LMFDB - Embedded newform 546.2.bv.a.317.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(317,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 4, 9]))

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

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

chi := DirichletCharacter("546.317");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bv (of order $12$, degree $4$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			317.27
Character	$\chi$	$=$	546.317
Dual form			546.2.bv.a.515.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +(-0.172608 - 1.72343i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.26981 - 0.340244i) q^{5} +(-0.612783 - 1.62003i) q^{6} +(-1.12113 - 2.39647i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.94041 + 0.594956i) q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} +(-0.172608 - 1.72343i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.26981 - 0.340244i) q^{5} +(-0.612783 - 1.62003i) q^{6} +(-1.12113 - 2.39647i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.94041 + 0.594956i) q^{9} +(1.13848 - 0.657301i) q^{10} +(-0.888483 - 0.238068i) q^{11} +(-1.01120 - 1.40623i) q^{12} +(-1.58383 - 3.23906i) q^{13} +(-1.70318 - 2.02464i) q^{14} +(-0.805566 - 2.12970i) q^{15} +(0.500000 - 0.866025i) q^{16} +(2.11756 + 3.66773i) q^{17} +(-2.68623 + 1.33572i) q^{18} +(0.896725 + 3.34662i) q^{19} +(0.929564 - 0.929564i) q^{20} +(-3.93663 + 2.34583i) q^{21} -0.919825 q^{22} +(3.61338 - 6.25856i) q^{23} +(-1.34070 - 1.09660i) q^{24} +(-2.83348 + 1.63591i) q^{25} +(-2.36819 - 2.71876i) q^{26} +(1.53290 + 4.96490i) q^{27} +(-2.16916 - 1.51484i) q^{28} -4.82542i q^{29} +(-1.32932 - 1.84863i) q^{30} +(10.3339 + 2.76895i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-0.256934 + 1.57233i) q^{33} +(2.99469 + 2.99469i) q^{34} +(-2.23900 - 2.66160i) q^{35} +(-2.24899 + 1.98545i) q^{36} +(-5.11817 + 1.37141i) q^{37} +(1.73234 + 3.00050i) q^{38} +(-5.30890 + 3.28871i) q^{39} +(0.657301 - 1.13848i) q^{40} +(0.501685 + 0.501685i) q^{41} +(-3.19535 + 3.28478i) q^{42} +2.84894i q^{43} +(-0.888483 + 0.238068i) q^{44} +(-3.53133 + 1.75594i) q^{45} +(1.87042 - 6.98052i) q^{46} +(-2.66163 - 9.93335i) q^{47} +(-1.57884 - 0.712231i) q^{48} +(-4.48615 + 5.37350i) q^{49} +(-2.31353 + 2.31353i) q^{50} +(5.95556 - 4.28255i) q^{51} +(-2.99117 - 2.01319i) q^{52} +(6.15237 - 3.55207i) q^{53} +(2.76568 + 4.39898i) q^{54} -1.20920 q^{55} +(-2.48732 - 0.901805i) q^{56} +(5.61288 - 2.12310i) q^{57} +(-1.24891 - 4.66100i) q^{58} +(10.5098 + 2.81610i) q^{59} +(-1.76249 - 1.44159i) q^{60} +(-3.88394 + 6.72719i) q^{61} +10.6984 q^{62} +(4.72237 + 6.37959i) q^{63} -1.00000i q^{64} +(-3.11323 - 3.57409i) q^{65} +(0.158769 + 1.58525i) q^{66} +(5.69940 + 1.52715i) q^{67} +(3.66773 + 2.11756i) q^{68} +(-11.4099 - 5.14713i) q^{69} +(-2.85158 - 1.99141i) q^{70} +(0.0481102 + 0.0481102i) q^{71} +(-1.65849 + 2.49988i) q^{72} +(-0.197835 + 0.738329i) q^{73} +(-4.58882 + 2.64936i) q^{74} +(3.30846 + 4.60093i) q^{75} +(2.44990 + 2.44990i) q^{76} +(0.425578 + 2.39613i) q^{77} +(-4.27682 + 4.55069i) q^{78} +(2.43891 - 4.22432i) q^{79} +(0.340244 - 1.26981i) q^{80} +(8.29205 - 3.49883i) q^{81} +(0.614436 + 0.354745i) q^{82} +(-5.78179 - 5.78179i) q^{83} +(-2.23631 + 3.99987i) q^{84} +(3.93682 + 3.93682i) q^{85} +(0.737361 + 2.75187i) q^{86} +(-8.31627 + 0.832908i) q^{87} +(-0.796592 + 0.459913i) q^{88} +(3.09511 + 11.5511i) q^{89} +(-2.95653 + 2.61008i) q^{90} +(-5.98663 + 7.42700i) q^{91} -7.22677i q^{92} +(2.98837 - 18.2876i) q^{93} +(-5.14188 - 8.90600i) q^{94} +(2.27734 + 3.94446i) q^{95} +(-1.70938 - 0.279329i) q^{96} +(-2.51747 + 2.51747i) q^{97} +(-2.94253 + 6.35150i) q^{98} +(2.75415 + 0.171411i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 16 q^{7}+O(q^{10}) $ 144 * q - 16 * q^7	$ 144 q - 16 q^{7} + 72 q^{16} + 16 q^{18} + 8 q^{19} + 8 q^{21} + 24 q^{27} - 8 q^{28} - 8 q^{31} + 12 q^{33} - 8 q^{37} + 16 q^{39} - 40 q^{45} + 8 q^{46} + 8 q^{52} - 12 q^{54} - 32 q^{55} + 16 q^{57} + 8 q^{58} - 32 q^{61} - 40 q^{63} - 32 q^{66} - 8 q^{67} + 16 q^{72} + 80 q^{73} - 16 q^{76} + 16 q^{78} - 112 q^{79} - 48 q^{81} + 16 q^{84} - 80 q^{85} + 96 q^{87} - 32 q^{91} + 36 q^{93} - 64 q^{94} - 144 q^{97} - 32 q^{99}+O(q^{100}) $ 144 * q - 16 * q^7 + 72 * q^16 + 16 * q^18 + 8 * q^19 + 8 * q^21 + 24 * q^27 - 8 * q^28 - 8 * q^31 + 12 * q^33 - 8 * q^37 + 16 * q^39 - 40 * q^45 + 8 * q^46 + 8 * q^52 - 12 * q^54 - 32 * q^55 + 16 * q^57 + 8 * q^58 - 32 * q^61 - 40 * q^63 - 32 * q^66 - 8 * q^67 + 16 * q^72 + 80 * q^73 - 16 * q^76 + 16 * q^78 - 112 * q^79 - 48 * q^81 + 16 * q^84 - 80 * q^85 + 96 * q^87 - 32 * q^91 + 36 * q^93 - 64 * q^94 - 144 * q^97 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$	−0.172608	−	1.72343i	−0.0996554	−	0.995022i
$3$	−0.172608	−	1.72343i	−0.0996554	−	0.995022i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	1.26981	−	0.340244i	0.567876	−	0.152162i	0.0365534	−	0.999332i	$-0.488362\pi$
$5$	1.26981	−	0.340244i	0.567876	−	0.152162i	0.531322	+	0.847170i	$0.321695\pi$
$6$	−0.612783	−	1.62003i	−0.250168	−	0.661374i
$7$	−1.12113	−	2.39647i	−0.423746	−	0.905781i
$7$	−1.12113	−	2.39647i	−0.423746	−	0.905781i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−2.94041	+	0.594956i	−0.980138	+	0.198319i
$10$	1.13848	−	0.657301i	0.360019	−	0.207857i
$11$	−0.888483	−	0.238068i	−0.267888	−	0.0717803i	0.122375	−	0.992484i	$-0.460949\pi$
$11$	−0.888483	−	0.238068i	−0.267888	−	0.0717803i	−0.390262	+	0.920704i	$0.627616\pi$
$12$	−1.01120	−	1.40623i	−0.291908	−	0.405943i
$13$	−1.58383	−	3.23906i	−0.439276	−	0.898352i
$13$	−1.58383	−	3.23906i	−0.439276	−	0.898352i
$14$	−1.70318	−	2.02464i	−0.455193	−	0.541109i
$15$	−0.805566	−	2.12970i	−0.207996	−	0.549885i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	2.11756	+	3.66773i	0.513585	+	0.889555i	0.999876	+	0.0157580i	$0.00501613\pi$
$17$	2.11756	+	3.66773i	0.513585	+	0.889555i	−0.486291	+	0.873797i	$0.661651\pi$
$18$	−2.68623	+	1.33572i	−0.633152	+	0.314832i
$19$	0.896725	+	3.34662i	0.205723	+	0.767768i	0.989228	+	0.146383i	$0.0467631\pi$
$19$	0.896725	+	3.34662i	0.205723	+	0.767768i	−0.783505	+	0.621385i	$0.786570\pi$
$20$	0.929564	−	0.929564i	0.207857	−	0.207857i
$21$	−3.93663	+	2.34583i	−0.859044	+	0.511903i
$22$	−0.919825			−0.196107
$23$	3.61338	−	6.25856i	0.753443	−	1.30500i	−0.192702	−	0.981257i	$-0.561725\pi$
$23$	3.61338	−	6.25856i	0.753443	−	1.30500i	0.946145	−	0.323743i	$-0.104941\pi$
$24$	−1.34070	−	1.09660i	−0.273669	−	0.223842i
$25$	−2.83348	+	1.63591i	−0.566696	+	0.327182i
$26$	−2.36819	−	2.71876i	−0.464441	−	0.533193i
$27$	1.53290	+	4.96490i	0.295007	+	0.955495i
$28$	−2.16916	−	1.51484i	−0.409933	−	0.286278i
$29$		−	4.82542i		−	0.896059i	−0.894019	−	0.448029i	$-0.852126\pi$
$29$		−	4.82542i		−	0.896059i	0.894019	−	0.448029i	$-0.147874\pi$
$30$	−1.32932	−	1.84863i	−0.242700	−	0.337512i
$31$	10.3339	+	2.76895i	1.85601	+	0.497318i	0.999813	−	0.0193253i	$-0.00615181\pi$
$31$	10.3339	+	2.76895i	1.85601	+	0.497318i	0.856201	+	0.516643i	$0.172818\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	−0.256934	+	1.57233i	−0.0447265	+	0.273707i
$34$	2.99469	+	2.99469i	0.513585	+	0.513585i
$35$	−2.23900	−	2.66160i	−0.378460	−	0.449893i
$36$	−2.24899	+	1.98545i	−0.374832	+	0.330909i
$37$	−5.11817	+	1.37141i	−0.841422	+	0.225458i	−0.653690	−	0.756762i	$-0.726780\pi$
$37$	−5.11817	+	1.37141i	−0.841422	+	0.225458i	−0.187731	+	0.982220i	$0.560113\pi$
$38$	1.73234	+	3.00050i	0.281022	+	0.486745i
$39$	−5.30890	+	3.28871i	−0.850104	+	0.526615i
$40$	0.657301	−	1.13848i	0.103928	−	0.180009i
$41$	0.501685	+	0.501685i	0.0783501	+	0.0783501i	0.745196	−	0.666846i	$-0.232356\pi$
$41$	0.501685	+	0.501685i	0.0783501	+	0.0783501i	−0.666846	+	0.745196i	$0.732356\pi$
$42$	−3.19535	+	3.28478i	−0.493053	+	0.506852i
$43$			2.84894i			0.434460i	0.976120	+	0.217230i	$0.0697021\pi$
$43$			2.84894i			0.434460i	−0.976120	+	0.217230i	$0.930298\pi$
$44$	−0.888483	+	0.238068i	−0.133944	+	0.0358901i
$45$	−3.53133	+	1.75594i	−0.526420	+	0.261760i
$46$	1.87042	−	6.98052i	0.275779	−	1.02922i
$47$	−2.66163	−	9.93335i	−0.388239	−	1.44893i	−0.832997	−	0.553277i	$-0.813377\pi$
$47$	−2.66163	−	9.93335i	−0.388239	−	1.44893i	0.444758	−	0.895651i	$-0.353290\pi$
$48$	−1.57884	−	0.712231i	−0.227886	−	0.102802i
$49$	−4.48615	+	5.37350i	−0.640879	+	0.767642i
$50$	−2.31353	+	2.31353i	−0.327182	+	0.327182i
$51$	5.95556	−	4.28255i	0.833945	−	0.599677i
$52$	−2.99117	−	2.01319i	−0.414800	−	0.279179i
$53$	6.15237	−	3.55207i	0.845093	−	0.487915i	−0.0138993	−	0.999903i	$-0.504424\pi$
$53$	6.15237	−	3.55207i	0.845093	−	0.487915i	0.858992	+	0.511989i	$0.171091\pi$
$54$	2.76568	+	4.39898i	0.376362	+	0.598625i
$55$	−1.20920			−0.163049
$56$	−2.48732	−	0.901805i	−0.332382	−	0.120509i
$57$	5.61288	−	2.12310i	0.743444	−	0.281211i
$58$	−1.24891	−	4.66100i	−0.163990	−	0.612019i
$59$	10.5098	+	2.81610i	1.36826	+	0.366625i	0.866844	−	0.498580i	$-0.166145\pi$
$59$	10.5098	+	2.81610i	1.36826	+	0.366625i	0.501418	+	0.865205i	$0.332812\pi$
$60$	−1.76249	−	1.44159i	−0.227536	−	0.186108i
$61$	−3.88394	+	6.72719i	−0.497288	+	0.861328i	−0.999995	−	0.00312876i	$-0.999004\pi$
$61$	−3.88394	+	6.72719i	−0.497288	+	0.861328i	0.502707	+	0.864457i	$0.332337\pi$
$62$	10.6984			1.35870
$63$	4.72237	+	6.37959i	0.594963	+	0.803753i
$64$		−	1.00000i		−	0.125000i
$65$	−3.11323	−	3.57409i	−0.386149	−	0.443311i
$66$	0.158769	+	1.58525i	0.0195432	+	0.195131i
$67$	5.69940	+	1.52715i	0.696292	+	0.186571i	0.589569	−	0.807718i	$-0.299298\pi$
$67$	5.69940	+	1.52715i	0.696292	+	0.186571i	0.106723	+	0.994289i	$0.465964\pi$
$68$	3.66773	+	2.11756i	0.444777	+	0.256792i
$69$	−11.4099	−	5.14713i	−1.37359	−	0.619642i
$70$	−2.85158	−	1.99141i	−0.340829	−	0.238020i
$71$	0.0481102	+	0.0481102i	0.00570963	+	0.00570963i	0.709956	−	0.704246i	$-0.248715\pi$
$71$	0.0481102	+	0.0481102i	0.00570963	+	0.00570963i	−0.704246	+	0.709956i	$0.748715\pi$
$72$	−1.65849	+	2.49988i	−0.195455	+	0.294614i
$73$	−0.197835	+	0.738329i	−0.0231548	+	0.0864149i	−0.976536	−	0.215353i	$-0.930910\pi$
$73$	−0.197835	+	0.738329i	−0.0231548	+	0.0864149i	0.953382	+	0.301767i	$0.0975766\pi$
$74$	−4.58882	+	2.64936i	−0.533440	+	0.307982i
$75$	3.30846	+	4.60093i	0.382028	+	0.531270i
$76$	2.44990	+	2.44990i	0.281022	+	0.281022i
$77$	0.425578	+	2.39613i	0.0484991	+	0.273064i
$78$	−4.27682	+	4.55069i	−0.484255	+	0.515264i
$79$	2.43891	−	4.22432i	0.274399	−	0.475273i	−0.695584	−	0.718444i	$-0.744854\pi$
$79$	2.43891	−	4.22432i	0.274399	−	0.475273i	0.969983	+	0.243172i	$0.0781878\pi$
$80$	0.340244	−	1.26981i	0.0380404	−	0.141969i
$81$	8.29205	−	3.49883i	0.921339	−	0.388759i
$82$	0.614436	+	0.354745i	0.0678532	+	0.0391750i
$83$	−5.78179	−	5.78179i	−0.634634	−	0.634634i	0.314593	−	0.949227i	$-0.398132\pi$
$83$	−5.78179	−	5.78179i	−0.634634	−	0.634634i	−0.949227	+	0.314593i	$0.898132\pi$
$84$	−2.23631	+	3.99987i	−0.244001	+	0.436421i
$85$	3.93682	+	3.93682i	0.427008	+	0.427008i
$86$	0.737361	+	2.75187i	0.0795116	+	0.296742i
$87$	−8.31627	+	0.832908i	−0.891598	+	0.0892971i
$88$	−0.796592	+	0.459913i	−0.0849170	+	0.0490268i
$89$	3.09511	+	11.5511i	0.328081	+	1.22441i	0.911178	+	0.412012i	$0.135174\pi$
$89$	3.09511	+	11.5511i	0.328081	+	1.22441i	−0.583097	+	0.812402i	$0.698159\pi$
$90$	−2.95653	+	2.61008i	−0.311646	+	0.275127i
$91$	−5.98663	+	7.42700i	−0.627569	+	0.778561i
$92$		−	7.22677i		−	0.753443i
$93$	2.98837	−	18.2876i	0.309880	−	1.89634i
$94$	−5.14188	−	8.90600i	−0.530344	−	0.918584i
$95$	2.27734	+	3.94446i	0.233650	+	0.404693i
$96$	−1.70938	−	0.279329i	−0.174463	−	0.0285089i
$97$	−2.51747	+	2.51747i	−0.255611	+	0.255611i	−0.823266	−	0.567656i	$-0.807851\pi$
$97$	−2.51747	+	2.51747i	−0.255611	+	0.255611i	0.567656	+	0.823266i	$0.307851\pi$
$98$	−2.94253	+	6.35150i	−0.297240	+	0.641598i
$99$	2.75415	+	0.171411i	0.276802	+	0.0172274i
$100$	−1.63591	+	2.83348i	−0.163591	+	0.283348i
$101$	8.86030	+	15.3465i	0.881633	+	1.52703i	0.849524	+	0.527549i	$0.176889\pi$
$101$	8.86030	+	15.3465i	0.881633	+	1.52703i	0.0321088	+	0.999484i	$0.489778\pi$
$102$	4.64422	−	5.67804i	0.459847	−	0.562210i
$103$	9.68096	+	5.58930i	0.953893	+	0.550730i	0.894288	−	0.447492i	$-0.147683\pi$
$103$	9.68096	+	5.58930i	0.953893	+	0.550730i	0.0596050	+	0.998222i	$0.481016\pi$
$104$	−3.41030	−	1.17042i	−0.334407	−	0.114769i
$105$	−4.20061	+	4.31817i	−0.409938	+	0.421411i
$106$	5.02339	−	5.02339i	0.487915	−	0.487915i
$107$	11.2953	+	6.52133i	1.09196	+	0.630441i	0.934097	−	0.357020i	$-0.116207\pi$
$107$	11.2953	+	6.52133i	1.09196	+	0.630441i	0.157860	+	0.987462i	$0.449541\pi$
$108$	3.80998	+	3.53328i	0.366616	+	0.339990i
$109$	11.9362	+	3.19830i	1.14328	+	0.306342i	0.780271	−	0.625442i	$-0.215081\pi$
$109$	11.9362	+	3.19830i	1.14328	+	0.306342i	0.363013	+	0.931784i	$0.381748\pi$
$110$	−1.16800	+	0.312965i	−0.111365	+	0.0298400i
$111$	3.24696	+	8.58408i	0.308188	+	0.814765i
$112$	−2.63597	−	0.227312i	−0.249076	−	0.0214789i
$113$		−	3.44414i		−	0.323998i	−0.986791	−	0.161999i	$-0.948206\pi$
$113$		−	3.44414i		−	0.323998i	0.986791	−	0.161999i	$-0.0517941\pi$
$114$	4.87213	−	3.50347i	0.456317	−	0.328130i
$115$	2.45886	−	9.17661i	0.229290	−	0.855723i
$116$	−2.41271	−	4.17894i	−0.224015	−	0.388005i
$117$	6.58421	+	8.58185i	0.608711	+	0.793392i
$118$	10.8806			1.00164
$119$	6.41555	−	9.18667i	0.588112	−	0.842141i
$120$	−2.07554	−	0.936301i	−0.189470	−	0.0854722i
$121$	−8.79355	−	5.07696i	−0.799414	−	0.461542i
$122$	−2.01048	+	7.50320i	−0.182020	+	0.679308i
$123$	0.778024	−	0.951214i	0.0701520	−	0.0857681i
$124$	10.3339	−	2.76895i	0.928007	−	0.248659i
$125$	−7.68919	+	7.68919i	−0.687742	+	0.687742i
$126$	6.21262	+	4.93998i	0.553464	+	0.440088i
$127$		−	13.1479i		−	1.16669i	−0.812225	−	0.583344i	$-0.801744\pi$
$127$		−	13.1479i		−	1.16669i	0.812225	−	0.583344i	$-0.198256\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	4.90995	−	0.491751i	0.432297	−	0.0432963i
$130$	−3.93219	−	2.64654i	−0.344876	−	0.232117i
$131$	9.48624	+	5.47688i	0.828817	+	0.478517i	0.853447	−	0.521179i	$-0.174508\pi$
$131$	9.48624	+	5.47688i	0.828817	+	0.478517i	−0.0246307	+	0.999697i	$0.507841\pi$
$132$	0.563653	+	1.49014i	0.0490597	+	0.129700i
$133$	7.01474	−	5.90096i	0.608255	−	0.511678i
$134$	5.90045			0.509721
$135$	3.63577	+	5.78291i	0.312917	+	0.497713i
$136$	4.09082	+	1.09613i	0.350785	+	0.0939925i
$137$	−10.4669	−	2.80461i	−0.894251	−	0.239614i	−0.217705	−	0.976015i	$-0.569857\pi$
$137$	−10.4669	−	2.80461i	−0.894251	−	0.239614i	−0.676546	+	0.736401i	$0.736524\pi$
$138$	−12.3533	−	2.01865i	−1.05158	−	0.171839i
$139$	−12.7355			−1.08021			−0.540105	−	0.841598i	$-0.681615\pi$
$139$	−12.7355			−1.08021			−0.540105	+	0.841598i	$0.681615\pi$
$140$	−3.26983	−	1.18552i	−0.276351	−	0.100194i
$141$	−16.6600	+	6.30171i	−1.40303	+	0.530700i
$142$	0.0589227	+	0.0340191i	0.00494469	+	0.00285482i
$143$	0.636091	+	3.25490i	0.0531926	+	0.272189i
$144$	−0.954959	+	2.84395i	−0.0795800	+	0.236996i
$145$	−1.64182	−	6.12736i	−0.136346	−	0.508850i
$146$			0.764375i			0.0632601i
$147$	10.0352	+	6.80405i	0.827688	+	0.561189i
$148$	−3.74676	+	3.74676i	−0.307982	+	0.307982i
$149$	−12.5818	+	3.37129i	−1.03074	+	0.276187i	−0.734272	−	0.678855i	$-0.762476\pi$
$149$	−12.5818	+	3.37129i	−1.03074	+	0.276187i	−0.296471	+	0.955042i	$0.595810\pi$
$150$	4.38653	+	3.58786i	0.358159	+	0.292948i
$151$	−3.06874	+	11.4527i	−0.249731	+	0.932007i	0.721216	+	0.692710i	$0.243584\pi$
$151$	−3.06874	+	11.4527i	−0.249731	+	0.932007i	−0.970946	+	0.239297i	$0.923083\pi$
$152$	3.00050	+	1.73234i	0.243373	+	0.140511i
$153$	−8.40865	−	9.52478i	−0.679799	−	0.770033i
$154$	1.03124	+	2.20433i	0.0830997	+	0.177630i
$155$	14.0641			1.12966
$156$	−2.95329	+	5.50255i	−0.236452	+	0.440557i
$157$	−1.07814	−	1.86740i	−0.0860451	−	0.149034i	0.819791	−	0.572663i	$-0.194090\pi$
$157$	−1.07814	−	1.86740i	−0.0860451	−	0.149034i	−0.905836	+	0.423628i	$0.860756\pi$
$158$	1.26247	−	4.71161i	0.100437	−	0.374836i
$159$	−7.18369	−	9.99005i	−0.569704	−	0.792263i
$160$		−	1.31460i		−	0.103928i
$161$	−19.0495	−	1.64273i	−1.50131	−	0.129465i
$162$	7.10395	−	5.52575i	0.558139	−	0.434144i
$163$	−10.4328	+	2.79546i	−0.817160	+	0.218957i	−0.643104	−	0.765778i	$-0.722354\pi$
$163$	−10.4328	+	2.79546i	−0.817160	+	0.218957i	−0.174056	+	0.984736i	$0.555687\pi$
$164$	0.685315	+	0.183630i	0.0535141	+	0.0143391i
$165$	0.208719	+	2.08398i	0.0162487	+	0.162237i
$166$	−7.08122	−	4.08834i	−0.549609	−	0.317317i
$167$	−4.58714	+	4.58714i	−0.354963	+	0.354963i	−0.861952	−	0.506989i	$-0.830758\pi$
$167$	−4.58714	+	4.58714i	−0.354963	+	0.354963i	0.506989	+	0.861952i	$0.330758\pi$
$168$	−1.12487	+	4.44237i	−0.0867852	+	0.342737i
$169$	−7.98296	+	10.2602i	−0.614074	+	0.789249i
$170$	4.82160	+	2.78375i	0.369800	+	0.213504i
$171$	−4.62783	−	9.30694i	−0.353899	−	0.711719i
$172$	1.42447	+	2.46726i	0.108615	+	0.188127i
$173$	8.44709	−	14.6308i	0.642220	−	1.11236i	−0.342716	−	0.939439i	$-0.611347\pi$
$173$	8.44709	−	14.6308i	0.642220	−	1.11236i	0.984936	−	0.172919i	$-0.0553198\pi$
$174$	−7.81733	+	2.95694i	−0.592630	+	0.224165i
$175$	7.09710	+	4.95629i	0.536491	+	0.374660i
$176$	−0.650415	+	0.650415i	−0.0490268	+	0.0490268i
$177$	3.03926	−	18.5990i	0.228445	−	1.39799i
$178$	5.97929	+	10.3564i	0.448167	+	0.776248i
$179$	−8.18902	−	14.1838i	−0.612076	−	1.06015i	−0.990890	−	0.134674i	$-0.957001\pi$
$179$	−8.18902	−	14.1838i	−0.612076	−	1.06015i	0.378814	−	0.925473i	$-0.376332\pi$
$180$	−2.18025	+	3.28635i	−0.162506	+	0.244950i
$181$		−	3.65978i		−	0.272029i	−0.990707	−	0.136014i	$-0.956571\pi$
$181$		−	3.65978i		−	0.272029i	0.990707	−	0.136014i	$-0.0434294\pi$
$182$	−3.86039	+	8.72338i	−0.286151	+	0.646620i
$183$	12.2642	+	5.53253i	0.906598	+	0.408976i
$184$	−1.87042	−	6.98052i	−0.137890	−	0.514611i
$185$	−6.03248	+	3.48285i	−0.443517	+	0.256064i
$186$	−1.84663	−	18.4379i	−0.135401	−	1.35193i
$187$	−1.00825	−	3.76284i	−0.0737305	−	0.275166i
$188$	−7.27172	−	7.27172i	−0.530344	−	0.530344i
$189$	10.1797	−	9.23984i	0.740461	−	0.672099i
$190$	3.22064	+	3.22064i	0.233650	+	0.233650i
$191$	−12.2195	−	7.05495i	−0.884174	−	0.510478i	−0.0121419	−	0.999926i	$-0.503865\pi$
$191$	−12.2195	−	7.05495i	−0.884174	−	0.510478i	−0.872033	+	0.489448i	$0.837198\pi$
$192$	−1.72343	+	0.172608i	−0.124378	+	0.0124569i
$193$	−0.695596	+	2.59600i	−0.0500701	+	0.186864i	−0.986432	−	0.164173i	$-0.947504\pi$
$193$	−0.695596	+	2.59600i	−0.0500701	+	0.186864i	0.936361	+	0.351037i	$0.114171\pi$
$194$	−1.78012	+	3.08326i	−0.127805	+	0.221365i
$195$	−5.62232	+	5.98235i	−0.402623	+	0.428405i
$196$	−1.19837	+	6.89666i	−0.0855981	+	0.492618i
$197$	15.1858	+	15.1858i	1.08194	+	1.08194i	0.996328	+	0.0856134i	$0.0272850\pi$
$197$	15.1858	+	15.1858i	1.08194	+	1.08194i	0.0856134	+	0.996328i	$0.472715\pi$
$198$	2.70467	−	0.547255i	0.192212	−	0.0388917i
$199$	−1.96754	+	1.13596i	−0.139475	+	0.0805261i	−0.568114	−	0.822950i	$-0.692327\pi$
$199$	−1.96754	+	1.13596i	−0.139475	+	0.0805261i	0.428639	+	0.903476i	$0.358993\pi$
$200$	−0.846810	+	3.16034i	−0.0598785	+	0.223470i
$201$	1.64817	−	10.0861i	0.116253	−	0.711419i
$202$	12.5304	+	12.5304i	0.881633	+	0.881633i
$203$	−11.5640	+	5.40991i	−0.811633	+	0.379701i
$204$	3.01639	−	6.68658i	0.211190	−	0.468154i
$205$	0.807740	+	0.466349i	0.0564150	+	0.0325712i
$206$	10.7977	+	2.89324i	0.752312	+	0.201581i
$207$	−6.90127	+	20.5526i	−0.479671	+	1.42850i
$208$	−3.59702	−	0.247889i	−0.249408	−	0.0171880i
$209$		−	3.18690i		−	0.220442i
$210$	−2.93985	+	5.25823i	−0.202869	+	0.362853i
$211$	−10.4053			−0.716331			−0.358165	−	0.933658i	$-0.616598\pi$
$211$	−10.4053			−0.716331			−0.358165	+	0.933658i	$0.616598\pi$
$212$	3.55207	−	6.15237i	0.243957	−	0.422546i
$213$	0.0746103	−	0.0912187i	0.00511221	−	0.00625021i
$214$	12.5983	+	3.37569i	0.861199	+	0.230758i
$215$	0.969336	+	3.61761i	0.0661082	+	0.246719i
$216$	4.59464	+	2.42679i	0.312626	+	0.165122i
$217$	−4.94985	−	27.8691i	−0.336018	−	1.89188i
$218$	12.3573			0.836942
$219$	1.30661	+	0.213512i	0.0882922	+	0.0144278i
$220$	−1.04720	+	0.604602i	−0.0706023	+	0.0407623i
$221$	8.52611	−	12.6680i	0.573528	−	0.852140i
$222$	5.35805	+	7.45121i	0.359609	+	0.500092i
$223$	−12.3431	+	12.3431i	−0.826555	+	0.826555i	−0.987038	−	0.160484i	$-0.948695\pi$
$223$	−12.3431	+	12.3431i	−0.826555	+	0.826555i	0.160484	+	0.987038i	$0.448695\pi$
$224$	−2.60498	+	0.462673i	−0.174053	+	0.0309136i
$225$	7.35831	−	6.49605i	0.490554	−	0.433070i
$226$	−0.891409	−	3.32679i	−0.0592957	−	0.221294i
$227$	−3.15723	+	11.7829i	−0.209553	+	0.782061i	0.778461	+	0.627693i	$0.216001\pi$
$227$	−3.15723	+	11.7829i	−0.209553	+	0.782061i	−0.988013	+	0.154368i	$0.950666\pi$
$228$	3.79935	−	4.64510i	0.251618	−	0.307629i
$229$	−24.6459	+	6.60384i	−1.62864	+	0.436394i	−0.953525	−	0.301314i	$-0.902575\pi$
$229$	−24.6459	+	6.60384i	−1.62864	+	0.436394i	−0.675120	+	0.737708i	$0.735908\pi$
$230$		−	9.50032i		−	0.626433i
$231$	4.05610	−	1.14704i	0.266872	−	0.0754700i
$232$	−3.41209	−	3.41209i	−0.224015	−	0.224015i
$233$	−1.81232	+	3.13902i	−0.118729	+	0.205644i	−0.919264	−	0.393641i	$-0.871215\pi$
$233$	−1.81232	+	3.13902i	−0.118729	+	0.205644i	0.800535	+	0.599286i	$0.204549\pi$
$234$	8.58101	+	6.58531i	0.560958	+	0.430495i
$235$	−6.75953	−	11.7078i	−0.440943	−	0.763736i
$236$	10.5098	−	2.81610i	0.684131	−	0.183312i
$237$	−7.70129	−	3.47414i	−0.500252	−	0.225669i
$238$	3.81926	−	10.5341i	0.247566	−	0.682825i
$239$	−13.4206	−	13.4206i	−0.868109	−	0.868109i	0.124154	−	0.992263i	$-0.460378\pi$
$239$	−13.4206	−	13.4206i	−0.868109	−	0.868109i	−0.992263	+	0.124154i	$0.960378\pi$
$240$	−2.24715	−	0.367207i	−0.145053	−	0.0237031i
$241$	−1.76180	+	6.57512i	−0.113487	+	0.423541i	−0.999169	−	0.0407517i	$-0.987025\pi$
$241$	−1.76180	+	6.57512i	−0.113487	+	0.423541i	0.885682	+	0.464293i	$0.153691\pi$
$242$	−9.80794	−	2.62803i	−0.630478	−	0.168936i
$243$	−7.46126	−	13.6868i	−0.478640	−	0.878011i
$244$			7.76789i			0.497288i
$245$	−3.86825	+	8.34969i	−0.247134	+	0.533442i
$246$	0.505321	−	1.12017i	0.0322181	−	0.0714194i
$247$	9.41963	−	8.20503i	0.599357	−	0.522073i
$248$	9.26508	−	5.34919i	0.588333	−	0.339674i
$249$	−8.96652	+	10.9625i	−0.568230	+	0.694720i
$250$	−5.43708	+	9.41729i	−0.343871	+	0.595602i
$251$	27.9262			1.76269			0.881344	−	0.472475i	$-0.156639\pi$
$251$	27.9262			1.76269			0.881344	+	0.472475i	$0.156639\pi$
$252$	7.27949	+	3.16371i	0.458565	+	0.199295i
$253$	−4.70039	+	4.70039i	−0.295511	+	0.295511i
$254$	−3.40293	−	12.6999i	−0.213519	−	0.796863i
$255$	6.10531	−	7.46436i	0.382329	−	0.467436i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	15.5288	−	26.8967i	0.968659	−	1.67777i	0.269215	−	0.963080i	$-0.413236\pi$
$257$	15.5288	−	26.8967i	0.968659	−	1.67777i	0.699445	−	0.714687i	$-0.253431\pi$
$258$	4.61537	−	1.74578i	0.287341	−	0.108688i
$259$	9.02466	+	10.7280i	0.560765	+	0.666607i
$260$	−4.48318	−	1.53864i	−0.278035	−	0.0954222i
$261$	2.87091	+	14.1887i	0.177705	+	0.878261i
$262$	10.5805	+	2.83504i	0.653667	+	0.175150i
$263$	−2.03208	+	1.17322i	−0.125303	+	0.0723439i	−0.561342	−	0.827584i	$-0.689715\pi$
$263$	−2.03208	+	1.17322i	−0.125303	+	0.0723439i	0.436038	+	0.899928i	$0.356381\pi$
$264$	0.930125	+	1.29348i	0.0572452	+	0.0796085i
$265$	6.60376	−	6.60376i	0.405666	−	0.405666i
$266$	5.24844	−	7.51544i	0.321802	−	0.460801i
$267$	19.3733	−	7.32802i	1.18562	−	0.448467i
$268$	5.69940	−	1.52715i	0.348146	−	0.0932855i
$269$	−5.01914	+	2.89780i	−0.306022	+	0.176682i	−0.645145	−	0.764060i	$-0.723203\pi$
$269$	−5.01914	+	2.89780i	−0.306022	+	0.176682i	0.339123	+	0.940742i	$0.389870\pi$
$270$	5.00861	+	4.64485i	0.304814	+	0.282677i
$271$	10.6951	−	2.86575i	0.649682	−	0.174082i	0.0810968	−	0.996706i	$-0.474158\pi$
$271$	10.6951	−	2.86575i	0.649682	−	0.174082i	0.568585	+	0.822625i	$0.307491\pi$
$272$	4.23513			0.256792
$273$	13.8332	+	9.03557i	0.837226	+	0.546857i
$274$	−10.8362			−0.654637
$275$	2.90696	−	0.778917i	0.175296	−	0.0469704i
$276$	−12.4548	+	1.24740i	−0.749692	+	0.0750846i
$277$	−24.0437	+	13.8817i	−1.44465	+	0.834068i	−0.998155	−	0.0607190i	$-0.980661\pi$
$277$	−24.0437	+	13.8817i	−1.44465	+	0.834068i	−0.446493	+	0.894787i	$0.647327\pi$
$278$	−12.3015	+	3.29619i	−0.737797	+	0.197692i
$279$	−32.0332	−	1.99366i	−1.91778	−	0.119357i
$280$	−3.46525	−	0.298825i	−0.207088	−	0.0178582i
$281$	12.1164	−	12.1164i	0.722802	−	0.722802i	−0.246373	−	0.969175i	$-0.579239\pi$
$281$	12.1164	−	12.1164i	0.722802	−	0.722802i	0.969175	+	0.246373i	$0.0792388\pi$
$282$	−14.4613	+	10.3989i	−0.861159	+	0.619246i
$283$	0.352051	−	0.203257i	0.0209273	−	0.0120824i	−0.489500	−	0.872003i	$-0.662821\pi$
$283$	0.352051	−	0.203257i	0.0209273	−	0.0120824i	0.510427	+	0.859921i	$0.329487\pi$
$284$	0.0657198	+	0.0176096i	0.00389975	+	0.00104494i
$285$	6.40491	−	4.60567i	0.379394	−	0.272817i
$286$	1.45685	+	2.97936i	0.0861452	+	0.176173i
$287$	0.639822	−	1.76473i	0.0377675	−	0.104169i
$288$	−0.186352	+	2.99421i	−0.0109809	+	0.176435i
$289$	−0.468155	+	0.810869i	−0.0275386	+	0.0476982i
$290$	−3.17176	−	5.49364i	−0.186252	−	0.322598i
$291$	4.77322	+	3.90415i	0.279811	+	0.228865i
$292$	0.197835	+	0.738329i	0.0115774	+	0.0432074i
$293$	−13.9031	+	13.9031i	−0.812230	+	0.812230i	−0.984968	−	0.172738i	$-0.944739\pi$
$293$	−13.9031	+	13.9031i	−0.812230	+	0.812230i	0.172738	+	0.984968i	$0.444739\pi$
$294$	11.4543	+	3.97491i	0.668026	+	0.231822i
$295$	14.3036			0.832789
$296$	−2.64936	+	4.58882i	−0.153991	+	0.266720i
$297$	−0.179974	−	4.77616i	−0.0104431	−	0.277141i
$298$	−11.2806	+	6.51283i	−0.653465	+	0.377278i
$299$	−25.9948	−	1.79144i	−1.50332	−	0.103602i
$300$	5.16567	+	2.33029i	0.298240	+	0.134540i
$301$	6.82741	−	3.19403i	0.393525	−	0.184101i
$302$			11.8567i			0.682277i
$303$	24.9192	−	17.9190i	1.43157	−	1.02942i
$304$	3.34662	+	0.896725i	0.191942	+	0.0514307i
$305$	−2.64298	+	9.86373i	−0.151336	+	0.564795i
$306$	−10.5873	−	7.02391i	−0.605237	−	0.401530i
$307$	−18.0506	−	18.0506i	−1.03020	−	1.03020i	−0.999529	−	0.0306724i	$-0.990235\pi$
$307$	−18.0506	−	18.0506i	−1.03020	−	1.03020i	−0.0306724	−	0.999529i	$-0.509765\pi$
$308$	1.56663	+	1.86232i	0.0892668	+	0.106115i
$309$	7.96175	−	17.6492i	0.452928	−	1.00403i
$310$	13.5849	−	3.64006i	0.771571	−	0.206742i
$311$	−0.878642	−	1.52185i	−0.0498232	−	0.0862963i	0.840038	−	0.542527i	$-0.182532\pi$
$311$	−0.878642	−	1.52185i	−0.0498232	−	0.0862963i	−0.889861	+	0.456231i	$0.849199\pi$
$312$	−1.42849	+	6.07943i	−0.0808723	+	0.344180i
$313$	4.46856	−	7.73978i	0.252578	−	0.437478i	−0.711657	−	0.702527i	$-0.752055\pi$
$313$	4.46856	−	7.73978i	0.252578	−	0.437478i	0.964235	+	0.265049i	$0.0853882\pi$
$314$	−1.52472	−	1.52472i	−0.0860451	−	0.0860451i
$315$	8.16712	+	6.49410i	0.460165	+	0.365901i
$316$		−	4.87782i		−	0.274399i
$317$	−1.54602	+	0.414254i	−0.0868329	+	0.0232668i	−0.301974	−	0.953316i	$-0.597646\pi$
$317$	−1.54602	+	0.414254i	−0.0868329	+	0.0232668i	0.215141	+	0.976583i	$0.430979\pi$
$318$	−9.52453	−	7.79037i	−0.534109	−	0.436862i
$319$	−1.14878	+	4.28731i	−0.0643193	+	0.240043i
$320$	−0.340244	−	1.26981i	−0.0190202	−	0.0709844i
$321$	9.28940	−	20.5923i	0.518484	−	1.14935i
$322$	−18.8256	+	3.34363i	−1.04911	+	0.186333i
$323$	−10.3756	+	10.3756i	−0.577315	+	0.577315i
$324$	5.43171	−	7.17610i	0.301762	−	0.398672i
$325$	9.78656	+	6.58679i	0.542861	+	0.365369i
$326$	−9.35379	+	5.40041i	−0.518059	+	0.299101i
$327$	3.45176	−	21.1233i	0.190883	−	1.16812i
$328$	0.709490			0.0391750
$329$	−20.8210	+	17.5151i	−1.14790	+	0.965637i
$330$	0.740980	+	1.95895i	0.0407896	+	0.107836i
$331$	−1.85234	−	6.91304i	−0.101814	−	0.379975i	0.896150	−	0.443751i	$-0.146352\pi$
$331$	−1.85234	−	6.91304i	−0.101814	−	0.379975i	−0.997964	+	0.0637757i	$0.979686\pi$
$332$	−7.89807	−	2.11628i	−0.433463	−	0.116146i
$333$	14.2336	−	7.07759i	0.779996	−	0.387850i
$334$	−3.24360	+	5.61807i	−0.177482	+	0.307407i
$335$	7.75674			0.423796
$336$	0.0632342	+	4.58214i	0.00344971	+	0.249976i
$337$		−	7.70230i		−	0.419571i	−0.977747	−	0.209786i	$-0.932723\pi$
$337$		−	7.70230i		−	0.419571i	0.977747	−	0.209786i	$-0.0672766\pi$
$338$	−5.05540	+	11.9768i	−0.274978	+	0.651450i
$339$	−5.93573	+	0.594487i	−0.322385	+	0.0322881i
$340$	5.37780	+	1.44098i	0.291652	+	0.0781480i
$341$	−8.52225	−	4.92032i	−0.461506	−	0.266450i
$342$	−6.87896	−	7.79204i	−0.371971	−	0.421345i
$343$	17.9070	+	4.72657i	0.966886	+	0.255211i
$344$	2.01451	+	2.01451i	0.108615	+	0.108615i
$345$	−16.2396	−	2.65372i	−0.874313	−	0.142871i
$346$	4.37253	−	16.3185i	0.235069	−	0.877289i
$347$	−15.3759	+	8.87726i	−0.825420	+	0.476556i	−0.852282	−	0.523083i	$-0.824782\pi$
$347$	−15.3759	+	8.87726i	−0.825420	+	0.476556i	0.0268622	+	0.999639i	$0.491448\pi$
$348$	−6.78565	+	4.87946i	−0.363749	+	0.261566i
$349$	−10.2613	−	10.2613i	−0.549274	−	0.549274i	0.376957	−	0.926231i	$-0.376970\pi$
$349$	−10.2613	−	10.2613i	−0.549274	−	0.549274i	−0.926231	+	0.376957i	$0.876970\pi$
$350$	8.13806	+	2.95054i	0.434997	+	0.157713i
$351$	13.6537	−	12.8287i	0.728781	−	0.684746i
$352$	−0.459913	+	0.796592i	−0.0245134	+	0.0424585i
$353$	3.86399	−	14.4206i	0.205660	−	0.767532i	−0.783588	−	0.621281i	$-0.786613\pi$
$353$	3.86399	−	14.4206i	0.205660	−	0.767532i	0.989248	−	0.146251i	$-0.0467207\pi$
$354$	−1.87808	−	18.7519i	−0.0998186	−	0.996651i
$355$	0.0774600	+	0.0447215i	0.00411115	+	0.00237357i
$356$	8.45600	+	8.45600i	0.448167	+	0.448167i
$357$	−16.9399	−	9.47105i	−0.896557	−	0.501261i
$358$	−11.5810	−	11.5810i	−0.612076	−	0.612076i
$359$	2.32206	+	8.66603i	0.122553	+	0.457376i	0.999741	−	0.0227728i	$-0.00724943\pi$
$359$	2.32206	+	8.66603i	0.122553	+	0.457376i	−0.877187	+	0.480149i	$0.840583\pi$
$360$	−1.25539	+	3.73866i	−0.0661650	+	0.197045i
$361$	6.05872	−	3.49800i	0.318880	−	0.184105i
$362$	−0.947220	−	3.53507i	−0.0497848	−	0.185799i
$363$	−7.23194	+	16.0314i	−0.379578	+	0.841430i
$364$	−1.47107	+	9.42528i	−0.0771052	+	0.494019i
$365$			1.00485i			0.0525962i
$366$	13.2783	+	2.16980i	0.694066	+	0.113417i
$367$	10.4015	+	18.0159i	0.542954	+	0.940424i	0.998733	+	0.0503305i	$0.0160275\pi$
$367$	10.4015	+	18.0159i	0.542954	+	0.940424i	−0.455779	+	0.890093i	$0.650639\pi$
$368$	−3.61338	−	6.25856i	−0.188361	−	0.326250i
$369$	−1.77364	−	1.17668i	−0.0923321	−	0.0612556i
$370$	−4.92550	+	4.92550i	−0.256064	+	0.256064i
$371$	−15.4100	−	10.7617i	−0.800048	−	0.558717i
$372$	−6.55579	−	17.3317i	−0.339902	−	0.898607i
$373$	−15.6928	+	27.1808i	−0.812544	+	1.40737i	0.0985336	+	0.995134i	$0.468585\pi$
$373$	−15.6928	+	27.1808i	−0.812544	+	1.40737i	−0.911078	+	0.412234i	$0.864749\pi$
$374$	−1.94779	−	3.37367i	−0.100718	−	0.174448i
$375$	14.5790	+	11.9246i	0.752856	+	0.615781i
$376$	−8.90600	−	5.14188i	−0.459292	−	0.265172i
$377$	−15.6298	+	7.64266i	−0.804976	+	0.393617i
$378$	7.44135	−	11.5597i	0.382742	−	0.594566i
$379$	4.22921	−	4.22921i	0.217240	−	0.217240i	−0.590094	−	0.807334i	$-0.700910\pi$
$379$	4.22921	−	4.22921i	0.217240	−	0.217240i	0.807334	+	0.590094i	$0.200910\pi$
$380$	3.94446	+	2.27734i	0.202347	+	0.116825i
$381$	−22.6595	+	2.26944i	−1.16088	+	0.116267i
$382$	−13.6291	−	3.65191i	−0.697326	−	0.186848i
$383$	10.6640	−	2.85742i	0.544906	−	0.146007i	0.0241433	−	0.999709i	$-0.492314\pi$
$383$	10.6640	−	2.85742i	0.544906	−	0.146007i	0.520763	+	0.853701i	$0.325648\pi$
$384$	−1.62003	+	0.612783i	−0.0826718	+	0.0312709i
$385$	1.35567	+	2.89782i	0.0690914	+	0.147687i
$386$			2.68758i			0.136794i
$387$	−1.69500	−	8.37707i	−0.0861615	−	0.425830i
$388$	−0.921459	+	3.43893i	−0.0467800	+	0.174585i
$389$	−17.7593	−	30.7599i	−0.900430	−	1.55959i	−0.826937	−	0.562295i	$-0.809919\pi$
$389$	−17.7593	−	30.7599i	−0.900430	−	1.55959i	−0.0734932	−	0.997296i	$-0.523415\pi$
$390$	−3.88240	+	7.23367i	−0.196593	+	0.366291i
$391$	30.6063			1.54783
$392$	0.627447	+	6.97182i	0.0316909	+	0.352130i
$393$	7.80161	−	17.2942i	0.393539	−	0.872378i
$394$	18.5987	+	10.7380i	0.936989	+	0.540971i
$395$	1.65965	−	6.19390i	0.0835060	−	0.311649i
$396$	2.47087	−	1.22863i	0.124166	−	0.0617408i
$397$	22.7284	−	6.09004i	1.14070	−	0.305651i	0.361469	−	0.932384i	$-0.382275\pi$
$397$	22.7284	−	6.09004i	1.14070	−	0.305651i	0.779234	+	0.626733i	$0.215608\pi$
$398$	−1.60649	+	1.60649i	−0.0805261	+	0.0805261i
$399$	−11.3807	−	11.0709i	−0.569747	−	0.554236i
$400$			3.27182i			0.163591i
$401$	8.04365	+	30.0193i	0.401681	+	1.49909i	0.810096	+	0.586297i	$0.199415\pi$
$401$	8.04365	+	30.0193i	0.401681	+	1.49909i	−0.408415	+	0.912796i	$0.633918\pi$
$402$	−1.01847	−	10.1690i	−0.0507965	−	0.507184i
$403$	−7.39830	−	37.8575i	−0.368536	−	1.88581i
$404$	15.3465	+	8.86030i	0.763517	+	0.440817i
$405$	9.33886	−	7.26417i	0.464052	−	0.360959i
$406$	−9.76977	+	8.21855i	−0.484865	+	0.407880i
$407$	4.87389			0.241590
$408$	1.18300	−	7.23944i	0.0585670	−	0.358406i
$409$	−8.52683	−	2.28476i	−0.421624	−	0.112974i	0.0417675	−	0.999127i	$-0.486701\pi$
$409$	−8.52683	−	2.28476i	−0.421624	−	0.112974i	−0.463392	+	0.886153i	$0.653368\pi$
$410$	0.900916	+	0.241400i	0.0444931	+	0.0119219i
$411$	−3.02686	+	18.5231i	−0.149304	+	0.913678i
$412$	11.1786			0.550730
$413$	−5.03414	−	28.3437i	−0.247714	−	1.39470i
$414$	−1.34672	+	21.6384i	−0.0661876	+	1.06347i
$415$	−9.30899	−	5.37455i	−0.456960	−	0.263826i
$416$	−3.53861	+	0.691534i	−0.173495	+	0.0339053i
$417$	2.19825	+	21.9487i	0.107649	+	1.07483i
$418$	−0.824830	−	3.07831i	−0.0403437	−	0.150565i
$419$			18.6589i			0.911548i	0.890095	+	0.455774i	$0.150638\pi$
$419$			18.6589i			0.911548i	−0.890095	+	0.455774i	$0.849362\pi$
$420$	−1.47875	+	5.83995i	−0.0721556	+	0.284961i
$421$	−23.8603	+	23.8603i	−1.16288	+	1.16288i	−0.179038	+	0.983842i	$0.557299\pi$
$421$	−23.8603	+	23.8603i	−1.16288	+	1.16288i	−0.983842	+	0.179038i	$0.942701\pi$
$422$	−10.0507	+	2.69309i	−0.489263	+	0.131098i
$423$	13.7362	+	27.6246i	0.667877	+	1.34315i
$424$	1.83869	−	6.86208i	0.0892946	−	0.333252i
$425$	−12.0002	−	6.92829i	−0.582093	−	0.336071i
$426$	0.0484589	−	0.107421i	0.00234784	−	0.00520457i
$427$	20.4759	+	1.76573i	0.990898	+	0.0854498i
$428$	13.0427			0.630441
$429$	5.49980	−	1.65808i	0.265533	−	0.0800529i
$430$	1.87261	+	3.24346i	0.0903054	+	0.156414i
$431$	−2.49215	+	9.30083i	−0.120043	+	0.448005i	−0.999615	−	0.0277606i	$-0.991162\pi$
$431$	−2.49215	+	9.30083i	−0.120043	+	0.448005i	0.879572	+	0.475766i	$0.157829\pi$
$432$	5.06618	+	1.15492i	0.243747	+	0.0555659i
$433$		−	22.4645i		−	1.07958i	−0.841801	−	0.539788i	$-0.818505\pi$
$433$		−	22.4645i		−	1.07958i	0.841801	−	0.539788i	$-0.181495\pi$
$434$	−11.9942	−	25.6384i	−0.575742	−	1.23068i
$435$	−10.2767	+	3.88720i	−0.492729	+	0.186377i
$436$	11.9362	−	3.19830i	0.571642	−	0.153171i
$437$	24.1853	+	6.48042i	1.15694	+	0.310001i
$438$	1.31735	−	0.131937i	0.0629452	−	0.00630421i
$439$	−14.4953	−	8.36888i	−0.691824	−	0.399425i	0.112471	−	0.993655i	$-0.464123\pi$
$439$	−14.4953	−	8.36888i	−0.691824	−	0.399425i	−0.804295	+	0.594230i	$0.797457\pi$
$440$	−0.855036	+	0.855036i	−0.0407623	+	0.0407623i
$441$	9.99414	−	18.4694i	0.475912	−	0.879493i
$442$	4.95688	−	14.4430i	0.235775	−	0.686985i
$443$	3.92321	+	2.26506i	0.186397	+	0.107616i	0.590295	−	0.807188i	$-0.299011\pi$
$443$	3.92321	+	2.26506i	0.186397	+	0.107616i	−0.403898	+	0.914804i	$0.632345\pi$
$444$	7.10399	+	5.81055i	0.337141	+	0.275757i
$445$	7.86039	+	13.6146i	0.372618	+	0.645394i
$446$	−8.72789	+	15.1171i	−0.413277	+	0.715817i
$447$	7.98190	+	21.1020i	0.377531	+	0.998089i
$448$	−2.39647	+	1.12113i	−0.113223	+	0.0529682i
$449$	−14.7451	+	14.7451i	−0.695867	+	0.695867i	−0.963516	−	0.267650i	$-0.913753\pi$
$449$	−14.7451	+	14.7451i	−0.695867	+	0.695867i	0.267650	+	0.963516i	$0.413753\pi$
$450$	5.42628	−	8.17917i	0.255797	−	0.385570i
$451$	−0.326303	−	0.565174i	−0.0153650	−	0.0266130i
$452$	−1.72207	−	2.98271i	−0.0809994	−	0.140295i
$453$	20.2676	+	3.31193i	0.952255	+	0.155608i
$454$			12.1986i			0.572508i
$455$	−5.07488	+	11.4678i	−0.237914	+	0.537618i
$456$	2.46765	−	5.47016i	0.115558	−	0.256164i
$457$	3.57187	+	13.3304i	0.167085	+	0.623570i	0.997765	+	0.0668199i	$0.0212853\pi$
$457$	3.57187	+	13.3304i	0.167085	+	0.623570i	−0.830680	+	0.556750i	$0.812048\pi$
$458$	−22.0969	+	12.7576i	−1.03252	+	0.596125i
$459$	−14.9639	+	16.1358i	−0.698454	+	0.753153i
$460$	−2.45886	−	9.17661i	−0.114645	−	0.427862i
$461$	12.5933	+	12.5933i	0.586529	+	0.586529i	0.936690	−	0.350161i	$-0.113873\pi$
$461$	12.5933	+	12.5933i	0.586529	+	0.586529i	−0.350161	+	0.936690i	$0.613873\pi$
$462$	3.62101	−	2.15776i	0.168465	−	0.100388i
$463$	8.53447	+	8.53447i	0.396631	+	0.396631i	0.877043	−	0.480412i	$-0.159513\pi$
$463$	8.53447	+	8.53447i	0.396631	+	0.396631i	−0.480412	+	0.877043i	$0.659513\pi$
$464$	−4.17894	−	2.41271i	−0.194002	−	0.112007i
$465$	−2.42758	−	24.2385i	−0.112577	−	1.12403i
$466$	−0.938124	+	3.50113i	−0.0434578	+	0.162187i
$467$	−6.58262	+	11.4014i	−0.304607	+	0.527595i	−0.977174	−	0.212441i	$-0.931859\pi$
$467$	−6.58262	+	11.4014i	−0.304607	+	0.527595i	0.672566	+	0.740037i	$0.265192\pi$
$468$	9.99302	+	4.13999i	0.461928	+	0.191371i
$469$	−2.72998	−	15.3706i	−0.126059	−	0.709747i
$470$	−9.55941	−	9.55941i	−0.440943	−	0.440943i
$471$	−3.03223	+	2.18043i	−0.139718	+	0.100469i
$472$	9.42285	−	5.44028i	0.433722	−	0.250409i
$473$	0.678243	−	2.53124i	0.0311856	−	0.116386i
$474$	−8.33804	−	1.36252i	−0.382979	−	0.0625826i
$475$	−8.01563	−	8.01563i	−0.367782	−	0.367782i
$476$	0.962694	−	11.1637i	0.0441250	−	0.511686i
$477$	−15.9772	+	14.1049i	−0.731545	+	0.645821i
$478$	−16.4369	−	9.48982i	−0.751804	−	0.434054i
$479$	−3.56379	−	0.954915i	−0.162834	−	0.0436312i	0.176481	−	0.984304i	$-0.443529\pi$
$479$	−3.56379	−	0.954915i	−0.162834	−	0.0436312i	−0.339315	+	0.940673i	$0.610195\pi$
$480$	−2.26562	+	0.226911i	−0.103411	+	0.0103570i
$481$	12.5484	+	14.4059i	0.572157	+	0.656855i
$482$			6.80707i			0.310054i
$483$	0.456979	+	33.1141i	0.0207933	+	1.50674i
$484$	−10.1539			−0.461542
$485$	−2.34015	+	4.05326i	−0.106261	+	0.184049i
$486$	−10.7494	−	11.2894i	−0.487605	−	0.512095i
$487$	35.6845	+	9.56163i	1.61702	+	0.433279i	0.950124	−	0.311873i	$-0.100956\pi$
$487$	35.6845	+	9.56163i	1.61702	+	0.433279i	0.666895	+	0.745152i	$0.267623\pi$
$488$	2.01048	+	7.50320i	0.0910100	+	0.339654i
$489$	6.61856	+	17.4977i	0.299302	+	0.791272i
$490$	−1.57538	+	9.06636i	−0.0711686	+	0.409577i
$491$	−7.92043			−0.357444			−0.178722	−	0.983900i	$-0.557196\pi$
$491$	−7.92043			−0.357444			−0.178722	+	0.983900i	$0.557196\pi$
$492$	0.198181	−	1.21279i	0.00893471	−	0.0546767i
$493$	17.6983	−	10.2181i	0.797093	−	0.460202i
$494$	6.97505	−	10.3634i	0.313822	−	0.466273i
$495$	3.55556	−	0.719423i	0.159811	−	0.0323357i
$496$	7.56490	−	7.56490i	0.339674	−	0.339674i
$497$	0.0613571	−	0.169232i	0.00275224	−	0.00759111i
$498$	−5.82369	+	12.9097i	−0.260966	+	0.578496i
$499$	−0.694278	−	2.59108i	−0.0310801	−	0.115993i	0.948643	−	0.316348i	$-0.102457\pi$
$499$	−0.694278	−	2.59108i	−0.0310801	−	0.115993i	−0.979723	+	0.200356i	$0.935790\pi$
$500$	−2.81444	+	10.5036i	−0.125866	+	0.469736i
$501$	8.69738	+	7.11383i	0.388570	+	0.317822i
$502$	26.9747	−	7.22784i	1.20394	−	0.322594i
$503$		−	38.7289i		−	1.72684i	−0.504488	−	0.863419i	$-0.668319\pi$
$503$		−	38.7289i		−	1.72684i	0.504488	−	0.863419i	$-0.331681\pi$
$504$	7.85027	+	1.17184i	0.349679	+	0.0521977i
$505$	16.4724	+	16.4724i	0.733014	+	0.733014i
$506$	−3.32368	+	5.75678i	−0.147756	+	0.255920i
$507$	19.0607	+	11.9871i	0.846516	+	0.532364i
$508$	−6.57396	−	11.3864i	−0.291672	−	0.505191i
$509$	−11.2815	+	3.02287i	−0.500044	+	0.133986i	−0.500020	−	0.866014i	$-0.666674\pi$
$509$	−11.2815	+	3.02287i	−0.500044	+	0.133986i	−2.33542e−5		1.00000i	$0.500007\pi$
$510$	3.96535	−	8.79019i	0.175589	−	0.389236i
$511$	1.99118	−	0.353655i	0.0880847	−	0.0156448i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−15.2410	+	9.58219i	−0.672908	+	0.423064i
$514$	8.03829	−	29.9993i	0.354554	−	1.32321i
$515$	14.1947	+	3.80345i	0.625493	+	0.167600i
$516$	4.00627	−	2.88084i	0.176366	−	0.126822i
$517$			9.45926i			0.416018i
$518$	11.4938	+	8.02672i	0.505007	+	0.352674i
$519$	−26.6731	−	12.0326i	−1.17082	−	0.528171i
$520$	−4.72865	−	0.325876i	−0.207365	−	0.0142906i
$521$	7.57419	−	4.37296i	0.331831	−	0.191583i	−0.324823	−	0.945775i	$-0.605305\pi$
$521$	7.57419	−	4.37296i	0.331831	−	0.191583i	0.656654	+	0.754192i	$0.271971\pi$
$522$	6.44540	+	12.9622i	0.282108	+	0.567341i
$523$	−13.1705	+	22.8120i	−0.575908	+	0.997501i	0.420035	+	0.907508i	$0.362018\pi$
$523$	−13.1705	+	22.8120i	−0.575908	+	0.997501i	−0.995942	+	0.0899932i	$0.971315\pi$
$524$	10.9538			0.478517
$525$	7.31680	−	13.0868i	0.319331	−	0.571157i
$526$	−1.65919	+	1.65919i	−0.0723439	+	0.0723439i
$527$	11.7268	+	43.7652i	0.510829	+	1.90644i
$528$	1.23321	+	1.00868i	0.0536686	+	0.0438970i
$529$	−14.6131	−	25.3106i	−0.635351	−	1.10046i
$530$	4.66956	−	8.08792i	0.202833	−	0.351317i
$531$	−32.5787	−	2.02761i	−1.41379	−	0.0879908i
$532$	3.12446	−	8.61775i	0.135463	−	0.373627i
$533$	0.830401	−	2.41957i	0.0359687	−	0.104803i
$534$	16.8165	−	12.0925i	0.727721	−	0.523293i
$535$	16.5617	+	4.43769i	0.716024	+	0.191858i
$536$	5.10994	−	2.95022i	0.220716	−	0.127430i
$537$	−23.0313	+	16.5614i	−0.993873	+	0.714679i
$538$	−4.09811	+	4.09811i	−0.176682	+	0.176682i
$539$	5.26513	−	3.70625i	0.226785	−	0.159639i
$540$	6.04012	+	3.19026i	0.259926	+	0.137287i
$541$	26.2800	−	7.04170i	1.12987	−	0.302747i	0.354996	−	0.934868i	$-0.384482\pi$
$541$	26.2800	−	7.04170i	1.12987	−	0.302747i	0.774869	+	0.632121i	$0.217816\pi$
$542$	9.58898	−	5.53620i	0.411882	−	0.237800i
$543$	−6.30736	+	0.631707i	−0.270675	+	0.0271092i
$544$	4.09082	−	1.09613i	0.175392	−	0.0469963i
$545$	16.2449			0.695856
$546$	15.7005	+	5.14738i	0.671918	+	0.220288i
$547$	2.60008			0.111171			0.0555857	−	0.998454i	$-0.482297\pi$
$547$	2.60008			0.111171			0.0555857	+	0.998454i	$0.482297\pi$
$548$	−10.4669	+	2.80461i	−0.447125	+	0.119807i
$549$	7.41802	−	22.0915i	0.316593	−	0.942841i
$550$	2.60631	−	1.50475i	0.111133	−	0.0641628i
$551$	16.1489	−	4.32708i	0.687965	−	0.184340i
$552$	−11.7076	+	4.42844i	−0.498308	+	0.188487i
$553$	−12.8578	−	1.10879i	−0.546769	−	0.0471504i
$554$	−19.6316	+	19.6316i	−0.834068	+	0.834068i
$555$	7.04370	+	9.79538i	0.298989	+	0.415791i
$556$	−11.0293	+	6.36774i	−0.467745	+	0.270053i
$557$	28.2933	+	7.58116i	1.19882	+	0.321224i	0.802368	−	0.596829i	$-0.203573\pi$
$557$	28.2933	+	7.58116i	1.19882	+	0.321224i	0.396457	+	0.918053i	$0.370240\pi$
$558$	−31.4577	+	6.36507i	−1.33171	+	0.269455i
$559$	9.22788	−	4.51225i	0.390298	−	0.190848i
$560$	−3.42452	+	0.608230i	−0.144712	+	0.0257024i
$561$	−6.31095	+	2.38714i	−0.266449	+	0.100785i
$562$	8.56757	−	14.8395i	0.361401	−	0.625965i
$563$	2.59433	+	4.49352i	0.109338	+	0.189379i	0.915502	−	0.402313i	$-0.131794\pi$
$563$	2.59433	+	4.49352i	0.109338	+	0.189379i	−0.806164	+	0.591692i	$0.798460\pi$
$564$	−11.2771	+	13.7874i	−0.474853	+	0.580556i
$565$	−1.17185	−	4.37340i	−0.0493001	−	0.183990i
$566$	0.287449	−	0.287449i	0.0120824	−	0.0120824i
$567$	−17.6813	−	15.9490i	−0.742545	−	0.669797i
$568$	0.0680381			0.00285482
$569$	1.75248	−	3.03538i	0.0734677	−	0.127250i	−0.826951	−	0.562274i	$-0.809927\pi$
$569$	1.75248	−	3.03538i	0.0734677	−	0.127250i	0.900419	+	0.435024i	$0.143260\pi$
$570$	4.99464	−	6.10645i	0.209202	−	0.255771i
$571$	−10.5172	+	6.07211i	−0.440132	+	0.254110i	−0.703653	−	0.710543i	$-0.748449\pi$
$571$	−10.5172	+	6.07211i	−0.440132	+	0.254110i	0.263522	+	0.964653i	$0.415116\pi$
$572$	2.17832	+	2.50078i	0.0910803	+	0.104563i
$573$	−10.0495	+	22.2772i	−0.419824	+	0.930645i
$574$	0.161275	−	1.87019i	0.00673151	−	0.0780604i
$575$			23.6447i			0.986052i
$576$	0.594956	+	2.94041i	0.0247898	+	0.122517i
$577$	−15.9093	−	4.26290i	−0.662315	−	0.177467i	−0.0880243	−	0.996118i	$-0.528055\pi$
$577$	−15.9093	−	4.26290i	−0.662315	−	0.177467i	−0.574290	+	0.818652i	$0.694722\pi$
$578$	−0.242335	+	0.904407i	−0.0100798	+	0.0376184i
$579$	4.59409	+	0.750719i	0.190924	+	0.0311988i
$580$	−4.48554	−	4.48554i	−0.186252	−	0.186252i
$581$	−7.37378	+	20.3380i	−0.305916	+	0.843763i
$582$	5.62105	+	2.53572i	0.233000	+	0.105109i
$583$	−6.31191	+	1.69127i	−0.261413	+	0.0700453i
$584$	0.382187	+	0.661968i	0.0158150	+	0.0273924i
$585$	11.2806	+	8.65706i	0.466396	+	0.357926i
$586$	−9.83100	+	17.0278i	−0.406115	+	0.703412i
$587$	15.8723	+	15.8723i	0.655121	+	0.655121i	0.954222	−	0.299101i	$-0.0966866\pi$
$587$	15.8723	+	15.8723i	0.655121	+	0.655121i	−0.299101	+	0.954222i	$0.596687\pi$
$588$	12.0927	+	0.874891i	0.498697	+	0.0360799i
$589$			37.0665i			1.52730i
$590$	13.8162	−	3.70205i	0.568805	−	0.152411i
$591$	23.5504	−	28.7928i	0.968735	−	1.18438i
$592$	−1.37141	+	5.11817i	−0.0563646	+	0.210355i
$593$	2.32926	+	8.69293i	0.0956514	+	0.356976i	0.997117	−	0.0758740i	$-0.0241747\pi$
$593$	2.32926	+	8.69293i	0.0956514	+	0.356976i	−0.901466	+	0.432850i	$0.857508\pi$
$594$	−1.41000	−	4.56684i	−0.0578531	−	0.187380i
$595$	5.02081	−	13.8482i	0.205833	−	0.567719i
$596$	−9.21053	+	9.21053i	−0.377278	+	0.377278i
$597$	2.29736	+	3.19484i	0.0940247	+	0.130756i
$598$	−25.5727	+	4.99756i	−1.04575	+	0.204365i
$599$	22.4584	−	12.9663i	0.917624	−	0.529791i	0.0347478	−	0.999396i	$-0.488937\pi$
$599$	22.4584	−	12.9663i	0.917624	−	0.529791i	0.882876	+	0.469606i	$0.155604\pi$
$600$	5.59278	+	0.913916i	0.228324	+	0.0373105i
$601$	46.0452			1.87822			0.939111	−	0.343614i	$-0.111651\pi$
$601$	46.0452			1.87822			0.939111	+	0.343614i	$0.111651\pi$
$602$	5.76810	−	4.85226i	0.235090	−	0.197763i
$603$	−17.6672	−	1.09956i	−0.719463	−	0.0447775i
$604$	3.06874	+	11.4527i	0.124865	+	0.466004i
$605$	−12.8935	−	3.45481i	−0.524197	−	0.140458i
$606$	19.4323	−	23.7580i	0.789385	−	0.965104i
$607$	14.2460	−	24.6748i	0.578228	−	1.00152i	−0.417455	−	0.908698i	$-0.637078\pi$
$607$	14.2460	−	24.6748i	0.578228	−	1.00152i	0.995683	−	0.0928221i	$-0.0295888\pi$
$608$	3.46468			0.140511
$609$	11.3196	+	18.9959i	0.458695	+	0.769753i
$610$			10.2117i			0.413459i
$611$	−27.9591	+	24.3539i	−1.13110	+	0.985254i
$612$	−12.0445	−	4.04438i	−0.486870	−	0.163484i
$613$	−7.14044	−	1.91328i	−0.288400	−	0.0772765i	0.111719	−	0.993740i	$-0.464364\pi$
$613$	−7.14044	−	1.91328i	−0.288400	−	0.0772765i	−0.400119	+	0.916463i	$0.631031\pi$
$614$	−22.1074	−	12.7637i	−0.892181	−	0.515101i
$615$	0.664296	−	1.47258i	0.0267870	−	0.0593800i
$616$	1.99525	+	1.39339i	0.0803908	+	0.0561413i
$617$	14.9269	+	14.9269i	0.600935	+	0.600935i	0.940561	−	0.339626i	$-0.110301\pi$
$617$	14.9269	+	14.9269i	0.600935	+	0.600935i	−0.339626	+	0.940561i	$0.610301\pi$
$618$	3.12251	−	19.1085i	0.125606	−	0.768655i
$619$	−2.18594	+	8.15804i	−0.0878604	+	0.327899i	−0.995840	−	0.0911139i	$-0.970957\pi$
$619$	−2.18594	+	8.15804i	−0.0878604	+	0.327899i	0.907980	+	0.419013i	$0.137624\pi$
$620$	12.1799	−	7.03206i	0.489156	−	0.282414i
$621$	36.6121	+	8.34630i	1.46919	+	0.334926i
$622$	−1.24259	−	1.24259i	−0.0498232	−	0.0498232i
$623$	24.2119	−	20.3676i	0.970029	−	0.816010i
$624$	0.193656	+	6.24199i	0.00775242	+	0.249880i
$625$	1.03196	−	1.78741i	0.0412784	−	0.0714962i
$626$	2.31310	−	8.63260i	0.0924500	−	0.345028i
$627$	−5.49239	+	0.550085i	−0.219345	+	0.0219683i
$628$	−1.86740	−	1.07814i	−0.0745172	−	0.0430225i
$629$	−15.8680	−	15.8680i	−0.632699	−	0.632699i
$630$	9.56963	+	4.15902i	0.381263	+	0.165699i
$631$	1.00215	+	1.00215i	0.0398951	+	0.0398951i	0.726773	−	0.686878i	$-0.241019\pi$
$631$	1.00215	+	1.00215i	0.0398951	+	0.0398951i	−0.686878	+	0.726773i	$0.741019\pi$
$632$	−1.26247	−	4.71161i	−0.0502185	−	0.187418i
$633$	1.79604	+	17.9328i	0.0713862	+	0.712765i
$634$	−1.38612	+	0.800277i	−0.0550499	+	0.0317831i
$635$	−4.47350	−	16.6953i	−0.177525	−	0.662534i
$636$	−11.2163	−	5.05979i	−0.444755	−	0.200634i
$637$	24.5104	+	6.02018i	0.971136	+	0.238528i
$638$			4.43855i			0.175724i
$639$	−0.170087	−	0.112840i	−0.00672855	−	0.00446390i
$640$	−0.657301	−	1.13848i	−0.0259821	−	0.0450023i
$641$	−0.698922	−	1.21057i	−0.0276058	−	0.0478146i	0.851892	−	0.523717i	$-0.175455\pi$
$641$	−0.698922	−	1.21057i	−0.0276058	−	0.0478146i	−0.879498	+	0.475902i	$0.842122\pi$
$642$	3.64320	−	22.2949i	0.143786	−	0.879908i
$643$	−30.2113	+	30.2113i	−1.19142	+	1.19142i	−0.214746	+	0.976670i	$0.568892\pi$
$643$	−30.2113	+	30.2113i	−1.19142	+	1.19142i	−0.976670	+	0.214746i	$0.931108\pi$
$644$	−17.3187	+	8.10212i	−0.682454	+	0.319268i
$645$	6.06738	−	2.29501i	0.238903	−	0.0903660i
$646$	−7.33668	+	12.7075i	−0.288658	+	0.499970i
$647$	14.8509	+	25.7224i	0.583847	+	1.01125i	0.995018	+	0.0996948i	$0.0317867\pi$
$647$	14.8509	+	25.7224i	0.583847	+	1.01125i	−0.411171	+	0.911558i	$0.634880\pi$
$648$	3.38932	−	8.33742i	0.133145	−	0.327525i
$649$	−8.66737	−	5.00411i	−0.340224	−	0.196428i
$650$	11.1579	+	3.82940i	0.437648	+	0.150202i
$651$	−47.1760	+	13.3412i	−1.84898	+	0.522881i
$652$	−7.63734	+	7.63734i	−0.299101	+	0.299101i
$653$	11.2686	+	6.50590i	0.440973	+	0.254596i	0.704010	−	0.710190i	$-0.251391\pi$
$653$	11.2686	+	6.50590i	0.440973	+	0.254596i	−0.263037	+	0.964786i	$0.584724\pi$
$654$	−2.13297	−	21.2969i	−0.0834058	−	0.832775i
$655$	13.9092	+	3.72695i	0.543477	+	0.145624i
$656$	0.685315	−	0.183630i	0.0267570	−	0.00716953i
$657$	0.142442	−	2.28870i	0.00555721	−	0.0892905i
$658$	−15.5783	+	22.3071i	−0.607304	+	0.869622i
$659$		−	9.45586i		−	0.368348i	−0.982894	−	0.184174i	$-0.941039\pi$
$659$		−	9.45586i		−	0.368348i	0.982894	−	0.184174i	$-0.0589610\pi$
$660$	1.22274	+	1.70042i	0.0475952	+	0.0661887i
$661$	−6.94162	+	25.9065i	−0.269998	+	1.00764i	0.689122	+	0.724645i	$0.257996\pi$
$661$	−6.94162	+	25.9065i	−0.269998	+	1.00764i	−0.959120	+	0.283000i	$0.908670\pi$
$662$	−3.57845	−	6.19806i	−0.139081	−	0.240895i
$663$	−23.3040	−	12.5075i	−0.905053	−	0.485753i
$664$	−8.17669			−0.317317
$665$	6.89961	−	9.87981i	0.267555	−	0.383123i
$666$	11.9168	−	10.5204i	0.461766	−	0.407656i
$667$	−30.2002	−	17.4361i	−1.16936	−	0.675129i
$668$	−1.67901	+	6.26615i	−0.0649628	+	0.242445i
$669$	23.4030	+	19.1419i	0.904811	+	0.740070i
$670$	7.49244	−	2.00759i	0.289458	−	0.0775601i
$671$	5.05235	−	5.05235i	0.195044	−	0.195044i
$672$	1.24702	+	4.40964i	0.0481050	+	0.170106i
$673$			34.7456i			1.33935i	0.742656	+	0.669673i	$0.233566\pi$
$673$			34.7456i			1.33935i	−0.742656	+	0.669673i	$0.766434\pi$
$674$	−1.99350	−	7.43985i	−0.0767868	−	0.286572i
$675$	−12.4656	−	11.5602i	−0.479800	−	0.444954i
$676$	−1.78333	+	12.8771i	−0.0685895	+	0.495273i
$677$	−11.3247	−	6.53833i	−0.435244	−	0.251288i	0.266334	−	0.963881i	$-0.414188\pi$
$677$	−11.3247	−	6.53833i	−0.435244	−	0.251288i	−0.701578	+	0.712592i	$0.747521\pi$
$678$	−5.57961	+	2.11051i	−0.214284	+	0.0810537i
$679$	8.85546	+	3.21065i	0.339841	+	0.123213i
$680$	5.56751			0.213504
$681$	20.8520	+	3.40743i	0.799051	+	0.130573i
$682$	−9.50533	−	2.54695i	−0.363978	−	0.0975276i
$683$	−36.0735	−	9.66587i	−1.38031	−	0.369854i	−0.509079	−	0.860720i	$-0.670014\pi$
$683$	−36.0735	−	9.66587i	−1.38031	−	0.369854i	−0.871235	+	0.490865i	$0.836681\pi$
$684$	−8.66129	−	5.74613i	−0.331173	−	0.219709i
$685$	−14.2453			−0.544283
$686$	18.5201	−	0.0691534i	0.707102	−	0.00264029i
$687$	15.6353	+	41.3355i	0.596525	+	1.57705i
$688$	2.46726	+	1.42447i	0.0940633	+	0.0543075i
$689$	−21.2497	−	14.3020i	−0.809548	−	0.544862i
$690$	−16.3731	+	1.63983i	−0.623314	+	0.0624274i
$691$	−3.44719	−	12.8651i	−0.131137	−	0.489411i	0.868847	−	0.495081i	$-0.164862\pi$
$691$	−3.44719	−	12.8651i	−0.131137	−	0.489411i	−0.999984	+	0.00567024i	$0.998195\pi$
$692$		−	16.8942i		−	0.642220i
$693$	−2.67697	−	6.79241i	−0.101689	−	0.258022i
$694$	−12.5543	+	12.5543i	−0.476556	+	0.476556i
$695$	−16.1716	+	4.33317i	−0.613425	+	0.164367i
$696$	−5.29154	+	6.46945i	−0.200575	+	0.245224i
$697$	−0.777695	+	2.90240i	−0.0294573	+	0.109936i
$698$	−12.5674	−	7.25582i	−0.475685	−	0.274637i
$699$	5.72271	+	2.58158i	0.216453	+	0.0976442i
$700$	8.62442	+	0.743723i	0.325972	+	0.0281101i
$701$	16.2274			0.612899			0.306450	−	0.951887i	$-0.400859\pi$
$701$	16.2274			0.612899			0.306450	+	0.951887i	$0.400859\pi$
$702$	9.86816	−	15.9254i	0.372450	−	0.601067i
$703$	−9.17917	−	15.8988i	−0.346199	−	0.599635i
$704$	−0.238068	+	0.888483i	−0.00897253	+	0.0334860i
$705$	−19.0109	+	13.6704i	−0.715991	+	0.514858i
$706$		−	14.9293i		−	0.561872i
$707$	26.8439	−	38.4388i	1.00957	−	1.44564i
$708$	−6.66742	−	17.6268i	−0.250577	−	0.662457i
$709$	−20.7567	+	5.56174i	−0.779533	+	0.208875i	−0.626579	−	0.779358i	$-0.715545\pi$
$709$	−20.7567	+	5.56174i	−0.779533	+	0.208875i	−0.152954	+	0.988233i	$0.548879\pi$
$710$	0.0863954	+	0.0231496i	0.00324236	+	0.000868788i
$711$	−4.65812	+	13.8723i	−0.174693	+	0.520251i
$712$	10.3564	+	5.97929i	0.388124	+	0.224083i
$713$	54.6698	−	54.6698i	2.04740	−	2.04740i
$714$	−18.8140	−	4.76395i	−0.704097	−	0.178286i
$715$	1.91518	+	3.91668i	0.0716235	+	0.146475i
$716$	−14.1838	−	8.18902i	−0.530074	−	0.306038i
$717$	−20.8130	+	25.4460i	−0.777276	+	0.950299i
$718$	4.48587	+	7.76975i	0.167411	+	0.289965i
$719$	5.65805	−	9.80002i	0.211010	−	0.365479i	−0.741021	−	0.671482i	$-0.765658\pi$
$719$	5.65805	−	9.80002i	0.211010	−	0.365479i	0.952031	+	0.306002i	$0.0989916\pi$
$720$	−0.244978	+	3.93619i	−0.00912980	+	0.146693i
$721$	2.54103	−	29.4665i	0.0946329	−	1.09739i
$722$	4.94692	−	4.94692i	0.184105	−	0.184105i
$723$	11.6359	+	1.90141i	0.432742	+	0.0707144i
$724$	−1.82989	−	3.16946i	−0.0680072	−	0.117792i
$725$	7.89396	+	13.6727i	0.293174	+	0.507793i
$726$	−2.83629	+	17.3569i	−0.105265	+	0.644175i
$727$		−	53.2858i		−	1.97626i	−0.153620	−	0.988130i	$-0.549093\pi$
$727$		−	53.2858i		−	1.97626i	0.153620	−	0.988130i	$-0.450907\pi$
$728$	1.01849	+	9.48487i	0.0377479	+	0.351532i
$729$	−22.3004	+	15.2214i	−0.825941	+	0.563756i
$730$	0.260074	+	0.970609i	0.00962577	+	0.0359239i
$731$	−10.4491	+	6.03282i	−0.386476	+	0.223132i
$732$	13.3874	−	1.34080i	0.494812	−	0.0495574i
$733$	4.31821	+	16.1158i	0.159497	+	0.595250i	0.998678	+	0.0513987i	$0.0163679\pi$
$733$	4.31821	+	16.1158i	0.159497	+	0.595250i	−0.839181	+	0.543852i	$0.816965\pi$
$734$	14.7099	+	14.7099i	0.542954	+	0.542954i
$735$	15.0578	+	5.22543i	0.555415	+	0.192743i
$736$	−5.11010	−	5.11010i	−0.188361	−	0.188361i
$737$	−4.70025	−	2.71369i	−0.173136	−	0.0999601i
$738$	−2.01775	−	0.677534i	−0.0742746	−	0.0249404i
$739$	1.39745	−	5.21534i	0.0514059	−	0.191849i	−0.935448	−	0.353464i	$-0.885004\pi$
$739$	1.39745	−	5.21534i	0.0514059	−	0.191849i	0.986854	+	0.161615i	$0.0516702\pi$
$740$	−3.48285	+	6.03248i	−0.128032	+	0.221758i
$741$	−15.7667	−	14.8178i	−0.579204	−	0.544346i
$742$	−17.6703	−	6.40655i	−0.648696	−	0.235192i
$743$	−32.5181	−	32.5181i	−1.19297	−	1.19297i	−0.976228	−	0.216745i	$-0.930456\pi$
$743$	−32.5181	−	32.5181i	−1.19297	−	1.19297i	−0.216745	−	0.976228i	$-0.569544\pi$
$744$	−10.8182	−	15.0444i	−0.396614	−	0.551554i
$745$	−14.8294	+	8.56178i	−0.543309	+	0.313679i
$746$	−8.12321	+	30.3162i	−0.297412	+	1.10996i
$747$	20.4408	+	13.5609i	0.747888	+	0.496169i
$748$	−2.75459	−	2.75459i	−0.100718	−	0.100718i
$749$	2.96475	−	34.3801i	0.108330	−	1.25622i
$750$	17.1685	+	7.74491i	0.626906	+	0.282804i
$751$	−27.8494	−	16.0789i	−1.01624	−	0.586726i	−0.103226	−	0.994658i	$-0.532917\pi$
$751$	−27.8494	−	16.0789i	−1.01624	−	0.586726i	−0.913012	+	0.407932i	$0.866250\pi$
$752$	−9.93335	−	2.66163i	−0.362232	−	0.0970598i
$753$	−4.82030	−	48.1289i	−0.175661	−	1.75391i
$754$	−13.1192	+	11.4275i	−0.477772	+	0.416166i
$755$			15.5868i			0.567264i
$756$	4.19592	−	13.0918i	0.152604	−	0.476143i
$757$	6.28135			0.228300			0.114150	−	0.993464i	$-0.463586\pi$
$757$	6.28135			0.228300			0.114150	+	0.993464i	$0.463586\pi$
$758$	2.99050	−	5.17970i	0.108620	−	0.188135i
$759$	8.91212	+	7.28947i	0.323489	+	0.264591i
$760$	4.39948	+	1.17884i	0.159586	+	0.0427609i
$761$	7.95550	+	29.6903i	0.288387	+	1.07627i	0.946329	+	0.323205i	$0.104760\pi$
$761$	7.95550	+	29.6903i	0.288387	+	1.07627i	−0.657942	+	0.753069i	$0.728573\pi$
$762$	−21.3000	+	8.05682i	−0.771618	+	0.291868i
$763$	−5.71738	−	32.1905i	−0.206983	−	1.16538i
$764$	−14.1099			−0.510478
$765$	−13.9181	−	9.23365i	−0.503211	−	0.333843i
$766$	9.56110	−	5.52011i	0.345457	−	0.199450i
$767$	−7.52429	−	38.5021i	−0.271686	−	1.39023i
$768$	−1.40623	+	1.01120i	−0.0507429	+	0.0364884i
$769$	4.35626	−	4.35626i	0.157091	−	0.157091i	−0.624185	−	0.781276i	$-0.714569\pi$
$769$	4.35626	−	4.35626i	0.157091	−	0.157091i	0.781276	+	0.624185i	$0.214569\pi$
$770$	2.05949	+	2.44821i	0.0742188	+	0.0882273i
$771$	−49.0349	−	22.1202i	−1.76595	−	0.796639i
$772$	0.695596	+	2.59600i	0.0250350	+	0.0934321i
$773$	3.29267	−	12.2884i	0.118429	−	0.441984i	−0.881091	−	0.472946i	$-0.843190\pi$
$773$	3.29267	−	12.2884i	0.118429	−	0.441984i	0.999521	+	0.0309622i	$0.00985716\pi$
$774$	−3.80538	−	7.65293i	−0.136782	−	0.275079i
$775$	−33.8105	+	9.05950i	−1.21451	+	0.325427i
$776$			3.56024i			0.127805i
$777$	16.9312	−	17.4051i	0.607405	−	0.624404i
$778$	−25.1154	−	25.1154i	−0.900430	−	0.900430i
$779$	−1.22908	+	2.12882i	−0.0440363	+	0.0762731i
$780$	−1.87790	+	7.99203i	−0.0672395	+	0.286160i
$781$	−0.0312916	−	0.0541986i	−0.00111970	−	0.00193938i
$782$	29.5634	−	7.92149i	1.05719	−	0.283272i
$783$	23.9577	−	7.39691i	0.856179	−	0.264344i
$784$	2.41051	+	6.57187i	0.0860896	+	0.234710i
$785$	−2.00440	−	2.00440i	−0.0715403	−	0.0715403i
$786$	3.05971	−	18.7241i	0.109136	−	0.667868i
$787$	−3.47797	+	12.9800i	−0.123976	+	0.462685i	−0.999801	−	0.0199435i	$-0.993651\pi$
$787$	−3.47797	+	12.9800i	−0.123976	+	0.462685i	0.875825	+	0.482629i	$0.160318\pi$
$788$	20.7442	+	5.55838i	0.738980	+	0.198009i
$789$	2.37272	+	3.29964i	0.0844709	+	0.117470i
$790$		−	6.41239i		−	0.228143i
$791$	−8.25379	+	3.86132i	−0.293471	+	0.137293i
$792$	2.06868	−	1.82627i	0.0735074	−	0.0648937i
$793$	27.9412	+	1.92558i	0.992223	+	0.0683792i
$794$	20.3777	−	11.7651i	0.723177	−	0.417526i
$795$	−12.5210	−	10.2412i	−0.444073	−	0.363219i
$796$	−1.13596	+	1.96754i	−0.0402631	+	0.0697376i
$797$	47.9895			1.69988			0.849938	−	0.526882i	$-0.176639\pi$
$797$	47.9895			1.69988			0.849938	+	0.526882i	$0.176639\pi$
$798$	−13.8582	−	7.74808i	−0.490577	−	0.274279i
$799$	30.7967	−	30.7967i	1.08951	−	1.08951i
$800$	0.846810	+	3.16034i	0.0299392	+	0.111735i
$801$	−15.9733	−	32.1236i	−0.564389	−	1.13503i
$802$	15.5391	+	26.9146i	0.548706	+	0.950387i
$803$	0.351545	−	0.608895i	0.0124058	−	0.0214874i
$804$	−3.61569	−	9.55891i	−0.127516	−	0.337117i
$805$	−24.7482	+	4.39554i	−0.872259	+	0.154922i
$806$	−16.9444	−	34.6527i	−0.596843	−	1.22059i
$807$	5.86050	+	8.14995i	0.206299	+	0.286892i
$808$	17.1168	+	4.58643i	0.602167	+	0.161350i
$809$	14.0434	−	8.10794i	0.493738	−	0.285060i	−0.232386	−	0.972624i	$-0.574653\pi$
$809$	14.0434	−	8.10794i	0.493738	−	0.285060i	0.726124	+	0.687564i	$0.241320\pi$
$810$	7.14054	−	9.43372i	0.250893	−	0.331467i
$811$	−10.0208	+	10.0208i	−0.351877	+	0.351877i	−0.860808	−	0.508930i	$-0.830041\pi$
$811$	−10.0208	+	10.0208i	−0.351877	+	0.351877i	0.508930	+	0.860808i	$0.330041\pi$
$812$	−7.30975	+	10.4671i	−0.256522	+	0.367324i
$813$	−6.78497	−	17.9376i	−0.237959	−	0.629099i
$814$	4.70782	−	1.26146i	0.165009	−	0.0442140i
$815$	−12.2965	+	7.09940i	−0.430728	+	0.248681i
$816$	−0.731018	−	7.29894i	−0.0255907	−	0.255514i
$817$	−9.53433	+	2.55472i	−0.333564	+	0.0893782i
$818$	−8.82762			−0.308650
$819$	13.1844	−	25.4002i	0.460701	−	0.887555i
$820$	0.932697			0.0325712
$821$	−31.1669	+	8.35113i	−1.08773	+	0.291457i	−0.757759	−	0.652534i	$-0.773706\pi$
$821$	−31.1669	+	8.35113i	−1.08773	+	0.291457i	−0.329971	+	0.943991i	$0.607039\pi$
$822$	1.87041	+	18.6754i	0.0652381	+	0.651378i
$823$	7.47304	−	4.31456i	0.260494	−	0.150396i	−0.364066	−	0.931373i	$-0.618612\pi$
$823$	7.47304	−	4.31456i	0.260494	−	0.150396i	0.624560	+	0.780977i	$0.285278\pi$
$824$	10.7977	−	2.89324i	0.376156	−	0.100791i
$825$	−1.84417	−	4.87549i	−0.0642058	−	0.169743i
$826$	−12.1985	−	26.0750i	−0.424440	−	0.907264i
$827$	21.1242	−	21.1242i	0.734560	−	0.734560i	−0.236960	−	0.971519i	$-0.576151\pi$
$827$	21.1242	−	21.1242i	0.734560	−	0.734560i	0.971519	+	0.236960i	$0.0761509\pi$
$828$	4.29961	+	21.2497i	0.149422	+	0.738477i
$829$	−23.6956	+	13.6807i	−0.822982	+	0.475149i	−0.851444	−	0.524446i	$-0.824272\pi$
$829$	−23.6956	+	13.6807i	−0.822982	+	0.475149i	0.0284617	+	0.999595i	$0.490939\pi$
$830$	−10.3828	−	2.78207i	−0.360393	−	0.0965670i
$831$	28.0742	+	39.0416i	0.973883	+	1.35434i
$832$	−3.23906	+	1.58383i	−0.112294	+	0.0549095i
$833$	−29.2082	−	5.07526i	−1.01201	−	0.175847i
$834$	7.80409	+	20.6319i	0.270234	+	0.714423i
$835$	−4.26404	+	7.38553i	−0.147563	+	0.255587i
$836$	−1.59345	−	2.75993i	−0.0551106	−	0.0954543i
$837$	2.09326	+	55.5510i	0.0723536	+	1.92012i
$838$	4.82929	+	18.0231i	0.166825	+	0.622599i
$839$	22.2010	−	22.2010i	0.766463	−	0.766463i	−0.211019	−	0.977482i	$-0.567678\pi$
$839$	22.2010	−	22.2010i	0.766463	−	0.766463i	0.977482	+	0.211019i	$0.0676781\pi$
$840$	0.0831279	+	6.02369i	0.00286818	+	0.207837i
$841$	5.71529			0.197079
$842$	−16.8718	+	29.2228i	−0.581440	+	1.00708i
$843$	−22.9731	−	18.7903i	−0.791235	−	0.647173i
$844$	−9.01126	+	5.20265i	−0.310180	+	0.179083i
$845$	−6.64584	+	15.7447i	−0.228624	+	0.541634i
$846$	20.4179	+	23.1281i	0.701983	+	0.795161i
$847$	−2.30811	+	26.7654i	−0.0793075	+	0.919671i
$848$		−	7.10414i		−	0.243957i
$849$	−0.411066	−	0.571652i	−0.0141077	−	0.0196190i
$850$	−13.3844	−	3.58635i	−0.459082	−	0.123011i
$851$	−9.91085	+	36.9878i	−0.339740	+	1.26793i
$852$	0.0190050	−	0.116303i	0.000651102	−	0.00398447i
$853$	24.0479	+	24.0479i	0.823385	+	0.823385i	0.986592	−	0.163206i	$-0.0521837\pi$
$853$	24.0479	+	24.0479i	0.823385	+	0.823385i	−0.163206	+	0.986592i	$0.552184\pi$
$854$	20.2352	−	3.59399i	0.692435	−	0.122984i
$855$	−9.04309	−	10.2434i	−0.309267	−	0.350318i
$856$	12.5983	−	3.37569i	0.430599	−	0.115379i
$857$	−1.40504	−	2.43360i	−0.0479952	−	0.0831302i	0.841030	−	0.540989i	$-0.181950\pi$
$857$	−1.40504	−	2.43360i	−0.0479952	−	0.0831302i	−0.889025	+	0.457859i	$0.848617\pi$
$858$	4.88326	−	3.02504i	0.166712	−	0.103273i
$859$	4.49403	−	7.78389i	0.153334	−	0.265583i	−0.779117	−	0.626879i	$-0.784332\pi$
$859$	4.49403	−	7.78389i	0.153334	−	0.265583i	0.932451	+	0.361296i	$0.117666\pi$
$860$	2.64828	+	2.64828i	0.0903054	+	0.0903054i
$861$	−3.15182	−	0.798081i	−0.107414	−	0.0271985i
$862$			9.62893i			0.327963i
$863$	−37.4257	+	10.0282i	−1.27399	+	0.341363i	−0.831557	−	0.555440i	$-0.812550\pi$
$863$	−37.4257	+	10.0282i	−1.27399	+	0.341363i	−0.442429	+	0.896803i	$0.645883\pi$
$864$	5.19247	−	0.195661i	0.176651	−	0.00665653i
$865$	5.74814	−	21.4524i	0.195443	−	0.729402i
$866$	−5.81424	−	21.6990i	−0.197576	−	0.737364i
$867$	1.47828	+	0.666870i	0.0502051	+	0.0226481i
$868$	−18.2213	−	21.6604i	−0.618470	−	0.735203i
$869$	−3.17261	+	3.17261i	−0.107623	+	0.107623i
$870$	−8.92043	+	6.41454i	−0.302431	+	0.217473i
$871$	−4.08036	−	20.8794i	−0.138258	−	0.707472i
$872$	10.7017	−	6.17865i	0.362406	−	0.209235i
$873$	5.90462	−	8.90019i	0.199841	−	0.301226i
$874$	25.0384			0.846937
$875$	27.0475	+	9.80637i	0.914371	+	0.331516i
$876$	1.23831	−	0.468396i	0.0418386	−	0.0158256i
$877$	−3.34265	−	12.4749i	−0.112873	−	0.421248i	0.886246	−	0.463215i	$-0.153304\pi$
$877$	−3.34265	−	12.4749i	−0.112873	−	0.421248i	−0.999119	+	0.0419669i	$0.986638\pi$
$878$	−16.1674	−	4.33205i	−0.545624	−	0.146200i
$879$	26.3609	+	21.5613i	0.889130	+	0.727244i
$880$	−0.604602	+	1.04720i	−0.0203811	+	0.0353012i
$881$	12.5016			0.421190			0.210595	−	0.977573i	$-0.432460\pi$
$881$	12.5016			0.421190			0.210595	+	0.977573i	$0.432460\pi$
$882$	4.87338	−	20.4267i	0.164095	−	0.687803i
$883$		−	50.4343i		−	1.69725i	−0.528996	−	0.848624i	$-0.677431\pi$
$883$		−	50.4343i		−	1.69725i	0.528996	−	0.848624i	$-0.322569\pi$
$884$	1.04984	−	15.2338i	0.0353101	−	0.512369i
$885$	−2.46892	−	24.6513i	−0.0829919	−	0.828643i
$886$	4.37577	+	1.17248i	0.147007	+	0.0393904i
$887$	−29.3630	−	16.9527i	−0.985912	−	0.569216i	−0.0818621	−	0.996644i	$-0.526087\pi$
$887$	−29.3630	−	16.9527i	−0.985912	−	0.569216i	−0.904050	+	0.427427i	$0.859420\pi$
$888$	8.36581	+	3.77391i	0.280738	+	0.126644i
$889$	−31.5086	+	14.7405i	−1.05676	+	0.494380i
$890$	11.1163	+	11.1163i	0.372618	+	0.372618i
$891$	−8.20031	+	1.13458i	−0.274721	+	0.0380098i
$892$	−4.51789	+	16.8610i	−0.151270	+	0.564547i
$893$	30.8564	−	17.8150i	1.03257	−	0.596155i
$894$	13.1715	+	18.3171i	0.440521	+	0.612614i
$895$	−15.2244	−	15.2244i	−0.508897	−	0.508897i
$896$	−2.02464	+	1.70318i	−0.0676386	+	0.0568992i
$897$	1.39950	+	45.1094i	0.0467280	+	1.50616i
$898$	−10.4264	+	18.0590i	−0.347933	+	0.602638i
$899$	13.3613	−	49.8652i	0.445626	−	1.66310i
$900$	3.12446	−	9.30490i	0.104149	−	0.310163i
$901$	26.0561	+	15.0435i	0.868054	+	0.501171i
$902$	−0.461463	−	0.461463i	−0.0153650	−	0.0153650i
$903$	−6.68314	−	11.2152i	−0.222401	−	0.373220i
$904$	−2.43538	−	2.43538i	−0.0809994	−	0.0809994i
$905$	−1.24522	−	4.64721i	−0.0413924	−	0.154479i
$906$	20.4342	−	2.04656i	0.678880	−	0.0679926i
$907$	18.1363	−	10.4710i	0.602207	−	0.347684i	−0.167702	−	0.985838i	$-0.553635\pi$
$907$	18.1363	−	10.4710i	0.602207	−	0.347684i	0.769909	+	0.638153i	$0.220301\pi$
$908$	3.15723	+	11.7829i	0.104776	+	0.391030i
$909$	−35.1834	−	39.8535i	−1.16696	−	1.32186i
$910$	−1.93388	+	12.3905i	−0.0641074	+	0.410741i
$911$		−	55.2824i		−	1.83159i	−0.401648	−	0.915794i	$-0.631562\pi$
$911$		−	55.2824i		−	1.83159i	0.401648	−	0.915794i	$-0.368438\pi$
$912$	0.967787	−	5.92245i	0.0320466	−	0.196112i
$913$	3.76056	+	6.51348i	0.124456	+	0.215565i
$914$	6.90033	+	11.9517i	0.228243	+	0.395328i
$915$	17.4556	+	2.85242i	0.577065	+	0.0942982i
$916$	−18.0420	+	18.0420i	−0.596125	+	0.596125i
$917$	2.48992	−	28.8738i	0.0822244	−	0.953496i
$918$	−10.2778	+	19.4589i	−0.339216	+	0.642239i
$919$	25.4360	−	44.0564i	0.839055	−	1.45329i	−0.0516312	−	0.998666i	$-0.516442\pi$
$919$	25.4360	−	44.0564i	0.839055	−	1.45329i	0.890686	−	0.454619i	$-0.150225\pi$
$920$	−4.75016	−	8.22752i	−0.156608	−	0.271253i
$921$	−27.9932	+	34.2246i	−0.922408	+	1.12774i
$922$	15.4236	+	8.90482i	0.507949	+	0.293265i
$923$	0.0796332	−	0.232030i	0.00262116	−	0.00763736i
$924$	2.93916	−	3.02142i	0.0966913	−	0.0993974i
$925$	12.2587	−	12.2587i	0.403064	−	0.403064i
$926$	10.4526	+	6.03478i	0.343492	+	0.198315i
$927$	−31.7914	−	10.6751i	−1.04417	−	0.350617i
$928$	−4.66100	−	1.24891i	−0.153005	−	0.0409975i
$929$	23.1429	−	6.20112i	0.759294	−	0.203452i	0.141657	−	0.989916i	$-0.454757\pi$
$929$	23.1429	−	6.20112i	0.759294	−	0.203452i	0.617637	+	0.786464i	$0.288090\pi$
$930$	−8.61826	−	22.7843i	−0.282604	−	0.747127i
$931$	−22.0059	−	10.1949i	−0.721214	−	0.334125i
$932$			3.62463i			0.118729i
$933$	−2.47114	+	1.77696i	−0.0809016	+	0.0581751i
$934$	−3.40742	+	12.7166i	−0.111494	+	0.416101i
$935$	−2.56057	−	4.43503i	−0.0837395	−	0.145041i
$936$	10.7240	+	1.41254i	0.350526	+	0.0461704i
$937$	−23.7691			−0.776501			−0.388251	−	0.921554i	$-0.626921\pi$
$937$	−23.7691			−0.776501			−0.388251	+	0.921554i	$0.626921\pi$
$938$	−6.61515	−	14.1403i	−0.215992	−	0.461696i
$939$	−14.1103	−	6.36530i	−0.460471	−	0.207724i
$940$	−11.7078	−	6.75953i	−0.381868	−	0.220471i
$941$	−1.04830	+	3.91230i	−0.0341735	+	0.127537i	−0.980905	−	0.194486i	$-0.937696\pi$
$941$	−1.04830	+	3.91230i	−0.0341735	+	0.127537i	0.946732	+	0.322023i	$0.104363\pi$
$942$	−2.36457	+	2.89093i	−0.0770419	+	0.0941916i
$943$	4.95261	−	1.32705i	0.161279	−	0.0432146i
$944$	7.69372	−	7.69372i	0.250409	−	0.250409i
$945$	9.78241	−	15.1964i	0.318222	−	0.494339i
$946$		−	2.62053i		−	0.0852008i
$947$	−8.91351	−	33.2657i	−0.289650	−	1.08099i	−0.945374	−	0.325988i	$-0.894303\pi$
$947$	−8.91351	−	33.2657i	−0.289650	−	1.08099i	0.655724	−	0.755001i	$-0.272364\pi$
$948$	−8.40658	+	0.841952i	−0.273033	+	0.0273453i
$949$	2.70483	−	0.528591i	0.0878024	−	0.0171588i
$950$	−9.81710	−	5.66790i	−0.318509	−	0.183891i
$951$	0.980792	+	2.59295i	0.0318044	+	0.0840820i
$952$	−1.95948	−	11.0324i	−0.0635070	−	0.357563i
$953$	14.8582			0.481304			0.240652	−	0.970611i	$-0.422639\pi$
$953$	14.8582			0.481304			0.240652	+	0.970611i	$0.422639\pi$
$954$	−11.7821	+	17.7595i	−0.381461	+	0.574986i
$955$	−17.9169	−	4.80081i	−0.579776	−	0.155351i
$956$	−18.3329	−	4.91229i	−0.592929	−	0.158875i
$957$	7.58715	+	1.23982i	0.245258	+	0.0400776i
$958$	−3.68951			−0.119203
$959$	5.01360	+	28.2280i	0.161898	+	0.911531i
$960$	−2.12970	+	0.805566i	−0.0687356	+	0.0259995i
$961$	72.2746	+	41.7278i	2.33144	+	1.34606i
$962$	15.8493	+	10.6673i	0.511003	+	0.343928i
$963$	−37.0927	−	12.4552i	−1.19530	−	0.401364i
$964$	1.76180	+	6.57512i	0.0567437	+	0.211770i
$965$			3.53309i			0.113734i
$966$	9.01196	+	31.8674i	0.289955	+	1.02532i
$967$	29.8428	−	29.8428i	0.959678	−	0.959678i	−0.0395396	−	0.999218i	$-0.512589\pi$
$967$	29.8428	−	29.8428i	0.959678	−	0.959678i	0.999218	+	0.0395396i	$0.0125891\pi$
$968$	−9.80794	+	2.62803i	−0.315239	+	0.0844680i
$969$	19.6726	+	16.0907i	0.631974	+	0.516909i
$970$	−1.21135	+	4.52083i	−0.0388942	+	0.145155i
$971$	34.4822	+	19.9083i	1.10659	+	0.638888i	0.937943	−	0.346789i	$-0.112728\pi$
$971$	34.4822	+	19.9083i	1.10659	+	0.638888i	0.168643	+	0.985677i	$0.446061\pi$
$972$	−13.3051	−	8.12252i	−0.426760	−	0.260530i
$973$	14.2781	+	30.5202i	0.457735	+	0.978434i
$974$	36.9433			1.18374
$975$	9.66263	−	18.0034i	0.309452	−	0.576569i
$976$	3.88394	+	6.72719i	0.124322	+	0.215332i
$977$	−10.7257	+	40.0290i	−0.343147	+	1.28064i	0.551615	+	0.834099i	$0.314012\pi$
$977$	−10.7257	+	40.0290i	−0.343147	+	1.28064i	−0.894762	+	0.446543i	$0.852655\pi$
$978$	10.9218	+	15.1884i	0.349240	+	0.485673i
$979$		−	10.9998i		−	0.351555i
$980$	0.824843	+	9.16517i	0.0263487	+	0.292771i
$981$	−37.0003	−	2.30280i	−1.18133	−	0.0735228i
$982$	−7.65055	+	2.04996i	−0.244139	+	0.0654168i
$983$	−49.2350	−	13.1925i	−1.57035	−	0.420774i	−0.634429	−	0.772981i	$-0.718765\pi$
$983$	−49.2350	−	13.1925i	−1.57035	−	0.420774i	−0.935922	+	0.352207i	$0.885431\pi$
$984$	−0.122464	−	1.22276i	−0.00390400	−	0.0389800i
$985$	24.4499	+	14.1162i	0.779038	+	0.449778i
$986$	14.4506	−	14.4506i	0.460202	−	0.460202i
$987$	33.7798	+	32.8602i	1.07522	+	1.04595i
$988$	4.05513	−	11.8156i	0.129011	−	0.375904i
$989$	17.8303	+	10.2943i	0.566970	+	0.327340i
$990$	3.24821	−	1.61516i	0.103235	−	0.0513330i
$991$	−24.0653	−	41.6823i	−0.764459	−	1.32408i	−0.940532	−	0.339704i	$-0.889673\pi$
$991$	−24.0653	−	41.6823i	−0.764459	−	1.32408i	0.176074	−	0.984377i	$-0.443660\pi$
$992$	5.34919	−	9.26508i	0.169837	−	0.294166i
$993$	−11.5944	+	4.38563i	−0.367937	+	0.139174i
$994$	0.0154659	−	0.179346i	0.000490547	−	0.00568852i
$995$	−2.11190	+	2.11190i	−0.0669516	+	0.0669516i
$996$	−2.28399	+	13.9771i	−0.0723710	+	0.442880i
$997$	−0.590212	−	1.02228i	−0.0186922	−	0.0323759i	0.856528	−	0.516101i	$-0.172617\pi$
$997$	−0.590212	−	1.02228i	−0.0186922	−	0.0323759i	−0.875220	+	0.483725i	$0.839284\pi$
$998$	−1.34124	−	2.32310i	−0.0424563	−	0.0735364i
$999$	−14.6546	−	23.3089i	−0.463650	−	0.737462i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bv.a.317.27	yes	144
3.2	odd	2	inner	546.2.bv.a.317.3	✓	144
7.4	even	3	inner	546.2.bv.a.473.3	yes	144
13.8	odd	4	inner	546.2.bv.a.359.27	yes	144
21.11	odd	6	inner	546.2.bv.a.473.27	yes	144
39.8	even	4	inner	546.2.bv.a.359.3	yes	144
91.60	odd	12	inner	546.2.bv.a.515.3	yes	144
273.242	even	12	inner	546.2.bv.a.515.27	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bv.a.317.3	✓	144	3.2	odd	2	inner
546.2.bv.a.317.27	yes	144	1.1	even	1	trivial
546.2.bv.a.359.3	yes	144	39.8	even	4	inner
546.2.bv.a.359.27	yes	144	13.8	odd	4	inner
546.2.bv.a.473.3	yes	144	7.4	even	3	inner
546.2.bv.a.473.27	yes	144	21.11	odd	6	inner
546.2.bv.a.515.3	yes	144	91.60	odd	12	inner
546.2.bv.a.515.27	yes	144	273.242	even	12	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(-0.172608 - 1.72343i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.26981 - 0.340244i) q^{5} +(-0.612783 - 1.62003i) q^{6} +(-1.12113 - 2.39647i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.94041 + 0.594956i) q^{9} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{2} +(-0.172608 - 1.72343i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.26981 - 0.340244i) q^{5} +(-0.612783 - 1.62003i) q^{6} +(-1.12113 - 2.39647i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.94041 + 0.594956i) q^{9} +(1.13848 - 0.657301i) q^{10} +(-0.888483 - 0.238068i) q^{11} +(-1.01120 - 1.40623i) q^{12} +(-1.58383 - 3.23906i) q^{13} +(-1.70318 - 2.02464i) q^{14} +(-0.805566 - 2.12970i) q^{15} +(0.500000 - 0.866025i) q^{16} +(2.11756 + 3.66773i) q^{17} +(-2.68623 + 1.33572i) q^{18} +(0.896725 + 3.34662i) q^{19} +(0.929564 - 0.929564i) q^{20} +(-3.93663 + 2.34583i) q^{21} -0.919825 q^{22} +(3.61338 - 6.25856i) q^{23} +(-1.34070 - 1.09660i) q^{24} +(-2.83348 + 1.63591i) q^{25} +(-2.36819 - 2.71876i) q^{26} +(1.53290 + 4.96490i) q^{27} +(-2.16916 - 1.51484i) q^{28} -4.82542i q^{29} +(-1.32932 - 1.84863i) q^{30} +(10.3339 + 2.76895i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-0.256934 + 1.57233i) q^{33} +(2.99469 + 2.99469i) q^{34} +(-2.23900 - 2.66160i) q^{35} +(-2.24899 + 1.98545i) q^{36} +(-5.11817 + 1.37141i) q^{37} +(1.73234 + 3.00050i) q^{38} +(-5.30890 + 3.28871i) q^{39} +(0.657301 - 1.13848i) q^{40} +(0.501685 + 0.501685i) q^{41} +(-3.19535 + 3.28478i) q^{42} +2.84894i q^{43} +(-0.888483 + 0.238068i) q^{44} +(-3.53133 + 1.75594i) q^{45} +(1.87042 - 6.98052i) q^{46} +(-2.66163 - 9.93335i) q^{47} +(-1.57884 - 0.712231i) q^{48} +(-4.48615 + 5.37350i) q^{49} +(-2.31353 + 2.31353i) q^{50} +(5.95556 - 4.28255i) q^{51} +(-2.99117 - 2.01319i) q^{52} +(6.15237 - 3.55207i) q^{53} +(2.76568 + 4.39898i) q^{54} -1.20920 q^{55} +(-2.48732 - 0.901805i) q^{56} +(5.61288 - 2.12310i) q^{57} +(-1.24891 - 4.66100i) q^{58} +(10.5098 + 2.81610i) q^{59} +(-1.76249 - 1.44159i) q^{60} +(-3.88394 + 6.72719i) q^{61} +10.6984 q^{62} +(4.72237 + 6.37959i) q^{63} -1.00000i q^{64} +(-3.11323 - 3.57409i) q^{65} +(0.158769 + 1.58525i) q^{66} +(5.69940 + 1.52715i) q^{67} +(3.66773 + 2.11756i) q^{68} +(-11.4099 - 5.14713i) q^{69} +(-2.85158 - 1.99141i) q^{70} +(0.0481102 + 0.0481102i) q^{71} +(-1.65849 + 2.49988i) q^{72} +(-0.197835 + 0.738329i) q^{73} +(-4.58882 + 2.64936i) q^{74} +(3.30846 + 4.60093i) q^{75} +(2.44990 + 2.44990i) q^{76} +(0.425578 + 2.39613i) q^{77} +(-4.27682 + 4.55069i) q^{78} +(2.43891 - 4.22432i) q^{79} +(0.340244 - 1.26981i) q^{80} +(8.29205 - 3.49883i) q^{81} +(0.614436 + 0.354745i) q^{82} +(-5.78179 - 5.78179i) q^{83} +(-2.23631 + 3.99987i) q^{84} +(3.93682 + 3.93682i) q^{85} +(0.737361 + 2.75187i) q^{86} +(-8.31627 + 0.832908i) q^{87} +(-0.796592 + 0.459913i) q^{88} +(3.09511 + 11.5511i) q^{89} +(-2.95653 + 2.61008i) q^{90} +(-5.98663 + 7.42700i) q^{91} -7.22677i q^{92} +(2.98837 - 18.2876i) q^{93} +(-5.14188 - 8.90600i) q^{94} +(2.27734 + 3.94446i) q^{95} +(-1.70938 - 0.279329i) q^{96} +(-2.51747 + 2.51747i) q^{97} +(-2.94253 + 6.35150i) q^{98} +(2.75415 + 0.171411i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 16 q^{7}+O(q^{10}) \) 144 * q - 16 * q^7	\( 144 q - 16 q^{7} + 72 q^{16} + 16 q^{18} + 8 q^{19} + 8 q^{21} + 24 q^{27} - 8 q^{28} - 8 q^{31} + 12 q^{33} - 8 q^{37} + 16 q^{39} - 40 q^{45} + 8 q^{46} + 8 q^{52} - 12 q^{54} - 32 q^{55} + 16 q^{57} + 8 q^{58} - 32 q^{61} - 40 q^{63} - 32 q^{66} - 8 q^{67} + 16 q^{72} + 80 q^{73} - 16 q^{76} + 16 q^{78} - 112 q^{79} - 48 q^{81} + 16 q^{84} - 80 q^{85} + 96 q^{87} - 32 q^{91} + 36 q^{93} - 64 q^{94} - 144 q^{97} - 32 q^{99}+O(q^{100}) \) 144 * q - 16 * q^7 + 72 * q^16 + 16 * q^18 + 8 * q^19 + 8 * q^21 + 24 * q^27 - 8 * q^28 - 8 * q^31 + 12 * q^33 - 8 * q^37 + 16 * q^39 - 40 * q^45 + 8 * q^46 + 8 * q^52 - 12 * q^54 - 32 * q^55 + 16 * q^57 + 8 * q^58 - 32 * q^61 - 40 * q^63 - 32 * q^66 - 8 * q^67 + 16 * q^72 + 80 * q^73 - 16 * q^76 + 16 * q^78 - 112 * q^79 - 48 * q^81 + 16 * q^84 - 80 * q^85 + 96 * q^87 - 32 * q^91 + 36 * q^93 - 64 * q^94 - 144 * q^97 - 32 * q^99

Introduction

L-functions

Modular forms

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Database

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