LMFDB - Embedded newform 819.2.s.e.289.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(289,819)]

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, 2]))

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

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

chi := DirichletCharacter("819.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.s (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			289.6
Root			$0.415625 - 0.719884i$ of defining polynomial
Character	$\chi$	$=$	819.289
Dual form			819.2.s.e.802.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.831251 q^{2} -1.30902 q^{4} +(1.30847 - 2.26634i) q^{5} +(1.78280 - 1.95490i) q^{7} -2.75063 q^{8} +(1.08767 - 1.88389i) q^{10} +(-0.924183 + 1.60073i) q^{11} +(2.74506 - 2.33765i) q^{13} +(1.48195 - 1.62501i) q^{14} +0.331582 q^{16} -6.83128 q^{17} +(-2.53494 - 4.39065i) q^{19} +(-1.71281 + 2.96668i) q^{20} +(-0.768228 + 1.33061i) q^{22} +1.27286 q^{23} +(-0.924183 - 1.60073i) q^{25} +(2.28184 - 1.94318i) q^{26} +(-2.33372 + 2.55900i) q^{28} +(-0.724496 - 1.25486i) q^{29} +(-3.09878 - 5.36725i) q^{31} +5.77688 q^{32} -5.67851 q^{34} +(-2.09772 - 6.59834i) q^{35} +7.87843 q^{37} +(-2.10717 - 3.64973i) q^{38} +(-3.59911 + 6.23384i) q^{40} +(-4.41239 - 7.64248i) q^{41} +(0.109598 - 0.189830i) q^{43} +(1.20978 - 2.09539i) q^{44} +1.05806 q^{46} +(-0.624016 + 1.08083i) q^{47} +(-0.643251 - 6.97038i) q^{49} +(-0.768228 - 1.33061i) q^{50} +(-3.59335 + 3.06004i) q^{52} +(-1.33947 - 2.32004i) q^{53} +(2.41853 + 4.18902i) q^{55} +(-4.90382 + 5.37720i) q^{56} +(-0.602238 - 1.04311i) q^{58} +12.0361 q^{59} +(4.36109 + 7.55363i) q^{61} +(-2.57586 - 4.46153i) q^{62} +4.13888 q^{64} +(-1.70607 - 9.27998i) q^{65} +(-6.91656 + 11.9798i) q^{67} +8.94230 q^{68} +(-1.74373 - 5.48488i) q^{70} +(-1.78833 + 3.09749i) q^{71} +(-3.26733 - 5.65918i) q^{73} +6.54896 q^{74} +(3.31829 + 5.74745i) q^{76} +(1.48163 + 4.66047i) q^{77} +(3.08084 - 5.33616i) q^{79} +(0.433865 - 0.751475i) q^{80} +(-3.66780 - 6.35282i) q^{82} +8.67738 q^{83} +(-8.93852 + 15.4820i) q^{85} +(0.0911037 - 0.157796i) q^{86} +(2.54208 - 4.40302i) q^{88} +15.1550 q^{89} +(0.324029 - 9.53389i) q^{91} -1.66620 q^{92} +(-0.518714 + 0.898438i) q^{94} -13.2676 q^{95} +(6.08221 - 10.5347i) q^{97} +(-0.534703 - 5.79414i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{4} + q^{7} - 12 q^{8} - 4 q^{10} + 2 q^{11} + 5 q^{13} + 7 q^{14} + 12 q^{16} - 4 q^{17} - 11 q^{19} + 20 q^{20} + 7 q^{22} + 8 q^{23} + 2 q^{25} - 33 q^{26} - q^{28} - 15 q^{29} + 3 q^{31}+ \cdots - 18 q^{98}+O(q^{100}) $ 16 * q + 12 * q^4 + q^7 - 12 * q^8 - 4 * q^10 + 2 * q^11 + 5 * q^13 + 7 * q^14 + 12 * q^16 - 4 * q^17 - 11 * q^19 + 20 * q^20 + 7 * q^22 + 8 * q^23 + 2 * q^25 - 33 * q^26 - q^28 - 15 * q^29 + 3 * q^31 + 6 * q^32 - 68 * q^34 - 8 * q^37 - 2 * q^38 - 25 * q^40 - 19 * q^41 + 11 * q^43 + 16 * q^44 - 4 * q^46 - 5 * q^47 + 7 * q^49 + 7 * q^50 - 18 * q^52 - 36 * q^53 - 15 * q^55 + 51 * q^56 + 20 * q^58 - 34 * q^59 - 22 * q^61 + 6 * q^62 - 20 * q^64 + 24 * q^65 + 26 * q^67 + 10 * q^68 + 46 * q^70 - 9 * q^71 - 6 * q^73 + 30 * q^74 - 16 * q^76 + 36 * q^77 + 16 * q^79 + 28 * q^80 - q^82 - 36 * q^83 - 4 * q^85 - 16 * q^86 + 24 * q^88 + 40 * q^89 - 10 * q^91 + 94 * q^92 - 20 * q^94 + 7 * q^97 - 18 * q^98

Character values

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

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

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 $

$2$	0.831251			0.587783			0.293892	−	0.955839i	$-0.405050\pi$
$2$	0.831251			0.587783			0.293892	+	0.955839i	$0.405050\pi$
$3$		0			0
$3$		0			0
$4$	−1.30902			−0.654511
$5$	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
$7$	1.78280	−	1.95490i	0.673835	−	0.738882i
$7$	1.78280	−	1.95490i	0.673835	−	0.738882i
$8$	−2.75063			−0.972494
$9$		0			0
$10$	1.08767	−	1.88389i	0.343950	−	0.595739i
$11$	−0.924183	+	1.60073i	−0.278652	+	0.482639i	−0.971050	−	0.238877i	$-0.923221\pi$
$11$	−0.924183	+	1.60073i	−0.278652	+	0.482639i	0.692398	+	0.721516i	$0.256554\pi$
$12$		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
$16$	0.331582			0.0828954
$17$	−6.83128			−1.65683			−0.828415	−	0.560115i	$-0.810757\pi$
$17$	−6.83128			−1.65683			−0.828415	+	0.560115i	$0.810757\pi$
$18$		0			0
$19$	−2.53494	−	4.39065i	−0.581556	−	1.00728i	−0.995295	−	0.0968885i	$-0.969111\pi$
$19$	−2.53494	−	4.39065i	−0.581556	−	1.00728i	0.413740	−	0.910395i	$-0.364222\pi$
$20$	−1.71281	+	2.96668i	−0.382997	+	0.663370i
$21$		0			0
$22$	−0.768228	+	1.33061i	−0.163787	+	0.283687i
$23$	1.27286			0.265409			0.132704	−	0.991156i	$-0.457634\pi$
$23$	1.27286			0.265409			0.132704	+	0.991156i	$0.457634\pi$
$24$		0			0
$25$	−0.924183	−	1.60073i	−0.184837	−	0.320146i
$26$	2.28184	−	1.94318i	0.447505	−	0.381088i
$27$		0			0
$28$	−2.33372	+	2.55900i	−0.441032	+	0.483606i
$29$	−0.724496	−	1.25486i	−0.134536	−	0.233022i	0.790884	−	0.611966i	$-0.209621\pi$
$29$	−0.724496	−	1.25486i	−0.134536	−	0.233022i	−0.925420	+	0.378943i	$0.876288\pi$
$30$		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	$-0.354545\pi$
$32$	5.77688			1.02122
$33$		0			0
$34$	−5.67851			−0.973857
$35$	−2.09772	−	6.59834i	−0.354579	−	1.11532i
$36$		0			0
$37$	7.87843			1.29521			0.647603	−	0.761978i	$-0.275771\pi$
$37$	7.87843			1.29521			0.647603	+	0.761978i	$0.275771\pi$
$38$	−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	−0.972130	−	0.234444i	$-0.924673\pi$
$41$	−4.41239	−	7.64248i	−0.689099	−	1.19355i	0.283031	−	0.959111i	$-0.408660\pi$
$42$		0			0
$43$	0.109598	−	0.189830i	0.0167136	−	0.0289488i	−0.857548	−	0.514405i	$-0.828013\pi$
$43$	0.109598	−	0.189830i	0.0167136	−	0.0289488i	0.874261	+	0.485456i	$0.161346\pi$
$44$	1.20978	−	2.09539i	0.182381	−	0.315892i
$45$		0			0
$46$	1.05806			0.156003
$47$	−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
$49$	−0.643251	−	6.97038i	−0.0918930	−	0.995769i
$50$	−0.768228	−	1.33061i	−0.108644	−	0.188177i
$51$		0			0
$52$	−3.59335	+	3.06004i	−0.498308	+	0.424351i
$53$	−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
$56$	−4.90382	+	5.37720i	−0.655300	+	0.718558i
$57$		0			0
$58$	−0.602238	−	1.04311i	−0.0790777	−	0.136967i
$59$	12.0361			1.56697			0.783483	−	0.621414i	$-0.213441\pi$
$59$	12.0361			1.56697			0.783483	+	0.621414i	$0.213441\pi$
$60$		0			0
$61$	4.36109	+	7.55363i	0.558381	+	0.967144i	0.997632	+	0.0687794i	$0.0219105\pi$
$61$	4.36109	+	7.55363i	0.558381	+	0.967144i	−0.439251	+	0.898364i	$0.644756\pi$
$62$	−2.57586	−	4.46153i	−0.327135	−	0.566615i
$63$		0			0
$64$	4.13888			0.517359
$65$	−1.70607	−	9.27998i	−0.211612	−	1.15104i
$66$		0			0
$67$	−6.91656	+	11.9798i	−0.844992	+	1.46357i	0.0406360	+	0.999174i	$0.487062\pi$
$67$	−6.91656	+	11.9798i	−0.844992	+	1.46357i	−0.885628	+	0.464395i	$0.846272\pi$
$68$	8.94230			1.08441
$69$		0			0
$70$	−1.74373	−	5.48488i	−0.208415	−	0.655569i
$71$	−1.78833	+	3.09749i	−0.212236	+	0.367604i	−0.952414	−	0.304807i	$-0.901408\pi$
$71$	−1.78833	+	3.09749i	−0.212236	+	0.367604i	0.740178	+	0.672411i	$0.234741\pi$
$72$		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	$0.958240\pi$
$74$	6.54896			0.761301
$75$		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	$0.0539956\pi$
$80$	0.433865	−	0.751475i	0.0485075	−	0.0840175i
$81$		0			0
$82$	−3.66780	−	6.35282i	−0.405041	−	0.701551i
$83$	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
$88$	2.54208	−	4.40302i	0.270987	−	0.469363i
$89$	15.1550			1.60643			0.803215	−	0.595690i	$-0.203121\pi$
$89$	15.1550			1.60643			0.803215	+	0.595690i	$0.203121\pi$
$90$		0			0
$91$	0.324029	−	9.53389i	0.0339674	−	0.999423i
$92$	−1.66620			−0.173713
$93$		0			0
$94$	−0.518714	+	0.898438i	−0.0535012	+	0.0926668i
$95$	−13.2676			−1.36122
$96$		0			0
$97$	6.08221	−	10.5347i	0.617554	−	1.06964i	−0.372376	−	0.928082i	$-0.621457\pi$
$97$	6.08221	−	10.5347i	0.617554	−	1.06964i	0.989931	−	0.141554i	$-0.0452098\pi$
$98$	−0.534703	−	5.79414i	−0.0540132	−	0.585296i
$99$		0			0
$100$	1.20978	+	2.09539i	0.120978	+	0.209539i
$101$	−2.29803	+	3.98031i	−0.228663	+	0.396056i	−0.957412	−	0.288725i	$-0.906769\pi$
$101$	−2.29803	+	3.98031i	−0.228663	+	0.396056i	0.728749	+	0.684781i	$0.240102\pi$
$102$		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
$107$	−7.21387			−0.697391			−0.348696	−	0.937236i	$-0.613375\pi$
$107$	−7.21387			−0.697391			−0.348696	+	0.937236i	$0.613375\pi$
$108$		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	$0.696543\pi$
$110$	2.01041	+	3.48212i	0.191685	+	0.332007i
$111$		0			0
$112$	0.591144	−	0.648208i	0.0558578	−	0.0612499i
$113$	−1.82527	+	3.16146i	−0.171707	+	0.297405i	−0.939017	−	0.343871i	$-0.888262\pi$
$113$	−1.82527	+	3.16146i	−0.171707	+	0.297405i	0.767310	+	0.641277i	$0.221595\pi$
$114$		0			0
$115$	1.66549	−	2.88472i	0.155308	−	0.269002i
$116$	0.948381	+	1.64264i	0.0880550	+	0.152516i
$117$		0			0
$118$	10.0050			0.921036
$119$	−12.1788	+	13.3545i	−1.11643	+	1.22420i
$120$		0			0
$121$	3.79177	+	6.56754i	0.344707	+	0.597049i
$122$	3.62516	+	6.27896i	0.328207	+	0.568471i
$123$		0			0
$124$	4.05637	+	7.02584i	0.364273	+	0.630939i
$125$	8.24763			0.737691
$126$		0			0
$127$	4.80639	+	8.32491i	0.426498	+	0.738716i	0.996559	−	0.0828862i	$-0.0264138\pi$
$127$	4.80639	+	8.32491i	0.426498	+	0.738716i	−0.570061	+	0.821602i	$0.693080\pi$
$128$	−8.11332			−0.717123
$129$		0			0
$130$	−1.41817	−	7.71399i	−0.124382	−	0.676562i
$131$	−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
$133$	−13.1026	−	2.87209i	−1.13614	−	0.249042i
$134$	−5.74940	+	9.95825i	−0.496672	+	0.860261i
$135$		0			0
$136$	18.7903			1.61126
$137$	10.5569			0.901934			0.450967	−	0.892541i	$-0.351079\pi$
$137$	10.5569			0.901934			0.450967	+	0.892541i	$0.351079\pi$
$138$		0			0
$139$	−4.57749	+	7.92845i	−0.388258	+	0.672482i	−0.992215	−	0.124534i	$-0.960256\pi$
$139$	−4.57749	+	7.92845i	−0.388258	+	0.672482i	0.603958	+	0.797016i	$0.293590\pi$
$140$	2.74595	+	8.63738i	0.232076	+	0.729992i
$141$		0			0
$142$	−1.48655	+	2.57479i	−0.124749	+	0.216071i
$143$	1.20501	+	6.55453i	0.100768	+	0.548117i
$144$		0			0
$145$	−3.79192			−0.314902
$146$	−2.71597	−	4.70420i	−0.224775	−	0.389322i
$147$		0			0
$148$	−10.3130			−0.847727
$149$	−5.45367	−	9.44604i	−0.446782	−	0.773850i	0.551392	−	0.834246i	$-0.314097\pi$
$149$	−5.45367	−	9.44604i	−0.446782	−	0.773850i	−0.998174	+	0.0603965i	$0.980763\pi$
$150$		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	$0.470166\pi$
$152$	6.97268	+	12.0770i	0.565559	+	0.979577i
$153$		0			0
$154$	1.23161	+	3.87402i	0.0992459	+	0.312177i
$155$	−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	$0.841707\pi$
$158$	2.56095	−	4.43569i	0.203738	−	0.352885i
$159$		0			0
$160$	7.55887	−	13.0924i	0.597581	−	1.03504i
$161$	2.26925	−	2.48830i	0.178842	−	0.196106i
$162$		0			0
$163$	−9.09253	−	15.7487i	−0.712182	−	1.23354i	−0.964036	−	0.265771i	$-0.914374\pi$
$163$	−9.09253	−	15.7487i	−0.712182	−	1.23354i	0.251854	−	0.967765i	$-0.418960\pi$
$164$	5.77591	+	10.0042i	0.451023	+	0.781194i
$165$		0			0
$166$	7.21308			0.559844
$167$	2.21154	+	3.83050i	0.171134	+	0.296413i	0.938817	−	0.344417i	$-0.111924\pi$
$167$	2.21154	+	3.83050i	0.171134	+	0.296413i	−0.767683	+	0.640830i	$0.778590\pi$
$168$		0			0
$169$	2.07076	−	12.8340i	0.159289	−	0.987232i
$170$	−7.43016	+	12.8694i	−0.569867	+	0.987039i
$171$		0			0
$172$	−0.143467	+	0.248491i	−0.0109392	+	0.0189473i
$173$	1.76022	+	3.04879i	0.133827	+	0.231795i	0.925149	−	0.379605i	$-0.123940\pi$
$173$	1.76022	+	3.04879i	0.133827	+	0.231795i	−0.791322	+	0.611400i	$0.790607\pi$
$174$		0			0
$175$	−4.77690	−	1.04710i	−0.361100	−	0.0791534i
$176$	−0.306442	+	0.530773i	−0.0230990	+	0.0400086i
$177$		0			0
$178$	12.5976			0.944232
$179$	5.41014	−	9.37064i	0.404373	−	0.700395i	−0.589875	−	0.807494i	$-0.700823\pi$
$179$	5.41014	−	9.37064i	0.404373	−	0.700395i	0.994248	+	0.107100i	$0.0341564\pi$
$180$		0			0
$181$	−23.0651			−1.71441			−0.857207	−	0.514973i	$-0.827802\pi$
$181$	−23.0651			−1.71441			−0.857207	+	0.514973i	$0.827802\pi$
$182$	0.269349	−	7.92505i	0.0199655	−	0.587444i
$183$		0			0
$184$	−3.50115			−0.258109
$185$	10.3087	−	17.8552i	0.757910	−	1.31274i
$186$		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
$191$	−0.914829	−	1.58453i	−0.0661947	−	0.114653i	0.831029	−	0.556230i	$-0.187753\pi$
$191$	−0.914829	−	1.58453i	−0.0661947	−	0.114653i	−0.897223	+	0.441577i	$0.854419\pi$
$192$		0			0
$193$	−1.57976	+	2.73622i	−0.113713	+	0.196957i	−0.917265	−	0.398278i	$-0.869608\pi$
$193$	−1.57976	+	2.73622i	−0.113713	+	0.196957i	0.803551	+	0.595235i	$0.202941\pi$
$194$	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	0.596117	−	0.802898i	$-0.296709\pi$
$197$	−5.57597	−	9.65786i	−0.397271	−	0.688094i	−0.993388	+	0.114804i	$0.963376\pi$
$198$		0			0
$199$	20.7497			1.47090			0.735452	−	0.677577i	$-0.236970\pi$
$199$	20.7497			1.47090			0.735452	+	0.677577i	$0.236970\pi$
$200$	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
$205$	−23.0939			−1.61295
$206$	−1.85044	+	3.20506i	−0.128926	+	0.223307i
$207$		0			0
$208$	0.910213	−	0.775123i	0.0631119	−	0.0537451i
$209$	9.37100			0.648206
$210$		0			0
$211$	8.16773	+	14.1469i	0.562289	+	0.973914i	0.997296	+	0.0734866i	$0.0234126\pi$
$211$	8.16773	+	14.1469i	0.562289	+	0.973914i	−0.435007	+	0.900427i	$0.643254\pi$
$212$	1.75340	+	3.03698i	0.120424	+	0.208581i
$213$		0			0
$214$	−5.99654			−0.409915
$215$	−0.286812	−	0.496773i	−0.0195604	−	0.0338796i
$216$		0			0
$217$	−16.0169	−	3.51092i	−1.08730	−	0.238337i
$218$	3.61577	+	6.26270i	0.244891	+	0.424163i
$219$		0			0
$220$	−3.16591	−	5.48351i	−0.213445	−	0.369698i
$221$	−18.7523	+	15.9692i	−1.26142	+	1.07420i
$222$		0			0
$223$	9.30867	+	16.1231i	0.623355	+	1.07968i	0.988857	+	0.148871i	$0.0475640\pi$
$223$	9.30867	+	16.1231i	0.623355	+	1.07968i	−0.365502	+	0.930811i	$0.619103\pi$
$224$	10.2990	−	11.2932i	0.688133	−	0.754560i
$225$		0			0
$226$	−1.51726	+	2.62797i	−0.100926	+	0.174810i
$227$	22.5455			1.49639			0.748197	−	0.663476i	$-0.230920\pi$
$227$	22.5455			1.49639			0.748197	+	0.663476i	$0.230920\pi$
$228$		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
$236$	−15.7555			−1.02560
$237$		0			0
$238$	−10.1236	+	11.1009i	−0.656219	+	0.719565i
$239$	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
$241$	19.4461			1.25263			0.626316	−	0.779569i	$-0.284562\pi$
$241$	19.4461			1.25263			0.626316	+	0.779569i	$0.284562\pi$
$242$	3.15191	+	5.45928i	0.202613	+	0.350936i
$243$		0			0
$244$	−5.70876	−	9.88787i	−0.365466	−	0.633006i
$245$	−16.6389	−	7.66271i	−1.06302	−	0.489552i
$246$		0			0
$247$	−17.2224	−	6.12680i	−1.09583	−	0.389839i
$248$	8.52359	+	14.7633i	0.541249	+	0.937470i
$249$		0			0
$250$	6.85585			0.433602
$251$	8.79293	−	15.2298i	0.555005	−	0.961297i	−0.442898	−	0.896572i	$-0.646050\pi$
$251$	8.79293	−	15.2298i	0.555005	−	0.961297i	0.997903	−	0.0647248i	$-0.0206170\pi$
$252$		0			0
$253$	−1.17635	+	2.03750i	−0.0739566	+	0.128097i
$254$	3.99531	+	6.92009i	0.250688	+	0.434205i
$255$		0			0
$256$	−15.0220			−0.938872
$257$	−15.1872			−0.947353			−0.473677	−	0.880699i	$-0.657073\pi$
$257$	−15.1872			−0.947353			−0.473677	+	0.880699i	$0.657073\pi$
$258$		0			0
$259$	14.0457	−	15.4015i	0.872755	−	0.957005i
$260$	2.23328	+	12.1477i	0.138502	+	0.753368i
$261$		0			0
$262$	−6.88289	+	11.9215i	−0.425226	+	0.736514i
$263$	−6.98496	+	12.0983i	−0.430711	+	0.746014i	−0.996935	−	0.0782380i	$-0.975071\pi$
$263$	−6.98496	+	12.0983i	−0.430711	+	0.746014i	0.566223	+	0.824252i	$0.308404\pi$
$264$		0			0
$265$	−7.01065			−0.430661
$266$	−10.8915	−	2.38743i	−0.667802	−	0.146383i
$267$		0			0
$268$	9.05393	−	15.6819i	0.553057	−	0.957922i
$269$	28.9256			1.76363			0.881813	−	0.471600i	$-0.156323\pi$
$269$	28.9256			1.76363			0.881813	+	0.471600i	$0.156323\pi$
$270$		0			0
$271$	−10.1175			−0.614595			−0.307297	−	0.951614i	$-0.599425\pi$
$271$	−10.1175			−0.614595			−0.307297	+	0.951614i	$0.599425\pi$
$272$	−2.26513			−0.137344
$273$		0			0
$274$	8.77541			0.530142
$275$	3.41646			0.206020
$276$		0			0
$277$	3.40639			0.204670			0.102335	−	0.994750i	$-0.467369\pi$
$277$	3.40639			0.204670			0.102335	+	0.994750i	$0.467369\pi$
$278$	−3.80504	+	6.59053i	−0.228211	+	0.395274i
$279$		0			0
$280$	5.77003	+	18.1496i	0.344825	+	1.08465i
$281$	−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
$283$	−5.23950	+	9.07507i	−0.311456	+	0.539457i	−0.978678	−	0.205402i	$-0.934150\pi$
$283$	−5.23950	+	9.07507i	−0.311456	+	0.539457i	0.667222	+	0.744859i	$0.267483\pi$
$284$	2.34097	−	4.05468i	0.138911	−	0.240601i
$285$		0			0
$286$	1.00167	+	5.44846i	0.0592299	+	0.322174i
$287$	−22.8067	−	4.99924i	−1.34623	−	0.295096i
$288$		0			0
$289$	29.6664			1.74508
$290$	−3.15204			−0.185094
$291$		0			0
$292$	4.27701	+	7.40799i	0.250293	+	0.433520i
$293$	4.61007	−	7.98488i	0.269323	−	0.466481i	−0.699364	−	0.714766i	$-0.746533\pi$
$293$	4.61007	−	7.98488i	0.269323	−	0.466481i	0.968687	+	0.248284i	$0.0798667\pi$
$294$		0			0
$295$	15.7489	−	27.2778i	0.916934	−	1.58818i
$296$	−21.6706			−1.25958
$297$		0			0
$298$	−4.53337	−	7.85203i	−0.262611	−	0.454856i
$299$	3.49407	−	2.97550i	0.202068	−	0.172077i
$300$		0			0
$301$	−0.175706	−	0.552682i	−0.0101275	−	0.0318561i
$302$	9.28524	+	16.0825i	0.534306	+	0.925445i
$303$		0			0
$304$	−0.840540	−	1.45586i	−0.0482083	−	0.0834992i
$305$	22.8254			1.30698
$306$		0			0
$307$	−16.1499			−0.921726			−0.460863	−	0.887471i	$-0.652460\pi$
$307$	−16.1499			−0.921726			−0.460863	+	0.887471i	$0.652460\pi$
$308$	−1.93949	−	6.10065i	−0.110513	−	0.347617i
$309$		0			0
$310$	−13.4818			−0.765712
$311$	−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
$319$	2.67827			0.149954
$320$	5.41559	−	9.38008i	0.302741	−	0.524362i
$321$		0			0
$322$	1.88632	−	2.06841i	0.105120	−	0.115268i
$323$	17.3169	+	29.9938i	0.963538	+	1.66890i
$324$		0			0
$325$	−6.27890	−	2.23369i	−0.348291	−	0.123903i
$326$	−7.55818	−	13.0911i	−0.418609	−	0.725052i
$327$		0			0
$328$	12.1368	+	21.0216i	0.670144	+	1.16072i
$329$	1.00041	+	3.14678i	0.0551544	+	0.173488i
$330$		0			0
$331$	6.20311	+	10.7441i	0.340954	+	0.590549i	0.984610	−	0.174766i	$-0.0559168\pi$
$331$	6.20311	+	10.7441i	0.340954	+	0.590549i	−0.643656	+	0.765315i	$0.722583\pi$
$332$	−11.3589			−0.623400
$333$		0			0
$334$	1.83834	+	3.18411i	0.100590	+	0.174226i
$335$	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	$0.642105\pi$
$338$	1.72132	−	10.6683i	0.0936276	−	0.580278i
$339$		0			0
$340$	11.7007	−	20.2662i	0.634561	−	1.09909i
$341$	11.4554			0.620343
$342$		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
$347$	12.9304			0.694142			0.347071	−	0.937839i	$-0.387176\pi$
$347$	12.9304			0.694142			0.347071	+	0.937839i	$0.387176\pi$
$348$		0			0
$349$	−1.67254	−	2.89693i	−0.0895292	−	0.155069i	0.817783	−	0.575527i	$-0.195203\pi$
$349$	−1.67254	−	2.89693i	−0.0895292	−	0.155069i	−0.907312	+	0.420458i	$0.861870\pi$
$350$	−3.97080	−	0.870404i	−0.212248	−	0.0465250i
$351$		0			0
$352$	−5.33890	+	9.24724i	−0.284564	+	0.492880i
$353$	3.00732	−	5.20882i	0.160063	−	0.277238i	−0.774828	−	0.632172i	$-0.782164\pi$
$353$	3.00732	−	5.20882i	0.160063	−	0.277238i	0.934891	+	0.354935i	$0.115497\pi$
$354$		0			0
$355$	4.67996	+	8.10593i	0.248387	+	0.430218i
$356$	−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
$361$	−3.35186	+	5.80559i	−0.176414	+	0.305557i
$362$	−19.1729			−1.00770
$363$		0			0
$364$	−0.424161	+	12.4801i	−0.0222321	+	0.654133i
$365$	−17.1008			−0.895097
$366$		0			0
$367$	4.04076	−	6.99881i	0.210926	−	0.365335i	−0.741078	−	0.671418i	$-0.765685\pi$
$367$	4.04076	−	6.99881i	0.210926	−	0.365335i	0.952005	+	0.306084i	$0.0990187\pi$
$368$	0.422056			0.0220012
$369$		0			0
$370$	8.56911	−	14.8421i	0.445487	−	0.771605i
$371$	−6.92345	−	1.51763i	−0.359448	−	0.0787913i
$372$		0			0
$373$	5.63854	+	9.76624i	0.291953	+	0.505677i	0.974271	−	0.225378i	$-0.0723617\pi$
$373$	5.63854	+	9.76624i	0.291953	+	0.505677i	−0.682319	+	0.731055i	$0.739028\pi$
$374$	5.24798	−	9.08977i	0.271367	−	0.470021i
$375$		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	0.539431	−	0.842030i	$-0.318639\pi$
$379$	−8.94558	−	15.4942i	−0.459504	−	0.795884i	−0.998935	+	0.0461461i	$0.985306\pi$
$380$	17.3675			0.890936
$381$		0			0
$382$	−0.760453	−	1.31714i	−0.0389081	−	0.0673909i
$383$	0.0190547	+	0.0330037i	0.000973650	+	0.00168641i	0.866512	−	0.499157i	$-0.166357\pi$
$383$	0.0190547	+	0.0330037i	0.000973650	+	0.00168641i	−0.865538	+	0.500843i	$0.833023\pi$
$384$		0			0
$385$	12.5009	+	2.74020i	0.637102	+	0.139653i
$386$	−1.31317	+	2.27448i	−0.0668388	+	0.115768i
$387$		0			0
$388$	−7.96174	+	13.7901i	−0.404196	+	0.700088i
$389$	−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
$392$	1.76934	+	19.1729i	0.0893654	+	0.968379i
$393$		0			0
$394$	−4.63503	−	8.02811i	−0.233509	−	0.404450i
$395$	−8.06236	−	13.9644i	−0.405661	−	0.702626i
$396$		0			0
$397$	−4.36570	−	7.56162i	−0.219108	−	0.379507i	0.735427	−	0.677604i	$-0.236981\pi$
$397$	−4.36570	−	7.56162i	−0.219108	−	0.379507i	−0.954536	+	0.298097i	$0.903648\pi$
$398$	17.2482			0.864573
$399$		0			0
$400$	−0.306442	−	0.530773i	−0.0153221	−	0.0265387i
$401$	−24.2837			−1.21267			−0.606336	−	0.795208i	$-0.707361\pi$
$401$	−24.2837			−1.21267			−0.606336	+	0.795208i	$0.707361\pi$
$402$		0			0
$403$	−21.0531	−	7.48956i	−1.04873	−	0.373082i
$404$	3.00818	−	5.21031i	0.149662	−	0.259223i
$405$		0			0
$406$	−3.11284	−	0.682337i	−0.154487	−	0.0338638i
$407$	−7.28111	+	12.6113i	−0.360911	+	0.625117i
$408$		0			0
$409$	−19.7226			−0.975221			−0.487610	−	0.873061i	$-0.662131\pi$
$409$	−19.7226			−0.975221			−0.487610	+	0.873061i	$0.662131\pi$
$410$	−19.1968			−0.948063
$411$		0			0
$412$	2.91400	−	5.04720i	0.143563	−	0.248658i
$413$	21.4579	−	23.5293i	1.05588	−	1.15780i
$414$		0			0
$415$	11.3541	−	19.6659i	0.557350	−	0.965359i
$416$	15.8579	−	13.5043i	0.777498	−	0.662105i
$417$		0			0
$418$	7.78965			0.381004
$419$	−11.0976	−	19.2216i	−0.542154	−	0.939039i	−0.998780	−	0.0493798i	$-0.984276\pi$
$419$	−11.0976	−	19.2216i	−0.542154	−	0.939039i	0.456626	−	0.889659i	$-0.349058\pi$
$420$		0			0
$421$	−1.85475			−0.0903949			−0.0451974	−	0.998978i	$-0.514392\pi$
$421$	−1.85475			−0.0903949			−0.0451974	+	0.998978i	$0.514392\pi$
$422$	6.78943	+	11.7596i	0.330504	+	0.572450i
$423$		0			0
$424$	3.68440	+	6.38156i	0.178930	+	0.309916i
$425$	6.31336	+	10.9351i	0.306243	+	0.530428i
$426$		0			0
$427$	22.5415	+	4.94112i	1.09086	+	0.239118i
$428$	9.44312			0.456450
$429$		0			0
$430$	−0.238413	−	0.412943i	−0.0114973	−	0.0199139i
$431$	−18.8935	+	32.7246i	−0.910069	+	1.57629i	−0.0961051	+	0.995371i	$0.530638\pi$
$431$	−18.8935	+	32.7246i	−0.910069	+	1.57629i	−0.813964	+	0.580915i	$0.802695\pi$
$432$		0			0
$433$	17.5680	−	30.4286i	0.844263	−	1.46231i	−0.0419959	−	0.999118i	$-0.513372\pi$
$433$	17.5680	−	30.4286i	0.844263	−	1.46231i	0.886259	−	0.463189i	$-0.153295\pi$
$434$	−13.3141	−	2.91846i	−0.639096	−	0.140091i
$435$		0			0
$436$	−5.69397	−	9.86225i	−0.272692	−	0.472316i
$437$	−3.22662	−	5.58867i	−0.154350	−	0.267342i
$438$		0			0
$439$	15.3475			0.732496			0.366248	−	0.930517i	$-0.380642\pi$
$439$	15.3475			0.732496			0.366248	+	0.930517i	$0.380642\pi$
$440$	−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
$445$	19.8299	−	34.3464i	0.940027	−	1.62817i
$446$	7.73784	+	13.4023i	0.366397	+	0.634619i
$447$		0			0
$448$	7.37879	−	8.09108i	0.348615	−	0.382268i
$449$	1.18131	−	2.04609i	0.0557494	−	0.0965607i	−0.836804	−	0.547503i	$-0.815579\pi$
$449$	1.18131	−	2.04609i	0.0557494	−	0.0965607i	0.892553	+	0.450942i	$0.148912\pi$
$450$		0			0
$451$	16.3114			0.768074
$452$	2.38932	−	4.13842i	0.112384	−	0.194655i
$453$		0			0
$454$	18.7409			0.879555
$455$	−21.1830	−	13.2092i	−0.993074	−	0.619255i
$456$		0			0
$457$	−16.7534			−0.783692			−0.391846	−	0.920031i	$-0.628163\pi$
$457$	−16.7534			−0.783692			−0.391846	+	0.920031i	$0.628163\pi$
$458$	8.00257	−	13.8608i	0.373935	−	0.647675i
$459$		0			0
$460$	−2.18017	+	3.77616i	−0.101651	+	0.176064i
$461$	−12.5469	+	21.7318i	−0.584366	+	1.01215i	0.410588	+	0.911821i	$0.365323\pi$
$461$	−12.5469	+	21.7318i	−0.584366	+	1.01215i	−0.994954	+	0.100330i	$0.968010\pi$
$462$		0			0
$463$	−0.254256			−0.0118163			−0.00590815	−	0.999983i	$-0.501881\pi$
$463$	−0.254256			−0.0118163			−0.00590815	+	0.999983i	$0.501881\pi$
$464$	−0.240230	−	0.416090i	−0.0111524	−	0.0193165i
$465$		0			0
$466$	9.49924	−	16.4532i	0.440044	−	0.762178i
$467$	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
$472$	−33.1068			−1.52386
$473$	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
$478$	9.35162			0.427733
$479$	−6.35400	+	11.0055i	−0.290322	+	0.502852i	−0.973886	−	0.227039i	$-0.927096\pi$
$479$	−6.35400	+	11.0055i	−0.290322	+	0.502852i	0.683564	+	0.729891i	$0.260429\pi$
$480$		0			0
$481$	21.6268	−	18.4170i	0.986098	−	0.839745i
$482$	16.1646			0.736277
$483$		0			0
$484$	−4.96351	−	8.59706i	−0.225614	−	0.390775i
$485$	−15.9168	−	27.5686i	−0.722743	−	1.25183i
$486$		0			0
$487$	20.4820			0.928126			0.464063	−	0.885802i	$-0.346391\pi$
$487$	20.4820			0.928126			0.464063	+	0.885802i	$0.346391\pi$
$488$	−11.9957	−	20.7772i	−0.543022	−	0.940541i
$489$		0			0
$490$	−13.8311	−	6.36963i	−0.624825	−	0.287751i
$491$	9.92098	+	17.1836i	0.447727	+	0.775487i	0.998238	−	0.0593417i	$-0.0189002\pi$
$491$	9.92098	+	17.1836i	0.447727	+	0.775487i	−0.550510	+	0.834828i	$0.685567\pi$
$492$		0			0
$493$	4.94924	+	8.57233i	0.222902	+	0.386078i
$494$	−14.3161	−	5.09291i	−0.644113	−	0.229141i
$495$		0			0
$496$	−1.02750	−	1.77968i	−0.0461361	−	0.0799100i
$497$	2.86703	+	9.01821i	0.128604	+	0.404522i
$498$		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	$0.952123\pi$
$500$	−10.7963			−0.482827
$501$		0			0
$502$	7.30913	−	12.6598i	0.326223	−	0.565034i
$503$	−6.62277	+	11.4710i	−0.295295	+	0.511465i	−0.975053	−	0.221970i	$-0.928751\pi$
$503$	−6.62277	+	11.4710i	−0.295295	+	0.511465i	0.679759	+	0.733436i	$0.262084\pi$
$504$		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
$509$	−27.0750			−1.20008			−0.600040	−	0.799970i	$-0.704849\pi$
$509$	−27.0750			−1.20008			−0.600040	+	0.799970i	$0.704849\pi$
$510$		0			0
$511$	−16.8881	−	3.70189i	−0.747086	−	0.163762i
$512$	3.73962			0.165270
$513$		0			0
$514$	−12.6244			−0.556838
$515$	5.82554	+	10.0901i	0.256704	+	0.444625i
$516$		0			0
$517$	−1.15341	−	1.99776i	−0.0507269	−	0.0878615i
$518$	11.6755	−	12.8025i	0.512991	−	0.562511i
$519$		0			0
$520$	4.69277	+	25.5258i	0.205791	+	1.11938i
$521$	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
$523$	33.5380			1.46651			0.733256	−	0.679952i	$-0.237999\pi$
$523$	33.5380			1.46651			0.733256	+	0.679952i	$0.237999\pi$
$524$	10.8389	−	18.7735i	0.473500	−	0.820126i
$525$		0			0
$526$	−5.80626	+	10.0567i	−0.253165	+	0.438494i
$527$	21.1686	+	36.6652i	0.922121	+	1.59716i
$528$		0			0
$529$	−21.3798			−0.929558
$530$	−5.82761			−0.253135
$531$		0			0
$532$	17.1515	+	3.75963i	0.743614	+	0.163001i
$533$	−29.9777	−	10.6645i	−1.29848	−	0.461929i
$534$		0			0
$535$	−9.43913	+	16.3491i	−0.408089	+	0.706831i
$536$	19.0249	−	32.9521i	0.821750	−	1.42331i
$537$		0			0
$538$	24.0444			1.03663
$539$	11.7522	+	5.41224i	0.506203	+	0.233122i
$540$		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	$0.230818\pi$
$542$	−8.41019			−0.361248
$543$		0			0
$544$	−39.4635			−1.69198
$545$	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	$0.735278\pi$
$548$	−13.8192			−0.590326
$549$		0			0
$550$	2.83993			0.121095
$551$	−3.67311	+	6.36201i	−0.156480	+	0.271031i
$552$		0			0
$553$	−4.93914	−	15.5360i	−0.210034	−	0.660659i
$554$	2.83157			0.120302
$555$		0			0
$556$	5.99203	−	10.3785i	0.254119	−	0.440147i
$557$	2.76650	−	4.79172i	0.117220	−	0.203032i	−0.801445	−	0.598069i	$-0.795935\pi$
$557$	2.76650	−	4.79172i	0.117220	−	0.203032i	0.918665	+	0.395037i	$0.129268\pi$
$558$		0			0
$559$	−0.142902	−	0.777298i	−0.00604410	−	0.0328762i
$560$	−0.695564	−	2.18789i	−0.0293929	−	0.0924553i
$561$		0			0
$562$	−7.81651			−0.329720
$563$	−12.3688			−0.521281			−0.260641	−	0.965436i	$-0.583934\pi$
$563$	−12.3688			−0.521281			−0.260641	+	0.965436i	$0.583934\pi$
$564$		0			0
$565$	4.77662	+	8.27335i	0.200954	+	0.348062i
$566$	−4.35534	+	7.54366i	−0.183068	+	0.317084i
$567$		0			0
$568$	4.91904	−	8.52003i	0.206398	−	0.357493i
$569$	−1.99446			−0.0836120			−0.0418060	−	0.999126i	$-0.513311\pi$
$569$	−1.99446			−0.0836120			−0.0418060	+	0.999126i	$0.513311\pi$
$570$		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	$0.986265\pi$
$572$	−1.57739	−	8.58002i	−0.0659539	−	0.358749i
$573$		0			0
$574$	−18.9581	−	4.15562i	−0.791294	−	0.173452i
$575$	−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	$0.893902\pi$
$578$	24.6603			1.02573
$579$		0			0
$580$	4.96371			0.206107
$581$	15.4700	−	16.9634i	0.641805	−	0.703760i
$582$		0			0
$583$	4.95168			0.205078
$584$	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	0.921614	−	0.388109i	$-0.126872\pi$
$587$	3.02112	+	5.23273i	0.124695	+	0.215978i	−0.796919	+	0.604086i	$0.793538\pi$
$588$		0			0
$589$	−15.7105	+	27.2113i	−0.647338	+	1.12122i
$590$	13.0912	−	22.6747i	0.538958	−	0.933503i
$591$		0			0
$592$	2.61234			0.107367
$593$	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
$595$	14.3301	+	45.0752i	0.587476	+	1.84790i
$596$	7.13898	+	12.3651i	0.292424	+	0.506493i
$597$		0			0
$598$	2.90445	−	2.47338i	0.118772	−	0.101144i
$599$	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	−0.936687	−	0.350168i	$-0.886125\pi$
$601$	−18.9159	−	32.7634i	−0.771598	−	1.33645i	0.165089	−	0.986279i	$-0.447209\pi$
$602$	−0.146056	−	0.459417i	−0.00595279	−	0.0187245i
$603$		0			0
$604$	−14.6220	−	25.3261i	−0.594962	−	1.03051i
$605$	19.8457			0.806841
$606$		0			0
$607$	−3.35449	−	5.81015i	−0.136155	−	0.235827i	0.789883	−	0.613257i	$-0.210141\pi$
$607$	−3.35449	−	5.81015i	−0.136155	−	0.235827i	−0.926038	+	0.377430i	$0.876808\pi$
$608$	−14.6441	−	25.3643i	−0.593895	−	1.02866i
$609$		0			0
$610$	18.9737			0.768221
$611$	0.813634	+	4.42567i	0.0329161	+	0.179043i
$612$		0			0
$613$	10.0836	−	17.4653i	0.407272	−	0.705416i	−0.587311	−	0.809362i	$-0.699813\pi$
$613$	10.0836	−	17.4653i	0.407272	−	0.705416i	0.994583	+	0.103945i	$0.0331467\pi$
$614$	−13.4247			−0.541775
$615$		0			0
$616$	−4.07542	−	12.8192i	−0.164203	−	0.516501i
$617$	2.98249	−	5.16582i	0.120071	−	0.207968i	−0.799725	−	0.600367i	$-0.795021\pi$
$617$	2.98249	−	5.16582i	0.120071	−	0.207968i	0.919795	+	0.392399i	$0.128355\pi$
$618$		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	$0.777857\pi$
$620$	21.2305			0.852639
$621$		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
$626$	−11.3764	+	19.7046i	−0.454694	+	0.787553i
$627$		0			0
$628$	0.431435	+	0.747267i	0.0172161	+	0.0298192i
$629$	−53.8198			−2.14594
$630$		0			0
$631$	−1.02888	+	1.78208i	−0.0409592	+	0.0709434i	−0.885778	−	0.464109i	$-0.846375\pi$
$631$	−1.02888	+	1.78208i	−0.0409592	+	0.0709434i	0.844819	+	0.535052i	$0.179708\pi$
$632$	−8.47423	+	14.6778i	−0.337087	+	0.583852i
$633$		0			0
$634$	5.14066	−	8.90388i	0.204162	−	0.353618i
$635$	25.1560			0.998287
$636$		0			0
$637$	−18.0601	−	17.6305i	−0.715567	−	0.698544i
$638$	2.22631			0.0881405
$639$		0			0
$640$	−10.6160	+	18.3875i	−0.419635	+	0.726830i
$641$	17.6623			0.697618			0.348809	−	0.937194i	$-0.386586\pi$
$641$	17.6623			0.697618			0.348809	+	0.937194i	$0.386586\pi$
$642$		0			0
$643$	−24.6023	+	42.6124i	−0.970219	+	1.68047i	−0.275334	+	0.961349i	$0.588788\pi$
$643$	−24.6023	+	42.6124i	−0.970219	+	1.68047i	−0.694885	+	0.719121i	$0.744545\pi$
$644$	−2.97050	+	3.25725i	−0.117054	+	0.128353i
$645$		0			0
$646$	14.3947	+	24.9323i	0.566352	+	0.980950i
$647$	−7.74797	+	13.4199i	−0.304604	+	0.527590i	−0.977173	−	0.212445i	$-0.931857\pi$
$647$	−7.74797	+	13.4199i	−0.304604	+	0.527590i	0.672569	+	0.740034i	$0.265191\pi$
$648$		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
$653$	36.7330			1.43748			0.718738	−	0.695281i	$-0.244720\pi$
$653$	36.7330			1.43748			0.718738	+	0.695281i	$0.244720\pi$
$654$		0			0
$655$	21.6687	+	37.5312i	0.846665	+	1.46647i
$656$	−1.46307	−	2.53411i	−0.0571232	−	0.0989402i
$657$		0			0
$658$	0.831593	+	2.61577i	0.0324189	+	0.101973i
$659$	5.48070	−	9.49284i	0.213498	−	0.369789i	−0.739309	−	0.673366i	$-0.764848\pi$
$659$	5.48070	−	9.49284i	0.213498	−	0.369789i	0.952807	+	0.303577i	$0.0981811\pi$
$660$		0			0
$661$	−8.03552	+	13.9179i	−0.312545	+	0.541344i	−0.978913	−	0.204279i	$-0.934515\pi$
$661$	−8.03552	+	13.9179i	−0.312545	+	0.541344i	0.666367	+	0.745624i	$0.267848\pi$
$662$	5.15634	+	8.93104i	0.200407	+	0.347115i
$663$		0			0
$664$	−23.8682			−0.926268
$665$	−23.6534	+	25.9367i	−0.917240	+	1.00578i
$666$		0			0
$667$	−0.922180	−	1.59726i	−0.0357069	−	0.0618462i
$668$	−2.89495	−	5.01421i	−0.112009	−	0.194005i
$669$		0			0
$670$	15.0458	+	26.0601i	0.581271	+	1.00679i
$671$	−16.1218			−0.622375
$672$		0			0
$673$	14.1074	+	24.4348i	0.543802	+	0.941892i	0.998681	+	0.0513390i	$0.0163489\pi$
$673$	14.1074	+	24.4348i	0.543802	+	0.941892i	−0.454880	+	0.890553i	$0.650318\pi$
$674$	−13.1769			−0.507554
$675$		0			0
$676$	−2.71067	+	16.8000i	−0.104257	+	0.646154i
$677$	−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
$679$	−9.75089	−	30.6713i	−0.374205	−	1.17706i
$680$	24.5866	−	42.5852i	0.942851	−	1.63307i
$681$		0			0
$682$	9.52228			0.364627
$683$	−48.3832			−1.85133			−0.925666	−	0.378341i	$-0.876495\pi$
$683$	−48.3832			−1.85133			−0.925666	+	0.378341i	$0.876495\pi$
$684$		0			0
$685$	13.8133	−	23.9254i	0.527781	−	0.914143i
$686$	−12.2802	−	9.28450i	−0.468861	−	0.354484i
$687$		0			0
$688$	0.0363408	−	0.0629441i	0.00138548	−	0.00239972i
$689$	−9.10039	−	3.23743i	−0.346697	−	0.123336i
$690$		0			0
$691$	−24.1060			−0.917035			−0.458518	−	0.888685i	$-0.651619\pi$
$691$	−24.1060			−0.917035			−0.458518	+	0.888685i	$0.651619\pi$
$692$	−2.30417	−	3.99093i	−0.0875913	−	0.151713i
$693$		0			0
$694$	10.7484			0.408005
$695$	11.9790	+	20.7483i	0.454390	+	0.787026i
$696$		0			0
$697$	30.1423	+	52.2079i	1.14172	+	1.97752i
$698$	−1.39030	−	2.40808i	−0.0526238	−	0.0911470i
$699$		0			0
$700$	6.25307	+	1.37068i	0.236344	+	0.0518068i
$701$	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
$704$	−3.82508	+	6.62523i	−0.144163	+	0.249698i
$705$		0			0
$706$	2.49983	−	4.32984i	0.0940825	−	0.162956i
$707$	3.68417	+	11.5885i	0.138557	+	0.435831i
$708$		0			0
$709$	−17.9722	−	31.1287i	−0.674959	−	1.16906i	−0.976481	−	0.215604i	$-0.930828\pi$
$709$	−17.9722	−	31.1287i	−0.674959	−	1.16906i	0.301522	−	0.953459i	$-0.402505\pi$
$710$	3.89022	+	6.73806i	0.145997	+	0.252875i
$711$		0			0
$712$	−41.6858			−1.56224
$713$	−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
$718$	−6.19253	+	10.7258i	−0.231103	+	0.400282i
$719$	5.09760	+	8.82930i	0.190108	+	0.329278i	0.945286	−	0.326243i	$-0.105783\pi$
$719$	5.09760	+	8.82930i	0.190108	+	0.329278i	−0.755178	+	0.655520i	$0.772449\pi$
$720$		0			0
$721$	3.56883	+	11.2257i	0.132910	+	0.418068i
$722$	−2.78624	+	4.82590i	−0.103693	+	0.179602i
$723$		0			0
$724$	30.1927			1.12210
$725$	−1.33913	+	2.31945i	−0.0497342	+	0.0861421i
$726$		0			0
$727$	−2.32372			−0.0861821			−0.0430911	−	0.999071i	$-0.513721\pi$
$727$	−2.32372			−0.0861821			−0.0430911	+	0.999071i	$0.513721\pi$
$728$	−0.891282	+	26.2242i	−0.0330331	+	0.971933i
$729$		0			0
$730$	−14.2151			−0.526123
$731$	−0.748697	+	1.29678i	−0.0276916	+	0.0479632i
$732$		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
$737$	−12.7843	−	22.1431i	−0.470917	−	0.815652i
$738$		0			0
$739$	−0.0105714	+	0.0183102i	−0.000388875	+	0.000673551i	−0.866220	−	0.499663i	$-0.833457\pi$
$739$	−0.0105714	+	0.0183102i	−0.000388875	+	0.000673551i	0.865831	+	0.500337i	$0.166790\pi$
$740$	−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	0.998658	+	0.0517853i	$0.0164911\pi$
$743$	14.8332	+	25.6918i	0.544176	+	0.942541i	−0.454482	+	0.890756i	$0.650176\pi$
$744$		0			0
$745$	−28.5439			−1.04577
$746$	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
$751$	12.6016			0.459838			0.229919	−	0.973210i	$-0.426154\pi$
$751$	12.6016			0.459838			0.229919	+	0.973210i	$0.426154\pi$
$752$	−0.206912	+	0.358382i	−0.00754531	+	0.0130689i
$753$		0			0
$754$	−4.09160	−	1.45557i	−0.149007	−	0.0530088i
$755$	58.4635			2.12770
$756$		0			0
$757$	−8.13319	−	14.0871i	−0.295606	−	0.512004i	0.679520	−	0.733657i	$-0.262188\pi$
$757$	−8.13319	−	14.0871i	−0.295606	−	0.512004i	−0.975126	+	0.221653i	$0.928855\pi$
$758$	−7.43602	−	12.8796i	−0.270089	−	0.467807i
$759$		0			0
$760$	36.4942			1.32378
$761$	23.1276	+	40.0581i	0.838374	+	1.45211i	0.891254	+	0.453505i	$0.149827\pi$
$761$	23.1276	+	40.0581i	0.838374	+	1.45211i	−0.0528802	+	0.998601i	$0.516840\pi$
$762$		0			0
$763$	22.4831	+	4.92832i	0.813944	+	0.178417i
$764$	1.19753	+	2.07419i	0.0433252	+	0.0750414i
$765$		0			0
$766$	0.0158392	+	0.0274344i	0.000572295	+	0.000991244i
$767$	33.0398	−	28.1362i	1.19300	−	1.01594i
$768$		0			0
$769$	19.2803	+	33.3944i	0.695264	+	1.20423i	0.970092	+	0.242739i	$0.0780460\pi$
$769$	19.2803	+	33.3944i	0.695264	+	1.20423i	−0.274827	+	0.961494i	$0.588621\pi$
$770$	10.3913	+	2.27779i	0.374478	+	0.0820859i
$771$		0			0
$772$	2.06794	−	3.58177i	0.0744267	−	0.128911i
$773$	10.3545			0.372424			0.186212	−	0.982510i	$-0.440379\pi$
$773$	10.3545			0.372424			0.186212	+	0.982510i	$0.440379\pi$
$774$		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
$782$	−7.22793			−0.258470
$783$		0			0
$784$	−0.213290	−	2.31125i	−0.00761751	−	0.0825447i
$785$	−1.72501			−0.0615683
$786$		0			0
$787$	34.2879			1.22223			0.611116	−	0.791541i	$-0.290721\pi$
$787$	34.2879			1.22223			0.611116	+	0.791541i	$0.290721\pi$
$788$	7.29906	+	12.6423i	0.260018	+	0.450365i
$789$		0			0
$790$	−6.70184	−	11.6079i	−0.238441	−	0.412992i
$791$	2.92624	+	9.20447i	0.104045	+	0.327273i
$792$		0			0
$793$	29.6293	+	10.5405i	1.05217	+	0.374304i
$794$	−3.62899	−	6.28560i	−0.128788	−	0.223068i
$795$		0			0
$796$	−27.1618			−0.962723
$797$	−6.60638	+	11.4426i	−0.234010	+	0.405317i	−0.958984	−	0.283459i	$-0.908518\pi$
$797$	−6.60638	+	11.4426i	−0.234010	+	0.405317i	0.724975	+	0.688776i	$0.241851\pi$
$798$		0			0
$799$	4.26283	−	7.38343i	0.150808	−	0.261207i
$800$	−5.33890	−	9.24724i	−0.188758	−	0.326939i
$801$		0			0
$802$	−20.1859			−0.712788
$803$	12.0784			0.426239
$804$		0			0
$805$	−2.67009	−	8.39875i	−0.0941083	−	0.296017i
$806$	−17.5004	−	6.22571i	−0.616426	−	0.219291i
$807$		0			0
$808$	6.32103	−	10.9484i	0.222373	−	0.385162i
$809$	−25.4875	+	44.1457i	−0.896094	+	1.55208i	−0.0636484	+	0.997972i	$0.520274\pi$
$809$	−25.4875	+	44.1457i	−0.896094	+	1.55208i	−0.832445	+	0.554107i	$0.813060\pi$
$810$		0			0
$811$	7.86969			0.276342			0.138171	−	0.990408i	$-0.455878\pi$
$811$	7.86969			0.276342			0.138171	+	0.990408i	$0.455878\pi$
$812$	4.90197	+	1.07452i	0.172026	+	0.0377082i
$813$		0			0
$814$	−6.05243	+	10.4831i	−0.212138	+	0.367433i
$815$	−47.5892			−1.66698
$816$		0			0
$817$	−1.11130			−0.0388795
$818$	−16.3944			−0.573218
$819$		0			0
$820$	30.2304			1.05569
$821$	41.6714			1.45434			0.727171	−	0.686457i	$-0.240835\pi$
$821$	41.6714			1.45434			0.727171	+	0.686457i	$0.240835\pi$
$822$		0			0
$823$	−15.7101			−0.547619			−0.273809	−	0.961784i	$-0.588284\pi$
$823$	−15.7101			−0.547619			−0.273809	+	0.961784i	$0.588284\pi$
$824$	6.12315	−	10.6056i	0.213310	−	0.369464i
$825$		0			0
$826$	17.8369	−	19.5588i	0.620626	−	0.680537i
$827$	−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
$829$	25.1510	−	43.5629i	0.873532	−	1.51300i	0.0152129	−	0.999884i	$-0.495157\pi$
$829$	25.1510	−	43.5629i	0.873532	−	1.51300i	0.858319	−	0.513117i	$-0.171509\pi$
$830$	9.43810	−	16.3473i	0.327601	−	0.567422i
$831$		0			0
$832$	11.3615	−	9.67525i	0.393889	−	0.335429i
$833$	4.39423	+	47.6167i	0.152251	+	1.64982i
$834$		0			0
$835$	11.5749			0.400567
$836$	−12.2668			−0.424258
$837$		0			0
$838$	−9.22491	−	15.9780i	−0.318669	−	0.551951i
$839$	19.2875	−	33.4069i	0.665877	−	1.15333i	−0.313170	−	0.949697i	$-0.601391\pi$
$839$	19.2875	−	33.4069i	0.665877	−	1.15333i	0.979047	−	0.203635i	$-0.0652757\pi$
$840$		0			0
$841$	13.4502	−	23.2964i	0.463800	−	0.803326i
$842$	−1.54176			−0.0531326
$843$		0			0
$844$	−10.6917	−	18.5186i	−0.368025	−	0.637437i
$845$	−26.3767	−	21.4860i	−0.907384	−	0.739139i
$846$		0			0
$847$	19.5988	+	4.29608i	0.673424	+	0.147615i
$848$	−0.444145	−	0.769282i	−0.0152520	−	0.0264173i
$849$		0			0
$850$	5.24798	+	9.08977i	0.180004	+	0.311777i
$851$	10.0281			0.343759
$852$		0			0
$853$	22.6889			0.776855			0.388427	−	0.921479i	$-0.373018\pi$
$853$	22.6889			0.776855			0.388427	+	0.921479i	$0.373018\pi$
$854$	18.7377	+	4.10731i	0.641190	+	0.140549i
$855$		0			0
$856$	19.8427			0.678209
$857$	−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
$865$	9.21277			0.313244
$866$	14.6034	−	25.2938i	0.496244	−	0.859520i
$867$		0			0
$868$	20.9665	+	4.59588i	0.711649	+	0.155994i
$869$	5.69451	+	9.86318i	0.193173	+	0.334586i
$870$		0			0
$871$	9.01828	+	49.0539i	0.305573	+	1.66213i
$872$	−11.9647	−	20.7234i	−0.405174	−	0.701783i
$873$		0			0
$874$	−2.68213	−	4.64558i	−0.0907244	−	0.157139i
$875$	14.7039	−	16.1233i	0.497082	−	0.545066i
$876$		0			0
$877$	6.29998	+	10.9119i	0.212735	+	0.368468i	0.952570	−	0.304321i	$-0.0984295\pi$
$877$	6.29998	+	10.9119i	0.212735	+	0.368468i	−0.739834	+	0.672789i	$0.765096\pi$
$878$	12.7576			0.430549
$879$		0			0
$880$	0.801940	+	1.38900i	0.0270334	+	0.0468232i
$881$	−0.0834951	−	0.144618i	−0.00281302	−	0.00487230i	0.864615	−	0.502434i	$-0.167562\pi$
$881$	−0.0834951	−	0.144618i	−0.00281302	−	0.00487230i	−0.867428	+	0.497562i	$0.834229\pi$
$882$		0			0
$883$	1.54174			0.0518836			0.0259418	−	0.999663i	$-0.491742\pi$
$883$	1.54174			0.0518836			0.0259418	+	0.999663i	$0.491742\pi$
$884$	24.5472	−	20.9040i	0.825611	−	0.703077i
$885$		0			0
$886$	12.0828	−	20.9280i	0.405928	−	0.703088i
$887$	10.3337			0.346971			0.173485	−	0.984836i	$-0.444497\pi$
$887$	10.3337			0.346971			0.173485	+	0.984836i	$0.444497\pi$
$888$		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
$893$	6.32737			0.211737
$894$		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
$899$	−4.49011	+	7.77709i	−0.149753	+	0.259381i
$900$		0			0
$901$	9.15033	+	15.8488i	0.304842	+	0.528001i
$902$	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
$907$	−11.9496	+	20.6973i	−0.396780	+	0.687242i	−0.993327	−	0.115336i	$-0.963206\pi$
$907$	−11.9496	+	20.6973i	−0.396780	+	0.687242i	0.596547	+	0.802578i	$0.296539\pi$
$908$	−29.5125			−0.979406
$909$		0			0
$910$	−17.6084	−	10.9801i	−0.583712	−	0.363988i
$911$	−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
$913$	−8.01949	+	13.8902i	−0.265406	+	0.459697i
$914$	−13.9263			−0.460641
$915$		0			0
$916$	−12.6021	+	21.8275i	−0.416386	+	0.721202i
$917$	13.2746	+	41.7552i	0.438366	+	1.37888i
$918$		0			0
$919$	27.1731	+	47.0652i	0.896359	+	1.55254i	0.832114	+	0.554605i	$0.187131\pi$
$919$	27.1731	+	47.0652i	0.896359	+	1.55254i	0.0642448	+	0.997934i	$0.479536\pi$
$920$	−4.58115	+	7.93479i	−0.151036	+	0.261602i
$921$		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
$926$	−0.211351			−0.00694542
$927$		0			0
$928$	−4.18533	−	7.24920i	−0.137390	−	0.237967i
$929$	8.33555	+	14.4376i	0.273480	+	0.473682i	0.969751	−	0.244098i	$-0.0784918\pi$
$929$	8.33555	+	14.4376i	0.273480	+	0.473682i	−0.696270	+	0.717780i	$0.745158\pi$
$930$		0			0
$931$	−28.9739	+	20.4938i	−0.949581	+	0.671657i
$932$	−14.9590	+	25.9098i	−0.490000	+	0.848704i
$933$		0			0
$934$	4.24898	−	7.35945i	0.139031	−	0.240808i
$935$	−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	$0.513266\pi$
$938$	9.21733	+	28.9930i	0.300957	+	0.946656i
$939$		0			0
$940$	−2.13765	−	3.70251i	−0.0697223	−	0.120763i
$941$	−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
$943$	−5.61634	−	9.72778i	−0.182893	−	0.316780i
$944$	3.99095			0.129894
$945$		0			0
$946$	0.168393	+	0.291665i	0.00547493	+	0.00948285i
$947$	−14.9857			−0.486969			−0.243485	−	0.969905i	$-0.578291\pi$
$947$	−14.9857			−0.486969			−0.243485	+	0.969905i	$0.578291\pi$
$948$		0			0
$949$	−22.1982	−	7.89694i	−0.720585	−	0.256345i
$950$	−3.89483	+	6.74604i	−0.126365	+	0.218870i
$951$		0			0
$952$	33.4994	−	36.7332i	1.08572	−	1.19053i
$953$	6.40858	−	11.1000i	0.207594	−	0.359564i	−0.743362	−	0.668889i	$-0.766770\pi$
$953$	6.40858	−	11.1000i	0.207594	−	0.359564i	0.950956	+	0.309326i	$0.100103\pi$
$954$		0			0
$955$	−4.78810			−0.154939
$956$	−14.7266			−0.476291
$957$		0			0
$958$	−5.28177	+	9.14829i	−0.170646	+	0.295568i
$959$	18.8208	−	20.6376i	0.607755	−	0.666423i
$960$		0			0
$961$	−3.70488	+	6.41704i	−0.119512	+	0.207001i
$962$	17.9773	−	15.3092i	0.579612	−	0.493588i
$963$		0			0
$964$	−25.4554			−0.819862
$965$	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	$0.407307\pi$
$968$	−10.4298	−	18.0649i	−0.335225	−	0.580627i
$969$		0			0
$970$	−13.2308	−	22.9165i	−0.424816	−	0.735803i
$971$	17.6534	+	30.5765i	0.566523	+	0.981247i	0.996906	+	0.0786007i	$0.0250452\pi$
$971$	17.6534	+	30.5765i	0.566523	+	0.981247i	−0.430383	+	0.902646i	$0.641621\pi$
$972$		0			0
$973$	7.33855	+	23.0834i	0.235263	+	0.740018i
$974$	17.0256			0.545537
$975$		0			0
$976$	1.44606	+	2.50465i	0.0462872	+	0.0801718i
$977$	9.55272	−	16.5458i	0.305618	−	0.529347i	−0.671780	−	0.740750i	$-0.734470\pi$
$977$	9.55272	−	16.5458i	0.305618	−	0.529347i	0.977399	+	0.211404i	$0.0678035\pi$
$978$		0			0
$979$	−14.0060	+	24.2591i	−0.447634	+	0.775325i
$980$	21.7807	+	10.0307i	0.695758	+	0.320417i
$981$		0			0
$982$	8.24682	+	14.2839i	0.263167	+	0.455818i
$983$	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
$985$	−29.1839			−0.929877
$986$	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
$991$	−27.9186	+	48.3564i	−0.886863	+	1.53609i	−0.0433004	+	0.999062i	$0.513787\pi$
$991$	−27.9186	+	48.3564i	−0.886863	+	1.53609i	−0.843563	+	0.537030i	$0.819546\pi$
$992$	−17.9013	−	31.0059i	−0.568367	−	0.984440i
$993$		0			0
$994$	2.38322	+	7.49640i	0.0755911	+	0.237771i
$995$	27.1503	−	47.0257i	0.860722	−	1.49081i
$996$		0			0
$997$	−22.8782			−0.724560			−0.362280	−	0.932069i	$-0.618002\pi$
$997$	−22.8782			−0.724560			−0.362280	+	0.932069i	$0.618002\pi$
$998$	−11.5892	+	20.0731i	−0.366850	+	0.635402i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.b.100.6	✓	16	39.35	odd	6
273.2.j.b.172.6	yes	16	21.11	odd	6
273.2.l.b.16.3	yes	16	3.2	odd	2
273.2.l.b.256.3	yes	16	273.74	odd	6
819.2.n.e.100.3		16	13.9	even	3
819.2.n.e.172.3		16	7.4	even	3
819.2.s.e.289.6		16	1.1	even	1	trivial
819.2.s.e.802.6		16	91.74	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+0.831251 q^{2} -1.30902 q^{4} +(1.30847 - 2.26634i) q^{5} +(1.78280 - 1.95490i) q^{7} -2.75063 q^{8} +(1.08767 - 1.88389i) q^{10} +(-0.924183 + 1.60073i) q^{11} +(2.74506 - 2.33765i) q^{13} +(1.48195 - 1.62501i) q^{14} +0.331582 q^{16} -6.83128 q^{17} +(-2.53494 - 4.39065i) q^{19} +(-1.71281 + 2.96668i) q^{20} +(-0.768228 + 1.33061i) q^{22} +1.27286 q^{23} +(-0.924183 - 1.60073i) q^{25} +(2.28184 - 1.94318i) q^{26} +(-2.33372 + 2.55900i) q^{28} +(-0.724496 - 1.25486i) q^{29} +(-3.09878 - 5.36725i) q^{31} +5.77688 q^{32} -5.67851 q^{34} +(-2.09772 - 6.59834i) q^{35} +7.87843 q^{37} +(-2.10717 - 3.64973i) q^{38} +(-3.59911 + 6.23384i) q^{40} +(-4.41239 - 7.64248i) q^{41} +(0.109598 - 0.189830i) q^{43} +(1.20978 - 2.09539i) q^{44} +1.05806 q^{46} +(-0.624016 + 1.08083i) q^{47} +(-0.643251 - 6.97038i) q^{49} +(-0.768228 - 1.33061i) q^{50} +(-3.59335 + 3.06004i) q^{52} +(-1.33947 - 2.32004i) q^{53} +(2.41853 + 4.18902i) q^{55} +(-4.90382 + 5.37720i) q^{56} +(-0.602238 - 1.04311i) q^{58} +12.0361 q^{59} +(4.36109 + 7.55363i) q^{61} +(-2.57586 - 4.46153i) q^{62} +4.13888 q^{64} +(-1.70607 - 9.27998i) q^{65} +(-6.91656 + 11.9798i) q^{67} +8.94230 q^{68} +(-1.74373 - 5.48488i) q^{70} +(-1.78833 + 3.09749i) q^{71} +(-3.26733 - 5.65918i) q^{73} +6.54896 q^{74} +(3.31829 + 5.74745i) q^{76} +(1.48163 + 4.66047i) q^{77} +(3.08084 - 5.33616i) q^{79} +(0.433865 - 0.751475i) q^{80} +(-3.66780 - 6.35282i) q^{82} +8.67738 q^{83} +(-8.93852 + 15.4820i) q^{85} +(0.0911037 - 0.157796i) q^{86} +(2.54208 - 4.40302i) q^{88} +15.1550 q^{89} +(0.324029 - 9.53389i) q^{91} -1.66620 q^{92} +(-0.518714 + 0.898438i) q^{94} -13.2676 q^{95} +(6.08221 - 10.5347i) q^{97} +(-0.534703 - 5.79414i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{4} + q^{7} - 12 q^{8} - 4 q^{10} + 2 q^{11} + 5 q^{13} + 7 q^{14} + 12 q^{16} - 4 q^{17} - 11 q^{19} + 20 q^{20} + 7 q^{22} + 8 q^{23} + 2 q^{25} - 33 q^{26} - q^{28} - 15 q^{29} + 3 q^{31}+ \cdots - 18 q^{98}+O(q^{100}) \) 16 * q + 12 * q^4 + q^7 - 12 * q^8 - 4 * q^10 + 2 * q^11 + 5 * q^13 + 7 * q^14 + 12 * q^16 - 4 * q^17 - 11 * q^19 + 20 * q^20 + 7 * q^22 + 8 * q^23 + 2 * q^25 - 33 * q^26 - q^28 - 15 * q^29 + 3 * q^31 + 6 * q^32 - 68 * q^34 - 8 * q^37 - 2 * q^38 - 25 * q^40 - 19 * q^41 + 11 * q^43 + 16 * q^44 - 4 * q^46 - 5 * q^47 + 7 * q^49 + 7 * q^50 - 18 * q^52 - 36 * q^53 - 15 * q^55 + 51 * q^56 + 20 * q^58 - 34 * q^59 - 22 * q^61 + 6 * q^62 - 20 * q^64 + 24 * q^65 + 26 * q^67 + 10 * q^68 + 46 * q^70 - 9 * q^71 - 6 * q^73 + 30 * q^74 - 16 * q^76 + 36 * q^77 + 16 * q^79 + 28 * q^80 - q^82 - 36 * q^83 - 4 * q^85 - 16 * q^86 + 24 * q^88 + 40 * q^89 - 10 * q^91 + 94 * q^92 - 20 * q^94 + 7 * q^97 - 18 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more