LMFDB - Embedded newform 441.2.s.c.362.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(362,441)]

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([1, 5]))

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

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

chi := DirichletCharacter("441.362");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 7x^{10} + 37x^{8} - 78x^{6} + 123x^{4} - 36x^{2} + 9 $ x^12 - 7x^10 + 37x^8 - 78x^6 + 123x^4 - 36*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			362.5
Root			$1.29589 - 0.748185i$ of defining polynomial
Character	$\chi$	$=$	441.362
Dual form			441.2.s.c.374.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.97141 - 1.13819i) q^{2} +(-1.70316 + 0.315036i) q^{3} +(1.59097 - 2.75564i) q^{4} +1.43429 q^{5} +(-2.99905 + 2.55959i) q^{6} -2.69056i q^{8} +(2.80150 - 1.07311i) q^{9} +O(q^{10})$	\(q+(1.97141 - 1.13819i) q^{2} +(-1.70316 + 0.315036i) q^{3} +(1.59097 - 2.75564i) q^{4} +1.43429 q^{5} +(-2.99905 + 2.55959i) q^{6} -2.69056i q^{8} +(2.80150 - 1.07311i) q^{9} +(2.82757 - 1.63250i) q^{10} -3.23490i q^{11} +(-1.84155 + 5.19451i) q^{12} +(4.43334 - 2.55959i) q^{13} +(-2.44282 + 0.451852i) q^{15} +(0.119562 + 0.207087i) q^{16} +(-0.545658 - 0.945107i) q^{17} +(4.30150 - 5.30420i) q^{18} +(-3.88768 - 2.24456i) q^{19} +(2.28191 - 3.95238i) q^{20} +(-3.68194 - 6.37731i) q^{22} +4.00844i q^{23} +(0.847623 + 4.58246i) q^{24} -2.94282 q^{25} +(5.82662 - 10.0920i) q^{26} +(-4.43334 + 2.71026i) q^{27} +(1.02859 + 0.593857i) q^{29} +(-4.30150 + 3.67119i) q^{30} +(3.24275 + 1.87220i) q^{31} +(5.13160 + 2.96273i) q^{32} +(1.01911 + 5.50955i) q^{33} +(-2.15143 - 1.24213i) q^{34} +(1.50000 - 9.42724i) q^{36} +(0.119562 - 0.207087i) q^{37} -10.2190 q^{38} +(-6.74433 + 5.75605i) q^{39} -3.85904i q^{40} +(3.71620 + 6.43664i) q^{41} +(-3.82326 + 6.62208i) q^{43} +(-8.91423 - 5.14663i) q^{44} +(4.01816 - 1.53915i) q^{45} +(4.56238 + 7.90228i) q^{46} +(-2.11042 - 3.65536i) q^{47} +(-0.268872 - 0.315036i) q^{48} +(-5.80150 + 3.34950i) q^{50} +(1.22708 + 1.43777i) q^{51} -16.2889i q^{52} +(-6.07442 + 3.50707i) q^{53} +(-5.65514 + 10.3890i) q^{54} -4.63977i q^{55} +(7.32846 + 2.59808i) q^{57} +2.70370 q^{58} +(-4.73531 + 8.20179i) q^{59} +(-2.64132 + 7.45043i) q^{60} +(2.82757 - 1.63250i) q^{61} +8.52371 q^{62} +13.0104 q^{64} +(6.35868 - 3.67119i) q^{65} +(8.28002 + 9.70164i) q^{66} +(-0.330095 + 0.571741i) q^{67} -3.47250 q^{68} +(-1.26280 - 6.82701i) q^{69} -3.82347i q^{71} +(-2.88727 - 7.53762i) q^{72} +(6.33127 - 3.65536i) q^{73} -0.544337i q^{74} +(5.01209 - 0.927093i) q^{75} +(-12.3704 + 7.14205i) q^{76} +(-6.74433 + 19.0239i) q^{78} +(-1.83009 - 3.16982i) q^{79} +(0.171486 + 0.297022i) q^{80} +(6.69686 - 6.01266i) q^{81} +(14.6523 + 8.45951i) q^{82} +(-5.45245 + 9.44392i) q^{83} +(-0.782630 - 1.35556i) q^{85} +17.4064i q^{86} +(-1.93894 - 0.687390i) q^{87} -8.70370 q^{88} +(-6.84573 + 11.8572i) q^{89} +(6.16959 - 7.60775i) q^{90} +(11.0458 + 6.37731i) q^{92} +(-6.11273 - 2.16708i) q^{93} +(-8.32102 - 4.80415i) q^{94} +(-5.57605 - 3.21934i) q^{95} +(-9.67330 - 3.42937i) q^{96} +(2.69709 + 1.55716i) q^{97} +(-3.47141 - 9.06259i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} + 2 q^{4}+O(q^{10}) $ 12 * q + 6 * q^2 + 2 * q^4	$ 12 q + 6 q^{2} + 2 q^{4} + 6 q^{15} + 2 q^{16} + 18 q^{18} - 10 q^{22} + 30 q^{29} - 18 q^{30} + 12 q^{32} + 18 q^{36} + 2 q^{37} - 12 q^{39} - 10 q^{43} - 54 q^{44} + 20 q^{46} - 36 q^{50} + 66 q^{51} + 12 q^{53} - 18 q^{57} - 4 q^{58} - 30 q^{60} + 16 q^{64} + 78 q^{65} + 12 q^{67} - 54 q^{72} - 12 q^{78} - 6 q^{79} + 24 q^{81} - 6 q^{85} - 68 q^{88} + 30 q^{92} - 54 q^{93} - 72 q^{95} - 24 q^{99}+O(q^{100}) $ 12 * q + 6 * q^2 + 2 * q^4 + 6 * q^15 + 2 * q^16 + 18 * q^18 - 10 * q^22 + 30 * q^29 - 18 * q^30 + 12 * q^32 + 18 * q^36 + 2 * q^37 - 12 * q^39 - 10 * q^43 - 54 * q^44 + 20 * q^46 - 36 * q^50 + 66 * q^51 + 12 * q^53 - 18 * q^57 - 4 * q^58 - 30 * q^60 + 16 * q^64 + 78 * q^65 + 12 * q^67 - 54 * q^72 - 12 * q^78 - 6 * q^79 + 24 * q^81 - 6 * q^85 - 68 * q^88 + 30 * q^92 - 54 * q^93 - 72 * q^95 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.97141	−	1.13819i	1.39400	−	0.804825i	0.400242	−	0.916409i	$-0.368926\pi$
$2$	1.97141	−	1.13819i	1.39400	−	0.804825i	0.993755	+	0.111585i	$0.0355926\pi$
$3$	−1.70316	+	0.315036i	−0.983320	+	0.181886i
$3$	−1.70316	+	0.315036i	−0.983320	+	0.181886i
$4$	1.59097	−	2.75564i	0.795486	−	1.37782i
$5$	1.43429			0.641433			0.320716	−	0.947175i	$-0.396076\pi$
$5$	1.43429			0.641433			0.320716	+	0.947175i	$0.396076\pi$
$6$	−2.99905	+	2.55959i	−1.22436	+	1.04495i
$7$		0			0
$7$		0			0
$8$		−	2.69056i		−	0.951257i
$9$	2.80150	−	1.07311i	0.933835	−	0.357704i
$10$	2.82757	−	1.63250i	0.894156	−	0.516241i
$11$		−	3.23490i		−	0.975359i	−0.873023	−	0.487679i	$-0.837843\pi$
$11$		−	3.23490i		−	0.975359i	0.873023	−	0.487679i	$-0.162157\pi$
$12$	−1.84155	+	5.19451i	−0.531610	+	1.49953i
$13$	4.43334	−	2.55959i	1.22959	−	0.709903i	0.262644	−	0.964893i	$-0.415406\pi$
$13$	4.43334	−	2.55959i	1.22959	−	0.709903i	0.966944	+	0.254990i	$0.0820722\pi$
$14$		0			0
$15$	−2.44282	+	0.451852i	−0.630733	+	0.116668i
$16$	0.119562	+	0.207087i	0.0298904	+	0.0517717i
$17$	−0.545658	−	0.945107i	−0.132341	−	0.229222i	0.792237	−	0.610213i	$-0.208916\pi$
$17$	−0.545658	−	0.945107i	−0.132341	−	0.229222i	−0.924579	+	0.380991i	$0.875583\pi$
$18$	4.30150	−	5.30420i	1.01387	−	1.25021i
$19$	−3.88768	−	2.24456i	−0.891896	−	0.514936i	−0.0173336	−	0.999850i	$-0.505518\pi$
$19$	−3.88768	−	2.24456i	−0.891896	−	0.514936i	−0.874562	+	0.484914i	$0.838851\pi$
$20$	2.28191	−	3.95238i	0.510251	−	0.883780i
$21$		0			0
$22$	−3.68194	−	6.37731i	−0.784993	−	1.35965i
$23$			4.00844i			0.835817i	0.908489	+	0.417909i	$0.137237\pi$
$23$			4.00844i			0.835817i	−0.908489	+	0.417909i	$0.862763\pi$
$24$	0.847623	+	4.58246i	0.173020	+	0.935390i
$25$	−2.94282			−0.588564
$26$	5.82662	−	10.0920i	1.14269	−	1.97921i
$27$	−4.43334	+	2.71026i	−0.853197	+	0.521589i
$28$		0			0
$29$	1.02859	+	0.593857i	0.191004	+	0.110276i	0.592453	−	0.805605i	$-0.298160\pi$
$29$	1.02859	+	0.593857i	0.191004	+	0.110276i	−0.401448	+	0.915882i	$0.631493\pi$
$30$	−4.30150	+	3.67119i	−0.785344	+	0.670264i
$31$	3.24275	+	1.87220i	0.582414	+	0.336257i	0.762092	−	0.647468i	$-0.224172\pi$
$31$	3.24275	+	1.87220i	0.582414	+	0.336257i	−0.179678	+	0.983726i	$0.557506\pi$
$32$	5.13160	+	2.96273i	0.907147	+	0.523742i
$33$	1.01911	+	5.50955i	0.177404	+	0.959089i
$34$	−2.15143	−	1.24213i	−0.368967	−	0.213023i
$35$		0			0
$36$	1.50000	−	9.42724i	0.250000	−	1.57121i
$37$	0.119562	−	0.207087i	0.0196558	−	0.0340449i	−0.856030	−	0.516926i	$-0.827076\pi$
$37$	0.119562	−	0.207087i	0.0196558	−	0.0340449i	0.875686	+	0.482881i	$0.160410\pi$
$38$	−10.2190			−1.65773
$39$	−6.74433	+	5.75605i	−1.07996	+	0.921706i
$40$		−	3.85904i		−	0.610168i
$41$	3.71620	+	6.43664i	0.580373	+	1.00523i	0.995435	+	0.0954418i	$0.0304264\pi$
$41$	3.71620	+	6.43664i	0.580373	+	1.00523i	−0.415062	+	0.909793i	$0.636240\pi$
$42$		0			0
$43$	−3.82326	+	6.62208i	−0.583041	+	1.00986i	0.412075	+	0.911150i	$0.364804\pi$
$43$	−3.82326	+	6.62208i	−0.583041	+	1.00986i	−0.995116	+	0.0987075i	$0.968529\pi$
$44$	−8.91423	−	5.14663i	−1.34387	−	0.775884i
$45$	4.01816	−	1.53915i	0.598992	−	0.229443i
$46$	4.56238	+	7.90228i	0.672686	+	1.16513i
$47$	−2.11042	−	3.65536i	−0.307837	−	0.533189i	0.670052	−	0.742314i	$-0.266272\pi$
$47$	−2.11042	−	3.65536i	−0.307837	−	0.533189i	−0.977889	+	0.209125i	$0.932939\pi$
$48$	−0.268872	−	0.315036i	−0.0388084	−	0.0454715i
$49$		0			0
$50$	−5.80150	+	3.34950i	−0.820457	+	0.473691i
$51$	1.22708	+	1.43777i	0.171826	+	0.201328i
$52$		−	16.2889i		−	2.25887i
$53$	−6.07442	+	3.50707i	−0.834386	+	0.481733i	−0.855352	−	0.518047i	$-0.826659\pi$
$53$	−6.07442	+	3.50707i	−0.834386	+	0.481733i	0.0209662	+	0.999780i	$0.493326\pi$
$54$	−5.65514	+	10.3890i	−0.769567	+	1.41377i
$55$		−	4.63977i		−	0.625627i
$56$		0			0
$57$	7.32846	+	2.59808i	0.970678	+	0.344124i
$58$	2.70370			0.355013
$59$	−4.73531	+	8.20179i	−0.616484	+	1.06778i	0.373638	+	0.927575i	$0.378110\pi$
$59$	−4.73531	+	8.20179i	−0.616484	+	1.06778i	−0.990122	+	0.140208i	$0.955223\pi$
$60$	−2.64132	+	7.45043i	−0.340992	+	0.961846i
$61$	2.82757	−	1.63250i	0.362033	−	0.209020i	−0.307939	−	0.951406i	$-0.599639\pi$
$61$	2.82757	−	1.63250i	0.362033	−	0.209020i	0.669972	+	0.742386i	$0.266306\pi$
$62$	8.52371			1.08251
$63$		0			0
$64$	13.0104			1.62630
$65$	6.35868	−	3.67119i	0.788698	−	0.455355i
$66$	8.28002	+	9.70164i	1.01920	+	1.19419i
$67$	−0.330095	+	0.571741i	−0.0403275	+	0.0698493i	−0.885485	−	0.464669i	$-0.846173\pi$
$67$	−0.330095	+	0.571741i	−0.0403275	+	0.0698493i	0.845157	+	0.534518i	$0.179507\pi$
$68$	−3.47250			−0.421103
$69$	−1.26280	−	6.82701i	−0.152023	−	0.821876i
$70$		0			0
$71$		−	3.82347i		−	0.453762i	−0.973922	−	0.226881i	$-0.927147\pi$
$71$		−	3.82347i		−	0.453762i	0.973922	−	0.226881i	$-0.0728529\pi$
$72$	−2.88727	−	7.53762i	−0.340269	−	0.888317i
$73$	6.33127	−	3.65536i	0.741020	−	0.427828i	−0.0814203	−	0.996680i	$-0.525946\pi$
$73$	6.33127	−	3.65536i	0.741020	−	0.427828i	0.822440	+	0.568852i	$0.192612\pi$
$74$		−	0.544337i		−	0.0632779i
$75$	5.01209	−	0.927093i	0.578747	−	0.107052i
$76$	−12.3704	+	7.14205i	−1.41898	+	0.819249i
$77$		0			0
$78$	−6.74433	+	19.0239i	−0.763644	+	2.15403i
$79$	−1.83009	−	3.16982i	−0.205902	−	0.356632i	0.744518	−	0.667602i	$-0.232679\pi$
$79$	−1.83009	−	3.16982i	−0.205902	−	0.356632i	−0.950420	+	0.310970i	$0.899346\pi$
$80$	0.171486	+	0.297022i	0.0191727	+	0.0332081i
$81$	6.69686	−	6.01266i	0.744096	−	0.668073i
$82$	14.6523	+	8.45951i	1.61808	+	0.934196i
$83$	−5.45245	+	9.44392i	−0.598484	+	1.03660i	0.394561	+	0.918870i	$0.370897\pi$
$83$	−5.45245	+	9.44392i	−0.598484	+	1.03660i	−0.993045	+	0.117735i	$0.962437\pi$
$84$		0			0
$85$	−0.782630	−	1.35556i	−0.0848882	−	0.147031i
$86$			17.4064i			1.87698i
$87$	−1.93894	−	0.687390i	−0.207876	−	0.0736960i
$88$	−8.70370			−0.927817
$89$	−6.84573	+	11.8572i	−0.725646	+	1.25686i	0.233061	+	0.972462i	$0.425126\pi$
$89$	−6.84573	+	11.8572i	−0.725646	+	1.25686i	−0.958708	+	0.284394i	$0.908208\pi$
$90$	6.16959	−	7.60775i	0.650332	−	0.801927i
$91$		0			0
$92$	11.0458	+	6.37731i	1.15161	+	0.664881i
$93$	−6.11273	−	2.16708i	−0.633860	−	0.224715i
$94$	−8.32102	−	4.80415i	−0.858248	−	0.495510i
$95$	−5.57605	−	3.21934i	−0.572091	−	0.330297i
$96$	−9.67330	−	3.42937i	−0.987277	−	0.350008i
$97$	2.69709	+	1.55716i	0.273848	+	0.158106i	0.630635	−	0.776080i	$-0.282795\pi$
$97$	2.69709	+	1.55716i	0.273848	+	0.158106i	−0.356787	+	0.934186i	$0.616128\pi$
$98$		0			0
$99$	−3.47141	−	9.06259i	−0.348890	−	0.910824i
$100$	−4.68194	+	8.10936i	−0.468194	+	0.810936i
$101$	−7.08942			−0.705424			−0.352712	−	0.935732i	$-0.614740\pi$
$101$	−7.08942			−0.705424			−0.352712	+	0.935732i	$0.614740\pi$
$102$	4.05555	+	1.43777i	0.401559	+	0.142360i
$103$			1.70352i			0.167853i	0.996472	+	0.0839265i	$0.0267461\pi$
$103$			1.70352i			0.167853i	−0.996472	+	0.0839265i	$0.973254\pi$
$104$	−6.88674	−	11.9282i	−0.675300	−	1.16965i
$105$		0			0
$106$	−7.98345	+	13.8277i	−0.775421	+	1.34307i
$107$	−4.27455	−	2.46791i	−0.413236	−	0.238582i	0.278943	−	0.960308i	$-0.410016\pi$
$107$	−4.27455	−	2.46791i	−0.413236	−	0.238582i	−0.692179	+	0.721726i	$0.743349\pi$
$108$	0.415178	+	16.5286i	0.0399506	+	1.59047i
$109$	−4.06922	−	7.04809i	−0.389760	−	0.675085i	0.602657	−	0.798001i	$-0.294109\pi$
$109$	−4.06922	−	7.04809i	−0.389760	−	0.675085i	−0.992417	+	0.122916i	$0.960776\pi$
$110$	−5.28096	−	9.14690i	−0.503520	−	0.872123i
$111$	−0.138393	+	0.390368i	−0.0131357	+	0.0370521i
$112$		0			0
$113$	−3.39699	+	1.96125i	−0.319562	+	0.184499i	−0.651197	−	0.758908i	$-0.725733\pi$
$113$	−3.39699	+	1.96125i	−0.319562	+	0.184499i	0.331635	+	0.943408i	$0.392400\pi$
$114$	17.4045	−	3.21934i	1.63008	−	0.301519i
$115$			5.74925i			0.536121i
$116$	3.27292	−	1.88962i	0.303883	−	0.175447i
$117$	9.67330	−	11.9282i	0.894297	−	1.10276i
$118$			21.5588i			1.98465i
$119$		0			0
$120$	1.21574	+	6.57256i	0.110981	+	0.599990i
$121$	0.535426			0.0486751
$122$	3.71620	−	6.43664i	0.336449	−	0.582746i
$123$	−8.35705	−	9.79190i	−0.753530	−	0.882905i
$124$	10.3182	−	5.95724i	0.926605	−	0.534976i
$125$	−11.3923			−1.01896
$126$		0			0
$127$	6.16827			0.547345			0.273673	−	0.961823i	$-0.411761\pi$
$127$	6.16827			0.547345			0.273673	+	0.961823i	$0.411761\pi$
$128$	15.3856	−	8.88290i	1.35991	−	0.785145i
$129$	4.42543	−	12.4829i	0.389637	−	1.09906i
$130$	8.35705	−	14.4748i	0.732962	−	1.26953i
$131$	−8.26275			−0.721920			−0.360960	−	0.932581i	$-0.617551\pi$
$131$	−8.26275			−0.721920			−0.360960	+	0.932581i	$0.617551\pi$
$132$	16.8037	+	5.95724i	1.46258	+	0.518511i
$133$		0			0
$134$			1.50285i			0.129826i
$135$	−6.35868	+	3.88728i	−0.547268	+	0.334564i
$136$	−2.54287	+	1.46813i	−0.218049	+	0.125891i
$137$			10.3481i			0.884096i	0.896991	+	0.442048i	$0.145748\pi$
$137$			10.3481i			0.884096i	−0.896991	+	0.442048i	$0.854252\pi$
$138$	−10.2600	−	12.0215i	−0.873386	−	1.02334i
$139$	15.4589	−	8.92521i	1.31121	−	0.757026i	0.328912	−	0.944361i	$-0.393318\pi$
$139$	15.4589	−	8.92521i	1.31121	−	0.757026i	0.982296	+	0.187334i	$0.0599848\pi$
$140$		0			0
$141$	4.74596	+	5.56081i	0.399682	+	0.468304i
$142$	−4.35185	−	7.53762i	−0.365199	−	0.632543i
$143$	−8.28002	−	14.3414i	−0.692410	−	1.19929i
$144$	0.557180	+	0.451852i	0.0464317	+	0.0376543i
$145$	1.47529	+	0.851761i	0.122516	+	0.0707349i
$146$	8.32102	−	14.4124i	0.688653	−	1.19278i
$147$		0			0
$148$	−0.380438	−	0.658939i	−0.0312718	−	0.0541644i
$149$		−	17.5235i		−	1.43558i	−0.696259	−	0.717790i	$-0.745154\pi$
$149$		−	17.5235i		−	1.43558i	0.696259	−	0.717790i	$-0.254846\pi$
$150$	8.82568	−	7.53242i	0.720613	−	0.615019i
$151$	1.10069			0.0895726			0.0447863	−	0.998997i	$-0.485739\pi$
$151$	1.10069			0.0895726			0.0447863	+	0.998997i	$0.485739\pi$
$152$	−6.03911	+	10.4601i	−0.489837	+	0.848422i
$153$	−2.54287	−	2.06217i	−0.205579	−	0.166717i
$154$		0			0
$155$	4.65103	+	2.68527i	0.373580	+	0.215686i
$156$	5.13160	+	27.7427i	0.410857	+	2.22119i
$157$	8.45150	+	4.87948i	0.674503	+	0.389425i	0.797781	−	0.602947i	$-0.206007\pi$
$157$	8.45150	+	4.87948i	0.674503	+	0.389425i	−0.123277	+	0.992372i	$0.539340\pi$
$158$	−7.21574	−	4.16601i	−0.574053	−	0.331430i
$159$	9.24085	−	7.88676i	0.732847	−	0.625460i
$160$	7.36019	+	4.24941i	0.581874	+	0.335945i
$161$		0			0
$162$	6.35868	−	19.4757i	0.499585	−	1.53016i
$163$	3.61273	−	6.25742i	0.282970	−	0.490119i	−0.689145	−	0.724624i	$-0.742013\pi$
$163$	3.61273	−	6.25742i	0.282970	−	0.490119i	0.972115	+	0.234505i	$0.0753468\pi$
$164$	23.6495			1.84671
$165$	1.46169	+	7.90228i	0.113793	+	0.615191i
$166$			24.8238i			1.92670i
$167$	−8.65419	−	14.9895i	−0.669681	−	1.15992i	−0.977993	−	0.208637i	$-0.933097\pi$
$167$	−8.65419	−	14.9895i	−0.669681	−	1.15992i	0.308312	−	0.951285i	$-0.400236\pi$
$168$		0			0
$169$	6.60301	−	11.4367i	0.507924	−	0.879750i
$170$	−3.08577	−	1.78157i	−0.236668	−	0.136640i
$171$	−13.3000	−	2.11621i	−1.01708	−	0.161831i
$172$	12.1654	+	21.0711i	0.927602	+	1.60665i
$173$	0.978103	+	1.69412i	0.0743638	+	0.128802i	0.900809	−	0.434215i	$-0.142974\pi$
$173$	0.978103	+	1.69412i	0.0743638	+	0.128802i	−0.826446	+	0.563017i	$0.809641\pi$
$174$	−4.60483	+	0.851761i	−0.349091	+	0.0645718i
$175$		0			0
$176$	0.669905	−	0.386770i	0.0504960	−	0.0291539i
$177$	5.48113	−	15.4608i	0.411987	−	1.16210i
$178$			31.1671i			2.33607i
$179$	20.0933	−	11.6009i	1.50184	−	0.867090i	0.501846	−	0.864957i	$-0.332655\pi$
$179$	20.0933	−	11.6009i	1.50184	−	0.867090i	0.999998	−	0.00213247i	$-0.000678788\pi$
$180$	2.15143	−	13.5214i	0.160358	−	1.00782i
$181$		−	10.2744i		−	0.763689i	−0.924226	−	0.381845i	$-0.875289\pi$
$181$		−	10.2744i		−	0.763689i	0.924226	−	0.381845i	$-0.124711\pi$
$182$		0			0
$183$	−4.30150	+	3.67119i	−0.317976	+	0.271382i
$184$	10.7850			0.795077
$185$	0.171486	−	0.297022i	0.0126079	−	0.0218375i
$186$	−14.5172	+	2.68527i	−1.06446	+	0.196894i
$187$	−3.05733	+	1.76515i	−0.223574	+	0.129080i
$188$	−13.4305			−0.979520
$189$		0			0
$190$	−14.6569			−1.06332
$191$	−19.6758	+	11.3598i	−1.42369	+	0.821968i	−0.996612	−	0.0822464i	$-0.973791\pi$
$191$	−19.6758	+	11.3598i	−1.42369	+	0.821968i	−0.427079	+	0.904215i	$0.640457\pi$
$192$	−22.1588	+	4.09874i	−1.59917	+	0.295801i
$193$	−8.43598	+	14.6116i	−0.607235	+	1.05176i	0.384459	+	0.923142i	$0.374388\pi$
$193$	−8.43598	+	14.6116i	−0.607235	+	1.05176i	−0.991694	+	0.128620i	$0.958945\pi$
$194$	7.08942			0.508991
$195$	−9.67330	+	8.25583i	−0.692719	+	0.591212i
$196$		0			0
$197$		−	8.94426i		−	0.637252i	−0.947880	−	0.318626i	$-0.896779\pi$
$197$		−	8.94426i		−	0.637252i	0.947880	−	0.318626i	$-0.103221\pi$
$198$	−17.1586	−	13.9149i	−1.21941	−	0.988891i
$199$	−5.01020	+	2.89264i	−0.355164	+	0.205054i	−0.666957	−	0.745096i	$-0.732404\pi$
$199$	−5.01020	+	2.89264i	−0.355164	+	0.205054i	0.311794	+	0.950150i	$0.399070\pi$
$200$			7.91784i			0.559876i
$201$	0.382085	−	1.07776i	0.0269502	−	0.0760192i
$202$	−13.9762	+	8.06914i	−0.983359	+	0.567743i
$203$		0			0
$204$	5.91423	−	1.09396i	0.414079	−	0.0765927i
$205$	5.33009	+	9.23200i	0.372270	+	0.644791i
$206$	1.93894	+	3.35834i	0.135092	+	0.233987i
$207$	4.30150	+	11.2297i	0.298975	+	0.780515i
$208$	1.06012	+	0.612058i	0.0735058	+	0.0424386i
$209$	−7.26091	+	12.5763i	−0.502248	+	0.869918i
$210$		0			0
$211$	−12.9451	−	22.4216i	−0.891180	−	1.54357i	−0.838462	−	0.544960i	$-0.816545\pi$
$211$	−12.9451	−	22.4216i	−0.891180	−	1.54357i	−0.0527186	−	0.998609i	$-0.516789\pi$
$212$			22.3186i			1.53285i
$213$	1.20453	+	6.51198i	0.0825330	+	0.446193i
$214$	−11.2359			−0.768067
$215$	−5.48365	+	9.49796i	−0.373982	+	0.647756i
$216$	7.29211	+	11.9282i	0.496165	+	0.811610i
$217$		0			0
$218$	−16.0442	−	9.26312i	−1.08665	−	0.627378i
$219$	−9.63160	+	8.22024i	−0.650843	+	0.555473i
$220$	−12.7856	−	7.38175i	−0.862003	−	0.497678i
$221$	−4.83818	−	2.79332i	−0.325451	−	0.187899i
$222$	0.171486	+	0.927093i	0.0115094	+	0.0622224i
$223$	15.4827	+	8.93892i	1.03680	+	0.598594i	0.918924	−	0.394435i	$-0.129060\pi$
$223$	15.4827	+	8.93892i	1.03680	+	0.598594i	0.117871	+	0.993029i	$0.462393\pi$
$224$		0			0
$225$	−8.24433	+	3.15798i	−0.549622	+	0.210532i
$226$	−4.46457	+	7.73287i	−0.296979	+	0.514383i
$227$	10.9673			0.727925			0.363963	−	0.931414i	$-0.381424\pi$
$227$	10.9673			0.727925			0.363963	+	0.931414i	$0.381424\pi$
$228$	18.8187	−	16.0612i	1.24630	−	1.06368i
$229$		−	19.4393i		−	1.28459i	−0.766459	−	0.642293i	$-0.777983\pi$
$229$		−	19.4393i		−	1.28459i	0.766459	−	0.642293i	$-0.222017\pi$
$230$	6.54377	+	11.3341i	0.431483	+	0.747351i
$231$		0			0
$232$	1.59781	−	2.76748i	0.104901	−	0.181694i
$233$	−2.54639	−	1.47016i	−0.166819	−	0.0963131i	0.414266	−	0.910156i	$-0.364038\pi$
$233$	−2.54639	−	1.47016i	−0.166819	−	0.0963131i	−0.581085	+	0.813843i	$0.697372\pi$
$234$	5.49346	−	34.5254i	0.359118	−	2.25700i
$235$	−3.02696	−	5.24284i	−0.197457	−	0.342005i
$236$	15.0675	+	26.0976i	0.980809	+	1.69881i
$237$	4.11555	+	4.82216i	0.267334	+	0.313233i
$238$		0			0
$239$	−10.7255	+	6.19234i	−0.693772	+	0.400549i	−0.805023	−	0.593243i	$-0.797847\pi$
$239$	−10.7255	+	6.19234i	−0.693772	+	0.400549i	0.111252	+	0.993792i	$0.464514\pi$
$240$	−0.385640	−	0.451852i	−0.0248930	−	0.0291669i
$241$		−	13.5034i		−	0.869828i	−0.900472	−	0.434914i	$-0.856779\pi$
$241$		−	13.5034i		−	0.869828i	0.900472	−	0.434914i	$-0.143221\pi$
$242$	1.05555	−	0.609419i	0.0678530	−	0.0391750i
$243$	−9.51162	+	12.3503i	−0.610171	+	0.792270i
$244$		−	10.3890i		−	0.665089i
$245$		0			0
$246$	−27.6202	−	9.79190i	−1.76100	−	0.624308i
$247$	−22.9806			−1.46222
$248$	5.03727	−	8.72481i	0.319867	−	0.554026i
$249$	6.31122	−	17.8022i	0.399957	−	1.12817i
$250$	−22.4589	+	12.9666i	−1.42042	+	0.820082i
$251$	7.51441			0.474305			0.237153	−	0.971472i	$-0.423786\pi$
$251$	7.51441			0.474305			0.237153	+	0.971472i	$0.423786\pi$
$252$		0			0
$253$	12.9669			0.815222
$254$	12.1602	−	7.02069i	0.762998	−	0.440517i
$255$	1.75999	+	2.06217i	0.110215	+	0.129138i
$256$	7.21053	−	12.4890i	0.450658	−	0.780563i
$257$	−7.75576			−0.483791			−0.241895	−	0.970302i	$-0.577769\pi$
$257$	−7.75576			−0.483791			−0.241895	+	0.970302i	$0.577769\pi$
$258$	−5.48365	−	29.6459i	−0.341397	−	1.84568i
$259$		0			0
$260$		−	23.3630i		−	1.44891i
$261$	3.51887	+	0.559900i	0.217813	+	0.0346569i
$262$	−16.2893	+	9.40462i	−1.00635	+	0.581019i
$263$			13.9866i			0.862449i	0.902245	+	0.431224i	$0.141918\pi$
$263$			13.9866i			0.862449i	−0.902245	+	0.431224i	$0.858082\pi$
$264$	14.8238	−	2.74198i	0.912341	−	0.168757i
$265$	−8.71246	+	5.03014i	−0.535202	+	0.308999i
$266$		0			0
$267$	7.92395	−	22.3513i	0.484938	−	1.36788i
$268$	1.05034	+	1.81925i	0.0641599	+	0.111128i
$269$	12.9160	+	22.3712i	0.787505	+	1.36400i	0.927491	+	0.373846i	$0.121961\pi$
$269$	12.9160	+	22.3712i	0.787505	+	1.36400i	−0.139986	+	0.990154i	$0.544706\pi$
$270$	−8.11109	+	14.9009i	−0.493625	+	0.906837i
$271$	−14.4225	−	8.32686i	−0.876107	−	0.505821i	−0.00673411	−	0.999977i	$-0.502144\pi$
$271$	−14.4225	−	8.32686i	−0.876107	−	0.505821i	−0.869373	+	0.494157i	$0.835477\pi$
$272$	0.130480	−	0.225997i	0.00791148	−	0.0137031i
$273$		0			0
$274$	11.7781	+	20.4003i	0.711542	+	1.23243i
$275$			9.51973i			0.574061i
$276$	−20.8219	−	7.38175i	−1.25333	−	0.444329i
$277$	31.4088			1.88717			0.943585	−	0.331130i	$-0.107430\pi$
$277$	31.4088			1.88717			0.943585	+	0.331130i	$0.107430\pi$
$278$	20.3172	−	35.1905i	1.21855	−	2.11059i
$279$	11.0937	+	1.76515i	0.664160	+	0.105677i
$280$		0			0
$281$	8.10464	+	4.67922i	0.483483	+	0.279139i	0.721867	−	0.692032i	$-0.243284\pi$
$281$	8.10464	+	4.67922i	0.483483	+	0.279139i	−0.238384	+	0.971171i	$0.576618\pi$
$282$	15.6855	+	5.56081i	0.934059	+	0.331141i
$283$	13.6603	+	7.88676i	0.812018	+	0.468819i	0.847656	−	0.530546i	$-0.178013\pi$
$283$	13.6603	+	7.88676i	0.812018	+	0.468819i	−0.0356380	+	0.999365i	$0.511346\pi$
$284$	−10.5361	−	6.08303i	−0.625203	−	0.360961i
$285$	10.5111	+	3.72639i	0.622625	+	0.220732i
$286$	−32.6466	−	18.8485i	−1.93044	−	1.11454i
$287$		0			0
$288$	17.5555	+	2.79332i	1.03447	+	0.164598i
$289$	7.90451	−	13.6910i	0.464971	−	0.805354i
$290$	3.87788			0.227717
$291$	−5.08414	−	1.80242i	−0.298037	−	0.105660i
$292$		−	23.2623i		−	1.36132i
$293$	12.4287	+	21.5271i	0.726090	+	1.25762i	0.958524	+	0.285013i	$0.0919978\pi$
$293$	12.4287	+	21.5271i	0.726090	+	1.25762i	−0.232434	+	0.972612i	$0.574669\pi$
$294$		0			0
$295$	−6.79179	+	11.7637i	−0.395433	+	0.684911i
$296$	−0.557180	−	0.321688i	−0.0323854	−	0.0186977i
$297$	8.76740	+	14.3414i	0.508736	+	0.832173i
$298$	−19.9451	−	34.5460i	−1.15539	−	2.00120i
$299$	10.2600	+	17.7708i	0.593349	+	1.02771i
$300$	5.41936	−	15.2865i	0.312887	−	0.882568i
$301$		0			0
$302$	2.16991	−	1.25280i	0.124864	−	0.0720903i
$303$	12.0744	−	2.23342i	0.693657	−	0.128307i
$304$		−	1.07345i		−	0.0615666i
$305$	4.05555	−	2.34147i	0.232220	−	0.134072i
$306$	−7.36019	−	1.17110i	−0.420754	−	0.0669476i
$307$		−	18.8878i		−	1.07799i	−0.842310	−	0.538993i	$-0.818805\pi$
$307$		−	18.8878i		−	1.07799i	0.842310	−	0.538993i	$-0.181195\pi$
$308$		0			0
$309$	−0.536670	−	2.90137i	−0.0305301	−	0.165053i
$310$	12.2255			0.694359
$311$	3.97716	−	6.88864i	0.225524	−	0.390619i	−0.730953	−	0.682428i	$-0.760924\pi$
$311$	3.97716	−	6.88864i	0.225524	−	0.390619i	0.956476	+	0.291809i	$0.0942573\pi$
$312$	15.4870	+	18.1460i	0.876780	+	1.02732i
$313$	−9.64210	+	5.56687i	−0.545004	+	0.314658i	−0.747104	−	0.664707i	$-0.768556\pi$
$313$	−9.64210	+	5.56687i	−0.545004	+	0.314658i	0.202101	+	0.979365i	$0.435223\pi$
$314$	22.2152			1.25367
$315$		0			0
$316$	−11.6465			−0.655168
$317$	20.1380	−	11.6267i	1.13107	−	0.653021i	0.186863	−	0.982386i	$-0.440168\pi$
$317$	20.1380	−	11.6267i	1.13107	−	0.653021i	0.944203	+	0.329365i	$0.106835\pi$
$318$	9.24085	−	26.0659i	0.518201	−	1.46170i
$319$	1.92107	−	3.32738i	0.107559	−	0.186298i
$320$	18.6607			1.04316
$321$	8.05772	+	2.85661i	0.449738	+	0.159441i
$322$		0			0
$323$			4.89904i			0.272590i
$324$	−5.91423	−	28.0201i	−0.328568	−	1.55667i
$325$	−13.0465	+	7.53242i	−0.723691	+	0.417823i
$326$		−	16.4479i		−	0.910967i
$327$	9.15093	+	10.7221i	0.506048	+	0.592932i
$328$	17.3182	−	9.99866i	0.956237	−	0.552084i
$329$		0			0
$330$	11.8759	+	13.9149i	0.653748	+	0.765992i
$331$	9.57962	+	16.5924i	0.526544	+	0.912000i	0.999522	+	0.0309261i	$0.00984566\pi$
$331$	9.57962	+	16.5924i	0.526544	+	0.912000i	−0.472978	+	0.881074i	$0.656821\pi$
$332$	17.3494	+	30.0500i	0.952171	+	1.64921i
$333$	0.112725	−	0.708458i	0.00617730	−	0.0388233i
$334$	−34.1219	−	19.7003i	−1.86707	−	1.07795i
$335$	−0.473451	+	0.820041i	−0.0258674	+	0.0448036i
$336$		0			0
$337$	14.2781	+	24.7304i	0.777779	+	1.34715i	0.933219	+	0.359307i	$0.116987\pi$
$337$	14.2781	+	24.7304i	0.777779	+	1.34715i	−0.155441	+	0.987845i	$0.549680\pi$
$338$		−	30.0620i		−	1.63516i
$339$	5.16775	−	4.41050i	0.280674	−	0.239545i
$340$	−4.98057			−0.270109
$341$	6.05638	−	10.4900i	0.327971	−	0.568063i
$342$	−28.6285	+	10.9661i	−1.54805	+	0.592978i
$343$		0			0
$344$	17.8171	+	10.2867i	0.960634	+	0.554622i
$345$	−1.81122	−	9.79190i	−0.0975128	−	0.527178i
$346$	3.85648	+	2.22654i	0.207326	+	0.119700i
$347$	−2.56690	−	1.48200i	−0.137798	−	0.0795578i	0.429516	−	0.903059i	$-0.358684\pi$
$347$	−2.56690	−	1.48200i	−0.137798	−	0.0795578i	−0.567314	+	0.823501i	$0.692017\pi$
$348$	−4.97900	+	4.24941i	−0.266902	+	0.227792i
$349$	−23.3885	−	13.5034i	−1.25196	−	0.722818i	−0.280460	−	0.959866i	$-0.590487\pi$
$349$	−23.3885	−	13.5034i	−1.25196	−	0.722818i	−0.971498	+	0.237048i	$0.923820\pi$
$350$		0			0
$351$	−12.7174	+	23.3630i	−0.678803	+	1.24703i
$352$	9.58414	−	16.6002i	0.510836	−	0.884794i
$353$	−29.6476			−1.57798			−0.788990	−	0.614405i	$-0.789396\pi$
$353$	−29.6476			−1.57798			−0.788990	+	0.614405i	$0.789396\pi$
$354$	−6.79179	−	36.7181i	−0.360980	−	1.95154i
$355$		−	5.48395i		−	0.291058i
$356$	21.7827	+	37.7288i	1.15448	+	1.99962i
$357$		0			0
$358$	26.4081	−	45.7401i	1.39571	−	2.41744i
$359$	21.3268	+	12.3130i	1.12559	+	0.649858i	0.942821	−	0.333299i	$-0.108162\pi$
$359$	21.3268	+	12.3130i	1.12559	+	0.649858i	0.182766	+	0.983157i	$0.441495\pi$
$360$	−4.14118	−	10.8111i	−0.218259	−	0.569796i
$361$	0.576055	+	0.997756i	0.0303187	+	0.0525135i
$362$	−11.6943	−	20.2550i	−0.614636	−	1.06458i
$363$	−0.911917	+	0.168678i	−0.0478632	+	0.00885332i
$364$		0			0
$365$	9.08087	−	5.24284i	0.475314	−	0.274423i
$366$	−4.30150	+	12.1334i	−0.224843	+	0.634221i
$367$			5.60720i			0.292694i	0.989233	+	0.146347i	$0.0467515\pi$
$367$			5.60720i			0.292694i	−0.989233	+	0.146347i	$0.953248\pi$
$368$	−0.830095	+	0.479256i	−0.0432717	+	0.0249829i
$369$	17.3182	+	14.0444i	0.901549	+	0.731122i
$370$		−	0.780736i		−	0.0405885i
$371$		0			0
$372$	−15.6969	+	13.3967i	−0.813844	+	0.694588i
$373$	−3.73353			−0.193315			−0.0966574	−	0.995318i	$-0.530815\pi$
$373$	−3.73353			−0.193315			−0.0966574	+	0.995318i	$0.530815\pi$
$374$	−4.01816	+	6.95966i	−0.207774	+	0.359876i
$375$	19.4029	−	3.58898i	1.00196	−	0.185334i
$376$	−9.83498	+	5.67823i	−0.507200	+	0.292832i
$377$	6.08012			0.313142
$378$		0			0
$379$	−30.4419			−1.56369			−0.781847	−	0.623470i	$-0.785722\pi$
$379$	−30.4419			−1.56369			−0.781847	+	0.623470i	$0.785722\pi$
$380$	−17.7427	+	10.2437i	−0.910181	+	0.525493i
$381$	−10.5055	+	1.94323i	−0.538216	+	0.0995545i
$382$	−25.8594	+	44.7897i	−1.32308	+	2.29164i
$383$	16.9850			0.867894			0.433947	−	0.900938i	$-0.357121\pi$
$383$	16.9850			0.867894			0.433947	+	0.900938i	$0.357121\pi$
$384$	−23.4058	+	19.9760i	−1.19442	+	1.01940i
$385$		0			0
$386$			38.4071i			1.95487i
$387$	−3.60464	+	22.6546i	−0.183234	+	1.15160i
$388$	8.58198	−	4.95481i	0.435684	−	0.251542i
$389$		−	10.8924i		−	0.552267i	−0.961119	−	0.276134i	$-0.910947\pi$
$389$		−	10.8924i		−	0.552267i	0.961119	−	0.276134i	$-0.0890532\pi$
$390$	−9.67330	+	27.2857i	−0.489827	+	1.38167i
$391$	3.78840	−	2.18724i	0.191588	−	0.110613i
$392$		0			0
$393$	14.0728	−	2.60306i	0.709878	−	0.131307i
$394$	−10.1803	−	17.6328i	−0.512877	−	0.888328i
$395$	−2.62488	−	4.54643i	−0.132072	−	0.228756i
$396$	−30.4962	−	4.85235i	−1.53249	−	0.243840i
$397$	−19.3154	−	11.1518i	−0.969412	−	0.559690i	−0.0703551	−	0.997522i	$-0.522413\pi$
$397$	−19.3154	−	11.1518i	−0.969412	−	0.559690i	−0.899057	+	0.437832i	$0.855747\pi$
$398$	−6.58477	+	11.4052i	−0.330065	+	0.571689i
$399$		0			0
$400$	−0.351848	−	0.609419i	−0.0175924	−	0.0304710i
$401$			24.0818i			1.20259i	0.799029	+	0.601293i	$0.205347\pi$
$401$			24.0818i			1.20259i	−0.799029	+	0.601293i	$0.794653\pi$
$402$	−0.473451	−	2.55959i	−0.0236136	−	0.127661i
$403$	19.1683			0.954840
$404$	−11.2791	+	19.5359i	−0.561155	+	0.971949i
$405$	9.60522	−	8.62388i	0.477287	−	0.428524i
$406$		0			0
$407$	−0.669905	−	0.386770i	−0.0332060	−	0.0191715i
$408$	3.86840	−	3.30155i	0.191514	−	0.163451i
$409$	−22.8191	−	13.1746i	−1.12833	−	0.651443i	−0.184817	−	0.982773i	$-0.559169\pi$
$409$	−22.8191	−	13.1746i	−1.12833	−	0.651443i	−0.943515	+	0.331330i	$0.892503\pi$
$410$	21.0156	+	12.1334i	1.03789	+	0.599224i
$411$	−3.26001	−	17.6244i	−0.160805	−	0.869349i
$412$	4.69430	+	2.71026i	0.231272	+	0.133525i
$413$		0			0
$414$	21.2616	+	17.2423i	1.04495	+	0.847414i
$415$	−7.82038	+	13.5453i	−0.383887	+	0.664912i
$416$	30.3335			1.48722
$417$	−23.5172	+	20.0712i	−1.15164	+	0.982889i
$418$			33.0573i			1.61689i
$419$	−16.1761	−	28.0178i	−0.790252	−	1.36876i	−0.925811	−	0.377988i	$-0.876616\pi$
$419$	−16.1761	−	28.0178i	−0.790252	−	1.36876i	0.135558	−	0.990769i	$-0.456717\pi$
$420$		0			0
$421$	−5.54746	+	9.60849i	−0.270367	+	0.468289i	−0.968956	−	0.247234i	$-0.920478\pi$
$421$	−5.54746	+	9.60849i	−0.270367	+	0.468289i	0.698589	+	0.715523i	$0.253812\pi$
$422$	−51.0404	−	29.4682i	−2.48461	−	1.43449i
$423$	−9.83498	−	7.97579i	−0.478193	−	0.387796i
$424$	9.43598	+	16.3436i	0.458252	+	0.793716i
$425$	1.60577	+	2.78128i	0.0778914	+	0.134912i
$426$	9.78651	+	11.4668i	0.474158	+	0.555568i
$427$		0			0
$428$	−13.6014	+	7.85276i	−0.657447	+	0.379577i
$429$	18.6202	+	21.8172i	0.898994	+	1.05334i
$430$			24.9658i			1.20396i
$431$	−14.1202	+	8.15233i	−0.680149	+	0.392684i	−0.799911	−	0.600119i	$-0.795120\pi$
$431$	−14.1202	+	8.15233i	−0.680149	+	0.392684i	0.119762	+	0.992803i	$0.461787\pi$
$432$	−1.09132	−	0.594044i	−0.0525060	−	0.0285810i
$433$			12.5359i			0.602438i	0.953555	+	0.301219i	$0.0973936\pi$
$433$			12.5359i			0.602438i	−0.953555	+	0.301219i	$0.902606\pi$
$434$		0			0
$435$	−2.78100	−	0.985915i	−0.133339	−	0.0472710i
$436$	−25.8960			−1.24020
$437$	8.99716	−	15.5835i	0.430393	−	0.745462i
$438$	−9.63160	+	27.1681i	−0.460216	+	1.29814i
$439$	16.1276	−	9.31127i	0.769728	−	0.444403i	−0.0630496	−	0.998010i	$-0.520083\pi$
$439$	16.1276	−	9.31127i	0.769728	−	0.444403i	0.832778	+	0.553608i	$0.186749\pi$
$440$	−12.4836			−0.595132
$441$		0			0
$442$	−12.7174			−0.604904
$443$	−4.11436	+	2.37543i	−0.195479	+	0.112860i	−0.594545	−	0.804062i	$-0.702668\pi$
$443$	−4.11436	+	2.37543i	−0.195479	+	0.112860i	0.399066	+	0.916922i	$0.369334\pi$
$444$	0.855536	+	1.00243i	0.0406020	+	0.0475730i
$445$	−9.81875	+	17.0066i	−0.465453	+	0.806189i
$446$	40.6969			1.92705
$447$	5.52053	+	29.8453i	0.261112	+	1.41163i
$448$		0			0
$449$		−	16.2393i		−	0.766379i	−0.923670	−	0.383189i	$-0.874826\pi$
$449$		−	16.2393i		−	0.766379i	0.923670	−	0.383189i	$-0.125174\pi$
$450$	−12.6586	+	15.6093i	−0.596730	+	0.735830i
$451$	20.8219	−	12.0215i	0.980465	−	0.566072i
$452$			12.4812i			0.587066i
$453$	−1.87465	+	0.346756i	−0.0880785	+	0.0162920i
$454$	21.6210	−	12.4829i	1.01473	−	0.585852i
$455$		0			0
$456$	6.99028	−	19.7177i	0.327350	−	0.923365i
$457$	2.87360	+	4.97722i	0.134421	+	0.232825i	0.925376	−	0.379050i	$-0.123749\pi$
$457$	2.87360	+	4.97722i	0.134421	+	0.232825i	−0.790955	+	0.611874i	$0.790416\pi$
$458$	−22.1257	−	38.3228i	−1.03387	−	1.79071i
$459$	4.98057	+	2.71111i	0.232473	+	0.126544i
$460$	15.8429	+	9.14690i	0.738679	+	0.426476i
$461$	18.1346	−	31.4101i	0.844613	−	1.46291i	−0.0413440	−	0.999145i	$-0.513164\pi$
$461$	18.1346	−	31.4101i	0.844613	−	1.46291i	0.885957	−	0.463768i	$-0.153503\pi$
$462$		0			0
$463$	14.6202	+	25.3230i	0.679461	+	1.17686i	0.975144	+	0.221574i	$0.0711195\pi$
$463$	14.6202	+	25.3230i	0.679461	+	1.17686i	−0.295683	+	0.955286i	$0.595547\pi$
$464$			0.284010i			0.0131848i
$465$	−8.76740	−	3.10821i	−0.406579	−	0.144140i
$466$	−6.69329			−0.310061
$467$	−1.32107	+	2.28817i	−0.0611320	+	0.105884i	−0.894972	−	0.446123i	$-0.852804\pi$
$467$	−1.32107	+	2.28817i	−0.0611320	+	0.105884i	0.833840	+	0.552007i	$0.186138\pi$
$468$	−17.4799	−	45.6336i	−0.808007	−	2.10941i
$469$		0			0
$470$	−11.9347	−	6.89053i	−0.550508	−	0.317836i
$471$	−15.9315	−	5.64800i	−0.734083	−	0.260246i
$472$	22.0674	+	12.7406i	1.01574	+	0.586435i
$473$	21.4218	+	12.3679i	0.984973	+	0.568675i
$474$	13.6020	+	4.82216i	0.624760	+	0.221489i
$475$	11.4408	+	6.60532i	0.524938	+	0.303073i
$476$		0			0
$477$	−13.2540	+	16.3436i	−0.606861	+	0.748322i
$478$	−14.0962	+	24.4153i	−0.644744	+	1.11673i
$479$	31.0819			1.42017			0.710083	−	0.704118i	$-0.248657\pi$
$479$	31.0819			1.42017			0.710083	+	0.704118i	$0.248657\pi$
$480$	−13.8743	−	4.91870i	−0.633272	−	0.224507i
$481$		−	1.22412i		−	0.0558149i
$482$	−15.3694	−	26.6207i	−0.700059	−	1.21254i
$483$		0			0
$484$	0.851848	−	1.47544i	0.0387204	−	0.0670657i
$485$	3.86840	+	2.23342i	0.175655	+	0.101414i
$486$	−4.69430	+	35.1735i	−0.212938	+	1.59550i
$487$	−17.4360	−	30.2000i	−0.790100	−	1.36849i	−0.925905	−	0.377757i	$-0.876695\pi$
$487$	−17.4360	−	30.2000i	−0.790100	−	1.36849i	0.135805	−	0.990736i	$-0.456638\pi$
$488$	−4.39234	−	7.60775i	−0.198832	−	0.344387i
$489$	−4.18174	+	11.7955i	−0.189105	+	0.533412i
$490$		0			0
$491$	−22.6758	+	13.0919i	−1.02334	+	0.590828i	−0.915071	−	0.403293i	$-0.867866\pi$
$491$	−22.6758	+	13.0919i	−1.02334	+	0.590828i	−0.108273	+	0.994121i	$0.534532\pi$
$492$	−40.2788	+	7.45043i	−1.81591	+	0.335891i
$493$		−	1.29617i		−	0.0583766i
$494$	−45.3041	+	26.1563i	−2.03833	+	1.17683i
$495$	−4.97900	−	12.9984i	−0.223789	−	0.584232i
$496$			0.895374i			0.0402035i
$497$		0			0
$498$	−7.82038	−	42.2789i	−0.350440	−	1.89456i
$499$	12.4782			0.558603			0.279302	−	0.960203i	$-0.409897\pi$
$499$	12.4782			0.558603			0.279302	+	0.960203i	$0.409897\pi$
$500$	−18.1248	+	31.3931i	−0.810566	+	1.40394i
$501$	19.4617	+	22.8031i	0.869484	+	1.01877i
$502$	14.8140	−	8.55285i	0.661180	−	0.381733i
$503$	−37.8479			−1.68756			−0.843778	−	0.536693i	$-0.819673\pi$
$503$	−37.8479			−1.68756			−0.843778	+	0.536693i	$0.819673\pi$
$504$		0			0
$505$	−10.1683			−0.452482
$506$	25.5631	−	14.7588i	1.13642	−	0.656111i
$507$	−7.64300	+	21.5588i	−0.339437	+	0.957460i
$508$	9.81354	−	16.9976i	0.435406	−	0.754145i
$509$	−35.3847			−1.56840			−0.784200	−	0.620508i	$-0.786926\pi$
$509$	−35.3847			−1.56840			−0.784200	+	0.620508i	$0.786926\pi$
$510$	5.81682	+	2.06217i	0.257573	+	0.0913144i
$511$		0			0
$512$			2.70367i			0.119486i
$513$	23.3187	−	0.585737i	1.02955	−	0.0258609i
$514$	−15.2898	+	8.82756i	−0.674403	+	0.389367i
$515$			2.44334i			0.107666i
$516$	−27.3577	−	32.0549i	−1.20436	−	1.41114i
$517$	−11.8247	+	6.82701i	−0.520051	+	0.300252i
$518$		0			0
$519$	−2.19957	−	2.57723i	−0.0965506	−	0.113128i
$520$	−9.87756	−	17.1084i	−0.433160	−	0.750255i
$521$	1.15939	+	2.00813i	0.0507940	+	0.0879777i	0.890304	−	0.455366i	$-0.150491\pi$
$521$	1.15939	+	2.00813i	0.0507940	+	0.0879777i	−0.839511	+	0.543343i	$0.817158\pi$
$522$	7.57442	−	2.90137i	0.331523	−	0.126990i
$523$	17.4799	+	10.0920i	0.764341	+	0.441293i	0.830852	−	0.556493i	$-0.187853\pi$
$523$	17.4799	+	10.0920i	0.764341	+	0.441293i	−0.0665110	+	0.997786i	$0.521187\pi$
$524$	−13.1458	+	22.7692i	−0.574277	+	0.994677i
$525$		0			0
$526$	15.9194	+	27.5733i	0.694120	+	1.20225i
$527$		−	4.08632i		−	0.178003i
$528$	−1.01911	+	0.869775i	−0.0443510	+	0.0378521i
$529$	6.93242			0.301409
$530$	−11.4506	+	19.8329i	−0.497380	+	0.861488i
$531$	−4.46454	+	28.0589i	−0.193745	+	1.21765i
$532$		0			0
$533$	32.9503	+	19.0239i	1.42724	+	0.824016i
$534$	−9.81875	−	53.0825i	−0.424899	−	2.29711i
$535$	−6.13093	−	3.53970i	−0.265063	−	0.153034i
$536$	1.53831	+	0.888141i	0.0664447	+	0.0383618i
$537$	−30.5674	+	26.0882i	−1.31908	+	1.12579i
$538$	50.9256	+	29.4019i	2.19556	+	1.26761i
$539$		0			0
$540$	0.595485	+	23.7068i	0.0256256	+	1.02018i
$541$	11.3856	−	19.7205i	0.489507	−	0.847851i	−0.510420	−	0.859925i	$-0.670510\pi$
$541$	11.3856	−	19.7205i	0.489507	−	0.847851i	0.999927	+	0.0120743i	$0.00384346\pi$
$542$	−37.9103			−1.62839
$543$	3.23680	+	17.4989i	0.138904	+	0.750951i
$544$		−	6.46655i		−	0.277251i
$545$	−5.83643	−	10.1090i	−0.250005	−	0.433022i
$546$		0			0
$547$	14.7918	−	25.6201i	0.632451	−	1.09544i	−0.354598	−	0.935019i	$-0.615382\pi$
$547$	14.7918	−	25.6201i	0.632451	−	1.09544i	0.987049	−	0.160419i	$-0.0512845\pi$
$548$	28.5156	+	16.4635i	1.21813	+	0.703286i
$549$	6.16959	−	7.60775i	0.263312	−	0.324691i
$550$	10.8353	+	18.7673i	0.462019	+	0.800240i
$551$	−2.66589	−	4.61745i	−0.113571	−	0.196710i
$552$	−18.3685	+	3.39765i	−0.781815	+	0.144613i
$553$		0			0
$554$	61.9196	−	35.7493i	2.63071	−	1.51884i
$555$	−0.198495	+	0.559900i	−0.00842564	+	0.0237664i
$556$		−	56.7990i		−	2.40881i
$557$	4.08250	−	2.35703i	0.172981	−	0.0998707i	−0.411010	−	0.911631i	$-0.634824\pi$
$557$	4.08250	−	2.35703i	0.172981	−	0.0998707i	0.583991	+	0.811760i	$0.301490\pi$
$558$	23.8792	−	9.14690i	1.01089	−	0.387219i
$559$			39.1439i			1.65561i
$560$		0			0
$561$	4.65103	−	3.96950i	0.196367	−	0.167592i
$562$	21.3034			0.898631
$563$	13.6742	−	23.6844i	0.576299	−	0.998179i	−0.419601	−	0.907709i	$-0.637830\pi$
$563$	13.6742	−	23.6844i	0.576299	−	0.998179i	0.995899	−	0.0904697i	$-0.0288368\pi$
$564$	22.8743	−	4.23109i	0.963181	−	0.178161i
$565$	−4.87226	+	2.81300i	−0.204977	+	0.118344i
$566$	35.9066			1.50927
$567$		0			0
$568$	−10.2873			−0.431645
$569$	−20.4018	+	11.7790i	−0.855288	+	0.493801i	−0.862432	−	0.506174i	$-0.831059\pi$
$569$	−20.4018	+	11.7790i	−0.855288	+	0.493801i	0.00714355	+	0.999974i	$0.497726\pi$
$570$	24.9631	−	4.61745i	1.04559	−	0.193404i
$571$	−9.59385	+	16.6170i	−0.401490	+	0.695401i	−0.993906	−	0.110231i	$-0.964841\pi$
$571$	−9.59385	+	16.6170i	−0.401490	+	0.695401i	0.592416	+	0.805632i	$0.298174\pi$
$572$	−52.6931			−2.20321
$573$	29.9323	−	25.5462i	1.25044	−	1.06721i
$574$		0			0
$575$		−	11.7961i		−	0.491932i
$576$	36.4487	−	13.9616i	1.51870	−	0.581734i
$577$	−1.93481	+	1.11706i	−0.0805472	+	0.0465039i	−0.539733	−	0.841836i	$-0.681475\pi$
$577$	−1.93481	+	1.11706i	−0.0805472	+	0.0465039i	0.459185	+	0.888340i	$0.348141\pi$
$578$		−	35.9875i		−	1.49688i
$579$	9.76466	−	27.5434i	0.405806	−	1.14467i
$580$	4.69430	−	2.71026i	0.194920	−	0.112537i
$581$		0			0
$582$	−12.0744	+	2.23342i	−0.500501	+	0.0925783i
$583$	11.3450	+	19.6501i	0.469862	+	0.813826i
$584$	−9.83498	−	17.0347i	−0.406974	−	0.704900i
$585$	13.8743	−	17.1084i	0.573631	−	0.707347i
$586$	49.0040	+	28.2925i	2.02434	+	1.16875i
$587$	12.9883	−	22.4963i	0.536083	−	0.928522i	−0.463028	−	0.886344i	$-0.653237\pi$
$587$	12.9883	−	22.4963i	0.536083	−	0.928522i	0.999110	−	0.0421784i	$-0.0134298\pi$
$588$		0			0
$589$	−8.40451	−	14.5570i	−0.346302	−	0.599813i
$590$			30.9215i			1.27302i
$591$	2.81776	+	15.2335i	0.115907	+	0.626623i
$592$	0.0571799			0.00235008
$593$	2.85877	−	4.95153i	0.117396	−	0.203335i	−0.801339	−	0.598210i	$-0.795879\pi$
$593$	2.85877	−	4.95153i	0.117396	−	0.203335i	0.918735	+	0.394875i	$0.129212\pi$
$594$	33.6075	+	18.2938i	1.37893	+	0.750604i
$595$		0			0
$596$	−48.2885	−	27.8794i	−1.97797	−	1.14198i
$597$	7.62188	−	6.50502i	0.311943	−	0.266233i
$598$	40.4532	+	23.3557i	1.65425	+	0.955084i
$599$	−21.8662	−	12.6245i	−0.893429	−	0.515822i	−0.0183665	−	0.999831i	$-0.505847\pi$
$599$	−21.8662	−	12.6245i	−0.893429	−	0.515822i	−0.875063	+	0.484010i	$0.839180\pi$
$600$	−2.49440	−	13.4853i	−0.101834	−	0.550537i
$601$	−40.2546	−	23.2410i	−1.64202	−	0.948021i	−0.980114	−	0.198435i	$-0.936414\pi$
$601$	−40.2546	−	23.2410i	−1.64202	−	0.948021i	−0.661907	−	0.749586i	$-0.730252\pi$
$602$		0			0
$603$	−0.311220	+	1.95596i	−0.0126739	+	0.0796530i
$604$	1.75116	−	3.03310i	0.0712538	−	0.123415i
$605$	0.767955			0.0312218
$606$	21.2616	−	18.1460i	0.863692	−	0.737132i
$607$			7.03681i			0.285615i	0.989750	+	0.142808i	$0.0456130\pi$
$607$			7.03681i			0.285615i	−0.989750	+	0.142808i	$0.954387\pi$
$608$	−13.3000	−	23.0363i	−0.539387	−	0.934246i
$609$		0			0
$610$	5.33009	−	9.23200i	0.215809	−	0.373793i
$611$	−18.7125	−	10.8036i	−0.757025	−	0.437069i
$612$	−9.72824	+	3.72639i	−0.393241	+	0.150630i
$613$	−3.27128	−	5.66602i	−0.132126	−	0.228849i	0.792370	−	0.610041i	$-0.208847\pi$
$613$	−3.27128	−	5.66602i	−0.132126	−	0.228849i	−0.924496	+	0.381192i	$0.875514\pi$
$614$	−21.4980	−	37.2357i	−0.867590	−	1.50271i
$615$	−11.9864	−	14.0444i	−0.483339	−	0.566324i
$616$		0			0
$617$	−30.0043	+	17.3230i	−1.20793	+	0.697396i	−0.962306	−	0.271970i	$-0.912325\pi$
$617$	−30.0043	+	17.3230i	−1.20793	+	0.697396i	−0.245620	+	0.969366i	$0.578992\pi$
$618$	−4.36032	−	5.10896i	−0.175398	−	0.205512i
$619$			16.9825i			0.682583i	0.939958	+	0.341291i	$0.110864\pi$
$619$			16.9825i			0.682583i	−0.939958	+	0.341291i	$0.889136\pi$
$620$	14.7993	−	8.54439i	0.594355	−	0.343151i
$621$	−10.8639	−	17.7708i	−0.435953	−	0.713117i
$622$		−	18.1071i		−	0.726029i
$623$		0			0
$624$	−1.99837	−	0.708458i	−0.0799986	−	0.0283610i
$625$	−1.62571			−0.0650284
$626$	−12.6724	+	21.9492i	−0.506489	+	0.877265i
$627$	8.40451	−	23.7068i	0.335644	−	0.946760i
$628$	26.8922	−	15.5262i	1.07312	−	0.619564i
$629$	−0.260959			−0.0104051
$630$		0			0
$631$	26.2438			1.04475			0.522374	−	0.852716i	$-0.325047\pi$
$631$	26.2438			1.04475			0.522374	+	0.852716i	$0.325047\pi$
$632$	−8.52859	+	4.92398i	−0.339249	+	0.195866i
$633$	29.1113	+	34.1095i	1.15707	+	1.35573i
$634$	26.4669	−	45.8420i	1.05113	−	1.82062i
$635$	8.84707			0.351085
$636$	−7.03115	−	38.0121i	−0.278803	−	1.50728i
$637$		0			0
$638$		−	8.74619i		−	0.346265i
$639$	−4.10301	−	10.7115i	−0.162313	−	0.423739i
$640$	22.0674	−	12.7406i	0.872292	−	0.503618i
$641$		−	19.0631i		−	0.752949i	−0.926427	−	0.376474i	$-0.877136\pi$
$641$		−	19.0631i		−	0.752949i	0.926427	−	0.376474i	$-0.122864\pi$
$642$	19.1365	−	3.53970i	0.755256	−	0.139701i
$643$	−15.3447	+	8.85928i	−0.605136	+	0.349376i	−0.771060	−	0.636763i	$-0.780273\pi$
$643$	−15.3447	+	8.85928i	−0.605136	+	0.349376i	0.165923	+	0.986139i	$0.446940\pi$
$644$		0			0
$645$	6.34733	−	17.9041i	0.249926	−	0.704973i
$646$	5.57605	+	9.65801i	0.219387	+	0.379989i
$647$	−10.8951	−	18.8709i	−0.428330	−	0.741890i	0.568395	−	0.822756i	$-0.307565\pi$
$647$	−10.8951	−	18.8709i	−0.428330	−	0.741890i	−0.996725	+	0.0808661i	$0.974231\pi$
$648$	−16.1774	−	18.0183i	−0.635509	−	0.707826i
$649$	26.5320	+	15.3182i	1.04147	+	0.601294i
$650$	−17.1467	+	29.6990i	−0.672549	+	1.16489i
$651$		0			0
$652$	−11.4955	−	19.9108i	−0.450198	−	0.779766i
$653$		−	15.1095i		−	0.591281i	−0.955299	−	0.295640i	$-0.904467\pi$
$653$		−	15.1095i		−	0.591281i	0.955299	−	0.295640i	$-0.0955330\pi$
$654$	30.2440	+	10.7221i	1.18264	+	0.419266i
$655$	−11.8512			−0.463063
$656$	−0.888629	+	1.53915i	−0.0346951	+	0.0600938i
$657$	13.8145	−	17.0347i	0.538954	−	0.664586i
$658$		0			0
$659$	−27.1850	−	15.6952i	−1.05898	−	0.611400i	−0.133827	−	0.991005i	$-0.542727\pi$
$659$	−27.1850	−	15.6952i	−1.05898	−	0.611400i	−0.925149	+	0.379605i	$0.876060\pi$
$660$	24.1014	+	8.54439i	0.938145	+	0.332590i
$661$	−37.8554	−	21.8558i	−1.47240	−	0.850093i	−0.472885	−	0.881124i	$-0.656787\pi$
$661$	−37.8554	−	21.8558i	−1.47240	−	0.850093i	−0.999518	+	0.0310314i	$0.990121\pi$
$662$	37.7707	+	21.8069i	1.46800	+	0.847551i
$663$	9.12018	+	3.23327i	0.354198	+	0.125570i
$664$	25.4095	+	14.6702i	0.986078	+	0.569312i
$665$		0			0
$666$	−0.584135	−	1.52496i	−0.0226348	−	0.0590912i
$667$	−2.38044	+	4.12304i	−0.0921709	+	0.159645i
$668$	−55.0743			−2.13089
$669$	−29.1855	−	10.3468i	−1.12838	−	0.400031i
$670$			2.15552i			0.0832749i
$671$	−5.28096	−	9.14690i	−0.203869	−	0.353112i
$672$		0			0
$673$	−4.60589	+	7.97763i	−0.177544	+	0.307515i	−0.941039	−	0.338299i	$-0.890149\pi$
$673$	−4.60589	+	7.97763i	−0.177544	+	0.307515i	0.763495	+	0.645814i	$0.223482\pi$
$674$	56.2960	+	32.5025i	2.16844	+	1.25195i
$675$	13.0465	−	7.97579i	0.502161	−	0.306988i
$676$	−21.0104	−	36.3911i	−0.808092	−	1.39966i
$677$	11.4194	+	19.7789i	0.438882	+	0.760165i	0.997604	−	0.0691899i	$-0.0220414\pi$
$677$	11.4194	+	19.7789i	0.438882	+	0.760165i	−0.558722	+	0.829355i	$0.688708\pi$
$678$	5.16775	−	14.5768i	0.198466	−	0.559819i
$679$		0			0
$680$	−3.64721	+	2.10571i	−0.139864	+	0.0807505i
$681$	−18.6791	+	3.45509i	−0.715783	+	0.132399i
$682$		−	27.5733i		−	1.05584i
$683$	29.6030	−	17.0913i	1.13273	−	0.653981i	0.188108	−	0.982148i	$-0.439764\pi$
$683$	29.6030	−	17.0913i	1.13273	−	0.653981i	0.944619	+	0.328168i	$0.106431\pi$
$684$	−26.9915	+	33.2833i	−1.03205	+	1.27262i
$685$			14.8421i			0.567088i
$686$		0			0
$687$	6.12408	+	33.1082i	0.233648	+	1.26316i
$688$	−1.82846			−0.0697094
$689$	−17.9533	+	31.0961i	−0.683967	+	1.18467i
$690$	−14.7157	−	17.2423i	−0.560218	−	0.656404i
$691$	−0.224082	+	0.129374i	−0.00852446	+	0.00492160i	−0.504256	−	0.863554i	$-0.668233\pi$
$691$	−0.224082	+	0.129374i	−0.00852446	+	0.00492160i	0.495732	+	0.868476i	$0.334900\pi$
$692$	6.22453			0.236621
$693$		0			0
$694$	−6.74720			−0.256120
$695$	22.1725	−	12.8013i	0.841052	−	0.485582i
$696$	−1.84947	+	5.21684i	−0.0701038	+	0.197744i
$697$	4.05555	−	7.02441i	0.153615	−	0.266069i
$698$	−61.4778			−2.32697
$699$	4.80005	+	1.70171i	0.181555	+	0.0643645i
$700$		0			0
$701$			5.16189i			0.194962i	0.995237	+	0.0974810i	$0.0310785\pi$
$701$			5.16189i			0.194962i	−0.995237	+	0.0974810i	$0.968921\pi$
$702$	1.52051	+	60.5329i	0.0573879	+	2.28467i
$703$	−0.929636	+	0.536725i	−0.0350619	+	0.0202430i
$704$		−	42.0873i		−	1.58623i
$705$	6.80707	+	7.97579i	0.256369	+	0.300386i
$706$	−58.4475	+	33.7447i	−2.19970	+	1.27000i
$707$		0			0
$708$	−33.8840	−	39.7016i	−1.27344	−	1.49208i
$709$	−11.7472	−	20.3468i	−0.441175	−	0.764138i	0.556602	−	0.830780i	$-0.312105\pi$
$709$	−11.7472	−	20.3468i	−0.441175	−	0.764138i	−0.997777	+	0.0666412i	$0.978772\pi$
$710$	−6.24180	−	10.8111i	−0.234251	−	0.405734i
$711$	−8.52859	−	6.91636i	−0.319847	−	0.259384i
$712$	31.9024	+	18.4189i	1.19559	+	0.690276i
$713$	−7.50460	+	12.9984i	−0.281050	+	0.486792i
$714$		0			0
$715$	−11.8759	−	20.5697i	−0.444134	−	0.769263i
$716$		−	73.8266i		−	2.75903i
$717$	16.3163	−	13.9254i	0.609345	−	0.520055i
$718$	56.0586			2.09209
$719$	−5.07828	+	8.79584i	−0.189388	+	0.328029i	−0.945046	−	0.326937i	$-0.893984\pi$
$719$	−5.07828	+	8.79584i	−0.189388	+	0.328029i	0.755658	+	0.654966i	$0.227317\pi$
$720$	0.799156	+	0.648085i	0.0297828	+	0.0241527i
$721$		0			0
$722$	2.27128	+	1.31132i	0.0845283	+	0.0488024i
$723$	4.25404	+	22.9984i	0.158209	+	0.855319i
$724$	−28.3126	−	16.3463i	−1.05223	−	0.607504i
$725$	−3.02696	−	1.74761i	−0.112418	−	0.0649047i
$726$	−1.60577	+	1.37047i	−0.0595958	+	0.0508630i
$727$	5.74874	+	3.31904i	0.213209	+	0.123096i	0.602802	−	0.797891i	$-0.294051\pi$
$727$	5.74874	+	3.31904i	0.213209	+	0.123096i	−0.389593	+	0.920987i	$0.627384\pi$
$728$		0			0
$729$	12.3090	−	24.0310i	0.455890	−	0.890036i
$730$	11.9347	−	20.6716i	0.441725	−	0.765089i
$731$	8.34476			0.308642
$732$	3.27292	+	17.6942i	0.120970	+	0.653995i
$733$		−	6.00594i		−	0.221834i	−0.993830	−	0.110917i	$-0.964621\pi$
$733$		−	6.00594i		−	0.221834i	0.993830	−	0.110917i	$-0.0353788\pi$
$734$	6.38209	+	11.0541i	0.235567	+	0.408014i
$735$		0			0
$736$	−11.8759	+	20.5697i	−0.437752	+	0.758209i
$737$	1.84953	+	1.06782i	0.0681281	+	0.0393338i
$738$	50.1265	+	7.97579i	1.84518	+	0.293593i
$739$	7.81930	+	13.5434i	0.287638	+	0.498203i	0.973245	−	0.229768i	$-0.0737968\pi$
$739$	7.81930	+	13.5434i	0.287638	+	0.498203i	−0.685608	+	0.727971i	$0.740463\pi$
$740$	−0.545658	−	0.945107i	−0.0200588	−	0.0347428i
$741$	39.1396	−	7.23970i	1.43783	−	0.265957i
$742$		0			0
$743$	27.3807	−	15.8083i	1.00450	−	0.579949i	0.0949246	−	0.995484i	$-0.469739\pi$
$743$	27.3807	−	15.8083i	1.00450	−	0.579949i	0.909577	+	0.415535i	$0.136406\pi$
$744$	−5.83065	+	16.4467i	−0.213762	+	0.602964i
$745$		−	25.1337i		−	0.920829i
$746$	−7.36032	+	4.24948i	−0.269480	+	0.155585i
$747$	−5.14068	+	32.3083i	−0.188088	+	1.18210i
$748$			11.2332i			0.410727i
$749$		0			0
$750$	34.1661	−	29.1596i	1.24757	−	1.06476i
$751$	−14.2736			−0.520851			−0.260426	−	0.965494i	$-0.583863\pi$
$751$	−14.2736			−0.520851			−0.260426	+	0.965494i	$0.583863\pi$
$752$	0.504652	−	0.874082i	0.0184028	−	0.0318745i
$753$	−12.7982	+	2.36731i	−0.466394	+	0.0862695i
$754$	11.9864	−	6.92036i	0.436519	−	0.252025i
$755$	1.57870			0.0574548
$756$		0			0
$757$	−10.8227			−0.393358			−0.196679	−	0.980468i	$-0.563016\pi$
$757$	−10.8227			−0.393358			−0.196679	+	0.980468i	$0.563016\pi$
$758$	−60.0134	+	34.6488i	−2.17979	+	1.25850i
$759$	−22.0847	+	4.08504i	−0.801624	+	0.148277i
$760$	−8.66182	+	15.0027i	−0.314197	+	0.544206i
$761$	5.86195			0.212496			0.106248	−	0.994340i	$-0.466116\pi$
$761$	5.86195			0.212496			0.106248	+	0.994340i	$0.466116\pi$
$762$	−18.4990	+	15.7882i	−0.670147	+	0.571948i
$763$		0			0
$764$			72.2926i			2.61546i
$765$	−3.64721	−	2.95774i	−0.131865	−	0.106937i
$766$	33.4844	−	19.3323i	1.20984	−	0.698503i
$767$			48.4818i			1.75058i
$768$	−8.34620	+	23.5424i	−0.301168	+	0.849511i
$769$	−27.5683	+	15.9166i	−0.994140	+	0.573967i	−0.906509	−	0.422186i	$-0.861263\pi$
$769$	−27.5683	+	15.9166i	−0.994140	+	0.573967i	−0.0876307	+	0.996153i	$0.527930\pi$
$770$		0			0
$771$	13.2093	−	2.44334i	0.475721	−	0.0879947i
$772$	26.8428	+	46.4931i	0.966094	+	1.67332i
$773$	9.51908	+	16.4875i	0.342378	+	0.593015i	0.984874	−	0.173274i	$-0.0554345\pi$
$773$	9.51908	+	16.4875i	0.342378	+	0.593015i	−0.642496	+	0.766289i	$0.722101\pi$
$774$	18.6791	+	48.7642i	0.671405	+	1.75279i
$775$	−9.54282	−	5.50955i	−0.342788	−	0.197909i
$776$	4.18965	−	7.25668i	0.150400	−	0.260500i
$777$		0			0
$778$	−12.3977	−	21.4734i	−0.444478	−	0.769859i
$779$		−	33.3648i		−	1.19542i
$780$	7.36019	+	39.7910i	0.263537	+	1.42475i
$781$	−12.3685			−0.442581
$782$	4.97900	−	8.62388i	0.178049	−	0.308389i
$783$	−6.16959	+	0.154972i	−0.220483	+	0.00553826i
$784$		0			0
$785$	12.1219	+	6.99857i	0.432649	+	0.249790i
$786$	24.7804	−	21.1493i	0.883889	−	0.754369i
$787$	−16.4123	−	9.47564i	−0.585035	−	0.337770i	0.178097	−	0.984013i	$-0.443006\pi$
$787$	−16.4123	−	9.47564i	−0.585035	−	0.337770i	−0.763132	+	0.646243i	$0.776339\pi$
$788$	−24.6472	−	14.2301i	−0.878020	−	0.506925i
$789$	−4.40627	−	23.8214i	−0.156867	−	0.848063i
$790$	−10.3494	−	5.97525i	−0.368216	−	0.212590i
$791$		0			0
$792$	−24.3834	+	9.34004i	−0.866428	+	0.331884i
$793$	8.35705	−	14.4748i	0.296768	−	0.514016i
$794$	−50.7714			−1.80181
$795$	13.2540	−	11.3119i	0.470072	−	0.401191i
$796$			18.4084i			0.652470i
$797$	26.7207	+	46.2816i	0.946497	+	1.63938i	0.752727	+	0.658333i	$0.228738\pi$
$797$	26.7207	+	46.2816i	0.946497	+	1.63938i	0.193770	+	0.981047i	$0.437929\pi$
$798$		0			0
$799$	−2.30314	+	3.98916i	−0.0814792	+	0.141126i
$800$	−15.1014	−	8.71878i	−0.533914	−	0.308256i
$801$	−6.45429	+	40.5641i	−0.228051	+	1.43326i
$802$	27.4097	+	47.4750i	0.967871	+	1.67640i
$803$	−11.8247	−	20.4810i	−0.417286	−	0.722760i
$804$	−2.36203	−	2.76757i	−0.0833024	−	0.0976048i
$805$		0			0
$806$	37.7885	−	21.8172i	1.33104	−	0.768479i
$807$	−29.0458	−	34.0328i	−1.02246	−	1.19801i
$808$			19.0745i			0.671040i
$809$	−2.23517	+	1.29047i	−0.0785842	+	0.0453706i	−0.538777	−	0.842448i	$-0.681114\pi$
$809$	−2.23517	+	1.29047i	−0.0785842	+	0.0453706i	0.460193	+	0.887819i	$0.347780\pi$
$810$	9.12018	−	27.9338i	0.320450	−	0.981494i
$811$		−	6.06938i		−	0.213125i	−0.994306	−	0.106562i	$-0.966016\pi$
$811$		−	6.06938i		−	0.213125i	0.994306	−	0.106562i	$-0.0339844\pi$
$812$		0			0
$813$	27.1871	+	9.63835i	0.953495	+	0.338032i
$814$	−1.76088			−0.0617187
$815$	5.18169	−	8.97494i	0.181507	−	0.314379i
$816$	−0.151030	+	0.426015i	−0.00528712	+	0.0149135i
$817$	29.7272	−	17.1630i	1.04002	−	0.600458i
$818$	−59.9811			−2.09719
$819$		0			0
$820$	33.9201			1.18454
$821$	−8.03938	+	4.64154i	−0.280576	+	0.161991i	−0.633684	−	0.773592i	$-0.718458\pi$
$821$	−8.03938	+	4.64154i	−0.280576	+	0.161991i	0.353108	+	0.935583i	$0.385125\pi$
$822$	−26.4868	−	31.0344i	−0.923834	−	1.08245i
$823$	−9.03448	+	15.6482i	−0.314922	+	0.545461i	−0.979421	−	0.201828i	$-0.935312\pi$
$823$	−9.03448	+	15.6482i	−0.314922	+	0.545461i	0.664499	+	0.747289i	$0.268645\pi$
$824$	4.58343			0.159671
$825$	−2.99905	−	16.2136i	−0.104414	−	0.564486i
$826$		0			0
$827$		−	48.5440i		−	1.68804i	−0.536310	−	0.844021i	$-0.680182\pi$
$827$		−	48.5440i		−	1.68804i	0.536310	−	0.844021i	$-0.319818\pi$
$828$	37.7885	+	6.01266i	1.31324	+	0.208954i
$829$	4.71804	−	2.72396i	0.163864	−	0.0946071i	−0.415825	−	0.909445i	$-0.636507\pi$
$829$	4.71804	−	2.72396i	0.163864	−	0.0946071i	0.579689	+	0.814837i	$0.303174\pi$
$830$			35.6044i			1.23585i
$831$	−53.4941	+	9.89488i	−1.85569	+	0.343250i
$832$	57.6796	−	33.3013i	1.99968	−	1.15452i
$833$		0			0
$834$	−23.5172	+	66.3357i	−0.814335	+	2.29702i
$835$	−12.4126	−	21.4992i	−0.429556	−	0.744012i
$836$	23.1038	+	40.0170i	0.799062	+	1.38402i
$837$	−19.4503	+	0.488568i	−0.672302	+	0.0168874i
$838$	−63.7793	−	36.8230i	−2.20322	−	1.27203i
$839$	24.2673	−	42.0322i	0.837801	−	1.45111i	−0.0539281	−	0.998545i	$-0.517174\pi$
$839$	24.2673	−	42.0322i	0.837801	−	1.45111i	0.891729	−	0.452569i	$-0.149492\pi$
$840$		0			0
$841$	−13.7947	−	23.8931i	−0.475678	−	0.823899i
$842$			25.2564i			0.870392i
$843$	−15.2776	−	5.41620i	−0.526189	−	0.186544i
$844$	−82.3814			−2.83569
$845$	9.47061	−	16.4036i	0.325799	−	0.564300i
$846$	−28.4668	−	4.52945i	−0.978708	−	0.155726i
$847$		0			0
$848$	−1.45254	−	0.838622i	−0.0498803	−	0.0287984i
$849$	−25.7502	−	9.12893i	−0.883745	−	0.313304i
$850$	6.33127	+	3.65536i	0.217161	+	0.125378i
$851$	0.830095	+	0.479256i	0.0284553	+	0.0164287i
$852$	19.8611	+	7.04112i	0.680429	+	0.241225i
$853$	10.7703	+	6.21823i	0.368768	+	0.212908i	0.672920	−	0.739715i	$-0.265040\pi$
$853$	10.7703	+	6.21823i	0.368768	+	0.212908i	−0.304152	+	0.952623i	$0.598373\pi$
$854$		0			0
$855$	−19.0761	−	3.03526i	−0.652387	−	0.103804i
$856$	−6.64007	+	11.5009i	−0.226953	+	0.393094i
$857$	10.5815			0.361459			0.180729	−	0.983533i	$-0.442154\pi$
$857$	10.5815			0.361459			0.180729	+	0.983533i	$0.442154\pi$
$858$	61.5404	+	21.8172i	2.10095	+	0.744827i
$859$			32.4993i			1.10886i	0.832230	+	0.554431i	$0.187064\pi$
$859$			32.4993i			1.10886i	−0.832230	+	0.554431i	$0.812936\pi$
$860$	17.4487	+	30.2220i	0.594995	+	1.03056i
$861$		0			0
$862$	−18.5579	+	32.1432i	−0.632084	+	1.09480i
$863$	21.8414	+	12.6102i	0.743491	+	0.429255i	0.823337	−	0.567552i	$-0.192110\pi$
$863$	21.8414	+	12.6102i	0.743491	+	0.429255i	−0.0798460	+	0.996807i	$0.525443\pi$
$864$	−30.7799	+	0.773151i	−1.04715	+	0.0263031i
$865$	1.40288	+	2.42986i	0.0476994	+	0.0826177i
$866$	14.2683	+	24.7135i	0.484857	+	0.839797i
$867$	−9.14949	+	25.8082i	−0.310733	+	0.876492i
$868$		0			0
$869$	−10.2540	+	5.92017i	−0.347844	+	0.200828i
$870$	−6.60464	+	1.22167i	−0.223918	+	0.0414185i
$871$			3.37963i			0.114514i
$872$	−18.9633	+	10.9485i	−0.642179	+	0.370762i
$873$	9.22692	+	1.46813i	0.312284	+	0.0496885i
$874$		−	40.9621i		−	1.38556i
$875$		0			0
$876$	7.32846	+	39.6194i	0.247606	+	1.33862i
$877$	−14.9579			−0.505091			−0.252546	−	0.967585i	$-0.581268\pi$
$877$	−14.9579			−0.505091			−0.252546	+	0.967585i	$0.581268\pi$
$878$	21.1961	−	36.7127i	0.715333	−	1.23899i
$879$	−27.9498	−	32.7486i	−0.942723	−	1.10458i
$880$	0.960836	−	0.554739i	0.0323898	−	0.0187003i
$881$	36.4482			1.22797			0.613985	−	0.789318i	$-0.289566\pi$
$881$	36.4482			1.22797			0.613985	+	0.789318i	$0.289566\pi$
$882$		0			0
$883$	15.9831			0.537873			0.268936	−	0.963158i	$-0.413328\pi$
$883$	15.9831			0.537873			0.268936	+	0.963158i	$0.413328\pi$
$884$	−15.3948	+	8.88819i	−0.517783	+	0.298942i
$885$	7.86151	−	22.1752i	0.264262	−	0.745410i
$886$	−5.40739	+	9.36588i	−0.181665	+	0.314653i
$887$	49.0416			1.64666			0.823329	−	0.567565i	$-0.192114\pi$
$887$	49.0416			1.64666			0.823329	+	0.567565i	$0.192114\pi$
$888$	1.05031	+	0.372354i	0.0352461	+	0.0124954i
$889$		0			0
$890$			44.7026i			1.49843i
$891$	−19.4503	−	21.6637i	−0.651611	−	0.725760i
$892$	49.2649	−	28.4431i	1.64951	−	0.952346i
$893$			18.9479i			0.634066i
$894$	44.8530	+	52.5539i	1.50011	+	1.75767i
$895$	28.8196	−	16.6390i	0.963332	−	0.556180i
$896$		0			0
$897$	−23.0728	−	27.0342i	−0.770378	−	0.902646i
$898$	−18.4834	−	32.0143i	−0.616801	−	1.06833i
$899$	2.22364	+	3.85145i	0.0741625	+	0.128453i
$900$	−4.41423	+	27.7427i	−0.147141	+	0.924756i
$901$	6.62911	+	3.82732i	0.220848	+	0.127506i
$902$	27.3657	−	47.3987i	0.911177	−	1.57820i
$903$		0			0
$904$	5.27687	+	9.13981i	0.175506	+	0.303986i
$905$		−	14.7364i		−	0.489855i
$906$	−3.30102	+	2.81731i	−0.109669	+	0.0935988i
$907$	−4.85829			−0.161317			−0.0806585	−	0.996742i	$-0.525702\pi$
$907$	−4.85829			−0.161317			−0.0806585	+	0.996742i	$0.525702\pi$
$908$	17.4487	−	30.2220i	0.579054	−	1.00295i
$909$	−19.8611	+	7.60775i	−0.658750	+	0.252333i
$910$		0			0
$911$	14.4945	+	8.36843i	0.480226	+	0.277258i	0.720510	−	0.693444i	$-0.243908\pi$
$911$	14.4945	+	8.36843i	0.480226	+	0.277258i	−0.240285	+	0.970702i	$0.577241\pi$
$912$	0.338175	+	1.82826i	0.0111981	+	0.0605397i
$913$	30.5501	+	17.6381i	1.01106	+	0.583737i
$914$	11.3301	+	6.54143i	0.374766	+	0.216371i
$915$	−6.16959	+	5.26554i	−0.203960	+	0.174073i
$916$	−53.5678	−	30.9274i	−1.76993	−	1.02187i
$917$		0			0
$918$	12.9045	−	0.324145i	0.425912	−	0.0106984i
$919$	−15.3200	+	26.5350i	−0.505360	+	0.875309i	0.494621	+	0.869109i	$0.335307\pi$
$919$	−15.3200	+	26.5350i	−0.505360	+	0.875309i	−0.999981	+	0.00620006i	$0.998026\pi$
$920$	15.4687			0.509989
$921$	5.95034	+	32.1690i	0.196071	+	1.06000i
$922$		−	82.5628i		−	2.71906i
$923$	−9.78651	−	16.9507i	−0.322127	−	0.557940i
$924$		0			0
$925$	−0.351848	+	0.609419i	−0.0115687	+	0.0200376i
$926$	57.6450	+	33.2814i	1.89433	+	1.09369i
$927$	1.82807	+	4.77243i	0.0600417	+	0.156747i
$928$	3.51887	+	6.09487i	0.115513	+	0.200074i
$929$	−14.8723	−	25.7595i	−0.487943	−	0.845142i	0.511961	−	0.859009i	$-0.328919\pi$
$929$	−14.8723	−	25.7595i	−0.487943	−	0.845142i	−0.999904	+	0.0138670i	$0.995586\pi$
$930$	−20.8219	+	3.85145i	−0.682777	+	0.126294i
$931$		0			0
$932$	−8.10245	+	4.67795i	−0.265405	+	0.153231i
$933$	−4.60357	+	12.9854i	−0.150714	+	0.425123i
$934$			6.01456i			0.196802i
$935$	−4.38508	+	2.53173i	−0.143408	+	0.0827964i
$936$	−32.0935	−	26.0266i	−1.04901	−	0.850706i
$937$		−	4.03712i		−	0.131887i	−0.997823	−	0.0659434i	$-0.978994\pi$
$937$		−	4.03712i		−	0.131887i	0.997823	−	0.0659434i	$-0.0210057\pi$
$938$		0			0
$939$	14.6683	−	12.5189i	0.478681	−	0.408538i
$940$	−19.2632			−0.628296
$941$	−7.20264	+	12.4753i	−0.234799	+	0.406684i	−0.959214	−	0.282680i	$-0.908777\pi$
$941$	−7.20264	+	12.4753i	−0.234799	+	0.406684i	0.724415	+	0.689364i	$0.242110\pi$
$942$	−37.8360	+	6.99857i	−1.23276	+	0.228026i
$943$	−25.8009	+	14.8962i	−0.840193	+	0.485085i
$944$	−2.26464			−0.0737079
$945$		0			0
$946$	56.3081			1.83073
$947$	−27.0334	+	15.6077i	−0.878467	+	0.507183i	−0.870153	−	0.492782i	$-0.835980\pi$
$947$	−27.0334	+	15.6077i	−0.878467	+	0.507183i	−0.00831468	+	0.999965i	$0.502647\pi$
$948$	19.8359	−	3.66907i	0.644239	−	0.119166i
$949$	18.7125	−	32.4109i	0.607432	−	1.05210i
$950$	30.0726			0.975682
$951$	−30.6355	+	26.1463i	−0.993423	+	0.847853i
$952$		0			0
$953$			8.55869i			0.277243i	0.990345	+	0.138622i	$0.0442672\pi$
$953$			8.55869i			0.277243i	−0.990345	+	0.138622i	$0.955733\pi$
$954$	−7.52696	+	47.3056i	−0.243694	+	1.53158i
$955$	−28.2207	+	16.2933i	−0.913202	+	0.527237i
$956$			39.4074i			1.27453i
$957$	−2.22364	+	6.27227i	−0.0718800	+	0.202754i
$958$	61.2751	−	35.3772i	1.97971	−	1.14298i
$959$		0			0
$960$	−31.7821	+	5.87877i	−1.02576	+	0.189737i
$961$	−8.48973	−	14.7046i	−0.273862	−	0.474343i
$962$	−1.39328	−	2.41323i	−0.0449212	−	0.0778058i
$963$	−14.6235	−	2.32680i	−0.471236	−	0.0749800i
$964$	−37.2104	−	21.4835i	−1.19847	−	0.691936i
$965$	−12.0996	+	20.9572i	−0.389501	+	0.674635i
$966$		0			0
$967$	16.0280	+	27.7614i	0.515427	+	0.892745i	0.999840	+	0.0179059i	$0.00569994\pi$
$967$	16.0280	+	27.7614i	0.515427	+	0.892745i	−0.484413	+	0.874840i	$0.660967\pi$
$968$		−	1.44060i		−	0.0463026i
$969$	−1.54337	−	8.34384i	−0.0495802	−	0.268043i
$970$	10.1683			0.326483
$971$	16.6183	−	28.7838i	0.533307	−	0.923715i	−0.465936	−	0.884818i	$-0.654282\pi$
$971$	16.6183	−	28.7838i	0.533307	−	0.923715i	0.999243	−	0.0388964i	$-0.0123842\pi$
$972$	18.9002	+	45.8596i	0.606225	+	1.47095i
$973$		0			0
$974$	−68.7469	−	39.6911i	−2.20279	−	1.27178i
$975$	19.8473	−	16.9390i	0.635623	−	0.542483i
$976$	0.676137	+	0.390368i	0.0216426	+	0.0124954i
$977$	−45.1558	−	26.0707i	−1.44466	−	0.834076i	−0.446507	−	0.894780i	$-0.647332\pi$
$977$	−45.1558	−	26.0707i	−1.44466	−	0.834076i	−0.998156	+	0.0607042i	$0.980665\pi$
$978$	5.18169	+	28.0134i	0.165692	+	0.895771i
$979$	38.3567	+	22.1453i	1.22589	+	0.707765i
$980$		0			0
$981$	−18.9633	−	15.3785i	−0.605453	−	0.490999i
$982$	−29.8022	+	51.6189i	−0.951026	+	1.64723i
$983$	−24.2385			−0.773087			−0.386544	−	0.922271i	$-0.626331\pi$
$983$	−24.2385			−0.773087			−0.386544	+	0.922271i	$0.626331\pi$
$984$	−26.3457	+	22.4852i	−0.839870	+	0.716801i
$985$		−	12.8286i		−	0.408755i
$986$	−1.47529	−	2.55528i	−0.0469829	−	0.0813768i
$987$		0			0
$988$	−36.5614	+	63.3263i	−1.16317	+	2.01468i
$989$	−26.5442	−	15.3253i	−0.844056	−	0.487316i
$990$	−24.6103	−	19.9580i	−0.782167	−	0.634307i
$991$	12.0991	+	20.9562i	0.384339	+	0.665695i	0.991677	−	0.128749i	$-0.0410960\pi$
$991$	12.0991	+	20.9562i	0.384339	+	0.665695i	−0.607338	+	0.794443i	$0.707763\pi$
$992$	11.0937	+	19.2148i	0.352224	+	0.610070i
$993$	−21.5428	−	25.2416i	−0.683641	−	0.801017i
$994$		0			0
$995$	−7.18607	+	4.14888i	−0.227814	+	0.131528i
$996$	−39.0156	−	45.7143i	−1.23626	−	1.44851i
$997$			10.1835i			0.322516i	0.986912	+	0.161258i	$0.0515551\pi$
$997$			10.1835i			0.322516i	−0.986912	+	0.161258i	$0.948445\pi$
$998$	24.5997	−	14.2027i	0.778691	−	0.449578i
$999$	0.0312007	+	1.24213i	0.000987146	+	0.0392992i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.s.c.362.5		12
3.2	odd	2		1323.2.s.c.656.1		12
7.2	even	3		63.2.o.a.20.2	yes	12
7.3	odd	6		441.2.i.c.227.5		12
7.4	even	3		441.2.i.c.227.6		12
7.5	odd	6		63.2.o.a.20.1	✓	12
7.6	odd	2	inner	441.2.s.c.362.6		12
9.4	even	3		1323.2.i.c.1097.5		12
9.5	odd	6		441.2.i.c.68.1		12
21.2	odd	6		189.2.o.a.62.6		12
21.5	even	6		189.2.o.a.62.5		12
21.11	odd	6		1323.2.i.c.521.2		12
21.17	even	6		1323.2.i.c.521.1		12
21.20	even	2		1323.2.s.c.656.2		12
28.19	even	6		1008.2.cc.a.209.5		12
28.23	odd	6		1008.2.cc.a.209.2		12
63.2	odd	6		567.2.c.c.566.1		12
63.4	even	3		1323.2.s.c.962.2		12
63.5	even	6		63.2.o.a.41.2	yes	12
63.13	odd	6		1323.2.i.c.1097.6		12
63.16	even	3		567.2.c.c.566.12		12
63.23	odd	6		63.2.o.a.41.1	yes	12
63.31	odd	6		1323.2.s.c.962.1		12
63.32	odd	6	inner	441.2.s.c.374.6		12
63.40	odd	6		189.2.o.a.125.6		12
63.41	even	6		441.2.i.c.68.2		12
63.47	even	6		567.2.c.c.566.2		12
63.58	even	3		189.2.o.a.125.5		12
63.59	even	6	inner	441.2.s.c.374.5		12
63.61	odd	6		567.2.c.c.566.11		12
84.23	even	6		3024.2.cc.a.2897.4		12
84.47	odd	6		3024.2.cc.a.2897.3		12
252.23	even	6		1008.2.cc.a.545.5		12
252.103	even	6		3024.2.cc.a.881.4		12
252.131	odd	6		1008.2.cc.a.545.2		12
252.247	odd	6		3024.2.cc.a.881.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.o.a.20.1	✓	12	7.5	odd	6
63.2.o.a.20.2	yes	12	7.2	even	3
63.2.o.a.41.1	yes	12	63.23	odd	6
63.2.o.a.41.2	yes	12	63.5	even	6
189.2.o.a.62.5		12	21.5	even	6
189.2.o.a.62.6		12	21.2	odd	6
189.2.o.a.125.5		12	63.58	even	3
189.2.o.a.125.6		12	63.40	odd	6
441.2.i.c.68.1		12	9.5	odd	6
441.2.i.c.68.2		12	63.41	even	6
441.2.i.c.227.5		12	7.3	odd	6
441.2.i.c.227.6		12	7.4	even	3
441.2.s.c.362.5		12	1.1	even	1	trivial
441.2.s.c.362.6		12	7.6	odd	2	inner
441.2.s.c.374.5		12	63.59	even	6	inner
441.2.s.c.374.6		12	63.32	odd	6	inner
567.2.c.c.566.1		12	63.2	odd	6
567.2.c.c.566.2		12	63.47	even	6
567.2.c.c.566.11		12	63.61	odd	6
567.2.c.c.566.12		12	63.16	even	3
1008.2.cc.a.209.2		12	28.23	odd	6
1008.2.cc.a.209.5		12	28.19	even	6
1008.2.cc.a.545.2		12	252.131	odd	6
1008.2.cc.a.545.5		12	252.23	even	6
1323.2.i.c.521.1		12	21.17	even	6
1323.2.i.c.521.2		12	21.11	odd	6
1323.2.i.c.1097.5		12	9.4	even	3
1323.2.i.c.1097.6		12	63.13	odd	6
1323.2.s.c.656.1		12	3.2	odd	2
1323.2.s.c.656.2		12	21.20	even	2
1323.2.s.c.962.1		12	63.31	odd	6
1323.2.s.c.962.2		12	63.4	even	3
3024.2.cc.a.881.3		12	252.247	odd	6
3024.2.cc.a.881.4		12	252.103	even	6
3024.2.cc.a.2897.3		12	84.47	odd	6
3024.2.cc.a.2897.4		12	84.23	even	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.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.97141 - 1.13819i) q^{2} +(-1.70316 + 0.315036i) q^{3} +(1.59097 - 2.75564i) q^{4} +1.43429 q^{5} +(-2.99905 + 2.55959i) q^{6} -2.69056i q^{8} +(2.80150 - 1.07311i) q^{9} +O(q^{10})\)	\(q+(1.97141 - 1.13819i) q^{2} +(-1.70316 + 0.315036i) q^{3} +(1.59097 - 2.75564i) q^{4} +1.43429 q^{5} +(-2.99905 + 2.55959i) q^{6} -2.69056i q^{8} +(2.80150 - 1.07311i) q^{9} +(2.82757 - 1.63250i) q^{10} -3.23490i q^{11} +(-1.84155 + 5.19451i) q^{12} +(4.43334 - 2.55959i) q^{13} +(-2.44282 + 0.451852i) q^{15} +(0.119562 + 0.207087i) q^{16} +(-0.545658 - 0.945107i) q^{17} +(4.30150 - 5.30420i) q^{18} +(-3.88768 - 2.24456i) q^{19} +(2.28191 - 3.95238i) q^{20} +(-3.68194 - 6.37731i) q^{22} +4.00844i q^{23} +(0.847623 + 4.58246i) q^{24} -2.94282 q^{25} +(5.82662 - 10.0920i) q^{26} +(-4.43334 + 2.71026i) q^{27} +(1.02859 + 0.593857i) q^{29} +(-4.30150 + 3.67119i) q^{30} +(3.24275 + 1.87220i) q^{31} +(5.13160 + 2.96273i) q^{32} +(1.01911 + 5.50955i) q^{33} +(-2.15143 - 1.24213i) q^{34} +(1.50000 - 9.42724i) q^{36} +(0.119562 - 0.207087i) q^{37} -10.2190 q^{38} +(-6.74433 + 5.75605i) q^{39} -3.85904i q^{40} +(3.71620 + 6.43664i) q^{41} +(-3.82326 + 6.62208i) q^{43} +(-8.91423 - 5.14663i) q^{44} +(4.01816 - 1.53915i) q^{45} +(4.56238 + 7.90228i) q^{46} +(-2.11042 - 3.65536i) q^{47} +(-0.268872 - 0.315036i) q^{48} +(-5.80150 + 3.34950i) q^{50} +(1.22708 + 1.43777i) q^{51} -16.2889i q^{52} +(-6.07442 + 3.50707i) q^{53} +(-5.65514 + 10.3890i) q^{54} -4.63977i q^{55} +(7.32846 + 2.59808i) q^{57} +2.70370 q^{58} +(-4.73531 + 8.20179i) q^{59} +(-2.64132 + 7.45043i) q^{60} +(2.82757 - 1.63250i) q^{61} +8.52371 q^{62} +13.0104 q^{64} +(6.35868 - 3.67119i) q^{65} +(8.28002 + 9.70164i) q^{66} +(-0.330095 + 0.571741i) q^{67} -3.47250 q^{68} +(-1.26280 - 6.82701i) q^{69} -3.82347i q^{71} +(-2.88727 - 7.53762i) q^{72} +(6.33127 - 3.65536i) q^{73} -0.544337i q^{74} +(5.01209 - 0.927093i) q^{75} +(-12.3704 + 7.14205i) q^{76} +(-6.74433 + 19.0239i) q^{78} +(-1.83009 - 3.16982i) q^{79} +(0.171486 + 0.297022i) q^{80} +(6.69686 - 6.01266i) q^{81} +(14.6523 + 8.45951i) q^{82} +(-5.45245 + 9.44392i) q^{83} +(-0.782630 - 1.35556i) q^{85} +17.4064i q^{86} +(-1.93894 - 0.687390i) q^{87} -8.70370 q^{88} +(-6.84573 + 11.8572i) q^{89} +(6.16959 - 7.60775i) q^{90} +(11.0458 + 6.37731i) q^{92} +(-6.11273 - 2.16708i) q^{93} +(-8.32102 - 4.80415i) q^{94} +(-5.57605 - 3.21934i) q^{95} +(-9.67330 - 3.42937i) q^{96} +(2.69709 + 1.55716i) q^{97} +(-3.47141 - 9.06259i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} + 2 q^{4}+O(q^{10}) \) 12 * q + 6 * q^2 + 2 * q^4	\( 12 q + 6 q^{2} + 2 q^{4} + 6 q^{15} + 2 q^{16} + 18 q^{18} - 10 q^{22} + 30 q^{29} - 18 q^{30} + 12 q^{32} + 18 q^{36} + 2 q^{37} - 12 q^{39} - 10 q^{43} - 54 q^{44} + 20 q^{46} - 36 q^{50} + 66 q^{51} + 12 q^{53} - 18 q^{57} - 4 q^{58} - 30 q^{60} + 16 q^{64} + 78 q^{65} + 12 q^{67} - 54 q^{72} - 12 q^{78} - 6 q^{79} + 24 q^{81} - 6 q^{85} - 68 q^{88} + 30 q^{92} - 54 q^{93} - 72 q^{95} - 24 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 + 2 * q^4 + 6 * q^15 + 2 * q^16 + 18 * q^18 - 10 * q^22 + 30 * q^29 - 18 * q^30 + 12 * q^32 + 18 * q^36 + 2 * q^37 - 12 * q^39 - 10 * q^43 - 54 * q^44 + 20 * q^46 - 36 * q^50 + 66 * q^51 + 12 * q^53 - 18 * q^57 - 4 * q^58 - 30 * q^60 + 16 * q^64 + 78 * q^65 + 12 * q^67 - 54 * q^72 - 12 * q^78 - 6 * q^79 + 24 * q^81 - 6 * q^85 - 68 * q^88 + 30 * q^92 - 54 * q^93 - 72 * q^95 - 24 * q^99

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