LMFDB - Embedded newform 420.2.bh.a.341.5

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			341.5
Root			$-1.08831 - 1.34743i$ of defining polynomial
Character	$\chi$	$=$	420.341
Dual form			420.2.bh.a.101.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.71107 + 0.268793i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(2.57325 + 0.615143i) q^{7} +(2.85550 + 0.919845i) q^{9} +O(q^{10})$	\(q+(1.71107 + 0.268793i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(2.57325 + 0.615143i) q^{7} +(2.85550 + 0.919845i) q^{9} +(-1.80606 + 1.04273i) q^{11} -0.245770i q^{13} +(-1.08831 + 1.34743i) q^{15} +(-0.471640 - 0.816904i) q^{17} +(-0.465563 - 0.268793i) q^{19} +(4.23765 + 1.74422i) q^{21} +(2.40010 + 1.38570i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(4.63871 + 2.34145i) q^{27} +0.267475i q^{29} +(0.981097 - 0.566436i) q^{31} +(-3.37057 + 1.29872i) q^{33} +(-1.81935 + 1.92093i) q^{35} +(3.08164 - 5.33755i) q^{37} +(0.0660611 - 0.420528i) q^{39} -2.38340 q^{41} -11.4354 q^{43} +(-2.22436 + 2.01301i) q^{45} +(6.23215 - 10.7944i) q^{47} +(6.24320 + 3.16583i) q^{49} +(-0.587429 - 1.52455i) q^{51} +(-10.8541 + 6.26660i) q^{53} -2.08546i q^{55} +(-0.724359 - 0.585062i) q^{57} +(-6.25478 - 10.8336i) q^{59} +(4.96556 + 2.86687i) q^{61} +(6.78207 + 4.12353i) q^{63} +(0.212843 + 0.122885i) q^{65} +(2.78001 + 4.81512i) q^{67} +(3.73427 + 3.01616i) q^{69} -10.1375i q^{71} +(-11.3758 + 6.56784i) q^{73} +(-0.622752 - 1.61622i) q^{75} +(-5.28887 + 1.57221i) q^{77} +(3.17314 - 5.49605i) q^{79} +(7.30777 + 5.25324i) q^{81} +1.06674 q^{83} +0.943279 q^{85} +(-0.0718953 + 0.457667i) q^{87} +(-0.463787 + 0.803302i) q^{89} +(0.151184 - 0.632426i) q^{91} +(1.83098 - 0.705499i) q^{93} +(0.465563 - 0.268793i) q^{95} +3.01245i q^{97} +(-6.11636 + 1.31622i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 10 q^{21} + 24 q^{23} - 5 q^{25} + 8 q^{27} + 15 q^{31} - 20 q^{33} + q^{35} - q^{37} + 15 q^{39} - 8 q^{41} - 26 q^{43} + 3 q^{45} + 14 q^{47} - 13 q^{49} - 44 q^{51} - 24 q^{53} + 18 q^{57} + 42 q^{61} - q^{63} + 9 q^{65} + 7 q^{67} - 14 q^{69} - 3 q^{73} - q^{75} - 26 q^{77} + q^{79} + 41 q^{81} - 8 q^{83} - 12 q^{85} - 26 q^{87} + 28 q^{89} - 11 q^{91} - 47 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 + 10 * q^21 + 24 * q^23 - 5 * q^25 + 8 * q^27 + 15 * q^31 - 20 * q^33 + q^35 - q^37 + 15 * q^39 - 8 * q^41 - 26 * q^43 + 3 * q^45 + 14 * q^47 - 13 * q^49 - 44 * q^51 - 24 * q^53 + 18 * q^57 + 42 * q^61 - q^63 + 9 * q^65 + 7 * q^67 - 14 * q^69 - 3 * q^73 - q^75 - 26 * q^77 + q^79 + 41 * q^81 - 8 * q^83 - 12 * q^85 - 26 * q^87 + 28 * q^89 - 11 * q^91 - 47 * q^93 - 3 * q^95 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$211$	$241$	$281$	$337$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

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
$3$	1.71107	+	0.268793i	0.987885	+	0.155188i
$3$	1.71107	+	0.268793i	0.987885	+	0.155188i
$4$		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
$9$	2.85550	+	0.919845i	0.951834	+	0.306615i
$10$		0			0
$11$	−1.80606	+	1.04273i	−0.544548	+	0.314395i	−0.746920	−	0.664914i	$-0.768468\pi$
$11$	−1.80606	+	1.04273i	−0.544548	+	0.314395i	0.202372	+	0.979309i	$0.435135\pi$
$12$		0			0
$13$		−	0.245770i		−	0.0681643i	−0.999419	−	0.0340821i	$-0.989149\pi$
$13$		−	0.245770i		−	0.0681643i	0.999419	−	0.0340821i	$-0.0108508\pi$
$14$		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	$-0.203158\pi$
$17$	−0.471640	−	0.816904i	−0.114389	−	0.198128i	−0.917536	+	0.397654i	$0.869824\pi$
$18$		0			0
$19$	−0.465563	−	0.268793i	−0.106807	−	0.0616653i	0.445645	−	0.895210i	$-0.352974\pi$
$19$	−0.465563	−	0.268793i	−0.106807	−	0.0616653i	−0.552452	+	0.833545i	$0.686308\pi$
$20$		0			0
$21$	4.23765	+	1.74422i	0.924731	+	0.380620i
$22$		0			0
$23$	2.40010	+	1.38570i	0.500456	+	0.288938i	0.728902	−	0.684618i	$-0.240031\pi$
$23$	2.40010	+	1.38570i	0.500456	+	0.288938i	−0.228446	+	0.973557i	$0.573364\pi$
$24$		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	−0.409301	−	0.912400i	$-0.634227\pi$
$31$	0.981097	−	0.566436i	0.176210	−	0.101735i	0.585511	+	0.810665i	$0.300894\pi$
$32$		0			0
$33$	−3.37057	+	1.29872i	−0.586741	+	0.226079i
$34$		0			0
$35$	−1.81935	+	1.92093i	−0.307527	+	0.324696i
$36$		0			0
$37$	3.08164	−	5.33755i	0.506618	−	0.877488i	−0.493353	−	0.869829i	$-0.664229\pi$
$37$	3.08164	−	5.33755i	0.506618	−	0.877488i	0.999971	−	0.00765857i	$-0.00243782\pi$
$38$		0			0
$39$	0.0660611	−	0.420528i	0.0105782	−	0.0673384i
$40$		0			0
$41$	−2.38340			−0.372224			−0.186112	−	0.982529i	$-0.559589\pi$
$41$	−2.38340			−0.372224			−0.186112	+	0.982529i	$0.559589\pi$
$42$		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
$45$	−2.22436	+	2.01301i	−0.331588	+	0.300082i
$46$		0			0
$47$	6.23215	−	10.7944i	0.909052	−	1.57452i	0.0936683	−	0.995603i	$-0.470141\pi$
$47$	6.23215	−	10.7944i	0.909052	−	1.57452i	0.815384	−	0.578921i	$-0.196526\pi$
$48$		0			0
$49$	6.24320	+	3.16583i	0.891885	+	0.452261i
$50$		0			0
$51$	−0.587429	−	1.52455i	−0.0822565	−	0.213480i
$52$		0			0
$53$	−10.8541	+	6.26660i	−1.49092	+	0.860784i	−0.999946	−	0.0103892i	$-0.996693\pi$
$53$	−10.8541	+	6.26660i	−1.49092	+	0.860784i	−0.490976	+	0.871173i	$0.663360\pi$
$54$		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	−0.909827	−	0.414987i	$-0.863786\pi$
$59$	−6.25478	−	10.8336i	−0.814303	−	1.41041i	0.0955244	−	0.995427i	$-0.469547\pi$
$60$		0			0
$61$	4.96556	+	2.86687i	0.635775	+	0.367065i	0.782985	−	0.622040i	$-0.213696\pi$
$61$	4.96556	+	2.86687i	0.635775	+	0.367065i	−0.147210	+	0.989105i	$0.547029\pi$
$62$		0			0
$63$	6.78207	+	4.12353i	0.854461	+	0.519516i
$64$		0			0
$65$	0.212843	+	0.122885i	0.0263999	+	0.0152420i
$66$		0			0
$67$	2.78001	+	4.81512i	0.339633	+	0.588261i	0.984364	−	0.176149i	$-0.0563639\pi$
$67$	2.78001	+	4.81512i	0.339633	+	0.588261i	−0.644731	+	0.764410i	$0.723031\pi$
$68$		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	−0.985520	−	0.169557i	$-0.945766\pi$
$73$	−11.3758	+	6.56784i	−1.33144	+	0.768707i	−0.345919	+	0.938264i	$0.612433\pi$
$74$		0			0
$75$	−0.622752	−	1.61622i	−0.0719092	−	0.186625i
$76$		0			0
$77$	−5.28887	+	1.57221i	−0.602722	+	0.179170i
$78$		0			0
$79$	3.17314	−	5.49605i	0.357007	−	0.618353i	−0.630453	−	0.776228i	$-0.717131\pi$
$79$	3.17314	−	5.49605i	0.357007	−	0.618353i	0.987459	+	0.157874i	$0.0504641\pi$
$80$		0			0
$81$	7.30777	+	5.25324i	0.811975	+	0.583693i
$82$		0			0
$83$	1.06674			0.117090			0.0585449	−	0.998285i	$-0.481354\pi$
$83$	1.06674			0.117090			0.0585449	+	0.998285i	$0.481354\pi$
$84$		0			0
$85$	0.943279			0.102313
$86$		0			0
$87$	−0.0718953	+	0.457667i	−0.00770798	+	0.0490671i
$88$		0			0
$89$	−0.463787	+	0.803302i	−0.0491613	+	0.0851499i	−0.889559	−	0.456820i	$-0.848988\pi$
$89$	−0.463787	+	0.803302i	−0.0491613	+	0.0851499i	0.840398	+	0.541970i	$0.182322\pi$
$90$		0			0
$91$	0.151184	−	0.632426i	0.0158483	−	0.0662963i
$92$		0			0
$93$	1.83098	−	0.705499i	0.189863	−	0.0731568i
$94$		0			0
$95$	0.465563	−	0.268793i	0.0477657	−	0.0275776i
$96$		0			0
$97$			3.01245i			0.305868i	0.988236	+	0.152934i	$0.0488722\pi$
$97$			3.01245i			0.305868i	−0.988236	+	0.152934i	$0.951128\pi$
$98$		0			0
$99$	−6.11636	+	1.31622i	−0.614717	+	0.132285i
$100$		0			0
$101$	−6.19049	−	10.7223i	−0.615977	−	1.06690i	−0.990212	−	0.139570i	$-0.955428\pi$
$101$	−6.19049	−	10.7223i	−0.615977	−	1.06690i	0.374235	−	0.927334i	$-0.377905\pi$
$102$		0			0
$103$	−14.5787	−	8.41703i	−1.43648	−	0.829355i	−0.438881	−	0.898545i	$-0.644625\pi$
$103$	−14.5787	−	8.41703i	−1.43648	−	0.829355i	−0.997603	+	0.0691903i	$0.977958\pi$
$104$		0			0
$105$	−3.62937	+	2.79780i	−0.354190	+	0.273038i
$106$		0			0
$107$	−11.1031	−	6.41036i	−1.07337	−	0.619713i	−0.144273	−	0.989538i	$-0.546084\pi$
$107$	−11.1031	−	6.41036i	−1.07337	−	0.619713i	−0.929101	+	0.369825i	$0.879418\pi$
$108$		0			0
$109$	1.79448	+	3.10813i	0.171880	+	0.297705i	0.939077	−	0.343707i	$-0.111683\pi$
$109$	1.79448	+	3.10813i	0.171880	+	0.297705i	−0.767197	+	0.641411i	$0.778349\pi$
$110$		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
$117$	0.226070	−	0.701796i	0.0209002	−	0.0648810i
$118$		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
$123$	−4.07815	−	0.640639i	−0.367714	−	0.0577645i
$124$		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
$129$	−19.5667	−	3.07374i	−1.72275	−	0.270628i
$130$		0			0
$131$	8.58199	−	14.8644i	0.749812	−	1.29871i	−0.198101	−	0.980182i	$-0.563477\pi$
$131$	8.58199	−	14.8644i	0.749812	−	1.29871i	0.947913	−	0.318530i	$-0.103189\pi$
$132$		0			0
$133$	−1.03266	−	0.978058i	−0.0895431	−	0.0848084i
$134$		0			0
$135$	−4.34711	+	2.84651i	−0.374140	+	0.244989i
$136$		0			0
$137$	−13.0137	+	7.51345i	−1.11183	+	0.641918i	−0.939304	−	0.343087i	$-0.888528\pi$
$137$	−13.0137	+	7.51345i	−1.11183	+	0.641918i	−0.172530	+	0.985004i	$0.555194\pi$
$138$		0			0
$139$		−	9.83141i		−	0.833889i	−0.908932	−	0.416945i	$-0.863101\pi$
$139$		−	9.83141i		−	0.833889i	0.908932	−	0.416945i	$-0.136899\pi$
$140$		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
$147$	9.83158	+	7.09507i	0.810895	+	0.585192i
$148$		0			0
$149$	19.9895	+	11.5409i	1.63760	+	0.945469i	0.981656	+	0.190658i	$0.0610623\pi$
$149$	19.9895	+	11.5409i	1.63760	+	0.945469i	0.655943	+	0.754810i	$0.272271\pi$
$150$		0			0
$151$	7.20527	+	12.4799i	0.586357	+	1.01560i	0.994705	+	0.102774i	$0.0327717\pi$
$151$	7.20527	+	12.4799i	0.586357	+	1.01560i	−0.408348	+	0.912826i	$0.633895\pi$
$152$		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	−0.574065	−	0.818809i	$-0.694635\pi$
$157$	−1.90441	+	1.09951i	−0.151988	+	0.0877506i	0.422077	+	0.906560i	$0.361301\pi$
$158$		0			0
$159$	−20.2565	+	7.80508i	−1.60644	+	0.618983i
$160$		0			0
$161$	5.32365	+	5.04216i	0.419563	+	0.397378i
$162$		0			0
$163$	−4.92757	+	8.53481i	−0.385957	+	0.668498i	−0.991902	−	0.127009i	$-0.959462\pi$
$163$	−4.92757	+	8.53481i	−0.385957	+	0.668498i	0.605944	+	0.795507i	$0.292795\pi$
$164$		0			0
$165$	0.560556	−	3.56836i	0.0436392	−	0.277796i
$166$		0			0
$167$	22.8349			1.76702			0.883509	−	0.468415i	$-0.155175\pi$
$167$	22.8349			1.76702			0.883509	+	0.468415i	$0.155175\pi$
$168$		0			0
$169$	12.9396			0.995354
$170$		0			0
$171$	−1.08217	−	1.19578i	−0.0827554	−	0.0914438i
$172$		0			0
$173$	−4.87085	+	8.43656i	−0.370324	+	0.641420i	−0.989615	−	0.143741i	$-0.954087\pi$
$173$	−4.87085	+	8.43656i	−0.370324	+	0.641420i	0.619291	+	0.785161i	$0.287420\pi$
$174$		0			0
$175$	−0.753894	−	2.53607i	−0.0569890	−	0.191709i
$176$		0			0
$177$	−7.79036	−	20.2182i	−0.585559	−	1.51970i
$178$		0			0
$179$	−15.6543	+	9.03800i	−1.17006	+	0.675532i	−0.953693	−	0.300781i	$-0.902753\pi$
$179$	−15.6543	+	9.03800i	−1.17006	+	0.675532i	−0.216363	+	0.976313i	$0.569419\pi$
$180$		0			0
$181$		−	17.7230i		−	1.31734i	−0.752433	−	0.658669i	$-0.771120\pi$
$181$		−	17.7230i		−	1.31734i	0.752433	−	0.658669i	$-0.228880\pi$
$182$		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
$189$	10.4962	+	8.87861i	0.763487	+	0.645824i
$190$		0			0
$191$	19.0353	+	10.9901i	1.37735	+	0.795212i	0.991840	−	0.127492i	$-0.0406927\pi$
$191$	19.0353	+	10.9901i	1.37735	+	0.795212i	0.385508	+	0.922704i	$0.374026\pi$
$192$		0			0
$193$	4.48820	+	7.77378i	0.323067	+	0.559569i	0.981119	−	0.193403i	$-0.0619526\pi$
$193$	4.48820	+	7.77378i	0.323067	+	0.559569i	−0.658052	+	0.752973i	$0.728619\pi$
$194$		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	0.209606	−	0.977786i	$-0.432782\pi$
$199$	16.3807	−	9.45740i	1.16120	−	0.670417i	0.951591	+	0.307368i	$0.0994484\pi$
$200$		0			0
$201$	3.46252	+	8.98625i	0.244227	+	0.633841i
$202$		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
$207$	5.57887	+	6.16459i	0.387758	+	0.428469i
$208$		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
$213$	2.72489	−	17.3460i	0.186706	−	1.18853i
$214$		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
$219$	−21.2302	+	8.18027i	−1.43460	+	0.552771i
$220$		0			0
$221$	−0.200770	+	0.115915i	−0.0135053	+	0.00779727i
$222$		0			0
$223$		−	13.5949i		−	0.910379i	−0.890395	−	0.455189i	$-0.849572\pi$
$223$		−	13.5949i		−	0.910379i	0.890395	−	0.455189i	$-0.150428\pi$
$224$		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	$-0.0582596\pi$
$227$	5.03260	+	8.71671i	0.334025	+	0.578549i	−0.649272	+	0.760556i	$0.724926\pi$
$228$		0			0
$229$	12.3651	+	7.13897i	0.817106	+	0.471756i	0.849418	−	0.527721i	$-0.176953\pi$
$229$	12.3651	+	7.13897i	0.817106	+	0.471756i	−0.0323114	+	0.999478i	$0.510287\pi$
$230$		0			0
$231$	−9.47221	+	1.26856i	−0.623225	+	0.0834648i
$232$		0			0
$233$	17.9716	+	10.3759i	1.17736	+	0.679750i	0.955403	−	0.295306i	$-0.0954218\pi$
$233$	17.9716	+	10.3759i	1.17736	+	0.679750i	0.221958	+	0.975056i	$0.428755\pi$
$234$		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	−0.896584	−	0.442874i	$-0.853959\pi$
$241$	−14.9239	+	8.61634i	−0.961336	+	0.555028i	−0.0647520	+	0.997901i	$0.520626\pi$
$242$		0			0
$243$	11.0921	+	10.9529i	0.711556	+	0.702630i
$244$		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
$249$	1.82526	+	0.286732i	0.115671	+	0.0181709i
$250$		0			0
$251$	−15.8276			−0.999031			−0.499516	−	0.866305i	$-0.666489\pi$
$251$	−15.8276			−0.999031			−0.499516	+	0.866305i	$0.666489\pi$
$252$		0			0
$253$	−5.77964			−0.363363
$254$		0			0
$255$	1.61401	+	0.253547i	0.101073	+	0.0158777i
$256$		0			0
$257$	9.10800	−	15.7755i	0.568141	−	0.984050i	−0.428609	−	0.903490i	$-0.640996\pi$
$257$	9.10800	−	15.7755i	0.568141	−	0.984050i	0.996750	−	0.0805593i	$-0.0256706\pi$
$258$		0			0
$259$	11.2132	−	11.8392i	0.696752	−	0.735651i
$260$		0			0
$261$	−0.246035	+	0.763775i	−0.0152292	+	0.0472765i
$262$		0			0
$263$	−4.55971	+	2.63255i	−0.281164	+	0.162330i	−0.633950	−	0.773374i	$-0.718568\pi$
$263$	−4.55971	+	2.63255i	−0.281164	+	0.162330i	0.352786	+	0.935704i	$0.385234\pi$
$264$		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	$-0.151612\pi$
$269$	0.775418	+	1.34306i	0.0472780	+	0.0818880i	−0.841418	+	0.540385i	$0.818279\pi$
$270$		0			0
$271$	−9.77676	−	5.64461i	−0.593896	−	0.342886i	0.172741	−	0.984967i	$-0.444738\pi$
$271$	−9.77676	−	5.64461i	−0.593896	−	0.342886i	−0.766636	+	0.642082i	$0.778071\pi$
$272$		0			0
$273$	0.428677	−	1.04149i	0.0259447	−	0.0630336i
$274$		0			0
$275$	1.80606	+	1.04273i	0.108910	+	0.0628790i
$276$		0			0
$277$	−8.54371	−	14.7981i	−0.513342	−	0.889134i	−0.999880	−	0.0154751i	$-0.995074\pi$
$277$	−8.54371	−	14.7981i	−0.513342	−	0.889134i	0.486538	−	0.873659i	$-0.338259\pi$
$278$		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	−0.859933	−	0.510407i	$-0.829495\pi$
$283$	−14.2634	+	8.23500i	−0.847874	+	0.489520i	0.0120590	+	0.999927i	$0.496161\pi$
$284$		0			0
$285$	0.868858	−	0.334783i	0.0514667	−	0.0198308i
$286$		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
$291$	−0.809725	+	5.15450i	−0.0474669	+	0.302162i
$292$		0			0
$293$	18.1748			1.06179			0.530893	−	0.847439i	$-0.321857\pi$
$293$	18.1748			1.06179			0.530893	+	0.847439i	$0.321857\pi$
$294$		0			0
$295$	12.5096			0.728335
$296$		0			0
$297$	−10.8193	+	0.608108i	−0.627799	+	0.0352860i
$298$		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
$303$	−7.71029	−	20.0104i	−0.442944	−	1.14957i
$304$		0			0
$305$	−4.96556	+	2.86687i	−0.284327	+	0.164156i
$306$		0			0
$307$			24.6960i			1.40948i	0.709468	+	0.704738i	$0.248935\pi$
$307$			24.6960i			1.40948i	−0.709468	+	0.704738i	$0.751065\pi$
$308$		0			0
$309$	−22.6827	−	18.3208i	−1.29038	−	1.04223i
$310$		0			0
$311$	11.5061	+	19.9291i	0.652448	+	1.13007i	0.982527	+	0.186120i	$0.0595914\pi$
$311$	11.5061	+	19.9291i	0.652448	+	1.13007i	−0.330079	+	0.943953i	$0.607075\pi$
$312$		0			0
$313$	2.73490	+	1.57900i	0.154586	+	0.0892502i	0.575298	−	0.817944i	$-0.304886\pi$
$313$	2.73490	+	1.57900i	0.154586	+	0.0892502i	−0.420712	+	0.907194i	$0.638220\pi$
$314$		0			0
$315$	−6.96212	+	3.81168i	−0.392271	+	0.214764i
$316$		0			0
$317$	−2.78696	−	1.60905i	−0.156531	−	0.0903734i	0.419688	−	0.907668i	$-0.362139\pi$
$317$	−2.78696	−	1.60905i	−0.156531	−	0.0903734i	−0.576220	+	0.817295i	$0.695473\pi$
$318$		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
$327$	2.23503	+	5.80056i	0.123598	+	0.320772i
$328$		0			0
$329$	22.6770	−	23.9430i	1.25022	−	1.32002i
$330$		0			0
$331$	−14.0918	+	24.4077i	−0.774554	+	1.34157i	0.160491	+	0.987037i	$0.448692\pi$
$331$	−14.0918	+	24.4077i	−0.774554	+	1.34157i	−0.935045	+	0.354529i	$0.884641\pi$
$332$		0			0
$333$	13.7093	−	12.4068i	0.751267	−	0.679886i
$334$		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
$339$	−0.269741	+	1.71711i	−0.0146503	+	0.0932604i
$340$		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
$345$	−4.47920	+	1.72590i	−0.241152	+	0.0929191i
$346$		0			0
$347$	13.3367	−	7.69997i	0.715953	−	0.413356i	−0.0973081	−	0.995254i	$-0.531023\pi$
$347$	13.3367	−	7.69997i	0.715953	−	0.413356i	0.813261	+	0.581898i	$0.197690\pi$
$348$		0			0
$349$			21.9727i			1.17617i	0.808799	+	0.588086i	$0.200118\pi$
$349$			21.9727i			1.17617i	−0.808799	+	0.588086i	$0.799882\pi$
$350$		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	$-0.319245\pi$
$353$	−8.66505	−	15.0083i	−0.461194	−	0.798811i	−0.999021	+	0.0442440i	$0.985912\pi$
$354$		0			0
$355$	8.77935	+	5.06876i	0.465959	+	0.269022i
$356$		0			0
$357$	−0.573783	−	4.28440i	−0.0303678	−	0.226754i
$358$		0			0
$359$	0.270990	+	0.156456i	0.0143023	+	0.00825745i	0.507134	−	0.861867i	$-0.330705\pi$
$359$	0.270990	+	0.156456i	0.0143023	+	0.00825745i	−0.492832	+	0.870125i	$0.664038\pi$
$360$		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	−0.414124	−	0.910220i	$-0.635912\pi$
$367$	3.20094	−	1.84807i	0.167088	−	0.0964682i	0.581212	+	0.813752i	$0.302579\pi$
$368$		0			0
$369$	−6.80579	−	2.19235i	−0.354295	−	0.114129i
$370$		0			0
$371$	−31.7851	+	9.44871i	−1.65020	+	0.490552i
$372$		0			0
$373$	0.351666	−	0.609103i	0.0182086	−	0.0315381i	−0.856778	−	0.515686i	$-0.827537\pi$
$373$	0.351666	−	0.609103i	0.0182086	−	0.0315381i	0.874986	+	0.484148i	$0.160870\pi$
$374$		0			0
$375$	1.71107	+	0.268793i	0.0883591	+	0.0138804i
$376$		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
$381$	−13.2795	−	2.08609i	−0.680331	−	0.106874i
$382$		0			0
$383$	14.7524	−	25.5519i	0.753813	−	1.30564i	−0.192150	−	0.981366i	$-0.561546\pi$
$383$	14.7524	−	25.5519i	0.753813	−	1.30564i	0.945963	−	0.324276i	$-0.105121\pi$
$384$		0			0
$385$	1.28286	−	5.36640i	0.0653804	−	0.273497i
$386$		0			0
$387$	−32.6537	−	10.5188i	−1.65988	−	0.534698i
$388$		0			0
$389$	−11.5224	+	6.65245i	−0.584208	+	0.337293i	−0.762804	−	0.646630i	$-0.776178\pi$
$389$	−11.5224	+	6.65245i	−0.584208	+	0.337293i	0.178596	+	0.983923i	$0.442845\pi$
$390$		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	0.400845	−	0.916146i	$-0.368717\pi$
$397$	−3.82832	−	2.21028i	−0.192138	−	0.110931i	−0.592983	+	0.805215i	$0.702050\pi$
$398$		0			0
$399$	−1.50406	−	1.95109i	−0.0752971	−	0.0976769i
$400$		0			0
$401$	25.4507	+	14.6940i	1.27095	+	0.733781i	0.975166	−	0.221475i	$-0.0710871\pi$
$401$	25.4507	+	14.6940i	1.27095	+	0.733781i	0.295780	+	0.955256i	$0.404420\pi$
$402$		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	−0.325862	−	0.945417i	$-0.605654\pi$
$409$	6.67308	−	3.85270i	0.329962	−	0.190504i	0.655824	+	0.754913i	$0.272321\pi$
$410$		0			0
$411$	−24.2868	+	9.35804i	−1.19798	+	0.461598i
$412$		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
$417$	2.64261	−	16.8222i	0.129409	−	0.823787i
$418$		0			0
$419$	−1.40692			−0.0687327			−0.0343663	−	0.999409i	$-0.510941\pi$
$419$	−1.40692			−0.0687327			−0.0343663	+	0.999409i	$0.510941\pi$
$420$		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
$423$	27.7251	−	25.0908i	1.34804	−	1.21996i
$424$		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
$429$	0.319187	+	0.828384i	0.0154105	+	0.0399947i
$430$		0			0
$431$	−9.16199	+	5.28968i	−0.441317	+	0.254795i	−0.704156	−	0.710045i	$-0.748675\pi$
$431$	−9.16199	+	5.28968i	−0.441317	+	0.254795i	0.262839	+	0.964840i	$0.415341\pi$
$432$		0			0
$433$			23.7164i			1.13974i	0.821735	+	0.569869i	$0.193006\pi$
$433$			23.7164i			1.13974i	−0.821735	+	0.569869i	$0.806994\pi$
$434$		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	0.0151058	−	0.999886i	$-0.495191\pi$
$439$	−17.6684	−	10.2009i	−0.843268	−	0.486861i	−0.858374	+	0.513025i	$0.828525\pi$
$440$		0			0
$441$	14.9154	+	14.7828i	0.710256	+	0.703943i
$442$		0			0
$443$	−0.475830	−	0.274720i	−0.0226074	−	0.0130524i	0.488654	−	0.872478i	$-0.337488\pi$
$443$	−0.475830	−	0.274720i	−0.0226074	−	0.0130524i	−0.511261	+	0.859425i	$0.670821\pi$
$444$		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
$453$	8.97420	+	23.2907i	0.421645	+	1.09429i
$454$		0			0
$455$	0.472105	+	0.447142i	0.0221326	+	0.0209623i
$456$		0			0
$457$	14.6946	−	25.4518i	0.687385	−	1.19059i	−0.285296	−	0.958439i	$-0.592092\pi$
$457$	14.6946	−	25.4518i	0.687385	−	1.19059i	0.972681	−	0.232146i	$-0.0745748\pi$
$458$		0			0
$459$	−0.275055	−	4.89370i	−0.0128385	−	0.228418i
$460$		0			0
$461$	−29.9734			−1.39600			−0.697999	−	0.716098i	$-0.745926\pi$
$461$	−29.9734			−1.39600			−0.697999	+	0.716098i	$0.745926\pi$
$462$		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
$465$	−0.304508	+	1.93842i	−0.0141212	+	0.0898921i
$466$		0			0
$467$	1.21626	−	2.10662i	0.0562817	−	0.0974828i	−0.836512	−	0.547949i	$-0.815409\pi$
$467$	1.21626	−	2.10662i	0.0562817	−	0.0974828i	0.892794	+	0.450466i	$0.148742\pi$
$468$		0			0
$469$	4.19167	+	14.1006i	0.193553	+	0.651105i
$470$		0			0
$471$	−3.55411	+	1.36945i	−0.163765	+	0.0631008i
$472$		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	$-0.0859432\pi$
$479$	5.49101	+	9.51071i	0.250891	+	0.434555i	−0.712881	+	0.701285i	$0.752610\pi$
$480$		0			0
$481$	−1.31181	−	0.757373i	−0.0598133	−	0.0345332i
$482$		0			0
$483$	7.75383	+	10.0584i	0.352812	+	0.457674i
$484$		0			0
$485$	−2.60886	−	1.50622i	−0.118462	−	0.0683941i
$486$		0			0
$487$	−13.4393	−	23.2776i	−0.608993	−	1.05481i	−0.991407	−	0.130816i	$-0.958240\pi$
$487$	−13.4393	−	23.2776i	−0.608993	−	1.05481i	0.382414	−	0.923991i	$-0.375093\pi$
$488$		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
$495$	1.91830	−	5.95503i	0.0862211	−	0.267659i
$496$		0			0
$497$	6.23602	−	26.0863i	0.279724	−	1.17013i
$498$		0			0
$499$	−2.58341	+	4.47460i	−0.115649	+	0.200311i	−0.918039	−	0.396490i	$-0.870228\pi$
$499$	−2.58341	+	4.47460i	−0.115649	+	0.200311i	0.802390	+	0.596800i	$0.203562\pi$
$500$		0			0
$501$	39.0720	+	6.13785i	1.74561	+	0.274219i
$502$		0			0
$503$	−42.2496			−1.88382			−0.941908	−	0.335872i	$-0.890969\pi$
$503$	−42.2496			−1.88382			−0.941908	+	0.335872i	$0.890969\pi$
$504$		0			0
$505$	12.3810			0.550947
$506$		0			0
$507$	22.1405	+	3.47807i	0.983295	+	0.154466i
$508$		0			0
$509$	−3.76320	+	6.51806i	−0.166801	+	0.288908i	−0.937293	−	0.348541i	$-0.886677\pi$
$509$	−3.76320	+	6.51806i	−0.166801	+	0.288908i	0.770492	+	0.637449i	$0.220010\pi$
$510$		0			0
$511$	−33.3130	+	9.90290i	−1.47368	+	0.438079i
$512$		0			0
$513$	−1.53024	−	2.33694i	−0.0675619	−	0.103179i
$514$		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	$-0.0197222\pi$
$521$	10.1668	+	17.6095i	0.445417	+	0.771484i	−0.552665	+	0.833404i	$0.686389\pi$
$522$		0			0
$523$	3.14832	+	1.81768i	0.137666	+	0.0794818i	0.567251	−	0.823545i	$-0.308007\pi$
$523$	3.14832	+	1.81768i	0.137666	+	0.0794818i	−0.429585	+	0.903026i	$0.641340\pi$
$524$		0			0
$525$	−0.608286	−	4.54202i	−0.0265478	−	0.198230i
$526$		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
$537$	−29.2149	+	11.2569i	−1.26071	+	0.485770i
$538$		0			0
$539$	−14.5767	+	0.792285i	−0.627863	+	0.0341261i
$540$		0			0
$541$	−9.20758	+	15.9480i	−0.395865	+	0.685658i	−0.993211	−	0.116325i	$-0.962888\pi$
$541$	−9.20758	+	15.9480i	−0.395865	+	0.685658i	0.597346	+	0.801983i	$0.296222\pi$
$542$		0			0
$543$	4.76381	−	30.3252i	0.204434	−	1.30138i
$544$		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
$549$	11.5421	+	12.7539i	0.492605	+	0.544323i
$550$		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
$555$	3.83819	+	9.96123i	0.162922	+	0.422831i
$556$		0			0
$557$	−33.9272	+	19.5879i	−1.43754	+	0.829965i	−0.997679	−	0.0680994i	$-0.978307\pi$
$557$	−33.9272	+	19.5879i	−1.43754	+	0.829965i	−0.439863	+	0.898065i	$0.644973\pi$
$558$		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	$-0.142162\pi$
$563$	1.82483	+	3.16069i	0.0769073	+	0.133207i	−0.825007	+	0.565123i	$0.808829\pi$
$564$		0			0
$565$	−0.869081	−	0.501764i	−0.0365625	−	0.0211094i
$566$		0			0
$567$	15.5732	+	18.0132i	0.654013	+	0.756483i
$568$		0			0
$569$	−17.1456	−	9.89902i	−0.718781	−	0.414988i	0.0955229	−	0.995427i	$-0.469548\pi$
$569$	−17.1456	−	9.89902i	−0.718781	−	0.414988i	−0.814304	+	0.580439i	$0.802881\pi$
$570$		0			0
$571$	−18.7342	−	32.4487i	−0.784004	−	1.35793i	−0.929592	−	0.368589i	$-0.879841\pi$
$571$	−18.7342	−	32.4487i	−0.784004	−	1.35793i	0.145589	−	0.989345i	$-0.453492\pi$
$572$		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	0.0368312	−	0.999322i	$-0.488274\pi$
$577$	22.1156	−	12.7684i	0.920685	−	0.531558i	0.883853	+	0.467764i	$0.154940\pi$
$578$		0			0
$579$	5.59007	+	14.5079i	0.232315	+	0.602926i
$580$		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
$585$	0.494738	+	0.546680i	0.0204549	+	0.0226024i
$586$		0			0
$587$	−7.57204			−0.312531			−0.156266	−	0.987715i	$-0.549946\pi$
$587$	−7.57204			−0.312531			−0.156266	+	0.987715i	$0.549946\pi$
$588$		0			0
$589$	−0.609016			−0.0250941
$590$		0			0
$591$	−5.99412	+	38.1571i	−0.246565	+	1.56957i
$592$		0			0
$593$	−1.58920	+	2.75258i	−0.0652606	+	0.113035i	−0.896810	−	0.442417i	$-0.854121\pi$
$593$	−1.58920	+	2.75258i	−0.0652606	+	0.113035i	0.831549	+	0.555452i	$0.187455\pi$
$594$		0			0
$595$	2.42729	+	0.580252i	0.0995092	+	0.0237880i
$596$		0			0
$597$	30.5706	−	11.7792i	1.25117	−	0.482092i
$598$		0			0
$599$	23.5750	−	13.6110i	0.963247	−	0.556131i	0.0660761	−	0.997815i	$-0.478952\pi$
$599$	23.5750	−	13.6110i	0.963247	−	0.556131i	0.897171	+	0.441684i	$0.145619\pi$
$600$		0			0
$601$			13.1953i			0.538247i	0.963106	+	0.269123i	$0.0867340\pi$
$601$			13.1953i			0.538247i	−0.963106	+	0.269123i	$0.913266\pi$
$602$		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	0.358518	−	0.933523i	$-0.383282\pi$
$607$	−6.66879	−	3.85023i	−0.270678	−	0.156276i	−0.629196	+	0.777247i	$0.716616\pi$
$608$		0			0
$609$	−0.466535	+	1.13347i	−0.0189050	+	0.0459303i
$610$		0			0
$611$	−2.65294	−	1.53167i	−0.107326	−	0.0619649i
$612$		0			0
$613$	14.4287	+	24.9912i	0.582769	+	1.00939i	0.995150	+	0.0983735i	$0.0313640\pi$
$613$	14.4287	+	24.9912i	0.582769	+	1.00939i	−0.412381	+	0.911012i	$0.635303\pi$
$614$		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	0.108530	−	0.994093i	$-0.465386\pi$
$619$	25.4695	−	14.7048i	1.02370	−	0.591036i	0.915175	+	0.403057i	$0.132052\pi$
$620$		0			0
$621$	7.88882	+	12.0476i	0.316567	+	0.483453i
$622$		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
$627$	1.91830	+	0.301347i	0.0766095	+	0.0120346i
$628$		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
$633$	34.9319	+	5.48747i	1.38842	+	0.218107i
$634$		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
$639$	9.32494	−	28.9477i	0.368889	−	1.14515i
$640$		0			0
$641$	27.8245	−	16.0645i	1.09900	−	0.634510i	0.163044	−	0.986619i	$-0.447869\pi$
$641$	27.8245	−	16.0645i	1.09900	−	0.634510i	0.935959	+	0.352109i	$0.114535\pi$
$642$		0			0
$643$		−	5.88352i		−	0.232024i	−0.993248	−	0.116012i	$-0.962989\pi$
$643$		−	5.88352i		−	0.232024i	0.993248	−	0.116012i	$-0.0370110\pi$
$644$		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	$-0.0381638\pi$
$647$	9.99202	+	17.3067i	0.392827	+	0.680396i	−0.599994	+	0.800004i	$0.704830\pi$
$648$		0			0
$649$	22.5930	+	13.0441i	0.886854	+	0.512025i
$650$		0			0
$651$	5.14554	−	0.689111i	0.201669	−	0.0270084i
$652$		0			0
$653$	−2.19720	−	1.26856i	−0.0859832	−	0.0496424i	0.456392	−	0.889779i	$-0.349142\pi$
$653$	−2.19720	−	1.26856i	−0.0859832	−	0.0496424i	−0.542375	+	0.840136i	$0.682475\pi$
$654$		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	0.0848363	−	0.996395i	$-0.472963\pi$
$661$	25.4569	−	14.6975i	0.990158	−	0.571668i	0.905321	+	0.424727i	$0.139630\pi$
$662$		0			0
$663$	−0.374688	+	0.144372i	−0.0145517	+	0.00560696i
$664$		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
$669$	3.65420	−	23.2617i	0.141279	−	0.899350i
$670$		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
$675$	−0.291594	−	5.18796i	−0.0112235	−	0.199685i
$676$		0			0
$677$	−19.2622	+	33.3630i	−0.740305	+	1.28225i	0.212051	+	0.977259i	$0.431986\pi$
$677$	−19.2622	+	33.3630i	−0.740305	+	1.28225i	−0.952356	+	0.304987i	$0.901348\pi$
$678$		0			0
$679$	−1.85309	+	7.75178i	−0.0711150	+	0.297486i
$680$		0			0
$681$	6.26812	+	16.2676i	0.240195	+	0.623376i
$682$		0			0
$683$	−8.24278	+	4.75897i	−0.315401	+	0.182097i	−0.649341	−	0.760497i	$-0.724955\pi$
$683$	−8.24278	+	4.75897i	−0.315401	+	0.182097i	0.333940	+	0.942594i	$0.391622\pi$
$684$		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	0.993067	−	0.117548i	$-0.0375033\pi$
$691$	36.4810	+	21.0623i	1.38780	+	0.801248i	0.394734	+	0.918795i	$0.370837\pi$
$692$		0			0
$693$	−16.5486	−	0.375477i	−0.628628	−	0.0142632i
$694$		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
$705$	7.76217	+	20.1451i	0.292340	+	0.758708i
$706$		0			0
$707$	−9.33395	−	31.3990i	−0.351039	−	1.18088i
$708$		0			0
$709$	12.6523	−	21.9145i	0.475168	−	0.823015i	−0.524427	−	0.851455i	$-0.675721\pi$
$709$	12.6523	−	21.9145i	0.475168	−	0.823015i	0.999596	+	0.0284398i	$0.00905390\pi$
$710$		0			0
$711$	14.1164	−	12.7752i	0.529407	−	0.479106i
$712$		0			0
$713$	3.13964			0.117581
$714$		0			0
$715$	−0.512543			−0.0191680
$716$		0			0
$717$	−1.30747	+	8.32300i	−0.0488282	+	0.310828i
$718$		0			0
$719$	7.70568	−	13.3466i	0.287373	−	0.497745i	−0.685809	−	0.727782i	$-0.740551\pi$
$719$	7.70568	−	13.3466i	0.287373	−	0.497745i	0.973182	+	0.230037i	$0.0738846\pi$
$720$		0			0
$721$	−32.3370	−	30.6271i	−1.20429	−	1.14061i
$722$		0			0
$723$	−27.8519	+	10.7317i	−1.03582	+	0.399116i
$724$		0			0
$725$	0.231640	−	0.133737i	0.00860289	−	0.00496688i
$726$		0			0
$727$			17.2053i			0.638109i	0.947736	+	0.319054i	$0.103365\pi$
$727$			17.2053i			0.638109i	−0.947736	+	0.319054i	$0.896635\pi$
$728$		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	0.420047	−	0.907502i	$-0.362014\pi$
$733$	−4.21946	−	2.43611i	−0.155849	−	0.0899797i	−0.575896	+	0.817523i	$0.695347\pi$
$734$		0			0
$735$	−11.0603	+	4.96686i	−0.407965	+	0.183205i
$736$		0			0
$737$	−10.0417	−	5.79760i	−0.369892	−	0.213557i
$738$		0			0
$739$	−11.2489	−	19.4836i	−0.413796	−	0.716716i	0.581505	−	0.813543i	$-0.302464\pi$
$739$	−11.2489	−	19.4836i	−0.413796	−	0.716716i	−0.995301	+	0.0968269i	$0.969131\pi$
$740$		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
$747$	3.04608	+	0.981235i	0.111450	+	0.0359015i
$748$		0			0
$749$	−24.6277	−	23.3254i	−0.899875	−	0.852292i
$750$		0			0
$751$	−13.4867	+	23.3597i	−0.492138	+	0.852409i	−0.999959	−	0.00905407i	$-0.997118\pi$
$751$	−13.4867	+	23.3597i	−0.492138	+	0.852409i	0.507821	+	0.861463i	$0.330451\pi$
$752$		0			0
$753$	−27.0821	−	4.25435i	−0.986928	−	0.155037i
$754$		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
$759$	−9.88936	−	1.55353i	−0.358961	−	0.0563894i
$760$		0			0
$761$	9.03998	−	15.6577i	0.327699	−	0.567591i	−0.654356	−	0.756187i	$-0.727060\pi$
$761$	9.03998	−	15.6577i	0.327699	−	0.567591i	0.982055	+	0.188595i	$0.0603935\pi$
$762$		0			0
$763$	2.70569	+	9.10184i	0.0979527	+	0.329509i
$764$		0			0
$765$	2.69353	+	0.867670i	0.0973849	+	0.0313707i
$766$		0			0
$767$	−2.66257	+	1.53724i	−0.0961398	+	0.0555064i
$768$		0			0
$769$			25.1297i			0.906199i	0.891460	+	0.453100i	$0.149682\pi$
$769$			25.1297i			0.906199i	−0.891460	+	0.453100i	$0.850318\pi$
$770$		0			0
$771$	19.8247	−	24.5448i	0.713971	−	0.883959i
$772$		0			0
$773$	16.3082	+	28.2467i	0.586567	+	1.01596i	0.994678	+	0.103031i	$0.0328541\pi$
$773$	16.3082	+	28.2467i	0.586567	+	1.01596i	−0.408112	+	0.912932i	$0.633813\pi$
$774$		0			0
$775$	−0.981097	−	0.566436i	−0.0352420	−	0.0203470i
$776$		0			0
$777$	22.3688	−	17.2436i	0.802475	−	0.618612i
$778$		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	−0.427287	−	0.904116i	$-0.640531\pi$
$787$	3.98518	−	2.30085i	0.142056	−	0.0820164i	0.569344	+	0.822100i	$0.307197\pi$
$788$		0			0
$789$	−8.50958	+	3.27885i	−0.302949	+	0.116730i
$790$		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
$795$	3.36883	−	21.4452i	0.119480	−	0.760581i
$796$		0			0
$797$	13.3722			0.473666			0.236833	−	0.971550i	$-0.423891\pi$
$797$	13.3722			0.473666			0.236833	+	0.971550i	$0.423891\pi$
$798$		0			0
$799$	−11.7573			−0.415944
$800$		0			0
$801$	−2.06326	+	1.86722i	−0.0729016	+	0.0659749i
$802$		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
$807$	0.965786	+	2.50650i	0.0339973	+	0.0882329i
$808$		0			0
$809$	−20.3694	+	11.7603i	−0.716152	+	0.413470i	−0.813335	−	0.581796i	$-0.802350\pi$
$809$	−20.3694	+	11.7603i	−0.716152	+	0.413470i	0.0971830	+	0.995267i	$0.469017\pi$
$810$		0			0
$811$		−	25.5058i		−	0.895628i	−0.894127	−	0.447814i	$-0.852203\pi$
$811$		−	25.5058i		−	0.895628i	0.894127	−	0.447814i	$-0.147797\pi$
$812$		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
$819$	1.01344	−	1.66683i	0.0354124	−	0.0582437i
$820$		0			0
$821$	−1.50477	−	0.868778i	−0.0525167	−	0.0303205i	0.473512	−	0.880788i	$-0.342986\pi$
$821$	−1.50477	−	0.868778i	−0.0525167	−	0.0303205i	−0.526028	+	0.850467i	$0.676319\pi$
$822$		0			0
$823$	−0.100180	−	0.173518i	−0.00349207	−	0.00604844i	0.864274	−	0.503021i	$-0.167778\pi$
$823$	−0.100180	−	0.173518i	−0.00349207	−	0.00604844i	−0.867766	+	0.496973i	$0.834445\pi$
$824$		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	−0.837462	−	0.546496i	$-0.815961\pi$
$829$	−22.5419	+	13.0146i	−0.782913	+	0.452015i	0.0545485	+	0.998511i	$0.482628\pi$
$830$		0			0
$831$	−10.6412	−	27.6171i	−0.369140	−	0.958027i
$832$		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
$837$	5.87730	−	0.330339i	0.203149	−	0.0114182i
$838$		0			0
$839$	2.46944			0.0852546			0.0426273	−	0.999091i	$-0.486427\pi$
$839$	2.46944			0.0852546			0.0426273	+	0.999091i	$0.486427\pi$
$840$		0			0
$841$	28.9285			0.997533
$842$		0			0
$843$	−4.09072	+	26.0405i	−0.140892	+	0.896881i
$844$		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
$849$	−26.6192	+	10.2567i	−0.913569	+	0.352010i
$850$		0			0
$851$	14.7925	−	8.54045i	0.507080	−	0.292763i
$852$		0			0
$853$		−	30.3776i		−	1.04011i	−0.854133	−	0.520055i	$-0.825912\pi$
$853$		−	30.3776i		−	1.04011i	0.854133	−	0.520055i	$-0.174088\pi$
$854$		0			0
$855$	1.57666	−	0.339293i	0.0539207	−	0.0116036i
$856$		0			0
$857$	−25.8422	−	44.7601i	−0.882754	−	1.52898i	−0.848266	−	0.529570i	$-0.822353\pi$
$857$	−25.8422	−	44.7601i	−0.882754	−	1.52898i	−0.0344882	−	0.999405i	$-0.510980\pi$
$858$		0			0
$859$	−21.0239	−	12.1381i	−0.717326	−	0.414148i	0.0964418	−	0.995339i	$-0.469254\pi$
$859$	−21.0239	−	12.1381i	−0.717326	−	0.414148i	−0.813768	+	0.581190i	$0.802587\pi$
$860$		0			0
$861$	−10.1000	−	4.15717i	−0.344207	−	0.141676i
$862$		0			0
$863$	−39.3631	−	22.7263i	−1.33993	−	0.773611i	−0.353137	−	0.935572i	$-0.614885\pi$
$863$	−39.3631	−	22.7263i	−1.33993	−	0.773611i	−0.986797	+	0.161960i	$0.948218\pi$
$864$		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
$873$	−2.77099	+	8.60205i	−0.0937837	+	0.291135i
$874$		0			0
$875$	2.57325	+	0.615143i	0.0869916	+	0.0207956i
$876$		0			0
$877$	−12.6911	+	21.9817i	−0.428549	+	0.742268i	−0.996744	−	0.0806254i	$-0.974308\pi$
$877$	−12.6911	+	21.9817i	−0.428549	+	0.742268i	0.568196	+	0.822893i	$0.307642\pi$
$878$		0			0
$879$	31.0984	+	4.88527i	1.04892	+	0.164776i
$880$		0			0
$881$	−42.5616			−1.43394			−0.716969	−	0.697105i	$-0.754471\pi$
$881$	−42.5616			−1.43394			−0.716969	+	0.697105i	$0.754471\pi$
$882$		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
$885$	21.4047	+	3.36248i	0.719511	+	0.113028i
$886$		0			0
$887$	−3.87420	+	6.71032i	−0.130083	+	0.225310i	−0.923708	−	0.383096i	$-0.874858\pi$
$887$	−3.87420	+	6.71032i	−0.130083	+	0.225310i	0.793625	+	0.608407i	$0.208191\pi$
$888$		0			0
$889$	−19.9709	−	4.77410i	−0.669802	−	0.160118i
$890$		0			0
$891$	−18.6760	−	1.86763i	−0.625669	−	0.0625680i
$892$		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
$903$	−48.4591	−	19.9458i	−1.61262	−	0.663755i
$904$		0			0
$905$	15.3485	+	8.86149i	0.510203	+	0.294566i
$906$		0			0
$907$	−22.7236	−	39.3584i	−0.754524	−	1.30687i	−0.945611	−	0.325300i	$-0.894535\pi$
$907$	−22.7236	−	39.3584i	−0.754524	−	1.30687i	0.191087	−	0.981573i	$-0.438799\pi$
$908$		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
$915$	−9.26700	+	3.57070i	−0.306358	+	0.118044i
$916$		0			0
$917$	31.2273	−	32.9707i	1.03122	−	1.08879i
$918$		0			0
$919$	−14.4006	+	24.9427i	−0.475034	+	0.822782i	−0.999591	−	0.0285927i	$-0.990897\pi$
$919$	−14.4006	+	24.9427i	−0.475034	+	0.822782i	0.524558	+	0.851375i	$0.324231\pi$
$920$		0			0
$921$	−6.63811	+	42.2565i	−0.218733	+	1.39240i
$922$		0			0
$923$	−2.49149			−0.0820085
$924$		0			0
$925$	−6.16327			−0.202647
$926$		0			0
$927$	−33.8872	−	37.4450i	−1.11300	−	1.22986i
$928$		0			0
$929$	15.9490	−	27.6244i	0.523269	−	0.906329i	−0.476364	−	0.879248i	$-0.658046\pi$
$929$	15.9490	−	27.6244i	0.523269	−	0.906329i	0.999633	−	0.0270805i	$-0.00862104\pi$
$930$		0			0
$931$	−2.05565	−	3.15202i	−0.0673711	−	0.103303i
$932$		0			0
$933$	14.3308	+	37.1927i	0.469171	+	1.21763i
$934$		0			0
$935$	−1.70362	+	0.983585i	−0.0557143	+	0.0321667i
$936$		0			0
$937$			36.5715i			1.19474i	0.801966	+	0.597370i	$0.203787\pi$
$937$			36.5715i			1.19474i	−0.801966	+	0.597370i	$0.796213\pi$
$938$		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	$-0.289742\pi$
$941$	−11.5675	−	20.0355i	−0.377091	−	0.653140i	−0.990638	+	0.136518i	$0.956409\pi$
$942$		0			0
$943$	−5.72040	−	3.30267i	−0.186282	−	0.107550i
$944$		0			0
$945$	−12.9372	+	4.65068i	−0.420847	+	0.151287i
$946$		0			0
$947$	29.4876	+	17.0247i	0.958220	+	0.553228i	0.895625	−	0.444811i	$-0.146729\pi$
$947$	29.4876	+	17.0247i	0.958220	+	0.553228i	0.0625952	+	0.998039i	$0.480062\pi$
$948$		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
$957$	−0.347376	−	0.901542i	−0.0112291	−	0.0291427i
$958$		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
$963$	−25.8083	−	28.5179i	−0.831661	−	0.918976i
$964$		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
$969$	−0.136303	+	0.867670i	−0.00437868	+	0.0278736i
$970$		0			0
$971$	−9.79452	+	16.9646i	−0.314321	+	0.544420i	−0.979293	−	0.202448i	$-0.935110\pi$
$971$	−9.79452	+	16.9646i	−0.314321	+	0.544420i	0.664972	+	0.746868i	$0.268444\pi$
$972$		0			0
$973$	6.04772	−	25.2986i	0.193881	−	0.811037i
$974$		0			0
$975$	−0.397219	+	0.153054i	−0.0127212	+	0.00490164i
$976$		0			0
$977$	26.5041	−	15.3022i	0.847942	−	0.489559i	−0.0120141	−	0.999928i	$-0.503824\pi$
$977$	26.5041	−	15.3022i	0.847942	−	0.489559i	0.859956	+	0.510368i	$0.170491\pi$
$978$		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	$-0.0180683\pi$
$983$	14.1107	+	24.4405i	0.450063	+	0.779532i	−0.548327	+	0.836264i	$0.684735\pi$
$984$		0			0
$985$	−19.3125	−	11.1501i	−0.615347	−	0.355271i
$986$		0			0
$987$	45.2375	−	34.8726i	1.43992	−	1.11001i
$988$		0			0
$989$	−27.4460	−	15.8460i	−0.872734	−	0.503873i
$990$		0			0
$991$	12.2999	+	21.3040i	0.390719	+	0.676745i	0.992545	−	0.121882i	$-0.0388931\pi$
$991$	12.2999	+	21.3040i	0.390719	+	0.676745i	−0.601826	+	0.798628i	$0.705560\pi$
$992$		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	0.530481	−	0.847697i	$-0.322011\pi$
$997$	48.3054	−	27.8892i	1.52985	−	0.883258i	0.999367	−	0.0355613i	$-0.0113219\pi$
$998$		0			0
$999$	26.7924	−	17.5438i	0.847675	−	0.555062i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bh.a.101.5	✓	10	21.17	even	6	inner
420.2.bh.a.341.5	yes	10	1.1	even	1	trivial
420.2.bh.b.101.3	yes	10	7.3	odd	6
420.2.bh.b.341.3	yes	10	3.2	odd	2
2100.2.bi.j.101.3		10	35.24	odd	6
2100.2.bi.j.1601.3		10	15.14	odd	2
2100.2.bi.k.101.1		10	105.59	even	6
2100.2.bi.k.1601.1		10	5.4	even	2
2100.2.bo.g.1349.1		20	15.2	even	4
2100.2.bo.g.1349.10		20	15.8	even	4
2100.2.bo.g.1949.1		20	35.3	even	12
2100.2.bo.g.1949.10		20	35.17	even	12
2100.2.bo.h.1349.5		20	5.3	odd	4
2100.2.bo.h.1349.6		20	5.2	odd	4
2100.2.bo.h.1949.5		20	105.17	odd	12
2100.2.bo.h.1949.6		20	105.38	odd	12
2940.2.d.a.881.7		10	7.5	odd	6
2940.2.d.a.881.8		10	21.2	odd	6
2940.2.d.b.881.3		10	21.5	even	6
2940.2.d.b.881.4		10	7.2	even	3

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)

\(f(q)\)	\(=\)	\(q+(1.71107 + 0.268793i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(2.57325 + 0.615143i) q^{7} +(2.85550 + 0.919845i) q^{9} +O(q^{10})\)	\(q+(1.71107 + 0.268793i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(2.57325 + 0.615143i) q^{7} +(2.85550 + 0.919845i) q^{9} +(-1.80606 + 1.04273i) q^{11} -0.245770i q^{13} +(-1.08831 + 1.34743i) q^{15} +(-0.471640 - 0.816904i) q^{17} +(-0.465563 - 0.268793i) q^{19} +(4.23765 + 1.74422i) q^{21} +(2.40010 + 1.38570i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(4.63871 + 2.34145i) q^{27} +0.267475i q^{29} +(0.981097 - 0.566436i) q^{31} +(-3.37057 + 1.29872i) q^{33} +(-1.81935 + 1.92093i) q^{35} +(3.08164 - 5.33755i) q^{37} +(0.0660611 - 0.420528i) q^{39} -2.38340 q^{41} -11.4354 q^{43} +(-2.22436 + 2.01301i) q^{45} +(6.23215 - 10.7944i) q^{47} +(6.24320 + 3.16583i) q^{49} +(-0.587429 - 1.52455i) q^{51} +(-10.8541 + 6.26660i) q^{53} -2.08546i q^{55} +(-0.724359 - 0.585062i) q^{57} +(-6.25478 - 10.8336i) q^{59} +(4.96556 + 2.86687i) q^{61} +(6.78207 + 4.12353i) q^{63} +(0.212843 + 0.122885i) q^{65} +(2.78001 + 4.81512i) q^{67} +(3.73427 + 3.01616i) q^{69} -10.1375i q^{71} +(-11.3758 + 6.56784i) q^{73} +(-0.622752 - 1.61622i) q^{75} +(-5.28887 + 1.57221i) q^{77} +(3.17314 - 5.49605i) q^{79} +(7.30777 + 5.25324i) q^{81} +1.06674 q^{83} +0.943279 q^{85} +(-0.0718953 + 0.457667i) q^{87} +(-0.463787 + 0.803302i) q^{89} +(0.151184 - 0.632426i) q^{91} +(1.83098 - 0.705499i) q^{93} +(0.465563 - 0.268793i) q^{95} +3.01245i q^{97} +(-6.11636 + 1.31622i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{3} - 5 q^{5} - 5 q^{7} - 3 q^{9}+O(q^{10}) \) 10 * q - q^3 - 5 * q^5 - 5 * q^7 - 3 * q^9	\( 10 q - q^{3} - 5 q^{5} - 5 q^{7} - 3 q^{9} - 6 q^{11} + 2 q^{15} + 6 q^{17} + 3 q^{19} + 10 q^{21} + 24 q^{23} - 5 q^{25} + 8 q^{27} + 15 q^{31} - 20 q^{33} + q^{35} - q^{37} + 15 q^{39} - 8 q^{41} - 26 q^{43} + 3 q^{45} + 14 q^{47} - 13 q^{49} - 44 q^{51} - 24 q^{53} + 18 q^{57} + 42 q^{61} - q^{63} + 9 q^{65} + 7 q^{67} - 14 q^{69} - 3 q^{73} - q^{75} - 26 q^{77} + q^{79} + 41 q^{81} - 8 q^{83} - 12 q^{85} - 26 q^{87} + 28 q^{89} - 11 q^{91} - 47 q^{93} - 3 q^{95} + 36 q^{99}+O(q^{100}) \) 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 + 10 * q^21 + 24 * q^23 - 5 * q^25 + 8 * q^27 + 15 * q^31 - 20 * q^33 + q^35 - q^37 + 15 * q^39 - 8 * q^41 - 26 * q^43 + 3 * q^45 + 14 * q^47 - 13 * q^49 - 44 * q^51 - 24 * q^53 + 18 * q^57 + 42 * q^61 - q^63 + 9 * q^65 + 7 * q^67 - 14 * q^69 - 3 * q^73 - q^75 - 26 * q^77 + q^79 + 41 * q^81 - 8 * q^83 - 12 * q^85 - 26 * q^87 + 28 * q^89 - 11 * q^91 - 47 * q^93 - 3 * q^95 + 36 * q^99

Introduction

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