LMFDB - Embedded newform 300.2.x.a.53.3

Newspace parameters

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

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			53.3
Character	$\chi$	$=$	300.53
Dual form			300.2.x.a.17.3

$q$-expansion

$f(q)$	$=$	$q+(-1.13130 - 1.31155i) q^{3} +(2.14441 + 0.633635i) q^{5} +(0.907947 - 0.907947i) q^{7} +(-0.440321 + 2.96751i) q^{9} +O(q^{10})$	\(q+(-1.13130 - 1.31155i) q^{3} +(2.14441 + 0.633635i) q^{5} +(0.907947 - 0.907947i) q^{7} +(-0.440321 + 2.96751i) q^{9} +(1.03855 + 0.337444i) q^{11} +(2.26685 - 4.44893i) q^{13} +(-1.59493 - 3.52933i) q^{15} +(2.19690 + 0.347955i) q^{17} +(-2.39954 - 3.30268i) q^{19} +(-2.21798 - 0.163656i) q^{21} +(-2.13422 - 4.18865i) q^{23} +(4.19701 + 2.71755i) q^{25} +(4.39017 - 2.77964i) q^{27} +(0.981024 + 0.712755i) q^{29} +(0.992266 - 0.720923i) q^{31} +(-0.732332 - 1.74385i) q^{33} +(2.52232 - 1.37171i) q^{35} +(6.47404 + 3.29869i) q^{37} +(-8.39948 + 2.06000i) q^{39} +(-8.57625 + 2.78659i) q^{41} +(1.48285 + 1.48285i) q^{43} +(-2.82455 + 6.08456i) q^{45} +(0.0645410 + 0.407496i) q^{47} +5.35127i q^{49} +(-2.02900 - 3.27499i) q^{51} +(-13.7949 + 2.18491i) q^{53} +(2.01325 + 1.38168i) q^{55} +(-1.61703 + 6.88343i) q^{57} +(3.76991 + 11.6026i) q^{59} +(0.344205 - 1.05936i) q^{61} +(2.29455 + 3.09413i) q^{63} +(7.68005 - 8.10400i) q^{65} +(-1.22742 + 7.74963i) q^{67} +(-3.07917 + 7.53776i) q^{69} +(-6.04759 + 8.32380i) q^{71} +(5.93345 - 3.02324i) q^{73} +(-1.18388 - 8.57895i) q^{75} +(1.24932 - 0.636563i) q^{77} +(-5.56738 + 7.66285i) q^{79} +(-8.61223 - 2.61331i) q^{81} +(2.79265 - 17.6321i) q^{83} +(4.49059 + 2.13819i) q^{85} +(-0.175018 - 2.09300i) q^{87} +(4.10757 - 12.6418i) q^{89} +(-1.98122 - 6.09757i) q^{91} +(-2.06808 - 0.485825i) q^{93} +(-3.05291 - 8.60274i) q^{95} +(-15.3339 + 2.42865i) q^{97} +(-1.45866 + 2.93331i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80q - 2q^{3} + 4q^{7} + O(q^{10}) $	$ 80q - 2q^{3} + 4q^{7} + 12q^{13} + 10q^{15} + 20q^{19} + 40q^{25} - 14q^{27} - 20q^{33} + 12q^{37} - 40q^{39} + 12q^{43} - 60q^{45} - 76q^{57} - 98q^{63} - 36q^{67} - 70q^{69} - 44q^{73} - 90q^{75} - 40q^{79} + 20q^{81} - 100q^{85} - 70q^{87} - 18q^{93} - 56q^{97} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$151$	$277$
$\chi(n)$	$-1$	$1$	$e\left(\frac{7}{20}\right)$

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	−0.514387	−	0.857558i	$-0.671980\pi$
$7$	0.907947	−	0.907947i	0.343172	−	0.343172i	0.857558	+	0.514387i	$0.171980\pi$
$8$		0			0
$9$	−0.440321	+	2.96751i	−0.146774	+	0.989170i
$10$		0			0
$11$	1.03855	+	0.337444i	0.313133	+	0.101743i	0.461367	−	0.887209i	$-0.347359\pi$
$11$	1.03855	+	0.337444i	0.313133	+	0.101743i	−0.148234	+	0.988952i	$0.547359\pi$
$12$		0			0
$13$	2.26685	−	4.44893i	0.628710	−	1.23391i	−0.328496	−	0.944505i	$-0.606542\pi$
$13$	2.26685	−	4.44893i	0.628710	−	1.23391i	0.957206	−	0.289407i	$-0.0934581\pi$
$14$		0			0
$15$	−1.59493	−	3.52933i	−0.411809	−	0.911270i
$16$		0			0
$17$	2.19690	+	0.347955i	0.532827	+	0.0843916i	0.417050	−	0.908884i	$-0.363064\pi$
$17$	2.19690	+	0.347955i	0.532827	+	0.0843916i	0.115777	+	0.993275i	$0.463064\pi$
$18$		0			0
$19$	−2.39954	−	3.30268i	−0.550491	−	0.757686i	0.439587	−	0.898200i	$-0.355125\pi$
$19$	−2.39954	−	3.30268i	−0.550491	−	0.757686i	−0.990079	+	0.140513i	$0.955125\pi$
$20$		0			0
$21$	−2.21798	−	0.163656i	−0.484002	−	0.0357128i
$22$		0			0
$23$	−2.13422	−	4.18865i	−0.445016	−	0.873394i	−0.999160	−	0.0409730i	$-0.986954\pi$
$23$	−2.13422	−	4.18865i	−0.445016	−	0.873394i	0.554144	−	0.832421i	$-0.313046\pi$
$24$		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	0.675134	−	0.737695i	$-0.264086\pi$
$29$	0.981024	+	0.712755i	0.182172	+	0.132355i	−0.492962	+	0.870051i	$0.664086\pi$
$30$		0			0
$31$	0.992266	−	0.720923i	0.178216	−	0.129482i	−0.495101	−	0.868836i	$-0.664869\pi$
$31$	0.992266	−	0.720923i	0.178216	−	0.129482i	0.673317	+	0.739354i	$0.264869\pi$
$32$		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	0.896284	−	0.443480i	$-0.146256\pi$
$37$	6.47404	+	3.29869i	1.06432	+	0.542301i	0.168040	+	0.985780i	$0.446256\pi$
$38$		0			0
$39$	−8.39948	+	2.06000i	−1.34499	+	0.329864i
$40$		0			0
$41$	−8.57625	+	2.78659i	−1.33938	+	0.435193i	−0.889108	−	0.457697i	$-0.848675\pi$
$41$	−8.57625	+	2.78659i	−1.33938	+	0.435193i	−0.450277	+	0.892889i	$0.648675\pi$
$42$		0			0
$43$	1.48285	+	1.48285i	0.226133	+	0.226133i	0.811075	−	0.584942i	$-0.198883\pi$
$43$	1.48285	+	1.48285i	0.226133	+	0.226133i	−0.584942	+	0.811075i	$0.698883\pi$
$44$		0			0
$45$	−2.82455	+	6.08456i	−0.421059	+	0.907033i
$46$		0			0
$47$	0.0645410	+	0.407496i	0.00941428	+	0.0594394i	0.991948	−	0.126644i	$-0.0404206\pi$
$47$	0.0645410	+	0.407496i	0.00941428	+	0.0594394i	−0.982534	+	0.186083i	$0.940421\pi$
$48$		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	$-0.958818\pi$
$53$	−13.7949	+	2.18491i	−1.89488	+	0.300120i	−0.903240	+	0.429136i	$0.858818\pi$
$54$		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	0.823400	+	0.567462i	$0.192075\pi$
$59$	3.76991	+	11.6026i	0.490801	+	1.51053i	−0.332599	+	0.943068i	$0.607925\pi$
$60$		0			0
$61$	0.344205	−	1.05936i	0.0440710	−	0.135637i	−0.926600	−	0.376049i	$-0.877283\pi$
$61$	0.344205	−	1.05936i	0.0440710	−	0.135637i	0.970671	+	0.240412i	$0.0772826\pi$
$62$		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	0.791877	+	0.610680i	$0.209104\pi$
$67$	−1.22742	+	7.74963i	−0.149953	+	0.946768i	−0.941831	+	0.336088i	$0.890896\pi$
$68$		0			0
$69$	−3.07917	+	7.53776i	−0.370689	+	0.907439i
$70$		0			0
$71$	−6.04759	+	8.32380i	−0.717717	+	0.987853i	0.281879	+	0.959450i	$0.409042\pi$
$71$	−6.04759	+	8.32380i	−0.717717	+	0.987853i	−0.999597	+	0.0284034i	$0.990958\pi$
$72$		0			0
$73$	5.93345	−	3.02324i	0.694458	−	0.353844i	−0.0708692	−	0.997486i	$-0.522577\pi$
$73$	5.93345	−	3.02324i	0.694458	−	0.353844i	0.765327	+	0.643642i	$0.222577\pi$
$74$		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	−0.997798	−	0.0663280i	$-0.978872\pi$
$79$	−5.56738	+	7.66285i	−0.626380	+	0.862138i	0.371418	+	0.928466i	$0.378872\pi$
$80$		0			0
$81$	−8.61223	−	2.61331i	−0.956915	−	0.290368i
$82$		0			0
$83$	2.79265	−	17.6321i	0.306534	−	1.93538i	−0.0444903	−	0.999010i	$-0.514166\pi$
$83$	2.79265	−	17.6321i	0.306534	−	1.93538i	0.351024	−	0.936367i	$-0.385834\pi$
$84$		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	−0.457274	−	0.889326i	$-0.651174\pi$
$89$	4.10757	−	12.6418i	0.435401	−	1.34003i	0.892675	−	0.450701i	$-0.148826\pi$
$90$		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	−0.874740	−	0.484592i	$-0.838968\pi$
$97$	−15.3339	+	2.42865i	−1.55692	+	0.246592i	−0.682180	+	0.731184i	$0.738968\pi$
$98$		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	0.965822	+	0.259207i	$0.0834613\pi$
$103$	1.29267	+	8.16157i	0.127370	+	0.804184i	−0.838452	+	0.544976i	$0.816539\pi$
$104$		0			0
$105$	−4.65256	−	1.75633i	−0.454043	−	0.171401i
$106$		0			0
$107$	6.56922	+	6.56922i	0.635071	+	0.635071i	0.949335	−	0.314265i	$-0.101758\pi$
$107$	6.56922	+	6.56922i	0.635071	+	0.635071i	−0.314265	+	0.949335i	$0.601758\pi$
$108$		0			0
$109$	18.5165	−	6.01639i	1.77356	−	0.576265i	0.775108	−	0.631829i	$-0.217696\pi$
$109$	18.5165	−	6.01639i	1.77356	−	0.576265i	0.998455	+	0.0555636i	$0.0176956\pi$
$110$		0			0
$111$	−2.99769	−	12.2228i	−0.284528	−	1.16014i
$112$		0			0
$113$	−5.59661	−	2.85162i	−0.526485	−	0.268258i	0.170482	−	0.985361i	$-0.445468\pi$
$113$	−5.59661	−	2.85162i	−0.526485	−	0.268258i	−0.696967	+	0.717103i	$0.745468\pi$
$114$		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	0.806655	−	0.591023i	$-0.201276\pi$
$127$	−1.64120	−	3.22104i	−0.145633	−	0.285821i	−0.952287	+	0.305203i	$0.901276\pi$
$128$		0			0
$129$	0.267283	−	3.62239i	0.0235329	−	0.318933i
$130$		0			0
$131$	6.57127	+	9.04457i	0.574134	+	0.790228i	0.993037	−	0.117803i	$-0.0375852\pi$
$131$	6.57127	+	9.04457i	0.574134	+	0.790228i	−0.418903	+	0.908031i	$0.637585\pi$
$132$		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	0.518970	+	0.854792i	$0.326316\pi$
$137$	−5.59033	+	10.9716i	−0.477615	+	0.937371i	−0.996585	+	0.0825788i	$0.973684\pi$
$138$		0			0
$139$	−15.7315	−	5.11149i	−1.33433	−	0.433551i	−0.446939	−	0.894565i	$-0.647486\pi$
$139$	−15.7315	−	5.11149i	−1.33433	−	0.433551i	−0.887393	+	0.461014i	$0.847486\pi$
$140$		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	−0.235751	−	0.971814i	$-0.575755\pi$
$157$	9.22284	−	9.22284i	0.736063	−	0.736063i	0.971814	+	0.235751i	$0.0757550\pi$
$158$		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	−0.873589	−	0.486665i	$-0.838213\pi$
$163$	0.429156	−	0.842267i	0.0336141	−	0.0659714i	0.907203	+	0.420694i	$0.138213\pi$
$164$		0			0
$165$	−0.465457	−	4.20357i	−0.0362357	−	0.327248i
$166$		0			0
$167$	−23.0479	−	3.65042i	−1.78350	−	0.282478i	−0.824494	−	0.565871i	$-0.808540\pi$
$167$	−23.0479	−	3.65042i	−1.78350	−	0.282478i	−0.959004	+	0.283393i	$0.908540\pi$
$168$		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	0.946671	−	0.322203i	$-0.104423\pi$
$173$	1.70415	+	3.34458i	0.129564	+	0.254284i	−0.817107	+	0.576487i	$0.804423\pi$
$174$		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	0.239021	−	0.971014i	$-0.423174\pi$
$179$	−8.16937	−	5.93539i	−0.610607	−	0.443632i	−0.849628	+	0.527382i	$0.823174\pi$
$180$		0			0
$181$	9.96400	−	7.23927i	0.740618	−	0.538091i	−0.152286	−	0.988336i	$-0.548664\pi$
$181$	9.96400	−	7.23927i	0.740618	−	0.538091i	0.892905	+	0.450246i	$0.148664\pi$
$182$		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	0.168885	−	0.985636i	$-0.445983\pi$
$191$	12.2290	−	3.97343i	0.884858	−	0.287508i	0.715973	+	0.698128i	$0.245983\pi$
$192$		0			0
$193$	−9.96950	−	9.96950i	−0.717620	−	0.717620i	0.250497	−	0.968117i	$-0.419406\pi$
$193$	−9.96950	−	9.96950i	−0.717620	−	0.717620i	−0.968117	+	0.250497i	$0.919406\pi$
$194$		0			0
$195$	−19.3172	−	0.904708i	−1.38334	−	0.0647875i
$196$		0			0
$197$	−1.20326	−	7.59705i	−0.0857284	−	0.541268i	−0.992751	−	0.120186i	$-0.961651\pi$
$197$	−1.20326	−	7.59705i	−0.0857284	−	0.541268i	0.907023	−	0.421081i	$-0.138349\pi$
$198$		0			0
$199$			16.0864i			1.14033i	0.821530	+	0.570166i	$0.193121\pi$
$199$			16.0864i			1.14033i	−0.821530	+	0.570166i	$0.806879\pi$
$200$		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	0.359903	+	0.932990i	$0.382810\pi$
$211$	−6.96750	+	21.4437i	−0.479662	+	1.47625i	−0.839565	+	0.543259i	$0.817190\pi$
$212$		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	−0.759676	−	0.650302i	$-0.774642\pi$
$223$	−10.1560	+	5.17474i	−0.680097	+	0.346526i	0.0795792	+	0.996829i	$0.474642\pi$
$224$		0			0
$225$	−9.91239	+	11.2581i	−0.660826	+	0.750539i
$226$		0			0
$227$	−12.6380	+	6.43937i	−0.838812	+	0.427396i	−0.819956	−	0.572426i	$-0.806002\pi$
$227$	−12.6380	+	6.43937i	−0.838812	+	0.427396i	−0.0188557	+	0.999822i	$0.506002\pi$
$228$		0			0
$229$	2.06221	−	2.83839i	0.136275	−	0.187566i	−0.735425	−	0.677606i	$-0.763018\pi$
$229$	2.06221	−	2.83839i	0.136275	−	0.187566i	0.871700	+	0.490039i	$0.163018\pi$
$230$		0			0
$231$	−2.24824	−	0.918407i	−0.147924	−	0.0604267i
$232$		0			0
$233$	0.450064	−	2.84159i	0.0294847	−	0.186159i	−0.968550	−	0.248818i	$-0.919958\pi$
$233$	0.450064	−	2.84159i	0.0294847	−	0.186159i	0.998035	+	0.0626588i	$0.0199580\pi$
$234$		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	−0.698153	−	0.715948i	$-0.745995\pi$
$239$	4.44446	−	13.6787i	0.287488	−	0.884798i	0.985642	−	0.168850i	$-0.0540054\pi$
$240$		0			0
$241$	0.877493	+	2.70064i	0.0565243	+	0.173964i	0.975333	−	0.220740i	$-0.0708472\pi$
$241$	0.877493	+	2.70064i	0.0565243	+	0.173964i	−0.918808	+	0.394704i	$0.870847\pi$
$242$		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	$0.132884\pi$
$251$			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
$255$	−2.27586	−	8.30857i	−0.142520	−	0.520303i
$256$		0			0
$257$	−9.47863	−	9.47863i	−0.591261	−	0.591261i	0.346711	−	0.937972i	$-0.387298\pi$
$257$	−9.47863	−	9.47863i	−0.591261	−	0.591261i	−0.937972	+	0.346711i	$0.887298\pi$
$258$		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	0.388813	−	0.921317i	$-0.372885\pi$
$263$	−2.07596	−	1.05775i	−0.128009	−	0.0652239i	−0.516822	+	0.856093i	$0.672885\pi$
$264$		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	0.361958	−	0.932194i	$-0.382108\pi$
$269$	22.3119	−	16.2105i	1.36038	−	0.988373i	0.998421	−	0.0561787i	$-0.0178917\pi$
$270$		0			0
$271$	25.5707	+	18.5782i	1.55331	+	1.12854i	0.941239	+	0.337740i	$0.109662\pi$
$271$	25.5707	+	18.5782i	1.55331	+	1.12854i	0.612069	+	0.790805i	$0.290338\pi$
$272$		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	0.965999	−	0.258547i	$-0.0832436\pi$
$277$	3.14609	+	6.17455i	0.189030	+	0.370993i	−0.776969	+	0.629539i	$0.783244\pi$
$278$		0			0
$279$	1.70243	+	3.26200i	0.101922	+	0.195291i
$280$		0			0
$281$	−3.62737	−	4.99264i	−0.216391	−	0.297836i	0.686998	−	0.726660i	$-0.258928\pi$
$281$	−3.62737	−	4.99264i	−0.216391	−	0.297836i	−0.903388	+	0.428823i	$0.858928\pi$
$282$		0			0
$283$	3.40261	+	0.538921i	0.202264	+	0.0320355i	0.256744	−	0.966479i	$-0.417350\pi$
$283$	3.40261	+	0.538921i	0.202264	+	0.0320355i	−0.0544801	+	0.998515i	$0.517350\pi$
$284$		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	−0.988924	−	0.148424i	$-0.952580\pi$
$293$	−14.3870	+	14.3870i	−0.840500	+	0.840500i	0.148424	+	0.988924i	$0.452580\pi$
$294$		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	0.286934	−	0.957950i	$-0.407364\pi$
$307$	21.8121	−	21.8121i	1.24488	−	1.24488i	0.957950	−	0.286934i	$-0.0926362\pi$
$308$		0			0
$309$	9.24191	−	10.9286i	0.525754	−	0.621705i
$310$		0			0
$311$	23.6419	+	7.68170i	1.34061	+	0.435589i	0.889522	−	0.456892i	$-0.151037\pi$
$311$	23.6419	+	7.68170i	1.34061	+	0.435589i	0.451084	+	0.892481i	$0.351037\pi$
$312$		0			0
$313$	−5.16865	+	10.1440i	−0.292149	+	0.573375i	−0.989699	−	0.143161i	$-0.954273\pi$
$313$	−5.16865	+	10.1440i	−0.292149	+	0.573375i	0.697550	+	0.716536i	$0.254273\pi$
$314$		0			0
$315$	2.95992	+	8.08900i	0.166773	+	0.455764i
$316$		0			0
$317$	−15.6631	−	2.48079i	−0.879728	−	0.139335i	−0.299799	−	0.954002i	$-0.596920\pi$
$317$	−15.6631	−	2.48079i	−0.879728	−	0.139335i	−0.579929	+	0.814667i	$0.696920\pi$
$318$		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	−0.831901	−	0.554924i	$-0.812747\pi$
$331$	−10.2103	+	7.41821i	−0.561209	+	0.407742i	0.270693	+	0.962666i	$0.412747\pi$
$332$		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	0.566090	−	0.824343i	$-0.308455\pi$
$337$	4.25752	+	2.16931i	0.231922	+	0.118170i	−0.334168	+	0.942513i	$0.608455\pi$
$338$		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	−0.971662	−	0.236374i	$-0.924041\pi$
$347$	−2.24653	−	14.1841i	−0.120600	−	0.761440i	0.851062	−	0.525066i	$-0.175959\pi$
$348$		0			0
$349$			20.9612i			1.12203i	0.827807	+	0.561013i	$0.189588\pi$
$349$			20.9612i			1.12203i	−0.827807	+	0.561013i	$0.810412\pi$
$350$		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	$-0.508245\pi$
$353$	4.85452	−	0.768881i	0.258380	−	0.0409234i	0.284281	+	0.958741i	$0.408245\pi$
$354$		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	0.866780	−	0.498690i	$-0.166185\pi$
$359$	−2.41734	−	7.43981i	−0.127582	−	0.392658i	−0.994363	+	0.106032i	$0.966185\pi$
$360$		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	−0.835192	−	0.549959i	$-0.814643\pi$
$367$	2.47261	−	15.6115i	0.129069	−	0.814912i	0.964261	−	0.264953i	$-0.0853565\pi$
$368$		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	−0.787144	−	0.616770i	$-0.788441\pi$
$373$	−14.5011	+	7.38868i	−0.750838	+	0.382571i	0.0363057	+	0.999341i	$0.488441\pi$
$374$		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	0.0590965	−	0.998252i	$-0.481178\pi$
$379$	19.2777	−	26.5335i	0.990229	−	1.36293i	0.931133	−	0.364681i	$-0.118822\pi$
$380$		0			0
$381$	−2.36786	+	5.79647i	−0.121309	+	0.296962i
$382$		0			0
$383$	−2.51909	+	15.9049i	−0.128720	+	0.812703i	0.835866	+	0.548933i	$0.184966\pi$
$383$	−2.51909	+	15.9049i	−0.128720	+	0.812703i	−0.964586	+	0.263770i	$0.915034\pi$
$384$		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	−0.525017	−	0.851092i	$-0.675941\pi$
$389$	7.88904	−	24.2800i	0.399990	−	1.23104i	0.925007	−	0.379951i	$-0.124059\pi$
$390$		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	−0.226809	−	0.973939i	$-0.572829\pi$
$397$	−2.82041	+	0.446710i	−0.141553	+	0.0224197i	0.0852560	+	0.996359i	$0.472829\pi$
$398$		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
$405$	−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	0.413986	−	0.910283i	$-0.364136\pi$
$409$	25.9665	−	8.43701i	1.28396	−	0.417183i	0.869973	+	0.493100i	$0.164136\pi$
$410$		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	−0.167624	−	0.985851i	$-0.553609\pi$
$419$	14.7007	−	10.6807i	0.718178	−	0.521787i	0.885802	+	0.464064i	$0.153609\pi$
$420$		0			0
$421$	−0.685185	−	0.497816i	−0.0333939	−	0.0242621i	0.570963	−	0.820976i	$-0.306570\pi$
$421$	−0.685185	−	0.497816i	−0.0333939	−	0.0242621i	−0.604357	+	0.796714i	$0.706570\pi$
$422$		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	0.989518	−	0.144407i	$-0.0461274\pi$
$431$	11.3436	+	15.6131i	0.546401	+	0.752057i	−0.443117	+	0.896464i	$0.646127\pi$
$432$		0			0
$433$	14.7512	+	2.33636i	0.708897	+	0.112278i	0.500463	−	0.865758i	$-0.333163\pi$
$433$	14.7512	+	2.33636i	0.708897	+	0.112278i	0.208434	+	0.978036i	$0.433163\pi$
$434$		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	0.397673	−	0.917527i	$-0.369818\pi$
$439$	3.77327	+	1.22601i	0.180088	+	0.0585143i	−0.217585	+	0.976041i	$0.569818\pi$
$440$		0			0
$441$	−15.8799	−	2.35627i	−0.756187	−	0.112204i
$442$		0			0
$443$	20.1922	−	20.1922i	0.959360	−	0.959360i	−0.0398456	−	0.999206i	$-0.512687\pi$
$443$	20.1922	−	20.1922i	0.959360	−	0.959360i	0.999206	+	0.0398456i	$0.0126866\pi$
$444$		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	−0.700377	−	0.713773i	$-0.746985\pi$
$457$	0.286369	−	0.286369i	0.0133958	−	0.0133958i	0.713773	+	0.700377i	$0.246985\pi$
$458$		0			0
$459$	10.6120	−	4.57902i	0.495324	−	0.213730i
$460$		0			0
$461$	−7.31001	−	2.37517i	−0.340461	−	0.110623i	0.133796	−	0.991009i	$-0.457283\pi$
$461$	−7.31001	−	2.37517i	−0.340461	−	0.110623i	−0.474257	+	0.880386i	$0.657283\pi$
$462$		0			0
$463$	−2.82556	+	5.54548i	−0.131315	+	0.257720i	−0.947297	−	0.320358i	$-0.896197\pi$
$463$	−2.82556	+	5.54548i	−0.131315	+	0.257720i	0.815982	+	0.578078i	$0.196197\pi$
$464$		0			0
$465$	−4.12698	−	2.35221i	−0.191384	−	0.109081i
$466$		0			0
$467$	−2.70390	−	0.428256i	−0.125122	−	0.0198173i	0.0935595	−	0.995614i	$-0.470175\pi$
$467$	−2.70390	−	0.428256i	−0.125122	−	0.0198173i	−0.218681	+	0.975796i	$0.570175\pi$
$468$		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	0.710057	−	0.704144i	$-0.248669\pi$
$479$	5.68590	+	4.13105i	0.259796	+	0.188753i	−0.450261	+	0.892897i	$0.648669\pi$
$480$		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	0.606049	−	0.795428i	$-0.292754\pi$
$487$	7.03443	+	3.58422i	0.318761	+	0.162417i	−0.287288	+	0.957844i	$0.592754\pi$
$488$		0			0
$489$	−1.59018	+	0.389997i	−0.0719104	+	0.0176363i
$490$		0			0
$491$	7.06686	−	2.29616i	0.318923	−	0.103624i	−0.145181	−	0.989405i	$-0.546376\pi$
$491$	7.06686	−	2.29616i	0.318923	−	0.103624i	0.464104	+	0.885781i	$0.346376\pi$
$492$		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	$0.123941\pi$
$499$			16.9596i			0.759216i	−0.925147	+	0.379608i	$0.876059\pi$
$500$		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	$-0.223731\pi$
$503$	37.8665	−	5.99747i	1.68839	−	0.267414i	0.925397	+	0.378998i	$0.123731\pi$
$504$		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	0.973537	+	0.228531i	$0.0733921\pi$
$509$	7.22530	+	22.2372i	0.320256	+	0.985646i	−0.653281	+	0.757116i	$0.726608\pi$
$510$		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	−0.653774	−	0.756690i	$-0.726815\pi$
$521$	6.11512	−	8.41674i	0.267908	−	0.368744i	0.921682	+	0.387946i	$0.126815\pi$
$522$		0			0
$523$	29.8122	−	15.1901i	1.30360	−	0.664216i	0.342263	−	0.939604i	$-0.388806\pi$
$523$	29.8122	−	15.1901i	1.30360	−	0.664216i	0.961333	+	0.275389i	$0.0888065\pi$
$524$		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	0.934209	−	0.356726i	$-0.116107\pi$
$541$	−0.727097	−	2.23777i	−0.0312603	−	0.0962094i	−0.965469	+	0.260517i	$0.916107\pi$
$542$		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	−0.978038	−	0.208426i	$-0.933166\pi$
$547$	−43.1229	+	6.82999i	−1.84380	+	0.292029i	−0.865762	+	0.500456i	$0.833166\pi$
$548$		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	0.621735	−	0.783228i	$-0.286428\pi$
$557$	−3.81138	−	3.81138i	−0.161493	−	0.161493i	−0.783228	+	0.621735i	$0.786428\pi$
$558$		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	−0.281981	−	0.959420i	$-0.590992\pi$
$563$	−29.0405	−	14.7969i	−1.22391	−	0.623615i	−0.941931	+	0.335805i	$0.890992\pi$
$564$		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	−0.623578	−	0.781761i	$-0.714322\pi$
$569$	−1.73598	+	1.26126i	−0.0727760	+	0.0528749i	0.550802	+	0.834636i	$0.314322\pi$
$570$		0			0
$571$	4.09296	+	2.97371i	0.171285	+	0.124446i	0.670125	−	0.742248i	$-0.266240\pi$
$571$	4.09296	+	2.97371i	0.171285	+	0.124446i	−0.498840	+	0.866694i	$0.666240\pi$
$572$		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	0.998382	+	0.0568682i	$0.0181115\pi$
$577$	10.9908	+	21.5708i	0.457555	+	0.898002i	−0.540827	+	0.841134i	$0.681889\pi$
$578$		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	−0.487255	−	0.873260i	$-0.662002\pi$
$587$	12.2504	−	24.0428i	0.505628	−	0.992352i	0.992883	−	0.119092i	$-0.0379983\pi$
$588$		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	−0.544927	−	0.838483i	$-0.683443\pi$
$593$	7.14857	−	7.14857i	0.293556	−	0.293556i	0.838483	+	0.544927i	$0.183443\pi$
$594$		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	−0.464632	−	0.885504i	$-0.653813\pi$
$607$	10.3692	−	10.3692i	0.420872	−	0.420872i	0.885504	+	0.464632i	$0.153813\pi$
$608$		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	−0.929203	−	0.369570i	$-0.879505\pi$
$613$	−2.08080	+	4.08379i	−0.0840425	+	0.164943i	0.845160	+	0.534513i	$0.179505\pi$
$614$		0			0
$615$	23.5133	+	25.8240i	0.948149	+	1.04132i
$616$		0			0
$617$	3.30490	+	0.523445i	0.133050	+	0.0210731i	0.222604	−	0.974909i	$-0.428544\pi$
$617$	3.30490	+	0.523445i	0.133050	+	0.0210731i	−0.0895540	+	0.995982i	$0.528544\pi$
$618$		0			0
$619$	−18.6414	−	25.6577i	−0.749260	−	1.03127i	−0.998032	−	0.0627063i	$-0.980027\pi$
$619$	−18.6414	−	25.6577i	−0.749260	−	1.03127i	0.248772	−	0.968562i	$-0.419973\pi$
$620$		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	−0.643753	−	0.765234i	$-0.722623\pi$
$631$	−2.88632	+	2.09703i	−0.114902	+	0.0834815i	0.528850	+	0.848715i	$0.322623\pi$
$632$		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	−0.784069	−	0.620674i	$-0.786859\pi$
$641$	−26.6743	+	8.66700i	−1.05357	+	0.342326i	−0.269502	+	0.963000i	$0.586859\pi$
$642$		0			0
$643$	−4.46449	−	4.46449i	−0.176062	−	0.176062i	0.613575	−	0.789637i	$-0.289731\pi$
$643$	−4.46449	−	4.46449i	−0.176062	−	0.176062i	−0.789637	+	0.613575i	$0.789731\pi$
$644$		0			0
$645$	2.86843	−	7.59853i	0.112945	−	0.299192i
$646$		0			0
$647$	2.38692	+	15.0704i	0.0938396	+	0.592480i	0.989135	+	0.147008i	$0.0469642\pi$
$647$	2.38692	+	15.0704i	0.0938396	+	0.592480i	−0.895296	+	0.445472i	$0.853036\pi$
$648$		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	$-0.691352\pi$
$653$	−21.6865	+	3.43481i	−0.848660	+	0.134415i	−0.283068	+	0.959100i	$0.591352\pi$
$654$		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	0.874651	−	0.484753i	$-0.161090\pi$
$659$	−3.02628	−	9.31393i	−0.117887	−	0.362819i	−0.992538	+	0.121934i	$0.961090\pi$
$660$		0			0
$661$	−14.2639	+	43.8997i	−0.554800	+	1.70750i	0.141671	+	0.989914i	$0.454753\pi$
$661$	−14.2639	+	43.8997i	−0.554800	+	1.70750i	−0.696471	+	0.717585i	$0.745247\pi$
$662$		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	−0.616769	−	0.787144i	$-0.711559\pi$
$673$	−8.88482	+	4.52704i	−0.342485	+	0.174505i	0.274285	+	0.961648i	$0.411559\pi$
$674$		0			0
$675$	25.9794	+	0.264307i	0.999948	+	0.0101732i
$676$		0			0
$677$	32.0266	−	16.3184i	1.23088	−	0.627167i	0.287154	−	0.957884i	$-0.407291\pi$
$677$	32.0266	−	16.3184i	1.23088	−	0.627167i	0.943730	+	0.330718i	$0.107291\pi$
$678$		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	−0.712237	−	0.701939i	$-0.752318\pi$
$683$	4.75779	−	30.0395i	0.182052	−	1.14943i	0.894289	−	0.447490i	$-0.147682\pi$
$684$		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	−0.999845	−	0.0176058i	$-0.994396\pi$
$691$	−5.29160	−	16.2859i	−0.201302	−	0.619543i	0.798543	−	0.601938i	$-0.205604\pi$
$692$		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	$0.244321\pi$
$701$			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
$705$	1.33525	−	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	−0.870811	−	0.491618i	$-0.836406\pi$
$709$	−34.2516	+	11.1290i	−1.28635	+	0.417959i	−0.415535	+	0.909577i	$0.636406\pi$
$710$		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	−0.970734	−	0.240158i	$-0.922801\pi$
$719$	−27.9485	+	20.3058i	−1.04230	+	0.757278i	−0.0715696	+	0.997436i	$0.522801\pi$
$720$		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	0.986706	+	0.162515i	$0.0519607\pi$
$727$	14.5118	+	28.4810i	0.538212	+	1.05630i	−0.448494	+	0.893786i	$0.648039\pi$
$728$		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	0.526522	−	0.850161i	$-0.323496\pi$
$733$	20.6997	+	3.27851i	0.764560	+	0.121094i	0.238038	+	0.971256i	$0.423496\pi$
$734$		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	0.161370	−	0.986894i	$-0.448409\pi$
$739$	−7.83354	−	2.54527i	−0.288162	−	0.0936294i	−0.449531	+	0.893265i	$0.648409\pi$
$740$		0			0
$741$	26.9584	+	22.7977i	0.990340	+	0.837495i
$742$		0			0
$743$	−30.1299	+	30.1299i	−1.10536	+	1.10536i	−0.111607	+	0.993752i	$0.535600\pi$
$743$	−30.1299	+	30.1299i	−1.10536	+	1.10536i	−0.993752	+	0.111607i	$0.964400\pi$
$744$		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	−0.728692	−	0.684842i	$-0.759871\pi$
$757$	−1.20647	+	1.20647i	−0.0438498	+	0.0438498i	0.684842	+	0.728692i	$0.259871\pi$
$758$		0			0
$759$	−5.74143	+	6.78925i	−0.208401	+	0.246434i
$760$		0			0
$761$	−41.1754	−	13.3787i	−1.49261	−	0.484978i	−0.554756	−	0.832013i	$-0.687189\pi$
$761$	−41.1754	−	13.3787i	−1.49261	−	0.484978i	−0.937852	+	0.347035i	$0.887189\pi$
$762$		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	0.310454	−	0.950589i	$-0.399519\pi$
$769$	−19.1217	−	26.3187i	−0.689545	−	0.949078i	−0.999999	+	0.00151094i	$0.999519\pi$
$770$		0			0
$771$	−1.70851	+	23.1549i	−0.0615306	+	0.833902i
$772$		0			0
$773$	−7.28640	−	14.3004i	−0.262074	−	0.514348i	0.722048	−	0.691843i	$-0.243201\pi$
$773$	−7.28640	−	14.3004i	−0.262074	−	0.514348i	−0.984122	+	0.177494i	$0.943201\pi$
$774$		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	0.409087	−	0.912495i	$-0.365847\pi$
$787$	−2.48782	−	1.26761i	−0.0886811	−	0.0451853i	−0.497769	+	0.867310i	$0.665847\pi$
$788$		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	−

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)

\(f(q)\)	\(=\)	\(q+(-1.13130 - 1.31155i) q^{3} +(2.14441 + 0.633635i) q^{5} +(0.907947 - 0.907947i) q^{7} +(-0.440321 + 2.96751i) q^{9} +O(q^{10})\)	\(q+(-1.13130 - 1.31155i) q^{3} +(2.14441 + 0.633635i) q^{5} +(0.907947 - 0.907947i) q^{7} +(-0.440321 + 2.96751i) q^{9} +(1.03855 + 0.337444i) q^{11} +(2.26685 - 4.44893i) q^{13} +(-1.59493 - 3.52933i) q^{15} +(2.19690 + 0.347955i) q^{17} +(-2.39954 - 3.30268i) q^{19} +(-2.21798 - 0.163656i) q^{21} +(-2.13422 - 4.18865i) q^{23} +(4.19701 + 2.71755i) q^{25} +(4.39017 - 2.77964i) q^{27} +(0.981024 + 0.712755i) q^{29} +(0.992266 - 0.720923i) q^{31} +(-0.732332 - 1.74385i) q^{33} +(2.52232 - 1.37171i) q^{35} +(6.47404 + 3.29869i) q^{37} +(-8.39948 + 2.06000i) q^{39} +(-8.57625 + 2.78659i) q^{41} +(1.48285 + 1.48285i) q^{43} +(-2.82455 + 6.08456i) q^{45} +(0.0645410 + 0.407496i) q^{47} +5.35127i q^{49} +(-2.02900 - 3.27499i) q^{51} +(-13.7949 + 2.18491i) q^{53} +(2.01325 + 1.38168i) q^{55} +(-1.61703 + 6.88343i) q^{57} +(3.76991 + 11.6026i) q^{59} +(0.344205 - 1.05936i) q^{61} +(2.29455 + 3.09413i) q^{63} +(7.68005 - 8.10400i) q^{65} +(-1.22742 + 7.74963i) q^{67} +(-3.07917 + 7.53776i) q^{69} +(-6.04759 + 8.32380i) q^{71} +(5.93345 - 3.02324i) q^{73} +(-1.18388 - 8.57895i) q^{75} +(1.24932 - 0.636563i) q^{77} +(-5.56738 + 7.66285i) q^{79} +(-8.61223 - 2.61331i) q^{81} +(2.79265 - 17.6321i) q^{83} +(4.49059 + 2.13819i) q^{85} +(-0.175018 - 2.09300i) q^{87} +(4.10757 - 12.6418i) q^{89} +(-1.98122 - 6.09757i) q^{91} +(-2.06808 - 0.485825i) q^{93} +(-3.05291 - 8.60274i) q^{95} +(-15.3339 + 2.42865i) q^{97} +(-1.45866 + 2.93331i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80q - 2q^{3} + 4q^{7} + O(q^{10}) \)	\( 80q - 2q^{3} + 4q^{7} + 12q^{13} + 10q^{15} + 20q^{19} + 40q^{25} - 14q^{27} - 20q^{33} + 12q^{37} - 40q^{39} + 12q^{43} - 60q^{45} - 76q^{57} - 98q^{63} - 36q^{67} - 70q^{69} - 44q^{73} - 90q^{75} - 40q^{79} + 20q^{81} - 100q^{85} - 70q^{87} - 18q^{93} - 56q^{97} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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