LMFDB - Embedded newform 1226.2.a.e.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1226,2,Mod(1,1226)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1226, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1226.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1226 = 2 \cdot 613 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1226.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:	$9.78965928781$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 4 x^{16} - 28 x^{15} + 120 x^{14} + 291 x^{13} - 1382 x^{12} - 1398 x^{11} + 7700 x^{10} + \cdots - 320 $ x^17 - 4x^16 - 28x^15 + 120x^14 + 291x^13 - 1382x^12 - 1398x^11 + 7700x^10 + 3456x^9 - 21974x^8 - 6336x^7 + 33062x^6 + 9753x^5 - 24446x^4 - 8368x^3 + 7000x^2 + 2384x - 320
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-0.926840$ of defining polynomial
Character	$\chi$	$=$	1226.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.926840 q^{3} +1.00000 q^{4} +0.613322 q^{5} +0.926840 q^{6} -4.30069 q^{7} -1.00000 q^{8} -2.14097 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.926840 q^{3} +1.00000 q^{4} +0.613322 q^{5} +0.926840 q^{6} -4.30069 q^{7} -1.00000 q^{8} -2.14097 q^{9} -0.613322 q^{10} -0.812094 q^{11} -0.926840 q^{12} -5.56948 q^{13} +4.30069 q^{14} -0.568452 q^{15} +1.00000 q^{16} -0.247362 q^{17} +2.14097 q^{18} +5.43006 q^{19} +0.613322 q^{20} +3.98605 q^{21} +0.812094 q^{22} -0.410501 q^{23} +0.926840 q^{24} -4.62384 q^{25} +5.56948 q^{26} +4.76486 q^{27} -4.30069 q^{28} +6.26185 q^{29} +0.568452 q^{30} +8.45616 q^{31} -1.00000 q^{32} +0.752681 q^{33} +0.247362 q^{34} -2.63771 q^{35} -2.14097 q^{36} +3.11260 q^{37} -5.43006 q^{38} +5.16202 q^{39} -0.613322 q^{40} +5.83087 q^{41} -3.98605 q^{42} -4.28708 q^{43} -0.812094 q^{44} -1.31310 q^{45} +0.410501 q^{46} -0.735067 q^{47} -0.926840 q^{48} +11.4959 q^{49} +4.62384 q^{50} +0.229265 q^{51} -5.56948 q^{52} +0.537458 q^{53} -4.76486 q^{54} -0.498075 q^{55} +4.30069 q^{56} -5.03279 q^{57} -6.26185 q^{58} +3.05642 q^{59} -0.568452 q^{60} -12.3973 q^{61} -8.45616 q^{62} +9.20763 q^{63} +1.00000 q^{64} -3.41588 q^{65} -0.752681 q^{66} -6.79764 q^{67} -0.247362 q^{68} +0.380469 q^{69} +2.63771 q^{70} +0.183966 q^{71} +2.14097 q^{72} +8.53553 q^{73} -3.11260 q^{74} +4.28556 q^{75} +5.43006 q^{76} +3.49256 q^{77} -5.16202 q^{78} +14.5278 q^{79} +0.613322 q^{80} +2.00664 q^{81} -5.83087 q^{82} -0.337683 q^{83} +3.98605 q^{84} -0.151713 q^{85} +4.28708 q^{86} -5.80373 q^{87} +0.812094 q^{88} -18.0121 q^{89} +1.31310 q^{90} +23.9526 q^{91} -0.410501 q^{92} -7.83751 q^{93} +0.735067 q^{94} +3.33037 q^{95} +0.926840 q^{96} -0.706123 q^{97} -11.4959 q^{98} +1.73867 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 17 q^{2} + 4 q^{3} + 17 q^{4} - 5 q^{5} - 4 q^{6} + 7 q^{7} - 17 q^{8} + 21 q^{9}+O(q^{10}) $ 17 * q - 17 * q^2 + 4 * q^3 + 17 * q^4 - 5 * q^5 - 4 * q^6 + 7 * q^7 - 17 * q^8 + 21 * q^9	\( 17 q - 17 q^{2} + 4 q^{3} + 17 q^{4} - 5 q^{5} - 4 q^{6} + 7 q^{7} - 17 q^{8} + 21 q^{9} + 5 q^{10} + 8 q^{11} + 4 q^{12} + 9 q^{13} - 7 q^{14} - 4 q^{15} + 17 q^{16} - q^{17} - 21 q^{18} + 32 q^{19} - 5 q^{20} + 6 q^{21} - 8 q^{22} - 5 q^{23} - 4 q^{24} + 30 q^{25} - 9 q^{26} + 16 q^{27} + 7 q^{28} + 3 q^{29} + 4 q^{30} + 27 q^{31} - 17 q^{32} - 14 q^{33} + q^{34} + 25 q^{35} + 21 q^{36} + 7 q^{37} - 32 q^{38} + 27 q^{39} + 5 q^{40} - 2 q^{41} - 6 q^{42} + 36 q^{43} + 8 q^{44} - q^{45} + 5 q^{46} - 3 q^{47} + 4 q^{48} + 52 q^{49} - 30 q^{50} + 40 q^{51} + 9 q^{52} - 20 q^{53} - 16 q^{54} + 48 q^{55} - 7 q^{56} + 12 q^{57} - 3 q^{58} + 34 q^{59} - 4 q^{60} + 49 q^{61} - 27 q^{62} + 27 q^{63} + 17 q^{64} - 6 q^{65} + 14 q^{66} + 36 q^{67} - q^{68} + 18 q^{69} - 25 q^{70} - q^{71} - 21 q^{72} + 24 q^{73} - 7 q^{74} + 35 q^{75} + 32 q^{76} - 6 q^{77} - 27 q^{78} + 43 q^{79} - 5 q^{80} + 37 q^{81} + 2 q^{82} + 10 q^{83} + 6 q^{84} + 16 q^{85} - 36 q^{86} + 28 q^{87} - 8 q^{88} - 12 q^{89} + q^{90} + 42 q^{91} - 5 q^{92} + 3 q^{93} + 3 q^{94} - 10 q^{95} - 4 q^{96} + 26 q^{97} - 52 q^{98} + 34 q^{99}+O(q^{100}) \) 17 * q - 17 * q^2 + 4 * q^3 + 17 * q^4 - 5 * q^5 - 4 * q^6 + 7 * q^7 - 17 * q^8 + 21 * q^9 + 5 * q^10 + 8 * q^11 + 4 * q^12 + 9 * q^13 - 7 * q^14 - 4 * q^15 + 17 * q^16 - q^17 - 21 * q^18 + 32 * q^19 - 5 * q^20 + 6 * q^21 - 8 * q^22 - 5 * q^23 - 4 * q^24 + 30 * q^25 - 9 * q^26 + 16 * q^27 + 7 * q^28 + 3 * q^29 + 4 * q^30 + 27 * q^31 - 17 * q^32 - 14 * q^33 + q^34 + 25 * q^35 + 21 * q^36 + 7 * q^37 - 32 * q^38 + 27 * q^39 + 5 * q^40 - 2 * q^41 - 6 * q^42 + 36 * q^43 + 8 * q^44 - q^45 + 5 * q^46 - 3 * q^47 + 4 * q^48 + 52 * q^49 - 30 * q^50 + 40 * q^51 + 9 * q^52 - 20 * q^53 - 16 * q^54 + 48 * q^55 - 7 * q^56 + 12 * q^57 - 3 * q^58 + 34 * q^59 - 4 * q^60 + 49 * q^61 - 27 * q^62 + 27 * q^63 + 17 * q^64 - 6 * q^65 + 14 * q^66 + 36 * q^67 - q^68 + 18 * q^69 - 25 * q^70 - q^71 - 21 * q^72 + 24 * q^73 - 7 * q^74 + 35 * q^75 + 32 * q^76 - 6 * q^77 - 27 * q^78 + 43 * q^79 - 5 * q^80 + 37 * q^81 + 2 * q^82 + 10 * q^83 + 6 * q^84 + 16 * q^85 - 36 * q^86 + 28 * q^87 - 8 * q^88 - 12 * q^89 + q^90 + 42 * q^91 - 5 * q^92 + 3 * q^93 + 3 * q^94 - 10 * q^95 - 4 * q^96 + 26 * q^97 - 52 * q^98 + 34 * 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
$3$	−0.926840	−0.535111	−0.267556	−	0.963542i	$-0.586216\pi$
$3$	−0.926840	−0.535111	−0.267556	+	0.963542i	$0.586216\pi$
$4$	1.00000	0.500000
$5$	0.613322	0.274286	0.137143	−	0.990551i	$-0.456208\pi$
$5$	0.613322	0.274286	0.137143	+	0.990551i	$0.456208\pi$
$6$	0.926840	0.378381
$7$	−4.30069	−1.62551	−0.812753	−	0.582608i	$-0.802032\pi$
$7$	−4.30069	−1.62551	−0.812753	+	0.582608i	$0.802032\pi$
$8$	−1.00000	−0.353553
$9$	−2.14097	−0.713656
$10$	−0.613322	−0.193949
$11$	−0.812094	−0.244855	−0.122428	−	0.992477i	$-0.539068\pi$
$11$	−0.812094	−0.244855	−0.122428	+	0.992477i	$0.539068\pi$
$12$	−0.926840	−0.267556
$13$	−5.56948	−1.54470	−0.772348	−	0.635200i	$-0.780918\pi$
$13$	−5.56948	−1.54470	−0.772348	+	0.635200i	$0.780918\pi$
$14$	4.30069	1.14941
$15$	−0.568452	−0.146774
$16$	1.00000	0.250000
$17$	−0.247362	−0.0599941	−0.0299970	−	0.999550i	$-0.509550\pi$
$17$	−0.247362	−0.0599941	−0.0299970	+	0.999550i	$0.509550\pi$
$18$	2.14097	0.504631
$19$	5.43006	1.24574	0.622870	−	0.782325i	$-0.285966\pi$
$19$	5.43006	1.24574	0.622870	+	0.782325i	$0.285966\pi$
$20$	0.613322	0.137143
$21$	3.98605	0.869827
$22$	0.812094	0.173139
$23$	−0.410501	−0.0855953	−0.0427977	−	0.999084i	$-0.513627\pi$
$23$	−0.410501	−0.0855953	−0.0427977	+	0.999084i	$0.513627\pi$
$24$	0.926840	0.189190
$25$	−4.62384	−0.924767
$26$	5.56948	1.09226
$27$	4.76486	0.916997
$28$	−4.30069	−0.812753
$29$	6.26185	1.16280	0.581398	−	0.813619i	$-0.302506\pi$
$29$	6.26185	1.16280	0.581398	+	0.813619i	$0.302506\pi$
$30$	0.568452	0.103785
$31$	8.45616	1.51877	0.759386	−	0.650641i	$-0.225500\pi$
$31$	8.45616	1.51877	0.759386	+	0.650641i	$0.225500\pi$
$32$	−1.00000	−0.176777
$33$	0.752681	0.131025
$34$	0.247362	0.0424222
$35$	−2.63771	−0.445854
$36$	−2.14097	−0.356828
$37$	3.11260	0.511708	0.255854	−	0.966715i	$-0.417643\pi$
$37$	3.11260	0.511708	0.255854	+	0.966715i	$0.417643\pi$
$38$	−5.43006	−0.880871
$39$	5.16202	0.826585
$40$	−0.613322	−0.0969747
$41$	5.83087	0.910629	0.455315	−	0.890331i	$-0.349527\pi$
$41$	5.83087	0.910629	0.455315	+	0.890331i	$0.349527\pi$
$42$	−3.98605	−0.615061
$43$	−4.28708	−0.653774	−0.326887	−	0.945063i	$-0.606000\pi$
$43$	−4.28708	−0.653774	−0.326887	+	0.945063i	$0.606000\pi$
$44$	−0.812094	−0.122428
$45$	−1.31310	−0.195746
$46$	0.410501	0.0605251
$47$	−0.735067	−0.107221	−0.0536103	−	0.998562i	$-0.517073\pi$
$47$	−0.735067	−0.107221	−0.0536103	+	0.998562i	$0.517073\pi$
$48$	−0.926840	−0.133778
$49$	11.4959	1.64227
$50$	4.62384	0.653909
$51$	0.229265	0.0321035
$52$	−5.56948	−0.772348
$53$	0.537458	0.0738256	0.0369128	−	0.999318i	$-0.488248\pi$
$53$	0.537458	0.0738256	0.0369128	+	0.999318i	$0.488248\pi$
$54$	−4.76486	−0.648415
$55$	−0.498075	−0.0671604
$56$	4.30069	0.574703
$57$	−5.03279	−0.666610
$58$	−6.26185	−0.822221
$59$	3.05642	0.397912	0.198956	−	0.980008i	$-0.436245\pi$
$59$	3.05642	0.397912	0.198956	+	0.980008i	$0.436245\pi$
$60$	−0.568452	−0.0733868
$61$	−12.3973	−1.58732	−0.793658	−	0.608364i	$-0.791826\pi$
$61$	−12.3973	−1.58732	−0.793658	+	0.608364i	$0.791826\pi$
$62$	−8.45616	−1.07393
$63$	9.20763	1.16005
$64$	1.00000	0.125000
$65$	−3.41588	−0.423688
$66$	−0.752681	−0.0926486
$67$	−6.79764	−0.830464	−0.415232	−	0.909716i	$-0.636300\pi$
$67$	−6.79764	−0.830464	−0.415232	+	0.909716i	$0.636300\pi$
$68$	−0.247362	−0.0299970
$69$	0.380469	0.0458031
$70$	2.63771	0.315266
$71$	0.183966	0.0218327	0.0109164	−	0.999940i	$-0.496525\pi$
$71$	0.183966	0.0218327	0.0109164	+	0.999940i	$0.496525\pi$
$72$	2.14097	0.252315
$73$	8.53553	0.999008	0.499504	−	0.866312i	$-0.333516\pi$
$73$	8.53553	0.999008	0.499504	+	0.866312i	$0.333516\pi$
$74$	−3.11260	−0.361833
$75$	4.28556	0.494854
$76$	5.43006	0.622870
$77$	3.49256	0.398014
$78$	−5.16202	−0.584484
$79$	14.5278	1.63450	0.817251	−	0.576282i	$-0.195497\pi$
$79$	14.5278	1.63450	0.817251	+	0.576282i	$0.195497\pi$
$80$	0.613322	0.0685715
$81$	2.00664	0.222960
$82$	−5.83087	−0.643912
$83$	−0.337683	−0.0370655	−0.0185328	−	0.999828i	$-0.505899\pi$
$83$	−0.337683	−0.0370655	−0.0185328	+	0.999828i	$0.505899\pi$
$84$	3.98605	0.434914
$85$	−0.151713	−0.0164555
$86$	4.28708	0.462288
$87$	−5.80373	−0.622226
$88$	0.812094	0.0865695
$89$	−18.0121	−1.90928	−0.954638	−	0.297769i	$-0.903758\pi$
$89$	−18.0121	−1.90928	−0.954638	+	0.297769i	$0.903758\pi$
$90$	1.31310	0.138413
$91$	23.9526	2.51091
$92$	−0.410501	−0.0427977
$93$	−7.83751	−0.812712
$94$	0.735067	0.0758164
$95$	3.33037	0.341689
$96$	0.926840	0.0945952
$97$	−0.706123	−0.0716960	−0.0358480	−	0.999357i	$-0.511413\pi$
$97$	−0.706123	−0.0716960	−0.0358480	+	0.999357i	$0.511413\pi$
$98$	−11.4959	−1.16126
$99$	1.73867	0.174742
$100$	−4.62384	−0.462384
$101$	−9.69344	−0.964534	−0.482267	−	0.876024i	$-0.660186\pi$
$101$	−9.69344	−0.964534	−0.482267	+	0.876024i	$0.660186\pi$
$102$	−0.229265	−0.0227006
$103$	4.50697	0.444085	0.222043	−	0.975037i	$-0.428728\pi$
$103$	4.50697	0.444085	0.222043	+	0.975037i	$0.428728\pi$
$104$	5.56948	0.546132
$105$	2.44473	0.238581
$106$	−0.537458	−0.0522026
$107$	16.8135	1.62543	0.812713	−	0.582664i	$-0.197990\pi$
$107$	16.8135	1.62543	0.812713	+	0.582664i	$0.197990\pi$
$108$	4.76486	0.458498
$109$	12.0827	1.15731	0.578656	−	0.815572i	$-0.303577\pi$
$109$	12.0827	1.15731	0.578656	+	0.815572i	$0.303577\pi$
$110$	0.498075	0.0474896
$111$	−2.88488	−0.273821
$112$	−4.30069	−0.406377
$113$	13.5418	1.27390	0.636952	−	0.770904i	$-0.280195\pi$
$113$	13.5418	1.27390	0.636952	+	0.770904i	$0.280195\pi$
$114$	5.03279	0.471364
$115$	−0.251769	−0.0234776
$116$	6.26185	0.581398
$117$	11.9241	1.10238
$118$	−3.05642	−0.281366
$119$	1.06383	0.0975208
$120$	0.568452	0.0518923
$121$	−10.3405	−0.940046
$122$	12.3973	1.12240
$123$	−5.40429	−0.487288
$124$	8.45616	0.759386
$125$	−5.90251	−0.527937
$126$	−9.20763	−0.820281
$127$	19.6307	1.74194	0.870971	−	0.491334i	$-0.163491\pi$
$127$	19.6307	1.74194	0.870971	+	0.491334i	$0.163491\pi$
$128$	−1.00000	−0.0883883
$129$	3.97344	0.349842
$130$	3.41588	0.299593
$131$	20.6647	1.80548	0.902740	−	0.430186i	$-0.141552\pi$
$131$	20.6647	1.80548	0.902740	+	0.430186i	$0.141552\pi$
$132$	0.752681	0.0655125
$133$	−23.3530	−2.02496
$134$	6.79764	0.587227
$135$	2.92239	0.251519
$136$	0.247362	0.0212111
$137$	−9.46216	−0.808407	−0.404203	−	0.914669i	$-0.632451\pi$
$137$	−9.46216	−0.808407	−0.404203	+	0.914669i	$0.632451\pi$
$138$	−0.380469	−0.0323876
$139$	−6.86593	−0.582361	−0.291180	−	0.956668i	$-0.594048\pi$
$139$	−6.86593	−0.582361	−0.291180	+	0.956668i	$0.594048\pi$
$140$	−2.63771	−0.222927
$141$	0.681290	0.0573749
$142$	−0.183966	−0.0154381
$143$	4.52294	0.378227
$144$	−2.14097	−0.178414
$145$	3.84053	0.318939
$146$	−8.53553	−0.706405
$147$	−10.6549	−0.878799
$148$	3.11260	0.255854
$149$	−6.43770	−0.527397	−0.263699	−	0.964605i	$-0.584942\pi$
$149$	−6.43770	−0.527397	−0.263699	+	0.964605i	$0.584942\pi$
$150$	−4.28556	−0.349914
$151$	8.34403	0.679028	0.339514	−	0.940601i	$-0.389737\pi$
$151$	8.34403	0.679028	0.339514	+	0.940601i	$0.389737\pi$
$152$	−5.43006	−0.440436
$153$	0.529594	0.0428151
$154$	−3.49256	−0.281439
$155$	5.18635	0.416578
$156$	5.16202	0.413292
$157$	−2.38130	−0.190048	−0.0950241	−	0.995475i	$-0.530293\pi$
$157$	−2.38130	−0.190048	−0.0950241	+	0.995475i	$0.530293\pi$
$158$	−14.5278	−1.15577
$159$	−0.498138	−0.0395049
$160$	−0.613322	−0.0484874
$161$	1.76544	0.139136
$162$	−2.00664	−0.157657
$163$	16.9060	1.32418	0.662090	−	0.749424i	$-0.269670\pi$
$163$	16.9060	1.32418	0.662090	+	0.749424i	$0.269670\pi$
$164$	5.83087	0.455315
$165$	0.461636	0.0359383
$166$	0.337683	0.0262093
$167$	−17.8651	−1.38244	−0.691220	−	0.722645i	$-0.742926\pi$
$167$	−17.8651	−1.38244	−0.691220	+	0.722645i	$0.742926\pi$
$168$	−3.98605	−0.307530
$169$	18.0191	1.38609
$170$	0.151713	0.0116358
$171$	−11.6256	−0.889030
$172$	−4.28708	−0.326887
$173$	0.837202	0.0636513	0.0318256	−	0.999493i	$-0.489868\pi$
$173$	0.837202	0.0636513	0.0318256	+	0.999493i	$0.489868\pi$
$174$	5.80373	0.439980
$175$	19.8857	1.50322
$176$	−0.812094	−0.0612139
$177$	−2.83281	−0.212927
$178$	18.0121	1.35006
$179$	−10.9794	−0.820637	−0.410318	−	0.911942i	$-0.634582\pi$
$179$	−10.9794	−0.820637	−0.410318	+	0.911942i	$0.634582\pi$
$180$	−1.31310	−0.0978729
$181$	−5.16051	−0.383578	−0.191789	−	0.981436i	$-0.561429\pi$
$181$	−5.16051	−0.383578	−0.191789	+	0.981436i	$0.561429\pi$
$182$	−23.9526	−1.77548
$183$	11.4904	0.849391
$184$	0.410501	0.0302625
$185$	1.90903	0.140354
$186$	7.83751	0.574674
$187$	0.200881	0.0146899
$188$	−0.735067	−0.0536103
$189$	−20.4922	−1.49058
$190$	−3.33037	−0.241611
$191$	−22.8080	−1.65033	−0.825166	−	0.564890i	$-0.808919\pi$
$191$	−22.8080	−1.65033	−0.825166	+	0.564890i	$0.808919\pi$
$192$	−0.926840	−0.0668889
$193$	24.9859	1.79853	0.899263	−	0.437409i	$-0.144104\pi$
$193$	24.9859	1.79853	0.899263	+	0.437409i	$0.144104\pi$
$194$	0.706123	0.0506967
$195$	3.16598	0.226721
$196$	11.4959	0.821136
$197$	−5.85052	−0.416832	−0.208416	−	0.978040i	$-0.566831\pi$
$197$	−5.85052	−0.416832	−0.208416	+	0.978040i	$0.566831\pi$
$198$	−1.73867	−0.123562
$199$	15.0230	1.06495	0.532476	−	0.846445i	$-0.321262\pi$
$199$	15.0230	1.06495	0.532476	+	0.846445i	$0.321262\pi$
$200$	4.62384	0.326955
$201$	6.30033	0.444391
$202$	9.69344	0.682028
$203$	−26.9303	−1.89013
$204$	0.229265	0.0160518
$205$	3.57620	0.249773
$206$	−4.50697	−0.314016
$207$	0.878869	0.0610856
$208$	−5.56948	−0.386174
$209$	−4.40971	−0.305026
$210$	−2.44473	−0.168703
$211$	15.5580	1.07106	0.535528	−	0.844517i	$-0.320113\pi$
$211$	15.5580	1.07106	0.535528	+	0.844517i	$0.320113\pi$
$212$	0.537458	0.0369128
$213$	−0.170507	−0.0116829
$214$	−16.8135	−1.14935
$215$	−2.62936	−0.179321
$216$	−4.76486	−0.324207
$217$	−36.3673	−2.46877
$218$	−12.0827	−0.818343
$219$	−7.91107	−0.534580
$220$	−0.498075	−0.0335802
$221$	1.37768	0.0926726
$222$	2.88488	0.193621
$223$	7.31293	0.489710	0.244855	−	0.969560i	$-0.421260\pi$
$223$	7.31293	0.489710	0.244855	+	0.969560i	$0.421260\pi$
$224$	4.30069	0.287352
$225$	9.89948	0.659965
$226$	−13.5418	−0.900786
$227$	7.49736	0.497617	0.248809	−	0.968553i	$-0.419961\pi$
$227$	7.49736	0.497617	0.248809	+	0.968553i	$0.419961\pi$
$228$	−5.03279	−0.333305
$229$	−22.2152	−1.46802	−0.734011	−	0.679138i	$-0.762354\pi$
$229$	−22.2152	−1.46802	−0.734011	+	0.679138i	$0.762354\pi$
$230$	0.251769	0.0166012
$231$	−3.23705	−0.212982
$232$	−6.26185	−0.411110
$233$	10.7762	0.705974	0.352987	−	0.935628i	$-0.385166\pi$
$233$	10.7762	0.705974	0.352987	+	0.935628i	$0.385166\pi$
$234$	−11.9241	−0.779501
$235$	−0.450833	−0.0294091
$236$	3.05642	0.198956
$237$	−13.4649	−0.874641
$238$	−1.06383	−0.0689576
$239$	−16.2655	−1.05213	−0.526065	−	0.850444i	$-0.676333\pi$
$239$	−16.2655	−1.05213	−0.526065	+	0.850444i	$0.676333\pi$
$240$	−0.568452	−0.0366934
$241$	22.9590	1.47892	0.739458	−	0.673203i	$-0.235082\pi$
$241$	22.9590	1.47892	0.739458	+	0.673203i	$0.235082\pi$
$242$	10.3405	0.664713
$243$	−16.1544	−1.03631
$244$	−12.3973	−0.793658
$245$	7.05069	0.450452
$246$	5.40429	0.344565
$247$	−30.2426	−1.92429
$248$	−8.45616	−0.536967
$249$	0.312978	0.0198342
$250$	5.90251	0.373308
$251$	4.77513	0.301404	0.150702	−	0.988579i	$-0.451847\pi$
$251$	4.77513	0.301404	0.150702	+	0.988579i	$0.451847\pi$
$252$	9.20763	0.580026
$253$	0.333365	0.0209585
$254$	−19.6307	−1.23174
$255$	0.140613	0.00880555
$256$	1.00000	0.0625000
$257$	−8.89232	−0.554687	−0.277344	−	0.960771i	$-0.589454\pi$
$257$	−8.89232	−0.554687	−0.277344	+	0.960771i	$0.589454\pi$
$258$	−3.97344	−0.247376
$259$	−13.3863	−0.831786
$260$	−3.41588	−0.211844
$261$	−13.4064	−0.829836
$262$	−20.6647	−1.27667
$263$	−22.7327	−1.40176	−0.700879	−	0.713281i	$-0.747209\pi$
$263$	−22.7327	−1.40176	−0.700879	+	0.713281i	$0.747209\pi$
$264$	−0.752681	−0.0463243
$265$	0.329635	0.0202493
$266$	23.3530	1.43186
$267$	16.6943	1.02168
$268$	−6.79764	−0.415232
$269$	−15.9281	−0.971152	−0.485576	−	0.874194i	$-0.661390\pi$
$269$	−15.9281	−0.971152	−0.485576	+	0.874194i	$0.661390\pi$
$270$	−2.92239	−0.177851
$271$	18.2010	1.10563	0.552816	−	0.833303i	$-0.313553\pi$
$271$	18.2010	1.10563	0.552816	+	0.833303i	$0.313553\pi$
$272$	−0.247362	−0.0149985
$273$	−22.2002	−1.34362
$274$	9.46216	0.571630
$275$	3.75499	0.226434
$276$	0.380469	0.0229015
$277$	−18.0087	−1.08204	−0.541019	−	0.841010i	$-0.681961\pi$
$277$	−18.0087	−1.08204	−0.541019	+	0.841010i	$0.681961\pi$
$278$	6.86593	0.411791
$279$	−18.1044	−1.08388
$280$	2.63771	0.157633
$281$	−9.93003	−0.592376	−0.296188	−	0.955130i	$-0.595716\pi$
$281$	−9.93003	−0.592376	−0.296188	+	0.955130i	$0.595716\pi$
$282$	−0.681290	−0.0405702
$283$	14.9457	0.888432	0.444216	−	0.895920i	$-0.353482\pi$
$283$	14.9457	0.888432	0.444216	+	0.895920i	$0.353482\pi$
$284$	0.183966	0.0109164
$285$	−3.08672	−0.182842
$286$	−4.52294	−0.267447
$287$	−25.0768	−1.48023
$288$	2.14097	0.126158
$289$	−16.9388	−0.996401
$290$	−3.84053	−0.225524
$291$	0.654464	0.0383653
$292$	8.53553	0.499504
$293$	0.705749	0.0412303	0.0206152	−	0.999787i	$-0.493438\pi$
$293$	0.705749	0.0412303	0.0206152	+	0.999787i	$0.493438\pi$
$294$	10.6549	0.621405
$295$	1.87457	0.109142
$296$	−3.11260	−0.180916
$297$	−3.86951	−0.224532
$298$	6.43770	0.372926
$299$	2.28628	0.132219
$300$	4.28556	0.247427
$301$	18.4374	1.06271
$302$	−8.34403	−0.480145
$303$	8.98427	0.516133
$304$	5.43006	0.311435
$305$	−7.60356	−0.435379
$306$	−0.529594	−0.0302749
$307$	−3.38803	−0.193365	−0.0966827	−	0.995315i	$-0.530823\pi$
$307$	−3.38803	−0.193365	−0.0966827	+	0.995315i	$0.530823\pi$
$308$	3.49256	0.199007
$309$	−4.17724	−0.237635
$310$	−5.18635	−0.294565
$311$	8.16099	0.462767	0.231384	−	0.972863i	$-0.425675\pi$
$311$	8.16099	0.462767	0.231384	+	0.972863i	$0.425675\pi$
$312$	−5.16202	−0.292242
$313$	−3.17712	−0.179582	−0.0897908	−	0.995961i	$-0.528620\pi$
$313$	−3.17712	−0.179582	−0.0897908	+	0.995961i	$0.528620\pi$
$314$	2.38130	0.134384
$315$	5.64724	0.318186
$316$	14.5278	0.817251
$317$	23.8445	1.33924	0.669621	−	0.742703i	$-0.266456\pi$
$317$	23.8445	1.33924	0.669621	+	0.742703i	$0.266456\pi$
$318$	0.498138	0.0279342
$319$	−5.08521	−0.284717
$320$	0.613322	0.0342857
$321$	−15.5835	−0.869784
$322$	−1.76544	−0.0983839
$323$	−1.34319	−0.0747371
$324$	2.00664	0.111480
$325$	25.7524	1.42848
$326$	−16.9060	−0.936337
$327$	−11.1987	−0.619291
$328$	−5.83087	−0.321956
$329$	3.16129	0.174288
$330$	−0.461636	−0.0254122
$331$	18.6849	1.02702	0.513508	−	0.858085i	$-0.328346\pi$
$331$	18.6849	1.02702	0.513508	+	0.858085i	$0.328346\pi$
$332$	−0.337683	−0.0185328
$333$	−6.66398	−0.365184
$334$	17.8651	0.977532
$335$	−4.16914	−0.227785
$336$	3.98605	0.217457
$337$	−6.75341	−0.367882	−0.183941	−	0.982937i	$-0.558885\pi$
$337$	−6.75341	−0.367882	−0.183941	+	0.982937i	$0.558885\pi$
$338$	−18.0191	−0.980110
$339$	−12.5511	−0.681680
$340$	−0.151713	−0.00822777
$341$	−6.86719	−0.371879
$342$	11.6256	0.628639
$343$	−19.3355	−1.04402
$344$	4.28708	0.231144
$345$	0.233350	0.0125631
$346$	−0.837202	−0.0450083
$347$	11.4668	0.615570	0.307785	−	0.951456i	$-0.400412\pi$
$347$	11.4668	0.615570	0.307785	+	0.951456i	$0.400412\pi$
$348$	−5.80373	−0.311113
$349$	28.5903	1.53040	0.765202	−	0.643790i	$-0.222639\pi$
$349$	28.5903	1.53040	0.765202	+	0.643790i	$0.222639\pi$
$350$	−19.8857	−1.06293
$351$	−26.5378	−1.41648
$352$	0.812094	0.0432847
$353$	27.9111	1.48556	0.742779	−	0.669537i	$-0.233507\pi$
$353$	27.9111	1.48556	0.742779	+	0.669537i	$0.233507\pi$
$354$	2.83281	0.150562
$355$	0.112830	0.00598840
$356$	−18.0121	−0.954638
$357$	−0.985997	−0.0521845
$358$	10.9794	0.580278
$359$	34.8379	1.83867	0.919336	−	0.393474i	$-0.128727\pi$
$359$	34.8379	1.83867	0.919336	+	0.393474i	$0.128727\pi$
$360$	1.31310	0.0692066
$361$	10.4855	0.551869
$362$	5.16051	0.271230
$363$	9.58400	0.503029
$364$	23.9526	1.25546
$365$	5.23503	0.274014
$366$	−11.4904	−0.600610
$367$	−21.7737	−1.13658	−0.568288	−	0.822829i	$-0.692394\pi$
$367$	−21.7737	−1.13658	−0.568288	+	0.822829i	$0.692394\pi$
$368$	−0.410501	−0.0213988
$369$	−12.4837	−0.649876
$370$	−1.90903	−0.0992456
$371$	−2.31144	−0.120004
$372$	−7.83751	−0.406356
$373$	15.3161	0.793035	0.396518	−	0.918027i	$-0.370219\pi$
$373$	15.3161	0.793035	0.396518	+	0.918027i	$0.370219\pi$
$374$	−0.200881	−0.0103873
$375$	5.47068	0.282505
$376$	0.735067	0.0379082
$377$	−34.8752	−1.79617
$378$	20.4922	1.05400
$379$	4.14465	0.212897	0.106448	−	0.994318i	$-0.466052\pi$
$379$	4.14465	0.212897	0.106448	+	0.994318i	$0.466052\pi$
$380$	3.33037	0.170845
$381$	−18.1945	−0.932133
$382$	22.8080	1.16696
$383$	9.14276	0.467173	0.233587	−	0.972336i	$-0.424954\pi$
$383$	9.14276	0.467173	0.233587	+	0.972336i	$0.424954\pi$
$384$	0.926840	0.0472976
$385$	2.14206	0.109170
$386$	−24.9859	−1.27175
$387$	9.17850	0.466570
$388$	−0.706123	−0.0358480
$389$	−23.7310	−1.20321	−0.601605	−	0.798793i	$-0.705472\pi$
$389$	−23.7310	−1.20321	−0.601605	+	0.798793i	$0.705472\pi$
$390$	−3.16598	−0.160316
$391$	0.101542	0.00513522
$392$	−11.4959	−0.580631
$393$	−19.1528	−0.966133
$394$	5.85052	0.294745
$395$	8.91020	0.448321
$396$	1.73867	0.0873712
$397$	8.35856	0.419504	0.209752	−	0.977755i	$-0.432734\pi$
$397$	8.35856	0.419504	0.209752	+	0.977755i	$0.432734\pi$
$398$	−15.0230	−0.753035
$399$	21.6445	1.08358
$400$	−4.62384	−0.231192
$401$	25.3323	1.26503	0.632517	−	0.774546i	$-0.282022\pi$
$401$	25.3323	1.26503	0.632517	+	0.774546i	$0.282022\pi$
$402$	−6.30033	−0.314232
$403$	−47.0964	−2.34604
$404$	−9.69344	−0.482267
$405$	1.23072	0.0611548
$406$	26.9303	1.33653
$407$	−2.52772	−0.125295
$408$	−0.229265	−0.0113503
$409$	−3.67900	−0.181915	−0.0909575	−	0.995855i	$-0.528993\pi$
$409$	−3.67900	−0.181915	−0.0909575	+	0.995855i	$0.528993\pi$
$410$	−3.57620	−0.176616
$411$	8.76991	0.432588
$412$	4.50697	0.222043
$413$	−13.1447	−0.646808
$414$	−0.878869	−0.0431940
$415$	−0.207108	−0.0101666
$416$	5.56948	0.273066
$417$	6.36362	0.311628
$418$	4.40971	0.215686
$419$	34.8876	1.70437	0.852185	−	0.523240i	$-0.175277\pi$
$419$	34.8876	1.70437	0.852185	+	0.523240i	$0.175277\pi$
$420$	2.44473	0.119291
$421$	19.8674	0.968279	0.484139	−	0.874991i	$-0.339133\pi$
$421$	19.8674	0.968279	0.484139	+	0.874991i	$0.339133\pi$
$422$	−15.5580	−0.757351
$423$	1.57375	0.0765186
$424$	−0.537458	−0.0261013
$425$	1.14376	0.0554806
$426$	0.170507	0.00826108
$427$	53.3171	2.58019
$428$	16.8135	0.812713
$429$	−4.19204	−0.202394
$430$	2.62936	0.126799
$431$	−38.4689	−1.85298	−0.926491	−	0.376316i	$-0.877191\pi$
$431$	−38.4689	−1.85298	−0.926491	+	0.376316i	$0.877191\pi$
$432$	4.76486	0.229249
$433$	24.0036	1.15354	0.576769	−	0.816907i	$-0.304313\pi$
$433$	24.0036	1.15354	0.576769	+	0.816907i	$0.304313\pi$
$434$	36.3673	1.74569
$435$	−3.55956	−0.170668
$436$	12.0827	0.578656
$437$	−2.22904	−0.106630
$438$	7.91107	0.378005
$439$	29.3726	1.40188	0.700938	−	0.713222i	$-0.252765\pi$
$439$	29.3726	1.40188	0.700938	+	0.713222i	$0.252765\pi$
$440$	0.498075	0.0237448
$441$	−24.6124	−1.17202
$442$	−1.37768	−0.0655294
$443$	−2.48716	−0.118168	−0.0590842	−	0.998253i	$-0.518818\pi$
$443$	−2.48716	−0.118168	−0.0590842	+	0.998253i	$0.518818\pi$
$444$	−2.88488	−0.136911
$445$	−11.0472	−0.523688
$446$	−7.31293	−0.346277
$447$	5.96672	0.282216
$448$	−4.30069	−0.203188
$449$	−23.8800	−1.12697	−0.563483	−	0.826128i	$-0.690539\pi$
$449$	−23.8800	−1.12697	−0.563483	+	0.826128i	$0.690539\pi$
$450$	−9.89948	−0.466666
$451$	−4.73522	−0.222973
$452$	13.5418	0.636952
$453$	−7.73358	−0.363355
$454$	−7.49736	−0.351868
$455$	14.6907	0.688708
$456$	5.03279	0.235682
$457$	3.36625	0.157466	0.0787332	−	0.996896i	$-0.474912\pi$
$457$	3.36625	0.157466	0.0787332	+	0.996896i	$0.474912\pi$
$458$	22.2152	1.03805
$459$	−1.17864	−0.0550144
$460$	−0.251769	−0.0117388
$461$	27.7553	1.29270	0.646348	−	0.763043i	$-0.276296\pi$
$461$	27.7553	1.29270	0.646348	+	0.763043i	$0.276296\pi$
$462$	3.23705	0.150601
$463$	−28.8211	−1.33943	−0.669714	−	0.742619i	$-0.733583\pi$
$463$	−28.8211	−1.33943	−0.669714	+	0.742619i	$0.733583\pi$
$464$	6.26185	0.290699
$465$	−4.80692	−0.222915
$466$	−10.7762	−0.499199
$467$	−18.1652	−0.840583	−0.420292	−	0.907389i	$-0.638072\pi$
$467$	−18.1652	−0.840583	−0.420292	+	0.907389i	$0.638072\pi$
$468$	11.9241	0.551191
$469$	29.2345	1.34992
$470$	0.450833	0.0207954
$471$	2.20708	0.101697
$472$	−3.05642	−0.140683
$473$	3.48151	0.160080
$474$	13.4649	0.618465
$475$	−25.1077	−1.15202
$476$	1.06383	0.0487604
$477$	−1.15068	−0.0526860
$478$	16.2655	0.743968
$479$	−36.4654	−1.66615	−0.833074	−	0.553162i	$-0.813421\pi$
$479$	−36.4654	−1.66615	−0.833074	+	0.553162i	$0.813421\pi$
$480$	0.568452	0.0259461
$481$	−17.3356	−0.790434
$482$	−22.9590	−1.04575
$483$	−1.63628	−0.0744532
$484$	−10.3405	−0.470023
$485$	−0.433081	−0.0196652
$486$	16.1544	0.732779
$487$	−32.8608	−1.48906	−0.744532	−	0.667587i	$-0.767327\pi$
$487$	−32.8608	−1.48906	−0.744532	+	0.667587i	$0.767327\pi$
$488$	12.3973	0.561201
$489$	−15.6692	−0.708584
$490$	−7.05069	−0.318518
$491$	−11.8666	−0.535532	−0.267766	−	0.963484i	$-0.586285\pi$
$491$	−11.8666	−0.535532	−0.267766	+	0.963484i	$0.586285\pi$
$492$	−5.40429	−0.243644
$493$	−1.54894	−0.0697609
$494$	30.2426	1.36068
$495$	1.06636	0.0479294
$496$	8.45616	0.379693
$497$	−0.791179	−0.0354892
$498$	−0.312978	−0.0140249
$499$	−3.50427	−0.156873	−0.0784363	−	0.996919i	$-0.524993\pi$
$499$	−3.50427	−0.156873	−0.0784363	+	0.996919i	$0.524993\pi$
$500$	−5.90251	−0.263968
$501$	16.5581	0.739759
$502$	−4.77513	−0.213125
$503$	−11.4687	−0.511364	−0.255682	−	0.966761i	$-0.582300\pi$
$503$	−11.4687	−0.511364	−0.255682	+	0.966761i	$0.582300\pi$
$504$	−9.20763	−0.410140
$505$	−5.94520	−0.264558
$506$	−0.333365	−0.0148199
$507$	−16.7008	−0.741710
$508$	19.6307	0.870971
$509$	4.30197	0.190682	0.0953408	−	0.995445i	$-0.469606\pi$
$509$	4.30197	0.190682	0.0953408	+	0.995445i	$0.469606\pi$
$510$	−0.140613	−0.00622646
$511$	−36.7086	−1.62389
$512$	−1.00000	−0.0441942
$513$	25.8734	1.14234
$514$	8.89232	0.392223
$515$	2.76423	0.121806
$516$	3.97344	0.174921
$517$	0.596943	0.0262535
$518$	13.3863	0.588161
$519$	−0.775953	−0.0340605
$520$	3.41588	0.149796
$521$	30.7835	1.34865	0.674326	−	0.738434i	$-0.264434\pi$
$521$	30.7835	1.34865	0.674326	+	0.738434i	$0.264434\pi$
$522$	13.4064	0.586783
$523$	13.9326	0.609229	0.304614	−	0.952476i	$-0.401472\pi$
$523$	13.9326	0.609229	0.304614	+	0.952476i	$0.401472\pi$
$524$	20.6647	0.902740
$525$	−18.4308	−0.804388
$526$	22.7327	0.991192
$527$	−2.09173	−0.0911173
$528$	0.752681	0.0327562
$529$	−22.8315	−0.992673
$530$	−0.329635	−0.0143184
$531$	−6.54369	−0.283972
$532$	−23.3530	−1.01248
$533$	−32.4749	−1.40665
$534$	−16.6943	−0.722434
$535$	10.3121	0.445832
$536$	6.79764	0.293613
$537$	10.1761	0.439132
$538$	15.9281	0.686708
$539$	−9.33575	−0.402119
$540$	2.92239	0.125760
$541$	1.54382	0.0663739	0.0331869	−	0.999449i	$-0.489434\pi$
$541$	1.54382	0.0663739	0.0331869	+	0.999449i	$0.489434\pi$
$542$	−18.2010	−0.781800
$543$	4.78297	0.205257
$544$	0.247362	0.0106056
$545$	7.41058	0.317434
$546$	22.2002	0.950082
$547$	−8.68580	−0.371378	−0.185689	−	0.982609i	$-0.559452\pi$
$547$	−8.68580	−0.371378	−0.185689	+	0.982609i	$0.559452\pi$
$548$	−9.46216	−0.404203
$549$	26.5423	1.13280
$550$	−3.75499	−0.160113
$551$	34.0022	1.44854
$552$	−0.380469	−0.0161938
$553$	−62.4794	−2.65689
$554$	18.0087	0.765117
$555$	−1.76936	−0.0751053
$556$	−6.86593	−0.291180
$557$	−34.4895	−1.46137	−0.730684	−	0.682716i	$-0.760799\pi$
$557$	−34.4895	−1.46137	−0.730684	+	0.682716i	$0.760799\pi$
$558$	18.1044	0.766419
$559$	23.8768	1.00988
$560$	−2.63771	−0.111463
$561$	−0.186185	−0.00786072
$562$	9.93003	0.418873
$563$	29.9981	1.26427	0.632134	−	0.774859i	$-0.282179\pi$
$563$	29.9981	1.26427	0.632134	+	0.774859i	$0.282179\pi$
$564$	0.681290	0.0286875
$565$	8.30547	0.349414
$566$	−14.9457	−0.628216
$567$	−8.62994	−0.362423
$568$	−0.183966	−0.00771903
$569$	21.7035	0.909859	0.454929	−	0.890527i	$-0.349664\pi$
$569$	21.7035	0.909859	0.454929	+	0.890527i	$0.349664\pi$
$570$	3.08672	0.129289
$571$	0.0233525	0.000977271 0	0.000488635	−	1.00000i	$-0.499844\pi$
$571$	0.0233525	0.000977271 0	0.000488635		1.00000i	$0.499844\pi$
$572$	4.52294	0.189114
$573$	21.1394	0.883112
$574$	25.0768	1.04668
$575$	1.89809	0.0791558
$576$	−2.14097	−0.0892070
$577$	5.73179	0.238618	0.119309	−	0.992857i	$-0.461932\pi$
$577$	5.73179	0.238618	0.119309	+	0.992857i	$0.461932\pi$
$578$	16.9388	0.704562
$579$	−23.1580	−0.962412
$580$	3.84053	0.159469
$581$	1.45227	0.0602503
$582$	−0.654464	−0.0271284
$583$	−0.436467	−0.0180766
$584$	−8.53553	−0.353203
$585$	7.31330	0.302368
$586$	−0.705749	−0.0291542
$587$	15.4386	0.637219	0.318609	−	0.947886i	$-0.396784\pi$
$587$	15.4386	0.637219	0.318609	+	0.947886i	$0.396784\pi$
$588$	−10.6549	−0.439399
$589$	45.9174	1.89199
$590$	−1.87457	−0.0771748
$591$	5.42250	0.223052
$592$	3.11260	0.127927
$593$	−5.38781	−0.221251	−0.110625	−	0.993862i	$-0.535285\pi$
$593$	−5.38781	−0.221251	−0.110625	+	0.993862i	$0.535285\pi$
$594$	3.86951	0.158768
$595$	0.652468	0.0267486
$596$	−6.43770	−0.263699
$597$	−13.9239	−0.569868
$598$	−2.28628	−0.0934928
$599$	−2.26577	−0.0925768	−0.0462884	−	0.998928i	$-0.514739\pi$
$599$	−2.26577	−0.0925768	−0.0462884	+	0.998928i	$0.514739\pi$
$600$	−4.28556	−0.174957
$601$	−11.0329	−0.450043	−0.225021	−	0.974354i	$-0.572245\pi$
$601$	−11.0329	−0.450043	−0.225021	+	0.974354i	$0.572245\pi$
$602$	−18.4374	−0.751452
$603$	14.5535	0.592665
$604$	8.34403	0.339514
$605$	−6.34206	−0.257841
$606$	−8.98427	−0.364961
$607$	23.2240	0.942634	0.471317	−	0.881964i	$-0.343779\pi$
$607$	23.2240	0.942634	0.471317	+	0.881964i	$0.343779\pi$
$608$	−5.43006	−0.220218
$609$	24.9600	1.01143
$610$	7.60356	0.307859
$611$	4.09394	0.165623
$612$	0.529594	0.0214076
$613$	1.00000	0.0403896
$613$	1.00000	0.0403896
$614$	3.38803	0.136730
$615$	−3.31457	−0.133656
$616$	−3.49256	−0.140719
$617$	−16.3274	−0.657318	−0.328659	−	0.944449i	$-0.606597\pi$
$617$	−16.3274	−0.657318	−0.328659	+	0.944449i	$0.606597\pi$
$618$	4.17724	0.168033
$619$	−25.9989	−1.04499	−0.522493	−	0.852644i	$-0.674998\pi$
$619$	−25.9989	−1.04499	−0.522493	+	0.852644i	$0.674998\pi$
$620$	5.18635	0.208289
$621$	−1.95598	−0.0784907
$622$	−8.16099	−0.327226
$623$	77.4643	3.10354
$624$	5.16202	0.206646
$625$	19.4990	0.779962
$626$	3.17712	0.126983
$627$	4.08710	0.163223
$628$	−2.38130	−0.0950241
$629$	−0.769939	−0.0306995
$630$	−5.64724	−0.224992
$631$	26.3784	1.05011	0.525054	−	0.851069i	$-0.324045\pi$
$631$	26.3784	1.05011	0.525054	+	0.851069i	$0.324045\pi$
$632$	−14.5278	−0.577884
$633$	−14.4198	−0.573134
$634$	−23.8445	−0.946988
$635$	12.0399	0.477790
$636$	−0.498138	−0.0197525
$637$	−64.0262	−2.53681
$638$	5.08521	0.201325
$639$	−0.393864	−0.0155810
$640$	−0.613322	−0.0242437
$641$	−21.7817	−0.860324	−0.430162	−	0.902752i	$-0.641544\pi$
$641$	−21.7817	−0.860324	−0.430162	+	0.902752i	$0.641544\pi$
$642$	15.5835	0.615030
$643$	0.624181	0.0246153	0.0123077	−	0.999924i	$-0.496082\pi$
$643$	0.624181	0.0246153	0.0123077	+	0.999924i	$0.496082\pi$
$644$	1.76544	0.0695679
$645$	2.43700	0.0959567
$646$	1.34319	0.0528471
$647$	47.2241	1.85657	0.928285	−	0.371871i	$-0.121283\pi$
$647$	47.2241	1.85657	0.928285	+	0.371871i	$0.121283\pi$
$648$	−2.00664	−0.0788283
$649$	−2.48210	−0.0974309
$650$	−25.7524	−1.01009
$651$	33.7067	1.32107
$652$	16.9060	0.662090
$653$	21.3764	0.836523	0.418261	−	0.908327i	$-0.362640\pi$
$653$	21.3764	0.836523	0.418261	+	0.908327i	$0.362640\pi$
$654$	11.1987	0.437905
$655$	12.6741	0.495218
$656$	5.83087	0.227657
$657$	−18.2743	−0.712948
$658$	−3.16129	−0.123240
$659$	41.4420	1.61435	0.807176	−	0.590311i	$-0.200995\pi$
$659$	41.4420	1.61435	0.807176	+	0.590311i	$0.200995\pi$
$660$	0.461636	0.0179692
$661$	−1.74064	−0.0677029	−0.0338514	−	0.999427i	$-0.510777\pi$
$661$	−1.74064	−0.0677029	−0.0338514	+	0.999427i	$0.510777\pi$
$662$	−18.6849	−0.726211
$663$	−1.27689	−0.0495902
$664$	0.337683	0.0131046
$665$	−14.3229	−0.555418
$666$	6.66398	0.258224
$667$	−2.57049	−0.0995299
$668$	−17.8651	−0.691220
$669$	−6.77792	−0.262049
$670$	4.16914	0.161068
$671$	10.0678	0.388663
$672$	−3.98605	−0.153765
$673$	25.3091	0.975595	0.487798	−	0.872957i	$-0.337800\pi$
$673$	25.3091	0.975595	0.487798	+	0.872957i	$0.337800\pi$
$674$	6.75341	0.260132
$675$	−22.0319	−0.848009
$676$	18.0191	0.693043
$677$	10.9018	0.418989	0.209494	−	0.977810i	$-0.432818\pi$
$677$	10.9018	0.418989	0.209494	+	0.977810i	$0.432818\pi$
$678$	12.5511	0.482021
$679$	3.03682	0.116542
$680$	0.151713	0.00581791
$681$	−6.94885	−0.266281
$682$	6.86719	0.262958
$683$	20.2808	0.776024	0.388012	−	0.921654i	$-0.373162\pi$
$683$	20.2808	0.776024	0.388012	+	0.921654i	$0.373162\pi$
$684$	−11.6256	−0.444515
$685$	−5.80335	−0.221735
$686$	19.3355	0.738233
$687$	20.5899	0.785555
$688$	−4.28708	−0.163444
$689$	−2.99336	−0.114038
$690$	−0.233350	−0.00888348
$691$	13.0102	0.494933	0.247466	−	0.968896i	$-0.420402\pi$
$691$	13.0102	0.494933	0.247466	+	0.968896i	$0.420402\pi$
$692$	0.837202	0.0318256
$693$	−7.47746	−0.284045
$694$	−11.4668	−0.435274
$695$	−4.21103	−0.159733
$696$	5.80373	0.219990
$697$	−1.44234	−0.0546324
$698$	−28.5903	−1.08216
$699$	−9.98783	−0.377775
$700$	19.8857	0.751608
$701$	34.4344	1.30057	0.650284	−	0.759691i	$-0.274650\pi$
$701$	34.4344	1.30057	0.650284	+	0.759691i	$0.274650\pi$
$702$	26.5378	1.00160
$703$	16.9016	0.637456
$704$	−0.812094	−0.0306069
$705$	0.417850	0.0157371
$706$	−27.9111	−1.05045
$707$	41.6885	1.56786
$708$	−2.83281	−0.106464
$709$	−10.9346	−0.410657	−0.205328	−	0.978693i	$-0.565826\pi$
$709$	−10.9346	−0.410657	−0.205328	+	0.978693i	$0.565826\pi$
$710$	−0.112830	−0.00423444
$711$	−31.1035	−1.16647
$712$	18.0121	0.675031
$713$	−3.47126	−0.130000
$714$	0.985997	0.0369000
$715$	2.77402	0.103742
$716$	−10.9794	−0.410318
$717$	15.0756	0.563007
$718$	−34.8379	−1.30014
$719$	33.5358	1.25067	0.625337	−	0.780355i	$-0.284962\pi$
$719$	33.5358	1.25067	0.625337	+	0.780355i	$0.284962\pi$
$720$	−1.31310	−0.0489364
$721$	−19.3831	−0.721864
$722$	−10.4855	−0.390230
$723$	−21.2793	−0.791385
$724$	−5.16051	−0.191789
$725$	−28.9538	−1.07532
$726$	−9.58400	−0.355695
$727$	20.4936	0.760064	0.380032	−	0.924973i	$-0.375913\pi$
$727$	20.4936	0.760064	0.380032	+	0.924973i	$0.375913\pi$
$728$	−23.9526	−0.887742
$729$	8.95263	0.331579
$730$	−5.23503	−0.193757
$731$	1.06046	0.0392226
$732$	11.4904	0.424696
$733$	23.5872	0.871213	0.435606	−	0.900137i	$-0.356534\pi$
$733$	23.5872	0.871213	0.435606	+	0.900137i	$0.356534\pi$
$734$	21.7737	0.803681
$735$	−6.53487	−0.241042
$736$	0.410501	0.0151313
$737$	5.52032	0.203344
$738$	12.4837	0.459532
$739$	−2.84419	−0.104625	−0.0523126	−	0.998631i	$-0.516659\pi$
$739$	−2.84419	−0.104625	−0.0523126	+	0.998631i	$0.516659\pi$
$740$	1.90903	0.0701772
$741$	28.0301	1.02971
$742$	2.31144	0.0848556
$743$	−36.0648	−1.32309	−0.661544	−	0.749906i	$-0.730099\pi$
$743$	−36.0648	−1.32309	−0.661544	+	0.749906i	$0.730099\pi$
$744$	7.83751	0.287337
$745$	−3.94838	−0.144658
$746$	−15.3161	−0.560761
$747$	0.722968	0.0264520
$748$	0.200881	0.00734494
$749$	−72.3098	−2.64214
$750$	−5.47068	−0.199761
$751$	−32.8806	−1.19983	−0.599914	−	0.800064i	$-0.704799\pi$
$751$	−32.8806	−1.19983	−0.599914	+	0.800064i	$0.704799\pi$
$752$	−0.735067	−0.0268051
$753$	−4.42579	−0.161285
$754$	34.8752	1.27008
$755$	5.11758	0.186248
$756$	−20.4922	−0.745292
$757$	6.78162	0.246482	0.123241	−	0.992377i	$-0.460671\pi$
$757$	6.78162	0.246482	0.123241	+	0.992377i	$0.460671\pi$
$758$	−4.14465	−0.150541
$759$	−0.308976	−0.0112151
$760$	−3.33037	−0.120805
$761$	−20.5159	−0.743700	−0.371850	−	0.928293i	$-0.621276\pi$
$761$	−20.5159	−0.743700	−0.371850	+	0.928293i	$0.621276\pi$
$762$	18.1945	0.659118
$763$	−51.9639	−1.88122
$764$	−22.8080	−0.825166
$765$	0.324812	0.0117436
$766$	−9.14276	−0.330341
$767$	−17.0227	−0.614653
$768$	−0.926840	−0.0334445
$769$	−28.5132	−1.02821	−0.514106	−	0.857727i	$-0.671876\pi$
$769$	−28.5132	−1.02821	−0.514106	+	0.857727i	$0.671876\pi$
$770$	−2.14206	−0.0771946
$771$	8.24176	0.296820
$772$	24.9859	0.899263
$773$	12.2489	0.440561	0.220280	−	0.975437i	$-0.429303\pi$
$773$	12.2489	0.440561	0.220280	+	0.975437i	$0.429303\pi$
$774$	−9.17850	−0.329915
$775$	−39.0999	−1.40451
$776$	0.706123	0.0253484
$777$	12.4070	0.445098
$778$	23.7310	0.850798
$779$	31.6620	1.13441
$780$	3.16598	0.113360
$781$	−0.149397	−0.00534586
$782$	−0.101542	−0.00363115
$783$	29.8368	1.06628
$784$	11.4959	0.410568
$785$	−1.46050	−0.0521275
$786$	19.1528	0.683159
$787$	−18.9134	−0.674189	−0.337095	−	0.941471i	$-0.609444\pi$
$787$	−18.9134	−0.674189	−0.337095	+	0.941471i	$0.609444\pi$
$788$	−5.85052	−0.208416
$789$	21.0696	0.750096
$790$	−8.91020	−0.317011
$791$	−58.2390	−2.07074
$792$	−1.73867	−0.0617808
$793$	69.0467	2.45192
$794$	−8.35856	−0.296634
$795$	−0.305519	−0.0108356
$796$	15.0230	0.532476
$797$	−24.4745	−0.866932	−0.433466	−	0.901170i	$-0.642710\pi$
$797$	−24.4745	−0.866932	−0.433466	+	0.901170i	$0.642710\pi$
$798$	−21.6445	−0.766206
$799$	0.181828	0.00643260
$800$	4.62384	0.163477
$801$	38.5633	1.36257
$802$	−25.3323	−0.894514
$803$	−6.93165	−0.244612
$804$	6.30033	0.222195
$805$	1.08278	0.0381630
$806$	47.0964	1.65890
$807$	14.7628	0.519675
$808$	9.69344	0.341014
$809$	15.0958	0.530742	0.265371	−	0.964146i	$-0.414506\pi$
$809$	15.0958	0.530742	0.265371	+	0.964146i	$0.414506\pi$
$810$	−1.23072	−0.0432430
$811$	8.01418	0.281416	0.140708	−	0.990051i	$-0.455062\pi$
$811$	8.01418	0.281416	0.140708	+	0.990051i	$0.455062\pi$
$812$	−26.9303	−0.945067
$813$	−16.8694	−0.591637
$814$	2.52772	0.0885967
$815$	10.3688	0.363204
$816$	0.229265	0.00802588
$817$	−23.2791	−0.814433
$818$	3.67900	0.128633
$819$	−51.2817	−1.79193
$820$	3.57620	0.124886
$821$	39.5232	1.37937	0.689685	−	0.724109i	$-0.257749\pi$
$821$	39.5232	1.37937	0.689685	+	0.724109i	$0.257749\pi$
$822$	−8.76991	−0.305886
$823$	−13.0704	−0.455605	−0.227803	−	0.973707i	$-0.573154\pi$
$823$	−13.0704	−0.455605	−0.227803	+	0.973707i	$0.573154\pi$
$824$	−4.50697	−0.157008
$825$	−3.48027	−0.121168
$826$	13.1447	0.457363
$827$	−12.0694	−0.419695	−0.209848	−	0.977734i	$-0.567297\pi$
$827$	−12.0694	−0.419695	−0.209848	+	0.977734i	$0.567297\pi$
$828$	0.878869	0.0305428
$829$	15.2448	0.529475	0.264737	−	0.964321i	$-0.414715\pi$
$829$	15.2448	0.529475	0.264737	+	0.964321i	$0.414715\pi$
$830$	0.207108	0.00718884
$831$	16.6912	0.579011
$832$	−5.56948	−0.193087
$833$	−2.84365	−0.0985267
$834$	−6.36362	−0.220354
$835$	−10.9570	−0.379184
$836$	−4.40971	−0.152513
$837$	40.2924	1.39271
$838$	−34.8876	−1.20517
$839$	−2.81736	−0.0972662	−0.0486331	−	0.998817i	$-0.515487\pi$
$839$	−2.81736	−0.0972662	−0.0486331	+	0.998817i	$0.515487\pi$
$840$	−2.44473	−0.0843513
$841$	10.2107	0.352095
$842$	−19.8674	−0.684677
$843$	9.20356	0.316987
$844$	15.5580	0.535528
$845$	11.0515	0.380184
$846$	−1.57375	−0.0541068
$847$	44.4713	1.52805
$848$	0.537458	0.0184564
$849$	−13.8523	−0.475410
$850$	−1.14376	−0.0392307
$851$	−1.27773	−0.0437999
$852$	−0.170507	−0.00584147
$853$	10.0437	0.343891	0.171946	−	0.985106i	$-0.444995\pi$
$853$	10.0437	0.343891	0.171946	+	0.985106i	$0.444995\pi$
$854$	−53.3171	−1.82447
$855$	−7.13022	−0.243848
$856$	−16.8135	−0.574675
$857$	−37.5879	−1.28398	−0.641989	−	0.766714i	$-0.721891\pi$
$857$	−37.5879	−1.28398	−0.641989	+	0.766714i	$0.721891\pi$
$858$	4.19204	0.143114
$859$	21.0944	0.719732	0.359866	−	0.933004i	$-0.382822\pi$
$859$	21.0944	0.719732	0.359866	+	0.933004i	$0.382822\pi$
$860$	−2.62936	−0.0896605
$861$	23.2422	0.792090
$862$	38.4689	1.31026
$863$	54.9243	1.86964	0.934822	−	0.355117i	$-0.115559\pi$
$863$	54.9243	1.86964	0.934822	+	0.355117i	$0.115559\pi$
$864$	−4.76486	−0.162104
$865$	0.513474	0.0174587
$866$	−24.0036	−0.815674
$867$	15.6996	0.533185
$868$	−36.3673	−1.23439
$869$	−11.7979	−0.400217
$870$	3.55956	0.120680
$871$	37.8593	1.28281
$872$	−12.0827	−0.409172
$873$	1.51179	0.0511662
$874$	2.22904	0.0753985
$875$	25.3849	0.858165
$876$	−7.91107	−0.267290
$877$	24.9954	0.844035	0.422017	−	0.906588i	$-0.361322\pi$
$877$	24.9954	0.844035	0.422017	+	0.906588i	$0.361322\pi$
$878$	−29.3726	−0.991276
$879$	−0.654117	−0.0220628
$880$	−0.498075	−0.0167901
$881$	−5.61754	−0.189260	−0.0946298	−	0.995513i	$-0.530167\pi$
$881$	−5.61754	−0.189260	−0.0946298	+	0.995513i	$0.530167\pi$
$882$	24.6124	0.828741
$883$	−3.79477	−0.127704	−0.0638521	−	0.997959i	$-0.520339\pi$
$883$	−3.79477	−0.127704	−0.0638521	+	0.997959i	$0.520339\pi$
$884$	1.37768	0.0463363
$885$	−1.73743	−0.0584029
$886$	2.48716	0.0835576
$887$	30.5307	1.02512	0.512560	−	0.858651i	$-0.328697\pi$
$887$	30.5307	1.02512	0.512560	+	0.858651i	$0.328697\pi$
$888$	2.88488	0.0968104
$889$	−84.4254	−2.83154
$890$	11.0472	0.370303
$891$	−1.62958	−0.0545930
$892$	7.31293	0.244855
$893$	−3.99146	−0.133569
$894$	−5.96672	−0.199557
$895$	−6.73389	−0.225089
$896$	4.30069	0.143676
$897$	−2.11901	−0.0707518
$898$	23.8800	0.796885
$899$	52.9512	1.76602
$900$	9.89948	0.329983
$901$	−0.132947	−0.00442910
$902$	4.73522	0.157665
$903$	−17.0885	−0.568671
$904$	−13.5418	−0.450393
$905$	−3.16506	−0.105210
$906$	7.73358	0.256931
$907$	−21.2662	−0.706133	−0.353067	−	0.935598i	$-0.614861\pi$
$907$	−21.2662	−0.706133	−0.353067	+	0.935598i	$0.614861\pi$
$908$	7.49736	0.248809
$909$	20.7533	0.688345
$910$	−14.6907	−0.486990
$911$	−13.8890	−0.460164	−0.230082	−	0.973171i	$-0.573899\pi$
$911$	−13.8890	−0.460164	−0.230082	+	0.973171i	$0.573899\pi$
$912$	−5.03279	−0.166652
$913$	0.274230	0.00907570
$914$	−3.36625	−0.111346
$915$	7.04728	0.232976
$916$	−22.2152	−0.734011
$917$	−88.8723	−2.93482
$918$	1.17864	0.0389011
$919$	−32.7378	−1.07992	−0.539960	−	0.841691i	$-0.681561\pi$
$919$	−32.7378	−1.07992	−0.539960	+	0.841691i	$0.681561\pi$
$920$	0.251769	0.00830059
$921$	3.14017	0.103472
$922$	−27.7553	−0.914073
$923$	−1.02459	−0.0337249
$924$	−3.23705	−0.106491
$925$	−14.3922	−0.473211
$926$	28.8211	0.947119
$927$	−9.64928	−0.316924
$928$	−6.26185	−0.205555
$929$	7.79703	0.255812	0.127906	−	0.991786i	$-0.459174\pi$
$929$	7.79703	0.255812	0.127906	+	0.991786i	$0.459174\pi$
$930$	4.80692	0.157625
$931$	62.4234	2.04585
$932$	10.7762	0.352987
$933$	−7.56394	−0.247632
$934$	18.1652	0.594382
$935$	0.123205	0.00402923
$936$	−11.9241	−0.389751
$937$	−7.89602	−0.257952	−0.128976	−	0.991648i	$-0.541169\pi$
$937$	−7.89602	−0.257952	−0.128976	+	0.991648i	$0.541169\pi$
$938$	−29.2345	−0.954541
$939$	2.94469	0.0960962
$940$	−0.450833	−0.0147045
$941$	−40.8241	−1.33083	−0.665414	−	0.746475i	$-0.731745\pi$
$941$	−40.8241	−1.33083	−0.665414	+	0.746475i	$0.731745\pi$
$942$	−2.20708	−0.0719106
$943$	−2.39358	−0.0779456
$944$	3.05642	0.0994779
$945$	−12.5683	−0.408846
$946$	−3.48151	−0.113194
$947$	−45.4382	−1.47654	−0.738272	−	0.674503i	$-0.764358\pi$
$947$	−45.4382	−1.47654	−0.738272	+	0.674503i	$0.764358\pi$
$948$	−13.4649	−0.437320
$949$	−47.5384	−1.54316
$950$	25.1077	0.814601
$951$	−22.1001	−0.716644
$952$	−1.06383	−0.0344788
$953$	−31.4201	−1.01780	−0.508898	−	0.860827i	$-0.669947\pi$
$953$	−31.4201	−1.01780	−0.508898	+	0.860827i	$0.669947\pi$
$954$	1.15068	0.0372547
$955$	−13.9887	−0.452663
$956$	−16.2655	−0.526065
$957$	4.71318	0.152355
$958$	36.4654	1.17814
$959$	40.6938	1.31407
$960$	−0.568452	−0.0183467
$961$	40.5066	1.30667
$962$	17.3356	0.558921
$963$	−35.9972	−1.15999
$964$	22.9590	0.739458
$965$	15.3244	0.493310
$966$	1.63628	0.0526463
$967$	14.8848	0.478664	0.239332	−	0.970938i	$-0.423072\pi$
$967$	14.8848	0.478664	0.239332	+	0.970938i	$0.423072\pi$
$968$	10.3405	0.332356
$969$	1.24492	0.0399927
$970$	0.433081	0.0139054
$971$	−24.6156	−0.789951	−0.394976	−	0.918692i	$-0.629247\pi$
$971$	−24.6156	−0.789951	−0.394976	+	0.918692i	$0.629247\pi$
$972$	−16.1544	−0.518153
$973$	29.5282	0.946631
$974$	32.8608	1.05293
$975$	−23.8683	−0.764398
$976$	−12.3973	−0.396829
$977$	17.9162	0.573190	0.286595	−	0.958052i	$-0.407477\pi$
$977$	17.9162	0.573190	0.286595	+	0.958052i	$0.407477\pi$
$978$	15.6692	0.501044
$979$	14.6275	0.467497
$980$	7.05069	0.225226
$981$	−25.8686	−0.825922
$982$	11.8666	0.378678
$983$	−59.3441	−1.89278	−0.946392	−	0.323022i	$-0.895301\pi$
$983$	−59.3441	−1.89278	−0.946392	+	0.323022i	$0.895301\pi$
$984$	5.40429	0.172282
$985$	−3.58825	−0.114331
$986$	1.54894	0.0493284
$987$	−2.93001	−0.0932634
$988$	−30.2426	−0.962145
$989$	1.75985	0.0559600
$990$	−1.06636	−0.0338912
$991$	−18.3182	−0.581897	−0.290948	−	0.956739i	$-0.593971\pi$
$991$	−18.3182	−0.581897	−0.290948	+	0.956739i	$0.593971\pi$
$992$	−8.45616	−0.268483
$993$	−17.3179	−0.549568
$994$	0.791179	0.0250947
$995$	9.21394	0.292102
$996$	0.312978	0.00991709
$997$	11.4964	0.364095	0.182047	−	0.983290i	$-0.441728\pi$
$997$	11.4964	0.364095	0.182047	+	0.983290i	$0.441728\pi$
$998$	3.50427	0.110926
$999$	14.8311	0.469235

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1226.2.a.e.1.7	✓	17
4.3	odd	2		9808.2.a.f.1.11		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1226.2.a.e.1.7	✓	17	1.1	even	1	trivial
9808.2.a.f.1.11		17	4.3	odd	2

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:	\( N \)	\(=\)	\( 1226 = 2 \cdot 613 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1226.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.926840 q^{3} +1.00000 q^{4} +0.613322 q^{5} +0.926840 q^{6} -4.30069 q^{7} -1.00000 q^{8} -2.14097 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.926840 q^{3} +1.00000 q^{4} +0.613322 q^{5} +0.926840 q^{6} -4.30069 q^{7} -1.00000 q^{8} -2.14097 q^{9} -0.613322 q^{10} -0.812094 q^{11} -0.926840 q^{12} -5.56948 q^{13} +4.30069 q^{14} -0.568452 q^{15} +1.00000 q^{16} -0.247362 q^{17} +2.14097 q^{18} +5.43006 q^{19} +0.613322 q^{20} +3.98605 q^{21} +0.812094 q^{22} -0.410501 q^{23} +0.926840 q^{24} -4.62384 q^{25} +5.56948 q^{26} +4.76486 q^{27} -4.30069 q^{28} +6.26185 q^{29} +0.568452 q^{30} +8.45616 q^{31} -1.00000 q^{32} +0.752681 q^{33} +0.247362 q^{34} -2.63771 q^{35} -2.14097 q^{36} +3.11260 q^{37} -5.43006 q^{38} +5.16202 q^{39} -0.613322 q^{40} +5.83087 q^{41} -3.98605 q^{42} -4.28708 q^{43} -0.812094 q^{44} -1.31310 q^{45} +0.410501 q^{46} -0.735067 q^{47} -0.926840 q^{48} +11.4959 q^{49} +4.62384 q^{50} +0.229265 q^{51} -5.56948 q^{52} +0.537458 q^{53} -4.76486 q^{54} -0.498075 q^{55} +4.30069 q^{56} -5.03279 q^{57} -6.26185 q^{58} +3.05642 q^{59} -0.568452 q^{60} -12.3973 q^{61} -8.45616 q^{62} +9.20763 q^{63} +1.00000 q^{64} -3.41588 q^{65} -0.752681 q^{66} -6.79764 q^{67} -0.247362 q^{68} +0.380469 q^{69} +2.63771 q^{70} +0.183966 q^{71} +2.14097 q^{72} +8.53553 q^{73} -3.11260 q^{74} +4.28556 q^{75} +5.43006 q^{76} +3.49256 q^{77} -5.16202 q^{78} +14.5278 q^{79} +0.613322 q^{80} +2.00664 q^{81} -5.83087 q^{82} -0.337683 q^{83} +3.98605 q^{84} -0.151713 q^{85} +4.28708 q^{86} -5.80373 q^{87} +0.812094 q^{88} -18.0121 q^{89} +1.31310 q^{90} +23.9526 q^{91} -0.410501 q^{92} -7.83751 q^{93} +0.735067 q^{94} +3.33037 q^{95} +0.926840 q^{96} -0.706123 q^{97} -11.4959 q^{98} +1.73867 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 17 q^{2} + 4 q^{3} + 17 q^{4} - 5 q^{5} - 4 q^{6} + 7 q^{7} - 17 q^{8} + 21 q^{9}+O(q^{10}) \) 17 * q - 17 * q^2 + 4 * q^3 + 17 * q^4 - 5 * q^5 - 4 * q^6 + 7 * q^7 - 17 * q^8 + 21 * q^9	\( 17 q - 17 q^{2} + 4 q^{3} + 17 q^{4} - 5 q^{5} - 4 q^{6} + 7 q^{7} - 17 q^{8} + 21 q^{9} + 5 q^{10} + 8 q^{11} + 4 q^{12} + 9 q^{13} - 7 q^{14} - 4 q^{15} + 17 q^{16} - q^{17} - 21 q^{18} + 32 q^{19} - 5 q^{20} + 6 q^{21} - 8 q^{22} - 5 q^{23} - 4 q^{24} + 30 q^{25} - 9 q^{26} + 16 q^{27} + 7 q^{28} + 3 q^{29} + 4 q^{30} + 27 q^{31} - 17 q^{32} - 14 q^{33} + q^{34} + 25 q^{35} + 21 q^{36} + 7 q^{37} - 32 q^{38} + 27 q^{39} + 5 q^{40} - 2 q^{41} - 6 q^{42} + 36 q^{43} + 8 q^{44} - q^{45} + 5 q^{46} - 3 q^{47} + 4 q^{48} + 52 q^{49} - 30 q^{50} + 40 q^{51} + 9 q^{52} - 20 q^{53} - 16 q^{54} + 48 q^{55} - 7 q^{56} + 12 q^{57} - 3 q^{58} + 34 q^{59} - 4 q^{60} + 49 q^{61} - 27 q^{62} + 27 q^{63} + 17 q^{64} - 6 q^{65} + 14 q^{66} + 36 q^{67} - q^{68} + 18 q^{69} - 25 q^{70} - q^{71} - 21 q^{72} + 24 q^{73} - 7 q^{74} + 35 q^{75} + 32 q^{76} - 6 q^{77} - 27 q^{78} + 43 q^{79} - 5 q^{80} + 37 q^{81} + 2 q^{82} + 10 q^{83} + 6 q^{84} + 16 q^{85} - 36 q^{86} + 28 q^{87} - 8 q^{88} - 12 q^{89} + q^{90} + 42 q^{91} - 5 q^{92} + 3 q^{93} + 3 q^{94} - 10 q^{95} - 4 q^{96} + 26 q^{97} - 52 q^{98} + 34 q^{99}+O(q^{100}) \) 17 * q - 17 * q^2 + 4 * q^3 + 17 * q^4 - 5 * q^5 - 4 * q^6 + 7 * q^7 - 17 * q^8 + 21 * q^9 + 5 * q^10 + 8 * q^11 + 4 * q^12 + 9 * q^13 - 7 * q^14 - 4 * q^15 + 17 * q^16 - q^17 - 21 * q^18 + 32 * q^19 - 5 * q^20 + 6 * q^21 - 8 * q^22 - 5 * q^23 - 4 * q^24 + 30 * q^25 - 9 * q^26 + 16 * q^27 + 7 * q^28 + 3 * q^29 + 4 * q^30 + 27 * q^31 - 17 * q^32 - 14 * q^33 + q^34 + 25 * q^35 + 21 * q^36 + 7 * q^37 - 32 * q^38 + 27 * q^39 + 5 * q^40 - 2 * q^41 - 6 * q^42 + 36 * q^43 + 8 * q^44 - q^45 + 5 * q^46 - 3 * q^47 + 4 * q^48 + 52 * q^49 - 30 * q^50 + 40 * q^51 + 9 * q^52 - 20 * q^53 - 16 * q^54 + 48 * q^55 - 7 * q^56 + 12 * q^57 - 3 * q^58 + 34 * q^59 - 4 * q^60 + 49 * q^61 - 27 * q^62 + 27 * q^63 + 17 * q^64 - 6 * q^65 + 14 * q^66 + 36 * q^67 - q^68 + 18 * q^69 - 25 * q^70 - q^71 - 21 * q^72 + 24 * q^73 - 7 * q^74 + 35 * q^75 + 32 * q^76 - 6 * q^77 - 27 * q^78 + 43 * q^79 - 5 * q^80 + 37 * q^81 + 2 * q^82 + 10 * q^83 + 6 * q^84 + 16 * q^85 - 36 * q^86 + 28 * q^87 - 8 * q^88 - 12 * q^89 + q^90 + 42 * q^91 - 5 * q^92 + 3 * q^93 + 3 * q^94 - 10 * q^95 - 4 * q^96 + 26 * q^97 - 52 * q^98 + 34 * q^99

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