LMFDB - Embedded newform 216.2.q.b.49.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(25,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, 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("216.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.q (of order $9$, degree $6$, 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:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			49.5
Character	$\chi$	$=$	216.49
Dual form			216.2.q.b.97.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.51177 + 0.845305i) q^{3} +(-3.37598 + 1.22876i) q^{5} +(0.462643 + 2.62378i) q^{7} +(1.57092 + 2.55582i) q^{9} +O(q^{10})$	\(q+(1.51177 + 0.845305i) q^{3} +(-3.37598 + 1.22876i) q^{5} +(0.462643 + 2.62378i) q^{7} +(1.57092 + 2.55582i) q^{9} +(0.236557 + 0.0860998i) q^{11} +(4.63259 + 3.88721i) q^{13} +(-6.14239 - 0.996131i) q^{15} +(2.21778 - 3.84131i) q^{17} +(-3.90542 - 6.76438i) q^{19} +(-1.51848 + 4.35764i) q^{21} +(0.688536 - 3.90488i) q^{23} +(6.05716 - 5.08256i) q^{25} +(0.214425 + 5.19173i) q^{27} +(-3.97795 + 3.33789i) q^{29} +(-0.0109744 + 0.0622391i) q^{31} +(0.284840 + 0.330126i) q^{33} +(-4.78586 - 8.28934i) q^{35} +(1.23341 - 2.13633i) q^{37} +(3.71755 + 9.79253i) q^{39} +(6.28083 + 5.27024i) q^{41} +(2.30259 + 0.838074i) q^{43} +(-8.44386 - 6.69811i) q^{45} +(-0.795962 - 4.51412i) q^{47} +(-0.0923337 + 0.0336067i) q^{49} +(6.59987 - 3.93249i) q^{51} +0.892650 q^{53} -0.904407 q^{55} +(-0.186140 - 13.5275i) q^{57} +(-4.57083 + 1.66365i) q^{59} +(-0.928071 - 5.26335i) q^{61} +(-5.97913 + 5.30418i) q^{63} +(-20.4159 - 7.43080i) q^{65} +(-2.29185 - 1.92309i) q^{67} +(4.34173 - 5.32128i) q^{69} +(3.66273 - 6.34403i) q^{71} +(3.20833 + 5.55700i) q^{73} +(13.4534 - 2.56353i) q^{75} +(-0.116465 + 0.660507i) q^{77} +(8.99771 - 7.54997i) q^{79} +(-4.06443 + 8.02997i) q^{81} +(-0.891052 + 0.747682i) q^{83} +(-2.76715 + 15.6933i) q^{85} +(-8.83530 + 1.68356i) q^{87} +(4.40320 + 7.62657i) q^{89} +(-8.05593 + 13.9533i) q^{91} +(-0.0692018 + 0.0848146i) q^{93} +(21.4964 + 18.0376i) q^{95} +(-1.78895 - 0.651123i) q^{97} +(0.151556 + 0.739853i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{7} - 6 q^{9}+O(q^{10}) $ 30 * q + 3 * q^7 - 6 * q^9	$ 30 q + 3 q^{7} - 6 q^{9} - 3 q^{11} - 12 q^{13} + 15 q^{15} + 6 q^{17} - 9 q^{19} + 30 q^{21} - 12 q^{23} + 24 q^{25} - 15 q^{27} - 9 q^{29} + 27 q^{31} - 30 q^{33} - 18 q^{35} - 15 q^{37} - 21 q^{39} - 15 q^{41} - 30 q^{43} + 15 q^{45} - 18 q^{47} + 15 q^{49} - 6 q^{51} - 18 q^{53} + 54 q^{55} - 72 q^{57} - 12 q^{59} + 6 q^{61} - 54 q^{63} - 54 q^{65} - 45 q^{67} + 9 q^{69} - 36 q^{73} + 69 q^{75} + 12 q^{77} + 45 q^{79} - 30 q^{81} - 3 q^{83} + 57 q^{85} - 60 q^{87} + 36 q^{89} - 39 q^{91} + 30 q^{93} + 51 q^{95} - 84 q^{97} + 162 q^{99}+O(q^{100}) $ 30 * q + 3 * q^7 - 6 * q^9 - 3 * q^11 - 12 * q^13 + 15 * q^15 + 6 * q^17 - 9 * q^19 + 30 * q^21 - 12 * q^23 + 24 * q^25 - 15 * q^27 - 9 * q^29 + 27 * q^31 - 30 * q^33 - 18 * q^35 - 15 * q^37 - 21 * q^39 - 15 * q^41 - 30 * q^43 + 15 * q^45 - 18 * q^47 + 15 * q^49 - 6 * q^51 - 18 * q^53 + 54 * q^55 - 72 * q^57 - 12 * q^59 + 6 * q^61 - 54 * q^63 - 54 * q^65 - 45 * q^67 + 9 * q^69 - 36 * q^73 + 69 * q^75 + 12 * q^77 + 45 * q^79 - 30 * q^81 - 3 * q^83 + 57 * q^85 - 60 * q^87 + 36 * q^89 - 39 * q^91 + 30 * q^93 + 51 * q^95 - 84 * q^97 + 162 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{9}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.51177	+	0.845305i	0.872823	+	0.488037i
$3$	1.51177	+	0.845305i	0.872823	+	0.488037i
$4$		0			0
$5$	−3.37598	+	1.22876i	−1.50978	+	0.549516i	−0.958572	−	0.284850i	$-0.908056\pi$
$5$	−3.37598	+	1.22876i	−1.50978	+	0.549516i	−0.551211	+	0.834366i	$0.685834\pi$
$6$		0			0
$7$	0.462643	+	2.62378i	0.174863	+	0.991696i	0.938302	+	0.345816i	$0.112398\pi$
$7$	0.462643	+	2.62378i	0.174863	+	0.991696i	−0.763440	+	0.645879i	$0.776491\pi$
$8$		0			0
$9$	1.57092	+	2.55582i	0.523639	+	0.851940i
$10$		0			0
$11$	0.236557	+	0.0860998i	0.0713247	+	0.0259601i	0.377436	−	0.926036i	$-0.376806\pi$
$11$	0.236557	+	0.0860998i	0.0713247	+	0.0259601i	−0.306111	+	0.951996i	$0.599028\pi$
$12$		0			0
$13$	4.63259	+	3.88721i	1.28485	+	1.07812i	0.992556	+	0.121788i	$0.0388628\pi$
$13$	4.63259	+	3.88721i	1.28485	+	1.07812i	0.292293	+	0.956329i	$0.405582\pi$
$14$		0			0
$15$	−6.14239	−	0.996131i	−1.58596	−	0.257200i
$16$		0			0
$17$	2.21778	−	3.84131i	0.537891	−	0.931655i	−0.461126	−	0.887335i	$-0.652554\pi$
$17$	2.21778	−	3.84131i	0.537891	−	0.931655i	0.999017	−	0.0443205i	$-0.0141123\pi$
$18$		0			0
$19$	−3.90542	−	6.76438i	−0.895965	−	1.55186i	−0.832606	−	0.553866i	$-0.813152\pi$
$19$	−3.90542	−	6.76438i	−0.895965	−	1.55186i	−0.0633585	−	0.997991i	$-0.520181\pi$
$20$		0			0
$21$	−1.51848	+	4.35764i	−0.331360	+	0.950914i
$22$		0			0
$23$	0.688536	−	3.90488i	0.143570	−	0.814225i	−0.824935	−	0.565228i	$-0.808788\pi$
$23$	0.688536	−	3.90488i	0.143570	−	0.814225i	0.968504	−	0.248996i	$-0.0801007\pi$
$24$		0			0
$25$	6.05716	−	5.08256i	1.21143	−	1.01651i
$26$		0			0
$27$	0.214425	+	5.19173i	0.0412661	+	0.999148i
$28$		0			0
$29$	−3.97795	+	3.33789i	−0.738686	+	0.619831i	−0.932485	−	0.361210i	$-0.882364\pi$
$29$	−3.97795	+	3.33789i	−0.738686	+	0.619831i	0.193798	+	0.981041i	$0.437919\pi$
$30$		0			0
$31$	−0.0109744	+	0.0622391i	−0.00197106	+	0.0111785i	−0.985777	−	0.168056i	$-0.946251\pi$
$31$	−0.0109744	+	0.0622391i	−0.00197106	+	0.0111785i	0.983806	+	0.179235i	$0.0573621\pi$
$32$		0			0
$33$	0.284840	+	0.330126i	0.0495843	+	0.0574676i
$34$		0			0
$35$	−4.78586	−	8.28934i	−0.808957	−	1.40115i
$36$		0			0
$37$	1.23341	−	2.13633i	0.202771	−	0.351210i	−0.746649	−	0.665218i	$-0.768338\pi$
$37$	1.23341	−	2.13633i	0.202771	−	0.351210i	0.949420	+	0.314008i	$0.101672\pi$
$38$		0			0
$39$	3.71755	+	9.79253i	0.595285	+	1.56806i
$40$		0			0
$41$	6.28083	+	5.27024i	0.980901	+	0.823073i	0.984225	−	0.176921i	$-0.0566137\pi$
$41$	6.28083	+	5.27024i	0.980901	+	0.823073i	−0.00332439	+	0.999994i	$0.501058\pi$
$42$		0			0
$43$	2.30259	+	0.838074i	0.351142	+	0.127805i	0.511568	−	0.859243i	$-0.329065\pi$
$43$	2.30259	+	0.838074i	0.351142	+	0.127805i	−0.160427	+	0.987048i	$0.551287\pi$
$44$		0			0
$45$	−8.44386	−	6.69811i	−1.25874	−	0.998496i
$46$		0			0
$47$	−0.795962	−	4.51412i	−0.116103	−	0.658452i	−0.986198	−	0.165569i	$-0.947054\pi$
$47$	−0.795962	−	4.51412i	−0.116103	−	0.658452i	0.870095	−	0.492884i	$-0.164057\pi$
$48$		0			0
$49$	−0.0923337	+	0.0336067i	−0.0131905	+	0.00480096i
$50$		0			0
$51$	6.59987	−	3.93249i	0.924166	−	0.550659i
$52$		0			0
$53$	0.892650			0.122615			0.0613075	−	0.998119i	$-0.480473\pi$
$53$	0.892650			0.122615			0.0613075	+	0.998119i	$0.480473\pi$
$54$		0			0
$55$	−0.904407			−0.121950
$56$		0			0
$57$	−0.186140	−	13.5275i	−0.0246549	−	1.79176i
$58$		0			0
$59$	−4.57083	+	1.66365i	−0.595072	+	0.216588i	−0.621959	−	0.783050i	$-0.713663\pi$
$59$	−4.57083	+	1.66365i	−0.595072	+	0.216588i	0.0268869	+	0.999638i	$0.491441\pi$
$60$		0			0
$61$	−0.928071	−	5.26335i	−0.118827	−	0.673903i	−0.984784	−	0.173784i	$-0.944401\pi$
$61$	−0.928071	−	5.26335i	−0.118827	−	0.673903i	0.865956	−	0.500119i	$-0.166711\pi$
$62$		0			0
$63$	−5.97913	+	5.30418i	−0.753300	+	0.668263i
$64$		0			0
$65$	−20.4159	−	7.43080i	−2.53229	−	0.921677i
$66$		0			0
$67$	−2.29185	−	1.92309i	−0.279994	−	0.234943i	0.491965	−	0.870615i	$-0.336279\pi$
$67$	−2.29185	−	1.92309i	−0.279994	−	0.234943i	−0.771960	+	0.635672i	$0.780723\pi$
$68$		0			0
$69$	4.34173	−	5.32128i	0.522683	−	0.640606i
$70$		0			0
$71$	3.66273	−	6.34403i	0.434686	−	0.752898i	−0.562584	−	0.826740i	$-0.690193\pi$
$71$	3.66273	−	6.34403i	0.434686	−	0.752898i	0.997270	+	0.0738419i	$0.0235260\pi$
$72$		0			0
$73$	3.20833	+	5.55700i	0.375507	+	0.650397i	0.990403	−	0.138211i	$-0.0441353\pi$
$73$	3.20833	+	5.55700i	0.375507	+	0.650397i	−0.614896	+	0.788608i	$0.710802\pi$
$74$		0			0
$75$	13.4534	−	2.56353i	1.55346	−	0.296011i
$76$		0			0
$77$	−0.116465	+	0.660507i	−0.0132724	+	0.0752718i
$78$		0			0
$79$	8.99771	−	7.54997i	1.01232	−	0.849438i	0.0236780	−	0.999720i	$-0.492462\pi$
$79$	8.99771	−	7.54997i	1.01232	−	0.849438i	0.988643	+	0.150281i	$0.0480179\pi$
$80$		0			0
$81$	−4.06443	+	8.02997i	−0.451603	+	0.892219i
$82$		0			0
$83$	−0.891052	+	0.747682i	−0.0978057	+	0.0820687i	−0.690379	−	0.723448i	$-0.742556\pi$
$83$	−0.891052	+	0.747682i	−0.0978057	+	0.0820687i	0.592574	+	0.805516i	$0.298112\pi$
$84$		0			0
$85$	−2.76715	+	15.6933i	−0.300140	+	1.70218i
$86$		0			0
$87$	−8.83530	+	1.68356i	−0.947243	+	0.180497i
$88$		0			0
$89$	4.40320	+	7.62657i	0.466738	+	0.808415i	0.999278	−	0.0379904i	$-0.0120956\pi$
$89$	4.40320	+	7.62657i	0.466738	+	0.808415i	−0.532540	+	0.846405i	$0.678762\pi$
$90$		0			0
$91$	−8.05593	+	13.9533i	−0.844491	+	1.46270i
$92$		0			0
$93$	−0.0692018	+	0.0848146i	−0.00717590	+	0.00879487i
$94$		0			0
$95$	21.4964	+	18.0376i	2.20548	+	1.85062i
$96$		0			0
$97$	−1.78895	−	0.651123i	−0.181640	−	0.0661115i	0.249599	−	0.968349i	$-0.419701\pi$
$97$	−1.78895	−	0.651123i	−0.181640	−	0.0661115i	−0.431239	+	0.902238i	$0.641923\pi$
$98$		0			0
$99$	0.151556	+	0.739853i	0.0152320	+	0.0743580i
$100$		0			0
$101$	1.15504	+	6.55056i	0.114931	+	0.651805i	0.986784	+	0.162039i	$0.0518069\pi$
$101$	1.15504	+	6.55056i	0.114931	+	0.651805i	−0.871854	+	0.489767i	$0.837082\pi$
$102$		0			0
$103$	−3.22518	+	1.17387i	−0.317787	+	0.115665i	−0.495989	−	0.868329i	$-0.665194\pi$
$103$	−3.22518	+	1.17387i	−0.317787	+	0.115665i	0.178202	+	0.983994i	$0.442972\pi$
$104$		0			0
$105$	−0.228103	−	16.5771i	−0.0222606	−	1.61776i
$106$		0			0
$107$	4.00352			0.387034			0.193517	−	0.981097i	$-0.438010\pi$
$107$	4.00352			0.387034			0.193517	+	0.981097i	$0.438010\pi$
$108$		0			0
$109$	−11.0315			−1.05663			−0.528315	−	0.849048i	$-0.677176\pi$
$109$	−11.0315			−1.05663			−0.528315	+	0.849048i	$0.677176\pi$
$110$		0			0
$111$	3.67049	−	2.18704i	0.348387	−	0.207585i
$112$		0			0
$113$	16.2619	−	5.91884i	1.52979	−	0.556797i	0.566219	−	0.824255i	$-0.308406\pi$
$113$	16.2619	−	5.91884i	1.52979	−	0.556797i	0.963570	+	0.267458i	$0.0861835\pi$
$114$		0			0
$115$	2.47366	+	14.0288i	0.230670	+	1.30820i
$116$		0			0
$117$	−2.65758	+	17.9466i	−0.245693	+	1.65916i
$118$		0			0
$119$	11.1048	+	4.04182i	1.01798	+	0.370513i
$120$		0			0
$121$	−8.37794	−	7.02993i	−0.761631	−	0.639084i
$122$		0			0
$123$	5.04023	+	13.2766i	0.454462	+	1.19711i
$124$		0			0
$125$	−5.22200	+	9.04478i	−0.467070	+	0.808989i
$126$		0			0
$127$	−10.4998	−	18.1862i	−0.931705	−	1.61376i	−0.780407	−	0.625272i	$-0.784988\pi$
$127$	−10.4998	−	18.1862i	−0.931705	−	1.61376i	−0.151298	−	0.988488i	$-0.548345\pi$
$128$		0			0
$129$	2.77257	+	3.21337i	0.244111	+	0.282921i
$130$		0			0
$131$	−1.58392	+	8.98286i	−0.138388	+	0.784836i	0.834053	+	0.551685i	$0.186015\pi$
$131$	−1.58392	+	8.98286i	−0.138388	+	0.784836i	−0.972441	+	0.233151i	$0.925096\pi$
$132$		0			0
$133$	15.9414	−	13.3765i	1.38230	−	1.15989i
$134$		0			0
$135$	−7.10325	−	17.2637i	−0.611351	−	1.48582i
$136$		0			0
$137$	−5.22571	+	4.38489i	−0.446463	+	0.374627i	−0.838121	−	0.545484i	$-0.816346\pi$
$137$	−5.22571	+	4.38489i	−0.446463	+	0.374627i	0.391658	+	0.920111i	$0.371901\pi$
$138$		0			0
$139$	−2.01234	+	11.4126i	−0.170685	+	0.968002i	0.772323	+	0.635230i	$0.219095\pi$
$139$	−2.01234	+	11.4126i	−0.170685	+	0.968002i	−0.943008	+	0.332771i	$0.892016\pi$
$140$		0			0
$141$	2.61250	−	7.49716i	0.220012	−	0.631375i
$142$		0			0
$143$	0.761185	+	1.31841i	0.0636535	+	0.110251i
$144$		0			0
$145$	9.32800	−	16.1566i	0.774649	−	1.34173i
$146$		0			0
$147$	−0.167996	−	0.0272444i	−0.0138560	−	0.00224708i
$148$		0			0
$149$	−12.3407	−	10.3551i	−1.01099	−	0.848320i	−0.0225202	−	0.999746i	$-0.507169\pi$
$149$	−12.3407	−	10.3551i	−1.01099	−	0.848320i	−0.988469	+	0.151426i	$0.951613\pi$
$150$		0			0
$151$	−16.4189	−	5.97600i	−1.33615	−	0.486320i	−0.427555	−	0.903989i	$-0.640625\pi$
$151$	−16.4189	−	5.97600i	−1.33615	−	0.486320i	−0.908599	+	0.417669i	$0.862847\pi$
$152$		0			0
$153$	13.3017	−	0.366135i	1.07538	−	0.0296002i
$154$		0			0
$155$	−0.0394271	−	0.223602i	−0.00316686	−	0.0179602i
$156$		0			0
$157$	−18.1467	+	6.60486i	−1.44826	+	0.527125i	−0.942106	−	0.335316i	$-0.891157\pi$
$157$	−18.1467	+	6.60486i	−1.44826	+	0.527125i	−0.506158	+	0.862441i	$0.668935\pi$
$158$		0			0
$159$	1.34948	+	0.754562i	0.107021	+	0.0598406i
$160$		0			0
$161$	10.5641			0.832568
$162$		0			0
$163$	−17.4282			−1.36508			−0.682541	−	0.730847i	$-0.739125\pi$
$163$	−17.4282			−1.36508			−0.682541	+	0.730847i	$0.739125\pi$
$164$		0			0
$165$	−1.36726	−	0.764500i	−0.106441	−	0.0595162i
$166$		0			0
$167$	−17.9726	+	6.54151i	−1.39077	+	0.506197i	−0.925424	−	0.378934i	$-0.876291\pi$
$167$	−17.9726	+	6.54151i	−1.39077	+	0.506197i	−0.465342	+	0.885131i	$0.654069\pi$
$168$		0			0
$169$	4.09311	+	23.2132i	0.314854	+	1.78563i
$170$		0			0
$171$	11.1535	−	20.6078i	0.852926	−	1.57592i
$172$		0			0
$173$	17.1850	+	6.25484i	1.30655	+	0.475547i	0.899126	−	0.437690i	$-0.144203\pi$
$173$	17.1850	+	6.25484i	1.30655	+	0.475547i	0.407428	+	0.913237i	$0.366426\pi$
$174$		0			0
$175$	16.1378	+	13.5412i	1.21990	+	1.02362i
$176$		0			0
$177$	−8.31635	−	1.34869i	−0.625095	−	0.101374i
$178$		0			0
$179$	9.81549	−	17.0009i	0.733644	−	1.27071i	−0.221671	−	0.975121i	$-0.571151\pi$
$179$	9.81549	−	17.0009i	0.733644	−	1.27071i	0.955316	−	0.295588i	$-0.0955155\pi$
$180$		0			0
$181$	4.21157	+	7.29465i	0.313043	+	0.542207i	0.979020	−	0.203766i	$-0.0653182\pi$
$181$	4.21157	+	7.29465i	0.313043	+	0.542207i	−0.665976	+	0.745973i	$0.731985\pi$
$182$		0			0
$183$	3.04611	−	8.74150i	0.225175	−	0.646190i
$184$		0			0
$185$	−1.53894	+	8.72776i	−0.113145	+	0.641678i
$186$		0			0
$187$	0.855368	−	0.717739i	0.0625507	−	0.0524863i
$188$		0			0
$189$	−13.5227	+	2.96452i	−0.983635	+	0.215637i
$190$		0			0
$191$	−1.26952	+	1.06525i	−0.0918591	+	0.0770790i	−0.687561	−	0.726127i	$-0.741319\pi$
$191$	−1.26952	+	1.06525i	−0.0918591	+	0.0770790i	0.595702	+	0.803206i	$0.296874\pi$
$192$		0			0
$193$	0.487673	−	2.76573i	0.0351035	−	0.199082i	−0.962212	−	0.272300i	$-0.912216\pi$
$193$	0.487673	−	2.76573i	0.0351035	−	0.199082i	0.997316	+	0.0732181i	$0.0233269\pi$
$194$		0			0
$195$	−24.5830	−	28.4914i	−1.76042	−	2.04031i
$196$		0			0
$197$	−5.01766	−	8.69085i	−0.357494	−	0.619197i	0.630048	−	0.776556i	$-0.283035\pi$
$197$	−5.01766	−	8.69085i	−0.357494	−	0.619197i	−0.987541	+	0.157359i	$0.949702\pi$
$198$		0			0
$199$	3.88094	−	6.72199i	0.275113	−	0.476509i	−0.695051	−	0.718960i	$-0.744618\pi$
$199$	3.88094	−	6.72199i	0.275113	−	0.476509i	0.970164	+	0.242452i	$0.0779515\pi$
$200$		0			0
$201$	−1.83916	−	4.84460i	−0.129725	−	0.341712i
$202$		0			0
$203$	−10.5983	−	8.89300i	−0.743853	−	0.624167i
$204$		0			0
$205$	−27.6798	−	10.0746i	−1.93324	−	0.703641i
$206$		0			0
$207$	11.0618	−	4.37448i	0.768849	−	0.304047i
$208$		0			0
$209$	−0.341443	−	1.93642i	−0.0236181	−	0.133945i
$210$		0			0
$211$	21.8036	−	7.93585i	1.50102	−	0.546327i	0.544696	−	0.838634i	$-0.316645\pi$
$211$	21.8036	−	7.93585i	1.50102	−	0.546327i	0.956325	+	0.292307i	$0.0944229\pi$
$212$		0			0
$213$	10.8999	−	6.49462i	0.746846	−	0.445004i
$214$		0			0
$215$	−8.80328			−0.600378
$216$		0			0
$217$	−0.168379			−0.0114303
$218$		0			0
$219$	0.152916	+	11.1129i	0.0103331	+	0.750943i
$220$		0			0
$221$	25.2061	−	9.17425i	1.69554	−	0.617127i
$222$		0			0
$223$	1.39918	+	7.93516i	0.0936963	+	0.531378i	0.995139	+	0.0984796i	$0.0313979\pi$
$223$	1.39918	+	7.93516i	0.0936963	+	0.531378i	−0.901443	+	0.432898i	$0.857491\pi$
$224$		0			0
$225$	22.5054	+	7.49672i	1.50036	+	0.499781i
$226$		0			0
$227$	−14.2874	−	5.20020i	−0.948291	−	0.345150i	−0.178856	−	0.983875i	$-0.557240\pi$
$227$	−14.2874	−	5.20020i	−0.948291	−	0.345150i	−0.769435	+	0.638726i	$0.779462\pi$
$228$		0			0
$229$	6.53852	+	5.48647i	0.432077	+	0.362556i	0.832735	−	0.553672i	$-0.186774\pi$
$229$	6.53852	+	5.48647i	0.432077	+	0.362556i	−0.400657	+	0.916228i	$0.631218\pi$
$230$		0			0
$231$	−0.734399	+	0.900089i	−0.0483199	+	0.0592215i
$232$		0			0
$233$	1.94977	−	3.37710i	0.127734	−	0.221241i	−0.795064	−	0.606525i	$-0.792563\pi$
$233$	1.94977	−	3.37710i	0.127734	−	0.221241i	0.922798	+	0.385284i	$0.125896\pi$
$234$		0			0
$235$	8.23390	+	14.2615i	0.537120	+	0.930320i
$236$		0			0
$237$	19.9845	−	3.80804i	1.29813	−	0.247359i
$238$		0			0
$239$	−3.01159	+	17.0796i	−0.194804	+	1.10479i	0.717895	+	0.696152i	$0.245106\pi$
$239$	−3.01159	+	17.0796i	−0.194804	+	1.10479i	−0.912698	+	0.408634i	$0.866005\pi$
$240$		0			0
$241$	−9.98016	+	8.37435i	−0.642879	+	0.539439i	−0.904901	−	0.425623i	$-0.860055\pi$
$241$	−9.98016	+	8.37435i	−0.642879	+	0.539439i	0.262022	+	0.965062i	$0.415611\pi$
$242$		0			0
$243$	−12.9323	+	8.70381i	−0.829606	+	0.558350i
$244$		0			0
$245$	0.270422	−	0.226911i	0.0172766	−	0.0144968i
$246$		0			0
$247$	8.20234	−	46.5178i	0.521903	−	2.95986i
$248$		0			0
$249$	−1.97909	+	0.377114i	−0.125420	+	0.0238986i
$250$		0			0
$251$	−4.09321	−	7.08965i	−0.258361	−	0.447495i	0.707442	−	0.706772i	$-0.249849\pi$
$251$	−4.09321	−	7.08965i	−0.258361	−	0.447495i	−0.965803	+	0.259277i	$0.916516\pi$
$252$		0			0
$253$	0.499088	−	0.864445i	0.0313774	−	0.0543472i
$254$		0			0
$255$	−17.4489	+	21.3856i	−1.09269	+	1.33922i
$256$		0			0
$257$	−19.0825	−	16.0121i	−1.19033	−	0.998809i	−0.999853	−	0.0171180i	$-0.994551\pi$
$257$	−19.0825	−	16.0121i	−1.19033	−	0.998809i	−0.190481	−	0.981691i	$-0.561005\pi$
$258$		0			0
$259$	6.17589	+	2.24784i	0.383751	+	0.139674i
$260$		0			0
$261$	−14.7801	−	4.92336i	−0.914864	−	0.304748i
$262$		0			0
$263$	2.37029	+	13.4426i	0.146158	+	0.828905i	0.966430	+	0.256931i	$0.0827113\pi$
$263$	2.37029	+	13.4426i	0.146158	+	0.828905i	−0.820271	+	0.571975i	$0.806178\pi$
$264$		0			0
$265$	−3.01357	+	1.09685i	−0.185122	+	0.0673788i
$266$		0			0
$267$	0.209865	+	15.2517i	0.0128436	+	0.933388i
$268$		0			0
$269$	13.0929			0.798290			0.399145	−	0.916888i	$-0.369307\pi$
$269$	13.0929			0.798290			0.399145	+	0.916888i	$0.369307\pi$
$270$		0			0
$271$	1.34477			0.0816892			0.0408446	−	0.999166i	$-0.486995\pi$
$271$	1.34477			0.0816892			0.0408446	+	0.999166i	$0.486995\pi$
$272$		0			0
$273$	−23.9735	+	14.2845i	−1.45094	+	0.864537i
$274$		0			0
$275$	1.87047	−	0.680796i	0.112794	−	0.0410535i
$276$		0			0
$277$	−2.36027	−	13.3857i	−0.141815	−	0.804271i	−0.969870	−	0.243624i	$-0.921664\pi$
$277$	−2.36027	−	13.3857i	−0.141815	−	0.804271i	0.828055	−	0.560647i	$-0.189447\pi$
$278$		0			0
$279$	−0.176312	+	0.0697238i	−0.0105555	+	0.00417426i
$280$		0			0
$281$	−2.95187	−	1.07439i	−0.176094	−	0.0640929i	0.252469	−	0.967605i	$-0.418758\pi$
$281$	−2.95187	−	1.07439i	−0.176094	−	0.0640929i	−0.428562	+	0.903512i	$0.640980\pi$
$282$		0			0
$283$	−9.09314	−	7.63005i	−0.540531	−	0.453560i	0.331188	−	0.943565i	$-0.392550\pi$
$283$	−9.09314	−	7.63005i	−0.540531	−	0.453560i	−0.871720	+	0.490005i	$0.836995\pi$
$284$		0			0
$285$	17.2504	+	45.4398i	1.02182	+	2.69162i
$286$		0			0
$287$	−10.9222	+	18.9178i	−0.644715	+	1.11668i
$288$		0			0
$289$	−1.33712	−	2.31596i	−0.0786543	−	0.136233i
$290$		0			0
$291$	−2.15408	−	2.49656i	−0.126275	−	0.146351i
$292$		0			0
$293$	0.335061	−	1.90022i	0.0195745	−	0.111012i	−0.973455	−	0.228878i	$-0.926494\pi$
$293$	0.335061	−	1.90022i	0.0195745	−	0.111012i	0.993030	+	0.117866i	$0.0376053\pi$
$294$		0			0
$295$	13.3868	−	11.2329i	0.779410	−	0.654003i
$296$		0			0
$297$	−0.396283	+	1.24660i	−0.0229947	+	0.0723352i
$298$		0			0
$299$	18.3688	−	15.4132i	1.06229	−	0.891371i
$300$		0			0
$301$	−1.13364	+	6.42922i	−0.0653422	+	0.370574i
$302$		0			0
$303$	−3.79106	+	10.8793i	−0.217791	+	0.625001i
$304$		0			0
$305$	9.60052	+	16.6286i	0.549724	+	0.952150i
$306$		0			0
$307$	2.53757	−	4.39520i	0.144827	−	0.250847i	−0.784482	−	0.620152i	$-0.787071\pi$
$307$	2.53757	−	4.39520i	0.144827	−	0.250847i	0.929308	+	0.369305i	$0.120404\pi$
$308$		0			0
$309$	−5.86803	−	0.951638i	−0.333820	−	0.0541368i
$310$		0			0
$311$	−4.10504	−	3.44454i	−0.232775	−	0.195322i	0.518938	−	0.854812i	$-0.326328\pi$
$311$	−4.10504	−	3.44454i	−0.232775	−	0.195322i	−0.751713	+	0.659490i	$0.770772\pi$
$312$		0			0
$313$	−11.2849	−	4.10737i	−0.637861	−	0.232162i	0.00278809	−	0.999996i	$-0.499113\pi$
$313$	−11.2849	−	4.10737i	−0.637861	−	0.232162i	−0.640649	+	0.767834i	$0.721335\pi$
$314$		0			0
$315$	13.6679	−	25.2537i	0.770098	−	1.42288i
$316$		0			0
$317$	−2.58119	−	14.6386i	−0.144974	−	0.822188i	−0.967388	−	0.253299i	$-0.918484\pi$
$317$	−2.58119	−	14.6386i	−0.144974	−	0.822188i	0.822414	−	0.568889i	$-0.192627\pi$
$318$		0			0
$319$	−1.22840	+	0.447102i	−0.0687774	+	0.0250329i
$320$		0			0
$321$	6.05241	+	3.38419i	0.337813	+	0.188887i
$322$		0			0
$323$	−34.6455			−1.92773
$324$		0			0
$325$	47.8173			2.65243
$326$		0			0
$327$	−16.6772	−	9.32502i	−0.922251	−	0.515675i
$328$		0			0
$329$	11.4758	−	4.17686i	0.632682	−	0.230278i
$330$		0			0
$331$	5.51797	+	31.2940i	0.303295	+	1.72007i	0.631423	+	0.775438i	$0.282471\pi$
$331$	5.51797	+	31.2940i	0.303295	+	1.72007i	−0.328128	+	0.944633i	$0.606418\pi$
$332$		0			0
$333$	7.39766	−	0.203624i	0.405389	−	0.0111585i
$334$		0			0
$335$	10.1003	+	3.67619i	0.551836	+	0.200852i
$336$		0			0
$337$	−2.13804	−	1.79403i	−0.116466	−	0.0977269i	0.582694	−	0.812691i	$-0.301998\pi$
$337$	−2.13804	−	1.79403i	−0.116466	−	0.0977269i	−0.699161	+	0.714964i	$0.746443\pi$
$338$		0			0
$339$	29.5875	+	4.79830i	1.60697	+	0.260608i
$340$		0			0
$341$	−0.00795485	+	0.0137782i	−0.000430779	+	0.000746131i
$342$		0			0
$343$	9.19400	+	15.9245i	0.496429	+	0.859841i
$344$		0			0
$345$	−8.11903	+	23.2994i	−0.437114	+	1.25440i
$346$		0			0
$347$	3.63935	−	20.6398i	0.195371	−	1.10800i	−0.716519	−	0.697568i	$-0.754266\pi$
$347$	3.63935	−	20.6398i	0.195371	−	1.10800i	0.911890	−	0.410435i	$-0.134623\pi$
$348$		0			0
$349$	15.9090	−	13.3493i	0.851590	−	0.714569i	−0.108549	−	0.994091i	$-0.534620\pi$
$349$	15.9090	−	13.3493i	0.851590	−	0.714569i	0.960139	+	0.279522i	$0.0901760\pi$
$350$		0			0
$351$	−19.1880	+	24.8847i	−1.02418	+	1.32824i
$352$		0			0
$353$	−1.91579	+	1.60754i	−0.101967	+	0.0855608i	−0.692346	−	0.721566i	$-0.743423\pi$
$353$	−1.91579	+	1.60754i	−0.101967	+	0.0855608i	0.590379	+	0.807126i	$0.298978\pi$
$354$		0			0
$355$	−4.57003	+	25.9179i	−0.242552	+	1.37558i
$356$		0			0
$357$	13.3714	+	15.4973i	0.707688	+	0.820202i
$358$		0			0
$359$	5.38348	+	9.32447i	0.284129	+	0.492127i	0.972398	−	0.233330i	$-0.0749621\pi$
$359$	5.38348	+	9.32447i	0.284129	+	0.492127i	−0.688268	+	0.725456i	$0.741629\pi$
$360$		0			0
$361$	−21.0046	+	36.3810i	−1.10551	+	1.91479i
$362$		0			0
$363$	−6.72312	−	17.7096i	−0.352872	−	0.929512i
$364$		0			0
$365$	−17.6594	−	14.8180i	−0.924337	−	0.775611i
$366$		0			0
$367$	12.0282	+	4.37791i	0.627867	+	0.228525i	0.636303	−	0.771439i	$-0.280463\pi$
$367$	12.0282	+	4.37791i	0.627867	+	0.228525i	−0.00843548	+	0.999964i	$0.502685\pi$
$368$		0			0
$369$	−3.60312	+	24.3318i	−0.187571	+	1.26666i
$370$		0			0
$371$	0.412978	+	2.34212i	0.0214408	+	0.121597i
$372$		0			0
$373$	12.0864	−	4.39910i	0.625811	−	0.227777i	−0.00959576	−	0.999954i	$-0.503054\pi$
$373$	12.0864	−	4.39910i	0.625811	−	0.227777i	0.635407	+	0.772177i	$0.280832\pi$
$374$		0			0
$375$	−15.5401	+	9.25947i	−0.802487	+	0.478157i
$376$		0			0
$377$	−31.4033			−1.61735
$378$		0			0
$379$	36.6813			1.88419			0.942097	−	0.335341i	$-0.108852\pi$
$379$	36.6813			1.88419			0.942097	+	0.335341i	$0.108852\pi$
$380$		0			0
$381$	−0.500441	−	36.3689i	−0.0256383	−	1.86323i
$382$		0			0
$383$	−0.425403	+	0.154834i	−0.0217371	+	0.00791164i	−0.352866	−	0.935674i	$-0.614793\pi$
$383$	−0.425403	+	0.154834i	−0.0217371	+	0.00791164i	0.331129	+	0.943586i	$0.392571\pi$
$384$		0			0
$385$	−0.418418	−	2.37296i	−0.0213245	−	0.120937i
$386$		0			0
$387$	1.47521	+	7.20155i	0.0749893	+	0.366075i
$388$		0			0
$389$	−9.29213	−	3.38206i	−0.471130	−	0.171477i	0.0955344	−	0.995426i	$-0.469544\pi$
$389$	−9.29213	−	3.38206i	−0.471130	−	0.171477i	−0.566664	+	0.823949i	$0.691766\pi$
$390$		0			0
$391$	−13.4729	−	11.3051i	−0.681352	−	0.571722i
$392$		0			0
$393$	−9.98778	+	12.2411i	−0.503817	+	0.617484i
$394$		0			0
$395$	−21.0990	+	36.5445i	−1.06161	+	1.83875i
$396$		0			0
$397$	3.62086	+	6.27151i	0.181726	+	0.314758i	0.942468	−	0.334296i	$-0.108498\pi$
$397$	3.62086	+	6.27151i	0.181726	+	0.314758i	−0.760743	+	0.649054i	$0.775165\pi$
$398$		0			0
$399$	35.4070	−	6.74679i	1.77257	−	0.337762i
$400$		0			0
$401$	1.33496	−	7.57093i	0.0666647	−	0.378074i	−0.933162	−	0.359456i	$-0.882962\pi$
$401$	1.33496	−	7.57093i	0.0666647	−	0.378074i	0.999827	−	0.0186182i	$-0.00592668\pi$
$402$		0			0
$403$	−0.292776	+	0.245668i	−0.0145842	+	0.0122376i
$404$		0			0
$405$	3.85456	−	32.1032i	0.191535	−	1.59522i
$406$		0			0
$407$	0.475710	−	0.399168i	0.0235800	−	0.0197860i
$408$		0			0
$409$	5.75411	−	32.6332i	0.284522	−	1.61361i	−0.422465	−	0.906379i	$-0.638835\pi$
$409$	5.75411	−	32.6332i	0.284522	−	1.61361i	0.706987	−	0.707227i	$-0.250054\pi$
$410$		0			0
$411$	−11.6067	+	2.21164i	−0.572515	+	0.109092i
$412$		0			0
$413$	−6.47971	−	11.2232i	−0.318846	−	0.552257i
$414$		0			0
$415$	2.08945	−	3.61904i	0.102567	−	0.177652i
$416$		0			0
$417$	−12.6893	+	15.5522i	−0.621398	+	0.761593i
$418$		0			0
$419$	3.63317	+	3.04859i	0.177492	+	0.148933i	0.727206	−	0.686420i	$-0.240819\pi$
$419$	3.63317	+	3.04859i	0.177492	+	0.148933i	−0.549714	+	0.835353i	$0.685263\pi$
$420$		0			0
$421$	−17.1712	−	6.24982i	−0.836875	−	0.304597i	−0.112197	−	0.993686i	$-0.535789\pi$
$421$	−17.1712	−	6.24982i	−0.836875	−	0.304597i	−0.724677	+	0.689088i	$0.758011\pi$
$422$		0			0
$423$	10.2869	−	9.12565i	0.500166	−	0.443704i
$424$		0			0
$425$	−6.09024	−	34.5394i	−0.295420	−	1.67541i
$426$		0			0
$427$	13.3805	−	4.87011i	0.647528	−	0.235681i
$428$		0			0
$429$	0.0362796	+	2.63657i	0.00175160	+	0.127295i
$430$		0			0
$431$	35.0994			1.69068			0.845338	−	0.534231i	$-0.179399\pi$
$431$	35.0994			1.69068			0.845338	+	0.534231i	$0.179399\pi$
$432$		0			0
$433$	−21.7509			−1.04528			−0.522642	−	0.852552i	$-0.675053\pi$
$433$	−21.7509			−1.04528			−0.522642	+	0.852552i	$0.675053\pi$
$434$		0			0
$435$	27.7591	−	16.5401i	1.33095	−	0.793036i
$436$		0			0
$437$	−29.1032	+	10.5927i	−1.39219	+	0.506717i
$438$		0			0
$439$	2.85448	+	16.1885i	0.136237	+	0.772637i	0.973991	+	0.226589i	$0.0727573\pi$
$439$	2.85448	+	16.1885i	0.136237	+	0.772637i	−0.837754	+	0.546048i	$0.816132\pi$
$440$		0			0
$441$	−0.230941	−	0.183195i	−0.0109972	−	0.00872356i
$442$		0			0
$443$	6.62622	+	2.41175i	0.314821	+	0.114586i	0.494598	−	0.869122i	$-0.335315\pi$
$443$	6.62622	+	2.41175i	0.314821	+	0.114586i	−0.179777	+	0.983707i	$0.557538\pi$
$444$		0			0
$445$	−24.2363	−	20.3367i	−1.14891	−	0.964050i
$446$		0			0
$447$	−9.90314	−	26.0862i	−0.468402	−	1.23383i
$448$		0			0
$449$	−8.27383	+	14.3307i	−0.390466	+	0.676307i	−0.992511	−	0.122155i	$-0.961019\pi$
$449$	−8.27383	+	14.3307i	−0.390466	+	0.676307i	0.602045	+	0.798462i	$0.294353\pi$
$450$		0			0
$451$	1.03201	+	1.78749i	0.0485954	+	0.0841697i
$452$		0			0
$453$	−19.7702	−	22.9134i	−0.928883	−	1.07656i
$454$		0			0
$455$	10.0515	−	57.0047i	0.471220	−	2.67242i
$456$		0			0
$457$	12.2054	−	10.2415i	0.570944	−	0.479079i	−0.311015	−	0.950405i	$-0.600669\pi$
$457$	12.2054	−	10.2415i	0.570944	−	0.479079i	0.881959	+	0.471326i	$0.156224\pi$
$458$		0			0
$459$	20.4186	+	10.6904i	0.953058	+	0.498987i
$460$		0			0
$461$	27.1019	−	22.7412i	1.26226	−	1.05916i	0.266824	−	0.963745i	$-0.414026\pi$
$461$	27.1019	−	22.7412i	1.26226	−	1.05916i	0.995437	−	0.0954179i	$-0.0304188\pi$
$462$		0			0
$463$	1.20303	−	6.82270i	0.0559094	−	0.317078i	−0.944008	−	0.329922i	$-0.892977\pi$
$463$	1.20303	−	6.82270i	0.0559094	−	0.317078i	0.999918	+	0.0128443i	$0.00408858\pi$
$464$		0			0
$465$	0.129407	−	0.371364i	0.00600112	−	0.0172216i
$466$		0			0
$467$	5.31035	+	9.19780i	0.245734	+	0.425623i	0.962338	−	0.271857i	$-0.0876378\pi$
$467$	5.31035	+	9.19780i	0.245734	+	0.425623i	−0.716604	+	0.697480i	$0.754304\pi$
$468$		0			0
$469$	3.98546	−	6.90302i	0.184032	−	0.318752i
$470$		0			0
$471$	−33.0168	−	5.35445i	−1.52133	−	0.246720i
$472$		0			0
$473$	0.472536	+	0.396505i	0.0217272	+	0.0182313i
$474$		0			0
$475$	−58.0361	−	21.1234i	−2.66288	−	0.969209i
$476$		0			0
$477$	1.40228	+	2.28145i	0.0642060	+	0.104461i
$478$		0			0
$479$	−1.03896	−	5.89222i	−0.0474712	−	0.269222i	0.951829	−	0.306630i	$-0.0992013\pi$
$479$	−1.03896	−	5.89222i	−0.0474712	−	0.269222i	−0.999300	+	0.0374072i	$0.988090\pi$
$480$		0			0
$481$	14.0182	−	5.10222i	0.639177	−	0.232641i
$482$		0			0
$483$	15.9705	+	8.92989i	0.726684	+	0.406324i
$484$		0			0
$485$	6.83951			0.310566
$486$		0			0
$487$	2.45291			0.111152			0.0555760	−	0.998454i	$-0.482300\pi$
$487$	2.45291			0.111152			0.0555760	+	0.998454i	$0.482300\pi$
$488$		0			0
$489$	−26.3475	−	14.7322i	−1.19148	−	0.666211i
$490$		0			0
$491$	−34.3786	+	12.5128i	−1.55148	+	0.564694i	−0.968765	−	0.247980i	$-0.920233\pi$
$491$	−34.3786	+	12.5128i	−1.55148	+	0.564694i	−0.582718	+	0.812674i	$0.698011\pi$
$492$		0			0
$493$	3.99967	+	22.6833i	0.180136	+	1.02160i
$494$		0			0
$495$	−1.42075	−	2.31150i	−0.0638579	−	0.103894i
$496$		0			0
$497$	18.3399	+	6.67517i	0.822656	+	0.299422i
$498$		0			0
$499$	−15.2254	−	12.7756i	−0.681580	−	0.571914i	0.234887	−	0.972023i	$-0.424528\pi$
$499$	−15.2254	−	12.7756i	−0.681580	−	0.571914i	−0.916468	+	0.400109i	$0.868972\pi$
$500$		0			0
$501$	−32.7001	−	5.30309i	−1.46093	−	0.236925i
$502$		0			0
$503$	0.869530	−	1.50607i	0.0387704	−	0.0671523i	−0.845989	−	0.533200i	$-0.820989\pi$
$503$	0.869530	−	1.50607i	0.0387704	−	0.0671523i	0.884759	+	0.466048i	$0.154323\pi$
$504$		0			0
$505$	−11.9484	−	20.6953i	−0.531698	−	0.920928i
$506$		0			0
$507$	−13.4344	+	38.5530i	−0.596641	+	1.71220i
$508$		0			0
$509$	−7.72083	+	43.7870i	−0.342220	+	1.94083i	−0.00334494	+	0.999994i	$0.501065\pi$
$509$	−7.72083	+	43.7870i	−0.342220	+	1.94083i	−0.338875	+	0.940831i	$0.610046\pi$
$510$		0			0
$511$	−13.0960	+	10.9889i	−0.579334	+	0.486119i
$512$		0			0
$513$	34.2814	−	21.7263i	1.51356	−	0.959241i
$514$		0			0
$515$	9.44574	−	7.92592i	0.416229	−	0.349258i
$516$		0			0
$517$	0.200374	−	1.13638i	0.00881246	−	0.0499779i
$518$		0			0
$519$	20.6926	+	23.9825i	0.908306	+	1.05272i
$520$		0			0
$521$	16.5887	+	28.7324i	0.726763	+	1.25879i	0.958244	+	0.285951i	$0.0923094\pi$
$521$	16.5887	+	28.7324i	0.726763	+	1.25879i	−0.231482	+	0.972839i	$0.574357\pi$
$522$		0			0
$523$	16.5503	−	28.6660i	0.723695	−	1.25348i	−0.235814	−	0.971798i	$-0.575776\pi$
$523$	16.5503	−	28.6660i	0.723695	−	1.25348i	0.959509	−	0.281678i	$-0.0908910\pi$
$524$		0			0
$525$	12.9502	+	34.1127i	0.565195	+	1.48880i
$526$		0			0
$527$	0.214741	+	0.180189i	0.00935426	+	0.00784915i
$528$		0			0
$529$	6.83890	+	2.48915i	0.297343	+	0.108224i
$530$		0			0
$531$	−11.4324	−	9.06877i	−0.496123	−	0.393551i
$532$		0			0
$533$	8.61000	+	48.8297i	0.372941	+	2.11505i
$534$		0			0
$535$	−13.5158	+	4.91934i	−0.584338	+	0.212682i
$536$		0			0
$537$	29.2098	−	17.4045i	1.26049	−	0.751058i
$538$		0			0
$539$	−0.0247357			−0.00106544
$540$		0			0
$541$	20.7206			0.890850			0.445425	−	0.895319i	$-0.353053\pi$
$541$	20.7206			0.890850			0.445425	+	0.895319i	$0.353053\pi$
$542$		0			0
$543$	0.200732	+	14.5879i	0.00861422	+	0.626027i
$544$		0			0
$545$	37.2422	−	13.5551i	1.59528	−	0.580635i
$546$		0			0
$547$	−4.65308	−	26.3889i	−0.198951	−	1.12831i	−0.906678	−	0.421823i	$-0.861390\pi$
$547$	−4.65308	−	26.3889i	−0.198951	−	1.12831i	0.707727	−	0.706486i	$-0.249721\pi$
$548$		0			0
$549$	11.9943	−	10.6403i	0.511903	−	0.454116i
$550$		0			0
$551$	38.1144	+	13.8725i	1.62373	+	0.590988i
$552$		0			0
$553$	23.9722	+	20.1151i	1.01940	+	0.855379i
$554$		0			0
$555$	−9.70415	+	11.8935i	−0.411918	+	0.504852i
$556$		0			0
$557$	22.0756	−	38.2360i	0.935373	−	1.62011i	0.161404	−	0.986888i	$-0.448398\pi$
$557$	22.0756	−	38.2360i	0.935373	−	1.62011i	0.773968	−	0.633224i	$-0.218269\pi$
$558$		0			0
$559$	7.40919	+	12.8331i	0.313375	+	0.542782i
$560$		0			0
$561$	1.89983	−	0.362012i	0.0802110	−	0.0152842i
$562$		0			0
$563$	3.61017	−	20.4743i	0.152151	−	0.862889i	−0.809194	−	0.587541i	$-0.800096\pi$
$563$	3.61017	−	20.4743i	0.152151	−	0.862889i	0.961345	−	0.275348i	$-0.0887929\pi$
$564$		0			0
$565$	−47.6269	+	39.9637i	−2.00368	+	1.68129i
$566$		0			0
$567$	−22.9493	−	6.94916i	−0.963778	−	0.291837i
$568$		0			0
$569$	−25.8535	+	21.6937i	−1.08384	+	0.909447i	−0.996234	−	0.0867085i	$-0.972365\pi$
$569$	−25.8535	+	21.6937i	−1.08384	+	0.909447i	−0.0876029	+	0.996155i	$0.527921\pi$
$570$		0			0
$571$	−0.146083	+	0.828480i	−0.00611340	+	0.0346708i	−0.987712	−	0.156286i	$-0.950048\pi$
$571$	−0.146083	+	0.828480i	−0.00611340	+	0.0346708i	0.981598	+	0.190957i	$0.0611590\pi$
$572$		0			0
$573$	−2.81969	+	0.537290i	−0.117794	+	0.0224456i
$574$		0			0
$575$	−15.6762	−	27.1520i	−0.653744	−	1.13232i
$576$		0			0
$577$	−18.7907	+	32.5464i	−0.782267	+	1.35493i	0.148352	+	0.988935i	$0.452603\pi$
$577$	−18.7907	+	32.5464i	−0.782267	+	1.35493i	−0.930618	+	0.365991i	$0.880730\pi$
$578$		0			0
$579$	3.07514	−	3.76893i	0.127798	−	0.156631i
$580$		0			0
$581$	−2.37399	−	1.99202i	−0.0984898	−	0.0826427i
$582$		0			0
$583$	0.211163	+	0.0768569i	0.00874547	+	0.00318309i
$584$		0			0
$585$	−13.0800	−	63.8526i	−0.540792	−	2.63998i
$586$		0			0
$587$	4.78337	+	27.1278i	0.197431	+	1.11969i	0.908914	+	0.416983i	$0.136912\pi$
$587$	4.78337	+	27.1278i	0.197431	+	1.11969i	−0.711484	+	0.702703i	$0.751976\pi$
$588$		0			0
$589$	0.463869	−	0.168834i	0.0191134	−	0.00695670i
$590$		0			0
$591$	−0.239152	−	17.3801i	−0.00983739	−	0.714920i
$592$		0			0
$593$	−11.5294			−0.473454			−0.236727	−	0.971576i	$-0.576075\pi$
$593$	−11.5294			−0.473454			−0.236727	+	0.971576i	$0.576075\pi$
$594$		0			0
$595$	−42.4560			−1.74052
$596$		0			0
$597$	11.5492	−	6.88154i	0.472679	−	0.281643i
$598$		0			0
$599$	−26.7327	+	9.72989i	−1.09227	+	0.397553i	−0.824460	−	0.565920i	$-0.808521\pi$
$599$	−26.7327	+	9.72989i	−1.09227	+	0.397553i	−0.267807	+	0.963473i	$0.586299\pi$
$600$		0			0
$601$	6.50493	+	36.8913i	0.265342	+	1.50483i	0.768061	+	0.640377i	$0.221222\pi$
$601$	6.50493	+	36.8913i	0.265342	+	1.50483i	−0.502719	+	0.864450i	$0.667667\pi$
$602$		0			0
$603$	1.31477	−	8.87859i	0.0535414	−	0.361564i
$604$		0			0
$605$	36.9218	+	13.4384i	1.50108	+	0.546350i
$606$		0			0
$607$	25.2286	+	21.1693i	1.02400	+	0.859236i	0.990125	−	0.140190i	$-0.0447714\pi$
$607$	25.2286	+	21.1693i	1.02400	+	0.859236i	0.0338731	+	0.999426i	$0.489216\pi$
$608$		0			0
$609$	−8.50488	−	22.4030i	−0.344635	−	0.907815i
$610$		0			0
$611$	13.8600	−	24.0061i	0.560714	−	0.971185i
$612$		0			0
$613$	−6.35437	−	11.0061i	−0.256651	−	0.444532i	0.708692	−	0.705518i	$-0.249286\pi$
$613$	−6.35437	−	11.0061i	−0.256651	−	0.444532i	−0.965343	+	0.260986i	$0.915952\pi$
$614$		0			0
$615$	−33.3294	−	38.6284i	−1.34397	−	1.55765i
$616$		0			0
$617$	2.69680	−	15.2943i	0.108569	−	0.615725i	−0.881166	−	0.472808i	$-0.843241\pi$
$617$	2.69680	−	15.2943i	0.108569	−	0.615725i	0.989735	−	0.142917i	$-0.0456484\pi$
$618$		0			0
$619$	−8.77717	+	7.36492i	−0.352784	+	0.296021i	−0.801907	−	0.597449i	$-0.796181\pi$
$619$	−8.77717	+	7.36492i	−0.352784	+	0.296021i	0.449123	+	0.893470i	$0.351737\pi$
$620$		0			0
$621$	20.4207	+	2.73739i	0.819456	+	0.109848i
$622$		0			0
$623$	−17.9733	+	15.0814i	−0.720086	+	0.604224i
$624$		0			0
$625$	−0.349680	+	1.98314i	−0.0139872	+	0.0793254i
$626$		0			0
$627$	1.12068	−	3.21605i	0.0447557	−	0.128437i
$628$		0			0
$629$	−5.47087	−	9.47583i	−0.218138	−	0.377826i
$630$		0			0
$631$	−9.82951	+	17.0252i	−0.391306	+	0.677763i	−0.992622	−	0.121249i	$-0.961310\pi$
$631$	−9.82951	+	17.0252i	−0.391306	+	0.677763i	0.601316	+	0.799012i	$0.294643\pi$
$632$		0			0
$633$	39.6703	+	6.43346i	1.57675	+	0.255707i
$634$		0			0
$635$	57.7934	+	48.4944i	2.29346	+	1.92444i
$636$		0			0
$637$	−0.558380	−	0.203234i	−0.0221238	−	0.00805242i
$638$		0			0
$639$	21.9681	−	0.604681i	0.869043	−	0.0239208i
$640$		0			0
$641$	2.52076	+	14.2959i	0.0995641	+	0.564656i	0.993253	+	0.115969i	$0.0369972\pi$
$641$	2.52076	+	14.2959i	0.0995641	+	0.564656i	−0.893689	+	0.448687i	$0.851892\pi$
$642$		0			0
$643$	−31.7247	+	11.5469i	−1.25110	+	0.455363i	−0.880773	−	0.473538i	$-0.842977\pi$
$643$	−31.7247	+	11.5469i	−1.25110	+	0.455363i	−0.370327	+	0.928901i	$0.620754\pi$
$644$		0			0
$645$	−13.3086	−	7.44145i	−0.524024	−	0.293007i
$646$		0			0
$647$	−2.50800			−0.0985998			−0.0492999	−	0.998784i	$-0.515699\pi$
$647$	−2.50800			−0.0985998			−0.0492999	+	0.998784i	$0.515699\pi$
$648$		0			0
$649$	−1.22450			−0.0480659
$650$		0			0
$651$	−0.254551	−	0.142331i	−0.00997663	−	0.00557841i
$652$		0			0
$653$	−25.8890	+	9.42282i	−1.01311	+	0.368743i	−0.794628	−	0.607097i	$-0.792334\pi$
$653$	−25.8890	+	9.42282i	−1.01311	+	0.368743i	−0.218486	+	0.975840i	$0.570112\pi$
$654$		0			0
$655$	−5.69045	−	32.2722i	−0.222344	−	1.26098i
$656$		0			0
$657$	−9.16265	+	16.9295i	−0.357469	+	0.660483i
$658$		0			0
$659$	−46.3222	−	16.8599i	−1.80446	−	0.656769i	−0.997840	−	0.0656960i	$-0.979073\pi$
$659$	−46.3222	−	16.8599i	−1.80446	−	0.656769i	−0.806618	−	0.591073i	$-0.798705\pi$
$660$		0			0
$661$	15.8483	+	13.2983i	0.616427	+	0.517244i	0.896678	−	0.442683i	$-0.145973\pi$
$661$	15.8483	+	13.2983i	0.616427	+	0.517244i	−0.280251	+	0.959927i	$0.590418\pi$
$662$		0			0
$663$	45.8609	+	7.43741i	1.78109	+	0.288845i
$664$		0			0
$665$	−37.3815	+	64.7467i	−1.44959	+	2.51077i
$666$		0			0
$667$	10.2951	+	17.8317i	0.398629	+	0.690446i
$668$		0			0
$669$	−4.59239	+	13.1789i	−0.177552	+	0.509526i
$670$		0			0
$671$	0.233632	−	1.32499i	0.00901925	−	0.0511507i
$672$		0			0
$673$	4.08301	−	3.42605i	0.157388	−	0.132065i	−0.560693	−	0.828024i	$-0.689465\pi$
$673$	4.08301	−	3.42605i	0.157388	−	0.132065i	0.718081	+	0.695959i	$0.245021\pi$
$674$		0			0
$675$	27.6861	+	30.3573i	1.06564	+	1.16845i
$676$		0			0
$677$	−2.48582	+	2.08585i	−0.0955377	+	0.0801657i	−0.689306	−	0.724471i	$-0.742084\pi$
$677$	−2.48582	+	2.08585i	−0.0955377	+	0.0801657i	0.593768	+	0.804636i	$0.297640\pi$
$678$		0			0
$679$	0.880760	−	4.99504i	0.0338005	−	0.191692i
$680$		0			0
$681$	−17.2036	−	19.9388i	−0.659244	−	0.764056i
$682$		0			0
$683$	15.2207	+	26.3631i	0.582405	+	1.00876i	0.995193	+	0.0979282i	$0.0312215\pi$
$683$	15.2207	+	26.3631i	0.582405	+	1.00876i	−0.412788	+	0.910827i	$0.635445\pi$
$684$		0			0
$685$	12.2539	−	21.2244i	0.468199	−	0.810944i
$686$		0			0
$687$	5.24702	+	13.8213i	0.200186	+	0.527317i
$688$		0			0
$689$	4.13528	+	3.46991i	0.157542	+	0.132193i
$690$		0			0
$691$	9.31401	+	3.39002i	0.354322	+	0.128963i	0.513048	−	0.858360i	$-0.328516\pi$
$691$	9.31401	+	3.39002i	0.354322	+	0.128963i	−0.158726	+	0.987323i	$0.550739\pi$
$692$		0			0
$693$	−1.87110	+	0.739939i	−0.0710770	+	0.0281080i
$694$		0			0
$695$	−7.22963	−	41.0012i	−0.274235	−	1.55527i
$696$		0			0
$697$	34.1742	−	12.4384i	1.29444	−	0.471137i
$698$		0			0
$699$	5.80230	−	3.45726i	0.219463	−	0.130766i
$700$		0			0
$701$	8.54939			0.322906			0.161453	−	0.986880i	$-0.448382\pi$
$701$	8.54939			0.322906			0.161453	+	0.986880i	$0.448382\pi$
$702$		0			0
$703$	−19.2679			−0.726704
$704$		0			0
$705$	0.392444	+	28.5204i	0.0147803	+	1.07414i
$706$		0			0
$707$	−16.6529	+	6.06115i	−0.626295	+	0.227953i
$708$		0			0
$709$	−1.32721	−	7.52700i	−0.0498445	−	0.282682i	0.949690	−	0.313192i	$-0.101398\pi$
$709$	−1.32721	−	7.52700i	−0.0498445	−	0.282682i	−0.999534	+	0.0305093i	$0.990287\pi$
$710$		0			0
$711$	33.4310	+	11.1361i	1.25376	+	0.417638i
$712$		0			0
$713$	0.235480	+	0.0857077i	0.00881879	+	0.00320978i
$714$		0			0
$715$	−4.18975	−	3.51562i	−0.156688	−	0.131477i
$716$		0			0
$717$	−18.9903	+	23.2747i	−0.709206	+	0.869211i
$718$		0			0
$719$	14.7522	−	25.5515i	0.550162	−	0.952909i	−0.448100	−	0.893984i	$-0.647899\pi$
$719$	14.7522	−	25.5515i	0.550162	−	0.952909i	0.998262	−	0.0589259i	$-0.0187676\pi$
$720$		0			0
$721$	−4.57209	−	7.91909i	−0.170273	−	0.294922i
$722$		0			0
$723$	−22.1666	+	4.22384i	−0.824386	+	0.157086i
$724$		0			0
$725$	−7.13001	+	40.4363i	−0.264802	+	1.50177i
$726$		0			0
$727$	−22.7771	+	19.1122i	−0.844755	+	0.708834i	−0.958628	−	0.284661i	$-0.908119\pi$
$727$	−22.7771	+	19.1122i	−0.844755	+	0.708834i	0.113873	+	0.993495i	$0.463674\pi$
$728$		0			0
$729$	−26.9080	+	2.22647i	−0.996594	+	0.0824619i
$730$		0			0
$731$	8.32595	−	6.98630i	0.307946	−	0.258398i
$732$		0			0
$733$	1.90789	−	10.8202i	0.0704695	−	0.399653i	−0.929087	−	0.369862i	$-0.879405\pi$
$733$	1.90789	−	10.8202i	0.0704695	−	0.399653i	0.999556	−	0.0297904i	$-0.00948398\pi$
$734$		0			0
$735$	0.600626	−	0.114449i	0.0221544	−	0.00422151i
$736$		0			0
$737$	−0.376576	−	0.652249i	−0.0138714	−	0.0240259i
$738$		0			0
$739$	−10.1521	+	17.5840i	−0.373452	+	0.646838i	−0.990094	−	0.140406i	$-0.955159\pi$
$739$	−10.1521	+	17.5840i	−0.373452	+	0.646838i	0.616642	+	0.787244i	$0.288493\pi$
$740$		0			0
$741$	51.7218	−	63.3909i	1.90005	−	2.32872i
$742$		0			0
$743$	1.72816	+	1.45010i	0.0634000	+	0.0531989i	0.673937	−	0.738789i	$-0.264602\pi$
$743$	1.72816	+	1.45010i	0.0634000	+	0.0531989i	−0.610537	+	0.791988i	$0.709046\pi$
$744$		0			0
$745$	54.3857	+	19.7948i	1.99254	+	0.725225i
$746$		0			0
$747$	−3.31071	−	1.10282i	−0.121133	−	0.0403502i
$748$		0			0
$749$	1.85220	+	10.5043i	0.0676779	+	0.383820i
$750$		0			0
$751$	−48.1636	+	17.5301i	−1.75751	+	0.639683i	−0.999915	−	0.0130363i	$-0.995850\pi$
$751$	−48.1636	+	17.5301i	−1.75751	+	0.639683i	−0.757600	+	0.652719i	$0.773628\pi$
$752$		0			0
$753$	−0.195091	−	14.1780i	−0.00710950	−	0.516673i
$754$		0			0
$755$	62.7730			2.28454
$756$		0			0
$757$	17.0855			0.620984			0.310492	−	0.950576i	$-0.399506\pi$
$757$	17.0855			0.620984			0.310492	+	0.950576i	$0.399506\pi$
$758$		0			0
$759$	1.48523	−	0.884964i	0.0539103	−	0.0321222i
$760$		0			0
$761$	−9.10650	+	3.31450i	−0.330110	+	0.120150i	−0.501758	−	0.865008i	$-0.667313\pi$
$761$	−9.10650	+	3.31450i	−0.330110	+	0.120150i	0.171648	+	0.985158i	$0.445091\pi$
$762$		0			0
$763$	−5.10367	−	28.9444i	−0.184765	−	1.04786i
$764$		0			0
$765$	−44.4562	+	17.5805i	−1.60732	+	0.635626i
$766$		0			0
$767$	−27.6417	−	10.0608i	−0.998085	−	0.363273i
$768$		0			0
$769$	−31.0485	−	26.0528i	−1.11964	−	0.939488i	−0.121052	−	0.992646i	$-0.538627\pi$
$769$	−31.0485	−	26.0528i	−1.11964	−	0.939488i	−0.998586	+	0.0531583i	$0.983071\pi$
$770$		0			0
$771$	−15.3133	−	40.3373i	−0.551495	−	1.45271i
$772$		0			0
$773$	8.03955	−	13.9249i	0.289163	−	0.500844i	−0.684447	−	0.729062i	$-0.739956\pi$
$773$	8.03955	−	13.9249i	0.289163	−	0.500844i	0.973610	+	0.228218i	$0.0732898\pi$
$774$		0			0
$775$	0.249860	+	0.432770i	0.00897523	+	0.0155456i
$776$		0			0
$777$	7.43643	+	8.61874i	0.266781	+	0.309195i
$778$		0			0
$779$	11.1207	−	63.0684i	0.398439	−	2.25966i
$780$		0			0
$781$	1.41266	−	1.18537i	0.0505491	−	0.0424157i
$782$		0			0
$783$	−18.1824	−	19.9367i	−0.649786	−	0.712479i
$784$		0			0
$785$	53.1471	−	44.5957i	1.89690	−	1.59169i
$786$		0			0
$787$	−0.141305	+	0.801378i	−0.00503697	+	0.0285661i	−0.987223	−	0.159347i	$-0.949061\pi$
$787$	−0.141305	+	0.801378i	−0.00503697	+	0.0285661i	0.982186	+	0.187913i	$0.0601723\pi$
$788$		0			0
$789$	−7.77975	+	22.3258i	−0.276966	+	0.794818i
$790$		0			0
$791$	23.0532	+	39.9293i	0.819676	+	1.41972i
$792$		0			0
$793$	16.1604	−	27.9906i	0.573871	−	0.993974i
$794$		0			0
$795$	−5.48300	−	0.889197i	−0.194462	−	0.0315366i
$796$		0			0
$797$	16.7875	+	14.0864i	0.594644	+	0.498966i	0.889719	−	0.456508i	$-0.150900\pi$
$797$	16.7875	+	14.0864i	0.594644	+	0.498966i	−0.295075	+	0.955474i	$0.595345\pi$
$798$		0			0
$799$	−19.1054	−	6.95381i	−0.675901	−	0.246008i
$800$		0			0
$801$	−12.5751	+	23.2345i	−0.444318	+	0.820951i
$802$		0			0
$803$	0.280498	+	1.59078i	0.00989856	+	0.0561375i
$804$		0			0
$805$	−35.6642	+	12.9807i	−1.25700	+	0.457509i
$806$		0			0
$807$	19.7936	+	11.0675i	0.696766	+	0.389595i
$808$		0			0
$809$	−26.2460			−0.922758			−0.461379	−	0.887203i	$-0.652645\pi$
$809$	−26.2460			−0.922758			−0.461379	+	0.887203i	$0.652645\pi$
$810$		0			0
$811$	4.97198			0.174590			0.0872950	−	0.996183i	$-0.472178\pi$
$811$	4.97198			0.174590			0.0872950	+	0.996183i	$0.472178\pi$
$812$		0			0
$813$	2.03299	+	1.13674i	0.0713002	+	0.0398673i
$814$		0			0
$815$	58.8372	−	21.4150i	2.06098	−	0.750135i
$816$		0			0
$817$	−3.32352	−	18.8486i	−0.116275	−	0.659430i
$818$		0			0
$819$	−48.3173	+	1.32996i	−1.68834	+	0.0464725i
$820$		0			0
$821$	−23.5297	−	8.56412i	−0.821193	−	0.298890i	−0.102954	−	0.994686i	$-0.532829\pi$
$821$	−23.5297	−	8.56412i	−0.821193	−	0.298890i	−0.718239	+	0.695796i	$0.755052\pi$
$822$		0			0
$823$	5.52379	+	4.63501i	0.192547	+	0.161566i	0.733965	−	0.679188i	$-0.237668\pi$
$823$	5.52379	+	4.63501i	0.192547	+	0.161566i	−0.541418	+	0.840754i	$0.682112\pi$
$824$		0			0
$825$	3.40321	+	0.551910i	0.118485	+	0.0192150i
$826$		0			0
$827$	−9.69443	+	16.7913i	−0.337108	+	0.583889i	−0.983888	−	0.178788i	$-0.942782\pi$
$827$	−9.69443	+	16.7913i	−0.337108	+	0.583889i	0.646779	+	0.762677i	$0.276116\pi$
$828$		0			0
$829$	5.87221	+	10.1710i	0.203950	+	0.353252i	0.949798	−	0.312865i	$-0.101289\pi$
$829$	5.87221	+	10.1710i	0.203950	+	0.353252i	−0.745848	+	0.666117i	$0.767955\pi$
$830$		0			0
$831$	7.74684	−	22.2313i	0.268735	−	0.771196i
$832$		0			0
$833$	−0.0756822	+	0.429215i	−0.00262223	+	0.0148714i
$834$		0			0
$835$	52.6373	−	44.1680i	1.82159	−	1.52850i
$836$		0			0
$837$	−0.325481	−	0.0436306i	−0.0112503	−	0.00150809i
$838$		0			0
$839$	−20.7446	+	17.4068i	−0.716183	+	0.600949i	−0.926326	−	0.376722i	$-0.877051\pi$
$839$	−20.7446	+	17.4068i	−0.716183	+	0.600949i	0.210144	+	0.977670i	$0.432607\pi$
$840$		0			0
$841$	−0.353269	+	2.00349i	−0.0121817	+	0.0690857i
$842$		0			0
$843$	−3.55437	−	4.11947i	−0.122419	−	0.141882i
$844$		0			0
$845$	−42.3415	−	73.3377i	−1.45659	−	2.52289i
$846$		0			0
$847$	14.5690	−	25.2342i	0.500596	−	0.867058i
$848$		0			0
$849$	−7.29705	−	19.2214i	−0.250434	−	0.659677i
$850$		0			0
$851$	−7.49287	−	6.28727i	−0.256852	−	0.215525i
$852$		0			0
$853$	37.1589	+	13.5247i	1.27229	+	0.463078i	0.887877	−	0.460082i	$-0.152180\pi$
$853$	37.1589	+	13.5247i	1.27229	+	0.463078i	0.384418	+	0.923159i	$0.374402\pi$
$854$		0			0
$855$	−12.3318	+	83.2765i	−0.421739	+	2.84800i
$856$		0			0
$857$	−3.38315	−	19.1868i	−0.115566	−	0.655408i	−0.986468	−	0.163952i	$-0.947576\pi$
$857$	−3.38315	−	19.1868i	−0.115566	−	0.655408i	0.870902	−	0.491456i	$-0.163535\pi$
$858$		0			0
$859$	28.3684	−	10.3252i	0.967916	−	0.352293i	0.190785	−	0.981632i	$-0.438897\pi$
$859$	28.3684	−	10.3252i	0.967916	−	0.352293i	0.777131	+	0.629339i	$0.216674\pi$
$860$		0			0
$861$	−32.5031	+	19.3668i	−1.10770	+	0.660018i
$862$		0			0
$863$	−37.1325			−1.26401			−0.632003	−	0.774966i	$-0.717767\pi$
$863$	−37.1325			−1.26401			−0.632003	+	0.774966i	$0.717767\pi$
$864$		0			0
$865$	−65.7020			−2.23393
$866$		0			0
$867$	−0.0637299	−	4.63149i	−0.00216438	−	0.157294i
$868$		0			0
$869$	2.77852	−	1.01130i	0.0942549	−	0.0343060i
$870$		0			0
$871$	−3.14176	−	17.8178i	−0.106454	−	0.603733i
$872$		0			0
$873$	−1.14613	−	5.59509i	−0.0387908	−	0.189365i
$874$		0			0
$875$	−26.1474	−	9.51689i	−0.883944	−	0.321729i
$876$		0			0
$877$	−4.04093	−	3.39074i	−0.136452	−	0.114497i	0.572007	−	0.820249i	$-0.306165\pi$
$877$	−4.04093	−	3.39074i	−0.136452	−	0.114497i	−0.708459	+	0.705752i	$0.750609\pi$
$878$		0			0
$879$	2.11281	−	2.58948i	0.0712632	−	0.0873410i
$880$		0			0
$881$	13.1005	−	22.6908i	0.441368	−	0.764471i	−0.556424	−	0.830899i	$-0.687827\pi$
$881$	13.1005	−	22.6908i	0.441368	−	0.764471i	0.997791	+	0.0664276i	$0.0211601\pi$
$882$		0			0
$883$	−7.90545	−	13.6926i	−0.266040	−	0.460794i	0.701796	−	0.712378i	$-0.252382\pi$
$883$	−7.90545	−	13.6926i	−0.266040	−	0.460794i	−0.967835	+	0.251584i	$0.919049\pi$
$884$		0			0
$885$	29.7330	−	5.66561i	0.999465	−	0.190447i
$886$		0			0
$887$	−7.96490	+	45.1712i	−0.267435	+	1.51670i	0.494575	+	0.869135i	$0.335324\pi$
$887$	−7.96490	+	45.1712i	−0.267435	+	1.51670i	−0.762010	+	0.647565i	$0.775787\pi$
$888$		0			0
$889$	42.8588	−	35.9628i	1.43744	−	1.20615i
$890$		0			0
$891$	−1.65285	+	1.54960i	−0.0553725	+	0.0519135i
$892$		0			0
$893$	−27.4267	+	23.0137i	−0.917800	+	0.770125i
$894$		0			0
$895$	−12.2469	+	69.4556i	−0.409368	+	2.32164i
$896$		0			0
$897$	40.7983	−	7.77410i	1.36222	−	0.259570i
$898$		0			0
$899$	−0.164092	−	0.284215i	−0.00547276	−	0.00947911i
$900$		0			0
$901$	1.97970	−	3.42895i	0.0659535	−	0.114235i
$902$		0			0
$903$	−7.14846	+	8.76124i	−0.237886	+	0.291556i
$904$		0			0
$905$	−23.1815	−	19.4516i	−0.770579	−	0.646592i
$906$		0			0
$907$	34.9858	+	12.7338i	1.16169	+	0.422819i	0.849699	−	0.527267i	$-0.176783\pi$
$907$	34.9858	+	12.7338i	1.16169	+	0.422819i	0.311987	+	0.950087i	$0.399006\pi$
$908$		0			0
$909$	−14.9276	+	13.2425i	−0.495117	+	0.439225i
$910$		0			0
$911$	−7.90962	−	44.8577i	−0.262057	−	1.48620i	−0.777285	−	0.629148i	$-0.783404\pi$
$911$	−7.90962	−	44.8577i	−0.262057	−	1.48620i	0.515228	−	0.857053i	$-0.327707\pi$
$912$		0			0
$913$	−0.275160	+	0.100150i	−0.00910647	+	0.00331448i
$914$		0			0
$915$	0.457580	+	33.2540i	0.0151271	+	1.09934i
$916$		0			0
$917$	−24.3018			−0.802517
$918$		0			0
$919$	−4.31393			−0.142303			−0.0711517	−	0.997466i	$-0.522667\pi$
$919$	−4.31393			−0.142303			−0.0711517	+	0.997466i	$0.522667\pi$
$920$		0			0
$921$	7.55152	−	4.49953i	0.248831	−	0.148264i
$922$		0			0
$923$	41.6285	−	15.1515i	1.37022	−	0.498719i
$924$		0			0
$925$	−3.38706	−	19.2090i	−0.111366	−	0.631587i
$926$		0			0
$927$	−8.06670	−	6.39893i	−0.264945	−	0.210169i
$928$		0			0
$929$	−12.5729	−	4.57617i	−0.412504	−	0.150139i	0.127428	−	0.991848i	$-0.459328\pi$
$929$	−12.5729	−	4.57617i	−0.412504	−	0.150139i	−0.539932	+	0.841709i	$0.681550\pi$
$930$		0			0
$931$	0.587930	+	0.493332i	0.0192686	+	0.0161683i
$932$		0			0
$933$	−3.29420	−	8.67737i	−0.107847	−	0.284084i
$934$		0			0
$935$	−2.00578	+	3.47411i	−0.0655960	+	0.113616i
$936$		0			0
$937$	−1.45814	−	2.52558i	−0.0476355	−	0.0825071i	0.841225	−	0.540686i	$-0.181835\pi$
$937$	−1.45814	−	2.52558i	−0.0476355	−	0.0825071i	−0.888860	+	0.458179i	$0.848502\pi$
$938$		0			0
$939$	−13.5883	−	15.7486i	−0.443436	−	0.513937i
$940$		0			0
$941$	−2.94961	+	16.7281i	−0.0961547	+	0.545320i	0.898233	+	0.439520i	$0.144851\pi$
$941$	−2.94961	+	16.7281i	−0.0961547	+	0.545320i	−0.994387	+	0.105800i	$0.966260\pi$
$942$		0			0
$943$	24.9043	−	20.8972i	0.810994	−	0.680505i
$944$		0			0
$945$	42.0098	−	26.6243i	1.36658	−	0.866088i
$946$		0			0
$947$	−31.7987	+	26.6823i	−1.03332	+	0.867058i	−0.991242	−	0.132057i	$-0.957842\pi$
$947$	−31.7987	+	26.6823i	−1.03332	+	0.867058i	−0.0420769	+	0.999114i	$0.513397\pi$
$948$		0			0
$949$	−6.73829	+	38.2147i	−0.218734	+	1.24050i
$950$		0			0
$951$	8.47195	−	24.3122i	0.274722	−	0.788377i
$952$		0			0
$953$	−18.3366	−	31.7599i	−0.593981	−	1.02881i	−0.993690	−	0.112163i	$-0.964222\pi$
$953$	−18.3366	−	31.7599i	−0.593981	−	1.02881i	0.399709	−	0.916642i	$-0.369111\pi$
$954$		0			0
$955$	2.97693	−	5.15619i	0.0963312	−	0.166851i
$956$		0			0
$957$	−2.23501	−	0.362459i	−0.0722475	−	0.0117166i
$958$		0			0
$959$	−13.9226	−	11.6825i	−0.449585	−	0.377247i
$960$		0			0
$961$	29.1267	+	10.6013i	0.939572	+	0.341976i
$962$		0			0
$963$	6.28920	+	10.2323i	0.202667	+	0.329730i
$964$		0			0
$965$	1.75203	+	9.93627i	0.0563999	+	0.319860i
$966$		0			0
$967$	39.2166	−	14.2737i	1.26112	−	0.459011i	0.376976	−	0.926223i	$-0.376964\pi$
$967$	39.2166	−	14.2737i	1.26112	−	0.459011i	0.884145	+	0.467212i	$0.154742\pi$
$968$		0			0
$969$	−52.3761	−	29.2860i	−1.68256	−	0.940802i
$970$		0			0
$971$	−19.6506			−0.630619			−0.315309	−	0.948989i	$-0.602108\pi$
$971$	−19.6506			−0.630619			−0.315309	+	0.948989i	$0.602108\pi$
$972$		0			0
$973$	−30.8751			−0.989809
$974$		0			0
$975$	72.2889	+	40.4202i	2.31510	+	1.29448i
$976$		0			0
$977$	13.3676	−	4.86543i	0.427669	−	0.155659i	−0.119213	−	0.992869i	$-0.538037\pi$
$977$	13.3676	−	4.86543i	0.427669	−	0.155659i	0.546882	+	0.837210i	$0.315815\pi$
$978$		0			0
$979$	0.384963	+	2.18323i	0.0123035	+	0.0697765i
$980$		0			0
$981$	−17.3297	−	28.1947i	−0.553293	−	0.900186i
$982$		0			0
$983$	−13.9025	−	5.06008i	−0.443419	−	0.161391i	0.110655	−	0.993859i	$-0.464705\pi$
$983$	−13.9025	−	5.06008i	−0.443419	−	0.161391i	−0.554074	+	0.832467i	$0.686928\pi$
$984$		0			0
$985$	27.6184	+	23.1746i	0.879997	+	0.738405i
$986$		0			0
$987$	20.8796	+	3.38611i	0.664604	+	0.107781i
$988$		0			0
$989$	4.85800	−	8.41430i	0.154475	−	0.267559i
$990$		0			0
$991$	6.45390	+	11.1785i	0.205015	+	0.355096i	0.950137	−	0.311831i	$-0.100942\pi$
$991$	6.45390	+	11.1785i	0.205015	+	0.355096i	−0.745123	+	0.666928i	$0.767609\pi$
$992$		0			0
$993$	−18.1110	+	51.9737i	−0.574736	+	1.64934i
$994$		0			0
$995$	−4.84229	+	27.4620i	−0.153511	+	0.870604i
$996$		0			0
$997$	−17.6135	+	14.7795i	−0.557825	+	0.468071i	−0.877580	−	0.479429i	$-0.840844\pi$
$997$	−17.6135	+	14.7795i	−0.557825	+	0.468071i	0.319756	+	0.947500i	$0.396399\pi$
$998$		0			0
$999$	11.3557	+	5.94545i	0.359279	+	0.188106i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.q.b.49.5	✓	30
3.2	odd	2		648.2.q.b.361.5		30
4.3	odd	2		432.2.u.f.49.1		30
27.4	even	9		5832.2.a.k.1.15		15
27.11	odd	18		648.2.q.b.289.5		30
27.16	even	9	inner	216.2.q.b.97.5	yes	30
27.23	odd	18		5832.2.a.l.1.1		15
108.43	odd	18		432.2.u.f.97.1		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.q.b.49.5	✓	30	1.1	even	1	trivial
216.2.q.b.97.5	yes	30	27.16	even	9	inner
432.2.u.f.49.1		30	4.3	odd	2
432.2.u.f.97.1		30	108.43	odd	18
648.2.q.b.289.5		30	27.11	odd	18
648.2.q.b.361.5		30	3.2	odd	2
5832.2.a.k.1.15		15	27.4	even	9
5832.2.a.l.1.1		15	27.23	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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.q (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.51177 + 0.845305i) q^{3} +(-3.37598 + 1.22876i) q^{5} +(0.462643 + 2.62378i) q^{7} +(1.57092 + 2.55582i) q^{9} +O(q^{10})\)	\(q+(1.51177 + 0.845305i) q^{3} +(-3.37598 + 1.22876i) q^{5} +(0.462643 + 2.62378i) q^{7} +(1.57092 + 2.55582i) q^{9} +(0.236557 + 0.0860998i) q^{11} +(4.63259 + 3.88721i) q^{13} +(-6.14239 - 0.996131i) q^{15} +(2.21778 - 3.84131i) q^{17} +(-3.90542 - 6.76438i) q^{19} +(-1.51848 + 4.35764i) q^{21} +(0.688536 - 3.90488i) q^{23} +(6.05716 - 5.08256i) q^{25} +(0.214425 + 5.19173i) q^{27} +(-3.97795 + 3.33789i) q^{29} +(-0.0109744 + 0.0622391i) q^{31} +(0.284840 + 0.330126i) q^{33} +(-4.78586 - 8.28934i) q^{35} +(1.23341 - 2.13633i) q^{37} +(3.71755 + 9.79253i) q^{39} +(6.28083 + 5.27024i) q^{41} +(2.30259 + 0.838074i) q^{43} +(-8.44386 - 6.69811i) q^{45} +(-0.795962 - 4.51412i) q^{47} +(-0.0923337 + 0.0336067i) q^{49} +(6.59987 - 3.93249i) q^{51} +0.892650 q^{53} -0.904407 q^{55} +(-0.186140 - 13.5275i) q^{57} +(-4.57083 + 1.66365i) q^{59} +(-0.928071 - 5.26335i) q^{61} +(-5.97913 + 5.30418i) q^{63} +(-20.4159 - 7.43080i) q^{65} +(-2.29185 - 1.92309i) q^{67} +(4.34173 - 5.32128i) q^{69} +(3.66273 - 6.34403i) q^{71} +(3.20833 + 5.55700i) q^{73} +(13.4534 - 2.56353i) q^{75} +(-0.116465 + 0.660507i) q^{77} +(8.99771 - 7.54997i) q^{79} +(-4.06443 + 8.02997i) q^{81} +(-0.891052 + 0.747682i) q^{83} +(-2.76715 + 15.6933i) q^{85} +(-8.83530 + 1.68356i) q^{87} +(4.40320 + 7.62657i) q^{89} +(-8.05593 + 13.9533i) q^{91} +(-0.0692018 + 0.0848146i) q^{93} +(21.4964 + 18.0376i) q^{95} +(-1.78895 - 0.651123i) q^{97} +(0.151556 + 0.739853i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{7} - 6 q^{9}+O(q^{10}) \) 30 * q + 3 * q^7 - 6 * q^9	\( 30 q + 3 q^{7} - 6 q^{9} - 3 q^{11} - 12 q^{13} + 15 q^{15} + 6 q^{17} - 9 q^{19} + 30 q^{21} - 12 q^{23} + 24 q^{25} - 15 q^{27} - 9 q^{29} + 27 q^{31} - 30 q^{33} - 18 q^{35} - 15 q^{37} - 21 q^{39} - 15 q^{41} - 30 q^{43} + 15 q^{45} - 18 q^{47} + 15 q^{49} - 6 q^{51} - 18 q^{53} + 54 q^{55} - 72 q^{57} - 12 q^{59} + 6 q^{61} - 54 q^{63} - 54 q^{65} - 45 q^{67} + 9 q^{69} - 36 q^{73} + 69 q^{75} + 12 q^{77} + 45 q^{79} - 30 q^{81} - 3 q^{83} + 57 q^{85} - 60 q^{87} + 36 q^{89} - 39 q^{91} + 30 q^{93} + 51 q^{95} - 84 q^{97} + 162 q^{99}+O(q^{100}) \) 30 * q + 3 * q^7 - 6 * q^9 - 3 * q^11 - 12 * q^13 + 15 * q^15 + 6 * q^17 - 9 * q^19 + 30 * q^21 - 12 * q^23 + 24 * q^25 - 15 * q^27 - 9 * q^29 + 27 * q^31 - 30 * q^33 - 18 * q^35 - 15 * q^37 - 21 * q^39 - 15 * q^41 - 30 * q^43 + 15 * q^45 - 18 * q^47 + 15 * q^49 - 6 * q^51 - 18 * q^53 + 54 * q^55 - 72 * q^57 - 12 * q^59 + 6 * q^61 - 54 * q^63 - 54 * q^65 - 45 * q^67 + 9 * q^69 - 36 * q^73 + 69 * q^75 + 12 * q^77 + 45 * q^79 - 30 * q^81 - 3 * q^83 + 57 * q^85 - 60 * q^87 + 36 * q^89 - 39 * q^91 + 30 * q^93 + 51 * q^95 - 84 * q^97 + 162 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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