LMFDB - Embedded newform 572.2.bv.a.41.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(41,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([0, 18, 5]))

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

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

chi := DirichletCharacter("572.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bv (of order $60$, degree $16$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$14$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			41.12
Character	$\chi$	$=$	572.41
Dual form			572.2.bv.a.293.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.43269 - 1.59116i) q^{3} +(-0.186319 + 0.0295100i) q^{5} +(0.938903 + 0.0492058i) q^{7} +(-0.165612 - 1.57570i) q^{9} +O(q^{10})$	\(q+(1.43269 - 1.59116i) q^{3} +(-0.186319 + 0.0295100i) q^{5} +(0.938903 + 0.0492058i) q^{7} +(-0.165612 - 1.57570i) q^{9} +(-0.887226 - 3.19575i) q^{11} +(0.930431 - 3.48343i) q^{13} +(-0.219982 + 0.338742i) q^{15} +(1.46378 - 0.651717i) q^{17} +(-0.00445075 - 0.00685355i) q^{19} +(1.42345 - 1.42345i) q^{21} +(5.06452 - 2.92400i) q^{23} +(-4.72144 + 1.53409i) q^{25} +(2.45214 + 1.78159i) q^{27} +(1.13451 + 5.33744i) q^{29} +(0.683018 - 4.31241i) q^{31} +(-6.35606 - 3.16679i) q^{33} +(-0.176388 + 0.0185391i) q^{35} +(-4.90314 - 3.18414i) q^{37} +(-4.20968 - 6.47113i) q^{39} +(11.0936 - 0.581388i) q^{41} +(-5.79926 + 10.0446i) q^{43} +(0.0773556 + 0.288695i) q^{45} +(3.03790 - 5.96221i) q^{47} +(-6.08254 - 0.639300i) q^{49} +(1.06015 - 3.26281i) q^{51} +(-11.1948 + 8.13352i) q^{53} +(0.259614 + 0.569248i) q^{55} +(-0.0172816 - 0.00273714i) q^{57} +(-0.0913913 + 1.74385i) q^{59} +(-0.809054 - 1.81716i) q^{61} +(-0.0779605 - 1.48758i) q^{63} +(-0.0705608 + 0.676487i) q^{65} +(8.32006 + 2.22935i) q^{67} +(2.60332 - 12.2476i) q^{69} +(-1.15825 + 3.01735i) q^{71} +(2.35679 + 4.62547i) q^{73} +(-4.32336 + 9.71043i) q^{75} +(-0.675769 - 3.04416i) q^{77} +(4.04902 + 5.57300i) q^{79} +(10.9972 - 2.33753i) q^{81} +(2.52972 + 15.9720i) q^{83} +(-0.253498 + 0.164624i) q^{85} +(10.1181 + 5.84169i) q^{87} +(1.46565 - 5.46989i) q^{89} +(1.04499 - 3.22482i) q^{91} +(-5.88318 - 7.26512i) q^{93} +(0.00103151 + 0.00114561i) q^{95} +(-5.32225 - 4.30987i) q^{97} +(-4.88860 + 1.92725i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 28 q^{9}+O(q^{10}) $ 224 * q + 28 * q^9	$ 224 q + 28 q^{9} + 16 q^{11} + 10 q^{13} - 28 q^{15} - 48 q^{23} + 24 q^{27} + 20 q^{29} + 4 q^{31} + 60 q^{33} + 50 q^{35} + 12 q^{37} - 40 q^{39} + 20 q^{41} + 64 q^{45} - 62 q^{47} + 100 q^{53} - 22 q^{55} + 12 q^{59} - 40 q^{61} - 80 q^{63} - 44 q^{67} - 152 q^{71} + 30 q^{73} - 120 q^{75} + 80 q^{79} + 72 q^{81} + 90 q^{83} - 40 q^{85} - 8 q^{89} - 36 q^{91} - 90 q^{93} - 42 q^{97} + 144 q^{99}+O(q^{100}) $ 224 * q + 28 * q^9 + 16 * q^11 + 10 * q^13 - 28 * q^15 - 48 * q^23 + 24 * q^27 + 20 * q^29 + 4 * q^31 + 60 * q^33 + 50 * q^35 + 12 * q^37 - 40 * q^39 + 20 * q^41 + 64 * q^45 - 62 * q^47 + 100 * q^53 - 22 * q^55 + 12 * q^59 - 40 * q^61 - 80 * q^63 - 44 * q^67 - 152 * q^71 + 30 * q^73 - 120 * q^75 + 80 * q^79 + 72 * q^81 + 90 * q^83 - 40 * q^85 - 8 * q^89 - 36 * q^91 - 90 * q^93 - 42 * q^97 + 144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{3}{10}\right)$

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
$3$	1.43269	−	1.59116i	0.827162	−	0.918656i	−0.170613	−	0.985338i	$-0.554575\pi$
$3$	1.43269	−	1.59116i	0.827162	−	0.918656i	0.997774	+	0.0666821i	$0.0212413\pi$
$4$		0			0
$5$	−0.186319	+	0.0295100i	−0.0833244	+	0.0131973i	−0.197957	−	0.980211i	$-0.563431\pi$
$5$	−0.186319	+	0.0295100i	−0.0833244	+	0.0131973i	0.114633	+	0.993408i	$0.463431\pi$
$6$		0			0
$7$	0.938903	+	0.0492058i	0.354872	+	0.0185981i	0.228939	−	0.973441i	$-0.426474\pi$
$7$	0.938903	+	0.0492058i	0.354872	+	0.0185981i	0.125933	+	0.992039i	$0.459808\pi$
$8$		0			0
$9$	−0.165612	−	1.57570i	−0.0552041	−	0.525232i
$10$		0			0
$11$	−0.887226	−	3.19575i	−0.267509	−	0.963555i
$11$	−0.887226	−	3.19575i	−0.267509	−	0.963555i
$12$		0			0
$13$	0.930431	−	3.48343i	0.258055	−	0.966130i
$13$	0.930431	−	3.48343i	0.258055	−	0.966130i
$14$		0			0
$15$	−0.219982	+	0.338742i	−0.0567990	+	0.0874628i
$16$		0			0
$17$	1.46378	−	0.651717i	0.355019	−	0.158065i	−0.221475	−	0.975166i	$-0.571087\pi$
$17$	1.46378	−	0.651717i	0.355019	−	0.158065i	0.576494	+	0.817101i	$0.304420\pi$
$18$		0			0
$19$	−0.00445075	−	0.00685355i	−0.00102107	−	0.00157231i	0.838160	−	0.545425i	$-0.183632\pi$
$19$	−0.00445075	−	0.00685355i	−0.00102107	−	0.00157231i	−0.839181	+	0.543853i	$0.816965\pi$
$20$		0			0
$21$	1.42345	−	1.42345i	0.310622	−	0.310622i
$22$		0			0
$23$	5.06452	−	2.92400i	1.05603	−	0.609697i	0.131696	−	0.991290i	$-0.457958\pi$
$23$	5.06452	−	2.92400i	1.05603	−	0.609697i	0.924330	+	0.381593i	$0.124625\pi$
$24$		0			0
$25$	−4.72144	+	1.53409i	−0.944288	+	0.306818i
$26$		0			0
$27$	2.45214	+	1.78159i	0.471915	+	0.342866i
$28$		0			0
$29$	1.13451	+	5.33744i	0.210673	+	0.991137i	0.948654	+	0.316316i	$0.102446\pi$
$29$	1.13451	+	5.33744i	0.210673	+	0.991137i	−0.737981	+	0.674821i	$0.764221\pi$
$30$		0			0
$31$	0.683018	−	4.31241i	0.122674	−	0.774531i	−0.847263	−	0.531174i	$-0.821751\pi$
$31$	0.683018	−	4.31241i	0.122674	−	0.774531i	0.969937	−	0.243358i	$-0.0782488\pi$
$32$		0			0
$33$	−6.35606	−	3.16679i	−1.10645	−	0.551268i
$34$		0			0
$35$	−0.176388	+	0.0185391i	−0.0298150	+	0.00313368i
$36$		0			0
$37$	−4.90314	−	3.18414i	−0.806071	−	0.523469i	0.0745906	−	0.997214i	$-0.476235\pi$
$37$	−4.90314	−	3.18414i	−0.806071	−	0.523469i	−0.880662	+	0.473745i	$0.842902\pi$
$38$		0			0
$39$	−4.20968	−	6.47113i	−0.674088	−	1.03621i
$40$		0			0
$41$	11.0936	−	0.581388i	1.73252	−	0.0907976i	0.840223	−	0.542242i	$-0.182424\pi$
$41$	11.0936	−	0.581388i	1.73252	−	0.0907976i	0.892299	+	0.451444i	$0.149091\pi$
$42$		0			0
$43$	−5.79926	+	10.0446i	−0.884378	+	1.53179i	−0.0379539	+	0.999279i	$0.512084\pi$
$43$	−5.79926	+	10.0446i	−0.884378	+	1.53179i	−0.846424	+	0.532509i	$0.821249\pi$
$44$		0			0
$45$	0.0773556	+	0.288695i	0.0115315	+	0.0430361i
$46$		0			0
$47$	3.03790	−	5.96221i	0.443123	−	0.869678i	−0.556132	−	0.831094i	$-0.687715\pi$
$47$	3.03790	−	5.96221i	0.443123	−	0.869678i	0.999255	−	0.0385842i	$-0.0122848\pi$
$48$		0			0
$49$	−6.08254	−	0.639300i	−0.868934	−	0.0913286i
$50$		0			0
$51$	1.06015	−	3.26281i	0.148451	−	0.456885i
$52$		0			0
$53$	−11.1948	+	8.13352i	−1.53773	+	1.11722i	−0.585987	+	0.810320i	$0.699293\pi$
$53$	−11.1948	+	8.13352i	−1.53773	+	1.11722i	−0.951740	+	0.306904i	$0.900707\pi$
$54$		0			0
$55$	0.259614	+	0.569248i	0.0350063	+	0.0767573i
$56$		0			0
$57$	−0.0172816	−	0.00273714i	−0.00228901	−	0.000362543i
$58$		0			0
$59$	−0.0913913	+	1.74385i	−0.0118981	+	0.227030i	0.986208	+	0.165512i	$0.0529275\pi$
$59$	−0.0913913	+	1.74385i	−0.0118981	+	0.227030i	−0.998106	+	0.0615182i	$0.980406\pi$
$60$		0			0
$61$	−0.809054	−	1.81716i	−0.103589	−	0.232664i	0.854314	−	0.519757i	$-0.173978\pi$
$61$	−0.809054	−	1.81716i	−0.103589	−	0.232664i	−0.957903	+	0.287093i	$0.907311\pi$
$62$		0			0
$63$	−0.0779605	−	1.48758i	−0.00982210	−	0.187417i
$64$		0			0
$65$	−0.0705608	+	0.676487i	−0.00875199	+	0.0839079i
$66$		0			0
$67$	8.32006	+	2.22935i	1.01646	+	0.272359i	0.728325	−	0.685232i	$-0.240299\pi$
$67$	8.32006	+	2.22935i	1.01646	+	0.272359i	0.288132	+	0.957591i	$0.406966\pi$
$68$		0			0
$69$	2.60332	−	12.2476i	0.313402	−	1.47444i
$70$		0			0
$71$	−1.15825	+	3.01735i	−0.137459	+	0.358094i	−0.984980	−	0.172668i	$-0.944761\pi$
$71$	−1.15825	+	3.01735i	−0.137459	+	0.358094i	0.847521	+	0.530763i	$0.178094\pi$
$72$		0			0
$73$	2.35679	+	4.62547i	0.275842	+	0.541370i	0.986816	−	0.161849i	$-0.0517456\pi$
$73$	2.35679	+	4.62547i	0.275842	+	0.541370i	−0.710974	+	0.703218i	$0.751746\pi$
$74$		0			0
$75$	−4.32336	+	9.71043i	−0.499219	+	1.12126i
$76$		0			0
$77$	−0.675769	−	3.04416i	−0.0770111	−	0.346914i
$78$		0			0
$79$	4.04902	+	5.57300i	0.455550	+	0.627011i	0.973579	−	0.228352i	$-0.0733338\pi$
$79$	4.04902	+	5.57300i	0.455550	+	0.627011i	−0.518028	+	0.855363i	$0.673334\pi$
$80$		0			0
$81$	10.9972	−	2.33753i	1.22191	−	0.259725i
$82$		0			0
$83$	2.52972	+	15.9720i	0.277673	+	1.75316i	0.593962	+	0.804493i	$0.297563\pi$
$83$	2.52972	+	15.9720i	0.277673	+	1.75316i	−0.316289	+	0.948663i	$0.602437\pi$
$84$		0			0
$85$	−0.253498	+	0.164624i	−0.0274957	+	0.0178559i
$86$		0			0
$87$	10.1181	+	5.84169i	1.08477	+	0.626295i
$88$		0			0
$89$	1.46565	−	5.46989i	0.155359	−	0.579808i	−0.843715	−	0.536791i	$-0.819636\pi$
$89$	1.46565	−	5.46989i	0.155359	−	0.579808i	0.999074	−	0.0430168i	$-0.0136969\pi$
$90$		0			0
$91$	1.04499	−	3.22482i	0.109545	−	0.338053i
$92$		0			0
$93$	−5.88318	−	7.26512i	−0.610057	−	0.753357i
$94$		0			0
$95$	0.00103151	+	0.00114561i	0.000105831	+	0.000117537i
$96$		0			0
$97$	−5.32225	−	4.30987i	−0.540393	−	0.437601i	0.319863	−	0.947464i	$-0.396363\pi$
$97$	−5.32225	−	4.30987i	−0.540393	−	0.437601i	−0.860256	+	0.509862i	$0.829696\pi$
$98$		0			0
$99$	−4.88860	+	1.92725i	−0.491323	+	0.193696i
$100$		0			0
$101$	−6.42285	−	2.85964i	−0.639097	−	0.284544i	0.0614939	−	0.998107i	$-0.480414\pi$
$101$	−6.42285	−	2.85964i	−0.639097	−	0.284544i	−0.700591	+	0.713563i	$0.747080\pi$
$102$		0			0
$103$	−7.32386	−	2.37967i	−0.721641	−	0.234475i	−0.0749066	−	0.997191i	$-0.523866\pi$
$103$	−7.32386	−	2.37967i	−0.721641	−	0.234475i	−0.646735	+	0.762715i	$0.723866\pi$
$104$		0			0
$105$	−0.223209	+	0.307222i	−0.0217830	+	0.0299817i
$106$		0			0
$107$	12.3025	+	11.0772i	1.18933	+	1.07087i	0.995965	+	0.0897459i	$0.0286055\pi$
$107$	12.3025	+	11.0772i	1.18933	+	1.07087i	0.193361	+	0.981128i	$0.438061\pi$
$108$		0			0
$109$	4.10271	+	4.10271i	0.392968	+	0.392968i	0.875744	−	0.482776i	$-0.160371\pi$
$109$	4.10271	+	4.10271i	0.392968	+	0.392968i	−0.482776	+	0.875744i	$0.660371\pi$
$110$		0			0
$111$	−12.0911	+	3.23981i	−1.14764	+	0.307509i
$112$		0			0
$113$	14.4201	+	3.06509i	1.35653	+	0.288340i	0.828074	−	0.560619i	$-0.189437\pi$
$113$	14.4201	+	3.06509i	1.35653	+	0.288340i	0.528459	+	0.848959i	$0.322770\pi$
$114$		0			0
$115$	−0.857330	+	0.694252i	−0.0799464	+	0.0647393i
$116$		0			0
$117$	−5.64292	−	0.889177i	−0.521688	−	0.0822045i
$118$		0			0
$119$	1.40642	−	0.539873i	0.128926	−	0.0494901i
$120$		0			0
$121$	−9.42566	+	5.67071i	−0.856878	+	0.515519i
$122$		0			0
$123$	14.9685	−	18.4846i	1.34966	−	1.66670i
$124$		0			0
$125$	1.67483	−	0.853367i	0.149801	−	0.0763275i
$126$		0			0
$127$	−0.313292	+	2.98078i	−0.0278002	+	0.264501i	0.971789	+	0.235851i	$0.0757877\pi$
$127$	−0.313292	+	2.98078i	−0.0278002	+	0.264501i	−0.999589	+	0.0286505i	$0.990879\pi$
$128$		0			0
$129$	7.67405	+	23.6183i	0.675663	+	2.07948i
$130$		0			0
$131$			8.36775i			0.731094i	0.930793	+	0.365547i	$0.119118\pi$
$131$			8.36775i			0.731094i	−0.930793	+	0.365547i	$0.880882\pi$
$132$		0			0
$133$	−0.00384159	−	0.00665383i	−0.000333108	−	0.000576960i
$134$		0			0
$135$	−0.509456	−	0.259581i	−0.0438470	−	0.0223411i
$136$		0			0
$137$	−6.48137	−	2.48796i	−0.553740	−	0.212561i	0.0653754	−	0.997861i	$-0.479176\pi$
$137$	−6.48137	−	2.48796i	−0.553740	−	0.212561i	−0.619116	+	0.785300i	$0.712509\pi$
$138$		0			0
$139$	1.97060	−	1.77434i	0.167145	−	0.150498i	−0.581314	−	0.813680i	$-0.697461\pi$
$139$	1.97060	−	1.77434i	0.167145	−	0.150498i	0.748458	+	0.663182i	$0.230794\pi$
$140$		0			0
$141$	−5.13447	−	13.3758i	−0.432401	−	1.12644i
$142$		0			0
$143$	−11.9577	+	0.117163i	−0.999952	+	0.00979769i
$144$		0			0
$145$	−0.368888	−	0.960987i	−0.0306345	−	0.0798056i
$146$		0			0
$147$	−9.73159	+	8.76236i	−0.802648	+	0.722708i
$148$		0			0
$149$	−0.153459	−	0.0589072i	−0.0125718	−	0.00482587i	0.352074	−	0.935972i	$-0.385477\pi$
$149$	−0.153459	−	0.0589072i	−0.0125718	−	0.00482587i	−0.364646	+	0.931146i	$0.618810\pi$
$150$		0			0
$151$	9.77366	+	4.97993i	0.795369	+	0.405261i	0.803946	−	0.594702i	$-0.202730\pi$
$151$	9.77366	+	4.97993i	0.795369	+	0.405261i	−0.00857688	+	0.999963i	$0.502730\pi$
$152$		0			0
$153$	−1.26933	−	2.19854i	−0.102619	−	0.177742i
$154$		0			0
$155$			0.823640i			0.0661563i
$156$		0			0
$157$	−0.512800	−	1.57824i	−0.0409259	−	0.125957i	0.928506	−	0.371317i	$-0.121094\pi$
$157$	−0.512800	−	1.57824i	−0.0409259	−	0.125957i	−0.969432	+	0.245360i	$0.921094\pi$
$158$		0			0
$159$	−3.09695	+	29.4655i	−0.245604	+	2.33677i
$160$		0			0
$161$	4.89897	−	2.49615i	0.386093	−	0.196724i
$162$		0			0
$163$	−13.7458	+	16.9746i	−1.07665	+	1.32956i	−0.135803	+	0.990736i	$0.543362\pi$
$163$	−13.7458	+	16.9746i	−1.07665	+	1.32956i	−0.940851	+	0.338821i	$0.889972\pi$
$164$		0			0
$165$	1.27771	+	0.402466i	0.0994695	+	0.0313319i
$166$		0			0
$167$	−1.04191	+	0.399953i	−0.0806256	+	0.0309493i	−0.398347	−	0.917235i	$-0.630416\pi$
$167$	−1.04191	+	0.399953i	−0.0806256	+	0.0309493i	0.317721	+	0.948184i	$0.397083\pi$
$168$		0			0
$169$	−11.2686	−	6.48219i	−0.866815	−	0.498630i
$170$		0			0
$171$	−0.0100620	+	0.00814806i	−0.000769462	+	0.000623098i
$172$		0			0
$173$	−1.27807	−	0.271663i	−0.0971700	−	0.0206541i	0.159070	−	0.987267i	$-0.449150\pi$
$173$	−1.27807	−	0.271663i	−0.0971700	−	0.0206541i	−0.256240	+	0.966613i	$0.582484\pi$
$174$		0			0
$175$	−4.50846	+	1.20804i	−0.340808	+	0.0913191i
$176$		0			0
$177$	2.64381	+	2.64381i	0.198721	+	0.198721i
$178$		0			0
$179$	4.08770	+	3.68058i	0.305529	+	0.275099i	0.807605	−	0.589724i	$-0.200764\pi$
$179$	4.08770	+	3.68058i	0.305529	+	0.275099i	−0.502076	+	0.864824i	$0.667430\pi$
$180$		0			0
$181$	−6.08403	+	8.37395i	−0.452222	+	0.622431i	−0.972873	−	0.231339i	$-0.925689\pi$
$181$	−6.08403	+	8.37395i	−0.452222	+	0.622431i	0.520651	+	0.853770i	$0.325689\pi$
$182$		0			0
$183$	−4.05052	−	1.31609i	−0.299423	−	0.0972884i
$184$		0			0
$185$	1.00751	+	0.448574i	0.0740738	+	0.0329798i
$186$		0			0
$187$	−3.38143	−	4.09966i	−0.247275	−	0.299797i
$188$		0			0
$189$	2.21466	+	1.79340i	0.161093	+	0.130450i
$190$		0			0
$191$	−6.28653	−	6.98190i	−0.454877	−	0.505193i	0.471460	−	0.881887i	$-0.343727\pi$
$191$	−6.28653	−	6.98190i	−0.454877	−	0.505193i	−0.926337	+	0.376695i	$0.877061\pi$
$192$		0			0
$193$	−8.32284	−	10.2779i	−0.599091	−	0.739816i	0.383919	−	0.923367i	$-0.374574\pi$
$193$	−8.32284	−	10.2779i	−0.599091	−	0.739816i	−0.983010	+	0.183551i	$0.941241\pi$
$194$		0			0
$195$	0.975307	+	1.08147i	0.0698432	+	0.0774454i
$196$		0			0
$197$	0.243861	−	0.910100i	0.0173743	−	0.0648419i	−0.956694	−	0.291094i	$-0.905981\pi$
$197$	0.243861	−	0.910100i	0.0173743	−	0.0648419i	0.974069	+	0.226252i	$0.0726474\pi$
$198$		0			0
$199$	2.60690	+	1.50509i	0.184798	+	0.106693i	0.589545	−	0.807735i	$-0.299307\pi$
$199$	2.60690	+	1.50509i	0.184798	+	0.106693i	−0.404747	+	0.914429i	$0.632640\pi$
$200$		0			0
$201$	15.4673	−	10.0446i	1.09098	−	0.708490i
$202$		0			0
$203$	0.802560	+	5.06716i	0.0563286	+	0.355645i
$204$		0			0
$205$	−2.04978	+	0.435695i	−0.143163	+	0.0304303i
$206$		0			0
$207$	−5.44609	−	7.49590i	−0.378529	−	0.521001i
$208$		0			0
$209$	−0.0179534	+	0.0203041i	−0.00124187	+	0.00140447i
$210$		0			0
$211$	−3.02931	+	6.80394i	−0.208546	+	0.468403i	−0.987288	−	0.158942i	$-0.949192\pi$
$211$	−3.02931	+	6.80394i	−0.208546	+	0.468403i	0.778742	+	0.627345i	$0.215858\pi$
$212$		0			0
$213$	3.14168	+	6.16589i	0.215264	+	0.422480i
$214$		0			0
$215$	0.784095	−	2.04264i	0.0534749	−	0.139307i
$216$		0			0
$217$	0.853484	−	4.01532i	0.0579382	−	0.272578i
$218$		0			0
$219$	10.7364	+	2.87681i	0.725498	+	0.194397i
$220$		0			0
$221$	−0.908265	−	5.70536i	−0.0610965	−	0.383784i
$222$		0			0
$223$	−0.891869	−	17.0179i	−0.0597240	−	1.13960i	−0.849977	−	0.526820i	$-0.823384\pi$
$223$	−0.891869	−	17.0179i	−0.0597240	−	1.13960i	0.790253	−	0.612781i	$-0.209949\pi$
$224$		0			0
$225$	3.19919	+	7.18549i	0.213279	+	0.479033i
$226$		0			0
$227$	0.104503	−	1.99404i	0.00693614	−	0.132349i	−0.992967	−	0.118396i	$-0.962225\pi$
$227$	0.104503	−	1.99404i	0.00693614	−	0.132349i	0.999903	−	0.0139538i	$-0.00444177\pi$
$228$		0			0
$229$	−20.3281	−	3.21965i	−1.34332	−	0.212760i	−0.556963	−	0.830537i	$-0.688033\pi$
$229$	−20.3281	−	3.21965i	−1.34332	−	0.212760i	−0.786353	+	0.617777i	$0.788033\pi$
$230$		0			0
$231$	−5.81191	−	3.28607i	−0.382395	−	0.216207i
$232$		0			0
$233$	−0.763464	+	0.554689i	−0.0500162	+	0.0363389i	−0.612512	−	0.790461i	$-0.709841\pi$
$233$	−0.763464	+	0.554689i	−0.0500162	+	0.0363389i	0.562496	+	0.826800i	$0.309841\pi$
$234$		0			0
$235$	−0.390073	+	1.20052i	−0.0254456	+	0.0783135i
$236$		0			0
$237$	14.6685	+	1.54172i	0.952821	+	0.100146i
$238$		0			0
$239$	−1.89496	+	3.71908i	−0.122575	+	0.240567i	−0.944138	−	0.329551i	$-0.893103\pi$
$239$	−1.89496	+	3.71908i	−0.122575	+	0.240567i	0.821563	+	0.570118i	$0.193103\pi$
$240$		0			0
$241$	−5.80718	−	21.6727i	−0.374073	−	1.39606i	−0.854694	−	0.519132i	$-0.826255\pi$
$241$	−5.80718	−	21.6727i	−0.374073	−	1.39606i	0.480621	−	0.876929i	$-0.340411\pi$
$242$		0			0
$243$	7.48963	−	12.9724i	0.480460	−	0.832181i
$244$		0			0
$245$	1.15216	−	0.0603821i	0.0736087	−	0.00385767i
$246$		0			0
$247$	−0.0280150	+	0.00912713i	−0.00178255	+	0.000580745i
$248$		0			0
$249$	29.0383	+	18.8577i	1.84023	+	1.19506i
$250$		0			0
$251$	17.1588	−	1.80346i	1.08305	−	0.113833i	0.453852	−	0.891077i	$-0.350050\pi$
$251$	17.1588	−	1.80346i	1.08305	−	0.113833i	0.629199	+	0.777244i	$0.283383\pi$
$252$		0			0
$253$	−13.8378	−	13.5907i	−0.869973	−	0.854440i
$254$		0			0
$255$	−0.101241	+	0.639210i	−0.00633995	+	0.0400289i
$256$		0			0
$257$	−0.440754	−	2.07359i	−0.0274935	−	0.129347i	0.962260	−	0.272130i	$-0.0877281\pi$
$257$	−0.440754	−	2.07359i	−0.0274935	−	0.129347i	−0.989754	+	0.142783i	$0.954395\pi$
$258$		0			0
$259$	−4.44690	−	3.23086i	−0.276317	−	0.200756i
$260$		0			0
$261$	8.22229	−	2.67158i	0.508947	−	0.165367i
$262$		0			0
$263$	15.2307	−	8.79347i	0.939168	−	0.542229i	0.0494684	−	0.998776i	$-0.484247\pi$
$263$	15.2307	−	8.79347i	0.939168	−	0.542229i	0.889699	+	0.456547i	$0.150914\pi$
$264$		0			0
$265$	1.84579	−	1.84579i	0.113386	−	0.113386i
$266$		0			0
$267$	−6.60365	−	10.1687i	−0.404137	−	0.622316i
$268$		0			0
$269$	12.9339	−	5.75853i	0.788592	−	0.351104i	0.0273953	−	0.999625i	$-0.491279\pi$
$269$	12.9339	−	5.75853i	0.788592	−	0.351104i	0.761197	+	0.648521i	$0.224612\pi$
$270$		0			0
$271$	13.0521	−	20.0985i	0.792859	−	1.22090i	−0.178654	−	0.983912i	$-0.557174\pi$
$271$	13.0521	−	20.0985i	0.792859	−	1.22090i	0.971513	−	0.236984i	$-0.0761591\pi$
$272$		0			0
$273$	−3.63406	−	6.28290i	−0.219944	−	0.380259i
$274$		0			0
$275$	9.09155	+	13.7275i	0.548241	+	0.827797i
$276$		0			0
$277$	−2.46278	−	23.4317i	−0.147974	−	1.40788i	−0.776514	−	0.630100i	$-0.783014\pi$
$277$	−2.46278	−	23.4317i	−0.147974	−	1.40788i	0.628540	−	0.777777i	$-0.283653\pi$
$278$		0			0
$279$	−6.90816	−	0.362041i	−0.413581	−	0.0216748i
$280$		0			0
$281$	20.5539	−	3.25541i	1.22614	−	0.194202i	0.490420	−	0.871486i	$-0.336844\pi$
$281$	20.5539	−	3.25541i	1.22614	−	0.194202i	0.735721	+	0.677285i	$0.236844\pi$
$282$		0			0
$283$	0.0859077	−	0.0954101i	0.00510668	−	0.00567154i	−0.740586	−	0.671962i	$-0.765452\pi$
$283$	0.0859077	−	0.0954101i	0.00510668	−	0.00567154i	0.745693	+	0.666290i	$0.232119\pi$
$284$		0			0
$285$	0.00330067			0.000195515
$286$		0			0
$287$	10.4444			0.616512
$288$		0			0
$289$	−9.65730	+	10.7255i	−0.568077	+	0.630913i
$290$		0			0
$291$	−14.4828	+	2.29385i	−0.848997	+	0.134468i
$292$		0			0
$293$	−24.8210	−	1.30082i	−1.45006	−	0.0759944i	−0.689040	−	0.724723i	$-0.741968\pi$
$293$	−24.8210	−	1.30082i	−1.45006	−	0.0759944i	−0.761020	+	0.648729i	$0.775301\pi$
$294$		0			0
$295$	−0.0344331	−	0.327609i	−0.00200477	−	0.0190742i
$296$		0			0
$297$	3.51790	−	9.41711i	0.204129	−	0.546436i
$298$		0			0
$299$	−5.47338	−	20.3625i	−0.316534	−	1.17759i
$300$		0			0
$301$	−5.93919	+	9.14556i	−0.342329	+	0.527141i
$302$		0			0
$303$	−13.7521	+	6.12281i	−0.790035	+	0.351746i
$304$		0			0
$305$	0.204367	+	0.314697i	0.0117020	+	0.0180195i
$306$		0			0
$307$	8.77640	−	8.77640i	0.500895	−	0.500895i	−0.410821	−	0.911716i	$-0.634758\pi$
$307$	8.77640	−	8.77640i	0.500895	−	0.500895i	0.911716	+	0.410821i	$0.134758\pi$
$308$		0			0
$309$	−14.2792	+	8.24411i	−0.812316	+	0.468991i
$310$		0			0
$311$	14.9120	−	4.84520i	0.845581	−	0.274746i	0.145987	−	0.989286i	$-0.453364\pi$
$311$	14.9120	−	4.84520i	0.845581	−	0.274746i	0.699594	+	0.714540i	$0.253364\pi$
$312$		0			0
$313$	25.7614	+	18.7167i	1.45612	+	1.05793i	0.984353	+	0.176209i	$0.0563834\pi$
$313$	25.7614	+	18.7167i	1.45612	+	1.05793i	0.471766	+	0.881724i	$0.343617\pi$
$314$		0			0
$315$	0.0584240	+	0.274863i	0.00329182	+	0.0154868i
$316$		0			0
$317$	3.53666	−	22.3296i	0.198639	−	1.25415i	−0.663768	−	0.747939i	$-0.731044\pi$
$317$	3.53666	−	22.3296i	0.198639	−	1.25415i	0.862407	−	0.506216i	$-0.168956\pi$
$318$		0			0
$319$	16.0506	−	8.36111i	0.898659	−	0.468133i
$320$		0			0
$321$	35.2512	−	3.70505i	1.96753	−	0.206796i
$322$		0			0
$323$	−0.0109815	−	0.00713147i	−0.000611027	−	0.000396806i
$324$		0			0
$325$	0.950920	+	17.8742i	0.0527475	+	0.991481i
$326$		0			0
$327$	12.4059	−	0.650168i	0.686051	−	0.0359544i
$328$		0			0
$329$	3.14567	−	5.44846i	0.173426	−	0.300383i
$330$		0			0
$331$	−7.46987	−	27.8779i	−0.410581	−	1.53231i	−0.793525	−	0.608538i	$-0.791756\pi$
$331$	−7.46987	−	27.8779i	−0.410581	−	1.53231i	0.382944	−	0.923772i	$-0.374910\pi$
$332$		0			0
$333$	−4.20521	+	8.25319i	−0.230444	+	0.452272i
$334$		0			0
$335$	−1.61597	−	0.169846i	−0.0882901	−	0.00927967i
$336$		0			0
$337$	−8.73216	+	26.8748i	−0.475671	+	1.46396i	0.369380	+	0.929278i	$0.379570\pi$
$337$	−8.73216	+	26.8748i	−0.475671	+	1.46396i	−0.845051	+	0.534686i	$0.820430\pi$
$338$		0			0
$339$	25.5366	−	18.5534i	1.38696	−	1.00768i
$340$		0			0
$341$	−14.3874	+	1.64332i	−0.779120	+	0.0889908i
$342$		0			0
$343$	−12.1798	−	1.92909i	−0.657646	−	0.104161i
$344$		0			0
$345$	−0.123619	+	2.35879i	−0.00665543	+	0.126993i
$346$		0			0
$347$	−9.55733	−	21.4661i	−0.513064	−	1.15236i	−0.965462	−	0.260545i	$-0.916098\pi$
$347$	−9.55733	−	21.4661i	−0.513064	−	1.15236i	0.452397	−	0.891817i	$-0.350569\pi$
$348$		0			0
$349$	1.56572	+	29.8758i	0.0838112	+	1.59921i	0.640145	+	0.768254i	$0.278874\pi$
$349$	1.56572	+	29.8758i	0.0838112	+	1.59921i	−0.556333	+	0.830959i	$0.687792\pi$
$350$		0			0
$351$	8.48758	−	6.88423i	0.453034	−	0.367453i
$352$		0			0
$353$	−17.5442	−	4.70095i	−0.933782	−	0.250206i	−0.240315	−	0.970695i	$-0.577251\pi$
$353$	−17.5442	−	4.70095i	−0.933782	−	0.250206i	−0.693467	+	0.720489i	$0.743918\pi$
$354$		0			0
$355$	0.126763	−	0.596371i	0.00672786	−	0.0316521i
$356$		0			0
$357$	1.15593	−	3.01130i	0.0611783	−	0.159375i
$358$		0			0
$359$	−9.90477	−	19.4392i	−0.522754	−	1.02596i	−0.989898	−	0.141781i	$-0.954717\pi$
$359$	−9.90477	−	19.4392i	−0.522754	−	1.02596i	0.467145	−	0.884181i	$-0.345283\pi$
$360$		0			0
$361$	7.72797	−	17.3573i	0.406735	−	0.913542i
$362$		0			0
$363$	−4.48102	+	23.1221i	−0.235192	+	1.21359i
$364$		0			0
$365$	−0.575613	−	0.792263i	−0.0301290	−	0.0414690i
$366$		0			0
$367$	−30.8579	+	6.55904i	−1.61077	+	0.342379i	−0.923373	−	0.383905i	$-0.874579\pi$
$367$	−30.8579	+	6.55904i	−1.61077	+	0.342379i	−0.687395	+	0.726284i	$0.741246\pi$
$368$		0			0
$369$	−2.75332	−	17.3838i	−0.143332	−	0.904964i
$370$		0			0
$371$	−10.9111	+	7.08573i	−0.566475	+	0.367873i
$372$		0			0
$373$	−17.7076	−	10.2235i	−0.916863	−	0.529351i	−0.0342303	−	0.999414i	$-0.510898\pi$
$373$	−17.7076	−	10.2235i	−0.916863	−	0.529351i	−0.882633	+	0.470063i	$0.844231\pi$
$374$		0			0
$375$	1.04166	−	3.88752i	0.0537910	−	0.200751i
$376$		0			0
$377$	19.6482	+	1.01414i	1.01193	+	0.0522308i
$378$		0			0
$379$	12.2241	+	15.0954i	0.627907	+	0.775401i	0.987485	−	0.157714i	$-0.0504125\pi$
$379$	12.2241	+	15.0954i	0.627907	+	0.775401i	−0.359577	+	0.933115i	$0.617079\pi$
$380$		0			0
$381$	4.29404	+	4.76902i	0.219990	+	0.244324i
$382$		0			0
$383$	−1.29057	−	1.04508i	−0.0659450	−	0.0534012i	0.595781	−	0.803147i	$-0.296843\pi$
$383$	−1.29057	−	1.04508i	−0.0659450	−	0.0534012i	−0.661726	+	0.749746i	$0.730176\pi$
$384$		0			0
$385$	0.215742	+	0.547243i	0.0109952	+	0.0278901i
$386$		0			0
$387$	16.7877	+	7.47436i	0.853366	+	0.379943i
$388$		0			0
$389$	−5.36014	−	1.74162i	−0.271770	−	0.0883034i	0.169962	−	0.985451i	$-0.445636\pi$
$389$	−5.36014	−	1.74162i	−0.271770	−	0.0883034i	−0.441732	+	0.897147i	$0.645636\pi$
$390$		0			0
$391$	5.50773	−	7.58074i	0.278538	−	0.383374i
$392$		0			0
$393$	13.3144	+	11.9884i	0.671624	+	0.604733i
$394$		0			0
$395$	−0.918869	−	0.918869i	−0.0462333	−	0.0462333i
$396$		0			0
$397$	−20.2433	+	5.42418i	−1.01598	+	0.272232i	−0.728127	−	0.685442i	$-0.759609\pi$
$397$	−20.2433	+	5.42418i	−1.01598	+	0.272232i	−0.287855	+	0.957674i	$0.592942\pi$
$398$		0			0
$399$	−0.0160911	−	0.00342027i	−0.000805562	−	0.000171227i
$400$		0			0
$401$	−17.7454	+	14.3699i	−0.886161	+	0.717599i	−0.960098	−	0.279664i	$-0.909777\pi$
$401$	−17.7454	+	14.3699i	−0.886161	+	0.717599i	0.0739367	+	0.997263i	$0.476444\pi$
$402$		0			0
$403$	−14.3865	−	6.39165i	−0.716641	−	0.318391i
$404$		0			0
$405$	−1.98001	+	0.760054i	−0.0983874	+	0.0377674i
$406$		0			0
$407$	−5.82552	+	18.4943i	−0.288760	+	0.916727i
$408$		0			0
$409$	−18.6974	+	23.0894i	−0.924528	+	1.14170i	0.0650763	+	0.997880i	$0.479271\pi$
$409$	−18.6974	+	23.0894i	−0.924528	+	1.14170i	−0.989604	+	0.143817i	$0.954062\pi$
$410$		0			0
$411$	−13.2445	+	6.74841i	−0.653303	+	0.332875i
$412$		0			0
$413$	−0.171615	+	1.63281i	−0.00844463	+	0.0803453i
$414$		0			0
$415$	−0.942670	−	2.90124i	−0.0462738	−	0.142416i
$416$		0			0
$417$		−	5.67762i		−	0.278034i
$418$		0			0
$419$	9.47878	+	16.4177i	0.463069	+	0.802058i	0.999112	−	0.0421321i	$-0.0134150\pi$
$419$	9.47878	+	16.4177i	0.463069	+	0.802058i	−0.536043	+	0.844190i	$0.680082\pi$
$420$		0			0
$421$	10.5458	+	5.37336i	0.513972	+	0.261882i	0.691683	−	0.722201i	$-0.256869\pi$
$421$	10.5458	+	5.37336i	0.513972	+	0.261882i	−0.177712	+	0.984083i	$0.556869\pi$
$422$		0			0
$423$	−9.89775	−	3.79939i	−0.481245	−	0.184733i
$424$		0			0
$425$	−5.91136	+	5.32261i	−0.286743	+	0.258185i
$426$		0			0
$427$	−0.670208	−	1.74595i	−0.0324336	−	0.0844925i
$428$		0			0
$429$	−16.9452	+	19.1944i	−0.818121	+	0.926716i
$430$		0			0
$431$	−1.73408	−	4.51743i	−0.0835277	−	0.217597i	0.885455	−	0.464725i	$-0.153847\pi$
$431$	−1.73408	−	4.51743i	−0.0835277	−	0.217597i	−0.968983	+	0.247128i	$0.920513\pi$
$432$		0			0
$433$	25.1022	−	22.6021i	1.20633	−	1.08619i	0.212291	−	0.977207i	$-0.431908\pi$
$433$	25.1022	−	22.6021i	1.20633	−	1.08619i	0.994044	−	0.108982i	$-0.0347591\pi$
$434$		0			0
$435$	−2.05758	−	0.789833i	−0.0986536	−	0.0378696i
$436$		0			0
$437$	−0.0425807	−	0.0216960i	−0.00203691	−	0.00103786i
$438$		0			0
$439$	−5.20052	−	9.00756i	−0.248207	−	0.429907i	0.714821	−	0.699307i	$-0.246508\pi$
$439$	−5.20052	−	9.00756i	−0.248207	−	0.429907i	−0.963028	+	0.269400i	$0.913175\pi$
$440$		0			0
$441$			9.69010i			0.461434i
$442$		0			0
$443$	−4.30285	−	13.2428i	−0.204435	−	0.629185i	−0.999736	−	0.0229710i	$-0.992687\pi$
$443$	−4.30285	−	13.2428i	−0.204435	−	0.629185i	0.795302	−	0.606214i	$-0.207313\pi$
$444$		0			0
$445$	−0.111662	+	1.06240i	−0.00529331	+	0.0503625i
$446$		0			0
$447$	−0.313589	+	0.159781i	−0.0148322	+	0.00755740i
$448$		0			0
$449$	−16.5213	+	20.4021i	−0.779689	+	0.962836i	−0.999920	−	0.0126115i	$-0.995986\pi$
$449$	−16.5213	+	20.4021i	−0.779689	+	0.962836i	0.220231	+	0.975448i	$0.429319\pi$
$450$		0			0
$451$	−11.7005	−	34.9364i	−0.550953	−	1.64509i
$452$		0			0
$453$	21.9264	−	8.41677i	1.03019	−	0.395454i
$454$		0			0
$455$	−0.0995369	+	0.631684i	−0.00466636	+	0.0296138i
$456$		0			0
$457$	−24.2561	+	19.6422i	−1.13465	+	0.918822i	−0.997425	−	0.0717179i	$-0.977152\pi$
$457$	−24.2561	+	19.6422i	−1.13465	+	0.918822i	−0.137226	+	0.990540i	$0.543819\pi$
$458$		0			0
$459$	4.75049	+	1.00975i	0.221734	+	0.0471310i
$460$		0			0
$461$	21.5571	−	5.77620i	1.00401	−	0.269024i	0.280887	−	0.959741i	$-0.409371\pi$
$461$	21.5571	−	5.77620i	1.00401	−	0.269024i	0.723125	+	0.690717i	$0.242705\pi$
$462$		0			0
$463$	−24.8262	−	24.8262i	−1.15377	−	1.15377i	−0.985790	−	0.167980i	$-0.946276\pi$
$463$	−24.8262	−	24.8262i	−1.15377	−	1.15377i	−0.167980	−	0.985790i	$-0.553724\pi$
$464$		0			0
$465$	1.31054	+	1.18002i	0.0607749	+	0.0547220i
$466$		0			0
$467$	−4.62639	+	6.36768i	−0.214084	+	0.294661i	−0.902531	−	0.430626i	$-0.858293\pi$
$467$	−4.62639	+	6.36768i	−0.214084	+	0.294661i	0.688447	+	0.725287i	$0.258293\pi$
$468$		0			0
$469$	7.70204	+	2.50254i	0.355647	+	0.115557i
$470$		0			0
$471$	−3.24591	−	1.44517i	−0.149564	−	0.0665900i
$472$		0			0
$473$	37.2453	+	9.62115i	1.71254	+	0.442381i
$474$		0			0
$475$	0.0315279	+	0.0255308i	0.00144660	+	0.00117143i
$476$		0			0
$477$	14.6700	+	16.2926i	0.671691	+	0.745989i
$478$		0			0
$479$	25.0686	+	30.9571i	1.14541	+	1.41447i	0.894849	+	0.446368i	$0.147283\pi$
$479$	25.0686	+	30.9571i	1.14541	+	1.41447i	0.250564	+	0.968100i	$0.419384\pi$
$480$		0			0
$481$	−15.6538	+	14.1171i	−0.713750	+	0.643686i
$482$		0			0
$483$	3.04692	−	11.3712i	0.138640	−	0.517410i
$484$		0			0
$485$	1.11882	+	0.645952i	0.0508031	+	0.0293312i
$486$		0			0
$487$	21.0248	−	13.6537i	0.952727	−	0.618708i	0.0281091	−	0.999605i	$-0.491051\pi$
$487$	21.0248	−	13.6537i	0.952727	−	0.618708i	0.924617	+	0.380897i	$0.124385\pi$
$488$		0			0
$489$	7.31595	+	46.1911i	0.330839	+	2.08883i
$490$		0			0
$491$	−35.1062	+	7.46205i	−1.58432	+	0.336758i	−0.914127	−	0.405429i	$-0.867122\pi$
$491$	−35.1062	+	7.46205i	−1.58432	+	0.336758i	−0.670193	+	0.742186i	$0.733789\pi$
$492$		0			0
$493$	5.13917	+	7.07346i	0.231457	+	0.318573i
$494$		0			0
$495$	0.853966	−	0.503347i	0.0383829	−	0.0226238i
$496$		0			0
$497$	−1.23596	+	2.77601i	−0.0554404	+	0.124521i
$498$		0			0
$499$	−4.64642	−	9.11911i	−0.208002	−	0.408227i	0.763311	−	0.646031i	$-0.223572\pi$
$499$	−4.64642	−	9.11911i	−0.208002	−	0.408227i	−0.971313	+	0.237804i	$0.923572\pi$
$500$		0			0
$501$	−0.856345	+	2.23086i	−0.0382587	+	0.0996673i
$502$		0			0
$503$	−0.395606	+	1.86118i	−0.0176392	+	0.0829859i	−0.986087	−	0.166232i	$-0.946840\pi$
$503$	−0.395606	+	1.86118i	−0.0176392	+	0.0829859i	0.968448	+	0.249218i	$0.0801734\pi$
$504$		0			0
$505$	1.28109	+	0.343266i	0.0570076	+	0.0152751i
$506$		0			0
$507$	−26.4585	+	8.64319i	−1.17507	+	0.383858i
$508$		0			0
$509$	1.92111	+	36.6569i	0.0851515	+	1.62479i	0.623331	+	0.781958i	$0.285779\pi$
$509$	1.92111	+	36.6569i	0.0851515	+	1.62479i	−0.538180	+	0.842830i	$0.680888\pi$
$510$		0			0
$511$	1.98520	+	4.45883i	0.0878201	+	0.197247i
$512$		0			0
$513$	0.00129632	−	0.0247353i	5.72340e−5	−	0.00109209i
$514$		0			0
$515$	1.43480	+	0.227250i	0.0632248	+	0.0100138i
$516$		0			0
$517$	−21.7491	−	4.41854i	−0.956522	−	0.194327i
$518$		0			0
$519$	−2.26333	+	1.64441i	−0.0993493	+	0.0721815i
$520$		0			0
$521$	−2.94005	+	9.04855i	−0.128806	+	0.396424i	−0.994575	−	0.104019i	$-0.966830\pi$
$521$	−2.94005	+	9.04855i	−0.128806	+	0.396424i	0.865769	+	0.500443i	$0.166830\pi$
$522$		0			0
$523$	−6.40683	−	0.673385i	−0.280151	−	0.0294451i	−0.0365892	−	0.999330i	$-0.511649\pi$
$523$	−6.40683	−	0.673385i	−0.280151	−	0.0294451i	−0.243562	+	0.969885i	$0.578316\pi$
$524$		0			0
$525$	−4.53703	+	8.90442i	−0.198012	+	0.388621i
$526$		0			0
$527$	−1.81068	−	6.75755i	−0.0788745	−	0.294364i
$528$		0			0
$529$	5.59959	−	9.69877i	0.243460	−	0.421686i
$530$		0			0
$531$	2.76291	−	0.144798i	0.119900	−	0.00628370i
$532$		0			0
$533$	8.29656	−	39.1846i	0.359364	−	1.69727i
$534$		0			0
$535$	−2.61908	−	1.70085i	−0.113233	−	0.0735341i
$536$		0			0
$537$	11.7128	−	1.23106i	0.505443	−	0.0531243i
$538$		0			0
$539$	3.35354	+	20.0055i	0.144447	+	0.861697i
$540$		0			0
$541$	0.590010	−	3.72518i	0.0253665	−	0.160158i	−0.971753	−	0.235998i	$-0.924164\pi$
$541$	0.590010	−	3.72518i	0.0253665	−	0.160158i	0.997120	+	0.0758406i	$0.0241640\pi$
$542$		0			0
$543$	4.60778	+	21.6779i	0.197739	+	0.930288i
$544$		0			0
$545$	−0.885484	−	0.643342i	−0.0379300	−	0.0275577i
$546$		0			0
$547$	−2.78066	+	0.903490i	−0.118892	+	0.0386305i	−0.367859	−	0.929882i	$-0.619909\pi$
$547$	−2.78066	+	0.903490i	−0.118892	+	0.0386305i	0.248967	+	0.968512i	$0.419909\pi$
$548$		0			0
$549$	−2.72931	+	1.57577i	−0.116484	+	0.0672521i
$550$		0			0
$551$	0.0315310	−	0.0315310i	0.00134327	−	0.00134327i
$552$		0			0
$553$	3.52741	+	5.43174i	0.150001	+	0.230981i
$554$		0			0
$555$	2.15720	−	0.960448i	0.0915681	−	0.0407687i
$556$		0			0
$557$	22.6233	−	34.8368i	0.958579	−	1.47608i	0.0809641	−	0.996717i	$-0.474200\pi$
$557$	22.6233	−	34.8368i	0.958579	−	1.47608i	0.877615	−	0.479366i	$-0.159133\pi$
$558$		0			0
$559$	29.5939	+	29.5471i	1.25169	+	1.24971i
$560$		0			0
$561$	−11.3677	−	0.493132i	−0.479946	−	0.0208201i
$562$		0			0
$563$	−2.54533	−	24.2172i	−0.107273	−	1.02063i	−0.907247	−	0.420599i	$-0.861820\pi$
$563$	−2.54533	−	24.2172i	−0.107273	−	1.02063i	0.799974	−	0.600035i	$-0.204847\pi$
$564$		0			0
$565$	−2.77720	−	0.145547i	−0.116838	−	0.00612320i
$566$		0			0
$567$	10.4403	−	1.65358i	0.438452	−	0.0694440i
$568$		0			0
$569$	8.93350	−	9.92166i	0.374512	−	0.415938i	−0.526196	−	0.850364i	$-0.676382\pi$
$569$	8.93350	−	9.92166i	0.374512	−	0.415938i	0.900708	+	0.434426i	$0.143049\pi$
$570$		0			0
$571$	39.3734			1.64772			0.823862	−	0.566791i	$-0.191815\pi$
$571$	39.3734			1.64772			0.823862	+	0.566791i	$0.191815\pi$
$572$		0			0
$573$	−20.1159			−0.840355
$574$		0			0
$575$	−19.4262	+	21.5749i	−0.810126	+	0.899737i
$576$		0			0
$577$	2.12669	−	0.336835i	0.0885353	−	0.0140226i	−0.112010	−	0.993707i	$-0.535729\pi$
$577$	2.12669	−	0.336835i	0.0885353	−	0.0140226i	0.200545	+	0.979685i	$0.435729\pi$
$578$		0			0
$579$	−28.2777	−	1.48197i	−1.17518	−	0.0615887i
$580$		0			0
$581$	1.58924	+	15.1206i	0.0659330	+	0.627310i
$582$		0			0
$583$	35.9250	+	28.5596i	1.48786	+	1.18282i
$584$		0			0
$585$	1.07762		0.000852173i	0.0445543		3.52330e-5i
$586$		0			0
$587$	6.29336	−	9.69092i	0.259755	−	0.399987i	−0.684598	−	0.728920i	$-0.740022\pi$
$587$	6.29336	−	9.69092i	0.259755	−	0.399987i	0.944353	+	0.328933i	$0.106689\pi$
$588$		0			0
$589$	−0.0325953	+	0.0145123i	−0.00134306	+	0.000597971i
$590$		0			0
$591$	−1.09874	−	1.69191i	−0.0451960	−	0.0695958i
$592$		0			0
$593$	−13.4004	+	13.4004i	−0.550288	+	0.550288i	−0.926524	−	0.376236i	$-0.877218\pi$
$593$	−13.4004	+	13.4004i	−0.550288	+	0.550288i	0.376236	+	0.926524i	$0.377218\pi$
$594$		0			0
$595$	−0.246111	+	0.142092i	−0.0100896	+	0.00582521i
$596$		0			0
$597$	6.12971	−	1.99167i	0.250873	−	0.0815134i
$598$		0			0
$599$	−2.92583	−	2.12574i	−0.119546	−	0.0868554i	0.526406	−	0.850234i	$-0.323539\pi$
$599$	−2.92583	−	2.12574i	−0.119546	−	0.0868554i	−0.645952	+	0.763378i	$0.723539\pi$
$600$		0			0
$601$	0.903563	+	4.25093i	0.0368571	+	0.173399i	0.992726	−	0.120394i	$-0.0384157\pi$
$601$	0.903563	+	4.25093i	0.0368571	+	0.173399i	−0.955869	+	0.293793i	$0.905082\pi$
$602$		0			0
$603$	2.13488	−	13.4791i	0.0869390	−	0.548911i
$604$		0			0
$605$	1.58884	−	1.33471i	0.0645954	−	0.0542638i
$606$		0			0
$607$	14.7059	−	1.54566i	0.596896	−	0.0627363i	0.198737	−	0.980053i	$-0.436316\pi$
$607$	14.7059	−	1.54566i	0.596896	−	0.0627363i	0.398159	+	0.917317i	$0.369649\pi$
$608$		0			0
$609$	9.21247	+	5.98265i	0.373308	+	0.242429i
$610$		0			0
$611$	−17.9424	−	16.1297i	−0.725872	−	0.652539i
$612$		0			0
$613$	−31.9342	+	1.67360i	−1.28981	+	0.0675960i	−0.684864	−	0.728671i	$-0.740138\pi$
$613$	−31.9342	+	1.67360i	−1.28981	+	0.0675960i	−0.604945	+	0.796267i	$0.706805\pi$
$614$		0			0
$615$	−2.24344	+	3.88575i	−0.0904641	+	0.156688i
$616$		0			0
$617$	−1.72038	−	6.42054i	−0.0692598	−	0.258481i	0.922611	−	0.385732i	$-0.126051\pi$
$617$	−1.72038	−	6.42054i	−0.0692598	−	0.258481i	−0.991871	+	0.127251i	$0.959385\pi$
$618$		0			0
$619$	7.10914	−	13.9525i	0.285740	−	0.560797i	−0.702866	−	0.711322i	$-0.748097\pi$
$619$	7.10914	−	13.9525i	0.285740	−	0.560797i	0.988606	+	0.150526i	$0.0480966\pi$
$620$		0			0
$621$	17.6283	+	1.85281i	0.707399	+	0.0743506i
$622$		0			0
$623$	1.64526	−	5.06358i	0.0659159	−	0.202868i
$624$		0			0
$625$	19.7946	−	14.3816i	0.791784	−	0.575265i
$626$		0			0
$627$	0.00658548	+	0.0576562i	0.000262999	+	0.00230257i
$628$		0			0
$629$	−9.25228	−	1.46542i	−0.368912	−	0.0584300i
$630$		0			0
$631$	−0.489259	+	9.33563i	−0.0194771	+	0.371645i	0.971450	+	0.237245i	$0.0762443\pi$
$631$	−0.489259	+	9.33563i	−0.0194771	+	0.371645i	−0.990927	+	0.134401i	$0.957089\pi$
$632$		0			0
$633$	6.48610	+	14.5680i	0.257799	+	0.579027i
$634$		0			0
$635$	−0.0295905	−	0.564621i	−0.00117426	−	0.0224063i
$636$		0			0
$637$	−7.88634	+	20.5933i	−0.312468	+	0.815935i
$638$		0			0
$639$	4.94626	+	1.32535i	0.195671	+	0.0524298i
$640$		0			0
$641$	3.16590	−	14.8944i	0.125046	−	0.588293i	−0.870349	−	0.492435i	$-0.836107\pi$
$641$	3.16590	−	14.8944i	0.125046	−	0.588293i	0.995395	−	0.0958585i	$-0.0305596\pi$
$642$		0			0
$643$	7.18109	−	18.7074i	0.283195	−	0.737747i	−0.716018	−	0.698081i	$-0.754037\pi$
$643$	7.18109	−	18.7074i	0.283195	−	0.737747i	0.999213	−	0.0396658i	$-0.0126293\pi$
$644$		0			0
$645$	−2.12680	−	4.17408i	−0.0837427	−	0.164354i
$646$		0			0
$647$	−14.4407	+	32.4344i	−0.567723	+	1.27513i	0.370415	+	0.928866i	$0.379215\pi$
$647$	−14.4407	+	32.4344i	−0.567723	+	1.27513i	−0.938138	+	0.346261i	$0.887451\pi$
$648$		0			0
$649$	5.65399	−	1.25512i	0.221939	−	0.0492679i
$650$		0			0
$651$	−5.16625	−	7.11073i	−0.202481	−	0.278691i
$652$		0			0
$653$	−14.3790	+	3.05636i	−0.562695	+	0.119605i	−0.480473	−	0.877010i	$-0.659535\pi$
$653$	−14.3790	+	3.05636i	−0.562695	+	0.119605i	−0.0822221	+	0.996614i	$0.526202\pi$
$654$		0			0
$655$	−0.246933	−	1.55907i	−0.00964846	−	0.0609180i
$656$		0			0
$657$	6.89801	−	4.47962i	0.269117	−	0.174767i
$658$		0			0
$659$	−26.4838	−	15.2904i	−1.03166	−	0.595631i	−0.114203	−	0.993457i	$-0.536431\pi$
$659$	−26.4838	−	15.2904i	−1.03166	−	0.595631i	−0.917461	+	0.397826i	$0.869765\pi$
$660$		0			0
$661$	−8.11588	+	30.2889i	−0.315671	+	1.17810i	0.607692	+	0.794173i	$0.292096\pi$
$661$	−8.11588	+	30.2889i	−0.315671	+	1.17810i	−0.923363	+	0.383928i	$0.874571\pi$
$662$		0			0
$663$	−10.3794	−	6.72879i	−0.403102	−	0.261325i
$664$		0			0
$665$	0.000912116		0.00112637i	3.53703e−5		4.36787e-5i
$666$		0			0
$667$	21.3524	+	23.7143i	0.826769	+	0.918220i
$668$		0			0
$669$	−28.3559	−	22.9622i	−1.09630	−	0.887769i
$670$		0			0
$671$	−5.08939	+	4.19777i	−0.196474	+	0.162053i
$672$		0			0
$673$	−0.518130	−	0.230686i	−0.0199725	−	0.00889231i	0.396726	−	0.917937i	$-0.370146\pi$
$673$	−0.518130	−	0.230686i	−0.0199725	−	0.00889231i	−0.416699	+	0.909045i	$0.636813\pi$
$674$		0			0
$675$	−14.3108	−	4.64985i	−0.550821	−	0.178973i
$676$		0			0
$677$	18.3723	−	25.2874i	0.706106	−	0.971872i	−0.293766	−	0.955877i	$-0.594909\pi$
$677$	18.3723	−	25.2874i	0.706106	−	0.971872i	0.999872	−	0.0159945i	$-0.00509143\pi$
$678$		0			0
$679$	−4.78501	−	4.30844i	−0.183632	−	0.165343i
$680$		0			0
$681$	−3.02312	−	3.02312i	−0.115846	−	0.115846i
$682$		0			0
$683$	30.9097	−	8.28222i	1.18273	−	0.316910i	0.386718	−	0.922198i	$-0.373609\pi$
$683$	30.9097	−	8.28222i	1.18273	−	0.316910i	0.796007	+	0.605288i	$0.206942\pi$
$684$		0			0
$685$	1.28102	+	0.272290i	0.0489453	+	0.0104037i
$686$		0			0
$687$	−34.2467	+	27.7324i	−1.30659	+	1.05806i
$688$		0			0
$689$	17.9165	+	46.5641i	0.682566	+	1.77395i
$690$		0			0
$691$	8.06797	−	3.09700i	0.306920	−	0.117816i	−0.200033	−	0.979789i	$-0.564105\pi$
$691$	8.06797	−	3.09700i	0.306920	−	0.117816i	0.506953	+	0.861974i	$0.330772\pi$
$692$		0			0
$693$	−4.68475	+	1.56896i	−0.177959	+	0.0595998i
$694$		0			0
$695$	−0.314800	+	0.388746i	−0.0119411	+	0.0147460i
$696$		0			0
$697$	15.8596	−	8.08088i	0.600726	−	0.306085i
$698$		0			0
$699$	−0.211206	+	2.00949i	−0.00798853	+	0.0760058i
$700$		0			0
$701$	8.78963	+	27.0517i	0.331980	+	1.02173i	0.968191	+	0.250213i	$0.0805008\pi$
$701$	8.78963	+	27.0517i	0.331980	+	1.02173i	−0.636211	+	0.771515i	$0.719499\pi$
$702$		0			0
$703$			0.0477757i			0.00180190i
$704$		0			0
$705$	1.35137	+	2.34064i	0.0508955	+	0.0881536i
$706$		0			0
$707$	−5.88972	−	3.00096i	−0.221506	−	0.112863i
$708$		0			0
$709$	−6.86829	−	2.63649i	−0.257944	−	0.0990155i	0.225960	−	0.974137i	$-0.427448\pi$
$709$	−6.86829	−	2.63649i	−0.257944	−	0.0990155i	−0.483904	+	0.875121i	$0.660782\pi$
$710$		0			0
$711$	8.11078	−	7.30298i	0.304178	−	0.273883i
$712$		0			0
$713$	−9.15033	−	23.8374i	−0.342683	−	0.892719i
$714$		0			0
$715$	2.22449	−	0.374702i	0.0831911	−	0.0140130i
$716$		0			0
$717$	3.20275	+	8.34346i	0.119609	+	0.311592i
$718$		0			0
$719$	−18.3739	+	16.5439i	−0.685231	+	0.616984i	−0.936390	−	0.350961i	$-0.885855\pi$
$719$	−18.3739	+	16.5439i	−0.685231	+	0.616984i	0.251159	+	0.967946i	$0.419188\pi$
$720$		0			0
$721$	−6.75930	−	2.59465i	−0.251730	−	0.0966299i
$722$		0			0
$723$	−42.8046	−	21.8100i	−1.59192	−	0.811123i
$724$		0			0
$725$	−13.5446	−	23.4599i	−0.503034	−	0.871281i
$726$		0			0
$727$			4.95510i			0.183774i	0.995769	+	0.0918872i	$0.0292899\pi$
$727$			4.95510i			0.183774i	−0.995769	+	0.0918872i	$0.970710\pi$
$728$		0			0
$729$	0.511830	+	1.57525i	0.0189567	+	0.0583426i
$730$		0			0
$731$	−1.94260	+	18.4826i	−0.0718496	+	0.683603i
$732$		0			0
$733$	27.0544	−	13.7849i	0.999276	−	0.509157i	0.123743	−	0.992314i	$-0.460510\pi$
$733$	27.0544	−	13.7849i	0.999276	−	0.509157i	0.875533	+	0.483158i	$0.160510\pi$
$734$		0			0
$735$	1.55460	−	1.91978i	0.0573424	−	0.0708120i
$736$		0			0
$737$	−0.257310	−	28.5668i	−0.00947812	−	1.05227i
$738$		0			0
$739$	−41.1710	+	15.8041i	−1.51450	+	0.581361i	−0.966850	−	0.255347i	$-0.917810\pi$
$739$	−41.1710	+	15.8041i	−1.51450	+	0.581361i	−0.547649	+	0.836708i	$0.684477\pi$
$740$		0			0
$741$	−0.0256140	+	0.0576526i	−0.000940954	+	0.00211792i
$742$		0			0
$743$	24.4759	−	19.8202i	0.897934	−	0.727133i	−0.0647097	−	0.997904i	$-0.520612\pi$
$743$	24.4759	−	19.8202i	0.897934	−	0.727133i	0.962644	+	0.270772i	$0.0872788\pi$
$744$		0			0
$745$	0.0303306	+	0.00644697i	0.00111123	+	0.000236199i
$746$		0			0
$747$	24.7481	−	6.63123i	0.905485	−	0.242624i
$748$		0			0
$749$	11.0058	+	11.0058i	0.402142	+	0.402142i
$750$		0			0
$751$	13.2153	+	11.8991i	0.482233	+	0.434204i	0.874048	−	0.485840i	$-0.161486\pi$
$751$	13.2153	+	11.8991i	0.482233	+	0.434204i	−0.391815	+	0.920044i	$0.628153\pi$
$752$		0			0
$753$	21.7135	−	29.8861i	0.791285	−	1.08911i
$754$		0			0
$755$	−1.96798	−	0.639434i	−0.0716220	−	0.0232714i
$756$		0			0
$757$	−32.7788	−	14.5940i	−1.19136	−	0.530430i	−0.287306	−	0.957839i	$-0.592760\pi$
$757$	−32.7788	−	14.5940i	−1.19136	−	0.530430i	−0.904058	+	0.427409i	$0.859426\pi$
$758$		0			0
$759$	−41.4501	+	2.54687i	−1.50454	+	0.0924454i
$760$		0			0
$761$	17.9333	+	14.5221i	0.650081	+	0.526425i	0.896673	−	0.442694i	$-0.145977\pi$
$761$	17.9333	+	14.5221i	0.650081	+	0.526425i	−0.246592	+	0.969119i	$0.579311\pi$
$762$		0			0
$763$	3.65017	+	4.05392i	0.132145	+	0.146762i
$764$		0			0
$765$	0.301379	+	0.372172i	0.0108964	+	0.0134559i
$766$		0			0
$767$	5.98955	+	1.94089i	0.216270	+	0.0700813i
$768$		0			0
$769$	−1.46373	+	5.46272i	−0.0527835	+	0.196991i	−0.987283	−	0.158975i	$-0.949181\pi$
$769$	−1.46373	+	5.46272i	−0.0527835	+	0.196991i	0.934499	+	0.355965i	$0.115848\pi$
$770$		0			0
$771$	−3.93087	−	2.26949i	−0.141567	−	0.0817336i
$772$		0			0
$773$	−28.3342	+	18.4005i	−1.01911	+	0.661819i	−0.942142	−	0.335215i	$-0.891191\pi$
$773$	−28.3342	+	18.4005i	−1.01911	+	0.661819i	−0.0769698	+	0.997033i	$0.524525\pi$
$774$		0			0
$775$	3.39079	+	21.4086i	0.121801	+	0.769019i
$776$		0			0
$777$	−11.5118	+	2.44691i	−0.412984	+	0.0877825i
$778$		0			0
$779$	−0.0533592	−	0.0734427i	−0.00191179	−	0.00263136i
$780$		0			0
$781$	10.6703	+	1.02442i	0.381815	+	0.0366566i
$782$		0			0
$783$	−6.72713	+	15.1094i	−0.240408	+	0.539965i
$784$		0			0
$785$	0.142118	+	0.278923i	0.00507242	+	0.00995519i
$786$		0			0
$787$	−13.4412	+	35.0155i	−0.479126	+	1.24817i	0.454765	+	0.890611i	$0.349723\pi$
$787$	−13.4412	+	35.0155i	−0.479126	+	1.24817i	−0.933892	+	0.357556i	$0.883610\pi$
$788$		0			0
$789$	7.82906	−	36.8328i	0.278722	−	1.31128i
$790$		0			0
$791$	13.3883	+	3.58738i	0.476033	+	0.127553i
$792$		0			0
$793$	−7.08274	+	1.12754i	−0.251515	+	0.0400400i
$794$		0			0
$795$	−0.292508	−	5.58138i	−0.0103742	−	0.197951i
$796$		0			0
$797$	−12.4336	−	27.9263i	−0.440420	−	0.989200i	−0.988283	−	0.152632i	$-0.951225\pi$
$797$	−12.4336	−	27.9263i	−0.440420	−	0.989200i	0.547863	−	0.836568i	$-0.315442\pi$
$798$		0			0
$799$	0.561142	−	10.7072i	0.0198518	−	0.378794i
$800$		0			0
$801$	−8.86162	−	1.40354i	−0.313110	−	0.0495918i
$802$		0			0
$803$	12.6908	−	11.6356i	0.447850	−	0.410610i
$804$		0			0
$805$	−0.839111	+	0.609650i	−0.0295748	+	0.0214873i
$806$		0			0
$807$	9.36744	−	28.8300i	0.329749	−	1.01486i
$808$		0			0
$809$	−3.13873	−	0.329894i	−0.110352	−	0.0115985i	0.0491915	−	0.998789i	$-0.484336\pi$
$809$	−3.13873	−	0.329894i	−0.110352	−	0.0115985i	−0.159543	+	0.987191i	$0.551002\pi$
$810$		0			0
$811$	8.35801	−	16.4035i	0.293489	−	0.576006i	−0.696432	−	0.717623i	$-0.745230\pi$
$811$	8.35801	−	16.4035i	0.293489	−	0.576006i	0.989921	+	0.141617i	$0.0452302\pi$
$812$		0			0
$813$	−13.2803	−	49.5628i	−0.465761	−	1.73824i
$814$		0			0
$815$	2.06018	−	3.56834i	0.0721650	−	0.124994i
$816$		0			0
$817$	0.0946523	−	0.00496052i	0.00331146	−	0.000173547i
$818$		0			0
$819$	−5.25440	−	1.11252i	−0.183604	−	0.0388745i
$820$		0			0
$821$	−9.98058	−	6.48146i	−0.348325	−	0.226205i	0.358604	−	0.933490i	$-0.383253\pi$
$821$	−9.98058	−	6.48146i	−0.348325	−	0.226205i	−0.706928	+	0.707285i	$0.749920\pi$
$822$		0			0
$823$	52.1682	−	5.48310i	1.81847	−	0.191129i	0.866883	−	0.498511i	$-0.166120\pi$
$823$	52.1682	−	5.48310i	1.81847	−	0.191129i	0.951586	+	0.307382i	$0.0994530\pi$
$824$		0			0
$825$	34.8679	+	5.20105i	1.21394	+	0.181077i
$826$		0			0
$827$	−3.10096	+	19.5787i	−0.107831	+	0.680817i	0.873258	+	0.487258i	$0.162003\pi$
$827$	−3.10096	+	19.5787i	−0.107831	+	0.680817i	−0.981089	+	0.193559i	$0.937997\pi$
$828$		0			0
$829$	−7.92960	−	37.3058i	−0.275406	−	1.29569i	−0.870556	−	0.492070i	$-0.836240\pi$
$829$	−7.92960	−	37.3058i	−0.275406	−	1.29569i	0.595149	−	0.803615i	$-0.297093\pi$
$830$		0			0
$831$	−40.8120	−	29.6517i	−1.41575	−	1.02861i
$832$		0			0
$833$	−9.32014	+	3.02830i	−0.322924	+	0.104924i
$834$		0			0
$835$	0.182326	−	0.105266i	0.00630964	−	0.00364287i
$836$		0			0
$837$	9.35778	−	9.35778i	0.323452	−	0.323452i
$838$		0			0
$839$	4.82661	+	7.43233i	0.166633	+	0.256592i	0.912116	−	0.409932i	$-0.134448\pi$
$839$	4.82661	+	7.43233i	0.166633	+	0.256592i	−0.745483	+	0.666525i	$0.767781\pi$
$840$		0			0
$841$	−0.708312	+	0.315361i	−0.0244246	+	0.0108745i
$842$		0			0
$843$	24.2673	−	37.3684i	0.835812	−	1.28704i
$844$		0			0
$845$	2.29084	+	0.875218i	0.0788074	+	0.0301084i
$846$		0			0
$847$	−9.12882	+	4.86045i	−0.313670	+	0.167007i
$848$		0			0
$849$	−0.0287340	−	0.273386i	−0.000986147	−	0.00938257i
$850$		0			0
$851$	−34.1425	−	1.78933i	−1.17039	−	0.0613375i
$852$		0			0
$853$	37.3408	−	5.91420i	1.27852	−	0.202498i	0.520013	−	0.854158i	$-0.325927\pi$
$853$	37.3408	−	5.91420i	1.27852	−	0.202498i	0.758512	+	0.651660i	$0.225927\pi$
$854$		0			0
$855$	0.00163430	−	0.00181507i	5.58918e−5	−	6.20741e-5i
$856$		0			0
$857$	−8.83344			−0.301745			−0.150872	−	0.988553i	$-0.548208\pi$
$857$	−8.83344			−0.301745			−0.150872	+	0.988553i	$0.548208\pi$
$858$		0			0
$859$	34.2215			1.16762			0.583811	−	0.811889i	$-0.301561\pi$
$859$	34.2215			1.16762			0.583811	+	0.811889i	$0.301561\pi$
$860$		0			0
$861$	14.9635	−	16.6187i	0.509955	−	0.566363i
$862$		0			0
$863$	1.60127	−	0.253616i	0.0545079	−	0.00863320i	−0.129121	−	0.991629i	$-0.541216\pi$
$863$	1.60127	−	0.253616i	0.0545079	−	0.00863320i	0.183629	+	0.982996i	$0.441216\pi$
$864$		0			0
$865$	0.246146	+	0.0129000i	0.00836922	+	0.000438612i
$866$		0			0
$867$	3.23013	+	30.7326i	0.109701	+	1.04373i
$868$		0			0
$869$	14.2175	−	17.8842i	0.482296	−	0.606679i
$870$		0			0
$871$	15.5070	−	26.9081i	0.525436	−	0.911747i
$872$		0			0
$873$	−5.90962	+	9.10002i	−0.200010	+	0.307989i
$874$		0			0
$875$	1.61449	−	0.718818i	0.0545798	−	0.0243005i
$876$		0			0
$877$	20.2557	+	31.1910i	0.683986	+	1.05325i	0.994708	+	0.102745i	$0.0327626\pi$
$877$	20.2557	+	31.1910i	0.683986	+	1.05325i	−0.310722	+	0.950501i	$0.600571\pi$
$878$		0			0
$879$	−37.6305	+	37.6305i	−1.26925	+	1.26925i
$880$		0			0
$881$	22.8226	−	13.1766i	0.768912	−	0.443932i	−0.0635741	−	0.997977i	$-0.520250\pi$
$881$	22.8226	−	13.1766i	0.768912	−	0.443932i	0.832487	+	0.554045i	$0.186917\pi$
$882$		0			0
$883$	−28.9078	+	9.39273i	−0.972826	+	0.316090i	−0.751956	−	0.659213i	$-0.770890\pi$
$883$	−28.9078	+	9.39273i	−0.972826	+	0.316090i	−0.220870	+	0.975303i	$0.570890\pi$
$884$		0			0
$885$	−0.570610	−	0.414573i	−0.0191809	−	0.0139357i
$886$		0			0
$887$	−6.33379	−	29.7981i	−0.212668	−	1.00052i	−0.946876	−	0.321599i	$-0.895780\pi$
$887$	−6.33379	−	29.7981i	−0.212668	−	1.00052i	0.734208	−	0.678924i	$-0.237554\pi$
$888$		0			0
$889$	−0.440823	+	2.78325i	−0.0147847	+	0.0933471i
$890$		0			0
$891$	−17.2271	−	33.0704i	−0.577131	−	1.10790i
$892$		0			0
$893$	−0.0543833	+	0.00571591i	−0.00181987	+	0.000191276i
$894$		0			0
$895$	−0.870230	−	0.565134i	−0.0290886	−	0.0188903i
$896$		0			0
$897$	−40.2416	−	20.4641i	−1.34363	−	0.683275i
$898$		0			0
$899$	23.7921	−	1.24689i	0.793511	−	0.0415861i
$900$		0			0
$901$	−11.0860	+	19.2015i	−0.369329	+	0.639696i
$902$		0			0
$903$	6.04303	+	22.5529i	0.201100	+	0.750514i
$904$		0			0
$905$	0.886455	−	1.73977i	0.0294668	−	0.0578318i
$906$		0			0
$907$	12.1952	+	1.28177i	0.404936	+	0.0425605i	0.304808	−	0.952414i	$-0.401408\pi$
$907$	12.1952	+	1.28177i	0.404936	+	0.0425605i	0.100129	+	0.994974i	$0.468075\pi$
$908$		0			0
$909$	−3.44221	+	10.5940i	−0.114171	+	0.351382i
$910$		0			0
$911$	−40.3741	+	29.3335i	−1.33765	+	0.971863i	−0.338128	+	0.941100i	$0.609794\pi$
$911$	−40.3741	+	29.3335i	−1.33765	+	0.971863i	−0.999527	+	0.0307625i	$0.990206\pi$
$912$		0			0
$913$	48.7982	−	22.2551i	1.61498	−	0.736537i
$914$		0			0
$915$	0.793527	+	0.125682i	0.0262332	+	0.00415493i
$916$		0			0
$917$	−0.411742	+	7.85651i	−0.0135969	+	0.259445i
$918$		0			0
$919$	11.5075	+	25.8463i	0.379597	+	0.852589i	0.997783	+	0.0665570i	$0.0212014\pi$
$919$	11.5075	+	25.8463i	0.379597	+	0.852589i	−0.618185	+	0.786032i	$0.712132\pi$
$920$		0			0
$921$	−1.39082	−	26.5385i	−0.0458291	−	0.874472i
$922$		0			0
$923$	9.43307	+	6.84214i	0.310493	+	0.225212i
$924$		0			0
$925$	28.0346	+	7.51185i	0.921773	+	0.246988i
$926$		0			0
$927$	−2.53671	+	11.9343i	−0.0833165	+	0.391973i
$928$		0			0
$929$	7.96590	−	20.7519i	0.261353	−	0.680847i	−0.738625	−	0.674117i	$-0.764524\pi$
$929$	7.96590	−	20.7519i	0.261353	−	0.680847i	0.999977	−	0.00673021i	$-0.00214231\pi$
$930$		0			0
$931$	0.0226904	+	0.0445323i	0.000743647	+	0.00145949i
$932$		0			0
$933$	13.6547	−	30.6690i	0.447035	−	1.00406i
$934$		0			0
$935$	0.751006	+	0.664059i	0.0245605	+	0.0217170i
$936$		0			0
$937$	−9.89376	−	13.6176i	−0.323215	−	0.444867i	0.616230	−	0.787566i	$-0.288659\pi$
$937$	−9.89376	−	13.6176i	−0.323215	−	0.444867i	−0.939445	+	0.342699i	$0.888659\pi$
$938$		0			0
$939$	66.6893	−	14.1752i	2.17632	−	0.462592i
$940$		0			0
$941$	1.21435	+	7.66712i	0.0395868	+	0.249941i	0.999544	−	0.0302067i	$-0.00961657\pi$
$941$	1.21435	+	7.66712i	0.0395868	+	0.249941i	−0.959957	+	0.280148i	$0.909617\pi$
$942$		0			0
$943$	54.4836	−	35.3820i	1.77423	−	1.15220i
$944$		0			0
$945$	−0.465557	−	0.268789i	−0.0151446	−	0.00874372i
$946$		0			0
$947$	10.7296	−	40.0435i	0.348666	−	1.30124i	−0.539605	−	0.841918i	$-0.681427\pi$
$947$	10.7296	−	40.0435i	0.348666	−	1.30124i	0.888271	−	0.459320i	$-0.151907\pi$
$948$		0			0
$949$	18.3053	−	3.90605i	0.594216	−	0.126796i
$950$		0			0
$951$	−30.4630	−	37.6187i	−0.987831	−	1.21987i
$952$		0			0
$953$	13.6365	+	15.1449i	0.441731	+	0.490592i	0.922360	−	0.386332i	$-0.126258\pi$
$953$	13.6365	+	15.1449i	0.441731	+	0.490592i	−0.480629	+	0.876924i	$0.659591\pi$
$954$		0			0
$955$	1.37734	+	1.11535i	0.0445696	+	0.0360917i
$956$		0			0
$957$	9.69155	−	37.5178i	0.313283	−	1.21278i
$958$		0			0
$959$	−5.96295	−	2.65488i	−0.192554	−	0.0857305i
$960$		0			0
$961$	11.3524	+	3.68862i	0.366207	+	0.118988i
$962$		0			0
$963$	15.4169	−	21.2195i	0.496801	−	0.683789i
$964$		0			0
$965$	1.85400	+	1.66935i	0.0596825	+	0.0537384i
$966$		0			0
$967$	37.6779	+	37.6779i	1.21164	+	1.21164i	0.970487	+	0.241154i	$0.0775258\pi$
$967$	37.6779	+	37.6779i	1.21164	+	1.21164i	0.241154	+	0.970487i	$0.422474\pi$
$968$		0			0
$969$	−0.0270803	+	0.00725616i	−0.000869946	+	0.000233101i
$970$		0			0
$971$	−20.3956	−	4.33523i	−0.654528	−	0.139124i	−0.131334	−	0.991338i	$-0.541926\pi$
$971$	−20.3956	−	4.33523i	−0.654528	−	0.139124i	−0.523193	+	0.852214i	$0.675259\pi$
$972$		0			0
$973$	1.93752	−	1.56897i	0.0621139	−	0.0502988i
$974$		0			0
$975$	29.8030	+	24.0950i	0.954461	+	0.771658i
$976$		0			0
$977$	1.36717	−	0.524808i	0.0437397	−	0.0167901i	−0.336400	−	0.941719i	$-0.609209\pi$
$977$	1.36717	−	0.524808i	0.0437397	−	0.0167901i	0.380139	+	0.924929i	$0.375876\pi$
$978$		0			0
$979$	−18.7808	+	0.169164i	−0.600237	+	0.00540651i
$980$		0			0
$981$	5.78516	−	7.14408i	0.184706	−	0.228093i
$982$		0			0
$983$	47.4174	−	24.1604i	1.51238	−	0.770596i	0.516080	−	0.856540i	$-0.327391\pi$
$983$	47.4174	−	24.1604i	1.51238	−	0.770596i	0.996300	+	0.0859441i	$0.0273907\pi$
$984$		0			0
$985$	−0.0185788	+	0.176765i	−0.000591969	+	0.00563221i
$986$		0			0
$987$	−4.16261	−	12.8112i	−0.132497	−	0.407785i
$988$		0			0
$989$			67.8282i			2.15681i
$990$		0			0
$991$	−24.1012	−	41.7445i	−0.765601	−	1.32606i	−0.939928	−	0.341372i	$-0.889109\pi$
$991$	−24.1012	−	41.7445i	−0.765601	−	1.32606i	0.174328	−	0.984688i	$-0.444225\pi$
$992$		0			0
$993$	−55.0602	−	28.0546i	−1.74728	−	0.890285i
$994$		0			0
$995$	−0.530131	−	0.203498i	−0.0168063	−	0.00645132i
$996$		0			0
$997$	−31.5608	+	28.4175i	−0.999542	+	0.899992i	−0.994988	−	0.0999979i	$-0.968116\pi$
$997$	−31.5608	+	28.4175i	−0.999542	+	0.899992i	−0.00455446	+	0.999990i	$0.501450\pi$
$998$		0			0
$999$	−6.35039	−	16.5433i	−0.200917	−	0.523408i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bv.a.41.12	✓	224
11.7	odd	10	inner	572.2.bv.a.249.3	yes	224
13.7	odd	12	inner	572.2.bv.a.85.3	yes	224
143.7	even	60	inner	572.2.bv.a.293.12	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bv.a.41.12	✓	224	1.1	even	1	trivial
572.2.bv.a.85.3	yes	224	13.7	odd	12	inner
572.2.bv.a.249.3	yes	224	11.7	odd	10	inner
572.2.bv.a.293.12	yes	224	143.7	even	60	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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bv (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(1.43269 - 1.59116i) q^{3} +(-0.186319 + 0.0295100i) q^{5} +(0.938903 + 0.0492058i) q^{7} +(-0.165612 - 1.57570i) q^{9} +O(q^{10})\)	\(q+(1.43269 - 1.59116i) q^{3} +(-0.186319 + 0.0295100i) q^{5} +(0.938903 + 0.0492058i) q^{7} +(-0.165612 - 1.57570i) q^{9} +(-0.887226 - 3.19575i) q^{11} +(0.930431 - 3.48343i) q^{13} +(-0.219982 + 0.338742i) q^{15} +(1.46378 - 0.651717i) q^{17} +(-0.00445075 - 0.00685355i) q^{19} +(1.42345 - 1.42345i) q^{21} +(5.06452 - 2.92400i) q^{23} +(-4.72144 + 1.53409i) q^{25} +(2.45214 + 1.78159i) q^{27} +(1.13451 + 5.33744i) q^{29} +(0.683018 - 4.31241i) q^{31} +(-6.35606 - 3.16679i) q^{33} +(-0.176388 + 0.0185391i) q^{35} +(-4.90314 - 3.18414i) q^{37} +(-4.20968 - 6.47113i) q^{39} +(11.0936 - 0.581388i) q^{41} +(-5.79926 + 10.0446i) q^{43} +(0.0773556 + 0.288695i) q^{45} +(3.03790 - 5.96221i) q^{47} +(-6.08254 - 0.639300i) q^{49} +(1.06015 - 3.26281i) q^{51} +(-11.1948 + 8.13352i) q^{53} +(0.259614 + 0.569248i) q^{55} +(-0.0172816 - 0.00273714i) q^{57} +(-0.0913913 + 1.74385i) q^{59} +(-0.809054 - 1.81716i) q^{61} +(-0.0779605 - 1.48758i) q^{63} +(-0.0705608 + 0.676487i) q^{65} +(8.32006 + 2.22935i) q^{67} +(2.60332 - 12.2476i) q^{69} +(-1.15825 + 3.01735i) q^{71} +(2.35679 + 4.62547i) q^{73} +(-4.32336 + 9.71043i) q^{75} +(-0.675769 - 3.04416i) q^{77} +(4.04902 + 5.57300i) q^{79} +(10.9972 - 2.33753i) q^{81} +(2.52972 + 15.9720i) q^{83} +(-0.253498 + 0.164624i) q^{85} +(10.1181 + 5.84169i) q^{87} +(1.46565 - 5.46989i) q^{89} +(1.04499 - 3.22482i) q^{91} +(-5.88318 - 7.26512i) q^{93} +(0.00103151 + 0.00114561i) q^{95} +(-5.32225 - 4.30987i) q^{97} +(-4.88860 + 1.92725i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 28 q^{9}+O(q^{10}) \) 224 * q + 28 * q^9	\( 224 q + 28 q^{9} + 16 q^{11} + 10 q^{13} - 28 q^{15} - 48 q^{23} + 24 q^{27} + 20 q^{29} + 4 q^{31} + 60 q^{33} + 50 q^{35} + 12 q^{37} - 40 q^{39} + 20 q^{41} + 64 q^{45} - 62 q^{47} + 100 q^{53} - 22 q^{55} + 12 q^{59} - 40 q^{61} - 80 q^{63} - 44 q^{67} - 152 q^{71} + 30 q^{73} - 120 q^{75} + 80 q^{79} + 72 q^{81} + 90 q^{83} - 40 q^{85} - 8 q^{89} - 36 q^{91} - 90 q^{93} - 42 q^{97} + 144 q^{99}+O(q^{100}) \) 224 * q + 28 * q^9 + 16 * q^11 + 10 * q^13 - 28 * q^15 - 48 * q^23 + 24 * q^27 + 20 * q^29 + 4 * q^31 + 60 * q^33 + 50 * q^35 + 12 * q^37 - 40 * q^39 + 20 * q^41 + 64 * q^45 - 62 * q^47 + 100 * q^53 - 22 * q^55 + 12 * q^59 - 40 * q^61 - 80 * q^63 - 44 * q^67 - 152 * q^71 + 30 * q^73 - 120 * q^75 + 80 * q^79 + 72 * q^81 + 90 * q^83 - 40 * q^85 - 8 * q^89 - 36 * q^91 - 90 * q^93 - 42 * q^97 + 144 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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