LMFDB - Embedded newform 1216.2.t.d.1185.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1216,2,Mod(353,1216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1216, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("1216.353");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1216 = 2^{6} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1216.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.70980888579$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1185.8
Character	$\chi$	$=$	1216.1185
Dual form			1216.2.t.d.353.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.495361 - 0.285997i) q^{3} +(-0.355705 + 0.205367i) q^{5} -0.565533 q^{7} +(-1.33641 + 2.31473i) q^{9} +O(q^{10})$	\(q+(0.495361 - 0.285997i) q^{3} +(-0.355705 + 0.205367i) q^{5} -0.565533 q^{7} +(-1.33641 + 2.31473i) q^{9} -0.623114i q^{11} +(-3.87518 - 2.23733i) q^{13} +(-0.117468 + 0.203461i) q^{15} +(-1.03509 - 1.79283i) q^{17} +(1.77510 + 3.98108i) q^{19} +(-0.280143 + 0.161740i) q^{21} +(-2.39843 + 4.15420i) q^{23} +(-2.41565 + 4.18403i) q^{25} +3.24482i q^{27} +(-2.28597 - 1.31981i) q^{29} -5.12745 q^{31} +(-0.178209 - 0.308666i) q^{33} +(0.201163 - 0.116142i) q^{35} -5.19500i q^{37} -2.55948 q^{39} +(1.11982 + 1.93958i) q^{41} +(0.626955 - 0.361972i) q^{43} -1.09782i q^{45} +(-4.18140 + 7.24240i) q^{47} -6.68017 q^{49} +(-1.02548 - 0.592064i) q^{51} +(-10.5214 - 6.07455i) q^{53} +(0.127967 + 0.221645i) q^{55} +(2.01789 + 1.46440i) q^{57} +(7.71649 - 4.45512i) q^{59} +(-0.0512168 - 0.0295700i) q^{61} +(0.755785 - 1.30906i) q^{63} +1.83789 q^{65} +(0.447132 + 0.258152i) q^{67} +2.74377i q^{69} +(4.32599 + 7.49284i) q^{71} +(2.86096 + 4.95533i) q^{73} +2.76347i q^{75} +0.352392i q^{77} +(4.50179 + 7.79733i) q^{79} +(-3.08123 - 5.33684i) q^{81} +10.2514i q^{83} +(0.736374 + 0.425145i) q^{85} -1.50984 q^{87} +(-4.25944 + 7.37756i) q^{89} +(2.19154 + 1.26529i) q^{91} +(-2.53994 + 1.46643i) q^{93} +(-1.44899 - 1.05155i) q^{95} +(-5.33679 - 9.24359i) q^{97} +(1.44234 + 0.832737i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{5} + 8 q^{9}+O(q^{10}) $ 24 * q - 6 * q^5 + 8 * q^9	$ 24 q - 6 q^{5} + 8 q^{9} + 30 q^{13} + 6 q^{17} + 24 q^{21} + 6 q^{25} + 42 q^{29} - 14 q^{33} - 24 q^{41} + 24 q^{49} - 18 q^{53} - 42 q^{57} + 18 q^{61} - 20 q^{65} - 16 q^{73} + 52 q^{81} - 78 q^{85} + 14 q^{89} + 60 q^{93} - 4 q^{97}+O(q^{100}) $ 24 * q - 6 * q^5 + 8 * q^9 + 30 * q^13 + 6 * q^17 + 24 * q^21 + 6 * q^25 + 42 * q^29 - 14 * q^33 - 24 * q^41 + 24 * q^49 - 18 * q^53 - 42 * q^57 + 18 * q^61 - 20 * q^65 - 16 * q^73 + 52 * q^81 - 78 * q^85 + 14 * q^89 + 60 * q^93 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times$.

$n$	$191$	$705$	$837$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.495361	−	0.285997i	0.285997	−	0.165120i	−0.350138	−	0.936698i	$-0.613865\pi$
$3$	0.495361	−	0.285997i	0.285997	−	0.165120i	0.636135	+	0.771578i	$0.280532\pi$
$4$		0			0
$5$	−0.355705	+	0.205367i	−0.159076	+	0.0918428i	−0.577425	−	0.816444i	$-0.695942\pi$
$5$	−0.355705	+	0.205367i	−0.159076	+	0.0918428i	0.418349	+	0.908287i	$0.362609\pi$
$6$		0			0
$7$	−0.565533			−0.213751			−0.106876	−	0.994272i	$-0.534085\pi$
$7$	−0.565533			−0.213751			−0.106876	+	0.994272i	$0.534085\pi$
$8$		0			0
$9$	−1.33641	+	2.31473i	−0.445471	+	0.771578i
$10$		0			0
$11$		−	0.623114i		−	0.187876i	−0.995578	−	0.0939380i	$-0.970054\pi$
$11$		−	0.623114i		−	0.187876i	0.995578	−	0.0939380i	$-0.0299456\pi$
$12$		0			0
$13$	−3.87518	−	2.23733i	−1.07478	−	0.620525i	−0.145297	−	0.989388i	$-0.546414\pi$
$13$	−3.87518	−	2.23733i	−1.07478	−	0.620525i	−0.929484	+	0.368863i	$0.879747\pi$
$14$		0			0
$15$	−0.117468	+	0.203461i	−0.0303302	+	0.0525334i
$16$		0			0
$17$	−1.03509	−	1.79283i	−0.251046	−	0.434824i	0.712768	−	0.701400i	$-0.247441\pi$
$17$	−1.03509	−	1.79283i	−0.251046	−	0.434824i	−0.963814	+	0.266575i	$0.914108\pi$
$18$		0			0
$19$	1.77510	+	3.98108i	0.407236	+	0.913323i
$19$	1.77510	+	3.98108i	0.407236	+	0.913323i
$20$		0			0
$21$	−0.280143	+	0.161740i	−0.0611322	+	0.0352947i
$22$		0			0
$23$	−2.39843	+	4.15420i	−0.500107	+	0.866210i	0.499893	+	0.866087i	$0.333373\pi$
$23$	−2.39843	+	4.15420i	−0.500107	+	0.866210i	−1.00000		0.000123335i	$0.999961\pi$
$24$		0			0
$25$	−2.41565	+	4.18403i	−0.483130	+	0.836805i
$26$		0			0
$27$			3.24482i			0.624465i
$28$		0			0
$29$	−2.28597	−	1.31981i	−0.424495	−	0.245082i	0.272504	−	0.962155i	$-0.412148\pi$
$29$	−2.28597	−	1.31981i	−0.424495	−	0.245082i	−0.696999	+	0.717072i	$0.745482\pi$
$30$		0			0
$31$	−5.12745			−0.920918			−0.460459	−	0.887681i	$-0.652315\pi$
$31$	−5.12745			−0.920918			−0.460459	+	0.887681i	$0.652315\pi$
$32$		0			0
$33$	−0.178209	−	0.308666i	−0.0310221	−	0.0537319i
$34$		0			0
$35$	0.201163	−	0.116142i	0.0340028	−	0.0196315i
$36$		0			0
$37$		−	5.19500i		−	0.854053i	−0.904239	−	0.427026i	$-0.859561\pi$
$37$		−	5.19500i		−	0.854053i	0.904239	−	0.427026i	$-0.140439\pi$
$38$		0			0
$39$	−2.55948			−0.409845
$40$		0			0
$41$	1.11982	+	1.93958i	0.174886	+	0.302911i	0.940122	−	0.340839i	$-0.110711\pi$
$41$	1.11982	+	1.93958i	0.174886	+	0.302911i	−0.765236	+	0.643750i	$0.777378\pi$
$42$		0			0
$43$	0.626955	−	0.361972i	0.0956097	−	0.0552003i	−0.451433	−	0.892305i	$-0.649087\pi$
$43$	0.626955	−	0.361972i	0.0956097	−	0.0552003i	0.547042	+	0.837105i	$0.315754\pi$
$44$		0			0
$45$		−	1.09782i		−	0.163653i
$46$		0			0
$47$	−4.18140	+	7.24240i	−0.609920	+	1.05641i	0.381333	+	0.924438i	$0.375465\pi$
$47$	−4.18140	+	7.24240i	−0.609920	+	1.05641i	−0.991253	+	0.131975i	$0.957868\pi$
$48$		0			0
$49$	−6.68017			−0.954310
$50$		0			0
$51$	−1.02548	−	0.592064i	−0.143597	−	0.0829055i
$52$		0			0
$53$	−10.5214	−	6.07455i	−1.44523	−	0.834403i	−0.447037	−	0.894515i	$-0.647521\pi$
$53$	−10.5214	−	6.07455i	−1.44523	−	0.834403i	−0.998192	+	0.0601121i	$0.980854\pi$
$54$		0			0
$55$	0.127967	+	0.221645i	0.0172551	+	0.0298866i
$56$		0			0
$57$	2.01789	+	1.46440i	0.267276	+	0.193964i
$58$		0			0
$59$	7.71649	−	4.45512i	1.00460	−	0.580007i	0.0949951	−	0.995478i	$-0.469716\pi$
$59$	7.71649	−	4.45512i	1.00460	−	0.580007i	0.909607	+	0.415471i	$0.136383\pi$
$60$		0			0
$61$	−0.0512168	−	0.0295700i	−0.00655764	−	0.00378605i	0.496718	−	0.867912i	$-0.334538\pi$
$61$	−0.0512168	−	0.0295700i	−0.00655764	−	0.00378605i	−0.503275	+	0.864126i	$0.667872\pi$
$62$		0			0
$63$	0.755785	−	1.30906i	0.0952199	−	0.164926i
$64$		0			0
$65$	1.83789			0.227963
$66$		0			0
$67$	0.447132	+	0.258152i	0.0546258	+	0.0315382i	0.527064	−	0.849825i	$-0.323293\pi$
$67$	0.447132	+	0.258152i	0.0546258	+	0.0315382i	−0.472438	+	0.881364i	$0.656626\pi$
$68$		0			0
$69$			2.74377i			0.330311i
$70$		0			0
$71$	4.32599	+	7.49284i	0.513401	+	0.889236i	0.999879	+	0.0155438i	$0.00494794\pi$
$71$	4.32599	+	7.49284i	0.513401	+	0.889236i	−0.486478	+	0.873693i	$0.661719\pi$
$72$		0			0
$73$	2.86096	+	4.95533i	0.334850	+	0.579977i	0.983456	−	0.181147i	$-0.0579811\pi$
$73$	2.86096	+	4.95533i	0.334850	+	0.579977i	−0.648606	+	0.761124i	$0.724648\pi$
$74$		0			0
$75$			2.76347i			0.319098i
$76$		0			0
$77$			0.352392i			0.0401587i
$78$		0			0
$79$	4.50179	+	7.79733i	0.506491	+	0.877268i	0.999972	+	0.00751132i	$0.00239095\pi$
$79$	4.50179	+	7.79733i	0.506491	+	0.877268i	−0.493481	+	0.869757i	$0.664276\pi$
$80$		0			0
$81$	−3.08123	−	5.33684i	−0.342359	−	0.592983i
$82$		0			0
$83$			10.2514i			1.12523i	0.826718	+	0.562617i	$0.190205\pi$
$83$			10.2514i			1.12523i	−0.826718	+	0.562617i	$0.809795\pi$
$84$		0			0
$85$	0.736374	+	0.425145i	0.0798709	+	0.0461135i
$86$		0			0
$87$	−1.50984			−0.161872
$88$		0			0
$89$	−4.25944	+	7.37756i	−0.451499	+	0.782020i	−0.998479	−	0.0551257i	$-0.982444\pi$
$89$	−4.25944	+	7.37756i	−0.451499	+	0.782020i	0.546980	+	0.837146i	$0.315777\pi$
$90$		0			0
$91$	2.19154	+	1.26529i	0.229736	+	0.132638i
$92$		0			0
$93$	−2.53994	+	1.46643i	−0.263379	+	0.152062i
$94$		0			0
$95$	−1.44899	−	1.05155i	−0.148664	−	0.107886i
$96$		0			0
$97$	−5.33679	−	9.24359i	−0.541869	−	0.938544i	−0.998797	−	0.0490405i	$-0.984384\pi$
$97$	−5.33679	−	9.24359i	−0.541869	−	0.938544i	0.456928	−	0.889504i	$-0.348950\pi$
$98$		0			0
$99$	1.44234	+	0.832737i	0.144961	+	0.0836933i
$100$		0			0
$101$	−4.57456	−	2.64113i	−0.455186	−	0.262802i	0.254832	−	0.966985i	$-0.417980\pi$
$101$	−4.57456	−	2.64113i	−0.455186	−	0.262802i	−0.710018	+	0.704184i	$0.751313\pi$
$102$		0			0
$103$	−13.5734			−1.33743			−0.668714	−	0.743520i	$-0.733155\pi$
$103$	−13.5734			−1.33743			−0.668714	+	0.743520i	$0.733155\pi$
$104$		0			0
$105$	0.0664322	−	0.115064i	0.00648312	−	0.0112291i
$106$		0			0
$107$		−	1.42282i		−	0.137549i	−0.997632	−	0.0687747i	$-0.978091\pi$
$107$		−	1.42282i		−	0.137549i	0.997632	−	0.0687747i	$-0.0219090\pi$
$108$		0			0
$109$	4.44778	−	2.56793i	0.426020	−	0.245963i	−0.271629	−	0.962402i	$-0.587562\pi$
$109$	4.44778	−	2.56793i	0.426020	−	0.245963i	0.697650	+	0.716439i	$0.254229\pi$
$110$		0			0
$111$	−1.48575	−	2.57340i	−0.141021	−	0.244256i
$112$		0			0
$113$	−3.40470			−0.320288			−0.160144	−	0.987094i	$-0.551196\pi$
$113$	−3.40470			−0.320288			−0.160144	+	0.987094i	$0.551196\pi$
$114$		0			0
$115$		−	1.97023i		−	0.183725i
$116$		0			0
$117$	10.3577	−	5.98000i	0.957566	−	0.552851i
$118$		0			0
$119$	0.585377	+	1.01390i	0.0536614	+	0.0929443i
$120$		0			0
$121$	10.6117			0.964703
$122$		0			0
$123$	1.10943	+	0.640527i	0.100034	+	0.0577544i
$124$		0			0
$125$		−	4.03804i		−	0.361173i
$126$		0			0
$127$	2.83599	−	4.91209i	0.251654	−	0.435877i	−0.712328	−	0.701847i	$-0.752359\pi$
$127$	2.83599	−	4.91209i	0.251654	−	0.435877i	0.963981	+	0.265970i	$0.0856923\pi$
$128$		0			0
$129$	0.207046	−	0.358614i	0.0182294	−	0.0315742i
$130$		0			0
$131$	6.82143	−	3.93835i	0.595991	−	0.344095i	−0.171472	−	0.985189i	$-0.554852\pi$
$131$	6.82143	−	3.93835i	0.595991	−	0.344095i	0.767463	+	0.641094i	$0.221519\pi$
$132$		0			0
$133$	−1.00388	−	2.25143i	−0.0870472	−	0.195224i
$134$		0			0
$135$	−0.666377	−	1.15420i	−0.0573526	−	0.0993376i
$136$		0			0
$137$	−4.05338	+	7.02067i	−0.346304	+	0.599816i	−0.985590	−	0.169153i	$-0.945897\pi$
$137$	−4.05338	+	7.02067i	−0.346304	+	0.599816i	0.639286	+	0.768969i	$0.279230\pi$
$138$		0			0
$139$	−7.50640	−	4.33382i	−0.636684	−	0.367590i	0.146652	−	0.989188i	$-0.453150\pi$
$139$	−7.50640	−	4.33382i	−0.636684	−	0.367590i	−0.783336	+	0.621598i	$0.786484\pi$
$140$		0			0
$141$			4.78347i			0.402841i
$142$		0			0
$143$	−1.39411	+	2.41468i	−0.116582	+	0.201925i
$144$		0			0
$145$	1.08418			0.0900361
$146$		0			0
$147$	−3.30910	+	1.91051i	−0.272930	+	0.157576i
$148$		0			0
$149$	−6.69747	+	3.86678i	−0.548678	+	0.316779i	−0.748589	−	0.663035i	$-0.769268\pi$
$149$	−6.69747	+	3.86678i	−0.548678	+	0.316779i	0.199911	+	0.979814i	$0.435935\pi$
$150$		0			0
$151$	10.2050			0.830469			0.415234	−	0.909714i	$-0.363700\pi$
$151$	10.2050			0.830469			0.415234	+	0.909714i	$0.363700\pi$
$152$		0			0
$153$	5.53322			0.447334
$154$		0			0
$155$	1.82386	−	1.05301i	0.146496	−	0.0845796i
$156$		0			0
$157$	3.94882	−	2.27985i	0.315150	−	0.181952i	−0.334079	−	0.942545i	$-0.608425\pi$
$157$	3.94882	−	2.27985i	0.315150	−	0.181952i	0.649229	+	0.760593i	$0.275092\pi$
$158$		0			0
$159$	−6.94920			−0.551107
$160$		0			0
$161$	1.35639	−	2.34934i	0.106898	−	0.185154i
$162$		0			0
$163$		−	12.1835i		−	0.954283i	−0.878827	−	0.477141i	$-0.841673\pi$
$163$		−	12.1835i		−	0.954283i	0.878827	−	0.477141i	$-0.158327\pi$
$164$		0			0
$165$	0.126780	+	0.0731962i	0.00986977	+	0.00569832i
$166$		0			0
$167$	5.79203	−	10.0321i	0.448201	−	0.776306i	−0.550068	−	0.835120i	$-0.685398\pi$
$167$	5.79203	−	10.0321i	0.448201	−	0.776306i	0.998269	+	0.0588134i	$0.0187317\pi$
$168$		0			0
$169$	3.51132	+	6.08179i	0.270102	+	0.467830i
$170$		0			0
$171$	−11.5874	−	1.21148i	−0.886111	−	0.0926444i
$172$		0			0
$173$	−4.80088	+	2.77179i	−0.365004	+	0.210735i	−0.671274	−	0.741210i	$-0.734252\pi$
$173$	−4.80088	+	2.77179i	−0.365004	+	0.210735i	0.306270	+	0.951945i	$0.400919\pi$
$174$		0			0
$175$	1.36613	−	2.36620i	0.103270	−	0.178868i
$176$		0			0
$177$	2.54830	−	4.41378i	0.191542	−	0.331760i
$178$		0			0
$179$			9.92221i			0.741621i	0.928709	+	0.370810i	$0.120920\pi$
$179$			9.92221i			0.741621i	−0.928709	+	0.370810i	$0.879080\pi$
$180$		0			0
$181$	16.6482	+	9.61185i	1.23745	+	0.714443i	0.968573	−	0.248731i	$-0.0800136\pi$
$181$	16.6482	+	9.61185i	1.23745	+	0.714443i	0.268879	+	0.963174i	$0.413347\pi$
$182$		0			0
$183$	−0.0338277			−0.00250062
$184$		0			0
$185$	1.06688	+	1.84789i	0.0784385	+	0.135860i
$186$		0			0
$187$	−1.11714	+	0.644979i	−0.0816931	+	0.0471655i
$188$		0			0
$189$		−	1.83505i		−	0.133480i
$190$		0			0
$191$	14.7297			1.06580			0.532900	−	0.846178i	$-0.321102\pi$
$191$	14.7297			1.06580			0.532900	+	0.846178i	$0.321102\pi$
$192$		0			0
$193$	−8.85598	−	15.3390i	−0.637467	−	1.10413i	−0.985987	−	0.166824i	$-0.946649\pi$
$193$	−8.85598	−	15.3390i	−0.637467	−	1.10413i	0.348519	−	0.937302i	$-0.386685\pi$
$194$		0			0
$195$	0.910421	−	0.525632i	0.0651966	−	0.0376413i
$196$		0			0
$197$			26.6926i			1.90177i	0.309547	+	0.950884i	$0.399822\pi$
$197$			26.6926i			1.90177i	−0.309547	+	0.950884i	$0.600178\pi$
$198$		0			0
$199$	6.43770	−	11.1504i	0.456356	−	0.790432i	−0.542409	−	0.840115i	$-0.682488\pi$
$199$	6.43770	−	11.1504i	0.456356	−	0.790432i	0.998765	+	0.0496824i	$0.0158209\pi$
$200$		0			0
$201$	0.295322			0.0208304
$202$		0			0
$203$	1.29279	+	0.746395i	0.0907363	+	0.0523866i
$204$		0			0
$205$	−0.796649	−	0.459946i	−0.0556404	−	0.0321240i
$206$		0			0
$207$	−6.41058	−	11.1034i	−0.445566	−	0.771743i
$208$		0			0
$209$	2.48067	−	1.10609i	0.171592	−	0.0765099i
$210$		0			0
$211$	−13.7910	+	7.96226i	−0.949414	+	0.548144i	−0.892899	−	0.450257i	$-0.851332\pi$
$211$	−13.7910	+	7.96226i	−0.949414	+	0.548144i	−0.0565152	+	0.998402i	$0.517999\pi$
$212$		0			0
$213$	4.28585	+	2.47444i	0.293662	+	0.169546i
$214$		0			0
$215$	−0.148674	+	0.257511i	−0.0101395	+	0.0175621i
$216$		0			0
$217$	2.89974			0.196847
$218$		0			0
$219$	2.83441	+	1.63645i	0.191532	+	0.110581i
$220$		0			0
$221$			9.26336i			0.623121i
$222$		0			0
$223$	2.43662	+	4.22035i	0.163168	+	0.282616i	0.936003	−	0.351991i	$-0.114495\pi$
$223$	2.43662	+	4.22035i	0.163168	+	0.282616i	−0.772835	+	0.634607i	$0.781162\pi$
$224$		0			0
$225$	−6.45660	−	11.1832i	−0.430440	−	0.745544i
$226$		0			0
$227$		−	21.2093i		−	1.40771i	−0.710344	−	0.703855i	$-0.751460\pi$
$227$		−	21.2093i		−	1.40771i	0.710344	−	0.703855i	$-0.248540\pi$
$228$		0			0
$229$			3.41777i			0.225853i	0.993603	+	0.112926i	$0.0360224\pi$
$229$			3.41777i			0.225853i	−0.993603	+	0.112926i	$0.963978\pi$
$230$		0			0
$231$	0.100783	+	0.174561i	0.00663102	+	0.0114853i
$232$		0			0
$233$	9.03289	+	15.6454i	0.591764	+	1.02497i	0.993995	+	0.109427i	$0.0349017\pi$
$233$	9.03289	+	15.6454i	0.591764	+	1.02497i	−0.402231	+	0.915538i	$0.631765\pi$
$234$		0			0
$235$		−	3.43488i		−	0.224067i
$236$		0			0
$237$	4.46002	+	2.57499i	0.289709	+	0.167264i
$238$		0			0
$239$	24.1989			1.56530			0.782649	−	0.622463i	$-0.213868\pi$
$239$	24.1989			1.56530			0.782649	+	0.622463i	$0.213868\pi$
$240$		0			0
$241$	6.33257	−	10.9683i	0.407917	−	0.706532i	−0.586740	−	0.809776i	$-0.699589\pi$
$241$	6.33257	−	10.9683i	0.407917	−	0.706532i	0.994656	+	0.103243i	$0.0329221\pi$
$242$		0			0
$243$	−11.4829	−	6.62967i	−0.736630	−	0.425293i
$244$		0			0
$245$	2.37617	−	1.37188i	0.151808	−	0.0876465i
$246$		0			0
$247$	2.02818	−	19.3989i	0.129050	−	1.23432i
$248$		0			0
$249$	2.93186	+	5.07813i	0.185799	+	0.321813i
$250$		0			0
$251$	−3.71329	−	2.14387i	−0.234381	−	0.135320i	0.378211	−	0.925720i	$-0.376540\pi$
$251$	−3.71329	−	2.14387i	−0.234381	−	0.135320i	−0.612591	+	0.790400i	$0.709873\pi$
$252$		0			0
$253$	2.58854	+	1.49449i	0.162740	+	0.0939581i
$254$		0			0
$255$	0.486361			0.0304571
$256$		0			0
$257$	9.67320	−	16.7545i	0.603398	−	1.04512i	−0.388905	−	0.921278i	$-0.627147\pi$
$257$	9.67320	−	16.7545i	0.603398	−	1.04512i	0.992303	−	0.123837i	$-0.0395201\pi$
$258$		0			0
$259$			2.93794i			0.182555i
$260$		0			0
$261$	6.11001	−	3.52761i	0.378200	−	0.218354i
$262$		0			0
$263$	6.72838	+	11.6539i	0.414890	+	0.718610i	0.995417	−	0.0956310i	$-0.0304869\pi$
$263$	6.72838	+	11.6539i	0.414890	+	0.718610i	−0.580527	+	0.814241i	$0.697154\pi$
$264$		0			0
$265$	4.99004			0.306536
$266$		0			0
$267$			4.87274i			0.298207i
$268$		0			0
$269$	8.03510	−	4.63907i	0.489909	−	0.282849i	−0.234628	−	0.972085i	$-0.575387\pi$
$269$	8.03510	−	4.63907i	0.489909	−	0.282849i	0.724537	+	0.689236i	$0.242054\pi$
$270$		0			0
$271$	−11.3590	−	19.6744i	−0.690010	−	1.19513i	−0.971834	−	0.235666i	$-0.924273\pi$
$271$	−11.3590	−	19.6744i	−0.690010	−	1.19513i	0.281824	−	0.959466i	$-0.409061\pi$
$272$		0			0
$273$	1.44747			0.0876048
$274$		0			0
$275$	2.60713	+	1.50523i	0.157216	+	0.0907685i
$276$		0			0
$277$		−	10.3729i		−	0.623249i	−0.950205	−	0.311625i	$-0.899127\pi$
$277$		−	10.3729i		−	0.623249i	0.950205	−	0.311625i	$-0.100873\pi$
$278$		0			0
$279$	6.85239	−	11.8687i	0.410242	−	0.710560i
$280$		0			0
$281$	−8.30802	+	14.3899i	−0.495615	+	0.858430i	−0.999987	−	0.00505593i	$-0.998391\pi$
$281$	−8.30802	+	14.3899i	−0.495615	+	0.858430i	0.504372	+	0.863486i	$0.331724\pi$
$282$		0			0
$283$	−10.9865	+	6.34305i	−0.653079	+	0.377055i	−0.789635	−	0.613577i	$-0.789730\pi$
$283$	−10.9865	+	6.34305i	−0.653079	+	0.377055i	0.136556	+	0.990632i	$0.456397\pi$
$284$		0			0
$285$	−1.01851	−	0.106487i	−0.0603315	−	0.00630776i
$286$		0			0
$287$	−0.633293	−	1.09690i	−0.0373821	−	0.0647477i
$288$		0			0
$289$	6.35718	−	11.0110i	0.373952	−	0.647704i
$290$		0			0
$291$	−5.28727	−	3.05261i	−0.309945	−	0.178947i
$292$		0			0
$293$			5.67796i			0.331710i	0.986150	+	0.165855i	$0.0530383\pi$
$293$			5.67796i			0.331710i	−0.986150	+	0.165855i	$0.946962\pi$
$294$		0			0
$295$	−1.82987	+	3.16942i	−0.106539	+	0.184531i
$296$		0			0
$297$	2.02189			0.117322
$298$		0			0
$299$	18.5887	−	10.7322i	1.07501	−	0.620657i
$300$		0			0
$301$	−0.354563	+	0.204707i	−0.0204367	+	0.0117991i
$302$		0			0
$303$	−3.02141			−0.173576
$304$		0			0
$305$	0.0242908			0.00139089
$306$		0			0
$307$	2.09500	−	1.20955i	0.119568	−	0.0690326i	−0.439023	−	0.898476i	$-0.644675\pi$
$307$	2.09500	−	1.20955i	0.119568	−	0.0690326i	0.558591	+	0.829443i	$0.311342\pi$
$308$		0			0
$309$	−6.72373	+	3.88195i	−0.382500	+	0.220836i
$310$		0			0
$311$	−18.0441			−1.02319			−0.511594	−	0.859227i	$-0.670945\pi$
$311$	−18.0441			−1.02319			−0.511594	+	0.859227i	$0.670945\pi$
$312$		0			0
$313$	0.902817	−	1.56372i	0.0510302	−	0.0883869i	−0.839382	−	0.543542i	$-0.817083\pi$
$313$	0.902817	−	1.56372i	0.0510302	−	0.0883869i	0.890412	+	0.455155i	$0.150416\pi$
$314$		0			0
$315$			0.620852i			0.0349810i
$316$		0			0
$317$	13.9141	+	8.03332i	0.781495	+	0.451196i	0.836960	−	0.547265i	$-0.184331\pi$
$317$	13.9141	+	8.03332i	0.781495	+	0.451196i	−0.0554651	+	0.998461i	$0.517664\pi$
$318$		0			0
$319$	−0.822391	+	1.42442i	−0.0460451	+	0.0797524i
$320$		0			0
$321$	−0.406922	−	0.704810i	−0.0227122	−	0.0393387i
$322$		0			0
$323$	5.30000	−	7.30322i	0.294900	−	0.406362i
$324$		0			0
$325$	18.7221	−	10.8092i	1.03852	−	0.599588i
$326$		0			0
$327$	1.46884	−	2.54410i	0.0812270	−	0.140689i
$328$		0			0
$329$	2.36472	−	4.09582i	0.130371	−	0.225810i
$330$		0			0
$331$		−	11.3991i		−	0.626550i	−0.949662	−	0.313275i	$-0.898574\pi$
$331$		−	11.3991i		−	0.626550i	0.949662	−	0.313275i	$-0.101426\pi$
$332$		0			0
$333$	12.0250	+	6.94266i	0.658968	+	0.380455i
$334$		0			0
$335$	−0.212063			−0.0115862
$336$		0			0
$337$	−11.6969	−	20.2597i	−0.637172	−	1.10361i	−0.986051	−	0.166446i	$-0.946771\pi$
$337$	−11.6969	−	20.2597i	−0.637172	−	1.10361i	0.348878	−	0.937168i	$-0.386563\pi$
$338$		0			0
$339$	−1.68656	+	0.973734i	−0.0916012	+	0.0528860i
$340$		0			0
$341$			3.19499i			0.173018i
$342$		0			0
$343$	7.73659			0.417736
$344$		0			0
$345$	−0.563479	−	0.975974i	−0.0303367	−	0.0525447i
$346$		0			0
$347$	−29.3846	+	16.9652i	−1.57745	+	0.910741i	−0.582235	+	0.813020i	$0.697822\pi$
$347$	−29.3846	+	16.9652i	−1.57745	+	0.910741i	−0.995214	+	0.0977205i	$0.968845\pi$
$348$		0			0
$349$			21.1792i			1.13370i	0.823821	+	0.566849i	$0.191838\pi$
$349$			21.1792i			1.13370i	−0.823821	+	0.566849i	$0.808162\pi$
$350$		0			0
$351$	7.25974	−	12.5742i	0.387496	−	0.671163i
$352$		0			0
$353$	7.34223			0.390787			0.195394	−	0.980725i	$-0.437402\pi$
$353$	7.34223			0.390787			0.195394	+	0.980725i	$0.437402\pi$
$354$		0			0
$355$	−3.07756	−	1.77683i	−0.163340	−	0.0943043i
$356$		0			0
$357$	0.579945	+	0.334832i	0.0306940	+	0.0177212i
$358$		0			0
$359$	15.1915	+	26.3125i	0.801778	+	1.38872i	0.918445	+	0.395549i	$0.129446\pi$
$359$	15.1915	+	26.3125i	0.801778	+	1.38872i	−0.116667	+	0.993171i	$0.537221\pi$
$360$		0			0
$361$	−12.6980	+	14.1336i	−0.668318	+	0.743876i
$362$		0			0
$363$	5.25663	−	3.03492i	0.275902	−	0.159292i
$364$		0			0
$365$	−2.03532	−	1.17509i	−0.106533	−	0.0615071i
$366$		0			0
$367$	14.3292	−	24.8189i	0.747979	−	1.29554i	−0.200811	−	0.979630i	$-0.564358\pi$
$367$	14.3292	−	24.8189i	0.747979	−	1.29554i	0.948790	−	0.315907i	$-0.102309\pi$
$368$		0			0
$369$	−5.98614			−0.311626
$370$		0			0
$371$	5.95021	+	3.43536i	0.308920	+	0.178355i
$372$		0			0
$373$			19.0463i			0.986178i	0.869979	+	0.493089i	$0.164132\pi$
$373$			19.0463i			0.986178i	−0.869979	+	0.493089i	$0.835868\pi$
$374$		0			0
$375$	−1.15487	−	2.00029i	−0.0596370	−	0.103294i
$376$		0			0
$377$	5.90570	+	10.2290i	0.304159	+	0.526819i
$378$		0			0
$379$			2.35677i			0.121059i	0.998166	+	0.0605296i	$0.0192789\pi$
$379$			2.35677i			0.121059i	−0.998166	+	0.0605296i	$0.980721\pi$
$380$		0			0
$381$		−	3.24434i		−	0.166213i
$382$		0			0
$383$	13.4562	+	23.3069i	0.687582	+	1.19093i	0.972618	+	0.232410i	$0.0746612\pi$
$383$	13.4562	+	23.3069i	0.687582	+	1.19093i	−0.285036	+	0.958517i	$0.592005\pi$
$384$		0			0
$385$	−0.0723695	−	0.125348i	−0.00368829	−	0.00638831i
$386$		0			0
$387$			1.93498i			0.0983604i
$388$		0			0
$389$	−26.1945	−	15.1234i	−1.32811	−	0.766786i	−0.343105	−	0.939297i	$-0.611479\pi$
$389$	−26.1945	−	15.1234i	−1.32811	−	0.766786i	−0.985008	+	0.172511i	$0.944812\pi$
$390$		0			0
$391$	9.93034			0.502199
$392$		0			0
$393$	2.25271	−	3.90181i	0.113634	−	0.196820i
$394$		0			0
$395$	−3.20262	−	1.84903i	−0.161141	−	0.0930350i
$396$		0			0
$397$	18.5519	−	10.7110i	0.931094	−	0.537567i	0.0439366	−	0.999034i	$-0.486010\pi$
$397$	18.5519	−	10.7110i	0.931094	−	0.537567i	0.887157	+	0.461467i	$0.152677\pi$
$398$		0			0
$399$	−1.14118	−	0.828166i	−0.0571306	−	0.0414601i
$400$		0			0
$401$	1.34850	+	2.33566i	0.0673407	+	0.116637i	0.897730	−	0.440546i	$-0.145215\pi$
$401$	1.34850	+	2.33566i	0.0673407	+	0.116637i	−0.830389	+	0.557184i	$0.811882\pi$
$402$		0			0
$403$	19.8698	+	11.4718i	0.989784	+	0.571452i
$404$		0			0
$405$	2.19202	+	1.26556i	0.108922	+	0.0628863i
$406$		0			0
$407$	−3.23708			−0.160456
$408$		0			0
$409$	2.90473	−	5.03114i	0.143630	−	0.248774i	−0.785231	−	0.619203i	$-0.787456\pi$
$409$	2.90473	−	5.03114i	0.143630	−	0.248774i	0.928861	+	0.370429i	$0.120789\pi$
$410$		0			0
$411$			4.63702i			0.228727i
$412$		0			0
$413$	−4.36393	+	2.51952i	−0.214735	+	0.123977i
$414$		0			0
$415$	−2.10529	−	3.64647i	−0.103345	−	0.178998i
$416$		0			0
$417$	−4.95783			−0.242786
$418$		0			0
$419$		−	38.9036i		−	1.90057i	−0.311389	−	0.950283i	$-0.600794\pi$
$419$		−	38.9036i		−	1.90057i	0.311389	−	0.950283i	$-0.399206\pi$
$420$		0			0
$421$	17.3148	−	9.99669i	0.843870	−	0.487209i	−0.0147077	−	0.999892i	$-0.504682\pi$
$421$	17.3148	−	9.99669i	0.843870	−	0.487209i	0.858578	+	0.512683i	$0.171348\pi$
$422$		0			0
$423$	−11.1762	−	19.3577i	−0.543403	−	0.941202i
$424$		0			0
$425$	10.0016			0.485151
$426$		0			0
$427$	0.0289648	+	0.0167228i	0.00140170	+	0.000809274i
$428$		0			0
$429$			1.59485i			0.0770000i
$430$		0			0
$431$	−12.2479	+	21.2139i	−0.589959	+	1.02184i	0.404279	+	0.914636i	$0.367523\pi$
$431$	−12.2479	+	21.2139i	−0.589959	+	1.02184i	−0.994237	+	0.107203i	$0.965811\pi$
$432$		0			0
$433$	−9.95963	+	17.2506i	−0.478629	+	0.829010i	−0.999700	−	0.0245034i	$-0.992200\pi$
$433$	−9.95963	+	17.2506i	−0.478629	+	0.829010i	0.521070	+	0.853514i	$0.325533\pi$
$434$		0			0
$435$	0.537059	−	0.310071i	0.0257500	−	0.0148668i
$436$		0			0
$437$	−20.7957	−	2.17422i	−0.994791	−	0.104007i
$438$		0			0
$439$	9.26447	+	16.0465i	0.442169	+	0.765859i	0.997850	−	0.0655361i	$-0.0208758\pi$
$439$	9.26447	+	16.0465i	0.442169	+	0.765859i	−0.555681	+	0.831396i	$0.687542\pi$
$440$		0			0
$441$	8.92746	−	15.4628i	0.425117	−	0.736325i
$442$		0			0
$443$	10.5509	+	6.09155i	0.501287	+	0.289418i	0.729245	−	0.684253i	$-0.239872\pi$
$443$	10.5509	+	6.09155i	0.501287	+	0.289418i	−0.227958	+	0.973671i	$0.573205\pi$
$444$		0			0
$445$		−	3.49899i		−	0.165868i
$446$		0			0
$447$	−2.21177	+	3.83091i	−0.104613	+	0.181196i
$448$		0			0
$449$	18.0800			0.853249			0.426624	−	0.904429i	$-0.359703\pi$
$449$	18.0800			0.853249			0.426624	+	0.904429i	$0.359703\pi$
$450$		0			0
$451$	1.20858	−	0.697773i	0.0569098	−	0.0328569i
$452$		0			0
$453$	5.05514	−	2.91859i	0.237511	−	0.137127i
$454$		0			0
$455$	−1.03939			−0.0487273
$456$		0			0
$457$	−3.47704			−0.162649			−0.0813246	−	0.996688i	$-0.525915\pi$
$457$	−3.47704			−0.162649			−0.0813246	+	0.996688i	$0.525915\pi$
$458$		0			0
$459$	5.81739	−	3.35867i	0.271533	−	0.156769i
$460$		0			0
$461$	−30.3222	+	17.5065i	−1.41225	+	0.815361i	−0.995600	−	0.0937072i	$-0.970128\pi$
$461$	−30.3222	+	17.5065i	−1.41225	+	0.815361i	−0.416647	+	0.909068i	$0.636795\pi$
$462$		0			0
$463$	−21.6790			−1.00751			−0.503755	−	0.863847i	$-0.668048\pi$
$463$	−21.6790			−1.00751			−0.503755	+	0.863847i	$0.668048\pi$
$464$		0			0
$465$	0.602313	−	1.04324i	0.0279316	−	0.0483790i
$466$		0			0
$467$			17.1508i			0.793643i	0.917896	+	0.396822i	$0.129887\pi$
$467$			17.1508i			0.793643i	−0.917896	+	0.396822i	$0.870113\pi$
$468$		0			0
$469$	−0.252868	−	0.145993i	−0.0116763	−	0.00674134i
$470$		0			0
$471$	1.30406	−	2.25870i	0.0600878	−	0.104075i
$472$		0			0
$473$	−0.225550	−	0.390664i	−0.0103708	−	0.0179628i
$474$		0			0
$475$	−20.9450	−	2.18983i	−0.961021	−	0.100476i
$476$		0			0
$477$	28.1219	−	16.2362i	1.28761	−	0.743404i
$478$		0			0
$479$	−14.4776	+	25.0759i	−0.661498	+	1.14575i	0.318724	+	0.947848i	$0.396746\pi$
$479$	−14.4776	+	25.0759i	−0.661498	+	1.14575i	−0.980222	+	0.197901i	$0.936588\pi$
$480$		0			0
$481$	−11.6229	+	20.1315i	−0.529961	+	0.917919i
$482$		0			0
$483$		−	1.55169i		−	0.0706044i
$484$		0			0
$485$	3.79665	+	2.19200i	0.172397	+	0.0995334i
$486$		0			0
$487$	−31.3183			−1.41917			−0.709584	−	0.704621i	$-0.751117\pi$
$487$	−31.3183			−1.41917			−0.709584	+	0.704621i	$0.751117\pi$
$488$		0			0
$489$	−3.48443	−	6.03521i	−0.157571	−	0.272922i
$490$		0			0
$491$	22.5766	−	13.0346i	1.01887	−	0.588245i	0.105093	−	0.994462i	$-0.466486\pi$
$491$	22.5766	−	13.0346i	1.01887	−	0.588245i	0.913776	+	0.406218i	$0.133153\pi$
$492$		0			0
$493$			5.46448i			0.246108i
$494$		0			0
$495$	−0.684066			−0.0307465
$496$		0			0
$497$	−2.44649	−	4.23745i	−0.109740	−	0.190075i
$498$		0			0
$499$	−14.5755	+	8.41515i	−0.652487	+	0.376714i	−0.789409	−	0.613868i	$-0.789613\pi$
$499$	−14.5755	+	8.41515i	−0.652487	+	0.376714i	0.136921	+	0.990582i	$0.456279\pi$
$500$		0			0
$501$		−	6.62600i		−	0.296028i
$502$		0			0
$503$	4.41768	−	7.65165i	0.196975	−	0.341170i	−0.750571	−	0.660789i	$-0.770222\pi$
$503$	4.41768	−	7.65165i	0.196975	−	0.341170i	0.947546	+	0.319619i	$0.103555\pi$
$504$		0			0
$505$	2.16960			0.0965458
$506$		0			0
$507$	3.47874	+	2.00845i	0.154496	+	0.0891985i
$508$		0			0
$509$	−38.6411	−	22.3094i	−1.71274	−	0.988849i	−0.930829	−	0.365454i	$-0.880914\pi$
$509$	−38.6411	−	22.3094i	−1.71274	−	0.988849i	−0.781907	−	0.623395i	$-0.785753\pi$
$510$		0			0
$511$	−1.61797	−	2.80240i	−0.0715746	−	0.123971i
$512$		0			0
$513$	−12.9179	+	5.75988i	−0.570339	+	0.254305i
$514$		0			0
$515$	4.82814	−	2.78753i	0.212753	−	0.122833i
$516$		0			0
$517$	4.51284	+	2.60549i	0.198475	+	0.114589i
$518$		0			0
$519$	−1.58544	+	2.74607i	−0.0695932	+	0.120539i
$520$		0			0
$521$	−11.0465			−0.483955			−0.241978	−	0.970282i	$-0.577796\pi$
$521$	−11.0465			−0.483955			−0.241978	+	0.970282i	$0.577796\pi$
$522$		0			0
$523$	21.7906	+	12.5808i	0.952838	+	0.550121i	0.893961	−	0.448144i	$-0.147915\pi$
$523$	21.7906	+	12.5808i	0.952838	+	0.550121i	0.0588767	+	0.998265i	$0.481248\pi$
$524$		0			0
$525$		−	1.56283i		−	0.0682076i
$526$		0			0
$527$	5.30737	+	9.19263i	0.231193	+	0.400437i
$528$		0			0
$529$	−0.00491365	−	0.00851069i	−0.000213637	−	0.000370030i
$530$		0			0
$531$			23.8155i			1.03350i
$532$		0			0
$533$		−	10.0216i		−	0.434084i
$534$		0			0
$535$	0.292200	+	0.506106i	0.0126329	+	0.0218808i
$536$		0			0
$537$	2.83772	+	4.91507i	0.122457	+	0.212101i
$538$		0			0
$539$			4.16251i			0.179292i
$540$		0			0
$541$	−26.9385	−	15.5529i	−1.15818	−	0.668673i	−0.207310	−	0.978275i	$-0.566471\pi$
$541$	−26.9385	−	15.5529i	−1.15818	−	0.668673i	−0.950866	+	0.309602i	$0.899804\pi$
$542$		0			0
$543$	10.9958			0.471876
$544$		0			0
$545$	−1.05473	+	1.82685i	−0.0451798	+	0.0782538i
$546$		0			0
$547$	−19.3115	−	11.1495i	−0.825700	−	0.476718i	0.0266781	−	0.999644i	$-0.491507\pi$
$547$	−19.3115	−	11.1495i	−0.825700	−	0.476718i	−0.852378	+	0.522926i	$0.824840\pi$
$548$		0			0
$549$	0.136893	−	0.0790355i	0.00584247	−	0.00337315i
$550$		0			0
$551$	1.19643	−	11.4434i	0.0509697	−	0.487507i
$552$		0			0
$553$	−2.54591	−	4.40964i	−0.108263	−	0.187517i
$554$		0			0
$555$	1.05698	+	0.610248i	0.0448663	+	0.0259036i
$556$		0			0
$557$	−24.0380	−	13.8784i	−1.01852	−	0.588045i	−0.104848	−	0.994488i	$-0.533436\pi$
$557$	−24.0380	−	13.8784i	−1.01852	−	0.588045i	−0.913676	+	0.406443i	$0.866769\pi$
$558$		0			0
$559$	−3.23941			−0.137013
$560$		0			0
$561$	−0.368923	+	0.638994i	−0.0155760	+	0.0269784i
$562$		0			0
$563$			30.7019i			1.29393i	0.762519	+	0.646966i	$0.223962\pi$
$563$			30.7019i			1.29393i	−0.762519	+	0.646966i	$0.776038\pi$
$564$		0			0
$565$	1.21107	−	0.699212i	0.0509502	−	0.0294161i
$566$		0			0
$567$	1.74254	+	3.01816i	0.0731796	+	0.126751i
$568$		0			0
$569$	−21.1756			−0.887726			−0.443863	−	0.896095i	$-0.646392\pi$
$569$	−21.1756			−0.887726			−0.443863	+	0.896095i	$0.646392\pi$
$570$		0			0
$571$			36.3708i			1.52207i	0.648710	+	0.761036i	$0.275309\pi$
$571$			36.3708i			1.52207i	−0.648710	+	0.761036i	$0.724691\pi$
$572$		0			0
$573$	7.29649	−	4.21263i	0.304815	−	0.175985i
$574$		0			0
$575$	−11.5875	−	20.0702i	−0.483233	−	0.836984i
$576$		0			0
$577$	−6.46302			−0.269059			−0.134530	−	0.990910i	$-0.542952\pi$
$577$	−6.46302			−0.269059			−0.134530	+	0.990910i	$0.542952\pi$
$578$		0			0
$579$	−8.77381	−	5.06556i	−0.364627	−	0.210517i
$580$		0			0
$581$		−	5.79749i		−	0.240520i
$582$		0			0
$583$	−3.78514	+	6.55605i	−0.156764	+	0.271524i
$584$		0			0
$585$	−2.45618	+	4.25424i	−0.101551	+	0.175891i
$586$		0			0
$587$	−7.78374	+	4.49395i	−0.321269	+	0.185485i	−0.651958	−	0.758255i	$-0.726052\pi$
$587$	−7.78374	+	4.49395i	−0.321269	+	0.185485i	0.330689	+	0.943740i	$0.392719\pi$
$588$		0			0
$589$	−9.10174	−	20.4128i	−0.375031	−	0.841095i
$590$		0			0
$591$	7.63399	+	13.2225i	0.314020	+	0.543899i
$592$		0			0
$593$	−12.5388	+	21.7178i	−0.514907	+	0.891845i	0.484944	+	0.874545i	$0.338840\pi$
$593$	−12.5388	+	21.7178i	−0.514907	+	0.891845i	−0.999850	+	0.0172992i	$0.994493\pi$
$594$		0			0
$595$	−0.416443	−	0.240434i	−0.0170725	−	0.00985682i
$596$		0			0
$597$		−	7.36464i		−	0.301415i
$598$		0			0
$599$	−23.0910	+	39.9948i	−0.943474	+	1.63415i	−0.184696	+	0.982796i	$0.559130\pi$
$599$	−23.0910	+	39.9948i	−0.943474	+	1.63415i	−0.758778	+	0.651349i	$0.774203\pi$
$600$		0			0
$601$	15.4513			0.630270			0.315135	−	0.949047i	$-0.397950\pi$
$601$	15.4513			0.630270			0.315135	+	0.949047i	$0.397950\pi$
$602$		0			0
$603$	−1.19510	+	0.689994i	−0.0486684	+	0.0280987i
$604$		0			0
$605$	−3.77465	+	2.17930i	−0.153461	+	0.0886009i
$606$		0			0
$607$	−10.7724			−0.437238			−0.218619	−	0.975810i	$-0.570155\pi$
$607$	−10.7724			−0.437238			−0.218619	+	0.975810i	$0.570155\pi$
$608$		0			0
$609$	0.853866			0.0346004
$610$		0			0
$611$	32.4073	−	18.7104i	1.31106	−	0.756941i
$612$		0			0
$613$	−29.0301	+	16.7605i	−1.17252	+	0.676952i	−0.954271	−	0.298942i	$-0.903366\pi$
$613$	−29.0301	+	16.7605i	−1.17252	+	0.676952i	−0.218244	+	0.975894i	$0.570033\pi$
$614$		0			0
$615$	−0.526172			−0.0212173
$616$		0			0
$617$	−8.26156	+	14.3094i	−0.332598	+	0.576076i	−0.983020	−	0.183496i	$-0.941258\pi$
$617$	−8.26156	+	14.3094i	−0.332598	+	0.576076i	0.650423	+	0.759572i	$0.274592\pi$
$618$		0			0
$619$		−	24.4924i		−	0.984431i	−0.870473	−	0.492216i	$-0.836187\pi$
$619$		−	24.4924i		−	0.984431i	0.870473	−	0.492216i	$-0.163813\pi$
$620$		0			0
$621$	−13.4796	−	7.78246i	−0.540918	−	0.312299i
$622$		0			0
$623$	2.40885	−	4.17225i	0.0965086	−	0.167158i
$624$		0			0
$625$	−11.2490	−	19.4838i	−0.449959	−	0.779351i
$626$		0			0
$627$	0.912488	−	1.25738i	0.0364413	−	0.0502148i
$628$		0			0
$629$	−9.31373	+	5.37729i	−0.371363	+	0.214406i
$630$		0			0
$631$	−14.4118	+	24.9620i	−0.573724	+	0.993720i	0.422455	+	0.906384i	$0.361169\pi$
$631$	−14.4118	+	24.9620i	−0.573724	+	0.993720i	−0.996179	+	0.0873357i	$0.972165\pi$
$632$		0			0
$633$	−4.55436	+	7.88838i	−0.181019	+	0.313535i
$634$		0			0
$635$			2.32967i			0.0924503i
$636$		0			0
$637$	25.8868	+	14.9458i	1.02567	+	0.592173i
$638$		0			0
$639$	−23.1252			−0.914820
$640$		0			0
$641$	16.9810	+	29.4120i	0.670710	+	1.16170i	0.977703	+	0.209992i	$0.0673437\pi$
$641$	16.9810	+	29.4120i	0.670710	+	1.16170i	−0.306994	+	0.951712i	$0.599323\pi$
$642$		0			0
$643$	8.60391	−	4.96747i	0.339305	−	0.195898i	−0.320660	−	0.947194i	$-0.603905\pi$
$643$	8.60391	−	4.96747i	0.339305	−	0.195898i	0.659965	+	0.751297i	$0.270571\pi$
$644$		0			0
$645$			0.170081i			0.00669694i
$646$		0			0
$647$	5.41778			0.212995			0.106497	−	0.994313i	$-0.466036\pi$
$647$	5.41778			0.212995			0.106497	+	0.994313i	$0.466036\pi$
$648$		0			0
$649$	−2.77605	−	4.80826i	−0.108969	−	0.188741i
$650$		0			0
$651$	1.43642	−	0.829317i	0.0562977	−	0.0325035i
$652$		0			0
$653$			36.9266i			1.44505i	0.691346	+	0.722524i	$0.257018\pi$
$653$			36.9266i			1.44505i	−0.691346	+	0.722524i	$0.742982\pi$
$654$		0			0
$655$	−1.61761	+	2.80179i	−0.0632053	+	0.109475i
$656$		0			0
$657$	−15.2937			−0.596663
$658$		0			0
$659$	13.4165	+	7.74604i	0.522634	+	0.301743i	0.738012	−	0.674788i	$-0.235765\pi$
$659$	13.4165	+	7.74604i	0.522634	+	0.301743i	−0.215378	+	0.976531i	$0.569098\pi$
$660$		0			0
$661$	−17.0451	−	9.84101i	−0.662979	−	0.382771i	0.130432	−	0.991457i	$-0.458363\pi$
$661$	−17.0451	−	9.84101i	−0.662979	−	0.382771i	−0.793411	+	0.608686i	$0.791697\pi$
$662$		0			0
$663$	2.64929	+	4.58870i	0.102890	+	0.178210i
$664$		0			0
$665$	0.819454	+	0.594684i	0.0317771	+	0.0230609i
$666$		0			0
$667$	10.9655	−	6.33093i	0.424586	−	0.245135i
$668$		0			0
$669$	2.41401	+	1.39373i	0.0933312	+	0.0538848i
$670$		0			0
$671$	−0.0184255	+	0.0319139i	−0.000711309	+	0.00123202i
$672$		0			0
$673$	17.4981			0.674502			0.337251	−	0.941415i	$-0.390503\pi$
$673$	17.4981			0.674502			0.337251	+	0.941415i	$0.390503\pi$
$674$		0			0
$675$	−13.5764	−	7.83834i	−0.522556	−	0.301698i
$676$		0			0
$677$		−	4.58479i		−	0.176208i	−0.996111	−	0.0881040i	$-0.971919\pi$
$677$		−	4.58479i		−	0.176208i	0.996111	−	0.0881040i	$-0.0280808\pi$
$678$		0			0
$679$	3.01813	+	5.22755i	0.115825	+	0.200615i
$680$		0			0
$681$	−6.06579	−	10.5062i	−0.232441	−	0.402600i
$682$		0			0
$683$		−	8.62342i		−	0.329966i	−0.986296	−	0.164983i	$-0.947243\pi$
$683$		−	8.62342i		−	0.329966i	0.986296	−	0.164983i	$-0.0527570\pi$
$684$		0			0
$685$		−	3.32972i		−	0.127222i
$686$		0			0
$687$	0.977471	+	1.69303i	0.0372928	+	0.0645931i
$688$		0			0
$689$	27.1816	+	47.0799i	1.03554	+	1.79360i
$690$		0			0
$691$			35.4700i			1.34934i	0.738118	+	0.674672i	$0.235715\pi$
$691$			35.4700i			1.34934i	−0.738118	+	0.674672i	$0.764285\pi$
$692$		0			0
$693$	−0.815693	−	0.470940i	−0.0309856	−	0.0178895i
$694$		0			0
$695$	3.56009			0.135042
$696$		0			0
$697$	2.31822	−	4.01527i	0.0878088	−	0.152089i
$698$		0			0
$699$	8.94908	+	5.16675i	0.338485	+	0.195424i
$700$		0			0
$701$	−13.5390	+	7.81676i	−0.511362	+	0.295235i	−0.733393	−	0.679805i	$-0.762065\pi$
$701$	−13.5390	+	7.81676i	−0.511362	+	0.295235i	0.222031	+	0.975040i	$0.428731\pi$
$702$		0			0
$703$	20.6817	−	9.22165i	0.780026	−	0.347801i
$704$		0			0
$705$	−0.982365	−	1.70151i	−0.0369980	−	0.0640824i
$706$		0			0
$707$	2.58707	+	1.49364i	0.0972966	+	0.0561742i
$708$		0			0
$709$	−27.8542	−	16.0816i	−1.04609	−	0.603958i	−0.124534	−	0.992215i	$-0.539744\pi$
$709$	−27.8542	−	16.0816i	−1.04609	−	0.603958i	−0.921551	+	0.388258i	$0.873077\pi$
$710$		0			0
$711$	−24.0650			−0.902507
$712$		0			0
$713$	12.2978	−	21.3005i	0.460557	−	0.797708i
$714$		0			0
$715$		−	1.14522i		−	0.0428287i
$716$		0			0
$717$	11.9872	−	6.92081i	0.447670	−	0.258462i
$718$		0			0
$719$	16.7342	+	28.9846i	0.624082	+	1.08094i	0.988718	+	0.149791i	$0.0478602\pi$
$719$	16.7342	+	28.9846i	0.624082	+	1.08094i	−0.364636	+	0.931150i	$0.618806\pi$
$720$		0			0
$721$	7.67621			0.285877
$722$		0			0
$723$		−	7.24437i		−	0.269421i
$724$		0			0
$725$	11.0442	−	6.37639i	0.410172	−	0.236813i
$726$		0			0
$727$	−19.4625	−	33.7100i	−0.721824	−	1.25024i	−0.960268	−	0.279080i	$-0.909971\pi$
$727$	−19.4625	−	33.7100i	−0.721824	−	1.25024i	0.238444	−	0.971156i	$-0.423363\pi$
$728$		0			0
$729$	10.9031			0.403819
$730$		0			0
$731$	−1.29791	−	0.749347i	−0.0480048	−	0.0277156i
$732$		0			0
$733$		−	45.8177i		−	1.69232i	−0.532932	−	0.846158i	$-0.678910\pi$
$733$		−	45.8177i		−	1.69232i	0.532932	−	0.846158i	$-0.321090\pi$
$734$		0			0
$735$	0.784709	−	1.35916i	0.0289444	−	0.0501332i
$736$		0			0
$737$	0.160858	−	0.278614i	0.00592528	−	0.0102629i
$738$		0			0
$739$	29.3064	−	16.9200i	1.07805	−	0.622414i	0.147682	−	0.989035i	$-0.452819\pi$
$739$	29.3064	−	16.9200i	1.07805	−	0.622414i	0.930370	+	0.366621i	$0.119486\pi$
$740$		0			0
$741$	−4.54333	−	10.1895i	−0.166904	−	0.374321i
$742$		0			0
$743$	1.57015	+	2.71958i	0.0576032	+	0.0997717i	0.893389	−	0.449284i	$-0.148321\pi$
$743$	1.57015	+	2.71958i	0.0576032	+	0.0997717i	−0.835786	+	0.549056i	$0.814988\pi$
$744$		0			0
$745$	1.58822	−	2.75087i	0.0581878	−	0.100784i
$746$		0			0
$747$	−23.7292	−	13.7001i	−0.868206	−	0.501259i
$748$		0			0
$749$			0.804652i			0.0294014i
$750$		0			0
$751$	−23.0858	+	39.9857i	−0.842412	+	1.45910i	0.0454379	+	0.998967i	$0.485532\pi$
$751$	−23.0858	+	39.9857i	−0.842412	+	1.45910i	−0.887850	+	0.460133i	$0.847802\pi$
$752$		0			0
$753$	−2.45256			−0.0893762
$754$		0			0
$755$	−3.62996	+	2.09576i	−0.132108	+	0.0762725i
$756$		0			0
$757$	14.6388	−	8.45169i	0.532055	−	0.307182i	−0.209798	−	0.977745i	$-0.567281\pi$
$757$	14.6388	−	8.45169i	0.532055	−	0.307182i	0.741853	+	0.670563i	$0.233947\pi$
$758$		0			0
$759$	1.70968			0.0620575
$760$		0			0
$761$	−39.6686			−1.43799			−0.718993	−	0.695018i	$-0.755396\pi$
$761$	−39.6686			−1.43799			−0.718993	+	0.695018i	$0.755396\pi$
$762$		0			0
$763$	−2.51537	+	1.45225i	−0.0910624	+	0.0525749i
$764$		0			0
$765$	−1.96820	+	1.13634i	−0.0711603	+	0.0410844i
$766$		0			0
$767$	−39.8703			−1.43963
$768$		0			0
$769$	−16.1994	+	28.0582i	−0.584166	+	1.01180i	0.410813	+	0.911719i	$0.365245\pi$
$769$	−16.1994	+	28.0582i	−0.584166	+	1.01180i	−0.994979	+	0.100085i	$0.968089\pi$
$770$		0			0
$771$		−	11.0660i		−	0.398533i
$772$		0			0
$773$	−2.91042	−	1.68033i	−0.104680	−	0.0604373i	0.446746	−	0.894661i	$-0.352583\pi$
$773$	−2.91042	−	1.68033i	−0.104680	−	0.0604373i	−0.551426	+	0.834224i	$0.685916\pi$
$774$		0			0
$775$	12.3861	−	21.4534i	0.444923	−	0.770629i
$776$		0			0
$777$	0.840242	+	1.45534i	0.0301435	+	0.0522101i
$778$		0			0
$779$	−5.73384	+	7.90103i	−0.205436	+	0.283084i
$780$		0			0
$781$	4.66890	−	2.69559i	0.167066	−	0.0964557i
$782$		0			0
$783$	4.28254	−	7.41757i	0.153045	−	0.265082i
$784$		0			0
$785$	−0.936410	+	1.62191i	−0.0334219	+	0.0578884i
$786$		0			0
$787$			47.0238i			1.67622i	0.545502	+	0.838109i	$0.316339\pi$
$787$			47.0238i			1.67622i	−0.545502	+	0.838109i	$0.683661\pi$
$788$		0			0
$789$	6.66595	+	3.84859i	0.237314	+	0.137013i
$790$		0			0
$791$	1.92547			0.0684619
$792$		0			0
$793$	0.132316	+	0.229178i	0.00469868	+	0.00813835i
$794$		0			0
$795$	2.47187	−	1.42713i	0.0876681	−	0.0506152i
$796$		0			0
$797$		−	3.27254i		−	0.115919i	−0.998319	−	0.0579596i	$-0.981541\pi$
$797$		−	3.27254i		−	0.115919i	0.998319	−	0.0579596i	$-0.0184595\pi$
$798$		0			0
$799$	17.3125			0.612472
$800$		0			0
$801$	−11.3847	−	19.7189i	−0.402259	−	0.696734i
$802$		0			0
$803$	3.08773	−	1.78270i	0.108964	−	0.0629103i
$804$		0			0
$805$			1.11423i			0.0392714i
$806$		0			0
$807$	2.65352	−	4.59603i	0.0934082	−	0.161788i
$808$		0			0
$809$	−39.4070			−1.38548			−0.692738	−	0.721190i	$-0.743596\pi$
$809$	−39.4070			−1.38548			−0.692738	+	0.721190i	$0.743596\pi$
$810$		0			0
$811$	−19.7726	−	11.4157i	−0.694309	−	0.400860i	0.110915	−	0.993830i	$-0.464622\pi$
$811$	−19.7726	−	11.4157i	−0.694309	−	0.400860i	−0.805224	+	0.592970i	$0.797955\pi$
$812$		0			0
$813$	−11.2536	−	6.49727i	−0.394681	−	0.227869i
$814$		0			0
$815$	2.50208	+	4.33373i	0.0876440	+	0.151804i
$816$		0			0
$817$	2.55395	+	1.85342i	0.0893514	+	0.0648430i
$818$		0			0
$819$	−5.85760	+	3.38188i	−0.204681	+	0.118173i
$820$		0			0
$821$	12.3194	+	7.11259i	0.429949	+	0.248231i	0.699325	−	0.714804i	$-0.253484\pi$
$821$	12.3194	+	7.11259i	0.429949	+	0.248231i	−0.269376	+	0.963035i	$0.586817\pi$
$822$		0			0
$823$	6.38028	−	11.0510i	0.222403	−	0.385213i	−0.733134	−	0.680084i	$-0.761943\pi$
$823$	6.38028	−	11.0510i	0.222403	−	0.385213i	0.955537	+	0.294871i	$0.0952767\pi$
$824$		0			0
$825$	1.72196			0.0599509
$826$		0			0
$827$	29.6616	+	17.1251i	1.03143	+	0.595499i	0.917395	−	0.397977i	$-0.130288\pi$
$827$	29.6616	+	17.1251i	1.03143	+	0.595499i	0.114040	+	0.993476i	$0.463621\pi$
$828$		0			0
$829$			50.6534i			1.75927i	0.475652	+	0.879633i	$0.342212\pi$
$829$			50.6534i			1.75927i	−0.475652	+	0.879633i	$0.657788\pi$
$830$		0			0
$831$	−2.96663	−	5.13835i	−0.102911	−	0.178247i
$832$		0			0
$833$	6.91457	+	11.9764i	0.239576	+	0.414957i
$834$		0			0
$835$			4.75796i			0.164656i
$836$		0			0
$837$		−	16.6376i		−	0.575081i
$838$		0			0
$839$	23.1996	+	40.1828i	0.800938	+	1.38726i	0.919000	+	0.394259i	$0.128999\pi$
$839$	23.1996	+	40.1828i	0.800938	+	1.38726i	−0.118062	+	0.993006i	$0.537668\pi$
$840$		0			0
$841$	−11.0162	−	19.0806i	−0.379869	−	0.657953i
$842$		0			0
$843$			9.50427i			0.327344i
$844$		0			0
$845$	−2.49799	−	1.44222i	−0.0859336	−	0.0496138i
$846$		0			0
$847$	−6.00128			−0.206206
$848$		0			0
$849$	−3.62818	+	6.28420i	−0.124519	+	0.215673i
$850$		0			0
$851$	21.5811	+	12.4598i	0.739789	+	0.427118i
$852$		0			0
$853$	−13.5431	+	7.81910i	−0.463706	+	0.267721i	−0.713601	−	0.700552i	$-0.752937\pi$
$853$	−13.5431	+	7.81910i	−0.463706	+	0.267721i	0.249895	+	0.968273i	$0.419604\pi$
$854$		0			0
$855$	4.37050	−	1.94874i	0.149468	−	0.0666454i
$856$		0			0
$857$	−25.6351	−	44.4013i	−0.875679	−	1.51672i	−0.856037	−	0.516914i	$-0.827081\pi$
$857$	−25.6351	−	44.4013i	−0.875679	−	1.51672i	−0.0196420	−	0.999807i	$-0.506253\pi$
$858$		0			0
$859$	11.0574	+	6.38399i	0.377274	+	0.217819i	0.676631	−	0.736322i	$-0.263439\pi$
$859$	11.0574	+	6.38399i	0.377274	+	0.217819i	−0.299358	+	0.954141i	$0.596772\pi$
$860$		0			0
$861$	−0.627417	−	0.362239i	−0.0213823	−	0.0123451i
$862$		0			0
$863$	−14.4704			−0.492577			−0.246289	−	0.969197i	$-0.579211\pi$
$863$	−14.4704			−0.492577			−0.246289	+	0.969197i	$0.579211\pi$
$864$		0			0
$865$	1.13847	−	1.97188i	0.0387090	−	0.0670459i
$866$		0			0
$867$		−	7.27253i		−	0.246988i
$868$		0			0
$869$	4.85863	−	2.80513i	0.164818	−	0.0951575i
$870$		0			0
$871$	−1.15514	−	2.00077i	−0.0391405	−	0.0677934i
$872$		0			0
$873$	28.5286			0.965546
$874$		0			0
$875$			2.28364i			0.0772013i
$876$		0			0
$877$	41.2494	−	23.8154i	1.39289	−	0.804188i	0.399260	−	0.916838i	$-0.369267\pi$
$877$	41.2494	−	23.8154i	1.39289	−	0.804188i	0.993635	+	0.112650i	$0.0359339\pi$
$878$		0			0
$879$	1.62388	+	2.81264i	0.0547720	+	0.0948679i
$880$		0			0
$881$	51.7908			1.74488			0.872438	−	0.488725i	$-0.162538\pi$
$881$	51.7908			1.74488			0.872438	+	0.488725i	$0.162538\pi$
$882$		0			0
$883$	−36.9253	−	21.3188i	−1.24264	−	0.717436i	−0.273005	−	0.962013i	$-0.588018\pi$
$883$	−36.9253	−	21.3188i	−1.24264	−	0.717436i	−0.969630	+	0.244577i	$0.921351\pi$
$884$		0			0
$885$			2.09334i			0.0703669i
$886$		0			0
$887$	−4.54128	+	7.86572i	−0.152481	+	0.264105i	−0.932139	−	0.362101i	$-0.882060\pi$
$887$	−4.54128	+	7.86572i	−0.152481	+	0.264105i	0.779658	+	0.626206i	$0.215393\pi$
$888$		0			0
$889$	−1.60385	+	2.77795i	−0.0537913	+	0.0931693i
$890$		0			0
$891$	−3.32546	+	1.91996i	−0.111407	+	0.0643210i
$892$		0			0
$893$	−36.2550	−	3.79052i	−1.21323	−	0.126845i
$894$		0			0
$895$	−2.03769	−	3.52938i	−0.0681125	−	0.117974i
$896$		0			0
$897$	6.13873	−	10.6326i	0.204966	−	0.355012i
$898$		0			0
$899$	11.7212	+	6.76725i	0.390925	+	0.225701i
$900$		0			0
$901$			25.1508i			0.837894i
$902$		0			0
$903$	−0.117091	+	0.202808i	−0.00389655	+	0.00674902i
$904$		0			0
$905$	−7.89581			−0.262466
$906$		0			0
$907$	9.13860	−	5.27618i	0.303442	−	0.175193i	−0.340546	−	0.940228i	$-0.610612\pi$
$907$	9.13860	−	5.27618i	0.303442	−	0.175193i	0.643988	+	0.765035i	$0.277279\pi$
$908$		0			0
$909$	12.2270	−	7.05926i	0.405544	−	0.234141i
$910$		0			0
$911$	29.0098			0.961137			0.480569	−	0.876957i	$-0.340430\pi$
$911$	29.0098			0.961137			0.480569	+	0.876957i	$0.340430\pi$
$912$		0			0
$913$	6.38778			0.211405
$914$		0			0
$915$	0.0120327	−	0.00694709i	0.000397789	−	0.000229664i
$916$		0			0
$917$	−3.85774	+	2.22727i	−0.127394	+	0.0735508i
$918$		0			0
$919$	−14.0200			−0.462476			−0.231238	−	0.972897i	$-0.574278\pi$
$919$	−14.0200			−0.462476			−0.231238	+	0.972897i	$0.574278\pi$
$920$		0			0
$921$	0.691854	−	1.19833i	0.0227974	−	0.0394862i
$922$		0			0
$923$		−	38.7148i		−	1.27431i
$924$		0			0
$925$	21.7360	+	12.5493i	0.714676	+	0.412618i
$926$		0			0
$927$	18.1397	−	31.4188i	0.595785	−	1.03193i
$928$		0			0
$929$	15.0890	+	26.1349i	0.495054	+	0.857459i	0.999984	−	0.00570137i	$-0.00181481\pi$
$929$	15.0890	+	26.1349i	0.495054	+	0.857459i	−0.504929	+	0.863161i	$0.668481\pi$
$930$		0			0
$931$	−11.8580	−	26.5943i	−0.388630	−	0.871594i
$932$		0			0
$933$	−8.93834	+	5.16056i	−0.292628	+	0.168949i
$934$		0			0
$935$	0.264914	−	0.458845i	0.00866362	−	0.0150058i
$936$		0			0
$937$	5.42494	−	9.39628i	0.177225	−	0.306963i	−0.763704	−	0.645567i	$-0.776621\pi$
$937$	5.42494	−	9.39628i	0.177225	−	0.306963i	0.940929	+	0.338604i	$0.109955\pi$
$938$		0			0
$939$		−	1.03281i		−	0.0337045i
$940$		0			0
$941$	31.4879	+	18.1795i	1.02648	+	0.592636i	0.915973	−	0.401240i	$-0.131421\pi$
$941$	31.4879	+	18.1795i	1.02648	+	0.592636i	0.110503	+	0.993876i	$0.464754\pi$
$942$		0			0
$943$	−10.7432			−0.349846
$944$		0			0
$945$	0.376858	+	0.652737i	0.0122592	+	0.0212336i
$946$		0			0
$947$	−49.9527	+	28.8402i	−1.62324	+	0.937180i	−0.637198	+	0.770700i	$0.719907\pi$
$947$	−49.9527	+	28.8402i	−1.62324	+	0.937180i	−0.986045	+	0.166480i	$0.946760\pi$
$948$		0			0
$949$		−	25.6037i		−	0.831130i
$950$		0			0
$951$	9.19001			0.298006
$952$		0			0
$953$	−8.57213	−	14.8474i	−0.277679	−	0.480954i	0.693129	−	0.720814i	$-0.256232\pi$
$953$	−8.57213	−	14.8474i	−0.277679	−	0.480954i	−0.970807	+	0.239860i	$0.922898\pi$
$954$		0			0
$955$	−5.23942	+	3.02498i	−0.169544	+	0.0978861i
$956$		0			0
$957$			0.940805i			0.0304119i
$958$		0			0
$959$	2.29232	−	3.97042i	0.0740229	−	0.128211i
$960$		0			0
$961$	−4.70924			−0.151911
$962$		0			0
$963$	3.29345	+	1.90148i	0.106130	+	0.0612742i
$964$		0			0
$965$	6.30024	+	3.63744i	0.202812	+	0.117093i
$966$		0			0
$967$	−16.2235	−	28.0999i	−0.521712	−	0.903631i	−0.999681	−	0.0252548i	$-0.991960\pi$
$967$	−16.2235	−	28.0999i	−0.521712	−	0.903631i	0.477969	−	0.878377i	$-0.341373\pi$
$968$		0			0
$969$	0.536717	−	5.13351i	0.0172418	−	0.164912i
$970$		0			0
$971$	37.5884	−	21.7017i	1.20627	−	0.696441i	0.244328	−	0.969693i	$-0.421433\pi$
$971$	37.5884	−	21.7017i	1.20627	−	0.696441i	0.961943	+	0.273252i	$0.0880993\pi$
$972$		0			0
$973$	4.24511	+	2.45092i	0.136092	+	0.0785728i
$974$		0			0
$975$	6.18280	−	10.7089i	0.198008	−	0.342960i
$976$		0			0
$977$	31.4161			1.00509			0.502544	−	0.864551i	$-0.332397\pi$
$977$	31.4161			1.00509			0.502544	+	0.864551i	$0.332397\pi$
$978$		0			0
$979$	4.59706	+	2.65412i	0.146923	+	0.0848259i
$980$		0			0
$981$			13.7272i			0.438277i
$982$		0			0
$983$	20.5214	+	35.5441i	0.654531	+	1.13368i	0.982011	+	0.188823i	$0.0604672\pi$
$983$	20.5214	+	35.5441i	0.654531	+	1.13368i	−0.327480	+	0.944858i	$0.606199\pi$
$984$		0			0
$985$	−5.48177	−	9.49470i	−0.174664	−	0.302526i
$986$		0			0
$987$		−	2.70521i		−	0.0861077i
$988$		0			0
$989$			3.47266i			0.110424i
$990$		0			0
$991$	17.2514	+	29.8803i	0.548009	+	0.949179i	0.998411	+	0.0563529i	$0.0179472\pi$
$991$	17.2514	+	29.8803i	0.548009	+	0.949179i	−0.450402	+	0.892826i	$0.648719\pi$
$992$		0			0
$993$	−3.26010	−	5.64665i	−0.103456	−	0.179191i
$994$		0			0
$995$			5.28835i			0.167652i
$996$		0			0
$997$	31.1621	+	17.9915i	0.986915	+	0.569796i	0.904351	−	0.426790i	$-0.140356\pi$
$997$	31.1621	+	17.9915i	0.986915	+	0.569796i	0.0825644	+	0.996586i	$0.473689\pi$
$998$		0			0
$999$	16.8568			0.533326

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1216.2.t.d.1185.8	yes	24
4.3	odd	2	inner	1216.2.t.d.1185.6	yes	24
8.3	odd	2		1216.2.t.e.1185.8	yes	24
8.5	even	2		1216.2.t.e.1185.6	yes	24
19.11	even	3		1216.2.t.e.353.6	yes	24
76.11	odd	6		1216.2.t.e.353.8	yes	24
152.11	odd	6	inner	1216.2.t.d.353.6	✓	24
152.125	even	6	inner	1216.2.t.d.353.8	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1216.2.t.d.353.6	✓	24	152.11	odd	6	inner
1216.2.t.d.353.8	yes	24	152.125	even	6	inner
1216.2.t.d.1185.6	yes	24	4.3	odd	2	inner
1216.2.t.d.1185.8	yes	24	1.1	even	1	trivial
1216.2.t.e.353.6	yes	24	19.11	even	3
1216.2.t.e.353.8	yes	24	76.11	odd	6
1216.2.t.e.1185.6	yes	24	8.5	even	2
1216.2.t.e.1185.8	yes	24	8.3	odd	2

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:	\( N \)	\(=\)	\( 1216 = 2^{6} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1216.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.495361 - 0.285997i) q^{3} +(-0.355705 + 0.205367i) q^{5} -0.565533 q^{7} +(-1.33641 + 2.31473i) q^{9} +O(q^{10})\)	\(q+(0.495361 - 0.285997i) q^{3} +(-0.355705 + 0.205367i) q^{5} -0.565533 q^{7} +(-1.33641 + 2.31473i) q^{9} -0.623114i q^{11} +(-3.87518 - 2.23733i) q^{13} +(-0.117468 + 0.203461i) q^{15} +(-1.03509 - 1.79283i) q^{17} +(1.77510 + 3.98108i) q^{19} +(-0.280143 + 0.161740i) q^{21} +(-2.39843 + 4.15420i) q^{23} +(-2.41565 + 4.18403i) q^{25} +3.24482i q^{27} +(-2.28597 - 1.31981i) q^{29} -5.12745 q^{31} +(-0.178209 - 0.308666i) q^{33} +(0.201163 - 0.116142i) q^{35} -5.19500i q^{37} -2.55948 q^{39} +(1.11982 + 1.93958i) q^{41} +(0.626955 - 0.361972i) q^{43} -1.09782i q^{45} +(-4.18140 + 7.24240i) q^{47} -6.68017 q^{49} +(-1.02548 - 0.592064i) q^{51} +(-10.5214 - 6.07455i) q^{53} +(0.127967 + 0.221645i) q^{55} +(2.01789 + 1.46440i) q^{57} +(7.71649 - 4.45512i) q^{59} +(-0.0512168 - 0.0295700i) q^{61} +(0.755785 - 1.30906i) q^{63} +1.83789 q^{65} +(0.447132 + 0.258152i) q^{67} +2.74377i q^{69} +(4.32599 + 7.49284i) q^{71} +(2.86096 + 4.95533i) q^{73} +2.76347i q^{75} +0.352392i q^{77} +(4.50179 + 7.79733i) q^{79} +(-3.08123 - 5.33684i) q^{81} +10.2514i q^{83} +(0.736374 + 0.425145i) q^{85} -1.50984 q^{87} +(-4.25944 + 7.37756i) q^{89} +(2.19154 + 1.26529i) q^{91} +(-2.53994 + 1.46643i) q^{93} +(-1.44899 - 1.05155i) q^{95} +(-5.33679 - 9.24359i) q^{97} +(1.44234 + 0.832737i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{5} + 8 q^{9}+O(q^{10}) \) 24 * q - 6 * q^5 + 8 * q^9	\( 24 q - 6 q^{5} + 8 q^{9} + 30 q^{13} + 6 q^{17} + 24 q^{21} + 6 q^{25} + 42 q^{29} - 14 q^{33} - 24 q^{41} + 24 q^{49} - 18 q^{53} - 42 q^{57} + 18 q^{61} - 20 q^{65} - 16 q^{73} + 52 q^{81} - 78 q^{85} + 14 q^{89} + 60 q^{93} - 4 q^{97}+O(q^{100}) \) 24 * q - 6 * q^5 + 8 * q^9 + 30 * q^13 + 6 * q^17 + 24 * q^21 + 6 * q^25 + 42 * q^29 - 14 * q^33 - 24 * q^41 + 24 * q^49 - 18 * q^53 - 42 * q^57 + 18 * q^61 - 20 * q^65 - 16 * q^73 + 52 * q^81 - 78 * q^85 + 14 * q^89 + 60 * q^93 - 4 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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