LMFDB - Embedded newform 4026.2.a.bc.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4026,2,Mod(1,4026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4026, 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("4026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4026 = 2 \cdot 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4026.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:	$32.1477718538$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - x^{8} - 30x^{7} + 7x^{6} + 284x^{5} + 100x^{4} - 777x^{3} - 250x^{2} + 574x - 68 $ x^9 - x^8 - 30x^7 + 7x^6 + 284x^5 + 100x^4 - 777x^3 - 250x^2 + 574*x - 68
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.60053$ of defining polynomial
Character	$\chi$	$=$	4026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.600528 q^{5} +1.00000 q^{6} +0.748033 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.600528 q^{5} +1.00000 q^{6} +0.748033 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.600528 q^{10} +1.00000 q^{11} +1.00000 q^{12} -3.37388 q^{13} +0.748033 q^{14} -0.600528 q^{15} +1.00000 q^{16} +1.61669 q^{17} +1.00000 q^{18} +1.26064 q^{19} -0.600528 q^{20} +0.748033 q^{21} +1.00000 q^{22} +5.33798 q^{23} +1.00000 q^{24} -4.63937 q^{25} -3.37388 q^{26} +1.00000 q^{27} +0.748033 q^{28} +3.93905 q^{29} -0.600528 q^{30} +6.73745 q^{31} +1.00000 q^{32} +1.00000 q^{33} +1.61669 q^{34} -0.449215 q^{35} +1.00000 q^{36} +0.919689 q^{37} +1.26064 q^{38} -3.37388 q^{39} -0.600528 q^{40} +10.3291 q^{41} +0.748033 q^{42} +0.371237 q^{43} +1.00000 q^{44} -0.600528 q^{45} +5.33798 q^{46} +1.78835 q^{47} +1.00000 q^{48} -6.44045 q^{49} -4.63937 q^{50} +1.61669 q^{51} -3.37388 q^{52} -8.73693 q^{53} +1.00000 q^{54} -0.600528 q^{55} +0.748033 q^{56} +1.26064 q^{57} +3.93905 q^{58} -1.55335 q^{59} -0.600528 q^{60} -1.00000 q^{61} +6.73745 q^{62} +0.748033 q^{63} +1.00000 q^{64} +2.02611 q^{65} +1.00000 q^{66} +6.96334 q^{67} +1.61669 q^{68} +5.33798 q^{69} -0.449215 q^{70} +7.20179 q^{71} +1.00000 q^{72} +11.0840 q^{73} +0.919689 q^{74} -4.63937 q^{75} +1.26064 q^{76} +0.748033 q^{77} -3.37388 q^{78} +15.8076 q^{79} -0.600528 q^{80} +1.00000 q^{81} +10.3291 q^{82} +5.44158 q^{83} +0.748033 q^{84} -0.970868 q^{85} +0.371237 q^{86} +3.93905 q^{87} +1.00000 q^{88} +10.6282 q^{89} -0.600528 q^{90} -2.52377 q^{91} +5.33798 q^{92} +6.73745 q^{93} +1.78835 q^{94} -0.757048 q^{95} +1.00000 q^{96} -17.4847 q^{97} -6.44045 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} + 9 q^{3} + 9 q^{4} + 8 q^{5} + 9 q^{6} + 9 q^{7} + 9 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q + 9 * q^2 + 9 * q^3 + 9 * q^4 + 8 * q^5 + 9 * q^6 + 9 * q^7 + 9 * q^8 + 9 * q^9	\( 9 q + 9 q^{2} + 9 q^{3} + 9 q^{4} + 8 q^{5} + 9 q^{6} + 9 q^{7} + 9 q^{8} + 9 q^{9} + 8 q^{10} + 9 q^{11} + 9 q^{12} + 8 q^{13} + 9 q^{14} + 8 q^{15} + 9 q^{16} + q^{17} + 9 q^{18} + 5 q^{19} + 8 q^{20} + 9 q^{21} + 9 q^{22} - q^{23} + 9 q^{24} + 23 q^{25} + 8 q^{26} + 9 q^{27} + 9 q^{28} - 14 q^{29} + 8 q^{30} + 25 q^{31} + 9 q^{32} + 9 q^{33} + q^{34} + 5 q^{35} + 9 q^{36} + 16 q^{37} + 5 q^{38} + 8 q^{39} + 8 q^{40} + 5 q^{41} + 9 q^{42} + 5 q^{43} + 9 q^{44} + 8 q^{45} - q^{46} + 8 q^{47} + 9 q^{48} + 30 q^{49} + 23 q^{50} + q^{51} + 8 q^{52} + q^{53} + 9 q^{54} + 8 q^{55} + 9 q^{56} + 5 q^{57} - 14 q^{58} + 4 q^{59} + 8 q^{60} - 9 q^{61} + 25 q^{62} + 9 q^{63} + 9 q^{64} - 14 q^{65} + 9 q^{66} - 4 q^{67} + q^{68} - q^{69} + 5 q^{70} + 20 q^{71} + 9 q^{72} + 15 q^{73} + 16 q^{74} + 23 q^{75} + 5 q^{76} + 9 q^{77} + 8 q^{78} - 2 q^{79} + 8 q^{80} + 9 q^{81} + 5 q^{82} + 21 q^{83} + 9 q^{84} - 16 q^{85} + 5 q^{86} - 14 q^{87} + 9 q^{88} + 10 q^{89} + 8 q^{90} - 19 q^{91} - q^{92} + 25 q^{93} + 8 q^{94} - 7 q^{95} + 9 q^{96} + 3 q^{97} + 30 q^{98} + 9 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 9 * q^3 + 9 * q^4 + 8 * q^5 + 9 * q^6 + 9 * q^7 + 9 * q^8 + 9 * q^9 + 8 * q^10 + 9 * q^11 + 9 * q^12 + 8 * q^13 + 9 * q^14 + 8 * q^15 + 9 * q^16 + q^17 + 9 * q^18 + 5 * q^19 + 8 * q^20 + 9 * q^21 + 9 * q^22 - q^23 + 9 * q^24 + 23 * q^25 + 8 * q^26 + 9 * q^27 + 9 * q^28 - 14 * q^29 + 8 * q^30 + 25 * q^31 + 9 * q^32 + 9 * q^33 + q^34 + 5 * q^35 + 9 * q^36 + 16 * q^37 + 5 * q^38 + 8 * q^39 + 8 * q^40 + 5 * q^41 + 9 * q^42 + 5 * q^43 + 9 * q^44 + 8 * q^45 - q^46 + 8 * q^47 + 9 * q^48 + 30 * q^49 + 23 * q^50 + q^51 + 8 * q^52 + q^53 + 9 * q^54 + 8 * q^55 + 9 * q^56 + 5 * q^57 - 14 * q^58 + 4 * q^59 + 8 * q^60 - 9 * q^61 + 25 * q^62 + 9 * q^63 + 9 * q^64 - 14 * q^65 + 9 * q^66 - 4 * q^67 + q^68 - q^69 + 5 * q^70 + 20 * q^71 + 9 * q^72 + 15 * q^73 + 16 * q^74 + 23 * q^75 + 5 * q^76 + 9 * q^77 + 8 * q^78 - 2 * q^79 + 8 * q^80 + 9 * q^81 + 5 * q^82 + 21 * q^83 + 9 * q^84 - 16 * q^85 + 5 * q^86 - 14 * q^87 + 9 * q^88 + 10 * q^89 + 8 * q^90 - 19 * q^91 - q^92 + 25 * q^93 + 8 * q^94 - 7 * q^95 + 9 * q^96 + 3 * q^97 + 30 * q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−0.600528	−0.268564	−0.134282	−	0.990943i	$-0.542873\pi$
$5$	−0.600528	−0.268564	−0.134282	+	0.990943i	$0.542873\pi$
$6$	1.00000	0.408248
$7$	0.748033	0.282730	0.141365	−	0.989958i	$-0.454851\pi$
$7$	0.748033	0.282730	0.141365	+	0.989958i	$0.454851\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−0.600528	−0.189904
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.00000	0.288675
$13$	−3.37388	−0.935745	−0.467873	−	0.883796i	$-0.654979\pi$
$13$	−3.37388	−0.935745	−0.467873	+	0.883796i	$0.654979\pi$
$14$	0.748033	0.199920
$15$	−0.600528	−0.155056
$16$	1.00000	0.250000
$17$	1.61669	0.392105	0.196053	−	0.980593i	$-0.437188\pi$
$17$	1.61669	0.392105	0.196053	+	0.980593i	$0.437188\pi$
$18$	1.00000	0.235702
$19$	1.26064	0.289210	0.144605	−	0.989489i	$-0.453809\pi$
$19$	1.26064	0.289210	0.144605	+	0.989489i	$0.453809\pi$
$20$	−0.600528	−0.134282
$21$	0.748033	0.163234
$22$	1.00000	0.213201
$23$	5.33798	1.11305	0.556523	−	0.830832i	$-0.312135\pi$
$23$	5.33798	1.11305	0.556523	+	0.830832i	$0.312135\pi$
$24$	1.00000	0.204124
$25$	−4.63937	−0.927873
$26$	−3.37388	−0.661672
$27$	1.00000	0.192450
$28$	0.748033	0.141365
$29$	3.93905	0.731463	0.365731	−	0.930720i	$-0.380819\pi$
$29$	3.93905	0.731463	0.365731	+	0.930720i	$0.380819\pi$
$30$	−0.600528	−0.109641
$31$	6.73745	1.21008	0.605041	−	0.796194i	$-0.293157\pi$
$31$	6.73745	1.21008	0.605041	+	0.796194i	$0.293157\pi$
$32$	1.00000	0.176777
$33$	1.00000	0.174078
$34$	1.61669	0.277260
$35$	−0.449215	−0.0759312
$36$	1.00000	0.166667
$37$	0.919689	0.151196	0.0755979	−	0.997138i	$-0.475913\pi$
$37$	0.919689	0.151196	0.0755979	+	0.997138i	$0.475913\pi$
$38$	1.26064	0.204502
$39$	−3.37388	−0.540253
$40$	−0.600528	−0.0949518
$41$	10.3291	1.61313	0.806566	−	0.591144i	$-0.201323\pi$
$41$	10.3291	1.61313	0.806566	+	0.591144i	$0.201323\pi$
$42$	0.748033	0.115424
$43$	0.371237	0.0566132	0.0283066	−	0.999599i	$-0.490989\pi$
$43$	0.371237	0.0566132	0.0283066	+	0.999599i	$0.490989\pi$
$44$	1.00000	0.150756
$45$	−0.600528	−0.0895214
$46$	5.33798	0.787042
$47$	1.78835	0.260857	0.130429	−	0.991458i	$-0.458365\pi$
$47$	1.78835	0.260857	0.130429	+	0.991458i	$0.458365\pi$
$48$	1.00000	0.144338
$49$	−6.44045	−0.920064
$50$	−4.63937	−0.656105
$51$	1.61669	0.226382
$52$	−3.37388	−0.467873
$53$	−8.73693	−1.20011	−0.600055	−	0.799959i	$-0.704855\pi$
$53$	−8.73693	−1.20011	−0.600055	+	0.799959i	$0.704855\pi$
$54$	1.00000	0.136083
$55$	−0.600528	−0.0809751
$56$	0.748033	0.0999602
$57$	1.26064	0.166976
$58$	3.93905	0.517222
$59$	−1.55335	−0.202229	−0.101115	−	0.994875i	$-0.532241\pi$
$59$	−1.55335	−0.202229	−0.101115	+	0.994875i	$0.532241\pi$
$60$	−0.600528	−0.0775278
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	6.73745	0.855657
$63$	0.748033	0.0942433
$64$	1.00000	0.125000
$65$	2.02611	0.251308
$66$	1.00000	0.123091
$67$	6.96334	0.850708	0.425354	−	0.905027i	$-0.360150\pi$
$67$	6.96334	0.850708	0.425354	+	0.905027i	$0.360150\pi$
$68$	1.61669	0.196053
$69$	5.33798	0.642617
$70$	−0.449215	−0.0536914
$71$	7.20179	0.854695	0.427348	−	0.904087i	$-0.359448\pi$
$71$	7.20179	0.854695	0.427348	+	0.904087i	$0.359448\pi$
$72$	1.00000	0.117851
$73$	11.0840	1.29728	0.648640	−	0.761095i	$-0.275338\pi$
$73$	11.0840	1.29728	0.648640	+	0.761095i	$0.275338\pi$
$74$	0.919689	0.106912
$75$	−4.63937	−0.535708
$76$	1.26064	0.144605
$77$	0.748033	0.0852463
$78$	−3.37388	−0.382016
$79$	15.8076	1.77849	0.889245	−	0.457432i	$-0.151231\pi$
$79$	15.8076	1.77849	0.889245	+	0.457432i	$0.151231\pi$
$80$	−0.600528	−0.0671410
$81$	1.00000	0.111111
$82$	10.3291	1.14066
$83$	5.44158	0.597291	0.298645	−	0.954364i	$-0.403465\pi$
$83$	5.44158	0.597291	0.298645	+	0.954364i	$0.403465\pi$
$84$	0.748033	0.0816171
$85$	−0.970868	−0.105305
$86$	0.371237	0.0400316
$87$	3.93905	0.422310
$88$	1.00000	0.106600
$89$	10.6282	1.12659	0.563295	−	0.826256i	$-0.309533\pi$
$89$	10.6282	1.12659	0.563295	+	0.826256i	$0.309533\pi$
$90$	−0.600528	−0.0633012
$91$	−2.52377	−0.264563
$92$	5.33798	0.556523
$93$	6.73745	0.698641
$94$	1.78835	0.184454
$95$	−0.757048	−0.0776715
$96$	1.00000	0.102062
$97$	−17.4847	−1.77531	−0.887653	−	0.460513i	$-0.847665\pi$
$97$	−17.4847	−1.77531	−0.887653	+	0.460513i	$0.847665\pi$
$98$	−6.44045	−0.650583
$99$	1.00000	0.100504
$100$	−4.63937	−0.463937
$101$	−13.0405	−1.29758	−0.648788	−	0.760970i	$-0.724724\pi$
$101$	−13.0405	−1.29758	−0.648788	+	0.760970i	$0.724724\pi$
$102$	1.61669	0.160076
$103$	6.66201	0.656427	0.328214	−	0.944604i	$-0.393553\pi$
$103$	6.66201	0.656427	0.328214	+	0.944604i	$0.393553\pi$
$104$	−3.37388	−0.330836
$105$	−0.449215	−0.0438389
$106$	−8.73693	−0.848606
$107$	−10.7711	−1.04128	−0.520638	−	0.853777i	$-0.674306\pi$
$107$	−10.7711	−1.04128	−0.520638	+	0.853777i	$0.674306\pi$
$108$	1.00000	0.0962250
$109$	7.81214	0.748267	0.374134	−	0.927375i	$-0.377940\pi$
$109$	7.81214	0.748267	0.374134	+	0.927375i	$0.377940\pi$
$110$	−0.600528	−0.0572581
$111$	0.919689	0.0872930
$112$	0.748033	0.0706825
$113$	−15.6519	−1.47241	−0.736205	−	0.676758i	$-0.763384\pi$
$113$	−15.6519	−1.47241	−0.736205	+	0.676758i	$0.763384\pi$
$114$	1.26064	0.118070
$115$	−3.20561	−0.298924
$116$	3.93905	0.365731
$117$	−3.37388	−0.311915
$118$	−1.55335	−0.142998
$119$	1.20934	0.110860
$120$	−0.600528	−0.0548204
$121$	1.00000	0.0909091
$122$	−1.00000	−0.0905357
$123$	10.3291	0.931343
$124$	6.73745	0.605041
$125$	5.78871	0.517758
$126$	0.748033	0.0666401
$127$	−16.1823	−1.43595	−0.717975	−	0.696069i	$-0.754931\pi$
$127$	−16.1823	−1.43595	−0.717975	+	0.696069i	$0.754931\pi$
$128$	1.00000	0.0883883
$129$	0.371237	0.0326856
$130$	2.02611	0.177701
$131$	−19.5243	−1.70584	−0.852922	−	0.522038i	$-0.825172\pi$
$131$	−19.5243	−1.70584	−0.852922	+	0.522038i	$0.825172\pi$
$132$	1.00000	0.0870388
$133$	0.942999	0.0817684
$134$	6.96334	0.601541
$135$	−0.600528	−0.0516852
$136$	1.61669	0.138630
$137$	19.6596	1.67963	0.839815	−	0.542872i	$-0.182663\pi$
$137$	19.6596	1.67963	0.839815	+	0.542872i	$0.182663\pi$
$138$	5.33798	0.454399
$139$	14.9071	1.26440	0.632201	−	0.774804i	$-0.282152\pi$
$139$	14.9071	1.26440	0.632201	+	0.774804i	$0.282152\pi$
$140$	−0.449215	−0.0379656
$141$	1.78835	0.150606
$142$	7.20179	0.604361
$143$	−3.37388	−0.282138
$144$	1.00000	0.0833333
$145$	−2.36551	−0.196445
$146$	11.0840	0.917316
$147$	−6.44045	−0.531199
$148$	0.919689	0.0755979
$149$	−7.06181	−0.578526	−0.289263	−	0.957250i	$-0.593410\pi$
$149$	−7.06181	−0.578526	−0.289263	+	0.957250i	$0.593410\pi$
$150$	−4.63937	−0.378803
$151$	0.654495	0.0532620	0.0266310	−	0.999645i	$-0.491522\pi$
$151$	0.654495	0.0532620	0.0266310	+	0.999645i	$0.491522\pi$
$152$	1.26064	0.102251
$153$	1.61669	0.130702
$154$	0.748033	0.0602782
$155$	−4.04603	−0.324985
$156$	−3.37388	−0.270126
$157$	10.3719	0.827764	0.413882	−	0.910330i	$-0.364173\pi$
$157$	10.3719	0.827764	0.413882	+	0.910330i	$0.364173\pi$
$158$	15.8076	1.25758
$159$	−8.73693	−0.692884
$160$	−0.600528	−0.0474759
$161$	3.99299	0.314692
$162$	1.00000	0.0785674
$163$	10.3180	0.808170	0.404085	−	0.914721i	$-0.367590\pi$
$163$	10.3180	0.808170	0.404085	+	0.914721i	$0.367590\pi$
$164$	10.3291	0.806566
$165$	−0.600528	−0.0467510
$166$	5.44158	0.422348
$167$	3.01833	0.233566	0.116783	−	0.993157i	$-0.462742\pi$
$167$	3.01833	0.233566	0.116783	+	0.993157i	$0.462742\pi$
$168$	0.748033	0.0577120
$169$	−1.61695	−0.124381
$170$	−0.970868	−0.0744622
$171$	1.26064	0.0964034
$172$	0.371237	0.0283066
$173$	−19.7437	−1.50109	−0.750544	−	0.660820i	$-0.770209\pi$
$173$	−19.7437	−1.50109	−0.750544	+	0.660820i	$0.770209\pi$
$174$	3.93905	0.298618
$175$	−3.47040	−0.262338
$176$	1.00000	0.0753778
$177$	−1.55335	−0.116757
$178$	10.6282	0.796620
$179$	10.9225	0.816385	0.408192	−	0.912896i	$-0.366159\pi$
$179$	10.9225	0.816385	0.408192	+	0.912896i	$0.366159\pi$
$180$	−0.600528	−0.0447607
$181$	−1.75742	−0.130628	−0.0653140	−	0.997865i	$-0.520805\pi$
$181$	−1.75742	−0.130628	−0.0653140	+	0.997865i	$0.520805\pi$
$182$	−2.52377	−0.187074
$183$	−1.00000	−0.0739221
$184$	5.33798	0.393521
$185$	−0.552299	−0.0406058
$186$	6.73745	0.494014
$187$	1.61669	0.118224
$188$	1.78835	0.130429
$189$	0.748033	0.0544114
$190$	−0.757048	−0.0549220
$191$	−12.8261	−0.928061	−0.464030	−	0.885819i	$-0.653597\pi$
$191$	−12.8261	−0.928061	−0.464030	+	0.885819i	$0.653597\pi$
$192$	1.00000	0.0721688
$193$	−2.07382	−0.149277	−0.0746384	−	0.997211i	$-0.523780\pi$
$193$	−2.07382	−0.149277	−0.0746384	+	0.997211i	$0.523780\pi$
$194$	−17.4847	−1.25533
$195$	2.02611	0.145093
$196$	−6.44045	−0.460032
$197$	−22.2990	−1.58874	−0.794369	−	0.607435i	$-0.792198\pi$
$197$	−22.2990	−1.58874	−0.794369	+	0.607435i	$0.792198\pi$
$198$	1.00000	0.0710669
$199$	5.97125	0.423291	0.211645	−	0.977347i	$-0.432118\pi$
$199$	5.97125	0.423291	0.211645	+	0.977347i	$0.432118\pi$
$200$	−4.63937	−0.328053
$201$	6.96334	0.491156
$202$	−13.0405	−0.917524
$203$	2.94654	0.206806
$204$	1.61669	0.113191
$205$	−6.20291	−0.433230
$206$	6.66201	0.464164
$207$	5.33798	0.371015
$208$	−3.37388	−0.233936
$209$	1.26064	0.0872002
$210$	−0.449215	−0.0309988
$211$	−1.30617	−0.0899206	−0.0449603	−	0.998989i	$-0.514316\pi$
$211$	−1.30617	−0.0899206	−0.0449603	+	0.998989i	$0.514316\pi$
$212$	−8.73693	−0.600055
$213$	7.20179	0.493458
$214$	−10.7711	−0.736294
$215$	−0.222938	−0.0152043
$216$	1.00000	0.0680414
$217$	5.03984	0.342127
$218$	7.81214	0.529105
$219$	11.0840	0.748985
$220$	−0.600528	−0.0404876
$221$	−5.45452	−0.366911
$222$	0.919689	0.0617255
$223$	22.5370	1.50919	0.754594	−	0.656192i	$-0.227834\pi$
$223$	22.5370	1.50919	0.754594	+	0.656192i	$0.227834\pi$
$224$	0.748033	0.0499801
$225$	−4.63937	−0.309291
$226$	−15.6519	−1.04115
$227$	−14.0429	−0.932063	−0.466032	−	0.884768i	$-0.654317\pi$
$227$	−14.0429	−0.932063	−0.466032	+	0.884768i	$0.654317\pi$
$228$	1.26064	0.0834878
$229$	−4.21543	−0.278563	−0.139282	−	0.990253i	$-0.544479\pi$
$229$	−4.21543	−0.278563	−0.139282	+	0.990253i	$0.544479\pi$
$230$	−3.20561	−0.211371
$231$	0.748033	0.0492170
$232$	3.93905	0.258611
$233$	−0.537423	−0.0352077	−0.0176039	−	0.999845i	$-0.505604\pi$
$233$	−0.537423	−0.0352077	−0.0176039	+	0.999845i	$0.505604\pi$
$234$	−3.37388	−0.220557
$235$	−1.07395	−0.0700569
$236$	−1.55335	−0.101115
$237$	15.8076	1.02681
$238$	1.20934	0.0783898
$239$	12.3260	0.797302	0.398651	−	0.917103i	$-0.369478\pi$
$239$	12.3260	0.797302	0.398651	+	0.917103i	$0.369478\pi$
$240$	−0.600528	−0.0387639
$241$	−9.76663	−0.629124	−0.314562	−	0.949237i	$-0.601858\pi$
$241$	−9.76663	−0.629124	−0.314562	+	0.949237i	$0.601858\pi$
$242$	1.00000	0.0642824
$243$	1.00000	0.0641500
$244$	−1.00000	−0.0640184
$245$	3.86767	0.247096
$246$	10.3291	0.658559
$247$	−4.25324	−0.270627
$248$	6.73745	0.427829
$249$	5.44158	0.344846
$250$	5.78871	0.366110
$251$	−3.61129	−0.227942	−0.113971	−	0.993484i	$-0.536357\pi$
$251$	−3.61129	−0.227942	−0.113971	+	0.993484i	$0.536357\pi$
$252$	0.748033	0.0471217
$253$	5.33798	0.335596
$254$	−16.1823	−1.01537
$255$	−0.970868	−0.0607981
$256$	1.00000	0.0625000
$257$	−16.4909	−1.02867	−0.514336	−	0.857589i	$-0.671962\pi$
$257$	−16.4909	−1.02867	−0.514336	+	0.857589i	$0.671962\pi$
$258$	0.371237	0.0231122
$259$	0.687958	0.0427476
$260$	2.02611	0.125654
$261$	3.93905	0.243821
$262$	−19.5243	−1.20621
$263$	−14.5435	−0.896793	−0.448396	−	0.893835i	$-0.648005\pi$
$263$	−14.5435	−0.896793	−0.448396	+	0.893835i	$0.648005\pi$
$264$	1.00000	0.0615457
$265$	5.24677	0.322306
$266$	0.942999	0.0578190
$267$	10.6282	0.650437
$268$	6.96334	0.425354
$269$	−11.1059	−0.677139	−0.338570	−	0.940941i	$-0.609943\pi$
$269$	−11.1059	−0.677139	−0.338570	+	0.940941i	$0.609943\pi$
$270$	−0.600528	−0.0365470
$271$	21.2573	1.29129	0.645644	−	0.763639i	$-0.276589\pi$
$271$	21.2573	1.29129	0.645644	+	0.763639i	$0.276589\pi$
$272$	1.61669	0.0980263
$273$	−2.52377	−0.152746
$274$	19.6596	1.18768
$275$	−4.63937	−0.279764
$276$	5.33798	0.321309
$277$	9.68120	0.581687	0.290844	−	0.956771i	$-0.406064\pi$
$277$	9.68120	0.581687	0.290844	+	0.956771i	$0.406064\pi$
$278$	14.9071	0.894068
$279$	6.73745	0.403361
$280$	−0.449215	−0.0268457
$281$	22.3772	1.33491	0.667456	−	0.744650i	$-0.267383\pi$
$281$	22.3772	1.33491	0.667456	+	0.744650i	$0.267383\pi$
$282$	1.78835	0.106495
$283$	−28.0955	−1.67011	−0.835054	−	0.550169i	$-0.814563\pi$
$283$	−28.0955	−1.67011	−0.835054	+	0.550169i	$0.814563\pi$
$284$	7.20179	0.427348
$285$	−0.757048	−0.0448437
$286$	−3.37388	−0.199502
$287$	7.72650	0.456081
$288$	1.00000	0.0589256
$289$	−14.3863	−0.846253
$290$	−2.36551	−0.138907
$291$	−17.4847	−1.02497
$292$	11.0840	0.648640
$293$	−14.9028	−0.870630	−0.435315	−	0.900278i	$-0.643363\pi$
$293$	−14.9028	−0.870630	−0.435315	+	0.900278i	$0.643363\pi$
$294$	−6.44045	−0.375614
$295$	0.932831	0.0543115
$296$	0.919689	0.0534558
$297$	1.00000	0.0580259
$298$	−7.06181	−0.409080
$299$	−18.0097	−1.04153
$300$	−4.63937	−0.267854
$301$	0.277698	0.0160062
$302$	0.654495	0.0376619
$303$	−13.0405	−0.749155
$304$	1.26064	0.0723025
$305$	0.600528	0.0343861
$306$	1.61669	0.0924201
$307$	0.0842553	0.00480870	0.00240435	−	0.999997i	$-0.499235\pi$
$307$	0.0842553	0.00480870	0.00240435	+	0.999997i	$0.499235\pi$
$308$	0.748033	0.0426232
$309$	6.66201	0.378988
$310$	−4.04603	−0.229799
$311$	9.30703	0.527753	0.263876	−	0.964556i	$-0.414999\pi$
$311$	9.30703	0.527753	0.263876	+	0.964556i	$0.414999\pi$
$312$	−3.37388	−0.191008
$313$	16.2487	0.918432	0.459216	−	0.888325i	$-0.348130\pi$
$313$	16.2487	0.918432	0.459216	+	0.888325i	$0.348130\pi$
$314$	10.3719	0.585318
$315$	−0.449215	−0.0253104
$316$	15.8076	0.889245
$317$	12.4700	0.700384	0.350192	−	0.936678i	$-0.386116\pi$
$317$	12.4700	0.700384	0.350192	+	0.936678i	$0.386116\pi$
$318$	−8.73693	−0.489943
$319$	3.93905	0.220544
$320$	−0.600528	−0.0335705
$321$	−10.7711	−0.601182
$322$	3.99299	0.222521
$323$	2.03806	0.113401
$324$	1.00000	0.0555556
$325$	15.6527	0.868253
$326$	10.3180	0.571463
$327$	7.81214	0.432012
$328$	10.3291	0.570329
$329$	1.33774	0.0737522
$330$	−0.600528	−0.0330580
$331$	5.25978	0.289104	0.144552	−	0.989497i	$-0.453826\pi$
$331$	5.25978	0.289104	0.144552	+	0.989497i	$0.453826\pi$
$332$	5.44158	0.298645
$333$	0.919689	0.0503986
$334$	3.01833	0.165156
$335$	−4.18168	−0.228470
$336$	0.748033	0.0408086
$337$	24.1448	1.31525	0.657625	−	0.753346i	$-0.271561\pi$
$337$	24.1448	1.31525	0.657625	+	0.753346i	$0.271561\pi$
$338$	−1.61695	−0.0879504
$339$	−15.6519	−0.850097
$340$	−0.970868	−0.0526527
$341$	6.73745	0.364854
$342$	1.26064	0.0681675
$343$	−10.0539	−0.542860
$344$	0.371237	0.0200158
$345$	−3.20561	−0.172584
$346$	−19.7437	−1.06143
$347$	−18.3114	−0.983008	−0.491504	−	0.870875i	$-0.663553\pi$
$347$	−18.3114	−0.983008	−0.491504	+	0.870875i	$0.663553\pi$
$348$	3.93905	0.211155
$349$	−2.13066	−0.114051	−0.0570257	−	0.998373i	$-0.518162\pi$
$349$	−2.13066	−0.114051	−0.0570257	+	0.998373i	$0.518162\pi$
$350$	−3.47040	−0.185501
$351$	−3.37388	−0.180084
$352$	1.00000	0.0533002
$353$	4.79482	0.255203	0.127601	−	0.991826i	$-0.459272\pi$
$353$	4.79482	0.255203	0.127601	+	0.991826i	$0.459272\pi$
$354$	−1.55335	−0.0825597
$355$	−4.32487	−0.229541
$356$	10.6282	0.563295
$357$	1.20934	0.0640050
$358$	10.9225	0.577271
$359$	−22.7159	−1.19890	−0.599449	−	0.800413i	$-0.704613\pi$
$359$	−22.7159	−1.19890	−0.599449	+	0.800413i	$0.704613\pi$
$360$	−0.600528	−0.0316506
$361$	−17.4108	−0.916357
$362$	−1.75742	−0.0923680
$363$	1.00000	0.0524864
$364$	−2.52377	−0.132282
$365$	−6.65623	−0.348403
$366$	−1.00000	−0.0522708
$367$	−27.2068	−1.42018	−0.710092	−	0.704109i	$-0.751347\pi$
$367$	−27.2068	−1.42018	−0.710092	+	0.704109i	$0.751347\pi$
$368$	5.33798	0.278262
$369$	10.3291	0.537711
$370$	−0.552299	−0.0287126
$371$	−6.53552	−0.339307
$372$	6.73745	0.349321
$373$	−4.48288	−0.232115	−0.116057	−	0.993243i	$-0.537026\pi$
$373$	−4.48288	−0.232115	−0.116057	+	0.993243i	$0.537026\pi$
$374$	1.61669	0.0835971
$375$	5.78871	0.298928
$376$	1.78835	0.0922270
$377$	−13.2899	−0.684463
$378$	0.748033	0.0384747
$379$	5.01577	0.257643	0.128821	−	0.991668i	$-0.458881\pi$
$379$	5.01577	0.257643	0.128821	+	0.991668i	$0.458881\pi$
$380$	−0.757048	−0.0388357
$381$	−16.1823	−0.829046
$382$	−12.8261	−0.656238
$383$	16.6703	0.851811	0.425905	−	0.904768i	$-0.359956\pi$
$383$	16.6703	0.851811	0.425905	+	0.904768i	$0.359956\pi$
$384$	1.00000	0.0510310
$385$	−0.449215	−0.0228941
$386$	−2.07382	−0.105555
$387$	0.371237	0.0188711
$388$	−17.4847	−0.887653
$389$	37.5232	1.90250	0.951252	−	0.308415i	$-0.0997986\pi$
$389$	37.5232	1.90250	0.951252	+	0.308415i	$0.0997986\pi$
$390$	2.02611	0.102596
$391$	8.62987	0.436431
$392$	−6.44045	−0.325292
$393$	−19.5243	−0.984870
$394$	−22.2990	−1.12341
$395$	−9.49288	−0.477639
$396$	1.00000	0.0502519
$397$	26.4230	1.32613	0.663066	−	0.748561i	$-0.269255\pi$
$397$	26.4230	1.32613	0.663066	+	0.748561i	$0.269255\pi$
$398$	5.97125	0.299312
$399$	0.942999	0.0472090
$400$	−4.63937	−0.231968
$401$	−30.7558	−1.53587	−0.767937	−	0.640526i	$-0.778717\pi$
$401$	−30.7558	−1.53587	−0.767937	+	0.640526i	$0.778717\pi$
$402$	6.96334	0.347300
$403$	−22.7313	−1.13233
$404$	−13.0405	−0.648788
$405$	−0.600528	−0.0298405
$406$	2.94654	0.146234
$407$	0.919689	0.0455873
$408$	1.61669	0.0800382
$409$	−12.3234	−0.609354	−0.304677	−	0.952456i	$-0.598549\pi$
$409$	−12.3234	−0.609354	−0.304677	+	0.952456i	$0.598549\pi$
$410$	−6.20291	−0.306340
$411$	19.6596	0.969735
$412$	6.66201	0.328214
$413$	−1.16196	−0.0571763
$414$	5.33798	0.262347
$415$	−3.26782	−0.160411
$416$	−3.37388	−0.165418
$417$	14.9071	0.730003
$418$	1.26064	0.0616598
$419$	38.1766	1.86505	0.932525	−	0.361106i	$-0.117601\pi$
$419$	38.1766	1.86505	0.932525	+	0.361106i	$0.117601\pi$
$420$	−0.449215	−0.0219194
$421$	−12.7073	−0.619318	−0.309659	−	0.950848i	$-0.600215\pi$
$421$	−12.7073	−0.619318	−0.309659	+	0.950848i	$0.600215\pi$
$422$	−1.30617	−0.0635835
$423$	1.78835	0.0869524
$424$	−8.73693	−0.424303
$425$	−7.50043	−0.363824
$426$	7.20179	0.348928
$427$	−0.748033	−0.0361999
$428$	−10.7711	−0.520638
$429$	−3.37388	−0.162892
$430$	−0.222938	−0.0107510
$431$	−14.2871	−0.688185	−0.344093	−	0.938936i	$-0.611813\pi$
$431$	−14.2871	−0.688185	−0.344093	+	0.938936i	$0.611813\pi$
$432$	1.00000	0.0481125
$433$	−24.3489	−1.17013	−0.585067	−	0.810985i	$-0.698932\pi$
$433$	−24.3489	−1.17013	−0.585067	+	0.810985i	$0.698932\pi$
$434$	5.03984	0.241920
$435$	−2.36551	−0.113417
$436$	7.81214	0.374134
$437$	6.72926	0.321904
$438$	11.0840	0.529613
$439$	−7.93790	−0.378855	−0.189428	−	0.981895i	$-0.560663\pi$
$439$	−7.93790	−0.378855	−0.189428	+	0.981895i	$0.560663\pi$
$440$	−0.600528	−0.0286290
$441$	−6.44045	−0.306688
$442$	−5.45452	−0.259445
$443$	−28.0951	−1.33484	−0.667419	−	0.744682i	$-0.732601\pi$
$443$	−28.0951	−1.33484	−0.667419	+	0.744682i	$0.732601\pi$
$444$	0.919689	0.0436465
$445$	−6.38255	−0.302562
$446$	22.5370	1.06716
$447$	−7.06181	−0.334012
$448$	0.748033	0.0353413
$449$	−28.7037	−1.35461	−0.677306	−	0.735701i	$-0.736853\pi$
$449$	−28.7037	−1.35461	−0.677306	+	0.735701i	$0.736853\pi$
$450$	−4.63937	−0.218702
$451$	10.3291	0.486378
$452$	−15.6519	−0.736205
$453$	0.654495	0.0307508
$454$	−14.0429	−0.659068
$455$	1.51560	0.0710522
$456$	1.26064	0.0590348
$457$	21.8471	1.02197	0.510983	−	0.859591i	$-0.329282\pi$
$457$	21.8471	1.02197	0.510983	+	0.859591i	$0.329282\pi$
$458$	−4.21543	−0.196974
$459$	1.61669	0.0754607
$460$	−3.20561	−0.149462
$461$	34.8711	1.62411	0.812055	−	0.583581i	$-0.198349\pi$
$461$	34.8711	1.62411	0.812055	+	0.583581i	$0.198349\pi$
$462$	0.748033	0.0348017
$463$	−31.4892	−1.46343	−0.731714	−	0.681612i	$-0.761279\pi$
$463$	−31.4892	−1.46343	−0.731714	+	0.681612i	$0.761279\pi$
$464$	3.93905	0.182866
$465$	−4.04603	−0.187630
$466$	−0.537423	−0.0248956
$467$	−15.1010	−0.698791	−0.349395	−	0.936975i	$-0.613613\pi$
$467$	−15.1010	−0.698791	−0.349395	+	0.936975i	$0.613613\pi$
$468$	−3.37388	−0.155958
$469$	5.20881	0.240521
$470$	−1.07395	−0.0495377
$471$	10.3719	0.477910
$472$	−1.55335	−0.0714988
$473$	0.371237	0.0170695
$474$	15.8076	0.726065
$475$	−5.84856	−0.268350
$476$	1.20934	0.0554300
$477$	−8.73693	−0.400037
$478$	12.3260	0.563778
$479$	−6.14658	−0.280845	−0.140422	−	0.990092i	$-0.544846\pi$
$479$	−6.14658	−0.280845	−0.140422	+	0.990092i	$0.544846\pi$
$480$	−0.600528	−0.0274102
$481$	−3.10292	−0.141481
$482$	−9.76663	−0.444858
$483$	3.99299	0.181687
$484$	1.00000	0.0454545
$485$	10.5001	0.476784
$486$	1.00000	0.0453609
$487$	31.2664	1.41682	0.708408	−	0.705803i	$-0.249414\pi$
$487$	31.2664	1.41682	0.708408	+	0.705803i	$0.249414\pi$
$488$	−1.00000	−0.0452679
$489$	10.3180	0.466597
$490$	3.86767	0.174723
$491$	1.81636	0.0819711	0.0409855	−	0.999160i	$-0.486950\pi$
$491$	1.81636	0.0819711	0.0409855	+	0.999160i	$0.486950\pi$
$492$	10.3291	0.465671
$493$	6.36823	0.286810
$494$	−4.25324	−0.191362
$495$	−0.600528	−0.0269917
$496$	6.73745	0.302521
$497$	5.38718	0.241648
$498$	5.44158	0.243843
$499$	0.0913402	0.00408895	0.00204447	−	0.999998i	$-0.499349\pi$
$499$	0.0913402	0.00408895	0.00204447	+	0.999998i	$0.499349\pi$
$500$	5.78871	0.258879
$501$	3.01833	0.134849
$502$	−3.61129	−0.161180
$503$	−24.9703	−1.11337	−0.556686	−	0.830723i	$-0.687927\pi$
$503$	−24.9703	−1.11337	−0.556686	+	0.830723i	$0.687927\pi$
$504$	0.748033	0.0333201
$505$	7.83116	0.348482
$506$	5.33798	0.237302
$507$	−1.61695	−0.0718112
$508$	−16.1823	−0.717975
$509$	−25.7241	−1.14020	−0.570100	−	0.821575i	$-0.693095\pi$
$509$	−25.7241	−1.14020	−0.570100	+	0.821575i	$0.693095\pi$
$510$	−0.970868	−0.0429908
$511$	8.29118	0.366780
$512$	1.00000	0.0441942
$513$	1.26064	0.0556585
$514$	−16.4909	−0.727381
$515$	−4.00072	−0.176293
$516$	0.371237	0.0163428
$517$	1.78835	0.0786514
$518$	0.687958	0.0302271
$519$	−19.7437	−0.866654
$520$	2.02611	0.0888507
$521$	−42.6430	−1.86823	−0.934113	−	0.356978i	$-0.883807\pi$
$521$	−42.6430	−1.86823	−0.934113	+	0.356978i	$0.883807\pi$
$522$	3.93905	0.172407
$523$	−4.98426	−0.217946	−0.108973	−	0.994045i	$-0.534756\pi$
$523$	−4.98426	−0.217946	−0.108973	+	0.994045i	$0.534756\pi$
$524$	−19.5243	−0.852922
$525$	−3.47040	−0.151461
$526$	−14.5435	−0.634128
$527$	10.8924	0.474480
$528$	1.00000	0.0435194
$529$	5.49405	0.238872
$530$	5.24677	0.227905
$531$	−1.55335	−0.0674097
$532$	0.942999	0.0408842
$533$	−34.8491	−1.50948
$534$	10.6282	0.459929
$535$	6.46832	0.279650
$536$	6.96334	0.300771
$537$	10.9225	0.471340
$538$	−11.1059	−0.478810
$539$	−6.44045	−0.277410
$540$	−0.600528	−0.0258426
$541$	−39.3180	−1.69041	−0.845206	−	0.534441i	$-0.820522\pi$
$541$	−39.3180	−1.69041	−0.845206	+	0.534441i	$0.820522\pi$
$542$	21.2573	0.913078
$543$	−1.75742	−0.0754182
$544$	1.61669	0.0693151
$545$	−4.69141	−0.200958
$546$	−2.52377	−0.108008
$547$	−42.6203	−1.82231	−0.911157	−	0.412059i	$-0.864810\pi$
$547$	−42.6203	−1.82231	−0.911157	+	0.412059i	$0.864810\pi$
$548$	19.6596	0.839815
$549$	−1.00000	−0.0426790
$550$	−4.63937	−0.197823
$551$	4.96571	0.211546
$552$	5.33798	0.227200
$553$	11.8246	0.502832
$554$	9.68120	0.411315
$555$	−0.552299	−0.0234438
$556$	14.9071	0.632201
$557$	10.8840	0.461171	0.230586	−	0.973052i	$-0.425936\pi$
$557$	10.8840	0.461171	0.230586	+	0.973052i	$0.425936\pi$
$558$	6.73745	0.285219
$559$	−1.25251	−0.0529755
$560$	−0.449215	−0.0189828
$561$	1.61669	0.0682568
$562$	22.3772	0.943925
$563$	30.2723	1.27583	0.637913	−	0.770108i	$-0.279798\pi$
$563$	30.2723	1.27583	0.637913	+	0.770108i	$0.279798\pi$
$564$	1.78835	0.0753030
$565$	9.39942	0.395437
$566$	−28.0955	−1.18094
$567$	0.748033	0.0314144
$568$	7.20179	0.302180
$569$	−38.1958	−1.60125	−0.800625	−	0.599166i	$-0.795499\pi$
$569$	−38.1958	−1.60125	−0.800625	+	0.599166i	$0.795499\pi$
$570$	−0.757048	−0.0317093
$571$	−2.00867	−0.0840601	−0.0420300	−	0.999116i	$-0.513383\pi$
$571$	−2.00867	−0.0840601	−0.0420300	+	0.999116i	$0.513383\pi$
$572$	−3.37388	−0.141069
$573$	−12.8261	−0.535816
$574$	7.72650	0.322498
$575$	−24.7649	−1.03277
$576$	1.00000	0.0416667
$577$	−14.8650	−0.618838	−0.309419	−	0.950926i	$-0.600135\pi$
$577$	−14.8650	−0.618838	−0.309419	+	0.950926i	$0.600135\pi$
$578$	−14.3863	−0.598391
$579$	−2.07382	−0.0861850
$580$	−2.36551	−0.0982224
$581$	4.07048	0.168872
$582$	−17.4847	−0.724766
$583$	−8.73693	−0.361847
$584$	11.0840	0.458658
$585$	2.02611	0.0837692
$586$	−14.9028	−0.615628
$587$	9.08738	0.375076	0.187538	−	0.982257i	$-0.439949\pi$
$587$	9.08738	0.375076	0.187538	+	0.982257i	$0.439949\pi$
$588$	−6.44045	−0.265600
$589$	8.49349	0.349968
$590$	0.932831	0.0384040
$591$	−22.2990	−0.917258
$592$	0.919689	0.0377990
$593$	38.0272	1.56159	0.780795	−	0.624787i	$-0.214814\pi$
$593$	38.0272	1.56159	0.780795	+	0.624787i	$0.214814\pi$
$594$	1.00000	0.0410305
$595$	−0.726242	−0.0297730
$596$	−7.06181	−0.289263
$597$	5.97125	0.244387
$598$	−18.0097	−0.736471
$599$	36.8970	1.50757	0.753786	−	0.657120i	$-0.228225\pi$
$599$	36.8970	1.50757	0.753786	+	0.657120i	$0.228225\pi$
$600$	−4.63937	−0.189401
$601$	17.1213	0.698392	0.349196	−	0.937050i	$-0.386455\pi$
$601$	17.1213	0.698392	0.349196	+	0.937050i	$0.386455\pi$
$602$	0.277698	0.0113181
$603$	6.96334	0.283569
$604$	0.654495	0.0266310
$605$	−0.600528	−0.0244149
$606$	−13.0405	−0.529733
$607$	−9.20705	−0.373703	−0.186851	−	0.982388i	$-0.559828\pi$
$607$	−9.20705	−0.373703	−0.186851	+	0.982388i	$0.559828\pi$
$608$	1.26064	0.0511256
$609$	2.94654	0.119400
$610$	0.600528	0.0243147
$611$	−6.03367	−0.244096
$612$	1.61669	0.0653509
$613$	−19.8503	−0.801745	−0.400872	−	0.916134i	$-0.631293\pi$
$613$	−19.8503	−0.801745	−0.400872	+	0.916134i	$0.631293\pi$
$614$	0.0842553	0.00340027
$615$	−6.20291	−0.250125
$616$	0.748033	0.0301391
$617$	−42.1748	−1.69789	−0.848947	−	0.528477i	$-0.822763\pi$
$617$	−42.1748	−1.69789	−0.848947	+	0.528477i	$0.822763\pi$
$618$	6.66201	0.267985
$619$	2.09824	0.0843356	0.0421678	−	0.999111i	$-0.486574\pi$
$619$	2.09824	0.0843356	0.0421678	+	0.999111i	$0.486574\pi$
$620$	−4.04603	−0.162492
$621$	5.33798	0.214206
$622$	9.30703	0.373178
$623$	7.95027	0.318521
$624$	−3.37388	−0.135063
$625$	19.7206	0.788822
$626$	16.2487	0.649430
$627$	1.26064	0.0503450
$628$	10.3719	0.413882
$629$	1.48685	0.0592847
$630$	−0.449215	−0.0178971
$631$	25.3717	1.01003	0.505016	−	0.863110i	$-0.331486\pi$
$631$	25.3717	1.01003	0.505016	+	0.863110i	$0.331486\pi$
$632$	15.8076	0.628791
$633$	−1.30617	−0.0519157
$634$	12.4700	0.495246
$635$	9.71794	0.385645
$636$	−8.73693	−0.346442
$637$	21.7293	0.860945
$638$	3.93905	0.155948
$639$	7.20179	0.284898
$640$	−0.600528	−0.0237379
$641$	34.8899	1.37807	0.689033	−	0.724730i	$-0.258035\pi$
$641$	34.8899	1.37807	0.689033	+	0.724730i	$0.258035\pi$
$642$	−10.7711	−0.425100
$643$	2.14306	0.0845139	0.0422570	−	0.999107i	$-0.486545\pi$
$643$	2.14306	0.0845139	0.0422570	+	0.999107i	$0.486545\pi$
$644$	3.99299	0.157346
$645$	−0.222938	−0.00877819
$646$	2.03806	0.0801865
$647$	−7.22845	−0.284179	−0.142090	−	0.989854i	$-0.545382\pi$
$647$	−7.22845	−0.284179	−0.142090	+	0.989854i	$0.545382\pi$
$648$	1.00000	0.0392837
$649$	−1.55335	−0.0609744
$650$	15.6527	0.613948
$651$	5.03984	0.197527
$652$	10.3180	0.404085
$653$	5.49278	0.214949	0.107475	−	0.994208i	$-0.465724\pi$
$653$	5.49278	0.214949	0.107475	+	0.994208i	$0.465724\pi$
$654$	7.81214	0.305479
$655$	11.7249	0.458129
$656$	10.3291	0.403283
$657$	11.0840	0.432427
$658$	1.33774	0.0521507
$659$	−27.0537	−1.05386	−0.526931	−	0.849908i	$-0.676658\pi$
$659$	−27.0537	−1.05386	−0.526931	+	0.849908i	$0.676658\pi$
$660$	−0.600528	−0.0233755
$661$	24.5145	0.953504	0.476752	−	0.879038i	$-0.341814\pi$
$661$	24.5145	0.953504	0.476752	+	0.879038i	$0.341814\pi$
$662$	5.25978	0.204427
$663$	−5.45452	−0.211836
$664$	5.44158	0.211174
$665$	−0.566297	−0.0219601
$666$	0.919689	0.0356372
$667$	21.0266	0.814152
$668$	3.01833	0.116783
$669$	22.5370	0.871330
$670$	−4.18168	−0.161552
$671$	−1.00000	−0.0386046
$672$	0.748033	0.0288560
$673$	−1.01371	−0.0390755	−0.0195378	−	0.999809i	$-0.506219\pi$
$673$	−1.01371	−0.0390755	−0.0195378	+	0.999809i	$0.506219\pi$
$674$	24.1448	0.930022
$675$	−4.63937	−0.178569
$676$	−1.61695	−0.0621903
$677$	−34.8826	−1.34065	−0.670324	−	0.742068i	$-0.733845\pi$
$677$	−34.8826	−1.34065	−0.670324	+	0.742068i	$0.733845\pi$
$678$	−15.6519	−0.601109
$679$	−13.0792	−0.501932
$680$	−0.970868	−0.0372311
$681$	−14.0429	−0.538127
$682$	6.73745	0.257990
$683$	−12.8392	−0.491279	−0.245639	−	0.969361i	$-0.578998\pi$
$683$	−12.8392	−0.491279	−0.245639	+	0.969361i	$0.578998\pi$
$684$	1.26064	0.0482017
$685$	−11.8061	−0.451089
$686$	−10.0539	−0.383860
$687$	−4.21543	−0.160829
$688$	0.371237	0.0141533
$689$	29.4773	1.12300
$690$	−3.20561	−0.122035
$691$	−32.5984	−1.24010	−0.620051	−	0.784561i	$-0.712888\pi$
$691$	−32.5984	−1.24010	−0.620051	+	0.784561i	$0.712888\pi$
$692$	−19.7437	−0.750544
$693$	0.748033	0.0284154
$694$	−18.3114	−0.695092
$695$	−8.95212	−0.339573
$696$	3.93905	0.149309
$697$	16.6990	0.632518
$698$	−2.13066	−0.0806465
$699$	−0.537423	−0.0203272
$700$	−3.47040	−0.131169
$701$	4.40381	0.166330	0.0831648	−	0.996536i	$-0.473497\pi$
$701$	4.40381	0.166330	0.0831648	+	0.996536i	$0.473497\pi$
$702$	−3.37388	−0.127339
$703$	1.15939	0.0437274
$704$	1.00000	0.0376889
$705$	−1.07395	−0.0404474
$706$	4.79482	0.180456
$707$	−9.75471	−0.366863
$708$	−1.55335	−0.0583785
$709$	−13.3793	−0.502471	−0.251236	−	0.967926i	$-0.580837\pi$
$709$	−13.3793	−0.502471	−0.251236	+	0.967926i	$0.580837\pi$
$710$	−4.32487	−0.162310
$711$	15.8076	0.592830
$712$	10.6282	0.398310
$713$	35.9644	1.34688
$714$	1.20934	0.0452584
$715$	2.02611	0.0757721
$716$	10.9225	0.408192
$717$	12.3260	0.460323
$718$	−22.7159	−0.847749
$719$	5.46905	0.203961	0.101981	−	0.994786i	$-0.467482\pi$
$719$	5.46905	0.203961	0.101981	+	0.994786i	$0.467482\pi$
$720$	−0.600528	−0.0223803
$721$	4.98340	0.185592
$722$	−17.4108	−0.647963
$723$	−9.76663	−0.363225
$724$	−1.75742	−0.0653140
$725$	−18.2747	−0.678705
$726$	1.00000	0.0371135
$727$	−4.39354	−0.162948	−0.0814738	−	0.996675i	$-0.525963\pi$
$727$	−4.39354	−0.162948	−0.0814738	+	0.996675i	$0.525963\pi$
$728$	−2.52377	−0.0935372
$729$	1.00000	0.0370370
$730$	−6.65623	−0.246358
$731$	0.600176	0.0221983
$732$	−1.00000	−0.0369611
$733$	−18.8338	−0.695642	−0.347821	−	0.937561i	$-0.613078\pi$
$733$	−18.8338	−0.695642	−0.347821	+	0.937561i	$0.613078\pi$
$734$	−27.2068	−1.00422
$735$	3.86767	0.142661
$736$	5.33798	0.196761
$737$	6.96334	0.256498
$738$	10.3291	0.380219
$739$	−20.7849	−0.764586	−0.382293	−	0.924041i	$-0.624865\pi$
$739$	−20.7849	−0.764586	−0.382293	+	0.924041i	$0.624865\pi$
$740$	−0.552299	−0.0203029
$741$	−4.25324	−0.156247
$742$	−6.53552	−0.239926
$743$	1.50202	0.0551038	0.0275519	−	0.999620i	$-0.491229\pi$
$743$	1.50202	0.0551038	0.0275519	+	0.999620i	$0.491229\pi$
$744$	6.73745	0.247007
$745$	4.24081	0.155371
$746$	−4.48288	−0.164130
$747$	5.44158	0.199097
$748$	1.61669	0.0591121
$749$	−8.05711	−0.294400
$750$	5.78871	0.211374
$751$	13.0878	0.477579	0.238790	−	0.971071i	$-0.423249\pi$
$751$	13.0878	0.477579	0.238790	+	0.971071i	$0.423249\pi$
$752$	1.78835	0.0652143
$753$	−3.61129	−0.131603
$754$	−13.2899	−0.483988
$755$	−0.393042	−0.0143043
$756$	0.748033	0.0272057
$757$	16.4585	0.598195	0.299097	−	0.954223i	$-0.403314\pi$
$757$	16.4585	0.598195	0.299097	+	0.954223i	$0.403314\pi$
$758$	5.01577	0.182181
$759$	5.33798	0.193756
$760$	−0.757048	−0.0274610
$761$	29.8670	1.08268	0.541339	−	0.840804i	$-0.317917\pi$
$761$	29.8670	1.08268	0.541339	+	0.840804i	$0.317917\pi$
$762$	−16.1823	−0.586224
$763$	5.84374	0.211558
$764$	−12.8261	−0.464030
$765$	−0.970868	−0.0351018
$766$	16.6703	0.602321
$767$	5.24082	0.189235
$768$	1.00000	0.0360844
$769$	1.78944	0.0645289	0.0322645	−	0.999479i	$-0.489728\pi$
$769$	1.78944	0.0645289	0.0322645	+	0.999479i	$0.489728\pi$
$770$	−0.449215	−0.0161886
$771$	−16.4909	−0.593904
$772$	−2.07382	−0.0746384
$773$	−21.5719	−0.775888	−0.387944	−	0.921683i	$-0.626815\pi$
$773$	−21.5719	−0.775888	−0.387944	+	0.921683i	$0.626815\pi$
$774$	0.371237	0.0133439
$775$	−31.2575	−1.12280
$776$	−17.4847	−0.627665
$777$	0.687958	0.0246803
$778$	37.5232	1.34527
$779$	13.0212	0.466534
$780$	2.02611	0.0725463
$781$	7.20179	0.257700
$782$	8.62987	0.308604
$783$	3.93905	0.140770
$784$	−6.44045	−0.230016
$785$	−6.22859	−0.222308
$786$	−19.5243	−0.696408
$787$	25.0599	0.893288	0.446644	−	0.894712i	$-0.352619\pi$
$787$	25.0599	0.893288	0.446644	+	0.894712i	$0.352619\pi$
$788$	−22.2990	−0.794369
$789$	−14.5435	−0.517764
$790$	−9.49288	−0.337741
$791$	−11.7082	−0.416295
$792$	1.00000	0.0355335
$793$	3.37388	0.119810
$794$	26.4230	0.937717
$795$	5.24677	0.186084
$796$	5.97125	0.211645
$797$	−34.1523	−1.20974	−0.604868	−	0.796326i	$-0.706774\pi$
$797$	−34.1523	−1.20974	−0.604868	+	0.796326i	$0.706774\pi$
$798$	0.942999	0.0333818
$799$	2.89121	0.102284
$800$	−4.63937	−0.164026
$801$	10.6282	0.375530
$802$	−30.7558	−1.08603
$803$	11.0840	0.391145
$804$	6.96334	0.245578
$805$	−2.39790	−0.0845149
$806$	−22.7313	−0.800677
$807$	−11.1059	−0.390947
$808$	−13.0405	−0.458762
$809$	−51.3850	−1.80660	−0.903300	−	0.429010i	$-0.858862\pi$
$809$	−51.3850	−1.80660	−0.903300	+	0.429010i	$0.858862\pi$
$810$	−0.600528	−0.0211004
$811$	−52.2122	−1.83342	−0.916710	−	0.399554i	$-0.869165\pi$
$811$	−52.2122	−1.83342	−0.916710	+	0.399554i	$0.869165\pi$
$812$	2.94654	0.103403
$813$	21.2573	0.745525
$814$	0.919689	0.0322351
$815$	−6.19626	−0.217046
$816$	1.61669	0.0565955
$817$	0.467996	0.0163731
$818$	−12.3234	−0.430879
$819$	−2.52377	−0.0881878
$820$	−6.20291	−0.216615
$821$	−33.1972	−1.15859	−0.579295	−	0.815118i	$-0.696672\pi$
$821$	−33.1972	−1.15859	−0.579295	+	0.815118i	$0.696672\pi$
$822$	19.6596	0.685706
$823$	20.2527	0.705965	0.352982	−	0.935630i	$-0.385168\pi$
$823$	20.2527	0.705965	0.352982	+	0.935630i	$0.385168\pi$
$824$	6.66201	0.232082
$825$	−4.63937	−0.161522
$826$	−1.16196	−0.0404297
$827$	12.1521	0.422569	0.211284	−	0.977425i	$-0.432235\pi$
$827$	12.1521	0.422569	0.211284	+	0.977425i	$0.432235\pi$
$828$	5.33798	0.185508
$829$	7.43492	0.258225	0.129113	−	0.991630i	$-0.458787\pi$
$829$	7.43492	0.258225	0.129113	+	0.991630i	$0.458787\pi$
$830$	−3.26782	−0.113428
$831$	9.68120	0.335837
$832$	−3.37388	−0.116968
$833$	−10.4122	−0.360762
$834$	14.9071	0.516190
$835$	−1.81259	−0.0627273
$836$	1.26064	0.0436001
$837$	6.73745	0.232880
$838$	38.1766	1.31879
$839$	36.1001	1.24632	0.623158	−	0.782096i	$-0.285849\pi$
$839$	36.1001	1.24632	0.623158	+	0.782096i	$0.285849\pi$
$840$	−0.449215	−0.0154994
$841$	−13.4839	−0.464962
$842$	−12.7073	−0.437924
$843$	22.3772	0.770711
$844$	−1.30617	−0.0449603
$845$	0.971023	0.0334042
$846$	1.78835	0.0614846
$847$	0.748033	0.0257027
$848$	−8.73693	−0.300027
$849$	−28.0955	−0.964237
$850$	−7.50043	−0.257262
$851$	4.90928	0.168288
$852$	7.20179	0.246729
$853$	50.3770	1.72488	0.862438	−	0.506162i	$-0.168936\pi$
$853$	50.3770	1.72488	0.862438	+	0.506162i	$0.168936\pi$
$854$	−0.748033	−0.0255972
$855$	−0.757048	−0.0258905
$856$	−10.7711	−0.368147
$857$	−55.0933	−1.88195	−0.940975	−	0.338476i	$-0.890088\pi$
$857$	−55.0933	−1.88195	−0.940975	+	0.338476i	$0.890088\pi$
$858$	−3.37388	−0.115182
$859$	45.3208	1.54633	0.773164	−	0.634207i	$-0.218673\pi$
$859$	45.3208	1.54633	0.773164	+	0.634207i	$0.218673\pi$
$860$	−0.222938	−0.00760213
$861$	7.72650	0.263319
$862$	−14.2871	−0.486620
$863$	−11.3309	−0.385707	−0.192853	−	0.981228i	$-0.561774\pi$
$863$	−11.3309	−0.385707	−0.192853	+	0.981228i	$0.561774\pi$
$864$	1.00000	0.0340207
$865$	11.8567	0.403139
$866$	−24.3489	−0.827409
$867$	−14.3863	−0.488585
$868$	5.03984	0.171063
$869$	15.8076	0.536235
$870$	−2.36551	−0.0801982
$871$	−23.4935	−0.796046
$872$	7.81214	0.264552
$873$	−17.4847	−0.591769
$874$	6.72926	0.227621
$875$	4.33015	0.146386
$876$	11.0840	0.374493
$877$	16.8916	0.570388	0.285194	−	0.958470i	$-0.407942\pi$
$877$	16.8916	0.570388	0.285194	+	0.958470i	$0.407942\pi$
$878$	−7.93790	−0.267891
$879$	−14.9028	−0.502658
$880$	−0.600528	−0.0202438
$881$	40.7768	1.37381	0.686903	−	0.726749i	$-0.258970\pi$
$881$	40.7768	1.37381	0.686903	+	0.726749i	$0.258970\pi$
$882$	−6.44045	−0.216861
$883$	−49.9531	−1.68106	−0.840528	−	0.541769i	$-0.817755\pi$
$883$	−49.9531	−1.68106	−0.840528	+	0.541769i	$0.817755\pi$
$884$	−5.45452	−0.183455
$885$	0.932831	0.0313568
$886$	−28.0951	−0.943873
$887$	27.2297	0.914284	0.457142	−	0.889394i	$-0.348873\pi$
$887$	27.2297	0.914284	0.457142	+	0.889394i	$0.348873\pi$
$888$	0.919689	0.0308627
$889$	−12.1049	−0.405986
$890$	−6.38255	−0.213944
$891$	1.00000	0.0335013
$892$	22.5370	0.754594
$893$	2.25446	0.0754426
$894$	−7.06181	−0.236182
$895$	−6.55926	−0.219252
$896$	0.748033	0.0249900
$897$	−18.0097	−0.601326
$898$	−28.7037	−0.957856
$899$	26.5392	0.885130
$900$	−4.63937	−0.154646
$901$	−14.1249	−0.470569
$902$	10.3291	0.343921
$903$	0.277698	0.00924121
$904$	−15.6519	−0.520576
$905$	1.05538	0.0350820
$906$	0.654495	0.0217441
$907$	−0.157384	−0.00522584	−0.00261292	−	0.999997i	$-0.500832\pi$
$907$	−0.157384	−0.00522584	−0.00261292	+	0.999997i	$0.500832\pi$
$908$	−14.0429	−0.466032
$909$	−13.0405	−0.432525
$910$	1.51560	0.0502415
$911$	4.07678	0.135070	0.0675348	−	0.997717i	$-0.478487\pi$
$911$	4.07678	0.135070	0.0675348	+	0.997717i	$0.478487\pi$
$912$	1.26064	0.0417439
$913$	5.44158	0.180090
$914$	21.8471	0.722639
$915$	0.600528	0.0198528
$916$	−4.21543	−0.139282
$917$	−14.6048	−0.482293
$918$	1.61669	0.0533588
$919$	22.3245	0.736417	0.368208	−	0.929743i	$-0.379971\pi$
$919$	22.3245	0.736417	0.368208	+	0.929743i	$0.379971\pi$
$920$	−3.20561	−0.105686
$921$	0.0842553	0.00277631
$922$	34.8711	1.14842
$923$	−24.2980	−0.799777
$924$	0.748033	0.0246085
$925$	−4.26677	−0.140291
$926$	−31.4892	−1.03480
$927$	6.66201	0.218809
$928$	3.93905	0.129306
$929$	1.07769	0.0353577	0.0176789	−	0.999844i	$-0.494372\pi$
$929$	1.07769	0.0353577	0.0176789	+	0.999844i	$0.494372\pi$
$930$	−4.04603	−0.132674
$931$	−8.11907	−0.266092
$932$	−0.537423	−0.0176039
$933$	9.30703	0.304698
$934$	−15.1010	−0.494120
$935$	−0.970868	−0.0317508
$936$	−3.37388	−0.110279
$937$	2.15606	0.0704352	0.0352176	−	0.999380i	$-0.488788\pi$
$937$	2.15606	0.0704352	0.0352176	+	0.999380i	$0.488788\pi$
$938$	5.20881	0.170074
$939$	16.2487	0.530257
$940$	−1.07395	−0.0350285
$941$	20.0132	0.652412	0.326206	−	0.945299i	$-0.394230\pi$
$941$	20.0132	0.652412	0.326206	+	0.945299i	$0.394230\pi$
$942$	10.3719	0.337933
$943$	55.1365	1.79549
$944$	−1.55335	−0.0505573
$945$	−0.449215	−0.0146130
$946$	0.371237	0.0120700
$947$	−45.9800	−1.49415	−0.747075	−	0.664740i	$-0.768542\pi$
$947$	−45.9800	−1.49415	−0.747075	+	0.664740i	$0.768542\pi$
$948$	15.8076	0.513406
$949$	−37.3960	−1.21392
$950$	−5.84856	−0.189752
$951$	12.4700	0.404367
$952$	1.20934	0.0391949
$953$	39.6331	1.28384	0.641921	−	0.766771i	$-0.278138\pi$
$953$	39.6331	1.28384	0.641921	+	0.766771i	$0.278138\pi$
$954$	−8.73693	−0.282869
$955$	7.70240	0.249244
$956$	12.3260	0.398651
$957$	3.93905	0.127331
$958$	−6.14658	−0.198587
$959$	14.7060	0.474882
$960$	−0.600528	−0.0193820
$961$	14.3933	0.464299
$962$	−3.10292	−0.100042
$963$	−10.7711	−0.347092
$964$	−9.76663	−0.314562
$965$	1.24539	0.0400904
$966$	3.99299	0.128472
$967$	−36.4860	−1.17331	−0.586655	−	0.809837i	$-0.699555\pi$
$967$	−36.4860	−1.17331	−0.586655	+	0.809837i	$0.699555\pi$
$968$	1.00000	0.0321412
$969$	2.03806	0.0654720
$970$	10.5001	0.337137
$971$	−40.1208	−1.28754	−0.643769	−	0.765220i	$-0.722630\pi$
$971$	−40.1208	−1.28754	−0.643769	+	0.765220i	$0.722630\pi$
$972$	1.00000	0.0320750
$973$	11.1510	0.357485
$974$	31.2664	1.00184
$975$	15.6527	0.501286
$976$	−1.00000	−0.0320092
$977$	−5.41498	−0.173241	−0.0866203	−	0.996241i	$-0.527607\pi$
$977$	−5.41498	−0.173241	−0.0866203	+	0.996241i	$0.527607\pi$
$978$	10.3180	0.329934
$979$	10.6282	0.339680
$980$	3.86767	0.123548
$981$	7.81214	0.249422
$982$	1.81636	0.0579623
$983$	31.0918	0.991674	0.495837	−	0.868415i	$-0.334861\pi$
$983$	31.0918	0.991674	0.495837	+	0.868415i	$0.334861\pi$
$984$	10.3291	0.329279
$985$	13.3912	0.426678
$986$	6.36823	0.202806
$987$	1.33774	0.0425808
$988$	−4.25324	−0.135314
$989$	1.98166	0.0630131
$990$	−0.600528	−0.0190860
$991$	13.5368	0.430011	0.215006	−	0.976613i	$-0.431023\pi$
$991$	13.5368	0.430011	0.215006	+	0.976613i	$0.431023\pi$
$992$	6.73745	0.213914
$993$	5.25978	0.166914
$994$	5.38718	0.170871
$995$	−3.58590	−0.113681
$996$	5.44158	0.172423
$997$	55.5304	1.75867	0.879333	−	0.476208i	$-0.157989\pi$
$997$	55.5304	1.75867	0.879333	+	0.476208i	$0.157989\pi$
$998$	0.0913402	0.00289132
$999$	0.919689	0.0290977

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.bc.1.3	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.bc.1.3	✓	9	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:	\( N \)	\(=\)	\( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.600528 q^{5} +1.00000 q^{6} +0.748033 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.600528 q^{5} +1.00000 q^{6} +0.748033 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.600528 q^{10} +1.00000 q^{11} +1.00000 q^{12} -3.37388 q^{13} +0.748033 q^{14} -0.600528 q^{15} +1.00000 q^{16} +1.61669 q^{17} +1.00000 q^{18} +1.26064 q^{19} -0.600528 q^{20} +0.748033 q^{21} +1.00000 q^{22} +5.33798 q^{23} +1.00000 q^{24} -4.63937 q^{25} -3.37388 q^{26} +1.00000 q^{27} +0.748033 q^{28} +3.93905 q^{29} -0.600528 q^{30} +6.73745 q^{31} +1.00000 q^{32} +1.00000 q^{33} +1.61669 q^{34} -0.449215 q^{35} +1.00000 q^{36} +0.919689 q^{37} +1.26064 q^{38} -3.37388 q^{39} -0.600528 q^{40} +10.3291 q^{41} +0.748033 q^{42} +0.371237 q^{43} +1.00000 q^{44} -0.600528 q^{45} +5.33798 q^{46} +1.78835 q^{47} +1.00000 q^{48} -6.44045 q^{49} -4.63937 q^{50} +1.61669 q^{51} -3.37388 q^{52} -8.73693 q^{53} +1.00000 q^{54} -0.600528 q^{55} +0.748033 q^{56} +1.26064 q^{57} +3.93905 q^{58} -1.55335 q^{59} -0.600528 q^{60} -1.00000 q^{61} +6.73745 q^{62} +0.748033 q^{63} +1.00000 q^{64} +2.02611 q^{65} +1.00000 q^{66} +6.96334 q^{67} +1.61669 q^{68} +5.33798 q^{69} -0.449215 q^{70} +7.20179 q^{71} +1.00000 q^{72} +11.0840 q^{73} +0.919689 q^{74} -4.63937 q^{75} +1.26064 q^{76} +0.748033 q^{77} -3.37388 q^{78} +15.8076 q^{79} -0.600528 q^{80} +1.00000 q^{81} +10.3291 q^{82} +5.44158 q^{83} +0.748033 q^{84} -0.970868 q^{85} +0.371237 q^{86} +3.93905 q^{87} +1.00000 q^{88} +10.6282 q^{89} -0.600528 q^{90} -2.52377 q^{91} +5.33798 q^{92} +6.73745 q^{93} +1.78835 q^{94} -0.757048 q^{95} +1.00000 q^{96} -17.4847 q^{97} -6.44045 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} + 9 q^{3} + 9 q^{4} + 8 q^{5} + 9 q^{6} + 9 q^{7} + 9 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q + 9 * q^2 + 9 * q^3 + 9 * q^4 + 8 * q^5 + 9 * q^6 + 9 * q^7 + 9 * q^8 + 9 * q^9	\( 9 q + 9 q^{2} + 9 q^{3} + 9 q^{4} + 8 q^{5} + 9 q^{6} + 9 q^{7} + 9 q^{8} + 9 q^{9} + 8 q^{10} + 9 q^{11} + 9 q^{12} + 8 q^{13} + 9 q^{14} + 8 q^{15} + 9 q^{16} + q^{17} + 9 q^{18} + 5 q^{19} + 8 q^{20} + 9 q^{21} + 9 q^{22} - q^{23} + 9 q^{24} + 23 q^{25} + 8 q^{26} + 9 q^{27} + 9 q^{28} - 14 q^{29} + 8 q^{30} + 25 q^{31} + 9 q^{32} + 9 q^{33} + q^{34} + 5 q^{35} + 9 q^{36} + 16 q^{37} + 5 q^{38} + 8 q^{39} + 8 q^{40} + 5 q^{41} + 9 q^{42} + 5 q^{43} + 9 q^{44} + 8 q^{45} - q^{46} + 8 q^{47} + 9 q^{48} + 30 q^{49} + 23 q^{50} + q^{51} + 8 q^{52} + q^{53} + 9 q^{54} + 8 q^{55} + 9 q^{56} + 5 q^{57} - 14 q^{58} + 4 q^{59} + 8 q^{60} - 9 q^{61} + 25 q^{62} + 9 q^{63} + 9 q^{64} - 14 q^{65} + 9 q^{66} - 4 q^{67} + q^{68} - q^{69} + 5 q^{70} + 20 q^{71} + 9 q^{72} + 15 q^{73} + 16 q^{74} + 23 q^{75} + 5 q^{76} + 9 q^{77} + 8 q^{78} - 2 q^{79} + 8 q^{80} + 9 q^{81} + 5 q^{82} + 21 q^{83} + 9 q^{84} - 16 q^{85} + 5 q^{86} - 14 q^{87} + 9 q^{88} + 10 q^{89} + 8 q^{90} - 19 q^{91} - q^{92} + 25 q^{93} + 8 q^{94} - 7 q^{95} + 9 q^{96} + 3 q^{97} + 30 q^{98} + 9 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 9 * q^3 + 9 * q^4 + 8 * q^5 + 9 * q^6 + 9 * q^7 + 9 * q^8 + 9 * q^9 + 8 * q^10 + 9 * q^11 + 9 * q^12 + 8 * q^13 + 9 * q^14 + 8 * q^15 + 9 * q^16 + q^17 + 9 * q^18 + 5 * q^19 + 8 * q^20 + 9 * q^21 + 9 * q^22 - q^23 + 9 * q^24 + 23 * q^25 + 8 * q^26 + 9 * q^27 + 9 * q^28 - 14 * q^29 + 8 * q^30 + 25 * q^31 + 9 * q^32 + 9 * q^33 + q^34 + 5 * q^35 + 9 * q^36 + 16 * q^37 + 5 * q^38 + 8 * q^39 + 8 * q^40 + 5 * q^41 + 9 * q^42 + 5 * q^43 + 9 * q^44 + 8 * q^45 - q^46 + 8 * q^47 + 9 * q^48 + 30 * q^49 + 23 * q^50 + q^51 + 8 * q^52 + q^53 + 9 * q^54 + 8 * q^55 + 9 * q^56 + 5 * q^57 - 14 * q^58 + 4 * q^59 + 8 * q^60 - 9 * q^61 + 25 * q^62 + 9 * q^63 + 9 * q^64 - 14 * q^65 + 9 * q^66 - 4 * q^67 + q^68 - q^69 + 5 * q^70 + 20 * q^71 + 9 * q^72 + 15 * q^73 + 16 * q^74 + 23 * q^75 + 5 * q^76 + 9 * q^77 + 8 * q^78 - 2 * q^79 + 8 * q^80 + 9 * q^81 + 5 * q^82 + 21 * q^83 + 9 * q^84 - 16 * q^85 + 5 * q^86 - 14 * q^87 + 9 * q^88 + 10 * q^89 + 8 * q^90 - 19 * q^91 - q^92 + 25 * q^93 + 8 * q^94 - 7 * q^95 + 9 * q^96 + 3 * q^97 + 30 * q^98 + 9 * q^99

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