LMFDB - Embedded newform 441.2.e.f.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(226,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("441.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 147)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.2
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	441.361
Dual form			441.2.e.f.226.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.207107 + 0.358719i) q^{2} +(0.914214 - 1.58346i) q^{4} +(-1.70711 - 2.95680i) q^{5} +1.58579 q^{8} +O(q^{10})$	\(q+(0.207107 + 0.358719i) q^{2} +(0.914214 - 1.58346i) q^{4} +(-1.70711 - 2.95680i) q^{5} +1.58579 q^{8} +(0.707107 - 1.22474i) q^{10} +(-1.00000 + 1.73205i) q^{11} -2.58579 q^{13} +(-1.50000 - 2.59808i) q^{16} +(1.12132 - 1.94218i) q^{17} +(-1.41421 - 2.44949i) q^{19} -6.24264 q^{20} -0.828427 q^{22} +(-3.82843 - 6.63103i) q^{23} +(-3.32843 + 5.76500i) q^{25} +(-0.535534 - 0.927572i) q^{26} +6.82843 q^{29} +(-0.585786 + 1.01461i) q^{31} +(2.20711 - 3.82282i) q^{32} +0.928932 q^{34} +(2.00000 + 3.46410i) q^{37} +(0.585786 - 1.01461i) q^{38} +(-2.70711 - 4.68885i) q^{40} +6.24264 q^{41} +5.65685 q^{43} +(1.82843 + 3.16693i) q^{44} +(1.58579 - 2.74666i) q^{46} +(1.41421 + 2.44949i) q^{47} -2.75736 q^{50} +(-2.36396 + 4.09450i) q^{52} +(-1.00000 + 1.73205i) q^{53} +6.82843 q^{55} +(1.41421 + 2.44949i) q^{58} +(0.585786 - 1.01461i) q^{59} +(6.12132 + 10.6024i) q^{61} -0.485281 q^{62} -4.17157 q^{64} +(4.41421 + 7.64564i) q^{65} +(2.82843 - 4.89898i) q^{67} +(-2.05025 - 3.55114i) q^{68} -9.31371 q^{71} +(6.94975 - 12.0373i) q^{73} +(-0.828427 + 1.43488i) q^{74} -5.17157 q^{76} +(-6.82843 - 11.8272i) q^{79} +(-5.12132 + 8.87039i) q^{80} +(1.29289 + 2.23936i) q^{82} +7.31371 q^{83} -7.65685 q^{85} +(1.17157 + 2.02922i) q^{86} +(-1.58579 + 2.74666i) q^{88} +(7.12132 + 12.3345i) q^{89} -14.0000 q^{92} +(-0.585786 + 1.01461i) q^{94} +(-4.82843 + 8.36308i) q^{95} -2.58579 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} - 4 q^{5} + 12 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^4 - 4 * q^5 + 12 * q^8	$ 4 q - 2 q^{2} - 2 q^{4} - 4 q^{5} + 12 q^{8} - 4 q^{11} - 16 q^{13} - 6 q^{16} - 4 q^{17} - 8 q^{20} + 8 q^{22} - 4 q^{23} - 2 q^{25} + 12 q^{26} + 16 q^{29} - 8 q^{31} + 6 q^{32} + 32 q^{34} + 8 q^{37} + 8 q^{38} - 8 q^{40} + 8 q^{41} - 4 q^{44} + 12 q^{46} - 28 q^{50} + 16 q^{52} - 4 q^{53} + 16 q^{55} + 8 q^{59} + 16 q^{61} + 32 q^{62} - 28 q^{64} + 12 q^{65} - 28 q^{68} + 8 q^{71} + 8 q^{73} + 8 q^{74} - 32 q^{76} - 16 q^{79} - 12 q^{80} + 8 q^{82} - 16 q^{83} - 8 q^{85} + 16 q^{86} - 12 q^{88} + 20 q^{89} - 56 q^{92} - 8 q^{94} - 8 q^{95} - 16 q^{97}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 - 4 * q^5 + 12 * q^8 - 4 * q^11 - 16 * q^13 - 6 * q^16 - 4 * q^17 - 8 * q^20 + 8 * q^22 - 4 * q^23 - 2 * q^25 + 12 * q^26 + 16 * q^29 - 8 * q^31 + 6 * q^32 + 32 * q^34 + 8 * q^37 + 8 * q^38 - 8 * q^40 + 8 * q^41 - 4 * q^44 + 12 * q^46 - 28 * q^50 + 16 * q^52 - 4 * q^53 + 16 * q^55 + 8 * q^59 + 16 * q^61 + 32 * q^62 - 28 * q^64 + 12 * q^65 - 28 * q^68 + 8 * q^71 + 8 * q^73 + 8 * q^74 - 32 * q^76 - 16 * q^79 - 12 * q^80 + 8 * q^82 - 16 * q^83 - 8 * q^85 + 16 * q^86 - 12 * q^88 + 20 * q^89 - 56 * q^92 - 8 * q^94 - 8 * q^95 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.207107	+	0.358719i	0.146447	+	0.253653i	0.929912	−	0.367783i	$-0.119883\pi$
$2$	0.207107	+	0.358719i	0.146447	+	0.253653i	−0.783465	+	0.621436i	$0.786550\pi$
$3$		0			0
$3$		0			0
$4$	0.914214	−	1.58346i	0.457107	−	0.791732i
$5$	−1.70711	−	2.95680i	−0.763441	−	1.32232i	−0.941067	−	0.338221i	$-0.890175\pi$
$5$	−1.70711	−	2.95680i	−0.763441	−	1.32232i	0.177625	−	0.984098i	$-0.443158\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	1.58579			0.560660
$9$		0			0
$10$	0.707107	−	1.22474i	0.223607	−	0.387298i
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	−0.976478	−	0.215615i	$-0.930824\pi$
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	0.674967	+	0.737848i	$0.264158\pi$
$12$		0			0
$13$	−2.58579			−0.717168			−0.358584	−	0.933497i	$-0.616740\pi$
$13$	−2.58579			−0.717168			−0.358584	+	0.933497i	$0.616740\pi$
$14$		0			0
$15$		0			0
$16$	−1.50000	−	2.59808i	−0.375000	−	0.649519i
$17$	1.12132	−	1.94218i	0.271960	−	0.471049i	−0.697404	−	0.716679i	$-0.745661\pi$
$17$	1.12132	−	1.94218i	0.271960	−	0.471049i	0.969364	+	0.245630i	$0.0789948\pi$
$18$		0			0
$19$	−1.41421	−	2.44949i	−0.324443	−	0.561951i	0.656957	−	0.753928i	$-0.271843\pi$
$19$	−1.41421	−	2.44949i	−0.324443	−	0.561951i	−0.981399	+	0.191977i	$0.938510\pi$
$20$	−6.24264			−1.39590
$21$		0			0
$22$	−0.828427			−0.176621
$23$	−3.82843	−	6.63103i	−0.798282	−	1.38267i	−0.920734	−	0.390191i	$-0.872409\pi$
$23$	−3.82843	−	6.63103i	−0.798282	−	1.38267i	0.122452	−	0.992474i	$-0.460924\pi$
$24$		0			0
$25$	−3.32843	+	5.76500i	−0.665685	+	1.15300i
$26$	−0.535534	−	0.927572i	−0.105027	−	0.181912i
$27$		0			0
$28$		0			0
$29$	6.82843			1.26801			0.634004	−	0.773330i	$-0.281410\pi$
$29$	6.82843			1.26801			0.634004	+	0.773330i	$0.281410\pi$
$30$		0			0
$31$	−0.585786	+	1.01461i	−0.105210	+	0.182230i	−0.913824	−	0.406110i	$-0.866885\pi$
$31$	−0.585786	+	1.01461i	−0.105210	+	0.182230i	0.808614	+	0.588340i	$0.200218\pi$
$32$	2.20711	−	3.82282i	0.390165	−	0.675786i
$33$		0			0
$34$	0.928932			0.159311
$35$		0			0
$36$		0			0
$37$	2.00000	+	3.46410i	0.328798	+	0.569495i	0.982274	−	0.187453i	$-0.0600231\pi$
$37$	2.00000	+	3.46410i	0.328798	+	0.569495i	−0.653476	+	0.756948i	$0.726690\pi$
$38$	0.585786	−	1.01461i	0.0950271	−	0.164592i
$39$		0			0
$40$	−2.70711	−	4.68885i	−0.428031	−	0.741372i
$41$	6.24264			0.974937			0.487468	−	0.873141i	$-0.337920\pi$
$41$	6.24264			0.974937			0.487468	+	0.873141i	$0.337920\pi$
$42$		0			0
$43$	5.65685			0.862662			0.431331	−	0.902194i	$-0.358044\pi$
$43$	5.65685			0.862662			0.431331	+	0.902194i	$0.358044\pi$
$44$	1.82843	+	3.16693i	0.275646	+	0.477432i
$45$		0			0
$46$	1.58579	−	2.74666i	0.233811	−	0.404973i
$47$	1.41421	+	2.44949i	0.206284	+	0.357295i	0.950541	−	0.310599i	$-0.100530\pi$
$47$	1.41421	+	2.44949i	0.206284	+	0.357295i	−0.744257	+	0.667893i	$0.767196\pi$
$48$		0			0
$49$		0			0
$50$	−2.75736			−0.389949
$51$		0			0
$52$	−2.36396	+	4.09450i	−0.327822	+	0.567805i
$53$	−1.00000	+	1.73205i	−0.137361	+	0.237915i	−0.926497	−	0.376303i	$-0.877195\pi$
$53$	−1.00000	+	1.73205i	−0.137361	+	0.237915i	0.789136	+	0.614218i	$0.210529\pi$
$54$		0			0
$55$	6.82843			0.920745
$56$		0			0
$57$		0			0
$58$	1.41421	+	2.44949i	0.185695	+	0.321634i
$59$	0.585786	−	1.01461i	0.0762629	−	0.132091i	−0.825372	−	0.564589i	$-0.809035\pi$
$59$	0.585786	−	1.01461i	0.0762629	−	0.132091i	0.901635	+	0.432498i	$0.142368\pi$
$60$		0			0
$61$	6.12132	+	10.6024i	0.783755	+	1.35750i	0.929740	+	0.368216i	$0.120031\pi$
$61$	6.12132	+	10.6024i	0.783755	+	1.35750i	−0.145985	+	0.989287i	$0.546635\pi$
$62$	−0.485281			−0.0616308
$63$		0			0
$64$	−4.17157			−0.521447
$65$	4.41421	+	7.64564i	0.547516	+	0.948325i
$66$		0			0
$67$	2.82843	−	4.89898i	0.345547	−	0.598506i	−0.639906	−	0.768453i	$-0.721027\pi$
$67$	2.82843	−	4.89898i	0.345547	−	0.598506i	0.985453	+	0.169948i	$0.0543599\pi$
$68$	−2.05025	−	3.55114i	−0.248630	−	0.430639i
$69$		0			0
$70$		0			0
$71$	−9.31371			−1.10533			−0.552667	−	0.833402i	$-0.686390\pi$
$71$	−9.31371			−1.10533			−0.552667	+	0.833402i	$0.686390\pi$
$72$		0			0
$73$	6.94975	−	12.0373i	0.813406	−	1.40886i	−0.0970601	−	0.995279i	$-0.530944\pi$
$73$	6.94975	−	12.0373i	0.813406	−	1.40886i	0.910467	−	0.413583i	$-0.135723\pi$
$74$	−0.828427	+	1.43488i	−0.0963027	+	0.166801i
$75$		0			0
$76$	−5.17157			−0.593220
$77$		0			0
$78$		0			0
$79$	−6.82843	−	11.8272i	−0.768258	−	1.33066i	−0.938507	−	0.345261i	$-0.887790\pi$
$79$	−6.82843	−	11.8272i	−0.768258	−	1.33066i	0.170249	−	0.985401i	$-0.445543\pi$
$80$	−5.12132	+	8.87039i	−0.572581	+	0.991739i
$81$		0			0
$82$	1.29289	+	2.23936i	0.142776	+	0.247296i
$83$	7.31371			0.802784			0.401392	−	0.915906i	$-0.368527\pi$
$83$	7.31371			0.802784			0.401392	+	0.915906i	$0.368527\pi$
$84$		0			0
$85$	−7.65685			−0.830502
$86$	1.17157	+	2.02922i	0.126334	+	0.218817i
$87$		0			0
$88$	−1.58579	+	2.74666i	−0.169045	+	0.292795i
$89$	7.12132	+	12.3345i	0.754858	+	1.30745i	0.945445	+	0.325783i	$0.105628\pi$
$89$	7.12132	+	12.3345i	0.754858	+	1.30745i	−0.190586	+	0.981670i	$0.561039\pi$
$90$		0			0
$91$		0			0
$92$	−14.0000			−1.45960
$93$		0			0
$94$	−0.585786	+	1.01461i	−0.0604193	+	0.104649i
$95$	−4.82843	+	8.36308i	−0.495386	+	0.858034i
$96$		0			0
$97$	−2.58579			−0.262547			−0.131273	−	0.991346i	$-0.541907\pi$
$97$	−2.58579			−0.262547			−0.131273	+	0.991346i	$0.541907\pi$
$98$		0			0
$99$		0			0
$100$	6.08579	+	10.5409i	0.608579	+	1.05409i
$101$	−1.46447	+	2.53653i	−0.145720	+	0.252394i	−0.929641	−	0.368466i	$-0.879883\pi$
$101$	−1.46447	+	2.53653i	−0.145720	+	0.252394i	0.783921	+	0.620860i	$0.213216\pi$
$102$		0			0
$103$	2.24264	+	3.88437i	0.220974	+	0.382738i	0.955104	−	0.296271i	$-0.0957431\pi$
$103$	2.24264	+	3.88437i	0.220974	+	0.382738i	−0.734130	+	0.679009i	$0.762410\pi$
$104$	−4.10051			−0.402088
$105$		0			0
$106$	−0.828427			−0.0804640
$107$	−0.171573	−	0.297173i	−0.0165866	−	0.0287288i	0.857613	−	0.514296i	$-0.171947\pi$
$107$	−0.171573	−	0.297173i	−0.0165866	−	0.0287288i	−0.874200	+	0.485567i	$0.838613\pi$
$108$		0			0
$109$	2.82843	−	4.89898i	0.270914	−	0.469237i	−0.698182	−	0.715920i	$-0.746007\pi$
$109$	2.82843	−	4.89898i	0.270914	−	0.469237i	0.969096	+	0.246683i	$0.0793407\pi$
$110$	1.41421	+	2.44949i	0.134840	+	0.233550i
$111$		0			0
$112$		0			0
$113$	5.31371			0.499872			0.249936	−	0.968262i	$-0.419590\pi$
$113$	5.31371			0.499872			0.249936	+	0.968262i	$0.419590\pi$
$114$		0			0
$115$	−13.0711	+	22.6398i	−1.21888	+	2.11117i
$116$	6.24264	−	10.8126i	0.579615	−	1.00392i
$117$		0			0
$118$	0.485281			0.0446738
$119$		0			0
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	−2.53553	+	4.39167i	−0.229556	+	0.397603i
$123$		0			0
$124$	1.07107	+	1.85514i	0.0961847	+	0.166597i
$125$	5.65685			0.505964
$126$		0			0
$127$	−1.65685			−0.147022			−0.0735110	−	0.997294i	$-0.523420\pi$
$127$	−1.65685			−0.147022			−0.0735110	+	0.997294i	$0.523420\pi$
$128$	−5.27817	−	9.14207i	−0.466529	−	0.808052i
$129$		0			0
$130$	−1.82843	+	3.16693i	−0.160364	+	0.277758i
$131$	7.65685	+	13.2621i	0.668982	+	1.15871i	0.978189	+	0.207717i	$0.0666032\pi$
$131$	7.65685	+	13.2621i	0.668982	+	1.15871i	−0.309207	+	0.950995i	$0.600063\pi$
$132$		0			0
$133$		0			0
$134$	2.34315			0.202417
$135$		0			0
$136$	1.77817	−	3.07989i	0.152477	−	0.264098i
$137$	7.07107	−	12.2474i	0.604122	−	1.04637i	−0.388067	−	0.921631i	$-0.626857\pi$
$137$	7.07107	−	12.2474i	0.604122	−	1.04637i	0.992190	−	0.124739i	$-0.0398094\pi$
$138$		0			0
$139$	17.6569			1.49763			0.748817	−	0.662776i	$-0.230622\pi$
$139$	17.6569			1.49763			0.748817	+	0.662776i	$0.230622\pi$
$140$		0			0
$141$		0			0
$142$	−1.92893	−	3.34101i	−0.161872	−	0.280371i
$143$	2.58579	−	4.47871i	0.216234	−	0.374529i
$144$		0			0
$145$	−11.6569	−	20.1903i	−0.968049	−	1.67671i
$146$	5.75736			0.476482
$147$		0			0
$148$	7.31371			0.601183
$149$	8.65685	+	14.9941i	0.709197	+	1.22837i	0.965155	+	0.261678i	$0.0842757\pi$
$149$	8.65685	+	14.9941i	0.709197	+	1.22837i	−0.255958	+	0.966688i	$0.582391\pi$
$150$		0			0
$151$	−6.00000	+	10.3923i	−0.488273	+	0.845714i	−0.999909	−	0.0134886i	$-0.995706\pi$
$151$	−6.00000	+	10.3923i	−0.488273	+	0.845714i	0.511636	+	0.859202i	$0.329040\pi$
$152$	−2.24264	−	3.88437i	−0.181902	−	0.315064i
$153$		0			0
$154$		0			0
$155$	4.00000			0.321288
$156$		0			0
$157$	5.87868	−	10.1822i	0.469170	−	0.812626i	−0.530209	−	0.847867i	$-0.677887\pi$
$157$	5.87868	−	10.1822i	0.469170	−	0.812626i	0.999379	+	0.0352411i	$0.0112199\pi$
$158$	2.82843	−	4.89898i	0.225018	−	0.389742i
$159$		0			0
$160$	−15.0711			−1.19147
$161$		0			0
$162$		0			0
$163$	5.65685	+	9.79796i	0.443079	+	0.767435i	0.997916	−	0.0645236i	$-0.0205528\pi$
$163$	5.65685	+	9.79796i	0.443079	+	0.767435i	−0.554837	+	0.831959i	$0.687219\pi$
$164$	5.70711	−	9.88500i	0.445650	−	0.771889i
$165$		0			0
$166$	1.51472	+	2.62357i	0.117565	+	0.203628i
$167$	−19.7990			−1.53209			−0.766046	−	0.642786i	$-0.777779\pi$
$167$	−19.7990			−1.53209			−0.766046	+	0.642786i	$0.777779\pi$
$168$		0			0
$169$	−6.31371			−0.485670
$170$	−1.58579	−	2.74666i	−0.121624	−	0.210659i
$171$		0			0
$172$	5.17157	−	8.95743i	0.394329	−	0.682997i
$173$	−10.5355	−	18.2481i	−0.801002	−	1.38738i	−0.918957	−	0.394357i	$-0.870967\pi$
$173$	−10.5355	−	18.2481i	−0.801002	−	1.38738i	0.117956	−	0.993019i	$-0.462366\pi$
$174$		0			0
$175$		0			0
$176$	6.00000			0.452267
$177$		0			0
$178$	−2.94975	+	5.10911i	−0.221093	+	0.382944i
$179$	−9.82843	+	17.0233i	−0.734611	+	1.27238i	0.220283	+	0.975436i	$0.429302\pi$
$179$	−9.82843	+	17.0233i	−0.734611	+	1.27238i	−0.954894	+	0.296948i	$0.904031\pi$
$180$		0			0
$181$	2.58579			0.192200			0.0961000	−	0.995372i	$-0.469363\pi$
$181$	2.58579			0.192200			0.0961000	+	0.995372i	$0.469363\pi$
$182$		0			0
$183$		0			0
$184$	−6.07107	−	10.5154i	−0.447565	−	0.775205i
$185$	6.82843	−	11.8272i	0.502036	−	0.869552i
$186$		0			0
$187$	2.24264	+	3.88437i	0.163998	+	0.284053i
$188$	5.17157			0.377176
$189$		0			0
$190$	−4.00000			−0.290191
$191$	−9.00000	−	15.5885i	−0.651217	−	1.12794i	−0.982828	−	0.184525i	$-0.940925\pi$
$191$	−9.00000	−	15.5885i	−0.651217	−	1.12794i	0.331611	−	0.943416i	$-0.392408\pi$
$192$		0			0
$193$	−2.65685	+	4.60181i	−0.191245	+	0.331245i	−0.945663	−	0.325149i	$-0.894586\pi$
$193$	−2.65685	+	4.60181i	−0.191245	+	0.331245i	0.754418	+	0.656394i	$0.227919\pi$
$194$	−0.535534	−	0.927572i	−0.0384491	−	0.0665958i
$195$		0			0
$196$		0			0
$197$	−2.00000			−0.142494			−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000			−0.142494			−0.0712470	+	0.997459i	$0.522698\pi$
$198$		0			0
$199$	10.8284	−	18.7554i	0.767607	−	1.32953i	−0.171250	−	0.985228i	$-0.554781\pi$
$199$	10.8284	−	18.7554i	0.767607	−	1.32953i	0.938857	−	0.344307i	$-0.111886\pi$
$200$	−5.27817	+	9.14207i	−0.373223	+	0.646442i
$201$		0			0
$202$	−1.21320			−0.0853607
$203$		0			0
$204$		0			0
$205$	−10.6569	−	18.4582i	−0.744307	−	1.28918i
$206$	−0.928932	+	1.60896i	−0.0647218	+	0.112101i
$207$		0			0
$208$	3.87868	+	6.71807i	0.268938	+	0.465814i
$209$	5.65685			0.391293
$210$		0			0
$211$	12.9706			0.892930			0.446465	−	0.894801i	$-0.352683\pi$
$211$	12.9706			0.892930			0.446465	+	0.894801i	$0.352683\pi$
$212$	1.82843	+	3.16693i	0.125577	+	0.217506i
$213$		0			0
$214$	0.0710678	−	0.123093i	0.00485810	−	0.00841447i
$215$	−9.65685	−	16.7262i	−0.658592	−	1.14071i
$216$		0			0
$217$		0			0
$218$	2.34315			0.158698
$219$		0			0
$220$	6.24264	−	10.8126i	0.420879	−	0.728983i
$221$	−2.89949	+	5.02207i	−0.195041	+	0.337821i
$222$		0			0
$223$	−24.9706			−1.67215			−0.836076	−	0.548613i	$-0.815156\pi$
$223$	−24.9706			−1.67215			−0.836076	+	0.548613i	$0.815156\pi$
$224$		0			0
$225$		0			0
$226$	1.10051	+	1.90613i	0.0732045	+	0.126794i
$227$	−11.8995	+	20.6105i	−0.789797	+	1.36797i	0.136294	+	0.990668i	$0.456481\pi$
$227$	−11.8995	+	20.6105i	−0.789797	+	1.36797i	−0.926091	+	0.377300i	$0.876852\pi$
$228$		0			0
$229$	−0.121320	−	0.210133i	−0.00801707	−	0.0138860i	0.861989	−	0.506927i	$-0.169219\pi$
$229$	−0.121320	−	0.210133i	−0.00801707	−	0.0138860i	−0.870006	+	0.493041i	$0.835885\pi$
$230$	−10.8284			−0.714005
$231$		0			0
$232$	10.8284			0.710921
$233$	−3.07107	−	5.31925i	−0.201192	−	0.348475i	0.747721	−	0.664014i	$-0.231148\pi$
$233$	−3.07107	−	5.31925i	−0.201192	−	0.348475i	−0.948913	+	0.315538i	$0.897815\pi$
$234$		0			0
$235$	4.82843	−	8.36308i	0.314972	−	0.545547i
$236$	−1.07107	−	1.85514i	−0.0697206	−	0.120760i
$237$		0			0
$238$		0			0
$239$	15.6569			1.01276			0.506379	−	0.862311i	$-0.330984\pi$
$239$	15.6569			1.01276			0.506379	+	0.862311i	$0.330984\pi$
$240$		0			0
$241$	−8.12132	+	14.0665i	−0.523140	+	0.906105i	0.476497	+	0.879176i	$0.341906\pi$
$241$	−8.12132	+	14.0665i	−0.523140	+	0.906105i	−0.999637	+	0.0269294i	$0.991427\pi$
$242$	−1.44975	+	2.51104i	−0.0931933	+	0.161416i
$243$		0			0
$244$	22.3848			1.43304
$245$		0			0
$246$		0			0
$247$	3.65685	+	6.33386i	0.232680	+	0.403014i
$248$	−0.928932	+	1.60896i	−0.0589873	+	0.102169i
$249$		0			0
$250$	1.17157	+	2.02922i	0.0740968	+	0.128339i
$251$	−12.4853			−0.788064			−0.394032	−	0.919097i	$-0.628920\pi$
$251$	−12.4853			−0.788064			−0.394032	+	0.919097i	$0.628920\pi$
$252$		0			0
$253$	15.3137			0.962765
$254$	−0.343146	−	0.594346i	−0.0215309	−	0.0372926i
$255$		0			0
$256$	−1.98528	+	3.43861i	−0.124080	+	0.214913i
$257$	−11.6066	−	20.1032i	−0.724000	−	1.25400i	−0.959384	−	0.282102i	$-0.908968\pi$
$257$	−11.6066	−	20.1032i	−0.724000	−	1.25400i	0.235384	−	0.971902i	$-0.424365\pi$
$258$		0			0
$259$		0			0
$260$	16.1421			1.00109
$261$		0			0
$262$	−3.17157	+	5.49333i	−0.195940	+	0.339379i
$263$	2.65685	−	4.60181i	0.163829	−	0.283760i	−0.772410	−	0.635124i	$-0.780949\pi$
$263$	2.65685	−	4.60181i	0.163829	−	0.283760i	0.936239	+	0.351365i	$0.114282\pi$
$264$		0			0
$265$	6.82843			0.419467
$266$		0			0
$267$		0			0
$268$	−5.17157	−	8.95743i	−0.315904	−	0.547162i
$269$	7.36396	−	12.7548i	0.448989	−	0.777671i	−0.549332	−	0.835604i	$-0.685118\pi$
$269$	7.36396	−	12.7548i	0.448989	−	0.777671i	0.998320	+	0.0579332i	$0.0184510\pi$
$270$		0			0
$271$	−5.07107	−	8.78335i	−0.308045	−	0.533550i	0.669889	−	0.742461i	$-0.266342\pi$
$271$	−5.07107	−	8.78335i	−0.308045	−	0.533550i	−0.977935	+	0.208911i	$0.933008\pi$
$272$	−6.72792			−0.407940
$273$		0			0
$274$	5.85786			0.353887
$275$	−6.65685	−	11.5300i	−0.401423	−	0.695286i
$276$		0			0
$277$	4.65685	−	8.06591i	0.279803	−	0.484633i	−0.691532	−	0.722345i	$-0.743064\pi$
$277$	4.65685	−	8.06591i	0.279803	−	0.484633i	0.971336	+	0.237712i	$0.0763974\pi$
$278$	3.65685	+	6.33386i	0.219324	+	0.379880i
$279$		0			0
$280$		0			0
$281$	−0.485281			−0.0289495			−0.0144747	−	0.999895i	$-0.504608\pi$
$281$	−0.485281			−0.0289495			−0.0144747	+	0.999895i	$0.504608\pi$
$282$		0			0
$283$	−4.24264	+	7.34847i	−0.252199	+	0.436821i	−0.964131	−	0.265427i	$-0.914487\pi$
$283$	−4.24264	+	7.34847i	−0.252199	+	0.436821i	0.711932	+	0.702248i	$0.247820\pi$
$284$	−8.51472	+	14.7479i	−0.505256	+	0.875128i
$285$		0			0
$286$	2.14214			0.126667
$287$		0			0
$288$		0			0
$289$	5.98528	+	10.3668i	0.352075	+	0.609812i
$290$	4.82843	−	8.36308i	0.283535	−	0.491097i
$291$		0			0
$292$	−12.7071	−	22.0094i	−0.743627	−	1.28800i
$293$	16.5858			0.968952			0.484476	−	0.874805i	$-0.339010\pi$
$293$	16.5858			0.968952			0.484476	+	0.874805i	$0.339010\pi$
$294$		0			0
$295$	−4.00000			−0.232889
$296$	3.17157	+	5.49333i	0.184344	+	0.319293i
$297$		0			0
$298$	−3.58579	+	6.21076i	−0.207719	+	0.359780i
$299$	9.89949	+	17.1464i	0.572503	+	0.991604i
$300$		0			0
$301$		0			0
$302$	−4.97056			−0.286024
$303$		0			0
$304$	−4.24264	+	7.34847i	−0.243332	+	0.421464i
$305$	20.8995	−	36.1990i	1.19670	−	2.07275i
$306$		0			0
$307$	−30.1421			−1.72030			−0.860151	−	0.510039i	$-0.829631\pi$
$307$	−30.1421			−1.72030			−0.860151	+	0.510039i	$0.829631\pi$
$308$		0			0
$309$		0			0
$310$	0.828427	+	1.43488i	0.0470515	+	0.0814956i
$311$	−3.07107	+	5.31925i	−0.174144	+	0.301627i	−0.939865	−	0.341547i	$-0.889049\pi$
$311$	−3.07107	+	5.31925i	−0.174144	+	0.301627i	0.765721	+	0.643173i	$0.222383\pi$
$312$		0			0
$313$	0.949747	+	1.64501i	0.0536829	+	0.0929815i	0.891618	−	0.452788i	$-0.149571\pi$
$313$	0.949747	+	1.64501i	0.0536829	+	0.0929815i	−0.837935	+	0.545770i	$0.816237\pi$
$314$	4.87006			0.274833
$315$		0			0
$316$	−24.9706			−1.40470
$317$	5.00000	+	8.66025i	0.280828	+	0.486408i	0.971589	−	0.236675i	$-0.0760576\pi$
$317$	5.00000	+	8.66025i	0.280828	+	0.486408i	−0.690761	+	0.723083i	$0.742724\pi$
$318$		0			0
$319$	−6.82843	+	11.8272i	−0.382319	+	0.662195i
$320$	7.12132	+	12.3345i	0.398094	+	0.689519i
$321$		0			0
$322$		0			0
$323$	−6.34315			−0.352942
$324$		0			0
$325$	8.60660	−	14.9071i	0.477408	−	0.826896i
$326$	−2.34315	+	4.05845i	−0.129775	+	0.224777i
$327$		0			0
$328$	9.89949			0.546608
$329$		0			0
$330$		0			0
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	0.915742	−	0.401768i	$-0.131604\pi$
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	−0.805812	+	0.592172i	$0.798271\pi$
$332$	6.68629	−	11.5810i	0.366958	−	0.635590i
$333$		0			0
$334$	−4.10051	−	7.10228i	−0.224370	−	0.388620i
$335$	−19.3137			−1.05522
$336$		0			0
$337$	−29.6569			−1.61551			−0.807756	−	0.589517i	$-0.799318\pi$
$337$	−29.6569			−1.61551			−0.807756	+	0.589517i	$0.799318\pi$
$338$	−1.30761	−	2.26485i	−0.0711247	−	0.123192i
$339$		0			0
$340$	−7.00000	+	12.1244i	−0.379628	+	0.657536i
$341$	−1.17157	−	2.02922i	−0.0634442	−	0.109889i
$342$		0			0
$343$		0			0
$344$	8.97056			0.483660
$345$		0			0
$346$	4.36396	−	7.55860i	0.234608	−	0.406353i
$347$	16.6569	−	28.8505i	0.894187	−	1.54878i	0.0593789	−	0.998236i	$-0.481088\pi$
$347$	16.6569	−	28.8505i	0.894187	−	1.54878i	0.834808	−	0.550541i	$-0.185579\pi$
$348$		0			0
$349$	9.89949			0.529908			0.264954	−	0.964261i	$-0.414643\pi$
$349$	9.89949			0.529908			0.264954	+	0.964261i	$0.414643\pi$
$350$		0			0
$351$		0			0
$352$	4.41421	+	7.64564i	0.235278	+	0.407514i
$353$	7.36396	−	12.7548i	0.391944	−	0.678867i	−0.600762	−	0.799428i	$-0.705136\pi$
$353$	7.36396	−	12.7548i	0.391944	−	0.678867i	0.992706	+	0.120561i	$0.0384693\pi$
$354$		0			0
$355$	15.8995	+	27.5387i	0.843858	+	1.46160i
$356$	26.0416			1.38020
$357$		0			0
$358$	−8.14214			−0.430325
$359$	−0.171573	−	0.297173i	−0.00905527	−	0.0156842i	0.861462	−	0.507822i	$-0.169549\pi$
$359$	−0.171573	−	0.297173i	−0.00905527	−	0.0156842i	−0.870518	+	0.492137i	$0.836216\pi$
$360$		0			0
$361$	5.50000	−	9.52628i	0.289474	−	0.501383i
$362$	0.535534	+	0.927572i	0.0281470	+	0.0487521i
$363$		0			0
$364$		0			0
$365$	−47.4558			−2.48395
$366$		0			0
$367$	−1.65685	+	2.86976i	−0.0864871	+	0.149800i	−0.906024	−	0.423226i	$-0.860897\pi$
$367$	−1.65685	+	2.86976i	−0.0864871	+	0.149800i	0.819537	+	0.573027i	$0.194231\pi$
$368$	−11.4853	+	19.8931i	−0.598712	+	1.03700i
$369$		0			0
$370$	5.65685			0.294086
$371$		0			0
$372$		0			0
$373$	5.34315	+	9.25460i	0.276658	+	0.479185i	0.970552	−	0.240892i	$-0.0774399\pi$
$373$	5.34315	+	9.25460i	0.276658	+	0.479185i	−0.693894	+	0.720077i	$0.744107\pi$
$374$	−0.928932	+	1.60896i	−0.0480339	+	0.0831972i
$375$		0			0
$376$	2.24264	+	3.88437i	0.115655	+	0.200321i
$377$	−17.6569			−0.909374
$378$		0			0
$379$	8.68629			0.446185			0.223092	−	0.974797i	$-0.428385\pi$
$379$	8.68629			0.446185			0.223092	+	0.974797i	$0.428385\pi$
$380$	8.82843	+	15.2913i	0.452889	+	0.784426i
$381$		0			0
$382$	3.72792	−	6.45695i	0.190737	−	0.330366i
$383$	9.17157	+	15.8856i	0.468645	+	0.811718i	0.999358	−	0.0358343i	$-0.0114088\pi$
$383$	9.17157	+	15.8856i	0.468645	+	0.811718i	−0.530712	+	0.847552i	$0.678076\pi$
$384$		0			0
$385$		0			0
$386$	−2.20101			−0.112028
$387$		0			0
$388$	−2.36396	+	4.09450i	−0.120012	+	0.207867i
$389$	−9.07107	+	15.7116i	−0.459921	+	0.796607i	−0.998956	−	0.0456762i	$-0.985456\pi$
$389$	−9.07107	+	15.7116i	−0.459921	+	0.796607i	0.539035	+	0.842283i	$0.318789\pi$
$390$		0			0
$391$	−17.1716			−0.868404
$392$		0			0
$393$		0			0
$394$	−0.414214	−	0.717439i	−0.0208678	−	0.0361441i
$395$	−23.3137	+	40.3805i	−1.17304	+	2.03176i
$396$		0			0
$397$	−1.19239	−	2.06528i	−0.0598442	−	0.103653i	0.834551	−	0.550931i	$-0.185727\pi$
$397$	−1.19239	−	2.06528i	−0.0598442	−	0.103653i	−0.894395	+	0.447277i	$0.852394\pi$
$398$	8.97056			0.449654
$399$		0			0
$400$	19.9706			0.998528
$401$	−3.07107	−	5.31925i	−0.153362	−	0.265630i	0.779100	−	0.626900i	$-0.215677\pi$
$401$	−3.07107	−	5.31925i	−0.153362	−	0.265630i	−0.932461	+	0.361270i	$0.882343\pi$
$402$		0			0
$403$	1.51472	−	2.62357i	0.0754535	−	0.130689i
$404$	2.67767	+	4.63786i	0.133219	+	0.230742i
$405$		0			0
$406$		0			0
$407$	−8.00000			−0.396545
$408$		0			0
$409$	−10.7071	+	18.5453i	−0.529432	+	0.917004i	0.469978	+	0.882678i	$0.344262\pi$
$409$	−10.7071	+	18.5453i	−0.529432	+	0.917004i	−0.999411	+	0.0343258i	$0.989072\pi$
$410$	4.41421	−	7.64564i	0.218002	−	0.377591i
$411$		0			0
$412$	8.20101			0.404035
$413$		0			0
$414$		0			0
$415$	−12.4853	−	21.6251i	−0.612878	−	1.06154i
$416$	−5.70711	+	9.88500i	−0.279814	+	0.484652i
$417$		0			0
$418$	1.17157	+	2.02922i	0.0573035	+	0.0992526i
$419$	33.1716			1.62054			0.810269	−	0.586059i	$-0.199321\pi$
$419$	33.1716			1.62054			0.810269	+	0.586059i	$0.199321\pi$
$420$		0			0
$421$	16.6274			0.810371			0.405185	−	0.914235i	$-0.367207\pi$
$421$	16.6274			0.810371			0.405185	+	0.914235i	$0.367207\pi$
$422$	2.68629	+	4.65279i	0.130767	+	0.226494i
$423$		0			0
$424$	−1.58579	+	2.74666i	−0.0770126	+	0.133390i
$425$	7.46447	+	12.9288i	0.362080	+	0.627141i
$426$		0			0
$427$		0			0
$428$	−0.627417			−0.0303273
$429$		0			0
$430$	4.00000	−	6.92820i	0.192897	−	0.334108i
$431$	−13.4853	+	23.3572i	−0.649563	+	1.12508i	0.333664	+	0.942692i	$0.391715\pi$
$431$	−13.4853	+	23.3572i	−0.649563	+	1.12508i	−0.983227	+	0.182384i	$0.941618\pi$
$432$		0			0
$433$	20.2426			0.972799			0.486400	−	0.873736i	$-0.338310\pi$
$433$	20.2426			0.972799			0.486400	+	0.873736i	$0.338310\pi$
$434$		0			0
$435$		0			0
$436$	−5.17157	−	8.95743i	−0.247673	−	0.428983i
$437$	−10.8284	+	18.7554i	−0.517994	+	0.897192i
$438$		0			0
$439$	6.34315	+	10.9867i	0.302742	+	0.524364i	0.976756	−	0.214354i	$-0.0687647\pi$
$439$	6.34315	+	10.9867i	0.302742	+	0.524364i	−0.674014	+	0.738718i	$0.735431\pi$
$440$	10.8284			0.516225
$441$		0			0
$442$	−2.40202			−0.114252
$443$	17.4853	+	30.2854i	0.830751	+	1.43890i	0.897444	+	0.441129i	$0.145422\pi$
$443$	17.4853	+	30.2854i	0.830751	+	1.43890i	−0.0666929	+	0.997774i	$0.521245\pi$
$444$		0			0
$445$	24.3137	−	42.1126i	1.15258	−	1.99633i
$446$	−5.17157	−	8.95743i	−0.244881	−	0.424146i
$447$		0			0
$448$		0			0
$449$	5.31371			0.250769			0.125385	−	0.992108i	$-0.459983\pi$
$449$	5.31371			0.250769			0.125385	+	0.992108i	$0.459983\pi$
$450$		0			0
$451$	−6.24264	+	10.8126i	−0.293954	+	0.509144i
$452$	4.85786	−	8.41407i	0.228495	−	0.395764i
$453$		0			0
$454$	−9.85786			−0.462652
$455$		0			0
$456$		0			0
$457$	9.00000	+	15.5885i	0.421002	+	0.729197i	0.996038	−	0.0889312i	$-0.0283451\pi$
$457$	9.00000	+	15.5885i	0.421002	+	0.729197i	−0.575036	+	0.818128i	$0.695012\pi$
$458$	0.0502525	−	0.0870399i	0.00234815	−	0.00406711i
$459$		0			0
$460$	23.8995	+	41.3951i	1.11432	+	1.93006i
$461$	−16.5858			−0.772477			−0.386239	−	0.922399i	$-0.626226\pi$
$461$	−16.5858			−0.772477			−0.386239	+	0.922399i	$0.626226\pi$
$462$		0			0
$463$	−26.6274			−1.23748			−0.618741	−	0.785595i	$-0.712357\pi$
$463$	−26.6274			−1.23748			−0.618741	+	0.785595i	$0.712357\pi$
$464$	−10.2426	−	17.7408i	−0.475503	−	0.823595i
$465$		0			0
$466$	1.27208	−	2.20330i	0.0589279	−	0.102066i
$467$	−0.100505	−	0.174080i	−0.00465082	−	0.00805546i	0.863691	−	0.504022i	$-0.168147\pi$
$467$	−0.100505	−	0.174080i	−0.00465082	−	0.00805546i	−0.868341	+	0.495967i	$0.834814\pi$
$468$		0			0
$469$		0			0
$470$	4.00000			0.184506
$471$		0			0
$472$	0.928932	−	1.60896i	0.0427576	−	0.0740583i
$473$	−5.65685	+	9.79796i	−0.260102	+	0.450511i
$474$		0			0
$475$	18.8284			0.863907
$476$		0			0
$477$		0			0
$478$	3.24264	+	5.61642i	0.148315	+	0.256889i
$479$	−0.928932	+	1.60896i	−0.0424440	+	0.0735152i	−0.886467	−	0.462792i	$-0.846848\pi$
$479$	−0.928932	+	1.60896i	−0.0424440	+	0.0735152i	0.844023	+	0.536307i	$0.180181\pi$
$480$		0			0
$481$	−5.17157	−	8.95743i	−0.235803	−	0.408424i
$482$	−6.72792			−0.306448
$483$		0			0
$484$	12.7990			0.581772
$485$	4.41421	+	7.64564i	0.200439	+	0.347171i
$486$		0			0
$487$	−13.3137	+	23.0600i	−0.603302	+	1.04495i	0.389016	+	0.921231i	$0.372815\pi$
$487$	−13.3137	+	23.0600i	−0.603302	+	1.04495i	−0.992317	+	0.123718i	$0.960518\pi$
$488$	9.70711	+	16.8132i	0.439420	+	0.761098i
$489$		0			0
$490$		0			0
$491$	−5.02944			−0.226975			−0.113488	−	0.993539i	$-0.536202\pi$
$491$	−5.02944			−0.226975			−0.113488	+	0.993539i	$0.536202\pi$
$492$		0			0
$493$	7.65685	−	13.2621i	0.344847	−	0.597293i
$494$	−1.51472	+	2.62357i	−0.0681504	+	0.118040i
$495$		0			0
$496$	3.51472			0.157816
$497$		0			0
$498$		0			0
$499$	−1.65685	−	2.86976i	−0.0741710	−	0.128468i	0.826554	−	0.562857i	$-0.190298\pi$
$499$	−1.65685	−	2.86976i	−0.0741710	−	0.128468i	−0.900725	+	0.434389i	$0.856964\pi$
$500$	5.17157	−	8.95743i	0.231280	−	0.400588i
$501$		0			0
$502$	−2.58579	−	4.47871i	−0.115409	−	0.199895i
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$	10.0000			0.444994
$506$	3.17157	+	5.49333i	0.140994	+	0.244208i
$507$		0			0
$508$	−1.51472	+	2.62357i	−0.0672048	+	0.116402i
$509$	−2.77817	−	4.81194i	−0.123140	−	0.213285i	0.797864	−	0.602837i	$-0.205963\pi$
$509$	−2.77817	−	4.81194i	−0.123140	−	0.213285i	−0.921005	+	0.389552i	$0.872630\pi$
$510$		0			0
$511$		0			0
$512$	−22.7574			−1.00574
$513$		0			0
$514$	4.80761	−	8.32703i	0.212055	−	0.367289i
$515$	7.65685	−	13.2621i	0.337401	−	0.584396i
$516$		0			0
$517$	−5.65685			−0.248788
$518$		0			0
$519$		0			0
$520$	7.00000	+	12.1244i	0.306970	+	0.531688i
$521$	17.7071	−	30.6696i	0.775762	−	1.34366i	−0.158603	−	0.987343i	$-0.550699\pi$
$521$	17.7071	−	30.6696i	0.775762	−	1.34366i	0.934365	−	0.356317i	$-0.115968\pi$
$522$		0			0
$523$	−12.8284	−	22.2195i	−0.560948	−	0.971590i	−0.997414	−	0.0718696i	$-0.977103\pi$
$523$	−12.8284	−	22.2195i	−0.560948	−	0.971590i	0.436466	−	0.899721i	$-0.356230\pi$
$524$	28.0000			1.22319
$525$		0			0
$526$	2.20101			0.0959686
$527$	1.31371	+	2.27541i	0.0572260	+	0.0991184i
$528$		0			0
$529$	−17.8137	+	30.8542i	−0.774509	+	1.34149i
$530$	1.41421	+	2.44949i	0.0614295	+	0.106399i
$531$		0			0
$532$		0			0
$533$	−16.1421			−0.699194
$534$		0			0
$535$	−0.585786	+	1.01461i	−0.0253258	+	0.0438655i
$536$	4.48528	−	7.76874i	0.193735	−	0.335558i
$537$		0			0
$538$	6.10051			0.263011
$539$		0			0
$540$		0			0
$541$	−8.65685	−	14.9941i	−0.372187	−	0.644647i	0.617715	−	0.786402i	$-0.288059\pi$
$541$	−8.65685	−	14.9941i	−0.372187	−	0.644647i	−0.989902	+	0.141755i	$0.954725\pi$
$542$	2.10051	−	3.63818i	0.0902244	−	0.156273i
$543$		0			0
$544$	−4.94975	−	8.57321i	−0.212219	−	0.367574i
$545$	−19.3137			−0.827308
$546$		0			0
$547$	−36.9706			−1.58075			−0.790374	−	0.612625i	$-0.790114\pi$
$547$	−36.9706			−1.58075			−0.790374	+	0.612625i	$0.790114\pi$
$548$	−12.9289	−	22.3936i	−0.552297	−	0.956606i
$549$		0			0
$550$	2.75736	−	4.77589i	0.117574	−	0.203644i
$551$	−9.65685	−	16.7262i	−0.411396	−	0.712558i
$552$		0			0
$553$		0			0
$554$	3.85786			0.163905
$555$		0			0
$556$	16.1421	−	27.9590i	0.684579	−	1.18573i
$557$	13.0000	−	22.5167i	0.550828	−	0.954062i	−0.447387	−	0.894340i	$-0.647645\pi$
$557$	13.0000	−	22.5167i	0.550828	−	0.954062i	0.998215	−	0.0597213i	$-0.0190212\pi$
$558$		0			0
$559$	−14.6274			−0.618674
$560$		0			0
$561$		0			0
$562$	−0.100505	−	0.174080i	−0.00423955	−	0.00734312i
$563$	0.585786	−	1.01461i	0.0246880	−	0.0427608i	−0.853417	−	0.521228i	$-0.825474\pi$
$563$	0.585786	−	1.01461i	0.0246880	−	0.0427608i	0.878105	+	0.478467i	$0.158807\pi$
$564$		0			0
$565$	−9.07107	−	15.7116i	−0.381623	−	0.660990i
$566$	−3.51472			−0.147735
$567$		0			0
$568$	−14.7696			−0.619717
$569$	−8.24264	−	14.2767i	−0.345549	−	0.598509i	0.639904	−	0.768455i	$-0.278974\pi$
$569$	−8.24264	−	14.2767i	−0.345549	−	0.598509i	−0.985453	+	0.169946i	$0.945641\pi$
$570$		0			0
$571$	−11.1716	+	19.3497i	−0.467516	+	0.809761i	−0.999311	−	0.0371118i	$-0.988184\pi$
$571$	−11.1716	+	19.3497i	−0.467516	+	0.809761i	0.531795	+	0.846873i	$0.321518\pi$
$572$	−4.72792	−	8.18900i	−0.197684	−	0.342399i
$573$		0			0
$574$		0			0
$575$	50.9706			2.12562
$576$		0			0
$577$	−16.9497	+	29.3578i	−0.705627	+	1.22218i	0.260837	+	0.965383i	$0.416001\pi$
$577$	−16.9497	+	29.3578i	−0.705627	+	1.22218i	−0.966465	+	0.256799i	$0.917332\pi$
$578$	−2.47918	+	4.29407i	−0.103120	+	0.178610i
$579$		0			0
$580$	−42.6274			−1.77001
$581$		0			0
$582$		0			0
$583$	−2.00000	−	3.46410i	−0.0828315	−	0.143468i
$584$	11.0208	−	19.0886i	0.456045	−	0.789892i
$585$		0			0
$586$	3.43503	+	5.94964i	0.141900	+	0.245778i
$587$	−22.8284			−0.942230			−0.471115	−	0.882072i	$-0.656148\pi$
$587$	−22.8284			−0.942230			−0.471115	+	0.882072i	$0.656148\pi$
$588$		0			0
$589$	3.31371			0.136539
$590$	−0.828427	−	1.43488i	−0.0341058	−	0.0590730i
$591$		0			0
$592$	6.00000	−	10.3923i	0.246598	−	0.427121i
$593$	3.46447	+	6.00063i	0.142269	+	0.246416i	0.928351	−	0.371706i	$-0.121227\pi$
$593$	3.46447	+	6.00063i	0.142269	+	0.246416i	−0.786082	+	0.618122i	$0.787894\pi$
$594$		0			0
$595$		0			0
$596$	31.6569			1.29672
$597$		0			0
$598$	−4.10051	+	7.10228i	−0.167682	+	0.290434i
$599$	−1.00000	+	1.73205i	−0.0408589	+	0.0707697i	−0.885732	−	0.464198i	$-0.846343\pi$
$599$	−1.00000	+	1.73205i	−0.0408589	+	0.0707697i	0.844873	+	0.534967i	$0.179676\pi$
$600$		0			0
$601$	15.0711			0.614762			0.307381	−	0.951587i	$-0.400547\pi$
$601$	15.0711			0.614762			0.307381	+	0.951587i	$0.400547\pi$
$602$		0			0
$603$		0			0
$604$	10.9706	+	19.0016i	0.446386	+	0.773163i
$605$	11.9497	−	20.6976i	0.485826	−	0.841476i
$606$		0			0
$607$	−9.17157	−	15.8856i	−0.372263	−	0.644778i	0.617651	−	0.786453i	$-0.288085\pi$
$607$	−9.17157	−	15.8856i	−0.372263	−	0.644778i	−0.989913	+	0.141675i	$0.954751\pi$
$608$	−12.4853			−0.506345
$609$		0			0
$610$	17.3137			0.701012
$611$	−3.65685	−	6.33386i	−0.147940	−	0.256240i
$612$		0			0
$613$	−2.34315	+	4.05845i	−0.0946388	+	0.163919i	−0.909458	−	0.415796i	$-0.863503\pi$
$613$	−2.34315	+	4.05845i	−0.0946388	+	0.163919i	0.814819	+	0.579715i	$0.196836\pi$
$614$	−6.24264	−	10.8126i	−0.251932	−	0.436360i
$615$		0			0
$616$		0			0
$617$	24.4853			0.985740			0.492870	−	0.870103i	$-0.335948\pi$
$617$	24.4853			0.985740			0.492870	+	0.870103i	$0.335948\pi$
$618$		0			0
$619$	14.4853	−	25.0892i	0.582213	−	1.00842i	−0.413004	−	0.910729i	$-0.635520\pi$
$619$	14.4853	−	25.0892i	0.582213	−	1.00842i	0.995217	−	0.0976926i	$-0.0311462\pi$
$620$	3.65685	−	6.33386i	0.146863	−	0.254374i
$621$		0			0
$622$	−2.54416			−0.102011
$623$		0			0
$624$		0			0
$625$	6.98528	+	12.0989i	0.279411	+	0.483954i
$626$	−0.393398	+	0.681386i	−0.0157234	+	0.0272337i
$627$		0			0
$628$	−10.7487	−	18.6174i	−0.428921	−	0.742914i
$629$	8.97056			0.357680
$630$		0			0
$631$	23.3137			0.928104			0.464052	−	0.885808i	$-0.346395\pi$
$631$	23.3137			0.928104			0.464052	+	0.885808i	$0.346395\pi$
$632$	−10.8284	−	18.7554i	−0.430732	−	0.746049i
$633$		0			0
$634$	−2.07107	+	3.58719i	−0.0822526	+	0.142466i
$635$	2.82843	+	4.89898i	0.112243	+	0.194410i
$636$		0			0
$637$		0			0
$638$	−5.65685			−0.223957
$639$		0			0
$640$	−18.0208	+	31.2130i	−0.712335	+	1.23380i
$641$	−5.41421	+	9.37769i	−0.213849	+	0.370397i	−0.952916	−	0.303235i	$-0.901933\pi$
$641$	−5.41421	+	9.37769i	−0.213849	+	0.370397i	0.739067	+	0.673632i	$0.235267\pi$
$642$		0			0
$643$	34.4264			1.35764			0.678822	−	0.734302i	$-0.262491\pi$
$643$	34.4264			1.35764			0.678822	+	0.734302i	$0.262491\pi$
$644$		0			0
$645$		0			0
$646$	−1.31371	−	2.27541i	−0.0516872	−	0.0895248i
$647$	−13.4142	+	23.2341i	−0.527367	+	0.913427i	0.472124	+	0.881532i	$0.343487\pi$
$647$	−13.4142	+	23.2341i	−0.527367	+	0.913427i	−0.999491	+	0.0318946i	$0.989846\pi$
$648$		0			0
$649$	1.17157	+	2.02922i	0.0459883	+	0.0796540i
$650$	7.12994			0.279659
$651$		0			0
$652$	20.6863			0.810138
$653$	18.2426	+	31.5972i	0.713890	+	1.23649i	0.963386	+	0.268118i	$0.0864016\pi$
$653$	18.2426	+	31.5972i	0.713890	+	1.23649i	−0.249497	+	0.968376i	$0.580265\pi$
$654$		0			0
$655$	26.1421	−	45.2795i	1.02146	−	1.76922i
$656$	−9.36396	−	16.2189i	−0.365601	−	0.633240i
$657$		0			0
$658$		0			0
$659$	−9.31371			−0.362811			−0.181405	−	0.983408i	$-0.558065\pi$
$659$	−9.31371			−0.362811			−0.181405	+	0.983408i	$0.558065\pi$
$660$		0			0
$661$	−11.7782	+	20.4004i	−0.458118	+	0.793483i	−0.998862	−	0.0477040i	$-0.984810\pi$
$661$	−11.7782	+	20.4004i	−0.458118	+	0.793483i	0.540744	+	0.841187i	$0.318143\pi$
$662$	−0.828427	+	1.43488i	−0.0321977	+	0.0557681i
$663$		0			0
$664$	11.5980			0.450089
$665$		0			0
$666$		0			0
$667$	−26.1421	−	45.2795i	−1.01223	−	1.75323i
$668$	−18.1005	+	31.3510i	−0.700330	+	1.21301i
$669$		0			0
$670$	−4.00000	−	6.92820i	−0.154533	−	0.267660i
$671$	−24.4853			−0.945244
$672$		0			0
$673$	23.3137			0.898677			0.449339	−	0.893361i	$-0.351660\pi$
$673$	23.3137			0.898677			0.449339	+	0.893361i	$0.351660\pi$
$674$	−6.14214	−	10.6385i	−0.236586	−	0.409779i
$675$		0			0
$676$	−5.77208	+	9.99753i	−0.222003	+	0.384520i
$677$	−15.7071	−	27.2055i	−0.603673	−	1.04559i	−0.992260	−	0.124180i	$-0.960370\pi$
$677$	−15.7071	−	27.2055i	−0.603673	−	1.04559i	0.388587	−	0.921412i	$-0.372963\pi$
$678$		0			0
$679$		0			0
$680$	−12.1421			−0.465630
$681$		0			0
$682$	0.485281	−	0.840532i	0.0185824	−	0.0321856i
$683$	−9.82843	+	17.0233i	−0.376074	+	0.651380i	−0.990487	−	0.137605i	$-0.956060\pi$
$683$	−9.82843	+	17.0233i	−0.376074	+	0.651380i	0.614413	+	0.788985i	$0.289393\pi$
$684$		0			0
$685$	−48.2843			−1.84485
$686$		0			0
$687$		0			0
$688$	−8.48528	−	14.6969i	−0.323498	−	0.560316i
$689$	2.58579	−	4.47871i	0.0985106	−	0.170625i
$690$		0			0
$691$	−0.343146	−	0.594346i	−0.0130539	−	0.0226100i	0.859425	−	0.511262i	$-0.170822\pi$
$691$	−0.343146	−	0.594346i	−0.0130539	−	0.0226100i	−0.872479	+	0.488652i	$0.837489\pi$
$692$	−38.5269			−1.46457
$693$		0			0
$694$	13.7990			0.523802
$695$	−30.1421	−	52.2077i	−1.14336	−	1.98035i
$696$		0			0
$697$	7.00000	−	12.1244i	0.265144	−	0.459243i
$698$	2.05025	+	3.55114i	0.0776032	+	0.134413i
$699$		0			0
$700$		0			0
$701$	17.1716			0.648561			0.324281	−	0.945961i	$-0.394878\pi$
$701$	17.1716			0.648561			0.324281	+	0.945961i	$0.394878\pi$
$702$		0			0
$703$	5.65685	−	9.79796i	0.213352	−	0.369537i
$704$	4.17157	−	7.22538i	0.157222	−	0.272317i
$705$		0			0
$706$	6.10051			0.229596
$707$		0			0
$708$		0			0
$709$	18.1421	+	31.4231i	0.681342	+	1.18012i	0.974571	+	0.224077i	$0.0719368\pi$
$709$	18.1421	+	31.4231i	0.681342	+	1.18012i	−0.293229	+	0.956042i	$0.594730\pi$
$710$	−6.58579	+	11.4069i	−0.247160	+	0.428094i
$711$		0			0
$712$	11.2929	+	19.5599i	0.423219	+	0.733037i
$713$	8.97056			0.335950
$714$		0			0
$715$	−17.6569			−0.660329
$716$	17.9706	+	31.1259i	0.671591	+	1.16323i
$717$		0			0
$718$	0.0710678	−	0.123093i	0.00265223	−	0.00459379i
$719$	−20.9706	−	36.3221i	−0.782070	−	1.35459i	−0.930734	−	0.365697i	$-0.880831\pi$
$719$	−20.9706	−	36.3221i	−0.782070	−	1.35459i	0.148664	−	0.988888i	$-0.452503\pi$
$720$		0			0
$721$		0			0
$722$	4.55635			0.169570
$723$		0			0
$724$	2.36396	−	4.09450i	0.0878559	−	0.152171i
$725$	−22.7279	+	39.3659i	−0.844094	+	1.46201i
$726$		0			0
$727$	−12.4853			−0.463053			−0.231527	−	0.972829i	$-0.574372\pi$
$727$	−12.4853			−0.463053			−0.231527	+	0.972829i	$0.574372\pi$
$728$		0			0
$729$		0			0
$730$	−9.82843	−	17.0233i	−0.363766	−	0.630062i
$731$	6.34315	−	10.9867i	0.234610	−	0.406356i
$732$		0			0
$733$	24.8492	+	43.0402i	0.917828	+	1.58972i	0.802708	+	0.596373i	$0.203392\pi$
$733$	24.8492	+	43.0402i	0.917828	+	1.58972i	0.115120	+	0.993352i	$0.463275\pi$
$734$	−1.37258			−0.0506630
$735$		0			0
$736$	−33.7990			−1.24585
$737$	5.65685	+	9.79796i	0.208373	+	0.360912i
$738$		0			0
$739$	−2.34315	+	4.05845i	−0.0861940	+	0.149292i	−0.905899	−	0.423493i	$-0.860804\pi$
$739$	−2.34315	+	4.05845i	−0.0861940	+	0.149292i	0.819705	+	0.572785i	$0.194137\pi$
$740$	−12.4853	−	21.6251i	−0.458968	−	0.794956i
$741$		0			0
$742$		0			0
$743$	50.9706			1.86993			0.934964	−	0.354742i	$-0.115431\pi$
$743$	50.9706			1.86993			0.934964	+	0.354742i	$0.115431\pi$
$744$		0			0
$745$	29.5563	−	51.1931i	1.08286	−	1.87557i
$746$	−2.21320	+	3.83338i	−0.0810311	+	0.140350i
$747$		0			0
$748$	8.20101			0.299859
$749$		0			0
$750$		0			0
$751$	−6.82843	−	11.8272i	−0.249173	−	0.431580i	0.714124	−	0.700020i	$-0.246825\pi$
$751$	−6.82843	−	11.8272i	−0.249173	−	0.431580i	−0.963297	+	0.268440i	$0.913492\pi$
$752$	4.24264	−	7.34847i	0.154713	−	0.267971i
$753$		0			0
$754$	−3.65685	−	6.33386i	−0.133175	−	0.230665i
$755$	40.9706			1.49107
$756$		0			0
$757$	26.3431			0.957458			0.478729	−	0.877963i	$-0.341098\pi$
$757$	26.3431			0.957458			0.478729	+	0.877963i	$0.341098\pi$
$758$	1.79899	+	3.11594i	0.0653423	+	0.113176i
$759$		0			0
$760$	−7.65685	+	13.2621i	−0.277743	+	0.481065i
$761$	9.26346	+	16.0448i	0.335800	+	0.581623i	0.983638	−	0.180155i	$-0.0576600\pi$
$761$	9.26346	+	16.0448i	0.335800	+	0.581623i	−0.647838	+	0.761778i	$0.724327\pi$
$762$		0			0
$763$		0			0
$764$	−32.9117			−1.19070
$765$		0			0
$766$	−3.79899	+	6.58004i	−0.137263	+	0.237747i
$767$	−1.51472	+	2.62357i	−0.0546933	+	0.0947316i
$768$		0			0
$769$	−29.6985			−1.07095			−0.535477	−	0.844550i	$-0.679868\pi$
$769$	−29.6985			−1.07095			−0.535477	+	0.844550i	$0.679868\pi$
$770$		0			0
$771$		0			0
$772$	4.85786	+	8.41407i	0.174838	+	0.302829i
$773$	4.77817	−	8.27604i	0.171859	−	0.297669i	−0.767211	−	0.641395i	$-0.778356\pi$
$773$	4.77817	−	8.27604i	0.171859	−	0.297669i	0.939070	+	0.343727i	$0.111689\pi$
$774$		0			0
$775$	−3.89949	−	6.75412i	−0.140074	−	0.242615i
$776$	−4.10051			−0.147200
$777$		0			0
$778$	−7.51472			−0.269416
$779$	−8.82843	−	15.2913i	−0.316311	−	0.547867i
$780$		0			0
$781$	9.31371	−	16.1318i	0.333271	−	0.577242i
$782$	−3.55635	−	6.15978i	−0.127175	−	0.220273i
$783$		0			0
$784$		0			0
$785$	−40.1421			−1.43273
$786$		0			0
$787$	12.3431	−	21.3790i	0.439986	−	0.762077i	−0.557702	−	0.830041i	$-0.688317\pi$
$787$	12.3431	−	21.3790i	0.439986	−	0.762077i	0.997688	+	0.0679637i	$0.0216502\pi$
$788$	−1.82843	+	3.16693i	−0.0651350	+	0.112817i
$789$		0			0
$790$	−19.3137			−0.687151
$791$		0			0
$792$		0			0
$793$	−15.8284	−	27.4156i	−0.562084	−	0.973558i
$794$	0.493903	−	0.855466i	0.0175280	−	0.0303593i
$795$		0			0
$796$	−19.7990	−	34.2929i	−0.701757	−	1.21548i
$797$	−8.38478			−0.297004			−0.148502	−	0.988912i	$-0.547445\pi$
$797$	−8.38478			−0.297004			−0.148502	+	0.988912i	$0.547445\pi$
$798$		0			0
$799$	6.34315			0.224404
$800$	14.6924	+	25.4480i	0.519454	+	0.899721i
$801$		0			0
$802$	1.27208	−	2.20330i	0.0449186	−	0.0778014i
$803$	13.8995	+	24.0746i	0.490503	+	0.849575i
$804$		0			0
$805$		0			0
$806$	1.25483			0.0441996
$807$		0			0
$808$	−2.32233	+	4.02239i	−0.0816993	+	0.141507i
$809$	9.97056	−	17.2695i	0.350546	−	0.607164i	−0.635799	−	0.771855i	$-0.719329\pi$
$809$	9.97056	−	17.2695i	0.350546	−	0.607164i	0.986345	+	0.164691i	$0.0526626\pi$
$810$		0			0
$811$	17.6569			0.620016			0.310008	−	0.950734i	$-0.399668\pi$
$811$	17.6569			0.620016			0.310008	+	0.950734i	$0.399668\pi$
$812$		0			0
$813$		0			0
$814$	−1.65685	−	2.86976i	−0.0580727	−	0.100585i
$815$	19.3137	−	33.4523i	0.676530	−	1.17178i
$816$		0			0
$817$	−8.00000	−	13.8564i	−0.279885	−	0.484774i
$818$	−8.87006			−0.310134
$819$		0			0
$820$	−38.9706			−1.36091
$821$	−5.34315	−	9.25460i	−0.186477	−	0.322988i	0.757596	−	0.652724i	$-0.226374\pi$
$821$	−5.34315	−	9.25460i	−0.186477	−	0.322988i	−0.944073	+	0.329736i	$0.893040\pi$
$822$		0			0
$823$	−4.48528	+	7.76874i	−0.156347	+	0.270801i	−0.933549	−	0.358451i	$-0.883305\pi$
$823$	−4.48528	+	7.76874i	−0.156347	+	0.270801i	0.777202	+	0.629252i	$0.216639\pi$
$824$	3.55635	+	6.15978i	0.123891	+	0.214586i
$825$		0			0
$826$		0			0
$827$	−47.6569			−1.65719			−0.828596	−	0.559848i	$-0.810860\pi$
$827$	−47.6569			−1.65719			−0.828596	+	0.559848i	$0.810860\pi$
$828$		0			0
$829$	−0.363961	+	0.630399i	−0.0126409	+	0.0218947i	−0.872277	−	0.489013i	$-0.837357\pi$
$829$	−0.363961	+	0.630399i	−0.0126409	+	0.0218947i	0.859636	+	0.510907i	$0.170690\pi$
$830$	5.17157	−	8.95743i	0.179508	−	0.310917i
$831$		0			0
$832$	10.7868			0.373965
$833$		0			0
$834$		0			0
$835$	33.7990	+	58.5416i	1.16966	+	2.02591i
$836$	5.17157	−	8.95743i	0.178863	−	0.309799i
$837$		0			0
$838$	6.87006	+	11.8993i	0.237322	+	0.411054i
$839$	50.8284			1.75479			0.877396	−	0.479767i	$-0.159279\pi$
$839$	50.8284			1.75479			0.877396	+	0.479767i	$0.159279\pi$
$840$		0			0
$841$	17.6274			0.607842
$842$	3.44365	+	5.96458i	0.118676	+	0.205553i
$843$		0			0
$844$	11.8579	−	20.5384i	0.408165	−	0.706962i
$845$	10.7782	+	18.6683i	0.370780	+	0.642211i
$846$		0			0
$847$		0			0
$848$	6.00000			0.206041
$849$		0			0
$850$	−3.09188	+	5.35530i	−0.106051	+	0.183685i
$851$	15.3137	−	26.5241i	0.524947	−	0.909235i
$852$		0			0
$853$	49.4975			1.69476			0.847381	−	0.530986i	$-0.178178\pi$
$853$	49.4975			1.69476			0.847381	+	0.530986i	$0.178178\pi$
$854$		0			0
$855$		0			0
$856$	−0.272078	−	0.471253i	−0.00929943	−	0.0161071i
$857$	−7.70711	+	13.3491i	−0.263270	+	0.455997i	−0.967109	−	0.254363i	$-0.918134\pi$
$857$	−7.70711	+	13.3491i	−0.263270	+	0.455997i	0.703839	+	0.710359i	$0.251468\pi$
$858$		0			0
$859$	28.7279	+	49.7582i	0.980184	+	1.69773i	0.661642	+	0.749820i	$0.269860\pi$
$859$	28.7279	+	49.7582i	0.980184	+	1.69773i	0.318542	+	0.947909i	$0.396807\pi$
$860$	−35.3137			−1.20419
$861$		0			0
$862$	−11.1716			−0.380505
$863$	8.65685	+	14.9941i	0.294683	+	0.510405i	0.974911	−	0.222595i	$-0.0714527\pi$
$863$	8.65685	+	14.9941i	0.294683	+	0.510405i	−0.680228	+	0.733000i	$0.738119\pi$
$864$		0			0
$865$	−35.9706	+	62.3028i	−1.22304	+	2.11836i
$866$	4.19239	+	7.26143i	0.142463	+	0.246753i
$867$		0			0
$868$		0			0
$869$	27.3137			0.926554
$870$		0			0
$871$	−7.31371	+	12.6677i	−0.247816	+	0.429229i
$872$	4.48528	−	7.76874i	0.151891	−	0.263083i
$873$		0			0
$874$	−8.97056			−0.303434
$875$		0			0
$876$		0			0
$877$	5.65685	+	9.79796i	0.191018	+	0.330854i	0.945588	−	0.325366i	$-0.105488\pi$
$877$	5.65685	+	9.79796i	0.191018	+	0.330854i	−0.754570	+	0.656220i	$0.772154\pi$
$878$	−2.62742	+	4.55082i	−0.0886710	+	0.153583i
$879$		0			0
$880$	−10.2426	−	17.7408i	−0.345279	−	0.598041i
$881$	21.7574			0.733024			0.366512	−	0.930413i	$-0.380552\pi$
$881$	21.7574			0.733024			0.366512	+	0.930413i	$0.380552\pi$
$882$		0			0
$883$	−4.68629			−0.157706			−0.0788531	−	0.996886i	$-0.525126\pi$
$883$	−4.68629			−0.157706			−0.0788531	+	0.996886i	$0.525126\pi$
$884$	5.30152	+	9.18249i	0.178309	+	0.308841i
$885$		0			0
$886$	−7.24264	+	12.5446i	−0.243321	+	0.421445i
$887$	1.41421	+	2.44949i	0.0474846	+	0.0822458i	0.888791	−	0.458313i	$-0.151546\pi$
$887$	1.41421	+	2.44949i	0.0474846	+	0.0822458i	−0.841306	+	0.540559i	$0.818213\pi$
$888$		0			0
$889$		0			0
$890$	20.1421			0.675166
$891$		0			0
$892$	−22.8284	+	39.5400i	−0.764352	+	1.32390i
$893$	4.00000	−	6.92820i	0.133855	−	0.231843i
$894$		0			0
$895$	67.1127			2.24333
$896$		0			0
$897$		0			0
$898$	1.10051	+	1.90613i	0.0367243	+	0.0636084i
$899$	−4.00000	+	6.92820i	−0.133407	+	0.231069i
$900$		0			0
$901$	2.24264	+	3.88437i	0.0747132	+	0.129407i
$902$	−5.17157			−0.172195
$903$		0			0
$904$	8.42641			0.280258
$905$	−4.41421	−	7.64564i	−0.146733	−	0.254150i
$906$		0			0
$907$	8.00000	−	13.8564i	0.265636	−	0.460094i	−0.702094	−	0.712084i	$-0.747752\pi$
$907$	8.00000	−	13.8564i	0.265636	−	0.460094i	0.967730	+	0.251990i	$0.0810849\pi$
$908$	21.7574	+	37.6849i	0.722043	+	1.25062i
$909$		0			0
$910$		0			0
$911$	1.02944			0.0341068			0.0170534	−	0.999855i	$-0.494571\pi$
$911$	1.02944			0.0341068			0.0170534	+	0.999855i	$0.494571\pi$
$912$		0			0
$913$	−7.31371	+	12.6677i	−0.242048	+	0.419240i
$914$	−3.72792	+	6.45695i	−0.123309	+	0.213577i
$915$		0			0
$916$	−0.443651			−0.0146586
$917$		0			0
$918$		0			0
$919$	4.14214	+	7.17439i	0.136636	+	0.236661i	0.926221	−	0.376980i	$-0.123037\pi$
$919$	4.14214	+	7.17439i	0.136636	+	0.236661i	−0.789585	+	0.613641i	$0.789704\pi$
$920$	−20.7279	+	35.9018i	−0.683379	+	1.18365i
$921$		0			0
$922$	−3.43503	−	5.94964i	−0.113127	−	0.195941i
$923$	24.0833			0.792710
$924$		0			0
$925$	−26.6274			−0.875504
$926$	−5.51472	−	9.55177i	−0.181225	−	0.313891i
$927$		0			0
$928$	15.0711	−	26.1039i	0.494732	−	0.856901i
$929$	19.6066	+	33.9596i	0.643272	+	1.11418i	0.984698	+	0.174271i	$0.0557568\pi$
$929$	19.6066	+	33.9596i	0.643272	+	1.11418i	−0.341426	+	0.939909i	$0.610910\pi$
$930$		0			0
$931$		0			0
$932$	−11.2304			−0.367866
$933$		0			0
$934$	0.0416306	−	0.0721062i	0.00136219	−	0.00235939i
$935$	7.65685	−	13.2621i	0.250406	−	0.433716i
$936$		0			0
$937$	−30.5858			−0.999194			−0.499597	−	0.866258i	$-0.666519\pi$
$937$	−30.5858			−0.999194			−0.499597	+	0.866258i	$0.666519\pi$
$938$		0			0
$939$		0			0
$940$	−8.82843	−	15.2913i	−0.287952	−	0.498747i
$941$	−17.6066	+	30.4955i	−0.573959	+	0.994126i	0.422195	+	0.906505i	$0.361260\pi$
$941$	−17.6066	+	30.4955i	−0.573959	+	0.994126i	−0.996154	+	0.0876208i	$0.972074\pi$
$942$		0			0
$943$	−23.8995	−	41.3951i	−0.778275	−	1.34801i
$944$	−3.51472			−0.114394
$945$		0			0
$946$	−4.68629			−0.152364
$947$	15.3431	+	26.5751i	0.498585	+	0.863575i	0.999999	−	0.00163285i	$-0.000519752\pi$
$947$	15.3431	+	26.5751i	0.498585	+	0.863575i	−0.501413	+	0.865208i	$0.667186\pi$
$948$		0			0
$949$	−17.9706	+	31.1259i	−0.583349	+	1.01039i
$950$	3.89949	+	6.75412i	0.126516	+	0.219133i
$951$		0			0
$952$		0			0
$953$	−2.00000			−0.0647864			−0.0323932	−	0.999475i	$-0.510313\pi$
$953$	−2.00000			−0.0647864			−0.0323932	+	0.999475i	$0.510313\pi$
$954$		0			0
$955$	−30.7279	+	53.2223i	−0.994332	+	1.72223i
$956$	14.3137	−	24.7921i	0.462938	−	0.801833i
$957$		0			0
$958$	−0.769553			−0.0248631
$959$		0			0
$960$		0			0
$961$	14.8137	+	25.6581i	0.477862	+	0.827681i
$962$	2.14214	−	3.71029i	0.0690652	−	0.119624i
$963$		0			0
$964$	14.8492	+	25.7196i	0.478262	+	0.828374i
$965$	18.1421			0.584016
$966$		0			0
$967$	33.6569			1.08233			0.541166	−	0.840916i	$-0.317983\pi$
$967$	33.6569			1.08233			0.541166	+	0.840916i	$0.317983\pi$
$968$	5.55025	+	9.61332i	0.178392	+	0.308984i
$969$		0			0
$970$	−1.82843	+	3.16693i	−0.0587073	+	0.101684i
$971$	25.3137	+	43.8446i	0.812356	+	1.40704i	0.911211	+	0.411939i	$0.135148\pi$
$971$	25.3137	+	43.8446i	0.812356	+	1.40704i	−0.0988557	+	0.995102i	$0.531518\pi$
$972$		0			0
$973$		0			0
$974$	−11.0294			−0.353406
$975$		0			0
$976$	18.3640	−	31.8073i	0.587816	−	1.01813i
$977$	−10.5858	+	18.3351i	−0.338669	+	0.586592i	−0.984183	−	0.177157i	$-0.943310\pi$
$977$	−10.5858	+	18.3351i	−0.338669	+	0.586592i	0.645513	+	0.763749i	$0.276643\pi$
$978$		0			0
$979$	−28.4853			−0.910394
$980$		0			0
$981$		0			0
$982$	−1.04163	−	1.80416i	−0.0332398	−	0.0575730i
$983$	26.6274	−	46.1200i	0.849283	−	1.47100i	−0.0325667	−	0.999470i	$-0.510368\pi$
$983$	26.6274	−	46.1200i	0.849283	−	1.47100i	0.881849	−	0.471531i	$-0.156299\pi$
$984$		0			0
$985$	3.41421	+	5.91359i	0.108786	+	0.188423i
$986$	6.34315			0.202007
$987$		0			0
$988$	13.3726			0.425439
$989$	−21.6569	−	37.5108i	−0.688648	−	1.19277i
$990$		0			0
$991$	6.48528	−	11.2328i	0.206012	−	0.356823i	−0.744443	−	0.667686i	$-0.767285\pi$
$991$	6.48528	−	11.2328i	0.206012	−	0.356823i	0.950455	+	0.310863i	$0.100618\pi$
$992$	2.58579	+	4.47871i	0.0820988	+	0.142199i
$993$		0			0
$994$		0			0
$995$	−73.9411			−2.34409
$996$		0			0
$997$	13.1924	−	22.8499i	0.417807	−	0.723663i	−0.577911	−	0.816099i	$-0.696132\pi$
$997$	13.1924	−	22.8499i	0.417807	−	0.723663i	0.995719	+	0.0924363i	$0.0294654\pi$
$998$	0.686292	−	1.18869i	0.0217242	−	0.0376274i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.e.f.361.2		4
3.2	odd	2		147.2.e.e.67.1		4
7.2	even	3	inner	441.2.e.f.226.2		4
7.3	odd	6		441.2.a.i.1.1		2
7.4	even	3		441.2.a.j.1.1		2
7.5	odd	6		441.2.e.g.226.2		4
7.6	odd	2		441.2.e.g.361.2		4
12.11	even	2		2352.2.q.bb.1537.2		4
21.2	odd	6		147.2.e.e.79.1		4
21.5	even	6		147.2.e.d.79.1		4
21.11	odd	6		147.2.a.d.1.2	✓	2
21.17	even	6		147.2.a.e.1.2	yes	2
21.20	even	2		147.2.e.d.67.1		4
28.3	even	6		7056.2.a.cf.1.1		2
28.11	odd	6		7056.2.a.cv.1.2		2
84.11	even	6		2352.2.a.be.1.1		2
84.23	even	6		2352.2.q.bb.961.2		4
84.47	odd	6		2352.2.q.bd.961.1		4
84.59	odd	6		2352.2.a.bc.1.2		2
84.83	odd	2		2352.2.q.bd.1537.1		4
105.59	even	6		3675.2.a.bd.1.1		2
105.74	odd	6		3675.2.a.bf.1.1		2
168.11	even	6		9408.2.a.dq.1.2		2
168.53	odd	6		9408.2.a.ef.1.2		2
168.59	odd	6		9408.2.a.dt.1.1		2
168.101	even	6		9408.2.a.di.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.a.d.1.2	✓	2	21.11	odd	6
147.2.a.e.1.2	yes	2	21.17	even	6
147.2.e.d.67.1		4	21.20	even	2
147.2.e.d.79.1		4	21.5	even	6
147.2.e.e.67.1		4	3.2	odd	2
147.2.e.e.79.1		4	21.2	odd	6
441.2.a.i.1.1		2	7.3	odd	6
441.2.a.j.1.1		2	7.4	even	3
441.2.e.f.226.2		4	7.2	even	3	inner
441.2.e.f.361.2		4	1.1	even	1	trivial
441.2.e.g.226.2		4	7.5	odd	6
441.2.e.g.361.2		4	7.6	odd	2
2352.2.a.bc.1.2		2	84.59	odd	6
2352.2.a.be.1.1		2	84.11	even	6
2352.2.q.bb.961.2		4	84.23	even	6
2352.2.q.bb.1537.2		4	12.11	even	2
2352.2.q.bd.961.1		4	84.47	odd	6
2352.2.q.bd.1537.1		4	84.83	odd	2
3675.2.a.bd.1.1		2	105.59	even	6
3675.2.a.bf.1.1		2	105.74	odd	6
7056.2.a.cf.1.1		2	28.3	even	6
7056.2.a.cv.1.2		2	28.11	odd	6
9408.2.a.di.1.1		2	168.101	even	6
9408.2.a.dq.1.2		2	168.11	even	6
9408.2.a.dt.1.1		2	168.59	odd	6
9408.2.a.ef.1.2		2	168.53	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.207107 + 0.358719i) q^{2} +(0.914214 - 1.58346i) q^{4} +(-1.70711 - 2.95680i) q^{5} +1.58579 q^{8} +O(q^{10})\)	\(q+(0.207107 + 0.358719i) q^{2} +(0.914214 - 1.58346i) q^{4} +(-1.70711 - 2.95680i) q^{5} +1.58579 q^{8} +(0.707107 - 1.22474i) q^{10} +(-1.00000 + 1.73205i) q^{11} -2.58579 q^{13} +(-1.50000 - 2.59808i) q^{16} +(1.12132 - 1.94218i) q^{17} +(-1.41421 - 2.44949i) q^{19} -6.24264 q^{20} -0.828427 q^{22} +(-3.82843 - 6.63103i) q^{23} +(-3.32843 + 5.76500i) q^{25} +(-0.535534 - 0.927572i) q^{26} +6.82843 q^{29} +(-0.585786 + 1.01461i) q^{31} +(2.20711 - 3.82282i) q^{32} +0.928932 q^{34} +(2.00000 + 3.46410i) q^{37} +(0.585786 - 1.01461i) q^{38} +(-2.70711 - 4.68885i) q^{40} +6.24264 q^{41} +5.65685 q^{43} +(1.82843 + 3.16693i) q^{44} +(1.58579 - 2.74666i) q^{46} +(1.41421 + 2.44949i) q^{47} -2.75736 q^{50} +(-2.36396 + 4.09450i) q^{52} +(-1.00000 + 1.73205i) q^{53} +6.82843 q^{55} +(1.41421 + 2.44949i) q^{58} +(0.585786 - 1.01461i) q^{59} +(6.12132 + 10.6024i) q^{61} -0.485281 q^{62} -4.17157 q^{64} +(4.41421 + 7.64564i) q^{65} +(2.82843 - 4.89898i) q^{67} +(-2.05025 - 3.55114i) q^{68} -9.31371 q^{71} +(6.94975 - 12.0373i) q^{73} +(-0.828427 + 1.43488i) q^{74} -5.17157 q^{76} +(-6.82843 - 11.8272i) q^{79} +(-5.12132 + 8.87039i) q^{80} +(1.29289 + 2.23936i) q^{82} +7.31371 q^{83} -7.65685 q^{85} +(1.17157 + 2.02922i) q^{86} +(-1.58579 + 2.74666i) q^{88} +(7.12132 + 12.3345i) q^{89} -14.0000 q^{92} +(-0.585786 + 1.01461i) q^{94} +(-4.82843 + 8.36308i) q^{95} -2.58579 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} - 4 q^{5} + 12 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^4 - 4 * q^5 + 12 * q^8	\( 4 q - 2 q^{2} - 2 q^{4} - 4 q^{5} + 12 q^{8} - 4 q^{11} - 16 q^{13} - 6 q^{16} - 4 q^{17} - 8 q^{20} + 8 q^{22} - 4 q^{23} - 2 q^{25} + 12 q^{26} + 16 q^{29} - 8 q^{31} + 6 q^{32} + 32 q^{34} + 8 q^{37} + 8 q^{38} - 8 q^{40} + 8 q^{41} - 4 q^{44} + 12 q^{46} - 28 q^{50} + 16 q^{52} - 4 q^{53} + 16 q^{55} + 8 q^{59} + 16 q^{61} + 32 q^{62} - 28 q^{64} + 12 q^{65} - 28 q^{68} + 8 q^{71} + 8 q^{73} + 8 q^{74} - 32 q^{76} - 16 q^{79} - 12 q^{80} + 8 q^{82} - 16 q^{83} - 8 q^{85} + 16 q^{86} - 12 q^{88} + 20 q^{89} - 56 q^{92} - 8 q^{94} - 8 q^{95} - 16 q^{97}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 - 4 * q^5 + 12 * q^8 - 4 * q^11 - 16 * q^13 - 6 * q^16 - 4 * q^17 - 8 * q^20 + 8 * q^22 - 4 * q^23 - 2 * q^25 + 12 * q^26 + 16 * q^29 - 8 * q^31 + 6 * q^32 + 32 * q^34 + 8 * q^37 + 8 * q^38 - 8 * q^40 + 8 * q^41 - 4 * q^44 + 12 * q^46 - 28 * q^50 + 16 * q^52 - 4 * q^53 + 16 * q^55 + 8 * q^59 + 16 * q^61 + 32 * q^62 - 28 * q^64 + 12 * q^65 - 28 * q^68 + 8 * q^71 + 8 * q^73 + 8 * q^74 - 32 * q^76 - 16 * q^79 - 12 * q^80 + 8 * q^82 - 16 * q^83 - 8 * q^85 + 16 * q^86 - 12 * q^88 + 20 * q^89 - 56 * q^92 - 8 * q^94 - 8 * q^95 - 16 * q^97

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