LMFDB - Embedded newform 592.2.bc.d.33.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [592,2,Mod(33,592)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(592, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 10]))

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

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

chi := DirichletCharacter("592.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 592 = 2^{4} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	592.bc (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.72714379966$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 24x^{10} + 264x^{8} - 1687x^{6} + 6600x^{4} - 15000x^{2} + 15625 $ x^12 - 24x^10 + 264x^8 - 1687x^6 + 6600x^4 - 15000*x^2 + 15625
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 74)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			33.2
Root			$2.14169 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	592.33
Dual form			592.2.bc.d.305.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.238878 + 1.35474i) q^{3} +(0.266044 - 0.223238i) q^{5} +(0.365982 - 0.307095i) q^{7} +(1.04081 - 0.378824i) q^{9} +O(q^{10})$	\(q+(0.238878 + 1.35474i) q^{3} +(0.266044 - 0.223238i) q^{5} +(0.365982 - 0.307095i) q^{7} +(1.04081 - 0.378824i) q^{9} +(1.29268 - 2.23899i) q^{11} +(4.21288 + 1.53336i) q^{13} +(0.365982 + 0.307095i) q^{15} +(-1.88864 + 0.687407i) q^{17} +(-0.611631 - 3.46873i) q^{19} +(0.503461 + 0.422454i) q^{21} +(2.60486 + 4.51175i) q^{23} +(-0.847296 + 4.80526i) q^{25} +(2.82530 + 4.89356i) q^{27} +(-0.114111 + 0.197646i) q^{29} +6.74658 q^{31} +(3.34205 + 1.21641i) q^{33} +(0.0288122 - 0.163402i) q^{35} +(2.42322 - 5.57925i) q^{37} +(-1.07095 + 6.07365i) q^{39} +(-10.0701 - 3.66521i) q^{41} -8.85889 q^{43} +(0.192334 - 0.333132i) q^{45} +(3.72890 + 6.45864i) q^{47} +(-1.17590 + 6.66887i) q^{49} +(-1.38241 - 2.39441i) q^{51} +(3.35194 + 2.81261i) q^{53} +(-0.155916 - 0.884246i) q^{55} +(4.55314 - 1.65721i) q^{57} +(-3.43016 - 2.87825i) q^{59} +(1.35175 + 0.491998i) q^{61} +(0.264583 - 0.458271i) q^{63} +(1.46312 - 0.532531i) q^{65} +(8.06111 - 6.76408i) q^{67} +(-5.49002 + 4.60667i) q^{69} +(-1.54193 - 8.74474i) q^{71} +7.18667 q^{73} -6.71229 q^{75} +(-0.214485 - 1.21641i) q^{77} +(-2.70857 + 2.27276i) q^{79} +(-3.40919 + 2.86065i) q^{81} +(1.32932 - 0.483834i) q^{83} +(-0.349006 + 0.604496i) q^{85} +(-0.295018 - 0.107378i) q^{87} +(2.92954 + 2.45818i) q^{89} +(2.01273 - 0.732572i) q^{91} +(1.61161 + 9.13989i) q^{93} +(-0.937074 - 0.786298i) q^{95} +(-9.24175 - 16.0072i) q^{97} +(0.497253 - 2.82006i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{3} - 6 q^{5} - 6 q^{7} - 3 q^{9}+O(q^{10}) $ 12 * q + 3 * q^3 - 6 * q^5 - 6 * q^7 - 3 * q^9	$ 12 q + 3 q^{3} - 6 q^{5} - 6 q^{7} - 3 q^{9} - 3 q^{11} - 6 q^{13} - 6 q^{15} - 3 q^{17} + 3 q^{19} - 33 q^{21} + 21 q^{23} - 6 q^{25} - 3 q^{27} + 6 q^{29} - 42 q^{31} + 57 q^{33} + 9 q^{35} - 3 q^{37} + 24 q^{39} - 21 q^{41} - 36 q^{43} - 6 q^{45} - 9 q^{47} - 12 q^{49} - 6 q^{53} - 36 q^{57} + 6 q^{59} - 18 q^{61} - 36 q^{63} + 3 q^{65} + 27 q^{67} - 12 q^{69} + 18 q^{71} + 54 q^{73} + 6 q^{75} + 51 q^{77} + 12 q^{79} - 36 q^{81} + 6 q^{83} + 3 q^{85} - 39 q^{87} - 15 q^{89} + 51 q^{91} + 45 q^{93} + 15 q^{95} - 42 q^{97} + 33 q^{99}+O(q^{100}) $ 12 * q + 3 * q^3 - 6 * q^5 - 6 * q^7 - 3 * q^9 - 3 * q^11 - 6 * q^13 - 6 * q^15 - 3 * q^17 + 3 * q^19 - 33 * q^21 + 21 * q^23 - 6 * q^25 - 3 * q^27 + 6 * q^29 - 42 * q^31 + 57 * q^33 + 9 * q^35 - 3 * q^37 + 24 * q^39 - 21 * q^41 - 36 * q^43 - 6 * q^45 - 9 * q^47 - 12 * q^49 - 6 * q^53 - 36 * q^57 + 6 * q^59 - 18 * q^61 - 36 * q^63 + 3 * q^65 + 27 * q^67 - 12 * q^69 + 18 * q^71 + 54 * q^73 + 6 * q^75 + 51 * q^77 + 12 * q^79 - 36 * q^81 + 6 * q^83 + 3 * q^85 - 39 * q^87 - 15 * q^89 + 51 * q^91 + 45 * q^93 + 15 * q^95 - 42 * q^97 + 33 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/592\mathbb{Z}\right)^\times$.

$n$	$113$	$149$	$223$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.238878	+	1.35474i	0.137916	+	0.782162i	0.972784	+	0.231712i	$0.0744326\pi$
$3$	0.238878	+	1.35474i	0.137916	+	0.782162i	−0.834868	+	0.550450i	$0.814456\pi$
$4$		0			0
$5$	0.266044	−	0.223238i	0.118979	−	0.0998350i	−0.581357	−	0.813649i	$-0.697478\pi$
$5$	0.266044	−	0.223238i	0.118979	−	0.0998350i	0.700336	+	0.713814i	$0.253034\pi$
$6$		0			0
$7$	0.365982	−	0.307095i	0.138328	−	0.116071i	−0.570998	−	0.820951i	$-0.693444\pi$
$7$	0.365982	−	0.307095i	0.138328	−	0.116071i	0.709326	+	0.704880i	$0.248999\pi$
$8$		0			0
$9$	1.04081	−	0.378824i	0.346937	−	0.126275i
$10$		0			0
$11$	1.29268	−	2.23899i	0.389758	−	0.675081i	−0.602659	−	0.797999i	$-0.705892\pi$
$11$	1.29268	−	2.23899i	0.389758	−	0.675081i	0.992417	+	0.122918i	$0.0392253\pi$
$12$		0			0
$13$	4.21288	+	1.53336i	1.16844	+	0.425278i	0.852106	−	0.523369i	$-0.175325\pi$
$13$	4.21288	+	1.53336i	1.16844	+	0.425278i	0.316336	+	0.948647i	$0.397547\pi$
$14$		0			0
$15$	0.365982	+	0.307095i	0.0944962	+	0.0792917i
$16$		0			0
$17$	−1.88864	+	0.687407i	−0.458062	+	0.166721i	−0.560737	−	0.827994i	$-0.689482\pi$
$17$	−1.88864	+	0.687407i	−0.458062	+	0.166721i	0.102675	+	0.994715i	$0.467260\pi$
$18$		0			0
$19$	−0.611631	−	3.46873i	−0.140318	−	0.795782i	−0.971008	−	0.239047i	$-0.923165\pi$
$19$	−0.611631	−	3.46873i	−0.140318	−	0.795782i	0.830690	−	0.556735i	$-0.187946\pi$
$20$		0			0
$21$	0.503461	+	0.422454i	0.109864	+	0.0921869i
$22$		0			0
$23$	2.60486	+	4.51175i	0.543151	+	0.940765i	0.998721	+	0.0505649i	$0.0161022\pi$
$23$	2.60486	+	4.51175i	0.543151	+	0.940765i	−0.455570	+	0.890200i	$0.650565\pi$
$24$		0			0
$25$	−0.847296	+	4.80526i	−0.169459	+	0.961051i
$26$		0			0
$27$	2.82530	+	4.89356i	0.543729	+	0.941767i
$28$		0			0
$29$	−0.114111	+	0.197646i	−0.0211899	+	0.0367019i	−0.876426	−	0.481537i	$-0.840079\pi$
$29$	−0.114111	+	0.197646i	−0.0211899	+	0.0367019i	0.855236	+	0.518239i	$0.173412\pi$
$30$		0			0
$31$	6.74658			1.21172			0.605861	−	0.795571i	$-0.292829\pi$
$31$	6.74658			1.21172			0.605861	+	0.795571i	$0.292829\pi$
$32$		0			0
$33$	3.34205	+	1.21641i	0.581776	+	0.211749i
$34$		0			0
$35$	0.0288122	−	0.163402i	0.00487015	−	0.0276200i
$36$		0			0
$37$	2.42322	−	5.57925i	0.398376	−	0.917222i
$37$	2.42322	−	5.57925i	0.398376	−	0.917222i
$38$		0			0
$39$	−1.07095	+	6.07365i	−0.171489	+	0.972563i
$40$		0			0
$41$	−10.0701	−	3.66521i	−1.57268	−	0.572410i	−0.599086	−	0.800685i	$-0.704469\pi$
$41$	−10.0701	−	3.66521i	−1.57268	−	0.572410i	−0.973597	+	0.228275i	$0.926691\pi$
$42$		0			0
$43$	−8.85889			−1.35097			−0.675484	−	0.737374i	$-0.736065\pi$
$43$	−8.85889			−1.35097			−0.675484	+	0.737374i	$0.736065\pi$
$44$		0			0
$45$	0.192334	−	0.333132i	0.0286715	−	0.0496604i
$46$		0			0
$47$	3.72890	+	6.45864i	0.543916	+	0.942090i	0.998674	+	0.0514750i	$0.0163923\pi$
$47$	3.72890	+	6.45864i	0.543916	+	0.942090i	−0.454758	+	0.890615i	$0.650274\pi$
$48$		0			0
$49$	−1.17590	+	6.66887i	−0.167986	+	0.952696i
$50$		0			0
$51$	−1.38241	−	2.39441i	−0.193577	−	0.335285i
$52$		0			0
$53$	3.35194	+	2.81261i	0.460424	+	0.386342i	0.843287	−	0.537464i	$-0.180617\pi$
$53$	3.35194	+	2.81261i	0.460424	+	0.386342i	−0.382863	+	0.923805i	$0.625062\pi$
$54$		0			0
$55$	−0.155916	−	0.884246i	−0.0210238	−	0.119232i
$56$		0			0
$57$	4.55314	−	1.65721i	0.603078	−	0.219502i
$58$		0			0
$59$	−3.43016	−	2.87825i	−0.446569	−	0.374716i	0.391592	−	0.920139i	$-0.371924\pi$
$59$	−3.43016	−	2.87825i	−0.446569	−	0.374716i	−0.838161	+	0.545423i	$0.816369\pi$
$60$		0			0
$61$	1.35175	+	0.491998i	0.173074	+	0.0629939i	0.427104	−	0.904203i	$-0.359534\pi$
$61$	1.35175	+	0.491998i	0.173074	+	0.0629939i	−0.254030	+	0.967196i	$0.581756\pi$
$62$		0			0
$63$	0.264583	−	0.458271i	0.0333343	−	0.0577367i
$64$		0			0
$65$	1.46312	−	0.532531i	0.181477	−	0.0660523i
$66$		0			0
$67$	8.06111	−	6.76408i	0.984822	−	0.826363i	1.18267e−5	−	1.00000i	$-0.499996\pi$
$67$	8.06111	−	6.76408i	0.984822	−	0.826363i	0.984810	+	0.173637i	$0.0555518\pi$
$68$		0			0
$69$	−5.49002	+	4.60667i	−0.660921	+	0.554578i
$70$		0			0
$71$	−1.54193	−	8.74474i	−0.182994	−	1.03781i	−0.928506	−	0.371318i	$-0.878906\pi$
$71$	−1.54193	−	8.74474i	−0.182994	−	1.03781i	0.745512	−	0.666492i	$-0.232205\pi$
$72$		0			0
$73$	7.18667			0.841136			0.420568	−	0.907261i	$-0.361831\pi$
$73$	7.18667			0.841136			0.420568	+	0.907261i	$0.361831\pi$
$74$		0			0
$75$	−6.71229			−0.775069
$76$		0			0
$77$	−0.214485	−	1.21641i	−0.0244429	−	0.138622i
$78$		0			0
$79$	−2.70857	+	2.27276i	−0.304738	+	0.255705i	−0.782313	−	0.622885i	$-0.785960\pi$
$79$	−2.70857	+	2.27276i	−0.304738	+	0.255705i	0.477575	+	0.878591i	$0.341516\pi$
$80$		0			0
$81$	−3.40919	+	2.86065i	−0.378799	+	0.317850i
$82$		0			0
$83$	1.32932	−	0.483834i	0.145912	−	0.0531077i	−0.268032	−	0.963410i	$-0.586373\pi$
$83$	1.32932	−	0.483834i	0.145912	−	0.0531077i	0.413944	+	0.910302i	$0.364151\pi$
$84$		0			0
$85$	−0.349006	+	0.604496i	−0.0378550	+	0.0655668i
$86$		0			0
$87$	−0.295018	−	0.107378i	−0.0316292	−	0.0115121i
$88$		0			0
$89$	2.92954	+	2.45818i	0.310531	+	0.260567i	0.784711	−	0.619861i	$-0.212811\pi$
$89$	2.92954	+	2.45818i	0.310531	+	0.260567i	−0.474180	+	0.880428i	$0.657256\pi$
$90$		0			0
$91$	2.01273	−	0.732572i	0.210991	−	0.0767944i
$92$		0			0
$93$	1.61161	+	9.13989i	0.167116	+	0.947762i
$94$		0			0
$95$	−0.937074	−	0.786298i	−0.0961417	−	0.0806725i
$96$		0			0
$97$	−9.24175	−	16.0072i	−0.938358	−	1.62528i	−0.768534	−	0.639809i	$-0.779013\pi$
$97$	−9.24175	−	16.0072i	−0.938358	−	1.62528i	−0.169824	−	0.985474i	$-0.554320\pi$
$98$		0			0
$99$	0.497253	−	2.82006i	0.0499758	−	0.283427i
$100$		0			0
$101$	−8.56431	−	14.8338i	−0.852180	−	1.47602i	−0.879236	−	0.476386i	$-0.841947\pi$
$101$	−8.56431	−	14.8338i	−0.852180	−	1.47602i	0.0270562	−	0.999634i	$-0.491387\pi$
$102$		0			0
$103$	−6.71012	+	11.6223i	−0.661167	+	1.14518i	0.319142	+	0.947707i	$0.396605\pi$
$103$	−6.71012	+	11.6223i	−0.661167	+	1.14518i	−0.980309	+	0.197468i	$0.936728\pi$
$104$		0			0
$105$	0.228251			0.0222750
$106$		0			0
$107$	−19.2261	−	6.99774i	−1.85866	−	0.676497i	−0.979984	−	0.199079i	$-0.936205\pi$
$107$	−19.2261	−	6.99774i	−1.85866	−	0.676497i	−0.878676	−	0.477418i	$-0.841573\pi$
$108$		0			0
$109$	1.85087	−	10.4968i	0.177281	−	1.00541i	−0.758197	−	0.652026i	$-0.773919\pi$
$109$	1.85087	−	10.4968i	0.177281	−	1.00541i	0.935478	−	0.353385i	$-0.114970\pi$
$110$		0			0
$111$	8.13730	+	1.95009i	0.772359	+	0.185094i
$112$		0			0
$113$	2.12063	−	12.0267i	0.199492	−	1.13138i	−0.706383	−	0.707830i	$-0.749674\pi$
$113$	2.12063	−	12.0267i	0.199492	−	1.13138i	0.905875	−	0.423546i	$-0.139215\pi$
$114$		0			0
$115$	1.70020	+	0.618823i	0.158545	+	0.0577055i
$116$		0			0
$117$	4.96568			0.459077
$118$		0			0
$119$	−0.480107	+	0.831570i	−0.0440114	+	0.0762299i
$120$		0			0
$121$	2.15795	+	3.73768i	0.196177	+	0.339789i
$122$		0			0
$123$	2.55990	−	14.5179i	0.230818	−	1.30904i
$124$		0			0
$125$	1.71554	+	2.97140i	0.153442	+	0.265770i
$126$		0			0
$127$	5.40029	+	4.53138i	0.479198	+	0.402095i	0.850136	−	0.526563i	$-0.176519\pi$
$127$	5.40029	+	4.53138i	0.479198	+	0.402095i	−0.370938	+	0.928658i	$0.620964\pi$
$128$		0			0
$129$	−2.11619	−	12.0015i	−0.186320	−	1.05668i
$130$		0			0
$131$	1.86532	−	0.678920i	0.162974	−	0.0593175i	−0.259245	−	0.965812i	$-0.583474\pi$
$131$	1.86532	−	0.678920i	0.162974	−	0.0593175i	0.422219	+	0.906494i	$0.361251\pi$
$132$		0			0
$133$	−1.28908	−	1.08167i	−0.111777	−	0.0937923i
$134$		0			0
$135$	1.84408	+	0.671192i	0.158713	+	0.0577670i
$136$		0			0
$137$	−8.69897	+	15.0671i	−0.743203	+	1.28727i	0.207826	+	0.978166i	$0.433361\pi$
$137$	−8.69897	+	15.0671i	−0.743203	+	1.28727i	−0.951029	+	0.309100i	$0.899972\pi$
$138$		0			0
$139$	0.692602	−	0.252086i	0.0587457	−	0.0213817i	−0.312480	−	0.949924i	$-0.601160\pi$
$139$	0.692602	−	0.252086i	0.0587457	−	0.0213817i	0.371226	+	0.928543i	$0.378938\pi$
$140$		0			0
$141$	−7.85905	+	6.59453i	−0.661852	+	0.555360i
$142$		0			0
$143$	8.87909	−	7.45044i	0.742507	−	0.623037i
$144$		0			0
$145$	0.0137635	+	0.0780564i	0.00114299	+	0.00648223i
$146$		0			0
$147$	−9.31551			−0.768330
$148$		0			0
$149$	−19.0346			−1.55938			−0.779689	−	0.626167i	$-0.784623\pi$
$149$	−19.0346			−1.55938			−0.779689	+	0.626167i	$0.784623\pi$
$150$		0			0
$151$	1.12385	+	6.37365i	0.0914574	+	0.518681i	0.995775	+	0.0918214i	$0.0292689\pi$
$151$	1.12385	+	6.37365i	0.0914574	+	0.518681i	−0.904318	+	0.426859i	$0.859620\pi$
$152$		0			0
$153$	−1.70531	+	1.43092i	−0.137866	+	0.115683i
$154$		0			0
$155$	1.79489	−	1.50609i	0.144169	−	0.120972i
$156$		0			0
$157$	−11.3628	+	4.13571i	−0.906847	+	0.330065i	−0.752993	−	0.658028i	$-0.771391\pi$
$157$	−11.3628	+	4.13571i	−0.906847	+	0.330065i	−0.153854	+	0.988094i	$0.549169\pi$
$158$		0			0
$159$	−3.00966	+	5.21289i	−0.238682	+	0.413409i
$160$		0			0
$161$	2.33887	+	0.851279i	0.184329	+	0.0670902i
$162$		0			0
$163$	−11.2965	−	9.47892i	−0.884813	−	0.742446i	0.0823498	−	0.996603i	$-0.473758\pi$
$163$	−11.2965	−	9.47892i	−0.884813	−	0.742446i	−0.967163	+	0.254157i	$0.918202\pi$
$164$		0			0
$165$	1.16068	−	0.422454i	0.0903590	−	0.0328880i
$166$		0			0
$167$	−1.44239	−	8.18020i	−0.111616	−	0.633003i	−0.988370	−	0.152066i	$-0.951408\pi$
$167$	−1.44239	−	8.18020i	−0.111616	−	0.633003i	0.876755	−	0.480937i	$-0.159704\pi$
$168$		0			0
$169$	5.43855	+	4.56349i	0.418350	+	0.351038i
$170$		0			0
$171$	−1.95063	−	3.37859i	−0.149168	−	0.258367i
$172$		0			0
$173$	−1.14829	+	6.51227i	−0.0873028	+	0.495119i	0.909533	+	0.415632i	$0.136439\pi$
$173$	−1.14829	+	6.51227i	−0.0873028	+	0.495119i	−0.996836	+	0.0794872i	$0.974672\pi$
$174$		0			0
$175$	1.16558	+	2.01884i	0.0881093	+	0.152610i
$176$		0			0
$177$	3.07990	−	5.33454i	0.231499	−	0.400968i
$178$		0			0
$179$	−4.53985			−0.339325			−0.169662	−	0.985502i	$-0.554268\pi$
$179$	−4.53985			−0.339325			−0.169662	+	0.985502i	$0.554268\pi$
$180$		0			0
$181$	1.46942	+	0.534826i	0.109221	+	0.0397533i	0.396053	−	0.918228i	$-0.370380\pi$
$181$	1.46942	+	0.534826i	0.109221	+	0.0397533i	−0.286831	+	0.957981i	$0.592602\pi$
$182$		0			0
$183$	−0.343627	+	1.94881i	−0.0254016	+	0.144060i
$184$		0			0
$185$	−0.600813	−	2.02528i	−0.0441727	−	0.148902i
$186$		0			0
$187$	−0.902307	+	5.11724i	−0.0659832	+	0.374209i
$188$		0			0
$189$	2.53680	+	0.923320i	0.184525	+	0.0671616i
$190$		0			0
$191$	−23.0183			−1.66555			−0.832773	−	0.553615i	$-0.813248\pi$
$191$	−23.0183			−1.66555			−0.832773	+	0.553615i	$0.813248\pi$
$192$		0			0
$193$	5.27705	−	9.14013i	0.379851	−	0.657921i	−0.611190	−	0.791484i	$-0.709309\pi$
$193$	5.27705	−	9.14013i	0.379851	−	0.657921i	0.991040	+	0.133564i	$0.0426420\pi$
$194$		0			0
$195$	1.07095	+	1.85494i	0.0766923	+	0.132835i
$196$		0			0
$197$	0.838489	−	4.75531i	0.0597399	−	0.338802i	−0.940259	−	0.340461i	$-0.889417\pi$
$197$	0.838489	−	4.75531i	0.0597399	−	0.338802i	0.999999	+	0.00165899i	$0.000528074\pi$
$198$		0			0
$199$	5.14608	+	8.91327i	0.364796	+	0.631845i	0.988743	−	0.149621i	$-0.0478054\pi$
$199$	5.14608	+	8.91327i	0.364796	+	0.631845i	−0.623947	+	0.781466i	$0.714472\pi$
$200$		0			0
$201$	11.0892	+	9.30495i	0.782173	+	0.656321i
$202$		0			0
$203$	0.0189336	+	0.107378i	0.00132888	+	0.00753644i
$204$		0			0
$205$	−3.49730	+	1.27291i	−0.244262	+	0.0889042i
$206$		0			0
$207$	4.42032	+	3.70909i	0.307234	+	0.257800i
$208$		0			0
$209$	−8.55710	−	3.11453i	−0.591907	−	0.215437i
$210$		0			0
$211$	0.685470	−	1.18727i	0.0471897	−	0.0817349i	−0.841466	−	0.540310i	$-0.818307\pi$
$211$	0.685470	−	1.18727i	0.0471897	−	0.0817349i	0.888655	+	0.458576i	$0.151640\pi$
$212$		0			0
$213$	11.4785	−	4.17785i	0.786497	−	0.286262i
$214$		0			0
$215$	−2.35686	+	1.97764i	−0.160736	+	0.134874i
$216$		0			0
$217$	2.46913	−	2.07184i	0.167615	−	0.140646i
$218$		0			0
$219$	1.71674	+	9.73610i	0.116006	+	0.657904i
$220$		0			0
$221$	−9.01064			−0.606121
$222$		0			0
$223$	29.2612			1.95947			0.979736	−	0.200292i	$-0.0641892\pi$
$223$	29.2612			1.95947			0.979736	+	0.200292i	$0.0641892\pi$
$224$		0			0
$225$	0.938471	+	5.32234i	0.0625648	+	0.354822i
$226$		0			0
$227$	−7.89376	+	6.62365i	−0.523927	+	0.439627i	−0.865998	−	0.500047i	$-0.833316\pi$
$227$	−7.89376	+	6.62365i	−0.523927	+	0.439627i	0.342071	+	0.939674i	$0.388872\pi$
$228$		0			0
$229$	12.0022	−	10.0711i	0.793128	−	0.665514i	−0.153389	−	0.988166i	$-0.549019\pi$
$229$	12.0022	−	10.0711i	0.793128	−	0.665514i	0.946518	+	0.322652i	$0.104574\pi$
$230$		0			0
$231$	1.59668	−	0.581145i	0.105054	−	0.0382366i
$232$		0			0
$233$	−3.60202	+	6.23888i	−0.235976	+	0.408723i	−0.959556	−	0.281518i	$-0.909162\pi$
$233$	−3.60202	+	6.23888i	−0.235976	+	0.408723i	0.723580	+	0.690241i	$0.242495\pi$
$234$		0			0
$235$	2.43387	+	0.885855i	0.158768	+	0.0577868i
$236$		0			0
$237$	−3.72602	−	3.12651i	−0.242031	−	0.203088i
$238$		0			0
$239$	−20.6291	+	7.50838i	−1.33439	+	0.485677i	−0.908040	−	0.418884i	$-0.862421\pi$
$239$	−20.6291	+	7.50838i	−1.33439	+	0.485677i	−0.426346	+	0.904560i	$0.640199\pi$
$240$		0			0
$241$	2.57180	+	14.5854i	0.165664	+	0.939527i	0.948377	+	0.317145i	$0.102724\pi$
$241$	2.57180	+	14.5854i	0.165664	+	0.939527i	−0.782713	+	0.622383i	$0.786165\pi$
$242$		0			0
$243$	8.29600	+	6.96117i	0.532189	+	0.446559i
$244$		0			0
$245$	1.17590	+	2.03672i	0.0751256	+	0.130121i
$246$		0			0
$247$	2.74210	−	15.5512i	0.174475	−	0.989499i
$248$		0			0
$249$	0.973018	+	1.68532i	0.0616625	+	0.106803i
$250$		0			0
$251$	6.64493	−	11.5094i	0.419424	−	0.726464i	−0.576457	−	0.817127i	$-0.695565\pi$
$251$	6.64493	−	11.5094i	0.419424	−	0.726464i	0.995882	+	0.0906631i	$0.0288986\pi$
$252$		0			0
$253$	13.4690			0.846790
$254$		0			0
$255$	−0.902307	−	0.328413i	−0.0565046	−	0.0205660i
$256$		0			0
$257$	3.03928	−	17.2366i	0.189585	−	1.07519i	−0.730336	−	0.683088i	$-0.760636\pi$
$257$	3.03928	−	17.2366i	0.189585	−	1.07519i	0.919921	−	0.392104i	$-0.128253\pi$
$258$		0			0
$259$	−0.826504	−	2.78607i	−0.0513565	−	0.173118i
$260$		0			0
$261$	−0.0438948	+	0.248940i	−0.00271702	+	0.0154090i
$262$		0			0
$263$	−13.2811	−	4.83392i	−0.818947	−	0.298072i	−0.101633	−	0.994822i	$-0.532407\pi$
$263$	−13.2811	−	4.83392i	−0.818947	−	0.298072i	−0.717314	+	0.696750i	$0.754629\pi$
$264$		0			0
$265$	1.51964			0.0933510
$266$		0			0
$267$	−2.63040	+	4.55599i	−0.160978	+	0.278822i
$268$		0			0
$269$	13.4051	+	23.2183i	0.817324	+	1.41565i	0.907647	+	0.419734i	$0.137876\pi$
$269$	13.4051	+	23.2183i	0.817324	+	1.41565i	−0.0903238	+	0.995912i	$0.528790\pi$
$270$		0			0
$271$	1.89500	−	10.7471i	0.115113	−	0.652838i	−0.871581	−	0.490251i	$-0.836905\pi$
$271$	1.89500	−	10.7471i	0.115113	−	0.652838i	0.986694	−	0.162587i	$-0.0519838\pi$
$272$		0			0
$273$	1.47324	+	2.55173i	0.0891647	+	0.154438i
$274$		0			0
$275$	9.66364	+	8.10875i	0.582739	+	0.488976i
$276$		0			0
$277$	1.06680	+	6.05012i	0.0640978	+	0.363517i	0.999938	+	0.0110932i	$0.00353116\pi$
$277$	1.06680	+	6.05012i	0.0640978	+	0.363517i	−0.935841	+	0.352423i	$0.885358\pi$
$278$		0			0
$279$	7.02191	−	2.55577i	0.420391	−	0.153010i
$280$		0			0
$281$	2.26215	+	1.89817i	0.134948	+	0.113235i	0.707763	−	0.706449i	$-0.249704\pi$
$281$	2.26215	+	1.89817i	0.134948	+	0.113235i	−0.572815	+	0.819685i	$0.694149\pi$
$282$		0			0
$283$	13.6016	+	4.95056i	0.808529	+	0.294280i	0.713016	−	0.701148i	$-0.247329\pi$
$283$	13.6016	+	4.95056i	0.808529	+	0.294280i	0.0955129	+	0.995428i	$0.469551\pi$
$284$		0			0
$285$	0.841386	−	1.45732i	0.0498394	−	0.0863244i
$286$		0			0
$287$	−4.81104	+	1.75108i	−0.283987	+	0.103363i
$288$		0			0
$289$	−9.92834	+	8.33086i	−0.584020	+	0.490051i
$290$		0			0
$291$	19.4780	−	16.3440i	1.14182	−	0.958100i
$292$		0			0
$293$	−2.18486	−	12.3910i	−0.127641	−	0.723888i	−0.979704	−	0.200449i	$-0.935760\pi$
$293$	−2.18486	−	12.3910i	−0.127641	−	0.723888i	0.852063	−	0.523439i	$-0.175351\pi$
$294$		0			0
$295$	−1.55511			−0.0905419
$296$		0			0
$297$	14.6089			0.847691
$298$		0			0
$299$	4.05581	+	23.0016i	0.234554	+	1.33022i
$300$		0			0
$301$	−3.24220	+	2.72053i	−0.186877	+	0.156808i
$302$		0			0
$303$	18.0502	−	15.1459i	1.03696	−	0.870110i
$304$		0			0
$305$	0.469459	−	0.170869i	0.0268811	−	0.00978393i
$306$		0			0
$307$	−9.44985	+	16.3676i	−0.539331	+	0.934149i	0.459609	+	0.888121i	$0.347990\pi$
$307$	−9.44985	+	16.3676i	−0.539331	+	0.934149i	−0.998940	+	0.0460279i	$0.985344\pi$
$308$		0			0
$309$	−17.3481	−	6.31419i	−0.986898	−	0.359201i
$310$		0			0
$311$	0.0868584	+	0.0728829i	0.00492529	+	0.00413281i	0.645247	−	0.763974i	$-0.276754\pi$
$311$	0.0868584	+	0.0728829i	0.00492529	+	0.00413281i	−0.640322	+	0.768107i	$0.721199\pi$
$312$		0			0
$313$	−8.62740	+	3.14012i	−0.487650	+	0.177490i	−0.574131	−	0.818764i	$-0.694660\pi$
$313$	−8.62740	+	3.14012i	−0.487650	+	0.177490i	0.0864813	+	0.996253i	$0.472438\pi$
$314$		0			0
$315$	−0.0319126	−	0.180985i	−0.00179807	−	0.0101974i
$316$		0			0
$317$	20.1198	+	16.8826i	1.13004	+	0.948219i	0.999068	−	0.0431670i	$-0.0137447\pi$
$317$	20.1198	+	16.8826i	1.13004	+	0.948219i	0.130975	+	0.991386i	$0.458189\pi$
$318$		0			0
$319$	0.295018	+	0.510986i	0.0165178	+	0.0286097i
$320$		0			0
$321$	4.88744	−	27.7181i	0.272791	−	1.54707i
$322$		0			0
$323$	3.53958	+	6.13074i	0.196948	+	0.341123i
$324$		0			0
$325$	−10.9378	+	18.9447i	−0.606717	+	1.05087i
$326$		0			0
$327$	14.6626			0.810844
$328$		0			0
$329$	3.34813	+	1.21862i	0.184588	+	0.0671847i
$330$		0			0
$331$	4.96254	−	28.1439i	0.272766	−	1.54693i	−0.473205	−	0.880952i	$-0.656903\pi$
$331$	4.96254	−	28.1439i	0.272766	−	1.54693i	0.745971	−	0.665979i	$-0.231986\pi$
$332$		0			0
$333$	0.408565	−	6.72491i	0.0223892	−	0.368523i
$334$		0			0
$335$	0.634617	−	3.59909i	0.0346728	−	0.196639i
$336$		0			0
$337$	9.18348	+	3.34251i	0.500256	+	0.182078i	0.579809	−	0.814752i	$-0.303127\pi$
$337$	9.18348	+	3.34251i	0.500256	+	0.182078i	−0.0795532	+	0.996831i	$0.525349\pi$
$338$		0			0
$339$	16.7997			0.912432
$340$		0			0
$341$	8.72118	−	15.1055i	0.472278	−	0.818010i
$342$		0			0
$343$	3.28977	+	5.69804i	0.177631	+	0.307665i
$344$		0			0
$345$	−0.432206	+	2.45116i	−0.0232692	+	0.131966i
$346$		0			0
$347$	8.28817	+	14.3555i	0.444932	+	0.770645i	0.998047	−	0.0624595i	$-0.0198944\pi$
$347$	8.28817	+	14.3555i	0.444932	+	0.770645i	−0.553115	+	0.833105i	$0.686561\pi$
$348$		0			0
$349$	14.3165	+	12.0129i	0.766342	+	0.643038i	0.939769	−	0.341809i	$-0.111040\pi$
$349$	14.3165	+	12.0129i	0.766342	+	0.643038i	−0.173427	+	0.984847i	$0.555484\pi$
$350$		0			0
$351$	4.39904	+	24.9482i	0.234803	+	1.33164i
$352$		0			0
$353$	−5.07813	+	1.84829i	−0.270282	+	0.0983745i	−0.473606	−	0.880737i	$-0.657048\pi$
$353$	−5.07813	+	1.84829i	−0.270282	+	0.0983745i	0.203324	+	0.979112i	$0.434826\pi$
$354$		0			0
$355$	−2.36238	−	1.98227i	−0.125382	−	0.105208i
$356$		0			0
$357$	−1.24125	−	0.451779i	−0.0656940	−	0.0239107i
$358$		0			0
$359$	−5.28319	+	9.15075i	−0.278836	+	0.482958i	−0.971096	−	0.238690i	$-0.923282\pi$
$359$	−5.28319	+	9.15075i	−0.278836	+	0.482958i	0.692260	+	0.721649i	$0.256615\pi$
$360$		0			0
$361$	6.19614	−	2.25521i	0.326113	−	0.118695i
$362$		0			0
$363$	−4.54811	+	3.81632i	−0.238714	+	0.200305i
$364$		0			0
$365$	1.91197	−	1.60434i	0.100077	−	0.0839748i
$366$		0			0
$367$	0.0374864	+	0.212596i	0.00195677	+	0.0110974i	0.985771	−	0.168097i	$-0.0537621\pi$
$367$	0.0374864	+	0.212596i	0.00195677	+	0.0110974i	−0.983814	+	0.179194i	$0.942651\pi$
$368$		0			0
$369$	−11.8695			−0.617902
$370$		0			0
$371$	2.09049			0.108533
$372$		0			0
$373$	−3.43905	−	19.5038i	−0.178067	−	1.00987i	−0.934543	−	0.355849i	$-0.884192\pi$
$373$	−3.43905	−	19.5038i	−0.178067	−	1.00987i	0.756476	−	0.654021i	$-0.226919\pi$
$374$		0			0
$375$	−3.61568	+	3.03391i	−0.186713	+	0.156671i
$376$		0			0
$377$	−0.783798	+	0.657684i	−0.0403676	+	0.0338725i
$378$		0			0
$379$	−21.7031	+	7.89927i	−1.11481	+	0.405758i	−0.832756	−	0.553640i	$-0.813239\pi$
$379$	−21.7031	+	7.89927i	−1.11481	+	0.405758i	−0.282056	+	0.959398i	$0.591016\pi$
$380$		0			0
$381$	−4.84885	+	8.39845i	−0.248414	+	0.430266i
$382$		0			0
$383$	−4.77929	−	1.73952i	−0.244210	−	0.0888853i	0.217015	−	0.976168i	$-0.430368\pi$
$383$	−4.77929	−	1.73952i	−0.244210	−	0.0888853i	−0.461226	+	0.887283i	$0.652590\pi$
$384$		0			0
$385$	−0.328611	−	0.275737i	−0.0167475	−	0.0140529i
$386$		0			0
$387$	−9.22042	+	3.35596i	−0.468701	+	0.170593i
$388$		0			0
$389$	−5.06138	−	28.7045i	−0.256622	−	1.45538i	−0.791874	−	0.610684i	$-0.790895\pi$
$389$	−5.06138	−	28.7045i	−0.256622	−	1.45538i	0.535252	−	0.844692i	$-0.320217\pi$
$390$		0			0
$391$	−8.02104	−	6.73045i	−0.405642	−	0.340374i
$392$		0			0
$393$	1.36535	+	2.36485i	0.0688726	+	0.119291i
$394$		0			0
$395$	−0.213234	+	1.20931i	−0.0107290	+	0.0608470i
$396$		0			0
$397$	7.99625	+	13.8499i	0.401320	+	0.695107i	0.993886	−	0.110416i	$-0.0352182\pi$
$397$	7.99625	+	13.8499i	0.401320	+	0.695107i	−0.592565	+	0.805522i	$0.701885\pi$
$398$		0			0
$399$	1.15745	−	2.00476i	0.0579448	−	0.100363i
$400$		0			0
$401$	−5.43983			−0.271652			−0.135826	−	0.990733i	$-0.543369\pi$
$401$	−5.43983			−0.271652			−0.135826	+	0.990733i	$0.543369\pi$
$402$		0			0
$403$	28.4225	+	10.3450i	1.41583	+	0.515319i
$404$		0			0
$405$	−0.268391	+	1.52212i	−0.0133365	+	0.0756348i
$406$		0			0
$407$	−9.35942	−	12.6378i	−0.463929	−	0.626431i
$408$		0			0
$409$	−6.55076	+	37.1512i	−0.323914	+	1.83701i	0.193283	+	0.981143i	$0.438086\pi$
$409$	−6.55076	+	37.1512i	−0.323914	+	1.83701i	−0.517198	+	0.855866i	$0.673025\pi$
$410$		0			0
$411$	−22.4900	−	8.18569i	−1.10935	−	0.403770i
$412$		0			0
$413$	−2.13927			−0.105267
$414$		0			0
$415$	0.245649	−	0.425477i	0.0120584	−	0.0208858i
$416$		0			0
$417$	0.506960	+	0.878080i	0.0248259	+	0.0429998i
$418$		0			0
$419$	−1.07518	+	6.09766i	−0.0525261	+	0.297890i	−0.999742	−	0.0227055i	$-0.992772\pi$
$419$	−1.07518	+	6.09766i	−0.0525261	+	0.297890i	0.947216	+	0.320596i	$0.103883\pi$
$420$		0			0
$421$	5.05431	+	8.75433i	0.246332	+	0.426660i	0.962505	−	0.271263i	$-0.0874412\pi$
$421$	5.05431	+	8.75433i	0.246332	+	0.426660i	−0.716173	+	0.697923i	$0.754108\pi$
$422$		0			0
$423$	6.32776	+	5.30962i	0.307666	+	0.258163i
$424$		0			0
$425$	−1.70293	−	9.65782i	−0.0826044	−	0.468473i
$426$		0			0
$427$	0.645808	−	0.235055i	0.0312528	−	0.0113751i
$428$		0			0
$429$	12.2145	+	10.2491i	0.589719	+	0.494833i
$430$		0			0
$431$	−32.1170	−	11.6896i	−1.54702	−	0.563070i	−0.579304	−	0.815111i	$-0.696676\pi$
$431$	−32.1170	−	11.6896i	−1.54702	−	0.563070i	−0.967716	+	0.252042i	$0.918898\pi$
$432$		0			0
$433$	0.343160	−	0.594370i	0.0164912	−	0.0285636i	−0.857662	−	0.514214i	$-0.828084\pi$
$433$	0.343160	−	0.594370i	0.0164912	−	0.0285636i	0.874153	+	0.485650i	$0.161417\pi$
$434$		0			0
$435$	−0.102459	+	0.0372919i	−0.00491252	+	0.00178801i
$436$		0			0
$437$	14.0568	−	11.7951i	0.672430	−	0.564236i
$438$		0			0
$439$	−16.4768	+	13.8257i	−0.786393	+	0.659862i	−0.944850	−	0.327503i	$-0.893793\pi$
$439$	−16.4768	+	13.8257i	−0.786393	+	0.659862i	0.158456	+	0.987366i	$0.449348\pi$
$440$		0			0
$441$	1.30244	+	7.38649i	0.0620208	+	0.351738i
$442$		0			0
$443$	28.5971			1.35869			0.679344	−	0.733820i	$-0.262264\pi$
$443$	28.5971			1.35869			0.679344	+	0.733820i	$0.262264\pi$
$444$		0			0
$445$	1.32815			0.0629602
$446$		0			0
$447$	−4.54695	−	25.7870i	−0.215063	−	1.21969i
$448$		0			0
$449$	−26.4813	+	22.2204i	−1.24973	+	1.04865i	−0.253031	+	0.967458i	$0.581427\pi$
$449$	−26.4813	+	22.2204i	−1.24973	+	1.04865i	−0.996699	+	0.0811896i	$0.974128\pi$
$450$		0			0
$451$	−21.2238	+	17.8089i	−0.999388	+	0.838587i
$452$		0			0
$453$	−8.36620	+	3.04505i	−0.393079	+	0.143069i
$454$		0			0
$455$	0.371937	−	0.644213i	0.0174367	−	0.0302012i
$456$		0			0
$457$	−30.9238	−	11.2553i	−1.44655	−	0.526503i	−0.504928	−	0.863162i	$-0.668481\pi$
$457$	−30.9238	−	11.2553i	−1.44655	−	0.526503i	−0.941627	+	0.336659i	$0.890703\pi$
$458$		0			0
$459$	−8.69983	−	7.30003i	−0.406074	−	0.340736i
$460$		0			0
$461$	17.0455	−	6.20405i	0.793888	−	0.288952i	0.0869368	−	0.996214i	$-0.472292\pi$
$461$	17.0455	−	6.20405i	0.793888	−	0.288952i	0.706951	+	0.707262i	$0.250070\pi$
$462$		0			0
$463$	−0.0589368	−	0.334247i	−0.00273903	−	0.0155338i	0.983408	−	0.181410i	$-0.0580660\pi$
$463$	−0.0589368	−	0.334247i	−0.00273903	−	0.0155338i	−0.986147	+	0.165876i	$0.946955\pi$
$464$		0			0
$465$	2.46913	+	2.07184i	0.114503	+	0.0960795i
$466$		0			0
$467$	−7.10101	−	12.2993i	−0.328596	−	0.569144i	0.653638	−	0.756808i	$-0.273242\pi$
$467$	−7.10101	−	12.2993i	−0.328596	−	0.569144i	−0.982233	+	0.187663i	$0.939909\pi$
$468$		0			0
$469$	0.873006	−	4.95106i	0.0403117	−	0.228619i
$470$		0			0
$471$	−8.31714	−	14.4057i	−0.383233	−	0.663780i
$472$		0			0
$473$	−11.4517	+	19.8350i	−0.526551	+	0.912013i
$474$		0			0
$475$	17.1864			0.788566
$476$		0			0
$477$	4.55421	+	1.65760i	0.208523	+	0.0758962i
$478$		0			0
$479$	5.90065	−	33.4642i	0.269608	−	1.52902i	−0.485979	−	0.873971i	$-0.661537\pi$
$479$	5.90065	−	33.4642i	0.269608	−	1.52902i	0.755586	−	0.655049i	$-0.227352\pi$
$480$		0			0
$481$	18.7637	−	19.7890i	0.855553	−	0.902301i
$482$		0			0
$483$	−0.594561	+	3.37192i	−0.0270534	+	0.153428i
$484$		0			0
$485$	−6.03213	−	2.19551i	−0.273905	−	0.0996932i
$486$		0			0
$487$	25.3330			1.14795			0.573974	−	0.818874i	$-0.305401\pi$
$487$	25.3330			1.14795			0.573974	+	0.818874i	$0.305401\pi$
$488$		0			0
$489$	10.1430	−	17.5682i	0.458683	−	0.794462i
$490$		0			0
$491$	10.6344	+	18.4193i	0.479922	+	0.831249i	0.999735	−	0.0230308i	$-0.00733158\pi$
$491$	10.6344	+	18.4193i	0.479922	+	0.831249i	−0.519813	+	0.854280i	$0.673998\pi$
$492$		0			0
$493$	0.0796507	−	0.451722i	0.00358729	−	0.0203445i
$494$		0			0
$495$	−0.497253	−	0.861267i	−0.0223499	−	0.0387111i
$496$		0			0
$497$	−3.24979	−	2.72690i	−0.145773	−	0.122318i
$498$		0			0
$499$	−2.85314	−	16.1810i	−0.127724	−	0.724359i	−0.979653	−	0.200701i	$-0.935678\pi$
$499$	−2.85314	−	16.1810i	−0.127724	−	0.724359i	0.851928	−	0.523658i	$-0.175433\pi$
$500$		0			0
$501$	10.7375	−	3.90814i	0.479717	−	0.174603i
$502$		0			0
$503$	−15.9979	−	13.4238i	−0.713311	−	0.598539i	0.212215	−	0.977223i	$-0.431932\pi$
$503$	−15.9979	−	13.4238i	−0.713311	−	0.598539i	−0.925526	+	0.378684i	$0.876377\pi$
$504$		0			0
$505$	−5.58995	−	2.03458i	−0.248750	−	0.0905375i
$506$		0			0
$507$	−4.88321	+	8.45796i	−0.216871	+	0.375631i
$508$		0			0
$509$	−37.6746	+	13.7124i	−1.66990	+	0.607793i	−0.991871	−	0.127245i	$-0.959386\pi$
$509$	−37.6746	+	13.7124i	−1.66990	+	0.607793i	−0.678026	+	0.735038i	$0.737164\pi$
$510$		0			0
$511$	2.63019	−	2.20699i	0.116353	−	0.0976317i
$512$		0			0
$513$	15.2464	−	12.7933i	0.673146	−	0.564837i
$514$		0			0
$515$	0.809339	+	4.58999i	0.0356637	+	0.202259i
$516$		0			0
$517$	19.2811			0.847982
$518$		0			0
$519$	−9.09676			−0.399303
$520$		0			0
$521$	1.59181	+	9.02760i	0.0697384	+	0.395506i	0.999618	+	0.0276419i	$0.00879982\pi$
$521$	1.59181	+	9.02760i	0.0697384	+	0.395506i	−0.929879	+	0.367864i	$0.880089\pi$
$522$		0			0
$523$	−22.7091	+	19.0552i	−0.993000	+	0.833226i	−0.985999	−	0.166749i	$-0.946673\pi$
$523$	−22.7091	+	19.0552i	−0.993000	+	0.833226i	−0.00700102	+	0.999975i	$0.502229\pi$
$524$		0			0
$525$	−2.45658	+	2.06131i	−0.107214	+	0.0899631i
$526$		0			0
$527$	−12.7418	+	4.63765i	−0.555043	+	0.202019i
$528$		0			0
$529$	−2.07059	+	3.58637i	−0.0900257	+	0.155929i
$530$		0			0
$531$	−4.66049	−	1.69628i	−0.202248	−	0.0736123i
$532$		0			0
$533$	−36.8039	−	30.8822i	−1.59415	−	1.33765i
$534$		0			0
$535$	−6.67716	+	2.43029i	−0.288679	+	0.105071i
$536$		0			0
$537$	−1.08447	−	6.15034i	−0.0467984	−	0.265407i
$538$		0			0
$539$	13.4115	+	11.2536i	0.577673	+	0.484725i
$540$		0			0
$541$	−14.4930	−	25.1027i	−0.623104	−	1.07925i	−0.988904	−	0.148554i	$-0.952538\pi$
$541$	−14.4930	−	25.1027i	−0.623104	−	1.07925i	0.365800	−	0.930693i	$-0.380795\pi$
$542$		0			0
$543$	−0.373540	+	2.11845i	−0.0160301	+	0.0909113i
$544$		0			0
$545$	−1.85087	−	3.20580i	−0.0792825	−	0.137321i
$546$		0			0
$547$	2.68304	−	4.64717i	0.114719	−	0.198699i	−0.802949	−	0.596048i	$-0.796737\pi$
$547$	2.68304	−	4.64717i	0.114719	−	0.198699i	0.917667	+	0.397350i	$0.130070\pi$
$548$		0			0
$549$	1.59330			0.0680003
$550$		0			0
$551$	0.755374	+	0.274934i	0.0321800	+	0.0117126i
$552$		0			0
$553$	−0.293334	+	1.66358i	−0.0124738	+	0.0707426i
$554$		0			0
$555$	2.60022	−	1.29774i	0.110373	−	0.0550861i
$556$		0			0
$557$	−2.03774	+	11.5566i	−0.0863416	+	0.489668i	0.910717	+	0.413030i	$0.135530\pi$
$557$	−2.03774	+	11.5566i	−0.0863416	+	0.489668i	−0.997059	+	0.0766376i	$0.975582\pi$
$558$		0			0
$559$	−37.3214	−	13.5839i	−1.57853	−	0.574537i
$560$		0			0
$561$	−7.14808			−0.301792
$562$		0			0
$563$	9.45929	−	16.3840i	0.398662	−	0.690502i	−0.594899	−	0.803800i	$-0.702808\pi$
$563$	9.45929	−	16.3840i	0.398662	−	0.690502i	0.993561	+	0.113298i	$0.0361415\pi$
$564$		0			0
$565$	−2.12063	−	3.67304i	−0.0892156	−	0.154526i
$566$		0			0
$567$	−0.369210	+	2.09390i	−0.0155054	+	0.0879353i
$568$		0			0
$569$	10.8074	+	18.7189i	0.453068	+	0.784737i	0.998575	−	0.0533694i	$-0.0169961\pi$
$569$	10.8074	+	18.7189i	0.453068	+	0.784737i	−0.545507	+	0.838107i	$0.683663\pi$
$570$		0			0
$571$	26.8881	+	22.5618i	1.12523	+	0.944181i	0.998857	−	0.0478018i	$-0.0152216\pi$
$571$	26.8881	+	22.5618i	1.12523	+	0.944181i	0.126374	+	0.991983i	$0.459666\pi$
$572$		0			0
$573$	−5.49856	−	31.1839i	−0.229706	−	1.30273i
$574$		0			0
$575$	−23.8872	+	8.69423i	−0.996165	+	0.362574i
$576$		0			0
$577$	−33.0040	−	27.6937i	−1.37398	−	1.15290i	−0.971382	−	0.237523i	$-0.923664\pi$
$577$	−33.0040	−	27.6937i	−1.37398	−	1.15290i	−0.402593	−	0.915379i	$-0.631891\pi$
$578$		0			0
$579$	13.6431	+	4.96568i	0.566988	+	0.206367i
$580$		0			0
$581$	0.337926	−	0.585304i	0.0140195	−	0.0242825i
$582$		0			0
$583$	10.6304	−	3.86915i	0.440266	−	0.160244i
$584$		0			0
$585$	1.32109	−	1.10853i	0.0546204	−	0.0458320i
$586$		0			0
$587$	15.6463	−	13.1288i	0.645790	−	0.541882i	−0.260000	−	0.965609i	$-0.583723\pi$
$587$	15.6463	−	13.1288i	0.645790	−	0.541882i	0.905790	+	0.423726i	$0.139278\pi$
$588$		0			0
$589$	−4.12642	−	23.4021i	−0.170026	−	0.964267i
$590$		0			0
$591$	6.64252			0.273237
$592$		0			0
$593$	−0.908005			−0.0372873			−0.0186436	−	0.999826i	$-0.505935\pi$
$593$	−0.908005			−0.0372873			−0.0186436	+	0.999826i	$0.505935\pi$
$594$		0			0
$595$	0.0579080	+	0.328413i	0.00237400	+	0.0134636i
$596$		0			0
$597$	−10.8459	+	9.10080i	−0.443894	+	0.372471i
$598$		0			0
$599$	9.44037	−	7.92141i	0.385723	−	0.323660i	−0.429221	−	0.903199i	$-0.641212\pi$
$599$	9.44037	−	7.92141i	0.385723	−	0.323660i	0.814944	+	0.579539i	$0.196767\pi$
$600$		0			0
$601$	32.2492	−	11.7377i	1.31547	−	0.478792i	0.413467	−	0.910519i	$-0.364318\pi$
$601$	32.2492	−	11.7377i	1.31547	−	0.478792i	0.902004	+	0.431727i	$0.142095\pi$
$602$		0			0
$603$	5.82769	−	10.0939i	0.237322	−	0.411054i
$604$		0			0
$605$	1.40850	+	0.512653i	0.0572637	+	0.0208423i
$606$		0			0
$607$	3.12973	+	2.62616i	0.127032	+	0.106593i	0.704090	−	0.710110i	$-0.251355\pi$
$607$	3.12973	+	2.62616i	0.127032	+	0.106593i	−0.577058	+	0.816703i	$0.695799\pi$
$608$		0			0
$609$	−0.140947	+	0.0513003i	−0.00571144	+	0.00207879i
$610$		0			0
$611$	5.80596	+	32.9272i	0.234884	+	1.33209i
$612$		0			0
$613$	15.2276	+	12.7775i	0.615036	+	0.516077i	0.896239	−	0.443572i	$-0.146289\pi$
$613$	15.2276	+	12.7775i	0.615036	+	0.516077i	−0.281202	+	0.959648i	$0.590733\pi$
$614$		0			0
$615$	−2.55990	−	4.43388i	−0.103225	−	0.178791i
$616$		0			0
$617$	0.664267	−	3.76724i	0.0267424	−	0.151664i	−0.968513	−	0.248964i	$-0.919910\pi$
$617$	0.664267	−	3.76724i	0.0267424	−	0.151664i	0.995255	+	0.0973009i	$0.0310209\pi$
$618$		0			0
$619$	−5.97516	−	10.3493i	−0.240162	−	0.415973i	0.720598	−	0.693353i	$-0.243867\pi$
$619$	−5.97516	−	10.3493i	−0.240162	−	0.415973i	−0.960760	+	0.277380i	$0.910534\pi$
$620$		0			0
$621$	−14.7190	+	25.4941i	−0.590654	+	1.02304i
$622$		0			0
$623$	1.82706			0.0731995
$624$		0			0
$625$	−21.8059	−	7.93669i	−0.872235	−	0.317468i
$626$		0			0
$627$	2.17529	−	12.3367i	0.0868727	−	0.492679i
$628$		0			0
$629$	−0.741374	+	12.2029i	−0.0295605	+	0.486562i
$630$		0			0
$631$	3.49888	−	19.8431i	0.139288	−	0.789942i	−0.832489	−	0.554041i	$-0.813085\pi$
$631$	3.49888	−	19.8431i	0.139288	−	0.789942i	0.971777	−	0.235901i	$-0.0758040\pi$
$632$		0			0
$633$	1.77219	+	0.645024i	0.0704381	+	0.0256374i
$634$		0			0
$635$	2.44829			0.0971575
$636$		0			0
$637$	−15.1797	+	26.2920i	−0.601442	+	1.04173i
$638$		0			0
$639$	−4.91758	−	8.51749i	−0.194536	−	0.336947i
$640$		0			0
$641$	5.23531	−	29.6909i	0.206782	−	1.17272i	−0.687828	−	0.725874i	$-0.741435\pi$
$641$	5.23531	−	29.6909i	0.206782	−	1.17272i	0.894610	−	0.446848i	$-0.147453\pi$
$642$		0			0
$643$	−6.52757	−	11.3061i	−0.257422	−	0.445868i	0.708128	−	0.706084i	$-0.249540\pi$
$643$	−6.52757	−	11.3061i	−0.257422	−	0.445868i	−0.965551	+	0.260215i	$0.916206\pi$
$644$		0			0
$645$	−3.24220	−	2.72053i	−0.127661	−	0.107121i
$646$		0			0
$647$	−8.16883	−	46.3278i	−0.321150	−	1.82133i	−0.535453	−	0.844565i	$-0.679859\pi$
$647$	−8.16883	−	46.3278i	−0.321150	−	1.82133i	0.214303	−	0.976767i	$-0.431252\pi$
$648$		0			0
$649$	−10.8785	+	3.95944i	−0.427017	+	0.155422i
$650$		0			0
$651$	3.39664	+	2.85012i	0.133125	+	0.111705i
$652$		0			0
$653$	25.9534	+	9.44628i	1.01564	+	0.369661i	0.795595	−	0.605829i	$-0.207158\pi$
$653$	25.9534	+	9.44628i	1.01564	+	0.369661i	0.220042	+	0.975491i	$0.429381\pi$
$654$		0			0
$655$	0.344697	−	0.597032i	0.0134684	−	0.0233280i
$656$		0			0
$657$	7.47996	−	2.72248i	0.291821	−	0.106214i
$658$		0			0
$659$	−27.5226	+	23.0942i	−1.07213	+	0.899624i	−0.995244	−	0.0974158i	$-0.968942\pi$
$659$	−27.5226	+	23.0942i	−1.07213	+	0.899624i	−0.0768864	+	0.997040i	$0.524498\pi$
$660$		0			0
$661$	30.2001	−	25.3409i	1.17465	−	0.985645i	0.174647	−	0.984631i	$-0.444122\pi$
$661$	30.2001	−	25.3409i	1.17465	−	0.985645i	0.999999	−	0.00101438i	$-0.000322887\pi$
$662$		0			0
$663$	−2.15244	−	12.2071i	−0.0835939	−	0.474085i
$664$		0			0
$665$	−0.584421			−0.0226629
$666$		0			0
$667$	−1.18897			−0.0460372
$668$		0			0
$669$	6.98984	+	39.6414i	0.270243	+	1.53262i
$670$		0			0
$671$	2.84896	−	2.39056i	0.109983	−	0.0922867i
$672$		0			0
$673$	11.6863	−	9.80600i	0.450475	−	0.377994i	−0.389137	−	0.921180i	$-0.627227\pi$
$673$	11.6863	−	9.80600i	0.450475	−	0.377994i	0.839612	+	0.543186i	$0.182782\pi$
$674$		0			0
$675$	−25.9087	+	9.42999i	−0.997226	+	0.362961i
$676$		0			0
$677$	−10.7029	+	18.5379i	−0.411345	+	0.712471i	−0.995037	−	0.0995043i	$-0.968274\pi$
$677$	−10.7029	+	18.5379i	−0.411345	+	0.712471i	0.583692	+	0.811975i	$0.301608\pi$
$678$		0			0
$679$	−8.29805	−	3.02024i	−0.318450	−	0.115906i
$680$		0			0
$681$	−10.8590	−	9.11178i	−0.416118	−	0.349164i
$682$		0			0
$683$	11.8657	−	4.31877i	0.454029	−	0.165253i	−0.104875	−	0.994485i	$-0.533444\pi$
$683$	11.8657	−	4.31877i	0.454029	−	0.165253i	0.558904	+	0.829232i	$0.311222\pi$
$684$		0			0
$685$	1.04922	+	5.95045i	0.0400888	+	0.227355i
$686$		0			0
$687$	16.5108	+	13.8542i	0.629925	+	0.528569i
$688$		0			0
$689$	9.80855	+	16.9889i	0.373676	+	0.647226i
$690$		0			0
$691$	0.596082	−	3.38055i	0.0226760	−	0.128602i	−0.971368	−	0.237579i	$-0.923646\pi$
$691$	0.596082	−	3.38055i	0.0226760	−	0.128602i	0.994044	+	0.108977i	$0.0347574\pi$
$692$		0			0
$693$	−0.684042	−	1.18480i	−0.0259846	−	0.0450067i
$694$		0			0
$695$	0.127988	−	0.221681i	0.00485485	−	0.00840884i
$696$		0			0
$697$	21.5382			0.815818
$698$		0			0
$699$	−9.31253	−	3.38948i	−0.352232	−	0.128202i
$700$		0			0
$701$	0.0325577	−	0.184644i	0.00122969	−	0.00697390i	−0.984187	−	0.177134i	$-0.943317\pi$
$701$	0.0325577	−	0.184644i	0.00122969	−	0.00697390i	0.985416	+	0.170160i	$0.0544285\pi$
$702$		0			0
$703$	−20.8350	−	4.99308i	−0.785808	−	0.188317i
$704$		0			0
$705$	−0.618709	+	3.50888i	−0.0233019	+	0.132152i
$706$		0			0
$707$	−7.68978	−	2.79885i	−0.289204	−	0.105262i
$708$		0			0
$709$	−48.4114			−1.81813			−0.909064	−	0.416656i	$-0.863202\pi$
$709$	−48.4114			−1.81813			−0.909064	+	0.416656i	$0.863202\pi$
$710$		0			0
$711$	−1.95813	+	3.39158i	−0.0734357	+	0.127194i
$712$		0			0
$713$	17.5739	+	30.4389i	0.658148	+	1.13995i
$714$		0			0
$715$	0.699012	−	3.96430i	0.0261416	−	0.148256i
$716$		0			0
$717$	−15.0998	−	26.1536i	−0.563911	−	0.976722i
$718$		0			0
$719$	34.9152	+	29.2973i	1.30212	+	1.09261i	0.989775	+	0.142635i	$0.0455575\pi$
$719$	34.9152	+	29.2973i	1.30212	+	1.09261i	0.312341	+	0.949970i	$0.398887\pi$
$720$		0			0
$721$	1.11336	+	6.31419i	0.0414637	+	0.235153i
$722$		0			0
$723$	−19.1451	+	6.96825i	−0.712015	+	0.259152i
$724$		0			0
$725$	−0.853053	−	0.715797i	−0.0316816	−	0.0265840i
$726$		0			0
$727$	39.4113	+	14.3445i	1.46168	+	0.532009i	0.945828	−	0.324667i	$-0.105252\pi$
$727$	39.4113	+	14.3445i	1.46168	+	0.532009i	0.515854	+	0.856676i	$0.327475\pi$
$728$		0			0
$729$	−14.1244	+	24.4643i	−0.523128	+	0.906084i
$730$		0			0
$731$	16.7312	−	6.08967i	0.618827	−	0.225234i
$732$		0			0
$733$	13.4938	−	11.3227i	0.498406	−	0.418212i	−0.358622	−	0.933483i	$-0.616753\pi$
$733$	13.4938	−	11.3227i	0.498406	−	0.418212i	0.857027	+	0.515271i	$0.172309\pi$
$734$		0			0
$735$	−2.47834	+	2.07957i	−0.0914149	+	0.0767062i
$736$		0			0
$737$	−4.72425	−	26.7925i	−0.174020	−	0.986916i
$738$		0			0
$739$	−39.4393			−1.45080			−0.725400	−	0.688328i	$-0.758345\pi$
$739$	−39.4393			−1.45080			−0.725400	+	0.688328i	$0.758345\pi$
$740$		0			0
$741$	21.7229			0.798011
$742$		0			0
$743$	−2.27755	−	12.9167i	−0.0835554	−	0.473866i	−0.997659	−	0.0683854i	$-0.978215\pi$
$743$	−2.27755	−	12.9167i	−0.0835554	−	0.473866i	0.914104	−	0.405481i	$-0.132896\pi$
$744$		0			0
$745$	−5.06406	+	4.24925i	−0.185533	+	0.155680i
$746$		0			0
$747$	1.20029	−	1.00716i	0.0439162	−	0.0368500i
$748$		0			0
$749$	−9.18539	+	3.34321i	−0.335627	+	0.122158i
$750$		0			0
$751$	−19.9893	+	34.6226i	−0.729421	+	1.26340i	0.227707	+	0.973730i	$0.426877\pi$
$751$	−19.9893	+	34.6226i	−0.729421	+	1.26340i	−0.957128	+	0.289665i	$0.906456\pi$
$752$		0			0
$753$	17.1796	+	6.25285i	0.626058	+	0.227866i
$754$		0			0
$755$	1.72183	+	1.44479i	0.0626639	+	0.0525813i
$756$		0			0
$757$	−26.2852	+	9.56703i	−0.955352	+	0.347720i	−0.772210	−	0.635367i	$-0.780849\pi$
$757$	−26.2852	+	9.56703i	−0.955352	+	0.347720i	−0.183141	+	0.983087i	$0.558627\pi$
$758$		0			0
$759$	3.21745	+	18.2471i	0.116786	+	0.662326i
$760$		0			0
$761$	−1.66744	−	1.39915i	−0.0604447	−	0.0507191i	0.612065	−	0.790808i	$-0.290339\pi$
$761$	−1.66744	−	1.39915i	−0.0604447	−	0.0507191i	−0.672510	+	0.740088i	$0.734784\pi$
$762$		0			0
$763$	−2.54614	−	4.41004i	−0.0921763	−	0.159654i
$764$		0			0
$765$	−0.134251	+	0.761377i	−0.00485387	+	0.0275276i
$766$		0			0
$767$	−10.0374	−	17.3854i	−0.362431	−	0.627749i
$768$		0			0
$769$	20.6905	−	35.8370i	0.746118	−	1.29231i	−0.203553	−	0.979064i	$-0.565249\pi$
$769$	20.6905	−	35.8370i	0.746118	−	1.29231i	0.949671	−	0.313250i	$-0.101418\pi$
$770$		0			0
$771$	24.0772			0.867121
$772$		0			0
$773$	11.5459	+	4.20237i	0.415278	+	0.151149i	0.541205	−	0.840891i	$-0.317968\pi$
$773$	11.5459	+	4.20237i	0.415278	+	0.151149i	−0.125927	+	0.992040i	$0.540191\pi$
$774$		0			0
$775$	−5.71635	+	32.4191i	−0.205338	+	1.16453i
$776$		0			0
$777$	3.57697	−	1.78523i	0.128323	−	0.0640448i
$778$		0			0
$779$	−6.55446	+	37.1722i	−0.234838	+	1.33183i
$780$		0			0
$781$	−21.5726	−	7.85179i	−0.771929	−	0.280959i
$782$		0			0
$783$	−1.28959			−0.0460862
$784$		0			0
$785$	−2.09975	+	3.63688i	−0.0749434	+	0.129806i
$786$		0			0
$787$	12.0763	+	20.9167i	0.430473	+	0.745601i	0.996914	−	0.0785015i	$-0.0250135\pi$
$787$	12.0763	+	20.9167i	0.430473	+	0.745601i	−0.566441	+	0.824102i	$0.691680\pi$
$788$		0			0
$789$	3.37617	−	19.1472i	0.120195	−	0.681658i
$790$		0			0
$791$	−2.91723	−	5.05279i	−0.103725	−	0.179657i
$792$		0			0
$793$	4.94036	+	4.14545i	0.175437	+	0.147209i
$794$		0			0
$795$	0.363009	+	2.05873i	0.0128746	+	0.0730156i
$796$		0			0
$797$	30.9648	−	11.2703i	1.09683	−	0.399214i	0.270684	−	0.962668i	$-0.412750\pi$
$797$	30.9648	−	11.2703i	1.09683	−	0.399214i	0.826147	+	0.563455i	$0.190528\pi$
$798$		0			0
$799$	−11.4823	−	9.63475i	−0.406213	−	0.340853i
$800$		0			0
$801$	3.98032	+	1.44872i	0.140638	+	0.0511879i
$802$		0			0
$803$	9.29008	−	16.0909i	0.327840	−	0.567835i
$804$		0			0
$805$	0.812281	−	0.295646i	0.0286291	−	0.0104202i
$806$		0			0
$807$	−28.2527	+	23.7068i	−0.994542	+	0.834520i
$808$		0			0
$809$	27.3400	−	22.9410i	0.961224	−	0.806563i	−0.0199275	−	0.999801i	$-0.506344\pi$
$809$	27.3400	−	22.9410i	0.961224	−	0.806563i	0.981152	+	0.193238i	$0.0618991\pi$
$810$		0			0
$811$	−5.88324	−	33.3655i	−0.206589	−	1.17162i	−0.894920	−	0.446226i	$-0.852768\pi$
$811$	−5.88324	−	33.3655i	−0.206589	−	1.17162i	0.688332	−	0.725396i	$-0.258343\pi$
$812$		0			0
$813$	15.0122			0.526501
$814$		0			0
$815$	−5.12143			−0.179396
$816$		0			0
$817$	5.41838	+	30.7291i	0.189565	+	1.07508i
$818$		0			0
$819$	1.81735	−	1.52494i	0.0635033	−	0.0532856i
$820$		0			0
$821$	−18.1645	+	15.2418i	−0.633945	+	0.531943i	−0.902152	−	0.431418i	$-0.858013\pi$
$821$	−18.1645	+	15.2418i	−0.633945	+	0.531943i	0.268207	+	0.963361i	$0.413569\pi$
$822$		0			0
$823$	23.3126	−	8.48508i	0.812625	−	0.295771i	0.0979172	−	0.995195i	$-0.468782\pi$
$823$	23.3126	−	8.48508i	0.812625	−	0.295771i	0.714708	+	0.699423i	$0.246560\pi$
$824$		0			0
$825$	−8.67685	+	15.0288i	−0.302089	+	0.523234i
$826$		0			0
$827$	49.8660	+	18.1497i	1.73401	+	0.631129i	0.998903	−	0.0468213i	$-0.0149091\pi$
$827$	49.8660	+	18.1497i	1.73401	+	0.631129i	0.735108	+	0.677950i	$0.237131\pi$
$828$		0			0
$829$	−4.78684	−	4.01663i	−0.166254	−	0.139503i	0.555865	−	0.831273i	$-0.312387\pi$
$829$	−4.78684	−	4.01663i	−0.166254	−	0.139503i	−0.722119	+	0.691769i	$0.756832\pi$
$830$		0			0
$831$	−7.94153	+	2.89048i	−0.275489	+	0.100270i
$832$		0			0
$833$	−2.36338	−	13.4034i	−0.0818863	−	0.464400i
$834$		0			0
$835$	−2.20987	−	1.85430i	−0.0764757	−	0.0641707i
$836$		0			0
$837$	19.0611	+	33.0148i	0.658849	+	1.14116i
$838$		0			0
$839$	−1.97545	+	11.2033i	−0.0682002	+	0.386783i	0.931532	+	0.363658i	$0.118472\pi$
$839$	−1.97545	+	11.2033i	−0.0682002	+	0.386783i	−0.999733	+	0.0231242i	$0.992639\pi$
$840$		0			0
$841$	14.4740	+	25.0696i	0.499102	+	0.864470i
$842$		0			0
$843$	−2.03115	+	3.51806i	−0.0699566	+	0.121168i
$844$		0			0
$845$	2.46564			0.0848206
$846$		0			0
$847$	1.93760	+	0.705227i	0.0665766	+	0.0242319i
$848$		0			0
$849$	−3.45763	+	19.6092i	−0.118666	+	0.672986i
$850$		0			0
$851$	31.4843	−	3.60017i	1.07927	−	0.123412i
$852$		0			0
$853$	−0.162161	+	0.919663i	−0.00555230	+	0.0314886i	−0.987458	−	0.157882i	$-0.949534\pi$
$853$	−0.162161	+	0.919663i	−0.00555230	+	0.0314886i	0.981906	+	0.189370i	$0.0606447\pi$
$854$		0			0
$855$	−1.27318	−	0.463401i	−0.0435420	−	0.0158480i
$856$		0			0
$857$	34.2745			1.17080			0.585398	−	0.810746i	$-0.300938\pi$
$857$	34.2745			1.17080			0.585398	+	0.810746i	$0.300938\pi$
$858$		0			0
$859$	−8.03105	+	13.9102i	−0.274016	+	0.474609i	−0.969886	−	0.243558i	$-0.921685\pi$
$859$	−8.03105	+	13.9102i	−0.274016	+	0.474609i	0.695871	+	0.718167i	$0.255019\pi$
$860$		0			0
$861$	−3.52151	−	6.09943i	−0.120013	−	0.207868i
$862$		0			0
$863$	1.11602	−	6.32926i	0.0379898	−	0.215451i	−0.959903	−	0.280331i	$-0.909556\pi$
$863$	1.11602	−	6.32926i	0.0379898	−	0.215451i	0.997893	+	0.0648808i	$0.0206667\pi$
$864$		0			0
$865$	1.14829	+	1.98889i	0.0390430	+	0.0676245i
$866$		0			0
$867$	−13.6578	−	11.4603i	−0.463845	−	0.389212i
$868$		0			0
$869$	1.58737	+	9.00241i	0.0538478	+	0.305386i
$870$		0			0
$871$	44.3322	−	16.1356i	1.50214	−	0.546735i
$872$		0			0
$873$	−15.6828	−	13.1594i	−0.530783	−	0.445380i
$874$		0			0
$875$	1.54036	+	0.560645i	0.0520736	+	0.0189533i
$876$		0			0
$877$	−21.9328	+	37.9888i	−0.740619	+	1.28279i	0.211595	+	0.977357i	$0.432134\pi$
$877$	−21.9328	+	37.9888i	−0.740619	+	1.28279i	−0.952214	+	0.305432i	$0.901199\pi$
$878$		0			0
$879$	16.2647	−	5.91985i	0.548594	−	0.199672i
$880$		0			0
$881$	−18.2452	+	15.3095i	−0.614696	+	0.515791i	−0.896131	−	0.443789i	$-0.853634\pi$
$881$	−18.2452	+	15.3095i	−0.614696	+	0.515791i	0.281436	+	0.959580i	$0.409189\pi$
$882$		0			0
$883$	−5.99963	+	5.03429i	−0.201904	+	0.169417i	−0.738133	−	0.674655i	$-0.764292\pi$
$883$	−5.99963	+	5.03429i	−0.201904	+	0.169417i	0.536230	+	0.844072i	$0.319848\pi$
$884$		0			0
$885$	−0.371481	−	2.10677i	−0.0124872	−	0.0708184i
$886$		0			0
$887$	37.5492			1.26078			0.630389	−	0.776280i	$-0.282896\pi$
$887$	37.5492			1.26078			0.630389	+	0.776280i	$0.282896\pi$
$888$		0			0
$889$	3.36798			0.112958
$890$		0			0
$891$	1.99797	+	11.3311i	0.0669346	+	0.379605i
$892$		0			0
$893$	20.1226	−	16.8849i	0.673377	−	0.565030i
$894$		0			0
$895$	−1.20780	+	1.01347i	−0.0403724	+	0.0338765i
$896$		0			0
$897$	−30.1925	+	10.9892i	−1.00810	+	0.366918i
$898$		0			0
$899$	−0.769858	+	1.33343i	−0.0256762	+	0.0444725i
$900$		0			0
$901$	−8.26400	−	3.00785i	−0.275314	−	0.100206i
$902$		0			0
$903$	−4.46010	−	3.74247i	−0.148423	−	0.124542i
$904$		0			0
$905$	0.510325	−	0.185743i	0.0169638	−	0.00617431i
$906$		0			0
$907$	−5.69564	−	32.3016i	−0.189120	−	1.07256i	−0.920546	−	0.390634i	$-0.872256\pi$
$907$	−5.69564	−	32.3016i	−0.189120	−	1.07256i	0.731426	−	0.681921i	$-0.238855\pi$
$908$		0			0
$909$	−14.5332	−	12.1948i	−0.482036	−	0.404477i
$910$		0			0
$911$	16.8114	+	29.1181i	0.556985	+	0.964727i	0.997746	+	0.0671021i	$0.0213753\pi$
$911$	16.8114	+	29.1181i	0.556985	+	0.964727i	−0.440761	+	0.897625i	$0.645291\pi$
$912$		0			0
$913$	0.635092	−	3.60179i	0.0210185	−	0.119202i
$914$		0			0
$915$	0.343627	+	0.595180i	0.0113600	+	0.0196760i
$916$		0			0
$917$	0.474180	−	0.821303i	0.0156588	−	0.0271218i
$918$		0			0
$919$	29.1313			0.960954			0.480477	−	0.877007i	$-0.340464\pi$
$919$	29.1313			0.960954			0.480477	+	0.877007i	$0.340464\pi$
$920$		0			0
$921$	−24.4313	−	8.89226i	−0.805038	−	0.293010i
$922$		0			0
$923$	6.91287	−	39.2049i	0.227540	−	1.29044i
$924$		0			0
$925$	24.7565	+	16.3715i	0.813989	+	0.538291i
$926$		0			0
$927$	−2.58117	+	14.6385i	−0.0847766	+	0.480792i
$928$		0			0
$929$	−28.9996	−	10.5550i	−0.951446	−	0.346298i	−0.180770	−	0.983525i	$-0.557859\pi$
$929$	−28.9996	−	10.5550i	−0.951446	−	0.346298i	−0.770676	+	0.637228i	$0.780081\pi$
$930$		0			0
$931$	23.8518			0.781710
$932$		0			0
$933$	−0.0779891	+	0.135081i	−0.00255325	+	0.00442235i
$934$		0			0
$935$	0.902307	+	1.56284i	0.0295086	+	0.0511104i
$936$		0			0
$937$	1.27251	−	7.21677i	0.0415711	−	0.235762i	−0.956942	−	0.290281i	$-0.906251\pi$
$937$	1.27251	−	7.21677i	0.0415711	−	0.235762i	0.998513	+	0.0545189i	$0.0173625\pi$
$938$		0			0
$939$	−6.31495	−	10.9378i	−0.206081	−	0.356942i
$940$		0			0
$941$	32.3208	+	27.1204i	1.05363	+	0.884098i	0.993470	−	0.114090i	$-0.0363954\pi$
$941$	32.3208	+	27.1204i	1.05363	+	0.884098i	0.0601572	+	0.998189i	$0.480840\pi$
$942$		0			0
$943$	−9.69464	−	54.9810i	−0.315701	−	1.79043i
$944$		0			0
$945$	0.881021	−	0.320666i	0.0286596	−	0.0104313i
$946$		0			0
$947$	29.9494	+	25.1305i	0.973224	+	0.816632i	0.983053	−	0.183320i	$-0.0586844\pi$
$947$	29.9494	+	25.1305i	0.973224	+	0.816632i	−0.00982951	+	0.999952i	$0.503129\pi$
$948$		0			0
$949$	30.2766	+	11.0198i	0.982819	+	0.357717i
$950$		0			0
$951$	−18.0653	+	31.2901i	−0.585809	+	1.01465i
$952$		0			0
$953$	1.14509	−	0.416780i	0.0370932	−	0.0135008i	−0.323407	−	0.946260i	$-0.604828\pi$
$953$	1.14509	−	0.416780i	0.0370932	−	0.0135008i	0.360500	+	0.932759i	$0.382606\pi$
$954$		0			0
$955$	−6.12389	+	5.13855i	−0.198164	+	0.166280i
$956$		0			0
$957$	−0.621782	+	0.521737i	−0.0200994	+	0.0168654i
$958$		0			0
$959$	1.44336	+	8.18569i	0.0466085	+	0.264330i
$960$		0			0
$961$	14.5164			0.468270
$962$		0			0
$963$	−22.6617			−0.730262
$964$		0			0
$965$	−0.636491	−	3.60972i	−0.0204894	−	0.116201i
$966$		0			0
$967$	−9.72067	+	8.15661i	−0.312596	+	0.262299i	−0.785564	−	0.618781i	$-0.787627\pi$
$967$	−9.72067	+	8.15661i	−0.312596	+	0.262299i	0.472968	+	0.881080i	$0.343183\pi$
$968$		0			0
$969$	−7.46005	+	6.25972i	−0.239651	+	0.201091i
$970$		0			0
$971$	0.827436	−	0.301162i	0.0265537	−	0.00966475i	−0.328709	−	0.944431i	$-0.606614\pi$
$971$	0.827436	−	0.301162i	0.0265537	−	0.00966475i	0.355263	+	0.934766i	$0.384391\pi$
$972$		0			0
$973$	0.176065	−	0.304954i	0.00564439	−	0.00977638i
$974$		0			0
$975$	−28.2781	−	10.2924i	−0.905623	−	0.329620i
$976$		0			0
$977$	35.8592	+	30.0895i	1.14724	+	0.962647i	0.999651	−	0.0264023i	$-0.00840510\pi$
$977$	35.8592	+	30.0895i	1.14724	+	0.962647i	0.147586	+	0.989049i	$0.452850\pi$
$978$		0			0
$979$	9.29081	−	3.38158i	0.296935	−	0.108076i
$980$		0			0
$981$	−2.05004	−	11.6263i	−0.0654526	−	0.371200i
$982$		0			0
$983$	26.4449	+	22.1899i	0.843460	+	0.707747i	0.958339	−	0.285633i	$-0.0922037\pi$
$983$	26.4449	+	22.1899i	0.843460	+	0.707747i	−0.114879	+	0.993379i	$0.536648\pi$
$984$		0			0
$985$	−0.838489	−	1.45231i	−0.0267165	−	0.0462743i
$986$		0			0
$987$	−0.851123	+	4.82696i	−0.0270915	+	0.153644i
$988$		0			0
$989$	−23.0762	−	39.9691i	−0.733780	−	1.27094i
$990$		0			0
$991$	−23.7701	+	41.1711i	−0.755083	+	1.30784i	0.190249	+	0.981736i	$0.439070\pi$
$991$	−23.7701	+	41.1711i	−0.755083	+	1.30784i	−0.945333	+	0.326107i	$0.894263\pi$
$992$		0			0
$993$	39.3133			1.24757
$994$		0			0
$995$	3.35887	+	1.22253i	0.106483	+	0.0387567i
$996$		0			0
$997$	9.31464	−	52.8259i	0.294998	−	1.67301i	−0.372215	−	0.928147i	$-0.621401\pi$
$997$	9.31464	−	52.8259i	0.294998	−	1.67301i	0.667212	−	0.744868i	$-0.267487\pi$
$998$		0			0
$999$	34.1487	−	3.90484i	1.08042	−	0.123544i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	592.2.bc.d.33.2		12
4.3	odd	2		74.2.f.b.33.1	yes	12
12.11	even	2		666.2.x.g.181.1		12
37.9	even	9	inner	592.2.bc.d.305.2		12
148.3	odd	18		2738.2.a.q.1.3		6
148.71	odd	18		2738.2.a.t.1.3		6
148.83	odd	18		74.2.f.b.9.1	✓	12
444.83	even	18		666.2.x.g.379.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.f.b.9.1	✓	12	148.83	odd	18
74.2.f.b.33.1	yes	12	4.3	odd	2
592.2.bc.d.33.2		12	1.1	even	1	trivial
592.2.bc.d.305.2		12	37.9	even	9	inner
666.2.x.g.181.1		12	12.11	even	2
666.2.x.g.379.1		12	444.83	even	18
2738.2.a.q.1.3		6	148.3	odd	18
2738.2.a.t.1.3		6	148.71	odd	18

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:	\( N \)	\(=\)	\( 592 = 2^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	592.bc (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.238878 + 1.35474i) q^{3} +(0.266044 - 0.223238i) q^{5} +(0.365982 - 0.307095i) q^{7} +(1.04081 - 0.378824i) q^{9} +O(q^{10})\)	\(q+(0.238878 + 1.35474i) q^{3} +(0.266044 - 0.223238i) q^{5} +(0.365982 - 0.307095i) q^{7} +(1.04081 - 0.378824i) q^{9} +(1.29268 - 2.23899i) q^{11} +(4.21288 + 1.53336i) q^{13} +(0.365982 + 0.307095i) q^{15} +(-1.88864 + 0.687407i) q^{17} +(-0.611631 - 3.46873i) q^{19} +(0.503461 + 0.422454i) q^{21} +(2.60486 + 4.51175i) q^{23} +(-0.847296 + 4.80526i) q^{25} +(2.82530 + 4.89356i) q^{27} +(-0.114111 + 0.197646i) q^{29} +6.74658 q^{31} +(3.34205 + 1.21641i) q^{33} +(0.0288122 - 0.163402i) q^{35} +(2.42322 - 5.57925i) q^{37} +(-1.07095 + 6.07365i) q^{39} +(-10.0701 - 3.66521i) q^{41} -8.85889 q^{43} +(0.192334 - 0.333132i) q^{45} +(3.72890 + 6.45864i) q^{47} +(-1.17590 + 6.66887i) q^{49} +(-1.38241 - 2.39441i) q^{51} +(3.35194 + 2.81261i) q^{53} +(-0.155916 - 0.884246i) q^{55} +(4.55314 - 1.65721i) q^{57} +(-3.43016 - 2.87825i) q^{59} +(1.35175 + 0.491998i) q^{61} +(0.264583 - 0.458271i) q^{63} +(1.46312 - 0.532531i) q^{65} +(8.06111 - 6.76408i) q^{67} +(-5.49002 + 4.60667i) q^{69} +(-1.54193 - 8.74474i) q^{71} +7.18667 q^{73} -6.71229 q^{75} +(-0.214485 - 1.21641i) q^{77} +(-2.70857 + 2.27276i) q^{79} +(-3.40919 + 2.86065i) q^{81} +(1.32932 - 0.483834i) q^{83} +(-0.349006 + 0.604496i) q^{85} +(-0.295018 - 0.107378i) q^{87} +(2.92954 + 2.45818i) q^{89} +(2.01273 - 0.732572i) q^{91} +(1.61161 + 9.13989i) q^{93} +(-0.937074 - 0.786298i) q^{95} +(-9.24175 - 16.0072i) q^{97} +(0.497253 - 2.82006i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{3} - 6 q^{5} - 6 q^{7} - 3 q^{9}+O(q^{10}) \) 12 * q + 3 * q^3 - 6 * q^5 - 6 * q^7 - 3 * q^9	\( 12 q + 3 q^{3} - 6 q^{5} - 6 q^{7} - 3 q^{9} - 3 q^{11} - 6 q^{13} - 6 q^{15} - 3 q^{17} + 3 q^{19} - 33 q^{21} + 21 q^{23} - 6 q^{25} - 3 q^{27} + 6 q^{29} - 42 q^{31} + 57 q^{33} + 9 q^{35} - 3 q^{37} + 24 q^{39} - 21 q^{41} - 36 q^{43} - 6 q^{45} - 9 q^{47} - 12 q^{49} - 6 q^{53} - 36 q^{57} + 6 q^{59} - 18 q^{61} - 36 q^{63} + 3 q^{65} + 27 q^{67} - 12 q^{69} + 18 q^{71} + 54 q^{73} + 6 q^{75} + 51 q^{77} + 12 q^{79} - 36 q^{81} + 6 q^{83} + 3 q^{85} - 39 q^{87} - 15 q^{89} + 51 q^{91} + 45 q^{93} + 15 q^{95} - 42 q^{97} + 33 q^{99}+O(q^{100}) \) 12 * q + 3 * q^3 - 6 * q^5 - 6 * q^7 - 3 * q^9 - 3 * q^11 - 6 * q^13 - 6 * q^15 - 3 * q^17 + 3 * q^19 - 33 * q^21 + 21 * q^23 - 6 * q^25 - 3 * q^27 + 6 * q^29 - 42 * q^31 + 57 * q^33 + 9 * q^35 - 3 * q^37 + 24 * q^39 - 21 * q^41 - 36 * q^43 - 6 * q^45 - 9 * q^47 - 12 * q^49 - 6 * q^53 - 36 * q^57 + 6 * q^59 - 18 * q^61 - 36 * q^63 + 3 * q^65 + 27 * q^67 - 12 * q^69 + 18 * q^71 + 54 * q^73 + 6 * q^75 + 51 * q^77 + 12 * q^79 - 36 * q^81 + 6 * q^83 + 3 * q^85 - 39 * q^87 - 15 * q^89 + 51 * q^91 + 45 * q^93 + 15 * q^95 - 42 * q^97 + 33 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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