LMFDB - Embedded newform 1456.2.cc.d.225.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1456,2,Mod(225,1456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1456, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 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("1456.225");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1456 = 2^{4} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1456.cc (of order $6$, degree $2$, not 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:	$11.6262185343$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 39 x^{10} - 140 x^{9} + 460 x^{8} - 1066 x^{7} + 2127 x^{6} - 3172 x^{5} + \cdots + 169 $ x^12 - 6x^11 + 39x^10 - 140x^9 + 460x^8 - 1066x^7 + 2127x^6 - 3172x^5 + 3842x^4 - 3394x^3 + 2141x^2 - 832*x + 169
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			225.6
Root			$0.500000 - 2.47866i$ of defining polynomial
Character	$\chi$	$=$	1456.225
Dual form			1456.2.cc.d.673.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.67234 - 2.89658i) q^{3} +1.56356i q^{5} +(0.866025 - 0.500000i) q^{7} +(-4.09347 - 7.09010i) q^{9} +O(q^{10})$	\(q+(1.67234 - 2.89658i) q^{3} +1.56356i q^{5} +(0.866025 - 0.500000i) q^{7} +(-4.09347 - 7.09010i) q^{9} +(2.48215 + 1.43307i) q^{11} +(2.99598 + 2.00602i) q^{13} +(4.52898 + 2.61481i) q^{15} +(-1.11481 - 1.93090i) q^{17} +(6.26657 - 3.61801i) q^{19} -3.34469i q^{21} +(0.833676 - 1.44397i) q^{23} +2.55529 q^{25} -17.3487 q^{27} +(-2.41379 + 4.18080i) q^{29} +0.597963i q^{31} +(8.30201 - 4.79317i) q^{33} +(0.781779 + 1.35408i) q^{35} +(0.0333971 + 0.0192818i) q^{37} +(10.8209 - 5.32335i) q^{39} +(-6.88896 - 3.97734i) q^{41} +(-5.04571 - 8.73942i) q^{43} +(11.0858 - 6.40037i) q^{45} -7.02636i q^{47} +(0.500000 - 0.866025i) q^{49} -7.45736 q^{51} -5.98404 q^{53} +(-2.24069 + 3.88098i) q^{55} -24.2022i q^{57} +(-0.776138 + 0.448103i) q^{59} +(7.12846 + 12.3469i) q^{61} +(-7.09010 - 4.09347i) q^{63} +(-3.13653 + 4.68438i) q^{65} +(1.42103 + 0.820432i) q^{67} +(-2.78838 - 4.82962i) q^{69} +(1.98724 - 1.14733i) q^{71} +11.2277i q^{73} +(4.27332 - 7.40161i) q^{75} +2.86614 q^{77} -4.26098 q^{79} +(-16.7326 + 28.9816i) q^{81} +4.94829i q^{83} +(3.01907 - 1.74306i) q^{85} +(8.07337 + 13.9835i) q^{87} +(2.09682 + 1.21060i) q^{89} +(3.59760 + 0.239275i) q^{91} +(1.73205 + 1.00000i) q^{93} +(5.65696 + 9.79815i) q^{95} +(-4.23338 + 2.44414i) q^{97} -23.4649i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{3} - 6 q^{9}+O(q^{10}) $ 12 * q + 2 * q^3 - 6 * q^9	$ 12 q + 2 q^{3} - 6 q^{9} + 18 q^{11} - 8 q^{13} + 6 q^{15} + 4 q^{17} - 12 q^{19} + 6 q^{23} - 24 q^{25} - 40 q^{27} - 10 q^{29} + 12 q^{33} - 2 q^{35} - 6 q^{37} + 54 q^{39} - 24 q^{41} - 26 q^{43} + 72 q^{45} + 6 q^{49} + 36 q^{51} + 36 q^{53} + 6 q^{55} - 6 q^{59} - 28 q^{61} - 34 q^{65} + 42 q^{67} + 32 q^{69} - 48 q^{71} + 48 q^{75} - 4 q^{77} - 44 q^{79} - 34 q^{81} + 54 q^{85} - 2 q^{87} + 12 q^{89} + 16 q^{91} - 32 q^{95} + 60 q^{97}+O(q^{100}) $ 12 * q + 2 * q^3 - 6 * q^9 + 18 * q^11 - 8 * q^13 + 6 * q^15 + 4 * q^17 - 12 * q^19 + 6 * q^23 - 24 * q^25 - 40 * q^27 - 10 * q^29 + 12 * q^33 - 2 * q^35 - 6 * q^37 + 54 * q^39 - 24 * q^41 - 26 * q^43 + 72 * q^45 + 6 * q^49 + 36 * q^51 + 36 * q^53 + 6 * q^55 - 6 * q^59 - 28 * q^61 - 34 * q^65 + 42 * q^67 + 32 * q^69 - 48 * q^71 + 48 * q^75 - 4 * q^77 - 44 * q^79 - 34 * q^81 + 54 * q^85 - 2 * q^87 + 12 * q^89 + 16 * q^91 - 32 * q^95 + 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times$.

$n$	$561$	$911$	$1093$	$1249$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$	$1$

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
$3$	1.67234	−	2.89658i	0.965528	−	1.67234i	0.257339	−	0.966321i	$-0.417154\pi$
$3$	1.67234	−	2.89658i	0.965528	−	1.67234i	0.708189	−	0.706023i	$-0.249512\pi$
$4$		0			0
$5$			1.56356i			0.699244i	0.936891	+	0.349622i	$0.113690\pi$
$5$			1.56356i			0.699244i	−0.936891	+	0.349622i	$0.886310\pi$
$6$		0			0
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$8$		0			0
$9$	−4.09347	−	7.09010i	−1.36449	−	2.36337i
$10$		0			0
$11$	2.48215	+	1.43307i	0.748396	+	0.432087i	0.825114	−	0.564966i	$-0.191111\pi$
$11$	2.48215	+	1.43307i	0.748396	+	0.432087i	−0.0767180	+	0.997053i	$0.524444\pi$
$12$		0			0
$13$	2.99598	+	2.00602i	0.830935	+	0.556370i
$13$	2.99598	+	2.00602i	0.830935	+	0.556370i
$14$		0			0
$15$	4.52898	+	2.61481i	1.16938	+	0.675140i
$16$		0			0
$17$	−1.11481	−	1.93090i	−0.270380	−	0.468312i	0.698579	−	0.715533i	$-0.253816\pi$
$17$	−1.11481	−	1.93090i	−0.270380	−	0.468312i	−0.968959	+	0.247221i	$0.920483\pi$
$18$		0			0
$19$	6.26657	−	3.61801i	1.43765	−	0.830028i	0.439964	−	0.898015i	$-0.354991\pi$
$19$	6.26657	−	3.61801i	1.43765	−	0.830028i	0.997686	+	0.0679872i	$0.0216577\pi$
$20$		0			0
$21$		−	3.34469i		−	0.729871i
$22$		0			0
$23$	0.833676	−	1.44397i	0.173833	−	0.301088i	−0.765924	−	0.642932i	$-0.777718\pi$
$23$	0.833676	−	1.44397i	0.173833	−	0.301088i	0.939757	+	0.341843i	$0.111051\pi$
$24$		0			0
$25$	2.55529			0.511058
$26$		0			0
$27$	−17.3487			−3.33876
$28$		0			0
$29$	−2.41379	+	4.18080i	−0.448229	+	0.776356i	−0.998271	−	0.0587816i	$-0.981278\pi$
$29$	−2.41379	+	4.18080i	−0.448229	+	0.776356i	0.550042	+	0.835137i	$0.314612\pi$
$30$		0			0
$31$			0.597963i			0.107397i	0.998557	+	0.0536987i	$0.0171010\pi$
$31$			0.597963i			0.107397i	−0.998557	+	0.0536987i	$0.982899\pi$
$32$		0			0
$33$	8.30201	−	4.79317i	1.44519	−	0.834384i
$34$		0			0
$35$	0.781779	+	1.35408i	0.132145	+	0.228881i
$36$		0			0
$37$	0.0333971	+	0.0192818i	0.00549045	+	0.00316991i	0.502743	−	0.864436i	$-0.332324\pi$
$37$	0.0333971	+	0.0192818i	0.00549045	+	0.00316991i	−0.497252	+	0.867606i	$0.665658\pi$
$38$		0			0
$39$	10.8209	−	5.32335i	1.73273	−	0.852418i
$40$		0			0
$41$	−6.88896	−	3.97734i	−1.07588	−	0.621157i	−0.146095	−	0.989271i	$-0.546670\pi$
$41$	−6.88896	−	3.97734i	−1.07588	−	0.621157i	−0.929781	+	0.368114i	$0.880004\pi$
$42$		0			0
$43$	−5.04571	−	8.73942i	−0.769463	−	1.33275i	−0.937854	−	0.347029i	$-0.887191\pi$
$43$	−5.04571	−	8.73942i	−0.769463	−	1.33275i	0.168391	−	0.985720i	$-0.446143\pi$
$44$		0			0
$45$	11.0858	−	6.40037i	1.65257	−	0.954111i
$46$		0			0
$47$		−	7.02636i		−	1.02490i	−0.858717	−	0.512450i	$-0.828738\pi$
$47$		−	7.02636i		−	1.02490i	0.858717	−	0.512450i	$-0.171262\pi$
$48$		0			0
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$		0			0
$51$	−7.45736			−1.04424
$52$		0			0
$53$	−5.98404			−0.821971			−0.410985	−	0.911642i	$-0.634815\pi$
$53$	−5.98404			−0.821971			−0.410985	+	0.911642i	$0.634815\pi$
$54$		0			0
$55$	−2.24069	+	3.88098i	−0.302134	+	0.523312i
$56$		0			0
$57$		−	24.2022i		−	3.20566i
$58$		0			0
$59$	−0.776138	+	0.448103i	−0.101044	+	0.0583381i	−0.549671	−	0.835381i	$-0.685247\pi$
$59$	−0.776138	+	0.448103i	−0.101044	+	0.0583381i	0.448626	+	0.893719i	$0.351913\pi$
$60$		0			0
$61$	7.12846	+	12.3469i	0.912706	+	1.58085i	0.810225	+	0.586119i	$0.199345\pi$
$61$	7.12846	+	12.3469i	0.912706	+	1.58085i	0.102481	+	0.994735i	$0.467322\pi$
$62$		0			0
$63$	−7.09010	−	4.09347i	−0.893268	−	0.515729i
$64$		0			0
$65$	−3.13653	+	4.68438i	−0.389038	+	0.581026i
$66$		0			0
$67$	1.42103	+	0.820432i	0.173606	+	0.100232i	0.584285	−	0.811548i	$-0.301375\pi$
$67$	1.42103	+	0.820432i	0.173606	+	0.100232i	−0.410679	+	0.911780i	$0.634708\pi$
$68$		0			0
$69$	−2.78838	−	4.82962i	−0.335682	−	0.581418i
$70$		0			0
$71$	1.98724	−	1.14733i	0.235841	−	0.136163i	−0.377422	−	0.926041i	$-0.623190\pi$
$71$	1.98724	−	1.14733i	0.235841	−	0.136163i	0.613264	+	0.789878i	$0.289856\pi$
$72$		0			0
$73$			11.2277i			1.31411i	0.753844	+	0.657054i	$0.228198\pi$
$73$			11.2277i			1.31411i	−0.753844	+	0.657054i	$0.771802\pi$
$74$		0			0
$75$	4.27332	−	7.40161i	0.493441	−	0.854664i
$76$		0			0
$77$	2.86614			0.326627
$78$		0			0
$79$	−4.26098			−0.479397			−0.239699	−	0.970847i	$-0.577049\pi$
$79$	−4.26098			−0.479397			−0.239699	+	0.970847i	$0.577049\pi$
$80$		0			0
$81$	−16.7326	+	28.9816i	−1.85917	+	3.22018i
$82$		0			0
$83$			4.94829i			0.543145i	0.962418	+	0.271572i	$0.0875437\pi$
$83$			4.94829i			0.543145i	−0.962418	+	0.271572i	$0.912456\pi$
$84$		0			0
$85$	3.01907	−	1.74306i	0.327465	−	0.189062i
$86$		0			0
$87$	8.07337	+	13.9835i	0.865556	+	1.49919i
$88$		0			0
$89$	2.09682	+	1.21060i	0.222263	+	0.128323i	0.606997	−	0.794704i	$-0.292374\pi$
$89$	2.09682	+	1.21060i	0.222263	+	0.128323i	−0.384735	+	0.923027i	$0.625707\pi$
$90$		0			0
$91$	3.59760	+	0.239275i	0.377131	+	0.0250828i
$92$		0			0
$93$	1.73205	+	1.00000i	0.179605	+	0.103695i
$94$		0			0
$95$	5.65696	+	9.79815i	0.580392	+	1.00527i
$96$		0			0
$97$	−4.23338	+	2.44414i	−0.429835	+	0.248165i	−0.699276	−	0.714852i	$-0.746494\pi$
$97$	−4.23338	+	2.44414i	−0.429835	+	0.248165i	0.269442	+	0.963017i	$0.413161\pi$
$98$		0			0
$99$		−	23.4649i		−	2.35831i
$100$		0			0
$101$	3.68373	−	6.38042i	0.366545	−	0.634875i	−0.622478	−	0.782638i	$-0.713874\pi$
$101$	3.68373	−	6.38042i	0.366545	−	0.634875i	0.989023	+	0.147763i	$0.0472072\pi$
$102$		0			0
$103$	5.78525			0.570038			0.285019	−	0.958522i	$-0.408000\pi$
$103$	5.78525			0.570038			0.285019	+	0.958522i	$0.408000\pi$
$104$		0			0
$105$	5.22961			0.510358
$106$		0			0
$107$	−0.514478	+	0.891102i	−0.0497365	+	0.0861461i	−0.889822	−	0.456308i	$-0.849171\pi$
$107$	−0.514478	+	0.891102i	−0.0497365	+	0.0861461i	0.840085	+	0.542454i	$0.182505\pi$
$108$		0			0
$109$		−	14.1535i		−	1.35566i	−0.735220	−	0.677829i	$-0.762921\pi$
$109$		−	14.1535i		−	1.35566i	0.735220	−	0.677829i	$-0.237079\pi$
$110$		0			0
$111$	0.111703	−	0.0644917i	0.0106024	−	0.00612128i
$112$		0			0
$113$	6.77051	+	11.7269i	0.636916	+	1.10317i	0.986106	+	0.166119i	$0.0531237\pi$
$113$	6.77051	+	11.7269i	0.636916	+	1.10317i	−0.349189	+	0.937052i	$0.613543\pi$
$114$		0			0
$115$	2.25773	+	1.30350i	0.210534	+	0.121552i
$116$		0			0
$117$	1.95893	−	29.4533i	0.181103	−	2.72296i
$118$		0			0
$119$	−1.93090	−	1.11481i	−0.177005	−	0.102194i
$120$		0			0
$121$	−1.39263	−	2.41210i	−0.126602	−	0.219282i
$122$		0			0
$123$	−23.0414	+	13.3030i	−2.07758	+	1.19949i
$124$		0			0
$125$			11.8131i			1.05660i
$126$		0			0
$127$	−4.92583	+	8.53178i	−0.437096	+	0.757073i	−0.997464	−	0.0711707i	$-0.977326\pi$
$127$	−4.92583	+	8.53178i	−0.437096	+	0.757073i	0.560368	+	0.828244i	$0.310660\pi$
$128$		0			0
$129$	−33.7526			−2.97175
$130$		0			0
$131$	−14.7923			−1.29241			−0.646204	−	0.763165i	$-0.723645\pi$
$131$	−14.7923			−1.29241			−0.646204	+	0.763165i	$0.723645\pi$
$132$		0			0
$133$	3.61801	−	6.26657i	0.313721	−	0.543381i
$134$		0			0
$135$		−	27.1257i		−	2.33461i
$136$		0			0
$137$	0.397503	−	0.229499i	0.0339610	−	0.0196074i	−0.482923	−	0.875663i	$-0.660425\pi$
$137$	0.397503	−	0.229499i	0.0339610	−	0.0196074i	0.516884	+	0.856055i	$0.327092\pi$
$138$		0			0
$139$	7.65731	+	13.2628i	0.649485	+	1.12494i	0.983246	+	0.182283i	$0.0583486\pi$
$139$	7.65731	+	13.2628i	0.649485	+	1.12494i	−0.333762	+	0.942658i	$0.608318\pi$
$140$		0			0
$141$	−20.3525	−	11.7505i	−1.71399	−	0.989570i
$142$		0			0
$143$	4.56170	+	9.27268i	0.381468	+	0.775421i
$144$		0			0
$145$	−6.53693	−	3.77410i	−0.542862	−	0.313422i
$146$		0			0
$147$	−1.67234	−	2.89658i	−0.137933	−	0.238906i
$148$		0			0
$149$	8.86563	−	5.11858i	0.726301	−	0.419330i	−0.0907665	−	0.995872i	$-0.528932\pi$
$149$	8.86563	−	5.11858i	0.726301	−	0.419330i	0.817067	+	0.576542i	$0.195598\pi$
$150$		0			0
$151$			15.2110i			1.23785i	0.785448	+	0.618927i	$0.212432\pi$
$151$			15.2110i			1.23785i	−0.785448	+	0.618927i	$0.787568\pi$
$152$		0			0
$153$	−9.12684	+	15.8082i	−0.737862	+	1.27801i
$154$		0			0
$155$	−0.934950			−0.0750970
$156$		0			0
$157$	−2.27419			−0.181500			−0.0907500	−	0.995874i	$-0.528926\pi$
$157$	−2.27419			−0.181500			−0.0907500	+	0.995874i	$0.528926\pi$
$158$		0			0
$159$	−10.0074	+	17.3333i	−0.793636	+	1.37462i
$160$		0			0
$161$		−	1.66735i		−	0.131406i
$162$		0			0
$163$	−0.00848066	+	0.00489631i	−0.000664256	+	0.000383509i	−0.500332	−	0.865834i	$-0.666789\pi$
$163$	−0.00848066	+	0.00489631i	−0.000664256	+	0.000383509i	0.499668	+	0.866217i	$0.333455\pi$
$164$		0			0
$165$	7.49440	+	12.9807i	0.583438	+	1.01054i
$166$		0			0
$167$	−21.6080	−	12.4754i	−1.67208	−	0.965376i	−0.966472	−	0.256773i	$-0.917341\pi$
$167$	−21.6080	−	12.4754i	−1.67208	−	0.965376i	−0.705608	−	0.708603i	$-0.749326\pi$
$168$		0			0
$169$	4.95177	+	12.0200i	0.380906	+	0.924614i
$170$		0			0
$171$	−51.3040	−	29.6204i	−3.92332	−	2.26513i
$172$		0			0
$173$	−1.60275	−	2.77604i	−0.121855	−	0.211058i	0.798644	−	0.601803i	$-0.205551\pi$
$173$	−1.60275	−	2.77604i	−0.121855	−	0.211058i	−0.920499	+	0.390745i	$0.872218\pi$
$174$		0			0
$175$	2.21294	−	1.27764i	0.167283	−	0.0965808i
$176$		0			0
$177$			2.99753i			0.225308i
$178$		0			0
$179$	7.89998	−	13.6832i	0.590472	−	1.02273i	−0.403697	−	0.914893i	$-0.632275\pi$
$179$	7.89998	−	13.6832i	0.590472	−	1.02273i	0.994169	−	0.107835i	$-0.0343917\pi$
$180$		0			0
$181$	9.11907			0.677815			0.338908	−	0.940820i	$-0.389943\pi$
$181$	9.11907			0.677815			0.338908	+	0.940820i	$0.389943\pi$
$182$		0			0
$183$	47.6850			3.52497
$184$		0			0
$185$	−0.0301482	+	0.0522183i	−0.00221654	+	0.00383916i
$186$		0			0
$187$		−	6.39038i		−	0.467311i
$188$		0			0
$189$	−15.0244	+	8.67434i	−1.09286	+	0.630966i
$190$		0			0
$191$	−1.63068	−	2.82443i	−0.117992	−	0.204368i	0.800980	−	0.598691i	$-0.204312\pi$
$191$	−1.63068	−	2.82443i	−0.117992	−	0.204368i	−0.918972	+	0.394323i	$0.870979\pi$
$192$		0			0
$193$	19.1158	+	11.0365i	1.37599	+	0.794426i	0.991674	−	0.128777i	$-0.0411051\pi$
$193$	19.1158	+	11.0365i	1.37599	+	0.794426i	0.384313	+	0.923203i	$0.374438\pi$
$194$		0			0
$195$	8.32336	+	16.9191i	0.596048	+	1.21160i
$196$		0			0
$197$	−4.56660	−	2.63653i	−0.325357	−	0.187845i	0.328421	−	0.944531i	$-0.393484\pi$
$197$	−4.56660	−	2.63653i	−0.325357	−	0.187845i	−0.653778	+	0.756687i	$0.726817\pi$
$198$		0			0
$199$	−4.43381	−	7.67958i	−0.314304	−	0.544391i	0.664985	−	0.746857i	$-0.268438\pi$
$199$	−4.43381	−	7.67958i	−0.314304	−	0.544391i	−0.979289	+	0.202466i	$0.935105\pi$
$200$		0			0
$201$	4.75290	−	2.74409i	0.335244	−	0.193553i
$202$		0			0
$203$			4.82757i			0.338829i
$204$		0			0
$205$	6.21881	−	10.7713i	0.434340	−	0.752300i
$206$		0			0
$207$	−13.6505			−0.948775
$208$		0			0
$209$	20.7394			1.43458
$210$		0			0
$211$	3.28453	−	5.68898i	0.226117	−	0.391646i	−0.730537	−	0.682873i	$-0.760730\pi$
$211$	3.28453	−	5.68898i	0.226117	−	0.391646i	0.956654	+	0.291227i	$0.0940636\pi$
$212$		0			0
$213$		−	7.67493i		−	0.525877i
$214$		0			0
$215$	13.6646	−	7.88925i	0.931917	−	0.538043i
$216$		0			0
$217$	0.298982	+	0.517851i	0.0202962	+	0.0351540i
$218$		0			0
$219$	32.5221	+	18.7766i	2.19764	+	1.26881i
$220$		0			0
$221$	0.533490	−	8.02126i	0.0358864	−	0.539568i
$222$		0			0
$223$	14.6463	+	8.45606i	0.980790	+	0.566260i	0.902509	−	0.430672i	$-0.141723\pi$
$223$	14.6463	+	8.45606i	0.980790	+	0.566260i	0.0782817	+	0.996931i	$0.475057\pi$
$224$		0			0
$225$	−10.4600	−	18.1172i	−0.697333	−	1.20782i
$226$		0			0
$227$	13.9709	−	8.06611i	0.927282	−	0.535367i	0.0413312	−	0.999146i	$-0.486840\pi$
$227$	13.9709	−	8.06611i	0.927282	−	0.535367i	0.885951	+	0.463779i	$0.153507\pi$
$228$		0			0
$229$		−	6.91184i		−	0.456747i	−0.973574	−	0.228374i	$-0.926659\pi$
$229$		−	6.91184i		−	0.456747i	0.973574	−	0.228374i	$-0.0733408\pi$
$230$		0			0
$231$	4.79317	−	8.30201i	0.315367	−	0.546232i
$232$		0			0
$233$	7.47405			0.489641			0.244821	−	0.969568i	$-0.421271\pi$
$233$	7.47405			0.489641			0.244821	+	0.969568i	$0.421271\pi$
$234$		0			0
$235$	10.9861			0.716656
$236$		0			0
$237$	−7.12582	+	12.3423i	−0.462872	+	0.801717i
$238$		0			0
$239$			19.8696i			1.28526i	0.766179	+	0.642628i	$0.222156\pi$
$239$			19.8696i			1.28526i	−0.766179	+	0.642628i	$0.777844\pi$
$240$		0			0
$241$	−9.21842	+	5.32226i	−0.593811	+	0.342837i	−0.766603	−	0.642121i	$-0.778054\pi$
$241$	−9.21842	+	5.32226i	−0.593811	+	0.342837i	0.172792	+	0.984958i	$0.444721\pi$
$242$		0			0
$243$	29.9422	+	51.8613i	1.92079	+	3.32691i
$244$		0			0
$245$	1.35408	+	0.781779i	0.0865090	+	0.0499460i
$246$		0			0
$247$	26.0323	+	1.73140i	1.65640	+	0.110166i
$248$		0			0
$249$	14.3331	+	8.27524i	0.908325	+	0.524422i
$250$		0			0
$251$	−7.95696	−	13.7819i	−0.502239	−	0.869904i	−0.999997	−	0.00258749i	$-0.999176\pi$
$251$	−7.95696	−	13.7819i	−0.502239	−	0.869904i	0.497757	−	0.867316i	$-0.334157\pi$
$252$		0			0
$253$	4.13861	−	2.38943i	0.260192	−	0.150222i
$254$		0			0
$255$		−	11.6600i		−	0.730178i
$256$		0			0
$257$	−15.5509	+	26.9350i	−0.970039	+	1.68016i	−0.274619	+	0.961553i	$0.588552\pi$
$257$	−15.5509	+	26.9350i	−0.970039	+	1.68016i	−0.695420	+	0.718603i	$0.744782\pi$
$258$		0			0
$259$	0.0385636			0.00239623
$260$		0			0
$261$	39.5230			2.44642
$262$		0			0
$263$	−14.1873	+	24.5732i	−0.874829	+	1.51525i	−0.0178837	+	0.999840i	$0.505693\pi$
$263$	−14.1873	+	24.5732i	−0.874829	+	1.51525i	−0.856945	+	0.515408i	$0.827640\pi$
$264$		0			0
$265$		−	9.35639i		−	0.574758i
$266$		0			0
$267$	7.01321	−	4.04908i	0.429202	−	0.247800i
$268$		0			0
$269$	10.7008	+	18.5344i	0.652441	+	1.13006i	0.982529	+	0.186111i	$0.0595883\pi$
$269$	10.7008	+	18.5344i	0.652441	+	1.13006i	−0.330088	+	0.943950i	$0.607078\pi$
$270$		0			0
$271$	−4.97667	−	2.87328i	−0.302311	−	0.174539i	0.341170	−	0.940002i	$-0.389177\pi$
$271$	−4.97667	−	2.87328i	−0.302311	−	0.174539i	−0.643481	+	0.765462i	$0.722510\pi$
$272$		0			0
$273$	6.70951	−	10.0206i	0.406078	−	0.606475i
$274$		0			0
$275$	6.34260	+	3.66190i	0.382473	+	0.220821i
$276$		0			0
$277$	13.3010	+	23.0380i	0.799180	+	1.38422i	0.920151	+	0.391564i	$0.128066\pi$
$277$	13.3010	+	23.0380i	0.799180	+	1.38422i	−0.120971	+	0.992656i	$0.538601\pi$
$278$		0			0
$279$	4.23962	−	2.44774i	0.253819	−	0.146543i
$280$		0			0
$281$		−	6.69143i		−	0.399177i	−0.979880	−	0.199589i	$-0.936039\pi$
$281$		−	6.69143i		−	0.399177i	0.979880	−	0.199589i	$-0.0639606\pi$
$282$		0			0
$283$	−9.96692	+	17.2632i	−0.592472	+	1.02619i	0.401426	+	0.915891i	$0.368515\pi$
$283$	−9.96692	+	17.2632i	−0.592472	+	1.02619i	−0.993898	+	0.110300i	$0.964819\pi$
$284$		0			0
$285$	37.8416			2.24154
$286$		0			0
$287$	−7.95469			−0.469550
$288$		0			0
$289$	6.01442	−	10.4173i	0.353789	−	0.612781i
$290$		0			0
$291$			16.3498i			0.958442i
$292$		0			0
$293$	−7.67375	+	4.43044i	−0.448305	+	0.258829i	−0.707114	−	0.707099i	$-0.750003\pi$
$293$	−7.67375	+	4.43044i	−0.448305	+	0.258829i	0.258809	+	0.965929i	$0.416670\pi$
$294$		0			0
$295$	−0.700635	−	1.21354i	−0.0407926	−	0.0706548i
$296$		0			0
$297$	−43.0620	−	24.8619i	−2.49871	−	1.44263i
$298$		0			0
$299$	5.39430	−	2.65373i	0.311961	−	0.153469i
$300$		0			0
$301$	−8.73942	−	5.04571i	−0.503732	−	0.290830i
$302$		0			0
$303$	−12.3209	−	21.3405i	−0.707820	−	1.22598i
$304$		0			0
$305$	−19.3050	+	11.1458i	−1.10540	+	0.638205i
$306$		0			0
$307$		−	8.34636i		−	0.476352i	−0.971222	−	0.238176i	$-0.923450\pi$
$307$		−	8.34636i		−	0.476352i	0.971222	−	0.238176i	$-0.0765495\pi$
$308$		0			0
$309$	9.67493	−	16.7575i	0.550387	−	0.953299i
$310$		0			0
$311$	6.68896			0.379296			0.189648	−	0.981852i	$-0.439265\pi$
$311$	6.68896			0.379296			0.189648	+	0.981852i	$0.439265\pi$
$312$		0			0
$313$	−21.3788			−1.20840			−0.604199	−	0.796833i	$-0.706507\pi$
$313$	−21.3788			−1.20840			−0.604199	+	0.796833i	$0.706507\pi$
$314$		0			0
$315$	6.40037	−	11.0858i	0.360620	−	0.624612i
$316$		0			0
$317$			31.6776i			1.77919i	0.456748	+	0.889596i	$0.349014\pi$
$317$			31.6776i			1.77919i	−0.456748	+	0.889596i	$0.650986\pi$
$318$		0			0
$319$	−11.9828	+	6.91825i	−0.670906	+	0.387348i
$320$		0			0
$321$	1.72077	+	2.98046i	0.0960439	+	0.166353i
$322$		0			0
$323$	−13.9720	−	8.06675i	−0.777424	−	0.448846i
$324$		0			0
$325$	7.65559	+	5.12596i	0.424656	+	0.284337i
$326$		0			0
$327$	−40.9967	−	23.6695i	−2.26713	−	1.30893i
$328$		0			0
$329$	−3.51318	−	6.08501i	−0.193688	−	0.335477i
$330$		0			0
$331$	21.3644	−	12.3347i	1.17429	−	0.677979i	0.219606	−	0.975589i	$-0.429523\pi$
$331$	21.3644	−	12.3347i	1.17429	−	0.677979i	0.954688	+	0.297609i	$0.0961893\pi$
$332$		0			0
$333$		−	0.315718i		−	0.0173012i
$334$		0			0
$335$	−1.28279	+	2.22186i	−0.0700865	+	0.121393i
$336$		0			0
$337$	28.0871			1.53000			0.765002	−	0.644028i	$-0.222738\pi$
$337$	28.0871			1.53000			0.765002	+	0.644028i	$0.222738\pi$
$338$		0			0
$339$	45.2905			2.45984
$340$		0			0
$341$	−0.856923	+	1.48423i	−0.0464050	+	0.0803757i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$		0			0
$345$	7.55139	−	4.35980i	0.406553	−	0.234724i
$346$		0			0
$347$	−5.05398	−	8.75374i	−0.271312	−	0.469926i	0.697886	−	0.716209i	$-0.254124\pi$
$347$	−5.05398	−	8.75374i	−0.271312	−	0.469926i	−0.969198	+	0.246283i	$0.920791\pi$
$348$		0			0
$349$	−15.0596	−	8.69465i	−0.806121	−	0.465414i	0.0394863	−	0.999220i	$-0.487428\pi$
$349$	−15.0596	−	8.69465i	−0.806121	−	0.465414i	−0.845607	+	0.533806i	$0.820761\pi$
$350$		0			0
$351$	−51.9763	−	34.8018i	−2.77429	−	1.85758i
$352$		0			0
$353$	2.88091	+	1.66329i	0.153335	+	0.0885282i	0.574704	−	0.818361i	$-0.305117\pi$
$353$	2.88091	+	1.66329i	0.153335	+	0.0885282i	−0.421369	+	0.906889i	$0.638450\pi$
$354$		0			0
$355$	1.79392	+	3.10716i	0.0952113	+	0.164911i
$356$		0			0
$357$	−6.45826	+	3.72868i	−0.341807	+	0.197343i
$358$		0			0
$359$			8.02414i			0.423498i	0.977324	+	0.211749i	$0.0679159\pi$
$359$			8.02414i			0.423498i	−0.977324	+	0.211749i	$0.932084\pi$
$360$		0			0
$361$	16.6800	−	28.8905i	0.877893	−	1.52055i
$362$		0			0
$363$	−9.31579			−0.488952
$364$		0			0
$365$	−17.5552			−0.918882
$366$		0			0
$367$	0.519540	−	0.899869i	0.0271198	−	0.0469728i	−0.852147	−	0.523302i	$-0.824700\pi$
$367$	0.519540	−	0.899869i	0.0271198	−	0.0469728i	0.879267	+	0.476330i	$0.158033\pi$
$368$		0			0
$369$			65.1245i			3.39025i
$370$		0			0
$371$	−5.18233	+	2.99202i	−0.269053	+	0.155338i
$372$		0			0
$373$	−13.6562	−	23.6532i	−0.707092	−	1.22472i	−0.965931	−	0.258798i	$-0.916673\pi$
$373$	−13.6562	−	23.6532i	−0.707092	−	1.22472i	0.258840	−	0.965920i	$-0.416660\pi$
$374$		0			0
$375$	34.2177	+	19.7556i	1.76700	+	1.02018i
$376$		0			0
$377$	−15.6184	+	7.68349i	−0.804390	+	0.395720i
$378$		0			0
$379$	1.91535	+	1.10583i	0.0983850	+	0.0568026i	0.548385	−	0.836226i	$-0.315243\pi$
$379$	1.91535	+	1.10583i	0.0983850	+	0.0568026i	−0.450000	+	0.893028i	$0.648576\pi$
$380$		0			0
$381$	16.4754	+	28.5361i	0.844058	+	1.46195i
$382$		0			0
$383$	−19.3458	+	11.1693i	−0.988522	+	0.570724i	−0.904832	−	0.425768i	$-0.860004\pi$
$383$	−19.3458	+	11.1693i	−0.988522	+	0.570724i	−0.0836900	+	0.996492i	$0.526671\pi$
$384$		0			0
$385$			4.48137i			0.228392i
$386$		0			0
$387$	−41.3089	+	71.5491i	−2.09985	+	3.63704i
$388$		0			0
$389$	−12.2604			−0.621629			−0.310814	−	0.950471i	$-0.600602\pi$
$389$	−12.2604			−0.621629			−0.310814	+	0.950471i	$0.600602\pi$
$390$		0			0
$391$	−3.71755			−0.188004
$392$		0			0
$393$	−24.7378	+	42.8471i	−1.24786	+	2.16135i
$394$		0			0
$395$		−	6.66228i		−	0.335216i
$396$		0			0
$397$	2.54193	−	1.46759i	0.127576	−	0.0736561i	−0.434854	−	0.900501i	$-0.643200\pi$
$397$	2.54193	−	1.46759i	0.127576	−	0.0736561i	0.562430	+	0.826845i	$0.309867\pi$
$398$		0			0
$399$	−12.1011	−	20.9597i	−0.605813	−	1.04930i
$400$		0			0
$401$	18.9229	+	10.9251i	0.944963	+	0.545575i	0.891513	−	0.452996i	$-0.149645\pi$
$401$	18.9229	+	10.9251i	0.944963	+	0.545575i	0.0534502	+	0.998571i	$0.482978\pi$
$402$		0			0
$403$	−1.19953	+	1.79148i	−0.0597526	+	0.0892402i
$404$		0			0
$405$	−45.3145	−	26.1623i	−2.25169	−	1.30002i
$406$		0			0
$407$	0.0552644	+	0.0957207i	0.00273935	+	0.00474470i
$408$		0			0
$409$	−6.39292	+	3.69095i	−0.316109	+	0.182506i	−0.649657	−	0.760227i	$-0.725088\pi$
$409$	−6.39292	+	3.69095i	−0.316109	+	0.182506i	0.333548	+	0.942733i	$0.391754\pi$
$410$		0			0
$411$		−	1.53520i		−	0.0757260i
$412$		0			0
$413$	−0.448103	+	0.776138i	−0.0220497	+	0.0381912i
$414$		0			0
$415$	−7.73693			−0.379791
$416$		0			0
$417$	51.2226			2.50838
$418$		0			0
$419$	−4.29137	+	7.43287i	−0.209647	+	0.363119i	−0.951603	−	0.307329i	$-0.900565\pi$
$419$	−4.29137	+	7.43287i	−0.209647	+	0.363119i	0.741956	+	0.670448i	$0.233898\pi$
$420$		0			0
$421$			7.49525i			0.365296i	0.983178	+	0.182648i	$0.0584669\pi$
$421$			7.49525i			0.365296i	−0.983178	+	0.182648i	$0.941533\pi$
$422$		0			0
$423$	−49.8176	+	28.7622i	−2.42221	+	1.39847i
$424$		0			0
$425$	−2.84865	−	4.93401i	−0.138180	−	0.239334i
$426$		0			0
$427$	12.3469	+	7.12846i	0.597507	+	0.344971i
$428$		0			0
$429$	34.4878	+	2.29377i	1.66509	+	0.110744i
$430$		0			0
$431$	14.2713	+	8.23956i	0.687426	+	0.396886i	0.802647	−	0.596454i	$-0.203424\pi$
$431$	14.2713	+	8.23956i	0.687426	+	0.396886i	−0.115221	+	0.993340i	$0.536758\pi$
$432$		0			0
$433$	−12.7805	−	22.1365i	−0.614192	−	1.06381i	−0.990526	−	0.137328i	$-0.956149\pi$
$433$	−12.7805	−	22.1365i	−0.614192	−	1.06381i	0.376333	−	0.926484i	$-0.377185\pi$
$434$		0			0
$435$	−21.8640	+	12.6232i	−1.04830	+	0.605235i
$436$		0			0
$437$		−	12.0650i		−	0.577146i
$438$		0			0
$439$	−4.60420	+	7.97470i	−0.219746	+	0.380612i	−0.954730	−	0.297473i	$-0.903856\pi$
$439$	−4.60420	+	7.97470i	−0.219746	+	0.380612i	0.734984	+	0.678084i	$0.237190\pi$
$440$		0			0
$441$	−8.18694			−0.389854
$442$		0			0
$443$	6.20759			0.294931			0.147466	−	0.989067i	$-0.452888\pi$
$443$	6.20759			0.294931			0.147466	+	0.989067i	$0.452888\pi$
$444$		0			0
$445$	−1.89284	+	3.27850i	−0.0897294	+	0.155416i
$446$		0			0
$447$		−	34.2401i		−	1.61950i
$448$		0			0
$449$	4.51968	−	2.60944i	0.213297	−	0.123147i	−0.389546	−	0.921007i	$-0.627368\pi$
$449$	4.51968	−	2.60944i	0.213297	−	0.123147i	0.602843	+	0.797860i	$0.294035\pi$
$450$		0			0
$451$	−11.3996	−	19.7447i	−0.536787	−	0.929743i
$452$		0			0
$453$	44.0600	+	25.4380i	2.07012	+	1.19518i
$454$		0			0
$455$	−0.374120	+	5.62506i	−0.0175390	+	0.263707i
$456$		0			0
$457$	−29.3870	−	16.9666i	−1.37467	−	0.793664i	−0.383155	−	0.923684i	$-0.625162\pi$
$457$	−29.3870	−	16.9666i	−1.37467	−	0.793664i	−0.991511	+	0.130021i	$0.958496\pi$
$458$		0			0
$459$	19.3404	+	33.4986i	0.902733	+	1.56358i
$460$		0			0
$461$	0.731583	−	0.422380i	0.0340732	−	0.0196722i	−0.482867	−	0.875694i	$-0.660404\pi$
$461$	0.731583	−	0.422380i	0.0340732	−	0.0196722i	0.516940	+	0.856022i	$0.327071\pi$
$462$		0			0
$463$			6.50221i			0.302183i	0.988520	+	0.151092i	$0.0482789\pi$
$463$			6.50221i			0.302183i	−0.988520	+	0.151092i	$0.951721\pi$
$464$		0			0
$465$	−1.56356	+	2.70816i	−0.0725082	+	0.125588i
$466$		0			0
$467$	−9.52759			−0.440884			−0.220442	−	0.975400i	$-0.570750\pi$
$467$	−9.52759			−0.440884			−0.220442	+	0.975400i	$0.570750\pi$
$468$		0			0
$469$	1.64086			0.0757681
$470$		0			0
$471$	−3.80322	+	6.58738i	−0.175243	+	0.303530i
$472$		0			0
$473$		−	28.9234i		−	1.32990i
$474$		0			0
$475$	16.0129	−	9.24505i	0.734722	−	0.424192i
$476$		0			0
$477$	24.4955	+	42.4274i	1.12157	+	1.94262i
$478$		0			0
$479$	2.46123	+	1.42099i	0.112457	+	0.0649268i	0.555173	−	0.831735i	$-0.312652\pi$
$479$	2.46123	+	1.42099i	0.112457	+	0.0649268i	−0.442717	+	0.896662i	$0.645985\pi$
$480$		0			0
$481$	0.0613773	+	0.124763i	0.00279856	+	0.00568871i
$482$		0			0
$483$	−4.82962	−	2.78838i	−0.219755	−	0.126876i
$484$		0			0
$485$	−3.82156	−	6.61913i	−0.173528	−	0.300559i
$486$		0			0
$487$	4.55853	−	2.63187i	0.206567	−	0.119261i	−0.393148	−	0.919475i	$-0.628614\pi$
$487$	4.55853	−	2.63187i	0.206567	−	0.119261i	0.599715	+	0.800214i	$0.295281\pi$
$488$		0			0
$489$			0.0327533i			0.00148115i
$490$		0			0
$491$	−11.4457	+	19.8245i	−0.516536	+	0.894666i	0.483280	+	0.875466i	$0.339445\pi$
$491$	−11.4457	+	19.8245i	−0.516536	+	0.894666i	−0.999816	+	0.0192004i	$0.993888\pi$
$492$		0			0
$493$	10.7636			0.484769
$494$		0			0
$495$	36.6887			1.64903
$496$		0			0
$497$	1.14733	−	1.98724i	0.0514648	−	0.0891397i
$498$		0			0
$499$		−	6.79877i		−	0.304355i	−0.988353	−	0.152177i	$-0.951372\pi$
$499$		−	6.79877i		−	0.304355i	0.988353	−	0.152177i	$-0.0486285\pi$
$500$		0			0
$501$	−72.2721	+	41.7263i	−3.22888	+	1.86419i
$502$		0			0
$503$	5.40300	+	9.35827i	0.240908	+	0.417265i	0.960973	−	0.276642i	$-0.0892215\pi$
$503$	5.40300	+	9.35827i	0.240908	+	0.417265i	−0.720065	+	0.693906i	$0.755888\pi$
$504$		0			0
$505$	9.97615	+	5.75973i	0.443933	+	0.256305i
$506$		0			0
$507$	43.0980	+	5.75832i	1.91405	+	0.255736i
$508$		0			0
$509$	−23.6593	−	13.6597i	−1.04868	−	0.605455i	−0.126400	−	0.991979i	$-0.540342\pi$
$509$	−23.6593	−	13.6597i	−1.04868	−	0.605455i	−0.922279	+	0.386524i	$0.873676\pi$
$510$		0			0
$511$	5.61387	+	9.72351i	0.248343	+	0.430143i
$512$		0			0
$513$	−108.717	+	62.7677i	−4.79996	+	2.77126i
$514$		0			0
$515$			9.04557i			0.398595i
$516$		0			0
$517$	10.0693	−	17.4405i	0.442846	−	0.767031i
$518$		0			0
$519$	−10.7214			−0.470616
$520$		0			0
$521$	−3.63580			−0.159287			−0.0796437	−	0.996823i	$-0.525378\pi$
$521$	−3.63580			−0.159287			−0.0796437	+	0.996823i	$0.525378\pi$
$522$		0			0
$523$	−3.59223	+	6.22193i	−0.157077	+	0.272066i	−0.933813	−	0.357760i	$-0.883541\pi$
$523$	−3.59223	+	6.22193i	−0.157077	+	0.272066i	0.776736	+	0.629826i	$0.216874\pi$
$524$		0			0
$525$		−	8.54664i		−	0.373006i
$526$		0			0
$527$	1.15461	−	0.666613i	0.0502955	−	0.0290381i
$528$		0			0
$529$	10.1100	+	17.5110i	0.439564	+	0.761347i
$530$		0			0
$531$	6.35419	+	3.66859i	0.275748	+	0.159203i
$532$		0			0
$533$	−12.6606	−	25.7354i	−0.548389	−	1.11473i
$534$		0			0
$535$	−1.39329	−	0.804416i	−0.0602371	−	0.0347779i
$536$		0			0
$537$	−26.4230	−	45.7659i	−1.14023	−	1.97494i
$538$		0			0
$539$	2.48215	−	1.43307i	0.106914	−	0.0617267i
$540$		0			0
$541$			0.445063i			0.0191347i	0.999954	+	0.00956737i	$0.00304543\pi$
$541$			0.445063i			0.0191347i	−0.999954	+	0.00956737i	$0.996955\pi$
$542$		0			0
$543$	15.2502	−	26.4142i	0.654450	−	1.13354i
$544$		0			0
$545$	22.1298			0.947935
$546$		0			0
$547$	5.67129			0.242487			0.121243	−	0.992623i	$-0.461312\pi$
$547$	5.67129			0.242487			0.121243	+	0.992623i	$0.461312\pi$
$548$		0			0
$549$	58.3603	−	101.083i	2.49076	−	4.31412i
$550$		0			0
$551$			34.9324i			1.48817i
$552$		0			0
$553$	−3.69011	+	2.13049i	−0.156920	+	0.0905976i
$554$		0			0
$555$	0.100836	+	0.174654i	0.00428027	+	0.00741364i
$556$		0			0
$557$	22.9561	+	13.2537i	0.972683	+	0.561579i	0.900053	−	0.435780i	$-0.143528\pi$
$557$	22.9561	+	13.2537i	0.972683	+	0.561579i	0.0726298	+	0.997359i	$0.476861\pi$
$558$		0			0
$559$	2.41462	−	36.3049i	0.102128	−	1.53553i
$560$		0			0
$561$	−18.5103	−	10.6869i	−0.781504	−	0.451202i
$562$		0			0
$563$	5.76880	+	9.99186i	0.243126	+	0.421107i	0.961603	−	0.274444i	$-0.0884938\pi$
$563$	5.76880	+	9.99186i	0.243126	+	0.421107i	−0.718477	+	0.695551i	$0.755160\pi$
$564$		0			0
$565$	−18.3356	+	10.5861i	−0.771386	+	0.445360i
$566$		0			0
$567$			33.4651i			1.40540i
$568$		0			0
$569$	−16.0791	+	27.8497i	−0.674069	+	1.16752i	0.302671	+	0.953095i	$0.402122\pi$
$569$	−16.0791	+	27.8497i	−0.674069	+	1.16752i	−0.976740	+	0.214427i	$0.931212\pi$
$570$		0			0
$571$	11.5540			0.483521			0.241761	−	0.970336i	$-0.422275\pi$
$571$	11.5540			0.483521			0.241761	+	0.970336i	$0.422275\pi$
$572$		0			0
$573$	−10.9083			−0.455699
$574$		0			0
$575$	2.13028	−	3.68976i	0.0888389	−	0.153873i
$576$		0			0
$577$		−	9.14050i		−	0.380524i	−0.981733	−	0.190262i	$-0.939066\pi$
$577$		−	9.14050i		−	0.380524i	0.981733	−	0.190262i	$-0.0609337\pi$
$578$		0			0
$579$	63.9364	−	36.9137i	2.65711	−	1.53408i
$580$		0			0
$581$	2.47414	+	4.28534i	0.102645	+	0.177786i
$582$		0			0
$583$	−14.8533	−	8.57554i	−0.615160	−	0.355163i
$584$		0			0
$585$	46.0520	+	3.06289i	1.90402	+	0.126635i
$586$		0			0
$587$	−37.0629	−	21.3983i	−1.52975	−	0.883201i	−0.999372	−	0.0354398i	$-0.988717\pi$
$587$	−37.0629	−	21.3983i	−1.52975	−	0.883201i	−0.530378	−	0.847761i	$-0.677950\pi$
$588$		0			0
$589$	2.16344	+	3.74718i	0.0891428	+	0.154400i
$590$		0			0
$591$	−15.2738	+	8.81836i	−0.628282	+	0.362739i
$592$		0			0
$593$			14.2439i			0.584927i	0.956277	+	0.292463i	$0.0944750\pi$
$593$			14.2439i			0.584927i	−0.956277	+	0.292463i	$0.905525\pi$
$594$		0			0
$595$	1.74306	−	3.01907i	0.0714586	−	0.123770i
$596$		0			0
$597$	−29.6594			−1.21388
$598$		0			0
$599$	−3.74735			−0.153113			−0.0765563	−	0.997065i	$-0.524392\pi$
$599$	−3.74735			−0.153113			−0.0765563	+	0.997065i	$0.524392\pi$
$600$		0			0
$601$	−5.33462	+	9.23984i	−0.217604	+	0.376901i	−0.954075	−	0.299568i	$-0.903157\pi$
$601$	−5.33462	+	9.23984i	−0.217604	+	0.376901i	0.736471	+	0.676469i	$0.236491\pi$
$602$		0			0
$603$		−	13.4337i		−	0.547061i
$604$		0			0
$605$	3.77145	−	2.17745i	0.153331	−	0.0885259i
$606$		0			0
$607$	4.82628	+	8.35936i	0.195893	+	0.339296i	0.947193	−	0.320665i	$-0.103906\pi$
$607$	4.82628	+	8.35936i	0.195893	+	0.339296i	−0.751300	+	0.659961i	$0.770573\pi$
$608$		0			0
$609$	13.9835	+	8.07337i	0.566639	+	0.327149i
$610$		0			0
$611$	14.0950	−	21.0508i	0.570223	−	0.851625i
$612$		0			0
$613$	−3.45968	−	1.99745i	−0.139735	−	0.0806761i	0.428503	−	0.903541i	$-0.359041\pi$
$613$	−3.45968	−	1.99745i	−0.139735	−	0.0806761i	−0.568238	+	0.822864i	$0.692375\pi$
$614$		0			0
$615$	−20.8000	−	36.0266i	−0.838736	−	1.45273i
$616$		0			0
$617$	2.80199	−	1.61773i	0.112804	−	0.0651273i	−0.442537	−	0.896750i	$-0.645921\pi$
$617$	2.80199	−	1.61773i	0.112804	−	0.0651273i	0.555340	+	0.831623i	$0.312588\pi$
$618$		0			0
$619$		−	39.2679i		−	1.57831i	−0.614193	−	0.789156i	$-0.710518\pi$
$619$		−	39.2679i		−	1.57831i	0.614193	−	0.789156i	$-0.289482\pi$
$620$		0			0
$621$	−14.4632	+	25.0510i	−0.580387	+	1.00526i
$622$		0			0
$623$	2.42120			0.0970033
$624$		0			0
$625$	−5.69406			−0.227763
$626$		0			0
$627$	34.6834	−	60.0735i	1.38512	−	2.39910i
$628$		0			0
$629$		−	0.0859819i		−	0.00342832i
$630$		0			0
$631$	−25.4983	+	14.7215i	−1.01507	+	0.586052i	−0.912673	−	0.408691i	$-0.865985\pi$
$631$	−25.4983	+	14.7215i	−1.01507	+	0.586052i	−0.102400	+	0.994743i	$0.532652\pi$
$632$		0			0
$633$	−10.9857	−	19.0279i	−0.436644	−	0.756290i
$634$		0			0
$635$	−13.3399	−	7.70181i	−0.529379	−	0.305637i
$636$		0			0
$637$	3.23525	−	1.59158i	0.128185	−	0.0630608i
$638$		0			0
$639$	−16.2694	−	9.39313i	−0.643606	−	0.371586i
$640$		0			0
$641$	2.04559	+	3.54307i	0.0807961	+	0.139943i	0.903592	−	0.428394i	$-0.140920\pi$
$641$	2.04559	+	3.54307i	0.0807961	+	0.139943i	−0.822796	+	0.568337i	$0.807587\pi$
$642$		0			0
$643$	−19.2672	+	11.1239i	−0.759825	+	0.438685i	−0.829233	−	0.558903i	$-0.811222\pi$
$643$	−19.2672	+	11.1239i	−0.759825	+	0.438685i	0.0694080	+	0.997588i	$0.477889\pi$
$644$		0			0
$645$		−	52.7742i		−	2.07798i
$646$		0			0
$647$	24.9292	−	43.1786i	0.980066	−	1.69752i	0.317980	−	0.948097i	$-0.396996\pi$
$647$	24.9292	−	43.1786i	0.980066	−	1.69752i	0.662086	−	0.749427i	$-0.269671\pi$
$648$		0			0
$649$	−2.56865			−0.100828
$650$		0			0
$651$	2.00000			0.0783862
$652$		0			0
$653$	−3.70177	+	6.41165i	−0.144861	+	0.250907i	−0.929321	−	0.369272i	$-0.879607\pi$
$653$	−3.70177	+	6.41165i	−0.144861	+	0.250907i	0.784460	+	0.620180i	$0.212940\pi$
$654$		0			0
$655$		−	23.1286i		−	0.903709i
$656$		0			0
$657$	79.6058	−	45.9604i	3.10572	−	1.79309i
$658$		0			0
$659$	15.0410	+	26.0518i	0.585914	+	1.01483i	0.994761	+	0.102230i	$0.0325977\pi$
$659$	15.0410	+	26.0518i	0.585914	+	1.01483i	−0.408847	+	0.912603i	$0.634069\pi$
$660$		0			0
$661$	23.0639	+	13.3160i	0.897082	+	0.517931i	0.876252	−	0.481852i	$-0.160036\pi$
$661$	23.0639	+	13.3160i	0.897082	+	0.517931i	0.0208300	+	0.999783i	$0.493369\pi$
$662$		0			0
$663$	−22.3421	−	14.9596i	−0.867694	−	0.580983i
$664$		0			0
$665$	9.79815	+	5.65696i	0.379956	+	0.219368i
$666$		0			0
$667$	4.02463	+	6.97087i	0.155834	+	0.269913i
$668$		0			0
$669$	48.9874	−	28.2829i	1.89396	−	1.09348i
$670$		0			0
$671$			40.8623i			1.57747i
$672$		0			0
$673$	−1.84652	+	3.19827i	−0.0711783	+	0.123284i	−0.899418	−	0.437090i	$-0.856009\pi$
$673$	−1.84652	+	3.19827i	−0.0711783	+	0.123284i	0.828240	+	0.560374i	$0.189343\pi$
$674$		0			0
$675$	−44.3309			−1.70630
$676$		0			0
$677$	−35.6533			−1.37027			−0.685134	−	0.728417i	$-0.740256\pi$
$677$	−35.6533			−1.37027			−0.685134	+	0.728417i	$0.740256\pi$
$678$		0			0
$679$	−2.44414	+	4.23338i	−0.0937976	+	0.162462i
$680$		0			0
$681$		−	53.9572i		−	2.06765i
$682$		0			0
$683$	26.2105	−	15.1326i	1.00292	−	0.579034i	0.0938062	−	0.995590i	$-0.470097\pi$
$683$	26.2105	−	15.1326i	1.00292	−	0.579034i	0.909110	+	0.416557i	$0.136763\pi$
$684$		0			0
$685$	0.358834	+	0.621519i	0.0137104	+	0.0237470i
$686$		0			0
$687$	−20.0207	−	11.5590i	−0.763838	−	0.441002i
$688$		0			0
$689$	−17.9280	−	12.0041i	−0.683004	−	0.457320i
$690$		0			0
$691$	−3.03377	−	1.75155i	−0.115410	−	0.0666320i	0.441184	−	0.897417i	$-0.354559\pi$
$691$	−3.03377	−	1.75155i	−0.115410	−	0.0666320i	−0.556594	+	0.830785i	$0.687892\pi$
$692$		0			0
$693$	−11.7324	−	20.3212i	−0.445679	−	0.771938i
$694$		0			0
$695$	−20.7372	+	11.9726i	−0.786608	+	0.454148i
$696$		0			0
$697$			17.7359i			0.671794i
$698$		0			0
$699$	12.4992	−	21.6492i	0.472762	−	0.818849i
$700$		0			0
$701$	−45.2243			−1.70810			−0.854048	−	0.520194i	$-0.825860\pi$
$701$	−45.2243			−1.70810			−0.854048	+	0.520194i	$0.825860\pi$
$702$		0			0
$703$	0.279047			0.0105245
$704$		0			0
$705$	18.3726	−	31.8222i	0.691951	−	1.19849i
$706$		0			0
$707$		−	7.36747i		−	0.277082i
$708$		0			0
$709$	2.59657	−	1.49913i	0.0975161	−	0.0563009i	−0.450449	−	0.892802i	$-0.648736\pi$
$709$	2.59657	−	1.49913i	0.0975161	−	0.0563009i	0.547965	+	0.836501i	$0.315403\pi$
$710$		0			0
$711$	17.4422	+	30.2107i	0.654133	+	1.13299i
$712$		0			0
$713$	0.863440	+	0.498507i	0.0323361	+	0.0186692i
$714$		0			0
$715$	−14.4984	+	7.13248i	−0.542208	+	0.266740i
$716$		0			0
$717$	57.5539	+	33.2287i	2.14939	+	1.24095i
$718$		0			0
$719$	10.0397	+	17.3892i	0.374417	+	0.648509i	0.990240	−	0.139376i	$-0.0445096\pi$
$719$	10.0397	+	17.3892i	0.374417	+	0.648509i	−0.615823	+	0.787885i	$0.711176\pi$
$720$		0			0
$721$	5.01017	−	2.89263i	0.186589	−	0.107727i
$722$		0			0
$723$			35.6026i			1.32407i
$724$		0			0
$725$	−6.16792	+	10.6832i	−0.229071	+	0.396762i
$726$		0			0
$727$	32.5895			1.20868			0.604338	−	0.796728i	$-0.293438\pi$
$727$	32.5895			1.20868			0.604338	+	0.796728i	$0.293438\pi$
$728$		0			0
$729$	99.8990			3.69996
$730$		0			0
$731$	−11.2500	+	19.4855i	−0.416095	+	0.720698i
$732$		0			0
$733$		−	18.5190i		−	0.684017i	−0.939697	−	0.342008i	$-0.888893\pi$
$733$		−	18.5190i		−	0.684017i	0.939697	−	0.342008i	$-0.111107\pi$
$734$		0			0
$735$	4.52898	−	2.61481i	0.167054	−	0.0964486i
$736$		0			0
$737$	2.35147	+	4.07287i	0.0866176	+	0.150026i
$738$		0			0
$739$	−13.7968	−	7.96559i	−0.507524	−	0.293019i	0.224291	−	0.974522i	$-0.427993\pi$
$739$	−13.7968	−	7.96559i	−0.507524	−	0.293019i	−0.731815	+	0.681503i	$0.761327\pi$
$740$		0			0
$741$	48.5501	−	72.5093i	1.78353	−	2.66370i
$742$		0			0
$743$	−10.5962	−	6.11773i	−0.388738	−	0.224438i	0.292875	−	0.956151i	$-0.405388\pi$
$743$	−10.5962	−	6.11773i	−0.388738	−	0.224438i	−0.681613	+	0.731713i	$0.738721\pi$
$744$		0			0
$745$	8.00319	+	13.8619i	0.293214	+	0.507862i
$746$		0			0
$747$	35.0838	−	20.2556i	1.28365	−	0.741115i
$748$		0			0
$749$			1.02896i			0.0375972i
$750$		0			0
$751$	10.4107	−	18.0318i	0.379891	−	0.657990i	−0.611155	−	0.791511i	$-0.709295\pi$
$751$	10.4107	−	18.0318i	0.379891	−	0.657990i	0.991046	+	0.133521i	$0.0426282\pi$
$752$		0			0
$753$	−53.2271			−1.93970
$754$		0			0
$755$	−23.7833			−0.865563
$756$		0			0
$757$	−13.5575	+	23.4823i	−0.492757	+	0.853480i	−0.999965	−	0.00834344i	$-0.997344\pi$
$757$	−13.5575	+	23.4823i	−0.492757	+	0.853480i	0.507208	+	0.861824i	$0.330678\pi$
$758$		0			0
$759$		−	15.9838i		−	0.580175i
$760$		0			0
$761$	41.8920	−	24.1864i	1.51858	−	0.876755i	0.518824	−	0.854881i	$-0.326370\pi$
$761$	41.8920	−	24.1864i	1.51858	−	0.876755i	0.999761	−	0.0218739i	$-0.00696324\pi$
$762$		0			0
$763$	−7.07674	−	12.2573i	−0.256195	−	0.443743i
$764$		0			0
$765$	−24.7170	−	14.2703i	−0.893644	−	0.515945i
$766$		0			0
$767$	−3.22419	−	0.214439i	−0.116419	−	0.00774296i
$768$		0			0
$769$	−15.0214	−	8.67264i	−0.541687	−	0.312743i	0.204075	−	0.978955i	$-0.434581\pi$
$769$	−15.0214	−	8.67264i	−0.541687	−	0.312743i	−0.745762	+	0.666212i	$0.767915\pi$
$770$		0			0
$771$	52.0129	+	90.0890i	1.87320	+	3.24448i
$772$		0			0
$773$	−12.1659	+	7.02398i	−0.437576	+	0.252635i	−0.702569	−	0.711616i	$-0.747964\pi$
$773$	−12.1659	+	7.02398i	−0.437576	+	0.252635i	0.264993	+	0.964250i	$0.414630\pi$
$774$		0			0
$775$			1.52797i			0.0548862i
$776$		0			0
$777$	0.0644917	−	0.111703i	0.00231363	−	0.00400732i
$778$		0			0
$779$	−57.5603			−2.06231
$780$		0			0
$781$	6.57682			0.235337
$782$		0			0
$783$	41.8760	−	72.5314i	1.49653	−	2.59206i
$784$		0			0
$785$		−	3.55582i		−	0.126913i
$786$		0			0
$787$	6.71670	−	3.87789i	0.239424	−	0.138232i	−0.375488	−	0.926827i	$-0.622525\pi$
$787$	6.71670	−	3.87789i	0.239424	−	0.138232i	0.614912	+	0.788596i	$0.289191\pi$
$788$		0			0
$789$	47.4522	+	82.1896i	1.68934	+	2.92603i
$790$		0			0
$791$	11.7269	+	6.77051i	0.416960	+	0.240732i
$792$		0			0
$793$	−3.41132	+	51.2908i	−0.121140	+	1.82139i
$794$		0			0
$795$	−27.1016	−	15.6471i	−0.961193	−	0.554945i
$796$		0			0
$797$	−16.9246	−	29.3143i	−0.599500	−	1.03836i	−0.992895	−	0.118995i	$-0.962033\pi$
$797$	−16.9246	−	29.3143i	−0.599500	−	1.03836i	0.393395	−	0.919370i	$-0.371301\pi$
$798$		0			0
$799$	−13.5672	+	7.83303i	−0.479973	+	0.277113i
$800$		0			0
$801$		−	19.8222i		−	0.700383i
$802$		0			0
$803$	−16.0901	+	27.8689i	−0.567808	+	0.983473i
$804$		0			0
$805$	2.60700			0.0918847
$806$		0			0
$807$	71.5819			2.51980
$808$		0			0
$809$	16.4170	−	28.4351i	0.577191	−	0.999723i	−0.418609	−	0.908166i	$-0.637482\pi$
$809$	16.4170	−	28.4351i	0.577191	−	0.999723i	0.995800	−	0.0915570i	$-0.0291844\pi$
$810$		0			0
$811$		−	12.2083i		−	0.428690i	−0.976758	−	0.214345i	$-0.931238\pi$
$811$		−	12.2083i		−	0.428690i	0.976758	−	0.214345i	$-0.0687617\pi$
$812$		0			0
$813$	−16.6454	+	9.61023i	−0.583780	+	0.337045i
$814$		0			0
$815$	−0.00765566	−	0.0132600i	−0.000268166	−	0.000464477i
$816$		0			0
$817$	−63.2386	−	36.5108i	−2.21244	−	1.27735i
$818$		0			0
$819$	−13.0302	−	26.4868i	−0.455312	−	0.925524i
$820$		0			0
$821$	41.1248	+	23.7434i	1.43526	+	0.828650i	0.997516	−	0.0704470i	$-0.0224426\pi$
$821$	41.1248	+	23.7434i	1.43526	+	0.828650i	0.437749	+	0.899097i	$0.355776\pi$
$822$		0			0
$823$	−11.0229	−	19.0923i	−0.384235	−	0.665515i	0.607427	−	0.794375i	$-0.292202\pi$
$823$	−11.0229	−	19.0923i	−0.384235	−	0.665515i	−0.991663	+	0.128860i	$0.958868\pi$
$824$		0			0
$825$	21.2140	−	12.2479i	0.738578	−	0.426418i
$826$		0			0
$827$		−	45.9092i		−	1.59642i	−0.602380	−	0.798209i	$-0.705781\pi$
$827$		−	45.9092i		−	1.59642i	0.602380	−	0.798209i	$-0.294219\pi$
$828$		0			0
$829$	13.3883	−	23.1893i	0.464996	−	0.805396i	−0.534206	−	0.845355i	$-0.679389\pi$
$829$	13.3883	−	23.1893i	0.464996	−	0.805396i	0.999201	+	0.0399584i	$0.0127225\pi$
$830$		0			0
$831$	88.9754			3.08652
$832$		0			0
$833$	−2.22961			−0.0772515
$834$		0			0
$835$	19.5060	−	33.7854i	0.675033	−	1.16919i
$836$		0			0
$837$		−	10.3739i		−	0.358574i
$838$		0			0
$839$	24.5960	−	14.2005i	0.849147	−	0.490255i	−0.0112158	−	0.999937i	$-0.503570\pi$
$839$	24.5960	−	14.2005i	0.849147	−	0.490255i	0.860363	+	0.509682i	$0.170237\pi$
$840$		0			0
$841$	2.84726	+	4.93160i	0.0981814	+	0.170055i
$842$		0			0
$843$	−19.3823	−	11.1904i	−0.667562	−	0.385417i
$844$		0			0
$845$	−18.7939	+	7.74238i	−0.646531	+	0.266346i
$846$		0			0
$847$	−2.41210	−	1.39263i	−0.0828806	−	0.0478512i
$848$		0			0
$849$	33.3362	+	57.7400i	1.14410	+	1.98163i
$850$		0			0
$851$	0.0556847	−	0.0321496i	0.00190885	−	0.00110207i
$852$		0			0
$853$			21.3316i			0.730379i	0.930933	+	0.365189i	$0.118996\pi$
$853$			21.3316i			0.730379i	−0.930933	+	0.365189i	$0.881004\pi$
$854$		0			0
$855$	46.3132	−	80.2168i	1.58388	−	2.74336i
$856$		0			0
$857$	−41.0823			−1.40335			−0.701673	−	0.712499i	$-0.747563\pi$
$857$	−41.0823			−1.40335			−0.701673	+	0.712499i	$0.747563\pi$
$858$		0			0
$859$	−28.8618			−0.984752			−0.492376	−	0.870383i	$-0.663871\pi$
$859$	−28.8618			−0.984752			−0.492376	+	0.870383i	$0.663871\pi$
$860$		0			0
$861$	−13.3030	+	23.0414i	−0.453364	+	0.785250i
$862$		0			0
$863$		−	22.7332i		−	0.773847i	−0.922112	−	0.386923i	$-0.873538\pi$
$863$		−	22.7332i		−	0.773847i	0.922112	−	0.386923i	$-0.126462\pi$
$864$		0			0
$865$	4.34050	−	2.50599i	0.147581	−	0.0852062i
$866$		0			0
$867$	−20.1163	−	34.8425i	−0.683187	−	1.18331i
$868$		0			0
$869$	−10.5764	−	6.10627i	−0.358779	−	0.207141i
$870$		0			0
$871$	2.61157	+	5.30861i	0.0884898	+	0.179875i
$872$		0			0
$873$	34.6584	+	20.0100i	1.17301	+	0.677238i
$874$		0			0
$875$	5.90656	+	10.2305i	0.199678	+	0.345853i
$876$		0			0
$877$	25.4765	−	14.7089i	0.860282	−	0.496684i	−0.00382498	−	0.999993i	$-0.501218\pi$
$877$	25.4765	−	14.7089i	0.860282	−	0.496684i	0.864107	+	0.503309i	$0.167884\pi$
$878$		0			0
$879$			29.6369i			0.999627i
$880$		0			0
$881$	2.11104	−	3.65644i	0.0711229	−	0.123188i	−0.828271	−	0.560328i	$-0.810675\pi$
$881$	2.11104	−	3.65644i	0.0711229	−	0.123188i	0.899394	+	0.437140i	$0.144008\pi$
$882$		0			0
$883$	−37.1982			−1.25182			−0.625910	−	0.779895i	$-0.715272\pi$
$883$	−37.1982			−1.25182			−0.625910	+	0.779895i	$0.715272\pi$
$884$		0			0
$885$	−4.68681			−0.157545
$886$		0			0
$887$	−28.0947	+	48.6614i	−0.943327	+	1.63389i	−0.184260	+	0.982878i	$0.558989\pi$
$887$	−28.0947	+	48.6614i	−0.943327	+	1.63389i	−0.759067	+	0.651013i	$0.774344\pi$
$888$		0			0
$889$			9.85165i			0.330414i
$890$		0			0
$891$	−83.0654	+	47.9578i	−2.78280	+	1.60665i
$892$		0			0
$893$	−25.4214	−	44.0312i	−0.850696	−	1.47345i
$894$		0			0
$895$	21.3944	+	12.3521i	0.715136	+	0.412884i
$896$		0			0
$897$	1.33438	−	20.0630i	0.0445536	−	0.669884i
$898$		0			0
$899$	−2.49997	−	1.44336i	−0.0833785	−	0.0481386i
$900$		0			0
$901$	6.67104	+	11.5546i	0.222245	+	0.384939i
$902$		0			0
$903$	−29.2306	+	16.8763i	−0.972734	+	0.561609i
$904$		0			0
$905$			14.2582i			0.473958i
$906$		0			0
$907$	0.326806	−	0.566045i	0.0108514	−	0.0187952i	−0.860549	−	0.509368i	$-0.829879\pi$
$907$	0.326806	−	0.566045i	0.0108514	−	0.0187952i	0.871400	+	0.490573i	$0.163212\pi$
$908$		0			0
$909$	−60.3170			−2.00059
$910$		0			0
$911$	−39.7806			−1.31799			−0.658995	−	0.752147i	$-0.729018\pi$
$911$	−39.7806			−1.31799			−0.658995	+	0.752147i	$0.729018\pi$
$912$		0			0
$913$	−7.09124	+	12.2824i	−0.234686	+	0.406487i
$914$		0			0
$915$			74.5582i			2.46482i
$916$		0			0
$917$	−12.8105	+	7.39614i	−0.423040	+	0.244242i
$918$		0			0
$919$	17.3028	+	29.9693i	0.570767	+	0.988597i	0.996487	+	0.0837423i	$0.0266872\pi$
$919$	17.3028	+	29.9693i	0.570767	+	0.988597i	−0.425721	+	0.904855i	$0.639979\pi$
$920$		0			0
$921$	−24.1759	−	13.9580i	−0.796624	−	0.459931i
$922$		0			0
$923$	8.25528	+	0.549054i	0.271726	+	0.0180723i
$924$		0			0
$925$	0.0853392	+	0.0492706i	0.00280593	+	0.00162001i
$926$		0			0
$927$	−23.6817	−	41.0180i	−0.777810	−	1.34721i
$928$		0			0
$929$	16.6889	−	9.63536i	0.547546	−	0.316126i	−0.200586	−	0.979676i	$-0.564285\pi$
$929$	16.6889	−	9.63536i	0.547546	−	0.316126i	0.748132	+	0.663550i	$0.230951\pi$
$930$		0			0
$931$		−	7.23602i		−	0.237151i
$932$		0			0
$933$	11.1862	−	19.3751i	0.366221	−	0.634314i
$934$		0			0
$935$	9.99172			0.326764
$936$		0			0
$937$	−50.9507			−1.66449			−0.832244	−	0.554410i	$-0.812944\pi$
$937$	−50.9507			−1.66449			−0.832244	+	0.554410i	$0.812944\pi$
$938$		0			0
$939$	−35.7526	+	61.9254i	−1.16674	+	2.02086i
$940$		0			0
$941$		−	24.3014i		−	0.792204i	−0.918207	−	0.396102i	$-0.870363\pi$
$941$		−	24.3014i		−	0.792204i	0.918207	−	0.396102i	$-0.129637\pi$
$942$		0			0
$943$	−11.4863	+	6.63163i	−0.374046	+	0.215956i
$944$		0			0
$945$	−13.5628	−	23.4915i	−0.441199	−	0.764179i
$946$		0			0
$947$	−22.2278	−	12.8332i	−0.722307	−	0.417024i	0.0932940	−	0.995639i	$-0.470260\pi$
$947$	−22.2278	−	12.8332i	−0.722307	−	0.417024i	−0.815601	+	0.578614i	$0.803594\pi$
$948$		0			0
$949$	−22.5231	+	33.6381i	−0.731130	+	1.09194i
$950$		0			0
$951$	91.7569	+	52.9759i	2.97542	+	1.71786i
$952$		0			0
$953$	2.40492	+	4.16544i	0.0779029	+	0.134932i	0.902345	−	0.431015i	$-0.141844\pi$
$953$	2.40492	+	4.16544i	0.0779029	+	0.134932i	−0.824442	+	0.565946i	$0.808511\pi$
$954$		0			0
$955$	4.41616	−	2.54967i	0.142903	−	0.0825053i
$956$		0			0
$957$			46.2788i			1.49598i
$958$		0			0
$959$	0.229499	−	0.397503i	0.00741090	−	0.0128361i
$960$		0			0
$961$	30.6424			0.988466
$962$		0			0
$963$	8.42400			0.271460
$964$		0			0
$965$	−17.2562	+	29.8887i	−0.555498	+	0.962150i
$966$		0			0
$967$		−	58.2044i		−	1.87173i	−0.352362	−	0.935864i	$-0.614622\pi$
$967$		−	58.2044i		−	1.87173i	0.352362	−	0.935864i	$-0.385378\pi$
$968$		0			0
$969$	−46.7321	+	26.9808i	−1.50125	+	0.866747i
$970$		0			0
$971$	−18.0669	−	31.2927i	−0.579793	−	1.00423i	−0.995503	−	0.0947336i	$-0.969800\pi$
$971$	−18.0669	−	31.2927i	−0.579793	−	1.00423i	0.415710	−	0.909497i	$-0.363533\pi$
$972$		0			0
$973$	13.2628	+	7.65731i	0.425187	+	0.245482i
$974$		0			0
$975$	27.6505	−	13.6027i	0.885526	−	0.435635i
$976$		0			0
$977$	14.4794	+	8.35970i	0.463238	+	0.267451i	0.713405	−	0.700752i	$-0.247152\pi$
$977$	14.4794	+	8.35970i	0.463238	+	0.267451i	−0.250167	+	0.968203i	$0.580485\pi$
$978$		0			0
$979$	3.46975	+	6.00978i	0.110894	+	0.192073i
$980$		0			0
$981$	−100.349	+	57.9368i	−3.20391	+	1.84978i
$982$		0			0
$983$			46.4764i			1.48237i	0.671303	+	0.741183i	$0.265735\pi$
$983$			46.4764i			1.48237i	−0.671303	+	0.741183i	$0.734265\pi$
$984$		0			0
$985$	4.12236	−	7.14014i	0.131349	−	0.227504i
$986$		0			0
$987$	−23.5010			−0.748045
$988$		0			0
$989$	−16.8259			−0.535033
$990$		0			0
$991$	17.6755	−	30.6148i	0.561480	−	0.972512i	−0.435887	−	0.900001i	$-0.643565\pi$
$991$	17.6755	−	30.6148i	0.561480	−	0.972512i	0.997368	−	0.0725110i	$-0.0231012\pi$
$992$		0			0
$993$		−	82.5118i		−	2.61843i
$994$		0			0
$995$	12.0075	−	6.93251i	0.380662	−	0.219775i
$996$		0			0
$997$	−0.743899	−	1.28847i	−0.0235595	−	0.0408063i	0.854005	−	0.520264i	$-0.174167\pi$
$997$	−0.743899	−	1.28847i	−0.0235595	−	0.0408063i	−0.877565	+	0.479458i	$0.840833\pi$
$998$		0			0
$999$	−0.579396	−	0.334514i	−0.0183313	−	0.0105836i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1456.2.cc.d.225.6		12
4.3	odd	2		182.2.m.b.43.1	✓	12
12.11	even	2		1638.2.bj.g.1135.4		12
13.10	even	6	inner	1456.2.cc.d.673.6		12
28.3	even	6		1274.2.v.d.667.4		12
28.11	odd	6		1274.2.v.e.667.6		12
28.19	even	6		1274.2.o.e.459.6		12
28.23	odd	6		1274.2.o.d.459.4		12
28.27	even	2		1274.2.m.c.589.3		12
52.7	even	12		2366.2.a.bf.1.6		6
52.19	even	12		2366.2.a.bh.1.6		6
52.23	odd	6		182.2.m.b.127.1	yes	12
52.35	odd	6		2366.2.d.r.337.12		12
52.43	odd	6		2366.2.d.r.337.6		12
156.23	even	6		1638.2.bj.g.127.6		12
364.23	odd	6		1274.2.v.e.361.6		12
364.75	even	6		1274.2.v.d.361.4		12
364.179	odd	6		1274.2.o.d.569.1		12
364.283	even	6		1274.2.o.e.569.3		12
364.335	even	6		1274.2.m.c.491.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.m.b.43.1	✓	12	4.3	odd	2
182.2.m.b.127.1	yes	12	52.23	odd	6
1274.2.m.c.491.3		12	364.335	even	6
1274.2.m.c.589.3		12	28.27	even	2
1274.2.o.d.459.4		12	28.23	odd	6
1274.2.o.d.569.1		12	364.179	odd	6
1274.2.o.e.459.6		12	28.19	even	6
1274.2.o.e.569.3		12	364.283	even	6
1274.2.v.d.361.4		12	364.75	even	6
1274.2.v.d.667.4		12	28.3	even	6
1274.2.v.e.361.6		12	364.23	odd	6
1274.2.v.e.667.6		12	28.11	odd	6
1456.2.cc.d.225.6		12	1.1	even	1	trivial
1456.2.cc.d.673.6		12	13.10	even	6	inner
1638.2.bj.g.127.6		12	156.23	even	6
1638.2.bj.g.1135.4		12	12.11	even	2
2366.2.a.bf.1.6		6	52.7	even	12
2366.2.a.bh.1.6		6	52.19	even	12
2366.2.d.r.337.6		12	52.43	odd	6
2366.2.d.r.337.12		12	52.35	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:	\( N \)	\(=\)	\( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1456.cc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.67234 - 2.89658i) q^{3} +1.56356i q^{5} +(0.866025 - 0.500000i) q^{7} +(-4.09347 - 7.09010i) q^{9} +O(q^{10})\)	\(q+(1.67234 - 2.89658i) q^{3} +1.56356i q^{5} +(0.866025 - 0.500000i) q^{7} +(-4.09347 - 7.09010i) q^{9} +(2.48215 + 1.43307i) q^{11} +(2.99598 + 2.00602i) q^{13} +(4.52898 + 2.61481i) q^{15} +(-1.11481 - 1.93090i) q^{17} +(6.26657 - 3.61801i) q^{19} -3.34469i q^{21} +(0.833676 - 1.44397i) q^{23} +2.55529 q^{25} -17.3487 q^{27} +(-2.41379 + 4.18080i) q^{29} +0.597963i q^{31} +(8.30201 - 4.79317i) q^{33} +(0.781779 + 1.35408i) q^{35} +(0.0333971 + 0.0192818i) q^{37} +(10.8209 - 5.32335i) q^{39} +(-6.88896 - 3.97734i) q^{41} +(-5.04571 - 8.73942i) q^{43} +(11.0858 - 6.40037i) q^{45} -7.02636i q^{47} +(0.500000 - 0.866025i) q^{49} -7.45736 q^{51} -5.98404 q^{53} +(-2.24069 + 3.88098i) q^{55} -24.2022i q^{57} +(-0.776138 + 0.448103i) q^{59} +(7.12846 + 12.3469i) q^{61} +(-7.09010 - 4.09347i) q^{63} +(-3.13653 + 4.68438i) q^{65} +(1.42103 + 0.820432i) q^{67} +(-2.78838 - 4.82962i) q^{69} +(1.98724 - 1.14733i) q^{71} +11.2277i q^{73} +(4.27332 - 7.40161i) q^{75} +2.86614 q^{77} -4.26098 q^{79} +(-16.7326 + 28.9816i) q^{81} +4.94829i q^{83} +(3.01907 - 1.74306i) q^{85} +(8.07337 + 13.9835i) q^{87} +(2.09682 + 1.21060i) q^{89} +(3.59760 + 0.239275i) q^{91} +(1.73205 + 1.00000i) q^{93} +(5.65696 + 9.79815i) q^{95} +(-4.23338 + 2.44414i) q^{97} -23.4649i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{3} - 6 q^{9}+O(q^{10}) \) 12 * q + 2 * q^3 - 6 * q^9	\( 12 q + 2 q^{3} - 6 q^{9} + 18 q^{11} - 8 q^{13} + 6 q^{15} + 4 q^{17} - 12 q^{19} + 6 q^{23} - 24 q^{25} - 40 q^{27} - 10 q^{29} + 12 q^{33} - 2 q^{35} - 6 q^{37} + 54 q^{39} - 24 q^{41} - 26 q^{43} + 72 q^{45} + 6 q^{49} + 36 q^{51} + 36 q^{53} + 6 q^{55} - 6 q^{59} - 28 q^{61} - 34 q^{65} + 42 q^{67} + 32 q^{69} - 48 q^{71} + 48 q^{75} - 4 q^{77} - 44 q^{79} - 34 q^{81} + 54 q^{85} - 2 q^{87} + 12 q^{89} + 16 q^{91} - 32 q^{95} + 60 q^{97}+O(q^{100}) \) 12 * q + 2 * q^3 - 6 * q^9 + 18 * q^11 - 8 * q^13 + 6 * q^15 + 4 * q^17 - 12 * q^19 + 6 * q^23 - 24 * q^25 - 40 * q^27 - 10 * q^29 + 12 * q^33 - 2 * q^35 - 6 * q^37 + 54 * q^39 - 24 * q^41 - 26 * q^43 + 72 * q^45 + 6 * q^49 + 36 * q^51 + 36 * q^53 + 6 * q^55 - 6 * q^59 - 28 * q^61 - 34 * q^65 + 42 * q^67 + 32 * q^69 - 48 * q^71 + 48 * q^75 - 4 * q^77 - 44 * q^79 - 34 * q^81 + 54 * q^85 - 2 * q^87 + 12 * q^89 + 16 * q^91 - 32 * q^95 + 60 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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