LMFDB - Embedded newform 420.2.bh.b.101.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [420,2,Mod(101,420)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(420, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 1]))

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

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

chi := DirichletCharacter("420.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	420.bh (of order $6$, degree $2$, 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:	$3.35371688489$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	10.0.29471584693248.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 2x^{8} - 4x^{7} + 13x^{6} - 36x^{5} + 39x^{4} - 36x^{3} + 54x^{2} - 162x + 243 $ x^10 - 2x^9 + 2x^8 - 4x^7 + 13x^6 - 36x^5 + 39x^4 - 36x^3 + 54x^2 - 162*x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.3
Root			$-1.08831 + 1.34743i$ of defining polynomial
Character	$\chi$	$=$	420.101
Dual form			420.2.bh.b.341.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.622752 + 1.61622i) q^{3} +(0.500000 + 0.866025i) q^{5} +(2.57325 - 0.615143i) q^{7} +(-2.22436 + 2.01301i) q^{9} +O(q^{10})$	\(q+(0.622752 + 1.61622i) q^{3} +(0.500000 + 0.866025i) q^{5} +(2.57325 - 0.615143i) q^{7} +(-2.22436 + 2.01301i) q^{9} +(1.80606 + 1.04273i) q^{11} +0.245770i q^{13} +(-1.08831 + 1.34743i) q^{15} +(0.471640 - 0.816904i) q^{17} +(-0.465563 + 0.268793i) q^{19} +(2.59670 + 3.77586i) q^{21} +(-2.40010 + 1.38570i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-4.63871 - 2.34145i) q^{27} +0.267475i q^{29} +(0.981097 + 0.566436i) q^{31} +(-0.560556 + 3.56836i) q^{33} +(1.81935 + 1.92093i) q^{35} +(3.08164 + 5.33755i) q^{37} +(-0.397219 + 0.153054i) q^{39} +2.38340 q^{41} -11.4354 q^{43} +(-2.85550 - 0.919845i) q^{45} +(-6.23215 - 10.7944i) q^{47} +(6.24320 - 3.16583i) q^{49} +(1.61401 + 0.253547i) q^{51} +(10.8541 + 6.26660i) q^{53} +2.08546i q^{55} +(-0.724359 - 0.585062i) q^{57} +(6.25478 - 10.8336i) q^{59} +(4.96556 - 2.86687i) q^{61} +(-4.48553 + 6.54828i) q^{63} +(-0.212843 + 0.122885i) q^{65} +(2.78001 - 4.81512i) q^{67} +(-3.73427 - 3.01616i) q^{69} -10.1375i q^{71} +(-11.3758 - 6.56784i) q^{73} +(-1.71107 - 0.268793i) q^{75} +(5.28887 + 1.57221i) q^{77} +(3.17314 + 5.49605i) q^{79} +(0.895549 - 8.95533i) q^{81} -1.06674 q^{83} +0.943279 q^{85} +(-0.432299 + 0.166571i) q^{87} +(0.463787 + 0.803302i) q^{89} +(0.151184 + 0.632426i) q^{91} +(-0.304508 + 1.93842i) q^{93} +(-0.465563 - 0.268793i) q^{95} -3.01245i q^{97} +(-6.11636 + 1.31622i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{3} + 5 q^{5} - 5 q^{7} + 3 q^{9}+O(q^{10}) $ 10 * q + q^3 + 5 * q^5 - 5 * q^7 + 3 * q^9	$ 10 q + q^{3} + 5 q^{5} - 5 q^{7} + 3 q^{9} + 6 q^{11} + 2 q^{15} - 6 q^{17} + 3 q^{19} + 12 q^{21} - 24 q^{23} - 5 q^{25} - 8 q^{27} + 15 q^{31} - 4 q^{33} - q^{35} - q^{37} - 21 q^{39} + 8 q^{41} - 26 q^{43} + 3 q^{45} - 14 q^{47} - 13 q^{49} + 40 q^{51} + 24 q^{53} + 18 q^{57} + 42 q^{61} - 49 q^{63} - 9 q^{65} + 7 q^{67} + 14 q^{69} - 3 q^{73} + q^{75} + 26 q^{77} + q^{79} - 13 q^{81} + 8 q^{83} - 12 q^{85} + 8 q^{87} - 28 q^{89} - 11 q^{91} + 25 q^{93} + 3 q^{95} + 36 q^{99}+O(q^{100}) $ 10 * q + q^3 + 5 * q^5 - 5 * q^7 + 3 * q^9 + 6 * q^11 + 2 * q^15 - 6 * q^17 + 3 * q^19 + 12 * q^21 - 24 * q^23 - 5 * q^25 - 8 * q^27 + 15 * q^31 - 4 * q^33 - q^35 - q^37 - 21 * q^39 + 8 * q^41 - 26 * q^43 + 3 * q^45 - 14 * q^47 - 13 * q^49 + 40 * q^51 + 24 * q^53 + 18 * q^57 + 42 * q^61 - 49 * q^63 - 9 * q^65 + 7 * q^67 + 14 * q^69 - 3 * q^73 + q^75 + 26 * q^77 + q^79 - 13 * q^81 + 8 * q^83 - 12 * q^85 + 8 * q^87 - 28 * q^89 - 11 * q^91 + 25 * q^93 + 3 * q^95 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/420\mathbb{Z}\right)^\times$.

$n$	$211$	$241$	$281$	$337$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.622752	+	1.61622i	0.359546	+	0.933127i
$3$	0.622752	+	1.61622i	0.359546	+	0.933127i
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	2.57325	−	0.615143i	0.972596	−	0.232502i
$7$	2.57325	−	0.615143i	0.972596	−	0.232502i
$8$		0			0
$9$	−2.22436	+	2.01301i	−0.741453	+	0.671005i
$10$		0			0
$11$	1.80606	+	1.04273i	0.544548	+	0.314395i	0.746920	−	0.664914i	$-0.231532\pi$
$11$	1.80606	+	1.04273i	0.544548	+	0.314395i	−0.202372	+	0.979309i	$0.564865\pi$
$12$		0			0
$13$			0.245770i			0.0681643i	0.999419	+	0.0340821i	$0.0108508\pi$
$13$			0.245770i			0.0681643i	−0.999419	+	0.0340821i	$0.989149\pi$
$14$		0			0
$15$	−1.08831	+	1.34743i	−0.281002	+	0.347905i
$16$		0			0
$17$	0.471640	−	0.816904i	0.114389	−	0.198128i	−0.803146	−	0.595782i	$-0.796842\pi$
$17$	0.471640	−	0.816904i	0.114389	−	0.198128i	0.917536	+	0.397654i	$0.130176\pi$
$18$		0			0
$19$	−0.465563	+	0.268793i	−0.106807	+	0.0616653i	−0.552452	−	0.833545i	$-0.686308\pi$
$19$	−0.465563	+	0.268793i	−0.106807	+	0.0616653i	0.445645	+	0.895210i	$0.352974\pi$
$20$		0			0
$21$	2.59670	+	3.77586i	0.566647	+	0.823960i
$22$		0			0
$23$	−2.40010	+	1.38570i	−0.500456	+	0.288938i	−0.728902	−	0.684618i	$-0.759969\pi$
$23$	−2.40010	+	1.38570i	−0.500456	+	0.288938i	0.228446	+	0.973557i	$0.426636\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	−4.63871	−	2.34145i	−0.892719	−	0.450613i
$28$		0			0
$29$			0.267475i			0.0496688i	0.999692	+	0.0248344i	$0.00790585\pi$
$29$			0.267475i			0.0496688i	−0.999692	+	0.0248344i	$0.992094\pi$
$30$		0			0
$31$	0.981097	+	0.566436i	0.176210	+	0.101735i	0.585511	−	0.810665i	$-0.300894\pi$
$31$	0.981097	+	0.566436i	0.176210	+	0.101735i	−0.409301	+	0.912400i	$0.634227\pi$
$32$		0			0
$33$	−0.560556	+	3.56836i	−0.0975803	+	0.621172i
$34$		0			0
$35$	1.81935	+	1.92093i	0.307527	+	0.324696i
$36$		0			0
$37$	3.08164	+	5.33755i	0.506618	+	0.877488i	0.999971	+	0.00765857i	$0.00243782\pi$
$37$	3.08164	+	5.33755i	0.506618	+	0.877488i	−0.493353	+	0.869829i	$0.664229\pi$
$38$		0			0
$39$	−0.397219	+	0.153054i	−0.0636059	+	0.0245082i
$40$		0			0
$41$	2.38340			0.372224			0.186112	−	0.982529i	$-0.440411\pi$
$41$	2.38340			0.372224			0.186112	+	0.982529i	$0.440411\pi$
$42$		0			0
$43$	−11.4354			−1.74388			−0.871938	−	0.489616i	$-0.837137\pi$
$43$	−11.4354			−1.74388			−0.871938	+	0.489616i	$0.837137\pi$
$44$		0			0
$45$	−2.85550	−	0.919845i	−0.425673	−	0.137122i
$46$		0			0
$47$	−6.23215	−	10.7944i	−0.909052	−	1.57452i	−0.815384	−	0.578921i	$-0.803474\pi$
$47$	−6.23215	−	10.7944i	−0.909052	−	1.57452i	−0.0936683	−	0.995603i	$-0.529859\pi$
$48$		0			0
$49$	6.24320	−	3.16583i	0.891885	−	0.452261i
$50$		0			0
$51$	1.61401	+	0.253547i	0.226007	+	0.0355036i
$52$		0			0
$53$	10.8541	+	6.26660i	1.49092	+	0.860784i	0.999946	−	0.0103892i	$-0.00330704\pi$
$53$	10.8541	+	6.26660i	1.49092	+	0.860784i	0.490976	+	0.871173i	$0.336640\pi$
$54$		0			0
$55$			2.08546i			0.281203i
$56$		0			0
$57$	−0.724359	−	0.585062i	−0.0959437	−	0.0774934i
$58$		0			0
$59$	6.25478	−	10.8336i	0.814303	−	1.41041i	−0.0955244	−	0.995427i	$-0.530453\pi$
$59$	6.25478	−	10.8336i	0.814303	−	1.41041i	0.909827	−	0.414987i	$-0.136214\pi$
$60$		0			0
$61$	4.96556	−	2.86687i	0.635775	−	0.367065i	−0.147210	−	0.989105i	$-0.547029\pi$
$61$	4.96556	−	2.86687i	0.635775	−	0.367065i	0.782985	+	0.622040i	$0.213696\pi$
$62$		0			0
$63$	−4.48553	+	6.54828i	−0.565124	+	0.825006i
$64$		0			0
$65$	−0.212843	+	0.122885i	−0.0263999	+	0.0152420i
$66$		0			0
$67$	2.78001	−	4.81512i	0.339633	−	0.588261i	−0.644731	−	0.764410i	$-0.723031\pi$
$67$	2.78001	−	4.81512i	0.339633	−	0.588261i	0.984364	+	0.176149i	$0.0563639\pi$
$68$		0			0
$69$	−3.73427	−	3.01616i	−0.449553	−	0.363103i
$70$		0			0
$71$		−	10.1375i		−	1.20310i	−0.798835	−	0.601551i	$-0.794550\pi$
$71$		−	10.1375i		−	1.20310i	0.798835	−	0.601551i	$-0.205450\pi$
$72$		0			0
$73$	−11.3758	−	6.56784i	−1.33144	−	0.768707i	−0.345919	−	0.938264i	$-0.612433\pi$
$73$	−11.3758	−	6.56784i	−1.33144	−	0.768707i	−0.985520	+	0.169557i	$0.945766\pi$
$74$		0			0
$75$	−1.71107	−	0.268793i	−0.197577	−	0.0310375i
$76$		0			0
$77$	5.28887	+	1.57221i	0.602722	+	0.179170i
$78$		0			0
$79$	3.17314	+	5.49605i	0.357007	+	0.618353i	0.987459	−	0.157874i	$-0.0504641\pi$
$79$	3.17314	+	5.49605i	0.357007	+	0.618353i	−0.630453	+	0.776228i	$0.717131\pi$
$80$		0			0
$81$	0.895549	−	8.95533i	0.0995055	−	0.995037i
$82$		0			0
$83$	−1.06674			−0.117090			−0.0585449	−	0.998285i	$-0.518646\pi$
$83$	−1.06674			−0.117090			−0.0585449	+	0.998285i	$0.518646\pi$
$84$		0			0
$85$	0.943279			0.102313
$86$		0			0
$87$	−0.432299	+	0.166571i	−0.0463473	+	0.0178582i
$88$		0			0
$89$	0.463787	+	0.803302i	0.0491613	+	0.0851499i	0.889559	−	0.456820i	$-0.151012\pi$
$89$	0.463787	+	0.803302i	0.0491613	+	0.0851499i	−0.840398	+	0.541970i	$0.817678\pi$
$90$		0			0
$91$	0.151184	+	0.632426i	0.0158483	+	0.0662963i
$92$		0			0
$93$	−0.304508	+	1.93842i	−0.0315760	+	0.201005i
$94$		0			0
$95$	−0.465563	−	0.268793i	−0.0477657	−	0.0275776i
$96$		0			0
$97$		−	3.01245i		−	0.305868i	−0.988236	−	0.152934i	$-0.951128\pi$
$97$		−	3.01245i		−	0.305868i	0.988236	−	0.152934i	$-0.0488722\pi$
$98$		0			0
$99$	−6.11636	+	1.31622i	−0.614717	+	0.132285i
$100$		0			0
$101$	6.19049	−	10.7223i	0.615977	−	1.06690i	−0.374235	−	0.927334i	$-0.622095\pi$
$101$	6.19049	−	10.7223i	0.615977	−	1.06690i	0.990212	−	0.139570i	$-0.0445720\pi$
$102$		0			0
$103$	−14.5787	+	8.41703i	−1.43648	+	0.829355i	−0.997603	−	0.0691903i	$-0.977958\pi$
$103$	−14.5787	+	8.41703i	−1.43648	+	0.829355i	−0.438881	+	0.898545i	$0.644625\pi$
$104$		0			0
$105$	−1.97164	+	4.13674i	−0.192412	+	0.403705i
$106$		0			0
$107$	11.1031	−	6.41036i	1.07337	−	0.619713i	0.144273	−	0.989538i	$-0.453916\pi$
$107$	11.1031	−	6.41036i	1.07337	−	0.619713i	0.929101	+	0.369825i	$0.120582\pi$
$108$		0			0
$109$	1.79448	−	3.10813i	0.171880	−	0.297705i	−0.767197	−	0.641411i	$-0.778349\pi$
$109$	1.79448	−	3.10813i	0.171880	−	0.297705i	0.939077	+	0.343707i	$0.111683\pi$
$110$		0			0
$111$	−6.70758	+	8.30459i	−0.636655	+	0.788236i
$112$		0			0
$113$			1.00353i			0.0944041i	0.998885	+	0.0472020i	$0.0150305\pi$
$113$			1.00353i			0.0944041i	−0.998885	+	0.0472020i	$0.984970\pi$
$114$		0			0
$115$	−2.40010	−	1.38570i	−0.223811	−	0.129217i
$116$		0			0
$117$	−0.494738	−	0.546680i	−0.0457385	−	0.0505406i
$118$		0			0
$119$	0.711132	−	2.39222i	0.0651894	−	0.219295i
$120$		0			0
$121$	−3.32543	−	5.75981i	−0.302312	−	0.523619i
$122$		0			0
$123$	1.48426	+	3.85210i	0.133832	+	0.347332i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−7.76096			−0.688674			−0.344337	−	0.938846i	$-0.611896\pi$
$127$	−7.76096			−0.688674			−0.344337	+	0.938846i	$0.611896\pi$
$128$		0			0
$129$	−7.12140	−	18.4821i	−0.627004	−	1.62726i
$130$		0			0
$131$	−8.58199	−	14.8644i	−0.749812	−	1.29871i	−0.947913	−	0.318530i	$-0.896811\pi$
$131$	−8.58199	−	14.8644i	−0.749812	−	1.29871i	0.198101	−	0.980182i	$-0.436523\pi$
$132$		0			0
$133$	−1.03266	+	0.978058i	−0.0895431	+	0.0848084i
$134$		0			0
$135$	−0.291594	−	5.18796i	−0.0250965	−	0.446509i
$136$		0			0
$137$	13.0137	+	7.51345i	1.11183	+	0.641918i	0.939304	−	0.343087i	$-0.111472\pi$
$137$	13.0137	+	7.51345i	1.11183	+	0.641918i	0.172530	+	0.985004i	$0.444806\pi$
$138$		0			0
$139$			9.83141i			0.833889i	0.908932	+	0.416945i	$0.136899\pi$
$139$			9.83141i			0.833889i	−0.908932	+	0.416945i	$0.863101\pi$
$140$		0			0
$141$	13.5651	−	16.7948i	1.14239	−	1.41438i
$142$		0			0
$143$	−0.256271	+	0.443875i	−0.0214305	+	0.0371187i
$144$		0			0
$145$	−0.231640	+	0.133737i	−0.0192367	+	0.0111063i
$146$		0			0
$147$	9.00466	+	8.11888i	0.742692	+	0.669634i
$148$		0			0
$149$	−19.9895	+	11.5409i	−1.63760	+	0.945469i	−0.655943	+	0.754810i	$0.727729\pi$
$149$	−19.9895	+	11.5409i	−1.63760	+	0.945469i	−0.981656	+	0.190658i	$0.938938\pi$
$150$		0			0
$151$	7.20527	−	12.4799i	0.586357	−	1.01560i	−0.408348	−	0.912826i	$-0.633895\pi$
$151$	7.20527	−	12.4799i	0.586357	−	1.01560i	0.994705	−	0.102774i	$-0.0327717\pi$
$152$		0			0
$153$	0.595343	+	2.76650i	0.0481306	+	0.223659i
$154$		0			0
$155$			1.13287i			0.0909945i
$156$		0			0
$157$	−1.90441	−	1.09951i	−0.151988	−	0.0877506i	0.422077	−	0.906560i	$-0.361301\pi$
$157$	−1.90441	−	1.09951i	−0.151988	−	0.0877506i	−0.574065	+	0.818809i	$0.694635\pi$
$158$		0			0
$159$	−3.36883	+	21.4452i	−0.267166	+	1.70071i
$160$		0			0
$161$	−5.32365	+	5.04216i	−0.419563	+	0.397378i
$162$		0			0
$163$	−4.92757	−	8.53481i	−0.385957	−	0.668498i	0.605944	−	0.795507i	$-0.292795\pi$
$163$	−4.92757	−	8.53481i	−0.385957	−	0.668498i	−0.991902	+	0.127009i	$0.959462\pi$
$164$		0			0
$165$	−3.37057	+	1.29872i	−0.262398	+	0.101106i
$166$		0			0
$167$	−22.8349			−1.76702			−0.883509	−	0.468415i	$-0.844825\pi$
$167$	−22.8349			−1.76702			−0.883509	+	0.468415i	$0.844825\pi$
$168$		0			0
$169$	12.9396			0.995354
$170$		0			0
$171$	0.494495	−	1.53508i	0.0378150	−	0.117390i
$172$		0			0
$173$	4.87085	+	8.43656i	0.370324	+	0.641420i	0.989615	−	0.143741i	$-0.0459133\pi$
$173$	4.87085	+	8.43656i	0.370324	+	0.641420i	−0.619291	+	0.785161i	$0.712580\pi$
$174$		0			0
$175$	−0.753894	+	2.53607i	−0.0569890	+	0.191709i
$176$		0			0
$177$	21.4047	+	3.36248i	1.60888	+	0.252739i
$178$		0			0
$179$	15.6543	+	9.03800i	1.17006	+	0.675532i	0.953693	−	0.300781i	$-0.0972473\pi$
$179$	15.6543	+	9.03800i	1.17006	+	0.675532i	0.216363	+	0.976313i	$0.430581\pi$
$180$		0			0
$181$			17.7230i			1.31734i	0.752433	+	0.658669i	$0.228880\pi$
$181$			17.7230i			1.31734i	−0.752433	+	0.658669i	$0.771120\pi$
$182$		0			0
$183$	7.72582	+	6.24011i	0.571109	+	0.461282i
$184$		0			0
$185$	−3.08164	+	5.33755i	−0.226566	+	0.392425i
$186$		0			0
$187$	1.70362	−	0.983585i	0.124581	−	0.0719269i
$188$		0			0
$189$	−13.3769	−	3.17167i	−0.973024	−	0.230705i
$190$		0			0
$191$	−19.0353	+	10.9901i	−1.37735	+	0.795212i	−0.991840	−	0.127492i	$-0.959307\pi$
$191$	−19.0353	+	10.9901i	−1.37735	+	0.795212i	−0.385508	+	0.922704i	$0.625974\pi$
$192$		0			0
$193$	4.48820	−	7.77378i	0.323067	−	0.559569i	−0.658052	−	0.752973i	$-0.728619\pi$
$193$	4.48820	−	7.77378i	0.323067	−	0.559569i	0.981119	+	0.193403i	$0.0619526\pi$
$194$		0			0
$195$	−0.331158	−	0.267475i	−0.0237147	−	0.0191543i
$196$		0			0
$197$			22.3002i			1.58882i	0.607382	+	0.794410i	$0.292220\pi$
$197$			22.3002i			1.58882i	−0.607382	+	0.794410i	$0.707780\pi$
$198$		0			0
$199$	16.3807	+	9.45740i	1.16120	+	0.670417i	0.951591	−	0.307368i	$-0.0994484\pi$
$199$	16.3807	+	9.45740i	1.16120	+	0.670417i	0.209606	+	0.977786i	$0.432782\pi$
$200$		0			0
$201$	9.51358	+	1.49449i	0.671036	+	0.105414i
$202$		0			0
$203$	0.164535	+	0.688279i	0.0115481	+	0.0483077i
$204$		0			0
$205$	1.19170	+	2.06408i	0.0832318	+	0.144162i
$206$		0			0
$207$	2.54926	−	7.91374i	0.177186	−	0.550043i
$208$		0			0
$209$	−1.12111			−0.0775490
$210$		0			0
$211$	20.4152			1.40544			0.702722	−	0.711465i	$-0.251968\pi$
$211$	20.4152			1.40544			0.702722	+	0.711465i	$0.251968\pi$
$212$		0			0
$213$	16.3845	−	6.31316i	1.12265	−	0.432571i
$214$		0			0
$215$	−5.71768	−	9.90331i	−0.389943	−	0.675400i
$216$		0			0
$217$	2.87304	+	0.854066i	0.195035	+	0.0579778i
$218$		0			0
$219$	3.53077	−	22.4760i	0.238588	−	1.51879i
$220$		0			0
$221$	0.200770	+	0.115915i	0.0135053	+	0.00779727i
$222$		0			0
$223$			13.5949i			0.910379i	0.890395	+	0.455189i	$0.150428\pi$
$223$			13.5949i			0.910379i	−0.890395	+	0.455189i	$0.849572\pi$
$224$		0			0
$225$	−0.631142	−	2.93286i	−0.0420761	−	0.195524i
$226$		0			0
$227$	−5.03260	+	8.71671i	−0.334025	+	0.578549i	−0.983297	−	0.182008i	$-0.941740\pi$
$227$	−5.03260	+	8.71671i	−0.334025	+	0.578549i	0.649272	+	0.760556i	$0.275074\pi$
$228$		0			0
$229$	12.3651	−	7.13897i	0.817106	−	0.471756i	−0.0323114	−	0.999478i	$-0.510287\pi$
$229$	12.3651	−	7.13897i	0.817106	−	0.471756i	0.849418	+	0.527721i	$0.176953\pi$
$230$		0			0
$231$	0.752603	+	9.52709i	0.0495176	+	0.626837i
$232$		0			0
$233$	−17.9716	+	10.3759i	−1.17736	+	0.679750i	−0.955403	−	0.295306i	$-0.904578\pi$
$233$	−17.9716	+	10.3759i	−1.17736	+	0.679750i	−0.221958	+	0.975056i	$0.571245\pi$
$234$		0			0
$235$	6.23215	−	10.7944i	0.406540	−	0.704149i
$236$		0			0
$237$	−6.90676	+	8.55118i	−0.448642	+	0.555459i
$238$		0			0
$239$			4.86422i			0.314640i	0.987548	+	0.157320i	$0.0502854\pi$
$239$			4.86422i			0.314640i	−0.987548	+	0.157320i	$0.949715\pi$
$240$		0			0
$241$	−14.9239	−	8.61634i	−0.961336	−	0.555028i	−0.0647520	−	0.997901i	$-0.520626\pi$
$241$	−14.9239	−	8.61634i	−0.961336	−	0.555028i	−0.896584	+	0.442874i	$0.853959\pi$
$242$		0			0
$243$	15.0315	−	4.12954i	0.964273	−	0.264910i
$244$		0			0
$245$	5.86329	+	3.82385i	0.374592	+	0.244297i
$246$		0			0
$247$	−0.0660611	−	0.114421i	−0.00420337	−	0.00728045i
$248$		0			0
$249$	−0.664314	−	1.72409i	−0.0420992	−	0.109260i
$250$		0			0
$251$	15.8276			0.999031			0.499516	−	0.866305i	$-0.333511\pi$
$251$	15.8276			0.999031			0.499516	+	0.866305i	$0.333511\pi$
$252$		0			0
$253$	−5.77964			−0.363363
$254$		0			0
$255$	0.587429	+	1.52455i	0.0367862	+	0.0954710i
$256$		0			0
$257$	−9.10800	−	15.7755i	−0.568141	−	0.984050i	−0.996750	−	0.0805593i	$-0.974329\pi$
$257$	−9.10800	−	15.7755i	−0.568141	−	0.984050i	0.428609	−	0.903490i	$-0.359004\pi$
$258$		0			0
$259$	11.2132	+	11.8392i	0.696752	+	0.735651i
$260$		0			0
$261$	−0.538431	−	0.594960i	−0.0333280	−	0.0368271i
$262$		0			0
$263$	4.55971	+	2.63255i	0.281164	+	0.162330i	0.633950	−	0.773374i	$-0.281432\pi$
$263$	4.55971	+	2.63255i	0.281164	+	0.162330i	−0.352786	+	0.935704i	$0.614766\pi$
$264$		0			0
$265$			12.5332i			0.769909i
$266$		0			0
$267$	−1.00949	+	1.24984i	−0.0617799	+	0.0764891i
$268$		0			0
$269$	−0.775418	+	1.34306i	−0.0472780	+	0.0818880i	−0.888696	−	0.458497i	$-0.848388\pi$
$269$	−0.775418	+	1.34306i	−0.0472780	+	0.0818880i	0.841418	+	0.540385i	$0.181721\pi$
$270$		0			0
$271$	−9.77676	+	5.64461i	−0.593896	+	0.342886i	−0.766636	−	0.642082i	$-0.778071\pi$
$271$	−9.77676	+	5.64461i	−0.593896	+	0.342886i	0.172741	+	0.984967i	$0.444738\pi$
$272$		0			0
$273$	−0.927992	+	0.638191i	−0.0561647	+	0.0386251i
$274$		0			0
$275$	−1.80606	+	1.04273i	−0.108910	+	0.0628790i
$276$		0			0
$277$	−8.54371	+	14.7981i	−0.513342	+	0.889134i	0.486538	+	0.873659i	$0.338259\pi$
$277$	−8.54371	+	14.7981i	−0.513342	+	0.889134i	−0.999880	+	0.0154751i	$0.995074\pi$
$278$		0			0
$279$	−3.32256	+	0.715003i	−0.198916	+	0.0428061i
$280$		0			0
$281$			15.2188i			0.907880i	0.891032	+	0.453940i	$0.149982\pi$
$281$			15.2188i			0.907880i	−0.891032	+	0.453940i	$0.850018\pi$
$282$		0			0
$283$	−14.2634	−	8.23500i	−0.847874	−	0.489520i	0.0120590	−	0.999927i	$-0.496161\pi$
$283$	−14.2634	−	8.23500i	−0.847874	−	0.489520i	−0.859933	+	0.510407i	$0.829495\pi$
$284$		0			0
$285$	0.144499	−	0.919845i	0.00855939	−	0.0544869i
$286$		0			0
$287$	6.13307	−	1.46613i	0.362023	−	0.0865429i
$288$		0			0
$289$	8.05511	+	13.9519i	0.473830	+	0.820698i
$290$		0			0
$291$	4.86879	−	1.87601i	0.285414	−	0.109974i
$292$		0			0
$293$	−18.1748			−1.06179			−0.530893	−	0.847439i	$-0.678143\pi$
$293$	−18.1748			−1.06179			−0.530893	+	0.847439i	$0.678143\pi$
$294$		0			0
$295$	12.5096			0.728335
$296$		0			0
$297$	−5.93628	−	9.06572i	−0.344458	−	0.526047i
$298$		0			0
$299$	−0.340563	−	0.589873i	−0.0196953	−	0.0341132i
$300$		0			0
$301$	−29.4260	+	7.03438i	−1.69609	+	0.405455i
$302$		0			0
$303$	21.1847	+	3.32792i	1.21703	+	0.191184i
$304$		0			0
$305$	4.96556	+	2.86687i	0.284327	+	0.164156i
$306$		0			0
$307$		−	24.6960i		−	1.40948i	−0.709468	−	0.704738i	$-0.751065\pi$
$307$		−	24.6960i		−	1.40948i	0.709468	−	0.704738i	$-0.248935\pi$
$308$		0			0
$309$	−22.6827	−	18.3208i	−1.29038	−	1.04223i
$310$		0			0
$311$	−11.5061	+	19.9291i	−0.652448	+	1.13007i	0.330079	+	0.943953i	$0.392925\pi$
$311$	−11.5061	+	19.9291i	−0.652448	+	1.13007i	−0.982527	+	0.186120i	$0.940409\pi$
$312$		0			0
$313$	2.73490	−	1.57900i	0.154586	−	0.0892502i	−0.420712	−	0.907194i	$-0.638220\pi$
$313$	2.73490	−	1.57900i	0.154586	−	0.0892502i	0.575298	+	0.817944i	$0.304886\pi$
$314$		0			0
$315$	−7.91374	−	0.610446i	−0.445889	−	0.0343947i
$316$		0			0
$317$	2.78696	−	1.60905i	0.156531	−	0.0903734i	−0.419688	−	0.907668i	$-0.637861\pi$
$317$	2.78696	−	1.60905i	0.156531	−	0.0903734i	0.576220	+	0.817295i	$0.304527\pi$
$318$		0			0
$319$	−0.278904	+	0.483076i	−0.0156156	+	0.0270471i
$320$		0			0
$321$	17.2750	+	13.9530i	0.964199	+	0.778780i
$322$		0			0
$323$			0.507093i			0.0282154i
$324$		0			0
$325$	−0.212843	−	0.122885i	−0.0118064	−	0.00681643i
$326$		0			0
$327$	6.14095	+	0.964686i	0.339595	+	0.0533472i
$328$		0			0
$329$	−22.6770	−	23.9430i	−1.25022	−	1.32002i
$330$		0			0
$331$	−14.0918	−	24.4077i	−0.774554	−	1.34157i	−0.935045	−	0.354529i	$-0.884641\pi$
$331$	−14.0918	−	24.4077i	−0.774554	−	1.34157i	0.160491	−	0.987037i	$-0.448692\pi$
$332$		0			0
$333$	−17.5992	−	5.66925i	−0.964432	−	0.310673i
$334$		0			0
$335$	5.56003			0.303777
$336$		0			0
$337$	−18.4497			−1.00502			−0.502510	−	0.864571i	$-0.667590\pi$
$337$	−18.4497			−1.00502			−0.502510	+	0.864571i	$0.667590\pi$
$338$		0			0
$339$	−1.62193	+	0.624950i	−0.0880910	+	0.0339426i
$340$		0			0
$341$	1.18128	+	2.04604i	0.0639699	+	0.110799i
$342$		0			0
$343$	14.1178	−	11.9869i	0.762292	−	0.647233i
$344$		0			0
$345$	0.744932	−	4.74205i	0.0401058	−	0.255304i
$346$		0			0
$347$	−13.3367	−	7.69997i	−0.715953	−	0.413356i	0.0973081	−	0.995254i	$-0.468977\pi$
$347$	−13.3367	−	7.69997i	−0.715953	−	0.413356i	−0.813261	+	0.581898i	$0.802310\pi$
$348$		0			0
$349$		−	21.9727i		−	1.17617i	−0.808799	−	0.588086i	$-0.799882\pi$
$349$		−	21.9727i		−	1.17617i	0.808799	−	0.588086i	$-0.200118\pi$
$350$		0			0
$351$	0.575458	−	1.14005i	0.0307157	−	0.0608516i
$352$		0			0
$353$	8.66505	−	15.0083i	0.461194	−	0.798811i	−0.537827	−	0.843055i	$-0.680755\pi$
$353$	8.66505	−	15.0083i	0.461194	−	0.798811i	0.999021	+	0.0442440i	$0.0140879\pi$
$354$		0			0
$355$	8.77935	−	5.06876i	0.465959	−	0.269022i
$356$		0			0
$357$	4.30922	−	0.340412i	0.228068	−	0.0180165i
$358$		0			0
$359$	−0.270990	+	0.156456i	−0.0143023	+	0.00825745i	−0.507134	−	0.861867i	$-0.669295\pi$
$359$	−0.270990	+	0.156456i	−0.0143023	+	0.00825745i	0.492832	+	0.870125i	$0.335962\pi$
$360$		0			0
$361$	−9.35550	+	16.2042i	−0.492395	+	0.852853i
$362$		0			0
$363$	7.23823	−	8.96158i	0.379909	−	0.470361i
$364$		0			0
$365$		−	13.1357i		−	0.687553i
$366$		0			0
$367$	3.20094	+	1.84807i	0.167088	+	0.0964682i	0.581212	−	0.813752i	$-0.302579\pi$
$367$	3.20094	+	1.84807i	0.167088	+	0.0964682i	−0.414124	+	0.910220i	$0.635912\pi$
$368$		0			0
$369$	−5.30153	+	4.79781i	−0.275987	+	0.249764i
$370$		0			0
$371$	31.7851	+	9.44871i	1.65020	+	0.490552i
$372$		0			0
$373$	0.351666	+	0.609103i	0.0182086	+	0.0315381i	0.874986	−	0.484148i	$-0.160870\pi$
$373$	0.351666	+	0.609103i	0.0182086	+	0.0315381i	−0.856778	+	0.515686i	$0.827537\pi$
$374$		0			0
$375$	−0.622752	−	1.61622i	−0.0321588	−	0.0834614i
$376$		0			0
$377$	−0.0657372			−0.00338564
$378$		0			0
$379$	−10.3929			−0.533849			−0.266924	−	0.963717i	$-0.586007\pi$
$379$	−10.3929			−0.533849			−0.266924	+	0.963717i	$0.586007\pi$
$380$		0			0
$381$	−4.83316	−	12.5435i	−0.247610	−	0.642621i
$382$		0			0
$383$	−14.7524	−	25.5519i	−0.753813	−	1.30564i	−0.945963	−	0.324276i	$-0.894879\pi$
$383$	−14.7524	−	25.5519i	−0.753813	−	1.30564i	0.192150	−	0.981366i	$-0.438454\pi$
$384$		0			0
$385$	1.28286	+	5.36640i	0.0653804	+	0.273497i
$386$		0			0
$387$	25.4364	−	23.0195i	1.29300	−	1.17015i
$388$		0			0
$389$	11.5224	+	6.65245i	0.584208	+	0.337293i	0.762804	−	0.646630i	$-0.223822\pi$
$389$	11.5224	+	6.65245i	0.584208	+	0.337293i	−0.178596	+	0.983923i	$0.557155\pi$
$390$		0			0
$391$			2.61420i			0.132206i
$392$		0			0
$393$	18.6798	−	23.1273i	0.942271	−	1.16662i
$394$		0			0
$395$	−3.17314	+	5.49605i	−0.159658	+	0.276536i
$396$		0			0
$397$	−3.82832	+	2.21028i	−0.192138	+	0.110931i	−0.592983	−	0.805215i	$-0.702050\pi$
$397$	−3.82832	+	2.21028i	−0.192138	+	0.110931i	0.400845	+	0.916146i	$0.368717\pi$
$398$		0			0
$399$	−2.22385	−	1.05992i	−0.111332	−	0.0530626i
$400$		0			0
$401$	−25.4507	+	14.6940i	−1.27095	+	0.733781i	−0.975166	−	0.221475i	$-0.928913\pi$
$401$	−25.4507	+	14.6940i	−1.27095	+	0.733781i	−0.295780	+	0.955256i	$0.595580\pi$
$402$		0			0
$403$	−0.139213	+	0.241124i	−0.00693469	+	0.0120112i
$404$		0			0
$405$	8.20332	−	3.70210i	0.407626	−	0.183959i
$406$		0			0
$407$			12.8533i			0.637112i
$408$		0			0
$409$	6.67308	+	3.85270i	0.329962	+	0.190504i	0.655824	−	0.754913i	$-0.272321\pi$
$409$	6.67308	+	3.85270i	0.329962	+	0.190504i	−0.325862	+	0.945417i	$0.605654\pi$
$410$		0			0
$411$	−4.03912	+	25.7120i	−0.199235	+	1.26828i
$412$		0			0
$413$	9.43088	−	31.7251i	0.464063	−	1.56109i
$414$		0			0
$415$	−0.533370	−	0.923823i	−0.0261821	−	0.0453487i
$416$		0			0
$417$	−15.8898	+	6.12253i	−0.778125	+	0.299822i
$418$		0			0
$419$	1.40692			0.0687327			0.0343663	−	0.999409i	$-0.489059\pi$
$419$	1.40692			0.0687327			0.0343663	+	0.999409i	$0.489059\pi$
$420$		0			0
$421$	−7.23785			−0.352751			−0.176375	−	0.984323i	$-0.556437\pi$
$421$	−7.23785			−0.352751			−0.176375	+	0.984323i	$0.556437\pi$
$422$		0			0
$423$	35.5918	+	11.4652i	1.73053	+	0.557458i
$424$		0			0
$425$	0.471640	+	0.816904i	0.0228779	+	0.0396256i
$426$		0			0
$427$	11.0141	−	10.4317i	0.533009	−	0.504825i
$428$		0			0
$429$	−0.876995	−	0.137768i	−0.0423417	−	0.00665149i
$430$		0			0
$431$	9.16199	+	5.28968i	0.441317	+	0.254795i	0.704156	−	0.710045i	$-0.251325\pi$
$431$	9.16199	+	5.28968i	0.441317	+	0.254795i	−0.262839	+	0.964840i	$0.584659\pi$
$432$		0			0
$433$		−	23.7164i		−	1.13974i	−0.821735	−	0.569869i	$-0.806994\pi$
$433$		−	23.7164i		−	1.13974i	0.821735	−	0.569869i	$-0.193006\pi$
$434$		0			0
$435$	−0.360404	−	0.291097i	−0.0172800	−	0.0139570i
$436$		0			0
$437$	0.744932	−	1.29026i	0.0356349	−	0.0617215i
$438$		0			0
$439$	−17.6684	+	10.2009i	−0.843268	+	0.486861i	−0.858374	−	0.513025i	$-0.828525\pi$
$439$	−17.6684	+	10.2009i	−0.843268	+	0.486861i	0.0151058	+	0.999886i	$0.495191\pi$
$440$		0			0
$441$	−7.51425	+	19.6096i	−0.357822	+	0.933790i
$442$		0			0
$443$	0.475830	−	0.274720i	0.0226074	−	0.0130524i	−0.488654	−	0.872478i	$-0.662512\pi$
$443$	0.475830	−	0.274720i	0.0226074	−	0.0130524i	0.511261	+	0.859425i	$0.329179\pi$
$444$		0			0
$445$	−0.463787	+	0.803302i	−0.0219856	+	0.0380802i
$446$		0			0
$447$	−31.1012	−	25.1203i	−1.47104	−	1.18815i
$448$		0			0
$449$			1.12469i			0.0530772i	0.999648	+	0.0265386i	$0.00844850\pi$
$449$			1.12469i			0.0530772i	−0.999648	+	0.0265386i	$0.991552\pi$
$450$		0			0
$451$	4.30456	+	2.48524i	0.202694	+	0.117025i
$452$		0			0
$453$	24.6574	+	3.87345i	1.15851	+	0.181991i
$454$		0			0
$455$	−0.472105	+	0.447142i	−0.0221326	+	0.0209623i
$456$		0			0
$457$	14.6946	+	25.4518i	0.687385	+	1.19059i	0.972681	+	0.232146i	$0.0745748\pi$
$457$	14.6946	+	25.4518i	0.687385	+	1.19059i	−0.285296	+	0.958439i	$0.592092\pi$
$458$		0			0
$459$	−4.10054	+	2.68505i	−0.191397	+	0.125328i
$460$		0			0
$461$	29.9734			1.39600			0.697999	−	0.716098i	$-0.254074\pi$
$461$	29.9734			1.39600			0.697999	+	0.716098i	$0.254074\pi$
$462$		0			0
$463$	13.0355			0.605809			0.302905	−	0.953021i	$-0.402044\pi$
$463$	13.0355			0.605809			0.302905	+	0.953021i	$0.402044\pi$
$464$		0			0
$465$	−1.83098	+	0.705499i	−0.0849095	+	0.0327167i
$466$		0			0
$467$	−1.21626	−	2.10662i	−0.0562817	−	0.0974828i	0.836512	−	0.547949i	$-0.184591\pi$
$467$	−1.21626	−	2.10662i	−0.0562817	−	0.0974828i	−0.892794	+	0.450466i	$0.851258\pi$
$468$		0			0
$469$	4.19167	−	14.1006i	0.193553	−	0.651105i
$470$		0			0
$471$	0.591082	−	3.76268i	0.0272356	−	0.173375i
$472$		0			0
$473$	−20.6530	−	11.9240i	−0.949624	−	0.548266i
$474$		0			0
$475$		−	0.537585i		−	0.0246661i
$476$		0			0
$477$	−36.7581	+	7.91023i	−1.68304	+	0.362184i
$478$		0			0
$479$	−5.49101	+	9.51071i	−0.250891	+	0.434555i	−0.963771	−	0.266730i	$-0.914057\pi$
$479$	−5.49101	+	9.51071i	−0.250891	+	0.434555i	0.712881	+	0.701285i	$0.247390\pi$
$480$		0			0
$481$	−1.31181	+	0.757373i	−0.0598133	+	0.0345332i
$482$		0			0
$483$	−11.4646	−	5.46420i	−0.521656	−	0.248630i
$484$		0			0
$485$	2.60886	−	1.50622i	0.118462	−	0.0683941i
$486$		0			0
$487$	−13.4393	+	23.2776i	−0.608993	+	1.05481i	0.382414	+	0.923991i	$0.375093\pi$
$487$	−13.4393	+	23.2776i	−0.608993	+	1.05481i	−0.991407	+	0.130816i	$0.958240\pi$
$488$		0			0
$489$	10.7255	−	13.2791i	0.485024	−	0.600503i
$490$		0			0
$491$		−	25.1295i		−	1.13408i	−0.823692	−	0.567038i	$-0.808089\pi$
$491$		−	25.1295i		−	1.13408i	0.823692	−	0.567038i	$-0.191911\pi$
$492$		0			0
$493$	0.218501	+	0.126152i	0.00984080	+	0.00568159i
$494$		0			0
$495$	−4.19806	−	4.63881i	−0.188689	−	0.208499i
$496$		0			0
$497$	−6.23602	−	26.0863i	−0.279724	−	1.17013i
$498$		0			0
$499$	−2.58341	−	4.47460i	−0.115649	−	0.200311i	0.802390	−	0.596800i	$-0.203562\pi$
$499$	−2.58341	−	4.47460i	−0.115649	−	0.200311i	−0.918039	+	0.396490i	$0.870228\pi$
$500$		0			0
$501$	−14.2205	−	36.9063i	−0.635324	−	1.64885i
$502$		0			0
$503$	42.2496			1.88382			0.941908	−	0.335872i	$-0.109031\pi$
$503$	42.2496			1.88382			0.941908	+	0.335872i	$0.109031\pi$
$504$		0			0
$505$	12.3810			0.550947
$506$		0			0
$507$	8.05816	+	20.9133i	0.357876	+	0.928792i
$508$		0			0
$509$	3.76320	+	6.51806i	0.166801	+	0.288908i	0.937293	−	0.348541i	$-0.113323\pi$
$509$	3.76320	+	6.51806i	0.166801	+	0.288908i	−0.770492	+	0.637449i	$0.779990\pi$
$510$		0			0
$511$	−33.3130	−	9.90290i	−1.47368	−	0.438079i
$512$		0			0
$513$	2.78897	−	0.156757i	0.123136	−	0.00692099i
$514$		0			0
$515$	−14.5787	−	8.41703i	−0.642415	−	0.370899i
$516$		0			0
$517$		−	25.9938i		−	1.14320i
$518$		0			0
$519$	−10.6020	+	13.1263i	−0.465378	+	0.576180i
$520$		0			0
$521$	−10.1668	+	17.6095i	−0.445417	+	0.771484i	−0.998081	−	0.0619196i	$-0.980278\pi$
$521$	−10.1668	+	17.6095i	−0.445417	+	0.771484i	0.552665	+	0.833404i	$0.313611\pi$
$522$		0			0
$523$	3.14832	−	1.81768i	0.137666	−	0.0794818i	−0.429585	−	0.903026i	$-0.641340\pi$
$523$	3.14832	−	1.81768i	0.137666	−	0.0794818i	0.567251	+	0.823545i	$0.308007\pi$
$524$		0			0
$525$	−4.56834	+	0.360881i	−0.199379	+	0.0157501i
$526$		0			0
$527$	0.925448	−	0.534308i	0.0403131	−	0.0232748i
$528$		0			0
$529$	−7.65967	+	13.2669i	−0.333029	+	0.576823i
$530$		0			0
$531$	7.89530	+	36.6888i	0.342627	+	1.59216i
$532$		0			0
$533$			0.585766i			0.0253724i
$534$		0			0
$535$	11.1031	+	6.41036i	0.480028	+	0.277144i
$536$		0			0
$537$	−4.85870	+	30.9293i	−0.209668	+	1.33470i
$538$		0			0
$539$	14.5767	+	0.792285i	0.627863	+	0.0341261i
$540$		0			0
$541$	−9.20758	−	15.9480i	−0.395865	−	0.685658i	0.597346	−	0.801983i	$-0.296222\pi$
$541$	−9.20758	−	15.9480i	−0.395865	−	0.685658i	−0.993211	+	0.116325i	$0.962888\pi$
$542$		0			0
$543$	−28.6443	+	11.0370i	−1.22924	+	0.473644i
$544$		0			0
$545$	3.58896			0.153734
$546$		0			0
$547$	−22.6376			−0.967915			−0.483957	−	0.875092i	$-0.660801\pi$
$547$	−22.6376			−0.967915			−0.483957	+	0.875092i	$0.660801\pi$
$548$		0			0
$549$	−5.27415	+	16.3727i	−0.225095	+	0.698770i
$550$		0			0
$551$	−0.0718953	−	0.124526i	−0.00306284	−	0.00530500i
$552$		0			0
$553$	11.5461	+	12.1907i	0.490992	+	0.518403i
$554$		0			0
$555$	−10.5458	−	1.65664i	−0.447643	−	0.0703206i
$556$		0			0
$557$	33.9272	+	19.5879i	1.43754	+	0.829965i	0.997679	−	0.0680994i	$-0.0216935\pi$
$557$	33.9272	+	19.5879i	1.43754	+	0.829965i	0.439863	+	0.898065i	$0.355027\pi$
$558$		0			0
$559$		−	2.81047i		−	0.118870i
$560$		0			0
$561$	2.65063	+	2.14090i	0.111910	+	0.0903889i
$562$		0			0
$563$	−1.82483	+	3.16069i	−0.0769073	+	0.133207i	−0.901914	−	0.431915i	$-0.857838\pi$
$563$	−1.82483	+	3.16069i	−0.0769073	+	0.133207i	0.825007	+	0.565123i	$0.191171\pi$
$564$		0			0
$565$	−0.869081	+	0.501764i	−0.0365625	+	0.0211094i
$566$		0			0
$567$	−3.20434	−	23.5952i	−0.134570	−	0.990904i
$568$		0			0
$569$	17.1456	−	9.89902i	0.718781	−	0.414988i	−0.0955229	−	0.995427i	$-0.530452\pi$
$569$	17.1456	−	9.89902i	0.718781	−	0.414988i	0.814304	+	0.580439i	$0.197119\pi$
$570$		0			0
$571$	−18.7342	+	32.4487i	−0.784004	+	1.35793i	0.145589	+	0.989345i	$0.453492\pi$
$571$	−18.7342	+	32.4487i	−0.784004	+	1.35793i	−0.929592	+	0.368589i	$0.879841\pi$
$572$		0			0
$573$	−29.6167	−	23.9213i	−1.23725	−	0.999326i
$574$		0			0
$575$		−	2.77140i		−	0.115575i
$576$		0			0
$577$	22.1156	+	12.7684i	0.920685	+	0.531558i	0.883853	−	0.467764i	$-0.154940\pi$
$577$	22.1156	+	12.7684i	0.920685	+	0.531558i	0.0368312	+	0.999322i	$0.488274\pi$
$578$		0			0
$579$	15.3592	+	2.41279i	0.638307	+	0.100272i
$580$		0			0
$581$	−2.74498	+	0.656198i	−0.113881	+	0.0272237i
$582$		0			0
$583$	13.0687	+	22.6357i	0.541252	+	0.937476i
$584$		0			0
$585$	0.226070	−	0.701796i	0.00934684	−	0.0290157i
$586$		0			0
$587$	7.57204			0.312531			0.156266	−	0.987715i	$-0.450054\pi$
$587$	7.57204			0.312531			0.156266	+	0.987715i	$0.450054\pi$
$588$		0			0
$589$	−0.609016			−0.0250941
$590$		0			0
$591$	−36.0420	+	13.8875i	−1.48257	+	0.571254i
$592$		0			0
$593$	1.58920	+	2.75258i	0.0652606	+	0.113035i	0.896810	−	0.442417i	$-0.145879\pi$
$593$	1.58920	+	2.75258i	0.0652606	+	0.113035i	−0.831549	+	0.555452i	$0.812545\pi$
$594$		0			0
$595$	2.42729	−	0.580252i	0.0995092	−	0.0237880i
$596$		0			0
$597$	−5.08416	+	32.3645i	−0.208081	+	1.32459i
$598$		0			0
$599$	−23.5750	−	13.6110i	−0.963247	−	0.556131i	−0.0660761	−	0.997815i	$-0.521048\pi$
$599$	−23.5750	−	13.6110i	−0.963247	−	0.556131i	−0.897171	+	0.441684i	$0.854381\pi$
$600$		0			0
$601$		−	13.1953i		−	0.538247i	−0.963106	−	0.269123i	$-0.913266\pi$
$601$		−	13.1953i		−	0.538247i	0.963106	−	0.269123i	$-0.0867340\pi$
$602$		0			0
$603$	3.50916	+	16.3068i	0.142904	+	0.664063i
$604$		0			0
$605$	3.32543	−	5.75981i	0.135198	−	0.234170i
$606$		0			0
$607$	−6.66879	+	3.85023i	−0.270678	+	0.156276i	−0.629196	−	0.777247i	$-0.716616\pi$
$607$	−6.66879	+	3.85023i	−0.270678	+	0.156276i	0.358518	+	0.933523i	$0.383282\pi$
$608$		0			0
$609$	−1.00995	+	0.694553i	−0.0409252	+	0.0281447i
$610$		0			0
$611$	2.65294	−	1.53167i	0.107326	−	0.0619649i
$612$		0			0
$613$	14.4287	−	24.9912i	0.582769	−	1.00939i	−0.412381	−	0.911012i	$-0.635303\pi$
$613$	14.4287	−	24.9912i	0.582769	−	1.00939i	0.995150	−	0.0983735i	$-0.0313640\pi$
$614$		0			0
$615$	−2.59388	+	3.21146i	−0.104596	+	0.129499i
$616$		0			0
$617$			31.5272i			1.26924i	0.772825	+	0.634619i	$0.218843\pi$
$617$			31.5272i			1.26924i	−0.772825	+	0.634619i	$0.781157\pi$
$618$		0			0
$619$	25.4695	+	14.7048i	1.02370	+	0.591036i	0.915175	−	0.403057i	$-0.132052\pi$
$619$	25.4695	+	14.7048i	1.02370	+	0.591036i	0.108530	+	0.994093i	$0.465386\pi$
$620$		0			0
$621$	14.3779	−	0.808125i	0.576966	−	0.0324289i
$622$		0			0
$623$	1.68758	+	1.78180i	0.0676116	+	0.0713863i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−0.698175	−	1.81197i	−0.0278824	−	0.0723631i
$628$		0			0
$629$	5.81369			0.231807
$630$		0			0
$631$	29.9987			1.19423			0.597115	−	0.802155i	$-0.296313\pi$
$631$	29.9987			1.19423			0.597115	+	0.802155i	$0.296313\pi$
$632$		0			0
$633$	12.7136	+	32.9956i	0.505322	+	1.31146i
$634$		0			0
$635$	−3.88048	−	6.72119i	−0.153992	−	0.266722i
$636$		0			0
$637$	0.778065	+	1.53439i	0.0308281	+	0.0607947i
$638$		0			0
$639$	20.4070	+	22.5495i	0.807287	+	0.892044i
$640$		0			0
$641$	−27.8245	−	16.0645i	−1.09900	−	0.634510i	−0.163044	−	0.986619i	$-0.552131\pi$
$641$	−27.8245	−	16.0645i	−1.09900	−	0.634510i	−0.935959	+	0.352109i	$0.885465\pi$
$642$		0			0
$643$			5.88352i			0.232024i	0.993248	+	0.116012i	$0.0370110\pi$
$643$			5.88352i			0.232024i	−0.993248	+	0.116012i	$0.962989\pi$
$644$		0			0
$645$	12.4453	−	15.4084i	0.490032	−	0.606704i
$646$		0			0
$647$	−9.99202	+	17.3067i	−0.392827	+	0.680396i	−0.992821	−	0.119608i	$-0.961836\pi$
$647$	−9.99202	+	17.3067i	−0.392827	+	0.680396i	0.599994	+	0.800004i	$0.295170\pi$
$648$		0			0
$649$	22.5930	−	13.0441i	0.886854	−	0.512025i
$650$		0			0
$651$	0.408832	+	5.17535i	0.0160234	+	0.202838i
$652$		0			0
$653$	2.19720	−	1.26856i	0.0859832	−	0.0496424i	−0.456392	−	0.889779i	$-0.650858\pi$
$653$	2.19720	−	1.26856i	0.0859832	−	0.0496424i	0.542375	+	0.840136i	$0.317525\pi$
$654$		0			0
$655$	8.58199	−	14.8644i	0.335326	−	0.580802i
$656$		0			0
$657$	38.5251	−	8.29047i	1.50301	−	0.323442i
$658$		0			0
$659$			28.5964i			1.11396i	0.830526	+	0.556979i	$0.188040\pi$
$659$			28.5964i			1.11396i	−0.830526	+	0.556979i	$0.811960\pi$
$660$		0			0
$661$	25.4569	+	14.6975i	0.990158	+	0.571668i	0.905321	−	0.424727i	$-0.139630\pi$
$661$	25.4569	+	14.6975i	0.990158	+	0.571668i	0.0848363	+	0.996395i	$0.472963\pi$
$662$		0			0
$663$	−0.0623141	+	0.396676i	−0.00242008	+	0.0154056i
$664$		0			0
$665$	−1.36335	−	0.405282i	−0.0528686	−	0.0157162i
$666$		0			0
$667$	−0.370640	−	0.641967i	−0.0143512	−	0.0248571i
$668$		0			0
$669$	−21.9723	+	8.46623i	−0.849499	+	0.327323i
$670$		0			0
$671$	11.9575			0.461613
$672$		0			0
$673$	−18.1428			−0.699354			−0.349677	−	0.936870i	$-0.613709\pi$
$673$	−18.1428			−0.699354			−0.349677	+	0.936870i	$0.613709\pi$
$674$		0			0
$675$	4.34711	−	2.84651i	0.167320	−	0.109562i
$676$		0			0
$677$	19.2622	+	33.3630i	0.740305	+	1.28225i	0.952356	+	0.304987i	$0.0986523\pi$
$677$	19.2622	+	33.3630i	0.740305	+	1.28225i	−0.212051	+	0.977259i	$0.568014\pi$
$678$		0			0
$679$	−1.85309	−	7.75178i	−0.0711150	−	0.297486i
$680$		0			0
$681$	−17.2222	−	2.70545i	−0.659957	−	0.103673i
$682$		0			0
$683$	8.24278	+	4.75897i	0.315401	+	0.182097i	0.649341	−	0.760497i	$-0.275045\pi$
$683$	8.24278	+	4.75897i	0.315401	+	0.182097i	−0.333940	+	0.942594i	$0.608378\pi$
$684$		0			0
$685$			15.0269i			0.574149i
$686$		0			0
$687$	19.2385	+	15.5389i	0.733996	+	0.592846i
$688$		0			0
$689$	−1.54014	+	2.66760i	−0.0586747	+	0.101628i
$690$		0			0
$691$	36.4810	−	21.0623i	1.38780	−	0.801248i	0.394734	−	0.918795i	$-0.370837\pi$
$691$	36.4810	−	21.0623i	1.38780	−	0.801248i	0.993067	+	0.117548i	$0.0375033\pi$
$692$		0			0
$693$	−14.9292	+	7.14939i	−0.567115	+	0.271583i
$694$		0			0
$695$	−8.51425	+	4.91570i	−0.322964	+	0.186463i
$696$		0			0
$697$	1.12410	−	1.94700i	0.0425785	−	0.0737481i
$698$		0			0
$699$	−27.9617	−	22.5846i	−1.05761	−	0.854226i
$700$		0			0
$701$		−	20.1103i		−	0.759555i	−0.925078	−	0.379778i	$-0.876001\pi$
$701$		−	20.1103i		−	0.759555i	0.925078	−	0.379778i	$-0.123999\pi$
$702$		0			0
$703$	−2.86939	−	1.65664i	−0.108221	−	0.0624815i
$704$		0			0
$705$	21.3272	+	3.35031i	0.803230	+	0.126180i
$706$		0			0
$707$	9.33395	−	31.3990i	0.351039	−	1.18088i
$708$		0			0
$709$	12.6523	+	21.9145i	0.475168	+	0.823015i	0.999596	−	0.0284398i	$-0.00905390\pi$
$709$	12.6523	+	21.9145i	0.475168	+	0.823015i	−0.524427	+	0.851455i	$0.675721\pi$
$710$		0			0
$711$	−18.1218	−	5.83760i	−0.679622	−	0.218927i
$712$		0			0
$713$	−3.13964			−0.117581
$714$		0			0
$715$	−0.512543			−0.0191680
$716$		0			0
$717$	−7.86166	+	3.02920i	−0.293599	+	0.113128i
$718$		0			0
$719$	−7.70568	−	13.3466i	−0.287373	−	0.497745i	0.685809	−	0.727782i	$-0.259449\pi$
$719$	−7.70568	−	13.3466i	−0.287373	−	0.497745i	−0.973182	+	0.230037i	$0.926115\pi$
$720$		0			0
$721$	−32.3370	+	30.6271i	−1.20429	+	1.14061i
$722$		0			0
$723$	4.63202	−	29.4863i	0.172267	−	1.09661i
$724$		0			0
$725$	−0.231640	−	0.133737i	−0.00860289	−	0.00496688i
$726$		0			0
$727$		−	17.2053i		−	0.638109i	−0.947736	−	0.319054i	$-0.896635\pi$
$727$		−	17.2053i		−	0.638109i	0.947736	−	0.319054i	$-0.103365\pi$
$728$		0			0
$729$	16.0352	+	21.7226i	0.593896	+	0.804542i
$730$		0			0
$731$	−5.39337	+	9.34159i	−0.199481	+	0.345511i
$732$		0			0
$733$	−4.21946	+	2.43611i	−0.155849	+	0.0899797i	−0.575896	−	0.817523i	$-0.695347\pi$
$733$	−4.21946	+	2.43611i	−0.155849	+	0.0899797i	0.420047	+	0.907502i	$0.362014\pi$
$734$		0			0
$735$	−2.52883	+	11.8577i	−0.0932772	+	0.437378i
$736$		0			0
$737$	10.0417	−	5.79760i	0.369892	−	0.213557i
$738$		0			0
$739$	−11.2489	+	19.4836i	−0.413796	+	0.716716i	−0.995301	−	0.0968269i	$-0.969131\pi$
$739$	−11.2489	+	19.4836i	−0.413796	+	0.716716i	0.581505	+	0.813543i	$0.302464\pi$
$740$		0			0
$741$	0.143791	−	0.178026i	0.00528228	−	0.00653993i
$742$		0			0
$743$			5.74923i			0.210919i	0.994424	+	0.105459i	$0.0336313\pi$
$743$			5.74923i			0.210919i	−0.994424	+	0.105459i	$0.966369\pi$
$744$		0			0
$745$	−19.9895	−	11.5409i	−0.732357	−	0.422826i
$746$		0			0
$747$	2.37281	−	2.14736i	0.0868167	−	0.0785678i
$748$		0			0
$749$	24.6277	−	23.3254i	0.899875	−	0.852292i
$750$		0			0
$751$	−13.4867	−	23.3597i	−0.492138	−	0.852409i	0.507821	−	0.861463i	$-0.330451\pi$
$751$	−13.4867	−	23.3597i	−0.492138	−	0.852409i	−0.999959	+	0.00905407i	$0.997118\pi$
$752$		0			0
$753$	9.85669	+	25.5810i	0.359198	+	0.932223i
$754$		0			0
$755$	14.4105			0.524454
$756$		0			0
$757$	−3.74640			−0.136165			−0.0680826	−	0.997680i	$-0.521688\pi$
$757$	−3.74640			−0.136165			−0.0680826	+	0.997680i	$0.521688\pi$
$758$		0			0
$759$	−3.59929	−	9.34120i	−0.130646	−	0.339064i
$760$		0			0
$761$	−9.03998	−	15.6577i	−0.327699	−	0.567591i	0.654356	−	0.756187i	$-0.272940\pi$
$761$	−9.03998	−	15.6577i	−0.327699	−	0.567591i	−0.982055	+	0.188595i	$0.939607\pi$
$762$		0			0
$763$	2.70569	−	9.10184i	0.0979527	−	0.329509i
$764$		0			0
$765$	−2.09819	+	1.89883i	−0.0758603	+	0.0686525i
$766$		0			0
$767$	2.66257	+	1.53724i	0.0961398	+	0.0555064i
$768$		0			0
$769$		−	25.1297i		−	0.906199i	−0.891460	−	0.453100i	$-0.850318\pi$
$769$		−	25.1297i		−	0.906199i	0.891460	−	0.453100i	$-0.149682\pi$
$770$		0			0
$771$	19.8247	−	24.5448i	0.713971	−	0.883959i
$772$		0			0
$773$	−16.3082	+	28.2467i	−0.586567	+	1.01596i	0.408112	+	0.912932i	$0.366187\pi$
$773$	−16.3082	+	28.2467i	−0.586567	+	1.01596i	−0.994678	+	0.103031i	$0.967146\pi$
$774$		0			0
$775$	−0.981097	+	0.566436i	−0.0352420	+	0.0203470i
$776$		0			0
$777$	−12.1518	+	25.4959i	−0.435942	+	0.914659i
$778$		0			0
$779$	−1.10962	+	0.640639i	−0.0397563	+	0.0229533i
$780$		0			0
$781$	10.5707	−	18.3090i	0.378249	−	0.655146i
$782$		0			0
$783$	0.626280	−	1.24074i	0.0223814	−	0.0443403i
$784$		0			0
$785$		−	2.19902i		−	0.0784865i
$786$		0			0
$787$	3.98518	+	2.30085i	0.142056	+	0.0820164i	0.569344	−	0.822100i	$-0.307197\pi$
$787$	3.98518	+	2.30085i	0.142056	+	0.0820164i	−0.427287	+	0.904116i	$0.640531\pi$
$788$		0			0
$789$	−1.41522	+	9.00894i	−0.0503832	+	0.320727i
$790$		0			0
$791$	0.617314	+	2.58233i	0.0219492	+	0.0918170i
$792$		0			0
$793$	0.704590	+	1.22038i	0.0250207	+	0.0433371i
$794$		0			0
$795$	−20.2565	+	7.80508i	−0.718423	+	0.276818i
$796$		0			0
$797$	−13.3722			−0.473666			−0.236833	−	0.971550i	$-0.576109\pi$
$797$	−13.3722			−0.473666			−0.236833	+	0.971550i	$0.576109\pi$
$798$		0			0
$799$	−11.7573			−0.415944
$800$		0			0
$801$	−2.64869	−	0.853224i	−0.0935868	−	0.0301472i
$802$		0			0
$803$	−13.6970	−	23.7238i	−0.483355	−	0.837196i
$804$		0			0
$805$	−7.02846	−	2.08934i	−0.247721	−	0.0736396i
$806$		0			0
$807$	−2.65358	−	0.416853i	−0.0934105	−	0.0146739i
$808$		0			0
$809$	20.3694	+	11.7603i	0.716152	+	0.413470i	0.813335	−	0.581796i	$-0.197650\pi$
$809$	20.3694	+	11.7603i	0.716152	+	0.413470i	−0.0971830	+	0.995267i	$0.530983\pi$
$810$		0			0
$811$			25.5058i			0.895628i	0.894127	+	0.447814i	$0.147797\pi$
$811$			25.5058i			0.895628i	−0.894127	+	0.447814i	$0.852203\pi$
$812$		0			0
$813$	−15.2115	−	12.2862i	−0.533489	−	0.430897i
$814$		0			0
$815$	4.92757	−	8.53481i	0.172605	−	0.298961i
$816$		0			0
$817$	5.32388	−	3.07374i	0.186259	−	0.107537i
$818$		0			0
$819$	−1.60937	−	1.10241i	−0.0562359	−	0.0385213i
$820$		0			0
$821$	1.50477	−	0.868778i	0.0525167	−	0.0303205i	−0.473512	−	0.880788i	$-0.657014\pi$
$821$	1.50477	−	0.868778i	0.0525167	−	0.0303205i	0.526028	+	0.850467i	$0.323681\pi$
$822$		0			0
$823$	−0.100180	+	0.173518i	−0.00349207	+	0.00604844i	−0.867766	−	0.496973i	$-0.834445\pi$
$823$	−0.100180	+	0.173518i	−0.00349207	+	0.00604844i	0.864274	+	0.503021i	$0.167778\pi$
$824$		0			0
$825$	−2.81001	−	2.26964i	−0.0978321	−	0.0790186i
$826$		0			0
$827$		−	21.7179i		−	0.755207i	−0.925967	−	0.377603i	$-0.876748\pi$
$827$		−	21.7179i		−	0.755207i	0.925967	−	0.377603i	$-0.123252\pi$
$828$		0			0
$829$	−22.5419	−	13.0146i	−0.782913	−	0.452015i	0.0545485	−	0.998511i	$-0.482628\pi$
$829$	−22.5419	−	13.0146i	−0.782913	−	0.452015i	−0.837462	+	0.546496i	$0.815961\pi$
$830$		0			0
$831$	−29.2377	−	4.59298i	−1.01425	−	0.159329i
$832$		0			0
$833$	0.358360	−	6.59322i	0.0124165	−	0.228442i
$834$		0			0
$835$	−11.4174	−	19.7756i	−0.395117	−	0.684363i
$836$		0			0
$837$	−3.22473	−	4.92472i	−0.111463	−	0.170223i
$838$		0			0
$839$	−2.46944			−0.0852546			−0.0426273	−	0.999091i	$-0.513573\pi$
$839$	−2.46944			−0.0852546			−0.0426273	+	0.999091i	$0.513573\pi$
$840$		0			0
$841$	28.9285			0.997533
$842$		0			0
$843$	−24.5971	+	9.47757i	−0.847168	+	0.326425i
$844$		0			0
$845$	6.46980	+	11.2060i	0.222568	+	0.385499i
$846$		0			0
$847$	−12.1003	−	12.7758i	−0.415770	−	0.438982i
$848$		0			0
$849$	4.42702	−	28.1813i	0.151935	−	0.967179i
$850$		0			0
$851$	−14.7925	−	8.54045i	−0.507080	−	0.292763i
$852$		0			0
$853$			30.3776i			1.04011i	0.854133	+	0.520055i	$0.174088\pi$
$853$			30.3776i			1.04011i	−0.854133	+	0.520055i	$0.825912\pi$
$854$		0			0
$855$	1.57666	−	0.339293i	0.0539207	−	0.0116036i
$856$		0			0
$857$	25.8422	−	44.7601i	0.882754	−	1.52898i	0.0344882	−	0.999405i	$-0.489020\pi$
$857$	25.8422	−	44.7601i	0.882754	−	1.52898i	0.848266	−	0.529570i	$-0.177647\pi$
$858$		0			0
$859$	−21.0239	+	12.1381i	−0.717326	+	0.414148i	−0.813768	−	0.581190i	$-0.802587\pi$
$859$	−21.0239	+	12.1381i	−0.717326	+	0.414148i	0.0964418	+	0.995339i	$0.469254\pi$
$860$		0			0
$861$	6.18897	+	8.99937i	0.210920	+	0.306698i
$862$		0			0
$863$	39.3631	−	22.7263i	1.33993	−	0.773611i	0.353137	−	0.935572i	$-0.385115\pi$
$863$	39.3631	−	22.7263i	1.33993	−	0.773611i	0.986797	+	0.161960i	$0.0517817\pi$
$864$		0			0
$865$	−4.87085	+	8.43656i	−0.165614	+	0.286852i
$866$		0			0
$867$	−17.5330	+	21.7074i	−0.595452	+	0.737223i
$868$		0			0
$869$			13.2349i			0.448964i
$870$		0			0
$871$	1.18341	+	0.683243i	0.0400984	+	0.0231508i
$872$		0			0
$873$	6.06410	+	6.70077i	0.205239	+	0.226787i
$874$		0			0
$875$	−2.57325	+	0.615143i	−0.0869916	+	0.0207956i
$876$		0			0
$877$	−12.6911	−	21.9817i	−0.428549	−	0.742268i	0.568196	−	0.822893i	$-0.307642\pi$
$877$	−12.6911	−	21.9817i	−0.428549	−	0.742268i	−0.996744	+	0.0806254i	$0.974308\pi$
$878$		0			0
$879$	−11.3184	−	29.3746i	−0.381761	−	0.990782i
$880$		0			0
$881$	42.5616			1.43394			0.716969	−	0.697105i	$-0.245529\pi$
$881$	42.5616			1.43394			0.716969	+	0.697105i	$0.245529\pi$
$882$		0			0
$883$	−6.16214			−0.207372			−0.103686	−	0.994610i	$-0.533064\pi$
$883$	−6.16214			−0.207372			−0.103686	+	0.994610i	$0.533064\pi$
$884$		0			0
$885$	7.79036	+	20.2182i	0.261870	+	0.679629i
$886$		0			0
$887$	3.87420	+	6.71032i	0.130083	+	0.225310i	0.923708	−	0.383096i	$-0.125142\pi$
$887$	3.87420	+	6.71032i	0.130083	+	0.225310i	−0.793625	+	0.608407i	$0.791809\pi$
$888$		0			0
$889$	−19.9709	+	4.77410i	−0.669802	+	0.160118i
$890$		0			0
$891$	10.9554	−	15.2401i	0.367020	−	0.510561i
$892$		0			0
$893$	5.80291	+	3.35031i	0.194187	+	0.112114i
$894$		0			0
$895$			18.0760i			0.604214i
$896$		0			0
$897$	0.741280	−	0.917771i	0.0247506	−	0.0306435i
$898$		0			0
$899$	−0.151507	+	0.262419i	−0.00505306	+	0.00875215i
$900$		0			0
$901$	10.2384	−	5.91116i	0.341091	−	0.196929i
$902$		0			0
$903$	−29.6943	−	43.1783i	−0.988163	−	1.43689i
$904$		0			0
$905$	−15.3485	+	8.86149i	−0.510203	+	0.294566i
$906$		0			0
$907$	−22.7236	+	39.3584i	−0.754524	+	1.30687i	0.191087	+	0.981573i	$0.438799\pi$
$907$	−22.7236	+	39.3584i	−0.754524	+	1.30687i	−0.945611	+	0.325300i	$0.894535\pi$
$908$		0			0
$909$	7.81416	+	36.3117i	0.259179	+	1.20438i
$910$		0			0
$911$		−	35.7765i		−	1.18533i	−0.805449	−	0.592665i	$-0.798076\pi$
$911$		−	35.7765i		−	1.18533i	0.805449	−	0.592665i	$-0.201924\pi$
$912$		0			0
$913$	−1.92660	−	1.11232i	−0.0637610	−	0.0368124i
$914$		0			0
$915$	−1.54119	+	9.81081i	−0.0509501	+	0.324335i
$916$		0			0
$917$	−31.2273	−	32.9707i	−1.03122	−	1.08879i
$918$		0			0
$919$	−14.4006	−	24.9427i	−0.475034	−	0.822782i	0.524558	−	0.851375i	$-0.324231\pi$
$919$	−14.4006	−	24.9427i	−0.475034	−	0.822782i	−0.999591	+	0.0285927i	$0.990897\pi$
$920$		0			0
$921$	39.9143	−	15.3795i	1.31522	−	0.506772i
$922$		0			0
$923$	2.49149			0.0820085
$924$		0			0
$925$	−6.16327			−0.202647
$926$		0			0
$927$	15.4847	−	48.0697i	0.508585	−	1.57882i
$928$		0			0
$929$	−15.9490	−	27.6244i	−0.523269	−	0.906329i	−0.999633	−	0.0270805i	$-0.991379\pi$
$929$	−15.9490	−	27.6244i	−0.523269	−	0.906329i	0.476364	−	0.879248i	$-0.341954\pi$
$930$		0			0
$931$	−2.05565	+	3.15202i	−0.0673711	+	0.103303i
$932$		0			0
$933$	−39.3753	−	6.18549i	−1.28909	−	0.202504i
$934$		0			0
$935$	1.70362	+	0.983585i	0.0557143	+	0.0321667i
$936$		0			0
$937$		−	36.5715i		−	1.19474i	−0.801966	−	0.597370i	$-0.796213\pi$
$937$		−	36.5715i		−	1.19474i	0.801966	−	0.597370i	$-0.203787\pi$
$938$		0			0
$939$	4.25518	+	3.43689i	0.138863	+	0.112159i
$940$		0			0
$941$	11.5675	−	20.0355i	0.377091	−	0.653140i	−0.613547	−	0.789658i	$-0.710258\pi$
$941$	11.5675	−	20.0355i	0.377091	−	0.653140i	0.990638	+	0.136518i	$0.0435912\pi$
$942$		0			0
$943$	−5.72040	+	3.30267i	−0.186282	+	0.107550i
$944$		0			0
$945$	−3.94169	−	13.1705i	−0.128223	−	0.428438i
$946$		0			0
$947$	−29.4876	+	17.0247i	−0.958220	+	0.553228i	−0.895625	−	0.444811i	$-0.853271\pi$
$947$	−29.4876	+	17.0247i	−0.958220	+	0.553228i	−0.0625952	+	0.998039i	$0.519938\pi$
$948$		0			0
$949$	1.61418	−	2.79583i	0.0523984	−	0.0907566i
$950$		0			0
$951$	4.33618	+	3.50231i	0.140610	+	0.113570i
$952$		0			0
$953$			4.08410i			0.132297i	0.997810	+	0.0661485i	$0.0210711\pi$
$953$			4.08410i			0.132297i	−0.997810	+	0.0661485i	$0.978929\pi$
$954$		0			0
$955$	−19.0353	−	10.9901i	−0.615969	−	0.355630i
$956$		0			0
$957$	−0.954447	−	0.149935i	−0.0308529	−	0.00484670i
$958$		0			0
$959$	38.1093	+	11.3287i	1.23061	+	0.365822i
$960$		0			0
$961$	−14.8583	−	25.7353i	−0.479300	−	0.830172i
$962$		0			0
$963$	−11.7931	+	36.6096i	−0.380026	+	1.17973i
$964$		0			0
$965$	8.97639			0.288960
$966$		0			0
$967$	−8.66642			−0.278693			−0.139347	−	0.990244i	$-0.544500\pi$
$967$	−8.66642			−0.278693			−0.139347	+	0.990244i	$0.544500\pi$
$968$		0			0
$969$	−0.819576	+	0.315793i	−0.0263286	+	0.0101447i
$970$		0			0
$971$	9.79452	+	16.9646i	0.314321	+	0.544420i	0.979293	−	0.202448i	$-0.0648898\pi$
$971$	9.79452	+	16.9646i	0.314321	+	0.544420i	−0.664972	+	0.746868i	$0.731556\pi$
$972$		0			0
$973$	6.04772	+	25.2986i	0.193881	+	0.811037i
$974$		0			0
$975$	0.0660611	−	0.420528i	0.00211565	−	0.0134677i
$976$		0			0
$977$	−26.5041	−	15.3022i	−0.847942	−	0.489559i	0.0120141	−	0.999928i	$-0.496176\pi$
$977$	−26.5041	−	15.3022i	−0.847942	−	0.489559i	−0.859956	+	0.510368i	$0.829509\pi$
$978$		0			0
$979$			1.93442i			0.0618242i
$980$		0			0
$981$	2.26514	+	10.5259i	0.0723204	+	0.336066i
$982$		0			0
$983$	−14.1107	+	24.4405i	−0.450063	+	0.779532i	−0.998389	−	0.0567327i	$-0.981932\pi$
$983$	−14.1107	+	24.4405i	−0.450063	+	0.779532i	0.548327	+	0.836264i	$0.315265\pi$
$984$		0			0
$985$	−19.3125	+	11.1501i	−0.615347	+	0.355271i
$986$		0			0
$987$	24.5751	−	51.5616i	0.782234	−	1.64122i
$988$		0			0
$989$	27.4460	−	15.8460i	0.872734	−	0.503873i
$990$		0			0
$991$	12.2999	−	21.3040i	0.390719	−	0.676745i	−0.601826	−	0.798628i	$-0.705560\pi$
$991$	12.2999	−	21.3040i	0.390719	−	0.676745i	0.992545	+	0.121882i	$0.0388931\pi$
$992$		0			0
$993$	30.6726	−	37.9754i	0.973364	−	1.20511i
$994$		0			0
$995$			18.9148i			0.599640i
$996$		0			0
$997$	48.3054	+	27.8892i	1.52985	+	0.883258i	0.999367	+	0.0355613i	$0.0113219\pi$
$997$	48.3054	+	27.8892i	1.52985	+	0.883258i	0.530481	+	0.847697i	$0.322011\pi$
$998$		0			0
$999$	−1.79718	−	31.9748i	−0.0568601	−	1.01164i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.bh.b.101.3	yes	10
3.2	odd	2		420.2.bh.a.101.5	✓	10
5.2	odd	4		2100.2.bo.g.1949.10		20
5.3	odd	4		2100.2.bo.g.1949.1		20
5.4	even	2		2100.2.bi.j.101.3		10
7.3	odd	6		2940.2.d.b.881.4		10
7.4	even	3		2940.2.d.a.881.7		10
7.5	odd	6		420.2.bh.a.341.5	yes	10
15.2	even	4		2100.2.bo.h.1949.5		20
15.8	even	4		2100.2.bo.h.1949.6		20
15.14	odd	2		2100.2.bi.k.101.1		10
21.5	even	6	inner	420.2.bh.b.341.3	yes	10
21.11	odd	6		2940.2.d.b.881.3		10
21.17	even	6		2940.2.d.a.881.8		10
35.12	even	12		2100.2.bo.h.1349.6		20
35.19	odd	6		2100.2.bi.k.1601.1		10
35.33	even	12		2100.2.bo.h.1349.5		20
105.47	odd	12		2100.2.bo.g.1349.1		20
105.68	odd	12		2100.2.bo.g.1349.10		20
105.89	even	6		2100.2.bi.j.1601.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bh.a.101.5	✓	10	3.2	odd	2
420.2.bh.a.341.5	yes	10	7.5	odd	6
420.2.bh.b.101.3	yes	10	1.1	even	1	trivial
420.2.bh.b.341.3	yes	10	21.5	even	6	inner
2100.2.bi.j.101.3		10	5.4	even	2
2100.2.bi.j.1601.3		10	105.89	even	6
2100.2.bi.k.101.1		10	15.14	odd	2
2100.2.bi.k.1601.1		10	35.19	odd	6
2100.2.bo.g.1349.1		20	105.47	odd	12
2100.2.bo.g.1349.10		20	105.68	odd	12
2100.2.bo.g.1949.1		20	5.3	odd	4
2100.2.bo.g.1949.10		20	5.2	odd	4
2100.2.bo.h.1349.5		20	35.33	even	12
2100.2.bo.h.1349.6		20	35.12	even	12
2100.2.bo.h.1949.5		20	15.2	even	4
2100.2.bo.h.1949.6		20	15.8	even	4
2940.2.d.a.881.7		10	7.4	even	3
2940.2.d.a.881.8		10	21.17	even	6
2940.2.d.b.881.3		10	21.11	odd	6
2940.2.d.b.881.4		10	7.3	odd	6

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:	\( N \)	\(=\)	\( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	420.bh (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.622752 + 1.61622i) q^{3} +(0.500000 + 0.866025i) q^{5} +(2.57325 - 0.615143i) q^{7} +(-2.22436 + 2.01301i) q^{9} +O(q^{10})\)	\(q+(0.622752 + 1.61622i) q^{3} +(0.500000 + 0.866025i) q^{5} +(2.57325 - 0.615143i) q^{7} +(-2.22436 + 2.01301i) q^{9} +(1.80606 + 1.04273i) q^{11} +0.245770i q^{13} +(-1.08831 + 1.34743i) q^{15} +(0.471640 - 0.816904i) q^{17} +(-0.465563 + 0.268793i) q^{19} +(2.59670 + 3.77586i) q^{21} +(-2.40010 + 1.38570i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-4.63871 - 2.34145i) q^{27} +0.267475i q^{29} +(0.981097 + 0.566436i) q^{31} +(-0.560556 + 3.56836i) q^{33} +(1.81935 + 1.92093i) q^{35} +(3.08164 + 5.33755i) q^{37} +(-0.397219 + 0.153054i) q^{39} +2.38340 q^{41} -11.4354 q^{43} +(-2.85550 - 0.919845i) q^{45} +(-6.23215 - 10.7944i) q^{47} +(6.24320 - 3.16583i) q^{49} +(1.61401 + 0.253547i) q^{51} +(10.8541 + 6.26660i) q^{53} +2.08546i q^{55} +(-0.724359 - 0.585062i) q^{57} +(6.25478 - 10.8336i) q^{59} +(4.96556 - 2.86687i) q^{61} +(-4.48553 + 6.54828i) q^{63} +(-0.212843 + 0.122885i) q^{65} +(2.78001 - 4.81512i) q^{67} +(-3.73427 - 3.01616i) q^{69} -10.1375i q^{71} +(-11.3758 - 6.56784i) q^{73} +(-1.71107 - 0.268793i) q^{75} +(5.28887 + 1.57221i) q^{77} +(3.17314 + 5.49605i) q^{79} +(0.895549 - 8.95533i) q^{81} -1.06674 q^{83} +0.943279 q^{85} +(-0.432299 + 0.166571i) q^{87} +(0.463787 + 0.803302i) q^{89} +(0.151184 + 0.632426i) q^{91} +(-0.304508 + 1.93842i) q^{93} +(-0.465563 - 0.268793i) q^{95} -3.01245i q^{97} +(-6.11636 + 1.31622i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{3} + 5 q^{5} - 5 q^{7} + 3 q^{9}+O(q^{10}) \) 10 * q + q^3 + 5 * q^5 - 5 * q^7 + 3 * q^9	\( 10 q + q^{3} + 5 q^{5} - 5 q^{7} + 3 q^{9} + 6 q^{11} + 2 q^{15} - 6 q^{17} + 3 q^{19} + 12 q^{21} - 24 q^{23} - 5 q^{25} - 8 q^{27} + 15 q^{31} - 4 q^{33} - q^{35} - q^{37} - 21 q^{39} + 8 q^{41} - 26 q^{43} + 3 q^{45} - 14 q^{47} - 13 q^{49} + 40 q^{51} + 24 q^{53} + 18 q^{57} + 42 q^{61} - 49 q^{63} - 9 q^{65} + 7 q^{67} + 14 q^{69} - 3 q^{73} + q^{75} + 26 q^{77} + q^{79} - 13 q^{81} + 8 q^{83} - 12 q^{85} + 8 q^{87} - 28 q^{89} - 11 q^{91} + 25 q^{93} + 3 q^{95} + 36 q^{99}+O(q^{100}) \) 10 * q + q^3 + 5 * q^5 - 5 * q^7 + 3 * q^9 + 6 * q^11 + 2 * q^15 - 6 * q^17 + 3 * q^19 + 12 * q^21 - 24 * q^23 - 5 * q^25 - 8 * q^27 + 15 * q^31 - 4 * q^33 - q^35 - q^37 - 21 * q^39 + 8 * q^41 - 26 * q^43 + 3 * q^45 - 14 * q^47 - 13 * q^49 + 40 * q^51 + 24 * q^53 + 18 * q^57 + 42 * q^61 - 49 * q^63 - 9 * q^65 + 7 * q^67 + 14 * q^69 - 3 * q^73 + q^75 + 26 * q^77 + q^79 - 13 * q^81 + 8 * q^83 - 12 * q^85 + 8 * q^87 - 28 * q^89 - 11 * q^91 + 25 * q^93 + 3 * q^95 + 36 * q^99

Introduction

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