LMFDB - Embedded newform 420.2.bh.b.341.2

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			341.2
Root			$0.527154 + 1.64988i$ of defining polynomial
Character	$\chi$	$=$	420.341
Dual form			420.2.bh.b.101.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16526 + 1.28147i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-1.80025 - 1.93884i) q^{7} +(-0.284326 - 2.98650i) q^{9} +O(q^{10})$	\(q+(-1.16526 + 1.28147i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-1.80025 - 1.93884i) q^{7} +(-0.284326 - 2.98650i) q^{9} +(-4.05595 + 2.34170i) q^{11} +2.18938i q^{13} +(0.527154 + 1.64988i) q^{15} +(-3.74984 - 6.49492i) q^{17} +(-0.638109 - 0.368412i) q^{19} +(4.58233 - 0.0477143i) q^{21} +(-6.99627 - 4.03930i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(4.15842 + 3.11570i) q^{27} -1.15414i q^{29} +(8.95201 - 5.16845i) q^{31} +(1.72543 - 7.92628i) q^{33} +(-2.57921 + 0.589646i) q^{35} +(2.30923 - 3.99970i) q^{37} +(-2.80562 - 2.55120i) q^{39} +1.43758 q^{41} -9.24142 q^{43} +(-2.72854 - 1.24701i) q^{45} +(-4.34224 + 7.52098i) q^{47} +(-0.518179 + 6.98079i) q^{49} +(12.6926 + 2.76298i) q^{51} +(-7.03514 + 4.06174i) q^{53} +4.68341i q^{55} +(1.21567 - 0.388420i) q^{57} +(-3.48730 - 6.04018i) q^{59} +(5.13811 + 2.96649i) q^{61} +(-5.27847 + 5.92771i) q^{63} +(1.89606 + 1.09469i) q^{65} +(0.691639 + 1.19795i) q^{67} +(13.3287 - 4.25866i) q^{69} +7.26258i q^{71} +(-0.211355 + 0.122026i) q^{73} +(1.69242 + 0.368412i) q^{75} +(11.8419 + 3.64817i) q^{77} +(-5.79653 + 10.0399i) q^{79} +(-8.83832 + 1.69828i) q^{81} +16.4610 q^{83} -7.49968 q^{85} +(1.47899 + 1.34488i) q^{87} +(-0.658248 + 1.14012i) q^{89} +(4.24485 - 3.94144i) q^{91} +(-3.80824 + 17.4943i) q^{93} +(-0.638109 + 0.368412i) q^{95} -4.84232i q^{97} +(8.14670 + 11.4473i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/420\mathbb{Z}\right)^\times$.

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

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
$3$	−1.16526	+	1.28147i	−0.672765	+	0.739857i
$3$	−1.16526	+	1.28147i	−0.672765	+	0.739857i
$4$		0			0
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	−1.80025	−	1.93884i	−0.680432	−	0.732812i
$7$	−1.80025	−	1.93884i	−0.680432	−	0.732812i
$8$		0			0
$9$	−0.284326	−	2.98650i	−0.0947754	−	0.995499i
$10$		0			0
$11$	−4.05595	+	2.34170i	−1.22292	+	0.706050i	−0.965538	−	0.260261i	$-0.916192\pi$
$11$	−4.05595	+	2.34170i	−1.22292	+	0.706050i	−0.257377	+	0.966311i	$0.582858\pi$
$12$		0			0
$13$			2.18938i			0.607225i	0.952796	+	0.303612i	$0.0981928\pi$
$13$			2.18938i			0.607225i	−0.952796	+	0.303612i	$0.901807\pi$
$14$		0			0
$15$	0.527154	+	1.64988i	0.136110	+	0.425998i
$16$		0			0
$17$	−3.74984	−	6.49492i	−0.909470	−	1.57525i	−0.814802	−	0.579740i	$-0.803154\pi$
$17$	−3.74984	−	6.49492i	−0.909470	−	1.57525i	−0.0946686	−	0.995509i	$-0.530179\pi$
$18$		0			0
$19$	−0.638109	−	0.368412i	−0.146392	−	0.0845196i	0.425015	−	0.905186i	$-0.360269\pi$
$19$	−0.638109	−	0.368412i	−0.146392	−	0.0845196i	−0.571407	+	0.820667i	$0.693602\pi$
$20$		0			0
$21$	4.58233	−	0.0477143i	0.999946	−	0.0104121i
$22$		0			0
$23$	−6.99627	−	4.03930i	−1.45882	−	0.842252i	−0.459870	−	0.887986i	$-0.652104\pi$
$23$	−6.99627	−	4.03930i	−1.45882	−	0.842252i	−0.998954	+	0.0457338i	$0.985437\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	4.15842	+	3.11570i	0.800288	+	0.599616i
$28$		0			0
$29$		−	1.15414i		−	0.214318i	−0.994242	−	0.107159i	$-0.965825\pi$
$29$		−	1.15414i		−	0.214318i	0.994242	−	0.107159i	$-0.0341754\pi$
$30$		0			0
$31$	8.95201	−	5.16845i	1.60783	−	0.928280i	0.617974	−	0.786199i	$-0.287954\pi$
$31$	8.95201	−	5.16845i	1.60783	−	0.928280i	0.989855	−	0.142081i	$-0.0453794\pi$
$32$		0			0
$33$	1.72543	−	7.92628i	0.300358	−	1.37979i
$34$		0			0
$35$	−2.57921	+	0.589646i	−0.435966	+	0.0996684i
$36$		0			0
$37$	2.30923	−	3.99970i	0.379635	−	0.657547i	−0.611374	−	0.791342i	$-0.709383\pi$
$37$	2.30923	−	3.99970i	0.379635	−	0.657547i	0.991009	+	0.133795i	$0.0427163\pi$
$38$		0			0
$39$	−2.80562	−	2.55120i	−0.449259	−	0.408519i
$40$		0			0
$41$	1.43758			0.224513			0.112256	−	0.993679i	$-0.464192\pi$
$41$	1.43758			0.224513			0.112256	+	0.993679i	$0.464192\pi$
$42$		0			0
$43$	−9.24142			−1.40930			−0.704651	−	0.709554i	$-0.748897\pi$
$43$	−9.24142			−1.40930			−0.704651	+	0.709554i	$0.748897\pi$
$44$		0			0
$45$	−2.72854	−	1.24701i	−0.406747	−	0.185894i
$46$		0			0
$47$	−4.34224	+	7.52098i	−0.633380	+	1.09705i	0.353475	+	0.935444i	$0.385000\pi$
$47$	−4.34224	+	7.52098i	−0.633380	+	1.09705i	−0.986856	+	0.161603i	$0.948333\pi$
$48$		0			0
$49$	−0.518179	+	6.98079i	−0.0740255	+	0.997256i
$50$		0			0
$51$	12.6926	+	2.76298i	1.77732	+	0.386894i
$52$		0			0
$53$	−7.03514	+	4.06174i	−0.966351	+	0.557923i	−0.898122	−	0.439747i	$-0.855068\pi$
$53$	−7.03514	+	4.06174i	−0.966351	+	0.557923i	−0.0682291	+	0.997670i	$0.521735\pi$
$54$		0			0
$55$			4.68341i			0.631511i
$56$		0			0
$57$	1.21567	−	0.388420i	0.161020	−	0.0514475i
$58$		0			0
$59$	−3.48730	−	6.04018i	−0.454008	−	0.786364i	0.544623	−	0.838681i	$-0.316673\pi$
$59$	−3.48730	−	6.04018i	−0.454008	−	0.786364i	−0.998631	+	0.0523168i	$0.983339\pi$
$60$		0			0
$61$	5.13811	+	2.96649i	0.657867	+	0.379820i	0.791464	−	0.611216i	$-0.209319\pi$
$61$	5.13811	+	2.96649i	0.657867	+	0.379820i	−0.133596	+	0.991036i	$0.542653\pi$
$62$		0			0
$63$	−5.27847	+	5.92771i	−0.665025	+	0.746821i
$64$		0			0
$65$	1.89606	+	1.09469i	0.235177	+	0.135780i
$66$		0			0
$67$	0.691639	+	1.19795i	0.0844971	+	0.146353i	0.905177	−	0.425035i	$-0.139738\pi$
$67$	0.691639	+	1.19795i	0.0844971	+	0.146353i	−0.820680	+	0.571389i	$0.806405\pi$
$68$		0			0
$69$	13.3287	−	4.25866i	1.60459	−	0.512683i
$70$		0			0
$71$			7.26258i			0.861909i	0.902374	+	0.430955i	$0.141823\pi$
$71$			7.26258i			0.861909i	−0.902374	+	0.430955i	$0.858177\pi$
$72$		0			0
$73$	−0.211355	+	0.122026i	−0.0247372	+	0.0142820i	−0.512318	−	0.858796i	$-0.671213\pi$
$73$	−0.211355	+	0.122026i	−0.0247372	+	0.0142820i	0.487580	+	0.873078i	$0.337880\pi$
$74$		0			0
$75$	1.69242	+	0.368412i	0.195423	+	0.0425406i
$76$		0			0
$77$	11.8419	+	3.64817i	1.34951	+	0.415747i
$78$		0			0
$79$	−5.79653	+	10.0399i	−0.652160	+	1.12957i	0.330438	+	0.943828i	$0.392804\pi$
$79$	−5.79653	+	10.0399i	−0.652160	+	1.12957i	−0.982598	+	0.185747i	$0.940530\pi$
$80$		0			0
$81$	−8.83832	+	1.69828i	−0.982035	+	0.188698i
$82$		0			0
$83$	16.4610			1.80683			0.903413	−	0.428772i	$-0.141054\pi$
$83$	16.4610			1.80683			0.903413	+	0.428772i	$0.141054\pi$
$84$		0			0
$85$	−7.49968			−0.813455
$86$		0			0
$87$	1.47899	+	1.34488i	0.158565	+	0.144186i
$88$		0			0
$89$	−0.658248	+	1.14012i	−0.0697741	+	0.120852i	−0.898802	−	0.438355i	$-0.855561\pi$
$89$	−0.658248	+	1.14012i	−0.0697741	+	0.120852i	0.829028	+	0.559208i	$0.188895\pi$
$90$		0			0
$91$	4.24485	−	3.94144i	0.444981	−	0.413175i
$92$		0			0
$93$	−3.80824	+	17.4943i	−0.394896	+	1.81408i
$94$		0			0
$95$	−0.638109	+	0.368412i	−0.0654686	+	0.0377983i
$96$		0			0
$97$		−	4.84232i		−	0.491663i	−0.969313	−	0.245832i	$-0.920939\pi$
$97$		−	4.84232i		−	0.491663i	0.969313	−	0.245832i	$-0.0790611\pi$
$98$		0			0
$99$	8.14670	+	11.4473i	0.818775	+	1.15049i
$100$		0			0
$101$	−1.38435	−	2.39776i	−0.137748	−	0.238586i	0.788896	−	0.614527i	$-0.210653\pi$
$101$	−1.38435	−	2.39776i	−0.137748	−	0.238586i	−0.926644	+	0.375941i	$0.877320\pi$
$102$		0			0
$103$	−7.07000	−	4.08187i	−0.696628	−	0.402199i	0.109462	−	0.993991i	$-0.465087\pi$
$103$	−7.07000	−	4.08187i	−0.696628	−	0.402199i	−0.806090	+	0.591792i	$0.798421\pi$
$104$		0			0
$105$	2.24984	−	3.99227i	0.219562	−	0.389606i
$106$		0			0
$107$	0.186331	+	0.107578i	0.0180133	+	0.0104000i	0.508980	−	0.860779i	$-0.330023\pi$
$107$	0.186331	+	0.107578i	0.0180133	+	0.0104000i	−0.490966	+	0.871179i	$0.663356\pi$
$108$		0			0
$109$	−1.08683	−	1.88245i	−0.104100	−	0.180306i	0.809270	−	0.587436i	$-0.199863\pi$
$109$	−1.08683	−	1.88245i	−0.104100	−	0.180306i	−0.913370	+	0.407131i	$0.866529\pi$
$110$		0			0
$111$	2.43464	+	7.61990i	0.231085	+	0.723249i
$112$		0			0
$113$		−	11.2195i		−	1.05544i	−0.849419	−	0.527719i	$-0.823048\pi$
$113$		−	11.2195i		−	1.05544i	0.849419	−	0.527719i	$-0.176952\pi$
$114$		0			0
$115$	−6.99627	+	4.03930i	−0.652406	+	0.376667i
$116$		0			0
$117$	6.53858	−	0.622499i	0.604492	−	0.0575500i
$118$		0			0
$119$	−5.84192	+	18.9628i	−0.535528	+	1.73832i
$120$		0			0
$121$	5.46716	−	9.46940i	0.497015	−	0.860854i
$122$		0			0
$123$	−1.67516	+	1.84222i	−0.151044	+	0.166107i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	17.2228			1.52828			0.764140	−	0.645051i	$-0.223164\pi$
$127$	17.2228			1.52828			0.764140	+	0.645051i	$0.223164\pi$
$128$		0			0
$129$	10.7687	−	11.8426i	0.948129	−	1.04268i
$130$		0			0
$131$	8.65810	−	14.9963i	0.756462	−	1.31023i	−0.188183	−	0.982134i	$-0.560260\pi$
$131$	8.65810	−	14.9963i	0.756462	−	1.31023i	0.944644	−	0.328096i	$-0.106407\pi$
$132$		0			0
$133$	0.434466	+	1.90042i	0.0376730	+	0.164788i
$134$		0			0
$135$	4.77748	−	2.04345i	0.411180	−	0.175872i
$136$		0			0
$137$	−9.68866	+	5.59375i	−0.827758	+	0.477907i	−0.853085	−	0.521773i	$-0.825271\pi$
$137$	−9.68866	+	5.59375i	−0.827758	+	0.477907i	0.0253261	+	0.999679i	$0.491938\pi$
$138$		0			0
$139$		−	2.16017i		−	0.183223i	−0.995795	−	0.0916116i	$-0.970798\pi$
$139$		−	2.16017i		−	0.183223i	0.995795	−	0.0916116i	$-0.0292018\pi$
$140$		0			0
$141$	−4.57805	−	14.3284i	−0.385542	−	1.20667i
$142$		0			0
$143$	−5.12688	−	8.88002i	−0.428731	−	0.742585i
$144$		0			0
$145$	−0.999514	−	0.577070i	−0.0830051	−	0.0479230i
$146$		0			0
$147$	−8.34186	−	8.79849i	−0.688025	−	0.725687i
$148$		0			0
$149$	−1.37427	−	0.793438i	−0.112585	−	0.0650010i	0.442650	−	0.896694i	$-0.354038\pi$
$149$	−1.37427	−	0.793438i	−0.112585	−	0.0650010i	−0.555235	+	0.831693i	$0.687372\pi$
$150$		0			0
$151$	−5.12229	−	8.87206i	−0.416846	−	0.721998i	0.578774	−	0.815488i	$-0.303531\pi$
$151$	−5.12229	−	8.87206i	−0.416846	−	0.721998i	−0.995620	+	0.0934894i	$0.970198\pi$
$152$		0			0
$153$	−18.3309	+	13.0456i	−1.48196	+	1.05467i
$154$		0			0
$155$		−	10.3369i		−	0.830279i
$156$		0			0
$157$	−5.62174	+	3.24572i	−0.448664	+	0.259036i	−0.707266	−	0.706948i	$-0.750072\pi$
$157$	−5.62174	+	3.24572i	−0.448664	+	0.259036i	0.258602	+	0.965984i	$0.416738\pi$
$158$		0			0
$159$	2.99279	−	13.7483i	0.237344	−	1.09031i
$160$		0			0
$161$	4.76352	+	20.8364i	0.375418	+	1.64214i
$162$		0			0
$163$	−2.68350	+	4.64797i	−0.210188	+	0.364057i	−0.951773	−	0.306802i	$-0.900741\pi$
$163$	−2.68350	+	4.64797i	−0.210188	+	0.364057i	0.741585	+	0.670859i	$0.234074\pi$
$164$		0			0
$165$	−6.00164	−	5.45740i	−0.467227	−	0.424858i
$166$		0			0
$167$	6.84082			0.529359			0.264679	−	0.964336i	$-0.414734\pi$
$167$	6.84082			0.529359			0.264679	+	0.964336i	$0.414734\pi$
$168$		0			0
$169$	8.20661			0.631278
$170$		0			0
$171$	−0.918831	+	2.01046i	−0.0702648	+	0.153744i
$172$		0			0
$173$	−5.81618	+	10.0739i	−0.442196	+	0.765906i	−0.997852	−	0.0655063i	$-0.979134\pi$
$173$	−5.81618	+	10.0739i	−0.442196	+	0.765906i	0.555656	+	0.831412i	$0.312467\pi$
$174$		0			0
$175$	−0.778956	+	2.52848i	−0.0588835	+	0.191135i
$176$		0			0
$177$	11.8039	+	2.56953i	0.887237	+	0.193138i
$178$		0			0
$179$	6.95741	−	4.01686i	0.520021	−	0.300234i	−0.216922	−	0.976189i	$-0.569602\pi$
$179$	6.95741	−	4.01686i	0.520021	−	0.300234i	0.736943	+	0.675955i	$0.236268\pi$
$180$		0			0
$181$			9.81789i			0.729758i	0.931055	+	0.364879i	$0.118890\pi$
$181$			9.81789i			0.729758i	−0.931055	+	0.364879i	$0.881110\pi$
$182$		0			0
$183$	−9.78871	+	3.12759i	−0.723602	+	0.231198i
$184$		0			0
$185$	−2.30923	−	3.99970i	−0.169778	−	0.294064i
$186$		0			0
$187$	30.4184	+	17.5620i	2.22441	+	1.28426i
$188$		0			0
$189$	−1.44537	−	13.6715i	−0.105136	−	0.994458i
$190$		0			0
$191$	−13.9054	−	8.02830i	−1.00616	−	0.580907i	−0.0960953	−	0.995372i	$-0.530635\pi$
$191$	−13.9054	−	8.02830i	−1.00616	−	0.580907i	−0.910065	+	0.414465i	$0.863969\pi$
$192$		0			0
$193$	−3.19143	−	5.52771i	−0.229724	−	0.397894i	0.728002	−	0.685575i	$-0.240449\pi$
$193$	−3.19143	−	5.52771i	−0.229724	−	0.397894i	−0.957726	+	0.287681i	$0.907116\pi$
$194$		0			0
$195$	−3.61222	+	1.15414i	−0.258676	+	0.0826497i
$196$		0			0
$197$		−	2.54995i		−	0.181677i	−0.995866	−	0.0908384i	$-0.971045\pi$
$197$		−	2.54995i		−	0.181677i	0.995866	−	0.0908384i	$-0.0289547\pi$
$198$		0			0
$199$	−6.27973	+	3.62561i	−0.445159	+	0.257012i	−0.705783	−	0.708428i	$-0.749405\pi$
$199$	−6.27973	+	3.62561i	−0.445159	+	0.257012i	0.260625	+	0.965440i	$0.416071\pi$
$200$		0			0
$201$	−2.34108	−	0.509617i	−0.165127	−	0.0359456i
$202$		0			0
$203$	−2.23769	+	2.07774i	−0.157055	+	0.145829i
$204$		0			0
$205$	0.718792	−	1.24498i	0.0502026	−	0.0869535i
$206$		0			0
$207$	−10.0741	+	22.0428i	−0.700200	+	1.53208i
$208$		0			0
$209$	3.45085			0.238700
$210$		0			0
$211$	−13.2654			−0.913230			−0.456615	−	0.889664i	$-0.650938\pi$
$211$	−13.2654			−0.913230			−0.456615	+	0.889664i	$0.650938\pi$
$212$		0			0
$213$	−9.30677	−	8.46281i	−0.637689	−	0.579862i
$214$		0			0
$215$	−4.62071	+	8.00330i	−0.315130	+	0.545821i
$216$		0			0
$217$	−26.1367	−	8.05198i	−1.77427	−	0.546604i
$218$		0			0
$219$	0.0899116	−	0.413037i	0.00607567	−	0.0279104i
$220$		0			0
$221$	14.2198	−	8.20983i	0.956530	−	0.552253i
$222$		0			0
$223$		−	28.1032i		−	1.88193i	−0.338506	−	0.940964i	$-0.609922\pi$
$223$		−	28.1032i		−	1.88193i	0.338506	−	0.940964i	$-0.390078\pi$
$224$		0			0
$225$	−2.44422	+	1.73948i	−0.162948	+	0.115965i
$226$		0			0
$227$	−6.71504	−	11.6308i	−0.445693	−	0.771963i	0.552407	−	0.833574i	$-0.313709\pi$
$227$	−6.71504	−	11.6308i	−0.445693	−	0.771963i	−0.998100	+	0.0616117i	$0.980376\pi$
$228$		0			0
$229$	−7.24605	−	4.18351i	−0.478833	−	0.276454i	0.241097	−	0.970501i	$-0.422493\pi$
$229$	−7.24605	−	4.18351i	−0.478833	−	0.276454i	−0.719930	+	0.694047i	$0.755826\pi$
$230$		0			0
$231$	−18.4740	+	10.9240i	−1.21550	+	0.718745i
$232$		0			0
$233$	7.07871	+	4.08689i	0.463742	+	0.267741i	0.713616	−	0.700537i	$-0.247056\pi$
$233$	7.07871	+	4.08689i	0.463742	+	0.267741i	−0.249875	+	0.968278i	$0.580389\pi$
$234$		0			0
$235$	4.34224	+	7.52098i	0.283256	+	0.490614i
$236$		0			0
$237$	−6.11132	−	19.1272i	−0.396973	−	1.24244i
$238$		0			0
$239$		−	12.5553i		−	0.812134i	−0.913843	−	0.406067i	$-0.866900\pi$
$239$		−	12.5553i		−	0.812134i	0.913843	−	0.406067i	$-0.133100\pi$
$240$		0			0
$241$	19.1154	−	11.0363i	1.23133	−	0.710910i	0.264025	−	0.964516i	$-0.414950\pi$
$241$	19.1154	−	11.0363i	1.23133	−	0.710910i	0.967308	+	0.253606i	$0.0816166\pi$
$242$		0			0
$243$	8.12267	−	13.3050i	0.521069	−	0.853514i
$244$		0			0
$245$	5.78646	+	3.93915i	0.369683	+	0.251663i
$246$		0			0
$247$	0.806595	−	1.39706i	0.0513224	−	0.0888930i
$248$		0			0
$249$	−19.1813	+	21.0942i	−1.21557	+	1.33679i
$250$		0			0
$251$	−1.66808			−0.105288			−0.0526441	−	0.998613i	$-0.516765\pi$
$251$	−1.66808			−0.105288			−0.0526441	+	0.998613i	$0.516765\pi$
$252$		0			0
$253$	37.8354			2.37869
$254$		0			0
$255$	8.73910	−	9.61061i	0.547264	−	0.601840i
$256$		0			0
$257$	−0.602166	+	1.04298i	−0.0375621	+	0.0650594i	−0.884195	−	0.467117i	$-0.845293\pi$
$257$	−0.602166	+	1.04298i	−0.0375621	+	0.0650594i	0.846633	+	0.532177i	$0.178626\pi$
$258$		0			0
$259$	−11.9120	+	2.72326i	−0.740173	+	0.169215i
$260$		0			0
$261$	−3.44683	+	0.328152i	−0.213354	+	0.0203121i
$262$		0			0
$263$	4.34275	−	2.50729i	0.267785	−	0.154606i	−0.360095	−	0.932915i	$-0.617256\pi$
$263$	4.34275	−	2.50729i	0.267785	−	0.154606i	0.627881	+	0.778310i	$0.283923\pi$
$264$		0			0
$265$			8.12348i			0.499021i
$266$		0			0
$267$	−0.693995	−	2.17206i	−0.0424718	−	0.132928i
$268$		0			0
$269$	7.94487	+	13.7609i	0.484407	+	0.839018i	0.999840	−	0.0179121i	$-0.00570189\pi$
$269$	7.94487	+	13.7609i	0.484407	+	0.839018i	−0.515432	+	0.856930i	$0.672369\pi$
$270$		0			0
$271$	−17.4197	−	10.0573i	−1.05817	−	0.610937i	−0.133248	−	0.991083i	$-0.542541\pi$
$271$	−17.4197	−	10.0573i	−1.05817	−	0.610937i	−0.924927	+	0.380146i	$0.875874\pi$
$272$		0			0
$273$	0.104465	+	10.0325i	0.00632250	+	0.607192i
$274$		0			0
$275$	4.05595	+	2.34170i	0.244583	+	0.141210i
$276$		0			0
$277$	−2.20512	−	3.81938i	−0.132493	−	0.229484i	0.792144	−	0.610334i	$-0.208965\pi$
$277$	−2.20512	−	3.81938i	−0.132493	−	0.229484i	−0.924637	+	0.380850i	$0.875631\pi$
$278$		0			0
$279$	−17.9808	−	25.2656i	−1.07648	−	1.51261i
$280$		0			0
$281$		−	17.9173i		−	1.06886i	−0.845213	−	0.534429i	$-0.820527\pi$
$281$		−	17.9173i		−	1.06886i	0.845213	−	0.534429i	$-0.179473\pi$
$282$		0			0
$283$	10.0054	−	5.77663i	0.594760	−	0.343385i	−0.172217	−	0.985059i	$-0.555093\pi$
$283$	10.0054	−	5.77663i	0.594760	−	0.343385i	0.766978	+	0.641674i	$0.221760\pi$
$284$		0			0
$285$	0.271455	−	1.24701i	0.0160796	−	0.0738667i
$286$		0			0
$287$	−2.58802	−	2.78724i	−0.152766	−	0.164526i
$288$		0			0
$289$	−19.6226	+	33.9874i	−1.15427	+	1.99926i
$290$		0			0
$291$	6.20529	+	5.64258i	0.363760	+	0.330774i
$292$		0			0
$293$	7.17953			0.419433			0.209716	−	0.977762i	$-0.432746\pi$
$293$	7.17953			0.419433			0.209716	+	0.977762i	$0.432746\pi$
$294$		0			0
$295$	−6.97460			−0.406077
$296$		0			0
$297$	−24.1624	−	2.89933i	−1.40204	−	0.168236i
$298$		0			0
$299$	8.84357	−	15.3175i	0.511437	−	0.885834i
$300$		0			0
$301$	16.6369	+	17.9176i	0.958934	+	1.03275i
$302$		0			0
$303$	4.68578	+	1.02002i	0.269191	+	0.0585987i
$304$		0			0
$305$	5.13811	−	2.96649i	0.294207	−	0.169861i
$306$		0			0
$307$		−	2.44348i		−	0.139457i	−0.997566	−	0.0697284i	$-0.977787\pi$
$307$		−	2.44348i		−	0.139457i	0.997566	−	0.0697284i	$-0.0222133\pi$
$308$		0			0
$309$	13.4692	−	4.30354i	0.766236	−	0.244820i
$310$		0			0
$311$	−2.56348	−	4.44007i	−0.145361	−	0.251773i	0.784146	−	0.620576i	$-0.213101\pi$
$311$	−2.56348	−	4.44007i	−0.145361	−	0.251773i	−0.929508	+	0.368803i	$0.879768\pi$
$312$		0			0
$313$	−1.41881	−	0.819152i	−0.0801961	−	0.0463012i	0.459366	−	0.888247i	$-0.348077\pi$
$313$	−1.41881	−	0.819152i	−0.0801961	−	0.0463012i	−0.539562	+	0.841946i	$0.681410\pi$
$314$		0			0
$315$	2.49431	+	7.53514i	0.140539	+	0.424557i
$316$		0			0
$317$	14.3446	+	8.28184i	0.805672	+	0.465155i	0.845451	−	0.534054i	$-0.179332\pi$
$317$	14.3446	+	8.28184i	0.805672	+	0.465155i	−0.0397789	+	0.999209i	$0.512665\pi$
$318$		0			0
$319$	2.70265	+	4.68113i	0.151320	+	0.262093i
$320$		0			0
$321$	−0.354983	+	0.113421i	−0.0198132	+	0.00633052i
$322$		0			0
$323$			5.52595i			0.307472i
$324$		0			0
$325$	1.89606	−	1.09469i	0.105174	−	0.0607225i
$326$		0			0
$327$	3.67874	+	0.800804i	0.203435	+	0.0442846i
$328$		0			0
$329$	22.3991	−	5.12077i	1.23490	−	0.282317i
$330$		0			0
$331$	11.9722	−	20.7364i	0.658049	−	1.13977i	−0.323071	−	0.946375i	$-0.604715\pi$
$331$	11.9722	−	20.7364i	0.658049	−	1.13977i	0.981120	−	0.193400i	$-0.0619513\pi$
$332$		0			0
$333$	−12.6017	−	5.75928i	−0.690567	−	0.315607i
$334$		0			0
$335$	1.38328			0.0755765
$336$		0			0
$337$	−9.25410			−0.504103			−0.252051	−	0.967714i	$-0.581105\pi$
$337$	−9.25410			−0.504103			−0.252051	+	0.967714i	$0.581105\pi$
$338$		0			0
$339$	14.3774	+	13.0736i	0.780872	+	0.710061i
$340$		0			0
$341$	−24.2059	+	41.9259i	−1.31083	+	2.27042i
$342$		0			0
$343$	14.4675	−	11.5625i	0.781170	−	0.624318i
$344$		0			0
$345$	2.97626	−	13.6724i	0.160236	−	0.736095i
$346$		0			0
$347$	23.0038	−	13.2812i	1.23491	−	0.712973i	0.266857	−	0.963736i	$-0.414015\pi$
$347$	23.0038	−	13.2812i	1.23491	−	0.712973i	0.968049	+	0.250763i	$0.0806814\pi$
$348$		0			0
$349$			14.8893i			0.797004i	0.917167	+	0.398502i	$0.130470\pi$
$349$			14.8893i			0.797004i	−0.917167	+	0.398502i	$0.869530\pi$
$350$		0			0
$351$	−6.82145	+	9.10436i	−0.364102	+	0.485955i
$352$		0			0
$353$	8.41481	+	14.5749i	0.447875	+	0.775743i	0.998248	−	0.0591766i	$-0.0188475\pi$
$353$	8.41481	+	14.5749i	0.447875	+	0.775743i	−0.550372	+	0.834919i	$0.685514\pi$
$354$		0			0
$355$	6.28957	+	3.63129i	0.333816	+	0.192729i
$356$		0			0
$357$	−17.4929	−	29.5829i	−0.925823	−	1.56569i
$358$		0			0
$359$	−24.3673	−	14.0685i	−1.28606	−	0.742506i	−0.308109	−	0.951351i	$-0.599696\pi$
$359$	−24.3673	−	14.0685i	−1.28606	−	0.742506i	−0.977949	+	0.208846i	$0.933029\pi$
$360$		0			0
$361$	−9.22854	−	15.9843i	−0.485713	−	0.841279i
$362$		0			0
$363$	5.76407	+	18.0403i	0.302535	+	0.946872i
$364$		0			0
$365$			0.244052i			0.0127742i
$366$		0			0
$367$	−12.7963	+	7.38797i	−0.667963	+	0.385649i	−0.795304	−	0.606210i	$-0.792689\pi$
$367$	−12.7963	+	7.38797i	−0.667963	+	0.385649i	0.127341	+	0.991859i	$0.459356\pi$
$368$		0			0
$369$	−0.408743	−	4.29334i	−0.0212783	−	0.223502i
$370$		0			0
$371$	20.5401	+	6.32783i	1.06639	+	0.328525i
$372$		0			0
$373$	10.9537	−	18.9723i	0.567159	−	0.982348i	−0.429687	−	0.902978i	$-0.641376\pi$
$373$	10.9537	−	18.9723i	0.567159	−	0.982348i	0.996845	−	0.0793696i	$-0.0252907\pi$
$374$		0			0
$375$	1.16526	−	1.28147i	0.0601739	−	0.0661748i
$376$		0			0
$377$	2.52685			0.130139
$378$		0			0
$379$	−8.15057			−0.418667			−0.209333	−	0.977844i	$-0.567129\pi$
$379$	−8.15057			−0.418667			−0.209333	+	0.977844i	$0.567129\pi$
$380$		0			0
$381$	−20.0691	+	22.0705i	−1.02817	+	1.13071i
$382$		0			0
$383$	−0.164775	+	0.285399i	−0.00841962	+	0.0145832i	−0.870205	−	0.492691i	$-0.836013\pi$
$383$	−0.164775	+	0.285399i	−0.00841962	+	0.0145832i	0.861785	+	0.507274i	$0.169347\pi$
$384$		0			0
$385$	9.08037	−	8.43132i	0.462778	−	0.429700i
$386$		0			0
$387$	2.62758	+	27.5995i	0.133567	+	1.40296i
$388$		0			0
$389$	−11.5387	+	6.66185i	−0.585033	+	0.337769i	−0.763131	−	0.646244i	$-0.776339\pi$
$389$	−11.5387	+	6.66185i	−0.585033	+	0.337769i	0.178098	+	0.984013i	$0.443006\pi$
$390$		0			0
$391$			60.5869i			3.06401i
$392$		0			0
$393$	9.12830	+	28.5697i	0.460462	+	1.44115i
$394$		0			0
$395$	5.79653	+	10.0399i	0.291655	+	0.505161i
$396$		0			0
$397$	−24.7694	−	14.3006i	−1.24314	−	0.717728i	−0.273409	−	0.961898i	$-0.588151\pi$
$397$	−24.7694	−	14.3006i	−1.24314	−	0.717728i	−0.969733	+	0.244169i	$0.921485\pi$
$398$		0			0
$399$	−2.94160	−	1.65774i	−0.147264	−	0.0829908i
$400$		0			0
$401$	24.2076	+	13.9763i	1.20887	+	0.697941i	0.962512	−	0.271238i	$-0.0874330\pi$
$401$	24.2076	+	13.9763i	1.20887	+	0.697941i	0.246357	+	0.969179i	$0.420766\pi$
$402$		0			0
$403$	11.3157	+	19.5994i	0.563675	+	0.976314i
$404$		0			0
$405$	−2.94841	+	8.50335i	−0.146507	+	0.422535i
$406$		0			0
$407$			21.6301i			1.07217i
$408$		0			0
$409$	0.852979	−	0.492468i	0.0421771	−	0.0243510i	−0.478763	−	0.877944i	$-0.658915\pi$
$409$	0.852979	−	0.492468i	0.0421771	−	0.0243510i	0.520940	+	0.853593i	$0.325581\pi$
$410$		0			0
$411$	4.12162	−	18.9339i	0.203304	−	0.933941i
$412$		0			0
$413$	−5.43290	+	17.6352i	−0.267336	+	0.867769i
$414$		0			0
$415$	8.23048	−	14.2556i	0.404018	−	0.699780i
$416$		0			0
$417$	2.76819	+	2.51716i	0.135559	+	0.123266i
$418$		0			0
$419$	31.2166			1.52503			0.762515	−	0.646970i	$-0.223964\pi$
$419$	31.2166			1.52503			0.762515	+	0.646970i	$0.223964\pi$
$420$		0			0
$421$	−34.7393			−1.69309			−0.846544	−	0.532319i	$-0.821321\pi$
$421$	−34.7393			−1.69309			−0.846544	+	0.532319i	$0.821321\pi$
$422$		0			0
$423$	23.6960	+	10.8297i	1.15214	+	0.526556i
$424$		0			0
$425$	−3.74984	+	6.49492i	−0.181894	+	0.315050i
$426$		0			0
$427$	−3.49836	−	15.3024i	−0.169297	−	0.740534i
$428$		0			0
$429$	17.3536	+	3.77761i	0.837841	+	0.182385i
$430$		0			0
$431$	15.9115	−	9.18649i	0.766429	−	0.442498i	−0.0651704	−	0.997874i	$-0.520759\pi$
$431$	15.9115	−	9.18649i	0.766429	−	0.442498i	0.831599	+	0.555376i	$0.187426\pi$
$432$		0			0
$433$		−	24.6833i		−	1.18621i	−0.805127	−	0.593103i	$-0.797903\pi$
$433$		−	24.6833i		−	1.18621i	0.805127	−	0.593103i	$-0.202097\pi$
$434$		0			0
$435$	1.90419	−	0.608409i	0.0912991	−	0.0291710i
$436$		0			0
$437$	2.97626	+	5.15503i	0.142374	+	0.246598i
$438$		0			0
$439$	−13.1758	−	7.60702i	−0.628844	−	0.363063i	0.151460	−	0.988463i	$-0.451602\pi$
$439$	−13.1758	−	7.60702i	−0.628844	−	0.363063i	−0.780304	+	0.625400i	$0.784936\pi$
$440$		0			0
$441$	20.9954	−	0.437285i	0.999783	−	0.0208231i
$442$		0			0
$443$	−26.1325	−	15.0876i	−1.24159	−	0.716834i	−0.272174	−	0.962248i	$-0.587743\pi$
$443$	−26.1325	−	15.0876i	−1.24159	−	0.716834i	−0.969418	+	0.245414i	$0.921076\pi$
$444$		0			0
$445$	0.658248	+	1.14012i	0.0312039	+	0.0540468i
$446$		0			0
$447$	2.61816	−	0.836527i	0.123835	−	0.0395664i
$448$		0			0
$449$			27.7596i			1.31006i	0.755603	+	0.655029i	$0.227344\pi$
$449$			27.7596i			1.31006i	−0.755603	+	0.655029i	$0.772656\pi$
$450$		0			0
$451$	−5.83077	+	3.36640i	−0.274560	+	0.158518i
$452$		0			0
$453$	17.3381	+	3.77423i	0.814614	+	0.177329i
$454$		0			0
$455$	−1.29096	−	5.64687i	−0.0605211	−	0.264729i
$456$		0			0
$457$	−16.9273	+	29.3189i	−0.791825	+	1.37148i	0.133011	+	0.991115i	$0.457535\pi$
$457$	−16.9273	+	29.3189i	−0.791825	+	1.37148i	−0.924836	+	0.380366i	$0.875798\pi$
$458$		0			0
$459$	4.64278	−	38.6919i	0.216707	−	1.80599i
$460$		0			0
$461$	−23.7084			−1.10421			−0.552104	−	0.833775i	$-0.686175\pi$
$461$	−23.7084			−1.10421			−0.552104	+	0.833775i	$0.686175\pi$
$462$		0			0
$463$	1.60640			0.0746559			0.0373280	−	0.999303i	$-0.488115\pi$
$463$	1.60640			0.0746559			0.0373280	+	0.999303i	$0.488115\pi$
$464$		0			0
$465$	13.2464	+	12.0452i	0.614287	+	0.558582i
$466$		0			0
$467$	−3.18589	+	5.51812i	−0.147425	+	0.255348i	−0.930275	−	0.366863i	$-0.880432\pi$
$467$	−3.18589	+	5.51812i	−0.147425	+	0.255348i	0.782850	+	0.622211i	$0.213765\pi$
$468$		0			0
$469$	1.07751	−	3.49759i	0.0497549	−	0.161504i
$470$		0			0
$471$	2.39152	−	10.9862i	0.110196	−	0.506217i
$472$		0			0
$473$	37.4827	−	21.6407i	1.72346	−	0.995039i
$474$		0			0
$475$			0.736825i			0.0338078i
$476$		0			0
$477$	14.1306	+	19.8556i	0.646998	+	0.909124i
$478$		0			0
$479$	1.66105	+	2.87702i	0.0758953	+	0.131455i	0.901475	−	0.432831i	$-0.142485\pi$
$479$	1.66105	+	2.87702i	0.0758953	+	0.131455i	−0.825580	+	0.564285i	$0.809152\pi$
$480$		0			0
$481$	8.75687	+	5.05578i	0.399279	+	0.230524i
$482$		0			0
$483$	−32.2519	−	18.1756i	−1.46751	−	0.827017i
$484$		0			0
$485$	−4.19357	−	2.42116i	−0.190420	−	0.109939i
$486$		0			0
$487$	10.3313	+	17.8943i	0.468155	+	0.810868i	0.999338	−	0.0363892i	$-0.0115856\pi$
$487$	10.3313	+	17.8943i	0.468155	+	0.810868i	−0.531183	+	0.847257i	$0.678252\pi$
$488$		0			0
$489$	−2.82924	−	8.85493i	−0.127943	−	0.400434i
$490$		0			0
$491$		−	15.1679i		−	0.684518i	−0.939606	−	0.342259i	$-0.888808\pi$
$491$		−	15.1679i		−	0.684518i	0.939606	−	0.342259i	$-0.111192\pi$
$492$		0			0
$493$	−7.49604	+	4.32784i	−0.337605	+	0.194916i
$494$		0			0
$495$	13.9870	−	1.33162i	0.628668	−	0.0598517i
$496$		0			0
$497$	14.0810	−	13.0745i	0.631617	−	0.586470i
$498$		0			0
$499$	−3.10558	+	5.37903i	−0.139025	+	0.240798i	−0.927128	−	0.374745i	$-0.877730\pi$
$499$	−3.10558	+	5.37903i	−0.139025	+	0.240798i	0.788103	+	0.615544i	$0.211064\pi$
$500$		0			0
$501$	−7.97136	+	8.76631i	−0.356134	+	0.391650i
$502$		0			0
$503$	5.52940			0.246544			0.123272	−	0.992373i	$-0.460661\pi$
$503$	5.52940			0.246544			0.123272	+	0.992373i	$0.460661\pi$
$504$		0			0
$505$	−2.76869			−0.123205
$506$		0			0
$507$	−9.56286	+	10.5165i	−0.424701	+	0.467055i
$508$		0			0
$509$	−14.8857	+	25.7827i	−0.659796	+	1.14280i	0.320872	+	0.947122i	$0.396024\pi$
$509$	−14.8857	+	25.7827i	−0.659796	+	1.14280i	−0.980668	+	0.195678i	$0.937309\pi$
$510$		0			0
$511$	0.617080	+	0.190105i	0.0272980	+	0.00840977i
$512$		0			0
$513$	−1.50566	−	3.52017i	−0.0664766	−	0.155419i
$514$		0			0
$515$	−7.07000	+	4.08187i	−0.311542	+	0.179869i
$516$		0			0
$517$		−	40.6729i		−	1.78879i
$518$		0			0
$519$	−6.13204	−	19.1920i	−0.269167	−	0.842436i
$520$		0			0
$521$	−11.2112	−	19.4183i	−0.491170	−	0.850732i	0.508778	−	0.860898i	$-0.330097\pi$
$521$	−11.2112	−	19.4183i	−0.491170	−	0.850732i	−0.999948	+	0.0101659i	$0.996764\pi$
$522$		0			0
$523$	20.3535	+	11.7511i	0.889996	+	0.513839i	0.873941	−	0.486032i	$-0.161556\pi$
$523$	20.3535	+	11.7511i	0.889996	+	0.513839i	0.0160547	+	0.999871i	$0.494889\pi$
$524$		0			0
$525$	−2.33249	−	3.94455i	−0.101798	−	0.172154i
$526$		0			0
$527$	−67.1372	−	38.7617i	−2.92454	−	1.68849i
$528$		0			0
$529$	21.1319	+	36.6015i	0.918778	+	1.59137i
$530$		0			0
$531$	−17.0474	+	12.1322i	−0.739796	+	0.526492i
$532$		0			0
$533$			3.14742i			0.136330i
$534$		0			0
$535$	0.186331	−	0.107578i	0.00805579	−	0.00465101i
$536$		0			0
$537$	−2.95972	+	13.5964i	−0.127721	+	0.586728i
$538$		0			0
$539$	−14.2453	−	29.5272i	−0.613586	−	1.27183i
$540$		0			0
$541$	−0.0653647	+	0.113215i	−0.00281025	+	0.00486749i	−0.867427	−	0.497564i	$-0.834228\pi$
$541$	−0.0653647	+	0.113215i	−0.00281025	+	0.00486749i	0.864617	+	0.502432i	$0.167561\pi$
$542$		0			0
$543$	−12.5813	−	11.4404i	−0.539916	−	0.490956i
$544$		0			0
$545$	−2.17366			−0.0931095
$546$		0			0
$547$	41.2183			1.76237			0.881184	−	0.472774i	$-0.156747\pi$
$547$	41.2183			1.76237			0.881184	+	0.472774i	$0.156747\pi$
$548$		0			0
$549$	7.39851	−	16.1884i	0.315761	−	0.690904i
$550$		0			0
$551$	−0.425199	+	0.736467i	−0.0181141	+	0.0313745i
$552$		0			0
$553$	29.9009	−	6.83580i	1.27152	−	0.290688i
$554$		0			0
$555$	7.81635	+	1.70150i	0.331786	+	0.0722245i
$556$		0			0
$557$	−5.03375	+	2.90624i	−0.213287	+	0.123141i	−0.602838	−	0.797864i	$-0.705963\pi$
$557$	−5.03375	+	2.90624i	−0.213287	+	0.123141i	0.389551	+	0.921005i	$0.372630\pi$
$558$		0			0
$559$		−	20.2330i		−	0.855764i
$560$		0			0
$561$	−57.9506	+	18.5158i	−2.44668	+	0.781737i
$562$		0			0
$563$	10.5187	+	18.2190i	0.443312	+	0.767838i	0.997933	−	0.0642647i	$-0.0204702\pi$
$563$	10.5187	+	18.2190i	0.443312	+	0.767838i	−0.554621	+	0.832103i	$0.687137\pi$
$564$		0			0
$565$	−9.71633	−	5.60973i	−0.408769	−	0.236003i
$566$		0			0
$567$	19.2039	+	14.0787i	0.806488	+	0.591251i
$568$		0			0
$569$	−30.2091	−	17.4412i	−1.26643	−	0.731173i	−0.292119	−	0.956382i	$-0.594360\pi$
$569$	−30.2091	−	17.4412i	−1.26643	−	0.731173i	−0.974311	+	0.225209i	$0.927694\pi$
$570$		0			0
$571$	−18.9889	−	32.8897i	−0.794661	−	1.37639i	−0.923054	−	0.384670i	$-0.874315\pi$
$571$	−18.9889	−	32.8897i	−0.794661	−	1.37639i	0.128394	−	0.991723i	$-0.459018\pi$
$572$		0			0
$573$	26.4915	−	8.46429i	1.10670	−	0.353601i
$574$		0			0
$575$			8.07860i			0.336901i
$576$		0			0
$577$	−4.69855	+	2.71271i	−0.195603	+	0.112932i	−0.594603	−	0.804019i	$-0.702691\pi$
$577$	−4.69855	+	2.71271i	−0.195603	+	0.112932i	0.399000	+	0.916951i	$0.369357\pi$
$578$		0			0
$579$	10.8024	+	2.35152i	0.448934	+	0.0977260i
$580$		0			0
$581$	−29.6339	−	31.9151i	−1.22942	−	1.32406i
$582$		0			0
$583$	19.0228	−	32.9484i	0.787844	−	1.36459i
$584$		0			0
$585$	2.73019	−	5.97382i	0.112879	−	0.246987i
$586$		0			0
$587$	−8.71317			−0.359631			−0.179816	−	0.983700i	$-0.557550\pi$
$587$	−8.71317			−0.359631			−0.179816	+	0.983700i	$0.557550\pi$
$588$		0			0
$589$	−7.61648			−0.313832
$590$		0			0
$591$	3.26769	+	2.97137i	0.134415	+	0.122226i
$592$		0			0
$593$	−9.79341	+	16.9627i	−0.402167	+	0.696574i	−0.993987	−	0.109496i	$-0.965076\pi$
$593$	−9.79341	+	16.9627i	−0.402167	+	0.696574i	0.591820	+	0.806070i	$0.298410\pi$
$594$		0			0
$595$	13.5013	+	14.5407i	0.553500	+	0.596109i
$596$		0			0
$597$	2.67144	−	12.2721i	0.109335	−	0.502262i
$598$		0			0
$599$	14.2397	−	8.22129i	0.581818	−	0.335913i	−0.180038	−	0.983660i	$-0.557622\pi$
$599$	14.2397	−	8.22129i	0.581818	−	0.335913i	0.761855	+	0.647747i	$0.224289\pi$
$600$		0			0
$601$			11.0177i			0.449420i	0.974426	+	0.224710i	$0.0721435\pi$
$601$			11.0177i			0.449420i	−0.974426	+	0.224710i	$0.927857\pi$
$602$		0			0
$603$	3.38103	−	2.40619i	0.137686	−	0.0979875i
$604$		0			0
$605$	−5.46716	−	9.46940i	−0.222272	−	0.384986i
$606$		0			0
$607$	10.5191	+	6.07323i	0.426959	+	0.246505i	0.698050	−	0.716049i	$-0.254051\pi$
$607$	10.5191	+	6.07323i	0.426959	+	0.246505i	−0.271091	+	0.962554i	$0.587385\pi$
$608$		0			0
$609$	−0.0550690	−	5.28865i	−0.00223151	−	0.214307i
$610$		0			0
$611$	−16.4663	−	9.50681i	−0.666154	−	0.384604i
$612$		0			0
$613$	8.26802	+	14.3206i	0.333942	+	0.578405i	0.983281	−	0.182094i	$-0.0582877\pi$
$613$	8.26802	+	14.3206i	0.333942	+	0.578405i	−0.649339	+	0.760499i	$0.724954\pi$
$614$		0			0
$615$	0.757828	+	2.37184i	0.0305586	+	0.0956420i
$616$		0			0
$617$		−	34.8433i		−	1.40274i	−0.712799	−	0.701368i	$-0.752573\pi$
$617$		−	34.8433i		−	1.40274i	0.712799	−	0.701368i	$-0.247427\pi$
$618$		0			0
$619$	−21.3120	+	12.3045i	−0.856603	+	0.494560i	−0.862873	−	0.505421i	$-0.831337\pi$
$619$	−21.3120	+	12.3045i	−0.856603	+	0.494560i	0.00627057	+	0.999980i	$0.498004\pi$
$620$		0			0
$621$	−16.5082	−	38.5954i	−0.662451	−	1.54878i
$622$		0			0
$623$	3.39552	−	0.776267i	0.136039	−	0.0311005i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	−4.02115	+	4.42216i	−0.160589	+	0.176604i
$628$		0			0
$629$	−34.6370			−1.38107
$630$		0			0
$631$	−37.4776			−1.49196			−0.745979	−	0.665969i	$-0.768018\pi$
$631$	−37.4776			−1.49196			−0.745979	+	0.665969i	$0.768018\pi$
$632$		0			0
$633$	15.4577	−	16.9992i	0.614389	−	0.675659i
$634$		0			0
$635$	8.61142	−	14.9154i	0.341734	−	0.591900i
$636$		0			0
$637$	−15.2836	−	1.13449i	−0.605559	−	0.0449501i
$638$		0			0
$639$	21.6897	−	2.06494i	0.858029	−	0.0816878i
$640$		0			0
$641$	13.6348	−	7.87204i	0.538541	−	0.310927i	−0.205946	−	0.978563i	$-0.566027\pi$
$641$	13.6348	−	7.87204i	0.538541	−	0.310927i	0.744488	+	0.667636i	$0.232694\pi$
$642$		0			0
$643$		−	11.7173i		−	0.462086i	−0.972943	−	0.231043i	$-0.925786\pi$
$643$		−	11.7173i		−	0.462086i	0.972943	−	0.231043i	$-0.0742139\pi$
$644$		0			0
$645$	−4.87164	−	15.2472i	−0.191821	−	0.600360i
$646$		0			0
$647$	13.2263	+	22.9086i	0.519980	+	0.900632i	0.999730	+	0.0232268i	$0.00739398\pi$
$647$	13.2263	+	22.9086i	0.519980	+	0.900632i	−0.479750	+	0.877405i	$0.659273\pi$
$648$		0			0
$649$	28.2886	+	16.3324i	1.11043	+	0.641105i
$650$		0			0
$651$	40.7744	−	24.1106i	1.59808	−	0.944971i
$652$		0			0
$653$	3.13762	+	1.81151i	0.122785	+	0.0708898i	0.560134	−	0.828402i	$-0.310749\pi$
$653$	3.13762	+	1.81151i	0.122785	+	0.0708898i	−0.437350	+	0.899292i	$0.644083\pi$
$654$		0			0
$655$	−8.65810	−	14.9963i	−0.338300	−	0.585953i
$656$		0			0
$657$	0.424523	+	0.596515i	0.0165622	+	0.0232723i
$658$		0			0
$659$			24.1855i			0.942132i	0.882098	+	0.471066i	$0.156131\pi$
$659$			24.1855i			0.942132i	−0.882098	+	0.471066i	$0.843869\pi$
$660$		0			0
$661$	13.7414	−	7.93363i	0.534480	−	0.308582i	−0.208359	−	0.978053i	$-0.566812\pi$
$661$	13.7414	−	7.93363i	0.534480	−	0.308582i	0.742839	+	0.669470i	$0.233479\pi$
$662$		0			0
$663$	−6.04921	+	27.7889i	−0.234932	+	1.07923i
$664$		0			0
$665$	1.86305	+	0.573954i	0.0722460	+	0.0222570i
$666$		0			0
$667$	−4.66192	+	8.07468i	−0.180510	+	0.312653i
$668$		0			0
$669$	36.0134	+	32.7476i	1.39236	+	1.26609i
$670$		0			0
$671$	−27.7866			−1.07269
$672$		0			0
$673$	−3.48623			−0.134384			−0.0671922	−	0.997740i	$-0.521404\pi$
$673$	−3.48623			−0.134384			−0.0671922	+	0.997740i	$0.521404\pi$
$674$		0			0
$675$	0.619064	−	5.15914i	0.0238278	−	0.198576i
$676$		0			0
$677$	−19.4486	+	33.6859i	−0.747469	+	1.29465i	0.201564	+	0.979475i	$0.435398\pi$
$677$	−19.4486	+	33.6859i	−0.747469	+	1.29465i	−0.949032	+	0.315179i	$0.897936\pi$
$678$		0			0
$679$	−9.38847	+	8.71741i	−0.360297	+	0.334543i
$680$		0			0
$681$	22.7293	+	4.94781i	0.870988	+	0.189600i
$682$		0			0
$683$	−10.4809	+	6.05116i	−0.401041	+	0.231541i	−0.686933	−	0.726721i	$-0.741044\pi$
$683$	−10.4809	+	6.05116i	−0.401041	+	0.231541i	0.285892	+	0.958262i	$0.407710\pi$
$684$		0			0
$685$			11.1875i			0.427453i
$686$		0			0
$687$	13.8046	−	4.41070i	0.526678	−	0.168279i
$688$		0			0
$689$	−8.89270	−	15.4026i	−0.338785	−	0.586792i
$690$		0			0
$691$	−18.7139	−	10.8044i	−0.711908	−	0.411021i	0.0998588	−	0.995002i	$-0.468161\pi$
$691$	−18.7139	−	10.8044i	−0.711908	−	0.411021i	−0.811767	+	0.583981i	$0.801494\pi$
$692$		0			0
$693$	7.52827	−	36.4031i	0.285975	−	1.38284i
$694$		0			0
$695$	−1.87076	−	1.08008i	−0.0709620	−	0.0409699i
$696$		0			0
$697$	−5.39071	−	9.33699i	−0.204188	−	0.353664i
$698$		0			0
$699$	−13.4858	+	4.30884i	−0.510079	+	0.162975i
$700$		0			0
$701$		−	25.2893i		−	0.955163i	−0.878587	−	0.477582i	$-0.841513\pi$
$701$		−	25.2893i		−	0.955163i	0.878587	−	0.477582i	$-0.158487\pi$
$702$		0			0
$703$	−2.94708	+	1.70150i	−0.111151	+	0.0641732i
$704$		0			0
$705$	−14.6977	−	3.19947i	−0.553549	−	0.120499i
$706$		0			0
$707$	−2.15669	+	7.00059i	−0.0811106	+	0.263284i
$708$		0			0
$709$	5.13129	−	8.88765i	0.192710	−	0.333783i	−0.753438	−	0.657519i	$-0.771606\pi$
$709$	5.13129	−	8.88765i	0.192710	−	0.333783i	0.946147	+	0.323737i	$0.104939\pi$
$710$		0			0
$711$	31.6322	+	14.4567i	1.18630	+	0.542169i
$712$		0			0
$713$	−83.5076			−3.12738
$714$		0			0
$715$	−10.2538			−0.383469
$716$		0			0
$717$	16.0892	+	14.6302i	0.600862	+	0.546375i
$718$		0			0
$719$	−24.3969	+	42.2566i	−0.909850	+	1.57591i	−0.0955793	+	0.995422i	$0.530470\pi$
$719$	−24.3969	+	42.2566i	−0.909850	+	1.57591i	−0.814271	+	0.580485i	$0.802863\pi$
$720$		0			0
$721$	4.81372	+	21.0560i	0.179272	+	0.784166i
$722$		0			0
$723$	−8.13181	+	37.3560i	−0.302425	+	1.38928i
$724$		0			0
$725$	−0.999514	+	0.577070i	−0.0371210	+	0.0214318i
$726$		0			0
$727$			9.98665i			0.370384i	0.982702	+	0.185192i	$0.0592907\pi$
$727$			9.98665i			0.370384i	−0.982702	+	0.185192i	$0.940709\pi$
$728$		0			0
$729$	7.58487	+	25.9127i	0.280921	+	0.959731i
$730$		0			0
$731$	34.6538	+	60.0222i	1.28172	+	2.22000i
$732$		0			0
$733$	−31.9630	−	18.4538i	−1.18058	−	0.681608i	−0.224432	−	0.974490i	$-0.572053\pi$
$733$	−31.9630	−	18.4538i	−1.18058	−	0.681608i	−0.956149	+	0.292881i	$0.905386\pi$
$734$		0			0
$735$	−11.7906	+	2.82502i	−0.434904	+	0.104202i
$736$		0			0
$737$	−5.61051	−	3.23923i	−0.206666	−	0.119318i
$738$		0			0
$739$	−19.7107	−	34.1399i	−0.725070	−	1.25586i	−0.958945	−	0.283591i	$-0.908474\pi$
$739$	−19.7107	−	34.1399i	−0.725070	−	1.25586i	0.233875	−	0.972267i	$-0.424859\pi$
$740$		0			0
$741$	0.850399	+	2.66157i	0.0312402	+	0.0977753i
$742$		0			0
$743$		−	12.7786i		−	0.468800i	−0.972140	−	0.234400i	$-0.924688\pi$
$743$		−	12.7786i		−	0.468800i	0.972140	−	0.234400i	$-0.0753125\pi$
$744$		0			0
$745$	−1.37427	+	0.793438i	−0.0503495	+	0.0290693i
$746$		0			0
$747$	−4.68028	−	49.1606i	−0.171243	−	1.79869i
$748$		0			0
$749$	−0.126866	−	0.554934i	−0.00463559	−	0.0202768i
$750$		0			0
$751$	−4.32518	+	7.49143i	−0.157828	+	0.273366i	−0.934085	−	0.357050i	$-0.883782\pi$
$751$	−4.32518	+	7.49143i	−0.157828	+	0.273366i	0.776257	+	0.630416i	$0.217116\pi$
$752$		0			0
$753$	1.94375	−	2.13759i	0.0708342	−	0.0778982i
$754$		0			0
$755$	−10.2446			−0.372838
$756$		0			0
$757$	26.6532			0.968727			0.484364	−	0.874867i	$-0.339051\pi$
$757$	26.6532			0.968727			0.484364	+	0.874867i	$0.339051\pi$
$758$		0			0
$759$	−44.0882	+	48.4849i	−1.60030	+	1.75989i
$760$		0			0
$761$	18.2462	−	31.6034i	0.661425	−	1.14562i	−0.318816	−	0.947817i	$-0.603285\pi$
$761$	18.2462	−	31.6034i	0.661425	−	1.14562i	0.980241	−	0.197805i	$-0.0633814\pi$
$762$		0			0
$763$	−1.69319	+	5.49607i	−0.0612975	+	0.198971i
$764$		0			0
$765$	2.13236	+	22.3978i	0.0770955	+	0.809793i
$766$		0			0
$767$	13.2242	−	7.63502i	0.477500	−	0.275685i
$768$		0			0
$769$		−	26.0781i		−	0.940400i	−0.882560	−	0.470200i	$-0.844182\pi$
$769$		−	26.0781i		−	0.940400i	0.882560	−	0.470200i	$-0.155818\pi$
$770$		0			0
$771$	−0.634868	−	1.98700i	−0.0228642	−	0.0715602i
$772$		0			0
$773$	−19.9307	−	34.5210i	−0.716858	−	1.24163i	−0.962239	−	0.272208i	$-0.912246\pi$
$773$	−19.9307	−	34.5210i	−0.716858	−	1.24163i	0.245381	−	0.969427i	$-0.421087\pi$
$774$		0			0
$775$	−8.95201	−	5.16845i	−0.321566	−	0.185656i
$776$		0			0
$777$	10.3908	−	18.4381i	0.372768	−	0.661464i
$778$		0			0
$779$	−0.917336	−	0.529624i	−0.0328670	−	0.0189757i
$780$		0			0
$781$	−17.0068	−	29.4566i	−0.608551	−	1.05404i
$782$		0			0
$783$	3.59595	−	4.79939i	0.128509	−	0.171516i
$784$		0			0
$785$			6.49143i			0.231689i
$786$		0			0
$787$	21.2458	−	12.2663i	0.757331	−	0.437245i	−0.0710057	−	0.997476i	$-0.522621\pi$
$787$	21.2458	−	12.2663i	0.757331	−	0.437245i	0.828337	+	0.560231i	$0.189288\pi$
$788$		0			0
$789$	−1.84743	+	8.48675i	−0.0657703	+	0.302136i
$790$		0			0
$791$	−21.7527	+	20.1978i	−0.773436	+	0.718153i
$792$		0			0
$793$	−6.49477	+	11.2493i	−0.230636	+	0.399473i
$794$		0			0
$795$	−10.4100	−	9.46599i	−0.369204	−	0.335724i
$796$		0			0
$797$	33.4163			1.18367			0.591834	−	0.806060i	$-0.298404\pi$
$797$	33.4163			1.18367			0.591834	+	0.806060i	$0.298404\pi$
$798$		0			0
$799$	65.1308			2.30416
$800$		0			0
$801$	3.59212	+	1.64169i	0.126921	+	0.0580062i
$802$		0			0
$803$	0.571497	−	0.989861i	0.0201677	−	0.0349315i
$804$		0			0
$805$	20.4266	+	6.29287i	0.719943	+	0.221795i
$806$		0			0
$807$	−26.8921	−	5.85398i	−0.946645	−	0.206070i
$808$		0			0
$809$	43.1974	−	24.9400i	1.51874	−	0.876845i	0.518984	−	0.854784i	$-0.326310\pi$
$809$	43.1974	−	24.9400i	1.51874	−	0.876845i	0.999757	−	0.0220612i	$-0.00702286\pi$
$810$		0			0
$811$			16.9220i			0.594210i	0.954845	+	0.297105i	$0.0960212\pi$
$811$			16.9220i			0.594210i	−0.954845	+	0.297105i	$0.903979\pi$
$812$		0			0
$813$	33.1867	−	10.6035i	1.16391	−	0.371880i
$814$		0			0
$815$	2.68350	+	4.64797i	0.0939990	+	0.162811i
$816$		0			0
$817$	5.89703	+	3.40465i	0.206311	+	0.119114i
$818$		0			0
$819$	−12.9780	−	11.5566i	−0.453489	−	0.403820i
$820$		0			0
$821$	0.856494	+	0.494497i	0.0298918	+	0.0172581i	0.514871	−	0.857267i	$-0.327840\pi$
$821$	0.856494	+	0.494497i	0.0298918	+	0.0172581i	−0.484980	+	0.874525i	$0.661173\pi$
$822$		0			0
$823$	17.8141	+	30.8549i	0.620960	+	1.07553i	0.989307	+	0.145846i	$0.0465906\pi$
$823$	17.8141	+	30.8549i	0.620960	+	1.07553i	−0.368347	+	0.929688i	$0.620076\pi$
$824$		0			0
$825$	−7.72707	+	2.46888i	−0.269022	+	0.0859552i
$826$		0			0
$827$			48.8191i			1.69761i	0.528709	+	0.848803i	$0.322676\pi$
$827$			48.8191i			1.69761i	−0.528709	+	0.848803i	$0.677324\pi$
$828$		0			0
$829$	11.5060	−	6.64300i	0.399621	−	0.230721i	−0.286700	−	0.958021i	$-0.592558\pi$
$829$	11.5060	−	6.64300i	0.399621	−	0.230721i	0.686320	+	0.727299i	$0.259225\pi$
$830$		0			0
$831$	7.46395	+	1.62479i	0.258922	+	0.0563632i
$832$		0			0
$833$	47.2828	−	22.8113i	1.63825	−	0.790366i
$834$		0			0
$835$	3.42041	−	5.92433i	0.118368	−	0.205020i
$836$		0			0
$837$	53.3295	+	6.39919i	1.84334	+	0.221189i
$838$		0			0
$839$	42.5549			1.46916			0.734579	−	0.678523i	$-0.237380\pi$
$839$	42.5549			1.46916			0.734579	+	0.678523i	$0.237380\pi$
$840$		0			0
$841$	27.6680			0.954068
$842$		0			0
$843$	22.9605	+	20.8784i	0.790802	+	0.719090i
$844$		0			0
$845$	4.10331	−	7.10714i	0.141158	−	0.244493i
$846$		0			0
$847$	−28.2019	+	6.44738i	−0.969028	+	0.221535i
$848$		0			0
$849$	−4.25637	+	19.5529i	−0.146078	+	0.671055i
$850$		0			0
$851$	−32.3120	+	18.6553i	−1.10764	+	0.639496i
$852$		0			0
$853$			27.4196i			0.938830i	0.882978	+	0.469415i	$0.155535\pi$
$853$			27.4196i			0.938830i	−0.882978	+	0.469415i	$0.844465\pi$
$854$		0			0
$855$	1.28169	+	1.80096i	0.0438330	+	0.0615916i
$856$		0			0
$857$	−4.27514	−	7.40476i	−0.146036	−	0.252942i	0.783723	−	0.621111i	$-0.213318\pi$
$857$	−4.27514	−	7.40476i	−0.146036	−	0.252942i	−0.929759	+	0.368169i	$0.879985\pi$
$858$		0			0
$859$	−2.23617	−	1.29105i	−0.0762970	−	0.0440501i	0.461366	−	0.887210i	$-0.347359\pi$
$859$	−2.23617	−	1.29105i	−0.0762970	−	0.0440501i	−0.537663	+	0.843160i	$0.680693\pi$
$860$		0			0
$861$	6.58748	−	0.0685934i	0.224501	−	0.00233766i
$862$		0			0
$863$	18.5478	+	10.7086i	0.631373	+	0.364523i	0.781284	−	0.624176i	$-0.214565\pi$
$863$	18.5478	+	10.7086i	0.631373	+	0.364523i	−0.149911	+	0.988700i	$0.547899\pi$
$864$		0			0
$865$	5.81618	+	10.0739i	0.197756	+	0.342524i
$866$		0			0
$867$	−20.6883	−	64.7500i	−0.702611	−	2.19903i
$868$		0			0
$869$		−	54.2950i		−	1.84183i
$870$		0			0
$871$	−2.62278	+	1.51426i	−0.0888694	+	0.0513088i
$872$		0			0
$873$	−14.4616	+	1.37680i	−0.489450	+	0.0465976i
$874$		0			0
$875$	1.80025	+	1.93884i	0.0608597	+	0.0655447i
$876$		0			0
$877$	−23.9665	+	41.5112i	−0.809291	+	1.40173i	0.104064	+	0.994571i	$0.466815\pi$
$877$	−23.9665	+	41.5112i	−0.809291	+	1.40173i	−0.913355	+	0.407163i	$0.866518\pi$
$878$		0			0
$879$	−8.36604	+	9.20035i	−0.282179	+	0.310320i
$880$		0			0
$881$	16.0526			0.540827			0.270413	−	0.962744i	$-0.412840\pi$
$881$	16.0526			0.540827			0.270413	+	0.962744i	$0.412840\pi$
$882$		0			0
$883$	−57.8898			−1.94815			−0.974073	−	0.226236i	$-0.927358\pi$
$883$	−57.8898			−1.94815			−0.974073	+	0.226236i	$0.927358\pi$
$884$		0			0
$885$	8.12724	−	8.93773i	0.273194	−	0.300439i
$886$		0			0
$887$	0.415272	−	0.719272i	0.0139435	−	0.0241508i	−0.858969	−	0.512027i	$-0.828895\pi$
$887$	0.415272	−	0.719272i	0.0139435	−	0.0241508i	0.872913	+	0.487876i	$0.162228\pi$
$888$		0			0
$889$	−31.0055	−	33.3923i	−1.03989	−	1.11994i
$890$		0			0
$891$	31.8709	−	27.5849i	1.06772	−	0.924128i
$892$		0			0
$893$	5.54164	−	3.19947i	0.185444	−	0.107066i
$894$		0			0
$895$		−	8.03372i		−	0.268538i
$896$		0			0
$897$	9.32383	+	29.1817i	0.311314	+	0.974348i
$898$		0			0
$899$	−5.96511	−	10.3319i	−0.198947	−	0.344587i
$900$		0			0
$901$	52.7613	+	30.4618i	1.75773	+	1.01483i
$902$		0			0
$903$	−42.3472	+	0.440948i	−1.40923	+	0.0146738i
$904$		0			0
$905$	8.50255	+	4.90895i	0.282634	+	0.163179i
$906$		0			0
$907$	21.9547	+	38.0267i	0.728995	+	1.26266i	0.957308	+	0.289069i	$0.0933456\pi$
$907$	21.9547	+	38.0267i	0.728995	+	1.26266i	−0.228313	+	0.973588i	$0.573321\pi$
$908$		0			0
$909$	−6.76729	+	4.81609i	−0.224457	+	0.159740i
$910$		0			0
$911$		−	1.64586i		−	0.0545299i	−0.999628	−	0.0272649i	$-0.991320\pi$
$911$		−	1.64586i		−	0.0545299i	0.999628	−	0.0272649i	$-0.00867978\pi$
$912$		0			0
$913$	−66.7649	+	38.5467i	−2.20959	+	1.27571i
$914$		0			0
$915$	−2.18578	+	10.0411i	−0.0722597	+	0.331947i
$916$		0			0
$917$	−44.6621	+	10.2104i	−1.47487	+	0.337178i
$918$		0			0
$919$	22.9387	−	39.7309i	0.756677	−	1.31060i	−0.187860	−	0.982196i	$-0.560155\pi$
$919$	22.9387	−	39.7309i	0.756677	−	1.31060i	0.944537	−	0.328406i	$-0.106512\pi$
$920$		0			0
$921$	3.13124	+	2.84730i	0.103178	+	0.0938216i
$922$		0			0
$923$	−15.9005			−0.523373
$924$		0			0
$925$	−4.61846			−0.151854
$926$		0			0
$927$	−10.1803	+	22.2751i	−0.334365	+	0.731611i
$928$		0			0
$929$	5.79774	−	10.0420i	0.190218	−	0.329467i	−0.755105	−	0.655604i	$-0.772414\pi$
$929$	5.79774	−	10.0420i	0.190218	−	0.329467i	0.945322	+	0.326137i	$0.105747\pi$
$930$		0			0
$931$	2.90247	−	4.26360i	0.0951245	−	0.139734i
$932$		0			0
$933$	8.67694	+	1.88883i	0.284070	+	0.0618376i
$934$		0			0
$935$	30.4184	−	17.5620i	0.994786	−	0.574340i
$936$		0			0
$937$		−	39.7618i		−	1.29896i	−0.760378	−	0.649481i	$-0.774986\pi$
$937$		−	39.7618i		−	1.29896i	0.760378	−	0.649481i	$-0.225014\pi$
$938$		0			0
$939$	2.70301	−	0.863638i	0.0882094	−	0.0281838i
$940$		0			0
$941$	20.7590	+	35.9557i	0.676724	+	1.17212i	0.975962	+	0.217942i	$0.0699345\pi$
$941$	20.7590	+	35.9557i	0.676724	+	1.17212i	−0.299237	+	0.954179i	$0.596732\pi$
$942$		0			0
$943$	−10.0577	−	5.80684i	−0.327525	−	0.189097i
$944$		0			0
$945$	−12.5626	−	5.58404i	−0.408661	−	0.181649i
$946$		0			0
$947$	26.5502	+	15.3288i	0.862767	+	0.498119i	0.864938	−	0.501879i	$-0.167358\pi$
$947$	26.5502	+	15.3288i	0.862767	+	0.498119i	−0.00217116	+	0.999998i	$0.500691\pi$
$948$		0			0
$949$	−0.267161	−	0.462736i	−0.00867241	−	0.0150211i
$950$		0			0
$951$	−27.3281	+	8.73161i	−0.886175	+	0.283142i
$952$		0			0
$953$			22.7409i			0.736650i	0.929697	+	0.368325i	$0.120069\pi$
$953$			22.7409i			0.736650i	−0.929697	+	0.368325i	$0.879931\pi$
$954$		0			0
$955$	−13.9054	+	8.02830i	−0.449969	+	0.259790i
$956$		0			0
$957$	−9.14803	−	1.99138i	−0.295714	−	0.0643723i
$958$		0			0
$959$	28.2874	+	8.71457i	0.913449	+	0.281408i
$960$		0			0
$961$	37.9257	−	65.6892i	1.22341	−	2.11901i
$962$		0			0
$963$	0.268303	−	0.587064i	0.00864595	−	0.0189179i
$964$		0			0
$965$	−6.38285			−0.205471
$966$		0			0
$967$	18.4381			0.592928			0.296464	−	0.955044i	$-0.404193\pi$
$967$	18.4381			0.592928			0.296464	+	0.955044i	$0.404193\pi$
$968$		0			0
$969$	−7.08134	−	6.43919i	−0.227485	−	0.206856i
$970$		0			0
$971$	−0.784910	+	1.35950i	−0.0251889	+	0.0436285i	−0.878345	−	0.478027i	$-0.841352\pi$
$971$	−0.784910	+	1.35950i	−0.0251889	+	0.0436285i	0.853156	+	0.521656i	$0.174685\pi$
$972$		0			0
$973$	−4.18822	+	3.88885i	−0.134268	+	0.124671i
$974$		0			0
$975$	−0.806595	+	3.70534i	−0.0258317	+	0.118666i
$976$		0			0
$977$	18.3718	−	10.6070i	0.587766	−	0.339347i	−0.176448	−	0.984310i	$-0.556461\pi$
$977$	18.3718	−	10.6070i	0.587766	−	0.339347i	0.764214	+	0.644963i	$0.223127\pi$
$978$		0			0
$979$		−	6.16569i		−	0.197056i
$980$		0			0
$981$	−5.31291	+	3.78105i	−0.169628	+	0.120720i
$982$		0			0
$983$	18.2639	+	31.6340i	0.582528	+	1.00897i	0.995179	+	0.0980782i	$0.0312695\pi$
$983$	18.2639	+	31.6340i	0.582528	+	1.00897i	−0.412651	+	0.910889i	$0.635397\pi$
$984$		0			0
$985$	−2.20833	−	1.27498i	−0.0703631	−	0.0406242i
$986$		0			0
$987$	−19.5387	+	34.6708i	−0.621924	+	1.10358i
$988$		0			0
$989$	64.6555	+	37.3289i	2.05592	+	1.18699i
$990$		0			0
$991$	9.43293	+	16.3383i	0.299647	+	0.519004i	0.976055	−	0.217523i	$-0.0697978\pi$
$991$	9.43293	+	16.3383i	0.299647	+	0.519004i	−0.676408	+	0.736527i	$0.736464\pi$
$992$		0			0
$993$	12.6223	+	39.5053i	0.400557	+	1.25366i
$994$		0			0
$995$			7.25121i			0.229879i
$996$		0			0
$997$	24.2658	−	14.0098i	0.768504	−	0.443696i	−0.0638366	−	0.997960i	$-0.520334\pi$
$997$	24.2658	−	14.0098i	0.768504	−	0.443696i	0.832341	+	0.554264i	$0.187000\pi$
$998$		0			0
$999$	22.0646	−	9.43757i	0.698093	−	0.298591i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.bh.b.341.2	yes	10
3.2	odd	2		420.2.bh.a.341.1	yes	10
5.2	odd	4		2100.2.bo.g.1349.8		20
5.3	odd	4		2100.2.bo.g.1349.3		20
5.4	even	2		2100.2.bi.j.1601.4		10
7.2	even	3		2940.2.d.a.881.5		10
7.3	odd	6		420.2.bh.a.101.1	✓	10
7.5	odd	6		2940.2.d.b.881.6		10
15.2	even	4		2100.2.bo.h.1349.7		20
15.8	even	4		2100.2.bo.h.1349.4		20
15.14	odd	2		2100.2.bi.k.1601.5		10
21.2	odd	6		2940.2.d.b.881.5		10
21.5	even	6		2940.2.d.a.881.6		10
21.17	even	6	inner	420.2.bh.b.101.2	yes	10
35.3	even	12		2100.2.bo.h.1949.7		20
35.17	even	12		2100.2.bo.h.1949.4		20
35.24	odd	6		2100.2.bi.k.101.5		10
105.17	odd	12		2100.2.bo.g.1949.3		20
105.38	odd	12		2100.2.bo.g.1949.8		20
105.59	even	6		2100.2.bi.j.101.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bh.a.101.1	✓	10	7.3	odd	6
420.2.bh.a.341.1	yes	10	3.2	odd	2
420.2.bh.b.101.2	yes	10	21.17	even	6	inner
420.2.bh.b.341.2	yes	10	1.1	even	1	trivial
2100.2.bi.j.101.4		10	105.59	even	6
2100.2.bi.j.1601.4		10	5.4	even	2
2100.2.bi.k.101.5		10	35.24	odd	6
2100.2.bi.k.1601.5		10	15.14	odd	2
2100.2.bo.g.1349.3		20	5.3	odd	4
2100.2.bo.g.1349.8		20	5.2	odd	4
2100.2.bo.g.1949.3		20	105.17	odd	12
2100.2.bo.g.1949.8		20	105.38	odd	12
2100.2.bo.h.1349.4		20	15.8	even	4
2100.2.bo.h.1349.7		20	15.2	even	4
2100.2.bo.h.1949.4		20	35.17	even	12
2100.2.bo.h.1949.7		20	35.3	even	12
2940.2.d.a.881.5		10	7.2	even	3
2940.2.d.a.881.6		10	21.5	even	6
2940.2.d.b.881.5		10	21.2	odd	6
2940.2.d.b.881.6		10	7.5	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)

\(f(q)\)	\(=\)	\(q+(-1.16526 + 1.28147i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-1.80025 - 1.93884i) q^{7} +(-0.284326 - 2.98650i) q^{9} +O(q^{10})\)	\(q+(-1.16526 + 1.28147i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-1.80025 - 1.93884i) q^{7} +(-0.284326 - 2.98650i) q^{9} +(-4.05595 + 2.34170i) q^{11} +2.18938i q^{13} +(0.527154 + 1.64988i) q^{15} +(-3.74984 - 6.49492i) q^{17} +(-0.638109 - 0.368412i) q^{19} +(4.58233 - 0.0477143i) q^{21} +(-6.99627 - 4.03930i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(4.15842 + 3.11570i) q^{27} -1.15414i q^{29} +(8.95201 - 5.16845i) q^{31} +(1.72543 - 7.92628i) q^{33} +(-2.57921 + 0.589646i) q^{35} +(2.30923 - 3.99970i) q^{37} +(-2.80562 - 2.55120i) q^{39} +1.43758 q^{41} -9.24142 q^{43} +(-2.72854 - 1.24701i) q^{45} +(-4.34224 + 7.52098i) q^{47} +(-0.518179 + 6.98079i) q^{49} +(12.6926 + 2.76298i) q^{51} +(-7.03514 + 4.06174i) q^{53} +4.68341i q^{55} +(1.21567 - 0.388420i) q^{57} +(-3.48730 - 6.04018i) q^{59} +(5.13811 + 2.96649i) q^{61} +(-5.27847 + 5.92771i) q^{63} +(1.89606 + 1.09469i) q^{65} +(0.691639 + 1.19795i) q^{67} +(13.3287 - 4.25866i) q^{69} +7.26258i q^{71} +(-0.211355 + 0.122026i) q^{73} +(1.69242 + 0.368412i) q^{75} +(11.8419 + 3.64817i) q^{77} +(-5.79653 + 10.0399i) q^{79} +(-8.83832 + 1.69828i) q^{81} +16.4610 q^{83} -7.49968 q^{85} +(1.47899 + 1.34488i) q^{87} +(-0.658248 + 1.14012i) q^{89} +(4.24485 - 3.94144i) q^{91} +(-3.80824 + 17.4943i) q^{93} +(-0.638109 + 0.368412i) q^{95} -4.84232i q^{97} +(8.14670 + 11.4473i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{3} + 5 q^{5} - 5 q^{7} + 3 q^{9}+O(q^{10}) \) 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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