LMFDB - Embedded newform 572.2.bg.a.9.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(9,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 18, 20]))

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

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

chi := DirichletCharacter("572.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bg (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			9.7
Character	$\chi$	$=$	572.9
Dual form			572.2.bg.a.445.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0692906 - 0.659256i) q^{3} +(0.701430 + 2.15878i) q^{5} +(-0.337098 + 3.20727i) q^{7} +(2.50463 - 0.532375i) q^{9} +O(q^{10})$	\(q+(-0.0692906 - 0.659256i) q^{3} +(0.701430 + 2.15878i) q^{5} +(-0.337098 + 3.20727i) q^{7} +(2.50463 - 0.532375i) q^{9} +(-3.06734 + 1.26152i) q^{11} +(-3.59215 + 0.310559i) q^{13} +(1.37458 - 0.612004i) q^{15} +(-2.72835 + 3.03014i) q^{17} +(-1.94543 - 0.866160i) q^{19} +2.13777 q^{21} +(-1.34133 + 2.32325i) q^{23} +(-0.123234 + 0.0895350i) q^{25} +(-1.13905 - 3.50563i) q^{27} +(3.09085 - 1.37613i) q^{29} +(-3.08363 + 9.49043i) q^{31} +(1.04420 + 1.93475i) q^{33} +(-7.16023 + 1.52195i) q^{35} +(9.01121 - 4.01205i) q^{37} +(0.453640 + 2.34663i) q^{39} +(1.02141 + 9.71811i) q^{41} +(1.33625 + 2.31446i) q^{43} +(2.90610 + 5.03351i) q^{45} +(10.7589 - 7.81683i) q^{47} +(-3.32591 - 0.706944i) q^{49} +(2.18668 + 1.58872i) q^{51} +(1.12082 - 3.44952i) q^{53} +(-4.87487 - 5.73683i) q^{55} +(-0.436221 + 1.34255i) q^{57} +(-0.846110 + 8.05020i) q^{59} +(6.44614 - 7.15916i) q^{61} +(0.863166 + 8.21247i) q^{63} +(-3.19007 - 7.53682i) q^{65} +(1.32719 - 2.29875i) q^{67} +(1.62456 + 0.723300i) q^{69} +(-0.991204 + 1.10084i) q^{71} +(-7.63977 - 5.55062i) q^{73} +(0.0675655 + 0.0750390i) q^{75} +(-3.01205 - 10.2630i) q^{77} +(-1.60582 + 4.94219i) q^{79} +(4.78544 - 2.13061i) q^{81} +(-1.13431 - 3.49105i) q^{83} +(-8.45514 - 3.76447i) q^{85} +(-1.12139 - 1.94231i) q^{87} +(-7.65590 + 13.2604i) q^{89} +(0.214859 - 11.6257i) q^{91} +(6.47029 + 1.37530i) q^{93} +(0.505267 - 4.80730i) q^{95} +(4.41850 - 0.939181i) q^{97} +(-7.01093 + 4.79262i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 8 q^{9}+O(q^{10}) $ 112 * q + 8 * q^9	$ 112 q + 8 q^{9} - 10 q^{11} + 11 q^{13} - 2 q^{15} + 4 q^{17} - 12 q^{19} - 40 q^{21} + 10 q^{23} - 16 q^{25} - 12 q^{27} + q^{29} + 4 q^{31} + 35 q^{33} - 5 q^{35} - 12 q^{37} + 21 q^{39} - 10 q^{41} - 32 q^{43} + 34 q^{45} + 70 q^{47} + 16 q^{49} - 48 q^{51} - 26 q^{53} + 10 q^{55} - 12 q^{57} - 5 q^{59} + 28 q^{61} + 34 q^{63} + 22 q^{65} - 68 q^{67} - 58 q^{69} + 44 q^{71} + 42 q^{73} - 24 q^{75} + 46 q^{77} - 24 q^{79} + 64 q^{81} - 114 q^{83} + 4 q^{85} - 30 q^{87} - 6 q^{89} + 77 q^{91} - 5 q^{93} - 36 q^{95} - 15 q^{97} - 40 q^{99}+O(q^{100}) $ 112 * q + 8 * q^9 - 10 * q^11 + 11 * q^13 - 2 * q^15 + 4 * q^17 - 12 * q^19 - 40 * q^21 + 10 * q^23 - 16 * q^25 - 12 * q^27 + q^29 + 4 * q^31 + 35 * q^33 - 5 * q^35 - 12 * q^37 + 21 * q^39 - 10 * q^41 - 32 * q^43 + 34 * q^45 + 70 * q^47 + 16 * q^49 - 48 * q^51 - 26 * q^53 + 10 * q^55 - 12 * q^57 - 5 * q^59 + 28 * q^61 + 34 * q^63 + 22 * q^65 - 68 * q^67 - 58 * q^69 + 44 * q^71 + 42 * q^73 - 24 * q^75 + 46 * q^77 - 24 * q^79 + 64 * q^81 - 114 * q^83 + 4 * q^85 - 30 * q^87 - 6 * q^89 + 77 * q^91 - 5 * q^93 - 36 * q^95 - 15 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{5}\right)$

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
$3$	−0.0692906	−	0.659256i	−0.0400049	−	0.380622i	−0.996146	−	0.0877140i	$-0.972044\pi$
$3$	−0.0692906	−	0.659256i	−0.0400049	−	0.380622i	0.956141	−	0.292908i	$-0.0946228\pi$
$4$		0			0
$5$	0.701430	+	2.15878i	0.313689	+	0.965435i	0.976291	+	0.216463i	$0.0694521\pi$
$5$	0.701430	+	2.15878i	0.313689	+	0.965435i	−0.662602	+	0.748972i	$0.730548\pi$
$6$		0			0
$7$	−0.337098	+	3.20727i	−0.127411	+	1.21223i	0.724772	+	0.688989i	$0.241945\pi$
$7$	−0.337098	+	3.20727i	−0.127411	+	1.21223i	−0.852183	+	0.523245i	$0.824721\pi$
$8$		0			0
$9$	2.50463	−	0.532375i	0.834875	−	0.177458i
$10$		0			0
$11$	−3.06734	+	1.26152i	−0.924837	+	0.380364i
$11$	−3.06734	+	1.26152i	−0.924837	+	0.380364i
$12$		0			0
$13$	−3.59215	+	0.310559i	−0.996284	+	0.0861336i
$13$	−3.59215	+	0.310559i	−0.996284	+	0.0861336i
$14$		0			0
$15$	1.37458	−	0.612004i	0.354916	−	0.158019i
$16$		0			0
$17$	−2.72835	+	3.03014i	−0.661722	+	0.734916i	−0.976801	−	0.214149i	$-0.931302\pi$
$17$	−2.72835	+	3.03014i	−0.661722	+	0.734916i	0.315079	+	0.949065i	$0.397969\pi$
$18$		0			0
$19$	−1.94543	−	0.866160i	−0.446312	−	0.198711i	0.171259	−	0.985226i	$-0.445216\pi$
$19$	−1.94543	−	0.866160i	−0.446312	−	0.198711i	−0.617571	+	0.786515i	$0.711883\pi$
$20$		0			0
$21$	2.13777			0.466499
$22$		0			0
$23$	−1.34133	+	2.32325i	−0.279686	+	0.484431i	−0.971307	−	0.237830i	$-0.923564\pi$
$23$	−1.34133	+	2.32325i	−0.279686	+	0.484431i	0.691620	+	0.722261i	$0.256897\pi$
$24$		0			0
$25$	−0.123234	+	0.0895350i	−0.0246469	+	0.0179070i
$26$		0			0
$27$	−1.13905	−	3.50563i	−0.219210	−	0.674659i
$28$		0			0
$29$	3.09085	−	1.37613i	0.573956	−	0.255542i	−0.0991686	−	0.995071i	$-0.531618\pi$
$29$	3.09085	−	1.37613i	0.573956	−	0.255542i	0.673125	+	0.739529i	$0.264952\pi$
$30$		0			0
$31$	−3.08363	+	9.49043i	−0.553836	+	1.70453i	0.145161	+	0.989408i	$0.453630\pi$
$31$	−3.08363	+	9.49043i	−0.553836	+	1.70453i	−0.698997	+	0.715124i	$0.746370\pi$
$32$		0			0
$33$	1.04420	+	1.93475i	0.181773	+	0.336796i
$34$		0			0
$35$	−7.16023	+	1.52195i	−1.21030	+	0.257257i
$36$		0			0
$37$	9.01121	−	4.01205i	1.48143	−	0.659577i	0.502653	−	0.864488i	$-0.332357\pi$
$37$	9.01121	−	4.01205i	1.48143	−	0.659577i	0.978781	+	0.204911i	$0.0656906\pi$
$38$		0			0
$39$	0.453640	+	2.34663i	0.0726405	+	0.375761i
$40$		0			0
$41$	1.02141	+	9.71811i	0.159518	+	1.51771i	0.722573	+	0.691294i	$0.242959\pi$
$41$	1.02141	+	9.71811i	0.159518	+	1.51771i	−0.563055	+	0.826419i	$0.690374\pi$
$42$		0			0
$43$	1.33625	+	2.31446i	0.203777	+	0.352952i	0.949742	−	0.313033i	$-0.101345\pi$
$43$	1.33625	+	2.31446i	0.203777	+	0.352952i	−0.745965	+	0.665985i	$0.768012\pi$
$44$		0			0
$45$	2.90610	+	5.03351i	0.433215	+	0.750351i
$46$		0			0
$47$	10.7589	−	7.81683i	1.56935	−	1.14020i	0.641581	−	0.767055i	$-0.278279\pi$
$47$	10.7589	−	7.81683i	1.56935	−	1.14020i	0.927772	−	0.373147i	$-0.121721\pi$
$48$		0			0
$49$	−3.32591	−	0.706944i	−0.475130	−	0.100992i
$50$		0			0
$51$	2.18668	+	1.58872i	0.306197	+	0.222465i
$52$		0			0
$53$	1.12082	−	3.44952i	0.153956	−	0.473828i	−0.844098	−	0.536190i	$-0.819863\pi$
$53$	1.12082	−	3.44952i	0.153956	−	0.473828i	0.998054	+	0.0623615i	$0.0198632\pi$
$54$		0			0
$55$	−4.87487	−	5.73683i	−0.657327	−	0.773554i
$56$		0			0
$57$	−0.436221	+	1.34255i	−0.0577789	+	0.177825i
$58$		0			0
$59$	−0.846110	+	8.05020i	−0.110154	+	1.04805i	0.790188	+	0.612864i	$0.209983\pi$
$59$	−0.846110	+	8.05020i	−0.110154	+	1.04805i	−0.900342	+	0.435182i	$0.856684\pi$
$60$		0			0
$61$	6.44614	−	7.15916i	0.825343	−	0.916636i	−0.172314	−	0.985042i	$-0.555125\pi$
$61$	6.44614	−	7.15916i	0.825343	−	0.916636i	0.997658	+	0.0684056i	$0.0217912\pi$
$62$		0			0
$63$	0.863166	+	8.21247i	0.108749	+	1.03467i
$64$		0			0
$65$	−3.19007	−	7.53682i	−0.395679	−	0.934828i
$66$		0			0
$67$	1.32719	−	2.29875i	0.162142	−	0.280837i	−0.773495	−	0.633802i	$-0.781493\pi$
$67$	1.32719	−	2.29875i	0.162142	−	0.280837i	0.935637	+	0.352965i	$0.114827\pi$
$68$		0			0
$69$	1.62456	+	0.723300i	0.195574	+	0.0870751i
$70$		0			0
$71$	−0.991204	+	1.10084i	−0.117634	+	0.130646i	−0.799085	−	0.601218i	$-0.794683\pi$
$71$	−0.991204	+	1.10084i	−0.117634	+	0.130646i	0.681451	+	0.731864i	$0.261349\pi$
$72$		0			0
$73$	−7.63977	−	5.55062i	−0.894167	−	0.649651i	0.0427939	−	0.999084i	$-0.486374\pi$
$73$	−7.63977	−	5.55062i	−0.894167	−	0.649651i	−0.936961	+	0.349433i	$0.886374\pi$
$74$		0			0
$75$	0.0675655	+	0.0750390i	0.00780179	+	0.00866476i
$76$		0			0
$77$	−3.01205	−	10.2630i	−0.343255	−	1.16958i
$78$		0			0
$79$	−1.60582	+	4.94219i	−0.180668	+	0.556040i	−0.999847	−	0.0174985i	$-0.994430\pi$
$79$	−1.60582	+	4.94219i	−0.180668	+	0.556040i	0.819178	+	0.573539i	$0.194430\pi$
$80$		0			0
$81$	4.78544	−	2.13061i	0.531715	−	0.236735i
$82$		0			0
$83$	−1.13431	−	3.49105i	−0.124507	−	0.383193i	0.869304	−	0.494278i	$-0.164567\pi$
$83$	−1.13431	−	3.49105i	−0.124507	−	0.383193i	−0.993811	+	0.111085i	$0.964567\pi$
$84$		0			0
$85$	−8.45514	−	3.76447i	−0.917088	−	0.408314i
$86$		0			0
$87$	−1.12139	−	1.94231i	−0.120226	−	0.208237i
$88$		0			0
$89$	−7.65590	+	13.2604i	−0.811524	+	1.40560i	0.100274	+	0.994960i	$0.468028\pi$
$89$	−7.65590	+	13.2604i	−0.811524	+	1.40560i	−0.911797	+	0.410640i	$0.865305\pi$
$90$		0			0
$91$	0.214859	−	11.6257i	0.0225234	−	1.21870i
$92$		0			0
$93$	6.47029	+	1.37530i	0.670938	+	0.142612i
$94$		0			0
$95$	0.505267	−	4.80730i	0.0518393	−	0.493218i
$96$		0			0
$97$	4.41850	−	0.939181i	0.448631	−	0.0953594i	0.0219446	−	0.999759i	$-0.493014\pi$
$97$	4.41850	−	0.939181i	0.448631	−	0.0953594i	0.426686	+	0.904400i	$0.359681\pi$
$98$		0			0
$99$	−7.01093	+	4.79262i	−0.704625	+	0.481676i
$100$		0			0
$101$	9.80419	+	10.8887i	0.975553	+	1.08346i	0.996493	+	0.0836805i	$0.0266675\pi$
$101$	9.80419	+	10.8887i	0.975553	+	1.08346i	−0.0209397	+	0.999781i	$0.506666\pi$
$102$		0			0
$103$	−14.8067	−	10.7577i	−1.45895	−	1.05999i	−0.983635	−	0.180170i	$-0.942335\pi$
$103$	−14.8067	−	10.7577i	−1.45895	−	1.05999i	−0.475312	−	0.879817i	$-0.657665\pi$
$104$		0			0
$105$	1.49949	+	4.61497i	0.146336	+	0.450375i
$106$		0			0
$107$	−1.05118	−	10.0013i	−0.101622	−	0.966866i	−0.919929	−	0.392085i	$-0.871754\pi$
$107$	−1.05118	−	10.0013i	−0.101622	−	0.966866i	0.818307	−	0.574781i	$-0.194913\pi$
$108$		0			0
$109$	5.84709			0.560050			0.280025	−	0.959993i	$-0.409657\pi$
$109$	5.84709			0.560050			0.280025	+	0.959993i	$0.409657\pi$
$110$		0			0
$111$	−3.26936	−	5.66269i	−0.310314	−	0.537479i
$112$		0			0
$113$	−4.00004	−	1.78093i	−0.376292	−	0.167536i	0.209871	−	0.977729i	$-0.432696\pi$
$113$	−4.00004	−	1.78093i	−0.376292	−	0.167536i	−0.586163	+	0.810193i	$0.699362\pi$
$114$		0			0
$115$	−5.95623	−	1.26604i	−0.555421	−	0.118058i
$116$		0			0
$117$	−8.83166	+	2.69020i	−0.816487	+	0.248709i
$118$		0			0
$119$	−8.79875	−	9.77200i	−0.806580	−	0.895798i
$120$		0			0
$121$	7.81712	−	7.73904i	0.710647	−	0.703549i
$122$		0			0
$123$	6.33594	−	1.34675i	0.571293	−	0.121432i
$124$		0			0
$125$	8.90211	+	6.46776i	0.796228	+	0.578494i
$126$		0			0
$127$	9.16157	+	1.94735i	0.812958	+	0.172800i	0.595588	−	0.803290i	$-0.296919\pi$
$127$	9.16157	+	1.94735i	0.812958	+	0.172800i	0.217370	+	0.976089i	$0.430252\pi$
$128$		0			0
$129$	1.43323	−	1.04130i	0.126189	−	0.0916817i
$130$		0			0
$131$	−6.63097			−0.579351			−0.289675	−	0.957125i	$-0.593547\pi$
$131$	−6.63097			−0.579351			−0.289675	+	0.957125i	$0.593547\pi$
$132$		0			0
$133$	3.43381	−	5.94753i	0.297749	−	0.515716i
$134$		0			0
$135$	6.76892	−	4.91790i	0.582575	−	0.423266i
$136$		0			0
$137$	4.51493	−	5.01434i	0.385737	−	0.428404i	−0.518737	−	0.854934i	$-0.673597\pi$
$137$	4.51493	−	5.01434i	0.385737	−	0.428404i	0.904473	+	0.426530i	$0.140264\pi$
$138$		0			0
$139$	1.49934	−	14.2653i	0.127173	−	1.20997i	−0.725761	−	0.687947i	$-0.758512\pi$
$139$	1.49934	−	14.2653i	0.127173	−	1.20997i	0.852934	−	0.522019i	$-0.174821\pi$
$140$		0			0
$141$	−5.89879	−	6.55126i	−0.496767	−	0.551716i
$142$		0			0
$143$	10.6266	−	5.48417i	0.888638	−	0.458610i
$144$		0			0
$145$	5.13878	+	5.70720i	0.426753	+	0.473957i
$146$		0			0
$147$	−0.235603	+	2.24161i	−0.0194322	+	0.184885i
$148$		0			0
$149$	5.33026	−	5.91986i	0.436672	−	0.484974i	−0.484134	−	0.874994i	$-0.660865\pi$
$149$	5.33026	−	5.91986i	0.436672	−	0.484974i	0.920806	+	0.390020i	$0.127532\pi$
$150$		0			0
$151$	9.08424	−	6.60009i	0.739265	−	0.537107i	−0.153216	−	0.988193i	$-0.548963\pi$
$151$	9.08424	−	6.60009i	0.739265	−	0.537107i	0.892481	+	0.451085i	$0.148963\pi$
$152$		0			0
$153$	−5.22032	+	9.04186i	−0.422038	+	0.730991i
$154$		0			0
$155$	−22.6507			−1.81935
$156$		0			0
$157$	7.05456	−	5.12544i	0.563015	−	0.409055i	−0.269546	−	0.962988i	$-0.586874\pi$
$157$	7.05456	−	5.12544i	0.563015	−	0.409055i	0.832561	+	0.553933i	$0.186874\pi$
$158$		0			0
$159$	−2.35178	−	0.499886i	−0.186508	−	0.0396435i
$160$		0			0
$161$	−6.99913	−	5.08517i	−0.551609	−	0.400767i
$162$		0			0
$163$	−9.84792	+	2.09324i	−0.771349	+	0.163955i	−0.576742	−	0.816926i	$-0.695676\pi$
$163$	−9.84792	+	2.09324i	−0.771349	+	0.163955i	−0.194606	+	0.980881i	$0.562343\pi$
$164$		0			0
$165$	−3.44426	+	3.61129i	−0.268135	+	0.281139i
$166$		0			0
$167$	11.1378	+	12.3698i	0.861870	+	0.957204i	0.999446	−	0.0332875i	$-0.0105977\pi$
$167$	11.1378	+	12.3698i	0.861870	+	0.957204i	−0.137576	+	0.990491i	$0.543931\pi$
$168$		0			0
$169$	12.8071	−	2.23115i	0.985162	−	0.171627i
$170$		0			0
$171$	−5.33369	−	1.13371i	−0.407877	−	0.0866970i
$172$		0			0
$173$	−0.408783	−	0.182002i	−0.0310792	−	0.0138374i	0.391138	−	0.920332i	$-0.372081\pi$
$173$	−0.408783	−	0.182002i	−0.0310792	−	0.0138374i	−0.422217	+	0.906495i	$0.638748\pi$
$174$		0			0
$175$	−0.245621	−	0.425428i	−0.0185672	−	0.0321593i
$176$		0			0
$177$	5.36577			0.403316
$178$		0			0
$179$	0.535200	+	5.09209i	0.0400027	+	0.380601i	0.996147	+	0.0877033i	$0.0279527\pi$
$179$	0.535200	+	5.09209i	0.0400027	+	0.380601i	−0.956144	+	0.292897i	$0.905381\pi$
$180$		0			0
$181$	2.11315	+	6.50359i	0.157069	+	0.483408i	0.998365	−	0.0571668i	$-0.0182067\pi$
$181$	2.11315	+	6.50359i	0.157069	+	0.483408i	−0.841296	+	0.540575i	$0.818207\pi$
$182$		0			0
$183$	−5.16637	−	3.75359i	−0.381909	−	0.277473i
$184$		0			0
$185$	14.9819	+	16.6390i	1.10149	+	1.22333i
$186$		0			0
$187$	4.54617	−	12.7363i	0.332449	−	0.931373i
$188$		0			0
$189$	11.6275	−	2.47149i	0.845774	−	0.179775i
$190$		0			0
$191$	0.0222553	−	0.211745i	0.00161034	−	0.0153213i	−0.993687	−	0.112186i	$-0.964215\pi$
$191$	0.0222553	−	0.211745i	0.00161034	−	0.0153213i	0.995298	+	0.0968647i	$0.0308814\pi$
$192$		0			0
$193$	−4.43164	−	0.941974i	−0.318996	−	0.0678048i	0.0456308	−	0.998958i	$-0.485470\pi$
$193$	−4.43164	−	0.941974i	−0.318996	−	0.0678048i	−0.364627	+	0.931154i	$0.618804\pi$
$194$		0			0
$195$	−4.74765	+	2.62530i	−0.339986	+	0.188002i
$196$		0			0
$197$	−10.0209	+	17.3567i	−0.713958	+	1.23661i	0.249402	+	0.968400i	$0.419766\pi$
$197$	−10.0209	+	17.3567i	−0.713958	+	1.23661i	−0.963360	+	0.268212i	$0.913567\pi$
$198$		0			0
$199$	5.47839	+	9.48885i	0.388353	+	0.672647i	0.992228	−	0.124432i	$-0.0397109\pi$
$199$	5.47839	+	9.48885i	0.388353	+	0.672647i	−0.603875	+	0.797079i	$0.706378\pi$
$200$		0			0
$201$	−1.60743	−	0.715673i	−0.113379	−	0.0504797i
$202$		0			0
$203$	3.37172	+	10.3771i	0.236648	+	0.728328i
$204$		0			0
$205$	−20.2628	+	9.02157i	−1.41521	+	0.630094i
$206$		0			0
$207$	−2.12269	+	6.53296i	−0.147537	+	0.454072i
$208$		0			0
$209$	7.05996	+	0.202603i	0.488348	+	0.0140143i
$210$		0			0
$211$	0.0247775	+	0.0275182i	0.00170575	+	0.00189443i	0.743997	−	0.668183i	$-0.232928\pi$
$211$	0.0247775	+	0.0275182i	0.00170575	+	0.00189443i	−0.742291	+	0.670077i	$0.766261\pi$
$212$		0			0
$213$	0.794419	+	0.577179i	0.0544327	+	0.0395477i
$214$		0			0
$215$	−4.05912	+	4.50811i	−0.276830	+	0.307451i
$216$		0			0
$217$	−29.3989	−	13.0892i	−1.99573	−	0.888555i
$218$		0			0
$219$	−3.12991	+	5.42117i	−0.211500	+	0.366329i
$220$		0			0
$221$	8.85960	−	11.7320i	0.595961	−	0.789181i
$222$		0			0
$223$	−2.31540	−	22.0296i	−0.155051	−	1.47521i	−0.744619	−	0.667490i	$-0.767369\pi$
$223$	−2.31540	−	22.0296i	−0.155051	−	1.47521i	0.589568	−	0.807718i	$-0.299298\pi$
$224$		0			0
$225$	−0.260990	+	0.289859i	−0.0173993	+	0.0193239i
$226$		0			0
$227$	−1.48005	+	14.0817i	−0.0982342	+	0.934636i	0.828771	+	0.559588i	$0.189041\pi$
$227$	−1.48005	+	14.0817i	−0.0982342	+	0.934636i	−0.927005	+	0.375048i	$0.877626\pi$
$228$		0			0
$229$	8.27234	−	25.4596i	0.546652	−	1.68242i	−0.170379	−	0.985379i	$-0.554499\pi$
$229$	8.27234	−	25.4596i	0.546652	−	1.68242i	0.717030	−	0.697042i	$-0.245501\pi$
$230$		0			0
$231$	−6.55726	+	2.69685i	−0.431436	+	0.177439i
$232$		0			0
$233$	−7.92258	+	24.3832i	−0.519026	+	1.59740i	0.256810	+	0.966462i	$0.417328\pi$
$233$	−7.92258	+	24.3832i	−0.519026	+	1.59740i	−0.775836	+	0.630935i	$0.782672\pi$
$234$		0			0
$235$	24.4214	+	17.7432i	1.59308	+	1.15744i
$236$		0			0
$237$	3.36944	+	0.716196i	0.218869	+	0.0465219i
$238$		0			0
$239$	19.1305	−	13.8991i	1.23745	−	0.899061i	0.240025	−	0.970767i	$-0.422844\pi$
$239$	19.1305	−	13.8991i	1.23745	−	0.899061i	0.997426	+	0.0717058i	$0.0228443\pi$
$240$		0			0
$241$	−12.7759	−	22.1285i	−0.822969	−	1.42542i	−0.903462	−	0.428669i	$-0.858983\pi$
$241$	−12.7759	−	22.1285i	−0.822969	−	1.42542i	0.0804926	−	0.996755i	$-0.474351\pi$
$242$		0			0
$243$	−7.26526	−	12.5838i	−0.466067	−	0.807251i
$244$		0			0
$245$	−0.806756	−	7.67577i	−0.0515417	−	0.490387i
$246$		0			0
$247$	7.25726	+	2.50721i	0.461769	+	0.159530i
$248$		0			0
$249$	−2.22290	+	0.989699i	−0.140871	+	0.0627196i
$250$		0			0
$251$	23.2846	−	4.94929i	1.46971	−	0.312396i	0.597635	−	0.801769i	$-0.296107\pi$
$251$	23.2846	−	4.94929i	1.46971	−	0.312396i	0.872075	+	0.489372i	$0.162774\pi$
$252$		0			0
$253$	1.18347	−	8.81831i	0.0744044	−	0.554402i
$254$		0			0
$255$	−1.89589	+	5.83494i	−0.118725	+	0.365398i
$256$		0			0
$257$	8.37924	−	3.73068i	0.522683	−	0.232713i	−0.128397	−	0.991723i	$-0.540983\pi$
$257$	8.37924	−	3.73068i	0.522683	−	0.232713i	0.651079	+	0.759010i	$0.274316\pi$
$258$		0			0
$259$	9.83006	+	30.2538i	0.610810	+	1.87988i
$260$		0			0
$261$	7.00880	−	5.09219i	0.433834	−	0.315199i
$262$		0			0
$263$	−3.20654	+	5.55389i	−0.197724	+	0.342468i	−0.947790	−	0.318895i	$-0.896688\pi$
$263$	−3.20654	+	5.55389i	−0.197724	+	0.342468i	0.750066	+	0.661363i	$0.230022\pi$
$264$		0			0
$265$	8.23292			0.505744
$266$		0			0
$267$	9.27248	+	4.12838i	0.567467	+	0.252652i
$268$		0			0
$269$	−15.0408	+	16.7045i	−0.917051	+	1.01849i	0.0827086	+	0.996574i	$0.473643\pi$
$269$	−15.0408	+	16.7045i	−0.917051	+	1.01849i	−0.999760	+	0.0219148i	$0.993024\pi$
$270$		0			0
$271$	−27.9153	+	12.4287i	−1.69574	+	0.754990i	−0.696435	+	0.717620i	$0.745231\pi$
$271$	−27.9153	+	12.4287i	−1.69574	+	0.754990i	−0.999301	+	0.0373704i	$0.988102\pi$
$272$		0			0
$273$	−7.67919	+	0.663903i	−0.464766	+	0.0401812i
$274$		0			0
$275$	0.265051	−	0.430097i	0.0159832	−	0.0259358i
$276$		0			0
$277$	−28.1441	+	5.98221i	−1.69101	+	0.359436i	−0.950047	−	0.312106i	$-0.898966\pi$
$277$	−28.1441	+	5.98221i	−1.69101	+	0.359436i	−0.740967	+	0.671542i	$0.765632\pi$
$278$		0			0
$279$	−2.67087	+	25.4116i	−0.159901	+	1.52135i
$280$		0			0
$281$	5.33615	+	16.4230i	0.318328	+	0.979713i	0.974363	+	0.224983i	$0.0722325\pi$
$281$	5.33615	+	16.4230i	0.318328	+	0.979713i	−0.656035	+	0.754731i	$0.727767\pi$
$282$		0			0
$283$	−0.327196	−	3.11306i	−0.0194498	−	0.185052i	0.980484	−	0.196601i	$-0.0629905\pi$
$283$	−0.327196	−	3.11306i	−0.0194498	−	0.185052i	−0.999933	+	0.0115489i	$0.996324\pi$
$284$		0			0
$285$	−3.20425			−0.189803
$286$		0			0
$287$	−31.5129			−1.86015
$288$		0			0
$289$	0.0391342	+	0.372337i	0.00230201	+	0.0219022i
$290$		0			0
$291$	−0.925321	−	2.84785i	−0.0542433	−	0.166944i
$292$		0			0
$293$	0.825595	−	7.85501i	0.0482318	−	0.458895i	−0.943576	−	0.331156i	$-0.892561\pi$
$293$	0.825595	−	7.85501i	0.0482318	−	0.458895i	0.991808	−	0.127739i	$-0.0407719\pi$
$294$		0			0
$295$	−17.9721	+	3.82008i	−1.04638	+	0.222414i
$296$		0			0
$297$	7.91628	+	9.31601i	0.459349	+	0.540570i
$298$		0			0
$299$	4.09675	−	8.76203i	0.236921	−	0.506721i
$300$		0			0
$301$	−7.87355	+	3.50553i	−0.453824	+	0.202055i
$302$		0			0
$303$	6.49907	−	7.21795i	0.373362	−	0.414660i
$304$		0			0
$305$	19.9765	+	8.89413i	1.14385	+	0.509276i
$306$		0			0
$307$	13.4432			0.767242			0.383621	−	0.923491i	$-0.374677\pi$
$307$	13.4432			0.767242			0.383621	+	0.923491i	$0.374677\pi$
$308$		0			0
$309$	−6.06611	+	10.5068i	−0.345089	+	0.597712i
$310$		0			0
$311$	−10.1940	+	7.40638i	−0.578049	+	0.419977i	−0.838020	−	0.545639i	$-0.816287\pi$
$311$	−10.1940	+	7.40638i	−0.578049	+	0.419977i	0.259971	+	0.965616i	$0.416287\pi$
$312$		0			0
$313$	5.10751	+	15.7193i	0.288694	+	0.888508i	0.985267	+	0.171022i	$0.0547071\pi$
$313$	5.10751	+	15.7193i	0.288694	+	0.888508i	−0.696573	+	0.717486i	$0.745293\pi$
$314$		0			0
$315$	−17.1235	+	7.62385i	−0.964797	+	0.429555i
$316$		0			0
$317$	3.26102	−	10.0364i	0.183157	−	0.563699i	−0.816755	−	0.576985i	$-0.804229\pi$
$317$	3.26102	−	10.0364i	0.183157	−	0.563699i	0.999912	+	0.0132859i	$0.00422915\pi$
$318$		0			0
$319$	−7.74465	+	8.12025i	−0.433617	+	0.454647i
$320$		0			0
$321$	−6.52060	+	1.38600i	−0.363944	+	0.0773588i
$322$		0			0
$323$	7.93239	−	3.53173i	0.441370	−	0.196511i
$324$		0			0
$325$	0.414871	−	0.359895i	0.0230129	−	0.0199634i
$326$		0			0
$327$	−0.405148	−	3.85473i	−0.0224048	−	0.213167i
$328$		0			0
$329$	21.4439	+	37.1419i	1.18224	+	2.04770i
$330$		0			0
$331$	0.126611	+	0.219296i	0.00695914	+	0.0120536i	0.869484	−	0.493961i	$-0.164451\pi$
$331$	0.126611	+	0.219296i	0.00695914	+	0.0120536i	−0.862525	+	0.506015i	$0.831118\pi$
$332$		0			0
$333$	20.4338	−	14.8460i	1.11976	−	0.813557i
$334$		0			0
$335$	5.89342	+	1.25269i	0.321992	+	0.0684416i
$336$		0			0
$337$	−16.0225	−	11.6411i	−0.872804	−	0.634129i	0.0585342	−	0.998285i	$-0.481357\pi$
$337$	−16.0225	−	11.6411i	−0.872804	−	0.634129i	−0.931338	+	0.364156i	$0.881357\pi$
$338$		0			0
$339$	−0.896925	+	2.76045i	−0.0487143	+	0.149927i
$340$		0			0
$341$	−2.51388	−	33.0004i	−0.136134	−	1.78707i
$342$		0			0
$343$	−3.58741	+	11.0409i	−0.193702	+	0.596153i
$344$		0			0
$345$	−0.421931	+	4.01440i	−0.0227160	+	0.216128i
$346$		0			0
$347$	3.78352	−	4.20202i	0.203110	−	0.225576i	−0.632981	−	0.774167i	$-0.718169\pi$
$347$	3.78352	−	4.20202i	0.203110	−	0.225576i	0.836091	+	0.548591i	$0.184836\pi$
$348$		0			0
$349$	1.63900	+	15.5940i	0.0877335	+	0.834728i	0.946574	+	0.322486i	$0.104518\pi$
$349$	1.63900	+	15.5940i	0.0877335	+	0.834728i	−0.858841	+	0.512243i	$0.828815\pi$
$350$		0			0
$351$	5.18034	+	12.2390i	0.276506	+	0.653270i
$352$		0			0
$353$	−9.65186	+	16.7175i	−0.513717	+	0.889783i	0.486157	+	0.873872i	$0.338398\pi$
$353$	−9.65186	+	16.7175i	−0.513717	+	0.889783i	−0.999873	+	0.0159117i	$0.994935\pi$
$354$		0			0
$355$	−3.07174	−	1.36763i	−0.163031	−	0.0725860i
$356$		0			0
$357$	−5.83258	+	6.47773i	−0.308693	+	0.342838i
$358$		0			0
$359$	15.6704	+	11.3852i	0.827052	+	0.600889i	0.918724	−	0.394901i	$-0.129221\pi$
$359$	15.6704	+	11.3852i	0.827052	+	0.600889i	−0.0916716	+	0.995789i	$0.529221\pi$
$360$		0			0
$361$	−9.67903	−	10.7496i	−0.509422	−	0.565771i
$362$		0			0
$363$	−5.64366	−	4.61724i	−0.296215	−	0.242342i
$364$		0			0
$365$	6.62379	−	20.3859i	0.346705	−	1.06705i
$366$		0			0
$367$	33.7353	−	15.0199i	1.76097	−	0.784034i	0.772053	−	0.635558i	$-0.219230\pi$
$367$	33.7353	−	15.0199i	1.76097	−	0.784034i	0.988916	−	0.148476i	$-0.0474369\pi$
$368$		0			0
$369$	7.73193	+	23.7964i	0.402508	+	1.23879i
$370$		0			0
$371$	10.6857	+	4.75759i	0.554775	+	0.247002i
$372$		0			0
$373$	−12.0401	−	20.8540i	−0.623411	−	1.07978i	−0.988846	−	0.148942i	$-0.952413\pi$
$373$	−12.0401	−	20.8540i	−0.623411	−	1.07978i	0.365435	−	0.930837i	$-0.380920\pi$
$374$		0			0
$375$	3.64708	−	6.31692i	0.188334	−	0.326204i
$376$		0			0
$377$	−10.6754	+	5.90318i	−0.549812	+	0.304029i
$378$		0			0
$379$	22.4306	+	4.76778i	1.15218	+	0.244904i	0.744118	−	0.668048i	$-0.232870\pi$
$379$	22.4306	+	4.76778i	1.15218	+	0.244904i	0.408066	+	0.912952i	$0.366203\pi$
$380$		0			0
$381$	0.648993	−	6.17475i	0.0332489	−	0.316342i
$382$		0			0
$383$	−13.1341	+	2.79175i	−0.671123	+	0.142652i	−0.530856	−	0.847462i	$-0.678129\pi$
$383$	−13.1341	+	2.79175i	−0.671123	+	0.142652i	−0.140267	+	0.990114i	$0.544796\pi$
$384$		0			0
$385$	20.0429	−	13.7011i	1.02148	−	0.698275i
$386$		0			0
$387$	4.57898	+	5.08547i	0.232763	+	0.258509i
$388$		0			0
$389$	3.93667	+	2.86016i	0.199597	+	0.145016i	0.683095	−	0.730330i	$-0.260634\pi$
$389$	3.93667	+	2.86016i	0.199597	+	0.145016i	−0.483497	+	0.875346i	$0.660634\pi$
$390$		0			0
$391$	−3.38015	−	10.4030i	−0.170942	−	0.526105i
$392$		0			0
$393$	0.459464	+	4.37151i	0.0231769	+	0.220513i
$394$		0			0
$395$	−11.7955			−0.593494
$396$		0			0
$397$	7.11553	+	12.3245i	0.357118	+	0.618547i	0.987478	−	0.157756i	$-0.0504259\pi$
$397$	7.11553	+	12.3245i	0.357118	+	0.618547i	−0.630360	+	0.776303i	$0.717093\pi$
$398$		0			0
$399$	−4.15887	−	1.85165i	−0.208204	−	0.0926984i
$400$		0			0
$401$	8.00947	+	1.70247i	0.399974	+	0.0850171i	0.403507	−	0.914977i	$-0.367791\pi$
$401$	8.00947	+	1.70247i	0.399974	+	0.0850171i	−0.00353282	+	0.999994i	$0.501125\pi$
$402$		0			0
$403$	8.12952	−	35.0487i	0.404960	−	1.74590i
$404$		0			0
$405$	7.95617	+	8.83622i	0.395345	+	0.439075i
$406$		0			0
$407$	−22.5791	+	23.6742i	−1.11921	+	1.17348i
$408$		0			0
$409$	−12.5160	+	2.66036i	−0.618878	+	0.131546i	−0.506673	−	0.862139i	$-0.669125\pi$
$409$	−12.5160	+	2.66036i	−0.618878	+	0.131546i	−0.112205	+	0.993685i	$0.535791\pi$
$410$		0			0
$411$	−3.61858	−	2.62905i	−0.178491	−	0.129681i
$412$		0			0
$413$	−25.5339	−	5.42741i	−1.25644	−	0.267065i
$414$		0			0
$415$	6.74077	−	4.89746i	0.330891	−	0.240407i
$416$		0			0
$417$	−9.50836			−0.465626
$418$		0			0
$419$	−7.39036	+	12.8005i	−0.361043	+	0.625345i	−0.988133	−	0.153602i	$-0.950913\pi$
$419$	−7.39036	+	12.8005i	−0.361043	+	0.625345i	0.627090	+	0.778947i	$0.284246\pi$
$420$		0			0
$421$	19.6316	−	14.2632i	0.956787	−	0.695146i	0.00438472	−	0.999990i	$-0.498604\pi$
$421$	19.6316	−	14.2632i	0.956787	−	0.695146i	0.952402	+	0.304844i	$0.0986043\pi$
$422$		0			0
$423$	22.7856	−	25.3060i	1.10788	−	1.23042i
$424$		0			0
$425$	0.0649229	−	0.617700i	0.00314922	−	0.0299628i
$426$		0			0
$427$	20.7884	+	23.0878i	1.00602	+	1.11730i
$428$		0			0
$429$	−4.35179	−	6.62562i	−0.210107	−	0.319888i
$430$		0			0
$431$	14.6806	+	16.3044i	0.707138	+	0.785356i	0.984495	−	0.175410i	$-0.0561253\pi$
$431$	14.6806	+	16.3044i	0.707138	+	0.785356i	−0.277357	+	0.960767i	$0.589459\pi$
$432$		0			0
$433$	0.616384	−	5.86451i	0.0296215	−	0.281830i	−0.969677	−	0.244389i	$-0.921413\pi$
$433$	0.616384	−	5.86451i	0.0296215	−	0.281830i	0.999299	−	0.0374412i	$-0.0119207\pi$
$434$		0			0
$435$	3.40643	−	3.78323i	0.163326	−	0.181392i
$436$		0			0
$437$	4.62177	−	3.35791i	0.221089	−	0.160631i
$438$		0			0
$439$	5.18768	−	8.98532i	0.247594	−	0.428846i	−0.715263	−	0.698855i	$-0.753693\pi$
$439$	5.18768	−	8.98532i	0.247594	−	0.428846i	0.962858	+	0.270009i	$0.0870267\pi$
$440$		0			0
$441$	−8.70651			−0.414596
$442$		0			0
$443$	7.42003	−	5.39097i	0.352536	−	0.256133i	−0.397396	−	0.917647i	$-0.630086\pi$
$443$	7.42003	−	5.39097i	0.352536	−	0.256133i	0.749932	+	0.661515i	$0.230086\pi$
$444$		0			0
$445$	−33.9964	−	7.22615i	−1.61158	−	0.342552i
$446$		0			0
$447$	−4.27204	−	3.10382i	−0.202060	−	0.146805i
$448$		0			0
$449$	−7.97308	+	1.69473i	−0.376273	+	0.0799793i	−0.392166	−	0.919894i	$-0.628274\pi$
$449$	−7.97308	+	1.69473i	−0.376273	+	0.0799793i	0.0158932	+	0.999874i	$0.494941\pi$
$450$		0			0
$451$	−15.3926	−	28.5202i	−0.724811	−	1.34296i
$452$		0			0
$453$	−4.98060	−	5.53151i	−0.234009	−	0.259893i
$454$		0			0
$455$	25.2480	−	7.69077i	1.18364	−	0.360549i
$456$		0			0
$457$	−8.88886	−	1.88939i	−0.415803	−	0.0883818i	−0.00474061	−	0.999989i	$-0.501509\pi$
$457$	−8.88886	−	1.88939i	−0.415803	−	0.0883818i	−0.411063	+	0.911607i	$0.634842\pi$
$458$		0			0
$459$	13.7303	+	6.11311i	0.640874	+	0.285335i
$460$		0			0
$461$	−18.7353	−	32.4504i	−0.872588	−	1.51137i	−0.859310	−	0.511456i	$-0.829106\pi$
$461$	−18.7353	−	32.4504i	−0.872588	−	1.51137i	−0.0132788	−	0.999912i	$-0.504227\pi$
$462$		0			0
$463$	−26.2782			−1.22125			−0.610625	−	0.791920i	$-0.709082\pi$
$463$	−26.2782			−1.22125			−0.610625	+	0.791920i	$0.709082\pi$
$464$		0			0
$465$	1.56948	+	14.9326i	0.0727829	+	0.692483i
$466$		0			0
$467$	−1.95000	−	6.00148i	−0.0902352	−	0.277715i	0.895747	−	0.444563i	$-0.146641\pi$
$467$	−1.95000	−	6.00148i	−0.0902352	−	0.277715i	−0.985983	+	0.166848i	$0.946641\pi$
$468$		0			0
$469$	6.92533	+	5.03155i	0.319782	+	0.232335i
$470$		0			0
$471$	−3.86779	−	4.29562i	−0.178218	−	0.197932i
$472$		0			0
$473$	−7.01849	−	5.41352i	−0.322711	−	0.248914i
$474$		0			0
$475$	0.317295	−	0.0674432i	0.0145585	−	0.00309451i
$476$		0			0
$477$	0.970790	−	9.23645i	0.0444494	−	0.422908i
$478$		0			0
$479$	6.30403	+	1.33996i	0.288038	+	0.0612244i	0.349665	−	0.936875i	$-0.386295\pi$
$479$	6.30403	+	1.33996i	0.288038	+	0.0612244i	−0.0616266	+	0.998099i	$0.519629\pi$
$480$		0			0
$481$	−31.1237	+	17.2104i	−1.41912	+	0.784727i
$482$		0			0
$483$	−2.86745	+	4.96657i	−0.130474	+	0.225987i
$484$		0			0
$485$	5.12675	+	8.87979i	0.232794	+	0.403211i
$486$		0			0
$487$	23.0027	+	10.2415i	1.04235	+	0.464085i	0.855228	−	0.518251i	$-0.173417\pi$
$487$	23.0027	+	10.2415i	1.04235	+	0.464085i	0.187124	+	0.982336i	$0.440083\pi$
$488$		0			0
$489$	2.06235	+	6.34726i	0.0932627	+	0.287033i
$490$		0			0
$491$	−6.03185	+	2.68555i	−0.272213	+	0.121197i	−0.538304	−	0.842751i	$-0.680935\pi$
$491$	−6.03185	+	2.68555i	−0.272213	+	0.121197i	0.266090	+	0.963948i	$0.414268\pi$
$492$		0			0
$493$	−4.26303	+	13.1203i	−0.191997	+	0.590907i
$494$		0			0
$495$	−15.2639	−	11.7734i	−0.686060	−	0.529173i
$496$		0			0
$497$	−3.19657	−	3.55015i	−0.143386	−	0.159246i
$498$		0			0
$499$	1.24755	+	0.906398i	0.0558480	+	0.0405760i	0.615359	−	0.788247i	$-0.289011\pi$
$499$	1.24755	+	0.906398i	0.0558480	+	0.0405760i	−0.559511	+	0.828823i	$0.689011\pi$
$500$		0			0
$501$	7.38312	−	8.19978i	0.329853	−	0.366339i
$502$		0			0
$503$	11.9139	+	5.30443i	0.531216	+	0.236513i	0.654774	−	0.755825i	$-0.272764\pi$
$503$	11.9139	+	5.30443i	0.531216	+	0.236513i	−0.123558	+	0.992337i	$0.539430\pi$
$504$		0			0
$505$	−16.6292	+	28.8027i	−0.739991	+	1.28170i
$506$		0			0
$507$	−2.35831	−	8.28856i	−0.104736	−	0.368108i
$508$		0			0
$509$	−4.32901	−	41.1878i	−0.191880	−	1.82562i	−0.490724	−	0.871315i	$-0.663268\pi$
$509$	−4.32901	−	41.1878i	−0.191880	−	1.82562i	0.298844	−	0.954302i	$-0.403399\pi$
$510$		0			0
$511$	20.3777	−	22.6317i	0.901455	−	1.00117i
$512$		0			0
$513$	−0.820501	+	7.80655i	−0.0362260	+	0.344668i
$514$		0			0
$515$	12.8376	−	39.5101i	0.565693	−	1.74103i
$516$		0			0
$517$	−23.1402	+	37.5495i	−1.01770	+	1.65143i
$518$		0			0
$519$	−0.0916610	+	0.282104i	−0.00402347	+	0.0123830i
$520$		0			0
$521$	−3.75641	−	2.72919i	−0.164571	−	0.119568i	0.502451	−	0.864605i	$-0.332432\pi$
$521$	−3.75641	−	2.72919i	−0.164571	−	0.119568i	−0.667023	+	0.745037i	$0.732432\pi$
$522$		0			0
$523$	−9.72557	−	2.06723i	−0.425269	−	0.0903938i	−0.00969497	−	0.999953i	$-0.503086\pi$
$523$	−9.72557	−	2.06723i	−0.425269	−	0.0903938i	−0.415574	+	0.909559i	$0.636419\pi$
$524$		0			0
$525$	−0.263447	+	0.191405i	−0.0114978	+	0.00835360i
$526$		0			0
$527$	−20.3441	−	35.2370i	−0.886203	−	1.53495i
$528$		0			0
$529$	7.90167	+	13.6861i	0.343551	+	0.595048i
$530$		0			0
$531$	2.16653	+	20.6132i	0.0940195	+	0.894536i
$532$		0			0
$533$	−6.68712	−	34.5917i	−0.289651	−	1.49833i
$534$		0			0
$535$	20.8533	−	9.28450i	0.901568	−	0.401404i
$536$		0			0
$537$	3.31991	−	0.705668i	0.143264	−	0.0304518i
$538$		0			0
$539$	11.0935	−	2.02728i	0.477831	−	0.0873210i
$540$		0			0
$541$	0.620918	−	1.91099i	0.0266954	−	0.0821599i	−0.936821	−	0.349809i	$-0.886247\pi$
$541$	0.620918	−	1.91099i	0.0266954	−	0.0821599i	0.963517	+	0.267649i	$0.0862466\pi$
$542$		0			0
$543$	4.14111	−	1.84374i	0.177712	−	0.0791225i
$544$		0			0
$545$	4.10132	+	12.6226i	0.175681	+	0.540692i
$546$		0			0
$547$	−5.97874	+	4.34381i	−0.255632	+	0.185728i	−0.708219	−	0.705992i	$-0.750501\pi$
$547$	−5.97874	+	4.34381i	−0.255632	+	0.185728i	0.452587	+	0.891720i	$0.350501\pi$
$548$		0			0
$549$	12.3338	−	21.3628i	0.526394	−	0.911741i
$550$		0			0
$551$	−7.20498			−0.306942
$552$		0			0
$553$	−15.3096	−	6.81629i	−0.651032	−	0.289858i
$554$		0			0
$555$	9.93128	−	11.0298i	0.421559	−	0.468189i
$556$		0			0
$557$	10.0062	−	4.45504i	0.423976	−	0.188766i	−0.183646	−	0.982992i	$-0.558790\pi$
$557$	10.0062	−	4.45504i	0.423976	−	0.188766i	0.607622	+	0.794226i	$0.292123\pi$
$558$		0			0
$559$	−5.51881	−	7.89891i	−0.233421	−	0.334088i
$560$		0			0
$561$	−8.71151	−	2.11458i	−0.367800	−	0.0892778i
$562$		0			0
$563$	−2.37184	+	0.504149i	−0.0999609	+	0.0212474i	−0.257621	−	0.966246i	$-0.582938\pi$
$563$	−2.37184	+	0.504149i	−0.0999609	+	0.0212474i	0.157660	+	0.987494i	$0.449605\pi$
$564$		0			0
$565$	1.03889	−	9.88439i	0.0437065	−	0.415839i
$566$		0			0
$567$	5.22029	+	16.0664i	0.219232	+	0.674726i
$568$		0			0
$569$	−1.66181	−	15.8111i	−0.0696667	−	0.662835i	−0.972509	−	0.232864i	$-0.925190\pi$
$569$	−1.66181	−	15.8111i	−0.0696667	−	0.662835i	0.902843	−	0.429971i	$-0.141476\pi$
$570$		0			0
$571$	36.2913			1.51874			0.759372	−	0.650657i	$-0.225506\pi$
$571$	36.2913			1.51874			0.759372	+	0.650657i	$0.225506\pi$
$572$		0			0
$573$	−0.141136			−0.00589605
$574$		0			0
$575$	−0.0427144	−	0.406400i	−0.00178131	−	0.0169481i
$576$		0			0
$577$	−0.298084	−	0.917409i	−0.0124094	−	0.0381922i	0.944660	−	0.328051i	$-0.106392\pi$
$577$	−0.298084	−	0.917409i	−0.0124094	−	0.0381922i	−0.957069	+	0.289859i	$0.906392\pi$
$578$		0			0
$579$	−0.313931	+	2.98685i	−0.0130465	+	0.124129i
$580$		0			0
$581$	11.5791	−	2.46122i	0.480383	−	0.102109i
$582$		0			0
$583$	0.913727	+	11.9948i	0.0378427	+	0.496773i
$584$		0			0
$585$	−12.0023	−	17.1786i	−0.496236	−	0.710248i
$586$		0			0
$587$	−31.6966	+	14.1123i	−1.30826	+	0.582475i	−0.938059	−	0.346476i	$-0.887378\pi$
$587$	−31.6966	+	14.1123i	−1.30826	+	0.582475i	−0.370202	+	0.928951i	$0.620711\pi$
$588$		0			0
$589$	14.2192	−	15.7920i	0.585892	−	0.650700i
$590$		0			0
$591$	12.1368	+	5.40367i	0.499243	+	0.222277i
$592$		0			0
$593$	27.5442			1.13110			0.565552	−	0.824713i	$-0.308663\pi$
$593$	27.5442			1.13110			0.565552	+	0.824713i	$0.308663\pi$
$594$		0			0
$595$	14.9239	−	25.8489i	0.611819	−	1.05970i
$596$		0			0
$597$	5.87598	−	4.26915i	0.240488	−	0.174725i
$598$		0			0
$599$	−1.61370	−	4.96647i	−0.0659341	−	0.202924i	0.912662	−	0.408716i	$-0.134023\pi$
$599$	−1.61370	−	4.96647i	−0.0659341	−	0.202924i	−0.978596	+	0.205791i	$0.934023\pi$
$600$		0			0
$601$	5.77657	−	2.57190i	0.235631	−	0.104910i	−0.285524	−	0.958371i	$-0.592168\pi$
$601$	5.77657	−	2.57190i	0.235631	−	0.104910i	0.521156	+	0.853462i	$0.325501\pi$
$602$		0			0
$603$	2.10031	−	6.46408i	0.0855311	−	0.263238i
$604$		0			0
$605$	22.1900	+	11.4470i	0.902153	+	0.465388i
$606$		0			0
$607$	38.7173	−	8.22961i	1.57149	−	0.334030i	0.661915	−	0.749579i	$-0.269744\pi$
$607$	38.7173	−	8.22961i	1.57149	−	0.334030i	0.909571	+	0.415549i	$0.136411\pi$
$608$		0			0
$609$	6.60752	−	2.94186i	0.267750	−	0.119210i
$610$		0			0
$611$	−36.2202	+	31.4205i	−1.46531	+	1.27114i
$612$		0			0
$613$	−3.12108	−	29.6951i	−0.126059	−	1.19937i	−0.856408	−	0.516299i	$-0.827309\pi$
$613$	−3.12108	−	29.6951i	−0.126059	−	1.19937i	0.730349	−	0.683074i	$-0.239357\pi$
$614$		0			0
$615$	7.35155	+	12.7332i	0.296443	+	0.513454i
$616$		0			0
$617$	−13.0736	−	22.6442i	−0.526325	−	0.911621i	−0.999530	−	0.0306688i	$-0.990236\pi$
$617$	−13.0736	−	22.6442i	−0.526325	−	0.911621i	0.473205	−	0.880952i	$-0.343097\pi$
$618$		0			0
$619$	29.3287	−	21.3086i	1.17882	−	0.856463i	0.186782	−	0.982401i	$-0.440194\pi$
$619$	29.3287	−	21.3086i	1.17882	−	0.856463i	0.992038	+	0.125938i	$0.0401941\pi$
$620$		0			0
$621$	9.67230	+	2.05591i	0.388136	+	0.0825008i
$622$		0			0
$623$	−39.9489	−	29.0246i	−1.60052	−	1.16285i
$624$		0			0
$625$	−7.95361	+	24.4787i	−0.318144	+	0.979148i
$626$		0			0
$627$	−0.355622	−	4.66836i	−0.0142022	−	0.186436i
$628$		0			0
$629$	−12.4287	+	38.2515i	−0.495563	+	1.52519i
$630$		0			0
$631$	−1.16090	+	11.0452i	−0.0462148	+	0.439704i	0.946810	+	0.321795i	$0.104286\pi$
$631$	−1.16090	+	11.0452i	−0.0462148	+	0.439704i	−0.993024	+	0.117910i	$0.962381\pi$
$632$		0			0
$633$	0.0164247	−	0.0182414i	0.000652822	−	0.000725033i
$634$		0			0
$635$	2.22230	+	21.1437i	0.0881891	+	0.839063i
$636$		0			0
$637$	12.1667	+	1.50656i	0.482063	+	0.0596920i
$638$		0			0
$639$	−1.89653	+	3.28489i	−0.0750257	+	0.129948i
$640$		0			0
$641$	−6.71738	−	2.99077i	−0.265320	−	0.118128i	0.269765	−	0.962926i	$-0.413054\pi$
$641$	−6.71738	−	2.99077i	−0.265320	−	0.118128i	−0.535086	+	0.844798i	$0.679721\pi$
$642$		0			0
$643$	−11.3755	+	12.6338i	−0.448608	+	0.498229i	−0.924451	−	0.381301i	$-0.875476\pi$
$643$	−11.3755	+	12.6338i	−0.448608	+	0.498229i	0.475843	+	0.879530i	$0.342143\pi$
$644$		0			0
$645$	3.25326	+	2.36363i	0.128097	+	0.0930678i
$646$		0			0
$647$	10.8145	+	12.0107i	0.425162	+	0.472190i	0.917225	−	0.398369i	$-0.130424\pi$
$647$	10.8145	+	12.0107i	0.425162	+	0.472190i	−0.492063	+	0.870559i	$0.663757\pi$
$648$		0			0
$649$	−7.56021	−	25.7601i	−0.296764	−	1.01117i
$650$		0			0
$651$	−6.59208	+	20.2884i	−0.258364	+	0.795163i
$652$		0			0
$653$	−6.08790	+	2.71051i	−0.238238	+	0.106070i	−0.522383	−	0.852711i	$-0.674957\pi$
$653$	−6.08790	+	2.71051i	−0.238238	+	0.106070i	0.284145	+	0.958781i	$0.408290\pi$
$654$		0			0
$655$	−4.65116	−	14.3148i	−0.181736	−	0.559326i
$656$		0			0
$657$	−22.0898	−	9.83500i	−0.861804	−	0.383700i
$658$		0			0
$659$	−13.5573	−	23.4819i	−0.528116	−	0.914723i	−0.999463	−	0.0327754i	$-0.989565\pi$
$659$	−13.5573	−	23.4819i	−0.528116	−	0.914723i	0.471347	−	0.881948i	$-0.343768\pi$
$660$		0			0
$661$	−8.60954	+	14.9122i	−0.334872	+	0.580016i	−0.983460	−	0.181124i	$-0.942026\pi$
$661$	−8.60954	+	14.9122i	−0.334872	+	0.580016i	0.648588	+	0.761140i	$0.275360\pi$
$662$		0			0
$663$	−8.34829	−	5.02783i	−0.324221	−	0.195265i
$664$		0			0
$665$	15.2480	+	3.24106i	0.591291	+	0.125683i
$666$		0			0
$667$	−0.948741	+	9.02667i	−0.0367354	+	0.349514i
$668$		0			0
$669$	−14.3627	+	3.05288i	−0.555293	+	0.118031i
$670$		0			0
$671$	−10.7410	+	30.0915i	−0.414653	+	1.16167i
$672$		0			0
$673$	29.3440	+	32.5898i	1.13113	+	1.25624i	0.962712	+	0.270528i	$0.0871984\pi$
$673$	29.3440	+	32.5898i	1.13113	+	1.25624i	0.168416	+	0.985716i	$0.446135\pi$
$674$		0			0
$675$	0.454247	+	0.330029i	0.0174840	+	0.0127028i
$676$		0			0
$677$	−8.31398	−	25.5878i	−0.319532	−	0.983419i	−0.973849	−	0.227198i	$-0.927044\pi$
$677$	−8.31398	−	25.5878i	−0.319532	−	0.983419i	0.654317	−	0.756221i	$-0.272956\pi$
$678$		0			0
$679$	1.52274	+	14.4879i	0.0584374	+	0.555995i
$680$		0			0
$681$	9.38600			0.359672
$682$		0			0
$683$	−6.15000	−	10.6521i	−0.235323	−	0.407592i	0.724043	−	0.689755i	$-0.242282\pi$
$683$	−6.15000	−	10.6521i	−0.235323	−	0.407592i	−0.959367	+	0.282163i	$0.908948\pi$
$684$		0			0
$685$	13.9918	+	6.22953i	0.534597	+	0.238018i
$686$		0			0
$687$	−17.3576	−	3.68948i	−0.662234	−	0.140762i
$688$		0			0
$689$	−2.95487	+	12.7393i	−0.112571	+	0.485328i
$690$		0			0
$691$	0.754614	+	0.838084i	0.0287069	+	0.0318822i	0.757327	−	0.653036i	$-0.226505\pi$
$691$	0.754614	+	0.838084i	0.0287069	+	0.0318822i	−0.728620	+	0.684918i	$0.759838\pi$
$692$		0			0
$693$	−13.0078	−	24.1015i	−0.494127	−	0.915541i
$694$		0			0
$695$	31.8473	−	6.76935i	1.20804	−	0.256776i
$696$		0			0
$697$	−32.2340	−	23.4194i	−1.22095	−	0.887071i
$698$		0			0
$699$	16.6237	+	3.53348i	0.628767	+	0.133649i
$700$		0			0
$701$	−33.1324	+	24.0721i	−1.25139	+	0.909190i	−0.998302	−	0.0582522i	$-0.981447\pi$
$701$	−33.1324	+	24.0721i	−1.25139	+	0.909190i	−0.253091	+	0.967442i	$0.581447\pi$
$702$		0			0
$703$	−21.0057			−0.792246
$704$		0			0
$705$	10.0051	−	17.3294i	0.376816	−	0.652664i
$706$		0			0
$707$	−38.2278	+	27.7741i	−1.43770	+	1.04455i
$708$		0			0
$709$	−15.1742	+	16.8526i	−0.569879	+	0.632914i	−0.957337	−	0.288973i	$-0.906686\pi$
$709$	−15.1742	+	16.8526i	−0.569879	+	0.632914i	0.387459	+	0.921887i	$0.373353\pi$
$710$		0			0
$711$	−1.39087	+	13.2332i	−0.0521617	+	0.496285i
$712$		0			0
$713$	−17.9125	−	19.8938i	−0.670828	−	0.745030i
$714$		0			0
$715$	19.2929	+	19.0936i	0.721513	+	0.714061i
$716$		0			0
$717$	−10.4887	−	11.6488i	−0.391706	−	0.435034i
$718$		0			0
$719$	−3.11162	+	29.6051i	−0.116044	+	1.10408i	0.769216	+	0.638989i	$0.220647\pi$
$719$	−3.11162	+	29.6051i	−0.116044	+	1.10408i	−0.885260	+	0.465096i	$0.846020\pi$
$720$		0			0
$721$	39.4941	−	43.8627i	1.47084	−	1.63353i
$722$		0			0
$723$	−13.7031	+	9.95590i	−0.509624	+	0.370264i
$724$		0			0
$725$	−0.257687	+	0.446326i	−0.00957024	+	0.0165761i
$726$		0			0
$727$	11.6028			0.430324			0.215162	−	0.976578i	$-0.430972\pi$
$727$	11.6028			0.430324			0.215162	+	0.976578i	$0.430972\pi$
$728$		0			0
$729$	4.92113	−	3.57541i	0.182264	−	0.132422i
$730$		0			0
$731$	−10.6589	−	2.26562i	−0.394234	−	0.0837970i
$732$		0			0
$733$	22.9065	+	16.6426i	0.846072	+	0.614707i	0.924060	−	0.382247i	$-0.124850\pi$
$733$	22.9065	+	16.6426i	0.846072	+	0.614707i	−0.0779884	+	0.996954i	$0.524850\pi$
$734$		0			0
$735$	−5.00439	+	1.06372i	−0.184590	+	0.0392358i
$736$		0			0
$737$	−1.17100	+	8.72533i	−0.0431342	+	0.321402i
$738$		0			0
$739$	−25.4494	−	28.2644i	−0.936170	−	1.03972i	−0.999130	−	0.0417056i	$-0.986721\pi$
$739$	−25.4494	−	28.2644i	−0.936170	−	1.03972i	0.0629604	−	0.998016i	$-0.479946\pi$
$740$		0			0
$741$	1.15003	−	4.95812i	0.0422475	−	0.182141i
$742$		0			0
$743$	38.5510	+	8.19427i	1.41430	+	0.300619i	0.850796	−	0.525496i	$-0.176120\pi$
$743$	38.5510	+	8.19427i	1.41430	+	0.300619i	0.563503	+	0.826114i	$0.309453\pi$
$744$		0			0
$745$	16.5185	+	7.35449i	0.605190	+	0.269448i
$746$		0			0
$747$	−4.69958	−	8.13990i	−0.171948	−	0.297823i
$748$		0			0
$749$	32.4313			1.18501
$750$		0			0
$751$	−2.93853	−	27.9583i	−0.107229	−	1.02021i	−0.907351	−	0.420375i	$-0.861899\pi$
$751$	−2.93853	−	27.9583i	−0.107229	−	1.02021i	0.800122	−	0.599837i	$-0.204768\pi$
$752$		0			0
$753$	−4.87625	−	15.0076i	−0.177700	−	0.546906i
$754$		0			0
$755$	20.6201	+	14.9814i	0.750442	+	0.545228i
$756$		0			0
$757$	14.2374	+	15.8123i	0.517469	+	0.574707i	0.944075	−	0.329730i	$-0.106958\pi$
$757$	14.2374	+	15.8123i	0.517469	+	0.574707i	−0.426606	+	0.904437i	$0.640291\pi$
$758$		0			0
$759$	−5.89553	−	0.169186i	−0.213994	−	0.00614107i
$760$		0			0
$761$	1.04692	−	0.222530i	0.0379508	−	0.00806669i	−0.188897	−	0.981997i	$-0.560491\pi$
$761$	1.04692	−	0.222530i	0.0379508	−	0.00806669i	0.226848	+	0.973930i	$0.427158\pi$
$762$		0			0
$763$	−1.97104	+	18.7532i	−0.0713565	+	0.678912i
$764$		0			0
$765$	−23.1811	−	4.92729i	−0.838113	−	0.178146i
$766$		0			0
$767$	0.539294	−	29.1803i	0.0194728	−	1.05364i
$768$		0			0
$769$	−19.2339	+	33.3140i	−0.693591	+	1.20133i	0.277063	+	0.960852i	$0.410639\pi$
$769$	−19.2339	+	33.3140i	−0.693591	+	1.20133i	−0.970653	+	0.240483i	$0.922694\pi$
$770$		0			0
$771$	−3.04007	−	5.26556i	−0.109486	−	0.189635i
$772$		0			0
$773$	−3.13808	−	1.39716i	−0.112869	−	0.0502525i	0.349525	−	0.936927i	$-0.386343\pi$
$773$	−3.13808	−	1.39716i	−0.112869	−	0.0502525i	−0.462394	+	0.886674i	$0.653010\pi$
$774$		0			0
$775$	−0.469717	−	1.44564i	−0.0168727	−	0.0519289i
$776$		0			0
$777$	19.2639	−	8.57683i	0.691088	−	0.307692i
$778$		0			0
$779$	6.43035	−	19.7906i	0.230391	−	0.709071i
$780$		0			0
$781$	1.65162	−	4.62709i	0.0590995	−	0.165570i
$782$		0			0
$783$	−8.34485	−	9.26789i	−0.298220	−	0.331207i
$784$		0			0
$785$	16.0130	+	11.6341i	0.571527	+	0.415239i
$786$		0			0
$787$	−15.6115	+	17.3383i	−0.556491	+	0.618045i	−0.954092	−	0.299513i	$-0.903176\pi$
$787$	−15.6115	+	17.3383i	−0.556491	+	0.618045i	0.397602	+	0.917558i	$0.369843\pi$
$788$		0			0
$789$	3.88362	+	1.72910i	0.138261	+	0.0615576i
$790$		0			0
$791$	7.06033	−	12.2288i	0.251036	−	0.434808i
$792$		0			0
$793$	−20.9322	+	27.7187i	−0.743323	+	0.984320i
$794$		0			0
$795$	−0.570464	−	5.42760i	−0.0202323	−	0.192497i
$796$		0			0
$797$	−25.6662	+	28.5052i	−0.909143	+	1.00971i	0.0907618	+	0.995873i	$0.471070\pi$
$797$	−25.6662	+	28.5052i	−0.909143	+	1.00971i	−0.999904	+	0.0138325i	$0.995597\pi$
$798$		0			0
$799$	−5.66807	+	53.9281i	−0.200522	+	1.90784i
$800$		0			0
$801$	−12.1157	+	37.2882i	−0.428086	+	1.31751i
$802$		0			0
$803$	30.4360	+	7.38787i	1.07406	+	0.260712i
$804$		0			0
$805$	6.06835	−	18.6765i	0.213881	−	0.658259i
$806$		0			0
$807$	12.0547	+	8.75825i	0.424345	+	0.308305i
$808$		0			0
$809$	14.8531	+	3.15713i	0.522208	+	0.110999i	0.461472	−	0.887155i	$-0.347322\pi$
$809$	14.8531	+	3.15713i	0.522208	+	0.110999i	0.0607368	+	0.998154i	$0.480655\pi$
$810$		0			0
$811$	6.71514	−	4.87883i	0.235800	−	0.171319i	−0.463610	−	0.886039i	$-0.653446\pi$
$811$	6.71514	−	4.87883i	0.235800	−	0.171319i	0.699410	+	0.714720i	$0.253446\pi$
$812$		0			0
$813$	10.1280	+	17.5422i	0.355203	+	0.615230i
$814$		0			0
$815$	−11.4265	−	19.7912i	−0.400252	−	0.693256i
$816$		0			0
$817$	−0.594893	−	5.66003i	−0.0208127	−	0.198019i
$818$		0			0
$819$	−5.65108	−	29.2324i	−0.197465	−	1.02146i
$820$		0			0
$821$	3.92720	−	1.74850i	0.137060	−	0.0610231i	−0.337061	−	0.941483i	$-0.609433\pi$
$821$	3.92720	−	1.74850i	0.137060	−	0.0610231i	0.474121	+	0.880460i	$0.342766\pi$
$822$		0			0
$823$	12.2113	−	2.59560i	0.425660	−	0.0904768i	0.00989947	−	0.999951i	$-0.496849\pi$
$823$	12.2113	−	2.59560i	0.425660	−	0.0904768i	0.415760	+	0.909474i	$0.363516\pi$
$824$		0			0
$825$	−0.301910	−	0.144935i	−0.0105111	−	0.00504598i
$826$		0			0
$827$	2.43714	−	7.50073i	0.0847475	−	0.260826i	−0.899699	−	0.436511i	$-0.856214\pi$
$827$	2.43714	−	7.50073i	0.0847475	−	0.260826i	0.984446	+	0.175685i	$0.0562140\pi$
$828$		0			0
$829$	−33.8873	+	15.0876i	−1.17695	+	0.524014i	−0.899584	−	0.436749i	$-0.856130\pi$
$829$	−33.8873	+	15.0876i	−1.17695	+	0.524014i	−0.277371	+	0.960763i	$0.589463\pi$
$830$		0			0
$831$	5.89393	+	18.1396i	0.204458	+	0.629257i
$832$		0			0
$833$	11.2164	−	8.14917i	0.388624	−	0.282352i
$834$		0			0
$835$	−18.8913	+	32.7206i	−0.653759	+	1.13234i
$836$		0			0
$837$	36.7824			1.27138
$838$		0			0
$839$	8.84282	+	3.93708i	0.305288	+	0.135923i	0.553663	−	0.832741i	$-0.313230\pi$
$839$	8.84282	+	3.93708i	0.305288	+	0.135923i	−0.248375	+	0.968664i	$0.579896\pi$
$840$		0			0
$841$	−11.7452	+	13.0444i	−0.405006	+	0.449805i
$842$		0			0
$843$	10.4572	−	4.65585i	0.360165	−	0.160356i
$844$		0			0
$845$	13.7998	+	26.0827i	0.474729	+	0.897272i
$846$		0			0
$847$	22.1860	+	27.6804i	0.762321	+	0.951110i
$848$		0			0
$849$	−2.02963	+	0.431412i	−0.0696569	+	0.0148060i
$850$		0			0
$851$	−2.76600	+	26.3168i	−0.0948174	+	0.902127i
$852$		0			0
$853$	2.94248	+	9.05601i	0.100748	+	0.310072i	0.988709	−	0.149847i	$-0.0478783\pi$
$853$	2.94248	+	9.05601i	0.100748	+	0.310072i	−0.887961	+	0.459919i	$0.847878\pi$
$854$		0			0
$855$	−1.29378	−	12.3095i	−0.0442463	−	0.420975i
$856$		0			0
$857$	39.6552			1.35460			0.677299	−	0.735708i	$-0.263151\pi$
$857$	39.6552			1.35460			0.677299	+	0.735708i	$0.263151\pi$
$858$		0			0
$859$	51.0153			1.74062			0.870309	−	0.492506i	$-0.163919\pi$
$859$	51.0153			1.74062			0.870309	+	0.492506i	$0.163919\pi$
$860$		0			0
$861$	2.18355	+	20.7751i	0.0744151	+	0.708012i
$862$		0			0
$863$	−3.96327	−	12.1977i	−0.134911	−	0.415215i	0.860665	−	0.509172i	$-0.170048\pi$
$863$	−3.96327	−	12.1977i	−0.134911	−	0.415215i	−0.995576	+	0.0939573i	$0.970048\pi$
$864$		0			0
$865$	0.106169	−	1.01013i	0.00360986	−	0.0343456i
$866$		0			0
$867$	0.242754	−	0.0515989i	0.00824435	−	0.00175239i
$868$		0			0
$869$	−1.30911	−	17.1851i	−0.0444087	−	0.582966i
$870$		0			0
$871$	−4.05355	+	8.66964i	−0.137349	+	0.293760i
$872$		0			0
$873$	10.5667	−	4.70459i	0.357628	−	0.159226i
$874$		0			0
$875$	−23.7447	+	26.3712i	−0.802718	+	0.891509i
$876$		0			0
$877$	−12.8020	−	5.69980i	−0.432292	−	0.192469i	0.179042	−	0.983841i	$-0.442700\pi$
$877$	−12.8020	−	5.69980i	−0.432292	−	0.192469i	−0.611334	+	0.791373i	$0.709367\pi$
$878$		0			0
$879$	−5.23567			−0.176595
$880$		0			0
$881$	7.01838	−	12.1562i	0.236455	−	0.409552i	−0.723239	−	0.690597i	$-0.757348\pi$
$881$	7.01838	−	12.1562i	0.236455	−	0.409552i	0.959695	+	0.281045i	$0.0906810\pi$
$882$		0			0
$883$	−20.4694	+	14.8719i	−0.688851	+	0.500479i	−0.876282	−	0.481798i	$-0.839984\pi$
$883$	−20.4694	+	14.8719i	−0.688851	+	0.500479i	0.187431	+	0.982278i	$0.439984\pi$
$884$		0			0
$885$	3.76371	+	11.5835i	0.126516	+	0.389375i
$886$		0			0
$887$	−4.53239	+	2.01795i	−0.152183	+	0.0677561i	−0.481415	−	0.876493i	$-0.659877\pi$
$887$	−4.53239	+	2.01795i	−0.152183	+	0.0677561i	0.329232	+	0.944249i	$0.393210\pi$
$888$		0			0
$889$	−9.33403	+	28.7272i	−0.313053	+	0.963479i
$890$		0			0
$891$	−11.9907	+	12.5723i	−0.401705	+	0.421186i
$892$		0			0
$893$	−27.7014	+	5.88811i	−0.926991	+	0.197038i
$894$		0			0
$895$	−10.6173	+	4.72712i	−0.354897	+	0.158010i
$896$		0			0
$897$	−6.06029	−	2.09368i	−0.202347	−	0.0699060i
$898$		0			0
$899$	3.52908	+	33.5770i	0.117702	+	1.11986i
$900$		0			0
$901$	7.39454	+	12.8077i	0.246348	+	0.426687i
$902$		0			0
$903$	2.85660	+	4.94778i	0.0950618	+	0.164652i
$904$		0			0
$905$	−12.5576	+	9.12363i	−0.417429	+	0.303280i
$906$		0			0
$907$	−15.4474	−	3.28345i	−0.512922	−	0.109025i	−0.0558231	−	0.998441i	$-0.517778\pi$
$907$	−15.4474	−	3.28345i	−0.512922	−	0.109025i	−0.457099	+	0.889416i	$0.651112\pi$
$908$		0			0
$909$	30.3527	+	22.0525i	1.00673	+	0.731435i
$910$		0			0
$911$	2.89337	−	8.90488i	0.0958616	−	0.295032i	−0.891616	−	0.452793i	$-0.850428\pi$
$911$	2.89337	−	8.90488i	0.0958616	−	0.295032i	0.987477	+	0.157761i	$0.0504276\pi$
$912$		0			0
$913$	7.88336	+	9.27728i	0.260901	+	0.307033i
$914$		0			0
$915$	4.47932	−	13.7859i	0.148082	−	0.455749i
$916$		0			0
$917$	2.23529	−	21.2673i	0.0738156	−	0.702309i
$918$		0			0
$919$	−3.64767	+	4.05115i	−0.120326	+	0.133635i	−0.800298	−	0.599603i	$-0.795325\pi$
$919$	−3.64767	+	4.05115i	−0.120326	+	0.133635i	0.679972	+	0.733238i	$0.261992\pi$
$920$		0			0
$921$	−0.931485	−	8.86249i	−0.0306935	−	0.292029i
$922$		0			0
$923$	3.21868	−	4.26222i	0.105944	−	0.140293i
$924$		0			0
$925$	−0.751272	+	1.30124i	−0.0247017	+	0.0427845i
$926$		0			0
$927$	−42.8124	−	19.0613i	−1.40614	−	0.626055i
$928$		0			0
$929$	−24.2314	+	26.9117i	−0.795007	+	0.882945i	−0.995305	−	0.0967905i	$-0.969142\pi$
$929$	−24.2314	+	26.9117i	−0.795007	+	0.882945i	0.200298	+	0.979735i	$0.435809\pi$
$930$		0			0
$931$	5.85799	+	4.25608i	0.191988	+	0.139487i
$932$		0			0
$933$	5.58905	+	6.20727i	0.182977	+	0.203217i
$934$		0			0
$935$	30.6837	+	0.880543i	1.00347	+	0.0287968i
$936$		0			0
$937$	−3.33423	+	10.2617i	−0.108925	+	0.335235i	−0.990632	−	0.136562i	$-0.956395\pi$
$937$	−3.33423	+	10.2617i	−0.108925	+	0.335235i	0.881707	+	0.471797i	$0.156395\pi$
$938$		0			0
$939$	10.0091	−	4.45636i	0.326636	−	0.145428i
$940$		0			0
$941$	−8.19884	−	25.2334i	−0.267275	−	0.822587i	−0.991161	−	0.132667i	$-0.957646\pi$
$941$	−8.19884	−	25.2334i	−0.267275	−	0.822587i	0.723886	−	0.689919i	$-0.242354\pi$
$942$		0			0
$943$	−23.9476	−	10.6622i	−0.779843	−	0.347208i
$944$		0			0
$945$	13.4913	+	23.3675i	0.438871	+	0.760146i
$946$		0			0
$947$	5.50706	−	9.53851i	0.178955	−	0.309960i	−0.762568	−	0.646909i	$-0.776062\pi$
$947$	5.50706	−	9.53851i	0.178955	−	0.309960i	0.941523	+	0.336949i	$0.109395\pi$
$948$		0			0
$949$	29.1670	+	17.5661i	0.946801	+	0.570218i
$950$		0			0
$951$	−6.84250	−	1.45442i	−0.221883	−	0.0471627i
$952$		0			0
$953$	5.96500	−	56.7532i	0.193225	−	1.83842i	−0.283031	−	0.959111i	$-0.591340\pi$
$953$	5.96500	−	56.7532i	0.193225	−	1.83842i	0.476257	−	0.879306i	$-0.341993\pi$
$954$		0			0
$955$	0.472721	−	0.100480i	0.0152969	−	0.00325145i
$956$		0			0
$957$	5.88995	+	4.54305i	0.190395	+	0.146856i
$958$		0			0
$959$	14.5604	+	16.1709i	0.470179	+	0.522186i
$960$		0			0
$961$	−55.4800	−	40.3086i	−1.78968	−	1.30028i
$962$		0			0
$963$	−7.95728	−	24.4900i	−0.256420	−	0.789179i
$964$		0			0
$965$	−1.07497	−	10.2277i	−0.0346045	−	0.329240i
$966$		0			0
$967$	19.1967			0.617325			0.308662	−	0.951172i	$-0.400119\pi$
$967$	19.1967			0.617325			0.308662	+	0.951172i	$0.400119\pi$
$968$		0			0
$969$	−2.87795	−	4.98476i	−0.0924531	−	0.160133i
$970$		0			0
$971$	−11.7058	−	5.21175i	−0.375657	−	0.167253i	0.210219	−	0.977654i	$-0.432582\pi$
$971$	−11.7058	−	5.21175i	−0.375657	−	0.167253i	−0.585875	+	0.810401i	$0.699249\pi$
$972$		0			0
$973$	45.2472	+	9.61759i	1.45056	+	0.308326i
$974$		0			0
$975$	−0.266009	−	0.248569i	−0.00851912	−	0.00796057i
$976$		0			0
$977$	−30.5728	−	33.9545i	−0.978110	−	1.08630i	−0.996255	−	0.0864661i	$-0.972443\pi$
$977$	−30.5728	−	33.9545i	−0.978110	−	1.08630i	0.0181445	−	0.999835i	$-0.494224\pi$
$978$		0			0
$979$	6.75491	−	50.3322i	0.215888	−	1.60863i
$980$		0			0
$981$	14.6448	−	3.11284i	0.467572	−	0.0993855i
$982$		0			0
$983$	−33.7339	−	24.5091i	−1.07594	−	0.781719i	−0.0989724	−	0.995090i	$-0.531556\pi$
$983$	−33.7339	−	24.5091i	−1.07594	−	0.781719i	−0.976971	+	0.213371i	$0.931556\pi$
$984$		0			0
$985$	−44.4982	−	9.45838i	−1.41783	−	0.301369i
$986$		0			0
$987$	23.0001	−	16.7106i	0.732102	−	0.531904i
$988$		0			0
$989$	−7.16943			−0.227975
$990$		0			0
$991$	7.87959	−	13.6479i	0.250303	−	0.433538i	−0.713306	−	0.700853i	$-0.752803\pi$
$991$	7.87959	−	13.6479i	0.250303	−	0.433538i	0.963609	+	0.267315i	$0.0861363\pi$
$992$		0			0
$993$	0.135799	−	0.0986639i	0.00430946	−	0.00313100i
$994$		0			0
$995$	−16.6416	+	18.4824i	−0.527575	+	0.585931i
$996$		0			0
$997$	−3.98205	+	37.8866i	−0.126113	+	1.19988i	0.730130	+	0.683308i	$0.239459\pi$
$997$	−3.98205	+	37.8866i	−0.126113	+	1.19988i	−0.856243	+	0.516574i	$0.827207\pi$
$998$		0			0
$999$	−24.3290	−	27.0200i	−0.769734	−	0.854876i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bg.a.9.7	✓	112
11.5	even	5	inner	572.2.bg.a.269.8	yes	112
13.3	even	3	inner	572.2.bg.a.185.8	yes	112
143.16	even	15	inner	572.2.bg.a.445.7	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bg.a.9.7	✓	112	1.1	even	1	trivial
572.2.bg.a.185.8	yes	112	13.3	even	3	inner
572.2.bg.a.269.8	yes	112	11.5	even	5	inner
572.2.bg.a.445.7	yes	112	143.16	even	15	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.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0692906 - 0.659256i) q^{3} +(0.701430 + 2.15878i) q^{5} +(-0.337098 + 3.20727i) q^{7} +(2.50463 - 0.532375i) q^{9} +O(q^{10})\)	\(q+(-0.0692906 - 0.659256i) q^{3} +(0.701430 + 2.15878i) q^{5} +(-0.337098 + 3.20727i) q^{7} +(2.50463 - 0.532375i) q^{9} +(-3.06734 + 1.26152i) q^{11} +(-3.59215 + 0.310559i) q^{13} +(1.37458 - 0.612004i) q^{15} +(-2.72835 + 3.03014i) q^{17} +(-1.94543 - 0.866160i) q^{19} +2.13777 q^{21} +(-1.34133 + 2.32325i) q^{23} +(-0.123234 + 0.0895350i) q^{25} +(-1.13905 - 3.50563i) q^{27} +(3.09085 - 1.37613i) q^{29} +(-3.08363 + 9.49043i) q^{31} +(1.04420 + 1.93475i) q^{33} +(-7.16023 + 1.52195i) q^{35} +(9.01121 - 4.01205i) q^{37} +(0.453640 + 2.34663i) q^{39} +(1.02141 + 9.71811i) q^{41} +(1.33625 + 2.31446i) q^{43} +(2.90610 + 5.03351i) q^{45} +(10.7589 - 7.81683i) q^{47} +(-3.32591 - 0.706944i) q^{49} +(2.18668 + 1.58872i) q^{51} +(1.12082 - 3.44952i) q^{53} +(-4.87487 - 5.73683i) q^{55} +(-0.436221 + 1.34255i) q^{57} +(-0.846110 + 8.05020i) q^{59} +(6.44614 - 7.15916i) q^{61} +(0.863166 + 8.21247i) q^{63} +(-3.19007 - 7.53682i) q^{65} +(1.32719 - 2.29875i) q^{67} +(1.62456 + 0.723300i) q^{69} +(-0.991204 + 1.10084i) q^{71} +(-7.63977 - 5.55062i) q^{73} +(0.0675655 + 0.0750390i) q^{75} +(-3.01205 - 10.2630i) q^{77} +(-1.60582 + 4.94219i) q^{79} +(4.78544 - 2.13061i) q^{81} +(-1.13431 - 3.49105i) q^{83} +(-8.45514 - 3.76447i) q^{85} +(-1.12139 - 1.94231i) q^{87} +(-7.65590 + 13.2604i) q^{89} +(0.214859 - 11.6257i) q^{91} +(6.47029 + 1.37530i) q^{93} +(0.505267 - 4.80730i) q^{95} +(4.41850 - 0.939181i) q^{97} +(-7.01093 + 4.79262i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 8 q^{9}+O(q^{10}) \) 112 * q + 8 * q^9	\( 112 q + 8 q^{9} - 10 q^{11} + 11 q^{13} - 2 q^{15} + 4 q^{17} - 12 q^{19} - 40 q^{21} + 10 q^{23} - 16 q^{25} - 12 q^{27} + q^{29} + 4 q^{31} + 35 q^{33} - 5 q^{35} - 12 q^{37} + 21 q^{39} - 10 q^{41} - 32 q^{43} + 34 q^{45} + 70 q^{47} + 16 q^{49} - 48 q^{51} - 26 q^{53} + 10 q^{55} - 12 q^{57} - 5 q^{59} + 28 q^{61} + 34 q^{63} + 22 q^{65} - 68 q^{67} - 58 q^{69} + 44 q^{71} + 42 q^{73} - 24 q^{75} + 46 q^{77} - 24 q^{79} + 64 q^{81} - 114 q^{83} + 4 q^{85} - 30 q^{87} - 6 q^{89} + 77 q^{91} - 5 q^{93} - 36 q^{95} - 15 q^{97} - 40 q^{99}+O(q^{100}) \) 112 * q + 8 * q^9 - 10 * q^11 + 11 * q^13 - 2 * q^15 + 4 * q^17 - 12 * q^19 - 40 * q^21 + 10 * q^23 - 16 * q^25 - 12 * q^27 + q^29 + 4 * q^31 + 35 * q^33 - 5 * q^35 - 12 * q^37 + 21 * q^39 - 10 * q^41 - 32 * q^43 + 34 * q^45 + 70 * q^47 + 16 * q^49 - 48 * q^51 - 26 * q^53 + 10 * q^55 - 12 * q^57 - 5 * q^59 + 28 * q^61 + 34 * q^63 + 22 * q^65 - 68 * q^67 - 58 * q^69 + 44 * q^71 + 42 * q^73 - 24 * q^75 + 46 * q^77 - 24 * q^79 + 64 * q^81 - 114 * q^83 + 4 * q^85 - 30 * q^87 - 6 * q^89 + 77 * q^91 - 5 * q^93 - 36 * q^95 - 15 * q^97 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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