LMFDB - Embedded newform 4730.2.a.bd.1.5

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} - 3 x^{10} - 25 x^{9} + 72 x^{8} + 216 x^{7} - 572 x^{6} - 767 x^{5} + 1665 x^{4} + 993 x^{3} + \cdots + 64 $ x^11 - 3x^10 - 25x^9 + 72x^8 + 216x^7 - 572x^6 - 767x^5 + 1665x^4 + 993x^3 - 1256x^2 + 96x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.183468$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -0.183468 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.183468 q^{6} -3.52029 q^{7} +1.00000 q^{8} -2.96634 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.183468 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.183468 q^{6} -3.52029 q^{7} +1.00000 q^{8} -2.96634 q^{9} +1.00000 q^{10} +1.00000 q^{11} -0.183468 q^{12} -4.25907 q^{13} -3.52029 q^{14} -0.183468 q^{15} +1.00000 q^{16} -0.133399 q^{17} -2.96634 q^{18} +2.57864 q^{19} +1.00000 q^{20} +0.645860 q^{21} +1.00000 q^{22} +3.03457 q^{23} -0.183468 q^{24} +1.00000 q^{25} -4.25907 q^{26} +1.09463 q^{27} -3.52029 q^{28} -1.44019 q^{29} -0.183468 q^{30} +9.53993 q^{31} +1.00000 q^{32} -0.183468 q^{33} -0.133399 q^{34} -3.52029 q^{35} -2.96634 q^{36} +5.20377 q^{37} +2.57864 q^{38} +0.781402 q^{39} +1.00000 q^{40} -5.06051 q^{41} +0.645860 q^{42} -1.00000 q^{43} +1.00000 q^{44} -2.96634 q^{45} +3.03457 q^{46} +7.87054 q^{47} -0.183468 q^{48} +5.39247 q^{49} +1.00000 q^{50} +0.0244744 q^{51} -4.25907 q^{52} +7.91666 q^{53} +1.09463 q^{54} +1.00000 q^{55} -3.52029 q^{56} -0.473097 q^{57} -1.44019 q^{58} -9.81709 q^{59} -0.183468 q^{60} +7.68968 q^{61} +9.53993 q^{62} +10.4424 q^{63} +1.00000 q^{64} -4.25907 q^{65} -0.183468 q^{66} +9.85223 q^{67} -0.133399 q^{68} -0.556746 q^{69} -3.52029 q^{70} +4.62209 q^{71} -2.96634 q^{72} +1.46897 q^{73} +5.20377 q^{74} -0.183468 q^{75} +2.57864 q^{76} -3.52029 q^{77} +0.781402 q^{78} -5.97343 q^{79} +1.00000 q^{80} +8.69819 q^{81} -5.06051 q^{82} +13.0423 q^{83} +0.645860 q^{84} -0.133399 q^{85} -1.00000 q^{86} +0.264228 q^{87} +1.00000 q^{88} +7.08632 q^{89} -2.96634 q^{90} +14.9932 q^{91} +3.03457 q^{92} -1.75027 q^{93} +7.87054 q^{94} +2.57864 q^{95} -0.183468 q^{96} +6.08942 q^{97} +5.39247 q^{98} -2.96634 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 11 q^{2} + 3 q^{3} + 11 q^{4} + 11 q^{5} + 3 q^{6} + 5 q^{7} + 11 q^{8} + 26 q^{9}+O(q^{10}) $ 11 * q + 11 * q^2 + 3 * q^3 + 11 * q^4 + 11 * q^5 + 3 * q^6 + 5 * q^7 + 11 * q^8 + 26 * q^9	\( 11 q + 11 q^{2} + 3 q^{3} + 11 q^{4} + 11 q^{5} + 3 q^{6} + 5 q^{7} + 11 q^{8} + 26 q^{9} + 11 q^{10} + 11 q^{11} + 3 q^{12} + q^{13} + 5 q^{14} + 3 q^{15} + 11 q^{16} + 8 q^{17} + 26 q^{18} + q^{19} + 11 q^{20} + 11 q^{22} + 20 q^{23} + 3 q^{24} + 11 q^{25} + q^{26} + 18 q^{27} + 5 q^{28} + 9 q^{29} + 3 q^{30} + 12 q^{31} + 11 q^{32} + 3 q^{33} + 8 q^{34} + 5 q^{35} + 26 q^{36} + 19 q^{37} + q^{38} - 18 q^{39} + 11 q^{40} + 9 q^{41} - 11 q^{43} + 11 q^{44} + 26 q^{45} + 20 q^{46} + 15 q^{47} + 3 q^{48} + 2 q^{49} + 11 q^{50} - 25 q^{51} + q^{52} + 35 q^{53} + 18 q^{54} + 11 q^{55} + 5 q^{56} - 25 q^{57} + 9 q^{58} + 13 q^{59} + 3 q^{60} + 9 q^{61} + 12 q^{62} + 22 q^{63} + 11 q^{64} + q^{65} + 3 q^{66} - q^{67} + 8 q^{68} + 12 q^{69} + 5 q^{70} + 14 q^{71} + 26 q^{72} - 20 q^{73} + 19 q^{74} + 3 q^{75} + q^{76} + 5 q^{77} - 18 q^{78} - 23 q^{79} + 11 q^{80} + 71 q^{81} + 9 q^{82} + 12 q^{83} + 8 q^{85} - 11 q^{86} + 6 q^{87} + 11 q^{88} - q^{89} + 26 q^{90} - 17 q^{91} + 20 q^{92} + 7 q^{93} + 15 q^{94} + q^{95} + 3 q^{96} + 17 q^{97} + 2 q^{98} + 26 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 + 3 * q^3 + 11 * q^4 + 11 * q^5 + 3 * q^6 + 5 * q^7 + 11 * q^8 + 26 * q^9 + 11 * q^10 + 11 * q^11 + 3 * q^12 + q^13 + 5 * q^14 + 3 * q^15 + 11 * q^16 + 8 * q^17 + 26 * q^18 + q^19 + 11 * q^20 + 11 * q^22 + 20 * q^23 + 3 * q^24 + 11 * q^25 + q^26 + 18 * q^27 + 5 * q^28 + 9 * q^29 + 3 * q^30 + 12 * q^31 + 11 * q^32 + 3 * q^33 + 8 * q^34 + 5 * q^35 + 26 * q^36 + 19 * q^37 + q^38 - 18 * q^39 + 11 * q^40 + 9 * q^41 - 11 * q^43 + 11 * q^44 + 26 * q^45 + 20 * q^46 + 15 * q^47 + 3 * q^48 + 2 * q^49 + 11 * q^50 - 25 * q^51 + q^52 + 35 * q^53 + 18 * q^54 + 11 * q^55 + 5 * q^56 - 25 * q^57 + 9 * q^58 + 13 * q^59 + 3 * q^60 + 9 * q^61 + 12 * q^62 + 22 * q^63 + 11 * q^64 + q^65 + 3 * q^66 - q^67 + 8 * q^68 + 12 * q^69 + 5 * q^70 + 14 * q^71 + 26 * q^72 - 20 * q^73 + 19 * q^74 + 3 * q^75 + q^76 + 5 * q^77 - 18 * q^78 - 23 * q^79 + 11 * q^80 + 71 * q^81 + 9 * q^82 + 12 * q^83 + 8 * q^85 - 11 * q^86 + 6 * q^87 + 11 * q^88 - q^89 + 26 * q^90 - 17 * q^91 + 20 * q^92 + 7 * q^93 + 15 * q^94 + q^95 + 3 * q^96 + 17 * q^97 + 2 * q^98 + 26 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−0.183468	−0.105925	−0.0529625	−	0.998596i	$-0.516866\pi$
$3$	−0.183468	−0.105925	−0.0529625	+	0.998596i	$0.516866\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.183468	−0.0749004
$7$	−3.52029	−1.33055	−0.665273	−	0.746600i	$-0.731685\pi$
$7$	−3.52029	−1.33055	−0.665273	+	0.746600i	$0.731685\pi$
$8$	1.00000	0.353553
$9$	−2.96634	−0.988780
$10$	1.00000	0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.183468	−0.0529625
$13$	−4.25907	−1.18125	−0.590627	−	0.806945i	$-0.701120\pi$
$13$	−4.25907	−1.18125	−0.590627	+	0.806945i	$0.701120\pi$
$14$	−3.52029	−0.940838
$15$	−0.183468	−0.0473711
$16$	1.00000	0.250000
$17$	−0.133399	−0.0323540	−0.0161770	−	0.999869i	$-0.505150\pi$
$17$	−0.133399	−0.0323540	−0.0161770	+	0.999869i	$0.505150\pi$
$18$	−2.96634	−0.699173
$19$	2.57864	0.591580	0.295790	−	0.955253i	$-0.404417\pi$
$19$	2.57864	0.591580	0.295790	+	0.955253i	$0.404417\pi$
$20$	1.00000	0.223607
$21$	0.645860	0.140938
$22$	1.00000	0.213201
$23$	3.03457	0.632752	0.316376	−	0.948634i	$-0.397534\pi$
$23$	3.03457	0.632752	0.316376	+	0.948634i	$0.397534\pi$
$24$	−0.183468	−0.0374502
$25$	1.00000	0.200000
$26$	−4.25907	−0.835273
$27$	1.09463	0.210662
$28$	−3.52029	−0.665273
$29$	−1.44019	−0.267437	−0.133718	−	0.991019i	$-0.542692\pi$
$29$	−1.44019	−0.267437	−0.133718	+	0.991019i	$0.542692\pi$
$30$	−0.183468	−0.0334965
$31$	9.53993	1.71342	0.856711	−	0.515797i	$-0.172504\pi$
$31$	9.53993	1.71342	0.856711	+	0.515797i	$0.172504\pi$
$32$	1.00000	0.176777
$33$	−0.183468	−0.0319376
$34$	−0.133399	−0.0228778
$35$	−3.52029	−0.595038
$36$	−2.96634	−0.494390
$37$	5.20377	0.855495	0.427747	−	0.903898i	$-0.359307\pi$
$37$	5.20377	0.855495	0.427747	+	0.903898i	$0.359307\pi$
$38$	2.57864	0.418310
$39$	0.781402	0.125124
$40$	1.00000	0.158114
$41$	−5.06051	−0.790319	−0.395159	−	0.918613i	$-0.629311\pi$
$41$	−5.06051	−0.790319	−0.395159	+	0.918613i	$0.629311\pi$
$42$	0.645860	0.0996584
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	1.00000	0.150756
$45$	−2.96634	−0.442196
$46$	3.03457	0.447424
$47$	7.87054	1.14804	0.574018	−	0.818843i	$-0.305384\pi$
$47$	7.87054	1.14804	0.574018	+	0.818843i	$0.305384\pi$
$48$	−0.183468	−0.0264813
$49$	5.39247	0.770353
$50$	1.00000	0.141421
$51$	0.0244744	0.00342710
$52$	−4.25907	−0.590627
$53$	7.91666	1.08744	0.543718	−	0.839268i	$-0.317016\pi$
$53$	7.91666	1.08744	0.543718	+	0.839268i	$0.317016\pi$
$54$	1.09463	0.148960
$55$	1.00000	0.134840
$56$	−3.52029	−0.470419
$57$	−0.473097	−0.0626632
$58$	−1.44019	−0.189106
$59$	−9.81709	−1.27808	−0.639038	−	0.769175i	$-0.720667\pi$
$59$	−9.81709	−1.27808	−0.639038	+	0.769175i	$0.720667\pi$
$60$	−0.183468	−0.0236856
$61$	7.68968	0.984562	0.492281	−	0.870436i	$-0.336163\pi$
$61$	7.68968	0.984562	0.492281	+	0.870436i	$0.336163\pi$
$62$	9.53993	1.21157
$63$	10.4424	1.31562
$64$	1.00000	0.125000
$65$	−4.25907	−0.528273
$66$	−0.183468	−0.0225833
$67$	9.85223	1.20364	0.601820	−	0.798631i	$-0.294442\pi$
$67$	9.85223	1.20364	0.601820	+	0.798631i	$0.294442\pi$
$68$	−0.133399	−0.0161770
$69$	−0.556746	−0.0670244
$70$	−3.52029	−0.420756
$71$	4.62209	0.548541	0.274271	−	0.961653i	$-0.411564\pi$
$71$	4.62209	0.548541	0.274271	+	0.961653i	$0.411564\pi$
$72$	−2.96634	−0.349586
$73$	1.46897	0.171930	0.0859651	−	0.996298i	$-0.472603\pi$
$73$	1.46897	0.171930	0.0859651	+	0.996298i	$0.472603\pi$
$74$	5.20377	0.604926
$75$	−0.183468	−0.0211850
$76$	2.57864	0.295790
$77$	−3.52029	−0.401175
$78$	0.781402	0.0884764
$79$	−5.97343	−0.672064	−0.336032	−	0.941851i	$-0.609085\pi$
$79$	−5.97343	−0.672064	−0.336032	+	0.941851i	$0.609085\pi$
$80$	1.00000	0.111803
$81$	8.69819	0.966466
$82$	−5.06051	−0.558840
$83$	13.0423	1.43157	0.715787	−	0.698318i	$-0.246068\pi$
$83$	13.0423	1.43157	0.715787	+	0.698318i	$0.246068\pi$
$84$	0.645860	0.0704691
$85$	−0.133399	−0.0144692
$86$	−1.00000	−0.107833
$87$	0.264228	0.0283283
$88$	1.00000	0.106600
$89$	7.08632	0.751149	0.375574	−	0.926792i	$-0.377445\pi$
$89$	7.08632	0.751149	0.375574	+	0.926792i	$0.377445\pi$
$90$	−2.96634	−0.312680
$91$	14.9932	1.57171
$92$	3.03457	0.316376
$93$	−1.75027	−0.181494
$94$	7.87054	0.811784
$95$	2.57864	0.264563
$96$	−0.183468	−0.0187251
$97$	6.08942	0.618287	0.309144	−	0.951015i	$-0.399958\pi$
$97$	6.08942	0.618287	0.309144	+	0.951015i	$0.399958\pi$
$98$	5.39247	0.544722
$99$	−2.96634	−0.298128
$100$	1.00000	0.100000
$101$	−9.80239	−0.975374	−0.487687	−	0.873018i	$-0.662159\pi$
$101$	−9.80239	−0.975374	−0.487687	+	0.873018i	$0.662159\pi$
$102$	0.0244744	0.00242333
$103$	−4.27733	−0.421458	−0.210729	−	0.977545i	$-0.567584\pi$
$103$	−4.27733	−0.421458	−0.210729	+	0.977545i	$0.567584\pi$
$104$	−4.25907	−0.417636
$105$	0.645860	0.0630295
$106$	7.91666	0.768934
$107$	3.19010	0.308399	0.154199	−	0.988040i	$-0.450720\pi$
$107$	3.19010	0.308399	0.154199	+	0.988040i	$0.450720\pi$
$108$	1.09463	0.105331
$109$	−5.21754	−0.499749	−0.249875	−	0.968278i	$-0.580389\pi$
$109$	−5.21754	−0.499749	−0.249875	+	0.968278i	$0.580389\pi$
$110$	1.00000	0.0953463
$111$	−0.954724	−0.0906184
$112$	−3.52029	−0.332637
$113$	10.4387	0.981994	0.490997	−	0.871161i	$-0.336633\pi$
$113$	10.4387	0.981994	0.490997	+	0.871161i	$0.336633\pi$
$114$	−0.473097	−0.0443096
$115$	3.03457	0.282975
$116$	−1.44019	−0.133718
$117$	12.6339	1.16800
$118$	−9.81709	−0.903736
$119$	0.469604	0.0430485
$120$	−0.183468	−0.0167482
$121$	1.00000	0.0909091
$122$	7.68968	0.696191
$123$	0.928440	0.0837146
$124$	9.53993	0.856711
$125$	1.00000	0.0894427
$126$	10.4424	0.930282
$127$	15.6171	1.38580	0.692898	−	0.721035i	$-0.256333\pi$
$127$	15.6171	1.38580	0.692898	+	0.721035i	$0.256333\pi$
$128$	1.00000	0.0883883
$129$	0.183468	0.0161534
$130$	−4.25907	−0.373545
$131$	−9.84360	−0.860039	−0.430020	−	0.902820i	$-0.641493\pi$
$131$	−9.84360	−0.860039	−0.430020	+	0.902820i	$0.641493\pi$
$132$	−0.183468	−0.0159688
$133$	−9.07757	−0.787125
$134$	9.85223	0.851103
$135$	1.09463	0.0942108
$136$	−0.133399	−0.0114389
$137$	16.1602	1.38066	0.690329	−	0.723495i	$-0.257466\pi$
$137$	16.1602	1.38066	0.690329	+	0.723495i	$0.257466\pi$
$138$	−0.556746	−0.0473934
$139$	−5.65496	−0.479647	−0.239824	−	0.970816i	$-0.577090\pi$
$139$	−5.65496	−0.479647	−0.239824	+	0.970816i	$0.577090\pi$
$140$	−3.52029	−0.297519
$141$	−1.44399	−0.121606
$142$	4.62209	0.387877
$143$	−4.25907	−0.356162
$144$	−2.96634	−0.247195
$145$	−1.44019	−0.119601
$146$	1.46897	0.121573
$147$	−0.989344	−0.0815997
$148$	5.20377	0.427747
$149$	4.87869	0.399678	0.199839	−	0.979829i	$-0.435958\pi$
$149$	4.87869	0.399678	0.199839	+	0.979829i	$0.435958\pi$
$150$	−0.183468	−0.0149801
$151$	−15.8367	−1.28877	−0.644387	−	0.764699i	$-0.722887\pi$
$151$	−15.8367	−1.28877	−0.644387	+	0.764699i	$0.722887\pi$
$152$	2.57864	0.209155
$153$	0.395707	0.0319910
$154$	−3.52029	−0.283673
$155$	9.53993	0.766266
$156$	0.781402	0.0625622
$157$	6.83916	0.545824	0.272912	−	0.962039i	$-0.412013\pi$
$157$	6.83916	0.545824	0.272912	+	0.962039i	$0.412013\pi$
$158$	−5.97343	−0.475221
$159$	−1.45245	−0.115187
$160$	1.00000	0.0790569
$161$	−10.6826	−0.841906
$162$	8.69819	0.683394
$163$	−13.8969	−1.08849	−0.544243	−	0.838927i	$-0.683183\pi$
$163$	−13.8969	−1.08849	−0.544243	+	0.838927i	$0.683183\pi$
$164$	−5.06051	−0.395159
$165$	−0.183468	−0.0142829
$166$	13.0423	1.01228
$167$	0.661555	0.0511926	0.0255963	−	0.999672i	$-0.491852\pi$
$167$	0.661555	0.0511926	0.0255963	+	0.999672i	$0.491852\pi$
$168$	0.645860	0.0498292
$169$	5.13970	0.395361
$170$	−0.133399	−0.0102312
$171$	−7.64912	−0.584943
$172$	−1.00000	−0.0762493
$173$	2.25636	0.171548	0.0857740	−	0.996315i	$-0.472664\pi$
$173$	2.25636	0.171548	0.0857740	+	0.996315i	$0.472664\pi$
$174$	0.264228	0.0200311
$175$	−3.52029	−0.266109
$176$	1.00000	0.0753778
$177$	1.80112	0.135380
$178$	7.08632	0.531142
$179$	4.21374	0.314949	0.157475	−	0.987523i	$-0.449665\pi$
$179$	4.21374	0.314949	0.157475	+	0.987523i	$0.449665\pi$
$180$	−2.96634	−0.221098
$181$	−14.0442	−1.04390	−0.521948	−	0.852977i	$-0.674794\pi$
$181$	−14.0442	−1.04390	−0.521948	+	0.852977i	$0.674794\pi$
$182$	14.9932	1.11137
$183$	−1.41081	−0.104290
$184$	3.03457	0.223712
$185$	5.20377	0.382589
$186$	−1.75027	−0.128336
$187$	−0.133399	−0.00975511
$188$	7.87054	0.574018
$189$	−3.85342	−0.280295
$190$	2.57864	0.187074
$191$	−5.84276	−0.422767	−0.211384	−	0.977403i	$-0.567797\pi$
$191$	−5.84276	−0.422767	−0.211384	+	0.977403i	$0.567797\pi$
$192$	−0.183468	−0.0132406
$193$	11.3153	0.814492	0.407246	−	0.913318i	$-0.366489\pi$
$193$	11.3153	0.814492	0.407246	+	0.913318i	$0.366489\pi$
$194$	6.08942	0.437195
$195$	0.781402	0.0559574
$196$	5.39247	0.385177
$197$	−7.21148	−0.513796	−0.256898	−	0.966438i	$-0.582701\pi$
$197$	−7.21148	−0.513796	−0.256898	+	0.966438i	$0.582701\pi$
$198$	−2.96634	−0.210809
$199$	10.9893	0.779007	0.389504	−	0.921025i	$-0.372647\pi$
$199$	10.9893	0.779007	0.389504	+	0.921025i	$0.372647\pi$
$200$	1.00000	0.0707107
$201$	−1.80756	−0.127496
$202$	−9.80239	−0.689694
$203$	5.06990	0.355837
$204$	0.0244744	0.00171355
$205$	−5.06051	−0.353441
$206$	−4.27733	−0.298016
$207$	−9.00158	−0.625653
$208$	−4.25907	−0.295314
$209$	2.57864	0.178368
$210$	0.645860	0.0445686
$211$	11.2353	0.773470	0.386735	−	0.922191i	$-0.373603\pi$
$211$	11.2353	0.773470	0.386735	+	0.922191i	$0.373603\pi$
$212$	7.91666	0.543718
$213$	−0.848004	−0.0581043
$214$	3.19010	0.218071
$215$	−1.00000	−0.0681994
$216$	1.09463	0.0744802
$217$	−33.5834	−2.27979
$218$	−5.21754	−0.353376
$219$	−0.269509	−0.0182117
$220$	1.00000	0.0674200
$221$	0.568156	0.0382183
$222$	−0.954724	−0.0640769
$223$	−25.4181	−1.70212	−0.851061	−	0.525067i	$-0.824040\pi$
$223$	−25.4181	−1.70212	−0.851061	+	0.525067i	$0.824040\pi$
$224$	−3.52029	−0.235210
$225$	−2.96634	−0.197756
$226$	10.4387	0.694375
$227$	−2.46747	−0.163772	−0.0818858	−	0.996642i	$-0.526094\pi$
$227$	−2.46747	−0.163772	−0.0818858	+	0.996642i	$0.526094\pi$
$228$	−0.473097	−0.0313316
$229$	−12.6781	−0.837795	−0.418897	−	0.908034i	$-0.637583\pi$
$229$	−12.6781	−0.837795	−0.418897	+	0.908034i	$0.637583\pi$
$230$	3.03457	0.200094
$231$	0.645860	0.0424945
$232$	−1.44019	−0.0945532
$233$	−10.2702	−0.672825	−0.336413	−	0.941715i	$-0.609214\pi$
$233$	−10.2702	−0.672825	−0.336413	+	0.941715i	$0.609214\pi$
$234$	12.6339	0.825901
$235$	7.87054	0.513417
$236$	−9.81709	−0.639038
$237$	1.09593	0.0711884
$238$	0.469604	0.0304399
$239$	−12.1694	−0.787175	−0.393587	−	0.919287i	$-0.628766\pi$
$239$	−12.1694	−0.787175	−0.393587	+	0.919287i	$0.628766\pi$
$240$	−0.183468	−0.0118428
$241$	11.2916	0.727357	0.363679	−	0.931524i	$-0.381521\pi$
$241$	11.2916	0.727357	0.363679	+	0.931524i	$0.381521\pi$
$242$	1.00000	0.0642824
$243$	−4.87973	−0.313035
$244$	7.68968	0.492281
$245$	5.39247	0.344512
$246$	0.928440	0.0591952
$247$	−10.9826	−0.698807
$248$	9.53993	0.605786
$249$	−2.39283	−0.151640
$250$	1.00000	0.0632456
$251$	17.3135	1.09282	0.546409	−	0.837518i	$-0.315994\pi$
$251$	17.3135	1.09282	0.546409	+	0.837518i	$0.315994\pi$
$252$	10.4424	0.657809
$253$	3.03457	0.190782
$254$	15.6171	0.979906
$255$	0.0244744	0.00153265
$256$	1.00000	0.0625000
$257$	19.2140	1.19854	0.599268	−	0.800549i	$-0.295458\pi$
$257$	19.2140	1.19854	0.599268	+	0.800549i	$0.295458\pi$
$258$	0.183468	0.0114222
$259$	−18.3188	−1.13828
$260$	−4.25907	−0.264136
$261$	4.27210	0.264436
$262$	−9.84360	−0.608140
$263$	6.49855	0.400718	0.200359	−	0.979723i	$-0.435789\pi$
$263$	6.49855	0.400718	0.200359	+	0.979723i	$0.435789\pi$
$264$	−0.183468	−0.0112917
$265$	7.91666	0.486316
$266$	−9.07757	−0.556581
$267$	−1.30011	−0.0795655
$268$	9.85223	0.601820
$269$	11.7237	0.714807	0.357404	−	0.933950i	$-0.383662\pi$
$269$	11.7237	0.714807	0.357404	+	0.933950i	$0.383662\pi$
$270$	1.09463	0.0666171
$271$	4.27789	0.259863	0.129932	−	0.991523i	$-0.458524\pi$
$271$	4.27789	0.259863	0.129932	+	0.991523i	$0.458524\pi$
$272$	−0.133399	−0.00808851
$273$	−2.75077	−0.166484
$274$	16.1602	0.976273
$275$	1.00000	0.0603023
$276$	−0.556746	−0.0335122
$277$	−18.7577	−1.12704	−0.563519	−	0.826103i	$-0.690553\pi$
$277$	−18.7577	−1.12704	−0.563519	+	0.826103i	$0.690553\pi$
$278$	−5.65496	−0.339162
$279$	−28.2987	−1.69420
$280$	−3.52029	−0.210378
$281$	6.87179	0.409937	0.204968	−	0.978769i	$-0.434291\pi$
$281$	6.87179	0.409937	0.204968	+	0.978769i	$0.434291\pi$
$282$	−1.44399	−0.0859883
$283$	3.66883	0.218089	0.109045	−	0.994037i	$-0.465221\pi$
$283$	3.66883	0.218089	0.109045	+	0.994037i	$0.465221\pi$
$284$	4.62209	0.274271
$285$	−0.473097	−0.0280238
$286$	−4.25907	−0.251844
$287$	17.8145	1.05156
$288$	−2.96634	−0.174793
$289$	−16.9822	−0.998953
$290$	−1.44019	−0.0845709
$291$	−1.11721	−0.0654921
$292$	1.46897	0.0859651
$293$	30.4846	1.78093	0.890466	−	0.455050i	$-0.150379\pi$
$293$	30.4846	1.78093	0.890466	+	0.455050i	$0.150379\pi$
$294$	−0.989344	−0.0576997
$295$	−9.81709	−0.571573
$296$	5.20377	0.302463
$297$	1.09463	0.0635169
$298$	4.87869	0.282615
$299$	−12.9245	−0.747441
$300$	−0.183468	−0.0105925
$301$	3.52029	0.202906
$302$	−15.8367	−0.911301
$303$	1.79842	0.103317
$304$	2.57864	0.147895
$305$	7.68968	0.440310
$306$	0.395707	0.0226211
$307$	−10.2159	−0.583054	−0.291527	−	0.956563i	$-0.594163\pi$
$307$	−10.2159	−0.583054	−0.291527	+	0.956563i	$0.594163\pi$
$308$	−3.52029	−0.200587
$309$	0.784752	0.0446430
$310$	9.53993	0.541832
$311$	−5.53935	−0.314108	−0.157054	−	0.987590i	$-0.550200\pi$
$311$	−5.53935	−0.314108	−0.157054	+	0.987590i	$0.550200\pi$
$312$	0.781402	0.0442382
$313$	1.38818	0.0784643	0.0392322	−	0.999230i	$-0.487509\pi$
$313$	1.38818	0.0784643	0.0392322	+	0.999230i	$0.487509\pi$
$314$	6.83916	0.385956
$315$	10.4424	0.588362
$316$	−5.97343	−0.336032
$317$	−7.70949	−0.433008	−0.216504	−	0.976282i	$-0.569465\pi$
$317$	−7.70949	−0.433008	−0.216504	+	0.976282i	$0.569465\pi$
$318$	−1.45245	−0.0814494
$319$	−1.44019	−0.0806352
$320$	1.00000	0.0559017
$321$	−0.585281	−0.0326672
$322$	−10.6826	−0.595318
$323$	−0.343988	−0.0191400
$324$	8.69819	0.483233
$325$	−4.25907	−0.236251
$326$	−13.8969	−0.769676
$327$	0.957249	0.0529360
$328$	−5.06051	−0.279420
$329$	−27.7066	−1.52751
$330$	−0.183468	−0.0100996
$331$	−8.96835	−0.492945	−0.246473	−	0.969150i	$-0.579272\pi$
$331$	−8.96835	−0.492945	−0.246473	+	0.969150i	$0.579272\pi$
$332$	13.0423	0.715787
$333$	−15.4362	−0.845896
$334$	0.661555	0.0361987
$335$	9.85223	0.538285
$336$	0.645860	0.0352346
$337$	31.6100	1.72191	0.860953	−	0.508685i	$-0.169868\pi$
$337$	31.6100	1.72191	0.860953	+	0.508685i	$0.169868\pi$
$338$	5.13970	0.279563
$339$	−1.91517	−0.104018
$340$	−0.133399	−0.00723458
$341$	9.53993	0.516616
$342$	−7.64912	−0.413617
$343$	5.65897	0.305556
$344$	−1.00000	−0.0539164
$345$	−0.556746	−0.0299742
$346$	2.25636	0.121303
$347$	13.0712	0.701698	0.350849	−	0.936432i	$-0.385893\pi$
$347$	13.0712	0.701698	0.350849	+	0.936432i	$0.385893\pi$
$348$	0.264228	0.0141641
$349$	11.6461	0.623401	0.311701	−	0.950180i	$-0.399101\pi$
$349$	11.6461	0.623401	0.311701	+	0.950180i	$0.399101\pi$
$350$	−3.52029	−0.188168
$351$	−4.66211	−0.248845
$352$	1.00000	0.0533002
$353$	12.4962	0.665106	0.332553	−	0.943085i	$-0.392090\pi$
$353$	12.4962	0.665106	0.332553	+	0.943085i	$0.392090\pi$
$354$	1.80112	0.0957283
$355$	4.62209	0.245315
$356$	7.08632	0.375574
$357$	−0.0861572	−0.00455992
$358$	4.21374	0.222703
$359$	−13.7833	−0.727457	−0.363729	−	0.931505i	$-0.618496\pi$
$359$	−13.7833	−0.727457	−0.363729	+	0.931505i	$0.618496\pi$
$360$	−2.96634	−0.156340
$361$	−12.3506	−0.650033
$362$	−14.0442	−0.738146
$363$	−0.183468	−0.00962955
$364$	14.9932	0.785857
$365$	1.46897	0.0768895
$366$	−1.41081	−0.0737441
$367$	−13.2415	−0.691201	−0.345601	−	0.938382i	$-0.612325\pi$
$367$	−13.2415	−0.691201	−0.345601	+	0.938382i	$0.612325\pi$
$368$	3.03457	0.158188
$369$	15.0112	0.781451
$370$	5.20377	0.270531
$371$	−27.8690	−1.44688
$372$	−1.75027	−0.0907472
$373$	2.27006	0.117539	0.0587697	−	0.998272i	$-0.481282\pi$
$373$	2.27006	0.117539	0.0587697	+	0.998272i	$0.481282\pi$
$374$	−0.133399	−0.00689790
$375$	−0.183468	−0.00947423
$376$	7.87054	0.405892
$377$	6.13388	0.315911
$378$	−3.85342	−0.198199
$379$	13.4425	0.690494	0.345247	−	0.938512i	$-0.387795\pi$
$379$	13.4425	0.690494	0.345247	+	0.938512i	$0.387795\pi$
$380$	2.57864	0.132281
$381$	−2.86524	−0.146791
$382$	−5.84276	−0.298942
$383$	−14.7914	−0.755804	−0.377902	−	0.925846i	$-0.623354\pi$
$383$	−14.7914	−0.755804	−0.377902	+	0.925846i	$0.623354\pi$
$384$	−0.183468	−0.00936254
$385$	−3.52029	−0.179411
$386$	11.3153	0.575933
$387$	2.96634	0.150788
$388$	6.08942	0.309144
$389$	2.66523	0.135133	0.0675663	−	0.997715i	$-0.478477\pi$
$389$	2.66523	0.135133	0.0675663	+	0.997715i	$0.478477\pi$
$390$	0.781402	0.0395678
$391$	−0.404809	−0.0204721
$392$	5.39247	0.272361
$393$	1.80598	0.0910998
$394$	−7.21148	−0.363309
$395$	−5.97343	−0.300556
$396$	−2.96634	−0.149064
$397$	10.1238	0.508097	0.254048	−	0.967192i	$-0.418238\pi$
$397$	10.1238	0.508097	0.254048	+	0.967192i	$0.418238\pi$
$398$	10.9893	0.550841
$399$	1.66544	0.0833763
$400$	1.00000	0.0500000
$401$	−0.955959	−0.0477383	−0.0238691	−	0.999715i	$-0.507599\pi$
$401$	−0.955959	−0.0477383	−0.0238691	+	0.999715i	$0.507599\pi$
$402$	−1.80756	−0.0901531
$403$	−40.6313	−2.02399
$404$	−9.80239	−0.487687
$405$	8.69819	0.432217
$406$	5.06990	0.251615
$407$	5.20377	0.257941
$408$	0.0244744	0.00121166
$409$	7.69938	0.380710	0.190355	−	0.981715i	$-0.439036\pi$
$409$	7.69938	0.380710	0.190355	+	0.981715i	$0.439036\pi$
$410$	−5.06051	−0.249921
$411$	−2.96487	−0.146246
$412$	−4.27733	−0.210729
$413$	34.5590	1.70054
$414$	−9.00158	−0.442403
$415$	13.0423	0.640220
$416$	−4.25907	−0.208818
$417$	1.03750	0.0508067
$418$	2.57864	0.126125
$419$	3.74719	0.183062	0.0915310	−	0.995802i	$-0.470824\pi$
$419$	3.74719	0.183062	0.0915310	+	0.995802i	$0.470824\pi$
$420$	0.645860	0.0315147
$421$	25.3342	1.23471	0.617357	−	0.786683i	$-0.288203\pi$
$421$	25.3342	1.23471	0.617357	+	0.786683i	$0.288203\pi$
$422$	11.2353	0.546926
$423$	−23.3467	−1.13515
$424$	7.91666	0.384467
$425$	−0.133399	−0.00647081
$426$	−0.848004	−0.0410859
$427$	−27.0699	−1.31001
$428$	3.19010	0.154199
$429$	0.781402	0.0377264
$430$	−1.00000	−0.0482243
$431$	9.64747	0.464702	0.232351	−	0.972632i	$-0.425358\pi$
$431$	9.64747	0.464702	0.232351	+	0.972632i	$0.425358\pi$
$432$	1.09463	0.0526654
$433$	2.11153	0.101474	0.0507368	−	0.998712i	$-0.483843\pi$
$433$	2.11153	0.101474	0.0507368	+	0.998712i	$0.483843\pi$
$434$	−33.5834	−1.61205
$435$	0.264228	0.0126688
$436$	−5.21754	−0.249875
$437$	7.82507	0.374324
$438$	−0.269509	−0.0128776
$439$	−17.7022	−0.844882	−0.422441	−	0.906390i	$-0.638827\pi$
$439$	−17.7022	−0.844882	−0.422441	+	0.906390i	$0.638827\pi$
$440$	1.00000	0.0476731
$441$	−15.9959	−0.761710
$442$	0.568156	0.0270244
$443$	11.3323	0.538413	0.269207	−	0.963082i	$-0.413239\pi$
$443$	11.3323	0.538413	0.269207	+	0.963082i	$0.413239\pi$
$444$	−0.954724	−0.0453092
$445$	7.08632	0.335924
$446$	−25.4181	−1.20358
$447$	−0.895081	−0.0423359
$448$	−3.52029	−0.166318
$449$	4.73346	0.223386	0.111693	−	0.993743i	$-0.464373\pi$
$449$	4.73346	0.223386	0.111693	+	0.993743i	$0.464373\pi$
$450$	−2.96634	−0.139835
$451$	−5.06051	−0.238290
$452$	10.4387	0.490997
$453$	2.90553	0.136514
$454$	−2.46747	−0.115804
$455$	14.9932	0.702892
$456$	−0.473097	−0.0221548
$457$	7.00766	0.327805	0.163902	−	0.986477i	$-0.447592\pi$
$457$	7.00766	0.327805	0.163902	+	0.986477i	$0.447592\pi$
$458$	−12.6781	−0.592410
$459$	−0.146023	−0.00681576
$460$	3.03457	0.141488
$461$	40.0454	1.86510	0.932551	−	0.361038i	$-0.117578\pi$
$461$	40.0454	1.86510	0.932551	+	0.361038i	$0.117578\pi$
$462$	0.645860	0.0300481
$463$	−32.4564	−1.50838	−0.754189	−	0.656657i	$-0.771970\pi$
$463$	−32.4564	−1.50838	−0.754189	+	0.656657i	$0.771970\pi$
$464$	−1.44019	−0.0668592
$465$	−1.75027	−0.0811668
$466$	−10.2702	−0.475759
$467$	−32.3156	−1.49539	−0.747694	−	0.664043i	$-0.768839\pi$
$467$	−32.3156	−1.49539	−0.747694	+	0.664043i	$0.768839\pi$
$468$	12.6339	0.584000
$469$	−34.6827	−1.60150
$470$	7.87054	0.363041
$471$	−1.25476	−0.0578165
$472$	−9.81709	−0.451868
$473$	−1.00000	−0.0459800
$474$	1.09593	0.0503378
$475$	2.57864	0.118316
$476$	0.469604	0.0215243
$477$	−23.4835	−1.07524
$478$	−12.1694	−0.556617
$479$	−9.73786	−0.444934	−0.222467	−	0.974940i	$-0.571411\pi$
$479$	−9.73786	−0.444934	−0.222467	+	0.974940i	$0.571411\pi$
$480$	−0.183468	−0.00837411
$481$	−22.1632	−1.01056
$482$	11.2916	0.514319
$483$	1.95991	0.0891790
$484$	1.00000	0.0454545
$485$	6.08942	0.276507
$486$	−4.87973	−0.221349
$487$	15.6510	0.709214	0.354607	−	0.935015i	$-0.384615\pi$
$487$	15.6510	0.709214	0.354607	+	0.935015i	$0.384615\pi$
$488$	7.68968	0.348095
$489$	2.54963	0.115298
$490$	5.39247	0.243607
$491$	−1.00346	−0.0452854	−0.0226427	−	0.999744i	$-0.507208\pi$
$491$	−1.00346	−0.0452854	−0.0226427	+	0.999744i	$0.507208\pi$
$492$	0.928440	0.0418573
$493$	0.192120	0.00865266
$494$	−10.9826	−0.494131
$495$	−2.96634	−0.133327
$496$	9.53993	0.428355
$497$	−16.2711	−0.729859
$498$	−2.39283	−0.107225
$499$	−11.3672	−0.508868	−0.254434	−	0.967090i	$-0.581889\pi$
$499$	−11.3672	−0.508868	−0.254434	+	0.967090i	$0.581889\pi$
$500$	1.00000	0.0447214
$501$	−0.121374	−0.00542259
$502$	17.3135	0.772739
$503$	0.0564895	0.00251874	0.00125937	−	0.999999i	$-0.499599\pi$
$503$	0.0564895	0.00251874	0.00125937	+	0.999999i	$0.499599\pi$
$504$	10.4424	0.465141
$505$	−9.80239	−0.436201
$506$	3.03457	0.134903
$507$	−0.942968	−0.0418787
$508$	15.6171	0.692898
$509$	−14.9513	−0.662705	−0.331352	−	0.943507i	$-0.607505\pi$
$509$	−14.9513	−0.662705	−0.331352	+	0.943507i	$0.607505\pi$
$510$	0.0244744	0.00108375
$511$	−5.17122	−0.228761
$512$	1.00000	0.0441942
$513$	2.82266	0.124623
$514$	19.2140	0.847493
$515$	−4.27733	−0.188482
$516$	0.183468	0.00807671
$517$	7.87054	0.346146
$518$	−18.3188	−0.804882
$519$	−0.413969	−0.0181712
$520$	−4.25907	−0.186773
$521$	30.3586	1.33003	0.665016	−	0.746829i	$-0.268425\pi$
$521$	30.3586	1.33003	0.665016	+	0.746829i	$0.268425\pi$
$522$	4.27210	0.186985
$523$	14.9630	0.654288	0.327144	−	0.944975i	$-0.393914\pi$
$523$	14.9630	0.654288	0.327144	+	0.944975i	$0.393914\pi$
$524$	−9.84360	−0.430020
$525$	0.645860	0.0281876
$526$	6.49855	0.283350
$527$	−1.27262	−0.0554361
$528$	−0.183468	−0.00798440
$529$	−13.7914	−0.599624
$530$	7.91666	0.343878
$531$	29.1208	1.26374
$532$	−9.07757	−0.393562
$533$	21.5531	0.933567
$534$	−1.30011	−0.0562613
$535$	3.19010	0.137920
$536$	9.85223	0.425551
$537$	−0.773084	−0.0333611
$538$	11.7237	0.505445
$539$	5.39247	0.232270
$540$	1.09463	0.0471054
$541$	−14.3947	−0.618876	−0.309438	−	0.950920i	$-0.600141\pi$
$541$	−14.3947	−0.618876	−0.309438	+	0.950920i	$0.600141\pi$
$542$	4.27789	0.183751
$543$	2.57665	0.110575
$544$	−0.133399	−0.00571944
$545$	−5.21754	−0.223495
$546$	−2.75077	−0.117722
$547$	3.73616	0.159747	0.0798733	−	0.996805i	$-0.474548\pi$
$547$	3.73616	0.159747	0.0798733	+	0.996805i	$0.474548\pi$
$548$	16.1602	0.690329
$549$	−22.8102	−0.973515
$550$	1.00000	0.0426401
$551$	−3.71373	−0.158210
$552$	−0.556746	−0.0236967
$553$	21.0282	0.894212
$554$	−18.7577	−0.796937
$555$	−0.954724	−0.0405258
$556$	−5.65496	−0.239824
$557$	30.3050	1.28406	0.642031	−	0.766679i	$-0.278092\pi$
$557$	30.3050	1.28406	0.642031	+	0.766679i	$0.278092\pi$
$558$	−28.2987	−1.19798
$559$	4.25907	0.180140
$560$	−3.52029	−0.148760
$561$	0.0244744	0.00103331
$562$	6.87179	0.289869
$563$	−24.7059	−1.04123	−0.520616	−	0.853791i	$-0.674298\pi$
$563$	−24.7059	−1.04123	−0.520616	+	0.853791i	$0.674298\pi$
$564$	−1.44399	−0.0608029
$565$	10.4387	0.439161
$566$	3.66883	0.154212
$567$	−30.6202	−1.28593
$568$	4.62209	0.193939
$569$	−44.5859	−1.86914	−0.934570	−	0.355780i	$-0.884215\pi$
$569$	−44.5859	−1.86914	−0.934570	+	0.355780i	$0.884215\pi$
$570$	−0.473097	−0.0198158
$571$	19.9492	0.834849	0.417424	−	0.908712i	$-0.362933\pi$
$571$	19.9492	0.834849	0.417424	+	0.908712i	$0.362933\pi$
$572$	−4.25907	−0.178081
$573$	1.07196	0.0447817
$574$	17.8145	0.743562
$575$	3.03457	0.126550
$576$	−2.96634	−0.123597
$577$	−18.1123	−0.754023	−0.377012	−	0.926209i	$-0.623048\pi$
$577$	−18.1123	−0.754023	−0.377012	+	0.926209i	$0.623048\pi$
$578$	−16.9822	−0.706367
$579$	−2.07599	−0.0862752
$580$	−1.44019	−0.0598007
$581$	−45.9126	−1.90478
$582$	−1.11721	−0.0463099
$583$	7.91666	0.327875
$584$	1.46897	0.0607865
$585$	12.6339	0.522346
$586$	30.4846	1.25931
$587$	−14.6425	−0.604361	−0.302180	−	0.953251i	$-0.597714\pi$
$587$	−14.6425	−0.604361	−0.302180	+	0.953251i	$0.597714\pi$
$588$	−0.989344	−0.0407999
$589$	24.6000	1.01363
$590$	−9.81709	−0.404163
$591$	1.32307	0.0544239
$592$	5.20377	0.213874
$593$	−4.65501	−0.191158	−0.0955791	−	0.995422i	$-0.530470\pi$
$593$	−4.65501	−0.191158	−0.0955791	+	0.995422i	$0.530470\pi$
$594$	1.09463	0.0449132
$595$	0.469604	0.0192519
$596$	4.87869	0.199839
$597$	−2.01617	−0.0825164
$598$	−12.9245	−0.528521
$599$	36.6204	1.49627	0.748134	−	0.663547i	$-0.230950\pi$
$599$	36.6204	1.49627	0.748134	+	0.663547i	$0.230950\pi$
$600$	−0.183468	−0.00749004
$601$	9.68570	0.395088	0.197544	−	0.980294i	$-0.436703\pi$
$601$	9.68570	0.395088	0.197544	+	0.980294i	$0.436703\pi$
$602$	3.52029	0.143476
$603$	−29.2250	−1.19014
$604$	−15.8367	−0.644387
$605$	1.00000	0.0406558
$606$	1.79842	0.0730559
$607$	20.8217	0.845127	0.422564	−	0.906333i	$-0.361130\pi$
$607$	20.8217	0.845127	0.422564	+	0.906333i	$0.361130\pi$
$608$	2.57864	0.104578
$609$	−0.930162	−0.0376921
$610$	7.68968	0.311346
$611$	−33.5212	−1.35612
$612$	0.395707	0.0159955
$613$	4.32585	0.174719	0.0873597	−	0.996177i	$-0.472157\pi$
$613$	4.32585	0.174719	0.0873597	+	0.996177i	$0.472157\pi$
$614$	−10.2159	−0.412281
$615$	0.928440	0.0374383
$616$	−3.52029	−0.141837
$617$	−10.5769	−0.425810	−0.212905	−	0.977073i	$-0.568292\pi$
$617$	−10.5769	−0.425810	−0.212905	+	0.977073i	$0.568292\pi$
$618$	0.784752	0.0315674
$619$	3.35452	0.134830	0.0674149	−	0.997725i	$-0.478525\pi$
$619$	3.35452	0.134830	0.0674149	+	0.997725i	$0.478525\pi$
$620$	9.53993	0.383133
$621$	3.32174	0.133297
$622$	−5.53935	−0.222108
$623$	−24.9459	−0.999438
$624$	0.781402	0.0312811
$625$	1.00000	0.0400000
$626$	1.38818	0.0554827
$627$	−0.473097	−0.0188937
$628$	6.83916	0.272912
$629$	−0.694179	−0.0276787
$630$	10.4424	0.416035
$631$	8.05059	0.320489	0.160244	−	0.987077i	$-0.448772\pi$
$631$	8.05059	0.320489	0.160244	+	0.987077i	$0.448772\pi$
$632$	−5.97343	−0.237610
$633$	−2.06131	−0.0819299
$634$	−7.70949	−0.306183
$635$	15.6171	0.619747
$636$	−1.45245	−0.0575934
$637$	−22.9669	−0.909983
$638$	−1.44019	−0.0570177
$639$	−13.7107	−0.542386
$640$	1.00000	0.0395285
$641$	33.7639	1.33359	0.666797	−	0.745239i	$-0.267665\pi$
$641$	33.7639	1.33359	0.666797	+	0.745239i	$0.267665\pi$
$642$	−0.585281	−0.0230992
$643$	−2.86228	−0.112877	−0.0564387	−	0.998406i	$-0.517975\pi$
$643$	−2.86228	−0.112877	−0.0564387	+	0.998406i	$0.517975\pi$
$644$	−10.6826	−0.420953
$645$	0.183468	0.00722403
$646$	−0.343988	−0.0135340
$647$	23.3407	0.917616	0.458808	−	0.888536i	$-0.348277\pi$
$647$	23.3407	0.917616	0.458808	+	0.888536i	$0.348277\pi$
$648$	8.69819	0.341697
$649$	−9.81709	−0.385354
$650$	−4.25907	−0.167055
$651$	6.16146	0.241487
$652$	−13.8969	−0.544243
$653$	33.9508	1.32860	0.664299	−	0.747467i	$-0.268730\pi$
$653$	33.9508	1.32860	0.664299	+	0.747467i	$0.268730\pi$
$654$	0.957249	0.0374314
$655$	−9.84360	−0.384621
$656$	−5.06051	−0.197580
$657$	−4.35747	−0.170001
$658$	−27.7066	−1.08012
$659$	−2.87064	−0.111824	−0.0559121	−	0.998436i	$-0.517807\pi$
$659$	−2.87064	−0.111824	−0.0559121	+	0.998436i	$0.517807\pi$
$660$	−0.183468	−0.00714147
$661$	−4.06471	−0.158099	−0.0790495	−	0.996871i	$-0.525189\pi$
$661$	−4.06471	−0.158099	−0.0790495	+	0.996871i	$0.525189\pi$
$662$	−8.96835	−0.348565
$663$	−0.104238	−0.00404828
$664$	13.0423	0.506138
$665$	−9.07757	−0.352013
$666$	−15.4362	−0.598139
$667$	−4.37037	−0.169221
$668$	0.661555	0.0255963
$669$	4.66340	0.180297
$670$	9.85223	0.380625
$671$	7.68968	0.296857
$672$	0.645860	0.0249146
$673$	36.8844	1.42179	0.710895	−	0.703298i	$-0.248290\pi$
$673$	36.8844	1.42179	0.710895	+	0.703298i	$0.248290\pi$
$674$	31.6100	1.21757
$675$	1.09463	0.0421323
$676$	5.13970	0.197681
$677$	−15.0185	−0.577208	−0.288604	−	0.957449i	$-0.593191\pi$
$677$	−15.0185	−0.577208	−0.288604	+	0.957449i	$0.593191\pi$
$678$	−1.91517	−0.0735517
$679$	−21.4366	−0.822660
$680$	−0.133399	−0.00511562
$681$	0.452700	0.0173475
$682$	9.53993	0.365303
$683$	−15.7849	−0.603994	−0.301997	−	0.953309i	$-0.597653\pi$
$683$	−15.7849	−0.603994	−0.301997	+	0.953309i	$0.597653\pi$
$684$	−7.64912	−0.292471
$685$	16.1602	0.617449
$686$	5.65897	0.216061
$687$	2.32603	0.0887435
$688$	−1.00000	−0.0381246
$689$	−33.7176	−1.28454
$690$	−0.556746	−0.0211950
$691$	−15.5546	−0.591725	−0.295863	−	0.955231i	$-0.595607\pi$
$691$	−15.5546	−0.591725	−0.295863	+	0.955231i	$0.595607\pi$
$692$	2.25636	0.0857740
$693$	10.4424	0.396674
$694$	13.0712	0.496176
$695$	−5.65496	−0.214505
$696$	0.264228	0.0100156
$697$	0.675067	0.0255700
$698$	11.6461	0.440811
$699$	1.88425	0.0712691
$700$	−3.52029	−0.133055
$701$	46.8307	1.76877	0.884385	−	0.466758i	$-0.154578\pi$
$701$	46.8307	1.76877	0.884385	+	0.466758i	$0.154578\pi$
$702$	−4.66211	−0.175960
$703$	13.4186	0.506094
$704$	1.00000	0.0376889
$705$	−1.44399	−0.0543838
$706$	12.4962	0.470301
$707$	34.5073	1.29778
$708$	1.80112	0.0676902
$709$	35.6343	1.33827	0.669136	−	0.743140i	$-0.266664\pi$
$709$	35.6343	1.33827	0.669136	+	0.743140i	$0.266664\pi$
$710$	4.62209	0.173464
$711$	17.7192	0.664523
$712$	7.08632	0.265571
$713$	28.9496	1.08417
$714$	−0.0861572	−0.00322435
$715$	−4.25907	−0.159280
$716$	4.21374	0.157475
$717$	2.23270	0.0833816
$718$	−13.7833	−0.514390
$719$	17.6334	0.657615	0.328808	−	0.944397i	$-0.393353\pi$
$719$	17.6334	0.657615	0.328808	+	0.944397i	$0.393353\pi$
$720$	−2.96634	−0.110549
$721$	15.0575	0.560769
$722$	−12.3506	−0.459643
$723$	−2.07165	−0.0770454
$724$	−14.0442	−0.521948
$725$	−1.44019	−0.0534873
$726$	−0.183468	−0.00680912
$727$	6.79375	0.251966	0.125983	−	0.992032i	$-0.459791\pi$
$727$	6.79375	0.251966	0.125983	+	0.992032i	$0.459791\pi$
$728$	14.9932	0.555685
$729$	−25.1993	−0.933307
$730$	1.46897	0.0543691
$731$	0.133399	0.00493394
$732$	−1.41081	−0.0521449
$733$	37.3508	1.37958	0.689791	−	0.724009i	$-0.257702\pi$
$733$	37.3508	1.37958	0.689791	+	0.724009i	$0.257702\pi$
$734$	−13.2415	−0.488753
$735$	−0.989344	−0.0364925
$736$	3.03457	0.111856
$737$	9.85223	0.362911
$738$	15.0112	0.552570
$739$	−30.0703	−1.10615	−0.553077	−	0.833130i	$-0.686546\pi$
$739$	−30.0703	−1.10615	−0.553077	+	0.833130i	$0.686546\pi$
$740$	5.20377	0.191294
$741$	2.01495	0.0740212
$742$	−27.8690	−1.02310
$743$	−50.1270	−1.83898	−0.919491	−	0.393112i	$-0.871398\pi$
$743$	−50.1270	−1.83898	−0.919491	+	0.393112i	$0.871398\pi$
$744$	−1.75027	−0.0641680
$745$	4.87869	0.178741
$746$	2.27006	0.0831130
$747$	−38.6878	−1.41551
$748$	−0.133399	−0.00487755
$749$	−11.2301	−0.410339
$750$	−0.183468	−0.00669929
$751$	50.0133	1.82501	0.912505	−	0.409066i	$-0.134145\pi$
$751$	50.0133	1.82501	0.912505	+	0.409066i	$0.134145\pi$
$752$	7.87054	0.287009
$753$	−3.17647	−0.115757
$754$	6.13388	0.223383
$755$	−15.8367	−0.576357
$756$	−3.85342	−0.140148
$757$	45.1606	1.64139	0.820694	−	0.571368i	$-0.193587\pi$
$757$	45.1606	1.64139	0.820694	+	0.571368i	$0.193587\pi$
$758$	13.4425	0.488253
$759$	−0.556746	−0.0202086
$760$	2.57864	0.0935371
$761$	−20.4806	−0.742422	−0.371211	−	0.928548i	$-0.621057\pi$
$761$	−20.4806	−0.742422	−0.371211	+	0.928548i	$0.621057\pi$
$762$	−2.86524	−0.103797
$763$	18.3673	0.664940
$764$	−5.84276	−0.211384
$765$	0.395707	0.0143068
$766$	−14.7914	−0.534434
$767$	41.8117	1.50973
$768$	−0.183468	−0.00662032
$769$	−8.45160	−0.304772	−0.152386	−	0.988321i	$-0.548696\pi$
$769$	−8.45160	−0.304772	−0.152386	+	0.988321i	$0.548696\pi$
$770$	−3.52029	−0.126863
$771$	−3.52515	−0.126955
$772$	11.3153	0.407246
$773$	−30.7615	−1.10642	−0.553208	−	0.833043i	$-0.686596\pi$
$773$	−30.7615	−1.10642	−0.553208	+	0.833043i	$0.686596\pi$
$774$	2.96634	0.106623
$775$	9.53993	0.342684
$776$	6.08942	0.218598
$777$	3.36091	0.120572
$778$	2.66523	0.0955532
$779$	−13.0492	−0.467537
$780$	0.781402	0.0279787
$781$	4.62209	0.165391
$782$	−0.404809	−0.0144760
$783$	−1.57648	−0.0563387
$784$	5.39247	0.192588
$785$	6.83916	0.244100
$786$	1.80598	0.0644173
$787$	−0.473732	−0.0168867	−0.00844336	−	0.999964i	$-0.502688\pi$
$787$	−0.473732	−0.0168867	−0.00844336	+	0.999964i	$0.502688\pi$
$788$	−7.21148	−0.256898
$789$	−1.19227	−0.0424460
$790$	−5.97343	−0.212525
$791$	−36.7475	−1.30659
$792$	−2.96634	−0.105404
$793$	−32.7509	−1.16302
$794$	10.1238	0.359279
$795$	−1.45245	−0.0515131
$796$	10.9893	0.389504
$797$	−6.43476	−0.227931	−0.113965	−	0.993485i	$-0.536355\pi$
$797$	−6.43476	−0.227931	−0.113965	+	0.993485i	$0.536355\pi$
$798$	1.66544	0.0589559
$799$	−1.04992	−0.0371436
$800$	1.00000	0.0353553
$801$	−21.0204	−0.742721
$802$	−0.955959	−0.0337561
$803$	1.46897	0.0518389
$804$	−1.80756	−0.0637479
$805$	−10.6826	−0.376512
$806$	−40.6313	−1.43117
$807$	−2.15092	−0.0757160
$808$	−9.80239	−0.344847
$809$	−39.4887	−1.38835	−0.694175	−	0.719807i	$-0.744231\pi$
$809$	−39.4887	−1.38835	−0.694175	+	0.719807i	$0.744231\pi$
$810$	8.69819	0.305623
$811$	−2.74330	−0.0963303	−0.0481652	−	0.998839i	$-0.515337\pi$
$811$	−2.74330	−0.0963303	−0.0481652	+	0.998839i	$0.515337\pi$
$812$	5.06990	0.177918
$813$	−0.784854	−0.0275260
$814$	5.20377	0.182392
$815$	−13.8969	−0.486786
$816$	0.0244744	0.000856776 0
$817$	−2.57864	−0.0902151
$818$	7.69938	0.269203
$819$	−44.4749	−1.55408
$820$	−5.06051	−0.176721
$821$	9.10177	0.317654	0.158827	−	0.987306i	$-0.449229\pi$
$821$	9.10177	0.317654	0.158827	+	0.987306i	$0.449229\pi$
$822$	−2.96487	−0.103412
$823$	11.8542	0.413211	0.206606	−	0.978424i	$-0.433758\pi$
$823$	11.8542	0.413211	0.206606	+	0.978424i	$0.433758\pi$
$824$	−4.27733	−0.149008
$825$	−0.183468	−0.00638752
$826$	34.5590	1.20246
$827$	1.19588	0.0415850	0.0207925	−	0.999784i	$-0.493381\pi$
$827$	1.19588	0.0415850	0.0207925	+	0.999784i	$0.493381\pi$
$828$	−9.00158	−0.312826
$829$	−25.2255	−0.876116	−0.438058	−	0.898947i	$-0.644334\pi$
$829$	−25.2255	−0.876116	−0.438058	+	0.898947i	$0.644334\pi$
$830$	13.0423	0.452704
$831$	3.44142	0.119382
$832$	−4.25907	−0.147657
$833$	−0.719351	−0.0249240
$834$	1.03750	0.0359258
$835$	0.661555	0.0228940
$836$	2.57864	0.0891841
$837$	10.4427	0.360952
$838$	3.74719	0.129444
$839$	−0.280934	−0.00969891	−0.00484945	−	0.999988i	$-0.501544\pi$
$839$	−0.280934	−0.00969891	−0.00484945	+	0.999988i	$0.501544\pi$
$840$	0.645860	0.0222843
$841$	−26.9259	−0.928478
$842$	25.3342	0.873075
$843$	−1.26075	−0.0434226
$844$	11.2353	0.386735
$845$	5.13970	0.176811
$846$	−23.3467	−0.802675
$847$	−3.52029	−0.120959
$848$	7.91666	0.271859
$849$	−0.673112	−0.0231011
$850$	−0.133399	−0.00457555
$851$	15.7912	0.541317
$852$	−0.848004	−0.0290521
$853$	26.1835	0.896505	0.448252	−	0.893907i	$-0.352047\pi$
$853$	26.1835	0.896505	0.448252	+	0.893907i	$0.352047\pi$
$854$	−27.0699	−0.926314
$855$	−7.64912	−0.261594
$856$	3.19010	0.109035
$857$	−56.6105	−1.93378	−0.966888	−	0.255200i	$-0.917859\pi$
$857$	−56.6105	−1.93378	−0.966888	+	0.255200i	$0.917859\pi$
$858$	0.781402	0.0266766
$859$	−34.4205	−1.17441	−0.587206	−	0.809438i	$-0.699772\pi$
$859$	−34.4205	−1.17441	−0.587206	+	0.809438i	$0.699772\pi$
$860$	−1.00000	−0.0340997
$861$	−3.26838	−0.111386
$862$	9.64747	0.328594
$863$	10.1856	0.346722	0.173361	−	0.984858i	$-0.444537\pi$
$863$	10.1856	0.346722	0.173361	+	0.984858i	$0.444537\pi$
$864$	1.09463	0.0372401
$865$	2.25636	0.0767186
$866$	2.11153	0.0717527
$867$	3.11569	0.105814
$868$	−33.5834	−1.13989
$869$	−5.97343	−0.202635
$870$	0.264228	0.00895818
$871$	−41.9613	−1.42181
$872$	−5.21754	−0.176688
$873$	−18.0633	−0.611350
$874$	7.82507	0.264687
$875$	−3.52029	−0.119008
$876$	−0.269509	−0.00910586
$877$	−50.1785	−1.69441	−0.847204	−	0.531267i	$-0.821716\pi$
$877$	−50.1785	−1.69441	−0.847204	+	0.531267i	$0.821716\pi$
$878$	−17.7022	−0.597422
$879$	−5.59295	−0.188645
$880$	1.00000	0.0337100
$881$	−12.6716	−0.426917	−0.213459	−	0.976952i	$-0.568473\pi$
$881$	−12.6716	−0.426917	−0.213459	+	0.976952i	$0.568473\pi$
$882$	−15.9959	−0.538610
$883$	−43.7809	−1.47335	−0.736673	−	0.676250i	$-0.763604\pi$
$883$	−43.7809	−1.47335	−0.736673	+	0.676250i	$0.763604\pi$
$884$	0.568156	0.0191092
$885$	1.80112	0.0605439
$886$	11.3323	0.380716
$887$	11.0680	0.371626	0.185813	−	0.982585i	$-0.440508\pi$
$887$	11.0680	0.371626	0.185813	+	0.982585i	$0.440508\pi$
$888$	−0.954724	−0.0320384
$889$	−54.9769	−1.84387
$890$	7.08632	0.237534
$891$	8.69819	0.291400
$892$	−25.4181	−0.851061
$893$	20.2953	0.679155
$894$	−0.895081	−0.0299360
$895$	4.21374	0.140850
$896$	−3.52029	−0.117605
$897$	2.37122	0.0791728
$898$	4.73346	0.157958
$899$	−13.7393	−0.458232
$900$	−2.96634	−0.0988780
$901$	−1.05608	−0.0351830
$902$	−5.06051	−0.168497
$903$	−0.645860	−0.0214929
$904$	10.4387	0.347187
$905$	−14.0442	−0.466844
$906$	2.90553	0.0965297
$907$	40.2315	1.33587	0.667933	−	0.744222i	$-0.267179\pi$
$907$	40.2315	1.33587	0.667933	+	0.744222i	$0.267179\pi$
$908$	−2.46747	−0.0818858
$909$	29.0772	0.964431
$910$	14.9932	0.497019
$911$	−58.4571	−1.93677	−0.968386	−	0.249458i	$-0.919747\pi$
$911$	−58.4571	−1.93677	−0.968386	+	0.249458i	$0.919747\pi$
$912$	−0.473097	−0.0156658
$913$	13.0423	0.431636
$914$	7.00766	0.231793
$915$	−1.41081	−0.0466398
$916$	−12.6781	−0.418897
$917$	34.6524	1.14432
$918$	−0.146023	−0.00481947
$919$	16.1188	0.531710	0.265855	−	0.964013i	$-0.414346\pi$
$919$	16.1188	0.531710	0.265855	+	0.964013i	$0.414346\pi$
$920$	3.03457	0.100047
$921$	1.87429	0.0617600
$922$	40.0454	1.31883
$923$	−19.6858	−0.647967
$924$	0.645860	0.0212472
$925$	5.20377	0.171099
$926$	−32.4564	−1.06658
$927$	12.6880	0.416729
$928$	−1.44019	−0.0472766
$929$	−20.0285	−0.657115	−0.328558	−	0.944484i	$-0.606563\pi$
$929$	−20.0285	−0.657115	−0.328558	+	0.944484i	$0.606563\pi$
$930$	−1.75027	−0.0573936
$931$	13.9052	0.455726
$932$	−10.2702	−0.336413
$933$	1.01629	0.0332719
$934$	−32.3156	−1.05740
$935$	−0.133399	−0.00436262
$936$	12.6339	0.412950
$937$	−42.4105	−1.38549	−0.692745	−	0.721183i	$-0.743599\pi$
$937$	−42.4105	−1.38549	−0.692745	+	0.721183i	$0.743599\pi$
$938$	−34.6827	−1.13243
$939$	−0.254685	−0.00831134
$940$	7.87054	0.256709
$941$	29.2397	0.953189	0.476594	−	0.879123i	$-0.341871\pi$
$941$	29.2397	0.953189	0.476594	+	0.879123i	$0.341871\pi$
$942$	−1.25476	−0.0408824
$943$	−15.3565	−0.500076
$944$	−9.81709	−0.319519
$945$	−3.85342	−0.125352
$946$	−1.00000	−0.0325128
$947$	−27.4901	−0.893308	−0.446654	−	0.894707i	$-0.647385\pi$
$947$	−27.4901	−0.893308	−0.446654	+	0.894707i	$0.647385\pi$
$948$	1.09593	0.0355942
$949$	−6.25646	−0.203093
$950$	2.57864	0.0836621
$951$	1.41444	0.0458664
$952$	0.469604	0.0152200
$953$	−38.5188	−1.24775	−0.623874	−	0.781525i	$-0.714442\pi$
$953$	−38.5188	−1.24775	−0.623874	+	0.781525i	$0.714442\pi$
$954$	−23.4835	−0.760306
$955$	−5.84276	−0.189067
$956$	−12.1694	−0.393587
$957$	0.264228	0.00854129
$958$	−9.73786	−0.314616
$959$	−56.8886	−1.83703
$960$	−0.183468	−0.00592139
$961$	60.0103	1.93581
$962$	−22.1632	−0.714572
$963$	−9.46293	−0.304939
$964$	11.2916	0.363679
$965$	11.3153	0.364252
$966$	1.95991	0.0630591
$967$	−38.3714	−1.23394	−0.616971	−	0.786986i	$-0.711640\pi$
$967$	−38.3714	−1.23394	−0.616971	+	0.786986i	$0.711640\pi$
$968$	1.00000	0.0321412
$969$	0.0631107	0.00202741
$970$	6.08942	0.195520
$971$	38.5806	1.23811	0.619055	−	0.785348i	$-0.287516\pi$
$971$	38.5806	1.23811	0.619055	+	0.785348i	$0.287516\pi$
$972$	−4.87973	−0.156517
$973$	19.9071	0.638193
$974$	15.6510	0.501490
$975$	0.781402	0.0250249
$976$	7.68968	0.246141
$977$	40.9038	1.30863	0.654314	−	0.756223i	$-0.272957\pi$
$977$	40.9038	1.30863	0.654314	+	0.756223i	$0.272957\pi$
$978$	2.54963	0.0815280
$979$	7.08632	0.226480
$980$	5.39247	0.172256
$981$	15.4770	0.494142
$982$	−1.00346	−0.0320216
$983$	−40.9526	−1.30619	−0.653093	−	0.757278i	$-0.726529\pi$
$983$	−40.9526	−1.30619	−0.653093	+	0.757278i	$0.726529\pi$
$984$	0.928440	0.0295976
$985$	−7.21148	−0.229777
$986$	0.192120	0.00611835
$987$	5.08327	0.161802
$988$	−10.9826	−0.349403
$989$	−3.03457	−0.0964938
$990$	−2.96634	−0.0942765
$991$	21.4744	0.682158	0.341079	−	0.940035i	$-0.389208\pi$
$991$	21.4744	0.682158	0.341079	+	0.940035i	$0.389208\pi$
$992$	9.53993	0.302893
$993$	1.64540	0.0522153
$994$	−16.2711	−0.516088
$995$	10.9893	0.348383
$996$	−2.39283	−0.0758199
$997$	−22.0956	−0.699774	−0.349887	−	0.936792i	$-0.613780\pi$
$997$	−22.0956	−0.699774	−0.349887	+	0.936792i	$0.613780\pi$
$998$	−11.3672	−0.359824
$999$	5.69621	0.180220

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.bd.1.5	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.bd.1.5	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.183468 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.183468 q^{6} -3.52029 q^{7} +1.00000 q^{8} -2.96634 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.183468 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.183468 q^{6} -3.52029 q^{7} +1.00000 q^{8} -2.96634 q^{9} +1.00000 q^{10} +1.00000 q^{11} -0.183468 q^{12} -4.25907 q^{13} -3.52029 q^{14} -0.183468 q^{15} +1.00000 q^{16} -0.133399 q^{17} -2.96634 q^{18} +2.57864 q^{19} +1.00000 q^{20} +0.645860 q^{21} +1.00000 q^{22} +3.03457 q^{23} -0.183468 q^{24} +1.00000 q^{25} -4.25907 q^{26} +1.09463 q^{27} -3.52029 q^{28} -1.44019 q^{29} -0.183468 q^{30} +9.53993 q^{31} +1.00000 q^{32} -0.183468 q^{33} -0.133399 q^{34} -3.52029 q^{35} -2.96634 q^{36} +5.20377 q^{37} +2.57864 q^{38} +0.781402 q^{39} +1.00000 q^{40} -5.06051 q^{41} +0.645860 q^{42} -1.00000 q^{43} +1.00000 q^{44} -2.96634 q^{45} +3.03457 q^{46} +7.87054 q^{47} -0.183468 q^{48} +5.39247 q^{49} +1.00000 q^{50} +0.0244744 q^{51} -4.25907 q^{52} +7.91666 q^{53} +1.09463 q^{54} +1.00000 q^{55} -3.52029 q^{56} -0.473097 q^{57} -1.44019 q^{58} -9.81709 q^{59} -0.183468 q^{60} +7.68968 q^{61} +9.53993 q^{62} +10.4424 q^{63} +1.00000 q^{64} -4.25907 q^{65} -0.183468 q^{66} +9.85223 q^{67} -0.133399 q^{68} -0.556746 q^{69} -3.52029 q^{70} +4.62209 q^{71} -2.96634 q^{72} +1.46897 q^{73} +5.20377 q^{74} -0.183468 q^{75} +2.57864 q^{76} -3.52029 q^{77} +0.781402 q^{78} -5.97343 q^{79} +1.00000 q^{80} +8.69819 q^{81} -5.06051 q^{82} +13.0423 q^{83} +0.645860 q^{84} -0.133399 q^{85} -1.00000 q^{86} +0.264228 q^{87} +1.00000 q^{88} +7.08632 q^{89} -2.96634 q^{90} +14.9932 q^{91} +3.03457 q^{92} -1.75027 q^{93} +7.87054 q^{94} +2.57864 q^{95} -0.183468 q^{96} +6.08942 q^{97} +5.39247 q^{98} -2.96634 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 11 q^{2} + 3 q^{3} + 11 q^{4} + 11 q^{5} + 3 q^{6} + 5 q^{7} + 11 q^{8} + 26 q^{9}+O(q^{10}) \) 11 * q + 11 * q^2 + 3 * q^3 + 11 * q^4 + 11 * q^5 + 3 * q^6 + 5 * q^7 + 11 * q^8 + 26 * q^9	\( 11 q + 11 q^{2} + 3 q^{3} + 11 q^{4} + 11 q^{5} + 3 q^{6} + 5 q^{7} + 11 q^{8} + 26 q^{9} + 11 q^{10} + 11 q^{11} + 3 q^{12} + q^{13} + 5 q^{14} + 3 q^{15} + 11 q^{16} + 8 q^{17} + 26 q^{18} + q^{19} + 11 q^{20} + 11 q^{22} + 20 q^{23} + 3 q^{24} + 11 q^{25} + q^{26} + 18 q^{27} + 5 q^{28} + 9 q^{29} + 3 q^{30} + 12 q^{31} + 11 q^{32} + 3 q^{33} + 8 q^{34} + 5 q^{35} + 26 q^{36} + 19 q^{37} + q^{38} - 18 q^{39} + 11 q^{40} + 9 q^{41} - 11 q^{43} + 11 q^{44} + 26 q^{45} + 20 q^{46} + 15 q^{47} + 3 q^{48} + 2 q^{49} + 11 q^{50} - 25 q^{51} + q^{52} + 35 q^{53} + 18 q^{54} + 11 q^{55} + 5 q^{56} - 25 q^{57} + 9 q^{58} + 13 q^{59} + 3 q^{60} + 9 q^{61} + 12 q^{62} + 22 q^{63} + 11 q^{64} + q^{65} + 3 q^{66} - q^{67} + 8 q^{68} + 12 q^{69} + 5 q^{70} + 14 q^{71} + 26 q^{72} - 20 q^{73} + 19 q^{74} + 3 q^{75} + q^{76} + 5 q^{77} - 18 q^{78} - 23 q^{79} + 11 q^{80} + 71 q^{81} + 9 q^{82} + 12 q^{83} + 8 q^{85} - 11 q^{86} + 6 q^{87} + 11 q^{88} - q^{89} + 26 q^{90} - 17 q^{91} + 20 q^{92} + 7 q^{93} + 15 q^{94} + q^{95} + 3 q^{96} + 17 q^{97} + 2 q^{98} + 26 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 + 3 * q^3 + 11 * q^4 + 11 * q^5 + 3 * q^6 + 5 * q^7 + 11 * q^8 + 26 * q^9 + 11 * q^10 + 11 * q^11 + 3 * q^12 + q^13 + 5 * q^14 + 3 * q^15 + 11 * q^16 + 8 * q^17 + 26 * q^18 + q^19 + 11 * q^20 + 11 * q^22 + 20 * q^23 + 3 * q^24 + 11 * q^25 + q^26 + 18 * q^27 + 5 * q^28 + 9 * q^29 + 3 * q^30 + 12 * q^31 + 11 * q^32 + 3 * q^33 + 8 * q^34 + 5 * q^35 + 26 * q^36 + 19 * q^37 + q^38 - 18 * q^39 + 11 * q^40 + 9 * q^41 - 11 * q^43 + 11 * q^44 + 26 * q^45 + 20 * q^46 + 15 * q^47 + 3 * q^48 + 2 * q^49 + 11 * q^50 - 25 * q^51 + q^52 + 35 * q^53 + 18 * q^54 + 11 * q^55 + 5 * q^56 - 25 * q^57 + 9 * q^58 + 13 * q^59 + 3 * q^60 + 9 * q^61 + 12 * q^62 + 22 * q^63 + 11 * q^64 + q^65 + 3 * q^66 - q^67 + 8 * q^68 + 12 * q^69 + 5 * q^70 + 14 * q^71 + 26 * q^72 - 20 * q^73 + 19 * q^74 + 3 * q^75 + q^76 + 5 * q^77 - 18 * q^78 - 23 * q^79 + 11 * q^80 + 71 * q^81 + 9 * q^82 + 12 * q^83 + 8 * q^85 - 11 * q^86 + 6 * q^87 + 11 * q^88 - q^89 + 26 * q^90 - 17 * q^91 + 20 * q^92 + 7 * q^93 + 15 * q^94 + q^95 + 3 * q^96 + 17 * q^97 + 2 * q^98 + 26 * q^99

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