LMFDB - Embedded newform 4730.2.a.bd.1.11

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			1.11
Root			$3.36929$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +3.36929 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.36929 q^{6} +3.52337 q^{7} +1.00000 q^{8} +8.35210 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +3.36929 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.36929 q^{6} +3.52337 q^{7} +1.00000 q^{8} +8.35210 q^{9} +1.00000 q^{10} +1.00000 q^{11} +3.36929 q^{12} -2.62672 q^{13} +3.52337 q^{14} +3.36929 q^{15} +1.00000 q^{16} -1.78745 q^{17} +8.35210 q^{18} -6.72497 q^{19} +1.00000 q^{20} +11.8713 q^{21} +1.00000 q^{22} -0.519567 q^{23} +3.36929 q^{24} +1.00000 q^{25} -2.62672 q^{26} +18.0328 q^{27} +3.52337 q^{28} +6.14594 q^{29} +3.36929 q^{30} -7.71059 q^{31} +1.00000 q^{32} +3.36929 q^{33} -1.78745 q^{34} +3.52337 q^{35} +8.35210 q^{36} -0.489223 q^{37} -6.72497 q^{38} -8.85018 q^{39} +1.00000 q^{40} -3.44928 q^{41} +11.8713 q^{42} -1.00000 q^{43} +1.00000 q^{44} +8.35210 q^{45} -0.519567 q^{46} -12.4364 q^{47} +3.36929 q^{48} +5.41417 q^{49} +1.00000 q^{50} -6.02242 q^{51} -2.62672 q^{52} -8.49059 q^{53} +18.0328 q^{54} +1.00000 q^{55} +3.52337 q^{56} -22.6584 q^{57} +6.14594 q^{58} -12.5689 q^{59} +3.36929 q^{60} -1.20105 q^{61} -7.71059 q^{62} +29.4276 q^{63} +1.00000 q^{64} -2.62672 q^{65} +3.36929 q^{66} -9.44187 q^{67} -1.78745 q^{68} -1.75057 q^{69} +3.52337 q^{70} +14.5533 q^{71} +8.35210 q^{72} +7.18081 q^{73} -0.489223 q^{74} +3.36929 q^{75} -6.72497 q^{76} +3.52337 q^{77} -8.85018 q^{78} -8.37633 q^{79} +1.00000 q^{80} +35.7013 q^{81} -3.44928 q^{82} -6.71066 q^{83} +11.8713 q^{84} -1.78745 q^{85} -1.00000 q^{86} +20.7074 q^{87} +1.00000 q^{88} +7.19424 q^{89} +8.35210 q^{90} -9.25492 q^{91} -0.519567 q^{92} -25.9792 q^{93} -12.4364 q^{94} -6.72497 q^{95} +3.36929 q^{96} +4.47632 q^{97} +5.41417 q^{98} +8.35210 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	3.36929	1.94526	0.972630	−	0.232361i	$-0.0746451\pi$
$3$	3.36929	1.94526	0.972630	+	0.232361i	$0.0746451\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	3.36929	1.37551
$7$	3.52337	1.33171	0.665855	−	0.746081i	$-0.268067\pi$
$7$	3.52337	1.33171	0.665855	+	0.746081i	$0.268067\pi$
$8$	1.00000	0.353553
$9$	8.35210	2.78403
$10$	1.00000	0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	3.36929	0.972630
$13$	−2.62672	−0.728521	−0.364261	−	0.931297i	$-0.618678\pi$
$13$	−2.62672	−0.728521	−0.364261	+	0.931297i	$0.618678\pi$
$14$	3.52337	0.941661
$15$	3.36929	0.869946
$16$	1.00000	0.250000
$17$	−1.78745	−0.433520	−0.216760	−	0.976225i	$-0.569549\pi$
$17$	−1.78745	−0.433520	−0.216760	+	0.976225i	$0.569549\pi$
$18$	8.35210	1.96861
$19$	−6.72497	−1.54281	−0.771407	−	0.636342i	$-0.780447\pi$
$19$	−6.72497	−1.54281	−0.771407	+	0.636342i	$0.780447\pi$
$20$	1.00000	0.223607
$21$	11.8713	2.59052
$22$	1.00000	0.213201
$23$	−0.519567	−0.108337	−0.0541687	−	0.998532i	$-0.517251\pi$
$23$	−0.519567	−0.108337	−0.0541687	+	0.998532i	$0.517251\pi$
$24$	3.36929	0.687753
$25$	1.00000	0.200000
$26$	−2.62672	−0.515142
$27$	18.0328	3.47041
$28$	3.52337	0.665855
$29$	6.14594	1.14127	0.570636	−	0.821203i	$-0.306697\pi$
$29$	6.14594	1.14127	0.570636	+	0.821203i	$0.306697\pi$
$30$	3.36929	0.615145
$31$	−7.71059	−1.38486	−0.692431	−	0.721484i	$-0.743460\pi$
$31$	−7.71059	−1.38486	−0.692431	+	0.721484i	$0.743460\pi$
$32$	1.00000	0.176777
$33$	3.36929	0.586518
$34$	−1.78745	−0.306545
$35$	3.52337	0.595559
$36$	8.35210	1.39202
$37$	−0.489223	−0.0804277	−0.0402138	−	0.999191i	$-0.512804\pi$
$37$	−0.489223	−0.0804277	−0.0402138	+	0.999191i	$0.512804\pi$
$38$	−6.72497	−1.09093
$39$	−8.85018	−1.41716
$40$	1.00000	0.158114
$41$	−3.44928	−0.538687	−0.269343	−	0.963044i	$-0.586807\pi$
$41$	−3.44928	−0.538687	−0.269343	+	0.963044i	$0.586807\pi$
$42$	11.8713	1.83178
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	1.00000	0.150756
$45$	8.35210	1.24506
$46$	−0.519567	−0.0766060
$47$	−12.4364	−1.81403	−0.907015	−	0.421099i	$-0.861644\pi$
$47$	−12.4364	−1.81403	−0.907015	+	0.421099i	$0.861644\pi$
$48$	3.36929	0.486315
$49$	5.41417	0.773453
$50$	1.00000	0.141421
$51$	−6.02242	−0.843308
$52$	−2.62672	−0.364261
$53$	−8.49059	−1.16627	−0.583136	−	0.812374i	$-0.698175\pi$
$53$	−8.49059	−1.16627	−0.583136	+	0.812374i	$0.698175\pi$
$54$	18.0328	2.45395
$55$	1.00000	0.134840
$56$	3.52337	0.470831
$57$	−22.6584	−3.00117
$58$	6.14594	0.807001
$59$	−12.5689	−1.63633	−0.818166	−	0.574983i	$-0.805009\pi$
$59$	−12.5689	−1.63633	−0.818166	+	0.574983i	$0.805009\pi$
$60$	3.36929	0.434973
$61$	−1.20105	−0.153778	−0.0768890	−	0.997040i	$-0.524499\pi$
$61$	−1.20105	−0.153778	−0.0768890	+	0.997040i	$0.524499\pi$
$62$	−7.71059	−0.979246
$63$	29.4276	3.70753
$64$	1.00000	0.125000
$65$	−2.62672	−0.325805
$66$	3.36929	0.414731
$67$	−9.44187	−1.15351	−0.576754	−	0.816918i	$-0.695681\pi$
$67$	−9.44187	−1.15351	−0.576754	+	0.816918i	$0.695681\pi$
$68$	−1.78745	−0.216760
$69$	−1.75057	−0.210744
$70$	3.52337	0.421124
$71$	14.5533	1.72716	0.863579	−	0.504213i	$-0.168217\pi$
$71$	14.5533	1.72716	0.863579	+	0.504213i	$0.168217\pi$
$72$	8.35210	0.984304
$73$	7.18081	0.840451	0.420225	−	0.907420i	$-0.361951\pi$
$73$	7.18081	0.840451	0.420225	+	0.907420i	$0.361951\pi$
$74$	−0.489223	−0.0568710
$75$	3.36929	0.389052
$76$	−6.72497	−0.771407
$77$	3.52337	0.401526
$78$	−8.85018	−1.00209
$79$	−8.37633	−0.942411	−0.471205	−	0.882024i	$-0.656181\pi$
$79$	−8.37633	−0.942411	−0.471205	+	0.882024i	$0.656181\pi$
$80$	1.00000	0.111803
$81$	35.7013	3.96681
$82$	−3.44928	−0.380909
$83$	−6.71066	−0.736591	−0.368295	−	0.929709i	$-0.620058\pi$
$83$	−6.71066	−0.736591	−0.368295	+	0.929709i	$0.620058\pi$
$84$	11.8713	1.29526
$85$	−1.78745	−0.193876
$86$	−1.00000	−0.107833
$87$	20.7074	2.22007
$88$	1.00000	0.106600
$89$	7.19424	0.762588	0.381294	−	0.924454i	$-0.375479\pi$
$89$	7.19424	0.762588	0.381294	+	0.924454i	$0.375479\pi$
$90$	8.35210	0.880389
$91$	−9.25492	−0.970179
$92$	−0.519567	−0.0541687
$93$	−25.9792	−2.69392
$94$	−12.4364	−1.28271
$95$	−6.72497	−0.689968
$96$	3.36929	0.343876
$97$	4.47632	0.454501	0.227251	−	0.973836i	$-0.427026\pi$
$97$	4.47632	0.454501	0.227251	+	0.973836i	$0.427026\pi$
$98$	5.41417	0.546914
$99$	8.35210	0.839418
$100$	1.00000	0.100000
$101$	2.44947	0.243731	0.121866	−	0.992547i	$-0.461112\pi$
$101$	2.44947	0.243731	0.121866	+	0.992547i	$0.461112\pi$
$102$	−6.02242	−0.596309
$103$	16.5881	1.63448	0.817238	−	0.576300i	$-0.195504\pi$
$103$	16.5881	1.63448	0.817238	+	0.576300i	$0.195504\pi$
$104$	−2.62672	−0.257571
$105$	11.8713	1.15852
$106$	−8.49059	−0.824679
$107$	−1.53018	−0.147928	−0.0739642	−	0.997261i	$-0.523565\pi$
$107$	−1.53018	−0.147928	−0.0739642	+	0.997261i	$0.523565\pi$
$108$	18.0328	1.73520
$109$	10.9169	1.04565	0.522825	−	0.852440i	$-0.324878\pi$
$109$	10.9169	1.04565	0.522825	+	0.852440i	$0.324878\pi$
$110$	1.00000	0.0953463
$111$	−1.64833	−0.156453
$112$	3.52337	0.332928
$113$	11.7993	1.10998	0.554992	−	0.831856i	$-0.312721\pi$
$113$	11.7993	1.10998	0.554992	+	0.831856i	$0.312721\pi$
$114$	−22.6584	−2.12215
$115$	−0.519567	−0.0484499
$116$	6.14594	0.570636
$117$	−21.9386	−2.02823
$118$	−12.5689	−1.15706
$119$	−6.29785	−0.577323
$120$	3.36929	0.307572
$121$	1.00000	0.0909091
$122$	−1.20105	−0.108738
$123$	−11.6216	−1.04789
$124$	−7.71059	−0.692431
$125$	1.00000	0.0894427
$126$	29.4276	2.62162
$127$	−11.4178	−1.01317	−0.506584	−	0.862191i	$-0.669092\pi$
$127$	−11.4178	−1.01317	−0.506584	+	0.862191i	$0.669092\pi$
$128$	1.00000	0.0883883
$129$	−3.36929	−0.296649
$130$	−2.62672	−0.230379
$131$	−14.8288	−1.29560	−0.647798	−	0.761812i	$-0.724310\pi$
$131$	−14.8288	−1.29560	−0.647798	+	0.761812i	$0.724310\pi$
$132$	3.36929	0.293259
$133$	−23.6946	−2.05458
$134$	−9.44187	−0.815653
$135$	18.0328	1.55201
$136$	−1.78745	−0.153272
$137$	21.0466	1.79813	0.899067	−	0.437811i	$-0.144246\pi$
$137$	21.0466	1.79813	0.899067	+	0.437811i	$0.144246\pi$
$138$	−1.75057	−0.149019
$139$	−14.3023	−1.21310	−0.606552	−	0.795044i	$-0.707448\pi$
$139$	−14.3023	−1.21310	−0.606552	+	0.795044i	$0.707448\pi$
$140$	3.52337	0.297779
$141$	−41.9017	−3.52876
$142$	14.5533	1.22129
$143$	−2.62672	−0.219657
$144$	8.35210	0.696008
$145$	6.14594	0.510392
$146$	7.18081	0.594288
$147$	18.2419	1.50457
$148$	−0.489223	−0.0402138
$149$	2.73710	0.224232	0.112116	−	0.993695i	$-0.464237\pi$
$149$	2.73710	0.224232	0.112116	+	0.993695i	$0.464237\pi$
$150$	3.36929	0.275101
$151$	−8.38168	−0.682092	−0.341046	−	0.940047i	$-0.610781\pi$
$151$	−8.38168	−0.682092	−0.341046	+	0.940047i	$0.610781\pi$
$152$	−6.72497	−0.545467
$153$	−14.9289	−1.20693
$154$	3.52337	0.283922
$155$	−7.71059	−0.619329
$156$	−8.85018	−0.708581
$157$	18.2881	1.45955	0.729775	−	0.683687i	$-0.239625\pi$
$157$	18.2881	1.45955	0.729775	+	0.683687i	$0.239625\pi$
$158$	−8.37633	−0.666385
$159$	−28.6072	−2.26870
$160$	1.00000	0.0790569
$161$	−1.83063	−0.144274
$162$	35.7013	2.80496
$163$	20.5678	1.61100	0.805498	−	0.592599i	$-0.201898\pi$
$163$	20.5678	1.61100	0.805498	+	0.592599i	$0.201898\pi$
$164$	−3.44928	−0.269343
$165$	3.36929	0.262299
$166$	−6.71066	−0.520848
$167$	12.1259	0.938334	0.469167	−	0.883109i	$-0.344554\pi$
$167$	12.1259	0.938334	0.469167	+	0.883109i	$0.344554\pi$
$168$	11.8713	0.915888
$169$	−6.10034	−0.469257
$170$	−1.78745	−0.137091
$171$	−56.1677	−4.29525
$172$	−1.00000	−0.0762493
$173$	−8.75459	−0.665600	−0.332800	−	0.942998i	$-0.607993\pi$
$173$	−8.75459	−0.665600	−0.332800	+	0.942998i	$0.607993\pi$
$174$	20.7074	1.56983
$175$	3.52337	0.266342
$176$	1.00000	0.0753778
$177$	−42.3482	−3.18309
$178$	7.19424	0.539231
$179$	5.07751	0.379511	0.189756	−	0.981831i	$-0.439230\pi$
$179$	5.07751	0.379511	0.189756	+	0.981831i	$0.439230\pi$
$180$	8.35210	0.622529
$181$	0.976028	0.0725476	0.0362738	−	0.999342i	$-0.488451\pi$
$181$	0.976028	0.0725476	0.0362738	+	0.999342i	$0.488451\pi$
$182$	−9.25492	−0.686020
$183$	−4.04667	−0.299138
$184$	−0.519567	−0.0383030
$185$	−0.489223	−0.0359684
$186$	−25.9792	−1.90489
$187$	−1.78745	−0.130711
$188$	−12.4364	−0.907015
$189$	63.5362	4.62158
$190$	−6.72497	−0.487881
$191$	8.46474	0.612487	0.306244	−	0.951953i	$-0.400928\pi$
$191$	8.46474	0.612487	0.306244	+	0.951953i	$0.400928\pi$
$192$	3.36929	0.243157
$193$	−16.4508	−1.18415	−0.592076	−	0.805882i	$-0.701691\pi$
$193$	−16.4508	−1.18415	−0.592076	+	0.805882i	$0.701691\pi$
$194$	4.47632	0.321381
$195$	−8.85018	−0.633774
$196$	5.41417	0.386726
$197$	−7.21327	−0.513924	−0.256962	−	0.966421i	$-0.582722\pi$
$197$	−7.21327	−0.513924	−0.256962	+	0.966421i	$0.582722\pi$
$198$	8.35210	0.593558
$199$	6.19696	0.439291	0.219645	−	0.975580i	$-0.429510\pi$
$199$	6.19696	0.439291	0.219645	+	0.975580i	$0.429510\pi$
$200$	1.00000	0.0707107
$201$	−31.8124	−2.24387
$202$	2.44947	0.172344
$203$	21.6544	1.51984
$204$	−6.02242	−0.421654
$205$	−3.44928	−0.240908
$206$	16.5881	1.15575
$207$	−4.33948	−0.301615
$208$	−2.62672	−0.182130
$209$	−6.72497	−0.465176
$210$	11.8713	0.819195
$211$	−19.7097	−1.35687	−0.678435	−	0.734661i	$-0.737341\pi$
$211$	−19.7097	−1.35687	−0.678435	+	0.734661i	$0.737341\pi$
$212$	−8.49059	−0.583136
$213$	49.0342	3.35977
$214$	−1.53018	−0.104601
$215$	−1.00000	−0.0681994
$216$	18.0328	1.22697
$217$	−27.1673	−1.84424
$218$	10.9169	0.739387
$219$	24.1942	1.63489
$220$	1.00000	0.0674200
$221$	4.69512	0.315828
$222$	−1.64833	−0.110629
$223$	−12.3429	−0.826539	−0.413269	−	0.910609i	$-0.635613\pi$
$223$	−12.3429	−0.826539	−0.413269	+	0.910609i	$0.635613\pi$
$224$	3.52337	0.235415
$225$	8.35210	0.556807
$226$	11.7993	0.784877
$227$	−6.05080	−0.401606	−0.200803	−	0.979632i	$-0.564355\pi$
$227$	−6.05080	−0.401606	−0.200803	+	0.979632i	$0.564355\pi$
$228$	−22.6584	−1.50059
$229$	−9.90690	−0.654667	−0.327333	−	0.944909i	$-0.606150\pi$
$229$	−9.90690	−0.654667	−0.327333	+	0.944909i	$0.606150\pi$
$230$	−0.519567	−0.0342593
$231$	11.8713	0.781072
$232$	6.14594	0.403500
$233$	−11.9592	−0.783474	−0.391737	−	0.920077i	$-0.628126\pi$
$233$	−11.9592	−0.783474	−0.391737	+	0.920077i	$0.628126\pi$
$234$	−21.9386	−1.43417
$235$	−12.4364	−0.811259
$236$	−12.5689	−0.818166
$237$	−28.2223	−1.83323
$238$	−6.29785	−0.408229
$239$	24.1628	1.56296	0.781480	−	0.623930i	$-0.214465\pi$
$239$	24.1628	1.56296	0.781480	+	0.623930i	$0.214465\pi$
$240$	3.36929	0.217487
$241$	−0.901945	−0.0580994	−0.0290497	−	0.999578i	$-0.509248\pi$
$241$	−0.901945	−0.0580994	−0.0290497	+	0.999578i	$0.509248\pi$
$242$	1.00000	0.0642824
$243$	66.1896	4.24606
$244$	−1.20105	−0.0768890
$245$	5.41417	0.345898
$246$	−11.6216	−0.740967
$247$	17.6646	1.12397
$248$	−7.71059	−0.489623
$249$	−22.6101	−1.43286
$250$	1.00000	0.0632456
$251$	17.5479	1.10761	0.553806	−	0.832646i	$-0.313175\pi$
$251$	17.5479	1.10761	0.553806	+	0.832646i	$0.313175\pi$
$252$	29.4276	1.85376
$253$	−0.519567	−0.0326649
$254$	−11.4178	−0.716418
$255$	−6.02242	−0.377139
$256$	1.00000	0.0625000
$257$	23.7691	1.48267	0.741337	−	0.671133i	$-0.234192\pi$
$257$	23.7691	1.48267	0.741337	+	0.671133i	$0.234192\pi$
$258$	−3.36929	−0.209763
$259$	−1.72371	−0.107106
$260$	−2.62672	−0.162902
$261$	51.3315	3.17734
$262$	−14.8288	−0.916125
$263$	−26.8757	−1.65723	−0.828614	−	0.559820i	$-0.810870\pi$
$263$	−26.8757	−1.65723	−0.828614	+	0.559820i	$0.810870\pi$
$264$	3.36929	0.207365
$265$	−8.49059	−0.521573
$266$	−23.6946	−1.45281
$267$	24.2395	1.48343
$268$	−9.44187	−0.576754
$269$	16.8546	1.02765	0.513823	−	0.857896i	$-0.328229\pi$
$269$	16.8546	1.02765	0.513823	+	0.857896i	$0.328229\pi$
$270$	18.0328	1.09744
$271$	22.6995	1.37890	0.689450	−	0.724334i	$-0.257853\pi$
$271$	22.6995	1.37890	0.689450	+	0.724334i	$0.257853\pi$
$272$	−1.78745	−0.108380
$273$	−31.1825	−1.88725
$274$	21.0466	1.27147
$275$	1.00000	0.0603023
$276$	−1.75057	−0.105372
$277$	28.1712	1.69264	0.846321	−	0.532674i	$-0.178813\pi$
$277$	28.1712	1.69264	0.846321	+	0.532674i	$0.178813\pi$
$278$	−14.3023	−0.857794
$279$	−64.3996	−3.85550
$280$	3.52337	0.210562
$281$	10.2932	0.614041	0.307020	−	0.951703i	$-0.400668\pi$
$281$	10.2932	0.614041	0.307020	+	0.951703i	$0.400668\pi$
$282$	−41.9017	−2.49521
$283$	10.6982	0.635941	0.317970	−	0.948101i	$-0.396999\pi$
$283$	10.6982	0.635941	0.317970	+	0.948101i	$0.396999\pi$
$284$	14.5533	0.863579
$285$	−22.6584	−1.34217
$286$	−2.62672	−0.155321
$287$	−12.1531	−0.717375
$288$	8.35210	0.492152
$289$	−13.8050	−0.812061
$290$	6.14594	0.360902
$291$	15.0820	0.884123
$292$	7.18081	0.420225
$293$	−5.76038	−0.336525	−0.168262	−	0.985742i	$-0.553816\pi$
$293$	−5.76038	−0.336525	−0.168262	+	0.985742i	$0.553816\pi$
$294$	18.2419	1.06389
$295$	−12.5689	−0.731790
$296$	−0.489223	−0.0284355
$297$	18.0328	1.04637
$298$	2.73710	0.158556
$299$	1.36476	0.0789260
$300$	3.36929	0.194526
$301$	−3.52337	−0.203084
$302$	−8.38168	−0.482312
$303$	8.25296	0.474120
$304$	−6.72497	−0.385704
$305$	−1.20105	−0.0687717
$306$	−14.9289	−0.853430
$307$	25.3431	1.44641	0.723203	−	0.690635i	$-0.242669\pi$
$307$	25.3431	1.44641	0.723203	+	0.690635i	$0.242669\pi$
$308$	3.52337	0.200763
$309$	55.8902	3.17948
$310$	−7.71059	−0.437932
$311$	−10.5760	−0.599711	−0.299855	−	0.953985i	$-0.596938\pi$
$311$	−10.5760	−0.599711	−0.299855	+	0.953985i	$0.596938\pi$
$312$	−8.85018	−0.501043
$313$	−5.79143	−0.327351	−0.163675	−	0.986514i	$-0.552335\pi$
$313$	−5.79143	−0.327351	−0.163675	+	0.986514i	$0.552335\pi$
$314$	18.2881	1.03206
$315$	29.4276	1.65806
$316$	−8.37633	−0.471205
$317$	13.9565	0.783875	0.391938	−	0.919992i	$-0.371805\pi$
$317$	13.9565	0.783875	0.391938	+	0.919992i	$0.371805\pi$
$318$	−28.6072	−1.60421
$319$	6.14594	0.344106
$320$	1.00000	0.0559017
$321$	−5.15563	−0.287759
$322$	−1.83063	−0.102017
$323$	12.0205	0.668841
$324$	35.7013	1.98340
$325$	−2.62672	−0.145704
$326$	20.5678	1.13915
$327$	36.7822	2.03406
$328$	−3.44928	−0.190455
$329$	−43.8179	−2.41576
$330$	3.36929	0.185473
$331$	31.2497	1.71764	0.858819	−	0.512279i	$-0.171199\pi$
$331$	31.2497	1.71764	0.858819	+	0.512279i	$0.171199\pi$
$332$	−6.71066	−0.368295
$333$	−4.08604	−0.223913
$334$	12.1259	0.663502
$335$	−9.44187	−0.515864
$336$	11.8713	0.647630
$337$	27.5117	1.49866	0.749329	−	0.662198i	$-0.230376\pi$
$337$	27.5117	1.49866	0.749329	+	0.662198i	$0.230376\pi$
$338$	−6.10034	−0.331815
$339$	39.7552	2.15921
$340$	−1.78745	−0.0969379
$341$	−7.71059	−0.417552
$342$	−56.1677	−3.03720
$343$	−5.58748	−0.301696
$344$	−1.00000	−0.0539164
$345$	−1.75057	−0.0942476
$346$	−8.75459	−0.470650
$347$	−28.6812	−1.53969	−0.769845	−	0.638231i	$-0.779666\pi$
$347$	−28.6812	−1.53969	−0.769845	+	0.638231i	$0.779666\pi$
$348$	20.7074	1.11003
$349$	−1.36803	−0.0732291	−0.0366145	−	0.999329i	$-0.511657\pi$
$349$	−1.36803	−0.0732291	−0.0366145	+	0.999329i	$0.511657\pi$
$350$	3.52337	0.188332
$351$	−47.3670	−2.52827
$352$	1.00000	0.0533002
$353$	0.0679674	0.00361754	0.00180877	−	0.999998i	$-0.499424\pi$
$353$	0.0679674	0.00361754	0.00180877	+	0.999998i	$0.499424\pi$
$354$	−42.3482	−2.25078
$355$	14.5533	0.772409
$356$	7.19424	0.381294
$357$	−21.2193	−1.12304
$358$	5.07751	0.268355
$359$	23.6952	1.25058	0.625291	−	0.780391i	$-0.284980\pi$
$359$	23.6952	1.25058	0.625291	+	0.780391i	$0.284980\pi$
$360$	8.35210	0.440194
$361$	26.2253	1.38028
$362$	0.976028	0.0512989
$363$	3.36929	0.176842
$364$	−9.25492	−0.485090
$365$	7.18081	0.375861
$366$	−4.04667	−0.211523
$367$	−12.8428	−0.670390	−0.335195	−	0.942149i	$-0.608802\pi$
$367$	−12.8428	−0.670390	−0.335195	+	0.942149i	$0.608802\pi$
$368$	−0.519567	−0.0270843
$369$	−28.8087	−1.49972
$370$	−0.489223	−0.0254335
$371$	−29.9155	−1.55314
$372$	−25.9792	−1.34696
$373$	−14.7058	−0.761435	−0.380718	−	0.924691i	$-0.624323\pi$
$373$	−14.7058	−0.761435	−0.380718	+	0.924691i	$0.624323\pi$
$374$	−1.78745	−0.0924267
$375$	3.36929	0.173989
$376$	−12.4364	−0.641356
$377$	−16.1437	−0.831441
$378$	63.5362	3.26795
$379$	−12.2308	−0.628252	−0.314126	−	0.949381i	$-0.601711\pi$
$379$	−12.2308	−0.628252	−0.314126	+	0.949381i	$0.601711\pi$
$380$	−6.72497	−0.344984
$381$	−38.4699	−1.97087
$382$	8.46474	0.433094
$383$	2.79629	0.142884	0.0714418	−	0.997445i	$-0.477240\pi$
$383$	2.79629	0.142884	0.0714418	+	0.997445i	$0.477240\pi$
$384$	3.36929	0.171938
$385$	3.52337	0.179568
$386$	−16.4508	−0.837321
$387$	−8.35210	−0.424561
$388$	4.47632	0.227251
$389$	1.00810	0.0511125	0.0255562	−	0.999673i	$-0.491864\pi$
$389$	1.00810	0.0511125	0.0255562	+	0.999673i	$0.491864\pi$
$390$	−8.85018	−0.448146
$391$	0.928699	0.0469663
$392$	5.41417	0.273457
$393$	−49.9624	−2.52027
$394$	−7.21327	−0.363399
$395$	−8.37633	−0.421459
$396$	8.35210	0.419709
$397$	13.3075	0.667883	0.333941	−	0.942594i	$-0.391621\pi$
$397$	13.3075	0.667883	0.333941	+	0.942594i	$0.391621\pi$
$398$	6.19696	0.310625
$399$	−79.8339	−3.99670
$400$	1.00000	0.0500000
$401$	37.1890	1.85713	0.928566	−	0.371167i	$-0.121042\pi$
$401$	37.1890	1.85713	0.928566	+	0.371167i	$0.121042\pi$
$402$	−31.8124	−1.58666
$403$	20.2536	1.00890
$404$	2.44947	0.121866
$405$	35.7013	1.77401
$406$	21.6544	1.07469
$407$	−0.489223	−0.0242499
$408$	−6.02242	−0.298154
$409$	34.0800	1.68515	0.842573	−	0.538582i	$-0.181040\pi$
$409$	34.0800	1.68515	0.842573	+	0.538582i	$0.181040\pi$
$410$	−3.44928	−0.170348
$411$	70.9121	3.49784
$412$	16.5881	0.817238
$413$	−44.2849	−2.17912
$414$	−4.33948	−0.213274
$415$	−6.71066	−0.329413
$416$	−2.62672	−0.128786
$417$	−48.1885	−2.35980
$418$	−6.72497	−0.328929
$419$	0.728657	0.0355972	0.0177986	−	0.999842i	$-0.494334\pi$
$419$	0.728657	0.0355972	0.0177986	+	0.999842i	$0.494334\pi$
$420$	11.8713	0.579258
$421$	22.7343	1.10800	0.554000	−	0.832517i	$-0.313101\pi$
$421$	22.7343	1.10800	0.554000	+	0.832517i	$0.313101\pi$
$422$	−19.7097	−0.959452
$423$	−103.870	−5.05032
$424$	−8.49059	−0.412340
$425$	−1.78745	−0.0867039
$426$	49.0342	2.37572
$427$	−4.23173	−0.204788
$428$	−1.53018	−0.0739642
$429$	−8.85018	−0.427291
$430$	−1.00000	−0.0482243
$431$	7.89446	0.380263	0.190131	−	0.981759i	$-0.439109\pi$
$431$	7.89446	0.380263	0.190131	+	0.981759i	$0.439109\pi$
$432$	18.0328	0.867602
$433$	−16.8347	−0.809026	−0.404513	−	0.914532i	$-0.632559\pi$
$433$	−16.8347	−0.809026	−0.404513	+	0.914532i	$0.632559\pi$
$434$	−27.1673	−1.30407
$435$	20.7074	0.992845
$436$	10.9169	0.522825
$437$	3.49408	0.167144
$438$	24.1942	1.15604
$439$	18.3768	0.877075	0.438538	−	0.898713i	$-0.355497\pi$
$439$	18.3768	0.877075	0.438538	+	0.898713i	$0.355497\pi$
$440$	1.00000	0.0476731
$441$	45.2197	2.15332
$442$	4.69512	0.223324
$443$	−1.42346	−0.0676306	−0.0338153	−	0.999428i	$-0.510766\pi$
$443$	−1.42346	−0.0676306	−0.0338153	+	0.999428i	$0.510766\pi$
$444$	−1.64833	−0.0782264
$445$	7.19424	0.341040
$446$	−12.3429	−0.584451
$447$	9.22208	0.436190
$448$	3.52337	0.166464
$449$	−3.89460	−0.183798	−0.0918989	−	0.995768i	$-0.529294\pi$
$449$	−3.89460	−0.183798	−0.0918989	+	0.995768i	$0.529294\pi$
$450$	8.35210	0.393722
$451$	−3.44928	−0.162420
$452$	11.7993	0.554992
$453$	−28.2403	−1.32685
$454$	−6.05080	−0.283978
$455$	−9.25492	−0.433877
$456$	−22.6584	−1.06108
$457$	31.4483	1.47109	0.735545	−	0.677476i	$-0.236926\pi$
$457$	31.4483	1.47109	0.735545	+	0.677476i	$0.236926\pi$
$458$	−9.90690	−0.462919
$459$	−32.2326	−1.50449
$460$	−0.519567	−0.0242250
$461$	−24.1399	−1.12431	−0.562155	−	0.827032i	$-0.690027\pi$
$461$	−24.1399	−1.12431	−0.562155	+	0.827032i	$0.690027\pi$
$462$	11.8713	0.552301
$463$	25.4482	1.18268	0.591339	−	0.806423i	$-0.298600\pi$
$463$	25.4482	1.18268	0.591339	+	0.806423i	$0.298600\pi$
$464$	6.14594	0.285318
$465$	−25.9792	−1.20476
$466$	−11.9592	−0.554000
$467$	−29.7761	−1.37787	−0.688937	−	0.724821i	$-0.741922\pi$
$467$	−29.7761	−1.37787	−0.688937	+	0.724821i	$0.741922\pi$
$468$	−21.9386	−1.01411
$469$	−33.2672	−1.53614
$470$	−12.4364	−0.573646
$471$	61.6179	2.83920
$472$	−12.5689	−0.578530
$473$	−1.00000	−0.0459800
$474$	−28.2223	−1.29629
$475$	−6.72497	−0.308563
$476$	−6.29785	−0.288661
$477$	−70.9143	−3.24694
$478$	24.1628	1.10518
$479$	16.1037	0.735797	0.367899	−	0.929866i	$-0.380077\pi$
$479$	16.1037	0.735797	0.367899	+	0.929866i	$0.380077\pi$
$480$	3.36929	0.153786
$481$	1.28505	0.0585933
$482$	−0.901945	−0.0410825
$483$	−6.16792	−0.280650
$484$	1.00000	0.0454545
$485$	4.47632	0.203259
$486$	66.1896	3.00242
$487$	31.1689	1.41240	0.706198	−	0.708015i	$-0.250409\pi$
$487$	31.1689	1.41240	0.706198	+	0.708015i	$0.250409\pi$
$488$	−1.20105	−0.0543688
$489$	69.2989	3.13380
$490$	5.41417	0.244587
$491$	−17.9732	−0.811117	−0.405559	−	0.914069i	$-0.632923\pi$
$491$	−17.9732	−0.811117	−0.405559	+	0.914069i	$0.632923\pi$
$492$	−11.6216	−0.523943
$493$	−10.9855	−0.494764
$494$	17.6646	0.794769
$495$	8.35210	0.375399
$496$	−7.71059	−0.346216
$497$	51.2767	2.30007
$498$	−22.6101	−1.01318
$499$	17.2203	0.770888	0.385444	−	0.922731i	$-0.374048\pi$
$499$	17.2203	0.770888	0.385444	+	0.922731i	$0.374048\pi$
$500$	1.00000	0.0447214
$501$	40.8558	1.82530
$502$	17.5479	0.783199
$503$	−14.0247	−0.625329	−0.312665	−	0.949864i	$-0.601222\pi$
$503$	−14.0247	−0.625329	−0.312665	+	0.949864i	$0.601222\pi$
$504$	29.4276	1.31081
$505$	2.44947	0.109000
$506$	−0.519567	−0.0230976
$507$	−20.5538	−0.912826
$508$	−11.4178	−0.506584
$509$	22.5137	0.997904	0.498952	−	0.866630i	$-0.333718\pi$
$509$	22.5137	0.997904	0.498952	+	0.866630i	$0.333718\pi$
$510$	−6.02242	−0.266677
$511$	25.3007	1.11924
$512$	1.00000	0.0441942
$513$	−121.270	−5.35420
$514$	23.7691	1.04841
$515$	16.5881	0.730960
$516$	−3.36929	−0.148325
$517$	−12.4364	−0.546950
$518$	−1.72371	−0.0757357
$519$	−29.4967	−1.29476
$520$	−2.62672	−0.115189
$521$	−30.2742	−1.32634	−0.663169	−	0.748469i	$-0.730789\pi$
$521$	−30.2742	−1.32634	−0.663169	+	0.748469i	$0.730789\pi$
$522$	51.3315	2.24672
$523$	−27.4712	−1.20123	−0.600617	−	0.799537i	$-0.705078\pi$
$523$	−27.4712	−1.20123	−0.600617	+	0.799537i	$0.705078\pi$
$524$	−14.8288	−0.647798
$525$	11.8713	0.518104
$526$	−26.8757	−1.17184
$527$	13.7823	0.600365
$528$	3.36929	0.146629
$529$	−22.7300	−0.988263
$530$	−8.49059	−0.368808
$531$	−104.977	−4.55560
$532$	−23.6946	−1.02729
$533$	9.06029	0.392445
$534$	24.2395	1.04894
$535$	−1.53018	−0.0661556
$536$	−9.44187	−0.407827
$537$	17.1076	0.738248
$538$	16.8546	0.726656
$539$	5.41417	0.233205
$540$	18.0328	0.776007
$541$	25.2174	1.08418	0.542090	−	0.840321i	$-0.317633\pi$
$541$	25.2174	1.08418	0.542090	+	0.840321i	$0.317633\pi$
$542$	22.6995	0.975029
$543$	3.28852	0.141124
$544$	−1.78745	−0.0766362
$545$	10.9169	0.467629
$546$	−31.1825	−1.33449
$547$	−6.48475	−0.277268	−0.138634	−	0.990344i	$-0.544271\pi$
$547$	−6.48475	−0.277268	−0.138634	+	0.990344i	$0.544271\pi$
$548$	21.0466	0.899067
$549$	−10.0312	−0.428123
$550$	1.00000	0.0426401
$551$	−41.3313	−1.76077
$552$	−1.75057	−0.0745093
$553$	−29.5129	−1.25502
$554$	28.1712	1.19688
$555$	−1.64833	−0.0699678
$556$	−14.3023	−0.606552
$557$	3.98598	0.168891	0.0844456	−	0.996428i	$-0.473088\pi$
$557$	3.98598	0.168891	0.0844456	+	0.996428i	$0.473088\pi$
$558$	−64.3996	−2.72625
$559$	2.62672	0.111098
$560$	3.52337	0.148890
$561$	−6.02242	−0.254267
$562$	10.2932	0.434192
$563$	23.4723	0.989239	0.494619	−	0.869110i	$-0.335307\pi$
$563$	23.4723	0.989239	0.494619	+	0.869110i	$0.335307\pi$
$564$	−41.9017	−1.76438
$565$	11.7993	0.496400
$566$	10.6982	0.449678
$567$	125.789	5.28264
$568$	14.5533	0.610643
$569$	−11.3127	−0.474252	−0.237126	−	0.971479i	$-0.576205\pi$
$569$	−11.3127	−0.474252	−0.237126	+	0.971479i	$0.576205\pi$
$570$	−22.6584	−0.949055
$571$	−4.40453	−0.184324	−0.0921620	−	0.995744i	$-0.529378\pi$
$571$	−4.40453	−0.184324	−0.0921620	+	0.995744i	$0.529378\pi$
$572$	−2.62672	−0.109829
$573$	28.5201	1.19145
$574$	−12.1531	−0.507261
$575$	−0.519567	−0.0216675
$576$	8.35210	0.348004
$577$	32.9166	1.37034	0.685169	−	0.728384i	$-0.259728\pi$
$577$	32.9166	1.37034	0.685169	+	0.728384i	$0.259728\pi$
$578$	−13.8050	−0.574214
$579$	−55.4273	−2.30348
$580$	6.14594	0.255196
$581$	−23.6442	−0.980925
$582$	15.0820	0.625169
$583$	−8.49059	−0.351644
$584$	7.18081	0.297144
$585$	−21.9386	−0.907051
$586$	−5.76038	−0.237959
$587$	−27.3420	−1.12853	−0.564263	−	0.825595i	$-0.690839\pi$
$587$	−27.3420	−1.12853	−0.564263	+	0.825595i	$0.690839\pi$
$588$	18.2419	0.752283
$589$	51.8535	2.13659
$590$	−12.5689	−0.517453
$591$	−24.3036	−0.999716
$592$	−0.489223	−0.0201069
$593$	−23.7824	−0.976627	−0.488313	−	0.872668i	$-0.662388\pi$
$593$	−23.7824	−0.976627	−0.488313	+	0.872668i	$0.662388\pi$
$594$	18.0328	0.739893
$595$	−6.29785	−0.258186
$596$	2.73710	0.112116
$597$	20.8793	0.854534
$598$	1.36476	0.0558091
$599$	23.8553	0.974702	0.487351	−	0.873206i	$-0.337963\pi$
$599$	23.8553	0.974702	0.487351	+	0.873206i	$0.337963\pi$
$600$	3.36929	0.137551
$601$	−29.0346	−1.18434	−0.592172	−	0.805812i	$-0.701729\pi$
$601$	−29.0346	−1.18434	−0.592172	+	0.805812i	$0.701729\pi$
$602$	−3.52337	−0.143602
$603$	−78.8594	−3.21140
$604$	−8.38168	−0.341046
$605$	1.00000	0.0406558
$606$	8.25296	0.335253
$607$	13.0721	0.530578	0.265289	−	0.964169i	$-0.414533\pi$
$607$	13.0721	0.530578	0.265289	+	0.964169i	$0.414533\pi$
$608$	−6.72497	−0.272734
$609$	72.9600	2.95649
$610$	−1.20105	−0.0486289
$611$	32.6668	1.32156
$612$	−14.9289	−0.603466
$613$	−27.1321	−1.09585	−0.547927	−	0.836526i	$-0.684583\pi$
$613$	−27.1321	−1.09585	−0.547927	+	0.836526i	$0.684583\pi$
$614$	25.3431	1.02276
$615$	−11.6216	−0.468629
$616$	3.52337	0.141961
$617$	−7.00947	−0.282191	−0.141095	−	0.989996i	$-0.545062\pi$
$617$	−7.00947	−0.282191	−0.141095	+	0.989996i	$0.545062\pi$
$618$	55.8902	2.24823
$619$	−35.7053	−1.43512	−0.717558	−	0.696499i	$-0.754740\pi$
$619$	−35.7053	−1.43512	−0.717558	+	0.696499i	$0.754740\pi$
$620$	−7.71059	−0.309665
$621$	−9.36924	−0.375975
$622$	−10.5760	−0.424059
$623$	25.3480	1.01555
$624$	−8.85018	−0.354291
$625$	1.00000	0.0400000
$626$	−5.79143	−0.231472
$627$	−22.6584	−0.904888
$628$	18.2881	0.729775
$629$	0.874459	0.0348670
$630$	29.4276	1.17242
$631$	−14.0630	−0.559840	−0.279920	−	0.960023i	$-0.590308\pi$
$631$	−14.0630	−0.559840	−0.279920	+	0.960023i	$0.590308\pi$
$632$	−8.37633	−0.333192
$633$	−66.4075	−2.63946
$634$	13.9565	0.554284
$635$	−11.4178	−0.453102
$636$	−28.6072	−1.13435
$637$	−14.2215	−0.563477
$638$	6.14594	0.243320
$639$	121.551	4.80847
$640$	1.00000	0.0395285
$641$	−15.7612	−0.622531	−0.311266	−	0.950323i	$-0.600753\pi$
$641$	−15.7612	−0.622531	−0.311266	+	0.950323i	$0.600753\pi$
$642$	−5.15563	−0.203476
$643$	−21.4915	−0.847541	−0.423771	−	0.905770i	$-0.639294\pi$
$643$	−21.4915	−0.847541	−0.423771	+	0.905770i	$0.639294\pi$
$644$	−1.83063	−0.0721370
$645$	−3.36929	−0.132666
$646$	12.0205	0.472942
$647$	0.575395	0.0226211	0.0113106	−	0.999936i	$-0.496400\pi$
$647$	0.575395	0.0226211	0.0113106	+	0.999936i	$0.496400\pi$
$648$	35.7013	1.40248
$649$	−12.5689	−0.493372
$650$	−2.62672	−0.103028
$651$	−91.5344	−3.58752
$652$	20.5678	0.805498
$653$	−0.341822	−0.0133765	−0.00668827	−	0.999978i	$-0.502129\pi$
$653$	−0.341822	−0.0133765	−0.00668827	+	0.999978i	$0.502129\pi$
$654$	36.7822	1.43830
$655$	−14.8288	−0.579408
$656$	−3.44928	−0.134672
$657$	59.9749	2.33984
$658$	−43.8179	−1.70820
$659$	−23.4777	−0.914562	−0.457281	−	0.889322i	$-0.651177\pi$
$659$	−23.4777	−0.914562	−0.457281	+	0.889322i	$0.651177\pi$
$660$	3.36929	0.131149
$661$	−40.2591	−1.56590	−0.782948	−	0.622087i	$-0.786285\pi$
$661$	−40.2591	−1.56590	−0.782948	+	0.622087i	$0.786285\pi$
$662$	31.2497	1.21455
$663$	15.8192	0.614368
$664$	−6.71066	−0.260424
$665$	−23.6946	−0.918837
$666$	−4.08604	−0.158331
$667$	−3.19323	−0.123642
$668$	12.1259	0.469167
$669$	−41.5866	−1.60783
$670$	−9.44187	−0.364771
$671$	−1.20105	−0.0463658
$672$	11.8713	0.457944
$673$	−48.7707	−1.87997	−0.939987	−	0.341211i	$-0.889163\pi$
$673$	−48.7707	−1.87997	−0.939987	+	0.341211i	$0.889163\pi$
$674$	27.5117	1.05971
$675$	18.0328	0.694081
$676$	−6.10034	−0.234628
$677$	−13.3430	−0.512812	−0.256406	−	0.966569i	$-0.582538\pi$
$677$	−13.3430	−0.512812	−0.256406	+	0.966569i	$0.582538\pi$
$678$	39.7552	1.52679
$679$	15.7717	0.605264
$680$	−1.78745	−0.0685455
$681$	−20.3869	−0.781228
$682$	−7.71059	−0.295254
$683$	−22.5569	−0.863117	−0.431559	−	0.902085i	$-0.642036\pi$
$683$	−22.5569	−0.863117	−0.431559	+	0.902085i	$0.642036\pi$
$684$	−56.1677	−2.14762
$685$	21.0466	0.804150
$686$	−5.58748	−0.213331
$687$	−33.3792	−1.27350
$688$	−1.00000	−0.0381246
$689$	22.3024	0.849654
$690$	−1.75057	−0.0666431
$691$	48.8063	1.85668	0.928339	−	0.371735i	$-0.121237\pi$
$691$	48.8063	1.85668	0.928339	+	0.371735i	$0.121237\pi$
$692$	−8.75459	−0.332800
$693$	29.4276	1.11786
$694$	−28.6812	−1.08872
$695$	−14.3023	−0.542516
$696$	20.7074	0.784913
$697$	6.16540	0.233531
$698$	−1.36803	−0.0517808
$699$	−40.2940	−1.52406
$700$	3.52337	0.133171
$701$	−18.1438	−0.685282	−0.342641	−	0.939466i	$-0.611321\pi$
$701$	−18.1438	−0.685282	−0.342641	+	0.939466i	$0.611321\pi$
$702$	−47.3670	−1.78775
$703$	3.29001	0.124085
$704$	1.00000	0.0376889
$705$	−41.9017	−1.57811
$706$	0.0679674	0.00255799
$707$	8.63039	0.324579
$708$	−42.3482	−1.59154
$709$	44.7911	1.68216	0.841082	−	0.540907i	$-0.181919\pi$
$709$	44.7911	1.68216	0.841082	+	0.540907i	$0.181919\pi$
$710$	14.5533	0.546175
$711$	−69.9599	−2.62370
$712$	7.19424	0.269616
$713$	4.00617	0.150032
$714$	−21.2193	−0.794111
$715$	−2.62672	−0.0982338
$716$	5.07751	0.189756
$717$	81.4114	3.04036
$718$	23.6952	0.884295
$719$	−23.0795	−0.860721	−0.430361	−	0.902657i	$-0.641614\pi$
$719$	−23.0795	−0.860721	−0.430361	+	0.902657i	$0.641614\pi$
$720$	8.35210	0.311264
$721$	58.4462	2.17665
$722$	26.2253	0.976004
$723$	−3.03891	−0.113018
$724$	0.976028	0.0362738
$725$	6.14594	0.228254
$726$	3.36929	0.125046
$727$	29.9578	1.11107	0.555537	−	0.831492i	$-0.312513\pi$
$727$	29.9578	1.11107	0.555537	+	0.831492i	$0.312513\pi$
$728$	−9.25492	−0.343010
$729$	115.908	4.29288
$730$	7.18081	0.265774
$731$	1.78745	0.0661111
$732$	−4.04667	−0.149569
$733$	−26.8616	−0.992156	−0.496078	−	0.868278i	$-0.665227\pi$
$733$	−26.8616	−0.992156	−0.496078	+	0.868278i	$0.665227\pi$
$734$	−12.8428	−0.474037
$735$	18.2419	0.672862
$736$	−0.519567	−0.0191515
$737$	−9.44187	−0.347796
$738$	−28.8087	−1.06046
$739$	29.7089	1.09286	0.546429	−	0.837505i	$-0.315987\pi$
$739$	29.7089	1.09286	0.546429	+	0.837505i	$0.315987\pi$
$740$	−0.489223	−0.0179842
$741$	59.5172	2.18642
$742$	−29.9155	−1.09823
$743$	−18.4070	−0.675289	−0.337644	−	0.941274i	$-0.609630\pi$
$743$	−18.4070	−0.675289	−0.337644	+	0.941274i	$0.609630\pi$
$744$	−25.9792	−0.952443
$745$	2.73710	0.100280
$746$	−14.7058	−0.538416
$747$	−56.0481	−2.05069
$748$	−1.78745	−0.0653555
$749$	−5.39141	−0.196998
$750$	3.36929	0.123029
$751$	11.4355	0.417289	0.208644	−	0.977992i	$-0.433095\pi$
$751$	11.4355	0.417289	0.208644	+	0.977992i	$0.433095\pi$
$752$	−12.4364	−0.453507
$753$	59.1238	2.15459
$754$	−16.1437	−0.587917
$755$	−8.38168	−0.305041
$756$	63.5362	2.31079
$757$	−48.0323	−1.74577	−0.872883	−	0.487930i	$-0.837752\pi$
$757$	−48.0323	−1.74577	−0.872883	+	0.487930i	$0.837752\pi$
$758$	−12.2308	−0.444241
$759$	−1.75057	−0.0635417
$760$	−6.72497	−0.243940
$761$	−13.2068	−0.478748	−0.239374	−	0.970927i	$-0.576942\pi$
$761$	−13.2068	−0.478748	−0.239374	+	0.970927i	$0.576942\pi$
$762$	−38.4699	−1.39362
$763$	38.4644	1.39250
$764$	8.46474	0.306244
$765$	−14.9289	−0.539757
$766$	2.79629	0.101034
$767$	33.0150	1.19210
$768$	3.36929	0.121579
$769$	−37.9294	−1.36777	−0.683885	−	0.729589i	$-0.739711\pi$
$769$	−37.9294	−1.36777	−0.683885	+	0.729589i	$0.739711\pi$
$770$	3.52337	0.126974
$771$	80.0849	2.88419
$772$	−16.4508	−0.592076
$773$	−17.0296	−0.612513	−0.306256	−	0.951949i	$-0.599076\pi$
$773$	−17.0296	−0.612513	−0.306256	+	0.951949i	$0.599076\pi$
$774$	−8.35210	−0.300210
$775$	−7.71059	−0.276973
$776$	4.47632	0.160691
$777$	−5.80769	−0.208350
$778$	1.00810	0.0361420
$779$	23.1963	0.831094
$780$	−8.85018	−0.316887
$781$	14.5533	0.520758
$782$	0.928699	0.0332102
$783$	110.828	3.96068
$784$	5.41417	0.193363
$785$	18.2881	0.652731
$786$	−49.9624	−1.78210
$787$	28.3763	1.01151	0.505753	−	0.862678i	$-0.331215\pi$
$787$	28.3763	1.01151	0.505753	+	0.862678i	$0.331215\pi$
$788$	−7.21327	−0.256962
$789$	−90.5521	−3.22374
$790$	−8.37633	−0.298016
$791$	41.5733	1.47818
$792$	8.35210	0.296779
$793$	3.15481	0.112031
$794$	13.3075	0.472264
$795$	−28.6072	−1.01459
$796$	6.19696	0.219645
$797$	−24.4614	−0.866467	−0.433233	−	0.901282i	$-0.642627\pi$
$797$	−24.4614	−0.866467	−0.433233	+	0.901282i	$0.642627\pi$
$798$	−79.8339	−2.82609
$799$	22.2293	0.786417
$800$	1.00000	0.0353553
$801$	60.0870	2.12307
$802$	37.1890	1.31319
$803$	7.18081	0.253405
$804$	−31.8124	−1.12194
$805$	−1.83063	−0.0645213
$806$	20.2536	0.713401
$807$	56.7882	1.99904
$808$	2.44947	0.0861719
$809$	−16.3102	−0.573437	−0.286718	−	0.958015i	$-0.592564\pi$
$809$	−16.3102	−0.573437	−0.286718	+	0.958015i	$0.592564\pi$
$810$	35.7013	1.25441
$811$	46.1801	1.62160	0.810801	−	0.585322i	$-0.199032\pi$
$811$	46.1801	1.62160	0.810801	+	0.585322i	$0.199032\pi$
$812$	21.6544	0.759922
$813$	76.4813	2.68232
$814$	−0.489223	−0.0171472
$815$	20.5678	0.720459
$816$	−6.02242	−0.210827
$817$	6.72497	0.235277
$818$	34.0800	1.19158
$819$	−77.2980	−2.70101
$820$	−3.44928	−0.120454
$821$	−21.9178	−0.764938	−0.382469	−	0.923968i	$-0.624926\pi$
$821$	−21.9178	−0.764938	−0.382469	+	0.923968i	$0.624926\pi$
$822$	70.9121	2.47334
$823$	27.0453	0.942741	0.471370	−	0.881935i	$-0.343760\pi$
$823$	27.0453	0.942741	0.471370	+	0.881935i	$0.343760\pi$
$824$	16.5881	0.577875
$825$	3.36929	0.117304
$826$	−44.2849	−1.54087
$827$	49.1125	1.70781	0.853905	−	0.520429i	$-0.174228\pi$
$827$	49.1125	1.70781	0.853905	+	0.520429i	$0.174228\pi$
$828$	−4.33948	−0.150807
$829$	−8.09839	−0.281269	−0.140634	−	0.990062i	$-0.544914\pi$
$829$	−8.09839	−0.281269	−0.140634	+	0.990062i	$0.544914\pi$
$830$	−6.71066	−0.232930
$831$	94.9168	3.29263
$832$	−2.62672	−0.0910652
$833$	−9.67754	−0.335307
$834$	−48.1885	−1.66863
$835$	12.1259	0.419636
$836$	−6.72497	−0.232588
$837$	−139.043	−4.80604
$838$	0.728657	0.0251711
$839$	26.6994	0.921766	0.460883	−	0.887461i	$-0.347533\pi$
$839$	26.6994	0.921766	0.460883	+	0.887461i	$0.347533\pi$
$840$	11.8713	0.409597
$841$	8.77253	0.302501
$842$	22.7343	0.783474
$843$	34.6808	1.19447
$844$	−19.7097	−0.678435
$845$	−6.10034	−0.209858
$846$	−103.870	−3.57111
$847$	3.52337	0.121065
$848$	−8.49059	−0.291568
$849$	36.0453	1.23707
$850$	−1.78745	−0.0613089
$851$	0.254184	0.00871332
$852$	49.0342	1.67989
$853$	−1.93285	−0.0661796	−0.0330898	−	0.999452i	$-0.510535\pi$
$853$	−1.93285	−0.0661796	−0.0330898	+	0.999452i	$0.510535\pi$
$854$	−4.23173	−0.144807
$855$	−56.1677	−1.92089
$856$	−1.53018	−0.0523006
$857$	−20.0598	−0.685231	−0.342616	−	0.939476i	$-0.611313\pi$
$857$	−20.0598	−0.685231	−0.342616	+	0.939476i	$0.611313\pi$
$858$	−8.85018	−0.302140
$859$	−36.5652	−1.24759	−0.623795	−	0.781588i	$-0.714410\pi$
$859$	−36.5652	−1.24759	−0.623795	+	0.781588i	$0.714410\pi$
$860$	−1.00000	−0.0340997
$861$	−40.9473	−1.39548
$862$	7.89446	0.268886
$863$	2.05194	0.0698489	0.0349244	−	0.999390i	$-0.488881\pi$
$863$	2.05194	0.0698489	0.0349244	+	0.999390i	$0.488881\pi$
$864$	18.0328	0.613487
$865$	−8.75459	−0.297665
$866$	−16.8347	−0.572068
$867$	−46.5131	−1.57967
$868$	−27.1673	−0.922118
$869$	−8.37633	−0.284147
$870$	20.7074	0.702048
$871$	24.8012	0.840355
$872$	10.9169	0.369693
$873$	37.3867	1.26535
$874$	3.49408	0.118189
$875$	3.52337	0.119112
$876$	24.1942	0.817447
$877$	26.6573	0.900152	0.450076	−	0.892990i	$-0.351397\pi$
$877$	26.6573	0.900152	0.450076	+	0.892990i	$0.351397\pi$
$878$	18.3768	0.620186
$879$	−19.4084	−0.654628
$880$	1.00000	0.0337100
$881$	−16.4419	−0.553942	−0.276971	−	0.960878i	$-0.589331\pi$
$881$	−16.4419	−0.553942	−0.276971	+	0.960878i	$0.589331\pi$
$882$	45.2197	1.52263
$883$	−48.0318	−1.61640	−0.808199	−	0.588909i	$-0.799558\pi$
$883$	−48.0318	−1.61640	−0.808199	+	0.588909i	$0.799558\pi$
$884$	4.69512	0.157914
$885$	−42.3482	−1.42352
$886$	−1.42346	−0.0478221
$887$	−21.1545	−0.710300	−0.355150	−	0.934809i	$-0.615570\pi$
$887$	−21.1545	−0.710300	−0.355150	+	0.934809i	$0.615570\pi$
$888$	−1.64833	−0.0553144
$889$	−40.2292	−1.34925
$890$	7.19424	0.241152
$891$	35.7013	1.19604
$892$	−12.3429	−0.413269
$893$	83.6342	2.79871
$894$	9.22208	0.308433
$895$	5.07751	0.169723
$896$	3.52337	0.117708
$897$	4.59826	0.153532
$898$	−3.89460	−0.129965
$899$	−47.3888	−1.58050
$900$	8.35210	0.278403
$901$	15.1765	0.505602
$902$	−3.44928	−0.114848
$903$	−11.8713	−0.395051
$904$	11.7993	0.392438
$905$	0.976028	0.0324443
$906$	−28.2403	−0.938221
$907$	15.8932	0.527724	0.263862	−	0.964560i	$-0.415004\pi$
$907$	15.8932	0.527724	0.263862	+	0.964560i	$0.415004\pi$
$908$	−6.05080	−0.200803
$909$	20.4582	0.678555
$910$	−9.25492	−0.306798
$911$	−34.1607	−1.13179	−0.565897	−	0.824476i	$-0.691470\pi$
$911$	−34.1607	−1.13179	−0.565897	+	0.824476i	$0.691470\pi$
$912$	−22.6584	−0.750294
$913$	−6.71066	−0.222090
$914$	31.4483	1.04022
$915$	−4.04667	−0.133779
$916$	−9.90690	−0.327333
$917$	−52.2473	−1.72536
$918$	−32.2326	−1.06383
$919$	−29.4284	−0.970753	−0.485376	−	0.874305i	$-0.661317\pi$
$919$	−29.4284	−0.970753	−0.485376	+	0.874305i	$0.661317\pi$
$920$	−0.519567	−0.0171296
$921$	85.3882	2.81364
$922$	−24.1399	−0.795007
$923$	−38.2274	−1.25827
$924$	11.8713	0.390536
$925$	−0.489223	−0.0160855
$926$	25.4482	0.836279
$927$	138.546	4.55044
$928$	6.14594	0.201750
$929$	−44.1944	−1.44997	−0.724986	−	0.688764i	$-0.758154\pi$
$929$	−44.1944	−1.44997	−0.724986	+	0.688764i	$0.758154\pi$
$930$	−25.9792	−0.851891
$931$	−36.4101	−1.19329
$932$	−11.9592	−0.391737
$933$	−35.6336	−1.16659
$934$	−29.7761	−0.974304
$935$	−1.78745	−0.0584558
$936$	−21.9386	−0.717087
$937$	−49.2700	−1.60958	−0.804790	−	0.593559i	$-0.797722\pi$
$937$	−49.2700	−1.60958	−0.804790	+	0.593559i	$0.797722\pi$
$938$	−33.2672	−1.08621
$939$	−19.5130	−0.636782
$940$	−12.4364	−0.405629
$941$	29.8833	0.974168	0.487084	−	0.873355i	$-0.338061\pi$
$941$	29.8833	0.974168	0.487084	+	0.873355i	$0.338061\pi$
$942$	61.6179	2.00762
$943$	1.79213	0.0583599
$944$	−12.5689	−0.409083
$945$	63.5362	2.06683
$946$	−1.00000	−0.0325128
$947$	21.6146	0.702382	0.351191	−	0.936304i	$-0.385777\pi$
$947$	21.6146	0.702382	0.351191	+	0.936304i	$0.385777\pi$
$948$	−28.2223	−0.916616
$949$	−18.8620	−0.612286
$950$	−6.72497	−0.218187
$951$	47.0235	1.52484
$952$	−6.29785	−0.204114
$953$	24.0589	0.779344	0.389672	−	0.920954i	$-0.372588\pi$
$953$	24.0589	0.779344	0.389672	+	0.920954i	$0.372588\pi$
$954$	−70.9143	−2.29593
$955$	8.46474	0.273913
$956$	24.1628	0.781480
$957$	20.7074	0.669376
$958$	16.1037	0.520287
$959$	74.1551	2.39459
$960$	3.36929	0.108743
$961$	28.4532	0.917844
$962$	1.28505	0.0414317
$963$	−12.7802	−0.411838
$964$	−0.901945	−0.0290497
$965$	−16.4508	−0.529569
$966$	−6.16792	−0.198450
$967$	−42.9907	−1.38249	−0.691243	−	0.722622i	$-0.742937\pi$
$967$	−42.9907	−1.38249	−0.691243	+	0.722622i	$0.742937\pi$
$968$	1.00000	0.0321412
$969$	40.5006	1.30107
$970$	4.47632	0.143726
$971$	−53.7588	−1.72520	−0.862601	−	0.505884i	$-0.831166\pi$
$971$	−53.7588	−1.72520	−0.862601	+	0.505884i	$0.831166\pi$
$972$	66.1896	2.12303
$973$	−50.3923	−1.61550
$974$	31.1689	0.998715
$975$	−8.85018	−0.283433
$976$	−1.20105	−0.0384445
$977$	1.83536	0.0587183	0.0293592	−	0.999569i	$-0.490653\pi$
$977$	1.83536	0.0587183	0.0293592	+	0.999569i	$0.490653\pi$
$978$	69.2989	2.21593
$979$	7.19424	0.229929
$980$	5.41417	0.172949
$981$	91.1792	2.91113
$982$	−17.9732	−0.573546
$983$	−25.8334	−0.823958	−0.411979	−	0.911193i	$-0.635162\pi$
$983$	−25.8334	−0.823958	−0.411979	+	0.911193i	$0.635162\pi$
$984$	−11.6216	−0.370483
$985$	−7.21327	−0.229834
$986$	−10.9855	−0.349851
$987$	−147.635	−4.69928
$988$	17.6646	0.561987
$989$	0.519567	0.0165213
$990$	8.35210	0.265447
$991$	11.6354	0.369612	0.184806	−	0.982775i	$-0.440834\pi$
$991$	11.6354	0.369612	0.184806	+	0.982775i	$0.440834\pi$
$992$	−7.71059	−0.244811
$993$	105.289	3.34125
$994$	51.2767	1.62640
$995$	6.19696	0.196457
$996$	−22.6101	−0.716430
$997$	7.52391	0.238284	0.119142	−	0.992877i	$-0.461986\pi$
$997$	7.52391	0.238284	0.119142	+	0.992877i	$0.461986\pi$
$998$	17.2203	0.545100
$999$	−8.82203	−0.279117

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.bd.1.11	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.bd.1.11	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +3.36929 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.36929 q^{6} +3.52337 q^{7} +1.00000 q^{8} +8.35210 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +3.36929 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.36929 q^{6} +3.52337 q^{7} +1.00000 q^{8} +8.35210 q^{9} +1.00000 q^{10} +1.00000 q^{11} +3.36929 q^{12} -2.62672 q^{13} +3.52337 q^{14} +3.36929 q^{15} +1.00000 q^{16} -1.78745 q^{17} +8.35210 q^{18} -6.72497 q^{19} +1.00000 q^{20} +11.8713 q^{21} +1.00000 q^{22} -0.519567 q^{23} +3.36929 q^{24} +1.00000 q^{25} -2.62672 q^{26} +18.0328 q^{27} +3.52337 q^{28} +6.14594 q^{29} +3.36929 q^{30} -7.71059 q^{31} +1.00000 q^{32} +3.36929 q^{33} -1.78745 q^{34} +3.52337 q^{35} +8.35210 q^{36} -0.489223 q^{37} -6.72497 q^{38} -8.85018 q^{39} +1.00000 q^{40} -3.44928 q^{41} +11.8713 q^{42} -1.00000 q^{43} +1.00000 q^{44} +8.35210 q^{45} -0.519567 q^{46} -12.4364 q^{47} +3.36929 q^{48} +5.41417 q^{49} +1.00000 q^{50} -6.02242 q^{51} -2.62672 q^{52} -8.49059 q^{53} +18.0328 q^{54} +1.00000 q^{55} +3.52337 q^{56} -22.6584 q^{57} +6.14594 q^{58} -12.5689 q^{59} +3.36929 q^{60} -1.20105 q^{61} -7.71059 q^{62} +29.4276 q^{63} +1.00000 q^{64} -2.62672 q^{65} +3.36929 q^{66} -9.44187 q^{67} -1.78745 q^{68} -1.75057 q^{69} +3.52337 q^{70} +14.5533 q^{71} +8.35210 q^{72} +7.18081 q^{73} -0.489223 q^{74} +3.36929 q^{75} -6.72497 q^{76} +3.52337 q^{77} -8.85018 q^{78} -8.37633 q^{79} +1.00000 q^{80} +35.7013 q^{81} -3.44928 q^{82} -6.71066 q^{83} +11.8713 q^{84} -1.78745 q^{85} -1.00000 q^{86} +20.7074 q^{87} +1.00000 q^{88} +7.19424 q^{89} +8.35210 q^{90} -9.25492 q^{91} -0.519567 q^{92} -25.9792 q^{93} -12.4364 q^{94} -6.72497 q^{95} +3.36929 q^{96} +4.47632 q^{97} +5.41417 q^{98} +8.35210 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 11 q^{2} + 3 q^{3} + 11 q^{4} + 11 q^{5} + 3 q^{6} + 5 q^{7} + 11 q^{8} + 26 q^{9}+O(q^{10}) \) 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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