LMFDB - Embedded newform 1386.2.bu.b.827.4

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			827.4
Character	$\chi$	$=$	1386.827
Dual form			1386.2.bu.b.1205.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-1.68374 + 0.547080i) q^{5} +(-0.587785 + 0.809017i) q^{7} +(0.809017 - 0.587785i) q^{8} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-1.68374 + 0.547080i) q^{5} +(-0.587785 + 0.809017i) q^{7} +(0.809017 - 0.587785i) q^{8} -1.77039i q^{10} +(-0.882736 + 3.19700i) q^{11} +(5.61541 + 1.82456i) q^{13} +(-0.587785 - 0.809017i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-2.35030 - 7.23348i) q^{17} +(2.36768 + 3.25883i) q^{19} +(1.68374 + 0.547080i) q^{20} +(-2.76774 - 1.82746i) q^{22} +5.31904i q^{23} +(-1.50940 + 1.09665i) q^{25} +(-3.47052 + 4.77675i) q^{26} +(0.951057 - 0.309017i) q^{28} +(-1.43507 - 1.04264i) q^{29} +(-0.558230 + 1.71805i) q^{31} -1.00000 q^{32} +7.60573 q^{34} +(0.547080 - 1.68374i) q^{35} +(-6.24119 - 4.53449i) q^{37} +(-3.83098 + 1.24476i) q^{38} +(-1.04061 + 1.43227i) q^{40} +(-5.68867 + 4.13306i) q^{41} -7.27378i q^{43} +(2.59329 - 2.06756i) q^{44} +(-5.05871 - 1.64367i) q^{46} +(1.37438 + 1.89167i) q^{47} +(-0.309017 - 0.951057i) q^{49} +(-0.576541 - 1.77441i) q^{50} +(-3.47052 - 4.77675i) q^{52} +(-9.89540 - 3.21521i) q^{53} +(-0.262715 - 5.86583i) q^{55} +1.00000i q^{56} +(1.43507 - 1.04264i) q^{58} +(-5.96760 + 8.21370i) q^{59} +(-4.06283 + 1.32009i) q^{61} +(-1.46146 - 1.06182i) q^{62} +(0.309017 - 0.951057i) q^{64} -10.4531 q^{65} +7.57214 q^{67} +(-2.35030 + 7.23348i) q^{68} +(1.43227 + 1.04061i) q^{70} +(-8.10283 + 2.63277i) q^{71} +(-6.05824 + 8.33845i) q^{73} +(6.24119 - 4.53449i) q^{74} -4.02813i q^{76} +(-2.06756 - 2.59329i) q^{77} +(-5.89055 - 1.91396i) q^{79} +(-1.04061 - 1.43227i) q^{80} +(-2.17288 - 6.68743i) q^{82} +(-1.63299 - 5.02583i) q^{83} +(7.91458 + 10.8935i) q^{85} +(6.91777 + 2.24772i) q^{86} +(1.16500 + 3.10528i) q^{88} -5.93010i q^{89} +(-4.77675 + 3.47052i) q^{91} +(3.12645 - 4.30319i) q^{92} +(-2.22379 + 0.722555i) q^{94} +(-5.76939 - 4.19170i) q^{95} +(-1.89206 + 5.82316i) q^{97} +1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−1.68374	+	0.547080i	−0.752991	+	0.244662i	−0.660268	−	0.751030i	$-0.729557\pi$
$5$	−1.68374	+	0.547080i	−0.752991	+	0.244662i	−0.0927233	+	0.995692i	$0.529557\pi$
$6$		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
$10$		−	1.77039i		−	0.559846i
$11$	−0.882736	+	3.19700i	−0.266155	+	0.963930i
$11$	−0.882736	+	3.19700i	−0.266155	+	0.963930i
$12$		0			0
$13$	5.61541	+	1.82456i	1.55743	+	0.506041i	0.956121	−	0.292972i	$-0.0946442\pi$
$13$	5.61541	+	1.82456i	1.55743	+	0.506041i	0.601314	+	0.799013i	$0.294644\pi$
$14$	−0.587785	−	0.809017i	−0.157092	−	0.216219i
$15$		0			0
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−2.35030	−	7.23348i	−0.570031	−	1.75438i	−0.652507	−	0.757783i	$-0.726283\pi$
$17$	−2.35030	−	7.23348i	−0.570031	−	1.75438i	0.0824755	−	0.996593i	$-0.473717\pi$
$18$		0			0
$19$	2.36768	+	3.25883i	0.543182	+	0.747626i	0.989067	−	0.147464i	$-0.0471111\pi$
$19$	2.36768	+	3.25883i	0.543182	+	0.747626i	−0.445885	+	0.895090i	$0.647111\pi$
$20$	1.68374	+	0.547080i	0.376496	+	0.122331i
$21$		0			0
$22$	−2.76774	−	1.82746i	−0.590085	−	0.389615i
$23$			5.31904i			1.10910i	0.832152	+	0.554548i	$0.187109\pi$
$23$			5.31904i			1.10910i	−0.832152	+	0.554548i	$0.812891\pi$
$24$		0			0
$25$	−1.50940	+	1.09665i	−0.301881	+	0.219329i
$26$	−3.47052	+	4.77675i	−0.680624	+	0.936799i
$27$		0			0
$28$	0.951057	−	0.309017i	0.179733	−	0.0583987i
$29$	−1.43507	−	1.04264i	−0.266486	−	0.193613i	0.446516	−	0.894776i	$-0.352665\pi$
$29$	−1.43507	−	1.04264i	−0.266486	−	0.193613i	−0.713001	+	0.701163i	$0.752665\pi$
$30$		0			0
$31$	−0.558230	+	1.71805i	−0.100261	+	0.308572i	−0.988589	−	0.150638i	$-0.951867\pi$
$31$	−0.558230	+	1.71805i	−0.100261	+	0.308572i	0.888328	+	0.459210i	$0.151867\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	7.60573			1.30437
$35$	0.547080	−	1.68374i	0.0924734	−	0.284604i
$36$		0			0
$37$	−6.24119	−	4.53449i	−1.02605	−	0.745466i	−0.0585323	−	0.998286i	$-0.518642\pi$
$37$	−6.24119	−	4.53449i	−1.02605	−	0.745466i	−0.967513	+	0.252820i	$0.918642\pi$
$38$	−3.83098	+	1.24476i	−0.621467	+	0.201927i
$39$		0			0
$40$	−1.04061	+	1.43227i	−0.164535	+	0.226462i
$41$	−5.68867	+	4.13306i	−0.888421	+	0.645476i	−0.935466	−	0.353417i	$-0.885020\pi$
$41$	−5.68867	+	4.13306i	−0.888421	+	0.645476i	0.0470449	+	0.998893i	$0.485020\pi$
$42$		0			0
$43$		−	7.27378i		−	1.10924i	−0.832104	−	0.554620i	$-0.812863\pi$
$43$		−	7.27378i		−	1.10924i	0.832104	−	0.554620i	$-0.187137\pi$
$44$	2.59329	−	2.06756i	0.390954	−	0.311697i
$45$		0			0
$46$	−5.05871	−	1.64367i	−0.745865	−	0.242346i
$47$	1.37438	+	1.89167i	0.200474	+	0.275929i	0.897403	−	0.441211i	$-0.145451\pi$
$47$	1.37438	+	1.89167i	0.200474	+	0.275929i	−0.696929	+	0.717140i	$0.745451\pi$
$48$		0			0
$49$	−0.309017	−	0.951057i	−0.0441453	−	0.135865i
$50$	−0.576541	−	1.77441i	−0.0815352	−	0.250940i
$51$		0			0
$52$	−3.47052	−	4.77675i	−0.481274	−	0.662417i
$53$	−9.89540	−	3.21521i	−1.35924	−	0.441643i	−0.463450	−	0.886123i	$-0.653388\pi$
$53$	−9.89540	−	3.21521i	−1.35924	−	0.441643i	−0.895789	+	0.444480i	$0.853388\pi$
$54$		0			0
$55$	−0.262715	−	5.86583i	−0.0354245	−	0.790949i
$56$			1.00000i			0.133631i
$57$		0			0
$58$	1.43507	−	1.04264i	0.188434	−	0.136905i
$59$	−5.96760	+	8.21370i	−0.776915	+	1.06933i	0.218700	+	0.975792i	$0.429818\pi$
$59$	−5.96760	+	8.21370i	−0.776915	+	1.06933i	−0.995615	+	0.0935403i	$0.970182\pi$
$60$		0			0
$61$	−4.06283	+	1.32009i	−0.520192	+	0.169020i	−0.557332	−	0.830290i	$-0.688175\pi$
$61$	−4.06283	+	1.32009i	−0.520192	+	0.169020i	0.0371407	+	0.999310i	$0.488175\pi$
$62$	−1.46146	−	1.06182i	−0.185606	−	0.134851i
$63$		0			0
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−10.4531			−1.29654
$66$		0			0
$67$	7.57214			0.925084			0.462542	−	0.886597i	$-0.346938\pi$
$67$	7.57214			0.925084			0.462542	+	0.886597i	$0.346938\pi$
$68$	−2.35030	+	7.23348i	−0.285016	+	0.877188i
$69$		0			0
$70$	1.43227	+	1.04061i	0.171189	+	0.124376i
$71$	−8.10283	+	2.63277i	−0.961629	+	0.312452i	−0.747432	−	0.664338i	$-0.768713\pi$
$71$	−8.10283	+	2.63277i	−0.961629	+	0.312452i	−0.214197	+	0.976791i	$0.568713\pi$
$72$		0			0
$73$	−6.05824	+	8.33845i	−0.709063	+	0.975942i	0.290753	+	0.956798i	$0.406094\pi$
$73$	−6.05824	+	8.33845i	−0.709063	+	0.975942i	−0.999817	+	0.0191438i	$0.993906\pi$
$74$	6.24119	−	4.53449i	0.725524	−	0.527124i
$75$		0			0
$76$		−	4.02813i		−	0.462058i
$77$	−2.06756	−	2.59329i	−0.235621	−	0.295533i
$78$		0			0
$79$	−5.89055	−	1.91396i	−0.662739	−	0.215337i	−0.0417160	−	0.999130i	$-0.513282\pi$
$79$	−5.89055	−	1.91396i	−0.662739	−	0.215337i	−0.621023	+	0.783793i	$0.713282\pi$
$80$	−1.04061	−	1.43227i	−0.116344	−	0.160133i
$81$		0			0
$82$	−2.17288	−	6.68743i	−0.239954	−	0.738503i
$83$	−1.63299	−	5.02583i	−0.179244	−	0.551656i	0.820558	−	0.571564i	$-0.193663\pi$
$83$	−1.63299	−	5.02583i	−0.179244	−	0.551656i	−0.999802	+	0.0199072i	$0.993663\pi$
$84$		0			0
$85$	7.91458	+	10.8935i	0.858457	+	1.18156i
$86$	6.91777	+	2.24772i	0.745963	+	0.242378i
$87$		0			0
$88$	1.16500	+	3.10528i	0.124189	+	0.331024i
$89$		−	5.93010i		−	0.628589i	−0.949325	−	0.314295i	$-0.898232\pi$
$89$		−	5.93010i		−	0.628589i	0.949325	−	0.314295i	$-0.101768\pi$
$90$		0			0
$91$	−4.77675	+	3.47052i	−0.500740	+	0.363809i
$92$	3.12645	−	4.30319i	0.325955	−	0.448639i
$93$		0			0
$94$	−2.22379	+	0.722555i	−0.229367	+	0.0745258i
$95$	−5.76939	−	4.19170i	−0.591927	−	0.430060i
$96$		0			0
$97$	−1.89206	+	5.82316i	−0.192110	+	0.591253i	0.807889	+	0.589335i	$0.200610\pi$
$97$	−1.89206	+	5.82316i	−0.192110	+	0.591253i	−0.999998	+	0.00191729i	$0.999390\pi$
$98$	1.00000			0.101015
$99$		0			0
$100$	1.86573			0.186573
$101$	−4.18375	+	12.8763i	−0.416299	+	1.28124i	0.494785	+	0.869015i	$0.335247\pi$
$101$	−4.18375	+	12.8763i	−0.416299	+	1.28124i	−0.911084	+	0.412221i	$0.864753\pi$
$102$		0			0
$103$	−4.54988	−	3.30568i	−0.448313	−	0.325718i	0.340617	−	0.940202i	$-0.389364\pi$
$103$	−4.54988	−	3.30568i	−0.448313	−	0.325718i	−0.788929	+	0.614484i	$0.789364\pi$
$104$	5.61541	−	1.82456i	0.550636	−	0.178913i
$105$		0			0
$106$	6.11570	−	8.41753i	0.594009	−	0.817583i
$107$	0.844054	−	0.613241i	0.0815978	−	0.0592843i	−0.546238	−	0.837630i	$-0.683941\pi$
$107$	0.844054	−	0.613241i	0.0815978	−	0.0592843i	0.627836	+	0.778345i	$0.283941\pi$
$108$		0			0
$109$		−	7.01137i		−	0.671567i	−0.941939	−	0.335784i	$-0.890999\pi$
$109$		−	7.01137i		−	0.671567i	0.941939	−	0.335784i	$-0.109001\pi$
$110$	5.65992	+	1.56279i	0.539652	+	0.149006i
$111$		0			0
$112$	−0.951057	−	0.309017i	−0.0898664	−	0.0291994i
$113$	5.21636	+	7.17971i	0.490714	+	0.675410i	0.980520	−	0.196422i	$-0.0629322\pi$
$113$	5.21636	+	7.17971i	0.490714	+	0.675410i	−0.489805	+	0.871832i	$0.662932\pi$
$114$		0			0
$115$	−2.90994	−	8.95587i	−0.271353	−	0.835139i
$116$	0.548148	+	1.68703i	0.0508943	+	0.156636i
$117$		0			0
$118$	−5.96760	−	8.21370i	−0.549362	−	0.756132i
$119$	7.23348	+	2.35030i	0.663092	+	0.215452i
$120$		0			0
$121$	−9.44155	−	5.64421i	−0.858323	−	0.513110i
$122$		−	4.27191i		−	0.386760i
$123$		0			0
$124$	1.46146	−	1.06182i	0.131243	−	0.0953539i
$125$	7.14453	−	9.83360i	0.639026	−	0.879544i
$126$		0			0
$127$	−0.251687	+	0.0817782i	−0.0223336	+	0.00725664i	−0.320163	−	0.947363i	$-0.603738\pi$
$127$	−0.251687	+	0.0817782i	−0.0223336	+	0.00725664i	0.297829	+	0.954619i	$0.403738\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$		0			0
$130$	3.23018	−	9.94146i	0.283305	−	0.871923i
$131$	−7.42431			−0.648665			−0.324333	−	0.945943i	$-0.605140\pi$
$131$	−7.42431			−0.648665			−0.324333	+	0.945943i	$0.605140\pi$
$132$		0			0
$133$	−4.02813			−0.349283
$134$	−2.33992	+	7.20153i	−0.202138	+	0.622117i
$135$		0			0
$136$	−6.15316	−	4.47053i	−0.527629	−	0.383345i
$137$	18.3467	−	5.96122i	1.56747	−	0.509301i	0.608678	−	0.793417i	$-0.291700\pi$
$137$	18.3467	−	5.96122i	1.56747	−	0.509301i	0.958790	+	0.284116i	$0.0917002\pi$
$138$		0			0
$139$	7.92992	−	10.9146i	0.672607	−	0.925765i	−0.327209	−	0.944952i	$-0.606108\pi$
$139$	7.92992	−	10.9146i	0.672607	−	0.925765i	0.999816	+	0.0191875i	$0.00610795\pi$
$140$	−1.43227	+	1.04061i	−0.121049	+	0.0879474i
$141$		0			0
$142$		−	8.51982i		−	0.714967i
$143$	−10.7900	+	16.3418i	−0.902307	+	1.36657i
$144$		0			0
$145$	2.98669	+	0.970435i	0.248031	+	0.0805902i
$146$	−6.05824	−	8.33845i	−0.501383	−	0.690095i
$147$		0			0
$148$	2.38392	+	7.33696i	0.195957	+	0.603095i
$149$	4.33452	+	13.3403i	0.355098	+	1.09288i	0.955953	+	0.293521i	$0.0948269\pi$
$149$	4.33452	+	13.3403i	0.355098	+	1.09288i	−0.600855	+	0.799358i	$0.705173\pi$
$150$		0			0
$151$	9.89971	+	13.6258i	0.805627	+	1.10885i	0.991983	+	0.126368i	$0.0403320\pi$
$151$	9.89971	+	13.6258i	0.805627	+	1.10885i	−0.186357	+	0.982482i	$0.559668\pi$
$152$	3.83098	+	1.24476i	0.310733	+	0.100963i
$153$		0			0
$154$	3.10528	−	1.16500i	0.250231	−	0.0938782i
$155$		−	3.19815i		−	0.256882i
$156$		0			0
$157$	−15.1742	+	11.0247i	−1.21103	+	0.879867i	−0.995324	−	0.0965902i	$-0.969206\pi$
$157$	−15.1742	+	11.0247i	−1.21103	+	0.879867i	−0.215709	+	0.976458i	$0.569206\pi$
$158$	3.64056	−	5.01080i	0.289627	−	0.398638i
$159$		0			0
$160$	1.68374	−	0.547080i	0.133111	−	0.0432505i
$161$	−4.30319	−	3.12645i	−0.339139	−	0.246399i
$162$		0			0
$163$	1.94098	−	5.97372i	0.152029	−	0.467898i	−0.845819	−	0.533471i	$-0.820888\pi$
$163$	1.94098	−	5.97372i	0.152029	−	0.467898i	0.997848	+	0.0655729i	$0.0208875\pi$
$164$	7.03158			0.549074
$165$		0			0
$166$	5.28447			0.410154
$167$	−0.535567	+	1.64830i	−0.0414434	+	0.127550i	−0.969638	−	0.244547i	$-0.921361\pi$
$167$	−0.535567	+	1.64830i	−0.0414434	+	0.127550i	0.928194	+	0.372096i	$0.121361\pi$
$168$		0			0
$169$	17.6866	+	12.8501i	1.36051	+	0.988467i
$170$	−12.8061	+	4.16094i	−0.982180	+	0.319130i
$171$		0			0
$172$	−4.27542	+	5.88461i	−0.325998	+	0.448697i
$173$	−6.42886	+	4.67084i	−0.488777	+	0.355117i	−0.804714	−	0.593663i	$-0.797681\pi$
$173$	−6.42886	+	4.67084i	−0.488777	+	0.355117i	0.315937	+	0.948780i	$0.397681\pi$
$174$		0			0
$175$		−	1.86573i		−	0.141036i
$176$	−3.31330	+	0.148394i	−0.249750	+	0.0111856i
$177$		0			0
$178$	5.63986	+	1.83250i	0.422725	+	0.137352i
$179$	−13.2640	−	18.2563i	−0.991399	−	1.36454i	−0.930457	−	0.366402i	$-0.880589\pi$
$179$	−13.2640	−	18.2563i	−0.991399	−	1.36454i	−0.0609423	−	0.998141i	$-0.519411\pi$
$180$		0			0
$181$	6.40149	+	19.7018i	0.475819	+	1.46442i	0.844850	+	0.535004i	$0.179690\pi$
$181$	6.40149	+	19.7018i	0.475819	+	1.46442i	−0.369031	+	0.929417i	$0.620310\pi$
$182$	−1.82456	−	5.61541i	−0.135245	−	0.416242i
$183$		0			0
$184$	3.12645	+	4.30319i	0.230485	+	0.317236i
$185$	12.9893	+	4.22047i	0.954990	+	0.310295i
$186$		0			0
$187$	25.2001	−	1.12864i	1.84281	−	0.0825346i
$188$		−	2.33824i		−	0.170533i
$189$		0			0
$190$	5.76939	−	4.19170i	0.418555	−	0.304098i
$191$	13.0063	−	17.9016i	0.941101	−	1.29531i	−0.0142676	−	0.999898i	$-0.504542\pi$
$191$	13.0063	−	17.9016i	0.941101	−	1.29531i	0.955369	−	0.295416i	$-0.0954583\pi$
$192$		0			0
$193$	−22.1086	+	7.18352i	−1.59141	+	0.517081i	−0.964964	−	0.262381i	$-0.915492\pi$
$193$	−22.1086	+	7.18352i	−1.59141	+	0.517081i	−0.626449	+	0.779463i	$0.715492\pi$
$194$	−4.95348	−	3.59891i	−0.355639	−	0.258387i
$195$		0			0
$196$	−0.309017	+	0.951057i	−0.0220726	+	0.0679326i
$197$	18.4121			1.31181			0.655904	−	0.754845i	$-0.272288\pi$
$197$	18.4121			1.31181			0.655904	+	0.754845i	$0.272288\pi$
$198$		0			0
$199$	−18.1730			−1.28825			−0.644126	−	0.764919i	$-0.722779\pi$
$199$	−18.1730			−1.28825			−0.644126	+	0.764919i	$0.722779\pi$
$200$	−0.576541	+	1.77441i	−0.0407676	+	0.125470i
$201$		0			0
$202$	−10.9532	−	7.95797i	−0.770665	−	0.559921i
$203$	1.68703	−	0.548148i	0.118406	−	0.0384725i
$204$		0			0
$205$	7.31712	−	10.0712i	0.511050	−	0.703400i
$206$	4.54988	−	3.30568i	0.317005	−	0.230317i
$207$		0			0
$208$			5.90439i			0.409396i
$209$	−12.5085	+	4.69276i	−0.865230	+	0.324605i
$210$		0			0
$211$	3.34195	+	1.08587i	0.230070	+	0.0747541i	0.421783	−	0.906697i	$-0.361404\pi$
$211$	3.34195	+	1.08587i	0.230070	+	0.0747541i	−0.191713	+	0.981451i	$0.561404\pi$
$212$	6.11570	+	8.41753i	0.420028	+	0.578119i
$213$		0			0
$214$	0.322400	+	0.992245i	0.0220388	+	0.0678285i
$215$	3.97934	+	12.2471i	0.271389	+	0.835248i
$216$		0			0
$217$	−1.06182	−	1.46146i	−0.0720808	−	0.0992107i
$218$	6.66821	+	2.16663i	0.451628	+	0.146743i
$219$		0			0
$220$	−3.23531	+	4.89998i	−0.218124	+	0.330356i
$221$		−	44.9072i		−	3.02079i
$222$		0			0
$223$	−5.82514	+	4.23221i	−0.390080	+	0.283410i	−0.765488	−	0.643450i	$-0.777503\pi$
$223$	−5.82514	+	4.23221i	−0.390080	+	0.283410i	0.375408	+	0.926860i	$0.377503\pi$
$224$	0.587785	−	0.809017i	0.0392731	−	0.0540547i
$225$		0			0
$226$	−8.44025	+	2.74240i	−0.561437	+	0.182422i
$227$	−2.43006	−	1.76554i	−0.161289	−	0.117183i	0.504213	−	0.863579i	$-0.331783\pi$
$227$	−2.43006	−	1.76554i	−0.161289	−	0.117183i	−0.665502	+	0.746396i	$0.731783\pi$
$228$		0			0
$229$	5.33724	−	16.4263i	0.352694	−	1.08548i	−0.604640	−	0.796499i	$-0.706683\pi$
$229$	5.33724	−	16.4263i	0.352694	−	1.08548i	0.957334	−	0.288983i	$-0.0933171\pi$
$230$	9.41676			0.620923
$231$		0			0
$232$	−1.77384			−0.116459
$233$	−1.82579	+	5.61922i	−0.119612	+	0.368127i	−0.992881	−	0.119111i	$-0.961996\pi$
$233$	−1.82579	+	5.61922i	−0.119612	+	0.368127i	0.873269	+	0.487238i	$0.161996\pi$
$234$		0			0
$235$	−3.34899	−	2.43319i	−0.218464	−	0.158724i
$236$	9.65578	−	3.13735i	0.628538	−	0.204224i
$237$		0			0
$238$	−4.47053	+	6.15316i	−0.289782	+	0.398850i
$239$	10.3250	−	7.50158i	0.667871	−	0.485237i	−0.201441	−	0.979501i	$-0.564562\pi$
$239$	10.3250	−	7.50158i	0.667871	−	0.485237i	0.869312	+	0.494264i	$0.164562\pi$
$240$		0			0
$241$		−	18.4692i		−	1.18970i	−0.803835	−	0.594852i	$-0.797211\pi$
$241$		−	18.4692i		−	1.18970i	0.803835	−	0.594852i	$-0.202789\pi$
$242$	8.28556	−	7.23530i	0.532616	−	0.465102i
$243$		0			0
$244$	4.06283	+	1.32009i	0.260096	+	0.0845102i
$245$	1.04061	+	1.43227i	0.0664820	+	0.0915046i
$246$		0			0
$247$	7.34956	+	22.6196i	0.467641	+	1.43925i
$248$	0.558230	+	1.71805i	0.0354476	+	0.109097i
$249$		0			0
$250$	7.14453	+	9.83360i	0.451860	+	0.621932i
$251$	28.0794	+	9.12356i	1.77236	+	0.575874i	0.998356	−	0.0573095i	$-0.0182522\pi$
$251$	28.0794	+	9.12356i	1.77236	+	0.575874i	0.774002	+	0.633184i	$0.218252\pi$
$252$		0			0
$253$	−17.0049	−	4.69531i	−1.06909	−	0.295191i
$254$		−	0.264640i		−	0.0166050i
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−0.904272	+	1.24462i	−0.0564069	+	0.0776375i	−0.836289	−	0.548289i	$-0.815279\pi$
$257$	−0.904272	+	1.24462i	−0.0564069	+	0.0776375i	0.779882	+	0.625927i	$0.215279\pi$
$258$		0			0
$259$	7.33696	−	2.38392i	0.455897	−	0.148130i
$260$	8.45671	+	6.14416i	0.524463	+	0.381045i
$261$		0			0
$262$	2.29424	−	7.06094i	0.141739	−	0.436226i
$263$	4.56189			0.281298			0.140649	−	0.990060i	$-0.455081\pi$
$263$	4.56189			0.281298			0.140649	+	0.990060i	$0.455081\pi$
$264$		0			0
$265$	18.4203			1.13155
$266$	1.24476	−	3.83098i	0.0763212	−	0.234892i
$267$		0			0
$268$	−6.12599	−	4.45079i	−0.374204	−	0.271875i
$269$	−7.91267	+	2.57098i	−0.482444	+	0.156756i	−0.540134	−	0.841579i	$-0.681626\pi$
$269$	−7.91267	+	2.57098i	−0.482444	+	0.156756i	0.0576900	+	0.998335i	$0.481626\pi$
$270$		0			0
$271$	−11.5277	+	15.8666i	−0.700261	+	0.963826i	0.299691	+	0.954036i	$0.403116\pi$
$271$	−11.5277	+	15.8666i	−0.700261	+	0.963826i	−0.999952	+	0.00978988i	$0.996884\pi$
$272$	6.15316	−	4.47053i	0.373090	−	0.271066i
$273$		0			0
$274$			19.2909i			1.16541i
$275$	−2.17357	−	5.79361i	−0.131071	−	0.349368i
$276$		0			0
$277$	26.8079	+	8.71042i	1.61073	+	0.523358i	0.969730	−	0.244181i	$-0.0785190\pi$
$277$	26.8079	+	8.71042i	1.61073	+	0.523358i	0.641002	+	0.767539i	$0.278519\pi$
$278$	7.92992	+	10.9146i	0.475605	+	0.654614i
$279$		0			0
$280$	−0.547080	−	1.68374i	−0.0326943	−	0.100623i
$281$	−4.05183	−	12.4703i	−0.241712	−	0.743914i	−0.996160	−	0.0875534i	$-0.972095\pi$
$281$	−4.05183	−	12.4703i	−0.241712	−	0.743914i	0.754448	−	0.656360i	$-0.227905\pi$
$282$		0			0
$283$	−8.74437	−	12.0356i	−0.519799	−	0.715442i	0.465734	−	0.884925i	$-0.345790\pi$
$283$	−8.74437	−	12.0356i	−0.519799	−	0.715442i	−0.985533	+	0.169483i	$0.945790\pi$
$284$	8.10283	+	2.63277i	0.480814	+	0.156226i
$285$		0			0
$286$	−12.2077	−	15.3118i	−0.721857	−	0.905408i
$287$		−	7.03158i		−	0.415061i
$288$		0			0
$289$	−33.0460	+	24.0093i	−1.94388	+	1.41231i
$290$	−1.84588	+	2.54063i	−0.108394	+	0.149191i
$291$		0			0
$292$	9.80244	−	3.18500i	0.573644	−	0.186388i
$293$	−2.72214	−	1.97775i	−0.159029	−	0.115541i	0.505425	−	0.862871i	$-0.331336\pi$
$293$	−2.72214	−	1.97775i	−0.159029	−	0.115541i	−0.664454	+	0.747329i	$0.731336\pi$
$294$		0			0
$295$	5.55433	−	17.0945i	0.323386	−	0.995279i
$296$	−7.71454			−0.448398
$297$		0			0
$298$	−14.0268			−0.812551
$299$	−9.70489	+	29.8686i	−0.561248	+	1.72734i
$300$		0			0
$301$	5.88461	+	4.27542i	0.339183	+	0.246431i
$302$	−16.0181	+	5.20458i	−0.921736	+	0.299490i
$303$		0			0
$304$	−2.36768	+	3.25883i	−0.135796	+	0.186906i
$305$	6.11854	−	4.44538i	0.350347	−	0.254542i
$306$		0			0
$307$			28.6813i			1.63693i	0.574557	+	0.818464i	$0.305174\pi$
$307$			28.6813i			1.63693i	−0.574557	+	0.818464i	$0.694826\pi$
$308$	0.148394	+	3.31330i	0.00845553	+	0.188793i
$309$		0			0
$310$	3.04162	+	0.988283i	0.172753	+	0.0561307i
$311$	5.67180	+	7.80657i	0.321618	+	0.442670i	0.938960	−	0.344025i	$-0.111791\pi$
$311$	5.67180	+	7.80657i	0.321618	+	0.442670i	−0.617342	+	0.786695i	$0.711791\pi$
$312$		0			0
$313$	5.72981	+	17.6345i	0.323868	+	0.996763i	0.971949	+	0.235192i	$0.0755719\pi$
$313$	5.72981	+	17.6345i	0.323868	+	0.996763i	−0.648081	+	0.761572i	$0.724428\pi$
$314$	−5.79603	−	17.8384i	−0.327089	−	1.00668i
$315$		0			0
$316$	3.64056	+	5.01080i	0.204797	+	0.281880i
$317$	−3.28961	−	1.06886i	−0.184763	−	0.0600331i	0.215174	−	0.976576i	$-0.430968\pi$
$317$	−3.28961	−	1.06886i	−0.184763	−	0.0600331i	−0.399937	+	0.916543i	$0.630968\pi$
$318$		0			0
$319$	4.60010	−	3.66754i	0.257556	−	0.205343i
$320$			1.77039i			0.0989677i
$321$		0			0
$322$	4.30319	−	3.12645i	0.239808	−	0.174230i
$323$	18.0079	−	24.7857i	1.00199	−	1.37912i
$324$		0			0
$325$	−10.4768	+	3.40413i	−0.581149	+	0.188827i
$326$	5.08155	+	3.69196i	0.281441	+	0.204479i
$327$		0			0
$328$	−2.17288	+	6.68743i	−0.119977	+	0.369252i
$329$	−2.33824			−0.128911
$330$		0			0
$331$	−11.5176			−0.633064			−0.316532	−	0.948582i	$-0.602518\pi$
$331$	−11.5176			−0.633064			−0.316532	+	0.948582i	$0.602518\pi$
$332$	−1.63299	+	5.02583i	−0.0896220	+	0.275828i
$333$		0			0
$334$	−1.40213	−	1.01871i	−0.0767212	−	0.0557412i
$335$	−12.7495	+	4.14256i	−0.696580	+	0.226332i
$336$		0			0
$337$	−16.6034	+	22.8527i	−0.904446	+	1.24486i	0.0645814	+	0.997912i	$0.479429\pi$
$337$	−16.6034	+	22.8527i	−0.904446	+	1.24486i	−0.969028	+	0.246951i	$0.920571\pi$
$338$	−17.6866	+	12.8501i	−0.962025	+	0.698952i
$339$		0			0
$340$		−	13.4651i		−	0.730247i
$341$	−4.99984	−	3.30125i	−0.270757	−	0.178773i
$342$		0			0
$343$	0.951057	+	0.309017i	0.0513522	+	0.0166853i
$344$	−4.27542	−	5.88461i	−0.230515	−	0.317277i
$345$		0			0
$346$	−2.45560	−	7.55757i	−0.132014	−	0.406298i
$347$	9.26084	+	28.5019i	0.497148	+	1.53006i	0.813582	+	0.581450i	$0.197514\pi$
$347$	9.26084	+	28.5019i	0.497148	+	1.53006i	−0.316435	+	0.948614i	$0.602486\pi$
$348$		0			0
$349$	19.2088	+	26.4387i	1.02822	+	1.41523i	0.906273	+	0.422693i	$0.138915\pi$
$349$	19.2088	+	26.4387i	1.02822	+	1.41523i	0.121951	+	0.992536i	$0.461085\pi$
$350$	1.77441	+	0.576541i	0.0948463	+	0.0308174i
$351$		0			0
$352$	0.882736	−	3.19700i	0.0470500	−	0.170400i
$353$			14.1629i			0.753817i	0.926250	+	0.376909i	$0.123013\pi$
$353$			14.1629i			0.753817i	−0.926250	+	0.376909i	$0.876987\pi$
$354$		0			0
$355$	12.2027	−	8.86579i	0.647653	−	0.470547i
$356$	−3.48563	+	4.79755i	−0.184738	+	0.254270i
$357$		0			0
$358$	21.4616	−	6.97330i	1.13428	−	0.368551i
$359$	17.7727	+	12.9126i	0.938005	+	0.681501i	0.947940	−	0.318450i	$-0.103162\pi$
$359$	17.7727	+	12.9126i	0.938005	+	0.681501i	−0.00993430	+	0.999951i	$0.503162\pi$
$360$		0			0
$361$	0.857265	−	2.63839i	0.0451192	−	0.138863i
$362$	−20.7157			−1.08879
$363$		0			0
$364$	5.90439			0.309474
$365$	5.63869	−	17.3541i	0.295143	−	0.908356i
$366$		0			0
$367$	17.3330	+	12.5932i	0.904776	+	0.657359i	0.939688	−	0.342032i	$-0.111115\pi$
$367$	17.3330	+	12.5932i	0.904776	+	0.657359i	−0.0349120	+	0.999390i	$0.511115\pi$
$368$	−5.05871	+	1.64367i	−0.263703	+	0.0856824i
$369$		0			0
$370$	−8.02781	+	11.0493i	−0.417346	+	0.574427i
$371$	8.41753	−	6.11570i	0.437017	−	0.317511i
$372$		0			0
$373$		−	12.4688i		−	0.645609i	−0.946466	−	0.322804i	$-0.895374\pi$
$373$		−	12.4688i		−	0.645609i	0.946466	−	0.322804i	$-0.104626\pi$
$374$	−6.71385	+	24.3155i	−0.347165	+	1.25732i
$375$		0			0
$376$	2.22379	+	0.722555i	0.114683	+	0.0372629i
$377$	−6.15615	−	8.47322i	−0.317058	−	0.436393i
$378$		0			0
$379$	−2.95365	−	9.09040i	−0.151719	−	0.466942i	0.846095	−	0.533032i	$-0.178948\pi$
$379$	−2.95365	−	9.09040i	−0.151719	−	0.466942i	−0.997814	+	0.0660900i	$0.978948\pi$
$380$	2.20371	+	6.78232i	0.113048	+	0.347926i
$381$		0			0
$382$	13.0063	+	17.9016i	0.665459	+	0.915926i
$383$	30.0796	+	9.77345i	1.53700	+	0.499400i	0.950546	−	0.310585i	$-0.100525\pi$
$383$	30.0796	+	9.77345i	1.53700	+	0.499400i	0.586450	+	0.809985i	$0.300525\pi$
$384$		0			0
$385$	4.89998	+	3.23531i	0.249726	+	0.164887i
$386$		−	23.2464i		−	1.18321i
$387$		0			0
$388$	4.95348	−	3.59891i	0.251475	−	0.182707i
$389$	−12.2106	+	16.8064i	−0.619101	+	0.852119i	−0.997287	−	0.0736106i	$-0.976548\pi$
$389$	−12.2106	+	16.8064i	−0.619101	+	0.852119i	0.378187	+	0.925729i	$0.376548\pi$
$390$		0			0
$391$	38.4751	−	12.5013i	1.94577	−	0.632219i
$392$	−0.809017	−	0.587785i	−0.0408615	−	0.0296876i
$393$		0			0
$394$	−5.68965	+	17.5109i	−0.286640	+	0.882188i
$395$	10.9652			0.551721
$396$		0			0
$397$	0.189938			0.00953270			0.00476635	−	0.999989i	$-0.498483\pi$
$397$	0.189938			0.00953270			0.00476635	+	0.999989i	$0.498483\pi$
$398$	5.61578	−	17.2836i	0.281493	−	0.866348i
$399$		0			0
$400$	−1.50940	−	1.09665i	−0.0754702	−	0.0548323i
$401$	−5.64724	+	1.83490i	−0.282010	+	0.0916305i	−0.446607	−	0.894730i	$-0.647368\pi$
$401$	−5.64724	+	1.83490i	−0.282010	+	0.0916305i	0.164597	+	0.986361i	$0.447368\pi$
$402$		0			0
$403$	−6.26938	+	8.62906i	−0.312300	+	0.429844i
$404$	10.9532	−	7.95797i	0.544942	−	0.395924i
$405$		0			0
$406$			1.77384i			0.0880344i
$407$	20.0061	−	15.9503i	0.991664	−	0.790627i
$408$		0			0
$409$	11.1080	+	3.60919i	0.549253	+	0.178463i	0.570480	−	0.821312i	$-0.306757\pi$
$409$	11.1080	+	3.60919i	0.549253	+	0.178463i	−0.0212268	+	0.999775i	$0.506757\pi$
$410$	7.31712	+	10.0712i	0.361367	+	0.497379i
$411$		0			0
$412$	1.73790	+	5.34870i	0.0856201	+	0.263511i
$413$	−3.13735	−	9.65578i	−0.154379	−	0.475130i
$414$		0			0
$415$	5.49906	+	7.56881i	0.269938	+	0.371538i
$416$	−5.61541	−	1.82456i	−0.275318	−	0.0894563i
$417$		0			0
$418$	−0.597750	−	13.3464i	−0.0292369	−	0.652795i
$419$			4.85503i			0.237184i	0.992943	+	0.118592i	$0.0378380\pi$
$419$			4.85503i			0.237184i	−0.992943	+	0.118592i	$0.962162\pi$
$420$		0			0
$421$	−7.84676	+	5.70100i	−0.382428	+	0.277850i	−0.762345	−	0.647170i	$-0.775952\pi$
$421$	−7.84676	+	5.70100i	−0.382428	+	0.277850i	0.379918	+	0.925020i	$0.375952\pi$
$422$	−2.06544	+	2.84284i	−0.100544	+	0.138387i
$423$		0			0
$424$	−9.89540	+	3.21521i	−0.480563	+	0.156144i
$425$	11.4801	+	8.34079i	0.556868	+	0.404588i
$426$		0			0
$427$	1.32009	−	4.06283i	0.0638837	−	0.196614i
$428$	−1.04331			−0.0504302
$429$		0			0
$430$	−12.8774			−0.621004
$431$	−1.69942	+	5.23027i	−0.0818581	+	0.251933i	−0.983607	−	0.180328i	$-0.942284\pi$
$431$	−1.69942	+	5.23027i	−0.0818581	+	0.251933i	0.901748	+	0.432261i	$0.142284\pi$
$432$		0			0
$433$	−0.0573287	−	0.0416517i	−0.00275504	−	0.00200165i	0.586407	−	0.810017i	$-0.300542\pi$
$433$	−0.0573287	−	0.0416517i	−0.00275504	−	0.00200165i	−0.589162	+	0.808015i	$0.700542\pi$
$434$	1.71805	−	0.558230i	0.0824693	−	0.0267959i
$435$		0			0
$436$	−4.12118	+	5.67231i	−0.197369	+	0.271655i
$437$	−17.3338	+	12.5938i	−0.829189	+	0.602441i
$438$		0			0
$439$		−	17.5467i		−	0.837461i	−0.908111	−	0.418730i	$-0.862475\pi$
$439$		−	17.5467i		−	0.837461i	0.908111	−	0.418730i	$-0.137525\pi$
$440$	−3.66039	−	4.59114i	−0.174502	−	0.218874i
$441$		0			0
$442$	42.7093	+	13.8771i	2.03147	+	0.660066i
$443$	−22.8566	−	31.4594i	−1.08595	−	1.49468i	−0.852798	−	0.522240i	$-0.825096\pi$
$443$	−22.8566	−	31.4594i	−1.08595	−	1.49468i	−0.233151	−	0.972441i	$-0.574904\pi$
$444$		0			0
$445$	3.24424	+	9.98474i	0.153792	+	0.473322i
$446$	−2.22501	−	6.84787i	−0.105357	−	0.324256i
$447$		0			0
$448$	0.587785	+	0.809017i	0.0277702	+	0.0382225i
$449$	−15.4407	−	5.01700i	−0.728693	−	0.236767i	−0.0789050	−	0.996882i	$-0.525142\pi$
$449$	−15.4407	−	5.01700i	−0.728693	−	0.236767i	−0.649788	+	0.760115i	$0.725142\pi$
$450$		0			0
$451$	−8.19178	−	21.8350i	−0.385736	−	1.02817i
$452$		−	8.87461i		−	0.417426i
$453$		0			0
$454$	2.43006	−	1.76554i	0.114048	−	0.0828610i
$455$	6.14416	−	8.45671i	0.288043	−	0.396457i
$456$		0			0
$457$	2.85698	−	0.928288i	0.133644	−	0.0434235i	−0.241431	−	0.970418i	$-0.577617\pi$
$457$	2.85698	−	0.928288i	0.133644	−	0.0434235i	0.375075	+	0.926994i	$0.377617\pi$
$458$	13.9731	+	10.1520i	0.652918	+	0.474373i
$459$		0			0
$460$	−2.90994	+	8.95587i	−0.135677	+	0.417570i
$461$	1.37050			0.0638304			0.0319152	−	0.999491i	$-0.489839\pi$
$461$	1.37050			0.0638304			0.0319152	+	0.999491i	$0.489839\pi$
$462$		0			0
$463$	39.0298			1.81387			0.906933	−	0.421274i	$-0.138417\pi$
$463$	39.0298			1.81387			0.906933	+	0.421274i	$0.138417\pi$
$464$	0.548148	−	1.68703i	0.0254471	−	0.0783182i
$465$		0			0
$466$	−4.77999	−	3.47287i	−0.221429	−	0.160878i
$467$	−0.619895	+	0.201416i	−0.0286853	+	0.00932043i	−0.323325	−	0.946288i	$-0.604801\pi$
$467$	−0.619895	+	0.201416i	−0.0286853	+	0.00932043i	0.294639	+	0.955609i	$0.404801\pi$
$468$		0			0
$469$	−4.45079	+	6.12599i	−0.205518	+	0.282872i
$470$	3.34899	−	2.43319i	0.154478	−	0.112235i
$471$		0			0
$472$			10.1527i			0.467315i
$473$	23.2542	+	6.42083i	1.06923	+	0.295230i
$474$		0			0
$475$	−7.14756	−	2.32238i	−0.327952	−	0.106558i
$476$	−4.47053	−	6.15316i	−0.204907	−	0.282030i
$477$		0			0
$478$	3.94381	+	12.1378i	0.180386	+	0.555171i
$479$	8.84635	+	27.2263i	0.404200	+	1.24400i	0.921562	+	0.388232i	$0.126914\pi$
$479$	8.84635	+	27.2263i	0.404200	+	1.24400i	−0.517362	+	0.855767i	$0.673086\pi$
$480$		0			0
$481$	−26.7734	−	36.8505i	−1.22076	−	1.68024i
$482$	17.5652	+	5.70729i	0.800075	+	0.259960i
$483$		0			0
$484$	4.32080	+	10.1159i	0.196400	+	0.459812i
$485$		−	10.8398i		−	0.492210i
$486$		0			0
$487$	27.1551	−	19.7294i	1.23052	−	0.894023i	0.233588	−	0.972336i	$-0.424953\pi$
$487$	27.1551	−	19.7294i	1.23052	−	0.894023i	0.996929	+	0.0783132i	$0.0249534\pi$
$488$	−2.51096	+	3.45605i	−0.113666	+	0.156448i
$489$		0			0
$490$	−1.68374	+	0.547080i	−0.0760636	+	0.0247146i
$491$	−10.5153	−	7.63978i	−0.474547	−	0.344779i	0.324664	−	0.945830i	$-0.394749\pi$
$491$	−10.5153	−	7.63978i	−0.474547	−	0.344779i	−0.799211	+	0.601051i	$0.794749\pi$
$492$		0			0
$493$	−4.16907	+	12.8311i	−0.187765	+	0.577882i
$494$	−23.7837			−1.07008
$495$		0			0
$496$	−1.80647			−0.0811129
$497$	2.63277	−	8.10283i	0.118096	−	0.363461i
$498$		0			0
$499$	−28.1430	−	20.4471i	−1.25985	−	0.915336i	−0.261101	−	0.965311i	$-0.584086\pi$
$499$	−28.1430	−	20.4471i	−1.25985	−	0.915336i	−0.998750	+	0.0499757i	$0.984086\pi$
$500$	−11.5601	+	3.75610i	−0.516983	+	0.167978i
$501$		0			0
$502$	−17.3540	+	23.8858i	−0.774549	+	1.06608i
$503$	2.02753	−	1.47308i	0.0904029	−	0.0656815i	−0.541666	−	0.840594i	$-0.682206\pi$
$503$	2.02753	−	1.47308i	0.0904029	−	0.0656815i	0.632069	+	0.774912i	$0.282206\pi$
$504$		0			0
$505$		−	23.9691i		−	1.06661i
$506$	9.72032	−	14.7217i	0.432121	−	0.654461i
$507$		0			0
$508$	0.251687	+	0.0817782i	0.0111668	+	0.00362832i
$509$	−5.85706	−	8.06156i	−0.259610	−	0.357322i	0.659238	−	0.751934i	$-0.270879\pi$
$509$	−5.85706	−	8.06156i	−0.259610	−	0.357322i	−0.918848	+	0.394612i	$0.870879\pi$
$510$		0			0
$511$	−3.18500	−	9.80244i	−0.140896	−	0.433634i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$		0			0
$514$	−0.904272	−	1.24462i	−0.0398857	−	0.0548980i
$515$	9.46927	+	3.07675i	0.417266	+	0.135578i
$516$		0			0
$517$	−7.26088	+	2.72404i	−0.319333	+	0.119803i
$518$			7.71454i			0.338957i
$519$		0			0
$520$	−8.45671	+	6.14416i	−0.370851	+	0.269439i
$521$	5.16252	−	7.10560i	0.226174	−	0.311302i	−0.680815	−	0.732455i	$-0.738374\pi$
$521$	5.16252	−	7.10560i	0.226174	−	0.311302i	0.906990	+	0.421153i	$0.138374\pi$
$522$		0			0
$523$	−32.4604	+	10.5470i	−1.41940	+	0.461190i	−0.915410	−	0.402522i	$-0.868134\pi$
$523$	−32.4604	+	10.5470i	−1.41940	+	0.461190i	−0.503986	+	0.863712i	$0.668134\pi$
$524$	6.00640	+	4.36390i	0.262391	+	0.190638i
$525$		0			0
$526$	−1.40970	+	4.33861i	−0.0614658	+	0.189172i
$527$	13.7395			0.598503
$528$		0			0
$529$	−5.29216			−0.230094
$530$	−5.69217	+	17.5187i	−0.247252	+	0.760964i
$531$		0			0
$532$	3.25883	+	2.36768i	0.141288	+	0.102652i
$533$	−39.4852	+	12.8295i	−1.71030	+	0.555709i
$534$		0			0
$535$	−1.08567	+	1.49430i	−0.0469378	+	0.0646044i
$536$	6.12599	−	4.45079i	0.264602	−	0.192245i
$537$		0			0
$538$		−	8.31988i		−	0.358695i
$539$	3.31330	−	0.148394i	0.142714	−	0.00639178i
$540$		0			0
$541$	−38.3744	−	12.4686i	−1.64985	−	0.536067i	−0.671139	−	0.741331i	$-0.734195\pi$
$541$	−38.3744	−	12.4686i	−1.64985	−	0.536067i	−0.978707	+	0.205264i	$0.934195\pi$
$542$	−11.5277	−	15.8666i	−0.495159	−	0.681528i
$543$		0			0
$544$	2.35030	+	7.23348i	0.100768	+	0.310133i
$545$	3.83578	+	11.8053i	0.164307	+	0.505684i
$546$		0			0
$547$	−2.38012	−	3.27596i	−0.101767	−	0.140070i	0.755097	−	0.655614i	$-0.227590\pi$
$547$	−2.38012	−	3.27596i	−0.101767	−	0.140070i	−0.856863	+	0.515544i	$0.827590\pi$
$548$	−18.3467	−	5.96122i	−0.783734	−	0.254651i
$549$		0			0
$550$	6.18172	−	0.276862i	0.263589	−	0.0118055i
$551$		−	7.14528i		−	0.304399i
$552$		0			0
$553$	5.01080	−	3.64056i	0.213081	−	0.154812i
$554$	−16.5682	+	22.8042i	−0.703916	+	0.968857i
$555$		0			0
$556$	−12.8309	+	4.16901i	−0.544151	+	0.176805i
$557$	−20.1013	−	14.6044i	−0.851718	−	0.618809i	0.0739014	−	0.997266i	$-0.476455\pi$
$557$	−20.1013	−	14.6044i	−0.851718	−	0.618809i	−0.925619	+	0.378456i	$0.876455\pi$
$558$		0			0
$559$	13.2714	−	40.8453i	0.561322	−	1.72757i
$560$	1.77039			0.0748125
$561$		0			0
$562$	13.1120			0.553097
$563$	−11.9456	+	36.7647i	−0.503447	+	1.54945i	0.299920	+	0.953964i	$0.403040\pi$
$563$	−11.9456	+	36.7647i	−0.503447	+	1.54945i	−0.803367	+	0.595485i	$0.796960\pi$
$564$		0			0
$565$	−12.7109	−	9.23499i	−0.534750	−	0.388519i
$566$	14.1487	−	4.59719i	0.594714	−	0.193234i
$567$		0			0
$568$	−5.00782	+	6.89268i	−0.210124	+	0.289210i
$569$	−29.9338	+	21.7482i	−1.25489	+	0.911731i	−0.998495	−	0.0548409i	$-0.982535\pi$
$569$	−29.9338	+	21.7482i	−1.25489	+	0.911731i	−0.256395	+	0.966572i	$0.582535\pi$
$570$		0			0
$571$		−	12.6501i		−	0.529392i	−0.964332	−	0.264696i	$-0.914728\pi$
$571$		−	12.6501i		−	0.529392i	0.964332	−	0.264696i	$-0.0852716\pi$
$572$	18.3348	−	6.87861i	0.766617	−	0.287609i
$573$		0			0
$574$	6.68743	+	2.17288i	0.279128	+	0.0906942i
$575$	−5.83310	−	8.02858i	−0.243257	−	0.334815i
$576$		0			0
$577$	−9.60131	−	29.5498i	−0.399708	−	1.23017i	−0.925234	−	0.379397i	$-0.876132\pi$
$577$	−9.60131	−	29.5498i	−0.399708	−	1.23017i	0.525526	−	0.850777i	$-0.323868\pi$
$578$	−12.6224	−	38.8479i	−0.525025	−	1.61586i
$579$		0			0
$580$	−1.84588	−	2.54063i	−0.0766459	−	0.105494i
$581$	5.02583	+	1.63299i	0.208506	+	0.0677479i
$582$		0			0
$583$	19.0140	−	28.7974i	0.787481	−	1.19267i
$584$			10.3069i			0.426502i
$585$		0			0
$586$	2.72214	−	1.97775i	0.112451	−	0.0817001i
$587$	5.68248	−	7.82127i	0.234541	−	0.322818i	−0.675481	−	0.737377i	$-0.736064\pi$
$587$	5.68248	−	7.82127i	0.234541	−	0.322818i	0.910023	+	0.414559i	$0.136064\pi$
$588$		0			0
$589$	−6.92055	+	2.24862i	−0.285156	+	0.0926529i
$590$	14.5414	+	10.5650i	0.598661	+	0.434953i
$591$		0			0
$592$	2.38392	−	7.33696i	0.0979787	−	0.301547i
$593$	16.4851			0.676960			0.338480	−	0.940974i	$-0.390087\pi$
$593$	16.4851			0.676960			0.338480	+	0.940974i	$0.390087\pi$
$594$		0			0
$595$	−13.4651			−0.552015
$596$	4.33452	−	13.3403i	0.177549	−	0.546439i
$597$		0			0
$598$	−25.4077	−	18.4598i	−1.03900	−	0.754877i
$599$	43.0406	−	13.9847i	1.75859	−	0.571401i	0.761539	−	0.648119i	$-0.224444\pi$
$599$	43.0406	−	13.9847i	1.75859	−	0.571401i	0.997053	+	0.0767180i	$0.0244441\pi$
$600$		0			0
$601$	−14.5593	+	20.0392i	−0.593887	+	0.817416i	−0.995132	−	0.0985552i	$-0.968578\pi$
$601$	−14.5593	+	20.0392i	−0.593887	+	0.817416i	0.401244	+	0.915971i	$0.368578\pi$
$602$	−5.88461	+	4.27542i	−0.239839	+	0.174253i
$603$		0			0
$604$		−	16.8424i		−	0.685307i
$605$	18.9849	+	4.33808i	0.771848	+	0.176368i
$606$		0			0
$607$	35.5163	+	11.5399i	1.44156	+	0.468392i	0.922384	−	0.386274i	$-0.126238\pi$
$607$	35.5163	+	11.5399i	1.44156	+	0.468392i	0.519178	+	0.854666i	$0.326238\pi$
$608$	−2.36768	−	3.25883i	−0.0960219	−	0.132163i
$609$		0			0
$610$	2.33708	+	7.19278i	0.0946254	+	0.291227i
$611$	4.26625	+	13.1302i	0.172594	+	0.531189i
$612$		0			0
$613$	13.8063	+	19.0027i	0.557631	+	0.767514i	0.991023	−	0.133692i	$-0.0426833\pi$
$613$	13.8063	+	19.0027i	0.557631	+	0.767514i	−0.433392	+	0.901206i	$0.642683\pi$
$614$	−27.2775	−	8.86301i	−1.10083	−	0.357682i
$615$		0			0
$616$	−3.19700	−	0.882736i	−0.128811	−	0.0355664i
$617$		−	13.5768i		−	0.546580i	−0.961932	−	0.273290i	$-0.911888\pi$
$617$		−	13.5768i		−	0.546580i	0.961932	−	0.273290i	$-0.0881119\pi$
$618$		0			0
$619$	−31.3288	+	22.7617i	−1.25921	+	0.914869i	−0.998719	−	0.0506068i	$-0.983884\pi$
$619$	−31.3288	+	22.7617i	−1.25921	+	0.914869i	−0.260491	+	0.965476i	$0.583884\pi$
$620$	−1.87983	+	2.58736i	−0.0754957	+	0.103911i
$621$		0			0
$622$	−9.17717	+	2.98184i	−0.367971	+	0.119561i
$623$	4.79755	+	3.48563i	0.192210	+	0.139649i
$624$		0			0
$625$	−3.76705	+	11.5938i	−0.150682	+	0.463752i
$626$	−18.5421			−0.741090
$627$		0			0
$628$	18.7564			0.748460
$629$	−18.1315	+	55.8029i	−0.722949	+	2.22501i
$630$		0			0
$631$	−9.16771	−	6.66073i	−0.364961	−	0.265159i	0.390158	−	0.920748i	$-0.372421\pi$
$631$	−9.16771	−	6.66073i	−0.364961	−	0.265159i	−0.755118	+	0.655589i	$0.772421\pi$
$632$	−5.89055	+	1.91396i	−0.234313	+	0.0761331i
$633$		0			0
$634$	2.03309	−	2.79831i	0.0807444	−	0.111135i
$635$	0.379037	−	0.275386i	0.0150416	−	0.0109284i
$636$		0			0
$637$		−	5.90439i		−	0.233941i
$638$	2.06653	+	5.50829i	0.0818145	+	0.218075i
$639$		0			0
$640$	−1.68374	−	0.547080i	−0.0665556	−	0.0216252i
$641$	−8.06465	−	11.1000i	−0.318535	−	0.438425i	0.619485	−	0.785009i	$-0.287342\pi$
$641$	−8.06465	−	11.1000i	−0.318535	−	0.438425i	−0.938019	+	0.346584i	$0.887342\pi$
$642$		0			0
$643$	3.55638	+	10.9454i	0.140250	+	0.431645i	0.996370	−	0.0851324i	$-0.0271313\pi$
$643$	3.55638	+	10.9454i	0.140250	+	0.431645i	−0.856120	+	0.516778i	$0.827131\pi$
$644$	1.64367	+	5.05871i	0.0647698	+	0.199341i
$645$		0			0
$646$	18.0079	+	24.7857i	0.708511	+	0.975182i
$647$	0.422199	+	0.137181i	0.0165984	+	0.00539313i	0.317304	−	0.948324i	$-0.397222\pi$
$647$	0.422199	+	0.137181i	0.0165984	+	0.00539313i	−0.300706	+	0.953717i	$0.597222\pi$
$648$		0			0
$649$	−20.9913	−	26.3289i	−0.823982	−	1.03350i
$650$		−	11.0160i		−	0.432082i
$651$		0			0
$652$	−5.08155	+	3.69196i	−0.199009	+	0.144588i
$653$	18.5462	−	25.5267i	0.725769	−	0.998936i	−0.273543	−	0.961860i	$-0.588196\pi$
$653$	18.5462	−	25.5267i	0.725769	−	0.998936i	0.999312	−	0.0370758i	$-0.0118043\pi$
$654$		0			0
$655$	12.5006	−	4.06169i	0.488439	−	0.158703i
$656$	−5.68867	−	4.13306i	−0.222105	−	0.161369i
$657$		0			0
$658$	0.722555	−	2.22379i	0.0281681	−	0.0866925i
$659$	30.5337			1.18942			0.594712	−	0.803939i	$-0.297266\pi$
$659$	30.5337			1.18942			0.594712	+	0.803939i	$0.297266\pi$
$660$		0			0
$661$	17.6757			0.687504			0.343752	−	0.939061i	$-0.388302\pi$
$661$	17.6757			0.687504			0.343752	+	0.939061i	$0.388302\pi$
$662$	3.55913	−	10.9539i	0.138330	−	0.425734i
$663$		0			0
$664$	−4.27522	−	3.10613i	−0.165911	−	0.120541i
$665$	6.78232	−	2.20371i	0.263007	−	0.0854562i
$666$		0			0
$667$	5.54584	−	7.63319i	0.214736	−	0.295558i
$668$	1.40213	−	1.01871i	0.0542501	−	0.0394150i
$669$		0			0
$670$		−	13.4056i		−	0.517904i
$671$	−0.633925	−	14.1541i	−0.0244724	−	0.546414i
$672$		0			0
$673$	18.7712	+	6.09914i	0.723578	+	0.235105i	0.647574	−	0.762003i	$-0.275784\pi$
$673$	18.7712	+	6.09914i	0.723578	+	0.235105i	0.0760042	+	0.997107i	$0.475784\pi$
$674$	−16.6034	−	22.8527i	−0.639540	−	0.880252i
$675$		0			0
$676$	−6.75569	−	20.7919i	−0.259834	−	0.799687i
$677$	−7.62616	−	23.4709i	−0.293097	−	0.902060i	−0.983854	−	0.178973i	$-0.942722\pi$
$677$	−7.62616	−	23.4709i	−0.293097	−	0.902060i	0.690757	−	0.723087i	$-0.257278\pi$
$678$		0			0
$679$	−3.59891	−	4.95348i	−0.138114	−	0.190097i
$680$	12.8061	+	4.16094i	0.491090	+	0.159565i
$681$		0			0
$682$	4.68471	−	3.73499i	0.179387	−	0.143020i
$683$		−	7.78423i		−	0.297855i	−0.988848	−	0.148928i	$-0.952418\pi$
$683$		−	7.78423i		−	0.297855i	0.988848	−	0.148928i	$-0.0475822\pi$
$684$		0			0
$685$	−27.6299	+	20.0743i	−1.05568	+	0.766998i
$686$	−0.587785	+	0.809017i	−0.0224417	+	0.0308884i
$687$		0			0
$688$	6.91777	−	2.24772i	0.263738	−	0.0856936i
$689$	−49.7004	−	36.1095i	−1.89344	−	1.37566i
$690$		0			0
$691$	2.57712	−	7.93156i	0.0980382	−	0.301731i	−0.889995	−	0.455970i	$-0.849293\pi$
$691$	2.57712	−	7.93156i	0.0980382	−	0.301731i	0.988034	+	0.154239i	$0.0492926\pi$
$692$	7.94650			0.302081
$693$		0			0
$694$	−29.9687			−1.13760
$695$	−7.38076	+	22.7156i	−0.279968	+	0.861654i
$696$		0			0
$697$	43.2665	+	31.4349i	1.63883	+	1.19068i
$698$	−31.0805	+	10.0987i	−1.17641	+	0.382240i
$699$		0			0
$700$	−1.09665	+	1.50940i	−0.0414493	+	0.0570501i
$701$	−9.69695	+	7.04525i	−0.366249	+	0.266095i	−0.755654	−	0.654971i	$-0.772681\pi$
$701$	−9.69695	+	7.04525i	−0.366249	+	0.266095i	0.389405	+	0.921067i	$0.372681\pi$
$702$		0			0
$703$		−	31.0752i		−	1.17202i
$704$	2.76774	+	1.82746i	0.104313	+	0.0688749i
$705$		0			0
$706$	−13.4698	−	4.37659i	−0.506941	−	0.164715i
$707$	−7.95797	−	10.9532i	−0.299290	−	0.411938i
$708$		0			0
$709$	−15.2246	−	46.8566i	−0.571773	−	1.75974i	−0.646912	−	0.762564i	$-0.723940\pi$
$709$	−15.2246	−	46.8566i	−0.571773	−	1.75974i	0.0751392	−	0.997173i	$-0.476060\pi$
$710$	4.66102	+	14.3451i	0.174925	+	0.538364i
$711$		0			0
$712$	−3.48563	−	4.79755i	−0.130629	−	0.179796i
$713$	−9.13840	−	2.96925i	−0.342236	−	0.111199i
$714$		0			0
$715$	9.22730	−	33.4184i	0.345081	−	1.24978i
$716$			22.5661i			0.843334i
$717$		0			0
$718$	−17.7727	+	12.9126i	−0.663270	+	0.481894i
$719$	16.5840	−	22.8259i	0.618479	−	0.851264i	−0.378762	−	0.925494i	$-0.623650\pi$
$719$	16.5840	−	22.8259i	0.618479	−	0.851264i	0.997241	+	0.0742305i	$0.0236500\pi$
$720$		0			0
$721$	5.34870	−	1.73790i	0.199196	−	0.0647227i
$722$	2.24435	+	1.63061i	0.0835260	+	0.0606852i
$723$		0			0
$724$	6.40149	−	19.7018i	0.237910	−	0.732210i
$725$	3.30951			0.122912
$726$		0			0
$727$	−11.3195			−0.419819			−0.209909	−	0.977721i	$-0.567317\pi$
$727$	−11.3195			−0.419819			−0.209909	+	0.977721i	$0.567317\pi$
$728$	−1.82456	+	5.61541i	−0.0676226	+	0.208121i
$729$		0			0
$730$	14.7623	+	10.7254i	0.546377	+	0.396966i
$731$	−52.6147	+	17.0956i	−1.94603	+	0.632302i
$732$		0			0
$733$	−7.20025	+	9.91030i	−0.265947	+	0.366045i	−0.921016	−	0.389524i	$-0.872640\pi$
$733$	−7.20025	+	9.91030i	−0.265947	+	0.366045i	0.655069	+	0.755569i	$0.272640\pi$
$734$	−17.3330	+	12.5932i	−0.639774	+	0.464823i
$735$		0			0
$736$		−	5.31904i		−	0.196062i
$737$	−6.68420	+	24.2081i	−0.246216	+	0.891716i
$738$		0			0
$739$	−10.9561	−	3.55986i	−0.403028	−	0.130952i	0.100487	−	0.994938i	$-0.467960\pi$
$739$	−10.9561	−	3.55986i	−0.403028	−	0.130952i	−0.503515	+	0.863987i	$0.667960\pi$
$740$	−8.02781	−	11.0493i	−0.295108	−	0.406182i
$741$		0			0
$742$	3.21521	+	9.89540i	0.118034	+	0.363272i
$743$	12.5933	+	38.7582i	0.462004	+	1.42190i	0.862712	+	0.505696i	$0.168764\pi$
$743$	12.5933	+	38.7582i	0.462004	+	1.42190i	−0.400708	+	0.916206i	$0.631236\pi$
$744$		0			0
$745$	−14.5964	−	20.0902i	−0.534771	−	0.736049i
$746$	11.8585	+	3.85306i	0.434171	+	0.141071i
$747$		0			0
$748$	−21.0507	−	13.8991i	−0.769690	−	0.508203i
$749$			1.04331i			0.0381216i
$750$		0			0
$751$	−5.30474	+	3.85412i	−0.193573	+	0.140639i	−0.680350	−	0.732887i	$-0.738172\pi$
$751$	−5.30474	+	3.85412i	−0.193573	+	0.140639i	0.486777	+	0.873526i	$0.338172\pi$
$752$	−1.37438	+	1.89167i	−0.0501185	+	0.0689822i
$753$		0			0
$754$	9.96087	−	3.23648i	0.362753	−	0.117866i
$755$	−24.1229	−	17.5263i	−0.877923	−	0.637848i
$756$		0			0
$757$	2.83843	−	8.73578i	0.103164	−	0.317507i	−0.886131	−	0.463435i	$-0.846617\pi$
$757$	2.83843	−	8.73578i	0.103164	−	0.317507i	0.989295	+	0.145928i	$0.0466167\pi$
$758$	9.55821			0.347170
$759$		0			0
$760$	−7.13135			−0.258681
$761$	−1.67453	+	5.15367i	−0.0607016	+	0.186820i	−0.976809	−	0.214113i	$-0.931314\pi$
$761$	−1.67453	+	5.15367i	−0.0607016	+	0.186820i	0.916107	+	0.400933i	$0.131314\pi$
$762$		0			0
$763$	5.67231	+	4.12118i	0.205352	+	0.149197i
$764$	−21.0446	+	6.83780i	−0.761367	+	0.247383i
$765$		0			0
$766$	−18.5902	+	25.5872i	−0.671692	+	0.924504i
$767$	−48.4969	+	35.2351i	−1.75112	+	1.27226i
$768$		0			0
$769$		−	46.1487i		−	1.66417i	−0.554651	−	0.832083i	$-0.687148\pi$
$769$		−	46.1487i		−	1.66417i	0.554651	−	0.832083i	$-0.312852\pi$
$770$	−4.59114	+	3.66039i	−0.165453	+	0.131911i
$771$		0			0
$772$	22.1086	+	7.18352i	0.795706	+	0.258541i
$773$	28.1412	+	38.7330i	1.01217	+	1.39313i	0.917553	+	0.397614i	$0.130162\pi$
$773$	28.1412	+	38.7330i	1.01217	+	1.39313i	0.0946141	+	0.995514i	$0.469838\pi$
$774$		0			0
$775$	−1.04150	−	3.20542i	−0.0374119	−	0.115142i
$776$	1.89206	+	5.82316i	0.0679210	+	0.209039i
$777$		0			0
$778$	−12.2106	−	16.8064i	−0.437770	−	0.602539i
$779$	−26.9378	−	8.75264i	−0.965148	−	0.313596i
$780$		0			0
$781$	−1.26429	−	28.2287i	−0.0452398	−	1.01010i
$782$			40.4552i			1.44667i
$783$		0			0
$784$	0.809017	−	0.587785i	0.0288935	−	0.0209923i
$785$	19.5180	−	26.8642i	0.696628	−	0.958826i
$786$		0			0
$787$	−12.5278	+	4.07051i	−0.446566	+	0.145098i	−0.523663	−	0.851925i	$-0.675435\pi$
$787$	−12.5278	+	4.07051i	−0.446566	+	0.145098i	0.0770969	+	0.997024i	$0.475435\pi$
$788$	−14.8957	−	10.8224i	−0.530637	−	0.385531i
$789$		0			0
$790$	−3.38844	+	10.4286i	−0.120555	+	0.371031i
$791$	−8.87461			−0.315545
$792$		0			0
$793$	−25.2230			−0.895696
$794$	−0.0586940	+	0.180642i	−0.00208297	+	0.00641073i
$795$		0			0
$796$	14.7023	+	10.6818i	0.521109	+	0.378608i
$797$	9.69949	−	3.15156i	0.343574	−	0.111634i	−0.132147	−	0.991230i	$-0.542187\pi$
$797$	9.69949	−	3.15156i	0.343574	−	0.111634i	0.475721	+	0.879596i	$0.342187\pi$
$798$		0			0
$799$	10.4532	−	14.3875i	0.369806	−	0.508995i
$800$	1.50940	−	1.09665i	0.0533655	−	0.0387723i
$801$		0			0
$802$		−	5.93786i		−	0.209673i
$803$	−21.3102	−	26.7288i	−0.752019	−	0.943239i
$804$		0			0
$805$	8.95587	+	2.90994i	0.315653	+	0.102562i
$806$	−6.26938	−	8.62906i	−0.220829	−	0.303946i
$807$		0			0
$808$	4.18375	+	12.8763i	0.147184	+	0.452985i
$809$	6.22410	+	19.1558i	0.218828	+	0.673483i	0.998860	+	0.0477430i	$0.0152028\pi$
$809$	6.22410	+	19.1558i	0.218828	+	0.673483i	−0.780032	+	0.625740i	$0.784797\pi$
$810$		0			0
$811$	4.16824	+	5.73709i	0.146367	+	0.201456i	0.875905	−	0.482483i	$-0.160265\pi$
$811$	4.16824	+	5.73709i	0.146367	+	0.201456i	−0.729538	+	0.683940i	$0.760265\pi$
$812$	−1.68703	−	0.548148i	−0.0592030	−	0.0192362i
$813$		0			0
$814$	8.98742	+	23.9558i	0.315009	+	0.839651i
$815$			11.1201i			0.389518i
$816$		0			0
$817$	23.7040	−	17.2219i	0.829297	−	0.602520i
$818$	−6.86510	+	9.44899i	−0.240032	+	0.330376i
$819$		0			0
$820$	−11.8393	+	3.84684i	−0.413448	+	0.134337i
$821$	45.9083	+	33.3543i	1.60221	+	1.16407i	0.883109	+	0.469169i	$0.155446\pi$
$821$	45.9083	+	33.3543i	1.60221	+	1.16407i	0.719101	+	0.694905i	$0.244554\pi$
$822$		0			0
$823$	6.04720	−	18.6114i	0.210792	−	0.648752i	−0.788633	−	0.614864i	$-0.789211\pi$
$823$	6.04720	−	18.6114i	0.210792	−	0.648752i	0.999426	−	0.0338880i	$-0.0107889\pi$
$824$	−5.62395			−0.195920
$825$		0			0
$826$	10.1527			0.353257
$827$	8.70129	−	26.7798i	0.302574	−	0.931226i	−0.677998	−	0.735064i	$-0.737152\pi$
$827$	8.70129	−	26.7798i	0.302574	−	0.931226i	0.980571	−	0.196162i	$-0.0628479\pi$
$828$		0			0
$829$	−23.1512	−	16.8203i	−0.804075	−	0.584195i	0.108032	−	0.994147i	$-0.465545\pi$
$829$	−23.1512	−	16.8203i	−0.804075	−	0.584195i	−0.912107	+	0.409953i	$0.865545\pi$
$830$	−8.89767	+	2.89103i	−0.308843	+	0.100349i
$831$		0			0
$832$	3.47052	−	4.77675i	0.120318	−	0.165604i
$833$	−6.15316	+	4.47053i	−0.213194	+	0.154895i
$834$		0			0
$835$		−	3.06831i		−	0.106183i
$836$	12.8779	+	3.55578i	0.445392	+	0.122979i
$837$		0			0
$838$	−4.61741	−	1.50029i	−0.159506	−	0.0518265i
$839$	19.6905	+	27.1017i	0.679792	+	0.935653i	0.999931	−	0.0117171i	$-0.00372975\pi$
$839$	19.6905	+	27.1017i	0.679792	+	0.935653i	−0.320139	+	0.947370i	$0.603730\pi$
$840$		0			0
$841$	−7.98916	−	24.5881i	−0.275488	−	0.847866i
$842$	−2.99720	−	9.22442i	−0.103290	−	0.317894i
$843$		0			0
$844$	−2.06544	−	2.84284i	−0.0710954	−	0.0978544i
$845$	−36.8097	−	11.9602i	−1.26629	−	0.411443i
$846$		0			0
$847$	10.1159	−	4.32080i	0.347585	−	0.148464i
$848$		−	10.4046i		−	0.357297i
$849$		0			0
$850$	−11.4801	+	8.34079i	−0.393765	+	0.286087i
$851$	24.1191	−	33.1971i	0.826793	−	1.13798i
$852$		0			0
$853$	16.6480	−	5.40927i	0.570018	−	0.185210i	−0.00980614	−	0.999952i	$-0.503121\pi$
$853$	16.6480	−	5.40927i	0.570018	−	0.185210i	0.579824	+	0.814742i	$0.303121\pi$
$854$	3.45605	+	2.51096i	0.118263	+	0.0859234i
$855$		0			0
$856$	0.322400	−	0.992245i	0.0110194	−	0.0339142i
$857$	9.41950			0.321764			0.160882	−	0.986974i	$-0.448566\pi$
$857$	9.41950			0.321764			0.160882	+	0.986974i	$0.448566\pi$
$858$		0			0
$859$	−52.7706			−1.80051			−0.900255	−	0.435363i	$-0.856620\pi$
$859$	−52.7706			−1.80051			−0.900255	+	0.435363i	$0.856620\pi$
$860$	3.97934	−	12.2471i	0.135694	−	0.417624i
$861$		0			0
$862$	−4.44913	−	3.23249i	−0.151538	−	0.110099i
$863$	1.60965	−	0.523005i	0.0547930	−	0.0178033i	−0.281492	−	0.959563i	$-0.590829\pi$
$863$	1.60965	−	0.523005i	0.0547930	−	0.0178033i	0.336285	+	0.941760i	$0.390829\pi$
$864$		0			0
$865$	8.26919	−	11.3816i	0.281161	−	0.386985i
$866$	0.0573287	−	0.0416517i	0.00194811	−	0.00141538i
$867$		0			0
$868$			1.80647i			0.0613156i
$869$	11.3187	−	17.1425i	0.383961	−	0.581521i
$870$		0			0
$871$	42.5207	+	13.8158i	1.44076	+	0.468130i
$872$	−4.12118	−	5.67231i	−0.139561	−	0.192089i
$873$		0			0
$874$	−6.62093	−	20.3771i	−0.223956	−	0.689267i
$875$	3.75610	+	11.5601i	0.126979	+	0.390802i
$876$		0			0
$877$	−8.62801	−	11.8754i	−0.291347	−	0.401005i	0.638104	−	0.769950i	$-0.279719\pi$
$877$	−8.62801	−	11.8754i	−0.291347	−	0.401005i	−0.929451	+	0.368945i	$0.879719\pi$
$878$	16.6879	+	5.42224i	0.563191	+	0.182992i
$879$		0			0
$880$	5.49756	−	2.06250i	0.185323	−	0.0695268i
$881$		−	27.0639i		−	0.911805i	−0.890030	−	0.455902i	$-0.849317\pi$
$881$		−	27.0639i		−	0.911805i	0.890030	−	0.455902i	$-0.150683\pi$
$882$		0			0
$883$	−21.4742	+	15.6019i	−0.722663	+	0.525045i	−0.887234	−	0.461320i	$-0.847376\pi$
$883$	−21.4742	+	15.6019i	−0.722663	+	0.525045i	0.164571	+	0.986365i	$0.447376\pi$
$884$	−26.3958	+	36.3307i	−0.887787	+	1.22193i
$885$		0			0
$886$	36.9827	−	12.0164i	1.24246	−	0.403700i
$887$	7.55079	+	5.48597i	0.253531	+	0.184201i	0.707290	−	0.706923i	$-0.249917\pi$
$887$	7.55079	+	5.48597i	0.253531	+	0.184201i	−0.453759	+	0.891124i	$0.649917\pi$
$888$		0			0
$889$	0.0817782	−	0.251687i	0.00274275	−	0.00844132i
$890$	−10.4986			−0.351913
$891$		0			0
$892$	7.20027			0.241083
$893$	−2.91054	+	8.95773i	−0.0973976	+	0.299759i
$894$		0			0
$895$	32.3208	+	23.4825i	1.08037	+	0.784932i
$896$	−0.951057	+	0.309017i	−0.0317726	+	0.0103235i
$897$		0			0
$898$	9.54290	−	13.1347i	0.318451	−	0.438310i
$899$	2.59241	−	1.88350i	0.0864617	−	0.0628181i
$900$		0			0
$901$			79.1349i			2.63637i
$902$	23.2978	−	1.04344i	0.775731	−	0.0347429i
$903$		0			0
$904$	8.44025	+	2.74240i	0.280719	+	0.0912110i
$905$	−21.5569	−	29.6705i	−0.716575	−	0.986281i
$906$		0			0
$907$	3.46960	+	10.6783i	0.115206	+	0.354569i	0.991990	−	0.126316i	$-0.0403155\pi$
$907$	3.46960	+	10.6783i	0.115206	+	0.354569i	−0.876784	+	0.480885i	$0.840315\pi$
$908$	0.928200	+	2.85671i	0.0308034	+	0.0948031i
$909$		0			0
$910$	6.14416	+	8.45671i	0.203677	+	0.280337i
$911$	16.8850	+	5.48626i	0.559424	+	0.181768i	0.575062	−	0.818110i	$-0.304978\pi$
$911$	16.8850	+	5.48626i	0.559424	+	0.181768i	−0.0156381	+	0.999878i	$0.504978\pi$
$912$		0			0
$913$	17.5090	−	0.784183i	0.579465	−	0.0259527i
$914$			3.00400i			0.0993636i
$915$		0			0
$916$	−13.9731	+	10.1520i	−0.461683	+	0.335432i
$917$	4.36390	−	6.00640i	0.144109	−	0.198349i
$918$		0			0
$919$	20.6791	−	6.71905i	0.682141	−	0.221641i	0.0526083	−	0.998615i	$-0.483247\pi$
$919$	20.6791	−	6.71905i	0.682141	−	0.221641i	0.629532	+	0.776974i	$0.283247\pi$
$920$	−7.61832	−	5.53503i	−0.251169	−	0.182485i
$921$		0			0
$922$	−0.423507	+	1.30342i	−0.0139475	+	0.0429259i
$923$	−50.3043			−1.65579
$924$		0			0
$925$	14.3932			0.473246
$926$	−12.0609	+	37.1195i	−0.396344	+	1.21982i
$927$		0			0
$928$	1.43507	+	1.04264i	0.0471085	+	0.0342263i
$929$	5.25902	−	1.70876i	0.172543	−	0.0560626i	−0.221472	−	0.975167i	$-0.571086\pi$
$929$	5.25902	−	1.70876i	0.172543	−	0.0560626i	0.394014	+	0.919104i	$0.371086\pi$
$930$		0			0
$931$	2.36768	−	3.25883i	0.0775974	−	0.106804i
$932$	4.77999	−	3.47287i	0.156574	−	0.113758i
$933$		0			0
$934$		−	0.651797i		−	0.0213274i
$935$	−41.8129	+	15.6868i	−1.36743	+	0.513013i
$936$		0			0
$937$	19.2488	+	6.25433i	0.628832	+	0.204320i	0.606058	−	0.795421i	$-0.292750\pi$
$937$	19.2488	+	6.25433i	0.628832	+	0.204320i	0.0227743	+	0.999741i	$0.492750\pi$
$938$	−4.45079	−	6.12599i	−0.145323	−	0.200021i
$939$		0			0
$940$	1.27920	+	3.93698i	0.0417230	+	0.128410i
$941$	0.783548	+	2.41151i	0.0255429	+	0.0786131i	0.963015	−	0.269446i	$-0.0868407\pi$
$941$	0.783548	+	2.41151i	0.0255429	+	0.0786131i	−0.937472	+	0.348060i	$0.886841\pi$
$942$		0			0
$943$	−21.9839	−	30.2582i	−0.715894	−	0.985344i
$944$	−9.65578	−	3.13735i	−0.314269	−	0.102112i
$945$		0			0
$946$	−13.2925	+	20.1319i	−0.432177	+	0.654546i
$947$			36.0730i			1.17221i	0.810234	+	0.586107i	$0.199340\pi$
$947$			36.0730i			1.17221i	−0.810234	+	0.586107i	$0.800660\pi$
$948$		0			0
$949$	−49.2335	+	35.7702i	−1.59819	+	1.16115i
$950$	4.41743	−	6.08008i	0.143320	−	0.197264i
$951$		0			0
$952$	7.23348	−	2.35030i	0.234438	−	0.0761736i
$953$	−35.0479	−	25.4638i	−1.13531	−	0.824852i	−0.148853	−	0.988859i	$-0.547558\pi$
$953$	−35.0479	−	25.4638i	−1.13531	−	0.824852i	−0.986459	+	0.164007i	$0.947558\pi$
$954$		0			0
$955$	−12.1056	+	37.2571i	−0.391727	+	1.20561i
$956$	−12.7624			−0.412767
$957$		0			0
$958$	−28.6274			−0.924908
$959$	−5.96122	+	18.3467i	−0.192498	+	0.592447i
$960$		0			0
$961$	22.4394	+	16.3032i	0.723853	+	0.525910i
$962$	43.3203	−	14.0756i	1.39670	−	0.453816i
$963$		0			0
$964$	−10.8559	+	14.9419i	−0.349645	+	0.481246i
$965$	33.2952	−	24.1904i	1.07181	−	0.778715i
$966$		0			0
$967$			53.4382i			1.71846i	0.511592	+	0.859229i	$0.329056\pi$
$967$			53.4382i			1.71846i	−0.511592	+	0.859229i	$0.670944\pi$
$968$	−10.9560	+	0.983348i	−0.352138	+	0.0316060i
$969$		0			0
$970$	10.3093	+	3.34968i	0.331010	+	0.107552i
$971$	13.1442	+	18.0914i	0.421817	+	0.580582i	0.966051	−	0.258352i	$-0.0831794\pi$
$971$	13.1442	+	18.0914i	0.421817	+	0.580582i	−0.544234	+	0.838934i	$0.683179\pi$
$972$		0			0
$973$	4.16901	+	12.8309i	0.133652	+	0.411339i
$974$	10.3723	+	31.9228i	0.332351	+	1.02287i
$975$		0			0
$976$	−2.51096	−	3.45605i	−0.0803740	−	0.110625i
$977$	12.1714	+	3.95472i	0.389397	+	0.126523i	0.497171	−	0.867653i	$-0.334372\pi$
$977$	12.1714	+	3.95472i	0.389397	+	0.126523i	−0.107774	+	0.994175i	$0.534372\pi$
$978$		0			0
$979$	18.9585	+	5.23471i	0.605916	+	0.167302i
$980$		−	1.77039i		−	0.0565530i
$981$		0			0
$982$	10.5153	−	7.63978i	0.335555	−	0.243795i
$983$	−16.7241	+	23.0188i	−0.533417	+	0.734186i	−0.987646	−	0.156699i	$-0.949915\pi$
$983$	−16.7241	+	23.0188i	−0.533417	+	0.734186i	0.454229	+	0.890885i	$0.349915\pi$
$984$		0			0
$985$	−31.0012	+	10.0729i	−0.987779	+	0.320949i
$986$	−10.9148	−	7.93003i	−0.347597	−	0.252544i
$987$		0			0
$988$	7.34956	−	22.6196i	0.233821	−	0.719626i
$989$	38.6895			1.23025
$990$		0			0
$991$	−18.0873			−0.574562			−0.287281	−	0.957846i	$-0.592751\pi$
$991$	−18.0873			−0.574562			−0.287281	+	0.957846i	$0.592751\pi$
$992$	0.558230	−	1.71805i	0.0177238	−	0.0545483i
$993$		0			0
$994$	6.89268	+	5.00782i	0.218622	+	0.158838i
$995$	30.5987	−	9.94210i	0.970042	−	0.315186i
$996$		0			0
$997$	12.8745	−	17.7202i	0.407740	−	0.561205i	−0.554926	−	0.831900i	$-0.687253\pi$
$997$	12.8745	−	17.7202i	0.407740	−	0.561205i	0.962665	+	0.270695i	$0.0872533\pi$
$998$	28.1430	−	20.4471i	0.890850	−	0.647240i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.bu.b.827.4	yes	48
3.2	odd	2		1386.2.bu.a.827.9	✓	48
11.6	odd	10		1386.2.bu.a.1205.9	yes	48
33.17	even	10	inner	1386.2.bu.b.1205.4	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1386.2.bu.a.827.9	✓	48	3.2	odd	2
1386.2.bu.a.1205.9	yes	48	11.6	odd	10
1386.2.bu.b.827.4	yes	48	1.1	even	1	trivial
1386.2.bu.b.1205.4	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)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-1.68374 + 0.547080i) q^{5} +(-0.587785 + 0.809017i) q^{7} +(0.809017 - 0.587785i) q^{8} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-1.68374 + 0.547080i) q^{5} +(-0.587785 + 0.809017i) q^{7} +(0.809017 - 0.587785i) q^{8} -1.77039i q^{10} +(-0.882736 + 3.19700i) q^{11} +(5.61541 + 1.82456i) q^{13} +(-0.587785 - 0.809017i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-2.35030 - 7.23348i) q^{17} +(2.36768 + 3.25883i) q^{19} +(1.68374 + 0.547080i) q^{20} +(-2.76774 - 1.82746i) q^{22} +5.31904i q^{23} +(-1.50940 + 1.09665i) q^{25} +(-3.47052 + 4.77675i) q^{26} +(0.951057 - 0.309017i) q^{28} +(-1.43507 - 1.04264i) q^{29} +(-0.558230 + 1.71805i) q^{31} -1.00000 q^{32} +7.60573 q^{34} +(0.547080 - 1.68374i) q^{35} +(-6.24119 - 4.53449i) q^{37} +(-3.83098 + 1.24476i) q^{38} +(-1.04061 + 1.43227i) q^{40} +(-5.68867 + 4.13306i) q^{41} -7.27378i q^{43} +(2.59329 - 2.06756i) q^{44} +(-5.05871 - 1.64367i) q^{46} +(1.37438 + 1.89167i) q^{47} +(-0.309017 - 0.951057i) q^{49} +(-0.576541 - 1.77441i) q^{50} +(-3.47052 - 4.77675i) q^{52} +(-9.89540 - 3.21521i) q^{53} +(-0.262715 - 5.86583i) q^{55} +1.00000i q^{56} +(1.43507 - 1.04264i) q^{58} +(-5.96760 + 8.21370i) q^{59} +(-4.06283 + 1.32009i) q^{61} +(-1.46146 - 1.06182i) q^{62} +(0.309017 - 0.951057i) q^{64} -10.4531 q^{65} +7.57214 q^{67} +(-2.35030 + 7.23348i) q^{68} +(1.43227 + 1.04061i) q^{70} +(-8.10283 + 2.63277i) q^{71} +(-6.05824 + 8.33845i) q^{73} +(6.24119 - 4.53449i) q^{74} -4.02813i q^{76} +(-2.06756 - 2.59329i) q^{77} +(-5.89055 - 1.91396i) q^{79} +(-1.04061 - 1.43227i) q^{80} +(-2.17288 - 6.68743i) q^{82} +(-1.63299 - 5.02583i) q^{83} +(7.91458 + 10.8935i) q^{85} +(6.91777 + 2.24772i) q^{86} +(1.16500 + 3.10528i) q^{88} -5.93010i q^{89} +(-4.77675 + 3.47052i) q^{91} +(3.12645 - 4.30319i) q^{92} +(-2.22379 + 0.722555i) q^{94} +(-5.76939 - 4.19170i) q^{95} +(-1.89206 + 5.82316i) q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 12 q^{2} - 12 q^{4} + 12 q^{8}+O(q^{10}) \) 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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