LMFDB - Embedded newform 1183.2.c.j.337.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(337,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("1183.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.c (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			337.13
Character	$\chi$	$=$	1183.337
Dual form			1183.2.c.j.337.12

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.149660i q^{2} +2.76031 q^{3} +1.97760 q^{4} -4.13443i q^{5} +0.413107i q^{6} +1.00000i q^{7} +0.595288i q^{8} +4.61930 q^{9} +O(q^{10})$	\(q+0.149660i q^{2} +2.76031 q^{3} +1.97760 q^{4} -4.13443i q^{5} +0.413107i q^{6} +1.00000i q^{7} +0.595288i q^{8} +4.61930 q^{9} +0.618759 q^{10} -2.55320i q^{11} +5.45879 q^{12} -0.149660 q^{14} -11.4123i q^{15} +3.86611 q^{16} -1.50360 q^{17} +0.691324i q^{18} +5.93185i q^{19} -8.17626i q^{20} +2.76031i q^{21} +0.382113 q^{22} -6.55752 q^{23} +1.64318i q^{24} -12.0935 q^{25} +4.46975 q^{27} +1.97760i q^{28} +0.283949 q^{29} +1.70797 q^{30} +1.95156i q^{31} +1.76918i q^{32} -7.04763i q^{33} -0.225029i q^{34} +4.13443 q^{35} +9.13513 q^{36} +5.66775i q^{37} -0.887760 q^{38} +2.46118 q^{40} +6.70206i q^{41} -0.413107 q^{42} +8.14248 q^{43} -5.04922i q^{44} -19.0982i q^{45} -0.981398i q^{46} -3.94423i q^{47} +10.6717 q^{48} -1.00000 q^{49} -1.80992i q^{50} -4.15040 q^{51} -1.08139 q^{53} +0.668943i q^{54} -10.5561 q^{55} -0.595288 q^{56} +16.3737i q^{57} +0.0424957i q^{58} -3.71413i q^{59} -22.5690i q^{60} +1.93905 q^{61} -0.292070 q^{62} +4.61930i q^{63} +7.46745 q^{64} +1.05475 q^{66} +3.38134i q^{67} -2.97352 q^{68} -18.1008 q^{69} +0.618759i q^{70} -5.36923i q^{71} +2.74981i q^{72} +2.62686i q^{73} -0.848236 q^{74} -33.3819 q^{75} +11.7308i q^{76} +2.55320 q^{77} +7.89503 q^{79} -15.9842i q^{80} -1.51999 q^{81} -1.00303 q^{82} +10.5270i q^{83} +5.45879i q^{84} +6.21653i q^{85} +1.21860i q^{86} +0.783786 q^{87} +1.51989 q^{88} -6.64469i q^{89} +2.85823 q^{90} -12.9682 q^{92} +5.38690i q^{93} +0.590294 q^{94} +24.5248 q^{95} +4.88347i q^{96} -0.504498i q^{97} -0.149660i q^{98} -11.7940i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 16 q^{3} - 30 q^{4} + 52 q^{9}+O(q^{10}) $ 24 * q + 16 * q^3 - 30 * q^4 + 52 * q^9	$ 24 q + 16 q^{3} - 30 q^{4} + 52 q^{9} + 12 q^{10} - 26 q^{12} + 6 q^{14} + 26 q^{16} - 62 q^{17} - 8 q^{22} - 36 q^{23} - 64 q^{25} + 64 q^{27} + 30 q^{29} + 20 q^{30} - 8 q^{35} - 98 q^{36} - 90 q^{38} - 40 q^{40} + 4 q^{42} + 44 q^{43} + 22 q^{48} - 24 q^{49} - 36 q^{51} + 106 q^{53} - 52 q^{55} - 24 q^{56} + 44 q^{61} - 38 q^{62} - 4 q^{64} - 68 q^{66} + 68 q^{68} - 6 q^{69} - 80 q^{74} - 30 q^{75} - 24 q^{77} + 4 q^{79} + 72 q^{81} + 64 q^{82} + 54 q^{87} + 96 q^{88} + 52 q^{90} + 104 q^{92} - 88 q^{94} - 58 q^{95}+O(q^{100}) $ 24 * q + 16 * q^3 - 30 * q^4 + 52 * q^9 + 12 * q^10 - 26 * q^12 + 6 * q^14 + 26 * q^16 - 62 * q^17 - 8 * q^22 - 36 * q^23 - 64 * q^25 + 64 * q^27 + 30 * q^29 + 20 * q^30 - 8 * q^35 - 98 * q^36 - 90 * q^38 - 40 * q^40 + 4 * q^42 + 44 * q^43 + 22 * q^48 - 24 * q^49 - 36 * q^51 + 106 * q^53 - 52 * q^55 - 24 * q^56 + 44 * q^61 - 38 * q^62 - 4 * q^64 - 68 * q^66 + 68 * q^68 - 6 * q^69 - 80 * q^74 - 30 * q^75 - 24 * q^77 + 4 * q^79 + 72 * q^81 + 64 * q^82 + 54 * q^87 + 96 * q^88 + 52 * q^90 + 104 * q^92 - 88 * q^94 - 58 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times$.

$n$	$339$	$1016$
$\chi(n)$	$1$	$-1$

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 $

$2$	0.149660i	0.105826i	0.998599	+	0.0529128i	$0.0168505\pi$
$2$	0.149660i	0.105826i	−0.998599	+	0.0529128i	$0.983149\pi$
$3$	2.76031	1.59366	0.796832	−	0.604201i	$-0.206508\pi$
$3$	2.76031	1.59366	0.796832	+	0.604201i	$0.206508\pi$
$4$	1.97760	0.988801
$5$	− 4.13443i	− 1.84897i	−0.381213	−	0.924487i	$-0.624494\pi$
$5$	− 4.13443i	− 1.84897i	0.381213	−	0.924487i	$-0.375506\pi$
$6$	0.413107i	0.168650i
$7$	1.00000i	0.377964i
$7$	1.00000i	0.377964i
$8$	0.595288i	0.210466i
$9$	4.61930	1.53977
$10$	0.618759	0.195669
$11$	− 2.55320i	− 0.769820i	−0.922954	−	0.384910i	$-0.874232\pi$
$11$	− 2.55320i	− 0.769820i	0.922954	−	0.384910i	$-0.125768\pi$
$12$	5.45879	1.57582
$13$	0	0
$13$	0	0
$14$	−0.149660	−0.0399983
$15$	− 11.4123i	− 2.94664i
$16$	3.86611	0.966528
$17$	−1.50360	−0.364676	−0.182338	−	0.983236i	$-0.558367\pi$
$17$	−1.50360	−0.364676	−0.182338	+	0.983236i	$0.558367\pi$
$18$	0.691324i	0.162947i
$19$	5.93185i	1.36086i	0.732813	+	0.680430i	$0.238207\pi$
$19$	5.93185i	1.36086i	−0.732813	+	0.680430i	$0.761793\pi$
$20$	− 8.17626i	− 1.82827i
$21$	2.76031i	0.602348i
$22$	0.382113	0.0814667
$23$	−6.55752	−1.36734	−0.683669	−	0.729792i	$-0.739617\pi$
$23$	−6.55752	−1.36734	−0.683669	+	0.729792i	$0.739617\pi$
$24$	1.64318i	0.335412i
$25$	−12.0935	−2.41871
$26$	0	0
$27$	4.46975	0.860205
$28$	1.97760i	0.373732i
$29$	0.283949	0.0527279	0.0263640	−	0.999652i	$-0.491607\pi$
$29$	0.283949	0.0527279	0.0263640	+	0.999652i	$0.491607\pi$
$30$	1.70797	0.311830
$31$	1.95156i	0.350510i	0.984523	+	0.175255i	$0.0560750\pi$
$31$	1.95156i	0.350510i	−0.984523	+	0.175255i	$0.943925\pi$
$32$	1.76918i	0.312749i
$33$	− 7.04763i	− 1.22683i
$34$	− 0.225029i	− 0.0385921i
$35$	4.13443	0.698847
$36$	9.13513	1.52252
$37$	5.66775i	0.931773i	0.884845	+	0.465886i	$0.154264\pi$
$37$	5.66775i	0.931773i	−0.884845	+	0.465886i	$0.845736\pi$
$38$	−0.887760	−0.144014
$39$	0	0
$40$	2.46118	0.389146
$41$	6.70206i	1.04669i	0.852122	+	0.523343i	$0.175315\pi$
$41$	6.70206i	1.04669i	−0.852122	+	0.523343i	$0.824685\pi$
$42$	−0.413107	−0.0637439
$43$	8.14248	1.24172	0.620858	−	0.783923i	$-0.286784\pi$
$43$	8.14248	1.24172	0.620858	+	0.783923i	$0.286784\pi$
$44$	− 5.04922i	− 0.761199i
$45$	− 19.0982i	− 2.84699i
$46$	− 0.981398i	− 0.144699i
$47$	− 3.94423i	− 0.575326i	−0.957732	−	0.287663i	$-0.907122\pi$
$47$	− 3.94423i	− 0.575326i	0.957732	−	0.287663i	$-0.0928783\pi$
$48$	10.6717	1.54032
$49$	−1.00000	−0.142857
$50$	− 1.80992i	− 0.255961i
$51$	−4.15040	−0.581172
$52$	0	0
$53$	−1.08139	−0.148541	−0.0742705	−	0.997238i	$-0.523663\pi$
$53$	−1.08139	−0.148541	−0.0742705	+	0.997238i	$0.523663\pi$
$54$	0.668943i	0.0910316i
$55$	−10.5561	−1.42338
$56$	−0.595288	−0.0795487
$57$	16.3737i	2.16875i
$58$	0.0424957i	0.00557997i
$59$	− 3.71413i	− 0.483538i	−0.970334	−	0.241769i	$-0.922272\pi$
$59$	− 3.71413i	− 0.483538i	0.970334	−	0.241769i	$-0.0777277\pi$
$60$	− 22.5690i	− 2.91364i
$61$	1.93905	0.248270	0.124135	−	0.992265i	$-0.460384\pi$
$61$	1.93905	0.248270	0.124135	+	0.992265i	$0.460384\pi$
$62$	−0.292070	−0.0370930
$63$	4.61930i	0.581977i
$64$	7.46745	0.933431
$65$	0	0
$66$	1.05475	0.129831
$67$	3.38134i	0.413096i	0.978436	+	0.206548i	$0.0662230\pi$
$67$	3.38134i	0.413096i	−0.978436	+	0.206548i	$0.933777\pi$
$68$	−2.97352	−0.360592
$69$	−18.1008	−2.17908
$70$	0.618759i	0.0739559i
$71$	− 5.36923i	− 0.637210i	−0.947888	−	0.318605i	$-0.896786\pi$
$71$	− 5.36923i	− 0.637210i	0.947888	−	0.318605i	$-0.103214\pi$
$72$	2.74981i	0.324068i
$73$	2.62686i	0.307451i	0.988114	+	0.153725i	$0.0491271\pi$
$73$	2.62686i	0.307451i	−0.988114	+	0.153725i	$0.950873\pi$
$74$	−0.848236	−0.0986054
$75$	−33.3819	−3.85461
$76$	11.7308i	1.34562i
$77$	2.55320	0.290965
$78$	0	0
$79$	7.89503	0.888260	0.444130	−	0.895962i	$-0.353513\pi$
$79$	7.89503	0.888260	0.444130	+	0.895962i	$0.353513\pi$
$80$	− 15.9842i	− 1.78709i
$81$	−1.51999	−0.168888
$82$	−1.00303	−0.110766
$83$	10.5270i	1.15549i	0.816218	+	0.577745i	$0.196067\pi$
$83$	10.5270i	1.15549i	−0.816218	+	0.577745i	$0.803933\pi$
$84$	5.45879i	0.595603i
$85$	6.21653i	0.674277i
$86$	1.21860i	0.131405i
$87$	0.783786	0.0840306
$88$	1.51989	0.162021
$89$	− 6.64469i	− 0.704336i	−0.935937	−	0.352168i	$-0.885445\pi$
$89$	− 6.64469i	− 0.704336i	0.935937	−	0.352168i	$-0.114555\pi$
$90$	2.85823	0.301284
$91$	0	0
$92$	−12.9682	−1.35202
$93$	5.38690i	0.558596i
$94$	0.590294	0.0608842
$95$	24.5248	2.51619
$96$	4.88347i	0.498418i
$97$	− 0.504498i	− 0.0512240i	−0.999672	−	0.0256120i	$-0.991847\pi$
$97$	− 0.504498i	− 0.0512240i	0.999672	−	0.0256120i	$-0.00815344\pi$
$98$	− 0.149660i	− 0.0151179i
$99$	− 11.7940i	− 1.18534i
$100$	−23.9162	−2.39162
$101$	7.18413	0.714847	0.357424	−	0.933942i	$-0.383655\pi$
$101$	7.18413	0.714847	0.357424	+	0.933942i	$0.383655\pi$
$102$	− 0.621148i	− 0.0615028i
$103$	−15.2582	−1.50343	−0.751716	−	0.659487i	$-0.770774\pi$
$103$	−15.2582	−1.50343	−0.751716	+	0.659487i	$0.770774\pi$
$104$	0	0
$105$	11.4123	1.11373
$106$	− 0.161841i	− 0.0157194i
$107$	−3.47375	−0.335820	−0.167910	−	0.985802i	$-0.553702\pi$
$107$	−3.47375	−0.335820	−0.167910	+	0.985802i	$0.553702\pi$
$108$	8.83939	0.850571
$109$	− 16.6557i	− 1.59533i	−0.603103	−	0.797663i	$-0.706069\pi$
$109$	− 16.6557i	− 1.59533i	0.603103	−	0.797663i	$-0.293931\pi$
$110$	− 1.57982i	− 0.150630i
$111$	15.6447i	1.48493i
$112$	3.86611i	0.365313i
$113$	18.2871	1.72031	0.860153	−	0.510036i	$-0.170368\pi$
$113$	18.2871	1.72031	0.860153	+	0.510036i	$0.170368\pi$
$114$	−2.45049	−0.229510
$115$	27.1116i	2.52817i
$116$	0.561537	0.0521374
$117$	0	0
$118$	0.555856	0.0511707
$119$	− 1.50360i	− 0.137835i
$120$	6.79360	0.620168
$121$	4.48114	0.407377
$122$	0.290199i	0.0262734i
$123$	18.4997i	1.66807i
$124$	3.85941i	0.346585i
$125$	29.3277i	2.62315i
$126$	−0.691324	−0.0615880
$127$	7.98164	0.708256	0.354128	−	0.935197i	$-0.384778\pi$
$127$	7.98164	0.708256	0.354128	+	0.935197i	$0.384778\pi$
$128$	4.65593i	0.411530i
$129$	22.4757	1.97888
$130$	0	0
$131$	−18.7232	−1.63586	−0.817929	−	0.575319i	$-0.804878\pi$
$131$	−18.7232	−1.63586	−0.817929	+	0.575319i	$0.804878\pi$
$132$	− 13.9374i	− 1.21310i
$133$	−5.93185	−0.514357
$134$	−0.506051	−0.0437161
$135$	− 18.4799i	− 1.59050i
$136$	− 0.895074i	− 0.0767520i
$137$	2.32575i	0.198703i	0.995052	+	0.0993513i	$0.0316768\pi$
$137$	2.32575i	0.198703i	−0.995052	+	0.0993513i	$0.968323\pi$
$138$	− 2.70896i	− 0.230602i
$139$	9.02263	0.765289	0.382645	−	0.923896i	$-0.375013\pi$
$139$	9.02263	0.765289	0.382645	+	0.923896i	$0.375013\pi$
$140$	8.17626	0.691020
$141$	− 10.8873i	− 0.916876i
$142$	0.803558	0.0674331
$143$	0	0
$144$	17.8587	1.48823
$145$	− 1.17397i	− 0.0974926i
$146$	−0.393136	−0.0325362
$147$	−2.76031	−0.227666
$148$	11.2086i	0.921338i
$149$	13.5260i	1.10809i	0.832486	+	0.554045i	$0.186917\pi$
$149$	13.5260i	1.10809i	−0.832486	+	0.554045i	$0.813083\pi$
$150$	− 4.99593i	− 0.407916i
$151$	− 5.02665i	− 0.409063i	−0.978860	−	0.204531i	$-0.934433\pi$
$151$	− 5.02665i	− 0.409063i	0.978860	−	0.204531i	$-0.0655671\pi$
$152$	−3.53116	−0.286415
$153$	−6.94557	−0.561516
$154$	0.382113i	0.0307915i
$155$	8.06859	0.648085
$156$	0	0
$157$	−11.4938	−0.917308	−0.458654	−	0.888615i	$-0.651668\pi$
$157$	−11.4938	−0.917308	−0.458654	+	0.888615i	$0.651668\pi$
$158$	1.18157i	0.0940006i
$159$	−2.98498	−0.236724
$160$	7.31455	0.578266
$161$	− 6.55752i	− 0.516805i
$162$	− 0.227482i	− 0.0178727i
$163$	− 12.8306i	− 1.00497i	−0.864586	−	0.502485i	$-0.832419\pi$
$163$	− 12.8306i	− 1.00497i	0.864586	−	0.502485i	$-0.167581\pi$
$164$	13.2540i	1.03496i
$165$	−29.1379	−2.26839
$166$	−1.57547	−0.122280
$167$	− 21.6586i	− 1.67600i	−0.545674	−	0.837998i	$-0.683726\pi$
$167$	− 21.6586i	− 1.67600i	0.545674	−	0.837998i	$-0.316274\pi$
$168$	−1.64318	−0.126774
$169$	0	0
$170$	−0.930366	−0.0713558
$171$	27.4010i	2.09540i
$172$	16.1026	1.22781
$173$	−16.3149	−1.24040	−0.620201	−	0.784443i	$-0.712949\pi$
$173$	−16.3149	−1.24040	−0.620201	+	0.784443i	$0.712949\pi$
$174$	0.117301i	0.00889259i
$175$	− 12.0935i	− 0.914185i
$176$	− 9.87098i	− 0.744053i
$177$	− 10.2521i	− 0.770598i
$178$	0.994444	0.0745367
$179$	1.42206	0.106290	0.0531450	−	0.998587i	$-0.483075\pi$
$179$	1.42206	0.106290	0.0531450	+	0.998587i	$0.483075\pi$
$180$	− 37.7686i	− 2.81510i
$181$	19.1896	1.42635	0.713174	−	0.700987i	$-0.247257\pi$
$181$	19.1896	1.42635	0.713174	+	0.700987i	$0.247257\pi$
$182$	0	0
$183$	5.35238	0.395660
$184$	− 3.90361i	− 0.287778i
$185$	23.4329	1.72282
$186$	−0.806204	−0.0591137
$187$	3.83900i	0.280735i
$188$	− 7.80012i	− 0.568883i
$189$	4.46975i	0.325127i
$190$	3.67039i	0.266278i
$191$	14.0009	1.01307	0.506536	−	0.862219i	$-0.330926\pi$
$191$	14.0009	1.01307	0.506536	+	0.862219i	$0.330926\pi$
$192$	20.6125	1.48758
$193$	− 1.26935i	− 0.0913695i	−0.998956	−	0.0456847i	$-0.985453\pi$
$193$	− 1.26935i	− 0.0913695i	0.998956	−	0.0456847i	$-0.0145470\pi$
$194$	0.0755031	0.00542081
$195$	0	0
$196$	−1.97760	−0.141257
$197$	2.82033i	0.200940i	0.994940	+	0.100470i	$0.0320346\pi$
$197$	2.82033i	0.200940i	−0.994940	+	0.100470i	$0.967965\pi$
$198$	1.76509	0.125440
$199$	−19.2600	−1.36530	−0.682652	−	0.730743i	$-0.739174\pi$
$199$	−19.2600	−1.36530	−0.682652	+	0.730743i	$0.739174\pi$
$200$	− 7.19913i	− 0.509055i
$201$	9.33353i	0.658337i
$202$	1.07518i	0.0756491i
$203$	0.283949i	0.0199293i
$204$	−8.20783	−0.574663
$205$	27.7092	1.93529
$206$	− 2.28354i	− 0.159102i
$207$	−30.2911	−2.10538
$208$	0	0
$209$	15.1452	1.04762
$210$	1.70797i	0.117861i
$211$	−12.8443	−0.884236	−0.442118	−	0.896957i	$-0.645773\pi$
$211$	−12.8443	−0.884236	−0.442118	+	0.896957i	$0.645773\pi$
$212$	−2.13857	−0.146877
$213$	− 14.8207i	− 1.01550i
$214$	− 0.519881i	− 0.0355383i
$215$	− 33.6645i	− 2.29590i
$216$	2.66079i	0.181044i
$217$	−1.95156	−0.132480
$218$	2.49269	0.168826
$219$	7.25094i	0.489973i
$220$	−20.8757	−1.40744
$221$	0	0
$222$	−2.34139	−0.157144
$223$	− 4.51539i	− 0.302373i	−0.988505	−	0.151187i	$-0.951691\pi$
$223$	− 4.51539i	− 0.302373i	0.988505	−	0.151187i	$-0.0483094\pi$
$224$	−1.76918	−0.118208
$225$	−55.8636	−3.72424
$226$	2.73685i	0.182052i
$227$	9.86924i	0.655044i	0.944843	+	0.327522i	$0.106214\pi$
$227$	9.86924i	0.655044i	−0.944843	+	0.327522i	$0.893786\pi$
$228$	32.3807i	2.14446i
$229$	4.44617i	0.293811i	0.989151	+	0.146906i	$0.0469313\pi$
$229$	4.44617i	0.293811i	−0.989151	+	0.146906i	$0.953069\pi$
$230$	−4.05752	−0.267545
$231$	7.04763	0.463700
$232$	0.169031i	0.0110974i
$233$	−27.6514	−1.81151	−0.905753	−	0.423806i	$-0.860694\pi$
$233$	−27.6514	−1.81151	−0.905753	+	0.423806i	$0.860694\pi$
$234$	0	0
$235$	−16.3072	−1.06376
$236$	− 7.34507i	− 0.478123i
$237$	21.7927	1.41559
$238$	0.225029	0.0145864
$239$	− 17.2370i	− 1.11497i	−0.830188	−	0.557483i	$-0.811767\pi$
$239$	− 17.2370i	− 1.11497i	0.830188	−	0.557483i	$-0.188233\pi$
$240$	− 44.1213i	− 2.84801i
$241$	26.4553i	1.70414i	0.523431	+	0.852068i	$0.324652\pi$
$241$	26.4553i	1.70414i	−0.523431	+	0.852068i	$0.675348\pi$
$242$	0.670648i	0.0431109i
$243$	−17.6049	−1.12936
$244$	3.83468	0.245490
$245$	4.13443i	0.264139i
$246$	−2.76867	−0.176524
$247$	0	0
$248$	−1.16174	−0.0737705
$249$	29.0578i	1.84146i
$250$	−4.38919	−0.277597
$251$	7.91803	0.499782	0.249891	−	0.968274i	$-0.419605\pi$
$251$	7.91803	0.499782	0.249891	+	0.968274i	$0.419605\pi$
$252$	9.13513i	0.575459i
$253$	16.7427i	1.05260i
$254$	1.19453i	0.0749516i
$255$	17.1595i	1.07457i
$256$	14.2381	0.889881
$257$	19.9720	1.24582	0.622910	−	0.782293i	$-0.285950\pi$
$257$	19.9720	1.24582	0.622910	+	0.782293i	$0.285950\pi$
$258$	3.36372i	0.209416i
$259$	−5.66775	−0.352177
$260$	0	0
$261$	1.31164	0.0811887
$262$	− 2.80212i	− 0.173116i
$263$	−2.88461	−0.177873	−0.0889364	−	0.996037i	$-0.528347\pi$
$263$	−2.88461	−0.177873	−0.0889364	+	0.996037i	$0.528347\pi$
$264$	4.19537	0.258207
$265$	4.47095i	0.274648i
$266$	− 0.887760i	− 0.0544321i
$267$	− 18.3414i	− 1.12247i
$268$	6.68694i	0.408470i
$269$	−12.5865	−0.767410	−0.383705	−	0.923456i	$-0.625352\pi$
$269$	−12.5865	−0.767410	−0.383705	+	0.923456i	$0.625352\pi$
$270$	2.76570	0.168315
$271$	− 21.4007i	− 1.30000i	−0.759934	−	0.650001i	$-0.774769\pi$
$271$	− 21.4007i	− 1.30000i	0.759934	−	0.650001i	$-0.225231\pi$
$272$	−5.81308	−0.352470
$273$	0	0
$274$	−0.348072	−0.0210278
$275$	30.8773i	1.86197i
$276$	−35.7961	−2.15467
$277$	13.6063	0.817524	0.408762	−	0.912641i	$-0.365961\pi$
$277$	13.6063	0.817524	0.408762	+	0.912641i	$0.365961\pi$
$278$	1.35033i	0.0809872i
$279$	9.01483i	0.539704i
$280$	2.46118i	0.147083i
$281$	30.7217i	1.83270i	0.400374	+	0.916352i	$0.368880\pi$
$281$	30.7217i	1.83270i	−0.400374	+	0.916352i	$0.631120\pi$
$282$	1.62939	0.0970289
$283$	−27.7843	−1.65160	−0.825802	−	0.563961i	$-0.809277\pi$
$283$	−27.7843	−1.65160	−0.825802	+	0.563961i	$0.809277\pi$
$284$	− 10.6182i	− 0.630074i
$285$	67.6961	4.00997
$286$	0	0
$287$	−6.70206	−0.395610
$288$	8.17236i	0.481561i
$289$	−14.7392	−0.867011
$290$	0.175696	0.0103172
$291$	− 1.39257i	− 0.0816338i
$292$	5.19488i	0.304008i
$293$	− 0.146791i	− 0.00857560i	−0.999991	−	0.00428780i	$-0.998635\pi$
$293$	− 0.146791i	− 0.00857560i	0.999991	−	0.00428780i	$-0.00136485\pi$
$294$	− 0.413107i	− 0.0240929i
$295$	−15.3558	−0.894050
$296$	−3.37394	−0.196107
$297$	− 11.4122i	− 0.662203i
$298$	−2.02430	−0.117264
$299$	0	0
$300$	−66.0160	−3.81144
$301$	8.14248i	0.469325i
$302$	0.752288	0.0432893
$303$	19.8304	1.13923
$304$	22.9332i	1.31531i
$305$	− 8.01688i	− 0.459045i
$306$	− 1.03947i	− 0.0594228i
$307$	− 31.6486i	− 1.80628i	−0.429342	−	0.903142i	$-0.641255\pi$
$307$	− 31.6486i	− 1.80628i	0.429342	−	0.903142i	$-0.358745\pi$
$308$	5.04922	0.287706
$309$	−42.1173	−2.39597
$310$	1.20754i	0.0685839i
$311$	−18.8608	−1.06950	−0.534748	−	0.845011i	$-0.679594\pi$
$311$	−18.8608	−1.06950	−0.534748	+	0.845011i	$0.679594\pi$
$312$	0	0
$313$	−33.7796	−1.90934	−0.954668	−	0.297674i	$-0.903789\pi$
$313$	−33.7796	−1.90934	−0.954668	+	0.297674i	$0.903789\pi$
$314$	− 1.72017i	− 0.0970746i
$315$	19.0982	1.07606
$316$	15.6132	0.878312
$317$	22.0847i	1.24040i	0.784443	+	0.620201i	$0.212949\pi$
$317$	22.0847i	1.24040i	−0.784443	+	0.620201i	$0.787051\pi$
$318$	− 0.446732i	− 0.0250515i
$319$	− 0.724979i	− 0.0405910i
$320$	− 30.8737i	− 1.72589i
$321$	−9.58860	−0.535184
$322$	0.981398	0.0546912
$323$	− 8.91912i	− 0.496273i
$324$	−3.00594	−0.166997
$325$	0	0
$326$	1.92023	0.106352
$327$	− 45.9748i	− 2.54241i
$328$	−3.98965	−0.220292
$329$	3.94423	0.217453
$330$	− 4.36078i	− 0.240053i
$331$	25.3399i	1.39281i	0.717650	+	0.696404i	$0.245218\pi$
$331$	25.3399i	1.39281i	−0.717650	+	0.696404i	$0.754782\pi$
$332$	20.8182i	1.14255i
$333$	26.1810i	1.43471i
$334$	3.24143	0.177363
$335$	13.9799	0.763804
$336$	10.6717i	0.582187i
$337$	26.2596	1.43045	0.715226	−	0.698893i	$-0.246324\pi$
$337$	26.2596	1.43045	0.715226	+	0.698893i	$0.246324\pi$
$338$	0	0
$339$	50.4780	2.74159
$340$	12.2938i	0.666726i
$341$	4.98273	0.269830
$342$	−4.10083	−0.221747
$343$	− 1.00000i	− 0.0539949i
$344$	4.84712i	0.261339i
$345$	74.8364i	4.02906i
$346$	− 2.44169i	− 0.131266i
$347$	−4.13355	−0.221901	−0.110950	−	0.993826i	$-0.535389\pi$
$347$	−4.13355	−0.221901	−0.110950	+	0.993826i	$0.535389\pi$
$348$	1.55002	0.0830896
$349$	− 4.02138i	− 0.215259i	−0.994191	−	0.107630i	$-0.965674\pi$
$349$	− 4.02138i	− 0.215259i	0.994191	−	0.107630i	$-0.0343261\pi$
$350$	1.80992	0.0967442
$351$	0	0
$352$	4.51707	0.240761
$353$	− 2.65565i	− 0.141346i	−0.997500	−	0.0706730i	$-0.977485\pi$
$353$	− 2.65565i	− 0.141346i	0.997500	−	0.0706730i	$-0.0225147\pi$
$354$	1.53433	0.0815489
$355$	−22.1987	−1.17819
$356$	− 13.1406i	− 0.696448i
$357$	− 4.15040i	− 0.219662i
$358$	0.212826i	0.0112482i
$359$	5.18529i	0.273669i	0.990594	+	0.136835i	$0.0436929\pi$
$359$	5.18529i	0.273669i	−0.990594	+	0.136835i	$0.956307\pi$
$360$	11.3689	0.599194
$361$	−16.1868	−0.851939
$362$	2.87191i	0.150944i
$363$	12.3693	0.649222
$364$	0	0
$365$	10.8606	0.568469
$366$	0.801037i	0.0418709i
$367$	−10.4931	−0.547737	−0.273869	−	0.961767i	$-0.588303\pi$
$367$	−10.4931	−0.547737	−0.273869	+	0.961767i	$0.588303\pi$
$368$	−25.3521	−1.32157
$369$	30.9588i	1.61165i
$370$	3.50697i	0.182319i
$371$	− 1.08139i	− 0.0561432i
$372$	10.6531i	0.552340i
$373$	−25.5655	−1.32373	−0.661866	−	0.749622i	$-0.730235\pi$
$373$	−25.5655	−1.32373	−0.661866	+	0.749622i	$0.730235\pi$
$374$	−0.574544	−0.0297090
$375$	80.9535i	4.18042i
$376$	2.34795	0.121087
$377$	0	0
$378$	−0.668943	−0.0344067
$379$	− 0.598162i	− 0.0307255i	−0.999882	−	0.0153627i	$-0.995110\pi$
$379$	− 0.598162i	− 0.0307255i	0.999882	−	0.0153627i	$-0.00489031\pi$
$380$	48.5003	2.48802
$381$	22.0318	1.12872
$382$	2.09538i	0.107209i
$383$	10.2676i	0.524649i	0.964980	+	0.262325i	$0.0844891\pi$
$383$	10.2676i	0.524649i	−0.964980	+	0.262325i	$0.915511\pi$
$384$	12.8518i	0.655841i
$385$	− 10.5561i	− 0.537986i
$386$	0.189970	0.00966923
$387$	37.6125	1.91195
$388$	− 0.997695i	− 0.0506503i
$389$	3.10131	0.157243	0.0786213	−	0.996905i	$-0.474948\pi$
$389$	3.10131	0.157243	0.0786213	+	0.996905i	$0.474948\pi$
$390$	0	0
$391$	9.85988	0.498636
$392$	− 0.595288i	− 0.0300666i
$393$	−51.6819	−2.60701
$394$	−0.422090	−0.0212646
$395$	− 32.6415i	− 1.64237i
$396$	− 23.3239i	− 1.17207i
$397$	8.88419i	0.445885i	0.974832	+	0.222942i	$0.0715662\pi$
$397$	8.88419i	0.445885i	−0.974832	+	0.222942i	$0.928434\pi$
$398$	− 2.88245i	− 0.144484i
$399$	−16.3737	−0.819712
$400$	−46.7550	−2.33775
$401$	− 5.31632i	− 0.265484i	−0.991151	−	0.132742i	$-0.957622\pi$
$401$	− 5.31632i	− 0.265484i	0.991151	−	0.132742i	$-0.0423782\pi$
$402$	−1.39686	−0.0696688
$403$	0	0
$404$	14.2073	0.706842
$405$	6.28431i	0.312270i
$406$	−0.0424957	−0.00210903
$407$	14.4709	0.717298
$408$	− 2.47068i	− 0.122317i
$409$	1.71205i	0.0846556i	0.999104	+	0.0423278i	$0.0134774\pi$
$409$	1.71205i	0.0846556i	−0.999104	+	0.0423278i	$0.986523\pi$
$410$	4.14696i	0.204804i
$411$	6.41980i	0.316665i
$412$	−30.1746	−1.48660
$413$	3.71413	0.182760
$414$	− 4.53337i	− 0.222803i
$415$	43.5232	2.13647
$416$	0	0
$417$	24.9052	1.21961
$418$	2.26663i	0.110865i
$419$	−6.33942	−0.309701	−0.154850	−	0.987938i	$-0.549490\pi$
$419$	−6.33942	−0.309701	−0.154850	+	0.987938i	$0.549490\pi$
$420$	22.5690	1.10125
$421$	− 33.7640i	− 1.64556i	−0.568362	−	0.822779i	$-0.692423\pi$
$421$	− 33.7640i	− 1.64556i	0.568362	−	0.822779i	$-0.307577\pi$
$422$	− 1.92227i	− 0.0935748i
$423$	− 18.2196i	− 0.885866i
$424$	− 0.643741i	− 0.0312628i
$425$	18.1838	0.882045
$426$	2.21807	0.107466
$427$	1.93905i	0.0938374i
$428$	−6.86969	−0.332059
$429$	0	0
$430$	5.03823	0.242965
$431$	− 29.7020i	− 1.43069i	−0.698770	−	0.715346i	$-0.746269\pi$
$431$	− 29.7020i	− 1.43069i	0.698770	−	0.715346i	$-0.253731\pi$
$432$	17.2806	0.831412
$433$	0.203068	0.00975884	0.00487942	−	0.999988i	$-0.498447\pi$
$433$	0.203068	0.00975884	0.00487942	+	0.999988i	$0.498447\pi$
$434$	− 0.292070i	− 0.0140198i
$435$	− 3.24051i	− 0.155370i
$436$	− 32.9383i	− 1.57746i
$437$	− 38.8982i	− 1.86075i
$438$	−1.08518	−0.0518517
$439$	−29.9951	−1.43159	−0.715794	−	0.698311i	$-0.753935\pi$
$439$	−29.9951	−1.43159	−0.715794	+	0.698311i	$0.753935\pi$
$440$	− 6.28389i	− 0.299573i
$441$	−4.61930	−0.219966
$442$	0	0
$443$	1.17113	0.0556421	0.0278211	−	0.999613i	$-0.491143\pi$
$443$	1.17113	0.0556421	0.0278211	+	0.999613i	$0.491143\pi$
$444$	30.9391i	1.46830i
$445$	−27.4720	−1.30230
$446$	0.675774	0.0319988
$447$	37.3358i	1.76592i
$448$	7.46745i	0.352804i
$449$	9.29361i	0.438593i	0.975658	+	0.219296i	$0.0703761\pi$
$449$	9.29361i	0.438593i	−0.975658	+	0.219296i	$0.929624\pi$
$450$	− 8.36054i	− 0.394120i
$451$	17.1117	0.805760
$452$	36.1646	1.70104
$453$	− 13.8751i	− 0.651909i
$454$	−1.47703	−0.0693205
$455$	0	0
$456$	−9.74708	−0.456449
$457$	− 30.3849i	− 1.42134i	−0.703523	−	0.710672i	$-0.748391\pi$
$457$	− 30.3849i	− 1.42134i	0.703523	−	0.710672i	$-0.251609\pi$
$458$	−0.665413	−0.0310927
$459$	−6.72072	−0.313696
$460$	53.6160i	2.49986i
$461$	− 27.9856i	− 1.30342i	−0.758468	−	0.651710i	$-0.774052\pi$
$461$	− 27.9856i	− 1.30342i	0.758468	−	0.651710i	$-0.225948\pi$
$462$	1.05475i	0.0490713i
$463$	4.38020i	0.203565i	0.994807	+	0.101783i	$0.0324546\pi$
$463$	4.38020i	0.203565i	−0.994807	+	0.101783i	$0.967545\pi$
$464$	1.09778	0.0509630
$465$	22.2718	1.03283
$466$	− 4.13831i	− 0.191704i
$467$	−9.59064	−0.443802	−0.221901	−	0.975069i	$-0.571226\pi$
$467$	−9.59064	−0.443802	−0.221901	+	0.975069i	$0.571226\pi$
$468$	0	0
$469$	−3.38134	−0.156136
$470$	− 2.44053i	− 0.112573i
$471$	−31.7265	−1.46188
$472$	2.21098	0.101768
$473$	− 20.7894i	− 0.955898i
$474$	3.26149i	0.149805i
$475$	− 71.7370i	− 3.29152i
$476$	− 2.97352i	− 0.136291i
$477$	−4.99528	−0.228718
$478$	2.57968	0.117992
$479$	0.637948i	0.0291486i	0.999894	+	0.0145743i	$0.00463931\pi$
$479$	0.637948i	0.0291486i	−0.999894	+	0.0145743i	$0.995361\pi$
$480$	20.1904	0.921561
$481$	0	0
$482$	−3.95930	−0.180341
$483$	− 18.1008i	− 0.823614i
$484$	8.86192	0.402815
$485$	−2.08581	−0.0947118
$486$	− 2.63475i	− 0.119515i
$487$	− 34.6352i	− 1.56947i	−0.619830	−	0.784736i	$-0.712799\pi$
$487$	− 34.6352i	− 1.56947i	0.619830	−	0.784736i	$-0.287201\pi$
$488$	1.15429i	0.0522525i
$489$	− 35.4164i	− 1.60159i
$490$	−0.618759	−0.0279527
$491$	−28.5890	−1.29020	−0.645101	−	0.764097i	$-0.723185\pi$
$491$	−28.5890	−1.29020	−0.645101	+	0.764097i	$0.723185\pi$
$492$	36.5851i	1.64938i
$493$	−0.426945	−0.0192286
$494$	0	0
$495$	−48.7615	−2.19167
$496$	7.54495i	0.338778i
$497$	5.36923	0.240843
$498$	−4.34879	−0.194874
$499$	− 35.1797i	− 1.57486i	−0.616403	−	0.787431i	$-0.711411\pi$
$499$	− 35.1797i	− 1.57486i	0.616403	−	0.787431i	$-0.288589\pi$
$500$	57.9986i	2.59377i
$501$	− 59.7845i	− 2.67097i
$502$	1.18501i	0.0528897i
$503$	9.42778	0.420364	0.210182	−	0.977662i	$-0.432594\pi$
$503$	9.42778	0.420364	0.210182	+	0.977662i	$0.432594\pi$
$504$	−2.74981	−0.122486
$505$	− 29.7023i	− 1.32173i
$506$	−2.50571	−0.111392
$507$	0	0
$508$	15.7845	0.700325
$509$	2.62920i	0.116537i	0.998301	+	0.0582686i	$0.0185580\pi$
$509$	2.62920i	0.116537i	−0.998301	+	0.0582686i	$0.981442\pi$
$510$	−2.56809	−0.113717
$511$	−2.62686	−0.116205
$512$	11.4427i	0.505703i
$513$	26.5139i	1.17062i
$514$	2.98901i	0.131840i
$515$	63.0839i	2.77981i
$516$	44.4481	1.95672
$517$	−10.0704	−0.442897
$518$	− 0.848236i	− 0.0372693i
$519$	−45.0343	−1.97678
$520$	0	0
$521$	19.6001	0.858696	0.429348	−	0.903139i	$-0.358743\pi$
$521$	19.6001	0.858696	0.429348	+	0.903139i	$0.358743\pi$
$522$	0.196300i	0.00859184i
$523$	−14.8982	−0.651452	−0.325726	−	0.945464i	$-0.605609\pi$
$523$	−14.8982	−0.651452	−0.325726	+	0.945464i	$0.605609\pi$
$524$	−37.0271	−1.61754
$525$	− 33.3819i	− 1.45690i
$526$	− 0.431711i	− 0.0188235i
$527$	− 2.93436i	− 0.127823i
$528$	− 27.2469i	− 1.18577i
$529$	20.0011	0.869612
$530$	−0.669122	−0.0290648
$531$	− 17.1567i	− 0.744535i
$532$	−11.7308	−0.508596
$533$	0	0
$534$	2.74497	0.118787
$535$	14.3620i	0.620922i
$536$	−2.01287	−0.0869427
$537$	3.92533	0.169390
$538$	− 1.88369i	− 0.0812116i
$539$	2.55320i	0.109974i
$540$	− 36.5459i	− 1.57268i
$541$	− 10.4746i	− 0.450339i	−0.974320	−	0.225170i	$-0.927706\pi$
$541$	− 10.4746i	− 0.450339i	0.974320	−	0.225170i	$-0.0722936\pi$
$542$	3.20283	0.137573
$543$	52.9691	2.27312
$544$	− 2.66013i	− 0.114052i
$545$	−68.8618	−2.94972
$546$	0	0
$547$	−24.9324	−1.06603	−0.533016	−	0.846105i	$-0.678942\pi$
$547$	−24.9324	−1.06603	−0.533016	+	0.846105i	$0.678942\pi$
$548$	4.59942i	0.196477i
$549$	8.95706	0.382278
$550$	−4.62109	−0.197044
$551$	1.68434i	0.0717553i
$552$	− 10.7752i	− 0.458622i
$553$	7.89503i	0.335731i
$554$	2.03632i	0.0865150i
$555$	64.6821	2.74560
$556$	17.8432	0.756719
$557$	33.0777i	1.40155i	0.713384	+	0.700774i	$0.247162\pi$
$557$	33.0777i	1.40155i	−0.713384	+	0.700774i	$0.752838\pi$
$558$	−1.34916	−0.0571144
$559$	0	0
$560$	15.9842	0.675455
$561$	10.5968i	0.447398i
$562$	−4.59781	−0.193947
$563$	4.54152	0.191402	0.0957012	−	0.995410i	$-0.469491\pi$
$563$	4.54152	0.191402	0.0957012	+	0.995410i	$0.469491\pi$
$564$	− 21.5307i	− 0.906608i
$565$	− 75.6068i	− 3.18080i
$566$	− 4.15819i	− 0.174782i
$567$	− 1.51999i	− 0.0638337i
$568$	3.19624	0.134111
$569$	20.8507	0.874105	0.437053	−	0.899436i	$-0.356022\pi$
$569$	20.8507	0.874105	0.437053	+	0.899436i	$0.356022\pi$
$570$	10.1314i	0.424357i
$571$	31.9139	1.33556	0.667778	−	0.744360i	$-0.267245\pi$
$571$	31.9139	1.33556	0.667778	+	0.744360i	$0.267245\pi$
$572$	0	0
$573$	38.6469	1.61450
$574$	− 1.00303i	− 0.0418656i
$575$	79.3036	3.30719
$576$	34.4944	1.43727
$577$	13.7190i	0.571129i	0.958359	+	0.285565i	$0.0921811\pi$
$577$	13.7190i	0.571129i	−0.958359	+	0.285565i	$0.907819\pi$
$578$	− 2.20587i	− 0.0917520i
$579$	− 3.50378i	− 0.145612i
$580$	− 2.32164i	− 0.0964008i
$581$	−10.5270	−0.436734
$582$	0.208412	0.00863894
$583$	2.76102i	0.114350i
$584$	−1.56374	−0.0647079
$585$	0	0
$586$	0.0219687	0.000907518 0
$587$	− 25.0820i	− 1.03525i	−0.855609	−	0.517623i	$-0.826817\pi$
$587$	− 25.0820i	− 1.03525i	0.855609	−	0.517623i	$-0.173183\pi$
$588$	−5.45879	−0.225117
$589$	−11.5764	−0.476995
$590$	− 2.29815i	− 0.0946134i
$591$	7.78497i	0.320231i
$592$	21.9122i	0.900585i
$593$	26.7388i	1.09803i	0.835812	+	0.549016i	$0.184997\pi$
$593$	26.7388i	1.09803i	−0.835812	+	0.549016i	$0.815003\pi$
$594$	1.70795	0.0700780
$595$	−6.21653	−0.254853
$596$	26.7490i	1.09568i
$597$	−53.1635	−2.17584
$598$	0	0
$599$	21.1279	0.863264	0.431632	−	0.902050i	$-0.357938\pi$
$599$	21.1279	0.863264	0.431632	+	0.902050i	$0.357938\pi$
$600$	− 19.8718i	− 0.811263i
$601$	26.0691	1.06338	0.531691	−	0.846938i	$-0.321557\pi$
$601$	26.0691	1.06338	0.531691	+	0.846938i	$0.321557\pi$
$602$	−1.21860	−0.0496665
$603$	15.6194i	0.636071i
$604$	− 9.94071i	− 0.404482i
$605$	− 18.5270i	− 0.753229i
$606$	2.96782i	0.120559i
$607$	11.0294	0.447670	0.223835	−	0.974627i	$-0.428142\pi$
$607$	11.0294	0.447670	0.223835	+	0.974627i	$0.428142\pi$
$608$	−10.4945	−0.425608
$609$	0.783786i	0.0317606i
$610$	1.19981	0.0485788
$611$	0	0
$612$	−13.7356	−0.555228
$613$	8.29847i	0.335172i	0.985857	+	0.167586i	$0.0535972\pi$
$613$	8.29847i	0.335172i	−0.985857	+	0.167586i	$0.946403\pi$
$614$	4.73654	0.191151
$615$	76.4859	3.08421
$616$	1.51989i	0.0612382i
$617$	19.8547i	0.799320i	0.916663	+	0.399660i	$0.130872\pi$
$617$	19.8547i	0.799320i	−0.916663	+	0.399660i	$0.869128\pi$
$618$	− 6.30327i	− 0.253555i
$619$	15.9751i	0.642093i	0.947063	+	0.321047i	$0.104035\pi$
$619$	15.9751i	0.642093i	−0.947063	+	0.321047i	$0.895965\pi$
$620$	15.9565	0.640827
$621$	−29.3105	−1.17619
$622$	− 2.82270i	− 0.113180i
$623$	6.64469	0.266214
$624$	0	0
$625$	60.7858	2.43143
$626$	− 5.05545i	− 0.202057i
$627$	41.8055	1.66955
$628$	−22.7302	−0.907035
$629$	− 8.52203i	− 0.339796i
$630$	2.85823i	0.113875i
$631$	29.5325i	1.17567i	0.808981	+	0.587835i	$0.200019\pi$
$631$	29.5325i	1.17567i	−0.808981	+	0.587835i	$0.799981\pi$
$632$	4.69981i	0.186949i
$633$	−35.4541	−1.40918
$634$	−3.30520	−0.131266
$635$	− 32.9996i	− 1.30955i
$636$	−5.90310	−0.234073
$637$	0	0
$638$	0.108500	0.00429557
$639$	− 24.8021i	− 0.981154i
$640$	19.2496	0.760909
$641$	−25.6564	−1.01337	−0.506683	−	0.862132i	$-0.669129\pi$
$641$	−25.6564	−1.01337	−0.506683	+	0.862132i	$0.669129\pi$
$642$	− 1.43503i	− 0.0566361i
$643$	27.8289i	1.09746i	0.835998	+	0.548732i	$0.184889\pi$
$643$	27.8289i	1.09746i	−0.835998	+	0.548732i	$0.815111\pi$
$644$	− 12.9682i	− 0.511017i
$645$	− 92.9244i	− 3.65890i
$646$	1.33484	0.0525184
$647$	−14.0636	−0.552899	−0.276449	−	0.961028i	$-0.589158\pi$
$647$	−14.0636	−0.552899	−0.276449	+	0.961028i	$0.589158\pi$
$648$	− 0.904834i	− 0.0355452i
$649$	−9.48293	−0.372238
$650$	0	0
$651$	−5.38690	−0.211129
$652$	− 25.3738i	− 0.993716i
$653$	32.1381	1.25766	0.628831	−	0.777542i	$-0.283534\pi$
$653$	32.1381	1.25766	0.628831	+	0.777542i	$0.283534\pi$
$654$	6.88059	0.269052
$655$	77.4100i	3.02466i
$656$	25.9109i	1.01165i
$657$	12.1342i	0.473402i
$658$	0.590294i	0.0230121i
$659$	38.7643	1.51004	0.755021	−	0.655700i	$-0.227627\pi$
$659$	38.7643	1.51004	0.755021	+	0.655700i	$0.227627\pi$
$660$	−57.6233	−2.24298
$661$	− 31.1898i	− 1.21314i	−0.795029	−	0.606571i	$-0.792545\pi$
$661$	− 31.1898i	− 1.21314i	0.795029	−	0.606571i	$-0.207455\pi$
$662$	−3.79237	−0.147395
$663$	0	0
$664$	−6.26660	−0.243191
$665$	24.5248i	0.951032i
$666$	−3.91825	−0.151829
$667$	−1.86200	−0.0720969
$668$	− 42.8321i	− 1.65723i
$669$	− 12.4639i	− 0.481881i
$670$	2.09223i	0.0808300i
$671$	− 4.95080i	− 0.191124i
$672$	−4.88347	−0.188384
$673$	6.51491	0.251131	0.125566	−	0.992085i	$-0.459925\pi$
$673$	6.51491	0.251131	0.125566	+	0.992085i	$0.459925\pi$
$674$	3.93001i	0.151379i
$675$	−54.0551	−2.08058
$676$	0	0
$677$	26.3121	1.01126	0.505629	−	0.862751i	$-0.331260\pi$
$677$	26.3121	1.01126	0.505629	+	0.862751i	$0.331260\pi$
$678$	7.55454i	0.290130i
$679$	0.504498	0.0193608
$680$	−3.70062	−0.141912
$681$	27.2421i	1.04392i
$682$	0.745715i	0.0285549i
$683$	20.2861i	0.776226i	0.921612	+	0.388113i	$0.126873\pi$
$683$	20.2861i	0.776226i	−0.921612	+	0.388113i	$0.873127\pi$
$684$	54.1882i	2.07194i
$685$	9.61567	0.367396
$686$	0.149660	0.00571404
$687$	12.2728i	0.468236i
$688$	31.4797	1.20015
$689$	0	0
$690$	−11.2000	−0.426377
$691$	− 8.37956i	− 0.318773i	−0.987216	−	0.159387i	$-0.949048\pi$
$691$	− 8.37956i	− 0.318773i	0.987216	−	0.159387i	$-0.0509517\pi$
$692$	−32.2645	−1.22651
$693$	11.7940	0.448017
$694$	− 0.618627i	− 0.0234828i
$695$	− 37.3034i	− 1.41500i
$696$	0.466578i	0.0176856i
$697$	− 10.0772i	− 0.381701i
$698$	0.601839	0.0227800
$699$	−76.3265	−2.88693
$700$	− 23.9162i	− 0.903947i
$701$	49.5870	1.87288	0.936438	−	0.350832i	$-0.114101\pi$
$701$	49.5870	1.87288	0.936438	+	0.350832i	$0.114101\pi$
$702$	0	0
$703$	−33.6203	−1.26801
$704$	− 19.0659i	− 0.718574i
$705$	−45.0128	−1.69528
$706$	0.397445	0.0149580
$707$	7.18413i	0.270187i
$708$	− 20.2746i	− 0.761968i
$709$	14.4361i	0.542160i	0.962557	+	0.271080i	$0.0873807\pi$
$709$	14.4361i	0.542160i	−0.962557	+	0.271080i	$0.912619\pi$
$710$	− 3.32226i	− 0.124682i
$711$	36.4695	1.36771
$712$	3.95550	0.148239
$713$	− 12.7974i	− 0.479266i
$714$	0.621148	0.0232459
$715$	0	0
$716$	2.81227	0.105100
$717$	− 47.5793i	− 1.77688i
$718$	−0.776031	−0.0289612
$719$	−19.6313	−0.732122	−0.366061	−	0.930591i	$-0.619294\pi$
$719$	−19.6313	−0.732122	−0.366061	+	0.930591i	$0.619294\pi$
$720$	− 73.8357i	− 2.75169i
$721$	− 15.2582i	− 0.568244i
$722$	− 2.42252i	− 0.0901569i
$723$	73.0248i	2.71582i
$724$	37.9493	1.41037
$725$	−3.43394	−0.127533
$726$	1.85119i	0.0687043i
$727$	36.3713	1.34894	0.674468	−	0.738304i	$-0.264373\pi$
$727$	36.3713	1.34894	0.674468	+	0.738304i	$0.264373\pi$
$728$	0	0
$729$	−44.0350	−1.63093
$730$	1.62539i	0.0601585i
$731$	−12.2430	−0.452825
$732$	10.5849	0.391228
$733$	− 24.4766i	− 0.904064i	−0.892002	−	0.452032i	$-0.850699\pi$
$733$	− 24.4766i	− 0.904064i	0.892002	−	0.452032i	$-0.149301\pi$
$734$	− 1.57040i	− 0.0579646i
$735$	11.4123i	0.420949i
$736$	− 11.6014i	− 0.427634i
$737$	8.63325	0.318010
$738$	−4.63329	−0.170554
$739$	36.3349i	1.33660i	0.743892	+	0.668300i	$0.232978\pi$
$739$	36.3349i	1.33660i	−0.743892	+	0.668300i	$0.767022\pi$
$740$	46.3410	1.70353
$741$	0	0
$742$	0.161841	0.00594139
$743$	− 1.66844i	− 0.0612092i	−0.999532	−	0.0306046i	$-0.990257\pi$
$743$	− 1.66844i	− 0.0612092i	0.999532	−	0.0306046i	$-0.00974327\pi$
$744$	−3.20676	−0.117565
$745$	55.9222	2.04883
$746$	− 3.82614i	− 0.140085i
$747$	48.6274i	1.77918i
$748$	7.59201i	0.277591i
$749$	− 3.47375i	− 0.126928i
$750$	−12.1155	−0.442396
$751$	25.6435	0.935743	0.467871	−	0.883797i	$-0.345021\pi$
$751$	25.6435	0.935743	0.467871	+	0.883797i	$0.345021\pi$
$752$	− 15.2489i	− 0.556069i
$753$	21.8562	0.796484
$754$	0	0
$755$	−20.7823	−0.756347
$756$	8.83939i	0.321486i
$757$	29.6442	1.07744	0.538719	−	0.842485i	$-0.318908\pi$
$757$	29.6442	1.07744	0.538719	+	0.842485i	$0.318908\pi$
$758$	0.0895209	0.00325154
$759$	46.2150i	1.67750i
$760$	14.5993i	0.529573i
$761$	− 28.5689i	− 1.03562i	−0.855495	−	0.517811i	$-0.826747\pi$
$761$	− 28.5689i	− 1.03562i	0.855495	−	0.517811i	$-0.173253\pi$
$762$	3.29728i	0.119448i
$763$	16.6557	0.602977
$764$	27.6883	1.00173
$765$	28.7160i	1.03823i
$766$	−1.53665	−0.0555213
$767$	0	0
$768$	39.3015	1.41817
$769$	26.6293i	0.960276i	0.877193	+	0.480138i	$0.159413\pi$
$769$	26.6293i	0.960276i	−0.877193	+	0.480138i	$0.840587\pi$
$770$	1.57982	0.0569327
$771$	55.1289	1.98542
$772$	− 2.51026i	− 0.0903462i
$773$	− 45.5999i	− 1.64011i	−0.572283	−	0.820056i	$-0.693942\pi$
$773$	− 45.5999i	− 1.64011i	0.572283	−	0.820056i	$-0.306058\pi$
$774$	5.62909i	0.202333i
$775$	− 23.6012i	− 0.847781i
$776$	0.300321	0.0107809
$777$	−15.6447	−0.561252
$778$	0.464142i	0.0166403i
$779$	−39.7556	−1.42439
$780$	0	0
$781$	−13.7087	−0.490537
$782$	1.47563i	0.0527684i
$783$	1.26918	0.0453568
$784$	−3.86611	−0.138075
$785$	47.5205i	1.69608i
$786$	− 7.73471i	− 0.275888i
$787$	27.5508i	0.982079i	0.871137	+	0.491040i	$0.163383\pi$
$787$	27.5508i	0.982079i	−0.871137	+	0.491040i	$0.836617\pi$
$788$	5.57749i	0.198690i
$789$	−7.96242	−0.283470
$790$	4.88512	0.173805
$791$	18.2871i	0.650215i
$792$	7.02083	0.249474
$793$	0	0
$794$	−1.32961	−0.0471860
$795$	12.3412i	0.437697i
$796$	−38.0886	−1.35001
$797$	−14.4713	−0.512599	−0.256299	−	0.966597i	$-0.582503\pi$
$797$	−14.4713	−0.512599	−0.256299	+	0.966597i	$0.582503\pi$
$798$	− 2.45049i	− 0.0867465i
$799$	5.93055i	0.209808i
$800$	− 21.3956i	− 0.756449i
$801$	− 30.6938i	− 1.08451i
$802$	0.795640	0.0280950
$803$	6.70691	0.236682
$804$	18.4580i	0.650964i
$805$	−27.1116	−0.955559
$806$	0	0
$807$	−34.7425	−1.22299
$808$	4.27662i	0.150451i
$809$	45.2178	1.58977	0.794886	−	0.606758i	$-0.207530\pi$
$809$	45.2178	1.58977	0.794886	+	0.606758i	$0.207530\pi$
$810$	−0.940510	−0.0330462
$811$	− 21.8610i	− 0.767644i	−0.923407	−	0.383822i	$-0.874608\pi$
$811$	− 21.8610i	− 0.767644i	0.923407	−	0.383822i	$-0.125392\pi$
$812$	0.561537i	0.0197061i
$813$	− 59.0726i	− 2.07176i
$814$	2.16572i	0.0759084i
$815$	−53.0473	−1.85816
$816$	−16.0459	−0.561719
$817$	48.2999i	1.68980i
$818$	−0.256226	−0.00895872
$819$	0	0
$820$	54.7978	1.91362
$821$	38.5812i	1.34649i	0.739417	+	0.673247i	$0.235101\pi$
$821$	38.5812i	1.34649i	−0.739417	+	0.673247i	$0.764899\pi$
$822$	−0.960786	−0.0335113
$823$	12.9067	0.449899	0.224949	−	0.974370i	$-0.427778\pi$
$823$	12.9067	0.449899	0.224949	+	0.974370i	$0.427778\pi$
$824$	− 9.08301i	− 0.316421i
$825$	85.2307i	2.96735i
$826$	0.555856i	0.0193407i
$827$	− 18.4205i	− 0.640544i	−0.947326	−	0.320272i	$-0.896226\pi$
$827$	− 18.4205i	− 0.640544i	0.947326	−	0.320272i	$-0.103774\pi$
$828$	−59.9038	−2.08180
$829$	−24.6596	−0.856464	−0.428232	−	0.903669i	$-0.640863\pi$
$829$	−24.6596	−0.856464	−0.428232	+	0.903669i	$0.640863\pi$
$830$	6.51368i	0.226093i
$831$	37.5576	1.30286
$832$	0	0
$833$	1.50360	0.0520966
$834$	3.72731i	0.129066i
$835$	−89.5461	−3.09887
$836$	29.9512	1.03588
$837$	8.72299i	0.301511i
$838$	− 0.948757i	− 0.0327743i
$839$	37.4397i	1.29256i	0.763100	+	0.646281i	$0.223677\pi$
$839$	37.4397i	1.29256i	−0.763100	+	0.646281i	$0.776323\pi$
$840$	6.79360i	0.234402i
$841$	−28.9194	−0.997220
$842$	5.05312	0.174142
$843$	84.8014i	2.92071i
$844$	−25.4009	−0.874333
$845$	0	0
$846$	2.72674	0.0937473
$847$	4.48114i	0.153974i
$848$	−4.18079	−0.143569
$849$	−76.6931	−2.63210
$850$	2.72139i	0.0933429i
$851$	− 37.1664i	− 1.27405i
$852$	− 29.3095i	− 1.00413i
$853$	− 17.6278i	− 0.603563i	−0.953377	−	0.301782i	$-0.902419\pi$
$853$	− 17.6278i	− 0.603563i	0.953377	−	0.301782i	$-0.0975814\pi$
$854$	−0.290199	−0.00993039
$855$	113.287	3.87435
$856$	− 2.06788i	− 0.0706786i
$857$	2.90411	0.0992026	0.0496013	−	0.998769i	$-0.484205\pi$
$857$	2.90411	0.0992026	0.0496013	+	0.998769i	$0.484205\pi$
$858$	0	0
$859$	18.7011	0.638074	0.319037	−	0.947742i	$-0.396640\pi$
$859$	18.7011	0.638074	0.319037	+	0.947742i	$0.396640\pi$
$860$	− 66.5750i	− 2.27019i
$861$	−18.4997	−0.630469
$862$	4.44519	0.151404
$863$	36.1575i	1.23082i	0.788208	+	0.615409i	$0.211009\pi$
$863$	36.1575i	1.23082i	−0.788208	+	0.615409i	$0.788991\pi$
$864$	7.90779i	0.269028i
$865$	67.4530i	2.29347i
$866$	0.0303912i	0.00103274i
$867$	−40.6847	−1.38172
$868$	−3.85941	−0.130997
$869$	− 20.1576i	− 0.683800i
$870$	0.484974	0.0164422
$871$	0	0
$872$	9.91493	0.335762
$873$	− 2.33042i	− 0.0788729i
$874$	5.82151	0.196915
$875$	−29.3277	−0.991458
$876$	14.3395i	0.484486i
$877$	16.1122i	0.544069i	0.962287	+	0.272035i	$0.0876965\pi$
$877$	16.1122i	0.544069i	−0.962287	+	0.272035i	$0.912303\pi$
$878$	− 4.48907i	− 0.151499i
$879$	− 0.405187i	− 0.0136666i
$880$	−40.8109	−1.37573
$881$	8.87299	0.298939	0.149469	−	0.988766i	$-0.452243\pi$
$881$	8.87299	0.298939	0.149469	+	0.988766i	$0.452243\pi$
$882$	− 0.691324i	− 0.0232781i
$883$	−14.8164	−0.498613	−0.249306	−	0.968425i	$-0.580203\pi$
$883$	−14.8164	−0.498613	−0.249306	+	0.968425i	$0.580203\pi$
$884$	0	0
$885$	−42.3868	−1.42482
$886$	0.175271i	0.00588836i
$887$	22.0508	0.740392	0.370196	−	0.928954i	$-0.379290\pi$
$887$	22.0508	0.740392	0.370196	+	0.928954i	$0.379290\pi$
$888$	−9.31312	−0.312528
$889$	7.98164i	0.267696i
$890$	− 4.11146i	− 0.137817i
$891$	3.88086i	0.130014i
$892$	− 8.92965i	− 0.298987i
$893$	23.3966	0.782937
$894$	−5.58768	−0.186880
$895$	− 5.87942i	− 0.196527i
$896$	−4.65593	−0.155544
$897$	0	0
$898$	−1.39088	−0.0464143
$899$	0.554142i	0.0184817i
$900$	−110.476	−3.68253
$901$	1.62598	0.0541694
$902$	2.56094i	0.0852700i
$903$	22.4757i	0.747946i
$904$	10.8861i	0.362066i
$905$	− 79.3379i	− 2.63728i
$906$	2.07655	0.0689886
$907$	10.0602	0.334044	0.167022	−	0.985953i	$-0.446585\pi$
$907$	10.0602	0.334044	0.167022	+	0.985953i	$0.446585\pi$
$908$	19.5174i	0.647709i
$909$	33.1856	1.10070
$910$	0	0
$911$	−33.0112	−1.09371	−0.546856	−	0.837227i	$-0.684175\pi$
$911$	−33.0112	−1.09371	−0.546856	+	0.837227i	$0.684175\pi$
$912$	63.3027i	2.09616i
$913$	26.8776	0.889519
$914$	4.54740	0.150415
$915$	− 22.1291i	− 0.731564i
$916$	8.79275i	0.290521i
$917$	− 18.7232i	− 0.618296i
$918$	− 1.00582i	− 0.0331971i
$919$	13.5362	0.446518	0.223259	−	0.974759i	$-0.428330\pi$
$919$	13.5362	0.446518	0.223259	+	0.974759i	$0.428330\pi$
$920$	−16.1392	−0.532094
$921$	− 87.3600i	− 2.87861i
$922$	4.18832	0.137935
$923$	0	0
$924$	13.9374	0.458507
$925$	− 68.5431i	− 2.25368i
$926$	−0.655541	−0.0215424
$927$	−70.4820	−2.31493
$928$	0.502356i	0.0164906i
$929$	− 16.5687i	− 0.543601i	−0.962354	−	0.271801i	$-0.912381\pi$
$929$	− 16.5687i	− 0.543601i	0.962354	−	0.271801i	$-0.0876191\pi$
$930$	3.33319i	0.109300i
$931$	− 5.93185i	− 0.194408i
$932$	−54.6835	−1.79122
$933$	−52.0615	−1.70442
$934$	− 1.43533i	− 0.0469656i
$935$	15.8721	0.519072
$936$	0	0
$937$	35.2063	1.15014	0.575070	−	0.818104i	$-0.304975\pi$
$937$	35.2063	1.15014	0.575070	+	0.818104i	$0.304975\pi$
$938$	− 0.506051i	− 0.0165231i
$939$	−93.2420	−3.04284
$940$	−32.2491	−1.05185
$941$	− 29.0236i	− 0.946142i	−0.881024	−	0.473071i	$-0.843145\pi$
$941$	− 29.0236i	− 0.946142i	0.881024	−	0.473071i	$-0.156855\pi$
$942$	− 4.74819i	− 0.154704i
$943$	− 43.9489i	− 1.43117i
$944$	− 14.3592i	− 0.467353i
$945$	18.4799	0.601151
$946$	3.11134	0.101158
$947$	− 43.1704i	− 1.40285i	−0.712744	−	0.701425i	$-0.752548\pi$
$947$	− 43.1704i	− 1.40285i	0.712744	−	0.701425i	$-0.247452\pi$
$948$	43.0973	1.39973
$949$	0	0
$950$	10.7362	0.348327
$951$	60.9606i	1.97678i
$952$	0.895074	0.0290095
$953$	−12.7569	−0.413236	−0.206618	−	0.978422i	$-0.566246\pi$
$953$	−12.7569	−0.413236	−0.206618	+	0.978422i	$0.566246\pi$
$954$	− 0.747593i	− 0.0242042i
$955$	− 57.8859i	− 1.87314i
$956$	− 34.0878i	− 1.10248i
$957$	− 2.00117i	− 0.0646885i
$958$	−0.0954753	−0.00308467
$959$	−2.32575	−0.0751025
$960$	− 85.2208i	− 2.75049i
$961$	27.1914	0.877143
$962$	0	0
$963$	−16.0463	−0.517083
$964$	52.3181i	1.68505i
$965$	−5.24802	−0.168940
$966$	2.70896	0.0871594
$967$	− 24.7647i	− 0.796380i	−0.917303	−	0.398190i	$-0.869639\pi$
$967$	− 24.7647i	− 0.796380i	0.917303	−	0.398190i	$-0.130361\pi$
$968$	2.66757i	0.0857390i
$969$	− 24.6195i	− 0.790893i
$970$	− 0.312162i	− 0.0100229i
$971$	6.83748	0.219425	0.109713	−	0.993963i	$-0.465007\pi$
$971$	6.83748	0.219425	0.109713	+	0.993963i	$0.465007\pi$
$972$	−34.8155	−1.11671
$973$	9.02263i	0.289252i
$974$	5.18351	0.166090
$975$	0	0
$976$	7.49660	0.239960
$977$	− 15.5220i	− 0.496594i	−0.968684	−	0.248297i	$-0.920129\pi$
$977$	− 15.5220i	− 0.496594i	0.968684	−	0.248297i	$-0.0798708\pi$
$978$	5.30042	0.169489
$979$	−16.9653	−0.542212
$980$	8.17626i	0.261181i
$981$	− 76.9376i	− 2.45643i
$982$	− 4.27862i	− 0.136536i
$983$	− 2.75887i	− 0.0879941i	−0.999032	−	0.0439971i	$-0.985991\pi$
$983$	− 2.75887i	− 0.0879941i	0.999032	−	0.0439971i	$-0.0140092\pi$
$984$	−11.0127	−0.351071
$985$	11.6605	0.371533
$986$	− 0.0638966i	− 0.00203488i
$987$	10.8873	0.346547
$988$	0	0
$989$	−53.3945	−1.69784
$990$	− 7.29765i	− 0.231935i
$991$	24.2991	0.771886	0.385943	−	0.922523i	$-0.373876\pi$
$991$	24.2991	0.771886	0.385943	+	0.922523i	$0.373876\pi$
$992$	−3.45265	−0.109622
$993$	69.9460i	2.21967i
$994$	0.803558i	0.0254873i
$995$	79.6291i	2.52441i
$996$	57.4647i	1.82084i
$997$	13.5557	0.429313	0.214657	−	0.976690i	$-0.431137\pi$
$997$	13.5557	0.429313	0.214657	+	0.976690i	$0.431137\pi$
$998$	5.26500	0.166661
$999$	25.3335i	0.801515i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.c.j.337.13		24
13.5	odd	4		1183.2.a.q.1.7	✓	12
13.8	odd	4		1183.2.a.r.1.6	yes	12
13.12	even	2	inner	1183.2.c.j.337.12		24
91.34	even	4		8281.2.a.cq.1.6		12
91.83	even	4		8281.2.a.cn.1.7		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1183.2.a.q.1.7	✓	12	13.5	odd	4
1183.2.a.r.1.6	yes	12	13.8	odd	4
1183.2.c.j.337.12		24	13.12	even	2	inner
1183.2.c.j.337.13		24	1.1	even	1	trivial
8281.2.a.cn.1.7		12	91.83	even	4
8281.2.a.cq.1.6		12	91.34	even	4

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:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+0.149660i q^{2} +2.76031 q^{3} +1.97760 q^{4} -4.13443i q^{5} +0.413107i q^{6} +1.00000i q^{7} +0.595288i q^{8} +4.61930 q^{9} +O(q^{10})\)	\(q+0.149660i q^{2} +2.76031 q^{3} +1.97760 q^{4} -4.13443i q^{5} +0.413107i q^{6} +1.00000i q^{7} +0.595288i q^{8} +4.61930 q^{9} +0.618759 q^{10} -2.55320i q^{11} +5.45879 q^{12} -0.149660 q^{14} -11.4123i q^{15} +3.86611 q^{16} -1.50360 q^{17} +0.691324i q^{18} +5.93185i q^{19} -8.17626i q^{20} +2.76031i q^{21} +0.382113 q^{22} -6.55752 q^{23} +1.64318i q^{24} -12.0935 q^{25} +4.46975 q^{27} +1.97760i q^{28} +0.283949 q^{29} +1.70797 q^{30} +1.95156i q^{31} +1.76918i q^{32} -7.04763i q^{33} -0.225029i q^{34} +4.13443 q^{35} +9.13513 q^{36} +5.66775i q^{37} -0.887760 q^{38} +2.46118 q^{40} +6.70206i q^{41} -0.413107 q^{42} +8.14248 q^{43} -5.04922i q^{44} -19.0982i q^{45} -0.981398i q^{46} -3.94423i q^{47} +10.6717 q^{48} -1.00000 q^{49} -1.80992i q^{50} -4.15040 q^{51} -1.08139 q^{53} +0.668943i q^{54} -10.5561 q^{55} -0.595288 q^{56} +16.3737i q^{57} +0.0424957i q^{58} -3.71413i q^{59} -22.5690i q^{60} +1.93905 q^{61} -0.292070 q^{62} +4.61930i q^{63} +7.46745 q^{64} +1.05475 q^{66} +3.38134i q^{67} -2.97352 q^{68} -18.1008 q^{69} +0.618759i q^{70} -5.36923i q^{71} +2.74981i q^{72} +2.62686i q^{73} -0.848236 q^{74} -33.3819 q^{75} +11.7308i q^{76} +2.55320 q^{77} +7.89503 q^{79} -15.9842i q^{80} -1.51999 q^{81} -1.00303 q^{82} +10.5270i q^{83} +5.45879i q^{84} +6.21653i q^{85} +1.21860i q^{86} +0.783786 q^{87} +1.51989 q^{88} -6.64469i q^{89} +2.85823 q^{90} -12.9682 q^{92} +5.38690i q^{93} +0.590294 q^{94} +24.5248 q^{95} +4.88347i q^{96} -0.504498i q^{97} -0.149660i q^{98} -11.7940i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 16 q^{3} - 30 q^{4} + 52 q^{9}+O(q^{10}) \) 24 * q + 16 * q^3 - 30 * q^4 + 52 * q^9	\( 24 q + 16 q^{3} - 30 q^{4} + 52 q^{9} + 12 q^{10} - 26 q^{12} + 6 q^{14} + 26 q^{16} - 62 q^{17} - 8 q^{22} - 36 q^{23} - 64 q^{25} + 64 q^{27} + 30 q^{29} + 20 q^{30} - 8 q^{35} - 98 q^{36} - 90 q^{38} - 40 q^{40} + 4 q^{42} + 44 q^{43} + 22 q^{48} - 24 q^{49} - 36 q^{51} + 106 q^{53} - 52 q^{55} - 24 q^{56} + 44 q^{61} - 38 q^{62} - 4 q^{64} - 68 q^{66} + 68 q^{68} - 6 q^{69} - 80 q^{74} - 30 q^{75} - 24 q^{77} + 4 q^{79} + 72 q^{81} + 64 q^{82} + 54 q^{87} + 96 q^{88} + 52 q^{90} + 104 q^{92} - 88 q^{94} - 58 q^{95}+O(q^{100}) \) 24 * q + 16 * q^3 - 30 * q^4 + 52 * q^9 + 12 * q^10 - 26 * q^12 + 6 * q^14 + 26 * q^16 - 62 * q^17 - 8 * q^22 - 36 * q^23 - 64 * q^25 + 64 * q^27 + 30 * q^29 + 20 * q^30 - 8 * q^35 - 98 * q^36 - 90 * q^38 - 40 * q^40 + 4 * q^42 + 44 * q^43 + 22 * q^48 - 24 * q^49 - 36 * q^51 + 106 * q^53 - 52 * q^55 - 24 * q^56 + 44 * q^61 - 38 * q^62 - 4 * q^64 - 68 * q^66 + 68 * q^68 - 6 * q^69 - 80 * q^74 - 30 * q^75 - 24 * q^77 + 4 * q^79 + 72 * q^81 + 64 * q^82 + 54 * q^87 + 96 * q^88 + 52 * q^90 + 104 * q^92 - 88 * q^94 - 58 * q^95

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