LMFDB - Embedded newform 4730.2.a.bd.1.10

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			1.10
Root			$3.07012$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +3.07012 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.07012 q^{6} -3.37856 q^{7} +1.00000 q^{8} +6.42564 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +3.07012 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.07012 q^{6} -3.37856 q^{7} +1.00000 q^{8} +6.42564 q^{9} +1.00000 q^{10} +1.00000 q^{11} +3.07012 q^{12} +3.03614 q^{13} -3.37856 q^{14} +3.07012 q^{15} +1.00000 q^{16} -6.45082 q^{17} +6.42564 q^{18} +4.05824 q^{19} +1.00000 q^{20} -10.3726 q^{21} +1.00000 q^{22} +5.27821 q^{23} +3.07012 q^{24} +1.00000 q^{25} +3.03614 q^{26} +10.5171 q^{27} -3.37856 q^{28} +8.50345 q^{29} +3.07012 q^{30} -3.47827 q^{31} +1.00000 q^{32} +3.07012 q^{33} -6.45082 q^{34} -3.37856 q^{35} +6.42564 q^{36} -8.91176 q^{37} +4.05824 q^{38} +9.32132 q^{39} +1.00000 q^{40} +1.40650 q^{41} -10.3726 q^{42} -1.00000 q^{43} +1.00000 q^{44} +6.42564 q^{45} +5.27821 q^{46} +13.4917 q^{47} +3.07012 q^{48} +4.41468 q^{49} +1.00000 q^{50} -19.8048 q^{51} +3.03614 q^{52} -1.18455 q^{53} +10.5171 q^{54} +1.00000 q^{55} -3.37856 q^{56} +12.4593 q^{57} +8.50345 q^{58} +2.68029 q^{59} +3.07012 q^{60} -0.371203 q^{61} -3.47827 q^{62} -21.7094 q^{63} +1.00000 q^{64} +3.03614 q^{65} +3.07012 q^{66} +11.2439 q^{67} -6.45082 q^{68} +16.2048 q^{69} -3.37856 q^{70} -5.77406 q^{71} +6.42564 q^{72} -14.4616 q^{73} -8.91176 q^{74} +3.07012 q^{75} +4.05824 q^{76} -3.37856 q^{77} +9.32132 q^{78} -1.29464 q^{79} +1.00000 q^{80} +13.0120 q^{81} +1.40650 q^{82} +10.1391 q^{83} -10.3726 q^{84} -6.45082 q^{85} -1.00000 q^{86} +26.1066 q^{87} +1.00000 q^{88} +1.36073 q^{89} +6.42564 q^{90} -10.2578 q^{91} +5.27821 q^{92} -10.6787 q^{93} +13.4917 q^{94} +4.05824 q^{95} +3.07012 q^{96} +3.69605 q^{97} +4.41468 q^{98} +6.42564 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	3.07012	1.77254	0.886268	−	0.463173i	$-0.153289\pi$
$3$	3.07012	1.77254	0.886268	+	0.463173i	$0.153289\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	3.07012	1.25337
$7$	−3.37856	−1.27698	−0.638488	−	0.769632i	$-0.720440\pi$
$7$	−3.37856	−1.27698	−0.638488	+	0.769632i	$0.720440\pi$
$8$	1.00000	0.353553
$9$	6.42564	2.14188
$10$	1.00000	0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	3.07012	0.886268
$13$	3.03614	0.842074	0.421037	−	0.907043i	$-0.361666\pi$
$13$	3.03614	0.842074	0.421037	+	0.907043i	$0.361666\pi$
$14$	−3.37856	−0.902959
$15$	3.07012	0.792702
$16$	1.00000	0.250000
$17$	−6.45082	−1.56455	−0.782277	−	0.622931i	$-0.785942\pi$
$17$	−6.45082	−1.56455	−0.782277	+	0.622931i	$0.785942\pi$
$18$	6.42564	1.51454
$19$	4.05824	0.931024	0.465512	−	0.885041i	$-0.345870\pi$
$19$	4.05824	0.931024	0.465512	+	0.885041i	$0.345870\pi$
$20$	1.00000	0.223607
$21$	−10.3726	−2.26349
$22$	1.00000	0.213201
$23$	5.27821	1.10058	0.550292	−	0.834972i	$-0.314516\pi$
$23$	5.27821	1.10058	0.550292	+	0.834972i	$0.314516\pi$
$24$	3.07012	0.626686
$25$	1.00000	0.200000
$26$	3.03614	0.595436
$27$	10.5171	2.02403
$28$	−3.37856	−0.638488
$29$	8.50345	1.57905	0.789526	−	0.613718i	$-0.210327\pi$
$29$	8.50345	1.57905	0.789526	+	0.613718i	$0.210327\pi$
$30$	3.07012	0.560525
$31$	−3.47827	−0.624717	−0.312358	−	0.949964i	$-0.601119\pi$
$31$	−3.47827	−0.624717	−0.312358	+	0.949964i	$0.601119\pi$
$32$	1.00000	0.176777
$33$	3.07012	0.534439
$34$	−6.45082	−1.10631
$35$	−3.37856	−0.571081
$36$	6.42564	1.07094
$37$	−8.91176	−1.46508	−0.732542	−	0.680721i	$-0.761666\pi$
$37$	−8.91176	−1.46508	−0.732542	+	0.680721i	$0.761666\pi$
$38$	4.05824	0.658334
$39$	9.32132	1.49261
$40$	1.00000	0.158114
$41$	1.40650	0.219659	0.109829	−	0.993950i	$-0.464970\pi$
$41$	1.40650	0.219659	0.109829	+	0.993950i	$0.464970\pi$
$42$	−10.3726	−1.60053
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	1.00000	0.150756
$45$	6.42564	0.957878
$46$	5.27821	0.778230
$47$	13.4917	1.96797	0.983983	−	0.178263i	$-0.0570476\pi$
$47$	13.4917	1.96797	0.983983	+	0.178263i	$0.0570476\pi$
$48$	3.07012	0.443134
$49$	4.41468	0.630669
$50$	1.00000	0.141421
$51$	−19.8048	−2.77323
$52$	3.03614	0.421037
$53$	−1.18455	−0.162710	−0.0813551	−	0.996685i	$-0.525925\pi$
$53$	−1.18455	−0.162710	−0.0813551	+	0.996685i	$0.525925\pi$
$54$	10.5171	1.43120
$55$	1.00000	0.134840
$56$	−3.37856	−0.451479
$57$	12.4593	1.65027
$58$	8.50345	1.11656
$59$	2.68029	0.348944	0.174472	−	0.984662i	$-0.444178\pi$
$59$	2.68029	0.348944	0.174472	+	0.984662i	$0.444178\pi$
$60$	3.07012	0.396351
$61$	−0.371203	−0.0475277	−0.0237639	−	0.999718i	$-0.507565\pi$
$61$	−0.371203	−0.0475277	−0.0237639	+	0.999718i	$0.507565\pi$
$62$	−3.47827	−0.441741
$63$	−21.7094	−2.73513
$64$	1.00000	0.125000
$65$	3.03614	0.376587
$66$	3.07012	0.377906
$67$	11.2439	1.37367	0.686834	−	0.726815i	$-0.259000\pi$
$67$	11.2439	1.37367	0.686834	+	0.726815i	$0.259000\pi$
$68$	−6.45082	−0.782277
$69$	16.2048	1.95082
$70$	−3.37856	−0.403815
$71$	−5.77406	−0.685255	−0.342627	−	0.939471i	$-0.611317\pi$
$71$	−5.77406	−0.685255	−0.342627	+	0.939471i	$0.611317\pi$
$72$	6.42564	0.757269
$73$	−14.4616	−1.69260	−0.846299	−	0.532708i	$-0.821174\pi$
$73$	−14.4616	−1.69260	−0.846299	+	0.532708i	$0.821174\pi$
$74$	−8.91176	−1.03597
$75$	3.07012	0.354507
$76$	4.05824	0.465512
$77$	−3.37856	−0.385023
$78$	9.32132	1.05543
$79$	−1.29464	−0.145659	−0.0728293	−	0.997344i	$-0.523203\pi$
$79$	−1.29464	−0.145659	−0.0728293	+	0.997344i	$0.523203\pi$
$80$	1.00000	0.111803
$81$	13.0120	1.44577
$82$	1.40650	0.155322
$83$	10.1391	1.11291	0.556456	−	0.830877i	$-0.312161\pi$
$83$	10.1391	1.11291	0.556456	+	0.830877i	$0.312161\pi$
$84$	−10.3726	−1.13174
$85$	−6.45082	−0.699690
$86$	−1.00000	−0.107833
$87$	26.1066	2.79892
$88$	1.00000	0.106600
$89$	1.36073	0.144237	0.0721184	−	0.997396i	$-0.477024\pi$
$89$	1.36073	0.144237	0.0721184	+	0.997396i	$0.477024\pi$
$90$	6.42564	0.677322
$91$	−10.2578	−1.07531
$92$	5.27821	0.550292
$93$	−10.6787	−1.10733
$94$	13.4917	1.39156
$95$	4.05824	0.416367
$96$	3.07012	0.313343
$97$	3.69605	0.375277	0.187638	−	0.982238i	$-0.439917\pi$
$97$	3.69605	0.375277	0.187638	+	0.982238i	$0.439917\pi$
$98$	4.41468	0.445950
$99$	6.42564	0.645802
$100$	1.00000	0.100000
$101$	−7.95747	−0.791798	−0.395899	−	0.918294i	$-0.629567\pi$
$101$	−7.95747	−0.791798	−0.395899	+	0.918294i	$0.629567\pi$
$102$	−19.8048	−1.96097
$103$	13.4872	1.32893	0.664467	−	0.747318i	$-0.268659\pi$
$103$	13.4872	1.32893	0.664467	+	0.747318i	$0.268659\pi$
$104$	3.03614	0.297718
$105$	−10.3726	−1.01226
$106$	−1.18455	−0.115054
$107$	−16.3136	−1.57710	−0.788549	−	0.614972i	$-0.789167\pi$
$107$	−16.3136	−1.57710	−0.788549	+	0.614972i	$0.789167\pi$
$108$	10.5171	1.01201
$109$	−11.2530	−1.07784	−0.538920	−	0.842357i	$-0.681167\pi$
$109$	−11.2530	−1.07784	−0.538920	+	0.842357i	$0.681167\pi$
$110$	1.00000	0.0953463
$111$	−27.3602	−2.59691
$112$	−3.37856	−0.319244
$113$	−9.00136	−0.846777	−0.423389	−	0.905948i	$-0.639159\pi$
$113$	−9.00136	−0.846777	−0.423389	+	0.905948i	$0.639159\pi$
$114$	12.4593	1.16692
$115$	5.27821	0.492196
$116$	8.50345	0.789526
$117$	19.5092	1.80362
$118$	2.68029	0.246740
$119$	21.7945	1.99790
$120$	3.07012	0.280262
$121$	1.00000	0.0909091
$122$	−0.371203	−0.0336072
$123$	4.31813	0.389353
$124$	−3.47827	−0.312358
$125$	1.00000	0.0894427
$126$	−21.7094	−1.93403
$127$	−7.69480	−0.682803	−0.341401	−	0.939918i	$-0.610902\pi$
$127$	−7.69480	−0.682803	−0.341401	+	0.939918i	$0.610902\pi$
$128$	1.00000	0.0883883
$129$	−3.07012	−0.270309
$130$	3.03614	0.266287
$131$	−5.35508	−0.467876	−0.233938	−	0.972252i	$-0.575161\pi$
$131$	−5.35508	−0.467876	−0.233938	+	0.972252i	$0.575161\pi$
$132$	3.07012	0.267220
$133$	−13.7110	−1.18890
$134$	11.2439	0.971329
$135$	10.5171	0.905172
$136$	−6.45082	−0.553153
$137$	−1.17847	−0.100683	−0.0503417	−	0.998732i	$-0.516031\pi$
$137$	−1.17847	−0.100683	−0.0503417	+	0.998732i	$0.516031\pi$
$138$	16.2048	1.37944
$139$	−12.3276	−1.04562	−0.522808	−	0.852450i	$-0.675116\pi$
$139$	−12.3276	−1.04562	−0.522808	+	0.852450i	$0.675116\pi$
$140$	−3.37856	−0.285541
$141$	41.4211	3.48829
$142$	−5.77406	−0.484548
$143$	3.03614	0.253895
$144$	6.42564	0.535470
$145$	8.50345	0.706173
$146$	−14.4616	−1.19685
$147$	13.5536	1.11788
$148$	−8.91176	−0.732542
$149$	−14.9618	−1.22572	−0.612860	−	0.790191i	$-0.709981\pi$
$149$	−14.9618	−1.22572	−0.612860	+	0.790191i	$0.709981\pi$
$150$	3.07012	0.250674
$151$	9.53712	0.776120	0.388060	−	0.921634i	$-0.373145\pi$
$151$	9.53712	0.776120	0.388060	+	0.921634i	$0.373145\pi$
$152$	4.05824	0.329167
$153$	−41.4507	−3.35109
$154$	−3.37856	−0.272252
$155$	−3.47827	−0.279382
$156$	9.32132	0.746303
$157$	2.60693	0.208056	0.104028	−	0.994574i	$-0.466827\pi$
$157$	2.60693	0.208056	0.104028	+	0.994574i	$0.466827\pi$
$158$	−1.29464	−0.102996
$159$	−3.63671	−0.288410
$160$	1.00000	0.0790569
$161$	−17.8328	−1.40542
$162$	13.0120	1.02232
$163$	−7.56597	−0.592612	−0.296306	−	0.955093i	$-0.595755\pi$
$163$	−7.56597	−0.592612	−0.296306	+	0.955093i	$0.595755\pi$
$164$	1.40650	0.109829
$165$	3.07012	0.239009
$166$	10.1391	0.786948
$167$	−0.931661	−0.0720941	−0.0360470	−	0.999350i	$-0.511477\pi$
$167$	−0.931661	−0.0720941	−0.0360470	+	0.999350i	$0.511477\pi$
$168$	−10.3726	−0.800263
$169$	−3.78185	−0.290912
$170$	−6.45082	−0.494755
$171$	26.0768	1.99414
$172$	−1.00000	−0.0762493
$173$	21.2614	1.61648	0.808238	−	0.588855i	$-0.200421\pi$
$173$	21.2614	1.61648	0.808238	+	0.588855i	$0.200421\pi$
$174$	26.1066	1.97914
$175$	−3.37856	−0.255395
$176$	1.00000	0.0753778
$177$	8.22881	0.618515
$178$	1.36073	0.101991
$179$	−9.75068	−0.728800	−0.364400	−	0.931242i	$-0.618726\pi$
$179$	−9.75068	−0.728800	−0.364400	+	0.931242i	$0.618726\pi$
$180$	6.42564	0.478939
$181$	−12.5959	−0.936248	−0.468124	−	0.883663i	$-0.655070\pi$
$181$	−12.5959	−0.936248	−0.468124	+	0.883663i	$0.655070\pi$
$182$	−10.2578	−0.760358
$183$	−1.13964	−0.0842446
$184$	5.27821	0.389115
$185$	−8.91176	−0.655206
$186$	−10.6787	−0.783002
$187$	−6.45082	−0.471731
$188$	13.4917	0.983983
$189$	−35.5328	−2.58463
$190$	4.05824	0.294416
$191$	−5.13297	−0.371409	−0.185704	−	0.982606i	$-0.559457\pi$
$191$	−5.13297	−0.371409	−0.185704	+	0.982606i	$0.559457\pi$
$192$	3.07012	0.221567
$193$	1.71715	0.123603	0.0618016	−	0.998088i	$-0.480315\pi$
$193$	1.71715	0.123603	0.0618016	+	0.998088i	$0.480315\pi$
$194$	3.69605	0.265361
$195$	9.32132	0.667514
$196$	4.41468	0.315334
$197$	15.9926	1.13942	0.569712	−	0.821844i	$-0.307055\pi$
$197$	15.9926	1.13942	0.569712	+	0.821844i	$0.307055\pi$
$198$	6.42564	0.456651
$199$	−8.18216	−0.580018	−0.290009	−	0.957024i	$-0.593658\pi$
$199$	−8.18216	−0.580018	−0.290009	+	0.957024i	$0.593658\pi$
$200$	1.00000	0.0707107
$201$	34.5203	2.43487
$202$	−7.95747	−0.559886
$203$	−28.7294	−2.01641
$204$	−19.8048	−1.38661
$205$	1.40650	0.0982343
$206$	13.4872	0.939698
$207$	33.9159	2.35732
$208$	3.03614	0.210518
$209$	4.05824	0.280714
$210$	−10.3726	−0.715777
$211$	−13.9718	−0.961859	−0.480930	−	0.876759i	$-0.659701\pi$
$211$	−13.9718	−0.961859	−0.480930	+	0.876759i	$0.659701\pi$
$212$	−1.18455	−0.0813551
$213$	−17.7271	−1.21464
$214$	−16.3136	−1.11518
$215$	−1.00000	−0.0681994
$216$	10.5171	0.715601
$217$	11.7516	0.797748
$218$	−11.2530	−0.762148
$219$	−44.3988	−3.00019
$220$	1.00000	0.0674200
$221$	−19.5856	−1.31747
$222$	−27.3602	−1.83630
$223$	29.4962	1.97521	0.987607	−	0.156950i	$-0.0501660\pi$
$223$	29.4962	1.97521	0.987607	+	0.156950i	$0.0501660\pi$
$224$	−3.37856	−0.225740
$225$	6.42564	0.428376
$226$	−9.00136	−0.598762
$227$	−3.42702	−0.227460	−0.113730	−	0.993512i	$-0.536280\pi$
$227$	−3.42702	−0.227460	−0.113730	+	0.993512i	$0.536280\pi$
$228$	12.4593	0.825137
$229$	7.82348	0.516990	0.258495	−	0.966013i	$-0.416773\pi$
$229$	7.82348	0.516990	0.258495	+	0.966013i	$0.416773\pi$
$230$	5.27821	0.348035
$231$	−10.3726	−0.682467
$232$	8.50345	0.558279
$233$	21.9475	1.43783	0.718916	−	0.695097i	$-0.244639\pi$
$233$	21.9475	1.43783	0.718916	+	0.695097i	$0.244639\pi$
$234$	19.5092	1.27535
$235$	13.4917	0.880101
$236$	2.68029	0.174472
$237$	−3.97471	−0.258185
$238$	21.7945	1.41273
$239$	−28.8116	−1.86367	−0.931833	−	0.362888i	$-0.881791\pi$
$239$	−28.8116	−1.86367	−0.931833	+	0.362888i	$0.881791\pi$
$240$	3.07012	0.198175
$241$	−19.8749	−1.28026	−0.640128	−	0.768268i	$-0.721119\pi$
$241$	−19.8749	−1.28026	−0.640128	+	0.768268i	$0.721119\pi$
$242$	1.00000	0.0642824
$243$	8.39690	0.538661
$244$	−0.371203	−0.0237639
$245$	4.41468	0.282044
$246$	4.31813	0.275314
$247$	12.3214	0.783991
$248$	−3.47827	−0.220871
$249$	31.1283	1.97268
$250$	1.00000	0.0632456
$251$	−4.96533	−0.313409	−0.156705	−	0.987646i	$-0.550087\pi$
$251$	−4.96533	−0.313409	−0.156705	+	0.987646i	$0.550087\pi$
$252$	−21.7094	−1.36757
$253$	5.27821	0.331838
$254$	−7.69480	−0.482814
$255$	−19.8048	−1.24022
$256$	1.00000	0.0625000
$257$	8.52444	0.531740	0.265870	−	0.964009i	$-0.414341\pi$
$257$	8.52444	0.531740	0.265870	+	0.964009i	$0.414341\pi$
$258$	−3.07012	−0.191137
$259$	30.1089	1.87088
$260$	3.03614	0.188293
$261$	54.6402	3.38214
$262$	−5.35508	−0.330838
$263$	25.5217	1.57374	0.786869	−	0.617120i	$-0.211701\pi$
$263$	25.5217	1.57374	0.786869	+	0.617120i	$0.211701\pi$
$264$	3.07012	0.188953
$265$	−1.18455	−0.0727663
$266$	−13.7110	−0.840676
$267$	4.17760	0.255665
$268$	11.2439	0.686834
$269$	1.96588	0.119862	0.0599309	−	0.998203i	$-0.480912\pi$
$269$	1.96588	0.119862	0.0599309	+	0.998203i	$0.480912\pi$
$270$	10.5171	0.640053
$271$	−23.9089	−1.45236	−0.726180	−	0.687504i	$-0.758706\pi$
$271$	−23.9089	−1.45236	−0.726180	+	0.687504i	$0.758706\pi$
$272$	−6.45082	−0.391138
$273$	−31.4927	−1.90602
$274$	−1.17847	−0.0711940
$275$	1.00000	0.0603023
$276$	16.2048	0.975412
$277$	31.3015	1.88072	0.940362	−	0.340174i	$-0.110486\pi$
$277$	31.3015	1.88072	0.940362	+	0.340174i	$0.110486\pi$
$278$	−12.3276	−0.739363
$279$	−22.3502	−1.33807
$280$	−3.37856	−0.201908
$281$	−22.6873	−1.35341	−0.676707	−	0.736253i	$-0.736593\pi$
$281$	−22.6873	−1.35341	−0.676707	+	0.736253i	$0.736593\pi$
$282$	41.4211	2.46659
$283$	−10.5728	−0.628485	−0.314242	−	0.949343i	$-0.601750\pi$
$283$	−10.5728	−0.628485	−0.314242	+	0.949343i	$0.601750\pi$
$284$	−5.77406	−0.342627
$285$	12.4593	0.738025
$286$	3.03614	0.179531
$287$	−4.75195	−0.280499
$288$	6.42564	0.378635
$289$	24.6131	1.44783
$290$	8.50345	0.499340
$291$	11.3473	0.665191
$292$	−14.4616	−0.846299
$293$	12.4906	0.729711	0.364855	−	0.931064i	$-0.381118\pi$
$293$	12.4906	0.729711	0.364855	+	0.931064i	$0.381118\pi$
$294$	13.5536	0.790462
$295$	2.68029	0.156052
$296$	−8.91176	−0.517986
$297$	10.5171	0.610267
$298$	−14.9618	−0.866715
$299$	16.0254	0.926773
$300$	3.07012	0.177254
$301$	3.37856	0.194737
$302$	9.53712	0.548800
$303$	−24.4304	−1.40349
$304$	4.05824	0.232756
$305$	−0.371203	−0.0212550
$306$	−41.4507	−2.36958
$307$	−14.5839	−0.832349	−0.416175	−	0.909285i	$-0.636629\pi$
$307$	−14.5839	−0.832349	−0.416175	+	0.909285i	$0.636629\pi$
$308$	−3.37856	−0.192511
$309$	41.4073	2.35558
$310$	−3.47827	−0.197553
$311$	1.10238	0.0625100	0.0312550	−	0.999511i	$-0.490050\pi$
$311$	1.10238	0.0625100	0.0312550	+	0.999511i	$0.490050\pi$
$312$	9.32132	0.527716
$313$	15.5252	0.877538	0.438769	−	0.898600i	$-0.355415\pi$
$313$	15.5252	0.877538	0.438769	+	0.898600i	$0.355415\pi$
$314$	2.60693	0.147118
$315$	−21.7094	−1.22319
$316$	−1.29464	−0.0728293
$317$	1.14284	0.0641883	0.0320941	−	0.999485i	$-0.489782\pi$
$317$	1.14284	0.0641883	0.0320941	+	0.999485i	$0.489782\pi$
$318$	−3.63671	−0.203936
$319$	8.50345	0.476102
$320$	1.00000	0.0559017
$321$	−50.0848	−2.79546
$322$	−17.8328	−0.993781
$323$	−26.1790	−1.45664
$324$	13.0120	0.722887
$325$	3.03614	0.168415
$326$	−7.56597	−0.419040
$327$	−34.5480	−1.91051
$328$	1.40650	0.0776610
$329$	−45.5825	−2.51305
$330$	3.07012	0.169005
$331$	−2.00407	−0.110153	−0.0550767	−	0.998482i	$-0.517540\pi$
$331$	−2.00407	−0.110153	−0.0550767	+	0.998482i	$0.517540\pi$
$332$	10.1391	0.556456
$333$	−57.2638	−3.13804
$334$	−0.931661	−0.0509782
$335$	11.2439	0.614323
$336$	−10.3726	−0.565871
$337$	−28.9249	−1.57564	−0.787819	−	0.615907i	$-0.788790\pi$
$337$	−28.9249	−1.57564	−0.787819	+	0.615907i	$0.788790\pi$
$338$	−3.78185	−0.205706
$339$	−27.6353	−1.50094
$340$	−6.45082	−0.349845
$341$	−3.47827	−0.188359
$342$	26.0768	1.41007
$343$	8.73466	0.471627
$344$	−1.00000	−0.0539164
$345$	16.2048	0.872435
$346$	21.2614	1.14302
$347$	−29.4836	−1.58276	−0.791380	−	0.611324i	$-0.790637\pi$
$347$	−29.4836	−1.58276	−0.791380	+	0.611324i	$0.790637\pi$
$348$	26.1066	1.39946
$349$	10.1203	0.541725	0.270863	−	0.962618i	$-0.412691\pi$
$349$	10.1203	0.541725	0.270863	+	0.962618i	$0.412691\pi$
$350$	−3.37856	−0.180592
$351$	31.9315	1.70438
$352$	1.00000	0.0533002
$353$	8.11526	0.431932	0.215966	−	0.976401i	$-0.430710\pi$
$353$	8.11526	0.431932	0.215966	+	0.976401i	$0.430710\pi$
$354$	8.22881	0.437356
$355$	−5.77406	−0.306455
$356$	1.36073	0.0721184
$357$	66.9118	3.54135
$358$	−9.75068	−0.515340
$359$	−26.5700	−1.40231	−0.701156	−	0.713008i	$-0.747332\pi$
$359$	−26.5700	−1.40231	−0.701156	+	0.713008i	$0.747332\pi$
$360$	6.42564	0.338661
$361$	−2.53068	−0.133194
$362$	−12.5959	−0.662028
$363$	3.07012	0.161140
$364$	−10.2578	−0.537654
$365$	−14.4616	−0.756953
$366$	−1.13964	−0.0595699
$367$	−21.9875	−1.14774	−0.573870	−	0.818947i	$-0.694558\pi$
$367$	−21.9875	−1.14774	−0.573870	+	0.818947i	$0.694558\pi$
$368$	5.27821	0.275146
$369$	9.03767	0.470483
$370$	−8.91176	−0.463300
$371$	4.00207	0.207777
$372$	−10.6787	−0.553666
$373$	−24.9535	−1.29204	−0.646021	−	0.763320i	$-0.723568\pi$
$373$	−24.9535	−1.29204	−0.646021	+	0.763320i	$0.723568\pi$
$374$	−6.45082	−0.333564
$375$	3.07012	0.158540
$376$	13.4917	0.695781
$377$	25.8177	1.32968
$378$	−35.5328	−1.82761
$379$	−21.9175	−1.12582	−0.562912	−	0.826517i	$-0.690319\pi$
$379$	−21.9175	−1.12582	−0.562912	+	0.826517i	$0.690319\pi$
$380$	4.05824	0.208183
$381$	−23.6240	−1.21029
$382$	−5.13297	−0.262626
$383$	−24.5396	−1.25391	−0.626957	−	0.779054i	$-0.715700\pi$
$383$	−24.5396	−1.25391	−0.626957	+	0.779054i	$0.715700\pi$
$384$	3.07012	0.156671
$385$	−3.37856	−0.172187
$386$	1.71715	0.0874007
$387$	−6.42564	−0.326634
$388$	3.69605	0.187638
$389$	1.83008	0.0927889	0.0463944	−	0.998923i	$-0.485227\pi$
$389$	1.83008	0.0927889	0.0463944	+	0.998923i	$0.485227\pi$
$390$	9.32132	0.472003
$391$	−34.0488	−1.72192
$392$	4.41468	0.222975
$393$	−16.4408	−0.829326
$394$	15.9926	0.805695
$395$	−1.29464	−0.0651405
$396$	6.42564	0.322901
$397$	−15.7985	−0.792906	−0.396453	−	0.918055i	$-0.629759\pi$
$397$	−15.7985	−0.792906	−0.396453	+	0.918055i	$0.629759\pi$
$398$	−8.18216	−0.410135
$399$	−42.0945	−2.10736
$400$	1.00000	0.0500000
$401$	29.1429	1.45533	0.727664	−	0.685934i	$-0.240606\pi$
$401$	29.1429	1.45533	0.727664	+	0.685934i	$0.240606\pi$
$402$	34.5203	1.72172
$403$	−10.5605	−0.526057
$404$	−7.95747	−0.395899
$405$	13.0120	0.646570
$406$	−28.7294	−1.42582
$407$	−8.91176	−0.441740
$408$	−19.8048	−0.980484
$409$	17.7146	0.875931	0.437966	−	0.898992i	$-0.355699\pi$
$409$	17.7146	0.875931	0.437966	+	0.898992i	$0.355699\pi$
$410$	1.40650	0.0694621
$411$	−3.61805	−0.178465
$412$	13.4872	0.664467
$413$	−9.05552	−0.445593
$414$	33.9159	1.66688
$415$	10.1391	0.497710
$416$	3.03614	0.148859
$417$	−37.8473	−1.85339
$418$	4.05824	0.198495
$419$	−17.7051	−0.864951	−0.432476	−	0.901646i	$-0.642360\pi$
$419$	−17.7051	−0.864951	−0.432476	+	0.901646i	$0.642360\pi$
$420$	−10.3726	−0.506131
$421$	23.8331	1.16156	0.580778	−	0.814062i	$-0.302749\pi$
$421$	23.8331	1.16156	0.580778	+	0.814062i	$0.302749\pi$
$422$	−13.9718	−0.680137
$423$	86.6928	4.21515
$424$	−1.18455	−0.0575268
$425$	−6.45082	−0.312911
$426$	−17.7271	−0.858879
$427$	1.25413	0.0606918
$428$	−16.3136	−0.788549
$429$	9.32132	0.450038
$430$	−1.00000	−0.0482243
$431$	−10.9452	−0.527210	−0.263605	−	0.964631i	$-0.584911\pi$
$431$	−10.9452	−0.527210	−0.263605	+	0.964631i	$0.584911\pi$
$432$	10.5171	0.506006
$433$	−8.95509	−0.430354	−0.215177	−	0.976575i	$-0.569033\pi$
$433$	−8.95509	−0.430354	−0.215177	+	0.976575i	$0.569033\pi$
$434$	11.7516	0.564093
$435$	26.1066	1.25172
$436$	−11.2530	−0.538920
$437$	21.4203	1.02467
$438$	−44.3988	−2.12145
$439$	−36.0956	−1.72275	−0.861375	−	0.507970i	$-0.830396\pi$
$439$	−36.0956	−1.72275	−0.861375	+	0.507970i	$0.830396\pi$
$440$	1.00000	0.0476731
$441$	28.3672	1.35082
$442$	−19.5856	−0.931592
$443$	−22.7491	−1.08084	−0.540422	−	0.841394i	$-0.681735\pi$
$443$	−22.7491	−1.08084	−0.540422	+	0.841394i	$0.681735\pi$
$444$	−27.3602	−1.29846
$445$	1.36073	0.0645047
$446$	29.4962	1.39669
$447$	−45.9346	−2.17263
$448$	−3.37856	−0.159622
$449$	−6.39980	−0.302025	−0.151013	−	0.988532i	$-0.548253\pi$
$449$	−6.39980	−0.302025	−0.151013	+	0.988532i	$0.548253\pi$
$450$	6.42564	0.302908
$451$	1.40650	0.0662295
$452$	−9.00136	−0.423389
$453$	29.2801	1.37570
$454$	−3.42702	−0.160838
$455$	−10.2578	−0.480893
$456$	12.4593	0.583460
$457$	34.8873	1.63196	0.815979	−	0.578082i	$-0.196198\pi$
$457$	34.8873	1.63196	0.815979	+	0.578082i	$0.196198\pi$
$458$	7.82348	0.365567
$459$	−67.8442	−3.16670
$460$	5.27821	0.246098
$461$	1.23455	0.0574986	0.0287493	−	0.999587i	$-0.490848\pi$
$461$	1.23455	0.0574986	0.0287493	+	0.999587i	$0.490848\pi$
$462$	−10.3726	−0.482577
$463$	37.6972	1.75194	0.875969	−	0.482368i	$-0.160223\pi$
$463$	37.6972	1.75194	0.875969	+	0.482368i	$0.160223\pi$
$464$	8.50345	0.394763
$465$	−10.6787	−0.495214
$466$	21.9475	1.01670
$467$	33.8607	1.56689	0.783444	−	0.621463i	$-0.213461\pi$
$467$	33.8607	1.56689	0.783444	+	0.621463i	$0.213461\pi$
$468$	19.5092	0.901811
$469$	−37.9884	−1.75414
$470$	13.4917	0.622325
$471$	8.00359	0.368786
$472$	2.68029	0.123370
$473$	−1.00000	−0.0459800
$474$	−3.97471	−0.182564
$475$	4.05824	0.186205
$476$	21.7945	0.998949
$477$	−7.61149	−0.348506
$478$	−28.8116	−1.31781
$479$	7.06624	0.322865	0.161432	−	0.986884i	$-0.448389\pi$
$479$	7.06624	0.322865	0.161432	+	0.986884i	$0.448389\pi$
$480$	3.07012	0.140131
$481$	−27.0574	−1.23371
$482$	−19.8749	−0.905278
$483$	−54.7488	−2.49116
$484$	1.00000	0.0454545
$485$	3.69605	0.167829
$486$	8.39690	0.380891
$487$	−31.2404	−1.41564	−0.707819	−	0.706394i	$-0.750321\pi$
$487$	−31.2404	−1.41564	−0.707819	+	0.706394i	$0.750321\pi$
$488$	−0.371203	−0.0168036
$489$	−23.2284	−1.05043
$490$	4.41468	0.199435
$491$	−18.8693	−0.851561	−0.425780	−	0.904827i	$-0.640000\pi$
$491$	−18.8693	−0.851561	−0.425780	+	0.904827i	$0.640000\pi$
$492$	4.31813	0.194676
$493$	−54.8542	−2.47051
$494$	12.3214	0.554366
$495$	6.42564	0.288811
$496$	−3.47827	−0.156179
$497$	19.5080	0.875054
$498$	31.1283	1.39489
$499$	39.8772	1.78515	0.892574	−	0.450900i	$-0.148897\pi$
$499$	39.8772	1.78515	0.892574	+	0.450900i	$0.148897\pi$
$500$	1.00000	0.0447214
$501$	−2.86031	−0.127789
$502$	−4.96533	−0.221614
$503$	−21.1035	−0.940958	−0.470479	−	0.882411i	$-0.655919\pi$
$503$	−21.1035	−0.940958	−0.470479	+	0.882411i	$0.655919\pi$
$504$	−21.7094	−0.967015
$505$	−7.95747	−0.354103
$506$	5.27821	0.234645
$507$	−11.6107	−0.515651
$508$	−7.69480	−0.341401
$509$	−7.82808	−0.346974	−0.173487	−	0.984836i	$-0.555503\pi$
$509$	−7.82808	−0.346974	−0.173487	+	0.984836i	$0.555503\pi$
$510$	−19.8048	−0.876971
$511$	48.8593	2.16141
$512$	1.00000	0.0441942
$513$	42.6811	1.88442
$514$	8.52444	0.375997
$515$	13.4872	0.594317
$516$	−3.07012	−0.135155
$517$	13.4917	0.593364
$518$	30.1089	1.32291
$519$	65.2752	2.86526
$520$	3.03614	0.133144
$521$	29.8760	1.30889	0.654446	−	0.756109i	$-0.272902\pi$
$521$	29.8760	1.30889	0.654446	+	0.756109i	$0.272902\pi$
$522$	54.6402	2.39153
$523$	−16.2209	−0.709288	−0.354644	−	0.935001i	$-0.615398\pi$
$523$	−16.2209	−0.709288	−0.354644	+	0.935001i	$0.615398\pi$
$524$	−5.35508	−0.233938
$525$	−10.3726	−0.452697
$526$	25.5217	1.11280
$527$	22.4377	0.977403
$528$	3.07012	0.133610
$529$	4.85954	0.211284
$530$	−1.18455	−0.0514535
$531$	17.2226	0.747396
$532$	−13.7110	−0.594448
$533$	4.27033	0.184969
$534$	4.17760	0.180782
$535$	−16.3136	−0.705300
$536$	11.2439	0.485665
$537$	−29.9358	−1.29182
$538$	1.96588	0.0847551
$539$	4.41468	0.190154
$540$	10.5171	0.452586
$541$	36.3420	1.56246	0.781232	−	0.624241i	$-0.214592\pi$
$541$	36.3420	1.56246	0.781232	+	0.624241i	$0.214592\pi$
$542$	−23.9089	−1.02697
$543$	−38.6710	−1.65953
$544$	−6.45082	−0.276577
$545$	−11.2530	−0.482024
$546$	−31.4927	−1.34776
$547$	1.37060	0.0586028	0.0293014	−	0.999571i	$-0.490672\pi$
$547$	1.37060	0.0586028	0.0293014	+	0.999571i	$0.490672\pi$
$548$	−1.17847	−0.0503417
$549$	−2.38522	−0.101799
$550$	1.00000	0.0426401
$551$	34.5091	1.47014
$552$	16.2048	0.689720
$553$	4.37403	0.186003
$554$	31.3015	1.32987
$555$	−27.3602	−1.16138
$556$	−12.3276	−0.522808
$557$	−4.38726	−0.185894	−0.0929471	−	0.995671i	$-0.529629\pi$
$557$	−4.38726	−0.185894	−0.0929471	+	0.995671i	$0.529629\pi$
$558$	−22.3502	−0.946157
$559$	−3.03614	−0.128415
$560$	−3.37856	−0.142770
$561$	−19.8048	−0.836159
$562$	−22.6873	−0.957008
$563$	8.62986	0.363705	0.181853	−	0.983326i	$-0.441791\pi$
$563$	8.62986	0.363705	0.181853	+	0.983326i	$0.441791\pi$
$564$	41.4211	1.74414
$565$	−9.00136	−0.378690
$566$	−10.5728	−0.444406
$567$	−43.9617	−1.84622
$568$	−5.77406	−0.242274
$569$	31.3864	1.31579	0.657894	−	0.753110i	$-0.271447\pi$
$569$	31.3864	1.31579	0.657894	+	0.753110i	$0.271447\pi$
$570$	12.4593	0.521862
$571$	−19.1620	−0.801907	−0.400953	−	0.916098i	$-0.631321\pi$
$571$	−19.1620	−0.801907	−0.400953	+	0.916098i	$0.631321\pi$
$572$	3.03614	0.126947
$573$	−15.7588	−0.658335
$574$	−4.75195	−0.198343
$575$	5.27821	0.220117
$576$	6.42564	0.267735
$577$	−20.4975	−0.853321	−0.426660	−	0.904412i	$-0.640310\pi$
$577$	−20.4975	−0.853321	−0.426660	+	0.904412i	$0.640310\pi$
$578$	24.6131	1.02377
$579$	5.27186	0.219091
$580$	8.50345	0.353087
$581$	−34.2556	−1.42116
$582$	11.3473	0.470361
$583$	−1.18455	−0.0490590
$584$	−14.4616	−0.598424
$585$	19.5092	0.806604
$586$	12.4906	0.515983
$587$	−9.70819	−0.400700	−0.200350	−	0.979724i	$-0.564208\pi$
$587$	−9.70819	−0.400700	−0.200350	+	0.979724i	$0.564208\pi$
$588$	13.5536	0.558941
$589$	−14.1157	−0.581626
$590$	2.68029	0.110346
$591$	49.0992	2.01967
$592$	−8.91176	−0.366271
$593$	15.7678	0.647508	0.323754	−	0.946141i	$-0.395055\pi$
$593$	15.7678	0.647508	0.323754	+	0.946141i	$0.395055\pi$
$594$	10.5171	0.431524
$595$	21.7945	0.893487
$596$	−14.9618	−0.612860
$597$	−25.1202	−1.02810
$598$	16.0254	0.655327
$599$	44.1126	1.80239	0.901195	−	0.433414i	$-0.142691\pi$
$599$	44.1126	1.80239	0.901195	+	0.433414i	$0.142691\pi$
$600$	3.07012	0.125337
$601$	−22.5246	−0.918796	−0.459398	−	0.888230i	$-0.651935\pi$
$601$	−22.5246	−0.918796	−0.459398	+	0.888230i	$0.651935\pi$
$602$	3.37856	0.137700
$603$	72.2496	2.94223
$604$	9.53712	0.388060
$605$	1.00000	0.0406558
$606$	−24.4304	−0.992417
$607$	−16.5929	−0.673484	−0.336742	−	0.941597i	$-0.609325\pi$
$607$	−16.5929	−0.673484	−0.336742	+	0.941597i	$0.609325\pi$
$608$	4.05824	0.164583
$609$	−88.2029	−3.57416
$610$	−0.371203	−0.0150296
$611$	40.9627	1.65717
$612$	−41.4507	−1.67554
$613$	8.38017	0.338472	0.169236	−	0.985576i	$-0.445870\pi$
$613$	8.38017	0.338472	0.169236	+	0.985576i	$0.445870\pi$
$614$	−14.5839	−0.588560
$615$	4.31813	0.174124
$616$	−3.37856	−0.136126
$617$	2.39460	0.0964028	0.0482014	−	0.998838i	$-0.484651\pi$
$617$	2.39460	0.0964028	0.0482014	+	0.998838i	$0.484651\pi$
$618$	41.4073	1.66565
$619$	16.5428	0.664912	0.332456	−	0.943119i	$-0.392123\pi$
$619$	16.5428	0.664912	0.332456	+	0.943119i	$0.392123\pi$
$620$	−3.47827	−0.139691
$621$	55.5117	2.22761
$622$	1.10238	0.0442012
$623$	−4.59730	−0.184187
$624$	9.32132	0.373151
$625$	1.00000	0.0400000
$626$	15.5252	0.620513
$627$	12.4593	0.497576
$628$	2.60693	0.104028
$629$	57.4882	2.29220
$630$	−21.7094	−0.864925
$631$	−3.38458	−0.134738	−0.0673689	−	0.997728i	$-0.521460\pi$
$631$	−3.38458	−0.134738	−0.0673689	+	0.997728i	$0.521460\pi$
$632$	−1.29464	−0.0514981
$633$	−42.8952	−1.70493
$634$	1.14284	0.0453880
$635$	−7.69480	−0.305359
$636$	−3.63671	−0.144205
$637$	13.4036	0.531070
$638$	8.50345	0.336655
$639$	−37.1021	−1.46773
$640$	1.00000	0.0395285
$641$	−34.9979	−1.38233	−0.691167	−	0.722695i	$-0.742903\pi$
$641$	−34.9979	−1.38233	−0.691167	+	0.722695i	$0.742903\pi$
$642$	−50.0848	−1.97669
$643$	−29.1725	−1.15045	−0.575226	−	0.817995i	$-0.695086\pi$
$643$	−29.1725	−1.15045	−0.575226	+	0.817995i	$0.695086\pi$
$644$	−17.8328	−0.702710
$645$	−3.07012	−0.120886
$646$	−26.1790	−1.03000
$647$	32.4939	1.27747	0.638733	−	0.769429i	$-0.279459\pi$
$647$	32.4939	1.27747	0.638733	+	0.769429i	$0.279459\pi$
$648$	13.0120	0.511158
$649$	2.68029	0.105211
$650$	3.03614	0.119087
$651$	36.0787	1.41404
$652$	−7.56597	−0.296306
$653$	28.5761	1.11827	0.559135	−	0.829076i	$-0.311133\pi$
$653$	28.5761	1.11827	0.559135	+	0.829076i	$0.311133\pi$
$654$	−34.5480	−1.35093
$655$	−5.35508	−0.209240
$656$	1.40650	0.0549146
$657$	−92.9249	−3.62534
$658$	−45.5825	−1.77699
$659$	30.4589	1.18651	0.593256	−	0.805014i	$-0.297842\pi$
$659$	30.4589	1.18651	0.593256	+	0.805014i	$0.297842\pi$
$660$	3.07012	0.119504
$661$	−40.1355	−1.56109	−0.780545	−	0.625100i	$-0.785058\pi$
$661$	−40.1355	−1.56109	−0.780545	+	0.625100i	$0.785058\pi$
$662$	−2.00407	−0.0778903
$663$	−60.1302	−2.33526
$664$	10.1391	0.393474
$665$	−13.7110	−0.531690
$666$	−57.2638	−2.21893
$667$	44.8830	1.73788
$668$	−0.931661	−0.0360470
$669$	90.5570	3.50114
$670$	11.2439	0.434392
$671$	−0.371203	−0.0143301
$672$	−10.3726	−0.400132
$673$	24.6920	0.951807	0.475903	−	0.879498i	$-0.342121\pi$
$673$	24.6920	0.951807	0.475903	+	0.879498i	$0.342121\pi$
$674$	−28.9249	−1.11414
$675$	10.5171	0.404805
$676$	−3.78185	−0.145456
$677$	−8.47640	−0.325775	−0.162887	−	0.986645i	$-0.552081\pi$
$677$	−8.47640	−0.325775	−0.162887	+	0.986645i	$0.552081\pi$
$678$	−27.6353	−1.06133
$679$	−12.4873	−0.479219
$680$	−6.45082	−0.247378
$681$	−10.5214	−0.403180
$682$	−3.47827	−0.133190
$683$	13.3837	0.512111	0.256056	−	0.966662i	$-0.417577\pi$
$683$	13.3837	0.512111	0.256056	+	0.966662i	$0.417577\pi$
$684$	26.0768	0.997072
$685$	−1.17847	−0.0450270
$686$	8.73466	0.333491
$687$	24.0190	0.916383
$688$	−1.00000	−0.0381246
$689$	−3.59646	−0.137014
$690$	16.2048	0.616904
$691$	8.44899	0.321415	0.160707	−	0.987002i	$-0.448622\pi$
$691$	8.44899	0.321415	0.160707	+	0.987002i	$0.448622\pi$
$692$	21.2614	0.808238
$693$	−21.7094	−0.824673
$694$	−29.4836	−1.11918
$695$	−12.3276	−0.467614
$696$	26.1066	0.989569
$697$	−9.07309	−0.343668
$698$	10.1203	0.383058
$699$	67.3816	2.54861
$700$	−3.37856	−0.127698
$701$	50.7461	1.91665	0.958326	−	0.285677i	$-0.0922185\pi$
$701$	50.7461	1.91665	0.958326	+	0.285677i	$0.0922185\pi$
$702$	31.9315	1.20518
$703$	−36.1661	−1.36403
$704$	1.00000	0.0376889
$705$	41.4211	1.56001
$706$	8.11526	0.305422
$707$	26.8848	1.01111
$708$	8.22881	0.309258
$709$	22.0055	0.826432	0.413216	−	0.910633i	$-0.364405\pi$
$709$	22.0055	0.826432	0.413216	+	0.910633i	$0.364405\pi$
$710$	−5.77406	−0.216697
$711$	−8.31891	−0.311984
$712$	1.36073	0.0509954
$713$	−18.3591	−0.687553
$714$	66.9118	2.50411
$715$	3.03614	0.113545
$716$	−9.75068	−0.364400
$717$	−88.4550	−3.30341
$718$	−26.5700	−0.991584
$719$	−23.5935	−0.879889	−0.439944	−	0.898025i	$-0.645002\pi$
$719$	−23.5935	−0.879889	−0.439944	+	0.898025i	$0.645002\pi$
$720$	6.42564	0.239470
$721$	−45.5673	−1.69702
$722$	−2.53068	−0.0941823
$723$	−61.0184	−2.26930
$724$	−12.5959	−0.468124
$725$	8.50345	0.315810
$726$	3.07012	0.113943
$727$	14.9978	0.556236	0.278118	−	0.960547i	$-0.410289\pi$
$727$	14.9978	0.556236	0.278118	+	0.960547i	$0.410289\pi$
$728$	−10.2578	−0.380179
$729$	−13.2564	−0.490979
$730$	−14.4616	−0.535247
$731$	6.45082	0.238592
$732$	−1.13964	−0.0421223
$733$	36.4038	1.34460	0.672302	−	0.740277i	$-0.265306\pi$
$733$	36.4038	1.34460	0.672302	+	0.740277i	$0.265306\pi$
$734$	−21.9875	−0.811574
$735$	13.5536	0.499932
$736$	5.27821	0.194558
$737$	11.2439	0.414176
$738$	9.03767	0.332681
$739$	18.3234	0.674036	0.337018	−	0.941498i	$-0.390582\pi$
$739$	18.3234	0.674036	0.337018	+	0.941498i	$0.390582\pi$
$740$	−8.91176	−0.327603
$741$	37.8282	1.38965
$742$	4.00207	0.146921
$743$	12.3281	0.452275	0.226138	−	0.974095i	$-0.427390\pi$
$743$	12.3281	0.452275	0.226138	+	0.974095i	$0.427390\pi$
$744$	−10.6787	−0.391501
$745$	−14.9618	−0.548159
$746$	−24.9535	−0.913612
$747$	65.1504	2.38373
$748$	−6.45082	−0.235865
$749$	55.1166	2.01392
$750$	3.07012	0.112105
$751$	51.4449	1.87725	0.938626	−	0.344937i	$-0.112100\pi$
$751$	51.4449	1.87725	0.938626	+	0.344937i	$0.112100\pi$
$752$	13.4917	0.491991
$753$	−15.2442	−0.555529
$754$	25.8177	0.940224
$755$	9.53712	0.347091
$756$	−35.5328	−1.29232
$757$	−39.5958	−1.43913	−0.719567	−	0.694423i	$-0.755660\pi$
$757$	−39.5958	−1.43913	−0.719567	+	0.694423i	$0.755660\pi$
$758$	−21.9175	−0.796078
$759$	16.2048	0.588195
$760$	4.05824	0.147208
$761$	−38.7516	−1.40474	−0.702371	−	0.711811i	$-0.747875\pi$
$761$	−38.7516	−1.40474	−0.702371	+	0.711811i	$0.747875\pi$
$762$	−23.6240	−0.855806
$763$	38.0189	1.37638
$764$	−5.13297	−0.185704
$765$	−41.4507	−1.49865
$766$	−24.5396	−0.886652
$767$	8.13773	0.293836
$768$	3.07012	0.110783
$769$	−12.7341	−0.459203	−0.229601	−	0.973285i	$-0.573742\pi$
$769$	−12.7341	−0.459203	−0.229601	+	0.973285i	$0.573742\pi$
$770$	−3.37856	−0.121755
$771$	26.1711	0.942528
$772$	1.71715	0.0618016
$773$	−2.43454	−0.0875645	−0.0437822	−	0.999041i	$-0.513941\pi$
$773$	−2.43454	−0.0875645	−0.0437822	+	0.999041i	$0.513941\pi$
$774$	−6.42564	−0.230965
$775$	−3.47827	−0.124943
$776$	3.69605	0.132680
$777$	92.4381	3.31620
$778$	1.83008	0.0656117
$779$	5.70792	0.204507
$780$	9.32132	0.333757
$781$	−5.77406	−0.206612
$782$	−34.0488	−1.21758
$783$	89.4320	3.19604
$784$	4.41468	0.157667
$785$	2.60693	0.0930453
$786$	−16.4408	−0.586422
$787$	18.6849	0.666044	0.333022	−	0.942919i	$-0.391932\pi$
$787$	18.6849	0.666044	0.333022	+	0.942919i	$0.391932\pi$
$788$	15.9926	0.569712
$789$	78.3549	2.78951
$790$	−1.29464	−0.0460613
$791$	30.4117	1.08131
$792$	6.42564	0.228325
$793$	−1.12703	−0.0400219
$794$	−15.7985	−0.560669
$795$	−3.63671	−0.128981
$796$	−8.18216	−0.290009
$797$	40.8335	1.44640	0.723198	−	0.690641i	$-0.242671\pi$
$797$	40.8335	1.44640	0.723198	+	0.690641i	$0.242671\pi$
$798$	−42.0945	−1.49013
$799$	−87.0325	−3.07899
$800$	1.00000	0.0353553
$801$	8.74355	0.308938
$802$	29.1429	1.02907
$803$	−14.4616	−0.510338
$804$	34.5203	1.21744
$805$	−17.8328	−0.628523
$806$	−10.5605	−0.371979
$807$	6.03549	0.212459
$808$	−7.95747	−0.279943
$809$	−8.94840	−0.314609	−0.157305	−	0.987550i	$-0.550280\pi$
$809$	−8.94840	−0.314609	−0.157305	+	0.987550i	$0.550280\pi$
$810$	13.0120	0.457194
$811$	28.5045	1.00093	0.500464	−	0.865758i	$-0.333163\pi$
$811$	28.5045	1.00093	0.500464	+	0.865758i	$0.333163\pi$
$812$	−28.7294	−1.00821
$813$	−73.4031	−2.57436
$814$	−8.91176	−0.312357
$815$	−7.56597	−0.265024
$816$	−19.8048	−0.693307
$817$	−4.05824	−0.141980
$818$	17.7146	0.619377
$819$	−65.9129	−2.30318
$820$	1.40650	0.0491171
$821$	17.4281	0.608244	0.304122	−	0.952633i	$-0.401637\pi$
$821$	17.4281	0.608244	0.304122	+	0.952633i	$0.401637\pi$
$822$	−3.61805	−0.126194
$823$	−48.7247	−1.69843	−0.849217	−	0.528043i	$-0.822926\pi$
$823$	−48.7247	−1.69843	−0.849217	+	0.528043i	$0.822926\pi$
$824$	13.4872	0.469849
$825$	3.07012	0.106888
$826$	−9.05552	−0.315082
$827$	−49.0197	−1.70458	−0.852292	−	0.523067i	$-0.824788\pi$
$827$	−49.0197	−1.70458	−0.852292	+	0.523067i	$0.824788\pi$
$828$	33.9159	1.17866
$829$	−10.1829	−0.353667	−0.176834	−	0.984241i	$-0.556585\pi$
$829$	−10.1829	−0.353667	−0.176834	+	0.984241i	$0.556585\pi$
$830$	10.1391	0.351934
$831$	96.0994	3.33365
$832$	3.03614	0.105259
$833$	−28.4783	−0.986715
$834$	−37.8473	−1.31055
$835$	−0.931661	−0.0322415
$836$	4.05824	0.140357
$837$	−36.5815	−1.26444
$838$	−17.7051	−0.611613
$839$	−32.9072	−1.13608	−0.568042	−	0.822999i	$-0.692299\pi$
$839$	−32.9072	−1.13608	−0.568042	+	0.822999i	$0.692299\pi$
$840$	−10.3726	−0.357889
$841$	43.3087	1.49340
$842$	23.8331	0.821344
$843$	−69.6529	−2.39897
$844$	−13.9718	−0.480930
$845$	−3.78185	−0.130100
$846$	86.6928	2.98056
$847$	−3.37856	−0.116089
$848$	−1.18455	−0.0406776
$849$	−32.4596	−1.11401
$850$	−6.45082	−0.221261
$851$	−47.0382	−1.61245
$852$	−17.7271	−0.607319
$853$	−1.17644	−0.0402806	−0.0201403	−	0.999797i	$-0.506411\pi$
$853$	−1.17644	−0.0402806	−0.0201403	+	0.999797i	$0.506411\pi$
$854$	1.25413	0.0429156
$855$	26.0768	0.891808
$856$	−16.3136	−0.557588
$857$	−18.4017	−0.628589	−0.314295	−	0.949325i	$-0.601768\pi$
$857$	−18.4017	−0.628589	−0.314295	+	0.949325i	$0.601768\pi$
$858$	9.32132	0.318225
$859$	28.4320	0.970086	0.485043	−	0.874490i	$-0.338804\pi$
$859$	28.4320	0.970086	0.485043	+	0.874490i	$0.338804\pi$
$860$	−1.00000	−0.0340997
$861$	−14.5891	−0.497194
$862$	−10.9452	−0.372793
$863$	0.245287	0.00834967	0.00417484	−	0.999991i	$-0.498671\pi$
$863$	0.245287	0.00834967	0.00417484	+	0.999991i	$0.498671\pi$
$864$	10.5171	0.357800
$865$	21.2614	0.722910
$866$	−8.95509	−0.304306
$867$	75.5652	2.56633
$868$	11.7516	0.398874
$869$	−1.29464	−0.0439177
$870$	26.1066	0.885098
$871$	34.1382	1.15673
$872$	−11.2530	−0.381074
$873$	23.7495	0.803798
$874$	21.4203	0.724551
$875$	−3.37856	−0.114216
$876$	−44.3988	−1.50009
$877$	31.8125	1.07423	0.537116	−	0.843508i	$-0.319514\pi$
$877$	31.8125	1.07423	0.537116	+	0.843508i	$0.319514\pi$
$878$	−36.0956	−1.21817
$879$	38.3478	1.29344
$880$	1.00000	0.0337100
$881$	28.2765	0.952660	0.476330	−	0.879267i	$-0.341967\pi$
$881$	28.2765	0.952660	0.476330	+	0.879267i	$0.341967\pi$
$882$	28.3672	0.955172
$883$	−5.75380	−0.193631	−0.0968153	−	0.995302i	$-0.530866\pi$
$883$	−5.75380	−0.193631	−0.0968153	+	0.995302i	$0.530866\pi$
$884$	−19.5856	−0.658735
$885$	8.22881	0.276608
$886$	−22.7491	−0.764272
$887$	50.5475	1.69722	0.848609	−	0.529020i	$-0.177440\pi$
$887$	50.5475	1.69722	0.848609	+	0.529020i	$0.177440\pi$
$888$	−27.3602	−0.918148
$889$	25.9973	0.871923
$890$	1.36073	0.0456117
$891$	13.0120	0.435917
$892$	29.4962	0.987607
$893$	54.7525	1.83222
$894$	−45.9346	−1.53628
$895$	−9.75068	−0.325929
$896$	−3.37856	−0.112870
$897$	49.1999	1.64274
$898$	−6.39980	−0.213564
$899$	−29.5773	−0.986459
$900$	6.42564	0.214188
$901$	7.64131	0.254569
$902$	1.40650	0.0468314
$903$	10.3726	0.345178
$904$	−9.00136	−0.299381
$905$	−12.5959	−0.418703
$906$	29.2801	0.972767
$907$	−12.3460	−0.409942	−0.204971	−	0.978768i	$-0.565710\pi$
$907$	−12.3460	−0.409942	−0.204971	+	0.978768i	$0.565710\pi$
$908$	−3.42702	−0.113730
$909$	−51.1319	−1.69594
$910$	−10.2578	−0.340042
$911$	−0.798881	−0.0264681	−0.0132340	−	0.999912i	$-0.504213\pi$
$911$	−0.798881	−0.0264681	−0.0132340	+	0.999912i	$0.504213\pi$
$912$	12.4593	0.412568
$913$	10.1391	0.335556
$914$	34.8873	1.15397
$915$	−1.13964	−0.0376753
$916$	7.82348	0.258495
$917$	18.0925	0.597466
$918$	−67.8442	−2.23919
$919$	15.8294	0.522163	0.261081	−	0.965317i	$-0.415921\pi$
$919$	15.8294	0.522163	0.261081	+	0.965317i	$0.415921\pi$
$920$	5.27821	0.174018
$921$	−44.7744	−1.47537
$922$	1.23455	0.0406576
$923$	−17.5309	−0.577035
$924$	−10.3726	−0.341233
$925$	−8.91176	−0.293017
$926$	37.6972	1.23881
$927$	86.6639	2.84642
$928$	8.50345	0.279139
$929$	−19.6599	−0.645019	−0.322509	−	0.946566i	$-0.604526\pi$
$929$	−19.6599	−0.645019	−0.322509	+	0.946566i	$0.604526\pi$
$930$	−10.6787	−0.350169
$931$	17.9158	0.587168
$932$	21.9475	0.718916
$933$	3.38442	0.110801
$934$	33.8607	1.10796
$935$	−6.45082	−0.210964
$936$	19.5092	0.637677
$937$	−13.5403	−0.442341	−0.221170	−	0.975235i	$-0.570988\pi$
$937$	−13.5403	−0.442341	−0.221170	+	0.975235i	$0.570988\pi$
$938$	−37.9884	−1.24036
$939$	47.6644	1.55547
$940$	13.4917	0.440051
$941$	52.4655	1.71033	0.855163	−	0.518359i	$-0.173457\pi$
$941$	52.4655	1.71033	0.855163	+	0.518359i	$0.173457\pi$
$942$	8.00359	0.260771
$943$	7.42381	0.241753
$944$	2.68029	0.0872359
$945$	−35.5328	−1.15588
$946$	−1.00000	−0.0325128
$947$	14.0563	0.456770	0.228385	−	0.973571i	$-0.426656\pi$
$947$	14.0563	0.456770	0.228385	+	0.973571i	$0.426656\pi$
$948$	−3.97471	−0.129093
$949$	−43.9073	−1.42529
$950$	4.05824	0.131667
$951$	3.50866	0.113776
$952$	21.7945	0.706364
$953$	18.3765	0.595275	0.297637	−	0.954679i	$-0.403801\pi$
$953$	18.3765	0.595275	0.297637	+	0.954679i	$0.403801\pi$
$954$	−7.61149	−0.246431
$955$	−5.13297	−0.166099
$956$	−28.8116	−0.931833
$957$	26.1066	0.843907
$958$	7.06624	0.228300
$959$	3.98153	0.128570
$960$	3.07012	0.0990877
$961$	−18.9016	−0.609729
$962$	−27.0574	−0.872364
$963$	−104.826	−3.37796
$964$	−19.8749	−0.640128
$965$	1.71715	0.0552771
$966$	−54.7488	−1.76151
$967$	35.1542	1.13048	0.565242	−	0.824925i	$-0.308783\pi$
$967$	35.1542	1.13048	0.565242	+	0.824925i	$0.308783\pi$
$968$	1.00000	0.0321412
$969$	−80.3727	−2.58194
$970$	3.69605	0.118673
$971$	−31.5593	−1.01279	−0.506394	−	0.862302i	$-0.669022\pi$
$971$	−31.5593	−1.01279	−0.506394	+	0.862302i	$0.669022\pi$
$972$	8.39690	0.269331
$973$	41.6497	1.33523
$974$	−31.2404	−1.00101
$975$	9.32132	0.298521
$976$	−0.371203	−0.0118819
$977$	−25.2610	−0.808172	−0.404086	−	0.914721i	$-0.632410\pi$
$977$	−25.2610	−0.808172	−0.404086	+	0.914721i	$0.632410\pi$
$978$	−23.2284	−0.742764
$979$	1.36073	0.0434890
$980$	4.41468	0.141022
$981$	−72.3076	−2.30860
$982$	−18.8693	−0.602144
$983$	−24.0758	−0.767899	−0.383949	−	0.923354i	$-0.625436\pi$
$983$	−24.0758	−0.767899	−0.383949	+	0.923354i	$0.625436\pi$
$984$	4.31813	0.137657
$985$	15.9926	0.509566
$986$	−54.8542	−1.74692
$987$	−139.944	−4.45446
$988$	12.3214	0.391996
$989$	−5.27821	−0.167837
$990$	6.42564	0.204220
$991$	−29.9041	−0.949936	−0.474968	−	0.880003i	$-0.657540\pi$
$991$	−29.9041	−0.949936	−0.474968	+	0.880003i	$0.657540\pi$
$992$	−3.47827	−0.110435
$993$	−6.15273	−0.195251
$994$	19.5080	0.618757
$995$	−8.18216	−0.259392
$996$	31.1283	0.986339
$997$	−38.8927	−1.23174	−0.615872	−	0.787846i	$-0.711196\pi$
$997$	−38.8927	−1.23174	−0.615872	+	0.787846i	$0.711196\pi$
$998$	39.8772	1.26229
$999$	−93.7263	−2.96537

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.bd.1.10	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.bd.1.10	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +3.07012 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.07012 q^{6} -3.37856 q^{7} +1.00000 q^{8} +6.42564 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +3.07012 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.07012 q^{6} -3.37856 q^{7} +1.00000 q^{8} +6.42564 q^{9} +1.00000 q^{10} +1.00000 q^{11} +3.07012 q^{12} +3.03614 q^{13} -3.37856 q^{14} +3.07012 q^{15} +1.00000 q^{16} -6.45082 q^{17} +6.42564 q^{18} +4.05824 q^{19} +1.00000 q^{20} -10.3726 q^{21} +1.00000 q^{22} +5.27821 q^{23} +3.07012 q^{24} +1.00000 q^{25} +3.03614 q^{26} +10.5171 q^{27} -3.37856 q^{28} +8.50345 q^{29} +3.07012 q^{30} -3.47827 q^{31} +1.00000 q^{32} +3.07012 q^{33} -6.45082 q^{34} -3.37856 q^{35} +6.42564 q^{36} -8.91176 q^{37} +4.05824 q^{38} +9.32132 q^{39} +1.00000 q^{40} +1.40650 q^{41} -10.3726 q^{42} -1.00000 q^{43} +1.00000 q^{44} +6.42564 q^{45} +5.27821 q^{46} +13.4917 q^{47} +3.07012 q^{48} +4.41468 q^{49} +1.00000 q^{50} -19.8048 q^{51} +3.03614 q^{52} -1.18455 q^{53} +10.5171 q^{54} +1.00000 q^{55} -3.37856 q^{56} +12.4593 q^{57} +8.50345 q^{58} +2.68029 q^{59} +3.07012 q^{60} -0.371203 q^{61} -3.47827 q^{62} -21.7094 q^{63} +1.00000 q^{64} +3.03614 q^{65} +3.07012 q^{66} +11.2439 q^{67} -6.45082 q^{68} +16.2048 q^{69} -3.37856 q^{70} -5.77406 q^{71} +6.42564 q^{72} -14.4616 q^{73} -8.91176 q^{74} +3.07012 q^{75} +4.05824 q^{76} -3.37856 q^{77} +9.32132 q^{78} -1.29464 q^{79} +1.00000 q^{80} +13.0120 q^{81} +1.40650 q^{82} +10.1391 q^{83} -10.3726 q^{84} -6.45082 q^{85} -1.00000 q^{86} +26.1066 q^{87} +1.00000 q^{88} +1.36073 q^{89} +6.42564 q^{90} -10.2578 q^{91} +5.27821 q^{92} -10.6787 q^{93} +13.4917 q^{94} +4.05824 q^{95} +3.07012 q^{96} +3.69605 q^{97} +4.41468 q^{98} +6.42564 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 11 q^{2} + 3 q^{3} + 11 q^{4} + 11 q^{5} + 3 q^{6} + 5 q^{7} + 11 q^{8} + 26 q^{9}+O(q^{10}) \) 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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