LMFDB - Embedded newform 512.2.k.a.17.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [512,2,Mod(17,512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(512, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("512.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.k (of order $32$, degree $16$, not 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:	$4.08834058349$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$15$ over $\Q(\zeta_{32})$
Twist minimal:	no (minimal twist has level 128)
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			17.1
Character	$\chi$	$=$	512.17
Dual form			512.2.k.a.241.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.46662 + 2.74386i) q^{3} +(-0.382125 - 0.313602i) q^{5} +(-1.98950 - 1.32934i) q^{7} +(-3.71107 - 5.55401i) q^{9} +O(q^{10})$	\(q+(-1.46662 + 2.74386i) q^{3} +(-0.382125 - 0.313602i) q^{5} +(-1.98950 - 1.32934i) q^{7} +(-3.71107 - 5.55401i) q^{9} +(1.05398 - 3.47451i) q^{11} +(2.05150 + 2.49975i) q^{13} +(1.42091 - 0.588561i) q^{15} +(-5.44241 - 2.25432i) q^{17} +(-3.91033 - 0.385134i) q^{19} +(6.56538 - 3.50927i) q^{21} +(1.15735 + 0.230211i) q^{23} +(-0.927778 - 4.66426i) q^{25} +(11.3934 - 1.12215i) q^{27} +(7.71499 - 2.34032i) q^{29} +(2.98655 - 2.98655i) q^{31} +(7.98777 + 7.98777i) q^{33} +(0.343354 + 1.13189i) q^{35} +(0.848768 + 8.61769i) q^{37} +(-9.86775 + 1.96282i) q^{39} +(-0.0242205 + 0.121765i) q^{41} +(-2.46052 - 4.60331i) q^{43} +(-0.323655 + 3.28612i) q^{45} +(1.36332 - 3.29134i) q^{47} +(-0.487818 - 1.17770i) q^{49} +(14.1675 - 11.6270i) q^{51} +(-8.90424 - 2.70107i) q^{53} +(-1.49236 + 0.997166i) q^{55} +(6.79174 - 10.1646i) q^{57} +(-3.77059 + 4.59448i) q^{59} +(-11.1794 - 5.97554i) q^{61} +15.9830i q^{63} -1.59857i q^{65} +(-7.51634 - 4.01757i) q^{67} +(-2.32906 + 2.83797i) q^{69} +(3.58681 - 5.36805i) q^{71} +(-5.06870 + 3.38680i) q^{73} +(14.1588 + 4.29501i) q^{75} +(-6.71571 + 5.51144i) q^{77} +(-3.35477 - 8.09914i) q^{79} +(-5.96214 + 14.3939i) q^{81} +(-0.129211 + 1.31190i) q^{83} +(1.37272 + 2.56818i) q^{85} +(-4.89349 + 24.6012i) q^{87} +(-8.16474 + 1.62407i) q^{89} +(-0.758424 - 7.70041i) q^{91} +(3.81453 + 12.5748i) q^{93} +(1.37346 + 1.37346i) q^{95} +(1.07767 - 1.07767i) q^{97} +(-23.2089 + 7.04033i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9}+O(q^{10}) $ 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9	$ 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9} + 16 q^{11} - 16 q^{13} + 16 q^{15} - 16 q^{17} + 16 q^{19} - 16 q^{21} + 16 q^{23} - 16 q^{25} + 16 q^{27} - 16 q^{29} + 16 q^{31} - 16 q^{33} + 16 q^{35} - 16 q^{37} + 16 q^{39} - 16 q^{41} + 16 q^{43} - 16 q^{45} + 16 q^{47} - 16 q^{49} + 16 q^{51} - 16 q^{53} + 16 q^{55} - 16 q^{57} + 16 q^{59} - 16 q^{61} + 16 q^{67} - 16 q^{69} + 16 q^{71} - 16 q^{73} + 16 q^{75} - 16 q^{77} + 16 q^{79} - 16 q^{81} + 16 q^{83} - 16 q^{85} + 16 q^{87} - 16 q^{89} + 16 q^{91} - 16 q^{93} + 16 q^{95} - 16 q^{97} + 16 q^{99}+O(q^{100}) $ 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9 + 16 * q^11 - 16 * q^13 + 16 * q^15 - 16 * q^17 + 16 * q^19 - 16 * q^21 + 16 * q^23 - 16 * q^25 + 16 * q^27 - 16 * q^29 + 16 * q^31 - 16 * q^33 + 16 * q^35 - 16 * q^37 + 16 * q^39 - 16 * q^41 + 16 * q^43 - 16 * q^45 + 16 * q^47 - 16 * q^49 + 16 * q^51 - 16 * q^53 + 16 * q^55 - 16 * q^57 + 16 * q^59 - 16 * q^61 + 16 * q^67 - 16 * q^69 + 16 * q^71 - 16 * q^73 + 16 * q^75 - 16 * q^77 + 16 * q^79 - 16 * q^81 + 16 * q^83 - 16 * q^85 + 16 * q^87 - 16 * q^89 + 16 * q^91 - 16 * q^93 + 16 * q^95 - 16 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{7}{32}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.46662	+	2.74386i	−0.846756	+	1.58417i	−0.0355789	+	0.999367i	$0.511328\pi$
$3$	−1.46662	+	2.74386i	−0.846756	+	1.58417i	−0.811177	+	0.584801i	$0.801172\pi$
$4$		0			0
$5$	−0.382125	−	0.313602i	−0.170891	−	0.140247i	0.545060	−	0.838397i	$-0.316507\pi$
$5$	−0.382125	−	0.313602i	−0.170891	−	0.140247i	−0.715952	+	0.698150i	$0.754007\pi$
$6$		0			0
$7$	−1.98950	−	1.32934i	−0.751961	−	0.502444i	0.119545	−	0.992829i	$-0.461856\pi$
$7$	−1.98950	−	1.32934i	−0.751961	−	0.502444i	−0.871506	+	0.490384i	$0.836856\pi$
$8$		0			0
$9$	−3.71107	−	5.55401i	−1.23702	−	1.85134i
$10$		0			0
$11$	1.05398	−	3.47451i	0.317787	−	1.04760i	−0.641960	−	0.766738i	$-0.721878\pi$
$11$	1.05398	−	3.47451i	0.317787	−	1.04760i	0.959747	−	0.280866i	$-0.0906216\pi$
$12$		0			0
$13$	2.05150	+	2.49975i	0.568982	+	0.693307i	0.975416	−	0.220373i	$-0.0707276\pi$
$13$	2.05150	+	2.49975i	0.568982	+	0.693307i	−0.406433	+	0.913681i	$0.633228\pi$
$14$		0			0
$15$	1.42091	−	0.588561i	0.366878	−	0.151966i
$16$		0			0
$17$	−5.44241	−	2.25432i	−1.31998	−	0.546753i	−0.392198	−	0.919881i	$-0.628285\pi$
$17$	−5.44241	−	2.25432i	−1.31998	−	0.546753i	−0.927780	+	0.373128i	$0.878285\pi$
$18$		0			0
$19$	−3.91033	−	0.385134i	−0.897092	−	0.0883558i	−0.361049	−	0.932547i	$-0.617581\pi$
$19$	−3.91033	−	0.385134i	−0.897092	−	0.0883558i	−0.536043	+	0.844191i	$0.680081\pi$
$20$		0			0
$21$	6.56538	−	3.50927i	1.43268	−	0.765785i
$22$		0			0
$23$	1.15735	+	0.230211i	0.241324	+	0.0480023i	0.314270	−	0.949334i	$-0.398240\pi$
$23$	1.15735	+	0.230211i	0.241324	+	0.0480023i	−0.0729464	+	0.997336i	$0.523240\pi$
$24$		0			0
$25$	−0.927778	−	4.66426i	−0.185556	−	0.932851i
$26$		0			0
$27$	11.3934	−	1.12215i	2.19267	−	0.215959i
$28$		0			0
$29$	7.71499	−	2.34032i	1.43264	−	0.434586i	0.523838	−	0.851818i	$-0.324500\pi$
$29$	7.71499	−	2.34032i	1.43264	−	0.434586i	0.908800	+	0.417232i	$0.137000\pi$
$30$		0			0
$31$	2.98655	−	2.98655i	0.536400	−	0.536400i	−0.386069	−	0.922470i	$-0.626167\pi$
$31$	2.98655	−	2.98655i	0.536400	−	0.536400i	0.922470	+	0.386069i	$0.126167\pi$
$32$		0			0
$33$	7.98777	+	7.98777i	1.39049	+	1.39049i
$34$		0			0
$35$	0.343354	+	1.13189i	0.0580374	+	0.191324i
$36$		0			0
$37$	0.848768	+	8.61769i	0.139537	+	1.41674i	0.768771	+	0.639524i	$0.220868\pi$
$37$	0.848768	+	8.61769i	0.139537	+	1.41674i	−0.629235	+	0.777215i	$0.716632\pi$
$38$		0			0
$39$	−9.86775	+	1.96282i	−1.58010	+	0.314302i
$40$		0			0
$41$	−0.0242205	+	0.121765i	−0.00378261	+	0.0190165i	−0.982630	−	0.185573i	$-0.940586\pi$
$41$	−0.0242205	+	0.121765i	−0.00378261	+	0.0190165i	0.978848	+	0.204589i	$0.0655859\pi$
$42$		0			0
$43$	−2.46052	−	4.60331i	−0.375226	−	0.701998i	0.621451	−	0.783453i	$-0.286543\pi$
$43$	−2.46052	−	4.60331i	−0.375226	−	0.701998i	−0.996677	+	0.0814546i	$0.974043\pi$
$44$		0			0
$45$	−0.323655	+	3.28612i	−0.0482476	+	0.489866i
$46$		0			0
$47$	1.36332	−	3.29134i	0.198860	−	0.480091i	−0.792720	−	0.609586i	$-0.791336\pi$
$47$	1.36332	−	3.29134i	0.198860	−	0.480091i	0.991580	+	0.129495i	$0.0413356\pi$
$48$		0			0
$49$	−0.487818	−	1.17770i	−0.0696883	−	0.168242i
$50$		0			0
$51$	14.1675	−	11.6270i	1.98385	−	1.62810i
$52$		0			0
$53$	−8.90424	−	2.70107i	−1.22309	−	0.371021i	−0.388272	−	0.921545i	$-0.626928\pi$
$53$	−8.90424	−	2.70107i	−1.22309	−	0.371021i	−0.834819	+	0.550524i	$0.814428\pi$
$54$		0			0
$55$	−1.49236	+	0.997166i	−0.201230	+	0.134458i
$56$		0			0
$57$	6.79174	−	10.1646i	0.899588	−	1.34633i
$58$		0			0
$59$	−3.77059	+	4.59448i	−0.490889	+	0.598150i	−0.958255	−	0.285914i	$-0.907703\pi$
$59$	−3.77059	+	4.59448i	−0.490889	+	0.598150i	0.467366	+	0.884064i	$0.345203\pi$
$60$		0			0
$61$	−11.1794	−	5.97554i	−1.43138	−	0.765089i	−0.440238	−	0.897881i	$-0.645106\pi$
$61$	−11.1794	−	5.97554i	−1.43138	−	0.765089i	−0.991144	+	0.132792i	$0.957606\pi$
$62$		0			0
$63$			15.9830i			2.01367i
$64$		0			0
$65$		−	1.59857i		−	0.198278i
$66$		0			0
$67$	−7.51634	−	4.01757i	−0.918267	−	0.490824i	−0.0566562	−	0.998394i	$-0.518044\pi$
$67$	−7.51634	−	4.01757i	−0.918267	−	0.490824i	−0.861611	+	0.507570i	$0.830544\pi$
$68$		0			0
$69$	−2.32906	+	2.83797i	−0.280386	+	0.341651i
$70$		0			0
$71$	3.58681	−	5.36805i	0.425677	−	0.637070i	−0.555196	−	0.831719i	$-0.687357\pi$
$71$	3.58681	−	5.36805i	0.425677	−	0.637070i	0.980873	+	0.194649i	$0.0623569\pi$
$72$		0			0
$73$	−5.06870	+	3.38680i	−0.593247	+	0.396395i	−0.815638	−	0.578563i	$-0.803614\pi$
$73$	−5.06870	+	3.38680i	−0.593247	+	0.396395i	0.222391	+	0.974958i	$0.428614\pi$
$74$		0			0
$75$	14.1588	+	4.29501i	1.63491	+	0.495946i
$76$		0			0
$77$	−6.71571	+	5.51144i	−0.765326	+	0.628087i
$78$		0			0
$79$	−3.35477	−	8.09914i	−0.377442	−	0.911224i	−0.992444	−	0.122699i	$-0.960845\pi$
$79$	−3.35477	−	8.09914i	−0.377442	−	0.911224i	0.615002	−	0.788525i	$-0.289155\pi$
$80$		0			0
$81$	−5.96214	+	14.3939i	−0.662460	+	1.59932i
$82$		0			0
$83$	−0.129211	+	1.31190i	−0.0141828	+	0.144000i	−0.999668	−	0.0257601i	$-0.991799\pi$
$83$	−0.129211	+	1.31190i	−0.0141828	+	0.144000i	0.985485	+	0.169760i	$0.0542994\pi$
$84$		0			0
$85$	1.37272	+	2.56818i	0.148893	+	0.278558i
$86$		0			0
$87$	−4.89349	+	24.6012i	−0.524637	+	2.63753i
$88$		0			0
$89$	−8.16474	+	1.62407i	−0.865460	+	0.172151i	−0.607805	−	0.794086i	$-0.707950\pi$
$89$	−8.16474	+	1.62407i	−0.865460	+	0.172151i	−0.257655	+	0.966237i	$0.582950\pi$
$90$		0			0
$91$	−0.758424	−	7.70041i	−0.0795044	−	0.807222i
$92$		0			0
$93$	3.81453	+	12.5748i	0.395548	+	1.30395i
$94$		0			0
$95$	1.37346	+	1.37346i	0.140914	+	0.140914i
$96$		0			0
$97$	1.07767	−	1.07767i	0.109420	−	0.109420i	−0.650277	−	0.759697i	$-0.725347\pi$
$97$	1.07767	−	1.07767i	0.109420	−	0.109420i	0.759697	+	0.650277i	$0.225347\pi$
$98$		0			0
$99$	−23.2089	+	7.04033i	−2.33258	+	0.707580i
$100$		0			0
$101$	9.12431	−	0.898666i	0.907903	−	0.0894207i	0.366726	−	0.930329i	$-0.380479\pi$
$101$	9.12431	−	0.898666i	0.907903	−	0.0894207i	0.541177	+	0.840908i	$0.317979\pi$
$102$		0			0
$103$	1.52549	+	7.66914i	0.150311	+	0.755662i	0.980243	+	0.197798i	$0.0633790\pi$
$103$	1.52549	+	7.66914i	0.150311	+	0.755662i	−0.829932	+	0.557864i	$0.811621\pi$
$104$		0			0
$105$	−3.60931	−	0.717936i	−0.352232	−	0.0700634i
$106$		0			0
$107$	0.739018	−	0.395013i	0.0714436	−	0.0381874i	−0.435288	−	0.900291i	$-0.643353\pi$
$107$	0.739018	−	0.395013i	0.0714436	−	0.0381874i	0.506732	+	0.862104i	$0.330853\pi$
$108$		0			0
$109$	−12.9892	−	1.27932i	−1.24414	−	0.122537i	−0.545560	−	0.838072i	$-0.683683\pi$
$109$	−12.9892	−	1.27932i	−1.24414	−	0.122537i	−0.698577	+	0.715535i	$0.746183\pi$
$110$		0			0
$111$	−24.8905	−	10.3100i	−2.36251	−	0.978582i
$112$		0			0
$113$	5.36691	−	2.22305i	0.504877	−	0.209127i	−0.115683	−	0.993286i	$-0.536906\pi$
$113$	5.36691	−	2.22305i	0.504877	−	0.209127i	0.620559	+	0.784159i	$0.286906\pi$
$114$		0			0
$115$	−0.370057	−	0.450916i	−0.0345080	−	0.0420481i
$116$		0			0
$117$	6.27042	−	20.6708i	0.579700	−	1.91102i
$118$		0			0
$119$	7.83092	+	11.7198i	0.717859	+	1.07435i
$120$		0			0
$121$	−1.81517	−	1.21286i	−0.165016	−	0.110260i
$122$		0			0
$123$	−0.298583	−	0.245041i	−0.0269223	−	0.0220946i
$124$		0			0
$125$	−2.27333	+	4.25310i	−0.203333	+	0.380409i
$126$		0			0
$127$	−1.76150			−0.156308			−0.0781538	−	0.996941i	$-0.524903\pi$
$127$	−1.76150			−0.156308			−0.0781538	+	0.996941i	$0.524903\pi$
$128$		0			0
$129$	16.2395			1.42981
$130$		0			0
$131$	2.96973	−	5.55597i	0.259467	−	0.485428i	−0.718132	−	0.695907i	$-0.755002\pi$
$131$	2.96973	−	5.55597i	0.259467	−	0.485428i	0.977598	+	0.210479i	$0.0675025\pi$
$132$		0			0
$133$	7.26764	+	5.96440i	0.630184	+	0.517179i
$134$		0			0
$135$	−4.70562	−	3.14420i	−0.404995	−	0.270609i
$136$		0			0
$137$	−1.88078	−	2.81478i	−0.160686	−	0.240483i	0.742386	−	0.669972i	$-0.233694\pi$
$137$	−1.88078	−	2.81478i	−0.160686	−	0.240483i	−0.903072	+	0.429489i	$0.858694\pi$
$138$		0			0
$139$	−6.43403	+	21.2102i	−0.545727	+	1.79902i	0.0536552	+	0.998560i	$0.482913\pi$
$139$	−6.43403	+	21.2102i	−0.545727	+	1.79902i	−0.599383	+	0.800463i	$0.704587\pi$
$140$		0			0
$141$	7.03150	+	8.56791i	0.592159	+	0.721548i
$142$		0			0
$143$	10.8477	−	4.49325i	0.907127	−	0.375744i
$144$		0			0
$145$	−3.68202	−	1.52514i	−0.305775	−	0.126656i
$146$		0			0
$147$	3.94688	+	0.388734i	0.325533	+	0.0320622i
$148$		0			0
$149$	17.7020	−	9.46193i	1.45021	−	0.775151i	0.456775	−	0.889582i	$-0.349005\pi$
$149$	17.7020	−	9.46193i	1.45021	−	0.775151i	0.993431	+	0.114431i	$0.0365045\pi$
$150$		0			0
$151$	−12.6804	−	2.52230i	−1.03192	−	0.205262i	−0.350047	−	0.936732i	$-0.613834\pi$
$151$	−12.6804	−	2.52230i	−1.03192	−	0.205262i	−0.681873	+	0.731471i	$0.738834\pi$
$152$		0			0
$153$	7.67665	+	38.5931i	0.620620	+	3.12007i
$154$		0			0
$155$	−2.07782	+	0.204648i	−0.166895	+	0.0164377i
$156$		0			0
$157$	−7.16468	+	2.17338i	−0.571803	+	0.173455i	−0.562928	−	0.826506i	$-0.690325\pi$
$157$	−7.16468	+	2.17338i	−0.571803	+	0.173455i	−0.00887537	+	0.999961i	$0.502825\pi$
$158$		0			0
$159$	20.4705	−	20.4705i	1.62342	−	1.62342i
$160$		0			0
$161$	−1.99652	−	1.99652i	−0.157348	−	0.157348i
$162$		0			0
$163$	2.39693	+	7.90161i	0.187742	+	0.618902i	0.999396	+	0.0347630i	$0.0110676\pi$
$163$	2.39693	+	7.90161i	0.187742	+	0.618902i	−0.811654	+	0.584139i	$0.801432\pi$
$164$		0			0
$165$	−0.547347	−	5.55731i	−0.0426109	−	0.432636i
$166$		0			0
$167$	18.8138	−	3.74230i	1.45586	−	0.289588i	0.597180	−	0.802107i	$-0.296288\pi$
$167$	18.8138	−	3.74230i	1.45586	−	0.289588i	0.858676	+	0.512519i	$0.171288\pi$
$168$		0			0
$169$	0.496036	−	2.49374i	0.0381566	−	0.191826i
$170$		0			0
$171$	12.3725	+	23.1473i	0.946147	+	1.77012i
$172$		0			0
$173$	0.886379	−	8.99956i	0.0673902	−	0.684224i	−0.900838	−	0.434155i	$-0.857047\pi$
$173$	0.886379	−	8.99956i	0.0673902	−	0.684224i	0.968228	−	0.250069i	$-0.0804531\pi$
$174$		0			0
$175$	−4.35458	+	10.5129i	−0.329175	+	0.794699i
$176$		0			0
$177$	−7.07656	−	17.0843i	−0.531907	−	1.28414i
$178$		0			0
$179$	−0.152731	+	0.125343i	−0.0114156	+	0.00936858i	−0.640084	−	0.768305i	$-0.721100\pi$
$179$	−0.152731	+	0.125343i	−0.0114156	+	0.00936858i	0.628668	+	0.777674i	$0.283600\pi$
$180$		0			0
$181$	4.25835	+	1.29176i	0.316521	+	0.0960156i	0.444548	−	0.895755i	$-0.353364\pi$
$181$	4.25835	+	1.29176i	0.316521	+	0.0960156i	−0.128027	+	0.991771i	$0.540864\pi$
$182$		0			0
$183$	32.7921	−	21.9110i	2.42406	−	1.61971i
$184$		0			0
$185$	2.37819	−	3.55921i	0.174848	−	0.261678i
$186$		0			0
$187$	−13.5688	+	16.5337i	−0.992252	+	1.20906i
$188$		0			0
$189$	−24.1590	−	12.9132i	−1.75731	−	0.939300i
$190$		0			0
$191$		−	11.0408i		−	0.798881i	−0.916759	−	0.399440i	$-0.869204\pi$
$191$		−	11.0408i		−	0.798881i	0.916759	−	0.399440i	$-0.130796\pi$
$192$		0			0
$193$		−	20.6630i		−	1.48735i	−0.668539	−	0.743677i	$-0.733080\pi$
$193$		−	20.6630i		−	1.48735i	0.668539	−	0.743677i	$-0.266920\pi$
$194$		0			0
$195$	4.38626	+	2.34450i	0.314106	+	0.167893i
$196$		0			0
$197$	−10.5122	+	12.8091i	−0.748963	+	0.912614i	−0.998444	−	0.0557661i	$-0.982240\pi$
$197$	−10.5122	+	12.8091i	−0.748963	+	0.912614i	0.249481	+	0.968380i	$0.419740\pi$
$198$		0			0
$199$	−4.93255	+	7.38208i	−0.349659	+	0.523302i	−0.964057	−	0.265694i	$-0.914399\pi$
$199$	−4.93255	+	7.38208i	−0.349659	+	0.523302i	0.614398	+	0.788996i	$0.289399\pi$
$200$		0			0
$201$	22.0473	−	14.7315i	1.55509	−	1.03908i
$202$		0			0
$203$	−18.4601	−	5.59980i	−1.29564	−	0.393029i
$204$		0			0
$205$	0.0474409	−	0.0389338i	0.00331342	−	0.00271925i
$206$		0			0
$207$	−3.01641	−	7.28225i	−0.209655	−	0.506152i
$208$		0			0
$209$	−5.45957	+	13.1806i	−0.377646	+	0.911719i
$210$		0			0
$211$	−0.436682	+	4.43371i	−0.0300625	+	0.305229i	0.968382	+	0.249472i	$0.0802572\pi$
$211$	−0.436682	+	4.43371i	−0.0300625	+	0.305229i	−0.998444	+	0.0557569i	$0.982243\pi$
$212$		0			0
$213$	9.46866	+	17.7146i	0.648782	+	1.21379i
$214$		0			0
$215$	−0.503380	+	2.53066i	−0.0343303	+	0.172590i
$216$		0			0
$217$	−9.91190	+	1.97160i	−0.672864	+	0.133841i
$218$		0			0
$219$	−1.85902	−	18.8750i	−0.125621	−	1.27545i
$220$		0			0
$221$	−5.52983	−	18.2294i	−0.371977	−	1.22624i
$222$		0			0
$223$	3.57635	+	3.57635i	0.239490	+	0.239490i	0.816639	−	0.577149i	$-0.195835\pi$
$223$	3.57635	+	3.57635i	0.239490	+	0.239490i	−0.577149	+	0.816639i	$0.695835\pi$
$224$		0			0
$225$	−22.4623	+	22.4623i	−1.49748	+	1.49748i
$226$		0			0
$227$	−2.51703	+	0.763533i	−0.167061	+	0.0506774i	−0.372707	−	0.927949i	$-0.621570\pi$
$227$	−2.51703	+	0.763533i	−0.167061	+	0.0506774i	0.205646	+	0.978626i	$0.434070\pi$
$228$		0			0
$229$	4.67196	−	0.460148i	0.308732	−	0.0304074i	0.0575350	−	0.998343i	$-0.481676\pi$
$229$	4.67196	−	0.460148i	0.308732	−	0.0304074i	0.251197	+	0.967936i	$0.419176\pi$
$230$		0			0
$231$	−5.27320	−	26.5102i	−0.346951	−	1.74424i
$232$		0			0
$233$	−5.85988	−	1.16560i	−0.383893	−	0.0763611i	−0.000628901	−	1.00000i	$-0.500200\pi$
$233$	−5.85988	−	1.16560i	−0.383893	−	0.0763611i	−0.383264	+	0.923639i	$0.625200\pi$
$234$		0			0
$235$	−1.55313	+	0.830164i	−0.101315	+	0.0541540i
$236$		0			0
$237$	27.1431	+	2.67336i	1.76313	+	0.173653i
$238$		0			0
$239$	18.4466	+	7.64084i	1.19321	+	0.494245i	0.888800	−	0.458296i	$-0.151540\pi$
$239$	18.4466	+	7.64084i	1.19321	+	0.494245i	0.304412	+	0.952540i	$0.401540\pi$
$240$		0			0
$241$	−8.17478	+	3.38610i	−0.526584	+	0.218118i	−0.630106	−	0.776509i	$-0.716989\pi$
$241$	−8.17478	+	3.38610i	−0.526584	+	0.218118i	0.103522	+	0.994627i	$0.466989\pi$
$242$		0			0
$243$	−8.96191	−	10.9201i	−0.574907	−	0.700526i
$244$		0			0
$245$	−0.182921	+	0.603008i	−0.0116864	+	0.0385248i
$246$		0			0
$247$	−7.05929	−	10.5650i	−0.449172	−	0.672233i
$248$		0			0
$249$	−3.41018	−	2.27861i	−0.216111	−	0.144401i
$250$		0			0
$251$	−9.15973	−	7.51719i	−0.578157	−	0.474481i	0.299285	−	0.954164i	$-0.403252\pi$
$251$	−9.15973	−	7.51719i	−0.578157	−	0.474481i	−0.877442	+	0.479683i	$0.840752\pi$
$252$		0			0
$253$	2.01969	−	3.77858i	0.126977	−	0.237557i
$254$		0			0
$255$	−9.05999			−0.567359
$256$		0			0
$257$	15.8663			0.989714			0.494857	−	0.868975i	$-0.335220\pi$
$257$	15.8663			0.989714			0.494857	+	0.868975i	$0.335220\pi$
$258$		0			0
$259$	9.76723	−	18.2732i	0.606906	−	1.13544i
$260$		0			0
$261$	−41.6290	−	34.1641i	−2.57677	−	2.11470i
$262$		0			0
$263$	21.8173	+	14.5779i	1.34532	+	0.898911i	0.999228	−	0.0392914i	$-0.0125101\pi$
$263$	21.8173	+	14.5779i	1.34532	+	0.898911i	0.346087	+	0.938202i	$0.387510\pi$
$264$		0			0
$265$	2.55547	+	3.82453i	0.156981	+	0.234939i
$266$		0			0
$267$	7.51838	−	24.7848i	0.460118	−	1.51680i
$268$		0			0
$269$	1.77108	+	2.15807i	0.107985	+	0.131580i	0.824198	−	0.566302i	$-0.191626\pi$
$269$	1.77108	+	2.15807i	0.107985	+	0.131580i	−0.716213	+	0.697881i	$0.754126\pi$
$270$		0			0
$271$	−4.80799	+	1.99153i	−0.292064	+	0.120977i	−0.523905	−	0.851777i	$-0.675525\pi$
$271$	−4.80799	+	1.99153i	−0.292064	+	0.120977i	0.231840	+	0.972754i	$0.425525\pi$
$272$		0			0
$273$	22.2412	+	9.21259i	1.34610	+	0.557571i
$274$		0			0
$275$	−17.1839	−	1.69246i	−1.03623	−	0.102059i
$276$		0			0
$277$	−9.24472	+	4.94141i	−0.555462	+	0.296900i	−0.725143	−	0.688599i	$-0.758226\pi$
$277$	−9.24472	+	4.94141i	−0.555462	+	0.296900i	0.169681	+	0.985499i	$0.445726\pi$
$278$		0			0
$279$	−27.6706	−	5.50403i	−1.65660	−	0.329518i
$280$		0			0
$281$	5.04370	+	25.3564i	0.300882	+	1.51264i	0.774879	+	0.632109i	$0.217811\pi$
$281$	5.04370	+	25.3564i	0.300882	+	1.51264i	−0.473997	+	0.880526i	$0.657189\pi$
$282$		0			0
$283$	−1.37868	+	0.135789i	−0.0819543	+	0.00807179i	−0.138911	−	0.990305i	$-0.544360\pi$
$283$	−1.37868	+	0.135789i	−0.0819543	+	0.00807179i	0.0569569	+	0.998377i	$0.481860\pi$
$284$		0			0
$285$	−5.78292	+	1.75423i	−0.342550	+	0.103912i
$286$		0			0
$287$	0.210054	−	0.210054i	0.0123991	−	0.0123991i
$288$		0			0
$289$	12.5170	+	12.5170i	0.736296	+	0.736296i
$290$		0			0
$291$	1.37643	+	4.53750i	0.0806880	+	0.265993i
$292$		0			0
$293$	0.406443	+	4.12668i	0.0237446	+	0.241083i	0.999730	+	0.0232463i	$0.00740018\pi$
$293$	0.406443	+	4.12668i	0.0237446	+	0.241083i	−0.975985	+	0.217837i	$0.930100\pi$
$294$		0			0
$295$	2.88167	−	0.573200i	0.167777	−	0.0333730i
$296$		0			0
$297$	8.10951	−	40.7693i	0.470562	−	2.36567i
$298$		0			0
$299$	1.79882	+	3.36536i	0.104029	+	0.194624i
$300$		0			0
$301$	−1.22417	+	12.4292i	−0.0705598	+	0.716405i
$302$		0			0
$303$	−10.9161	+	26.3538i	−0.627115	+	1.51399i
$304$		0			0
$305$	2.39801	+	5.78930i	0.137309	+	0.331494i
$306$		0			0
$307$	3.44005	−	2.82317i	0.196334	−	0.161127i	−0.531090	−	0.847315i	$-0.678217\pi$
$307$	3.44005	−	2.82317i	0.196334	−	0.161127i	0.727424	+	0.686188i	$0.240717\pi$
$308$		0			0
$309$	−23.2803	−	7.06202i	−1.32437	−	0.401744i
$310$		0			0
$311$	−21.5073	+	14.3708i	−1.21957	+	0.814890i	−0.987471	−	0.157802i	$-0.949559\pi$
$311$	−21.5073	+	14.3708i	−1.21957	+	0.814890i	−0.232099	+	0.972692i	$0.574559\pi$
$312$		0			0
$313$	0.910773	−	1.36307i	0.0514799	−	0.0770452i	−0.804837	−	0.593496i	$-0.797747\pi$
$313$	0.910773	−	1.36307i	0.0514799	−	0.0770452i	0.856317	+	0.516451i	$0.172747\pi$
$314$		0			0
$315$	5.01230	−	6.10750i	0.282411	−	0.344119i
$316$		0			0
$317$	−1.86323	−	0.995915i	−0.104649	−	0.0559362i	0.418242	−	0.908336i	$-0.362647\pi$
$317$	−1.86323	−	0.995915i	−0.104649	−	0.0559362i	−0.522891	+	0.852400i	$0.675147\pi$
$318$		0			0
$319$		−	29.2725i		−	1.63894i
$320$		0			0
$321$			2.60710i			0.145514i
$322$		0			0
$323$	20.4134	+	10.9112i	1.13583	+	0.607115i
$324$		0			0
$325$	9.75616	−	11.8879i	0.541174	−	0.659423i
$326$		0			0
$327$	22.5605	−	33.7642i	1.24760	−	1.86716i
$328$		0			0
$329$	−7.08764	+	4.73581i	−0.390754	+	0.261094i
$330$		0			0
$331$	29.4439	+	8.93172i	1.61839	+	0.490932i	0.964150	−	0.265359i	$-0.0854904\pi$
$331$	29.4439	+	8.93172i	1.61839	+	0.490932i	0.654236	+	0.756291i	$0.272990\pi$
$332$		0			0
$333$	44.7129	−	36.6949i	2.45025	−	2.01087i
$334$		0			0
$335$	1.61226	+	3.89235i	0.0880874	+	0.212662i
$336$		0			0
$337$	3.59802	−	8.68639i	0.195997	−	0.473178i	−0.795074	−	0.606512i	$-0.792568\pi$
$337$	3.59802	−	8.68639i	0.195997	−	0.473178i	0.991071	+	0.133334i	$0.0425683\pi$
$338$		0			0
$339$	−1.77151	+	17.9864i	−0.0962151	+	0.976889i
$340$		0			0
$341$	−7.22903	−	13.5246i	−0.391474	−	0.732396i
$342$		0			0
$343$	−3.86267	+	19.4190i	−0.208565	+	1.04852i
$344$		0			0
$345$	1.77998	−	0.354061i	0.0958311	−	0.0190620i
$346$		0			0
$347$	−2.60352	−	26.4340i	−0.139764	−	1.41905i	−0.767713	−	0.640794i	$-0.778605\pi$
$347$	−2.60352	−	26.4340i	−0.139764	−	1.41905i	0.627949	−	0.778255i	$-0.283895\pi$
$348$		0			0
$349$	−1.46537	−	4.83068i	−0.0784395	−	0.258580i	0.908946	−	0.416913i	$-0.136888\pi$
$349$	−1.46537	−	4.83068i	−0.0784395	−	0.258580i	−0.987386	+	0.158333i	$0.949388\pi$
$350$		0			0
$351$	26.1787	+	26.1787i	1.39731	+	1.39731i
$352$		0			0
$353$	15.6624	−	15.6624i	0.833625	−	0.833625i	−0.154386	−	0.988011i	$-0.549340\pi$
$353$	15.6624	−	15.6624i	0.833625	−	0.833625i	0.988011	+	0.154386i	$0.0493398\pi$
$354$		0			0
$355$	−3.05404	+	0.926433i	−0.162092	+	0.0491700i
$356$		0			0
$357$	−43.6425	+	4.29841i	−2.30981	+	0.227496i
$358$		0			0
$359$	0.133722	+	0.672265i	0.00705757	+	0.0354808i	0.984154	−	0.177318i	$-0.0567421\pi$
$359$	0.133722	+	0.672265i	0.00705757	+	0.0354808i	−0.977096	+	0.212799i	$0.931742\pi$
$360$		0			0
$361$	−3.49255	−	0.694711i	−0.183818	−	0.0365637i
$362$		0			0
$363$	5.99009	−	3.20177i	0.314398	−	0.168049i
$364$		0			0
$365$	2.99898	+	0.295374i	0.156974	+	0.0154606i
$366$		0			0
$367$	19.4149	+	8.04193i	1.01345	+	0.419786i	0.826713	−	0.562624i	$-0.190208\pi$
$367$	19.4149	+	8.04193i	1.01345	+	0.419786i	0.186739	+	0.982410i	$0.440208\pi$
$368$		0			0
$369$	0.766167	−	0.317357i	0.0398851	−	0.0165209i
$370$		0			0
$371$	14.1244	+	17.2106i	0.733300	+	0.893529i
$372$		0			0
$373$	−7.31590	+	24.1173i	−0.378803	+	1.24875i	0.535784	+	0.844355i	$0.320016\pi$
$373$	−7.31590	+	24.1173i	−0.378803	+	1.24875i	−0.914586	+	0.404390i	$0.867484\pi$
$374$		0			0
$375$	−8.33579	−	12.4754i	−0.430458	−	0.644226i
$376$		0			0
$377$	21.6775	+	14.4844i	1.11645	+	0.745986i
$378$		0			0
$379$	−22.8733	−	18.7716i	−1.17492	−	0.964232i	−0.175127	−	0.984546i	$-0.556033\pi$
$379$	−22.8733	−	18.7716i	−1.17492	−	0.964232i	−0.999794	+	0.0203139i	$0.993533\pi$
$380$		0			0
$381$	2.58345	−	4.83330i	0.132354	−	0.247618i
$382$		0			0
$383$	−5.95953			−0.304518			−0.152259	−	0.988341i	$-0.548655\pi$
$383$	−5.95953			−0.304518			−0.152259	+	0.988341i	$0.548655\pi$
$384$		0			0
$385$	4.29464			0.218875
$386$		0			0
$387$	−16.4357	+	30.7490i	−0.835472	+	1.56306i
$388$		0			0
$389$	27.6432	+	22.6862i	1.40157	+	1.15024i	0.968541	+	0.248856i	$0.0800544\pi$
$389$	27.6432	+	22.6862i	1.40157	+	1.15024i	0.433027	+	0.901381i	$0.357446\pi$
$390$		0			0
$391$	−5.77979	−	3.86193i	−0.292297	−	0.195306i
$392$		0			0
$393$	10.8893	+	16.2970i	0.549294	+	0.822077i
$394$		0			0
$395$	−1.25796	+	4.14695i	−0.0632950	+	0.208656i
$396$		0			0
$397$	2.12968	+	2.59502i	0.106885	+	0.130240i	0.823705	−	0.567018i	$-0.191903\pi$
$397$	2.12968	+	2.59502i	0.106885	+	0.130240i	−0.716820	+	0.697258i	$0.754403\pi$
$398$		0			0
$399$	−27.0244	+	11.1939i	−1.35291	+	0.560394i
$400$		0			0
$401$	2.77760	+	1.15052i	0.138707	+	0.0574542i	0.450957	−	0.892546i	$-0.351083\pi$
$401$	2.77760	+	1.15052i	0.138707	+	0.0574542i	−0.312250	+	0.950000i	$0.601083\pi$
$402$		0			0
$403$	13.5925	+	1.33875i	0.677093	+	0.0666878i
$404$		0			0
$405$	6.79223	−	3.63052i	0.337509	−	0.180402i
$406$		0			0
$407$	30.8368	+	6.13382i	1.52852	+	0.304042i
$408$		0			0
$409$	−7.49046	−	37.6571i	−0.370380	−	1.86202i	−0.493664	−	0.869652i	$-0.664343\pi$
$409$	−7.49046	−	37.6571i	−0.370380	−	1.86202i	0.123285	−	0.992371i	$-0.460657\pi$
$410$		0			0
$411$	10.4818	−	1.03236i	0.517028	−	0.0509228i
$412$		0			0
$413$	13.6092	−	4.12831i	0.669666	−	0.203141i
$414$		0			0
$415$	0.460791	−	0.460791i	0.0226193	−	0.0226193i
$416$		0			0
$417$	−48.7614	−	48.7614i	−2.38786	−	2.38786i
$418$		0			0
$419$	−9.78724	−	32.2642i	−0.478138	−	1.57621i	−0.781863	−	0.623450i	$-0.785730\pi$
$419$	−9.78724	−	32.2642i	−0.478138	−	1.57621i	0.303725	−	0.952760i	$-0.401770\pi$
$420$		0			0
$421$	1.25211	+	12.7129i	0.0610241	+	0.619588i	0.976250	+	0.216647i	$0.0695121\pi$
$421$	1.25211	+	12.7129i	0.0610241	+	0.619588i	−0.915226	+	0.402941i	$0.867988\pi$
$422$		0			0
$423$	−23.3395	+	4.64252i	−1.13481	+	0.225727i
$424$		0			0
$425$	−5.46537	+	27.4763i	−0.265110	+	1.33280i
$426$		0			0
$427$	14.2980	+	26.7497i	0.691928	+	1.29451i
$428$		0			0
$429$	−3.58059	+	36.3543i	−0.172873	+	1.75520i
$430$		0			0
$431$	−0.964421	+	2.32832i	−0.0464545	+	0.112151i	−0.945403	−	0.325902i	$-0.894332\pi$
$431$	−0.964421	+	2.32832i	−0.0464545	+	0.112151i	0.898949	+	0.438053i	$0.144332\pi$
$432$		0			0
$433$	6.66026	+	16.0793i	0.320072	+	0.772721i	0.999249	+	0.0387471i	$0.0123367\pi$
$433$	6.66026	+	16.0793i	0.320072	+	0.772721i	−0.679177	+	0.733974i	$0.737663\pi$
$434$		0			0
$435$	9.58491	−	7.86613i	0.459561	−	0.377152i
$436$		0			0
$437$	−4.43696	−	1.34594i	−0.212248	−	0.0643848i
$438$		0			0
$439$	−23.8764	+	15.9537i	−1.13956	+	0.761427i	−0.974396	−	0.224839i	$-0.927814\pi$
$439$	−23.8764	+	15.9537i	−1.13956	+	0.761427i	−0.165161	+	0.986267i	$0.552814\pi$
$440$		0			0
$441$	−4.73061	+	7.07986i	−0.225267	+	0.337136i
$442$		0			0
$443$	3.69075	−	4.49720i	0.175353	−	0.213668i	−0.677916	−	0.735139i	$-0.737117\pi$
$443$	3.69075	−	4.49720i	0.175353	−	0.213668i	0.853269	+	0.521471i	$0.174617\pi$
$444$		0			0
$445$	3.62926	+	1.93988i	0.172043	+	0.0919591i
$446$		0			0
$447$			62.4489i			2.95373i
$448$		0			0
$449$		−	9.01473i		−	0.425432i	−0.977114	−	0.212716i	$-0.931769\pi$
$449$		−	9.01473i		−	0.425432i	0.977114	−	0.212716i	$-0.0682309\pi$
$450$		0			0
$451$	0.397545	+	0.212492i	0.0187197	+	0.0100059i
$452$		0			0
$453$	25.5183	−	31.0941i	1.19895	−	1.46093i
$454$		0			0
$455$	−2.12505	+	3.18036i	−0.0996238	+	0.149098i
$456$		0			0
$457$	14.5711	−	9.73608i	0.681606	−	0.455435i	−0.165954	−	0.986133i	$-0.553070\pi$
$457$	14.5711	−	9.73608i	0.681606	−	0.455435i	0.847560	+	0.530699i	$0.178070\pi$
$458$		0			0
$459$	−64.5373	−	19.5772i	−3.01235	−	0.913785i
$460$		0			0
$461$	26.9629	−	22.1279i	1.25579	−	1.03060i	0.257865	−	0.966181i	$-0.416981\pi$
$461$	26.9629	−	22.1279i	1.25579	−	1.03060i	0.997923	−	0.0644176i	$-0.0205190\pi$
$462$		0			0
$463$	−1.25485	−	3.02948i	−0.0583178	−	0.140792i	0.892035	−	0.451967i	$-0.149277\pi$
$463$	−1.25485	−	3.02948i	−0.0583178	−	0.140792i	−0.950353	+	0.311175i	$0.899277\pi$
$464$		0			0
$465$	2.48586	−	6.00140i	0.115279	−	0.278308i
$466$		0			0
$467$	−1.75127	+	17.7809i	−0.0810391	+	0.822804i	0.865649	+	0.500652i	$0.166906\pi$
$467$	−1.75127	+	17.7809i	−0.0810391	+	0.822804i	−0.946688	+	0.322152i	$0.895594\pi$
$468$		0			0
$469$	9.61305	+	17.9847i	0.443889	+	0.830458i
$470$		0			0
$471$	4.54443	−	22.8464i	0.209396	−	1.05271i
$472$		0			0
$473$	−18.5876	+	3.69730i	−0.854658	+	0.170002i
$474$		0			0
$475$	1.83156	+	18.5961i	0.0840376	+	0.853248i
$476$		0			0
$477$	18.0425	+	59.4781i	0.826109	+	2.72332i
$478$		0			0
$479$	−15.9297	−	15.9297i	−0.727849	−	0.727849i	0.242342	−	0.970191i	$-0.422084\pi$
$479$	−15.9297	−	15.9297i	−0.727849	−	0.727849i	−0.970191	+	0.242342i	$0.922084\pi$
$480$		0			0
$481$	−19.8009	+	19.8009i	−0.902841	+	0.902841i
$482$		0			0
$483$	8.40630	−	2.55002i	0.382500	−	0.116030i
$484$		0			0
$485$	−0.749761	+	0.0738450i	−0.0340449	+	0.00335313i
$486$		0			0
$487$	−6.03588	−	30.3444i	−0.273512	−	1.37504i	−0.836226	−	0.548385i	$-0.815243\pi$
$487$	−6.03588	−	30.3444i	−0.273512	−	1.37504i	0.562714	−	0.826652i	$-0.309757\pi$
$488$		0			0
$489$	−25.1963	−	5.01185i	−1.13942	−	0.226644i
$490$		0			0
$491$	−22.5067	+	12.0301i	−1.01571	+	0.542910i	−0.893249	−	0.449563i	$-0.851580\pi$
$491$	−22.5067	+	12.0301i	−1.01571	+	0.542910i	−0.122464	+	0.992473i	$0.539080\pi$
$492$		0			0
$493$	−47.2639	−	4.65509i	−2.12866	−	0.209655i
$494$		0			0
$495$	11.0765	+	4.58805i	0.497854	+	0.206218i
$496$		0			0
$497$	−14.2719	+	5.91163i	−0.640184	+	0.265173i
$498$		0			0
$499$	−7.28184	−	8.87294i	−0.325980	−	0.397207i	0.584072	−	0.811702i	$-0.301458\pi$
$499$	−7.28184	−	8.87294i	−0.325980	−	0.397207i	−0.910052	+	0.414494i	$0.863958\pi$
$500$		0			0
$501$	−17.3244	+	57.1110i	−0.773998	+	2.55153i
$502$		0			0
$503$	−16.4572	−	24.6299i	−0.733788	−	1.09819i	−0.991262	−	0.131907i	$-0.957890\pi$
$503$	−16.4572	−	24.6299i	−0.733788	−	1.09819i	0.257474	−	0.966285i	$-0.417110\pi$
$504$		0			0
$505$	−3.76845	−	2.51800i	−0.167694	−	0.112049i
$506$		0			0
$507$	6.11498	+	5.01843i	0.271576	+	0.222876i
$508$		0			0
$509$	9.02818	−	16.8905i	0.400167	−	0.748660i	−0.598454	−	0.801157i	$-0.704218\pi$
$509$	9.02818	−	16.8905i	0.400167	−	0.748660i	0.998621	+	0.0524973i	$0.0167181\pi$
$510$		0			0
$511$	14.5864			0.645265
$512$		0			0
$513$	−44.9843			−1.98610
$514$		0			0
$515$	1.82213	−	3.40896i	0.0802926	−	0.150217i
$516$		0			0
$517$	−9.99888	−	8.20587i	−0.439750	−	0.360894i
$518$		0			0
$519$	23.3935	+	15.6311i	1.02686	+	0.686128i
$520$		0			0
$521$	7.24339	+	10.8405i	0.317339	+	0.474931i	0.955508	−	0.294965i	$-0.0953080\pi$
$521$	7.24339	+	10.8405i	0.317339	+	0.474931i	−0.638169	+	0.769896i	$0.720308\pi$
$522$		0			0
$523$	6.66226	−	21.9625i	0.291320	−	0.960355i	−0.682087	−	0.731271i	$-0.738927\pi$
$523$	6.66226	−	21.9625i	0.291320	−	0.960355i	0.973407	−	0.229083i	$-0.0735727\pi$
$524$		0			0
$525$	−22.4593	−	27.3668i	−0.980206	−	1.19438i
$526$		0			0
$527$	−22.9867	+	9.52139i	−1.00131	+	0.414758i
$528$		0			0
$529$	−19.9628	−	8.26885i	−0.867947	−	0.359515i
$530$		0			0
$531$	39.5107	+	3.89146i	1.71462	+	0.168875i
$532$		0			0
$533$	−0.354070	+	0.189255i	−0.0153365	+	0.00819753i
$534$		0			0
$535$	−0.406274	−	0.0808130i	−0.0175648	−	0.00349385i
$536$		0			0
$537$	−0.119925	−	0.602903i	−0.00517514	−	0.0260172i
$538$		0			0
$539$	−4.60607	+	0.453658i	−0.198397	+	0.0195404i
$540$		0			0
$541$	19.0167	−	5.76864i	0.817590	−	0.248013i	0.146331	−	0.989236i	$-0.453254\pi$
$541$	19.0167	−	5.76864i	0.817590	−	0.248013i	0.671259	+	0.741223i	$0.265754\pi$
$542$		0			0
$543$	−9.78980	+	9.78980i	−0.420121	+	0.420121i
$544$		0			0
$545$	4.56229	+	4.56229i	0.195427	+	0.195427i
$546$		0			0
$547$	−0.237817	−	0.783978i	−0.0101683	−	0.0335205i	0.951709	−	0.307000i	$-0.0993253\pi$
$547$	−0.237817	−	0.783978i	−0.0101683	−	0.0335205i	−0.961878	+	0.273480i	$0.911825\pi$
$548$		0			0
$549$	8.29952	+	84.2664i	0.354215	+	3.59640i
$550$		0			0
$551$	−31.0695	+	6.18011i	−1.32361	+	0.263282i
$552$		0			0
$553$	−4.09220	+	20.5729i	−0.174018	+	0.874849i
$554$		0			0
$555$	6.27806	+	11.7454i	0.266489	+	0.498566i
$556$		0			0
$557$	−1.14433	+	11.6186i	−0.0484868	+	0.492295i	0.940020	+	0.341119i	$0.110806\pi$
$557$	−1.14433	+	11.6186i	−0.0484868	+	0.492295i	−0.988507	+	0.151176i	$0.951694\pi$
$558$		0			0
$559$	6.45940	−	15.5944i	0.273203	−	0.659571i
$560$		0			0
$561$	−25.4657	−	61.4797i	−1.07516	−	2.59568i
$562$		0			0
$563$	−12.9857	+	10.6571i	−0.547281	+	0.449142i	−0.866955	−	0.498386i	$-0.833926\pi$
$563$	−12.9857	+	10.6571i	−0.547281	+	0.449142i	0.319675	+	0.947527i	$0.396426\pi$
$564$		0			0
$565$	−2.74798	−	0.833592i	−0.115609	−	0.0350695i
$566$		0			0
$567$	30.9961	−	20.7109i	1.30171	−	0.869777i
$568$		0			0
$569$	−10.1550	+	15.1981i	−0.425721	+	0.637136i	−0.980881	−	0.194607i	$-0.937657\pi$
$569$	−10.1550	+	15.1981i	−0.425721	+	0.637136i	0.555161	+	0.831743i	$0.312657\pi$
$570$		0			0
$571$	−10.3530	+	12.6151i	−0.433257	+	0.527926i	−0.943175	−	0.332298i	$-0.892176\pi$
$571$	−10.3530	+	12.6151i	−0.433257	+	0.527926i	0.509917	+	0.860224i	$0.329676\pi$
$572$		0			0
$573$	30.2943	+	16.1926i	1.26556	+	0.676457i
$574$		0			0
$575$		−	5.61175i		−	0.234026i
$576$		0			0
$577$			40.3079i			1.67804i	0.544102	+	0.839019i	$0.316871\pi$
$577$			40.3079i			1.67804i	−0.544102	+	0.839019i	$0.683129\pi$
$578$		0			0
$579$	56.6964	+	30.3048i	2.35622	+	1.25943i
$580$		0			0
$581$	2.00104	−	2.43827i	0.0830170	−	0.101157i
$582$		0			0
$583$	−18.7698	+	28.0910i	−0.777366	+	1.16341i
$584$		0			0
$585$	−8.87848	+	5.93241i	−0.367080	+	0.245275i
$586$		0			0
$587$	−8.13898	−	2.46893i	−0.335932	−	0.101904i	0.117812	−	0.993036i	$-0.462412\pi$
$587$	−8.13898	−	2.46893i	−0.335932	−	0.101904i	−0.453744	+	0.891132i	$0.649912\pi$
$588$		0			0
$589$	−12.8286	+	10.5282i	−0.528595	+	0.433806i
$590$		0			0
$591$	−19.7291	−	47.6302i	−0.811545	−	1.95924i
$592$		0			0
$593$	1.78154	−	4.30101i	0.0731590	−	0.176621i	−0.883070	−	0.469242i	$-0.844527\pi$
$593$	1.78154	−	4.30101i	0.0731590	−	0.176621i	0.956229	+	0.292620i	$0.0945272\pi$
$594$		0			0
$595$	0.682961	−	6.93422i	0.0279987	−	0.284275i
$596$		0			0
$597$	−13.0212	−	24.3610i	−0.532922	−	0.997028i
$598$		0			0
$599$	5.62494	−	28.2785i	0.229829	−	1.15543i	−0.677668	−	0.735368i	$-0.737009\pi$
$599$	5.62494	−	28.2785i	0.229829	−	1.15543i	0.907497	−	0.420059i	$-0.137991\pi$
$600$		0			0
$601$	47.4604	−	9.44046i	1.93595	−	0.385084i	0.936546	−	0.350546i	$-0.114004\pi$
$601$	47.4604	−	9.44046i	1.93595	−	0.385084i	0.999403	−	0.0345386i	$-0.0109962\pi$
$602$		0			0
$603$	5.58006	+	56.6553i	0.227238	+	2.30718i
$604$		0			0
$605$	0.313268	+	1.03271i	0.0127361	+	0.0419855i
$606$		0			0
$607$	−4.54088	−	4.54088i	−0.184308	−	0.184308i	0.608922	−	0.793230i	$-0.291602\pi$
$607$	−4.54088	−	4.54088i	−0.184308	−	0.184308i	−0.793230	+	0.608922i	$0.791602\pi$
$608$		0			0
$609$	42.4390	−	42.4390i	1.71972	−	1.71972i
$610$		0			0
$611$	11.0244	−	3.34421i	0.445999	−	0.135292i
$612$		0			0
$613$	−5.18337	+	0.510517i	−0.209354	+	0.0206196i	−0.202151	−	0.979354i	$-0.564793\pi$
$613$	−5.18337	+	0.510517i	−0.209354	+	0.0206196i	−0.00720369	+	0.999974i	$0.502293\pi$
$614$		0			0
$615$	0.0372508	+	0.187272i	0.00150210	+	0.00755156i
$616$		0			0
$617$	−12.3036	−	2.44734i	−0.495325	−	0.0985262i	−0.0588944	−	0.998264i	$-0.518758\pi$
$617$	−12.3036	−	2.44734i	−0.495325	−	0.0985262i	−0.436430	+	0.899738i	$0.643758\pi$
$618$		0			0
$619$	23.8551	−	12.7508i	0.958818	−	0.512499i	0.0837434	−	0.996487i	$-0.473312\pi$
$619$	23.8551	−	12.7508i	0.958818	−	0.512499i	0.875074	+	0.483989i	$0.160812\pi$
$620$		0			0
$621$	13.4445	+	1.32417i	0.539509	+	0.0531370i
$622$		0			0
$623$	18.4027	+	7.62265i	0.737289	+	0.305395i
$624$		0			0
$625$	−19.7657	+	8.18722i	−0.790628	+	0.327489i
$626$		0			0
$627$	−28.1585	−	34.3112i	−1.12454	−	1.37026i
$628$		0			0
$629$	14.8077	−	48.8144i	0.590421	−	1.94636i
$630$		0			0
$631$	23.0068	+	34.4321i	0.915885	+	1.37072i	0.928712	+	0.370801i	$0.120917\pi$
$631$	23.0068	+	34.4321i	0.915885	+	1.37072i	−0.0128271	+	0.999918i	$0.504083\pi$
$632$		0			0
$633$	−11.5250	−	7.70078i	−0.458079	−	0.306078i
$634$		0			0
$635$	0.673112	+	0.552409i	0.0267116	+	0.0219217i
$636$		0			0
$637$	1.94320	−	3.63547i	0.0769923	−	0.144042i
$638$		0			0
$639$	−43.1251			−1.70600
$640$		0			0
$641$	46.0864			1.82030			0.910152	−	0.414275i	$-0.135965\pi$
$641$	46.0864			1.82030			0.910152	+	0.414275i	$0.135965\pi$
$642$		0			0
$643$	7.06951	−	13.2261i	0.278794	−	0.521588i	−0.703082	−	0.711108i	$-0.748193\pi$
$643$	7.06951	−	13.2261i	0.278794	−	0.521588i	0.981877	+	0.189521i	$0.0606935\pi$
$644$		0			0
$645$	−6.20552	−	5.09274i	−0.244342	−	0.200526i
$646$		0			0
$647$	37.7713	+	25.2380i	1.48494	+	0.992208i	0.992550	+	0.121836i	$0.0388781\pi$
$647$	37.7713	+	25.2380i	1.48494	+	0.992208i	0.492394	+	0.870372i	$0.336122\pi$
$648$		0			0
$649$	11.9894	+	17.9434i	0.470626	+	0.704342i
$650$		0			0
$651$	9.12723	−	30.0885i	0.357724	−	1.17926i
$652$		0			0
$653$	2.20684	+	2.68905i	0.0863604	+	0.105230i	0.814398	−	0.580307i	$-0.197067\pi$
$653$	2.20684	+	2.68905i	0.0863604	+	0.105230i	−0.728038	+	0.685537i	$0.759567\pi$
$654$		0			0
$655$	−2.87717	+	1.19176i	−0.112420	+	0.0465661i
$656$		0			0
$657$	37.6206	+	15.5830i	1.46772	+	0.607950i
$658$		0			0
$659$	−4.17215	−	0.410921i	−0.162524	−	0.0160072i	0.0164279	−	0.999865i	$-0.494771\pi$
$659$	−4.17215	−	0.410921i	−0.162524	−	0.0160072i	−0.178952	+	0.983858i	$0.557271\pi$
$660$		0			0
$661$	40.4332	−	21.6120i	1.57267	−	0.840608i	0.572888	−	0.819634i	$-0.305823\pi$
$661$	40.4332	−	21.6120i	1.57267	−	0.840608i	0.999780	−	0.0209747i	$-0.00667693\pi$
$662$		0			0
$663$	58.1291	+	11.5626i	2.25755	+	0.449054i
$664$		0			0
$665$	−0.906700	−	4.55829i	−0.0351603	−	0.176763i
$666$		0			0
$667$	9.46770	−	0.932487i	0.366591	−	0.0361060i
$668$		0			0
$669$	−15.0582	+	4.56784i	−0.582182	+	0.176603i
$670$		0			0
$671$	−32.5450	+	32.5450i	−1.25639	+	1.25639i
$672$		0			0
$673$	−17.3196	−	17.3196i	−0.667623	−	0.667623i	0.289542	−	0.957165i	$-0.406497\pi$
$673$	−17.3196	−	17.3196i	−0.667623	−	0.667623i	−0.957165	+	0.289542i	$0.906497\pi$
$674$		0			0
$675$	−15.8046	−	52.1007i	−0.608319	−	2.00536i
$676$		0			0
$677$	−3.81846	−	38.7695i	−0.146755	−	1.49003i	−0.733183	−	0.680032i	$-0.761966\pi$
$677$	−3.81846	−	38.7695i	−0.146755	−	1.49003i	0.586427	−	0.810002i	$-0.300534\pi$
$678$		0			0
$679$	−3.57661	+	0.711431i	−0.137258	+	0.0273022i
$680$		0			0
$681$	1.59651	−	8.02619i	0.0611784	−	0.307564i
$682$		0			0
$683$	−22.2076	−	41.5474i	−0.849749	−	1.58977i	−0.806902	−	0.590686i	$-0.798857\pi$
$683$	−22.2076	−	41.5474i	−0.849749	−	1.58977i	−0.0428470	−	0.999082i	$-0.513643\pi$
$684$		0			0
$685$	−0.164029	+	1.66542i	−0.00626723	+	0.0636322i
$686$		0			0
$687$	−5.58942	+	13.4941i	−0.213250	+	0.514830i
$688$		0			0
$689$	−11.5150	−	27.7997i	−0.438686	−	1.05908i
$690$		0			0
$691$	27.5371	−	22.5991i	1.04756	−	0.859711i	0.0572199	−	0.998362i	$-0.481776\pi$
$691$	27.5371	−	22.5991i	1.04756	−	0.859711i	0.990341	+	0.138650i	$0.0442764\pi$
$692$		0			0
$693$	55.5331	+	16.8458i	2.10953	+	0.639918i
$694$		0			0
$695$	9.11015	−	6.08721i	0.345568	−	0.230901i
$696$		0			0
$697$	0.406315	−	0.608093i	0.0153903	−	0.0230332i
$698$		0			0
$699$	11.7925	−	14.3692i	0.446033	−	0.543492i
$700$		0			0
$701$	−13.5322	−	7.23312i	−0.511105	−	0.273191i	0.195620	−	0.980680i	$-0.437328\pi$
$701$	−13.5322	−	7.23312i	−0.511105	−	0.273191i	−0.706725	+	0.707489i	$0.749828\pi$
$702$		0			0
$703$		−	34.0249i		−	1.28327i
$704$		0			0
$705$		−	5.47911i		−	0.206355i
$706$		0			0
$707$	−19.3475	−	10.3414i	−0.727637	−	0.388930i
$708$		0			0
$709$	−5.29658	+	6.45390i	−0.198917	+	0.242381i	−0.862910	−	0.505358i	$-0.831361\pi$
$709$	−5.29658	+	6.45390i	−0.198917	+	0.242381i	0.663993	+	0.747739i	$0.268861\pi$
$710$		0			0
$711$	−32.5329	+	48.6889i	−1.22008	+	1.82598i
$712$		0			0
$713$	4.14402	−	2.76894i	0.155195	−	0.103698i
$714$		0			0
$715$	−5.55425	−	1.68486i	−0.207717	−	0.0630103i
$716$		0			0
$717$	−48.0196	+	39.4087i	−1.79333	+	1.47174i
$718$		0			0
$719$	2.11732	+	5.11167i	0.0789628	+	0.190633i	0.958431	−	0.285325i	$-0.0921015\pi$
$719$	2.11732	+	5.11167i	0.0789628	+	0.190633i	−0.879468	+	0.475958i	$0.842101\pi$
$720$		0			0
$721$	7.15995	−	17.2857i	0.266651	−	0.643751i
$722$		0			0
$723$	2.69833	−	27.3966i	0.100352	−	1.01889i
$724$		0			0
$725$	−18.0736	−	33.8134i	−0.671238	−	1.25580i
$726$		0			0
$727$	−2.18296	+	10.9745i	−0.0809616	+	0.407021i	0.918958	+	0.394355i	$0.129032\pi$
$727$	−2.18296	+	10.9745i	−0.0809616	+	0.407021i	−0.999920	+	0.0126663i	$0.995968\pi$
$728$		0			0
$729$	−2.73434	+	0.543894i	−0.101272	+	0.0201442i
$730$		0			0
$731$	3.01383	+	30.5999i	0.111470	+	1.13178i
$732$		0			0
$733$	−10.6612	−	35.1453i	−0.393780	−	1.29812i	−0.900066	−	0.435754i	$-0.856482\pi$
$733$	−10.6612	−	35.1453i	−0.393780	−	1.29812i	0.506285	−	0.862366i	$-0.331018\pi$
$734$		0			0
$735$	−1.38629	−	1.38629i	−0.0511342	−	0.0511342i
$736$		0			0
$737$	−21.8811	+	21.8811i	−0.806002	+	0.806002i
$738$		0			0
$739$	23.6308	−	7.16833i	0.869273	−	0.263691i	0.176021	−	0.984386i	$-0.443677\pi$
$739$	23.6308	−	7.16833i	0.869273	−	0.263691i	0.693252	+	0.720695i	$0.256177\pi$
$740$		0			0
$741$	39.3421	−	3.87486i	1.44527	−	0.142347i
$742$		0			0
$743$	−1.46411	−	7.36058i	−0.0537130	−	0.270034i	0.944591	−	0.328250i	$-0.106459\pi$
$743$	−1.46411	−	7.36058i	−0.0537130	−	0.270034i	−0.998304	+	0.0582161i	$0.981459\pi$
$744$		0			0
$745$	−9.73166	−	1.93575i	−0.356540	−	0.0709203i
$746$		0			0
$747$	7.76585	−	4.15093i	0.284137	−	0.151875i
$748$		0			0
$749$	−1.99539	−	0.196528i	−0.0729098	−	0.00718099i
$750$		0			0
$751$	−1.31921	−	0.546433i	−0.0481385	−	0.0199396i	0.358484	−	0.933536i	$-0.383294\pi$
$751$	−1.31921	−	0.546433i	−0.0481385	−	0.0199396i	−0.406623	+	0.913596i	$0.633294\pi$
$752$		0			0
$753$	34.0600	−	14.1081i	1.24122	−	0.514128i
$754$		0			0
$755$	4.05451	+	4.94044i	0.147559	+	0.179801i
$756$		0			0
$757$	1.05228	−	3.46889i	0.0382456	−	0.126079i	−0.935739	−	0.352694i	$-0.885266\pi$
$757$	1.05228	−	3.46889i	0.0382456	−	0.126079i	0.973984	+	0.226615i	$0.0727658\pi$
$758$		0			0
$759$	7.40576	+	11.0835i	0.268812	+	0.402306i
$760$		0			0
$761$	−12.7093	−	8.49211i	−0.460713	−	0.307839i	0.303466	−	0.952842i	$-0.401856\pi$
$761$	−12.7093	−	8.49211i	−0.460713	−	0.307839i	−0.764180	+	0.645003i	$0.776856\pi$
$762$		0			0
$763$	24.1413	+	19.8123i	0.873974	+	0.717252i
$764$		0			0
$765$	9.16944	−	17.1548i	0.331522	−	0.620233i
$766$		0			0
$767$	−19.2204			−0.694009
$768$		0			0
$769$	12.1126			0.436791			0.218395	−	0.975860i	$-0.429918\pi$
$769$	12.1126			0.436791			0.218395	+	0.975860i	$0.429918\pi$
$770$		0			0
$771$	−23.2699	+	43.5349i	−0.838046	+	1.56787i
$772$		0			0
$773$	17.2242	+	14.1355i	0.619510	+	0.508419i	0.890989	−	0.454026i	$-0.150013\pi$
$773$	17.2242	+	14.1355i	0.619510	+	0.508419i	−0.271478	+	0.962445i	$0.587513\pi$
$774$		0			0
$775$	−16.7009	−	11.1592i	−0.599914	−	0.400850i
$776$		0			0
$777$	35.8143	+	53.5998i	1.28483	+	1.92288i
$778$		0			0
$779$	0.141606	−	0.466813i	0.00507357	−	0.0167253i
$780$		0			0
$781$	−14.8709	−	18.1202i	−0.532122	−	0.648393i
$782$		0			0
$783$	85.2739	−	35.3216i	3.04744	−	1.26229i
$784$		0			0
$785$	3.41938	+	1.41635i	0.122043	+	0.0505518i
$786$		0			0
$787$	26.7767	+	2.63728i	0.954487	+	0.0940088i	0.563255	−	0.826283i	$-0.309549\pi$
$787$	26.7767	+	2.63728i	0.954487	+	0.0940088i	0.391232	+	0.920292i	$0.372049\pi$
$788$		0			0
$789$	−71.9975	+	38.4835i	−2.56318	+	1.37005i
$790$		0			0
$791$	−13.6327	−	2.71171i	−0.484722	−	0.0964172i
$792$		0			0
$793$	−7.99720	−	40.2047i	−0.283989	−	1.42771i
$794$		0			0
$795$	−14.2419	+	1.40270i	−0.505108	+	0.0497488i
$796$		0			0
$797$	−11.6531	+	3.53493i	−0.412775	+	0.125214i	−0.489840	−	0.871812i	$-0.662945\pi$
$797$	−11.6531	+	3.53493i	−0.412775	+	0.125214i	0.0770656	+	0.997026i	$0.475445\pi$
$798$		0			0
$799$	−14.8395	+	14.8395i	−0.524983	+	0.524983i
$800$		0			0
$801$	39.3200	+	39.3200i	1.38930	+	1.38930i
$802$		0			0
$803$	6.42515	+	21.1809i	0.226739	+	0.747457i
$804$		0			0
$805$	0.136808	+	1.38903i	0.00482183	+	0.0489569i
$806$		0			0
$807$	−8.51895	+	1.69452i	−0.299881	+	0.0596501i
$808$		0			0
$809$	−6.51202	+	32.7381i	−0.228950	+	1.15101i	0.679712	+	0.733479i	$0.262105\pi$
$809$	−6.51202	+	32.7381i	−0.228950	+	1.15101i	−0.908662	+	0.417532i	$0.862895\pi$
$810$		0			0
$811$	−2.94097	−	5.50217i	−0.103271	−	0.193207i	0.824979	−	0.565164i	$-0.191187\pi$
$811$	−2.94097	−	5.50217i	−0.103271	−	0.193207i	−0.928250	+	0.371957i	$0.878687\pi$
$812$		0			0
$813$	1.58702	−	16.1133i	0.0556592	−	0.565117i
$814$		0			0
$815$	1.56203	−	3.77108i	0.0547156	−	0.132095i
$816$		0			0
$817$	7.84856	+	18.9481i	0.274586	+	0.662910i
$818$		0			0
$819$	−39.9536	+	32.7890i	−1.39609	+	1.14574i
$820$		0			0
$821$	−33.2581	−	10.0887i	−1.16072	−	0.352099i	−0.349551	−	0.936917i	$-0.613666\pi$
$821$	−33.2581	−	10.0887i	−1.16072	−	0.352099i	−0.811165	+	0.584818i	$0.801166\pi$
$822$		0			0
$823$	4.24506	−	2.83646i	0.147973	−	0.0988727i	−0.479380	−	0.877608i	$-0.659138\pi$
$823$	4.24506	−	2.83646i	0.147973	−	0.0988727i	0.627353	+	0.778735i	$0.284138\pi$
$824$		0			0
$825$	29.8461	−	44.6679i	1.03911	−	1.55514i
$826$		0			0
$827$	1.04227	−	1.27000i	0.0362431	−	0.0441624i	−0.754573	−	0.656216i	$-0.772156\pi$
$827$	1.04227	−	1.27000i	0.0362431	−	0.0441624i	0.790817	+	0.612053i	$0.209656\pi$
$828$		0			0
$829$	4.97341	+	2.65834i	0.172734	+	0.0923280i	0.555498	−	0.831518i	$-0.312528\pi$
$829$	4.97341	+	2.65834i	0.172734	+	0.0923280i	−0.382764	+	0.923846i	$0.625028\pi$
$830$		0			0
$831$		−	32.6134i		−	1.13135i
$832$		0			0
$833$			7.50921i			0.260179i
$834$		0			0
$835$	−8.36281	−	4.47002i	−0.289407	−	0.154691i
$836$		0			0
$837$	30.6757	−	37.3784i	1.06031	−	1.29199i
$838$		0			0
$839$	3.37521	−	5.05136i	0.116525	−	0.174392i	−0.768622	−	0.639703i	$-0.779057\pi$
$839$	3.37521	−	5.05136i	0.116525	−	0.174392i	0.885147	+	0.465311i	$0.154057\pi$
$840$		0			0
$841$	29.9314	−	19.9995i	1.03212	−	0.689638i
$842$		0			0
$843$	−76.9716	−	23.3491i	−2.65104	−	0.804185i
$844$		0			0
$845$	−0.971589	+	0.797363i	−0.0334237	+	0.0274301i
$846$		0			0
$847$	1.99898	+	4.82597i	0.0686859	+	0.165822i
$848$		0			0
$849$	1.64943	−	3.98207i	0.0566082	−	0.136664i
$850$		0			0
$851$	−1.00157	+	10.1691i	−0.0343332	+	0.348591i
$852$		0			0
$853$	−13.3629	−	25.0002i	−0.457536	−	0.855989i	−0.999875	−	0.0158296i	$-0.994961\pi$
$853$	−13.3629	−	25.0002i	−0.457536	−	0.855989i	0.542339	−	0.840160i	$-0.317539\pi$
$854$		0			0
$855$	2.53120	−	12.7252i	0.0865651	−	0.435192i
$856$		0			0
$857$	6.80551	−	1.35370i	0.232472	−	0.0462415i	−0.0774795	−	0.996994i	$-0.524687\pi$
$857$	6.80551	−	1.35370i	0.232472	−	0.0462415i	0.309951	+	0.950752i	$0.399687\pi$
$858$		0			0
$859$	−2.11669	−	21.4911i	−0.0722206	−	0.733268i	−0.961298	−	0.275511i	$-0.911153\pi$
$859$	−2.11669	−	21.4911i	−0.0722206	−	0.733268i	0.889077	−	0.457757i	$-0.151347\pi$
$860$		0			0
$861$	0.268289	+	0.884429i	0.00914325	+	0.0301413i
$862$		0			0
$863$	13.7300	+	13.7300i	0.467374	+	0.467374i	0.901063	−	0.433689i	$-0.142788\pi$
$863$	13.7300	+	13.7300i	0.467374	+	0.467374i	−0.433689	+	0.901063i	$0.642788\pi$
$864$		0			0
$865$	−3.16099	+	3.16099i	−0.107477	+	0.107477i
$866$		0			0
$867$	−52.7027	+	15.9872i	−1.78988	+	0.542954i
$868$		0			0
$869$	−31.6764	+	3.11985i	−1.07455	+	0.105834i
$870$		0			0
$871$	−5.37680	−	27.0310i	−0.182186	−	0.915911i
$872$		0			0
$873$	−9.98466	−	1.98607i	−0.337930	−	0.0672184i
$874$		0			0
$875$	10.1766	−	5.43951i	0.344032	−	0.183889i
$876$		0			0
$877$	−36.3320	−	3.57839i	−1.22685	−	0.120834i	−0.536240	−	0.844065i	$-0.680156\pi$
$877$	−36.3320	−	3.57839i	−1.22685	−	0.120834i	−0.690606	+	0.723231i	$0.742656\pi$
$878$		0			0
$879$	−11.9191	−	4.93707i	−0.402023	−	0.166523i
$880$		0			0
$881$	−44.8606	+	18.5819i	−1.51139	+	0.626039i	−0.975844	−	0.218467i	$-0.929894\pi$
$881$	−44.8606	+	18.5819i	−1.51139	+	0.626039i	−0.535547	+	0.844506i	$0.679894\pi$
$882$		0			0
$883$	−19.7643	−	24.0829i	−0.665122	−	0.810453i	0.325722	−	0.945466i	$-0.394393\pi$
$883$	−19.7643	−	24.0829i	−0.665122	−	0.810453i	−0.990844	+	0.135012i	$0.956893\pi$
$884$		0			0
$885$	−2.65355	+	8.74757i	−0.0891980	+	0.294046i
$886$		0			0
$887$	−26.0238	−	38.9474i	−0.873794	−	1.30772i	−0.950517	−	0.310672i	$-0.899446\pi$
$887$	−26.0238	−	38.9474i	−0.873794	−	1.30772i	0.0767234	−	0.997052i	$-0.475554\pi$
$888$		0			0
$889$	3.50450	+	2.34163i	0.117537	+	0.0785359i
$890$		0			0
$891$	43.7277	+	35.8864i	1.46493	+	1.20224i
$892$		0			0
$893$	−6.59863	+	12.3452i	−0.220815	+	0.413116i
$894$		0			0
$895$	0.0976701			0.00326475
$896$		0			0
$897$	−11.8723			−0.396404
$898$		0			0
$899$	16.0517	−	30.0307i	0.535355	−	1.00158i
$900$		0			0
$901$	42.3714	+	34.7733i	1.41160	+	1.15847i
$902$		0			0
$903$	−32.3085	−	21.5879i	−1.07516	−	0.718399i
$904$		0			0
$905$	−1.22213	−	1.82904i	−0.0406248	−	0.0607993i
$906$		0			0
$907$	−13.5900	+	44.8002i	−0.451248	+	1.48757i	0.376474	+	0.926427i	$0.377136\pi$
$907$	−13.5900	+	44.8002i	−0.451248	+	1.48757i	−0.827722	+	0.561138i	$0.810364\pi$
$908$		0			0
$909$	−38.8522	−	47.3415i	−1.28865	−	1.57022i
$910$		0			0
$911$	15.5659	−	6.44760i	0.515721	−	0.213619i	−0.109615	−	0.993974i	$-0.534962\pi$
$911$	15.5659	−	6.44760i	0.515721	−	0.213619i	0.625336	+	0.780356i	$0.284962\pi$
$912$		0			0
$913$	4.42204	+	1.83167i	0.146348	+	0.0606194i
$914$		0			0
$915$	−19.4020	−	1.91093i	−0.641410	−	0.0631734i
$916$		0			0
$917$	−13.2941	+	7.10583i	−0.439009	+	0.234655i
$918$		0			0
$919$	−52.2467	−	10.3925i	−1.72346	−	0.342818i	−0.768567	−	0.639769i	$-0.779030\pi$
$919$	−52.2467	−	10.3925i	−1.72346	−	0.342818i	−0.954893	+	0.296951i	$0.904030\pi$
$920$		0			0
$921$	2.70114	+	13.5795i	0.0890055	+	0.447461i
$922$		0			0
$923$	20.7771	−	2.04637i	0.683888	−	0.0673570i
$924$		0			0
$925$	39.4076	−	11.9542i	1.29572	−	0.393051i
$926$		0			0
$927$	36.9333	−	36.9333i	1.21305	−	1.21305i
$928$		0			0
$929$	−24.8899	−	24.8899i	−0.816610	−	0.816610i	0.169005	−	0.985615i	$-0.445945\pi$
$929$	−24.8899	−	24.8899i	−0.816610	−	0.816610i	−0.985615	+	0.169005i	$0.945945\pi$
$930$		0			0
$931$	1.45396	+	4.79306i	0.0476516	+	0.157086i
$932$		0			0
$933$	−7.88814	−	80.0896i	−0.258246	−	2.62202i
$934$		0			0
$935$	10.3700	−	2.06272i	0.339135	−	0.0674581i
$936$		0			0
$937$	0.642936	−	3.23226i	0.0210038	−	0.105593i	−0.968861	−	0.247604i	$-0.920357\pi$
$937$	0.642936	−	3.23226i	0.0210038	−	0.105593i	0.989865	+	0.142011i	$0.0453568\pi$
$938$		0			0
$939$	2.40431	+	4.49814i	0.0784616	+	0.146791i
$940$		0			0
$941$	1.21405	−	12.3265i	0.0395770	−	0.401832i	−0.954904	−	0.296915i	$-0.904042\pi$
$941$	1.21405	−	12.3265i	0.0395770	−	0.401832i	0.994481	−	0.104917i	$-0.0334578\pi$
$942$		0			0
$943$	−0.0560632	+	0.135349i	−0.00182567	+	0.00440755i
$944$		0			0
$945$	5.18213	+	12.5108i	0.168575	+	0.406975i
$946$		0			0
$947$	−27.7811	+	22.7993i	−0.902763	+	0.740878i	−0.966386	−	0.257096i	$-0.917234\pi$
$947$	−27.7811	+	22.7993i	−0.902763	+	0.740878i	0.0636231	+	0.997974i	$0.479734\pi$
$948$		0			0
$949$	−18.8646	−	5.72251i	−0.612370	−	0.185760i
$950$		0			0
$951$	5.46530	−	3.65180i	0.177225	−	0.118418i
$952$		0			0
$953$	15.0183	−	22.4765i	0.486492	−	0.728087i	−0.504293	−	0.863533i	$-0.668247\pi$
$953$	15.0183	−	22.4765i	0.486492	−	0.728087i	0.990785	+	0.135446i	$0.0432467\pi$
$954$		0			0
$955$	−3.46240	+	4.21895i	−0.112041	+	0.136522i
$956$		0			0
$957$	80.3195	+	42.9317i	2.59636	+	1.38778i
$958$		0			0
$959$			8.10022i			0.261570i
$960$		0			0
$961$			13.1610i			0.424549i
$962$		0			0
$963$	−4.93646	−	2.63859i	−0.159075	−	0.0850274i
$964$		0			0
$965$	−6.47995	+	7.89585i	−0.208597	+	0.254176i
$966$		0			0
$967$	23.3269	−	34.9112i	0.750143	−	1.12267i	−0.238317	−	0.971187i	$-0.576596\pi$
$967$	23.3269	−	34.9112i	0.750143	−	1.12267i	0.988460	−	0.151481i	$-0.0484042\pi$
$968$		0			0
$969$	−59.8776	+	40.0089i	−1.92354	+	1.28527i
$970$		0			0
$971$	54.6133	+	16.5668i	1.75263	+	0.531653i	0.992938	−	0.118636i	$-0.0378520\pi$
$971$	54.6133	+	16.5668i	1.75263	+	0.531653i	0.759687	+	0.650289i	$0.225352\pi$
$972$		0			0
$973$	40.9961	−	33.6446i	1.31427	−	1.07860i
$974$		0			0
$975$	18.3102	+	44.2046i	0.586394	+	1.41568i
$976$		0			0
$977$	−8.95883	+	21.6285i	−0.286618	+	0.691958i	−0.999961	−	0.00885781i	$-0.997180\pi$
$977$	−8.95883	+	21.6285i	−0.286618	+	0.691958i	0.713342	+	0.700816i	$0.247180\pi$
$978$		0			0
$979$	−2.96264	+	30.0802i	−0.0946864	+	0.961367i
$980$		0			0
$981$	41.0984	+	76.8896i	1.31217	+	2.45490i
$982$		0			0
$983$	−1.61099	+	8.09899i	−0.0513826	+	0.258318i	−0.997935	−	0.0642324i	$-0.979540\pi$
$983$	−1.61099	+	8.09899i	−0.0513826	+	0.258318i	0.946552	+	0.322550i	$0.104540\pi$
$984$		0			0
$985$	8.03394	−	1.59805i	0.255983	−	0.0509181i
$986$		0			0
$987$	−2.59950	−	26.3932i	−0.0827430	−	0.840103i
$988$		0			0
$989$	−1.78795	−	5.89407i	−0.0568534	−	0.187421i
$990$		0			0
$991$	28.9139	+	28.9139i	0.918479	+	0.918479i	0.996919	−	0.0784399i	$-0.0249939\pi$
$991$	28.9139	+	28.9139i	0.918479	+	0.918479i	−0.0784399	+	0.996919i	$0.524994\pi$
$992$		0			0
$993$	−67.6906	+	67.6906i	−2.14810	+	2.14810i
$994$		0			0
$995$	4.19989	−	1.27402i	0.133145	−	0.0403892i
$996$		0			0
$997$	25.9301	−	2.55390i	0.821216	−	0.0808827i	0.321323	−	0.946970i	$-0.395873\pi$
$997$	25.9301	−	2.55390i	0.821216	−	0.0808827i	0.499893	+	0.866087i	$0.333373\pi$
$998$		0			0
$999$	19.3407	+	97.2325i	0.611914	+	3.07630i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.k.a.17.1		240
4.3	odd	2		128.2.k.a.45.7	yes	240
128.37	even	32	inner	512.2.k.a.241.1		240
128.91	odd	32		128.2.k.a.37.7	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.2.k.a.37.7	✓	240	128.91	odd	32
128.2.k.a.45.7	yes	240	4.3	odd	2
512.2.k.a.17.1		240	1.1	even	1	trivial
512.2.k.a.241.1		240	128.37	even	32	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:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.k (of order \(32\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.46662 + 2.74386i) q^{3} +(-0.382125 - 0.313602i) q^{5} +(-1.98950 - 1.32934i) q^{7} +(-3.71107 - 5.55401i) q^{9} +O(q^{10})\)	\(q+(-1.46662 + 2.74386i) q^{3} +(-0.382125 - 0.313602i) q^{5} +(-1.98950 - 1.32934i) q^{7} +(-3.71107 - 5.55401i) q^{9} +(1.05398 - 3.47451i) q^{11} +(2.05150 + 2.49975i) q^{13} +(1.42091 - 0.588561i) q^{15} +(-5.44241 - 2.25432i) q^{17} +(-3.91033 - 0.385134i) q^{19} +(6.56538 - 3.50927i) q^{21} +(1.15735 + 0.230211i) q^{23} +(-0.927778 - 4.66426i) q^{25} +(11.3934 - 1.12215i) q^{27} +(7.71499 - 2.34032i) q^{29} +(2.98655 - 2.98655i) q^{31} +(7.98777 + 7.98777i) q^{33} +(0.343354 + 1.13189i) q^{35} +(0.848768 + 8.61769i) q^{37} +(-9.86775 + 1.96282i) q^{39} +(-0.0242205 + 0.121765i) q^{41} +(-2.46052 - 4.60331i) q^{43} +(-0.323655 + 3.28612i) q^{45} +(1.36332 - 3.29134i) q^{47} +(-0.487818 - 1.17770i) q^{49} +(14.1675 - 11.6270i) q^{51} +(-8.90424 - 2.70107i) q^{53} +(-1.49236 + 0.997166i) q^{55} +(6.79174 - 10.1646i) q^{57} +(-3.77059 + 4.59448i) q^{59} +(-11.1794 - 5.97554i) q^{61} +15.9830i q^{63} -1.59857i q^{65} +(-7.51634 - 4.01757i) q^{67} +(-2.32906 + 2.83797i) q^{69} +(3.58681 - 5.36805i) q^{71} +(-5.06870 + 3.38680i) q^{73} +(14.1588 + 4.29501i) q^{75} +(-6.71571 + 5.51144i) q^{77} +(-3.35477 - 8.09914i) q^{79} +(-5.96214 + 14.3939i) q^{81} +(-0.129211 + 1.31190i) q^{83} +(1.37272 + 2.56818i) q^{85} +(-4.89349 + 24.6012i) q^{87} +(-8.16474 + 1.62407i) q^{89} +(-0.758424 - 7.70041i) q^{91} +(3.81453 + 12.5748i) q^{93} +(1.37346 + 1.37346i) q^{95} +(1.07767 - 1.07767i) q^{97} +(-23.2089 + 7.04033i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9}+O(q^{10}) \) 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9	\( 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9} + 16 q^{11} - 16 q^{13} + 16 q^{15} - 16 q^{17} + 16 q^{19} - 16 q^{21} + 16 q^{23} - 16 q^{25} + 16 q^{27} - 16 q^{29} + 16 q^{31} - 16 q^{33} + 16 q^{35} - 16 q^{37} + 16 q^{39} - 16 q^{41} + 16 q^{43} - 16 q^{45} + 16 q^{47} - 16 q^{49} + 16 q^{51} - 16 q^{53} + 16 q^{55} - 16 q^{57} + 16 q^{59} - 16 q^{61} + 16 q^{67} - 16 q^{69} + 16 q^{71} - 16 q^{73} + 16 q^{75} - 16 q^{77} + 16 q^{79} - 16 q^{81} + 16 q^{83} - 16 q^{85} + 16 q^{87} - 16 q^{89} + 16 q^{91} - 16 q^{93} + 16 q^{95} - 16 q^{97} + 16 q^{99}+O(q^{100}) \) 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9 + 16 * q^11 - 16 * q^13 + 16 * q^15 - 16 * q^17 + 16 * q^19 - 16 * q^21 + 16 * q^23 - 16 * q^25 + 16 * q^27 - 16 * q^29 + 16 * q^31 - 16 * q^33 + 16 * q^35 - 16 * q^37 + 16 * q^39 - 16 * q^41 + 16 * q^43 - 16 * q^45 + 16 * q^47 - 16 * q^49 + 16 * q^51 - 16 * q^53 + 16 * q^55 - 16 * q^57 + 16 * q^59 - 16 * q^61 + 16 * q^67 - 16 * q^69 + 16 * q^71 - 16 * q^73 + 16 * q^75 - 16 * q^77 + 16 * q^79 - 16 * q^81 + 16 * q^83 - 16 * q^85 + 16 * q^87 - 16 * q^89 + 16 * q^91 - 16 * q^93 + 16 * q^95 - 16 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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