LMFDB - Embedded newform 324.3.k.a.17.3

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			17.3
Character	$\chi$	$=$	324.17
Dual form			324.3.k.a.305.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.92426 - 0.515626i) q^{5} +(0.715829 - 0.600652i) q^{7} +O(q^{10})$	$q+(-2.92426 - 0.515626i) q^{5} +(0.715829 - 0.600652i) q^{7} +(-5.89850 + 1.04007i) q^{11} +(-9.53387 + 3.47005i) q^{13} +(-6.81408 - 3.93411i) q^{17} +(-2.29223 - 3.97026i) q^{19} +(-22.9203 + 27.3153i) q^{23} +(-15.2069 - 5.53485i) q^{25} +(-3.20583 + 8.80793i) q^{29} +(-41.5801 - 34.8898i) q^{31} +(-2.40298 + 1.38736i) q^{35} +(-9.21875 + 15.9673i) q^{37} +(3.70267 + 10.1730i) q^{41} +(-9.70581 - 55.0444i) q^{43} +(46.8929 + 55.8847i) q^{47} +(-8.35713 + 47.3957i) q^{49} -44.8133i q^{53} +17.7851 q^{55} +(-81.5042 - 14.3714i) q^{59} +(47.6825 - 40.0104i) q^{61} +(29.6688 - 5.23141i) q^{65} +(-31.9873 + 11.6424i) q^{67} +(-60.7133 - 35.0528i) q^{71} +(68.4607 + 118.577i) q^{73} +(-3.59760 + 4.28745i) q^{77} +(41.4241 + 15.0772i) q^{79} +(31.4310 - 86.3561i) q^{83} +(17.8976 + 15.0179i) q^{85} +(86.0608 - 49.6872i) q^{89} +(-4.74033 + 8.21049i) q^{91} +(4.65591 + 12.7920i) q^{95} +(-4.81594 - 27.3125i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−2.92426	−	0.515626i	−0.584852	−	0.103125i	−0.126610	−	0.991953i	$-0.540410\pi$
$5$	−2.92426	−	0.515626i	−0.584852	−	0.103125i	−0.458242	+	0.888827i	$0.651521\pi$
$6$		0			0
$7$	0.715829	−	0.600652i	0.102261	−	0.0858074i	−0.590224	−	0.807240i	$-0.700960\pi$
$7$	0.715829	−	0.600652i	0.102261	−	0.0858074i	0.692485	+	0.721432i	$0.256516\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−5.89850	+	1.04007i	−0.536228	+	0.0945514i	−0.435203	−	0.900332i	$-0.643323\pi$
$11$	−5.89850	+	1.04007i	−0.536228	+	0.0945514i	−0.101025	+	0.994884i	$0.532212\pi$
$12$		0			0
$13$	−9.53387	+	3.47005i	−0.733375	+	0.266927i	−0.681593	−	0.731732i	$-0.738712\pi$
$13$	−9.53387	+	3.47005i	−0.733375	+	0.266927i	−0.0517821	+	0.998658i	$0.516490\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−6.81408	−	3.93411i	−0.400828	−	0.231418i	0.286013	−	0.958226i	$-0.407670\pi$
$17$	−6.81408	−	3.93411i	−0.400828	−	0.231418i	−0.686841	+	0.726807i	$0.741003\pi$
$18$		0			0
$19$	−2.29223	−	3.97026i	−0.120644	−	0.208961i	0.799378	−	0.600828i	$-0.205163\pi$
$19$	−2.29223	−	3.97026i	−0.120644	−	0.208961i	−0.920022	+	0.391867i	$0.871829\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−22.9203	+	27.3153i	−0.996534	+	1.18762i	−0.0143130	+	0.999898i	$0.504556\pi$
$23$	−22.9203	+	27.3153i	−0.996534	+	1.18762i	−0.982221	+	0.187726i	$0.939888\pi$
$24$		0			0
$25$	−15.2069	−	5.53485i	−0.608275	−	0.221394i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.20583	+	8.80793i	−0.110546	+	0.303722i	−0.982613	−	0.185663i	$-0.940557\pi$
$29$	−3.20583	+	8.80793i	−0.110546	+	0.303722i	0.872068	+	0.489385i	$0.162779\pi$
$30$		0			0
$31$	−41.5801	−	34.8898i	−1.34129	−	1.12548i	−0.981292	−	0.192527i	$-0.938332\pi$
$31$	−41.5801	−	34.8898i	−1.34129	−	1.12548i	−0.360002	−	0.932952i	$-0.617224\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2.40298	+	1.38736i	−0.0686566	+	0.0396389i
$36$		0			0
$37$	−9.21875	+	15.9673i	−0.249155	+	0.431550i	−0.963292	−	0.268457i	$-0.913486\pi$
$37$	−9.21875	+	15.9673i	−0.249155	+	0.431550i	0.714136	+	0.700007i	$0.246820\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.70267	+	10.1730i	0.0903090	+	0.248122i	0.976622	−	0.214965i	$-0.0689639\pi$
$41$	3.70267	+	10.1730i	0.0903090	+	0.248122i	−0.886313	+	0.463087i	$0.846742\pi$
$42$		0			0
$43$	−9.70581	−	55.0444i	−0.225716	−	1.28010i	−0.861311	−	0.508078i	$-0.830356\pi$
$43$	−9.70581	−	55.0444i	−0.225716	−	1.28010i	0.635594	−	0.772023i	$-0.280755\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	46.8929	+	55.8847i	0.997720	+	1.18904i	0.981946	+	0.189161i	$0.0605768\pi$
$47$	46.8929	+	55.8847i	0.997720	+	1.18904i	0.0157742	+	0.999876i	$0.494979\pi$
$48$		0			0
$49$	−8.35713	+	47.3957i	−0.170554	+	0.967258i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	44.8133i		−	0.845534i	−0.906238	−	0.422767i	$-0.861059\pi$
$53$		−	44.8133i		−	0.845534i	0.906238	−	0.422767i	$-0.138941\pi$
$54$		0			0
$55$	17.7851			0.323365
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−81.5042	−	14.3714i	−1.38143	−	0.243583i	−0.566937	−	0.823761i	$-0.691872\pi$
$59$	−81.5042	−	14.3714i	−1.38143	−	0.243583i	−0.814490	+	0.580178i	$0.802983\pi$
$60$		0			0
$61$	47.6825	−	40.0104i	0.781681	−	0.655908i	−0.161990	−	0.986792i	$-0.551791\pi$
$61$	47.6825	−	40.0104i	0.781681	−	0.655908i	0.943671	+	0.330884i	$0.107347\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	29.6688	−	5.23141i	0.456443	−	0.0804832i
$66$		0			0
$67$	−31.9873	+	11.6424i	−0.477423	+	0.173768i	−0.569512	−	0.821983i	$-0.692868\pi$
$67$	−31.9873	+	11.6424i	−0.477423	+	0.173768i	0.0920892	+	0.995751i	$0.470646\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−60.7133	−	35.0528i	−0.855117	−	0.493702i	0.00725708	−	0.999974i	$-0.497690\pi$
$71$	−60.7133	−	35.0528i	−0.855117	−	0.493702i	−0.862374	+	0.506272i	$0.831023\pi$
$72$		0			0
$73$	68.4607	+	118.577i	0.937818	+	1.62435i	0.769530	+	0.638611i	$0.220491\pi$
$73$	68.4607	+	118.577i	0.937818	+	1.62435i	0.168288	+	0.985738i	$0.446176\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−3.59760	+	4.28745i	−0.0467221	+	0.0556812i
$78$		0			0
$79$	41.4241	+	15.0772i	0.524356	+	0.190850i	0.590617	−	0.806952i	$-0.298885\pi$
$79$	41.4241	+	15.0772i	0.524356	+	0.190850i	−0.0662604	+	0.997802i	$0.521107\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	31.4310	−	86.3561i	0.378687	−	1.04043i	−0.593214	−	0.805045i	$-0.702141\pi$
$83$	31.4310	−	86.3561i	0.378687	−	1.04043i	0.971901	−	0.235390i	$-0.0756366\pi$
$84$		0			0
$85$	17.8976	+	15.0179i	0.210560	+	0.176681i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	86.0608	−	49.6872i	0.966975	−	0.558283i	0.0686623	−	0.997640i	$-0.478127\pi$
$89$	86.0608	−	49.6872i	0.966975	−	0.558283i	0.898313	+	0.439357i	$0.144794\pi$
$90$		0			0
$91$	−4.74033	+	8.21049i	−0.0520915	+	0.0902252i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	4.65591	+	12.7920i	0.0490096	+	0.134653i
$96$		0			0
$97$	−4.81594	−	27.3125i	−0.0496488	−	0.281573i	0.949868	−	0.312651i	$-0.101217\pi$
$97$	−4.81594	−	27.3125i	−0.0496488	−	0.281573i	−0.999517	+	0.0310783i	$0.990106\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	114.677	+	136.666i	1.13541	+	1.35313i	0.926988	+	0.375092i	$0.122389\pi$
$101$	114.677	+	136.666i	1.13541	+	1.35313i	0.208424	+	0.978039i	$0.433167\pi$
$102$		0			0
$103$	−0.915345	+	5.19118i	−0.00888684	+	0.0503998i	−0.988929	−	0.148391i	$-0.952590\pi$
$103$	−0.915345	+	5.19118i	−0.00888684	+	0.0503998i	0.980042	+	0.198791i	$0.0637016\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	153.946i		−	1.43875i	−0.694623	−	0.719374i	$-0.744429\pi$
$107$		−	153.946i		−	1.43875i	0.694623	−	0.719374i	$-0.255571\pi$
$108$		0			0
$109$	145.335			1.33335			0.666675	−	0.745348i	$-0.267717\pi$
$109$	145.335			1.33335			0.666675	+	0.745348i	$0.267717\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	62.4372	+	11.0094i	0.552542	+	0.0974280i	0.442946	−	0.896548i	$-0.353933\pi$
$113$	62.4372	+	11.0094i	0.552542	+	0.0974280i	0.109596	+	0.993976i	$0.465044\pi$
$114$		0			0
$115$	81.1094	−	68.0589i	0.705299	−	0.591816i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−7.24074	+	1.27674i	−0.0608466	+	0.0107289i
$120$		0			0
$121$	−79.9922	+	29.1148i	−0.661092	+	0.240618i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	105.904	+	61.1436i	0.847230	+	0.489149i
$126$		0			0
$127$	32.0199	+	55.4601i	0.252125	+	0.436694i	0.964111	−	0.265501i	$-0.0855372\pi$
$127$	32.0199	+	55.4601i	0.252125	+	0.436694i	−0.711986	+	0.702194i	$0.752204\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−77.4031	+	92.2454i	−0.590863	+	0.704164i	−0.975772	−	0.218791i	$-0.929789\pi$
$131$	−77.4031	+	92.2454i	−0.590863	+	0.704164i	0.384908	+	0.922955i	$0.374233\pi$
$132$		0			0
$133$	−4.02559	−	1.46519i	−0.0302676	−	0.0110165i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	55.4867	−	152.448i	0.405012	−	1.11276i	−0.554767	−	0.832006i	$-0.687193\pi$
$137$	55.4867	−	152.448i	0.405012	−	1.11276i	0.959779	−	0.280756i	$-0.0905852\pi$
$138$		0			0
$139$	−81.5779	−	68.4520i	−0.586892	−	0.492461i	0.300311	−	0.953841i	$-0.402910\pi$
$139$	−81.5779	−	68.4520i	−0.586892	−	0.492461i	−0.887202	+	0.461381i	$0.847354\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	52.6265	−	30.3839i	0.368018	−	0.212475i
$144$		0			0
$145$	13.9163	−	24.1037i	0.0959743	−	0.166232i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−5.26909	−	14.4767i	−0.0353630	−	0.0971590i	0.920755	−	0.390142i	$-0.127574\pi$
$149$	−5.26909	−	14.4767i	−0.0353630	−	0.0971590i	−0.956118	+	0.292983i	$0.905352\pi$
$150$		0			0
$151$	0.522463	+	2.96303i	0.00346002	+	0.0196227i	0.986489	−	0.163828i	$-0.0523843\pi$
$151$	0.522463	+	2.96303i	0.00346002	+	0.0196227i	−0.983029	+	0.183451i	$0.941273\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	103.601	+	123.467i	0.668393	+	0.796560i
$156$		0			0
$157$	−9.84877	+	55.8551i	−0.0627310	+	0.355765i	0.937244	+	0.348675i	$0.113368\pi$
$157$	−9.84877	+	55.8551i	−0.0627310	+	0.355765i	−0.999975	+	0.00709063i	$0.997743\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			33.3202i			0.206958i
$162$		0			0
$163$	−68.0676			−0.417592			−0.208796	−	0.977959i	$-0.566955\pi$
$163$	−68.0676			−0.417592			−0.208796	+	0.977959i	$0.566955\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−105.878	−	18.6691i	−0.633998	−	0.111791i	−0.152593	−	0.988289i	$-0.548762\pi$
$167$	−105.878	−	18.6691i	−0.633998	−	0.111791i	−0.481405	+	0.876498i	$0.659873\pi$
$168$		0			0
$169$	−50.6080	+	42.4652i	−0.299456	+	0.251273i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−265.492	+	46.8135i	−1.53464	+	0.270598i	−0.876167	−	0.482007i	$-0.839908\pi$
$173$	−265.492	+	46.8135i	−1.53464	+	0.270598i	−0.658472	+	0.752606i	$0.728797\pi$
$174$		0			0
$175$	−14.2100	+	5.17203i	−0.0812002	+	0.0295545i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−187.227	−	108.096i	−1.04596	−	0.603887i	−0.124447	−	0.992226i	$-0.539716\pi$
$179$	−187.227	−	108.096i	−1.04596	−	0.603887i	−0.921517	+	0.388339i	$0.873049\pi$
$180$		0			0
$181$	−62.0552	−	107.483i	−0.342847	−	0.593828i	0.642114	−	0.766610i	$-0.278058\pi$
$181$	−62.0552	−	107.483i	−0.342847	−	0.593828i	−0.984960	+	0.172782i	$0.944724\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	35.1912	−	41.9393i	0.190223	−	0.226699i
$186$		0			0
$187$	44.2846	+	16.1183i	0.236816	+	0.0861940i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	34.5227	−	94.8505i	0.180747	−	0.496599i	−0.815921	−	0.578164i	$-0.803769\pi$
$191$	34.5227	−	94.8505i	0.180747	−	0.496599i	0.996668	+	0.0815645i	$0.0259917\pi$
$192$		0			0
$193$	149.819	+	125.713i	0.776264	+	0.651362i	0.942305	−	0.334756i	$-0.108654\pi$
$193$	149.819	+	125.713i	0.776264	+	0.651362i	−0.166041	+	0.986119i	$0.553098\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−213.741	+	123.403i	−1.08498	+	0.626412i	−0.932235	−	0.361854i	$-0.882144\pi$
$197$	−213.741	+	123.403i	−1.08498	+	0.626412i	−0.152743	+	0.988266i	$0.548811\pi$
$198$		0			0
$199$	−79.4674	+	137.642i	−0.399334	+	0.691666i	−0.993644	−	0.112570i	$-0.964092\pi$
$199$	−79.4674	+	137.642i	−0.399334	+	0.691666i	0.594310	+	0.804236i	$0.297425\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	2.99568	+	8.23055i	0.0147570	+	0.0405446i
$204$		0			0
$205$	−5.58211	−	31.6577i	−0.0272298	−	0.154428i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	17.6501	+	21.0345i	0.0844501	+	0.100644i
$210$		0			0
$211$	60.4264	−	342.695i	0.286381	−	1.62415i	−0.413930	−	0.910309i	$-0.635844\pi$
$211$	60.4264	−	342.695i	0.286381	−	1.62415i	0.700311	−	0.713838i	$-0.253045\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$			165.969i			0.771947i
$216$		0			0
$217$	−50.7209			−0.233737
$218$		0			0
$219$		0			0
$220$		0			0
$221$	78.6161	+	13.8621i	0.355729	+	0.0627246i
$222$		0			0
$223$	−120.247	+	100.900i	−0.539226	+	0.452465i	−0.871273	−	0.490798i	$-0.836705\pi$
$223$	−120.247	+	100.900i	−0.539226	+	0.452465i	0.332047	+	0.943263i	$0.392261\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−357.998	+	63.1248i	−1.57709	+	0.278083i	−0.892568	−	0.450914i	$-0.851098\pi$
$227$	−357.998	+	63.1248i	−1.57709	+	0.278083i	−0.684518	+	0.728996i	$0.739987\pi$
$228$		0			0
$229$	−84.0632	+	30.5965i	−0.367088	+	0.133609i	−0.518977	−	0.854788i	$-0.673687\pi$
$229$	−84.0632	+	30.5965i	−0.367088	+	0.133609i	0.151888	+	0.988398i	$0.451465\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	160.610	+	92.7281i	0.689312	+	0.397975i	0.803354	−	0.595501i	$-0.203047\pi$
$233$	160.610	+	92.7281i	0.689312	+	0.397975i	−0.114042	+	0.993476i	$0.536380\pi$
$234$		0			0
$235$	−108.311	−	187.601i	−0.460899	−	0.798301i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−19.8929	+	23.7075i	−0.0832341	+	0.0991945i	−0.806054	−	0.591842i	$-0.798401\pi$
$239$	−19.8929	+	23.7075i	−0.0832341	+	0.0991945i	0.722820	+	0.691036i	$0.242846\pi$
$240$		0			0
$241$	−329.180	−	119.812i	−1.36589	−	0.497144i	−0.448020	−	0.894023i	$-0.647871\pi$
$241$	−329.180	−	119.812i	−1.36589	−	0.497144i	−0.917871	+	0.396880i	$0.870093\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	48.8769	−	134.288i	0.199497	−	0.548115i
$246$		0			0
$247$	35.6308	+	29.8978i	0.144254	+	0.121044i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−41.0932	+	23.7252i	−0.163718	+	0.0945226i	−0.579620	−	0.814887i	$-0.696799\pi$
$251$	−41.0932	+	23.7252i	−0.163718	+	0.0945226i	0.415902	+	0.909409i	$0.363466\pi$
$252$		0			0
$253$	106.786	−	184.958i	0.422078	−	0.731060i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−39.9077	−	109.645i	−0.155283	−	0.426636i	0.837519	−	0.546409i	$-0.184006\pi$
$257$	−39.9077	−	109.645i	−0.155283	−	0.426636i	−0.992801	+	0.119773i	$0.961783\pi$
$258$		0			0
$259$	2.99176	+	16.9671i	0.0115512	+	0.0655102i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	205.463	+	244.861i	0.781227	+	0.931030i	0.998988	−	0.0449723i	$-0.0143200\pi$
$263$	205.463	+	244.861i	0.781227	+	0.931030i	−0.217762	+	0.976002i	$0.569876\pi$
$264$		0			0
$265$	−23.1069	+	131.046i	−0.0871959	+	0.494512i
$266$		0			0
$267$		0			0
$268$		0			0
$269$			347.341i			1.29123i	0.763662	+	0.645616i	$0.223399\pi$
$269$			347.341i			1.29123i	−0.763662	+	0.645616i	$0.776601\pi$
$270$		0			0
$271$	−464.981			−1.71580			−0.857898	−	0.513821i	$-0.828230\pi$
$271$	−464.981			−1.71580			−0.857898	+	0.513821i	$0.828230\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	95.4545	+	16.8312i	0.347107	+	0.0612044i
$276$		0			0
$277$	−104.098	+	87.3486i	−0.375805	+	0.315338i	−0.811053	−	0.584973i	$-0.801105\pi$
$277$	−104.098	+	87.3486i	−0.375805	+	0.315338i	0.435248	+	0.900311i	$0.356661\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−531.265	+	93.6763i	−1.89062	+	0.333367i	−0.993995	−	0.109422i	$-0.965100\pi$
$281$	−531.265	+	93.6763i	−1.89062	+	0.333367i	−0.896626	+	0.442789i	$0.853989\pi$
$282$		0			0
$283$	279.334	−	101.669i	0.987048	−	0.359256i	0.202471	−	0.979288i	$-0.435103\pi$
$283$	279.334	−	101.669i	0.987048	−	0.359256i	0.784576	+	0.620032i	$0.212881\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	8.76090	+	5.05811i	0.0305258	+	0.0176241i
$288$		0			0
$289$	−113.546	−	196.667i	−0.392891	−	0.680507i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	345.127	−	411.306i	1.17791	−	1.40378i	0.282071	−	0.959393i	$-0.408979\pi$
$293$	345.127	−	411.306i	1.17791	−	1.40378i	0.895837	−	0.444383i	$-0.146577\pi$
$294$		0			0
$295$	230.929	+	84.0514i	0.782811	+	0.284920i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	123.734	−	339.955i	0.413825	−	1.13697i
$300$		0			0
$301$	−40.0102	−	33.5725i	−0.132924	−	0.111537i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−160.067	+	92.4145i	−0.524809	+	0.302998i
$306$		0			0
$307$	15.9704	−	27.6615i	0.0520208	−	0.0901027i	−0.838842	−	0.544374i	$-0.816767\pi$
$307$	15.9704	−	27.6615i	0.0520208	−	0.0901027i	0.890863	+	0.454272i	$0.150100\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	121.282	+	333.220i	0.389975	+	1.07145i	0.967012	+	0.254730i	$0.0819866\pi$
$311$	121.282	+	333.220i	0.389975	+	1.07145i	−0.577037	+	0.816718i	$0.695791\pi$
$312$		0			0
$313$	72.9700	+	413.834i	0.233131	+	1.32215i	0.846514	+	0.532366i	$0.178697\pi$
$313$	72.9700	+	413.834i	0.233131	+	1.32215i	−0.613383	+	0.789786i	$0.710192\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−162.451	−	193.602i	−0.512464	−	0.610731i	0.446318	−	0.894875i	$-0.352735\pi$
$317$	−162.451	−	193.602i	−0.512464	−	0.610731i	−0.958782	+	0.284144i	$0.908291\pi$
$318$		0			0
$319$	9.74875	−	55.2879i	0.0305603	−	0.173316i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			36.0716i			0.111677i
$324$		0			0
$325$	164.187			0.505190
$326$		0			0
$327$		0			0
$328$		0			0
$329$	67.1345	+	11.8376i	0.204056	+	0.0359806i
$330$		0			0
$331$	−121.834	+	102.231i	−0.368080	+	0.308855i	−0.808001	−	0.589181i	$-0.799451\pi$
$331$	−121.834	+	102.231i	−0.368080	+	0.308855i	0.439922	+	0.898036i	$0.355006\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	99.5424	−	17.5520i	0.297142	−	0.0523941i
$336$		0			0
$337$	499.639	−	181.854i	1.48261	−	0.539626i	0.531117	−	0.847298i	$-0.321772\pi$
$337$	499.639	−	181.854i	1.48261	−	0.539626i	0.951492	+	0.307673i	$0.0995501\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	281.548	+	162.552i	0.825654	+	0.476692i
$342$		0			0
$343$	45.3800	+	78.6004i	0.132303	+	0.229156i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	57.0006	−	67.9306i	0.164267	−	0.195765i	−0.677632	−	0.735401i	$-0.736994\pi$
$347$	57.0006	−	67.9306i	0.164267	−	0.195765i	0.841898	+	0.539636i	$0.181438\pi$
$348$		0			0
$349$	54.9200	+	19.9893i	0.157364	+	0.0572758i	0.419501	−	0.907755i	$-0.362205\pi$
$349$	54.9200	+	19.9893i	0.157364	+	0.0572758i	−0.262137	+	0.965031i	$0.584427\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	154.431	−	424.296i	0.437482	−	1.20197i	−0.503643	−	0.863912i	$-0.668007\pi$
$353$	154.431	−	424.296i	0.437482	−	1.20197i	0.941125	−	0.338060i	$-0.109771\pi$
$354$		0			0
$355$	159.467	+	133.809i	0.449204	+	0.376927i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	354.208	−	204.502i	0.986653	−	0.569644i	0.0823810	−	0.996601i	$-0.473748\pi$
$359$	354.208	−	204.502i	0.986653	−	0.569644i	0.904272	+	0.426956i	$0.140414\pi$
$360$		0			0
$361$	169.991	−	294.434i	0.470890	−	0.815606i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−139.055	−	382.052i	−0.380974	−	1.04672i
$366$		0			0
$367$	94.4979	+	535.924i	0.257487	+	1.46028i	0.789606	+	0.613614i	$0.210285\pi$
$367$	94.4979	+	535.924i	0.257487	+	1.46028i	−0.532119	+	0.846670i	$0.678604\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−26.9172	−	32.0786i	−0.0725530	−	0.0864654i
$372$		0			0
$373$	−39.2174	+	222.413i	−0.105140	+	0.596281i	0.886024	+	0.463640i	$0.153457\pi$
$373$	−39.2174	+	222.413i	−0.105140	+	0.596281i	−0.991164	+	0.132641i	$0.957654\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	95.0981i		−	0.252250i
$378$		0			0
$379$	174.665			0.460857			0.230428	−	0.973089i	$-0.425987\pi$
$379$	174.665			0.460857			0.230428	+	0.973089i	$0.425987\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	567.725	+	100.105i	1.48231	+	0.261372i	0.855501	−	0.517800i	$-0.173249\pi$
$383$	567.725	+	100.105i	1.48231	+	0.261372i	0.626810	+	0.779172i	$0.284360\pi$
$384$		0			0
$385$	12.7311	−	10.6826i	0.0330677	−	0.0277471i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−674.651	+	118.959i	−1.73432	+	0.305808i	−0.949465	−	0.313872i	$-0.898374\pi$
$389$	−674.651	+	118.959i	−1.73432	+	0.305808i	−0.784855	+	0.619679i	$0.787263\pi$
$390$		0			0
$391$	263.642	−	95.9579i	0.674277	−	0.245417i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−113.361	−	65.4489i	−0.286989	−	0.165693i
$396$		0			0
$397$	28.9985	+	50.2268i	0.0730440	+	0.126516i	0.900234	−	0.435406i	$-0.143395\pi$
$397$	28.9985	+	50.2268i	0.0730440	+	0.126516i	−0.827190	+	0.561922i	$0.810062\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−21.2804	+	25.3610i	−0.0530683	+	0.0632443i	−0.791926	−	0.610618i	$-0.790921\pi$
$401$	−21.2804	+	25.3610i	−0.0530683	+	0.0632443i	0.738857	+	0.673862i	$0.235366\pi$
$402$		0			0
$403$	517.489	+	188.350i	1.28409	+	0.467371i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	37.7698	−	103.772i	0.0928004	−	0.254967i
$408$		0			0
$409$	151.962	+	127.512i	0.371546	+	0.311764i	0.809373	−	0.587295i	$-0.199807\pi$
$409$	151.962	+	127.512i	0.371546	+	0.311764i	−0.437827	+	0.899059i	$0.644252\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−66.9752	+	38.6682i	−0.162168	+	0.0936275i
$414$		0			0
$415$	−136.440	+	236.321i	−0.328771	+	0.569448i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−124.159	−	341.125i	−0.296323	−	0.814140i	−0.995107	−	0.0988073i	$-0.968497\pi$
$419$	−124.159	−	341.125i	−0.296323	−	0.814140i	0.698784	−	0.715333i	$-0.253725\pi$
$420$		0			0
$421$	−82.0540	−	465.352i	−0.194903	−	1.10535i	−0.912557	−	0.408949i	$-0.865895\pi$
$421$	−82.0540	−	465.352i	−0.194903	−	1.10535i	0.717655	−	0.696399i	$-0.245216\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	81.8462	+	97.5405i	0.192579	+	0.229507i
$426$		0			0
$427$	10.1002	−	57.2812i	0.0236539	−	0.134148i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			144.354i			0.334927i	0.985878	+	0.167464i	$0.0535577\pi$
$431$			144.354i			0.334927i	−0.985878	+	0.167464i	$0.946442\pi$
$432$		0			0
$433$	−25.2858			−0.0583967			−0.0291984	−	0.999574i	$-0.509295\pi$
$433$	−25.2858			−0.0583967			−0.0291984	+	0.999574i	$0.509295\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	160.988	+	28.3865i	0.368393	+	0.0649576i
$438$		0			0
$439$	−119.871	+	100.583i	−0.273054	+	0.229119i	−0.769024	−	0.639220i	$-0.779257\pi$
$439$	−119.871	+	100.583i	−0.273054	+	0.229119i	0.495970	+	0.868340i	$0.334813\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	522.960	−	92.2120i	1.18050	−	0.208153i	0.451246	−	0.892400i	$-0.350980\pi$
$443$	522.960	−	92.2120i	1.18050	−	0.208153i	0.729251	+	0.684246i	$0.239869\pi$
$444$		0			0
$445$	−277.284	+	100.923i	−0.623111	+	0.226794i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	210.795	+	121.703i	0.469477	+	0.271052i	0.716021	−	0.698079i	$-0.245962\pi$
$449$	210.795	+	121.703i	0.469477	+	0.271052i	−0.246544	+	0.969132i	$0.579295\pi$
$450$		0			0
$451$	−32.4208	−	56.1545i	−0.0718865	−	0.124511i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	18.0955	−	21.5654i	0.0397704	−	0.0473965i
$456$		0			0
$457$	−610.104	−	222.060i	−1.33502	−	0.485908i	−0.426780	−	0.904356i	$-0.640352\pi$
$457$	−610.104	−	222.060i	−1.33502	−	0.485908i	−0.908241	+	0.418448i	$0.862574\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−10.4561	+	28.7278i	−0.0226813	+	0.0623162i	−0.950517	−	0.310674i	$-0.899445\pi$
$461$	−10.4561	+	28.7278i	−0.0226813	+	0.0623162i	0.927835	+	0.372990i	$0.121667\pi$
$462$		0			0
$463$	−6.55388	−	5.49936i	−0.0141553	−	0.0118777i	0.635683	−	0.771951i	$-0.280719\pi$
$463$	−6.55388	−	5.49936i	−0.0141553	−	0.0118777i	−0.649838	+	0.760073i	$0.725163\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	92.6402	−	53.4858i	0.198373	−	0.114531i	−0.397523	−	0.917592i	$-0.630130\pi$
$467$	92.6402	−	53.4858i	0.198373	−	0.114531i	0.595896	+	0.803061i	$0.296797\pi$
$468$		0			0
$469$	−15.9044	+	27.5472i	−0.0339113	+	0.0587361i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	114.499	+	314.585i	0.242071	+	0.665084i
$474$		0			0
$475$	12.8829	+	73.0624i	0.0271218	+	0.153816i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	367.547	+	438.026i	0.767322	+	0.914459i	0.998287	−	0.0585028i	$-0.0186327\pi$
$479$	367.547	+	438.026i	0.767322	+	0.914459i	−0.230965	+	0.972962i	$0.574188\pi$
$480$		0			0
$481$	32.4830	−	184.220i	0.0675322	−	0.382994i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			82.3522i			0.169798i
$486$		0			0
$487$	−51.4408			−0.105628			−0.0528140	−	0.998604i	$-0.516819\pi$
$487$	−51.4408			−0.105628			−0.0528140	+	0.998604i	$0.516819\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−520.792	−	91.8297i	−1.06068	−	0.187026i	−0.384020	−	0.923325i	$-0.625461\pi$
$491$	−520.792	−	91.8297i	−1.06068	−	0.187026i	−0.676656	+	0.736299i	$0.736572\pi$
$492$		0			0
$493$	56.4961	−	47.4059i	0.114597	−	0.0961580i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−64.5149	+	11.3757i	−0.129809	+	0.0228888i
$498$		0			0
$499$	−11.9189	+	4.33813i	−0.0238856	+	0.00869364i	−0.353935	−	0.935270i	$-0.615157\pi$
$499$	−11.9189	+	4.33813i	−0.0238856	+	0.00869364i	0.330050	+	0.943964i	$0.392934\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−239.874	−	138.491i	−0.476886	−	0.275330i	0.242232	−	0.970218i	$-0.422121\pi$
$503$	−239.874	−	138.491i	−0.476886	−	0.275330i	−0.719118	+	0.694888i	$0.755454\pi$
$504$		0			0
$505$	−264.876	−	458.778i	−0.524506	−	0.908471i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	160.021	−	190.705i	0.314382	−	0.374666i	−0.585594	−	0.810604i	$-0.699139\pi$
$509$	160.021	−	190.705i	0.314382	−	0.374666i	0.899977	+	0.435938i	$0.143583\pi$
$510$		0			0
$511$	120.230	+	43.7601i	0.235284	+	0.0856362i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	5.35341	−	14.7084i	0.0103950	−	0.0285600i
$516$		0			0
$517$	−334.721	−	280.865i	−0.647430	−	0.543259i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−770.317	+	444.742i	−1.47853	+	0.853632i	−0.999705	−	0.0242755i	$-0.992272\pi$
$521$	−770.317	+	444.742i	−1.47853	+	0.853632i	−0.478829	+	0.877908i	$0.658939\pi$
$522$		0			0
$523$	−236.647	+	409.884i	−0.452479	+	0.783717i	−0.998539	−	0.0540291i	$-0.982794\pi$
$523$	−236.647	+	409.884i	−0.452479	+	0.783717i	0.546060	+	0.837746i	$0.316127\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	146.070	+	401.323i	0.277172	+	0.761523i
$528$		0			0
$529$	−128.928	−	731.188i	−0.243721	−	1.38221i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−70.6015	−	84.1396i	−0.132461	−	0.157860i
$534$		0			0
$535$	−79.3786	+	450.178i	−0.148371	+	0.841455i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	288.255i		−	0.534797i
$540$		0			0
$541$	−54.9995			−0.101663			−0.0508314	−	0.998707i	$-0.516187\pi$
$541$	−54.9995			−0.101663			−0.0508314	+	0.998707i	$0.516187\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−424.998	−	74.9386i	−0.779813	−	0.137502i
$546$		0			0
$547$	572.073	−	480.027i	1.04584	−	0.877562i	0.0531884	−	0.998584i	$-0.483062\pi$
$547$	572.073	−	480.027i	1.04584	−	0.877562i	0.992650	+	0.121022i	$0.0386172\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	42.3183	−	7.46185i	0.0768027	−	0.0135424i
$552$		0			0
$553$	38.7087	−	14.0888i	0.0699976	−	0.0254771i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−30.6029	−	17.6686i	−0.0549424	−	0.0317210i	0.472277	−	0.881450i	$-0.343432\pi$
$557$	−30.6029	−	17.6686i	−0.0549424	−	0.0317210i	−0.527220	+	0.849729i	$0.676765\pi$
$558$		0			0
$559$	283.540	+	491.106i	0.507228	+	0.878544i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−438.510	+	522.596i	−0.778882	+	0.928235i	−0.998882	−	0.0472647i	$-0.984950\pi$
$563$	−438.510	+	522.596i	−0.778882	+	0.928235i	0.220001	+	0.975500i	$0.429394\pi$
$564$		0			0
$565$	−176.906	−	64.3885i	−0.313108	−	0.113962i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−309.078	+	849.184i	−0.543195	+	1.49242i	0.299538	+	0.954084i	$0.403167\pi$
$569$	−309.078	+	849.184i	−0.543195	+	1.49242i	−0.842733	+	0.538331i	$0.819055\pi$
$570$		0			0
$571$	−495.403	−	415.692i	−0.867606	−	0.728008i	0.0959867	−	0.995383i	$-0.469399\pi$
$571$	−495.403	−	415.692i	−0.867606	−	0.728008i	−0.963593	+	0.267375i	$0.913844\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	499.733	−	288.521i	0.869100	−	0.501775i
$576$		0			0
$577$	165.488	−	286.633i	0.286807	−	0.496765i	−0.686239	−	0.727377i	$-0.740739\pi$
$577$	165.488	−	286.633i	0.286807	−	0.496765i	0.973046	+	0.230612i	$0.0740727\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−29.3707	−	80.6952i	−0.0505519	−	0.138890i
$582$		0			0
$583$	46.6088	+	264.331i	0.0799464	+	0.453399i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	9.19148	+	10.9540i	0.0156584	+	0.0186610i	0.773817	−	0.633409i	$-0.218345\pi$
$587$	9.19148	+	10.9540i	0.0156584	+	0.0186610i	−0.758158	+	0.652070i	$0.773901\pi$
$588$		0			0
$589$	−43.2106	+	245.059i	−0.0733626	+	0.416060i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	834.096i		−	1.40657i	−0.710908	−	0.703285i	$-0.751716\pi$
$593$		−	834.096i		−	1.40657i	0.710908	−	0.703285i	$-0.248284\pi$
$594$		0			0
$595$	21.8321			0.0366927
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−764.371	−	134.779i	−1.27608	−	0.225007i	−0.505764	−	0.862672i	$-0.668789\pi$
$599$	−764.371	−	134.779i	−1.27608	−	0.225007i	−0.770314	+	0.637665i	$0.779900\pi$
$600$		0			0
$601$	−327.998	+	275.223i	−0.545754	+	0.457942i	−0.873500	−	0.486824i	$-0.838155\pi$
$601$	−327.998	+	275.223i	−0.545754	+	0.457942i	0.327746	+	0.944766i	$0.393711\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	248.930	−	43.8931i	0.411455	−	0.0725507i
$606$		0			0
$607$	−1085.37	+	395.041i	−1.78808	+	0.650809i	−0.788733	+	0.614736i	$0.789263\pi$
$607$	−1085.37	+	395.041i	−1.78808	+	0.650809i	−0.999349	+	0.0360730i	$0.988515\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−640.993	−	370.077i	−1.04909	−	0.605691i
$612$		0			0
$613$	496.301	+	859.619i	0.809627	+	1.40231i	0.913123	+	0.407685i	$0.133664\pi$
$613$	496.301	+	859.619i	0.809627	+	1.40231i	−0.103496	+	0.994630i	$0.533003\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−623.221	+	742.726i	−1.01008	+	1.20377i	−0.0311651	+	0.999514i	$0.509922\pi$
$617$	−623.221	+	742.726i	−1.01008	+	1.20377i	−0.978918	+	0.204255i	$0.934523\pi$
$618$		0			0
$619$	−666.834	−	242.708i	−1.07728	−	0.392096i	−0.258383	−	0.966043i	$-0.583190\pi$
$619$	−666.834	−	242.708i	−1.07728	−	0.392096i	−0.818893	+	0.573946i	$0.805412\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	31.7601	−	87.2601i	0.0509792	−	0.140064i
$624$		0			0
$625$	31.7560	+	26.6464i	0.0508095	+	0.0426343i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	125.635	−	72.5352i	0.199737	−	0.115318i
$630$		0			0
$631$	27.0548	−	46.8602i	0.0428760	−	0.0742634i	−0.843791	−	0.536672i	$-0.819681\pi$
$631$	27.0548	−	46.8602i	0.0428760	−	0.0742634i	0.886667	+	0.462408i	$0.153015\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−65.0379	−	178.690i	−0.102422	−	0.281402i
$636$		0			0
$637$	−84.7893	−	480.864i	−0.133107	−	0.754888i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−182.928	−	218.005i	−0.285380	−	0.340102i	0.604242	−	0.796801i	$-0.293476\pi$
$641$	−182.928	−	218.005i	−0.285380	−	0.340102i	−0.889621	+	0.456699i	$0.849032\pi$
$642$		0			0
$643$	143.731	−	815.136i	0.223531	−	1.26771i	−0.641942	−	0.766753i	$-0.721871\pi$
$643$	143.731	−	815.136i	0.223531	−	1.26771i	0.865473	−	0.500955i	$-0.167018\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			592.934i			0.916436i	0.888840	+	0.458218i	$0.151512\pi$
$647$			592.934i			0.916436i	−0.888840	+	0.458218i	$0.848488\pi$
$648$		0			0
$649$	495.700			0.763791
$650$		0			0
$651$		0			0
$652$		0			0
$653$	50.0324	+	8.82206i	0.0766193	+	0.0135100i	0.211826	−	0.977307i	$-0.432059\pi$
$653$	50.0324	+	8.82206i	0.0766193	+	0.0135100i	−0.135207	+	0.990817i	$0.543170\pi$
$654$		0			0
$655$	273.911	−	229.839i	0.418185	−	0.350899i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	17.8256	−	3.14313i	0.0270494	−	0.00476954i	−0.160107	−	0.987100i	$-0.551184\pi$
$659$	17.8256	−	3.14313i	0.0270494	−	0.00476954i	0.187157	+	0.982330i	$0.440073\pi$
$660$		0			0
$661$	−901.414	+	328.088i	−1.36371	+	0.496351i	−0.917200	−	0.398427i	$-0.869556\pi$
$661$	−901.414	+	328.088i	−1.36371	+	0.496351i	−0.446512	+	0.894778i	$0.647334\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	11.0164	+	6.36031i	0.0165660	+	0.00956437i
$666$		0			0
$667$	−167.113	−	289.449i	−0.250545	−	0.433956i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−239.642	+	285.594i	−0.357142	+	0.425625i
$672$		0			0
$673$	936.382	+	340.815i	1.39136	+	0.506412i	0.925601	−	0.378502i	$-0.123561\pi$
$673$	936.382	+	340.815i	1.39136	+	0.506412i	0.465755	+	0.884914i	$0.345783\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−206.246	+	566.655i	−0.304647	+	0.837010i	0.689030	+	0.724732i	$0.258037\pi$
$677$	−206.246	+	566.655i	−0.304647	+	0.837010i	−0.993677	+	0.112277i	$0.964186\pi$
$678$		0			0
$679$	−19.8527	−	16.6584i	−0.0292381	−	0.0245337i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	413.524	−	238.748i	0.605452	−	0.349558i	−0.165731	−	0.986171i	$-0.552998\pi$
$683$	413.524	−	238.748i	0.605452	−	0.349558i	0.771184	+	0.636613i	$0.219665\pi$
$684$		0			0
$685$	−240.864	+	417.189i	−0.351626	+	0.609034i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	155.504	+	427.244i	0.225696	+	0.620093i
$690$		0			0
$691$	−71.3995	−	404.927i	−0.103328	−	0.586001i	−0.991875	−	0.127216i	$-0.959396\pi$
$691$	−71.3995	−	404.927i	−0.103328	−	0.586001i	0.888547	−	0.458785i	$-0.151715\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	203.260	+	242.235i	0.292460	+	0.348540i
$696$		0			0
$697$	14.7914	−	83.8863i	0.0212216	−	0.120353i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	857.375i		−	1.22307i	−0.791216	−	0.611537i	$-0.790552\pi$
$701$		−	857.375i		−	1.22307i	0.791216	−	0.611537i	$-0.209448\pi$
$702$		0			0
$703$	84.5260			0.120236
$704$		0			0
$705$		0			0
$706$		0			0
$707$	164.178	+	28.9489i	0.232217	+	0.0409461i
$708$		0			0
$709$	507.834	−	426.123i	0.716268	−	0.601020i	−0.210082	−	0.977684i	$-0.567373\pi$
$709$	507.834	−	426.123i	0.716268	−	0.601020i	0.926350	+	0.376664i	$0.122929\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	1906.06	−	336.089i	2.67329	−	0.471373i
$714$		0			0
$715$	−169.560	+	61.7150i	−0.237147	+	0.0863146i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−273.812	−	158.085i	−0.380823	−	0.219868i	0.297353	−	0.954768i	$-0.403896\pi$
$719$	−273.812	−	158.085i	−0.380823	−	0.219868i	−0.678176	+	0.734899i	$0.737229\pi$
$720$		0			0
$721$	2.46286	+	4.26580i	0.00341589	+	0.00591650i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	97.5012	−	116.197i	0.134484	−	0.160272i
$726$		0			0
$727$	−357.493	−	130.117i	−0.491738	−	0.178978i	0.0842365	−	0.996446i	$-0.473155\pi$
$727$	−357.493	−	130.117i	−0.491738	−	0.178978i	−0.575974	+	0.817468i	$0.695377\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−150.414	+	413.260i	−0.205765	+	0.565336i
$732$		0			0
$733$	382.389	+	320.862i	0.521676	+	0.437738i	0.865216	−	0.501400i	$-0.167181\pi$
$733$	382.389	+	320.862i	0.521676	+	0.437738i	−0.343540	+	0.939138i	$0.611626\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	176.568	−	101.942i	0.239577	−	0.138320i
$738$		0			0
$739$	384.461	−	665.906i	0.520245	−	0.901090i	−0.479478	−	0.877554i	$-0.659174\pi$
$739$	384.461	−	665.906i	0.520245	−	0.901090i	0.999723	−	0.0235367i	$-0.00749264\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	121.256	+	333.147i	0.163197	+	0.448381i	0.994156	−	0.107953i	$-0.0344296\pi$
$743$	121.256	+	333.147i	0.163197	+	0.448381i	−0.830959	+	0.556334i	$0.812207\pi$
$744$		0			0
$745$	7.94362	+	45.0505i	0.0106626	+	0.0604705i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−92.4679	−	110.199i	−0.123455	−	0.147128i
$750$		0			0
$751$	−56.1994	+	318.723i	−0.0748327	+	0.424398i	0.924258	+	0.381768i	$0.124685\pi$
$751$	−56.1994	+	318.723i	−0.0748327	+	0.424398i	−0.999091	+	0.0426296i	$0.986426\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		−	8.93408i		−	0.0118332i
$756$		0			0
$757$	−158.961			−0.209988			−0.104994	−	0.994473i	$-0.533482\pi$
$757$	−158.961			−0.209988			−0.104994	+	0.994473i	$0.533482\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	39.6236	+	6.98671i	0.0520678	+	0.00918096i	0.199621	−	0.979873i	$-0.436029\pi$
$761$	39.6236	+	6.98671i	0.0520678	+	0.00918096i	−0.147554	+	0.989054i	$0.547140\pi$
$762$		0			0
$763$	104.035	−	87.2958i	0.136350	−	0.114411i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	826.920	−	145.808i	1.07812	−	0.190102i
$768$		0			0
$769$	−387.461	+	141.024i	−0.503851	+	0.183387i	−0.581425	−	0.813600i	$-0.697505\pi$
$769$	−387.461	+	141.024i	−0.503851	+	0.183387i	0.0775744	+	0.996987i	$0.475282\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	1135.88	+	655.799i	1.46944	+	0.848382i	0.999413	−	0.0342695i	$-0.0109105\pi$
$773$	1135.88	+	655.799i	1.46944	+	0.848382i	0.470028	+	0.882651i	$0.344244\pi$
$774$		0			0
$775$	439.193	+	760.705i	0.566701	+	0.981555i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	31.9021	−	38.0194i	0.0409526	−	0.0488054i
$780$		0			0
$781$	394.575	+	143.614i	0.505218	+	0.183884i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	57.6007	−	158.257i	0.0733767	−	0.201601i
$786$		0			0
$787$	−355.669	−	298.441i	−0.451930	−	0.379214i	0.388222	−	0.921566i	$-0.373089\pi$
$787$	−355.669	−	298.441i	−0.451930	−	0.379214i	−0.840151	+	0.542352i	$0.817534\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	51.3071	−	29.6222i	0.0648636	−	0.0374490i
$792$		0			0
$793$	−315.761	+	546.915i	−0.398186	+	0.689678i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−279.835	−	768.839i	−0.351110	−	0.964667i	−0.982014	−	0.188806i	$-0.939538\pi$
$797$	−279.835	−	768.839i	−0.351110	−	0.964667i	0.630904	−	0.775861i	$-0.282684\pi$
$798$		0			0
$799$	−99.6749	−	565.285i	−0.124750	−	0.707490i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−527.144	−	628.226i	−0.656468	−	0.782349i
$804$		0			0
$805$	17.1808	−	97.4370i	0.0213426	−	0.121040i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	787.781i		−	0.973771i	−0.873466	−	0.486886i	$-0.838133\pi$
$809$		−	787.781i		−	0.973771i	0.873466	−	0.486886i	$-0.161867\pi$
$810$		0			0
$811$	781.305			0.963384			0.481692	−	0.876341i	$-0.340022\pi$
$811$	781.305			0.963384			0.481692	+	0.876341i	$0.340022\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	199.047	+	35.0974i	0.244230	+	0.0430643i
$816$		0			0
$817$	−196.292	+	164.709i	−0.240260	+	0.201602i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	262.358	−	46.2608i	0.319559	−	0.0563469i	−0.0115678	−	0.999933i	$-0.503682\pi$
$821$	262.358	−	46.2608i	0.319559	−	0.0563469i	0.331127	+	0.943586i	$0.392571\pi$
$822$		0			0
$823$	1115.33	−	405.945i	1.35519	−	0.493251i	0.440629	−	0.897689i	$-0.354755\pi$
$823$	1115.33	−	405.945i	1.35519	−	0.493251i	0.914565	+	0.404439i	$0.132533\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−678.939	−	391.985i	−0.820966	−	0.473985i	0.0297836	−	0.999556i	$-0.490518\pi$
$827$	−678.939	−	391.985i	−0.820966	−	0.473985i	−0.850749	+	0.525572i	$0.823852\pi$
$828$		0			0
$829$	489.138	+	847.212i	0.590034	+	1.02197i	0.994227	+	0.107295i	$0.0342190\pi$
$829$	489.138	+	847.212i	0.590034	+	1.02197i	−0.404193	+	0.914674i	$0.632448\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	243.406	−	290.080i	0.292204	−	0.348235i
$834$		0			0
$835$	299.987	+	109.187i	0.359266	+	0.130762i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−355.297	+	976.171i	−0.423477	+	1.16349i	0.526227	+	0.850344i	$0.323606\pi$
$839$	−355.297	+	976.171i	−0.423477	+	1.16349i	−0.949704	+	0.313149i	$0.898616\pi$
$840$		0			0
$841$	576.941	+	484.111i	0.686018	+	0.575637i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	169.887	−	98.0844i	0.201050	−	0.116076i
$846$		0			0
$847$	−39.7729	+	68.8886i	−0.0469573	+	0.0813325i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−224.857	−	617.790i	−0.264227	−	0.725957i
$852$		0			0
$853$	164.358	+	932.120i	0.192682	+	1.09275i	0.915681	+	0.401906i	$0.131652\pi$
$853$	164.358	+	932.120i	0.192682	+	1.09275i	−0.722999	+	0.690849i	$0.757237\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	194.366	+	231.636i	0.226798	+	0.270287i	0.867428	−	0.497562i	$-0.165771\pi$
$857$	194.366	+	231.636i	0.226798	+	0.270287i	−0.640631	+	0.767849i	$0.721327\pi$
$858$		0			0
$859$	−150.742	+	854.900i	−0.175485	+	0.995227i	0.762097	+	0.647463i	$0.224170\pi$
$859$	−150.742	+	854.900i	−0.175485	+	0.995227i	−0.937582	+	0.347764i	$0.886941\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			179.663i			0.208184i	0.994568	+	0.104092i	$0.0331936\pi$
$863$			179.663i			0.208184i	−0.994568	+	0.104092i	$0.966806\pi$
$864$		0			0
$865$	800.508			0.925442
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−260.022	−	45.8488i	−0.299219	−	0.0527605i
$870$		0			0
$871$	264.563	−	221.995i	0.303747	−	0.254874i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	112.535	−	19.8429i	0.128611	−	0.0226777i
$876$		0			0
$877$	573.067	−	208.579i	0.653440	−	0.237833i	0.00603862	−	0.999982i	$-0.498078\pi$
$877$	573.067	−	208.579i	0.653440	−	0.237833i	0.647402	+	0.762149i	$0.275856\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−662.997	−	382.782i	−0.752551	−	0.434485i	0.0740639	−	0.997253i	$-0.476403\pi$
$881$	−662.997	−	382.782i	−0.752551	−	0.434485i	−0.826615	+	0.562768i	$0.809736\pi$
$882$		0			0
$883$	−256.800	−	444.790i	−0.290826	−	0.503726i	0.683179	−	0.730251i	$-0.260597\pi$
$883$	−256.800	−	444.790i	−0.290826	−	0.503726i	−0.974005	+	0.226525i	$0.927263\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	213.850	−	254.857i	0.241094	−	0.287325i	−0.631906	−	0.775045i	$-0.717727\pi$
$887$	213.850	−	254.857i	0.241094	−	0.287325i	0.873000	+	0.487721i	$0.162172\pi$
$888$		0			0
$889$	56.2329	+	20.4671i	0.0632541	+	0.0230226i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	114.388	−	314.278i	0.128094	−	0.351935i
$894$		0			0
$895$	491.765	+	412.640i	0.549458	+	0.461050i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	440.606	−	254.384i	0.490107	−	0.282963i
$900$		0			0
$901$	−176.300	+	305.361i	−0.195672	+	0.338914i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	126.045	+	346.305i	0.139276	+	0.382658i
$906$		0			0
$907$	−142.000	−	805.323i	−0.156560	−	0.887897i	−0.957345	−	0.288946i	$-0.906695\pi$
$907$	−142.000	−	805.323i	−0.156560	−	0.887897i	0.800785	−	0.598952i	$-0.204416\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−1004.82	−	1197.50i	−1.10299	−	1.31449i	−0.945007	−	0.327049i	$-0.893946\pi$
$911$	−1004.82	−	1197.50i	−1.10299	−	1.31449i	−0.157982	−	0.987442i	$-0.550499\pi$
$912$		0			0
$913$	−95.5801	+	542.062i	−0.104688	+	0.593715i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			112.524i			0.122709i
$918$		0			0
$919$	−826.055			−0.898863			−0.449431	−	0.893315i	$-0.648373\pi$
$919$	−826.055			−0.898863			−0.449431	+	0.893315i	$0.648373\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	700.468	+	123.511i	0.758903	+	0.133815i
$924$		0			0
$925$	228.565	−	191.789i	0.247098	−	0.207340i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1285.74	−	226.711i	1.38401	−	0.244038i	0.568453	−	0.822716i	$-0.307542\pi$
$929$	1285.74	−	226.711i	1.38401	−	0.244038i	0.815556	+	0.578678i	$0.196431\pi$
$930$		0			0
$931$	207.330	−	75.4618i	0.222696	−	0.0810545i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−121.189	−	69.9684i	−0.129614	−	0.0748325i
$936$		0			0
$937$	−409.103	−	708.588i	−0.436610	−	0.756230i	0.560816	−	0.827941i	$-0.310488\pi$
$937$	−409.103	−	708.588i	−0.436610	−	0.756230i	−0.997425	+	0.0717104i	$0.977154\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	120.852	−	144.026i	0.128430	−	0.153056i	−0.697997	−	0.716100i	$-0.745925\pi$
$941$	120.852	−	144.026i	0.128430	−	0.153056i	0.826427	+	0.563044i	$0.190370\pi$
$942$		0			0
$943$	−362.745	−	132.028i	−0.384671	−	0.140009i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−431.659	+	1185.97i	−0.455817	+	1.25235i	0.472755	+	0.881194i	$0.343260\pi$
$947$	−431.659	+	1185.97i	−0.455817	+	1.25235i	−0.928572	+	0.371153i	$0.878963\pi$
$948$		0			0
$949$	−1064.16	−	892.940i	−1.12135	−	0.940928i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−789.863	+	456.027i	−0.828817	+	0.478518i	−0.853447	−	0.521179i	$-0.825492\pi$
$953$	−789.863	+	456.027i	−0.828817	+	0.478518i	0.0246304	+	0.999697i	$0.492159\pi$
$954$		0			0
$955$	−149.861	+	259.567i	−0.156922	+	0.271798i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−51.8494	−	142.455i	−0.0540661	−	0.148545i
$960$		0			0
$961$	344.727	+	1955.05i	0.358717	+	2.03439i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−373.289	−	444.868i	−0.386828	−	0.461003i
$966$		0			0
$967$	172.790	−	979.942i	0.178687	−	1.01338i	−0.755115	−	0.655592i	$-0.772419\pi$
$967$	172.790	−	979.942i	0.178687	−	1.01338i	0.933802	−	0.357791i	$-0.116470\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$			1477.87i			1.52201i	0.648746	+	0.761005i	$0.275294\pi$
$971$			1477.87i			1.52201i	−0.648746	+	0.761005i	$0.724706\pi$
$972$		0			0
$973$	−99.5116			−0.102273
$974$		0			0
$975$		0			0
$976$		0			0
$977$	150.970	+	26.6200i	0.154524	+	0.0272467i	0.250375	−	0.968149i	$-0.419446\pi$
$977$	150.970	+	26.6200i	0.154524	+	0.0272467i	−0.0958511	+	0.995396i	$0.530557\pi$
$978$		0			0
$979$	−455.952	+	382.589i	−0.465732	+	0.390796i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	84.1552	−	14.8388i	0.0856106	−	0.0150955i	−0.130679	−	0.991425i	$-0.541716\pi$
$983$	84.1552	−	14.8388i	0.0856106	−	0.0150955i	0.216289	+	0.976329i	$0.430605\pi$
$984$		0			0
$985$	688.664	−	250.653i	0.699151	−	0.254470i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	1726.02	+	996.515i	1.74521	+	1.00760i
$990$		0			0
$991$	−793.570	−	1374.50i	−0.800777	−	1.38699i	−0.919106	−	0.394011i	$-0.871087\pi$
$991$	−793.570	−	1374.50i	−0.800777	−	1.38699i	0.118329	−	0.992974i	$-0.462246\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	303.355	−	361.524i	0.304879	−	0.363341i
$996$		0			0
$997$	453.729	+	165.144i	0.455094	+	0.165641i	0.559388	−	0.828906i	$-0.311036\pi$
$997$	453.729	+	165.144i	0.455094	+	0.165641i	−0.104294	+	0.994546i	$0.533258\pi$
$998$		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.17.3		36
3.2	odd	2		108.3.k.a.77.5	✓	36
12.11	even	2		432.3.bc.b.401.2		36
27.7	even	9		108.3.k.a.101.5	yes	36
27.13	even	9		2916.3.c.b.1457.14		36
27.14	odd	18		2916.3.c.b.1457.23		36
27.20	odd	18	inner	324.3.k.a.305.3		36
108.7	odd	18		432.3.bc.b.209.2		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.k.a.77.5	✓	36	3.2	odd	2
108.3.k.a.101.5	yes	36	27.7	even	9
324.3.k.a.17.3		36	1.1	even	1	trivial
324.3.k.a.305.3		36	27.20	odd	18	inner
432.3.bc.b.209.2		36	108.7	odd	18
432.3.bc.b.401.2		36	12.11	even	2
2916.3.c.b.1457.14		36	27.13	even	9
2916.3.c.b.1457.23		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)

\(f(q)\)	\(=\)	\(q+(-2.92426 - 0.515626i) q^{5} +(0.715829 - 0.600652i) q^{7} +O(q^{10})\)	\(q+(-2.92426 - 0.515626i) q^{5} +(0.715829 - 0.600652i) q^{7} +(-5.89850 + 1.04007i) q^{11} +(-9.53387 + 3.47005i) q^{13} +(-6.81408 - 3.93411i) q^{17} +(-2.29223 - 3.97026i) q^{19} +(-22.9203 + 27.3153i) q^{23} +(-15.2069 - 5.53485i) q^{25} +(-3.20583 + 8.80793i) q^{29} +(-41.5801 - 34.8898i) q^{31} +(-2.40298 + 1.38736i) q^{35} +(-9.21875 + 15.9673i) q^{37} +(3.70267 + 10.1730i) q^{41} +(-9.70581 - 55.0444i) q^{43} +(46.8929 + 55.8847i) q^{47} +(-8.35713 + 47.3957i) q^{49} -44.8133i q^{53} +17.7851 q^{55} +(-81.5042 - 14.3714i) q^{59} +(47.6825 - 40.0104i) q^{61} +(29.6688 - 5.23141i) q^{65} +(-31.9873 + 11.6424i) q^{67} +(-60.7133 - 35.0528i) q^{71} +(68.4607 + 118.577i) q^{73} +(-3.59760 + 4.28745i) q^{77} +(41.4241 + 15.0772i) q^{79} +(31.4310 - 86.3561i) q^{83} +(17.8976 + 15.0179i) q^{85} +(86.0608 - 49.6872i) q^{89} +(-4.74033 + 8.21049i) q^{91} +(4.65591 + 12.7920i) q^{95} +(-4.81594 - 27.3125i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 9 q^{5}+O(q^{10}) \) 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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