LMFDB - Embedded newform 1568.2.i.v.961.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1568,2,Mod(961,1568)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1568, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("1568.961");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1568 = 2^{5} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1568.i (of order $3$, 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:	$12.5205430369$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 224)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.2
Root			$0.809017 + 1.40126i$ of defining polynomial
Character	$\chi$	$=$	1568.961
Dual form			1568.2.i.v.1537.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.61803 + 2.80252i) q^{3} +(0.618034 - 1.07047i) q^{5} +(-3.73607 + 6.47106i) q^{9} +O(q^{10})$	\(q+(1.61803 + 2.80252i) q^{3} +(0.618034 - 1.07047i) q^{5} +(-3.73607 + 6.47106i) q^{9} +(-1.23607 - 2.14093i) q^{11} +5.23607 q^{13} +4.00000 q^{15} +(2.23607 + 3.87298i) q^{17} +(-1.61803 + 2.80252i) q^{19} +(-2.00000 + 3.46410i) q^{23} +(1.73607 + 3.00696i) q^{25} -14.4721 q^{27} +4.47214 q^{29} +(-3.23607 - 5.60503i) q^{31} +(4.00000 - 6.92820i) q^{33} +(-2.23607 + 3.87298i) q^{37} +(8.47214 + 14.6742i) q^{39} +0.472136 q^{41} -2.47214 q^{43} +(4.61803 + 7.99867i) q^{45} +(-0.763932 + 1.32317i) q^{47} +(-7.23607 + 12.5332i) q^{51} +(5.00000 + 8.66025i) q^{53} -3.05573 q^{55} -10.4721 q^{57} +(2.38197 + 4.12569i) q^{59} +(-3.38197 + 5.85774i) q^{61} +(3.23607 - 5.60503i) q^{65} +(-2.00000 - 3.46410i) q^{67} -12.9443 q^{69} +12.9443 q^{71} +(-7.47214 - 12.9421i) q^{73} +(-5.61803 + 9.73072i) q^{75} +(2.47214 - 4.28187i) q^{79} +(-12.2082 - 21.1452i) q^{81} -4.76393 q^{83} +5.52786 q^{85} +(7.23607 + 12.5332i) q^{87} +(3.00000 - 5.19615i) q^{89} +(10.4721 - 18.1383i) q^{93} +(2.00000 + 3.46410i) q^{95} +3.52786 q^{97} +18.4721 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 2 q^{5} - 6 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 - 2 * q^5 - 6 * q^9	$ 4 q + 2 q^{3} - 2 q^{5} - 6 q^{9} + 4 q^{11} + 12 q^{13} + 16 q^{15} - 2 q^{19} - 8 q^{23} - 2 q^{25} - 40 q^{27} - 4 q^{31} + 16 q^{33} + 16 q^{39} - 16 q^{41} + 8 q^{43} + 14 q^{45} - 12 q^{47} - 20 q^{51} + 20 q^{53} - 48 q^{55} - 24 q^{57} + 14 q^{59} - 18 q^{61} + 4 q^{65} - 8 q^{67} - 16 q^{69} + 16 q^{71} - 12 q^{73} - 18 q^{75} - 8 q^{79} - 22 q^{81} - 28 q^{83} + 40 q^{85} + 20 q^{87} + 12 q^{89} + 24 q^{93} + 8 q^{95} + 32 q^{97} + 56 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 - 2 * q^5 - 6 * q^9 + 4 * q^11 + 12 * q^13 + 16 * q^15 - 2 * q^19 - 8 * q^23 - 2 * q^25 - 40 * q^27 - 4 * q^31 + 16 * q^33 + 16 * q^39 - 16 * q^41 + 8 * q^43 + 14 * q^45 - 12 * q^47 - 20 * q^51 + 20 * q^53 - 48 * q^55 - 24 * q^57 + 14 * q^59 - 18 * q^61 + 4 * q^65 - 8 * q^67 - 16 * q^69 + 16 * q^71 - 12 * q^73 - 18 * q^75 - 8 * q^79 - 22 * q^81 - 28 * q^83 + 40 * q^85 + 20 * q^87 + 12 * q^89 + 24 * q^93 + 8 * q^95 + 32 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1568\mathbb{Z}\right)^\times$.

$n$	$197$	$1471$	$1473$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.61803	+	2.80252i	0.934172	+	1.61803i	0.776103	+	0.630606i	$0.217194\pi$
$3$	1.61803	+	2.80252i	0.934172	+	1.61803i	0.158069	+	0.987428i	$0.449473\pi$
$4$		0			0
$5$	0.618034	−	1.07047i	0.276393	−	0.478727i	−0.694092	−	0.719886i	$-0.744194\pi$
$5$	0.618034	−	1.07047i	0.276393	−	0.478727i	0.970486	+	0.241159i	$0.0775275\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−3.73607	+	6.47106i	−1.24536	+	2.15702i
$10$		0			0
$11$	−1.23607	−	2.14093i	−0.372689	−	0.645515i	0.617290	−	0.786736i	$-0.288231\pi$
$11$	−1.23607	−	2.14093i	−0.372689	−	0.645515i	−0.989978	+	0.141221i	$0.954897\pi$
$12$		0			0
$13$	5.23607			1.45222			0.726112	−	0.687576i	$-0.241325\pi$
$13$	5.23607			1.45222			0.726112	+	0.687576i	$0.241325\pi$
$14$		0			0
$15$	4.00000			1.03280
$16$		0			0
$17$	2.23607	+	3.87298i	0.542326	+	0.939336i	0.998770	+	0.0495842i	$0.0157896\pi$
$17$	2.23607	+	3.87298i	0.542326	+	0.939336i	−0.456444	+	0.889752i	$0.650877\pi$
$18$		0			0
$19$	−1.61803	+	2.80252i	−0.371202	+	0.642942i	−0.989751	−	0.142805i	$-0.954388\pi$
$19$	−1.61803	+	2.80252i	−0.371202	+	0.642942i	0.618548	+	0.785747i	$0.287721\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	−0.995639	−	0.0932891i	$-0.970262\pi$
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	0.578610	+	0.815604i	$0.303595\pi$
$24$		0			0
$25$	1.73607	+	3.00696i	0.347214	+	0.601392i
$26$		0			0
$27$	−14.4721			−2.78516
$28$		0			0
$29$	4.47214			0.830455			0.415227	−	0.909718i	$-0.363702\pi$
$29$	4.47214			0.830455			0.415227	+	0.909718i	$0.363702\pi$
$30$		0			0
$31$	−3.23607	−	5.60503i	−0.581215	−	1.00669i	−0.995336	−	0.0964719i	$-0.969244\pi$
$31$	−3.23607	−	5.60503i	−0.581215	−	1.00669i	0.414121	−	0.910222i	$-0.364089\pi$
$32$		0			0
$33$	4.00000	−	6.92820i	0.696311	−	1.20605i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−2.23607	+	3.87298i	−0.367607	+	0.636715i	−0.989191	−	0.146633i	$-0.953156\pi$
$37$	−2.23607	+	3.87298i	−0.367607	+	0.636715i	0.621584	+	0.783348i	$0.286490\pi$
$38$		0			0
$39$	8.47214	+	14.6742i	1.35663	+	2.34975i
$40$		0			0
$41$	0.472136			0.0737352			0.0368676	−	0.999320i	$-0.488262\pi$
$41$	0.472136			0.0737352			0.0368676	+	0.999320i	$0.488262\pi$
$42$		0			0
$43$	−2.47214			−0.376997			−0.188499	−	0.982073i	$-0.560362\pi$
$43$	−2.47214			−0.376997			−0.188499	+	0.982073i	$0.560362\pi$
$44$		0			0
$45$	4.61803	+	7.99867i	0.688416	+	1.19237i
$46$		0			0
$47$	−0.763932	+	1.32317i	−0.111431	+	0.193004i	−0.916347	−	0.400384i	$-0.868877\pi$
$47$	−0.763932	+	1.32317i	−0.111431	+	0.193004i	0.804916	+	0.593388i	$0.202210\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−7.23607	+	12.5332i	−1.01325	+	1.75500i
$52$		0			0
$53$	5.00000	+	8.66025i	0.686803	+	1.18958i	0.972867	+	0.231367i	$0.0743197\pi$
$53$	5.00000	+	8.66025i	0.686803	+	1.18958i	−0.286064	+	0.958211i	$0.592347\pi$
$54$		0			0
$55$	−3.05573			−0.412034
$56$		0			0
$57$	−10.4721			−1.38707
$58$		0			0
$59$	2.38197	+	4.12569i	0.310106	+	0.537119i	0.978385	−	0.206792i	$-0.0663023\pi$
$59$	2.38197	+	4.12569i	0.310106	+	0.537119i	−0.668279	+	0.743910i	$0.732969\pi$
$60$		0			0
$61$	−3.38197	+	5.85774i	−0.433016	+	0.750006i	−0.997131	−	0.0756898i	$-0.975884\pi$
$61$	−3.38197	+	5.85774i	−0.433016	+	0.750006i	0.564115	+	0.825696i	$0.309217\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	3.23607	−	5.60503i	0.401385	−	0.695219i
$66$		0			0
$67$	−2.00000	−	3.46410i	−0.244339	−	0.423207i	0.717607	−	0.696449i	$-0.245238\pi$
$67$	−2.00000	−	3.46410i	−0.244339	−	0.423207i	−0.961946	+	0.273241i	$0.911904\pi$
$68$		0			0
$69$	−12.9443			−1.55831
$70$		0			0
$71$	12.9443			1.53620			0.768101	−	0.640328i	$-0.221202\pi$
$71$	12.9443			1.53620			0.768101	+	0.640328i	$0.221202\pi$
$72$		0			0
$73$	−7.47214	−	12.9421i	−0.874547	−	1.51476i	−0.857244	−	0.514910i	$-0.827825\pi$
$73$	−7.47214	−	12.9421i	−0.874547	−	1.51476i	−0.0173032	−	0.999850i	$-0.505508\pi$
$74$		0			0
$75$	−5.61803	+	9.73072i	−0.648715	+	1.12361i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	2.47214	−	4.28187i	0.278137	−	0.481747i	−0.692785	−	0.721144i	$-0.743616\pi$
$79$	2.47214	−	4.28187i	0.278137	−	0.481747i	0.970922	+	0.239397i	$0.0769497\pi$
$80$		0			0
$81$	−12.2082	−	21.1452i	−1.35647	−	2.34947i
$82$		0			0
$83$	−4.76393			−0.522909			−0.261455	−	0.965216i	$-0.584202\pi$
$83$	−4.76393			−0.522909			−0.261455	+	0.965216i	$0.584202\pi$
$84$		0			0
$85$	5.52786			0.599581
$86$		0			0
$87$	7.23607	+	12.5332i	0.775788	+	1.34370i
$88$		0			0
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	−0.662071	−	0.749441i	$-0.730322\pi$
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	0.980071	+	0.198650i	$0.0636557\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	10.4721	−	18.1383i	1.08591	−	1.88085i
$94$		0			0
$95$	2.00000	+	3.46410i	0.205196	+	0.355409i
$96$		0			0
$97$	3.52786			0.358200			0.179100	−	0.983831i	$-0.442681\pi$
$97$	3.52786			0.358200			0.179100	+	0.983831i	$0.442681\pi$
$98$		0			0
$99$	18.4721			1.85652
$100$		0			0
$101$	−5.85410	−	10.1396i	−0.582505	−	1.00893i	−0.995181	−	0.0980505i	$-0.968739\pi$
$101$	−5.85410	−	10.1396i	−0.582505	−	1.00893i	0.412677	−	0.910878i	$-0.364594\pi$
$102$		0			0
$103$	7.23607	−	12.5332i	0.712991	−	1.23494i	−0.250738	−	0.968055i	$-0.580673\pi$
$103$	7.23607	−	12.5332i	0.712991	−	1.23494i	0.963729	−	0.266882i	$-0.0859933\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.47214	−	7.74597i	0.432338	−	0.748831i	−0.564736	−	0.825271i	$-0.691022\pi$
$107$	4.47214	−	7.74597i	0.432338	−	0.748831i	0.997074	+	0.0764405i	$0.0243555\pi$
$108$		0			0
$109$	0.236068	+	0.408882i	0.0226112	+	0.0391638i	0.877110	−	0.480290i	$-0.159469\pi$
$109$	0.236068	+	0.408882i	0.0226112	+	0.0391638i	−0.854498	+	0.519454i	$0.826135\pi$
$110$		0			0
$111$	−14.4721			−1.37363
$112$		0			0
$113$	−3.52786			−0.331874			−0.165937	−	0.986136i	$-0.553065\pi$
$113$	−3.52786			−0.331874			−0.165937	+	0.986136i	$0.553065\pi$
$114$		0			0
$115$	2.47214	+	4.28187i	0.230528	+	0.399286i
$116$		0			0
$117$	−19.5623	+	33.8829i	−1.80854	+	3.13248i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	2.44427	−	4.23360i	0.222207	−	0.384873i
$122$		0			0
$123$	0.763932	+	1.32317i	0.0688814	+	0.119306i
$124$		0			0
$125$	10.4721			0.936656
$126$		0			0
$127$	−8.94427			−0.793676			−0.396838	−	0.917889i	$-0.629892\pi$
$127$	−8.94427			−0.793676			−0.396838	+	0.917889i	$0.629892\pi$
$128$		0			0
$129$	−4.00000	−	6.92820i	−0.352180	−	0.609994i
$130$		0			0
$131$	0.854102	−	1.47935i	0.0746232	−	0.129251i	−0.826299	−	0.563232i	$-0.809558\pi$
$131$	0.854102	−	1.47935i	0.0746232	−	0.129251i	0.900922	+	0.433980i	$0.142891\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−8.94427	+	15.4919i	−0.769800	+	1.33333i
$136$		0			0
$137$	1.47214	+	2.54981i	0.125773	+	0.217845i	0.922035	−	0.387107i	$-0.126526\pi$
$137$	1.47214	+	2.54981i	0.125773	+	0.217845i	−0.796262	+	0.604952i	$0.793192\pi$
$138$		0			0
$139$	−3.23607			−0.274480			−0.137240	−	0.990538i	$-0.543823\pi$
$139$	−3.23607			−0.274480			−0.137240	+	0.990538i	$0.543823\pi$
$140$		0			0
$141$	−4.94427			−0.416383
$142$		0			0
$143$	−6.47214	−	11.2101i	−0.541227	−	0.937433i
$144$		0			0
$145$	2.76393	−	4.78727i	0.229532	−	0.397561i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	7.47214	−	12.9421i	0.612141	−	1.06026i	−0.378738	−	0.925504i	$-0.623642\pi$
$149$	7.47214	−	12.9421i	0.612141	−	1.06026i	0.990879	−	0.134756i	$-0.0430249\pi$
$150$		0			0
$151$	−4.47214	−	7.74597i	−0.363937	−	0.630358i	0.624668	−	0.780891i	$-0.285234\pi$
$151$	−4.47214	−	7.74597i	−0.363937	−	0.630358i	−0.988605	+	0.150533i	$0.951901\pi$
$152$		0			0
$153$	−33.4164			−2.70156
$154$		0			0
$155$	−8.00000			−0.642575
$156$		0			0
$157$	−2.61803	−	4.53457i	−0.208942	−	0.361898i	0.742440	−	0.669913i	$-0.233669\pi$
$157$	−2.61803	−	4.53457i	−0.208942	−	0.361898i	−0.951381	+	0.308015i	$0.900335\pi$
$158$		0			0
$159$	−16.1803	+	28.0252i	−1.28318	+	2.22254i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−11.7082	+	20.2792i	−0.917057	+	1.58839i	−0.113196	+	0.993573i	$0.536109\pi$
$163$	−11.7082	+	20.2792i	−0.917057	+	1.58839i	−0.803861	+	0.594817i	$0.797224\pi$
$164$		0			0
$165$	−4.94427	−	8.56373i	−0.384911	−	0.666685i
$166$		0			0
$167$	−3.41641			−0.264370			−0.132185	−	0.991225i	$-0.542199\pi$
$167$	−3.41641			−0.264370			−0.132185	+	0.991225i	$0.542199\pi$
$168$		0			0
$169$	14.4164			1.10895
$170$		0			0
$171$	−12.0902	−	20.9408i	−0.924558	−	1.60138i
$172$		0			0
$173$	3.85410	−	6.67550i	0.293022	−	0.507529i	−0.681501	−	0.731817i	$-0.738672\pi$
$173$	3.85410	−	6.67550i	0.293022	−	0.507529i	0.974523	+	0.224288i	$0.0720058\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−7.70820	+	13.3510i	−0.579384	+	1.00352i
$178$		0			0
$179$	12.4721	+	21.6024i	0.932211	+	1.61464i	0.779533	+	0.626361i	$0.215456\pi$
$179$	12.4721	+	21.6024i	0.932211	+	1.61464i	0.152678	+	0.988276i	$0.451210\pi$
$180$		0			0
$181$	10.1803			0.756699			0.378349	−	0.925663i	$-0.376492\pi$
$181$	10.1803			0.756699			0.378349	+	0.925663i	$0.376492\pi$
$182$		0			0
$183$	−21.8885			−1.61805
$184$		0			0
$185$	2.76393	+	4.78727i	0.203208	+	0.351967i
$186$		0			0
$187$	5.52786	−	9.57454i	0.404237	−	0.700160i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	6.47214	−	11.2101i	0.468307	−	0.811132i	−0.531037	−	0.847349i	$-0.678197\pi$
$191$	6.47214	−	11.2101i	0.468307	−	0.811132i	0.999344	+	0.0362168i	$0.0115307\pi$
$192$		0			0
$193$	4.23607	+	7.33708i	0.304919	+	0.528135i	0.977243	−	0.212122i	$-0.0680373\pi$
$193$	4.23607	+	7.33708i	0.304919	+	0.528135i	−0.672324	+	0.740257i	$0.734704\pi$
$194$		0			0
$195$	20.9443			1.49985
$196$		0			0
$197$	−6.94427			−0.494759			−0.247379	−	0.968919i	$-0.579569\pi$
$197$	−6.94427			−0.494759			−0.247379	+	0.968919i	$0.579569\pi$
$198$		0			0
$199$	5.70820	+	9.88690i	0.404644	+	0.700864i	0.994280	−	0.106805i	$-0.0340622\pi$
$199$	5.70820	+	9.88690i	0.404644	+	0.700864i	−0.589636	+	0.807669i	$0.700729\pi$
$200$		0			0
$201$	6.47214	−	11.2101i	0.456509	−	0.790697i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	0.291796	−	0.505406i	0.0203799	−	0.0352991i
$206$		0			0
$207$	−14.9443	−	25.8842i	−1.03870	−	1.79908i
$208$		0			0
$209$	8.00000			0.553372
$210$		0			0
$211$	−12.0000			−0.826114			−0.413057	−	0.910705i	$-0.635539\pi$
$211$	−12.0000			−0.826114			−0.413057	+	0.910705i	$0.635539\pi$
$212$		0			0
$213$	20.9443	+	36.2765i	1.43508	+	2.48563i
$214$		0			0
$215$	−1.52786	+	2.64634i	−0.104199	+	0.180479i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	24.1803	−	41.8816i	1.63396	−	2.83009i
$220$		0			0
$221$	11.7082	+	20.2792i	0.787579	+	1.36413i
$222$		0			0
$223$	−4.94427			−0.331093			−0.165546	−	0.986202i	$-0.552939\pi$
$223$	−4.94427			−0.331093			−0.165546	+	0.986202i	$0.552939\pi$
$224$		0			0
$225$	−25.9443			−1.72962
$226$		0			0
$227$	6.38197	+	11.0539i	0.423586	+	0.733672i	0.996287	−	0.0860918i	$-0.0274378\pi$
$227$	6.38197	+	11.0539i	0.423586	+	0.733672i	−0.572701	+	0.819764i	$0.694104\pi$
$228$		0			0
$229$	12.7984	−	22.1674i	0.845740	−	1.46487i	−0.0392364	−	0.999230i	$-0.512493\pi$
$229$	12.7984	−	22.1674i	0.845740	−	1.46487i	0.884977	−	0.465635i	$-0.154174\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−9.94427	+	17.2240i	−0.651471	+	1.12838i	0.331295	+	0.943527i	$0.392514\pi$
$233$	−9.94427	+	17.2240i	−0.651471	+	1.12838i	−0.982766	+	0.184854i	$0.940819\pi$
$234$		0			0
$235$	0.944272	+	1.63553i	0.0615975	+	0.106690i
$236$		0			0
$237$	16.0000			1.03931
$238$		0			0
$239$	21.8885			1.41585			0.707926	−	0.706287i	$-0.249631\pi$
$239$	21.8885			1.41585			0.707926	+	0.706287i	$0.249631\pi$
$240$		0			0
$241$	−1.76393	−	3.05522i	−0.113625	−	0.196804i	0.803604	−	0.595164i	$-0.202913\pi$
$241$	−1.76393	−	3.05522i	−0.113625	−	0.196804i	−0.917229	+	0.398360i	$0.869580\pi$
$242$		0			0
$243$	17.7984	−	30.8277i	1.14177	−	1.97760i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−8.47214	+	14.6742i	−0.539069	+	0.933695i
$248$		0			0
$249$	−7.70820	−	13.3510i	−0.488488	−	0.846085i
$250$		0			0
$251$	17.7082			1.11773			0.558866	−	0.829258i	$-0.311237\pi$
$251$	17.7082			1.11773			0.558866	+	0.829258i	$0.311237\pi$
$252$		0			0
$253$	9.88854			0.621687
$254$		0			0
$255$	8.94427	+	15.4919i	0.560112	+	0.970143i
$256$		0			0
$257$	7.00000	−	12.1244i	0.436648	−	0.756297i	−0.560781	−	0.827964i	$-0.689499\pi$
$257$	7.00000	−	12.1244i	0.436648	−	0.756297i	0.997429	+	0.0716680i	$0.0228322\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−16.7082	+	28.9395i	−1.03421	+	1.79131i
$262$		0			0
$263$	−14.4721	−	25.0665i	−0.892390	−	1.54567i	−0.837002	−	0.547200i	$-0.815694\pi$
$263$	−14.4721	−	25.0665i	−0.892390	−	1.54567i	−0.0553884	−	0.998465i	$-0.517640\pi$
$264$		0			0
$265$	12.3607			0.759311
$266$		0			0
$267$	19.4164			1.18826
$268$		0			0
$269$	−9.09017	−	15.7446i	−0.554237	−	0.959967i	−0.997962	−	0.0638044i	$-0.979677\pi$
$269$	−9.09017	−	15.7446i	−0.554237	−	0.959967i	0.443725	−	0.896163i	$-0.353657\pi$
$270$		0			0
$271$	12.0000	−	20.7846i	0.728948	−	1.26258i	−0.228380	−	0.973572i	$-0.573343\pi$
$271$	12.0000	−	20.7846i	0.728948	−	1.26258i	0.957328	−	0.289003i	$-0.0933238\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	4.29180	−	7.43361i	0.258805	−	0.448263i
$276$		0			0
$277$	13.9443	+	24.1522i	0.837830	+	1.45116i	0.891705	+	0.452617i	$0.149509\pi$
$277$	13.9443	+	24.1522i	0.837830	+	1.45116i	−0.0538751	+	0.998548i	$0.517157\pi$
$278$		0			0
$279$	48.3607			2.89528
$280$		0			0
$281$	26.0000			1.55103			0.775515	−	0.631329i	$-0.217490\pi$
$281$	26.0000			1.55103			0.775515	+	0.631329i	$0.217490\pi$
$282$		0			0
$283$	−8.09017	−	14.0126i	−0.480911	−	0.832962i	0.518849	−	0.854866i	$-0.326361\pi$
$283$	−8.09017	−	14.0126i	−0.480911	−	0.832962i	−0.999760	+	0.0219039i	$0.993027\pi$
$284$		0			0
$285$	−6.47214	+	11.2101i	−0.383376	+	0.664027i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−1.50000	+	2.59808i	−0.0882353	+	0.152828i
$290$		0			0
$291$	5.70820	+	9.88690i	0.334621	+	0.579580i
$292$		0			0
$293$	−17.2361			−1.00694			−0.503471	−	0.864012i	$-0.667944\pi$
$293$	−17.2361			−1.00694			−0.503471	+	0.864012i	$0.667944\pi$
$294$		0			0
$295$	5.88854			0.342844
$296$		0			0
$297$	17.8885	+	30.9839i	1.03800	+	1.79787i
$298$		0			0
$299$	−10.4721	+	18.1383i	−0.605619	+	1.04896i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	18.9443	−	32.8124i	1.08832	−	1.88503i
$304$		0			0
$305$	4.18034	+	7.24056i	0.239366	+	0.414593i
$306$		0			0
$307$	24.1803			1.38004			0.690022	−	0.723788i	$-0.257601\pi$
$307$	24.1803			1.38004			0.690022	+	0.723788i	$0.257601\pi$
$308$		0			0
$309$	46.8328			2.66423
$310$		0			0
$311$	−4.00000	−	6.92820i	−0.226819	−	0.392862i	0.730044	−	0.683400i	$-0.239499\pi$
$311$	−4.00000	−	6.92820i	−0.226819	−	0.392862i	−0.956864	+	0.290537i	$0.906166\pi$
$312$		0			0
$313$	−0.236068	+	0.408882i	−0.0133434	+	0.0231114i	−0.872620	−	0.488400i	$-0.837581\pi$
$313$	−0.236068	+	0.408882i	−0.0133434	+	0.0231114i	0.859277	+	0.511511i	$0.170914\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−13.4721	+	23.3344i	−0.756671	+	1.31059i	0.187869	+	0.982194i	$0.439842\pi$
$317$	−13.4721	+	23.3344i	−0.756671	+	1.31059i	−0.944540	+	0.328398i	$0.893491\pi$
$318$		0			0
$319$	−5.52786	−	9.57454i	−0.309501	−	0.536071i
$320$		0			0
$321$	28.9443			1.61551
$322$		0			0
$323$	−14.4721			−0.805251
$324$		0			0
$325$	9.09017	+	15.7446i	0.504232	+	0.873355i
$326$		0			0
$327$	−0.763932	+	1.32317i	−0.0422455	+	0.0731714i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−6.76393	+	11.7155i	−0.371779	+	0.643941i	−0.989839	−	0.142190i	$-0.954586\pi$
$331$	−6.76393	+	11.7155i	−0.371779	+	0.643941i	0.618060	+	0.786131i	$0.287919\pi$
$332$		0			0
$333$	−16.7082	−	28.9395i	−0.915604	−	1.58587i
$334$		0			0
$335$	−4.94427			−0.270134
$336$		0			0
$337$	−34.3607			−1.87175			−0.935873	−	0.352338i	$-0.885387\pi$
$337$	−34.3607			−1.87175			−0.935873	+	0.352338i	$0.885387\pi$
$338$		0			0
$339$	−5.70820	−	9.88690i	−0.310027	−	0.536983i
$340$		0			0
$341$	−8.00000	+	13.8564i	−0.433224	+	0.750366i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−8.00000	+	13.8564i	−0.430706	+	0.746004i
$346$		0			0
$347$	1.23607	+	2.14093i	0.0663556	+	0.114931i	0.897295	−	0.441432i	$-0.145529\pi$
$347$	1.23607	+	2.14093i	0.0663556	+	0.114931i	−0.830939	+	0.556364i	$0.812196\pi$
$348$		0			0
$349$	−4.65248			−0.249041			−0.124521	−	0.992217i	$-0.539739\pi$
$349$	−4.65248			−0.249041			−0.124521	+	0.992217i	$0.539739\pi$
$350$		0			0
$351$	−75.7771			−4.04468
$352$		0			0
$353$	−9.94427	−	17.2240i	−0.529280	−	0.916740i	−0.999417	−	0.0341465i	$-0.989129\pi$
$353$	−9.94427	−	17.2240i	−0.529280	−	0.916740i	0.470137	−	0.882594i	$-0.344205\pi$
$354$		0			0
$355$	8.00000	−	13.8564i	0.424596	−	0.735422i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−0.472136	+	0.817763i	−0.0249184	+	0.0431599i	−0.878216	−	0.478265i	$-0.841266\pi$
$359$	−0.472136	+	0.817763i	−0.0249184	+	0.0431599i	0.853297	+	0.521425i	$0.174599\pi$
$360$		0			0
$361$	4.26393	+	7.38535i	0.224417	+	0.388702i
$362$		0			0
$363$	15.8197			0.830317
$364$		0			0
$365$	−18.4721			−0.966876
$366$		0			0
$367$	−15.4164	−	26.7020i	−0.804730	−	1.39383i	−0.916473	−	0.400096i	$-0.868977\pi$
$367$	−15.4164	−	26.7020i	−0.804730	−	1.39383i	0.111743	−	0.993737i	$-0.464357\pi$
$368$		0			0
$369$	−1.76393	+	3.05522i	−0.0918266	+	0.159048i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	7.47214	−	12.9421i	0.386893	−	0.670118i	−0.605137	−	0.796121i	$-0.706882\pi$
$373$	7.47214	−	12.9421i	0.386893	−	0.670118i	0.992030	+	0.126004i	$0.0402151\pi$
$374$		0			0
$375$	16.9443	+	29.3483i	0.874998	+	1.51554i
$376$		0			0
$377$	23.4164			1.20601
$378$		0			0
$379$	−31.4164			−1.61375			−0.806876	−	0.590721i	$-0.798844\pi$
$379$	−31.4164			−1.61375			−0.806876	+	0.590721i	$0.798844\pi$
$380$		0			0
$381$	−14.4721	−	25.0665i	−0.741430	−	1.28419i
$382$		0			0
$383$	−5.70820	+	9.88690i	−0.291676	+	0.505197i	−0.974206	−	0.225660i	$-0.927546\pi$
$383$	−5.70820	+	9.88690i	−0.291676	+	0.505197i	0.682530	+	0.730857i	$0.260879\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	9.23607	−	15.9973i	0.469496	−	0.813190i
$388$		0			0
$389$	−2.23607	−	3.87298i	−0.113373	−	0.196368i	0.803755	−	0.594960i	$-0.202832\pi$
$389$	−2.23607	−	3.87298i	−0.113373	−	0.196368i	−0.917128	+	0.398592i	$0.869499\pi$
$390$		0			0
$391$	−17.8885			−0.904663
$392$		0			0
$393$	5.52786			0.278844
$394$		0			0
$395$	−3.05573	−	5.29268i	−0.153750	−	0.266303i
$396$		0			0
$397$	5.38197	−	9.32184i	0.270113	−	0.467850i	−0.698777	−	0.715339i	$-0.746272\pi$
$397$	5.38197	−	9.32184i	0.270113	−	0.467850i	0.968891	+	0.247489i	$0.0796056\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	16.2361	−	28.1217i	0.810791	−	1.40433i	−0.101521	−	0.994833i	$-0.532371\pi$
$401$	16.2361	−	28.1217i	0.810791	−	1.40433i	0.912311	−	0.409497i	$-0.134296\pi$
$402$		0			0
$403$	−16.9443	−	29.3483i	−0.844054	−	1.46194i
$404$		0			0
$405$	−30.1803			−1.49967
$406$		0			0
$407$	11.0557			0.548012
$408$		0			0
$409$	−2.70820	−	4.69075i	−0.133912	−	0.231943i	0.791269	−	0.611468i	$-0.209421\pi$
$409$	−2.70820	−	4.69075i	−0.133912	−	0.231943i	−0.925181	+	0.379525i	$0.876087\pi$
$410$		0			0
$411$	−4.76393	+	8.25137i	−0.234987	+	0.407010i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−2.94427	+	5.09963i	−0.144529	+	0.250331i
$416$		0			0
$417$	−5.23607	−	9.06914i	−0.256411	−	0.444117i
$418$		0			0
$419$	−0.180340			−0.00881018			−0.00440509	−	0.999990i	$-0.501402\pi$
$419$	−0.180340			−0.00881018			−0.00440509	+	0.999990i	$0.501402\pi$
$420$		0			0
$421$	−2.00000			−0.0974740			−0.0487370	−	0.998812i	$-0.515520\pi$
$421$	−2.00000			−0.0974740			−0.0487370	+	0.998812i	$0.515520\pi$
$422$		0			0
$423$	−5.70820	−	9.88690i	−0.277542	−	0.480717i
$424$		0			0
$425$	−7.76393	+	13.4475i	−0.376606	+	0.652301i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	20.9443	−	36.2765i	1.01120	−	1.75145i
$430$		0			0
$431$	14.0000	+	24.2487i	0.674356	+	1.16802i	0.976657	+	0.214807i	$0.0689121\pi$
$431$	14.0000	+	24.2487i	0.674356	+	1.16802i	−0.302300	+	0.953213i	$0.597755\pi$
$432$		0			0
$433$	−17.4164			−0.836979			−0.418490	−	0.908222i	$-0.637440\pi$
$433$	−17.4164			−0.836979			−0.418490	+	0.908222i	$0.637440\pi$
$434$		0			0
$435$	17.8885			0.857690
$436$		0			0
$437$	−6.47214	−	11.2101i	−0.309604	−	0.536250i
$438$		0			0
$439$	16.0000	−	27.7128i	0.763638	−	1.32266i	−0.177325	−	0.984152i	$-0.556744\pi$
$439$	16.0000	−	27.7128i	0.763638	−	1.32266i	0.940963	−	0.338508i	$-0.109922\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−10.9443	+	18.9560i	−0.519978	+	0.900628i	0.479752	+	0.877404i	$0.340727\pi$
$443$	−10.9443	+	18.9560i	−0.519978	+	0.900628i	−0.999730	+	0.0232244i	$0.992607\pi$
$444$		0			0
$445$	−3.70820	−	6.42280i	−0.175786	−	0.304470i
$446$		0			0
$447$	48.3607			2.28738
$448$		0			0
$449$	27.8885			1.31614			0.658071	−	0.752956i	$-0.271373\pi$
$449$	27.8885			1.31614			0.658071	+	0.752956i	$0.271373\pi$
$450$		0			0
$451$	−0.583592	−	1.01081i	−0.0274803	−	0.0475972i
$452$		0			0
$453$	14.4721	−	25.0665i	0.679960	−	1.17773i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	8.23607	−	14.2653i	0.385267	−	0.667302i	−0.606539	−	0.795054i	$-0.707443\pi$
$457$	8.23607	−	14.2653i	0.385267	−	0.667302i	0.991806	+	0.127752i	$0.0407760\pi$
$458$		0			0
$459$	−32.3607	−	56.0503i	−1.51047	−	2.61621i
$460$		0			0
$461$	8.29180			0.386187			0.193094	−	0.981180i	$-0.438148\pi$
$461$	8.29180			0.386187			0.193094	+	0.981180i	$0.438148\pi$
$462$		0			0
$463$	35.7771			1.66270			0.831351	−	0.555748i	$-0.187568\pi$
$463$	35.7771			1.66270			0.831351	+	0.555748i	$0.187568\pi$
$464$		0			0
$465$	−12.9443	−	22.4201i	−0.600276	−	1.03971i
$466$		0			0
$467$	−13.0344	+	22.5763i	−0.603162	+	1.04471i	0.389177	+	0.921163i	$0.372759\pi$
$467$	−13.0344	+	22.5763i	−0.603162	+	1.04471i	−0.992339	+	0.123544i	$0.960574\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	8.47214	−	14.6742i	0.390375	−	0.676150i
$472$		0			0
$473$	3.05573	+	5.29268i	0.140503	+	0.243358i
$474$		0			0
$475$	−11.2361			−0.515546
$476$		0			0
$477$	−74.7214			−3.42126
$478$		0			0
$479$	17.7082	+	30.6715i	0.809108	+	1.40142i	0.913482	+	0.406879i	$0.133383\pi$
$479$	17.7082	+	30.6715i	0.809108	+	1.40142i	−0.104374	+	0.994538i	$0.533284\pi$
$480$		0			0
$481$	−11.7082	+	20.2792i	−0.533848	+	0.924652i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	2.18034	−	3.77646i	0.0990041	−	0.171480i
$486$		0			0
$487$	−10.0000	−	17.3205i	−0.453143	−	0.784867i	0.545436	−	0.838152i	$-0.316364\pi$
$487$	−10.0000	−	17.3205i	−0.453143	−	0.784867i	−0.998579	+	0.0532853i	$0.983031\pi$
$488$		0			0
$489$	−75.7771			−3.42676
$490$		0			0
$491$	2.11146			0.0952887			0.0476443	−	0.998864i	$-0.484829\pi$
$491$	2.11146			0.0952887			0.0476443	+	0.998864i	$0.484829\pi$
$492$		0			0
$493$	10.0000	+	17.3205i	0.450377	+	0.780076i
$494$		0			0
$495$	11.4164	−	19.7738i	0.513129	−	0.888766i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	6.94427	−	12.0278i	0.310868	−	0.538440i	−0.667682	−	0.744446i	$-0.732714\pi$
$499$	6.94427	−	12.0278i	0.310868	−	0.538440i	0.978551	+	0.206007i	$0.0660469\pi$
$500$		0			0
$501$	−5.52786	−	9.57454i	−0.246967	−	0.427759i
$502$		0			0
$503$	12.9443			0.577157			0.288578	−	0.957456i	$-0.406817\pi$
$503$	12.9443			0.577157			0.288578	+	0.957456i	$0.406817\pi$
$504$		0			0
$505$	−14.4721			−0.644002
$506$		0			0
$507$	23.3262	+	40.4022i	1.03595	+	1.79433i
$508$		0			0
$509$	0.437694	−	0.758108i	0.0194004	−	0.0336026i	−0.856162	−	0.516707i	$-0.827158\pi$
$509$	0.437694	−	0.758108i	0.0194004	−	0.0336026i	0.875563	+	0.483105i	$0.160491\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	23.4164	−	40.5584i	1.03386	−	1.79070i
$514$		0			0
$515$	−8.94427	−	15.4919i	−0.394132	−	0.682656i
$516$		0			0
$517$	3.77709			0.166116
$518$		0			0
$519$	24.9443			1.09493
$520$		0			0
$521$	16.7082	+	28.9395i	0.732000	+	1.26786i	0.956027	+	0.293278i	$0.0947461\pi$
$521$	16.7082	+	28.9395i	0.732000	+	1.26786i	−0.224028	+	0.974583i	$0.571921\pi$
$522$		0			0
$523$	8.85410	−	15.3358i	0.387163	−	0.670586i	−0.604904	−	0.796299i	$-0.706788\pi$
$523$	8.85410	−	15.3358i	0.387163	−	0.670586i	0.992067	+	0.125713i	$0.0401218\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	14.4721	−	25.0665i	0.630416	−	1.09191i
$528$		0			0
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$		0			0
$531$	−35.5967			−1.54477
$532$		0			0
$533$	2.47214			0.107080
$534$		0			0
$535$	−5.52786	−	9.57454i	−0.238990	−	0.413944i
$536$		0			0
$537$	−40.3607	+	69.9067i	−1.74169	+	3.01670i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	11.4721	−	19.8703i	0.493226	−	0.854292i	−0.506744	−	0.862097i	$-0.669151\pi$
$541$	11.4721	−	19.8703i	0.493226	−	0.854292i	0.999970	+	0.00780476i	$0.00248436\pi$
$542$		0			0
$543$	16.4721	+	28.5306i	0.706887	+	1.22436i
$544$		0			0
$545$	0.583592			0.0249983
$546$		0			0
$547$	−31.4164			−1.34327			−0.671634	−	0.740883i	$-0.734407\pi$
$547$	−31.4164			−1.34327			−0.671634	+	0.740883i	$0.734407\pi$
$548$		0			0
$549$	−25.2705	−	43.7698i	−1.07852	−	1.86805i
$550$		0			0
$551$	−7.23607	+	12.5332i	−0.308267	+	0.533934i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−8.94427	+	15.4919i	−0.379663	+	0.657596i
$556$		0			0
$557$	−13.4721	−	23.3344i	−0.570833	−	0.988711i	−0.996481	−	0.0838224i	$-0.973287\pi$
$557$	−13.4721	−	23.3344i	−0.570833	−	0.988711i	0.425648	−	0.904889i	$-0.360046\pi$
$558$		0			0
$559$	−12.9443			−0.547484
$560$		0			0
$561$	35.7771			1.51051
$562$		0			0
$563$	20.0902	+	34.7972i	0.846700	+	1.46653i	0.884137	+	0.467228i	$0.154747\pi$
$563$	20.0902	+	34.7972i	0.846700	+	1.46653i	−0.0374372	+	0.999299i	$0.511919\pi$
$564$		0			0
$565$	−2.18034	+	3.77646i	−0.0917276	+	0.158877i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	9.18034	−	15.9008i	0.384860	−	0.666597i	−0.606890	−	0.794786i	$-0.707583\pi$
$569$	9.18034	−	15.9008i	0.384860	−	0.666597i	0.991750	+	0.128189i	$0.0409164\pi$
$570$		0			0
$571$	2.76393	+	4.78727i	0.115667	+	0.200341i	0.918046	−	0.396474i	$-0.129766\pi$
$571$	2.76393	+	4.78727i	0.115667	+	0.200341i	−0.802379	+	0.596815i	$0.796433\pi$
$572$		0			0
$573$	41.8885			1.74992
$574$		0			0
$575$	−13.8885			−0.579192
$576$		0			0
$577$	3.00000	+	5.19615i	0.124892	+	0.216319i	0.921691	−	0.387926i	$-0.126808\pi$
$577$	3.00000	+	5.19615i	0.124892	+	0.216319i	−0.796799	+	0.604245i	$0.793475\pi$
$578$		0			0
$579$	−13.7082	+	23.7433i	−0.569694	+	0.986738i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	12.3607	−	21.4093i	0.511927	−	0.886684i
$584$		0			0
$585$	24.1803	+	41.8816i	0.999734	+	1.73159i
$586$		0			0
$587$	9.70820			0.400700			0.200350	−	0.979724i	$-0.435792\pi$
$587$	9.70820			0.400700			0.200350	+	0.979724i	$0.435792\pi$
$588$		0			0
$589$	20.9443			0.862994
$590$		0			0
$591$	−11.2361	−	19.4614i	−0.462190	−	0.800537i
$592$		0			0
$593$	10.4164	−	18.0417i	0.427751	−	0.740886i	−0.568922	−	0.822391i	$-0.692639\pi$
$593$	10.4164	−	18.0417i	0.427751	−	0.740886i	0.996673	+	0.0815055i	$0.0259728\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−18.4721	+	31.9947i	−0.756014	+	1.30945i
$598$		0			0
$599$	8.94427	+	15.4919i	0.365453	+	0.632983i	0.988849	−	0.148923i	$-0.0475807\pi$
$599$	8.94427	+	15.4919i	0.365453	+	0.632983i	−0.623396	+	0.781907i	$0.714247\pi$
$600$		0			0
$601$	−41.7771			−1.70412			−0.852061	−	0.523442i	$-0.824648\pi$
$601$	−41.7771			−1.70412			−0.852061	+	0.523442i	$0.824648\pi$
$602$		0			0
$603$	29.8885			1.21716
$604$		0			0
$605$	−3.02129	−	5.23302i	−0.122833	−	0.212753i
$606$		0			0
$607$	12.9443	−	22.4201i	0.525392	−	0.910005i	−0.474171	−	0.880433i	$-0.657252\pi$
$607$	12.9443	−	22.4201i	0.525392	−	0.910005i	0.999563	−	0.0295724i	$-0.00941457\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−4.00000	+	6.92820i	−0.161823	+	0.280285i
$612$		0			0
$613$	−1.29180	−	2.23746i	−0.0521752	−	0.0903700i	0.838758	−	0.544504i	$-0.183282\pi$
$613$	−1.29180	−	2.23746i	−0.0521752	−	0.0903700i	−0.890933	+	0.454134i	$0.849949\pi$
$614$		0			0
$615$	1.88854			0.0761534
$616$		0			0
$617$	−10.3607			−0.417105			−0.208553	−	0.978011i	$-0.566875\pi$
$617$	−10.3607			−0.417105			−0.208553	+	0.978011i	$0.566875\pi$
$618$		0			0
$619$	−5.03444	−	8.71991i	−0.202351	−	0.350483i	0.746934	−	0.664898i	$-0.231525\pi$
$619$	−5.03444	−	8.71991i	−0.202351	−	0.350483i	−0.949286	+	0.314415i	$0.898192\pi$
$620$		0			0
$621$	28.9443	−	50.1329i	1.16149	−	2.01177i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−2.20820	+	3.82472i	−0.0883282	+	0.152989i
$626$		0			0
$627$	12.9443	+	22.4201i	0.516944	+	0.895374i
$628$		0			0
$629$	−20.0000			−0.797452
$630$		0			0
$631$	−27.0557			−1.07707			−0.538536	−	0.842603i	$-0.681022\pi$
$631$	−27.0557			−1.07707			−0.538536	+	0.842603i	$0.681022\pi$
$632$		0			0
$633$	−19.4164	−	33.6302i	−0.771733	−	1.33668i
$634$		0			0
$635$	−5.52786	+	9.57454i	−0.219367	+	0.379954i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−48.3607	+	83.7632i	−1.91312	+	3.31362i
$640$		0			0
$641$	−20.7082	−	35.8677i	−0.817925	−	1.41669i	−0.907209	−	0.420681i	$-0.861791\pi$
$641$	−20.7082	−	35.8677i	−0.817925	−	1.41669i	0.0892837	−	0.996006i	$-0.471542\pi$
$642$		0			0
$643$	−30.2918			−1.19459			−0.597296	−	0.802021i	$-0.703758\pi$
$643$	−30.2918			−1.19459			−0.597296	+	0.802021i	$0.703758\pi$
$644$		0			0
$645$	−9.88854			−0.389361
$646$		0			0
$647$	−12.1803	−	21.0970i	−0.478859	−	0.829407i	0.520848	−	0.853650i	$-0.325616\pi$
$647$	−12.1803	−	21.0970i	−0.478859	−	0.829407i	−0.999706	+	0.0242423i	$0.992283\pi$
$648$		0			0
$649$	5.88854	−	10.1993i	0.231146	−	0.400356i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−8.70820	+	15.0831i	−0.340778	+	0.590245i	−0.984577	−	0.174949i	$-0.944024\pi$
$653$	−8.70820	+	15.0831i	−0.340778	+	0.590245i	0.643799	+	0.765195i	$0.277357\pi$
$654$		0			0
$655$	−1.05573	−	1.82857i	−0.0412507	−	0.0714483i
$656$		0			0
$657$	111.666			4.35649
$658$		0			0
$659$	−25.3050			−0.985741			−0.492870	−	0.870103i	$-0.664052\pi$
$659$	−25.3050			−0.985741			−0.492870	+	0.870103i	$0.664052\pi$
$660$		0			0
$661$	−4.32624	−	7.49326i	−0.168271	−	0.291454i	0.769541	−	0.638597i	$-0.220485\pi$
$661$	−4.32624	−	7.49326i	−0.168271	−	0.291454i	−0.937812	+	0.347143i	$0.887152\pi$
$662$		0			0
$663$	−37.8885	+	65.6249i	−1.47147	+	2.54866i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−8.94427	+	15.4919i	−0.346324	+	0.599850i
$668$		0			0
$669$	−8.00000	−	13.8564i	−0.309298	−	0.535720i
$670$		0			0
$671$	16.7214			0.645521
$672$		0			0
$673$	14.9443			0.576059			0.288030	−	0.957621i	$-0.407000\pi$
$673$	14.9443			0.576059			0.288030	+	0.957621i	$0.407000\pi$
$674$		0			0
$675$	−25.1246	−	43.5171i	−0.967047	−	1.67497i
$676$		0			0
$677$	−21.0902	+	36.5292i	−0.810561	+	1.40393i	0.101911	+	0.994794i	$0.467504\pi$
$677$	−21.0902	+	36.5292i	−0.810561	+	1.40393i	−0.912472	+	0.409139i	$0.865829\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−20.6525	+	35.7711i	−0.791405	+	1.37075i
$682$		0			0
$683$	23.8885	+	41.3762i	0.914070	+	1.58322i	0.808258	+	0.588829i	$0.200411\pi$
$683$	23.8885	+	41.3762i	0.914070	+	1.58322i	0.105812	+	0.994386i	$0.466256\pi$
$684$		0			0
$685$	3.63932			0.139051
$686$		0			0
$687$	82.8328			3.16027
$688$		0			0
$689$	26.1803	+	45.3457i	0.997392	+	1.72753i
$690$		0			0
$691$	−4.09017	+	7.08438i	−0.155597	+	0.269503i	−0.933276	−	0.359159i	$-0.883064\pi$
$691$	−4.09017	+	7.08438i	−0.155597	+	0.269503i	0.777679	+	0.628662i	$0.216397\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−2.00000	+	3.46410i	−0.0758643	+	0.131401i
$696$		0			0
$697$	1.05573	+	1.82857i	0.0399886	+	0.0692622i
$698$		0			0
$699$	−64.3607			−2.43434
$700$		0			0
$701$	−14.5836			−0.550815			−0.275407	−	0.961328i	$-0.588813\pi$
$701$	−14.5836			−0.550815			−0.275407	+	0.961328i	$0.588813\pi$
$702$		0			0
$703$	−7.23607	−	12.5332i	−0.272913	−	0.472700i
$704$		0			0
$705$	−3.05573	+	5.29268i	−0.115085	+	0.199334i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−23.1803	+	40.1495i	−0.870556	+	1.50785i	−0.00913331	+	0.999958i	$0.502907\pi$
$709$	−23.1803	+	40.1495i	−0.870556	+	1.50785i	−0.861423	+	0.507889i	$0.830426\pi$
$710$		0			0
$711$	18.4721	+	31.9947i	0.692759	+	1.19989i
$712$		0			0
$713$	25.8885			0.969534
$714$		0			0
$715$	−16.0000			−0.598366
$716$		0			0
$717$	35.4164	+	61.3430i	1.32265	+	2.29090i
$718$		0			0
$719$	23.5967	−	40.8708i	0.880010	−	1.52422i	0.0286822	−	0.999589i	$-0.490869\pi$
$719$	23.5967	−	40.8708i	0.880010	−	1.52422i	0.851328	−	0.524634i	$-0.175798\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	5.70820	−	9.88690i	0.212290	−	0.367698i
$724$		0			0
$725$	7.76393	+	13.4475i	0.288345	+	0.499429i
$726$		0			0
$727$	−32.3607			−1.20019			−0.600096	−	0.799928i	$-0.704871\pi$
$727$	−32.3607			−1.20019			−0.600096	+	0.799928i	$0.704871\pi$
$728$		0			0
$729$	41.9443			1.55349
$730$		0			0
$731$	−5.52786	−	9.57454i	−0.204455	−	0.354127i
$732$		0			0
$733$	4.61803	−	7.99867i	0.170571	−	0.295438i	−0.768049	−	0.640391i	$-0.778772\pi$
$733$	4.61803	−	7.99867i	0.170571	−	0.295438i	0.938620	+	0.344954i	$0.112105\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−4.94427	+	8.56373i	−0.182125	+	0.315449i
$738$		0			0
$739$	−11.7082	−	20.2792i	−0.430693	−	0.745983i	0.566240	−	0.824240i	$-0.308398\pi$
$739$	−11.7082	−	20.2792i	−0.430693	−	0.745983i	−0.996933	+	0.0782579i	$0.975064\pi$
$740$		0			0
$741$	−54.8328			−2.01433
$742$		0			0
$743$	7.05573			0.258850			0.129425	−	0.991589i	$-0.458687\pi$
$743$	7.05573			0.258850			0.129425	+	0.991589i	$0.458687\pi$
$744$		0			0
$745$	−9.23607	−	15.9973i	−0.338383	−	0.586097i
$746$		0			0
$747$	17.7984	−	30.8277i	0.651208	−	1.12793i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−18.0000	+	31.1769i	−0.656829	+	1.13766i	0.324603	+	0.945851i	$0.394769\pi$
$751$	−18.0000	+	31.1769i	−0.656829	+	1.13766i	−0.981432	+	0.191811i	$0.938564\pi$
$752$		0			0
$753$	28.6525	+	49.6275i	1.04415	+	1.80853i
$754$		0			0
$755$	−11.0557			−0.402359
$756$		0			0
$757$	−23.3050			−0.847033			−0.423516	−	0.905888i	$-0.639204\pi$
$757$	−23.3050			−0.847033			−0.423516	+	0.905888i	$0.639204\pi$
$758$		0			0
$759$	16.0000	+	27.7128i	0.580763	+	1.00591i
$760$		0			0
$761$	6.23607	−	10.8012i	0.226057	−	0.391543i	−0.730579	−	0.682828i	$-0.760750\pi$
$761$	6.23607	−	10.8012i	0.226057	−	0.391543i	0.956636	+	0.291286i	$0.0940830\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−20.6525	+	35.7711i	−0.746692	+	1.29331i
$766$		0			0
$767$	12.4721	+	21.6024i	0.450343	+	0.780016i
$768$		0			0
$769$	26.3607			0.950590			0.475295	−	0.879826i	$-0.342341\pi$
$769$	26.3607			0.950590			0.475295	+	0.879826i	$0.342341\pi$
$770$		0			0
$771$	45.3050			1.63162
$772$		0			0
$773$	−8.90983	−	15.4323i	−0.320464	−	0.555060i	0.660120	−	0.751161i	$-0.270506\pi$
$773$	−8.90983	−	15.4323i	−0.320464	−	0.555060i	−0.980584	+	0.196100i	$0.937172\pi$
$774$		0			0
$775$	11.2361	−	19.4614i	0.403611	−	0.699076i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−0.763932	+	1.32317i	−0.0273707	+	0.0474075i
$780$		0			0
$781$	−16.0000	−	27.7128i	−0.572525	−	0.991642i
$782$		0			0
$783$	−64.7214			−2.31295
$784$		0			0
$785$	−6.47214			−0.231000
$786$		0			0
$787$	12.8541	+	22.2640i	0.458199	+	0.793624i	0.998866	−	0.0476126i	$-0.0151613\pi$
$787$	12.8541	+	22.2640i	0.458199	+	0.793624i	−0.540667	+	0.841237i	$0.681828\pi$
$788$		0			0
$789$	46.8328	−	81.1168i	1.66729	−	2.88784i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−17.7082	+	30.6715i	−0.628837	+	1.08918i
$794$		0			0
$795$	20.0000	+	34.6410i	0.709327	+	1.22859i
$796$		0			0
$797$	−29.8197			−1.05627			−0.528133	−	0.849161i	$-0.677108\pi$
$797$	−29.8197			−1.05627			−0.528133	+	0.849161i	$0.677108\pi$
$798$		0			0
$799$	−6.83282			−0.241728
$800$		0			0
$801$	22.4164	+	38.8264i	0.792045	+	1.37186i
$802$		0			0
$803$	−18.4721	+	31.9947i	−0.651868	+	1.12907i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	29.4164	−	50.9507i	1.03551	−	1.79355i
$808$		0			0
$809$	−4.70820	−	8.15485i	−0.165532	−	0.286709i	0.771312	−	0.636457i	$-0.219601\pi$
$809$	−4.70820	−	8.15485i	−0.165532	−	0.286709i	−0.936844	+	0.349748i	$0.886267\pi$
$810$		0			0
$811$	23.0132			0.808101			0.404051	−	0.914737i	$-0.367602\pi$
$811$	23.0132			0.808101			0.404051	+	0.914737i	$0.367602\pi$
$812$		0			0
$813$	77.6656			2.72385
$814$		0			0
$815$	14.4721	+	25.0665i	0.506937	+	0.878040i
$816$		0			0
$817$	4.00000	−	6.92820i	0.139942	−	0.242387i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−19.9443	+	34.5445i	−0.696060	+	1.20561i	0.273762	+	0.961797i	$0.411732\pi$
$821$	−19.9443	+	34.5445i	−0.696060	+	1.20561i	−0.969822	+	0.243814i	$0.921601\pi$
$822$		0			0
$823$	−25.8885	−	44.8403i	−0.902418	−	1.56303i	−0.824346	−	0.566086i	$-0.808457\pi$
$823$	−25.8885	−	44.8403i	−0.902418	−	1.56303i	−0.0780717	−	0.996948i	$-0.524876\pi$
$824$		0			0
$825$	27.7771			0.967074
$826$		0			0
$827$	32.9443			1.14558			0.572792	−	0.819701i	$-0.305860\pi$
$827$	32.9443			1.14558			0.572792	+	0.819701i	$0.305860\pi$
$828$		0			0
$829$	−3.38197	−	5.85774i	−0.117461	−	0.203448i	0.801300	−	0.598263i	$-0.204142\pi$
$829$	−3.38197	−	5.85774i	−0.117461	−	0.203448i	−0.918761	+	0.394815i	$0.870809\pi$
$830$		0			0
$831$	−45.1246	+	78.1581i	−1.56536	+	2.71128i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−2.11146	+	3.65715i	−0.0730700	+	0.126561i
$836$		0			0
$837$	46.8328	+	81.1168i	1.61878	+	2.80381i
$838$		0			0
$839$	−30.4721			−1.05201			−0.526007	−	0.850480i	$-0.676312\pi$
$839$	−30.4721			−1.05201			−0.526007	+	0.850480i	$0.676312\pi$
$840$		0			0
$841$	−9.00000			−0.310345
$842$		0			0
$843$	42.0689	+	72.8654i	1.44893	+	2.50962i
$844$		0			0
$845$	8.90983	−	15.4323i	0.306507	−	0.530887i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	26.1803	−	45.3457i	0.898507	−	1.55626i
$850$		0			0
$851$	−8.94427	−	15.4919i	−0.306606	−	0.531057i
$852$		0			0
$853$	0.291796			0.00999091			0.00499545	−	0.999988i	$-0.498410\pi$
$853$	0.291796			0.00999091			0.00499545	+	0.999988i	$0.498410\pi$
$854$		0			0
$855$	−29.8885			−1.02217
$856$		0			0
$857$	18.2361	+	31.5858i	0.622932	+	1.07895i	0.988937	+	0.148337i	$0.0473921\pi$
$857$	18.2361	+	31.5858i	0.622932	+	1.07895i	−0.366005	+	0.930613i	$0.619275\pi$
$858$		0			0
$859$	28.0902	−	48.6536i	0.958424	−	1.66004i	0.232094	−	0.972693i	$-0.425442\pi$
$859$	28.0902	−	48.6536i	0.958424	−	1.66004i	0.726330	−	0.687346i	$-0.241224\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	1.52786	−	2.64634i	0.0520091	−	0.0900824i	−0.838849	−	0.544365i	$-0.816771\pi$
$863$	1.52786	−	2.64634i	0.0520091	−	0.0900824i	0.890858	+	0.454282i	$0.150104\pi$
$864$		0			0
$865$	−4.76393	−	8.25137i	−0.161979	−	0.280555i
$866$		0			0
$867$	−9.70820			−0.329708
$868$		0			0
$869$	−12.2229			−0.414634
$870$		0			0
$871$	−10.4721	−	18.1383i	−0.354835	−	0.614592i
$872$		0			0
$873$	−13.1803	+	22.8290i	−0.446087	+	0.772645i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	6.70820	−	11.6190i	0.226520	−	0.392344i	−0.730254	−	0.683175i	$-0.760598\pi$
$877$	6.70820	−	11.6190i	0.226520	−	0.392344i	0.956774	+	0.290831i	$0.0939318\pi$
$878$		0			0
$879$	−27.8885	−	48.3044i	−0.940657	−	1.62927i
$880$		0			0
$881$	−28.8328			−0.971402			−0.485701	−	0.874125i	$-0.661436\pi$
$881$	−28.8328			−0.971402			−0.485701	+	0.874125i	$0.661436\pi$
$882$		0			0
$883$	40.9443			1.37788			0.688942	−	0.724816i	$-0.258075\pi$
$883$	40.9443			1.37788			0.688942	+	0.724816i	$0.258075\pi$
$884$		0			0
$885$	9.52786	+	16.5027i	0.320276	+	0.554734i
$886$		0			0
$887$	−14.6525	+	25.3788i	−0.491982	+	0.852138i	−0.999957	−	0.00923379i	$-0.997061\pi$
$887$	−14.6525	+	25.3788i	−0.491982	+	0.852138i	0.507975	+	0.861372i	$0.330394\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−30.1803	+	52.2739i	−1.01108	+	1.75124i
$892$		0			0
$893$	−2.47214	−	4.28187i	−0.0827269	−	0.143287i
$894$		0			0
$895$	30.8328			1.03063
$896$		0			0
$897$	−67.7771			−2.26301
$898$		0			0
$899$	−14.4721	−	25.0665i	−0.482673	−	0.836014i
$900$		0			0
$901$	−22.3607	+	38.7298i	−0.744942	+	1.29028i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	6.29180	−	10.8977i	0.209146	−	0.362252i
$906$		0			0
$907$	8.47214	+	14.6742i	0.281313	+	0.487248i	0.971708	−	0.236184i	$-0.0758969\pi$
$907$	8.47214	+	14.6742i	0.281313	+	0.487248i	−0.690396	+	0.723432i	$0.742564\pi$
$908$		0			0
$909$	87.4853			2.90170
$910$		0			0
$911$	18.8328			0.623959			0.311980	−	0.950089i	$-0.399008\pi$
$911$	18.8328			0.623959			0.311980	+	0.950089i	$0.399008\pi$
$912$		0			0
$913$	5.88854	+	10.1993i	0.194882	+	0.337546i
$914$		0			0
$915$	−13.5279	+	23.4309i	−0.447217	+	0.774603i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−17.8885	+	30.9839i	−0.590089	+	1.02206i	0.404131	+	0.914701i	$0.367574\pi$
$919$	−17.8885	+	30.9839i	−0.590089	+	1.02206i	−0.994220	+	0.107362i	$0.965759\pi$
$920$		0			0
$921$	39.1246	+	67.7658i	1.28920	+	2.23296i
$922$		0			0
$923$	67.7771			2.23091
$924$		0			0
$925$	−15.5279			−0.510553
$926$		0			0
$927$	54.0689	+	93.6501i	1.77586	+	3.07587i
$928$		0			0
$929$	−7.65248	+	13.2545i	−0.251070	+	0.434865i	−0.963821	−	0.266552i	$-0.914116\pi$
$929$	−7.65248	+	13.2545i	−0.251070	+	0.434865i	0.712751	+	0.701417i	$0.247449\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	12.9443	−	22.4201i	0.423776	−	0.734002i
$934$		0			0
$935$	−6.83282	−	11.8348i	−0.223457	−	0.387039i
$936$		0			0
$937$	−26.9443			−0.880231			−0.440115	−	0.897941i	$-0.645063\pi$
$937$	−26.9443			−0.880231			−0.440115	+	0.897941i	$0.645063\pi$
$938$		0			0
$939$	−1.52786			−0.0498600
$940$		0			0
$941$	−6.79837	−	11.7751i	−0.221621	−	0.383858i	0.733680	−	0.679496i	$-0.237801\pi$
$941$	−6.79837	−	11.7751i	−0.221621	−	0.383858i	−0.955300	+	0.295637i	$0.904468\pi$
$942$		0			0
$943$	−0.944272	+	1.63553i	−0.0307497	+	0.0532601i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	15.7082	−	27.2074i	0.510448	−	0.884122i	−0.489479	−	0.872015i	$-0.662813\pi$
$947$	15.7082	−	27.2074i	0.510448	−	0.884122i	0.999927	−	0.0121067i	$-0.00385377\pi$
$948$		0			0
$949$	−39.1246	−	67.7658i	−1.27004	−	2.19977i
$950$		0			0
$951$	−87.1935			−2.82744
$952$		0			0
$953$	16.1115			0.521901			0.260951	−	0.965352i	$-0.415964\pi$
$953$	16.1115			0.521901			0.260951	+	0.965352i	$0.415964\pi$
$954$		0			0
$955$	−8.00000	−	13.8564i	−0.258874	−	0.448383i
$956$		0			0
$957$	17.8885	−	30.9839i	0.578254	−	1.00157i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−5.44427	+	9.42976i	−0.175622	+	0.304186i
$962$		0			0
$963$	33.4164	+	57.8789i	1.07683	+	1.86512i
$964$		0			0
$965$	10.4721			0.337110
$966$		0			0
$967$	−5.88854			−0.189363			−0.0946814	−	0.995508i	$-0.530183\pi$
$967$	−5.88854			−0.189363			−0.0946814	+	0.995508i	$0.530183\pi$
$968$		0			0
$969$	−23.4164	−	40.5584i	−0.752243	−	1.30292i
$970$		0			0
$971$	−13.6180	+	23.5871i	−0.437024	+	0.756947i	−0.997458	−	0.0712516i	$-0.977301\pi$
$971$	−13.6180	+	23.5871i	−0.437024	+	0.756947i	0.560435	+	0.828199i	$0.310634\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−29.4164	+	50.9507i	−0.942079	+	1.63173i
$976$		0			0
$977$	−20.4164	−	35.3623i	−0.653179	−	1.13134i	−0.982347	−	0.187068i	$-0.940102\pi$
$977$	−20.4164	−	35.3623i	−0.653179	−	1.13134i	0.329168	−	0.944271i	$-0.393232\pi$
$978$		0			0
$979$	−14.8328			−0.474059
$980$		0			0
$981$	−3.52786			−0.112636
$982$		0			0
$983$	7.23607	+	12.5332i	0.230795	+	0.399748i	0.958042	−	0.286627i	$-0.0925341\pi$
$983$	7.23607	+	12.5332i	0.230795	+	0.399748i	−0.727247	+	0.686375i	$0.759201\pi$
$984$		0			0
$985$	−4.29180	+	7.43361i	−0.136748	+	0.236854i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	4.94427	−	8.56373i	0.157219	−	0.272311i
$990$		0			0
$991$	12.0000	+	20.7846i	0.381193	+	0.660245i	0.991233	−	0.132125i	$-0.0421802\pi$
$991$	12.0000	+	20.7846i	0.381193	+	0.660245i	−0.610040	+	0.792370i	$0.708847\pi$
$992$		0			0
$993$	−43.7771			−1.38922
$994$		0			0
$995$	14.1115			0.447363
$996$		0			0
$997$	20.0344	+	34.7007i	0.634497	+	1.09898i	0.986621	+	0.163028i	$0.0521261\pi$
$997$	20.0344	+	34.7007i	0.634497	+	1.09898i	−0.352124	+	0.935953i	$0.614541\pi$
$998$		0			0
$999$	32.3607	−	56.0503i	1.02385	−	1.77335i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1568.2.i.v.961.2		4
4.3	odd	2		1568.2.i.m.961.1		4
7.2	even	3		224.2.a.c.1.1	✓	2
7.3	odd	6		1568.2.i.n.1537.1		4
7.4	even	3	inner	1568.2.i.v.1537.2		4
7.5	odd	6		1568.2.a.v.1.2		2
7.6	odd	2		1568.2.i.n.961.1		4
21.2	odd	6		2016.2.a.r.1.2		2
28.3	even	6		1568.2.i.w.1537.2		4
28.11	odd	6		1568.2.i.m.1537.1		4
28.19	even	6		1568.2.a.k.1.1		2
28.23	odd	6		224.2.a.d.1.2	yes	2
28.27	even	2		1568.2.i.w.961.2		4
35.9	even	6		5600.2.a.bk.1.2		2
56.5	odd	6		3136.2.a.bf.1.1		2
56.19	even	6		3136.2.a.by.1.2		2
56.37	even	6		448.2.a.j.1.2		2
56.51	odd	6		448.2.a.i.1.1		2
84.23	even	6		2016.2.a.o.1.2		2
112.37	even	12		1792.2.b.k.897.4		4
112.51	odd	12		1792.2.b.m.897.4		4
112.93	even	12		1792.2.b.k.897.1		4
112.107	odd	12		1792.2.b.m.897.1		4
140.79	odd	6		5600.2.a.z.1.1		2
168.107	even	6		4032.2.a.bv.1.1		2
168.149	odd	6		4032.2.a.bw.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.a.c.1.1	✓	2	7.2	even	3
224.2.a.d.1.2	yes	2	28.23	odd	6
448.2.a.i.1.1		2	56.51	odd	6
448.2.a.j.1.2		2	56.37	even	6
1568.2.a.k.1.1		2	28.19	even	6
1568.2.a.v.1.2		2	7.5	odd	6
1568.2.i.m.961.1		4	4.3	odd	2
1568.2.i.m.1537.1		4	28.11	odd	6
1568.2.i.n.961.1		4	7.6	odd	2
1568.2.i.n.1537.1		4	7.3	odd	6
1568.2.i.v.961.2		4	1.1	even	1	trivial
1568.2.i.v.1537.2		4	7.4	even	3	inner
1568.2.i.w.961.2		4	28.27	even	2
1568.2.i.w.1537.2		4	28.3	even	6
1792.2.b.k.897.1		4	112.93	even	12
1792.2.b.k.897.4		4	112.37	even	12
1792.2.b.m.897.1		4	112.107	odd	12
1792.2.b.m.897.4		4	112.51	odd	12
2016.2.a.o.1.2		2	84.23	even	6
2016.2.a.r.1.2		2	21.2	odd	6
3136.2.a.bf.1.1		2	56.5	odd	6
3136.2.a.by.1.2		2	56.19	even	6
4032.2.a.bv.1.1		2	168.107	even	6
4032.2.a.bw.1.1		2	168.149	odd	6
5600.2.a.z.1.1		2	140.79	odd	6
5600.2.a.bk.1.2		2	35.9	even	6

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:	\( N \)	\(=\)	\( 1568 = 2^{5} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1568.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.61803 + 2.80252i) q^{3} +(0.618034 - 1.07047i) q^{5} +(-3.73607 + 6.47106i) q^{9} +O(q^{10})\)	\(q+(1.61803 + 2.80252i) q^{3} +(0.618034 - 1.07047i) q^{5} +(-3.73607 + 6.47106i) q^{9} +(-1.23607 - 2.14093i) q^{11} +5.23607 q^{13} +4.00000 q^{15} +(2.23607 + 3.87298i) q^{17} +(-1.61803 + 2.80252i) q^{19} +(-2.00000 + 3.46410i) q^{23} +(1.73607 + 3.00696i) q^{25} -14.4721 q^{27} +4.47214 q^{29} +(-3.23607 - 5.60503i) q^{31} +(4.00000 - 6.92820i) q^{33} +(-2.23607 + 3.87298i) q^{37} +(8.47214 + 14.6742i) q^{39} +0.472136 q^{41} -2.47214 q^{43} +(4.61803 + 7.99867i) q^{45} +(-0.763932 + 1.32317i) q^{47} +(-7.23607 + 12.5332i) q^{51} +(5.00000 + 8.66025i) q^{53} -3.05573 q^{55} -10.4721 q^{57} +(2.38197 + 4.12569i) q^{59} +(-3.38197 + 5.85774i) q^{61} +(3.23607 - 5.60503i) q^{65} +(-2.00000 - 3.46410i) q^{67} -12.9443 q^{69} +12.9443 q^{71} +(-7.47214 - 12.9421i) q^{73} +(-5.61803 + 9.73072i) q^{75} +(2.47214 - 4.28187i) q^{79} +(-12.2082 - 21.1452i) q^{81} -4.76393 q^{83} +5.52786 q^{85} +(7.23607 + 12.5332i) q^{87} +(3.00000 - 5.19615i) q^{89} +(10.4721 - 18.1383i) q^{93} +(2.00000 + 3.46410i) q^{95} +3.52786 q^{97} +18.4721 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 2 q^{5} - 6 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 - 2 * q^5 - 6 * q^9	\( 4 q + 2 q^{3} - 2 q^{5} - 6 q^{9} + 4 q^{11} + 12 q^{13} + 16 q^{15} - 2 q^{19} - 8 q^{23} - 2 q^{25} - 40 q^{27} - 4 q^{31} + 16 q^{33} + 16 q^{39} - 16 q^{41} + 8 q^{43} + 14 q^{45} - 12 q^{47} - 20 q^{51} + 20 q^{53} - 48 q^{55} - 24 q^{57} + 14 q^{59} - 18 q^{61} + 4 q^{65} - 8 q^{67} - 16 q^{69} + 16 q^{71} - 12 q^{73} - 18 q^{75} - 8 q^{79} - 22 q^{81} - 28 q^{83} + 40 q^{85} + 20 q^{87} + 12 q^{89} + 24 q^{93} + 8 q^{95} + 32 q^{97} + 56 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 - 2 * q^5 - 6 * q^9 + 4 * q^11 + 12 * q^13 + 16 * q^15 - 2 * q^19 - 8 * q^23 - 2 * q^25 - 40 * q^27 - 4 * q^31 + 16 * q^33 + 16 * q^39 - 16 * q^41 + 8 * q^43 + 14 * q^45 - 12 * q^47 - 20 * q^51 + 20 * q^53 - 48 * q^55 - 24 * q^57 + 14 * q^59 - 18 * q^61 + 4 * q^65 - 8 * q^67 - 16 * q^69 + 16 * q^71 - 12 * q^73 - 18 * q^75 - 8 * q^79 - 22 * q^81 - 28 * q^83 + 40 * q^85 + 20 * q^87 + 12 * q^89 + 24 * q^93 + 8 * q^95 + 32 * q^97 + 56 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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