LMFDB - Embedded newform 4730.2.a.bb.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4730,2,Mod(1,4730)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4730, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4730.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4730 = 2 \cdot 5 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4730.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:	$37.7692401561$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - x^{10} - 22 x^{9} + 21 x^{8} + 165 x^{7} - 130 x^{6} - 535 x^{5} + 323 x^{4} + 710 x^{3} + \cdots + 128 $ x^11 - x^10 - 22x^9 + 21x^8 + 165x^7 - 130x^6 - 535x^5 + 323x^4 + 710x^3 - 343x^2 - 261*x + 128
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-1.80931$ of defining polynomial
Character	$\chi$	$=$	4730.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.80931 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.80931 q^{6} +4.53794 q^{7} -1.00000 q^{8} +0.273608 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.80931 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.80931 q^{6} +4.53794 q^{7} -1.00000 q^{8} +0.273608 q^{9} +1.00000 q^{10} -1.00000 q^{11} +1.80931 q^{12} +1.28672 q^{13} -4.53794 q^{14} -1.80931 q^{15} +1.00000 q^{16} -2.49948 q^{17} -0.273608 q^{18} +4.30450 q^{19} -1.00000 q^{20} +8.21054 q^{21} +1.00000 q^{22} -0.713282 q^{23} -1.80931 q^{24} +1.00000 q^{25} -1.28672 q^{26} -4.93289 q^{27} +4.53794 q^{28} -4.09374 q^{29} +1.80931 q^{30} +6.87649 q^{31} -1.00000 q^{32} -1.80931 q^{33} +2.49948 q^{34} -4.53794 q^{35} +0.273608 q^{36} +2.58524 q^{37} -4.30450 q^{38} +2.32807 q^{39} +1.00000 q^{40} +2.61453 q^{41} -8.21054 q^{42} +1.00000 q^{43} -1.00000 q^{44} -0.273608 q^{45} +0.713282 q^{46} +7.75858 q^{47} +1.80931 q^{48} +13.5929 q^{49} -1.00000 q^{50} -4.52234 q^{51} +1.28672 q^{52} +7.15552 q^{53} +4.93289 q^{54} +1.00000 q^{55} -4.53794 q^{56} +7.78817 q^{57} +4.09374 q^{58} -2.05592 q^{59} -1.80931 q^{60} -7.20843 q^{61} -6.87649 q^{62} +1.24162 q^{63} +1.00000 q^{64} -1.28672 q^{65} +1.80931 q^{66} +4.88949 q^{67} -2.49948 q^{68} -1.29055 q^{69} +4.53794 q^{70} -10.4518 q^{71} -0.273608 q^{72} -4.33504 q^{73} -2.58524 q^{74} +1.80931 q^{75} +4.30450 q^{76} -4.53794 q^{77} -2.32807 q^{78} +14.1763 q^{79} -1.00000 q^{80} -9.74596 q^{81} -2.61453 q^{82} +14.5435 q^{83} +8.21054 q^{84} +2.49948 q^{85} -1.00000 q^{86} -7.40684 q^{87} +1.00000 q^{88} +3.85436 q^{89} +0.273608 q^{90} +5.83904 q^{91} -0.713282 q^{92} +12.4417 q^{93} -7.75858 q^{94} -4.30450 q^{95} -1.80931 q^{96} +10.0330 q^{97} -13.5929 q^{98} -0.273608 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 11 q^{2} - q^{3} + 11 q^{4} - 11 q^{5} + q^{6} + 6 q^{7} - 11 q^{8} + 12 q^{9}+O(q^{10}) $ 11 * q - 11 * q^2 - q^3 + 11 * q^4 - 11 * q^5 + q^6 + 6 * q^7 - 11 * q^8 + 12 * q^9	\( 11 q - 11 q^{2} - q^{3} + 11 q^{4} - 11 q^{5} + q^{6} + 6 q^{7} - 11 q^{8} + 12 q^{9} + 11 q^{10} - 11 q^{11} - q^{12} + 4 q^{13} - 6 q^{14} + q^{15} + 11 q^{16} - 10 q^{17} - 12 q^{18} + 14 q^{19} - 11 q^{20} - 2 q^{21} + 11 q^{22} - 18 q^{23} + q^{24} + 11 q^{25} - 4 q^{26} + 2 q^{27} + 6 q^{28} - 6 q^{29} - q^{30} + 13 q^{31} - 11 q^{32} + q^{33} + 10 q^{34} - 6 q^{35} + 12 q^{36} + q^{37} - 14 q^{38} + 12 q^{39} + 11 q^{40} + 12 q^{41} + 2 q^{42} + 11 q^{43} - 11 q^{44} - 12 q^{45} + 18 q^{46} - 5 q^{47} - q^{48} + 31 q^{49} - 11 q^{50} + q^{51} + 4 q^{52} - 27 q^{53} - 2 q^{54} + 11 q^{55} - 6 q^{56} - 5 q^{57} + 6 q^{58} + 11 q^{59} + q^{60} + 36 q^{61} - 13 q^{62} + 17 q^{63} + 11 q^{64} - 4 q^{65} - q^{66} + 18 q^{67} - 10 q^{68} + 14 q^{69} + 6 q^{70} - 14 q^{71} - 12 q^{72} - 11 q^{73} - q^{74} - q^{75} + 14 q^{76} - 6 q^{77} - 12 q^{78} + 28 q^{79} - 11 q^{80} + 7 q^{81} - 12 q^{82} - 4 q^{83} - 2 q^{84} + 10 q^{85} - 11 q^{86} + 38 q^{87} + 11 q^{88} - 7 q^{89} + 12 q^{90} + 14 q^{91} - 18 q^{92} - 3 q^{93} + 5 q^{94} - 14 q^{95} + q^{96} - q^{97} - 31 q^{98} - 12 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - q^3 + 11 * q^4 - 11 * q^5 + q^6 + 6 * q^7 - 11 * q^8 + 12 * q^9 + 11 * q^10 - 11 * q^11 - q^12 + 4 * q^13 - 6 * q^14 + q^15 + 11 * q^16 - 10 * q^17 - 12 * q^18 + 14 * q^19 - 11 * q^20 - 2 * q^21 + 11 * q^22 - 18 * q^23 + q^24 + 11 * q^25 - 4 * q^26 + 2 * q^27 + 6 * q^28 - 6 * q^29 - q^30 + 13 * q^31 - 11 * q^32 + q^33 + 10 * q^34 - 6 * q^35 + 12 * q^36 + q^37 - 14 * q^38 + 12 * q^39 + 11 * q^40 + 12 * q^41 + 2 * q^42 + 11 * q^43 - 11 * q^44 - 12 * q^45 + 18 * q^46 - 5 * q^47 - q^48 + 31 * q^49 - 11 * q^50 + q^51 + 4 * q^52 - 27 * q^53 - 2 * q^54 + 11 * q^55 - 6 * q^56 - 5 * q^57 + 6 * q^58 + 11 * q^59 + q^60 + 36 * q^61 - 13 * q^62 + 17 * q^63 + 11 * q^64 - 4 * q^65 - q^66 + 18 * q^67 - 10 * q^68 + 14 * q^69 + 6 * q^70 - 14 * q^71 - 12 * q^72 - 11 * q^73 - q^74 - q^75 + 14 * q^76 - 6 * q^77 - 12 * q^78 + 28 * q^79 - 11 * q^80 + 7 * q^81 - 12 * q^82 - 4 * q^83 - 2 * q^84 + 10 * q^85 - 11 * q^86 + 38 * q^87 + 11 * q^88 - 7 * q^89 + 12 * q^90 + 14 * q^91 - 18 * q^92 - 3 * q^93 + 5 * q^94 - 14 * q^95 + q^96 - q^97 - 31 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.80931	1.04461	0.522303	−	0.852760i	$-0.325073\pi$
$3$	1.80931	1.04461	0.522303	+	0.852760i	$0.325073\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.80931	−0.738648
$7$	4.53794	1.71518	0.857589	−	0.514335i	$-0.171961\pi$
$7$	4.53794	1.71518	0.857589	+	0.514335i	$0.171961\pi$
$8$	−1.00000	−0.353553
$9$	0.273608	0.0912027
$10$	1.00000	0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.80931	0.522303
$13$	1.28672	0.356871	0.178436	−	0.983952i	$-0.442896\pi$
$13$	1.28672	0.356871	0.178436	+	0.983952i	$0.442896\pi$
$14$	−4.53794	−1.21281
$15$	−1.80931	−0.467162
$16$	1.00000	0.250000
$17$	−2.49948	−0.606213	−0.303106	−	0.952957i	$-0.598024\pi$
$17$	−2.49948	−0.606213	−0.303106	+	0.952957i	$0.598024\pi$
$18$	−0.273608	−0.0644900
$19$	4.30450	0.987519	0.493760	−	0.869598i	$-0.335622\pi$
$19$	4.30450	0.987519	0.493760	+	0.869598i	$0.335622\pi$
$20$	−1.00000	−0.223607
$21$	8.21054	1.79169
$22$	1.00000	0.213201
$23$	−0.713282	−0.148730	−0.0743648	−	0.997231i	$-0.523693\pi$
$23$	−0.713282	−0.148730	−0.0743648	+	0.997231i	$0.523693\pi$
$24$	−1.80931	−0.369324
$25$	1.00000	0.200000
$26$	−1.28672	−0.252346
$27$	−4.93289	−0.949336
$28$	4.53794	0.857589
$29$	−4.09374	−0.760188	−0.380094	−	0.924948i	$-0.624108\pi$
$29$	−4.09374	−0.760188	−0.380094	+	0.924948i	$0.624108\pi$
$30$	1.80931	0.330334
$31$	6.87649	1.23505	0.617527	−	0.786550i	$-0.288135\pi$
$31$	6.87649	1.23505	0.617527	+	0.786550i	$0.288135\pi$
$32$	−1.00000	−0.176777
$33$	−1.80931	−0.314961
$34$	2.49948	0.428657
$35$	−4.53794	−0.767051
$36$	0.273608	0.0456013
$37$	2.58524	0.425010	0.212505	−	0.977160i	$-0.431838\pi$
$37$	2.58524	0.425010	0.212505	+	0.977160i	$0.431838\pi$
$38$	−4.30450	−0.698281
$39$	2.32807	0.372790
$40$	1.00000	0.158114
$41$	2.61453	0.408322	0.204161	−	0.978937i	$-0.434553\pi$
$41$	2.61453	0.408322	0.204161	+	0.978937i	$0.434553\pi$
$42$	−8.21054	−1.26691
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−1.00000	−0.150756
$45$	−0.273608	−0.0407871
$46$	0.713282	0.105168
$47$	7.75858	1.13171	0.565853	−	0.824506i	$-0.308547\pi$
$47$	7.75858	1.13171	0.565853	+	0.824506i	$0.308547\pi$
$48$	1.80931	0.261152
$49$	13.5929	1.94184
$50$	−1.00000	−0.141421
$51$	−4.52234	−0.633254
$52$	1.28672	0.178436
$53$	7.15552	0.982887	0.491443	−	0.870909i	$-0.336469\pi$
$53$	7.15552	0.982887	0.491443	+	0.870909i	$0.336469\pi$
$54$	4.93289	0.671282
$55$	1.00000	0.134840
$56$	−4.53794	−0.606407
$57$	7.78817	1.03157
$58$	4.09374	0.537534
$59$	−2.05592	−0.267658	−0.133829	−	0.991004i	$-0.542727\pi$
$59$	−2.05592	−0.267658	−0.133829	+	0.991004i	$0.542727\pi$
$60$	−1.80931	−0.233581
$61$	−7.20843	−0.922945	−0.461473	−	0.887154i	$-0.652679\pi$
$61$	−7.20843	−0.922945	−0.461473	+	0.887154i	$0.652679\pi$
$62$	−6.87649	−0.873315
$63$	1.24162	0.156429
$64$	1.00000	0.125000
$65$	−1.28672	−0.159598
$66$	1.80931	0.222711
$67$	4.88949	0.597346	0.298673	−	0.954356i	$-0.403456\pi$
$67$	4.88949	0.597346	0.298673	+	0.954356i	$0.403456\pi$
$68$	−2.49948	−0.303106
$69$	−1.29055	−0.155364
$70$	4.53794	0.542387
$71$	−10.4518	−1.24040	−0.620202	−	0.784442i	$-0.712949\pi$
$71$	−10.4518	−1.24040	−0.620202	+	0.784442i	$0.712949\pi$
$72$	−0.273608	−0.0322450
$73$	−4.33504	−0.507378	−0.253689	−	0.967286i	$-0.581644\pi$
$73$	−4.33504	−0.507378	−0.253689	+	0.967286i	$0.581644\pi$
$74$	−2.58524	−0.300527
$75$	1.80931	0.208921
$76$	4.30450	0.493760
$77$	−4.53794	−0.517146
$78$	−2.32807	−0.263602
$79$	14.1763	1.59496	0.797479	−	0.603347i	$-0.206166\pi$
$79$	14.1763	1.59496	0.797479	+	0.603347i	$0.206166\pi$
$80$	−1.00000	−0.111803
$81$	−9.74596	−1.08288
$82$	−2.61453	−0.288727
$83$	14.5435	1.59635	0.798176	−	0.602424i	$-0.205798\pi$
$83$	14.5435	1.59635	0.798176	+	0.602424i	$0.205798\pi$
$84$	8.21054	0.895843
$85$	2.49948	0.271107
$86$	−1.00000	−0.107833
$87$	−7.40684	−0.794097
$88$	1.00000	0.106600
$89$	3.85436	0.408561	0.204280	−	0.978912i	$-0.434515\pi$
$89$	3.85436	0.408561	0.204280	+	0.978912i	$0.434515\pi$
$90$	0.273608	0.0288408
$91$	5.83904	0.612098
$92$	−0.713282	−0.0743648
$93$	12.4417	1.29014
$94$	−7.75858	−0.800236
$95$	−4.30450	−0.441632
$96$	−1.80931	−0.184662
$97$	10.0330	1.01870	0.509349	−	0.860560i	$-0.329886\pi$
$97$	10.0330	1.01870	0.509349	+	0.860560i	$0.329886\pi$
$98$	−13.5929	−1.37309
$99$	−0.273608	−0.0274986
$100$	1.00000	0.100000
$101$	17.9835	1.78942	0.894710	−	0.446647i	$-0.147382\pi$
$101$	17.9835	1.78942	0.894710	+	0.446647i	$0.147382\pi$
$102$	4.52234	0.447778
$103$	19.5618	1.92748	0.963740	−	0.266843i	$-0.0859806\pi$
$103$	19.5618	1.92748	0.963740	+	0.266843i	$0.0859806\pi$
$104$	−1.28672	−0.126173
$105$	−8.21054	−0.801267
$106$	−7.15552	−0.695006
$107$	−10.3310	−0.998735	−0.499367	−	0.866390i	$-0.666434\pi$
$107$	−10.3310	−0.998735	−0.499367	+	0.866390i	$0.666434\pi$
$108$	−4.93289	−0.474668
$109$	−15.6482	−1.49882	−0.749411	−	0.662105i	$-0.769663\pi$
$109$	−15.6482	−1.49882	−0.749411	+	0.662105i	$0.769663\pi$
$110$	−1.00000	−0.0953463
$111$	4.67750	0.443968
$112$	4.53794	0.428795
$113$	0.00194142	0.000182633 0	9.13167e−5	−	1.00000i	$-0.499971\pi$
$113$	0.00194142	0.000182633 0	9.13167e−5		1.00000i	$0.499971\pi$
$114$	−7.78817	−0.729429
$115$	0.713282	0.0665139
$116$	−4.09374	−0.380094
$117$	0.352056	0.0325476
$118$	2.05592	0.189263
$119$	−11.3425	−1.03976
$120$	1.80931	0.165167
$121$	1.00000	0.0909091
$122$	7.20843	0.652621
$123$	4.73051	0.426535
$124$	6.87649	0.617527
$125$	−1.00000	−0.0894427
$126$	−1.24162	−0.110612
$127$	1.99032	0.176612	0.0883062	−	0.996093i	$-0.471855\pi$
$127$	1.99032	0.176612	0.0883062	+	0.996093i	$0.471855\pi$
$128$	−1.00000	−0.0883883
$129$	1.80931	0.159301
$130$	1.28672	0.112853
$131$	−6.17996	−0.539945	−0.269973	−	0.962868i	$-0.587015\pi$
$131$	−6.17996	−0.539945	−0.269973	+	0.962868i	$0.587015\pi$
$132$	−1.80931	−0.157480
$133$	19.5335	1.69377
$134$	−4.88949	−0.422387
$135$	4.93289	0.424556
$136$	2.49948	0.214329
$137$	−18.9373	−1.61792	−0.808961	−	0.587863i	$-0.799969\pi$
$137$	−18.9373	−1.61792	−0.808961	+	0.587863i	$0.799969\pi$
$138$	1.29055	0.109859
$139$	−10.0357	−0.851220	−0.425610	−	0.904907i	$-0.639940\pi$
$139$	−10.0357	−0.851220	−0.425610	+	0.904907i	$0.639940\pi$
$140$	−4.53794	−0.383526
$141$	14.0377	1.18219
$142$	10.4518	0.877098
$143$	−1.28672	−0.107601
$144$	0.273608	0.0228007
$145$	4.09374	0.339966
$146$	4.33504	0.358771
$147$	24.5937	2.02846
$148$	2.58524	0.212505
$149$	14.0528	1.15125	0.575625	−	0.817714i	$-0.304759\pi$
$149$	14.0528	1.15125	0.575625	+	0.817714i	$0.304759\pi$
$150$	−1.80931	−0.147730
$151$	−11.3656	−0.924919	−0.462460	−	0.886640i	$-0.653033\pi$
$151$	−11.3656	−0.924919	−0.462460	+	0.886640i	$0.653033\pi$
$152$	−4.30450	−0.349141
$153$	−0.683878	−0.0552883
$154$	4.53794	0.365677
$155$	−6.87649	−0.552333
$156$	2.32807	0.186395
$157$	16.9897	1.35593	0.677963	−	0.735096i	$-0.262863\pi$
$157$	16.9897	1.35593	0.677963	+	0.735096i	$0.262863\pi$
$158$	−14.1763	−1.12781
$159$	12.9466	1.02673
$160$	1.00000	0.0790569
$161$	−3.23683	−0.255098
$162$	9.74596	0.765715
$163$	−18.7453	−1.46825	−0.734124	−	0.679015i	$-0.762407\pi$
$163$	−18.7453	−1.46825	−0.734124	+	0.679015i	$0.762407\pi$
$164$	2.61453	0.204161
$165$	1.80931	0.140855
$166$	−14.5435	−1.12879
$167$	15.7842	1.22142	0.610711	−	0.791854i	$-0.290884\pi$
$167$	15.7842	1.22142	0.610711	+	0.791854i	$0.290884\pi$
$168$	−8.21054	−0.633457
$169$	−11.3444	−0.872643
$170$	−2.49948	−0.191701
$171$	1.17774	0.0900644
$172$	1.00000	0.0762493
$173$	23.4793	1.78510	0.892548	−	0.450953i	$-0.148916\pi$
$173$	23.4793	1.78510	0.892548	+	0.450953i	$0.148916\pi$
$174$	7.40684	0.561511
$175$	4.53794	0.343036
$176$	−1.00000	−0.0753778
$177$	−3.71980	−0.279598
$178$	−3.85436	−0.288896
$179$	−0.0200101	−0.00149563	−0.000747813	−	1.00000i	$-0.500238\pi$
$179$	−0.0200101	−0.00149563	−0.000747813		1.00000i	$0.500238\pi$
$180$	−0.273608	−0.0203935
$181$	15.0756	1.12056	0.560280	−	0.828303i	$-0.310693\pi$
$181$	15.0756	1.12056	0.560280	+	0.828303i	$0.310693\pi$
$182$	−5.83904	−0.432819
$183$	−13.0423	−0.964115
$184$	0.713282	0.0525839
$185$	−2.58524	−0.190070
$186$	−12.4417	−0.912270
$187$	2.49948	0.182780
$188$	7.75858	0.565853
$189$	−22.3851	−1.62828
$190$	4.30450	0.312281
$191$	−22.3644	−1.61823	−0.809114	−	0.587651i	$-0.800053\pi$
$191$	−22.3644	−1.61823	−0.809114	+	0.587651i	$0.800053\pi$
$192$	1.80931	0.130576
$193$	−17.6534	−1.27072	−0.635361	−	0.772216i	$-0.719149\pi$
$193$	−17.6534	−1.27072	−0.635361	+	0.772216i	$0.719149\pi$
$194$	−10.0330	−0.720328
$195$	−2.32807	−0.166717
$196$	13.5929	0.970919
$197$	−0.716160	−0.0510243	−0.0255122	−	0.999675i	$-0.508122\pi$
$197$	−0.716160	−0.0510243	−0.0255122	+	0.999675i	$0.508122\pi$
$198$	0.273608	0.0194445
$199$	−10.1363	−0.718547	−0.359273	−	0.933232i	$-0.616975\pi$
$199$	−10.1363	−0.718547	−0.359273	+	0.933232i	$0.616975\pi$
$200$	−1.00000	−0.0707107
$201$	8.84660	0.623991
$202$	−17.9835	−1.26531
$203$	−18.5771	−1.30386
$204$	−4.52234	−0.316627
$205$	−2.61453	−0.182607
$206$	−19.5618	−1.36293
$207$	−0.195160	−0.0135645
$208$	1.28672	0.0892178
$209$	−4.30450	−0.297748
$210$	8.21054	0.566581
$211$	27.1396	1.86837	0.934184	−	0.356792i	$-0.116130\pi$
$211$	27.1396	1.86837	0.934184	+	0.356792i	$0.116130\pi$
$212$	7.15552	0.491443
$213$	−18.9106	−1.29573
$214$	10.3310	0.706212
$215$	−1.00000	−0.0681994
$216$	4.93289	0.335641
$217$	31.2051	2.11834
$218$	15.6482	1.05983
$219$	−7.84344	−0.530011
$220$	1.00000	0.0674200
$221$	−3.21613	−0.216340
$222$	−4.67750	−0.313933
$223$	−26.9918	−1.80750	−0.903752	−	0.428057i	$-0.859198\pi$
$223$	−26.9918	−1.80750	−0.903752	+	0.428057i	$0.859198\pi$
$224$	−4.53794	−0.303204
$225$	0.273608	0.0182405
$226$	−0.00194142	−0.000129141 0
$227$	16.1933	1.07479	0.537395	−	0.843331i	$-0.319408\pi$
$227$	16.1933	1.07479	0.537395	+	0.843331i	$0.319408\pi$
$228$	7.78817	0.515784
$229$	−3.67036	−0.242544	−0.121272	−	0.992619i	$-0.538697\pi$
$229$	−3.67036	−0.242544	−0.121272	+	0.992619i	$0.538697\pi$
$230$	−0.713282	−0.0470324
$231$	−8.21054	−0.540214
$232$	4.09374	0.268767
$233$	2.89466	0.189636	0.0948179	−	0.995495i	$-0.469773\pi$
$233$	2.89466	0.189636	0.0948179	+	0.995495i	$0.469773\pi$
$234$	−0.352056	−0.0230146
$235$	−7.75858	−0.506114
$236$	−2.05592	−0.133829
$237$	25.6493	1.66610
$238$	11.3425	0.735224
$239$	−24.6223	−1.59269	−0.796343	−	0.604845i	$-0.793235\pi$
$239$	−24.6223	−1.59269	−0.796343	+	0.604845i	$0.793235\pi$
$240$	−1.80931	−0.116791
$241$	13.6048	0.876365	0.438182	−	0.898886i	$-0.355622\pi$
$241$	13.6048	0.876365	0.438182	+	0.898886i	$0.355622\pi$
$242$	−1.00000	−0.0642824
$243$	−2.83481	−0.181853
$244$	−7.20843	−0.461473
$245$	−13.5929	−0.868416
$246$	−4.73051	−0.301606
$247$	5.53867	0.352417
$248$	−6.87649	−0.436657
$249$	26.3136	1.66756
$250$	1.00000	0.0632456
$251$	26.1525	1.65073	0.825366	−	0.564599i	$-0.190969\pi$
$251$	26.1525	1.65073	0.825366	+	0.564599i	$0.190969\pi$
$252$	1.24162	0.0782145
$253$	0.713282	0.0448437
$254$	−1.99032	−0.124884
$255$	4.52234	0.283200
$256$	1.00000	0.0625000
$257$	−22.3009	−1.39109	−0.695547	−	0.718481i	$-0.744838\pi$
$257$	−22.3009	−1.39109	−0.695547	+	0.718481i	$0.744838\pi$
$258$	−1.80931	−0.112643
$259$	11.7316	0.728968
$260$	−1.28672	−0.0797989
$261$	−1.12008	−0.0693312
$262$	6.17996	0.381799
$263$	8.00847	0.493824	0.246912	−	0.969038i	$-0.420584\pi$
$263$	8.00847	0.493824	0.246912	+	0.969038i	$0.420584\pi$
$264$	1.80931	0.111355
$265$	−7.15552	−0.439560
$266$	−19.5335	−1.19768
$267$	6.97373	0.426785
$268$	4.88949	0.298673
$269$	28.5272	1.73933	0.869666	−	0.493640i	$-0.164334\pi$
$269$	28.5272	1.73933	0.869666	+	0.493640i	$0.164334\pi$
$270$	−4.93289	−0.300206
$271$	−10.0036	−0.607678	−0.303839	−	0.952723i	$-0.598268\pi$
$271$	−10.0036	−0.607678	−0.303839	+	0.952723i	$0.598268\pi$
$272$	−2.49948	−0.151553
$273$	10.5646	0.639402
$274$	18.9373	1.14404
$275$	−1.00000	−0.0603023
$276$	−1.29055	−0.0776820
$277$	22.9013	1.37600	0.688002	−	0.725709i	$-0.258488\pi$
$277$	22.9013	1.37600	0.688002	+	0.725709i	$0.258488\pi$
$278$	10.0357	0.601903
$279$	1.88146	0.112640
$280$	4.53794	0.271194
$281$	29.4235	1.75526	0.877630	−	0.479339i	$-0.159124\pi$
$281$	29.4235	1.75526	0.877630	+	0.479339i	$0.159124\pi$
$282$	−14.0377	−0.835932
$283$	9.51051	0.565341	0.282671	−	0.959217i	$-0.408780\pi$
$283$	9.51051	0.565341	0.282671	+	0.959217i	$0.408780\pi$
$284$	−10.4518	−0.620202
$285$	−7.78817	−0.461332
$286$	1.28672	0.0760852
$287$	11.8646	0.700345
$288$	−0.273608	−0.0161225
$289$	−10.7526	−0.632506
$290$	−4.09374	−0.240392
$291$	18.1528	1.06414
$292$	−4.33504	−0.253689
$293$	3.18399	0.186011	0.0930054	−	0.995666i	$-0.470353\pi$
$293$	3.18399	0.186011	0.0930054	+	0.995666i	$0.470353\pi$
$294$	−24.5937	−1.43433
$295$	2.05592	0.119700
$296$	−2.58524	−0.150264
$297$	4.93289	0.286235
$298$	−14.0528	−0.814056
$299$	−0.917793	−0.0530773
$300$	1.80931	0.104461
$301$	4.53794	0.261562
$302$	11.3656	0.654017
$303$	32.5377	1.86924
$304$	4.30450	0.246880
$305$	7.20843	0.412754
$306$	0.683878	0.0390947
$307$	−26.7734	−1.52804	−0.764019	−	0.645194i	$-0.776777\pi$
$307$	−26.7734	−1.52804	−0.764019	+	0.645194i	$0.776777\pi$
$308$	−4.53794	−0.258573
$309$	35.3934	2.01346
$310$	6.87649	0.390558
$311$	−24.5195	−1.39037	−0.695187	−	0.718829i	$-0.744678\pi$
$311$	−24.5195	−1.39037	−0.695187	+	0.718829i	$0.744678\pi$
$312$	−2.32807	−0.131801
$313$	25.0633	1.41666	0.708332	−	0.705879i	$-0.249448\pi$
$313$	25.0633	1.41666	0.708332	+	0.705879i	$0.249448\pi$
$314$	−16.9897	−0.958784
$315$	−1.24162	−0.0699571
$316$	14.1763	0.797479
$317$	−29.6933	−1.66774	−0.833870	−	0.551960i	$-0.813880\pi$
$317$	−29.6933	−1.66774	−0.833870	+	0.551960i	$0.813880\pi$
$318$	−12.9466	−0.726008
$319$	4.09374	0.229205
$320$	−1.00000	−0.0559017
$321$	−18.6920	−1.04328
$322$	3.23683	0.180381
$323$	−10.7590	−0.598647
$324$	−9.74596	−0.541442
$325$	1.28672	0.0713743
$326$	18.7453	1.03821
$327$	−28.3124	−1.56568
$328$	−2.61453	−0.144364
$329$	35.2079	1.94108
$330$	−1.80931	−0.0995993
$331$	27.3999	1.50604	0.753018	−	0.658000i	$-0.228597\pi$
$331$	27.3999	1.50604	0.753018	+	0.658000i	$0.228597\pi$
$332$	14.5435	0.798176
$333$	0.707341	0.0387621
$334$	−15.7842	−0.863675
$335$	−4.88949	−0.267141
$336$	8.21054	0.447922
$337$	−14.1951	−0.773258	−0.386629	−	0.922235i	$-0.626361\pi$
$337$	−14.1951	−0.773258	−0.386629	+	0.922235i	$0.626361\pi$
$338$	11.3444	0.617052
$339$	0.00351263	0.000190780 0
$340$	2.49948	0.135553
$341$	−6.87649	−0.372383
$342$	−1.17774	−0.0636852
$343$	29.9180	1.61542
$344$	−1.00000	−0.0539164
$345$	1.29055	0.0694809
$346$	−23.4793	−1.26225
$347$	−14.9223	−0.801069	−0.400534	−	0.916282i	$-0.631176\pi$
$347$	−14.9223	−0.801069	−0.400534	+	0.916282i	$0.631176\pi$
$348$	−7.40684	−0.397048
$349$	−31.3875	−1.68013	−0.840067	−	0.542483i	$-0.817484\pi$
$349$	−31.3875	−1.68013	−0.840067	+	0.542483i	$0.817484\pi$
$350$	−4.53794	−0.242563
$351$	−6.34724	−0.338791
$352$	1.00000	0.0533002
$353$	11.3874	0.606090	0.303045	−	0.952976i	$-0.401997\pi$
$353$	11.3874	0.606090	0.303045	+	0.952976i	$0.401997\pi$
$354$	3.71980	0.197705
$355$	10.4518	0.554725
$356$	3.85436	0.204280
$357$	−20.5221	−1.08614
$358$	0.0200101	0.00105757
$359$	10.9849	0.579759	0.289880	−	0.957063i	$-0.406385\pi$
$359$	10.9849	0.579759	0.289880	+	0.957063i	$0.406385\pi$
$360$	0.273608	0.0144204
$361$	−0.471312	−0.0248059
$362$	−15.0756	−0.792356
$363$	1.80931	0.0949642
$364$	5.83904	0.306049
$365$	4.33504	0.226907
$366$	13.0423	0.681732
$367$	−29.5964	−1.54492	−0.772459	−	0.635065i	$-0.780973\pi$
$367$	−29.5964	−1.54492	−0.772459	+	0.635065i	$0.780973\pi$
$368$	−0.713282	−0.0371824
$369$	0.715358	0.0372400
$370$	2.58524	0.134400
$371$	32.4713	1.68583
$372$	12.4417	0.645072
$373$	−24.7257	−1.28025	−0.640125	−	0.768271i	$-0.721117\pi$
$373$	−24.7257	−1.28025	−0.640125	+	0.768271i	$0.721117\pi$
$374$	−2.49948	−0.129245
$375$	−1.80931	−0.0934324
$376$	−7.75858	−0.400118
$377$	−5.26748	−0.271289
$378$	22.3851	1.15137
$379$	−8.11573	−0.416877	−0.208439	−	0.978035i	$-0.566838\pi$
$379$	−8.11573	−0.416877	−0.208439	+	0.978035i	$0.566838\pi$
$380$	−4.30450	−0.220816
$381$	3.60111	0.184490
$382$	22.3644	1.14426
$383$	−18.4543	−0.942972	−0.471486	−	0.881874i	$-0.656282\pi$
$383$	−18.4543	−0.942972	−0.471486	+	0.881874i	$0.656282\pi$
$384$	−1.80931	−0.0923310
$385$	4.53794	0.231275
$386$	17.6534	0.898536
$387$	0.273608	0.0139083
$388$	10.0330	0.509349
$389$	13.2506	0.671830	0.335915	−	0.941892i	$-0.390954\pi$
$389$	13.2506	0.671830	0.335915	+	0.941892i	$0.390954\pi$
$390$	2.32807	0.117887
$391$	1.78283	0.0901618
$392$	−13.5929	−0.686543
$393$	−11.1815	−0.564031
$394$	0.716160	0.0360796
$395$	−14.1763	−0.713287
$396$	−0.273608	−0.0137493
$397$	−1.89992	−0.0953542	−0.0476771	−	0.998863i	$-0.515182\pi$
$397$	−1.89992	−0.0953542	−0.0476771	+	0.998863i	$0.515182\pi$
$398$	10.1363	0.508089
$399$	35.3422	1.76932
$400$	1.00000	0.0500000
$401$	29.6511	1.48070	0.740352	−	0.672219i	$-0.234659\pi$
$401$	29.6511	1.48070	0.740352	+	0.672219i	$0.234659\pi$
$402$	−8.84660	−0.441229
$403$	8.84810	0.440755
$404$	17.9835	0.894710
$405$	9.74596	0.484281
$406$	18.5771	0.921967
$407$	−2.58524	−0.128145
$408$	4.52234	0.223889
$409$	−22.3016	−1.10275	−0.551373	−	0.834259i	$-0.685896\pi$
$409$	−22.3016	−1.10275	−0.551373	+	0.834259i	$0.685896\pi$
$410$	2.61453	0.129123
$411$	−34.2634	−1.69009
$412$	19.5618	0.963740
$413$	−9.32964	−0.459082
$414$	0.195160	0.00959158
$415$	−14.5435	−0.713910
$416$	−1.28672	−0.0630865
$417$	−18.1578	−0.889190
$418$	4.30450	0.210540
$419$	−6.62038	−0.323427	−0.161713	−	0.986838i	$-0.551702\pi$
$419$	−6.62038	−0.323427	−0.161713	+	0.986838i	$0.551702\pi$
$420$	−8.21054	−0.400633
$421$	15.4538	0.753175	0.376587	−	0.926381i	$-0.377098\pi$
$421$	15.4538	0.753175	0.376587	+	0.926381i	$0.377098\pi$
$422$	−27.1396	−1.32114
$423$	2.12281	0.103215
$424$	−7.15552	−0.347503
$425$	−2.49948	−0.121243
$426$	18.9106	0.916222
$427$	−32.7114	−1.58302
$428$	−10.3310	−0.499367
$429$	−2.32807	−0.112400
$430$	1.00000	0.0482243
$431$	−2.64134	−0.127229	−0.0636145	−	0.997975i	$-0.520263\pi$
$431$	−2.64134	−0.127229	−0.0636145	+	0.997975i	$0.520263\pi$
$432$	−4.93289	−0.237334
$433$	−16.1858	−0.777839	−0.388919	−	0.921272i	$-0.627152\pi$
$433$	−16.1858	−0.777839	−0.388919	+	0.921272i	$0.627152\pi$
$434$	−31.2051	−1.49789
$435$	7.40684	0.355131
$436$	−15.6482	−0.749411
$437$	−3.07032	−0.146873
$438$	7.84344	0.374774
$439$	35.5178	1.69517	0.847586	−	0.530658i	$-0.178055\pi$
$439$	35.5178	1.69517	0.847586	+	0.530658i	$0.178055\pi$
$440$	−1.00000	−0.0476731
$441$	3.71912	0.177101
$442$	3.21613	0.152975
$443$	−39.7320	−1.88772	−0.943862	−	0.330339i	$-0.892837\pi$
$443$	−39.7320	−1.88772	−0.943862	+	0.330339i	$0.892837\pi$
$444$	4.67750	0.221984
$445$	−3.85436	−0.182714
$446$	26.9918	1.27810
$447$	25.4259	1.20260
$448$	4.53794	0.214397
$449$	4.55922	0.215163	0.107581	−	0.994196i	$-0.465689\pi$
$449$	4.55922	0.215163	0.107581	+	0.994196i	$0.465689\pi$
$450$	−0.273608	−0.0128980
$451$	−2.61453	−0.123114
$452$	0.00194142	9.13167e−5 0
$453$	−20.5639	−0.966177
$454$	−16.1933	−0.759991
$455$	−5.83904	−0.273739
$456$	−7.78817	−0.364715
$457$	14.5725	0.681673	0.340837	−	0.940123i	$-0.389290\pi$
$457$	14.5725	0.681673	0.340837	+	0.940123i	$0.389290\pi$
$458$	3.67036	0.171505
$459$	12.3297	0.575499
$460$	0.713282	0.0332570
$461$	37.2850	1.73653	0.868267	−	0.496097i	$-0.165234\pi$
$461$	37.2850	1.73653	0.868267	+	0.496097i	$0.165234\pi$
$462$	8.21054	0.381989
$463$	13.2646	0.616457	0.308229	−	0.951312i	$-0.400264\pi$
$463$	13.2646	0.616457	0.308229	+	0.951312i	$0.400264\pi$
$464$	−4.09374	−0.190047
$465$	−12.4417	−0.576970
$466$	−2.89466	−0.134093
$467$	−18.9504	−0.876922	−0.438461	−	0.898750i	$-0.644476\pi$
$467$	−18.9504	−0.876922	−0.438461	+	0.898750i	$0.644476\pi$
$468$	0.352056	0.0162738
$469$	22.1882	1.02455
$470$	7.75858	0.357877
$471$	30.7397	1.41641
$472$	2.05592	0.0946315
$473$	−1.00000	−0.0459800
$474$	−25.6493	−1.17811
$475$	4.30450	0.197504
$476$	−11.3425	−0.519882
$477$	1.95781	0.0896419
$478$	24.6223	1.12620
$479$	0.0755036	0.00344985	0.00172492	−	0.999999i	$-0.499451\pi$
$479$	0.0755036	0.00344985	0.00172492	+	0.999999i	$0.499451\pi$
$480$	1.80931	0.0825834
$481$	3.32647	0.151674
$482$	−13.6048	−0.619683
$483$	−5.85643	−0.266477
$484$	1.00000	0.0454545
$485$	−10.0330	−0.455575
$486$	2.83481	0.128589
$487$	16.1032	0.729706	0.364853	−	0.931065i	$-0.381119\pi$
$487$	16.1032	0.729706	0.364853	+	0.931065i	$0.381119\pi$
$488$	7.20843	0.326310
$489$	−33.9162	−1.53374
$490$	13.5929	0.614063
$491$	−2.33686	−0.105461	−0.0527304	−	0.998609i	$-0.516792\pi$
$491$	−2.33686	−0.105461	−0.0527304	+	0.998609i	$0.516792\pi$
$492$	4.73051	0.213268
$493$	10.2322	0.460836
$494$	−5.53867	−0.249197
$495$	0.273608	0.0122978
$496$	6.87649	0.308763
$497$	−47.4297	−2.12751
$498$	−26.3136	−1.17914
$499$	−14.5428	−0.651023	−0.325512	−	0.945538i	$-0.605537\pi$
$499$	−14.5428	−0.651023	−0.325512	+	0.945538i	$0.605537\pi$
$500$	−1.00000	−0.0447214
$501$	28.5586	1.27590
$502$	−26.1525	−1.16724
$503$	34.3695	1.53246	0.766229	−	0.642567i	$-0.222131\pi$
$503$	34.3695	1.53246	0.766229	+	0.642567i	$0.222131\pi$
$504$	−1.24162	−0.0553060
$505$	−17.9835	−0.800253
$506$	−0.713282	−0.0317093
$507$	−20.5255	−0.911568
$508$	1.99032	0.0883062
$509$	17.8363	0.790580	0.395290	−	0.918556i	$-0.370644\pi$
$509$	17.8363	0.790580	0.395290	+	0.918556i	$0.370644\pi$
$510$	−4.52234	−0.200252
$511$	−19.6721	−0.870245
$512$	−1.00000	−0.0441942
$513$	−21.2336	−0.937487
$514$	22.3009	0.983652
$515$	−19.5618	−0.861995
$516$	1.80931	0.0796505
$517$	−7.75858	−0.341222
$518$	−11.7316	−0.515458
$519$	42.4813	1.86472
$520$	1.28672	0.0564263
$521$	−3.88070	−0.170016	−0.0850082	−	0.996380i	$-0.527092\pi$
$521$	−3.88070	−0.170016	−0.0850082	+	0.996380i	$0.527092\pi$
$522$	1.12008	0.0490245
$523$	2.12930	0.0931078	0.0465539	−	0.998916i	$-0.485176\pi$
$523$	2.12930	0.0931078	0.0465539	+	0.998916i	$0.485176\pi$
$524$	−6.17996	−0.269973
$525$	8.21054	0.358337
$526$	−8.00847	−0.349186
$527$	−17.1876	−0.748705
$528$	−1.80931	−0.0787402
$529$	−22.4912	−0.977880
$530$	7.15552	0.310816
$531$	−0.562517	−0.0244112
$532$	19.5335	0.846886
$533$	3.36417	0.145718
$534$	−6.97373	−0.301783
$535$	10.3310	0.446648
$536$	−4.88949	−0.211194
$537$	−0.0362045	−0.00156234
$538$	−28.5272	−1.22989
$539$	−13.5929	−0.585486
$540$	4.93289	0.212278
$541$	−7.50761	−0.322777	−0.161389	−	0.986891i	$-0.551597\pi$
$541$	−7.50761	−0.322777	−0.161389	+	0.986891i	$0.551597\pi$
$542$	10.0036	0.429693
$543$	27.2764	1.17054
$544$	2.49948	0.107164
$545$	15.6482	0.670293
$546$	−10.5646	−0.452125
$547$	−29.8435	−1.27601	−0.638007	−	0.770030i	$-0.720241\pi$
$547$	−29.8435	−1.27601	−0.638007	+	0.770030i	$0.720241\pi$
$548$	−18.9373	−0.808961
$549$	−1.97229	−0.0841751
$550$	1.00000	0.0426401
$551$	−17.6215	−0.750700
$552$	1.29055	0.0549294
$553$	64.3311	2.73564
$554$	−22.9013	−0.972981
$555$	−4.67750	−0.198549
$556$	−10.0357	−0.425610
$557$	5.53462	0.234509	0.117255	−	0.993102i	$-0.462591\pi$
$557$	5.53462	0.234509	0.117255	+	0.993102i	$0.462591\pi$
$558$	−1.88146	−0.0796487
$559$	1.28672	0.0544224
$560$	−4.53794	−0.191763
$561$	4.52234	0.190933
$562$	−29.4235	−1.24116
$563$	23.7525	1.00105	0.500524	−	0.865723i	$-0.333141\pi$
$563$	23.7525	1.00105	0.500524	+	0.865723i	$0.333141\pi$
$564$	14.0377	0.591093
$565$	−0.00194142	−8.16762e−5 0
$566$	−9.51051	−0.399757
$567$	−44.2266	−1.85734
$568$	10.4518	0.438549
$569$	−7.35422	−0.308305	−0.154152	−	0.988047i	$-0.549265\pi$
$569$	−7.35422	−0.308305	−0.154152	+	0.988047i	$0.549265\pi$
$570$	7.78817	0.326211
$571$	4.55128	0.190465	0.0952326	−	0.995455i	$-0.469641\pi$
$571$	4.55128	0.190465	0.0952326	+	0.995455i	$0.469641\pi$
$572$	−1.28672	−0.0538004
$573$	−40.4641	−1.69041
$574$	−11.8646	−0.495218
$575$	−0.713282	−0.0297459
$576$	0.273608	0.0114003
$577$	−31.6243	−1.31654	−0.658269	−	0.752783i	$-0.728711\pi$
$577$	−31.6243	−1.31654	−0.658269	+	0.752783i	$0.728711\pi$
$578$	10.7526	0.447249
$579$	−31.9405	−1.32740
$580$	4.09374	0.169983
$581$	65.9973	2.73803
$582$	−18.1528	−0.752459
$583$	−7.15552	−0.296352
$584$	4.33504	0.179385
$585$	−0.352056	−0.0145557
$586$	−3.18399	−0.131529
$587$	−7.14164	−0.294767	−0.147383	−	0.989079i	$-0.547085\pi$
$587$	−7.14164	−0.294767	−0.147383	+	0.989079i	$0.547085\pi$
$588$	24.5937	1.01423
$589$	29.5998	1.21964
$590$	−2.05592	−0.0846410
$591$	−1.29576	−0.0533003
$592$	2.58524	0.106253
$593$	29.2853	1.20260	0.601302	−	0.799022i	$-0.294649\pi$
$593$	29.2853	1.20260	0.601302	+	0.799022i	$0.294649\pi$
$594$	−4.93289	−0.202399
$595$	11.3425	0.464996
$596$	14.0528	0.575625
$597$	−18.3398	−0.750598
$598$	0.917793	0.0375313
$599$	−4.16821	−0.170308	−0.0851542	−	0.996368i	$-0.527138\pi$
$599$	−4.16821	−0.170308	−0.0851542	+	0.996368i	$0.527138\pi$
$600$	−1.80931	−0.0738648
$601$	40.9185	1.66910	0.834550	−	0.550932i	$-0.185728\pi$
$601$	40.9185	1.66910	0.834550	+	0.550932i	$0.185728\pi$
$602$	−4.53794	−0.184952
$603$	1.33780	0.0544796
$604$	−11.3656	−0.462460
$605$	−1.00000	−0.0406558
$606$	−32.5377	−1.32175
$607$	33.1708	1.34636	0.673181	−	0.739478i	$-0.264928\pi$
$607$	33.1708	1.34636	0.673181	+	0.739478i	$0.264928\pi$
$608$	−4.30450	−0.174570
$609$	−33.6118	−1.36202
$610$	−7.20843	−0.291861
$611$	9.98310	0.403873
$612$	−0.683878	−0.0276441
$613$	2.87391	0.116076	0.0580382	−	0.998314i	$-0.481515\pi$
$613$	2.87391	0.116076	0.0580382	+	0.998314i	$0.481515\pi$
$614$	26.7734	1.08049
$615$	−4.73051	−0.190752
$616$	4.53794	0.182839
$617$	4.33161	0.174384	0.0871920	−	0.996192i	$-0.472211\pi$
$617$	4.33161	0.174384	0.0871920	+	0.996192i	$0.472211\pi$
$618$	−35.3934	−1.42373
$619$	−4.96649	−0.199620	−0.0998100	−	0.995007i	$-0.531823\pi$
$619$	−4.96649	−0.199620	−0.0998100	+	0.995007i	$0.531823\pi$
$620$	−6.87649	−0.276166
$621$	3.51854	0.141194
$622$	24.5195	0.983142
$623$	17.4908	0.700755
$624$	2.32807	0.0931975
$625$	1.00000	0.0400000
$626$	−25.0633	−1.00173
$627$	−7.78817	−0.311030
$628$	16.9897	0.677963
$629$	−6.46174	−0.257647
$630$	1.24162	0.0494672
$631$	−25.7883	−1.02662	−0.513309	−	0.858204i	$-0.671580\pi$
$631$	−25.7883	−1.02662	−0.513309	+	0.858204i	$0.671580\pi$
$632$	−14.1763	−0.563903
$633$	49.1040	1.95171
$634$	29.6933	1.17927
$635$	−1.99032	−0.0789835
$636$	12.9466	0.513365
$637$	17.4902	0.692986
$638$	−4.09374	−0.162073
$639$	−2.85970	−0.113128
$640$	1.00000	0.0395285
$641$	−0.739713	−0.0292169	−0.0146085	−	0.999893i	$-0.504650\pi$
$641$	−0.739713	−0.0292169	−0.0146085	+	0.999893i	$0.504650\pi$
$642$	18.6920	0.737714
$643$	9.59710	0.378473	0.189236	−	0.981932i	$-0.439399\pi$
$643$	9.59710	0.378473	0.189236	+	0.981932i	$0.439399\pi$
$644$	−3.23683	−0.127549
$645$	−1.80931	−0.0712416
$646$	10.7590	0.423307
$647$	−32.0119	−1.25852	−0.629258	−	0.777196i	$-0.716641\pi$
$647$	−32.0119	−1.25852	−0.629258	+	0.777196i	$0.716641\pi$
$648$	9.74596	0.382858
$649$	2.05592	0.0807020
$650$	−1.28672	−0.0504692
$651$	56.4597	2.21283
$652$	−18.7453	−0.734124
$653$	−33.5007	−1.31098	−0.655491	−	0.755203i	$-0.727538\pi$
$653$	−33.5007	−1.31098	−0.655491	+	0.755203i	$0.727538\pi$
$654$	28.3124	1.10710
$655$	6.17996	0.241471
$656$	2.61453	0.102080
$657$	−1.18610	−0.0462743
$658$	−35.2079	−1.37255
$659$	12.1853	0.474672	0.237336	−	0.971428i	$-0.423726\pi$
$659$	12.1853	0.474672	0.237336	+	0.971428i	$0.423726\pi$
$660$	1.80931	0.0704274
$661$	16.2883	0.633541	0.316770	−	0.948502i	$-0.397401\pi$
$661$	16.2883	0.633541	0.316770	+	0.948502i	$0.397401\pi$
$662$	−27.3999	−1.06493
$663$	−5.81897	−0.225990
$664$	−14.5435	−0.564396
$665$	−19.5335	−0.757478
$666$	−0.707341	−0.0274089
$667$	2.91999	0.113062
$668$	15.7842	0.610711
$669$	−48.8365	−1.88813
$670$	4.88949	0.188897
$671$	7.20843	0.278278
$672$	−8.21054	−0.316728
$673$	−1.53360	−0.0591159	−0.0295580	−	0.999563i	$-0.509410\pi$
$673$	−1.53360	−0.0591159	−0.0295580	+	0.999563i	$0.509410\pi$
$674$	14.1951	0.546776
$675$	−4.93289	−0.189867
$676$	−11.3444	−0.436321
$677$	21.6667	0.832718	0.416359	−	0.909200i	$-0.363306\pi$
$677$	21.6667	0.832718	0.416359	+	0.909200i	$0.363306\pi$
$678$	−0.00351263	−0.000134902 0
$679$	45.5291	1.74725
$680$	−2.49948	−0.0958507
$681$	29.2988	1.12273
$682$	6.87649	0.263314
$683$	48.0157	1.83727	0.918636	−	0.395106i	$-0.129292\pi$
$683$	48.0157	1.83727	0.918636	+	0.395106i	$0.129292\pi$
$684$	1.17774	0.0450322
$685$	18.9373	0.723556
$686$	−29.9180	−1.14227
$687$	−6.64083	−0.253363
$688$	1.00000	0.0381246
$689$	9.20714	0.350764
$690$	−1.29055	−0.0491304
$691$	−20.4041	−0.776209	−0.388105	−	0.921615i	$-0.626870\pi$
$691$	−20.4041	−0.776209	−0.388105	+	0.921615i	$0.626870\pi$
$692$	23.4793	0.892548
$693$	−1.24162	−0.0471651
$694$	14.9223	0.566441
$695$	10.0357	0.380677
$696$	7.40684	0.280756
$697$	−6.53498	−0.247530
$698$	31.3875	1.18803
$699$	5.23735	0.198095
$700$	4.53794	0.171518
$701$	8.71773	0.329264	0.164632	−	0.986355i	$-0.447356\pi$
$701$	8.71773	0.329264	0.164632	+	0.986355i	$0.447356\pi$
$702$	6.34724	0.239561
$703$	11.1281	0.419706
$704$	−1.00000	−0.0376889
$705$	−14.0377	−0.528690
$706$	−11.3874	−0.428571
$707$	81.6078	3.06918
$708$	−3.71980	−0.139799
$709$	−3.71148	−0.139388	−0.0696938	−	0.997568i	$-0.522202\pi$
$709$	−3.71148	−0.139388	−0.0696938	+	0.997568i	$0.522202\pi$
$710$	−10.4518	−0.392250
$711$	3.87875	0.145464
$712$	−3.85436	−0.144448
$713$	−4.90488	−0.183689
$714$	20.5221	0.768019
$715$	1.28672	0.0481205
$716$	−0.0200101	−0.000747813 0
$717$	−44.5495	−1.66373
$718$	−10.9849	−0.409952
$719$	−12.7644	−0.476033	−0.238016	−	0.971261i	$-0.576497\pi$
$719$	−12.7644	−0.476033	−0.238016	+	0.971261i	$0.576497\pi$
$720$	−0.273608	−0.0101968
$721$	88.7701	3.30597
$722$	0.471312	0.0175404
$723$	24.6154	0.915456
$724$	15.0756	0.560280
$725$	−4.09374	−0.152038
$726$	−1.80931	−0.0671498
$727$	−22.8600	−0.847831	−0.423916	−	0.905702i	$-0.639345\pi$
$727$	−22.8600	−0.847831	−0.423916	+	0.905702i	$0.639345\pi$
$728$	−5.83904	−0.216409
$729$	24.1088	0.892920
$730$	−4.33504	−0.160447
$731$	−2.49948	−0.0924466
$732$	−13.0423	−0.482057
$733$	28.4960	1.05253	0.526263	−	0.850322i	$-0.323593\pi$
$733$	28.4960	1.05253	0.526263	+	0.850322i	$0.323593\pi$
$734$	29.5964	1.09242
$735$	−24.5937	−0.907153
$736$	0.713282	0.0262919
$737$	−4.88949	−0.180107
$738$	−0.715358	−0.0263327
$739$	5.62330	0.206857	0.103428	−	0.994637i	$-0.467019\pi$
$739$	5.62330	0.206857	0.103428	+	0.994637i	$0.467019\pi$
$740$	−2.58524	−0.0950351
$741$	10.0212	0.368137
$742$	−32.4713	−1.19206
$743$	−24.5104	−0.899198	−0.449599	−	0.893230i	$-0.648433\pi$
$743$	−24.5104	−0.899198	−0.449599	+	0.893230i	$0.648433\pi$
$744$	−12.4417	−0.456135
$745$	−14.0528	−0.514854
$746$	24.7257	0.905273
$747$	3.97921	0.145592
$748$	2.49948	0.0913900
$749$	−46.8814	−1.71301
$750$	1.80931	0.0660667
$751$	15.1572	0.553092	0.276546	−	0.961001i	$-0.410810\pi$
$751$	15.1572	0.553092	0.276546	+	0.961001i	$0.410810\pi$
$752$	7.75858	0.282926
$753$	47.3180	1.72436
$754$	5.26748	0.191830
$755$	11.3656	0.413636
$756$	−22.3851	−0.814140
$757$	29.0010	1.05406	0.527029	−	0.849847i	$-0.323306\pi$
$757$	29.0010	1.05406	0.527029	+	0.849847i	$0.323306\pi$
$758$	8.11573	0.294777
$759$	1.29055	0.0468440
$760$	4.30450	0.156140
$761$	12.2831	0.445260	0.222630	−	0.974903i	$-0.428536\pi$
$761$	12.2831	0.445260	0.222630	+	0.974903i	$0.428536\pi$
$762$	−3.60111	−0.130454
$763$	−71.0103	−2.57075
$764$	−22.3644	−0.809114
$765$	0.683878	0.0247257
$766$	18.4543	0.666782
$767$	−2.64539	−0.0955196
$768$	1.80931	0.0652879
$769$	44.5197	1.60542	0.802711	−	0.596368i	$-0.203390\pi$
$769$	44.5197	1.60542	0.802711	+	0.596368i	$0.203390\pi$
$770$	−4.53794	−0.163536
$771$	−40.3493	−1.45315
$772$	−17.6534	−0.635361
$773$	−9.80872	−0.352795	−0.176398	−	0.984319i	$-0.556444\pi$
$773$	−9.80872	−0.352795	−0.176398	+	0.984319i	$0.556444\pi$
$774$	−0.273608	−0.00983464
$775$	6.87649	0.247011
$776$	−10.0330	−0.360164
$777$	21.2262	0.761485
$778$	−13.2506	−0.475056
$779$	11.2543	0.403225
$780$	−2.32807	−0.0833584
$781$	10.4518	0.373996
$782$	−1.78283	−0.0637540
$783$	20.1940	0.721673
$784$	13.5929	0.485459
$785$	−16.9897	−0.606388
$786$	11.1815	0.398830
$787$	−43.1246	−1.53723	−0.768614	−	0.639713i	$-0.779053\pi$
$787$	−43.1246	−1.53723	−0.768614	+	0.639713i	$0.779053\pi$
$788$	−0.716160	−0.0255122
$789$	14.4898	0.515851
$790$	14.1763	0.504370
$791$	0.00881004	0.000313249 0
$792$	0.273608	0.00972224
$793$	−9.27522	−0.329373
$794$	1.89992	0.0674256
$795$	−12.9466	−0.459168
$796$	−10.1363	−0.359273
$797$	−16.2719	−0.576379	−0.288189	−	0.957573i	$-0.593053\pi$
$797$	−16.2719	−0.576379	−0.288189	+	0.957573i	$0.593053\pi$
$798$	−35.3422	−1.25110
$799$	−19.3924	−0.686054
$800$	−1.00000	−0.0353553
$801$	1.05458	0.0372619
$802$	−29.6511	−1.04702
$803$	4.33504	0.152980
$804$	8.84660	0.311996
$805$	3.23683	0.114083
$806$	−8.84810	−0.311661
$807$	51.6146	1.81692
$808$	−17.9835	−0.632656
$809$	−27.0641	−0.951523	−0.475761	−	0.879574i	$-0.657827\pi$
$809$	−27.0641	−0.951523	−0.475761	+	0.879574i	$0.657827\pi$
$810$	−9.74596	−0.342438
$811$	−10.1074	−0.354919	−0.177460	−	0.984128i	$-0.556788\pi$
$811$	−10.1074	−0.354919	−0.177460	+	0.984128i	$0.556788\pi$
$812$	−18.5771	−0.651929
$813$	−18.0997	−0.634784
$814$	2.58524	0.0906124
$815$	18.7453	0.656621
$816$	−4.52234	−0.158313
$817$	4.30450	0.150595
$818$	22.3016	0.779759
$819$	1.59761	0.0558250
$820$	−2.61453	−0.0913035
$821$	−8.85984	−0.309211	−0.154605	−	0.987976i	$-0.549411\pi$
$821$	−8.85984	−0.309211	−0.154605	+	0.987976i	$0.549411\pi$
$822$	34.2634	1.19507
$823$	−31.6527	−1.10334	−0.551671	−	0.834062i	$-0.686010\pi$
$823$	−31.6527	−1.10334	−0.551671	+	0.834062i	$0.686010\pi$
$824$	−19.5618	−0.681467
$825$	−1.80931	−0.0629921
$826$	9.32964	0.324620
$827$	−23.8599	−0.829689	−0.414845	−	0.909892i	$-0.636164\pi$
$827$	−23.8599	−0.829689	−0.414845	+	0.909892i	$0.636164\pi$
$828$	−0.195160	−0.00678227
$829$	−12.2759	−0.426360	−0.213180	−	0.977013i	$-0.568382\pi$
$829$	−12.2759	−0.426360	−0.213180	+	0.977013i	$0.568382\pi$
$830$	14.5435	0.504811
$831$	41.4355	1.43738
$832$	1.28672	0.0446089
$833$	−33.9751	−1.17717
$834$	18.1578	0.628752
$835$	−15.7842	−0.546236
$836$	−4.30450	−0.148874
$837$	−33.9210	−1.17248
$838$	6.62038	0.228697
$839$	12.4611	0.430206	0.215103	−	0.976591i	$-0.430991\pi$
$839$	12.4611	0.430206	0.215103	+	0.976591i	$0.430991\pi$
$840$	8.21054	0.283291
$841$	−12.2413	−0.422115
$842$	−15.4538	−0.532575
$843$	53.2363	1.83356
$844$	27.1396	0.934184
$845$	11.3444	0.390258
$846$	−2.12281	−0.0729837
$847$	4.53794	0.155925
$848$	7.15552	0.245722
$849$	17.2075	0.590559
$850$	2.49948	0.0857315
$851$	−1.84400	−0.0632116
$852$	−18.9106	−0.647867
$853$	−11.4093	−0.390646	−0.195323	−	0.980739i	$-0.562575\pi$
$853$	−11.4093	−0.390646	−0.195323	+	0.980739i	$0.562575\pi$
$854$	32.7114	1.11936
$855$	−1.17774	−0.0402780
$856$	10.3310	0.353106
$857$	−25.7559	−0.879804	−0.439902	−	0.898046i	$-0.644987\pi$
$857$	−25.7559	−0.879804	−0.439902	+	0.898046i	$0.644987\pi$
$858$	2.32807	0.0794791
$859$	−37.9418	−1.29456	−0.647279	−	0.762253i	$-0.724093\pi$
$859$	−37.9418	−1.29456	−0.647279	+	0.762253i	$0.724093\pi$
$860$	−1.00000	−0.0340997
$861$	21.4667	0.731584
$862$	2.64134	0.0899645
$863$	0.963151	0.0327860	0.0163930	−	0.999866i	$-0.494782\pi$
$863$	0.963151	0.0327860	0.0163930	+	0.999866i	$0.494782\pi$
$864$	4.93289	0.167820
$865$	−23.4793	−0.798319
$866$	16.1858	0.550015
$867$	−19.4548	−0.660720
$868$	31.2051	1.05917
$869$	−14.1763	−0.480898
$870$	−7.40684	−0.251116
$871$	6.29139	0.213176
$872$	15.6482	0.529913
$873$	2.74511	0.0929080
$874$	3.07032	0.103855
$875$	−4.53794	−0.153410
$876$	−7.84344	−0.265005
$877$	−51.4027	−1.73575	−0.867873	−	0.496787i	$-0.834513\pi$
$877$	−51.4027	−1.73575	−0.867873	+	0.496787i	$0.834513\pi$
$878$	−35.5178	−1.19867
$879$	5.76083	0.194308
$880$	1.00000	0.0337100
$881$	−6.17209	−0.207943	−0.103971	−	0.994580i	$-0.533155\pi$
$881$	−6.17209	−0.207943	−0.103971	+	0.994580i	$0.533155\pi$
$882$	−3.71912	−0.125229
$883$	33.3931	1.12377	0.561884	−	0.827216i	$-0.310077\pi$
$883$	33.3931	1.12377	0.561884	+	0.827216i	$0.310077\pi$
$884$	−3.21613	−0.108170
$885$	3.71980	0.125040
$886$	39.7320	1.33482
$887$	−29.4796	−0.989829	−0.494915	−	0.868942i	$-0.664801\pi$
$887$	−29.4796	−0.989829	−0.494915	+	0.868942i	$0.664801\pi$
$888$	−4.67750	−0.156966
$889$	9.03195	0.302922
$890$	3.85436	0.129198
$891$	9.74596	0.326502
$892$	−26.9918	−0.903752
$893$	33.3968	1.11758
$894$	−25.4259	−0.850368
$895$	0.0200101	0.000668865 0
$896$	−4.53794	−0.151602
$897$	−1.66057	−0.0554449
$898$	−4.55922	−0.152143
$899$	−28.1505	−0.938872
$900$	0.273608	0.00912027
$901$	−17.8851	−0.595839
$902$	2.61453	0.0870545
$903$	8.21054	0.273230
$904$	−0.00194142	−6.45707e−5 0
$905$	−15.0756	−0.501130
$906$	20.5639	0.683190
$907$	2.62122	0.0870360	0.0435180	−	0.999053i	$-0.486143\pi$
$907$	2.62122	0.0870360	0.0435180	+	0.999053i	$0.486143\pi$
$908$	16.1933	0.537395
$909$	4.92042	0.163200
$910$	5.83904	0.193562
$911$	−5.21219	−0.172688	−0.0863438	−	0.996265i	$-0.527518\pi$
$911$	−5.21219	−0.172688	−0.0863438	+	0.996265i	$0.527518\pi$
$912$	7.78817	0.257892
$913$	−14.5435	−0.481318
$914$	−14.5725	−0.482016
$915$	13.0423	0.431165
$916$	−3.67036	−0.121272
$917$	−28.0443	−0.926103
$918$	−12.3297	−0.406940
$919$	−0.383739	−0.0126584	−0.00632918	−	0.999980i	$-0.502015\pi$
$919$	−0.383739	−0.0126584	−0.00632918	+	0.999980i	$0.502015\pi$
$920$	−0.713282	−0.0235162
$921$	−48.4414	−1.59620
$922$	−37.2850	−1.22792
$923$	−13.4486	−0.442664
$924$	−8.21054	−0.270107
$925$	2.58524	0.0850020
$926$	−13.2646	−0.435901
$927$	5.35226	0.175791
$928$	4.09374	0.134383
$929$	−21.7734	−0.714361	−0.357181	−	0.934035i	$-0.616262\pi$
$929$	−21.7734	−0.714361	−0.357181	+	0.934035i	$0.616262\pi$
$930$	12.4417	0.407980
$931$	58.5104	1.91760
$932$	2.89466	0.0948179
$933$	−44.3634	−1.45239
$934$	18.9504	0.620077
$935$	−2.49948	−0.0817417
$936$	−0.352056	−0.0115073
$937$	−21.3384	−0.697096	−0.348548	−	0.937291i	$-0.613325\pi$
$937$	−21.3384	−0.697096	−0.348548	+	0.937291i	$0.613325\pi$
$938$	−22.1882	−0.724470
$939$	45.3474	1.47986
$940$	−7.75858	−0.253057
$941$	−33.1664	−1.08119	−0.540596	−	0.841282i	$-0.681801\pi$
$941$	−33.1664	−1.08119	−0.540596	+	0.841282i	$0.681801\pi$
$942$	−30.7397	−1.00155
$943$	−1.86490	−0.0607295
$944$	−2.05592	−0.0669146
$945$	22.3851	0.728189
$946$	1.00000	0.0325128
$947$	−2.99219	−0.0972331	−0.0486166	−	0.998818i	$-0.515481\pi$
$947$	−2.99219	−0.0972331	−0.0486166	+	0.998818i	$0.515481\pi$
$948$	25.6493	0.833052
$949$	−5.57798	−0.181069
$950$	−4.30450	−0.139656
$951$	−53.7244	−1.74213
$952$	11.3425	0.367612
$953$	−30.6329	−0.992296	−0.496148	−	0.868238i	$-0.665253\pi$
$953$	−30.6329	−0.992296	−0.496148	+	0.868238i	$0.665253\pi$
$954$	−1.95781	−0.0633864
$955$	22.3644	0.723694
$956$	−24.6223	−0.796343
$957$	7.40684	0.239429
$958$	−0.0755036	−0.00243941
$959$	−85.9362	−2.77502
$960$	−1.80931	−0.0583953
$961$	16.2861	0.525357
$962$	−3.32647	−0.107250
$963$	−2.82664	−0.0910873
$964$	13.6048	0.438182
$965$	17.6534	0.568284
$966$	5.85643	0.188428
$967$	−4.71248	−0.151543	−0.0757716	−	0.997125i	$-0.524142\pi$
$967$	−4.71248	−0.151543	−0.0757716	+	0.997125i	$0.524142\pi$
$968$	−1.00000	−0.0321412
$969$	−19.4664	−0.625350
$970$	10.0330	0.322140
$971$	13.9972	0.449193	0.224597	−	0.974452i	$-0.427894\pi$
$971$	13.9972	0.449193	0.224597	+	0.974452i	$0.427894\pi$
$972$	−2.83481	−0.0909264
$973$	−45.5415	−1.45999
$974$	−16.1032	−0.515980
$975$	2.32807	0.0745580
$976$	−7.20843	−0.230736
$977$	−36.0644	−1.15380	−0.576902	−	0.816814i	$-0.695738\pi$
$977$	−36.0644	−1.15380	−0.576902	+	0.816814i	$0.695738\pi$
$978$	33.9162	1.08452
$979$	−3.85436	−0.123186
$980$	−13.5929	−0.434208
$981$	−4.28146	−0.136697
$982$	2.33686	0.0745721
$983$	−25.3547	−0.808689	−0.404345	−	0.914607i	$-0.632500\pi$
$983$	−25.3547	−0.808689	−0.404345	+	0.914607i	$0.632500\pi$
$984$	−4.73051	−0.150803
$985$	0.716160	0.0228188
$986$	−10.2322	−0.325860
$987$	63.7021	2.02766
$988$	5.53867	0.176209
$989$	−0.713282	−0.0226811
$990$	−0.273608	−0.00869584
$991$	7.09576	0.225404	0.112702	−	0.993629i	$-0.464049\pi$
$991$	7.09576	0.225404	0.112702	+	0.993629i	$0.464049\pi$
$992$	−6.87649	−0.218329
$993$	49.5750	1.57322
$994$	47.4297	1.50438
$995$	10.1363	0.321344
$996$	26.3136	0.833780
$997$	−31.3283	−0.992176	−0.496088	−	0.868272i	$-0.665231\pi$
$997$	−31.3283	−0.992176	−0.496088	+	0.868272i	$0.665231\pi$
$998$	14.5428	0.460343
$999$	−12.7527	−0.403477

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.bb.1.9	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.bb.1.9	✓	11	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4730.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.80931 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.80931 q^{6} +4.53794 q^{7} -1.00000 q^{8} +0.273608 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.80931 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.80931 q^{6} +4.53794 q^{7} -1.00000 q^{8} +0.273608 q^{9} +1.00000 q^{10} -1.00000 q^{11} +1.80931 q^{12} +1.28672 q^{13} -4.53794 q^{14} -1.80931 q^{15} +1.00000 q^{16} -2.49948 q^{17} -0.273608 q^{18} +4.30450 q^{19} -1.00000 q^{20} +8.21054 q^{21} +1.00000 q^{22} -0.713282 q^{23} -1.80931 q^{24} +1.00000 q^{25} -1.28672 q^{26} -4.93289 q^{27} +4.53794 q^{28} -4.09374 q^{29} +1.80931 q^{30} +6.87649 q^{31} -1.00000 q^{32} -1.80931 q^{33} +2.49948 q^{34} -4.53794 q^{35} +0.273608 q^{36} +2.58524 q^{37} -4.30450 q^{38} +2.32807 q^{39} +1.00000 q^{40} +2.61453 q^{41} -8.21054 q^{42} +1.00000 q^{43} -1.00000 q^{44} -0.273608 q^{45} +0.713282 q^{46} +7.75858 q^{47} +1.80931 q^{48} +13.5929 q^{49} -1.00000 q^{50} -4.52234 q^{51} +1.28672 q^{52} +7.15552 q^{53} +4.93289 q^{54} +1.00000 q^{55} -4.53794 q^{56} +7.78817 q^{57} +4.09374 q^{58} -2.05592 q^{59} -1.80931 q^{60} -7.20843 q^{61} -6.87649 q^{62} +1.24162 q^{63} +1.00000 q^{64} -1.28672 q^{65} +1.80931 q^{66} +4.88949 q^{67} -2.49948 q^{68} -1.29055 q^{69} +4.53794 q^{70} -10.4518 q^{71} -0.273608 q^{72} -4.33504 q^{73} -2.58524 q^{74} +1.80931 q^{75} +4.30450 q^{76} -4.53794 q^{77} -2.32807 q^{78} +14.1763 q^{79} -1.00000 q^{80} -9.74596 q^{81} -2.61453 q^{82} +14.5435 q^{83} +8.21054 q^{84} +2.49948 q^{85} -1.00000 q^{86} -7.40684 q^{87} +1.00000 q^{88} +3.85436 q^{89} +0.273608 q^{90} +5.83904 q^{91} -0.713282 q^{92} +12.4417 q^{93} -7.75858 q^{94} -4.30450 q^{95} -1.80931 q^{96} +10.0330 q^{97} -13.5929 q^{98} -0.273608 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 11 q^{2} - q^{3} + 11 q^{4} - 11 q^{5} + q^{6} + 6 q^{7} - 11 q^{8} + 12 q^{9}+O(q^{10}) \) 11 * q - 11 * q^2 - q^3 + 11 * q^4 - 11 * q^5 + q^6 + 6 * q^7 - 11 * q^8 + 12 * q^9	\( 11 q - 11 q^{2} - q^{3} + 11 q^{4} - 11 q^{5} + q^{6} + 6 q^{7} - 11 q^{8} + 12 q^{9} + 11 q^{10} - 11 q^{11} - q^{12} + 4 q^{13} - 6 q^{14} + q^{15} + 11 q^{16} - 10 q^{17} - 12 q^{18} + 14 q^{19} - 11 q^{20} - 2 q^{21} + 11 q^{22} - 18 q^{23} + q^{24} + 11 q^{25} - 4 q^{26} + 2 q^{27} + 6 q^{28} - 6 q^{29} - q^{30} + 13 q^{31} - 11 q^{32} + q^{33} + 10 q^{34} - 6 q^{35} + 12 q^{36} + q^{37} - 14 q^{38} + 12 q^{39} + 11 q^{40} + 12 q^{41} + 2 q^{42} + 11 q^{43} - 11 q^{44} - 12 q^{45} + 18 q^{46} - 5 q^{47} - q^{48} + 31 q^{49} - 11 q^{50} + q^{51} + 4 q^{52} - 27 q^{53} - 2 q^{54} + 11 q^{55} - 6 q^{56} - 5 q^{57} + 6 q^{58} + 11 q^{59} + q^{60} + 36 q^{61} - 13 q^{62} + 17 q^{63} + 11 q^{64} - 4 q^{65} - q^{66} + 18 q^{67} - 10 q^{68} + 14 q^{69} + 6 q^{70} - 14 q^{71} - 12 q^{72} - 11 q^{73} - q^{74} - q^{75} + 14 q^{76} - 6 q^{77} - 12 q^{78} + 28 q^{79} - 11 q^{80} + 7 q^{81} - 12 q^{82} - 4 q^{83} - 2 q^{84} + 10 q^{85} - 11 q^{86} + 38 q^{87} + 11 q^{88} - 7 q^{89} + 12 q^{90} + 14 q^{91} - 18 q^{92} - 3 q^{93} + 5 q^{94} - 14 q^{95} + q^{96} - q^{97} - 31 q^{98} - 12 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - q^3 + 11 * q^4 - 11 * q^5 + q^6 + 6 * q^7 - 11 * q^8 + 12 * q^9 + 11 * q^10 - 11 * q^11 - q^12 + 4 * q^13 - 6 * q^14 + q^15 + 11 * q^16 - 10 * q^17 - 12 * q^18 + 14 * q^19 - 11 * q^20 - 2 * q^21 + 11 * q^22 - 18 * q^23 + q^24 + 11 * q^25 - 4 * q^26 + 2 * q^27 + 6 * q^28 - 6 * q^29 - q^30 + 13 * q^31 - 11 * q^32 + q^33 + 10 * q^34 - 6 * q^35 + 12 * q^36 + q^37 - 14 * q^38 + 12 * q^39 + 11 * q^40 + 12 * q^41 + 2 * q^42 + 11 * q^43 - 11 * q^44 - 12 * q^45 + 18 * q^46 - 5 * q^47 - q^48 + 31 * q^49 - 11 * q^50 + q^51 + 4 * q^52 - 27 * q^53 - 2 * q^54 + 11 * q^55 - 6 * q^56 - 5 * q^57 + 6 * q^58 + 11 * q^59 + q^60 + 36 * q^61 - 13 * q^62 + 17 * q^63 + 11 * q^64 - 4 * q^65 - q^66 + 18 * q^67 - 10 * q^68 + 14 * q^69 + 6 * q^70 - 14 * q^71 - 12 * q^72 - 11 * q^73 - q^74 - q^75 + 14 * q^76 - 6 * q^77 - 12 * q^78 + 28 * q^79 - 11 * q^80 + 7 * q^81 - 12 * q^82 - 4 * q^83 - 2 * q^84 + 10 * q^85 - 11 * q^86 + 38 * q^87 + 11 * q^88 - 7 * q^89 + 12 * q^90 + 14 * q^91 - 18 * q^92 - 3 * q^93 + 5 * q^94 - 14 * q^95 + q^96 - q^97 - 31 * q^98 - 12 * q^99

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