LMFDB - Embedded newform 896.2.q.d.703.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [896,2,Mod(703,896)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(896, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("896.703");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.q (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} - 24x^{14} + 226x^{12} - 972x^{10} + 1575x^{8} + 252x^{6} + 550x^{4} + 156x^{2} + 49 $ x^16 - 24x^14 + 226x^12 - 972x^10 + 1575x^8 + 252x^6 + 550x^4 + 156*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			703.5
Root			$0.526379 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	896.703
Dual form			896.2.q.d.831.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.20586 + 0.696202i) q^{3} +(-2.07821 - 3.59957i) q^{5} +(-0.632797 + 2.56896i) q^{7} +(-0.530605 - 0.919035i) q^{9} +O(q^{10})$	\(q+(1.20586 + 0.696202i) q^{3} +(-2.07821 - 3.59957i) q^{5} +(-0.632797 + 2.56896i) q^{7} +(-0.530605 - 0.919035i) q^{9} +(-2.36310 + 4.09302i) q^{11} -3.68997 q^{13} -5.78742i q^{15} +(2.28389 + 1.31860i) q^{17} +(-0.698106 + 0.403051i) q^{19} +(-2.55158 + 2.65725i) q^{21} +(-4.73969 + 2.73646i) q^{23} +(-6.13792 + 10.6312i) q^{25} -5.65485i q^{27} -3.88464i q^{29} +(-0.515984 + 0.893710i) q^{31} +(-5.69914 + 3.29040i) q^{33} +(10.5622 - 3.06105i) q^{35} +(-1.03237 + 0.596037i) q^{37} +(-4.44957 - 2.56896i) q^{39} +6.47477i q^{41} -10.2758 q^{43} +(-2.20542 + 3.81990i) q^{45} +(3.98009 + 6.89371i) q^{47} +(-6.19914 - 3.25126i) q^{49} +(1.83603 + 3.18010i) q^{51} +(2.32572 + 1.34275i) q^{53} +19.6441 q^{55} -1.12242 q^{57} +(2.38243 + 1.37550i) q^{59} +(-0.819529 - 1.41947i) q^{61} +(2.69673 - 0.781542i) q^{63} +(7.66853 + 13.2823i) q^{65} +(2.45914 - 4.25936i) q^{67} -7.62052 q^{69} -11.7693i q^{71} +(-10.5226 - 6.07521i) q^{73} +(-14.8029 + 8.54647i) q^{75} +(-9.01944 - 8.66078i) q^{77} +(-12.2126 + 7.05096i) q^{79} +(2.34510 - 4.06183i) q^{81} -7.37993i q^{83} -10.9614i q^{85} +(2.70449 - 4.68432i) q^{87} +(15.8983 - 9.17887i) q^{89} +(2.33500 - 9.47938i) q^{91} +(-1.24441 + 0.718458i) q^{93} +(2.90162 + 1.67525i) q^{95} -1.83807i q^{97} +5.01550 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{3} + 8 q^{9}+O(q^{10}) $ 16 * q + 12 * q^3 + 8 * q^9	$ 16 q + 12 q^{3} + 8 q^{9} - 4 q^{11} - 12 q^{19} - 16 q^{25} + 24 q^{33} + 20 q^{35} + 16 q^{49} - 52 q^{51} + 48 q^{57} + 60 q^{59} + 24 q^{65} + 12 q^{67} - 24 q^{73} - 120 q^{75} - 32 q^{81} + 24 q^{89} + 72 q^{91} + 64 q^{99}+O(q^{100}) $ 16 * q + 12 * q^3 + 8 * q^9 - 4 * q^11 - 12 * q^19 - 16 * q^25 + 24 * q^33 + 20 * q^35 + 16 * q^49 - 52 * q^51 + 48 * q^57 + 60 * q^59 + 24 * q^65 + 12 * q^67 - 24 * q^73 - 120 * q^75 - 32 * q^81 + 24 * q^89 + 72 * q^91 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$-1$

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
$3$	1.20586	+	0.696202i	0.696202	+	0.401952i	0.805931	−	0.592009i	$-0.201665\pi$
$3$	1.20586	+	0.696202i	0.696202	+	0.401952i	−0.109729	+	0.993962i	$0.534998\pi$
$4$		0			0
$5$	−2.07821	−	3.59957i	−0.929404	−	1.60978i	−0.784320	−	0.620356i	$-0.786988\pi$
$5$	−2.07821	−	3.59957i	−0.929404	−	1.60978i	−0.145084	−	0.989419i	$-0.546345\pi$
$6$		0			0
$7$	−0.632797	+	2.56896i	−0.239175	+	0.970977i
$7$	−0.632797	+	2.56896i	−0.239175	+	0.970977i
$8$		0			0
$9$	−0.530605	−	0.919035i	−0.176868	−	0.306345i
$10$		0			0
$11$	−2.36310	+	4.09302i	−0.712503	+	1.23409i	0.251412	+	0.967880i	$0.419105\pi$
$11$	−2.36310	+	4.09302i	−0.712503	+	1.23409i	−0.963915	+	0.266211i	$0.914228\pi$
$12$		0			0
$13$	−3.68997			−1.02341			−0.511706	−	0.859160i	$-0.670986\pi$
$13$	−3.68997			−1.02341			−0.511706	+	0.859160i	$0.670986\pi$
$14$		0			0
$15$		−	5.78742i		−	1.49431i
$16$		0			0
$17$	2.28389	+	1.31860i	0.553925	+	0.319809i	0.750703	−	0.660639i	$-0.229715\pi$
$17$	2.28389	+	1.31860i	0.553925	+	0.319809i	−0.196779	+	0.980448i	$0.563048\pi$
$18$		0			0
$19$	−0.698106	+	0.403051i	−0.160156	+	0.0924663i	−0.577936	−	0.816082i	$-0.696142\pi$
$19$	−0.698106	+	0.403051i	−0.160156	+	0.0924663i	0.417780	+	0.908548i	$0.362808\pi$
$20$		0			0
$21$	−2.55158	+	2.65725i	−0.556800	+	0.579859i
$22$		0			0
$23$	−4.73969	+	2.73646i	−0.988294	+	0.570592i	−0.904764	−	0.425913i	$-0.859953\pi$
$23$	−4.73969	+	2.73646i	−0.988294	+	0.570592i	−0.0835302	+	0.996505i	$0.526620\pi$
$24$		0			0
$25$	−6.13792	+	10.6312i	−1.22758	+	2.12624i
$26$		0			0
$27$		−	5.65485i		−	1.08828i
$28$		0			0
$29$		−	3.88464i		−	0.721360i	−0.932690	−	0.360680i	$-0.882545\pi$
$29$		−	3.88464i		−	0.721360i	0.932690	−	0.360680i	$-0.117455\pi$
$30$		0			0
$31$	−0.515984	+	0.893710i	−0.0926734	+	0.160515i	−0.908635	−	0.417591i	$-0.862875\pi$
$31$	−0.515984	+	0.893710i	−0.0926734	+	0.160515i	0.815962	+	0.578106i	$0.196208\pi$
$32$		0			0
$33$	−5.69914	+	3.29040i	−0.992092	+	0.572785i
$34$		0			0
$35$	10.5622	−	3.06105i	1.78534	−	0.517412i
$36$		0			0
$37$	−1.03237	+	0.596037i	−0.169720	+	0.0979879i	−0.582454	−	0.812864i	$-0.697907\pi$
$37$	−1.03237	+	0.596037i	−0.169720	+	0.0979879i	0.412734	+	0.910852i	$0.364574\pi$
$38$		0			0
$39$	−4.44957	−	2.56896i	−0.712502	−	0.411363i
$40$		0			0
$41$			6.47477i			1.01119i	0.862771	+	0.505595i	$0.168727\pi$
$41$			6.47477i			1.01119i	−0.862771	+	0.505595i	$0.831273\pi$
$42$		0			0
$43$	−10.2758			−1.56705			−0.783526	−	0.621359i	$-0.786581\pi$
$43$	−10.2758			−1.56705			−0.783526	+	0.621359i	$0.786581\pi$
$44$		0			0
$45$	−2.20542	+	3.81990i	−0.328765	+	0.569437i
$46$		0			0
$47$	3.98009	+	6.89371i	0.580555	+	1.00555i	0.995414	+	0.0956650i	$0.0304978\pi$
$47$	3.98009	+	6.89371i	0.580555	+	1.00555i	−0.414858	+	0.909886i	$0.636169\pi$
$48$		0			0
$49$	−6.19914	−	3.25126i	−0.885591	−	0.464466i
$50$		0			0
$51$	1.83603	+	3.18010i	0.257096	+	0.445303i
$52$		0			0
$53$	2.32572	+	1.34275i	0.319462	+	0.184441i	0.651153	−	0.758947i	$-0.274286\pi$
$53$	2.32572	+	1.34275i	0.319462	+	0.184441i	−0.331691	+	0.943388i	$0.607619\pi$
$54$		0			0
$55$	19.6441			2.64881
$56$		0			0
$57$	−1.12242			−0.148668
$58$		0			0
$59$	2.38243	+	1.37550i	0.310166	+	0.179074i	0.647001	−	0.762489i	$-0.276023\pi$
$59$	2.38243	+	1.37550i	0.310166	+	0.179074i	−0.336835	+	0.941564i	$0.609356\pi$
$60$		0			0
$61$	−0.819529	−	1.41947i	−0.104930	−	0.181744i	0.808780	−	0.588112i	$-0.200129\pi$
$61$	−0.819529	−	1.41947i	−0.104930	−	0.181744i	−0.913710	+	0.406368i	$0.866795\pi$
$62$		0			0
$63$	2.69673	−	0.781542i	0.339756	−	0.0984650i
$64$		0			0
$65$	7.66853	+	13.2823i	0.951164	+	1.64746i
$66$		0			0
$67$	2.45914	−	4.25936i	0.300432	−	0.520363i	−0.675802	−	0.737083i	$-0.736202\pi$
$67$	2.45914	−	4.25936i	0.300432	−	0.520363i	0.976234	+	0.216720i	$0.0695358\pi$
$68$		0			0
$69$	−7.62052			−0.917403
$70$		0			0
$71$		−	11.7693i		−	1.39676i	−0.715729	−	0.698378i	$-0.753905\pi$
$71$		−	11.7693i		−	1.39676i	0.715729	−	0.698378i	$-0.246095\pi$
$72$		0			0
$73$	−10.5226	−	6.07521i	−1.23157	−	0.711049i	−0.264215	−	0.964464i	$-0.585113\pi$
$73$	−10.5226	−	6.07521i	−1.23157	−	0.711049i	−0.967358	+	0.253415i	$0.918446\pi$
$74$		0			0
$75$	−14.8029	+	8.54647i	−1.70929	+	0.986862i
$76$		0			0
$77$	−9.01944	−	8.66078i	−1.02786	−	0.986987i
$78$		0			0
$79$	−12.2126	+	7.05096i	−1.37403	+	0.793295i	−0.991432	−	0.130622i	$-0.958303\pi$
$79$	−12.2126	+	7.05096i	−1.37403	+	0.793295i	−0.382594	+	0.923916i	$0.624969\pi$
$80$		0			0
$81$	2.34510	−	4.06183i	0.260567	−	0.451315i
$82$		0			0
$83$		−	7.37993i		−	0.810053i	−0.914305	−	0.405026i	$-0.867262\pi$
$83$		−	7.37993i		−	0.810053i	0.914305	−	0.405026i	$-0.132738\pi$
$84$		0			0
$85$		−	10.9614i		−	1.18893i
$86$		0			0
$87$	2.70449	−	4.68432i	0.289952	−	0.502212i
$88$		0			0
$89$	15.8983	−	9.17887i	1.68521	−	0.972958i	0.727116	−	0.686514i	$-0.240860\pi$
$89$	15.8983	−	9.17887i	1.68521	−	0.972958i	0.958097	−	0.286444i	$-0.0924733\pi$
$90$		0			0
$91$	2.33500	−	9.47938i	0.244775	−	0.993710i
$92$		0			0
$93$	−1.24441	+	0.718458i	−0.129039	+	0.0745006i
$94$		0			0
$95$	2.90162	+	1.67525i	0.297700	+	0.171877i
$96$		0			0
$97$		−	1.83807i		−	0.186628i	−0.995637	−	0.0933139i	$-0.970254\pi$
$97$		−	1.83807i		−	0.186628i	0.995637	−	0.0933139i	$-0.0297460\pi$
$98$		0			0
$99$	5.01550			0.504077
$100$		0			0
$101$	−1.39892	+	2.42300i	−0.139198	+	0.241097i	−0.927193	−	0.374584i	$-0.877786\pi$
$101$	−1.39892	+	2.42300i	−0.139198	+	0.241097i	0.787996	+	0.615681i	$0.211119\pi$
$102$		0			0
$103$	−1.50146	−	2.60060i	−0.147943	−	0.256244i	0.782524	−	0.622620i	$-0.213932\pi$
$103$	−1.50146	−	2.60060i	−0.147943	−	0.256244i	−0.930467	+	0.366376i	$0.880598\pi$
$104$		0			0
$105$	14.8677	+	3.66226i	1.45094	+	0.357400i
$106$		0			0
$107$	−5.10982	−	8.85047i	−0.493985	−	0.855607i	0.505991	−	0.862539i	$-0.331127\pi$
$107$	−5.10982	−	8.85047i	−0.493985	−	0.855607i	−0.999976	+	0.00693167i	$0.997794\pi$
$108$		0			0
$109$	−4.70239	−	2.71493i	−0.450407	−	0.260043i	0.257595	−	0.966253i	$-0.417070\pi$
$109$	−4.70239	−	2.71493i	−0.450407	−	0.260043i	−0.708002	+	0.706210i	$0.750403\pi$
$110$		0			0
$111$	−1.65985			−0.157546
$112$		0			0
$113$	8.70807			0.819186			0.409593	−	0.912268i	$-0.365671\pi$
$113$	8.70807			0.819186			0.409593	+	0.912268i	$0.365671\pi$
$114$		0			0
$115$	19.7002	+	11.3739i	1.83705	+	1.06062i
$116$		0			0
$117$	1.95792	+	3.39121i	0.181009	+	0.313517i
$118$		0			0
$119$	−4.83268	+	5.03282i	−0.443011	+	0.461358i
$120$		0			0
$121$	−5.66853	−	9.81818i	−0.515321	−	0.892562i
$122$		0			0
$123$	−4.50775	+	7.80766i	−0.406450	+	0.703993i
$124$		0			0
$125$	30.2415			2.70488
$126$		0			0
$127$			7.76928i			0.689412i	0.938711	+	0.344706i	$0.112021\pi$
$127$			7.76928i			0.689412i	−0.938711	+	0.344706i	$0.887979\pi$
$128$		0			0
$129$	−12.3912	−	7.15407i	−1.09099	−	0.629881i
$130$		0			0
$131$	−0.595007	+	0.343528i	−0.0519860	+	0.0300141i	−0.525768	−	0.850628i	$-0.676222\pi$
$131$	−0.595007	+	0.343528i	−0.0519860	+	0.0300141i	0.473782	+	0.880642i	$0.342889\pi$
$132$		0			0
$133$	−0.593665	−	2.04846i	−0.0514773	−	0.177624i
$134$		0			0
$135$	−20.3550	+	11.7520i	−1.75188	+	1.01145i
$136$		0			0
$137$	0.222679	−	0.385692i	0.0190248	−	0.0329519i	−0.856356	−	0.516385i	$-0.827277\pi$
$137$	0.222679	−	0.385692i	0.0190248	−	0.0329519i	0.875381	+	0.483434i	$0.160611\pi$
$138$		0			0
$139$			13.1355i			1.11414i	0.830465	+	0.557071i	$0.188075\pi$
$139$			13.1355i			1.11414i	−0.830465	+	0.557071i	$0.811925\pi$
$140$		0			0
$141$			11.0838i			0.933422i
$142$		0			0
$143$	8.71978	−	15.1031i	0.729184	−	1.26298i
$144$		0			0
$145$	−13.9830	+	8.07310i	−1.16123	+	0.670435i
$146$		0			0
$147$	−5.21174	−	8.23641i	−0.429857	−	0.679328i
$148$		0			0
$149$	4.83527	−	2.79164i	0.396120	−	0.228700i	−0.288688	−	0.957423i	$-0.593219\pi$
$149$	4.83527	−	2.79164i	0.396120	−	0.228700i	0.684809	+	0.728723i	$0.259886\pi$
$150$		0			0
$151$	7.89592	+	4.55871i	0.642561	+	0.370983i	0.785600	−	0.618734i	$-0.212354\pi$
$151$	7.89592	+	4.55871i	0.642561	+	0.370983i	−0.143040	+	0.989717i	$0.545688\pi$
$152$		0			0
$153$		−	2.79863i		−	0.226256i
$154$		0			0
$155$	4.28929			0.344524
$156$		0			0
$157$	−9.58580	+	16.6031i	−0.765030	+	1.32507i	0.175200	+	0.984533i	$0.443943\pi$
$157$	−9.58580	+	16.6031i	−0.765030	+	1.32507i	−0.940231	+	0.340539i	$0.889391\pi$
$158$		0			0
$159$	1.86965	+	3.23834i	0.148273	+	0.256817i
$160$		0			0
$161$	−4.03061	−	13.9077i	−0.317656	−	1.09608i
$162$		0			0
$163$	−4.79414	−	8.30370i	−0.375506	−	0.650396i	0.614896	−	0.788608i	$-0.289198\pi$
$163$	−4.79414	−	8.30370i	−0.375506	−	0.650396i	−0.990403	+	0.138212i	$0.955864\pi$
$164$		0			0
$165$	23.6880	+	13.6763i	1.84411	+	1.06470i
$166$		0			0
$167$	−7.92465			−0.613228			−0.306614	−	0.951834i	$-0.599196\pi$
$167$	−7.92465			−0.613228			−0.306614	+	0.951834i	$0.599196\pi$
$168$		0			0
$169$	0.615852			0.0473732
$170$		0			0
$171$	0.740837	+	0.427722i	0.0566532	+	0.0327088i
$172$		0			0
$173$	6.70800	+	11.6186i	0.510000	+	0.883346i	0.999933	+	0.0115858i	$0.00368795\pi$
$173$	6.70800	+	11.6186i	0.510000	+	0.883346i	−0.489933	+	0.871760i	$0.662979\pi$
$174$		0			0
$175$	−23.4271	−	22.4955i	−1.77092	−	1.70050i
$176$		0			0
$177$	1.91525	+	3.31730i	0.143959	+	0.249344i
$178$		0			0
$179$	−6.67760	+	11.5659i	−0.499107	+	0.864479i	−0.999999	−	0.00103054i	$-0.999672\pi$
$179$	−6.67760	+	11.5659i	−0.499107	+	0.864479i	0.500892	+	0.865510i	$0.333005\pi$
$180$		0			0
$181$	3.49016			0.259421			0.129711	−	0.991552i	$-0.458595\pi$
$181$	3.49016			0.259421			0.129711	+	0.991552i	$0.458595\pi$
$182$		0			0
$183$		−	2.28223i		−	0.168707i
$184$		0			0
$185$	4.29095	+	2.47738i	0.315477	+	0.182141i
$186$		0			0
$187$	−10.7941	+	6.23200i	−0.789346	+	0.455729i
$188$		0			0
$189$	14.5271	+	3.57837i	1.05669	+	0.260288i
$190$		0			0
$191$	15.8821	−	9.16956i	1.14919	−	0.663486i	0.200501	−	0.979693i	$-0.435743\pi$
$191$	15.8821	−	9.16956i	1.14919	−	0.663486i	0.948690	+	0.316207i	$0.102410\pi$
$192$		0			0
$193$	4.91525	−	8.51345i	0.353807	−	0.612812i	−0.633106	−	0.774065i	$-0.718220\pi$
$193$	4.91525	−	8.51345i	0.353807	−	0.612812i	0.986913	+	0.161253i	$0.0515536\pi$
$194$		0			0
$195$			21.3554i			1.52929i
$196$		0			0
$197$			14.7895i			1.05371i	0.849956	+	0.526853i	$0.176628\pi$
$197$			14.7895i			1.05371i	−0.849956	+	0.526853i	$0.823372\pi$
$198$		0			0
$199$	−0.975475	+	1.68957i	−0.0691496	+	0.119771i	−0.898527	−	0.438918i	$-0.855362\pi$
$199$	−0.975475	+	1.68957i	−0.0691496	+	0.119771i	0.829378	+	0.558688i	$0.188695\pi$
$200$		0			0
$201$	5.93075	−	3.42412i	0.418323	−	0.241519i
$202$		0			0
$203$	9.97949	+	2.45819i	0.700423	+	0.172531i
$204$		0			0
$205$	23.3064	−	13.4560i	1.62779	−	0.939804i
$206$		0			0
$207$	5.02981	+	2.90396i	0.349596	+	0.201839i
$208$		0			0
$209$		−	3.80981i		−	0.263530i
$210$		0			0
$211$	15.5748			1.07222			0.536108	−	0.844149i	$-0.319894\pi$
$211$	15.5748			1.07222			0.536108	+	0.844149i	$0.319894\pi$
$212$		0			0
$213$	8.19380	−	14.1921i	0.561430	−	0.972425i
$214$		0			0
$215$	21.3554	+	36.9886i	1.45643	+	2.52260i
$216$		0			0
$217$	−1.96939	−	1.89108i	−0.133691	−	0.128375i
$218$		0			0
$219$	−8.45914	−	14.6517i	−0.571616	−	0.990068i
$220$		0			0
$221$	−8.42748	−	4.86561i	−0.566893	−	0.327296i
$222$		0			0
$223$	1.10497			0.0739941			0.0369970	−	0.999315i	$-0.488221\pi$
$223$	1.10497			0.0739941			0.0369970	+	0.999315i	$0.488221\pi$
$224$		0			0
$225$	13.0273			0.868484
$226$		0			0
$227$	−8.71567	−	5.03199i	−0.578479	−	0.333985i	0.182050	−	0.983289i	$-0.441727\pi$
$227$	−8.71567	−	5.03199i	−0.578479	−	0.333985i	−0.760529	+	0.649304i	$0.775060\pi$
$228$		0			0
$229$	−6.34145	−	10.9837i	−0.419055	−	0.725824i	0.576790	−	0.816893i	$-0.304305\pi$
$229$	−6.34145	−	10.9837i	−0.419055	−	0.725824i	−0.995845	+	0.0910683i	$0.970972\pi$
$230$		0			0
$231$	−4.84651	−	16.7230i	−0.318877	−	1.10029i
$232$		0			0
$233$	−10.4218	−	18.0511i	−0.682756	−	1.18257i	−0.974136	−	0.225961i	$-0.927448\pi$
$233$	−10.4218	−	18.0511i	−0.682756	−	1.18257i	0.291381	−	0.956607i	$-0.405885\pi$
$234$		0			0
$235$	16.5429	−	28.6532i	1.07914	−	1.86913i
$236$		0			0
$237$	−19.6356			−1.27547
$238$		0			0
$239$			19.4138i			1.25577i	0.778305	+	0.627886i	$0.216080\pi$
$239$			19.4138i			1.25577i	−0.778305	+	0.627886i	$0.783920\pi$
$240$		0			0
$241$	10.6836	+	6.16820i	0.688193	+	0.397329i	0.802935	−	0.596067i	$-0.203271\pi$
$241$	10.6836	+	6.16820i	0.688193	+	0.397329i	−0.114742	+	0.993395i	$0.536604\pi$
$242$		0			0
$243$	−9.03601	+	5.21694i	−0.579660	+	0.334667i
$244$		0			0
$245$	1.17997	+	29.0710i	0.0753853	+	1.85728i
$246$		0			0
$247$	2.57599	−	1.48725i	0.163906	−	0.0946312i
$248$		0			0
$249$	5.13792	−	8.89915i	0.325603	−	0.563961i
$250$		0			0
$251$			26.4577i			1.67000i	0.550251	+	0.834999i	$0.314532\pi$
$251$			26.4577i			1.67000i	−0.550251	+	0.834999i	$0.685468\pi$
$252$		0			0
$253$		−	25.8662i		−	1.62619i
$254$		0			0
$255$	7.63132	−	13.2178i	0.477892	−	0.827733i
$256$		0			0
$257$	19.4985	−	11.2575i	1.21628	−	0.702222i	0.252164	−	0.967685i	$-0.418858\pi$
$257$	19.4985	−	11.2575i	1.21628	−	0.702222i	0.964121	+	0.265462i	$0.0855246\pi$
$258$		0			0
$259$	−0.877918	−	3.02928i	−0.0545512	−	0.188230i
$260$		0			0
$261$	−3.57012	+	2.06121i	−0.220985	+	0.127586i
$262$		0			0
$263$	−13.7717	−	7.95110i	−0.849200	−	0.490286i	0.0111808	−	0.999937i	$-0.496441\pi$
$263$	−13.7717	−	7.95110i	−0.849200	−	0.490286i	−0.860381	+	0.509652i	$0.829774\pi$
$264$		0			0
$265$		−	11.1621i		−	0.685682i
$266$		0			0
$267$	25.5614			1.56433
$268$		0			0
$269$	−3.11103	+	5.38846i	−0.189683	+	0.328540i	−0.945144	−	0.326653i	$-0.894079\pi$
$269$	−3.11103	+	5.38846i	−0.189683	+	0.328540i	0.755462	+	0.655193i	$0.227413\pi$
$270$		0			0
$271$	7.49068	+	12.9742i	0.455027	+	0.788129i	0.998690	−	0.0511743i	$-0.0162964\pi$
$271$	7.49068	+	12.9742i	0.455027	+	0.788129i	−0.543663	+	0.839304i	$0.682963\pi$
$272$		0			0
$273$	9.41525	−	9.80515i	0.569837	−	0.593435i
$274$		0			0
$275$	−29.0091	−	50.2453i	−1.74932	−	3.02990i
$276$		0			0
$277$	6.20167	+	3.58053i	0.372622	+	0.215133i	0.674603	−	0.738180i	$-0.264315\pi$
$277$	6.20167	+	3.58053i	0.372622	+	0.215133i	−0.301981	+	0.953314i	$0.597648\pi$
$278$		0			0
$279$	1.09513			0.0655640
$280$		0			0
$281$	−9.18363			−0.547850			−0.273925	−	0.961751i	$-0.588322\pi$
$281$	−9.18363			−0.547850			−0.273925	+	0.961751i	$0.588322\pi$
$282$		0			0
$283$	−0.145830	−	0.0841948i	−0.00866867	−	0.00500486i	0.495659	−	0.868517i	$-0.334926\pi$
$283$	−0.145830	−	0.0841948i	−0.00866867	−	0.00500486i	−0.504328	+	0.863512i	$0.668260\pi$
$284$		0			0
$285$	2.33263	+	4.04023i	0.138173	+	0.239323i
$286$		0			0
$287$	−16.6335	−	4.09722i	−0.981842	−	0.241851i
$288$		0			0
$289$	−5.02256	−	8.69934i	−0.295445	−	0.511726i
$290$		0			0
$291$	1.27967	−	2.21645i	0.0750155	−	0.129931i
$292$		0			0
$293$	−14.7893			−0.864001			−0.432001	−	0.901873i	$-0.642192\pi$
$293$	−14.7893			−0.864001			−0.432001	+	0.901873i	$0.642192\pi$
$294$		0			0
$295$		−	11.4343i		−	0.665730i
$296$		0			0
$297$	23.1454	+	13.3630i	1.34303	+	0.775400i
$298$		0			0
$299$	17.4893	−	10.0975i	1.01143	−	0.583951i
$300$		0			0
$301$	6.50253	−	26.3983i	0.374800	−	1.52157i
$302$		0			0
$303$	−3.37379	+	1.94786i	−0.193819	+	0.111902i
$304$		0			0
$305$	−3.40631	+	5.89990i	−0.195045	+	0.337827i
$306$		0			0
$307$			12.2442i			0.698813i	0.936971	+	0.349407i	$0.113617\pi$
$307$			12.2442i			0.698813i	−0.936971	+	0.349407i	$0.886383\pi$
$308$		0			0
$309$		−	4.18127i		−	0.237864i
$310$		0			0
$311$	13.0325	−	22.5730i	0.739008	−	1.28000i	−0.213935	−	0.976848i	$-0.568628\pi$
$311$	13.0325	−	22.5730i	0.739008	−	1.28000i	0.952942	−	0.303151i	$-0.0980387\pi$
$312$		0			0
$313$	−13.7301	+	7.92710i	−0.776074	+	0.448066i	−0.835037	−	0.550194i	$-0.814554\pi$
$313$	−13.7301	+	7.92710i	−0.776074	+	0.448066i	0.0589634	+	0.998260i	$0.481220\pi$
$314$		0			0
$315$	−8.41759	−	8.08286i	−0.474278	−	0.455418i
$316$		0			0
$317$	−23.8270	+	13.7565i	−1.33826	+	0.772644i	−0.986549	−	0.163466i	$-0.947733\pi$
$317$	−23.8270	+	13.7565i	−1.33826	+	0.772644i	−0.351709	+	0.936109i	$0.614399\pi$
$318$		0			0
$319$	15.8999	+	9.17981i	0.890224	+	0.513971i
$320$		0			0
$321$		−	14.2299i		−	0.794234i
$322$		0			0
$323$	−2.12586			−0.118286
$324$		0			0
$325$	22.6487	−	39.2288i	1.25633	−	2.17602i
$326$		0			0
$327$	−3.78028	−	6.54763i	−0.209050	−	0.362085i
$328$		0			0
$329$	−20.2283	+	5.86237i	−1.11522	+	0.323203i
$330$		0			0
$331$	−8.45914	−	14.6517i	−0.464956	−	0.805328i	0.534243	−	0.845331i	$-0.320597\pi$
$331$	−8.45914	−	14.6517i	−0.464956	−	0.805328i	−0.999200	+	0.0400026i	$0.987263\pi$
$332$		0			0
$333$	1.09556	+	0.632521i	0.0600362	+	0.0346619i
$334$		0			0
$335$	−20.4425			−1.11689
$336$		0			0
$337$	−17.2288			−0.938510			−0.469255	−	0.883063i	$-0.655478\pi$
$337$	−17.2288			−0.938510			−0.469255	+	0.883063i	$0.655478\pi$
$338$		0			0
$339$	10.5007	+	6.06258i	0.570319	+	0.329274i
$340$		0			0
$341$	−2.43865	−	4.22386i	−0.132060	−	0.228735i
$342$		0			0
$343$	12.2752	−	13.8680i	0.662797	−	0.748799i
$344$		0			0
$345$	15.8371	+	27.4306i	0.852639	+	1.47681i
$346$		0			0
$347$	−15.0976	+	26.1497i	−0.810479	+	1.40379i	0.102049	+	0.994779i	$0.467460\pi$
$347$	−15.0976	+	26.1497i	−0.810479	+	1.40379i	−0.912529	+	0.409012i	$0.865873\pi$
$348$		0			0
$349$	23.8353			1.27587			0.637936	−	0.770089i	$-0.279788\pi$
$349$	23.8353			1.27587			0.637936	+	0.770089i	$0.279788\pi$
$350$		0			0
$351$			20.8662i			1.11376i
$352$		0			0
$353$	5.12282	+	2.95766i	0.272660	+	0.157421i	0.630096	−	0.776517i	$-0.283016\pi$
$353$	5.12282	+	2.95766i	0.272660	+	0.157421i	−0.357436	+	0.933938i	$0.616349\pi$
$354$		0			0
$355$	−42.3643	+	24.4591i	−2.24846	+	1.29815i
$356$		0			0
$357$	−9.33139	+	2.70434i	−0.493869	+	0.143129i
$358$		0			0
$359$	−4.99982	+	2.88665i	−0.263881	+	0.152352i	−0.626103	−	0.779740i	$-0.715351\pi$
$359$	−4.99982	+	2.88665i	−0.263881	+	0.152352i	0.362223	+	0.932091i	$0.382018\pi$
$360$		0			0
$361$	−9.17510	+	15.8917i	−0.482900	+	0.836407i
$362$		0			0
$363$		−	15.7858i		−	0.828538i
$364$		0			0
$365$			50.5022i			2.64341i
$366$		0			0
$367$	4.37926	−	7.58509i	0.228595	−	0.395939i	−0.728797	−	0.684730i	$-0.759920\pi$
$367$	4.37926	−	7.58509i	0.228595	−	0.395939i	0.957392	+	0.288791i	$0.0932534\pi$
$368$		0			0
$369$	5.95055	−	3.43555i	0.309773	−	0.178848i
$370$		0			0
$371$	−4.92119	+	5.12499i	−0.255495	+	0.266076i
$372$		0			0
$373$	−27.9028	+	16.1097i	−1.44475	+	0.834127i	−0.998161	−	0.0606123i	$-0.980695\pi$
$373$	−27.9028	+	16.1097i	−1.44475	+	0.834127i	−0.446589	+	0.894739i	$0.647361\pi$
$374$		0			0
$375$	36.4669	+	21.0542i	1.88314	+	1.08723i
$376$		0			0
$377$			14.3342i			0.738248i
$378$		0			0
$379$	32.1289			1.65035			0.825176	−	0.564876i	$-0.191076\pi$
$379$	32.1289			1.65035			0.825176	+	0.564876i	$0.191076\pi$
$380$		0			0
$381$	−5.40899	+	9.36864i	−0.277111	+	0.479970i
$382$		0			0
$383$	11.8334	+	20.4961i	0.604660	+	1.04730i	0.992105	+	0.125410i	$0.0400245\pi$
$383$	11.8334	+	20.4961i	0.604660	+	1.04730i	−0.387445	+	0.921893i	$0.626642\pi$
$384$		0			0
$385$	−12.4307	+	50.4650i	−0.633530	+	2.57194i
$386$		0			0
$387$	5.45242	+	9.44387i	0.277162	+	0.480059i
$388$		0			0
$389$	4.56952	+	2.63821i	0.231684	+	0.133763i	0.611349	−	0.791361i	$-0.290627\pi$
$389$	4.56952	+	2.63821i	0.231684	+	0.133763i	−0.379665	+	0.925124i	$0.623961\pi$
$390$		0			0
$391$	−14.4332			−0.729921
$392$		0			0
$393$	−0.956659			−0.0482570
$394$		0			0
$395$	50.7608	+	29.3068i	2.55405	+	1.47458i
$396$		0			0
$397$	1.01243	+	1.75357i	0.0508122	+	0.0880093i	0.890313	−	0.455349i	$-0.150486\pi$
$397$	1.01243	+	1.75357i	0.0508122	+	0.0880093i	−0.839501	+	0.543359i	$0.817152\pi$
$398$		0			0
$399$	0.710265	−	2.88346i	0.0355577	−	0.144353i
$400$		0			0
$401$	−10.6008	−	18.3610i	−0.529376	−	0.916906i	−0.999413	−	0.0342597i	$-0.989093\pi$
$401$	−10.6008	−	18.3610i	−0.529376	−	0.916906i	0.470037	−	0.882647i	$-0.344241\pi$
$402$		0			0
$403$	1.90396	−	3.29776i	0.0948432	−	0.164273i
$404$		0			0
$405$	−19.4945			−0.968687
$406$		0			0
$407$		−	5.63399i		−	0.279267i
$408$		0			0
$409$	−28.0804	−	16.2122i	−1.38849	−	0.801644i	−0.395343	−	0.918534i	$-0.629374\pi$
$409$	−28.0804	−	16.2122i	−1.38849	−	0.801644i	−0.993145	+	0.116890i	$0.962708\pi$
$410$		0			0
$411$	0.537039	−	0.310060i	0.0264902	−	0.0152941i
$412$		0			0
$413$	−5.04119	+	5.24996i	−0.248061	+	0.258334i
$414$		0			0
$415$	−26.5646	+	15.3371i	−1.30400	+	0.752867i
$416$		0			0
$417$	−9.14499	+	15.8396i	−0.447832	+	0.775668i
$418$		0			0
$419$			9.20577i			0.449731i	0.974390	+	0.224866i	$0.0721943\pi$
$419$			9.20577i			0.449731i	−0.974390	+	0.224866i	$0.927806\pi$
$420$		0			0
$421$		−	16.7895i		−	0.818269i	−0.912474	−	0.409135i	$-0.865831\pi$
$421$		−	16.7895i		−	0.818269i	0.912474	−	0.409135i	$-0.134169\pi$
$422$		0			0
$423$	4.22371	−	7.31568i	0.205364	−	0.355700i
$424$		0			0
$425$	−28.0367	+	16.1870i	−1.35998	+	0.785184i
$426$		0			0
$427$	4.16515	−	1.20711i	0.201566	−	0.0584159i
$428$		0			0
$429$	21.0296	−	12.1415i	1.01532	−	0.586195i
$430$		0			0
$431$	−18.3005	−	10.5658i	−0.881502	−	0.508935i	−0.0103485	−	0.999946i	$-0.503294\pi$
$431$	−18.3005	−	10.5658i	−0.881502	−	0.508935i	−0.871153	+	0.491011i	$0.836627\pi$
$432$		0			0
$433$			26.7782i			1.28688i	0.765497	+	0.643439i	$0.222493\pi$
$433$			26.7782i			1.28688i	−0.765497	+	0.643439i	$0.777507\pi$
$434$		0			0
$435$	−22.4820			−1.07793
$436$		0			0
$437$	2.20587	−	3.82068i	0.105521	−	0.182768i
$438$		0			0
$439$	0.0980721	+	0.169866i	0.00468073	+	0.00810725i	0.868356	−	0.495941i	$-0.165177\pi$
$439$	0.0980721	+	0.169866i	0.00468073	+	0.00810725i	−0.863676	+	0.504048i	$0.831843\pi$
$440$		0			0
$441$	0.301267	+	7.42236i	0.0143460	+	0.353446i
$442$		0			0
$443$	2.20204	+	3.81404i	0.104622	+	0.181211i	0.913584	−	0.406651i	$-0.133303\pi$
$443$	2.20204	+	3.81404i	0.104622	+	0.181211i	−0.808962	+	0.587861i	$0.799970\pi$
$444$		0			0
$445$	−66.0799	−	38.1513i	−3.13249	−	1.80854i
$446$		0			0
$447$	7.77419			0.367706
$448$		0			0
$449$	−28.1195			−1.32704			−0.663520	−	0.748158i	$-0.730938\pi$
$449$	−28.1195			−1.32704			−0.663520	+	0.748158i	$0.730938\pi$
$450$		0			0
$451$	−26.5014	−	15.3006i	−1.24790	−	0.720476i
$452$		0			0
$453$	6.34757	+	10.9943i	0.298235	+	0.516558i
$454$		0			0
$455$	−38.9743	+	11.2952i	−1.82714	+	0.529526i
$456$		0			0
$457$	15.6581	+	27.1207i	0.732456	+	1.26865i	0.955830	+	0.293919i	$0.0949594\pi$
$457$	15.6581	+	27.1207i	0.732456	+	1.26865i	−0.223374	+	0.974733i	$0.571707\pi$
$458$		0			0
$459$	7.45651	−	12.9150i	0.348040	−	0.602823i
$460$		0			0
$461$	3.93305			0.183181			0.0915903	−	0.995797i	$-0.470805\pi$
$461$	3.93305			0.183181			0.0915903	+	0.995797i	$0.470805\pi$
$462$		0			0
$463$		−	25.8507i		−	1.20138i	−0.799481	−	0.600692i	$-0.794892\pi$
$463$		−	25.8507i		−	1.20138i	0.799481	−	0.600692i	$-0.205108\pi$
$464$		0			0
$465$	5.17228	+	2.98622i	0.239859	+	0.138482i
$466$		0			0
$467$	−2.95865	+	1.70818i	−0.136910	+	0.0790450i	−0.566891	−	0.823793i	$-0.691854\pi$
$467$	−2.95865	+	1.70818i	−0.136910	+	0.0790450i	0.429981	+	0.902838i	$0.358520\pi$
$468$		0			0
$469$	9.38599	+	9.01275i	0.433405	+	0.416170i
$470$		0			0
$471$	−23.1182	+	13.3473i	−1.06523	+	0.615012i
$472$		0			0
$473$	24.2829	−	42.0592i	1.11653	−	1.93389i
$474$		0			0
$475$		−	9.89560i		−	0.454041i
$476$		0			0
$477$		−	2.84989i		−	0.130487i
$478$		0			0
$479$	0.336615	−	0.583034i	0.0153803	−	0.0266395i	−0.858233	−	0.513261i	$-0.828437\pi$
$479$	0.336615	−	0.583034i	0.0153803	−	0.0266395i	0.873613	+	0.486621i	$0.161771\pi$
$480$		0			0
$481$	3.80940	−	2.19936i	0.173694	−	0.100282i
$482$		0			0
$483$	4.82225	−	19.5768i	0.219420	−	0.890777i
$484$		0			0
$485$	−6.61626	+	3.81990i	−0.300429	+	0.173453i
$486$		0			0
$487$	−22.1931	−	12.8132i	−1.00566	−	0.580620i	−0.0957449	−	0.995406i	$-0.530523\pi$
$487$	−22.1931	−	12.8132i	−1.00566	−	0.580620i	−0.909919	+	0.414785i	$0.863857\pi$
$488$		0			0
$489$		−	13.3508i		−	0.603743i
$490$		0			0
$491$	−11.1931			−0.505136			−0.252568	−	0.967579i	$-0.581275\pi$
$491$	−11.1931			−0.505136			−0.252568	+	0.967579i	$0.581275\pi$
$492$		0			0
$493$	5.12230	−	8.87209i	0.230697	−	0.399579i
$494$		0			0
$495$	−10.4233	−	18.0536i	−0.468491	−	0.811451i
$496$		0			0
$497$	30.2348	+	7.44757i	1.35622	+	0.334069i
$498$		0			0
$499$	17.7962	+	30.8239i	0.796667	+	1.37987i	0.921775	+	0.387725i	$0.126739\pi$
$499$	17.7962	+	30.8239i	0.796667	+	1.37987i	−0.125108	+	0.992143i	$0.539928\pi$
$500$		0			0
$501$	−9.55600	−	5.51716i	−0.426931	−	0.246489i
$502$		0			0
$503$	35.2598			1.57216			0.786079	−	0.618127i	$-0.212108\pi$
$503$	35.2598			1.57216			0.786079	+	0.618127i	$0.212108\pi$
$504$		0			0
$505$	11.6290			0.517483
$506$		0			0
$507$	0.742630	+	0.428757i	0.0329813	+	0.0190418i
$508$		0			0
$509$	−5.76818	−	9.99078i	−0.255670	−	0.442833i	0.709407	−	0.704799i	$-0.248963\pi$
$509$	−5.76818	−	9.99078i	−0.255670	−	0.442833i	−0.965077	+	0.261965i	$0.915629\pi$
$510$		0			0
$511$	22.2656	−	23.1877i	0.984973	−	1.02576i
$512$		0			0
$513$	2.27919	+	3.94768i	0.100629	+	0.174294i
$514$		0			0
$515$	−6.24068	+	10.8092i	−0.274997	+	0.476309i
$516$		0			0
$517$	−37.6214			−1.65459
$518$		0			0
$519$			18.6805i			0.819983i
$520$		0			0
$521$	20.3305	+	11.7378i	0.890695	+	0.514243i	0.874170	−	0.485620i	$-0.161406\pi$
$521$	20.3305	+	11.7378i	0.890695	+	0.514243i	0.0165252	+	0.999863i	$0.494740\pi$
$522$		0			0
$523$	−32.9353	+	19.0152i	−1.44016	+	0.831477i	−0.997860	−	0.0653897i	$-0.979171\pi$
$523$	−32.9353	+	19.0152i	−1.44016	+	0.831477i	−0.442301	+	0.896867i	$0.645838\pi$
$524$		0			0
$525$	−12.5883	−	43.4363i	−0.549399	−	1.89572i
$526$		0			0
$527$	−2.35690	+	1.36076i	−0.102668	+	0.0592755i
$528$		0			0
$529$	3.47646	−	6.02140i	0.151150	−	0.261800i
$530$		0			0
$531$		−	2.91938i		−	0.126690i
$532$		0			0
$533$		−	23.8917i		−	1.03486i
$534$		0			0
$535$	−21.2386	+	36.7863i	−0.918224	+	1.59041i
$536$		0			0
$537$	−16.1045	+	9.29792i	−0.694959	+	0.401235i
$538$		0			0
$539$	27.9567	−	17.6901i	1.20418	−	0.761966i
$540$		0			0
$541$	−18.0532	+	10.4230i	−0.776166	+	0.448120i	−0.835070	−	0.550144i	$-0.814573\pi$
$541$	−18.0532	+	10.4230i	−0.776166	+	0.448120i	0.0589038	+	0.998264i	$0.481239\pi$
$542$		0			0
$543$	4.20863	+	2.42985i	0.180610	+	0.104275i
$544$		0			0
$545$			22.5688i			0.966740i
$546$		0			0
$547$	−1.93035			−0.0825357			−0.0412678	−	0.999148i	$-0.513140\pi$
$547$	−1.93035			−0.0825357			−0.0412678	+	0.999148i	$0.513140\pi$
$548$		0			0
$549$	−0.869693	+	1.50635i	−0.0371176	+	0.0642896i
$550$		0			0
$551$	1.56571	+	2.71189i	0.0667015	+	0.115530i
$552$		0			0
$553$	−10.3855	−	35.8356i	−0.441638	−	1.52388i
$554$		0			0
$555$	3.44952	+	5.97474i	0.146424	+	0.253614i
$556$		0			0
$557$	−28.5515	−	16.4842i	−1.20977	−	0.698458i	−0.247057	−	0.969001i	$-0.579464\pi$
$557$	−28.5515	−	16.4842i	−1.20977	−	0.698458i	−0.962708	+	0.270543i	$0.912797\pi$
$558$		0			0
$559$	37.9175			1.60374
$560$		0			0
$561$	−17.3549			−0.732726
$562$		0			0
$563$	−15.5561	−	8.98129i	−0.655610	−	0.378516i	0.134993	−	0.990847i	$-0.456899\pi$
$563$	−15.5561	−	8.98129i	−0.655610	−	0.378516i	−0.790602	+	0.612330i	$0.790232\pi$
$564$		0			0
$565$	−18.0972	−	31.3453i	−0.761355	−	1.31871i
$566$		0			0
$567$	8.95072	+	8.59479i	0.375895	+	0.360947i
$568$		0			0
$569$	6.87571	+	11.9091i	0.288245	+	0.499254i	0.973391	−	0.229151i	$-0.0735951\pi$
$569$	6.87571	+	11.9091i	0.288245	+	0.499254i	−0.685146	+	0.728406i	$0.740262\pi$
$570$		0			0
$571$	0.935886	−	1.62100i	0.0391656	−	0.0678369i	−0.845778	−	0.533535i	$-0.820863\pi$
$571$	0.935886	−	1.62100i	0.0391656	−	0.0678369i	0.884944	+	0.465698i	$0.154197\pi$
$572$		0			0
$573$	25.5355			1.06676
$574$		0			0
$575$		−	67.1848i		−	2.80180i
$576$		0			0
$577$	2.28242	+	1.31775i	0.0950183	+	0.0548589i	0.546756	−	0.837292i	$-0.315862\pi$
$577$	2.28242	+	1.31775i	0.0950183	+	0.0548589i	−0.451738	+	0.892151i	$0.649196\pi$
$578$		0			0
$579$	11.8542	−	6.84401i	0.492643	−	0.284427i
$580$		0			0
$581$	18.9588	+	4.67000i	0.786542	+	0.193744i
$582$		0			0
$583$	−10.9918	+	6.34613i	−0.455235	+	0.262830i
$584$		0			0
$585$	8.13792	−	14.0953i	0.336462	−	0.582769i
$586$		0			0
$587$			2.51566i			0.103833i	0.998651	+	0.0519163i	$0.0165329\pi$
$587$			2.51566i			0.103833i	−0.998651	+	0.0519163i	$0.983467\pi$
$588$		0			0
$589$		−	0.831872i		−	0.0342767i
$590$		0			0
$591$	−10.2965	+	17.8340i	−0.423540	+	0.733593i
$592$		0			0
$593$	−16.0848	+	9.28654i	−0.660522	+	0.381352i	−0.792476	−	0.609903i	$-0.791208\pi$
$593$	−16.0848	+	9.28654i	−0.660522	+	0.381352i	0.131954	+	0.991256i	$0.457875\pi$
$594$		0			0
$595$	28.1593	+	6.93632i	1.15442	+	0.284361i
$596$		0			0
$597$	−2.35257	+	1.35826i	−0.0962842	+	0.0555897i
$598$		0			0
$599$	−16.4021	−	9.46973i	−0.670170	−	0.386923i	0.125971	−	0.992034i	$-0.459795\pi$
$599$	−16.4021	−	9.46973i	−0.670170	−	0.386923i	−0.796141	+	0.605111i	$0.793129\pi$
$600$		0			0
$601$			16.1462i			0.658618i	0.944222	+	0.329309i	$0.106816\pi$
$601$			16.1462i			0.658618i	−0.944222	+	0.329309i	$0.893184\pi$
$602$		0			0
$603$	−5.21933			−0.212548
$604$		0			0
$605$	−23.5608	+	40.8085i	−0.957883	+	1.65910i
$606$		0			0
$607$	9.71399	+	16.8251i	0.394279	+	0.682911i	0.993009	−	0.118040i	$-0.0376611\pi$
$607$	9.71399	+	16.8251i	0.394279	+	0.682911i	−0.598730	+	0.800951i	$0.704328\pi$
$608$		0			0
$609$	10.3225	+	9.91197i	0.418287	+	0.401653i
$610$		0			0
$611$	−14.6864	−	25.4376i	−0.594147	−	1.02909i
$612$		0			0
$613$	13.2420	+	7.64527i	0.534839	+	0.308790i	0.742985	−	0.669308i	$-0.233409\pi$
$613$	13.2420	+	7.64527i	0.534839	+	0.308790i	−0.208145	+	0.978098i	$0.566743\pi$
$614$		0			0
$615$	37.4722			1.51103
$616$		0			0
$617$	29.9971			1.20764			0.603818	−	0.797122i	$-0.293645\pi$
$617$	29.9971			1.20764			0.603818	+	0.797122i	$0.293645\pi$
$618$		0			0
$619$	−8.33436	−	4.81184i	−0.334986	−	0.193404i	0.323067	−	0.946376i	$-0.395286\pi$
$619$	−8.33436	−	4.81184i	−0.334986	−	0.193404i	−0.658053	+	0.752972i	$0.728620\pi$
$620$		0			0
$621$	15.4743	+	26.8022i	0.620961	+	1.07554i
$622$		0			0
$623$	13.5198	+	46.6504i	0.541659	+	1.86901i
$624$		0			0
$625$	−32.1586	−	55.7004i	−1.28634	−	2.22801i
$626$		0			0
$627$	2.65240	−	4.59409i	0.105927	−	0.183470i
$628$		0			0
$629$	−3.14375			−0.125349
$630$		0			0
$631$			16.6431i			0.662552i	0.943534	+	0.331276i	$0.107479\pi$
$631$			16.6431i			0.662552i	−0.943534	+	0.331276i	$0.892521\pi$
$632$		0			0
$633$	18.7810	+	10.8432i	0.746479	+	0.430980i
$634$		0			0
$635$	27.9661	−	16.1462i	1.10980	−	0.640743i
$636$		0			0
$637$	22.8746	+	11.9971i	0.906325	+	0.475341i
$638$		0			0
$639$	−10.8164	+	6.24484i	−0.427890	+	0.247042i
$640$		0			0
$641$	−4.44585	+	7.70044i	−0.175601	+	0.304149i	−0.940369	−	0.340156i	$-0.889520\pi$
$641$	−4.44585	+	7.70044i	−0.175601	+	0.304149i	0.764768	+	0.644305i	$0.222853\pi$
$642$		0			0
$643$		−	31.1319i		−	1.22772i	−0.789413	−	0.613862i	$-0.789615\pi$
$643$		−	31.1319i		−	1.22772i	0.789413	−	0.613862i	$-0.210385\pi$
$644$		0			0
$645$			59.4707i			2.34165i
$646$		0			0
$647$	16.2830	−	28.2030i	0.640151	−	1.10877i	−0.345247	−	0.938512i	$-0.612205\pi$
$647$	16.2830	−	28.2030i	0.640151	−	1.10877i	0.985399	−	0.170263i	$-0.0544617\pi$
$648$		0			0
$649$	−11.2599	+	6.50088i	−0.441988	+	0.255182i
$650$		0			0
$651$	−1.05824	−	3.65147i	−0.0414755	−	0.143112i
$652$		0			0
$653$	30.5163	−	17.6186i	1.19420	−	0.689469i	0.234940	−	0.972010i	$-0.424511\pi$
$653$	30.5163	−	17.6186i	1.19420	−	0.689469i	0.959255	+	0.282541i	$0.0911772\pi$
$654$		0			0
$655$	2.47310	+	1.42785i	0.0966321	+	0.0557906i
$656$		0			0
$657$			12.8941i			0.503048i
$658$		0			0
$659$	−39.4975			−1.53861			−0.769303	−	0.638884i	$-0.779396\pi$
$659$	−39.4975			−1.53861			−0.769303	+	0.638884i	$0.779396\pi$
$660$		0			0
$661$	7.96057	−	13.7881i	0.309630	−	0.536295i	−0.668651	−	0.743576i	$-0.733128\pi$
$661$	7.96057	−	13.7881i	0.309630	−	0.536295i	0.978281	+	0.207281i	$0.0664614\pi$
$662$		0			0
$663$	−6.77489	−	11.7345i	−0.263115	−	0.455728i
$664$		0			0
$665$	−6.13980	+	6.39406i	−0.238091	+	0.247951i
$666$		0			0
$667$	10.6302	+	18.4120i	0.411602	+	0.712915i
$668$		0			0
$669$	1.33243	+	0.769280i	0.0515148	+	0.0297421i
$670$		0			0
$671$	7.74654			0.299052
$672$		0			0
$673$	−38.7175			−1.49245			−0.746224	−	0.665695i	$-0.768135\pi$
$673$	−38.7175			−1.49245			−0.746224	+	0.665695i	$0.768135\pi$
$674$		0			0
$675$	60.1178	+	34.7090i	2.31393	+	1.33595i
$676$		0			0
$677$	0.572823	+	0.992158i	0.0220154	+	0.0381317i	0.876823	−	0.480813i	$-0.159658\pi$
$677$	0.572823	+	0.992158i	0.0220154	+	0.0381317i	−0.854808	+	0.518945i	$0.826325\pi$
$678$		0			0
$679$	4.72193	+	1.16313i	0.181211	+	0.0446367i
$680$		0			0
$681$	−7.00657	−	12.1357i	−0.268492	−	0.465042i
$682$		0			0
$683$	−18.4264	+	31.9154i	−0.705066	+	1.22121i	0.261602	+	0.965176i	$0.415749\pi$
$683$	−18.4264	+	31.9154i	−0.705066	+	1.22121i	−0.966668	+	0.256034i	$0.917584\pi$
$684$		0			0
$685$	−1.85110			−0.0707268
$686$		0			0
$687$		−	17.6597i		−	0.673761i
$688$		0			0
$689$	−8.58181	−	4.95471i	−0.326941	−	0.188759i
$690$		0			0
$691$	−3.66564	+	2.11636i	−0.139448	+	0.0805102i	−0.568101	−	0.822959i	$-0.692322\pi$
$691$	−3.66564	+	2.11636i	−0.139448	+	0.0805102i	0.428653	+	0.903469i	$0.358988\pi$
$692$		0			0
$693$	−3.17380	+	12.8846i	−0.120563	+	0.489447i
$694$		0			0
$695$	47.2822	−	27.2984i	1.79352	−	1.03549i
$696$		0			0
$697$	−8.53767	+	14.7877i	−0.323387	+	0.560123i
$698$		0			0
$699$		−	29.0228i		−	1.09774i
$700$		0			0
$701$		−	23.6873i		−	0.894655i	−0.894370	−	0.447328i	$-0.852376\pi$
$701$		−	23.6873i		−	0.894655i	0.894370	−	0.447328i	$-0.147624\pi$
$702$		0			0
$703$	0.480467	−	0.832194i	0.0181212	−	0.0313868i
$704$		0			0
$705$	39.8968	−	23.0344i	1.50260	−	0.867527i
$706$		0			0
$707$	−5.33936	−	5.12703i	−0.200807	−	0.192822i
$708$		0			0
$709$	35.8535	−	20.7000i	1.34651	−	0.777405i	0.358753	−	0.933433i	$-0.383202\pi$
$709$	35.8535	−	20.7000i	1.34651	−	0.777405i	0.987753	+	0.156027i	$0.0498688\pi$
$710$		0			0
$711$	12.9602	+	7.48255i	0.486044	+	0.280618i
$712$		0			0
$713$		−	5.64788i		−	0.211515i
$714$		0			0
$715$	−72.4862			−2.71083
$716$		0			0
$717$	−13.5159	+	23.4102i	−0.504761	+	0.874272i
$718$		0			0
$719$	−7.97793	−	13.8182i	−0.297527	−	0.515331i	0.678043	−	0.735022i	$-0.262828\pi$
$719$	−7.97793	−	13.8182i	−0.297527	−	0.515331i	−0.975569	+	0.219691i	$0.929495\pi$
$720$		0			0
$721$	7.63095	−	2.21153i	0.284192	−	0.0823618i
$722$		0			0
$723$	8.58862	+	14.8759i	0.319414	+	0.553242i
$724$		0			0
$725$	41.2984	+	23.8436i	1.53378	+	0.885530i
$726$		0			0
$727$	−19.2245			−0.712998			−0.356499	−	0.934296i	$-0.616030\pi$
$727$	−19.2245			−0.712998			−0.356499	+	0.934296i	$0.616030\pi$
$728$		0			0
$729$	−28.5988			−1.05921
$730$		0			0
$731$	−23.4689	−	13.5498i	−0.868029	−	0.501157i
$732$		0			0
$733$	11.3309	+	19.6257i	0.418516	+	0.724890i	0.995790	−	0.0916596i	$-0.0292172\pi$
$733$	11.3309	+	19.6257i	0.418516	+	0.724890i	−0.577275	+	0.816550i	$0.695884\pi$
$734$		0			0
$735$	−18.8164	+	35.8770i	−0.694055	+	1.32334i
$736$		0			0
$737$	11.6224	+	20.1306i	0.428117	+	0.741521i
$738$		0			0
$739$	−13.3722	+	23.1614i	−0.491905	+	0.852005i	−0.999957	−	0.00932191i	$-0.997033\pi$
$739$	−13.3722	+	23.1614i	−0.491905	+	0.852005i	0.508051	+	0.861327i	$0.330366\pi$
$740$		0			0
$741$	4.14170			0.152149
$742$		0			0
$743$		−	21.4114i		−	0.785508i	−0.919643	−	0.392754i	$-0.871522\pi$
$743$		−	21.4114i		−	0.785508i	0.919643	−	0.392754i	$-0.128478\pi$
$744$		0			0
$745$	−20.0974	−	11.6032i	−0.736312	−	0.425110i
$746$		0			0
$747$	−6.78242	+	3.91583i	−0.248156	+	0.143273i
$748$		0			0
$749$	25.9700	−	7.52638i	0.948923	−	0.275008i
$750$		0			0
$751$	−13.6677	+	7.89107i	−0.498743	+	0.287949i	−0.728194	−	0.685371i	$-0.759640\pi$
$751$	−13.6677	+	7.89107i	−0.498743	+	0.287949i	0.229451	+	0.973320i	$0.426307\pi$
$752$		0			0
$753$	−18.4199	+	31.9043i	−0.671260	+	1.16266i
$754$		0			0
$755$		−	37.8958i		−	1.37917i
$756$		0			0
$757$			17.1426i			0.623059i	0.950236	+	0.311530i	$0.100841\pi$
$757$			17.1426i			0.623059i	−0.950236	+	0.311530i	$0.899159\pi$
$758$		0			0
$759$	18.0081	−	31.1909i	0.653653	−	1.13216i
$760$		0			0
$761$	10.7542	−	6.20893i	0.389839	−	0.225073i	−0.292252	−	0.956341i	$-0.594404\pi$
$761$	10.7542	−	6.20893i	0.389839	−	0.225073i	0.682090	+	0.731268i	$0.261071\pi$
$762$		0			0
$763$	9.95021	−	10.3623i	0.360222	−	0.375139i
$764$		0			0
$765$	−10.0739	+	5.81615i	−0.364222	+	0.210283i
$766$		0			0
$767$	−8.79108	−	5.07553i	−0.317427	−	0.183267i
$768$		0			0
$769$		−	44.3368i		−	1.59883i	−0.600782	−	0.799413i	$-0.705144\pi$
$769$		−	44.3368i		−	1.59883i	0.600782	−	0.799413i	$-0.294856\pi$
$770$		0			0
$771$	31.3499			1.12904
$772$		0			0
$773$	25.8172	−	44.7167i	0.928580	−	1.60835i	0.142879	−	0.989740i	$-0.454364\pi$
$773$	25.8172	−	44.7167i	0.928580	−	1.60835i	0.785701	−	0.618607i	$-0.212303\pi$
$774$		0			0
$775$	−6.33414	−	10.9711i	−0.227529	−	0.394092i
$776$		0			0
$777$	1.05035	−	4.26409i	0.0376810	−	0.152973i
$778$		0			0
$779$	−2.60967	−	4.52008i	−0.0935010	−	0.161949i
$780$		0			0
$781$	48.1719	+	27.8120i	1.72373	+	0.995193i
$782$		0			0
$783$	−21.9670			−0.785038
$784$		0			0
$785$	79.6853			2.84409
$786$		0			0
$787$	10.8258	+	6.25029i	0.385899	+	0.222799i	0.680382	−	0.732858i	$-0.261814\pi$
$787$	10.8258	+	6.25029i	0.385899	+	0.222799i	−0.294483	+	0.955657i	$0.595147\pi$
$788$		0			0
$789$	−11.0711	−	19.1758i	−0.394143	−	0.682676i
$790$		0			0
$791$	−5.51044	+	22.3707i	−0.195929	+	0.795411i
$792$		0			0
$793$	3.02404	+	5.23778i	0.107387	+	0.185999i
$794$		0			0
$795$	7.77107	−	13.4599i	0.275612	−	0.477373i
$796$		0			0
$797$	26.1284			0.925514			0.462757	−	0.886485i	$-0.346860\pi$
$797$	26.1284			0.925514			0.462757	+	0.886485i	$0.346860\pi$
$798$		0			0
$799$			20.9926i			0.742666i
$800$		0			0
$801$	−16.8714	−	9.74071i	−0.596122	−	0.344171i
$802$		0			0
$803$	49.7319	−	28.7127i	1.75500	−	1.01325i
$804$		0			0
$805$	−41.6853	+	43.4116i	−1.46921	+	1.53006i
$806$		0			0
$807$	−7.50291	+	4.33181i	−0.264115	+	0.152487i
$808$		0			0
$809$	14.0974	−	24.4174i	0.495638	−	0.858471i	−0.504349	−	0.863500i	$-0.668267\pi$
$809$	14.0974	−	24.4174i	0.495638	−	0.858471i	0.999987	+	0.00502905i	$0.00160080\pi$
$810$		0			0
$811$			3.63616i			0.127683i	0.997960	+	0.0638414i	$0.0203352\pi$
$811$			3.63616i			0.127683i	−0.997960	+	0.0638414i	$0.979665\pi$
$812$		0			0
$813$			20.8601i			0.731596i
$814$		0			0
$815$	−19.9265	+	34.5137i	−0.697994	+	1.20896i
$816$		0			0
$817$	7.17363	−	4.14170i	0.250973	−	0.144900i
$818$		0			0
$819$	−9.95085	+	2.88386i	−0.347711	+	0.100770i
$820$		0			0
$821$	−29.2291	+	16.8754i	−1.02010	+	0.588956i	−0.914133	−	0.405413i	$-0.867128\pi$
$821$	−29.2291	+	16.8754i	−1.02010	+	0.588956i	−0.105968	+	0.994369i	$0.533794\pi$
$822$		0			0
$823$	−32.7497	−	18.9080i	−1.14158	−	0.659093i	−0.194760	−	0.980851i	$-0.562393\pi$
$823$	−32.7497	−	18.9080i	−1.14158	−	0.659093i	−0.946822	+	0.321758i	$0.895726\pi$
$824$		0			0
$825$		−	80.7848i		−	2.81257i
$826$		0			0
$827$	−0.873832			−0.0303861			−0.0151931	−	0.999885i	$-0.504836\pi$
$827$	−0.873832			−0.0303861			−0.0151931	+	0.999885i	$0.504836\pi$
$828$		0			0
$829$	7.21806	−	12.5020i	0.250693	−	0.434214i	−0.713023	−	0.701140i	$-0.752675\pi$
$829$	7.21806	−	12.5020i	0.250693	−	0.434214i	0.963717	+	0.266926i	$0.0860080\pi$
$830$		0			0
$831$	4.98555	+	8.63523i	0.172947	+	0.299553i
$832$		0			0
$833$	−9.87101	−	15.5997i	−0.342010	−	0.540499i
$834$		0			0
$835$	16.4691	+	28.5253i	0.569937	+	0.987160i
$836$		0			0
$837$	5.05379	+	2.91781i	0.174685	+	0.100854i
$838$		0			0
$839$	−37.7316			−1.30264			−0.651319	−	0.758804i	$-0.725784\pi$
$839$	−37.7316			−1.30264			−0.651319	+	0.758804i	$0.725784\pi$
$840$		0			0
$841$	13.9096			0.479640
$842$		0			0
$843$	−11.0742	−	6.39366i	−0.381414	−	0.220209i
$844$		0			0
$845$	−1.27987	−	2.21680i	−0.0440289	−	0.0762603i
$846$		0			0
$847$	28.8096	−	8.34932i	0.989909	−	0.286886i
$848$		0			0
$849$	−0.117233	−	0.203054i	−0.00402343	−	0.00696879i
$850$		0			0
$851$	3.26207	−	5.65006i	0.111822	−	0.193682i
$852$		0			0
$853$	27.7787			0.951126			0.475563	−	0.879682i	$-0.342244\pi$
$853$	27.7787			0.951126			0.475563	+	0.879682i	$0.342244\pi$
$854$		0			0
$855$		−	3.55559i		−	0.121599i
$856$		0			0
$857$	12.6891	+	7.32607i	0.433452	+	0.250254i	0.700816	−	0.713342i	$-0.252819\pi$
$857$	12.6891	+	7.32607i	0.433452	+	0.250254i	−0.267364	+	0.963596i	$0.586153\pi$
$858$		0			0
$859$	−4.00523	+	2.31242i	−0.136657	+	0.0788988i	−0.566770	−	0.823876i	$-0.691807\pi$
$859$	−4.00523	+	2.31242i	−0.136657	+	0.0788988i	0.430113	+	0.902775i	$0.358474\pi$
$860$		0			0
$861$	−17.2051	−	16.5209i	−0.586348	−	0.563031i
$862$		0			0
$863$	−24.2969	+	14.0278i	−0.827076	+	0.477512i	−0.852850	−	0.522155i	$-0.825128\pi$
$863$	−24.2969	+	14.0278i	−0.827076	+	0.477512i	0.0257746	+	0.999668i	$0.491795\pi$
$864$		0			0
$865$	27.8813	−	48.2918i	0.947992	−	1.64197i
$866$		0			0
$867$		−	13.9869i		−	0.475019i
$868$		0			0
$869$		−	66.6486i		−	2.26090i
$870$		0			0
$871$	−9.07415	+	15.7169i	−0.307466	+	0.532547i
$872$		0			0
$873$	−1.68925	+	0.975290i	−0.0571725	+	0.0330086i
$874$		0			0
$875$	−19.1367	+	77.6893i	−0.646940	+	2.62638i
$876$		0			0
$877$	−31.1732	+	17.9978i	−1.05264	+	0.607744i	−0.923388	−	0.383868i	$-0.874592\pi$
$877$	−31.1732	+	17.9978i	−1.05264	+	0.607744i	−0.129255	+	0.991611i	$0.541259\pi$
$878$		0			0
$879$	−17.8338	−	10.2964i	−0.601519	−	0.347287i
$880$		0			0
$881$		−	20.2724i		−	0.682994i	−0.939883	−	0.341497i	$-0.889066\pi$
$881$		−	20.2724i		−	0.682994i	0.939883	−	0.341497i	$-0.110934\pi$
$882$		0			0
$883$	33.7734			1.13657			0.568283	−	0.822833i	$-0.307608\pi$
$883$	33.7734			1.13657			0.568283	+	0.822833i	$0.307608\pi$
$884$		0			0
$885$	7.96057	−	13.7881i	0.267592	−	0.463482i
$886$		0			0
$887$	−1.52190	−	2.63600i	−0.0511003	−	0.0885082i	0.839344	−	0.543601i	$-0.182939\pi$
$887$	−1.52190	−	2.63600i	−0.0511003	−	0.0885082i	−0.890444	+	0.455093i	$0.849606\pi$
$888$		0			0
$889$	−19.9590	−	4.91638i	−0.669403	−	0.164890i
$890$		0			0
$891$	11.0834	+	19.1971i	0.371309	+	0.643126i
$892$		0			0
$893$	−5.55704	−	3.20836i	−0.185959	−	0.107364i
$894$		0			0
$895$	55.5099			1.85549
$896$		0			0
$897$	28.1195			0.938882
$898$		0			0
$899$	3.47174	+	2.00441i	0.115789	+	0.0668509i
$900$		0			0
$901$	3.54112	+	6.13340i	0.117972	+	0.204333i
$902$		0			0
$903$	26.2197	−	27.3055i	0.872535	−	0.908669i
$904$		0			0
$905$	−7.25328	−	12.5631i	−0.241107	−	0.417610i
$906$		0			0
$907$	11.9344	−	20.6710i	0.396276	−	0.686371i	−0.596987	−	0.802251i	$-0.703636\pi$
$907$	11.9344	−	20.6710i	0.396276	−	0.686371i	0.993263	+	0.115880i	$0.0369689\pi$
$908$		0			0
$909$	2.96909			0.0984786
$910$		0			0
$911$			13.6058i			0.450782i	0.974268	+	0.225391i	$0.0723659\pi$
$911$			13.6058i			0.450782i	−0.974268	+	0.225391i	$0.927634\pi$
$912$		0			0
$913$	30.2062	+	17.4396i	0.999679	+	0.577165i
$914$		0			0
$915$	−8.21505	+	4.74296i	−0.271581	+	0.156797i
$916$		0			0
$917$	−0.505991	−	1.74593i	−0.0167093	−	0.0576558i
$918$		0			0
$919$	13.2691	−	7.66093i	0.437708	−	0.252711i	−0.264917	−	0.964271i	$-0.585345\pi$
$919$	13.2691	−	7.66093i	0.437708	−	0.252711i	0.702625	+	0.711560i	$0.252011\pi$
$920$		0			0
$921$	−8.52444	+	14.7648i	−0.280890	+	0.486515i
$922$		0			0
$923$			43.4282i			1.42946i
$924$		0			0
$925$		−	14.6337i		−	0.481154i
$926$		0			0
$927$	−1.59336	+	2.75978i	−0.0523328	+	0.0906431i
$928$		0			0
$929$	45.5296	−	26.2865i	1.49378	−	0.862433i	0.493804	−	0.869573i	$-0.335606\pi$
$929$	45.5296	−	26.2865i	1.49378	−	0.862433i	0.999975	+	0.00713973i	$0.00227267\pi$
$930$		0			0
$931$	5.63808	−	0.228844i	0.184781	−	0.00750007i
$932$		0			0
$933$	31.4308	−	18.1466i	1.02900	−	0.594092i
$934$		0			0
$935$	44.8650	+	25.9028i	1.46724	+	0.847113i
$936$		0			0
$937$			55.5022i			1.81318i	0.422015	+	0.906589i	$0.361323\pi$
$937$			55.5022i			1.81318i	−0.422015	+	0.906589i	$0.638677\pi$
$938$		0			0
$939$	−22.0755			−0.720405
$940$		0			0
$941$	11.0357	−	19.1144i	0.359753	−	0.623110i	−0.628166	−	0.778079i	$-0.716194\pi$
$941$	11.0357	−	19.1144i	0.359753	−	0.623110i	0.987919	+	0.154969i	$0.0495276\pi$
$942$		0			0
$943$	−17.7180	−	30.6884i	−0.576977	−	0.999353i
$944$		0			0
$945$	−17.3098	−	59.7278i	−0.563087	−	1.94295i
$946$		0			0
$947$	1.54086	+	2.66884i	0.0500712	+	0.0867258i	0.889975	−	0.456010i	$-0.150722\pi$
$947$	1.54086	+	2.66884i	0.0500712	+	0.0867258i	−0.839904	+	0.542736i	$0.817389\pi$
$948$		0			0
$949$	38.8279	+	22.4173i	1.26041	+	0.727697i
$950$		0			0
$951$	−38.3093			−1.24226
$952$		0			0
$953$	13.8174			0.447588			0.223794	−	0.974636i	$-0.428156\pi$
$953$	13.8174			0.447588			0.223794	+	0.974636i	$0.428156\pi$
$954$		0			0
$955$	−66.0129	−	38.1126i	−2.13613	−	1.23329i
$956$		0			0
$957$	12.7820	+	22.1391i	0.413184	+	0.715655i
$958$		0			0
$959$	0.849917	+	0.816119i	0.0274452	+	0.0263539i
$960$		0			0
$961$	14.9675	+	25.9245i	0.482823	+	0.836274i
$962$		0			0
$963$	−5.42260	+	9.39221i	−0.174741	+	0.302660i
$964$		0			0
$965$	−40.8597			−1.31532
$966$		0			0
$967$			42.3520i			1.36195i	0.732308	+	0.680974i	$0.238443\pi$
$967$			42.3520i			1.36195i	−0.732308	+	0.680974i	$0.761557\pi$
$968$		0			0
$969$	−2.56349	−	1.48003i	−0.0823510	−	0.0475454i
$970$		0			0
$971$	−16.0539	+	9.26873i	−0.515195	+	0.297448i	−0.734966	−	0.678104i	$-0.762802\pi$
$971$	−16.0539	+	9.26873i	−0.515195	+	0.297448i	0.219772	+	0.975551i	$0.429469\pi$
$972$		0			0
$973$	−33.7447	−	8.31213i	−1.08181	−	0.266475i
$974$		0			0
$975$	54.6223	−	31.5362i	1.74931	−	1.00997i
$976$		0			0
$977$	−15.0075	+	25.9937i	−0.480131	+	0.831612i	−0.999740	−	0.0227924i	$-0.992744\pi$
$977$	−15.0075	+	25.9937i	−0.480131	+	0.831612i	0.519609	+	0.854404i	$0.326078\pi$
$978$		0			0
$979$			86.7625i			2.77294i
$980$		0			0
$981$			5.76222i			0.183973i
$982$		0			0
$983$	−26.2129	+	45.4020i	−0.836061	+	1.44810i	0.0571028	+	0.998368i	$0.481814\pi$
$983$	−26.2129	+	45.4020i	−0.836061	+	1.44810i	−0.893164	+	0.449732i	$0.851520\pi$
$984$		0			0
$985$	53.2357	−	30.7357i	1.69623	−	0.979320i
$986$		0			0
$987$	−28.4738	−	7.01378i	−0.906331	−	0.223251i
$988$		0			0
$989$	48.7044	−	28.1195i	1.54871	−	0.894147i
$990$		0			0
$991$	−45.7531	−	26.4156i	−1.45340	−	0.839119i	−0.454724	−	0.890632i	$-0.650262\pi$
$991$	−45.7531	−	26.4156i	−1.45340	−	0.839119i	−0.998672	+	0.0515137i	$0.983595\pi$
$992$		0			0
$993$		−	23.5571i		−	0.747562i
$994$		0			0
$995$	8.10898			0.257072
$996$		0			0
$997$	−26.9722	+	46.7173i	−0.854220	+	1.47955i	0.0231474	+	0.999732i	$0.492631\pi$
$997$	−26.9722	+	46.7173i	−0.854220	+	1.47955i	−0.877367	+	0.479820i	$0.840702\pi$
$998$		0			0
$999$	3.37050	+	5.83787i	0.106638	+	0.184702i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.q.d.703.5	yes	16
4.3	odd	2		896.2.q.a.703.3	✓	16
7.5	odd	6	inner	896.2.q.d.831.6	yes	16
8.3	odd	2	inner	896.2.q.d.703.6	yes	16
8.5	even	2		896.2.q.a.703.4	yes	16
28.19	even	6		896.2.q.a.831.4	yes	16
56.5	odd	6		896.2.q.a.831.3	yes	16
56.19	even	6	inner	896.2.q.d.831.5	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
896.2.q.a.703.3	✓	16	4.3	odd	2
896.2.q.a.703.4	yes	16	8.5	even	2
896.2.q.a.831.3	yes	16	56.5	odd	6
896.2.q.a.831.4	yes	16	28.19	even	6
896.2.q.d.703.5	yes	16	1.1	even	1	trivial
896.2.q.d.703.6	yes	16	8.3	odd	2	inner
896.2.q.d.831.5	yes	16	56.19	even	6	inner
896.2.q.d.831.6	yes	16	7.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.20586 + 0.696202i) q^{3} +(-2.07821 - 3.59957i) q^{5} +(-0.632797 + 2.56896i) q^{7} +(-0.530605 - 0.919035i) q^{9} +O(q^{10})\)	\(q+(1.20586 + 0.696202i) q^{3} +(-2.07821 - 3.59957i) q^{5} +(-0.632797 + 2.56896i) q^{7} +(-0.530605 - 0.919035i) q^{9} +(-2.36310 + 4.09302i) q^{11} -3.68997 q^{13} -5.78742i q^{15} +(2.28389 + 1.31860i) q^{17} +(-0.698106 + 0.403051i) q^{19} +(-2.55158 + 2.65725i) q^{21} +(-4.73969 + 2.73646i) q^{23} +(-6.13792 + 10.6312i) q^{25} -5.65485i q^{27} -3.88464i q^{29} +(-0.515984 + 0.893710i) q^{31} +(-5.69914 + 3.29040i) q^{33} +(10.5622 - 3.06105i) q^{35} +(-1.03237 + 0.596037i) q^{37} +(-4.44957 - 2.56896i) q^{39} +6.47477i q^{41} -10.2758 q^{43} +(-2.20542 + 3.81990i) q^{45} +(3.98009 + 6.89371i) q^{47} +(-6.19914 - 3.25126i) q^{49} +(1.83603 + 3.18010i) q^{51} +(2.32572 + 1.34275i) q^{53} +19.6441 q^{55} -1.12242 q^{57} +(2.38243 + 1.37550i) q^{59} +(-0.819529 - 1.41947i) q^{61} +(2.69673 - 0.781542i) q^{63} +(7.66853 + 13.2823i) q^{65} +(2.45914 - 4.25936i) q^{67} -7.62052 q^{69} -11.7693i q^{71} +(-10.5226 - 6.07521i) q^{73} +(-14.8029 + 8.54647i) q^{75} +(-9.01944 - 8.66078i) q^{77} +(-12.2126 + 7.05096i) q^{79} +(2.34510 - 4.06183i) q^{81} -7.37993i q^{83} -10.9614i q^{85} +(2.70449 - 4.68432i) q^{87} +(15.8983 - 9.17887i) q^{89} +(2.33500 - 9.47938i) q^{91} +(-1.24441 + 0.718458i) q^{93} +(2.90162 + 1.67525i) q^{95} -1.83807i q^{97} +5.01550 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{3} + 8 q^{9}+O(q^{10}) \) 16 * q + 12 * q^3 + 8 * q^9	\( 16 q + 12 q^{3} + 8 q^{9} - 4 q^{11} - 12 q^{19} - 16 q^{25} + 24 q^{33} + 20 q^{35} + 16 q^{49} - 52 q^{51} + 48 q^{57} + 60 q^{59} + 24 q^{65} + 12 q^{67} - 24 q^{73} - 120 q^{75} - 32 q^{81} + 24 q^{89} + 72 q^{91} + 64 q^{99}+O(q^{100}) \) 16 * q + 12 * q^3 + 8 * q^9 - 4 * q^11 - 12 * q^19 - 16 * q^25 + 24 * q^33 + 20 * q^35 + 16 * q^49 - 52 * q^51 + 48 * q^57 + 60 * q^59 + 24 * q^65 + 12 * q^67 - 24 * q^73 - 120 * q^75 - 32 * q^81 + 24 * q^89 + 72 * q^91 + 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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