LMFDB - Embedded newform 324.3.k.a.17.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,3,Mod(17,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 11]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("324.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.k (of order $18$, degree $6$, 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:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			17.2
Character	$\chi$	$=$	324.17
Dual form			324.3.k.a.305.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.29223 - 0.580508i) q^{5} +(3.84473 - 3.22611i) q^{7} +O(q^{10})$	$q+(-3.29223 - 0.580508i) q^{5} +(3.84473 - 3.22611i) q^{7} +(-7.73764 + 1.36435i) q^{11} +(13.9363 - 5.07239i) q^{13} +(-18.4112 - 10.6297i) q^{17} +(-12.0316 - 20.8393i) q^{19} +(13.5318 - 16.1265i) q^{23} +(-12.9905 - 4.72817i) q^{25} +(10.7443 - 29.5197i) q^{29} +(3.12883 + 2.62540i) q^{31} +(-14.5305 + 8.38919i) q^{35} +(20.6961 - 35.8467i) q^{37} +(1.46139 + 4.01515i) q^{41} +(-2.94313 - 16.6913i) q^{43} +(-42.4392 - 50.5770i) q^{47} +(-4.13462 + 23.4486i) q^{49} +63.0022i q^{53} +26.2661 q^{55} +(75.1069 + 13.2434i) q^{59} +(-76.5149 + 64.2036i) q^{61} +(-48.8259 + 8.60932i) q^{65} +(83.0701 - 30.2350i) q^{67} +(-4.34219 - 2.50696i) q^{71} +(-19.2797 - 33.3934i) q^{73} +(-25.3476 + 30.2080i) q^{77} +(-35.9010 - 13.0669i) q^{79} +(48.8367 - 134.178i) q^{83} +(54.4433 + 45.6833i) q^{85} +(-75.2075 + 43.4211i) q^{89} +(37.2171 - 64.4618i) q^{91} +(27.5133 + 75.5921i) q^{95} +(28.6111 + 162.262i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 9 q^{5}+O(q^{10}) $ 36 * q + 9 * q^5	$ 36 q + 9 q^{5} - 36 q^{11} + 18 q^{23} - 9 q^{25} + 18 q^{29} + 45 q^{31} + 243 q^{35} + 198 q^{41} + 90 q^{43} + 243 q^{47} + 72 q^{49} - 252 q^{59} - 144 q^{61} - 747 q^{65} + 108 q^{67} - 324 q^{71} - 63 q^{73} - 495 q^{77} + 36 q^{79} + 27 q^{83} - 180 q^{85} + 567 q^{89} + 99 q^{91} + 1044 q^{95} - 216 q^{97}+O(q^{100}) $ 36 * q + 9 * q^5 - 36 * q^11 + 18 * q^23 - 9 * q^25 + 18 * q^29 + 45 * q^31 + 243 * q^35 + 198 * q^41 + 90 * q^43 + 243 * q^47 + 72 * q^49 - 252 * q^59 - 144 * q^61 - 747 * q^65 + 108 * q^67 - 324 * q^71 - 63 * q^73 - 495 * q^77 + 36 * q^79 + 27 * q^83 - 180 * q^85 + 567 * q^89 + 99 * q^91 + 1044 * q^95 - 216 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$1$	$e\left(\frac{11}{18}\right)$

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			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−3.29223	−	0.580508i	−0.658445	−	0.116102i	−0.165565	−	0.986199i	$-0.552945\pi$
$5$	−3.29223	−	0.580508i	−0.658445	−	0.116102i	−0.492880	+	0.870097i	$0.664056\pi$
$6$		0			0
$7$	3.84473	−	3.22611i	0.549247	−	0.460873i	−0.325439	−	0.945563i	$-0.605512\pi$
$7$	3.84473	−	3.22611i	0.549247	−	0.460873i	0.874686	+	0.484690i	$0.161068\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−7.73764	+	1.36435i	−0.703422	+	0.124032i	−0.513907	−	0.857846i	$-0.671803\pi$
$11$	−7.73764	+	1.36435i	−0.703422	+	0.124032i	−0.189514	+	0.981878i	$0.560691\pi$
$12$		0			0
$13$	13.9363	−	5.07239i	1.07202	−	0.390183i	0.255088	−	0.966918i	$-0.417895\pi$
$13$	13.9363	−	5.07239i	1.07202	−	0.390183i	0.816932	+	0.576734i	$0.195673\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−18.4112	−	10.6297i	−1.08301	−	0.625278i	−0.151305	−	0.988487i	$-0.548348\pi$
$17$	−18.4112	−	10.6297i	−1.08301	−	0.625278i	−0.931707	+	0.363210i	$0.881681\pi$
$18$		0			0
$19$	−12.0316	−	20.8393i	−0.633241	−	1.09681i	−0.986885	−	0.161425i	$-0.948391\pi$
$19$	−12.0316	−	20.8393i	−0.633241	−	1.09681i	0.353644	−	0.935380i	$-0.384942\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	13.5318	−	16.1265i	0.588338	−	0.701153i	−0.386948	−	0.922102i	$-0.626471\pi$
$23$	13.5318	−	16.1265i	0.588338	−	0.701153i	0.975286	+	0.220948i	$0.0709151\pi$
$24$		0			0
$25$	−12.9905	−	4.72817i	−0.519622	−	0.189127i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	10.7443	−	29.5197i	0.370492	−	1.01792i	−0.604679	−	0.796469i	$-0.706699\pi$
$29$	10.7443	−	29.5197i	0.370492	−	1.01792i	0.975172	−	0.221450i	$-0.0710790\pi$
$30$		0			0
$31$	3.12883	+	2.62540i	0.100930	+	0.0846904i	0.691856	−	0.722035i	$-0.256793\pi$
$31$	3.12883	+	2.62540i	0.100930	+	0.0846904i	−0.590926	+	0.806726i	$0.701238\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−14.5305	+	8.38919i	−0.415157	+	0.239691i
$36$		0			0
$37$	20.6961	−	35.8467i	0.559354	−	0.968829i	−0.438197	−	0.898879i	$-0.644383\pi$
$37$	20.6961	−	35.8467i	0.559354	−	0.968829i	0.997550	−	0.0699503i	$-0.0222841\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.46139	+	4.01515i	0.0356438	+	0.0979304i	0.956238	−	0.292590i	$-0.0945172\pi$
$41$	1.46139	+	4.01515i	0.0356438	+	0.0979304i	−0.920594	+	0.390521i	$0.872295\pi$
$42$		0			0
$43$	−2.94313	−	16.6913i	−0.0684448	−	0.388170i	−0.999716	−	0.0238424i	$-0.992410\pi$
$43$	−2.94313	−	16.6913i	−0.0684448	−	0.388170i	0.931271	−	0.364327i	$-0.118701\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−42.4392	−	50.5770i	−0.902961	−	1.07611i	−0.996753	−	0.0805150i	$-0.974344\pi$
$47$	−42.4392	−	50.5770i	−0.902961	−	1.07611i	0.0937926	−	0.995592i	$-0.470101\pi$
$48$		0			0
$49$	−4.13462	+	23.4486i	−0.0843799	+	0.478542i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			63.0022i			1.18872i	0.804199	+	0.594361i	$0.202595\pi$
$53$			63.0022i			1.18872i	−0.804199	+	0.594361i	$0.797405\pi$
$54$		0			0
$55$	26.2661			0.477565
$56$		0			0
$57$		0			0
$58$		0			0
$59$	75.1069	+	13.2434i	1.27300	+	0.224464i	0.769005	−	0.639243i	$-0.220752\pi$
$59$	75.1069	+	13.2434i	1.27300	+	0.224464i	0.503994	+	0.863707i	$0.331863\pi$
$60$		0			0
$61$	−76.5149	+	64.2036i	−1.25434	+	1.05252i	−0.258081	+	0.966123i	$0.583090\pi$
$61$	−76.5149	+	64.2036i	−1.25434	+	1.05252i	−0.996261	+	0.0863948i	$0.972465\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−48.8259	+	8.60932i	−0.751168	+	0.132451i
$66$		0			0
$67$	83.0701	−	30.2350i	1.23985	−	0.451269i	0.362892	−	0.931831i	$-0.381790\pi$
$67$	83.0701	−	30.2350i	1.23985	−	0.451269i	0.876961	+	0.480562i	$0.159567\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−4.34219	−	2.50696i	−0.0611576	−	0.0353093i	0.469109	−	0.883140i	$-0.344575\pi$
$71$	−4.34219	−	2.50696i	−0.0611576	−	0.0353093i	−0.530267	+	0.847831i	$0.677908\pi$
$72$		0			0
$73$	−19.2797	−	33.3934i	−0.264106	−	0.457444i	0.703223	−	0.710969i	$-0.251743\pi$
$73$	−19.2797	−	33.3934i	−0.264106	−	0.457444i	−0.967329	+	0.253525i	$0.918410\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−25.3476	+	30.2080i	−0.329189	+	0.392312i
$78$		0			0
$79$	−35.9010	−	13.0669i	−0.454443	−	0.165404i	0.104649	−	0.994509i	$-0.466628\pi$
$79$	−35.9010	−	13.0669i	−0.454443	−	0.165404i	−0.559092	+	0.829105i	$0.688850\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	48.8367	−	134.178i	0.588394	−	1.61660i	−0.185045	−	0.982730i	$-0.559243\pi$
$83$	48.8367	−	134.178i	0.588394	−	1.61660i	0.773439	−	0.633870i	$-0.218535\pi$
$84$		0			0
$85$	54.4433	+	45.6833i	0.640509	+	0.537451i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−75.2075	+	43.4211i	−0.845028	+	0.487877i	−0.858970	−	0.512026i	$-0.828895\pi$
$89$	−75.2075	+	43.4211i	−0.845028	+	0.487877i	0.0139421	+	0.999903i	$0.495562\pi$
$90$		0			0
$91$	37.2171	−	64.4618i	0.408979	−	0.708372i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	27.5133	+	75.5921i	0.289614	+	0.795707i
$96$		0			0
$97$	28.6111	+	162.262i	0.294960	+	1.67280i	0.667366	+	0.744730i	$0.267422\pi$
$97$	28.6111	+	162.262i	0.294960	+	1.67280i	−0.372406	+	0.928070i	$0.621467\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	115.316	+	137.429i	1.14174	+	1.36068i	0.922956	+	0.384906i	$0.125766\pi$
$101$	115.316	+	137.429i	1.14174	+	1.36068i	0.218789	+	0.975772i	$0.429789\pi$
$102$		0			0
$103$	−22.2865	+	126.393i	−0.216374	+	1.22712i	0.662133	+	0.749387i	$0.269651\pi$
$103$	−22.2865	+	126.393i	−0.216374	+	1.22712i	−0.878507	+	0.477730i	$0.841460\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			63.4953i			0.593414i	0.954969	+	0.296707i	$0.0958885\pi$
$107$			63.4953i			0.593414i	−0.954969	+	0.296707i	$0.904111\pi$
$108$		0			0
$109$	−139.796			−1.28253			−0.641264	−	0.767320i	$-0.721590\pi$
$109$	−139.796			−1.28253			−0.641264	+	0.767320i	$0.721590\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	144.495	+	25.4784i	1.27872	+	0.225472i	0.771436	−	0.636307i	$-0.219539\pi$
$113$	144.495	+	25.4784i	1.27872	+	0.225472i	0.507282	+	0.861780i	$0.330650\pi$
$114$		0			0
$115$	−53.9112	+	45.2369i	−0.468793	+	0.393364i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−105.079	+	18.5282i	−0.883014	+	0.155699i
$120$		0			0
$121$	−55.6932	+	20.2707i	−0.460274	+	0.167526i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	112.401	+	64.8950i	0.899212	+	0.519160i
$126$		0			0
$127$	−0.267714	−	0.463695i	−0.00210799	−	0.00365114i	0.864969	−	0.501824i	$-0.167338\pi$
$127$	−0.267714	−	0.463695i	−0.00210799	−	0.00365114i	−0.867077	+	0.498173i	$0.834004\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	130.988	−	156.105i	0.999905	−	1.19164i	0.0184728	−	0.999829i	$-0.494120\pi$
$131$	130.988	−	156.105i	0.999905	−	1.19164i	0.981432	−	0.191811i	$-0.0614360\pi$
$132$		0			0
$133$	−113.488	−	41.3062i	−0.853293	−	0.310573i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	32.7898	−	90.0892i	0.239341	−	0.657585i	−0.760623	−	0.649193i	$-0.775107\pi$
$137$	32.7898	−	90.0892i	0.239341	−	0.657585i	0.999965	−	0.00839175i	$-0.00267121\pi$
$138$		0			0
$139$	128.457	+	107.788i	0.924150	+	0.775454i	0.974758	−	0.223265i	$-0.0716715\pi$
$139$	128.457	+	107.788i	0.924150	+	0.775454i	−0.0506082	+	0.998719i	$0.516116\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−100.913	+	58.2623i	−0.705687	+	0.407429i
$144$		0			0
$145$	−52.5090	+	90.9483i	−0.362131	+	0.627229i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	32.0183	+	87.9696i	0.214888	+	0.590400i	0.999565	−	0.0295053i	$-0.00939319\pi$
$149$	32.0183	+	87.9696i	0.214888	+	0.590400i	−0.784677	+	0.619905i	$0.787171\pi$
$150$		0			0
$151$	−25.6981	−	145.741i	−0.170186	−	0.965175i	−0.943554	−	0.331217i	$-0.892541\pi$
$151$	−25.6981	−	145.741i	−0.170186	−	0.965175i	0.773368	−	0.633957i	$-0.218570\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−8.77676	−	10.4597i	−0.0566242	−	0.0674821i
$156$		0			0
$157$	21.1322	−	119.847i	0.134600	−	0.763356i	−0.840537	−	0.541754i	$-0.817760\pi$
$157$	21.1322	−	119.847i	0.134600	−	0.763356i	0.975137	−	0.221602i	$-0.0711285\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	105.657i		−	0.656255i
$162$		0			0
$163$	205.502			1.26075			0.630374	−	0.776292i	$-0.282902\pi$
$163$	205.502			1.26075			0.630374	+	0.776292i	$0.282902\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−95.6208	−	16.8605i	−0.572580	−	0.100961i	−0.120141	−	0.992757i	$-0.538335\pi$
$167$	−95.6208	−	16.8605i	−0.572580	−	0.100961i	−0.452439	+	0.891796i	$0.649446\pi$
$168$		0			0
$169$	39.0289	−	32.7491i	0.230940	−	0.193782i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−154.139	+	27.1789i	−0.890979	+	0.157104i	−0.600355	−	0.799734i	$-0.704974\pi$
$173$	−154.139	+	27.1789i	−0.890979	+	0.157104i	−0.290624	+	0.956837i	$0.593863\pi$
$174$		0			0
$175$	−65.1987	+	23.7304i	−0.372564	+	0.135602i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−132.107	−	76.2720i	−0.738027	−	0.426100i	0.0833243	−	0.996522i	$-0.473446\pi$
$179$	−132.107	−	76.2720i	−0.738027	−	0.426100i	−0.821352	+	0.570422i	$0.806780\pi$
$180$		0			0
$181$	−81.1057	−	140.479i	−0.448098	−	0.776128i	0.550164	−	0.835056i	$-0.314565\pi$
$181$	−81.1057	−	140.479i	−0.448098	−	0.776128i	−0.998262	+	0.0589281i	$0.981232\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−88.9456	+	106.001i	−0.480787	+	0.572979i
$186$		0			0
$187$	156.962	+	57.1295i	0.839369	+	0.305505i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	82.9169	−	227.812i	0.434120	−	1.19273i	−0.509141	−	0.860683i	$-0.670037\pi$
$191$	82.9169	−	227.812i	0.434120	−	1.19273i	0.943261	−	0.332052i	$-0.107741\pi$
$192$		0			0
$193$	−43.7249	−	36.6895i	−0.226554	−	0.190101i	0.522444	−	0.852673i	$-0.325020\pi$
$193$	−43.7249	−	36.6895i	−0.226554	−	0.190101i	−0.748998	+	0.662572i	$0.769465\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	35.3547	−	20.4121i	0.179466	−	0.103615i	−0.407576	−	0.913171i	$-0.633626\pi$
$197$	35.3547	−	20.4121i	0.179466	−	0.103615i	0.587042	+	0.809557i	$0.300293\pi$
$198$		0			0
$199$	80.0281	−	138.613i	0.402151	−	0.696546i	−0.591834	−	0.806060i	$-0.701596\pi$
$199$	80.0281	−	138.613i	0.402151	−	0.696546i	0.993985	+	0.109514i	$0.0349293\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−53.9248	−	148.157i	−0.265639	−	0.729838i
$204$		0			0
$205$	−2.48041	−	14.0671i	−0.0120996	−	0.0686201i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	121.528	+	144.832i	0.581475	+	0.692975i
$210$		0			0
$211$	34.5437	−	195.907i	0.163714	−	0.928469i	−0.786666	−	0.617379i	$-0.788195\pi$
$211$	34.5437	−	195.907i	0.163714	−	0.928469i	0.950380	−	0.311091i	$-0.100694\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$			56.6601i			0.263535i
$216$		0			0
$217$	20.4993			0.0944670
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−310.502	−	54.7498i	−1.40498	−	0.247737i
$222$		0			0
$223$	73.2087	−	61.4294i	0.328290	−	0.275468i	−0.463712	−	0.885986i	$-0.653483\pi$
$223$	73.2087	−	61.4294i	0.328290	−	0.275468i	0.792003	+	0.610517i	$0.209038\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−324.544	+	57.2258i	−1.42971	+	0.252096i	−0.834293	−	0.551322i	$-0.814124\pi$
$227$	−324.544	+	57.2258i	−1.42971	+	0.252096i	−0.595416	+	0.803418i	$0.703013\pi$
$228$		0			0
$229$	132.032	−	48.0559i	0.576561	−	0.209851i	−0.0372475	−	0.999306i	$-0.511859\pi$
$229$	132.032	−	48.0559i	0.576561	−	0.209851i	0.613808	+	0.789455i	$0.289637\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−26.4879	−	15.2928i	−0.113682	−	0.0656343i	0.442081	−	0.896975i	$-0.354240\pi$
$233$	−26.4879	−	15.2928i	−0.113682	−	0.0656343i	−0.555763	+	0.831341i	$0.687574\pi$
$234$		0			0
$235$	110.359	+	191.147i	0.469613	+	0.813393i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−63.2822	+	75.4168i	−0.264779	+	0.315551i	−0.882010	−	0.471231i	$-0.843810\pi$
$239$	−63.2822	+	75.4168i	−0.264779	+	0.315551i	0.617231	+	0.786782i	$0.288254\pi$
$240$		0			0
$241$	157.850	+	57.4525i	0.654977	+	0.238392i	0.648066	−	0.761584i	$-0.275578\pi$
$241$	157.850	+	57.4525i	0.654977	+	0.238392i	0.00691103	+	0.999976i	$0.497800\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	27.2242	−	74.7978i	0.111119	−	0.305297i
$246$		0			0
$247$	−273.380	−	229.393i	−1.10680	−	0.928718i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	342.158	−	197.545i	1.36318	−	0.787031i	0.373132	−	0.927778i	$-0.378284\pi$
$251$	342.158	−	197.545i	1.36318	−	0.787031i	0.990046	+	0.140748i	$0.0449506\pi$
$252$		0			0
$253$	−82.7016	+	143.243i	−0.326884	+	0.566180i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−132.409	−	363.791i	−0.515211	−	1.41553i	−0.875741	−	0.482782i	$-0.839626\pi$
$257$	−132.409	−	363.791i	−0.515211	−	1.41553i	0.360530	−	0.932748i	$-0.382596\pi$
$258$		0			0
$259$	−36.0745	−	204.589i	−0.139284	−	0.789917i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	309.848	+	369.262i	1.17813	+	1.40404i	0.895648	+	0.444764i	$0.146713\pi$
$263$	309.848	+	369.262i	1.17813	+	1.40404i	0.282480	+	0.959273i	$0.408843\pi$
$264$		0			0
$265$	36.5733	−	207.418i	0.138013	−	0.782708i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		−	482.527i		−	1.79378i	−0.442254	−	0.896890i	$-0.645821\pi$
$269$		−	482.527i		−	1.79378i	0.442254	−	0.896890i	$-0.354179\pi$
$270$		0			0
$271$	−129.558			−0.478073			−0.239037	−	0.971011i	$-0.576832\pi$
$271$	−129.558			−0.478073			−0.239037	+	0.971011i	$0.576832\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	106.967	+	18.8612i	0.388971	+	0.0685861i
$276$		0			0
$277$	220.907	−	185.363i	0.797500	−	0.669182i	−0.150090	−	0.988672i	$-0.547956\pi$
$277$	220.907	−	185.363i	0.797500	−	0.669182i	0.947589	+	0.319491i	$0.103512\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−97.7251	+	17.2316i	−0.347776	+	0.0613223i	−0.344808	−	0.938673i	$-0.612056\pi$
$281$	−97.7251	+	17.2316i	−0.347776	+	0.0613223i	−0.00296825	+	0.999996i	$0.500945\pi$
$282$		0			0
$283$	−478.772	+	174.259i	−1.69177	+	0.615755i	−0.994847	−	0.101387i	$-0.967672\pi$
$283$	−478.772	+	174.259i	−1.69177	+	0.615755i	−0.696927	+	0.717142i	$0.745450\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	18.5720	+	10.7225i	0.0647107	+	0.0373607i
$288$		0			0
$289$	81.4819	+	141.131i	0.281944	+	0.488342i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−176.106	+	209.875i	−0.601044	+	0.716297i	−0.977688	−	0.210061i	$-0.932634\pi$
$293$	−176.106	+	209.875i	−0.601044	+	0.716297i	0.376644	+	0.926358i	$0.377078\pi$
$294$		0			0
$295$	−239.581	−	87.2004i	−0.812139	−	0.295595i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	106.782	−	293.382i	0.357131	−	0.981210i
$300$		0			0
$301$	−65.1635	−	54.6786i	−0.216490	−	0.181657i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	289.175	−	166.955i	0.948115	−	0.547394i
$306$		0			0
$307$	−99.6479	+	172.595i	−0.324586	+	0.562200i	−0.981429	−	0.191828i	$-0.938558\pi$
$307$	−99.6479	+	172.595i	−0.324586	+	0.562200i	0.656842	+	0.754028i	$0.271892\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	52.3102	+	143.721i	0.168200	+	0.462125i	0.994941	−	0.100457i	$-0.0320303\pi$
$311$	52.3102	+	143.721i	0.168200	+	0.462125i	−0.826742	+	0.562582i	$0.809808\pi$
$312$		0			0
$313$	54.6584	+	309.983i	0.174628	+	0.990362i	0.938573	+	0.345081i	$0.112149\pi$
$313$	54.6584	+	309.983i	0.174628	+	0.990362i	−0.763945	+	0.645281i	$0.776740\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	363.366	+	433.042i	1.14626	+	1.36606i	0.919962	+	0.392007i	$0.128219\pi$
$317$	363.366	+	433.042i	1.14626	+	1.36606i	0.226302	+	0.974057i	$0.427336\pi$
$318$		0			0
$319$	−42.8601	+	243.071i	−0.134358	+	0.761980i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			511.569i			1.58381i
$324$		0			0
$325$	−205.023			−0.630839
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−326.334	−	57.5415i	−0.991896	−	0.174898i
$330$		0			0
$331$	179.324	−	150.471i	0.541765	−	0.454595i	−0.330376	−	0.943850i	$-0.607175\pi$
$331$	179.324	−	150.471i	0.541765	−	0.454595i	0.872141	+	0.489254i	$0.162731\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−291.037	+	51.3177i	−0.868768	+	0.153187i
$336$		0			0
$337$	314.566	−	114.493i	0.933430	−	0.339741i	0.169862	−	0.985468i	$-0.445668\pi$
$337$	314.566	−	114.493i	0.933430	−	0.339741i	0.763568	+	0.645727i	$0.223446\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−27.7918	−	16.0456i	−0.0815008	−	0.0470545i
$342$		0			0
$343$	182.715	+	316.472i	0.532697	+	0.922658i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	117.252	−	139.736i	0.337902	−	0.402696i	−0.570158	−	0.821535i	$-0.693118\pi$
$347$	117.252	−	139.736i	0.337902	−	0.402696i	0.908061	+	0.418838i	$0.137563\pi$
$348$		0			0
$349$	432.031	+	157.246i	1.23791	+	0.450563i	0.876300	−	0.481766i	$-0.160004\pi$
$349$	432.031	+	157.246i	1.23791	+	0.450563i	0.361612	+	0.932329i	$0.382227\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−132.162	+	363.113i	−0.374397	+	1.02865i	0.599245	+	0.800566i	$0.295468\pi$
$353$	−132.162	+	363.113i	−0.374397	+	1.02865i	−0.973642	+	0.228082i	$0.926755\pi$
$354$		0			0
$355$	12.8402	+	10.7742i	0.0361694	+	0.0303498i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−273.060	+	157.651i	−0.760613	+	0.439140i	−0.829516	−	0.558483i	$-0.811383\pi$
$359$	−273.060	+	157.651i	−0.760613	+	0.439140i	0.0689028	+	0.997623i	$0.478050\pi$
$360$		0			0
$361$	−109.018	+	188.824i	−0.301988	+	0.523059i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	44.0880	+	121.131i	0.120789	+	0.331865i
$366$		0			0
$367$	−42.0211	−	238.314i	−0.114499	−	0.649356i	−0.986997	−	0.160738i	$-0.948612\pi$
$367$	−42.0211	−	238.314i	−0.114499	−	0.649356i	0.872498	−	0.488618i	$-0.162499\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	203.252	+	242.226i	0.547849	+	0.652901i
$372$		0			0
$373$	−41.0443	+	232.774i	−0.110038	+	0.624058i	0.879050	+	0.476730i	$0.158178\pi$
$373$	−41.0443	+	232.774i	−0.110038	+	0.624058i	−0.989088	+	0.147327i	$0.952933\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	465.893i		−	1.23579i
$378$		0			0
$379$	317.201			0.836941			0.418471	−	0.908230i	$-0.362566\pi$
$379$	317.201			0.836941			0.418471	+	0.908230i	$0.362566\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	187.986	+	33.1470i	0.490824	+	0.0865456i	0.413582	−	0.910467i	$-0.364277\pi$
$383$	187.986	+	33.1470i	0.490824	+	0.0865456i	0.0772422	+	0.997012i	$0.475389\pi$
$384$		0			0
$385$	100.986	−	84.7373i	0.262301	−	0.220097i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	145.576	−	25.6689i	0.374231	−	0.0659870i	0.0166304	−	0.999862i	$-0.494706\pi$
$389$	145.576	−	25.6689i	0.374231	−	0.0659870i	0.357600	+	0.933875i	$0.383595\pi$
$390$		0			0
$391$	−420.557	+	153.070i	−1.07559	+	0.391484i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	110.609	+	63.8601i	0.280023	+	0.161671i
$396$		0			0
$397$	62.1813	+	107.701i	0.156628	+	0.271288i	0.933651	−	0.358185i	$-0.116604\pi$
$397$	62.1813	+	107.701i	0.156628	+	0.271288i	−0.777023	+	0.629473i	$0.783271\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	114.173	−	136.066i	0.284720	−	0.339316i	−0.604661	−	0.796483i	$-0.706691\pi$
$401$	114.173	−	136.066i	0.284720	−	0.339316i	0.889381	+	0.457167i	$0.151136\pi$
$402$		0			0
$403$	56.9213	+	20.7177i	0.141244	+	0.0514086i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−111.231	+	305.606i	−0.273296	+	0.750874i
$408$		0			0
$409$	−318.028	−	266.857i	−0.777574	−	0.652462i	0.165063	−	0.986283i	$-0.447217\pi$
$409$	−318.028	−	266.857i	−0.777574	−	0.652462i	−0.942636	+	0.333821i	$0.891662\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	331.490	−	191.386i	0.802639	−	0.463404i
$414$		0			0
$415$	−238.673	+	413.394i	−0.575116	+	0.996129i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	29.2696	+	80.4176i	0.0698559	+	0.191927i	0.969708	−	0.244268i	$-0.0785478\pi$
$419$	29.2696	+	80.4176i	0.0698559	+	0.191927i	−0.899852	+	0.436196i	$0.856326\pi$
$420$		0			0
$421$	−15.7075	−	89.0816i	−0.0373099	−	0.211595i	0.960453	−	0.278441i	$-0.0898176\pi$
$421$	−15.7075	−	89.0816i	−0.0373099	−	0.211595i	−0.997763	+	0.0668456i	$0.978706\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	188.913	+	225.137i	0.444500	+	0.529735i
$426$		0			0
$427$	−87.0510	+	493.691i	−0.203866	+	1.15618i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			374.477i			0.868856i	0.900707	+	0.434428i	$0.143049\pi$
$431$			374.477i			0.868856i	−0.900707	+	0.434428i	$0.856951\pi$
$432$		0			0
$433$	−277.375			−0.640589			−0.320295	−	0.947318i	$-0.603782\pi$
$433$	−277.375			−0.640589			−0.320295	+	0.947318i	$0.603782\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−498.874	−	87.9650i	−1.14159	−	0.201293i
$438$		0			0
$439$	−324.228	+	272.059i	−0.738560	+	0.619725i	−0.932450	−	0.361298i	$-0.882334\pi$
$439$	−324.228	+	272.059i	−0.738560	+	0.619725i	0.193891	+	0.981023i	$0.437889\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	45.7212	−	8.06188i	0.103208	−	0.0181984i	−0.121806	−	0.992554i	$-0.538868\pi$
$443$	45.7212	−	8.06188i	0.103208	−	0.0181984i	0.225014	+	0.974356i	$0.427757\pi$
$444$		0			0
$445$	272.806	−	99.2934i	0.613048	−	0.223131i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	414.555	+	239.343i	0.923285	+	0.533059i	0.884681	−	0.466196i	$-0.154376\pi$
$449$	414.555	+	239.343i	0.923285	+	0.533059i	0.0386031	+	0.999255i	$0.487709\pi$
$450$		0			0
$451$	−16.7858	−	29.0739i	−0.0372191	−	0.0644654i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−159.948	+	190.618i	−0.351533	+	0.418941i
$456$		0			0
$457$	41.7129	+	15.1823i	0.0912756	+	0.0332216i	0.387254	−	0.921973i	$-0.373424\pi$
$457$	41.7129	+	15.1823i	0.0912756	+	0.0332216i	−0.295979	+	0.955195i	$0.595646\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	242.819	−	667.139i	0.526722	−	1.44716i	−0.336186	−	0.941796i	$-0.609137\pi$
$461$	242.819	−	667.139i	0.526722	−	1.44716i	0.862908	−	0.505361i	$-0.168641\pi$
$462$		0			0
$463$	−281.800	−	236.458i	−0.608639	−	0.510709i	0.285570	−	0.958358i	$-0.407817\pi$
$463$	−281.800	−	236.458i	−0.608639	−	0.510709i	−0.894209	+	0.447649i	$0.852261\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	96.0048	−	55.4284i	0.205578	−	0.118690i	−0.393677	−	0.919249i	$-0.628797\pi$
$467$	96.0048	−	55.4284i	0.205578	−	0.118690i	0.599255	+	0.800559i	$0.295464\pi$
$468$		0			0
$469$	221.840	−	384.239i	0.473007	−	0.819272i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	45.5457	+	125.136i	0.0962912	+	0.264558i
$474$		0			0
$475$	57.7649	+	327.601i	0.121610	+	0.689687i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−243.096	−	289.711i	−0.507508	−	0.604825i	0.450072	−	0.892992i	$-0.351398\pi$
$479$	−243.096	−	289.711i	−0.507508	−	0.604825i	−0.957580	+	0.288168i	$0.906954\pi$
$480$		0			0
$481$	106.598	−	604.548i	0.221618	−	1.25686i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	550.811i		−	1.13569i
$486$		0			0
$487$	1.09062			0.00223946			0.00111973	−	0.999999i	$-0.499644\pi$
$487$	1.09062			0.00223946			0.00111973	+	0.999999i	$0.499644\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	262.868	+	46.3508i	0.535374	+	0.0944008i	0.434797	−	0.900528i	$-0.356820\pi$
$491$	262.868	+	46.3508i	0.535374	+	0.0944008i	0.100577	+	0.994929i	$0.467931\pi$
$492$		0			0
$493$	−511.601	+	429.284i	−1.03773	+	0.870759i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−24.7823	+	4.36978i	−0.0498637	+	0.00879231i
$498$		0			0
$499$	479.243	−	174.430i	0.960407	−	0.349560i	0.186214	−	0.982509i	$-0.440378\pi$
$499$	479.243	−	174.430i	0.960407	−	0.349560i	0.774193	+	0.632950i	$0.218156\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	37.0503	+	21.3910i	0.0736586	+	0.0425268i	0.536377	−	0.843979i	$-0.319793\pi$
$503$	37.0503	+	21.3910i	0.0736586	+	0.0425268i	−0.462718	+	0.886505i	$0.653126\pi$
$504$		0			0
$505$	−299.869	−	519.388i	−0.593800	−	1.02849i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−29.4414	+	35.0868i	−0.0578416	+	0.0689329i	−0.794189	−	0.607670i	$-0.792104\pi$
$509$	−29.4414	+	35.0868i	−0.0578416	+	0.0689329i	0.736348	+	0.676603i	$0.236549\pi$
$510$		0			0
$511$	−181.856	−	66.1902i	−0.355883	−	0.129531i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	146.744	−	403.177i	0.284941	−	0.782868i
$516$		0			0
$517$	397.384	+	333.445i	0.768634	+	0.644961i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−688.716	+	397.630i	−1.32191	+	0.763206i	−0.984033	−	0.177984i	$-0.943042\pi$
$521$	−688.716	+	397.630i	−1.32191	+	0.763206i	−0.337878	+	0.941190i	$0.609709\pi$
$522$		0			0
$523$	−46.6948	+	80.8777i	−0.0892826	+	0.154642i	−0.907208	−	0.420682i	$-0.861791\pi$
$523$	−46.6948	+	80.8777i	−0.0892826	+	0.154642i	0.817926	+	0.575324i	$0.195124\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−29.6983	−	81.5954i	−0.0563535	−	0.154830i
$528$		0			0
$529$	14.9036	+	84.5225i	0.0281732	+	0.159778i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	40.7328	+	48.5434i	0.0764217	+	0.0910758i
$534$		0			0
$535$	36.8596	−	209.041i	0.0688964	−	0.390731i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	187.078i		−	0.347083i
$540$		0			0
$541$	534.141			0.987322			0.493661	−	0.869654i	$-0.335658\pi$
$541$	534.141			0.987322			0.493661	+	0.869654i	$0.335658\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	460.239	+	81.1525i	0.844474	+	0.148904i
$546$		0			0
$547$	518.621	−	435.175i	0.948119	−	0.795566i	−0.0308612	−	0.999524i	$-0.509825\pi$
$547$	518.621	−	435.175i	0.948119	−	0.795566i	0.978980	+	0.203958i	$0.0653805\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−744.440	+	131.265i	−1.35107	+	0.238230i
$552$		0			0
$553$	−180.185	+	65.5819i	−0.325832	+	0.118593i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−241.945	−	139.687i	−0.434372	−	0.250785i	0.266835	−	0.963742i	$-0.414022\pi$
$557$	−241.945	−	139.687i	−0.434372	−	0.250785i	−0.701208	+	0.712957i	$0.747355\pi$
$558$		0			0
$559$	−125.681	−	217.686i	−0.224832	−	0.389420i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−158.912	+	189.384i	−0.282260	+	0.336384i	−0.888482	−	0.458911i	$-0.848240\pi$
$563$	−158.912	+	189.384i	−0.282260	+	0.336384i	0.606223	+	0.795295i	$0.292684\pi$
$564$		0			0
$565$	−460.920	−	167.761i	−0.815788	−	0.296923i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	37.4528	−	102.901i	0.0658221	−	0.180845i	−0.902421	−	0.430855i	$-0.858212\pi$
$569$	37.4528	−	102.901i	0.0658221	−	0.180845i	0.968243	+	0.250011i	$0.0804341\pi$
$570$		0			0
$571$	563.689	+	472.991i	0.987196	+	0.828356i	0.985159	−	0.171642i	$-0.0549072\pi$
$571$	563.689	+	472.991i	0.987196	+	0.828356i	0.00203684	+	0.999998i	$0.499352\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−252.034	+	145.512i	−0.438320	+	0.253064i
$576$		0			0
$577$	386.640	−	669.680i	0.670086	−	1.16062i	−0.307793	−	0.951453i	$-0.599590\pi$
$577$	386.640	−	669.680i	0.670086	−	1.16062i	0.977879	−	0.209170i	$-0.0670763\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−245.108	−	673.430i	−0.421873	−	1.15909i
$582$		0			0
$583$	−85.9574	−	487.489i	−0.147440	−	0.836173i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−731.963	−	872.319i	−1.24696	−	1.48606i	−0.809832	−	0.586662i	$-0.800442\pi$
$587$	−731.963	−	872.319i	−1.24696	−	1.48606i	−0.437123	−	0.899402i	$-0.644003\pi$
$588$		0			0
$589$	17.0668	−	96.7904i	0.0289758	−	0.164330i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			509.063i			0.858454i	0.903197	+	0.429227i	$0.141214\pi$
$593$			509.063i			0.858454i	−0.903197	+	0.429227i	$0.858786\pi$
$594$		0			0
$595$	356.699			0.599494
$596$		0			0
$597$		0			0
$598$		0			0
$599$	226.854	+	40.0005i	0.378721	+	0.0667788i	0.359769	−	0.933042i	$-0.382856\pi$
$599$	226.854	+	40.0005i	0.378721	+	0.0667788i	0.0189528	+	0.999820i	$0.493967\pi$
$600$		0			0
$601$	451.492	−	378.846i	0.751234	−	0.630360i	−0.184595	−	0.982815i	$-0.559097\pi$
$601$	451.492	−	378.846i	0.751234	−	0.630360i	0.935829	+	0.352455i	$0.114653\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	195.122	−	34.4053i	0.322516	−	0.0568682i
$606$		0			0
$607$	−54.2617	+	19.7497i	−0.0893933	+	0.0325365i	−0.386330	−	0.922361i	$-0.626257\pi$
$607$	−54.2617	+	19.7497i	−0.0893933	+	0.0325365i	0.296936	+	0.954897i	$0.404035\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−847.989	−	489.587i	−1.38787	−	0.801288i
$612$		0			0
$613$	−76.5325	−	132.558i	−0.124849	−	0.216245i	0.796825	−	0.604210i	$-0.206511\pi$
$613$	−76.5325	−	132.558i	−0.124849	−	0.216245i	−0.921674	+	0.387965i	$0.873178\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	419.858	−	500.368i	0.680483	−	0.810969i	−0.309686	−	0.950839i	$-0.600224\pi$
$617$	419.858	−	500.368i	0.680483	−	0.810969i	0.990170	+	0.139870i	$0.0446685\pi$
$618$		0			0
$619$	−421.315	−	153.346i	−0.680639	−	0.247732i	−0.0215170	−	0.999768i	$-0.506850\pi$
$619$	−421.315	−	153.346i	−0.680639	−	0.247732i	−0.659122	+	0.752036i	$0.729072\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−149.071	+	409.570i	−0.239280	+	0.657415i
$624$		0			0
$625$	−67.6293	−	56.7477i	−0.108207	−	0.0907964i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−762.081	+	439.987i	−1.21157	+	0.699503i
$630$		0			0
$631$	541.164	−	937.323i	0.857629	−	1.48546i	−0.0165560	−	0.999863i	$-0.505270\pi$
$631$	541.164	−	937.323i	0.857629	−	1.48546i	0.874185	−	0.485594i	$-0.161396\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	0.612198	+	1.68200i	0.000964091	+	0.00264882i
$636$		0			0
$637$	61.3191	+	347.758i	0.0962623	+	0.545931i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−773.511	−	921.835i	−1.20673	−	1.43812i	−0.867516	−	0.497409i	$-0.834285\pi$
$641$	−773.511	−	921.835i	−1.20673	−	1.43812i	−0.339210	−	0.940711i	$-0.610160\pi$
$642$		0			0
$643$	−56.2865	+	319.217i	−0.0875373	+	0.496449i	0.909243	+	0.416266i	$0.136662\pi$
$643$	−56.2865	+	319.217i	−0.0875373	+	0.496449i	−0.996780	+	0.0801828i	$0.974450\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			1013.29i			1.56614i	0.621936	+	0.783068i	$0.286346\pi$
$647$			1013.29i			1.56614i	−0.621936	+	0.783068i	$0.713654\pi$
$648$		0			0
$649$	−599.219			−0.923296
$650$		0			0
$651$		0			0
$652$		0			0
$653$	121.194	+	21.3698i	0.185596	+	0.0327256i	0.265673	−	0.964063i	$-0.414406\pi$
$653$	121.194	+	21.3698i	0.185596	+	0.0327256i	−0.0800776	+	0.996789i	$0.525517\pi$
$654$		0			0
$655$	−521.861	+	437.893i	−0.796734	+	0.668539i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	1053.37	−	185.738i	1.59844	−	0.281848i	0.697761	−	0.716330i	$-0.254180\pi$
$659$	1053.37	−	185.738i	1.59844	−	0.281848i	0.900681	+	0.434482i	$0.143068\pi$
$660$		0			0
$661$	395.481	−	143.943i	0.598307	−	0.217766i	−0.0250719	−	0.999686i	$-0.507981\pi$
$661$	395.481	−	143.943i	0.598307	−	0.217766i	0.623379	+	0.781920i	$0.285759\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	349.650	+	201.870i	0.525789	+	0.303564i
$666$		0			0
$667$	−330.661	−	572.721i	−0.495743	−	0.858652i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	504.448	−	601.178i	0.751786	−	0.895943i
$672$		0			0
$673$	370.766	+	134.948i	0.550915	+	0.200517i	0.602453	−	0.798154i	$-0.294190\pi$
$673$	370.766	+	134.948i	0.550915	+	0.200517i	−0.0515378	+	0.998671i	$0.516412\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−36.9501	+	101.520i	−0.0545792	+	0.149955i	−0.963986	−	0.265952i	$-0.914314\pi$
$677$	−36.9501	+	101.520i	−0.0545792	+	0.149955i	0.909407	+	0.415907i	$0.136536\pi$
$678$		0			0
$679$	633.475	+	531.549i	0.932953	+	0.782841i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	728.407	−	420.546i	1.06648	−	0.615733i	0.139263	−	0.990255i	$-0.455527\pi$
$683$	728.407	−	420.546i	1.06648	−	0.615733i	0.927218	+	0.374522i	$0.122193\pi$
$684$		0			0
$685$	−160.249	+	277.559i	−0.233940	+	0.405196i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	319.572	+	878.016i	0.463820	+	1.27433i
$690$		0			0
$691$	−20.0201	−	113.540i	−0.0289727	−	0.164312i	0.966889	−	0.255199i	$-0.0821410\pi$
$691$	−20.0201	−	113.540i	−0.0289727	−	0.164312i	−0.995861	+	0.0908868i	$0.971030\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−360.337	−	429.433i	−0.518471	−	0.617889i
$696$		0			0
$697$	15.7739	−	89.4580i	0.0226311	−	0.128347i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	535.100i		−	0.763337i	−0.924299	−	0.381669i	$-0.875350\pi$
$701$		−	535.100i		−	0.763337i	0.924299	−	0.381669i	$-0.124650\pi$
$702$		0			0
$703$	−996.027			−1.41682
$704$		0			0
$705$		0			0
$706$		0			0
$707$	886.719	+	156.352i	1.25420	+	0.221149i
$708$		0			0
$709$	−926.997	+	777.843i	−1.30747	+	1.09710i	−0.318668	+	0.947866i	$0.603236\pi$
$709$	−926.997	+	777.843i	−1.30747	+	1.09710i	−0.988802	+	0.149232i	$0.952320\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	84.6772	−	14.9309i	0.118762	−	0.0209409i
$714$		0			0
$715$	366.051	−	133.232i	0.511960	−	0.186338i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−729.678	−	421.280i	−1.01485	−	0.585925i	−0.102243	−	0.994759i	$-0.532602\pi$
$719$	−729.678	−	421.280i	−1.01485	−	0.585925i	−0.912608	+	0.408835i	$0.865935\pi$
$720$		0			0
$721$	322.072	+	557.845i	0.446702	+	0.773711i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−279.148	+	332.676i	−0.385032	+	0.458863i
$726$		0			0
$727$	−455.096	−	165.641i	−0.625991	−	0.227842i	0.00949432	−	0.999955i	$-0.496978\pi$
$727$	−455.096	−	165.641i	−0.625991	−	0.227842i	−0.635486	+	0.772113i	$0.719200\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−123.237	+	338.592i	−0.168587	+	0.463190i
$732$		0			0
$733$	864.616	+	725.499i	1.17956	+	0.989767i	0.999982	+	0.00602310i	$0.00191722\pi$
$733$	864.616	+	725.499i	1.17956	+	0.989767i	0.179577	+	0.983744i	$0.442527\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−601.515	+	347.285i	−0.816167	+	0.471214i
$738$		0			0
$739$	339.017	−	587.195i	0.458751	−	0.794580i	−0.540144	−	0.841572i	$-0.681630\pi$
$739$	339.017	−	587.195i	0.458751	−	0.794580i	0.998895	+	0.0469925i	$0.0149637\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	252.722	+	694.348i	0.340137	+	0.934520i	0.985354	+	0.170520i	$0.0545448\pi$
$743$	252.722	+	694.348i	0.340137	+	0.934520i	−0.645217	+	0.763999i	$0.723233\pi$
$744$		0			0
$745$	−54.3445	−	308.203i	−0.0729456	−	0.413695i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	204.843	+	244.122i	0.273488	+	0.325931i
$750$		0			0
$751$	−22.4168	+	127.132i	−0.0298493	+	0.169284i	−0.996088	−	0.0883639i	$-0.971836\pi$
$751$	−22.4168	+	127.132i	−0.0298493	+	0.169284i	0.966239	+	0.257647i	$0.0829473\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			494.732i			0.655274i
$756$		0			0
$757$	−27.2878			−0.0360474			−0.0180237	−	0.999838i	$-0.505737\pi$
$757$	−27.2878			−0.0360474			−0.0180237	+	0.999838i	$0.505737\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	45.8686	+	8.08787i	0.0602741	+	0.0106280i	0.203704	−	0.979033i	$-0.434702\pi$
$761$	45.8686	+	8.08787i	0.0602741	+	0.0106280i	−0.143430	+	0.989660i	$0.545813\pi$
$762$		0			0
$763$	−537.476	+	450.996i	−0.704424	+	0.591082i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	1113.89	−	196.408i	1.45226	−	0.256073i
$768$		0			0
$769$	−546.071	+	198.754i	−0.710105	+	0.258457i	−0.671719	−	0.740806i	$-0.734444\pi$
$769$	−546.071	+	198.754i	−0.710105	+	0.258457i	−0.0383859	+	0.999263i	$0.512222\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	908.006	+	524.237i	1.17465	+	0.678185i	0.954771	−	0.297341i	$-0.0961000\pi$
$773$	908.006	+	524.237i	1.17465	+	0.678185i	0.219880	+	0.975527i	$0.429433\pi$
$774$		0			0
$775$	−28.2319	−	48.8991i	−0.0364282	−	0.0630956i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	66.0900	−	78.7630i	0.0848395	−	0.101108i
$780$		0			0
$781$	37.0187	+	13.4737i	0.0473991	+	0.0172518i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−139.144	+	382.296i	−0.177254	+	0.487001i
$786$		0			0
$787$	−538.335	−	451.716i	−0.684034	−	0.573972i	0.233148	−	0.972441i	$-0.425097\pi$
$787$	−538.335	−	451.716i	−0.684034	−	0.573972i	−0.917182	+	0.398469i	$0.869542\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	637.740	−	368.200i	0.806246	−	0.465486i
$792$		0			0
$793$	−740.666	+	1282.87i	−0.934005	+	1.61774i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	193.340	+	531.197i	0.242585	+	0.666496i	0.999909	+	0.0134576i	$0.00428381\pi$
$797$	193.340	+	531.197i	0.242585	+	0.666496i	−0.757325	+	0.653038i	$0.773494\pi$
$798$		0			0
$799$	243.737	+	1382.30i	0.305052	+	1.73004i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	194.740	+	232.082i	0.242515	+	0.289019i
$804$		0			0
$805$	−61.3348	+	347.847i	−0.0761923	+	0.432108i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			575.984i			0.711970i	0.934492	+	0.355985i	$0.115855\pi$
$809$			575.984i			0.711970i	−0.934492	+	0.355985i	$0.884145\pi$
$810$		0			0
$811$	1178.94			1.45369			0.726844	−	0.686803i	$-0.240986\pi$
$811$	1178.94			1.45369			0.726844	+	0.686803i	$0.240986\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−676.559	−	119.296i	−0.830133	−	0.146375i
$816$		0			0
$817$	−312.425	+	262.155i	−0.382405	+	0.320876i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−307.195	+	54.1668i	−0.374172	+	0.0659766i	−0.357572	−	0.933886i	$-0.616395\pi$
$821$	−307.195	+	54.1668i	−0.374172	+	0.0659766i	−0.0165999	+	0.999862i	$0.505284\pi$
$822$		0			0
$823$	−257.317	+	93.6558i	−0.312658	+	0.113798i	−0.493583	−	0.869699i	$-0.664313\pi$
$823$	−257.317	+	93.6558i	−0.312658	+	0.113798i	0.180925	+	0.983497i	$0.442091\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−100.202	−	57.8518i	−0.121164	−	0.0699539i	0.438193	−	0.898881i	$-0.355619\pi$
$827$	−100.202	−	57.8518i	−0.121164	−	0.0699539i	−0.559357	+	0.828927i	$0.688952\pi$
$828$		0			0
$829$	−667.505	−	1156.15i	−0.805192	−	1.39463i	−0.916161	−	0.400810i	$-0.868729\pi$
$829$	−667.505	−	1156.15i	−0.805192	−	1.39463i	0.110969	−	0.993824i	$-0.464605\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	325.375	−	387.767i	0.390606	−	0.465506i
$834$		0			0
$835$	305.018	+	111.017i	0.365291	+	0.132955i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	90.3892	−	248.342i	0.107734	−	0.295998i	−0.874097	−	0.485751i	$-0.838546\pi$
$839$	90.3892	−	248.342i	0.107734	−	0.295998i	0.981832	+	0.189753i	$0.0607686\pi$
$840$		0			0
$841$	−111.727	−	93.7502i	−0.132850	−	0.111475i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−147.503	+	85.1609i	−0.174560	+	0.100782i
$846$		0			0
$847$	−148.730	+	257.607i	−0.175596	+	0.304141i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−298.028	−	818.825i	−0.350209	−	0.962192i
$852$		0			0
$853$	−5.27063	−	29.8912i	−0.00617893	−	0.0350424i	0.981562	−	0.191142i	$-0.0612191\pi$
$853$	−5.27063	−	29.8912i	−0.00617893	−	0.0350424i	−0.987741	+	0.156099i	$0.950108\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−983.369	−	1171.93i	−1.14745	−	1.36748i	−0.919157	−	0.393892i	$-0.871128\pi$
$857$	−983.369	−	1171.93i	−1.14745	−	1.36748i	−0.228298	−	0.973591i	$-0.573316\pi$
$858$		0			0
$859$	84.9511	−	481.781i	0.0988953	−	0.560863i	−0.894589	−	0.446891i	$-0.852531\pi$
$859$	84.9511	−	481.781i	0.0988953	−	0.560863i	0.993484	−	0.113973i	$-0.0363576\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			1081.12i			1.25275i	0.779523	+	0.626373i	$0.215461\pi$
$863$			1081.12i			1.25275i	−0.779523	+	0.626373i	$0.784539\pi$
$864$		0			0
$865$	523.239			0.604901
$866$		0			0
$867$		0			0
$868$		0			0
$869$	295.617	+	52.1253i	0.340181	+	0.0599831i
$870$		0			0
$871$	1004.32	−	842.727i	1.15307	−	0.967540i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	641.511	−	113.116i	0.733156	−	0.129275i
$876$		0			0
$877$	−455.586	+	165.820i	−0.519482	+	0.189076i	−0.588436	−	0.808544i	$-0.700256\pi$
$877$	−455.586	+	165.820i	−0.519482	+	0.189076i	0.0689539	+	0.997620i	$0.478034\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	735.532	+	424.660i	0.834883	+	0.482020i	0.855522	−	0.517767i	$-0.173237\pi$
$881$	735.532	+	424.660i	0.834883	+	0.482020i	−0.0206385	+	0.999787i	$0.506570\pi$
$882$		0			0
$883$	521.855	+	903.879i	0.591002	+	1.02365i	0.994098	+	0.108488i	$0.0346009\pi$
$883$	521.855	+	903.879i	0.591002	+	1.02365i	−0.403095	+	0.915158i	$0.632066\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−363.271	+	432.930i	−0.409551	+	0.488083i	−0.930907	−	0.365255i	$-0.880982\pi$
$887$	−363.271	+	432.930i	−0.409551	+	0.488083i	0.521357	+	0.853339i	$0.325426\pi$
$888$		0			0
$889$	−2.52522	−	0.919105i	−0.00284052	−	0.00103386i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−543.380	+	1492.92i	−0.608488	+	1.67181i
$894$		0			0
$895$	390.649	+	327.794i	0.436480	+	0.366250i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	111.118	−	64.1540i	0.123602	−	0.0713615i
$900$		0			0
$901$	669.696	−	1159.95i	0.743281	−	1.28740i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	185.469	+	509.572i	0.204938	+	0.563063i
$906$		0			0
$907$	30.7561	+	174.426i	0.0339097	+	0.192311i	0.997057	−	0.0766628i	$-0.0244265\pi$
$907$	30.7561	+	174.426i	0.0339097	+	0.192311i	−0.963147	+	0.268974i	$0.913315\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−305.717	−	364.340i	−0.335584	−	0.399934i	0.571692	−	0.820468i	$-0.306287\pi$
$911$	−305.717	−	364.340i	−0.335584	−	0.399934i	−0.907277	+	0.420534i	$0.861843\pi$
$912$		0			0
$913$	−194.815	+	1104.85i	−0.213379	+	1.21013i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	1022.76i		−	1.11533i
$918$		0			0
$919$	−816.349			−0.888301			−0.444151	−	0.895952i	$-0.646494\pi$
$919$	−816.349			−0.888301			−0.444151	+	0.895952i	$0.646494\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−73.2301	−	12.9125i	−0.0793393	−	0.0139897i
$924$		0			0
$925$	−438.343	+	367.813i	−0.473884	+	0.397636i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	874.083	−	154.124i	0.940885	−	0.165903i	0.317889	−	0.948128i	$-0.397026\pi$
$929$	874.083	−	154.124i	0.940885	−	0.165903i	0.622997	+	0.782225i	$0.285915\pi$
$930$		0			0
$931$	538.398	−	195.961i	0.578301	−	0.210484i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−483.591	−	279.201i	−0.517209	−	0.298611i
$936$		0			0
$937$	578.240	+	1001.54i	0.617118	+	1.06888i	0.990009	+	0.141005i	$0.0450332\pi$
$937$	578.240	+	1001.54i	0.617118	+	1.06888i	−0.372891	+	0.927875i	$0.621633\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−536.252	+	639.080i	−0.569874	+	0.679150i	−0.971605	−	0.236608i	$-0.923964\pi$
$941$	−536.252	+	639.080i	−0.569874	+	0.679150i	0.401731	+	0.915758i	$0.368409\pi$
$942$		0			0
$943$	84.5256	+	30.7648i	0.0896348	+	0.0326244i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−245.105	+	673.420i	−0.258822	+	0.711108i	0.740418	+	0.672146i	$0.234627\pi$
$947$	−245.105	+	673.420i	−0.258822	+	0.711108i	−0.999241	+	0.0389621i	$0.987595\pi$
$948$		0			0
$949$	−438.071	−	367.585i	−0.461614	−	0.387340i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−753.336	+	434.939i	−0.790489	+	0.456389i	−0.840135	−	0.542378i	$-0.817524\pi$
$953$	−753.336	+	434.939i	−0.790489	+	0.456389i	0.0496456	+	0.998767i	$0.484191\pi$
$954$		0			0
$955$	−405.228	+	701.876i	−0.424323	+	0.734949i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−164.570	−	452.152i	−0.171606	−	0.471482i
$960$		0			0
$961$	−163.979	−	929.971i	−0.170634	−	0.967712i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	122.654	+	146.173i	0.127102	+	0.151474i
$966$		0			0
$967$	220.746	−	1251.91i	0.228279	−	1.29464i	−0.628036	−	0.778184i	$-0.716141\pi$
$967$	220.746	−	1251.91i	0.228279	−	1.29464i	0.856316	−	0.516453i	$-0.172748\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		−	982.851i		−	1.01221i	−0.862473	−	0.506103i	$-0.831086\pi$
$971$		−	982.851i		−	1.01221i	0.862473	−	0.506103i	$-0.168914\pi$
$972$		0			0
$973$	841.617			0.864971
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1061.38	+	187.149i	1.08636	+	0.191555i	0.688027	−	0.725685i	$-0.258477\pi$
$977$	1061.38	+	187.149i	1.08636	+	0.191555i	0.398335	+	0.917240i	$0.369588\pi$
$978$		0			0
$979$	522.687	−	438.586i	0.533899	−	0.447994i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−38.4037	+	6.77162i	−0.0390679	+	0.00688872i	−0.193148	−	0.981170i	$-0.561870\pi$
$983$	−38.4037	+	6.77162i	−0.0390679	+	0.00688872i	0.154080	+	0.988058i	$0.450759\pi$
$984$		0			0
$985$	−128.245	+	46.6774i	−0.130198	+	0.0473882i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−308.998	−	178.400i	−0.312435	−	0.180385i
$990$		0			0
$991$	−34.5103	−	59.7737i	−0.0348237	−	0.0603165i	0.848088	−	0.529855i	$-0.177754\pi$
$991$	−34.5103	−	59.7737i	−0.0348237	−	0.0603165i	−0.882912	+	0.469538i	$0.844420\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−343.936	+	409.887i	−0.345665	+	0.411947i
$996$		0			0
$997$	−1114.73	−	405.729i	−1.11808	−	0.406950i	−0.284132	−	0.958785i	$-0.591705\pi$
$997$	−1114.73	−	405.729i	−1.11808	−	0.406950i	−0.833953	+	0.551836i	$0.813928\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.k.a.17.2		36
3.2	odd	2		108.3.k.a.77.1	✓	36
12.11	even	2		432.3.bc.b.401.6		36
27.7	even	9		108.3.k.a.101.1	yes	36
27.13	even	9		2916.3.c.b.1457.13		36
27.14	odd	18		2916.3.c.b.1457.24		36
27.20	odd	18	inner	324.3.k.a.305.2		36
108.7	odd	18		432.3.bc.b.209.6		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.k.a.77.1	✓	36	3.2	odd	2
108.3.k.a.101.1	yes	36	27.7	even	9
324.3.k.a.17.2		36	1.1	even	1	trivial
324.3.k.a.305.2		36	27.20	odd	18	inner
432.3.bc.b.209.6		36	108.7	odd	18
432.3.bc.b.401.6		36	12.11	even	2
2916.3.c.b.1457.13		36	27.13	even	9
2916.3.c.b.1457.24		36	27.14	odd	18

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.k (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.29223 - 0.580508i) q^{5} +(3.84473 - 3.22611i) q^{7} +O(q^{10})\)	\(q+(-3.29223 - 0.580508i) q^{5} +(3.84473 - 3.22611i) q^{7} +(-7.73764 + 1.36435i) q^{11} +(13.9363 - 5.07239i) q^{13} +(-18.4112 - 10.6297i) q^{17} +(-12.0316 - 20.8393i) q^{19} +(13.5318 - 16.1265i) q^{23} +(-12.9905 - 4.72817i) q^{25} +(10.7443 - 29.5197i) q^{29} +(3.12883 + 2.62540i) q^{31} +(-14.5305 + 8.38919i) q^{35} +(20.6961 - 35.8467i) q^{37} +(1.46139 + 4.01515i) q^{41} +(-2.94313 - 16.6913i) q^{43} +(-42.4392 - 50.5770i) q^{47} +(-4.13462 + 23.4486i) q^{49} +63.0022i q^{53} +26.2661 q^{55} +(75.1069 + 13.2434i) q^{59} +(-76.5149 + 64.2036i) q^{61} +(-48.8259 + 8.60932i) q^{65} +(83.0701 - 30.2350i) q^{67} +(-4.34219 - 2.50696i) q^{71} +(-19.2797 - 33.3934i) q^{73} +(-25.3476 + 30.2080i) q^{77} +(-35.9010 - 13.0669i) q^{79} +(48.8367 - 134.178i) q^{83} +(54.4433 + 45.6833i) q^{85} +(-75.2075 + 43.4211i) q^{89} +(37.2171 - 64.4618i) q^{91} +(27.5133 + 75.5921i) q^{95} +(28.6111 + 162.262i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 9 q^{5}+O(q^{10}) \) 36 * q + 9 * q^5	\( 36 q + 9 q^{5} - 36 q^{11} + 18 q^{23} - 9 q^{25} + 18 q^{29} + 45 q^{31} + 243 q^{35} + 198 q^{41} + 90 q^{43} + 243 q^{47} + 72 q^{49} - 252 q^{59} - 144 q^{61} - 747 q^{65} + 108 q^{67} - 324 q^{71} - 63 q^{73} - 495 q^{77} + 36 q^{79} + 27 q^{83} - 180 q^{85} + 567 q^{89} + 99 q^{91} + 1044 q^{95} - 216 q^{97}+O(q^{100}) \) 36 * q + 9 * q^5 - 36 * q^11 + 18 * q^23 - 9 * q^25 + 18 * q^29 + 45 * q^31 + 243 * q^35 + 198 * q^41 + 90 * q^43 + 243 * q^47 + 72 * q^49 - 252 * q^59 - 144 * q^61 - 747 * q^65 + 108 * q^67 - 324 * q^71 - 63 * q^73 - 495 * q^77 + 36 * q^79 + 27 * q^83 - 180 * q^85 + 567 * q^89 + 99 * q^91 + 1044 * q^95 - 216 * q^97

Introduction

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