LMFDB - Embedded newform 300.2.x.a.17.10

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			17.10
Character	$\chi$	$=$	300.17
Dual form			300.2.x.a.53.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.66741 + 0.468765i) q^{3} +(-0.354250 - 2.20783i) q^{5} +(-1.67035 - 1.67035i) q^{7} +(2.56052 + 1.56325i) q^{9} +O(q^{10})$	\(q+(1.66741 + 0.468765i) q^{3} +(-0.354250 - 2.20783i) q^{5} +(-1.67035 - 1.67035i) q^{7} +(2.56052 + 1.56325i) q^{9} +(5.27981 - 1.71551i) q^{11} +(-1.00207 - 1.96667i) q^{13} +(0.444271 - 3.84742i) q^{15} +(4.25837 - 0.674459i) q^{17} +(-4.59013 + 6.31777i) q^{19} +(-2.00216 - 3.56817i) q^{21} +(-1.53667 + 3.01588i) q^{23} +(-4.74901 + 1.56425i) q^{25} +(3.53664 + 3.80686i) q^{27} +(-0.409155 + 0.297269i) q^{29} +(2.41697 + 1.75603i) q^{31} +(9.60778 - 0.385478i) q^{33} +(-3.09613 + 4.27958i) q^{35} +(-7.68210 + 3.91423i) q^{37} +(-0.748954 - 3.74898i) q^{39} +(-4.48088 - 1.45593i) q^{41} +(5.88737 - 5.88737i) q^{43} +(2.54432 - 6.20697i) q^{45} +(0.527820 - 3.33252i) q^{47} -1.41984i q^{49} +(7.41661 + 0.871573i) q^{51} +(-5.21091 - 0.825328i) q^{53} +(-5.65793 - 11.0492i) q^{55} +(-10.6152 + 8.38263i) q^{57} +(-3.17139 + 9.76054i) q^{59} +(1.65928 + 5.10673i) q^{61} +(-1.66580 - 6.88815i) q^{63} +(-3.98709 + 2.90909i) q^{65} +(0.707187 + 4.46500i) q^{67} +(-3.97600 + 4.30838i) q^{69} +(6.04875 + 8.32540i) q^{71} +(-1.93067 - 0.983727i) q^{73} +(-8.65182 + 0.382074i) q^{75} +(-11.6847 - 5.95363i) q^{77} +(10.1110 + 13.9166i) q^{79} +(4.11252 + 8.00545i) q^{81} +(-1.93251 - 12.2014i) q^{83} +(-2.99762 - 9.16282i) q^{85} +(-0.821579 + 0.303872i) q^{87} +(-1.43321 - 4.41098i) q^{89} +(-1.61123 + 4.95884i) q^{91} +(3.20692 + 4.06102i) q^{93} +(15.5746 + 7.89614i) q^{95} +(-15.9942 - 2.53324i) q^{97} +(16.2008 + 3.86104i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.66741	+	0.468765i	0.962680	+	0.270642i
$3$	1.66741	+	0.468765i	0.962680	+	0.270642i
$4$		0			0
$5$	−0.354250	−	2.20783i	−0.158426	−	0.987371i
$5$	−0.354250	−	2.20783i	−0.158426	−	0.987371i
$6$		0			0
$7$	−1.67035	−	1.67035i	−0.631334	−	0.631334i	0.317068	−	0.948403i	$-0.397302\pi$
$7$	−1.67035	−	1.67035i	−0.631334	−	0.631334i	−0.948403	+	0.317068i	$0.897302\pi$
$8$		0			0
$9$	2.56052	+	1.56325i	0.853506	+	0.521082i
$10$		0			0
$11$	5.27981	−	1.71551i	1.59192	−	0.517247i	0.626830	−	0.779156i	$-0.284352\pi$
$11$	5.27981	−	1.71551i	1.59192	−	0.517247i	0.965092	+	0.261910i	$0.0843522\pi$
$12$		0			0
$13$	−1.00207	−	1.96667i	−0.277924	−	0.545456i	0.709279	−	0.704928i	$-0.249021\pi$
$13$	−1.00207	−	1.96667i	−0.277924	−	0.545456i	−0.987202	+	0.159472i	$0.949021\pi$
$14$		0			0
$15$	0.444271	−	3.84742i	0.114710	−	0.993399i
$16$		0			0
$17$	4.25837	−	0.674459i	1.03281	−	0.163580i	0.383053	−	0.923726i	$-0.374872\pi$
$17$	4.25837	−	0.674459i	1.03281	−	0.163580i	0.649753	+	0.760146i	$0.274872\pi$
$18$		0			0
$19$	−4.59013	+	6.31777i	−1.05305	+	1.44940i	−0.166911	+	0.985972i	$0.553379\pi$
$19$	−4.59013	+	6.31777i	−1.05305	+	1.44940i	−0.886137	+	0.463423i	$0.846621\pi$
$20$		0			0
$21$	−2.00216	−	3.56817i	−0.436908	−	0.778638i
$22$		0			0
$23$	−1.53667	+	3.01588i	−0.320418	+	0.628855i	−0.993892	−	0.110355i	$-0.964801\pi$
$23$	−1.53667	+	3.01588i	−0.320418	+	0.628855i	0.673475	+	0.739210i	$0.264801\pi$
$24$		0			0
$25$	−4.74901	+	1.56425i	−0.949803	+	0.312850i
$26$		0			0
$27$	3.53664	+	3.80686i	0.680627	+	0.732630i
$28$		0			0
$29$	−0.409155	+	0.297269i	−0.0759783	+	0.0552014i	−0.625126	−	0.780524i	$-0.714952\pi$
$29$	−0.409155	+	0.297269i	−0.0759783	+	0.0552014i	0.549148	+	0.835725i	$0.314952\pi$
$30$		0			0
$31$	2.41697	+	1.75603i	0.434101	+	0.315393i	0.783287	−	0.621661i	$-0.213542\pi$
$31$	2.41697	+	1.75603i	0.434101	+	0.315393i	−0.349186	+	0.937054i	$0.613542\pi$
$32$		0			0
$33$	9.60778	−	0.385478i	1.67250	−	0.0671031i
$34$		0			0
$35$	−3.09613	+	4.27958i	−0.523342	+	0.723381i
$36$		0			0
$37$	−7.68210	+	3.91423i	−1.26293	+	0.643495i	−0.951755	−	0.306858i	$-0.900722\pi$
$37$	−7.68210	+	3.91423i	−1.26293	+	0.643495i	−0.311174	+	0.950353i	$0.600722\pi$
$38$		0			0
$39$	−0.748954	−	3.74898i	−0.119929	−	0.600317i
$40$		0			0
$41$	−4.48088	−	1.45593i	−0.699796	−	0.227377i	−0.0625543	−	0.998042i	$-0.519925\pi$
$41$	−4.48088	−	1.45593i	−0.699796	−	0.227377i	−0.637242	+	0.770664i	$0.719925\pi$
$42$		0			0
$43$	5.88737	−	5.88737i	0.897816	−	0.897816i	−0.0974269	−	0.995243i	$-0.531061\pi$
$43$	5.88737	−	5.88737i	0.897816	−	0.897816i	0.995243	+	0.0974269i	$0.0310612\pi$
$44$		0			0
$45$	2.54432	−	6.20697i	0.379284	−	0.925280i
$46$		0			0
$47$	0.527820	−	3.33252i	0.0769905	−	0.486099i	−0.918821	−	0.394673i	$-0.870858\pi$
$47$	0.527820	−	3.33252i	0.0769905	−	0.486099i	0.995812	−	0.0914252i	$-0.0291423\pi$
$48$		0			0
$49$		−	1.41984i		−	0.202834i
$50$		0			0
$51$	7.41661	+	0.871573i	1.03853	+	0.122045i
$52$		0			0
$53$	−5.21091	−	0.825328i	−0.715774	−	0.113367i	−0.212083	−	0.977252i	$-0.568025\pi$
$53$	−5.21091	−	0.825328i	−0.715774	−	0.113367i	−0.503691	+	0.863884i	$0.668025\pi$
$54$		0			0
$55$	−5.65793	−	11.0492i	−0.762916	−	1.48987i
$56$		0			0
$57$	−10.6152	+	8.38263i	−1.40601	+	1.11031i
$58$		0			0
$59$	−3.17139	+	9.76054i	−0.412880	+	1.27071i	0.501254	+	0.865300i	$0.332872\pi$
$59$	−3.17139	+	9.76054i	−0.412880	+	1.27071i	−0.914134	+	0.405413i	$0.867128\pi$
$60$		0			0
$61$	1.65928	+	5.10673i	0.212449	+	0.653850i	0.999325	+	0.0367391i	$0.0116970\pi$
$61$	1.65928	+	5.10673i	0.212449	+	0.653850i	−0.786876	+	0.617111i	$0.788303\pi$
$62$		0			0
$63$	−1.66580	−	6.88815i	−0.209871	−	0.867825i
$64$		0			0
$65$	−3.98709	+	2.90909i	−0.494537	+	0.360828i
$66$		0			0
$67$	0.707187	+	4.46500i	0.0863966	+	0.545487i	0.992482	+	0.122392i	$0.0390564\pi$
$67$	0.707187	+	4.46500i	0.0863966	+	0.545487i	−0.906085	+	0.423095i	$0.860944\pi$
$68$		0			0
$69$	−3.97600	+	4.30838i	−0.478654	+	0.518668i
$70$		0			0
$71$	6.04875	+	8.32540i	0.717855	+	0.988043i	0.999592	+	0.0285511i	$0.00908934\pi$
$71$	6.04875	+	8.32540i	0.717855	+	0.988043i	−0.281737	+	0.959492i	$0.590911\pi$
$72$		0			0
$73$	−1.93067	−	0.983727i	−0.225968	−	0.115136i	0.337342	−	0.941382i	$-0.390472\pi$
$73$	−1.93067	−	0.983727i	−0.225968	−	0.115136i	−0.563310	+	0.826246i	$0.690472\pi$
$74$		0			0
$75$	−8.65182	+	0.382074i	−0.999026	+	0.0441181i
$76$		0			0
$77$	−11.6847	−	5.95363i	−1.33159	−	0.678479i
$78$		0			0
$79$	10.1110	+	13.9166i	1.13757	+	1.56574i	0.772811	+	0.634637i	$0.218850\pi$
$79$	10.1110	+	13.9166i	1.13757	+	1.56574i	0.364764	+	0.931100i	$0.381150\pi$
$80$		0			0
$81$	4.11252	+	8.00545i	0.456946	+	0.889494i
$82$		0			0
$83$	−1.93251	−	12.2014i	−0.212121	−	1.33928i	−0.832085	−	0.554648i	$-0.812853\pi$
$83$	−1.93251	−	12.2014i	−0.212121	−	1.33928i	0.619964	−	0.784630i	$-0.287147\pi$
$84$		0			0
$85$	−2.99762	−	9.16282i	−0.325137	−	0.993847i
$86$		0			0
$87$	−0.821579	+	0.303872i	−0.0880826	+	0.0325785i
$88$		0			0
$89$	−1.43321	−	4.41098i	−0.151920	−	0.467563i	0.845915	−	0.533317i	$-0.179055\pi$
$89$	−1.43321	−	4.41098i	−0.151920	−	0.467563i	−0.997836	+	0.0657541i	$0.979055\pi$
$90$		0			0
$91$	−1.61123	+	4.95884i	−0.168902	+	0.519828i
$92$		0			0
$93$	3.20692	+	4.06102i	0.332542	+	0.421108i
$94$		0			0
$95$	15.5746	+	7.89614i	1.59792	+	0.810127i
$96$		0			0
$97$	−15.9942	−	2.53324i	−1.62397	−	0.257211i	−0.722921	−	0.690931i	$-0.757201\pi$
$97$	−15.9942	−	2.53324i	−1.62397	−	0.257211i	−0.901048	+	0.433720i	$0.857201\pi$
$98$		0			0
$99$	16.2008	+	3.86104i	1.62824	+	0.388049i
$100$		0			0
$101$		−	4.67239i		−	0.464920i	−0.972606	−	0.232460i	$-0.925322\pi$
$101$		−	4.67239i		−	0.464920i	0.972606	−	0.232460i	$-0.0746775\pi$
$102$		0			0
$103$	−1.07022	+	6.75713i	−0.105452	+	0.665800i	0.877169	+	0.480181i	$0.159429\pi$
$103$	−1.07022	+	6.75713i	−0.105452	+	0.665800i	−0.982622	+	0.185619i	$0.940571\pi$
$104$		0			0
$105$	−7.16864	+	5.68446i	−0.699587	+	0.554746i
$106$		0			0
$107$	2.84075	−	2.84075i	0.274626	−	0.274626i	−0.556334	−	0.830959i	$-0.687792\pi$
$107$	2.84075	−	2.84075i	0.274626	−	0.274626i	0.830959	+	0.556334i	$0.187792\pi$
$108$		0			0
$109$	−10.7758	−	3.50126i	−1.03213	−	0.335360i	−0.256499	−	0.966544i	$-0.582569\pi$
$109$	−10.7758	−	3.50126i	−1.03213	−	0.335360i	−0.775633	+	0.631185i	$0.782569\pi$
$110$		0			0
$111$	−14.6441	+	2.92552i	−1.38995	+	0.277678i
$112$		0			0
$113$	−3.85613	+	1.96480i	−0.362754	+	0.184833i	−0.625862	−	0.779934i	$-0.715253\pi$
$113$	−3.85613	+	1.96480i	−0.362754	+	0.184833i	0.263108	+	0.964767i	$0.415253\pi$
$114$		0			0
$115$	7.20292	+	2.32432i	0.671675	+	0.216744i
$116$		0			0
$117$	0.508576	−	6.60217i	0.0470179	−	0.610371i
$118$		0			0
$119$	−8.23957	−	5.98640i	−0.755320	−	0.548772i
$120$		0			0
$121$	16.0342	−	11.6495i	1.45765	−	1.05905i
$122$		0			0
$123$	−6.78898	−	4.52811i	−0.612142	−	0.408286i
$124$		0			0
$125$	5.13593	+	9.93087i	0.459372	+	0.888244i
$126$		0			0
$127$	−0.759425	+	1.49046i	−0.0673881	+	0.132257i	−0.922243	−	0.386610i	$-0.873646\pi$
$127$	−0.759425	+	1.49046i	−0.0673881	+	0.132257i	0.854855	+	0.518867i	$0.173646\pi$
$128$		0			0
$129$	12.5765	−	7.05688i	1.10730	−	0.621323i
$130$		0			0
$131$	2.70065	−	3.71712i	0.235957	−	0.324767i	−0.674575	−	0.738207i	$-0.735673\pi$
$131$	2.70065	−	3.71712i	0.235957	−	0.324767i	0.910531	+	0.413440i	$0.135673\pi$
$132$		0			0
$133$	18.2200	−	2.88577i	1.57988	−	0.250228i
$134$		0			0
$135$	7.15203	−	9.15688i	0.615549	−	0.788099i
$136$		0			0
$137$	4.03906	+	7.92710i	0.345080	+	0.677258i	0.996690	−	0.0812966i	$-0.0259061\pi$
$137$	4.03906	+	7.92710i	0.345080	+	0.677258i	−0.651610	+	0.758554i	$0.725906\pi$
$138$		0			0
$139$	3.53260	−	1.14781i	0.299631	−	0.0973561i	−0.155343	−	0.987861i	$-0.549648\pi$
$139$	3.53260	−	1.14781i	0.299631	−	0.0973561i	0.454975	+	0.890504i	$0.349648\pi$
$140$		0			0
$141$	2.44226	−	5.30926i	0.205676	−	0.447121i
$142$		0			0
$143$	−8.66458	−	8.66458i	−0.724568	−	0.724568i
$144$		0			0
$145$	0.801262	+	0.798037i	0.0665412	+	0.0662734i
$146$		0			0
$147$	0.665570	−	2.36745i	0.0548953	−	0.195264i
$148$		0			0
$149$	16.5291			1.35411			0.677057	−	0.735931i	$-0.263255\pi$
$149$	16.5291			1.35411			0.677057	+	0.735931i	$0.263255\pi$
$150$		0			0
$151$	−5.27383			−0.429178			−0.214589	−	0.976704i	$-0.568841\pi$
$151$	−5.27383			−0.429178			−0.214589	+	0.976704i	$0.568841\pi$
$152$		0			0
$153$	11.9580	+	4.92992i	0.966745	+	0.398560i
$154$		0			0
$155$	3.02081	−	5.95833i	0.242637	−	0.478585i
$156$		0			0
$157$	7.79069	+	7.79069i	0.621765	+	0.621765i	0.945982	−	0.324218i	$-0.105101\pi$
$157$	7.79069	+	7.79069i	0.621765	+	0.621765i	−0.324218	+	0.945982i	$0.605101\pi$
$158$		0			0
$159$	−8.30185	−	3.81885i	−0.658379	−	0.302855i
$160$		0			0
$161$	7.60437	−	2.47081i	0.599308	−	0.194727i
$162$		0			0
$163$	−7.02791	−	13.7931i	−0.550469	−	1.08036i	−0.983825	−	0.179133i	$-0.942671\pi$
$163$	−7.02791	−	13.7931i	−0.550469	−	1.08036i	0.433356	−	0.901223i	$-0.357329\pi$
$164$		0			0
$165$	−4.25463	−	21.0758i	−0.331222	−	1.64075i
$166$		0			0
$167$	9.92370	−	1.57176i	0.767919	−	0.121626i	0.239829	−	0.970815i	$-0.422908\pi$
$167$	9.92370	−	1.57176i	0.767919	−	0.121626i	0.528090	+	0.849189i	$0.322908\pi$
$168$		0			0
$169$	4.77756	−	6.57575i	0.367505	−	0.505827i
$170$		0			0
$171$	−21.6293	+	9.00126i	−1.65404	+	0.688344i
$172$		0			0
$173$	6.65343	−	13.0581i	0.505851	−	0.992789i	−0.486997	−	0.873404i	$-0.661908\pi$
$173$	6.65343	−	13.0581i	0.505851	−	0.992789i	0.992848	−	0.119385i	$-0.0380923\pi$
$174$		0			0
$175$	10.5454	+	5.31968i	0.797156	+	0.402130i
$176$		0			0
$177$	−9.86341	+	14.7882i	−0.741379	+	1.11155i
$178$		0			0
$179$	−12.3066	+	8.94125i	−0.919837	+	0.668301i	−0.943483	−	0.331420i	$-0.892472\pi$
$179$	−12.3066	+	8.94125i	−0.919837	+	0.668301i	0.0236465	+	0.999720i	$0.492472\pi$
$180$		0			0
$181$	0.447095	+	0.324833i	0.0332323	+	0.0241447i	0.604277	−	0.796774i	$-0.293462\pi$
$181$	0.447095	+	0.324833i	0.0332323	+	0.0241447i	−0.571045	+	0.820919i	$0.693462\pi$
$182$		0			0
$183$	0.372842	+	9.29283i	0.0275612	+	0.686946i
$184$		0			0
$185$	11.3633	+	15.5741i	0.835448	+	1.14503i
$186$		0			0
$187$	21.3263	−	10.8663i	1.55954	−	0.794623i
$188$		0			0
$189$	0.451355	−	12.2662i	0.0328312	−	0.892238i
$190$		0			0
$191$	20.5690	+	6.68327i	1.48832	+	0.483585i	0.936587	−	0.350435i	$-0.113966\pi$
$191$	20.5690	+	6.68327i	1.48832	+	0.483585i	0.551734	+	0.834020i	$0.313966\pi$
$192$		0			0
$193$	−3.71609	+	3.71609i	−0.267490	+	0.267490i	−0.828088	−	0.560598i	$-0.810571\pi$
$193$	−3.71609	+	3.71609i	−0.267490	+	0.267490i	0.560598	+	0.828088i	$0.310571\pi$
$194$		0			0
$195$	−8.01179	+	2.98164i	−0.573736	+	0.213520i
$196$		0			0
$197$	3.06376	−	19.3438i	0.218284	−	1.37819i	−0.598442	−	0.801166i	$-0.704213\pi$
$197$	3.06376	−	19.3438i	0.218284	−	1.37819i	0.816726	−	0.577026i	$-0.195787\pi$
$198$		0			0
$199$		−	1.77115i		−	0.125553i	−0.998028	−	0.0627766i	$-0.980004\pi$
$199$		−	1.77115i		−	0.125553i	0.998028	−	0.0627766i	$-0.0199956\pi$
$200$		0			0
$201$	−0.913865	+	7.77649i	−0.0644590	+	0.548512i
$202$		0			0
$203$	1.17998	+	0.186890i	0.0828182	+	0.0131171i
$204$		0			0
$205$	−1.62708	+	10.4088i	−0.113640	+	0.726980i
$206$		0			0
$207$	−8.64924	+	5.32003i	−0.601164	+	0.369768i
$208$		0			0
$209$	−13.3968	+	41.2310i	−0.926674	+	2.85201i
$210$		0			0
$211$	0.990096	+	3.04720i	0.0681610	+	0.209778i	0.979335	−	0.202243i	$-0.0648230\pi$
$211$	0.990096	+	3.04720i	0.0681610	+	0.209778i	−0.911174	+	0.412021i	$0.864823\pi$
$212$		0			0
$213$	6.18311	+	16.7173i	0.423659	+	1.14545i
$214$		0			0
$215$	−15.0839	−	10.9127i	−1.02871	−	0.744240i
$216$		0			0
$217$	−1.10400	−	6.97039i	−0.0749445	−	0.473181i
$218$		0			0
$219$	−2.75809	−	2.54531i	−0.186374	−	0.171996i
$220$		0			0
$221$	−5.59361	−	7.69895i	−0.376267	−	0.517887i
$222$		0			0
$223$	−2.15039	−	1.09568i	−0.144001	−	0.0733720i	0.380505	−	0.924779i	$-0.375750\pi$
$223$	−2.15039	−	1.09568i	−0.144001	−	0.0733720i	−0.524506	+	0.851407i	$0.675750\pi$
$224$		0			0
$225$	−14.6052	−	3.41860i	−0.973683	−	0.227906i
$226$		0			0
$227$	−14.3886	−	7.33136i	−0.955005	−	0.486599i	−0.0942105	−	0.995552i	$-0.530033\pi$
$227$	−14.3886	−	7.33136i	−0.955005	−	0.486599i	−0.860794	+	0.508953i	$0.830033\pi$
$228$		0			0
$229$	−10.1726	−	14.0013i	−0.672222	−	0.925235i	0.327586	−	0.944821i	$-0.393765\pi$
$229$	−10.1726	−	14.0013i	−0.672222	−	0.925235i	−0.999808	+	0.0195869i	$0.993765\pi$
$230$		0			0
$231$	−16.6923	−	15.4045i	−1.09827	−	1.01354i
$232$		0			0
$233$	2.40288	+	15.1712i	0.157418	+	0.993898i	0.932272	+	0.361758i	$0.117823\pi$
$233$	2.40288	+	15.1712i	0.157418	+	0.993898i	−0.774854	+	0.632140i	$0.782177\pi$
$234$		0			0
$235$	−7.54462	+	0.0152120i	−0.492157	+	0.000992319i
$236$		0			0
$237$	10.3356	+	27.9443i	0.671367	+	1.81518i
$238$		0			0
$239$	−6.17815	−	19.0144i	−0.399631	−	1.22994i	−0.925296	−	0.379247i	$-0.876183\pi$
$239$	−6.17815	−	19.0144i	−0.399631	−	1.22994i	0.525664	−	0.850692i	$-0.323817\pi$
$240$		0			0
$241$	1.32659	−	4.08282i	0.0854532	−	0.262998i	−0.899195	−	0.437548i	$-0.855847\pi$
$241$	1.32659	−	4.08282i	0.0854532	−	0.262998i	0.984648	+	0.174550i	$0.0558471\pi$
$242$		0			0
$243$	3.10458	+	15.2762i	0.199159	+	0.979967i
$244$		0			0
$245$	−3.13476	+	0.502978i	−0.200272	+	0.0321341i
$246$		0			0
$247$	17.0246	+	2.69643i	1.08325	+	0.171570i
$248$		0			0
$249$	2.49730	−	21.2506i	0.158260	−	1.34671i
$250$		0			0
$251$		−	7.64733i		−	0.482695i	−0.970439	−	0.241347i	$-0.922411\pi$
$251$		−	7.64733i		−	0.482695i	0.970439	−	0.241347i	$-0.0775893\pi$
$252$		0			0
$253$	−2.93953	+	18.5595i	−0.184807	+	1.16682i
$254$		0			0
$255$	−0.703055	−	16.6834i	−0.0440270	−	1.04475i
$256$		0			0
$257$	6.23777	−	6.23777i	0.389101	−	0.389101i	−0.485266	−	0.874367i	$-0.661277\pi$
$257$	6.23777	−	6.23777i	0.389101	−	0.389101i	0.874367	+	0.485266i	$0.161277\pi$
$258$		0			0
$259$	19.3700	+	6.29368i	1.20359	+	0.391070i
$260$		0			0
$261$	−1.51236	+	0.121551i	−0.0936124	+	0.00752384i
$262$		0			0
$263$	−15.4727	+	7.88374i	−0.954088	+	0.486132i	−0.860484	−	0.509478i	$-0.829839\pi$
$263$	−15.4727	+	7.88374i	−0.954088	+	0.486132i	−0.0936037	+	0.995610i	$0.529839\pi$
$264$		0			0
$265$	0.0237862	+	11.7972i	0.00146118	+	0.724695i
$266$		0			0
$267$	−0.322045	−	8.02676i	−0.0197088	−	0.491230i
$268$		0			0
$269$	−17.2020	−	12.4980i	−1.04883	−	0.762017i	−0.0768379	−	0.997044i	$-0.524482\pi$
$269$	−17.2020	−	12.4980i	−1.04883	−	0.762017i	−0.971989	+	0.235026i	$0.924482\pi$
$270$		0			0
$271$	−7.79739	+	5.66514i	−0.473658	+	0.344133i	−0.798865	−	0.601510i	$-0.794566\pi$
$271$	−7.79739	+	5.66514i	−0.473658	+	0.344133i	0.325207	+	0.945643i	$0.394566\pi$
$272$		0			0
$273$	−5.01111	+	7.51314i	−0.303286	+	0.454716i
$274$		0			0
$275$	−22.3904	+	16.4059i	−1.35019	+	0.989315i
$276$		0			0
$277$	14.6228	−	28.6988i	0.878596	−	1.72434i	0.214455	−	0.976734i	$-0.431202\pi$
$277$	14.6228	−	28.6988i	0.878596	−	1.72434i	0.664141	−	0.747608i	$-0.268798\pi$
$278$		0			0
$279$	3.44359	+	8.27468i	0.206162	+	0.495392i
$280$		0			0
$281$	1.62290	−	2.23373i	0.0968141	−	0.133253i	−0.757862	−	0.652415i	$-0.773756\pi$
$281$	1.62290	−	2.23373i	0.0968141	−	0.133253i	0.854676	+	0.519162i	$0.173756\pi$
$282$		0			0
$283$	−15.0519	+	2.38398i	−0.894741	+	0.141713i	−0.586838	−	0.809705i	$-0.699627\pi$
$283$	−15.0519	+	2.38398i	−0.894741	+	0.141713i	−0.307903	+	0.951418i	$0.599627\pi$
$284$		0			0
$285$	22.2678	+	20.4669i	1.31903	+	1.21236i
$286$		0			0
$287$	5.05274	+	9.91657i	0.298254	+	0.585356i
$288$		0			0
$289$	1.51085	−	0.490904i	0.0888733	−	0.0288767i
$290$		0			0
$291$	−25.4815	−	11.7215i	−1.49375	−	0.687126i
$292$		0			0
$293$	−7.47364	−	7.47364i	−0.436615	−	0.436615i	0.454256	−	0.890871i	$-0.349905\pi$
$293$	−7.47364	−	7.47364i	−0.436615	−	0.436615i	−0.890871	+	0.454256i	$0.849905\pi$
$294$		0			0
$295$	22.6731	+	3.54421i	1.32008	+	0.206352i
$296$		0			0
$297$	25.2035	+	14.0323i	1.46246	+	0.814238i
$298$		0			0
$299$	7.47109			0.432064
$300$		0			0
$301$	−19.6680			−1.13364
$302$		0			0
$303$	2.19025	−	7.79080i	0.125827	−	0.447570i
$304$		0			0
$305$	10.6870	−	5.47246i	0.611935	−	0.313352i
$306$		0			0
$307$	3.64430	+	3.64430i	0.207991	+	0.207991i	0.803413	−	0.595422i	$-0.203015\pi$
$307$	3.64430	+	3.64430i	0.207991	+	0.207991i	−0.595422	+	0.803413i	$0.703015\pi$
$308$		0			0
$309$	−4.95201	+	10.7652i	−0.281710	+	0.612413i
$310$		0			0
$311$	−7.97750	+	2.59205i	−0.452363	+	0.146982i	−0.526332	−	0.850279i	$-0.676433\pi$
$311$	−7.97750	+	2.59205i	−0.452363	+	0.146982i	0.0739696	+	0.997260i	$0.476433\pi$
$312$		0			0
$313$	4.02979	+	7.90891i	0.227777	+	0.447038i	0.976403	−	0.215954i	$-0.0692863\pi$
$313$	4.02979	+	7.90891i	0.227777	+	0.447038i	−0.748626	+	0.662992i	$0.769286\pi$
$314$		0			0
$315$	−14.6177	+	6.11792i	−0.823616	+	0.344706i
$316$		0			0
$317$	14.6748	−	2.32426i	0.824218	−	0.130543i	0.269943	−	0.962876i	$-0.412995\pi$
$317$	14.6748	−	2.32426i	0.824218	−	0.130543i	0.554276	+	0.832333i	$0.312995\pi$
$318$		0			0
$319$	−1.65029	+	2.27143i	−0.0923987	+	0.127176i
$320$		0			0
$321$	6.06834	−	3.40505i	0.338702	−	0.190051i
$322$		0			0
$323$	−15.2854	+	29.9992i	−0.850501	+	1.66920i
$324$		0			0
$325$	7.83519	+	7.77226i	0.434618	+	0.431127i
$326$		0			0
$327$	−16.3264	−	10.8893i	−0.902850	−	0.602182i
$328$		0			0
$329$	−6.44814	+	4.68485i	−0.355497	+	0.258284i
$330$		0			0
$331$	−9.59179	−	6.96885i	−0.527213	−	0.383042i	0.292101	−	0.956387i	$-0.405646\pi$
$331$	−9.59179	−	6.96885i	−0.527213	−	0.383042i	−0.819314	+	0.573345i	$0.805646\pi$
$332$		0			0
$333$	−25.7891	−	1.98657i	−1.41323	−	0.108864i
$334$		0			0
$335$	9.60743	−	3.14307i	0.524910	−	0.171725i
$336$		0			0
$337$	−9.98022	+	5.08518i	−0.543657	+	0.277007i	−0.704176	−	0.710026i	$-0.748683\pi$
$337$	−9.98022	+	5.08518i	−0.543657	+	0.277007i	0.160519	+	0.987033i	$0.448683\pi$
$338$		0			0
$339$	−7.35078	+	1.46851i	−0.399240	+	0.0797583i
$340$		0			0
$341$	15.7736	+	5.12517i	0.854191	+	0.277543i
$342$		0			0
$343$	−14.0641	+	14.0641i	−0.759390	+	0.759390i
$344$		0			0
$345$	10.9207	+	7.25208i	0.587949	+	0.390439i
$346$		0			0
$347$	4.46050	−	28.1625i	0.239452	−	1.51184i	−0.515972	−	0.856606i	$-0.672569\pi$
$347$	4.46050	−	28.1625i	0.239452	−	1.51184i	0.755424	−	0.655236i	$-0.227431\pi$
$348$		0			0
$349$		−	24.5531i		−	1.31430i	−0.753761	−	0.657149i	$-0.771762\pi$
$349$		−	24.5531i		−	1.31430i	0.753761	−	0.657149i	$-0.228238\pi$
$350$		0			0
$351$	3.94287	−	10.7701i	0.210455	−	0.574867i
$352$		0			0
$353$	−7.23776	−	1.14635i	−0.385227	−	0.0610140i	−0.0391827	−	0.999232i	$-0.512475\pi$
$353$	−7.23776	−	1.14635i	−0.385227	−	0.0610140i	−0.346045	+	0.938218i	$0.612475\pi$
$354$		0			0
$355$	16.2383	−	16.3039i	0.861838	−	0.865320i
$356$		0			0
$357$	−10.9325	−	13.8442i	−0.578611	−	0.732713i
$358$		0			0
$359$	−3.41890	+	10.5223i	−0.180443	+	0.555345i	−0.999840	−	0.0178804i	$-0.994308\pi$
$359$	−3.41890	+	10.5223i	−0.180443	+	0.555345i	0.819397	+	0.573226i	$0.194308\pi$
$360$		0			0
$361$	−12.9736	−	39.9287i	−0.682821	−	2.10151i
$362$		0			0
$363$	32.1965	−	11.9083i	1.68988	−	0.625023i
$364$		0			0
$365$	−1.48796	+	4.61108i	−0.0778833	+	0.241355i
$366$		0			0
$367$	5.39806	+	34.0820i	0.281776	+	1.77907i	0.570142	+	0.821546i	$0.306888\pi$
$367$	5.39806	+	34.0820i	0.281776	+	1.77907i	−0.288366	+	0.957520i	$0.593112\pi$
$368$		0			0
$369$	−9.19741	−	10.7327i	−0.478798	−	0.558719i
$370$		0			0
$371$	7.32548	+	10.0827i	0.380320	+	0.523465i
$372$		0			0
$373$	14.7942	+	7.53802i	0.766014	+	0.390304i	0.792913	−	0.609335i	$-0.208563\pi$
$373$	14.7942	+	7.53802i	0.766014	+	0.390304i	−0.0268992	+	0.999638i	$0.508563\pi$
$374$		0			0
$375$	3.90846	+	18.9664i	0.201832	+	0.979420i
$376$		0			0
$377$	0.994631	+	0.506790i	0.0512261	+	0.0261010i
$378$		0			0
$379$	−20.3628	−	28.0270i	−1.04597	−	1.43965i	−0.892255	−	0.451532i	$-0.850878\pi$
$379$	−20.3628	−	28.0270i	−1.04597	−	1.43965i	−0.153711	−	0.988116i	$-0.549122\pi$
$380$		0			0
$381$	−1.96495	+	2.12921i	−0.100667	+	0.109083i
$382$		0			0
$383$	−3.45899	−	21.8392i	−0.176746	−	1.11593i	−0.903359	−	0.428885i	$-0.858906\pi$
$383$	−3.45899	−	21.8392i	−0.176746	−	1.11593i	0.726613	−	0.687047i	$-0.241094\pi$
$384$		0			0
$385$	−9.00530	+	27.9068i	−0.458953	+	1.42226i
$386$		0			0
$387$	24.2781	−	5.87131i	1.23413	−	0.298455i
$388$		0			0
$389$	−0.876383	−	2.69723i	−0.0444344	−	0.136755i	0.926378	−	0.376595i	$-0.122905\pi$
$389$	−0.876383	−	2.69723i	−0.0444344	−	0.136755i	−0.970812	+	0.239840i	$0.922905\pi$
$390$		0			0
$391$	−4.50961	+	13.8792i	−0.228061	+	0.701899i
$392$		0			0
$393$	6.24555	−	4.93200i	0.315046	−	0.248787i
$394$		0			0
$395$	27.1436	−	27.2533i	1.36574	−	1.37126i
$396$		0			0
$397$	−29.9879	−	4.74962i	−1.50505	−	0.238377i	−0.651205	−	0.758902i	$-0.725736\pi$
$397$	−29.9879	−	4.74962i	−1.50505	−	0.238377i	−0.853846	+	0.520525i	$0.825736\pi$
$398$		0			0
$399$	31.7331	+	3.72915i	1.58864	+	0.186691i
$400$		0			0
$401$			33.3974i			1.66779i	0.551925	+	0.833894i	$0.313893\pi$
$401$			33.3974i			1.66779i	−0.551925	+	0.833894i	$0.686107\pi$
$402$		0			0
$403$	1.03157	−	6.51305i	0.0513859	−	0.324438i
$404$		0			0
$405$	16.2178	−	11.9157i	0.805869	−	0.592094i
$406$		0			0
$407$	−33.8451	+	33.8451i	−1.67764	+	1.67764i
$408$		0			0
$409$	15.7176	+	5.10695i	0.777184	+	0.252522i	0.670637	−	0.741785i	$-0.266021\pi$
$409$	15.7176	+	5.10695i	0.777184	+	0.252522i	0.106547	+	0.994308i	$0.466021\pi$
$410$		0			0
$411$	3.01882	+	15.1111i	0.148908	+	0.745375i
$412$		0			0
$413$	21.6009	−	11.0062i	1.06291	−	0.541580i
$414$		0			0
$415$	−26.2540	+	8.58901i	−1.28876	+	0.421618i
$416$		0			0
$417$	6.42835	−	0.257915i	0.314798	−	0.0126301i
$418$		0			0
$419$	0.401580	+	0.291765i	0.0196184	+	0.0142536i	0.597551	−	0.801831i	$-0.296140\pi$
$419$	0.401580	+	0.291765i	0.0196184	+	0.0142536i	−0.577933	+	0.816084i	$0.696140\pi$
$420$		0			0
$421$	−5.08407	+	3.69379i	−0.247782	+	0.180025i	−0.704743	−	0.709462i	$-0.748938\pi$
$421$	−5.08407	+	3.69379i	−0.247782	+	0.180025i	0.456961	+	0.889487i	$0.348938\pi$
$422$		0			0
$423$	6.56105	−	7.70788i	0.319009	−	0.374770i
$424$		0			0
$425$	−19.1680	+	9.86416i	−0.929786	+	0.478482i
$426$		0			0
$427$	5.75847	−	11.3016i	0.278672	−	0.546924i
$428$		0			0
$429$	−10.3858	−	18.5091i	−0.501429	−	0.893626i
$430$		0			0
$431$	7.36561	−	10.1379i	0.354789	−	0.488325i	−0.593899	−	0.804540i	$-0.702412\pi$
$431$	7.36561	−	10.1379i	0.354789	−	0.488325i	0.948688	+	0.316215i	$0.102412\pi$
$432$		0			0
$433$	−26.6433	+	4.21988i	−1.28039	+	0.202795i	−0.759320	−	0.650717i	$-0.774468\pi$
$433$	−26.6433	+	4.21988i	−1.28039	+	0.202795i	−0.521074	+	0.853512i	$0.674468\pi$
$434$		0			0
$435$	0.961941	+	1.70626i	0.0461216	+	0.0818089i
$436$		0			0
$437$	−12.0001	−	23.5516i	−0.574045	−	1.12663i
$438$		0			0
$439$	−10.8500	+	3.52537i	−0.517841	+	0.168257i	−0.556265	−	0.831005i	$-0.687766\pi$
$439$	−10.8500	+	3.52537i	−0.517841	+	0.168257i	0.0384243	+	0.999262i	$0.487766\pi$
$440$		0			0
$441$	2.21956	−	3.63552i	0.105693	−	0.173120i
$442$		0			0
$443$	15.4331	+	15.4331i	0.733251	+	0.733251i	0.971262	−	0.238011i	$-0.0764956\pi$
$443$	15.4331	+	15.4331i	0.733251	+	0.733251i	−0.238011	+	0.971262i	$0.576496\pi$
$444$		0			0
$445$	−9.23097	+	4.72688i	−0.437590	+	0.224076i
$446$		0			0
$447$	27.5608	+	7.74825i	1.30358	+	0.366480i
$448$		0			0
$449$	34.8771			1.64595			0.822975	−	0.568077i	$-0.192312\pi$
$449$	34.8771			1.64595			0.822975	+	0.568077i	$0.192312\pi$
$450$		0			0
$451$	−26.1558			−1.23163
$452$		0			0
$453$	−8.79364	−	2.47218i	−0.413161	−	0.116153i
$454$		0			0
$455$	11.5190	+	1.80064i	0.540021	+	0.0844152i
$456$		0			0
$457$	23.6405	+	23.6405i	1.10585	+	1.10585i	0.993690	+	0.112165i	$0.0357786\pi$
$457$	23.6405	+	23.6405i	1.10585	+	1.10585i	0.112165	+	0.993690i	$0.464221\pi$
$458$		0			0
$459$	17.6279	+	13.8257i	0.822800	+	0.645327i
$460$		0			0
$461$	11.6988	−	3.80117i	0.544868	−	0.177038i	−0.0236333	−	0.999721i	$-0.507523\pi$
$461$	11.6988	−	3.80117i	0.544868	−	0.177038i	0.568501	+	0.822682i	$0.307523\pi$
$462$		0			0
$463$	8.22226	+	16.1371i	0.382121	+	0.749955i	0.999321	−	0.0368518i	$-0.0117330\pi$
$463$	8.22226	+	16.1371i	0.382121	+	0.749955i	−0.617200	+	0.786806i	$0.711733\pi$
$464$		0			0
$465$	7.82998	−	8.51895i	0.363107	−	0.395057i
$466$		0			0
$467$	16.3946	−	2.59664i	0.758650	−	0.120158i	0.234887	−	0.972023i	$-0.424528\pi$
$467$	16.3946	−	2.59664i	0.758650	−	0.120158i	0.523763	+	0.851864i	$0.324528\pi$
$468$		0			0
$469$	6.27688	−	8.63938i	0.289839	−	0.398930i
$470$		0			0
$471$	9.33828	+	16.6423i	0.430285	+	0.766836i
$472$		0			0
$473$	20.9843	−	41.1841i	0.964860	−	1.89365i
$474$		0			0
$475$	11.9160	−	37.1833i	0.546744	−	1.70609i
$476$		0			0
$477$	−12.0525	−	10.2592i	−0.551844	−	0.469737i
$478$		0			0
$479$	21.0507	−	15.2942i	0.961831	−	0.698811i	0.00825583	−	0.999966i	$-0.497372\pi$
$479$	21.0507	−	15.2942i	0.961831	−	0.698811i	0.953575	+	0.301155i	$0.0973721\pi$
$480$		0			0
$481$	15.3960	+	11.1858i	0.701996	+	0.510030i
$482$		0			0
$483$	13.8378	−	0.555194i	0.629644	−	0.0252622i
$484$		0			0
$485$	0.0730088	+	36.2099i	0.00331516	+	1.64421i
$486$		0			0
$487$	12.2935	−	6.26384i	0.557071	−	0.283842i	−0.152702	−	0.988272i	$-0.548797\pi$
$487$	12.2935	−	6.26384i	0.557071	−	0.283842i	0.709773	+	0.704430i	$0.248797\pi$
$488$		0			0
$489$	−5.25272	−	26.2931i	−0.237536	−	1.18902i
$490$		0			0
$491$	−21.5354	−	6.99728i	−0.971879	−	0.315783i	−0.220305	−	0.975431i	$-0.570705\pi$
$491$	−21.5354	−	6.99728i	−0.971879	−	0.315783i	−0.751574	+	0.659648i	$0.770705\pi$
$492$		0			0
$493$	−1.54184	+	1.54184i	−0.0694409	+	0.0694409i
$494$		0			0
$495$	2.78537	−	37.1364i	0.125193	−	1.66916i
$496$		0			0
$497$	3.80280	−	24.0099i	0.170579	−	1.07699i
$498$		0			0
$499$			7.12077i			0.318770i	0.987217	+	0.159385i	$0.0509511\pi$
$499$			7.12077i			0.318770i	−0.987217	+	0.159385i	$0.949049\pi$
$500$		0			0
$501$	17.2837	+	2.03111i	0.772178	+	0.0907434i
$502$		0			0
$503$	−20.1311	−	3.18846i	−0.897602	−	0.142166i	−0.309449	−	0.950916i	$-0.600145\pi$
$503$	−20.1311	−	3.18846i	−0.897602	−	0.142166i	−0.588153	+	0.808750i	$0.700145\pi$
$504$		0			0
$505$	−10.3158	+	1.65520i	−0.459049	+	0.0736553i
$506$		0			0
$507$	11.0486	−	8.72492i	0.490687	−	0.387487i
$508$		0			0
$509$	0.874684	−	2.69200i	0.0387697	−	0.119321i	−0.929799	−	0.368069i	$-0.880019\pi$
$509$	0.874684	−	2.69200i	0.0387697	−	0.119321i	0.968568	+	0.248748i	$0.0800191\pi$
$510$		0			0
$511$	1.58173	+	4.86808i	0.0699718	+	0.215351i
$512$		0			0
$513$	−40.2845	+	4.86973i	−1.77860	+	0.215004i
$514$		0			0
$515$	15.2977	−	0.0308443i	0.674098	−	0.00135916i
$516$		0			0
$517$	−2.93020	−	18.5006i	−0.128870	−	0.813654i
$518$		0			0
$519$	17.2152	−	18.6543i	0.755663	−	0.818834i
$520$		0			0
$521$	−21.4218	−	29.4846i	−0.938507	−	1.29174i	−0.956447	−	0.291905i	$-0.905711\pi$
$521$	−21.4218	−	29.4846i	−0.938507	−	1.29174i	0.0179402	−	0.999839i	$-0.494289\pi$
$522$		0			0
$523$	−12.8556	−	6.55024i	−0.562135	−	0.286422i	0.149743	−	0.988725i	$-0.452155\pi$
$523$	−12.8556	−	6.55024i	−0.562135	−	0.286422i	−0.711878	+	0.702303i	$0.752155\pi$
$524$		0			0
$525$	15.0898	+	13.8134i	0.658573	+	0.602866i
$526$		0			0
$527$	11.4767	+	5.84769i	0.499934	+	0.254729i
$528$		0			0
$529$	6.78486	+	9.33856i	0.294994	+	0.406025i
$530$		0			0
$531$	−23.3785	+	20.0344i	−1.01454	+	0.869418i
$532$		0			0
$533$	1.62682	+	10.2713i	0.0704655	+	0.444901i
$534$		0			0
$535$	−7.27822	−	5.26555i	−0.314665	−	0.227650i
$536$		0			0
$537$	−24.7115	+	9.13985i	−1.06638	+	0.394414i
$538$		0			0
$539$	−2.43575	−	7.49647i	−0.104915	−	0.322896i
$540$		0			0
$541$	−9.28677	+	28.5817i	−0.399269	+	1.22882i	0.526317	+	0.850288i	$0.323572\pi$
$541$	−9.28677	+	28.5817i	−0.399269	+	1.22882i	−0.925586	+	0.378536i	$0.876428\pi$
$542$		0			0
$543$	0.593220	+	0.751213i	0.0254575	+	0.0322376i
$544$		0			0
$545$	−3.91286	+	25.0314i	−0.167609	+	1.07223i
$546$		0			0
$547$	−32.6302	−	5.16812i	−1.39517	−	0.220973i	−0.586839	−	0.809704i	$-0.699628\pi$
$547$	−32.6302	−	5.16812i	−1.39517	−	0.220973i	−0.808329	+	0.588731i	$0.799628\pi$
$548$		0			0
$549$	−3.73447	+	15.6697i	−0.159383	+	0.668769i
$550$		0			0
$551$		−	3.94945i		−	0.168252i
$552$		0			0
$553$	6.35668	−	40.1345i	0.270314	−	1.70669i
$554$		0			0
$555$	11.6467	+	31.2952i	0.494376	+	1.32841i
$556$		0			0
$557$	−21.8255	+	21.8255i	−0.924778	+	0.924778i	−0.997362	−	0.0725847i	$-0.976875\pi$
$557$	−21.8255	+	21.8255i	−0.924778	+	0.924778i	0.0725847	+	0.997362i	$0.476875\pi$
$558$		0			0
$559$	−17.4781	−	5.67897i	−0.739243	−	0.240195i
$560$		0			0
$561$	40.6535	−	8.12157i	1.71639	−	0.342893i
$562$		0			0
$563$	1.53782	−	0.783556i	0.0648112	−	0.0330230i	−0.421285	−	0.906929i	$-0.638421\pi$
$563$	1.53782	−	0.783556i	0.0648112	−	0.0330230i	0.486096	+	0.873906i	$0.338421\pi$
$564$		0			0
$565$	5.70397	+	7.81765i	0.239968	+	0.328891i
$566$		0			0
$567$	6.50258	−	20.2413i	0.273083	−	0.850054i
$568$		0			0
$569$	−10.8632	−	7.89256i	−0.455408	−	0.330873i	0.336319	−	0.941748i	$-0.390818\pi$
$569$	−10.8632	−	7.89256i	−0.455408	−	0.330873i	−0.791727	+	0.610875i	$0.790818\pi$
$570$		0			0
$571$	13.8833	−	10.0868i	0.580999	−	0.422121i	−0.258085	−	0.966122i	$-0.583091\pi$
$571$	13.8833	−	10.0868i	0.580999	−	0.422121i	0.839084	+	0.544001i	$0.183091\pi$
$572$		0			0
$573$	31.1641	+	20.7858i	1.30190	+	0.868339i
$574$		0			0
$575$	2.58007	−	16.7262i	0.107596	−	0.697531i
$576$		0			0
$577$	−5.02409	+	9.86033i	−0.209156	+	0.410491i	−0.971623	−	0.236536i	$-0.923988\pi$
$577$	−5.02409	+	9.86033i	−0.209156	+	0.410491i	0.762467	+	0.647027i	$0.223988\pi$
$578$		0			0
$579$	−7.93823	+	4.45428i	−0.329902	+	0.185114i
$580$		0			0
$581$	−17.1527	+	23.6086i	−0.711613	+	0.979451i
$582$		0			0
$583$	−28.9285	+	4.58182i	−1.19810	+	0.189760i
$584$		0			0
$585$	−14.7566	+	1.21597i	−0.610112	+	0.0502743i
$586$		0			0
$587$	9.65285	+	18.9448i	0.398416	+	0.781935i	0.999856	−	0.0169832i	$-0.00540617\pi$
$587$	9.65285	+	18.9448i	0.398416	+	0.781935i	−0.601440	+	0.798918i	$0.705406\pi$
$588$		0			0
$589$	−22.1884	+	7.20945i	−0.914258	+	0.297060i
$590$		0			0
$591$	14.1763	−	30.8180i	0.583134	−	1.26768i
$592$		0			0
$593$	−12.3241	−	12.3241i	−0.506090	−	0.506090i	0.407234	−	0.913324i	$-0.366493\pi$
$593$	−12.3241	−	12.3241i	−0.506090	−	0.506090i	−0.913324	+	0.407234i	$0.866493\pi$
$594$		0			0
$595$	−10.2981	+	20.3122i	−0.422180	+	0.832720i
$596$		0			0
$597$	0.830251	−	2.95323i	0.0339799	−	0.120868i
$598$		0			0
$599$	13.1359			0.536716			0.268358	−	0.963319i	$-0.413519\pi$
$599$	13.1359			0.536716			0.268358	+	0.963319i	$0.413519\pi$
$600$		0			0
$601$	39.9534			1.62973			0.814867	−	0.579648i	$-0.196810\pi$
$601$	39.9534			1.62973			0.814867	+	0.579648i	$0.196810\pi$
$602$		0			0
$603$	−5.16914	+	12.5382i	−0.210503	+	0.510596i
$604$		0			0
$605$	−31.4003	−	31.2739i	−1.27660	−	1.27147i
$606$		0			0
$607$	−8.63234	−	8.63234i	−0.350376	−	0.350376i	0.509874	−	0.860249i	$-0.329692\pi$
$607$	−8.63234	−	8.63234i	−0.350376	−	0.350376i	−0.860249	+	0.509874i	$0.829692\pi$
$608$		0			0
$609$	1.87990	+	0.864755i	0.0761774	+	0.0350416i
$610$		0			0
$611$	−7.08288	+	2.30137i	−0.286543	+	0.0931034i
$612$		0			0
$613$	12.3185	+	24.1765i	0.497541	+	0.976480i	0.994099	+	0.108476i	$0.0345971\pi$
$613$	12.3185	+	24.1765i	0.497541	+	0.976480i	−0.496558	+	0.868004i	$0.665403\pi$
$614$		0			0
$615$	−7.59228	+	16.5930i	−0.306150	+	0.669094i
$616$		0			0
$617$	−16.2868	+	2.57957i	−0.655681	+	0.103850i	−0.475406	−	0.879766i	$-0.657699\pi$
$617$	−16.2868	+	2.57957i	−0.655681	+	0.103850i	−0.180275	+	0.983616i	$0.557699\pi$
$618$		0			0
$619$	−7.86705	+	10.8281i	−0.316203	+	0.435216i	−0.937303	−	0.348515i	$-0.886686\pi$
$619$	−7.86705	+	10.8281i	−0.316203	+	0.435216i	0.621100	+	0.783731i	$0.286686\pi$
$620$		0			0
$621$	−16.9157	+	4.81622i	−0.678803	+	0.193268i
$622$		0			0
$623$	−4.97392	+	9.76187i	−0.199276	+	0.391101i
$624$		0			0
$625$	20.1063	−	14.8573i	0.804250	−	0.594291i
$626$		0			0
$627$	−41.6656	+	62.4691i	−1.66396	+	2.49478i
$628$		0			0
$629$	−30.0732	+	21.8495i	−1.19910	+	0.871196i
$630$		0			0
$631$	16.8778	+	12.2624i	0.671894	+	0.488160i	0.870659	−	0.491887i	$-0.163693\pi$
$631$	16.8778	+	12.2624i	0.671894	+	0.488160i	−0.198764	+	0.980047i	$0.563693\pi$
$632$		0			0
$633$	0.222476	+	5.54506i	0.00884261	+	0.220396i
$634$		0			0
$635$	3.55970	+	1.14869i	0.141262	+	0.0455842i
$636$		0			0
$637$	−2.79235	+	1.42277i	−0.110637	+	0.0563723i
$638$		0			0
$639$	2.47330	+	30.7730i	0.0978421	+	1.21736i
$640$		0			0
$641$	−19.5368	−	6.34790i	−0.771658	−	0.250727i	−0.103383	−	0.994642i	$-0.532967\pi$
$641$	−19.5368	−	6.34790i	−0.771658	−	0.250727i	−0.668275	+	0.743915i	$0.732967\pi$
$642$		0			0
$643$	20.8324	−	20.8324i	0.821549	−	0.821549i	−0.164781	−	0.986330i	$-0.552692\pi$
$643$	20.8324	−	20.8324i	0.821549	−	0.821549i	0.986330	+	0.164781i	$0.0526917\pi$
$644$		0			0
$645$	−20.0356	−	25.2668i	−0.788901	−	0.994878i
$646$		0			0
$647$	−6.10259	+	38.5303i	−0.239918	+	1.51478i	0.513988	+	0.857798i	$0.328168\pi$
$647$	−6.10259	+	38.5303i	−0.239918	+	1.51478i	−0.753905	+	0.656983i	$0.771832\pi$
$648$		0			0
$649$			56.9743i			2.23644i
$650$		0			0
$651$	1.42665	−	12.1400i	0.0559149	−	0.475805i
$652$		0			0
$653$	32.1247	+	5.08805i	1.25714	+	0.199111i	0.749235	−	0.662304i	$-0.230421\pi$
$653$	32.1247	+	5.08805i	1.25714	+	0.199111i	0.507901	+	0.861415i	$0.330421\pi$
$654$		0			0
$655$	−9.16347	−	4.64577i	−0.358047	−	0.181525i
$656$		0			0
$657$	−3.40571	−	5.53697i	−0.132870	−	0.216018i
$658$		0			0
$659$	−6.17031	+	18.9903i	−0.240361	+	0.739755i	0.756004	+	0.654567i	$0.227149\pi$
$659$	−6.17031	+	18.9903i	−0.240361	+	0.739755i	−0.996365	+	0.0851880i	$0.972851\pi$
$660$		0			0
$661$	−4.21748	−	12.9801i	−0.164041	−	0.504866i	0.834923	−	0.550366i	$-0.185512\pi$
$661$	−4.21748	−	12.9801i	−0.164041	−	0.504866i	−0.998964	+	0.0455001i	$0.985512\pi$
$662$		0			0
$663$	−5.71786	−	15.4594i	−0.222063	−	0.600393i
$664$		0			0
$665$	−12.8257	−	39.2044i	−0.497361	−	1.52028i
$666$		0			0
$667$	−0.267791	−	1.69077i	−0.0103689	−	0.0654668i
$668$		0			0
$669$	−3.07197	−	2.83497i	−0.118769	−	0.109606i
$670$		0			0
$671$	17.5213	+	24.1161i	0.676404	+	0.930990i
$672$		0			0
$673$	−1.04272	−	0.531291i	−0.0401938	−	0.0204798i	0.433778	−	0.901020i	$-0.357180\pi$
$673$	−1.04272	−	0.531291i	−0.0401938	−	0.0204798i	−0.473972	+	0.880540i	$0.657180\pi$
$674$		0			0
$675$	−22.7504	−	12.5466i	−0.875664	−	0.482920i
$676$		0			0
$677$	2.46293	+	1.25493i	0.0946581	+	0.0482307i	0.500679	−	0.865633i	$-0.333084\pi$
$677$	2.46293	+	1.25493i	0.0946581	+	0.0482307i	−0.406020	+	0.913864i	$0.633084\pi$
$678$		0			0
$679$	22.4846	+	30.9474i	0.862881	+	1.18765i
$680$		0			0
$681$	−20.5550	−	18.9693i	−0.787670	−	0.726903i
$682$		0			0
$683$	4.28310	+	27.0424i	0.163888	+	1.03475i	0.923283	+	0.384119i	$0.125495\pi$
$683$	4.28310	+	27.0424i	0.163888	+	1.03475i	−0.759395	+	0.650630i	$0.774505\pi$
$684$		0			0
$685$	16.0708	−	11.7257i	0.614035	−	0.448017i
$686$		0			0
$687$	−10.3985	−	28.1145i	−0.396728	−	1.07264i
$688$		0			0
$689$	3.59854	+	11.0752i	0.137094	+	0.421931i
$690$		0			0
$691$	6.92199	−	21.3037i	0.263325	−	0.810430i	−0.728750	−	0.684780i	$-0.759898\pi$
$691$	6.92199	−	21.3037i	0.263325	−	0.810430i	0.992075	−	0.125650i	$-0.0401017\pi$
$692$		0			0
$693$	−20.6118	−	33.5104i	−0.782977	−	1.27296i
$694$		0			0
$695$	−3.78560	−	7.39276i	−0.143596	−	0.280424i
$696$		0			0
$697$	−20.0632	−	3.17770i	−0.759948	−	0.120364i
$698$		0			0
$699$	−3.10513	+	26.4230i	−0.117447	+	0.999410i
$700$		0			0
$701$		−	19.9094i		−	0.751969i	−0.926626	−	0.375985i	$-0.877305\pi$
$701$		−	19.9094i		−	0.751969i	0.926626	−	0.375985i	$-0.122695\pi$
$702$		0			0
$703$	10.5326	−	66.5005i	0.397246	−	2.50811i
$704$		0			0
$705$	−12.5871	−	3.51129i	−0.474058	−	0.132243i
$706$		0			0
$707$	−7.80455	+	7.80455i	−0.293520	+	0.293520i
$708$		0			0
$709$	−16.9259	−	5.49956i	−0.635666	−	0.206540i	−0.0265827	−	0.999647i	$-0.508463\pi$
$709$	−16.9259	−	5.49956i	−0.635666	−	0.206540i	−0.609083	+	0.793106i	$0.708463\pi$
$710$		0			0
$711$	4.13431	+	51.4396i	0.155049	+	1.92914i
$712$		0			0
$713$	−9.01008	+	4.59086i	−0.337430	+	0.171929i
$714$		0			0
$715$	−16.0605	+	22.1993i	−0.600627	+	0.830208i
$716$		0			0
$717$	−1.38824	−	34.6009i	−0.0518447	−	1.29219i
$718$		0			0
$719$	−33.9545	−	24.6694i	−1.26629	−	0.920014i	−0.267242	−	0.963629i	$-0.586112\pi$
$719$	−33.9545	−	24.6694i	−1.26629	−	0.920014i	−0.999048	+	0.0436153i	$0.986112\pi$
$720$		0			0
$721$	13.0745	−	9.49915i	0.486918	−	0.353767i
$722$		0			0
$723$	4.12586	−	6.18589i	0.153442	−	0.230056i
$724$		0			0
$725$	1.47808	−	2.05175i	0.0548946	−	0.0762002i
$726$		0			0
$727$	11.3404	−	22.2569i	0.420594	−	0.825462i	−0.579352	−	0.815077i	$-0.696694\pi$
$727$	11.3404	−	22.2569i	0.420594	−	0.825462i	0.999946	−	0.0103844i	$-0.00330552\pi$
$728$		0			0
$729$	−1.98433	+	26.9270i	−0.0734935	+	0.997296i
$730$		0			0
$731$	21.0998	−	29.0414i	0.780405	−	1.07413i
$732$		0			0
$733$	30.1622	−	4.77723i	1.11407	−	0.176451i	0.427852	−	0.903849i	$-0.359270\pi$
$733$	30.1622	−	4.77723i	1.11407	−	0.176451i	0.686216	+	0.727398i	$0.259270\pi$
$734$		0			0
$735$	−5.46271	−	0.630793i	−0.201495	−	0.0232672i
$736$		0			0
$737$	11.3936	+	22.3612i	0.419688	+	0.823684i
$738$		0			0
$739$	18.0849	−	5.87616i	0.665266	−	0.216158i	0.0431325	−	0.999069i	$-0.486266\pi$
$739$	18.0849	−	5.87616i	0.665266	−	0.216158i	0.622133	+	0.782911i	$0.286266\pi$
$740$		0			0
$741$	27.1230	+	12.4766i	0.996388	+	0.458339i
$742$		0			0
$743$	21.7526	+	21.7526i	0.798025	+	0.798025i	0.982784	−	0.184759i	$-0.0591505\pi$
$743$	21.7526	+	21.7526i	0.798025	+	0.798025i	−0.184759	+	0.982784i	$0.559150\pi$
$744$		0			0
$745$	−5.85543	−	36.4934i	−0.214526	−	1.33701i
$746$		0			0
$747$	14.1256	−	34.2629i	0.516828	−	1.25361i
$748$		0			0
$749$	−9.49011			−0.346761
$750$		0			0
$751$	−2.51184			−0.0916583			−0.0458292	−	0.998949i	$-0.514593\pi$
$751$	−2.51184			−0.0916583			−0.0458292	+	0.998949i	$0.514593\pi$
$752$		0			0
$753$	3.58480	−	12.7512i	0.130637	−	0.464681i
$754$		0			0
$755$	1.86826	+	11.6437i	0.0679928	+	0.423758i
$756$		0			0
$757$	10.6543	+	10.6543i	0.387238	+	0.387238i	0.873701	−	0.486463i	$-0.161713\pi$
$757$	10.6543	+	10.6543i	0.387238	+	0.387238i	−0.486463	+	0.873701i	$0.661713\pi$
$758$		0			0
$759$	−13.6014	+	29.5683i	−0.493700	+	1.07326i
$760$		0			0
$761$	−25.2259	+	8.19638i	−0.914437	+	0.297119i	−0.728183	−	0.685383i	$-0.759635\pi$
$761$	−25.2259	+	8.19638i	−0.914437	+	0.297119i	−0.186254	+	0.982502i	$0.559635\pi$
$762$		0			0
$763$	12.1510	+	23.8477i	0.439896	+	0.863344i
$764$		0			0
$765$	6.64829	−	28.1476i	0.240370	−	1.01768i
$766$		0			0
$767$	22.3737	−	3.54365i	0.807867	−	0.127954i
$768$		0			0
$769$	12.4291	−	17.1072i	0.448206	−	0.616903i	−0.523805	−	0.851838i	$-0.675488\pi$
$769$	12.4291	−	17.1072i	0.448206	−	0.616903i	0.972011	+	0.234935i	$0.0754878\pi$
$770$		0			0
$771$	13.3250	−	7.47688i	0.479887	−	0.269273i
$772$		0			0
$773$	−16.4953	+	32.3738i	−0.593294	+	1.16441i	0.377840	+	0.925871i	$0.376667\pi$
$773$	−16.4953	+	32.3738i	−0.593294	+	1.16441i	−0.971134	+	0.238534i	$0.923333\pi$
$774$		0			0
$775$	−14.2251	−	4.55868i	−0.510981	−	0.163753i
$776$		0			0
$777$	29.3474	+	19.5741i	1.05283	+	0.702218i
$778$		0			0
$779$	29.7660	−	21.6263i	1.06648	−	0.774842i
$780$		0			0
$781$	46.2186	+	33.5798i	1.65383	+	1.20158i
$782$		0			0
$783$	−2.57870	−	0.506263i	−0.0921551	−	0.0180924i
$784$		0			0
$785$	14.4406	−	19.9604i	0.515409	−	0.712416i
$786$		0			0
$787$	−25.7846	+	13.1379i	−0.919122	+	0.468316i	−0.848505	−	0.529188i	$-0.822497\pi$
$787$	−25.7846	+	13.1379i	−0.919122	+	0.468316i	−0.0706170	+	0.997504i	$0.522497\pi$
$788$		0			0
$789$	−29.4950	+	5.89237i	−1.05005	+	0.209774i
$790$		0			0
$791$	9.72301	+	3.15920i	0.345710	+	0.112328i
$792$		0			0
$793$	8.38054	−	8.38054i	0.297602	−	0.297602i
$794$		0			0
$795$	−5.49044	+	19.6819i	−0.194726	+	0.698045i
$796$		0			0
$797$	−1.30431	+	8.23509i	−0.0462010	+	0.291702i	−0.999961	−	0.00886857i	$-0.997177\pi$
$797$	−1.30431	+	8.23509i	−0.0462010	+	0.291702i	0.953760	+	0.300570i	$0.0971770\pi$
$798$		0			0
$799$		−	14.5471i		−	0.514640i
$800$		0			0
$801$	3.22568	−	13.5349i	0.113974	−	0.478231i
$802$		0			0
$803$	−11.8812	−	1.88179i	−0.419278	−	0.0664070i
$804$		0			0
$805$	−8.14898	−	15.9139i	−0.287214	−	0.560890i
$806$		0			0
$807$	−22.8242	−	28.9030i	−0.803451	−	1.01744i
$808$		0			0
$809$	10.7932	−	33.2182i	0.379470	−	1.16789i	−0.560943	−	0.827854i	$-0.689561\pi$
$809$	10.7932	−	33.2182i	0.379470	−	1.16789i	0.940413	−	0.340034i	$-0.110439\pi$
$810$		0			0
$811$	−0.408186	−	1.25627i	−0.0143333	−	0.0441135i	0.943634	−	0.330991i	$-0.107383\pi$
$811$	−0.408186	−	1.25627i	−0.0143333	−	0.0441135i	−0.957967	+	0.286877i	$0.907383\pi$
$812$		0			0
$813$	−15.6571	+	5.79097i	−0.549118	+	0.203098i
$814$		0			0
$815$	−27.9631	+	20.4026i	−0.979504	+	0.714673i
$816$		0			0
$817$	10.1713	+	64.2188i	0.355848	+	2.24673i
$818$		0			0
$819$	−11.8775	+	10.1785i	−0.415032	+	0.355664i
$820$		0			0
$821$	−7.54308	−	10.3822i	−0.263255	−	0.362340i	0.656843	−	0.754027i	$-0.271891\pi$
$821$	−7.54308	−	10.3822i	−0.263255	−	0.362340i	−0.920098	+	0.391688i	$0.871891\pi$
$822$		0			0
$823$	33.4192	+	17.0279i	1.16492	+	0.593556i	0.926015	−	0.377487i	$-0.123212\pi$
$823$	33.4192	+	17.0279i	1.16492	+	0.593556i	0.238905	+	0.971043i	$0.423212\pi$
$824$		0			0
$825$	−45.0245	+	16.8596i	−1.56755	+	0.586976i
$826$		0			0
$827$	14.4342	+	7.35461i	0.501928	+	0.255745i	0.686574	−	0.727060i	$-0.259114\pi$
$827$	14.4342	+	7.35461i	0.501928	+	0.255745i	−0.184646	+	0.982805i	$0.559114\pi$
$828$		0			0
$829$	8.37217	+	11.5233i	0.290777	+	0.400221i	0.929266	−	0.369410i	$-0.120440\pi$
$829$	8.37217	+	11.5233i	0.290777	+	0.400221i	−0.638489	+	0.769631i	$0.720440\pi$
$830$		0			0
$831$	37.8351	−	40.9980i	1.31249	−	1.42220i
$832$		0			0
$833$	−0.957623	−	6.04619i	−0.0331797	−	0.209488i
$834$		0			0
$835$	−6.98565	−	21.3530i	−0.241748	−	0.738952i
$836$		0			0
$837$	1.86300	+	15.4115i	0.0643946	+	0.532700i
$838$		0			0
$839$	−12.4231	−	38.2343i	−0.428892	−	1.32000i	−0.899217	−	0.437502i	$-0.855863\pi$
$839$	−12.4231	−	38.2343i	−0.428892	−	1.32000i	0.470325	−	0.882493i	$-0.344137\pi$
$840$		0			0
$841$	−8.88245	+	27.3374i	−0.306291	+	0.942668i
$842$		0			0
$843$	3.75313	−	2.96379i	0.129265	−	0.102078i
$844$		0			0
$845$	−16.2106	−	8.21857i	−0.557661	−	0.282727i
$846$		0			0
$847$	−46.2416	−	7.32395i	−1.58888	−	0.251654i
$848$		0			0
$849$	−26.2152	−	3.08071i	−0.899703	−	0.105730i
$850$		0			0
$851$		−	29.1832i		−	1.00039i
$852$		0			0
$853$	−4.09833	+	25.8759i	−0.140324	+	0.885973i	0.812613	+	0.582804i	$0.198045\pi$
$853$	−4.09833	+	25.8759i	−0.140324	+	0.885973i	−0.952937	+	0.303169i	$0.901955\pi$
$854$		0			0
$855$	27.5354	+	44.5652i	0.941692	+	1.52410i
$856$		0			0
$857$	33.2839	−	33.2839i	1.13696	−	1.13696i	0.147964	−	0.988993i	$-0.452728\pi$
$857$	33.2839	−	33.2839i	1.13696	−	1.13696i	0.988993	−	0.147964i	$-0.0472720\pi$
$858$		0			0
$859$	30.3820	+	9.87171i	1.03662	+	0.336818i	0.777405	−	0.629001i	$-0.216536\pi$
$859$	30.3820	+	9.87171i	1.03662	+	0.336818i	0.259216	+	0.965819i	$0.416536\pi$
$860$		0			0
$861$	3.77646	+	18.9035i	0.128701	+	0.644231i
$862$		0			0
$863$	28.4236	−	14.4825i	0.967549	−	0.492991i	0.102530	−	0.994730i	$-0.467306\pi$
$863$	28.4236	−	14.4825i	0.967549	−	0.492991i	0.865019	+	0.501739i	$0.167306\pi$
$864$		0			0
$865$	−31.1870	−	10.0638i	−1.06039	−	0.342180i
$866$		0			0
$867$	2.74932	−	0.110307i	0.0933718	−	0.00374621i
$868$		0			0
$869$	77.2581	+	56.1313i	2.62080	+	1.90412i
$870$		0			0
$871$	8.07253	−	5.86504i	0.273527	−	0.198729i
$872$		0			0
$873$	−36.9935	−	31.4894i	−1.25204	−	1.06575i
$874$		0			0
$875$	8.00925	−	25.1669i	0.270762	−	0.850796i
$876$		0			0
$877$	11.9289	−	23.4117i	0.402809	−	0.790558i	−0.597124	−	0.802149i	$-0.703690\pi$
$877$	11.9289	−	23.4117i	0.402809	−	0.790558i	0.999933	+	0.0115917i	$0.00368982\pi$
$878$		0			0
$879$	−8.95825	−	15.9650i	−0.302154	−	0.538487i
$880$		0			0
$881$	−5.23004	+	7.19854i	−0.176205	+	0.242525i	−0.887980	−	0.459883i	$-0.847892\pi$
$881$	−5.23004	+	7.19854i	−0.176205	+	0.242525i	0.711775	+	0.702407i	$0.247892\pi$
$882$		0			0
$883$	45.7465	−	7.24553i	1.53949	−	0.243831i	0.671724	−	0.740802i	$-0.265554\pi$
$883$	45.7465	−	7.24553i	1.53949	−	0.243831i	0.867768	+	0.496970i	$0.165554\pi$
$884$		0			0
$885$	36.1439	+	16.5380i	1.21496	+	0.555918i
$886$		0			0
$887$	−1.61971	−	3.17886i	−0.0543846	−	0.106736i	0.862215	−	0.506543i	$-0.169077\pi$
$887$	−1.61971	−	3.17886i	−0.0543846	−	0.106736i	−0.916599	+	0.399808i	$0.869077\pi$
$888$		0			0
$889$	3.75810	−	1.22108i	0.126042	−	0.0409537i
$890$		0			0
$891$	35.4467	+	35.2122i	1.18751	+	1.17965i
$892$		0			0
$893$	18.6314	+	18.6314i	0.623475	+	0.623475i
$894$		0			0
$895$	24.1004	+	24.0034i	0.805586	+	0.802344i
$896$		0			0
$897$	12.4574	+	3.50218i	0.415940	+	0.116935i
$898$		0			0
$899$	−1.51093			−0.0503924
$900$		0			0
$901$	−22.7466			−0.757800
$902$		0			0
$903$	−32.7946	−	9.21966i	−1.09134	−	0.306811i
$904$		0			0
$905$	0.558793	−	1.10218i	0.0185749	−	0.0366377i
$906$		0			0
$907$	−8.84343	−	8.84343i	−0.293641	−	0.293641i	0.544876	−	0.838517i	$-0.316577\pi$
$907$	−8.84343	−	8.84343i	−0.293641	−	0.293641i	−0.838517	+	0.544876i	$0.816577\pi$
$908$		0			0
$909$	7.30410	−	11.9637i	0.242262	−	0.396812i
$910$		0			0
$911$	−30.2562	+	9.83082i	−1.00243	+	0.325710i	−0.763837	−	0.645410i	$-0.776687\pi$
$911$	−30.2562	+	9.83082i	−1.00243	+	0.325710i	−0.238595	+	0.971119i	$0.576687\pi$
$912$		0			0
$913$	−31.1350	−	61.1058i	−1.03042	−	2.02231i
$914$		0			0
$915$	20.3849	−	4.11516i	0.673904	−	0.136043i
$916$		0			0
$917$	−10.7199	+	1.69787i	−0.354004	+	0.0560687i
$918$		0			0
$919$	−12.0511	+	16.5869i	−0.397529	+	0.547152i	−0.960122	−	0.279582i	$-0.909804\pi$
$919$	−12.0511	+	16.5869i	−0.397529	+	0.547152i	0.562593	+	0.826734i	$0.309804\pi$
$920$		0			0
$921$	4.36823	+	7.78487i	0.143938	+	0.256520i
$922$		0			0
$923$	10.3120	−	20.2385i	0.339425	−	0.666159i
$924$		0			0
$925$	30.3596	−	30.6054i	0.998217	−	1.00630i
$926$		0			0
$927$	−13.3034	+	15.6287i	−0.436941	+	0.513315i
$928$		0			0
$929$	35.8841	−	26.0713i	1.17732	−	0.855373i	0.185453	−	0.982653i	$-0.440625\pi$
$929$	35.8841	−	26.0713i	1.17732	−	0.855373i	0.991867	+	0.127281i	$0.0406249\pi$
$930$		0			0
$931$	8.97020	+	6.51723i	0.293987	+	0.213594i
$932$		0			0
$933$	−14.5168	+	0.582436i	−0.475260	+	0.0190681i
$934$		0			0
$935$	−31.5458	−	43.2355i	−1.03166	−	1.41395i
$936$		0			0
$937$	−1.10010	+	0.560530i	−0.0359388	+	0.0183117i	−0.471868	−	0.881669i	$-0.656420\pi$
$937$	−1.10010	+	0.560530i	−0.0359388	+	0.0183117i	0.435929	+	0.899981i	$0.356420\pi$
$938$		0			0
$939$	3.01190	+	15.0764i	0.0982895	+	0.492000i
$940$		0			0
$941$	−33.2056	−	10.7891i	−1.08247	−	0.351716i	−0.287138	−	0.957889i	$-0.592704\pi$
$941$	−33.2056	−	10.7891i	−1.08247	−	0.351716i	−0.795333	+	0.606173i	$0.792704\pi$
$942$		0			0
$943$	11.2765	−	11.2765i	0.367214	−	0.367214i
$944$		0			0
$945$	−27.2416	+	3.34881i	−0.886171	+	0.108937i
$946$		0			0
$947$	−6.31969	+	39.9009i	−0.205362	+	1.29661i	0.642457	+	0.766321i	$0.277915\pi$
$947$	−6.31969	+	39.9009i	−0.205362	+	1.29661i	−0.847820	+	0.530285i	$0.822085\pi$
$948$		0			0
$949$			4.78275i			0.155255i
$950$		0			0
$951$	25.5584	+	3.00353i	0.828789	+	0.0973962i
$952$		0			0
$953$	51.8286	+	8.20885i	1.67889	+	0.265911i	0.921876	−	0.387484i	$-0.126656\pi$
$953$	51.8286	+	8.20885i	1.67889	+	0.265911i	0.757017	+	0.653395i	$0.226656\pi$
$954$		0			0
$955$	7.46895	−	47.7804i	0.241689	−	1.54614i
$956$		0			0
$957$	−3.81649	+	3.01381i	−0.123369	+	0.0974228i
$958$		0			0
$959$	6.49440	−	19.9877i	0.209715	−	0.645437i
$960$		0			0
$961$	−6.82142	−	20.9942i	−0.220046	−	0.677232i
$962$		0			0
$963$	11.7146	−	2.83300i	0.377497	−	0.0912921i
$964$		0			0
$965$	9.52092	+	6.88807i	0.306489	+	0.221735i
$966$		0			0
$967$	2.62324	+	16.5625i	0.0843578	+	0.532614i	0.993288	+	0.115666i	$0.0369003\pi$
$967$	2.62324	+	16.5625i	0.0843578	+	0.532614i	−0.908930	+	0.416948i	$0.863100\pi$
$968$		0			0
$969$	−39.5496	+	42.8558i	−1.27052	+	1.37673i
$970$		0			0
$971$	29.3538	+	40.4020i	0.942008	+	1.29656i	0.954987	+	0.296647i	$0.0958685\pi$
$971$	29.3538	+	40.4020i	0.942008	+	1.29656i	−0.0129790	+	0.999916i	$0.504131\pi$
$972$		0			0
$973$	−7.81794	−	3.98344i	−0.250632	−	0.127703i
$974$		0			0
$975$	9.42113	+	16.6324i	0.301718	+	0.532663i
$976$		0			0
$977$	−54.4219	−	27.7294i	−1.74111	−	0.887141i	−0.967265	−	0.253768i	$-0.918330\pi$
$977$	−54.4219	−	27.7294i	−1.74111	−	0.887141i	−0.773847	−	0.633373i	$-0.781670\pi$
$978$		0			0
$979$	−15.1342	−	20.8304i	−0.483691	−	0.665743i
$980$		0			0
$981$	−22.1182	−	25.8102i	−0.706181	−	0.824058i
$982$		0			0
$983$	−1.42079	−	8.97053i	−0.0453163	−	0.286116i	0.954615	−	0.297843i	$-0.0962671\pi$
$983$	−1.42079	−	8.97053i	−0.0453163	−	0.286116i	−0.999931	+	0.0117271i	$0.996267\pi$
$984$		0			0
$985$	−43.7932	+	0.0882988i	−1.39537	+	0.00281343i
$986$		0			0
$987$	−12.9478	+	4.78891i	−0.412133	+	0.152433i
$988$		0			0
$989$	8.70868	+	26.8026i	0.276920	+	0.852272i
$990$		0			0
$991$	4.23922	−	13.0470i	0.134663	−	0.414451i	−0.860874	−	0.508818i	$-0.830083\pi$
$991$	4.23922	−	13.0470i	0.134663	−	0.414451i	0.995537	+	0.0943669i	$0.0300827\pi$
$992$		0			0
$993$	−12.7267	−	16.1162i	−0.403870	−	0.511433i
$994$		0			0
$995$	−3.91039	+	0.627429i	−0.123968	+	0.0198908i
$996$		0			0
$997$	19.1620	+	3.03495i	0.606865	+	0.0961180i	0.452302	−	0.891865i	$-0.350603\pi$
$997$	19.1620	+	3.03495i	0.606865	+	0.0961180i	0.154563	+	0.987983i	$0.450603\pi$
$998$		0			0
$999$	−42.0697	−	15.4014i	−1.33103	−	0.487280i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.x.a.17.10	yes	80
3.2	odd	2	inner	300.2.x.a.17.1	✓	80
25.3	odd	20	inner	300.2.x.a.53.1	yes	80
75.53	even	20	inner	300.2.x.a.53.10	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.x.a.17.1	✓	80	3.2	odd	2	inner
300.2.x.a.17.10	yes	80	1.1	even	1	trivial
300.2.x.a.53.1	yes	80	25.3	odd	20	inner
300.2.x.a.53.10	yes	80	75.53	even	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.66741 + 0.468765i) q^{3} +(-0.354250 - 2.20783i) q^{5} +(-1.67035 - 1.67035i) q^{7} +(2.56052 + 1.56325i) q^{9} +O(q^{10})\)	\(q+(1.66741 + 0.468765i) q^{3} +(-0.354250 - 2.20783i) q^{5} +(-1.67035 - 1.67035i) q^{7} +(2.56052 + 1.56325i) q^{9} +(5.27981 - 1.71551i) q^{11} +(-1.00207 - 1.96667i) q^{13} +(0.444271 - 3.84742i) q^{15} +(4.25837 - 0.674459i) q^{17} +(-4.59013 + 6.31777i) q^{19} +(-2.00216 - 3.56817i) q^{21} +(-1.53667 + 3.01588i) q^{23} +(-4.74901 + 1.56425i) q^{25} +(3.53664 + 3.80686i) q^{27} +(-0.409155 + 0.297269i) q^{29} +(2.41697 + 1.75603i) q^{31} +(9.60778 - 0.385478i) q^{33} +(-3.09613 + 4.27958i) q^{35} +(-7.68210 + 3.91423i) q^{37} +(-0.748954 - 3.74898i) q^{39} +(-4.48088 - 1.45593i) q^{41} +(5.88737 - 5.88737i) q^{43} +(2.54432 - 6.20697i) q^{45} +(0.527820 - 3.33252i) q^{47} -1.41984i q^{49} +(7.41661 + 0.871573i) q^{51} +(-5.21091 - 0.825328i) q^{53} +(-5.65793 - 11.0492i) q^{55} +(-10.6152 + 8.38263i) q^{57} +(-3.17139 + 9.76054i) q^{59} +(1.65928 + 5.10673i) q^{61} +(-1.66580 - 6.88815i) q^{63} +(-3.98709 + 2.90909i) q^{65} +(0.707187 + 4.46500i) q^{67} +(-3.97600 + 4.30838i) q^{69} +(6.04875 + 8.32540i) q^{71} +(-1.93067 - 0.983727i) q^{73} +(-8.65182 + 0.382074i) q^{75} +(-11.6847 - 5.95363i) q^{77} +(10.1110 + 13.9166i) q^{79} +(4.11252 + 8.00545i) q^{81} +(-1.93251 - 12.2014i) q^{83} +(-2.99762 - 9.16282i) q^{85} +(-0.821579 + 0.303872i) q^{87} +(-1.43321 - 4.41098i) q^{89} +(-1.61123 + 4.95884i) q^{91} +(3.20692 + 4.06102i) q^{93} +(15.5746 + 7.89614i) q^{95} +(-15.9942 - 2.53324i) q^{97} +(16.2008 + 3.86104i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{3} + 4 q^{7}+O(q^{10}) \) 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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