LMFDB - Embedded newform 4730.2.a.bc.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4730.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$37.7692401561$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 24x^{9} - x^{8} + 200x^{7} + 14x^{6} - 653x^{5} - 26x^{4} + 620x^{3} - 177x^{2} - 90x + 32 $ x^11 - 24x^9 - x^8 + 200x^7 + 14x^6 - 653x^5 - 26x^4 + 620x^3 - 177x^2 - 90x + 32
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$2.70832$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +2.70832 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.70832 q^{6} +4.04483 q^{7} -1.00000 q^{8} +4.33498 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.70832 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.70832 q^{6} +4.04483 q^{7} -1.00000 q^{8} +4.33498 q^{9} +1.00000 q^{10} +1.00000 q^{11} +2.70832 q^{12} -2.85628 q^{13} -4.04483 q^{14} -2.70832 q^{15} +1.00000 q^{16} -1.89678 q^{17} -4.33498 q^{18} -4.91241 q^{19} -1.00000 q^{20} +10.9547 q^{21} -1.00000 q^{22} +9.36806 q^{23} -2.70832 q^{24} +1.00000 q^{25} +2.85628 q^{26} +3.61555 q^{27} +4.04483 q^{28} +4.37185 q^{29} +2.70832 q^{30} +6.54125 q^{31} -1.00000 q^{32} +2.70832 q^{33} +1.89678 q^{34} -4.04483 q^{35} +4.33498 q^{36} +4.13131 q^{37} +4.91241 q^{38} -7.73572 q^{39} +1.00000 q^{40} -7.48146 q^{41} -10.9547 q^{42} -1.00000 q^{43} +1.00000 q^{44} -4.33498 q^{45} -9.36806 q^{46} -5.08979 q^{47} +2.70832 q^{48} +9.36066 q^{49} -1.00000 q^{50} -5.13709 q^{51} -2.85628 q^{52} -4.71878 q^{53} -3.61555 q^{54} -1.00000 q^{55} -4.04483 q^{56} -13.3044 q^{57} -4.37185 q^{58} +3.28788 q^{59} -2.70832 q^{60} +10.7714 q^{61} -6.54125 q^{62} +17.5343 q^{63} +1.00000 q^{64} +2.85628 q^{65} -2.70832 q^{66} +12.5824 q^{67} -1.89678 q^{68} +25.3717 q^{69} +4.04483 q^{70} +2.60458 q^{71} -4.33498 q^{72} +1.95416 q^{73} -4.13131 q^{74} +2.70832 q^{75} -4.91241 q^{76} +4.04483 q^{77} +7.73572 q^{78} +10.2123 q^{79} -1.00000 q^{80} -3.21288 q^{81} +7.48146 q^{82} +14.6750 q^{83} +10.9547 q^{84} +1.89678 q^{85} +1.00000 q^{86} +11.8404 q^{87} -1.00000 q^{88} -9.18154 q^{89} +4.33498 q^{90} -11.5532 q^{91} +9.36806 q^{92} +17.7158 q^{93} +5.08979 q^{94} +4.91241 q^{95} -2.70832 q^{96} +10.6870 q^{97} -9.36066 q^{98} +4.33498 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 11 q^{2} + 11 q^{4} - 11 q^{5} - 11 q^{8} + 15 q^{9}+O(q^{10}) $ 11 * q - 11 * q^2 + 11 * q^4 - 11 * q^5 - 11 * q^8 + 15 * q^9	$ 11 q - 11 q^{2} + 11 q^{4} - 11 q^{5} - 11 q^{8} + 15 q^{9} + 11 q^{10} + 11 q^{11} - q^{13} + 11 q^{16} - 15 q^{17} - 15 q^{18} + 14 q^{19} - 11 q^{20} + 7 q^{21} - 11 q^{22} - 2 q^{23} + 11 q^{25} + q^{26} + 3 q^{27} + 6 q^{29} + 13 q^{31} - 11 q^{32} + 15 q^{34} + 15 q^{36} + 16 q^{37} - 14 q^{38} + 4 q^{39} + 11 q^{40} - 7 q^{41} - 7 q^{42} - 11 q^{43} + 11 q^{44} - 15 q^{45} + 2 q^{46} - 19 q^{47} + 23 q^{49} - 11 q^{50} + 32 q^{51} - q^{52} - 16 q^{53} - 3 q^{54} - 11 q^{55} - 2 q^{57} - 6 q^{58} + 7 q^{59} + 20 q^{61} - 13 q^{62} + 11 q^{64} + q^{65} + 9 q^{67} - 15 q^{68} + 10 q^{69} + 13 q^{71} - 15 q^{72} + 20 q^{73} - 16 q^{74} + 14 q^{76} - 4 q^{78} + 13 q^{79} - 11 q^{80} + 19 q^{81} + 7 q^{82} - 6 q^{83} + 7 q^{84} + 15 q^{85} + 11 q^{86} - 23 q^{87} - 11 q^{88} + 10 q^{89} + 15 q^{90} + 43 q^{91} - 2 q^{92} + 22 q^{93} + 19 q^{94} - 14 q^{95} + 3 q^{97} - 23 q^{98} + 15 q^{99}+O(q^{100}) $ 11 * q - 11 * q^2 + 11 * q^4 - 11 * q^5 - 11 * q^8 + 15 * q^9 + 11 * q^10 + 11 * q^11 - q^13 + 11 * q^16 - 15 * q^17 - 15 * q^18 + 14 * q^19 - 11 * q^20 + 7 * q^21 - 11 * q^22 - 2 * q^23 + 11 * q^25 + q^26 + 3 * q^27 + 6 * q^29 + 13 * q^31 - 11 * q^32 + 15 * q^34 + 15 * q^36 + 16 * q^37 - 14 * q^38 + 4 * q^39 + 11 * q^40 - 7 * q^41 - 7 * q^42 - 11 * q^43 + 11 * q^44 - 15 * q^45 + 2 * q^46 - 19 * q^47 + 23 * q^49 - 11 * q^50 + 32 * q^51 - q^52 - 16 * q^53 - 3 * q^54 - 11 * q^55 - 2 * q^57 - 6 * q^58 + 7 * q^59 + 20 * q^61 - 13 * q^62 + 11 * q^64 + q^65 + 9 * q^67 - 15 * q^68 + 10 * q^69 + 13 * q^71 - 15 * q^72 + 20 * q^73 - 16 * q^74 + 14 * q^76 - 4 * q^78 + 13 * q^79 - 11 * q^80 + 19 * q^81 + 7 * q^82 - 6 * q^83 + 7 * q^84 + 15 * q^85 + 11 * q^86 - 23 * q^87 - 11 * q^88 + 10 * q^89 + 15 * q^90 + 43 * q^91 - 2 * q^92 + 22 * q^93 + 19 * q^94 - 14 * q^95 + 3 * q^97 - 23 * q^98 + 15 * 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
$3$	2.70832	1.56365	0.781824	−	0.623499i	$-0.214290\pi$
$3$	2.70832	1.56365	0.781824	+	0.623499i	$0.214290\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.70832	−1.10567
$7$	4.04483	1.52880	0.764401	−	0.644741i	$-0.223035\pi$
$7$	4.04483	1.52880	0.764401	+	0.644741i	$0.223035\pi$
$8$	−1.00000	−0.353553
$9$	4.33498	1.44499
$10$	1.00000	0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.70832	0.781824
$13$	−2.85628	−0.792190	−0.396095	−	0.918210i	$-0.629635\pi$
$13$	−2.85628	−0.792190	−0.396095	+	0.918210i	$0.629635\pi$
$14$	−4.04483	−1.08103
$15$	−2.70832	−0.699284
$16$	1.00000	0.250000
$17$	−1.89678	−0.460037	−0.230019	−	0.973186i	$-0.573879\pi$
$17$	−1.89678	−0.460037	−0.230019	+	0.973186i	$0.573879\pi$
$18$	−4.33498	−1.02177
$19$	−4.91241	−1.12698	−0.563492	−	0.826122i	$-0.690542\pi$
$19$	−4.91241	−1.12698	−0.563492	+	0.826122i	$0.690542\pi$
$20$	−1.00000	−0.223607
$21$	10.9547	2.39051
$22$	−1.00000	−0.213201
$23$	9.36806	1.95337	0.976687	−	0.214667i	$-0.0688666\pi$
$23$	9.36806	1.95337	0.976687	+	0.214667i	$0.0688666\pi$
$24$	−2.70832	−0.552833
$25$	1.00000	0.200000
$26$	2.85628	0.560163
$27$	3.61555	0.695814
$28$	4.04483	0.764401
$29$	4.37185	0.811832	0.405916	−	0.913910i	$-0.366952\pi$
$29$	4.37185	0.811832	0.405916	+	0.913910i	$0.366952\pi$
$30$	2.70832	0.494469
$31$	6.54125	1.17484	0.587422	−	0.809281i	$-0.300143\pi$
$31$	6.54125	1.17484	0.587422	+	0.809281i	$0.300143\pi$
$32$	−1.00000	−0.176777
$33$	2.70832	0.471458
$34$	1.89678	0.325295
$35$	−4.04483	−0.683701
$36$	4.33498	0.722497
$37$	4.13131	0.679183	0.339592	−	0.940573i	$-0.389711\pi$
$37$	4.13131	0.679183	0.339592	+	0.940573i	$0.389711\pi$
$38$	4.91241	0.796897
$39$	−7.73572	−1.23871
$40$	1.00000	0.158114
$41$	−7.48146	−1.16841	−0.584204	−	0.811607i	$-0.698593\pi$
$41$	−7.48146	−1.16841	−0.584204	+	0.811607i	$0.698593\pi$
$42$	−10.9547	−1.69034
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	1.00000	0.150756
$45$	−4.33498	−0.646221
$46$	−9.36806	−1.38124
$47$	−5.08979	−0.742422	−0.371211	−	0.928548i	$-0.621057\pi$
$47$	−5.08979	−0.742422	−0.371211	+	0.928548i	$0.621057\pi$
$48$	2.70832	0.390912
$49$	9.36066	1.33724
$50$	−1.00000	−0.141421
$51$	−5.13709	−0.719336
$52$	−2.85628	−0.396095
$53$	−4.71878	−0.648174	−0.324087	−	0.946027i	$-0.605057\pi$
$53$	−4.71878	−0.648174	−0.324087	+	0.946027i	$0.605057\pi$
$54$	−3.61555	−0.492015
$55$	−1.00000	−0.134840
$56$	−4.04483	−0.540513
$57$	−13.3044	−1.76220
$58$	−4.37185	−0.574052
$59$	3.28788	0.428045	0.214022	−	0.976829i	$-0.431343\pi$
$59$	3.28788	0.428045	0.214022	+	0.976829i	$0.431343\pi$
$60$	−2.70832	−0.349642
$61$	10.7714	1.37913	0.689567	−	0.724222i	$-0.257801\pi$
$61$	10.7714	1.37913	0.689567	+	0.724222i	$0.257801\pi$
$62$	−6.54125	−0.830740
$63$	17.5343	2.20911
$64$	1.00000	0.125000
$65$	2.85628	0.354278
$66$	−2.70832	−0.333371
$67$	12.5824	1.53719	0.768595	−	0.639735i	$-0.220956\pi$
$67$	12.5824	1.53719	0.768595	+	0.639735i	$0.220956\pi$
$68$	−1.89678	−0.230019
$69$	25.3717	3.05439
$70$	4.04483	0.483450
$71$	2.60458	0.309106	0.154553	−	0.987984i	$-0.450606\pi$
$71$	2.60458	0.309106	0.154553	+	0.987984i	$0.450606\pi$
$72$	−4.33498	−0.510883
$73$	1.95416	0.228718	0.114359	−	0.993440i	$-0.463519\pi$
$73$	1.95416	0.228718	0.114359	+	0.993440i	$0.463519\pi$
$74$	−4.13131	−0.480255
$75$	2.70832	0.312730
$76$	−4.91241	−0.563492
$77$	4.04483	0.460951
$78$	7.73572	0.875897
$79$	10.2123	1.14897	0.574487	−	0.818513i	$-0.305201\pi$
$79$	10.2123	1.14897	0.574487	+	0.818513i	$0.305201\pi$
$80$	−1.00000	−0.111803
$81$	−3.21288	−0.356986
$82$	7.48146	0.826189
$83$	14.6750	1.61079	0.805393	−	0.592741i	$-0.201954\pi$
$83$	14.6750	1.61079	0.805393	+	0.592741i	$0.201954\pi$
$84$	10.9547	1.19525
$85$	1.89678	0.205735
$86$	1.00000	0.107833
$87$	11.8404	1.26942
$88$	−1.00000	−0.106600
$89$	−9.18154	−0.973242	−0.486621	−	0.873613i	$-0.661771\pi$
$89$	−9.18154	−0.973242	−0.486621	+	0.873613i	$0.661771\pi$
$90$	4.33498	0.456947
$91$	−11.5532	−1.21110
$92$	9.36806	0.976687
$93$	17.7158	1.83704
$94$	5.08979	0.524972
$95$	4.91241	0.504002
$96$	−2.70832	−0.276416
$97$	10.6870	1.08510	0.542549	−	0.840024i	$-0.317459\pi$
$97$	10.6870	1.08510	0.542549	+	0.840024i	$0.317459\pi$
$98$	−9.36066	−0.945570
$99$	4.33498	0.435682
$100$	1.00000	0.100000
$101$	−13.5533	−1.34861	−0.674303	−	0.738455i	$-0.735556\pi$
$101$	−13.5533	−1.34861	−0.674303	+	0.738455i	$0.735556\pi$
$102$	5.13709	0.508647
$103$	−0.255588	−0.0251838	−0.0125919	−	0.999921i	$-0.504008\pi$
$103$	−0.255588	−0.0251838	−0.0125919	+	0.999921i	$0.504008\pi$
$104$	2.85628	0.280081
$105$	−10.9547	−1.06907
$106$	4.71878	0.458328
$107$	5.81507	0.562164	0.281082	−	0.959684i	$-0.409307\pi$
$107$	5.81507	0.562164	0.281082	+	0.959684i	$0.409307\pi$
$108$	3.61555	0.347907
$109$	5.39841	0.517074	0.258537	−	0.966001i	$-0.416760\pi$
$109$	5.39841	0.517074	0.258537	+	0.966001i	$0.416760\pi$
$110$	1.00000	0.0953463
$111$	11.1889	1.06200
$112$	4.04483	0.382201
$113$	−6.52360	−0.613688	−0.306844	−	0.951760i	$-0.599273\pi$
$113$	−6.52360	−0.613688	−0.306844	+	0.951760i	$0.599273\pi$
$114$	13.3044	1.24607
$115$	−9.36806	−0.873576
$116$	4.37185	0.405916
$117$	−12.3819	−1.14471
$118$	−3.28788	−0.302673
$119$	−7.67216	−0.703306
$120$	2.70832	0.247234
$121$	1.00000	0.0909091
$122$	−10.7714	−0.975195
$123$	−20.2622	−1.82698
$124$	6.54125	0.587422
$125$	−1.00000	−0.0894427
$126$	−17.5343	−1.56208
$127$	−9.18735	−0.815245	−0.407623	−	0.913150i	$-0.633642\pi$
$127$	−9.18735	−0.815245	−0.407623	+	0.913150i	$0.633642\pi$
$128$	−1.00000	−0.0883883
$129$	−2.70832	−0.238454
$130$	−2.85628	−0.250512
$131$	20.4633	1.78788	0.893942	−	0.448183i	$-0.147929\pi$
$131$	20.4633	1.78788	0.893942	+	0.448183i	$0.147929\pi$
$132$	2.70832	0.235729
$133$	−19.8699	−1.72294
$134$	−12.5824	−1.08696
$135$	−3.61555	−0.311177
$136$	1.89678	0.162648
$137$	16.4966	1.40940	0.704699	−	0.709506i	$-0.251082\pi$
$137$	16.4966	1.40940	0.704699	+	0.709506i	$0.251082\pi$
$138$	−25.3717	−2.15978
$139$	−19.4736	−1.65173	−0.825866	−	0.563866i	$-0.809314\pi$
$139$	−19.4736	−1.65173	−0.825866	+	0.563866i	$0.809314\pi$
$140$	−4.04483	−0.341851
$141$	−13.7848	−1.16089
$142$	−2.60458	−0.218571
$143$	−2.85628	−0.238854
$144$	4.33498	0.361249
$145$	−4.37185	−0.363062
$146$	−1.95416	−0.161728
$147$	25.3516	2.09097
$148$	4.13131	0.339592
$149$	7.37064	0.603826	0.301913	−	0.953335i	$-0.402375\pi$
$149$	7.37064	0.603826	0.301913	+	0.953335i	$0.402375\pi$
$150$	−2.70832	−0.221133
$151$	−2.43421	−0.198093	−0.0990467	−	0.995083i	$-0.531579\pi$
$151$	−2.43421	−0.198093	−0.0990467	+	0.995083i	$0.531579\pi$
$152$	4.91241	0.398449
$153$	−8.22251	−0.664751
$154$	−4.04483	−0.325942
$155$	−6.54125	−0.525406
$156$	−7.73572	−0.619353
$157$	1.27033	0.101384	0.0506918	−	0.998714i	$-0.483857\pi$
$157$	1.27033	0.101384	0.0506918	+	0.998714i	$0.483857\pi$
$158$	−10.2123	−0.812448
$159$	−12.7799	−1.01352
$160$	1.00000	0.0790569
$161$	37.8922	2.98632
$162$	3.21288	0.252427
$163$	−7.37078	−0.577324	−0.288662	−	0.957431i	$-0.593210\pi$
$163$	−7.37078	−0.577324	−0.288662	+	0.957431i	$0.593210\pi$
$164$	−7.48146	−0.584204
$165$	−2.70832	−0.210842
$166$	−14.6750	−1.13900
$167$	−17.5280	−1.35636	−0.678179	−	0.734897i	$-0.737231\pi$
$167$	−17.5280	−1.35636	−0.678179	+	0.734897i	$0.737231\pi$
$168$	−10.9547	−0.845172
$169$	−4.84166	−0.372435
$170$	−1.89678	−0.145476
$171$	−21.2952	−1.62848
$172$	−1.00000	−0.0762493
$173$	12.9715	0.986207	0.493103	−	0.869971i	$-0.335862\pi$
$173$	12.9715	0.986207	0.493103	+	0.869971i	$0.335862\pi$
$174$	−11.8404	−0.897615
$175$	4.04483	0.305761
$176$	1.00000	0.0753778
$177$	8.90461	0.669311
$178$	9.18154	0.688186
$179$	−18.5448	−1.38611	−0.693053	−	0.720887i	$-0.743735\pi$
$179$	−18.5448	−1.38611	−0.693053	+	0.720887i	$0.743735\pi$
$180$	−4.33498	−0.323110
$181$	11.7870	0.876123	0.438062	−	0.898945i	$-0.355665\pi$
$181$	11.7870	0.876123	0.438062	+	0.898945i	$0.355665\pi$
$182$	11.5532	0.856379
$183$	29.1723	2.15648
$184$	−9.36806	−0.690622
$185$	−4.13131	−0.303740
$186$	−17.7158	−1.29898
$187$	−1.89678	−0.138706
$188$	−5.08979	−0.371211
$189$	14.6243	1.06376
$190$	−4.91241	−0.356383
$191$	19.7824	1.43140	0.715702	−	0.698406i	$-0.246107\pi$
$191$	19.7824	1.43140	0.715702	+	0.698406i	$0.246107\pi$
$192$	2.70832	0.195456
$193$	1.71350	0.123341	0.0616703	−	0.998097i	$-0.480357\pi$
$193$	1.71350	0.123341	0.0616703	+	0.998097i	$0.480357\pi$
$194$	−10.6870	−0.767280
$195$	7.73572	0.553966
$196$	9.36066	0.668619
$197$	−20.7792	−1.48046	−0.740229	−	0.672355i	$-0.765283\pi$
$197$	−20.7792	−1.48046	−0.740229	+	0.672355i	$0.765283\pi$
$198$	−4.33498	−0.308074
$199$	−27.1079	−1.92163	−0.960813	−	0.277197i	$-0.910594\pi$
$199$	−27.1079	−1.92163	−0.960813	+	0.277197i	$0.910594\pi$
$200$	−1.00000	−0.0707107
$201$	34.0773	2.40362
$202$	13.5533	0.953608
$203$	17.6834	1.24113
$204$	−5.13709	−0.359668
$205$	7.48146	0.522528
$206$	0.255588	0.0178077
$207$	40.6104	2.82261
$208$	−2.85628	−0.198047
$209$	−4.91241	−0.339798
$210$	10.9547	0.755945
$211$	−12.8802	−0.886711	−0.443355	−	0.896346i	$-0.646212\pi$
$211$	−12.8802	−0.886711	−0.443355	+	0.896346i	$0.646212\pi$
$212$	−4.71878	−0.324087
$213$	7.05402	0.483333
$214$	−5.81507	−0.397510
$215$	1.00000	0.0681994
$216$	−3.61555	−0.246007
$217$	26.4583	1.79610
$218$	−5.39841	−0.365627
$219$	5.29250	0.357634
$220$	−1.00000	−0.0674200
$221$	5.41774	0.364437
$222$	−11.1889	−0.750950
$223$	14.9881	1.00368	0.501839	−	0.864961i	$-0.332657\pi$
$223$	14.9881	1.00368	0.501839	+	0.864961i	$0.332657\pi$
$224$	−4.04483	−0.270257
$225$	4.33498	0.288999
$226$	6.52360	0.433943
$227$	−13.5172	−0.897165	−0.448582	−	0.893741i	$-0.648071\pi$
$227$	−13.5172	−0.897165	−0.448582	+	0.893741i	$0.648071\pi$
$228$	−13.3044	−0.881102
$229$	27.6701	1.82849	0.914246	−	0.405160i	$-0.132784\pi$
$229$	27.6701	1.82849	0.914246	+	0.405160i	$0.132784\pi$
$230$	9.36806	0.617711
$231$	10.9547	0.720766
$232$	−4.37185	−0.287026
$233$	−17.1457	−1.12325	−0.561627	−	0.827390i	$-0.689825\pi$
$233$	−17.1457	−1.12325	−0.561627	+	0.827390i	$0.689825\pi$
$234$	12.3819	0.809432
$235$	5.08979	0.332021
$236$	3.28788	0.214022
$237$	27.6582	1.79659
$238$	7.67216	0.497312
$239$	−14.1295	−0.913964	−0.456982	−	0.889476i	$-0.651070\pi$
$239$	−14.1295	−0.913964	−0.456982	+	0.889476i	$0.651070\pi$
$240$	−2.70832	−0.174821
$241$	9.61164	0.619140	0.309570	−	0.950877i	$-0.399815\pi$
$241$	9.61164	0.619140	0.309570	+	0.950877i	$0.399815\pi$
$242$	−1.00000	−0.0642824
$243$	−19.5482	−1.25401
$244$	10.7714	0.689567
$245$	−9.36066	−0.598031
$246$	20.2622	1.29187
$247$	14.0312	0.892785
$248$	−6.54125	−0.415370
$249$	39.7445	2.51870
$250$	1.00000	0.0632456
$251$	−15.9616	−1.00748	−0.503742	−	0.863854i	$-0.668044\pi$
$251$	−15.9616	−1.00748	−0.503742	+	0.863854i	$0.668044\pi$
$252$	17.5343	1.10456
$253$	9.36806	0.588965
$254$	9.18735	0.576465
$255$	5.13709	0.321697
$256$	1.00000	0.0625000
$257$	−22.7281	−1.41774	−0.708871	−	0.705338i	$-0.750795\pi$
$257$	−22.7281	−1.41774	−0.708871	+	0.705338i	$0.750795\pi$
$258$	2.70832	0.168612
$259$	16.7105	1.03834
$260$	2.85628	0.177139
$261$	18.9519	1.17309
$262$	−20.4633	−1.26422
$263$	−22.9912	−1.41770	−0.708849	−	0.705360i	$-0.750785\pi$
$263$	−22.9912	−1.41770	−0.708849	+	0.705360i	$0.750785\pi$
$264$	−2.70832	−0.166685
$265$	4.71878	0.289872
$266$	19.8699	1.21830
$267$	−24.8665	−1.52181
$268$	12.5824	0.768595
$269$	−11.9105	−0.726194	−0.363097	−	0.931751i	$-0.618281\pi$
$269$	−11.9105	−0.726194	−0.363097	+	0.931751i	$0.618281\pi$
$270$	3.61555	0.220036
$271$	−2.81686	−0.171112	−0.0855560	−	0.996333i	$-0.527267\pi$
$271$	−2.81686	−0.171112	−0.0855560	+	0.996333i	$0.527267\pi$
$272$	−1.89678	−0.115009
$273$	−31.2897	−1.89374
$274$	−16.4966	−0.996595
$275$	1.00000	0.0603023
$276$	25.3717	1.52719
$277$	−4.42159	−0.265668	−0.132834	−	0.991138i	$-0.542408\pi$
$277$	−4.42159	−0.265668	−0.132834	+	0.991138i	$0.542408\pi$
$278$	19.4736	1.16795
$279$	28.3562	1.69764
$280$	4.04483	0.241725
$281$	−15.3484	−0.915609	−0.457805	−	0.889053i	$-0.651364\pi$
$281$	−15.3484	−0.915609	−0.457805	+	0.889053i	$0.651364\pi$
$282$	13.7848	0.820871
$283$	24.7174	1.46930	0.734648	−	0.678448i	$-0.237347\pi$
$283$	24.7174	1.46930	0.734648	+	0.678448i	$0.237347\pi$
$284$	2.60458	0.154553
$285$	13.3044	0.788082
$286$	2.85628	0.168895
$287$	−30.2612	−1.78627
$288$	−4.33498	−0.255441
$289$	−13.4022	−0.788366
$290$	4.37185	0.256724
$291$	28.9437	1.69671
$292$	1.95416	0.114359
$293$	−23.6853	−1.38371	−0.691854	−	0.722037i	$-0.743206\pi$
$293$	−23.6853	−1.38371	−0.691854	+	0.722037i	$0.743206\pi$
$294$	−25.3516	−1.47854
$295$	−3.28788	−0.191428
$296$	−4.13131	−0.240127
$297$	3.61555	0.209796
$298$	−7.37064	−0.426969
$299$	−26.7578	−1.54744
$300$	2.70832	0.156365
$301$	−4.04483	−0.233140
$302$	2.43421	0.140073
$303$	−36.7067	−2.10874
$304$	−4.91241	−0.281746
$305$	−10.7714	−0.616768
$306$	8.22251	0.470050
$307$	34.3695	1.96157	0.980787	−	0.195082i	$-0.0624973\pi$
$307$	34.3695	1.96157	0.980787	+	0.195082i	$0.0624973\pi$
$308$	4.04483	0.230476
$309$	−0.692214	−0.0393787
$310$	6.54125	0.371518
$311$	6.87137	0.389640	0.194820	−	0.980839i	$-0.437588\pi$
$311$	6.87137	0.389640	0.194820	+	0.980839i	$0.437588\pi$
$312$	7.73572	0.437949
$313$	23.0116	1.30069	0.650345	−	0.759639i	$-0.274624\pi$
$313$	23.0116	1.30069	0.650345	+	0.759639i	$0.274624\pi$
$314$	−1.27033	−0.0716890
$315$	−17.5343	−0.987944
$316$	10.2123	0.574487
$317$	32.2079	1.80898	0.904488	−	0.426498i	$-0.140253\pi$
$317$	32.2079	1.80898	0.904488	+	0.426498i	$0.140253\pi$
$318$	12.7799	0.716664
$319$	4.37185	0.244777
$320$	−1.00000	−0.0559017
$321$	15.7490	0.879026
$322$	−37.8922	−2.11165
$323$	9.31776	0.518454
$324$	−3.21288	−0.178493
$325$	−2.85628	−0.158438
$326$	7.37078	0.408230
$327$	14.6206	0.808522
$328$	7.48146	0.413095
$329$	−20.5874	−1.13502
$330$	2.70832	0.149088
$331$	−1.27623	−0.0701479	−0.0350740	−	0.999385i	$-0.511167\pi$
$331$	−1.27623	−0.0701479	−0.0350740	+	0.999385i	$0.511167\pi$
$332$	14.6750	0.805393
$333$	17.9092	0.981415
$334$	17.5280	0.959090
$335$	−12.5824	−0.687453
$336$	10.9547	0.597627
$337$	−1.21714	−0.0663020	−0.0331510	−	0.999450i	$-0.510554\pi$
$337$	−1.21714	−0.0663020	−0.0331510	+	0.999450i	$0.510554\pi$
$338$	4.84166	0.263351
$339$	−17.6680	−0.959593
$340$	1.89678	0.102867
$341$	6.54125	0.354229
$342$	21.2952	1.15151
$343$	9.54849	0.515570
$344$	1.00000	0.0539164
$345$	−25.3717	−1.36596
$346$	−12.9715	−0.697354
$347$	7.83504	0.420607	0.210303	−	0.977636i	$-0.432555\pi$
$347$	7.83504	0.420607	0.210303	+	0.977636i	$0.432555\pi$
$348$	11.8404	0.634710
$349$	9.38789	0.502522	0.251261	−	0.967919i	$-0.419155\pi$
$349$	9.38789	0.502522	0.251261	+	0.967919i	$0.419155\pi$
$350$	−4.04483	−0.216205
$351$	−10.3270	−0.551217
$352$	−1.00000	−0.0533002
$353$	−18.2133	−0.969396	−0.484698	−	0.874682i	$-0.661071\pi$
$353$	−18.2133	−0.969396	−0.484698	+	0.874682i	$0.661071\pi$
$354$	−8.90461	−0.473275
$355$	−2.60458	−0.138237
$356$	−9.18154	−0.486621
$357$	−20.7786	−1.09972
$358$	18.5448	0.980124
$359$	−24.3713	−1.28627	−0.643135	−	0.765753i	$-0.722367\pi$
$359$	−24.3713	−1.28627	−0.643135	+	0.765753i	$0.722367\pi$
$360$	4.33498	0.228474
$361$	5.13173	0.270091
$362$	−11.7870	−0.619513
$363$	2.70832	0.142150
$364$	−11.5532	−0.605551
$365$	−1.95416	−0.102286
$366$	−29.1723	−1.52486
$367$	−4.16844	−0.217591	−0.108795	−	0.994064i	$-0.534699\pi$
$367$	−4.16844	−0.217591	−0.108795	+	0.994064i	$0.534699\pi$
$368$	9.36806	0.488344
$369$	−32.4320	−1.68834
$370$	4.13131	0.214777
$371$	−19.0867	−0.990930
$372$	17.7158	0.918521
$373$	3.31919	0.171861	0.0859304	−	0.996301i	$-0.472614\pi$
$373$	3.31919	0.171861	0.0859304	+	0.996301i	$0.472614\pi$
$374$	1.89678	0.0980802
$375$	−2.70832	−0.139857
$376$	5.08979	0.262486
$377$	−12.4872	−0.643125
$378$	−14.6243	−0.752193
$379$	−4.23557	−0.217567	−0.108783	−	0.994065i	$-0.534695\pi$
$379$	−4.23557	−0.217567	−0.108783	+	0.994065i	$0.534695\pi$
$380$	4.91241	0.252001
$381$	−24.8823	−1.27476
$382$	−19.7824	−1.01216
$383$	30.2887	1.54768	0.773840	−	0.633382i	$-0.218334\pi$
$383$	30.2887	1.54768	0.773840	+	0.633382i	$0.218334\pi$
$384$	−2.70832	−0.138208
$385$	−4.04483	−0.206144
$386$	−1.71350	−0.0872149
$387$	−4.33498	−0.220360
$388$	10.6870	0.542549
$389$	21.2137	1.07558	0.537788	−	0.843080i	$-0.319260\pi$
$389$	21.2137	1.07558	0.537788	+	0.843080i	$0.319260\pi$
$390$	−7.73572	−0.391713
$391$	−17.7692	−0.898625
$392$	−9.36066	−0.472785
$393$	55.4210	2.79562
$394$	20.7792	1.04684
$395$	−10.2123	−0.513837
$396$	4.33498	0.217841
$397$	−14.5716	−0.731326	−0.365663	−	0.930747i	$-0.619158\pi$
$397$	−14.5716	−0.731326	−0.365663	+	0.930747i	$0.619158\pi$
$398$	27.1079	1.35879
$399$	−53.8139	−2.69406
$400$	1.00000	0.0500000
$401$	−0.267924	−0.0133795	−0.00668974	−	0.999978i	$-0.502129\pi$
$401$	−0.267924	−0.0133795	−0.00668974	+	0.999978i	$0.502129\pi$
$402$	−34.0773	−1.69962
$403$	−18.6837	−0.930699
$404$	−13.5533	−0.674303
$405$	3.21288	0.159649
$406$	−17.6834	−0.877612
$407$	4.13131	0.204781
$408$	5.13709	0.254324
$409$	32.1069	1.58758	0.793791	−	0.608191i	$-0.208104\pi$
$409$	32.1069	1.58758	0.793791	+	0.608191i	$0.208104\pi$
$410$	−7.48146	−0.369483
$411$	44.6780	2.20380
$412$	−0.255588	−0.0125919
$413$	13.2989	0.654396
$414$	−40.6104	−1.99589
$415$	−14.6750	−0.720366
$416$	2.85628	0.140041
$417$	−52.7408	−2.58273
$418$	4.91241	0.240274
$419$	10.1712	0.496893	0.248447	−	0.968646i	$-0.420080\pi$
$419$	10.1712	0.496893	0.248447	+	0.968646i	$0.420080\pi$
$420$	−10.9547	−0.534534
$421$	18.2272	0.888341	0.444171	−	0.895942i	$-0.353498\pi$
$421$	18.2272	0.888341	0.444171	+	0.895942i	$0.353498\pi$
$422$	12.8802	0.626999
$423$	−22.0642	−1.07280
$424$	4.71878	0.229164
$425$	−1.89678	−0.0920074
$426$	−7.05402	−0.341768
$427$	43.5684	2.10842
$428$	5.81507	0.281082
$429$	−7.73572	−0.373484
$430$	−1.00000	−0.0482243
$431$	−22.7041	−1.09362	−0.546808	−	0.837258i	$-0.684157\pi$
$431$	−22.7041	−1.09362	−0.546808	+	0.837258i	$0.684157\pi$
$432$	3.61555	0.173953
$433$	−9.93944	−0.477659	−0.238830	−	0.971062i	$-0.576764\pi$
$433$	−9.93944	−0.477659	−0.238830	+	0.971062i	$0.576764\pi$
$434$	−26.4583	−1.27004
$435$	−11.8404	−0.567702
$436$	5.39841	0.258537
$437$	−46.0197	−2.20142
$438$	−5.29250	−0.252885
$439$	−33.7547	−1.61102	−0.805512	−	0.592579i	$-0.798110\pi$
$439$	−33.7547	−1.61102	−0.805512	+	0.592579i	$0.798110\pi$
$440$	1.00000	0.0476731
$441$	40.5783	1.93230
$442$	−5.41774	−0.257696
$443$	14.8799	0.706964	0.353482	−	0.935441i	$-0.384998\pi$
$443$	14.8799	0.706964	0.353482	+	0.935441i	$0.384998\pi$
$444$	11.1889	0.531002
$445$	9.18154	0.435247
$446$	−14.9881	−0.709708
$447$	19.9620	0.944171
$448$	4.04483	0.191100
$449$	−16.2263	−0.765767	−0.382883	−	0.923797i	$-0.625069\pi$
$449$	−16.2263	−0.765767	−0.382883	+	0.923797i	$0.625069\pi$
$450$	−4.33498	−0.204353
$451$	−7.48146	−0.352288
$452$	−6.52360	−0.306844
$453$	−6.59262	−0.309748
$454$	13.5172	0.634391
$455$	11.5532	0.541621
$456$	13.3044	0.623033
$457$	21.4406	1.00295	0.501475	−	0.865172i	$-0.332791\pi$
$457$	21.4406	1.00295	0.501475	+	0.865172i	$0.332791\pi$
$458$	−27.6701	−1.29294
$459$	−6.85792	−0.320100
$460$	−9.36806	−0.436788
$461$	24.1546	1.12499	0.562496	−	0.826800i	$-0.309841\pi$
$461$	24.1546	1.12499	0.562496	+	0.826800i	$0.309841\pi$
$462$	−10.9547	−0.509658
$463$	−16.7099	−0.776573	−0.388287	−	0.921539i	$-0.626933\pi$
$463$	−16.7099	−0.776573	−0.388287	+	0.921539i	$0.626933\pi$
$464$	4.37185	0.202958
$465$	−17.7158	−0.821550
$466$	17.1457	0.794261
$467$	5.35756	0.247918	0.123959	−	0.992287i	$-0.460441\pi$
$467$	5.35756	0.247918	0.123959	+	0.992287i	$0.460441\pi$
$468$	−12.3819	−0.572355
$469$	50.8939	2.35006
$470$	−5.08979	−0.234775
$471$	3.44046	0.158528
$472$	−3.28788	−0.151337
$473$	−1.00000	−0.0459800
$474$	−27.6582	−1.27038
$475$	−4.91241	−0.225397
$476$	−7.67216	−0.351653
$477$	−20.4558	−0.936607
$478$	14.1295	0.646270
$479$	9.93243	0.453824	0.226912	−	0.973915i	$-0.427137\pi$
$479$	9.93243	0.453824	0.226912	+	0.973915i	$0.427137\pi$
$480$	2.70832	0.123617
$481$	−11.8002	−0.538042
$482$	−9.61164	−0.437798
$483$	102.624	4.66956
$484$	1.00000	0.0454545
$485$	−10.6870	−0.485271
$486$	19.5482	0.886722
$487$	−38.9964	−1.76709	−0.883547	−	0.468342i	$-0.844851\pi$
$487$	−38.9964	−1.76709	−0.883547	+	0.468342i	$0.844851\pi$
$488$	−10.7714	−0.487598
$489$	−19.9624	−0.902732
$490$	9.36066	0.422872
$491$	−11.2544	−0.507905	−0.253953	−	0.967217i	$-0.581731\pi$
$491$	−11.2544	−0.507905	−0.253953	+	0.967217i	$0.581731\pi$
$492$	−20.2622	−0.913489
$493$	−8.29244	−0.373473
$494$	−14.0312	−0.631294
$495$	−4.33498	−0.194843
$496$	6.54125	0.293711
$497$	10.5351	0.472563
$498$	−39.7445	−1.78099
$499$	−24.7057	−1.10598	−0.552990	−	0.833188i	$-0.686513\pi$
$499$	−24.7057	−1.10598	−0.552990	+	0.833188i	$0.686513\pi$
$500$	−1.00000	−0.0447214
$501$	−47.4714	−2.12087
$502$	15.9616	0.712399
$503$	−21.2900	−0.949274	−0.474637	−	0.880182i	$-0.657421\pi$
$503$	−21.2900	−0.949274	−0.474637	+	0.880182i	$0.657421\pi$
$504$	−17.5343	−0.781039
$505$	13.5533	0.603115
$506$	−9.36806	−0.416461
$507$	−13.1127	−0.582357
$508$	−9.18735	−0.407623
$509$	−15.0541	−0.667262	−0.333631	−	0.942704i	$-0.608274\pi$
$509$	−15.0541	−0.667262	−0.333631	+	0.942704i	$0.608274\pi$
$510$	−5.13709	−0.227474
$511$	7.90427	0.349664
$512$	−1.00000	−0.0441942
$513$	−17.7611	−0.784171
$514$	22.7281	1.00250
$515$	0.255588	0.0112626
$516$	−2.70832	−0.119227
$517$	−5.08979	−0.223849
$518$	−16.7105	−0.734215
$519$	35.1310	1.54208
$520$	−2.85628	−0.125256
$521$	33.2202	1.45540	0.727702	−	0.685893i	$-0.240588\pi$
$521$	33.2202	1.45540	0.727702	+	0.685893i	$0.240588\pi$
$522$	−18.9519	−0.829502
$523$	5.89141	0.257613	0.128807	−	0.991670i	$-0.458885\pi$
$523$	5.89141	0.257613	0.128807	+	0.991670i	$0.458885\pi$
$524$	20.4633	0.893942
$525$	10.9547	0.478102
$526$	22.9912	1.00246
$527$	−12.4073	−0.540472
$528$	2.70832	0.117864
$529$	64.7605	2.81567
$530$	−4.71878	−0.204971
$531$	14.2529	0.618522
$532$	−19.8699	−0.861468
$533$	21.3692	0.925601
$534$	24.8665	1.07608
$535$	−5.81507	−0.251407
$536$	−12.5824	−0.543479
$537$	−50.2253	−2.16738
$538$	11.9105	0.513496
$539$	9.36066	0.403192
$540$	−3.61555	−0.155589
$541$	−19.9432	−0.857426	−0.428713	−	0.903441i	$-0.641033\pi$
$541$	−19.9432	−0.857426	−0.428713	+	0.903441i	$0.641033\pi$
$542$	2.81686	0.120994
$543$	31.9230	1.36995
$544$	1.89678	0.0813238
$545$	−5.39841	−0.231243
$546$	31.2897	1.33907
$547$	−14.8281	−0.634003	−0.317002	−	0.948425i	$-0.602676\pi$
$547$	−14.8281	−0.634003	−0.317002	+	0.948425i	$0.602676\pi$
$548$	16.4966	0.704699
$549$	46.6938	1.99284
$550$	−1.00000	−0.0426401
$551$	−21.4763	−0.914921
$552$	−25.3717	−1.07989
$553$	41.3071	1.75656
$554$	4.42159	0.187855
$555$	−11.1889	−0.474942
$556$	−19.4736	−0.825866
$557$	16.7162	0.708288	0.354144	−	0.935191i	$-0.384772\pi$
$557$	16.7162	0.708288	0.354144	+	0.935191i	$0.384772\pi$
$558$	−28.3562	−1.20041
$559$	2.85628	0.120808
$560$	−4.04483	−0.170925
$561$	−5.13709	−0.216888
$562$	15.3484	0.647433
$563$	5.78145	0.243659	0.121829	−	0.992551i	$-0.461124\pi$
$563$	5.78145	0.243659	0.121829	+	0.992551i	$0.461124\pi$
$564$	−13.7848	−0.580444
$565$	6.52360	0.274450
$566$	−24.7174	−1.03895
$567$	−12.9955	−0.545762
$568$	−2.60458	−0.109286
$569$	−33.0360	−1.38494	−0.692470	−	0.721447i	$-0.743478\pi$
$569$	−33.0360	−1.38494	−0.692470	+	0.721447i	$0.743478\pi$
$570$	−13.3044	−0.557258
$571$	23.4619	0.981848	0.490924	−	0.871202i	$-0.336659\pi$
$571$	23.4619	0.981848	0.490924	+	0.871202i	$0.336659\pi$
$572$	−2.85628	−0.119427
$573$	53.5770	2.23821
$574$	30.2612	1.26308
$575$	9.36806	0.390675
$576$	4.33498	0.180624
$577$	−4.41345	−0.183734	−0.0918671	−	0.995771i	$-0.529284\pi$
$577$	−4.41345	−0.183734	−0.0918671	+	0.995771i	$0.529284\pi$
$578$	13.4022	0.557459
$579$	4.64071	0.192861
$580$	−4.37185	−0.181531
$581$	59.3578	2.46257
$582$	−28.9437	−1.19976
$583$	−4.71878	−0.195432
$584$	−1.95416	−0.0808639
$585$	12.3819	0.511930
$586$	23.6853	0.978429
$587$	−20.4850	−0.845506	−0.422753	−	0.906245i	$-0.638936\pi$
$587$	−20.4850	−0.845506	−0.422753	+	0.906245i	$0.638936\pi$
$588$	25.3516	1.04548
$589$	−32.1333	−1.32403
$590$	3.28788	0.135360
$591$	−56.2767	−2.31491
$592$	4.13131	0.169796
$593$	−1.98781	−0.0816294	−0.0408147	−	0.999167i	$-0.512995\pi$
$593$	−1.98781	−0.0816294	−0.0408147	+	0.999167i	$0.512995\pi$
$594$	−3.61555	−0.148348
$595$	7.67216	0.314528
$596$	7.37064	0.301913
$597$	−73.4167	−3.00475
$598$	26.7578	1.09421
$599$	−19.5327	−0.798085	−0.399043	−	0.916932i	$-0.630657\pi$
$599$	−19.5327	−0.798085	−0.399043	+	0.916932i	$0.630657\pi$
$600$	−2.70832	−0.110567
$601$	25.8154	1.05303	0.526515	−	0.850166i	$-0.323498\pi$
$601$	25.8154	1.05303	0.526515	+	0.850166i	$0.323498\pi$
$602$	4.04483	0.164855
$603$	54.5447	2.22123
$604$	−2.43421	−0.0990467
$605$	−1.00000	−0.0406558
$606$	36.7067	1.49111
$607$	−30.6337	−1.24339	−0.621693	−	0.783261i	$-0.713555\pi$
$607$	−30.6337	−1.24339	−0.621693	+	0.783261i	$0.713555\pi$
$608$	4.91241	0.199224
$609$	47.8923	1.94069
$610$	10.7714	0.436121
$611$	14.5379	0.588140
$612$	−8.22251	−0.332375
$613$	−30.2220	−1.22066	−0.610329	−	0.792148i	$-0.708963\pi$
$613$	−30.2220	−1.22066	−0.610329	+	0.792148i	$0.708963\pi$
$614$	−34.3695	−1.38704
$615$	20.2622	0.817049
$616$	−4.04483	−0.162971
$617$	15.2824	0.615248	0.307624	−	0.951508i	$-0.400466\pi$
$617$	15.2824	0.615248	0.307624	+	0.951508i	$0.400466\pi$
$618$	0.692214	0.0278449
$619$	4.01260	0.161280	0.0806399	−	0.996743i	$-0.474304\pi$
$619$	4.01260	0.161280	0.0806399	+	0.996743i	$0.474304\pi$
$620$	−6.54125	−0.262703
$621$	33.8707	1.35919
$622$	−6.87137	−0.275517
$623$	−37.1378	−1.48789
$624$	−7.73572	−0.309676
$625$	1.00000	0.0400000
$626$	−23.0116	−0.919727
$627$	−13.3044	−0.531325
$628$	1.27033	0.0506918
$629$	−7.83619	−0.312449
$630$	17.5343	0.698582
$631$	43.0031	1.71193	0.855963	−	0.517037i	$-0.172965\pi$
$631$	43.0031	1.71193	0.855963	+	0.517037i	$0.172965\pi$
$632$	−10.2123	−0.406224
$633$	−34.8837	−1.38650
$634$	−32.2079	−1.27914
$635$	9.18735	0.364589
$636$	−12.7799	−0.506758
$637$	−26.7367	−1.05935
$638$	−4.37185	−0.173083
$639$	11.2908	0.446657
$640$	1.00000	0.0395285
$641$	33.2712	1.31413	0.657067	−	0.753832i	$-0.271797\pi$
$641$	33.2712	1.31413	0.657067	+	0.753832i	$0.271797\pi$
$642$	−15.7490	−0.621565
$643$	27.7268	1.09344	0.546720	−	0.837316i	$-0.315876\pi$
$643$	27.7268	1.09344	0.546720	+	0.837316i	$0.315876\pi$
$644$	37.8922	1.49316
$645$	2.70832	0.106640
$646$	−9.31776	−0.366602
$647$	−47.2651	−1.85818	−0.929091	−	0.369850i	$-0.879409\pi$
$647$	−47.2651	−1.85818	−0.929091	+	0.369850i	$0.879409\pi$
$648$	3.21288	0.126214
$649$	3.28788	0.129060
$650$	2.85628	0.112033
$651$	71.6574	2.80847
$652$	−7.37078	−0.288662
$653$	5.77390	0.225950	0.112975	−	0.993598i	$-0.463962\pi$
$653$	5.77390	0.225950	0.112975	+	0.993598i	$0.463962\pi$
$654$	−14.6206	−0.571711
$655$	−20.4633	−0.799566
$656$	−7.48146	−0.292102
$657$	8.47127	0.330496
$658$	20.5874	0.802579
$659$	−18.6577	−0.726801	−0.363400	−	0.931633i	$-0.618384\pi$
$659$	−18.6577	−0.726801	−0.363400	+	0.931633i	$0.618384\pi$
$660$	−2.70832	−0.105421
$661$	17.3663	0.675472	0.337736	−	0.941241i	$-0.390339\pi$
$661$	17.3663	0.675472	0.337736	+	0.941241i	$0.390339\pi$
$662$	1.27623	0.0496021
$663$	14.6730	0.569851
$664$	−14.6750	−0.569499
$665$	19.8699	0.770520
$666$	−17.9092	−0.693966
$667$	40.9557	1.58581
$668$	−17.5280	−0.678179
$669$	40.5926	1.56940
$670$	12.5824	0.486102
$671$	10.7714	0.415825
$672$	−10.9547	−0.422586
$673$	−18.1960	−0.701404	−0.350702	−	0.936487i	$-0.614057\pi$
$673$	−18.1960	−0.701404	−0.350702	+	0.936487i	$0.614057\pi$
$674$	1.21714	0.0468826
$675$	3.61555	0.139163
$676$	−4.84166	−0.186218
$677$	−40.4919	−1.55623	−0.778115	−	0.628122i	$-0.783824\pi$
$677$	−40.4919	−1.55623	−0.778115	+	0.628122i	$0.783824\pi$
$678$	17.6680	0.678534
$679$	43.2270	1.65890
$680$	−1.89678	−0.0727382
$681$	−36.6087	−1.40285
$682$	−6.54125	−0.250477
$683$	−1.20560	−0.0461310	−0.0230655	−	0.999734i	$-0.507343\pi$
$683$	−1.20560	−0.0461310	−0.0230655	+	0.999734i	$0.507343\pi$
$684$	−21.2952	−0.814242
$685$	−16.4966	−0.630302
$686$	−9.54849	−0.364563
$687$	74.9394	2.85912
$688$	−1.00000	−0.0381246
$689$	13.4782	0.513477
$690$	25.3717	0.965883
$691$	−14.5834	−0.554780	−0.277390	−	0.960757i	$-0.589469\pi$
$691$	−14.5834	−0.554780	−0.277390	+	0.960757i	$0.589469\pi$
$692$	12.9715	0.493103
$693$	17.5343	0.666072
$694$	−7.83504	−0.297414
$695$	19.4736	0.738677
$696$	−11.8404	−0.448808
$697$	14.1907	0.537511
$698$	−9.38789	−0.355337
$699$	−46.4361	−1.75637
$700$	4.04483	0.152880
$701$	27.6308	1.04360	0.521800	−	0.853068i	$-0.325261\pi$
$701$	27.6308	1.04360	0.521800	+	0.853068i	$0.325261\pi$
$702$	10.3270	0.389769
$703$	−20.2947	−0.765428
$704$	1.00000	0.0376889
$705$	13.7848	0.519165
$706$	18.2133	0.685467
$707$	−54.8209	−2.06175
$708$	8.90461	0.334656
$709$	39.9186	1.49917	0.749587	−	0.661906i	$-0.230252\pi$
$709$	39.9186	1.49917	0.749587	+	0.661906i	$0.230252\pi$
$710$	2.60458	0.0977480
$711$	44.2702	1.66026
$712$	9.18154	0.344093
$713$	61.2788	2.29491
$714$	20.7786	0.777621
$715$	2.85628	0.106819
$716$	−18.5448	−0.693053
$717$	−38.2673	−1.42912
$718$	24.3713	0.909530
$719$	17.1626	0.640058	0.320029	−	0.947408i	$-0.396307\pi$
$719$	17.1626	0.640058	0.320029	+	0.947408i	$0.396307\pi$
$720$	−4.33498	−0.161555
$721$	−1.03381	−0.0385011
$722$	−5.13173	−0.190983
$723$	26.0314	0.968117
$724$	11.7870	0.438062
$725$	4.37185	0.162366
$726$	−2.70832	−0.100515
$727$	−30.4282	−1.12852	−0.564261	−	0.825597i	$-0.690839\pi$
$727$	−30.4282	−1.12852	−0.564261	+	0.825597i	$0.690839\pi$
$728$	11.5532	0.428189
$729$	−43.3040	−1.60385
$730$	1.95416	0.0723269
$731$	1.89678	0.0701550
$732$	29.1723	1.07824
$733$	−43.3507	−1.60120	−0.800598	−	0.599202i	$-0.795485\pi$
$733$	−43.3507	−1.60120	−0.800598	+	0.599202i	$0.795485\pi$
$734$	4.16844	0.153860
$735$	−25.3516	−0.935110
$736$	−9.36806	−0.345311
$737$	12.5824	0.463480
$738$	32.4320	1.19384
$739$	6.10610	0.224617	0.112308	−	0.993673i	$-0.464176\pi$
$739$	6.10610	0.224617	0.112308	+	0.993673i	$0.464176\pi$
$740$	−4.13131	−0.151870
$741$	38.0010	1.39600
$742$	19.0867	0.700693
$743$	22.1516	0.812664	0.406332	−	0.913726i	$-0.366808\pi$
$743$	22.1516	0.812664	0.406332	+	0.913726i	$0.366808\pi$
$744$	−17.7158	−0.649492
$745$	−7.37064	−0.270039
$746$	−3.31919	−0.121524
$747$	63.6157	2.32758
$748$	−1.89678	−0.0693532
$749$	23.5210	0.859437
$750$	2.70832	0.0988938
$751$	28.1991	1.02900	0.514500	−	0.857491i	$-0.327978\pi$
$751$	28.1991	1.02900	0.514500	+	0.857491i	$0.327978\pi$
$752$	−5.08979	−0.185606
$753$	−43.2289	−1.57535
$754$	12.4872	0.454758
$755$	2.43421	0.0885900
$756$	14.6243	0.531881
$757$	27.4697	0.998404	0.499202	−	0.866486i	$-0.333627\pi$
$757$	27.4697	0.998404	0.499202	+	0.866486i	$0.333627\pi$
$758$	4.23557	0.153843
$759$	25.3717	0.920933
$760$	−4.91241	−0.178192
$761$	25.9156	0.939441	0.469720	−	0.882815i	$-0.344355\pi$
$761$	25.9156	0.939441	0.469720	+	0.882815i	$0.344355\pi$
$762$	24.8823	0.901389
$763$	21.8357	0.790505
$764$	19.7824	0.715702
$765$	8.22251	0.297286
$766$	−30.2887	−1.09437
$767$	−9.39110	−0.339093
$768$	2.70832	0.0977280
$769$	27.3732	0.987104	0.493552	−	0.869716i	$-0.335698\pi$
$769$	27.3732	0.987104	0.493552	+	0.869716i	$0.335698\pi$
$770$	4.04483	0.145766
$771$	−61.5550	−2.21685
$772$	1.71350	0.0616703
$773$	4.67904	0.168293	0.0841466	−	0.996453i	$-0.473184\pi$
$773$	4.67904	0.168293	0.0841466	+	0.996453i	$0.473184\pi$
$774$	4.33498	0.155818
$775$	6.54125	0.234969
$776$	−10.6870	−0.383640
$777$	45.2572	1.62359
$778$	−21.2137	−0.760548
$779$	36.7520	1.31678
$780$	7.73572	0.276983
$781$	2.60458	0.0931990
$782$	17.7692	0.635424
$783$	15.8067	0.564884
$784$	9.36066	0.334309
$785$	−1.27033	−0.0453401
$786$	−55.4210	−1.97680
$787$	−30.7752	−1.09702	−0.548509	−	0.836145i	$-0.684804\pi$
$787$	−30.7752	−1.09702	−0.548509	+	0.836145i	$0.684804\pi$
$788$	−20.7792	−0.740229
$789$	−62.2675	−2.21678
$790$	10.2123	0.363338
$791$	−26.3869	−0.938209
$792$	−4.33498	−0.154037
$793$	−30.7661	−1.09254
$794$	14.5716	0.517126
$795$	12.7799	0.453258
$796$	−27.1079	−0.960813
$797$	−35.0881	−1.24288	−0.621441	−	0.783461i	$-0.713453\pi$
$797$	−35.0881	−1.24288	−0.621441	+	0.783461i	$0.713453\pi$
$798$	53.8139	1.90499
$799$	9.65422	0.341542
$800$	−1.00000	−0.0353553
$801$	−39.8018	−1.40633
$802$	0.267924	0.00946072
$803$	1.95416	0.0689610
$804$	34.0773	1.20181
$805$	−37.8922	−1.33552
$806$	18.6837	0.658104
$807$	−32.2573	−1.13551
$808$	13.5533	0.476804
$809$	−16.9260	−0.595088	−0.297544	−	0.954708i	$-0.596167\pi$
$809$	−16.9260	−0.595088	−0.297544	+	0.954708i	$0.596167\pi$
$810$	−3.21288	−0.112889
$811$	9.47222	0.332615	0.166307	−	0.986074i	$-0.446816\pi$
$811$	9.47222	0.332615	0.166307	+	0.986074i	$0.446816\pi$
$812$	17.6834	0.620566
$813$	−7.62895	−0.267559
$814$	−4.13131	−0.144802
$815$	7.37078	0.258187
$816$	−5.13709	−0.179834
$817$	4.91241	0.171863
$818$	−32.1069	−1.12259
$819$	−50.0828	−1.75004
$820$	7.48146	0.261264
$821$	24.9322	0.870139	0.435070	−	0.900397i	$-0.356724\pi$
$821$	24.9322	0.870139	0.435070	+	0.900397i	$0.356724\pi$
$822$	−44.6780	−1.55832
$823$	−46.4329	−1.61855	−0.809275	−	0.587430i	$-0.800140\pi$
$823$	−46.4329	−1.61855	−0.809275	+	0.587430i	$0.800140\pi$
$824$	0.255588	0.00890383
$825$	2.70832	0.0942915
$826$	−13.2989	−0.462728
$827$	−17.8977	−0.622364	−0.311182	−	0.950350i	$-0.600725\pi$
$827$	−17.8977	−0.622364	−0.311182	+	0.950350i	$0.600725\pi$
$828$	40.6104	1.41131
$829$	−12.8051	−0.444739	−0.222369	−	0.974963i	$-0.571379\pi$
$829$	−12.8051	−0.444739	−0.222369	+	0.974963i	$0.571379\pi$
$830$	14.6750	0.509375
$831$	−11.9751	−0.415411
$832$	−2.85628	−0.0990237
$833$	−17.7551	−0.615179
$834$	52.7408	1.82626
$835$	17.5280	0.606582
$836$	−4.91241	−0.169899
$837$	23.6503	0.817472
$838$	−10.1712	−0.351357
$839$	−20.4350	−0.705496	−0.352748	−	0.935718i	$-0.614753\pi$
$839$	−20.4350	−0.705496	−0.352748	+	0.935718i	$0.614753\pi$
$840$	10.9547	0.377973
$841$	−9.88692	−0.340928
$842$	−18.2272	−0.628152
$843$	−41.5683	−1.43169
$844$	−12.8802	−0.443355
$845$	4.84166	0.166558
$846$	22.0642	0.758581
$847$	4.04483	0.138982
$848$	−4.71878	−0.162043
$849$	66.9425	2.29746
$850$	1.89678	0.0650591
$851$	38.7023	1.32670
$852$	7.05402	0.241667
$853$	−8.48540	−0.290535	−0.145267	−	0.989392i	$-0.546404\pi$
$853$	−8.48540	−0.290535	−0.145267	+	0.989392i	$0.546404\pi$
$854$	−43.5684	−1.49088
$855$	21.2952	0.728280
$856$	−5.81507	−0.198755
$857$	−8.07843	−0.275954	−0.137977	−	0.990435i	$-0.544060\pi$
$857$	−8.07843	−0.275954	−0.137977	+	0.990435i	$0.544060\pi$
$858$	7.73572	0.264093
$859$	−7.56788	−0.258213	−0.129106	−	0.991631i	$-0.541211\pi$
$859$	−7.56788	−0.258213	−0.129106	+	0.991631i	$0.541211\pi$
$860$	1.00000	0.0340997
$861$	−81.9571	−2.79309
$862$	22.7041	0.773303
$863$	−19.9501	−0.679110	−0.339555	−	0.940586i	$-0.610277\pi$
$863$	−19.9501	−0.679110	−0.339555	+	0.940586i	$0.610277\pi$
$864$	−3.61555	−0.123004
$865$	−12.9715	−0.441045
$866$	9.93944	0.337756
$867$	−36.2975	−1.23273
$868$	26.4583	0.898052
$869$	10.2123	0.346429
$870$	11.8404	0.401426
$871$	−35.9390	−1.21775
$872$	−5.39841	−0.182813
$873$	46.3279	1.56796
$874$	46.0197	1.55664
$875$	−4.04483	−0.136740
$876$	5.29250	0.178817
$877$	−3.67241	−0.124008	−0.0620042	−	0.998076i	$-0.519749\pi$
$877$	−3.67241	−0.124008	−0.0620042	+	0.998076i	$0.519749\pi$
$878$	33.7547	1.13917
$879$	−64.1472	−2.16363
$880$	−1.00000	−0.0337100
$881$	−33.7421	−1.13680	−0.568401	−	0.822752i	$-0.692438\pi$
$881$	−33.7421	−1.13680	−0.568401	+	0.822752i	$0.692438\pi$
$882$	−40.5783	−1.36634
$883$	37.7724	1.27114	0.635571	−	0.772042i	$-0.280765\pi$
$883$	37.7724	1.27114	0.635571	+	0.772042i	$0.280765\pi$
$884$	5.41774	0.182218
$885$	−8.90461	−0.299325
$886$	−14.8799	−0.499899
$887$	−22.0366	−0.739917	−0.369958	−	0.929048i	$-0.620628\pi$
$887$	−22.0366	−0.739917	−0.369958	+	0.929048i	$0.620628\pi$
$888$	−11.1889	−0.375475
$889$	−37.1613	−1.24635
$890$	−9.18154	−0.307766
$891$	−3.21288	−0.107635
$892$	14.9881	0.501839
$893$	25.0031	0.836698
$894$	−19.9620	−0.667630
$895$	18.5448	0.619885
$896$	−4.04483	−0.135128
$897$	−72.4686	−2.41966
$898$	16.2263	0.541479
$899$	28.5974	0.953776
$900$	4.33498	0.144499
$901$	8.95049	0.298184
$902$	7.48146	0.249105
$903$	−10.9547	−0.364549
$904$	6.52360	0.216972
$905$	−11.7870	−0.391814
$906$	6.59262	0.219025
$907$	−37.5345	−1.24631	−0.623157	−	0.782097i	$-0.714150\pi$
$907$	−37.5345	−1.24631	−0.623157	+	0.782097i	$0.714150\pi$
$908$	−13.5172	−0.448582
$909$	−58.7534	−1.94873
$910$	−11.5532	−0.382984
$911$	−24.7356	−0.819526	−0.409763	−	0.912192i	$-0.634389\pi$
$911$	−24.7356	−0.819526	−0.409763	+	0.912192i	$0.634389\pi$
$912$	−13.3044	−0.440551
$913$	14.6750	0.485670
$914$	−21.4406	−0.709192
$915$	−29.1723	−0.964407
$916$	27.6701	0.914246
$917$	82.7704	2.73332
$918$	6.85792	0.226345
$919$	12.4542	0.410827	0.205413	−	0.978675i	$-0.434146\pi$
$919$	12.4542	0.410827	0.205413	+	0.978675i	$0.434146\pi$
$920$	9.36806	0.308856
$921$	93.0836	3.06721
$922$	−24.1546	−0.795490
$923$	−7.43940	−0.244871
$924$	10.9547	0.360383
$925$	4.13131	0.135837
$926$	16.7099	0.549120
$927$	−1.10797	−0.0363905
$928$	−4.37185	−0.143513
$929$	−27.7875	−0.911677	−0.455839	−	0.890062i	$-0.650661\pi$
$929$	−27.7875	−0.911677	−0.455839	+	0.890062i	$0.650661\pi$
$930$	17.7158	0.580923
$931$	−45.9834	−1.50704
$932$	−17.1457	−0.561627
$933$	18.6099	0.609260
$934$	−5.35756	−0.175305
$935$	1.89678	0.0620314
$936$	12.3819	0.404716
$937$	−41.3679	−1.35143	−0.675716	−	0.737162i	$-0.736165\pi$
$937$	−41.3679	−1.35143	−0.675716	+	0.737162i	$0.736165\pi$
$938$	−50.8939	−1.66174
$939$	62.3226	2.03382
$940$	5.08979	0.166011
$941$	−39.6111	−1.29129	−0.645643	−	0.763640i	$-0.723410\pi$
$941$	−39.6111	−1.29129	−0.645643	+	0.763640i	$0.723410\pi$
$942$	−3.44046	−0.112096
$943$	−70.0867	−2.28234
$944$	3.28788	0.107011
$945$	−14.6243	−0.475729
$946$	1.00000	0.0325128
$947$	−12.4090	−0.403238	−0.201619	−	0.979464i	$-0.564620\pi$
$947$	−12.4090	−0.403238	−0.201619	+	0.979464i	$0.564620\pi$
$948$	27.6582	0.898296
$949$	−5.58164	−0.181188
$950$	4.91241	0.159379
$951$	87.2292	2.82860
$952$	7.67216	0.248656
$953$	−44.1657	−1.43067	−0.715334	−	0.698783i	$-0.753725\pi$
$953$	−44.1657	−1.43067	−0.715334	+	0.698783i	$0.753725\pi$
$954$	20.4558	0.662281
$955$	−19.7824	−0.640143
$956$	−14.1295	−0.456982
$957$	11.8404	0.382744
$958$	−9.93243	−0.320902
$959$	66.7259	2.15469
$960$	−2.70832	−0.0874106
$961$	11.7880	0.380257
$962$	11.8002	0.380453
$963$	25.2082	0.812323
$964$	9.61164	0.309570
$965$	−1.71350	−0.0551596
$966$	−102.624	−3.30188
$967$	43.9565	1.41354	0.706772	−	0.707441i	$-0.250151\pi$
$967$	43.9565	1.41354	0.706772	+	0.707441i	$0.250151\pi$
$968$	−1.00000	−0.0321412
$969$	25.2354	0.810679
$970$	10.6870	0.343138
$971$	32.5353	1.04411	0.522053	−	0.852913i	$-0.325166\pi$
$971$	32.5353	1.04411	0.522053	+	0.852913i	$0.325166\pi$
$972$	−19.5482	−0.627007
$973$	−78.7676	−2.52517
$974$	38.9964	1.24952
$975$	−7.73572	−0.247741
$976$	10.7714	0.344784
$977$	−16.2614	−0.520249	−0.260124	−	0.965575i	$-0.583764\pi$
$977$	−16.2614	−0.520249	−0.260124	+	0.965575i	$0.583764\pi$
$978$	19.9624	0.638328
$979$	−9.18154	−0.293443
$980$	−9.36066	−0.299015
$981$	23.4020	0.747169
$982$	11.2544	0.359143
$983$	−50.8673	−1.62242	−0.811208	−	0.584758i	$-0.801190\pi$
$983$	−50.8673	−1.62242	−0.811208	+	0.584758i	$0.801190\pi$
$984$	20.2622	0.645934
$985$	20.7792	0.662081
$986$	8.29244	0.264085
$987$	−55.7571	−1.77477
$988$	14.0312	0.446392
$989$	−9.36806	−0.297887
$990$	4.33498	0.137775
$991$	42.2774	1.34298	0.671492	−	0.741011i	$-0.265654\pi$
$991$	42.2774	1.34298	0.671492	+	0.741011i	$0.265654\pi$
$992$	−6.54125	−0.207685
$993$	−3.45644	−0.109687
$994$	−10.5351	−0.334152
$995$	27.1079	0.859377
$996$	39.7445	1.25935
$997$	21.9281	0.694469	0.347234	−	0.937778i	$-0.387121\pi$
$997$	21.9281	0.694469	0.347234	+	0.937778i	$0.387121\pi$
$998$	24.7057	0.782046
$999$	14.9370	0.472585

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.bc.1.10	✓	11	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.70832 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.70832 q^{6} +4.04483 q^{7} -1.00000 q^{8} +4.33498 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.70832 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.70832 q^{6} +4.04483 q^{7} -1.00000 q^{8} +4.33498 q^{9} +1.00000 q^{10} +1.00000 q^{11} +2.70832 q^{12} -2.85628 q^{13} -4.04483 q^{14} -2.70832 q^{15} +1.00000 q^{16} -1.89678 q^{17} -4.33498 q^{18} -4.91241 q^{19} -1.00000 q^{20} +10.9547 q^{21} -1.00000 q^{22} +9.36806 q^{23} -2.70832 q^{24} +1.00000 q^{25} +2.85628 q^{26} +3.61555 q^{27} +4.04483 q^{28} +4.37185 q^{29} +2.70832 q^{30} +6.54125 q^{31} -1.00000 q^{32} +2.70832 q^{33} +1.89678 q^{34} -4.04483 q^{35} +4.33498 q^{36} +4.13131 q^{37} +4.91241 q^{38} -7.73572 q^{39} +1.00000 q^{40} -7.48146 q^{41} -10.9547 q^{42} -1.00000 q^{43} +1.00000 q^{44} -4.33498 q^{45} -9.36806 q^{46} -5.08979 q^{47} +2.70832 q^{48} +9.36066 q^{49} -1.00000 q^{50} -5.13709 q^{51} -2.85628 q^{52} -4.71878 q^{53} -3.61555 q^{54} -1.00000 q^{55} -4.04483 q^{56} -13.3044 q^{57} -4.37185 q^{58} +3.28788 q^{59} -2.70832 q^{60} +10.7714 q^{61} -6.54125 q^{62} +17.5343 q^{63} +1.00000 q^{64} +2.85628 q^{65} -2.70832 q^{66} +12.5824 q^{67} -1.89678 q^{68} +25.3717 q^{69} +4.04483 q^{70} +2.60458 q^{71} -4.33498 q^{72} +1.95416 q^{73} -4.13131 q^{74} +2.70832 q^{75} -4.91241 q^{76} +4.04483 q^{77} +7.73572 q^{78} +10.2123 q^{79} -1.00000 q^{80} -3.21288 q^{81} +7.48146 q^{82} +14.6750 q^{83} +10.9547 q^{84} +1.89678 q^{85} +1.00000 q^{86} +11.8404 q^{87} -1.00000 q^{88} -9.18154 q^{89} +4.33498 q^{90} -11.5532 q^{91} +9.36806 q^{92} +17.7158 q^{93} +5.08979 q^{94} +4.91241 q^{95} -2.70832 q^{96} +10.6870 q^{97} -9.36066 q^{98} +4.33498 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 11 q^{2} + 11 q^{4} - 11 q^{5} - 11 q^{8} + 15 q^{9}+O(q^{10}) \) 11 * q - 11 * q^2 + 11 * q^4 - 11 * q^5 - 11 * q^8 + 15 * q^9	\( 11 q - 11 q^{2} + 11 q^{4} - 11 q^{5} - 11 q^{8} + 15 q^{9} + 11 q^{10} + 11 q^{11} - q^{13} + 11 q^{16} - 15 q^{17} - 15 q^{18} + 14 q^{19} - 11 q^{20} + 7 q^{21} - 11 q^{22} - 2 q^{23} + 11 q^{25} + q^{26} + 3 q^{27} + 6 q^{29} + 13 q^{31} - 11 q^{32} + 15 q^{34} + 15 q^{36} + 16 q^{37} - 14 q^{38} + 4 q^{39} + 11 q^{40} - 7 q^{41} - 7 q^{42} - 11 q^{43} + 11 q^{44} - 15 q^{45} + 2 q^{46} - 19 q^{47} + 23 q^{49} - 11 q^{50} + 32 q^{51} - q^{52} - 16 q^{53} - 3 q^{54} - 11 q^{55} - 2 q^{57} - 6 q^{58} + 7 q^{59} + 20 q^{61} - 13 q^{62} + 11 q^{64} + q^{65} + 9 q^{67} - 15 q^{68} + 10 q^{69} + 13 q^{71} - 15 q^{72} + 20 q^{73} - 16 q^{74} + 14 q^{76} - 4 q^{78} + 13 q^{79} - 11 q^{80} + 19 q^{81} + 7 q^{82} - 6 q^{83} + 7 q^{84} + 15 q^{85} + 11 q^{86} - 23 q^{87} - 11 q^{88} + 10 q^{89} + 15 q^{90} + 43 q^{91} - 2 q^{92} + 22 q^{93} + 19 q^{94} - 14 q^{95} + 3 q^{97} - 23 q^{98} + 15 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 + 11 * q^4 - 11 * q^5 - 11 * q^8 + 15 * q^9 + 11 * q^10 + 11 * q^11 - q^13 + 11 * q^16 - 15 * q^17 - 15 * q^18 + 14 * q^19 - 11 * q^20 + 7 * q^21 - 11 * q^22 - 2 * q^23 + 11 * q^25 + q^26 + 3 * q^27 + 6 * q^29 + 13 * q^31 - 11 * q^32 + 15 * q^34 + 15 * q^36 + 16 * q^37 - 14 * q^38 + 4 * q^39 + 11 * q^40 - 7 * q^41 - 7 * q^42 - 11 * q^43 + 11 * q^44 - 15 * q^45 + 2 * q^46 - 19 * q^47 + 23 * q^49 - 11 * q^50 + 32 * q^51 - q^52 - 16 * q^53 - 3 * q^54 - 11 * q^55 - 2 * q^57 - 6 * q^58 + 7 * q^59 + 20 * q^61 - 13 * q^62 + 11 * q^64 + q^65 + 9 * q^67 - 15 * q^68 + 10 * q^69 + 13 * q^71 - 15 * q^72 + 20 * q^73 - 16 * q^74 + 14 * q^76 - 4 * q^78 + 13 * q^79 - 11 * q^80 + 19 * q^81 + 7 * q^82 - 6 * q^83 + 7 * q^84 + 15 * q^85 + 11 * q^86 - 23 * q^87 - 11 * q^88 + 10 * q^89 + 15 * q^90 + 43 * q^91 - 2 * q^92 + 22 * q^93 + 19 * q^94 - 14 * q^95 + 3 * q^97 - 23 * q^98 + 15 * q^99

Introduction

L-functions

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