LMFDB - Embedded newform 5290.2.a.be.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5290,2,Mod(1,5290)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5290, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("5290.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5290 = 2 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5290.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:	$42.2408626693$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.252973568.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 11x^{4} + 18x^{3} + 19x^{2} - 20x + 4 $ x^6 - 2x^5 - 11x^4 + 18x^3 + 19x^2 - 20*x + 4
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			1.2
Root			$2.14320$ of defining polynomial
Character	$\chi$	$=$	5290.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.14320 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.14320 q^{6} +3.62422 q^{7} -1.00000 q^{8} +1.59329 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.14320 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.14320 q^{6} +3.62422 q^{7} -1.00000 q^{8} +1.59329 q^{9} +1.00000 q^{10} -5.65190 q^{11} -2.14320 q^{12} -0.701307 q^{13} -3.62422 q^{14} +2.14320 q^{15} +1.00000 q^{16} +5.75992 q^{17} -1.59329 q^{18} -2.95455 q^{19} -1.00000 q^{20} -7.76742 q^{21} +5.65190 q^{22} +2.14320 q^{24} +1.00000 q^{25} +0.701307 q^{26} +3.01486 q^{27} +3.62422 q^{28} +0.108020 q^{29} -2.14320 q^{30} -2.03263 q^{31} -1.00000 q^{32} +12.1131 q^{33} -5.75992 q^{34} -3.62422 q^{35} +1.59329 q^{36} -2.92292 q^{37} +2.95455 q^{38} +1.50304 q^{39} +1.00000 q^{40} +8.21568 q^{41} +7.76742 q^{42} +7.57058 q^{43} -5.65190 q^{44} -1.59329 q^{45} -10.2794 q^{47} -2.14320 q^{48} +6.13499 q^{49} -1.00000 q^{50} -12.3446 q^{51} -0.701307 q^{52} -6.83903 q^{53} -3.01486 q^{54} +5.65190 q^{55} -3.62422 q^{56} +6.33219 q^{57} -0.108020 q^{58} -5.41182 q^{59} +2.14320 q^{60} +7.06611 q^{61} +2.03263 q^{62} +5.77443 q^{63} +1.00000 q^{64} +0.701307 q^{65} -12.1131 q^{66} -15.0179 q^{67} +5.75992 q^{68} +3.62422 q^{70} +10.1553 q^{71} -1.59329 q^{72} +1.89490 q^{73} +2.92292 q^{74} -2.14320 q^{75} -2.95455 q^{76} -20.4837 q^{77} -1.50304 q^{78} +9.07568 q^{79} -1.00000 q^{80} -11.2413 q^{81} -8.21568 q^{82} +15.2530 q^{83} -7.76742 q^{84} -5.75992 q^{85} -7.57058 q^{86} -0.231507 q^{87} +5.65190 q^{88} +2.95606 q^{89} +1.59329 q^{90} -2.54169 q^{91} +4.35633 q^{93} +10.2794 q^{94} +2.95455 q^{95} +2.14320 q^{96} +0.0397873 q^{97} -6.13499 q^{98} -9.00510 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - 6 q^{5} + 2 q^{6} - 2 q^{7} - 6 q^{8} + 8 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 6 * q^5 + 2 * q^6 - 2 * q^7 - 6 * q^8 + 8 * q^9	\( 6 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - 6 q^{5} + 2 q^{6} - 2 q^{7} - 6 q^{8} + 8 q^{9} + 6 q^{10} - 10 q^{11} - 2 q^{12} - 2 q^{13} + 2 q^{14} + 2 q^{15} + 6 q^{16} + 10 q^{17} - 8 q^{18} - 2 q^{19} - 6 q^{20} - 12 q^{21} + 10 q^{22} + 2 q^{24} + 6 q^{25} + 2 q^{26} - 8 q^{27} - 2 q^{28} - 2 q^{30} - 2 q^{31} - 6 q^{32} + 22 q^{33} - 10 q^{34} + 2 q^{35} + 8 q^{36} + 4 q^{37} + 2 q^{38} + 24 q^{39} + 6 q^{40} + 6 q^{41} + 12 q^{42} - 12 q^{43} - 10 q^{44} - 8 q^{45} + 8 q^{47} - 2 q^{48} + 8 q^{49} - 6 q^{50} - 34 q^{51} - 2 q^{52} - 36 q^{53} + 8 q^{54} + 10 q^{55} + 2 q^{56} - 32 q^{57} + 16 q^{59} + 2 q^{60} + 10 q^{61} + 2 q^{62} + 48 q^{63} + 6 q^{64} + 2 q^{65} - 22 q^{66} - 16 q^{67} + 10 q^{68} - 2 q^{70} - 2 q^{71} - 8 q^{72} + 4 q^{73} - 4 q^{74} - 2 q^{75} - 2 q^{76} - 16 q^{77} - 24 q^{78} + 20 q^{79} - 6 q^{80} + 34 q^{81} - 6 q^{82} - 8 q^{83} - 12 q^{84} - 10 q^{85} + 12 q^{86} - 12 q^{87} + 10 q^{88} - 12 q^{89} + 8 q^{90} - 38 q^{91} - 28 q^{93} - 8 q^{94} + 2 q^{95} + 2 q^{96} - 2 q^{97} - 8 q^{98} - 50 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 6 * q^5 + 2 * q^6 - 2 * q^7 - 6 * q^8 + 8 * q^9 + 6 * q^10 - 10 * q^11 - 2 * q^12 - 2 * q^13 + 2 * q^14 + 2 * q^15 + 6 * q^16 + 10 * q^17 - 8 * q^18 - 2 * q^19 - 6 * q^20 - 12 * q^21 + 10 * q^22 + 2 * q^24 + 6 * q^25 + 2 * q^26 - 8 * q^27 - 2 * q^28 - 2 * q^30 - 2 * q^31 - 6 * q^32 + 22 * q^33 - 10 * q^34 + 2 * q^35 + 8 * q^36 + 4 * q^37 + 2 * q^38 + 24 * q^39 + 6 * q^40 + 6 * q^41 + 12 * q^42 - 12 * q^43 - 10 * q^44 - 8 * q^45 + 8 * q^47 - 2 * q^48 + 8 * q^49 - 6 * q^50 - 34 * q^51 - 2 * q^52 - 36 * q^53 + 8 * q^54 + 10 * q^55 + 2 * q^56 - 32 * q^57 + 16 * q^59 + 2 * q^60 + 10 * q^61 + 2 * q^62 + 48 * q^63 + 6 * q^64 + 2 * q^65 - 22 * q^66 - 16 * q^67 + 10 * q^68 - 2 * q^70 - 2 * q^71 - 8 * q^72 + 4 * q^73 - 4 * q^74 - 2 * q^75 - 2 * q^76 - 16 * q^77 - 24 * q^78 + 20 * q^79 - 6 * q^80 + 34 * q^81 - 6 * q^82 - 8 * q^83 - 12 * q^84 - 10 * q^85 + 12 * q^86 - 12 * q^87 + 10 * q^88 - 12 * q^89 + 8 * q^90 - 38 * q^91 - 28 * q^93 - 8 * q^94 + 2 * q^95 + 2 * q^96 - 2 * q^97 - 8 * q^98 - 50 * 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
$3$	−2.14320	−1.23737	−0.618687	−	0.785637i	$-0.712335\pi$
$3$	−2.14320	−1.23737	−0.618687	+	0.785637i	$0.712335\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.14320	0.874956
$7$	3.62422	1.36983	0.684914	−	0.728624i	$-0.259840\pi$
$7$	3.62422	1.36983	0.684914	+	0.728624i	$0.259840\pi$
$8$	−1.00000	−0.353553
$9$	1.59329	0.531096
$10$	1.00000	0.316228
$11$	−5.65190	−1.70411	−0.852056	−	0.523451i	$-0.824644\pi$
$11$	−5.65190	−1.70411	−0.852056	+	0.523451i	$0.824644\pi$
$12$	−2.14320	−0.618687
$13$	−0.701307	−0.194507	−0.0972537	−	0.995260i	$-0.531006\pi$
$13$	−0.701307	−0.194507	−0.0972537	+	0.995260i	$0.531006\pi$
$14$	−3.62422	−0.968614
$15$	2.14320	0.553371
$16$	1.00000	0.250000
$17$	5.75992	1.39699	0.698493	−	0.715617i	$-0.253854\pi$
$17$	5.75992	1.39699	0.698493	+	0.715617i	$0.253854\pi$
$18$	−1.59329	−0.375541
$19$	−2.95455	−0.677821	−0.338911	−	0.940819i	$-0.610058\pi$
$19$	−2.95455	−0.677821	−0.338911	+	0.940819i	$0.610058\pi$
$20$	−1.00000	−0.223607
$21$	−7.76742	−1.69499
$22$	5.65190	1.20499
$23$	0	0
$23$	0	0
$24$	2.14320	0.437478
$25$	1.00000	0.200000
$26$	0.701307	0.137538
$27$	3.01486	0.580210
$28$	3.62422	0.684914
$29$	0.108020	0.0200588	0.0100294	−	0.999950i	$-0.496807\pi$
$29$	0.108020	0.0200588	0.0100294	+	0.999950i	$0.496807\pi$
$30$	−2.14320	−0.391292
$31$	−2.03263	−0.365071	−0.182536	−	0.983199i	$-0.558431\pi$
$31$	−2.03263	−0.365071	−0.182536	+	0.983199i	$0.558431\pi$
$32$	−1.00000	−0.176777
$33$	12.1131	2.10862
$34$	−5.75992	−0.987818
$35$	−3.62422	−0.612606
$36$	1.59329	0.265548
$37$	−2.92292	−0.480524	−0.240262	−	0.970708i	$-0.577233\pi$
$37$	−2.92292	−0.480524	−0.240262	+	0.970708i	$0.577233\pi$
$38$	2.95455	0.479292
$39$	1.50304	0.240679
$40$	1.00000	0.158114
$41$	8.21568	1.28307	0.641536	−	0.767093i	$-0.278297\pi$
$41$	8.21568	1.28307	0.641536	+	0.767093i	$0.278297\pi$
$42$	7.76742	1.19854
$43$	7.57058	1.15450	0.577251	−	0.816567i	$-0.304125\pi$
$43$	7.57058	1.15450	0.577251	+	0.816567i	$0.304125\pi$
$44$	−5.65190	−0.852056
$45$	−1.59329	−0.237513
$46$	0	0
$47$	−10.2794	−1.49940	−0.749701	−	0.661777i	$-0.769803\pi$
$47$	−10.2794	−1.49940	−0.749701	+	0.661777i	$0.769803\pi$
$48$	−2.14320	−0.309344
$49$	6.13499	0.876428
$50$	−1.00000	−0.141421
$51$	−12.3446	−1.72859
$52$	−0.701307	−0.0972537
$53$	−6.83903	−0.939414	−0.469707	−	0.882822i	$-0.655640\pi$
$53$	−6.83903	−0.939414	−0.469707	+	0.882822i	$0.655640\pi$
$54$	−3.01486	−0.410271
$55$	5.65190	0.762102
$56$	−3.62422	−0.484307
$57$	6.33219	0.838719
$58$	−0.108020	−0.0141837
$59$	−5.41182	−0.704558	−0.352279	−	0.935895i	$-0.614593\pi$
$59$	−5.41182	−0.704558	−0.352279	+	0.935895i	$0.614593\pi$
$60$	2.14320	0.276685
$61$	7.06611	0.904723	0.452361	−	0.891835i	$-0.350582\pi$
$61$	7.06611	0.904723	0.452361	+	0.891835i	$0.350582\pi$
$62$	2.03263	0.258144
$63$	5.77443	0.727509
$64$	1.00000	0.125000
$65$	0.701307	0.0869864
$66$	−12.1131	−1.49102
$67$	−15.0179	−1.83473	−0.917366	−	0.398044i	$-0.869689\pi$
$67$	−15.0179	−1.83473	−0.917366	+	0.398044i	$0.869689\pi$
$68$	5.75992	0.698493
$69$	0	0
$70$	3.62422	0.433178
$71$	10.1553	1.20521	0.602607	−	0.798038i	$-0.294128\pi$
$71$	10.1553	1.20521	0.602607	+	0.798038i	$0.294128\pi$
$72$	−1.59329	−0.187771
$73$	1.89490	0.221782	0.110891	−	0.993833i	$-0.464630\pi$
$73$	1.89490	0.221782	0.110891	+	0.993833i	$0.464630\pi$
$74$	2.92292	0.339782
$75$	−2.14320	−0.247475
$76$	−2.95455	−0.338911
$77$	−20.4837	−2.33434
$78$	−1.50304	−0.170185
$79$	9.07568	1.02109	0.510547	−	0.859850i	$-0.329443\pi$
$79$	9.07568	1.02109	0.510547	+	0.859850i	$0.329443\pi$
$80$	−1.00000	−0.111803
$81$	−11.2413	−1.24903
$82$	−8.21568	−0.907270
$83$	15.2530	1.67424	0.837119	−	0.547021i	$-0.184238\pi$
$83$	15.2530	1.67424	0.837119	+	0.547021i	$0.184238\pi$
$84$	−7.76742	−0.847495
$85$	−5.75992	−0.624751
$86$	−7.57058	−0.816356
$87$	−0.231507	−0.0248202
$88$	5.65190	0.602494
$89$	2.95606	0.313342	0.156671	−	0.987651i	$-0.449924\pi$
$89$	2.95606	0.313342	0.156671	+	0.987651i	$0.449924\pi$
$90$	1.59329	0.167947
$91$	−2.54169	−0.266442
$92$	0	0
$93$	4.35633	0.451730
$94$	10.2794	1.06024
$95$	2.95455	0.303131
$96$	2.14320	0.218739
$97$	0.0397873	0.00403979	0.00201990	−	0.999998i	$-0.499357\pi$
$97$	0.0397873	0.00403979	0.00201990	+	0.999998i	$0.499357\pi$
$98$	−6.13499	−0.619728
$99$	−9.00510	−0.905046
$100$	1.00000	0.100000
$101$	−15.5832	−1.55058	−0.775292	−	0.631603i	$-0.782397\pi$
$101$	−15.5832	−1.55058	−0.775292	+	0.631603i	$0.782397\pi$
$102$	12.3446	1.22230
$103$	−18.8929	−1.86157	−0.930784	−	0.365569i	$-0.880874\pi$
$103$	−18.8929	−1.86157	−0.930784	+	0.365569i	$0.880874\pi$
$104$	0.701307	0.0687688
$105$	7.76742	0.758022
$106$	6.83903	0.664266
$107$	−18.7351	−1.81119	−0.905597	−	0.424139i	$-0.860577\pi$
$107$	−18.7351	−1.81119	−0.905597	+	0.424139i	$0.860577\pi$
$108$	3.01486	0.290105
$109$	18.5471	1.77649	0.888247	−	0.459366i	$-0.151923\pi$
$109$	18.5471	1.77649	0.888247	+	0.459366i	$0.151923\pi$
$110$	−5.65190	−0.538887
$111$	6.26438	0.594589
$112$	3.62422	0.342457
$113$	19.7811	1.86085	0.930424	−	0.366486i	$-0.119439\pi$
$113$	19.7811	1.86085	0.930424	+	0.366486i	$0.119439\pi$
$114$	−6.33219	−0.593064
$115$	0	0
$116$	0.108020	0.0100294
$117$	−1.11738	−0.103302
$118$	5.41182	0.498198
$119$	20.8752	1.91363
$120$	−2.14320	−0.195646
$121$	20.9440	1.90400
$122$	−7.06611	−0.639736
$123$	−17.6078	−1.58764
$124$	−2.03263	−0.182536
$125$	−1.00000	−0.0894427
$126$	−5.77443	−0.514427
$127$	11.1184	0.986600	0.493300	−	0.869859i	$-0.335790\pi$
$127$	11.1184	0.986600	0.493300	+	0.869859i	$0.335790\pi$
$128$	−1.00000	−0.0883883
$129$	−16.2252	−1.42855
$130$	−0.701307	−0.0615087
$131$	−10.9195	−0.954043	−0.477022	−	0.878892i	$-0.658284\pi$
$131$	−10.9195	−0.954043	−0.477022	+	0.878892i	$0.658284\pi$
$132$	12.1131	1.05431
$133$	−10.7080	−0.928498
$134$	15.0179	1.29735
$135$	−3.01486	−0.259478
$136$	−5.75992	−0.493909
$137$	−20.0368	−1.71186	−0.855928	−	0.517095i	$-0.827013\pi$
$137$	−20.0368	−1.71186	−0.855928	+	0.517095i	$0.827013\pi$
$138$	0	0
$139$	−1.91324	−0.162279	−0.0811396	−	0.996703i	$-0.525856\pi$
$139$	−1.91324	−0.162279	−0.0811396	+	0.996703i	$0.525856\pi$
$140$	−3.62422	−0.306303
$141$	22.0307	1.85532
$142$	−10.1553	−0.852216
$143$	3.96371	0.331462
$144$	1.59329	0.132774
$145$	−0.108020	−0.00897055
$146$	−1.89490	−0.156823
$147$	−13.1485	−1.08447
$148$	−2.92292	−0.240262
$149$	4.90529	0.401857	0.200928	−	0.979606i	$-0.435604\pi$
$149$	4.90529	0.401857	0.200928	+	0.979606i	$0.435604\pi$
$150$	2.14320	0.174991
$151$	15.7568	1.28227	0.641136	−	0.767427i	$-0.278463\pi$
$151$	15.7568	1.28227	0.641136	+	0.767427i	$0.278463\pi$
$152$	2.95455	0.239646
$153$	9.17720	0.741933
$154$	20.4837	1.65063
$155$	2.03263	0.163265
$156$	1.50304	0.120339
$157$	3.37046	0.268992	0.134496	−	0.990914i	$-0.457058\pi$
$157$	3.37046	0.268992	0.134496	+	0.990914i	$0.457058\pi$
$158$	−9.07568	−0.722022
$159$	14.6574	1.16241
$160$	1.00000	0.0790569
$161$	0	0
$162$	11.2413	0.883200
$163$	20.0989	1.57427	0.787134	−	0.616783i	$-0.211564\pi$
$163$	20.0989	1.57427	0.787134	+	0.616783i	$0.211564\pi$
$164$	8.21568	0.641536
$165$	−12.1131	−0.943005
$166$	−15.2530	−1.18387
$167$	−3.02734	−0.234262	−0.117131	−	0.993116i	$-0.537370\pi$
$167$	−3.02734	−0.234262	−0.117131	+	0.993116i	$0.537370\pi$
$168$	7.76742	0.599269
$169$	−12.5082	−0.962167
$170$	5.75992	0.441766
$171$	−4.70745	−0.359988
$172$	7.57058	0.577251
$173$	−1.05450	−0.0801722	−0.0400861	−	0.999196i	$-0.512763\pi$
$173$	−1.05450	−0.0801722	−0.0400861	+	0.999196i	$0.512763\pi$
$174$	0.231507	0.0175505
$175$	3.62422	0.273966
$176$	−5.65190	−0.426028
$177$	11.5986	0.871803
$178$	−2.95606	−0.221566
$179$	−6.19889	−0.463327	−0.231663	−	0.972796i	$-0.574417\pi$
$179$	−6.19889	−0.463327	−0.231663	+	0.972796i	$0.574417\pi$
$180$	−1.59329	−0.118757
$181$	6.99109	0.519643	0.259822	−	0.965657i	$-0.416336\pi$
$181$	6.99109	0.519643	0.259822	+	0.965657i	$0.416336\pi$
$182$	2.54169	0.188403
$183$	−15.1441	−1.11948
$184$	0	0
$185$	2.92292	0.214897
$186$	−4.35633	−0.319421
$187$	−32.5545	−2.38062
$188$	−10.2794	−0.749701
$189$	10.9265	0.794788
$190$	−2.95455	−0.214346
$191$	−2.55965	−0.185210	−0.0926050	−	0.995703i	$-0.529519\pi$
$191$	−2.55965	−0.185210	−0.0926050	+	0.995703i	$0.529519\pi$
$192$	−2.14320	−0.154672
$193$	9.80330	0.705657	0.352829	−	0.935688i	$-0.385220\pi$
$193$	9.80330	0.705657	0.352829	+	0.935688i	$0.385220\pi$
$194$	−0.0397873	−0.00285656
$195$	−1.50304	−0.107635
$196$	6.13499	0.438214
$197$	4.99436	0.355833	0.177917	−	0.984046i	$-0.443064\pi$
$197$	4.99436	0.355833	0.177917	+	0.984046i	$0.443064\pi$
$198$	9.00510	0.639964
$199$	18.5829	1.31731	0.658654	−	0.752446i	$-0.271126\pi$
$199$	18.5829	1.31731	0.658654	+	0.752446i	$0.271126\pi$
$200$	−1.00000	−0.0707107
$201$	32.1864	2.27025
$202$	15.5832	1.09643
$203$	0.391488	0.0274770
$204$	−12.3446	−0.864297
$205$	−8.21568	−0.573808
$206$	18.8929	1.31633
$207$	0	0
$208$	−0.701307	−0.0486269
$209$	16.6988	1.15508
$210$	−7.76742	−0.536003
$211$	9.02953	0.621619	0.310809	−	0.950472i	$-0.399400\pi$
$211$	9.02953	0.621619	0.310809	+	0.950472i	$0.399400\pi$
$212$	−6.83903	−0.469707
$213$	−21.7648	−1.49130
$214$	18.7351	1.28071
$215$	−7.57058	−0.516309
$216$	−3.01486	−0.205135
$217$	−7.36671	−0.500085
$218$	−18.5471	−1.25617
$219$	−4.06115	−0.274427
$220$	5.65190	0.381051
$221$	−4.03947	−0.271724
$222$	−6.26438	−0.420438
$223$	2.43215	0.162868	0.0814342	−	0.996679i	$-0.474050\pi$
$223$	2.43215	0.162868	0.0814342	+	0.996679i	$0.474050\pi$
$224$	−3.62422	−0.242154
$225$	1.59329	0.106219
$226$	−19.7811	−1.31582
$227$	−3.14282	−0.208597	−0.104298	−	0.994546i	$-0.533260\pi$
$227$	−3.14282	−0.208597	−0.104298	+	0.994546i	$0.533260\pi$
$228$	6.33219	0.419359
$229$	−2.57758	−0.170331	−0.0851655	−	0.996367i	$-0.527142\pi$
$229$	−2.57758	−0.170331	−0.0851655	+	0.996367i	$0.527142\pi$
$230$	0	0
$231$	43.9007	2.88845
$232$	−0.108020	−0.00709184
$233$	−15.2254	−0.997451	−0.498726	−	0.866760i	$-0.666198\pi$
$233$	−15.2254	−0.997451	−0.498726	+	0.866760i	$0.666198\pi$
$234$	1.11738	0.0730456
$235$	10.2794	0.670553
$236$	−5.41182	−0.352279
$237$	−19.4510	−1.26348
$238$	−20.8752	−1.35314
$239$	−13.0119	−0.841672	−0.420836	−	0.907137i	$-0.638263\pi$
$239$	−13.0119	−0.841672	−0.420836	+	0.907137i	$0.638263\pi$
$240$	2.14320	0.138343
$241$	−7.36585	−0.474476	−0.237238	−	0.971452i	$-0.576242\pi$
$241$	−7.36585	−0.474476	−0.237238	+	0.971452i	$0.576242\pi$
$242$	−20.9440	−1.34633
$243$	15.0477	0.965311
$244$	7.06611	0.452361
$245$	−6.13499	−0.391950
$246$	17.6078	1.12263
$247$	2.07205	0.131841
$248$	2.03263	0.129072
$249$	−32.6902	−2.07166
$250$	1.00000	0.0632456
$251$	−14.9747	−0.945193	−0.472596	−	0.881279i	$-0.656683\pi$
$251$	−14.9747	−0.945193	−0.472596	+	0.881279i	$0.656683\pi$
$252$	5.77443	0.363755
$253$	0	0
$254$	−11.1184	−0.697632
$255$	12.3446	0.773051
$256$	1.00000	0.0625000
$257$	−15.8440	−0.988319	−0.494160	−	0.869371i	$-0.664524\pi$
$257$	−15.8440	−0.988319	−0.494160	+	0.869371i	$0.664524\pi$
$258$	16.2252	1.01014
$259$	−10.5933	−0.658236
$260$	0.701307	0.0434932
$261$	0.172106	0.0106531
$262$	10.9195	0.674611
$263$	−16.4581	−1.01485	−0.507426	−	0.861696i	$-0.669403\pi$
$263$	−16.4581	−1.01485	−0.507426	+	0.861696i	$0.669403\pi$
$264$	−12.1131	−0.745511
$265$	6.83903	0.420119
$266$	10.7080	0.656547
$267$	−6.33541	−0.387721
$268$	−15.0179	−0.917366
$269$	19.5034	1.18915	0.594573	−	0.804042i	$-0.297321\pi$
$269$	19.5034	1.18915	0.594573	+	0.804042i	$0.297321\pi$
$270$	3.01486	0.183479
$271$	−17.6799	−1.07398	−0.536988	−	0.843590i	$-0.680438\pi$
$271$	−17.6799	−1.07398	−0.536988	+	0.843590i	$0.680438\pi$
$272$	5.75992	0.349246
$273$	5.44734	0.329688
$274$	20.0368	1.21046
$275$	−5.65190	−0.340822
$276$	0	0
$277$	−10.4314	−0.626759	−0.313380	−	0.949628i	$-0.601461\pi$
$277$	−10.4314	−0.626759	−0.313380	+	0.949628i	$0.601461\pi$
$278$	1.91324	0.114749
$279$	−3.23856	−0.193888
$280$	3.62422	0.216589
$281$	−18.9887	−1.13277	−0.566386	−	0.824140i	$-0.691659\pi$
$281$	−18.9887	−1.13277	−0.566386	+	0.824140i	$0.691659\pi$
$282$	−22.0307	−1.31191
$283$	8.72453	0.518620	0.259310	−	0.965794i	$-0.416505\pi$
$283$	8.72453	0.518620	0.259310	+	0.965794i	$0.416505\pi$
$284$	10.1553	0.602607
$285$	−6.33219	−0.375086
$286$	−3.96371	−0.234379
$287$	29.7754	1.75759
$288$	−1.59329	−0.0938853
$289$	16.1767	0.951568
$290$	0.108020	0.00634314
$291$	−0.0852720	−0.00499873
$292$	1.89490	0.110891
$293$	−21.0909	−1.23214	−0.616071	−	0.787690i	$-0.711277\pi$
$293$	−21.0909	−1.23214	−0.616071	+	0.787690i	$0.711277\pi$
$294$	13.1485	0.766835
$295$	5.41182	0.315088
$296$	2.92292	0.169891
$297$	−17.0397	−0.988743
$298$	−4.90529	−0.284156
$299$	0	0
$300$	−2.14320	−0.123737
$301$	27.4375	1.58147
$302$	−15.7568	−0.906703
$303$	33.3978	1.91865
$304$	−2.95455	−0.169455
$305$	−7.06611	−0.404604
$306$	−9.17720	−0.524626
$307$	3.81306	0.217623	0.108812	−	0.994062i	$-0.465295\pi$
$307$	3.81306	0.217623	0.108812	+	0.994062i	$0.465295\pi$
$308$	−20.4837	−1.16717
$309$	40.4911	2.30346
$310$	−2.03263	−0.115446
$311$	30.0329	1.70301	0.851503	−	0.524349i	$-0.175691\pi$
$311$	30.0329	1.70301	0.851503	+	0.524349i	$0.175691\pi$
$312$	−1.50304	−0.0850927
$313$	−4.92191	−0.278203	−0.139101	−	0.990278i	$-0.544421\pi$
$313$	−4.92191	−0.278203	−0.139101	+	0.990278i	$0.544421\pi$
$314$	−3.37046	−0.190206
$315$	−5.77443	−0.325352
$316$	9.07568	0.510547
$317$	−15.0206	−0.843638	−0.421819	−	0.906680i	$-0.638608\pi$
$317$	−15.0206	−0.843638	−0.421819	+	0.906680i	$0.638608\pi$
$318$	−14.6574	−0.821945
$319$	−0.610517	−0.0341824
$320$	−1.00000	−0.0559017
$321$	40.1531	2.24113
$322$	0	0
$323$	−17.0180	−0.946906
$324$	−11.2413	−0.624517
$325$	−0.701307	−0.0389015
$326$	−20.0989	−1.11317
$327$	−39.7501	−2.19819
$328$	−8.21568	−0.453635
$329$	−37.2548	−2.05392
$330$	12.1131	0.666805
$331$	19.8388	1.09044	0.545221	−	0.838293i	$-0.316446\pi$
$331$	19.8388	1.09044	0.545221	+	0.838293i	$0.316446\pi$
$332$	15.2530	0.837119
$333$	−4.65704	−0.255204
$334$	3.02734	0.165649
$335$	15.0179	0.820517
$336$	−7.76742	−0.423747
$337$	−15.8819	−0.865143	−0.432571	−	0.901600i	$-0.642394\pi$
$337$	−15.8819	−0.865143	−0.432571	+	0.901600i	$0.642394\pi$
$338$	12.5082	0.680355
$339$	−42.3947	−2.30256
$340$	−5.75992	−0.312375
$341$	11.4882	0.622122
$342$	4.70745	0.254550
$343$	−3.13498	−0.169273
$344$	−7.57058	−0.408178
$345$	0	0
$346$	1.05450	0.0566903
$347$	−16.3479	−0.877602	−0.438801	−	0.898584i	$-0.644597\pi$
$347$	−16.3479	−0.877602	−0.438801	+	0.898584i	$0.644597\pi$
$348$	−0.231507	−0.0124101
$349$	−8.66167	−0.463648	−0.231824	−	0.972758i	$-0.574469\pi$
$349$	−8.66167	−0.463648	−0.231824	+	0.972758i	$0.574469\pi$
$350$	−3.62422	−0.193723
$351$	−2.11434	−0.112855
$352$	5.65190	0.301247
$353$	21.7992	1.16026	0.580128	−	0.814526i	$-0.303003\pi$
$353$	21.7992	1.16026	0.580128	+	0.814526i	$0.303003\pi$
$354$	−11.5986	−0.616458
$355$	−10.1553	−0.538989
$356$	2.95606	0.156671
$357$	−44.7397	−2.36788
$358$	6.19889	0.327622
$359$	−36.7307	−1.93857	−0.969285	−	0.245940i	$-0.920903\pi$
$359$	−36.7307	−1.93857	−0.969285	+	0.245940i	$0.920903\pi$
$360$	1.59329	0.0839736
$361$	−10.2706	−0.540558
$362$	−6.99109	−0.367443
$363$	−44.8870	−2.35596
$364$	−2.54169	−0.133221
$365$	−1.89490	−0.0991838
$366$	15.1441	0.791593
$367$	−26.7231	−1.39494	−0.697468	−	0.716616i	$-0.745690\pi$
$367$	−26.7231	−1.39494	−0.697468	+	0.716616i	$0.745690\pi$
$368$	0	0
$369$	13.0899	0.681434
$370$	−2.92292	−0.151955
$371$	−24.7862	−1.28683
$372$	4.35633	0.225865
$373$	10.4703	0.542131	0.271065	−	0.962561i	$-0.412624\pi$
$373$	10.4703	0.542131	0.271065	+	0.962561i	$0.412624\pi$
$374$	32.5545	1.68335
$375$	2.14320	0.110674
$376$	10.2794	0.530119
$377$	−0.0757550	−0.00390158
$378$	−10.9265	−0.562000
$379$	−28.6874	−1.47357	−0.736787	−	0.676125i	$-0.763658\pi$
$379$	−28.6874	−1.47357	−0.736787	+	0.676125i	$0.763658\pi$
$380$	2.95455	0.151565
$381$	−23.8289	−1.22079
$382$	2.55965	0.130963
$383$	−32.7748	−1.67471	−0.837357	−	0.546656i	$-0.815900\pi$
$383$	−32.7748	−1.67471	−0.837357	+	0.546656i	$0.815900\pi$
$384$	2.14320	0.109369
$385$	20.4837	1.04395
$386$	−9.80330	−0.498975
$387$	12.0621	0.613151
$388$	0.0397873	0.00201990
$389$	7.92228	0.401675	0.200838	−	0.979625i	$-0.435634\pi$
$389$	7.92228	0.401675	0.200838	+	0.979625i	$0.435634\pi$
$390$	1.50304	0.0761093
$391$	0	0
$392$	−6.13499	−0.309864
$393$	23.4027	1.18051
$394$	−4.99436	−0.251612
$395$	−9.07568	−0.456647
$396$	−9.00510	−0.452523
$397$	−2.11254	−0.106025	−0.0530126	−	0.998594i	$-0.516882\pi$
$397$	−2.11254	−0.106025	−0.0530126	+	0.998594i	$0.516882\pi$
$398$	−18.5829	−0.931477
$399$	22.9493	1.14890
$400$	1.00000	0.0500000
$401$	−7.66365	−0.382704	−0.191352	−	0.981521i	$-0.561287\pi$
$401$	−7.66365	−0.382704	−0.191352	+	0.981521i	$0.561287\pi$
$402$	−32.1864	−1.60531
$403$	1.42550	0.0710091
$404$	−15.5832	−0.775292
$405$	11.2413	0.558585
$406$	−0.391488	−0.0194292
$407$	16.5200	0.818867
$408$	12.3446	0.611150
$409$	−11.0602	−0.546891	−0.273445	−	0.961888i	$-0.588163\pi$
$409$	−11.0602	−0.546891	−0.273445	+	0.961888i	$0.588163\pi$
$410$	8.21568	0.405743
$411$	42.9427	2.11821
$412$	−18.8929	−0.930784
$413$	−19.6136	−0.965124
$414$	0	0
$415$	−15.2530	−0.748742
$416$	0.701307	0.0343844
$417$	4.10045	0.200800
$418$	−16.6988	−0.816767
$419$	−29.0798	−1.42064	−0.710320	−	0.703879i	$-0.751450\pi$
$419$	−29.0798	−1.42064	−0.710320	+	0.703879i	$0.751450\pi$
$420$	7.76742	0.379011
$421$	−12.8151	−0.624572	−0.312286	−	0.949988i	$-0.601095\pi$
$421$	−12.8151	−0.624572	−0.312286	+	0.949988i	$0.601095\pi$
$422$	−9.02953	−0.439551
$423$	−16.3780	−0.796326
$424$	6.83903	0.332133
$425$	5.75992	0.279397
$426$	21.7648	1.05451
$427$	25.6092	1.23931
$428$	−18.7351	−0.905597
$429$	−8.49501	−0.410143
$430$	7.57058	0.365086
$431$	−17.2129	−0.829117	−0.414559	−	0.910023i	$-0.636064\pi$
$431$	−17.2129	−0.829117	−0.414559	+	0.910023i	$0.636064\pi$
$432$	3.01486	0.145053
$433$	−28.6378	−1.37625	−0.688123	−	0.725594i	$-0.741565\pi$
$433$	−28.6378	−1.37625	−0.688123	+	0.725594i	$0.741565\pi$
$434$	7.36671	0.353613
$435$	0.231507	0.0110999
$436$	18.5471	0.888247
$437$	0	0
$438$	4.06115	0.194049
$439$	−12.1307	−0.578968	−0.289484	−	0.957183i	$-0.593484\pi$
$439$	−12.1307	−0.578968	−0.289484	+	0.957183i	$0.593484\pi$
$440$	−5.65190	−0.269444
$441$	9.77480	0.465467
$442$	4.03947	0.192138
$443$	−2.26916	−0.107811	−0.0539056	−	0.998546i	$-0.517167\pi$
$443$	−2.26916	−0.107811	−0.0539056	+	0.998546i	$0.517167\pi$
$444$	6.26438	0.297294
$445$	−2.95606	−0.140131
$446$	−2.43215	−0.115165
$447$	−10.5130	−0.497247
$448$	3.62422	0.171228
$449$	−1.70442	−0.0804366	−0.0402183	−	0.999191i	$-0.512805\pi$
$449$	−1.70442	−0.0804366	−0.0402183	+	0.999191i	$0.512805\pi$
$450$	−1.59329	−0.0751083
$451$	−46.4342	−2.18650
$452$	19.7811	0.930424
$453$	−33.7700	−1.58665
$454$	3.14282	0.147500
$455$	2.54169	0.119156
$456$	−6.33219	−0.296532
$457$	10.8806	0.508972	0.254486	−	0.967077i	$-0.418094\pi$
$457$	10.8806	0.508972	0.254486	+	0.967077i	$0.418094\pi$
$458$	2.57758	0.120442
$459$	17.3654	0.810545
$460$	0	0
$461$	−25.4457	−1.18512	−0.592562	−	0.805525i	$-0.701883\pi$
$461$	−25.4457	−1.18512	−0.592562	+	0.805525i	$0.701883\pi$
$462$	−43.9007	−2.04244
$463$	14.0114	0.651165	0.325582	−	0.945514i	$-0.394440\pi$
$463$	14.0114	0.651165	0.325582	+	0.945514i	$0.394440\pi$
$464$	0.108020	0.00501469
$465$	−4.35633	−0.202020
$466$	15.2254	0.705305
$467$	−38.6762	−1.78972	−0.894860	−	0.446347i	$-0.852725\pi$
$467$	−38.6762	−1.78972	−0.894860	+	0.446347i	$0.852725\pi$
$468$	−1.11738	−0.0516510
$469$	−54.4283	−2.51327
$470$	−10.2794	−0.474153
$471$	−7.22356	−0.332844
$472$	5.41182	0.249099
$473$	−42.7881	−1.96740
$474$	19.4510	0.893412
$475$	−2.95455	−0.135564
$476$	20.8752	0.956815
$477$	−10.8965	−0.498918
$478$	13.0119	0.595152
$479$	−24.2801	−1.10939	−0.554694	−	0.832055i	$-0.687165\pi$
$479$	−24.2801	−1.10939	−0.554694	+	0.832055i	$0.687165\pi$
$480$	−2.14320	−0.0978230
$481$	2.04986	0.0934656
$482$	7.36585	0.335505
$483$	0	0
$484$	20.9440	0.951998
$485$	−0.0397873	−0.00180665
$486$	−15.0477	−0.682578
$487$	5.92164	0.268335	0.134167	−	0.990959i	$-0.457164\pi$
$487$	5.92164	0.268335	0.134167	+	0.990959i	$0.457164\pi$
$488$	−7.06611	−0.319868
$489$	−43.0759	−1.94796
$490$	6.13499	0.277151
$491$	−19.1979	−0.866389	−0.433195	−	0.901300i	$-0.642614\pi$
$491$	−19.1979	−0.866389	−0.433195	+	0.901300i	$0.642614\pi$
$492$	−17.6078	−0.793821
$493$	0.622185	0.0280218
$494$	−2.07205	−0.0932259
$495$	9.00510	0.404749
$496$	−2.03263	−0.0912678
$497$	36.8052	1.65094
$498$	32.6902	1.46488
$499$	12.9910	0.581557	0.290779	−	0.956790i	$-0.406086\pi$
$499$	12.9910	0.581557	0.290779	+	0.956790i	$0.406086\pi$
$500$	−1.00000	−0.0447214
$501$	6.48818	0.289870
$502$	14.9747	0.668352
$503$	−22.9622	−1.02383	−0.511916	−	0.859036i	$-0.671064\pi$
$503$	−22.9622	−1.02383	−0.511916	+	0.859036i	$0.671064\pi$
$504$	−5.77443	−0.257213
$505$	15.5832	0.693442
$506$	0	0
$507$	26.8075	1.19056
$508$	11.1184	0.493300
$509$	40.4517	1.79299	0.896496	−	0.443052i	$-0.146104\pi$
$509$	40.4517	1.79299	0.896496	+	0.443052i	$0.146104\pi$
$510$	−12.3446	−0.546629
$511$	6.86755	0.303803
$512$	−1.00000	−0.0441942
$513$	−8.90757	−0.393279
$514$	15.8440	0.698847
$515$	18.8929	0.832519
$516$	−16.2252	−0.714276
$517$	58.0980	2.55515
$518$	10.5933	0.465443
$519$	2.26000	0.0992031
$520$	−0.701307	−0.0307543
$521$	9.15633	0.401146	0.200573	−	0.979679i	$-0.435720\pi$
$521$	9.15633	0.401146	0.200573	+	0.979679i	$0.435720\pi$
$522$	−0.172106	−0.00753289
$523$	6.31248	0.276025	0.138013	−	0.990430i	$-0.455929\pi$
$523$	6.31248	0.276025	0.138013	+	0.990430i	$0.455929\pi$
$524$	−10.9195	−0.477022
$525$	−7.76742	−0.338998
$526$	16.4581	0.717608
$527$	−11.7078	−0.509999
$528$	12.1131	0.527156
$529$	0	0
$530$	−6.83903	−0.297069
$531$	−8.62258	−0.374188
$532$	−10.7080	−0.464249
$533$	−5.76171	−0.249567
$534$	6.33541	0.274160
$535$	18.7351	0.809991
$536$	15.0179	0.648676
$537$	13.2854	0.573309
$538$	−19.5034	−0.840853
$539$	−34.6744	−1.49353
$540$	−3.01486	−0.129739
$541$	21.9234	0.942562	0.471281	−	0.881983i	$-0.343792\pi$
$541$	21.9234	0.942562	0.471281	+	0.881983i	$0.343792\pi$
$542$	17.6799	0.759416
$543$	−14.9833	−0.642994
$544$	−5.75992	−0.246954
$545$	−18.5471	−0.794472
$546$	−5.44734	−0.233125
$547$	−10.4619	−0.447317	−0.223658	−	0.974668i	$-0.571800\pi$
$547$	−10.4619	−0.447317	−0.223658	+	0.974668i	$0.571800\pi$
$548$	−20.0368	−0.855928
$549$	11.2583	0.480494
$550$	5.65190	0.240998
$551$	−0.319150	−0.0135963
$552$	0	0
$553$	32.8923	1.39872
$554$	10.4314	0.443186
$555$	−6.26438	−0.265908
$556$	−1.91324	−0.0811396
$557$	9.75719	0.413425	0.206713	−	0.978402i	$-0.433723\pi$
$557$	9.75719	0.413425	0.206713	+	0.978402i	$0.433723\pi$
$558$	3.23856	0.137099
$559$	−5.30929	−0.224559
$560$	−3.62422	−0.153151
$561$	69.7706	2.94572
$562$	18.9887	0.800990
$563$	−19.8031	−0.834603	−0.417301	−	0.908768i	$-0.637024\pi$
$563$	−19.8031	−0.834603	−0.417301	+	0.908768i	$0.637024\pi$
$564$	22.0307	0.927661
$565$	−19.7811	−0.832196
$566$	−8.72453	−0.366719
$567$	−40.7410	−1.71096
$568$	−10.1553	−0.426108
$569$	0.0887021	0.00371858	0.00185929	−	0.999998i	$-0.499408\pi$
$569$	0.0887021	0.00371858	0.00185929	+	0.999998i	$0.499408\pi$
$570$	6.33219	0.265226
$571$	−33.7514	−1.41245	−0.706226	−	0.707986i	$-0.749604\pi$
$571$	−33.7514	−1.41245	−0.706226	+	0.707986i	$0.749604\pi$
$572$	3.96371	0.165731
$573$	5.48583	0.229174
$574$	−29.7754	−1.24280
$575$	0	0
$576$	1.59329	0.0663870
$577$	−25.9768	−1.08143	−0.540714	−	0.841207i	$-0.681846\pi$
$577$	−25.9768	−1.08143	−0.540714	+	0.841207i	$0.681846\pi$
$578$	−16.1767	−0.672860
$579$	−21.0104	−0.873162
$580$	−0.108020	−0.00448528
$581$	55.2804	2.29342
$582$	0.0852720	0.00353464
$583$	38.6535	1.60087
$584$	−1.89490	−0.0784117
$585$	1.11738	0.0461981
$586$	21.0909	0.871257
$587$	−6.51747	−0.269005	−0.134502	−	0.990913i	$-0.542944\pi$
$587$	−6.51747	−0.269005	−0.134502	+	0.990913i	$0.542944\pi$
$588$	−13.1485	−0.542235
$589$	6.00552	0.247453
$590$	−5.41182	−0.222801
$591$	−10.7039	−0.440299
$592$	−2.92292	−0.120131
$593$	42.3735	1.74007	0.870035	−	0.492991i	$-0.164096\pi$
$593$	42.3735	1.74007	0.870035	+	0.492991i	$0.164096\pi$
$594$	17.0397	0.699147
$595$	−20.8752	−0.855801
$596$	4.90529	0.200928
$597$	−39.8268	−1.63000
$598$	0	0
$599$	−37.6611	−1.53879	−0.769396	−	0.638772i	$-0.779443\pi$
$599$	−37.6611	−1.53879	−0.769396	+	0.638772i	$0.779443\pi$
$600$	2.14320	0.0874956
$601$	13.0609	0.532765	0.266383	−	0.963867i	$-0.414171\pi$
$601$	13.0609	0.532765	0.266383	+	0.963867i	$0.414171\pi$
$602$	−27.4375	−1.11827
$603$	−23.9279	−0.974418
$604$	15.7568	0.641136
$605$	−20.9440	−0.851493
$606$	−33.3978	−1.35669
$607$	−12.9234	−0.524546	−0.262273	−	0.964994i	$-0.584472\pi$
$607$	−12.9234	−0.524546	−0.262273	+	0.964994i	$0.584472\pi$
$608$	2.95455	0.119823
$609$	−0.839034	−0.0339994
$610$	7.06611	0.286099
$611$	7.20900	0.291645
$612$	9.17720	0.370966
$613$	−34.9885	−1.41317	−0.706586	−	0.707627i	$-0.749766\pi$
$613$	−34.9885	−1.41317	−0.706586	+	0.707627i	$0.749766\pi$
$614$	−3.81306	−0.153883
$615$	17.6078	0.710015
$616$	20.4837	0.825313
$617$	−10.9082	−0.439148	−0.219574	−	0.975596i	$-0.570467\pi$
$617$	−10.9082	−0.439148	−0.219574	+	0.975596i	$0.570467\pi$
$618$	−40.4911	−1.62879
$619$	−10.3314	−0.415255	−0.207627	−	0.978208i	$-0.566574\pi$
$619$	−10.3314	−0.415255	−0.207627	+	0.978208i	$0.566574\pi$
$620$	2.03263	0.0816324
$621$	0	0
$622$	−30.0329	−1.20421
$623$	10.7134	0.429224
$624$	1.50304	0.0601696
$625$	1.00000	0.0400000
$626$	4.92191	0.196719
$627$	−35.7889	−1.42927
$628$	3.37046	0.134496
$629$	−16.8358	−0.671286
$630$	5.77443	0.230059
$631$	14.7605	0.587605	0.293803	−	0.955866i	$-0.405079\pi$
$631$	14.7605	0.587605	0.293803	+	0.955866i	$0.405079\pi$
$632$	−9.07568	−0.361011
$633$	−19.3521	−0.769175
$634$	15.0206	0.596542
$635$	−11.1184	−0.441221
$636$	14.6574	0.581203
$637$	−4.30251	−0.170472
$638$	0.610517	0.0241706
$639$	16.1803	0.640084
$640$	1.00000	0.0395285
$641$	−4.26896	−0.168614	−0.0843070	−	0.996440i	$-0.526868\pi$
$641$	−4.26896	−0.168614	−0.0843070	+	0.996440i	$0.526868\pi$
$642$	−40.1531	−1.58472
$643$	−7.91513	−0.312142	−0.156071	−	0.987746i	$-0.549883\pi$
$643$	−7.91513	−0.312142	−0.156071	+	0.987746i	$0.549883\pi$
$644$	0	0
$645$	16.2252	0.638868
$646$	17.0180	0.669564
$647$	23.5732	0.926757	0.463379	−	0.886160i	$-0.346637\pi$
$647$	23.5732	0.926757	0.463379	+	0.886160i	$0.346637\pi$
$648$	11.2413	0.441600
$649$	30.5870	1.20065
$650$	0.701307	0.0275075
$651$	15.7883	0.618792
$652$	20.0989	0.787134
$653$	8.34034	0.326383	0.163191	−	0.986594i	$-0.447821\pi$
$653$	8.34034	0.326383	0.163191	+	0.986594i	$0.447821\pi$
$654$	39.7501	1.55435
$655$	10.9195	0.426661
$656$	8.21568	0.320768
$657$	3.01912	0.117787
$658$	37.2548	1.45234
$659$	29.4295	1.14641	0.573204	−	0.819412i	$-0.305700\pi$
$659$	29.4295	1.14641	0.573204	+	0.819412i	$0.305700\pi$
$660$	−12.1131	−0.471503
$661$	−13.1410	−0.511126	−0.255563	−	0.966792i	$-0.582261\pi$
$661$	−13.1410	−0.511126	−0.255563	+	0.966792i	$0.582261\pi$
$662$	−19.8388	−0.771059
$663$	8.65737	0.336224
$664$	−15.2530	−0.591933
$665$	10.7080	0.415237
$666$	4.65704	0.180457
$667$	0	0
$668$	−3.02734	−0.117131
$669$	−5.21256	−0.201529
$670$	−15.0179	−0.580193
$671$	−39.9369	−1.54175
$672$	7.76742	0.299635
$673$	20.9503	0.807573	0.403786	−	0.914853i	$-0.367694\pi$
$673$	20.9503	0.807573	0.403786	+	0.914853i	$0.367694\pi$
$674$	15.8819	0.611748
$675$	3.01486	0.116042
$676$	−12.5082	−0.481083
$677$	−6.04395	−0.232288	−0.116144	−	0.993232i	$-0.537053\pi$
$677$	−6.04395	−0.232288	−0.116144	+	0.993232i	$0.537053\pi$
$678$	42.3947	1.62816
$679$	0.144198	0.00553382
$680$	5.75992	0.220883
$681$	6.73569	0.258112
$682$	−11.4882	−0.439907
$683$	37.0179	1.41645	0.708225	−	0.705987i	$-0.249496\pi$
$683$	37.0179	1.41645	0.708225	+	0.705987i	$0.249496\pi$
$684$	−4.70745	−0.179994
$685$	20.0368	0.765565
$686$	3.13498	0.119694
$687$	5.52425	0.210763
$688$	7.57058	0.288625
$689$	4.79626	0.182723
$690$	0	0
$691$	9.61281	0.365688	0.182844	−	0.983142i	$-0.441470\pi$
$691$	9.61281	0.365688	0.182844	+	0.983142i	$0.441470\pi$
$692$	−1.05450	−0.0400861
$693$	−32.6365	−1.23976
$694$	16.3479	0.620559
$695$	1.91324	0.0725735
$696$	0.231507	0.00877527
$697$	47.3216	1.79243
$698$	8.66167	0.327849
$699$	32.6311	1.23422
$700$	3.62422	0.136983
$701$	−33.1202	−1.25093	−0.625467	−	0.780251i	$-0.715091\pi$
$701$	−33.1202	−1.25093	−0.625467	+	0.780251i	$0.715091\pi$
$702$	2.11434	0.0798007
$703$	8.63592	0.325710
$704$	−5.65190	−0.213014
$705$	−22.0307	−0.829725
$706$	−21.7992	−0.820424
$707$	−56.4769	−2.12403
$708$	11.5986	0.435901
$709$	27.5989	1.03650	0.518250	−	0.855229i	$-0.326584\pi$
$709$	27.5989	1.03650	0.518250	+	0.855229i	$0.326584\pi$
$710$	10.1553	0.381122
$711$	14.4602	0.542298
$712$	−2.95606	−0.110783
$713$	0	0
$714$	44.7397	1.67434
$715$	−3.96371	−0.148234
$716$	−6.19889	−0.231663
$717$	27.8871	1.04146
$718$	36.7307	1.37078
$719$	−6.25376	−0.233226	−0.116613	−	0.993177i	$-0.537204\pi$
$719$	−6.25376	−0.233226	−0.116613	+	0.993177i	$0.537204\pi$
$720$	−1.59329	−0.0593783
$721$	−68.4719	−2.55003
$722$	10.2706	0.382232
$723$	15.7865	0.587105
$724$	6.99109	0.259822
$725$	0.108020	0.00401175
$726$	44.8870	1.66591
$727$	−21.4421	−0.795242	−0.397621	−	0.917550i	$-0.630164\pi$
$727$	−21.4421	−0.795242	−0.397621	+	0.917550i	$0.630164\pi$
$728$	2.54169	0.0942014
$729$	1.47370	0.0545814
$730$	1.89490	0.0701335
$731$	43.6059	1.61282
$732$	−15.1441	−0.559741
$733$	5.15218	0.190300	0.0951500	−	0.995463i	$-0.469667\pi$
$733$	5.15218	0.190300	0.0951500	+	0.995463i	$0.469667\pi$
$734$	26.7231	0.986368
$735$	13.1485	0.484989
$736$	0	0
$737$	84.8798	3.12659
$738$	−13.0899	−0.481847
$739$	41.3781	1.52212	0.761059	−	0.648682i	$-0.224680\pi$
$739$	41.3781	1.52212	0.761059	+	0.648682i	$0.224680\pi$
$740$	2.92292	0.107449
$741$	−4.44081	−0.163137
$742$	24.7862	0.909930
$743$	32.8302	1.20442	0.602211	−	0.798337i	$-0.294286\pi$
$743$	32.8302	1.20442	0.602211	+	0.798337i	$0.294286\pi$
$744$	−4.35633	−0.159711
$745$	−4.90529	−0.179716
$746$	−10.4703	−0.383344
$747$	24.3025	0.889181
$748$	−32.5545	−1.19031
$749$	−67.9003	−2.48102
$750$	−2.14320	−0.0782584
$751$	−15.1276	−0.552015	−0.276008	−	0.961155i	$-0.589012\pi$
$751$	−15.1276	−0.552015	−0.276008	+	0.961155i	$0.589012\pi$
$752$	−10.2794	−0.374851
$753$	32.0937	1.16956
$754$	0.0757550	0.00275883
$755$	−15.7568	−0.573450
$756$	10.9265	0.397394
$757$	−11.4986	−0.417922	−0.208961	−	0.977924i	$-0.567008\pi$
$757$	−11.4986	−0.417922	−0.208961	+	0.977924i	$0.567008\pi$
$758$	28.6874	1.04197
$759$	0	0
$760$	−2.95455	−0.107173
$761$	25.3630	0.919407	0.459704	−	0.888072i	$-0.347956\pi$
$761$	25.3630	0.919407	0.459704	+	0.888072i	$0.347956\pi$
$762$	23.8289	0.863231
$763$	67.2190	2.43349
$764$	−2.55965	−0.0926050
$765$	−9.17720	−0.331802
$766$	32.7748	1.18420
$767$	3.79534	0.137042
$768$	−2.14320	−0.0773359
$769$	−3.16577	−0.114160	−0.0570802	−	0.998370i	$-0.518179\pi$
$769$	−3.16577	−0.114160	−0.0570802	+	0.998370i	$0.518179\pi$
$770$	−20.4837	−0.738183
$771$	33.9567	1.22292
$772$	9.80330	0.352829
$773$	16.1893	0.582289	0.291144	−	0.956679i	$-0.405964\pi$
$773$	16.1893	0.582289	0.291144	+	0.956679i	$0.405964\pi$
$774$	−12.0621	−0.433563
$775$	−2.03263	−0.0730143
$776$	−0.0397873	−0.00142828
$777$	22.7035	0.814484
$778$	−7.92228	−0.284027
$779$	−24.2737	−0.869694
$780$	−1.50304	−0.0538174
$781$	−57.3968	−2.05382
$782$	0	0
$783$	0.325664	0.0116383
$784$	6.13499	0.219107
$785$	−3.37046	−0.120297
$786$	−23.4027	−0.834746
$787$	47.9770	1.71019	0.855097	−	0.518468i	$-0.173497\pi$
$787$	47.9770	1.71019	0.855097	+	0.518468i	$0.173497\pi$
$788$	4.99436	0.177917
$789$	35.2730	1.25575
$790$	9.07568	0.322898
$791$	71.6910	2.54904
$792$	9.00510	0.319982
$793$	−4.95551	−0.175975
$794$	2.11254	0.0749711
$795$	−14.6574	−0.519844
$796$	18.5829	0.658654
$797$	3.56358	0.126228	0.0631142	−	0.998006i	$-0.479897\pi$
$797$	3.56358	0.126228	0.0631142	+	0.998006i	$0.479897\pi$
$798$	−22.9493	−0.812395
$799$	−59.2084	−2.09464
$800$	−1.00000	−0.0353553
$801$	4.70985	0.166414
$802$	7.66365	0.270613
$803$	−10.7098	−0.377941
$804$	32.1864	1.13513
$805$	0	0
$806$	−1.42550	−0.0502110
$807$	−41.7997	−1.47142
$808$	15.5832	0.548214
$809$	38.7389	1.36199	0.680994	−	0.732289i	$-0.261548\pi$
$809$	38.7389	1.36199	0.680994	+	0.732289i	$0.261548\pi$
$810$	−11.2413	−0.394979
$811$	17.0303	0.598013	0.299007	−	0.954251i	$-0.403345\pi$
$811$	17.0303	0.598013	0.299007	+	0.954251i	$0.403345\pi$
$812$	0.391488	0.0137385
$813$	37.8914	1.32891
$814$	−16.5200	−0.579027
$815$	−20.0989	−0.704034
$816$	−12.3446	−0.432149
$817$	−22.3677	−0.782546
$818$	11.0602	0.386710
$819$	−4.04964	−0.141506
$820$	−8.21568	−0.286904
$821$	10.6529	0.371790	0.185895	−	0.982570i	$-0.440482\pi$
$821$	10.6529	0.371790	0.185895	+	0.982570i	$0.440482\pi$
$822$	−42.9427	−1.49780
$823$	−36.6760	−1.27844	−0.639222	−	0.769022i	$-0.720744\pi$
$823$	−36.6760	−1.27844	−0.639222	+	0.769022i	$0.720744\pi$
$824$	18.8929	0.658164
$825$	12.1131	0.421725
$826$	19.6136	0.682445
$827$	−15.8686	−0.551804	−0.275902	−	0.961186i	$-0.588977\pi$
$827$	−15.8686	−0.551804	−0.275902	+	0.961186i	$0.588977\pi$
$828$	0	0
$829$	−15.4316	−0.535961	−0.267981	−	0.963424i	$-0.586356\pi$
$829$	−15.4316	−0.535961	−0.267981	+	0.963424i	$0.586356\pi$
$830$	15.2530	0.529441
$831$	22.3564	0.775536
$832$	−0.701307	−0.0243134
$833$	35.3371	1.22436
$834$	−4.10045	−0.141987
$835$	3.02734	0.104765
$836$	16.6988	0.577542
$837$	−6.12810	−0.211818
$838$	29.0798	1.00454
$839$	42.5730	1.46978	0.734891	−	0.678185i	$-0.237233\pi$
$839$	42.5730	1.46978	0.734891	+	0.678185i	$0.237233\pi$
$840$	−7.76742	−0.268001
$841$	−28.9883	−0.999598
$842$	12.8151	0.441639
$843$	40.6965	1.40166
$844$	9.02953	0.310809
$845$	12.5082	0.430294
$846$	16.3780	0.563087
$847$	75.9056	2.60815
$848$	−6.83903	−0.234853
$849$	−18.6984	−0.641727
$850$	−5.75992	−0.197564
$851$	0	0
$852$	−21.7648	−0.745651
$853$	−46.9390	−1.60716	−0.803580	−	0.595196i	$-0.797074\pi$
$853$	−46.9390	−1.60716	−0.803580	+	0.595196i	$0.797074\pi$
$854$	−25.6092	−0.876328
$855$	4.70745	0.160992
$856$	18.7351	0.640354
$857$	−7.28247	−0.248764	−0.124382	−	0.992234i	$-0.539695\pi$
$857$	−7.28247	−0.248764	−0.124382	+	0.992234i	$0.539695\pi$
$858$	8.49501	0.290015
$859$	−14.7861	−0.504495	−0.252248	−	0.967663i	$-0.581170\pi$
$859$	−14.7861	−0.504495	−0.252248	+	0.967663i	$0.581170\pi$
$860$	−7.57058	−0.258154
$861$	−63.8146	−2.17480
$862$	17.2129	0.586275
$863$	4.10510	0.139739	0.0698696	−	0.997556i	$-0.477742\pi$
$863$	4.10510	0.139739	0.0698696	+	0.997556i	$0.477742\pi$
$864$	−3.01486	−0.102568
$865$	1.05450	0.0358541
$866$	28.6378	0.973153
$867$	−34.6697	−1.17745
$868$	−7.36671	−0.250042
$869$	−51.2948	−1.74006
$870$	−0.231507	−0.00784884
$871$	10.5322	0.356869
$872$	−18.5471	−0.628085
$873$	0.0633926	0.00214552
$874$	0	0
$875$	−3.62422	−0.122521
$876$	−4.06115	−0.137213
$877$	−15.6429	−0.528224	−0.264112	−	0.964492i	$-0.585079\pi$
$877$	−15.6429	−0.528224	−0.264112	+	0.964492i	$0.585079\pi$
$878$	12.1307	0.409392
$879$	45.2019	1.52462
$880$	5.65190	0.190525
$881$	23.5955	0.794953	0.397476	−	0.917612i	$-0.369886\pi$
$881$	23.5955	0.794953	0.397476	+	0.917612i	$0.369886\pi$
$882$	−9.77480	−0.329135
$883$	−42.7284	−1.43792	−0.718962	−	0.695049i	$-0.755383\pi$
$883$	−42.7284	−1.43792	−0.718962	+	0.695049i	$0.755383\pi$
$884$	−4.03947	−0.135862
$885$	−11.5986	−0.389882
$886$	2.26916	0.0762340
$887$	−4.03265	−0.135403	−0.0677015	−	0.997706i	$-0.521567\pi$
$887$	−4.03265	−0.135403	−0.0677015	+	0.997706i	$0.521567\pi$
$888$	−6.26438	−0.210219
$889$	40.2956	1.35147
$890$	2.95606	0.0990873
$891$	63.5347	2.12849
$892$	2.43215	0.0814342
$893$	30.3710	1.01633
$894$	10.5130	0.351607
$895$	6.19889	0.207206
$896$	−3.62422	−0.121077
$897$	0	0
$898$	1.70442	0.0568772
$899$	−0.219564	−0.00732288
$900$	1.59329	0.0531096
$901$	−39.3923	−1.31235
$902$	46.4342	1.54609
$903$	−58.8038	−1.95687
$904$	−19.7811	−0.657909
$905$	−6.99109	−0.232392
$906$	33.7700	1.12193
$907$	32.9469	1.09398	0.546992	−	0.837138i	$-0.315773\pi$
$907$	32.9469	1.09398	0.546992	+	0.837138i	$0.315773\pi$
$908$	−3.14282	−0.104298
$909$	−24.8285	−0.823509
$910$	−2.54169	−0.0842563
$911$	2.80548	0.0929497	0.0464749	−	0.998919i	$-0.485201\pi$
$911$	2.80548	0.0929497	0.0464749	+	0.998919i	$0.485201\pi$
$912$	6.33219	0.209680
$913$	−86.2086	−2.85309
$914$	−10.8806	−0.359897
$915$	15.1441	0.500647
$916$	−2.57758	−0.0851655
$917$	−39.5748	−1.30688
$918$	−17.3654	−0.573142
$919$	−42.7489	−1.41015	−0.705077	−	0.709130i	$-0.749088\pi$
$919$	−42.7489	−1.41015	−0.705077	+	0.709130i	$0.749088\pi$
$920$	0	0
$921$	−8.17214	−0.269281
$922$	25.4457	0.838009
$923$	−7.12199	−0.234423
$924$	43.9007	1.44423
$925$	−2.92292	−0.0961049
$926$	−14.0114	−0.460443
$927$	−30.1017	−0.988671
$928$	−0.108020	−0.00354592
$929$	45.5563	1.49465	0.747327	−	0.664456i	$-0.231337\pi$
$929$	45.5563	1.49465	0.747327	+	0.664456i	$0.231337\pi$
$930$	4.35633	0.142850
$931$	−18.1262	−0.594061
$932$	−15.2254	−0.498726
$933$	−64.3663	−2.10726
$934$	38.6762	1.26552
$935$	32.5545	1.06465
$936$	1.11738	0.0365228
$937$	3.62593	0.118454	0.0592270	−	0.998245i	$-0.481136\pi$
$937$	3.62593	0.118454	0.0592270	+	0.998245i	$0.481136\pi$
$938$	54.4283	1.77715
$939$	10.5486	0.344241
$940$	10.2794	0.335276
$941$	31.7504	1.03503	0.517517	−	0.855673i	$-0.326856\pi$
$941$	31.7504	1.03503	0.517517	+	0.855673i	$0.326856\pi$
$942$	7.22356	0.235356
$943$	0	0
$944$	−5.41182	−0.176140
$945$	−10.9265	−0.355440
$946$	42.7881	1.39116
$947$	−34.3408	−1.11593	−0.557963	−	0.829866i	$-0.688417\pi$
$947$	−34.3408	−1.11593	−0.557963	+	0.829866i	$0.688417\pi$
$948$	−19.4510	−0.631738
$949$	−1.32891	−0.0431382
$950$	2.95455	0.0958584
$951$	32.1920	1.04390
$952$	−20.8752	−0.676570
$953$	23.9256	0.775027	0.387513	−	0.921864i	$-0.373334\pi$
$953$	23.9256	0.775027	0.387513	+	0.921864i	$0.373334\pi$
$954$	10.8965	0.352789
$955$	2.55965	0.0828284
$956$	−13.0119	−0.420836
$957$	1.30846	0.0422964
$958$	24.2801	0.784455
$959$	−72.6177	−2.34495
$960$	2.14320	0.0691713
$961$	−26.8684	−0.866723
$962$	−2.04986	−0.0660902
$963$	−29.8505	−0.961917
$964$	−7.36585	−0.237238
$965$	−9.80330	−0.315580
$966$	0	0
$967$	−44.1277	−1.41905	−0.709526	−	0.704679i	$-0.751091\pi$
$967$	−44.1277	−1.41905	−0.709526	+	0.704679i	$0.751091\pi$
$968$	−20.9440	−0.673164
$969$	36.4729	1.17168
$970$	0.0397873	0.00127749
$971$	−26.8795	−0.862605	−0.431302	−	0.902207i	$-0.641946\pi$
$971$	−26.8795	−0.862605	−0.431302	+	0.902207i	$0.641946\pi$
$972$	15.0477	0.482656
$973$	−6.93402	−0.222294
$974$	−5.92164	−0.189741
$975$	1.50304	0.0481357
$976$	7.06611	0.226181
$977$	−6.17896	−0.197682	−0.0988412	−	0.995103i	$-0.531514\pi$
$977$	−6.17896	−0.197682	−0.0988412	+	0.995103i	$0.531514\pi$
$978$	43.0759	1.37741
$979$	−16.7073	−0.533969
$980$	−6.13499	−0.195975
$981$	29.5509	0.943488
$982$	19.1979	0.612630
$983$	16.5719	0.528562	0.264281	−	0.964446i	$-0.414865\pi$
$983$	16.5719	0.528562	0.264281	+	0.964446i	$0.414865\pi$
$984$	17.6078	0.561316
$985$	−4.99436	−0.159133
$986$	−0.622185	−0.0198144
$987$	79.8443	2.54147
$988$	2.07205	0.0659207
$989$	0	0
$990$	−9.00510	−0.286201
$991$	−48.0855	−1.52749	−0.763744	−	0.645520i	$-0.776641\pi$
$991$	−48.0855	−1.52749	−0.763744	+	0.645520i	$0.776641\pi$
$992$	2.03263	0.0645361
$993$	−42.5185	−1.34928
$994$	−36.8052	−1.16739
$995$	−18.5829	−0.589118
$996$	−32.6902	−1.03583
$997$	−41.2167	−1.30535	−0.652673	−	0.757640i	$-0.726353\pi$
$997$	−41.2167	−1.30535	−0.652673	+	0.757640i	$0.726353\pi$
$998$	−12.9910	−0.411223
$999$	−8.81219	−0.278805

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5290.2.a.be.1.2	✓	6
23.22	odd	2		5290.2.a.bf.1.2	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5290.2.a.be.1.2	✓	6	1.1	even	1	trivial
5290.2.a.bf.1.2	yes	6	23.22	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:	\( N \)	\(=\)	\( 5290 = 2 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5290.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.14320 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.14320 q^{6} +3.62422 q^{7} -1.00000 q^{8} +1.59329 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.14320 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.14320 q^{6} +3.62422 q^{7} -1.00000 q^{8} +1.59329 q^{9} +1.00000 q^{10} -5.65190 q^{11} -2.14320 q^{12} -0.701307 q^{13} -3.62422 q^{14} +2.14320 q^{15} +1.00000 q^{16} +5.75992 q^{17} -1.59329 q^{18} -2.95455 q^{19} -1.00000 q^{20} -7.76742 q^{21} +5.65190 q^{22} +2.14320 q^{24} +1.00000 q^{25} +0.701307 q^{26} +3.01486 q^{27} +3.62422 q^{28} +0.108020 q^{29} -2.14320 q^{30} -2.03263 q^{31} -1.00000 q^{32} +12.1131 q^{33} -5.75992 q^{34} -3.62422 q^{35} +1.59329 q^{36} -2.92292 q^{37} +2.95455 q^{38} +1.50304 q^{39} +1.00000 q^{40} +8.21568 q^{41} +7.76742 q^{42} +7.57058 q^{43} -5.65190 q^{44} -1.59329 q^{45} -10.2794 q^{47} -2.14320 q^{48} +6.13499 q^{49} -1.00000 q^{50} -12.3446 q^{51} -0.701307 q^{52} -6.83903 q^{53} -3.01486 q^{54} +5.65190 q^{55} -3.62422 q^{56} +6.33219 q^{57} -0.108020 q^{58} -5.41182 q^{59} +2.14320 q^{60} +7.06611 q^{61} +2.03263 q^{62} +5.77443 q^{63} +1.00000 q^{64} +0.701307 q^{65} -12.1131 q^{66} -15.0179 q^{67} +5.75992 q^{68} +3.62422 q^{70} +10.1553 q^{71} -1.59329 q^{72} +1.89490 q^{73} +2.92292 q^{74} -2.14320 q^{75} -2.95455 q^{76} -20.4837 q^{77} -1.50304 q^{78} +9.07568 q^{79} -1.00000 q^{80} -11.2413 q^{81} -8.21568 q^{82} +15.2530 q^{83} -7.76742 q^{84} -5.75992 q^{85} -7.57058 q^{86} -0.231507 q^{87} +5.65190 q^{88} +2.95606 q^{89} +1.59329 q^{90} -2.54169 q^{91} +4.35633 q^{93} +10.2794 q^{94} +2.95455 q^{95} +2.14320 q^{96} +0.0397873 q^{97} -6.13499 q^{98} -9.00510 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - 6 q^{5} + 2 q^{6} - 2 q^{7} - 6 q^{8} + 8 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 6 * q^5 + 2 * q^6 - 2 * q^7 - 6 * q^8 + 8 * q^9	\( 6 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - 6 q^{5} + 2 q^{6} - 2 q^{7} - 6 q^{8} + 8 q^{9} + 6 q^{10} - 10 q^{11} - 2 q^{12} - 2 q^{13} + 2 q^{14} + 2 q^{15} + 6 q^{16} + 10 q^{17} - 8 q^{18} - 2 q^{19} - 6 q^{20} - 12 q^{21} + 10 q^{22} + 2 q^{24} + 6 q^{25} + 2 q^{26} - 8 q^{27} - 2 q^{28} - 2 q^{30} - 2 q^{31} - 6 q^{32} + 22 q^{33} - 10 q^{34} + 2 q^{35} + 8 q^{36} + 4 q^{37} + 2 q^{38} + 24 q^{39} + 6 q^{40} + 6 q^{41} + 12 q^{42} - 12 q^{43} - 10 q^{44} - 8 q^{45} + 8 q^{47} - 2 q^{48} + 8 q^{49} - 6 q^{50} - 34 q^{51} - 2 q^{52} - 36 q^{53} + 8 q^{54} + 10 q^{55} + 2 q^{56} - 32 q^{57} + 16 q^{59} + 2 q^{60} + 10 q^{61} + 2 q^{62} + 48 q^{63} + 6 q^{64} + 2 q^{65} - 22 q^{66} - 16 q^{67} + 10 q^{68} - 2 q^{70} - 2 q^{71} - 8 q^{72} + 4 q^{73} - 4 q^{74} - 2 q^{75} - 2 q^{76} - 16 q^{77} - 24 q^{78} + 20 q^{79} - 6 q^{80} + 34 q^{81} - 6 q^{82} - 8 q^{83} - 12 q^{84} - 10 q^{85} + 12 q^{86} - 12 q^{87} + 10 q^{88} - 12 q^{89} + 8 q^{90} - 38 q^{91} - 28 q^{93} - 8 q^{94} + 2 q^{95} + 2 q^{96} - 2 q^{97} - 8 q^{98} - 50 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 6 * q^5 + 2 * q^6 - 2 * q^7 - 6 * q^8 + 8 * q^9 + 6 * q^10 - 10 * q^11 - 2 * q^12 - 2 * q^13 + 2 * q^14 + 2 * q^15 + 6 * q^16 + 10 * q^17 - 8 * q^18 - 2 * q^19 - 6 * q^20 - 12 * q^21 + 10 * q^22 + 2 * q^24 + 6 * q^25 + 2 * q^26 - 8 * q^27 - 2 * q^28 - 2 * q^30 - 2 * q^31 - 6 * q^32 + 22 * q^33 - 10 * q^34 + 2 * q^35 + 8 * q^36 + 4 * q^37 + 2 * q^38 + 24 * q^39 + 6 * q^40 + 6 * q^41 + 12 * q^42 - 12 * q^43 - 10 * q^44 - 8 * q^45 + 8 * q^47 - 2 * q^48 + 8 * q^49 - 6 * q^50 - 34 * q^51 - 2 * q^52 - 36 * q^53 + 8 * q^54 + 10 * q^55 + 2 * q^56 - 32 * q^57 + 16 * q^59 + 2 * q^60 + 10 * q^61 + 2 * q^62 + 48 * q^63 + 6 * q^64 + 2 * q^65 - 22 * q^66 - 16 * q^67 + 10 * q^68 - 2 * q^70 - 2 * q^71 - 8 * q^72 + 4 * q^73 - 4 * q^74 - 2 * q^75 - 2 * q^76 - 16 * q^77 - 24 * q^78 + 20 * q^79 - 6 * q^80 + 34 * q^81 - 6 * q^82 - 8 * q^83 - 12 * q^84 - 10 * q^85 + 12 * q^86 - 12 * q^87 + 10 * q^88 - 12 * q^89 + 8 * q^90 - 38 * q^91 - 28 * q^93 - 8 * q^94 + 2 * q^95 + 2 * q^96 - 2 * q^97 - 8 * q^98 - 50 * q^99

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