LMFDB - Embedded newform 819.2.n.e.100.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(100,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

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

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

chi := DirichletCharacter("819.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.n (of order $3$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 11 x^{14} - 4 x^{13} + 87 x^{12} - 35 x^{11} + 326 x^{10} - 205 x^{9} + 895 x^{8} - 481 x^{7} + \cdots + 1 $ x^16 + 11x^14 - 4x^13 + 87x^12 - 35x^11 + 326x^10 - 205x^9 + 895x^8 - 481x^7 + 1005x^6 - 544x^5 + 811x^4 - 312x^3 + 195x^2 + 13x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.3
Root			$0.415625 + 0.719884i$ of defining polynomial
Character	$\chi$	$=$	819.100
Dual form			819.2.n.e.172.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415625 - 0.719884i) q^{2} +(0.654511 - 1.13365i) q^{4} +(1.30847 - 2.26634i) q^{5} +(0.801591 + 2.52140i) q^{7} -2.75063 q^{8} +O(q^{10})$	\(q+(-0.415625 - 0.719884i) q^{2} +(0.654511 - 1.13365i) q^{4} +(1.30847 - 2.26634i) q^{5} +(0.801591 + 2.52140i) q^{7} -2.75063 q^{8} -2.17533 q^{10} +1.84837 q^{11} +(2.74506 + 2.33765i) q^{13} +(1.48195 - 1.62501i) q^{14} +(-0.165791 - 0.287158i) q^{16} +(3.41564 - 5.91607i) q^{17} +5.06988 q^{19} +(-1.71281 - 2.96668i) q^{20} +(-0.768228 - 1.33061i) q^{22} +(-0.636428 - 1.10233i) q^{23} +(-0.924183 - 1.60073i) q^{25} +(0.541921 - 2.94772i) q^{26} +(3.38302 + 0.741562i) q^{28} +(-0.724496 + 1.25486i) q^{29} +(-3.09878 - 5.36725i) q^{31} +(-2.88844 + 5.00293i) q^{32} -5.67851 q^{34} +(6.76319 + 1.48250i) q^{35} +(-3.93922 - 6.82292i) q^{37} +(-2.10717 - 3.64973i) q^{38} +(-3.59911 + 6.23384i) q^{40} +(-4.41239 + 7.64248i) q^{41} +(0.109598 + 0.189830i) q^{43} +(1.20978 - 2.09539i) q^{44} +(-0.529032 + 0.916310i) q^{46} +(-0.624016 + 1.08083i) q^{47} +(-5.71490 + 4.04226i) q^{49} +(-0.768228 + 1.33061i) q^{50} +(4.44675 - 1.58191i) q^{52} +(-1.33947 - 2.32004i) q^{53} +(2.41853 - 4.18902i) q^{55} +(-2.20488 - 6.93543i) q^{56} +1.20448 q^{58} +(-6.01804 + 10.4236i) q^{59} -8.72218 q^{61} +(-2.57586 + 4.46153i) q^{62} +4.13888 q^{64} +(8.88974 - 3.16249i) q^{65} +13.8331 q^{67} +(-4.47115 - 7.74426i) q^{68} +(-1.74373 - 5.48488i) q^{70} +(-1.78833 - 3.09749i) q^{71} +(-3.26733 - 5.65918i) q^{73} +(-3.27448 + 5.67156i) q^{74} +(3.31829 - 5.74745i) q^{76} +(1.48163 + 4.66047i) q^{77} +(3.08084 - 5.33616i) q^{79} -0.867729 q^{80} +7.33560 q^{82} +8.67738 q^{83} +(-8.93852 - 15.4820i) q^{85} +(0.0911037 - 0.157796i) q^{86} -5.08417 q^{88} +(-7.57751 - 13.1246i) q^{89} +(-3.69373 + 8.79524i) q^{91} -1.66620 q^{92} +1.03743 q^{94} +(6.63379 - 11.4901i) q^{95} +(6.08221 + 10.5347i) q^{97} +(5.28522 + 2.43400i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{4} + q^{7} - 12 q^{8}+O(q^{10}) $ 16 * q - 6 * q^4 + q^7 - 12 * q^8	$ 16 q - 6 q^{4} + q^{7} - 12 q^{8} + 8 q^{10} - 4 q^{11} + 5 q^{13} + 7 q^{14} - 6 q^{16} + 2 q^{17} + 22 q^{19} + 20 q^{20} + 7 q^{22} - 4 q^{23} + 2 q^{25} + 6 q^{26} - 7 q^{28} - 15 q^{29} + 3 q^{31} - 3 q^{32} - 68 q^{34} + 12 q^{35} + 4 q^{37} - 2 q^{38} - 25 q^{40} - 19 q^{41} + 11 q^{43} + 16 q^{44} + 2 q^{46} - 5 q^{47} + 13 q^{49} + 7 q^{50} + 36 q^{52} - 36 q^{53} - 15 q^{55} - 39 q^{56} - 40 q^{58} + 17 q^{59} + 44 q^{61} + 6 q^{62} - 20 q^{64} + 21 q^{65} - 52 q^{67} - 5 q^{68} + 46 q^{70} - 9 q^{71} - 6 q^{73} - 15 q^{74} - 16 q^{76} + 36 q^{77} + 16 q^{79} - 56 q^{80} + 2 q^{82} - 36 q^{83} - 4 q^{85} - 16 q^{86} - 48 q^{88} - 20 q^{89} - 7 q^{91} + 94 q^{92} + 40 q^{94} + 7 q^{97} + 3 q^{98}+O(q^{100}) $ 16 * q - 6 * q^4 + q^7 - 12 * q^8 + 8 * q^10 - 4 * q^11 + 5 * q^13 + 7 * q^14 - 6 * q^16 + 2 * q^17 + 22 * q^19 + 20 * q^20 + 7 * q^22 - 4 * q^23 + 2 * q^25 + 6 * q^26 - 7 * q^28 - 15 * q^29 + 3 * q^31 - 3 * q^32 - 68 * q^34 + 12 * q^35 + 4 * q^37 - 2 * q^38 - 25 * q^40 - 19 * q^41 + 11 * q^43 + 16 * q^44 + 2 * q^46 - 5 * q^47 + 13 * q^49 + 7 * q^50 + 36 * q^52 - 36 * q^53 - 15 * q^55 - 39 * q^56 - 40 * q^58 + 17 * q^59 + 44 * q^61 + 6 * q^62 - 20 * q^64 + 21 * q^65 - 52 * q^67 - 5 * q^68 + 46 * q^70 - 9 * q^71 - 6 * q^73 - 15 * q^74 - 16 * q^76 + 36 * q^77 + 16 * q^79 - 56 * q^80 + 2 * q^82 - 36 * q^83 - 4 * q^85 - 16 * q^86 - 48 * q^88 - 20 * q^89 - 7 * q^91 + 94 * q^92 + 40 * q^94 + 7 * q^97 + 3 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.415625	−	0.719884i	−0.293892	−	0.509035i	0.680835	−	0.732437i	$-0.261617\pi$
$2$	−0.415625	−	0.719884i	−0.293892	−	0.509035i	−0.974726	+	0.223402i	$0.928284\pi$
$3$		0			0
$3$		0			0
$4$	0.654511	−	1.13365i	0.327255	−	0.566823i
$5$	1.30847	−	2.26634i	0.585165	−	1.01354i	−0.409690	−	0.912225i	$-0.634363\pi$
$5$	1.30847	−	2.26634i	0.585165	−	1.01354i	0.994855	−	0.101311i	$-0.0323037\pi$
$6$		0			0
$7$	0.801591	+	2.52140i	0.302973	+	0.952999i
$7$	0.801591	+	2.52140i	0.302973	+	0.952999i
$8$	−2.75063			−0.972494
$9$		0			0
$10$	−2.17533			−0.687901
$11$	1.84837			0.557303			0.278652	−	0.960392i	$-0.410113\pi$
$11$	1.84837			0.557303			0.278652	+	0.960392i	$0.410113\pi$
$12$		0			0
$13$	2.74506	+	2.33765i	0.761344	+	0.648348i
$13$	2.74506	+	2.33765i	0.761344	+	0.648348i
$14$	1.48195	−	1.62501i	0.396069	−	0.434302i
$15$		0			0
$16$	−0.165791	−	0.287158i	−0.0414477	−	0.0717896i
$17$	3.41564	−	5.91607i	0.828415	−	1.43486i	−0.0708664	−	0.997486i	$-0.522576\pi$
$17$	3.41564	−	5.91607i	0.828415	−	1.43486i	0.899281	−	0.437371i	$-0.144090\pi$
$18$		0			0
$19$	5.06988			1.16311			0.581556	−	0.813507i	$-0.302444\pi$
$19$	5.06988			1.16311			0.581556	+	0.813507i	$0.302444\pi$
$20$	−1.71281	−	2.96668i	−0.382997	−	0.663370i
$21$		0			0
$22$	−0.768228	−	1.33061i	−0.163787	−	0.283687i
$23$	−0.636428	−	1.10233i	−0.132704	−	0.229851i	0.792014	−	0.610503i	$-0.209033\pi$
$23$	−0.636428	−	1.10233i	−0.132704	−	0.229851i	−0.924718	+	0.380652i	$0.875699\pi$
$24$		0			0
$25$	−0.924183	−	1.60073i	−0.184837	−	0.320146i
$26$	0.541921	−	2.94772i	0.106279	−	0.578095i
$27$		0			0
$28$	3.38302	+	0.741562i	0.639331	+	0.140142i
$29$	−0.724496	+	1.25486i	−0.134536	+	0.233022i	−0.925420	−	0.378943i	$-0.876288\pi$
$29$	−0.724496	+	1.25486i	−0.134536	+	0.233022i	0.790884	+	0.611966i	$0.209621\pi$
$30$		0			0
$31$	−3.09878	−	5.36725i	−0.556557	−	0.963986i	−0.997781	−	0.0665883i	$-0.978789\pi$
$31$	−3.09878	−	5.36725i	−0.556557	−	0.963986i	0.441223	−	0.897397i	$-0.354545\pi$
$32$	−2.88844	+	5.00293i	−0.510609	+	0.884401i
$33$		0			0
$34$	−5.67851			−0.973857
$35$	6.76319	+	1.48250i	1.14319	+	0.250588i
$36$		0			0
$37$	−3.93922	−	6.82292i	−0.647603	−	1.12168i	−0.983694	−	0.179852i	$-0.942438\pi$
$37$	−3.93922	−	6.82292i	−0.647603	−	1.12168i	0.336090	−	0.941830i	$-0.390895\pi$
$38$	−2.10717	−	3.64973i	−0.341829	−	0.592064i
$39$		0			0
$40$	−3.59911	+	6.23384i	−0.569069	+	0.985657i
$41$	−4.41239	+	7.64248i	−0.689099	+	1.19355i	0.283031	+	0.959111i	$0.408660\pi$
$41$	−4.41239	+	7.64248i	−0.689099	+	1.19355i	−0.972130	+	0.234444i	$0.924673\pi$
$42$		0			0
$43$	0.109598	+	0.189830i	0.0167136	+	0.0289488i	0.874261	−	0.485456i	$-0.161346\pi$
$43$	0.109598	+	0.189830i	0.0167136	+	0.0289488i	−0.857548	+	0.514405i	$0.828013\pi$
$44$	1.20978	−	2.09539i	0.182381	−	0.315892i
$45$		0			0
$46$	−0.529032	+	0.916310i	−0.0780015	+	0.135103i
$47$	−0.624016	+	1.08083i	−0.0910220	+	0.157655i	−0.907941	−	0.419097i	$-0.862347\pi$
$47$	−0.624016	+	1.08083i	−0.0910220	+	0.157655i	0.816919	+	0.576752i	$0.195680\pi$
$48$		0			0
$49$	−5.71490	+	4.04226i	−0.816415	+	0.577466i
$50$	−0.768228	+	1.33061i	−0.108644	+	0.188177i
$51$		0			0
$52$	4.44675	−	1.58191i	0.616653	−	0.219372i
$53$	−1.33947	−	2.32004i	−0.183991	−	0.318682i	0.759245	−	0.650805i	$-0.225568\pi$
$53$	−1.33947	−	2.32004i	−0.183991	−	0.318682i	−0.943236	+	0.332123i	$0.892235\pi$
$54$		0			0
$55$	2.41853	−	4.18902i	0.326114	−	0.564847i
$56$	−2.20488	−	6.93543i	−0.294639	−	0.926786i
$57$		0			0
$58$	1.20448			0.158155
$59$	−6.01804	+	10.4236i	−0.783483	+	1.35703i	0.146419	+	0.989223i	$0.453225\pi$
$59$	−6.01804	+	10.4236i	−0.783483	+	1.35703i	−0.929901	+	0.367809i	$0.880108\pi$
$60$		0			0
$61$	−8.72218			−1.11676			−0.558381	−	0.829585i	$-0.688577\pi$
$61$	−8.72218			−1.11676			−0.558381	+	0.829585i	$0.688577\pi$
$62$	−2.57586	+	4.46153i	−0.327135	+	0.566615i
$63$		0			0
$64$	4.13888			0.517359
$65$	8.88974	−	3.16249i	1.10264	−	0.392259i
$66$		0			0
$67$	13.8331			1.68998			0.844992	−	0.534779i	$-0.179605\pi$
$67$	13.8331			1.68998			0.844992	+	0.534779i	$0.179605\pi$
$68$	−4.47115	−	7.74426i	−0.542207	−	0.939129i
$69$		0			0
$70$	−1.74373	−	5.48488i	−0.208415	−	0.655569i
$71$	−1.78833	−	3.09749i	−0.212236	−	0.367604i	0.740178	−	0.672411i	$-0.234741\pi$
$71$	−1.78833	−	3.09749i	−0.212236	−	0.367604i	−0.952414	+	0.304807i	$0.901408\pi$
$72$		0			0
$73$	−3.26733	−	5.65918i	−0.382412	−	0.662357i	0.608994	−	0.793175i	$-0.291573\pi$
$73$	−3.26733	−	5.65918i	−0.382412	−	0.662357i	−0.991406	+	0.130817i	$0.958240\pi$
$74$	−3.27448	+	5.67156i	−0.380650	+	0.659306i
$75$		0			0
$76$	3.31829	−	5.74745i	0.380634	−	0.659278i
$77$	1.48163	+	4.66047i	0.168848	+	0.531110i
$78$		0			0
$79$	3.08084	−	5.33616i	0.346621	−	0.600365i	−0.639026	−	0.769185i	$-0.720662\pi$
$79$	3.08084	−	5.33616i	0.346621	−	0.600365i	0.985647	+	0.168820i	$0.0539956\pi$
$80$	−0.867729			−0.0970151
$81$		0			0
$82$	7.33560			0.810082
$83$	8.67738			0.952467			0.476233	−	0.879319i	$-0.342002\pi$
$83$	8.67738			0.952467			0.476233	+	0.879319i	$0.342002\pi$
$84$		0			0
$85$	−8.93852	−	15.4820i	−0.969519	−	1.67926i
$86$	0.0911037	−	0.157796i	0.00982396	−	0.0170156i
$87$		0			0
$88$	−5.08417			−0.541974
$89$	−7.57751	−	13.1246i	−0.803215	−	1.39121i	−0.917490	−	0.397760i	$-0.869788\pi$
$89$	−7.57751	−	13.1246i	−0.803215	−	1.39121i	0.114275	−	0.993449i	$-0.463546\pi$
$90$		0			0
$91$	−3.69373	+	8.79524i	−0.387209	+	0.921992i
$92$	−1.66620			−0.173713
$93$		0			0
$94$	1.03743			0.107002
$95$	6.63379	−	11.4901i	0.680612	−	1.17885i
$96$		0			0
$97$	6.08221	+	10.5347i	0.617554	+	1.06964i	0.989931	+	0.141554i	$0.0452098\pi$
$97$	6.08221	+	10.5347i	0.617554	+	1.06964i	−0.372376	+	0.928082i	$0.621457\pi$
$98$	5.28522	+	2.43400i	0.533888	+	0.245871i
$99$		0			0
$100$	−2.41955			−0.241955
$101$	4.59607			0.457326			0.228663	−	0.973506i	$-0.426565\pi$
$101$	4.59607			0.457326			0.228663	+	0.973506i	$0.426565\pi$
$102$		0			0
$103$	−2.22609	+	3.85570i	−0.219343	+	0.379914i	−0.954607	−	0.297867i	$-0.903725\pi$
$103$	−2.22609	+	3.85570i	−0.219343	+	0.379914i	0.735264	+	0.677781i	$0.237058\pi$
$104$	−7.55065	−	6.43001i	−0.740402	−	0.630515i
$105$		0			0
$106$	−1.11344	+	1.92853i	−0.108147	+	0.187316i
$107$	3.60694	+	6.24740i	0.348696	+	0.603959i	0.986018	−	0.166639i	$-0.0532913\pi$
$107$	3.60694	+	6.24740i	0.348696	+	0.603959i	−0.637322	+	0.770597i	$0.719958\pi$
$108$		0			0
$109$	4.34979	+	7.53406i	0.416635	+	0.721632i	0.995599	−	0.0937209i	$-0.0298761\pi$
$109$	4.34979	+	7.53406i	0.416635	+	0.721632i	−0.578964	+	0.815353i	$0.696543\pi$
$110$	−4.02081			−0.383369
$111$		0			0
$112$	0.591144	−	0.648208i	0.0558578	−	0.0612499i
$113$	−1.82527	−	3.16146i	−0.171707	−	0.297405i	0.767310	−	0.641277i	$-0.221595\pi$
$113$	−1.82527	−	3.16146i	−0.171707	−	0.297405i	−0.939017	+	0.343871i	$0.888262\pi$
$114$		0			0
$115$	−3.33099			−0.310616
$116$	0.948381	+	1.64264i	0.0880550	+	0.152516i
$117$		0			0
$118$	10.0050			0.921036
$119$	17.6547	+	3.86993i	1.61840	+	0.354756i
$120$		0			0
$121$	−7.58354			−0.689413
$122$	3.62516	+	6.27896i	0.328207	+	0.568471i
$123$		0			0
$124$	−8.11274			−0.728546
$125$	8.24763			0.737691
$126$		0			0
$127$	4.80639	−	8.32491i	0.426498	−	0.738716i	−0.570061	−	0.821602i	$-0.693080\pi$
$127$	4.80639	−	8.32491i	0.426498	−	0.738716i	0.996559	+	0.0828862i	$0.0264138\pi$
$128$	4.05666	+	7.02634i	0.358562	+	0.621047i
$129$		0			0
$130$	−5.97143	−	5.08517i	−0.523729	−	0.445999i
$131$	−8.28016	+	14.3417i	−0.723441	+	1.25304i	0.236172	+	0.971711i	$0.424107\pi$
$131$	−8.28016	+	14.3417i	−0.723441	+	1.25304i	−0.959613	+	0.281325i	$0.909226\pi$
$132$		0			0
$133$	4.06397	+	12.7832i	0.352391	+	1.10844i
$134$	−5.74940	−	9.95825i	−0.496672	−	0.860261i
$135$		0			0
$136$	−9.39516	+	16.2729i	−0.805628	+	1.39539i
$137$	−5.27844	+	9.14252i	−0.450967	+	0.781098i	−0.998446	−	0.0557212i	$-0.982254\pi$
$137$	−5.27844	+	9.14252i	−0.450967	+	0.781098i	0.547479	+	0.836819i	$0.315588\pi$
$138$		0			0
$139$	−4.57749	−	7.92845i	−0.388258	−	0.672482i	0.603958	−	0.797016i	$-0.293590\pi$
$139$	−4.57749	−	7.92845i	−0.388258	−	0.672482i	−0.992215	+	0.124534i	$0.960256\pi$
$140$	6.10721	−	6.69676i	0.516154	−	0.565979i
$141$		0			0
$142$	−1.48655	+	2.57479i	−0.124749	+	0.216071i
$143$	5.07388	+	4.32084i	0.424299	+	0.361327i
$144$		0			0
$145$	1.89596	+	3.28390i	0.157451	+	0.272713i
$146$	−2.71597	+	4.70420i	−0.224775	+	0.389322i
$147$		0			0
$148$	−10.3130			−0.847727
$149$	10.9073			0.893565			0.446782	−	0.894643i	$-0.352570\pi$
$149$	10.9073			0.893565			0.446782	+	0.894643i	$0.352570\pi$
$150$		0			0
$151$	11.1702	+	19.3474i	0.909018	+	1.57447i	0.815430	+	0.578855i	$0.196500\pi$
$151$	11.1702	+	19.3474i	0.909018	+	1.57447i	0.0935880	+	0.995611i	$0.470166\pi$
$152$	−13.9454			−1.13112
$153$		0			0
$154$	2.73919	−	3.00361i	0.220730	−	0.242038i
$155$	−16.2186			−1.30271
$156$		0			0
$157$	−0.329586	−	0.570859i	−0.0263038	−	0.0455595i	0.852574	−	0.522607i	$-0.175040\pi$
$157$	−0.329586	−	0.570859i	−0.0263038	−	0.0455595i	−0.878878	+	0.477047i	$0.841707\pi$
$158$	−5.12190			−0.407476
$159$		0			0
$160$	7.55887	+	13.0924i	0.597581	+	1.03504i
$161$	2.26925	−	2.48830i	0.178842	−	0.196106i
$162$		0			0
$163$	18.1851			1.42436			0.712182	−	0.701995i	$-0.247707\pi$
$163$	18.1851			1.42436			0.712182	+	0.701995i	$0.247707\pi$
$164$	5.77591	+	10.0042i	0.451023	+	0.781194i
$165$		0			0
$166$	−3.60654	−	6.24671i	−0.279922	−	0.484839i
$167$	2.21154	−	3.83050i	0.171134	−	0.296413i	−0.767683	−	0.640830i	$-0.778590\pi$
$167$	2.21154	−	3.83050i	0.171134	−	0.296413i	0.938817	+	0.344417i	$0.111924\pi$
$168$		0			0
$169$	2.07076	+	12.8340i	0.159289	+	0.987232i
$170$	−7.43016	+	12.8694i	−0.569867	+	0.987039i
$171$		0			0
$172$	0.286933			0.0218784
$173$	−3.52044			−0.267654			−0.133827	−	0.991005i	$-0.542727\pi$
$173$	−3.52044			−0.267654			−0.133827	+	0.991005i	$0.542727\pi$
$174$		0			0
$175$	3.29527	−	3.61337i	0.249099	−	0.273145i
$176$	−0.306442	−	0.530773i	−0.0230990	−	0.0400086i
$177$		0			0
$178$	−6.29881	+	10.9099i	−0.472116	+	0.817729i
$179$	−10.8203			−0.808746			−0.404373	−	0.914594i	$-0.632510\pi$
$179$	−10.8203			−0.808746			−0.404373	+	0.914594i	$0.632510\pi$
$180$		0			0
$181$	−23.0651			−1.71441			−0.857207	−	0.514973i	$-0.827802\pi$
$181$	−23.0651			−1.71441			−0.857207	+	0.514973i	$0.827802\pi$
$182$	7.86677	−	0.996466i	0.583124	−	0.0738630i
$183$		0			0
$184$	1.75058	+	3.03209i	0.129054	+	0.223529i
$185$	−20.6174			−1.51582
$186$		0			0
$187$	6.31336	−	10.9351i	0.461678	−	0.799650i
$188$	0.816850	+	1.41483i	0.0595749	+	0.103187i
$189$		0			0
$190$	−11.0287			−0.800105
$191$	1.82966			0.132389			0.0661947	−	0.997807i	$-0.478914\pi$
$191$	1.82966			0.132389			0.0661947	+	0.997807i	$0.478914\pi$
$192$		0			0
$193$	3.15951			0.227427			0.113713	−	0.993514i	$-0.463725\pi$
$193$	3.15951			0.227427			0.113713	+	0.993514i	$0.463725\pi$
$194$	5.05584	−	8.75697i	0.362988	−	0.628714i
$195$		0			0
$196$	0.842029	+	9.12438i	0.0601450	+	0.651742i
$197$	−5.57597	+	9.65786i	−0.397271	+	0.688094i	−0.993388	−	0.114804i	$-0.963376\pi$
$197$	−5.57597	+	9.65786i	−0.397271	+	0.688094i	0.596117	+	0.802898i	$0.296709\pi$
$198$		0			0
$199$	−10.3748	+	17.9697i	−0.735452	+	1.27384i	0.219072	+	0.975709i	$0.429697\pi$
$199$	−10.3748	+	17.9697i	−0.735452	+	1.27384i	−0.954525	+	0.298132i	$0.903636\pi$
$200$	2.54208	+	4.40302i	0.179752	+	0.311340i
$201$		0			0
$202$	−1.91024	−	3.30864i	−0.134404	−	0.232795i
$203$	−3.74476	−	0.820855i	−0.262831	−	0.0576127i
$204$		0			0
$205$	11.5469	+	19.9999i	0.806474	+	1.39685i
$206$	3.70088			0.257853
$207$		0			0
$208$	0.216169	−	1.17583i	0.0149887	−	0.0815291i
$209$	9.37100			0.648206
$210$		0			0
$211$	8.16773	−	14.1469i	0.562289	−	0.973914i	−0.435007	−	0.900427i	$-0.643254\pi$
$211$	8.16773	−	14.1469i	0.562289	−	0.973914i	0.997296	−	0.0734866i	$-0.0234126\pi$
$212$	−3.50680			−0.240848
$213$		0			0
$214$	2.99827	−	5.19316i	0.204957	−	0.354997i
$215$	0.573624			0.0391208
$216$		0			0
$217$	11.0490	−	12.1156i	0.750056	−	0.822460i
$218$	3.61577	−	6.26270i	0.244891	−	0.424163i
$219$		0			0
$220$	−3.16591	−	5.48351i	−0.213445	−	0.369698i
$221$	23.2059	−	8.25540i	1.56100	−	0.555318i
$222$		0			0
$223$	9.30867	−	16.1231i	0.623355	−	1.07968i	−0.365502	−	0.930811i	$-0.619103\pi$
$223$	9.30867	−	16.1231i	0.623355	−	1.07968i	0.988857	−	0.148871i	$-0.0475640\pi$
$224$	−14.9297	−	3.27261i	−0.997534	−	0.218660i
$225$		0			0
$226$	−1.51726	+	2.62797i	−0.100926	+	0.174810i
$227$	−11.2727	+	19.5249i	−0.748197	+	1.29592i	0.200489	+	0.979696i	$0.435747\pi$
$227$	−11.2727	+	19.5249i	−0.748197	+	1.29592i	−0.948686	+	0.316220i	$0.897586\pi$
$228$		0			0
$229$	9.62713	−	16.6747i	0.636179	−	1.10189i	−0.350085	−	0.936718i	$-0.613847\pi$
$229$	9.62713	−	16.6747i	0.636179	−	1.10189i	0.986264	−	0.165176i	$-0.0528193\pi$
$230$	1.38444	+	2.39793i	0.0912875	+	0.158115i
$231$		0			0
$232$	1.99282	−	3.45166i	0.130835	−	0.226613i
$233$	11.4276	−	19.7933i	0.748650	−	1.29670i	−0.199820	−	0.979833i	$-0.564036\pi$
$233$	11.4276	−	19.7933i	0.748650	−	1.29670i	0.948470	−	0.316867i	$-0.102631\pi$
$234$		0			0
$235$	1.63301	+	2.82846i	0.106526	+	0.184508i
$236$	7.87775	+	13.6447i	0.512798	+	0.888192i
$237$		0			0
$238$	−4.55185	−	14.3178i	−0.295052	−	0.928085i
$239$	11.2501			0.727705			0.363853	−	0.931457i	$-0.381461\pi$
$239$	11.2501			0.727705			0.363853	+	0.931457i	$0.381461\pi$
$240$		0			0
$241$	−9.72305	+	16.8408i	−0.626316	+	1.08481i	0.361968	+	0.932190i	$0.382105\pi$
$241$	−9.72305	+	16.8408i	−0.626316	+	1.08481i	−0.988285	+	0.152621i	$0.951228\pi$
$242$	3.15191	+	5.45928i	0.202613	+	0.350936i
$243$		0			0
$244$	−5.70876	+	9.88787i	−0.365466	+	0.633006i
$245$	1.68335	+	18.2411i	0.107545	+	1.16538i
$246$		0			0
$247$	13.9172	+	11.8516i	0.885528	+	0.754101i
$248$	8.52359	+	14.7633i	0.541249	+	0.937470i
$249$		0			0
$250$	−3.42793	−	5.93734i	−0.216801	−	0.375510i
$251$	8.79293	+	15.2298i	0.555005	+	0.961297i	0.997903	+	0.0647248i	$0.0206170\pi$
$251$	8.79293	+	15.2298i	0.555005	+	0.961297i	−0.442898	+	0.896572i	$0.646050\pi$
$252$		0			0
$253$	−1.17635	−	2.03750i	−0.0739566	−	0.128097i
$254$	−7.99063			−0.501377
$255$		0			0
$256$	7.51098	−	13.0094i	0.469436	−	0.813087i
$257$	7.59362	+	13.1525i	0.473677	+	0.820432i	0.999546	−	0.0301333i	$-0.00959318\pi$
$257$	7.59362	+	13.1525i	0.473677	+	0.820432i	−0.525869	+	0.850565i	$0.676260\pi$
$258$		0			0
$259$	14.0457	−	15.4015i	0.872755	−	0.957005i
$260$	2.23328	−	12.1477i	0.138502	−	0.753368i
$261$		0			0
$262$	13.7658			0.850453
$263$	13.9699			0.861422			0.430711	−	0.902490i	$-0.358263\pi$
$263$	13.9699			0.861422			0.430711	+	0.902490i	$0.358263\pi$
$264$		0			0
$265$	−7.01065			−0.430661
$266$	7.51333	−	8.23862i	0.460672	−	0.505142i
$267$		0			0
$268$	9.05393	−	15.6819i	0.553057	−	0.957922i
$269$	−14.4628	+	25.0503i	−0.881813	+	1.52734i	−0.0324890	+	0.999472i	$0.510343\pi$
$269$	−14.4628	+	25.0503i	−0.881813	+	1.52734i	−0.849324	+	0.527872i	$0.822990\pi$
$270$		0			0
$271$	5.05875	+	8.76202i	0.307297	+	0.532255i	0.977770	−	0.209679i	$-0.0672421\pi$
$271$	5.05875	+	8.76202i	0.307297	+	0.532255i	−0.670473	+	0.741934i	$0.733909\pi$
$272$	−2.26513			−0.137344
$273$		0			0
$274$	8.77541			0.530142
$275$	−1.70823	−	2.95874i	−0.103010	−	0.178419i
$276$		0			0
$277$	−1.70320	+	2.95002i	−0.102335	+	0.177250i	−0.912646	−	0.408750i	$-0.865965\pi$
$277$	−1.70320	+	2.95002i	−0.102335	+	0.177250i	0.810311	+	0.586000i	$0.199298\pi$
$278$	−3.80504	+	6.59053i	−0.228211	+	0.395274i
$279$		0			0
$280$	−18.6030	−	4.07780i	−1.11174	−	0.243695i
$281$	−9.40331			−0.560954			−0.280477	−	0.959861i	$-0.590493\pi$
$281$	−9.40331			−0.560954			−0.280477	+	0.959861i	$0.590493\pi$
$282$		0			0
$283$	10.4790			0.622911			0.311456	−	0.950261i	$-0.399183\pi$
$283$	10.4790			0.622911			0.311456	+	0.950261i	$0.399183\pi$
$284$	−4.68194			−0.277822
$285$		0			0
$286$	1.00167	−	5.44846i	0.0592299	−	0.322174i
$287$	−22.8067	−	4.99924i	−1.34623	−	0.295096i
$288$		0			0
$289$	−14.8332	−	25.6919i	−0.872542	−	1.51129i
$290$	1.57602	−	2.72975i	0.0925470	−	0.160296i
$291$		0			0
$292$	−8.55401			−0.500586
$293$	4.61007	+	7.98488i	0.269323	+	0.466481i	0.968687	−	0.248284i	$-0.0798667\pi$
$293$	4.61007	+	7.98488i	0.269323	+	0.466481i	−0.699364	+	0.714766i	$0.746533\pi$
$294$		0			0
$295$	15.7489	+	27.2778i	0.916934	+	1.58818i
$296$	10.8353	+	18.7673i	0.629790	+	1.09083i
$297$		0			0
$298$	−4.53337	−	7.85203i	−0.262611	−	0.454856i
$299$	0.829819	−	4.51371i	0.0479897	−	0.261034i
$300$		0			0
$301$	−0.390784	+	0.428507i	−0.0225244	+	0.0246987i
$302$	9.28524	−	16.0825i	0.534306	−	0.925445i
$303$		0			0
$304$	−0.840540	−	1.45586i	−0.0482083	−	0.0834992i
$305$	−11.4127	+	19.7674i	−0.653490	+	1.13188i
$306$		0			0
$307$	−16.1499			−0.921726			−0.460863	−	0.887471i	$-0.652460\pi$
$307$	−16.1499			−0.921726			−0.460863	+	0.887471i	$0.652460\pi$
$308$	6.25307	+	1.37068i	0.356302	+	0.0781016i
$309$		0			0
$310$	6.74088	+	11.6755i	0.382856	+	0.663126i
$311$	−15.2138	−	26.3510i	−0.862694	−	1.49423i	−0.869319	−	0.494252i	$-0.835442\pi$
$311$	−15.2138	−	26.3510i	−0.862694	−	1.49423i	0.00662478	−	0.999978i	$-0.497891\pi$
$312$		0			0
$313$	−13.6859	+	23.7047i	−0.773574	+	1.33987i	0.162018	+	0.986788i	$0.448200\pi$
$313$	−13.6859	+	23.7047i	−0.773574	+	1.33987i	−0.935592	+	0.353082i	$0.885134\pi$
$314$	−0.273968	+	0.474527i	−0.0154609	+	0.0267791i
$315$		0			0
$316$	−4.03288	−	6.98516i	−0.226867	−	0.392946i
$317$	6.18424	−	10.7114i	0.347342	−	0.601613i	−0.638435	−	0.769676i	$-0.720418\pi$
$317$	6.18424	−	10.7114i	0.347342	−	0.601613i	0.985776	+	0.168063i	$0.0537511\pi$
$318$		0			0
$319$	−1.33913	+	2.31945i	−0.0749771	+	0.129864i
$320$	5.41559	−	9.38008i	0.302741	−	0.524362i
$321$		0			0
$322$	−2.73445	−	0.599394i	−0.152385	−	0.0334029i
$323$	17.3169	−	29.9938i	0.963538	−	1.66890i
$324$		0			0
$325$	1.20501	−	6.55453i	0.0668421	−	0.363580i
$326$	−7.55818	−	13.0911i	−0.418609	−	0.725052i
$327$		0			0
$328$	12.1368	−	21.0216i	0.670144	−	1.16072i
$329$	−3.22540	−	0.707011i	−0.177822	−	0.0389788i
$330$		0			0
$331$	−12.4062			−0.681907			−0.340954	−	0.940080i	$-0.610750\pi$
$331$	−12.4062			−0.681907			−0.340954	+	0.940080i	$0.610750\pi$
$332$	5.67944	−	9.83708i	0.311700	−	0.539880i
$333$		0			0
$334$	−3.67669			−0.201179
$335$	18.1002	−	31.3505i	0.988920	−	1.71286i
$336$		0			0
$337$	−15.8519			−0.863506			−0.431753	−	0.901992i	$-0.642105\pi$
$337$	−15.8519			−0.863506			−0.431753	+	0.901992i	$0.642105\pi$
$338$	8.37835	−	6.82485i	0.455722	−	0.371223i
$339$		0			0
$340$	−23.4014			−1.26912
$341$	−5.72768	−	9.92063i	−0.310171	−	0.537232i
$342$		0			0
$343$	−14.7732	−	11.1693i	−0.797676	−	0.603086i
$344$	−0.301464	−	0.522151i	−0.0162539	−	0.0281525i
$345$		0			0
$346$	1.46318	+	2.53431i	0.0786613	+	0.136245i
$347$	−6.46521	+	11.1981i	−0.347071	+	0.601144i	−0.985728	−	0.168347i	$-0.946157\pi$
$347$	−6.46521	+	11.1981i	−0.347071	+	0.601144i	0.638657	+	0.769492i	$0.279490\pi$
$348$		0			0
$349$	−1.67254	+	2.89693i	−0.0895292	+	0.155069i	−0.907312	−	0.420458i	$-0.861870\pi$
$349$	−1.67254	+	2.89693i	−0.0895292	+	0.155069i	0.817783	+	0.575527i	$0.195203\pi$
$350$	−3.97080	−	0.870404i	−0.212248	−	0.0465250i
$351$		0			0
$352$	−5.33890	+	9.24724i	−0.284564	+	0.492880i
$353$	−6.01463			−0.320127			−0.160063	−	0.987107i	$-0.551170\pi$
$353$	−6.01463			−0.320127			−0.160063	+	0.987107i	$0.551170\pi$
$354$		0			0
$355$	−9.35992			−0.496773
$356$	−19.8383			−1.05143
$357$		0			0
$358$	4.49719	+	7.78936i	0.237684	+	0.411680i
$359$	−7.44965	+	12.9032i	−0.393177	+	0.681003i	−0.992867	−	0.119230i	$-0.961958\pi$
$359$	−7.44965	+	12.9032i	−0.393177	+	0.681003i	0.599689	+	0.800233i	$0.295291\pi$
$360$		0			0
$361$	6.70372			0.352827
$362$	9.58643	+	16.6042i	0.503852	+	0.872697i
$363$		0			0
$364$	7.55311	+	9.94397i	0.395890	+	0.521206i
$365$	−17.1008			−0.895097
$366$		0			0
$367$	−8.08153			−0.421852			−0.210926	−	0.977502i	$-0.567648\pi$
$367$	−8.08153			−0.421852			−0.210926	+	0.977502i	$0.567648\pi$
$368$	−0.211028	+	0.365511i	−0.0110006	+	0.0190536i
$369$		0			0
$370$	8.56911	+	14.8421i	0.445487	+	0.771605i
$371$	4.77603	−	5.23707i	0.247959	−	0.271895i
$372$		0			0
$373$	−11.2771			−0.583905			−0.291953	−	0.956433i	$-0.594305\pi$
$373$	−11.2771			−0.583905			−0.291953	+	0.956433i	$0.594305\pi$
$374$	−10.4960			−0.542733
$375$		0			0
$376$	1.71643	−	2.97295i	0.0885184	−	0.153318i
$377$	−4.92222	+	1.75106i	−0.253507	+	0.0901843i
$378$		0			0
$379$	−8.94558	+	15.4942i	−0.459504	+	0.795884i	−0.998935	−	0.0461461i	$-0.985306\pi$
$379$	−8.94558	+	15.4942i	−0.459504	+	0.795884i	0.539431	+	0.842030i	$0.318639\pi$
$380$	−8.68377	−	15.0407i	−0.445468	−	0.771573i
$381$		0			0
$382$	−0.760453	−	1.31714i	−0.0389081	−	0.0673909i
$383$	−0.0381094			−0.00194730			−0.000973650	−	1.00000i	$-0.500310\pi$
$383$	−0.0381094			−0.00194730			−0.000973650		1.00000i	$0.500310\pi$
$384$		0			0
$385$	12.5009	+	2.74020i	0.637102	+	0.139653i
$386$	−1.31317	−	2.27448i	−0.0668388	−	0.115768i
$387$		0			0
$388$	15.9235			0.808392
$389$	−19.5855	−	33.9231i	−0.993025	−	1.71997i	−0.598622	−	0.801032i	$-0.704285\pi$
$389$	−19.5855	−	33.9231i	−0.993025	−	1.71997i	−0.394403	−	0.918938i	$-0.629049\pi$
$390$		0			0
$391$	−8.69525			−0.439737
$392$	15.7196	−	11.1188i	0.793958	−	0.561582i
$393$		0			0
$394$	9.27006			0.467019
$395$	−8.06236	−	13.9644i	−0.405661	−	0.702626i
$396$		0			0
$397$	8.73141			0.438217			0.219108	−	0.975701i	$-0.429685\pi$
$397$	8.73141			0.438217			0.219108	+	0.975701i	$0.429685\pi$
$398$	17.2482			0.864573
$399$		0			0
$400$	−0.306442	+	0.530773i	−0.0153221	+	0.0265387i
$401$	12.1419	+	21.0303i	0.606336	+	1.05021i	0.991839	+	0.127498i	$0.0406948\pi$
$401$	12.1419	+	21.0303i	0.606336	+	1.05021i	−0.385503	+	0.922707i	$0.625972\pi$
$402$		0			0
$403$	4.04040	−	21.9773i	0.201267	−	1.09477i
$404$	3.00818	−	5.21031i	0.149662	−	0.259223i
$405$		0			0
$406$	0.965497	+	3.03696i	0.0479168	+	0.150722i
$407$	−7.28111	−	12.6113i	−0.360911	−	0.625117i
$408$		0			0
$409$	9.86131	−	17.0803i	0.487610	−	0.844566i	−0.512288	−	0.858814i	$-0.671202\pi$
$409$	9.86131	−	17.0803i	0.487610	−	0.844566i	0.999898	+	0.0142477i	$0.00453532\pi$
$410$	9.59841	−	16.6249i	0.474032	−	0.821047i
$411$		0			0
$412$	2.91400	+	5.04720i	0.143563	+	0.248658i
$413$	−31.1060	−	6.81846i	−1.53062	−	0.335514i
$414$		0			0
$415$	11.3541	−	19.6659i	0.557350	−	0.965359i
$416$	−19.6241	+	6.98119i	−0.962149	+	0.342281i
$417$		0			0
$418$	−3.89483	−	6.74604i	−0.190502	−	0.329959i
$419$	−11.0976	+	19.2216i	−0.542154	+	0.939039i	0.456626	+	0.889659i	$0.349058\pi$
$419$	−11.0976	+	19.2216i	−0.542154	+	0.939039i	−0.998780	+	0.0493798i	$0.984276\pi$
$420$		0			0
$421$	−1.85475			−0.0903949			−0.0451974	−	0.998978i	$-0.514392\pi$
$421$	−1.85475			−0.0903949			−0.0451974	+	0.998978i	$0.514392\pi$
$422$	−13.5789			−0.661009
$423$		0			0
$424$	3.68440	+	6.38156i	0.178930	+	0.309916i
$425$	−12.6267			−0.612485
$426$		0			0
$427$	−6.99163	−	21.9921i	−0.338349	−	1.06427i
$428$	9.44312			0.456450
$429$		0			0
$430$	−0.238413	−	0.412943i	−0.0114973	−	0.0199139i
$431$	37.7871			1.82014			0.910069	−	0.414456i	$-0.136028\pi$
$431$	37.7871			1.82014			0.910069	+	0.414456i	$0.136028\pi$
$432$		0			0
$433$	17.5680	+	30.4286i	0.844263	+	1.46231i	0.886259	+	0.463189i	$0.153295\pi$
$433$	17.5680	+	30.4286i	0.844263	+	1.46231i	−0.0419959	+	0.999118i	$0.513372\pi$
$434$	−13.3141	−	2.91846i	−0.639096	−	0.140091i
$435$		0			0
$436$	11.3879			0.545384
$437$	−3.22662	−	5.58867i	−0.154350	−	0.267342i
$438$		0			0
$439$	−7.67375	−	13.2913i	−0.366248	−	0.634360i	0.622727	−	0.782439i	$-0.286025\pi$
$439$	−7.67375	−	13.2913i	−0.366248	−	0.634360i	−0.988976	+	0.148078i	$0.952691\pi$
$440$	−6.65247	+	11.5224i	−0.317144	+	0.549310i
$441$		0			0
$442$	−15.5879	−	13.2744i	−0.741440	−	0.631398i
$443$	14.5356	−	25.1765i	0.690609	−	1.19617i	−0.281030	−	0.959699i	$-0.590676\pi$
$443$	14.5356	−	25.1765i	0.690609	−	1.19617i	0.971639	−	0.236471i	$-0.0759907\pi$
$444$		0			0
$445$	−39.6598			−1.88005
$446$	−15.4757			−0.732795
$447$		0			0
$448$	3.31769	+	10.4358i	0.156746	+	0.493043i
$449$	1.18131	+	2.04609i	0.0557494	+	0.0965607i	0.892553	−	0.450942i	$-0.148912\pi$
$449$	1.18131	+	2.04609i	0.0557494	+	0.0965607i	−0.836804	+	0.547503i	$0.815579\pi$
$450$		0			0
$451$	−8.15570	+	14.1261i	−0.384037	+	0.665172i
$452$	−4.77864			−0.224768
$453$		0			0
$454$	18.7409			0.879555
$455$	15.0998	+	19.8795i	0.707891	+	0.931967i
$456$		0			0
$457$	8.37672	+	14.5089i	0.391846	+	0.678698i	0.992693	−	0.120667i	$-0.0385032\pi$
$457$	8.37672	+	14.5089i	0.391846	+	0.678698i	−0.600847	+	0.799364i	$0.705170\pi$
$458$	−16.0051			−0.747871
$459$		0			0
$460$	−2.18017	+	3.77616i	−0.101651	+	0.176064i
$461$	−12.5469	−	21.7318i	−0.584366	−	1.01215i	−0.994954	−	0.100330i	$-0.968010\pi$
$461$	−12.5469	−	21.7318i	−0.584366	−	1.01215i	0.410588	−	0.911821i	$-0.365323\pi$
$462$		0			0
$463$	−0.254256			−0.0118163			−0.00590815	−	0.999983i	$-0.501881\pi$
$463$	−0.254256			−0.0118163			−0.00590815	+	0.999983i	$0.501881\pi$
$464$	0.480459			0.0223048
$465$		0			0
$466$	−18.9985			−0.880088
$467$	5.11155	−	8.85346i	0.236534	−	0.409689i	−0.723183	−	0.690656i	$-0.757322\pi$
$467$	5.11155	−	8.85346i	0.236534	−	0.409689i	0.959717	+	0.280967i	$0.0906551\pi$
$468$		0			0
$469$	11.0885	+	34.8788i	0.512020	+	1.61055i
$470$	1.35744	−	2.35116i	0.0626141	−	0.108451i
$471$		0			0
$472$	16.5534	−	28.6713i	0.761932	−	1.31970i
$473$	0.202578	+	0.350875i	0.00931453	+	0.0161332i
$474$		0			0
$475$	−4.68550	−	8.11552i	−0.214985	−	0.372366i
$476$	15.9423	−	17.4813i	0.730715	−	0.801253i
$477$		0			0
$478$	−4.67581	−	8.09874i	−0.213866	−	0.370428i
$479$	12.7080			0.580643			0.290322	−	0.956929i	$-0.406238\pi$
$479$	12.7080			0.580643			0.290322	+	0.956929i	$0.406238\pi$
$480$		0			0
$481$	5.13622	−	27.9379i	0.234191	−	1.27386i
$482$	16.1646			0.736277
$483$		0			0
$484$	−4.96351	+	8.59706i	−0.225614	+	0.390775i
$485$	31.8335			1.44549
$486$		0			0
$487$	−10.2410	+	17.7379i	−0.464063	+	0.803781i	−0.999159	−	0.0410108i	$-0.986942\pi$
$487$	−10.2410	+	17.7379i	−0.464063	+	0.803781i	0.535096	+	0.844791i	$0.320276\pi$
$488$	23.9915			1.08604
$489$		0			0
$490$	12.4318	−	8.79327i	0.561612	−	0.397239i
$491$	9.92098	−	17.1836i	0.447727	−	0.775487i	−0.550510	−	0.834828i	$-0.685567\pi$
$491$	9.92098	−	17.1836i	0.447727	−	0.775487i	0.998238	+	0.0593417i	$0.0189002\pi$
$492$		0			0
$493$	4.94924	+	8.57233i	0.222902	+	0.386078i
$494$	2.74748	−	14.9446i	0.123615	−	0.672389i
$495$		0			0
$496$	−1.02750	+	1.77968i	−0.0461361	+	0.0799100i
$497$	6.37648	−	6.99202i	0.286024	−	0.313635i
$498$		0			0
$499$	−13.9419	+	24.1480i	−0.624124	+	1.08101i	0.364585	+	0.931170i	$0.381211\pi$
$499$	−13.9419	+	24.1480i	−0.624124	+	1.08101i	−0.988710	+	0.149845i	$0.952123\pi$
$500$	5.39817	−	9.34990i	0.241413	−	0.418140i
$501$		0			0
$502$	7.30913	−	12.6598i	0.326223	−	0.565034i
$503$	−6.62277	−	11.4710i	−0.295295	−	0.511465i	0.679759	−	0.733436i	$-0.262084\pi$
$503$	−6.62277	−	11.4710i	−0.295295	−	0.511465i	−0.975053	+	0.221970i	$0.928751\pi$
$504$		0			0
$505$	6.01381	−	10.4162i	0.267611	−	0.463516i
$506$	−0.977844	+	1.69368i	−0.0434705	+	0.0752931i
$507$		0			0
$508$	−6.29167	−	10.8975i	−0.279148	−	0.483498i
$509$	13.5375	+	23.4477i	0.600040	+	1.03930i	0.992814	+	0.119665i	$0.0381819\pi$
$509$	13.5375	+	23.4477i	0.600040	+	1.03930i	−0.392775	+	0.919635i	$0.628485\pi$
$510$		0			0
$511$	11.6500	−	12.7746i	0.515365	−	0.565115i
$512$	3.73962			0.165270
$513$		0			0
$514$	6.31220	−	10.9331i	0.278419	−	0.482236i
$515$	5.82554	+	10.0901i	0.256704	+	0.444625i
$516$		0			0
$517$	−1.15341	+	1.99776i	−0.0507269	+	0.0878615i
$518$	−16.9251	−	3.70999i	−0.743645	−	0.163008i
$519$		0			0
$520$	−24.4524	+	8.69883i	−1.07231	+	0.381469i
$521$	11.6257	+	20.1363i	0.509331	+	0.882187i	0.999942	+	0.0108082i	$0.00344041\pi$
$521$	11.6257	+	20.1363i	0.509331	+	0.882187i	−0.490611	+	0.871379i	$0.663226\pi$
$522$		0			0
$523$	−16.7690	−	29.0447i	−0.733256	−	1.27004i	−0.955484	−	0.295043i	$-0.904666\pi$
$523$	−16.7690	−	29.0447i	−0.733256	−	1.27004i	0.222228	−	0.974995i	$-0.428667\pi$
$524$	10.8389	+	18.7735i	0.473500	+	0.820126i
$525$		0			0
$526$	−5.80626	−	10.0567i	−0.253165	−	0.438494i
$527$	−42.3373			−1.84424
$528$		0			0
$529$	10.6899	−	18.5155i	0.464779	−	0.805021i
$530$	2.91380	+	5.04685i	0.126568	+	0.219221i
$531$		0			0
$532$	17.1515	+	3.75963i	0.743614	+	0.163001i
$533$	−29.9777	+	10.6645i	−1.29848	+	0.461929i
$534$		0			0
$535$	18.8783			0.816178
$536$	−38.0498			−1.64350
$537$		0			0
$538$	24.0444			1.03663
$539$	−10.5632	+	7.47158i	−0.454991	+	0.321824i
$540$		0			0
$541$	−4.65598	+	8.06439i	−0.200176	+	0.346715i	−0.948585	−	0.316522i	$-0.897485\pi$
$541$	−4.65598	+	8.06439i	−0.200176	+	0.346715i	0.748409	+	0.663238i	$0.230818\pi$
$542$	4.20509	−	7.28343i	0.180624	−	0.312850i
$543$		0			0
$544$	19.7318	+	34.1764i	0.845992	+	1.46530i
$545$	22.7663			0.975200
$546$		0			0
$547$	−31.5111			−1.34732			−0.673658	−	0.739043i	$-0.735278\pi$
$547$	−31.5111			−1.34732			−0.673658	+	0.739043i	$0.735278\pi$
$548$	6.90959	+	11.9678i	0.295163	+	0.511237i
$549$		0			0
$550$	−1.41997	+	2.45945i	−0.0605476	+	0.104871i
$551$	−3.67311	+	6.36201i	−0.156480	+	0.271031i
$552$		0			0
$553$	15.9242	+	3.49059i	0.677165	+	0.148435i
$554$	2.83157			0.120302
$555$		0			0
$556$	−11.9841			−0.508238
$557$	−5.53300			−0.234441			−0.117220	−	0.993106i	$-0.537398\pi$
$557$	−5.53300			−0.234441			−0.117220	+	0.993106i	$0.537398\pi$
$558$		0			0
$559$	−0.142902	+	0.777298i	−0.00604410	+	0.0328762i
$560$	−0.695564	−	2.18789i	−0.0293929	−	0.0924553i
$561$		0			0
$562$	3.90826	+	6.76930i	0.164860	+	0.285546i
$563$	6.18438	−	10.7117i	0.260641	−	0.451443i	−0.705772	−	0.708439i	$-0.749400\pi$
$563$	6.18438	−	10.7117i	0.260641	−	0.451443i	0.966412	+	0.256997i	$0.0827329\pi$
$564$		0			0
$565$	−9.55324			−0.401908
$566$	−4.35534	−	7.54366i	−0.183068	−	0.317084i
$567$		0			0
$568$	4.91904	+	8.52003i	0.206398	+	0.357493i
$569$	0.997229	+	1.72725i	0.0418060	+	0.0724101i	0.886171	−	0.463358i	$-0.153356\pi$
$569$	0.997229	+	1.72725i	0.0418060	+	0.0724101i	−0.844365	+	0.535768i	$0.820022\pi$
$570$		0			0
$571$	−11.0440	−	19.1288i	−0.462179	−	0.800517i	0.536891	−	0.843652i	$-0.319599\pi$
$571$	−11.0440	−	19.1288i	−0.462179	−	0.800517i	−0.999069	+	0.0431350i	$0.986265\pi$
$572$	8.21921	−	2.92395i	0.343663	−	0.122257i
$573$		0			0
$574$	5.88015	+	18.4960i	0.245433	+	0.772007i
$575$	−1.17635	+	2.03750i	−0.0490573	+	0.0849697i
$576$		0			0
$577$	−4.54321	−	7.86907i	−0.189136	−	0.327594i	0.755826	−	0.654772i	$-0.227235\pi$
$577$	−4.54321	−	7.86907i	−0.189136	−	0.327594i	−0.944963	+	0.327179i	$0.893902\pi$
$578$	−12.3301	+	21.3564i	−0.512866	+	0.888310i
$579$		0			0
$580$	4.96371			0.206107
$581$	6.95572	+	21.8791i	0.288572	+	0.907700i
$582$		0			0
$583$	−2.47584	−	4.28828i	−0.102539	−	0.177602i
$584$	8.98721	+	15.5663i	0.371893	+	0.644138i
$585$		0			0
$586$	3.83213	−	6.63744i	0.158304	−	0.274190i
$587$	3.02112	−	5.23273i	0.124695	−	0.215978i	−0.796919	−	0.604086i	$-0.793538\pi$
$587$	3.02112	−	5.23273i	0.124695	−	0.215978i	0.921614	+	0.388109i	$0.126872\pi$
$588$		0			0
$589$	−15.7105	−	27.2113i	−0.647338	−	1.12122i
$590$	13.0912	−	22.6747i	0.538958	−	0.933503i
$591$		0			0
$592$	−1.30617	+	2.26236i	−0.0536834	+	0.0929823i
$593$	6.67095	−	11.5544i	0.273943	−	0.474484i	−0.695925	−	0.718115i	$-0.745005\pi$
$593$	6.67095	−	11.5544i	0.273943	−	0.474484i	0.969868	+	0.243631i	$0.0783386\pi$
$594$		0			0
$595$	31.8712	−	34.9478i	1.30659	−	1.43272i
$596$	7.13898	−	12.3651i	0.292424	−	0.506493i
$597$		0			0
$598$	−3.59424	+	1.27864i	−0.146979	+	0.0522874i
$599$	15.0725	+	26.1063i	0.615844	+	1.06667i	0.990236	+	0.139402i	$0.0445181\pi$
$599$	15.0725	+	26.1063i	0.615844	+	1.06667i	−0.374392	+	0.927270i	$0.622149\pi$
$600$		0			0
$601$	−18.9159	+	32.7634i	−0.771598	+	1.33645i	0.165089	+	0.986279i	$0.447209\pi$
$601$	−18.9159	+	32.7634i	−0.771598	+	1.33645i	−0.936687	+	0.350168i	$0.886125\pi$
$602$	0.470895	+	0.103221i	0.0191922	+	0.00420696i
$603$		0			0
$604$	29.2441			1.18992
$605$	−9.92283	+	17.1869i	−0.403421	+	0.698745i
$606$		0			0
$607$	6.70899			0.272309			0.136155	−	0.990688i	$-0.456526\pi$
$607$	6.70899			0.272309			0.136155	+	0.990688i	$0.456526\pi$
$608$	−14.6441	+	25.3643i	−0.593895	+	1.02866i
$609$		0			0
$610$	18.9737			0.768221
$611$	−4.23956	+	1.50821i	−0.171514	+	0.0610156i
$612$		0			0
$613$	−20.1672			−0.814544			−0.407272	−	0.913307i	$-0.633520\pi$
$613$	−20.1672			−0.814544			−0.407272	+	0.913307i	$0.633520\pi$
$614$	6.71233	+	11.6261i	0.270888	+	0.469191i
$615$		0			0
$616$	−4.07542	−	12.8192i	−0.164203	−	0.516501i
$617$	2.98249	+	5.16582i	0.120071	+	0.207968i	0.919795	−	0.392399i	$-0.128355\pi$
$617$	2.98249	+	5.16582i	0.120071	+	0.207968i	−0.799725	+	0.600367i	$0.795021\pi$
$618$		0			0
$619$	4.31420	+	7.47242i	0.173402	+	0.300342i	0.939607	−	0.342255i	$-0.111191\pi$
$619$	4.31420	+	7.47242i	0.173402	+	0.300342i	−0.766205	+	0.642596i	$0.777857\pi$
$620$	−10.6153	+	18.3862i	−0.426320	+	0.738407i
$621$		0			0
$622$	−12.6465	+	21.9043i	−0.507077	+	0.878283i
$623$	27.0184	−	29.6265i	1.08247	−	1.18696i
$624$		0			0
$625$	15.4127	−	26.6956i	0.616507	−	1.06782i
$626$	22.7529			0.909388
$627$		0			0
$628$	−0.862869			−0.0344322
$629$	−53.8198			−2.14594
$630$		0			0
$631$	−1.02888	−	1.78208i	−0.0409592	−	0.0709434i	0.844819	−	0.535052i	$-0.179708\pi$
$631$	−1.02888	−	1.78208i	−0.0409592	−	0.0709434i	−0.885778	+	0.464109i	$0.846375\pi$
$632$	−8.47423	+	14.6778i	−0.337087	+	0.583852i
$633$		0			0
$634$	−10.2813			−0.408323
$635$	−12.5780	−	21.7858i	−0.499144	−	0.864542i
$636$		0			0
$637$	−25.1372	−	2.26318i	−0.995971	−	0.0896706i
$638$	2.22631			0.0881405
$639$		0			0
$640$	21.2321			0.839271
$641$	−8.83114	+	15.2960i	−0.348809	+	0.604155i	−0.986038	−	0.166519i	$-0.946747\pi$
$641$	−8.83114	+	15.2960i	−0.348809	+	0.604155i	0.637229	+	0.770674i	$0.280080\pi$
$642$		0			0
$643$	−24.6023	−	42.6124i	−0.970219	−	1.68047i	−0.694885	−	0.719121i	$-0.744545\pi$
$643$	−24.6023	−	42.6124i	−0.970219	−	1.68047i	−0.275334	−	0.961349i	$-0.588788\pi$
$644$	−1.33561	−	4.20115i	−0.0526304	−	0.165548i
$645$		0			0
$646$	−28.7894			−1.13270
$647$	15.4959			0.609208			0.304604	−	0.952479i	$-0.401476\pi$
$647$	15.4959			0.609208			0.304604	+	0.952479i	$0.401476\pi$
$648$		0			0
$649$	−11.1235	+	19.2666i	−0.436637	+	0.756278i
$650$	−5.21934	+	1.85676i	−0.204719	+	0.0728281i
$651$		0			0
$652$	11.9023	−	20.6154i	0.466131	−	0.807363i
$653$	−18.3665	−	31.8117i	−0.718738	−	1.24489i	−0.961500	−	0.274804i	$-0.911387\pi$
$653$	−18.3665	−	31.8117i	−0.718738	−	1.24489i	0.242763	−	0.970086i	$-0.421946\pi$
$654$		0			0
$655$	21.6687	+	37.5312i	0.846665	+	1.46647i
$656$	2.92613			0.114246
$657$		0			0
$658$	0.831593	+	2.61577i	0.0324189	+	0.101973i
$659$	5.48070	+	9.49284i	0.213498	+	0.369789i	0.952807	−	0.303577i	$-0.0981811\pi$
$659$	5.48070	+	9.49284i	0.213498	+	0.369789i	−0.739309	+	0.673366i	$0.764848\pi$
$660$		0			0
$661$	16.0710			0.625091			0.312545	−	0.949903i	$-0.398818\pi$
$661$	16.0710			0.625091			0.312545	+	0.949903i	$0.398818\pi$
$662$	5.15634	+	8.93104i	0.200407	+	0.347115i
$663$		0			0
$664$	−23.8682			−0.926268
$665$	34.2886	+	7.51609i	1.32965	+	0.291462i
$666$		0			0
$667$	1.84436			0.0714139
$668$	−2.89495	−	5.01421i	−0.112009	−	0.194005i
$669$		0			0
$670$	−30.0916			−1.16254
$671$	−16.1218			−0.622375
$672$		0			0
$673$	14.1074	−	24.4348i	0.543802	−	0.941892i	−0.454880	−	0.890553i	$-0.650318\pi$
$673$	14.1074	−	24.4348i	0.543802	−	0.941892i	0.998681	−	0.0513390i	$-0.0163489\pi$
$674$	6.58844	+	11.4115i	0.253777	+	0.439555i
$675$		0			0
$676$	15.9046	+	6.05249i	0.611714	+	0.232788i
$677$	−17.5358	+	30.3729i	−0.673956	+	1.16733i	0.302817	+	0.953049i	$0.402073\pi$
$677$	−17.5358	+	30.3729i	−0.673956	+	1.16733i	−0.976773	+	0.214277i	$0.931260\pi$
$678$		0			0
$679$	−21.6867	+	23.7802i	−0.832259	+	0.912600i
$680$	24.5866	+	42.5852i	0.942851	+	1.63307i
$681$		0			0
$682$	−4.76114	+	8.24654i	−0.182313	+	0.315776i
$683$	24.1916	−	41.9011i	0.925666	−	1.60330i	0.135181	−	0.990821i	$-0.456839\pi$
$683$	24.1916	−	41.9011i	0.925666	−	1.60330i	0.790486	−	0.612480i	$-0.209828\pi$
$684$		0			0
$685$	13.8133	+	23.9254i	0.527781	+	0.914143i
$686$	−1.90050	+	15.2772i	−0.0725615	+	0.583287i
$687$		0			0
$688$	0.0363408	−	0.0629441i	0.00138548	−	0.00239972i
$689$	1.74650	−	9.49988i	0.0665363	−	0.361917i
$690$		0			0
$691$	12.0530	+	20.8764i	0.458518	+	0.794176i	0.998883	−	0.0472547i	$-0.0150473\pi$
$691$	12.0530	+	20.8764i	0.458518	+	0.794176i	−0.540365	+	0.841431i	$0.681714\pi$
$692$	−2.30417	+	3.99093i	−0.0875913	+	0.151713i
$693$		0			0
$694$	10.7484			0.408005
$695$	−23.9580			−0.908779
$696$		0			0
$697$	30.1423	+	52.2079i	1.14172	+	1.97752i
$698$	2.78061			0.105248
$699$		0			0
$700$	−1.93949	−	6.10065i	−0.0733059	−	0.230583i
$701$	3.07792			0.116251			0.0581257	−	0.998309i	$-0.481488\pi$
$701$	3.07792			0.116251			0.0581257	+	0.998309i	$0.481488\pi$
$702$		0			0
$703$	−19.9714	−	34.5914i	−0.753235	−	1.30464i
$704$	7.65016			0.288326
$705$		0			0
$706$	2.49983	+	4.32984i	0.0940825	+	0.162956i
$707$	3.68417	+	11.5885i	0.138557	+	0.435831i
$708$		0			0
$709$	35.9444			1.34992			0.674959	−	0.737855i	$-0.264161\pi$
$709$	35.9444			1.34992			0.674959	+	0.737855i	$0.264161\pi$
$710$	3.89022	+	6.73806i	0.145997	+	0.252875i
$711$		0			0
$712$	20.8429	+	36.1010i	0.781121	+	1.35294i
$713$	−3.94430	+	6.83173i	−0.147715	+	0.255850i
$714$		0			0
$715$	16.4315	−	5.84544i	0.614503	−	0.218607i
$716$	−7.08200	+	12.2664i	−0.264667	+	0.458416i
$717$		0			0
$718$	12.3851			0.462206
$719$	−10.1952			−0.380217			−0.190108	−	0.981763i	$-0.560884\pi$
$719$	−10.1952			−0.380217			−0.190108	+	0.981763i	$0.560884\pi$
$720$		0			0
$721$	−11.5062	−	2.52217i	−0.428513	−	0.0939303i
$722$	−2.78624	−	4.82590i	−0.103693	−	0.179602i
$723$		0			0
$724$	−15.0963	+	26.1476i	−0.561051	+	0.971769i
$725$	2.67827			0.0994683
$726$		0			0
$727$	−2.32372			−0.0861821			−0.0430911	−	0.999071i	$-0.513721\pi$
$727$	−2.32372			−0.0861821			−0.0430911	+	0.999071i	$0.513721\pi$
$728$	10.1601	−	24.1924i	0.376558	−	0.896632i
$729$		0			0
$730$	7.10753	+	12.3106i	0.263061	+	0.455636i
$731$	1.49739			0.0553831
$732$		0			0
$733$	2.91958	−	5.05685i	0.107837	−	0.186779i	−0.807057	−	0.590474i	$-0.798941\pi$
$733$	2.91958	−	5.05685i	0.107837	−	0.186779i	0.914894	+	0.403695i	$0.132274\pi$
$734$	3.35889	+	5.81777i	0.123979	+	0.214738i
$735$		0			0
$736$	7.35314			0.271040
$737$	25.5687			0.941834
$738$		0			0
$739$	0.0211428			0.000777749			0.000388875	−	1.00000i	$-0.499876\pi$
$739$	0.0211428			0.000777749			0.000388875		1.00000i	$0.499876\pi$
$740$	−13.4943	+	23.3728i	−0.496060	+	0.859201i
$741$		0			0
$742$	−5.75513	−	1.26153i	−0.211277	−	0.0463122i
$743$	14.8332	−	25.6918i	0.544176	−	0.942541i	−0.454482	−	0.890756i	$-0.650176\pi$
$743$	14.8332	−	25.6918i	0.544176	−	0.942541i	0.998658	−	0.0517853i	$-0.0164911\pi$
$744$		0			0
$745$	14.2719	−	24.7197i	0.522883	−	0.905660i
$746$	4.68704	+	8.11819i	0.171605	+	0.297228i
$747$		0			0
$748$	−8.26432	−	14.3142i	−0.302173	−	0.523380i
$749$	−12.8609	+	14.1024i	−0.469927	+	0.515290i
$750$		0			0
$751$	−6.30078	−	10.9133i	−0.229919	−	0.398231i	0.727865	−	0.685720i	$-0.240513\pi$
$751$	−6.30078	−	10.9133i	−0.229919	−	0.398231i	−0.957784	+	0.287489i	$0.907179\pi$
$752$	0.413824			0.0150906
$753$		0			0
$754$	3.30636	+	2.81565i	0.120411	+	0.102540i
$755$	58.4635			2.12770
$756$		0			0
$757$	−8.13319	+	14.0871i	−0.295606	+	0.512004i	−0.975126	−	0.221653i	$-0.928855\pi$
$757$	−8.13319	+	14.0871i	−0.295606	+	0.512004i	0.679520	+	0.733657i	$0.262188\pi$
$758$	14.8720			0.540177
$759$		0			0
$760$	−18.2471	+	31.6049i	−0.661891	+	1.14643i
$761$	−46.2551			−1.67675			−0.838374	−	0.545096i	$-0.816493\pi$
$761$	−46.2551			−1.67675			−0.838374	+	0.545096i	$0.816493\pi$
$762$		0			0
$763$	−15.5096	+	17.0068i	−0.561486	+	0.615687i
$764$	1.19753	−	2.07419i	0.0433252	−	0.0750414i
$765$		0			0
$766$	0.0158392	+	0.0274344i	0.000572295	+	0.000991244i
$767$	−40.8866	+	14.5452i	−1.47633	+	0.525198i
$768$		0			0
$769$	19.2803	−	33.3944i	0.695264	−	1.20423i	−0.274827	−	0.961494i	$-0.588621\pi$
$769$	19.2803	−	33.3944i	0.695264	−	1.20423i	0.970092	−	0.242739i	$-0.0780460\pi$
$770$	−3.22305	−	10.1381i	−0.116151	−	0.365351i
$771$		0			0
$772$	2.06794	−	3.58177i	0.0744267	−	0.128911i
$773$	−5.17723	+	8.96723i	−0.186212	+	0.322529i	−0.943984	−	0.329990i	$-0.892954\pi$
$773$	−5.17723	+	8.96723i	−0.186212	+	0.322529i	0.757772	+	0.652519i	$0.226288\pi$
$774$		0			0
$775$	−5.72768	+	9.92063i	−0.205744	+	0.356360i
$776$	−16.7299	−	28.9770i	−0.600568	−	1.04021i
$777$		0			0
$778$	−16.2805	+	28.1986i	−0.583683	+	1.01097i
$779$	−22.3703	+	38.7465i	−0.801499	+	1.38824i
$780$		0			0
$781$	−3.30550	−	5.72529i	−0.118280	−	0.204867i
$782$	3.61397	+	6.25957i	0.129235	+	0.223842i
$783$		0			0
$784$	2.10825	+	0.970911i	0.0752946	+	0.0346754i
$785$	−1.72501			−0.0615683
$786$		0			0
$787$	−17.1440	+	29.6942i	−0.611116	+	1.05848i	0.379937	+	0.925012i	$0.375946\pi$
$787$	−17.1440	+	29.6942i	−0.611116	+	1.05848i	−0.991053	+	0.133471i	$0.957388\pi$
$788$	7.29906	+	12.6423i	0.260018	+	0.450365i
$789$		0			0
$790$	−6.70184	+	11.6079i	−0.238441	+	0.412992i
$791$	6.50818	−	7.13643i	0.231404	−	0.253742i
$792$		0			0
$793$	−23.9430	−	20.3894i	−0.850239	−	0.724050i
$794$	−3.62899	−	6.28560i	−0.128788	−	0.223068i
$795$		0			0
$796$	13.5809	+	23.5228i	0.481362	+	0.833743i
$797$	−6.60638	−	11.4426i	−0.234010	−	0.405317i	0.724975	−	0.688776i	$-0.241851\pi$
$797$	−6.60638	−	11.4426i	−0.234010	−	0.405317i	−0.958984	+	0.283459i	$0.908518\pi$
$798$		0			0
$799$	4.26283	+	7.38343i	0.150808	+	0.261207i
$800$	10.6778			0.377517
$801$		0			0
$802$	10.0929	−	17.4815i	0.356394	−	0.617293i
$803$	−6.03922	−	10.4602i	−0.213120	−	0.369134i
$804$		0			0
$805$	−2.67009	−	8.39875i	−0.0941083	−	0.296017i
$806$	−17.5004	+	6.22571i	−0.616426	+	0.219291i
$807$		0			0
$808$	−12.6421			−0.444746
$809$	50.9750			1.79219			0.896094	−	0.443865i	$-0.146393\pi$
$809$	50.9750			1.79219			0.896094	+	0.443865i	$0.146393\pi$
$810$		0			0
$811$	7.86969			0.276342			0.138171	−	0.990408i	$-0.455878\pi$
$811$	7.86969			0.276342			0.138171	+	0.990408i	$0.455878\pi$
$812$	−3.38155	+	3.70798i	−0.118669	+	0.130124i
$813$		0			0
$814$	−6.05243	+	10.4831i	−0.212138	+	0.367433i
$815$	23.7946	−	41.2135i	0.833488	−	1.44364i
$816$		0			0
$817$	0.555650	+	0.962415i	0.0194397	+	0.0336706i
$818$	−16.3944			−0.573218
$819$		0			0
$820$	30.2304			1.05569
$821$	−20.8357	−	36.0885i	−0.727171	−	1.25950i	−0.958074	−	0.286520i	$-0.907502\pi$
$821$	−20.8357	−	36.0885i	−0.727171	−	1.25950i	0.230904	−	0.972977i	$-0.425832\pi$
$822$		0			0
$823$	7.85504	−	13.6053i	0.273809	−	0.474252i	−0.696025	−	0.718018i	$-0.745050\pi$
$823$	7.85504	−	13.6053i	0.273809	−	0.474252i	0.969834	+	0.243766i	$0.0783829\pi$
$824$	6.12315	−	10.6056i	0.213310	−	0.369464i
$825$		0			0
$826$	8.01993	+	25.2266i	0.279049	+	0.877746i
$827$	−33.6343			−1.16958			−0.584789	−	0.811185i	$-0.698823\pi$
$827$	−33.6343			−1.16958			−0.584789	+	0.811185i	$0.698823\pi$
$828$		0			0
$829$	−50.3021			−1.74706			−0.873532	−	0.486767i	$-0.838176\pi$
$829$	−50.3021			−1.74706			−0.873532	+	0.486767i	$0.838176\pi$
$830$	−18.8762			−0.655202
$831$		0			0
$832$	11.3615	+	9.67525i	0.393889	+	0.335429i
$833$	4.39423	+	47.6167i	0.152251	+	1.64982i
$834$		0			0
$835$	−5.78746	−	10.0242i	−0.200283	−	0.346901i
$836$	6.13342	−	10.6234i	0.212129	−	0.367418i
$837$		0			0
$838$	18.4498			0.637338
$839$	19.2875	+	33.4069i	0.665877	+	1.15333i	0.979047	+	0.203635i	$0.0652757\pi$
$839$	19.2875	+	33.4069i	0.665877	+	1.15333i	−0.313170	+	0.949697i	$0.601391\pi$
$840$		0			0
$841$	13.4502	+	23.2964i	0.463800	+	0.803326i
$842$	0.770881	+	1.33520i	0.0265663	+	0.0460142i
$843$		0			0
$844$	−10.6917	−	18.5186i	−0.368025	−	0.637437i
$845$	31.7957	+	12.0999i	1.09381	+	0.416248i
$846$		0			0
$847$	−6.07890	−	19.1211i	−0.208874	−	0.657010i
$848$	−0.444145	+	0.769282i	−0.0152520	+	0.0264173i
$849$		0			0
$850$	5.24798	+	9.08977i	0.180004	+	0.311777i
$851$	−5.01406	+	8.68460i	−0.171880	+	0.297704i
$852$		0			0
$853$	22.6889			0.776855			0.388427	−	0.921479i	$-0.373018\pi$
$853$	22.6889			0.776855			0.388427	+	0.921479i	$0.373018\pi$
$854$	−12.9259	+	14.1736i	−0.442314	+	0.485012i
$855$		0			0
$856$	−9.92134	−	17.1843i	−0.339104	−	0.587346i
$857$	−10.2901	−	17.8230i	−0.351504	−	0.608822i	0.635009	−	0.772504i	$-0.280996\pi$
$857$	−10.2901	−	17.8230i	−0.351504	−	0.608822i	−0.986513	+	0.163682i	$0.947663\pi$
$858$		0			0
$859$	1.81131	−	3.13729i	0.0618012	−	0.107043i	−0.833469	−	0.552566i	$-0.813649\pi$
$859$	1.81131	−	3.13729i	0.0618012	−	0.107043i	0.895271	+	0.445523i	$0.146982\pi$
$860$	0.375443	−	0.650286i	0.0128025	−	0.0221746i
$861$		0			0
$862$	−15.7053	−	27.2023i	−0.534923	−	0.926515i
$863$	3.99010	−	6.91105i	0.135824	−	0.235255i	−0.790088	−	0.612994i	$-0.789965\pi$
$863$	3.99010	−	6.91105i	0.135824	−	0.235255i	0.925912	+	0.377739i	$0.123298\pi$
$864$		0			0
$865$	−4.60639	+	7.97850i	−0.156622	+	0.271277i
$866$	14.6034	−	25.2938i	0.496244	−	0.859520i
$867$		0			0
$868$	−6.50310	−	20.4555i	−0.220730	−	0.694304i
$869$	5.69451	−	9.86318i	0.193173	−	0.334586i
$870$		0			0
$871$	37.9728	+	32.3370i	1.28666	+	1.09570i
$872$	−11.9647	−	20.7234i	−0.405174	−	0.701783i
$873$		0			0
$874$	−2.68213	+	4.64558i	−0.0907244	+	0.157139i
$875$	6.61123	+	20.7956i	0.223500	+	0.703019i
$876$		0			0
$877$	−12.6000			−0.425470			−0.212735	−	0.977110i	$-0.568237\pi$
$877$	−12.6000			−0.425470			−0.212735	+	0.977110i	$0.568237\pi$
$878$	−6.37881	+	11.0484i	−0.215275	+	0.372866i
$879$		0			0
$880$	−1.60388			−0.0540668
$881$	−0.0834951	+	0.144618i	−0.00281302	+	0.00487230i	−0.867428	−	0.497562i	$-0.834229\pi$
$881$	−0.0834951	+	0.144618i	−0.00281302	+	0.00487230i	0.864615	+	0.502434i	$0.167562\pi$
$882$		0			0
$883$	1.54174			0.0518836			0.0259418	−	0.999663i	$-0.491742\pi$
$883$	1.54174			0.0518836			0.0259418	+	0.999663i	$0.491742\pi$
$884$	5.82979	−	31.7105i	0.196077	−	1.06654i
$885$		0			0
$886$	−24.1655			−0.811857
$887$	−5.16683	−	8.94922i	−0.173485	−	0.300485i	0.766151	−	0.642661i	$-0.222170\pi$
$887$	−5.16683	−	8.94922i	−0.173485	−	0.300485i	−0.939636	+	0.342176i	$0.888836\pi$
$888$		0			0
$889$	24.8432	+	5.44565i	0.833213	+	0.182641i
$890$	16.4836	+	28.5504i	0.552532	+	0.957013i
$891$		0			0
$892$	−12.1852	−	21.1055i	−0.407992	−	0.706663i
$893$	−3.16369	+	5.47967i	−0.105869	+	0.183370i
$894$		0			0
$895$	−14.1580	+	24.5224i	−0.473250	+	0.819693i
$896$	−14.4644	+	15.8607i	−0.483223	+	0.529869i
$897$		0			0
$898$	0.981963	−	1.70081i	0.0327685	−	0.0567568i
$899$	8.98022			0.299507
$900$		0			0
$901$	−18.3007			−0.609684
$902$	13.5589			0.451461
$903$		0			0
$904$	5.02064	+	8.69600i	0.166984	+	0.289225i
$905$	−30.1799	+	52.2732i	−1.00321	+	1.73762i
$906$		0			0
$907$	23.8992			0.793559			0.396780	−	0.917914i	$-0.370128\pi$
$907$	23.8992			0.793559			0.396780	+	0.917914i	$0.370128\pi$
$908$	14.7562	+	25.5586i	0.489703	+	0.848191i
$909$		0			0
$910$	8.03510	−	19.1326i	0.266361	−	0.634239i
$911$	−14.3304			−0.474786			−0.237393	−	0.971414i	$-0.576293\pi$
$911$	−14.3304			−0.474786			−0.237393	+	0.971414i	$0.576293\pi$
$912$		0			0
$913$	16.0390			0.530813
$914$	6.96315	−	12.0605i	0.230321	−	0.398927i
$915$		0			0
$916$	−12.6021	−	21.8275i	−0.416386	−	0.721202i
$917$	−42.7983	−	9.38143i	−1.41333	−	0.309802i
$918$		0			0
$919$	−54.3463			−1.79272			−0.896359	−	0.443329i	$-0.853797\pi$
$919$	−54.3463			−1.79272			−0.896359	+	0.443329i	$0.853797\pi$
$920$	9.16231			0.302072
$921$		0			0
$922$	−10.4296	+	18.0646i	−0.343480	+	0.594926i
$923$	2.33175	−	12.6833i	0.0767506	−	0.417476i
$924$		0			0
$925$	−7.28111	+	12.6113i	−0.239402	+	0.414656i
$926$	0.105675	+	0.183035i	0.00347271	+	0.00601491i
$927$		0			0
$928$	−4.18533	−	7.24920i	−0.137390	−	0.237967i
$929$	−16.6711			−0.546961			−0.273480	−	0.961878i	$-0.588175\pi$
$929$	−16.6711			−0.546961			−0.273480	+	0.961878i	$0.588175\pi$
$930$		0			0
$931$	−28.9739	+	20.4938i	−0.949581	+	0.671657i
$932$	−14.9590	−	25.9098i	−0.490000	−	0.848704i
$933$		0			0
$934$	−8.49796			−0.278062
$935$	−16.5217	−	28.6164i	−0.540316	−	0.935855i
$936$		0			0
$937$	−2.55078			−0.0833303			−0.0416651	−	0.999132i	$-0.513266\pi$
$937$	−2.55078			−0.0833303			−0.0416651	+	0.999132i	$0.513266\pi$
$938$	20.5000	−	22.4790i	0.669350	−	0.733964i
$939$		0			0
$940$	4.27529			0.139445
$941$	−17.3944	−	30.1280i	−0.567041	−	0.982144i	−0.996857	−	0.0792275i	$-0.974755\pi$
$941$	−17.3944	−	30.1280i	−0.567041	−	0.982144i	0.429815	−	0.902917i	$-0.358579\pi$
$942$		0			0
$943$	11.2327			0.365786
$944$	3.99095			0.129894
$945$		0			0
$946$	0.168393	−	0.291665i	0.00547493	−	0.00948285i
$947$	7.49284	+	12.9780i	0.243485	+	0.421728i	0.961704	−	0.274088i	$-0.0883761\pi$
$947$	7.49284	+	12.9780i	0.243485	+	0.421728i	−0.718220	+	0.695816i	$0.755043\pi$
$948$		0			0
$949$	4.26017	−	23.1727i	0.138291	−	0.752218i
$950$	−3.89483	+	6.74604i	−0.126365	+	0.218870i
$951$		0			0
$952$	−48.5615	−	10.6447i	−1.57389	−	0.344998i
$953$	6.40858	+	11.1000i	0.207594	+	0.359564i	0.950956	−	0.309326i	$-0.100103\pi$
$953$	6.40858	+	11.1000i	0.207594	+	0.359564i	−0.743362	+	0.668889i	$0.766770\pi$
$954$		0			0
$955$	2.39405	−	4.14662i	0.0774697	−	0.134181i
$956$	7.36328	−	12.7536i	0.238146	−	0.412480i
$957$		0			0
$958$	−5.28177	−	9.14829i	−0.170646	−	0.295568i
$959$	−27.2831	−	5.98048i	−0.881017	−	0.193120i
$960$		0			0
$961$	−3.70488	+	6.41704i	−0.119512	+	0.207001i
$962$	−22.2468	+	7.91421i	−0.717265	+	0.255164i
$963$		0			0
$964$	12.7277	+	22.0450i	0.409931	+	0.710021i
$965$	4.13413	−	7.16052i	0.133082	−	0.230505i
$966$		0			0
$967$	17.8560			0.574209			0.287105	−	0.957899i	$-0.407307\pi$
$967$	17.8560			0.574209			0.287105	+	0.957899i	$0.407307\pi$
$968$	20.8595			0.670450
$969$		0			0
$970$	−13.2308	−	22.9165i	−0.424816	−	0.735803i
$971$	−35.3067			−1.13305			−0.566523	−	0.824046i	$-0.691712\pi$
$971$	−35.3067			−1.13305			−0.566523	+	0.824046i	$0.691712\pi$
$972$		0			0
$973$	16.3215	−	17.8971i	0.523243	−	0.573753i
$974$	17.0256			0.545537
$975$		0			0
$976$	1.44606	+	2.50465i	0.0462872	+	0.0801718i
$977$	−19.1054			−0.611237			−0.305618	−	0.952154i	$-0.598863\pi$
$977$	−19.1054			−0.611237			−0.305618	+	0.952154i	$0.598863\pi$
$978$		0			0
$979$	−14.0060	−	24.2591i	−0.447634	−	0.775325i
$980$	21.7807	+	10.0307i	0.695758	+	0.320417i
$981$		0			0
$982$	−16.4936			−0.526333
$983$	18.4765	+	32.0022i	0.589308	+	1.02071i	0.994323	+	0.106402i	$0.0339331\pi$
$983$	18.4765	+	32.0022i	0.589308	+	1.02071i	−0.405015	+	0.914310i	$0.632734\pi$
$984$		0			0
$985$	14.5920	+	25.2740i	0.464939	+	0.805297i
$986$	4.11406	−	7.12576i	0.131018	−	0.226930i
$987$		0			0
$988$	22.5445	−	8.02012i	0.717236	−	0.255154i
$989$	0.139503	−	0.241626i	0.00443593	−	0.00768326i
$990$		0			0
$991$	55.8372			1.77373			0.886863	−	0.462032i	$-0.152879\pi$
$991$	55.8372			1.77373			0.886863	+	0.462032i	$0.152879\pi$
$992$	35.8026			1.13673
$993$		0			0
$994$	−7.68368	−	1.68427i	−0.243711	−	0.0534218i
$995$	27.1503	+	47.0257i	0.860722	+	1.49081i
$996$		0			0
$997$	11.4391	−	19.8131i	0.362280	−	0.627488i	−0.626056	−	0.779778i	$-0.715332\pi$
$997$	11.4391	−	19.8131i	0.362280	−	0.627488i	0.988336	+	0.152291i	$0.0486650\pi$
$998$	23.1784			0.733699
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.n.e.100.3		16
3.2	odd	2		273.2.j.b.100.6	✓	16
7.4	even	3		819.2.s.e.802.6		16
13.3	even	3		819.2.s.e.289.6		16
21.11	odd	6		273.2.l.b.256.3	yes	16
39.29	odd	6		273.2.l.b.16.3	yes	16
91.81	even	3	inner	819.2.n.e.172.3		16
273.263	odd	6		273.2.j.b.172.6	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.b.100.6	✓	16	3.2	odd	2
273.2.j.b.172.6	yes	16	273.263	odd	6
273.2.l.b.16.3	yes	16	39.29	odd	6
273.2.l.b.256.3	yes	16	21.11	odd	6
819.2.n.e.100.3		16	1.1	even	1	trivial
819.2.n.e.172.3		16	91.81	even	3	inner
819.2.s.e.289.6		16	13.3	even	3
819.2.s.e.802.6		16	7.4	even	3

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.n (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.415625 - 0.719884i) q^{2} +(0.654511 - 1.13365i) q^{4} +(1.30847 - 2.26634i) q^{5} +(0.801591 + 2.52140i) q^{7} -2.75063 q^{8} +O(q^{10})\)	\(q+(-0.415625 - 0.719884i) q^{2} +(0.654511 - 1.13365i) q^{4} +(1.30847 - 2.26634i) q^{5} +(0.801591 + 2.52140i) q^{7} -2.75063 q^{8} -2.17533 q^{10} +1.84837 q^{11} +(2.74506 + 2.33765i) q^{13} +(1.48195 - 1.62501i) q^{14} +(-0.165791 - 0.287158i) q^{16} +(3.41564 - 5.91607i) q^{17} +5.06988 q^{19} +(-1.71281 - 2.96668i) q^{20} +(-0.768228 - 1.33061i) q^{22} +(-0.636428 - 1.10233i) q^{23} +(-0.924183 - 1.60073i) q^{25} +(0.541921 - 2.94772i) q^{26} +(3.38302 + 0.741562i) q^{28} +(-0.724496 + 1.25486i) q^{29} +(-3.09878 - 5.36725i) q^{31} +(-2.88844 + 5.00293i) q^{32} -5.67851 q^{34} +(6.76319 + 1.48250i) q^{35} +(-3.93922 - 6.82292i) q^{37} +(-2.10717 - 3.64973i) q^{38} +(-3.59911 + 6.23384i) q^{40} +(-4.41239 + 7.64248i) q^{41} +(0.109598 + 0.189830i) q^{43} +(1.20978 - 2.09539i) q^{44} +(-0.529032 + 0.916310i) q^{46} +(-0.624016 + 1.08083i) q^{47} +(-5.71490 + 4.04226i) q^{49} +(-0.768228 + 1.33061i) q^{50} +(4.44675 - 1.58191i) q^{52} +(-1.33947 - 2.32004i) q^{53} +(2.41853 - 4.18902i) q^{55} +(-2.20488 - 6.93543i) q^{56} +1.20448 q^{58} +(-6.01804 + 10.4236i) q^{59} -8.72218 q^{61} +(-2.57586 + 4.46153i) q^{62} +4.13888 q^{64} +(8.88974 - 3.16249i) q^{65} +13.8331 q^{67} +(-4.47115 - 7.74426i) q^{68} +(-1.74373 - 5.48488i) q^{70} +(-1.78833 - 3.09749i) q^{71} +(-3.26733 - 5.65918i) q^{73} +(-3.27448 + 5.67156i) q^{74} +(3.31829 - 5.74745i) q^{76} +(1.48163 + 4.66047i) q^{77} +(3.08084 - 5.33616i) q^{79} -0.867729 q^{80} +7.33560 q^{82} +8.67738 q^{83} +(-8.93852 - 15.4820i) q^{85} +(0.0911037 - 0.157796i) q^{86} -5.08417 q^{88} +(-7.57751 - 13.1246i) q^{89} +(-3.69373 + 8.79524i) q^{91} -1.66620 q^{92} +1.03743 q^{94} +(6.63379 - 11.4901i) q^{95} +(6.08221 + 10.5347i) q^{97} +(5.28522 + 2.43400i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{4} + q^{7} - 12 q^{8}+O(q^{10}) \) 16 * q - 6 * q^4 + q^7 - 12 * q^8	\( 16 q - 6 q^{4} + q^{7} - 12 q^{8} + 8 q^{10} - 4 q^{11} + 5 q^{13} + 7 q^{14} - 6 q^{16} + 2 q^{17} + 22 q^{19} + 20 q^{20} + 7 q^{22} - 4 q^{23} + 2 q^{25} + 6 q^{26} - 7 q^{28} - 15 q^{29} + 3 q^{31} - 3 q^{32} - 68 q^{34} + 12 q^{35} + 4 q^{37} - 2 q^{38} - 25 q^{40} - 19 q^{41} + 11 q^{43} + 16 q^{44} + 2 q^{46} - 5 q^{47} + 13 q^{49} + 7 q^{50} + 36 q^{52} - 36 q^{53} - 15 q^{55} - 39 q^{56} - 40 q^{58} + 17 q^{59} + 44 q^{61} + 6 q^{62} - 20 q^{64} + 21 q^{65} - 52 q^{67} - 5 q^{68} + 46 q^{70} - 9 q^{71} - 6 q^{73} - 15 q^{74} - 16 q^{76} + 36 q^{77} + 16 q^{79} - 56 q^{80} + 2 q^{82} - 36 q^{83} - 4 q^{85} - 16 q^{86} - 48 q^{88} - 20 q^{89} - 7 q^{91} + 94 q^{92} + 40 q^{94} + 7 q^{97} + 3 q^{98}+O(q^{100}) \) 16 * q - 6 * q^4 + q^7 - 12 * q^8 + 8 * q^10 - 4 * q^11 + 5 * q^13 + 7 * q^14 - 6 * q^16 + 2 * q^17 + 22 * q^19 + 20 * q^20 + 7 * q^22 - 4 * q^23 + 2 * q^25 + 6 * q^26 - 7 * q^28 - 15 * q^29 + 3 * q^31 - 3 * q^32 - 68 * q^34 + 12 * q^35 + 4 * q^37 - 2 * q^38 - 25 * q^40 - 19 * q^41 + 11 * q^43 + 16 * q^44 + 2 * q^46 - 5 * q^47 + 13 * q^49 + 7 * q^50 + 36 * q^52 - 36 * q^53 - 15 * q^55 - 39 * q^56 - 40 * q^58 + 17 * q^59 + 44 * q^61 + 6 * q^62 - 20 * q^64 + 21 * q^65 - 52 * q^67 - 5 * q^68 + 46 * q^70 - 9 * q^71 - 6 * q^73 - 15 * q^74 - 16 * q^76 + 36 * q^77 + 16 * q^79 - 56 * q^80 + 2 * q^82 - 36 * q^83 - 4 * q^85 - 16 * q^86 - 48 * q^88 - 20 * q^89 - 7 * q^91 + 94 * q^92 + 40 * q^94 + 7 * q^97 + 3 * q^98

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