.45071	−0.725357	−	0.688373i	$-0.758325\pi$
$647$	−36.9006	−1.45071	−0.725357	+	0.688373i	$0.758325\pi$
$648$	2.83909	0.111530
$649$	8.43373	0.331053
$650$	−1.08931	−0.0427261
$651$	−3.83756	−0.150406
$652$	0.123836	0.00484979
$653$	−18.8451	−0.737465	−0.368732	−	0.929536i	$-0.620208\pi$
$653$	−18.8451	−0.737465	−0.368732	+	0.929536i	$0.620208\pi$
$654$	3.75546	0.146850
$655$	12.6945	0.496014
$656$	28.2700	1.10376
$657$	−5.29412	−0.206543
$658$	−30.0535	−1.17161
$659$	−3.81566	−0.148637	−0.0743186	−	0.997235i	$-0.523678\pi$
$659$	−3.81566	−0.148637	−0.0743186	+	0.997235i	$0.523678\pi$
$660$	0.0330012	0.00128457
$661$	−10.1002	−0.392851	−0.196426	−	0.980519i	$-0.562933\pi$
$661$	−10.1002	−0.392851	−0.196426	+	0.980519i	$0.562933\pi$
$662$	0.956520	0.0371762
$663$	0.386358	0.0150049
$664$	−22.5633	−0.875626
$665$	−33.1781	−1.28659
$666$	2.30713	0.0893995
$667$	−39.9583	−1.54719
$668$	−0.0974487	−0.00377040
$669$	−3.76935	−0.145732
$670$	−0.882604	−0.0340980
$671$	4.36845	0.168642
$672$	−0.307181	−0.0118498
$673$	7.93623	0.305919	0.152960	−	0.988232i	$-0.451120\pi$
$673$	7.93623	0.305919	0.152960	+	0.988232i	$0.451120\pi$
$674$	9.69985	0.373624
$675$	2.00126	0.0770285
$676$	0.195634	0.00752440
$677$	−16.5865	−0.637470	−0.318735	−	0.947844i	$-0.603258\pi$
$677$	−16.5865	−0.637470	−0.318735	+	0.947844i	$0.603258\pi$
$678$	−22.4119	−0.860723
$679$	−28.6568	−1.09975
$680$	−4.91641	−0.188536
$681$	−22.7085	−0.870191
$682$	−1.89733	−0.0726524
$683$	−31.0278	−1.18725	−0.593623	−	0.804743i	$-0.702303\pi$
$683$	−31.0278	−1.18725	−0.593623	+	0.804743i	$0.702303\pi$
$684$	0.0817689	0.00312651
$685$	9.04431	0.345565
$686$	−6.41246	−0.244829
$687$	−13.3848	−0.510662
$688$	1.06999	0.0407931
$689$	2.18422	0.0832120
$690$	−18.2652	−0.695345
$691$	5.27130	0.200530	0.100265	−	0.994961i	$-0.468031\pi$
$691$	5.27130	0.200530	0.100265	+	0.994961i	$0.468031\pi$
$692$	0.0240644	0.000914790 0
$693$	4.46534	0.169624
$694$	0.769797	0.0292211
$695$	−34.0871	−1.29300
$696$	15.1526	0.574357
$697$	−7.12213	−0.269770
$698$	−20.8945	−0.790869
$699$	21.8099	0.824926
$700$	−0.108676	−0.00410755
$701$	−13.2234	−0.499442	−0.249721	−	0.968318i	$-0.580339\pi$
$701$	−13.2234	−0.499442	−0.249721	+	0.968318i	$0.580339\pi$
$702$	−0.544310	−0.0205436
$703$	8.79604	0.331749
$704$	−10.0896	−0.380268
$705$	−10.3561	−0.390034
$706$	34.3781	1.29384
$707$	14.1067	0.530537
$708$	−0.102564	−0.00385458
$709$	15.1764	0.569963	0.284981	−	0.958533i	$-0.408013\pi$
$709$	15.1764	0.569963	0.284981	+	0.958533i	$0.408013\pi$
$710$	−4.85159	−0.182077
$711$	−1.00000	−0.0375029
$712$	−30.5396	−1.14452
$713$	−8.05459	−0.301647
$714$	−5.02536	−0.188069
$715$	−0.837534	−0.0313220
$716$	−0.281760	−0.0105299
$717$	4.91225	0.183451
$718$	0.188764	0.00704462
$719$	−23.4274	−0.873695	−0.436847	−	0.899536i	$-0.643905\pi$
$719$	−23.4274	−0.873695	−0.436847	+	0.899536i	$0.643905\pi$
$720$	6.87362	0.256165
$721$	23.3455	0.869432
$722$	−13.8765	−0.516429
$723$	8.09964	0.301229
$724$	0.119595	0.00444471
$725$	10.6810	0.396681
$726$	−13.2893	−0.493213
$727$	−7.04357	−0.261232	−0.130616	−	0.991433i	$-0.541695\pi$
$727$	−7.04357	−0.261232	−0.130616	+	0.991433i	$0.541695\pi$
$728$	3.91274	0.145016
$729$	1.00000	0.0370370
$730$	−12.9157	−0.478033
$731$	−0.269566	−0.00997025
$732$	−0.0531254	−0.00196357
$733$	−27.3557	−1.01040	−0.505202	−	0.863001i	$-0.668582\pi$
$733$	−27.3557	−1.01040	−0.505202	+	0.863001i	$0.668582\pi$
$734$	41.0664	1.51579
$735$	9.91214	0.365615
$736$	−0.644737	−0.0237653
$737$	0.452880	0.0166821
$738$	10.0338	0.369350
$739$	−8.33567	−0.306633	−0.153316	−	0.988177i	$-0.548995\pi$
$739$	−8.33567	−0.306633	−0.153316	+	0.988177i	$0.548995\pi$
$740$	−0.0431721	−0.00158704
$741$	−2.07521	−0.0762346
$742$	−28.4101	−1.04297
$743$	29.7530	1.09153	0.545766	−	0.837938i	$-0.316239\pi$
$743$	29.7530	1.09153	0.545766	+	0.837938i	$0.316239\pi$
$744$	3.05438	0.111979
$745$	−21.6154	−0.791928
$746$	−28.5470	−1.04518
$747$	−7.94738	−0.290779
$748$	0.0190572	0.000696802 0
$749$	38.3045	1.39962
$750$	17.0805	0.623693
$751$	−36.8412	−1.34436	−0.672178	−	0.740389i	$-0.734641\pi$
$751$	−36.8412	−1.34436	−0.672178	+	0.740389i	$0.734641\pi$
$752$	23.7380	0.865636
$753$	−17.1853	−0.626269
$754$	−2.90505	−0.105796
$755$	−5.84735	−0.212807
$756$	−0.0543036	−0.00197500
$757$	−10.5231	−0.382470	−0.191235	−	0.981544i	$-0.561249\pi$
$757$	−10.5231	−0.382470	−0.191235	+	0.981544i	$0.561249\pi$
$758$	−31.2143	−1.13375
$759$	9.37222	0.340190
$760$	26.4070	0.957883
$761$	8.38938	0.304115	0.152057	−	0.988372i	$-0.451410\pi$
$761$	8.38938	0.304115	0.152057	+	0.988372i	$0.451410\pi$
$762$	−9.95200	−0.360523
$763$	−9.50865	−0.344236
$764$	0.229912	0.00831794
$765$	−1.73169	−0.0626093
$766$	37.8625	1.36803
$767$	2.60296	0.0939873
$768$	0.365345	0.0131833
$769$	−22.9995	−0.829383	−0.414692	−	0.909962i	$-0.636111\pi$
$769$	−22.9995	−0.829383	−0.414692	+	0.909962i	$0.636111\pi$
$770$	10.8938	0.392585
$771$	−4.36695	−0.157272
$772$	−0.0587200	−0.00211338
$773$	−36.0048	−1.29500	−0.647502	−	0.762064i	$-0.724186\pi$
$773$	−36.0048	−1.29500	−0.647502	+	0.762064i	$0.724186\pi$
$774$	0.379770	0.0136505
$775$	2.15302	0.0773386
$776$	22.8084	0.818773
$777$	−5.84155	−0.209564
$778$	39.2365	1.40670
$779$	38.2543	1.37060
$780$	0.0101854	0.000364695 0
$781$	2.48944	0.0890791
$782$	−10.5476	−0.377183
$783$	5.33712	0.190733
$784$	−22.7203	−0.811440
$785$	−21.9204	−0.782372
$786$	−10.3276	−0.368374
$787$	−31.7819	−1.13290	−0.566451	−	0.824095i	$-0.691684\pi$
$787$	−31.7819	−1.13290	−0.566451	+	0.824095i	$0.691684\pi$
$788$	0.00294431	0.000104887 0
$789$	5.66396	0.201642
$790$	−2.43964	−0.0867984
$791$	56.7458	2.01765
$792$	−3.55404	−0.126287
$793$	1.34827	0.0478783
$794$	−17.9496	−0.637008
$795$	−9.78982	−0.347209
$796$	−0.126316	−0.00447716
$797$	3.39114	0.120120	0.0600601	−	0.998195i	$-0.480871\pi$
$797$	3.39114	0.120120	0.0600601	+	0.998195i	$0.480871\pi$
$798$	26.9922	0.955513
$799$	−5.98037	−0.211570
$800$	0.172340	0.00609314
$801$	−10.7568	−0.380074
$802$	−7.70475	−0.272064
$803$	6.62730	0.233872
$804$	−0.00550755	−0.000194236 0
$805$	46.2467	1.62998
$806$	−0.585585	−0.0206263
$807$	−18.8787	−0.664560
$808$	−11.2277	−0.394991
$809$	45.3452	1.59425	0.797126	−	0.603813i	$-0.206353\pi$
$809$	45.3452	1.59425	0.797126	+	0.603813i	$0.206353\pi$
$810$	2.43964	0.0857201
$811$	−39.5104	−1.38740	−0.693699	−	0.720265i	$-0.744020\pi$
$811$	−39.5104	−1.38740	−0.693699	+	0.720265i	$0.744020\pi$
$812$	−0.289825	−0.0101709
$813$	6.69421	0.234776
$814$	−2.88812	−0.101229
$815$	14.0864	0.493424
$816$	3.96932	0.138954
$817$	1.44789	0.0506552
$818$	−39.1584	−1.36914
$819$	1.37817	0.0481571
$820$	−0.187757	−0.00655677
$821$	−44.6929	−1.55979	−0.779896	−	0.625910i	$-0.784728\pi$
$821$	−44.6929	−1.55979	−0.779896	+	0.625910i	$0.784728\pi$
$822$	−7.35803	−0.256641
$823$	46.6086	1.62467	0.812336	−	0.583189i	$-0.198195\pi$
$823$	46.6086	1.62467	0.812336	+	0.583189i	$0.198195\pi$
$824$	−18.5811	−0.647302
$825$	−2.50522	−0.0872207
$826$	−33.8567	−1.17802
$827$	47.5404	1.65314	0.826570	−	0.562834i	$-0.190289\pi$
$827$	47.5404	1.65314	0.826570	+	0.562834i	$0.190289\pi$
$828$	−0.113977	−0.00396097
$829$	−38.4508	−1.33545	−0.667726	−	0.744407i	$-0.732732\pi$
$829$	−38.4508	−1.33545	−0.667726	+	0.744407i	$0.732732\pi$
$830$	−19.3887	−0.672992
$831$	18.3818	0.637657
$832$	−3.11403	−0.107960
$833$	5.72398	0.198324
$834$	27.7317	0.960271
$835$	−11.0848	−0.383605
$836$	−0.102360	−0.00354020
$837$	1.07583	0.0371861
$838$	−47.4127	−1.63784
$839$	23.9217	0.825869	0.412935	−	0.910761i	$-0.364504\pi$
$839$	23.9217	0.825869	0.412935	+	0.910761i	$0.364504\pi$
$840$	−17.5372	−0.605090
$841$	−0.515114	−0.0177625
$842$	4.62285	0.159314
$843$	6.38236	0.219820
$844$	0.0868346	0.00298897
$845$	22.2534	0.765541
$846$	8.42527	0.289667
$847$	33.6479	1.15616
$848$	22.4399	0.770591
$849$	−19.6260	−0.673562
$850$	2.81942	0.0967052
$851$	−12.2607	−0.420292
$852$	−0.0302744	−0.00103718
$853$	−3.93467	−0.134720	−0.0673602	−	0.997729i	$-0.521458\pi$
$853$	−3.93467	−0.134720	−0.0673602	+	0.997729i	$0.521458\pi$
$854$	−17.5369	−0.600100
$855$	9.30123	0.318095
$856$	−30.4872	−1.04203
$857$	47.8127	1.63325	0.816626	−	0.577168i	$-0.195842\pi$
$857$	47.8127	1.63325	0.816626	+	0.577168i	$0.195842\pi$
$858$	0.681379	0.0232619
$859$	−22.6530	−0.772909	−0.386455	−	0.922308i	$-0.626300\pi$
$859$	−22.6530	−0.772909	−0.386455	+	0.922308i	$0.626300\pi$
$860$	−0.00710643	−0.000242327 0
$861$	−25.4051	−0.865805
$862$	−28.7332	−0.978658
$863$	−1.53813	−0.0523587	−0.0261793	−	0.999657i	$-0.508334\pi$
$863$	−1.53813	−0.0523587	−0.0261793	+	0.999657i	$0.508334\pi$
$864$	0.0861158	0.00292972
$865$	2.73732	0.0930718
$866$	1.12619	0.0382696
$867$	−1.00000	−0.0339618
$868$	−0.0584215	−0.00198295
$869$	1.25182	0.0424652
$870$	13.0206	0.441441
$871$	0.139776	0.00473611
$872$	7.56809	0.256288
$873$	8.03370	0.271900
$874$	56.6534	1.91633
$875$	−43.2471	−1.46202
$876$	−0.0805956	−0.00272307
$877$	50.7414	1.71342	0.856708	−	0.515802i	$-0.172506\pi$
$877$	50.7414	1.71342	0.856708	+	0.515802i	$0.172506\pi$
$878$	0.208406	0.00703336
$879$	11.0492	0.372679
$880$	−8.60455	−0.290059
$881$	−0.191888	−0.00646486	−0.00323243	−	0.999995i	$-0.501029\pi$
$881$	−0.191888	−0.00646486	−0.00323243	+	0.999995i	$0.501029\pi$
$882$	−8.06406	−0.271531
$883$	24.4718	0.823542	0.411771	−	0.911287i	$-0.364910\pi$
$883$	24.4718	0.823542	0.411771	+	0.911287i	$0.364910\pi$
$884$	0.00588176	0.000197825 0
$885$	−11.6666	−0.392170
$886$	−12.1276	−0.407435
$887$	−10.6508	−0.357618	−0.178809	−	0.983884i	$-0.557224\pi$
$887$	−10.6508	−0.357618	−0.178809	+	0.983884i	$0.557224\pi$
$888$	4.64939	0.156023
$889$	25.1980	0.845113
$890$	−26.2427	−0.879658
$891$	−1.25182	−0.0419376
$892$	−0.0573831	−0.00192133
$893$	32.1217	1.07491
$894$	17.5853	0.588141
$895$	−32.0503	−1.07132
$896$	39.8899	1.33263
$897$	2.89261	0.0965815
$898$	43.0510	1.43663
$899$	5.74184	0.191501
$900$	0.0304664	0.00101555
$901$	−5.65334	−0.188340
$902$	−12.5605	−0.418220
$903$	−0.961559	−0.0319987
$904$	−45.1650	−1.50216
$905$	13.6039	0.452210
$906$	4.75713	0.158045
$907$	32.9523	1.09416	0.547081	−	0.837080i	$-0.315739\pi$
$907$	32.9523	1.09416	0.547081	+	0.837080i	$0.315739\pi$
$908$	−0.345705	−0.0114726
$909$	−3.95470	−0.131169
$910$	3.36223	0.111457
$911$	41.6461	1.37980	0.689898	−	0.723907i	$-0.257655\pi$
$911$	41.6461	1.37980	0.689898	+	0.723907i	$0.257655\pi$
$912$	−21.3200	−0.705975
$913$	9.94871	0.329254
$914$	30.7952	1.01861
$915$	−6.04302	−0.199776
$916$	−0.203765	−0.00673258
$917$	26.1491	0.863519
$918$	1.40882	0.0464980
$919$	−10.6195	−0.350303	−0.175152	−	0.984541i	$-0.556042\pi$
$919$	−10.6195	−0.350303	−0.175152	+	0.984541i	$0.556042\pi$
$920$	−36.8085	−1.21354
$921$	−25.1560	−0.828918
$922$	−32.5048	−1.07049
$923$	0.768332	0.0252900
$924$	0.0679785	0.00223633
$925$	3.27733	0.107758
$926$	29.6343	0.973844
$927$	−6.54473	−0.214957
$928$	0.459611	0.0150875
$929$	13.9635	0.458129	0.229064	−	0.973411i	$-0.426433\pi$
$929$	13.9635	0.458129	0.229064	+	0.973411i	$0.426433\pi$
$930$	2.62463	0.0860651
$931$	−30.7446	−1.00761
$932$	0.332025	0.0108758
$933$	−11.7833	−0.385769
$934$	14.9044	0.487685
$935$	2.16776	0.0708935
$936$	−1.09691	−0.0358535
$937$	−50.8511	−1.66123	−0.830617	−	0.556844i	$-0.812012\pi$
$937$	−50.8511	−1.66123	−0.830617	+	0.556844i	$0.812012\pi$
$938$	−1.81806	−0.0593618
$939$	−20.7912	−0.678496
$940$	−0.157658	−0.00514222
$941$	−48.1332	−1.56910	−0.784549	−	0.620067i	$-0.787106\pi$
$941$	−48.1332	−1.56910	−0.784549	+	0.620067i	$0.787106\pi$
$942$	17.8334	0.581044
$943$	−53.3224	−1.73642
$944$	26.7419	0.870376
$945$	−6.17705	−0.200939
$946$	−0.475404	−0.0154567
$947$	−22.5213	−0.731843	−0.365922	−	0.930646i	$-0.619246\pi$
$947$	−22.5213	−0.731843	−0.365922	+	0.930646i	$0.619246\pi$
$948$	−0.0152236	−0.000494439 0
$949$	2.04543	0.0663974
$950$	−15.1436	−0.491324
$951$	23.9367	0.776201
$952$	−10.1272	−0.328225
$953$	−2.25295	−0.0729804	−0.0364902	−	0.999334i	$-0.511618\pi$
$953$	−2.25295	−0.0729804	−0.0364902	+	0.999334i	$0.511618\pi$
$954$	7.96455	0.257862
$955$	26.1526	0.846278
$956$	0.0747822	0.00241863
$957$	−6.68113	−0.215970
$958$	−16.5428	−0.534472
$959$	18.6302	0.601600
$960$	13.9573	0.450471
$961$	−29.8426	−0.962664
$962$	−0.891380	−0.0287392
$963$	−10.7384	−0.346039
$964$	0.123306	0.00397141
$965$	−6.67941	−0.215018
$966$	−37.6242	−1.21054
$967$	−24.5223	−0.788584	−0.394292	−	0.918985i	$-0.629010\pi$
$967$	−24.5223	−0.788584	−0.394292	+	0.918985i	$0.629010\pi$
$968$	−26.7810	−0.860773
$969$	5.37119	0.172548
$970$	19.5993	0.629296
$971$	−44.8682	−1.43989	−0.719944	−	0.694032i	$-0.755833\pi$
$971$	−44.8682	−1.43989	−0.719944	+	0.694032i	$0.755833\pi$
$972$	0.0152236	0.000488297 0
$973$	−70.2154	−2.25100
$974$	37.0601	1.18748
$975$	−0.773204	−0.0247623
$976$	13.8516	0.443380
$977$	−18.4116	−0.589039	−0.294520	−	0.955645i	$-0.595160\pi$
$977$	−18.4116	−0.589039	−0.294520	+	0.955645i	$0.595160\pi$
$978$	−11.4600	−0.366451
$979$	13.4656	0.430363
$980$	0.150898	0.00482028
$981$	2.66568	0.0851085
$982$	−58.5465	−1.86829
$983$	−44.6440	−1.42392	−0.711961	−	0.702219i	$-0.752193\pi$
$983$	−44.6440	−1.42392	−0.711961	+	0.702219i	$0.752193\pi$
$984$	20.2204	0.644602
$985$	0.334916	0.0106713
$986$	7.51905	0.239455
$987$	−21.3324	−0.679018
$988$	−0.0315921	−0.00100508
$989$	−2.01820	−0.0641751
$990$	−3.05399	−0.0970623
$991$	−5.32983	−0.169308	−0.0846539	−	0.996410i	$-0.526978\pi$
$991$	−5.32983	−0.169308	−0.0846539	+	0.996410i	$0.526978\pi$
$992$	0.0926459	0.00294151
$993$	0.678951	0.0215459
$994$	−9.99369	−0.316981
$995$	−14.3685	−0.455512
$996$	−0.120988	−0.00383364
$997$	−12.8262	−0.406210	−0.203105	−	0.979157i	$-0.565103\pi$
$997$	−12.8262	−0.406210	−0.203105	+	0.979157i	$0.565103\pi$
$998$	3.58118	0.113360
$999$	1.63763	0.0518124

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.i.1.8	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.i.1.8	✓	25	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q-1.40882 q^{2} -1.00000 q^{3} -0.0152236 q^{4} -1.73169 q^{5} +1.40882 q^{6} -3.56707 q^{7} +2.83909 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.40882 q^{2} -1.00000 q^{3} -0.0152236 q^{4} -1.73169 q^{5} +1.40882 q^{6} -3.56707 q^{7} +2.83909 q^{8} +1.00000 q^{9} +2.43964 q^{10} -1.25182 q^{11} +0.0152236 q^{12} -0.386358 q^{13} +5.02536 q^{14} +1.73169 q^{15} -3.96932 q^{16} +1.00000 q^{17} -1.40882 q^{18} -5.37119 q^{19} +0.0263625 q^{20} +3.56707 q^{21} +1.76359 q^{22} +7.48686 q^{23} -2.83909 q^{24} -2.00126 q^{25} +0.544310 q^{26} -1.00000 q^{27} +0.0543036 q^{28} -5.33712 q^{29} -2.43964 q^{30} -1.07583 q^{31} -0.0861158 q^{32} +1.25182 q^{33} -1.40882 q^{34} +6.17705 q^{35} -0.0152236 q^{36} -1.63763 q^{37} +7.56705 q^{38} +0.386358 q^{39} -4.91641 q^{40} -7.12213 q^{41} -5.02536 q^{42} -0.269566 q^{43} +0.0190572 q^{44} -1.73169 q^{45} -10.5476 q^{46} -5.98037 q^{47} +3.96932 q^{48} +5.72398 q^{49} +2.81942 q^{50} -1.00000 q^{51} +0.00588176 q^{52} -5.65334 q^{53} +1.40882 q^{54} +2.16776 q^{55} -10.1272 q^{56} +5.37119 q^{57} +7.51905 q^{58} -6.73716 q^{59} -0.0263625 q^{60} -3.48968 q^{61} +1.51565 q^{62} -3.56707 q^{63} +8.05996 q^{64} +0.669052 q^{65} -1.76359 q^{66} -0.361777 q^{67} -0.0152236 q^{68} -7.48686 q^{69} -8.70235 q^{70} -1.98865 q^{71} +2.83909 q^{72} -5.29412 q^{73} +2.30713 q^{74} +2.00126 q^{75} +0.0817689 q^{76} +4.46534 q^{77} -0.544310 q^{78} -1.00000 q^{79} +6.87362 q^{80} +1.00000 q^{81} +10.0338 q^{82} -7.94738 q^{83} -0.0543036 q^{84} -1.73169 q^{85} +0.379770 q^{86} +5.33712 q^{87} -3.55404 q^{88} -10.7568 q^{89} +2.43964 q^{90} +1.37817 q^{91} -0.113977 q^{92} +1.07583 q^{93} +8.42527 q^{94} +9.30123 q^{95} +0.0861158 q^{96} +8.03370 q^{97} -8.06406 q^{98} -1.25182 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 2 q^{2} - 25 q^{3} + 26 q^{4} - 2 q^{5} + 2 q^{6} + 12 q^{7} + 25 q^{9}+O(q^{10}) \) 25 * q - 2 * q^2 - 25 * q^3 + 26 * q^4 - 2 * q^5 + 2 * q^6 + 12 * q^7 + 25 * q^9	\( 25 q - 2 q^{2} - 25 q^{3} + 26 q^{4} - 2 q^{5} + 2 q^{6} + 12 q^{7} + 25 q^{9} + 19 q^{10} + 19 q^{11} - 26 q^{12} + 4 q^{13} + 15 q^{14} + 2 q^{15} + 32 q^{16} + 25 q^{17} - 2 q^{18} + 29 q^{19} - 8 q^{20} - 12 q^{21} + 23 q^{22} + 6 q^{23} + 15 q^{25} - 8 q^{26} - 25 q^{27} + 23 q^{28} + 11 q^{29} - 19 q^{30} + 38 q^{31} - 27 q^{32} - 19 q^{33} - 2 q^{34} + 20 q^{35} + 26 q^{36} + 8 q^{37} - 25 q^{38} - 4 q^{39} + 48 q^{40} + 24 q^{41} - 15 q^{42} + 11 q^{43} + 6 q^{44} - 2 q^{45} + 25 q^{46} + 23 q^{47} - 32 q^{48} + 21 q^{49} - 21 q^{50} - 25 q^{51} + 31 q^{52} - 16 q^{53} + 2 q^{54} - 11 q^{55} + 18 q^{56} - 29 q^{57} - 5 q^{58} + 27 q^{59} + 8 q^{60} + 40 q^{61} - 34 q^{62} + 12 q^{63} + 46 q^{64} - 19 q^{65} - 23 q^{66} + 24 q^{67} + 26 q^{68} - 6 q^{69} + 17 q^{70} + 19 q^{71} + 13 q^{73} - 56 q^{74} - 15 q^{75} + 21 q^{76} - 30 q^{77} + 8 q^{78} - 25 q^{79} - 40 q^{80} + 25 q^{81} + 61 q^{82} + q^{83} - 23 q^{84} - 2 q^{85} + 62 q^{86} - 11 q^{87} - q^{88} - 10 q^{89} + 19 q^{90} + 50 q^{91} + 18 q^{92} - 38 q^{93} + 15 q^{94} + 14 q^{95} + 27 q^{96} + 19 q^{97} - 23 q^{98} + 19 q^{99}+O(q^{100}) \) 25 * q - 2 * q^2 - 25 * q^3 + 26 * q^4 - 2 * q^5 + 2 * q^6 + 12 * q^7 + 25 * q^9 + 19 * q^10 + 19 * q^11 - 26 * q^12 + 4 * q^13 + 15 * q^14 + 2 * q^15 + 32 * q^16 + 25 * q^17 - 2 * q^18 + 29 * q^19 - 8 * q^20 - 12 * q^21 + 23 * q^22 + 6 * q^23 + 15 * q^25 - 8 * q^26 - 25 * q^27 + 23 * q^28 + 11 * q^29 - 19 * q^30 + 38 * q^31 - 27 * q^32 - 19 * q^33 - 2 * q^34 + 20 * q^35 + 26 * q^36 + 8 * q^37 - 25 * q^38 - 4 * q^39 + 48 * q^40 + 24 * q^41 - 15 * q^42 + 11 * q^43 + 6 * q^44 - 2 * q^45 + 25 * q^46 + 23 * q^47 - 32 * q^48 + 21 * q^49 - 21 * q^50 - 25 * q^51 + 31 * q^52 - 16 * q^53 + 2 * q^54 - 11 * q^55 + 18 * q^56 - 29 * q^57 - 5 * q^58 + 27 * q^59 + 8 * q^60 + 40 * q^61 - 34 * q^62 + 12 * q^63 + 46 * q^64 - 19 * q^65 - 23 * q^66 + 24 * q^67 + 26 * q^68 - 6 * q^69 + 17 * q^70 + 19 * q^71 + 13 * q^73 - 56 * q^74 - 15 * q^75 + 21 * q^76 - 30 * q^77 + 8 * q^78 - 25 * q^79 - 40 * q^80 + 25 * q^81 + 61 * q^82 + q^83 - 23 * q^84 - 2 * q^85 + 62 * q^86 - 11 * q^87 - q^88 - 10 * q^89 + 19 * q^90 + 50 * q^91 + 18 * q^92 - 38 * q^93 + 15 * q^94 + 14 * q^95 + 27 * q^96 + 19 * q^97 - 23 * q^98 + 19 * q^99

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