LMFDB - Embedded newform 300.2.x.a.17.3

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			17.3
Character	$\chi$	$=$	300.17
Dual form			300.2.x.a.53.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.13130 + 1.31155i) q^{3} +(2.14441 - 0.633635i) q^{5} +(0.907947 + 0.907947i) q^{7} +(-0.440321 - 2.96751i) q^{9} +O(q^{10})$	\(q+(-1.13130 + 1.31155i) q^{3} +(2.14441 - 0.633635i) q^{5} +(0.907947 + 0.907947i) q^{7} +(-0.440321 - 2.96751i) q^{9} +(1.03855 - 0.337444i) q^{11} +(2.26685 + 4.44893i) q^{13} +(-1.59493 + 3.52933i) q^{15} +(2.19690 - 0.347955i) q^{17} +(-2.39954 + 3.30268i) q^{19} +(-2.21798 + 0.163656i) q^{21} +(-2.13422 + 4.18865i) q^{23} +(4.19701 - 2.71755i) q^{25} +(4.39017 + 2.77964i) q^{27} +(0.981024 - 0.712755i) q^{29} +(0.992266 + 0.720923i) q^{31} +(-0.732332 + 1.74385i) q^{33} +(2.52232 + 1.37171i) q^{35} +(6.47404 - 3.29869i) q^{37} +(-8.39948 - 2.06000i) q^{39} +(-8.57625 - 2.78659i) q^{41} +(1.48285 - 1.48285i) q^{43} +(-2.82455 - 6.08456i) q^{45} +(0.0645410 - 0.407496i) q^{47} -5.35127i q^{49} +(-2.02900 + 3.27499i) q^{51} +(-13.7949 - 2.18491i) q^{53} +(2.01325 - 1.38168i) q^{55} +(-1.61703 - 6.88343i) q^{57} +(3.76991 - 11.6026i) q^{59} +(0.344205 + 1.05936i) q^{61} +(2.29455 - 3.09413i) q^{63} +(7.68005 + 8.10400i) q^{65} +(-1.22742 - 7.74963i) q^{67} +(-3.07917 - 7.53776i) q^{69} +(-6.04759 - 8.32380i) q^{71} +(5.93345 + 3.02324i) q^{73} +(-1.18388 + 8.57895i) q^{75} +(1.24932 + 0.636563i) q^{77} +(-5.56738 - 7.66285i) q^{79} +(-8.61223 + 2.61331i) q^{81} +(2.79265 + 17.6321i) q^{83} +(4.49059 - 2.13819i) q^{85} +(-0.175018 + 2.09300i) q^{87} +(4.10757 + 12.6418i) q^{89} +(-1.98122 + 6.09757i) q^{91} +(-2.06808 + 0.485825i) q^{93} +(-3.05291 + 8.60274i) q^{95} +(-15.3339 - 2.42865i) q^{97} +(-1.45866 - 2.93331i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.13130	+	1.31155i	−0.653156	+	0.757223i
$3$	−1.13130	+	1.31155i	−0.653156	+	0.757223i
$4$		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
$9$	−0.440321	−	2.96751i	−0.146774	−	0.989170i
$10$		0			0
$11$	1.03855	−	0.337444i	0.313133	−	0.101743i	−0.148234	−	0.988952i	$-0.547359\pi$
$11$	1.03855	−	0.337444i	0.313133	−	0.101743i	0.461367	+	0.887209i	$0.347359\pi$
$12$		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
$15$	−1.59493	+	3.52933i	−0.411809	+	0.911270i
$16$		0			0
$17$	2.19690	−	0.347955i	0.532827	−	0.0843916i	0.115777	−	0.993275i	$-0.463064\pi$
$17$	2.19690	−	0.347955i	0.532827	−	0.0843916i	0.417050	+	0.908884i	$0.363064\pi$
$18$		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
$21$	−2.21798	+	0.163656i	−0.484002	+	0.0357128i
$22$		0			0
$23$	−2.13422	+	4.18865i	−0.445016	+	0.873394i	0.554144	+	0.832421i	$0.313046\pi$
$23$	−2.13422	+	4.18865i	−0.445016	+	0.873394i	−0.999160	+	0.0409730i	$0.986954\pi$
$24$		0			0
$25$	4.19701	−	2.71755i	0.839403	−	0.543510i
$26$		0			0
$27$	4.39017	+	2.77964i	0.844889	+	0.534942i
$28$		0			0
$29$	0.981024	−	0.712755i	0.182172	−	0.132355i	−0.492962	−	0.870051i	$-0.664086\pi$
$29$	0.981024	−	0.712755i	0.182172	−	0.132355i	0.675134	+	0.737695i	$0.264086\pi$
$30$		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
$33$	−0.732332	+	1.74385i	−0.127483	+	0.303566i
$34$		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
$39$	−8.39948	−	2.06000i	−1.34499	−	0.329864i
$40$		0			0
$41$	−8.57625	−	2.78659i	−1.33938	−	0.435193i	−0.450277	−	0.892889i	$-0.648675\pi$
$41$	−8.57625	−	2.78659i	−1.33938	−	0.435193i	−0.889108	+	0.457697i	$0.848675\pi$
$42$		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
$45$	−2.82455	−	6.08456i	−0.421059	−	0.907033i
$46$		0			0
$47$	0.0645410	−	0.407496i	0.00941428	−	0.0594394i	−0.982534	−	0.186083i	$-0.940421\pi$
$47$	0.0645410	−	0.407496i	0.00941428	−	0.0594394i	0.991948	+	0.126644i	$0.0404206\pi$
$48$		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	−0.903240	−	0.429136i	$-0.858818\pi$
$53$	−13.7949	−	2.18491i	−1.89488	−	0.300120i	−0.991642	+	0.129017i	$0.958818\pi$
$54$		0			0
$55$	2.01325	−	1.38168i	0.271467	−	0.186305i
$56$		0			0
$57$	−1.61703	−	6.88343i	−0.214181	−	0.911732i
$58$		0			0
$59$	3.76991	−	11.6026i	0.490801	−	1.51053i	−0.332599	−	0.943068i	$-0.607925\pi$
$59$	3.76991	−	11.6026i	0.490801	−	1.51053i	0.823400	−	0.567462i	$-0.192075\pi$
$60$		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
$63$	2.29455	−	3.09413i	0.289087	−	0.389824i
$64$		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
$69$	−3.07917	−	7.53776i	−0.370689	−	0.907439i
$70$		0			0
$71$	−6.04759	−	8.32380i	−0.717717	−	0.987853i	−0.999597	−	0.0284034i	$-0.990958\pi$
$71$	−6.04759	−	8.32380i	−0.717717	−	0.987853i	0.281879	−	0.959450i	$-0.409042\pi$
$72$		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
$75$	−1.18388	+	8.57895i	−0.136703	+	0.990612i
$76$		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
$81$	−8.61223	+	2.61331i	−0.956915	+	0.290368i
$82$		0			0
$83$	2.79265	+	17.6321i	0.306534	+	1.93538i	0.351024	+	0.936367i	$0.385834\pi$
$83$	2.79265	+	17.6321i	0.306534	+	1.93538i	−0.0444903	+	0.999010i	$0.514166\pi$
$84$		0			0
$85$	4.49059	−	2.13819i	0.487073	−	0.231920i
$86$		0			0
$87$	−0.175018	+	2.09300i	−0.0187639	+	0.224393i
$88$		0			0
$89$	4.10757	+	12.6418i	0.435401	+	1.34003i	0.892675	+	0.450701i	$0.148826\pi$
$89$	4.10757	+	12.6418i	0.435401	+	1.34003i	−0.457274	+	0.889326i	$0.651174\pi$
$90$		0			0
$91$	−1.98122	+	6.09757i	−0.207688	+	0.639199i
$92$		0			0
$93$	−2.06808	+	0.485825i	−0.214450	+	0.0503777i
$94$		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	$-0.817814\pi$
$101$		−	10.8863i		−	1.08323i	0.840628	−	0.541613i	$-0.182186\pi$
$102$		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
$105$	−4.65256	+	1.75633i	−0.454043	+	0.171401i
$106$		0			0
$107$	6.56922	−	6.56922i	0.635071	−	0.635071i	−0.314265	−	0.949335i	$-0.601758\pi$
$107$	6.56922	−	6.56922i	0.635071	−	0.635071i	0.949335	+	0.314265i	$0.101758\pi$
$108$		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
$111$	−2.99769	+	12.2228i	−0.284528	+	1.16014i
$112$		0			0
$113$	−5.59661	+	2.85162i	−0.526485	+	0.268258i	−0.696967	−	0.717103i	$-0.745468\pi$
$113$	−5.59661	+	2.85162i	−0.526485	+	0.268258i	0.170482	+	0.985361i	$0.445468\pi$
$114$		0			0
$115$	−1.92258	+	10.3345i	−0.179282	+	0.963698i
$116$		0			0
$117$	12.2041	−	8.68585i	1.12827	−	0.803007i
$118$		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
$123$	13.3571	−	8.09570i	1.20437	−	0.729964i
$124$		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
$129$	0.267283	+	3.62239i	0.0235329	+	0.318933i
$130$		0			0
$131$	6.57127	−	9.04457i	0.574134	−	0.790228i	−0.418903	−	0.908031i	$-0.637585\pi$
$131$	6.57127	−	9.04457i	0.574134	−	0.790228i	0.993037	+	0.117803i	$0.0375852\pi$
$132$		0			0
$133$	−5.17731	+	0.820005i	−0.448930	+	0.0711034i
$134$		0			0
$135$	11.1756	+	3.17894i	0.961844	+	0.273599i
$136$		0			0
$137$	−5.59033	−	10.9716i	−0.477615	−	0.937371i	−0.996585	−	0.0825788i	$-0.973684\pi$
$137$	−5.59033	−	10.9716i	−0.477615	−	0.937371i	0.518970	−	0.854792i	$-0.326316\pi$
$138$		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
$141$	0.461436	+	0.545649i	0.0388599	+	0.0459519i
$142$		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
$147$	7.01845	+	6.05389i	0.578872	+	0.499316i
$148$		0			0
$149$	7.21459			0.591042			0.295521	−	0.955336i	$-0.404507\pi$
$149$	7.21459			0.591042			0.295521	+	0.955336i	$0.404507\pi$
$150$		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
$153$	−1.99990	−	6.36612i	−0.161683	−	0.514670i
$154$		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
$159$	18.4718	−	15.6210i	1.46491	−	1.23882i
$160$		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
$165$	−0.465457	+	4.20357i	−0.0362357	+	0.327248i
$166$		0			0
$167$	−23.0479	+	3.65042i	−1.78350	+	0.282478i	−0.959004	−	0.283393i	$-0.908540\pi$
$167$	−23.0479	+	3.65042i	−1.78350	+	0.282478i	−0.824494	+	0.565871i	$0.808540\pi$
$168$		0			0
$169$	−7.01322	+	9.65287i	−0.539479	+	0.742529i
$170$		0			0
$171$	10.8573	+	5.66641i	0.830278	+	0.433321i
$172$		0			0
$173$	1.70415	−	3.34458i	0.129564	−	0.254284i	−0.817107	−	0.576487i	$-0.804423\pi$
$173$	1.70415	−	3.34458i	0.129564	−	0.254284i	0.946671	+	0.322203i	$0.104423\pi$
$174$		0			0
$175$	6.27806	+	1.34328i	0.474576	+	0.101542i
$176$		0			0
$177$	10.9525	+	18.0704i	0.823239	+	1.35826i
$178$		0			0
$179$	−8.16937	+	5.93539i	−0.610607	+	0.443632i	−0.849628	−	0.527382i	$-0.823174\pi$
$179$	−8.16937	+	5.93539i	−0.610607	+	0.443632i	0.239021	+	0.971014i	$0.423174\pi$
$180$		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
$183$	−1.77880	−	0.747007i	−0.131492	−	0.0552203i
$184$		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
$189$	1.46227	+	6.50981i	0.106365	+	0.473519i
$190$		0			0
$191$	12.2290	+	3.97343i	0.884858	+	0.287508i	0.715973	−	0.698128i	$-0.245983\pi$
$191$	12.2290	+	3.97343i	0.884858	+	0.287508i	0.168885	+	0.985636i	$0.445983\pi$
$192$		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
$195$	−19.3172	+	0.904708i	−1.38334	+	0.0647875i
$196$		0			0
$197$	−1.20326	+	7.59705i	−0.0857284	+	0.541268i	0.907023	+	0.421081i	$0.138349\pi$
$197$	−1.20326	+	7.59705i	−0.0857284	+	0.541268i	−0.992751	+	0.120186i	$0.961651\pi$
$198$		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
$207$	13.3696	+	4.48898i	0.929252	+	0.312006i
$208$		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
$213$	17.7587	+	1.48500i	1.21681	+	0.101750i
$214$		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
$219$	−10.6776	+	4.36181i	−0.721528	+	0.294744i
$220$		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
$225$	−9.91239	−	11.2581i	−0.660826	−	0.750539i
$226$		0			0
$227$	−12.6380	−	6.43937i	−0.838812	−	0.427396i	−0.0188557	−	0.999822i	$-0.506002\pi$
$227$	−12.6380	−	6.43937i	−0.838812	−	0.427396i	−0.819956	+	0.572426i	$0.806002\pi$
$228$		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
$231$	−2.24824	+	0.918407i	−0.147924	+	0.0604267i
$232$		0			0
$233$	0.450064	+	2.84159i	0.0294847	+	0.186159i	0.998035	−	0.0626588i	$-0.0199580\pi$
$233$	0.450064	+	2.84159i	0.0294847	+	0.186159i	−0.968550	+	0.248818i	$0.919958\pi$
$234$		0			0
$235$	−0.119801	−	0.914735i	−0.00781496	−	0.0596708i
$236$		0			0
$237$	16.3486	+	1.36708i	1.06195	+	0.0888015i
$238$		0			0
$239$	4.44446	+	13.6787i	0.287488	+	0.884798i	0.985642	+	0.168850i	$0.0540054\pi$
$239$	4.44446	+	13.6787i	0.287488	+	0.884798i	−0.698153	+	0.715948i	$0.745995\pi$
$240$		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
$243$	6.31553	−	14.2518i	0.405142	−	0.914254i
$244$		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	$-0.867116\pi$
$251$		−	12.8469i		−	0.810891i	0.914119	−	0.405445i	$-0.132884\pi$
$252$		0			0
$253$	−0.803054	+	5.07028i	−0.0504876	+	0.318766i
$254$		0			0
$255$	−2.27586	+	8.30857i	−0.142520	+	0.520303i
$256$		0			0
$257$	−9.47863	+	9.47863i	−0.591261	+	0.591261i	−0.937972	−	0.346711i	$-0.887298\pi$
$257$	−9.47863	+	9.47863i	−0.591261	+	0.591261i	0.346711	+	0.937972i	$0.387298\pi$
$258$		0			0
$259$	8.87311	+	2.88305i	0.551348	+	0.179144i
$260$		0			0
$261$	−2.54707	−	2.59736i	−0.157660	−	0.160772i
$262$		0			0
$263$	−2.07596	+	1.05775i	−0.128009	+	0.0652239i	−0.516822	−	0.856093i	$-0.672885\pi$
$263$	−2.07596	+	1.05775i	−0.128009	+	0.0652239i	0.388813	+	0.921317i	$0.372885\pi$
$264$		0			0
$265$	−30.9665	+	4.05562i	−1.90226	+	0.249135i
$266$		0			0
$267$	−21.2272	−	8.91438i	−1.29908	−	0.545551i
$268$		0			0
$269$	22.3119	+	16.2105i	1.36038	+	0.988373i	0.998421	+	0.0561787i	$0.0178917\pi$
$269$	22.3119	+	16.2105i	1.36038	+	0.988373i	0.361958	+	0.932194i	$0.382108\pi$
$270$		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
$273$	−5.75591	−	9.49665i	−0.348363	−	0.574763i
$274$		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
$279$	1.70243	−	3.26200i	0.101922	−	0.195291i
$280$		0			0
$281$	−3.62737	+	4.99264i	−0.216391	+	0.297836i	−0.903388	−	0.428823i	$-0.858928\pi$
$281$	−3.62737	+	4.99264i	−0.216391	+	0.297836i	0.686998	+	0.726660i	$0.258928\pi$
$282$		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
$285$	−7.82916	−	13.7363i	−0.463759	−	0.813669i
$286$		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
$291$	20.5325	−	17.3636i	1.20364	−	1.01787i
$292$		0			0
$293$	−14.3870	−	14.3870i	−0.840500	−	0.840500i	0.148424	−	0.988924i	$-0.452580\pi$
$293$	−14.3870	−	14.3870i	−0.840500	−	0.840500i	−0.988924	+	0.148424i	$0.952580\pi$
$294$		0			0
$295$	0.732441	−	27.2695i	0.0426444	−	1.58769i
$296$		0			0
$297$	5.49736	+	1.40535i	0.318989	+	0.0815466i
$298$		0			0
$299$	−23.4730			−1.35748
$300$		0			0
$301$	2.69270			0.155205
$302$		0			0
$303$	14.2779	+	12.3157i	0.820244	+	0.707516i
$304$		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
$309$	9.24191	+	10.9286i	0.525754	+	0.621705i
$310$		0			0
$311$	23.6419	−	7.68170i	1.34061	−	0.435589i	0.451084	−	0.892481i	$-0.351037\pi$
$311$	23.6419	−	7.68170i	1.34061	−	0.435589i	0.889522	+	0.456892i	$0.151037\pi$
$312$		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
$315$	2.95992	−	8.08900i	0.166773	−	0.455764i
$316$		0			0
$317$	−15.6631	+	2.48079i	−0.879728	+	0.139335i	−0.579929	−	0.814667i	$-0.696920\pi$
$317$	−15.6631	+	2.48079i	−0.879728	+	0.139335i	−0.299799	+	0.954002i	$0.596920\pi$
$318$		0			0
$319$	0.778322	−	1.07127i	0.0435777	−	0.0599795i
$320$		0			0
$321$	1.18410	+	16.0476i	0.0660898	+	0.895691i
$322$		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
$327$	−28.8385	+	17.4790i	−1.59478	+	0.966591i
$328$		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
$333$	−12.6395	−	17.7593i	−0.692642	−	0.973203i
$334$		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
$339$	2.59141	−	10.5663i	0.140746	−	0.573881i
$340$		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
$345$	−11.3792	−	14.2130i	−0.612636	−	0.765202i
$346$		0			0
$347$	−2.24653	+	14.1841i	−0.120600	+	0.761440i	0.851062	+	0.525066i	$0.175959\pi$
$347$	−2.24653	+	14.1841i	−0.120600	+	0.761440i	−0.971662	+	0.236374i	$0.924041\pi$
$348$		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	0.284281	−	0.958741i	$-0.408245\pi$
$353$	4.85452	+	0.768881i	0.258380	+	0.0409234i	−0.0259004	+	0.999665i	$0.508245\pi$
$354$		0			0
$355$	−18.2428	−	14.0177i	−0.968227	−	0.743982i
$356$		0			0
$357$	−4.81574	+	1.13129i	−0.254876	+	0.0598744i
$358$		0			0
$359$	−2.41734	+	7.43981i	−0.127582	+	0.392658i	−0.994363	−	0.106032i	$-0.966185\pi$
$359$	−2.41734	+	7.43981i	−0.127582	+	0.392658i	0.866780	+	0.498690i	$0.166185\pi$
$360$		0			0
$361$	0.721413	+	2.22028i	0.0379691	+	0.116857i
$362$		0			0
$363$	1.41554	−	16.9281i	0.0742967	−	0.888495i
$364$		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
$369$	−4.49294	+	26.6771i	−0.233893	+	1.38875i
$370$		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
$375$	2.89719	+	19.1470i	0.149610	+	0.988745i
$376$		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
$381$	−2.36786	−	5.79647i	−0.121309	−	0.296962i
$382$		0			0
$383$	−2.51909	−	15.9049i	−0.128720	−	0.812703i	−0.964586	−	0.263770i	$-0.915034\pi$
$383$	−2.51909	−	15.9049i	−0.128720	−	0.812703i	0.835866	−	0.548933i	$-0.184966\pi$
$384$		0			0
$385$	3.08242	+	0.573438i	0.157094	+	0.0292251i
$386$		0			0
$387$	−5.05331	−	3.74745i	−0.256874	−	0.190494i
$388$		0			0
$389$	7.88904	+	24.2800i	0.399990	+	1.23104i	0.925007	+	0.379951i	$0.124059\pi$
$389$	7.88904	+	24.2800i	0.399990	+	1.23104i	−0.525017	+	0.851092i	$0.675941\pi$
$390$		0			0
$391$	−3.23122	+	9.94467i	−0.163410	+	0.502924i
$392$		0			0
$393$	4.42832	+	18.8507i	0.223379	+	0.950890i
$394$		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	$0.242650\pi$
$401$			27.6582i			1.38119i	−0.723244	+	0.690593i	$0.757350\pi$
$402$		0			0
$403$	−0.958028	+	6.04875i	−0.0477228	+	0.301310i
$404$		0			0
$405$	−16.8123	+	11.0610i	−0.835410	+	0.549627i
$406$		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
$411$	20.7142	+	5.08023i	1.02176	+	0.250589i
$412$		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
$417$	11.0931	−	26.4153i	0.543232	−	1.29356i
$418$		0			0
$419$	14.7007	+	10.6807i	0.718178	+	0.521787i	0.885802	−	0.464064i	$-0.153609\pi$
$419$	14.7007	+	10.6807i	0.718178	+	0.521787i	−0.167624	+	0.985851i	$0.553609\pi$
$420$		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
$423$	−1.23767	−	0.0120971i	−0.0601775	−	0.000588183i
$424$		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
$429$	−9.41837	+	0.694947i	−0.454723	+	0.0335524i
$430$		0			0
$431$	11.3436	−	15.6131i	0.546401	−	0.752057i	−0.443117	−	0.896464i	$-0.646127\pi$
$431$	11.3436	−	15.6131i	0.546401	−	0.752057i	0.989518	+	0.144407i	$0.0461274\pi$
$432$		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
$435$	0.950886	+	4.59916i	0.0455915	+	0.220513i
$436$		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
$441$	−15.8799	+	2.35627i	−0.756187	+	0.112204i
$442$		0			0
$443$	20.1922	+	20.1922i	0.959360	+	0.959360i	0.999206	−	0.0398456i	$-0.0126866\pi$
$443$	20.1922	+	20.1922i	0.959360	+	0.959360i	−0.0398456	+	0.999206i	$0.512687\pi$
$444$		0			0
$445$	16.8186	+	24.5065i	0.797278	+	1.16172i
$446$		0			0
$447$	−8.16186	+	9.46228i	−0.386043	+	0.447551i
$448$		0			0
$449$	−19.6086			−0.925387			−0.462693	−	0.886518i	$-0.653117\pi$
$449$	−19.6086			−0.925387			−0.462693	+	0.886518i	$0.653117\pi$
$450$		0			0
$451$	−9.84714			−0.463684
$452$		0			0
$453$	9.72335	−	11.2726i	0.456843	−	0.529631i
$454$		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
$459$	10.6120	+	4.57902i	0.495324	+	0.213730i
$460$		0			0
$461$	−7.31001	+	2.37517i	−0.340461	+	0.110623i	−0.474257	−	0.880386i	$-0.657283\pi$
$461$	−7.31001	+	2.37517i	−0.340461	+	0.110623i	0.133796	+	0.991009i	$0.457283\pi$
$462$		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
$465$	−4.12698	+	2.35221i	−0.191384	+	0.109081i
$466$		0			0
$467$	−2.70390	+	0.428256i	−0.125122	+	0.0198173i	−0.218681	−	0.975796i	$-0.570175\pi$
$467$	−2.70390	+	0.428256i	−0.125122	+	0.0198173i	0.0935595	+	0.995614i	$0.470175\pi$
$468$		0			0
$469$	5.92182	−	8.15069i	0.273444	−	0.376364i
$470$		0			0
$471$	−22.5300	+	1.66241i	−1.03813	+	0.0765997i
$472$		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
$477$	−0.409524	+	41.8987i	−0.0187508	+	1.91841i
$478$		0			0
$479$	5.68590	−	4.13105i	0.259796	−	0.188753i	−0.450261	−	0.892897i	$-0.648669\pi$
$479$	5.68590	−	4.13105i	0.259796	−	0.188753i	0.710057	+	0.704144i	$0.248669\pi$
$480$		0			0
$481$	29.3513	+	21.3249i	1.33830	+	0.972334i
$482$		0			0
$483$	4.04816	−	9.63961i	0.184198	−	0.438617i
$484$		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
$489$	−1.59018	−	0.389997i	−0.0719104	−	0.0176363i
$490$		0			0
$491$	7.06686	+	2.29616i	0.318923	+	0.103624i	0.464104	−	0.885781i	$-0.346376\pi$
$491$	7.06686	+	2.29616i	0.318923	+	0.103624i	−0.145181	+	0.989405i	$0.546376\pi$
$492$		0			0
$493$	1.90721	−	1.90721i	0.0858963	−	0.0858963i
$494$		0			0
$495$	−4.98662	−	5.36597i	−0.224132	−	0.241182i
$496$		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	0.925397	−	0.378998i	$-0.123731\pi$
$503$	37.8665	+	5.99747i	1.68839	+	0.267414i	0.762988	+	0.646412i	$0.223731\pi$
$504$		0			0
$505$	−6.89793	−	23.3447i	−0.306954	−	1.03882i
$506$		0			0
$507$	−4.72616	−	20.1185i	−0.209896	−	0.893493i
$508$		0			0
$509$	7.22530	−	22.2372i	0.320256	−	0.985646i	−0.653281	−	0.757116i	$-0.726608\pi$
$509$	7.22530	−	22.2372i	0.320256	−	0.985646i	0.973537	−	0.228531i	$-0.0733921\pi$
$510$		0			0
$511$	2.64231	+	8.13220i	0.116889	+	0.359747i
$512$		0			0
$513$	−19.7146	+	7.82947i	−0.870422	+	0.345679i
$514$		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
$519$	2.45868	+	6.01880i	0.107924	+	0.264196i
$520$		0			0
$521$	6.11512	+	8.41674i	0.267908	+	0.368744i	0.921682	−	0.387946i	$-0.126815\pi$
$521$	6.11512	+	8.41674i	0.267908	+	0.368744i	−0.653774	+	0.756690i	$0.726815\pi$
$522$		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
$525$	−8.86414	+	6.71433i	−0.386863	+	0.293037i
$526$		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
$531$	−36.0908	−	6.07839i	−1.56621	−	0.263780i
$532$		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
$537$	1.45745	−	17.4292i	0.0628935	−	0.752127i
$538$		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
$543$	−20.7669	+	4.87849i	−0.891194	+	0.209356i
$544$		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
$555$	1.31652	+	28.1102i	0.0558832	+	1.19321i
$556$		0			0
$557$	−3.81138	+	3.81138i	−0.161493	+	0.161493i	−0.783228	−	0.621735i	$-0.786428\pi$
$557$	−3.81138	+	3.81138i	−0.161493	+	0.161493i	0.621735	+	0.783228i	$0.286428\pi$
$558$		0			0
$559$	9.95852	+	3.23572i	0.421200	+	0.136856i
$560$		0			0
$561$	−1.00208	+	4.08589i	−0.0423078	+	0.172507i
$562$		0			0
$563$	−29.0405	+	14.7969i	−1.22391	+	0.623615i	−0.941931	−	0.335805i	$-0.890992\pi$
$563$	−29.0405	+	14.7969i	−1.22391	+	0.623615i	−0.281981	+	0.959420i	$0.590992\pi$
$564$		0			0
$565$	−10.1946	+	9.66125i	−0.428889	+	0.406452i
$566$		0			0
$567$	−10.1922	−	5.44670i	−0.428032	−	0.228740i
$568$		0			0
$569$	−1.73598	−	1.26126i	−0.0727760	−	0.0528749i	0.550802	−	0.834636i	$-0.314322\pi$
$569$	−1.73598	−	1.26126i	−0.0727760	−	0.0528749i	−0.623578	+	0.781761i	$0.714322\pi$
$570$		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
$573$	−19.0460	+	11.5438i	−0.795658	+	0.482247i
$574$		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
$579$	−1.79699	−	24.3540i	−0.0746804	−	1.01212i
$580$		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
$585$	20.6670	−	26.3590i	0.854476	−	1.08981i
$586$		0			0
$587$	12.2504	+	24.0428i	0.505628	+	0.992352i	0.992883	+	0.119092i	$0.0379983\pi$
$587$	12.2504	+	24.0428i	0.505628	+	0.992352i	−0.487255	+	0.873260i	$0.662002\pi$
$588$		0			0
$589$	−4.76196	+	1.54725i	−0.196213	+	0.0637535i
$590$		0			0
$591$	−8.60267	−	10.1727i	−0.353866	−	0.418448i
$592$		0			0
$593$	7.14857	+	7.14857i	0.293556	+	0.293556i	0.838483	−	0.544927i	$-0.183443\pi$
$593$	7.14857	+	7.14857i	0.293556	+	0.293556i	−0.544927	+	0.838483i	$0.683443\pi$
$594$		0			0
$595$	6.01858	+	2.13585i	0.246738	+	0.0875614i
$596$		0			0
$597$	21.0980	+	18.1985i	0.863485	+	0.744815i
$598$		0			0
$599$	−20.6392			−0.843294			−0.421647	−	0.906760i	$-0.638548\pi$
$599$	−20.6392			−0.843294			−0.421647	+	0.906760i	$0.638548\pi$
$600$		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
$603$	−22.4567	+	7.05471i	−0.914506	+	0.287290i
$604$		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
$609$	−2.05924	+	1.74143i	−0.0834446	+	0.0705661i
$610$		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
$615$	23.5133	−	25.8240i	0.948149	−	1.04132i
$616$		0			0
$617$	3.30490	−	0.523445i	0.133050	−	0.0210731i	−0.0895540	−	0.995982i	$-0.528544\pi$
$617$	3.30490	−	0.523445i	0.133050	−	0.0210731i	0.222604	+	0.974909i	$0.428544\pi$
$618$		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
$621$	−21.0126	+	12.4565i	−0.843205	+	0.499862i
$622$		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
$627$	−4.00213	−	6.60310i	−0.159830	−	0.263702i
$628$		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
$633$	36.0068	+	15.1211i	1.43114	+	0.601010i
$634$		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
$639$	−22.0381	+	21.6114i	−0.871813	+	0.854935i
$640$		0			0
$641$	−26.6743	−	8.66700i	−1.05357	−	0.342326i	−0.269502	−	0.963000i	$-0.586859\pi$
$641$	−26.6743	−	8.66700i	−1.05357	−	0.342326i	−0.784069	+	0.620674i	$0.786859\pi$
$642$		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
$645$	2.86843	+	7.59853i	0.112945	+	0.299192i
$646$		0			0
$647$	2.38692	−	15.0704i	0.0938396	−	0.592480i	−0.895296	−	0.445472i	$-0.853036\pi$
$647$	2.38692	−	15.0704i	0.0938396	−	0.592480i	0.989135	−	0.147008i	$-0.0469642\pi$
$648$		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	−0.283068	−	0.959100i	$-0.591352\pi$
$653$	−21.6865	−	3.43481i	−0.848660	−	0.134415i	−0.565592	+	0.824685i	$0.691352\pi$
$654$		0			0
$655$	8.36055	−	23.5591i	0.326674	−	0.920529i
$656$		0			0
$657$	6.35888	−	18.9388i	0.248084	−	0.738872i
$658$		0			0
$659$	−3.02628	+	9.31393i	−0.117887	+	0.362819i	−0.992538	−	0.121934i	$-0.961090\pi$
$659$	−3.02628	+	9.31393i	−0.117887	+	0.362819i	0.874651	+	0.484753i	$0.161090\pi$
$660$		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
$663$	−19.1696	−	1.60298i	−0.744487	−	0.0622546i
$664$		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
$669$	18.2764	−	7.46591i	0.706607	−	0.288649i
$670$		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
$675$	25.9794	−	0.264307i	0.999948	−	0.0101732i
$676$		0			0
$677$	32.0266	+	16.3184i	1.23088	+	0.627167i	0.943730	−	0.330718i	$-0.107291\pi$
$677$	32.0266	+	16.3184i	1.23088	+	0.627167i	0.287154	+	0.957884i	$0.407291\pi$
$678$		0			0
$679$	−11.7173	−	16.1274i	−0.449668	−	0.618914i
$680$		0			0
$681$	22.7429	−	9.29046i	0.871510	−	0.356011i
$682$		0			0
$683$	4.75779	+	30.0395i	0.182052	+	1.14943i	0.894289	+	0.447490i	$0.147682\pi$
$683$	4.75779	+	30.0395i	0.182052	+	1.14943i	−0.712237	+	0.701939i	$0.752318\pi$
$684$		0			0
$685$	−18.9400	−	19.9855i	−0.723660	−	0.763607i
$686$		0			0
$687$	−6.05567	−	0.506380i	−0.231038	−	0.0193196i
$688$		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
$693$	1.33890	−	3.98768i	0.0508607	−	0.151479i
$694$		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	$-0.755679\pi$
$701$		−	36.7694i		−	1.38876i	0.719609	−	0.694380i	$-0.244321\pi$
$702$		0			0
$703$	−4.64018	+	29.2970i	−0.175008	+	1.10496i
$704$		0			0
$705$	1.33525	+	0.877715i	0.0502885	+	0.0330567i
$706$		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
$711$	−20.2881	+	19.8954i	−0.760865	+	0.746135i
$712$		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
$717$	−22.9682	−	9.64553i	−0.857765	−	0.360219i
$718$		0			0
$719$	−27.9485	−	20.3058i	−1.04230	−	0.757278i	−0.0715696	−	0.997436i	$-0.522801\pi$
$719$	−27.9485	−	20.3058i	−1.04230	−	0.757278i	−0.970734	+	0.240158i	$0.922801\pi$
$720$		0			0
$721$	8.58395	−	6.23660i	0.319683	−	0.232263i
$722$		0			0
$723$	2.54932	+	4.20611i	0.0948102	+	0.156427i
$724$		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
$729$	11.5472	+	24.4062i	0.427673	+	0.903933i
$730$		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
$735$	18.8864	+	8.53490i	0.696635	+	0.314815i
$736$		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
$741$	26.9584	−	22.7977i	0.990340	−	0.837495i
$742$		0			0
$743$	−30.1299	−	30.1299i	−1.10536	−	1.10536i	−0.993752	−	0.111607i	$-0.964400\pi$
$743$	−30.1299	−	30.1299i	−1.10536	−	1.10536i	−0.111607	−	0.993752i	$-0.535600\pi$
$744$		0			0
$745$	15.4711	−	4.57141i	0.566816	−	0.167484i
$746$		0			0
$747$	51.0938	−	16.0510i	1.86943	−	0.587276i
$748$		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
$753$	16.8494	+	14.5337i	0.614025	+	0.529638i
$754$		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
$759$	−5.74143	−	6.78925i	−0.208401	−	0.246434i
$760$		0			0
$761$	−41.1754	+	13.3787i	−1.49261	+	0.484978i	−0.937852	−	0.347035i	$-0.887189\pi$
$761$	−41.1754	+	13.3787i	−1.49261	+	0.484978i	−0.554756	+	0.832013i	$0.687189\pi$
$762$		0			0
$763$	11.3495	+	22.2746i	0.410878	+	0.806394i
$764$		0			0
$765$	−8.32241	−	12.3844i	−0.300898	−	0.447758i
$766$		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
$771$	−1.70851	−	23.1549i	−0.0615306	−	0.833902i
$772$		0			0
$773$	−7.28640	+	14.3004i	−0.262074	+	0.514348i	−0.984122	−	0.177494i	$-0.943201\pi$
$773$	−7.28640	+	14.3004i	−0.262074	+	0.514348i	0.722048	+	0.691843i	$0.243201\pi$
$774$		0			0
$775$	6.12370	+	0.329194i	0.219970	+	0.0118250i
$776$		0			0
$777$	−13.8194	+	8.37593i	−0.495769	+	0.300485i
$778$		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
$783$	6.28806	−	0.402223i	0.224717	−	0.0143743i
$784$		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
$789$	0.961237	−	3.91936i	0.0342209	−	0.139533i
$790$		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
$795$	29.7133	−	45.2022i	1.05382	−	1.60316i
$796$		0			0
$797$	−7.08694	+	44.7452i	−0.251032	+	1.58496i	0.463981	+	0.885845i	$0.346421\pi$
$797$	−7.08694	+	44.7452i	−0.251032	+	1.58496i	−0.715014	+	0.699111i	$0.753579\pi$
$798$		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
$807$	−46.5023	+	10.9241i	−1.63696	+	0.384548i
$808$		0			0
$809$	10.6570	−	32.7987i	0.374679	−	1.15314i	−0.569016	−	0.822326i	$-0.692676\pi$
$809$	10.6570	−	32.7987i	0.374679	−	1.15314i	0.943695	−	0.330816i	$-0.107324\pi$
$810$		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
$813$	−4.56191	+	54.5547i	−0.159993	+	1.91332i
$814$		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
$819$	18.9670	+	3.19441i	0.662760	+	0.111622i
$820$		0			0
$821$	16.6270	+	22.8851i	0.580287	+	0.798697i	0.993727	−	0.111835i	$-0.0356728\pi$
$821$	16.6270	+	22.8851i	0.580287	+	0.798697i	−0.413440	+	0.910531i	$0.635673\pi$
$822$		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
$825$	1.66540	+	9.30912i	0.0579817	+	0.324102i
$826$		0			0
$827$	34.2714	+	17.4622i	1.19173	+	0.607219i	0.933400	−	0.358837i	$-0.116827\pi$
$827$	34.2714	+	17.4622i	1.19173	+	0.607219i	0.258334	+	0.966056i	$0.416827\pi$
$828$		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
$831$	4.53905	+	11.1115i	0.157458	+	0.385454i
$832$		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
$837$	2.35231	+	5.92312i	0.0813076	+	0.204733i
$838$		0			0
$839$	−4.25109	−	13.0835i	−0.146764	−	0.451693i	0.850470	−	0.526024i	$-0.176318\pi$
$839$	−4.25109	−	13.0835i	−0.146764	−	0.451693i	−0.997234	+	0.0743309i	$0.976318\pi$
$840$		0			0
$841$	−8.50711	+	26.1822i	−0.293348	+	0.902834i
$842$		0			0
$843$	−2.44446	−	10.4056i	−0.0841915	−	0.358390i
$844$		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
$855$	26.8730	+	5.27156i	0.919036	+	0.180284i
$856$		0			0
$857$	17.0033	−	17.0033i	0.580821	−	0.580821i	−0.354308	−	0.935129i	$-0.615283\pi$
$857$	17.0033	−	17.0033i	0.580821	−	0.580821i	0.935129	+	0.354308i	$0.115283\pi$
$858$		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
$861$	19.4780	+	4.77704i	0.663807	+	0.162801i
$862$		0			0
$863$	4.75115	−	2.42083i	0.161731	−	0.0824062i	−0.371251	−	0.928532i	$-0.621071\pi$
$863$	4.75115	−	2.42083i	0.161731	−	0.0824062i	0.532982	+	0.846126i	$0.321071\pi$
$864$		0			0
$865$	1.53516	−	8.25197i	0.0521969	−	0.280575i
$866$		0			0
$867$	8.08291	−	19.2473i	0.274510	−	0.653672i
$868$		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
$873$	−0.455210	+	46.5729i	−0.0154065	+	1.57625i
$874$		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
$879$	35.1454	−	2.59325i	1.18542	−	0.0874682i
$880$		0			0
$881$	−8.93089	+	12.2923i	−0.300889	+	0.414139i	−0.932513	−	0.361136i	$-0.882389\pi$
$881$	−8.93089	+	12.2923i	−0.300889	+	0.414139i	0.631624	+	0.775275i	$0.282389\pi$
$882$		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
$885$	34.9367	+	31.8106i	1.17438	+	1.06930i
$886$		0			0
$887$	17.1951	+	33.7472i	0.577354	+	1.13312i	0.976355	+	0.216171i	$0.0693569\pi$
$887$	17.1951	+	33.7472i	0.577354	+	1.13312i	−0.399001	+	0.916950i	$0.630643\pi$
$888$		0			0
$889$	−4.41465	+	1.43441i	−0.148063	+	0.0481085i
$890$		0			0
$891$	−8.06235	+	5.62019i	−0.270099	+	0.188283i
$892$		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
$897$	26.5550	−	30.7860i	0.886645	−	1.02791i
$898$		0			0
$899$	1.48728			0.0496035
$900$		0			0
$901$	−31.0664			−1.03497
$902$		0			0
$903$	−3.04626	+	3.53161i	−0.101373	+	0.117525i
$904$		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
$909$	−32.3052	+	4.79346i	−1.07149	+	0.158989i
$910$		0			0
$911$	−7.41217	+	2.40836i	−0.245576	+	0.0797925i	−0.429219	−	0.903201i	$-0.641211\pi$
$911$	−7.41217	+	2.40836i	−0.245576	+	0.0797925i	0.183643	+	0.982993i	$0.441211\pi$
$912$		0			0
$913$	8.85014	+	17.3694i	0.292897	+	0.574843i
$914$		0			0
$915$	−4.28780	−	0.474783i	−0.141750	−	0.0156959i
$916$		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
$921$	−53.2838	+	3.93162i	−1.75576	+	0.129551i
$922$		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
$927$	−24.7887	−	0.242289i	−0.814169	−	0.00795780i
$928$		0			0
$929$	−9.49314	+	6.89717i	−0.311460	+	0.226289i	−0.732523	−	0.680743i	$-0.761657\pi$
$929$	−9.49314	+	6.89717i	−0.311460	+	0.226289i	0.421063	+	0.907032i	$0.361657\pi$
$930$		0			0
$931$	17.6735	+	12.8406i	0.579226	+	0.420832i
$932$		0			0
$933$	−16.6711	+	39.6978i	−0.545787	+	1.29965i
$934$		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
$939$	19.1517	+	4.69702i	0.624992	+	0.153281i
$940$		0			0
$941$	31.7416	+	10.3135i	1.03475	+	0.336210i	0.776665	−	0.629914i	$-0.216910\pi$
$941$	31.7416	+	10.3135i	1.03475	+	0.336210i	0.258082	+	0.966123i	$0.416910\pi$
$942$		0			0
$943$	29.9757	−	29.9757i	0.976143	−	0.976143i
$944$		0			0
$945$	7.26056	+	13.0332i	0.236186	+	0.423969i
$946$		0			0
$947$	0.422572	−	2.66801i	0.0137317	−	0.0866988i	−0.979871	−	0.199633i	$-0.936025\pi$
$947$	0.422572	−	2.66801i	0.0137317	−	0.0866988i	0.993602	+	0.112934i	$0.0360250\pi$
$948$		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	0.492637	−	0.870235i	$-0.336033\pi$
$953$	21.3701	+	3.38469i	0.692245	+	0.109641i	0.199608	+	0.979876i	$0.436033\pi$
$954$		0			0
$955$	28.7417	+	0.771982i	0.930059	+	0.0249808i
$956$		0			0
$957$	0.524505	+	2.23273i	0.0169549	+	0.0721741i
$958$		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
$963$	−22.3868	−	16.6017i	−0.721404	−	0.534981i
$964$		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
$969$	−5.94758	−	14.5596i	−0.191064	−	0.467721i
$970$		0			0
$971$	−23.2793	−	32.0412i	−0.747069	−	1.02825i	−0.998181	−	0.0602944i	$-0.980796\pi$
$971$	−23.2793	−	32.0412i	−0.747069	−	1.02825i	0.251111	−	0.967958i	$-0.419204\pi$
$972$		0			0
$973$	−18.9244	−	9.64244i	−0.606687	−	0.309122i
$974$		0			0
$975$	−40.8509	+	14.1801i	−1.30828	+	0.454128i
$976$		0			0
$977$	−36.2603	−	18.4756i	−1.16007	−	0.591085i	−0.235417	−	0.971894i	$-0.575646\pi$
$977$	−36.2603	−	18.4756i	−1.16007	−	0.591085i	−0.924654	+	0.380809i	$0.875646\pi$
$978$		0			0
$979$	8.53179	+	11.7430i	0.272677	+	0.375308i
$980$		0			0
$981$	9.70047	−	57.5972i	0.309712	−	1.83894i
$982$		0			0
$983$	1.75697	+	11.0931i	0.0560387	+	0.353814i	0.999735	+	0.0230024i	$0.00732255\pi$
$983$	1.75697	+	11.0931i	0.0560387	+	0.353814i	−0.943697	+	0.330812i	$0.892677\pi$
$984$		0			0
$985$	2.23348	+	17.0536i	0.0711646	+	0.543374i
$986$		0			0
$987$	−0.0764612	+	0.914379i	−0.00243379	+	0.0291050i
$988$		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
$993$	21.2803	−	4.99908i	0.675308	−	0.158641i
$994$		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.17.3	✓	80
3.2	odd	2	inner	300.2.x.a.17.6	yes	80
25.3	odd	20	inner	300.2.x.a.53.6	yes	80
75.53	even	20	inner	300.2.x.a.53.3	yes	80

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

\(f(q)\)	\(=\)	\(q+(-1.13130 + 1.31155i) q^{3} +(2.14441 - 0.633635i) q^{5} +(0.907947 + 0.907947i) q^{7} +(-0.440321 - 2.96751i) q^{9} +O(q^{10})\)	\(q+(-1.13130 + 1.31155i) q^{3} +(2.14441 - 0.633635i) q^{5} +(0.907947 + 0.907947i) q^{7} +(-0.440321 - 2.96751i) q^{9} +(1.03855 - 0.337444i) q^{11} +(2.26685 + 4.44893i) q^{13} +(-1.59493 + 3.52933i) q^{15} +(2.19690 - 0.347955i) q^{17} +(-2.39954 + 3.30268i) q^{19} +(-2.21798 + 0.163656i) q^{21} +(-2.13422 + 4.18865i) q^{23} +(4.19701 - 2.71755i) q^{25} +(4.39017 + 2.77964i) q^{27} +(0.981024 - 0.712755i) q^{29} +(0.992266 + 0.720923i) q^{31} +(-0.732332 + 1.74385i) q^{33} +(2.52232 + 1.37171i) q^{35} +(6.47404 - 3.29869i) q^{37} +(-8.39948 - 2.06000i) q^{39} +(-8.57625 - 2.78659i) q^{41} +(1.48285 - 1.48285i) q^{43} +(-2.82455 - 6.08456i) q^{45} +(0.0645410 - 0.407496i) q^{47} -5.35127i q^{49} +(-2.02900 + 3.27499i) q^{51} +(-13.7949 - 2.18491i) q^{53} +(2.01325 - 1.38168i) q^{55} +(-1.61703 - 6.88343i) q^{57} +(3.76991 - 11.6026i) q^{59} +(0.344205 + 1.05936i) q^{61} +(2.29455 - 3.09413i) q^{63} +(7.68005 + 8.10400i) q^{65} +(-1.22742 - 7.74963i) q^{67} +(-3.07917 - 7.53776i) q^{69} +(-6.04759 - 8.32380i) q^{71} +(5.93345 + 3.02324i) q^{73} +(-1.18388 + 8.57895i) q^{75} +(1.24932 + 0.636563i) q^{77} +(-5.56738 - 7.66285i) q^{79} +(-8.61223 + 2.61331i) q^{81} +(2.79265 + 17.6321i) q^{83} +(4.49059 - 2.13819i) q^{85} +(-0.175018 + 2.09300i) q^{87} +(4.10757 + 12.6418i) q^{89} +(-1.98122 + 6.09757i) q^{91} +(-2.06808 + 0.485825i) q^{93} +(-3.05291 + 8.60274i) q^{95} +(-15.3339 - 2.42865i) q^{97} +(-1.45866 - 2.93331i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{3} + 4 q^{7}+O(q^{10}) \) 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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