LMFDB - Embedded newform 324.3.k.a.89.2

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			89.2
Character	$\chi$	$=$	324.89
Dual form			324.3.k.a.233.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.68656 - 3.20172i) q^{5} +(-4.88621 + 1.77844i) q^{7} +O(q^{10})$	$q+(-2.68656 - 3.20172i) q^{5} +(-4.88621 + 1.77844i) q^{7} +(4.52170 - 5.38875i) q^{11} +(3.33062 + 18.8889i) q^{13} +(-20.3965 + 11.7759i) q^{17} +(-11.7859 + 20.4138i) q^{19} +(-8.16612 + 22.4362i) q^{23} +(1.30781 - 7.41698i) q^{25} +(-21.2148 - 3.74075i) q^{29} +(24.0093 + 8.73866i) q^{31} +(18.8212 + 10.8664i) q^{35} +(-6.81584 - 11.8054i) q^{37} +(-50.7253 + 8.94424i) q^{41} +(3.55532 + 2.98327i) q^{43} +(-1.64224 - 4.51203i) q^{47} +(-16.8239 + 14.1170i) q^{49} +67.3308i q^{53} -29.4011 q^{55} +(-55.7367 - 66.4244i) q^{59} +(50.3038 - 18.3091i) q^{61} +(51.5290 - 61.4098i) q^{65} +(3.49276 + 19.8084i) q^{67} +(85.2808 - 49.2369i) q^{71} +(-69.6234 + 120.591i) q^{73} +(-12.5104 + 34.3721i) q^{77} +(18.3268 - 103.937i) q^{79} +(79.2540 + 13.9746i) q^{83} +(92.4995 + 33.6671i) q^{85} +(58.0744 + 33.5293i) q^{89} +(-49.8668 - 86.3718i) q^{91} +(97.0226 - 17.1077i) q^{95} +(-112.041 - 94.0132i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

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

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
$5$	−2.68656	−	3.20172i	−0.537312	−	0.640344i	0.427271	−	0.904124i	$-0.359475\pi$
$5$	−2.68656	−	3.20172i	−0.537312	−	0.640344i	−0.964583	+	0.263780i	$0.915031\pi$
$6$		0			0
$7$	−4.88621	+	1.77844i	−0.698031	+	0.254062i	−0.666570	−	0.745443i	$-0.732238\pi$
$7$	−4.88621	+	1.77844i	−0.698031	+	0.254062i	−0.0314608	+	0.999505i	$0.510016\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	4.52170	−	5.38875i	0.411064	−	0.489886i	−0.520297	−	0.853986i	$-0.674179\pi$
$11$	4.52170	−	5.38875i	0.411064	−	0.489886i	0.931360	+	0.364099i	$0.118623\pi$
$12$		0			0
$13$	3.33062	+	18.8889i	0.256202	+	1.45299i	0.792970	+	0.609261i	$0.208534\pi$
$13$	3.33062	+	18.8889i	0.256202	+	1.45299i	−0.536768	+	0.843730i	$0.680355\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−20.3965	+	11.7759i	−1.19979	+	0.692701i	−0.960509	−	0.278249i	$-0.910246\pi$
$17$	−20.3965	+	11.7759i	−1.19979	+	0.692701i	−0.239284	+	0.970950i	$0.576913\pi$
$18$		0			0
$19$	−11.7859	+	20.4138i	−0.620310	+	1.07441i	0.369118	+	0.929383i	$0.379660\pi$
$19$	−11.7859	+	20.4138i	−0.620310	+	1.07441i	−0.989428	+	0.145026i	$0.953674\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−8.16612	+	22.4362i	−0.355049	+	0.975489i	0.625674	+	0.780085i	$0.284824\pi$
$23$	−8.16612	+	22.4362i	−0.355049	+	0.975489i	−0.980723	+	0.195404i	$0.937398\pi$
$24$		0			0
$25$	1.30781	−	7.41698i	0.0523125	−	0.296679i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−21.2148	−	3.74075i	−0.731546	−	0.128991i	−0.204547	−	0.978857i	$-0.565572\pi$
$29$	−21.2148	−	3.74075i	−0.731546	−	0.128991i	−0.527000	+	0.849866i	$0.676683\pi$
$30$		0			0
$31$	24.0093	+	8.73866i	0.774492	+	0.281892i	0.698874	−	0.715245i	$-0.253685\pi$
$31$	24.0093	+	8.73866i	0.774492	+	0.281892i	0.0756183	+	0.997137i	$0.475907\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	18.8212	+	10.8664i	0.537747	+	0.310469i
$36$		0			0
$37$	−6.81584	−	11.8054i	−0.184212	−	0.319064i	0.759099	−	0.650975i	$-0.225640\pi$
$37$	−6.81584	−	11.8054i	−0.184212	−	0.319064i	−0.943311	+	0.331911i	$0.892307\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−50.7253	+	8.94424i	−1.23720	+	0.218152i	−0.753716	−	0.657200i	$-0.771741\pi$
$41$	−50.7253	+	8.94424i	−1.23720	+	0.218152i	−0.483486	+	0.875352i	$0.660630\pi$
$42$		0			0
$43$	3.55532	+	2.98327i	0.0826818	+	0.0693783i	0.683192	−	0.730239i	$-0.260591\pi$
$43$	3.55532	+	2.98327i	0.0826818	+	0.0693783i	−0.600510	+	0.799617i	$0.705036\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.64224	−	4.51203i	−0.0349413	−	0.0960006i	0.920995	−	0.389574i	$-0.127378\pi$
$47$	−1.64224	−	4.51203i	−0.0349413	−	0.0960006i	−0.955937	+	0.293573i	$0.905156\pi$
$48$		0			0
$49$	−16.8239	+	14.1170i	−0.343346	+	0.288101i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			67.3308i			1.27039i	0.772351	+	0.635196i	$0.219081\pi$
$53$			67.3308i			1.27039i	−0.772351	+	0.635196i	$0.780919\pi$
$54$		0			0
$55$	−29.4011			−0.534565
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−55.7367	−	66.4244i	−0.944690	−	1.12584i	−0.991909	−	0.126953i	$-0.959480\pi$
$59$	−55.7367	−	66.4244i	−0.944690	−	1.12584i	0.0472185	−	0.998885i	$-0.484964\pi$
$60$		0			0
$61$	50.3038	−	18.3091i	0.824653	−	0.300149i	0.104991	−	0.994473i	$-0.466519\pi$
$61$	50.3038	−	18.3091i	0.824653	−	0.300149i	0.719663	+	0.694324i	$0.244297\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	51.5290	−	61.4098i	0.792753	−	0.944767i
$66$		0			0
$67$	3.49276	+	19.8084i	0.0521307	+	0.295648i	0.999715	−	0.0238568i	$-0.00759458\pi$
$67$	3.49276	+	19.8084i	0.0521307	+	0.295648i	−0.947585	+	0.319505i	$0.896483\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	85.2808	−	49.2369i	1.20114	−	0.693477i	0.240329	−	0.970691i	$-0.422745\pi$
$71$	85.2808	−	49.2369i	1.20114	−	0.693477i	0.960808	+	0.277214i	$0.0894112\pi$
$72$		0			0
$73$	−69.6234	+	120.591i	−0.953745	+	1.65193i	−0.216530	+	0.976276i	$0.569474\pi$
$73$	−69.6234	+	120.591i	−0.953745	+	1.65193i	−0.737215	+	0.675659i	$0.763859\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−12.5104	+	34.3721i	−0.162473	+	0.446391i
$78$		0			0
$79$	18.3268	−	103.937i	0.231985	−	1.31565i	−0.616886	−	0.787053i	$-0.711606\pi$
$79$	18.3268	−	103.937i	0.231985	−	1.31565i	0.848871	−	0.528600i	$-0.177283\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	79.2540	+	13.9746i	0.954867	+	0.168369i	0.629311	−	0.777154i	$-0.283337\pi$
$83$	79.2540	+	13.9746i	0.954867	+	0.168369i	0.325557	+	0.945523i	$0.394448\pi$
$84$		0			0
$85$	92.4995	+	33.6671i	1.08823	+	0.396083i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	58.0744	+	33.5293i	0.652521	+	0.376733i	0.789421	−	0.613852i	$-0.210381\pi$
$89$	58.0744	+	33.5293i	0.652521	+	0.376733i	−0.136900	+	0.990585i	$0.543714\pi$
$90$		0			0
$91$	−49.8668	−	86.3718i	−0.547987	−	0.949141i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	97.0226	−	17.1077i	1.02129	−	0.180081i
$96$		0			0
$97$	−112.041	−	94.0132i	−1.15506	−	0.969208i	−0.155232	−	0.987878i	$-0.549612\pi$
$97$	−112.041	−	94.0132i	−1.15506	−	0.969208i	−0.999826	+	0.0186698i	$0.994057\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−33.7340	−	92.6834i	−0.334000	−	0.917657i	−0.987060	−	0.160351i	$-0.948737\pi$
$101$	−33.7340	−	92.6834i	−0.334000	−	0.917657i	0.653060	−	0.757306i	$-0.273485\pi$
$102$		0			0
$103$	107.050	−	89.8257i	1.03932	−	0.872094i	0.0473903	−	0.998876i	$-0.484910\pi$
$103$	107.050	−	89.8257i	1.03932	−	0.872094i	0.991931	+	0.126783i	$0.0404651\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			73.3054i			0.685098i	0.939500	+	0.342549i	$0.111290\pi$
$107$			73.3054i			0.685098i	−0.939500	+	0.342549i	$0.888710\pi$
$108$		0			0
$109$	−82.6310			−0.758083			−0.379041	−	0.925380i	$-0.623746\pi$
$109$	−82.6310			−0.758083			−0.379041	+	0.925380i	$0.623746\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−111.471	−	132.846i	−0.986466	−	1.17562i	−0.984457	−	0.175627i	$-0.943805\pi$
$113$	−111.471	−	132.846i	−0.986466	−	1.17562i	−0.00200959	−	0.999998i	$-0.500640\pi$
$114$		0			0
$115$	93.7733	−	34.1307i	0.815420	−	0.296789i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	78.7188	−	93.8134i	0.661503	−	0.788348i
$120$		0			0
$121$	12.4186	+	70.4291i	0.102633	+	0.582059i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−117.750	+	67.9832i	−0.942003	+	0.543866i
$126$		0			0
$127$	111.534	−	193.183i	0.878223	−	1.52113i	0.0249327	−	0.999689i	$-0.492063\pi$
$127$	111.534	−	193.183i	0.878223	−	1.52113i	0.853290	−	0.521437i	$-0.174604\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−76.0508	+	208.948i	−0.580540	+	1.59502i	0.206719	+	0.978400i	$0.433721\pi$
$131$	−76.0508	+	208.948i	−0.580540	+	1.59502i	−0.787260	+	0.616621i	$0.788501\pi$
$132$		0			0
$133$	21.2838	−	120.706i	0.160029	−	0.907567i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	159.835	+	28.1833i	1.16668	+	0.205717i	0.723247	−	0.690590i	$-0.242649\pi$
$137$	159.835	+	28.1833i	1.16668	+	0.205717i	0.443434	+	0.896307i	$0.353760\pi$
$138$		0			0
$139$	−71.5107	−	26.0278i	−0.514466	−	0.187250i	0.0717232	−	0.997425i	$-0.477150\pi$
$139$	−71.5107	−	26.0278i	−0.514466	−	0.187250i	−0.586189	+	0.810174i	$0.699372\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	116.848	+	67.4620i	0.817116	+	0.471762i
$144$		0			0
$145$	45.0181	+	77.9737i	0.310470	+	0.537749i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	90.4646	−	15.9514i	0.607145	−	0.107056i	0.138380	−	0.990379i	$-0.455810\pi$
$149$	90.4646	−	15.9514i	0.607145	−	0.107056i	0.468765	+	0.883323i	$0.344699\pi$
$150$		0			0
$151$	37.2582	+	31.2633i	0.246743	+	0.207042i	0.757768	−	0.652524i	$-0.226290\pi$
$151$	37.2582	+	31.2633i	0.246743	+	0.207042i	−0.511025	+	0.859566i	$0.670734\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−36.5236	−	100.348i	−0.235636	−	0.647405i
$156$		0			0
$157$	−78.3333	+	65.7295i	−0.498938	+	0.418659i	−0.857217	−	0.514956i	$-0.827808\pi$
$157$	−78.3333	+	65.7295i	−0.498938	+	0.418659i	0.358278	+	0.933615i	$0.383364\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	124.151i		−	0.771125i
$162$		0			0
$163$	−42.0106			−0.257734			−0.128867	−	0.991662i	$-0.541134\pi$
$163$	−42.0106			−0.257734			−0.128867	+	0.991662i	$0.541134\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	7.62167	+	9.08316i	0.0456388	+	0.0543902i	0.788381	−	0.615187i	$-0.210920\pi$
$167$	7.62167	+	9.08316i	0.0456388	+	0.0543902i	−0.742742	+	0.669578i	$0.766475\pi$
$168$		0			0
$169$	−186.889	+	68.0220i	−1.10585	+	0.402497i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−119.692	+	142.643i	−0.691860	+	0.824527i	−0.991579	−	0.129500i	$-0.958663\pi$
$173$	−119.692	+	142.643i	−0.691860	+	0.824527i	0.299719	+	0.954028i	$0.403107\pi$
$174$		0			0
$175$	6.80037	+	38.5668i	0.0388592	+	0.220382i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	82.0051	−	47.3456i	0.458129	−	0.264501i	−0.253128	−	0.967433i	$-0.581459\pi$
$179$	82.0051	−	47.3456i	0.458129	−	0.264501i	0.711257	+	0.702932i	$0.248126\pi$
$180$		0			0
$181$	−56.7101	+	98.2247i	−0.313315	+	0.542678i	−0.979078	−	0.203486i	$-0.934773\pi$
$181$	−56.7101	+	98.2247i	−0.313315	+	0.542678i	0.665763	+	0.746164i	$0.268106\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−19.4863	+	53.5383i	−0.105332	+	0.289396i
$186$		0			0
$187$	−28.7693	+	163.159i	−0.153846	+	0.872506i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−305.366	−	53.8443i	−1.59878	−	0.281907i	−0.697970	−	0.716127i	$-0.745913\pi$
$191$	−305.366	−	53.8443i	−1.59878	−	0.281907i	−0.900807	+	0.434220i	$0.857024\pi$
$192$		0			0
$193$	207.986	+	75.7007i	1.07765	+	0.392232i	0.819031	−	0.573749i	$-0.194511\pi$
$193$	207.986	+	75.7007i	1.07765	+	0.392232i	0.258616	+	0.965980i	$0.416734\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−129.101	−	74.5366i	−0.655336	−	0.378359i	0.135161	−	0.990824i	$-0.456845\pi$
$197$	−129.101	−	74.5366i	−0.655336	−	0.378359i	−0.790498	+	0.612465i	$0.790178\pi$
$198$		0			0
$199$	84.5042	+	146.366i	0.424644	+	0.735506i	0.996387	−	0.0849273i	$-0.0270658\pi$
$199$	84.5042	+	146.366i	0.424644	+	0.735506i	−0.571743	+	0.820433i	$0.693732\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	110.313	−	19.4511i	0.543413	−	0.0958184i
$204$		0			0
$205$	164.913	+	138.379i	0.804456	+	0.675019i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	56.7124	+	155.816i	0.271351	+	0.745531i
$210$		0			0
$211$	−163.282	+	137.010i	−0.773849	+	0.649337i	−0.941692	−	0.336477i	$-0.890765\pi$
$211$	−163.282	+	137.010i	−0.773849	+	0.649337i	0.167842	+	0.985814i	$0.446320\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		−	19.3978i		−	0.0902225i
$216$		0			0
$217$	−132.856			−0.612238
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−290.367	−	346.046i	−1.31388	−	1.56582i
$222$		0			0
$223$	51.1847	−	18.6297i	0.229528	−	0.0835412i	−0.224696	−	0.974429i	$-0.572139\pi$
$223$	51.1847	−	18.6297i	0.229528	−	0.0835412i	0.454224	+	0.890888i	$0.349917\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−56.5301	+	67.3699i	−0.249031	+	0.296784i	−0.876050	−	0.482220i	$-0.839830\pi$
$227$	−56.5301	+	67.3699i	−0.249031	+	0.296784i	0.627019	+	0.779004i	$0.284275\pi$
$228$		0			0
$229$	−45.0976	−	255.761i	−0.196933	−	1.11686i	−0.909639	−	0.415399i	$-0.863642\pi$
$229$	−45.0976	−	255.761i	−0.196933	−	1.11686i	0.712706	−	0.701462i	$-0.247469\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−188.673	+	108.930i	−0.809753	+	0.467511i	−0.846870	−	0.531800i	$-0.821516\pi$
$233$	−188.673	+	108.930i	−0.809753	+	0.467511i	0.0371169	+	0.999311i	$0.488183\pi$
$234$		0			0
$235$	−10.0343	+	17.3798i	−0.0426989	+	0.0739567i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−103.904	+	285.473i	−0.434744	+	1.19445i	0.508125	+	0.861284i	$0.330339\pi$
$239$	−103.904	+	285.473i	−0.434744	+	1.19445i	−0.942868	+	0.333165i	$0.891883\pi$
$240$		0			0
$241$	−33.0793	+	187.602i	−0.137259	+	0.778432i	0.836002	+	0.548727i	$0.184887\pi$
$241$	−33.0793	+	187.602i	−0.137259	+	0.778432i	−0.973260	+	0.229705i	$0.926224\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	90.3970	+	15.9394i	0.368967	+	0.0650589i
$246$		0			0
$247$	−424.847	−	154.632i	−1.72003	−	0.626040i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−244.229	−	141.006i	−0.973023	−	0.561775i	−0.0728668	−	0.997342i	$-0.523215\pi$
$251$	−244.229	−	141.006i	−0.973023	−	0.561775i	−0.900157	+	0.435566i	$0.856548\pi$
$252$		0			0
$253$	83.9786	+	145.455i	0.331931	+	0.574921i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	425.035	−	74.9451i	1.65383	−	0.291615i	0.732609	−	0.680649i	$-0.238302\pi$
$257$	425.035	−	74.9451i	1.65383	−	0.291615i	0.921223	+	0.389034i	$0.127191\pi$
$258$		0			0
$259$	54.2988	+	45.5621i	0.209648	+	0.175915i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	111.156	+	305.400i	0.422648	+	1.16121i	0.950186	+	0.311684i	$0.100893\pi$
$263$	111.156	+	305.400i	0.422648	+	1.16121i	−0.527538	+	0.849531i	$0.676885\pi$
$264$		0			0
$265$	215.574	−	180.888i	0.813488	−	0.682597i
$266$		0			0
$267$		0			0
$268$		0			0
$269$			222.465i			0.827009i	0.910502	+	0.413504i	$0.135695\pi$
$269$			222.465i			0.827009i	−0.910502	+	0.413504i	$0.864305\pi$
$270$		0			0
$271$	416.652			1.53746			0.768730	−	0.639574i	$-0.220889\pi$
$271$	416.652			1.53746			0.768730	+	0.639574i	$0.220889\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−34.0547	−	40.5848i	−0.123835	−	0.147581i
$276$		0			0
$277$	−55.3380	+	20.1414i	−0.199776	+	0.0727126i	−0.439971	−	0.898012i	$-0.645011\pi$
$277$	−55.3380	+	20.1414i	−0.199776	+	0.0727126i	0.240194	+	0.970725i	$0.422789\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−187.499	+	223.452i	−0.667255	+	0.795204i	−0.988408	−	0.151824i	$-0.951485\pi$
$281$	−187.499	+	223.452i	−0.667255	+	0.795204i	0.321152	+	0.947028i	$0.395930\pi$
$282$		0			0
$283$	15.3422	+	87.0101i	0.0542128	+	0.307456i	0.999842	−	0.0177914i	$-0.00566349\pi$
$283$	15.3422	+	87.0101i	0.0542128	+	0.307456i	−0.945629	+	0.325248i	$0.894552\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	231.948	−	133.915i	0.808181	−	0.466603i
$288$		0			0
$289$	132.844	−	230.093i	0.459668	−	0.796169i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−105.430	+	289.667i	−0.359830	+	0.988624i	0.619258	+	0.785187i	$0.287433\pi$
$293$	−105.430	+	289.667i	−0.359830	+	0.988624i	−0.979088	+	0.203437i	$0.934789\pi$
$294$		0			0
$295$	−62.9322	+	356.906i	−0.213330	+	1.20985i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−450.994	−	79.5224i	−1.50834	−	0.265961i
$300$		0			0
$301$	−22.6776	−	8.25397i	−0.0753408	−	0.0274218i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−193.765	−	111.870i	−0.635295	−	0.366788i
$306$		0			0
$307$	−93.8952	−	162.631i	−0.305847	−	0.529743i	0.671602	−	0.740912i	$-0.265606\pi$
$307$	−93.8952	−	162.631i	−0.305847	−	0.529743i	−0.977450	+	0.211169i	$0.932273\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	551.764	−	97.2909i	1.77416	−	0.312833i	0.811664	−	0.584124i	$-0.198562\pi$
$311$	551.764	−	97.2909i	1.77416	−	0.312833i	0.962497	+	0.271292i	$0.0874509\pi$
$312$		0			0
$313$	−229.337	−	192.436i	−0.732706	−	0.614813i	0.198162	−	0.980169i	$-0.436503\pi$
$313$	−229.337	−	192.436i	−0.732706	−	0.614813i	−0.930868	+	0.365356i	$0.880947\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	50.1956	+	137.911i	0.158346	+	0.435051i	0.993342	−	0.115205i	$-0.0367523\pi$
$317$	50.1956	+	137.911i	0.158346	+	0.435051i	−0.834996	+	0.550256i	$0.814530\pi$
$318$		0			0
$319$	−116.085	+	97.4069i	−0.363903	+	0.305351i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	555.158i		−	1.71876i
$324$		0			0
$325$	144.454			0.444475
$326$		0			0
$327$		0			0
$328$		0			0
$329$	16.0487	+	19.1261i	0.0487803	+	0.0581340i
$330$		0			0
$331$	−203.791	+	74.1738i	−0.615683	+	0.224090i	−0.630988	−	0.775793i	$-0.717350\pi$
$331$	−203.791	+	74.1738i	−0.615683	+	0.224090i	0.0153052	+	0.999883i	$0.495128\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	54.0374	−	64.3993i	0.161306	−	0.192237i
$336$		0			0
$337$	−11.0619	−	62.7349i	−0.0328245	−	0.186157i	0.963987	−	0.265949i	$-0.0856854\pi$
$337$	−11.0619	−	62.7349i	−0.0328245	−	0.186157i	−0.996812	+	0.0797923i	$0.974574\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	155.653	−	89.8664i	0.456461	−	0.263538i
$342$		0			0
$343$	184.494	−	319.554i	0.537884	−	0.931643i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	31.7255	−	87.1651i	0.0914280	−	0.251196i	−0.885547	−	0.464549i	$-0.846216\pi$
$347$	31.7255	−	87.1651i	0.0914280	−	0.251196i	0.976975	+	0.213353i	$0.0684385\pi$
$348$		0			0
$349$	41.7475	−	236.762i	0.119620	−	0.678401i	−0.864738	−	0.502223i	$-0.832516\pi$
$349$	41.7475	−	236.762i	0.119620	−	0.678401i	0.984358	−	0.176178i	$-0.0563733\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	326.982	+	57.6557i	0.926294	+	0.163331i	0.616393	−	0.787438i	$-0.288593\pi$
$353$	326.982	+	57.6557i	0.926294	+	0.163331i	0.309900	+	0.950769i	$0.399704\pi$
$354$		0			0
$355$	−386.754	−	140.767i	−1.08945	−	0.396527i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−56.4254	−	32.5772i	−0.157174	−	0.0907444i	0.419350	−	0.907825i	$-0.362258\pi$
$359$	−56.4254	−	32.5772i	−0.157174	−	0.0907444i	−0.576524	+	0.817080i	$0.695591\pi$
$360$		0			0
$361$	−97.3142	−	168.553i	−0.269569	−	0.466906i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	573.146	−	101.061i	1.57026	−	0.276880i
$366$		0			0
$367$	305.024	+	255.946i	0.831129	+	0.697400i	0.955550	−	0.294830i	$-0.0952630\pi$
$367$	305.024	+	255.946i	0.831129	+	0.697400i	−0.124421	+	0.992229i	$0.539707\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−119.744	−	328.993i	−0.322759	−	0.886773i
$372$		0			0
$373$	106.450	−	89.3225i	0.285390	−	0.239471i	−0.488842	−	0.872372i	$-0.662581\pi$
$373$	106.450	−	89.3225i	0.285390	−	0.239471i	0.774232	+	0.632902i	$0.218136\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	413.184i		−	1.09598i
$378$		0			0
$379$	447.841			1.18164			0.590819	−	0.806804i	$-0.298805\pi$
$379$	447.841			1.18164			0.590819	+	0.806804i	$0.298805\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	318.172	+	379.182i	0.830735	+	0.990031i	0.999990	+	0.00445916i	$0.00141940\pi$
$383$	318.172	+	379.182i	0.830735	+	0.990031i	−0.169255	+	0.985572i	$0.554136\pi$
$384$		0			0
$385$	143.660	−	52.2879i	0.373143	−	0.135813i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	297.166	−	354.149i	0.763924	−	0.910409i	−0.234165	−	0.972197i	$-0.575236\pi$
$389$	297.166	−	354.149i	0.763924	−	0.910409i	0.998089	+	0.0617877i	$0.0196802\pi$
$390$		0			0
$391$	−97.6470	−	553.784i	−0.249737	−	1.41633i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−382.012	+	220.555i	−0.967119	+	0.558366i
$396$		0			0
$397$	−36.0513	+	62.4427i	−0.0908094	+	0.157286i	−0.907852	−	0.419291i	$-0.862279\pi$
$397$	−36.0513	+	62.4427i	−0.0908094	+	0.157286i	0.817043	+	0.576577i	$0.195612\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	81.0353	−	222.643i	0.202083	−	0.555218i	−0.796709	−	0.604364i	$-0.793427\pi$
$401$	81.0353	−	222.643i	0.202083	−	0.555218i	0.998792	+	0.0491451i	$0.0156497\pi$
$402$		0			0
$403$	−85.0978	+	482.613i	−0.211161	+	1.19755i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−94.4354	−	16.6515i	−0.232028	−	0.0409128i
$408$		0			0
$409$	46.7510	+	17.0160i	0.114306	+	0.0416038i	0.398540	−	0.917151i	$-0.369517\pi$
$409$	46.7510	+	17.0160i	0.114306	+	0.0416038i	−0.284234	+	0.958755i	$0.591739\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	390.473	+	225.440i	0.945456	+	0.545859i
$414$		0			0
$415$	−168.178	−	291.293i	−0.405248	−	0.701910i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−31.7034	+	5.59016i	−0.0756643	+	0.0133417i	−0.211352	−	0.977410i	$-0.567787\pi$
$419$	−31.7034	+	5.59016i	−0.0756643	+	0.0133417i	0.135688	+	0.990752i	$0.456676\pi$
$420$		0			0
$421$	−214.696	−	180.151i	−0.509967	−	0.427913i	0.351151	−	0.936319i	$-0.385790\pi$
$421$	−214.696	−	180.151i	−0.509967	−	0.427913i	−0.861117	+	0.508406i	$0.830235\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	60.6669	+	166.681i	0.142746	+	0.392190i
$426$		0			0
$427$	−213.234	+	178.924i	−0.499377	+	0.419027i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	109.024i		−	0.252955i	−0.991969	−	0.126478i	$-0.959633\pi$
$431$		−	109.024i		−	0.252955i	0.991969	−	0.126478i	$-0.0403672\pi$
$432$		0			0
$433$	364.275			0.841282			0.420641	−	0.907227i	$-0.361805\pi$
$433$	364.275			0.841282			0.420641	+	0.907227i	$0.361805\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−361.763	−	431.132i	−0.827833	−	0.986573i
$438$		0			0
$439$	−275.236	+	100.178i	−0.626961	+	0.228195i	−0.635908	−	0.771765i	$-0.719374\pi$
$439$	−275.236	+	100.178i	−0.626961	+	0.228195i	0.00894720	+	0.999960i	$0.497152\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−424.424	+	505.809i	−0.958068	+	1.14178i	0.0317580	+	0.999496i	$0.489889\pi$
$443$	−424.424	+	505.809i	−0.958068	+	1.14178i	−0.989826	+	0.142285i	$0.954555\pi$
$444$		0			0
$445$	−48.6691	−	276.016i	−0.109369	−	0.620261i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	73.8335	−	42.6278i	0.164440	−	0.0949394i	−0.415522	−	0.909583i	$-0.636401\pi$
$449$	73.8335	−	42.6278i	0.164440	−	0.0949394i	0.579961	+	0.814644i	$0.303068\pi$
$450$		0			0
$451$	−181.166	+	313.789i	−0.401699	+	0.695763i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−142.568	+	391.703i	−0.313336	+	0.860885i
$456$		0			0
$457$	92.6648	−	525.528i	0.202768	−	1.14995i	−0.698147	−	0.715955i	$-0.745992\pi$
$457$	92.6648	−	525.528i	0.202768	−	1.14995i	0.900914	−	0.433997i	$-0.142897\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	657.017	+	115.850i	1.42520	+	0.251301i	0.832456	−	0.554091i	$-0.186934\pi$
$461$	657.017	+	115.850i	1.42520	+	0.251301i	0.592743	+	0.805392i	$0.298045\pi$
$462$		0			0
$463$	417.085	+	151.807i	0.900831	+	0.327876i	0.750586	−	0.660773i	$-0.229771\pi$
$463$	417.085	+	151.807i	0.900831	+	0.327876i	0.150246	+	0.988649i	$0.451994\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	199.055	+	114.925i	0.426242	+	0.246091i	0.697745	−	0.716347i	$-0.254187\pi$
$467$	199.055	+	114.925i	0.426242	+	0.246091i	−0.271502	+	0.962438i	$0.587520\pi$
$468$		0			0
$469$	−52.2944	−	90.5765i	−0.111502	−	0.193127i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	32.1521	−	5.66929i	0.0679749	−	0.0119858i
$474$		0			0
$475$	135.995	+	114.113i	0.286304	+	0.240238i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	143.940	+	395.471i	0.300501	+	0.825619i	0.994413	+	0.105559i	$0.0336633\pi$
$479$	143.940	+	395.471i	0.300501	+	0.825619i	−0.693912	+	0.720060i	$0.744114\pi$
$480$		0			0
$481$	200.289	−	168.063i	0.416402	−	0.349403i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			611.294i			1.26040i
$486$		0			0
$487$	−528.889			−1.08601			−0.543007	−	0.839728i	$-0.682714\pi$
$487$	−528.889			−1.08601			−0.543007	+	0.839728i	$0.682714\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−388.337	−	462.802i	−0.790911	−	0.942571i	0.208460	−	0.978031i	$-0.433155\pi$
$491$	−388.337	−	462.802i	−0.790911	−	0.942571i	−0.999371	+	0.0354597i	$0.988710\pi$
$492$		0			0
$493$	476.759	−	173.526i	0.967056	−	0.351980i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−329.135	+	392.248i	−0.662244	+	0.789232i
$498$		0			0
$499$	81.1625	+	460.295i	0.162650	+	0.922436i	0.951454	+	0.307791i	$0.0995897\pi$
$499$	81.1625	+	460.295i	0.162650	+	0.922436i	−0.788804	+	0.614645i	$0.789299\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	340.414	−	196.538i	0.676767	−	0.390732i	−0.121869	−	0.992546i	$-0.538889\pi$
$503$	340.414	−	196.538i	0.676767	−	0.390732i	0.798636	+	0.601815i	$0.205555\pi$
$504$		0			0
$505$	−206.118	+	357.006i	−0.408154	+	0.706943i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	88.2803	−	242.548i	0.173439	−	0.476519i	−0.822266	−	0.569103i	$-0.807290\pi$
$509$	88.2803	−	242.548i	0.173439	−	0.476519i	0.995705	+	0.0925841i	$0.0295127\pi$
$510$		0			0
$511$	125.731	−	713.055i	0.246049	−	1.39541i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−575.193	−	101.422i	−1.11688	−	0.196936i
$516$		0			0
$517$	−31.7399	−	11.5524i	−0.0613925	−	0.0223450i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−610.780	−	352.634i	−1.17232	−	0.676840i	−0.218096	−	0.975927i	$-0.569985\pi$
$521$	−610.780	−	352.634i	−1.17232	−	0.676840i	−0.954226	+	0.299087i	$0.903318\pi$
$522$		0			0
$523$	157.023	+	271.972i	0.300235	+	0.520023i	0.976189	−	0.216921i	$-0.0696015\pi$
$523$	157.023	+	271.972i	0.300235	+	0.520023i	−0.675954	+	0.736944i	$0.736268\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−592.610	+	104.493i	−1.12450	+	0.198279i
$528$		0			0
$529$	−31.4618	−	26.3996i	−0.0594742	−	0.0499047i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−337.893	−	928.354i	−0.633946	−	1.74175i
$534$		0			0
$535$	234.703	−	196.939i	0.438698	−	0.368111i
$536$		0			0
$537$		0			0
$538$		0			0
$539$			154.493i			0.286628i
$540$		0			0
$541$	−430.803			−0.796309			−0.398155	−	0.917318i	$-0.630349\pi$
$541$	−430.803			−0.796309			−0.398155	+	0.917318i	$0.630349\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	221.993	+	264.561i	0.407327	+	0.485433i
$546$		0			0
$547$	−119.598	+	43.5300i	−0.218643	+	0.0795796i	−0.449019	−	0.893522i	$-0.648227\pi$
$547$	−119.598	+	43.5300i	−0.218643	+	0.0795796i	0.230376	+	0.973102i	$0.426004\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	326.398	−	388.986i	0.592375	−	0.705965i
$552$		0			0
$553$	95.2958	+	540.450i	0.172325	+	0.977305i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−205.962	+	118.912i	−0.369770	+	0.213487i	−0.673358	−	0.739316i	$-0.735149\pi$
$557$	−205.962	+	118.912i	−0.369770	+	0.213487i	0.303588	+	0.952803i	$0.401815\pi$
$558$		0			0
$559$	−44.5091	+	77.0921i	−0.0796228	+	0.137911i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−311.664	+	856.289i	−0.553577	+	1.52094i	0.275215	+	0.961383i	$0.411251\pi$
$563$	−311.664	+	856.289i	−0.553577	+	1.52094i	−0.828792	+	0.559557i	$0.810971\pi$
$564$		0			0
$565$	−125.861	+	713.795i	−0.222764	+	1.26335i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	346.766	+	61.1442i	0.609430	+	0.107459i	0.469842	−	0.882751i	$-0.344311\pi$
$569$	346.766	+	61.1442i	0.609430	+	0.107459i	0.139588	+	0.990210i	$0.455422\pi$
$570$		0			0
$571$	−109.923	−	40.0089i	−0.192510	−	0.0700681i	0.243966	−	0.969784i	$-0.421551\pi$
$571$	−109.923	−	40.0089i	−0.192510	−	0.0700681i	−0.436476	+	0.899716i	$0.643774\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	155.729	+	89.9104i	0.270834	+	0.156366i
$576$		0			0
$577$	368.143	+	637.643i	0.638030	+	1.10510i	0.985865	+	0.167544i	$0.0535838\pi$
$577$	368.143	+	637.643i	0.638030	+	1.10510i	−0.347834	+	0.937556i	$0.613083\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−412.105	+	72.6652i	−0.709303	+	0.125069i
$582$		0			0
$583$	362.829	+	304.450i	0.622348	+	0.522212i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−28.4590	−	78.1905i	−0.0484821	−	0.133204i	0.913088	−	0.407762i	$-0.133691\pi$
$587$	−28.4590	−	78.1905i	−0.0484821	−	0.133204i	−0.961570	+	0.274558i	$0.911468\pi$
$588$		0			0
$589$	−461.359	+	387.126i	−0.783293	+	0.657261i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			775.560i			1.30786i	0.756556	+	0.653929i	$0.226880\pi$
$593$			775.560i			1.30786i	−0.756556	+	0.653929i	$0.773120\pi$
$594$		0			0
$595$	−511.847			−0.860247
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−302.130	−	360.064i	−0.504390	−	0.601108i	0.452426	−	0.891802i	$-0.350559\pi$
$599$	−302.130	−	360.064i	−0.504390	−	0.601108i	−0.956816	+	0.290693i	$0.906114\pi$
$600$		0			0
$601$	−481.410	+	175.219i	−0.801015	+	0.291546i	−0.709907	−	0.704295i	$-0.751263\pi$
$601$	−481.410	+	175.219i	−0.801015	+	0.291546i	−0.0911082	+	0.995841i	$0.529041\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	192.131	−	228.973i	0.317572	−	0.378467i
$606$		0			0
$607$	84.9380	+	481.708i	0.139931	+	0.793587i	0.971298	+	0.237864i	$0.0764474\pi$
$607$	84.9380	+	481.708i	0.139931	+	0.793587i	−0.831368	+	0.555723i	$0.812442\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	79.7575	−	46.0480i	0.130536	−	0.0753650i
$612$		0			0
$613$	−61.1107	+	105.847i	−0.0996912	+	0.172670i	−0.911557	−	0.411174i	$-0.865119\pi$
$613$	−61.1107	+	105.847i	−0.0996912	+	0.172670i	0.811866	+	0.583844i	$0.198452\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	228.283	−	627.201i	0.369988	−	1.01653i	−0.605377	−	0.795939i	$-0.706978\pi$
$617$	228.283	−	627.201i	0.369988	−	1.01653i	0.975365	−	0.220595i	$-0.0708000\pi$
$618$		0			0
$619$	−109.522	+	621.131i	−0.176934	+	1.00344i	0.758954	+	0.651144i	$0.225711\pi$
$619$	−109.522	+	621.131i	−0.176934	+	1.00344i	−0.935888	+	0.352298i	$0.885400\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−343.393	−	60.5495i	−0.551193	−	0.0971902i
$624$		0			0
$625$	357.077	+	129.965i	0.571323	+	0.207945i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	278.038	+	160.525i	0.442032	+	0.255207i
$630$		0			0
$631$	0.442857	+	0.767050i	0.000701833	+	0.00121561i	0.866376	−	0.499392i	$-0.166443\pi$
$631$	0.442857	+	0.767050i	0.000701833	+	0.00121561i	−0.865674	+	0.500608i	$0.833110\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−918.161	+	161.897i	−1.44592	+	0.254955i
$636$		0			0
$637$	−322.688	−	270.767i	−0.506574	−	0.425066i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−100.064	−	274.923i	−0.156106	−	0.428897i	0.836843	−	0.547443i	$-0.184399\pi$
$641$	−100.064	−	274.923i	−0.156106	−	0.428897i	−0.992949	+	0.118546i	$0.962177\pi$
$642$		0			0
$643$	−368.253	+	309.001i	−0.572710	+	0.480561i	−0.882544	−	0.470230i	$-0.844171\pi$
$643$	−368.253	+	309.001i	−0.572710	+	0.480561i	0.309834	+	0.950791i	$0.399727\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			283.657i			0.438419i	0.975678	+	0.219209i	$0.0703477\pi$
$647$			283.657i			0.438419i	−0.975678	+	0.219209i	$0.929652\pi$
$648$		0			0
$649$	−609.969			−0.939860
$650$		0			0
$651$		0			0
$652$		0			0
$653$	530.766	+	632.542i	0.812811	+	0.968670i	0.999907	−	0.0136713i	$-0.00435185\pi$
$653$	530.766	+	632.542i	0.812811	+	0.968670i	−0.187096	+	0.982342i	$0.559907\pi$
$654$		0			0
$655$	873.307	−	317.858i	1.33329	−	0.485279i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	760.069	−	905.814i	1.15337	−	1.37453i	0.238317	−	0.971187i	$-0.423404\pi$
$659$	760.069	−	905.814i	1.15337	−	1.37453i	0.915050	−	0.403341i	$-0.132151\pi$
$660$		0			0
$661$	213.726	+	1212.10i	0.323338	+	1.83374i	0.521108	+	0.853491i	$0.325519\pi$
$661$	213.726	+	1212.10i	0.323338	+	1.83374i	−0.197770	+	0.980248i	$0.563370\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−443.648	+	256.140i	−0.667140	+	0.385173i
$666$		0			0
$667$	257.171	−	445.434i	0.385564	−	0.667817i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	128.796	−	353.863i	0.191946	−	0.527367i
$672$		0			0
$673$	202.091	−	1146.11i	0.300284	−	1.70299i	−0.344631	−	0.938738i	$-0.611996\pi$
$673$	202.091	−	1146.11i	0.300284	−	1.70299i	0.644915	−	0.764255i	$-0.276893\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	137.416	+	24.2302i	0.202978	+	0.0357905i	0.274213	−	0.961669i	$-0.411583\pi$
$677$	137.416	+	24.2302i	0.202978	+	0.0357905i	−0.0712346	+	0.997460i	$0.522694\pi$
$678$		0			0
$679$	714.651	+	260.112i	1.05250	+	0.383080i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	415.978	+	240.165i	0.609046	+	0.351633i	0.772592	−	0.634903i	$-0.218960\pi$
$683$	415.978	+	240.165i	0.609046	+	0.351633i	−0.163546	+	0.986536i	$0.552293\pi$
$684$		0			0
$685$	−339.172	−	587.463i	−0.495142	−	0.857611i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1271.80	+	224.253i	−1.84587	+	0.325476i
$690$		0			0
$691$	−918.527	−	770.736i	−1.32927	−	1.11539i	−0.984247	−	0.176798i	$-0.943426\pi$
$691$	−918.527	−	770.736i	−1.32927	−	1.11539i	−0.345025	−	0.938594i	$-0.612129\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	108.784	+	298.882i	0.156524	+	0.430047i
$696$		0			0
$697$	929.291	−	779.767i	1.33327	−	1.11875i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	105.488i		−	0.150482i	−0.997165	−	0.0752410i	$-0.976027\pi$
$701$		−	105.488i		−	0.150482i	0.997165	−	0.0752410i	$-0.0239726\pi$
$702$		0			0
$703$	321.323			0.457074
$704$		0			0
$705$		0			0
$706$		0			0
$707$	329.663	+	392.877i	0.466284	+	0.555696i
$708$		0			0
$709$	166.245	−	60.5082i	0.234478	−	0.0853431i	−0.222109	−	0.975022i	$-0.571294\pi$
$709$	166.245	−	60.5082i	0.234478	−	0.0853431i	0.456587	+	0.889679i	$0.349072\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−392.125	+	467.317i	−0.549965	+	0.655423i
$714$		0			0
$715$	−97.9238	−	555.353i	−0.136956	−	0.776718i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−276.181	+	159.453i	−0.384119	+	0.221771i	−0.679609	−	0.733575i	$-0.737850\pi$
$719$	−276.181	+	159.453i	−0.384119	+	0.221771i	0.295490	+	0.955346i	$0.404517\pi$
$720$		0			0
$721$	−363.320	+	629.289i	−0.503911	+	0.872800i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−55.4901	+	152.458i	−0.0765381	+	0.210287i
$726$		0			0
$727$	133.363	−	756.339i	0.183443	−	1.04036i	−0.744497	−	0.667626i	$-0.767311\pi$
$727$	133.363	−	756.339i	0.183443	−	1.04036i	0.927940	−	0.372730i	$-0.121578\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−107.647	−	18.9810i	−0.147259	−	0.0259658i
$732$		0			0
$733$	599.501	+	218.200i	0.817873	+	0.297681i	0.716872	−	0.697205i	$-0.245573\pi$
$733$	599.501	+	218.200i	0.817873	+	0.297681i	0.101001	+	0.994886i	$0.467795\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	122.536	+	70.7461i	0.166263	+	0.0959920i
$738$		0			0
$739$	−47.0509	−	81.4946i	−0.0636684	−	0.110277i	0.832434	−	0.554124i	$-0.186947\pi$
$739$	−47.0509	−	81.4946i	−0.0636684	−	0.110277i	−0.896103	+	0.443847i	$0.853613\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	532.414	−	93.8789i	0.716573	−	0.126351i	0.196538	−	0.980496i	$-0.437030\pi$
$743$	532.414	−	93.8789i	0.716573	−	0.126351i	0.520035	+	0.854145i	$0.325919\pi$
$744$		0			0
$745$	−294.110	−	246.788i	−0.394779	−	0.331259i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−130.369	−	358.186i	−0.174057	−	0.478219i
$750$		0			0
$751$	−212.859	+	178.610i	−0.283434	+	0.237829i	−0.773409	−	0.633907i	$-0.781450\pi$
$751$	−212.859	+	178.610i	−0.283434	+	0.237829i	0.489975	+	0.871736i	$0.337006\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		−	203.281i		−	0.269246i
$756$		0			0
$757$	−401.897			−0.530908			−0.265454	−	0.964124i	$-0.585522\pi$
$757$	−401.897			−0.530908			−0.265454	+	0.964124i	$0.585522\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	31.3411	+	37.3509i	0.0411841	+	0.0490813i	0.786243	−	0.617917i	$-0.212023\pi$
$761$	31.3411	+	37.3509i	0.0411841	+	0.0490813i	−0.745059	+	0.666998i	$0.767579\pi$
$762$		0			0
$763$	403.753	−	146.954i	0.529165	−	0.192600i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	1069.05	−	1274.04i	1.39380	−	1.66107i
$768$		0			0
$769$	−213.365	−	1210.05i	−0.277457	−	1.57354i	−0.731046	−	0.682328i	$-0.760968\pi$
$769$	−213.365	−	1210.05i	−0.277457	−	1.57354i	0.453589	−	0.891211i	$-0.350144\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	334.794	−	193.294i	0.433110	−	0.250056i	−0.267560	−	0.963541i	$-0.586218\pi$
$773$	334.794	−	193.294i	0.433110	−	0.250056i	0.700671	+	0.713485i	$0.252884\pi$
$774$		0			0
$775$	96.2141	−	166.648i	0.124147	−	0.215029i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	415.257	−	1140.91i	0.533064	−	1.46458i
$780$		0			0
$781$	120.289	−	682.191i	0.154019	−	0.873484i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	420.894	+	74.2150i	0.536171	+	0.0945415i
$786$		0			0
$787$	156.999	+	57.1429i	0.199490	+	0.0726085i	0.439833	−	0.898080i	$-0.355038\pi$
$787$	156.999	+	57.1429i	0.199490	+	0.0726085i	−0.240343	+	0.970688i	$0.577260\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	780.927	+	450.868i	0.987266	+	0.569998i
$792$		0			0
$793$	513.382	+	889.203i	0.647392	+	1.12132i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−1205.18	+	212.506i	−1.51214	+	0.266632i	−0.867340	−	0.497716i	$-0.834172\pi$
$797$	−1205.18	+	212.506i	−1.51214	+	0.266632i	−0.644805	+	0.764348i	$0.723061\pi$
$798$		0			0
$799$	86.6292	+	72.6905i	0.108422	+	0.0909769i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	335.020	+	920.460i	0.417211	+	1.14628i
$804$		0			0
$805$	−397.497	+	333.540i	−0.493785	+	0.414335i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	86.8246i		−	0.107323i	−0.998559	−	0.0536617i	$-0.982911\pi$
$809$		−	86.8246i		−	0.107323i	0.998559	−	0.0536617i	$-0.0170892\pi$
$810$		0			0
$811$	−1587.52			−1.95748			−0.978740	−	0.205105i	$-0.934247\pi$
$811$	−1587.52			−1.95748			−0.978740	+	0.205105i	$0.934247\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	112.864	+	134.506i	0.138483	+	0.165038i
$816$		0			0
$817$	−102.802	+	37.4169i	−0.125829	+	0.0457980i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−296.471	+	353.321i	−0.361110	+	0.430354i	−0.915758	−	0.401731i	$-0.868409\pi$
$821$	−296.471	+	353.321i	−0.361110	+	0.430354i	0.554648	+	0.832085i	$0.312853\pi$
$822$		0			0
$823$	−37.6079	−	213.285i	−0.0456962	−	0.259156i	0.953398	−	0.301716i	$-0.0975596\pi$
$823$	−37.6079	−	213.285i	−0.0456962	−	0.259156i	−0.999094	+	0.0425606i	$0.986448\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−91.8908	+	53.0532i	−0.111113	+	0.0641514i	−0.554527	−	0.832166i	$-0.687101\pi$
$827$	−91.8908	+	53.0532i	−0.111113	+	0.0641514i	0.443413	+	0.896317i	$0.353767\pi$
$828$		0			0
$829$	562.231	−	973.812i	0.678204	−	1.17468i	−0.297318	−	0.954779i	$-0.596092\pi$
$829$	562.231	−	973.812i	0.678204	−	1.17468i	0.975521	−	0.219904i	$-0.0705746\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	176.909	−	486.053i	0.212376	−	0.583497i
$834$		0			0
$835$	8.60562	−	48.8049i	0.0103061	−	0.0584490i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	515.140	+	90.8331i	0.613993	+	0.108263i	0.471992	−	0.881603i	$-0.343535\pi$
$839$	515.140	+	90.8331i	0.613993	+	0.108263i	0.142001	+	0.989866i	$0.454646\pi$
$840$		0			0
$841$	−354.205	−	128.920i	−0.421172	−	0.153294i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	719.875	+	415.620i	0.851923	+	0.491858i
$846$		0			0
$847$	−185.933	−	322.046i	−0.219520	−	0.380220i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	320.527	−	56.5176i	0.376648	−	0.0664132i
$852$		0			0
$853$	1294.14	+	1085.91i	1.51716	+	1.27305i	0.848092	+	0.529849i	$0.177751\pi$
$853$	1294.14	+	1085.91i	1.51716	+	1.27305i	0.669069	+	0.743200i	$0.266693\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−178.884	−	491.480i	−0.208733	−	0.573489i	0.790508	−	0.612452i	$-0.209817\pi$
$857$	−178.884	−	491.480i	−0.208733	−	0.573489i	−0.999241	+	0.0389630i	$0.987595\pi$
$858$		0			0
$859$	568.283	−	476.846i	0.661563	−	0.555117i	−0.248992	−	0.968506i	$-0.580099\pi$
$859$	568.283	−	476.846i	0.661563	−	0.555117i	0.910555	+	0.413388i	$0.135655\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			520.182i			0.602761i	0.953504	+	0.301380i	$0.0974474\pi$
$863$			520.182i			0.602761i	−0.953504	+	0.301380i	$0.902553\pi$
$864$		0			0
$865$	778.263			0.899726
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−477.220	−	568.729i	−0.549160	−	0.654463i
$870$		0			0
$871$	−362.526	+	131.949i	−0.416218	+	0.151491i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	454.450	−	541.592i	0.519371	−	0.618963i
$876$		0			0
$877$	124.891	+	708.290i	0.142407	+	0.807628i	0.969413	+	0.245435i	$0.0789309\pi$
$877$	124.891	+	708.290i	0.142407	+	0.807628i	−0.827006	+	0.562193i	$0.809958\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	871.566	−	503.199i	0.989292	−	0.571168i	0.0842293	−	0.996446i	$-0.473157\pi$
$881$	871.566	−	503.199i	0.989292	−	0.571168i	0.905063	+	0.425279i	$0.139824\pi$
$882$		0			0
$883$	−329.836	+	571.293i	−0.373541	+	0.646991i	−0.990107	−	0.140311i	$-0.955190\pi$
$883$	−329.836	+	571.293i	−0.373541	+	0.646991i	0.616567	+	0.787303i	$0.288523\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	540.115	−	1483.95i	0.608923	−	1.67300i	−0.123659	−	0.992325i	$-0.539463\pi$
$887$	540.115	−	1483.95i	0.608923	−	1.67300i	0.732582	−	0.680679i	$-0.238315\pi$
$888$		0			0
$889$	−201.417	+	1142.29i	−0.226565	+	1.28492i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	111.463	+	19.6539i	0.124818	+	0.0220088i
$894$		0			0
$895$	−371.899	−	135.360i	−0.415530	−	0.151240i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−476.664	−	275.202i	−0.530215	−	0.306120i
$900$		0			0
$901$	−792.881	−	1373.31i	−0.880002	−	1.52421i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	466.843	−	82.3170i	0.515849	−	0.0909580i
$906$		0			0
$907$	−267.023	−	224.059i	−0.294402	−	0.247033i	0.483608	−	0.875285i	$-0.339326\pi$
$907$	−267.023	−	224.059i	−0.294402	−	0.247033i	−0.778010	+	0.628252i	$0.783771\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	44.6619	+	122.708i	0.0490252	+	0.134696i	0.961789	−	0.273793i	$-0.0882783\pi$
$911$	44.6619	+	122.708i	0.0490252	+	0.134696i	−0.912764	+	0.408488i	$0.866056\pi$
$912$		0			0
$913$	433.668	−	363.891i	0.474993	−	0.398566i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	1156.22i		−	1.26087i
$918$		0			0
$919$	995.800			1.08357			0.541785	−	0.840517i	$-0.317749\pi$
$919$	995.800			1.08357			0.541785	+	0.840517i	$0.317749\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	1214.07	+	1446.87i	1.31535	+	1.56757i
$924$		0			0
$925$	−96.4741	+	35.1137i	−0.104296	+	0.0379607i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−499.513	+	595.297i	−0.537689	+	0.640793i	−0.964668	−	0.263469i	$-0.915133\pi$
$929$	−499.513	+	595.297i	−0.537689	+	0.640793i	0.426979	+	0.904262i	$0.359578\pi$
$930$		0			0
$931$	−89.8951	−	509.820i	−0.0965576	−	0.547605i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	599.678	−	346.224i	0.641367	−	0.370293i
$936$		0			0
$937$	−308.703	+	534.690i	−0.329459	+	0.570640i	−0.982405	−	0.186765i	$-0.940200\pi$
$937$	−308.703	+	534.690i	−0.329459	+	0.570640i	0.652945	+	0.757405i	$0.273533\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−329.276	+	904.678i	−0.349921	+	0.961400i	0.632473	+	0.774582i	$0.282040\pi$
$941$	−329.276	+	904.678i	−0.349921	+	0.961400i	−0.982394	+	0.186818i	$0.940182\pi$
$942$		0			0
$943$	213.554	−	1211.12i	0.226462	−	1.28433i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−988.466	−	174.293i	−1.04379	−	0.184048i	−0.374634	−	0.927173i	$-0.622232\pi$
$947$	−988.466	−	174.293i	−1.04379	−	0.184048i	−0.669153	+	0.743125i	$0.733343\pi$
$948$		0			0
$949$	−2509.72	−	913.464i	−2.64460	−	0.962555i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−970.138	−	560.110i	−1.01798	−	0.587733i	−0.104464	−	0.994529i	$-0.533313\pi$
$953$	−970.138	−	560.110i	−1.01798	−	0.587733i	−0.913519	+	0.406796i	$0.866646\pi$
$954$		0			0
$955$	647.991	+	1122.35i	0.678524	+	1.17524i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−831.111	+	146.547i	−0.866644	+	0.152813i
$960$		0			0
$961$	−236.088	−	198.101i	−0.245669	−	0.206141i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−316.395	−	869.287i	−0.327870	−	0.900815i
$966$		0			0
$967$	−106.712	+	89.5422i	−0.110354	+	0.0925980i	−0.696295	−	0.717756i	$-0.745169\pi$
$967$	−106.712	+	89.5422i	−0.110354	+	0.0925980i	0.585941	+	0.810354i	$0.300725\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		−	218.013i		−	0.224524i	−0.993679	−	0.112262i	$-0.964190\pi$
$971$		−	218.013i		−	0.224524i	0.993679	−	0.112262i	$-0.0358096\pi$
$972$		0			0
$973$	395.706			0.406686
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1088.10	+	1296.75i	1.11372	+	1.32728i	0.939492	+	0.342571i	$0.111298\pi$
$977$	1088.10	+	1296.75i	1.11372	+	1.32728i	0.174226	+	0.984706i	$0.444258\pi$
$978$		0			0
$979$	443.276	−	161.339i	0.452784	−	0.164800i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−1029.81	+	1227.28i	−1.04762	+	1.24850i	−0.0798107	+	0.996810i	$0.525432\pi$
$983$	−1029.81	+	1227.28i	−1.04762	+	1.24850i	−0.967807	+	0.251692i	$0.919013\pi$
$984$		0			0
$985$	108.193	+	613.593i	0.109841	+	0.622937i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−95.9664	+	55.4062i	−0.0970338	+	0.0560225i
$990$		0			0
$991$	−1.33401	+	2.31057i	−0.00134612	+	0.00233155i	−0.866698	−	0.498834i	$-0.833762\pi$
$991$	−1.33401	+	2.31057i	−0.00134612	+	0.00233155i	0.865352	+	0.501165i	$0.167095\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	241.596	−	663.779i	0.242810	−	0.667114i
$996$		0			0
$997$	−271.205	+	1538.08i	−0.272021	+	1.54271i	0.476249	+	0.879311i	$0.341996\pi$
$997$	−271.205	+	1538.08i	−0.272021	+	1.54271i	−0.748269	+	0.663395i	$0.769115\pi$
$998$		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.89.2		36
3.2	odd	2		108.3.k.a.29.3	✓	36
12.11	even	2		432.3.bc.b.353.4		36
27.11	odd	18		2916.3.c.b.1457.26		36
27.13	even	9		108.3.k.a.41.3	yes	36
27.14	odd	18	inner	324.3.k.a.233.2		36
27.16	even	9		2916.3.c.b.1457.11		36
108.67	odd	18		432.3.bc.b.257.4		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.k.a.29.3	✓	36	3.2	odd	2
108.3.k.a.41.3	yes	36	27.13	even	9
324.3.k.a.89.2		36	1.1	even	1	trivial
324.3.k.a.233.2		36	27.14	odd	18	inner
432.3.bc.b.257.4		36	108.67	odd	18
432.3.bc.b.353.4		36	12.11	even	2
2916.3.c.b.1457.11		36	27.16	even	9
2916.3.c.b.1457.26		36	27.11	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)

\(f(q)\)	\(=\)	\(q+(-2.68656 - 3.20172i) q^{5} +(-4.88621 + 1.77844i) q^{7} +O(q^{10})\)	\(q+(-2.68656 - 3.20172i) q^{5} +(-4.88621 + 1.77844i) q^{7} +(4.52170 - 5.38875i) q^{11} +(3.33062 + 18.8889i) q^{13} +(-20.3965 + 11.7759i) q^{17} +(-11.7859 + 20.4138i) q^{19} +(-8.16612 + 22.4362i) q^{23} +(1.30781 - 7.41698i) q^{25} +(-21.2148 - 3.74075i) q^{29} +(24.0093 + 8.73866i) q^{31} +(18.8212 + 10.8664i) q^{35} +(-6.81584 - 11.8054i) q^{37} +(-50.7253 + 8.94424i) q^{41} +(3.55532 + 2.98327i) q^{43} +(-1.64224 - 4.51203i) q^{47} +(-16.8239 + 14.1170i) q^{49} +67.3308i q^{53} -29.4011 q^{55} +(-55.7367 - 66.4244i) q^{59} +(50.3038 - 18.3091i) q^{61} +(51.5290 - 61.4098i) q^{65} +(3.49276 + 19.8084i) q^{67} +(85.2808 - 49.2369i) q^{71} +(-69.6234 + 120.591i) q^{73} +(-12.5104 + 34.3721i) q^{77} +(18.3268 - 103.937i) q^{79} +(79.2540 + 13.9746i) q^{83} +(92.4995 + 33.6671i) q^{85} +(58.0744 + 33.5293i) q^{89} +(-49.8668 - 86.3718i) q^{91} +(97.0226 - 17.1077i) q^{95} +(-112.041 - 94.0132i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 9 q^{5}+O(q^{10}) \) 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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