LMFDB - Embedded newform 224.3.n.a.17.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,3,Mod(17,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("224.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	224.n (of order $6$, degree $2$, 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:	$6.10355792167$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.7
Character	$\chi$	$=$	224.17
Dual form			224.3.n.a.145.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.126628 + 0.219326i) q^{3} +(-1.78589 - 3.09325i) q^{5} +(-2.89466 - 6.37346i) q^{7} +(4.46793 + 7.73868i) q^{9} +O(q^{10})$	\(q+(-0.126628 + 0.219326i) q^{3} +(-1.78589 - 3.09325i) q^{5} +(-2.89466 - 6.37346i) q^{7} +(4.46793 + 7.73868i) q^{9} +(-6.82675 - 3.94142i) q^{11} -18.1529 q^{13} +0.904575 q^{15} +(-8.26180 - 4.76995i) q^{17} +(-12.4094 - 21.4938i) q^{19} +(1.76441 + 0.172184i) q^{21} +(-2.14949 - 3.72303i) q^{23} +(6.12120 - 10.6022i) q^{25} -4.54237 q^{27} -28.3630i q^{29} +(28.2372 + 16.3027i) q^{31} +(1.72891 - 0.998189i) q^{33} +(-14.5452 + 20.3362i) q^{35} +(-25.9006 + 14.9537i) q^{37} +(2.29867 - 3.98141i) q^{39} -45.2606i q^{41} +24.9109i q^{43} +(15.9585 - 27.6409i) q^{45} +(-44.0432 + 25.4284i) q^{47} +(-32.2419 + 36.8979i) q^{49} +(2.09235 - 1.20802i) q^{51} +(54.3930 + 31.4038i) q^{53} +28.1558i q^{55} +6.28554 q^{57} +(37.0048 - 64.0942i) q^{59} +(25.2994 + 43.8198i) q^{61} +(36.3890 - 50.8770i) q^{63} +(32.4191 + 56.1515i) q^{65} +(108.673 + 62.7422i) q^{67} +1.08875 q^{69} +5.33822 q^{71} +(-23.6569 - 13.6583i) q^{73} +(1.55023 + 2.68508i) q^{75} +(-5.35941 + 54.9191i) q^{77} +(-51.5380 - 89.2664i) q^{79} +(-39.6362 + 68.6519i) q^{81} -51.5695 q^{83} +34.0744i q^{85} +(6.22075 + 3.59155i) q^{87} +(133.222 - 76.9158i) q^{89} +(52.5464 + 115.697i) q^{91} +(-7.15123 + 4.12877i) q^{93} +(-44.3238 + 76.7711i) q^{95} +47.0436i q^{97} -70.4400i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{7} - 32 q^{9}+O(q^{10}) $ 28 * q + 4 * q^7 - 32 * q^9	$ 28 q + 4 q^{7} - 32 q^{9} - 28 q^{15} - 6 q^{17} - 30 q^{23} - 32 q^{25} + 6 q^{31} - 6 q^{33} + 20 q^{39} + 294 q^{47} - 20 q^{49} + 124 q^{57} - 432 q^{63} - 52 q^{65} + 136 q^{71} + 234 q^{73} + 162 q^{79} - 18 q^{81} - 48 q^{87} - 150 q^{89} - 290 q^{95}+O(q^{100}) $ 28 * q + 4 * q^7 - 32 * q^9 - 28 * q^15 - 6 * q^17 - 30 * q^23 - 32 * q^25 + 6 * q^31 - 6 * q^33 + 20 * q^39 + 294 * q^47 - 20 * q^49 + 124 * q^57 - 432 * q^63 - 52 * q^65 + 136 * q^71 + 234 * q^73 + 162 * q^79 - 18 * q^81 - 48 * q^87 - 150 * q^89 - 290 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

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
$3$	−0.126628	+	0.219326i	−0.0422093	+	0.0731087i	−0.886358	−	0.463000i	$-0.846773\pi$
$3$	−0.126628	+	0.219326i	−0.0422093	+	0.0731087i	0.844149	+	0.536109i	$0.180106\pi$
$4$		0			0
$5$	−1.78589	−	3.09325i	−0.357178	−	0.618650i	0.630310	−	0.776343i	$-0.282928\pi$
$5$	−1.78589	−	3.09325i	−0.357178	−	0.618650i	−0.987488	+	0.157693i	$0.949594\pi$
$6$		0			0
$7$	−2.89466	−	6.37346i	−0.413522	−	0.910494i
$7$	−2.89466	−	6.37346i	−0.413522	−	0.910494i
$8$		0			0
$9$	4.46793	+	7.73868i	0.496437	+	0.859854i
$10$		0			0
$11$	−6.82675	−	3.94142i	−0.620613	−	0.358311i	0.156494	−	0.987679i	$-0.449981\pi$
$11$	−6.82675	−	3.94142i	−0.620613	−	0.358311i	−0.777108	+	0.629368i	$0.783314\pi$
$12$		0			0
$13$	−18.1529			−1.39638			−0.698189	−	0.715914i	$-0.746010\pi$
$13$	−18.1529			−1.39638			−0.698189	+	0.715914i	$0.746010\pi$
$14$		0			0
$15$	0.904575			0.0603050
$16$		0			0
$17$	−8.26180	−	4.76995i	−0.485988	−	0.280585i	0.236920	−	0.971529i	$-0.423862\pi$
$17$	−8.26180	−	4.76995i	−0.485988	−	0.280585i	−0.722909	+	0.690944i	$0.757195\pi$
$18$		0			0
$19$	−12.4094	−	21.4938i	−0.653129	−	1.13125i	−0.982359	−	0.187003i	$-0.940123\pi$
$19$	−12.4094	−	21.4938i	−0.653129	−	1.13125i	0.329231	−	0.944250i	$-0.393211\pi$
$20$		0			0
$21$	1.76441	+	0.172184i	0.0840196	+	0.00819925i
$22$		0			0
$23$	−2.14949	−	3.72303i	−0.0934563	−	0.161871i	0.815507	−	0.578747i	$-0.196458\pi$
$23$	−2.14949	−	3.72303i	−0.0934563	−	0.161871i	−0.908963	+	0.416876i	$0.863125\pi$
$24$		0			0
$25$	6.12120	−	10.6022i	0.244848	−	0.424089i
$26$		0			0
$27$	−4.54237			−0.168236
$28$		0			0
$29$		−	28.3630i		−	0.978035i	−0.872274	−	0.489017i	$-0.837356\pi$
$29$		−	28.3630i		−	0.978035i	0.872274	−	0.489017i	$-0.162644\pi$
$30$		0			0
$31$	28.2372	+	16.3027i	0.910876	+	0.525895i	0.880713	−	0.473650i	$-0.157064\pi$
$31$	28.2372	+	16.3027i	0.910876	+	0.525895i	0.0301634	+	0.999545i	$0.490397\pi$
$32$		0			0
$33$	1.72891	−	0.998189i	0.0523914	−	0.0302482i
$34$		0			0
$35$	−14.5452	+	20.3362i	−0.415576	+	0.581034i
$36$		0			0
$37$	−25.9006	+	14.9537i	−0.700017	+	0.404155i	−0.807354	−	0.590068i	$-0.799101\pi$
$37$	−25.9006	+	14.9537i	−0.700017	+	0.404155i	0.107337	+	0.994223i	$0.465768\pi$
$38$		0			0
$39$	2.29867	−	3.98141i	0.0589402	−	0.102087i
$40$		0			0
$41$		−	45.2606i		−	1.10392i	−0.833872	−	0.551958i	$-0.813881\pi$
$41$		−	45.2606i		−	1.10392i	0.833872	−	0.551958i	$-0.186119\pi$
$42$		0			0
$43$			24.9109i			0.579323i	0.957129	+	0.289661i	$0.0935427\pi$
$43$			24.9109i			0.579323i	−0.957129	+	0.289661i	$0.906457\pi$
$44$		0			0
$45$	15.9585	−	27.6409i	0.354632	−	0.614242i
$46$		0			0
$47$	−44.0432	+	25.4284i	−0.937090	+	0.541029i	−0.889047	−	0.457816i	$-0.848632\pi$
$47$	−44.0432	+	25.4284i	−0.937090	+	0.541029i	−0.0480430	+	0.998845i	$0.515298\pi$
$48$		0			0
$49$	−32.2419	+	36.8979i	−0.657998	+	0.753019i
$50$		0			0
$51$	2.09235	−	1.20802i	0.0410265	−	0.0236867i
$52$		0			0
$53$	54.3930	+	31.4038i	1.02628	+	0.592525i	0.915918	−	0.401366i	$-0.131465\pi$
$53$	54.3930	+	31.4038i	1.02628	+	0.592525i	0.110365	+	0.993891i	$0.464798\pi$
$54$		0			0
$55$			28.1558i			0.511924i
$56$		0			0
$57$	6.28554			0.110273
$58$		0			0
$59$	37.0048	−	64.0942i	0.627200	−	1.08634i	−0.360912	−	0.932600i	$-0.617534\pi$
$59$	37.0048	−	64.0942i	0.627200	−	1.08634i	0.988111	−	0.153741i	$-0.0491323\pi$
$60$		0			0
$61$	25.2994	+	43.8198i	0.414743	+	0.718357i	0.995401	−	0.0957908i	$-0.0305380\pi$
$61$	25.2994	+	43.8198i	0.414743	+	0.718357i	−0.580658	+	0.814148i	$0.697205\pi$
$62$		0			0
$63$	36.3890	−	50.8770i	0.577604	−	0.807571i
$64$		0			0
$65$	32.4191	+	56.1515i	0.498755	+	0.863869i
$66$		0			0
$67$	108.673	+	62.7422i	1.62198	+	0.936451i	0.986389	+	0.164426i	$0.0525772\pi$
$67$	108.673	+	62.7422i	1.62198	+	0.936451i	0.635592	+	0.772025i	$0.280756\pi$
$68$		0			0
$69$	1.08875			0.0157789
$70$		0			0
$71$	5.33822			0.0751863			0.0375931	−	0.999293i	$-0.488031\pi$
$71$	5.33822			0.0751863			0.0375931	+	0.999293i	$0.488031\pi$
$72$		0			0
$73$	−23.6569	−	13.6583i	−0.324067	−	0.187100i	0.329137	−	0.944282i	$-0.393242\pi$
$73$	−23.6569	−	13.6583i	−0.324067	−	0.187100i	−0.653204	+	0.757182i	$0.726576\pi$
$74$		0			0
$75$	1.55023	+	2.68508i	0.0206697	+	0.0358010i
$76$		0			0
$77$	−5.35941	+	54.9191i	−0.0696027	+	0.713234i
$78$		0			0
$79$	−51.5380	−	89.2664i	−0.652380	−	1.12995i	−0.982544	−	0.186031i	$-0.940437\pi$
$79$	−51.5380	−	89.2664i	−0.652380	−	1.12995i	0.330164	−	0.943924i	$-0.392896\pi$
$80$		0			0
$81$	−39.6362	+	68.6519i	−0.489336	+	0.847554i
$82$		0			0
$83$	−51.5695			−0.621319			−0.310660	−	0.950521i	$-0.600550\pi$
$83$	−51.5695			−0.621319			−0.310660	+	0.950521i	$0.600550\pi$
$84$		0			0
$85$			34.0744i			0.400876i
$86$		0			0
$87$	6.22075	+	3.59155i	0.0715029	+	0.0412822i
$88$		0			0
$89$	133.222	−	76.9158i	1.49688	−	0.864222i	0.496883	−	0.867818i	$-0.334478\pi$
$89$	133.222	−	76.9158i	1.49688	−	0.864222i	0.999994	+	0.00359545i	$0.00114447\pi$
$90$		0			0
$91$	52.5464	+	115.697i	0.577433	+	1.27139i
$92$		0			0
$93$	−7.15123	+	4.12877i	−0.0768950	+	0.0443953i
$94$		0			0
$95$	−44.3238	+	76.7711i	−0.466566	+	0.808117i
$96$		0			0
$97$			47.0436i			0.484986i	0.970153	+	0.242493i	$0.0779651\pi$
$97$			47.0436i			0.484986i	−0.970153	+	0.242493i	$0.922035\pi$
$98$		0			0
$99$		−	70.4400i		−	0.711516i
$100$		0			0
$101$	74.6727	−	129.337i	0.739333	−	1.28056i	−0.213462	−	0.976951i	$-0.568474\pi$
$101$	74.6727	−	129.337i	0.739333	−	1.28056i	0.952796	−	0.303612i	$-0.0981926\pi$
$102$		0			0
$103$	17.1847	−	9.92160i	0.166842	−	0.0963262i	−0.414254	−	0.910161i	$-0.635957\pi$
$103$	17.1847	−	9.92160i	0.166842	−	0.0963262i	0.581096	+	0.813835i	$0.302624\pi$
$104$		0			0
$105$	−2.61843	−	5.76527i	−0.0249375	−	0.0549073i
$106$		0			0
$107$	7.91877	−	4.57190i	0.0740072	−	0.0427281i	−0.462540	−	0.886599i	$-0.653062\pi$
$107$	7.91877	−	4.57190i	0.0740072	−	0.0427281i	0.536547	+	0.843870i	$0.319728\pi$
$108$		0			0
$109$	103.229	+	59.5992i	0.947053	+	0.546781i	0.892164	−	0.451711i	$-0.149186\pi$
$109$	103.229	+	59.5992i	0.947053	+	0.546781i	0.0548888	+	0.998492i	$0.482520\pi$
$110$		0			0
$111$		−	7.57425i		−	0.0682365i
$112$		0			0
$113$	−124.011			−1.09744			−0.548720	−	0.836006i	$-0.684885\pi$
$113$	−124.011			−1.09744			−0.548720	+	0.836006i	$0.684885\pi$
$114$		0			0
$115$	−7.67752	+	13.2979i	−0.0667611	+	0.115634i
$116$		0			0
$117$	−81.1059	−	140.480i	−0.693213	−	1.20068i
$118$		0			0
$119$	−6.48601	+	66.4636i	−0.0545043	+	0.558518i
$120$		0			0
$121$	−29.4303	−	50.9749i	−0.243226	−	0.421280i
$122$		0			0
$123$	9.92683	+	5.73126i	0.0807059	+	0.0465956i
$124$		0			0
$125$	−133.022			−1.06417
$126$		0			0
$127$	57.6144			0.453656			0.226828	−	0.973935i	$-0.427164\pi$
$127$	57.6144			0.453656			0.226828	+	0.973935i	$0.427164\pi$
$128$		0			0
$129$	−5.46361	−	3.15441i	−0.0423535	−	0.0244528i
$130$		0			0
$131$	−62.1497	−	107.646i	−0.474425	−	0.821728i	0.525146	−	0.851012i	$-0.324011\pi$
$131$	−62.1497	−	107.646i	−0.474425	−	0.821728i	−0.999571	+	0.0292837i	$0.990677\pi$
$132$		0			0
$133$	−101.069	+	141.308i	−0.759915	+	1.06247i
$134$		0			0
$135$	8.11216	+	14.0507i	0.0600901	+	0.104079i
$136$		0			0
$137$	84.7404	−	146.775i	0.618543	−	1.07135i	−0.371208	−	0.928550i	$-0.621056\pi$
$137$	84.7404	−	146.775i	0.618543	−	1.07135i	0.989752	−	0.142799i	$-0.0456102\pi$
$138$		0			0
$139$	−266.497			−1.91725			−0.958624	−	0.284677i	$-0.908114\pi$
$139$	−266.497			−1.91725			−0.958624	+	0.284677i	$0.908114\pi$
$140$		0			0
$141$		−	12.8798i		−	0.0913459i
$142$		0			0
$143$	123.925	+	71.5483i	0.866610	+	0.500338i
$144$		0			0
$145$	−87.7339	+	50.6532i	−0.605061	+	0.349332i
$146$		0			0
$147$	−4.00996	−	11.7438i	−0.0272786	−	0.0798899i
$148$		0			0
$149$	−26.6902	+	15.4096i	−0.179129	+	0.103420i	−0.586883	−	0.809672i	$-0.699645\pi$
$149$	−26.6902	+	15.4096i	−0.179129	+	0.103420i	0.407754	+	0.913092i	$0.366312\pi$
$150$		0			0
$151$	11.7448	−	20.3425i	0.0777800	−	0.134719i	−0.824512	−	0.565845i	$-0.808550\pi$
$151$	11.7448	−	20.3425i	0.0777800	−	0.134719i	0.902292	+	0.431126i	$0.141884\pi$
$152$		0			0
$153$		−	85.2473i		−	0.557172i
$154$		0			0
$155$		−	116.460i		−	0.751352i
$156$		0			0
$157$	63.8147	−	110.530i	0.406463	−	0.704015i	−0.588028	−	0.808841i	$-0.700095\pi$
$157$	63.8147	−	110.530i	0.406463	−	0.704015i	0.994491	+	0.104826i	$0.0334287\pi$
$158$		0			0
$159$	−13.7754	+	7.95320i	−0.0866374	+	0.0500202i
$160$		0			0
$161$	−17.5065	+	24.4766i	−0.108736	+	0.152029i
$162$		0			0
$163$	−138.291	+	79.8421i	−0.848409	+	0.489829i	−0.860114	−	0.510103i	$-0.829607\pi$
$163$	−138.291	+	79.8421i	−0.848409	+	0.489829i	0.0117050	+	0.999931i	$0.496274\pi$
$164$		0			0
$165$	−6.17530	−	3.56531i	−0.0374261	−	0.0216080i
$166$		0			0
$167$		−	142.792i		−	0.855042i	−0.904005	−	0.427521i	$-0.859387\pi$
$167$		−	142.792i		−	0.855042i	0.904005	−	0.427521i	$-0.140613\pi$
$168$		0			0
$169$	160.528			0.949869
$170$		0			0
$171$	110.889	−	192.066i	0.648474	−	1.12319i
$172$		0			0
$173$	−97.8898	−	169.550i	−0.565837	−	0.980059i	−0.996971	−	0.0777710i	$-0.975220\pi$
$173$	−97.8898	−	169.550i	−0.565837	−	0.980059i	0.431134	−	0.902288i	$-0.358114\pi$
$174$		0			0
$175$	−85.2916	−	8.32338i	−0.487380	−	0.0475622i
$176$		0			0
$177$	9.37168	+	16.2322i	0.0529474	+	0.0917075i
$178$		0			0
$179$	129.477	+	74.7535i	0.723334	+	0.417617i	0.815979	−	0.578082i	$-0.196199\pi$
$179$	129.477	+	74.7535i	0.723334	+	0.417617i	−0.0926444	+	0.995699i	$0.529532\pi$
$180$		0			0
$181$	−91.2994			−0.504417			−0.252208	−	0.967673i	$-0.581157\pi$
$181$	−91.2994			−0.504417			−0.252208	+	0.967673i	$0.581157\pi$
$182$		0			0
$183$	−12.8144			−0.0700242
$184$		0			0
$185$	92.5114	+	53.4115i	0.500062	+	0.288711i
$186$		0			0
$187$	37.6008	+	65.1265i	0.201074	+	0.348270i
$188$		0			0
$189$	13.1486	+	28.9506i	0.0695693	+	0.153178i
$190$		0			0
$191$	13.9140	+	24.0997i	0.0728480	+	0.126176i	0.900148	−	0.435583i	$-0.143458\pi$
$191$	13.9140	+	24.0997i	0.0728480	+	0.126176i	−0.827300	+	0.561760i	$0.810125\pi$
$192$		0			0
$193$	−121.192	+	209.911i	−0.627938	+	1.08762i	0.360027	+	0.932942i	$0.382767\pi$
$193$	−121.192	+	209.911i	−0.627938	+	1.08762i	−0.987965	+	0.154678i	$0.950566\pi$
$194$		0			0
$195$	−16.4207			−0.0842085
$196$		0			0
$197$		−	94.7050i		−	0.480736i	−0.970682	−	0.240368i	$-0.922732\pi$
$197$		−	94.7050i		−	0.480736i	0.970682	−	0.240368i	$-0.0772682\pi$
$198$		0			0
$199$	−267.738	−	154.579i	−1.34542	−	0.776778i	−0.357823	−	0.933790i	$-0.616481\pi$
$199$	−267.738	−	154.579i	−1.34542	−	0.776778i	−0.987597	+	0.157011i	$0.949814\pi$
$200$		0			0
$201$	−27.5220	+	15.8899i	−0.136926	+	0.0790540i
$202$		0			0
$203$	−180.770	+	82.1012i	−0.890494	+	0.404439i
$204$		0			0
$205$	−140.002	+	80.8304i	−0.682938	+	0.394295i
$206$		0			0
$207$	19.2076	−	33.2685i	0.0927903	−	0.160717i
$208$		0			0
$209$			195.644i			0.936094i
$210$		0			0
$211$			125.864i			0.596514i	0.954486	+	0.298257i	$0.0964052\pi$
$211$			125.864i			0.596514i	−0.954486	+	0.298257i	$0.903595\pi$
$212$		0			0
$213$	−0.675969	+	1.17081i	−0.00317356	+	0.00549677i
$214$		0			0
$215$	77.0556	−	44.4881i	0.358398	−	0.206921i
$216$		0			0
$217$	22.1679	−	227.159i	0.102156	−	1.04682i
$218$		0			0
$219$	5.99125	−	3.45905i	0.0273573	−	0.0157947i
$220$		0			0
$221$	149.976	+	86.5885i	0.678623	+	0.391803i
$222$		0			0
$223$			8.94619i			0.0401174i	0.999799	+	0.0200587i	$0.00638532\pi$
$223$			8.94619i			0.0401174i	−0.999799	+	0.0200587i	$0.993615\pi$
$224$		0			0
$225$	109.396			0.486206
$226$		0			0
$227$	136.347	−	236.160i	0.600647	−	1.04035i	−0.392076	−	0.919933i	$-0.628243\pi$
$227$	136.347	−	236.160i	0.600647	−	1.04035i	0.992723	−	0.120419i	$-0.0384237\pi$
$228$		0			0
$229$	165.611	+	286.846i	0.723191	+	1.25260i	0.959714	+	0.280978i	$0.0906588\pi$
$229$	165.611	+	286.846i	0.723191	+	1.25260i	−0.236523	+	0.971626i	$0.576008\pi$
$230$		0			0
$231$	−11.3665	−	8.12975i	−0.0492058	−	0.0351937i
$232$		0			0
$233$	−79.1185	−	137.037i	−0.339564	−	0.588143i	0.644786	−	0.764363i	$-0.276946\pi$
$233$	−79.1185	−	137.037i	−0.339564	−	0.588143i	−0.984351	+	0.176220i	$0.943613\pi$
$234$		0			0
$235$	157.313	+	90.8245i	0.669416	+	0.386487i
$236$		0			0
$237$	26.1046			0.110146
$238$		0			0
$239$	−48.9981			−0.205013			−0.102507	−	0.994732i	$-0.532686\pi$
$239$	−48.9981			−0.205013			−0.102507	+	0.994732i	$0.532686\pi$
$240$		0			0
$241$	170.914	+	98.6771i	0.709186	+	0.409449i	0.810759	−	0.585379i	$-0.199054\pi$
$241$	170.914	+	98.6771i	0.709186	+	0.409449i	−0.101574	+	0.994828i	$0.532388\pi$
$242$		0			0
$243$	−30.4787	−	52.7907i	−0.125427	−	0.217246i
$244$		0			0
$245$	171.715	+	33.8367i	0.700878	+	0.138109i
$246$		0			0
$247$	225.267	+	390.175i	0.912014	+	1.57965i
$248$		0			0
$249$	6.53014	−	11.3105i	0.0262255	−	0.0454239i
$250$		0			0
$251$	315.497			1.25696			0.628480	−	0.777826i	$-0.283677\pi$
$251$	315.497			1.25696			0.628480	+	0.777826i	$0.283677\pi$
$252$		0			0
$253$			33.8883i			0.133946i
$254$		0			0
$255$	−7.47341	−	4.31478i	−0.0293075	−	0.0169207i
$256$		0			0
$257$	−329.533	+	190.256i	−1.28223	+	0.740296i	−0.977256	−	0.212065i	$-0.931981\pi$
$257$	−329.533	+	190.256i	−1.28223	+	0.740296i	−0.304974	+	0.952361i	$0.598648\pi$
$258$		0			0
$259$	170.281	+	121.791i	0.657454	+	0.470234i
$260$		0			0
$261$	219.492	−	126.724i	0.840967	−	0.485532i
$262$		0			0
$263$	98.1636	−	170.024i	0.373246	−	0.646480i	−0.616817	−	0.787106i	$-0.711578\pi$
$263$	98.1636	−	170.024i	0.373246	−	0.646480i	0.990063	+	0.140626i	$0.0449116\pi$
$264$		0			0
$265$		−	224.335i		−	0.846547i
$266$		0			0
$267$			38.9588i			0.145913i
$268$		0			0
$269$	−51.1557	+	88.6043i	−0.190170	+	0.329384i	−0.945306	−	0.326184i	$-0.894237\pi$
$269$	−51.1557	+	88.6043i	−0.190170	+	0.329384i	0.755137	+	0.655568i	$0.227571\pi$
$270$		0			0
$271$	221.981	−	128.161i	0.819118	−	0.472918i	−0.0309944	−	0.999520i	$-0.509867\pi$
$271$	221.981	−	128.161i	0.819118	−	0.472918i	0.850112	+	0.526602i	$0.176534\pi$
$272$		0			0
$273$	−32.0292	−	3.12564i	−0.117323	−	0.0114492i
$274$		0			0
$275$	−83.5757	+	48.2525i	−0.303912	+	0.175464i
$276$		0			0
$277$	170.372	+	98.3646i	0.615063	+	0.355107i	0.774944	−	0.632029i	$-0.217778\pi$
$277$	170.372	+	98.3646i	0.615063	+	0.355107i	−0.159881	+	0.987136i	$0.551111\pi$
$278$		0			0
$279$			291.358i			1.04429i
$280$		0			0
$281$	−70.2923			−0.250151			−0.125075	−	0.992147i	$-0.539917\pi$
$281$	−70.2923			−0.250151			−0.125075	+	0.992147i	$0.539917\pi$
$282$		0			0
$283$	−148.495	+	257.201i	−0.524718	+	0.908838i	0.474868	+	0.880057i	$0.342496\pi$
$283$	−148.495	+	257.201i	−0.524718	+	0.908838i	−0.999586	+	0.0287807i	$0.990838\pi$
$284$		0			0
$285$	−11.2253	−	19.4427i	−0.0393869	−	0.0682201i
$286$		0			0
$287$	−288.466	+	131.014i	−1.00511	+	0.456494i
$288$		0			0
$289$	−98.9951	−	171.465i	−0.342544	−	0.593303i
$290$		0			0
$291$	−10.3179	−	5.95704i	−0.0354567	−	0.0204709i
$292$		0			0
$293$	−135.561			−0.462665			−0.231333	−	0.972875i	$-0.574309\pi$
$293$	−135.561			−0.462665			−0.231333	+	0.972875i	$0.574309\pi$
$294$		0			0
$295$	−264.346			−0.896087
$296$		0			0
$297$	31.0096	+	17.9034i	0.104409	+	0.0602808i
$298$		0			0
$299$	39.0196	+	67.5839i	0.130500	+	0.226033i
$300$		0			0
$301$	158.768	−	72.1084i	0.527470	−	0.239563i
$302$		0			0
$303$	18.9113	+	32.7553i	0.0624136	+	0.108103i
$304$		0			0
$305$	90.3637	−	156.515i	0.296274	−	0.513162i
$306$		0			0
$307$	76.2052			0.248225			0.124113	−	0.992268i	$-0.460392\pi$
$307$	76.2052			0.248225			0.124113	+	0.992268i	$0.460392\pi$
$308$		0			0
$309$			5.02541i			0.0162635i
$310$		0			0
$311$	171.554	+	99.0468i	0.551621	+	0.318479i	0.749776	−	0.661692i	$-0.230161\pi$
$311$	171.554	+	99.0468i	0.551621	+	0.318479i	−0.198154	+	0.980171i	$0.563495\pi$
$312$		0			0
$313$	−47.9693	+	27.6951i	−0.153257	+	0.0884827i	−0.574667	−	0.818387i	$-0.694868\pi$
$313$	−47.9693	+	27.6951i	−0.153257	+	0.0884827i	0.421411	+	0.906870i	$0.361535\pi$
$314$		0			0
$315$	−222.362	−	21.6997i	−0.705912	−	0.0688881i
$316$		0			0
$317$	259.080	−	149.580i	0.817289	−	0.471862i	−0.0321920	−	0.999482i	$-0.510249\pi$
$317$	259.080	−	149.580i	0.817289	−	0.471862i	0.849481	+	0.527620i	$0.176915\pi$
$318$		0			0
$319$	−111.791	+	193.627i	−0.350441	+	0.606981i
$320$		0			0
$321$			2.31572i			0.00721409i
$322$		0			0
$323$			236.770i			0.733034i
$324$		0			0
$325$	−111.117	+	192.461i	−0.341900	+	0.592188i
$326$		0			0
$327$	−26.1433	+	15.0938i	−0.0799490	+	0.0461586i
$328$		0			0
$329$	289.557	+	207.101i	0.880111	+	0.629487i
$330$		0			0
$331$	325.087	−	187.689i	0.982135	−	0.567036i	0.0792209	−	0.996857i	$-0.474757\pi$
$331$	325.087	−	187.689i	0.982135	−	0.567036i	0.902914	+	0.429821i	$0.141423\pi$
$332$		0			0
$333$	−231.445	−	133.625i	−0.695029	−	0.401275i
$334$		0			0
$335$		−	448.203i		−	1.33792i
$336$		0			0
$337$	−4.99043			−0.0148084			−0.00740419	−	0.999973i	$-0.502357\pi$
$337$	−4.99043			−0.0148084			−0.00740419	+	0.999973i	$0.502357\pi$
$338$		0			0
$339$	15.7032	−	27.1988i	0.0463222	−	0.0802324i
$340$		0			0
$341$	−128.512	−	222.589i	−0.376868	−	0.652755i
$342$		0			0
$343$	328.497	+	98.6856i	0.957717	+	0.287713i
$344$		0			0
$345$	−1.94438	−	3.36776i	−0.00563588	−	0.00976163i
$346$		0			0
$347$	−320.772	−	185.198i	−0.924414	−	0.533711i	−0.0393734	−	0.999225i	$-0.512536\pi$
$347$	−320.772	−	185.198i	−0.924414	−	0.533711i	−0.885041	+	0.465514i	$0.845870\pi$
$348$		0			0
$349$	−25.6801			−0.0735821			−0.0367910	−	0.999323i	$-0.511714\pi$
$349$	−25.6801			−0.0735821			−0.0367910	+	0.999323i	$0.511714\pi$
$350$		0			0
$351$	82.4571			0.234921
$352$		0			0
$353$	−229.938	−	132.755i	−0.651383	−	0.376076i	0.137603	−	0.990487i	$-0.456060\pi$
$353$	−229.938	−	132.755i	−0.651383	−	0.376076i	−0.788986	+	0.614411i	$0.789394\pi$
$354$		0			0
$355$	−9.53348	−	16.5125i	−0.0268549	−	0.0465140i
$356$		0			0
$357$	−13.7559	−	9.83871i	−0.0385319	−	0.0275594i
$358$		0			0
$359$	−275.228	−	476.709i	−0.766651	−	1.32788i	−0.939369	−	0.342908i	$-0.888588\pi$
$359$	−275.228	−	476.709i	−0.766651	−	1.32788i	0.172718	−	0.984971i	$-0.444745\pi$
$360$		0			0
$361$	−127.489	+	220.817i	−0.353155	+	0.611682i
$362$		0			0
$363$	14.9068			0.0410656
$364$		0			0
$365$			97.5689i			0.267312i
$366$		0			0
$367$	−180.099	−	103.980i	−0.490732	−	0.283324i	0.234146	−	0.972201i	$-0.424771\pi$
$367$	−180.099	−	103.980i	−0.490732	−	0.283324i	−0.724878	+	0.688877i	$0.758104\pi$
$368$		0			0
$369$	350.257	−	202.221i	0.949207	−	0.548025i
$370$		0			0
$371$	42.7018	−	437.575i	0.115099	−	1.17945i
$372$		0			0
$373$	−393.539	+	227.210i	−1.05507	+	0.609142i	−0.924063	−	0.382240i	$-0.875153\pi$
$373$	−393.539	+	227.210i	−1.05507	+	0.609142i	−0.131002	+	0.991382i	$0.541820\pi$
$374$		0			0
$375$	16.8443	−	29.1751i	0.0449180	−	0.0778003i
$376$		0			0
$377$			514.871i			1.36570i
$378$		0			0
$379$		−	373.244i		−	0.984813i	−0.870365	−	0.492406i	$-0.836117\pi$
$379$		−	373.244i		−	0.984813i	0.870365	−	0.492406i	$-0.163883\pi$
$380$		0			0
$381$	−7.29559	+	12.6363i	−0.0191485	+	0.0331662i
$382$		0			0
$383$	270.298	−	156.056i	0.705738	−	0.407458i	−0.103743	−	0.994604i	$-0.533082\pi$
$383$	270.298	−	156.056i	0.705738	−	0.407458i	0.809481	+	0.587146i	$0.199749\pi$
$384$		0			0
$385$	179.450	−	81.5014i	0.466103	−	0.211692i
$386$		0			0
$387$	−192.777	+	111.300i	−0.498133	+	0.287597i
$388$		0			0
$389$	−439.628	−	253.819i	−1.13015	−	0.652492i	−0.186177	−	0.982516i	$-0.559610\pi$
$389$	−439.628	−	253.819i	−1.13015	−	0.652492i	−0.943973	+	0.330024i	$0.892943\pi$
$390$		0			0
$391$			41.0120i			0.104890i
$392$		0			0
$393$	31.4796			0.0801007
$394$		0			0
$395$	−184.082	+	318.840i	−0.466031	+	0.807190i
$396$		0			0
$397$	95.6487	+	165.668i	0.240929	+	0.417301i	0.960979	−	0.276621i	$-0.0892146\pi$
$397$	95.6487	+	165.668i	0.240929	+	0.417301i	−0.720050	+	0.693922i	$0.755881\pi$
$398$		0			0
$399$	−18.1945	−	40.0606i	−0.0456002	−	0.100402i
$400$		0			0
$401$	61.2011	+	106.004i	0.152621	+	0.264348i	0.932190	−	0.361968i	$-0.117895\pi$
$401$	61.2011	+	106.004i	0.152621	+	0.264348i	−0.779569	+	0.626316i	$0.784562\pi$
$402$		0			0
$403$	−512.587	−	295.942i	−1.27193	−	0.734347i
$404$		0			0
$405$	283.143			0.699120
$406$		0			0
$407$	235.756			0.579254
$408$		0			0
$409$	−4.57744	−	2.64279i	−0.0111918	−	0.00646158i	0.494394	−	0.869238i	$-0.335390\pi$
$409$	−4.57744	−	2.64279i	−0.0111918	−	0.00646158i	−0.505585	+	0.862777i	$0.668723\pi$
$410$		0			0
$411$	21.4610	+	37.1716i	0.0522166	+	0.0904418i
$412$		0			0
$413$	−515.617	−	50.3178i	−1.24847	−	0.121835i
$414$		0			0
$415$	92.0975	+	159.517i	0.221922	+	0.384379i
$416$		0			0
$417$	33.7460	−	58.4498i	0.0809257	−	0.140167i
$418$		0			0
$419$	−34.7160			−0.0828545			−0.0414272	−	0.999142i	$-0.513190\pi$
$419$	−34.7160			−0.0828545			−0.0414272	+	0.999142i	$0.513190\pi$
$420$		0			0
$421$		−	394.337i		−	0.936669i	−0.883551	−	0.468334i	$-0.844854\pi$
$421$		−	394.337i		−	0.936669i	0.883551	−	0.468334i	$-0.155146\pi$
$422$		0			0
$423$	−393.564	−	227.224i	−0.930412	−	0.537173i
$424$		0			0
$425$	−101.144	+	58.3956i	−0.237986	+	0.137401i
$426$		0			0
$427$	206.050	−	288.088i	0.482554	−	0.674678i
$428$		0			0
$429$	−31.3848	+	18.1200i	−0.0731581	+	0.0422378i
$430$		0			0
$431$	−215.872	+	373.901i	−0.500862	+	0.867519i	0.499137	+	0.866523i	$0.333650\pi$
$431$	−215.872	+	373.901i	−0.500862	+	0.867519i	−1.00000		0.000995912i	$0.999683\pi$
$432$		0			0
$433$		−	318.535i		−	0.735647i	−0.929896	−	0.367823i	$-0.880103\pi$
$433$		−	318.535i		−	0.735647i	0.929896	−	0.367823i	$-0.119897\pi$
$434$		0			0
$435$		−	25.6565i		−	0.0589803i
$436$		0			0
$437$	−53.3481	+	92.4016i	−0.122078	+	0.211445i
$438$		0			0
$439$	−532.799	+	307.612i	−1.21366	+	0.700710i	−0.963556	−	0.267508i	$-0.913800\pi$
$439$	−532.799	+	307.612i	−1.21366	+	0.700710i	−0.250109	+	0.968218i	$0.580467\pi$
$440$		0			0
$441$	−429.596	−	84.6525i	−0.974141	−	0.191956i
$442$		0			0
$443$	−86.4553	+	49.9150i	−0.195159	+	0.112675i	−0.594395	−	0.804173i	$-0.702609\pi$
$443$	−86.4553	+	49.9150i	−0.195159	+	0.112675i	0.399237	+	0.916848i	$0.369275\pi$
$444$		0			0
$445$	−475.840	−	274.726i	−1.06930	−	0.617362i
$446$		0			0
$447$		−	7.80515i		−	0.0174612i
$448$		0			0
$449$	−75.3168			−0.167743			−0.0838717	−	0.996477i	$-0.526729\pi$
$449$	−75.3168			−0.167743			−0.0838717	+	0.996477i	$0.526729\pi$
$450$		0			0
$451$	−178.391	+	308.983i	−0.395546	+	0.685105i
$452$		0			0
$453$	2.97443	+	5.15187i	0.00656608	+	0.0113728i
$454$		0			0
$455$	264.037	−	369.161i	0.580301	−	0.811343i
$456$		0			0
$457$	104.447	+	180.907i	0.228549	+	0.395858i	0.957378	−	0.288837i	$-0.0932687\pi$
$457$	104.447	+	180.907i	0.228549	+	0.395858i	−0.728830	+	0.684695i	$0.759935\pi$
$458$		0			0
$459$	37.5281	+	21.6669i	0.0817606	+	0.0472045i
$460$		0			0
$461$	751.461			1.63007			0.815034	−	0.579413i	$-0.196718\pi$
$461$	751.461			1.63007			0.815034	+	0.579413i	$0.196718\pi$
$462$		0			0
$463$	3.56075			0.00769060			0.00384530	−	0.999993i	$-0.498776\pi$
$463$	3.56075			0.00769060			0.00384530	+	0.999993i	$0.498776\pi$
$464$		0			0
$465$	25.5426	+	14.7470i	0.0549304	+	0.0317141i
$466$		0			0
$467$	206.945	+	358.440i	0.443138	+	0.767537i	0.997920	−	0.0644583i	$-0.0205320\pi$
$467$	206.945	+	358.440i	0.443138	+	0.767537i	−0.554783	+	0.831995i	$0.687199\pi$
$468$		0			0
$469$	85.3146	−	874.238i	0.181908	−	1.86405i
$470$		0			0
$471$	16.1615	+	27.9925i	0.0343131	+	0.0594320i
$472$		0			0
$473$	98.1843	−	170.060i	0.207578	−	0.359535i
$474$		0			0
$475$	−303.843			−0.639669
$476$		0			0
$477$			561.240i			1.17660i
$478$		0			0
$479$	785.798	+	453.681i	1.64050	+	0.947142i	0.980657	+	0.195737i	$0.0627098\pi$
$479$	785.798	+	453.681i	1.64050	+	0.947142i	0.659841	+	0.751405i	$0.270624\pi$
$480$		0			0
$481$	470.172	−	271.454i	0.977488	−	0.564353i
$482$		0			0
$483$	−3.15154	−	6.93907i	−0.00652494	−	0.0143666i
$484$		0			0
$485$	145.518	−	84.0147i	0.300037	−	0.173226i
$486$		0			0
$487$	421.452	−	729.977i	0.865405	−	1.49893i	−0.00123943	−	0.999999i	$-0.500395\pi$
$487$	421.452	−	729.977i	0.865405	−	1.49893i	0.866644	−	0.498926i	$-0.166272\pi$
$488$		0			0
$489$		−	40.4410i		−	0.0827014i
$490$		0			0
$491$			144.126i			0.293535i	0.989171	+	0.146768i	$0.0468870\pi$
$491$			144.126i			0.293535i	−0.989171	+	0.146768i	$0.953113\pi$
$492$		0			0
$493$	−135.290	+	234.329i	−0.274422	+	0.475313i
$494$		0			0
$495$	−217.889	+	125.798i	−0.440179	+	0.254138i
$496$		0			0
$497$	−15.4523	−	34.0229i	−0.0310912	−	0.0684566i
$498$		0			0
$499$	330.101	−	190.584i	0.661526	−	0.381932i	−0.131332	−	0.991338i	$-0.541926\pi$
$499$	330.101	−	190.584i	0.661526	−	0.381932i	0.792858	+	0.609406i	$0.208592\pi$
$500$		0			0
$501$	31.3180	+	18.0815i	0.0625110	+	0.0360908i
$502$		0			0
$503$			936.429i			1.86169i	0.365418	+	0.930843i	$0.380926\pi$
$503$			936.429i			1.86169i	−0.365418	+	0.930843i	$0.619074\pi$
$504$		0			0
$505$	−533.429			−1.05629
$506$		0			0
$507$	−20.3273	+	35.2080i	−0.0400933	+	0.0694437i
$508$		0			0
$509$	167.592	+	290.278i	0.329258	+	0.570291i	0.982365	−	0.186975i	$-0.0598682\pi$
$509$	167.592	+	290.278i	0.329258	+	0.570291i	−0.653107	+	0.757265i	$0.726535\pi$
$510$		0			0
$511$	−18.5721	+	190.312i	−0.0363446	+	0.372431i
$512$		0			0
$513$	56.3682	+	97.6327i	0.109880	+	0.190317i
$514$		0			0
$515$	−61.3800	−	35.4378i	−0.119185	−	0.0688112i
$516$		0			0
$517$	400.896			0.775427
$518$		0			0
$519$	49.5824			0.0955345
$520$		0			0
$521$	−421.675	−	243.454i	−0.809357	−	0.467283i	0.0373754	−	0.999301i	$-0.488100\pi$
$521$	−421.675	−	243.454i	−0.809357	−	0.467283i	−0.846733	+	0.532019i	$0.821434\pi$
$522$		0			0
$523$	86.3132	+	149.499i	0.165035	+	0.285849i	0.936668	−	0.350220i	$-0.113893\pi$
$523$	86.3132	+	149.499i	0.165035	+	0.285849i	−0.771633	+	0.636068i	$0.780560\pi$
$524$		0			0
$525$	12.6258	−	17.6527i	0.0240492	−	0.0336242i
$526$		0			0
$527$	−155.527	−	269.380i	−0.295117	−	0.511157i
$528$		0			0
$529$	255.259	−	442.122i	0.482532	−	0.835770i
$530$		0			0
$531$	661.339			1.24546
$532$		0			0
$533$			821.611i			1.54148i
$534$		0			0
$535$	−28.2841	−	16.3298i	−0.0528675	−	0.0305230i
$536$		0			0
$537$	−32.7908	+	18.9318i	−0.0610629	+	0.0352547i
$538$		0			0
$539$	365.538	−	124.814i	0.678178	−	0.231566i
$540$		0			0
$541$	500.736	−	289.100i	0.925574	−	0.534381i	0.0401652	−	0.999193i	$-0.487212\pi$
$541$	500.736	−	289.100i	0.925574	−	0.534381i	0.885409	+	0.464812i	$0.153878\pi$
$542$		0			0
$543$	11.5611	−	20.0244i	0.0212911	−	0.0368773i
$544$		0			0
$545$		−	425.750i		−	0.781193i
$546$		0			0
$547$		−	454.579i		−	0.831040i	−0.909584	−	0.415520i	$-0.863600\pi$
$547$		−	454.579i		−	0.831040i	0.909584	−	0.415520i	$-0.136400\pi$
$548$		0			0
$549$	−226.071	+	391.567i	−0.411788	+	0.713237i
$550$		0			0
$551$	−609.629	+	351.969i	−1.10640	+	0.638783i
$552$		0			0
$553$	−419.751	+	586.871i	−0.759043	+	1.06125i
$554$		0			0
$555$	−23.4291	+	13.5268i	−0.0422145	+	0.0243726i
$556$		0			0
$557$	25.2401	+	14.5724i	0.0453143	+	0.0261622i	0.522486	−	0.852648i	$-0.325005\pi$
$557$	25.2401	+	14.5724i	0.0453143	+	0.0261622i	−0.477172	+	0.878810i	$0.658338\pi$
$558$		0			0
$559$		−	452.205i		−	0.808953i
$560$		0			0
$561$	−19.0453			−0.0339488
$562$		0			0
$563$	−514.005	+	890.283i	−0.912975	+	1.58132i	−0.103136	+	0.994667i	$0.532888\pi$
$563$	−514.005	+	890.283i	−0.912975	+	1.58132i	−0.809839	+	0.586652i	$0.800446\pi$
$564$		0			0
$565$	221.469	+	383.596i	0.391981	+	0.678931i
$566$		0			0
$567$	552.283	+	53.8959i	0.974044	+	0.0950544i
$568$		0			0
$569$	409.852	+	709.885i	0.720303	+	1.24760i	0.960878	+	0.276971i	$0.0893305\pi$
$569$	409.852	+	709.885i	0.720303	+	1.24760i	−0.240576	+	0.970630i	$0.577336\pi$
$570$		0			0
$571$	−140.820	−	81.3023i	−0.246620	−	0.142386i	0.371596	−	0.928395i	$-0.378811\pi$
$571$	−140.820	−	81.3023i	−0.246620	−	0.142386i	−0.618215	+	0.786009i	$0.712144\pi$
$572$		0			0
$573$	−7.04760			−0.0122995
$574$		0			0
$575$	−52.6299			−0.0915303
$576$		0			0
$577$	131.878	+	76.1400i	0.228559	+	0.131958i	0.609907	−	0.792473i	$-0.291207\pi$
$577$	131.878	+	76.1400i	0.228559	+	0.131958i	−0.381348	+	0.924431i	$0.624540\pi$
$578$		0			0
$579$	−30.6926	−	53.1611i	−0.0530097	−	0.0918154i
$580$		0			0
$581$	149.276	+	328.676i	0.256930	+	0.565708i
$582$		0			0
$583$	−247.551	−	428.772i	−0.424617	−	0.735457i
$584$		0			0
$585$	−289.692	+	501.762i	−0.495201	+	0.857713i
$586$		0			0
$587$	894.404			1.52369			0.761843	−	0.647761i	$-0.224295\pi$
$587$	894.404			1.52369			0.761843	+	0.647761i	$0.224295\pi$
$588$		0			0
$589$		−	809.232i		−	1.37391i
$590$		0			0
$591$	20.7713	+	11.9923i	0.0351460	+	0.0202916i
$592$		0			0
$593$	164.729	−	95.1064i	0.277789	−	0.160382i	−0.354633	−	0.935006i	$-0.615394\pi$
$593$	164.729	−	95.1064i	0.277789	−	0.160382i	0.632422	+	0.774624i	$0.282061\pi$
$594$		0			0
$595$	217.172	−	98.6338i	0.364995	−	0.165771i
$596$		0			0
$597$	67.8064	−	39.1480i	0.113579	−	0.0655746i
$598$		0			0
$599$	−146.832	+	254.320i	−0.245128	+	0.424574i	−0.962168	−	0.272458i	$-0.912163\pi$
$599$	−146.832	+	254.320i	−0.245128	+	0.424574i	0.717040	+	0.697033i	$0.245497\pi$
$600$		0			0
$601$			597.574i			0.994299i	0.867665	+	0.497150i	$0.165620\pi$
$601$			597.574i			0.994299i	−0.867665	+	0.497150i	$0.834380\pi$
$602$		0			0
$603$			1121.31i			1.85956i
$604$		0			0
$605$	−105.119	+	182.071i	−0.173750	+	0.300944i
$606$		0			0
$607$	10.6620	−	6.15569i	0.0175650	−	0.0101412i	−0.491192	−	0.871051i	$-0.663439\pi$
$607$	10.6620	−	6.15569i	0.0175650	−	0.0101412i	0.508757	+	0.860910i	$0.330105\pi$
$608$		0			0
$609$	4.88366	−	50.0440i	0.00801915	−	0.0821740i
$610$		0			0
$611$	799.512	−	461.599i	1.30853	−	0.755481i
$612$		0			0
$613$	−118.897	−	68.6451i	−0.193959	−	0.111982i	0.399876	−	0.916569i	$-0.369053\pi$
$613$	−118.897	−	68.6451i	−0.193959	−	0.111982i	−0.593835	+	0.804587i	$0.702387\pi$
$614$		0			0
$615$		−	40.9416i		−	0.0665717i
$616$		0			0
$617$	290.516			0.470853			0.235427	−	0.971892i	$-0.424351\pi$
$617$	290.516			0.470853			0.235427	+	0.971892i	$0.424351\pi$
$618$		0			0
$619$	51.1586	−	88.6092i	0.0826471	−	0.143149i	−0.821739	−	0.569864i	$-0.806996\pi$
$619$	51.1586	−	88.6092i	0.0826471	−	0.143149i	0.904386	+	0.426715i	$0.140329\pi$
$620$		0			0
$621$	9.76379	+	16.9114i	0.0157227	+	0.0272325i
$622$		0			0
$623$	−875.851	−	626.440i	−1.40586	−	1.00552i
$624$		0			0
$625$	84.5320	+	146.414i	0.135251	+	0.234262i
$626$		0			0
$627$	−42.9098	−	24.7740i	−0.0684366	−	0.0395119i
$628$		0			0
$629$	285.315			0.453600
$630$		0			0
$631$	562.739			0.891820			0.445910	−	0.895078i	$-0.352880\pi$
$631$	562.739			0.891820			0.445910	+	0.895078i	$0.352880\pi$
$632$		0			0
$633$	−27.6054	−	15.9380i	−0.0436104	−	0.0251785i
$634$		0			0
$635$	−102.893	−	178.216i	−0.162036	−	0.280655i
$636$		0			0
$637$	585.284	−	669.805i	0.918814	−	1.05150i
$638$		0			0
$639$	23.8508	+	41.3108i	0.0373252	+	0.0646492i
$640$		0			0
$641$	376.275	−	651.727i	0.587012	−	1.01673i	−0.407610	−	0.913156i	$-0.633638\pi$
$641$	376.275	−	651.727i	0.587012	−	1.01673i	0.994621	−	0.103578i	$-0.0330291\pi$
$642$		0			0
$643$	−253.143			−0.393690			−0.196845	−	0.980435i	$-0.563070\pi$
$643$	−253.143			−0.393690			−0.196845	+	0.980435i	$0.563070\pi$
$644$		0			0
$645$			22.5337i			0.0349360i
$646$		0			0
$647$	−485.492	−	280.299i	−0.750374	−	0.433229i	0.0754551	−	0.997149i	$-0.475959\pi$
$647$	−485.492	−	280.299i	−0.750374	−	0.433229i	−0.825829	+	0.563921i	$0.809292\pi$
$648$		0			0
$649$	−505.244	+	291.703i	−0.778497	+	0.449465i
$650$		0			0
$651$	47.0149	+	33.6267i	0.0722195	+	0.0516539i
$652$		0			0
$653$	−602.396	+	347.793i	−0.922505	+	0.532609i	−0.884433	−	0.466666i	$-0.845455\pi$
$653$	−602.396	+	347.793i	−0.922505	+	0.532609i	−0.0380717	+	0.999275i	$0.512122\pi$
$654$		0			0
$655$	−221.985	+	384.489i	−0.338908	+	0.587007i
$656$		0			0
$657$		−	244.097i		−	0.371533i
$658$		0			0
$659$			323.387i			0.490724i	0.969432	+	0.245362i	$0.0789068\pi$
$659$			323.387i			0.490724i	−0.969432	+	0.245362i	$0.921093\pi$
$660$		0			0
$661$	−15.5168	+	26.8758i	−0.0234747	+	0.0406593i	−0.877524	−	0.479533i	$-0.840806\pi$
$661$	−15.5168	+	26.8758i	−0.0234747	+	0.0406593i	0.854049	+	0.520192i	$0.174140\pi$
$662$		0			0
$663$	−37.9822	+	21.9291i	−0.0572884	+	0.0330755i
$664$		0			0
$665$	617.600	+	60.2699i	0.928721	+	0.0906315i
$666$		0			0
$667$	−105.596	+	60.9661i	−0.158315	+	0.0914035i
$668$		0			0
$669$	−1.96213	−	1.13284i	−0.00293293	−	0.00169333i
$670$		0			0
$671$		−	398.862i		−	0.594429i
$672$		0			0
$673$	1011.75			1.50334			0.751670	−	0.659539i	$-0.229249\pi$
$673$	1011.75			1.50334			0.751670	+	0.659539i	$0.229249\pi$
$674$		0			0
$675$	−27.8047	+	48.1592i	−0.0411922	+	0.0713469i
$676$		0			0
$677$	34.7377	+	60.1674i	0.0513112	+	0.0888736i	0.890540	−	0.454905i	$-0.150327\pi$
$677$	34.7377	+	60.1674i	0.0513112	+	0.0888736i	−0.839229	+	0.543778i	$0.816993\pi$
$678$		0			0
$679$	299.831	−	136.175i	0.441577	−	0.200553i
$680$		0			0
$681$	34.5307	+	59.8089i	0.0507058	+	0.0878251i
$682$		0			0
$683$	−824.530	−	476.042i	−1.20722	−	0.696987i	−0.245067	−	0.969506i	$-0.578810\pi$
$683$	−824.530	−	476.042i	−1.20722	−	0.696987i	−0.962150	+	0.272519i	$0.912143\pi$
$684$		0			0
$685$	−605.348			−0.883720
$686$		0			0
$687$	−83.8839			−0.122102
$688$		0			0
$689$	−987.391	−	570.070i	−1.43308	−	0.827388i
$690$		0			0
$691$	−34.0754	−	59.0204i	−0.0493132	−	0.0854130i	0.840315	−	0.542098i	$-0.182370\pi$
$691$	−34.0754	−	59.0204i	−0.0493132	−	0.0854130i	−0.889628	+	0.456685i	$0.849037\pi$
$692$		0			0
$693$	−448.947	+	203.900i	−0.647831	+	0.294228i
$694$		0			0
$695$	475.935	+	824.343i	0.684798	+	1.18611i
$696$		0			0
$697$	−215.891	+	373.934i	−0.309743	+	0.536490i
$698$		0			0
$699$	40.0745			0.0573311
$700$		0			0
$701$			1.67276i			0.00238625i	0.999999	+	0.00119312i	$0.000379783\pi$
$701$			1.67276i			0.00238625i	−0.999999	+	0.00119312i	$0.999620\pi$
$702$		0			0
$703$	642.825	+	371.135i	0.914403	+	0.527931i
$704$		0			0
$705$	−39.8404	+	23.0019i	−0.0565112	+	0.0326267i
$706$		0			0
$707$	−1040.47	−	101.537i	−1.47168	−	0.143617i
$708$		0			0
$709$	−45.7969	+	26.4408i	−0.0645936	+	0.0372931i	−0.531949	−	0.846776i	$-0.678540\pi$
$709$	−45.7969	+	26.4408i	−0.0645936	+	0.0372931i	0.467355	+	0.884070i	$0.345207\pi$
$710$		0			0
$711$	460.536	−	797.673i	0.647731	−	1.12190i
$712$		0			0
$713$		−	140.171i		−	0.196593i
$714$		0			0
$715$		−	511.109i		−	0.714838i
$716$		0			0
$717$	6.20454	−	10.7466i	0.00865347	−	0.0149882i
$718$		0			0
$719$	824.178	−	475.840i	1.14628	−	0.661808i	0.198305	−	0.980140i	$-0.436456\pi$
$719$	824.178	−	475.840i	1.14628	−	0.661808i	0.947979	+	0.318333i	$0.103123\pi$
$720$		0			0
$721$	−112.979	−	80.8064i	−0.156697	−	0.112075i
$722$		0			0
$723$	−43.2849	+	24.9906i	−0.0598685	+	0.0345651i
$724$		0			0
$725$	−300.711	−	173.615i	−0.414774	−	0.239470i
$726$		0			0
$727$			1061.98i			1.46078i	0.683032	+	0.730388i	$0.260661\pi$
$727$			1061.98i			1.46078i	−0.683032	+	0.730388i	$0.739339\pi$
$728$		0			0
$729$	−698.013			−0.957494
$730$		0			0
$731$	118.824	−	205.809i	0.162550	−	0.281544i
$732$		0			0
$733$	0.148102	+	0.256519i	0.000202048	+	0.000349958i	0.866126	−	0.499825i	$-0.166602\pi$
$733$	0.148102	+	0.256519i	0.000202048	+	0.000349958i	−0.865924	+	0.500175i	$0.833269\pi$
$734$		0			0
$735$	−29.1652	+	33.3769i	−0.0396806	+	0.0454108i
$736$		0			0
$737$	−494.588	−	856.651i	−0.671082	−	1.16235i
$738$		0			0
$739$	176.276	+	101.773i	0.238533	+	0.137717i	0.614502	−	0.788915i	$-0.289357\pi$
$739$	176.276	+	101.773i	0.238533	+	0.137717i	−0.375969	+	0.926632i	$0.622690\pi$
$740$		0			0
$741$	−114.101			−0.153982
$742$		0			0
$743$	−1142.13			−1.53718			−0.768592	−	0.639739i	$-0.779042\pi$
$743$	−1142.13			−1.53718			−0.768592	+	0.639739i	$0.779042\pi$
$744$		0			0
$745$	95.3315	+	55.0397i	0.127962	+	0.0738788i
$746$		0			0
$747$	−230.409	−	399.080i	−0.308446	−	0.534244i
$748$		0			0
$749$	−52.0610	−	37.2358i	−0.0695073	−	0.0497141i
$750$		0			0
$751$	−396.068	−	686.010i	−0.527387	−	0.913462i	−0.999490	−	0.0319185i	$-0.989838\pi$
$751$	−396.068	−	686.010i	−0.527387	−	0.913462i	0.472103	−	0.881543i	$-0.343495\pi$
$752$		0			0
$753$	−39.9508	+	69.1967i	−0.0530554	+	0.0918947i
$754$		0			0
$755$	−83.8995			−0.111125
$756$		0			0
$757$		−	1179.34i		−	1.55792i	−0.627076	−	0.778958i	$-0.715748\pi$
$757$		−	1179.34i		−	1.55792i	0.627076	−	0.778958i	$-0.284252\pi$
$758$		0			0
$759$	−7.43259	−	4.29121i	−0.00979260	−	0.00565376i
$760$		0			0
$761$	197.869	−	114.240i	0.260011	−	0.150118i	−0.364328	−	0.931271i	$-0.618701\pi$
$761$	197.869	−	114.240i	0.260011	−	0.150118i	0.624340	+	0.781153i	$0.285368\pi$
$762$		0			0
$763$	81.0408	−	830.443i	0.106213	−	1.08839i
$764$		0			0
$765$	−263.691	+	152.242i	−0.344694	+	0.199009i
$766$		0			0
$767$	−671.744	+	1163.49i	−0.875807	+	1.51694i
$768$		0			0
$769$		−	83.4232i		−	0.108483i	−0.998528	−	0.0542414i	$-0.982726\pi$
$769$		−	83.4232i		−	0.108483i	0.998528	−	0.0542414i	$-0.0172740\pi$
$770$		0			0
$771$		−	96.3670i		−	0.124990i
$772$		0			0
$773$	285.318	−	494.186i	0.369105	−	0.639309i	−0.620321	−	0.784348i	$-0.712998\pi$
$773$	285.318	−	494.186i	0.369105	−	0.639309i	0.989426	+	0.145039i	$0.0463309\pi$
$774$		0			0
$775$	345.691	−	199.585i	0.446052	−	0.257528i
$776$		0			0
$777$	−48.2742	+	21.9249i	−0.0621289	+	0.0282173i
$778$		0			0
$779$	−972.822	+	561.659i	−1.24881	+	0.721000i
$780$		0			0
$781$	−36.4427	−	21.0402i	−0.0466616	−	0.0269401i
$782$		0			0
$783$			128.835i			0.164540i
$784$		0			0
$785$	−455.864			−0.580718
$786$		0			0
$787$	382.719	−	662.888i	0.486301	−	0.842298i	−0.513575	−	0.858045i	$-0.671679\pi$
$787$	382.719	−	662.888i	0.486301	−	0.842298i	0.999876	+	0.0157470i	$0.00501262\pi$
$788$		0			0
$789$	24.8605	+	43.0597i	0.0315089	+	0.0545750i
$790$		0			0
$791$	358.968	+	790.377i	0.453816	+	0.999212i
$792$		0			0
$793$	−459.257	−	795.456i	−0.579138	−	1.00310i
$794$		0			0
$795$	49.2025	+	28.4071i	0.0618900	+	0.0357322i
$796$		0			0
$797$	−577.729			−0.724880			−0.362440	−	0.932007i	$-0.618056\pi$
$797$	−577.729			−0.724880			−0.362440	+	0.932007i	$0.618056\pi$
$798$		0			0
$799$	485.168			0.607220
$800$		0			0
$801$	1190.45	+	687.309i	1.48621	+	0.858063i
$802$		0			0
$803$	107.666	+	186.484i	0.134080	+	0.232234i
$804$		0			0
$805$	106.977	+	10.4396i	0.132891	+	0.0129685i
$806$		0			0
$807$	−12.9555	−	22.4396i	−0.0160539	−	0.0278062i
$808$		0			0
$809$	41.4824	−	71.8496i	0.0512761	−	0.0888128i	−0.839248	−	0.543749i	$-0.817004\pi$
$809$	41.4824	−	71.8496i	0.0512761	−	0.0888128i	0.890524	+	0.454936i	$0.150338\pi$
$810$		0			0
$811$	−525.164			−0.647552			−0.323776	−	0.946134i	$-0.604952\pi$
$811$	−525.164			−0.647552			−0.323776	+	0.946134i	$0.604952\pi$
$812$		0			0
$813$			64.9150i			0.0798462i
$814$		0			0
$815$	493.944	+	285.178i	0.606066	+	0.349912i
$816$		0			0
$817$	535.429	−	309.130i	0.655360	−	0.378372i
$818$		0			0
$819$	−660.567	+	923.565i	−0.806553	+	1.12767i
$820$		0			0
$821$	506.369	−	292.352i	0.616771	−	0.356093i	−0.158840	−	0.987304i	$-0.550775\pi$
$821$	506.369	−	292.352i	0.616771	−	0.356093i	0.775611	+	0.631211i	$0.217442\pi$
$822$		0			0
$823$	590.484	−	1022.75i	0.717478	−	1.24271i	−0.244518	−	0.969645i	$-0.578630\pi$
$823$	590.484	−	1022.75i	0.717478	−	1.24271i	0.961996	−	0.273063i	$-0.0880368\pi$
$824$		0			0
$825$		−	24.4405i		−	0.0296248i
$826$		0			0
$827$			336.806i			0.407262i	0.979048	+	0.203631i	$0.0652743\pi$
$827$			336.806i			0.407262i	−0.979048	+	0.203631i	$0.934726\pi$
$828$		0			0
$829$	−184.145	+	318.949i	−0.222130	+	0.384740i	−0.955454	−	0.295139i	$-0.904634\pi$
$829$	−184.145	+	318.949i	−0.222130	+	0.384740i	0.733325	+	0.679878i	$0.237967\pi$
$830$		0			0
$831$	−43.1479	+	24.9114i	−0.0519228	+	0.0299777i
$832$		0			0
$833$	442.378	−	151.051i	0.531066	−	0.181334i
$834$		0			0
$835$	−441.692	+	255.011i	−0.528972	+	0.305402i
$836$		0			0
$837$	−128.264	−	74.0530i	−0.153242	−	0.0884743i
$838$		0			0
$839$		−	709.889i		−	0.846113i	−0.906103	−	0.423056i	$-0.860957\pi$
$839$		−	709.889i		−	0.846113i	0.906103	−	0.423056i	$-0.139043\pi$
$840$		0			0
$841$	36.5402			0.0434485
$842$		0			0
$843$	8.90098	−	15.4169i	0.0105587	−	0.0182882i
$844$		0			0
$845$	−286.685	−	496.553i	−0.339272	−	0.587637i
$846$		0			0
$847$	−239.695	+	335.128i	−0.282993	+	0.395664i
$848$		0			0
$849$	−37.6073	−	65.1377i	−0.0442960	−	0.0767229i
$850$		0			0
$851$	111.347	+	64.2860i	0.130842	+	0.0755417i
$852$		0			0
$853$	−1136.65			−1.33253			−0.666267	−	0.745713i	$-0.732109\pi$
$853$	−1136.65			−1.33253			−0.666267	+	0.745713i	$0.732109\pi$
$854$		0			0
$855$	−792.143			−0.926483
$856$		0			0
$857$	578.645	+	334.081i	0.675198	+	0.389826i	0.798043	−	0.602600i	$-0.205869\pi$
$857$	578.645	+	334.081i	0.675198	+	0.389826i	−0.122845	+	0.992426i	$0.539202\pi$
$858$		0			0
$859$	100.378	+	173.859i	0.116854	+	0.202397i	0.918519	−	0.395376i	$-0.129386\pi$
$859$	100.378	+	173.859i	0.116854	+	0.202397i	−0.801665	+	0.597773i	$0.796052\pi$
$860$		0			0
$861$	7.79316	−	79.8582i	0.00905129	−	0.0927506i
$862$		0			0
$863$	21.7855	+	37.7337i	0.0252440	+	0.0437238i	0.878371	−	0.477979i	$-0.158630\pi$
$863$	21.7855	+	37.7337i	0.0252440	+	0.0437238i	−0.853127	+	0.521703i	$0.825297\pi$
$864$		0			0
$865$	−349.641	+	605.596i	−0.404209	+	0.700111i
$866$		0			0
$867$	50.1422			0.0578342
$868$		0			0
$869$			812.533i			0.935020i
$870$		0			0
$871$	−1972.73	−	1138.95i	−2.26490	−	1.30764i
$872$		0			0
$873$	−364.056	+	210.188i	−0.417017	+	0.240765i
$874$		0			0
$875$	385.052	+	847.808i	0.440059	+	0.968923i
$876$		0			0
$877$	129.242	−	74.6180i	0.147368	−	0.0850832i	−0.424503	−	0.905427i	$-0.639551\pi$
$877$	129.242	−	74.6180i	0.147368	−	0.0850832i	0.571871	+	0.820343i	$0.306218\pi$
$878$		0			0
$879$	17.1658	−	29.7321i	0.0195288	−	0.0338249i
$880$		0			0
$881$			865.257i			0.982130i	0.871123	+	0.491065i	$0.163392\pi$
$881$			865.257i			0.982130i	−0.871123	+	0.491065i	$0.836608\pi$
$882$		0			0
$883$		−	1476.24i		−	1.67184i	−0.548850	−	0.835921i	$-0.684934\pi$
$883$		−	1476.24i		−	1.67184i	0.548850	−	0.835921i	$-0.315066\pi$
$884$		0			0
$885$	33.4736	−	57.9779i	0.0378233	−	0.0655118i
$886$		0			0
$887$	518.166	−	299.163i	0.584178	−	0.337275i	−0.178614	−	0.983919i	$-0.557161\pi$
$887$	518.166	−	299.163i	0.584178	−	0.337275i	0.762792	+	0.646644i	$0.223828\pi$
$888$		0			0
$889$	−166.774	−	367.203i	−0.187597	−	0.413051i
$890$		0			0
$891$	541.172	−	312.446i	0.607376	−	0.350669i
$892$		0			0
$893$	1093.10	+	631.104i	1.22408	+	0.706723i
$894$		0			0
$895$		−	534.006i		−	0.596655i
$896$		0			0
$897$	−19.7639			−0.0220333
$898$		0			0
$899$	462.395	−	800.891i	0.514343	−	0.890869i
$900$		0			0
$901$	−299.589	−	518.904i	−0.332508	−	0.575920i
$902$		0			0
$903$	−4.28926	+	43.9530i	−0.00475001	+	0.0486744i
$904$		0			0
$905$	163.051	+	282.412i	0.180167	+	0.312058i
$906$		0			0
$907$	1463.00	+	844.666i	1.61301	+	0.931274i	0.988667	+	0.150128i	$0.0479687\pi$
$907$	1463.00	+	844.666i	1.61301	+	0.931274i	0.624348	+	0.781146i	$0.285365\pi$
$908$		0			0
$909$	1334.53			1.46813
$910$		0			0
$911$	813.339			0.892798			0.446399	−	0.894834i	$-0.352706\pi$
$911$	813.339			0.892798			0.446399	+	0.894834i	$0.352706\pi$
$912$		0			0
$913$	352.052	+	203.257i	0.385599	+	0.222626i
$914$		0			0
$915$	22.8852	+	39.6382i	0.0250111	+	0.0433205i
$916$		0			0
$917$	−506.178	+	707.708i	−0.551993	+	0.771764i
$918$		0			0
$919$	751.489	+	1301.62i	0.817724	+	1.41634i	0.907355	+	0.420365i	$0.138098\pi$
$919$	751.489	+	1301.62i	0.817724	+	1.41634i	−0.0896310	+	0.995975i	$0.528569\pi$
$920$		0			0
$921$	−9.64971	+	16.7138i	−0.0104774	+	0.0181474i
$922$		0			0
$923$	−96.9043			−0.104988
$924$		0			0
$925$			366.139i			0.395826i
$926$		0			0
$927$	153.560	+	88.6581i	0.165653	+	0.0956398i
$928$		0			0
$929$	−1301.71	+	751.543i	−1.40120	+	0.808981i	−0.994515	−	0.104589i	$-0.966647\pi$
$929$	−1301.71	+	751.543i	−1.40120	+	0.808981i	−0.406681	+	0.913570i	$0.633314\pi$
$930$		0			0
$931$	1193.18	+	235.118i	1.28161	+	0.252543i
$932$		0			0
$933$	−43.4471	+	25.0842i	−0.0465671	+	0.0268855i
$934$		0			0
$935$	134.302	−	232.618i	0.143638	−	0.248789i
$936$		0			0
$937$		−	419.349i		−	0.447545i	−0.974641	−	0.223772i	$-0.928163\pi$
$937$		−	419.349i		−	0.447545i	0.974641	−	0.223772i	$-0.0718372\pi$
$938$		0			0
$939$		−	14.0279i		−	0.0149392i
$940$		0			0
$941$	261.680	−	453.243i	0.278087	−	0.481661i	−0.692822	−	0.721108i	$-0.743633\pi$
$941$	261.680	−	453.243i	0.278087	−	0.481661i	0.970909	+	0.239448i	$0.0769664\pi$
$942$		0			0
$943$	−168.507	+	97.2874i	−0.178692	+	0.103168i
$944$		0			0
$945$	66.0695	−	92.3744i	0.0699148	−	0.0977507i
$946$		0			0
$947$	311.949	−	180.104i	0.329408	−	0.190184i	−0.326170	−	0.945311i	$-0.605758\pi$
$947$	311.949	−	180.104i	0.329408	−	0.190184i	0.655578	+	0.755127i	$0.272425\pi$
$948$		0			0
$949$	429.441	+	247.938i	0.452520	+	0.261262i
$950$		0			0
$951$			75.7642i			0.0796679i
$952$		0			0
$953$	1242.81			1.30410			0.652051	−	0.758175i	$-0.273909\pi$
$953$	1242.81			1.30410			0.652051	+	0.758175i	$0.273909\pi$
$954$		0			0
$955$	49.6976	−	86.0789i	0.0520394	−	0.0901349i
$956$		0			0
$957$	−28.3116	−	49.0372i	−0.0295838	−	0.0512406i
$958$		0			0
$959$	−1180.76	−	115.227i	−1.23124	−	0.120153i
$960$		0			0
$961$	51.0585	+	88.4359i	0.0531306	+	0.0920248i
$962$		0			0
$963$	70.7610	+	40.8539i	0.0734798	+	0.0424236i
$964$		0			0
$965$	865.742			0.897142
$966$		0			0
$967$	−81.8793			−0.0846735			−0.0423368	−	0.999103i	$-0.513480\pi$
$967$	−81.8793			−0.0846735			−0.0423368	+	0.999103i	$0.513480\pi$
$968$		0			0
$969$	−51.9298	−	29.9817i	−0.0535912	−	0.0309409i
$970$		0			0
$971$	−409.052	−	708.499i	−0.421269	−	0.729660i	0.574795	−	0.818298i	$-0.305082\pi$
$971$	−409.052	−	708.499i	−0.421269	−	0.729660i	−0.996064	+	0.0886380i	$0.971749\pi$
$972$		0			0
$973$	771.419	+	1698.51i	0.792825	+	1.74564i
$974$		0			0
$975$	−28.1412	−	48.7419i	−0.0288627	−	0.0499917i
$976$		0			0
$977$	−448.155	+	776.227i	−0.458705	+	0.794500i	−0.998893	−	0.0470441i	$-0.985020\pi$
$977$	−448.155	+	776.227i	−0.458705	+	0.794500i	0.540188	+	0.841544i	$0.318353\pi$
$978$		0			0
$979$	−1212.63			−1.23864
$980$		0			0
$981$			1065.14i			1.08577i
$982$		0			0
$983$	−852.404	−	492.136i	−0.867146	−	0.500647i	−0.000746983	−	1.00000i	$-0.500238\pi$
$983$	−852.404	−	492.136i	−0.867146	−	0.500647i	−0.866399	+	0.499353i	$0.833571\pi$
$984$		0			0
$985$	−292.947	+	169.133i	−0.297408	+	0.171708i
$986$		0			0
$987$	−82.0887	+	37.2825i	−0.0831699	+	0.0377736i
$988$		0			0
$989$	92.7440	−	53.5458i	0.0937756	−	0.0541414i
$990$		0			0
$991$	−612.037	+	1060.08i	−0.617596	+	1.06971i	0.372327	+	0.928101i	$0.378560\pi$
$991$	−612.037	+	1060.08i	−0.617596	+	1.06971i	−0.989923	+	0.141606i	$0.954774\pi$
$992$		0			0
$993$			95.0667i			0.0957368i
$994$		0			0
$995$			1104.24i			1.10979i
$996$		0			0
$997$	186.825	−	323.590i	0.187387	−	0.324563i	−0.756991	−	0.653425i	$-0.773332\pi$
$997$	186.825	−	323.590i	0.187387	−	0.324563i	0.944378	+	0.328861i	$0.106665\pi$
$998$		0			0
$999$	117.650	−	67.9254i	0.117768	−	0.0679934i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.3.n.a.17.7		28
4.3	odd	2		56.3.j.a.45.12	yes	28
7.3	odd	6		1568.3.h.a.881.14		28
7.4	even	3		1568.3.h.a.881.16		28
7.5	odd	6	inner	224.3.n.a.145.8		28
8.3	odd	2		56.3.j.a.45.2	yes	28
8.5	even	2	inner	224.3.n.a.17.8		28
28.3	even	6		392.3.h.a.293.16		28
28.11	odd	6		392.3.h.a.293.15		28
28.19	even	6		56.3.j.a.5.2	✓	28
28.23	odd	6		392.3.j.e.117.2		28
28.27	even	2		392.3.j.e.325.12		28
56.3	even	6		392.3.h.a.293.13		28
56.5	odd	6	inner	224.3.n.a.145.7		28
56.11	odd	6		392.3.h.a.293.14		28
56.19	even	6		56.3.j.a.5.12	yes	28
56.27	even	2		392.3.j.e.325.2		28
56.45	odd	6		1568.3.h.a.881.15		28
56.51	odd	6		392.3.j.e.117.12		28
56.53	even	6		1568.3.h.a.881.13		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.j.a.5.2	✓	28	28.19	even	6
56.3.j.a.5.12	yes	28	56.19	even	6
56.3.j.a.45.2	yes	28	8.3	odd	2
56.3.j.a.45.12	yes	28	4.3	odd	2
224.3.n.a.17.7		28	1.1	even	1	trivial
224.3.n.a.17.8		28	8.5	even	2	inner
224.3.n.a.145.7		28	56.5	odd	6	inner
224.3.n.a.145.8		28	7.5	odd	6	inner
392.3.h.a.293.13		28	56.3	even	6
392.3.h.a.293.14		28	56.11	odd	6
392.3.h.a.293.15		28	28.11	odd	6
392.3.h.a.293.16		28	28.3	even	6
392.3.j.e.117.2		28	28.23	odd	6
392.3.j.e.117.12		28	56.51	odd	6
392.3.j.e.325.2		28	56.27	even	2
392.3.j.e.325.12		28	28.27	even	2
1568.3.h.a.881.13		28	56.53	even	6
1568.3.h.a.881.14		28	7.3	odd	6
1568.3.h.a.881.15		28	56.45	odd	6
1568.3.h.a.881.16		28	7.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	224.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.126628 + 0.219326i) q^{3} +(-1.78589 - 3.09325i) q^{5} +(-2.89466 - 6.37346i) q^{7} +(4.46793 + 7.73868i) q^{9} +O(q^{10})\)	\(q+(-0.126628 + 0.219326i) q^{3} +(-1.78589 - 3.09325i) q^{5} +(-2.89466 - 6.37346i) q^{7} +(4.46793 + 7.73868i) q^{9} +(-6.82675 - 3.94142i) q^{11} -18.1529 q^{13} +0.904575 q^{15} +(-8.26180 - 4.76995i) q^{17} +(-12.4094 - 21.4938i) q^{19} +(1.76441 + 0.172184i) q^{21} +(-2.14949 - 3.72303i) q^{23} +(6.12120 - 10.6022i) q^{25} -4.54237 q^{27} -28.3630i q^{29} +(28.2372 + 16.3027i) q^{31} +(1.72891 - 0.998189i) q^{33} +(-14.5452 + 20.3362i) q^{35} +(-25.9006 + 14.9537i) q^{37} +(2.29867 - 3.98141i) q^{39} -45.2606i q^{41} +24.9109i q^{43} +(15.9585 - 27.6409i) q^{45} +(-44.0432 + 25.4284i) q^{47} +(-32.2419 + 36.8979i) q^{49} +(2.09235 - 1.20802i) q^{51} +(54.3930 + 31.4038i) q^{53} +28.1558i q^{55} +6.28554 q^{57} +(37.0048 - 64.0942i) q^{59} +(25.2994 + 43.8198i) q^{61} +(36.3890 - 50.8770i) q^{63} +(32.4191 + 56.1515i) q^{65} +(108.673 + 62.7422i) q^{67} +1.08875 q^{69} +5.33822 q^{71} +(-23.6569 - 13.6583i) q^{73} +(1.55023 + 2.68508i) q^{75} +(-5.35941 + 54.9191i) q^{77} +(-51.5380 - 89.2664i) q^{79} +(-39.6362 + 68.6519i) q^{81} -51.5695 q^{83} +34.0744i q^{85} +(6.22075 + 3.59155i) q^{87} +(133.222 - 76.9158i) q^{89} +(52.5464 + 115.697i) q^{91} +(-7.15123 + 4.12877i) q^{93} +(-44.3238 + 76.7711i) q^{95} +47.0436i q^{97} -70.4400i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{7} - 32 q^{9}+O(q^{10}) \) 28 * q + 4 * q^7 - 32 * q^9	\( 28 q + 4 q^{7} - 32 q^{9} - 28 q^{15} - 6 q^{17} - 30 q^{23} - 32 q^{25} + 6 q^{31} - 6 q^{33} + 20 q^{39} + 294 q^{47} - 20 q^{49} + 124 q^{57} - 432 q^{63} - 52 q^{65} + 136 q^{71} + 234 q^{73} + 162 q^{79} - 18 q^{81} - 48 q^{87} - 150 q^{89} - 290 q^{95}+O(q^{100}) \) 28 * q + 4 * q^7 - 32 * q^9 - 28 * q^15 - 6 * q^17 - 30 * q^23 - 32 * q^25 + 6 * q^31 - 6 * q^33 + 20 * q^39 + 294 * q^47 - 20 * q^49 + 124 * q^57 - 432 * q^63 - 52 * q^65 + 136 * q^71 + 234 * q^73 + 162 * q^79 - 18 * q^81 - 48 * q^87 - 150 * q^89 - 290 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more