LMFDB - Embedded newform 231.2.l.a.32.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(32,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("231.32");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.l (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.12745506816.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 8x^{6} + 55x^{4} - 72x^{2} + 81 $ x^8 - 8x^6 + 55x^4 - 72*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			32.1
Root			$-2.23256 - 1.28897i$ of defining polynomial
Character	$\chi$	$=$	231.32
Dual form			231.2.l.a.65.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.724745 - 1.57313i) q^{3} +(1.00000 - 1.73205i) q^{4} +(1.22474 - 0.707107i) q^{5} +(-1.32288 - 2.29129i) q^{7} +(-1.94949 + 2.28024i) q^{9} +O(q^{10})$	\(q+(-0.724745 - 1.57313i) q^{3} +(1.00000 - 1.73205i) q^{4} +(1.22474 - 0.707107i) q^{5} +(-1.32288 - 2.29129i) q^{7} +(-1.94949 + 2.28024i) q^{9} +(-2.23256 + 2.45269i) q^{11} +(-3.44949 - 0.317837i) q^{12} +4.58258i q^{13} +(-2.00000 - 1.41421i) q^{15} +(-2.00000 - 3.46410i) q^{16} +(3.24037 - 5.61249i) q^{17} +(3.96863 - 2.29129i) q^{19} -2.82843i q^{20} +(-2.64575 + 3.74166i) q^{21} +(4.89898 - 2.82843i) q^{23} +(-1.50000 + 2.59808i) q^{25} +(5.00000 + 1.41421i) q^{27} -5.29150 q^{28} -6.48074 q^{29} +(0.500000 - 0.866025i) q^{31} +(5.47644 + 1.73453i) q^{33} +(-3.24037 - 1.87083i) q^{35} +(2.00000 + 5.65685i) q^{36} +(3.50000 + 6.06218i) q^{37} +(7.20900 - 3.32120i) q^{39} +6.48074 q^{41} -4.58258i q^{43} +(2.01563 + 6.31959i) q^{44} +(-0.775255 + 4.17121i) q^{45} +(4.89898 - 2.82843i) q^{47} +(-4.00000 + 5.65685i) q^{48} +(-3.50000 + 6.06218i) q^{49} +(-11.1776 - 1.02991i) q^{51} +(7.93725 + 4.58258i) q^{52} +(6.12372 + 3.53553i) q^{53} +(-1.00000 + 4.58258i) q^{55} +(-6.48074 - 4.58258i) q^{57} +(2.44949 + 1.41421i) q^{59} +(-4.44949 + 2.04989i) q^{60} +(7.80362 + 1.45037i) q^{63} -8.00000 q^{64} +(3.24037 + 5.61249i) q^{65} +(0.500000 - 0.866025i) q^{67} +(-6.48074 - 11.2250i) q^{68} +(-8.00000 - 5.65685i) q^{69} +1.41421i q^{71} +(3.96863 + 2.29129i) q^{73} +(5.17423 + 0.476756i) q^{75} -9.16515i q^{76} +(8.57321 + 1.87083i) q^{77} +(-11.9059 + 6.87386i) q^{79} +(-4.89898 - 2.82843i) q^{80} +(-1.39898 - 8.89060i) q^{81} -6.48074 q^{83} +(3.83499 + 8.32423i) q^{84} -9.16515i q^{85} +(4.69688 + 10.1951i) q^{87} +(-13.4722 + 7.77817i) q^{89} +(10.5000 - 6.06218i) q^{91} -11.3137i q^{92} +(-1.72474 - 0.158919i) q^{93} +(3.24037 - 5.61249i) q^{95} +8.00000 q^{97} +(-1.24037 - 9.87226i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} + 8 q^{4} + 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^3 + 8 * q^4 + 4 * q^9	$ 8 q + 4 q^{3} + 8 q^{4} + 4 q^{9} - 8 q^{12} - 16 q^{15} - 16 q^{16} - 12 q^{25} + 40 q^{27} + 4 q^{31} + 4 q^{33} + 16 q^{36} + 28 q^{37} - 16 q^{45} - 32 q^{48} - 28 q^{49} - 8 q^{55} - 16 q^{60} - 64 q^{64} + 4 q^{67} - 64 q^{69} + 12 q^{75} + 28 q^{81} + 84 q^{91} - 4 q^{93} + 64 q^{97} + 16 q^{99}+O(q^{100}) $ 8 * q + 4 * q^3 + 8 * q^4 + 4 * q^9 - 8 * q^12 - 16 * q^15 - 16 * q^16 - 12 * q^25 + 40 * q^27 + 4 * q^31 + 4 * q^33 + 16 * q^36 + 28 * q^37 - 16 * q^45 - 32 * q^48 - 28 * q^49 - 8 * q^55 - 16 * q^60 - 64 * q^64 + 4 * q^67 - 64 * q^69 + 12 * q^75 + 28 * q^81 + 84 * q^91 - 4 * q^93 + 64 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

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			0		0.866025	−	0.500000i	$-0.166667\pi$
$2$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$3$	−0.724745	−	1.57313i	−0.418432	−	0.908248i
$3$	−0.724745	−	1.57313i	−0.418432	−	0.908248i
$4$	1.00000	−	1.73205i	0.500000	−	0.866025i
$5$	1.22474	−	0.707107i	0.547723	−	0.316228i	−0.200480	−	0.979698i	$-0.564250\pi$
$5$	1.22474	−	0.707107i	0.547723	−	0.316228i	0.748203	+	0.663470i	$0.230917\pi$
$6$		0			0
$7$	−1.32288	−	2.29129i	−0.500000	−	0.866025i
$7$	−1.32288	−	2.29129i	−0.500000	−	0.866025i
$8$		0			0
$9$	−1.94949	+	2.28024i	−0.649830	+	0.760080i
$10$		0			0
$11$	−2.23256	+	2.45269i	−0.673141	+	0.739514i
$11$	−2.23256	+	2.45269i	−0.673141	+	0.739514i
$12$	−3.44949	−	0.317837i	−0.995782	−	0.0917517i
$13$			4.58258i			1.27098i	0.772110	+	0.635489i	$0.219201\pi$
$13$			4.58258i			1.27098i	−0.772110	+	0.635489i	$0.780799\pi$
$14$		0			0
$15$	−2.00000	−	1.41421i	−0.516398	−	0.365148i
$16$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$17$	3.24037	−	5.61249i	0.785905	−	1.36123i	−0.142552	−	0.989787i	$-0.545531\pi$
$17$	3.24037	−	5.61249i	0.785905	−	1.36123i	0.928457	−	0.371440i	$-0.121136\pi$
$18$		0			0
$19$	3.96863	−	2.29129i	0.910465	−	0.525657i	0.0298846	−	0.999553i	$-0.490486\pi$
$19$	3.96863	−	2.29129i	0.910465	−	0.525657i	0.880581	+	0.473896i	$0.157153\pi$
$20$		−	2.82843i		−	0.632456i
$21$	−2.64575	+	3.74166i	−0.577350	+	0.816497i
$22$		0			0
$23$	4.89898	−	2.82843i	1.02151	−	0.589768i	0.106967	−	0.994263i	$-0.465886\pi$
$23$	4.89898	−	2.82843i	1.02151	−	0.589768i	0.914540	+	0.404495i	$0.132553\pi$
$24$		0			0
$25$	−1.50000	+	2.59808i	−0.300000	+	0.519615i
$26$		0			0
$27$	5.00000	+	1.41421i	0.962250	+	0.272166i
$28$	−5.29150			−1.00000
$29$	−6.48074			−1.20344			−0.601722	−	0.798706i	$-0.705518\pi$
$29$	−6.48074			−1.20344			−0.601722	+	0.798706i	$0.705518\pi$
$30$		0			0
$31$	0.500000	−	0.866025i	0.0898027	−	0.155543i	−0.817625	−	0.575751i	$-0.804710\pi$
$31$	0.500000	−	0.866025i	0.0898027	−	0.155543i	0.907428	+	0.420208i	$0.138043\pi$
$32$		0			0
$33$	5.47644	+	1.73453i	0.953326	+	0.301944i
$34$		0			0
$35$	−3.24037	−	1.87083i	−0.547723	−	0.316228i
$36$	2.00000	+	5.65685i	0.333333	+	0.942809i
$37$	3.50000	+	6.06218i	0.575396	+	0.996616i	0.995998	+	0.0893706i	$0.0284856\pi$
$37$	3.50000	+	6.06218i	0.575396	+	0.996616i	−0.420602	+	0.907245i	$0.638181\pi$
$38$		0			0
$39$	7.20900	−	3.32120i	1.15436	−	0.531817i
$40$		0			0
$41$	6.48074			1.01212			0.506061	−	0.862498i	$-0.331101\pi$
$41$	6.48074			1.01212			0.506061	+	0.862498i	$0.331101\pi$
$42$		0			0
$43$		−	4.58258i		−	0.698836i	−0.936967	−	0.349418i	$-0.886379\pi$
$43$		−	4.58258i		−	0.698836i	0.936967	−	0.349418i	$-0.113621\pi$
$44$	2.01563	+	6.31959i	0.303867	+	0.952714i
$45$	−0.775255	+	4.17121i	−0.115568	+	0.621807i
$46$		0			0
$47$	4.89898	−	2.82843i	0.714590	−	0.412568i	−0.0981685	−	0.995170i	$-0.531298\pi$
$47$	4.89898	−	2.82843i	0.714590	−	0.412568i	0.812758	+	0.582601i	$0.197965\pi$
$48$	−4.00000	+	5.65685i	−0.577350	+	0.816497i
$49$	−3.50000	+	6.06218i	−0.500000	+	0.866025i
$50$		0			0
$51$	−11.1776	−	1.02991i	−1.56518	−	0.144216i
$52$	7.93725	+	4.58258i	1.10070	+	0.635489i
$53$	6.12372	+	3.53553i	0.841158	+	0.485643i	0.857658	−	0.514221i	$-0.171919\pi$
$53$	6.12372	+	3.53553i	0.841158	+	0.485643i	−0.0164995	+	0.999864i	$0.505252\pi$
$54$		0			0
$55$	−1.00000	+	4.58258i	−0.134840	+	0.617914i
$56$		0			0
$57$	−6.48074	−	4.58258i	−0.858395	−	0.606977i
$58$		0			0
$59$	2.44949	+	1.41421i	0.318896	+	0.184115i	0.650901	−	0.759163i	$-0.274391\pi$
$59$	2.44949	+	1.41421i	0.318896	+	0.184115i	−0.332004	+	0.943278i	$0.607725\pi$
$60$	−4.44949	+	2.04989i	−0.574427	+	0.264639i
$61$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$61$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$62$		0			0
$63$	7.80362	+	1.45037i	0.983163	+	0.182729i
$64$	−8.00000			−1.00000
$65$	3.24037	+	5.61249i	0.401918	+	0.696143i
$66$		0			0
$67$	0.500000	−	0.866025i	0.0610847	−	0.105802i	−0.833866	−	0.551967i	$-0.813877\pi$
$67$	0.500000	−	0.866025i	0.0610847	−	0.105802i	0.894951	+	0.446165i	$0.147211\pi$
$68$	−6.48074	−	11.2250i	−0.785905	−	1.36123i
$69$	−8.00000	−	5.65685i	−0.963087	−	0.681005i
$70$		0			0
$71$			1.41421i			0.167836i	0.996473	+	0.0839181i	$0.0267434\pi$
$71$			1.41421i			0.167836i	−0.996473	+	0.0839181i	$0.973257\pi$
$72$		0			0
$73$	3.96863	+	2.29129i	0.464493	+	0.268175i	0.713931	−	0.700216i	$-0.246913\pi$
$73$	3.96863	+	2.29129i	0.464493	+	0.268175i	−0.249439	+	0.968391i	$0.580246\pi$
$74$		0			0
$75$	5.17423	+	0.476756i	0.597469	+	0.0550510i
$76$		−	9.16515i		−	1.05131i
$77$	8.57321	+	1.87083i	0.977008	+	0.213201i
$78$		0			0
$79$	−11.9059	+	6.87386i	−1.33952	+	0.773370i	−0.986736	−	0.162336i	$-0.948097\pi$
$79$	−11.9059	+	6.87386i	−1.33952	+	0.773370i	−0.352781	+	0.935706i	$0.614764\pi$
$80$	−4.89898	−	2.82843i	−0.547723	−	0.316228i
$81$	−1.39898	−	8.89060i	−0.155442	−	0.987845i
$82$		0			0
$83$	−6.48074			−0.711354			−0.355677	−	0.934609i	$-0.615750\pi$
$83$	−6.48074			−0.711354			−0.355677	+	0.934609i	$0.615750\pi$
$84$	3.83499	+	8.32423i	0.418432	+	0.908248i
$85$		−	9.16515i		−	0.994100i
$86$		0			0
$87$	4.69688	+	10.1951i	0.503559	+	1.09303i
$88$		0			0
$89$	−13.4722	+	7.77817i	−1.42805	+	0.824485i	−0.996967	−	0.0778275i	$-0.975202\pi$
$89$	−13.4722	+	7.77817i	−1.42805	+	0.824485i	−0.431083	+	0.902312i	$0.641868\pi$
$90$		0			0
$91$	10.5000	−	6.06218i	1.10070	−	0.635489i
$92$		−	11.3137i		−	1.17954i
$93$	−1.72474	−	0.158919i	−0.178848	−	0.0164791i
$94$		0			0
$95$	3.24037	−	5.61249i	0.332455	−	0.575829i
$96$		0			0
$97$	8.00000			0.812277			0.406138	−	0.913812i	$-0.366875\pi$
$97$	8.00000			0.812277			0.406138	+	0.913812i	$0.366875\pi$
$98$		0			0
$99$	−1.24037	−	9.87226i	−0.124662	−	0.992199i
$100$	3.00000	+	5.19615i	0.300000	+	0.519615i
$101$	6.48074	−	11.2250i	0.644858	−	1.11693i	−0.339477	−	0.940615i	$-0.610250\pi$
$101$	6.48074	−	11.2250i	0.644858	−	1.11693i	0.984334	−	0.176312i	$-0.0564167\pi$
$102$		0			0
$103$	−2.50000	−	4.33013i	−0.246332	−	0.426660i	0.716173	−	0.697923i	$-0.245892\pi$
$103$	−2.50000	−	4.33013i	−0.246332	−	0.426660i	−0.962505	+	0.271263i	$0.912559\pi$
$104$		0			0
$105$	−0.594619	+	6.45340i	−0.0580289	+	0.629788i
$106$		0			0
$107$	6.48074	+	11.2250i	0.626517	+	1.08516i	0.988245	+	0.152876i	$0.0488534\pi$
$107$	6.48074	+	11.2250i	0.626517	+	1.08516i	−0.361729	+	0.932283i	$0.617813\pi$
$108$	7.44949	−	7.24604i	0.716827	−	0.697251i
$109$	3.96863	+	2.29129i	0.380126	+	0.219466i	0.677873	−	0.735179i	$-0.262902\pi$
$109$	3.96863	+	2.29129i	0.380126	+	0.219466i	−0.297747	+	0.954645i	$0.596235\pi$
$110$		0			0
$111$	7.00000	−	9.89949i	0.664411	−	0.939618i
$112$	−5.29150	+	9.16515i	−0.500000	+	0.866025i
$113$			14.1421i			1.33038i	0.746674	+	0.665190i	$0.231650\pi$
$113$			14.1421i			1.33038i	−0.746674	+	0.665190i	$0.768350\pi$
$114$		0			0
$115$	4.00000	−	6.92820i	0.373002	−	0.646058i
$116$	−6.48074	+	11.2250i	−0.601722	+	1.04221i
$117$	−10.4494	−	8.93368i	−0.966044	−	0.825919i
$118$		0			0
$119$	−17.1464			−1.57181
$120$		0			0
$121$	−1.03137	−	10.9515i	−0.0937612	−	0.995595i
$122$		0			0
$123$	−4.69688	−	10.1951i	−0.423504	−	0.919258i
$124$	−1.00000	−	1.73205i	−0.0898027	−	0.155543i
$125$			11.3137i			1.01193i
$126$		0			0
$127$		−	13.7477i		−	1.21991i	−0.792435	−	0.609957i	$-0.791187\pi$
$127$		−	13.7477i		−	1.21991i	0.792435	−	0.609957i	$-0.208813\pi$
$128$		0			0
$129$	−7.20900	+	3.32120i	−0.634717	+	0.292415i
$130$		0			0
$131$	3.24037	+	5.61249i	0.283112	+	0.490365i	0.972150	−	0.234361i	$-0.0752997\pi$
$131$	3.24037	+	5.61249i	0.283112	+	0.490365i	−0.689037	+	0.724726i	$0.741966\pi$
$132$	8.48074	−	7.75094i	0.738154	−	0.674633i
$133$	−10.5000	−	6.06218i	−0.910465	−	0.525657i
$134$		0			0
$135$	7.12372	−	1.80348i	0.613113	−	0.155219i
$136$		0			0
$137$	−8.57321	−	4.94975i	−0.732459	−	0.422885i	0.0868620	−	0.996220i	$-0.472316\pi$
$137$	−8.57321	−	4.94975i	−0.732459	−	0.422885i	−0.819321	+	0.573335i	$0.805649\pi$
$138$		0			0
$139$			4.58258i			0.388689i	0.980933	+	0.194344i	$0.0622580\pi$
$139$			4.58258i			0.388689i	−0.980933	+	0.194344i	$0.937742\pi$
$140$	−6.48074	+	3.74166i	−0.547723	+	0.316228i
$141$	−8.00000	−	5.65685i	−0.673722	−	0.476393i
$142$		0			0
$143$	−11.2396	−	10.2309i	−0.939906	−	0.855548i
$144$	11.7980	+	2.19275i	0.983163	+	0.182729i
$145$	−7.93725	+	4.58258i	−0.659153	+	0.380562i
$146$		0			0
$147$	12.0732	+	1.11243i	0.995782	+	0.0917517i
$148$	14.0000			1.15079
$149$	3.24037	+	5.61249i	0.265461	+	0.459793i	0.967684	−	0.252164i	$-0.0811424\pi$
$149$	3.24037	+	5.61249i	0.265461	+	0.459793i	−0.702223	+	0.711957i	$0.747809\pi$
$150$		0			0
$151$	7.93725	+	4.58258i	0.645925	+	0.372925i	0.786893	−	0.617089i	$-0.211688\pi$
$151$	7.93725	+	4.58258i	0.645925	+	0.372925i	−0.140969	+	0.990014i	$0.545022\pi$
$152$		0			0
$153$	6.48074	+	18.3303i	0.523937	+	1.48192i
$154$		0			0
$155$		−	1.41421i		−	0.113592i
$156$	1.45651	−	15.8075i	0.116614	−	1.26562i
$157$	−4.00000	+	6.92820i	−0.319235	+	0.552931i	−0.980329	−	0.197372i	$-0.936759\pi$
$157$	−4.00000	+	6.92820i	−0.319235	+	0.552931i	0.661094	+	0.750303i	$0.270093\pi$
$158$		0			0
$159$	1.12372	−	12.1958i	0.0891171	−	0.967189i
$160$		0			0
$161$	−12.9615	−	7.48331i	−1.02151	−	0.589768i
$162$		0			0
$163$	−1.00000	−	1.73205i	−0.0783260	−	0.135665i	0.824202	−	0.566296i	$-0.191624\pi$
$163$	−1.00000	−	1.73205i	−0.0783260	−	0.135665i	−0.902528	+	0.430632i	$0.858291\pi$
$164$	6.48074	−	11.2250i	0.506061	−	0.876523i
$165$	7.93374	−	1.74807i	0.617641	−	0.136087i
$166$		0			0
$167$	−12.9615			−1.00299			−0.501495	−	0.865161i	$-0.667216\pi$
$167$	−12.9615			−1.00299			−0.501495	+	0.865161i	$0.667216\pi$
$168$		0			0
$169$	−8.00000			−0.615385
$170$		0			0
$171$	−2.51211	+	13.5163i	−0.192106	+	1.03361i
$172$	−7.93725	−	4.58258i	−0.605210	−	0.349418i
$173$	9.72111	+	16.8375i	0.739082	+	1.28013i	0.952909	+	0.303257i	$0.0980739\pi$
$173$	9.72111	+	16.8375i	0.739082	+	1.28013i	−0.213827	+	0.976872i	$0.568593\pi$
$174$		0			0
$175$	7.93725			0.600000
$176$	12.9615	+	2.82843i	0.977008	+	0.213201i
$177$	0.449490	−	4.87832i	0.0337857	−	0.366677i
$178$		0			0
$179$	−15.9217	−	9.19239i	−1.19004	−	0.687071i	−0.231726	−	0.972781i	$-0.574437\pi$
$179$	−15.9217	−	9.19239i	−1.19004	−	0.687071i	−0.958316	+	0.285710i	$0.907771\pi$
$180$	6.44949	+	5.51399i	0.480717	+	0.410989i
$181$	−13.0000			−0.966282			−0.483141	−	0.875542i	$-0.660504\pi$
$181$	−13.0000			−0.966282			−0.483141	+	0.875542i	$0.660504\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	8.57321	+	4.94975i	0.630315	+	0.363913i
$186$		0			0
$187$	6.53137	+	20.4778i	0.477621	+	1.49749i
$188$		−	11.3137i		−	0.825137i
$189$	−3.37401	−	13.3273i	−0.245423	−	0.969416i
$190$		0			0
$191$	−17.1464	+	9.89949i	−1.24067	+	0.716302i	−0.969231	−	0.246153i	$-0.920834\pi$
$191$	−17.1464	+	9.89949i	−1.24067	+	0.716302i	−0.271441	+	0.962455i	$0.587500\pi$
$192$	5.79796	+	12.5851i	0.418432	+	0.908248i
$193$	−11.9059	−	6.87386i	−0.857004	−	0.494792i	0.00600382	−	0.999982i	$-0.498089\pi$
$193$	−11.9059	−	6.87386i	−0.857004	−	0.494792i	−0.863008	+	0.505190i	$0.831422\pi$
$194$		0			0
$195$	6.48074	−	9.16515i	0.464095	−	0.656330i
$196$	7.00000	+	12.1244i	0.500000	+	0.866025i
$197$		0			0			−	1.00000i	$-0.5\pi$
$197$		0			0				1.00000i	$0.5\pi$
$198$		0			0
$199$	−1.00000	+	1.73205i	−0.0708881	+	0.122782i	−0.899291	−	0.437351i	$-0.855917\pi$
$199$	−1.00000	+	1.73205i	−0.0708881	+	0.122782i	0.828403	+	0.560133i	$0.189250\pi$
$200$		0			0
$201$	−1.72474	−	0.158919i	−0.121654	−	0.0112093i
$202$		0			0
$203$	8.57321	+	14.8492i	0.601722	+	1.04221i
$204$	−12.9615	+	18.3303i	−0.907485	+	1.28338i
$205$	7.93725	−	4.58258i	0.554362	−	0.320061i
$206$		0			0
$207$	−3.10102	+	16.6848i	−0.215536	+	1.15968i
$208$	15.8745	−	9.16515i	1.10070	−	0.635489i
$209$	−3.24037	+	14.8492i	−0.224141	+	1.02714i
$210$		0			0
$211$			18.3303i			1.26191i	0.775819	+	0.630955i	$0.217337\pi$
$211$			18.3303i			1.26191i	−0.775819	+	0.630955i	$0.782663\pi$
$212$	12.2474	−	7.07107i	0.841158	−	0.485643i
$213$	2.22474	−	1.02494i	0.152437	−	0.0702280i
$214$		0			0
$215$	−3.24037	−	5.61249i	−0.220991	−	0.382768i
$216$		0			0
$217$	−2.64575			−0.179605
$218$		0			0
$219$	0.728257	−	7.90377i	0.0492110	−	0.534088i
$220$	6.93725	+	6.31463i	0.467710	+	0.425732i
$221$	25.7196	+	14.8492i	1.73009	+	0.998868i
$222$		0			0
$223$	−4.00000			−0.267860			−0.133930	−	0.990991i	$-0.542760\pi$
$223$	−4.00000			−0.267860			−0.133930	+	0.990991i	$0.542760\pi$
$224$		0			0
$225$	−3.00000	−	8.48528i	−0.200000	−	0.565685i
$226$		0			0
$227$	6.48074	−	11.2250i	0.430142	−	0.745028i	−0.566743	−	0.823894i	$-0.691797\pi$
$227$	6.48074	−	11.2250i	0.430142	−	0.745028i	0.996885	+	0.0788669i	$0.0251302\pi$
$228$	−14.4180	+	6.64240i	−0.954855	+	0.439903i
$229$	−5.50000	−	9.52628i	−0.363450	−	0.629514i	0.625076	−	0.780564i	$-0.285068\pi$
$229$	−5.50000	−	9.52628i	−0.363450	−	0.629514i	−0.988526	+	0.151050i	$0.951735\pi$
$230$		0			0
$231$	−3.27033	−	14.8427i	−0.215172	−	0.976576i
$232$		0			0
$233$	−3.24037	−	5.61249i	−0.212284	−	0.367686i	0.740145	−	0.672447i	$-0.234757\pi$
$233$	−3.24037	−	5.61249i	−0.212284	−	0.367686i	−0.952429	+	0.304761i	$0.901423\pi$
$234$		0			0
$235$	4.00000	−	6.92820i	0.260931	−	0.451946i
$236$	4.89898	−	2.82843i	0.318896	−	0.184115i
$237$	19.4422	+	13.7477i	1.26291	+	0.893011i
$238$		0			0
$239$	6.48074			0.419204			0.209602	−	0.977787i	$-0.432783\pi$
$239$	6.48074			0.419204			0.209602	+	0.977787i	$0.432783\pi$
$240$	−0.898979	+	9.75663i	−0.0580289	+	0.629788i
$241$	−15.8745	−	9.16515i	−1.02257	−	0.590379i	−0.107721	−	0.994181i	$-0.534355\pi$
$241$	−15.8745	−	9.16515i	−1.02257	−	0.590379i	−0.914846	+	0.403802i	$0.867688\pi$
$242$		0			0
$243$	−12.9722	+	8.64420i	−0.832167	+	0.554526i
$244$		0			0
$245$			9.89949i			0.632456i
$246$		0			0
$247$	10.5000	+	18.1865i	0.668099	+	1.15718i
$248$		0			0
$249$	4.69688	+	10.1951i	0.297653	+	0.646086i
$250$		0			0
$251$		−	7.07107i		−	0.446322i	−0.974782	−	0.223161i	$-0.928362\pi$
$251$		−	7.07107i		−	0.446322i	0.974782	−	0.223161i	$-0.0716375\pi$
$252$	10.3157	−	12.0659i	0.649830	−	0.760080i
$253$	−4.00000	+	18.3303i	−0.251478	+	1.15242i
$254$		0			0
$255$	−14.4180	+	6.64240i	−0.902890	+	0.415963i
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	15.9217	−	9.19239i	0.993167	−	0.573405i	0.0869478	−	0.996213i	$-0.472289\pi$
$257$	15.9217	−	9.19239i	0.993167	−	0.573405i	0.906220	+	0.422807i	$0.138955\pi$
$258$		0			0
$259$	9.26013	−	16.0390i	0.575396	−	0.996616i
$260$	12.9615			0.803837
$261$	12.6341	−	14.7776i	0.782033	−	0.914713i
$262$		0			0
$263$	−3.24037	+	5.61249i	−0.199810	+	0.346081i	−0.948467	−	0.316877i	$-0.897366\pi$
$263$	−3.24037	+	5.61249i	−0.199810	+	0.346081i	0.748657	+	0.662958i	$0.230699\pi$
$264$		0			0
$265$	10.0000			0.614295
$266$		0			0
$267$	22.0000	+	15.5563i	1.34638	+	0.952033i
$268$	−1.00000	−	1.73205i	−0.0610847	−	0.105802i
$269$	−4.89898	−	2.82843i	−0.298696	−	0.172452i	0.343161	−	0.939277i	$-0.388502\pi$
$269$	−4.89898	−	2.82843i	−0.298696	−	0.172452i	−0.641857	+	0.766824i	$0.721836\pi$
$270$		0			0
$271$	−7.93725	+	4.58258i	−0.482154	+	0.278372i	−0.721314	−	0.692609i	$-0.756461\pi$
$271$	−7.93725	+	4.58258i	−0.482154	+	0.278372i	0.239160	+	0.970980i	$0.423128\pi$
$272$	−25.9230			−1.57181
$273$	−17.1464	−	12.1244i	−1.03775	−	0.733799i
$274$		0			0
$275$	−3.02344	−	9.47939i	−0.182320	−	0.571629i
$276$	−17.7980	+	8.19955i	−1.07131	+	0.493555i
$277$	19.8431	+	11.4564i	1.19226	+	0.688351i	0.958818	−	0.284020i	$-0.0916684\pi$
$277$	19.8431	+	11.4564i	1.19226	+	0.688351i	0.233440	+	0.972371i	$0.425002\pi$
$278$		0			0
$279$	1.00000	+	2.82843i	0.0598684	+	0.169334i
$280$		0			0
$281$	12.9615			0.773217			0.386609	−	0.922244i	$-0.373646\pi$
$281$	12.9615			0.773217			0.386609	+	0.922244i	$0.373646\pi$
$282$		0			0
$283$	−11.9059	−	6.87386i	−0.707731	−	0.408609i	0.102489	−	0.994734i	$-0.467319\pi$
$283$	−11.9059	−	6.87386i	−0.707731	−	0.408609i	−0.810220	+	0.586125i	$0.800653\pi$
$284$	2.44949	+	1.41421i	0.145350	+	0.0839181i
$285$	−11.1776	−	1.02991i	−0.662105	−	0.0610066i
$286$		0			0
$287$	−8.57321	−	14.8492i	−0.506061	−	0.876523i
$288$		0			0
$289$	−12.5000	−	21.6506i	−0.735294	−	1.27357i
$290$		0			0
$291$	−5.79796	−	12.5851i	−0.339882	−	0.737749i
$292$	7.93725	−	4.58258i	0.464493	−	0.268175i
$293$	−12.9615			−0.757218			−0.378609	−	0.925557i	$-0.623597\pi$
$293$	−12.9615			−0.757218			−0.378609	+	0.925557i	$0.623597\pi$
$294$		0			0
$295$	4.00000			0.232889
$296$		0			0
$297$	−14.6314	+	9.10613i	−0.849001	+	0.528392i
$298$		0			0
$299$	12.9615	+	22.4499i	0.749582	+	1.29831i
$300$	6.00000	−	8.48528i	0.346410	−	0.489898i
$301$	−10.5000	+	6.06218i	−0.605210	+	0.349418i
$302$		0			0
$303$	−22.3552	−	2.05982i	−1.28428	−	0.118334i
$304$	−15.8745	−	9.16515i	−0.910465	−	0.525657i
$305$		0			0
$306$		0			0
$307$		−	13.7477i		−	0.784624i	−0.919832	−	0.392312i	$-0.871675\pi$
$307$		−	13.7477i		−	0.784624i	0.919832	−	0.392312i	$-0.128325\pi$
$308$	11.8136	−	12.9784i	0.673141	−	0.739514i
$309$	−5.00000	+	7.07107i	−0.284440	+	0.402259i
$310$		0			0
$311$	13.4722	+	7.77817i	0.763938	+	0.441060i	0.830708	−	0.556709i	$-0.187936\pi$
$311$	13.4722	+	7.77817i	0.763938	+	0.441060i	−0.0667698	+	0.997768i	$0.521269\pi$
$312$		0			0
$313$	−8.50000	−	14.7224i	−0.480448	−	0.832161i	0.519300	−	0.854592i	$-0.326193\pi$
$313$	−8.50000	−	14.7224i	−0.480448	−	0.832161i	−0.999748	+	0.0224310i	$0.992859\pi$
$314$		0			0
$315$	10.5830	−	3.74166i	0.596285	−	0.210819i
$316$			27.4955i			1.54674i
$317$	8.57321	−	4.94975i	0.481520	−	0.278006i	−0.239530	−	0.970889i	$-0.576993\pi$
$317$	8.57321	−	4.94975i	0.481520	−	0.278006i	0.721050	+	0.692883i	$0.243660\pi$
$318$		0			0
$319$	14.4686	−	15.8952i	0.810088	−	0.889963i
$320$	−9.79796	+	5.65685i	−0.547723	+	0.316228i
$321$	12.9615	−	18.3303i	0.723439	−	1.02310i
$322$		0			0
$323$		−	29.6985i		−	1.65247i
$324$	−16.7980	−	6.46750i	−0.933220	−	0.359306i
$325$	−11.9059	−	6.87386i	−0.660419	−	0.381293i
$326$		0			0
$327$	0.728257	−	7.90377i	0.0402727	−	0.437080i
$328$		0			0
$329$	−12.9615	−	7.48331i	−0.714590	−	0.412568i
$330$		0			0
$331$	3.50000	+	6.06218i	0.192377	+	0.333207i	0.946038	−	0.324057i	$-0.105047\pi$
$331$	3.50000	+	6.06218i	0.192377	+	0.333207i	−0.753660	+	0.657264i	$0.771714\pi$
$332$	−6.48074	+	11.2250i	−0.355677	+	0.616050i
$333$	−20.6464	−	3.83732i	−1.13142	−	0.210284i
$334$		0			0
$335$		−	1.41421i		−	0.0772667i
$336$	18.2530	+	1.68184i	0.995782	+	0.0917517i
$337$			4.58258i			0.249629i	0.992180	+	0.124814i	$0.0398335\pi$
$337$			4.58258i			0.249629i	−0.992180	+	0.124814i	$0.960166\pi$
$338$		0			0
$339$	22.2474	−	10.2494i	1.20832	−	0.556673i
$340$	−15.8745	−	9.16515i	−0.860916	−	0.497050i
$341$	1.00781	+	3.15980i	0.0545761	+	0.171113i
$342$		0			0
$343$	18.5203			1.00000
$344$		0			0
$345$	−13.7980	−	1.27135i	−0.742857	−	0.0684471i
$346$		0			0
$347$	9.72111	−	16.8375i	0.521857	−	0.903882i	−0.477820	−	0.878458i	$-0.658573\pi$
$347$	9.72111	−	16.8375i	0.521857	−	0.903882i	0.999677	−	0.0254244i	$-0.00809372\pi$
$348$	22.3552	+	2.05982i	1.19837	+	0.110418i
$349$			9.16515i			0.490599i	0.969447	+	0.245300i	$0.0788863\pi$
$349$			9.16515i			0.490599i	−0.969447	+	0.245300i	$0.921114\pi$
$350$		0			0
$351$	−6.48074	+	22.9129i	−0.345916	+	1.22300i
$352$		0			0
$353$	−12.2474	−	7.07107i	−0.651866	−	0.376355i	0.137305	−	0.990529i	$-0.456156\pi$
$353$	−12.2474	−	7.07107i	−0.651866	−	0.376355i	−0.789171	+	0.614174i	$0.789489\pi$
$354$		0			0
$355$	1.00000	+	1.73205i	0.0530745	+	0.0919277i
$356$			31.1127i			1.64897i
$357$	12.4268	+	26.9736i	0.657695	+	1.42759i
$358$		0			0
$359$	6.48074	+	11.2250i	0.342040	+	0.592431i	0.984811	−	0.173627i	$-0.0555487\pi$
$359$	6.48074	+	11.2250i	0.342040	+	0.592431i	−0.642771	+	0.766058i	$0.722215\pi$
$360$		0			0
$361$	1.00000	−	1.73205i	0.0526316	−	0.0911606i
$362$		0			0
$363$	−16.4807	+	9.55956i	−0.865015	+	0.501747i
$364$		−	24.2487i		−	1.27098i
$365$	6.48074			0.339217
$366$		0			0
$367$	0.500000	−	0.866025i	0.0260998	−	0.0452062i	−0.852680	−	0.522433i	$-0.825025\pi$
$367$	0.500000	−	0.866025i	0.0260998	−	0.0452062i	0.878780	+	0.477227i	$0.158358\pi$
$368$	−19.5959	−	11.3137i	−1.02151	−	0.589768i
$369$	−12.6341	+	14.7776i	−0.657707	+	0.769293i
$370$		0			0
$371$		−	18.7083i		−	0.971286i
$372$	−2.00000	+	2.82843i	−0.103695	+	0.146647i
$373$	−3.96863	+	2.29129i	−0.205488	+	0.118638i	−0.599213	−	0.800590i	$-0.704520\pi$
$373$	−3.96863	+	2.29129i	−0.205488	+	0.118638i	0.393725	+	0.919228i	$0.371186\pi$
$374$		0			0
$375$	17.7980	−	8.19955i	0.919083	−	0.423423i
$376$		0			0
$377$		−	29.6985i		−	1.52955i
$378$		0			0
$379$	11.0000			0.565032			0.282516	−	0.959263i	$-0.408831\pi$
$379$	11.0000			0.565032			0.282516	+	0.959263i	$0.408831\pi$
$380$	−6.48074	−	11.2250i	−0.332455	−	0.575829i
$381$	−21.6270	+	9.96359i	−1.10798	+	0.510450i
$382$		0			0
$383$	1.22474	−	0.707107i	0.0625815	−	0.0361315i	−0.468383	−	0.883526i	$-0.655163\pi$
$383$	1.22474	−	0.707107i	0.0625815	−	0.0361315i	0.530964	+	0.847394i	$0.321830\pi$
$384$		0			0
$385$	11.8229	−	3.77089i	0.602550	−	0.192182i
$386$		0			0
$387$	10.4494	+	8.93368i	0.531171	+	0.454125i
$388$	8.00000	−	13.8564i	0.406138	−	0.703452i
$389$	2.44949	+	1.41421i	0.124194	+	0.0717035i	0.560810	−	0.827945i	$-0.310490\pi$
$389$	2.44949	+	1.41421i	0.124194	+	0.0717035i	−0.436616	+	0.899648i	$0.643823\pi$
$390$		0			0
$391$		−	36.6606i		−	1.85401i
$392$		0			0
$393$	6.48074	−	9.16515i	0.326910	−	0.462321i
$394$		0			0
$395$	−9.72111	+	16.8375i	−0.489122	+	0.847184i
$396$	−18.3396	−	7.72387i	−0.921601	−	0.388139i
$397$	12.5000	+	21.6506i	0.627357	+	1.08661i	0.988080	+	0.153941i	$0.0491966\pi$
$397$	12.5000	+	21.6506i	0.627357	+	1.08661i	−0.360723	+	0.932673i	$0.617470\pi$
$398$		0			0
$399$	−1.92679	+	20.9114i	−0.0964599	+	1.04688i
$400$	12.0000			0.600000
$401$	12.2474	−	7.07107i	0.611608	−	0.353112i	−0.161986	−	0.986793i	$-0.551790\pi$
$401$	12.2474	−	7.07107i	0.611608	−	0.353112i	0.773595	+	0.633681i	$0.218457\pi$
$402$		0			0
$403$	3.96863	+	2.29129i	0.197691	+	0.114137i
$404$	−12.9615	−	22.4499i	−0.644858	−	1.11693i
$405$	−8.00000	−	9.89949i	−0.397523	−	0.491910i
$406$		0			0
$407$	−22.6826	−	4.94975i	−1.12433	−	0.245350i
$408$		0			0
$409$	11.9059	+	6.87386i	0.588708	+	0.339891i	0.764586	−	0.644521i	$-0.222943\pi$
$409$	11.9059	+	6.87386i	0.588708	+	0.339891i	−0.175879	+	0.984412i	$0.556277\pi$
$410$		0			0
$411$	−1.57321	+	17.0741i	−0.0776009	+	0.842203i
$412$	−10.0000			−0.492665
$413$		−	7.48331i		−	0.368230i
$414$		0			0
$415$	−7.93725	+	4.58258i	−0.389624	+	0.224950i
$416$		0			0
$417$	7.20900	−	3.32120i	0.353026	−	0.162640i
$418$		0			0
$419$			1.41421i			0.0690889i	0.999403	+	0.0345444i	$0.0109980\pi$
$419$			1.41421i			0.0690889i	−0.999403	+	0.0345444i	$0.989002\pi$
$420$	10.5830	+	7.48331i	0.516398	+	0.365148i
$421$	17.0000			0.828529			0.414265	−	0.910156i	$-0.364039\pi$
$421$	17.0000			0.828529			0.414265	+	0.910156i	$0.364039\pi$
$422$		0			0
$423$	−3.10102	+	16.6848i	−0.150777	+	0.811244i
$424$		0			0
$425$	9.72111	+	16.8375i	0.471543	+	0.816737i
$426$		0			0
$427$		0			0
$428$	25.9230			1.25303
$429$	−7.94863	+	25.0962i	−0.383764	+	1.21166i
$430$		0			0
$431$	−6.48074	+	11.2250i	−0.312166	+	0.540688i	−0.978831	−	0.204670i	$-0.934388\pi$
$431$	−6.48074	+	11.2250i	−0.312166	+	0.540688i	0.666665	+	0.745358i	$0.267721\pi$
$432$	−5.10102	−	20.1489i	−0.245423	−	0.969416i
$433$	11.0000			0.528626			0.264313	−	0.964437i	$-0.414855\pi$
$433$	11.0000			0.528626			0.264313	+	0.964437i	$0.414855\pi$
$434$		0			0
$435$	12.9615	+	9.16515i	0.621455	+	0.439435i
$436$	7.93725	−	4.58258i	0.380126	−	0.219466i
$437$	12.9615	−	22.4499i	0.620032	−	1.07393i
$438$		0			0
$439$	−23.8118	+	13.7477i	−1.13647	+	0.656143i	−0.945555	−	0.325463i	$-0.894480\pi$
$439$	−23.8118	+	13.7477i	−1.13647	+	0.656143i	−0.190918	+	0.981606i	$0.561147\pi$
$440$		0			0
$441$	−7.00000	−	19.7990i	−0.333333	−	0.942809i
$442$		0			0
$443$	−6.12372	+	3.53553i	−0.290947	+	0.167978i	−0.638369	−	0.769731i	$-0.720391\pi$
$443$	−6.12372	+	3.53553i	−0.290947	+	0.167978i	0.347422	+	0.937709i	$0.387057\pi$
$444$	−10.1464	−	22.0239i	−0.481528	−	1.04521i
$445$	−11.0000	+	19.0526i	−0.521450	+	0.903178i
$446$		0			0
$447$	6.48074	−	9.16515i	0.306529	−	0.433497i
$448$	10.5830	+	18.3303i	0.500000	+	0.866025i
$449$			1.41421i			0.0667409i	0.999443	+	0.0333704i	$0.0106241\pi$
$449$			1.41421i			0.0667409i	−0.999443	+	0.0333704i	$0.989376\pi$
$450$		0			0
$451$	−14.4686	+	15.8952i	−0.681301	+	0.748478i
$452$	24.4949	+	14.1421i	1.15214	+	0.665190i
$453$	1.45651	−	15.8075i	0.0684330	−	0.742703i
$454$		0			0
$455$	8.57321	−	14.8492i	0.401918	−	0.696143i
$456$		0			0
$457$	35.7176	−	20.6216i	1.67080	−	0.964637i	0.703610	−	0.710586i	$-0.251570\pi$
$457$	35.7176	−	20.6216i	1.67080	−	0.964637i	0.967191	−	0.254051i	$-0.0817631\pi$
$458$		0			0
$459$	24.1391	−	23.4799i	1.12672	−	1.09595i
$460$	−8.00000	−	13.8564i	−0.373002	−	0.646058i
$461$	−25.9230			−1.20735			−0.603676	−	0.797229i	$-0.706298\pi$
$461$	−25.9230			−1.20735			−0.603676	+	0.797229i	$0.706298\pi$
$462$		0			0
$463$	−25.0000			−1.16185			−0.580924	−	0.813958i	$-0.697309\pi$
$463$	−25.0000			−1.16185			−0.580924	+	0.813958i	$0.697309\pi$
$464$	12.9615	+	22.4499i	0.601722	+	1.04221i
$465$	−2.22474	+	1.02494i	−0.103170	+	0.0475306i
$466$		0			0
$467$	15.9217	−	9.19239i	0.736768	−	0.425373i	−0.0841252	−	0.996455i	$-0.526810\pi$
$467$	15.9217	−	9.19239i	0.736768	−	0.425373i	0.820893	+	0.571082i	$0.193476\pi$
$468$	−25.9230	+	9.16515i	−1.19829	+	0.423659i
$469$	−2.64575			−0.122169
$470$		0			0
$471$	13.7980	+	1.27135i	0.635776	+	0.0585807i
$472$		0			0
$473$	11.2396	+	10.2309i	0.516799	+	0.470416i
$474$		0			0
$475$			13.7477i			0.630789i
$476$	−17.1464	+	29.6985i	−0.785905	+	1.36123i
$477$	−20.0000	+	7.07107i	−0.915737	+	0.323762i
$478$		0			0
$479$	−3.24037	+	5.61249i	−0.148056	+	0.256441i	−0.930509	−	0.366269i	$-0.880635\pi$
$479$	−3.24037	+	5.61249i	−0.148056	+	0.256441i	0.782453	+	0.622710i	$0.213968\pi$
$480$		0			0
$481$	−27.7804	+	16.0390i	−1.26668	+	0.731316i
$482$		0			0
$483$	−2.37848	+	25.8136i	−0.108224	+	1.17456i
$484$	−20.0000	−	9.16515i	−0.909091	−	0.416598i
$485$	9.79796	−	5.65685i	0.444902	−	0.256865i
$486$		0			0
$487$	−14.5000	+	25.1147i	−0.657058	+	1.13806i	0.324316	+	0.945949i	$0.394866\pi$
$487$	−14.5000	+	25.1147i	−0.657058	+	1.13806i	−0.981374	+	0.192109i	$0.938467\pi$
$488$		0			0
$489$	−2.00000	+	2.82843i	−0.0904431	+	0.127906i
$490$		0			0
$491$	6.48074			0.292472			0.146236	−	0.989250i	$-0.453284\pi$
$491$	6.48074			0.292472			0.146236	+	0.989250i	$0.453284\pi$
$492$	−22.3552	−	2.05982i	−1.00785	−	0.0928639i
$493$	−21.0000	+	36.3731i	−0.945792	+	1.63816i
$494$		0			0
$495$	−8.49988	−	11.2139i	−0.382041	−	0.504028i
$496$	−4.00000			−0.179605
$497$	3.24037	−	1.87083i	0.145350	−	0.0839181i
$498$		0			0
$499$	−2.50000	−	4.33013i	−0.111915	−	0.193843i	0.804627	−	0.593780i	$-0.202365\pi$
$499$	−2.50000	−	4.33013i	−0.111915	−	0.193843i	−0.916542	+	0.399937i	$0.869032\pi$
$500$	19.5959	+	11.3137i	0.876356	+	0.505964i
$501$	9.39377	+	20.3901i	0.419683	+	0.910964i
$502$		0			0
$503$	19.4422			0.866886			0.433443	−	0.901181i	$-0.357299\pi$
$503$	19.4422			0.866886			0.433443	+	0.901181i	$0.357299\pi$
$504$		0			0
$505$		−	18.3303i		−	0.815688i
$506$		0			0
$507$	5.79796	+	12.5851i	0.257496	+	0.558922i
$508$	−23.8118	−	13.7477i	−1.05648	−	0.609957i
$509$	26.9444	−	15.5563i	1.19429	−	0.689523i	0.235013	−	0.971992i	$-0.424487\pi$
$509$	26.9444	−	15.5563i	1.19429	−	0.689523i	0.959276	+	0.282469i	$0.0911535\pi$
$510$		0			0
$511$		−	12.1244i		−	0.536350i
$512$		0			0
$513$	23.0835	−	5.84395i	1.01916	−	0.258017i
$514$		0			0
$515$	−6.12372	−	3.53553i	−0.269844	−	0.155794i
$516$	−1.45651	+	15.8075i	−0.0641194	+	0.695888i
$517$	−4.00000	+	18.3303i	−0.175920	+	0.806166i
$518$		0			0
$519$	19.4422	−	27.4955i	0.853419	−	1.20692i
$520$		0			0
$521$	6.12372	+	3.53553i	0.268285	+	0.154895i	0.628108	−	0.778126i	$-0.283830\pi$
$521$	6.12372	+	3.53553i	0.268285	+	0.154895i	−0.359823	+	0.933021i	$0.617163\pi$
$522$		0			0
$523$	3.96863	−	2.29129i	0.173536	−	0.100191i	−0.410716	−	0.911763i	$-0.634721\pi$
$523$	3.96863	−	2.29129i	0.173536	−	0.100191i	0.584252	+	0.811572i	$0.301388\pi$
$524$	12.9615			0.566225
$525$	−5.75248	−	12.4863i	−0.251059	−	0.544949i
$526$		0			0
$527$	−3.24037	−	5.61249i	−0.141153	−	0.244484i
$528$	−4.94428	−	22.4400i	−0.215172	−	0.976576i
$529$	4.50000	−	7.79423i	0.195652	−	0.338880i
$530$		0			0
$531$	−8.00000	+	2.82843i	−0.347170	+	0.122743i
$532$	−21.0000	+	12.1244i	−0.910465	+	0.525657i
$533$			29.6985i			1.28638i
$534$		0			0
$535$	15.8745	+	9.16515i	0.686315	+	0.396244i
$536$		0			0
$537$	−2.92168	+	31.7090i	−0.126080	+	1.36835i
$538$		0			0
$539$	−7.05469	−	22.1186i	−0.303867	−	0.952714i
$540$	4.00000	−	14.1421i	0.172133	−	0.608581i
$541$	27.7804	−	16.0390i	1.19437	−	0.689571i	0.235077	−	0.971977i	$-0.424466\pi$
$541$	27.7804	−	16.0390i	1.19437	−	0.689571i	0.959295	+	0.282406i	$0.0911324\pi$
$542$		0			0
$543$	9.42168	+	20.4507i	0.404323	+	0.877624i
$544$		0			0
$545$	6.48074			0.277604
$546$		0			0
$547$			9.16515i			0.391874i	0.980617	+	0.195937i	$0.0627747\pi$
$547$			9.16515i			0.391874i	−0.980617	+	0.195937i	$0.937225\pi$
$548$	−17.1464	+	9.89949i	−0.732459	+	0.422885i
$549$		0			0
$550$		0			0
$551$	−25.7196	+	14.8492i	−1.09569	+	0.632599i
$552$		0			0
$553$	31.5000	+	18.1865i	1.33952	+	0.773370i
$554$		0			0
$555$	1.57321	−	17.0741i	0.0667792	−	0.724755i
$556$	7.93725	+	4.58258i	0.336615	+	0.194344i
$557$	−16.2019	+	28.0624i	−0.686494	+	1.18904i	0.286470	+	0.958089i	$0.407518\pi$
$557$	−16.2019	+	28.0624i	−0.686494	+	1.18904i	−0.972965	+	0.230954i	$0.925815\pi$
$558$		0			0
$559$	21.0000			0.888205
$560$			14.9666i			0.632456i
$561$	27.4807	−	25.1159i	1.16024	−	1.06039i
$562$		0			0
$563$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$563$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$564$	−17.7980	+	8.19955i	−0.749429	+	0.345263i
$565$	10.0000	+	17.3205i	0.420703	+	0.728679i
$566$		0			0
$567$	−18.5203	+	14.9666i	−0.777778	+	0.628539i
$568$		0			0
$569$	−19.4422	−	33.6749i	−0.815060	−	1.41173i	−0.909285	−	0.416175i	$-0.863370\pi$
$569$	−19.4422	−	33.6749i	−0.815060	−	1.41173i	0.0942242	−	0.995551i	$-0.469963\pi$
$570$		0			0
$571$	11.9059	+	6.87386i	0.498246	+	0.287662i	0.727989	−	0.685589i	$-0.240455\pi$
$571$	11.9059	+	6.87386i	0.498246	+	0.287662i	−0.229743	+	0.973251i	$0.573789\pi$
$572$	−28.9600	+	9.23676i	−1.21088	+	0.386208i
$573$	28.0000	+	19.7990i	1.16972	+	0.827115i
$574$		0			0
$575$			16.9706i			0.707721i
$576$	15.5959	−	18.2419i	0.649830	−	0.760080i
$577$	21.5000	−	37.2391i	0.895057	−	1.55028i	0.0613223	−	0.998118i	$-0.480468\pi$
$577$	21.5000	−	37.2391i	0.895057	−	1.55028i	0.833734	−	0.552166i	$-0.186198\pi$
$578$		0			0
$579$	−2.18477	+	23.7113i	−0.0907959	+	0.985409i
$580$			18.3303i			0.761124i
$581$	8.57321	+	14.8492i	0.355677	+	0.616050i
$582$		0			0
$583$	−22.3431	+	7.12631i	−0.925358	+	0.295142i
$584$		0			0
$585$	−19.1149	−	3.55267i	−0.790303	−	0.146885i
$586$		0			0
$587$		−	2.82843i		−	0.116742i	−0.998295	−	0.0583708i	$-0.981409\pi$
$587$		−	2.82843i		−	0.116742i	0.998295	−	0.0583708i	$-0.0185906\pi$
$588$	14.0000	−	19.7990i	0.577350	−	0.816497i
$589$		−	4.58258i		−	0.188822i
$590$		0			0
$591$		0			0
$592$	14.0000	−	24.2487i	0.575396	−	0.996616i
$593$	−12.9615	−	22.4499i	−0.532264	−	0.921909i	−0.999290	−	0.0376652i	$-0.988008\pi$
$593$	−12.9615	−	22.4499i	−0.532264	−	0.921909i	0.467026	−	0.884243i	$-0.345325\pi$
$594$		0			0
$595$	−21.0000	+	12.1244i	−0.860916	+	0.497050i
$596$	12.9615			0.530923
$597$	3.44949	+	0.317837i	0.141178	+	0.0130082i
$598$		0			0
$599$	−23.2702	−	13.4350i	−0.950793	−	0.548940i	−0.0574656	−	0.998347i	$-0.518302\pi$
$599$	−23.2702	−	13.4350i	−0.950793	−	0.548940i	−0.893327	+	0.449407i	$0.851635\pi$
$600$		0			0
$601$		−	4.58258i		−	0.186927i	−0.995623	−	0.0934636i	$-0.970206\pi$
$601$		−	4.58258i		−	0.186927i	0.995623	−	0.0934636i	$-0.0297939\pi$
$602$		0			0
$603$	1.00000	+	2.82843i	0.0407231	+	0.115182i
$604$	15.8745	−	9.16515i	0.645925	−	0.372925i
$605$	−9.00708	−	12.6836i	−0.366190	−	0.515660i
$606$		0			0
$607$	19.8431	−	11.4564i	0.805408	−	0.465003i	−0.0399507	−	0.999202i	$-0.512720\pi$
$607$	19.8431	−	11.4564i	0.805408	−	0.465003i	0.845359	+	0.534199i	$0.179387\pi$
$608$		0			0
$609$	17.1464	−	24.2487i	0.694808	−	0.982607i
$610$		0			0
$611$	12.9615	+	22.4499i	0.524365	+	0.908228i
$612$	38.2298	+	7.10533i	1.54535	+	0.287216i
$613$	−31.7490	−	18.3303i	−1.28233	−	0.740354i	−0.305057	−	0.952334i	$-0.598675\pi$
$613$	−31.7490	−	18.3303i	−1.28233	−	0.740354i	−0.977274	+	0.211980i	$0.932009\pi$
$614$		0			0
$615$	−12.9615	−	9.16515i	−0.522657	−	0.369575i
$616$		0			0
$617$		−	24.0416i		−	0.967880i	−0.875101	−	0.483940i	$-0.839205\pi$
$617$		−	24.0416i		−	0.967880i	0.875101	−	0.483940i	$-0.160795\pi$
$618$		0			0
$619$	9.50000	−	16.4545i	0.381837	−	0.661361i	−0.609488	−	0.792796i	$-0.708625\pi$
$619$	9.50000	−	16.4545i	0.381837	−	0.661361i	0.991325	+	0.131434i	$0.0419582\pi$
$620$	−2.44949	−	1.41421i	−0.0983739	−	0.0567962i
$621$	28.4949	−	7.21393i	1.14346	−	0.289485i
$622$		0			0
$623$	35.6441	+	20.5791i	1.42805	+	0.824485i
$624$	−25.9230	−	18.3303i	−1.03775	−	0.733799i
$625$	0.500000	+	0.866025i	0.0200000	+	0.0346410i
$626$		0			0
$627$	25.7083	−	5.66438i	1.02669	−	0.226214i
$628$	8.00000	+	13.8564i	0.319235	+	0.552931i
$629$	45.3652			1.80883
$630$		0			0
$631$	14.0000			0.557331			0.278666	−	0.960388i	$-0.410108\pi$
$631$	14.0000			0.557331			0.278666	+	0.960388i	$0.410108\pi$
$632$		0			0
$633$	28.8360	−	13.2848i	1.14613	−	0.528023i
$634$		0			0
$635$	−9.72111	−	16.8375i	−0.385771	−	0.668174i
$636$	−20.0000	−	14.1421i	−0.793052	−	0.560772i
$637$	−27.7804	−	16.0390i	−1.10070	−	0.635489i
$638$		0			0
$639$	−3.22474	−	2.75699i	−0.127569	−	0.109065i
$640$		0			0
$641$	−34.2929	−	19.7990i	−1.35449	−	0.782013i	−0.365612	−	0.930767i	$-0.619140\pi$
$641$	−34.2929	−	19.7990i	−1.35449	−	0.782013i	−0.988874	+	0.148754i	$0.952474\pi$
$642$		0			0
$643$	−25.0000			−0.985904			−0.492952	−	0.870057i	$-0.664082\pi$
$643$	−25.0000			−0.985904			−0.492952	+	0.870057i	$0.664082\pi$
$644$	−25.9230	+	14.9666i	−1.02151	+	0.589768i
$645$	−6.48074	+	9.16515i	−0.255179	+	0.360877i
$646$		0			0
$647$	−19.5959	−	11.3137i	−0.770395	−	0.444788i	0.0626205	−	0.998037i	$-0.480054\pi$
$647$	−19.5959	−	11.3137i	−0.770395	−	0.444788i	−0.833016	+	0.553250i	$0.813388\pi$
$648$		0			0
$649$	−8.93725	+	2.85052i	−0.350818	+	0.111893i
$650$		0			0
$651$	1.91749	+	4.16212i	0.0751525	+	0.163126i
$652$	−4.00000			−0.156652
$653$	−20.8207	+	12.0208i	−0.814775	+	0.470411i	−0.848612	−	0.529017i	$-0.822561\pi$
$653$	−20.8207	+	12.0208i	−0.814775	+	0.470411i	0.0338360	+	0.999427i	$0.489228\pi$
$654$		0			0
$655$	7.93725	+	4.58258i	0.310134	+	0.179056i
$656$	−12.9615	−	22.4499i	−0.506061	−	0.876523i
$657$	−12.9615	+	4.58258i	−0.505676	+	0.178783i
$658$		0			0
$659$	−45.3652			−1.76718			−0.883588	−	0.468264i	$-0.844879\pi$
$659$	−45.3652			−1.76718			−0.883588	+	0.468264i	$0.844879\pi$
$660$	4.90600	−	15.4897i	0.190966	−	0.602936i
$661$	18.5000	−	32.0429i	0.719567	−	1.24633i	−0.241605	−	0.970375i	$-0.577674\pi$
$661$	18.5000	−	32.0429i	0.719567	−	1.24633i	0.961172	−	0.275951i	$-0.0889928\pi$
$662$		0			0
$663$	4.71964	−	51.2223i	0.183296	−	1.98931i
$664$		0			0
$665$	−17.1464			−0.664910
$666$		0			0
$667$	−31.7490	+	18.3303i	−1.22933	+	0.709752i
$668$	−12.9615	+	22.4499i	−0.501495	+	0.868614i
$669$	2.89898	+	6.29253i	0.112081	+	0.243283i
$670$		0			0
$671$		0			0
$672$		0			0
$673$		−	4.58258i		−	0.176645i	−0.996092	−	0.0883227i	$-0.971849\pi$
$673$		−	4.58258i		−	0.176645i	0.996092	−	0.0883227i	$-0.0281507\pi$
$674$		0			0
$675$	−11.1742	+	10.8691i	−0.430096	+	0.418350i
$676$	−8.00000	+	13.8564i	−0.307692	+	0.532939i
$677$	19.4422	+	33.6749i	0.747225	+	1.29423i	0.949148	+	0.314831i	$0.101948\pi$
$677$	19.4422	+	33.6749i	0.747225	+	1.29423i	−0.201923	+	0.979401i	$0.564719\pi$
$678$		0			0
$679$	−10.5830	−	18.3303i	−0.406138	−	0.703452i
$680$		0			0
$681$	−22.3552	−	2.05982i	−0.856655	−	0.0789325i
$682$		0			0
$683$	17.1464	+	9.89949i	0.656090	+	0.378794i	0.790785	−	0.612093i	$-0.209672\pi$
$683$	17.1464	+	9.89949i	0.656090	+	0.378794i	−0.134696	+	0.990887i	$0.543006\pi$
$684$	20.8987	+	17.8674i	0.799083	+	0.683176i
$685$	−14.0000			−0.534913
$686$		0			0
$687$	−11.0000	+	15.5563i	−0.419676	+	0.593512i
$688$	−15.8745	+	9.16515i	−0.605210	+	0.349418i
$689$	−16.2019	+	28.0624i	−0.617241	+	1.06909i
$690$		0			0
$691$	−23.5000	−	40.7032i	−0.893982	−	1.54842i	−0.835059	−	0.550160i	$-0.814567\pi$
$691$	−23.5000	−	40.7032i	−0.893982	−	1.54842i	−0.0589228	−	0.998263i	$-0.518767\pi$
$692$	38.8844			1.47816
$693$	−20.9793	+	15.9018i	−0.796939	+	0.604060i
$694$		0			0
$695$	3.24037	+	5.61249i	0.122914	+	0.212894i
$696$		0			0
$697$	21.0000	−	36.3731i	0.795432	−	1.37773i
$698$		0			0
$699$	−6.48074	+	9.16515i	−0.245124	+	0.346658i
$700$	7.93725	−	13.7477i	0.300000	−	0.519615i
$701$	−19.4422			−0.734323			−0.367161	−	0.930157i	$-0.619670\pi$
$701$	−19.4422			−0.734323			−0.367161	+	0.930157i	$0.619670\pi$
$702$		0			0
$703$	27.7804	+	16.0390i	1.04776	+	0.604923i
$704$	17.8605	−	19.6215i	0.673141	−	0.739514i
$705$	−13.7980	−	1.27135i	−0.519661	−	0.0478818i
$706$		0			0
$707$	−34.2929			−1.28972
$708$	−8.00000	−	5.65685i	−0.300658	−	0.212598i
$709$	8.00000	+	13.8564i	0.300446	+	0.520388i	0.976237	−	0.216705i	$-0.0695310\pi$
$709$	8.00000	+	13.8564i	0.300446	+	0.520388i	−0.675791	+	0.737093i	$0.736198\pi$
$710$		0			0
$711$	7.53634	−	40.5488i	0.282635	−	1.52070i
$712$		0			0
$713$		−	5.65685i		−	0.211851i
$714$		0			0
$715$	−21.0000	−	4.58258i	−0.785355	−	0.171379i
$716$	−31.8434	+	18.3848i	−1.19004	+	0.687071i
$717$	−4.69688	−	10.1951i	−0.175408	−	0.380742i
$718$		0			0
$719$	−39.1918	+	22.6274i	−1.46161	+	0.843860i	−0.999086	−	0.0427471i	$-0.986389\pi$
$719$	−39.1918	+	22.6274i	−1.46161	+	0.843860i	−0.462523	+	0.886607i	$0.653056\pi$
$720$	16.0000	−	5.65685i	0.596285	−	0.210819i
$721$	−6.61438	+	11.4564i	−0.246332	+	0.426660i
$722$		0			0
$723$	−2.91303	+	31.6151i	−0.108337	+	1.17578i
$724$	−13.0000	+	22.5167i	−0.483141	+	0.836825i
$725$	9.72111	−	16.8375i	0.361033	−	0.625328i
$726$		0			0
$727$	−1.00000			−0.0370879			−0.0185440	−	0.999828i	$-0.505903\pi$
$727$	−1.00000			−0.0370879			−0.0185440	+	0.999828i	$0.505903\pi$
$728$		0			0
$729$	23.0000	+	14.1421i	0.851852	+	0.523783i
$730$		0			0
$731$	−25.7196	−	14.8492i	−0.951275	−	0.549219i
$732$		0			0
$733$	43.6549	−	25.2042i	1.61243	−	0.930937i	0.623625	−	0.781723i	$-0.285659\pi$
$733$	43.6549	−	25.2042i	1.61243	−	0.930937i	0.988805	−	0.149214i	$-0.0476743\pi$
$734$		0			0
$735$	15.5732	−	7.17461i	0.574427	−	0.264639i
$736$		0			0
$737$	1.00781	+	3.15980i	0.0371233	+	0.116393i
$738$		0			0
$739$	27.7804	+	16.0390i	1.02192	+	0.590005i	0.914659	−	0.404226i	$-0.132459\pi$
$739$	27.7804	+	16.0390i	1.02192	+	0.590005i	0.107259	+	0.994231i	$0.465793\pi$
$740$	17.1464	−	9.89949i	0.630315	−	0.363913i
$741$	21.0000	−	29.6985i	0.771454	−	1.09100i
$742$		0			0
$743$	−32.4037			−1.18878			−0.594388	−	0.804178i	$-0.702606\pi$
$743$	−32.4037			−1.18878			−0.594388	+	0.804178i	$0.702606\pi$
$744$		0			0
$745$	7.93725	+	4.58258i	0.290798	+	0.167893i
$746$		0			0
$747$	12.6341	−	14.7776i	0.462259	−	0.540685i
$748$	42.0000	+	9.16515i	1.53567	+	0.335111i
$749$	17.1464	−	29.6985i	0.626517	−	1.08516i
$750$		0			0
$751$	−2.50000	−	4.33013i	−0.0912263	−	0.158009i	0.816801	−	0.576919i	$-0.195745\pi$
$751$	−2.50000	−	4.33013i	−0.0912263	−	0.158009i	−0.908027	+	0.418911i	$0.862412\pi$
$752$	−19.5959	−	11.3137i	−0.714590	−	0.412568i
$753$	−11.1237	+	5.12472i	−0.405371	+	0.186755i
$754$		0			0
$755$	12.9615			0.471717
$756$	−26.4575	−	7.48331i	−0.962250	−	0.272166i
$757$	32.0000			1.16306			0.581530	−	0.813525i	$-0.302454\pi$
$757$	32.0000			1.16306			0.581530	+	0.813525i	$0.302454\pi$
$758$		0			0
$759$	31.7350	−	6.99226i	1.15191	−	0.253803i
$760$		0			0
$761$	3.24037	+	5.61249i	0.117463	+	0.203452i	0.918762	−	0.394812i	$-0.129190\pi$
$761$	3.24037	+	5.61249i	0.117463	+	0.203452i	−0.801298	+	0.598265i	$0.795857\pi$
$762$		0			0
$763$		−	12.1244i		−	0.438931i
$764$			39.5980i			1.43260i
$765$	20.8987	+	17.8674i	0.755595	+	0.645996i
$766$		0			0
$767$	−6.48074	+	11.2250i	−0.234006	+	0.405310i
$768$	27.5959	+	2.54270i	0.995782	+	0.0917517i
$769$			32.0780i			1.15676i	0.815766	+	0.578382i	$0.196316\pi$
$769$			32.0780i			1.15676i	−0.815766	+	0.578382i	$0.803684\pi$
$770$		0			0
$771$	−26.0000	−	18.3848i	−0.936367	−	0.662112i
$772$	−23.8118	+	13.7477i	−0.857004	+	0.494792i
$773$	46.5403	+	26.8701i	1.67394	+	0.966449i	0.965399	+	0.260778i	$0.0839790\pi$
$773$	46.5403	+	26.8701i	1.67394	+	0.966449i	0.708540	+	0.705671i	$0.249354\pi$
$774$		0			0
$775$	1.50000	+	2.59808i	0.0538816	+	0.0933257i
$776$		0			0
$777$	−31.9427	−	2.94321i	−1.14594	−	0.105587i
$778$		0			0
$779$	25.7196	−	14.8492i	0.921502	−	0.532029i
$780$	−9.39377	−	20.3901i	−0.336351	−	0.730084i
$781$	−3.46863	−	3.15731i	−0.124117	−	0.112978i
$782$		0			0
$783$	−32.4037	−	9.16515i	−1.15801	−	0.327536i
$784$	28.0000			1.00000
$785$			11.3137i			0.403804i
$786$		0			0
$787$	−23.8118	−	13.7477i	−0.848798	−	0.490054i	0.0114473	−	0.999934i	$-0.496356\pi$
$787$	−23.8118	−	13.7477i	−0.848798	−	0.490054i	−0.860245	+	0.509881i	$0.829689\pi$
$788$		0			0
$789$	11.1776	+	1.02991i	0.397934	+	0.0366658i
$790$		0			0
$791$	32.4037	−	18.7083i	1.15214	−	0.665190i
$792$		0			0
$793$		0			0
$794$		0			0
$795$	−7.24745	−	15.7313i	−0.257041	−	0.557932i
$796$	2.00000	+	3.46410i	0.0708881	+	0.122782i
$797$		−	11.3137i		−	0.400752i	−0.979719	−	0.200376i	$-0.935784\pi$
$797$		−	11.3137i		−	0.400752i	0.979719	−	0.200376i	$-0.0642164\pi$
$798$		0			0
$799$		−	36.6606i		−	1.29696i
$800$		0			0
$801$	8.52781	−	45.8833i	0.301315	−	1.62121i
$802$		0			0
$803$	−14.4800	+	4.61838i	−0.510988	+	0.162979i
$804$	−2.00000	+	2.82843i	−0.0705346	+	0.0997509i
$805$	−21.1660			−0.746004
$806$		0			0
$807$	−0.898979	+	9.75663i	−0.0316456	+	0.343450i
$808$		0			0
$809$	−6.48074	+	11.2250i	−0.227851	+	0.394649i	−0.957171	−	0.289524i	$-0.906503\pi$
$809$	−6.48074	+	11.2250i	−0.227851	+	0.394649i	0.729320	+	0.684173i	$0.239836\pi$
$810$		0			0
$811$		−	27.4955i		−	0.965496i	−0.875759	−	0.482748i	$-0.839639\pi$
$811$		−	27.4955i		−	0.965496i	0.875759	−	0.482748i	$-0.160361\pi$
$812$	34.2929			1.20344
$813$	12.9615	+	9.16515i	0.454579	+	0.321436i
$814$		0			0
$815$	−2.44949	−	1.41421i	−0.0858019	−	0.0495377i
$816$	18.7875	+	40.7802i	0.657695	+	1.42759i
$817$	−10.5000	−	18.1865i	−0.367348	−	0.636266i
$818$		0			0
$819$	−6.64643	+	35.7607i	−0.232245	+	1.24958i
$820$		−	18.3303i		−	0.640122i
$821$	−9.72111	−	16.8375i	−0.339269	−	0.587631i	0.645026	−	0.764160i	$-0.276846\pi$
$821$	−9.72111	−	16.8375i	−0.339269	−	0.587631i	−0.984295	+	0.176529i	$0.943513\pi$
$822$		0			0
$823$	−7.00000	+	12.1244i	−0.244005	+	0.422628i	−0.961851	−	0.273573i	$-0.911795\pi$
$823$	−7.00000	+	12.1244i	−0.244005	+	0.422628i	0.717847	+	0.696201i	$0.245128\pi$
$824$		0			0
$825$	−12.7211	+	11.6264i	−0.442892	+	0.404780i
$826$		0			0
$827$	−38.8844			−1.35214			−0.676072	−	0.736835i	$-0.736319\pi$
$827$	−38.8844			−1.35214			−0.676072	+	0.736835i	$0.736319\pi$
$828$	25.7980	+	22.0560i	0.896541	+	0.766498i
$829$	−23.5000	+	40.7032i	−0.816189	+	1.41368i	0.0922825	+	0.995733i	$0.470584\pi$
$829$	−23.5000	+	40.7032i	−0.816189	+	1.41368i	−0.908471	+	0.417947i	$0.862750\pi$
$830$		0			0
$831$	3.64128	−	39.5189i	0.126315	−	1.37089i
$832$		−	36.6606i		−	1.27098i
$833$	22.6826	+	39.2874i	0.785905	+	1.36123i
$834$		0			0
$835$	−15.8745	+	9.16515i	−0.549360	+	0.317173i
$836$	22.4793	+	20.4617i	0.777462	+	0.707684i
$837$	3.72474	−	3.62302i	0.128746	−	0.125230i
$838$		0			0
$839$			1.41421i			0.0488241i	0.999702	+	0.0244120i	$0.00777136\pi$
$839$			1.41421i			0.0488241i	−0.999702	+	0.0244120i	$0.992229\pi$
$840$		0			0
$841$	13.0000			0.448276
$842$		0			0
$843$	−9.39377	−	20.3901i	−0.323539	−	0.702273i
$844$	31.7490	+	18.3303i	1.09285	+	0.630955i
$845$	−9.79796	+	5.65685i	−0.337060	+	0.194602i
$846$		0			0
$847$	−23.7288	+	16.8507i	−0.815330	+	0.578997i
$848$		−	28.2843i		−	0.971286i
$849$	−2.18477	+	23.7113i	−0.0749811	+	0.813770i
$850$		0			0
$851$	34.2929	+	19.7990i	1.17554	+	0.678701i
$852$	0.449490	−	4.87832i	0.0153993	−	0.167128i
$853$			22.9129i			0.784522i	0.919854	+	0.392261i	$0.128307\pi$
$853$			22.9129i			0.784522i	−0.919854	+	0.392261i	$0.871693\pi$
$854$		0			0
$855$	6.48074	+	18.3303i	0.221637	+	0.626883i
$856$		0			0
$857$	25.9230	−	44.8999i	0.885512	−	1.53375i	0.0403853	−	0.999184i	$-0.487141\pi$
$857$	25.9230	−	44.8999i	0.885512	−	1.53375i	0.845126	−	0.534567i	$-0.179525\pi$
$858$		0			0
$859$	20.0000	+	34.6410i	0.682391	+	1.18194i	0.974249	+	0.225475i	$0.0723932\pi$
$859$	20.0000	+	34.6410i	0.682391	+	1.18194i	−0.291858	+	0.956462i	$0.594273\pi$
$860$	−12.9615			−0.441983
$861$	−17.1464	+	24.2487i	−0.584349	+	0.826394i
$862$		0			0
$863$	8.57321	−	4.94975i	0.291836	−	0.168491i	−0.346934	−	0.937890i	$-0.612777\pi$
$863$	8.57321	−	4.94975i	0.291836	−	0.168491i	0.638769	+	0.769398i	$0.279444\pi$
$864$		0			0
$865$	23.8118	+	13.7477i	0.809624	+	0.467437i
$866$		0			0
$867$	−25.0000	+	35.3553i	−0.849045	+	1.20073i
$868$	−2.64575	+	4.58258i	−0.0898027	+	0.155543i
$869$	9.72111	−	44.5477i	0.329766	−	1.51118i
$870$		0			0
$871$	3.96863	+	2.29129i	0.134472	+	0.0776373i
$872$		0			0
$873$	−15.5959	+	18.2419i	−0.527842	+	0.617395i
$874$		0			0
$875$	25.9230	−	14.9666i	0.876356	−	0.505964i
$876$	−12.9615	−	9.16515i	−0.437928	−	0.309662i
$877$	−15.8745	+	9.16515i	−0.536044	+	0.309485i	−0.743474	−	0.668765i	$-0.766823\pi$
$877$	−15.8745	+	9.16515i	−0.536044	+	0.309485i	0.207430	+	0.978250i	$0.433490\pi$
$878$		0			0
$879$	9.39377	+	20.3901i	0.316844	+	0.687742i
$880$	17.8745	−	5.70105i	0.602550	−	0.192182i
$881$			52.3259i			1.76290i	0.472273	+	0.881452i	$0.343434\pi$
$881$			52.3259i			1.76290i	−0.472273	+	0.881452i	$0.656566\pi$
$882$		0			0
$883$	−49.0000			−1.64898			−0.824491	−	0.565876i	$-0.808538\pi$
$883$	−49.0000			−1.64898			−0.824491	+	0.565876i	$0.808538\pi$
$884$	51.4393	−	29.6985i	1.73009	−	0.998868i
$885$	−2.89898	−	6.29253i	−0.0974481	−	0.211521i
$886$		0			0
$887$	−6.48074	−	11.2250i	−0.217602	−	0.376898i	0.736472	−	0.676468i	$-0.236490\pi$
$887$	−6.48074	−	11.2250i	−0.217602	−	0.376898i	−0.954074	+	0.299570i	$0.903157\pi$
$888$		0			0
$889$	−31.5000	+	18.1865i	−1.05648	+	0.609957i
$890$		0			0
$891$	24.9292	+	16.4175i	0.835160	+	0.550008i
$892$	−4.00000	+	6.92820i	−0.133930	+	0.231973i
$893$	12.9615	−	22.4499i	0.433739	−	0.751259i
$894$		0			0
$895$	−26.0000			−0.869084
$896$		0			0
$897$	25.9230	−	36.6606i	0.865543	−	1.22406i
$898$		0			0
$899$	−3.24037	+	5.61249i	−0.108072	+	0.187187i
$900$	−17.6969	−	3.28913i	−0.589898	−	0.109638i
$901$	39.6863	−	22.9129i	1.32214	−	0.763339i
$902$		0			0
$903$	17.1464	+	12.1244i	0.570597	+	0.403473i
$904$		0			0
$905$	−15.9217	+	9.19239i	−0.529255	+	0.305565i
$906$		0			0
$907$	−20.5000	+	35.5070i	−0.680691	+	1.17899i	0.294079	+	0.955781i	$0.404987\pi$
$907$	−20.5000	+	35.5070i	−0.680691	+	1.17899i	−0.974770	+	0.223211i	$0.928346\pi$
$908$	−12.9615	−	22.4499i	−0.430142	−	0.745028i
$909$	12.9615	+	36.6606i	0.429905	+	1.21596i
$910$		0			0
$911$			48.0833i			1.59307i	0.604593	+	0.796535i	$0.293336\pi$
$911$			48.0833i			1.59307i	−0.604593	+	0.796535i	$0.706664\pi$
$912$	−2.91303	+	31.6151i	−0.0964599	+	1.04688i
$913$	14.4686	−	15.8952i	0.478842	−	0.526056i
$914$		0			0
$915$		0			0
$916$	−22.0000			−0.726900
$917$	8.57321	−	14.8492i	0.283112	−	0.490365i
$918$		0			0
$919$	−43.6549	+	25.2042i	−1.44004	+	0.831409i	−0.997852	−	0.0655125i	$-0.979132\pi$
$919$	−43.6549	+	25.2042i	−1.44004	+	0.831409i	−0.442190	+	0.896921i	$0.645798\pi$
$920$		0			0
$921$	−21.6270	+	9.96359i	−0.712634	+	0.328312i
$922$		0			0
$923$	−6.48074			−0.213316
$924$	−28.9786	−	9.17829i	−0.953326	−	0.301944i
$925$	−21.0000			−0.690476
$926$		0			0
$927$	14.7474	+	2.74094i	0.484370	+	0.0900243i
$928$		0			0
$929$	37.9671	−	21.9203i	1.24566	−	0.719182i	0.275419	−	0.961324i	$-0.411183\pi$
$929$	37.9671	−	21.9203i	1.24566	−	0.719182i	0.970241	+	0.242142i	$0.0778501\pi$
$930$		0			0
$931$			32.0780i			1.05131i
$932$	−12.9615			−0.424567
$933$	2.47219	−	26.8307i	0.0809360	−	0.878399i
$934$		0			0
$935$	22.4793	+	20.4617i	0.735151	+	0.669170i
$936$		0			0
$937$			13.7477i			0.449119i	0.974460	+	0.224559i	$0.0720943\pi$
$937$			13.7477i			0.449119i	−0.974460	+	0.224559i	$0.927906\pi$
$938$		0			0
$939$	−17.0000	+	24.0416i	−0.554774	+	0.784569i
$940$	−8.00000	−	13.8564i	−0.260931	−	0.451946i
$941$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$941$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$942$		0			0
$943$	31.7490	−	18.3303i	1.03389	−	0.596917i
$944$		−	11.3137i		−	0.368230i
$945$	−13.5561	−	13.9367i	−0.440980	−	0.453362i
$946$		0			0
$947$	−17.1464	+	9.89949i	−0.557184	+	0.321690i	−0.752014	−	0.659147i	$-0.770918\pi$
$947$	−17.1464	+	9.89949i	−0.557184	+	0.321690i	0.194830	+	0.980837i	$0.437584\pi$
$948$	43.2540	−	19.9272i	1.40482	−	0.647205i
$949$	−10.5000	+	18.1865i	−0.340844	+	0.590360i
$950$		0			0
$951$	−14.0000	−	9.89949i	−0.453981	−	0.321013i
$952$		0			0
$953$	−19.4422			−0.629795			−0.314898	−	0.949126i	$-0.601970\pi$
$953$	−19.4422			−0.629795			−0.314898	+	0.949126i	$0.601970\pi$
$954$		0			0
$955$	−14.0000	+	24.2487i	−0.453029	+	0.784670i
$956$	6.48074	−	11.2250i	0.209602	−	0.363042i
$957$	−35.4914	−	11.2411i	−1.14727	−	0.363372i
$958$		0			0
$959$			26.1916i			0.845771i
$960$	16.0000	+	11.3137i	0.516398	+	0.365148i
$961$	15.0000	+	25.9808i	0.483871	+	0.838089i
$962$		0			0
$963$	−38.2298	−	7.10533i	−1.23194	−	0.228966i
$964$	−31.7490	+	18.3303i	−1.02257	+	0.590379i
$965$	−19.4422			−0.625867
$966$		0			0
$967$			4.58258i			0.147366i	0.997282	+	0.0736828i	$0.0234753\pi$
$967$			4.58258i			0.147366i	−0.997282	+	0.0736828i	$0.976525\pi$
$968$		0			0
$969$	−46.7196	+	21.5238i	−1.50085	+	0.691445i
$970$		0			0
$971$	41.6413	−	24.0416i	1.33633	−	0.771533i	0.350072	−	0.936723i	$-0.386157\pi$
$971$	41.6413	−	24.0416i	1.33633	−	0.771533i	0.986262	+	0.165190i	$0.0528238\pi$
$972$	2.00000	+	31.1127i	0.0641500	+	0.997940i
$973$	10.5000	−	6.06218i	0.336615	−	0.194344i
$974$		0			0
$975$	−2.18477	+	23.7113i	−0.0699686	+	0.759370i
$976$		0			0
$977$	−45.3156	−	26.1630i	−1.44977	−	0.837027i	−0.451306	−	0.892369i	$-0.649042\pi$
$977$	−45.3156	−	26.1630i	−1.44977	−	0.837027i	−0.998467	+	0.0553424i	$0.982375\pi$
$978$		0			0
$979$	11.0000	−	50.4083i	0.351562	−	1.61106i
$980$	17.1464	+	9.89949i	0.547723	+	0.316228i
$981$	−12.9615	+	4.58258i	−0.413828	+	0.146310i
$982$		0			0
$983$	13.4722	+	7.77817i	0.429696	+	0.248085i	0.699217	−	0.714909i	$-0.253532\pi$
$983$	13.4722	+	7.77817i	0.429696	+	0.248085i	−0.269521	+	0.962995i	$0.586865\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−2.37848	+	25.8136i	−0.0757077	+	0.821656i
$988$	42.0000			1.33620
$989$	−12.9615	−	22.4499i	−0.412151	−	0.713867i
$990$		0			0
$991$	27.5000	−	47.6314i	0.873566	−	1.51306i	0.0152841	−	0.999883i	$-0.495135\pi$
$991$	27.5000	−	47.6314i	0.873566	−	1.51306i	0.858282	−	0.513178i	$-0.171532\pi$
$992$		0			0
$993$	7.00000	−	9.89949i	0.222138	−	0.314151i
$994$		0			0
$995$			2.82843i			0.0896672i
$996$	22.3552	+	2.05982i	0.708353	+	0.0652679i
$997$	19.8431	+	11.4564i	0.628438	+	0.362829i	0.780147	−	0.625596i	$-0.215144\pi$
$997$	19.8431	+	11.4564i	0.628438	+	0.362829i	−0.151709	+	0.988425i	$0.548478\pi$
$998$		0			0
$999$	8.92679	+	35.2606i	0.282431	+	1.11560i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.l.a.32.1	✓	8
3.2	odd	2	inner	231.2.l.a.32.3	yes	8
7.2	even	3	inner	231.2.l.a.65.4	yes	8
11.10	odd	2	inner	231.2.l.a.32.2	yes	8
21.2	odd	6	inner	231.2.l.a.65.2	yes	8
33.32	even	2	inner	231.2.l.a.32.4	yes	8
77.65	odd	6	inner	231.2.l.a.65.3	yes	8
231.65	even	6	inner	231.2.l.a.65.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.l.a.32.1	✓	8	1.1	even	1	trivial
231.2.l.a.32.2	yes	8	11.10	odd	2	inner
231.2.l.a.32.3	yes	8	3.2	odd	2	inner
231.2.l.a.32.4	yes	8	33.32	even	2	inner
231.2.l.a.65.1	yes	8	231.65	even	6	inner
231.2.l.a.65.2	yes	8	21.2	odd	6	inner
231.2.l.a.65.3	yes	8	77.65	odd	6	inner
231.2.l.a.65.4	yes	8	7.2	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.724745 - 1.57313i) q^{3} +(1.00000 - 1.73205i) q^{4} +(1.22474 - 0.707107i) q^{5} +(-1.32288 - 2.29129i) q^{7} +(-1.94949 + 2.28024i) q^{9} +O(q^{10})\)	\(q+(-0.724745 - 1.57313i) q^{3} +(1.00000 - 1.73205i) q^{4} +(1.22474 - 0.707107i) q^{5} +(-1.32288 - 2.29129i) q^{7} +(-1.94949 + 2.28024i) q^{9} +(-2.23256 + 2.45269i) q^{11} +(-3.44949 - 0.317837i) q^{12} +4.58258i q^{13} +(-2.00000 - 1.41421i) q^{15} +(-2.00000 - 3.46410i) q^{16} +(3.24037 - 5.61249i) q^{17} +(3.96863 - 2.29129i) q^{19} -2.82843i q^{20} +(-2.64575 + 3.74166i) q^{21} +(4.89898 - 2.82843i) q^{23} +(-1.50000 + 2.59808i) q^{25} +(5.00000 + 1.41421i) q^{27} -5.29150 q^{28} -6.48074 q^{29} +(0.500000 - 0.866025i) q^{31} +(5.47644 + 1.73453i) q^{33} +(-3.24037 - 1.87083i) q^{35} +(2.00000 + 5.65685i) q^{36} +(3.50000 + 6.06218i) q^{37} +(7.20900 - 3.32120i) q^{39} +6.48074 q^{41} -4.58258i q^{43} +(2.01563 + 6.31959i) q^{44} +(-0.775255 + 4.17121i) q^{45} +(4.89898 - 2.82843i) q^{47} +(-4.00000 + 5.65685i) q^{48} +(-3.50000 + 6.06218i) q^{49} +(-11.1776 - 1.02991i) q^{51} +(7.93725 + 4.58258i) q^{52} +(6.12372 + 3.53553i) q^{53} +(-1.00000 + 4.58258i) q^{55} +(-6.48074 - 4.58258i) q^{57} +(2.44949 + 1.41421i) q^{59} +(-4.44949 + 2.04989i) q^{60} +(7.80362 + 1.45037i) q^{63} -8.00000 q^{64} +(3.24037 + 5.61249i) q^{65} +(0.500000 - 0.866025i) q^{67} +(-6.48074 - 11.2250i) q^{68} +(-8.00000 - 5.65685i) q^{69} +1.41421i q^{71} +(3.96863 + 2.29129i) q^{73} +(5.17423 + 0.476756i) q^{75} -9.16515i q^{76} +(8.57321 + 1.87083i) q^{77} +(-11.9059 + 6.87386i) q^{79} +(-4.89898 - 2.82843i) q^{80} +(-1.39898 - 8.89060i) q^{81} -6.48074 q^{83} +(3.83499 + 8.32423i) q^{84} -9.16515i q^{85} +(4.69688 + 10.1951i) q^{87} +(-13.4722 + 7.77817i) q^{89} +(10.5000 - 6.06218i) q^{91} -11.3137i q^{92} +(-1.72474 - 0.158919i) q^{93} +(3.24037 - 5.61249i) q^{95} +8.00000 q^{97} +(-1.24037 - 9.87226i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} + 8 q^{4} + 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^3 + 8 * q^4 + 4 * q^9	\( 8 q + 4 q^{3} + 8 q^{4} + 4 q^{9} - 8 q^{12} - 16 q^{15} - 16 q^{16} - 12 q^{25} + 40 q^{27} + 4 q^{31} + 4 q^{33} + 16 q^{36} + 28 q^{37} - 16 q^{45} - 32 q^{48} - 28 q^{49} - 8 q^{55} - 16 q^{60} - 64 q^{64} + 4 q^{67} - 64 q^{69} + 12 q^{75} + 28 q^{81} + 84 q^{91} - 4 q^{93} + 64 q^{97} + 16 q^{99}+O(q^{100}) \) 8 * q + 4 * q^3 + 8 * q^4 + 4 * q^9 - 8 * q^12 - 16 * q^15 - 16 * q^16 - 12 * q^25 + 40 * q^27 + 4 * q^31 + 4 * q^33 + 16 * q^36 + 28 * q^37 - 16 * q^45 - 32 * q^48 - 28 * q^49 - 8 * q^55 - 16 * q^60 - 64 * q^64 + 4 * q^67 - 64 * q^69 + 12 * q^75 + 28 * q^81 + 84 * q^91 - 4 * q^93 + 64 * q^97 + 16 * q^99

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