LMFDB - Embedded newform 448.2.z.a.47.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [448,2,Mod(47,448)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(448, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 10]))

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

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

chi := DirichletCharacter("448.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	448.z (of order $12$, degree $4$, 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:	$3.57729801055$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			47.11
Character	$\chi$	$=$	448.47
Dual form			448.2.z.a.143.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.388227 - 1.44888i) q^{3} +(2.81809 - 0.755106i) q^{5} +(1.47726 - 2.19493i) q^{7} +(0.649537 + 0.375010i) q^{9} +O(q^{10})$	\(q+(0.388227 - 1.44888i) q^{3} +(2.81809 - 0.755106i) q^{5} +(1.47726 - 2.19493i) q^{7} +(0.649537 + 0.375010i) q^{9} +(-0.0165920 + 0.0619222i) q^{11} +(-3.62997 + 3.62997i) q^{13} -4.37624i q^{15} +(3.26044 - 1.88242i) q^{17} +(-2.13834 + 0.572967i) q^{19} +(-2.60668 - 2.99251i) q^{21} +(-3.80570 + 6.59167i) q^{23} +(3.04134 - 1.75592i) q^{25} +(3.97748 - 3.97748i) q^{27} +(-4.74233 - 4.74233i) q^{29} +(0.329500 + 0.570711i) q^{31} +(0.0832764 + 0.0480797i) q^{33} +(2.50566 - 7.30100i) q^{35} +(-1.08717 - 4.05737i) q^{37} +(3.85014 + 6.66865i) q^{39} +7.67610 q^{41} +(2.54426 + 2.54426i) q^{43} +(2.11363 + 0.566345i) q^{45} +(-2.62703 + 4.55014i) q^{47} +(-2.63540 - 6.48496i) q^{49} +(-1.46161 - 5.45480i) q^{51} +(-10.1607 - 2.72255i) q^{53} +0.187031i q^{55} +3.32064i q^{57} +(-2.43435 - 0.652282i) q^{59} +(1.84853 + 6.89881i) q^{61} +(1.78266 - 0.871698i) q^{63} +(-7.48858 + 12.9706i) q^{65} +(-5.98832 - 1.60456i) q^{67} +(8.07307 + 8.07307i) q^{69} -1.08883 q^{71} +(-0.0232448 - 0.0402613i) q^{73} +(-1.36339 - 5.08824i) q^{75} +(0.111404 + 0.127893i) q^{77} +(15.2466 + 8.80264i) q^{79} +(-3.09370 - 5.35845i) q^{81} +(5.07720 + 5.07720i) q^{83} +(7.76681 - 7.76681i) q^{85} +(-8.71217 + 5.02997i) q^{87} +(-4.47814 + 7.75636i) q^{89} +(2.60510 + 13.3299i) q^{91} +(0.954814 - 0.255842i) q^{93} +(-5.59340 + 3.22935i) q^{95} +1.85612i q^{97} +(-0.0339986 + 0.0339986i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 6 q^{3} - 6 q^{5} + 8 q^{7}+O(q^{10}) $ 56 * q + 6 * q^3 - 6 * q^5 + 8 * q^7	$ 56 q + 6 q^{3} - 6 q^{5} + 8 q^{7} - 2 q^{11} - 12 q^{17} + 6 q^{19} - 10 q^{21} + 12 q^{23} - 24 q^{29} - 12 q^{33} + 2 q^{35} + 6 q^{37} + 4 q^{39} + 12 q^{45} - 8 q^{49} + 34 q^{51} + 6 q^{53} - 42 q^{59} - 6 q^{61} - 4 q^{65} - 6 q^{67} + 80 q^{71} - 24 q^{75} + 10 q^{77} - 8 q^{81} - 28 q^{85} + 12 q^{87} - 16 q^{91} + 10 q^{93} + 16 q^{99}+O(q^{100}) $ 56 * q + 6 * q^3 - 6 * q^5 + 8 * q^7 - 2 * q^11 - 12 * q^17 + 6 * q^19 - 10 * q^21 + 12 * q^23 - 24 * q^29 - 12 * q^33 + 2 * q^35 + 6 * q^37 + 4 * q^39 + 12 * q^45 - 8 * q^49 + 34 * q^51 + 6 * q^53 - 42 * q^59 - 6 * q^61 - 4 * q^65 - 6 * q^67 + 80 * q^71 - 24 * q^75 + 10 * q^77 - 8 * q^81 - 28 * q^85 + 12 * q^87 - 16 * q^91 + 10 * q^93 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.388227	−	1.44888i	0.224143	−	0.836512i	−0.758603	−	0.651553i	$-0.774118\pi$
$3$	0.388227	−	1.44888i	0.224143	−	0.836512i	0.982746	−	0.184960i	$-0.0592154\pi$
$4$		0			0
$5$	2.81809	−	0.755106i	1.26029	−	0.337694i	0.433987	−	0.900919i	$-0.357106\pi$
$5$	2.81809	−	0.755106i	1.26029	−	0.337694i	0.826303	+	0.563225i	$0.190440\pi$
$6$		0			0
$7$	1.47726	−	2.19493i	0.558352	−	0.829604i
$7$	1.47726	−	2.19493i	0.558352	−	0.829604i
$8$		0			0
$9$	0.649537	+	0.375010i	0.216512	+	0.125003i
$10$		0			0
$11$	−0.0165920	+	0.0619222i	−0.00500267	+	0.0186702i	−0.968382	−	0.249472i	$-0.919743\pi$
$11$	−0.0165920	+	0.0619222i	−0.00500267	+	0.0186702i	0.963379	+	0.268142i	$0.0864097\pi$
$12$		0			0
$13$	−3.62997	+	3.62997i	−1.00677	+	1.00677i	−0.00679491	+	0.999977i	$0.502163\pi$
$13$	−3.62997	+	3.62997i	−1.00677	+	1.00677i	−0.999977	+	0.00679491i	$0.997837\pi$
$14$		0			0
$15$		−	4.37624i		−	1.12994i
$16$		0			0
$17$	3.26044	−	1.88242i	0.790773	−	0.456553i	−0.0494614	−	0.998776i	$-0.515750\pi$
$17$	3.26044	−	1.88242i	0.790773	−	0.456553i	0.840235	+	0.542223i	$0.182417\pi$
$18$		0			0
$19$	−2.13834	+	0.572967i	−0.490569	+	0.131448i	−0.495620	−	0.868540i	$-0.665059\pi$
$19$	−2.13834	+	0.572967i	−0.490569	+	0.131448i	0.00505063	+	0.999987i	$0.498392\pi$
$20$		0			0
$21$	−2.60668	−	2.99251i	−0.568824	−	0.653018i
$22$		0			0
$23$	−3.80570	+	6.59167i	−0.793543	+	1.37446i	0.130217	+	0.991486i	$0.458433\pi$
$23$	−3.80570	+	6.59167i	−0.793543	+	1.37446i	−0.923760	+	0.382972i	$0.874901\pi$
$24$		0			0
$25$	3.04134	−	1.75592i	0.608269	−	0.351184i
$26$		0			0
$27$	3.97748	−	3.97748i	0.765466	−	0.765466i
$28$		0			0
$29$	−4.74233	−	4.74233i	−0.880628	−	0.880628i	0.112971	−	0.993598i	$-0.463963\pi$
$29$	−4.74233	−	4.74233i	−0.880628	−	0.880628i	−0.993598	+	0.112971i	$0.963963\pi$
$30$		0			0
$31$	0.329500	+	0.570711i	0.0591800	+	0.102503i	0.894098	−	0.447872i	$-0.147818\pi$
$31$	0.329500	+	0.570711i	0.0591800	+	0.102503i	−0.834918	+	0.550375i	$0.814485\pi$
$32$		0			0
$33$	0.0832764	+	0.0480797i	0.0144966	+	0.00836960i
$34$		0			0
$35$	2.50566	−	7.30100i	0.423533	−	1.23409i
$36$		0			0
$37$	−1.08717	−	4.05737i	−0.178729	−	0.667027i	−0.995886	−	0.0906119i	$-0.971118\pi$
$37$	−1.08717	−	4.05737i	−0.178729	−	0.667027i	0.817157	−	0.576415i	$-0.195549\pi$
$38$		0			0
$39$	3.85014	+	6.66865i	0.616516	+	1.06784i
$40$		0			0
$41$	7.67610			1.19881			0.599403	−	0.800447i	$-0.295405\pi$
$41$	7.67610			1.19881			0.599403	+	0.800447i	$0.295405\pi$
$42$		0			0
$43$	2.54426	+	2.54426i	0.387995	+	0.387995i	0.873972	−	0.485976i	$-0.161536\pi$
$43$	2.54426	+	2.54426i	0.387995	+	0.387995i	−0.485976	+	0.873972i	$0.661536\pi$
$44$		0			0
$45$	2.11363	+	0.566345i	0.315081	+	0.0844258i
$46$		0			0
$47$	−2.62703	+	4.55014i	−0.383191	+	0.663707i	−0.991516	−	0.129981i	$-0.958508\pi$
$47$	−2.62703	+	4.55014i	−0.383191	+	0.663707i	0.608325	+	0.793688i	$0.291842\pi$
$48$		0			0
$49$	−2.63540	−	6.48496i	−0.376486	−	0.926422i
$50$		0			0
$51$	−1.46161	−	5.45480i	−0.204666	−	0.763825i
$52$		0			0
$53$	−10.1607	−	2.72255i	−1.39568	−	0.373970i	−0.518886	−	0.854843i	$-0.673653\pi$
$53$	−10.1607	−	2.72255i	−1.39568	−	0.373970i	−0.876790	+	0.480873i	$0.840320\pi$
$54$		0			0
$55$			0.187031i			0.0252193i
$56$		0			0
$57$			3.32064i			0.439830i
$58$		0			0
$59$	−2.43435	−	0.652282i	−0.316925	−	0.0849199i	0.0968497	−	0.995299i	$-0.469123\pi$
$59$	−2.43435	−	0.652282i	−0.316925	−	0.0849199i	−0.413775	+	0.910379i	$0.635790\pi$
$60$		0			0
$61$	1.84853	+	6.89881i	0.236680	+	0.883302i	0.977384	+	0.211471i	$0.0678253\pi$
$61$	1.84853	+	6.89881i	0.236680	+	0.883302i	−0.740704	+	0.671831i	$0.765508\pi$
$62$		0			0
$63$	1.78266	−	0.871698i	0.224594	−	0.109824i
$64$		0			0
$65$	−7.48858	+	12.9706i	−0.928844	+	1.60881i
$66$		0			0
$67$	−5.98832	−	1.60456i	−0.731589	−	0.196029i	−0.126252	−	0.991998i	$-0.540295\pi$
$67$	−5.98832	−	1.60456i	−0.731589	−	0.196029i	−0.605337	+	0.795969i	$0.706962\pi$
$68$		0			0
$69$	8.07307	+	8.07307i	0.971884	+	0.971884i
$70$		0			0
$71$	−1.08883			−0.129221			−0.0646104	−	0.997911i	$-0.520580\pi$
$71$	−1.08883			−0.129221			−0.0646104	+	0.997911i	$0.520580\pi$
$72$		0			0
$73$	−0.0232448	−	0.0402613i	−0.00272060	−	0.00471222i	0.864662	−	0.502354i	$-0.167533\pi$
$73$	−0.0232448	−	0.0402613i	−0.00272060	−	0.00471222i	−0.867383	+	0.497642i	$0.834199\pi$
$74$		0			0
$75$	−1.36339	−	5.08824i	−0.157431	−	0.587540i
$76$		0			0
$77$	0.111404	+	0.127893i	0.0126957	+	0.0145748i
$78$		0			0
$79$	15.2466	+	8.80264i	1.71538	+	0.990374i	0.926897	+	0.375316i	$0.122466\pi$
$79$	15.2466	+	8.80264i	1.71538	+	0.990374i	0.788482	+	0.615058i	$0.210867\pi$
$80$		0			0
$81$	−3.09370	−	5.35845i	−0.343745	−	0.595383i
$82$		0			0
$83$	5.07720	+	5.07720i	0.557295	+	0.557295i	0.928536	−	0.371241i	$-0.121068\pi$
$83$	5.07720	+	5.07720i	0.557295	+	0.557295i	−0.371241	+	0.928536i	$0.621068\pi$
$84$		0			0
$85$	7.76681	−	7.76681i	0.842429	−	0.842429i
$86$		0			0
$87$	−8.71217	+	5.02997i	−0.934042	+	0.539270i
$88$		0			0
$89$	−4.47814	+	7.75636i	−0.474681	+	0.822172i	−0.999580	−	0.0289926i	$-0.990770\pi$
$89$	−4.47814	+	7.75636i	−0.474681	+	0.822172i	0.524898	+	0.851165i	$0.324103\pi$
$90$		0			0
$91$	2.60510	+	13.3299i	0.273089	+	1.39736i
$92$		0			0
$93$	0.954814	−	0.255842i	0.0990096	−	0.0265295i
$94$		0			0
$95$	−5.59340	+	3.22935i	−0.573870	+	0.331324i
$96$		0			0
$97$			1.85612i			0.188460i	0.995550	+	0.0942302i	$0.0300390\pi$
$97$			1.85612i			0.188460i	−0.995550	+	0.0942302i	$0.969961\pi$
$98$		0			0
$99$	−0.0339986	+	0.0339986i	−0.00341698	+	0.00341698i
$100$		0			0
$101$	−4.53028	+	16.9072i	−0.450780	+	1.68233i	0.249427	+	0.968393i	$0.419758\pi$
$101$	−4.53028	+	16.9072i	−0.450780	+	1.68233i	−0.700207	+	0.713940i	$0.746909\pi$
$102$		0			0
$103$	−6.82381	−	3.93973i	−0.672370	−	0.388193i	0.124604	−	0.992207i	$-0.460234\pi$
$103$	−6.82381	−	3.93973i	−0.672370	−	0.388193i	−0.796974	+	0.604014i	$0.793567\pi$
$104$		0			0
$105$	−9.60552	−	6.46484i	−0.937403	−	0.630904i
$106$		0			0
$107$	−8.07325	+	2.16322i	−0.780470	+	0.209126i	−0.626992	−	0.779026i	$-0.715714\pi$
$107$	−8.07325	+	2.16322i	−0.780470	+	0.209126i	−0.153478	+	0.988152i	$0.549048\pi$
$108$		0			0
$109$	2.09025	−	7.80091i	0.200210	−	0.747192i	−0.790647	−	0.612272i	$-0.790256\pi$
$109$	2.09025	−	7.80091i	0.200210	−	0.747192i	0.990857	−	0.134920i	$-0.0430777\pi$
$110$		0			0
$111$	−6.30072			−0.598037
$112$		0			0
$113$	12.8566			1.20945			0.604725	−	0.796434i	$-0.293283\pi$
$113$	12.8566			1.20945			0.604725	+	0.796434i	$0.293283\pi$
$114$		0			0
$115$	−5.74741	+	21.4496i	−0.535949	+	2.00019i
$116$		0			0
$117$	−3.71907	+	0.996523i	−0.343829	+	0.0921286i
$118$		0			0
$119$	0.684755	−	9.93725i	0.0627714	−	0.910946i
$120$		0			0
$121$	9.52272	+	5.49795i	0.865702	+	0.499813i
$122$		0			0
$123$	2.98007	−	11.1218i	0.268704	−	1.00282i
$124$		0			0
$125$	−3.07005	+	3.07005i	−0.274594	+	0.274594i
$126$		0			0
$127$		−	15.3580i		−	1.36280i	−0.731912	−	0.681399i	$-0.761372\pi$
$127$		−	15.3580i		−	1.36280i	0.731912	−	0.681399i	$-0.238628\pi$
$128$		0			0
$129$	4.67408	−	2.69858i	0.411529	−	0.237597i
$130$		0			0
$131$	0.328184	−	0.0879366i	0.0286736	−	0.00768306i	−0.244454	−	0.969661i	$-0.578609\pi$
$131$	0.328184	−	0.0879366i	0.0286736	−	0.00768306i	0.273127	+	0.961978i	$0.411942\pi$
$132$		0			0
$133$	−1.90127	+	5.53992i	−0.164861	+	0.480372i
$134$		0			0
$135$	8.20549	−	14.2123i	0.706216	−	1.22320i
$136$		0			0
$137$	−7.82357	+	4.51694i	−0.668412	+	0.385908i	−0.795475	−	0.605987i	$-0.792778\pi$
$137$	−7.82357	+	4.51694i	−0.668412	+	0.385908i	0.127062	+	0.991895i	$0.459445\pi$
$138$		0			0
$139$	3.85776	−	3.85776i	0.327211	−	0.327211i	−0.524314	−	0.851525i	$-0.675678\pi$
$139$	3.85776	−	3.85776i	0.327211	−	0.327211i	0.851525	+	0.524314i	$0.175678\pi$
$140$		0			0
$141$	5.57274	+	5.57274i	0.469309	+	0.469309i
$142$		0			0
$143$	−0.164547	−	0.285004i	−0.0137601	−	0.0238332i
$144$		0			0
$145$	−16.9453	−	9.78336i	−1.40723	−	0.812464i
$146$		0			0
$147$	−10.4191	+	1.30076i	−0.859350	+	0.107284i
$148$		0			0
$149$	−1.65112	−	6.16207i	−0.135265	−	0.504816i	−0.999997	−	0.00258197i	$-0.999178\pi$
$149$	−1.65112	−	6.16207i	−0.135265	−	0.504816i	0.864732	−	0.502234i	$-0.167489\pi$
$150$		0			0
$151$	−1.70746	−	2.95741i	−0.138951	−	0.240671i	0.788149	−	0.615485i	$-0.211040\pi$
$151$	−1.70746	−	2.95741i	−0.138951	−	0.240671i	−0.927100	+	0.374814i	$0.877707\pi$
$152$		0			0
$153$	2.82370			0.228283
$154$		0			0
$155$	1.35951	+	1.35951i	0.109198	+	0.109198i
$156$		0			0
$157$	−4.54025	−	1.21656i	−0.362352	−	0.0970918i	0.0730497	−	0.997328i	$-0.476727\pi$
$157$	−4.54025	−	1.21656i	−0.362352	−	0.0970918i	−0.435401	+	0.900236i	$0.643394\pi$
$158$		0			0
$159$	−7.88930	+	13.6647i	−0.625662	+	1.08368i
$160$		0			0
$161$	8.84621	+	18.0908i	0.697179	+	1.42576i
$162$		0			0
$163$	−0.420383	−	1.56889i	−0.0329269	−	0.122885i	0.947506	−	0.319737i	$-0.103595\pi$
$163$	−0.420383	−	1.56889i	−0.0329269	−	0.122885i	−0.980433	+	0.196852i	$0.936928\pi$
$164$		0			0
$165$	0.270986	+	0.0726105i	0.0210962	+	0.00565272i
$166$		0			0
$167$			7.81760i			0.604944i	0.953158	+	0.302472i	$0.0978118\pi$
$167$			7.81760i			0.604944i	−0.953158	+	0.302472i	$0.902188\pi$
$168$		0			0
$169$		−	13.3533i		−	1.02718i
$170$		0			0
$171$	−1.60380	−	0.429737i	−0.122646	−	0.0328628i
$172$		0			0
$173$	−1.07228	−	4.00179i	−0.0815237	−	0.304251i	0.913110	−	0.407714i	$-0.133674\pi$
$173$	−1.07228	−	4.00179i	−0.0815237	−	0.304251i	−0.994633	+	0.103464i	$0.967007\pi$
$174$		0			0
$175$	0.638740	−	9.26948i	0.0482842	−	0.700707i
$176$		0			0
$177$	−1.89016	+	3.27385i	−0.142073	+	0.246078i
$178$		0			0
$179$	10.7595	+	2.88301i	0.804205	+	0.215486i	0.637429	−	0.770509i	$-0.279998\pi$
$179$	10.7595	+	2.88301i	0.804205	+	0.215486i	0.166776	+	0.985995i	$0.446664\pi$
$180$		0			0
$181$	4.50721	+	4.50721i	0.335018	+	0.335018i	0.854489	−	0.519470i	$-0.173871\pi$
$181$	4.50721	+	4.50721i	0.335018	+	0.335018i	−0.519470	+	0.854489i	$0.673871\pi$
$182$		0			0
$183$	10.7132			0.791943
$184$		0			0
$185$	−6.12749	−	10.6131i	−0.450502	−	0.780292i
$186$		0			0
$187$	0.0624661	+	0.233127i	0.00456797	+	0.0170479i
$188$		0			0
$189$	−2.85450	−	14.6060i	−0.207634	−	1.06243i
$190$		0			0
$191$	−14.4515	−	8.34360i	−1.04568	−	0.603722i	−0.124241	−	0.992252i	$-0.539650\pi$
$191$	−14.4515	−	8.34360i	−1.04568	−	0.603722i	−0.921436	+	0.388530i	$0.872983\pi$
$192$		0			0
$193$	−1.36382	−	2.36220i	−0.0981697	−	0.170035i	0.812757	−	0.582602i	$-0.197965\pi$
$193$	−1.36382	−	2.36220i	−0.0981697	−	0.170035i	−0.910927	+	0.412567i	$0.864632\pi$
$194$		0			0
$195$	15.8856	+	15.8856i	1.13759	+	1.13759i
$196$		0			0
$197$	3.88713	−	3.88713i	0.276947	−	0.276947i	−0.554942	−	0.831889i	$-0.687260\pi$
$197$	3.88713	−	3.88713i	0.276947	−	0.276947i	0.831889	+	0.554942i	$0.187260\pi$
$198$		0			0
$199$	12.5878	−	7.26759i	0.892329	−	0.515186i	0.0176251	−	0.999845i	$-0.494389\pi$
$199$	12.5878	−	7.26759i	0.892329	−	0.515186i	0.874703	+	0.484659i	$0.161056\pi$
$200$		0			0
$201$	−4.64965	+	8.05343i	−0.327961	+	0.568045i
$202$		0			0
$203$	−17.4147	+	3.40341i	−1.22227	+	0.238872i
$204$		0			0
$205$	21.6320	−	5.79627i	1.51084	−	0.404829i
$206$		0			0
$207$	−4.94389	+	2.85435i	−0.343624	+	0.198391i
$208$		0			0
$209$		−	0.141917i		−	0.00981663i
$210$		0			0
$211$	18.5514	−	18.5514i	1.27713	−	1.27713i	0.334867	−	0.942265i	$-0.391308\pi$
$211$	18.5514	−	18.5514i	1.27713	−	1.27713i	0.942265	−	0.334867i	$-0.108692\pi$
$212$		0			0
$213$	−0.422714	+	1.57759i	−0.0289639	+	0.108095i
$214$		0			0
$215$	9.09114	+	5.24877i	0.620010	+	0.357963i
$216$		0			0
$217$	1.73943	+	0.119860i	0.118080	+	0.00813664i
$218$		0			0
$219$	−0.0673581	+	0.0180485i	−0.00455164	+	0.00121961i
$220$		0			0
$221$	−5.00219	+	18.6684i	−0.336483	+	1.25577i
$222$		0			0
$223$	22.7321			1.52225			0.761126	−	0.648604i	$-0.224647\pi$
$223$	22.7321			1.52225			0.761126	+	0.648604i	$0.224647\pi$
$224$		0			0
$225$	2.63395			0.175597
$226$		0			0
$227$	−0.466286	+	1.74020i	−0.0309485	+	0.115501i	−0.979672	−	0.200605i	$-0.935709\pi$
$227$	−0.466286	+	1.74020i	−0.0309485	+	0.115501i	0.948724	+	0.316107i	$0.102376\pi$
$228$		0			0
$229$	14.3174	−	3.83633i	0.946119	−	0.253512i	0.247404	−	0.968912i	$-0.420422\pi$
$229$	14.3174	−	3.83633i	0.946119	−	0.253512i	0.698715	+	0.715400i	$0.253756\pi$
$230$		0			0
$231$	0.228552	−	0.111759i	0.0150376	−	0.00735323i
$232$		0			0
$233$	−18.4936	−	10.6773i	−1.21156	−	0.699493i	−0.248460	−	0.968642i	$-0.579924\pi$
$233$	−18.4936	−	10.6773i	−1.21156	−	0.699493i	−0.963099	+	0.269149i	$0.913258\pi$
$234$		0			0
$235$	−3.96737	+	14.8064i	−0.258802	+	0.965864i
$236$		0			0
$237$	18.6731	−	18.6731i	1.21295	−	1.21295i
$238$		0			0
$239$			0.632980i			0.0409441i	0.999790	+	0.0204720i	$0.00651691\pi$
$239$			0.632980i			0.0409441i	−0.999790	+	0.0204720i	$0.993483\pi$
$240$		0			0
$241$	16.2105	−	9.35914i	1.04421	−	0.602875i	0.123188	−	0.992383i	$-0.460688\pi$
$241$	16.2105	−	9.35914i	1.04421	−	0.602875i	0.921023	+	0.389508i	$0.127355\pi$
$242$		0			0
$243$	7.33519	−	1.96546i	0.470553	−	0.126084i
$244$		0			0
$245$	−12.3236	−	16.2852i	−0.787329	−	1.04042i
$246$		0			0
$247$	5.68226	−	9.84196i	0.361553	−	0.626229i
$248$		0			0
$249$	9.32737	−	5.38516i	0.591098	−	0.341271i
$250$		0			0
$251$	−11.0434	+	11.0434i	−0.697054	+	0.697054i	−0.963774	−	0.266720i	$-0.914060\pi$
$251$	−11.0434	+	11.0434i	−0.697054	+	0.697054i	0.266720	+	0.963774i	$0.414060\pi$
$252$		0			0
$253$	−0.345026	−	0.345026i	−0.0216916	−	0.0216916i
$254$		0			0
$255$	−8.23791	−	14.2685i	−0.515878	−	0.893526i
$256$		0			0
$257$	−26.9179	−	15.5411i	−1.67909	−	0.969425i	−0.962240	−	0.272201i	$-0.912248\pi$
$257$	−26.9179	−	15.5411i	−1.67909	−	0.969425i	−0.716853	−	0.697224i	$-0.754418\pi$
$258$		0			0
$259$	−10.5117	−	3.60753i	−0.653162	−	0.224161i
$260$		0			0
$261$	−1.30189	−	4.85874i	−0.0805853	−	0.300748i
$262$		0			0
$263$	−6.47429	−	11.2138i	−0.399222	−	0.691473i	0.594408	−	0.804164i	$-0.297386\pi$
$263$	−6.47429	−	11.2138i	−0.399222	−	0.691473i	−0.993630	+	0.112691i	$0.964053\pi$
$264$		0			0
$265$	−30.6896			−1.88525
$266$		0			0
$267$	9.49952	+	9.49952i	0.581361	+	0.581361i
$268$		0			0
$269$	−1.48882	−	0.398929i	−0.0907751	−	0.0243231i	0.213146	−	0.977020i	$-0.431629\pi$
$269$	−1.48882	−	0.398929i	−0.0907751	−	0.0243231i	−0.303921	+	0.952697i	$0.598296\pi$
$270$		0			0
$271$	−5.33475	+	9.24005i	−0.324063	+	0.561293i	−0.981322	−	0.192371i	$-0.938382\pi$
$271$	−5.33475	+	9.24005i	−0.324063	+	0.561293i	0.657259	+	0.753664i	$0.271716\pi$
$272$		0			0
$273$	20.3249	+	1.40054i	1.23012	+	0.0847647i
$274$		0			0
$275$	0.0582685	+	0.217461i	0.00351372	+	0.0131134i
$276$		0			0
$277$	24.0573	+	6.44615i	1.44547	+	0.387311i	0.894444	−	0.447180i	$-0.147572\pi$
$277$	24.0573	+	6.44615i	1.44547	+	0.387311i	0.551022	+	0.834491i	$0.314238\pi$
$278$		0			0
$279$			0.494264i			0.0295908i
$280$		0			0
$281$		−	15.2176i		−	0.907808i	−0.891051	−	0.453904i	$-0.850031\pi$
$281$		−	15.2176i		−	0.907808i	0.891051	−	0.453904i	$-0.149969\pi$
$282$		0			0
$283$	21.6985	+	5.81408i	1.28984	+	0.345611i	0.837599	−	0.546285i	$-0.183958\pi$
$283$	21.6985	+	5.81408i	1.28984	+	0.345611i	0.452240	+	0.891896i	$0.350625\pi$
$284$		0			0
$285$	2.50744	+	9.35789i	0.148528	+	0.554314i
$286$		0			0
$287$	11.3396	−	16.8485i	0.669356	−	0.994534i
$288$		0			0
$289$	−1.41301	+	2.44741i	−0.0831184	+	0.143965i
$290$		0			0
$291$	2.68930	+	0.720595i	0.157649	+	0.0422421i
$292$		0			0
$293$	6.75242	+	6.75242i	0.394480	+	0.394480i	0.876281	−	0.481800i	$-0.160017\pi$
$293$	6.75242	+	6.75242i	0.394480	+	0.394480i	−0.481800	+	0.876281i	$0.660017\pi$
$294$		0			0
$295$	−7.35277			−0.428095
$296$		0			0
$297$	0.180300	+	0.312288i	0.0104621	+	0.0181208i
$298$		0			0
$299$	−10.1130	−	37.7421i	−0.584848	−	2.18268i
$300$		0			0
$301$	9.34298	−	1.82593i	0.538521	−	0.105245i
$302$		0			0
$303$	22.7378	+	13.1277i	1.30625	+	0.754166i
$304$		0			0
$305$	10.4187	+	18.0457i	0.596571	+	1.03329i
$306$		0			0
$307$	−13.0278	−	13.0278i	−0.743535	−	0.743535i	0.229721	−	0.973257i	$-0.426219\pi$
$307$	−13.0278	−	13.0278i	−0.743535	−	0.743535i	−0.973257	+	0.229721i	$0.926219\pi$
$308$		0			0
$309$	−8.35739	+	8.35739i	−0.475435	+	0.475435i
$310$		0			0
$311$	0.115702	−	0.0668004i	0.00656084	−	0.00378790i	−0.496716	−	0.867913i	$-0.665461\pi$
$311$	0.115702	−	0.0668004i	0.00656084	−	0.00378790i	0.503277	+	0.864125i	$0.332128\pi$
$312$		0			0
$313$	0.970543	−	1.68103i	0.0548583	−	0.0950174i	−0.837292	−	0.546756i	$-0.815863\pi$
$313$	0.970543	−	1.68103i	0.0548583	−	0.0950174i	0.892150	+	0.451738i	$0.149196\pi$
$314$		0			0
$315$	4.36547	−	3.80262i	0.245966	−	0.214253i
$316$		0			0
$317$	−10.7114	+	2.87011i	−0.601613	+	0.161202i	−0.546755	−	0.837293i	$-0.684137\pi$
$317$	−10.7114	+	2.87011i	−0.601613	+	0.161202i	−0.0548575	+	0.998494i	$0.517470\pi$
$318$		0			0
$319$	0.372340	−	0.214970i	0.0208470	−	0.0120360i
$320$		0			0
$321$			12.5370i			0.699747i
$322$		0			0
$323$	−5.89337	+	5.89337i	−0.327916	+	0.327916i
$324$		0			0
$325$	−4.66604	+	17.4139i	−0.258826	+	0.965950i
$326$		0			0
$327$	−10.4911	−	6.05705i	−0.580160	−	0.334956i
$328$		0			0
$329$	6.10643	+	12.4879i	0.336658	+	0.688479i
$330$		0			0
$331$	−24.2423	+	6.49571i	−1.33248	+	0.357037i	−0.853639	−	0.520865i	$-0.825609\pi$
$331$	−24.2423	+	6.49571i	−1.33248	+	0.357037i	−0.478840	+	0.877902i	$0.658943\pi$
$332$		0			0
$333$	0.815399	−	3.04311i	0.0446836	−	0.166761i
$334$		0			0
$335$	−18.0873			−0.988212
$336$		0			0
$337$	−21.4362			−1.16770			−0.583851	−	0.811861i	$-0.698455\pi$
$337$	−21.4362			−1.16770			−0.583851	+	0.811861i	$0.698455\pi$
$338$		0			0
$339$	4.99129	−	18.6278i	0.271090	−	1.01172i
$340$		0			0
$341$	−0.0408067	+	0.0109341i	−0.00220981	+	0.000592116i
$342$		0			0
$343$	−18.1272	−	3.79545i	−0.978776	−	0.204935i
$344$		0			0
$345$	28.8467	+	16.6547i	1.55305	+	0.896656i
$346$		0			0
$347$	1.16752	−	4.35725i	0.0626758	−	0.233909i	−0.927481	−	0.373870i	$-0.878031\pi$
$347$	1.16752	−	4.35725i	0.0626758	−	0.233909i	0.990157	+	0.139960i	$0.0446975\pi$
$348$		0			0
$349$	−13.4710	+	13.4710i	−0.721087	+	0.721087i	−0.968827	−	0.247739i	$-0.920312\pi$
$349$	−13.4710	+	13.4710i	−0.721087	+	0.721087i	0.247739	+	0.968827i	$0.420312\pi$
$350$		0			0
$351$			28.8762i			1.54130i
$352$		0			0
$353$	−14.8316	+	8.56303i	−0.789407	+	0.455764i	−0.839754	−	0.542968i	$-0.817301\pi$
$353$	−14.8316	+	8.56303i	−0.789407	+	0.455764i	0.0503468	+	0.998732i	$0.483967\pi$
$354$		0			0
$355$	−3.06844	+	0.822185i	−0.162856	+	0.0436371i
$356$		0			0
$357$	−14.1321	−	4.85004i	−0.747948	−	0.256691i
$358$		0			0
$359$	−9.24447	+	16.0119i	−0.487904	+	0.845075i	−0.999903	−	0.0139109i	$-0.995572\pi$
$359$	−9.24447	+	16.0119i	−0.487904	+	0.845075i	0.511999	+	0.858986i	$0.328905\pi$
$360$		0			0
$361$	−12.2103	+	7.04960i	−0.642646	+	0.371032i
$362$		0			0
$363$	11.6628	−	11.6628i	0.612141	−	0.612141i
$364$		0			0
$365$	−0.0959077	−	0.0959077i	−0.00502004	−	0.00502004i
$366$		0			0
$367$	−12.2336	−	21.1892i	−0.638587	−	1.10607i	−0.985743	−	0.168258i	$-0.946186\pi$
$367$	−12.2336	−	21.1892i	−0.638587	−	1.10607i	0.347156	−	0.937807i	$-0.387148\pi$
$368$		0			0
$369$	4.98591	+	2.87862i	0.259556	+	0.149855i
$370$		0			0
$371$	−20.9858	+	18.2800i	−1.08953	+	0.949052i
$372$		0			0
$373$	−5.27316	−	19.6797i	−0.273034	−	1.01898i	−0.957147	−	0.289601i	$-0.906477\pi$
$373$	−5.27316	−	19.6797i	−0.273034	−	1.01898i	0.684114	−	0.729376i	$-0.260189\pi$
$374$		0			0
$375$	3.25627	+	5.64002i	0.168153	+	0.291249i
$376$		0			0
$377$	34.4290			1.77318
$378$		0			0
$379$	−24.7561	−	24.7561i	−1.27163	−	1.27163i	−0.945230	−	0.326404i	$-0.894163\pi$
$379$	−24.7561	−	24.7561i	−1.27163	−	1.27163i	−0.326404	−	0.945230i	$-0.605837\pi$
$380$		0			0
$381$	−22.2519	−	5.96237i	−1.14000	−	0.305462i
$382$		0			0
$383$	−9.84997	+	17.0606i	−0.503310	+	0.871758i	0.496683	+	0.867932i	$0.334551\pi$
$383$	−9.84997	+	17.0606i	−0.503310	+	0.871758i	−0.999993	+	0.00382628i	$0.998782\pi$
$384$		0			0
$385$	0.410520	+	0.276294i	0.0209220	+	0.0140812i
$386$		0			0
$387$	0.698466	+	2.60671i	0.0355050	+	0.132507i
$388$		0			0
$389$	2.83524	+	0.759700i	0.143752	+	0.0385183i	0.329978	−	0.943989i	$-0.392959\pi$
$389$	2.83524	+	0.759700i	0.143752	+	0.0385183i	−0.186225	+	0.982507i	$0.559625\pi$
$390$		0			0
$391$			28.6557i			1.44918i
$392$		0			0
$393$		−	0.509639i		−	0.0257079i
$394$		0			0
$395$	49.6133	+	13.2939i	2.49632	+	0.668886i
$396$		0			0
$397$	2.96194	+	11.0541i	0.148656	+	0.554791i	0.999565	+	0.0294787i	$0.00938472\pi$
$397$	2.96194	+	11.0541i	0.148656	+	0.554791i	−0.850910	+	0.525312i	$0.823949\pi$
$398$		0			0
$399$	7.28857	+	4.90546i	0.364885	+	0.245580i
$400$		0			0
$401$	2.80472	−	4.85792i	0.140061	−	0.242593i	−0.787458	−	0.616368i	$-0.788603\pi$
$401$	2.80472	−	4.85792i	0.140061	−	0.242593i	0.927519	+	0.373775i	$0.121937\pi$
$402$		0			0
$403$	−3.26774	−	0.875587i	−0.162778	−	0.0436161i
$404$		0			0
$405$	−12.7645	−	12.7645i	−0.634275	−	0.634275i
$406$		0			0
$407$	0.269279			0.0133477
$408$		0			0
$409$	16.8193	+	29.1319i	0.831662	+	1.44048i	0.896719	+	0.442600i	$0.145944\pi$
$409$	16.8193	+	29.1319i	0.831662	+	1.44048i	−0.0650570	+	0.997882i	$0.520723\pi$
$410$		0			0
$411$	3.50719	+	13.0890i	0.172997	+	0.645634i
$412$		0			0
$413$	−5.02788	+	4.37963i	−0.247406	+	0.215507i
$414$		0			0
$415$	18.1419	+	10.4742i	0.890549	+	0.514158i
$416$		0			0
$417$	−4.09175	−	7.08712i	−0.200374	−	0.347058i
$418$		0			0
$419$	−7.47278	−	7.47278i	−0.365069	−	0.365069i	0.500606	−	0.865675i	$-0.333111\pi$
$419$	−7.47278	−	7.47278i	−0.365069	−	0.365069i	−0.865675	+	0.500606i	$0.833111\pi$
$420$		0			0
$421$	−10.0923	+	10.0923i	−0.491866	+	0.491866i	−0.908894	−	0.417028i	$-0.863072\pi$
$421$	−10.0923	+	10.0923i	−0.491866	+	0.491866i	0.417028	+	0.908894i	$0.363072\pi$
$422$		0			0
$423$	−3.41270	+	1.97032i	−0.165931	+	0.0958004i
$424$		0			0
$425$	6.61075	−	11.4502i	0.320669	−	0.555414i
$426$		0			0
$427$	17.8731	+	6.13395i	0.864942	+	0.296843i
$428$		0			0
$429$	−0.476818	+	0.127763i	−0.0230210	+	0.00616846i
$430$		0			0
$431$	6.09461	−	3.51872i	0.293567	−	0.169491i	−0.345982	−	0.938241i	$-0.612454\pi$
$431$	6.09461	−	3.51872i	0.293567	−	0.169491i	0.639549	+	0.768750i	$0.279121\pi$
$432$		0			0
$433$		−	38.5837i		−	1.85422i	−0.374795	−	0.927108i	$-0.622287\pi$
$433$		−	38.5837i		−	1.85422i	0.374795	−	0.927108i	$-0.377713\pi$
$434$		0			0
$435$	−20.7536	+	20.7536i	−0.995057	+	0.995057i
$436$		0			0
$437$	4.36108	−	16.2758i	0.208619	−	0.778576i
$438$		0			0
$439$	15.4436	+	8.91638i	0.737084	+	0.425555i	0.821008	−	0.570917i	$-0.193412\pi$
$439$	15.4436	+	8.91638i	0.737084	+	0.425555i	−0.0839243	+	0.996472i	$0.526745\pi$
$440$		0			0
$441$	0.720134	−	5.20052i	0.0342921	−	0.247644i
$442$		0			0
$443$	−8.51469	+	2.28150i	−0.404545	+	0.108397i	−0.455353	−	0.890311i	$-0.650487\pi$
$443$	−8.51469	+	2.28150i	−0.404545	+	0.108397i	0.0508081	+	0.998708i	$0.483820\pi$
$444$		0			0
$445$	−6.76294	+	25.2396i	−0.320594	+	1.19647i
$446$		0			0
$447$	−9.56912			−0.452604
$448$		0			0
$449$	14.4915			0.683898			0.341949	−	0.939718i	$-0.388913\pi$
$449$	14.4915			0.683898			0.341949	+	0.939718i	$0.388913\pi$
$450$		0			0
$451$	−0.127362	+	0.475321i	−0.00599723	+	0.0223820i
$452$		0			0
$453$	−4.94783	+	1.32577i	−0.232469	+	0.0622899i
$454$		0			0
$455$	17.4069	+	35.5978i	0.816050	+	1.66885i
$456$		0			0
$457$	−2.59164	−	1.49628i	−0.121232	−	0.0699932i	0.438158	−	0.898898i	$-0.355631\pi$
$457$	−2.59164	−	1.49628i	−0.121232	−	0.0699932i	−0.559390	+	0.828905i	$0.688964\pi$
$458$		0			0
$459$	5.48107	−	20.4556i	0.255834	−	0.954786i
$460$		0			0
$461$	6.89015	−	6.89015i	0.320906	−	0.320906i	−0.528209	−	0.849115i	$-0.677136\pi$
$461$	6.89015	−	6.89015i	0.320906	−	0.320906i	0.849115	+	0.528209i	$0.177136\pi$
$462$		0			0
$463$		−	28.9432i		−	1.34511i	−0.740049	−	0.672553i	$-0.765198\pi$
$463$		−	28.9432i		−	1.34511i	0.740049	−	0.672553i	$-0.234802\pi$
$464$		0			0
$465$	2.49757	−	1.44197i	0.115822	−	0.0668698i
$466$		0			0
$467$	23.9512	−	6.41771i	1.10833	−	0.296976i	0.342177	−	0.939635i	$-0.388836\pi$
$467$	23.9512	−	6.41771i	1.10833	−	0.296976i	0.766152	+	0.642659i	$0.222169\pi$
$468$		0			0
$469$	−12.3682	+	10.7736i	−0.571111	+	0.497476i
$470$		0			0
$471$	−3.52530	+	6.10599i	−0.162437	+	0.281349i
$472$		0			0
$473$	−0.199760	+	0.115332i	−0.00918498	+	0.00530295i
$474$		0			0
$475$	−5.49735	+	5.49735i	−0.252236	+	0.252236i
$476$		0			0
$477$	−5.57876	−	5.57876i	−0.255434	−	0.255434i
$478$		0			0
$479$	5.53947	+	9.59464i	0.253105	+	0.438390i	0.964379	−	0.264524i	$-0.0852149\pi$
$479$	5.53947	+	9.59464i	0.253105	+	0.438390i	−0.711274	+	0.702915i	$0.751882\pi$
$480$		0			0
$481$	18.6745	+	10.7817i	0.851484	+	0.491604i
$482$		0			0
$483$	29.6458	−	5.79377i	1.34893	−	0.263626i
$484$		0			0
$485$	1.40157	+	5.23072i	0.0636419	+	0.237515i
$486$		0			0
$487$	−11.0071	−	19.0648i	−0.498779	−	0.863910i	0.501220	−	0.865320i	$-0.332885\pi$
$487$	−11.0071	−	19.0648i	−0.498779	−	0.863910i	−0.999999	+	0.00140957i	$0.999551\pi$
$488$		0			0
$489$	−2.43634			−0.110175
$490$		0			0
$491$	18.0641	+	18.0641i	0.815221	+	0.815221i	0.985411	−	0.170191i	$-0.0544383\pi$
$491$	18.0641	+	18.0641i	0.815221	+	0.815221i	−0.170191	+	0.985411i	$0.554438\pi$
$492$		0			0
$493$	−24.3891	−	6.53504i	−1.09843	−	0.294324i
$494$		0			0
$495$	−0.0701387	+	0.121484i	−0.00315250	+	0.00546029i
$496$		0			0
$497$	−1.60849	+	2.38991i	−0.0721507	+	0.107202i
$498$		0			0
$499$	−0.618516	−	2.30833i	−0.0276886	−	0.103335i	0.950699	−	0.310116i	$-0.100368\pi$
$499$	−0.618516	−	2.30833i	−0.0276886	−	0.103335i	−0.978387	+	0.206781i	$0.933701\pi$
$500$		0			0
$501$	11.3268	+	3.03500i	0.506043	+	0.135594i
$502$		0			0
$503$		−	15.2639i		−	0.680582i	−0.940320	−	0.340291i	$-0.889474\pi$
$503$		−	15.2639i		−	0.680582i	0.940320	−	0.340291i	$-0.110526\pi$
$504$		0			0
$505$			51.0670i			2.27245i
$506$		0			0
$507$	−19.3474	−	5.18412i	−0.859248	−	0.230235i
$508$		0			0
$509$	−4.48980	−	16.7561i	−0.199007	−	0.742703i	−0.991193	−	0.132424i	$-0.957724\pi$
$509$	−4.48980	−	16.7561i	−0.199007	−	0.742703i	0.792186	−	0.610279i	$-0.208943\pi$
$510$		0			0
$511$	−0.122709	−	0.00845563i	−0.00542833	−	0.000374055i
$512$		0			0
$513$	−6.22624	+	10.7842i	−0.274895	+	0.476133i
$514$		0			0
$515$	−22.2051	−	5.94983i	−0.978472	−	0.262181i
$516$		0			0
$517$	−0.238167	−	0.238167i	−0.0104746	−	0.0104746i
$518$		0			0
$519$	−6.21441			−0.272782
$520$		0			0
$521$	3.31388	+	5.73981i	0.145184	+	0.251466i	0.929441	−	0.368970i	$-0.120289\pi$
$521$	3.31388	+	5.73981i	0.145184	+	0.251466i	−0.784258	+	0.620435i	$0.786956\pi$
$522$		0			0
$523$	6.67146	+	24.8982i	0.291723	+	1.08872i	0.943785	+	0.330559i	$0.107237\pi$
$523$	6.67146	+	24.8982i	0.291723	+	1.08872i	−0.652063	+	0.758165i	$0.726096\pi$
$524$		0			0
$525$	−13.1824	−	4.52412i	−0.575327	−	0.197449i
$526$		0			0
$527$	2.14863	+	1.24051i	0.0935959	+	0.0540376i
$528$		0			0
$529$	−17.4667	−	30.2532i	−0.759422	−	1.31536i
$530$		0			0
$531$	−1.33659	−	1.33659i	−0.0580030	−	0.0580030i
$532$		0			0
$533$	−27.8640	+	27.8640i	−1.20692	+	1.20692i
$534$		0			0
$535$	−21.1177	+	12.1923i	−0.912999	+	0.527120i
$536$		0			0
$537$	8.35428	−	14.4700i	0.360514	−	0.624428i
$538$		0			0
$539$	0.445289	−	0.0555915i	0.0191800	−	0.00239450i
$540$		0			0
$541$	−6.62484	+	1.77512i	−0.284824	+	0.0763184i	−0.398403	−	0.917211i	$-0.630435\pi$
$541$	−6.62484	+	1.77512i	−0.284824	+	0.0763184i	0.113579	+	0.993529i	$0.463769\pi$
$542$		0			0
$543$	8.28024	−	4.78060i	0.355339	−	0.205155i
$544$		0			0
$545$		−	23.5621i		−	1.00929i
$546$		0			0
$547$	−8.23199	+	8.23199i	−0.351974	+	0.351974i	−0.860844	−	0.508869i	$-0.830064\pi$
$547$	−8.23199	+	8.23199i	−0.351974	+	0.351974i	0.508869	+	0.860844i	$0.330064\pi$
$548$		0			0
$549$	−1.38644	+	5.17425i	−0.0591716	+	0.220832i
$550$		0			0
$551$	12.8579	+	7.42351i	0.547765	+	0.316252i
$552$		0			0
$553$	41.8444	−	20.4614i	1.77940	−	0.870108i
$554$		0			0
$555$	−17.7560	+	4.75771i	−0.753701	+	0.201953i
$556$		0			0
$557$	7.05595	−	26.3332i	0.298970	−	1.11577i	−0.639043	−	0.769171i	$-0.720669\pi$
$557$	7.05595	−	26.3332i	0.298970	−	1.11577i	0.938013	−	0.346600i	$-0.112664\pi$
$558$		0			0
$559$	−18.4711			−0.781246
$560$		0			0
$561$	0.362024			0.0152847
$562$		0			0
$563$	0.167327	−	0.624473i	0.00705199	−	0.0263184i	−0.962310	−	0.271954i	$-0.912330\pi$
$563$	0.167327	−	0.624473i	0.00705199	−	0.0263184i	0.969362	+	0.245636i	$0.0789967\pi$
$564$		0			0
$565$	36.2312	−	9.70813i	1.52426	−	0.408424i
$566$		0			0
$567$	−16.3316	−	1.12538i	−0.685863	−	0.0472614i
$568$		0			0
$569$	−17.1431	−	9.89757i	−0.718676	−	0.414928i	0.0955892	−	0.995421i	$-0.469526\pi$
$569$	−17.1431	−	9.89757i	−0.718676	−	0.414928i	−0.814265	+	0.580493i	$0.802860\pi$
$570$		0			0
$571$	−2.77408	+	10.3530i	−0.116092	+	0.433260i	−0.999366	−	0.0355961i	$-0.988667\pi$
$571$	−2.77408	+	10.3530i	−0.116092	+	0.433260i	0.883275	+	0.468856i	$0.155334\pi$
$572$		0			0
$573$	−17.6994	+	17.6994i	−0.739402	+	0.739402i
$574$		0			0
$575$			26.7300i			1.11472i
$576$		0			0
$577$	−20.6057	+	11.8967i	−0.857828	+	0.495267i	−0.863284	−	0.504718i	$-0.831597\pi$
$577$	−20.6057	+	11.8967i	−0.857828	+	0.495267i	0.00545613	+	0.999985i	$0.498263\pi$
$578$		0			0
$579$	−3.95202	+	1.05894i	−0.164240	+	0.0440081i
$580$		0			0
$581$	18.6444	−	3.64373i	0.773501	−	0.151168i
$582$		0			0
$583$	0.337172	−	0.583999i	0.0139642	−	0.0241868i
$584$		0			0
$585$	−9.72822	+	5.61659i	−0.402212	+	0.232217i
$586$		0			0
$587$	18.9775	−	18.9775i	0.783286	−	0.783286i	−0.197098	−	0.980384i	$-0.563152\pi$
$587$	18.9775	−	18.9775i	0.783286	−	0.783286i	0.980384	+	0.197098i	$0.0631518\pi$
$588$		0			0
$589$	−1.03158	−	1.03158i	−0.0425056	−	0.0425056i
$590$		0			0
$591$	−4.12291	−	7.14109i	−0.169594	−	0.293745i
$592$		0			0
$593$	0.728860	+	0.420807i	0.0299307	+	0.0172805i	0.514891	−	0.857256i	$-0.327833\pi$
$593$	0.728860	+	0.420807i	0.0299307	+	0.0172805i	−0.484960	+	0.874536i	$0.661166\pi$
$594$		0			0
$595$	−5.57397	−	28.5212i	−0.228511	−	1.16925i
$596$		0			0
$597$	−5.64295	−	21.0598i	−0.230951	−	0.861919i
$598$		0			0
$599$	0.848110	+	1.46897i	0.0346529	+	0.0600205i	0.882832	−	0.469689i	$-0.155634\pi$
$599$	0.848110	+	1.46897i	0.0346529	+	0.0600205i	−0.848179	+	0.529710i	$0.822301\pi$
$600$		0			0
$601$	−28.0938			−1.14597			−0.572984	−	0.819566i	$-0.694214\pi$
$601$	−28.0938			−1.14597			−0.572984	+	0.819566i	$0.694214\pi$
$602$		0			0
$603$	−3.28790	−	3.28790i	−0.133894	−	0.133894i
$604$		0			0
$605$	30.9875	+	8.30306i	1.25982	+	0.337568i
$606$		0			0
$607$	19.5443	−	33.8517i	0.793277	−	1.37400i	−0.130650	−	0.991428i	$-0.541707\pi$
$607$	19.5443	−	33.8517i	0.793277	−	1.37400i	0.923927	−	0.382568i	$-0.124960\pi$
$608$		0			0
$609$	−1.82972	+	26.5531i	−0.0741441	+	1.07599i
$610$		0			0
$611$	−6.98085	−	26.0529i	−0.282415	−	1.05399i
$612$		0			0
$613$	−7.15084	−	1.91606i	−0.288820	−	0.0773891i	0.111500	−	0.993764i	$-0.464434\pi$
$613$	−7.15084	−	1.91606i	−0.288820	−	0.0773891i	−0.400320	+	0.916375i	$0.631101\pi$
$614$		0			0
$615$		−	33.5925i		−	1.35458i
$616$		0			0
$617$		−	11.3503i		−	0.456945i	−0.973550	−	0.228472i	$-0.926627\pi$
$617$		−	11.3503i		−	0.456945i	0.973550	−	0.228472i	$-0.0733731\pi$
$618$		0			0
$619$	−29.8682	−	8.00317i	−1.20051	−	0.321675i	−0.397476	−	0.917613i	$-0.630114\pi$
$619$	−29.8682	−	8.00317i	−1.20051	−	0.321675i	−0.803030	+	0.595938i	$0.796780\pi$
$620$		0			0
$621$	11.0811	+	41.3553i	0.444670	+	1.65953i
$622$		0			0
$623$	10.4093	+	21.2873i	0.417038	+	0.852859i
$624$		0			0
$625$	−15.1131	+	26.1766i	−0.604524	+	1.04707i
$626$		0			0
$627$	−0.205621	−	0.0550961i	−0.00821173	−	0.00220033i
$628$		0			0
$629$	−11.1823	−	11.1823i	−0.445868	−	0.445868i
$630$		0			0
$631$	11.1640			0.444430			0.222215	−	0.974998i	$-0.428671\pi$
$631$	11.1640			0.444430			0.222215	+	0.974998i	$0.428671\pi$
$632$		0			0
$633$	−19.6767	−	34.0810i	−0.782077	−	1.35460i
$634$		0			0
$635$	−11.5969	−	43.2802i	−0.460209	−	1.71752i
$636$		0			0
$637$	33.1066	+	13.9737i	1.31173	+	0.553660i
$638$		0			0
$639$	−0.707238	−	0.408324i	−0.0279779	−	0.0161531i
$640$		0			0
$641$	3.95262	+	6.84614i	0.156119	+	0.270406i	0.933466	−	0.358666i	$-0.116768\pi$
$641$	3.95262	+	6.84614i	0.156119	+	0.270406i	−0.777347	+	0.629072i	$0.783435\pi$
$642$		0			0
$643$	1.49041	+	1.49041i	0.0587758	+	0.0587758i	0.735884	−	0.677108i	$-0.236767\pi$
$643$	1.49041	+	1.49041i	0.0587758	+	0.0587758i	−0.677108	+	0.735884i	$0.736767\pi$
$644$		0			0
$645$	11.1343	−	11.1343i	0.438412	−	0.438412i
$646$		0			0
$647$	−8.79347	+	5.07691i	−0.345707	+	0.199594i	−0.662793	−	0.748803i	$-0.730629\pi$
$647$	−8.79347	+	5.07691i	−0.345707	+	0.199594i	0.317086	+	0.948397i	$0.397296\pi$
$648$		0			0
$649$	0.0807815	−	0.139918i	0.00317095	−	0.00549225i
$650$		0			0
$651$	0.848955	−	2.47369i	0.0332732	−	0.0969516i
$652$		0			0
$653$	20.3975	−	5.46551i	0.798218	−	0.213882i	0.163416	−	0.986557i	$-0.447749\pi$
$653$	20.3975	−	5.46551i	0.798218	−	0.213882i	0.634801	+	0.772675i	$0.281082\pi$
$654$		0			0
$655$	0.858452	−	0.495627i	0.0335425	−	0.0193658i
$656$		0			0
$657$		−	0.0348682i		−	0.00136034i
$658$		0			0
$659$	12.2016	−	12.2016i	0.475308	−	0.475308i	−0.428319	−	0.903627i	$-0.640894\pi$
$659$	12.2016	−	12.2016i	0.475308	−	0.475308i	0.903627	+	0.428319i	$0.140894\pi$
$660$		0			0
$661$	10.8248	−	40.3987i	0.421036	−	1.57133i	−0.351393	−	0.936228i	$-0.614292\pi$
$661$	10.8248	−	40.3987i	0.421036	−	1.57133i	0.772429	−	0.635101i	$-0.219041\pi$
$662$		0			0
$663$	25.1063	+	14.4952i	0.975049	+	0.562945i
$664$		0			0
$665$	−1.17472	+	17.0477i	−0.0455537	+	0.661081i
$666$		0			0
$667$	49.3077	−	13.2120i	1.90920	−	0.511569i
$668$		0			0
$669$	8.82520	−	32.9361i	0.341202	−	1.27338i
$670$		0			0
$671$	−0.457860			−0.0176755
$672$		0			0
$673$	28.4793			1.09780			0.548899	−	0.835889i	$-0.315047\pi$
$673$	28.4793			1.09780			0.548899	+	0.835889i	$0.315047\pi$
$674$		0			0
$675$	5.11274	−	19.0810i	0.196790	−	0.734429i
$676$		0			0
$677$	30.3235	−	8.12515i	1.16543	−	0.312275i	0.376295	−	0.926500i	$-0.377198\pi$
$677$	30.3235	−	8.12515i	1.16543	−	0.312275i	0.789131	+	0.614225i	$0.210531\pi$
$678$		0			0
$679$	4.07405	+	2.74197i	0.156348	+	0.105227i
$680$		0			0
$681$	2.34033	+	1.35119i	0.0896815	+	0.0517776i
$682$		0			0
$683$	−0.723851	+	2.70145i	−0.0276974	+	0.103368i	−0.978391	−	0.206764i	$-0.933707\pi$
$683$	−0.723851	+	2.70145i	−0.0276974	+	0.103368i	0.950693	+	0.310132i	$0.100373\pi$
$684$		0			0
$685$	−18.6368	+	18.6368i	−0.712075	+	0.712075i
$686$		0			0
$687$		−	22.2336i		−	0.848263i
$688$		0			0
$689$	46.7657	−	27.0002i	1.78163	−	1.02863i
$690$		0			0
$691$	18.0563	−	4.83818i	0.686895	−	0.184053i	0.101542	−	0.994831i	$-0.467623\pi$
$691$	18.0563	−	4.83818i	0.686895	−	0.184053i	0.585353	+	0.810778i	$0.300956\pi$
$692$		0			0
$693$	0.0243996	+	0.124849i	0.000926865	+	0.00474263i
$694$		0			0
$695$	7.95850	−	13.7845i	0.301883	−	0.522877i
$696$		0			0
$697$	25.0275	−	14.4496i	0.947984	−	0.547319i
$698$		0			0
$699$	−22.6499	+	22.6499i	−0.856697	+	0.856697i
$700$		0			0
$701$	−8.68328	−	8.68328i	−0.327963	−	0.327963i	0.523848	−	0.851811i	$-0.324496\pi$
$701$	−8.68328	−	8.68328i	−0.327963	−	0.327963i	−0.851811	+	0.523848i	$0.824496\pi$
$702$		0			0
$703$	4.64947	+	8.05312i	0.175358	+	0.303729i
$704$		0			0
$705$	19.9125	+	11.4965i	0.749949	+	0.432983i
$706$		0			0
$707$	30.4177	+	34.9200i	1.14398	+	1.31330i
$708$		0			0
$709$	5.08085	+	18.9620i	0.190815	+	0.712132i	0.993311	+	0.115474i	$0.0368385\pi$
$709$	5.08085	+	18.9620i	0.190815	+	0.712132i	−0.802495	+	0.596658i	$0.796495\pi$
$710$		0			0
$711$	6.60216	+	11.4353i	0.247600	+	0.428857i
$712$		0			0
$713$	−5.01591			−0.187847
$714$		0			0
$715$	−0.678917	−	0.678917i	−0.0253901	−	0.0253901i
$716$		0			0
$717$	0.917114	+	0.245740i	0.0342502	+	0.00917733i
$718$		0			0
$719$	0.995256	−	1.72383i	0.0371168	−	0.0642882i	−0.846870	−	0.531800i	$-0.821516\pi$
$719$	0.995256	−	1.72383i	0.0371168	−	0.0642882i	0.883987	+	0.467511i	$0.154849\pi$
$720$		0			0
$721$	−18.7280	+	9.15776i	−0.697466	+	0.341053i
$722$		0			0
$723$	−7.26694	−	27.1206i	−0.270260	−	1.00863i
$724$		0			0
$725$	−22.7502	−	6.09590i	−0.844921	−	0.226396i
$726$		0			0
$727$		−	24.4403i		−	0.906440i	−0.891399	−	0.453220i	$-0.850275\pi$
$727$		−	24.4403i		−	0.906440i	0.891399	−	0.453220i	$-0.149725\pi$
$728$		0			0
$729$		−	29.9531i		−	1.10937i
$730$		0			0
$731$	13.0848	+	3.50605i	0.483957	+	0.129676i
$732$		0			0
$733$	−6.67020	−	24.8935i	−0.246369	−	0.919463i	−0.972690	−	0.232107i	$-0.925438\pi$
$733$	−6.67020	−	24.8935i	−0.246369	−	0.919463i	0.726321	−	0.687356i	$-0.241229\pi$
$734$		0			0
$735$	−28.3797	+	11.5332i	−1.04680	+	0.425407i
$736$		0			0
$737$	0.198716	−	0.344187i	0.00731980	−	0.0126783i
$738$		0			0
$739$	30.3564	+	8.13399i	1.11668	+	0.299214i	0.769539	−	0.638600i	$-0.220486\pi$
$739$	30.3564	+	8.13399i	1.11668	+	0.299214i	0.347141	+	0.937813i	$0.387153\pi$
$740$		0			0
$741$	−12.0538	−	12.0538i	−0.442809	−	0.442809i
$742$		0			0
$743$	−12.7380			−0.467313			−0.233656	−	0.972319i	$-0.575069\pi$
$743$	−12.7380			−0.467313			−0.233656	+	0.972319i	$0.575069\pi$
$744$		0			0
$745$	−9.30603	−	16.1185i	−0.340947	−	0.590537i
$746$		0			0
$747$	1.39383	+	5.20183i	0.0509975	+	0.190325i
$748$		0			0
$749$	−7.17818	+	20.9158i	−0.262285	+	0.764248i
$750$		0			0
$751$	−12.0504	−	6.95728i	−0.439724	−	0.253875i	0.263757	−	0.964589i	$-0.415038\pi$
$751$	−12.0504	−	6.95728i	−0.439724	−	0.253875i	−0.703481	+	0.710715i	$0.748372\pi$
$752$		0			0
$753$	11.7132	+	20.2879i	0.426854	+	0.739334i
$754$		0			0
$755$	−7.04496	−	7.04496i	−0.256392	−	0.256392i
$756$		0			0
$757$	−6.51961	+	6.51961i	−0.236959	+	0.236959i	−0.815590	−	0.578631i	$-0.803587\pi$
$757$	−6.51961	+	6.51961i	−0.236959	+	0.236959i	0.578631	+	0.815590i	$0.303587\pi$
$758$		0			0
$759$	−0.633850	+	0.365954i	−0.0230073	+	0.0132833i
$760$		0			0
$761$	−10.3566	+	17.9382i	−0.375428	+	0.650260i	−0.990391	−	0.138296i	$-0.955838\pi$
$761$	−10.3566	+	17.9382i	−0.375428	+	0.650260i	0.614963	+	0.788556i	$0.289171\pi$
$762$		0			0
$763$	−14.0346	−	16.1119i	−0.508086	−	0.583291i
$764$		0			0
$765$	7.95746	−	2.13220i	0.287703	−	0.0770897i
$766$		0			0
$767$	11.2044	−	6.46885i	0.404567	−	0.233577i
$768$		0			0
$769$			2.25846i			0.0814421i	0.999171	+	0.0407210i	$0.0129655\pi$
$769$			2.25846i			0.0814421i	−0.999171	+	0.0407210i	$0.987035\pi$
$770$		0			0
$771$	−32.9674	+	32.9674i	−1.18729	+	1.18729i
$772$		0			0
$773$	−0.149388	+	0.557523i	−0.00537311	+	0.0200527i	−0.968560	−	0.248779i	$-0.919971\pi$
$773$	−0.149388	+	0.557523i	−0.00537311	+	0.0200527i	0.963187	+	0.268831i	$0.0866375\pi$
$774$		0			0
$775$	2.00425	+	1.15715i	0.0719947	+	0.0415661i
$776$		0			0
$777$	−9.30780	+	13.8296i	−0.333915	+	0.496134i
$778$		0			0
$779$	−16.4141	+	4.39815i	−0.588097	+	0.157580i
$780$		0			0
$781$	0.0180659	−	0.0674229i	0.000646450	−	0.00241258i
$782$		0			0
$783$	−37.7250			−1.34818
$784$		0			0
$785$	−13.7135			−0.489455
$786$		0			0
$787$	−8.19123	+	30.5701i	−0.291986	+	1.08971i	0.651596	+	0.758566i	$0.274100\pi$
$787$	−8.19123	+	30.5701i	−0.291986	+	1.08971i	−0.943582	+	0.331140i	$0.892567\pi$
$788$		0			0
$789$	−18.7610	+	5.02699i	−0.667909	+	0.178966i
$790$		0			0
$791$	18.9926	−	28.2194i	0.675299	−	1.00337i
$792$		0			0
$793$	−31.7526	−	18.3323i	−1.12757	−	0.651001i
$794$		0			0
$795$	−11.9145	+	44.4656i	−0.422564	+	1.57703i
$796$		0			0
$797$	17.1473	−	17.1473i	0.607387	−	0.607387i	−0.334875	−	0.942263i	$-0.608694\pi$
$797$	17.1473	−	17.1473i	0.607387	−	0.607387i	0.942263	+	0.334875i	$0.108694\pi$
$798$		0			0
$799$			19.7806i			0.699789i
$800$		0			0
$801$	−5.81743	+	3.35870i	−0.205549	+	0.118674i
$802$		0			0
$803$	0.00287874		0.000771357i	0.000101589		2.72206e-5i
$804$		0			0
$805$	38.5900	+	44.3019i	1.36012	+	1.56144i
$806$		0			0
$807$	−1.15600	+	2.00225i	−0.0406932	+	0.0704826i
$808$		0			0
$809$	−5.51003	+	3.18122i	−0.193722	+	0.111846i	−0.593724	−	0.804669i	$-0.702343\pi$
$809$	−5.51003	+	3.18122i	−0.193722	+	0.111846i	0.400002	+	0.916514i	$0.369010\pi$
$810$		0			0
$811$	9.98197	−	9.98197i	0.350514	−	0.350514i	−0.509787	−	0.860301i	$-0.670276\pi$
$811$	9.98197	−	9.98197i	0.350514	−	0.350514i	0.860301	+	0.509787i	$0.170276\pi$
$812$		0			0
$813$	11.3167	+	11.3167i	0.396892	+	0.396892i
$814$		0			0
$815$	−2.36936	−	4.10385i	−0.0829949	−	0.143751i
$816$		0			0
$817$	−6.89826	−	3.98271i	−0.241340	−	0.139337i
$818$		0			0
$819$	−3.30675	+	9.63522i	−0.115547	+	0.336682i
$820$		0			0
$821$	12.1404	+	45.3088i	0.423704	+	1.58129i	0.766736	+	0.641963i	$0.221880\pi$
$821$	12.1404	+	45.3088i	0.423704	+	1.58129i	−0.343031	+	0.939324i	$0.611454\pi$
$822$		0			0
$823$	18.5100	+	32.0602i	0.645218	+	1.11755i	0.984251	+	0.176775i	$0.0565666\pi$
$823$	18.5100	+	32.0602i	0.645218	+	1.11755i	−0.339034	+	0.940774i	$0.610100\pi$
$824$		0			0
$825$	0.337696			0.0117571
$826$		0			0
$827$	2.13977	+	2.13977i	0.0744071	+	0.0744071i	0.743331	−	0.668924i	$-0.233245\pi$
$827$	2.13977	+	2.13977i	0.0744071	+	0.0744071i	−0.668924	+	0.743331i	$0.733245\pi$
$828$		0			0
$829$	27.5450	+	7.38067i	0.956678	+	0.256341i	0.703194	−	0.710998i	$-0.251757\pi$
$829$	27.5450	+	7.38067i	0.956678	+	0.256341i	0.253485	+	0.967339i	$0.418423\pi$
$830$		0			0
$831$	18.6794	−	32.3537i	0.647982	−	1.12234i
$832$		0			0
$833$	−20.8000	−	16.1829i	−0.720676	−	0.560704i
$834$		0			0
$835$	5.90311	+	22.0307i	0.204286	+	0.762405i
$836$		0			0
$837$	3.58057	+	0.959411i	0.123763	+	0.0331621i
$838$		0			0
$839$		−	39.5103i		−	1.36405i	−0.731330	−	0.682023i	$-0.761100\pi$
$839$		−	39.5103i		−	1.36405i	0.731330	−	0.682023i	$-0.238900\pi$
$840$		0			0
$841$			15.9793i			0.551011i
$842$		0			0
$843$	−22.0486	−	5.90789i	−0.759392	−	0.203479i
$844$		0			0
$845$	−10.0832	−	37.6309i	−0.346872	−	1.29454i
$846$		0			0
$847$	26.1351	−	12.7798i	0.898013	−	0.439118i
$848$		0			0
$849$	16.8478	−	29.1813i	0.578216	−	1.00150i
$850$		0			0
$851$	30.8822	+	8.27487i	1.05863	+	0.283659i
$852$		0			0
$853$	13.2644	+	13.2644i	0.454165	+	0.454165i	0.896734	−	0.442570i	$-0.145933\pi$
$853$	13.2644	+	13.2644i	0.454165	+	0.454165i	−0.442570	+	0.896734i	$0.645933\pi$
$854$		0			0
$855$	−4.84416			−0.165667
$856$		0			0
$857$	3.96984	+	6.87597i	0.135607	+	0.234879i	0.925829	−	0.377942i	$-0.123368\pi$
$857$	3.96984	+	6.87597i	0.135607	+	0.234879i	−0.790222	+	0.612821i	$0.790035\pi$
$858$		0			0
$859$	9.90335	+	36.9598i	0.337898	+	1.26105i	0.900693	+	0.434456i	$0.143059\pi$
$859$	9.90335	+	36.9598i	0.337898	+	1.26105i	−0.562795	+	0.826596i	$0.690274\pi$
$860$		0			0
$861$	−20.0091	−	22.9708i	−0.681909	−	0.782842i
$862$		0			0
$863$	−43.1275	−	24.8997i	−1.46808	−	0.847595i	−0.468717	−	0.883349i	$-0.655284\pi$
$863$	−43.1275	−	24.8997i	−1.46808	−	0.847595i	−0.999361	+	0.0357536i	$0.988617\pi$
$864$		0			0
$865$	−6.04356	−	10.4677i	−0.205487	−	0.355914i
$866$		0			0
$867$	2.99744	+	2.99744i	0.101798	+	0.101798i
$868$		0			0
$869$	−0.798050	+	0.798050i	−0.0270720	+	0.0270720i
$870$		0			0
$871$	27.5619	−	15.9129i	0.933900	−	0.539187i
$872$		0			0
$873$	−0.696064	+	1.20562i	−0.0235582	+	0.0408040i
$874$		0			0
$875$	2.20327	+	11.2738i	0.0744842	+	0.381124i
$876$		0			0
$877$	7.34403	−	1.96783i	0.247990	−	0.0664488i	−0.132682	−	0.991159i	$-0.542359\pi$
$877$	7.34403	−	1.96783i	0.247990	−	0.0664488i	0.380673	+	0.924710i	$0.375692\pi$
$878$		0			0
$879$	12.4049	−	7.16199i	0.418408	−	0.241568i
$880$		0			0
$881$			15.5915i			0.525291i	0.964892	+	0.262645i	$0.0845949\pi$
$881$			15.5915i			0.525291i	−0.964892	+	0.262645i	$0.915405\pi$
$882$		0			0
$883$	−38.0811	+	38.0811i	−1.28153	+	1.28153i	−0.341736	+	0.939796i	$0.611015\pi$
$883$	−38.0811	+	38.0811i	−1.28153	+	1.28153i	−0.939796	+	0.341736i	$0.888985\pi$
$884$		0			0
$885$	−2.85454	+	10.6533i	−0.0959544	+	0.358107i
$886$		0			0
$887$	−42.5365	−	24.5585i	−1.42824	−	0.824593i	−0.431255	−	0.902230i	$-0.641929\pi$
$887$	−42.5365	−	24.5585i	−1.42824	−	0.824593i	−0.996982	+	0.0776375i	$0.975262\pi$
$888$		0			0
$889$	−33.7096	−	22.6877i	−1.13058	−	0.760921i
$890$		0			0
$891$	0.383138	−	0.102661i	0.0128356	−	0.00343929i
$892$		0			0
$893$	3.01040	−	11.2350i	0.100739	−	0.375963i
$894$		0			0
$895$	32.4983			1.08630
$896$		0			0
$897$	−58.6100			−1.95693
$898$		0			0
$899$	1.14390	−	4.26909i	0.0381512	−	0.142382i
$900$		0			0
$901$	−38.2533	+	10.2499i	−1.27440	+	0.341475i
$902$		0			0
$903$	0.981645	−	14.2458i	0.0326671	−	0.474069i
$904$		0			0
$905$	16.1052	+	9.29833i	0.535354	+	0.309087i
$906$		0			0
$907$	−3.61344	+	13.4855i	−0.119982	+	0.447780i	−0.999611	−	0.0278807i	$-0.991124\pi$
$907$	−3.61344	+	13.4855i	−0.119982	+	0.447780i	0.879629	+	0.475660i	$0.157791\pi$
$908$		0			0
$909$	−9.28298	+	9.28298i	−0.307897	+	0.307897i
$910$		0			0
$911$			22.9755i			0.761211i	0.924737	+	0.380606i	$0.124284\pi$
$911$			22.9755i			0.761211i	−0.924737	+	0.380606i	$0.875716\pi$
$912$		0			0
$913$	−0.398632	+	0.230150i	−0.0131928	+	0.00761686i
$914$		0			0
$915$	30.1908	−	8.08961i	0.998078	−	0.267434i
$916$		0			0
$917$	0.291799	−	0.850245i	0.00963604	−	0.0280776i
$918$		0			0
$919$	18.7608	−	32.4947i	0.618862	−	1.07190i	−0.370832	−	0.928700i	$-0.620927\pi$
$919$	18.7608	−	32.4947i	0.618862	−	1.07190i	0.989694	−	0.143200i	$-0.0457392\pi$
$920$		0			0
$921$	−23.9335	+	13.8180i	−0.788635	+	0.455319i
$922$		0			0
$923$	3.95243	−	3.95243i	0.130096	−	0.130096i
$924$		0			0
$925$	−10.4309	−	10.4309i	−0.342965	−	0.342965i
$926$		0			0
$927$	−2.95488	−	5.11800i	−0.0970510	−	0.168097i
$928$		0			0
$929$	11.3306	+	6.54174i	0.371746	+	0.214627i	0.674221	−	0.738530i	$-0.264480\pi$
$929$	11.3306	+	6.54174i	0.371746	+	0.214627i	−0.302475	+	0.953157i	$0.597813\pi$
$930$		0			0
$931$	9.35105	+	12.3570i	0.306468	+	0.404986i
$932$		0			0
$933$	−0.0518674	−	0.193572i	−0.00169806	−	0.00633725i
$934$		0			0
$935$	0.352071	+	0.609804i	0.0115139	+	0.0199427i
$936$		0			0
$937$	−12.8178			−0.418739			−0.209370	−	0.977837i	$-0.567141\pi$
$937$	−12.8178			−0.418739			−0.209370	+	0.977837i	$0.567141\pi$
$938$		0			0
$939$	−2.05882	−	2.05882i	−0.0671871	−	0.0671871i
$940$		0			0
$941$	31.0245	+	8.31298i	1.01137	+	0.270995i	0.726201	−	0.687482i	$-0.241284\pi$
$941$	31.0245	+	8.31298i	1.01137	+	0.270995i	0.285167	+	0.958478i	$0.407951\pi$
$942$		0			0
$943$	−29.2129	+	50.5983i	−0.951304	+	1.64771i
$944$		0			0
$945$	−19.0734	−	39.0058i	−0.620457	−	1.26886i
$946$		0			0
$947$	10.3703	+	38.7026i	0.336991	+	1.25767i	0.901695	+	0.432373i	$0.142324\pi$
$947$	10.3703	+	38.7026i	0.336991	+	1.25767i	−0.564704	+	0.825293i	$0.691010\pi$
$948$		0			0
$949$	0.230525	+	0.0617690i	0.00748316	+	0.00200511i
$950$		0			0
$951$			16.6338i			0.539389i
$952$		0			0
$953$			53.3527i			1.72826i	0.503266	+	0.864132i	$0.332132\pi$
$953$			53.3527i			1.72826i	−0.503266	+	0.864132i	$0.667868\pi$
$954$		0			0
$955$	−47.0261	−	12.6006i	−1.52173	−	0.407746i
$956$		0			0
$957$	−0.166915	−	0.622934i	−0.00539558	−	0.0201366i
$958$		0			0
$959$	−1.64310	+	23.8448i	−0.0530584	+	0.769990i
$960$		0			0
$961$	15.2829	−	26.4707i	0.492995	−	0.853893i
$962$		0			0
$963$	−6.05511	−	1.62246i	−0.195123	−	0.0522831i
$964$		0			0
$965$	−5.62708	−	5.62708i	−0.181142	−	0.181142i
$966$		0			0
$967$	−13.7500			−0.442169			−0.221085	−	0.975255i	$-0.570960\pi$
$967$	−13.7500			−0.442169			−0.221085	+	0.975255i	$0.570960\pi$
$968$		0			0
$969$	6.25084	+	10.8268i	0.200806	+	0.347806i
$970$		0			0
$971$	−3.00563	−	11.2172i	−0.0964554	−	0.359976i	0.900781	−	0.434274i	$-0.142995\pi$
$971$	−3.00563	−	11.2172i	−0.0964554	−	0.359976i	−0.997236	+	0.0742978i	$0.976328\pi$
$972$		0			0
$973$	−2.76858	−	14.1664i	−0.0887566	−	0.454154i
$974$		0			0
$975$	23.4192	+	13.5211i	0.750016	+	0.433022i
$976$		0			0
$977$	9.47758	+	16.4156i	0.303215	+	0.525183i	0.976862	−	0.213870i	$-0.0686068\pi$
$977$	9.47758	+	16.4156i	0.303215	+	0.525183i	−0.673648	+	0.739053i	$0.735273\pi$
$978$		0			0
$979$	−0.405989	−	0.405989i	−0.0129755	−	0.0129755i
$980$		0			0
$981$	4.28312	−	4.28312i	0.136749	−	0.136749i
$982$		0			0
$983$	29.7964	−	17.2029i	0.950357	−	0.548689i	0.0571649	−	0.998365i	$-0.481794\pi$
$983$	29.7964	−	17.2029i	0.950357	−	0.548689i	0.893192	+	0.449676i	$0.148461\pi$
$984$		0			0
$985$	8.01911	−	13.8895i	0.255510	−	0.442557i
$986$		0			0
$987$	20.4641	−	3.99936i	0.651381	−	0.127301i
$988$		0			0
$989$	−26.4536	+	7.08821i	−0.841174	+	0.225392i
$990$		0			0
$991$	−49.1173	+	28.3579i	−1.56026	+	0.900817i	−0.563032	+	0.826435i	$0.690365\pi$
$991$	−49.1173	+	28.3579i	−1.56026	+	0.900817i	−0.997230	+	0.0743822i	$0.976302\pi$
$992$		0			0
$993$			37.6461i			1.19466i
$994$		0			0
$995$	29.9859	−	29.9859i	0.950618	−	0.950618i
$996$		0			0
$997$	9.18819	−	34.2908i	0.290993	−	1.08600i	−0.653355	−	0.757052i	$-0.726639\pi$
$997$	9.18819	−	34.2908i	0.290993	−	1.08600i	0.944348	−	0.328949i	$-0.106694\pi$
$998$		0			0
$999$	−20.4623	−	11.8139i	−0.647398	−	0.373775i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	448.2.z.a.47.11		56
4.3	odd	2		112.2.v.a.19.3	yes	56
7.3	odd	6	inner	448.2.z.a.367.11		56
8.3	odd	2		896.2.z.b.607.11		56
8.5	even	2		896.2.z.a.607.4		56
16.3	odd	4		896.2.z.a.159.4		56
16.5	even	4		112.2.v.a.75.8	yes	56
16.11	odd	4	inner	448.2.z.a.271.11		56
16.13	even	4		896.2.z.b.159.11		56
28.3	even	6		112.2.v.a.3.8	✓	56
28.11	odd	6		784.2.w.f.227.8		56
28.19	even	6		784.2.j.a.195.22		56
28.23	odd	6		784.2.j.a.195.21		56
28.27	even	2		784.2.w.f.19.3		56
56.3	even	6		896.2.z.b.479.11		56
56.45	odd	6		896.2.z.a.479.4		56
112.3	even	12		896.2.z.a.31.4		56
112.5	odd	12		784.2.j.a.587.21		56
112.37	even	12		784.2.j.a.587.22		56
112.45	odd	12		896.2.z.b.31.11		56
112.53	even	12		784.2.w.f.619.3		56
112.59	even	12	inner	448.2.z.a.143.11		56
112.69	odd	4		784.2.w.f.411.8		56
112.101	odd	12		112.2.v.a.59.3	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.8	✓	56	28.3	even	6
112.2.v.a.19.3	yes	56	4.3	odd	2
112.2.v.a.59.3	yes	56	112.101	odd	12
112.2.v.a.75.8	yes	56	16.5	even	4
448.2.z.a.47.11		56	1.1	even	1	trivial
448.2.z.a.143.11		56	112.59	even	12	inner
448.2.z.a.271.11		56	16.11	odd	4	inner
448.2.z.a.367.11		56	7.3	odd	6	inner
784.2.j.a.195.21		56	28.23	odd	6
784.2.j.a.195.22		56	28.19	even	6
784.2.j.a.587.21		56	112.5	odd	12
784.2.j.a.587.22		56	112.37	even	12
784.2.w.f.19.3		56	28.27	even	2
784.2.w.f.227.8		56	28.11	odd	6
784.2.w.f.411.8		56	112.69	odd	4
784.2.w.f.619.3		56	112.53	even	12
896.2.z.a.31.4		56	112.3	even	12
896.2.z.a.159.4		56	16.3	odd	4
896.2.z.a.479.4		56	56.45	odd	6
896.2.z.a.607.4		56	8.5	even	2
896.2.z.b.31.11		56	112.45	odd	12
896.2.z.b.159.11		56	16.13	even	4
896.2.z.b.479.11		56	56.3	even	6
896.2.z.b.607.11		56	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	448.z (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.388227 - 1.44888i) q^{3} +(2.81809 - 0.755106i) q^{5} +(1.47726 - 2.19493i) q^{7} +(0.649537 + 0.375010i) q^{9} +O(q^{10})\)	\(q+(0.388227 - 1.44888i) q^{3} +(2.81809 - 0.755106i) q^{5} +(1.47726 - 2.19493i) q^{7} +(0.649537 + 0.375010i) q^{9} +(-0.0165920 + 0.0619222i) q^{11} +(-3.62997 + 3.62997i) q^{13} -4.37624i q^{15} +(3.26044 - 1.88242i) q^{17} +(-2.13834 + 0.572967i) q^{19} +(-2.60668 - 2.99251i) q^{21} +(-3.80570 + 6.59167i) q^{23} +(3.04134 - 1.75592i) q^{25} +(3.97748 - 3.97748i) q^{27} +(-4.74233 - 4.74233i) q^{29} +(0.329500 + 0.570711i) q^{31} +(0.0832764 + 0.0480797i) q^{33} +(2.50566 - 7.30100i) q^{35} +(-1.08717 - 4.05737i) q^{37} +(3.85014 + 6.66865i) q^{39} +7.67610 q^{41} +(2.54426 + 2.54426i) q^{43} +(2.11363 + 0.566345i) q^{45} +(-2.62703 + 4.55014i) q^{47} +(-2.63540 - 6.48496i) q^{49} +(-1.46161 - 5.45480i) q^{51} +(-10.1607 - 2.72255i) q^{53} +0.187031i q^{55} +3.32064i q^{57} +(-2.43435 - 0.652282i) q^{59} +(1.84853 + 6.89881i) q^{61} +(1.78266 - 0.871698i) q^{63} +(-7.48858 + 12.9706i) q^{65} +(-5.98832 - 1.60456i) q^{67} +(8.07307 + 8.07307i) q^{69} -1.08883 q^{71} +(-0.0232448 - 0.0402613i) q^{73} +(-1.36339 - 5.08824i) q^{75} +(0.111404 + 0.127893i) q^{77} +(15.2466 + 8.80264i) q^{79} +(-3.09370 - 5.35845i) q^{81} +(5.07720 + 5.07720i) q^{83} +(7.76681 - 7.76681i) q^{85} +(-8.71217 + 5.02997i) q^{87} +(-4.47814 + 7.75636i) q^{89} +(2.60510 + 13.3299i) q^{91} +(0.954814 - 0.255842i) q^{93} +(-5.59340 + 3.22935i) q^{95} +1.85612i q^{97} +(-0.0339986 + 0.0339986i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 6 q^{3} - 6 q^{5} + 8 q^{7}+O(q^{10}) \) 56 * q + 6 * q^3 - 6 * q^5 + 8 * q^7	\( 56 q + 6 q^{3} - 6 q^{5} + 8 q^{7} - 2 q^{11} - 12 q^{17} + 6 q^{19} - 10 q^{21} + 12 q^{23} - 24 q^{29} - 12 q^{33} + 2 q^{35} + 6 q^{37} + 4 q^{39} + 12 q^{45} - 8 q^{49} + 34 q^{51} + 6 q^{53} - 42 q^{59} - 6 q^{61} - 4 q^{65} - 6 q^{67} + 80 q^{71} - 24 q^{75} + 10 q^{77} - 8 q^{81} - 28 q^{85} + 12 q^{87} - 16 q^{91} + 10 q^{93} + 16 q^{99}+O(q^{100}) \) 56 * q + 6 * q^3 - 6 * q^5 + 8 * q^7 - 2 * q^11 - 12 * q^17 + 6 * q^19 - 10 * q^21 + 12 * q^23 - 24 * q^29 - 12 * q^33 + 2 * q^35 + 6 * q^37 + 4 * q^39 + 12 * q^45 - 8 * q^49 + 34 * q^51 + 6 * q^53 - 42 * q^59 - 6 * q^61 - 4 * q^65 - 6 * q^67 + 80 * q^71 - 24 * q^75 + 10 * q^77 - 8 * q^81 - 28 * q^85 + 12 * q^87 - 16 * q^91 + 10 * q^93 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more