LMFDB - Embedded newform 936.2.bi.b.361.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [936,2,Mod(361,936)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(936, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))

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

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

chi := DirichletCharacter("936.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.bi (of order $6$, degree $2$, 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:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.195105024.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 4x^{5} - 20x^{4} + 12x^{3} + 45x^{2} - 108x + 81 $ x^8 - 4x^7 + 5x^6 + 4x^5 - 20x^4 + 12x^3 + 45x^2 - 108*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.4
Root			$1.72124 + 0.193255i$ of defining polynomial
Character	$\chi$	$=$	936.361
Dual form			936.2.bi.b.433.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.17452i q^{5} +(2.98127 + 1.72124i) q^{7} +O(q^{10})$	$q+3.17452i q^{5} +(2.98127 + 1.72124i) q^{7} +(2.98127 - 1.72124i) q^{11} +(-0.362708 + 3.58726i) q^{13} +(0.886509 - 1.53548i) q^{17} +(-2.88434 - 1.66527i) q^{19} +(0.193255 + 0.334727i) q^{23} -5.07759 q^{25} +(-2.28801 - 3.96296i) q^{29} +11.0401i q^{31} +(-5.46410 + 9.46410i) q^{35} +(-1.40307 + 0.810063i) q^{37} +(1.96410 - 1.13397i) q^{41} +(5.36778 - 9.29726i) q^{43} +8.11192i q^{47} +(2.42531 + 4.20075i) q^{49} -11.6536 q^{53} +(5.46410 + 9.46410i) q^{55} +(5.47970 + 3.16371i) q^{59} +(-1.21042 + 2.09651i) q^{61} +(-11.3878 - 1.15142i) q^{65} +(-7.91867 + 4.57185i) q^{67} +(8.88434 + 5.12937i) q^{71} -8.40150i q^{73} +11.8506 q^{77} +8.22385 q^{79} -1.11506i q^{83} +(4.87441 + 2.81424i) q^{85} +(15.4339 - 8.91075i) q^{89} +(-7.25585 + 10.0703i) q^{91} +(5.28645 - 9.15640i) q^{95} +(3.88205 + 2.24130i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{7}+O(q^{10}) $ 8 * q - 6 * q^7	$ 8 q - 6 q^{7} - 6 q^{11} + 6 q^{13} - 6 q^{19} - 2 q^{23} - 20 q^{25} + 8 q^{29} - 16 q^{35} - 24 q^{37} - 12 q^{41} + 6 q^{43} + 2 q^{49} - 20 q^{53} + 16 q^{55} - 18 q^{59} - 4 q^{61} - 14 q^{65} - 42 q^{67} + 54 q^{71} + 60 q^{77} + 16 q^{79} + 6 q^{85} + 18 q^{89} - 46 q^{91} - 16 q^{95} + 30 q^{97}+O(q^{100}) $ 8 * q - 6 * q^7 - 6 * q^11 + 6 * q^13 - 6 * q^19 - 2 * q^23 - 20 * q^25 + 8 * q^29 - 16 * q^35 - 24 * q^37 - 12 * q^41 + 6 * q^43 + 2 * q^49 - 20 * q^53 + 16 * q^55 - 18 * q^59 - 4 * q^61 - 14 * q^65 - 42 * q^67 + 54 * q^71 + 60 * q^77 + 16 * q^79 + 6 * q^85 + 18 * q^89 - 46 * q^91 - 16 * q^95 + 30 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$			3.17452i			1.41969i	0.704358	+	0.709845i	$0.251235\pi$
$5$			3.17452i			1.41969i	−0.704358	+	0.709845i	$0.748765\pi$
$6$		0			0
$7$	2.98127	+	1.72124i	1.12681	+	0.650566i	0.943132	−	0.332420i	$-0.107865\pi$
$7$	2.98127	+	1.72124i	1.12681	+	0.650566i	0.183682	+	0.982986i	$0.441198\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.98127	−	1.72124i	0.898886	−	0.518972i	0.0220475	−	0.999757i	$-0.492982\pi$
$11$	2.98127	−	1.72124i	0.898886	−	0.518972i	0.876839	+	0.480785i	$0.159648\pi$
$12$		0			0
$13$	−0.362708	+	3.58726i	−0.100597	+	0.994927i
$13$	−0.362708	+	3.58726i	−0.100597	+	0.994927i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.886509	−	1.53548i	0.215010	−	0.372408i	−0.738266	−	0.674510i	$-0.764355\pi$
$17$	0.886509	−	1.53548i	0.215010	−	0.372408i	0.953276	+	0.302102i	$0.0976882\pi$
$18$		0			0
$19$	−2.88434	−	1.66527i	−0.661713	−	0.382040i	0.131217	−	0.991354i	$-0.458112\pi$
$19$	−2.88434	−	1.66527i	−0.661713	−	0.382040i	−0.792929	+	0.609314i	$0.791445\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.193255	+	0.334727i	0.0402964	+	0.0697953i	0.885470	−	0.464696i	$-0.153836\pi$
$23$	0.193255	+	0.334727i	0.0402964	+	0.0697953i	−0.845174	+	0.534492i	$0.820503\pi$
$24$		0			0
$25$	−5.07759			−1.01552
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.28801	−	3.96296i	−0.424873	−	0.735902i	0.571535	−	0.820578i	$-0.306348\pi$
$29$	−2.28801	−	3.96296i	−0.424873	−	0.735902i	−0.996409	+	0.0846752i	$0.973015\pi$
$30$		0			0
$31$			11.0401i			1.98287i	0.130618	+	0.991433i	$0.458304\pi$
$31$			11.0401i			1.98287i	−0.130618	+	0.991433i	$0.541696\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−5.46410	+	9.46410i	−0.923602	+	1.59973i
$36$		0			0
$37$	−1.40307	+	0.810063i	−0.230663	+	0.133174i	−0.610878	−	0.791725i	$-0.709183\pi$
$37$	−1.40307	+	0.810063i	−0.230663	+	0.133174i	0.380215	+	0.924898i	$0.375850\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.96410	−	1.13397i	0.306741	−	0.177097i	−0.338726	−	0.940885i	$-0.609996\pi$
$41$	1.96410	−	1.13397i	0.306741	−	0.177097i	0.645467	+	0.763788i	$0.276663\pi$
$42$		0			0
$43$	5.36778	−	9.29726i	0.818578	−	1.41782i	−0.0881515	−	0.996107i	$-0.528096\pi$
$43$	5.36778	−	9.29726i	0.818578	−	1.41782i	0.906730	−	0.421712i	$-0.138571\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			8.11192i			1.18325i	0.806215	+	0.591623i	$0.201513\pi$
$47$			8.11192i			1.18325i	−0.806215	+	0.591623i	$0.798487\pi$
$48$		0			0
$49$	2.42531	+	4.20075i	0.346472	+	0.600107i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−11.6536			−1.60075			−0.800374	−	0.599501i	$-0.795366\pi$
$53$	−11.6536			−1.60075			−0.800374	+	0.599501i	$0.795366\pi$
$54$		0			0
$55$	5.46410	+	9.46410i	0.736779	+	1.27614i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	5.47970	+	3.16371i	0.713396	+	0.411880i	0.812317	−	0.583216i	$-0.198206\pi$
$59$	5.47970	+	3.16371i	0.713396	+	0.411880i	−0.0989209	+	0.995095i	$0.531539\pi$
$60$		0			0
$61$	−1.21042	+	2.09651i	−0.154979	+	0.268431i	−0.933051	−	0.359744i	$-0.882864\pi$
$61$	−1.21042	+	2.09651i	−0.154979	+	0.268431i	0.778073	+	0.628174i	$0.216197\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−11.3878	−	1.15142i	−1.41249	−	0.142817i
$66$		0			0
$67$	−7.91867	+	4.57185i	−0.967420	+	0.558540i	−0.898449	−	0.439079i	$-0.855305\pi$
$67$	−7.91867	+	4.57185i	−0.967420	+	0.558540i	−0.0689710	+	0.997619i	$0.521972\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	8.88434	+	5.12937i	1.05438	+	0.608745i	0.923872	−	0.382703i	$-0.125007\pi$
$71$	8.88434	+	5.12937i	1.05438	+	0.608745i	0.130505	+	0.991448i	$0.458340\pi$
$72$		0			0
$73$		−	8.40150i		−	0.983322i	−0.870787	−	0.491661i	$-0.836390\pi$
$73$		−	8.40150i		−	0.983322i	0.870787	−	0.491661i	$-0.163610\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	11.8506			1.35050
$78$		0			0
$79$	8.22385			0.925255			0.462628	−	0.886553i	$-0.346907\pi$
$79$	8.22385			0.925255			0.462628	+	0.886553i	$0.346907\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		−	1.11506i		−	0.122393i	−0.998126	−	0.0611967i	$-0.980508\pi$
$83$		−	1.11506i		−	0.122393i	0.998126	−	0.0611967i	$-0.0194917\pi$
$84$		0			0
$85$	4.87441	+	2.81424i	0.528704	+	0.305248i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	15.4339	−	8.91075i	1.63599	−	0.944538i	0.653793	−	0.756674i	$-0.273177\pi$
$89$	15.4339	−	8.91075i	1.63599	−	0.944538i	0.982195	−	0.187864i	$-0.0601565\pi$
$90$		0			0
$91$	−7.25585	+	10.0703i	−0.760620	+	1.05565i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	5.28645	−	9.15640i	0.542378	−	0.939426i
$96$		0			0
$97$	3.88205	+	2.24130i	0.394162	+	0.227570i	0.683962	−	0.729518i	$-0.260255\pi$
$97$	3.88205	+	2.24130i	0.394162	+	0.227570i	−0.289800	+	0.957087i	$0.593589\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−0.0984958	−	0.170600i	−0.00980070	−	0.0169753i	0.861083	−	0.508464i	$-0.169786\pi$
$101$	−0.0984958	−	0.170600i	−0.00980070	−	0.0169753i	−0.870884	+	0.491488i	$0.836453\pi$
$102$		0			0
$103$	−6.34904			−0.625590			−0.312795	−	0.949821i	$-0.601265\pi$
$103$	−6.34904			−0.625590			−0.312795	+	0.949821i	$0.601265\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.57976	−	4.46828i	−0.249395	−	0.431965i	0.713963	−	0.700183i	$-0.246898\pi$
$107$	−2.57976	−	4.46828i	−0.249395	−	0.431965i	−0.963358	+	0.268218i	$0.913565\pi$
$108$		0			0
$109$		−	10.9282i		−	1.04673i	−0.852108	−	0.523366i	$-0.824676\pi$
$109$		−	10.9282i		−	1.04673i	0.852108	−	0.523366i	$-0.175324\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−5.46254	+	9.46139i	−0.513872	+	0.890053i	0.485998	+	0.873960i	$0.338456\pi$
$113$	−5.46254	+	9.46139i	−0.513872	+	0.890053i	−0.999871	+	0.0160929i	$0.994877\pi$
$114$		0			0
$115$	−1.06260	+	0.613491i	−0.0990877	+	0.0572083i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	5.28584	−	3.05178i	0.484552	−	0.279756i
$120$		0			0
$121$	0.425305	−	0.736650i	0.0386641	−	0.0669682i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	0.246319i		−	0.0220315i
$126$		0			0
$127$	−4.30518	−	7.45679i	−0.382023	−	0.661683i	0.609328	−	0.792918i	$-0.291439\pi$
$127$	−4.30518	−	7.45679i	−0.382023	−	0.661683i	−0.991351	+	0.131235i	$0.958106\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	3.19699			0.279322			0.139661	−	0.990199i	$-0.455399\pi$
$131$	3.19699			0.279322			0.139661	+	0.990199i	$0.455399\pi$
$132$		0			0
$133$	−5.73266	−	9.92925i	−0.497084	−	0.860975i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−6.99843	−	4.04055i	−0.597917	−	0.345207i	0.170305	−	0.985391i	$-0.445525\pi$
$137$	−6.99843	−	4.04055i	−0.597917	−	0.345207i	−0.768222	+	0.640184i	$0.778858\pi$
$138$		0			0
$139$	5.90368	−	10.2255i	0.500743	−	0.867313i	−0.499256	−	0.866454i	$-0.666393\pi$
$139$	5.90368	−	10.2255i	0.500743	−	0.867313i	1.00000		0.000858394i	$-0.000273235\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	5.09319	+	11.3189i	0.425914	+	0.946533i
$144$		0			0
$145$	12.5805	−	7.26335i	1.04475	−	0.603188i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−14.9892	−	8.65404i	−1.22797	−	0.708966i	−0.261362	−	0.965241i	$-0.584172\pi$
$149$	−14.9892	−	8.65404i	−1.22797	−	0.708966i	−0.966604	+	0.256274i	$0.917505\pi$
$150$		0			0
$151$		−	2.81628i		−	0.229185i	−0.993413	−	0.114593i	$-0.963444\pi$
$151$		−	2.81628i		−	0.229185i	0.993413	−	0.114593i	$-0.0365563\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−35.0471			−2.81505
$156$		0			0
$157$	−13.1997			−1.05345			−0.526724	−	0.850037i	$-0.676580\pi$
$157$	−13.1997			−1.05345			−0.526724	+	0.850037i	$0.676580\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			1.33055i			0.104862i
$162$		0			0
$163$	15.9095	+	9.18534i	1.24613	+	0.719451i	0.970334	−	0.241766i	$-0.0777267\pi$
$163$	15.9095	+	9.18534i	1.24613	+	0.719451i	0.275791	+	0.961217i	$0.411060\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−9.01873	+	5.20697i	−0.697890	+	0.402927i	−0.806561	−	0.591151i	$-0.798674\pi$
$167$	−9.01873	+	5.20697i	−0.697890	+	0.402927i	0.108671	+	0.994078i	$0.465341\pi$
$168$		0			0
$169$	−12.7369	−	2.60226i	−0.979760	−	0.200174i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	3.22988	−	5.59432i	0.245563	−	0.425328i	−0.716727	−	0.697354i	$-0.754360\pi$
$173$	3.22988	−	5.59432i	0.245563	−	0.425328i	0.962290	+	0.272026i	$0.0876938\pi$
$174$		0			0
$175$	−15.1377	−	8.73973i	−1.14430	−	0.660662i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	4.59476	+	7.95836i	0.343428	+	0.594835i	0.985067	−	0.172172i	$-0.0550784\pi$
$179$	4.59476	+	7.95836i	0.343428	+	0.594835i	−0.641639	+	0.767007i	$0.721745\pi$
$180$		0			0
$181$	1.95240			0.145121			0.0725603	−	0.997364i	$-0.476883\pi$
$181$	1.95240			0.145121			0.0725603	+	0.997364i	$0.476883\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−2.57156	−	4.45408i	−0.189065	−	0.327470i
$186$		0			0
$187$		−	6.10356i		−	0.446337i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	8.60975	−	14.9125i	0.622980	−	1.07903i	−0.365948	−	0.930635i	$-0.619255\pi$
$191$	8.60975	−	14.9125i	0.622980	−	1.07903i	0.988928	−	0.148398i	$-0.0474115\pi$
$192$		0			0
$193$	7.64192	−	4.41206i	0.550077	−	0.317587i	−0.199076	−	0.979984i	$-0.563794\pi$
$193$	7.64192	−	4.41206i	0.550077	−	0.317587i	0.749153	+	0.662397i	$0.230461\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	11.9698	−	6.91075i	0.852811	−	0.492371i	−0.00878717	−	0.999961i	$-0.502797\pi$
$197$	11.9698	−	6.91075i	0.852811	−	0.492371i	0.861598	+	0.507591i	$0.169464\pi$
$198$		0			0
$199$	12.4604	−	21.5820i	0.883292	−	1.52991i	0.0356328	−	0.999365i	$-0.488655\pi$
$199$	12.4604	−	21.5820i	0.883292	−	1.52991i	0.847659	−	0.530541i	$-0.178011\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		−	15.7528i		−	1.10563i
$204$		0			0
$205$	3.59983	+	6.23508i	0.251423	+	0.435477i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−11.4653			−0.793072
$210$		0			0
$211$	3.38277	+	5.85913i	0.232880	+	0.403359i	0.958654	−	0.284573i	$-0.0918518\pi$
$211$	3.38277	+	5.85913i	0.232880	+	0.403359i	−0.725775	+	0.687932i	$0.758519\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	29.5144	+	17.0401i	2.01286	+	1.16213i
$216$		0			0
$217$	−19.0027	+	32.9136i	−1.28998	+	2.23432i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	5.18662	+	3.73707i	0.348890	+	0.251383i
$222$		0			0
$223$	20.3987	−	11.7772i	1.36600	−	0.788660i	0.375584	−	0.926788i	$-0.377442\pi$
$223$	20.3987	−	11.7772i	1.36600	−	0.788660i	0.990414	+	0.138129i	$0.0441088\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−10.9721	−	6.33473i	−0.728242	−	0.420451i	0.0895368	−	0.995984i	$-0.471461\pi$
$227$	−10.9721	−	6.33473i	−0.728242	−	0.420451i	−0.817779	+	0.575533i	$0.804795\pi$
$228$		0			0
$229$			2.92820i			0.193501i	0.995309	+	0.0967506i	$0.0308449\pi$
$229$			2.92820i			0.193501i	−0.995309	+	0.0967506i	$0.969155\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	6.22385			0.407738			0.203869	−	0.978998i	$-0.434648\pi$
$233$	6.22385			0.407738			0.203869	+	0.978998i	$0.434648\pi$
$234$		0			0
$235$	−25.7515			−1.67984
$236$		0			0
$237$		0			0
$238$		0			0
$239$		−	16.4910i		−	1.06671i	−0.845891	−	0.533356i	$-0.820931\pi$
$239$		−	16.4910i		−	1.06671i	0.845891	−	0.533356i	$-0.179069\pi$
$240$		0			0
$241$	−13.6564	−	7.88452i	−0.879686	−	0.507887i	−0.00913098	−	0.999958i	$-0.502907\pi$
$241$	−13.6564	−	7.88452i	−0.879686	−	0.507887i	−0.870555	+	0.492071i	$0.836240\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−13.3354	+	7.69919i	−0.851966	+	0.491883i
$246$		0			0
$247$	7.01994	−	9.74287i	0.446668	−	0.619924i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	7.93194	−	13.7385i	0.500660	−	0.867168i	−0.499340	−	0.866406i	$-0.666424\pi$
$251$	7.93194	−	13.7385i	0.500660	−	0.867168i	1.00000		0.000761843i	$-0.000242502\pi$
$252$		0			0
$253$	1.15229	+	0.665273i	0.0724437	+	0.0418254i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	7.61192	+	13.1842i	0.474819	+	0.822410i	0.999584	−	0.0288366i	$-0.00918025\pi$
$257$	7.61192	+	13.1842i	0.474819	+	0.822410i	−0.524765	+	0.851247i	$0.675847\pi$
$258$		0			0
$259$	−5.57724			−0.346553
$260$		0			0
$261$		0			0
$262$		0			0
$263$	2.71995	+	4.71110i	0.167720	+	0.290499i	0.937618	−	0.347668i	$-0.113026\pi$
$263$	2.71995	+	4.71110i	0.167720	+	0.290499i	−0.769898	+	0.638167i	$0.779693\pi$
$264$		0			0
$265$		−	36.9947i		−	2.27256i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	8.88784	−	15.3942i	0.541901	−	0.938600i	−0.456894	−	0.889521i	$-0.651038\pi$
$269$	8.88784	−	15.3942i	0.541901	−	0.938600i	0.998795	−	0.0490791i	$-0.0156287\pi$
$270$		0			0
$271$	−0.856073	+	0.494254i	−0.0520027	+	0.0300238i	−0.525776	−	0.850623i	$-0.676225\pi$
$271$	−0.856073	+	0.494254i	−0.0520027	+	0.0300238i	0.473773	+	0.880647i	$0.342892\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−15.1377	+	8.73973i	−0.912835	+	0.527026i
$276$		0			0
$277$	1.02670	−	1.77829i	0.0616884	−	0.106847i	−0.833532	−	0.552471i	$-0.813685\pi$
$277$	1.02670	−	1.77829i	0.0616884	−	0.106847i	0.895220	+	0.445624i	$0.147018\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$			1.20451i			0.0718552i	0.999354	+	0.0359276i	$0.0114386\pi$
$281$			1.20451i			0.0718552i	−0.999354	+	0.0359276i	$0.988561\pi$
$282$		0			0
$283$	0.856073	+	1.48276i	0.0508883	+	0.0881411i	0.890347	−	0.455282i	$-0.150461\pi$
$283$	0.856073	+	1.48276i	0.0508883	+	0.0881411i	−0.839459	+	0.543423i	$0.817128\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	7.80735			0.460853
$288$		0			0
$289$	6.92820	+	12.0000i	0.407541	+	0.705882i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	2.24041	+	1.29350i	0.130886	+	0.0755672i	0.564013	−	0.825766i	$-0.309257\pi$
$293$	2.24041	+	1.29350i	0.130886	+	0.0755672i	−0.433127	+	0.901333i	$0.642590\pi$
$294$		0			0
$295$	−10.0433	+	17.3954i	−0.584741	+	1.01280i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.27085	+	0.571847i	−0.0734950	+	0.0330707i
$300$		0			0
$301$	32.0056	−	18.4784i	1.84477	−	1.06508i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−6.65542	−	3.84251i	−0.381088	−	0.220021i
$306$		0			0
$307$		−	12.3358i		−	0.704040i	−0.935993	−	0.352020i	$-0.885495\pi$
$307$		−	12.3358i		−	0.704040i	0.935993	−	0.352020i	$-0.114505\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	4.74303			0.268952			0.134476	−	0.990917i	$-0.457065\pi$
$311$	4.74303			0.268952			0.134476	+	0.990917i	$0.457065\pi$
$312$		0			0
$313$	−0.230114			−0.0130068			−0.00650339	−	0.999979i	$-0.502070\pi$
$313$	−0.230114			−0.0130068			−0.00650339	+	0.999979i	$0.502070\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	5.87888i		−	0.330191i	−0.986278	−	0.165095i	$-0.947207\pi$
$317$		−	5.87888i		−	0.330191i	0.986278	−	0.165095i	$-0.0527932\pi$
$318$		0			0
$319$	−13.6424	−	7.87642i	−0.763826	−	0.440995i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−5.11398	+	2.95256i	−0.284550	+	0.164285i
$324$		0			0
$325$	1.84168	−	18.2147i	0.102158	−	1.01037i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−13.9625	+	24.1838i	−0.769780	+	1.33330i
$330$		0			0
$331$	11.1065	+	6.41232i	0.610466	+	0.352453i	0.773148	−	0.634226i	$-0.218681\pi$
$331$	11.1065	+	6.41232i	0.610466	+	0.352453i	−0.162682	+	0.986679i	$0.552014\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−14.5134	−	25.1380i	−0.792953	−	1.37344i
$336$		0			0
$337$	30.5456			1.66392			0.831962	−	0.554833i	$-0.187218\pi$
$337$	30.5456			1.66392			0.831962	+	0.554833i	$0.187218\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	19.0027	+	32.9136i	1.02905	+	1.78237i
$342$		0			0
$343$		−	7.39921i		−	0.399520i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−6.19325	+	10.7270i	−0.332471	+	0.575857i	−0.982996	−	0.183628i	$-0.941216\pi$
$347$	−6.19325	+	10.7270i	−0.332471	+	0.575857i	0.650524	+	0.759485i	$0.274549\pi$
$348$		0			0
$349$	−15.1651	+	8.75557i	−0.811769	+	0.468675i	−0.847570	−	0.530684i	$-0.821935\pi$
$349$	−15.1651	+	8.75557i	−0.811769	+	0.468675i	0.0358011	+	0.999359i	$0.488602\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	19.7983	−	11.4306i	1.05376	−	0.608387i	0.130059	−	0.991506i	$-0.458483\pi$
$353$	19.7983	−	11.4306i	1.05376	−	0.608387i	0.923699	+	0.383119i	$0.125150\pi$
$354$		0			0
$355$	−16.2833	+	28.2035i	−0.864229	+	1.49689i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	20.4310i		−	1.07831i	−0.842208	−	0.539153i	$-0.818744\pi$
$359$		−	20.4310i		−	1.07831i	0.842208	−	0.539153i	$-0.181256\pi$
$360$		0			0
$361$	−3.95373	−	6.84806i	−0.208091	−	0.360424i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	26.6708			1.39601
$366$		0			0
$367$	12.2810	+	21.2713i	0.641062	+	1.11035i	0.985196	+	0.171432i	$0.0548393\pi$
$367$	12.2810	+	21.2713i	0.641062	+	1.11035i	−0.344134	+	0.938921i	$0.611827\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−34.7426	−	20.0586i	−1.80374	−	1.04139i
$372$		0			0
$373$	−2.52826	+	4.37908i	−0.130909	+	0.226740i	−0.924027	−	0.382327i	$-0.875123\pi$
$373$	−2.52826	+	4.37908i	−0.130909	+	0.226740i	0.793118	+	0.609067i	$0.208456\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	15.0460	−	6.77031i	0.774910	−	0.348688i
$378$		0			0
$379$	−3.45144	+	1.99269i	−0.177288	+	0.102358i	−0.586018	−	0.810298i	$-0.699305\pi$
$379$	−3.45144	+	1.99269i	−0.177288	+	0.102358i	0.408730	+	0.912656i	$0.365972\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−1.97814	−	1.14208i	−0.101078	−	0.0583574i	0.448609	−	0.893728i	$-0.351920\pi$
$383$	−1.97814	−	1.14208i	−0.101078	−	0.0583574i	−0.549687	+	0.835371i	$0.685253\pi$
$384$		0			0
$385$			37.6200i			1.91729i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−19.9727			−1.01265			−0.506327	−	0.862341i	$-0.668997\pi$
$389$	−19.9727			−1.01265			−0.506327	+	0.862341i	$0.668997\pi$
$390$		0			0
$391$	0.685288			0.0346565
$392$		0			0
$393$		0			0
$394$		0			0
$395$			26.1068i			1.31358i
$396$		0			0
$397$	12.8605	+	7.42502i	0.645451	+	0.372651i	0.786711	−	0.617321i	$-0.211782\pi$
$397$	12.8605	+	7.42502i	0.645451	+	0.372651i	−0.141260	+	0.989972i	$0.545115\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−12.5877	+	7.26753i	−0.628601	+	0.362923i	−0.780210	−	0.625517i	$-0.784888\pi$
$401$	−12.5877	+	7.26753i	−0.628601	+	0.362923i	0.151609	+	0.988441i	$0.451555\pi$
$402$		0			0
$403$	−39.6038	−	4.00434i	−1.97281	−	0.199470i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−2.78862	+	4.83003i	−0.138227	+	0.239416i
$408$		0			0
$409$	−15.3550	−	8.86519i	−0.759254	−	0.438355i	0.0697741	−	0.997563i	$-0.477772\pi$
$409$	−15.3550	−	8.86519i	−0.759254	−	0.438355i	−0.829028	+	0.559208i	$0.811105\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	10.8910	+	18.8637i	0.535910	+	0.928223i
$414$		0			0
$415$	3.53977			0.173761
$416$		0			0
$417$		0			0
$418$		0			0
$419$	17.5824	+	30.4537i	0.858958	+	1.48776i	0.872924	+	0.487856i	$0.162221\pi$
$419$	17.5824	+	30.4537i	0.858958	+	1.48776i	−0.0139663	+	0.999902i	$0.504446\pi$
$420$		0			0
$421$			21.4186i			1.04388i	0.852982	+	0.521941i	$0.174792\pi$
$421$			21.4186i			1.04388i	−0.852982	+	0.521941i	$0.825208\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−4.50133	+	7.79654i	−0.218347	+	0.378188i
$426$		0			0
$427$	−7.21718	+	4.16684i	−0.349264	+	0.201647i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	7.56743	−	4.36906i	0.364510	−	0.210450i	−0.306547	−	0.951855i	$-0.599174\pi$
$431$	7.56743	−	4.36906i	0.364510	−	0.210450i	0.671057	+	0.741405i	$0.265840\pi$
$432$		0			0
$433$	−13.9610	+	24.1811i	−0.670921	+	1.16207i	0.306722	+	0.951799i	$0.400768\pi$
$433$	−13.9610	+	24.1811i	−0.670921	+	1.16207i	−0.977643	+	0.210271i	$0.932565\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		−	1.28729i		−	0.0615793i
$438$		0			0
$439$	9.79755	+	16.9698i	0.467611	+	0.809927i	0.999315	−	0.0370038i	$-0.0117814\pi$
$439$	9.79755	+	16.9698i	0.467611	+	0.809927i	−0.531704	+	0.846930i	$0.678448\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−19.1521			−0.909942			−0.454971	−	0.890506i	$-0.650350\pi$
$443$	−19.1521			−0.909942			−0.454971	+	0.890506i	$0.650350\pi$
$444$		0			0
$445$	28.2874	+	48.9952i	1.34095	+	2.32259i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	16.3851	+	9.45992i	0.773259	+	0.446441i	0.834036	−	0.551710i	$-0.186025\pi$
$449$	16.3851	+	9.45992i	0.773259	+	0.446441i	−0.0607770	+	0.998151i	$0.519358\pi$
$450$		0			0
$451$	3.90368	−	6.76136i	0.183817	−	0.318380i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−31.9683	−	23.0339i	−1.49870	−	1.07984i
$456$		0			0
$457$	9.55027	−	5.51385i	0.446743	−	0.257927i	−0.259711	−	0.965686i	$-0.583627\pi$
$457$	9.55027	−	5.51385i	0.446743	−	0.257927i	0.706454	+	0.707759i	$0.250294\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−8.27788	−	4.77923i	−0.385539	−	0.222591i	0.294686	−	0.955594i	$-0.404785\pi$
$461$	−8.27788	−	4.77923i	−0.385539	−	0.222591i	−0.680225	+	0.733003i	$0.738118\pi$
$462$		0			0
$463$		−	17.1151i		−	0.795404i	−0.917515	−	0.397702i	$-0.869808\pi$
$463$		−	17.1151i		−	0.795404i	0.917515	−	0.397702i	$-0.130192\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	4.86196			0.224985			0.112492	−	0.993653i	$-0.464117\pi$
$467$	4.86196			0.224985			0.112492	+	0.993653i	$0.464117\pi$
$468$		0			0
$469$	−31.4769			−1.45347
$470$		0			0
$471$		0			0
$472$		0			0
$473$		−	36.9568i		−	1.69928i
$474$		0			0
$475$	14.6455	+	8.45558i	0.671981	+	0.387969i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−16.2003	+	9.35322i	−0.740209	+	0.427360i	−0.822145	−	0.569278i	$-0.807223\pi$
$479$	−16.2003	+	9.35322i	−0.740209	+	0.427360i	0.0819364	+	0.996638i	$0.473890\pi$
$480$		0			0
$481$	−2.39700	−	5.32700i	−0.109294	−	0.242890i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−7.11506	+	12.3236i	−0.323078	+	0.559588i
$486$		0			0
$487$	3.03321	+	1.75123i	0.137448	+	0.0793556i	0.567147	−	0.823616i	$-0.308047\pi$
$487$	3.03321	+	1.75123i	0.137448	+	0.0793556i	−0.429699	+	0.902972i	$0.641380\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	10.9005	+	18.8803i	0.491935	+	0.852056i	0.999957	−	0.00928817i	$-0.00295656\pi$
$491$	10.9005	+	18.8803i	0.491935	+	0.852056i	−0.508022	+	0.861344i	$0.669623\pi$
$492$		0			0
$493$	−8.11338			−0.365408
$494$		0			0
$495$		0			0
$496$		0			0
$497$	17.6577	+	30.5841i	0.792057	+	1.37188i
$498$		0			0
$499$		−	35.3505i		−	1.58251i	−0.611489	−	0.791253i	$-0.709429\pi$
$499$		−	35.3505i		−	1.58251i	0.611489	−	0.791253i	$-0.290571\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	11.3003	−	19.5727i	0.503856	−	0.872705i	−0.496134	−	0.868246i	$-0.665247\pi$
$503$	11.3003	−	19.5727i	0.503856	−	0.872705i	0.999990	−	0.00445881i	$-0.00141929\pi$
$504$		0			0
$505$	0.541573	−	0.312677i	0.0240997	−	0.0139139i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−12.9670	+	7.48652i	−0.574754	+	0.331834i	−0.759046	−	0.651037i	$-0.774334\pi$
$509$	−12.9670	+	7.48652i	−0.574754	+	0.331834i	0.184292	+	0.982872i	$0.441001\pi$
$510$		0			0
$511$	14.4610	−	25.0471i	0.639716	−	1.10802i
$512$		0			0
$513$		0			0
$514$		0			0
$515$		−	20.1552i		−	0.888144i
$516$		0			0
$517$	13.9625	+	24.1838i	0.614072	+	1.06360i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−17.7101			−0.775896			−0.387948	−	0.921681i	$-0.626816\pi$
$521$	−17.7101			−0.775896			−0.387948	+	0.921681i	$0.626816\pi$
$522$		0			0
$523$	4.79441	+	8.30417i	0.209645	+	0.363116i	0.951603	−	0.307331i	$-0.0994358\pi$
$523$	4.79441	+	8.30417i	0.209645	+	0.363116i	−0.741958	+	0.670447i	$0.766102\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	16.9519	+	9.78717i	0.738436	+	0.426336i
$528$		0			0
$529$	11.4253	−	19.7892i	0.496752	−	0.860400i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	3.35547	+	7.45705i	0.145341	+	0.323001i
$534$		0			0
$535$	14.1847	−	8.18952i	0.613256	−	0.354064i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	14.4610	+	8.34904i	0.622878	+	0.359619i
$540$		0			0
$541$		−	24.1149i		−	1.03678i	−0.855145	−	0.518389i	$-0.826532\pi$
$541$		−	24.1149i		−	1.03678i	0.855145	−	0.518389i	$-0.173468\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	34.6918			1.48603
$546$		0			0
$547$	26.1392			1.11763			0.558816	−	0.829292i	$-0.311256\pi$
$547$	26.1392			1.11763			0.558816	+	0.829292i	$0.311256\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$			15.2407i			0.649274i
$552$		0			0
$553$	24.5175	+	14.1552i	1.04259	+	0.601940i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−15.2220	+	8.78843i	−0.644977	+	0.372378i	−0.786529	−	0.617553i	$-0.788124\pi$
$557$	−15.2220	+	8.78843i	−0.644977	+	0.372378i	0.141552	+	0.989931i	$0.454791\pi$
$558$		0			0
$559$	31.4048	+	22.6278i	1.32828	+	0.957054i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	16.8693	−	29.2186i	0.710958	−	1.23142i	−0.253540	−	0.967325i	$-0.581595\pi$
$563$	16.8693	−	29.2186i	0.710958	−	1.23142i	0.964498	−	0.264091i	$-0.0850718\pi$
$564$		0			0
$565$	−30.0354	−	17.3409i	−1.26360	−	0.729539i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−22.5083	−	38.9856i	−0.943599	−	1.63436i	−0.758533	−	0.651635i	$-0.774084\pi$
$569$	−22.5083	−	38.9856i	−0.943599	−	1.63436i	−0.185066	−	0.982726i	$-0.559250\pi$
$570$		0			0
$571$	−35.4624			−1.48406			−0.742028	−	0.670369i	$-0.766136\pi$
$571$	−35.4624			−1.48406			−0.742028	+	0.670369i	$0.766136\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−0.981268	−	1.69961i	−0.0409217	−	0.0708785i
$576$		0			0
$577$			26.1530i			1.08876i	0.838838	+	0.544382i	$0.183236\pi$
$577$			26.1530i			1.08876i	−0.838838	+	0.544382i	$0.816764\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	1.91928	−	3.32428i	0.0796250	−	0.137914i
$582$		0			0
$583$	−34.7426	+	20.0586i	−1.43889	+	0.830743i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−9.35451	+	5.40083i	−0.386102	+	0.222916i	−0.680470	−	0.732776i	$-0.738224\pi$
$587$	−9.35451	+	5.40083i	−0.386102	+	0.222916i	0.294368	+	0.955692i	$0.404891\pi$
$588$		0			0
$589$	18.3848	−	31.8435i	0.757534	−	1.31209i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			44.4421i			1.82502i	0.409058	+	0.912508i	$0.365857\pi$
$593$			44.4421i			1.82502i	−0.409058	+	0.912508i	$0.634143\pi$
$594$		0			0
$595$	9.68795	+	16.7800i	0.397167	+	0.687914i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	15.7312			0.642760			0.321380	−	0.946950i	$-0.395853\pi$
$599$	15.7312			0.642760			0.321380	+	0.946950i	$0.395853\pi$
$600$		0			0
$601$	14.8447	+	25.7118i	0.605528	+	1.04881i	0.991968	+	0.126491i	$0.0403714\pi$
$601$	14.8447	+	25.7118i	0.605528	+	1.04881i	−0.386440	+	0.922315i	$0.626295\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	2.33851	+	1.35014i	0.0950741	+	0.0548911i
$606$		0			0
$607$	−18.2677	+	31.6406i	−0.741464	+	1.28425i	0.210365	+	0.977623i	$0.432535\pi$
$607$	−18.2677	+	31.6406i	−0.741464	+	1.28425i	−0.951829	+	0.306630i	$0.900799\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−29.0996	−	2.94226i	−1.17724	−	0.119031i
$612$		0			0
$613$	−29.0380	+	16.7651i	−1.17284	+	0.677137i	−0.954346	−	0.298702i	$-0.903446\pi$
$613$	−29.0380	+	16.7651i	−1.17284	+	0.677137i	−0.218489	+	0.975839i	$0.570113\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	18.9769	+	10.9563i	0.763981	+	0.441085i	0.830723	−	0.556685i	$-0.187927\pi$
$617$	18.9769	+	10.9563i	0.763981	+	0.441085i	−0.0667420	+	0.997770i	$0.521260\pi$
$618$		0			0
$619$		−	3.13533i		−	0.126020i	−0.998013	−	0.0630098i	$-0.979930\pi$
$619$		−	3.13533i		−	0.126020i	0.998013	−	0.0630098i	$-0.0200699\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	61.3500			2.45794
$624$		0			0
$625$	−24.6060			−0.984241
$626$		0			0
$627$		0			0
$628$		0			0
$629$			2.87251i			0.114535i
$630$		0			0
$631$	0.251510	+	0.145209i	0.0100124	+	0.00578069i	0.504998	−	0.863121i	$-0.331493\pi$
$631$	0.251510	+	0.145209i	0.0100124	+	0.00578069i	−0.494985	+	0.868901i	$0.664827\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	23.6717	−	13.6669i	0.939385	−	0.542354i
$636$		0			0
$637$	−15.9489	+	7.17656i	−0.631917	+	0.284346i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−7.43255	+	12.8735i	−0.293568	+	0.508475i	−0.974651	−	0.223732i	$-0.928176\pi$
$641$	−7.43255	+	12.8735i	−0.293568	+	0.508475i	0.681083	+	0.732206i	$0.261509\pi$
$642$		0			0
$643$	−0.806474	−	0.465618i	−0.0318042	−	0.0183622i	0.484014	−	0.875060i	$-0.339179\pi$
$643$	−0.806474	−	0.465618i	−0.0318042	−	0.0183622i	−0.515818	+	0.856698i	$0.672512\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−7.76349	−	13.4468i	−0.305214	−	0.528646i	0.672095	−	0.740465i	$-0.265395\pi$
$647$	−7.76349	−	13.4468i	−0.305214	−	0.528646i	−0.977309	+	0.211819i	$0.932061\pi$
$648$		0			0
$649$	21.7819			0.855016
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−4.10903	−	7.11704i	−0.160799	−	0.278511i	0.774357	−	0.632749i	$-0.218074\pi$
$653$	−4.10903	−	7.11704i	−0.160799	−	0.278511i	−0.935155	+	0.354238i	$0.884740\pi$
$654$		0			0
$655$			10.1489i			0.396551i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−16.8751	+	29.2286i	−0.657362	+	1.13858i	0.323934	+	0.946080i	$0.394994\pi$
$659$	−16.8751	+	29.2286i	−0.657362	+	1.13858i	−0.981296	+	0.192505i	$0.938339\pi$
$660$		0			0
$661$	−5.20295	+	3.00392i	−0.202371	+	0.116839i	−0.597761	−	0.801674i	$-0.703943\pi$
$661$	−5.20295	+	3.00392i	−0.202371	+	0.116839i	0.395390	+	0.918513i	$0.370610\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	31.5206	−	18.1984i	1.22232	−	0.705705i
$666$		0			0
$667$	0.884338	−	1.53172i	0.0342417	−	0.0593084i
$668$		0			0
$669$		0			0
$670$		0			0
$671$			8.33368i			0.321718i
$672$		0			0
$673$	−11.5476	−	20.0010i	−0.445127	−	0.770983i	0.552934	−	0.833225i	$-0.313508\pi$
$673$	−11.5476	−	20.0010i	−0.445127	−	0.770983i	−0.998061	+	0.0622420i	$0.980175\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−47.1723			−1.81298			−0.906490	−	0.422227i	$-0.861248\pi$
$677$	−47.1723			−1.81298			−0.906490	+	0.422227i	$0.861248\pi$
$678$		0			0
$679$	7.71561	+	13.3638i	0.296098	+	0.512857i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−36.3780	−	21.0028i	−1.39196	−	0.803651i	−0.398431	−	0.917198i	$-0.630445\pi$
$683$	−36.3780	−	21.0028i	−1.39196	−	0.803651i	−0.993533	+	0.113547i	$0.963779\pi$
$684$		0			0
$685$	12.8268	−	22.2167i	0.490087	−	0.848856i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	4.22686	−	41.8046i	0.161031	−	1.59263i
$690$		0			0
$691$	22.7253	−	13.1204i	0.864510	−	0.499125i	−0.00100968	−	0.999999i	$-0.500321\pi$
$691$	22.7253	−	13.1204i	0.864510	−	0.499125i	0.865520	+	0.500874i	$0.166988\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	32.4610	+	18.7413i	1.23131	+	0.710900i
$696$		0			0
$697$		−	4.02112i		−	0.152311i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−23.6200			−0.892116			−0.446058	−	0.895004i	$-0.647173\pi$
$701$	−23.6200			−0.892116			−0.446058	+	0.895004i	$0.647173\pi$
$702$		0			0
$703$	5.39590			0.203510
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	0.678138i		−	0.0255040i
$708$		0			0
$709$	−3.72212	−	2.14897i	−0.139787	−	0.0807063i	0.428475	−	0.903553i	$-0.359051\pi$
$709$	−3.72212	−	2.14897i	−0.139787	−	0.0807063i	−0.568263	+	0.822847i	$0.692384\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−3.69543	+	2.13356i	−0.138395	+	0.0799023i
$714$		0			0
$715$	−35.9321	+	16.1685i	−1.34378	+	0.604666i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	0.0530646	−	0.0919106i	0.00197898	−	0.00342769i	−0.865034	−	0.501713i	$-0.832703\pi$
$719$	0.0530646	−	0.0919106i	0.00197898	−	0.00342769i	0.867013	+	0.498285i	$0.166037\pi$
$720$		0			0
$721$	−18.9282	−	10.9282i	−0.704923	−	0.406988i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	11.6176	+	20.1223i	0.431467	+	0.747322i
$726$		0			0
$727$	−9.79643			−0.363329			−0.181665	−	0.983361i	$-0.558149\pi$
$727$	−9.79643			−0.363329			−0.181665	+	0.983361i	$0.558149\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−9.51717	−	16.4842i	−0.352005	−	0.609691i
$732$		0			0
$733$			1.98379i			0.0732731i	0.999329	+	0.0366366i	$0.0116644\pi$
$733$			1.98379i			0.0732731i	−0.999329	+	0.0366366i	$0.988336\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−15.7385	+	27.2598i	−0.579733	+	1.00413i
$738$		0			0
$739$	−4.50190	+	2.59917i	−0.165605	+	0.0956121i	−0.580512	−	0.814252i	$-0.697148\pi$
$739$	−4.50190	+	2.59917i	−0.165605	+	0.0956121i	0.414907	+	0.909864i	$0.363814\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−15.9989	+	9.23696i	−0.586942	+	0.338871i	−0.763887	−	0.645350i	$-0.776712\pi$
$743$	−15.9989	+	9.23696i	−0.586942	+	0.338871i	0.176945	+	0.984221i	$0.443378\pi$
$744$		0			0
$745$	27.4724	−	47.5837i	1.00651	−	1.74333i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		−	17.7615i		−	0.648992i
$750$		0			0
$751$	−18.3646	−	31.8085i	−0.670135	−	1.16071i	−0.977865	−	0.209235i	$-0.932903\pi$
$751$	−18.3646	−	31.8085i	−0.670135	−	1.16071i	0.307730	−	0.951474i	$-0.400431\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	8.94034			0.325372
$756$		0			0
$757$	12.7385	+	22.0636i	0.462987	+	0.801917i	0.999108	−	0.0422241i	$-0.0134444\pi$
$757$	12.7385	+	22.0636i	0.462987	+	0.801917i	−0.536121	+	0.844141i	$0.680111\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−28.6834	−	16.5604i	−1.03977	−	0.600312i	−0.120003	−	0.992774i	$-0.538290\pi$
$761$	−28.6834	−	16.5604i	−1.03977	−	0.600312i	−0.919769	+	0.392461i	$0.871624\pi$
$762$		0			0
$763$	18.8100	−	32.5799i	0.680968	−	1.17947i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−13.3366	+	18.5096i	−0.481556	+	0.668344i
$768$		0			0
$769$	2.15542	−	1.24443i	0.0777264	−	0.0448754i	−0.460633	−	0.887591i	$-0.652378\pi$
$769$	2.15542	−	1.24443i	0.0777264	−	0.0448754i	0.538359	+	0.842715i	$0.319044\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	13.8492	+	7.99582i	0.498120	+	0.287590i	0.727937	−	0.685644i	$-0.240479\pi$
$773$	13.8492	+	7.99582i	0.498120	+	0.287590i	−0.229817	+	0.973234i	$0.573813\pi$
$774$		0			0
$775$		−	56.0573i		−	2.01364i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−7.55351			−0.270633
$780$		0			0
$781$	35.3155			1.26369
$782$		0			0
$783$		0			0
$784$		0			0
$785$		−	41.9026i		−	1.49557i
$786$		0			0
$787$	25.0453	+	14.4599i	0.892769	+	0.515441i	0.874847	−	0.484399i	$-0.160962\pi$
$787$	25.0453	+	14.4599i	0.892769	+	0.515441i	0.0179219	+	0.999839i	$0.494295\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−32.5706	+	18.8046i	−1.15808	+	0.668615i
$792$		0			0
$793$	−7.08170	−	5.10252i	−0.251479	−	0.181196i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	3.54893	−	6.14693i	0.125710	−	0.217736i	−0.796300	−	0.604901i	$-0.793213\pi$
$797$	3.54893	−	6.14693i	0.125710	−	0.217736i	0.922010	+	0.387166i	$0.126546\pi$
$798$		0			0
$799$	12.4557	+	7.19130i	0.440651	+	0.254410i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−14.4610	−	25.0471i	−0.510317	−	0.883894i
$804$		0			0
$805$	−4.22385			−0.148871
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−3.26868	−	5.66151i	−0.114921	−	0.199048i	0.802827	−	0.596211i	$-0.203328\pi$
$809$	−3.26868	−	5.66151i	−0.114921	−	0.199048i	−0.917748	+	0.397163i	$0.869995\pi$
$810$		0			0
$811$		−	16.3358i		−	0.573627i	−0.957986	−	0.286813i	$-0.907404\pi$
$811$		−	16.3358i		−	0.573627i	0.957986	−	0.286813i	$-0.0925959\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−29.1591	+	50.5050i	−1.02140	+	1.76911i
$816$		0			0
$817$	−30.9650	+	17.8776i	−1.08333	+	0.625459i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	35.9698	−	20.7672i	1.25535	−	0.724779i	0.283186	−	0.959065i	$-0.408609\pi$
$821$	35.9698	−	20.7672i	1.25535	−	0.724779i	0.972168	+	0.234286i	$0.0752752\pi$
$822$		0			0
$823$	−2.66922	+	4.62322i	−0.0930431	+	0.161155i	−0.908790	−	0.417253i	$-0.862993\pi$
$823$	−2.66922	+	4.62322i	−0.0930431	+	0.161155i	0.815747	+	0.578409i	$0.196326\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	22.2608i		−	0.774085i	−0.922062	−	0.387043i	$-0.873497\pi$
$827$		−	22.2608i		−	0.774085i	0.922062	−	0.387043i	$-0.126503\pi$
$828$		0			0
$829$	−20.2276	−	35.0352i	−0.702532	−	1.21682i	−0.967575	−	0.252585i	$-0.918719\pi$
$829$	−20.2276	−	35.0352i	−0.702532	−	1.21682i	0.265042	−	0.964237i	$-0.414614\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	8.60022			0.297980
$834$		0			0
$835$	−16.5296	−	28.6302i	−0.572032	−	0.990788i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	3.42482	+	1.97732i	0.118238	+	0.0682647i	0.557953	−	0.829873i	$-0.311587\pi$
$839$	3.42482	+	1.97732i	0.118238	+	0.0682647i	−0.439715	+	0.898138i	$0.644920\pi$
$840$		0			0
$841$	4.02999	−	6.98015i	0.138965	−	0.240695i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	8.26092	−	40.4335i	0.284184	−	1.39096i
$846$		0			0
$847$	2.53590	−	1.46410i	0.0871345	−	0.0503071i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−0.542299	−	0.313097i	−0.0185898	−	0.0107328i
$852$		0			0
$853$		−	27.7953i		−	0.951692i	−0.879529	−	0.475846i	$-0.842142\pi$
$853$		−	27.7953i		−	0.951692i	0.879529	−	0.475846i	$-0.157858\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−16.5940			−0.566839			−0.283419	−	0.958996i	$-0.591469\pi$
$857$	−16.5940			−0.566839			−0.283419	+	0.958996i	$0.591469\pi$
$858$		0			0
$859$	−36.5932			−1.24854			−0.624271	−	0.781208i	$-0.714604\pi$
$859$	−36.5932			−1.24854			−0.624271	+	0.781208i	$0.714604\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			10.4107i			0.354384i	0.984176	+	0.177192i	$0.0567014\pi$
$863$			10.4107i			0.354384i	−0.984176	+	0.177192i	$0.943299\pi$
$864$		0			0
$865$	17.7593	+	10.2533i	0.603834	+	0.348624i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	24.5175	−	14.1552i	0.831699	−	0.480182i
$870$		0			0
$871$	−13.5282	−	30.0646i	−0.458387	−	1.01870i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	0.423973	−	0.734343i	0.0143329	−	0.0248253i
$876$		0			0
$877$	−5.92136	−	3.41870i	−0.199950	−	0.115441i	0.396682	−	0.917956i	$-0.370162\pi$
$877$	−5.92136	−	3.41870i	−0.199950	−	0.115441i	−0.596632	+	0.802515i	$0.703495\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	8.77024	+	15.1905i	0.295477	+	0.511781i	0.975096	−	0.221784i	$-0.0711881\pi$
$881$	8.77024	+	15.1905i	0.295477	+	0.511781i	−0.679619	+	0.733565i	$0.737855\pi$
$882$		0			0
$883$	3.95506			0.133098			0.0665492	−	0.997783i	$-0.478801\pi$
$883$	3.95506			0.133098			0.0665492	+	0.997783i	$0.478801\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	10.0889	+	17.4744i	0.338750	+	0.586733i	0.984198	−	0.177072i	$-0.0566624\pi$
$887$	10.0889	+	17.4744i	0.338750	+	0.586733i	−0.645448	+	0.763805i	$0.723329\pi$
$888$		0			0
$889$		−	29.6409i		−	0.994124i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	13.5086	−	23.3975i	0.452047	−	0.782969i
$894$		0			0
$895$	−25.2640	+	14.5862i	−0.844482	+	0.487562i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	43.7515	−	25.2600i	1.45920	−	0.842467i
$900$		0			0
$901$	−10.3310	+	17.8939i	−0.344177	+	0.596132i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			6.19793i			0.206026i
$906$		0			0
$907$	15.5242	+	26.8887i	0.515472	+	0.892823i	0.999839	+	0.0179583i	$0.00571660\pi$
$907$	15.5242	+	26.8887i	0.515472	+	0.892823i	−0.484367	+	0.874865i	$0.660950\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	25.2956			0.838082			0.419041	−	0.907967i	$-0.362366\pi$
$911$	25.2956			0.838082			0.419041	+	0.907967i	$0.362366\pi$
$912$		0			0
$913$	−1.91928	−	3.32428i	−0.0635188	−	0.110018i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	9.53109	+	5.50278i	0.314744	+	0.181718i
$918$		0			0
$919$	−24.2447	+	41.9931i	−0.799760	+	1.38522i	0.120012	+	0.992772i	$0.461707\pi$
$919$	−24.2447	+	41.9931i	−0.799760	+	1.38522i	−0.919772	+	0.392452i	$0.871627\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−21.6228	+	30.0100i	−0.711724	+	0.987790i
$924$		0			0
$925$	7.12422	−	4.11317i	0.234243	−	0.135240i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−35.8923	−	20.7224i	−1.17759	−	0.679881i	−0.222133	−	0.975016i	$-0.571302\pi$
$929$	−35.8923	−	20.7224i	−1.17759	−	0.679881i	−0.955455	+	0.295135i	$0.904635\pi$
$930$		0			0
$931$		−	16.1552i		−	0.529465i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	19.3759			0.633660
$936$		0			0
$937$	14.5402			0.475009			0.237504	−	0.971386i	$-0.423671\pi$
$937$	14.5402			0.475009			0.237504	+	0.971386i	$0.423671\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		−	38.0803i		−	1.24138i	−0.784056	−	0.620690i	$-0.786852\pi$
$941$		−	38.0803i		−	1.24138i	0.784056	−	0.620690i	$-0.213148\pi$
$942$		0			0
$943$	0.759143	+	0.438292i	0.0247211	+	0.0142727i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	39.5704	−	22.8460i	1.28586	−	0.742394i	0.307950	−	0.951402i	$-0.400357\pi$
$947$	39.5704	−	22.8460i	1.28586	−	0.742394i	0.977914	+	0.209008i	$0.0670236\pi$
$948$		0			0
$949$	30.1384	+	3.04729i	0.978334	+	0.0989193i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	17.9712	−	31.1271i	0.582145	−	1.00831i	−0.413080	−	0.910695i	$-0.635547\pi$
$953$	17.9712	−	31.1271i	0.582145	−	1.00831i	0.995225	−	0.0976101i	$-0.0311198\pi$
$954$		0			0
$955$	47.3402	+	27.3319i	1.53189	+	0.884438i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−13.9095	−	24.0919i	−0.449160	−	0.777968i
$960$		0			0
$961$	−90.8844			−2.93176
$962$		0			0
$963$		0			0
$964$		0			0
$965$	14.0062	+	24.2594i	0.450875	+	0.780939i
$966$		0			0
$967$			40.3763i			1.29842i	0.760611	+	0.649208i	$0.224899\pi$
$967$			40.3763i			1.29842i	−0.760611	+	0.649208i	$0.775101\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	4.89013	−	8.46996i	0.156932	−	0.271814i	−0.776829	−	0.629712i	$-0.783173\pi$
$971$	4.89013	−	8.46996i	0.156932	−	0.271814i	0.933761	+	0.357898i	$0.116506\pi$
$972$		0			0
$973$	35.2009	−	20.3232i	1.12849	−	0.651533i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−48.6158	+	28.0683i	−1.55536	+	0.897986i	−0.557667	+	0.830065i	$0.688303\pi$
$977$	−48.6158	+	28.0683i	−1.55536	+	0.897986i	−0.997691	+	0.0679208i	$0.978363\pi$
$978$		0			0
$979$	30.6750	−	53.1307i	0.980378	−	1.69806i
$980$		0			0
$981$		0			0
$982$		0			0
$983$		−	18.9028i		−	0.602906i	−0.953481	−	0.301453i	$-0.902528\pi$
$983$		−	18.9028i		−	0.602906i	0.953481	−	0.301453i	$-0.0974716\pi$
$984$		0			0
$985$	21.9383	+	37.9983i	0.699014	+	1.21073i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	4.14939			0.131943
$990$		0			0
$991$	1.82002	+	3.15236i	0.0578147	+	0.100138i	0.893484	−	0.449095i	$-0.148253\pi$
$991$	1.82002	+	3.15236i	0.0578147	+	0.100138i	−0.835669	+	0.549233i	$0.814920\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	68.5125	+	39.5557i	2.17199	+	1.25400i
$996$		0			0
$997$	5.20729	−	9.01929i	0.164916	−	0.285644i	−0.771709	−	0.635976i	$-0.780598\pi$
$997$	5.20729	−	9.01929i	0.164916	−	0.285644i	0.936626	+	0.350332i	$0.113931\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.bi.b.361.4		8
3.2	odd	2		104.2.o.a.49.2	yes	8
4.3	odd	2		1872.2.by.n.1297.4		8
12.11	even	2		208.2.w.c.49.3		8
13.4	even	6	inner	936.2.bi.b.433.1		8
24.5	odd	2		832.2.w.g.257.3		8
24.11	even	2		832.2.w.i.257.2		8
39.2	even	12		1352.2.a.l.1.3		4
39.5	even	4		1352.2.i.l.1329.2		8
39.8	even	4		1352.2.i.k.1329.2		8
39.11	even	12		1352.2.a.k.1.3		4
39.17	odd	6		104.2.o.a.17.2	✓	8
39.20	even	12		1352.2.i.k.529.2		8
39.23	odd	6		1352.2.f.f.337.6		8
39.29	odd	6		1352.2.f.f.337.5		8
39.32	even	12		1352.2.i.l.529.2		8
39.35	odd	6		1352.2.o.f.1161.2		8
39.38	odd	2		1352.2.o.f.361.2		8
52.43	odd	6		1872.2.by.n.433.1		8
156.11	odd	12		2704.2.a.bd.1.2		4
156.23	even	6		2704.2.f.q.337.4		8
156.95	even	6		208.2.w.c.17.3		8
156.107	even	6		2704.2.f.q.337.3		8
156.119	odd	12		2704.2.a.be.1.2		4
312.173	odd	6		832.2.w.g.641.3		8
312.251	even	6		832.2.w.i.641.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.o.a.17.2	✓	8	39.17	odd	6
104.2.o.a.49.2	yes	8	3.2	odd	2
208.2.w.c.17.3		8	156.95	even	6
208.2.w.c.49.3		8	12.11	even	2
832.2.w.g.257.3		8	24.5	odd	2
832.2.w.g.641.3		8	312.173	odd	6
832.2.w.i.257.2		8	24.11	even	2
832.2.w.i.641.2		8	312.251	even	6
936.2.bi.b.361.4		8	1.1	even	1	trivial
936.2.bi.b.433.1		8	13.4	even	6	inner
1352.2.a.k.1.3		4	39.11	even	12
1352.2.a.l.1.3		4	39.2	even	12
1352.2.f.f.337.5		8	39.29	odd	6
1352.2.f.f.337.6		8	39.23	odd	6
1352.2.i.k.529.2		8	39.20	even	12
1352.2.i.k.1329.2		8	39.8	even	4
1352.2.i.l.529.2		8	39.32	even	12
1352.2.i.l.1329.2		8	39.5	even	4
1352.2.o.f.361.2		8	39.38	odd	2
1352.2.o.f.1161.2		8	39.35	odd	6
1872.2.by.n.433.1		8	52.43	odd	6
1872.2.by.n.1297.4		8	4.3	odd	2
2704.2.a.bd.1.2		4	156.11	odd	12
2704.2.a.be.1.2		4	156.119	odd	12
2704.2.f.q.337.3		8	156.107	even	6
2704.2.f.q.337.4		8	156.23	even	6

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:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+3.17452i q^{5} +(2.98127 + 1.72124i) q^{7} +O(q^{10})\)	\(q+3.17452i q^{5} +(2.98127 + 1.72124i) q^{7} +(2.98127 - 1.72124i) q^{11} +(-0.362708 + 3.58726i) q^{13} +(0.886509 - 1.53548i) q^{17} +(-2.88434 - 1.66527i) q^{19} +(0.193255 + 0.334727i) q^{23} -5.07759 q^{25} +(-2.28801 - 3.96296i) q^{29} +11.0401i q^{31} +(-5.46410 + 9.46410i) q^{35} +(-1.40307 + 0.810063i) q^{37} +(1.96410 - 1.13397i) q^{41} +(5.36778 - 9.29726i) q^{43} +8.11192i q^{47} +(2.42531 + 4.20075i) q^{49} -11.6536 q^{53} +(5.46410 + 9.46410i) q^{55} +(5.47970 + 3.16371i) q^{59} +(-1.21042 + 2.09651i) q^{61} +(-11.3878 - 1.15142i) q^{65} +(-7.91867 + 4.57185i) q^{67} +(8.88434 + 5.12937i) q^{71} -8.40150i q^{73} +11.8506 q^{77} +8.22385 q^{79} -1.11506i q^{83} +(4.87441 + 2.81424i) q^{85} +(15.4339 - 8.91075i) q^{89} +(-7.25585 + 10.0703i) q^{91} +(5.28645 - 9.15640i) q^{95} +(3.88205 + 2.24130i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{7}+O(q^{10}) \) 8 * q - 6 * q^7	\( 8 q - 6 q^{7} - 6 q^{11} + 6 q^{13} - 6 q^{19} - 2 q^{23} - 20 q^{25} + 8 q^{29} - 16 q^{35} - 24 q^{37} - 12 q^{41} + 6 q^{43} + 2 q^{49} - 20 q^{53} + 16 q^{55} - 18 q^{59} - 4 q^{61} - 14 q^{65} - 42 q^{67} + 54 q^{71} + 60 q^{77} + 16 q^{79} + 6 q^{85} + 18 q^{89} - 46 q^{91} - 16 q^{95} + 30 q^{97}+O(q^{100}) \) 8 * q - 6 * q^7 - 6 * q^11 + 6 * q^13 - 6 * q^19 - 2 * q^23 - 20 * q^25 + 8 * q^29 - 16 * q^35 - 24 * q^37 - 12 * q^41 + 6 * q^43 + 2 * q^49 - 20 * q^53 + 16 * q^55 - 18 * q^59 - 4 * q^61 - 14 * q^65 - 42 * q^67 + 54 * q^71 + 60 * q^77 + 16 * q^79 + 6 * q^85 + 18 * q^89 - 46 * q^91 - 16 * q^95 + 30 * q^97

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