LMFDB - Embedded newform 4730.2.a.ba.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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} - 21x^{8} + 22x^{7} + 138x^{6} - 154x^{5} - 291x^{4} + 327x^{3} + 97x^{2} - 124x + 16 $ x^10 - x^9 - 21x^8 + 22x^7 + 138x^6 - 154x^5 - 291x^4 + 327x^3 + 97x^2 - 124x + 16
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			$0.530117$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -0.530117 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.530117 q^{6} -4.20387 q^{7} +1.00000 q^{8} -2.71898 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.530117 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.530117 q^{6} -4.20387 q^{7} +1.00000 q^{8} -2.71898 q^{9} -1.00000 q^{10} -1.00000 q^{11} -0.530117 q^{12} -0.777655 q^{13} -4.20387 q^{14} +0.530117 q^{15} +1.00000 q^{16} +2.87312 q^{17} -2.71898 q^{18} +0.898341 q^{19} -1.00000 q^{20} +2.22855 q^{21} -1.00000 q^{22} -7.76347 q^{23} -0.530117 q^{24} +1.00000 q^{25} -0.777655 q^{26} +3.03173 q^{27} -4.20387 q^{28} -0.772355 q^{29} +0.530117 q^{30} +0.403576 q^{31} +1.00000 q^{32} +0.530117 q^{33} +2.87312 q^{34} +4.20387 q^{35} -2.71898 q^{36} +11.7007 q^{37} +0.898341 q^{38} +0.412249 q^{39} -1.00000 q^{40} -2.98268 q^{41} +2.22855 q^{42} -1.00000 q^{43} -1.00000 q^{44} +2.71898 q^{45} -7.76347 q^{46} -13.4353 q^{47} -0.530117 q^{48} +10.6726 q^{49} +1.00000 q^{50} -1.52309 q^{51} -0.777655 q^{52} +4.31450 q^{53} +3.03173 q^{54} +1.00000 q^{55} -4.20387 q^{56} -0.476226 q^{57} -0.772355 q^{58} +7.25702 q^{59} +0.530117 q^{60} -5.45118 q^{61} +0.403576 q^{62} +11.4302 q^{63} +1.00000 q^{64} +0.777655 q^{65} +0.530117 q^{66} -1.80675 q^{67} +2.87312 q^{68} +4.11555 q^{69} +4.20387 q^{70} -0.857078 q^{71} -2.71898 q^{72} -2.74543 q^{73} +11.7007 q^{74} -0.530117 q^{75} +0.898341 q^{76} +4.20387 q^{77} +0.412249 q^{78} +10.6284 q^{79} -1.00000 q^{80} +6.54976 q^{81} -2.98268 q^{82} +12.9453 q^{83} +2.22855 q^{84} -2.87312 q^{85} -1.00000 q^{86} +0.409439 q^{87} -1.00000 q^{88} -2.57923 q^{89} +2.71898 q^{90} +3.26917 q^{91} -7.76347 q^{92} -0.213943 q^{93} -13.4353 q^{94} -0.898341 q^{95} -0.530117 q^{96} +7.47313 q^{97} +10.6726 q^{98} +2.71898 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} - q^{3} + 10 q^{4} - 10 q^{5} - q^{6} + 3 q^{7} + 10 q^{8} + 13 q^{9}+O(q^{10}) $ 10 * q + 10 * q^2 - q^3 + 10 * q^4 - 10 * q^5 - q^6 + 3 * q^7 + 10 * q^8 + 13 * q^9	\( 10 q + 10 q^{2} - q^{3} + 10 q^{4} - 10 q^{5} - q^{6} + 3 q^{7} + 10 q^{8} + 13 q^{9} - 10 q^{10} - 10 q^{11} - q^{12} + 6 q^{13} + 3 q^{14} + q^{15} + 10 q^{16} + 3 q^{17} + 13 q^{18} + 3 q^{19} - 10 q^{20} + 11 q^{21} - 10 q^{22} - 6 q^{23} - q^{24} + 10 q^{25} + 6 q^{26} + 8 q^{27} + 3 q^{28} + 14 q^{29} + q^{30} + 6 q^{31} + 10 q^{32} + q^{33} + 3 q^{34} - 3 q^{35} + 13 q^{36} + 10 q^{37} + 3 q^{38} + 24 q^{39} - 10 q^{40} + 26 q^{41} + 11 q^{42} - 10 q^{43} - 10 q^{44} - 13 q^{45} - 6 q^{46} + 3 q^{47} - q^{48} + 33 q^{49} + 10 q^{50} + 18 q^{51} + 6 q^{52} - 9 q^{53} + 8 q^{54} + 10 q^{55} + 3 q^{56} + 18 q^{57} + 14 q^{58} - 9 q^{59} + q^{60} + 22 q^{61} + 6 q^{62} - q^{63} + 10 q^{64} - 6 q^{65} + q^{66} + 18 q^{67} + 3 q^{68} + 6 q^{69} - 3 q^{70} + 27 q^{71} + 13 q^{72} + 28 q^{73} + 10 q^{74} - q^{75} + 3 q^{76} - 3 q^{77} + 24 q^{78} + 3 q^{79} - 10 q^{80} + 30 q^{81} + 26 q^{82} - 11 q^{83} + 11 q^{84} - 3 q^{85} - 10 q^{86} + 30 q^{87} - 10 q^{88} + 16 q^{89} - 13 q^{90} + 32 q^{91} - 6 q^{92} + 52 q^{93} + 3 q^{94} - 3 q^{95} - q^{96} + 22 q^{97} + 33 q^{98} - 13 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 - q^3 + 10 * q^4 - 10 * q^5 - q^6 + 3 * q^7 + 10 * q^8 + 13 * q^9 - 10 * q^10 - 10 * q^11 - q^12 + 6 * q^13 + 3 * q^14 + q^15 + 10 * q^16 + 3 * q^17 + 13 * q^18 + 3 * q^19 - 10 * q^20 + 11 * q^21 - 10 * q^22 - 6 * q^23 - q^24 + 10 * q^25 + 6 * q^26 + 8 * q^27 + 3 * q^28 + 14 * q^29 + q^30 + 6 * q^31 + 10 * q^32 + q^33 + 3 * q^34 - 3 * q^35 + 13 * q^36 + 10 * q^37 + 3 * q^38 + 24 * q^39 - 10 * q^40 + 26 * q^41 + 11 * q^42 - 10 * q^43 - 10 * q^44 - 13 * q^45 - 6 * q^46 + 3 * q^47 - q^48 + 33 * q^49 + 10 * q^50 + 18 * q^51 + 6 * q^52 - 9 * q^53 + 8 * q^54 + 10 * q^55 + 3 * q^56 + 18 * q^57 + 14 * q^58 - 9 * q^59 + q^60 + 22 * q^61 + 6 * q^62 - q^63 + 10 * q^64 - 6 * q^65 + q^66 + 18 * q^67 + 3 * q^68 + 6 * q^69 - 3 * q^70 + 27 * q^71 + 13 * q^72 + 28 * q^73 + 10 * q^74 - q^75 + 3 * q^76 - 3 * q^77 + 24 * q^78 + 3 * q^79 - 10 * q^80 + 30 * q^81 + 26 * q^82 - 11 * q^83 + 11 * q^84 - 3 * q^85 - 10 * q^86 + 30 * q^87 - 10 * q^88 + 16 * q^89 - 13 * q^90 + 32 * q^91 - 6 * q^92 + 52 * q^93 + 3 * q^94 - 3 * q^95 - q^96 + 22 * q^97 + 33 * q^98 - 13 * 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
$3$	−0.530117	−0.306063	−0.153032	−	0.988221i	$-0.548904\pi$
$3$	−0.530117	−0.306063	−0.153032	+	0.988221i	$0.548904\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.530117	−0.216419
$7$	−4.20387	−1.58892	−0.794458	−	0.607320i	$-0.792245\pi$
$7$	−4.20387	−1.58892	−0.794458	+	0.607320i	$0.792245\pi$
$8$	1.00000	0.353553
$9$	−2.71898	−0.906325
$10$	−1.00000	−0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.530117	−0.153032
$13$	−0.777655	−0.215683	−0.107841	−	0.994168i	$-0.534394\pi$
$13$	−0.777655	−0.215683	−0.107841	+	0.994168i	$0.534394\pi$
$14$	−4.20387	−1.12353
$15$	0.530117	0.136876
$16$	1.00000	0.250000
$17$	2.87312	0.696833	0.348417	−	0.937340i	$-0.386719\pi$
$17$	2.87312	0.696833	0.348417	+	0.937340i	$0.386719\pi$
$18$	−2.71898	−0.640869
$19$	0.898341	0.206094	0.103047	−	0.994677i	$-0.467141\pi$
$19$	0.898341	0.206094	0.103047	+	0.994677i	$0.467141\pi$
$20$	−1.00000	−0.223607
$21$	2.22855	0.486309
$22$	−1.00000	−0.213201
$23$	−7.76347	−1.61879	−0.809397	−	0.587261i	$-0.800206\pi$
$23$	−7.76347	−1.61879	−0.809397	+	0.587261i	$0.800206\pi$
$24$	−0.530117	−0.108210
$25$	1.00000	0.200000
$26$	−0.777655	−0.152511
$27$	3.03173	0.583456
$28$	−4.20387	−0.794458
$29$	−0.772355	−0.143423	−0.0717113	−	0.997425i	$-0.522846\pi$
$29$	−0.772355	−0.143423	−0.0717113	+	0.997425i	$0.522846\pi$
$30$	0.530117	0.0967857
$31$	0.403576	0.0724844	0.0362422	−	0.999343i	$-0.488461\pi$
$31$	0.403576	0.0724844	0.0362422	+	0.999343i	$0.488461\pi$
$32$	1.00000	0.176777
$33$	0.530117	0.0922816
$34$	2.87312	0.492736
$35$	4.20387	0.710585
$36$	−2.71898	−0.453163
$37$	11.7007	1.92358	0.961791	−	0.273785i	$-0.0882755\pi$
$37$	11.7007	1.92358	0.961791	+	0.273785i	$0.0882755\pi$
$38$	0.898341	0.145730
$39$	0.412249	0.0660126
$40$	−1.00000	−0.158114
$41$	−2.98268	−0.465817	−0.232908	−	0.972499i	$-0.574824\pi$
$41$	−2.98268	−0.465817	−0.232908	+	0.972499i	$0.574824\pi$
$42$	2.22855	0.343872
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−1.00000	−0.150756
$45$	2.71898	0.405321
$46$	−7.76347	−1.14466
$47$	−13.4353	−1.95974	−0.979872	−	0.199626i	$-0.936027\pi$
$47$	−13.4353	−1.95974	−0.979872	+	0.199626i	$0.936027\pi$
$48$	−0.530117	−0.0765158
$49$	10.6726	1.52465
$50$	1.00000	0.141421
$51$	−1.52309	−0.213275
$52$	−0.777655	−0.107841
$53$	4.31450	0.592643	0.296321	−	0.955088i	$-0.404240\pi$
$53$	4.31450	0.592643	0.296321	+	0.955088i	$0.404240\pi$
$54$	3.03173	0.412566
$55$	1.00000	0.134840
$56$	−4.20387	−0.561766
$57$	−0.476226	−0.0630777
$58$	−0.772355	−0.101415
$59$	7.25702	0.944783	0.472392	−	0.881389i	$-0.343391\pi$
$59$	7.25702	0.944783	0.472392	+	0.881389i	$0.343391\pi$
$60$	0.530117	0.0684378
$61$	−5.45118	−0.697952	−0.348976	−	0.937132i	$-0.613471\pi$
$61$	−5.45118	−0.697952	−0.348976	+	0.937132i	$0.613471\pi$
$62$	0.403576	0.0512542
$63$	11.4302	1.44007
$64$	1.00000	0.125000
$65$	0.777655	0.0964563
$66$	0.530117	0.0652529
$67$	−1.80675	−0.220730	−0.110365	−	0.993891i	$-0.535202\pi$
$67$	−1.80675	−0.220730	−0.110365	+	0.993891i	$0.535202\pi$
$68$	2.87312	0.348417
$69$	4.11555	0.495454
$70$	4.20387	0.502459
$71$	−0.857078	−0.101716	−0.0508582	−	0.998706i	$-0.516196\pi$
$71$	−0.857078	−0.101716	−0.0508582	+	0.998706i	$0.516196\pi$
$72$	−2.71898	−0.320434
$73$	−2.74543	−0.321328	−0.160664	−	0.987009i	$-0.551364\pi$
$73$	−2.74543	−0.321328	−0.160664	+	0.987009i	$0.551364\pi$
$74$	11.7007	1.36018
$75$	−0.530117	−0.0612127
$76$	0.898341	0.103047
$77$	4.20387	0.479076
$78$	0.412249	0.0466780
$79$	10.6284	1.19579	0.597897	−	0.801573i	$-0.296003\pi$
$79$	10.6284	1.19579	0.597897	+	0.801573i	$0.296003\pi$
$80$	−1.00000	−0.111803
$81$	6.54976	0.727751
$82$	−2.98268	−0.329382
$83$	12.9453	1.42093	0.710463	−	0.703734i	$-0.248485\pi$
$83$	12.9453	1.42093	0.710463	+	0.703734i	$0.248485\pi$
$84$	2.22855	0.243154
$85$	−2.87312	−0.311633
$86$	−1.00000	−0.107833
$87$	0.409439	0.0438964
$88$	−1.00000	−0.106600
$89$	−2.57923	−0.273397	−0.136699	−	0.990613i	$-0.543649\pi$
$89$	−2.57923	−0.273397	−0.136699	+	0.990613i	$0.543649\pi$
$90$	2.71898	0.286605
$91$	3.26917	0.342702
$92$	−7.76347	−0.809397
$93$	−0.213943	−0.0221848
$94$	−13.4353	−1.38575
$95$	−0.898341	−0.0921679
$96$	−0.530117	−0.0541049
$97$	7.47313	0.758782	0.379391	−	0.925236i	$-0.376134\pi$
$97$	7.47313	0.758782	0.379391	+	0.925236i	$0.376134\pi$
$98$	10.6726	1.07809
$99$	2.71898	0.273267
$100$	1.00000	0.100000
$101$	16.0837	1.60039	0.800196	−	0.599738i	$-0.204729\pi$
$101$	16.0837	1.60039	0.800196	+	0.599738i	$0.204729\pi$
$102$	−1.52309	−0.150808
$103$	12.7206	1.25340	0.626698	−	0.779262i	$-0.284406\pi$
$103$	12.7206	1.25340	0.626698	+	0.779262i	$0.284406\pi$
$104$	−0.777655	−0.0762554
$105$	−2.22855	−0.217484
$106$	4.31450	0.419062
$107$	−5.99220	−0.579288	−0.289644	−	0.957134i	$-0.593537\pi$
$107$	−5.99220	−0.579288	−0.289644	+	0.957134i	$0.593537\pi$
$108$	3.03173	0.291728
$109$	19.9333	1.90926	0.954631	−	0.297790i	$-0.0962494\pi$
$109$	19.9333	1.90926	0.954631	+	0.297790i	$0.0962494\pi$
$110$	1.00000	0.0953463
$111$	−6.20274	−0.588738
$112$	−4.20387	−0.397229
$113$	0.526577	0.0495362	0.0247681	−	0.999693i	$-0.492115\pi$
$113$	0.526577	0.0495362	0.0247681	+	0.999693i	$0.492115\pi$
$114$	−0.476226	−0.0446027
$115$	7.76347	0.723947
$116$	−0.772355	−0.0717113
$117$	2.11443	0.195479
$118$	7.25702	0.668063
$119$	−12.0782	−1.10721
$120$	0.530117	0.0483929
$121$	1.00000	0.0909091
$122$	−5.45118	−0.493527
$123$	1.58117	0.142569
$124$	0.403576	0.0362422
$125$	−1.00000	−0.0894427
$126$	11.4302	1.01829
$127$	−0.475972	−0.0422357	−0.0211179	−	0.999777i	$-0.506723\pi$
$127$	−0.475972	−0.0422357	−0.0211179	+	0.999777i	$0.506723\pi$
$128$	1.00000	0.0883883
$129$	0.530117	0.0466742
$130$	0.777655	0.0682049
$131$	−0.917399	−0.0801535	−0.0400767	−	0.999197i	$-0.512760\pi$
$131$	−0.917399	−0.0801535	−0.0400767	+	0.999197i	$0.512760\pi$
$132$	0.530117	0.0461408
$133$	−3.77651	−0.327465
$134$	−1.80675	−0.156080
$135$	−3.03173	−0.260930
$136$	2.87312	0.246368
$137$	−11.3839	−0.972595	−0.486297	−	0.873793i	$-0.661653\pi$
$137$	−11.3839	−0.972595	−0.486297	+	0.873793i	$0.661653\pi$
$138$	4.11555	0.350339
$139$	−10.8998	−0.924508	−0.462254	−	0.886748i	$-0.652959\pi$
$139$	−10.8998	−0.924508	−0.462254	+	0.886748i	$0.652959\pi$
$140$	4.20387	0.355292
$141$	7.12230	0.599806
$142$	−0.857078	−0.0719244
$143$	0.777655	0.0650308
$144$	−2.71898	−0.226581
$145$	0.772355	0.0641406
$146$	−2.74543	−0.227213
$147$	−5.65771	−0.466640
$148$	11.7007	0.961791
$149$	21.4451	1.75685	0.878425	−	0.477881i	$-0.158595\pi$
$149$	21.4451	1.75685	0.878425	+	0.477881i	$0.158595\pi$
$150$	−0.530117	−0.0432839
$151$	−6.83197	−0.555978	−0.277989	−	0.960584i	$-0.589668\pi$
$151$	−6.83197	−0.555978	−0.277989	+	0.960584i	$0.589668\pi$
$152$	0.898341	0.0728651
$153$	−7.81194	−0.631558
$154$	4.20387	0.338758
$155$	−0.403576	−0.0324160
$156$	0.412249	0.0330063
$157$	18.3879	1.46752	0.733759	−	0.679410i	$-0.237764\pi$
$157$	18.3879	1.46752	0.733759	+	0.679410i	$0.237764\pi$
$158$	10.6284	0.845553
$159$	−2.28719	−0.181386
$160$	−1.00000	−0.0790569
$161$	32.6366	2.57213
$162$	6.54976	0.514597
$163$	3.65630	0.286384	0.143192	−	0.989695i	$-0.454263\pi$
$163$	3.65630	0.286384	0.143192	+	0.989695i	$0.454263\pi$
$164$	−2.98268	−0.232908
$165$	−0.530117	−0.0412696
$166$	12.9453	1.00475
$167$	−3.50087	−0.270906	−0.135453	−	0.990784i	$-0.543249\pi$
$167$	−3.50087	−0.270906	−0.135453	+	0.990784i	$0.543249\pi$
$168$	2.22855	0.171936
$169$	−12.3953	−0.953481
$170$	−2.87312	−0.220358
$171$	−2.44257	−0.186788
$172$	−1.00000	−0.0762493
$173$	−0.169891	−0.0129165	−0.00645827	−	0.999979i	$-0.502056\pi$
$173$	−0.169891	−0.0129165	−0.00645827	+	0.999979i	$0.502056\pi$
$174$	0.409439	0.0310395
$175$	−4.20387	−0.317783
$176$	−1.00000	−0.0753778
$177$	−3.84707	−0.289163
$178$	−2.57923	−0.193321
$179$	1.23979	0.0926662	0.0463331	−	0.998926i	$-0.485246\pi$
$179$	1.23979	0.0926662	0.0463331	+	0.998926i	$0.485246\pi$
$180$	2.71898	0.202660
$181$	−0.760444	−0.0565234	−0.0282617	−	0.999601i	$-0.508997\pi$
$181$	−0.760444	−0.0565234	−0.0282617	+	0.999601i	$0.508997\pi$
$182$	3.26917	0.242327
$183$	2.88977	0.213618
$184$	−7.76347	−0.572330
$185$	−11.7007	−0.860252
$186$	−0.213943	−0.0156870
$187$	−2.87312	−0.210103
$188$	−13.4353	−0.979872
$189$	−12.7450	−0.927063
$190$	−0.898341	−0.0651725
$191$	15.8970	1.15027	0.575134	−	0.818059i	$-0.304950\pi$
$191$	15.8970	1.15027	0.575134	+	0.818059i	$0.304950\pi$
$192$	−0.530117	−0.0382579
$193$	−9.92872	−0.714685	−0.357342	−	0.933973i	$-0.616317\pi$
$193$	−9.92872	−0.714685	−0.357342	+	0.933973i	$0.616317\pi$
$194$	7.47313	0.536540
$195$	−0.412249	−0.0295217
$196$	10.6726	0.762326
$197$	7.15450	0.509737	0.254868	−	0.966976i	$-0.417968\pi$
$197$	7.15450	0.509737	0.254868	+	0.966976i	$0.417968\pi$
$198$	2.71898	0.193229
$199$	21.9261	1.55430	0.777151	−	0.629314i	$-0.216664\pi$
$199$	21.9261	1.55430	0.777151	+	0.629314i	$0.216664\pi$
$200$	1.00000	0.0707107
$201$	0.957790	0.0675573
$202$	16.0837	1.13165
$203$	3.24688	0.227886
$204$	−1.52309	−0.106638
$205$	2.98268	0.208320
$206$	12.7206	0.886285
$207$	21.1087	1.46715
$208$	−0.777655	−0.0539207
$209$	−0.898341	−0.0621396
$210$	−2.22855	−0.153784
$211$	−2.15992	−0.148695	−0.0743474	−	0.997232i	$-0.523687\pi$
$211$	−2.15992	−0.148695	−0.0743474	+	0.997232i	$0.523687\pi$
$212$	4.31450	0.296321
$213$	0.454352	0.0311317
$214$	−5.99220	−0.409619
$215$	1.00000	0.0681994
$216$	3.03173	0.206283
$217$	−1.69658	−0.115172
$218$	19.9333	1.35005
$219$	1.45540	0.0983468
$220$	1.00000	0.0674200
$221$	−2.23430	−0.150295
$222$	−6.20274	−0.416301
$223$	0.492756	0.0329974	0.0164987	−	0.999864i	$-0.494748\pi$
$223$	0.492756	0.0329974	0.0164987	+	0.999864i	$0.494748\pi$
$224$	−4.20387	−0.280883
$225$	−2.71898	−0.181265
$226$	0.526577	0.0350274
$227$	−2.29324	−0.152207	−0.0761037	−	0.997100i	$-0.524248\pi$
$227$	−2.29324	−0.152207	−0.0761037	+	0.997100i	$0.524248\pi$
$228$	−0.476226	−0.0315389
$229$	16.7314	1.10564	0.552820	−	0.833301i	$-0.313552\pi$
$229$	16.7314	1.10564	0.552820	+	0.833301i	$0.313552\pi$
$230$	7.76347	0.511908
$231$	−2.22855	−0.146628
$232$	−0.772355	−0.0507076
$233$	−11.8076	−0.773542	−0.386771	−	0.922176i	$-0.626410\pi$
$233$	−11.8076	−0.773542	−0.386771	+	0.922176i	$0.626410\pi$
$234$	2.11443	0.138224
$235$	13.4353	0.876424
$236$	7.25702	0.472392
$237$	−5.63432	−0.365988
$238$	−12.0782	−0.782915
$239$	6.50130	0.420534	0.210267	−	0.977644i	$-0.432567\pi$
$239$	6.50130	0.420534	0.210267	+	0.977644i	$0.432567\pi$
$240$	0.530117	0.0342189
$241$	3.92330	0.252722	0.126361	−	0.991984i	$-0.459670\pi$
$241$	3.92330	0.252722	0.126361	+	0.991984i	$0.459670\pi$
$242$	1.00000	0.0642824
$243$	−12.5673	−0.806194
$244$	−5.45118	−0.348976
$245$	−10.6726	−0.681845
$246$	1.58117	0.100812
$247$	−0.698600	−0.0444509
$248$	0.403576	0.0256271
$249$	−6.86250	−0.434893
$250$	−1.00000	−0.0632456
$251$	14.2418	0.898932	0.449466	−	0.893297i	$-0.351614\pi$
$251$	14.2418	0.898932	0.449466	+	0.893297i	$0.351614\pi$
$252$	11.4302	0.720037
$253$	7.76347	0.488085
$254$	−0.475972	−0.0298652
$255$	1.52309	0.0953795
$256$	1.00000	0.0625000
$257$	−21.5296	−1.34298	−0.671490	−	0.741014i	$-0.734345\pi$
$257$	−21.5296	−1.34298	−0.671490	+	0.741014i	$0.734345\pi$
$258$	0.530117	0.0330037
$259$	−49.1882	−3.05641
$260$	0.777655	0.0482281
$261$	2.10001	0.129988
$262$	−0.917399	−0.0566771
$263$	2.01696	0.124371	0.0621854	−	0.998065i	$-0.480193\pi$
$263$	2.01696	0.124371	0.0621854	+	0.998065i	$0.480193\pi$
$264$	0.530117	0.0326265
$265$	−4.31450	−0.265038
$266$	−3.77651	−0.231553
$267$	1.36729	0.0836769
$268$	−1.80675	−0.110365
$269$	−13.5392	−0.825498	−0.412749	−	0.910845i	$-0.635431\pi$
$269$	−13.5392	−0.825498	−0.412749	+	0.910845i	$0.635431\pi$
$270$	−3.03173	−0.184505
$271$	−17.0826	−1.03769	−0.518847	−	0.854867i	$-0.673638\pi$
$271$	−17.0826	−1.03769	−0.518847	+	0.854867i	$0.673638\pi$
$272$	2.87312	0.174208
$273$	−1.73304	−0.104888
$274$	−11.3839	−0.687728
$275$	−1.00000	−0.0603023
$276$	4.11555	0.247727
$277$	−16.1511	−0.970428	−0.485214	−	0.874395i	$-0.661258\pi$
$277$	−16.1511	−0.970428	−0.485214	+	0.874395i	$0.661258\pi$
$278$	−10.8998	−0.653726
$279$	−1.09731	−0.0656944
$280$	4.20387	0.251230
$281$	−31.0472	−1.85212	−0.926059	−	0.377379i	$-0.876825\pi$
$281$	−31.0472	−1.85212	−0.926059	+	0.377379i	$0.876825\pi$
$282$	7.12230	0.424127
$283$	11.2979	0.671592	0.335796	−	0.941935i	$-0.390995\pi$
$283$	11.2979	0.671592	0.335796	+	0.941935i	$0.390995\pi$
$284$	−0.857078	−0.0508582
$285$	0.476226	0.0282092
$286$	0.777655	0.0459837
$287$	12.5388	0.740143
$288$	−2.71898	−0.160217
$289$	−8.74519	−0.514423
$290$	0.772355	0.0453542
$291$	−3.96164	−0.232235
$292$	−2.74543	−0.160664
$293$	−3.38273	−0.197621	−0.0988105	−	0.995106i	$-0.531504\pi$
$293$	−3.38273	−0.197621	−0.0988105	+	0.995106i	$0.531504\pi$
$294$	−5.65771	−0.329964
$295$	−7.25702	−0.422520
$296$	11.7007	0.680089
$297$	−3.03173	−0.175919
$298$	21.4451	1.24228
$299$	6.03730	0.349146
$300$	−0.530117	−0.0306063
$301$	4.20387	0.242307
$302$	−6.83197	−0.393136
$303$	−8.52627	−0.489821
$304$	0.898341	0.0515234
$305$	5.45118	0.312134
$306$	−7.81194	−0.446579
$307$	−8.05888	−0.459945	−0.229972	−	0.973197i	$-0.573864\pi$
$307$	−8.05888	−0.459945	−0.229972	+	0.973197i	$0.573864\pi$
$308$	4.20387	0.239538
$309$	−6.74340	−0.383619
$310$	−0.403576	−0.0229216
$311$	4.03269	0.228673	0.114337	−	0.993442i	$-0.463526\pi$
$311$	4.03269	0.228673	0.114337	+	0.993442i	$0.463526\pi$
$312$	0.412249	0.0233390
$313$	−9.90253	−0.559724	−0.279862	−	0.960040i	$-0.590289\pi$
$313$	−9.90253	−0.559724	−0.279862	+	0.960040i	$0.590289\pi$
$314$	18.3879	1.03769
$315$	−11.4302	−0.644021
$316$	10.6284	0.597897
$317$	−3.45405	−0.193999	−0.0969995	−	0.995284i	$-0.530925\pi$
$317$	−3.45405	−0.193999	−0.0969995	+	0.995284i	$0.530925\pi$
$318$	−2.28719	−0.128259
$319$	0.772355	0.0432436
$320$	−1.00000	−0.0559017
$321$	3.17657	0.177299
$322$	32.6366	1.81877
$323$	2.58104	0.143613
$324$	6.54976	0.363875
$325$	−0.777655	−0.0431366
$326$	3.65630	0.202504
$327$	−10.5670	−0.584355
$328$	−2.98268	−0.164691
$329$	56.4804	3.11387
$330$	−0.530117	−0.0291820
$331$	−12.7324	−0.699835	−0.349917	−	0.936781i	$-0.613790\pi$
$331$	−12.7324	−0.699835	−0.349917	+	0.936781i	$0.613790\pi$
$332$	12.9453	0.710463
$333$	−31.8139	−1.74339
$334$	−3.50087	−0.191559
$335$	1.80675	0.0987133
$336$	2.22855	0.121577
$337$	−20.6853	−1.12680	−0.563400	−	0.826184i	$-0.690507\pi$
$337$	−20.6853	−1.12680	−0.563400	+	0.826184i	$0.690507\pi$
$338$	−12.3953	−0.674213
$339$	−0.279147	−0.0151612
$340$	−2.87312	−0.155817
$341$	−0.403576	−0.0218549
$342$	−2.44257	−0.132079
$343$	−15.4390	−0.833627
$344$	−1.00000	−0.0539164
$345$	−4.11555	−0.221574
$346$	−0.169891	−0.00913338
$347$	21.4809	1.15315	0.576577	−	0.817043i	$-0.304388\pi$
$347$	21.4809	1.15315	0.576577	+	0.817043i	$0.304388\pi$
$348$	0.409439	0.0219482
$349$	11.3138	0.605613	0.302807	−	0.953052i	$-0.402076\pi$
$349$	11.3138	0.605613	0.302807	+	0.953052i	$0.402076\pi$
$350$	−4.20387	−0.224707
$351$	−2.35764	−0.125841
$352$	−1.00000	−0.0533002
$353$	11.6504	0.620089	0.310045	−	0.950722i	$-0.399656\pi$
$353$	11.6504	0.620089	0.310045	+	0.950722i	$0.399656\pi$
$354$	−3.84707	−0.204469
$355$	0.857078	0.0454890
$356$	−2.57923	−0.136699
$357$	6.40288	0.338876
$358$	1.23979	0.0655249
$359$	−1.89076	−0.0997903	−0.0498951	−	0.998754i	$-0.515889\pi$
$359$	−1.89076	−0.0997903	−0.0498951	+	0.998754i	$0.515889\pi$
$360$	2.71898	0.143303
$361$	−18.1930	−0.957525
$362$	−0.760444	−0.0399681
$363$	−0.530117	−0.0278239
$364$	3.26917	0.171351
$365$	2.74543	0.143702
$366$	2.88977	0.151050
$367$	−28.5057	−1.48799	−0.743993	−	0.668187i	$-0.767071\pi$
$367$	−28.5057	−1.48799	−0.743993	+	0.668187i	$0.767071\pi$
$368$	−7.76347	−0.404699
$369$	8.10984	0.422181
$370$	−11.7007	−0.608290
$371$	−18.1376	−0.941659
$372$	−0.213943	−0.0110924
$373$	36.4135	1.88542	0.942711	−	0.333610i	$-0.108267\pi$
$373$	36.4135	1.88542	0.942711	+	0.333610i	$0.108267\pi$
$374$	−2.87312	−0.148565
$375$	0.530117	0.0273751
$376$	−13.4353	−0.692874
$377$	0.600626	0.0309338
$378$	−12.7450	−0.655532
$379$	−13.6723	−0.702297	−0.351148	−	0.936320i	$-0.614209\pi$
$379$	−13.6723	−0.702297	−0.351148	+	0.936320i	$0.614209\pi$
$380$	−0.898341	−0.0460839
$381$	0.252321	0.0129268
$382$	15.8970	0.813362
$383$	6.58673	0.336566	0.168283	−	0.985739i	$-0.446178\pi$
$383$	6.58673	0.336566	0.168283	+	0.985739i	$0.446178\pi$
$384$	−0.530117	−0.0270524
$385$	−4.20387	−0.214249
$386$	−9.92872	−0.505358
$387$	2.71898	0.138213
$388$	7.47313	0.379391
$389$	20.5761	1.04325	0.521626	−	0.853174i	$-0.325326\pi$
$389$	20.5761	1.04325	0.521626	+	0.853174i	$0.325326\pi$
$390$	−0.412249	−0.0208750
$391$	−22.3054	−1.12803
$392$	10.6726	0.539046
$393$	0.486329	0.0245320
$394$	7.15450	0.360438
$395$	−10.6284	−0.534775
$396$	2.71898	0.136634
$397$	−11.3120	−0.567733	−0.283867	−	0.958864i	$-0.591617\pi$
$397$	−11.3120	−0.567733	−0.283867	+	0.958864i	$0.591617\pi$
$398$	21.9261	1.09906
$399$	2.00200	0.100225
$400$	1.00000	0.0500000
$401$	26.2385	1.31029	0.655143	−	0.755505i	$-0.272608\pi$
$401$	26.2385	1.31029	0.655143	+	0.755505i	$0.272608\pi$
$402$	0.957790	0.0477702
$403$	−0.313843	−0.0156336
$404$	16.0837	0.800196
$405$	−6.54976	−0.325460
$406$	3.24688	0.161140
$407$	−11.7007	−0.579982
$408$	−1.52309	−0.0754042
$409$	27.9533	1.38220	0.691102	−	0.722758i	$-0.257126\pi$
$409$	27.9533	1.38220	0.691102	+	0.722758i	$0.257126\pi$
$410$	2.98268	0.147304
$411$	6.03482	0.297676
$412$	12.7206	0.626698
$413$	−30.5076	−1.50118
$414$	21.1087	1.03743
$415$	−12.9453	−0.635458
$416$	−0.777655	−0.0381277
$417$	5.77816	0.282958
$418$	−0.898341	−0.0439393
$419$	4.63297	0.226336	0.113168	−	0.993576i	$-0.463900\pi$
$419$	4.63297	0.226336	0.113168	+	0.993576i	$0.463900\pi$
$420$	−2.22855	−0.108742
$421$	16.0041	0.779990	0.389995	−	0.920817i	$-0.372477\pi$
$421$	16.0041	0.779990	0.389995	+	0.920817i	$0.372477\pi$
$422$	−2.15992	−0.105143
$423$	36.5303	1.77617
$424$	4.31450	0.209531
$425$	2.87312	0.139367
$426$	0.454352	0.0220134
$427$	22.9161	1.10899
$428$	−5.99220	−0.289644
$429$	−0.412249	−0.0199035
$430$	1.00000	0.0482243
$431$	−28.6674	−1.38086	−0.690429	−	0.723400i	$-0.742578\pi$
$431$	−28.6674	−1.38086	−0.690429	+	0.723400i	$0.742578\pi$
$432$	3.03173	0.145864
$433$	3.69875	0.177751	0.0888754	−	0.996043i	$-0.471673\pi$
$433$	3.69875	0.177751	0.0888754	+	0.996043i	$0.471673\pi$
$434$	−1.69658	−0.0814386
$435$	−0.409439	−0.0196311
$436$	19.9333	0.954631
$437$	−6.97424	−0.333623
$438$	1.45540	0.0695417
$439$	17.9788	0.858082	0.429041	−	0.903285i	$-0.358852\pi$
$439$	17.9788	0.858082	0.429041	+	0.903285i	$0.358852\pi$
$440$	1.00000	0.0476731
$441$	−29.0184	−1.38183
$442$	−2.23430	−0.106275
$443$	−2.38221	−0.113182	−0.0565911	−	0.998397i	$-0.518023\pi$
$443$	−2.38221	−0.113182	−0.0565911	+	0.998397i	$0.518023\pi$
$444$	−6.20274	−0.294369
$445$	2.57923	0.122267
$446$	0.492756	0.0233327
$447$	−11.3684	−0.537707
$448$	−4.20387	−0.198614
$449$	24.0347	1.13427	0.567134	−	0.823626i	$-0.308052\pi$
$449$	24.0347	1.13427	0.567134	+	0.823626i	$0.308052\pi$
$450$	−2.71898	−0.128174
$451$	2.98268	0.140449
$452$	0.526577	0.0247681
$453$	3.62175	0.170164
$454$	−2.29324	−0.107627
$455$	−3.26917	−0.153261
$456$	−0.476226	−0.0223013
$457$	−22.7775	−1.06549	−0.532744	−	0.846277i	$-0.678839\pi$
$457$	−22.7775	−1.06549	−0.532744	+	0.846277i	$0.678839\pi$
$458$	16.7314	0.781806
$459$	8.71051	0.406572
$460$	7.76347	0.361974
$461$	24.6623	1.14864	0.574318	−	0.818632i	$-0.305267\pi$
$461$	24.6623	1.14864	0.574318	+	0.818632i	$0.305267\pi$
$462$	−2.22855	−0.103681
$463$	−32.9021	−1.52909	−0.764546	−	0.644570i	$-0.777037\pi$
$463$	−32.9021	−1.52909	−0.764546	+	0.644570i	$0.777037\pi$
$464$	−0.772355	−0.0358557
$465$	0.213943	0.00992135
$466$	−11.8076	−0.546977
$467$	−35.1298	−1.62561	−0.812807	−	0.582534i	$-0.802061\pi$
$467$	−35.1298	−1.62561	−0.812807	+	0.582534i	$0.802061\pi$
$468$	2.11443	0.0977394
$469$	7.59535	0.350721
$470$	13.4353	0.619726
$471$	−9.74777	−0.449153
$472$	7.25702	0.334031
$473$	1.00000	0.0459800
$474$	−5.63432	−0.258793
$475$	0.898341	0.0412187
$476$	−12.0782	−0.553605
$477$	−11.7310	−0.537127
$478$	6.50130	0.297363
$479$	0.262120	0.0119766	0.00598828	−	0.999982i	$-0.498094\pi$
$479$	0.262120	0.0119766	0.00598828	+	0.999982i	$0.498094\pi$
$480$	0.530117	0.0241964
$481$	−9.09911	−0.414884
$482$	3.92330	0.178701
$483$	−17.3012	−0.787234
$484$	1.00000	0.0454545
$485$	−7.47313	−0.339338
$486$	−12.5673	−0.570065
$487$	19.7458	0.894765	0.447383	−	0.894343i	$-0.352356\pi$
$487$	19.7458	0.894765	0.447383	+	0.894343i	$0.352356\pi$
$488$	−5.45118	−0.246763
$489$	−1.93827	−0.0876515
$490$	−10.6726	−0.482137
$491$	−27.1090	−1.22341	−0.611707	−	0.791085i	$-0.709517\pi$
$491$	−27.1090	−1.22341	−0.611707	+	0.791085i	$0.709517\pi$
$492$	1.58117	0.0712847
$493$	−2.21907	−0.0999417
$494$	−0.698600	−0.0314315
$495$	−2.71898	−0.122209
$496$	0.403576	0.0181211
$497$	3.60305	0.161619
$498$	−6.86250	−0.307516
$499$	−1.95916	−0.0877040	−0.0438520	−	0.999038i	$-0.513963\pi$
$499$	−1.95916	−0.0877040	−0.0438520	+	0.999038i	$0.513963\pi$
$500$	−1.00000	−0.0447214
$501$	1.85587	0.0829143
$502$	14.2418	0.635641
$503$	−21.9621	−0.979244	−0.489622	−	0.871935i	$-0.662865\pi$
$503$	−21.9621	−0.979244	−0.489622	+	0.871935i	$0.662865\pi$
$504$	11.4302	0.509143
$505$	−16.0837	−0.715717
$506$	7.76347	0.345128
$507$	6.57094	0.291826
$508$	−0.475972	−0.0211179
$509$	35.5714	1.57668	0.788338	−	0.615243i	$-0.210942\pi$
$509$	35.5714	1.57668	0.788338	+	0.615243i	$0.210942\pi$
$510$	1.52309	0.0674435
$511$	11.5414	0.510564
$512$	1.00000	0.0441942
$513$	2.72353	0.120247
$514$	−21.5296	−0.949630
$515$	−12.7206	−0.560536
$516$	0.530117	0.0233371
$517$	13.4353	0.590885
$518$	−49.1882	−2.16121
$519$	0.0900619	0.00395328
$520$	0.777655	0.0341024
$521$	−16.9703	−0.743481	−0.371741	−	0.928337i	$-0.621239\pi$
$521$	−16.9703	−0.743481	−0.371741	+	0.928337i	$0.621239\pi$
$522$	2.10001	0.0919151
$523$	21.4970	0.939997	0.469999	−	0.882667i	$-0.344254\pi$
$523$	21.4970	0.939997	0.469999	+	0.882667i	$0.344254\pi$
$524$	−0.917399	−0.0400767
$525$	2.22855	0.0972617
$526$	2.01696	0.0879434
$527$	1.15952	0.0505095
$528$	0.530117	0.0230704
$529$	37.2714	1.62050
$530$	−4.31450	−0.187410
$531$	−19.7317	−0.856281
$532$	−3.77651	−0.163733
$533$	2.31950	0.100469
$534$	1.36729	0.0591685
$535$	5.99220	0.259066
$536$	−1.80675	−0.0780398
$537$	−0.657234	−0.0283617
$538$	−13.5392	−0.583715
$539$	−10.6726	−0.459700
$540$	−3.03173	−0.130465
$541$	34.1605	1.46867	0.734337	−	0.678785i	$-0.237493\pi$
$541$	34.1605	1.46867	0.734337	+	0.678785i	$0.237493\pi$
$542$	−17.0826	−0.733760
$543$	0.403125	0.0172997
$544$	2.87312	0.123184
$545$	−19.9333	−0.853848
$546$	−1.73304	−0.0741673
$547$	−2.87159	−0.122780	−0.0613901	−	0.998114i	$-0.519553\pi$
$547$	−2.87159	−0.122780	−0.0613901	+	0.998114i	$0.519553\pi$
$548$	−11.3839	−0.486297
$549$	14.8216	0.632572
$550$	−1.00000	−0.0426401
$551$	−0.693838	−0.0295585
$552$	4.11555	0.175169
$553$	−44.6806	−1.90001
$554$	−16.1511	−0.686196
$555$	6.20274	0.263292
$556$	−10.8998	−0.462254
$557$	10.0224	0.424663	0.212332	−	0.977198i	$-0.431894\pi$
$557$	10.0224	0.424663	0.212332	+	0.977198i	$0.431894\pi$
$558$	−1.09731	−0.0464530
$559$	0.777655	0.0328913
$560$	4.20387	0.177646
$561$	1.52309	0.0643049
$562$	−31.0472	−1.30965
$563$	−17.5498	−0.739636	−0.369818	−	0.929104i	$-0.620580\pi$
$563$	−17.5498	−0.739636	−0.369818	+	0.929104i	$0.620580\pi$
$564$	7.12230	0.299903
$565$	−0.526577	−0.0221533
$566$	11.2979	0.474887
$567$	−27.5344	−1.15633
$568$	−0.857078	−0.0359622
$569$	15.0904	0.632622	0.316311	−	0.948656i	$-0.397556\pi$
$569$	15.0904	0.632622	0.316311	+	0.948656i	$0.397556\pi$
$570$	0.476226	0.0199469
$571$	39.9509	1.67190	0.835948	−	0.548809i	$-0.184919\pi$
$571$	39.9509	1.67190	0.835948	+	0.548809i	$0.184919\pi$
$572$	0.777655	0.0325154
$573$	−8.42728	−0.352055
$574$	12.5388	0.523360
$575$	−7.76347	−0.323759
$576$	−2.71898	−0.113291
$577$	−23.2545	−0.968099	−0.484050	−	0.875041i	$-0.660835\pi$
$577$	−23.2545	−0.968099	−0.484050	+	0.875041i	$0.660835\pi$
$578$	−8.74519	−0.363752
$579$	5.26338	0.218739
$580$	0.772355	0.0320703
$581$	−54.4202	−2.25773
$582$	−3.96164	−0.164215
$583$	−4.31450	−0.178689
$584$	−2.74543	−0.113607
$585$	−2.11443	−0.0874208
$586$	−3.38273	−0.139739
$587$	−28.4059	−1.17244	−0.586218	−	0.810153i	$-0.699384\pi$
$587$	−28.4059	−1.17244	−0.586218	+	0.810153i	$0.699384\pi$
$588$	−5.65771	−0.233320
$589$	0.362549	0.0149386
$590$	−7.25702	−0.298767
$591$	−3.79272	−0.156012
$592$	11.7007	0.480896
$593$	12.5327	0.514657	0.257329	−	0.966324i	$-0.417158\pi$
$593$	12.5327	0.514657	0.257329	+	0.966324i	$0.417158\pi$
$594$	−3.03173	−0.124393
$595$	12.0782	0.495159
$596$	21.4451	0.878425
$597$	−11.6234	−0.475715
$598$	6.03730	0.246884
$599$	21.6022	0.882644	0.441322	−	0.897349i	$-0.354510\pi$
$599$	21.6022	0.882644	0.441322	+	0.897349i	$0.354510\pi$
$600$	−0.530117	−0.0216419
$601$	−15.9463	−0.650464	−0.325232	−	0.945634i	$-0.605442\pi$
$601$	−15.9463	−0.650464	−0.325232	+	0.945634i	$0.605442\pi$
$602$	4.20387	0.171337
$603$	4.91251	0.200053
$604$	−6.83197	−0.277989
$605$	−1.00000	−0.0406558
$606$	−8.52627	−0.346356
$607$	33.2431	1.34930	0.674649	−	0.738139i	$-0.264295\pi$
$607$	33.2431	1.34930	0.674649	+	0.738139i	$0.264295\pi$
$608$	0.898341	0.0364326
$609$	−1.72123	−0.0697477
$610$	5.45118	0.220712
$611$	10.4481	0.422683
$612$	−7.81194	−0.315779
$613$	29.9919	1.21136	0.605680	−	0.795708i	$-0.292901\pi$
$613$	29.9919	1.21136	0.605680	+	0.795708i	$0.292901\pi$
$614$	−8.05888	−0.325230
$615$	−1.58117	−0.0637590
$616$	4.20387	0.169379
$617$	36.0682	1.45205	0.726025	−	0.687669i	$-0.241366\pi$
$617$	36.0682	1.45205	0.726025	+	0.687669i	$0.241366\pi$
$618$	−6.74340	−0.271259
$619$	−24.1634	−0.971207	−0.485604	−	0.874179i	$-0.661400\pi$
$619$	−24.1634	−0.971207	−0.485604	+	0.874179i	$0.661400\pi$
$620$	−0.403576	−0.0162080
$621$	−23.5367	−0.944496
$622$	4.03269	0.161696
$623$	10.8427	0.434405
$624$	0.412249	0.0165031
$625$	1.00000	0.0400000
$626$	−9.90253	−0.395785
$627$	0.476226	0.0190186
$628$	18.3879	0.733759
$629$	33.6175	1.34042
$630$	−11.4302	−0.455391
$631$	23.1907	0.923205	0.461603	−	0.887087i	$-0.347275\pi$
$631$	23.1907	0.923205	0.461603	+	0.887087i	$0.347275\pi$
$632$	10.6284	0.422777
$633$	1.14501	0.0455100
$634$	−3.45405	−0.137178
$635$	0.475972	0.0188884
$636$	−2.28719	−0.0906931
$637$	−8.29958	−0.328841
$638$	0.772355	0.0305778
$639$	2.33037	0.0921881
$640$	−1.00000	−0.0395285
$641$	14.4448	0.570535	0.285267	−	0.958448i	$-0.407918\pi$
$641$	14.4448	0.570535	0.285267	+	0.958448i	$0.407918\pi$
$642$	3.17657	0.125369
$643$	17.8388	0.703492	0.351746	−	0.936095i	$-0.385588\pi$
$643$	17.8388	0.703492	0.351746	+	0.936095i	$0.385588\pi$
$644$	32.6366	1.28606
$645$	−0.530117	−0.0208733
$646$	2.58104	0.101550
$647$	2.96125	0.116419	0.0582094	−	0.998304i	$-0.481461\pi$
$647$	2.96125	0.116419	0.0582094	+	0.998304i	$0.481461\pi$
$648$	6.54976	0.257299
$649$	−7.25702	−0.284863
$650$	−0.777655	−0.0305022
$651$	0.899388	0.0352498
$652$	3.65630	0.143192
$653$	−17.5556	−0.687002	−0.343501	−	0.939152i	$-0.611613\pi$
$653$	−17.5556	−0.687002	−0.343501	+	0.939152i	$0.611613\pi$
$654$	−10.5670	−0.413202
$655$	0.917399	0.0358457
$656$	−2.98268	−0.116454
$657$	7.46476	0.291228
$658$	56.4804	2.20184
$659$	35.8973	1.39836	0.699181	−	0.714945i	$-0.253548\pi$
$659$	35.8973	1.39836	0.699181	+	0.714945i	$0.253548\pi$
$660$	−0.530117	−0.0206348
$661$	−11.0879	−0.431269	−0.215635	−	0.976474i	$-0.569182\pi$
$661$	−11.0879	−0.431269	−0.215635	+	0.976474i	$0.569182\pi$
$662$	−12.7324	−0.494858
$663$	1.18444	0.0459998
$664$	12.9453	0.502373
$665$	3.77651	0.146447
$666$	−31.8139	−1.23276
$667$	5.99615	0.232172
$668$	−3.50087	−0.135453
$669$	−0.261219	−0.0100993
$670$	1.80675	0.0698009
$671$	5.45118	0.210441
$672$	2.22855	0.0859680
$673$	3.54049	0.136476	0.0682380	−	0.997669i	$-0.478262\pi$
$673$	3.54049	0.136476	0.0682380	+	0.997669i	$0.478262\pi$
$674$	−20.6853	−0.796768
$675$	3.03173	0.116691
$676$	−12.3953	−0.476740
$677$	24.0665	0.924951	0.462476	−	0.886632i	$-0.346961\pi$
$677$	24.0665	0.924951	0.462476	+	0.886632i	$0.346961\pi$
$678$	−0.279147	−0.0107206
$679$	−31.4161	−1.20564
$680$	−2.87312	−0.110179
$681$	1.21568	0.0465851
$682$	−0.403576	−0.0154537
$683$	−11.9770	−0.458286	−0.229143	−	0.973393i	$-0.573592\pi$
$683$	−11.9770	−0.458286	−0.229143	+	0.973393i	$0.573592\pi$
$684$	−2.44257	−0.0933939
$685$	11.3839	0.434958
$686$	−15.4390	−0.589463
$687$	−8.86959	−0.338396
$688$	−1.00000	−0.0381246
$689$	−3.35520	−0.127823
$690$	−4.11555	−0.156676
$691$	6.30216	0.239746	0.119873	−	0.992789i	$-0.461751\pi$
$691$	6.30216	0.239746	0.119873	+	0.992789i	$0.461751\pi$
$692$	−0.169891	−0.00645827
$693$	−11.4302	−0.434199
$694$	21.4809	0.815403
$695$	10.8998	0.413452
$696$	0.409439	0.0155197
$697$	−8.56960	−0.324597
$698$	11.3138	0.428233
$699$	6.25941	0.236753
$700$	−4.20387	−0.158892
$701$	28.4593	1.07489	0.537447	−	0.843297i	$-0.319389\pi$
$701$	28.4593	1.07489	0.537447	+	0.843297i	$0.319389\pi$
$702$	−2.35764	−0.0889834
$703$	10.5112	0.396438
$704$	−1.00000	−0.0376889
$705$	−7.12230	−0.268241
$706$	11.6504	0.438469
$707$	−67.6140	−2.54289
$708$	−3.84707	−0.144582
$709$	−25.1571	−0.944794	−0.472397	−	0.881386i	$-0.656611\pi$
$709$	−25.1571	−0.944794	−0.472397	+	0.881386i	$0.656611\pi$
$710$	0.857078	0.0321655
$711$	−28.8985	−1.08378
$712$	−2.57923	−0.0966606
$713$	−3.13315	−0.117337
$714$	6.40288	0.239622
$715$	−0.777655	−0.0290827
$716$	1.23979	0.0463331
$717$	−3.44645	−0.128710
$718$	−1.89076	−0.0705624
$719$	31.2069	1.16382	0.581910	−	0.813253i	$-0.302305\pi$
$719$	31.2069	1.16382	0.581910	+	0.813253i	$0.302305\pi$
$720$	2.71898	0.101330
$721$	−53.4758	−1.99154
$722$	−18.1930	−0.677073
$723$	−2.07981	−0.0773490
$724$	−0.760444	−0.0282617
$725$	−0.772355	−0.0286845
$726$	−0.530117	−0.0196745
$727$	−20.2289	−0.750250	−0.375125	−	0.926974i	$-0.622400\pi$
$727$	−20.2289	−0.750250	−0.375125	+	0.926974i	$0.622400\pi$
$728$	3.26917	0.121163
$729$	−12.9871	−0.481004
$730$	2.74543	0.101613
$731$	−2.87312	−0.106266
$732$	2.88977	0.106809
$733$	17.0895	0.631214	0.315607	−	0.948890i	$-0.397792\pi$
$733$	17.0895	0.631214	0.315607	+	0.948890i	$0.397792\pi$
$734$	−28.5057	−1.05217
$735$	5.65771	0.208688
$736$	−7.76347	−0.286165
$737$	1.80675	0.0665525
$738$	8.10984	0.298527
$739$	17.8370	0.656146	0.328073	−	0.944652i	$-0.393601\pi$
$739$	17.8370	0.656146	0.328073	+	0.944652i	$0.393601\pi$
$740$	−11.7007	−0.430126
$741$	0.370340	0.0136048
$742$	−18.1376	−0.665854
$743$	4.74256	0.173988	0.0869938	−	0.996209i	$-0.472274\pi$
$743$	4.74256	0.173988	0.0869938	+	0.996209i	$0.472274\pi$
$744$	−0.213943	−0.00784351
$745$	−21.4451	−0.785687
$746$	36.4135	1.33319
$747$	−35.1978	−1.28782
$748$	−2.87312	−0.105052
$749$	25.1905	0.920440
$750$	0.530117	0.0193571
$751$	9.95689	0.363332	0.181666	−	0.983360i	$-0.441851\pi$
$751$	9.95689	0.363332	0.181666	+	0.983360i	$0.441851\pi$
$752$	−13.4353	−0.489936
$753$	−7.54980	−0.275130
$754$	0.600626	0.0218735
$755$	6.83197	0.248641
$756$	−12.7450	−0.463531
$757$	37.4627	1.36160	0.680802	−	0.732467i	$-0.261631\pi$
$757$	37.4627	1.36160	0.680802	+	0.732467i	$0.261631\pi$
$758$	−13.6723	−0.496599
$759$	−4.11555	−0.149385
$760$	−0.898341	−0.0325863
$761$	3.82440	0.138634	0.0693172	−	0.997595i	$-0.477918\pi$
$761$	3.82440	0.138634	0.0693172	+	0.997595i	$0.477918\pi$
$762$	0.252321	0.00914063
$763$	−83.7971	−3.03366
$764$	15.8970	0.575134
$765$	7.81194	0.282441
$766$	6.58673	0.237988
$767$	−5.64346	−0.203773
$768$	−0.530117	−0.0191290
$769$	52.2398	1.88382	0.941908	−	0.335872i	$-0.109031\pi$
$769$	52.2398	1.88382	0.941908	+	0.335872i	$0.109031\pi$
$770$	−4.20387	−0.151497
$771$	11.4132	0.411037
$772$	−9.92872	−0.357342
$773$	−19.0154	−0.683936	−0.341968	−	0.939712i	$-0.611093\pi$
$773$	−19.0154	−0.683936	−0.341968	+	0.939712i	$0.611093\pi$
$774$	2.71898	0.0977316
$775$	0.403576	0.0144969
$776$	7.47313	0.268270
$777$	26.0755	0.935455
$778$	20.5761	0.737690
$779$	−2.67947	−0.0960018
$780$	−0.412249	−0.0147609
$781$	0.857078	0.0306686
$782$	−22.3054	−0.797638
$783$	−2.34157	−0.0836809
$784$	10.6726	0.381163
$785$	−18.3879	−0.656294
$786$	0.486329	0.0173468
$787$	30.6964	1.09421	0.547105	−	0.837064i	$-0.315730\pi$
$787$	30.6964	1.09421	0.547105	+	0.837064i	$0.315730\pi$
$788$	7.15450	0.254868
$789$	−1.06922	−0.0380653
$790$	−10.6284	−0.378143
$791$	−2.21366	−0.0787088
$792$	2.71898	0.0966146
$793$	4.23914	0.150536
$794$	−11.3120	−0.401448
$795$	2.28719	0.0811184
$796$	21.9261	0.777151
$797$	7.29739	0.258487	0.129243	−	0.991613i	$-0.458745\pi$
$797$	7.29739	0.258487	0.129243	+	0.991613i	$0.458745\pi$
$798$	2.00200	0.0708699
$799$	−38.6013	−1.36562
$800$	1.00000	0.0353553
$801$	7.01285	0.247787
$802$	26.2385	0.926512
$803$	2.74543	0.0968841
$804$	0.957790	0.0337786
$805$	−32.6366	−1.15029
$806$	−0.313843	−0.0110546
$807$	7.17735	0.252655
$808$	16.0837	0.565824
$809$	21.0913	0.741531	0.370765	−	0.928727i	$-0.379095\pi$
$809$	21.0913	0.741531	0.370765	+	0.928727i	$0.379095\pi$
$810$	−6.54976	−0.230135
$811$	−28.7356	−1.00904	−0.504522	−	0.863399i	$-0.668331\pi$
$811$	−28.7356	−1.00904	−0.504522	+	0.863399i	$0.668331\pi$
$812$	3.24688	0.113943
$813$	9.05577	0.317600
$814$	−11.7007	−0.410109
$815$	−3.65630	−0.128075
$816$	−1.52309	−0.0533188
$817$	−0.898341	−0.0314290
$818$	27.9533	0.977365
$819$	−8.88878	−0.310599
$820$	2.98268	0.104160
$821$	−51.4859	−1.79687	−0.898434	−	0.439108i	$-0.855295\pi$
$821$	−51.4859	−1.79687	−0.898434	+	0.439108i	$0.855295\pi$
$822$	6.03482	0.210488
$823$	15.0384	0.524204	0.262102	−	0.965040i	$-0.415584\pi$
$823$	15.0384	0.524204	0.262102	+	0.965040i	$0.415584\pi$
$824$	12.7206	0.443143
$825$	0.530117	0.0184563
$826$	−30.5076	−1.06149
$827$	16.2427	0.564815	0.282408	−	0.959294i	$-0.408867\pi$
$827$	16.2427	0.564815	0.282408	+	0.959294i	$0.408867\pi$
$828$	21.1087	0.733577
$829$	−31.9983	−1.11135	−0.555674	−	0.831401i	$-0.687540\pi$
$829$	−31.9983	−1.11135	−0.555674	+	0.831401i	$0.687540\pi$
$830$	−12.9453	−0.449336
$831$	8.56200	0.297013
$832$	−0.777655	−0.0269603
$833$	30.6635	1.06243
$834$	5.77816	0.200081
$835$	3.50087	0.121153
$836$	−0.898341	−0.0310698
$837$	1.22353	0.0422915
$838$	4.63297	0.160043
$839$	−2.85256	−0.0984811	−0.0492406	−	0.998787i	$-0.515680\pi$
$839$	−2.85256	−0.0984811	−0.0492406	+	0.998787i	$0.515680\pi$
$840$	−2.22855	−0.0768922
$841$	−28.4035	−0.979430
$842$	16.0041	0.551537
$843$	16.4586	0.566865
$844$	−2.15992	−0.0743474
$845$	12.3953	0.426410
$846$	36.5303	1.25594
$847$	−4.20387	−0.144447
$848$	4.31450	0.148161
$849$	−5.98922	−0.205550
$850$	2.87312	0.0985471
$851$	−90.8379	−3.11388
$852$	0.454352	0.0155658
$853$	−36.4149	−1.24682	−0.623412	−	0.781894i	$-0.714254\pi$
$853$	−36.4149	−1.24682	−0.623412	+	0.781894i	$0.714254\pi$
$854$	22.9161	0.784172
$855$	2.44257	0.0835341
$856$	−5.99220	−0.204809
$857$	−43.1171	−1.47285	−0.736425	−	0.676519i	$-0.763488\pi$
$857$	−43.1171	−1.47285	−0.736425	+	0.676519i	$0.763488\pi$
$858$	−0.412249	−0.0140739
$859$	55.4004	1.89024	0.945119	−	0.326727i	$-0.105946\pi$
$859$	55.4004	1.89024	0.945119	+	0.326727i	$0.105946\pi$
$860$	1.00000	0.0340997
$861$	−6.64704	−0.226531
$862$	−28.6674	−0.976414
$863$	12.1683	0.414215	0.207108	−	0.978318i	$-0.433595\pi$
$863$	12.1683	0.414215	0.207108	+	0.978318i	$0.433595\pi$
$864$	3.03173	0.103141
$865$	0.169891	0.00577645
$866$	3.69875	0.125689
$867$	4.63598	0.157446
$868$	−1.69658	−0.0575858
$869$	−10.6284	−0.360545
$870$	−0.409439	−0.0138813
$871$	1.40503	0.0476076
$872$	19.9333	0.675026
$873$	−20.3193	−0.687703
$874$	−6.97424	−0.235907
$875$	4.20387	0.142117
$876$	1.45540	0.0491734
$877$	15.9386	0.538207	0.269104	−	0.963111i	$-0.413273\pi$
$877$	15.9386	0.538207	0.269104	+	0.963111i	$0.413273\pi$
$878$	17.9788	0.606755
$879$	1.79324	0.0604845
$880$	1.00000	0.0337100
$881$	26.0567	0.877872	0.438936	−	0.898518i	$-0.355355\pi$
$881$	26.0567	0.877872	0.438936	+	0.898518i	$0.355355\pi$
$882$	−29.0184	−0.977102
$883$	3.66814	0.123443	0.0617213	−	0.998093i	$-0.480341\pi$
$883$	3.66814	0.123443	0.0617213	+	0.998093i	$0.480341\pi$
$884$	−2.23430	−0.0751475
$885$	3.84707	0.129318
$886$	−2.38221	−0.0800318
$887$	15.6634	0.525925	0.262963	−	0.964806i	$-0.415300\pi$
$887$	15.6634	0.525925	0.262963	+	0.964806i	$0.415300\pi$
$888$	−6.20274	−0.208150
$889$	2.00093	0.0671090
$890$	2.57923	0.0864558
$891$	−6.54976	−0.219425
$892$	0.492756	0.0164987
$893$	−12.0695	−0.403891
$894$	−11.3684	−0.380216
$895$	−1.23979	−0.0414416
$896$	−4.20387	−0.140442
$897$	−3.20048	−0.106861
$898$	24.0347	0.802048
$899$	−0.311704	−0.0103959
$900$	−2.71898	−0.0906325
$901$	12.3961	0.412973
$902$	2.98268	0.0993124
$903$	−2.22855	−0.0741614
$904$	0.526577	0.0175137
$905$	0.760444	0.0252780
$906$	3.62175	0.120324
$907$	−5.01320	−0.166461	−0.0832303	−	0.996530i	$-0.526524\pi$
$907$	−5.01320	−0.166461	−0.0832303	+	0.996530i	$0.526524\pi$
$908$	−2.29324	−0.0761037
$909$	−43.7313	−1.45048
$910$	−3.26917	−0.108372
$911$	−43.9744	−1.45694	−0.728468	−	0.685080i	$-0.759767\pi$
$911$	−43.9744	−1.45694	−0.728468	+	0.685080i	$0.759767\pi$
$912$	−0.476226	−0.0157694
$913$	−12.9453	−0.428425
$914$	−22.7775	−0.753413
$915$	−2.88977	−0.0955327
$916$	16.7314	0.552820
$917$	3.85663	0.127357
$918$	8.71051	0.287490
$919$	−54.3302	−1.79219	−0.896095	−	0.443863i	$-0.853608\pi$
$919$	−54.3302	−1.79219	−0.896095	+	0.443863i	$0.853608\pi$
$920$	7.76347	0.255954
$921$	4.27215	0.140772
$922$	24.6623	0.812208
$923$	0.666511	0.0219385
$924$	−2.22855	−0.0733138
$925$	11.7007	0.384716
$926$	−32.9021	−1.08123
$927$	−34.5870	−1.13599
$928$	−0.772355	−0.0253538
$929$	39.5302	1.29694	0.648471	−	0.761239i	$-0.275409\pi$
$929$	39.5302	1.29694	0.648471	+	0.761239i	$0.275409\pi$
$930$	0.213943	0.00701545
$931$	9.58760	0.314221
$932$	−11.8076	−0.386771
$933$	−2.13780	−0.0699884
$934$	−35.1298	−1.14948
$935$	2.87312	0.0939610
$936$	2.11443	0.0691122
$937$	−26.2820	−0.858595	−0.429298	−	0.903163i	$-0.641239\pi$
$937$	−26.2820	−0.858595	−0.429298	+	0.903163i	$0.641239\pi$
$938$	7.59535	0.247997
$939$	5.24950	0.171311
$940$	13.4353	0.438212
$941$	−38.1061	−1.24222	−0.621111	−	0.783722i	$-0.713319\pi$
$941$	−38.1061	−1.24222	−0.621111	+	0.783722i	$0.713319\pi$
$942$	−9.74777	−0.317599
$943$	23.1559	0.754061
$944$	7.25702	0.236196
$945$	12.7450	0.414595
$946$	1.00000	0.0325128
$947$	50.9022	1.65410	0.827050	−	0.562129i	$-0.190018\pi$
$947$	50.9022	1.65410	0.827050	+	0.562129i	$0.190018\pi$
$948$	−5.63432	−0.182994
$949$	2.13500	0.0693050
$950$	0.898341	0.0291460
$951$	1.83105	0.0593760
$952$	−12.0782	−0.391458
$953$	−4.81248	−0.155892	−0.0779458	−	0.996958i	$-0.524836\pi$
$953$	−4.81248	−0.155892	−0.0779458	+	0.996958i	$0.524836\pi$
$954$	−11.7310	−0.379806
$955$	−15.8970	−0.514415
$956$	6.50130	0.210267
$957$	−0.409439	−0.0132353
$958$	0.262120	0.00846870
$959$	47.8566	1.54537
$960$	0.530117	0.0171095
$961$	−30.8371	−0.994746
$962$	−9.09911	−0.293367
$963$	16.2927	0.525023
$964$	3.92330	0.126361
$965$	9.92872	0.319617
$966$	−17.3012	−0.556658
$967$	−33.0779	−1.06371	−0.531857	−	0.846834i	$-0.678506\pi$
$967$	−33.0779	−1.06371	−0.531857	+	0.846834i	$0.678506\pi$
$968$	1.00000	0.0321412
$969$	−1.36825	−0.0439547
$970$	−7.47313	−0.239948
$971$	−12.3131	−0.395146	−0.197573	−	0.980288i	$-0.563306\pi$
$971$	−12.3131	−0.395146	−0.197573	+	0.980288i	$0.563306\pi$
$972$	−12.5673	−0.403097
$973$	45.8213	1.46896
$974$	19.7458	0.632695
$975$	0.412249	0.0132025
$976$	−5.45118	−0.174488
$977$	17.8560	0.571265	0.285633	−	0.958339i	$-0.407796\pi$
$977$	17.8560	0.571265	0.285633	+	0.958339i	$0.407796\pi$
$978$	−1.93827	−0.0619790
$979$	2.57923	0.0824324
$980$	−10.6726	−0.340922
$981$	−54.1981	−1.73041
$982$	−27.1090	−0.865084
$983$	−50.5273	−1.61157	−0.805785	−	0.592208i	$-0.798256\pi$
$983$	−50.5273	−1.61157	−0.805785	+	0.592208i	$0.798256\pi$
$984$	1.58117	0.0504059
$985$	−7.15450	−0.227961
$986$	−2.21907	−0.0706695
$987$	−29.9413	−0.953041
$988$	−0.698600	−0.0222254
$989$	7.76347	0.246864
$990$	−2.71898	−0.0864147
$991$	61.1956	1.94394	0.971971	−	0.235102i	$-0.0755425\pi$
$991$	61.1956	1.94394	0.971971	+	0.235102i	$0.0755425\pi$
$992$	0.403576	0.0128135
$993$	6.74965	0.214194
$994$	3.60305	0.114282
$995$	−21.9261	−0.695105
$996$	−6.86250	−0.217447
$997$	34.6998	1.09895	0.549476	−	0.835509i	$-0.314827\pi$
$997$	34.6998	1.09895	0.549476	+	0.835509i	$0.314827\pi$
$998$	−1.95916	−0.0620161
$999$	35.4733	1.12233

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.ba.1.5	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.ba.1.5	✓	10	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.530117 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.530117 q^{6} -4.20387 q^{7} +1.00000 q^{8} -2.71898 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.530117 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.530117 q^{6} -4.20387 q^{7} +1.00000 q^{8} -2.71898 q^{9} -1.00000 q^{10} -1.00000 q^{11} -0.530117 q^{12} -0.777655 q^{13} -4.20387 q^{14} +0.530117 q^{15} +1.00000 q^{16} +2.87312 q^{17} -2.71898 q^{18} +0.898341 q^{19} -1.00000 q^{20} +2.22855 q^{21} -1.00000 q^{22} -7.76347 q^{23} -0.530117 q^{24} +1.00000 q^{25} -0.777655 q^{26} +3.03173 q^{27} -4.20387 q^{28} -0.772355 q^{29} +0.530117 q^{30} +0.403576 q^{31} +1.00000 q^{32} +0.530117 q^{33} +2.87312 q^{34} +4.20387 q^{35} -2.71898 q^{36} +11.7007 q^{37} +0.898341 q^{38} +0.412249 q^{39} -1.00000 q^{40} -2.98268 q^{41} +2.22855 q^{42} -1.00000 q^{43} -1.00000 q^{44} +2.71898 q^{45} -7.76347 q^{46} -13.4353 q^{47} -0.530117 q^{48} +10.6726 q^{49} +1.00000 q^{50} -1.52309 q^{51} -0.777655 q^{52} +4.31450 q^{53} +3.03173 q^{54} +1.00000 q^{55} -4.20387 q^{56} -0.476226 q^{57} -0.772355 q^{58} +7.25702 q^{59} +0.530117 q^{60} -5.45118 q^{61} +0.403576 q^{62} +11.4302 q^{63} +1.00000 q^{64} +0.777655 q^{65} +0.530117 q^{66} -1.80675 q^{67} +2.87312 q^{68} +4.11555 q^{69} +4.20387 q^{70} -0.857078 q^{71} -2.71898 q^{72} -2.74543 q^{73} +11.7007 q^{74} -0.530117 q^{75} +0.898341 q^{76} +4.20387 q^{77} +0.412249 q^{78} +10.6284 q^{79} -1.00000 q^{80} +6.54976 q^{81} -2.98268 q^{82} +12.9453 q^{83} +2.22855 q^{84} -2.87312 q^{85} -1.00000 q^{86} +0.409439 q^{87} -1.00000 q^{88} -2.57923 q^{89} +2.71898 q^{90} +3.26917 q^{91} -7.76347 q^{92} -0.213943 q^{93} -13.4353 q^{94} -0.898341 q^{95} -0.530117 q^{96} +7.47313 q^{97} +10.6726 q^{98} +2.71898 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} - q^{3} + 10 q^{4} - 10 q^{5} - q^{6} + 3 q^{7} + 10 q^{8} + 13 q^{9}+O(q^{10}) \) 10 * q + 10 * q^2 - q^3 + 10 * q^4 - 10 * q^5 - q^6 + 3 * q^7 + 10 * q^8 + 13 * q^9	\( 10 q + 10 q^{2} - q^{3} + 10 q^{4} - 10 q^{5} - q^{6} + 3 q^{7} + 10 q^{8} + 13 q^{9} - 10 q^{10} - 10 q^{11} - q^{12} + 6 q^{13} + 3 q^{14} + q^{15} + 10 q^{16} + 3 q^{17} + 13 q^{18} + 3 q^{19} - 10 q^{20} + 11 q^{21} - 10 q^{22} - 6 q^{23} - q^{24} + 10 q^{25} + 6 q^{26} + 8 q^{27} + 3 q^{28} + 14 q^{29} + q^{30} + 6 q^{31} + 10 q^{32} + q^{33} + 3 q^{34} - 3 q^{35} + 13 q^{36} + 10 q^{37} + 3 q^{38} + 24 q^{39} - 10 q^{40} + 26 q^{41} + 11 q^{42} - 10 q^{43} - 10 q^{44} - 13 q^{45} - 6 q^{46} + 3 q^{47} - q^{48} + 33 q^{49} + 10 q^{50} + 18 q^{51} + 6 q^{52} - 9 q^{53} + 8 q^{54} + 10 q^{55} + 3 q^{56} + 18 q^{57} + 14 q^{58} - 9 q^{59} + q^{60} + 22 q^{61} + 6 q^{62} - q^{63} + 10 q^{64} - 6 q^{65} + q^{66} + 18 q^{67} + 3 q^{68} + 6 q^{69} - 3 q^{70} + 27 q^{71} + 13 q^{72} + 28 q^{73} + 10 q^{74} - q^{75} + 3 q^{76} - 3 q^{77} + 24 q^{78} + 3 q^{79} - 10 q^{80} + 30 q^{81} + 26 q^{82} - 11 q^{83} + 11 q^{84} - 3 q^{85} - 10 q^{86} + 30 q^{87} - 10 q^{88} + 16 q^{89} - 13 q^{90} + 32 q^{91} - 6 q^{92} + 52 q^{93} + 3 q^{94} - 3 q^{95} - q^{96} + 22 q^{97} + 33 q^{98} - 13 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 - q^3 + 10 * q^4 - 10 * q^5 - q^6 + 3 * q^7 + 10 * q^8 + 13 * q^9 - 10 * q^10 - 10 * q^11 - q^12 + 6 * q^13 + 3 * q^14 + q^15 + 10 * q^16 + 3 * q^17 + 13 * q^18 + 3 * q^19 - 10 * q^20 + 11 * q^21 - 10 * q^22 - 6 * q^23 - q^24 + 10 * q^25 + 6 * q^26 + 8 * q^27 + 3 * q^28 + 14 * q^29 + q^30 + 6 * q^31 + 10 * q^32 + q^33 + 3 * q^34 - 3 * q^35 + 13 * q^36 + 10 * q^37 + 3 * q^38 + 24 * q^39 - 10 * q^40 + 26 * q^41 + 11 * q^42 - 10 * q^43 - 10 * q^44 - 13 * q^45 - 6 * q^46 + 3 * q^47 - q^48 + 33 * q^49 + 10 * q^50 + 18 * q^51 + 6 * q^52 - 9 * q^53 + 8 * q^54 + 10 * q^55 + 3 * q^56 + 18 * q^57 + 14 * q^58 - 9 * q^59 + q^60 + 22 * q^61 + 6 * q^62 - q^63 + 10 * q^64 - 6 * q^65 + q^66 + 18 * q^67 + 3 * q^68 + 6 * q^69 - 3 * q^70 + 27 * q^71 + 13 * q^72 + 28 * q^73 + 10 * q^74 - q^75 + 3 * q^76 - 3 * q^77 + 24 * q^78 + 3 * q^79 - 10 * q^80 + 30 * q^81 + 26 * q^82 - 11 * q^83 + 11 * q^84 - 3 * q^85 - 10 * q^86 + 30 * q^87 - 10 * q^88 + 16 * q^89 - 13 * q^90 + 32 * q^91 - 6 * q^92 + 52 * q^93 + 3 * q^94 - 3 * q^95 - q^96 + 22 * q^97 + 33 * q^98 - 13 * q^99

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