LMFDB - Embedded newform 300.2.x.a.17.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(17,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 10, 13]))

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

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

chi := DirichletCharacter("300.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.x (of order $20$, degree $8$, 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:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			17.6
Character	$\chi$	$=$	300.17
Dual form			300.2.x.a.53.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.670639 + 1.59695i) q^{3} +(-2.14441 + 0.633635i) q^{5} +(0.907947 + 0.907947i) q^{7} +(-2.10049 + 2.14195i) q^{9} +O(q^{10})$	\(q+(0.670639 + 1.59695i) q^{3} +(-2.14441 + 0.633635i) q^{5} +(0.907947 + 0.907947i) q^{7} +(-2.10049 + 2.14195i) q^{9} +(-1.03855 + 0.337444i) q^{11} +(2.26685 + 4.44893i) q^{13} +(-2.45001 - 2.99958i) q^{15} +(-2.19690 + 0.347955i) q^{17} +(-2.39954 + 3.30268i) q^{19} +(-0.841039 + 2.05885i) q^{21} +(2.13422 - 4.18865i) q^{23} +(4.19701 - 2.71755i) q^{25} +(-4.82925 - 1.91789i) q^{27} +(-0.981024 + 0.712755i) q^{29} +(0.992266 + 0.720923i) q^{31} +(-1.23537 - 1.43220i) q^{33} +(-2.52232 - 1.37171i) q^{35} +(6.47404 - 3.29869i) q^{37} +(-5.58448 + 6.60366i) q^{39} +(8.57625 + 2.78659i) q^{41} +(1.48285 - 1.48285i) q^{43} +(3.14709 - 5.92417i) q^{45} +(-0.0645410 + 0.407496i) q^{47} -5.35127i q^{49} +(-2.02900 - 3.27499i) q^{51} +(13.7949 + 2.18491i) q^{53} +(2.01325 - 1.38168i) q^{55} +(-6.88343 - 1.61703i) q^{57} +(-3.76991 + 11.6026i) q^{59} +(0.344205 + 1.05936i) q^{61} +(-3.85191 + 0.0376491i) q^{63} +(-7.68005 - 8.10400i) q^{65} +(-1.22742 - 7.74963i) q^{67} +(8.12035 + 0.599171i) q^{69} +(6.04759 + 8.32380i) q^{71} +(5.93345 + 3.02324i) q^{73} +(7.15447 + 4.87992i) q^{75} +(-1.24932 - 0.636563i) q^{77} +(-5.56738 - 7.66285i) q^{79} +(-0.175918 - 8.99828i) q^{81} +(-2.79265 - 17.6321i) q^{83} +(4.49059 - 2.13819i) q^{85} +(-1.79615 - 1.08864i) q^{87} +(-4.10757 - 12.6418i) q^{89} +(-1.98122 + 6.09757i) q^{91} +(-0.485825 + 2.06808i) q^{93} +(3.05291 - 8.60274i) q^{95} +(-15.3339 - 2.42865i) q^{97} +(1.45866 - 2.93331i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 2 q^{3} + 4 q^{7}+O(q^{10}) $ 80 * q - 2 * q^3 + 4 * q^7	$ 80 q - 2 q^{3} + 4 q^{7} + 12 q^{13} + 10 q^{15} + 20 q^{19} + 40 q^{25} - 14 q^{27} - 20 q^{33} + 12 q^{37} - 40 q^{39} + 12 q^{43} - 60 q^{45} - 76 q^{57} - 98 q^{63} - 36 q^{67} - 70 q^{69} - 44 q^{73} - 90 q^{75} - 40 q^{79} + 20 q^{81} - 100 q^{85} - 70 q^{87} - 18 q^{93} - 56 q^{97}+O(q^{100}) $ 80 * q - 2 * q^3 + 4 * q^7 + 12 * q^13 + 10 * q^15 + 20 * q^19 + 40 * q^25 - 14 * q^27 - 20 * q^33 + 12 * q^37 - 40 * q^39 + 12 * q^43 - 60 * q^45 - 76 * q^57 - 98 * q^63 - 36 * q^67 - 70 * q^69 - 44 * q^73 - 90 * q^75 - 40 * q^79 + 20 * q^81 - 100 * q^85 - 70 * q^87 - 18 * q^93 - 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$-1$	$1$	$e\left(\frac{13}{20}\right)$

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
$3$	0.670639	+	1.59695i	0.387194	+	0.921998i
$3$	0.670639	+	1.59695i	0.387194	+	0.921998i
$4$		0			0
$5$	−2.14441	+	0.633635i	−0.959011	+	0.283370i
$5$	−2.14441	+	0.633635i	−0.959011	+	0.283370i
$6$		0			0
$7$	0.907947	+	0.907947i	0.343172	+	0.343172i	0.857558	−	0.514387i	$-0.171980\pi$
$7$	0.907947	+	0.907947i	0.343172	+	0.343172i	−0.514387	+	0.857558i	$0.671980\pi$
$8$		0			0
$9$	−2.10049	+	2.14195i	−0.700162	+	0.713984i
$10$		0			0
$11$	−1.03855	+	0.337444i	−0.313133	+	0.101743i	−0.461367	−	0.887209i	$-0.652641\pi$
$11$	−1.03855	+	0.337444i	−0.313133	+	0.101743i	0.148234	+	0.988952i	$0.452641\pi$
$12$		0			0
$13$	2.26685	+	4.44893i	0.628710	+	1.23391i	0.957206	+	0.289407i	$0.0934581\pi$
$13$	2.26685	+	4.44893i	0.628710	+	1.23391i	−0.328496	+	0.944505i	$0.606542\pi$
$14$		0			0
$15$	−2.45001	−	2.99958i	−0.632590	−	0.774487i
$16$		0			0
$17$	−2.19690	+	0.347955i	−0.532827	+	0.0843916i	−0.417050	−	0.908884i	$-0.636936\pi$
$17$	−2.19690	+	0.347955i	−0.532827	+	0.0843916i	−0.115777	+	0.993275i	$0.536936\pi$
$18$		0			0
$19$	−2.39954	+	3.30268i	−0.550491	+	0.757686i	−0.990079	−	0.140513i	$-0.955125\pi$
$19$	−2.39954	+	3.30268i	−0.550491	+	0.757686i	0.439587	+	0.898200i	$0.355125\pi$
$20$		0			0
$21$	−0.841039	+	2.05885i	−0.183530	+	0.449278i
$22$		0			0
$23$	2.13422	−	4.18865i	0.445016	−	0.873394i	−0.554144	−	0.832421i	$-0.686954\pi$
$23$	2.13422	−	4.18865i	0.445016	−	0.873394i	0.999160	−	0.0409730i	$-0.0130458\pi$
$24$		0			0
$25$	4.19701	−	2.71755i	0.839403	−	0.543510i
$26$		0			0
$27$	−4.82925	−	1.91789i	−0.929390	−	0.369098i
$28$		0			0
$29$	−0.981024	+	0.712755i	−0.182172	+	0.132355i	−0.675134	−	0.737695i	$-0.735914\pi$
$29$	−0.981024	+	0.712755i	−0.182172	+	0.132355i	0.492962	+	0.870051i	$0.335914\pi$
$30$		0			0
$31$	0.992266	+	0.720923i	0.178216	+	0.129482i	0.673317	−	0.739354i	$-0.264869\pi$
$31$	0.992266	+	0.720923i	0.178216	+	0.129482i	−0.495101	+	0.868836i	$0.664869\pi$
$32$		0			0
$33$	−1.23537	−	1.43220i	−0.215050	−	0.249314i
$34$		0			0
$35$	−2.52232	−	1.37171i	−0.426350	−	0.231861i
$36$		0			0
$37$	6.47404	−	3.29869i	1.06432	−	0.542301i	0.168040	−	0.985780i	$-0.446256\pi$
$37$	6.47404	−	3.29869i	1.06432	−	0.542301i	0.896284	+	0.443480i	$0.146256\pi$
$38$		0			0
$39$	−5.58448	+	6.60366i	−0.894233	+	1.05743i
$40$		0			0
$41$	8.57625	+	2.78659i	1.33938	+	0.435193i	0.889108	−	0.457697i	$-0.151325\pi$
$41$	8.57625	+	2.78659i	1.33938	+	0.435193i	0.450277	+	0.892889i	$0.351325\pi$
$42$		0			0
$43$	1.48285	−	1.48285i	0.226133	−	0.226133i	−0.584942	−	0.811075i	$-0.698883\pi$
$43$	1.48285	−	1.48285i	0.226133	−	0.226133i	0.811075	+	0.584942i	$0.198883\pi$
$44$		0			0
$45$	3.14709	−	5.92417i	0.469141	−	0.883123i
$46$		0			0
$47$	−0.0645410	+	0.407496i	−0.00941428	+	0.0594394i	−0.991948	−	0.126644i	$-0.959579\pi$
$47$	−0.0645410	+	0.407496i	−0.00941428	+	0.0594394i	0.982534	+	0.186083i	$0.0595794\pi$
$48$		0			0
$49$		−	5.35127i		−	0.764466i
$50$		0			0
$51$	−2.02900	−	3.27499i	−0.284116	−	0.458590i
$52$		0			0
$53$	13.7949	+	2.18491i	1.89488	+	0.300120i	0.991642	−	0.129017i	$-0.0411821\pi$
$53$	13.7949	+	2.18491i	1.89488	+	0.300120i	0.903240	+	0.429136i	$0.141182\pi$
$54$		0			0
$55$	2.01325	−	1.38168i	0.271467	−	0.186305i
$56$		0			0
$57$	−6.88343	−	1.61703i	−0.911732	−	0.214181i
$58$		0			0
$59$	−3.76991	+	11.6026i	−0.490801	+	1.51053i	0.332599	+	0.943068i	$0.392075\pi$
$59$	−3.76991	+	11.6026i	−0.490801	+	1.51053i	−0.823400	+	0.567462i	$0.807925\pi$
$60$		0			0
$61$	0.344205	+	1.05936i	0.0440710	+	0.135637i	0.970671	−	0.240412i	$-0.0772826\pi$
$61$	0.344205	+	1.05936i	0.0440710	+	0.135637i	−0.926600	+	0.376049i	$0.877283\pi$
$62$		0			0
$63$	−3.85191	+	0.0376491i	−0.485295	+	0.00474334i
$64$		0			0
$65$	−7.68005	−	8.10400i	−0.952593	−	1.00518i
$66$		0			0
$67$	−1.22742	−	7.74963i	−0.149953	−	0.946768i	−0.941831	−	0.336088i	$-0.890896\pi$
$67$	−1.22742	−	7.74963i	−0.149953	−	0.946768i	0.791877	−	0.610680i	$-0.209104\pi$
$68$		0			0
$69$	8.12035	+	0.599171i	0.977575	+	0.0721317i
$70$		0			0
$71$	6.04759	+	8.32380i	0.717717	+	0.987853i	0.999597	+	0.0284034i	$0.00904228\pi$
$71$	6.04759	+	8.32380i	0.717717	+	0.987853i	−0.281879	+	0.959450i	$0.590958\pi$
$72$		0			0
$73$	5.93345	+	3.02324i	0.694458	+	0.353844i	0.765327	−	0.643642i	$-0.222577\pi$
$73$	5.93345	+	3.02324i	0.694458	+	0.353844i	−0.0708692	+	0.997486i	$0.522577\pi$
$74$		0			0
$75$	7.15447	+	4.87992i	0.826127	+	0.563484i
$76$		0			0
$77$	−1.24932	−	0.636563i	−0.142374	−	0.0725431i
$78$		0			0
$79$	−5.56738	−	7.66285i	−0.626380	−	0.862138i	0.371418	−	0.928466i	$-0.378872\pi$
$79$	−5.56738	−	7.66285i	−0.626380	−	0.862138i	−0.997798	+	0.0663280i	$0.978872\pi$
$80$		0			0
$81$	−0.175918	−	8.99828i	−0.0195464	−	0.999809i
$82$		0			0
$83$	−2.79265	−	17.6321i	−0.306534	−	1.93538i	−0.351024	−	0.936367i	$-0.614166\pi$
$83$	−2.79265	−	17.6321i	−0.306534	−	1.93538i	0.0444903	−	0.999010i	$-0.485834\pi$
$84$		0			0
$85$	4.49059	−	2.13819i	0.487073	−	0.231920i
$86$		0			0
$87$	−1.79615	−	1.08864i	−0.192567	−	0.116715i
$88$		0			0
$89$	−4.10757	−	12.6418i	−0.435401	−	1.34003i	−0.892675	−	0.450701i	$-0.851174\pi$
$89$	−4.10757	−	12.6418i	−0.435401	−	1.34003i	0.457274	−	0.889326i	$-0.348826\pi$
$90$		0			0
$91$	−1.98122	+	6.09757i	−0.207688	+	0.639199i
$92$		0			0
$93$	−0.485825	+	2.06808i	−0.0503777	+	0.214450i
$94$		0			0
$95$	3.05291	−	8.60274i	0.313221	−	0.882622i
$96$		0			0
$97$	−15.3339	−	2.42865i	−1.55692	−	0.246592i	−0.682180	−	0.731184i	$-0.738968\pi$
$97$	−15.3339	−	2.42865i	−1.55692	−	0.246592i	−0.874740	+	0.484592i	$0.838968\pi$
$98$		0			0
$99$	1.45866	−	2.93331i	0.146601	−	0.294809i
$100$		0			0
$101$			10.8863i			1.08323i	0.840628	+	0.541613i	$0.182186\pi$
$101$			10.8863i			1.08323i	−0.840628	+	0.541613i	$0.817814\pi$
$102$		0			0
$103$	1.29267	−	8.16157i	0.127370	−	0.804184i	−0.838452	−	0.544976i	$-0.816539\pi$
$103$	1.29267	−	8.16157i	0.127370	−	0.804184i	0.965822	−	0.259207i	$-0.0834613\pi$
$104$		0			0
$105$	0.498977	−	4.94793i	0.0486952	−	0.482869i
$106$		0			0
$107$	−6.56922	+	6.56922i	−0.635071	+	0.635071i	−0.949335	−	0.314265i	$-0.898242\pi$
$107$	−6.56922	+	6.56922i	−0.635071	+	0.635071i	0.314265	+	0.949335i	$0.398242\pi$
$108$		0			0
$109$	18.5165	+	6.01639i	1.77356	+	0.576265i	0.998455	−	0.0555636i	$-0.0176956\pi$
$109$	18.5165	+	6.01639i	1.77356	+	0.576265i	0.775108	+	0.631829i	$0.217696\pi$
$110$		0			0
$111$	9.60957	+	8.12647i	0.912100	+	0.771330i
$112$		0			0
$113$	5.59661	−	2.85162i	0.526485	−	0.268258i	−0.170482	−	0.985361i	$-0.554532\pi$
$113$	5.59661	−	2.85162i	0.526485	−	0.268258i	0.696967	+	0.717103i	$0.254532\pi$
$114$		0			0
$115$	−1.92258	+	10.3345i	−0.179282	+	0.963698i
$116$		0			0
$117$	−14.2909	−	4.48945i	−1.32119	−	0.415050i
$118$		0			0
$119$	−2.31060	−	1.67875i	−0.211812	−	0.153890i
$120$		0			0
$121$	−7.93448	+	5.76474i	−0.721316	+	0.524067i
$122$		0			0
$123$	1.30153	+	15.5646i	0.117355	+	1.40341i
$124$		0			0
$125$	−7.27820	+	8.48692i	−0.650982	+	0.759093i
$126$		0			0
$127$	−1.64120	+	3.22104i	−0.145633	+	0.285821i	−0.952287	−	0.305203i	$-0.901276\pi$
$127$	−1.64120	+	3.22104i	−0.145633	+	0.285821i	0.806655	+	0.591023i	$0.201276\pi$
$128$		0			0
$129$	3.36250	+	1.37358i	0.296052	+	0.120937i
$130$		0			0
$131$	−6.57127	+	9.04457i	−0.574134	+	0.790228i	−0.993037	−	0.117803i	$-0.962415\pi$
$131$	−6.57127	+	9.04457i	−0.574134	+	0.790228i	0.418903	+	0.908031i	$0.362415\pi$
$132$		0			0
$133$	−5.17731	+	0.820005i	−0.448930	+	0.0711034i
$134$		0			0
$135$	11.5712	+	1.05276i	0.995887	+	0.0906075i
$136$		0			0
$137$	5.59033	+	10.9716i	0.477615	+	0.937371i	0.996585	+	0.0825788i	$0.0263156\pi$
$137$	5.59033	+	10.9716i	0.477615	+	0.937371i	−0.518970	+	0.854792i	$0.673684\pi$
$138$		0			0
$139$	−15.7315	+	5.11149i	−1.33433	+	0.433551i	−0.887393	−	0.461014i	$-0.847486\pi$
$139$	−15.7315	+	5.11149i	−1.33433	+	0.433551i	−0.446939	+	0.894565i	$0.647486\pi$
$140$		0			0
$141$	−0.694034	+	0.170214i	−0.0584482	+	0.0143346i
$142$		0			0
$143$	−3.85549	−	3.85549i	−0.322412	−	0.322412i
$144$		0			0
$145$	1.65209	−	2.15005i	0.137199	−	0.178552i
$146$		0			0
$147$	8.54569	−	3.58877i	0.704837	−	0.295997i
$148$		0			0
$149$	−7.21459			−0.591042			−0.295521	−	0.955336i	$-0.595493\pi$
$149$	−7.21459			−0.591042			−0.295521	+	0.955336i	$0.595493\pi$
$150$		0			0
$151$	−8.59485			−0.699439			−0.349719	−	0.936854i	$-0.613723\pi$
$151$	−8.59485			−0.699439			−0.349719	+	0.936854i	$0.613723\pi$
$152$		0			0
$153$	3.86926	−	5.43654i	0.312811	−	0.439518i
$154$		0			0
$155$	−2.58463	−	0.917223i	−0.207603	−	0.0736732i
$156$		0			0
$157$	9.22284	+	9.22284i	0.736063	+	0.736063i	0.971814	−	0.235751i	$-0.0757550\pi$
$157$	9.22284	+	9.22284i	0.736063	+	0.736063i	−0.235751	+	0.971814i	$0.575755\pi$
$158$		0			0
$159$	5.76225	+	23.4951i	0.456977	+	1.86328i
$160$		0			0
$161$	5.74083	−	1.86531i	0.452441	−	0.147007i
$162$		0			0
$163$	0.429156	+	0.842267i	0.0336141	+	0.0659714i	0.907203	−	0.420694i	$-0.138213\pi$
$163$	0.429156	+	0.842267i	0.0336141	+	0.0659714i	−0.873589	+	0.486665i	$0.838213\pi$
$164$		0			0
$165$	3.55663	+	2.28845i	0.276884	+	0.178156i
$166$		0			0
$167$	23.0479	−	3.65042i	1.78350	−	0.282478i	0.824494	−	0.565871i	$-0.191460\pi$
$167$	23.0479	−	3.65042i	1.78350	−	0.282478i	0.959004	+	0.283393i	$0.0914601\pi$
$168$		0			0
$169$	−7.01322	+	9.65287i	−0.539479	+	0.742529i
$170$		0			0
$171$	−2.03399	−	12.0769i	−0.155543	−	0.923545i
$172$		0			0
$173$	−1.70415	+	3.34458i	−0.129564	+	0.254284i	−0.946671	−	0.322203i	$-0.895577\pi$
$173$	−1.70415	+	3.34458i	−0.129564	+	0.254284i	0.817107	+	0.576487i	$0.195577\pi$
$174$		0			0
$175$	6.27806	+	1.34328i	0.474576	+	0.101542i
$176$		0			0
$177$	−21.0570	+	1.76080i	−1.58274	+	0.132350i
$178$		0			0
$179$	8.16937	−	5.93539i	0.610607	−	0.443632i	−0.239021	−	0.971014i	$-0.576826\pi$
$179$	8.16937	−	5.93539i	0.610607	−	0.443632i	0.849628	+	0.527382i	$0.176826\pi$
$180$		0			0
$181$	9.96400	+	7.23927i	0.740618	+	0.538091i	0.892905	−	0.450246i	$-0.148664\pi$
$181$	9.96400	+	7.23927i	0.740618	+	0.538091i	−0.152286	+	0.988336i	$0.548664\pi$
$182$		0			0
$183$	−1.46090	+	1.26012i	−0.107993	+	0.0931510i
$184$		0			0
$185$	−11.7928	+	11.1759i	−0.867027	+	0.821670i
$186$		0			0
$187$	2.16417	−	1.10270i	0.158260	−	0.0806373i
$188$		0			0
$189$	−2.64336	−	6.12605i	−0.192276	−	0.445604i
$190$		0			0
$191$	−12.2290	−	3.97343i	−0.884858	−	0.287508i	−0.168885	−	0.985636i	$-0.554017\pi$
$191$	−12.2290	−	3.97343i	−0.884858	−	0.287508i	−0.715973	+	0.698128i	$0.754017\pi$
$192$		0			0
$193$	−9.96950	+	9.96950i	−0.717620	+	0.717620i	−0.968117	−	0.250497i	$-0.919406\pi$
$193$	−9.96950	+	9.96950i	−0.717620	+	0.717620i	0.250497	+	0.968117i	$0.419406\pi$
$194$		0			0
$195$	7.79112	−	17.6995i	0.557934	−	1.26749i
$196$		0			0
$197$	1.20326	−	7.59705i	0.0857284	−	0.541268i	−0.907023	−	0.421081i	$-0.861651\pi$
$197$	1.20326	−	7.59705i	0.0857284	−	0.541268i	0.992751	−	0.120186i	$-0.0383493\pi$
$198$		0			0
$199$		−	16.0864i		−	1.14033i	−0.821530	−	0.570166i	$-0.806879\pi$
$199$		−	16.0864i		−	1.14033i	0.821530	−	0.570166i	$-0.193121\pi$
$200$		0			0
$201$	11.5526	−	7.15733i	0.814858	−	0.504839i
$202$		0			0
$203$	−1.53786	−	0.243573i	−0.107937	−	0.0170955i
$204$		0			0
$205$	−20.1567	−	0.541395i	−1.40780	−	0.0378127i
$206$		0			0
$207$	4.48898	+	13.3696i	0.312006	+	0.929252i
$208$		0			0
$209$	1.37756	−	4.23969i	0.0952877	−	0.293265i
$210$		0			0
$211$	−6.96750	−	21.4437i	−0.479662	−	1.47625i	−0.839565	−	0.543259i	$-0.817190\pi$
$211$	−6.96750	−	21.4437i	−0.479662	−	1.47625i	0.359903	−	0.932990i	$-0.382810\pi$
$212$		0			0
$213$	−9.23692	+	15.2400i	−0.632903	+	1.04422i
$214$		0			0
$215$	−2.24026	+	4.11944i	−0.152785	+	0.280943i
$216$		0			0
$217$	0.246365	+	1.55548i	0.0167243	+	0.105593i
$218$		0			0
$219$	−0.848758	+	11.5029i	−0.0573538	+	0.777295i
$220$		0			0
$221$	−6.52807	−	8.98512i	−0.439126	−	0.604404i
$222$		0			0
$223$	−10.1560	−	5.17474i	−0.680097	−	0.346526i	0.0795792	−	0.996829i	$-0.474642\pi$
$223$	−10.1560	−	5.17474i	−0.680097	−	0.346526i	−0.759676	+	0.650302i	$0.774642\pi$
$224$		0			0
$225$	−2.99491	+	14.6980i	−0.199661	+	0.979865i
$226$		0			0
$227$	12.6380	+	6.43937i	0.838812	+	0.427396i	0.819956	−	0.572426i	$-0.193998\pi$
$227$	12.6380	+	6.43937i	0.838812	+	0.427396i	0.0188557	+	0.999822i	$0.493998\pi$
$228$		0			0
$229$	2.06221	+	2.83839i	0.136275	+	0.187566i	0.871700	−	0.490039i	$-0.163018\pi$
$229$	2.06221	+	2.83839i	0.136275	+	0.187566i	−0.735425	+	0.677606i	$0.763018\pi$
$230$		0			0
$231$	0.178711	−	2.42201i	0.0117583	−	0.159357i
$232$		0			0
$233$	−0.450064	−	2.84159i	−0.0294847	−	0.186159i	0.968550	−	0.248818i	$-0.0800420\pi$
$233$	−0.450064	−	2.84159i	−0.0294847	−	0.186159i	−0.998035	+	0.0626588i	$0.980042\pi$
$234$		0			0
$235$	−0.119801	−	0.914735i	−0.00781496	−	0.0596708i
$236$		0			0
$237$	8.50346	−	14.0298i	0.552359	−	0.911335i
$238$		0			0
$239$	−4.44446	−	13.6787i	−0.287488	−	0.884798i	−0.985642	−	0.168850i	$-0.945995\pi$
$239$	−4.44446	−	13.6787i	−0.287488	−	0.884798i	0.698153	−	0.715948i	$-0.254005\pi$
$240$		0			0
$241$	0.877493	−	2.70064i	0.0565243	−	0.173964i	−0.918808	−	0.394704i	$-0.870847\pi$
$241$	0.877493	−	2.70064i	0.0565243	−	0.173964i	0.975333	+	0.220740i	$0.0708472\pi$
$242$		0			0
$243$	14.2518	−	6.31553i	0.914254	−	0.405142i
$244$		0			0
$245$	3.39075	+	11.4753i	0.216627	+	0.733131i
$246$		0			0
$247$	−20.1328	−	3.18872i	−1.28102	−	0.202893i
$248$		0			0
$249$	26.2847	−	16.2845i	1.66573	−	1.03199i
$250$		0			0
$251$			12.8469i			0.810891i	0.914119	+	0.405445i	$0.132884\pi$
$251$			12.8469i			0.810891i	−0.914119	+	0.405445i	$0.867116\pi$
$252$		0			0
$253$	−0.803054	+	5.07028i	−0.0504876	+	0.318766i
$254$		0			0
$255$	6.42615	+	5.73728i	0.402421	+	0.359283i
$256$		0			0
$257$	9.47863	−	9.47863i	0.591261	−	0.591261i	−0.346711	−	0.937972i	$-0.612702\pi$
$257$	9.47863	−	9.47863i	0.591261	−	0.591261i	0.937972	+	0.346711i	$0.112702\pi$
$258$		0			0
$259$	8.87311	+	2.88305i	0.551348	+	0.179144i
$260$		0			0
$261$	0.533938	−	3.59844i	0.0330500	−	0.222738i
$262$		0			0
$263$	2.07596	−	1.05775i	0.128009	−	0.0652239i	−0.388813	−	0.921317i	$-0.627115\pi$
$263$	2.07596	−	1.05775i	0.128009	−	0.0652239i	0.516822	+	0.856093i	$0.327115\pi$
$264$		0			0
$265$	−30.9665	+	4.05562i	−1.90226	+	0.249135i
$266$		0			0
$267$	17.4336	−	15.0377i	1.06692	−	0.920289i
$268$		0			0
$269$	−22.3119	−	16.2105i	−1.36038	−	0.988373i	−0.998421	−	0.0561787i	$-0.982108\pi$
$269$	−22.3119	−	16.2105i	−1.36038	−	0.988373i	−0.361958	−	0.932194i	$-0.617892\pi$
$270$		0			0
$271$	25.5707	−	18.5782i	1.55331	−	1.12854i	0.612069	−	0.790805i	$-0.290338\pi$
$271$	25.5707	−	18.5782i	1.55331	−	1.12854i	0.941239	−	0.337740i	$-0.109662\pi$
$272$		0			0
$273$	−11.0662	+	0.925364i	−0.669756	+	0.0560056i
$274$		0			0
$275$	−3.44177	+	4.23855i	−0.207546	+	0.255594i
$276$		0			0
$277$	3.14609	−	6.17455i	0.189030	−	0.370993i	−0.776969	−	0.629539i	$-0.783244\pi$
$277$	3.14609	−	6.17455i	0.189030	−	0.370993i	0.965999	+	0.258547i	$0.0832436\pi$
$278$		0			0
$279$	−3.62842	+	0.611097i	−0.217228	+	0.0365854i
$280$		0			0
$281$	3.62737	−	4.99264i	0.216391	−	0.297836i	−0.686998	−	0.726660i	$-0.741072\pi$
$281$	3.62737	−	4.99264i	0.216391	−	0.297836i	0.903388	+	0.428823i	$0.141072\pi$
$282$		0			0
$283$	3.40261	−	0.538921i	0.202264	−	0.0320355i	−0.0544801	−	0.998515i	$-0.517350\pi$
$283$	3.40261	−	0.538921i	0.202264	−	0.0320355i	0.256744	+	0.966479i	$0.417350\pi$
$284$		0			0
$285$	15.7855	−	0.894002i	0.935054	−	0.0529561i
$286$		0			0
$287$	5.25670	+	10.3169i	0.310293	+	0.608985i
$288$		0			0
$289$	−11.4626	+	3.72444i	−0.674274	+	0.219085i
$290$		0			0
$291$	−6.40508	−	26.1162i	−0.375473	−	1.53096i
$292$		0			0
$293$	14.3870	+	14.3870i	0.840500	+	0.840500i	0.988924	−	0.148424i	$-0.0474199\pi$
$293$	14.3870	+	14.3870i	0.840500	+	0.840500i	−0.148424	+	0.988924i	$0.547420\pi$
$294$		0			0
$295$	0.732441	−	27.2695i	0.0426444	−	1.58769i
$296$		0			0
$297$	5.66258	+	0.362213i	0.328576	+	0.0210177i
$298$		0			0
$299$	23.4730			1.35748
$300$		0			0
$301$	2.69270			0.155205
$302$		0			0
$303$	−17.3848	+	7.30077i	−0.998732	+	0.419418i
$304$		0			0
$305$	−1.40936	−	2.05360i	−0.0806999	−	0.117589i
$306$		0			0
$307$	21.8121	+	21.8121i	1.24488	+	1.24488i	0.957950	+	0.286934i	$0.0926362\pi$
$307$	21.8121	+	21.8121i	1.24488	+	1.24488i	0.286934	+	0.957950i	$0.407364\pi$
$308$		0			0
$309$	13.9005	−	3.40915i	0.790773	−	0.193940i
$310$		0			0
$311$	−23.6419	+	7.68170i	−1.34061	+	0.435589i	−0.889522	−	0.456892i	$-0.848963\pi$
$311$	−23.6419	+	7.68170i	−1.34061	+	0.435589i	−0.451084	+	0.892481i	$0.648963\pi$
$312$		0			0
$313$	−5.16865	−	10.1440i	−0.292149	−	0.573375i	0.697550	−	0.716536i	$-0.254273\pi$
$313$	−5.16865	−	10.1440i	−0.292149	−	0.573375i	−0.989699	+	0.143161i	$0.954273\pi$
$314$		0			0
$315$	8.23623	−	2.52144i	0.464059	−	0.142067i
$316$		0			0
$317$	15.6631	−	2.48079i	0.879728	−	0.139335i	0.299799	−	0.954002i	$-0.403080\pi$
$317$	15.6631	−	2.48079i	0.879728	−	0.139335i	0.579929	+	0.814667i	$0.303080\pi$
$318$		0			0
$319$	0.778322	−	1.07127i	0.0435777	−	0.0599795i
$320$		0			0
$321$	−14.8963	−	6.08513i	−0.831429	−	0.339639i
$322$		0			0
$323$	4.12236	−	8.09060i	0.229375	−	0.450173i
$324$		0			0
$325$	21.6042	+	12.5120i	1.19838	+	0.694040i
$326$		0			0
$327$	2.81006	+	33.6048i	0.155397	+	1.85835i
$328$		0			0
$329$	−0.428585	+	0.311385i	−0.0236286	+	0.0171672i
$330$		0			0
$331$	−10.2103	−	7.41821i	−0.561209	−	0.407742i	0.270693	−	0.962666i	$-0.412747\pi$
$331$	−10.2103	−	7.41821i	−0.561209	−	0.407742i	−0.831901	+	0.554924i	$0.812747\pi$
$332$		0			0
$333$	−6.53299	+	20.7959i	−0.358006	+	1.13961i
$334$		0			0
$335$	7.54253	+	15.8407i	0.412093	+	0.865468i
$336$		0			0
$337$	4.25752	−	2.16931i	0.231922	−	0.118170i	−0.334168	−	0.942513i	$-0.608455\pi$
$337$	4.25752	−	2.16931i	0.231922	−	0.118170i	0.566090	+	0.824343i	$0.308455\pi$
$338$		0			0
$339$	8.30719	+	7.02510i	0.451185	+	0.381551i
$340$		0			0
$341$	−1.27378	−	0.413878i	−0.0689793	−	0.0224127i
$342$		0			0
$343$	11.2143	−	11.2143i	0.605515	−	0.605515i
$344$		0			0
$345$	−17.7930	+	3.86047i	−0.957945	+	0.207840i
$346$		0			0
$347$	2.24653	−	14.1841i	0.120600	−	0.761440i	−0.851062	−	0.525066i	$-0.824041\pi$
$347$	2.24653	−	14.1841i	0.120600	−	0.761440i	0.971662	−	0.236374i	$-0.0759592\pi$
$348$		0			0
$349$		−	20.9612i		−	1.12203i	−0.827807	−	0.561013i	$-0.810412\pi$
$349$		−	20.9612i		−	1.12203i	0.827807	−	0.561013i	$-0.189588\pi$
$350$		0			0
$351$	−2.41461	−	25.8326i	−0.128882	−	1.37884i
$352$		0			0
$353$	−4.85452	−	0.768881i	−0.258380	−	0.0409234i	0.0259004	−	0.999665i	$-0.491755\pi$
$353$	−4.85452	−	0.768881i	−0.258380	−	0.0409234i	−0.284281	+	0.958741i	$0.591755\pi$
$354$		0			0
$355$	−18.2428	−	14.0177i	−0.968227	−	0.743982i
$356$		0			0
$357$	1.13129	−	4.81574i	0.0598744	−	0.254876i
$358$		0			0
$359$	2.41734	−	7.43981i	0.127582	−	0.392658i	−0.866780	−	0.498690i	$-0.833815\pi$
$359$	2.41734	−	7.43981i	0.127582	−	0.392658i	0.994363	+	0.106032i	$0.0338146\pi$
$360$		0			0
$361$	0.721413	+	2.22028i	0.0379691	+	0.116857i
$362$		0			0
$363$	−14.5272	−	8.80489i	−0.762478	−	0.462137i
$364$		0			0
$365$	−14.6394	−	2.72344i	−0.766261	−	0.142552i
$366$		0			0
$367$	2.47261	+	15.6115i	0.129069	+	0.814912i	0.964261	+	0.264953i	$0.0853565\pi$
$367$	2.47261	+	15.6115i	0.129069	+	0.814912i	−0.835192	+	0.549959i	$0.814643\pi$
$368$		0			0
$369$	−23.9830	+	12.5167i	−1.24851	+	0.651594i
$370$		0			0
$371$	10.5413	+	14.5089i	0.547277	+	0.753262i
$372$		0			0
$373$	−14.5011	−	7.38868i	−0.750838	−	0.382571i	0.0363057	−	0.999341i	$-0.488441\pi$
$373$	−14.5011	−	7.38868i	−0.750838	−	0.382571i	−0.787144	+	0.616770i	$0.788441\pi$
$374$		0			0
$375$	−18.4342	−	5.93124i	−0.951939	−	0.306288i
$376$		0			0
$377$	−5.39483	−	2.74880i	−0.277848	−	0.141571i
$378$		0			0
$379$	19.2777	+	26.5335i	0.990229	+	1.36293i	0.931133	+	0.364681i	$0.118822\pi$
$379$	19.2777	+	26.5335i	0.990229	+	1.36293i	0.0590965	+	0.998252i	$0.481178\pi$
$380$		0			0
$381$	−6.24448	−	0.460757i	−0.319914	−	0.0236053i
$382$		0			0
$383$	2.51909	+	15.9049i	0.128720	+	0.812703i	0.964586	+	0.263770i	$0.0849659\pi$
$383$	2.51909	+	15.9049i	0.128720	+	0.812703i	−0.835866	+	0.548933i	$0.815034\pi$
$384$		0			0
$385$	3.08242	+	0.573438i	0.157094	+	0.0292251i
$386$		0			0
$387$	0.0614883	+	6.29091i	0.00312563	+	0.319785i
$388$		0			0
$389$	−7.88904	−	24.2800i	−0.399990	−	1.23104i	−0.925007	−	0.379951i	$-0.875941\pi$
$389$	−7.88904	−	24.2800i	−0.399990	−	1.23104i	0.525017	−	0.851092i	$-0.324059\pi$
$390$		0			0
$391$	−3.23122	+	9.94467i	−0.163410	+	0.502924i
$392$		0			0
$393$	−18.8507	−	4.42832i	−0.950890	−	0.223379i
$394$		0			0
$395$	16.7942	+	12.9046i	0.845009	+	0.649302i
$396$		0			0
$397$	−2.82041	−	0.446710i	−0.141553	−	0.0224197i	0.0852560	−	0.996359i	$-0.472829\pi$
$397$	−2.82041	−	0.446710i	−0.141553	−	0.0224197i	−0.226809	+	0.973939i	$0.572829\pi$
$398$		0			0
$399$	−4.78161	−	7.71796i	−0.239380	−	0.386381i
$400$		0			0
$401$		−	27.6582i		−	1.38119i	−0.723244	−	0.690593i	$-0.757350\pi$
$401$		−	27.6582i		−	1.38119i	0.723244	−	0.690593i	$-0.242650\pi$
$402$		0			0
$403$	−0.958028	+	6.04875i	−0.0477228	+	0.301310i
$404$		0			0
$405$	6.07886	+	19.1846i	0.302061	+	0.953289i
$406$		0			0
$407$	−5.61046	+	5.61046i	−0.278100	+	0.278100i
$408$		0			0
$409$	25.9665	+	8.43701i	1.28396	+	0.417183i	0.869973	−	0.493100i	$-0.164136\pi$
$409$	25.9665	+	8.43701i	1.28396	+	0.417183i	0.413986	+	0.910283i	$0.364136\pi$
$410$		0			0
$411$	−13.7721	+	16.2855i	−0.679325	+	0.803304i
$412$		0			0
$413$	−13.9574	+	7.11166i	−0.686800	+	0.349942i
$414$		0			0
$415$	17.1609	+	36.0410i	0.842397	+	1.76918i
$416$		0			0
$417$	−18.7130	−	21.6945i	−0.916378	−	1.06238i
$418$		0			0
$419$	−14.7007	−	10.6807i	−0.718178	−	0.521787i	0.167624	−	0.985851i	$-0.446391\pi$
$419$	−14.7007	−	10.6807i	−0.718178	−	0.521787i	−0.885802	+	0.464064i	$0.846391\pi$
$420$		0			0
$421$	−0.685185	+	0.497816i	−0.0333939	+	0.0242621i	−0.604357	−	0.796714i	$-0.706570\pi$
$421$	−0.685185	+	0.497816i	−0.0333939	+	0.0242621i	0.570963	+	0.820976i	$0.306570\pi$
$422$		0			0
$423$	−0.737270	−	0.994184i	−0.0358473	−	0.0483389i
$424$		0			0
$425$	−8.27485	+	7.43057i	−0.401389	+	0.360435i
$426$		0			0
$427$	−0.649318	+	1.27436i	−0.0314227	+	0.0616705i
$428$		0			0
$429$	3.57137	−	8.74265i	0.172427	−	0.422099i
$430$		0			0
$431$	−11.3436	+	15.6131i	−0.546401	+	0.752057i	−0.989518	−	0.144407i	$-0.953873\pi$
$431$	−11.3436	+	15.6131i	−0.546401	+	0.752057i	0.443117	+	0.896464i	$0.353873\pi$
$432$		0			0
$433$	14.7512	−	2.33636i	0.708897	−	0.112278i	0.208434	−	0.978036i	$-0.433163\pi$
$433$	14.7512	−	2.33636i	0.708897	−	0.112278i	0.500463	+	0.865758i	$0.333163\pi$
$434$		0			0
$435$	4.54148	+	1.19640i	0.217747	+	0.0573629i
$436$		0			0
$437$	8.71262	+	17.0995i	0.416781	+	0.817979i
$438$		0			0
$439$	3.77327	−	1.22601i	0.180088	−	0.0585143i	−0.217585	−	0.976041i	$-0.569818\pi$
$439$	3.77327	−	1.22601i	0.180088	−	0.0585143i	0.397673	+	0.917527i	$0.369818\pi$
$440$		0			0
$441$	11.4622	+	11.2403i	0.545817	+	0.535250i
$442$		0			0
$443$	−20.1922	−	20.1922i	−0.959360	−	0.959360i	0.0398456	−	0.999206i	$-0.487313\pi$
$443$	−20.1922	−	20.1922i	−0.959360	−	0.959360i	−0.999206	+	0.0398456i	$0.987313\pi$
$444$		0			0
$445$	16.8186	+	24.5065i	0.797278	+	1.16172i
$446$		0			0
$447$	−4.83839	−	11.5213i	−0.228848	−	0.544940i
$448$		0			0
$449$	19.6086			0.925387			0.462693	−	0.886518i	$-0.346883\pi$
$449$	19.6086			0.925387			0.462693	+	0.886518i	$0.346883\pi$
$450$		0			0
$451$	−9.84714			−0.463684
$452$		0			0
$453$	−5.76404	−	13.7255i	−0.270818	−	0.644882i
$454$		0			0
$455$	0.384923	−	14.3311i	0.0180455	−	0.671851i
$456$		0			0
$457$	0.286369	+	0.286369i	0.0133958	+	0.0133958i	0.713773	−	0.700377i	$-0.246985\pi$
$457$	0.286369	+	0.286369i	0.0133958	+	0.0133958i	−0.700377	+	0.713773i	$0.746985\pi$
$458$		0			0
$459$	11.2767	+	2.53305i	0.526353	+	0.118233i
$460$		0			0
$461$	7.31001	−	2.37517i	0.340461	−	0.110623i	−0.133796	−	0.991009i	$-0.542717\pi$
$461$	7.31001	−	2.37517i	0.340461	−	0.110623i	0.474257	+	0.880386i	$0.342717\pi$
$462$		0			0
$463$	−2.82556	−	5.54548i	−0.131315	−	0.257720i	0.815982	−	0.578078i	$-0.196197\pi$
$463$	−2.82556	−	5.54548i	−0.131315	−	0.257720i	−0.947297	+	0.320358i	$0.896197\pi$
$464$		0			0
$465$	−0.268596	−	4.74265i	−0.0124559	−	0.219935i
$466$		0			0
$467$	2.70390	−	0.428256i	0.125122	−	0.0198173i	−0.0935595	−	0.995614i	$-0.529825\pi$
$467$	2.70390	−	0.428256i	0.125122	−	0.0198173i	0.218681	+	0.975796i	$0.429825\pi$
$468$		0			0
$469$	5.92182	−	8.15069i	0.273444	−	0.376364i
$470$		0			0
$471$	−8.54320	+	20.9136i	−0.393650	+	0.963647i
$472$		0			0
$473$	−1.03963	+	2.04039i	−0.0478023	+	0.0938172i
$474$		0			0
$475$	−1.09570	+	20.3822i	−0.0502740	+	0.935202i
$476$		0			0
$477$	−33.6561	+	24.9588i	−1.54101	+	1.14278i
$478$		0			0
$479$	−5.68590	+	4.13105i	−0.259796	+	0.188753i	−0.710057	−	0.704144i	$-0.751331\pi$
$479$	−5.68590	+	4.13105i	−0.259796	+	0.188753i	0.450261	+	0.892897i	$0.351331\pi$
$480$		0			0
$481$	29.3513	+	21.3249i	1.33830	+	0.972334i
$482$		0			0
$483$	6.82883	+	7.91686i	0.310723	+	0.360230i
$484$		0			0
$485$	34.4211	−	4.50806i	1.56298	−	0.204700i
$486$		0			0
$487$	7.03443	−	3.58422i	0.318761	−	0.162417i	−0.287288	−	0.957844i	$-0.592754\pi$
$487$	7.03443	−	3.58422i	0.318761	−	0.162417i	0.606049	+	0.795428i	$0.292754\pi$
$488$		0			0
$489$	−1.05725	+	1.25020i	−0.0478104	+	0.0565359i
$490$		0			0
$491$	−7.06686	−	2.29616i	−0.318923	−	0.103624i	0.145181	−	0.989405i	$-0.453624\pi$
$491$	−7.06686	−	2.29616i	−0.318923	−	0.103624i	−0.464104	+	0.885781i	$0.653624\pi$
$492$		0			0
$493$	1.90721	−	1.90721i	0.0858963	−	0.0858963i
$494$		0			0
$495$	−1.26932	+	7.21449i	−0.0570519	+	0.324267i
$496$		0			0
$497$	−2.06667	+	13.0485i	−0.0927030	+	0.585303i
$498$		0			0
$499$		−	16.9596i		−	0.759216i	−0.925147	−	0.379608i	$-0.876059\pi$
$499$		−	16.9596i		−	0.759216i	0.925147	−	0.379608i	$-0.123941\pi$
$500$		0			0
$501$	21.2863	+	34.3581i	0.951004	+	1.53501i
$502$		0			0
$503$	−37.8665	−	5.99747i	−1.68839	−	0.267414i	−0.762988	−	0.646412i	$-0.776269\pi$
$503$	−37.8665	−	5.99747i	−1.68839	−	0.267414i	−0.925397	+	0.378998i	$0.876269\pi$
$504$		0			0
$505$	−6.89793	−	23.3447i	−0.306954	−	1.03882i
$506$		0			0
$507$	−20.1185	−	4.72616i	−0.893493	−	0.209896i
$508$		0			0
$509$	−7.22530	+	22.2372i	−0.320256	+	0.985646i	0.653281	+	0.757116i	$0.273392\pi$
$509$	−7.22530	+	22.2372i	−0.320256	+	0.985646i	−0.973537	+	0.228531i	$0.926608\pi$
$510$		0			0
$511$	2.64231	+	8.13220i	0.116889	+	0.359747i
$512$		0			0
$513$	17.9221	−	11.3474i	0.791282	−	0.501001i
$514$		0			0
$515$	2.39945	+	18.3209i	0.105732	+	0.807313i
$516$		0			0
$517$	−0.0704782	−	0.444982i	−0.00309963	−	0.0195703i
$518$		0			0
$519$	−6.48399	−	0.478430i	−0.284616	−	0.0210008i
$520$		0			0
$521$	−6.11512	−	8.41674i	−0.267908	−	0.368744i	0.653774	−	0.756690i	$-0.273185\pi$
$521$	−6.11512	−	8.41674i	−0.267908	−	0.368744i	−0.921682	+	0.387946i	$0.873185\pi$
$522$		0			0
$523$	29.8122	+	15.1901i	1.30360	+	0.664216i	0.961333	−	0.275389i	$-0.0888065\pi$
$523$	29.8122	+	15.1901i	1.30360	+	0.664216i	0.342263	+	0.939604i	$0.388806\pi$
$524$		0			0
$525$	2.06517	+	10.9266i	0.0901314	+	0.476875i
$526$		0			0
$527$	−2.43076	−	1.23853i	−0.105886	−	0.0539514i
$528$		0			0
$529$	0.529182	+	0.728357i	0.0230079	+	0.0316677i
$530$		0			0
$531$	−16.9336	−	32.4461i	−0.734854	−	1.40804i
$532$		0			0
$533$	7.04366	+	44.4719i	0.305095	+	1.92629i
$534$		0			0
$535$	9.92464	−	18.2496i	0.429079	−	0.788999i
$536$		0			0
$537$	14.9572	+	9.06555i	0.645451	+	0.391207i
$538$		0			0
$539$	1.80575	+	5.55753i	0.0777792	+	0.239380i
$540$		0			0
$541$	−0.727097	+	2.23777i	−0.0312603	+	0.0962094i	−0.965469	−	0.260517i	$-0.916107\pi$
$541$	−0.727097	+	2.23777i	−0.0312603	+	0.0962094i	0.934209	+	0.356726i	$0.116107\pi$
$542$		0			0
$543$	−4.87849	+	20.7669i	−0.209356	+	0.891194i
$544$		0			0
$545$	−43.5193	−	1.16890i	−1.86416	−	0.0500701i
$546$		0			0
$547$	−43.1229	−	6.82999i	−1.84380	−	0.292029i	−0.865762	−	0.500456i	$-0.833166\pi$
$547$	−43.1229	−	6.82999i	−1.84380	−	0.292029i	−0.978038	+	0.208426i	$0.933166\pi$
$548$		0			0
$549$	−2.99209	−	1.48789i	−0.127699	−	0.0635016i
$550$		0			0
$551$		−	4.95029i		−	0.210889i
$552$		0			0
$553$	1.90257	−	12.0123i	0.0809055	−	0.510817i
$554$		0			0
$555$	−25.7561	−	11.3375i	−1.09329	−	0.481252i
$556$		0			0
$557$	3.81138	−	3.81138i	0.161493	−	0.161493i	−0.621735	−	0.783228i	$-0.713572\pi$
$557$	3.81138	−	3.81138i	0.161493	−	0.161493i	0.783228	+	0.621735i	$0.213572\pi$
$558$		0			0
$559$	9.95852	+	3.23572i	0.421200	+	0.136856i
$560$		0			0
$561$	3.21233	+	2.71655i	0.135625	+	0.114693i
$562$		0			0
$563$	29.0405	−	14.7969i	1.22391	−	0.623615i	0.281981	−	0.959420i	$-0.409008\pi$
$563$	29.0405	−	14.7969i	1.22391	−	0.623615i	0.941931	+	0.335805i	$0.109008\pi$
$564$		0			0
$565$	−10.1946	+	9.66125i	−0.428889	+	0.406452i
$566$		0			0
$567$	8.01024	−	8.32968i	0.336398	−	0.349814i
$568$		0			0
$569$	1.73598	+	1.26126i	0.0727760	+	0.0528749i	0.623578	−	0.781761i	$-0.285678\pi$
$569$	1.73598	+	1.26126i	0.0727760	+	0.0528749i	−0.550802	+	0.834636i	$0.685678\pi$
$570$		0			0
$571$	4.09296	−	2.97371i	0.171285	−	0.124446i	−0.498840	−	0.866694i	$-0.666240\pi$
$571$	4.09296	−	2.97371i	0.171285	−	0.124446i	0.670125	+	0.742248i	$0.266240\pi$
$572$		0			0
$573$	−1.85586	−	22.1938i	−0.0775297	−	0.927158i
$574$		0			0
$575$	−2.42549	−	23.3797i	−0.101150	−	0.975000i
$576$		0			0
$577$	10.9908	−	21.5708i	0.457555	−	0.898002i	−0.540827	−	0.841134i	$-0.681889\pi$
$577$	10.9908	−	21.5708i	0.457555	−	0.898002i	0.998382	−	0.0568682i	$-0.0181115\pi$
$578$		0			0
$579$	−22.6067	−	9.23483i	−0.939502	−	0.383786i
$580$		0			0
$581$	13.4734	−	18.5446i	0.558973	−	0.769360i
$582$		0			0
$583$	−15.0640	+	2.38590i	−0.623886	+	0.0988138i
$584$		0			0
$585$	33.4902	+	0.572036i	1.38465	+	0.0236508i
$586$		0			0
$587$	−12.2504	−	24.0428i	−0.505628	−	0.992352i	−0.992883	−	0.119092i	$-0.962002\pi$
$587$	−12.2504	−	24.0428i	−0.505628	−	0.992352i	0.487255	−	0.873260i	$-0.337998\pi$
$588$		0			0
$589$	−4.76196	+	1.54725i	−0.196213	+	0.0637535i
$590$		0			0
$591$	12.9391	−	3.17335i	0.532241	−	0.130534i
$592$		0			0
$593$	−7.14857	−	7.14857i	−0.293556	−	0.293556i	0.544927	−	0.838483i	$-0.316557\pi$
$593$	−7.14857	−	7.14857i	−0.293556	−	0.293556i	−0.838483	+	0.544927i	$0.816557\pi$
$594$		0			0
$595$	6.01858	+	2.13585i	0.246738	+	0.0875614i
$596$		0			0
$597$	25.6891	−	10.7881i	1.05138	−	0.441529i
$598$		0			0
$599$	20.6392			0.843294			0.421647	−	0.906760i	$-0.361452\pi$
$599$	20.6392			0.843294			0.421647	+	0.906760i	$0.361452\pi$
$600$		0			0
$601$	−7.30272			−0.297884			−0.148942	−	0.988846i	$-0.547587\pi$
$601$	−7.30272			−0.297884			−0.148942	+	0.988846i	$0.547587\pi$
$602$		0			0
$603$	19.1775	+	13.6489i	0.780969	+	0.555827i
$604$		0			0
$605$	13.3621	−	17.3895i	0.543245	−	0.706985i
$606$		0			0
$607$	10.3692	+	10.3692i	0.420872	+	0.420872i	0.885504	−	0.464632i	$-0.153813\pi$
$607$	10.3692	+	10.3692i	0.420872	+	0.420872i	−0.464632	+	0.885504i	$0.653813\pi$
$608$		0			0
$609$	−0.642376	−	2.61923i	−0.0260304	−	0.106137i
$610$		0			0
$611$	−1.95923	+	0.636592i	−0.0792619	+	0.0257537i
$612$		0			0
$613$	−2.08080	−	4.08379i	−0.0840425	−	0.164943i	0.845160	−	0.534513i	$-0.179505\pi$
$613$	−2.08080	−	4.08379i	−0.0840425	−	0.164943i	−0.929203	+	0.369570i	$0.879505\pi$
$614$		0			0
$615$	−12.6533	−	32.5523i	−0.510230	−	1.31263i
$616$		0			0
$617$	−3.30490	+	0.523445i	−0.133050	+	0.0210731i	−0.222604	−	0.974909i	$-0.571456\pi$
$617$	−3.30490	+	0.523445i	−0.133050	+	0.0210731i	0.0895540	+	0.995982i	$0.471456\pi$
$618$		0			0
$619$	−18.6414	+	25.6577i	−0.749260	+	1.03127i	0.248772	+	0.968562i	$0.419973\pi$
$619$	−18.6414	+	25.6577i	−0.749260	+	1.03127i	−0.998032	+	0.0627063i	$0.980027\pi$
$620$		0			0
$621$	−18.3401	+	16.1349i	−0.735962	+	0.647469i
$622$		0			0
$623$	7.74862	−	15.2075i	0.310442	−	0.609277i
$624$		0			0
$625$	10.2299	−	22.8112i	0.409194	−	0.912447i
$626$		0			0
$627$	7.69441	−	0.643413i	0.307285	−	0.0256954i
$628$		0			0
$629$	−13.0750	+	9.49957i	−0.521336	+	0.378773i
$630$		0			0
$631$	−2.88632	−	2.09703i	−0.114902	−	0.0834815i	0.528850	−	0.848715i	$-0.322623\pi$
$631$	−2.88632	−	2.09703i	−0.114902	−	0.0834815i	−0.643753	+	0.765234i	$0.722623\pi$
$632$		0			0
$633$	29.5719	−	25.5077i	1.17538	−	1.01384i
$634$		0			0
$635$	1.47845	−	7.94715i	0.0586705	−	0.315373i
$636$		0			0
$637$	23.8074	−	12.1305i	0.943285	−	0.480628i
$638$		0			0
$639$	−30.5321	−	4.53037i	−1.20783	−	0.179219i
$640$		0			0
$641$	26.6743	+	8.66700i	1.05357	+	0.342326i	0.784069	−	0.620674i	$-0.213141\pi$
$641$	26.6743	+	8.66700i	1.05357	+	0.342326i	0.269502	+	0.963000i	$0.413141\pi$
$642$		0			0
$643$	−4.46449	+	4.46449i	−0.176062	+	0.176062i	−0.789637	−	0.613575i	$-0.789731\pi$
$643$	−4.46449	+	4.46449i	−0.176062	+	0.176062i	0.613575	+	0.789637i	$0.289731\pi$
$644$		0			0
$645$	−8.08094	−	0.814927i	−0.318187	−	0.0320877i
$646$		0			0
$647$	−2.38692	+	15.0704i	−0.0938396	+	0.592480i	0.895296	+	0.445472i	$0.146964\pi$
$647$	−2.38692	+	15.0704i	−0.0938396	+	0.592480i	−0.989135	+	0.147008i	$0.953036\pi$
$648$		0			0
$649$		−	13.3220i		−	0.522933i
$650$		0			0
$651$	−2.31881	+	1.43660i	−0.0908812	+	0.0563048i
$652$		0			0
$653$	21.6865	+	3.43481i	0.848660	+	0.134415i	0.565592	−	0.824685i	$-0.308648\pi$
$653$	21.6865	+	3.43481i	0.848660	+	0.134415i	0.283068	+	0.959100i	$0.408648\pi$
$654$		0			0
$655$	8.36055	−	23.5591i	0.326674	−	0.920529i
$656$		0			0
$657$	−18.9388	+	6.35888i	−0.738872	+	0.248084i
$658$		0			0
$659$	3.02628	−	9.31393i	0.117887	−	0.362819i	−0.874651	−	0.484753i	$-0.838910\pi$
$659$	3.02628	−	9.31393i	0.117887	−	0.362819i	0.992538	+	0.121934i	$0.0389095\pi$
$660$		0			0
$661$	−14.2639	−	43.8997i	−0.554800	−	1.70750i	−0.696471	−	0.717585i	$-0.745247\pi$
$661$	−14.2639	−	43.8997i	−0.554800	−	1.70750i	0.141671	−	0.989914i	$-0.454753\pi$
$662$		0			0
$663$	9.97079	−	16.4508i	0.387233	−	0.638895i
$664$		0			0
$665$	10.5827	−	5.03895i	0.410380	−	0.195402i
$666$		0			0
$667$	0.891759	+	5.63034i	0.0345290	+	0.218008i
$668$		0			0
$669$	1.45278	−	19.6890i	0.0561677	−	0.761221i
$670$		0			0
$671$	−0.714946	−	0.984039i	−0.0276002	−	0.0379884i
$672$		0			0
$673$	−8.88482	−	4.52704i	−0.342485	−	0.174505i	0.274285	−	0.961648i	$-0.411559\pi$
$673$	−8.88482	−	4.52704i	−0.342485	−	0.174505i	−0.616769	+	0.787144i	$0.711559\pi$
$674$		0			0
$675$	−25.4804	+	5.07433i	−0.980741	+	0.195311i
$676$		0			0
$677$	−32.0266	−	16.3184i	−1.23088	−	0.627167i	−0.287154	−	0.957884i	$-0.592709\pi$
$677$	−32.0266	−	16.3184i	−1.23088	−	0.627167i	−0.943730	+	0.330718i	$0.892709\pi$
$678$		0			0
$679$	−11.7173	−	16.1274i	−0.449668	−	0.618914i
$680$		0			0
$681$	−1.80782	+	24.5007i	−0.0692757	+	0.938868i
$682$		0			0
$683$	−4.75779	−	30.0395i	−0.182052	−	1.14943i	−0.894289	−	0.447490i	$-0.852318\pi$
$683$	−4.75779	−	30.0395i	−0.182052	−	1.14943i	0.712237	−	0.701939i	$-0.247682\pi$
$684$		0			0
$685$	−18.9400	−	19.9855i	−0.723660	−	0.763607i
$686$		0			0
$687$	−3.14976	+	5.19678i	−0.120171	+	0.198270i
$688$		0			0
$689$	21.5505	+	66.3257i	0.821009	+	2.52681i
$690$		0			0
$691$	−5.29160	+	16.2859i	−0.201302	+	0.619543i	0.798543	+	0.601938i	$0.205604\pi$
$691$	−5.29160	+	16.2859i	−0.201302	+	0.619543i	−0.999845	+	0.0176058i	$0.994396\pi$
$692$		0			0
$693$	3.98768	−	1.33890i	0.151479	−	0.0508607i
$694$		0			0
$695$	30.4961	−	20.9292i	1.15678	−	0.793889i
$696$		0			0
$697$	−19.8108	−	3.13772i	−0.750387	−	0.118850i
$698$		0			0
$699$	4.23605	−	2.62441i	0.160222	−	0.0992644i
$700$		0			0
$701$			36.7694i			1.38876i	0.719609	+	0.694380i	$0.244321\pi$
$701$			36.7694i			1.38876i	−0.719609	+	0.694380i	$0.755679\pi$
$702$		0			0
$703$	−4.64018	+	29.2970i	−0.175008	+	1.10496i
$704$		0			0
$705$	1.38044	−	0.804773i	0.0519904	−	0.0303095i
$706$		0			0
$707$	−9.88417	+	9.88417i	−0.371732	+	0.371732i
$708$		0			0
$709$	−34.2516	−	11.1290i	−1.28635	−	0.417959i	−0.415535	−	0.909577i	$-0.636406\pi$
$709$	−34.2516	−	11.1290i	−1.28635	−	0.417959i	−0.870811	+	0.491618i	$0.836406\pi$
$710$		0			0
$711$	28.1077	+	4.17063i	1.05412	+	0.156411i
$712$		0			0
$713$	5.13741	−	2.61764i	0.192398	−	0.0980315i
$714$		0			0
$715$	10.7107	+	5.82478i	0.400558	+	0.217835i
$716$		0			0
$717$	18.8635	−	16.2710i	0.704469	−	0.607652i
$718$		0			0
$719$	27.9485	+	20.3058i	1.04230	+	0.757278i	0.970734	−	0.240158i	$-0.0771992\pi$
$719$	27.9485	+	20.3058i	1.04230	+	0.757278i	0.0715696	+	0.997436i	$0.477199\pi$
$720$		0			0
$721$	8.58395	−	6.23660i	0.319683	−	0.232263i
$722$		0			0
$723$	4.90127	−	0.409848i	0.182280	−	0.0152424i
$724$		0			0
$725$	−2.18042	+	5.65742i	−0.0809788	+	0.210111i
$726$		0			0
$727$	14.5118	−	28.4810i	0.538212	−	1.05630i	−0.448494	−	0.893786i	$-0.648039\pi$
$727$	14.5118	−	28.4810i	0.538212	−	1.05630i	0.986706	−	0.162515i	$-0.0519607\pi$
$728$		0			0
$729$	19.6434	+	18.5240i	0.727533	+	0.686072i
$730$		0			0
$731$	−2.74172	+	3.77365i	−0.101406	+	0.139574i
$732$		0			0
$733$	20.6997	−	3.27851i	0.764560	−	0.121094i	0.238038	−	0.971256i	$-0.423496\pi$
$733$	20.6997	−	3.27851i	0.764560	−	0.121094i	0.526522	+	0.850161i	$0.323496\pi$
$734$		0			0
$735$	−16.0515	+	13.1106i	−0.592069	+	0.483594i
$736$		0			0
$737$	3.88980	+	7.63416i	0.143283	+	0.281208i
$738$		0			0
$739$	−7.83354	+	2.54527i	−0.288162	+	0.0936294i	−0.449531	−	0.893265i	$-0.648409\pi$
$739$	−7.83354	+	2.54527i	−0.288162	+	0.0936294i	0.161370	+	0.986894i	$0.448409\pi$
$740$		0			0
$741$	−8.40961	−	34.2895i	−0.308935	−	1.25966i
$742$		0			0
$743$	30.1299	+	30.1299i	1.10536	+	1.10536i	0.993752	+	0.111607i	$0.0355998\pi$
$743$	30.1299	+	30.1299i	1.10536	+	1.10536i	0.111607	+	0.993752i	$0.464400\pi$
$744$		0			0
$745$	15.4711	−	4.57141i	0.566816	−	0.167484i
$746$		0			0
$747$	43.6331	+	31.0543i	1.59645	+	1.13622i
$748$		0			0
$749$	−11.9290			−0.435876
$750$		0			0
$751$	−26.7528			−0.976225			−0.488113	−	0.872781i	$-0.662314\pi$
$751$	−26.7528			−0.976225			−0.488113	+	0.872781i	$0.662314\pi$
$752$		0			0
$753$	−20.5159	+	8.61565i	−0.747640	+	0.313972i
$754$		0			0
$755$	18.4309	−	5.44600i	0.670769	−	0.198200i
$756$		0			0
$757$	−1.20647	−	1.20647i	−0.0438498	−	0.0438498i	0.684842	−	0.728692i	$-0.259871\pi$
$757$	−1.20647	−	1.20647i	−0.0438498	−	0.0438498i	−0.728692	+	0.684842i	$0.759871\pi$
$758$		0			0
$759$	−8.63554	+	2.11790i	−0.313450	+	0.0768747i
$760$		0			0
$761$	41.1754	−	13.3787i	1.49261	−	0.484978i	0.554756	−	0.832013i	$-0.312811\pi$
$761$	41.1754	−	13.3787i	1.49261	−	0.484978i	0.937852	+	0.347035i	$0.112811\pi$
$762$		0			0
$763$	11.3495	+	22.2746i	0.410878	+	0.806394i
$764$		0			0
$765$	−4.85251	+	14.1099i	−0.175443	+	0.510144i
$766$		0			0
$767$	−60.1650	+	9.52920i	−2.17243	+	0.344080i
$768$		0			0
$769$	−19.1217	+	26.3187i	−0.689545	+	0.949078i	−0.999999	−	0.00151094i	$-0.999519\pi$
$769$	−19.1217	+	26.3187i	−0.689545	+	0.949078i	0.310454	+	0.950589i	$0.399519\pi$
$770$		0			0
$771$	21.4936	+	8.78014i	0.774074	+	0.316209i
$772$		0			0
$773$	7.28640	−	14.3004i	0.262074	−	0.514348i	−0.722048	−	0.691843i	$-0.756799\pi$
$773$	7.28640	−	14.3004i	0.262074	−	0.514348i	0.984122	+	0.177494i	$0.0567992\pi$
$774$		0			0
$775$	6.12370	+	0.329194i	0.219970	+	0.0118250i
$776$		0			0
$777$	1.34658	+	16.1034i	0.0483082	+	0.577706i
$778$		0			0
$779$	−29.7822	+	21.6381i	−1.06706	+	0.775264i
$780$		0			0
$781$	−9.08951	−	6.60392i	−0.325248	−	0.236307i
$782$		0			0
$783$	6.10460	−	1.56058i	0.218161	−	0.0557707i
$784$		0			0
$785$	−25.6215	−	13.9337i	−0.914470	−	0.497314i
$786$		0			0
$787$	−2.48782	+	1.26761i	−0.0886811	+	0.0451853i	−0.497769	−	0.867310i	$-0.665847\pi$
$787$	−2.48782	+	1.26761i	−0.0886811	+	0.0451853i	0.409087	+	0.912495i	$0.365847\pi$
$788$		0			0
$789$	3.08140	+	2.60583i	0.109701	+	0.0927700i
$790$		0			0
$791$	7.67054	+	2.49231i	0.272733	+	0.0886164i
$792$		0			0
$793$	−3.93274	+	3.93274i	−0.139656	+	0.139656i
$794$		0			0
$795$	−27.2440	−	46.7320i	−0.966244	−	1.65741i
$796$		0			0
$797$	7.08694	−	44.7452i	0.251032	−	1.58496i	−0.463981	−	0.885845i	$-0.653579\pi$
$797$	7.08694	−	44.7452i	0.251032	−	1.58496i	0.715014	−	0.699111i	$-0.246421\pi$
$798$		0			0
$799$		−	0.917687i		−	0.0324654i
$800$		0			0
$801$	35.7060	+	17.7557i	1.26161	+	0.627367i
$802$		0			0
$803$	−7.18233	−	1.13757i	−0.253459	−	0.0401439i
$804$		0			0
$805$	−11.1288	+	7.63759i	−0.392238	+	0.269190i
$806$		0			0
$807$	10.9241	−	46.5023i	0.384548	−	1.63696i
$808$		0			0
$809$	−10.6570	+	32.7987i	−0.374679	+	1.15314i	0.569016	+	0.822326i	$0.307324\pi$
$809$	−10.6570	+	32.7987i	−0.374679	+	1.15314i	−0.943695	+	0.330816i	$0.892676\pi$
$810$		0			0
$811$	16.9534	+	52.1772i	0.595315	+	1.83219i	0.553154	+	0.833079i	$0.313424\pi$
$811$	16.9534	+	52.1772i	0.595315	+	1.83219i	0.0421604	+	0.999111i	$0.486576\pi$
$812$		0			0
$813$	46.8171	+	28.3758i	1.64195	+	0.995182i
$814$		0			0
$815$	−1.45398	−	1.53424i	−0.0509306	−	0.0537421i
$816$		0			0
$817$	1.33923	+	8.45555i	0.0468536	+	0.295822i
$818$		0			0
$819$	−8.89918	−	17.0515i	−0.310962	−	0.595829i
$820$		0			0
$821$	−16.6270	−	22.8851i	−0.580287	−	0.798697i	0.413440	−	0.910531i	$-0.364327\pi$
$821$	−16.6270	−	22.8851i	−0.580287	−	0.798697i	−0.993727	+	0.111835i	$0.964327\pi$
$822$		0			0
$823$	4.59265	+	2.34007i	0.160090	+	0.0815698i	0.532200	−	0.846619i	$-0.321366\pi$
$823$	4.59265	+	2.34007i	0.160090	+	0.0815698i	−0.372110	+	0.928189i	$0.621366\pi$
$824$		0			0
$825$	−9.07693	−	2.65378i	−0.316018	−	0.0923929i
$826$		0			0
$827$	−34.2714	−	17.4622i	−1.19173	−	0.607219i	−0.258334	−	0.966056i	$-0.583173\pi$
$827$	−34.2714	−	17.4622i	−1.19173	−	0.607219i	−0.933400	+	0.358837i	$0.883173\pi$
$828$		0			0
$829$	−17.9690	−	24.7323i	−0.624091	−	0.858987i	0.373552	−	0.927609i	$-0.378140\pi$
$829$	−17.9690	−	24.7323i	−0.624091	−	0.858987i	−0.997643	+	0.0686222i	$0.978140\pi$
$830$		0			0
$831$	11.9703	+	0.883246i	0.415246	+	0.0306395i
$832$		0			0
$833$	1.86200	+	11.7562i	0.0645145	+	0.407329i
$834$		0			0
$835$	−47.1111	+	22.4319i	−1.63035	+	0.776289i
$836$		0			0
$837$	−3.40925	−	5.38458i	−0.117841	−	0.186118i
$838$		0			0
$839$	4.25109	+	13.0835i	0.146764	+	0.451693i	0.997234	−	0.0743309i	$-0.0236821\pi$
$839$	4.25109	+	13.0835i	0.146764	+	0.451693i	−0.850470	+	0.526024i	$0.823682\pi$
$840$		0			0
$841$	−8.50711	+	26.1822i	−0.293348	+	0.902834i
$842$		0			0
$843$	10.4056	+	2.44446i	0.358390	+	0.0841915i
$844$		0			0
$845$	8.92285	−	25.1436i	0.306955	−	0.864965i
$846$		0			0
$847$	−12.4382	−	1.97001i	−0.427380	−	0.0676904i
$848$		0			0
$849$	3.14255	+	5.07237i	0.107852	+	0.174083i
$850$		0			0
$851$		−	34.1576i		−	1.17091i
$852$		0			0
$853$	−4.81039	+	30.3716i	−0.164705	+	1.03991i	0.757396	+	0.652956i	$0.226471\pi$
$853$	−4.81039	+	30.3716i	−0.164705	+	1.03991i	−0.922101	+	0.386949i	$0.873529\pi$
$854$		0			0
$855$	12.0141	+	24.6091i	0.410872	+	0.841614i
$856$		0			0
$857$	−17.0033	+	17.0033i	−0.580821	+	0.580821i	−0.935129	−	0.354308i	$-0.884717\pi$
$857$	−17.0033	+	17.0033i	−0.580821	+	0.580821i	0.354308	+	0.935129i	$0.384717\pi$
$858$		0			0
$859$	−24.2527	−	7.88017i	−0.827490	−	0.268868i	−0.135502	−	0.990777i	$-0.543265\pi$
$859$	−24.2527	−	7.88017i	−0.827490	−	0.268868i	−0.691988	+	0.721909i	$0.743265\pi$
$860$		0			0
$861$	−12.9501	+	15.3136i	−0.441339	+	0.521885i
$862$		0			0
$863$	−4.75115	+	2.42083i	−0.161731	+	0.0824062i	−0.532982	−	0.846126i	$-0.678929\pi$
$863$	−4.75115	+	2.42083i	−0.161731	+	0.0824062i	0.371251	+	0.928532i	$0.378929\pi$
$864$		0			0
$865$	1.53516	−	8.25197i	0.0521969	−	0.280575i
$866$		0			0
$867$	−13.6350	−	15.8075i	−0.463070	−	0.536851i
$868$		0			0
$869$	8.36776	+	6.07953i	0.283857	+	0.206234i
$870$		0			0
$871$	31.6952	−	23.0279i	1.07395	−	0.780272i
$872$		0			0
$873$	37.4107	−	27.7431i	1.26616	−	0.938962i
$874$		0			0
$875$	−14.3139	+	1.09746i	−0.483898	+	0.0371008i
$876$		0			0
$877$	0.238108	−	0.467313i	0.00804034	−	0.0157801i	−0.886951	−	0.461863i	$-0.847181\pi$
$877$	0.238108	−	0.467313i	0.00804034	−	0.0157801i	0.894992	+	0.446083i	$0.147181\pi$
$878$		0			0
$879$	−13.3268	+	32.6239i	−0.449503	+	1.10038i
$880$		0			0
$881$	8.93089	−	12.2923i	0.300889	−	0.414139i	−0.631624	−	0.775275i	$-0.717611\pi$
$881$	8.93089	−	12.2923i	0.300889	−	0.414139i	0.932513	+	0.361136i	$0.117611\pi$
$882$		0			0
$883$	−39.0132	+	6.17909i	−1.31290	+	0.207943i	−0.773333	−	0.634000i	$-0.781412\pi$
$883$	−39.0132	+	6.17909i	−1.31290	+	0.207943i	−0.539566	+	0.841943i	$0.681412\pi$
$884$		0			0
$885$	44.0392	−	17.1183i	1.48036	−	0.575427i
$886$		0			0
$887$	−17.1951	−	33.7472i	−0.577354	−	1.13312i	−0.976355	−	0.216171i	$-0.930643\pi$
$887$	−17.1951	−	33.7472i	−0.577354	−	1.13312i	0.399001	−	0.916950i	$-0.369357\pi$
$888$		0			0
$889$	−4.41465	+	1.43441i	−0.148063	+	0.0481085i
$890$		0			0
$891$	3.21911	+	9.28576i	0.107844	+	0.311085i
$892$		0			0
$893$	−1.19096	−	1.19096i	−0.0398540	−	0.0398540i
$894$		0			0
$895$	−13.7576	+	17.9043i	−0.459867	+	0.598476i
$896$		0			0
$897$	15.7419	+	37.4851i	0.525607	+	1.25159i
$898$		0			0
$899$	−1.48728			−0.0496035
$900$		0			0
$901$	−31.0664			−1.03497
$902$		0			0
$903$	1.80583	+	4.30011i	0.0600944	+	0.143099i
$904$		0			0
$905$	−25.9540	−	9.21045i	−0.862740	−	0.306166i
$906$		0			0
$907$	26.2182	+	26.2182i	0.870561	+	0.870561i	0.992533	−	0.121973i	$-0.0389220\pi$
$907$	26.2182	+	26.2182i	0.870561	+	0.870561i	−0.121973	+	0.992533i	$0.538922\pi$
$908$		0			0
$909$	−23.3179	−	22.8665i	−0.773406	−	0.758433i
$910$		0			0
$911$	7.41217	−	2.40836i	0.245576	−	0.0797925i	−0.183643	−	0.982993i	$-0.558789\pi$
$911$	7.41217	−	2.40836i	0.245576	−	0.0797925i	0.429219	+	0.903201i	$0.358789\pi$
$912$		0			0
$913$	8.85014	+	17.3694i	0.292897	+	0.574843i
$914$		0			0
$915$	2.33431	−	3.62790i	0.0771699	−	0.119935i
$916$		0			0
$917$	−14.1783	+	2.24563i	−0.468210	+	0.0741572i
$918$		0			0
$919$	−6.54187	+	9.00411i	−0.215796	+	0.297018i	−0.903168	−	0.429288i	$-0.858765\pi$
$919$	−6.54187	+	9.00411i	−0.215796	+	0.297018i	0.687371	+	0.726306i	$0.258765\pi$
$920$		0			0
$921$	−20.2048	+	49.4609i	−0.665770	+	1.62979i
$922$		0			0
$923$	−23.3231	+	45.7741i	−0.767688	+	1.50667i
$924$		0			0
$925$	18.2073	−	31.4381i	0.598652	−	1.03368i
$926$		0			0
$927$	14.7665	+	19.9121i	0.484994	+	0.653999i
$928$		0			0
$929$	9.49314	−	6.89717i	0.311460	−	0.226289i	−0.421063	−	0.907032i	$-0.638343\pi$
$929$	9.49314	−	6.89717i	0.311460	−	0.226289i	0.732523	+	0.680743i	$0.238343\pi$
$930$		0			0
$931$	17.6735	+	12.8406i	0.579226	+	0.420832i
$932$		0			0
$933$	−28.1224	−	32.6032i	−0.920687	−	1.06738i
$934$		0			0
$935$	−3.94216	+	3.73593i	−0.128922	+	0.122178i
$936$		0			0
$937$	−28.5913	+	14.5680i	−0.934038	+	0.475916i	−0.853650	−	0.520848i	$-0.825616\pi$
$937$	−28.5913	+	14.5680i	−0.934038	+	0.475916i	−0.0803881	+	0.996764i	$0.525616\pi$
$938$		0			0
$939$	12.7332	−	15.0571i	0.415533	−	0.491369i
$940$		0			0
$941$	−31.7416	−	10.3135i	−1.03475	−	0.336210i	−0.258082	−	0.966123i	$-0.583090\pi$
$941$	−31.7416	−	10.3135i	−1.03475	−	0.336210i	−0.776665	+	0.629914i	$0.783090\pi$
$942$		0			0
$943$	29.9757	−	29.9757i	0.976143	−	0.976143i
$944$		0			0
$945$	9.55014	+	11.4618i	0.310666	+	0.372854i
$946$		0			0
$947$	−0.422572	+	2.66801i	−0.0137317	+	0.0866988i	−0.993602	−	0.112934i	$-0.963975\pi$
$947$	−0.422572	+	2.66801i	−0.0137317	+	0.0866988i	0.979871	+	0.199633i	$0.0639750\pi$
$948$		0			0
$949$			33.2508i			1.07937i
$950$		0			0
$951$	14.4660	+	23.3495i	0.469092	+	0.757158i
$952$		0			0
$953$	−21.3701	−	3.38469i	−0.692245	−	0.109641i	−0.199608	−	0.979876i	$-0.563967\pi$
$953$	−21.3701	−	3.38469i	−0.692245	−	0.109641i	−0.492637	+	0.870235i	$0.663967\pi$
$954$		0			0
$955$	28.7417	+	0.771982i	0.930059	+	0.0249808i
$956$		0			0
$957$	2.23273	+	0.524505i	0.0721741	+	0.0169549i
$958$		0			0
$959$	−4.88595	+	15.0374i	−0.157775	+	0.485583i
$960$		0			0
$961$	−9.11467	−	28.0521i	−0.294021	−	0.904905i
$962$		0			0
$963$	−0.272401	−	27.8695i	−0.00877799	−	0.898083i
$964$		0			0
$965$	15.0617	−	27.6957i	0.484853	−	0.891557i
$966$		0			0
$967$	−2.16077	−	13.6426i	−0.0694857	−	0.438716i	−0.997764	−	0.0668302i	$-0.978711\pi$
$967$	−2.16077	−	13.6426i	−0.0694857	−	0.438716i	0.928279	−	0.371885i	$-0.121289\pi$
$968$		0			0
$969$	15.6849	+	1.15733i	0.503871	+	0.0371788i
$970$		0			0
$971$	23.2793	+	32.0412i	0.747069	+	1.02825i	0.998181	+	0.0602944i	$0.0192040\pi$
$971$	23.2793	+	32.0412i	0.747069	+	1.02825i	−0.251111	+	0.967958i	$0.580796\pi$
$972$		0			0
$973$	−18.9244	−	9.64244i	−0.606687	−	0.309122i
$974$		0			0
$975$	−5.49237	+	42.8918i	−0.175896	+	1.37364i
$976$		0			0
$977$	36.2603	+	18.4756i	1.16007	+	0.591085i	0.924654	−	0.380809i	$-0.124354\pi$
$977$	36.2603	+	18.4756i	1.16007	+	0.591085i	0.235417	+	0.971894i	$0.424354\pi$
$978$		0			0
$979$	8.53179	+	11.7430i	0.272677	+	0.375308i
$980$		0			0
$981$	−51.7805	+	27.0242i	−1.65323	+	0.862816i
$982$		0			0
$983$	−1.75697	−	11.0931i	−0.0560387	−	0.353814i	−0.999735	−	0.0230024i	$-0.992677\pi$
$983$	−1.75697	−	11.0931i	−0.0560387	−	0.353814i	0.943697	−	0.330812i	$-0.107323\pi$
$984$		0			0
$985$	2.23348	+	17.0536i	0.0711646	+	0.543374i
$986$		0			0
$987$	−0.784691	−	0.475600i	−0.0249770	−	0.0151385i
$988$		0			0
$989$	−3.04641	−	9.37590i	−0.0968703	−	0.298136i
$990$		0			0
$991$	−8.60678	+	26.4889i	−0.273403	+	0.841449i	0.716234	+	0.697860i	$0.245864\pi$
$991$	−8.60678	+	26.4889i	−0.273403	+	0.841449i	−0.989637	+	0.143589i	$0.954136\pi$
$992$		0			0
$993$	4.99908	−	21.2803i	0.158641	−	0.675308i
$994$		0			0
$995$	10.1929	+	34.4958i	0.323136	+	1.09359i
$996$		0			0
$997$	−52.2022	−	8.26801i	−1.65326	−	0.261851i	−0.741012	−	0.671491i	$-0.765654\pi$
$997$	−52.2022	−	8.26801i	−1.65326	−	0.261851i	−0.912247	+	0.409641i	$0.865654\pi$
$998$		0			0
$999$	−37.5913	+	3.51371i	−1.18934	+	0.111169i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.x.a.17.6	yes	80
3.2	odd	2	inner	300.2.x.a.17.3	✓	80
25.3	odd	20	inner	300.2.x.a.53.3	yes	80
75.53	even	20	inner	300.2.x.a.53.6	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.x.a.17.3	✓	80	3.2	odd	2	inner
300.2.x.a.17.6	yes	80	1.1	even	1	trivial
300.2.x.a.53.3	yes	80	25.3	odd	20	inner
300.2.x.a.53.6	yes	80	75.53	even	20	inner

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.x (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.670639 + 1.59695i) q^{3} +(-2.14441 + 0.633635i) q^{5} +(0.907947 + 0.907947i) q^{7} +(-2.10049 + 2.14195i) q^{9} +O(q^{10})\)	\(q+(0.670639 + 1.59695i) q^{3} +(-2.14441 + 0.633635i) q^{5} +(0.907947 + 0.907947i) q^{7} +(-2.10049 + 2.14195i) q^{9} +(-1.03855 + 0.337444i) q^{11} +(2.26685 + 4.44893i) q^{13} +(-2.45001 - 2.99958i) q^{15} +(-2.19690 + 0.347955i) q^{17} +(-2.39954 + 3.30268i) q^{19} +(-0.841039 + 2.05885i) q^{21} +(2.13422 - 4.18865i) q^{23} +(4.19701 - 2.71755i) q^{25} +(-4.82925 - 1.91789i) q^{27} +(-0.981024 + 0.712755i) q^{29} +(0.992266 + 0.720923i) q^{31} +(-1.23537 - 1.43220i) q^{33} +(-2.52232 - 1.37171i) q^{35} +(6.47404 - 3.29869i) q^{37} +(-5.58448 + 6.60366i) q^{39} +(8.57625 + 2.78659i) q^{41} +(1.48285 - 1.48285i) q^{43} +(3.14709 - 5.92417i) q^{45} +(-0.0645410 + 0.407496i) q^{47} -5.35127i q^{49} +(-2.02900 - 3.27499i) q^{51} +(13.7949 + 2.18491i) q^{53} +(2.01325 - 1.38168i) q^{55} +(-6.88343 - 1.61703i) q^{57} +(-3.76991 + 11.6026i) q^{59} +(0.344205 + 1.05936i) q^{61} +(-3.85191 + 0.0376491i) q^{63} +(-7.68005 - 8.10400i) q^{65} +(-1.22742 - 7.74963i) q^{67} +(8.12035 + 0.599171i) q^{69} +(6.04759 + 8.32380i) q^{71} +(5.93345 + 3.02324i) q^{73} +(7.15447 + 4.87992i) q^{75} +(-1.24932 - 0.636563i) q^{77} +(-5.56738 - 7.66285i) q^{79} +(-0.175918 - 8.99828i) q^{81} +(-2.79265 - 17.6321i) q^{83} +(4.49059 - 2.13819i) q^{85} +(-1.79615 - 1.08864i) q^{87} +(-4.10757 - 12.6418i) q^{89} +(-1.98122 + 6.09757i) q^{91} +(-0.485825 + 2.06808i) q^{93} +(3.05291 - 8.60274i) q^{95} +(-15.3339 - 2.42865i) q^{97} +(1.45866 - 2.93331i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{3} + 4 q^{7}+O(q^{10}) \) 80 * q - 2 * q^3 + 4 * q^7	\( 80 q - 2 q^{3} + 4 q^{7} + 12 q^{13} + 10 q^{15} + 20 q^{19} + 40 q^{25} - 14 q^{27} - 20 q^{33} + 12 q^{37} - 40 q^{39} + 12 q^{43} - 60 q^{45} - 76 q^{57} - 98 q^{63} - 36 q^{67} - 70 q^{69} - 44 q^{73} - 90 q^{75} - 40 q^{79} + 20 q^{81} - 100 q^{85} - 70 q^{87} - 18 q^{93} - 56 q^{97}+O(q^{100}) \) 80 * q - 2 * q^3 + 4 * q^7 + 12 * q^13 + 10 * q^15 + 20 * q^19 + 40 * q^25 - 14 * q^27 - 20 * q^33 + 12 * q^37 - 40 * q^39 + 12 * q^43 - 60 * q^45 - 76 * q^57 - 98 * q^63 - 36 * q^67 - 70 * q^69 - 44 * q^73 - 90 * q^75 - 40 * q^79 + 20 * q^81 - 100 * q^85 - 70 * q^87 - 18 * q^93 - 56 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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