LMFDB - Embedded newform 231.2.l.a.32.4

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			32.4
Root			$-1.00781 - 0.581861i$ of defining polynomial
Character	$\chi$	$=$	231.32
Dual form			231.2.l.a.65.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.72474 - 0.158919i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-1.22474 + 0.707107i) q^{5} +(1.32288 + 2.29129i) q^{7} +(2.94949 - 0.548188i) q^{9} +O(q^{10})$	\(q+(1.72474 - 0.158919i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-1.22474 + 0.707107i) q^{5} +(1.32288 + 2.29129i) q^{7} +(2.94949 - 0.548188i) q^{9} +(-1.00781 + 3.15980i) q^{11} +(1.44949 - 3.14626i) q^{12} -4.58258i q^{13} +(-2.00000 + 1.41421i) q^{15} +(-2.00000 - 3.46410i) q^{16} +(3.24037 - 5.61249i) q^{17} +(-3.96863 + 2.29129i) q^{19} +2.82843i q^{20} +(2.64575 + 3.74166i) q^{21} +(-4.89898 + 2.82843i) q^{23} +(-1.50000 + 2.59808i) q^{25} +(5.00000 - 1.41421i) q^{27} +5.29150 q^{28} -6.48074 q^{29} +(0.500000 - 0.866025i) q^{31} +(-1.23607 + 5.61000i) q^{33} +(-3.24037 - 1.87083i) q^{35} +(2.00000 - 5.65685i) q^{36} +(3.50000 + 6.06218i) q^{37} +(-0.728257 - 7.90377i) q^{39} +6.48074 q^{41} +4.58258i q^{43} +(4.46512 + 4.90538i) q^{44} +(-3.22474 + 2.75699i) q^{45} +(-4.89898 + 2.82843i) q^{47} +(-4.00000 - 5.65685i) q^{48} +(-3.50000 + 6.06218i) q^{49} +(4.69688 - 10.1951i) q^{51} +(-7.93725 - 4.58258i) q^{52} +(-6.12372 - 3.53553i) q^{53} +(-1.00000 - 4.58258i) q^{55} +(-6.48074 + 4.58258i) q^{57} +(-2.44949 - 1.41421i) q^{59} +(0.449490 + 4.87832i) q^{60} +(5.15787 + 6.03295i) q^{63} -8.00000 q^{64} +(3.24037 + 5.61249i) q^{65} +(0.500000 - 0.866025i) q^{67} +(-6.48074 - 11.2250i) q^{68} +(-8.00000 + 5.65685i) q^{69} -1.41421i q^{71} +(-3.96863 - 2.29129i) q^{73} +(-2.17423 + 4.71940i) q^{75} +9.16515i q^{76} +(-8.57321 + 1.87083i) q^{77} +(11.9059 - 6.87386i) q^{79} +(4.89898 + 2.82843i) q^{80} +(8.39898 - 3.23375i) q^{81} -6.48074 q^{83} +(9.12649 - 0.840918i) q^{84} +9.16515i q^{85} +(-11.1776 + 1.02991i) q^{87} +(13.4722 - 7.77817i) q^{89} +(10.5000 - 6.06218i) q^{91} +11.3137i q^{92} +(0.724745 - 1.57313i) q^{93} +(3.24037 - 5.61249i) q^{95} +8.00000 q^{97} +(-1.24037 + 9.87226i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$0.833333\pi$
$3$	1.72474	−	0.158919i	0.995782	−	0.0917517i
$3$	1.72474	−	0.158919i	0.995782	−	0.0917517i
$4$	1.00000	−	1.73205i	0.500000	−	0.866025i
$5$	−1.22474	+	0.707107i	−0.547723	+	0.316228i	−0.748203	−	0.663470i	$-0.769083\pi$
$5$	−1.22474	+	0.707107i	−0.547723	+	0.316228i	0.200480	+	0.979698i	$0.435750\pi$
$6$		0			0
$7$	1.32288	+	2.29129i	0.500000	+	0.866025i
$7$	1.32288	+	2.29129i	0.500000	+	0.866025i
$8$		0			0
$9$	2.94949	−	0.548188i	0.983163	−	0.182729i
$10$		0			0
$11$	−1.00781	+	3.15980i	−0.303867	+	0.952714i
$11$	−1.00781	+	3.15980i	−0.303867	+	0.952714i
$12$	1.44949	−	3.14626i	0.418432	−	0.908248i
$13$		−	4.58258i		−	1.27098i	−0.772110	−	0.635489i	$-0.780799\pi$
$13$		−	4.58258i		−	1.27098i	0.772110	−	0.635489i	$-0.219201\pi$
$14$		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	−0.880581	−	0.473896i	$-0.842847\pi$
$19$	−3.96863	+	2.29129i	−0.910465	+	0.525657i	−0.0298846	+	0.999553i	$0.509514\pi$
$20$			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	−0.914540	−	0.404495i	$-0.867447\pi$
$23$	−4.89898	+	2.82843i	−1.02151	+	0.589768i	−0.106967	+	0.994263i	$0.534114\pi$
$24$		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
$33$	−1.23607	+	5.61000i	−0.215172	+	0.976576i
$34$		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
$39$	−0.728257	−	7.90377i	−0.116614	−	1.26562i
$40$		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	$0.113621\pi$
$43$			4.58258i			0.698836i	−0.936967	+	0.349418i	$0.886379\pi$
$44$	4.46512	+	4.90538i	0.673141	+	0.739514i
$45$	−3.22474	+	2.75699i	−0.480717	+	0.410989i
$46$		0			0
$47$	−4.89898	+	2.82843i	−0.714590	+	0.412568i	−0.812758	−	0.582601i	$-0.802035\pi$
$47$	−4.89898	+	2.82843i	−0.714590	+	0.412568i	0.0981685	+	0.995170i	$0.468702\pi$
$48$	−4.00000	−	5.65685i	−0.577350	−	0.816497i
$49$	−3.50000	+	6.06218i	−0.500000	+	0.866025i
$50$		0			0
$51$	4.69688	−	10.1951i	0.657695	−	1.42759i
$52$	−7.93725	−	4.58258i	−1.10070	−	0.635489i
$53$	−6.12372	−	3.53553i	−0.841158	−	0.485643i	0.0164995	−	0.999864i	$-0.494748\pi$
$53$	−6.12372	−	3.53553i	−0.841158	−	0.485643i	−0.857658	+	0.514221i	$0.828081\pi$
$54$		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	0.332004	−	0.943278i	$-0.392275\pi$
$59$	−2.44949	−	1.41421i	−0.318896	−	0.184115i	−0.650901	+	0.759163i	$0.725609\pi$
$60$	0.449490	+	4.87832i	0.0580289	+	0.629788i
$61$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$61$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$62$		0			0
$63$	5.15787	+	6.03295i	0.649830	+	0.760080i
$64$	−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	$-0.973257\pi$
$71$		−	1.41421i		−	0.167836i	0.996473	−	0.0839181i	$-0.0267434\pi$
$72$		0			0
$73$	−3.96863	−	2.29129i	−0.464493	−	0.268175i	0.249439	−	0.968391i	$-0.419754\pi$
$73$	−3.96863	−	2.29129i	−0.464493	−	0.268175i	−0.713931	+	0.700216i	$0.753087\pi$
$74$		0			0
$75$	−2.17423	+	4.71940i	−0.251059	+	0.544949i
$76$			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	0.352781	−	0.935706i	$-0.385236\pi$
$79$	11.9059	−	6.87386i	1.33952	−	0.773370i	0.986736	+	0.162336i	$0.0519028\pi$
$80$	4.89898	+	2.82843i	0.547723	+	0.316228i
$81$	8.39898	−	3.23375i	0.933220	−	0.359306i
$82$		0			0
$83$	−6.48074			−0.711354			−0.355677	−	0.934609i	$-0.615750\pi$
$83$	−6.48074			−0.711354			−0.355677	+	0.934609i	$0.615750\pi$
$84$	9.12649	−	0.840918i	0.995782	−	0.0917517i
$85$			9.16515i			0.994100i
$86$		0			0
$87$	−11.1776	+	1.02991i	−1.19837	+	0.110418i
$88$		0			0
$89$	13.4722	−	7.77817i	1.42805	−	0.824485i	0.431083	−	0.902312i	$-0.358132\pi$
$89$	13.4722	−	7.77817i	1.42805	−	0.824485i	0.996967	+	0.0778275i	$0.0247983\pi$
$90$		0			0
$91$	10.5000	−	6.06218i	1.10070	−	0.635489i
$92$			11.3137i			1.17954i
$93$	0.724745	−	1.57313i	0.0751525	−	0.163126i
$94$		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
$105$	−5.88612	−	2.71175i	−0.574427	−	0.264639i
$106$		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	$0.617813\pi$
$108$	2.55051	−	10.0745i	0.245423	−	0.969416i
$109$	−3.96863	−	2.29129i	−0.380126	−	0.219466i	0.297747	−	0.954645i	$-0.403765\pi$
$109$	−3.96863	−	2.29129i	−0.380126	−	0.219466i	−0.677873	+	0.735179i	$0.737098\pi$
$110$		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	$-0.768350\pi$
$113$		−	14.1421i		−	1.33038i	0.746674	−	0.665190i	$-0.231650\pi$
$114$		0			0
$115$	4.00000	−	6.92820i	0.373002	−	0.646058i
$116$	−6.48074	+	11.2250i	−0.601722	+	1.04221i
$117$	−2.51211	−	13.5163i	−0.232245	−	1.24958i
$118$		0			0
$119$	17.1464			1.57181
$120$		0			0
$121$	−8.96863	−	6.36897i	−0.815330	−	0.578997i
$122$		0			0
$123$	11.1776	−	1.02991i	1.00785	−	0.0928639i
$124$	−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	$0.208813\pi$
$127$			13.7477i			1.21991i	−0.792435	+	0.609957i	$0.791187\pi$
$128$		0			0
$129$	0.728257	+	7.90377i	0.0641194	+	0.695888i
$130$		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
$135$	−5.12372	+	5.26758i	−0.440980	+	0.453362i
$136$		0			0
$137$	8.57321	+	4.94975i	0.732459	+	0.422885i	0.819321	−	0.573335i	$-0.194351\pi$
$137$	8.57321	+	4.94975i	0.732459	+	0.422885i	−0.0868620	+	0.996220i	$0.527684\pi$
$138$		0			0
$139$		−	4.58258i		−	0.388689i	−0.980933	−	0.194344i	$-0.937742\pi$
$139$		−	4.58258i		−	0.388689i	0.980933	−	0.194344i	$-0.0622580\pi$
$140$	−6.48074	+	3.74166i	−0.547723	+	0.316228i
$141$	−8.00000	+	5.65685i	−0.673722	+	0.476393i
$142$		0			0
$143$	14.4800	+	4.61838i	1.21088	+	0.386208i
$144$	−7.79796	−	9.12096i	−0.649830	−	0.760080i
$145$	7.93725	−	4.58258i	0.659153	−	0.380562i
$146$		0			0
$147$	−5.07321	+	11.0119i	−0.418432	+	0.908248i
$148$	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	0.140969	−	0.990014i	$-0.454978\pi$
$151$	−7.93725	−	4.58258i	−0.645925	−	0.372925i	−0.786893	+	0.617089i	$0.788312\pi$
$152$		0			0
$153$	6.48074	−	18.3303i	0.523937	−	1.48192i
$154$		0			0
$155$			1.41421i			0.113592i
$156$	−14.4180	−	6.64240i	−1.15436	−	0.531817i
$157$	−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
$159$	−11.1237	−	5.12472i	−0.882169	−	0.406417i
$160$		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
$165$	−2.45300	−	7.74486i	−0.190966	−	0.602936i
$166$		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
$171$	−10.4494	+	8.93368i	−0.799083	+	0.683176i
$172$	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
$177$	−4.44949	−	2.04989i	−0.334444	−	0.154079i
$178$		0			0
$179$	15.9217	+	9.19239i	1.19004	+	0.687071i	0.958316	−	0.285710i	$-0.0922293\pi$
$179$	15.9217	+	9.19239i	1.19004	+	0.687071i	0.231726	+	0.972781i	$0.425563\pi$
$180$	1.55051	+	8.34242i	0.115568	+	0.621807i
$181$	−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
$187$	14.4686	+	15.8952i	1.05805	+	1.16238i
$188$			11.3137i			0.825137i
$189$	9.85475	+	9.58561i	0.716827	+	0.697251i
$190$		0			0
$191$	17.1464	−	9.89949i	1.24067	−	0.716302i	0.271441	−	0.962455i	$-0.412500\pi$
$191$	17.1464	−	9.89949i	1.24067	−	0.716302i	0.969231	+	0.246153i	$0.0791665\pi$
$192$	−13.7980	+	1.27135i	−0.995782	+	0.0917517i
$193$	11.9059	+	6.87386i	0.857004	+	0.494792i	0.863008	−	0.505190i	$-0.168578\pi$
$193$	11.9059	+	6.87386i	0.857004	+	0.494792i	−0.00600382	+	0.999982i	$0.501911\pi$
$194$		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
$201$	0.724745	−	1.57313i	0.0511196	−	0.110960i
$202$		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
$207$	−12.8990	+	11.0280i	−0.896541	+	0.766498i
$208$	−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	$-0.782663\pi$
$211$		−	18.3303i		−	1.26191i	0.775819	−	0.630955i	$-0.217337\pi$
$212$	−12.2474	+	7.07107i	−0.841158	+	0.485643i
$213$	−0.224745	−	2.43916i	−0.0153993	−	0.167128i
$214$		0			0
$215$	−3.24037	−	5.61249i	−0.220991	−	0.382768i
$216$		0			0
$217$	2.64575			0.179605
$218$		0			0
$219$	−7.20900	−	3.32120i	−0.487139	−	0.224426i
$220$	−8.93725	−	2.85052i	−0.602550	−	0.192182i
$221$	−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	$0.0251302\pi$
$228$	1.45651	+	15.8075i	0.0964599	+	1.04688i
$229$	−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
$231$	−14.4893	+	4.58915i	−0.953326	+	0.301944i
$232$		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	$0.432783\pi$
$240$	8.89898	+	4.09978i	0.574427	+	0.264639i
$241$	15.8745	+	9.16515i	1.02257	+	0.590379i	0.914846	−	0.403802i	$-0.132312\pi$
$241$	15.8745	+	9.16515i	1.02257	+	0.590379i	0.107721	+	0.994181i	$0.465645\pi$
$242$		0			0
$243$	13.9722	−	6.91215i	0.896317	−	0.443415i
$244$		0			0
$245$		−	9.89949i		−	0.632456i
$246$		0			0
$247$	10.5000	+	18.1865i	0.668099	+	1.15718i
$248$		0			0
$249$	−11.1776	+	1.02991i	−0.708353	+	0.0652679i
$250$		0			0
$251$			7.07107i			0.446322i	0.974782	+	0.223161i	$0.0716375\pi$
$251$			7.07107i			0.446322i	−0.974782	+	0.223161i	$0.928362\pi$
$252$	15.6072	−	2.90074i	0.983163	−	0.182729i
$253$	−4.00000	−	18.3303i	−0.251478	−	1.15242i
$254$		0			0
$255$	1.45651	+	15.8075i	0.0912104	+	0.989907i
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	−15.9217	+	9.19239i	−0.993167	+	0.573405i	−0.906220	−	0.422807i	$-0.861045\pi$
$257$	−15.9217	+	9.19239i	−0.993167	+	0.573405i	−0.0869478	+	0.996213i	$0.527711\pi$
$258$		0			0
$259$	−9.26013	+	16.0390i	−0.575396	+	0.996616i
$260$	12.9615			0.803837
$261$	−19.1149	+	3.55267i	−1.18318	+	0.219904i
$262$		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	0.641857	−	0.766824i	$-0.278164\pi$
$269$	4.89898	+	2.82843i	0.298696	+	0.172452i	−0.343161	+	0.939277i	$0.611498\pi$
$270$		0			0
$271$	7.93725	−	4.58258i	0.482154	−	0.278372i	−0.239160	−	0.970980i	$-0.576872\pi$
$271$	7.93725	−	4.58258i	0.482154	−	0.278372i	0.721314	+	0.692609i	$0.243539\pi$
$272$	−25.9230			−1.57181
$273$	17.1464	−	12.1244i	1.03775	−	0.733799i
$274$		0			0
$275$	−6.69767	−	7.35807i	−0.403885	−	0.443708i
$276$	1.79796	+	19.5133i	0.108224	+	1.17456i
$277$	−19.8431	−	11.4564i	−1.19226	−	0.688351i	−0.233440	−	0.972371i	$-0.574998\pi$
$277$	−19.8431	−	11.4564i	−1.19226	−	0.688351i	−0.958818	+	0.284020i	$0.908332\pi$
$278$		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	0.810220	−	0.586125i	$-0.199347\pi$
$283$	11.9059	+	6.87386i	0.707731	+	0.408609i	−0.102489	+	0.994734i	$0.532681\pi$
$284$	−2.44949	−	1.41421i	−0.145350	−	0.0839181i
$285$	4.69688	−	10.1951i	0.278219	−	0.603903i
$286$		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
$291$	13.7980	−	1.27135i	0.808851	−	0.0745278i
$292$	−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
$297$	−0.570437	+	17.2242i	−0.0331001	+	0.999452i
$298$		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
$303$	9.39377	−	20.3901i	0.539658	−	1.17138i
$304$	15.8745	+	9.16515i	0.910465	+	0.525657i
$305$		0			0
$306$		0			0
$307$			13.7477i			0.784624i	0.919832	+	0.392312i	$0.128325\pi$
$307$			13.7477i			0.784624i	−0.919832	+	0.392312i	$0.871675\pi$
$308$	−5.33284	+	16.7201i	−0.303867	+	0.952714i
$309$	−5.00000	−	7.07107i	−0.284440	−	0.402259i
$310$		0			0
$311$	−13.4722	−	7.77817i	−0.763938	−	0.441060i	0.0667698	−	0.997768i	$-0.478731\pi$
$311$	−13.4722	−	7.77817i	−0.763938	−	0.441060i	−0.830708	+	0.556709i	$0.812064\pi$
$312$		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	−0.721050	−	0.692883i	$-0.756340\pi$
$317$	−8.57321	+	4.94975i	−0.481520	+	0.278006i	0.239530	+	0.970889i	$0.423007\pi$
$318$		0			0
$319$	6.53137	−	20.4778i	0.365687	−	1.14654i
$320$	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
$324$	2.79796	−	17.7812i	0.155442	−	0.987845i
$325$	11.9059	+	6.87386i	0.660419	+	0.381293i
$326$		0			0
$327$	−7.20900	−	3.32120i	−0.398658	−	0.183663i
$328$		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
$333$	13.6464	+	15.9617i	0.747820	+	0.874694i
$334$		0			0
$335$			1.41421i			0.0772667i
$336$	7.66998	−	16.6485i	0.418432	−	0.908248i
$337$		−	4.58258i		−	0.249629i	−0.992180	−	0.124814i	$-0.960166\pi$
$337$		−	4.58258i		−	0.249629i	0.992180	−	0.124814i	$-0.0398335\pi$
$338$		0			0
$339$	−2.24745	−	24.3916i	−0.122065	−	1.32477i
$340$	15.8745	+	9.16515i	0.860916	+	0.497050i
$341$	2.23256	+	2.45269i	0.120900	+	0.132821i
$342$		0			0
$343$	−18.5203			−1.00000
$344$		0			0
$345$	5.79796	−	12.5851i	0.312152	−	0.677557i
$346$		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	$-0.00809372\pi$
$348$	−9.39377	+	20.3901i	−0.503559	+	1.09303i
$349$		−	9.16515i		−	0.490599i	−0.969447	−	0.245300i	$-0.921114\pi$
$349$		−	9.16515i		−	0.490599i	0.969447	−	0.245300i	$-0.0788863\pi$
$350$		0			0
$351$	−6.48074	−	22.9129i	−0.345916	−	1.22300i
$352$		0			0
$353$	12.2474	+	7.07107i	0.651866	+	0.376355i	0.789171	−	0.614174i	$-0.210511\pi$
$353$	12.2474	+	7.07107i	0.651866	+	0.376355i	−0.137305	+	0.990529i	$0.543844\pi$
$354$		0			0
$355$	1.00000	+	1.73205i	0.0530745	+	0.0919277i
$356$		−	31.1127i		−	1.64897i
$357$	29.5732	−	2.72489i	1.56518	−	0.144216i
$358$		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
$369$	19.1149	−	3.55267i	0.995081	−	0.184944i
$370$		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	−0.393725	−	0.919228i	$-0.628814\pi$
$373$	3.96863	−	2.29129i	0.205488	−	0.118638i	0.599213	+	0.800590i	$0.295480\pi$
$374$		0			0
$375$	−1.79796	−	19.5133i	−0.0928462	−	1.00766i
$376$		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
$381$	2.18477	+	23.7113i	0.111929	+	1.21477i
$382$		0			0
$383$	−1.22474	+	0.707107i	−0.0625815	+	0.0361315i	−0.530964	−	0.847394i	$-0.678170\pi$
$383$	−1.22474	+	0.707107i	−0.0625815	+	0.0361315i	0.468383	+	0.883526i	$0.344837\pi$
$384$		0			0
$385$	9.17712	−	8.35347i	0.467710	−	0.425732i
$386$		0			0
$387$	2.51211	+	13.5163i	0.127698	+	0.687070i
$388$	8.00000	−	13.8564i	0.406138	−	0.703452i
$389$	−2.44949	−	1.41421i	−0.124194	−	0.0717035i	0.436616	−	0.899648i	$-0.356177\pi$
$389$	−2.44949	−	1.41421i	−0.124194	−	0.0717035i	−0.560810	+	0.827945i	$0.689510\pi$
$390$		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
$396$	15.8589	+	12.0206i	0.796939	+	0.604060i
$397$	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
$399$	−19.0732	−	8.78706i	−0.954855	−	0.439903i
$400$	12.0000			0.600000
$401$	−12.2474	+	7.07107i	−0.611608	+	0.353112i	−0.773595	−	0.633681i	$-0.781543\pi$
$401$	−12.2474	+	7.07107i	−0.611608	+	0.353112i	0.161986	+	0.986793i	$0.448210\pi$
$402$		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	0.175879	−	0.984412i	$-0.443723\pi$
$409$	−11.9059	−	6.87386i	−0.588708	−	0.339891i	−0.764586	+	0.644521i	$0.777057\pi$
$410$		0			0
$411$	15.5732	+	7.17461i	0.768170	+	0.353897i
$412$	−10.0000			−0.492665
$413$		−	7.48331i		−	0.368230i
$414$		0			0
$415$	7.93725	−	4.58258i	0.389624	−	0.224950i
$416$		0			0
$417$	−0.728257	−	7.90377i	−0.0356629	−	0.387049i
$418$		0			0
$419$		−	1.41421i		−	0.0690889i	−0.999403	−	0.0345444i	$-0.989002\pi$
$419$		−	1.41421i		−	0.0690889i	0.999403	−	0.0345444i	$-0.0109980\pi$
$420$	−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
$423$	−12.8990	+	11.0280i	−0.627170	+	0.536199i
$424$		0			0
$425$	9.72111	+	16.8375i	0.471543	+	0.816737i
$426$		0			0
$427$		0			0
$428$	25.9230			1.25303
$429$	25.7083	+	5.66438i	1.24121	+	0.273479i
$430$		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	$0.267721\pi$
$432$	−14.8990	−	14.4921i	−0.716827	−	0.697251i
$433$	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	0.190918	−	0.981606i	$-0.438853\pi$
$439$	23.8118	−	13.7477i	1.13647	−	0.656143i	0.945555	+	0.325463i	$0.105520\pi$
$440$		0			0
$441$	−7.00000	+	19.7990i	−0.333333	+	0.942809i
$442$		0			0
$443$	6.12372	−	3.53553i	0.290947	−	0.167978i	−0.347422	−	0.937709i	$-0.612943\pi$
$443$	6.12372	−	3.53553i	0.290947	−	0.167978i	0.638369	+	0.769731i	$0.279609\pi$
$444$	24.1464	−	2.22486i	1.14594	−	0.105587i
$445$	−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	$-0.989376\pi$
$449$		−	1.41421i		−	0.0667409i	0.999443	−	0.0333704i	$-0.0106241\pi$
$450$		0			0
$451$	−6.53137	+	20.4778i	−0.307550	+	0.964263i
$452$	−24.4949	−	14.1421i	−1.15214	−	0.665190i
$453$	−14.4180	−	6.64240i	−0.677416	−	0.312087i
$454$		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	$0.748430\pi$
$457$	−35.7176	+	20.6216i	−1.67080	+	0.964637i	−0.967191	+	0.254051i	$0.918237\pi$
$458$		0			0
$459$	8.26460	−	32.6450i	0.385758	−	1.52374i
$460$	−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
$465$	0.224745	+	2.43916i	0.0104223	+	0.113113i
$466$		0			0
$467$	−15.9217	+	9.19239i	−0.736768	+	0.425373i	−0.820893	−	0.571082i	$-0.806524\pi$
$467$	−15.9217	+	9.19239i	−0.736768	+	0.425373i	0.0841252	+	0.996455i	$0.473190\pi$
$468$	−25.9230	−	9.16515i	−1.19829	−	0.423659i
$469$	2.64575			0.122169
$470$		0			0
$471$	−5.79796	+	12.5851i	−0.267156	+	0.579889i
$472$		0			0
$473$	−14.4800	−	4.61838i	−0.665791	−	0.212353i
$474$		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
$483$	−23.5445	−	10.8470i	−1.07131	−	0.493555i
$484$	−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	$0.453284\pi$
$492$	9.39377	−	20.3901i	0.423504	−	0.919258i
$493$	−21.0000	+	36.3731i	−0.945792	+	1.63816i
$494$		0			0
$495$	−5.46160	−	12.9681i	−0.245481	−	0.582871i
$496$	−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
$501$	−22.3552	+	2.05982i	−0.998759	+	0.0920260i
$502$		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
$507$	−13.7980	+	1.27135i	−0.612789	+	0.0564626i
$508$	23.8118	+	13.7477i	1.05648	+	0.609957i
$509$	−26.9444	+	15.5563i	−1.19429	+	0.689523i	−0.959276	−	0.282469i	$-0.908846\pi$
$509$	−26.9444	+	15.5563i	−1.19429	+	0.689523i	−0.235013	+	0.971992i	$0.575513\pi$
$510$		0			0
$511$		−	12.1244i		−	0.536350i
$512$		0			0
$513$	−16.6028	+	17.0689i	−0.733030	+	0.753611i
$514$		0			0
$515$	6.12372	+	3.53553i	0.269844	+	0.155794i
$516$	14.4180	+	6.64240i	0.634717	+	0.292415i
$517$	−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	0.359823	−	0.933021i	$-0.382837\pi$
$521$	−6.12372	−	3.53553i	−0.268285	−	0.154895i	−0.628108	+	0.778126i	$0.716170\pi$
$522$		0			0
$523$	−3.96863	+	2.29129i	−0.173536	+	0.100191i	−0.584252	−	0.811572i	$-0.698612\pi$
$523$	−3.96863	+	2.29129i	−0.173536	+	0.100191i	0.410716	+	0.911763i	$0.365279\pi$
$524$	12.9615			0.566225
$525$	−13.6897	+	1.26138i	−0.597469	+	0.0550510i
$526$		0			0
$527$	−3.24037	−	5.61249i	−0.141153	−	0.244484i
$528$	21.9058	−	6.93814i	0.953326	−	0.301944i
$529$	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
$537$	28.9217	+	13.3243i	1.24806	+	0.574985i
$538$		0			0
$539$	−15.6279	−	17.1688i	−0.673141	−	0.739514i
$540$	4.00000	+	14.1421i	0.172133	+	0.608581i
$541$	−27.7804	+	16.0390i	−1.19437	+	0.689571i	−0.959295	−	0.282406i	$-0.908868\pi$
$541$	−27.7804	+	16.0390i	−1.19437	+	0.689571i	−0.235077	+	0.971977i	$0.575534\pi$
$542$		0			0
$543$	−22.4217	+	2.06594i	−0.962207	+	0.0886581i
$544$		0			0
$545$	6.48074			0.277604
$546$		0			0
$547$		−	9.16515i		−	0.391874i	−0.980617	−	0.195937i	$-0.937225\pi$
$547$		−	9.16515i		−	0.391874i	0.980617	−	0.195937i	$-0.0627747\pi$
$548$	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
$555$	−15.5732	−	7.17461i	−0.661046	−	0.304545i
$556$	−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	$0.166667\pi$
$564$	1.79796	+	19.5133i	0.0757077	+	0.821656i
$565$	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	0.229743	−	0.973251i	$-0.426211\pi$
$571$	−11.9059	−	6.87386i	−0.498246	−	0.287662i	−0.727989	+	0.685589i	$0.759545\pi$
$572$	22.4793	−	20.4617i	0.939906	−	0.855548i
$573$	28.0000	−	19.7990i	1.16972	−	0.827115i
$574$		0			0
$575$		−	16.9706i		−	0.707721i
$576$	−23.5959	+	4.38551i	−0.983163	+	0.182729i
$577$	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
$579$	21.6270	+	9.96359i	0.898787	+	0.414073i
$580$		−	18.3303i		−	0.761124i
$581$	−8.57321	−	14.8492i	−0.355677	−	0.616050i
$582$		0			0
$583$	17.3431	−	15.7866i	0.718279	−	0.653813i
$584$		0			0
$585$	12.6341	+	14.7776i	0.522357	+	0.610980i
$586$		0			0
$587$			2.82843i			0.116742i	0.998295	+	0.0583708i	$0.0185906\pi$
$587$			2.82843i			0.116742i	−0.998295	+	0.0583708i	$0.981409\pi$
$588$	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
$597$	−1.44949	+	3.14626i	−0.0593237	+	0.128768i
$598$		0			0
$599$	23.2702	+	13.4350i	0.950793	+	0.548940i	0.893327	−	0.449407i	$-0.148365\pi$
$599$	23.2702	+	13.4350i	0.950793	+	0.548940i	0.0574656	+	0.998347i	$0.481698\pi$
$600$		0			0
$601$			4.58258i			0.186927i	0.995623	+	0.0934636i	$0.0297939\pi$
$601$			4.58258i			0.186927i	−0.995623	+	0.0934636i	$0.970206\pi$
$602$		0			0
$603$	1.00000	−	2.82843i	0.0407231	−	0.115182i
$604$	−15.8745	+	9.16515i	−0.645925	+	0.372925i
$605$	15.4878	+	1.45858i	0.629669	+	0.0592998i
$606$		0			0
$607$	−19.8431	+	11.4564i	−0.805408	+	0.465003i	−0.845359	−	0.534199i	$-0.820613\pi$
$607$	−19.8431	+	11.4564i	−0.805408	+	0.465003i	0.0399507	+	0.999202i	$0.487280\pi$
$608$		0			0
$609$	−17.1464	−	24.2487i	−0.694808	−	0.982607i
$610$		0			0
$611$	12.9615	+	22.4499i	0.524365	+	0.908228i
$612$	−25.2683	−	29.5553i	−1.02141	−	1.19470i
$613$	31.7490	+	18.3303i	1.28233	+	0.740354i	0.977274	−	0.211980i	$-0.0679912\pi$
$613$	31.7490	+	18.3303i	1.28233	+	0.740354i	0.305057	+	0.952334i	$0.401325\pi$
$614$		0			0
$615$	−12.9615	+	9.16515i	−0.522657	+	0.369575i
$616$		0			0
$617$			24.0416i			0.967880i	0.875101	+	0.483940i	$0.160795\pi$
$617$			24.0416i			0.967880i	−0.875101	+	0.483940i	$0.839205\pi$
$618$		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
$621$	−20.4949	+	21.0703i	−0.822432	+	0.845524i
$622$		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
$627$	−7.94863	−	25.0962i	−0.317438	−	1.00225i
$628$	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
$633$	−2.91303	−	31.6151i	−0.115782	−	1.25659i
$634$		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
$639$	−0.775255	−	4.17121i	−0.0306686	−	0.165010i
$640$		0			0
$641$	34.2929	+	19.7990i	1.35449	+	0.782013i	0.988874	−	0.148754i	$-0.0475263\pi$
$641$	34.2929	+	19.7990i	1.35449	+	0.782013i	0.365612	+	0.930767i	$0.380860\pi$
$642$		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	0.833016	−	0.553250i	$-0.186612\pi$
$647$	19.5959	+	11.3137i	0.770395	+	0.444788i	−0.0626205	+	0.998037i	$0.519946\pi$
$648$		0			0
$649$	6.93725	−	6.31463i	0.272311	−	0.247871i
$650$		0			0
$651$	4.56325	−	0.420459i	0.178848	−	0.0164791i
$652$	−4.00000			−0.156652
$653$	20.8207	−	12.0208i	0.814775	−	0.470411i	−0.0338360	−	0.999427i	$-0.510772\pi$
$653$	20.8207	−	12.0208i	0.814775	−	0.470411i	0.848612	+	0.529017i	$0.177439\pi$
$654$		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	$0.844879\pi$
$660$	−15.8675	−	3.49613i	−0.617641	−	0.136087i
$661$	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
$663$	−46.7196	−	21.5238i	−1.81444	−	0.835916i
$664$		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
$669$	−6.89898	+	0.635674i	−0.266730	+	0.0245766i
$670$		0			0
$671$		0			0
$672$		0			0
$673$			4.58258i			0.176645i	0.996092	+	0.0883227i	$0.0281507\pi$
$673$			4.58258i			0.176645i	−0.996092	+	0.0883227i	$0.971849\pi$
$674$		0			0
$675$	−3.82577	+	15.1117i	−0.147254	+	0.581650i
$676$	−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
$681$	9.39377	−	20.3901i	0.359970	−	0.781351i
$682$		0			0
$683$	−17.1464	−	9.89949i	−0.656090	−	0.378794i	0.134696	−	0.990887i	$-0.456994\pi$
$683$	−17.1464	−	9.89949i	−0.656090	−	0.378794i	−0.790785	+	0.612093i	$0.790328\pi$
$684$	5.02423	+	27.0325i	0.192106	+	1.03361i
$685$	−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
$693$	−24.2610	+	10.2177i	−0.921601	+	0.388139i
$694$		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
$704$	8.06250	−	25.2784i	0.303867	−	0.952714i
$705$	5.79796	−	12.5851i	0.218364	−	0.473981i
$706$		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
$711$	31.3481	−	26.8011i	1.17565	−	1.00512i
$712$		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
$717$	11.1776	−	1.02991i	0.417436	−	0.0384627i
$718$		0			0
$719$	39.1918	−	22.6274i	1.46161	−	0.843860i	0.462523	−	0.886607i	$-0.346944\pi$
$719$	39.1918	−	22.6274i	1.46161	−	0.843860i	0.999086	+	0.0427471i	$0.0136110\pi$
$720$	16.0000	+	5.65685i	0.596285	+	0.210819i
$721$	6.61438	−	11.4564i	0.246332	−	0.426660i
$722$		0			0
$723$	28.8360	+	13.2848i	1.07242	+	0.494067i
$724$	−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	$0.714341\pi$
$733$	−43.6549	+	25.2042i	−1.61243	+	0.930937i	−0.988805	+	0.149214i	$0.952326\pi$
$734$		0			0
$735$	−1.57321	−	17.0741i	−0.0580289	−	0.629788i
$736$		0			0
$737$	2.23256	+	2.45269i	0.0822373	+	0.0903460i
$738$		0			0
$739$	−27.7804	−	16.0390i	−1.02192	−	0.590005i	−0.107259	−	0.994231i	$-0.534207\pi$
$739$	−27.7804	−	16.0390i	−1.02192	−	0.590005i	−0.914659	+	0.404226i	$0.867541\pi$
$740$	−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
$747$	−19.1149	+	3.55267i	−0.699377	+	0.129985i
$748$	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
$753$	1.12372	+	12.1958i	0.0409508	+	0.444439i
$754$		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
$759$	−9.81201	−	30.9794i	−0.356153	−	1.12448i
$760$		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
$765$	5.02423	+	27.0325i	0.181651	+	0.977363i
$766$		0			0
$767$	−6.48074	+	11.2250i	−0.234006	+	0.405310i
$768$	−11.5959	+	25.1701i	−0.418432	+	0.908248i
$769$		−	32.0780i		−	1.15676i	−0.815766	−	0.578382i	$-0.803684\pi$
$769$		−	32.0780i		−	1.15676i	0.815766	−	0.578382i	$-0.196316\pi$
$770$		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	$-0.916021\pi$
$773$	−46.5403	−	26.8701i	−1.67394	−	0.966449i	−0.708540	−	0.705671i	$-0.750646\pi$
$774$		0			0
$775$	1.50000	+	2.59808i	0.0538816	+	0.0933257i
$776$		0			0
$777$	−13.4225	+	29.1348i	−0.481528	+	1.04521i
$778$		0			0
$779$	−25.7196	+	14.8492i	−0.921502	+	0.532029i
$780$	22.3552	−	2.05982i	0.800446	−	0.0737534i
$781$	4.46863	+	1.42526i	0.159900	+	0.0509999i
$782$		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	0.860245	−	0.509881i	$-0.170311\pi$
$787$	23.8118	+	13.7477i	0.848798	+	0.490054i	−0.0114473	+	0.999934i	$0.503644\pi$
$788$		0			0
$789$	−4.69688	+	10.1951i	−0.167213	+	0.362954i
$790$		0			0
$791$	32.4037	−	18.7083i	1.15214	−	0.665190i
$792$		0			0
$793$		0			0
$794$		0			0
$795$	17.2474	−	1.58919i	0.611704	−	0.0563626i
$796$	2.00000	+	3.46410i	0.0708881	+	0.122782i
$797$			11.3137i			0.400752i	0.979719	+	0.200376i	$0.0642164\pi$
$797$			11.3137i			0.400752i	−0.979719	+	0.200376i	$0.935784\pi$
$798$		0			0
$799$			36.6606i			1.29696i
$800$		0			0
$801$	35.4722	−	30.3269i	1.25335	−	1.07155i
$802$		0			0
$803$	11.2396	−	10.2309i	0.396638	−	0.361039i
$804$	−2.00000	−	2.82843i	−0.0705346	−	0.0997509i
$805$	21.1660			0.746004
$806$		0			0
$807$	8.89898	+	4.09978i	0.313259	+	0.144319i
$808$		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	$0.160361\pi$
$811$			27.4955i			0.965496i	−0.875759	+	0.482748i	$0.839639\pi$
$812$	−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
$816$	−44.7105	+	4.11964i	−1.56518	+	0.144216i
$817$	−10.5000	−	18.1865i	−0.367348	−	0.636266i
$818$		0			0
$819$	27.6464	−	23.6363i	0.966044	−	0.825919i
$820$			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	$0.736319\pi$
$828$	6.20204	+	33.3697i	0.215536	+	1.15968i
$829$	−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
$831$	−36.0450	−	16.6060i	−1.25039	−	0.576055i
$832$			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
$836$	−28.9600	−	9.23676i	−1.00160	−	0.319460i
$837$	1.27526	−	5.03723i	0.0440793	−	0.174112i
$838$		0			0
$839$		−	1.41421i		−	0.0488241i	−0.999702	−	0.0244120i	$-0.992229\pi$
$839$		−	1.41421i		−	0.0488241i	0.999702	−	0.0244120i	$-0.00777136\pi$
$840$		0			0
$841$	13.0000			0.448276
$842$		0			0
$843$	22.3552	−	2.05982i	0.769956	−	0.0709440i
$844$	−31.7490	−	18.3303i	−1.09285	−	0.630955i
$845$	9.79796	−	5.65685i	0.337060	−	0.194602i
$846$		0			0
$847$	2.72876	−	28.9751i	0.0937612	−	0.995595i
$848$			28.2843i			0.971286i
$849$	21.6270	+	9.96359i	0.742236	+	0.341950i
$850$		0			0
$851$	−34.2929	−	19.7990i	−1.17554	−	0.678701i
$852$	−4.44949	−	2.04989i	−0.152437	−	0.0702280i
$853$		−	22.9129i		−	0.784522i	−0.919854	−	0.392261i	$-0.871693\pi$
$853$		−	22.9129i		−	0.784522i	0.919854	−	0.392261i	$-0.128307\pi$
$854$		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	−0.638769	−	0.769398i	$-0.720556\pi$
$863$	−8.57321	+	4.94975i	−0.291836	+	0.168491i	0.346934	+	0.937890i	$0.387223\pi$
$864$		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
$873$	23.5959	−	4.38551i	0.798601	−	0.148427i
$874$		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	−0.207430	−	0.978250i	$-0.566510\pi$
$877$	15.8745	−	9.16515i	0.536044	−	0.309485i	0.743474	+	0.668765i	$0.233177\pi$
$878$		0			0
$879$	−22.3552	+	2.05982i	−0.754024	+	0.0694760i
$880$	−13.8745	+	12.6293i	−0.467710	+	0.425732i
$881$		−	52.3259i		−	1.76290i	−0.472273	−	0.881452i	$-0.656566\pi$
$881$		−	52.3259i		−	1.76290i	0.472273	−	0.881452i	$-0.343434\pi$
$882$		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
$885$	6.89898	−	0.635674i	0.231907	−	0.0213680i
$886$		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
$891$	1.75340	+	29.7981i	0.0587410	+	0.998273i
$892$	−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
$900$	11.6969	+	13.6814i	0.389898	+	0.456048i
$901$	−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	$-0.706664\pi$
$911$		−	48.0833i		−	1.59307i	0.604593	−	0.796535i	$-0.293336\pi$
$912$	28.8360	+	13.2848i	0.954855	+	0.439903i
$913$	6.53137	−	20.4778i	0.216157	−	0.677717i
$914$		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	0.442190	−	0.896921i	$-0.354202\pi$
$919$	43.6549	−	25.2042i	1.44004	−	0.831409i	0.997852	+	0.0655125i	$0.0208682\pi$
$920$		0			0
$921$	2.18477	+	23.7113i	0.0719906	+	0.781315i
$922$		0			0
$923$	−6.48074			−0.213316
$924$	−6.54066	+	29.6853i	−0.215172	+	0.976576i
$925$	−21.0000			−0.690476
$926$		0			0
$927$	−9.74745	−	11.4012i	−0.320148	−	0.374464i
$928$		0			0
$929$	−37.9671	+	21.9203i	−1.24566	+	0.719182i	−0.970241	−	0.242142i	$-0.922150\pi$
$929$	−37.9671	+	21.9203i	−1.24566	+	0.719182i	−0.275419	+	0.961324i	$0.588817\pi$
$930$		0			0
$931$		−	32.0780i		−	1.05131i
$932$	−12.9615			−0.424567
$933$	−24.4722	−	11.2744i	−0.801184	−	0.369107i
$934$		0			0
$935$	−28.9600	−	9.23676i	−0.947094	−	0.302074i
$936$		0			0
$937$		−	13.7477i		−	0.449119i	−0.974460	−	0.224559i	$-0.927906\pi$
$937$		−	13.7477i		−	0.449119i	0.974460	−	0.224559i	$-0.0720943\pi$
$938$		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
$945$	−18.8476	−	4.77157i	−0.613113	−	0.155219i
$946$		0			0
$947$	17.1464	−	9.89949i	0.557184	−	0.321690i	−0.194830	−	0.980837i	$-0.562416\pi$
$947$	17.1464	−	9.89949i	0.557184	−	0.321690i	0.752014	+	0.659147i	$0.229082\pi$
$948$	−4.36954	−	47.4226i	−0.141916	−	1.54022i
$949$	−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
$957$	8.01064	−	36.3570i	0.258947	−	1.17525i
$958$		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
$963$	25.2683	+	29.5553i	0.814259	+	0.952405i
$964$	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	$-0.976525\pi$
$967$		−	4.58258i		−	0.147366i	0.997282	−	0.0736828i	$-0.0234753\pi$
$968$		0			0
$969$	4.71964	+	51.2223i	0.151617	+	1.64550i
$970$		0			0
$971$	−41.6413	+	24.0416i	−1.33633	+	0.771533i	−0.986262	−	0.165190i	$-0.947176\pi$
$971$	−41.6413	+	24.0416i	−1.33633	+	0.771533i	−0.350072	+	0.936723i	$0.613843\pi$
$972$	2.00000	−	31.1127i	0.0641500	−	0.997940i
$973$	10.5000	−	6.06218i	0.336615	−	0.194344i
$974$		0			0
$975$	21.6270	+	9.96359i	0.692618	+	0.319090i
$976$		0			0
$977$	45.3156	+	26.1630i	1.44977	+	0.837027i	0.998467	−	0.0553424i	$-0.0176250\pi$
$977$	45.3156	+	26.1630i	1.44977	+	0.837027i	0.451306	+	0.892369i	$0.350958\pi$
$978$		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	0.269521	−	0.962995i	$-0.413135\pi$
$983$	−13.4722	−	7.77817i	−0.429696	−	0.248085i	−0.699217	+	0.714909i	$0.746468\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−23.5445	−	10.8470i	−0.749429	−	0.345263i
$988$	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
$996$	−9.39377	+	20.3901i	−0.297653	+	0.646086i
$997$	−19.8431	−	11.4564i	−0.628438	−	0.362829i	0.151709	−	0.988425i	$-0.451522\pi$
$997$	−19.8431	−	11.4564i	−0.628438	−	0.362829i	−0.780147	+	0.625596i	$0.784856\pi$
$998$		0			0
$999$	26.0732	+	25.3611i	0.824920	+	0.802391i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(1.72474 - 0.158919i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-1.22474 + 0.707107i) q^{5} +(1.32288 + 2.29129i) q^{7} +(2.94949 - 0.548188i) q^{9} +O(q^{10})\)	\(q+(1.72474 - 0.158919i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-1.22474 + 0.707107i) q^{5} +(1.32288 + 2.29129i) q^{7} +(2.94949 - 0.548188i) q^{9} +(-1.00781 + 3.15980i) q^{11} +(1.44949 - 3.14626i) q^{12} -4.58258i q^{13} +(-2.00000 + 1.41421i) q^{15} +(-2.00000 - 3.46410i) q^{16} +(3.24037 - 5.61249i) q^{17} +(-3.96863 + 2.29129i) q^{19} +2.82843i q^{20} +(2.64575 + 3.74166i) q^{21} +(-4.89898 + 2.82843i) q^{23} +(-1.50000 + 2.59808i) q^{25} +(5.00000 - 1.41421i) q^{27} +5.29150 q^{28} -6.48074 q^{29} +(0.500000 - 0.866025i) q^{31} +(-1.23607 + 5.61000i) q^{33} +(-3.24037 - 1.87083i) q^{35} +(2.00000 - 5.65685i) q^{36} +(3.50000 + 6.06218i) q^{37} +(-0.728257 - 7.90377i) q^{39} +6.48074 q^{41} +4.58258i q^{43} +(4.46512 + 4.90538i) q^{44} +(-3.22474 + 2.75699i) q^{45} +(-4.89898 + 2.82843i) q^{47} +(-4.00000 - 5.65685i) q^{48} +(-3.50000 + 6.06218i) q^{49} +(4.69688 - 10.1951i) q^{51} +(-7.93725 - 4.58258i) q^{52} +(-6.12372 - 3.53553i) q^{53} +(-1.00000 - 4.58258i) q^{55} +(-6.48074 + 4.58258i) q^{57} +(-2.44949 - 1.41421i) q^{59} +(0.449490 + 4.87832i) q^{60} +(5.15787 + 6.03295i) q^{63} -8.00000 q^{64} +(3.24037 + 5.61249i) q^{65} +(0.500000 - 0.866025i) q^{67} +(-6.48074 - 11.2250i) q^{68} +(-8.00000 + 5.65685i) q^{69} -1.41421i q^{71} +(-3.96863 - 2.29129i) q^{73} +(-2.17423 + 4.71940i) q^{75} +9.16515i q^{76} +(-8.57321 + 1.87083i) q^{77} +(11.9059 - 6.87386i) q^{79} +(4.89898 + 2.82843i) q^{80} +(8.39898 - 3.23375i) q^{81} -6.48074 q^{83} +(9.12649 - 0.840918i) q^{84} +9.16515i q^{85} +(-11.1776 + 1.02991i) q^{87} +(13.4722 - 7.77817i) q^{89} +(10.5000 - 6.06218i) q^{91} +11.3137i q^{92} +(0.724745 - 1.57313i) q^{93} +(3.24037 - 5.61249i) q^{95} +8.00000 q^{97} +(-1.24037 + 9.87226i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} + 8 q^{4} + 4 q^{9}+O(q^{10}) \) 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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