LMFDB - Embedded newform 4026.2.a.ba.1.1

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:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 2x^{6} - 16x^{5} + 19x^{4} + 85x^{3} - 23x^{2} - 162x - 82 $ x^7 - 2x^6 - 16x^5 + 19x^4 + 85x^3 - 23x^2 - 162x - 82
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.69874$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.69874 q^{5} -1.00000 q^{6} +3.64759 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.69874 q^{5} -1.00000 q^{6} +3.64759 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.69874 q^{10} +1.00000 q^{11} +1.00000 q^{12} -6.50332 q^{13} -3.64759 q^{14} -3.69874 q^{15} +1.00000 q^{16} -6.91664 q^{17} -1.00000 q^{18} +2.83464 q^{19} -3.69874 q^{20} +3.64759 q^{21} -1.00000 q^{22} -5.46514 q^{23} -1.00000 q^{24} +8.68066 q^{25} +6.50332 q^{26} +1.00000 q^{27} +3.64759 q^{28} -2.39962 q^{29} +3.69874 q^{30} +3.76640 q^{31} -1.00000 q^{32} +1.00000 q^{33} +6.91664 q^{34} -13.4915 q^{35} +1.00000 q^{36} +1.16536 q^{37} -2.83464 q^{38} -6.50332 q^{39} +3.69874 q^{40} +4.51168 q^{41} -3.64759 q^{42} +10.2104 q^{43} +1.00000 q^{44} -3.69874 q^{45} +5.46514 q^{46} +7.72959 q^{47} +1.00000 q^{48} +6.30488 q^{49} -8.68066 q^{50} -6.91664 q^{51} -6.50332 q^{52} -5.76187 q^{53} -1.00000 q^{54} -3.69874 q^{55} -3.64759 q^{56} +2.83464 q^{57} +2.39962 q^{58} +11.4982 q^{59} -3.69874 q^{60} +1.00000 q^{61} -3.76640 q^{62} +3.64759 q^{63} +1.00000 q^{64} +24.0541 q^{65} -1.00000 q^{66} +0.969284 q^{67} -6.91664 q^{68} -5.46514 q^{69} +13.4915 q^{70} +10.7462 q^{71} -1.00000 q^{72} -1.00688 q^{73} -1.16536 q^{74} +8.68066 q^{75} +2.83464 q^{76} +3.64759 q^{77} +6.50332 q^{78} -13.5551 q^{79} -3.69874 q^{80} +1.00000 q^{81} -4.51168 q^{82} +12.3442 q^{83} +3.64759 q^{84} +25.5829 q^{85} -10.2104 q^{86} -2.39962 q^{87} -1.00000 q^{88} +12.3329 q^{89} +3.69874 q^{90} -23.7214 q^{91} -5.46514 q^{92} +3.76640 q^{93} -7.72959 q^{94} -10.4846 q^{95} -1.00000 q^{96} -12.7934 q^{97} -6.30488 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 7 q^{2} + 7 q^{3} + 7 q^{4} - 5 q^{5} - 7 q^{6} + 9 q^{7} - 7 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - 7 * q^2 + 7 * q^3 + 7 * q^4 - 5 * q^5 - 7 * q^6 + 9 * q^7 - 7 * q^8 + 7 * q^9	\( 7 q - 7 q^{2} + 7 q^{3} + 7 q^{4} - 5 q^{5} - 7 q^{6} + 9 q^{7} - 7 q^{8} + 7 q^{9} + 5 q^{10} + 7 q^{11} + 7 q^{12} + 4 q^{13} - 9 q^{14} - 5 q^{15} + 7 q^{16} - 6 q^{17} - 7 q^{18} + 9 q^{19} - 5 q^{20} + 9 q^{21} - 7 q^{22} - 8 q^{23} - 7 q^{24} + 4 q^{25} - 4 q^{26} + 7 q^{27} + 9 q^{28} - 4 q^{29} + 5 q^{30} + 17 q^{31} - 7 q^{32} + 7 q^{33} + 6 q^{34} - 3 q^{35} + 7 q^{36} + 19 q^{37} - 9 q^{38} + 4 q^{39} + 5 q^{40} + 5 q^{41} - 9 q^{42} + 24 q^{43} + 7 q^{44} - 5 q^{45} + 8 q^{46} + 6 q^{47} + 7 q^{48} + 24 q^{49} - 4 q^{50} - 6 q^{51} + 4 q^{52} + 3 q^{53} - 7 q^{54} - 5 q^{55} - 9 q^{56} + 9 q^{57} + 4 q^{58} + 10 q^{59} - 5 q^{60} + 7 q^{61} - 17 q^{62} + 9 q^{63} + 7 q^{64} + 16 q^{65} - 7 q^{66} + 22 q^{67} - 6 q^{68} - 8 q^{69} + 3 q^{70} + q^{71} - 7 q^{72} + 32 q^{73} - 19 q^{74} + 4 q^{75} + 9 q^{76} + 9 q^{77} - 4 q^{78} - 8 q^{79} - 5 q^{80} + 7 q^{81} - 5 q^{82} - 30 q^{83} + 9 q^{84} + 3 q^{85} - 24 q^{86} - 4 q^{87} - 7 q^{88} + 5 q^{89} + 5 q^{90} + 15 q^{91} - 8 q^{92} + 17 q^{93} - 6 q^{94} - 21 q^{95} - 7 q^{96} + 14 q^{97} - 24 q^{98} + 7 q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 + 7 * q^3 + 7 * q^4 - 5 * q^5 - 7 * q^6 + 9 * q^7 - 7 * q^8 + 7 * q^9 + 5 * q^10 + 7 * q^11 + 7 * q^12 + 4 * q^13 - 9 * q^14 - 5 * q^15 + 7 * q^16 - 6 * q^17 - 7 * q^18 + 9 * q^19 - 5 * q^20 + 9 * q^21 - 7 * q^22 - 8 * q^23 - 7 * q^24 + 4 * q^25 - 4 * q^26 + 7 * q^27 + 9 * q^28 - 4 * q^29 + 5 * q^30 + 17 * q^31 - 7 * q^32 + 7 * q^33 + 6 * q^34 - 3 * q^35 + 7 * q^36 + 19 * q^37 - 9 * q^38 + 4 * q^39 + 5 * q^40 + 5 * q^41 - 9 * q^42 + 24 * q^43 + 7 * q^44 - 5 * q^45 + 8 * q^46 + 6 * q^47 + 7 * q^48 + 24 * q^49 - 4 * q^50 - 6 * q^51 + 4 * q^52 + 3 * q^53 - 7 * q^54 - 5 * q^55 - 9 * q^56 + 9 * q^57 + 4 * q^58 + 10 * q^59 - 5 * q^60 + 7 * q^61 - 17 * q^62 + 9 * q^63 + 7 * q^64 + 16 * q^65 - 7 * q^66 + 22 * q^67 - 6 * q^68 - 8 * q^69 + 3 * q^70 + q^71 - 7 * q^72 + 32 * q^73 - 19 * q^74 + 4 * q^75 + 9 * q^76 + 9 * q^77 - 4 * q^78 - 8 * q^79 - 5 * q^80 + 7 * q^81 - 5 * q^82 - 30 * q^83 + 9 * q^84 + 3 * q^85 - 24 * q^86 - 4 * q^87 - 7 * q^88 + 5 * q^89 + 5 * q^90 + 15 * q^91 - 8 * q^92 + 17 * q^93 - 6 * q^94 - 21 * q^95 - 7 * q^96 + 14 * q^97 - 24 * q^98 + 7 * 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
$5$	−3.69874	−1.65413	−0.827063	−	0.562109i	$-0.809990\pi$
$5$	−3.69874	−1.65413	−0.827063	+	0.562109i	$0.809990\pi$
$6$	−1.00000	−0.408248
$7$	3.64759	1.37866	0.689329	−	0.724449i	$-0.257906\pi$
$7$	3.64759	1.37866	0.689329	+	0.724449i	$0.257906\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	3.69874	1.16964
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.00000	0.288675
$13$	−6.50332	−1.80370	−0.901848	−	0.432053i	$-0.857789\pi$
$13$	−6.50332	−1.80370	−0.901848	+	0.432053i	$0.857789\pi$
$14$	−3.64759	−0.974858
$15$	−3.69874	−0.955010
$16$	1.00000	0.250000
$17$	−6.91664	−1.67753	−0.838766	−	0.544492i	$-0.816723\pi$
$17$	−6.91664	−1.67753	−0.838766	+	0.544492i	$0.816723\pi$
$18$	−1.00000	−0.235702
$19$	2.83464	0.650311	0.325155	−	0.945661i	$-0.394583\pi$
$19$	2.83464	0.650311	0.325155	+	0.945661i	$0.394583\pi$
$20$	−3.69874	−0.827063
$21$	3.64759	0.795968
$22$	−1.00000	−0.213201
$23$	−5.46514	−1.13956	−0.569780	−	0.821797i	$-0.692971\pi$
$23$	−5.46514	−1.13956	−0.569780	+	0.821797i	$0.692971\pi$
$24$	−1.00000	−0.204124
$25$	8.68066	1.73613
$26$	6.50332	1.27541
$27$	1.00000	0.192450
$28$	3.64759	0.689329
$29$	−2.39962	−0.445599	−0.222799	−	0.974864i	$-0.571520\pi$
$29$	−2.39962	−0.445599	−0.222799	+	0.974864i	$0.571520\pi$
$30$	3.69874	0.675294
$31$	3.76640	0.676465	0.338232	−	0.941063i	$-0.390171\pi$
$31$	3.76640	0.676465	0.338232	+	0.941063i	$0.390171\pi$
$32$	−1.00000	−0.176777
$33$	1.00000	0.174078
$34$	6.91664	1.18619
$35$	−13.4915	−2.28047
$36$	1.00000	0.166667
$37$	1.16536	0.191584	0.0957921	−	0.995401i	$-0.469462\pi$
$37$	1.16536	0.191584	0.0957921	+	0.995401i	$0.469462\pi$
$38$	−2.83464	−0.459839
$39$	−6.50332	−1.04136
$40$	3.69874	0.584822
$41$	4.51168	0.704607	0.352303	−	0.935886i	$-0.385399\pi$
$41$	4.51168	0.704607	0.352303	+	0.935886i	$0.385399\pi$
$42$	−3.64759	−0.562835
$43$	10.2104	1.55707	0.778537	−	0.627598i	$-0.215962\pi$
$43$	10.2104	1.55707	0.778537	+	0.627598i	$0.215962\pi$
$44$	1.00000	0.150756
$45$	−3.69874	−0.551375
$46$	5.46514	0.805790
$47$	7.72959	1.12748	0.563738	−	0.825953i	$-0.309363\pi$
$47$	7.72959	1.12748	0.563738	+	0.825953i	$0.309363\pi$
$48$	1.00000	0.144338
$49$	6.30488	0.900697
$50$	−8.68066	−1.22763
$51$	−6.91664	−0.968524
$52$	−6.50332	−0.901848
$53$	−5.76187	−0.791454	−0.395727	−	0.918368i	$-0.629507\pi$
$53$	−5.76187	−0.791454	−0.395727	+	0.918368i	$0.629507\pi$
$54$	−1.00000	−0.136083
$55$	−3.69874	−0.498738
$56$	−3.64759	−0.487429
$57$	2.83464	0.375457
$58$	2.39962	0.315086
$59$	11.4982	1.49694	0.748470	−	0.663169i	$-0.230789\pi$
$59$	11.4982	1.49694	0.748470	+	0.663169i	$0.230789\pi$
$60$	−3.69874	−0.477505
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	−3.76640	−0.478333
$63$	3.64759	0.459553
$64$	1.00000	0.125000
$65$	24.0541	2.98354
$66$	−1.00000	−0.123091
$67$	0.969284	0.118417	0.0592084	−	0.998246i	$-0.481142\pi$
$67$	0.969284	0.118417	0.0592084	+	0.998246i	$0.481142\pi$
$68$	−6.91664	−0.838766
$69$	−5.46514	−0.657925
$70$	13.4915	1.61254
$71$	10.7462	1.27534	0.637668	−	0.770311i	$-0.279899\pi$
$71$	10.7462	1.27534	0.637668	+	0.770311i	$0.279899\pi$
$72$	−1.00000	−0.117851
$73$	−1.00688	−0.117846	−0.0589230	−	0.998263i	$-0.518767\pi$
$73$	−1.00688	−0.117846	−0.0589230	+	0.998263i	$0.518767\pi$
$74$	−1.16536	−0.135471
$75$	8.68066	1.00236
$76$	2.83464	0.325155
$77$	3.64759	0.415681
$78$	6.50332	0.736356
$79$	−13.5551	−1.52507	−0.762536	−	0.646946i	$-0.776046\pi$
$79$	−13.5551	−1.52507	−0.762536	+	0.646946i	$0.776046\pi$
$80$	−3.69874	−0.413531
$81$	1.00000	0.111111
$82$	−4.51168	−0.498232
$83$	12.3442	1.35496	0.677478	−	0.735543i	$-0.263073\pi$
$83$	12.3442	1.35496	0.677478	+	0.735543i	$0.263073\pi$
$84$	3.64759	0.397984
$85$	25.5829	2.77485
$86$	−10.2104	−1.10102
$87$	−2.39962	−0.257267
$88$	−1.00000	−0.106600
$89$	12.3329	1.30728	0.653640	−	0.756806i	$-0.273241\pi$
$89$	12.3329	1.30728	0.653640	+	0.756806i	$0.273241\pi$
$90$	3.69874	0.389881
$91$	−23.7214	−2.48668
$92$	−5.46514	−0.569780
$93$	3.76640	0.390557
$94$	−7.72959	−0.797246
$95$	−10.4846	−1.07570
$96$	−1.00000	−0.102062
$97$	−12.7934	−1.29897	−0.649486	−	0.760374i	$-0.725016\pi$
$97$	−12.7934	−1.29897	−0.649486	+	0.760374i	$0.725016\pi$
$98$	−6.30488	−0.636889
$99$	1.00000	0.100504
$100$	8.68066	0.868066
$101$	7.96896	0.792941	0.396470	−	0.918047i	$-0.370235\pi$
$101$	7.96896	0.792941	0.396470	+	0.918047i	$0.370235\pi$
$102$	6.91664	0.684850
$103$	−2.18334	−0.215131	−0.107565	−	0.994198i	$-0.534305\pi$
$103$	−2.18334	−0.215131	−0.107565	+	0.994198i	$0.534305\pi$
$104$	6.50332	0.637703
$105$	−13.4915	−1.31663
$106$	5.76187	0.559643
$107$	−17.1374	−1.65674	−0.828369	−	0.560183i	$-0.810731\pi$
$107$	−17.1374	−1.65674	−0.828369	+	0.560183i	$0.810731\pi$
$108$	1.00000	0.0962250
$109$	5.41836	0.518984	0.259492	−	0.965745i	$-0.416445\pi$
$109$	5.41836	0.518984	0.259492	+	0.965745i	$0.416445\pi$
$110$	3.69874	0.352661
$111$	1.16536	0.110611
$112$	3.64759	0.344664
$113$	−2.58852	−0.243508	−0.121754	−	0.992560i	$-0.538852\pi$
$113$	−2.58852	−0.243508	−0.121754	+	0.992560i	$0.538852\pi$
$114$	−2.83464	−0.265488
$115$	20.2141	1.88497
$116$	−2.39962	−0.222799
$117$	−6.50332	−0.601232
$118$	−11.4982	−1.05850
$119$	−25.2290	−2.31274
$120$	3.69874	0.337647
$121$	1.00000	0.0909091
$122$	−1.00000	−0.0905357
$123$	4.51168	0.406805
$124$	3.76640	0.338232
$125$	−13.6138	−1.21766
$126$	−3.64759	−0.324953
$127$	−18.3296	−1.62649	−0.813246	−	0.581920i	$-0.802302\pi$
$127$	−18.3296	−1.62649	−0.813246	+	0.581920i	$0.802302\pi$
$128$	−1.00000	−0.0883883
$129$	10.2104	0.898978
$130$	−24.0541	−2.10968
$131$	−3.07667	−0.268810	−0.134405	−	0.990926i	$-0.542912\pi$
$131$	−3.07667	−0.268810	−0.134405	+	0.990926i	$0.542912\pi$
$132$	1.00000	0.0870388
$133$	10.3396	0.896556
$134$	−0.969284	−0.0837333
$135$	−3.69874	−0.318337
$136$	6.91664	0.593097
$137$	−9.79553	−0.836889	−0.418444	−	0.908242i	$-0.637425\pi$
$137$	−9.79553	−0.836889	−0.418444	+	0.908242i	$0.637425\pi$
$138$	5.46514	0.465223
$139$	7.05576	0.598461	0.299231	−	0.954181i	$-0.403270\pi$
$139$	7.05576	0.598461	0.299231	+	0.954181i	$0.403270\pi$
$140$	−13.4915	−1.14024
$141$	7.72959	0.650949
$142$	−10.7462	−0.901799
$143$	−6.50332	−0.543835
$144$	1.00000	0.0833333
$145$	8.87558	0.737077
$146$	1.00688	0.0833298
$147$	6.30488	0.520018
$148$	1.16536	0.0957921
$149$	18.0296	1.47704	0.738520	−	0.674231i	$-0.235525\pi$
$149$	18.0296	1.47704	0.738520	+	0.674231i	$0.235525\pi$
$150$	−8.68066	−0.708773
$151$	13.2195	1.07579	0.537895	−	0.843012i	$-0.319220\pi$
$151$	13.2195	1.07579	0.537895	+	0.843012i	$0.319220\pi$
$152$	−2.83464	−0.229920
$153$	−6.91664	−0.559177
$154$	−3.64759	−0.293931
$155$	−13.9309	−1.11896
$156$	−6.50332	−0.520682
$157$	7.70630	0.615030	0.307515	−	0.951543i	$-0.400503\pi$
$157$	7.70630	0.615030	0.307515	+	0.951543i	$0.400503\pi$
$158$	13.5551	1.07839
$159$	−5.76187	−0.456946
$160$	3.69874	0.292411
$161$	−19.9345	−1.57106
$162$	−1.00000	−0.0785674
$163$	13.6846	1.07186	0.535930	−	0.844263i	$-0.319961\pi$
$163$	13.6846	1.07186	0.535930	+	0.844263i	$0.319961\pi$
$164$	4.51168	0.352303
$165$	−3.69874	−0.287946
$166$	−12.3442	−0.958099
$167$	11.5056	0.890330	0.445165	−	0.895449i	$-0.353145\pi$
$167$	11.5056	0.890330	0.445165	+	0.895449i	$0.353145\pi$
$168$	−3.64759	−0.281417
$169$	29.2932	2.25332
$170$	−25.5829	−1.96212
$171$	2.83464	0.216770
$172$	10.2104	0.778537
$173$	−1.61191	−0.122551	−0.0612755	−	0.998121i	$-0.519517\pi$
$173$	−1.61191	−0.122551	−0.0612755	+	0.998121i	$0.519517\pi$
$174$	2.39962	0.181915
$175$	31.6635	2.39353
$176$	1.00000	0.0753778
$177$	11.4982	0.864259
$178$	−12.3329	−0.924386
$179$	9.95847	0.744331	0.372166	−	0.928166i	$-0.378615\pi$
$179$	9.95847	0.744331	0.372166	+	0.928166i	$0.378615\pi$
$180$	−3.69874	−0.275688
$181$	2.83988	0.211087	0.105543	−	0.994415i	$-0.466342\pi$
$181$	2.83988	0.211087	0.105543	+	0.994415i	$0.466342\pi$
$182$	23.7214	1.75835
$183$	1.00000	0.0739221
$184$	5.46514	0.402895
$185$	−4.31037	−0.316904
$186$	−3.76640	−0.276166
$187$	−6.91664	−0.505795
$188$	7.72959	0.563738
$189$	3.64759	0.265323
$190$	10.4846	0.760632
$191$	−22.5566	−1.63214	−0.816068	−	0.577957i	$-0.803850\pi$
$191$	−22.5566	−1.63214	−0.816068	+	0.577957i	$0.803850\pi$
$192$	1.00000	0.0721688
$193$	0.0975677	0.00702308	0.00351154	−	0.999994i	$-0.498882\pi$
$193$	0.0975677	0.00702308	0.00351154	+	0.999994i	$0.498882\pi$
$194$	12.7934	0.918511
$195$	24.0541	1.72255
$196$	6.30488	0.450349
$197$	10.7143	0.763365	0.381683	−	0.924293i	$-0.375345\pi$
$197$	10.7143	0.763365	0.381683	+	0.924293i	$0.375345\pi$
$198$	−1.00000	−0.0710669
$199$	−0.00203644	−0.000144359 0	−7.21796e−5	−	1.00000i	$-0.500023\pi$
$199$	−0.00203644	−0.000144359 0	−7.21796e−5		1.00000i	$0.500023\pi$
$200$	−8.68066	−0.613816
$201$	0.969284	0.0683680
$202$	−7.96896	−0.560694
$203$	−8.75283	−0.614328
$204$	−6.91664	−0.484262
$205$	−16.6875	−1.16551
$206$	2.18334	0.152120
$207$	−5.46514	−0.379853
$208$	−6.50332	−0.450924
$209$	2.83464	0.196076
$210$	13.4915	0.930999
$211$	23.0220	1.58490	0.792449	−	0.609938i	$-0.208806\pi$
$211$	23.0220	1.58490	0.792449	+	0.609938i	$0.208806\pi$
$212$	−5.76187	−0.395727
$213$	10.7462	0.736316
$214$	17.1374	1.17149
$215$	−37.7657	−2.57560
$216$	−1.00000	−0.0680414
$217$	13.7383	0.932613
$218$	−5.41836	−0.366977
$219$	−1.00688	−0.0680385
$220$	−3.69874	−0.249369
$221$	44.9811	3.02576
$222$	−1.16536	−0.0782139
$223$	−12.2002	−0.816987	−0.408493	−	0.912761i	$-0.633946\pi$
$223$	−12.2002	−0.816987	−0.408493	+	0.912761i	$0.633946\pi$
$224$	−3.64759	−0.243715
$225$	8.68066	0.578711
$226$	2.58852	0.172186
$227$	26.6039	1.76576	0.882880	−	0.469599i	$-0.155601\pi$
$227$	26.6039	1.76576	0.882880	+	0.469599i	$0.155601\pi$
$228$	2.83464	0.187729
$229$	27.0506	1.78755	0.893777	−	0.448513i	$-0.148046\pi$
$229$	27.0506	1.78755	0.893777	+	0.448513i	$0.148046\pi$
$230$	−20.2141	−1.33288
$231$	3.64759	0.239994
$232$	2.39962	0.157543
$233$	15.9166	1.04273	0.521366	−	0.853333i	$-0.325423\pi$
$233$	15.9166	1.04273	0.521366	+	0.853333i	$0.325423\pi$
$234$	6.50332	0.425135
$235$	−28.5897	−1.86499
$236$	11.4982	0.748470
$237$	−13.5551	−0.880500
$238$	25.2290	1.63536
$239$	−10.3123	−0.667047	−0.333524	−	0.942742i	$-0.608238\pi$
$239$	−10.3123	−0.667047	−0.333524	+	0.942742i	$0.608238\pi$
$240$	−3.69874	−0.238753
$241$	16.1203	1.03840	0.519200	−	0.854653i	$-0.326230\pi$
$241$	16.1203	1.03840	0.519200	+	0.854653i	$0.326230\pi$
$242$	−1.00000	−0.0642824
$243$	1.00000	0.0641500
$244$	1.00000	0.0640184
$245$	−23.3201	−1.48987
$246$	−4.51168	−0.287655
$247$	−18.4346	−1.17296
$248$	−3.76640	−0.239166
$249$	12.3442	0.782284
$250$	13.6138	0.861013
$251$	25.2647	1.59470	0.797348	−	0.603520i	$-0.206236\pi$
$251$	25.2647	1.59470	0.797348	+	0.603520i	$0.206236\pi$
$252$	3.64759	0.229776
$253$	−5.46514	−0.343590
$254$	18.3296	1.15010
$255$	25.5829	1.60206
$256$	1.00000	0.0625000
$257$	−6.36362	−0.396952	−0.198476	−	0.980106i	$-0.563599\pi$
$257$	−6.36362	−0.396952	−0.198476	+	0.980106i	$0.563599\pi$
$258$	−10.2104	−0.635673
$259$	4.25075	0.264129
$260$	24.0541	1.49177
$261$	−2.39962	−0.148533
$262$	3.07667	0.190077
$263$	7.20703	0.444405	0.222202	−	0.975001i	$-0.428675\pi$
$263$	7.20703	0.444405	0.222202	+	0.975001i	$0.428675\pi$
$264$	−1.00000	−0.0615457
$265$	21.3117	1.30917
$266$	−10.3396	−0.633961
$267$	12.3329	0.754758
$268$	0.969284	0.0592084
$269$	18.8237	1.14770	0.573851	−	0.818960i	$-0.305449\pi$
$269$	18.8237	1.14770	0.573851	+	0.818960i	$0.305449\pi$
$270$	3.69874	0.225098
$271$	−17.3219	−1.05223	−0.526116	−	0.850413i	$-0.676352\pi$
$271$	−17.3219	−1.05223	−0.526116	+	0.850413i	$0.676352\pi$
$272$	−6.91664	−0.419383
$273$	−23.7214	−1.43569
$274$	9.79553	0.591770
$275$	8.68066	0.523464
$276$	−5.46514	−0.328962
$277$	2.06809	0.124259	0.0621297	−	0.998068i	$-0.480211\pi$
$277$	2.06809	0.124259	0.0621297	+	0.998068i	$0.480211\pi$
$278$	−7.05576	−0.423176
$279$	3.76640	0.225488
$280$	13.4915	0.806269
$281$	−15.2178	−0.907819	−0.453909	−	0.891048i	$-0.649971\pi$
$281$	−15.2178	−0.907819	−0.453909	+	0.891048i	$0.649971\pi$
$282$	−7.72959	−0.460290
$283$	20.1102	1.19542	0.597712	−	0.801711i	$-0.296077\pi$
$283$	20.1102	1.19542	0.597712	+	0.801711i	$0.296077\pi$
$284$	10.7462	0.637668
$285$	−10.4846	−0.621053
$286$	6.50332	0.384549
$287$	16.4568	0.971412
$288$	−1.00000	−0.0589256
$289$	30.8399	1.81411
$290$	−8.87558	−0.521192
$291$	−12.7934	−0.749961
$292$	−1.00688	−0.0589230
$293$	17.6641	1.03195	0.515975	−	0.856604i	$-0.327430\pi$
$293$	17.6641	1.03195	0.515975	+	0.856604i	$0.327430\pi$
$294$	−6.30488	−0.367708
$295$	−42.5289	−2.47613
$296$	−1.16536	−0.0677353
$297$	1.00000	0.0580259
$298$	−18.0296	−1.04443
$299$	35.5415	2.05542
$300$	8.68066	0.501178
$301$	37.2434	2.14667
$302$	−13.2195	−0.760699
$303$	7.96896	0.457805
$304$	2.83464	0.162578
$305$	−3.69874	−0.211789
$306$	6.91664	0.395398
$307$	−26.8533	−1.53260	−0.766300	−	0.642483i	$-0.777904\pi$
$307$	−26.8533	−1.53260	−0.766300	+	0.642483i	$0.777904\pi$
$308$	3.64759	0.207840
$309$	−2.18334	−0.124206
$310$	13.9309	0.791223
$311$	−30.0582	−1.70445	−0.852223	−	0.523179i	$-0.824746\pi$
$311$	−30.0582	−1.70445	−0.852223	+	0.523179i	$0.824746\pi$
$312$	6.50332	0.368178
$313$	−2.50660	−0.141682	−0.0708408	−	0.997488i	$-0.522568\pi$
$313$	−2.50660	−0.141682	−0.0708408	+	0.997488i	$0.522568\pi$
$314$	−7.70630	−0.434892
$315$	−13.4915	−0.760158
$316$	−13.5551	−0.762536
$317$	−5.30701	−0.298072	−0.149036	−	0.988832i	$-0.547617\pi$
$317$	−5.30701	−0.298072	−0.149036	+	0.988832i	$0.547617\pi$
$318$	5.76187	0.323110
$319$	−2.39962	−0.134353
$320$	−3.69874	−0.206766
$321$	−17.1374	−0.956518
$322$	19.9345	1.11091
$323$	−19.6062	−1.09092
$324$	1.00000	0.0555556
$325$	−56.4531	−3.13146
$326$	−13.6846	−0.757919
$327$	5.41836	0.299636
$328$	−4.51168	−0.249116
$329$	28.1943	1.55440
$330$	3.69874	0.203609
$331$	−10.0513	−0.552468	−0.276234	−	0.961090i	$-0.589086\pi$
$331$	−10.0513	−0.552468	−0.276234	+	0.961090i	$0.589086\pi$
$332$	12.3442	0.677478
$333$	1.16536	0.0638614
$334$	−11.5056	−0.629558
$335$	−3.58513	−0.195876
$336$	3.64759	0.198992
$337$	8.00391	0.436001	0.218000	−	0.975949i	$-0.430047\pi$
$337$	8.00391	0.436001	0.218000	+	0.975949i	$0.430047\pi$
$338$	−29.2932	−1.59334
$339$	−2.58852	−0.140589
$340$	25.5829	1.38742
$341$	3.76640	0.203962
$342$	−2.83464	−0.153280
$343$	−2.53551	−0.136905
$344$	−10.2104	−0.550509
$345$	20.2141	1.08829
$346$	1.61191	0.0866566
$347$	−20.2057	−1.08470	−0.542351	−	0.840152i	$-0.682466\pi$
$347$	−20.2057	−1.08470	−0.542351	+	0.840152i	$0.682466\pi$
$348$	−2.39962	−0.128633
$349$	−16.8778	−0.903450	−0.451725	−	0.892157i	$-0.649191\pi$
$349$	−16.8778	−0.903450	−0.451725	+	0.892157i	$0.649191\pi$
$350$	−31.6635	−1.69248
$351$	−6.50332	−0.347122
$352$	−1.00000	−0.0533002
$353$	18.5805	0.988938	0.494469	−	0.869195i	$-0.335363\pi$
$353$	18.5805	0.988938	0.494469	+	0.869195i	$0.335363\pi$
$354$	−11.4982	−0.611123
$355$	−39.7473	−2.10957
$356$	12.3329	0.653640
$357$	−25.2290	−1.33526
$358$	−9.95847	−0.526322
$359$	−36.0630	−1.90333	−0.951667	−	0.307132i	$-0.900631\pi$
$359$	−36.0630	−1.90333	−0.951667	+	0.307132i	$0.900631\pi$
$360$	3.69874	0.194941
$361$	−10.9648	−0.577096
$362$	−2.83988	−0.149261
$363$	1.00000	0.0524864
$364$	−23.7214	−1.24334
$365$	3.72418	0.194932
$366$	−1.00000	−0.0522708
$367$	3.99558	0.208567	0.104284	−	0.994548i	$-0.466745\pi$
$367$	3.99558	0.208567	0.104284	+	0.994548i	$0.466745\pi$
$368$	−5.46514	−0.284890
$369$	4.51168	0.234869
$370$	4.31037	0.224085
$371$	−21.0169	−1.09114
$372$	3.76640	0.195279
$373$	34.5760	1.79028	0.895139	−	0.445786i	$-0.147076\pi$
$373$	34.5760	1.79028	0.895139	+	0.445786i	$0.147076\pi$
$374$	6.91664	0.357651
$375$	−13.6138	−0.703014
$376$	−7.72959	−0.398623
$377$	15.6055	0.803725
$378$	−3.64759	−0.187612
$379$	14.9005	0.765387	0.382693	−	0.923875i	$-0.374997\pi$
$379$	14.9005	0.765387	0.382693	+	0.923875i	$0.374997\pi$
$380$	−10.4846	−0.537848
$381$	−18.3296	−0.939056
$382$	22.5566	1.15409
$383$	6.93216	0.354217	0.177109	−	0.984191i	$-0.443326\pi$
$383$	6.93216	0.354217	0.177109	+	0.984191i	$0.443326\pi$
$384$	−1.00000	−0.0510310
$385$	−13.4915	−0.687589
$386$	−0.0975677	−0.00496606
$387$	10.2104	0.519025
$388$	−12.7934	−0.649486
$389$	−5.04981	−0.256036	−0.128018	−	0.991772i	$-0.540861\pi$
$389$	−5.04981	−0.256036	−0.128018	+	0.991772i	$0.540861\pi$
$390$	−24.0541	−1.21803
$391$	37.8004	1.91165
$392$	−6.30488	−0.318445
$393$	−3.07667	−0.155197
$394$	−10.7143	−0.539781
$395$	50.1369	2.52266
$396$	1.00000	0.0502519
$397$	−22.6016	−1.13434	−0.567170	−	0.823601i	$-0.691962\pi$
$397$	−22.6016	−1.13434	−0.567170	+	0.823601i	$0.691962\pi$
$398$	0.00203644	0.000102077 0
$399$	10.3396	0.517627
$400$	8.68066	0.434033
$401$	2.60134	0.129905	0.0649523	−	0.997888i	$-0.479310\pi$
$401$	2.60134	0.129905	0.0649523	+	0.997888i	$0.479310\pi$
$402$	−0.969284	−0.0483435
$403$	−24.4941	−1.22014
$404$	7.96896	0.396470
$405$	−3.69874	−0.183792
$406$	8.75283	0.434396
$407$	1.16536	0.0577648
$408$	6.91664	0.342425
$409$	−9.04616	−0.447304	−0.223652	−	0.974669i	$-0.571798\pi$
$409$	−9.04616	−0.447304	−0.223652	+	0.974669i	$0.571798\pi$
$410$	16.6875	0.824139
$411$	−9.79553	−0.483178
$412$	−2.18334	−0.107565
$413$	41.9407	2.06377
$414$	5.46514	0.268597
$415$	−45.6581	−2.24127
$416$	6.50332	0.318851
$417$	7.05576	0.345522
$418$	−2.83464	−0.138647
$419$	−13.1890	−0.644326	−0.322163	−	0.946684i	$-0.604410\pi$
$419$	−13.1890	−0.644326	−0.322163	+	0.946684i	$0.604410\pi$
$420$	−13.4915	−0.658316
$421$	36.0504	1.75699	0.878493	−	0.477754i	$-0.158549\pi$
$421$	36.0504	1.75699	0.878493	+	0.477754i	$0.158549\pi$
$422$	−23.0220	−1.12069
$423$	7.72959	0.375826
$424$	5.76187	0.279821
$425$	−60.0411	−2.91242
$426$	−10.7462	−0.520654
$427$	3.64759	0.176519
$428$	−17.1374	−0.828369
$429$	−6.50332	−0.313983
$430$	37.7657	1.82122
$431$	18.4753	0.889925	0.444963	−	0.895549i	$-0.353217\pi$
$431$	18.4753	0.889925	0.444963	+	0.895549i	$0.353217\pi$
$432$	1.00000	0.0481125
$433$	−20.1477	−0.968237	−0.484119	−	0.875002i	$-0.660860\pi$
$433$	−20.1477	−0.968237	−0.484119	+	0.875002i	$0.660860\pi$
$434$	−13.7383	−0.659457
$435$	8.87558	0.425551
$436$	5.41836	0.259492
$437$	−15.4917	−0.741068
$438$	1.00688	0.0481105
$439$	21.3023	1.01670	0.508351	−	0.861150i	$-0.330255\pi$
$439$	21.3023	1.01670	0.508351	+	0.861150i	$0.330255\pi$
$440$	3.69874	0.176330
$441$	6.30488	0.300232
$442$	−44.9811	−2.13953
$443$	32.6077	1.54924	0.774620	−	0.632427i	$-0.217941\pi$
$443$	32.6077	1.54924	0.774620	+	0.632427i	$0.217941\pi$
$444$	1.16536	0.0553056
$445$	−45.6160	−2.16241
$446$	12.2002	0.577697
$447$	18.0296	0.852770
$448$	3.64759	0.172332
$449$	−38.5893	−1.82114	−0.910570	−	0.413354i	$-0.864357\pi$
$449$	−38.5893	−1.82114	−0.910570	+	0.413354i	$0.864357\pi$
$450$	−8.68066	−0.409210
$451$	4.51168	0.212447
$452$	−2.58852	−0.121754
$453$	13.2195	0.621108
$454$	−26.6039	−1.24858
$455$	87.7393	4.11328
$456$	−2.83464	−0.132744
$457$	1.36144	0.0636854	0.0318427	−	0.999493i	$-0.489862\pi$
$457$	1.36144	0.0636854	0.0318427	+	0.999493i	$0.489862\pi$
$458$	−27.0506	−1.26399
$459$	−6.91664	−0.322841
$460$	20.2141	0.942487
$461$	−32.7190	−1.52387	−0.761937	−	0.647651i	$-0.775751\pi$
$461$	−32.7190	−1.52387	−0.761937	+	0.647651i	$0.775751\pi$
$462$	−3.64759	−0.169701
$463$	25.4768	1.18401	0.592003	−	0.805935i	$-0.298337\pi$
$463$	25.4768	1.18401	0.592003	+	0.805935i	$0.298337\pi$
$464$	−2.39962	−0.111400
$465$	−13.9309	−0.646031
$466$	−15.9166	−0.737323
$467$	15.9601	0.738548	0.369274	−	0.929321i	$-0.379606\pi$
$467$	15.9601	0.738548	0.369274	+	0.929321i	$0.379606\pi$
$468$	−6.50332	−0.300616
$469$	3.53554	0.163256
$470$	28.5897	1.31875
$471$	7.70630	0.355088
$472$	−11.4982	−0.529248
$473$	10.2104	0.469476
$474$	13.5551	0.622608
$475$	24.6065	1.12903
$476$	−25.2290	−1.15637
$477$	−5.76187	−0.263818
$478$	10.3123	0.471674
$479$	−4.28727	−0.195890	−0.0979451	−	0.995192i	$-0.531227\pi$
$479$	−4.28727	−0.195890	−0.0979451	+	0.995192i	$0.531227\pi$
$480$	3.69874	0.168824
$481$	−7.57872	−0.345560
$482$	−16.1203	−0.734260
$483$	−19.9345	−0.907053
$484$	1.00000	0.0454545
$485$	47.3194	2.14866
$486$	−1.00000	−0.0453609
$487$	32.4067	1.46849	0.734243	−	0.678887i	$-0.237537\pi$
$487$	32.4067	1.46849	0.734243	+	0.678887i	$0.237537\pi$
$488$	−1.00000	−0.0452679
$489$	13.6846	0.618838
$490$	23.3201	1.05349
$491$	−25.1654	−1.13570	−0.567850	−	0.823132i	$-0.692225\pi$
$491$	−25.1654	−1.13570	−0.567850	+	0.823132i	$0.692225\pi$
$492$	4.51168	0.203402
$493$	16.5973	0.747507
$494$	18.4346	0.829410
$495$	−3.69874	−0.166246
$496$	3.76640	0.169116
$497$	39.1976	1.75825
$498$	−12.3442	−0.553159
$499$	4.19779	0.187919	0.0939595	−	0.995576i	$-0.470048\pi$
$499$	4.19779	0.187919	0.0939595	+	0.995576i	$0.470048\pi$
$500$	−13.6138	−0.608828
$501$	11.5056	0.514032
$502$	−25.2647	−1.12762
$503$	−28.8169	−1.28488	−0.642441	−	0.766335i	$-0.722078\pi$
$503$	−28.8169	−1.28488	−0.642441	+	0.766335i	$0.722078\pi$
$504$	−3.64759	−0.162476
$505$	−29.4751	−1.31162
$506$	5.46514	0.242955
$507$	29.2932	1.30096
$508$	−18.3296	−0.813246
$509$	18.5571	0.822527	0.411264	−	0.911516i	$-0.365088\pi$
$509$	18.5571	0.822527	0.411264	+	0.911516i	$0.365088\pi$
$510$	−25.5829	−1.13283
$511$	−3.67267	−0.162469
$512$	−1.00000	−0.0441942
$513$	2.83464	0.125152
$514$	6.36362	0.280687
$515$	8.07560	0.355853
$516$	10.2104	0.449489
$517$	7.72959	0.339947
$518$	−4.25075	−0.186767
$519$	−1.61191	−0.0707548
$520$	−24.0541	−1.05484
$521$	23.9087	1.04746	0.523730	−	0.851885i	$-0.324540\pi$
$521$	23.9087	1.04746	0.523730	+	0.851885i	$0.324540\pi$
$522$	2.39962	0.105029
$523$	27.9126	1.22053	0.610266	−	0.792196i	$-0.291062\pi$
$523$	27.9126	1.22053	0.610266	+	0.792196i	$0.291062\pi$
$524$	−3.07667	−0.134405
$525$	31.6635	1.38191
$526$	−7.20703	−0.314242
$527$	−26.0508	−1.13479
$528$	1.00000	0.0435194
$529$	6.86770	0.298596
$530$	−21.3117	−0.925720
$531$	11.4982	0.498980
$532$	10.3396	0.448278
$533$	−29.3409	−1.27090
$534$	−12.3329	−0.533695
$535$	63.3869	2.74045
$536$	−0.969284	−0.0418667
$537$	9.95847	0.429740
$538$	−18.8237	−0.811548
$539$	6.30488	0.271570
$540$	−3.69874	−0.159168
$541$	−34.4761	−1.48224	−0.741121	−	0.671371i	$-0.765706\pi$
$541$	−34.4761	−1.48224	−0.741121	+	0.671371i	$0.765706\pi$
$542$	17.3219	0.744041
$543$	2.83988	0.121871
$544$	6.91664	0.296549
$545$	−20.0411	−0.858466
$546$	23.7214	1.01518
$547$	−30.4935	−1.30381	−0.651903	−	0.758302i	$-0.726029\pi$
$547$	−30.4935	−1.30381	−0.651903	+	0.758302i	$0.726029\pi$
$548$	−9.79553	−0.418444
$549$	1.00000	0.0426790
$550$	−8.68066	−0.370145
$551$	−6.80207	−0.289778
$552$	5.46514	0.232612
$553$	−49.4435	−2.10255
$554$	−2.06809	−0.0878647
$555$	−4.31037	−0.182965
$556$	7.05576	0.299231
$557$	−41.4311	−1.75549	−0.877746	−	0.479127i	$-0.840953\pi$
$557$	−41.4311	−1.75549	−0.877746	+	0.479127i	$0.840953\pi$
$558$	−3.76640	−0.159444
$559$	−66.4016	−2.80849
$560$	−13.4915	−0.570118
$561$	−6.91664	−0.292021
$562$	15.2178	0.641925
$563$	−2.27624	−0.0959320	−0.0479660	−	0.998849i	$-0.515274\pi$
$563$	−2.27624	−0.0959320	−0.0479660	+	0.998849i	$0.515274\pi$
$564$	7.72959	0.325474
$565$	9.57426	0.402792
$566$	−20.1102	−0.845293
$567$	3.64759	0.153184
$568$	−10.7462	−0.450900
$569$	28.7019	1.20325	0.601624	−	0.798780i	$-0.294521\pi$
$569$	28.7019	1.20325	0.601624	+	0.798780i	$0.294521\pi$
$570$	10.4846	0.439151
$571$	2.30952	0.0966503	0.0483251	−	0.998832i	$-0.484612\pi$
$571$	2.30952	0.0966503	0.0483251	+	0.998832i	$0.484612\pi$
$572$	−6.50332	−0.271917
$573$	−22.5566	−0.942314
$574$	−16.4568	−0.686892
$575$	−47.4410	−1.97843
$576$	1.00000	0.0416667
$577$	−19.7554	−0.822429	−0.411214	−	0.911539i	$-0.634895\pi$
$577$	−19.7554	−0.822429	−0.411214	+	0.911539i	$0.634895\pi$
$578$	−30.8399	−1.28277
$579$	0.0975677	0.00405477
$580$	8.87558	0.368538
$581$	45.0267	1.86802
$582$	12.7934	0.530303
$583$	−5.76187	−0.238632
$584$	1.00688	0.0416649
$585$	24.0541	0.994514
$586$	−17.6641	−0.729699
$587$	−8.74499	−0.360944	−0.180472	−	0.983580i	$-0.557763\pi$
$587$	−8.74499	−0.360944	−0.180472	+	0.983580i	$0.557763\pi$
$588$	6.30488	0.260009
$589$	10.6764	0.439912
$590$	42.5289	1.75089
$591$	10.7143	0.440729
$592$	1.16536	0.0478961
$593$	8.10884	0.332990	0.166495	−	0.986042i	$-0.446755\pi$
$593$	8.10884	0.332990	0.166495	+	0.986042i	$0.446755\pi$
$594$	−1.00000	−0.0410305
$595$	93.3156	3.82557
$596$	18.0296	0.738520
$597$	−0.00203644	−8.33458e−5 0
$598$	−35.5415	−1.45340
$599$	48.4470	1.97949	0.989745	−	0.142846i	$-0.0456253\pi$
$599$	48.4470	1.97949	0.989745	+	0.142846i	$0.0456253\pi$
$600$	−8.68066	−0.354387
$601$	5.82350	0.237546	0.118773	−	0.992921i	$-0.462104\pi$
$601$	5.82350	0.237546	0.118773	+	0.992921i	$0.462104\pi$
$602$	−37.2434	−1.51793
$603$	0.969284	0.0394723
$604$	13.2195	0.537895
$605$	−3.69874	−0.150375
$606$	−7.96896	−0.323717
$607$	−25.9124	−1.05175	−0.525876	−	0.850561i	$-0.676262\pi$
$607$	−25.9124	−1.05175	−0.525876	+	0.850561i	$0.676262\pi$
$608$	−2.83464	−0.114960
$609$	−8.75283	−0.354683
$610$	3.69874	0.149758
$611$	−50.2680	−2.03363
$612$	−6.91664	−0.279589
$613$	−9.20575	−0.371817	−0.185908	−	0.982567i	$-0.559523\pi$
$613$	−9.20575	−0.371817	−0.185908	+	0.982567i	$0.559523\pi$
$614$	26.8533	1.08371
$615$	−16.6875	−0.672907
$616$	−3.64759	−0.146965
$617$	18.9290	0.762052	0.381026	−	0.924564i	$-0.375571\pi$
$617$	18.9290	0.762052	0.381026	+	0.924564i	$0.375571\pi$
$618$	2.18334	0.0878267
$619$	−8.61057	−0.346088	−0.173044	−	0.984914i	$-0.555360\pi$
$619$	−8.61057	−0.346088	−0.173044	+	0.984914i	$0.555360\pi$
$620$	−13.9309	−0.559479
$621$	−5.46514	−0.219308
$622$	30.0582	1.20523
$623$	44.9851	1.80229
$624$	−6.50332	−0.260341
$625$	6.95061	0.278024
$626$	2.50660	0.100184
$627$	2.83464	0.113205
$628$	7.70630	0.307515
$629$	−8.06039	−0.321389
$630$	13.4915	0.537513
$631$	45.2205	1.80020	0.900099	−	0.435685i	$-0.143494\pi$
$631$	45.2205	1.80020	0.900099	+	0.435685i	$0.143494\pi$
$632$	13.5551	0.539194
$633$	23.0220	0.915041
$634$	5.30701	0.210768
$635$	67.7965	2.69042
$636$	−5.76187	−0.228473
$637$	−41.0026	−1.62458
$638$	2.39962	0.0950020
$639$	10.7462	0.425112
$640$	3.69874	0.146205
$641$	33.0023	1.30351	0.651757	−	0.758428i	$-0.274032\pi$
$641$	33.0023	1.30351	0.651757	+	0.758428i	$0.274032\pi$
$642$	17.1374	0.676361
$643$	9.32073	0.367574	0.183787	−	0.982966i	$-0.441164\pi$
$643$	9.32073	0.367574	0.183787	+	0.982966i	$0.441164\pi$
$644$	−19.9345	−0.785531
$645$	−37.7657	−1.48702
$646$	19.6062	0.771395
$647$	35.2423	1.38552	0.692760	−	0.721168i	$-0.256395\pi$
$647$	35.2423	1.38552	0.692760	+	0.721168i	$0.256395\pi$
$648$	−1.00000	−0.0392837
$649$	11.4982	0.451344
$650$	56.4531	2.21427
$651$	13.7383	0.538445
$652$	13.6846	0.535930
$653$	9.19942	0.360001	0.180001	−	0.983667i	$-0.442390\pi$
$653$	9.19942	0.360001	0.180001	+	0.983667i	$0.442390\pi$
$654$	−5.41836	−0.211875
$655$	11.3798	0.444645
$656$	4.51168	0.176152
$657$	−1.00688	−0.0392820
$658$	−28.1943	−1.09913
$659$	−34.6571	−1.35005	−0.675025	−	0.737795i	$-0.735867\pi$
$659$	−34.6571	−1.35005	−0.675025	+	0.737795i	$0.735867\pi$
$660$	−3.69874	−0.143973
$661$	−34.4153	−1.33860	−0.669299	−	0.742993i	$-0.733406\pi$
$661$	−34.4153	−1.33860	−0.669299	+	0.742993i	$0.733406\pi$
$662$	10.0513	0.390654
$663$	44.9811	1.74692
$664$	−12.3442	−0.479049
$665$	−38.2434	−1.48302
$666$	−1.16536	−0.0451568
$667$	13.1143	0.507786
$668$	11.5056	0.445165
$669$	−12.2002	−0.471687
$670$	3.58513	0.138506
$671$	1.00000	0.0386046
$672$	−3.64759	−0.140709
$673$	9.16813	0.353405	0.176703	−	0.984264i	$-0.443457\pi$
$673$	9.16813	0.353405	0.176703	+	0.984264i	$0.443457\pi$
$674$	−8.00391	−0.308299
$675$	8.68066	0.334119
$676$	29.2932	1.12666
$677$	10.6017	0.407455	0.203728	−	0.979028i	$-0.434694\pi$
$677$	10.6017	0.407455	0.203728	+	0.979028i	$0.434694\pi$
$678$	2.58852	0.0994115
$679$	−46.6650	−1.79084
$680$	−25.5829	−0.981058
$681$	26.6039	1.01946
$682$	−3.76640	−0.144223
$683$	39.5040	1.51158	0.755790	−	0.654814i	$-0.227253\pi$
$683$	39.5040	1.51158	0.755790	+	0.654814i	$0.227253\pi$
$684$	2.83464	0.108385
$685$	36.2311	1.38432
$686$	2.53551	0.0968063
$687$	27.0506	1.03204
$688$	10.2104	0.389269
$689$	37.4713	1.42754
$690$	−20.2141	−0.769538
$691$	−29.2933	−1.11437	−0.557185	−	0.830388i	$-0.688119\pi$
$691$	−29.2933	−1.11437	−0.557185	+	0.830388i	$0.688119\pi$
$692$	−1.61191	−0.0612755
$693$	3.64759	0.138560
$694$	20.2057	0.767000
$695$	−26.0974	−0.989931
$696$	2.39962	0.0909575
$697$	−31.2057	−1.18200
$698$	16.8778	0.638836
$699$	15.9166	0.602022
$700$	31.6635	1.19677
$701$	−2.97495	−0.112362	−0.0561811	−	0.998421i	$-0.517892\pi$
$701$	−2.97495	−0.112362	−0.0561811	+	0.998421i	$0.517892\pi$
$702$	6.50332	0.245452
$703$	3.30338	0.124589
$704$	1.00000	0.0376889
$705$	−28.5897	−1.07675
$706$	−18.5805	−0.699285
$707$	29.0675	1.09319
$708$	11.4982	0.432129
$709$	19.6008	0.736123	0.368061	−	0.929801i	$-0.380022\pi$
$709$	19.6008	0.736123	0.368061	+	0.929801i	$0.380022\pi$
$710$	39.7473	1.49169
$711$	−13.5551	−0.508357
$712$	−12.3329	−0.462193
$713$	−20.5839	−0.770872
$714$	25.2290	0.944173
$715$	24.0541	0.899571
$716$	9.95847	0.372166
$717$	−10.3123	−0.385120
$718$	36.0630	1.34586
$719$	30.4387	1.13517	0.567587	−	0.823314i	$-0.307877\pi$
$719$	30.4387	1.13517	0.567587	+	0.823314i	$0.307877\pi$
$720$	−3.69874	−0.137844
$721$	−7.96391	−0.296592
$722$	10.9648	0.408068
$723$	16.1203	0.599521
$724$	2.83988	0.105543
$725$	−20.8303	−0.773619
$726$	−1.00000	−0.0371135
$727$	42.5351	1.57754	0.788770	−	0.614688i	$-0.210718\pi$
$727$	42.5351	1.57754	0.788770	+	0.614688i	$0.210718\pi$
$728$	23.7214	0.879174
$729$	1.00000	0.0370370
$730$	−3.72418	−0.137838
$731$	−70.6218	−2.61204
$732$	1.00000	0.0369611
$733$	5.42907	0.200527	0.100264	−	0.994961i	$-0.468031\pi$
$733$	5.42907	0.200527	0.100264	+	0.994961i	$0.468031\pi$
$734$	−3.99558	−0.147479
$735$	−23.3201	−0.860175
$736$	5.46514	0.201448
$737$	0.969284	0.0357040
$738$	−4.51168	−0.166077
$739$	−34.4472	−1.26716	−0.633581	−	0.773676i	$-0.718416\pi$
$739$	−34.4472	−1.26716	−0.633581	+	0.773676i	$0.718416\pi$
$740$	−4.31037	−0.158452
$741$	−18.4346	−0.677211
$742$	21.0169	0.771556
$743$	−37.9311	−1.39156	−0.695779	−	0.718256i	$-0.744941\pi$
$743$	−37.9311	−1.39156	−0.695779	+	0.718256i	$0.744941\pi$
$744$	−3.76640	−0.138083
$745$	−66.6867	−2.44321
$746$	−34.5760	−1.26592
$747$	12.3442	0.451652
$748$	−6.91664	−0.252898
$749$	−62.5103	−2.28407
$750$	13.6138	0.497106
$751$	2.19981	0.0802724	0.0401362	−	0.999194i	$-0.487221\pi$
$751$	2.19981	0.0802724	0.0401362	+	0.999194i	$0.487221\pi$
$752$	7.72959	0.281869
$753$	25.2647	0.920698
$754$	−15.6055	−0.568320
$755$	−48.8956	−1.77949
$756$	3.64759	0.132661
$757$	−25.0762	−0.911409	−0.455704	−	0.890131i	$-0.650613\pi$
$757$	−25.0762	−0.911409	−0.455704	+	0.890131i	$0.650613\pi$
$758$	−14.9005	−0.541210
$759$	−5.46514	−0.198372
$760$	10.4846	0.380316
$761$	−16.7026	−0.605470	−0.302735	−	0.953075i	$-0.597900\pi$
$761$	−16.7026	−0.605470	−0.302735	+	0.953075i	$0.597900\pi$
$762$	18.3296	0.664013
$763$	19.7639	0.715502
$764$	−22.5566	−0.816068
$765$	25.5829	0.924950
$766$	−6.93216	−0.250469
$767$	−74.7766	−2.70003
$768$	1.00000	0.0360844
$769$	−33.7835	−1.21826	−0.609132	−	0.793069i	$-0.708482\pi$
$769$	−33.7835	−1.21826	−0.609132	+	0.793069i	$0.708482\pi$
$770$	13.4915	0.486199
$771$	−6.36362	−0.229180
$772$	0.0975677	0.00351154
$773$	−29.9272	−1.07641	−0.538203	−	0.842815i	$-0.680897\pi$
$773$	−29.9272	−1.07641	−0.538203	+	0.842815i	$0.680897\pi$
$774$	−10.2104	−0.367006
$775$	32.6948	1.17443
$776$	12.7934	0.459256
$777$	4.25075	0.152495
$778$	5.04981	0.181045
$779$	12.7890	0.458213
$780$	24.0541	0.861274
$781$	10.7462	0.384528
$782$	−37.8004	−1.35174
$783$	−2.39962	−0.0857556
$784$	6.30488	0.225174
$785$	−28.5036	−1.01734
$786$	3.07667	0.109741
$787$	20.0109	0.713313	0.356657	−	0.934236i	$-0.383917\pi$
$787$	20.0109	0.713313	0.356657	+	0.934236i	$0.383917\pi$
$788$	10.7143	0.381683
$789$	7.20703	0.256577
$790$	−50.1369	−1.78379
$791$	−9.44185	−0.335714
$792$	−1.00000	−0.0355335
$793$	−6.50332	−0.230940
$794$	22.6016	0.802100
$795$	21.3117	0.755847
$796$	−0.00203644	−7.21796e−5 0
$797$	18.2188	0.645342	0.322671	−	0.946511i	$-0.395419\pi$
$797$	18.2188	0.645342	0.322671	+	0.946511i	$0.395419\pi$
$798$	−10.3396	−0.366017
$799$	−53.4628	−1.89138
$800$	−8.68066	−0.306908
$801$	12.3329	0.435760
$802$	−2.60134	−0.0918564
$803$	−1.00688	−0.0355319
$804$	0.969284	0.0341840
$805$	73.7327	2.59874
$806$	24.4941	0.862767
$807$	18.8237	0.662626
$808$	−7.96896	−0.280347
$809$	20.8083	0.731581	0.365791	−	0.930697i	$-0.380799\pi$
$809$	20.8083	0.731581	0.365791	+	0.930697i	$0.380799\pi$
$810$	3.69874	0.129960
$811$	3.92339	0.137769	0.0688845	−	0.997625i	$-0.478056\pi$
$811$	3.92339	0.137769	0.0688845	+	0.997625i	$0.478056\pi$
$812$	−8.75283	−0.307164
$813$	−17.3219	−0.607507
$814$	−1.16536	−0.0408459
$815$	−50.6157	−1.77299
$816$	−6.91664	−0.242131
$817$	28.9429	1.01258
$818$	9.04616	0.316291
$819$	−23.7214	−0.828893
$820$	−16.6875	−0.582754
$821$	−48.3619	−1.68784	−0.843921	−	0.536468i	$-0.819758\pi$
$821$	−48.3619	−1.68784	−0.843921	+	0.536468i	$0.819758\pi$
$822$	9.79553	0.341658
$823$	−29.4541	−1.02671	−0.513353	−	0.858177i	$-0.671597\pi$
$823$	−29.4541	−1.02671	−0.513353	+	0.858177i	$0.671597\pi$
$824$	2.18334	0.0760602
$825$	8.68066	0.302222
$826$	−41.9407	−1.45930
$827$	2.99790	0.104247	0.0521235	−	0.998641i	$-0.483401\pi$
$827$	2.99790	0.104247	0.0521235	+	0.998641i	$0.483401\pi$
$828$	−5.46514	−0.189927
$829$	1.15623	0.0401575	0.0200787	−	0.999798i	$-0.493608\pi$
$829$	1.15623	0.0401575	0.0200787	+	0.999798i	$0.493608\pi$
$830$	45.6581	1.58482
$831$	2.06809	0.0717412
$832$	−6.50332	−0.225462
$833$	−43.6086	−1.51095
$834$	−7.05576	−0.244321
$835$	−42.5562	−1.47272
$836$	2.83464	0.0980380
$837$	3.76640	0.130186
$838$	13.1890	0.455607
$839$	51.5830	1.78084	0.890421	−	0.455139i	$-0.150410\pi$
$839$	51.5830	1.78084	0.890421	+	0.455139i	$0.150410\pi$
$840$	13.4915	0.465500
$841$	−23.2418	−0.801442
$842$	−36.0504	−1.24238
$843$	−15.2178	−0.524130
$844$	23.0220	0.792449
$845$	−108.348	−3.72728
$846$	−7.72959	−0.265749
$847$	3.64759	0.125333
$848$	−5.76187	−0.197864
$849$	20.1102	0.690179
$850$	60.0411	2.05939
$851$	−6.36886	−0.218322
$852$	10.7462	0.368158
$853$	−19.6920	−0.674240	−0.337120	−	0.941462i	$-0.609453\pi$
$853$	−19.6920	−0.674240	−0.337120	+	0.941462i	$0.609453\pi$
$854$	−3.64759	−0.124818
$855$	−10.4846	−0.358565
$856$	17.1374	0.585745
$857$	47.7707	1.63182	0.815909	−	0.578181i	$-0.196237\pi$
$857$	47.7707	1.63182	0.815909	+	0.578181i	$0.196237\pi$
$858$	6.50332	0.222020
$859$	−14.2196	−0.485168	−0.242584	−	0.970130i	$-0.577995\pi$
$859$	−14.2196	−0.485168	−0.242584	+	0.970130i	$0.577995\pi$
$860$	−37.7657	−1.28780
$861$	16.4568	0.560845
$862$	−18.4753	−0.629272
$863$	−36.1683	−1.23118	−0.615592	−	0.788065i	$-0.711083\pi$
$863$	−36.1683	−1.23118	−0.615592	+	0.788065i	$0.711083\pi$
$864$	−1.00000	−0.0340207
$865$	5.96202	0.202715
$866$	20.1477	0.684647
$867$	30.8399	1.04738
$868$	13.7383	0.466307
$869$	−13.5551	−0.459826
$870$	−8.87558	−0.300910
$871$	−6.30356	−0.213588
$872$	−5.41836	−0.183489
$873$	−12.7934	−0.432990
$874$	15.4917	0.524014
$875$	−49.6575	−1.67873
$876$	−1.00688	−0.0340192
$877$	12.9223	0.436356	0.218178	−	0.975909i	$-0.429989\pi$
$877$	12.9223	0.436356	0.218178	+	0.975909i	$0.429989\pi$
$878$	−21.3023	−0.718917
$879$	17.6641	0.595796
$880$	−3.69874	−0.124684
$881$	−1.33492	−0.0449747	−0.0224874	−	0.999747i	$-0.507159\pi$
$881$	−1.33492	−0.0449747	−0.0224874	+	0.999747i	$0.507159\pi$
$882$	−6.30488	−0.212296
$883$	−32.6078	−1.09734	−0.548669	−	0.836040i	$-0.684865\pi$
$883$	−32.6078	−1.09734	−0.548669	+	0.836040i	$0.684865\pi$
$884$	44.9811	1.51288
$885$	−42.5289	−1.42959
$886$	−32.6077	−1.09548
$887$	−11.2083	−0.376337	−0.188169	−	0.982137i	$-0.560255\pi$
$887$	−11.2083	−0.376337	−0.188169	+	0.982137i	$0.560255\pi$
$888$	−1.16536	−0.0391070
$889$	−66.8589	−2.24238
$890$	45.6160	1.52905
$891$	1.00000	0.0335013
$892$	−12.2002	−0.408493
$893$	21.9106	0.733210
$894$	−18.0296	−0.602999
$895$	−36.8338	−1.23122
$896$	−3.64759	−0.121857
$897$	35.5415	1.18670
$898$	38.5893	1.28774
$899$	−9.03794	−0.301432
$900$	8.68066	0.289355
$901$	39.8528	1.32769
$902$	−4.51168	−0.150223
$903$	37.2434	1.23938
$904$	2.58852	0.0860929
$905$	−10.5040	−0.349164
$906$	−13.2195	−0.439190
$907$	23.8792	0.792895	0.396448	−	0.918057i	$-0.370243\pi$
$907$	23.8792	0.792895	0.396448	+	0.918057i	$0.370243\pi$
$908$	26.6039	0.882880
$909$	7.96896	0.264314
$910$	−87.7393	−2.90853
$911$	12.1377	0.402138	0.201069	−	0.979577i	$-0.435558\pi$
$911$	12.1377	0.402138	0.201069	+	0.979577i	$0.435558\pi$
$912$	2.83464	0.0938643
$913$	12.3442	0.408535
$914$	−1.36144	−0.0450324
$915$	−3.69874	−0.122277
$916$	27.0506	0.893777
$917$	−11.2224	−0.370597
$918$	6.91664	0.228283
$919$	1.96753	0.0649029	0.0324515	−	0.999473i	$-0.489669\pi$
$919$	1.96753	0.0649029	0.0324515	+	0.999473i	$0.489669\pi$
$920$	−20.2141	−0.666439
$921$	−26.8533	−0.884847
$922$	32.7190	1.07754
$923$	−69.8858	−2.30032
$924$	3.64759	0.119997
$925$	10.1161	0.332616
$926$	−25.4768	−0.837219
$927$	−2.18334	−0.0717102
$928$	2.39962	0.0787715
$929$	36.6010	1.20084	0.600420	−	0.799685i	$-0.295000\pi$
$929$	36.6010	1.20084	0.600420	+	0.799685i	$0.295000\pi$
$930$	13.9309	0.456813
$931$	17.8721	0.585733
$932$	15.9166	0.521366
$933$	−30.0582	−0.984062
$934$	−15.9601	−0.522232
$935$	25.5829	0.836649
$936$	6.50332	0.212568
$937$	27.5202	0.899045	0.449522	−	0.893269i	$-0.351594\pi$
$937$	27.5202	0.899045	0.449522	+	0.893269i	$0.351594\pi$
$938$	−3.53554	−0.115440
$939$	−2.50660	−0.0817999
$940$	−28.5897	−0.932494
$941$	13.6361	0.444523	0.222262	−	0.974987i	$-0.428656\pi$
$941$	13.6361	0.444523	0.222262	+	0.974987i	$0.428656\pi$
$942$	−7.70630	−0.251085
$943$	−24.6570	−0.802941
$944$	11.4982	0.374235
$945$	−13.4915	−0.438877
$946$	−10.2104	−0.331969
$947$	22.1851	0.720920	0.360460	−	0.932775i	$-0.382620\pi$
$947$	22.1851	0.720920	0.360460	+	0.932775i	$0.382620\pi$
$948$	−13.5551	−0.440250
$949$	6.54804	0.212559
$950$	−24.6065	−0.798342
$951$	−5.30701	−0.172092
$952$	25.2290	0.817678
$953$	0.107268	0.00347475	0.00173737	−	0.999998i	$-0.499447\pi$
$953$	0.107268	0.00347475	0.00173737	+	0.999998i	$0.499447\pi$
$954$	5.76187	0.186548
$955$	83.4308	2.69976
$956$	−10.3123	−0.333524
$957$	−2.39962	−0.0775688
$958$	4.28727	0.138515
$959$	−35.7300	−1.15378
$960$	−3.69874	−0.119376
$961$	−16.8143	−0.542395
$962$	7.57872	0.244348
$963$	−17.1374	−0.552246
$964$	16.1203	0.519200
$965$	−0.360877	−0.0116171
$966$	19.9345	0.641384
$967$	−0.153177	−0.00492583	−0.00246292	−	0.999997i	$-0.500784\pi$
$967$	−0.153177	−0.00492583	−0.00246292	+	0.999997i	$0.500784\pi$
$968$	−1.00000	−0.0321412
$969$	−19.6062	−0.629841
$970$	−47.3194	−1.51933
$971$	−33.8986	−1.08786	−0.543929	−	0.839131i	$-0.683064\pi$
$971$	−33.8986	−1.08786	−0.543929	+	0.839131i	$0.683064\pi$
$972$	1.00000	0.0320750
$973$	25.7365	0.825073
$974$	−32.4067	−1.03838
$975$	−56.4531	−1.80795
$976$	1.00000	0.0320092
$977$	−12.8168	−0.410046	−0.205023	−	0.978757i	$-0.565727\pi$
$977$	−12.8168	−0.410046	−0.205023	+	0.978757i	$0.565727\pi$
$978$	−13.6846	−0.437585
$979$	12.3329	0.394160
$980$	−23.3201	−0.744933
$981$	5.41836	0.172995
$982$	25.1654	0.803061
$983$	−11.2009	−0.357252	−0.178626	−	0.983917i	$-0.557165\pi$
$983$	−11.2009	−0.357252	−0.178626	+	0.983917i	$0.557165\pi$
$984$	−4.51168	−0.143827
$985$	−39.6295	−1.26270
$986$	−16.5973	−0.528567
$987$	28.1943	0.897436
$988$	−18.4346	−0.586482
$989$	−55.8013	−1.77438
$990$	3.69874	0.117554
$991$	2.08247	0.0661518	0.0330759	−	0.999453i	$-0.489470\pi$
$991$	2.08247	0.0661518	0.0330759	+	0.999453i	$0.489470\pi$
$992$	−3.76640	−0.119583
$993$	−10.0513	−0.318967
$994$	−39.1976	−1.24327
$995$	0.00753224	0.000238788 0
$996$	12.3442	0.391142
$997$	17.6320	0.558411	0.279206	−	0.960231i	$-0.409929\pi$
$997$	17.6320	0.558411	0.279206	+	0.960231i	$0.409929\pi$
$998$	−4.19779	−0.132879
$999$	1.16536	0.0368704

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.ba.1.1	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.ba.1.1	✓	7	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.69874 q^{5} -1.00000 q^{6} +3.64759 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.69874 q^{5} -1.00000 q^{6} +3.64759 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.69874 q^{10} +1.00000 q^{11} +1.00000 q^{12} -6.50332 q^{13} -3.64759 q^{14} -3.69874 q^{15} +1.00000 q^{16} -6.91664 q^{17} -1.00000 q^{18} +2.83464 q^{19} -3.69874 q^{20} +3.64759 q^{21} -1.00000 q^{22} -5.46514 q^{23} -1.00000 q^{24} +8.68066 q^{25} +6.50332 q^{26} +1.00000 q^{27} +3.64759 q^{28} -2.39962 q^{29} +3.69874 q^{30} +3.76640 q^{31} -1.00000 q^{32} +1.00000 q^{33} +6.91664 q^{34} -13.4915 q^{35} +1.00000 q^{36} +1.16536 q^{37} -2.83464 q^{38} -6.50332 q^{39} +3.69874 q^{40} +4.51168 q^{41} -3.64759 q^{42} +10.2104 q^{43} +1.00000 q^{44} -3.69874 q^{45} +5.46514 q^{46} +7.72959 q^{47} +1.00000 q^{48} +6.30488 q^{49} -8.68066 q^{50} -6.91664 q^{51} -6.50332 q^{52} -5.76187 q^{53} -1.00000 q^{54} -3.69874 q^{55} -3.64759 q^{56} +2.83464 q^{57} +2.39962 q^{58} +11.4982 q^{59} -3.69874 q^{60} +1.00000 q^{61} -3.76640 q^{62} +3.64759 q^{63} +1.00000 q^{64} +24.0541 q^{65} -1.00000 q^{66} +0.969284 q^{67} -6.91664 q^{68} -5.46514 q^{69} +13.4915 q^{70} +10.7462 q^{71} -1.00000 q^{72} -1.00688 q^{73} -1.16536 q^{74} +8.68066 q^{75} +2.83464 q^{76} +3.64759 q^{77} +6.50332 q^{78} -13.5551 q^{79} -3.69874 q^{80} +1.00000 q^{81} -4.51168 q^{82} +12.3442 q^{83} +3.64759 q^{84} +25.5829 q^{85} -10.2104 q^{86} -2.39962 q^{87} -1.00000 q^{88} +12.3329 q^{89} +3.69874 q^{90} -23.7214 q^{91} -5.46514 q^{92} +3.76640 q^{93} -7.72959 q^{94} -10.4846 q^{95} -1.00000 q^{96} -12.7934 q^{97} -6.30488 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 7 q^{2} + 7 q^{3} + 7 q^{4} - 5 q^{5} - 7 q^{6} + 9 q^{7} - 7 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - 7 * q^2 + 7 * q^3 + 7 * q^4 - 5 * q^5 - 7 * q^6 + 9 * q^7 - 7 * q^8 + 7 * q^9	\( 7 q - 7 q^{2} + 7 q^{3} + 7 q^{4} - 5 q^{5} - 7 q^{6} + 9 q^{7} - 7 q^{8} + 7 q^{9} + 5 q^{10} + 7 q^{11} + 7 q^{12} + 4 q^{13} - 9 q^{14} - 5 q^{15} + 7 q^{16} - 6 q^{17} - 7 q^{18} + 9 q^{19} - 5 q^{20} + 9 q^{21} - 7 q^{22} - 8 q^{23} - 7 q^{24} + 4 q^{25} - 4 q^{26} + 7 q^{27} + 9 q^{28} - 4 q^{29} + 5 q^{30} + 17 q^{31} - 7 q^{32} + 7 q^{33} + 6 q^{34} - 3 q^{35} + 7 q^{36} + 19 q^{37} - 9 q^{38} + 4 q^{39} + 5 q^{40} + 5 q^{41} - 9 q^{42} + 24 q^{43} + 7 q^{44} - 5 q^{45} + 8 q^{46} + 6 q^{47} + 7 q^{48} + 24 q^{49} - 4 q^{50} - 6 q^{51} + 4 q^{52} + 3 q^{53} - 7 q^{54} - 5 q^{55} - 9 q^{56} + 9 q^{57} + 4 q^{58} + 10 q^{59} - 5 q^{60} + 7 q^{61} - 17 q^{62} + 9 q^{63} + 7 q^{64} + 16 q^{65} - 7 q^{66} + 22 q^{67} - 6 q^{68} - 8 q^{69} + 3 q^{70} + q^{71} - 7 q^{72} + 32 q^{73} - 19 q^{74} + 4 q^{75} + 9 q^{76} + 9 q^{77} - 4 q^{78} - 8 q^{79} - 5 q^{80} + 7 q^{81} - 5 q^{82} - 30 q^{83} + 9 q^{84} + 3 q^{85} - 24 q^{86} - 4 q^{87} - 7 q^{88} + 5 q^{89} + 5 q^{90} + 15 q^{91} - 8 q^{92} + 17 q^{93} - 6 q^{94} - 21 q^{95} - 7 q^{96} + 14 q^{97} - 24 q^{98} + 7 q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 + 7 * q^3 + 7 * q^4 - 5 * q^5 - 7 * q^6 + 9 * q^7 - 7 * q^8 + 7 * q^9 + 5 * q^10 + 7 * q^11 + 7 * q^12 + 4 * q^13 - 9 * q^14 - 5 * q^15 + 7 * q^16 - 6 * q^17 - 7 * q^18 + 9 * q^19 - 5 * q^20 + 9 * q^21 - 7 * q^22 - 8 * q^23 - 7 * q^24 + 4 * q^25 - 4 * q^26 + 7 * q^27 + 9 * q^28 - 4 * q^29 + 5 * q^30 + 17 * q^31 - 7 * q^32 + 7 * q^33 + 6 * q^34 - 3 * q^35 + 7 * q^36 + 19 * q^37 - 9 * q^38 + 4 * q^39 + 5 * q^40 + 5 * q^41 - 9 * q^42 + 24 * q^43 + 7 * q^44 - 5 * q^45 + 8 * q^46 + 6 * q^47 + 7 * q^48 + 24 * q^49 - 4 * q^50 - 6 * q^51 + 4 * q^52 + 3 * q^53 - 7 * q^54 - 5 * q^55 - 9 * q^56 + 9 * q^57 + 4 * q^58 + 10 * q^59 - 5 * q^60 + 7 * q^61 - 17 * q^62 + 9 * q^63 + 7 * q^64 + 16 * q^65 - 7 * q^66 + 22 * q^67 - 6 * q^68 - 8 * q^69 + 3 * q^70 + q^71 - 7 * q^72 + 32 * q^73 - 19 * q^74 + 4 * q^75 + 9 * q^76 + 9 * q^77 - 4 * q^78 - 8 * q^79 - 5 * q^80 + 7 * q^81 - 5 * q^82 - 30 * q^83 + 9 * q^84 + 3 * q^85 - 24 * q^86 - 4 * q^87 - 7 * q^88 + 5 * q^89 + 5 * q^90 + 15 * q^91 - 8 * q^92 + 17 * q^93 - 6 * q^94 - 21 * q^95 - 7 * q^96 + 14 * q^97 - 24 * q^98 + 7 * q^99

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