LMFDB - Embedded newform 1386.2.bu.b.827.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(701,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("1386.701");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.bu (of order $10$, degree $4$, 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:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			827.3
Character	$\chi$	$=$	1386.827
Dual form			1386.2.bu.b.1205.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-2.76118 + 0.897162i) q^{5} +(0.587785 - 0.809017i) q^{7} +(0.809017 - 0.587785i) q^{8} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-2.76118 + 0.897162i) q^{5} +(0.587785 - 0.809017i) q^{7} +(0.809017 - 0.587785i) q^{8} -2.90328i q^{10} +(-3.28299 - 0.471165i) q^{11} +(3.88352 + 1.26183i) q^{13} +(0.587785 + 0.809017i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-1.06536 - 3.27883i) q^{17} +(-0.0378351 - 0.0520755i) q^{19} +(2.76118 + 0.897162i) q^{20} +(1.46260 - 2.97671i) q^{22} -1.52863i q^{23} +(2.77413 - 2.01552i) q^{25} +(-2.40015 + 3.30352i) q^{26} +(-0.951057 + 0.309017i) q^{28} +(0.0763776 + 0.0554915i) q^{29} +(0.598908 - 1.84325i) q^{31} -1.00000 q^{32} +3.44757 q^{34} +(-0.897162 + 2.76118i) q^{35} +(5.85528 + 4.25411i) q^{37} +(0.0612185 - 0.0198911i) q^{38} +(-1.70650 + 2.34880i) q^{40} +(6.78292 - 4.92808i) q^{41} -0.0378105i q^{43} +(2.37905 + 2.31087i) q^{44} +(1.45382 + 0.472374i) q^{46} +(4.84017 + 6.66193i) q^{47} +(-0.309017 - 0.951057i) q^{49} +(1.05962 + 3.26119i) q^{50} +(-2.40015 - 3.30352i) q^{52} +(10.4855 + 3.40696i) q^{53} +(9.48763 - 1.64440i) q^{55} -1.00000i q^{56} +(-0.0763776 + 0.0554915i) q^{58} +(-6.86594 + 9.45016i) q^{59} +(0.515879 - 0.167619i) q^{61} +(1.56796 + 1.13919i) q^{62} +(0.309017 - 0.951057i) q^{64} -11.8552 q^{65} +3.96105 q^{67} +(-1.06536 + 3.27883i) q^{68} +(-2.34880 - 1.70650i) q^{70} +(11.6649 - 3.79017i) q^{71} +(0.957782 - 1.31827i) q^{73} +(-5.85528 + 4.25411i) q^{74} +0.0643689i q^{76} +(-2.31087 + 2.37905i) q^{77} +(6.83971 + 2.22236i) q^{79} +(-1.70650 - 2.34880i) q^{80} +(2.59084 + 7.97380i) q^{82} +(4.45599 + 13.7141i) q^{83} +(5.88329 + 8.09765i) q^{85} +(0.0359599 + 0.0116841i) q^{86} +(-2.93294 + 1.54851i) q^{88} -8.76582i q^{89} +(3.30352 - 2.40015i) q^{91} +(-0.898508 + 1.23669i) q^{92} +(-7.83156 + 2.54463i) q^{94} +(0.151190 + 0.109846i) q^{95} +(-1.89380 + 5.82852i) q^{97} +1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 12 q^{2} - 12 q^{4} + 12 q^{8}+O(q^{10}) $ 48 * q + 12 * q^2 - 12 * q^4 + 12 * q^8	$ 48 q + 12 q^{2} - 12 q^{4} + 12 q^{8} - 4 q^{11} - 12 q^{16} - 24 q^{17} + 4 q^{22} + 24 q^{25} - 40 q^{26} + 16 q^{29} + 40 q^{31} - 48 q^{32} - 16 q^{34} + 12 q^{35} + 16 q^{37} + 40 q^{38} - 24 q^{41} - 4 q^{44} - 40 q^{46} + 40 q^{47} + 12 q^{49} - 4 q^{50} - 40 q^{52} + 40 q^{53} - 32 q^{55} - 16 q^{58} + 40 q^{61} + 40 q^{62} - 12 q^{64} + 48 q^{67} - 24 q^{68} + 8 q^{70} + 40 q^{73} - 16 q^{74} - 32 q^{77} + 40 q^{79} - 16 q^{82} + 16 q^{83} - 20 q^{85} + 4 q^{88} + 20 q^{92} + 52 q^{95} - 8 q^{97} + 48 q^{98}+O(q^{100}) $ 48 * q + 12 * q^2 - 12 * q^4 + 12 * q^8 - 4 * q^11 - 12 * q^16 - 24 * q^17 + 4 * q^22 + 24 * q^25 - 40 * q^26 + 16 * q^29 + 40 * q^31 - 48 * q^32 - 16 * q^34 + 12 * q^35 + 16 * q^37 + 40 * q^38 - 24 * q^41 - 4 * q^44 - 40 * q^46 + 40 * q^47 + 12 * q^49 - 4 * q^50 - 40 * q^52 + 40 * q^53 - 32 * q^55 - 16 * q^58 + 40 * q^61 + 40 * q^62 - 12 * q^64 + 48 * q^67 - 24 * q^68 + 8 * q^70 + 40 * q^73 - 16 * q^74 - 32 * q^77 + 40 * q^79 - 16 * q^82 + 16 * q^83 - 20 * q^85 + 4 * q^88 + 20 * q^92 + 52 * q^95 - 8 * q^97 + 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{10}\right)$

Coefficient data

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

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

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

$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$3$		0			0
$3$		0			0
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−2.76118	+	0.897162i	−1.23484	+	0.401223i	−0.852464	−	0.522785i	$-0.824893\pi$
$5$	−2.76118	+	0.897162i	−1.23484	+	0.401223i	−0.382373	+	0.924008i	$0.624893\pi$
$6$		0			0
$7$	0.587785	−	0.809017i	0.222162	−	0.305780i
$7$	0.587785	−	0.809017i	0.222162	−	0.305780i
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$		0			0
$10$		−	2.90328i		−	0.918097i
$11$	−3.28299	−	0.471165i	−0.989858	−	0.142062i
$11$	−3.28299	−	0.471165i	−0.989858	−	0.142062i
$12$		0			0
$13$	3.88352	+	1.26183i	1.07710	+	0.349970i	0.793247	−	0.608900i	$-0.208389\pi$
$13$	3.88352	+	1.26183i	1.07710	+	0.349970i	0.283848	+	0.958869i	$0.408389\pi$
$14$	0.587785	+	0.809017i	0.157092	+	0.216219i
$15$		0			0
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−1.06536	−	3.27883i	−0.258387	−	0.795234i	−0.993143	−	0.116903i	$-0.962703\pi$
$17$	−1.06536	−	3.27883i	−0.258387	−	0.795234i	0.734756	−	0.678331i	$-0.237297\pi$
$18$		0			0
$19$	−0.0378351	−	0.0520755i	−0.00867996	−	0.0119469i	0.804655	−	0.593743i	$-0.202350\pi$
$19$	−0.0378351	−	0.0520755i	−0.00867996	−	0.0119469i	−0.813335	+	0.581796i	$0.802350\pi$
$20$	2.76118	+	0.897162i	0.617419	+	0.200611i
$21$		0			0
$22$	1.46260	−	2.97671i	0.311828	−	0.634636i
$23$		−	1.52863i		−	0.318742i	−0.987219	−	0.159371i	$-0.949053\pi$
$23$		−	1.52863i		−	0.318742i	0.987219	−	0.159371i	$-0.0509466\pi$
$24$		0			0
$25$	2.77413	−	2.01552i	0.554826	−	0.403105i
$26$	−2.40015	+	3.30352i	−0.470708	+	0.647874i
$27$		0			0
$28$	−0.951057	+	0.309017i	−0.179733	+	0.0583987i
$29$	0.0763776	+	0.0554915i	0.0141830	+	0.0103045i	0.594854	−	0.803834i	$-0.297210\pi$
$29$	0.0763776	+	0.0554915i	0.0141830	+	0.0103045i	−0.580671	+	0.814138i	$0.697210\pi$
$30$		0			0
$31$	0.598908	−	1.84325i	0.107567	−	0.331057i	−0.882757	−	0.469829i	$-0.844316\pi$
$31$	0.598908	−	1.84325i	0.107567	−	0.331057i	0.990324	+	0.138772i	$0.0443155\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	3.44757			0.591253
$35$	−0.897162	+	2.76118i	−0.151648	+	0.466725i
$36$		0			0
$37$	5.85528	+	4.25411i	0.962602	+	0.699371i	0.953754	−	0.300590i	$-0.0971835\pi$
$37$	5.85528	+	4.25411i	0.962602	+	0.699371i	0.00884813	+	0.999961i	$0.497184\pi$
$38$	0.0612185	−	0.0198911i	0.00993094	−	0.00322676i
$39$		0			0
$40$	−1.70650	+	2.34880i	−0.269822	+	0.371378i
$41$	6.78292	−	4.92808i	1.05931	−	0.769636i	0.0853522	−	0.996351i	$-0.472798\pi$
$41$	6.78292	−	4.92808i	1.05931	−	0.769636i	0.973961	+	0.226715i	$0.0727985\pi$
$42$		0			0
$43$		−	0.0378105i		−	0.00576605i	−0.999996	−	0.00288302i	$-0.999082\pi$
$43$		−	0.0378105i		−	0.00576605i	0.999996	−	0.00288302i	$-0.000917696\pi$
$44$	2.37905	+	2.31087i	0.358655	+	0.348377i
$45$		0			0
$46$	1.45382	+	0.472374i	0.214354	+	0.0696477i
$47$	4.84017	+	6.66193i	0.706012	+	0.971742i	0.999874	+	0.0158938i	$0.00505937\pi$
$47$	4.84017	+	6.66193i	0.706012	+	0.971742i	−0.293862	+	0.955848i	$0.594941\pi$
$48$		0			0
$49$	−0.309017	−	0.951057i	−0.0441453	−	0.135865i
$50$	1.05962	+	3.26119i	0.149853	+	0.461202i
$51$		0			0
$52$	−2.40015	−	3.30352i	−0.332841	−	0.458116i
$53$	10.4855	+	3.40696i	1.44030	+	0.467982i	0.921991	−	0.387212i	$-0.126562\pi$
$53$	10.4855	+	3.40696i	1.44030	+	0.467982i	0.518309	+	0.855194i	$0.326562\pi$
$54$		0			0
$55$	9.48763	−	1.64440i	1.27931	−	0.221731i
$56$		−	1.00000i		−	0.133631i
$57$		0			0
$58$	−0.0763776	+	0.0554915i	−0.0100289	+	0.00728640i
$59$	−6.86594	+	9.45016i	−0.893870	+	1.23031i	0.0785128	+	0.996913i	$0.474983\pi$
$59$	−6.86594	+	9.45016i	−0.893870	+	1.23031i	−0.972382	+	0.233393i	$0.925017\pi$
$60$		0			0
$61$	0.515879	−	0.167619i	0.0660516	−	0.0214615i	−0.275805	−	0.961214i	$-0.588944\pi$
$61$	0.515879	−	0.167619i	0.0660516	−	0.0214615i	0.341856	+	0.939752i	$0.388944\pi$
$62$	1.56796	+	1.13919i	0.199131	+	0.144677i
$63$		0			0
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−11.8552			−1.47045
$66$		0			0
$67$	3.96105			0.483919			0.241960	−	0.970286i	$-0.422210\pi$
$67$	3.96105			0.483919			0.241960	+	0.970286i	$0.422210\pi$
$68$	−1.06536	+	3.27883i	−0.129194	+	0.397617i
$69$		0			0
$70$	−2.34880	−	1.70650i	−0.280735	−	0.203966i
$71$	11.6649	−	3.79017i	1.38437	−	0.449810i	0.480268	−	0.877122i	$-0.340539\pi$
$71$	11.6649	−	3.79017i	1.38437	−	0.449810i	0.904104	+	0.427312i	$0.140539\pi$
$72$		0			0
$73$	0.957782	−	1.31827i	0.112100	−	0.154292i	−0.749280	−	0.662253i	$-0.769600\pi$
$73$	0.957782	−	1.31827i	0.112100	−	0.154292i	0.861380	+	0.507961i	$0.169600\pi$
$74$	−5.85528	+	4.25411i	−0.680662	+	0.494530i
$75$		0			0
$76$			0.0643689i			0.00738362i
$77$	−2.31087	+	2.37905i	−0.263348	+	0.271118i
$78$		0			0
$79$	6.83971	+	2.22236i	0.769527	+	0.250034i	0.667362	−	0.744733i	$-0.267423\pi$
$79$	6.83971	+	2.22236i	0.769527	+	0.250034i	0.102165	+	0.994768i	$0.467423\pi$
$80$	−1.70650	−	2.34880i	−0.190793	−	0.262604i
$81$		0			0
$82$	2.59084	+	7.97380i	0.286111	+	0.880558i
$83$	4.45599	+	13.7141i	0.489108	+	1.50532i	0.825941	+	0.563756i	$0.190644\pi$
$83$	4.45599	+	13.7141i	0.489108	+	1.50532i	−0.336833	+	0.941564i	$0.609356\pi$
$84$		0			0
$85$	5.88329	+	8.09765i	0.638132	+	0.878313i
$86$	0.0359599	+	0.0116841i	0.00387766	+	0.00125993i
$87$		0			0
$88$	−2.93294	+	1.54851i	−0.312652	+	0.165072i
$89$		−	8.76582i		−	0.929175i	−0.885527	−	0.464587i	$-0.846203\pi$
$89$		−	8.76582i		−	0.929175i	0.885527	−	0.464587i	$-0.153797\pi$
$90$		0			0
$91$	3.30352	−	2.40015i	0.346303	−	0.251604i
$92$	−0.898508	+	1.23669i	−0.0936759	+	0.128934i
$93$		0			0
$94$	−7.83156	+	2.54463i	−0.807764	+	0.262458i
$95$	0.151190	+	0.109846i	0.0155117	+	0.0112699i
$96$		0			0
$97$	−1.89380	+	5.82852i	−0.192286	+	0.591797i	0.807711	+	0.589579i	$0.200706\pi$
$97$	−1.89380	+	5.82852i	−0.192286	+	0.591797i	−0.999998	+	0.00221843i	$0.999294\pi$
$98$	1.00000			0.101015
$99$		0			0
$100$	−3.42902			−0.342902
$101$	−2.16914	+	6.67593i	−0.215838	+	0.664280i	0.783255	+	0.621700i	$0.213558\pi$
$101$	−2.16914	+	6.67593i	−0.215838	+	0.664280i	−0.999093	+	0.0425799i	$0.986442\pi$
$102$		0			0
$103$	−2.56655	−	1.86471i	−0.252890	−	0.183735i	0.454117	−	0.890942i	$-0.349955\pi$
$103$	−2.56655	−	1.86471i	−0.252890	−	0.183735i	−0.707007	+	0.707207i	$0.749955\pi$
$104$	3.88352	−	1.26183i	0.380811	−	0.123733i
$105$		0			0
$106$	−6.48042	+	8.91953i	−0.629434	+	0.866342i
$107$	5.14692	−	3.73946i	0.497571	−	0.361507i	−0.310517	−	0.950568i	$-0.600502\pi$
$107$	5.14692	−	3.73946i	0.497571	−	0.361507i	0.808089	+	0.589061i	$0.200502\pi$
$108$		0			0
$109$		−	18.5954i		−	1.78112i	−0.454868	−	0.890559i	$-0.650314\pi$
$109$		−	18.5954i		−	1.78112i	0.454868	−	0.890559i	$-0.349686\pi$
$110$	−1.36792	+	9.53142i	−0.130426	+	0.908785i
$111$		0			0
$112$	0.951057	+	0.309017i	0.0898664	+	0.0291994i
$113$	5.80584	+	7.99106i	0.546168	+	0.751735i	0.989486	−	0.144629i	$-0.0461988\pi$
$113$	5.80584	+	7.99106i	0.546168	+	0.751735i	−0.443318	+	0.896364i	$0.646199\pi$
$114$		0			0
$115$	1.37143	+	4.22083i	0.127887	+	0.393595i
$116$	−0.0291736	−	0.0897872i	−0.00270870	−	0.00833653i
$117$		0			0
$118$	−6.86594	−	9.45016i	−0.632061	−	0.869958i
$119$	−3.27883	−	1.06536i	−0.300570	−	0.0976611i
$120$		0			0
$121$	10.5560	+	3.09366i	0.959637	+	0.281242i
$122$			0.542428i			0.0491091i
$123$		0			0
$124$	−1.56796	+	1.13919i	−0.140807	+	0.102302i
$125$	2.68089	−	3.68993i	0.239786	−	0.330037i
$126$		0			0
$127$	0.151159	−	0.0491145i	0.0134132	−	0.00435821i	−0.302303	−	0.953212i	$-0.597755\pi$
$127$	0.151159	−	0.0491145i	0.0134132	−	0.00435821i	0.315716	+	0.948854i	$0.397755\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$		0			0
$130$	3.66345	−	11.2749i	0.321306	−	0.988878i
$131$	−3.15860			−0.275969			−0.137984	−	0.990434i	$-0.544062\pi$
$131$	−3.15860			−0.275969			−0.137984	+	0.990434i	$0.544062\pi$
$132$		0			0
$133$	−0.0643689			−0.00558149
$134$	−1.22403	+	3.76718i	−0.105740	+	0.325435i
$135$		0			0
$136$	−2.78914	−	2.02643i	−0.239167	−	0.173765i
$137$	9.73699	−	3.16374i	0.831888	−	0.270297i	0.138047	−	0.990426i	$-0.455917\pi$
$137$	9.73699	−	3.16374i	0.831888	−	0.270297i	0.693840	+	0.720129i	$0.255917\pi$
$138$		0			0
$139$	−1.60822	+	2.21353i	−0.136408	+	0.187749i	−0.871756	−	0.489940i	$-0.837019\pi$
$139$	−1.60822	+	2.21353i	−0.136408	+	0.187749i	0.735348	+	0.677689i	$0.237019\pi$
$140$	2.34880	−	1.70650i	0.198510	−	0.144226i
$141$		0			0
$142$			12.2652i			1.02928i
$143$	−12.1550	−	5.97236i	−1.01645	−	0.499434i
$144$		0			0
$145$	−0.260677	−	0.0846991i	−0.0216481	−	0.00703388i
$146$	0.957782	+	1.31827i	0.0792666	+	0.109101i
$147$		0			0
$148$	−2.23652	−	6.88329i	−0.183841	−	0.565803i
$149$	−3.52337	−	10.8438i	−0.288646	−	0.888361i	−0.985282	−	0.170936i	$-0.945321\pi$
$149$	−3.52337	−	10.8438i	−0.288646	−	0.888361i	0.696636	−	0.717425i	$-0.254679\pi$
$150$		0			0
$151$	−6.48858	−	8.93076i	−0.528033	−	0.726775i	0.458796	−	0.888542i	$-0.348281\pi$
$151$	−6.48858	−	8.93076i	−0.528033	−	0.726775i	−0.986829	+	0.161766i	$0.948281\pi$
$152$	−0.0612185	−	0.0198911i	−0.00496547	−	0.00161338i
$153$		0			0
$154$	−1.54851	−	2.93294i	−0.124783	−	0.236343i
$155$			5.62686i			0.451960i
$156$		0			0
$157$	−5.91263	+	4.29577i	−0.471879	+	0.342840i	−0.798173	−	0.602428i	$-0.794200\pi$
$157$	−5.91263	+	4.29577i	−0.471879	+	0.342840i	0.326294	+	0.945268i	$0.394200\pi$
$158$	−4.22717	+	5.81820i	−0.336296	+	0.462871i
$159$		0			0
$160$	2.76118	−	0.897162i	0.218290	−	0.0709269i
$161$	−1.23669	−	0.898508i	−0.0974648	−	0.0708124i
$162$		0			0
$163$	6.34877	−	19.5395i	0.497274	−	1.53045i	−0.316108	−	0.948723i	$-0.602376\pi$
$163$	6.34877	−	19.5395i	0.497274	−	1.53045i	0.813382	−	0.581729i	$-0.197624\pi$
$164$	−8.38414			−0.654692
$165$		0			0
$166$	−14.4199			−1.11920
$167$	0.782089	−	2.40702i	0.0605198	−	0.186261i	−0.916226	−	0.400662i	$-0.868780\pi$
$167$	0.782089	−	2.40702i	0.0605198	−	0.186261i	0.976746	+	0.214401i	$0.0687801\pi$
$168$		0			0
$169$	2.97231	+	2.15951i	0.228639	+	0.166116i
$170$	−9.51936	+	3.09303i	−0.730101	+	0.237224i
$171$		0			0
$172$	−0.0222245	+	0.0305893i	−0.00169460	+	0.00233242i
$173$	12.3728	−	8.98934i	0.940684	−	0.683447i	−0.00790110	−	0.999969i	$-0.502515\pi$
$173$	12.3728	−	8.98934i	0.940684	−	0.683447i	0.948585	+	0.316522i	$0.102515\pi$
$174$		0			0
$175$		−	3.42902i		−	0.259209i
$176$	−0.566394	−	3.26790i	−0.0426935	−	0.246328i
$177$		0			0
$178$	8.33679	+	2.70879i	0.624869	+	0.203032i
$179$	13.6962	+	18.8512i	1.02370	+	1.40900i	0.909577	+	0.415535i	$0.136405\pi$
$179$	13.6962	+	18.8512i	1.02370	+	1.40900i	0.114122	+	0.993467i	$0.463595\pi$
$180$		0			0
$181$	0.386072	+	1.18821i	0.0286965	+	0.0883187i	0.964379	−	0.264524i	$-0.0852150\pi$
$181$	0.386072	+	1.18821i	0.0286965	+	0.0883187i	−0.935683	+	0.352843i	$0.885215\pi$
$182$	1.26183	+	3.88352i	0.0935333	+	0.287866i
$183$		0			0
$184$	−0.898508	−	1.23669i	−0.0662389	−	0.0911700i
$185$	−19.9841	−	6.49323i	−1.46926	−	0.477392i
$186$		0			0
$187$	1.95268	+	11.2663i	0.142794	+	0.823875i
$188$		−	8.23459i		−	0.600569i
$189$		0			0
$190$	−0.151190	+	0.109846i	−0.0109685	+	0.00796905i
$191$	1.24557	−	1.71437i	0.0901260	−	0.124048i	−0.761573	−	0.648079i	$-0.775573\pi$
$191$	1.24557	−	1.71437i	0.0901260	−	0.124048i	0.851699	+	0.524031i	$0.175573\pi$
$192$		0			0
$193$	−0.273363	+	0.0888211i	−0.0196771	+	0.00639348i	−0.318839	−	0.947809i	$-0.603293\pi$
$193$	−0.273363	+	0.0888211i	−0.0196771	+	0.00639348i	0.299162	+	0.954202i	$0.403293\pi$
$194$	−4.95804	−	3.60223i	−0.355966	−	0.258625i
$195$		0			0
$196$	−0.309017	+	0.951057i	−0.0220726	+	0.0679326i
$197$	−14.2903			−1.01814			−0.509072	−	0.860724i	$-0.670011\pi$
$197$	−14.2903			−1.01814			−0.509072	+	0.860724i	$0.670011\pi$
$198$		0			0
$199$	−22.8730			−1.62142			−0.810710	−	0.585448i	$-0.800919\pi$
$199$	−22.8730			−1.62142			−0.810710	+	0.585448i	$0.800919\pi$
$200$	1.05962	−	3.26119i	0.0749267	−	0.230601i
$201$		0			0
$202$	−5.67889	−	4.12595i	−0.399565	−	0.290301i
$203$	0.0897872	−	0.0291736i	0.00630183	−	0.00204759i
$204$		0			0
$205$	−14.3076	+	19.6927i	−0.999284	+	1.37540i
$206$	2.56655	−	1.86471i	0.178820	−	0.129921i
$207$		0			0
$208$			4.08338i			0.283131i
$209$	0.0996759	+	0.188790i	0.00689473	+	0.0130589i
$210$		0			0
$211$	19.2566	+	6.25684i	1.32568	+	0.430739i	0.884441	−	0.466652i	$-0.154540\pi$
$211$	19.2566	+	6.25684i	1.32568	+	0.430739i	0.441237	+	0.897391i	$0.354540\pi$
$212$	−6.48042	−	8.91953i	−0.445077	−	0.612596i
$213$		0			0
$214$	1.96595	+	6.05057i	0.134389	+	0.413608i
$215$	0.0339221	+	0.104402i	0.00231347	+	0.00712013i
$216$		0			0
$217$	−1.13919	−	1.56796i	−0.0773333	−	0.106440i
$218$	17.6853	+	5.74630i	1.19780	+	0.389188i
$219$		0			0
$220$	−8.64221	−	4.24634i	−0.582657	−	0.286288i
$221$		−	14.0777i		−	0.946970i
$222$		0			0
$223$	−9.35522	+	6.79697i	−0.626472	+	0.455159i	−0.855176	−	0.518337i	$-0.826551\pi$
$223$	−9.35522	+	6.79697i	−0.626472	+	0.455159i	0.228704	+	0.973496i	$0.426551\pi$
$224$	−0.587785	+	0.809017i	−0.0392731	+	0.0540547i
$225$		0			0
$226$	−9.39405	+	3.05231i	−0.624883	+	0.203037i
$227$	−20.7760	−	15.0947i	−1.37895	−	1.00187i	−0.996977	−	0.0776969i	$-0.975243\pi$
$227$	−20.7760	−	15.0947i	−1.37895	−	1.00187i	−0.381977	−	0.924172i	$-0.624757\pi$
$228$		0			0
$229$	−0.218009	+	0.670962i	−0.0144064	+	0.0443384i	−0.958001	−	0.286764i	$-0.907421\pi$
$229$	−0.218009	+	0.670962i	−0.0144064	+	0.0443384i	0.943595	+	0.331102i	$0.107421\pi$
$230$	−4.43804			−0.292636
$231$		0			0
$232$	0.0944078			0.00619818
$233$	5.16449	−	15.8947i	0.338337	−	1.04130i	−0.626717	−	0.779247i	$-0.715602\pi$
$233$	5.16449	−	15.8947i	0.338337	−	1.04130i	0.965055	−	0.262049i	$-0.0843981\pi$
$234$		0			0
$235$	−19.3414	−	14.0524i	−1.26169	−	0.916675i
$236$	11.1093	−	3.60964i	0.723156	−	0.234968i
$237$		0			0
$238$	2.02643	−	2.78914i	0.131354	−	0.180793i
$239$	6.73997	−	4.89688i	0.435972	−	0.316753i	−0.348060	−	0.937472i	$-0.613159\pi$
$239$	6.73997	−	4.89688i	0.435972	−	0.316753i	0.784033	+	0.620720i	$0.213159\pi$
$240$		0			0
$241$			25.7676i			1.65984i	0.557883	+	0.829919i	$0.311614\pi$
$241$			25.7676i			1.65984i	−0.557883	+	0.829919i	$0.688386\pi$
$242$	−6.20423	+	9.08337i	−0.398823	+	0.583901i
$243$		0			0
$244$	−0.515879	−	0.167619i	−0.0330258	−	0.0107307i
$245$	1.70650	+	2.34880i	0.109024	+	0.150059i
$246$		0			0
$247$	−0.0812228	−	0.249978i	−0.00516808	−	0.0159057i
$248$	−0.598908	−	1.84325i	−0.0380307	−	0.117046i
$249$		0			0
$250$	2.68089	+	3.68993i	0.169554	+	0.233372i
$251$	4.67261	+	1.51822i	0.294932	+	0.0958294i	0.452746	−	0.891640i	$-0.350444\pi$
$251$	4.67261	+	1.51822i	0.294932	+	0.0958294i	−0.157813	+	0.987469i	$0.550444\pi$
$252$		0			0
$253$	−0.720239	+	5.01848i	−0.0452810	+	0.315509i
$254$			0.158938i			0.00997265i
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	11.7504	−	16.1730i	0.732967	−	1.00884i	−0.266025	−	0.963966i	$-0.585710\pi$
$257$	11.7504	−	16.1730i	0.732967	−	1.00884i	0.998993	−	0.0448770i	$-0.0142896\pi$
$258$		0			0
$259$	6.88329	−	2.23652i	0.427707	−	0.138970i
$260$	9.59104	+	6.96830i	0.594811	+	0.432155i
$261$		0			0
$262$	0.976062	−	3.00401i	0.0603013	−	0.185588i
$263$	5.56665			0.343255			0.171627	−	0.985162i	$-0.445098\pi$
$263$	5.56665			0.343255			0.171627	+	0.985162i	$0.445098\pi$
$264$		0			0
$265$	−32.0091			−1.96630
$266$	0.0198911	−	0.0612185i	0.00121960	−	0.00375354i
$267$		0			0
$268$	−3.20456	−	2.32825i	−0.195750	−	0.142220i
$269$	12.4950	−	4.05989i	0.761836	−	0.247536i	0.0977697	−	0.995209i	$-0.468829\pi$
$269$	12.4950	−	4.05989i	0.761836	−	0.247536i	0.664067	+	0.747673i	$0.268829\pi$
$270$		0			0
$271$	−7.05116	+	9.70509i	−0.428328	+	0.589542i	−0.967568	−	0.252609i	$-0.918711\pi$
$271$	−7.05116	+	9.70509i	−0.428328	+	0.589542i	0.539241	+	0.842152i	$0.318711\pi$
$272$	2.78914	−	2.02643i	0.169117	−	0.122870i
$273$		0			0
$274$			10.2381i			0.618505i
$275$	−10.0571	+	5.30987i	−0.606465	+	0.320197i
$276$		0			0
$277$	12.8149	+	4.16381i	0.769973	+	0.250179i	0.667553	−	0.744562i	$-0.267342\pi$
$277$	12.8149	+	4.16381i	0.769973	+	0.250179i	0.102420	+	0.994741i	$0.467342\pi$
$278$	−1.60822	−	2.21353i	−0.0964547	−	0.132758i
$279$		0			0
$280$	0.897162	+	2.76118i	0.0536157	+	0.165012i
$281$	−0.193175	−	0.594530i	−0.0115238	−	0.0354667i	0.945129	−	0.326697i	$-0.105936\pi$
$281$	−0.193175	−	0.594530i	−0.0115238	−	0.0354667i	−0.956653	+	0.291230i	$0.905936\pi$
$282$		0			0
$283$	19.1079	+	26.2997i	1.13585	+	1.56336i	0.776458	+	0.630169i	$0.217014\pi$
$283$	19.1079	+	26.2997i	1.13585	+	1.56336i	0.359388	+	0.933188i	$0.382986\pi$
$284$	−11.6649	−	3.79017i	−0.692186	−	0.224905i
$285$		0			0
$286$	9.43616	−	9.71455i	0.557972	−	0.574434i
$287$		−	8.38414i		−	0.494900i
$288$		0			0
$289$	4.13753	−	3.00609i	0.243384	−	0.176829i
$290$	0.161107	−	0.221745i	0.00946055	−	0.0130213i
$291$		0			0
$292$	−1.54972	+	0.503536i	−0.0906907	+	0.0294672i
$293$	22.9793	+	16.6954i	1.34246	+	0.975357i	0.999350	+	0.0360629i	$0.0114817\pi$
$293$	22.9793	+	16.6954i	1.34246	+	0.975357i	0.343114	+	0.939294i	$0.388518\pi$
$294$		0			0
$295$	10.4798	−	32.2535i	0.610157	−	1.87787i
$296$	7.23752			0.420672
$297$		0			0
$298$	11.4019			0.660493
$299$	1.92888	−	5.93648i	0.111550	−	0.343316i
$300$		0			0
$301$	−0.0305893	−	0.0222245i	−0.00176314	−	0.00128100i
$302$	10.4987	−	3.41125i	0.604135	−	0.196295i
$303$		0			0
$304$	0.0378351	−	0.0520755i	0.00216999	−	0.00298674i
$305$	−1.27405	+	0.925655i	−0.0729521	+	0.0530028i
$306$		0			0
$307$		−	15.4510i		−	0.881837i	−0.897547	−	0.440918i	$-0.854653\pi$
$307$		−	15.4510i		−	0.881837i	0.897547	−	0.440918i	$-0.145347\pi$
$308$	3.26790	−	0.566394i	0.186206	−	0.0322733i
$309$		0			0
$310$	−5.35146	−	1.73879i	−0.303942	−	0.0987569i
$311$	−12.0920	−	16.6432i	−0.685675	−	0.943751i	0.314309	−	0.949321i	$-0.398227\pi$
$311$	−12.0920	−	16.6432i	−0.685675	−	0.943751i	−0.999984	+	0.00556977i	$0.998227\pi$
$312$		0			0
$313$	7.25345	+	22.3238i	0.409989	+	1.26182i	0.916656	+	0.399676i	$0.130877\pi$
$313$	7.25345	+	22.3238i	0.409989	+	1.26182i	−0.506667	+	0.862142i	$0.669123\pi$
$314$	−2.25842	−	6.95071i	−0.127450	−	0.392251i
$315$		0			0
$316$	−4.22717	−	5.81820i	−0.237797	−	0.327299i
$317$	−30.9693	−	10.0625i	−1.73941	−	0.565168i	−0.744652	−	0.667453i	$-0.767385\pi$
$317$	−30.9693	−	10.0625i	−1.73941	−	0.565168i	−0.994755	+	0.102285i	$0.967385\pi$
$318$		0			0
$319$	−0.224601	−	0.218164i	−0.0125752	−	0.0122149i
$320$			2.90328i			0.162298i
$321$		0			0
$322$	1.23669	−	0.898508i	0.0689180	−	0.0500719i
$323$	−0.130439	+	0.179534i	−0.00725782	+	0.00998954i
$324$		0			0
$325$	13.3167	−	4.32684i	0.738675	−	0.240010i
$326$	16.6213	+	12.0761i	0.920569	+	0.668832i
$327$		0			0
$328$	2.59084	−	7.97380i	0.143055	−	0.440279i
$329$	8.23459			0.453988
$330$		0			0
$331$	−27.3406			−1.50277			−0.751386	−	0.659863i	$-0.770615\pi$
$331$	−27.3406			−1.50277			−0.751386	+	0.659863i	$0.770615\pi$
$332$	4.45599	−	13.7141i	0.244554	−	0.752660i
$333$		0			0
$334$	2.04753	+	1.48762i	0.112036	+	0.0813990i
$335$	−10.9372	+	3.55370i	−0.597562	+	0.194160i
$336$		0			0
$337$	11.2616	−	15.5003i	0.613459	−	0.844353i	−0.383398	−	0.923583i	$-0.625246\pi$
$337$	11.2616	−	15.5003i	0.613459	−	0.844353i	0.996856	+	0.0792301i	$0.0252462\pi$
$338$	−2.97231	+	2.15951i	−0.161672	+	0.117462i
$339$		0			0
$340$		−	10.0092i		−	0.542828i
$341$	−2.83468	+	5.76918i	−0.153507	+	0.312418i
$342$		0			0
$343$	−0.951057	−	0.309017i	−0.0513522	−	0.0166853i
$344$	−0.0222245	−	0.0305893i	−0.00119826	−	0.00164927i
$345$		0			0
$346$	4.72598	+	14.5451i	0.254070	+	0.781947i
$347$	−7.01974	−	21.6045i	−0.376839	−	1.15979i	−0.942229	−	0.334968i	$-0.891274\pi$
$347$	−7.01974	−	21.6045i	−0.376839	−	1.15979i	0.565390	−	0.824824i	$-0.308726\pi$
$348$		0			0
$349$	19.3649	+	26.6535i	1.03658	+	1.42673i	0.899891	+	0.436115i	$0.143646\pi$
$349$	19.3649	+	26.6535i	1.03658	+	1.42673i	0.136688	+	0.990614i	$0.456354\pi$
$350$	3.26119	+	1.05962i	0.174318	+	0.0566393i
$351$		0			0
$352$	3.28299	+	0.471165i	0.174984	+	0.0251132i
$353$		−	20.5891i		−	1.09585i	−0.836528	−	0.547925i	$-0.815418\pi$
$353$		−	20.5891i		−	1.09585i	0.836528	−	0.547925i	$-0.184582\pi$
$354$		0			0
$355$	−28.8086	+	20.9307i	−1.52900	+	1.11088i
$356$	−5.15242	+	7.09169i	−0.273078	+	0.375859i
$357$		0			0
$358$	−22.1609	+	7.20050i	−1.17124	+	0.380558i
$359$	−0.183939	−	0.133640i	−0.00970793	−	0.00705323i	0.582921	−	0.812529i	$-0.301910\pi$
$359$	−0.183939	−	0.133640i	−0.00970793	−	0.00705323i	−0.592629	+	0.805476i	$0.701910\pi$
$360$		0			0
$361$	5.87004	−	18.0661i	0.308950	−	0.950849i
$362$	−1.24935			−0.0656646
$363$		0			0
$364$	−4.08338			−0.214027
$365$	−1.46190	+	4.49928i	−0.0765195	+	0.235503i
$366$		0			0
$367$	−15.3692	−	11.1664i	−0.802268	−	0.582881i	0.109311	−	0.994008i	$-0.465136\pi$
$367$	−15.3692	−	11.1664i	−0.802268	−	0.582881i	−0.911578	+	0.411126i	$0.865136\pi$
$368$	1.45382	−	0.472374i	0.0757854	−	0.0246242i
$369$		0			0
$370$	12.3509	−	16.9995i	0.642090	−	0.883761i
$371$	8.91953	−	6.48042i	0.463079	−	0.336447i
$372$		0			0
$373$		−	29.5333i		−	1.52918i	−0.644518	−	0.764589i	$-0.722942\pi$
$373$		−	29.5333i		−	1.52918i	0.644518	−	0.764589i	$-0.277058\pi$
$374$	−11.3183	−	1.62437i	−0.585256	−	0.0839944i
$375$		0			0
$376$	7.83156	+	2.54463i	0.403882	+	0.131229i
$377$	0.226593	+	0.311878i	0.0116701	+	0.0160626i
$378$		0			0
$379$	−11.0742	−	34.0829i	−0.568844	−	1.75072i	−0.656244	−	0.754549i	$-0.727856\pi$
$379$	−11.0742	−	34.0829i	−0.568844	−	1.75072i	0.0874003	−	0.996173i	$-0.472144\pi$
$380$	−0.0577493	−	0.177734i	−0.00296248	−	0.00911757i
$381$		0			0
$382$	1.24557	+	1.71437i	0.0637287	+	0.0877150i
$383$	−18.1529	−	5.89825i	−0.927572	−	0.301386i	−0.194003	−	0.981001i	$-0.562147\pi$
$383$	−18.1529	−	5.89825i	−0.927572	−	0.301386i	−0.733569	+	0.679615i	$0.762147\pi$
$384$		0			0
$385$	4.24634	−	8.64221i	0.216414	−	0.440448i
$386$		−	0.287431i		−	0.0146299i
$387$		0			0
$388$	4.95804	−	3.60223i	0.251706	−	0.182875i
$389$	7.16896	−	9.86723i	0.363481	−	0.500288i	−0.587634	−	0.809127i	$-0.699940\pi$
$389$	7.16896	−	9.86723i	0.363481	−	0.500288i	0.951114	+	0.308839i	$0.0999403\pi$
$390$		0			0
$391$	−5.01213	+	1.62854i	−0.253474	+	0.0823588i
$392$	−0.809017	−	0.587785i	−0.0408615	−	0.0296876i
$393$		0			0
$394$	4.41595	−	13.5909i	0.222473	−	0.684700i
$395$	−20.8795			−1.05056
$396$		0			0
$397$	15.7715			0.791550			0.395775	−	0.918347i	$-0.370476\pi$
$397$	15.7715			0.791550			0.395775	+	0.918347i	$0.370476\pi$
$398$	7.06813	−	21.7535i	0.354293	−	1.09040i
$399$		0			0
$400$	2.77413	+	2.01552i	0.138707	+	0.100776i
$401$	−32.3236	+	10.5026i	−1.61416	+	0.524473i	−0.970554	−	0.240882i	$-0.922563\pi$
$401$	−32.3236	+	10.5026i	−1.61416	+	0.524473i	−0.643608	+	0.765355i	$0.722563\pi$
$402$		0			0
$403$	4.65174	−	6.40258i	0.231720	−	0.318935i
$404$	5.67889	−	4.12595i	0.282535	−	0.205274i
$405$		0			0
$406$			0.0944078i			0.00468538i
$407$	−17.2184	−	16.7250i	−0.853485	−	0.829027i
$408$		0			0
$409$	7.84466	+	2.54889i	0.387894	+	0.126034i	0.496470	−	0.868054i	$-0.334629\pi$
$409$	7.84466	+	2.54889i	0.387894	+	0.126034i	−0.108576	+	0.994088i	$0.534629\pi$
$410$	−14.3076	−	19.6927i	−0.706600	−	0.972552i
$411$		0			0
$412$	0.980336	+	3.01716i	0.0482977	+	0.148645i
$413$	3.60964	+	11.1093i	0.177619	+	0.546654i
$414$		0			0
$415$	−24.6076	−	33.8694i	−1.20794	−	1.66258i
$416$	−3.88352	−	1.26183i	−0.190405	−	0.0618665i
$417$		0			0
$418$	−0.210351	+	0.0364581i	−0.0102886	+	0.00178323i
$419$			11.6703i			0.570129i	0.958508	+	0.285065i	$0.0920151\pi$
$419$			11.6703i			0.570129i	−0.958508	+	0.285065i	$0.907985\pi$
$420$		0			0
$421$	−17.1270	+	12.4435i	−0.834718	+	0.606458i	−0.920890	−	0.389822i	$-0.872536\pi$
$421$	−17.1270	+	12.4435i	−0.834718	+	0.606458i	0.0861723	+	0.996280i	$0.472536\pi$
$422$	−11.9012	+	16.3806i	−0.579343	+	0.797397i
$423$		0			0
$424$	10.4855	−	3.40696i	0.509223	−	0.165457i
$425$	−9.56401	−	6.94866i	−0.463923	−	0.337059i
$426$		0			0
$427$	0.167619	−	0.515879i	0.00811167	−	0.0249652i
$428$	−6.36194			−0.307516
$429$		0			0
$430$	−0.109774			−0.00529379
$431$	−2.68055	+	8.24990i	−0.129118	+	0.397384i	−0.994629	−	0.103506i	$-0.966994\pi$
$431$	−2.68055	+	8.24990i	−0.129118	+	0.397384i	0.865511	+	0.500890i	$0.166994\pi$
$432$		0			0
$433$	1.74570	+	1.26832i	0.0838928	+	0.0609517i	0.628941	−	0.777453i	$-0.283489\pi$
$433$	1.74570	+	1.26832i	0.0838928	+	0.0609517i	−0.545048	+	0.838405i	$0.683489\pi$
$434$	1.84325	−	0.598908i	0.0884788	−	0.0287485i
$435$		0			0
$436$	−10.9301	+	15.0440i	−0.523457	+	0.720477i
$437$	−0.0796044	+	0.0578360i	−0.00380799	+	0.00276667i
$438$		0			0
$439$		−	13.3235i		−	0.635895i	−0.948108	−	0.317947i	$-0.897006\pi$
$439$		−	13.3235i		−	0.635895i	0.948108	−	0.317947i	$-0.102994\pi$
$440$	6.70910	−	6.90703i	0.319844	−	0.329280i
$441$		0			0
$442$	13.3887	+	4.35026i	0.636836	+	0.206921i
$443$	2.69009	+	3.70260i	0.127810	+	0.175916i	0.868126	−	0.496343i	$-0.165324\pi$
$443$	2.69009	+	3.70260i	0.127810	+	0.175916i	−0.740316	+	0.672259i	$0.765324\pi$
$444$		0			0
$445$	7.86436	+	24.2040i	0.372806	+	1.14738i
$446$	−3.57338	−	10.9977i	−0.169204	−	0.520757i
$447$		0			0
$448$	−0.587785	−	0.809017i	−0.0277702	−	0.0382225i
$449$	33.5904	+	10.9142i	1.58523	+	0.515072i	0.963397	−	0.268080i	$-0.0863892\pi$
$449$	33.5904	+	10.9142i	1.58523	+	0.515072i	0.621831	+	0.783152i	$0.286389\pi$
$450$		0			0
$451$	−24.5902	+	12.9829i	−1.15791	+	0.611343i
$452$		−	9.87749i		−	0.464598i
$453$		0			0
$454$	20.7760	−	15.0947i	0.975068	−	0.708428i
$455$	−6.96830	+	9.59104i	−0.326679	+	0.449635i
$456$		0			0
$457$	−8.80751	+	2.86173i	−0.411998	+	0.133866i	−0.507680	−	0.861546i	$-0.669497\pi$
$457$	−8.80751	+	2.86173i	−0.411998	+	0.133866i	0.0956821	+	0.995412i	$0.469497\pi$
$458$	−0.570755	−	0.414677i	−0.0266696	−	0.0193766i
$459$		0			0
$460$	1.37143	−	4.22083i	0.0639433	−	0.196797i
$461$	6.71222			0.312619			0.156310	−	0.987708i	$-0.450040\pi$
$461$	6.71222			0.312619			0.156310	+	0.987708i	$0.450040\pi$
$462$		0			0
$463$	−17.9304			−0.833296			−0.416648	−	0.909068i	$-0.636795\pi$
$463$	−17.9304			−0.833296			−0.416648	+	0.909068i	$0.636795\pi$
$464$	−0.0291736	+	0.0897872i	−0.00135435	+	0.00416827i
$465$		0			0
$466$	13.5208	+	9.82345i	0.626340	+	0.455063i
$467$	−16.9351	+	5.50256i	−0.783665	+	0.254628i	−0.673404	−	0.739274i	$-0.735169\pi$
$467$	−16.9351	+	5.50256i	−0.783665	+	0.254628i	−0.110261	+	0.993903i	$0.535169\pi$
$468$		0			0
$469$	2.32825	−	3.20456i	0.107508	−	0.147973i
$470$	19.3414	−	14.0524i	0.892153	−	0.648187i
$471$		0			0
$472$			11.6810i			0.537663i
$473$	−0.0178150	+	0.124131i	−0.000819134	+	0.00570757i
$474$		0			0
$475$	−0.209919	−	0.0682068i	−0.00963174	−	0.00312954i
$476$	2.02643	+	2.78914i	0.0928813	+	0.127840i
$477$		0			0
$478$	2.57444	+	7.92331i	0.117752	+	0.362404i
$479$	0.784841	+	2.41549i	0.0358603	+	0.110367i	0.967384	−	0.253313i	$-0.0815203\pi$
$479$	0.784841	+	2.41549i	0.0358603	+	0.110367i	−0.931524	+	0.363680i	$0.881520\pi$
$480$		0			0
$481$	17.3711	+	23.9093i	0.792055	+	1.09017i
$482$	−24.5065	−	7.96263i	−1.11624	−	0.362688i
$483$		0			0
$484$	−6.72158	−	8.70749i	−0.305526	−	0.395795i
$485$		−	17.7927i		−	0.807923i
$486$		0			0
$487$	−22.9319	+	16.6610i	−1.03914	+	0.754982i	−0.970118	−	0.242633i	$-0.921989\pi$
$487$	−22.9319	+	16.6610i	−1.03914	+	0.754982i	−0.0690252	+	0.997615i	$0.521989\pi$
$488$	0.318831	−	0.438833i	0.0144328	−	0.0198650i
$489$		0			0
$490$	−2.76118	+	0.897162i	−0.124737	+	0.0405296i
$491$	29.5530	+	21.4715i	1.33371	+	0.968996i	0.999650	+	0.0264440i	$0.00841837\pi$
$491$	29.5530	+	21.4715i	1.33371	+	0.968996i	0.334059	+	0.942552i	$0.391582\pi$
$492$		0			0
$493$	0.100578	−	0.309547i	0.00452981	−	0.0139413i
$494$	0.262842			0.0118258
$495$		0			0
$496$	1.93811			0.0870235
$497$	3.79017	−	11.6649i	0.170012	−	0.523244i
$498$		0			0
$499$	5.73001	+	4.16309i	0.256510	+	0.186366i	0.708607	−	0.705603i	$-0.249324\pi$
$499$	5.73001	+	4.16309i	0.256510	+	0.186366i	−0.452097	+	0.891969i	$0.649324\pi$
$500$	−4.33777	+	1.40943i	−0.193991	+	0.0630315i
$501$		0			0
$502$	−2.88783	+	3.97476i	−0.128890	+	0.177402i
$503$	−7.19429	+	5.22696i	−0.320777	+	0.233058i	−0.736507	−	0.676430i	$-0.763526\pi$
$503$	−7.19429	+	5.22696i	−0.320777	+	0.233058i	0.415730	+	0.909488i	$0.363526\pi$
$504$		0			0
$505$		−	20.3795i		−	0.906877i
$506$	−4.55029	−	2.23578i	−0.202285	−	0.0993927i
$507$		0			0
$508$	−0.151159	−	0.0491145i	−0.00670659	−	0.00217910i
$509$	24.5966	+	33.8543i	1.09022	+	1.50057i	0.847741	+	0.530410i	$0.177962\pi$
$509$	24.5966	+	33.8543i	1.09022	+	1.50057i	0.242484	+	0.970156i	$0.422038\pi$
$510$		0			0
$511$	−0.503536	−	1.54972i	−0.0222751	−	0.0685557i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$		0			0
$514$	11.7504	+	16.1730i	0.518286	+	0.713360i
$515$	8.75966	+	2.84619i	0.385997	+	0.125418i
$516$		0			0
$517$	−12.7514	−	24.1515i	−0.560804	−	1.06218i
$518$			7.23752i			0.317998i
$519$		0			0
$520$	−9.59104	+	6.96830i	−0.420595	+	0.305580i
$521$	15.2277	−	20.9591i	0.667138	−	0.918237i	−0.332553	−	0.943084i	$-0.607910\pi$
$521$	15.2277	−	20.9591i	0.667138	−	0.918237i	0.999691	+	0.0248479i	$0.00791015\pi$
$522$		0			0
$523$	39.4780	−	12.8272i	1.72625	−	0.560894i	0.733355	−	0.679846i	$-0.237954\pi$
$523$	39.4780	−	12.8272i	1.72625	−	0.560894i	0.992900	+	0.118952i	$0.0379535\pi$
$524$	2.55536	+	1.85658i	0.111632	+	0.0811051i
$525$		0			0
$526$	−1.72019	+	5.29420i	−0.0750039	+	0.230838i
$527$	−6.68175			−0.291062
$528$		0			0
$529$	20.6633			0.898404
$530$	9.89134	−	30.4424i	0.429652	−	1.32233i
$531$		0			0
$532$	0.0520755	+	0.0378351i	0.00225776	+	0.00164036i
$533$	32.5600	−	10.5794i	1.41033	−	0.458244i
$534$		0			0
$535$	−10.8567	+	14.9429i	−0.469375	+	0.646039i
$536$	3.20456	−	2.32825i	0.138416	−	0.100565i
$537$		0			0
$538$			13.1381i			0.566422i
$539$	0.566394	+	3.26790i	0.0243963	+	0.140759i
$540$		0			0
$541$	38.8334	+	12.6177i	1.66958	+	0.542478i	0.982845	−	0.184432i	$-0.0590447\pi$
$541$	38.8334	+	12.6177i	1.66958	+	0.542478i	0.686732	+	0.726911i	$0.259045\pi$
$542$	−7.05116	−	9.70509i	−0.302873	−	0.416869i
$543$		0			0
$544$	1.06536	+	3.27883i	0.0456768	+	0.140579i
$545$	16.6831	+	51.3453i	0.714625	+	2.19939i
$546$		0			0
$547$	0.657765	+	0.905336i	0.0281240	+	0.0387094i	0.822847	−	0.568262i	$-0.192384\pi$
$547$	0.657765	+	0.905336i	0.0281240	+	0.0387094i	−0.794723	+	0.606972i	$0.792384\pi$
$548$	−9.73699	−	3.16374i	−0.415944	−	0.135148i
$549$		0			0
$550$	−1.94217	−	11.2057i	−0.0828145	−	0.477812i
$551$		−	0.00607693i		−	0.000258886i
$552$		0			0
$553$	5.81820	−	4.22717i	0.247415	−	0.179758i
$554$	−7.92005	+	10.9010i	−0.336491	+	0.463139i
$555$		0			0
$556$	2.60216	−	0.845492i	0.110356	−	0.0358568i
$557$	37.9008	+	27.5365i	1.60591	+	1.16676i	0.874782	+	0.484517i	$0.161004\pi$
$557$	37.9008	+	27.5365i	1.60591	+	1.16676i	0.731125	+	0.682243i	$0.238996\pi$
$558$		0			0
$559$	0.0477105	−	0.146838i	0.00201794	−	0.00621058i
$560$	−2.90328			−0.122686
$561$		0			0
$562$	0.625126			0.0263694
$563$	−6.61141	+	20.3478i	−0.278638	+	0.857559i	0.709596	+	0.704609i	$0.248877\pi$
$563$	−6.61141	+	20.3478i	−0.278638	+	0.857559i	−0.988234	+	0.152950i	$0.951123\pi$
$564$		0			0
$565$	−23.2003	−	16.8560i	−0.976042	−	0.709136i
$566$	−30.9172	+	10.0456i	−1.29955	+	0.422248i
$567$		0			0
$568$	7.20932	−	9.92278i	0.302496	−	0.416351i
$569$	−10.3810	+	7.54221i	−0.435193	+	0.316186i	−0.783722	−	0.621112i	$-0.786681\pi$
$569$	−10.3810	+	7.54221i	−0.435193	+	0.316186i	0.348529	+	0.937298i	$0.386681\pi$
$570$		0			0
$571$			27.0490i			1.13196i	0.824417	+	0.565982i	$0.191503\pi$
$571$			27.0490i			1.13196i	−0.824417	+	0.565982i	$0.808497\pi$
$572$	6.32315	+	11.9763i	0.264384	+	0.500754i
$573$		0			0
$574$	7.97380	+	2.59084i	0.332820	+	0.108140i
$575$	−3.08100	−	4.24063i	−0.128486	−	0.176846i
$576$		0			0
$577$	−0.0320017	−	0.0984911i	−0.00133225	−	0.00410024i	0.950388	−	0.311066i	$-0.100686\pi$
$577$	−0.0320017	−	0.0984911i	−0.00133225	−	0.00410024i	−0.951720	+	0.306966i	$0.900686\pi$
$578$	1.58040	+	4.86396i	0.0657359	+	0.202314i
$579$		0			0
$580$	0.161107	+	0.221745i	0.00668962	+	0.00920747i
$581$	13.7141	+	4.45599i	0.568958	+	0.184866i
$582$		0			0
$583$	−32.8186	−	16.1254i	−1.35921	−	0.667847i
$584$		−	1.62948i		−	0.0674282i
$585$		0			0
$586$	−22.9793	+	16.6954i	−0.949265	+	0.689681i
$587$	6.00676	−	8.26760i	0.247926	−	0.341240i	−0.666858	−	0.745185i	$-0.732361\pi$
$587$	6.00676	−	8.26760i	0.247926	−	0.341240i	0.914783	+	0.403945i	$0.132361\pi$
$588$		0			0
$589$	−0.118648	+	0.0385510i	−0.00488880	+	0.00158847i
$590$	27.4364	+	19.9337i	1.12954	+	0.820659i
$591$		0			0
$592$	−2.23652	+	6.88329i	−0.0919203	+	0.282902i
$593$	−23.5824			−0.968414			−0.484207	−	0.874953i	$-0.660892\pi$
$593$	−23.5824			−0.968414			−0.484207	+	0.874953i	$0.660892\pi$
$594$		0			0
$595$	10.0092			0.410339
$596$	−3.52337	+	10.8438i	−0.144323	+	0.444181i
$597$		0			0
$598$	5.04987	+	3.66895i	0.206505	+	0.150034i
$599$	−2.29668	+	0.746238i	−0.0938399	+	0.0304904i	−0.355561	−	0.934653i	$-0.615710\pi$
$599$	−2.29668	+	0.746238i	−0.0938399	+	0.0304904i	0.261721	+	0.965144i	$0.415710\pi$
$600$		0			0
$601$	−17.9565	+	24.7150i	−0.732461	+	1.00815i	0.266556	+	0.963819i	$0.414114\pi$
$601$	−17.9565	+	24.7150i	−0.732461	+	1.00815i	−0.999017	+	0.0443268i	$0.985886\pi$
$602$	0.0305893	−	0.0222245i	0.00124673	−	0.000905801i
$603$		0			0
$604$			11.0390i			0.449172i
$605$	−31.9225	+	0.928295i	−1.29784	+	0.0377405i
$606$		0			0
$607$	−20.1055	−	6.53267i	−0.816056	−	0.265153i	−0.128896	−	0.991658i	$-0.541143\pi$
$607$	−20.1055	−	6.53267i	−0.816056	−	0.265153i	−0.687161	+	0.726505i	$0.741143\pi$
$608$	0.0378351	+	0.0520755i	0.00153442	+	0.00211194i
$609$		0			0
$610$	−0.486645	−	1.49774i	−0.0197037	−	0.0606417i
$611$	10.3907	+	31.9792i	0.420362	+	1.29374i
$612$		0			0
$613$	−8.98479	−	12.3665i	−0.362892	−	0.499478i	0.588060	−	0.808818i	$-0.299892\pi$
$613$	−8.98479	−	12.3665i	−0.362892	−	0.499478i	−0.950952	+	0.309340i	$0.899892\pi$
$614$	14.6948	+	4.77463i	0.593034	+	0.192688i
$615$		0			0
$616$	−0.471165	+	3.28299i	−0.0189838	+	0.132275i
$617$			25.5352i			1.02801i	0.857788	+	0.514004i	$0.171838\pi$
$617$			25.5352i			1.02801i	−0.857788	+	0.514004i	$0.828162\pi$
$618$		0			0
$619$	−34.5185	+	25.0792i	−1.38742	+	1.00802i	−0.391272	+	0.920275i	$0.627965\pi$
$619$	−34.5185	+	25.0792i	−1.38742	+	1.00802i	−0.996143	+	0.0877415i	$0.972035\pi$
$620$	3.30738	−	4.55222i	0.132828	−	0.182822i
$621$		0			0
$622$	19.5653	−	6.35715i	0.784497	−	0.254898i
$623$	−7.09169	−	5.15242i	−0.284123	−	0.206427i
$624$		0			0
$625$	−9.39008	+	28.8997i	−0.375603	+	1.15599i
$626$	−23.4727			−0.938157
$627$		0			0
$628$	7.30841			0.291637
$629$	7.71054	−	23.7306i	0.307440	−	0.946202i
$630$		0			0
$631$	−24.3131	−	17.6645i	−0.967889	−	0.703213i	−0.0129195	−	0.999917i	$-0.504113\pi$
$631$	−24.3131	−	17.6645i	−0.967889	−	0.703213i	−0.954969	+	0.296704i	$0.904113\pi$
$632$	6.83971	−	2.22236i	0.272069	−	0.0884005i
$633$		0			0
$634$	19.1401	−	26.3440i	0.760149	−	1.04626i
$635$	−0.373313	+	0.271228i	−0.0148145	+	0.0107634i
$636$		0			0
$637$		−	4.08338i		−	0.161789i
$638$	0.276892	−	0.146192i	0.0109623	−	0.00578778i
$639$		0			0
$640$	−2.76118	−	0.897162i	−0.109145	−	0.0354634i
$641$	22.0414	+	30.3373i	0.870582	+	1.19825i	0.978941	+	0.204141i	$0.0654402\pi$
$641$	22.0414	+	30.3373i	0.870582	+	1.19825i	−0.108360	+	0.994112i	$0.534560\pi$
$642$		0			0
$643$	8.27213	+	25.4590i	0.326221	+	1.00401i	0.970886	+	0.239540i	$0.0769968\pi$
$643$	8.27213	+	25.4590i	0.326221	+	1.00401i	−0.644665	+	0.764465i	$0.723003\pi$
$644$	0.472374	+	1.45382i	0.0186141	+	0.0572884i
$645$		0			0
$646$	−0.130439	−	0.179534i	−0.00513206	−	0.00706367i
$647$	−26.5968	−	8.64183i	−1.04563	−	0.339746i	−0.264677	−	0.964337i	$-0.585266\pi$
$647$	−26.5968	−	8.64183i	−1.04563	−	0.339746i	−0.780952	+	0.624591i	$0.785266\pi$
$648$		0			0
$649$	26.9934	−	27.7898i	1.05958	−	1.09084i
$650$			14.0020i			0.549202i
$651$		0			0
$652$	−16.6213	+	12.0761i	−0.650940	+	0.472936i
$653$	−0.0544533	+	0.0749486i	−0.00213092	+	0.00293296i	−0.810081	−	0.586318i	$-0.800577\pi$
$653$	−0.0544533	+	0.0749486i	−0.00213092	+	0.00293296i	0.807950	+	0.589251i	$0.200577\pi$
$654$		0			0
$655$	8.72148	−	2.83378i	0.340776	−	0.110725i
$656$	6.78292	+	4.92808i	0.264828	+	0.192409i
$657$		0			0
$658$	−2.54463	+	7.83156i	−0.0992000	+	0.305306i
$659$	−3.43723			−0.133895			−0.0669477	−	0.997756i	$-0.521326\pi$
$659$	−3.43723			−0.133895			−0.0669477	+	0.997756i	$0.521326\pi$
$660$		0			0
$661$	2.90902			0.113148			0.0565740	−	0.998398i	$-0.481982\pi$
$661$	2.90902			0.113148			0.0565740	+	0.998398i	$0.481982\pi$
$662$	8.44870	−	26.0024i	0.328368	−	1.01061i
$663$		0			0
$664$	11.6659	+	8.47579i	0.452726	+	0.328925i
$665$	0.177734	−	0.0577493i	0.00689223	−	0.00223942i
$666$		0			0
$667$	0.0848262	−	0.116753i	0.00328448	−	0.00452070i
$668$	−2.04753	+	1.48762i	−0.0792215	+	0.0575578i
$669$		0			0
$670$		−	11.5000i		−	0.444285i
$671$	−1.77260	+	0.307228i	−0.0684305	+	0.0118604i
$672$		0			0
$673$	36.4522	+	11.8440i	1.40513	+	0.456554i	0.910845	−	0.412748i	$-0.135431\pi$
$673$	36.4522	+	11.8440i	1.40513	+	0.456554i	0.494283	+	0.869301i	$0.335431\pi$
$674$	11.2616	+	15.5003i	0.433781	+	0.597048i
$675$		0			0
$676$	−1.13532	−	3.49416i	−0.0436662	−	0.134391i
$677$	3.05280	+	9.39556i	0.117329	+	0.361101i	0.992426	−	0.122847i	$-0.0392025\pi$
$677$	3.05280	+	9.39556i	0.117329	+	0.361101i	−0.875097	+	0.483948i	$0.839202\pi$
$678$		0			0
$679$	3.60223	+	4.95804i	0.138241	+	0.190272i
$680$	9.51936	+	3.09303i	0.365051	+	0.118612i
$681$		0			0
$682$	−4.61085	−	4.47872i	−0.176558	−	0.171499i
$683$			44.3014i			1.69515i	0.530678	+	0.847574i	$0.321937\pi$
$683$			44.3014i			1.69515i	−0.530678	+	0.847574i	$0.678063\pi$
$684$		0			0
$685$	−24.0472	+	17.4713i	−0.918797	+	0.667545i
$686$	0.587785	−	0.809017i	0.0224417	−	0.0308884i
$687$		0			0
$688$	0.0359599	−	0.0116841i	0.00137096	−	0.000445452i
$689$	36.4218	+	26.4620i	1.38756	+	1.00812i
$690$		0			0
$691$	6.13501	−	18.8816i	0.233387	−	0.718291i	−0.763944	−	0.645282i	$-0.776740\pi$
$691$	6.13501	−	18.8816i	0.233387	−	0.718291i	0.997331	−	0.0730088i	$-0.0232601\pi$
$692$	−15.2936			−0.581375
$693$		0			0
$694$	22.7163			0.862301
$695$	2.45470	−	7.55478i	0.0931119	−	0.286569i
$696$		0			0
$697$	−23.3846	−	16.9899i	−0.885754	−	0.643538i
$698$	−31.3331	+	10.1807i	−1.18597	+	0.385346i
$699$		0			0
$700$	−2.01552	+	2.77413i	−0.0761797	+	0.104852i
$701$	−19.5803	+	14.2259i	−0.739537	+	0.537305i	−0.892566	−	0.450916i	$-0.851097\pi$
$701$	−19.5803	+	14.2259i	−0.739537	+	0.537305i	0.153029	+	0.988222i	$0.451097\pi$
$702$		0			0
$703$		−	0.465871i		−	0.0175707i
$704$	−1.46260	+	2.97671i	−0.0551239	+	0.112189i
$705$		0			0
$706$	19.5814	+	6.36239i	0.736957	+	0.239452i
$707$	4.12595	+	5.67889i	0.155172	+	0.213576i
$708$		0			0
$709$	1.07393	+	3.30521i	0.0403322	+	0.124130i	0.969195	−	0.246293i	$-0.0792127\pi$
$709$	1.07393	+	3.30521i	0.0403322	+	0.124130i	−0.928863	+	0.370423i	$0.879213\pi$
$710$	−11.0039	−	33.8665i	−0.412969	−	1.27099i
$711$		0			0
$712$	−5.15242	−	7.09169i	−0.193095	−	0.265772i
$713$	−2.81765	−	0.915510i	−0.105522	−	0.0342861i
$714$		0			0
$715$	38.9204	+	5.58575i	1.45554	+	0.208895i
$716$		−	23.3013i		−	0.870811i
$717$		0			0
$718$	0.183939	−	0.133640i	0.00686455	−	0.00498738i
$719$	−3.18905	+	4.38935i	−0.118931	+	0.163695i	−0.864332	−	0.502922i	$-0.832258\pi$
$719$	−3.18905	+	4.38935i	−0.118931	+	0.163695i	0.745400	+	0.666617i	$0.232258\pi$
$720$		0			0
$721$	−3.01716	+	0.980336i	−0.112365	+	0.0365096i
$722$	15.3680	+	11.1655i	0.571937	+	0.415536i
$723$		0			0
$724$	0.386072	−	1.18821i	0.0143482	−	0.0441594i
$725$	0.323726			0.0120229
$726$		0			0
$727$	−3.74048			−0.138727			−0.0693634	−	0.997591i	$-0.522097\pi$
$727$	−3.74048			−0.138727			−0.0693634	+	0.997591i	$0.522097\pi$
$728$	1.26183	−	3.88352i	0.0467666	−	0.143933i
$729$		0			0
$730$	−3.82731	−	2.78071i	−0.141655	−	0.102919i
$731$	−0.123974	+	0.0402817i	−0.00458535	+	0.00148987i
$732$		0			0
$733$	−3.51179	+	4.83357i	−0.129711	+	0.178532i	−0.868933	−	0.494930i	$-0.835194\pi$
$733$	−3.51179	+	4.83357i	−0.129711	+	0.178532i	0.739222	+	0.673462i	$0.235194\pi$
$734$	15.3692	−	11.1664i	0.567289	−	0.412159i
$735$		0			0
$736$			1.52863i			0.0563462i
$737$	−13.0041	−	1.86631i	−0.479011	−	0.0687464i
$738$		0			0
$739$	37.4323	+	12.1625i	1.37697	+	0.447404i	0.901671	−	0.432422i	$-0.142341\pi$
$739$	37.4323	+	12.1625i	1.37697	+	0.447404i	0.475296	+	0.879826i	$0.342341\pi$
$740$	12.3509	+	16.9995i	0.454026	+	0.624914i
$741$		0			0
$742$	3.40696	+	10.4855i	0.125073	+	0.384936i
$743$	−1.97913	−	6.09115i	−0.0726074	−	0.223463i	0.908167	−	0.418608i	$-0.137482\pi$
$743$	−1.97913	−	6.09115i	−0.0726074	−	0.223463i	−0.980774	+	0.195146i	$0.937482\pi$
$744$		0			0
$745$	19.4573	+	26.7807i	0.712862	+	0.981170i
$746$	28.0879	+	9.12630i	1.02837	+	0.334138i
$747$		0			0
$748$	5.04243	−	10.2624i	0.184369	−	0.375231i
$749$		−	6.36194i		−	0.232460i
$750$		0			0
$751$	31.3055	−	22.7448i	1.14235	−	0.829969i	0.154909	−	0.987929i	$-0.450492\pi$
$751$	31.3055	−	22.7448i	1.14235	−	0.829969i	0.987446	+	0.157959i	$0.0504915\pi$
$752$	−4.84017	+	6.66193i	−0.176503	+	0.242935i
$753$		0			0
$754$	−0.366635	+	0.119127i	−0.0133521	+	0.00433835i
$755$	25.9285	+	18.8381i	0.943634	+	0.685590i
$756$		0			0
$757$	−4.06770	+	12.5191i	−0.147843	+	0.455014i	−0.997366	−	0.0725381i	$-0.976890\pi$
$757$	−4.06770	+	12.5191i	−0.147843	+	0.455014i	0.849523	+	0.527552i	$0.176890\pi$
$758$	35.8369			1.30165
$759$		0			0
$760$	0.186881			0.00677888
$761$	6.67169	−	20.5334i	0.241849	−	0.744333i	−0.754290	−	0.656541i	$-0.772019\pi$
$761$	6.67169	−	20.5334i	0.241849	−	0.744333i	0.996139	−	0.0877923i	$-0.0279812\pi$
$762$		0			0
$763$	−15.0440	−	10.9301i	−0.544630	−	0.395697i
$764$	−2.01537	+	0.654833i	−0.0729135	+	0.0236910i
$765$		0			0
$766$	11.2191	−	15.4418i	0.405364	−	0.557935i
$767$	−38.5886	+	28.0362i	−1.39335	+	1.01233i
$768$		0			0
$769$		−	25.6929i		−	0.926508i	−0.886225	−	0.463254i	$-0.846682\pi$
$769$		−	25.6929i		−	0.926508i	0.886225	−	0.463254i	$-0.153318\pi$
$770$	6.90703	+	6.70910i	0.248912	+	0.241779i
$771$		0			0
$772$	0.273363	+	0.0888211i	0.00983856	+	0.00319674i
$773$	−11.2827	−	15.5292i	−0.405809	−	0.558548i	0.556381	−	0.830927i	$-0.312189\pi$
$773$	−11.2827	−	15.5292i	−0.405809	−	0.558548i	−0.962190	+	0.272379i	$0.912189\pi$
$774$		0			0
$775$	−2.05366	−	6.32053i	−0.0737698	−	0.227040i
$776$	1.89380	+	5.82852i	0.0679835	+	0.209232i
$777$		0			0
$778$	7.16896	+	9.86723i	0.257020	+	0.353757i
$779$	−0.513264	−	0.166770i	−0.0183896	−	0.00597514i
$780$		0			0
$781$	−40.0816	+	6.94695i	−1.43423	+	0.248582i
$782$		−	5.27007i		−	0.188457i
$783$		0			0
$784$	0.809017	−	0.587785i	0.0288935	−	0.0209923i
$785$	12.4718	−	17.1660i	0.445138	−	0.612680i
$786$		0			0
$787$	−27.3852	+	8.89798i	−0.976175	+	0.317179i	−0.753306	−	0.657670i	$-0.771542\pi$
$787$	−27.3852	+	8.89798i	−0.976175	+	0.317179i	−0.222869	+	0.974848i	$0.571542\pi$
$788$	11.5611	+	8.39964i	0.411848	+	0.299225i
$789$		0			0
$790$	6.45211	−	19.8576i	0.229556	−	0.706500i
$791$	9.87749			0.351203
$792$		0			0
$793$	2.21494			0.0786547
$794$	−4.87367	+	14.9996i	−0.172960	+	0.532316i
$795$		0			0
$796$	18.5046	+	13.4444i	0.655878	+	0.476524i
$797$	−39.8741	+	12.9559i	−1.41241	+	0.458921i	−0.913184	−	0.407548i	$-0.866384\pi$
$797$	−39.8741	+	12.9559i	−1.41241	+	0.458921i	−0.499231	+	0.866469i	$0.666384\pi$
$798$		0			0
$799$	16.6868	−	22.9674i	0.590337	−	0.812530i
$800$	−2.77413	+	2.01552i	−0.0980804	+	0.0712596i
$801$		0			0
$802$		−	33.9870i		−	1.20012i
$803$	−3.76551	+	3.87660i	−0.132882	+	0.136802i
$804$		0			0
$805$	4.22083	+	1.37143i	0.148765	+	0.0483366i
$806$	4.65174	+	6.40258i	0.163851	+	0.225521i
$807$		0			0
$808$	2.16914	+	6.67593i	0.0763101	+	0.234858i
$809$	13.4595	+	41.4242i	0.473212	+	1.45640i	0.848354	+	0.529430i	$0.177594\pi$
$809$	13.4595	+	41.4242i	0.473212	+	1.45640i	−0.375142	+	0.926967i	$0.622406\pi$
$810$		0			0
$811$	−4.86798	−	6.70020i	−0.170938	−	0.235276i	0.714950	−	0.699176i	$-0.246450\pi$
$811$	−4.86798	−	6.70020i	−0.170938	−	0.235276i	−0.885888	+	0.463900i	$0.846450\pi$
$812$	−0.0897872	−	0.0291736i	−0.00315091	−	0.00102379i
$813$		0			0
$814$	21.2272	−	11.2074i	0.744013	−	0.392818i
$815$			59.6480i			2.08938i
$816$		0			0
$817$	−0.00196900	+	0.00143056i	−6.88866e−5	+	5.00491e-5i
$818$	−4.84827	+	6.67307i	−0.169516	+	0.233318i
$819$		0			0
$820$	23.1501	−	7.52193i	0.808438	−	0.262677i
$821$	−21.6653	−	15.7408i	−0.756126	−	0.549358i	0.141594	−	0.989925i	$-0.454777\pi$
$821$	−21.6653	−	15.7408i	−0.756126	−	0.549358i	−0.897720	+	0.440567i	$0.854777\pi$
$822$		0			0
$823$	5.49250	−	16.9042i	0.191457	−	0.589243i	−0.808543	−	0.588437i	$-0.799744\pi$
$823$	5.49250	−	16.9042i	0.191457	−	0.589243i	1.00000		0.000805798i	$-0.000256494\pi$
$824$	−3.17243			−0.110517
$825$		0			0
$826$	−11.6810			−0.406435
$827$	−3.09201	+	9.51622i	−0.107520	+	0.330911i	−0.990314	−	0.138849i	$-0.955660\pi$
$827$	−3.09201	+	9.51622i	−0.107520	+	0.330911i	0.882794	+	0.469760i	$0.155660\pi$
$828$		0			0
$829$	−10.2437	−	7.44246i	−0.355777	−	0.258487i	0.395511	−	0.918461i	$-0.370567\pi$
$829$	−10.2437	−	7.44246i	−0.355777	−	0.258487i	−0.751289	+	0.659974i	$0.770567\pi$
$830$	39.8159	−	12.9370i	1.38203	−	0.449049i
$831$		0			0
$832$	2.40015	−	3.30352i	0.0832102	−	0.114529i
$833$	−2.78914	+	2.02643i	−0.0966380	+	0.0702116i
$834$		0			0
$835$			7.34788i			0.254284i
$836$	0.0303284	−	0.211322i	0.00104893	−	0.00730873i
$837$		0			0
$838$	−11.0991	−	3.60631i	−0.383411	−	0.124578i
$839$	17.4133	+	23.9674i	0.601174	+	0.827445i	0.995815	−	0.0913901i	$-0.0291310\pi$
$839$	17.4133	+	23.9674i	0.601174	+	0.827445i	−0.394641	+	0.918835i	$0.629131\pi$
$840$		0			0
$841$	−8.95874	−	27.5722i	−0.308922	−	0.950764i
$842$	−6.54192	−	20.1340i	−0.225450	−	0.693862i
$843$		0			0
$844$	−11.9012	−	16.3806i	−0.409657	−	0.563845i
$845$	−10.1445	−	3.29615i	−0.348981	−	0.113391i
$846$		0			0
$847$	8.70749	−	6.72158i	0.299193	−	0.230956i
$848$			11.0251i			0.378605i
$849$		0			0
$850$	9.56401	−	6.94866i	0.328043	−	0.238337i
$851$	6.50297	−	8.95057i	0.222919	−	0.306822i
$852$		0			0
$853$	32.5133	−	10.5642i	1.11323	−	0.361712i	0.306052	−	0.952015i	$-0.400992\pi$
$853$	32.5133	−	10.5642i	1.11323	−	0.361712i	0.807182	+	0.590303i	$0.200992\pi$
$854$	0.438833	+	0.318831i	0.0150166	+	0.0109102i
$855$		0			0
$856$	1.96595	−	6.05057i	0.0671947	−	0.206804i
$857$	14.6611			0.500812			0.250406	−	0.968141i	$-0.419436\pi$
$857$	14.6611			0.500812			0.250406	+	0.968141i	$0.419436\pi$
$858$		0			0
$859$	−41.9691			−1.43197			−0.715983	−	0.698118i	$-0.754021\pi$
$859$	−41.9691			−1.43197			−0.715983	+	0.698118i	$0.754021\pi$
$860$	0.0339221	−	0.104402i	0.00115674	−	0.00356007i
$861$		0			0
$862$	−7.01778	−	5.09872i	−0.239027	−	0.173663i
$863$	40.2269	−	13.0705i	1.36934	−	0.444925i	0.470189	−	0.882566i	$-0.344186\pi$
$863$	40.2269	−	13.0705i	1.36934	−	0.444925i	0.899150	+	0.437641i	$0.144186\pi$
$864$		0			0
$865$	−26.0985	+	35.9216i	−0.887377	+	1.22137i
$866$	−1.74570	+	1.26832i	−0.0593212	+	0.0430993i
$867$		0			0
$868$			1.93811i			0.0657836i
$869$	−21.4076	−	10.5186i	−0.726202	−	0.356819i
$870$		0			0
$871$	15.3828	+	4.99819i	0.521227	+	0.169357i
$872$	−10.9301	−	15.0440i	−0.370140	−	0.509454i
$873$		0			0
$874$	−0.0304062	−	0.0935806i	−0.00102850	−	0.00316541i
$875$	−1.40943	−	4.33777i	−0.0476473	−	0.146643i
$876$		0			0
$877$	34.4945	+	47.4777i	1.16480	+	1.60321i	0.691673	+	0.722211i	$0.256874\pi$
$877$	34.4945	+	47.4777i	1.16480	+	1.60321i	0.473125	+	0.880995i	$0.343126\pi$
$878$	12.6714	+	4.11718i	0.427638	+	0.138948i
$879$		0			0
$880$	4.49575	+	8.51513i	0.151552	+	0.287045i
$881$			15.3118i			0.515866i	0.966163	+	0.257933i	$0.0830414\pi$
$881$			15.3118i			0.515866i	−0.966163	+	0.257933i	$0.916959\pi$
$882$		0			0
$883$	14.2078	−	10.3225i	0.478129	−	0.347381i	−0.322472	−	0.946579i	$-0.604514\pi$
$883$	14.2078	−	10.3225i	0.478129	−	0.347381i	0.800601	+	0.599198i	$0.204514\pi$
$884$	−8.27468	+	11.3891i	−0.278308	+	0.383057i
$885$		0			0
$886$	−4.35266	+	1.41427i	−0.146231	+	0.0475132i
$887$	−41.2455	−	29.9666i	−1.38489	−	1.00618i	−0.996404	−	0.0847268i	$-0.972998\pi$
$887$	−41.2455	−	29.9666i	−1.38489	−	1.00618i	−0.388486	−	0.921455i	$-0.627002\pi$
$888$		0			0
$889$	0.0491145	−	0.151159i	0.00164725	−	0.00506971i
$890$	−25.4496			−0.853072
$891$		0			0
$892$	11.5637			0.387181
$893$	0.163795	−	0.504109i	0.00548119	−	0.0168694i
$894$		0			0
$895$	−54.7301	−	39.7638i	−1.82943	−	1.32916i
$896$	0.951057	−	0.309017i	0.0317726	−	0.0103235i
$897$		0			0
$898$	−20.7600	+	28.5737i	−0.692770	+	0.953516i
$899$	0.148028	−	0.107548i	0.00493700	−	0.00358694i
$900$		0			0
$901$		−	38.0099i		−	1.26630i
$902$	−4.74873	−	27.3986i	−0.158115	−	0.912273i
$903$		0			0
$904$	9.39405	+	3.05231i	0.312441	+	0.101518i
$905$	−2.13203	−	2.93448i	−0.0708710	−	0.0975456i
$906$		0			0
$907$	9.48228	+	29.1835i	0.314854	+	0.969021i	0.975814	+	0.218600i	$0.0701491\pi$
$907$	9.48228	+	29.1835i	0.314854	+	0.969021i	−0.660960	+	0.750421i	$0.729851\pi$
$908$	7.93574	+	24.4237i	0.263357	+	0.810529i
$909$		0			0
$910$	−6.96830	−	9.59104i	−0.230997	−	0.317940i
$911$	−15.0510	−	4.89038i	−0.498663	−	0.162025i	0.0488772	−	0.998805i	$-0.484436\pi$
$911$	−15.0510	−	4.89038i	−0.498663	−	0.162025i	−0.547540	+	0.836779i	$0.684436\pi$
$912$		0			0
$913$	−8.16733	−	47.1228i	−0.270299	−	1.55954i
$914$		−	9.26076i		−	0.306319i
$915$		0			0
$916$	0.570755	−	0.414677i	0.0188583	−	0.0137013i
$917$	−1.85658	+	2.55536i	−0.0613097	+	0.0843856i
$918$		0			0
$919$	9.85394	−	3.20174i	0.325051	−	0.105616i	−0.141946	−	0.989874i	$-0.545336\pi$
$919$	9.85394	−	3.20174i	0.325051	−	0.105616i	0.466997	+	0.884259i	$0.345336\pi$
$920$	3.59045	+	2.60862i	0.118374	+	0.0860036i
$921$		0			0
$922$	−2.07419	+	6.38370i	−0.0683098	+	0.210236i
$923$	50.0836			1.64852
$924$		0			0
$925$	24.8176			0.815997
$926$	5.54080	−	17.0528i	0.182082	−	0.560390i
$927$		0			0
$928$	−0.0763776	−	0.0554915i	−0.00250722	−	0.00182160i
$929$	−33.1127	+	10.7590i	−1.08639	+	0.352990i	−0.796851	−	0.604175i	$-0.793503\pi$
$929$	−33.1127	+	10.7590i	−1.08639	+	0.352990i	−0.289541	+	0.957166i	$0.593503\pi$
$930$		0			0
$931$	−0.0378351	+	0.0520755i	−0.00123999	+	0.00170671i
$932$	−13.5208	+	9.82345i	−0.442889	+	0.321778i
$933$		0			0
$934$		−	17.8067i		−	0.582652i
$935$	−15.4994	−	29.3565i	−0.506885	−	0.960059i
$936$		0			0
$937$	−17.4137	−	5.65805i	−0.568880	−	0.184840i	0.0104327	−	0.999946i	$-0.496679\pi$
$937$	−17.4137	−	5.65805i	−0.568880	−	0.184840i	−0.579313	+	0.815105i	$0.696679\pi$
$938$	2.32825	+	3.20456i	0.0760200	+	0.104633i
$939$		0			0
$940$	7.38776	+	22.7372i	0.240962	+	0.741605i
$941$	−3.15920	−	9.72302i	−0.102987	−	0.316961i	0.886266	−	0.463177i	$-0.153291\pi$
$941$	−3.15920	−	9.72302i	−0.102987	−	0.316961i	−0.989253	+	0.146216i	$0.953291\pi$
$942$		0			0
$943$	−7.53322	−	10.3686i	−0.245315	−	0.337648i
$944$	−11.1093	−	3.60964i	−0.361578	−	0.117484i
$945$		0			0
$946$	−0.112551	−	0.0553018i	−0.00365934	−	0.00179802i
$947$		−	15.2239i		−	0.494711i	−0.968925	−	0.247356i	$-0.920438\pi$
$947$		−	15.2239i		−	0.494711i	0.968925	−	0.247356i	$-0.0795616\pi$
$948$		0			0
$949$	5.38301	−	3.91098i	0.174740	−	0.126956i
$950$	0.129737	−	0.178568i	0.00420923	−	0.00579350i
$951$		0			0
$952$	−3.27883	+	1.06536i	−0.106268	+	0.0345284i
$953$	−30.6675	−	22.2813i	−0.993419	−	0.721761i	−0.0327515	−	0.999464i	$-0.510427\pi$
$953$	−30.6675	−	22.2813i	−0.993419	−	0.721761i	−0.960667	+	0.277703i	$0.910427\pi$
$954$		0			0
$955$	−1.90116	+	5.85117i	−0.0615201	+	0.189339i
$956$	−8.33106			−0.269446
$957$		0			0
$958$	−2.53980			−0.0820572
$959$	3.16374	−	9.73699i	0.102163	−	0.314424i
$960$		0			0
$961$	22.0407	+	16.0135i	0.710989	+	0.516564i
$962$	−28.1071	+	9.13254i	−0.906209	+	0.294445i
$963$		0			0
$964$	15.1458	−	20.8464i	0.487814	−	0.671419i
$965$	0.675118	−	0.490502i	0.0217328	−	0.0157898i
$966$		0			0
$967$			4.55649i			0.146527i	0.997313	+	0.0732634i	$0.0233414\pi$
$967$			4.55649i			0.146527i	−0.997313	+	0.0732634i	$0.976659\pi$
$968$	10.3584	−	3.70184i	0.332931	−	0.118982i
$969$		0			0
$970$	16.9218	+	5.49823i	0.543327	+	0.176538i
$971$	16.3499	+	22.5037i	0.524693	+	0.722178i	0.986310	−	0.164901i	$-0.0527305\pi$
$971$	16.3499	+	22.5037i	0.524693	+	0.722178i	−0.461617	+	0.887079i	$0.652730\pi$
$972$		0			0
$973$	0.845492	+	2.60216i	0.0271052	+	0.0834213i
$974$	−8.75920	−	26.9581i	−0.280663	−	0.863792i
$975$		0			0
$976$	0.318831	+	0.438833i	0.0102055	+	0.0140467i
$977$	−31.2291	−	10.1470i	−0.999108	−	0.324630i	−0.236599	−	0.971607i	$-0.576033\pi$
$977$	−31.2291	−	10.1470i	−0.999108	−	0.324630i	−0.762509	+	0.646977i	$0.776033\pi$
$978$		0			0
$979$	−4.13015	+	28.7781i	−0.132000	+	0.919751i
$980$		−	2.90328i		−	0.0927418i
$981$		0			0
$982$	−29.5530	+	21.4715i	−0.943075	+	0.685184i
$983$	−18.3090	+	25.2001i	−0.583965	+	0.803759i	−0.994123	−	0.108255i	$-0.965474\pi$
$983$	−18.3090	+	25.2001i	−0.583965	+	0.803759i	0.410158	+	0.912014i	$0.365474\pi$
$984$		0			0
$985$	39.4582	−	12.8207i	1.25724	−	0.408503i
$986$	0.263317	+	0.191311i	0.00838572	+	0.00609258i
$987$		0			0
$988$	−0.0812228	+	0.249978i	−0.00258404	+	0.00795286i
$989$	−0.0577984			−0.00183788
$990$		0			0
$991$	17.8058			0.565620			0.282810	−	0.959176i	$-0.408733\pi$
$991$	17.8058			0.565620			0.282810	+	0.959176i	$0.408733\pi$
$992$	−0.598908	+	1.84325i	−0.0190153	+	0.0585232i
$993$		0			0
$994$	9.92278	+	7.20932i	0.314732	+	0.228666i
$995$	63.1563	−	20.5207i	2.00219	−	0.650551i
$996$		0			0
$997$	−5.38048	+	7.40560i	−0.170402	+	0.234538i	−0.885674	−	0.464309i	$-0.846303\pi$
$997$	−5.38048	+	7.40560i	−0.170402	+	0.234538i	0.715272	+	0.698846i	$0.246303\pi$
$998$	−5.73001	+	4.16309i	−0.181380	+	0.131780i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.bu.b.827.3	yes	48
3.2	odd	2		1386.2.bu.a.827.10	✓	48
11.6	odd	10		1386.2.bu.a.1205.10	yes	48
33.17	even	10	inner	1386.2.bu.b.1205.3	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1386.2.bu.a.827.10	✓	48	3.2	odd	2
1386.2.bu.a.1205.10	yes	48	11.6	odd	10
1386.2.bu.b.827.3	yes	48	1.1	even	1	trivial
1386.2.bu.b.1205.3	yes	48	33.17	even	10	inner

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:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.bu (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-2.76118 + 0.897162i) q^{5} +(0.587785 - 0.809017i) q^{7} +(0.809017 - 0.587785i) q^{8} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-2.76118 + 0.897162i) q^{5} +(0.587785 - 0.809017i) q^{7} +(0.809017 - 0.587785i) q^{8} -2.90328i q^{10} +(-3.28299 - 0.471165i) q^{11} +(3.88352 + 1.26183i) q^{13} +(0.587785 + 0.809017i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-1.06536 - 3.27883i) q^{17} +(-0.0378351 - 0.0520755i) q^{19} +(2.76118 + 0.897162i) q^{20} +(1.46260 - 2.97671i) q^{22} -1.52863i q^{23} +(2.77413 - 2.01552i) q^{25} +(-2.40015 + 3.30352i) q^{26} +(-0.951057 + 0.309017i) q^{28} +(0.0763776 + 0.0554915i) q^{29} +(0.598908 - 1.84325i) q^{31} -1.00000 q^{32} +3.44757 q^{34} +(-0.897162 + 2.76118i) q^{35} +(5.85528 + 4.25411i) q^{37} +(0.0612185 - 0.0198911i) q^{38} +(-1.70650 + 2.34880i) q^{40} +(6.78292 - 4.92808i) q^{41} -0.0378105i q^{43} +(2.37905 + 2.31087i) q^{44} +(1.45382 + 0.472374i) q^{46} +(4.84017 + 6.66193i) q^{47} +(-0.309017 - 0.951057i) q^{49} +(1.05962 + 3.26119i) q^{50} +(-2.40015 - 3.30352i) q^{52} +(10.4855 + 3.40696i) q^{53} +(9.48763 - 1.64440i) q^{55} -1.00000i q^{56} +(-0.0763776 + 0.0554915i) q^{58} +(-6.86594 + 9.45016i) q^{59} +(0.515879 - 0.167619i) q^{61} +(1.56796 + 1.13919i) q^{62} +(0.309017 - 0.951057i) q^{64} -11.8552 q^{65} +3.96105 q^{67} +(-1.06536 + 3.27883i) q^{68} +(-2.34880 - 1.70650i) q^{70} +(11.6649 - 3.79017i) q^{71} +(0.957782 - 1.31827i) q^{73} +(-5.85528 + 4.25411i) q^{74} +0.0643689i q^{76} +(-2.31087 + 2.37905i) q^{77} +(6.83971 + 2.22236i) q^{79} +(-1.70650 - 2.34880i) q^{80} +(2.59084 + 7.97380i) q^{82} +(4.45599 + 13.7141i) q^{83} +(5.88329 + 8.09765i) q^{85} +(0.0359599 + 0.0116841i) q^{86} +(-2.93294 + 1.54851i) q^{88} -8.76582i q^{89} +(3.30352 - 2.40015i) q^{91} +(-0.898508 + 1.23669i) q^{92} +(-7.83156 + 2.54463i) q^{94} +(0.151190 + 0.109846i) q^{95} +(-1.89380 + 5.82852i) q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 12 q^{2} - 12 q^{4} + 12 q^{8}+O(q^{10}) \) 48 * q + 12 * q^2 - 12 * q^4 + 12 * q^8	\( 48 q + 12 q^{2} - 12 q^{4} + 12 q^{8} - 4 q^{11} - 12 q^{16} - 24 q^{17} + 4 q^{22} + 24 q^{25} - 40 q^{26} + 16 q^{29} + 40 q^{31} - 48 q^{32} - 16 q^{34} + 12 q^{35} + 16 q^{37} + 40 q^{38} - 24 q^{41} - 4 q^{44} - 40 q^{46} + 40 q^{47} + 12 q^{49} - 4 q^{50} - 40 q^{52} + 40 q^{53} - 32 q^{55} - 16 q^{58} + 40 q^{61} + 40 q^{62} - 12 q^{64} + 48 q^{67} - 24 q^{68} + 8 q^{70} + 40 q^{73} - 16 q^{74} - 32 q^{77} + 40 q^{79} - 16 q^{82} + 16 q^{83} - 20 q^{85} + 4 q^{88} + 20 q^{92} + 52 q^{95} - 8 q^{97} + 48 q^{98}+O(q^{100}) \) 48 * q + 12 * q^2 - 12 * q^4 + 12 * q^8 - 4 * q^11 - 12 * q^16 - 24 * q^17 + 4 * q^22 + 24 * q^25 - 40 * q^26 + 16 * q^29 + 40 * q^31 - 48 * q^32 - 16 * q^34 + 12 * q^35 + 16 * q^37 + 40 * q^38 - 24 * q^41 - 4 * q^44 - 40 * q^46 + 40 * q^47 + 12 * q^49 - 4 * q^50 - 40 * q^52 + 40 * q^53 - 32 * q^55 - 16 * q^58 + 40 * q^61 + 40 * q^62 - 12 * q^64 + 48 * q^67 - 24 * q^68 + 8 * q^70 + 40 * q^73 - 16 * q^74 - 32 * q^77 + 40 * q^79 - 16 * q^82 + 16 * q^83 - 20 * q^85 + 4 * q^88 + 20 * q^92 + 52 * q^95 - 8 * q^97 + 48 * q^98

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