LMFDB - Embedded newform 256.2.i.a.17.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [256,2,Mod(17,256)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(256, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("256.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	256.i (of order $16$, degree $8$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.04417029174$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 64)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			17.4
Character	$\chi$	$=$	256.17
Dual form			256.2.i.a.241.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.477374 + 0.714441i) q^{3} +(0.0517508 + 0.260169i) q^{5} +(0.515195 + 1.24379i) q^{7} +(0.865510 - 2.08953i) q^{9} +O(q^{10})$	\(q+(0.477374 + 0.714441i) q^{3} +(0.0517508 + 0.260169i) q^{5} +(0.515195 + 1.24379i) q^{7} +(0.865510 - 2.08953i) q^{9} +(4.11495 + 2.74952i) q^{11} +(-0.650168 + 3.26862i) q^{13} +(-0.161171 + 0.161171i) q^{15} +(1.10212 + 1.10212i) q^{17} +(-2.56547 - 0.510304i) q^{19} +(-0.642674 + 0.961830i) q^{21} +(-3.70792 - 1.53587i) q^{23} +(4.55439 - 1.88649i) q^{25} +(4.43424 - 0.882025i) q^{27} +(-5.46390 + 3.65086i) q^{29} -8.22961i q^{31} +4.25245i q^{33} +(-0.296934 + 0.198405i) q^{35} +(7.58710 - 1.50917i) q^{37} +(-2.64561 + 1.09585i) q^{39} +(-10.4659 - 4.33512i) q^{41} +(-2.31618 + 3.46640i) q^{43} +(0.588420 + 0.117044i) q^{45} +(-2.33317 - 2.33317i) q^{47} +(3.66816 - 3.66816i) q^{49} +(-0.261277 + 1.31353i) q^{51} +(-3.33837 - 2.23063i) q^{53} +(-0.502388 + 1.21287i) q^{55} +(-0.860108 - 2.07648i) q^{57} +(-1.16241 - 5.84382i) q^{59} +(-6.89488 - 10.3189i) q^{61} +3.04484 q^{63} -0.884038 q^{65} +(-1.94793 - 2.91529i) q^{67} +(-0.672776 - 3.38227i) q^{69} +(5.39337 + 13.0208i) q^{71} +(-0.375531 + 0.906612i) q^{73} +(3.52193 + 2.35328i) q^{75} +(-1.29983 + 6.53468i) q^{77} +(-1.20158 + 1.20158i) q^{79} +(-2.05082 - 2.05082i) q^{81} +(-15.1088 - 3.00532i) q^{83} +(-0.229702 + 0.343773i) q^{85} +(-5.21666 - 2.16081i) q^{87} +(-1.66533 + 0.689803i) q^{89} +(-4.40044 + 0.875301i) q^{91} +(5.87957 - 3.92860i) q^{93} -0.693864i q^{95} +15.4207i q^{97} +(9.30674 - 6.21857i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 8 q^{3} - 8 q^{5} + 8 q^{7} - 8 q^{9}+O(q^{10}) $ 56 * q + 8 * q^3 - 8 * q^5 + 8 * q^7 - 8 * q^9	$ 56 q + 8 q^{3} - 8 q^{5} + 8 q^{7} - 8 q^{9} + 8 q^{11} - 8 q^{13} + 8 q^{15} - 8 q^{17} + 8 q^{19} - 8 q^{21} + 8 q^{23} - 8 q^{25} + 8 q^{27} - 8 q^{29} + 8 q^{35} - 8 q^{37} + 8 q^{39} - 8 q^{41} + 8 q^{43} - 8 q^{45} + 8 q^{47} - 8 q^{49} - 24 q^{51} - 8 q^{53} - 56 q^{55} - 8 q^{57} - 56 q^{59} - 8 q^{61} - 64 q^{63} - 16 q^{65} - 72 q^{67} - 8 q^{69} - 56 q^{71} - 8 q^{73} - 56 q^{75} - 8 q^{77} - 24 q^{79} - 8 q^{81} + 8 q^{83} - 8 q^{85} + 8 q^{87} - 8 q^{89} + 8 q^{91} + 16 q^{93} - 16 q^{99}+O(q^{100}) $ 56 * q + 8 * q^3 - 8 * q^5 + 8 * q^7 - 8 * q^9 + 8 * q^11 - 8 * q^13 + 8 * q^15 - 8 * q^17 + 8 * q^19 - 8 * q^21 + 8 * q^23 - 8 * q^25 + 8 * q^27 - 8 * q^29 + 8 * q^35 - 8 * q^37 + 8 * q^39 - 8 * q^41 + 8 * q^43 - 8 * q^45 + 8 * q^47 - 8 * q^49 - 24 * q^51 - 8 * q^53 - 56 * q^55 - 8 * q^57 - 56 * q^59 - 8 * q^61 - 64 * q^63 - 16 * q^65 - 72 * q^67 - 8 * q^69 - 56 * q^71 - 8 * q^73 - 56 * q^75 - 8 * q^77 - 24 * q^79 - 8 * q^81 + 8 * q^83 - 8 * q^85 + 8 * q^87 - 8 * q^89 + 8 * q^91 + 16 * q^93 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{7}{16}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.477374	+	0.714441i	0.275612	+	0.412483i	0.943291	−	0.331967i	$-0.107712\pi$
$3$	0.477374	+	0.714441i	0.275612	+	0.412483i	−0.667679	+	0.744449i	$0.732712\pi$
$4$		0			0
$5$	0.0517508	+	0.260169i	0.0231436	+	0.116351i	0.990630	−	0.136571i	$-0.0436083\pi$
$5$	0.0517508	+	0.260169i	0.0231436	+	0.116351i	−0.967487	+	0.252922i	$0.918608\pi$
$6$		0			0
$7$	0.515195	+	1.24379i	0.194725	+	0.470109i	0.990841	−	0.135036i	$-0.0431151\pi$
$7$	0.515195	+	1.24379i	0.194725	+	0.470109i	−0.796115	+	0.605145i	$0.793115\pi$
$8$		0			0
$9$	0.865510	−	2.08953i	0.288503	−	0.696509i
$10$		0			0
$11$	4.11495	+	2.74952i	1.24071	+	0.829013i	0.990275	−	0.139122i	$-0.0444280\pi$
$11$	4.11495	+	2.74952i	1.24071	+	0.829013i	0.250430	+	0.968135i	$0.419428\pi$
$12$		0			0
$13$	−0.650168	+	3.26862i	−0.180324	+	0.906551i	0.779597	+	0.626281i	$0.215424\pi$
$13$	−0.650168	+	3.26862i	−0.180324	+	0.906551i	−0.959921	+	0.280269i	$0.909576\pi$
$14$		0			0
$15$	−0.161171	+	0.161171i	−0.0416141	+	0.0416141i
$16$		0			0
$17$	1.10212	+	1.10212i	0.267304	+	0.267304i	0.828013	−	0.560709i	$-0.189471\pi$
$17$	1.10212	+	1.10212i	0.267304	+	0.267304i	−0.560709	+	0.828013i	$0.689471\pi$
$18$		0			0
$19$	−2.56547	−	0.510304i	−0.588560	−	0.117072i	−0.108178	−	0.994132i	$-0.534502\pi$
$19$	−2.56547	−	0.510304i	−0.588560	−	0.117072i	−0.480381	+	0.877060i	$0.659502\pi$
$20$		0			0
$21$	−0.642674	+	0.961830i	−0.140243	+	0.209889i
$22$		0			0
$23$	−3.70792	−	1.53587i	−0.773154	−	0.320251i	−0.0390048	−	0.999239i	$-0.512419\pi$
$23$	−3.70792	−	1.53587i	−0.773154	−	0.320251i	−0.734149	+	0.678988i	$0.762419\pi$
$24$		0			0
$25$	4.55439	−	1.88649i	0.910878	−	0.377298i
$26$		0			0
$27$	4.43424	−	0.882025i	0.853370	−	0.169746i
$28$		0			0
$29$	−5.46390	+	3.65086i	−1.01462	+	0.677948i	−0.947487	−	0.319795i	$-0.896386\pi$
$29$	−5.46390	+	3.65086i	−1.01462	+	0.677948i	−0.0671349	+	0.997744i	$0.521386\pi$
$30$		0			0
$31$		−	8.22961i		−	1.47808i	−0.673661	−	0.739041i	$-0.735279\pi$
$31$		−	8.22961i		−	1.47808i	0.673661	−	0.739041i	$-0.264721\pi$
$32$		0			0
$33$			4.25245i			0.740256i
$34$		0			0
$35$	−0.296934	+	0.198405i	−0.0501909	+	0.0335365i
$36$		0			0
$37$	7.58710	−	1.50917i	1.24731	−	0.248106i	0.473087	−	0.881016i	$-0.343140\pi$
$37$	7.58710	−	1.50917i	1.24731	−	0.248106i	0.774225	+	0.632910i	$0.218140\pi$
$38$		0			0
$39$	−2.64561	+	1.09585i	−0.423636	+	0.175476i
$40$		0			0
$41$	−10.4659	−	4.33512i	−1.63450	−	0.677032i	−0.638774	−	0.769394i	$-0.720558\pi$
$41$	−10.4659	−	4.33512i	−1.63450	−	0.677032i	−0.995725	+	0.0923624i	$0.970558\pi$
$42$		0			0
$43$	−2.31618	+	3.46640i	−0.353213	+	0.528621i	−0.964948	−	0.262442i	$-0.915472\pi$
$43$	−2.31618	+	3.46640i	−0.353213	+	0.528621i	0.611734	+	0.791063i	$0.290472\pi$
$44$		0			0
$45$	0.588420	+	0.117044i	0.0877165	+	0.0174479i
$46$		0			0
$47$	−2.33317	−	2.33317i	−0.340328	−	0.340328i	0.516163	−	0.856490i	$-0.327360\pi$
$47$	−2.33317	−	2.33317i	−0.340328	−	0.340328i	−0.856490	+	0.516163i	$0.827360\pi$
$48$		0			0
$49$	3.66816	−	3.66816i	0.524023	−	0.524023i
$50$		0			0
$51$	−0.261277	+	1.31353i	−0.0365860	+	0.183930i
$52$		0			0
$53$	−3.33837	−	2.23063i	−0.458560	−	0.306400i	0.304750	−	0.952432i	$-0.401427\pi$
$53$	−3.33837	−	2.23063i	−0.458560	−	0.306400i	−0.763310	+	0.646032i	$0.776427\pi$
$54$		0			0
$55$	−0.502388	+	1.21287i	−0.0677420	+	0.163544i
$56$		0			0
$57$	−0.860108	−	2.07648i	−0.113924	−	0.275037i
$58$		0			0
$59$	−1.16241	−	5.84382i	−0.151333	−	0.760800i	−0.979677	−	0.200581i	$-0.935717\pi$
$59$	−1.16241	−	5.84382i	−0.151333	−	0.760800i	0.828345	−	0.560219i	$-0.189283\pi$
$60$		0			0
$61$	−6.89488	−	10.3189i	−0.882799	−	1.32120i	−0.946323	−	0.323222i	$-0.895234\pi$
$61$	−6.89488	−	10.3189i	−0.882799	−	1.32120i	0.0635241	−	0.997980i	$-0.479766\pi$
$62$		0			0
$63$	3.04484			0.383614
$64$		0			0
$65$	−0.884038			−0.109651
$66$		0			0
$67$	−1.94793	−	2.91529i	−0.237978	−	0.356159i	0.693187	−	0.720758i	$-0.256206\pi$
$67$	−1.94793	−	2.91529i	−0.237978	−	0.356159i	−0.931165	+	0.364599i	$0.881206\pi$
$68$		0			0
$69$	−0.672776	−	3.38227i	−0.0809927	−	0.407178i
$70$		0			0
$71$	5.39337	+	13.0208i	0.640076	+	1.54528i	0.826577	+	0.562824i	$0.190285\pi$
$71$	5.39337	+	13.0208i	0.640076	+	1.54528i	−0.186501	+	0.982455i	$0.559715\pi$
$72$		0			0
$73$	−0.375531	+	0.906612i	−0.0439526	+	0.106111i	−0.944331	−	0.328996i	$-0.893290\pi$
$73$	−0.375531	+	0.906612i	−0.0439526	+	0.106111i	0.900379	+	0.435107i	$0.143290\pi$
$74$		0			0
$75$	3.52193	+	2.35328i	0.406678	+	0.271733i
$76$		0			0
$77$	−1.29983	+	6.53468i	−0.148129	+	0.744696i
$78$		0			0
$79$	−1.20158	+	1.20158i	−0.135189	+	0.135189i	−0.771463	−	0.636274i	$-0.780475\pi$
$79$	−1.20158	+	1.20158i	−0.135189	+	0.135189i	0.636274	+	0.771463i	$0.280475\pi$
$80$		0			0
$81$	−2.05082	−	2.05082i	−0.227869	−	0.227869i
$82$		0			0
$83$	−15.1088	−	3.00532i	−1.65840	−	0.329877i	−0.725012	−	0.688736i	$-0.758166\pi$
$83$	−15.1088	−	3.00532i	−1.65840	−	0.329877i	−0.933392	+	0.358859i	$0.883166\pi$
$84$		0			0
$85$	−0.229702	+	0.343773i	−0.0249147	+	0.0372874i
$86$		0			0
$87$	−5.21666	−	2.16081i	−0.559284	−	0.231663i
$88$		0			0
$89$	−1.66533	+	0.689803i	−0.176525	+	0.0731189i	−0.469195	−	0.883094i	$-0.655456\pi$
$89$	−1.66533	+	0.689803i	−0.176525	+	0.0731189i	0.292671	+	0.956213i	$0.405456\pi$
$90$		0			0
$91$	−4.40044	+	0.875301i	−0.461291	+	0.0917565i
$92$		0			0
$93$	5.87957	−	3.92860i	0.609683	−	0.407377i
$94$		0			0
$95$		−	0.693864i		−	0.0711889i
$96$		0			0
$97$			15.4207i			1.56574i	0.622188	+	0.782868i	$0.286244\pi$
$97$			15.4207i			1.56574i	−0.622188	+	0.782868i	$0.713756\pi$
$98$		0			0
$99$	9.30674	−	6.21857i	0.935363	−	0.624989i
$100$		0			0
$101$	8.24786	−	1.64060i	0.820692	−	0.163246i	0.233152	−	0.972440i	$-0.425096\pi$
$101$	8.24786	−	1.64060i	0.820692	−	0.163246i	0.587541	+	0.809195i	$0.300096\pi$
$102$		0			0
$103$	9.41219	−	3.89866i	0.927410	−	0.384146i	0.132715	−	0.991154i	$-0.457631\pi$
$103$	9.41219	−	3.89866i	0.927410	−	0.384146i	0.794695	+	0.607008i	$0.207631\pi$
$104$		0			0
$105$	−0.283497	−	0.117428i	−0.0276665	−	0.0114598i
$106$		0			0
$107$	−1.05984	+	1.58616i	−0.102459	+	0.153340i	−0.879156	−	0.476533i	$-0.841893\pi$
$107$	−1.05984	+	1.58616i	−0.102459	+	0.153340i	0.776698	+	0.629873i	$0.216893\pi$
$108$		0			0
$109$	4.24989	+	0.845355i	0.407065	+	0.0809704i	0.394376	−	0.918949i	$-0.370961\pi$
$109$	4.24989	+	0.845355i	0.407065	+	0.0809704i	0.0126894	+	0.999919i	$0.495961\pi$
$110$		0			0
$111$	4.70010	+	4.70010i	0.446114	+	0.446114i
$112$		0			0
$113$	1.13449	−	1.13449i	0.106724	−	0.106724i	−0.651728	−	0.758453i	$-0.725956\pi$
$113$	1.13449	−	1.13449i	0.106724	−	0.106724i	0.758453	+	0.651728i	$0.225956\pi$
$114$		0			0
$115$	0.207698	−	1.04417i	0.0193679	−	0.0973690i
$116$		0			0
$117$	6.26713	+	4.18756i	0.579397	+	0.387140i
$118$		0			0
$119$	−0.803001	+	1.93862i	−0.0736110	+	0.177713i
$120$		0			0
$121$	5.16345	+	12.4657i	0.469404	+	1.13324i
$122$		0			0
$123$	−1.89897	−	9.54675i	−0.171224	−	0.860801i
$124$		0			0
$125$	1.46337	+	2.19008i	0.130888	+	0.195887i
$126$		0			0
$127$	18.1894			1.61405			0.807025	−	0.590517i	$-0.201076\pi$
$127$	18.1894			1.61405			0.807025	+	0.590517i	$0.201076\pi$
$128$		0			0
$129$	−3.58222			−0.315397
$130$		0			0
$131$	5.01304	+	7.50254i	0.437991	+	0.655500i	0.983143	−	0.182837i	$-0.0585281\pi$
$131$	5.01304	+	7.50254i	0.437991	+	0.655500i	−0.545152	+	0.838337i	$0.683528\pi$
$132$		0			0
$133$	−0.687007	−	3.45382i	−0.0595711	−	0.299484i
$134$		0			0
$135$	0.458950	+	1.10800i	0.0395002	+	0.0953618i
$136$		0			0
$137$	−2.99585	+	7.23263i	−0.255953	+	0.617925i	−0.998663	−	0.0516877i	$-0.983540\pi$
$137$	−2.99585	+	7.23263i	−0.255953	+	0.617925i	0.742710	+	0.669613i	$0.233540\pi$
$138$		0			0
$139$	−2.95817	−	1.97658i	−0.250908	−	0.167652i	0.423756	−	0.905777i	$-0.360712\pi$
$139$	−2.95817	−	1.97658i	−0.250908	−	0.167652i	−0.674664	+	0.738125i	$0.735712\pi$
$140$		0			0
$141$	0.553117	−	2.78071i	0.0465808	−	0.234178i
$142$		0			0
$143$	−11.6625	+	11.6625i	−0.975271	+	0.975271i
$144$		0			0
$145$	−1.23260	−	1.23260i	−0.102362	−	0.102362i
$146$		0			0
$147$	4.37177	+	0.869599i	0.360577	+	0.0717233i
$148$		0			0
$149$	−4.93832	+	7.39072i	−0.404563	+	0.605472i	−0.976680	−	0.214701i	$-0.931122\pi$
$149$	−4.93832	+	7.39072i	−0.404563	+	0.605472i	0.572117	+	0.820172i	$0.306122\pi$
$150$		0			0
$151$	3.73549	+	1.54729i	0.303990	+	0.125917i	0.529464	−	0.848332i	$-0.322393\pi$
$151$	3.73549	+	1.54729i	0.303990	+	0.125917i	−0.225474	+	0.974249i	$0.572393\pi$
$152$		0			0
$153$	3.25681	−	1.34902i	0.263298	−	0.109061i
$154$		0			0
$155$	2.14109	−	0.425888i	0.171976	−	0.0342082i
$156$		0			0
$157$	9.49118	−	6.34180i	0.757478	−	0.506131i	−0.115848	−	0.993267i	$-0.536958\pi$
$157$	9.49118	−	6.34180i	0.757478	−	0.506131i	0.873326	+	0.487136i	$0.161958\pi$
$158$		0			0
$159$		−	3.44991i		−	0.273596i
$160$		0			0
$161$		−	5.40314i		−	0.425827i
$162$		0			0
$163$	−0.00315871	+	0.00211058i	−0.000247409	+	0.000165314i	−0.555694	−	0.831387i	$-0.687547\pi$
$163$	−0.00315871	+	0.00211058i	−0.000247409	+	0.000165314i	0.555447	+	0.831552i	$0.312547\pi$
$164$		0			0
$165$	−1.10635	+	0.220067i	−0.0861295	+	0.0171322i
$166$		0			0
$167$	4.28839	−	1.77631i	0.331846	−	0.137455i	−0.210538	−	0.977586i	$-0.567522\pi$
$167$	4.28839	−	1.77631i	0.331846	−	0.137455i	0.542384	+	0.840131i	$0.317522\pi$
$168$		0			0
$169$	1.74931	+	0.724587i	0.134562	+	0.0557374i
$170$		0			0
$171$	−3.28674	+	4.91895i	−0.251343	+	0.376161i
$172$		0			0
$173$	7.26821	+	1.44574i	0.552592	+	0.109917i	0.463485	−	0.886105i	$-0.346599\pi$
$173$	7.26821	+	1.44574i	0.552592	+	0.109917i	0.0891066	+	0.996022i	$0.471599\pi$
$174$		0			0
$175$	4.69280	+	4.69280i	0.354742	+	0.354742i
$176$		0			0
$177$	3.62016	−	3.62016i	0.272108	−	0.272108i
$178$		0			0
$179$	−2.46773	+	12.4061i	−0.184447	+	0.927277i	0.772056	+	0.635554i	$0.219228\pi$
$179$	−2.46773	+	12.4061i	−0.184447	+	0.927277i	−0.956503	+	0.291722i	$0.905772\pi$
$180$		0			0
$181$	−13.4674	−	8.99863i	−1.00102	−	0.668863i	−0.0568753	−	0.998381i	$-0.518114\pi$
$181$	−13.4674	−	8.99863i	−1.00102	−	0.668863i	−0.944149	+	0.329518i	$0.893114\pi$
$182$		0			0
$183$	4.08082	−	9.85197i	0.301663	−	0.728279i
$184$		0			0
$185$	0.785277	+	1.89583i	0.0577347	+	0.139384i
$186$		0			0
$187$	1.50487	+	7.56549i	0.110047	+	0.553244i
$188$		0			0
$189$	3.38155	+	5.06085i	0.245972	+	0.368123i
$190$		0			0
$191$	−17.2169			−1.24577			−0.622885	−	0.782313i	$-0.714040\pi$
$191$	−17.2169			−1.24577			−0.622885	+	0.782313i	$0.714040\pi$
$192$		0			0
$193$	−12.7608			−0.918541			−0.459270	−	0.888296i	$-0.651889\pi$
$193$	−12.7608			−0.918541			−0.459270	+	0.888296i	$0.651889\pi$
$194$		0			0
$195$	−0.422017	−	0.631593i	−0.0302213	−	0.0452293i
$196$		0			0
$197$	−0.972213	−	4.88764i	−0.0692673	−	0.348230i	0.930573	−	0.366107i	$-0.119309\pi$
$197$	−0.972213	−	4.88764i	−0.0692673	−	0.348230i	−0.999840	+	0.0178765i	$0.994309\pi$
$198$		0			0
$199$	−8.85562	−	21.3794i	−0.627758	−	1.51554i	−0.842402	−	0.538850i	$-0.818859\pi$
$199$	−8.85562	−	21.3794i	−0.627758	−	1.51554i	0.214643	−	0.976692i	$-0.431141\pi$
$200$		0			0
$201$	1.15291	−	2.78337i	0.0813199	−	0.196324i
$202$		0			0
$203$	−7.35589	−	4.91505i	−0.516282	−	0.344969i
$204$		0			0
$205$	0.586244	−	2.94725i	0.0409450	−	0.205845i
$206$		0			0
$207$	−6.41848	+	6.41848i	−0.446115	+	0.446115i
$208$		0			0
$209$	−9.15371	−	9.15371i	−0.633175	−	0.633175i
$210$		0			0
$211$	3.65496	+	0.727017i	0.251618	+	0.0500499i	0.319288	−	0.947658i	$-0.396556\pi$
$211$	3.65496	+	0.727017i	0.251618	+	0.0500499i	−0.0676697	+	0.997708i	$0.521556\pi$
$212$		0			0
$213$	−6.72790	+	10.0690i	−0.460988	+	0.689918i
$214$		0			0
$215$	−1.02171	−	0.423207i	−0.0696802	−	0.0288625i
$216$		0			0
$217$	10.2359	−	4.23985i	0.694859	−	0.287820i
$218$		0			0
$219$	−0.826990	+	0.164498i	−0.0558828	+	0.0111158i
$220$		0			0
$221$	−4.31898	+	2.88585i	−0.290526	+	0.194123i
$222$		0			0
$223$			23.7016i			1.58718i	0.608456	+	0.793588i	$0.291789\pi$
$223$			23.7016i			1.58718i	−0.608456	+	0.793588i	$0.708211\pi$
$224$		0			0
$225$		−	11.1493i		−	0.743286i
$226$		0			0
$227$	8.78436	−	5.86952i	0.583039	−	0.389574i	−0.228785	−	0.973477i	$-0.573475\pi$
$227$	8.78436	−	5.86952i	0.583039	−	0.389574i	0.811823	+	0.583903i	$0.198475\pi$
$228$		0			0
$229$	−14.0985	+	2.80436i	−0.931653	+	0.185317i	−0.637508	−	0.770444i	$-0.720035\pi$
$229$	−14.0985	+	2.80436i	−0.931653	+	0.185317i	−0.294145	+	0.955761i	$0.595035\pi$
$230$		0			0
$231$	−5.28915	+	2.19084i	−0.348001	+	0.144147i
$232$		0			0
$233$	5.04386	+	2.08924i	0.330435	+	0.136870i	0.541732	−	0.840551i	$-0.317769\pi$
$233$	5.04386	+	2.08924i	0.330435	+	0.136870i	−0.211297	+	0.977422i	$0.567769\pi$
$234$		0			0
$235$	0.486274	−	0.727761i	0.0317210	−	0.0474739i
$236$		0			0
$237$	−1.43207	−	0.284856i	−0.0930228	−	0.0185034i
$238$		0			0
$239$	−13.6816	−	13.6816i	−0.884992	−	0.884992i	0.109045	−	0.994037i	$-0.465221\pi$
$239$	−13.6816	−	13.6816i	−0.884992	−	0.884992i	−0.994037	+	0.109045i	$0.965221\pi$
$240$		0			0
$241$	2.22031	−	2.22031i	0.143023	−	0.143023i	−0.631970	−	0.774993i	$-0.717753\pi$
$241$	2.22031	−	2.22031i	0.143023	−	0.143023i	0.774993	+	0.631970i	$0.217753\pi$
$242$		0			0
$243$	3.13226	−	15.7469i	0.200934	−	1.01016i
$244$		0			0
$245$	1.14417	+	0.764510i	0.0730983	+	0.0488427i
$246$		0			0
$247$	3.33598	−	8.05376i	0.212263	−	0.512448i
$248$		0			0
$249$	−5.06542	−	12.2290i	−0.321008	−	0.774981i
$250$		0			0
$251$	−0.729724	−	3.66857i	−0.0460598	−	0.231558i	0.950898	−	0.309505i	$-0.100163\pi$
$251$	−0.729724	−	3.66857i	−0.0460598	−	0.231558i	−0.996957	+	0.0779471i	$0.975163\pi$
$252$		0			0
$253$	−11.0350	−	16.5150i	−0.693764	−	1.03829i
$254$		0			0
$255$	−0.355259			−0.0222472
$256$		0			0
$257$	17.3864			1.08453			0.542267	−	0.840206i	$-0.317566\pi$
$257$	17.3864			1.08453			0.542267	+	0.840206i	$0.317566\pi$
$258$		0			0
$259$	5.78593	+	8.65925i	0.359520	+	0.538060i
$260$		0			0
$261$	2.89951	+	14.5768i	0.179475	+	0.902283i
$262$		0			0
$263$	−0.656941	−	1.58600i	−0.0405087	−	0.0977967i	0.902330	−	0.431045i	$-0.141855\pi$
$263$	−0.656941	−	1.58600i	−0.0405087	−	0.0977967i	−0.942839	+	0.333249i	$0.891855\pi$
$264$		0			0
$265$	0.407576	−	0.983975i	0.0250372	−	0.0604451i
$266$		0			0
$267$	−1.28781	−	0.860487i	−0.0788127	−	0.0526609i
$268$		0			0
$269$	−1.25541	+	6.31135i	−0.0765434	+	0.384810i	0.923456	+	0.383704i	$0.125352\pi$
$269$	−1.25541	+	6.31135i	−0.0765434	+	0.384810i	−0.999999	+	0.00110539i	$0.999648\pi$
$270$		0			0
$271$	17.1048	−	17.1048i	1.03904	−	1.03904i	0.0398353	−	0.999206i	$-0.487317\pi$
$271$	17.1048	−	17.1048i	1.03904	−	1.03904i	0.999206	−	0.0398353i	$-0.0126833\pi$
$272$		0			0
$273$	−2.72601	−	2.72601i	−0.164985	−	0.164985i
$274$		0			0
$275$	23.9280	+	4.75958i	1.44292	+	0.287014i
$276$		0			0
$277$	−4.08114	+	6.10786i	−0.245212	+	0.366985i	−0.933576	−	0.358380i	$-0.883329\pi$
$277$	−4.08114	+	6.10786i	−0.245212	+	0.366985i	0.688364	+	0.725365i	$0.258329\pi$
$278$		0			0
$279$	−17.1960	−	7.12281i	−1.02950	−	0.426432i
$280$		0			0
$281$	−16.8252	+	6.96925i	−1.00371	+	0.415750i	−0.823156	−	0.567815i	$-0.807789\pi$
$281$	−16.8252	+	6.96925i	−1.00371	+	0.415750i	−0.180554	+	0.983565i	$0.557789\pi$
$282$		0			0
$283$	−22.3174	+	4.43920i	−1.32663	+	0.263883i	−0.807022	−	0.590522i	$-0.798922\pi$
$283$	−22.3174	+	4.43920i	−1.32663	+	0.263883i	−0.519608	+	0.854405i	$0.673922\pi$
$284$		0			0
$285$	0.495725	−	0.331233i	0.0293642	−	0.0196205i
$286$		0			0
$287$		−	15.2508i		−	0.900228i
$288$		0			0
$289$		−	14.5707i		−	0.857097i
$290$		0			0
$291$	−11.0172	+	7.36145i	−0.645839	+	0.431536i
$292$		0			0
$293$	−23.6486	+	4.70399i	−1.38156	+	0.274810i	−0.829274	−	0.558842i	$-0.811246\pi$
$293$	−23.6486	+	4.70399i	−1.38156	+	0.274810i	−0.552290	+	0.833652i	$0.686246\pi$
$294$		0			0
$295$	1.46022	−	0.604844i	0.0850174	−	0.0352154i
$296$		0			0
$297$	20.6718	+	8.56256i	1.19950	+	0.496850i
$298$		0			0
$299$	7.43093	−	11.1212i	0.429742	−	0.643154i
$300$		0			0
$301$	−5.50476	−	1.09497i	−0.317289	−	0.0631127i
$302$		0			0
$303$	5.10943	+	5.10943i	0.293529	+	0.293529i
$304$		0			0
$305$	2.32784	−	2.32784i	0.133292	−	0.133292i
$306$		0			0
$307$	−1.72081	+	8.65108i	−0.0982116	+	0.493743i	0.900101	+	0.435681i	$0.143492\pi$
$307$	−1.72081	+	8.65108i	−0.0982116	+	0.493743i	−0.998313	+	0.0580626i	$0.981508\pi$
$308$		0			0
$309$	7.27850	+	4.86334i	0.414059	+	0.276666i
$310$		0			0
$311$	−1.49356	+	3.60578i	−0.0846923	+	0.204465i	−0.960552	−	0.278101i	$-0.910295\pi$
$311$	−1.49356	+	3.60578i	−0.0846923	+	0.204465i	0.875860	+	0.482566i	$0.160295\pi$
$312$		0			0
$313$	8.26474	+	19.9529i	0.467151	+	1.12780i	0.965401	+	0.260769i	$0.0839760\pi$
$313$	8.26474	+	19.9529i	0.467151	+	1.12780i	−0.498250	+	0.867033i	$0.666024\pi$
$314$		0			0
$315$	0.157573	+	0.792172i	0.00887822	+	0.0446338i
$316$		0			0
$317$	16.4821	+	24.6672i	0.925727	+	1.38545i	0.922728	+	0.385452i	$0.125955\pi$
$317$	16.4821	+	24.6672i	0.925727	+	1.38545i	0.00299906	+	0.999996i	$0.499045\pi$
$318$		0			0
$319$	−32.5219			−1.82087
$320$		0			0
$321$	−1.63916			−0.0914890
$322$		0			0
$323$	−2.26505	−	3.38988i	−0.126030	−	0.188618i
$324$		0			0
$325$	3.20509	+	16.1131i	0.177786	+	0.893793i
$326$		0			0
$327$	1.42483	+	3.43985i	0.0787933	+	0.190224i
$328$		0			0
$329$	1.69994	−	4.10401i	0.0937206	−	0.226261i
$330$		0			0
$331$	0.162367	+	0.108490i	0.00892448	+	0.00596315i	0.560024	−	0.828476i	$-0.310792\pi$
$331$	0.162367	+	0.108490i	0.00892448	+	0.00596315i	−0.551100	+	0.834439i	$0.685792\pi$
$332$		0			0
$333$	3.41327	−	17.1597i	0.187046	−	0.940343i
$334$		0			0
$335$	0.657660	−	0.657660i	0.0359318	−	0.0359318i
$336$		0			0
$337$	6.58517	+	6.58517i	0.358717	+	0.358717i	0.863340	−	0.504623i	$-0.168368\pi$
$337$	6.58517	+	6.58517i	0.358717	+	0.358717i	−0.504623	+	0.863340i	$0.668368\pi$
$338$		0			0
$339$	1.35211	+	0.268951i	0.0734364	+	0.0146074i
$340$		0			0
$341$	22.6275	−	33.8645i	1.22535	−	1.83386i
$342$		0			0
$343$	15.1588	+	6.27897i	0.818497	+	0.339032i
$344$		0			0
$345$	0.845145	−	0.350070i	0.0455011	−	0.0188472i
$346$		0			0
$347$	24.8134	−	4.93570i	1.33206	−	0.264962i	0.522818	−	0.852444i	$-0.324881\pi$
$347$	24.8134	−	4.93570i	1.33206	−	0.264962i	0.809237	+	0.587482i	$0.199881\pi$
$348$		0			0
$349$	−10.7430	+	7.17827i	−0.575062	+	0.384244i	−0.808825	−	0.588050i	$-0.799896\pi$
$349$	−10.7430	+	7.17827i	−0.575062	+	0.384244i	0.233763	+	0.972294i	$0.424896\pi$
$350$		0			0
$351$			15.0673i			0.804232i
$352$		0			0
$353$		−	15.3080i		−	0.814764i	−0.913258	−	0.407382i	$-0.866442\pi$
$353$		−	15.3080i		−	0.814764i	0.913258	−	0.407382i	$-0.133558\pi$
$354$		0			0
$355$	−3.10848	+	2.07702i	−0.164981	+	0.110237i
$356$		0			0
$357$	−1.76836	+	0.351749i	−0.0935915	+	0.0186165i
$358$		0			0
$359$	−7.28425	+	3.01723i	−0.384448	+	0.159243i	−0.566533	−	0.824039i	$-0.691715\pi$
$359$	−7.28425	+	3.01723i	−0.384448	+	0.159243i	0.182085	+	0.983283i	$0.441715\pi$
$360$		0			0
$361$	−11.2325	−	4.65264i	−0.591183	−	0.244876i
$362$		0			0
$363$	−6.44108	+	9.63976i	−0.338069	+	0.505956i
$364$		0			0
$365$	−0.255306	−	0.0507835i	−0.0133633	−	0.00265813i
$366$		0			0
$367$	9.38201	+	9.38201i	0.489737	+	0.489737i	0.908223	−	0.418486i	$-0.137439\pi$
$367$	9.38201	+	9.38201i	0.489737	+	0.489737i	−0.418486	+	0.908223i	$0.637439\pi$
$368$		0			0
$369$	−18.1167	+	18.1167i	−0.943118	+	0.943118i
$370$		0			0
$371$	1.05452	−	5.30144i	0.0547480	−	0.275237i
$372$		0			0
$373$	1.73641	+	1.16023i	0.0899078	+	0.0600745i	0.599712	−	0.800216i	$-0.295282\pi$
$373$	1.73641	+	1.16023i	0.0899078	+	0.0600745i	−0.509804	+	0.860291i	$0.670282\pi$
$374$		0			0
$375$	−0.866112	+	2.09098i	−0.0447258	+	0.107978i
$376$		0			0
$377$	−8.38081	−	20.2331i	−0.431634	−	1.04206i
$378$		0			0
$379$	6.02722	+	30.3009i	0.309597	+	1.55645i	0.751711	+	0.659492i	$0.229229\pi$
$379$	6.02722	+	30.3009i	0.309597	+	1.55645i	−0.442114	+	0.896959i	$0.645771\pi$
$380$		0			0
$381$	8.68317	+	12.9953i	0.444852	+	0.665768i
$382$		0			0
$383$	28.6473			1.46381			0.731904	−	0.681408i	$-0.238632\pi$
$383$	28.6473			1.46381			0.731904	+	0.681408i	$0.238632\pi$
$384$		0			0
$385$	−1.76739			−0.0900744
$386$		0			0
$387$	5.23847	+	7.83992i	0.266286	+	0.398525i
$388$		0			0
$389$	−1.69036	−	8.49804i	−0.0857049	−	0.430868i	−0.999685	−	0.0251080i	$-0.992007\pi$
$389$	−1.69036	−	8.49804i	−0.0857049	−	0.430868i	0.913980	−	0.405760i	$-0.132993\pi$
$390$		0			0
$391$	−2.39386	−	5.77929i	−0.121063	−	0.292271i
$392$		0			0
$393$	−2.96703	+	7.16304i	−0.149667	+	0.361328i
$394$		0			0
$395$	−0.374798	−	0.250432i	−0.0188581	−	0.0126006i
$396$		0			0
$397$	3.77514	−	18.9789i	0.189469	−	0.952525i	−0.762653	−	0.646808i	$-0.776104\pi$
$397$	3.77514	−	18.9789i	0.189469	−	0.952525i	0.952122	−	0.305718i	$-0.0988963\pi$
$398$		0			0
$399$	2.13959	−	2.13959i	0.107113	−	0.107113i
$400$		0			0
$401$	22.1086	+	22.1086i	1.10405	+	1.10405i	0.993917	+	0.110133i	$0.0351275\pi$
$401$	22.1086	+	22.1086i	1.10405	+	1.10405i	0.110133	+	0.993917i	$0.464872\pi$
$402$		0			0
$403$	26.8994	+	5.35063i	1.33996	+	0.266534i
$404$		0			0
$405$	0.427427	−	0.639690i	0.0212390	−	0.0317864i
$406$		0			0
$407$	35.3701	+	14.6508i	1.75323	+	0.726212i
$408$		0			0
$409$	−0.412610	+	0.170909i	−0.0204023	+	0.00845089i	−0.392861	−	0.919598i	$-0.628515\pi$
$409$	−0.412610	+	0.170909i	−0.0204023	+	0.00845089i	0.372459	+	0.928049i	$0.378515\pi$
$410$		0			0
$411$	−6.59743	+	1.31231i	−0.325427	+	0.0647315i
$412$		0			0
$413$	6.66962	−	4.45650i	0.328191	−	0.219290i
$414$		0			0
$415$		−	4.08636i		−	0.200591i
$416$		0			0
$417$		−	3.05701i		−	0.149702i
$418$		0			0
$419$	−24.9030	+	16.6397i	−1.21659	+	0.812901i	−0.987052	−	0.160398i	$-0.948722\pi$
$419$	−24.9030	+	16.6397i	−1.21659	+	0.812901i	−0.229541	+	0.973299i	$0.573722\pi$
$420$		0			0
$421$	27.6476	−	5.49946i	1.34746	−	0.268027i	0.531955	−	0.846772i	$-0.321457\pi$
$421$	27.6476	−	5.49946i	1.34746	−	0.268027i	0.815508	+	0.578745i	$0.196457\pi$
$422$		0			0
$423$	−6.89460	+	2.85584i	−0.335227	+	0.138856i
$424$		0			0
$425$	7.09863	+	2.94035i	0.344334	+	0.142628i
$426$		0			0
$427$	9.28237	−	13.8920i	0.449205	−	0.672283i
$428$		0			0
$429$	−13.8996	−	2.76480i	−0.671079	−	0.133486i
$430$		0			0
$431$	−5.47861	−	5.47861i	−0.263896	−	0.263896i	0.562739	−	0.826635i	$-0.309748\pi$
$431$	−5.47861	−	5.47861i	−0.263896	−	0.263896i	−0.826635	+	0.562739i	$0.809748\pi$
$432$		0			0
$433$	−13.9653	+	13.9653i	−0.671130	+	0.671130i	−0.957977	−	0.286847i	$-0.907393\pi$
$433$	−13.9653	+	13.9653i	−0.671130	+	0.671130i	0.286847	+	0.957977i	$0.407393\pi$
$434$		0			0
$435$	0.292209	−	1.46903i	0.0140103	−	0.0704348i
$436$		0			0
$437$	8.72880	+	5.83240i	0.417555	+	0.279001i
$438$		0			0
$439$	−7.32429	+	17.6824i	−0.349569	+	0.843935i	0.647102	+	0.762404i	$0.275981\pi$
$439$	−7.32429	+	17.6824i	−0.349569	+	0.843935i	−0.996671	+	0.0815308i	$0.974019\pi$
$440$		0			0
$441$	−4.48989	−	10.8395i	−0.213804	−	0.516169i
$442$		0			0
$443$	−1.03061	−	5.18121i	−0.0489656	−	0.246167i	0.948549	−	0.316631i	$-0.102552\pi$
$443$	−1.03061	−	5.18121i	−0.0489656	−	0.246167i	−0.997514	+	0.0704647i	$0.977552\pi$
$444$		0			0
$445$	−0.265647	−	0.397569i	−0.0125929	−	0.0188466i
$446$		0			0
$447$	−7.63766			−0.361249
$448$		0			0
$449$	25.4195			1.19962			0.599809	−	0.800143i	$-0.295243\pi$
$449$	25.4195			1.19962			0.599809	+	0.800143i	$0.295243\pi$
$450$		0			0
$451$	−31.1472	−	46.6151i	−1.46666	−	2.19502i
$452$		0			0
$453$	0.677779	+	3.40743i	0.0318449	+	0.160095i
$454$		0			0
$455$	−0.455452	−	1.09956i	−0.0213519	−	0.0515481i
$456$		0			0
$457$	0.410387	−	0.990763i	0.0191971	−	0.0463459i	−0.913990	−	0.405736i	$-0.867015\pi$
$457$	0.410387	−	0.990763i	0.0191971	−	0.0463459i	0.933187	+	0.359390i	$0.117015\pi$
$458$		0			0
$459$	5.85917	+	3.91497i	0.273483	+	0.182735i
$460$		0			0
$461$	−0.499040	+	2.50885i	−0.0232426	+	0.116849i	−0.990665	−	0.136320i	$-0.956473\pi$
$461$	−0.499040	+	2.50885i	−0.0232426	+	0.116849i	0.967422	+	0.253168i	$0.0814726\pi$
$462$		0			0
$463$	23.9046	−	23.9046i	1.11094	−	1.11094i	0.117915	−	0.993024i	$-0.462379\pi$
$463$	23.9046	−	23.9046i	1.11094	−	1.11094i	0.993024	−	0.117915i	$-0.0376211\pi$
$464$		0			0
$465$	1.32637	+	1.32637i	0.0615090	+	0.0615090i
$466$		0			0
$467$	−32.9221	−	6.54862i	−1.52345	−	0.303034i	−0.638833	−	0.769345i	$-0.720583\pi$
$467$	−32.9221	−	6.54862i	−1.52345	−	0.303034i	−0.884621	+	0.466311i	$0.845583\pi$
$468$		0			0
$469$	2.62244	−	3.92476i	0.121093	−	0.181229i
$470$		0			0
$471$	9.06169	+	3.75347i	0.417540	+	0.172951i
$472$		0			0
$473$	−19.0619	+	7.89570i	−0.876468	+	0.363045i
$474$		0			0
$475$	−12.6468	+	2.51561i	−0.580277	+	0.115424i
$476$		0			0
$477$	−7.55034	+	5.04498i	−0.345706	+	0.230994i
$478$		0			0
$479$			17.7201i			0.809654i	0.914393	+	0.404827i	$0.132668\pi$
$479$			17.7201i			0.809654i	−0.914393	+	0.404827i	$0.867332\pi$
$480$		0			0
$481$			25.7805i			1.17549i
$482$		0			0
$483$	3.86023	−	2.57932i	0.175647	−	0.117363i
$484$		0			0
$485$	−4.01198	+	0.798033i	−0.182175	+	0.0362368i
$486$		0			0
$487$	−22.3630	+	9.26304i	−1.01336	+	0.419749i	−0.826680	−	0.562672i	$-0.809773\pi$
$487$	−22.3630	+	9.26304i	−1.01336	+	0.419749i	−0.186682	+	0.982420i	$0.559773\pi$
$488$		0			0
$489$	−0.00301577	−	0.00124917i	−0.000136378	−	5.64896e-5i
$490$		0			0
$491$	16.5333	−	24.7438i	0.746136	−	1.11667i	−0.243051	−	0.970013i	$-0.578148\pi$
$491$	16.5333	−	24.7438i	0.746136	−	1.11667i	0.989187	−	0.146658i	$-0.0468517\pi$
$492$		0			0
$493$	−10.0456	−	1.99819i	−0.452430	−	0.0899940i
$494$		0			0
$495$	2.09951	+	2.09951i	0.0943658	+	0.0943658i
$496$		0			0
$497$	−13.4165	+	13.4165i	−0.601810	+	0.601810i
$498$		0			0
$499$	5.85555	−	29.4378i	0.262130	−	1.31782i	−0.595419	−	0.803416i	$-0.703014\pi$
$499$	5.85555	−	29.4378i	0.262130	−	1.31782i	0.857549	−	0.514402i	$-0.171986\pi$
$500$		0			0
$501$	3.31624	+	2.21584i	0.148159	+	0.0989964i
$502$		0			0
$503$	−2.73931	+	6.61328i	−0.122140	+	0.294871i	−0.973109	−	0.230343i	$-0.926015\pi$
$503$	−2.73931	+	6.61328i	−0.122140	+	0.294871i	0.850970	+	0.525215i	$0.176015\pi$
$504$		0			0
$505$	0.853666	+	2.06093i	0.0379876	+	0.0917102i
$506$		0			0
$507$	0.317400	+	1.59568i	0.0140962	+	0.0708665i
$508$		0			0
$509$	3.41939	+	5.11748i	0.151562	+	0.226829i	0.899479	−	0.436963i	$-0.143946\pi$
$509$	3.41939	+	5.11748i	0.151562	+	0.226829i	−0.747917	+	0.663792i	$0.768946\pi$
$510$		0			0
$511$	−1.32111			−0.0584423
$512$		0			0
$513$	−11.8260			−0.522131
$514$		0			0
$515$	1.50140	+	2.24700i	0.0661594	+	0.0990145i
$516$		0			0
$517$	−3.18578	−	16.0160i	−0.140110	−	0.704382i
$518$		0			0
$519$	2.43676	+	5.88286i	0.106962	+	0.258229i
$520$		0			0
$521$	5.10532	−	12.3253i	0.223668	−	0.539983i	−0.771715	−	0.635969i	$-0.780601\pi$
$521$	5.10532	−	12.3253i	0.223668	−	0.539983i	0.995383	+	0.0959866i	$0.0306006\pi$
$522$		0			0
$523$	−22.7053	−	15.1712i	−0.992835	−	0.663391i	−0.0507311	−	0.998712i	$-0.516155\pi$
$523$	−22.7053	−	15.1712i	−0.992835	−	0.663391i	−0.942104	+	0.335321i	$0.891155\pi$
$524$		0			0
$525$	−1.11251	+	5.59295i	−0.0485538	+	0.244096i
$526$		0			0
$527$	9.07003	−	9.07003i	0.395097	−	0.395097i
$528$		0			0
$529$	−4.87371	−	4.87371i	−0.211900	−	0.211900i
$530$		0			0
$531$	−13.2169	−	2.62900i	−0.573564	−	0.114089i
$532$		0			0
$533$	20.9744	−	31.3905i	0.908504	−	1.35967i
$534$		0			0
$535$	−0.467517	−	0.193652i	−0.0202125	−	0.00837231i
$536$		0			0
$537$	−10.0415	+	4.15931i	−0.433321	+	0.179488i
$538$		0			0
$539$	25.1800	−	5.00861i	1.08458	−	0.215736i
$540$		0			0
$541$	−1.36491	+	0.912006i	−0.0586822	+	0.0392102i	−0.584565	−	0.811347i	$-0.698735\pi$
$541$	−1.36491	+	0.912006i	−0.0586822	+	0.0392102i	0.525883	+	0.850557i	$0.323735\pi$
$542$		0			0
$543$		−	13.9174i		−	0.597252i
$544$		0			0
$545$			1.14944i			0.0492364i
$546$		0			0
$547$	−35.6558	+	23.8244i	−1.52453	+	1.01866i	−0.540361	+	0.841434i	$0.681712\pi$
$547$	−35.6558	+	23.8244i	−1.52453	+	1.01866i	−0.984170	+	0.177225i	$0.943288\pi$
$548$		0			0
$549$	−27.5292	+	5.47591i	−1.17492	+	0.233706i
$550$		0			0
$551$	15.8805	−	6.57794i	0.676534	−	0.280230i
$552$		0			0
$553$	−2.11357	−	0.875469i	−0.0898782	−	0.0372287i
$554$		0			0
$555$	−0.979585	+	1.46605i	−0.0415811	+	0.0622305i
$556$		0			0
$557$	−2.38952	−	0.475305i	−0.101247	−	0.0201393i	0.144207	−	0.989548i	$-0.453937\pi$
$557$	−2.38952	−	0.475305i	−0.101247	−	0.0201393i	−0.245454	+	0.969408i	$0.578937\pi$
$558$		0			0
$559$	−9.82443	−	9.82443i	−0.415529	−	0.415529i
$560$		0			0
$561$	−4.68671	+	4.68671i	−0.197873	+	0.197873i
$562$		0			0
$563$	−2.89115	+	14.5348i	−0.121847	+	0.612567i	0.870811	+	0.491617i	$0.163594\pi$
$563$	−2.89115	+	14.5348i	−0.121847	+	0.612567i	−0.992659	+	0.120950i	$0.961406\pi$
$564$		0			0
$565$	0.353871	+	0.236449i	0.0148874	+	0.00994748i
$566$		0			0
$567$	1.49422	−	3.60736i	0.0627512	−	0.151495i
$568$		0			0
$569$	−13.6164	−	32.8729i	−0.570829	−	1.37810i	−0.900851	−	0.434129i	$-0.857056\pi$
$569$	−13.6164	−	32.8729i	−0.570829	−	1.37810i	0.330022	−	0.943973i	$-0.392944\pi$
$570$		0			0
$571$	4.08279	+	20.5256i	0.170859	+	0.858968i	0.967180	+	0.254093i	$0.0817769\pi$
$571$	4.08279	+	20.5256i	0.170859	+	0.858968i	−0.796321	+	0.604875i	$0.793223\pi$
$572$		0			0
$573$	−8.21890	−	12.3005i	−0.343350	−	0.513859i
$574$		0			0
$575$	−19.7847			−0.825079
$576$		0			0
$577$	−13.2749			−0.552640			−0.276320	−	0.961066i	$-0.589115\pi$
$577$	−13.2749			−0.552640			−0.276320	+	0.961066i	$0.589115\pi$
$578$		0			0
$579$	−6.09167	−	9.11682i	−0.253161	−	0.378882i
$580$		0			0
$581$	−4.04598	−	20.3405i	−0.167855	−	0.843866i
$582$		0			0
$583$	−7.60407	−	18.3578i	−0.314928	−	0.760304i
$584$		0			0
$585$	−0.765144	+	1.84722i	−0.0316348	+	0.0763732i
$586$		0			0
$587$	5.72679	+	3.82652i	0.236370	+	0.157937i	0.668114	−	0.744059i	$-0.267102\pi$
$587$	5.72679	+	3.82652i	0.236370	+	0.157937i	−0.431744	+	0.901996i	$0.642102\pi$
$588$		0			0
$589$	−4.19960	+	21.1128i	−0.173042	+	0.869939i
$590$		0			0
$591$	3.02782	−	3.02782i	0.124548	−	0.124548i
$592$		0			0
$593$	5.93109	+	5.93109i	0.243561	+	0.243561i	0.818321	−	0.574761i	$-0.194905\pi$
$593$	5.93109	+	5.93109i	0.243561	+	0.243561i	−0.574761	+	0.818321i	$0.694905\pi$
$594$		0			0
$595$	−0.545923	−	0.108591i	−0.0223807	−	0.00445179i
$596$		0			0
$597$	11.0468	−	16.5328i	0.452117	−	0.676642i
$598$		0			0
$599$	−8.60956	−	3.56620i	−0.351777	−	0.145711i	0.199796	−	0.979838i	$-0.435972\pi$
$599$	−8.60956	−	3.56620i	−0.351777	−	0.145711i	−0.551573	+	0.834127i	$0.685972\pi$
$600$		0			0
$601$	−9.04530	+	3.74668i	−0.368965	+	0.152830i	−0.559459	−	0.828858i	$-0.688991\pi$
$601$	−9.04530	+	3.74668i	−0.368965	+	0.152830i	0.190494	+	0.981688i	$0.438991\pi$
$602$		0			0
$603$	−7.77753	+	1.54705i	−0.316725	+	0.0630006i
$604$		0			0
$605$	−2.97596	+	1.98847i	−0.120990	+	0.0808430i
$606$		0			0
$607$			34.8085i			1.41283i	0.707796	+	0.706417i	$0.249689\pi$
$607$			34.8085i			1.41283i	−0.707796	+	0.706417i	$0.750311\pi$
$608$		0			0
$609$		−	7.60167i		−	0.308035i
$610$		0			0
$611$	9.14318	−	6.10928i	0.369894	−	0.247155i
$612$		0			0
$613$	14.7093	−	2.92585i	0.594101	−	0.118174i	0.111123	−	0.993807i	$-0.464555\pi$
$613$	14.7093	−	2.92585i	0.594101	−	0.118174i	0.482978	+	0.875632i	$0.339555\pi$
$614$		0			0
$615$	2.38549	−	0.988103i	0.0961923	−	0.0398442i
$616$		0			0
$617$	7.99200	+	3.31040i	0.321746	+	0.133272i	0.537710	−	0.843130i	$-0.319289\pi$
$617$	7.99200	+	3.31040i	0.321746	+	0.133272i	−0.215964	+	0.976401i	$0.569289\pi$
$618$		0			0
$619$	4.66067	−	6.97519i	0.187328	−	0.280356i	−0.725904	−	0.687796i	$-0.758578\pi$
$619$	4.66067	−	6.97519i	0.187328	−	0.280356i	0.913232	+	0.407440i	$0.133578\pi$
$620$		0			0
$621$	−17.7965	−	3.53994i	−0.714147	−	0.142053i
$622$		0			0
$623$	−1.71594	−	1.71594i	−0.0687477	−	0.0687477i
$624$		0			0
$625$	16.9348	−	16.9348i	0.677393	−	0.677393i
$626$		0			0
$627$	2.17004	−	10.9095i	0.0866631	−	0.435685i
$628$		0			0
$629$	10.0252	+	6.69862i	0.399731	+	0.267092i
$630$		0			0
$631$	−12.6693	+	30.5864i	−0.504358	+	1.21763i	0.442731	+	0.896654i	$0.354010\pi$
$631$	−12.6693	+	30.5864i	−0.504358	+	1.21763i	−0.947089	+	0.320972i	$0.895990\pi$
$632$		0			0
$633$	1.22537	+	2.95831i	0.0487042	+	0.117582i
$634$		0			0
$635$	0.941317	+	4.73232i	0.0373550	+	0.187796i
$636$		0			0
$637$	9.60488	+	14.3747i	0.380559	+	0.569547i
$638$		0			0
$639$	31.8752			1.26096
$640$		0			0
$641$	10.2292			0.404030			0.202015	−	0.979382i	$-0.435251\pi$
$641$	10.2292			0.404030			0.202015	+	0.979382i	$0.435251\pi$
$642$		0			0
$643$	4.22568	+	6.32418i	0.166645	+	0.249401i	0.905388	−	0.424586i	$-0.139580\pi$
$643$	4.22568	+	6.32418i	0.166645	+	0.249401i	−0.738743	+	0.673987i	$0.764580\pi$
$644$		0			0
$645$	−0.185383	−	0.931982i	−0.00729944	−	0.0366968i
$646$		0			0
$647$	7.05188	+	17.0247i	0.277238	+	0.669311i	0.999757	−	0.0220394i	$-0.00701594\pi$
$647$	7.05188	+	17.0247i	0.277238	+	0.669311i	−0.722519	+	0.691351i	$0.757016\pi$
$648$		0			0
$649$	11.2845	−	27.2431i	0.442954	−	1.06939i
$650$		0			0
$651$	7.91549	+	5.28896i	0.310232	+	0.207291i
$652$		0			0
$653$	5.75170	−	28.9158i	0.225081	−	1.13156i	−0.688604	−	0.725138i	$-0.741776\pi$
$653$	5.75170	−	28.9158i	0.225081	−	1.13156i	0.913685	−	0.406423i	$-0.133224\pi$
$654$		0			0
$655$	−1.69250	+	1.69250i	−0.0661314	+	0.0661314i
$656$		0			0
$657$	1.56936	+	1.56936i	0.0612267	+	0.0612267i
$658$		0			0
$659$	4.76397	+	0.947613i	0.185578	+	0.0369138i	0.287004	−	0.957929i	$-0.407341\pi$
$659$	4.76397	+	0.947613i	0.185578	+	0.0369138i	−0.101426	+	0.994843i	$0.532341\pi$
$660$		0			0
$661$	−14.3165	+	21.4261i	−0.556846	+	0.833378i	−0.997945	−	0.0640799i	$-0.979589\pi$
$661$	−14.3165	+	21.4261i	−0.556846	+	0.833378i	0.441099	+	0.897458i	$0.354589\pi$
$662$		0			0
$663$	−4.12354	−	1.70802i	−0.160145	−	0.0663342i
$664$		0			0
$665$	0.863022	−	0.357475i	0.0334665	−	0.0138623i
$666$		0			0
$667$	25.8670	−	5.14526i	1.00157	−	0.199225i
$668$		0			0
$669$	−16.9334	+	11.3145i	−0.654683	+	0.437445i
$670$		0			0
$671$		−	61.4195i		−	2.37107i
$672$		0			0
$673$			7.18022i			0.276777i	0.990378	+	0.138389i	$0.0441923\pi$
$673$			7.18022i			0.276777i	−0.990378	+	0.138389i	$0.955808\pi$
$674$		0			0
$675$	18.5313	−	12.3822i	0.713271	−	0.476592i
$676$		0			0
$677$	0.516673	−	0.102773i	0.0198574	−	0.00394987i	−0.185152	−	0.982710i	$-0.559278\pi$
$677$	0.516673	−	0.102773i	0.0198574	−	0.00394987i	0.205009	+	0.978760i	$0.434278\pi$
$678$		0			0
$679$	−19.1801	+	7.94467i	−0.736066	+	0.304888i
$680$		0			0
$681$	8.38686	+	3.47395i	0.321385	+	0.133122i
$682$		0			0
$683$	−10.6617	+	15.9564i	−0.407960	+	0.610555i	−0.977380	−	0.211492i	$-0.932168\pi$
$683$	−10.6617	+	15.9564i	−0.407960	+	0.610555i	0.569420	+	0.822047i	$0.307168\pi$
$684$		0			0
$685$	−2.03674	−	0.405133i	−0.0778199	−	0.0154793i
$686$		0			0
$687$	−8.73379	−	8.73379i	−0.333215	−	0.333215i
$688$		0			0
$689$	9.46156	−	9.46156i	0.360457	−	0.360457i
$690$		0			0
$691$	−8.09941	+	40.7185i	−0.308116	+	1.54901i	0.447677	+	0.894195i	$0.352251\pi$
$691$	−8.09941	+	40.7185i	−0.308116	+	1.54901i	−0.755794	+	0.654810i	$0.772749\pi$
$692$		0			0
$693$	12.5294	+	8.37187i	0.475952	+	0.318021i
$694$		0			0
$695$	0.361158	−	0.871912i	0.0136995	−	0.0330735i
$696$		0			0
$697$	−6.75687	−	16.3125i	−0.255935	−	0.617881i
$698$		0			0
$699$	0.915174	+	4.60089i	0.0346151	+	0.174022i
$700$		0			0
$701$	2.87333	+	4.30025i	0.108524	+	0.162418i	0.881756	−	0.471705i	$-0.156361\pi$
$701$	2.87333	+	4.30025i	0.108524	+	0.162418i	−0.773232	+	0.634123i	$0.781361\pi$
$702$		0			0
$703$	−20.2346			−0.763164
$704$		0			0
$705$	0.752077			0.0283249
$706$		0			0
$707$	6.28982	+	9.41338i	0.236553	+	0.354027i
$708$		0			0
$709$	8.49385	+	42.7015i	0.318993	+	1.60369i	0.724286	+	0.689500i	$0.242170\pi$
$709$	8.49385	+	42.7015i	0.318993	+	1.60369i	−0.405292	+	0.914187i	$0.632830\pi$
$710$		0			0
$711$	1.47076	+	3.55073i	0.0551578	+	0.133163i
$712$		0			0
$713$	−12.6396	+	30.5147i	−0.473357	+	1.14278i
$714$		0			0
$715$	−3.63778	−	2.43068i	−0.136045	−	0.0909024i
$716$		0			0
$717$	3.24346	−	16.3060i	0.121129	−	0.608958i
$718$		0			0
$719$	−4.80412	+	4.80412i	−0.179163	+	0.179163i	−0.790991	−	0.611828i	$-0.790435\pi$
$719$	−4.80412	+	4.80412i	−0.179163	+	0.179163i	0.611828	+	0.790991i	$0.290435\pi$
$720$		0			0
$721$	9.69822	+	9.69822i	0.361181	+	0.361181i
$722$		0			0
$723$	2.64620	+	0.526363i	0.0984134	+	0.0195756i
$724$		0			0
$725$	−17.9974	+	26.9350i	−0.668408	+	1.00034i
$726$		0			0
$727$	−3.79111	−	1.57033i	−0.140604	−	0.0582402i	0.311272	−	0.950321i	$-0.399245\pi$
$727$	−3.79111	−	1.57033i	−0.140604	−	0.0582402i	−0.451876	+	0.892081i	$0.649245\pi$
$728$		0			0
$729$	4.70693	−	1.94968i	0.174331	−	0.0722102i
$730$		0			0
$731$	−6.37310	+	1.26769i	−0.235718	+	0.0468872i
$732$		0			0
$733$	37.2568	−	24.8942i	1.37611	−	0.919488i	0.376136	−	0.926564i	$-0.377253\pi$
$733$	37.2568	−	24.8942i	1.37611	−	0.919488i	0.999975	+	0.00707651i	$0.00225254\pi$
$734$		0			0
$735$			1.18240i			0.0436134i
$736$		0			0
$737$		−	17.3522i		−	0.639175i
$738$		0			0
$739$	29.8791	−	19.9646i	1.09912	−	0.734409i	0.132645	−	0.991164i	$-0.457653\pi$
$739$	29.8791	−	19.9646i	1.09912	−	0.734409i	0.966477	+	0.256754i	$0.0826531\pi$
$740$		0			0
$741$	7.34645	−	1.46130i	0.269878	−	0.0536822i
$742$		0			0
$743$	18.9414	−	7.84578i	0.694892	−	0.287834i	−0.00714476	−	0.999974i	$-0.502274\pi$
$743$	18.9414	−	7.84578i	0.694892	−	0.287834i	0.702037	+	0.712141i	$0.252274\pi$
$744$		0			0
$745$	−2.17840	−	0.902321i	−0.0798102	−	0.0330585i
$746$		0			0
$747$	−19.3565	+	28.9691i	−0.708218	+	1.05992i
$748$		0			0
$749$	−2.51888	−	0.501036i	−0.0920379	−	0.0183075i
$750$		0			0
$751$	5.62839	+	5.62839i	0.205383	+	0.205383i	0.802302	−	0.596919i	$-0.203609\pi$
$751$	5.62839	+	5.62839i	0.205383	+	0.205383i	−0.596919	+	0.802302i	$0.703609\pi$
$752$		0			0
$753$	2.27263	−	2.27263i	0.0828191	−	0.0828191i
$754$		0			0
$755$	−0.209242	+	1.05193i	−0.00761510	+	0.0382837i
$756$		0			0
$757$	−17.5865	−	11.7509i	−0.639192	−	0.427095i	0.193293	−	0.981141i	$-0.438083\pi$
$757$	−17.5865	−	11.7509i	−0.639192	−	0.427095i	−0.832486	+	0.554046i	$0.813083\pi$
$758$		0			0
$759$	6.53120	−	15.7677i	0.237068	−	0.572332i
$760$		0			0
$761$	8.96561	+	21.6449i	0.325003	+	0.784627i	0.998949	+	0.0458456i	$0.0145982\pi$
$761$	8.96561	+	21.6449i	0.325003	+	0.784627i	−0.673946	+	0.738781i	$0.735402\pi$
$762$		0			0
$763$	1.13808	+	5.72150i	0.0412011	+	0.207132i
$764$		0			0
$765$	0.519514	+	0.777507i	0.0187831	+	0.0281108i
$766$		0			0
$767$	19.8570			0.716993
$768$		0			0
$769$	6.14218			0.221493			0.110746	−	0.993849i	$-0.464676\pi$
$769$	6.14218			0.221493			0.110746	+	0.993849i	$0.464676\pi$
$770$		0			0
$771$	8.29983	+	12.4216i	0.298911	+	0.447352i
$772$		0			0
$773$	3.65565	+	18.3782i	0.131485	+	0.661018i	0.989162	+	0.146830i	$0.0469069\pi$
$773$	3.65565	+	18.3782i	0.131485	+	0.661018i	−0.857677	+	0.514189i	$0.828093\pi$
$774$		0			0
$775$	−15.5251	−	37.4808i	−0.557677	−	1.34635i
$776$		0			0
$777$	−3.42447	+	8.26741i	−0.122852	+	0.296592i
$778$		0			0
$779$	24.6378	+	16.4624i	0.882739	+	0.589827i
$780$		0			0
$781$	−13.6074	+	68.4090i	−0.486911	+	2.44787i
$782$		0			0
$783$	−21.0081	+	21.0081i	−0.750768	+	0.750768i
$784$		0			0
$785$	2.14111	+	2.14111i	0.0764196	+	0.0764196i
$786$		0			0
$787$	43.2635	+	8.60564i	1.54218	+	0.306758i	0.891650	−	0.452726i	$-0.149548\pi$
$787$	43.2635	+	8.60564i	1.54218	+	0.306758i	0.650526	+	0.759484i	$0.274548\pi$
$788$		0			0
$789$	0.819494	−	1.22646i	0.0291747	−	0.0436631i
$790$		0			0
$791$	1.99556	+	0.826587i	0.0709539	+	0.0293901i
$792$		0			0
$793$	38.2114	−	15.8277i	1.35693	−	0.562058i
$794$		0			0
$795$	0.897558	−	0.178535i	0.0318331	−	0.00633200i
$796$		0			0
$797$	−39.2600	+	26.2327i	−1.39066	+	0.929211i	−0.390700	+	0.920518i	$0.627767\pi$
$797$	−39.2600	+	26.2327i	−1.39066	+	0.929211i	−0.999962	+	0.00869271i	$0.997233\pi$
$798$		0			0
$799$		−	5.14287i		−	0.181942i
$800$		0			0
$801$			4.07679i			0.144046i
$802$		0			0
$803$	−4.03804	+	2.69813i	−0.142499	+	0.0952151i
$804$		0			0
$805$	1.40573	−	0.279617i	0.0495454	−	0.00985520i
$806$		0			0
$807$	−5.10839	+	2.11596i	−0.179824	+	0.0744854i
$808$		0			0
$809$	−14.5037	−	6.00764i	−0.509924	−	0.211217i	0.112861	−	0.993611i	$-0.463999\pi$
$809$	−14.5037	−	6.00764i	−0.509924	−	0.211217i	−0.622784	+	0.782394i	$0.713999\pi$
$810$		0			0
$811$	15.8735	−	23.7564i	0.557395	−	0.834200i	−0.440586	−	0.897710i	$-0.645229\pi$
$811$	15.8735	−	23.7564i	0.557395	−	0.834200i	0.997981	+	0.0635100i	$0.0202295\pi$
$812$		0			0
$813$	20.3857	+	4.05498i	0.714959	+	0.142214i
$814$		0			0
$815$	−0.000712573	0	0.000712573i	−2.49603e−5	0	2.49603e-5i
$816$		0			0
$817$	7.71100	−	7.71100i	0.269774	−	0.269774i
$818$		0			0
$819$	−1.97966	+	9.95241i	−0.0691749	+	0.347765i
$820$		0			0
$821$	−10.7690	−	7.19563i	−0.375842	−	0.251129i	0.353274	−	0.935520i	$-0.385068\pi$
$821$	−10.7690	−	7.19563i	−0.375842	−	0.251129i	−0.729116	+	0.684391i	$0.760068\pi$
$822$		0			0
$823$	5.78447	−	13.9649i	0.201634	−	0.486788i	−0.790425	−	0.612558i	$-0.790140\pi$
$823$	5.78447	−	13.9649i	0.201634	−	0.486788i	0.992059	+	0.125771i	$0.0401404\pi$
$824$		0			0
$825$	8.02219	+	19.3673i	0.279297	+	0.674282i
$826$		0			0
$827$	−6.95283	−	34.9542i	−0.241774	−	1.21548i	−0.890687	−	0.454616i	$-0.849776\pi$
$827$	−6.95283	−	34.9542i	−0.241774	−	1.21548i	0.648914	−	0.760862i	$-0.275224\pi$
$828$		0			0
$829$	−15.3694	−	23.0020i	−0.533802	−	0.798891i	0.462335	−	0.886705i	$-0.347012\pi$
$829$	−15.3694	−	23.0020i	−0.533802	−	0.798891i	−0.996137	+	0.0878145i	$0.972012\pi$
$830$		0			0
$831$	−6.31193			−0.218959
$832$		0			0
$833$	8.08551			0.280146
$834$		0			0
$835$	0.684068	+	1.02378i	0.0236732	+	0.0354294i
$836$		0			0
$837$	−7.25872	−	36.4920i	−0.250898	−	1.26135i
$838$		0			0
$839$	11.8401	+	28.5844i	0.408764	+	0.986844i	0.985463	+	0.169887i	$0.0543404\pi$
$839$	11.8401	+	28.5844i	0.408764	+	0.986844i	−0.576699	+	0.816956i	$0.695660\pi$
$840$		0			0
$841$	5.42762	−	13.1034i	0.187159	−	0.451843i
$842$		0			0
$843$	−13.0111	−	8.69371i	−0.448125	−	0.299427i
$844$		0			0
$845$	−0.0979868	+	0.492613i	−0.00337085	+	0.0169464i
$846$		0			0
$847$	−12.8445	+	12.8445i	−0.441342	+	0.441342i
$848$		0			0
$849$	−13.8253	−	13.8253i	−0.474482	−	0.474482i
$850$		0			0
$851$	−30.4502	−	6.05693i	−1.04382	−	0.207629i
$852$		0			0
$853$	−25.8867	+	38.7421i	−0.886343	+	1.32651i	0.0582640	+	0.998301i	$0.481443\pi$
$853$	−25.8867	+	38.7421i	−0.886343	+	1.32651i	−0.944607	+	0.328204i	$0.893557\pi$
$854$		0			0
$855$	−1.44985	−	0.600546i	−0.0495837	−	0.0205383i
$856$		0			0
$857$	11.6236	−	4.81466i	0.397055	−	0.164466i	−0.175216	−	0.984530i	$-0.556062\pi$
$857$	11.6236	−	4.81466i	0.397055	−	0.164466i	0.572271	+	0.820064i	$0.306062\pi$
$858$		0			0
$859$	−7.21770	+	1.43569i	−0.246265	+	0.0489851i	−0.316679	−	0.948533i	$-0.602568\pi$
$859$	−7.21770	+	1.43569i	−0.246265	+	0.0489851i	0.0704144	+	0.997518i	$0.477568\pi$
$860$		0			0
$861$	10.8958	−	7.28035i	0.371329	−	0.248114i
$862$		0			0
$863$			51.3234i			1.74707i	0.486761	+	0.873535i	$0.338178\pi$
$863$			51.3234i			1.74707i	−0.486761	+	0.873535i	$0.661822\pi$
$864$		0			0
$865$			1.96578i			0.0668384i
$866$		0			0
$867$	10.4099	−	6.95566i	0.353538	−	0.236226i
$868$		0			0
$869$	−8.24825	+	1.64068i	−0.279803	+	0.0556562i
$870$		0			0
$871$	10.7954	−	4.47162i	0.365790	−	0.151515i
$872$		0			0
$873$	32.2220	+	13.3468i	1.09055	+	0.451720i
$874$		0			0
$875$	−1.97009	+	2.94844i	−0.0666011	+	0.0996755i
$876$		0			0
$877$	41.5765	+	8.27007i	1.40394	+	0.279260i	0.838217	−	0.545337i	$-0.183598\pi$
$877$	41.5765	+	8.27007i	1.40394	+	0.279260i	0.565720	+	0.824597i	$0.308598\pi$
$878$		0			0
$879$	−14.6499	−	14.6499i	−0.494130	−	0.494130i
$880$		0			0
$881$	19.0362	−	19.0362i	0.641347	−	0.641347i	−0.309539	−	0.950887i	$-0.600175\pi$
$881$	19.0362	−	19.0362i	0.641347	−	0.641347i	0.950887	+	0.309539i	$0.100175\pi$
$882$		0			0
$883$	6.24157	−	31.3785i	0.210046	−	1.05597i	−0.721519	−	0.692395i	$-0.756556\pi$
$883$	6.24157	−	31.3785i	0.210046	−	1.05597i	0.931565	−	0.363576i	$-0.118444\pi$
$884$		0			0
$885$	1.12920	+	0.754506i	0.0379576	+	0.0253624i
$886$		0			0
$887$	17.9162	−	43.2535i	0.601567	−	1.45231i	−0.270401	−	0.962748i	$-0.587156\pi$
$887$	17.9162	−	43.2535i	0.601567	−	1.45231i	0.871968	−	0.489563i	$-0.162844\pi$
$888$		0			0
$889$	9.37110	+	22.6238i	0.314297	+	0.758779i
$890$		0			0
$891$	−2.80025	−	14.0778i	−0.0938118	−	0.471624i
$892$		0			0
$893$	4.79505	+	7.17630i	0.160460	+	0.240146i
$894$		0			0
$895$	−3.35539			−0.112158
$896$		0			0
$897$	11.4928			0.383732
$898$		0			0
$899$	30.0452	+	44.9658i	1.00206	+	1.49969i
$900$		0			0
$901$	−1.22087	−	6.13771i	−0.0406729	−	0.204477i
$902$		0			0
$903$	−1.84554	−	4.45554i	−0.0614158	−	0.148271i
$904$		0			0
$905$	1.64421	−	3.96948i	0.0546555	−	0.131950i
$906$		0			0
$907$	6.59470	+	4.40644i	0.218974	+	0.146313i	0.660219	−	0.751073i	$-0.270463\pi$
$907$	6.59470	+	4.40644i	0.218974	+	0.146313i	−0.441246	+	0.897386i	$0.645463\pi$
$908$		0			0
$909$	3.71053	−	18.6541i	0.123070	−	0.618717i
$910$		0			0
$911$	0.693019	−	0.693019i	0.0229608	−	0.0229608i	−0.695533	−	0.718494i	$-0.744832\pi$
$911$	0.693019	−	0.693019i	0.0229608	−	0.0229608i	0.718494	+	0.695533i	$0.244832\pi$
$912$		0			0
$913$	−53.9087	−	53.9087i	−1.78412	−	1.78412i
$914$		0			0
$915$	2.77436	+	0.551855i	0.0917175	+	0.0182437i
$916$		0			0
$917$	−6.74890	+	10.1004i	−0.222868	+	0.333546i
$918$		0			0
$919$	−24.9456	−	10.3328i	−0.822879	−	0.340848i	−0.0687992	−	0.997631i	$-0.521917\pi$
$919$	−24.9456	−	10.3328i	−0.822879	−	0.340848i	−0.754080	+	0.656783i	$0.771917\pi$
$920$		0			0
$921$	−7.00216	+	2.90039i	−0.230729	+	0.0955710i
$922$		0			0
$923$	−46.0664	+	9.16318i	−1.51630	+	0.301610i
$924$		0			0
$925$	31.7076	−	21.1863i	1.04254	−	0.696602i
$926$		0			0
$927$		−	23.0413i		−	0.756777i
$928$		0			0
$929$			12.4630i			0.408898i	0.978877	+	0.204449i	$0.0655402\pi$
$929$			12.4630i			0.408898i	−0.978877	+	0.204449i	$0.934460\pi$
$930$		0			0
$931$	−11.2824	+	7.53868i	−0.369767	+	0.247070i
$932$		0			0
$933$	−3.28911	+	0.654245i	−0.107681	+	0.0214190i
$934$		0			0
$935$	−1.89043	+	0.783040i	−0.0618235	+	0.0256081i
$936$		0			0
$937$	−53.2713	−	22.0657i	−1.74030	−	0.720855i	−0.998752	−	0.0499537i	$-0.984093\pi$
$937$	−53.2713	−	22.0657i	−1.74030	−	0.720855i	−0.741547	−	0.670901i	$-0.765907\pi$
$938$		0			0
$939$	−10.3098	+	15.4297i	−0.336446	+	0.503528i
$940$		0			0
$941$	−15.5300	−	3.08911i	−0.506264	−	0.100702i	−0.0646512	−	0.997908i	$-0.520593\pi$
$941$	−15.5300	−	3.08911i	−0.506264	−	0.100702i	−0.441613	+	0.897206i	$0.645593\pi$
$942$		0			0
$943$	32.1485	+	32.1485i	1.04690	+	1.04690i
$944$		0			0
$945$	−1.14168	+	1.14168i	−0.0371387	+	0.0371387i
$946$		0			0
$947$	2.16365	−	10.8774i	0.0703092	−	0.353468i	−0.929576	−	0.368631i	$-0.879827\pi$
$947$	2.16365	−	10.8774i	0.0703092	−	0.353468i	0.999885	+	0.0151628i	$0.00482666\pi$
$948$		0			0
$949$	−2.71921	−	1.81692i	−0.0882692	−	0.0589796i
$950$		0			0
$951$	−9.75513	+	23.5510i	−0.316332	+	0.763693i
$952$		0			0
$953$	13.7909	+	33.2942i	0.446731	+	1.07850i	0.973539	+	0.228520i	$0.0733887\pi$
$953$	13.7909	+	33.2942i	0.446731	+	1.07850i	−0.526808	+	0.849984i	$0.676611\pi$
$954$		0			0
$955$	−0.890987	−	4.47929i	−0.0288317	−	0.144947i
$956$		0			0
$957$	−15.5251	−	23.2350i	−0.501855	−	0.751079i
$958$		0			0
$959$	−10.5393			−0.340333
$960$		0			0
$961$	−36.7264			−1.18472
$962$		0			0
$963$	2.39703	+	3.58741i	0.0772431	+	0.115603i
$964$		0			0
$965$	−0.660380	−	3.31995i	−0.0212584	−	0.106873i
$966$		0			0
$967$	9.21382	+	22.2441i	0.296296	+	0.715323i	0.999988	+	0.00481755i	$0.00153348\pi$
$967$	9.21382	+	22.2441i	0.296296	+	0.715323i	−0.703692	+	0.710505i	$0.748467\pi$
$968$		0			0
$969$	1.34060	−	3.23648i	0.0430661	−	0.103971i
$970$		0			0
$971$	−11.1713	−	7.46439i	−0.358503	−	0.239544i	0.363255	−	0.931690i	$-0.381665\pi$
$971$	−11.1713	−	7.46439i	−0.358503	−	0.239544i	−0.721757	+	0.692146i	$0.756665\pi$
$972$		0			0
$973$	0.934424	−	4.69767i	0.0299563	−	0.150600i
$974$		0			0
$975$	−9.98182	+	9.98182i	−0.319674	+	0.319674i
$976$		0			0
$977$	−7.40597	−	7.40597i	−0.236938	−	0.236938i	0.578643	−	0.815581i	$-0.303582\pi$
$977$	−7.40597	−	7.40597i	−0.236938	−	0.236938i	−0.815581	+	0.578643i	$0.803582\pi$
$978$		0			0
$979$	−8.74939	−	1.74036i	−0.279632	−	0.0556222i
$980$		0			0
$981$	5.44472	−	8.14859i	0.173836	−	0.260165i
$982$		0			0
$983$	−46.6330	−	19.3160i	−1.48736	−	0.616085i	−0.516620	−	0.856215i	$-0.672810\pi$
$983$	−46.6330	−	19.3160i	−1.48736	−	0.616085i	−0.970741	+	0.240129i	$0.922810\pi$
$984$		0			0
$985$	1.22130	−	0.505878i	0.0389138	−	0.0161186i
$986$		0			0
$987$	3.74358	−	0.744644i	0.119159	−	0.0237023i
$988$		0			0
$989$	13.9121	−	9.29579i	0.442380	−	0.295589i
$990$		0			0
$991$		−	12.4779i		−	0.396374i	−0.980164	−	0.198187i	$-0.936495\pi$
$991$		−	12.4779i		−	0.396374i	0.980164	−	0.198187i	$-0.0635053\pi$
$992$		0			0
$993$			0.167792i			0.00532471i
$994$		0			0
$995$	5.10395	−	3.41035i	0.161806	−	0.108115i
$996$		0			0
$997$	1.42739	−	0.283926i	0.0452060	−	0.00899203i	−0.172436	−	0.985021i	$-0.555164\pi$
$997$	1.42739	−	0.283926i	0.0452060	−	0.00899203i	0.217642	+	0.976029i	$0.430164\pi$
$998$		0			0
$999$	32.3119	−	13.3840i	1.02230	−	0.423452i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.2.i.a.17.4		56
4.3	odd	2		64.2.i.a.45.7	yes	56
8.3	odd	2		512.2.i.b.289.4		56
8.5	even	2		512.2.i.a.289.4		56
12.11	even	2		576.2.bd.a.109.1		56
64.5	even	16		512.2.i.a.225.4		56
64.27	odd	16		64.2.i.a.37.7	✓	56
64.37	even	16	inner	256.2.i.a.241.4		56
64.59	odd	16		512.2.i.b.225.4		56
192.155	even	16		576.2.bd.a.37.1		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.37.7	✓	56	64.27	odd	16
64.2.i.a.45.7	yes	56	4.3	odd	2
256.2.i.a.17.4		56	1.1	even	1	trivial
256.2.i.a.241.4		56	64.37	even	16	inner
512.2.i.a.225.4		56	64.5	even	16
512.2.i.a.289.4		56	8.5	even	2
512.2.i.b.225.4		56	64.59	odd	16
512.2.i.b.289.4		56	8.3	odd	2
576.2.bd.a.37.1		56	192.155	even	16
576.2.bd.a.109.1		56	12.11	even	2

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:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	256.i (of order \(16\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.477374 + 0.714441i) q^{3} +(0.0517508 + 0.260169i) q^{5} +(0.515195 + 1.24379i) q^{7} +(0.865510 - 2.08953i) q^{9} +O(q^{10})\)	\(q+(0.477374 + 0.714441i) q^{3} +(0.0517508 + 0.260169i) q^{5} +(0.515195 + 1.24379i) q^{7} +(0.865510 - 2.08953i) q^{9} +(4.11495 + 2.74952i) q^{11} +(-0.650168 + 3.26862i) q^{13} +(-0.161171 + 0.161171i) q^{15} +(1.10212 + 1.10212i) q^{17} +(-2.56547 - 0.510304i) q^{19} +(-0.642674 + 0.961830i) q^{21} +(-3.70792 - 1.53587i) q^{23} +(4.55439 - 1.88649i) q^{25} +(4.43424 - 0.882025i) q^{27} +(-5.46390 + 3.65086i) q^{29} -8.22961i q^{31} +4.25245i q^{33} +(-0.296934 + 0.198405i) q^{35} +(7.58710 - 1.50917i) q^{37} +(-2.64561 + 1.09585i) q^{39} +(-10.4659 - 4.33512i) q^{41} +(-2.31618 + 3.46640i) q^{43} +(0.588420 + 0.117044i) q^{45} +(-2.33317 - 2.33317i) q^{47} +(3.66816 - 3.66816i) q^{49} +(-0.261277 + 1.31353i) q^{51} +(-3.33837 - 2.23063i) q^{53} +(-0.502388 + 1.21287i) q^{55} +(-0.860108 - 2.07648i) q^{57} +(-1.16241 - 5.84382i) q^{59} +(-6.89488 - 10.3189i) q^{61} +3.04484 q^{63} -0.884038 q^{65} +(-1.94793 - 2.91529i) q^{67} +(-0.672776 - 3.38227i) q^{69} +(5.39337 + 13.0208i) q^{71} +(-0.375531 + 0.906612i) q^{73} +(3.52193 + 2.35328i) q^{75} +(-1.29983 + 6.53468i) q^{77} +(-1.20158 + 1.20158i) q^{79} +(-2.05082 - 2.05082i) q^{81} +(-15.1088 - 3.00532i) q^{83} +(-0.229702 + 0.343773i) q^{85} +(-5.21666 - 2.16081i) q^{87} +(-1.66533 + 0.689803i) q^{89} +(-4.40044 + 0.875301i) q^{91} +(5.87957 - 3.92860i) q^{93} -0.693864i q^{95} +15.4207i q^{97} +(9.30674 - 6.21857i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 8 q^{3} - 8 q^{5} + 8 q^{7} - 8 q^{9}+O(q^{10}) \) 56 * q + 8 * q^3 - 8 * q^5 + 8 * q^7 - 8 * q^9	\( 56 q + 8 q^{3} - 8 q^{5} + 8 q^{7} - 8 q^{9} + 8 q^{11} - 8 q^{13} + 8 q^{15} - 8 q^{17} + 8 q^{19} - 8 q^{21} + 8 q^{23} - 8 q^{25} + 8 q^{27} - 8 q^{29} + 8 q^{35} - 8 q^{37} + 8 q^{39} - 8 q^{41} + 8 q^{43} - 8 q^{45} + 8 q^{47} - 8 q^{49} - 24 q^{51} - 8 q^{53} - 56 q^{55} - 8 q^{57} - 56 q^{59} - 8 q^{61} - 64 q^{63} - 16 q^{65} - 72 q^{67} - 8 q^{69} - 56 q^{71} - 8 q^{73} - 56 q^{75} - 8 q^{77} - 24 q^{79} - 8 q^{81} + 8 q^{83} - 8 q^{85} + 8 q^{87} - 8 q^{89} + 8 q^{91} + 16 q^{93} - 16 q^{99}+O(q^{100}) \) 56 * q + 8 * q^3 - 8 * q^5 + 8 * q^7 - 8 * q^9 + 8 * q^11 - 8 * q^13 + 8 * q^15 - 8 * q^17 + 8 * q^19 - 8 * q^21 + 8 * q^23 - 8 * q^25 + 8 * q^27 - 8 * q^29 + 8 * q^35 - 8 * q^37 + 8 * q^39 - 8 * q^41 + 8 * q^43 - 8 * q^45 + 8 * q^47 - 8 * q^49 - 24 * q^51 - 8 * q^53 - 56 * q^55 - 8 * q^57 - 56 * q^59 - 8 * q^61 - 64 * q^63 - 16 * q^65 - 72 * q^67 - 8 * q^69 - 56 * q^71 - 8 * q^73 - 56 * q^75 - 8 * q^77 - 24 * q^79 - 8 * q^81 + 8 * q^83 - 8 * q^85 + 8 * q^87 - 8 * q^89 + 8 * q^91 + 16 * q^93 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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