LMFDB - Embedded newform 968.2.i.o.9.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [968,2,Mod(9,968)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(968, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("968.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 968 = 2^{3} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	968.i (of order $5$, 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:	$7.72951891566$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.324000000.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 9x^{4} + 27x^{2} + 81 $ x^8 + 3x^6 + 9x^4 + 27*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			9.1
Root			$0.535233 + 1.64728i$ of defining polynomial
Character	$\chi$	$=$	968.9
Dual form			968.2.i.o.753.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.21028 + 1.60586i) q^{3} +(-1.15327 - 3.54939i) q^{5} +(2.21028 + 1.60586i) q^{7} +(1.37948 - 4.24561i) q^{9} +O(q^{10})$	\(q+(-2.21028 + 1.60586i) q^{3} +(-1.15327 - 3.54939i) q^{5} +(2.21028 + 1.60586i) q^{7} +(1.37948 - 4.24561i) q^{9} +(-1.37948 + 4.24561i) q^{13} +(8.24886 + 5.99315i) q^{15} +(-0.700835 - 2.15695i) q^{17} +(2.64383 - 1.92085i) q^{19} -7.46410 q^{21} -2.19615 q^{23} +(-7.22307 + 5.24787i) q^{25} +(1.23607 + 3.80423i) q^{27} +(-3.61153 - 2.62393i) q^{29} +(-1.46228 + 4.50045i) q^{31} +(3.15078 - 9.69712i) q^{35} +(-4.63733 - 3.36921i) q^{37} +(-3.76882 - 11.5992i) q^{39} +(6.25536 - 4.54479i) q^{41} -8.00000 q^{43} -16.6603 q^{45} +(2.64383 - 1.92085i) q^{47} +(0.143415 + 0.441387i) q^{49} +(5.01279 + 3.64201i) q^{51} +(0.369631 - 1.13761i) q^{53} +(-2.75897 + 8.49123i) q^{57} +(-10.8927 - 7.91400i) q^{59} +(-2.01970 - 6.21601i) q^{61} +(9.86689 - 7.16872i) q^{63} +16.6603 q^{65} -0.196152 q^{67} +(4.85410 - 3.52671i) q^{69} +(0.783636 + 2.41178i) q^{71} +(-7.22307 - 5.24787i) q^{73} +(7.53764 - 23.1985i) q^{75} +(5.12612 - 15.7766i) q^{79} +(1.99350 + 1.44836i) q^{81} +(-0.678648 - 2.08867i) q^{83} +(-6.84760 + 4.97507i) q^{85} +12.1962 q^{87} -16.4641 q^{89} +(-9.86689 + 7.16872i) q^{91} +(-3.99503 - 12.2955i) q^{93} +(-9.86689 - 7.16872i) q^{95} +(-3.68602 + 11.3444i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} + 4 q^{5} + 2 q^{7} - 2 q^{9}+O(q^{10}) $ 8 * q - 2 * q^3 + 4 * q^5 + 2 * q^7 - 2 * q^9	$ 8 q - 2 q^{3} + 4 q^{5} + 2 q^{7} - 2 q^{9} + 2 q^{13} + 10 q^{15} + 8 q^{17} + 10 q^{19} - 32 q^{21} + 24 q^{23} - 4 q^{25} - 8 q^{27} - 2 q^{29} + 6 q^{31} - 10 q^{35} - 8 q^{37} + 14 q^{39} + 12 q^{41} - 64 q^{43} - 64 q^{45} + 10 q^{47} + 6 q^{49} + 2 q^{51} + 8 q^{53} + 4 q^{57} - 20 q^{59} + 20 q^{61} + 14 q^{63} + 64 q^{65} + 40 q^{67} + 12 q^{69} - 12 q^{71} - 4 q^{73} - 28 q^{75} - 2 q^{79} - 2 q^{81} - 6 q^{83} - 10 q^{85} + 56 q^{87} - 104 q^{89} - 14 q^{91} + 12 q^{93} - 14 q^{95} + 10 q^{97}+O(q^{100}) $ 8 * q - 2 * q^3 + 4 * q^5 + 2 * q^7 - 2 * q^9 + 2 * q^13 + 10 * q^15 + 8 * q^17 + 10 * q^19 - 32 * q^21 + 24 * q^23 - 4 * q^25 - 8 * q^27 - 2 * q^29 + 6 * q^31 - 10 * q^35 - 8 * q^37 + 14 * q^39 + 12 * q^41 - 64 * q^43 - 64 * q^45 + 10 * q^47 + 6 * q^49 + 2 * q^51 + 8 * q^53 + 4 * q^57 - 20 * q^59 + 20 * q^61 + 14 * q^63 + 64 * q^65 + 40 * q^67 + 12 * q^69 - 12 * q^71 - 4 * q^73 - 28 * q^75 - 2 * q^79 - 2 * q^81 - 6 * q^83 - 10 * q^85 + 56 * q^87 - 104 * q^89 - 14 * q^91 + 12 * q^93 - 14 * q^95 + 10 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/968\mathbb{Z}\right)^\times$.

$n$	$485$	$727$	$849$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

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
$3$	−2.21028	+	1.60586i	−1.27610	+	0.927143i	−0.999428	−	0.0338203i	$-0.989233\pi$
$3$	−2.21028	+	1.60586i	−1.27610	+	0.927143i	−0.276675	+	0.960963i	$0.589233\pi$
$4$		0			0
$5$	−1.15327	−	3.54939i	−0.515757	−	1.58734i	−0.781901	−	0.623403i	$-0.785750\pi$
$5$	−1.15327	−	3.54939i	−0.515757	−	1.58734i	0.266144	−	0.963933i	$-0.414250\pi$
$6$		0			0
$7$	2.21028	+	1.60586i	0.835406	+	0.606958i	0.921083	−	0.389365i	$-0.127306\pi$
$7$	2.21028	+	1.60586i	0.835406	+	0.606958i	−0.0856778	+	0.996323i	$0.527306\pi$
$8$		0			0
$9$	1.37948	−	4.24561i	0.459828	−	1.41520i
$10$		0			0
$11$		0			0
$11$		0			0
$12$		0			0
$13$	−1.37948	+	4.24561i	−0.382600	+	1.17752i	0.555607	+	0.831445i	$0.312486\pi$
$13$	−1.37948	+	4.24561i	−0.382600	+	1.17752i	−0.938207	+	0.346076i	$0.887514\pi$
$14$		0			0
$15$	8.24886	+	5.99315i	2.12985	+	1.54742i
$16$		0			0
$17$	−0.700835	−	2.15695i	−0.169977	−	0.523137i	0.829391	−	0.558668i	$-0.188688\pi$
$17$	−0.700835	−	2.15695i	−0.169977	−	0.523137i	−0.999369	+	0.0355317i	$0.988688\pi$
$18$		0			0
$19$	2.64383	−	1.92085i	0.606535	−	0.440674i	−0.241657	−	0.970362i	$-0.577691\pi$
$19$	2.64383	−	1.92085i	0.606535	−	0.440674i	0.848193	+	0.529688i	$0.177691\pi$
$20$		0			0
$21$	−7.46410			−1.62880
$22$		0			0
$23$	−2.19615			−0.457929			−0.228965	−	0.973435i	$-0.573534\pi$
$23$	−2.19615			−0.457929			−0.228965	+	0.973435i	$0.573534\pi$
$24$		0			0
$25$	−7.22307	+	5.24787i	−1.44461	+	1.04957i
$26$		0			0
$27$	1.23607	+	3.80423i	0.237881	+	0.732124i
$28$		0			0
$29$	−3.61153	−	2.62393i	−0.670645	−	0.487252i	0.199596	−	0.979878i	$-0.436037\pi$
$29$	−3.61153	−	2.62393i	−0.670645	−	0.487252i	−0.870241	+	0.492626i	$0.836037\pi$
$30$		0			0
$31$	−1.46228	+	4.50045i	−0.262634	+	0.808304i	0.729595	+	0.683879i	$0.239709\pi$
$31$	−1.46228	+	4.50045i	−0.262634	+	0.808304i	−0.992229	+	0.124425i	$0.960291\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	3.15078	−	9.69712i	0.532580	−	1.63911i
$36$		0			0
$37$	−4.63733	−	3.36921i	−0.762372	−	0.553896i	0.137265	−	0.990534i	$-0.456169\pi$
$37$	−4.63733	−	3.36921i	−0.762372	−	0.553896i	−0.899637	+	0.436639i	$0.856169\pi$
$38$		0			0
$39$	−3.76882	−	11.5992i	−0.603494	−	1.85736i
$40$		0			0
$41$	6.25536	−	4.54479i	0.976923	−	0.709776i	0.0199043	−	0.999802i	$-0.493664\pi$
$41$	6.25536	−	4.54479i	0.976923	−	0.709776i	0.957019	+	0.290026i	$0.0936638\pi$
$42$		0			0
$43$	−8.00000			−1.21999			−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000			−1.21999			−0.609994	+	0.792406i	$0.708828\pi$
$44$		0			0
$45$	−16.6603			−2.48356
$46$		0			0
$47$	2.64383	−	1.92085i	0.385642	−	0.280185i	−0.378026	−	0.925795i	$-0.623397\pi$
$47$	2.64383	−	1.92085i	0.385642	−	0.280185i	0.763667	+	0.645610i	$0.223397\pi$
$48$		0			0
$49$	0.143415	+	0.441387i	0.0204879	+	0.0630553i
$50$		0			0
$51$	5.01279	+	3.64201i	0.701931	+	0.509983i
$52$		0			0
$53$	0.369631	−	1.13761i	0.0507728	−	0.156263i	−0.922455	−	0.386104i	$-0.873821\pi$
$53$	0.369631	−	1.13761i	0.0507728	−	0.156263i	0.973228	+	0.229841i	$0.0738207\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−2.75897	+	8.49123i	−0.365434	+	1.12469i
$58$		0			0
$59$	−10.8927	−	7.91400i	−1.41811	−	1.03032i	−0.992080	−	0.125604i	$-0.959913\pi$
$59$	−10.8927	−	7.91400i	−1.41811	−	1.03032i	−0.426027	−	0.904711i	$-0.640087\pi$
$60$		0			0
$61$	−2.01970	−	6.21601i	−0.258597	−	0.795878i	−0.993100	−	0.117273i	$-0.962585\pi$
$61$	−2.01970	−	6.21601i	−0.258597	−	0.795878i	0.734503	−	0.678605i	$-0.237415\pi$
$62$		0			0
$63$	9.86689	−	7.16872i	1.24311	−	0.903174i
$64$		0			0
$65$	16.6603			2.06645
$66$		0			0
$67$	−0.196152			−0.0239638			−0.0119819	−	0.999928i	$-0.503814\pi$
$67$	−0.196152			−0.0239638			−0.0119819	+	0.999928i	$0.503814\pi$
$68$		0			0
$69$	4.85410	−	3.52671i	0.584365	−	0.424566i
$70$		0			0
$71$	0.783636	+	2.41178i	0.0930004	+	0.286226i	0.986727	−	0.162385i	$-0.0519188\pi$
$71$	0.783636	+	2.41178i	0.0930004	+	0.286226i	−0.893727	+	0.448611i	$0.851919\pi$
$72$		0			0
$73$	−7.22307	−	5.24787i	−0.845396	−	0.614216i	0.0784766	−	0.996916i	$-0.474994\pi$
$73$	−7.22307	−	5.24787i	−0.845396	−	0.614216i	−0.923873	+	0.382700i	$0.874994\pi$
$74$		0			0
$75$	7.53764	−	23.1985i	0.870371	−	2.67873i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	5.12612	−	15.7766i	0.576733	−	1.77500i	−0.0534678	−	0.998570i	$-0.517027\pi$
$79$	5.12612	−	15.7766i	0.576733	−	1.77500i	0.630201	−	0.776432i	$-0.282973\pi$
$80$		0			0
$81$	1.99350	+	1.44836i	0.221500	+	0.160929i
$82$		0			0
$83$	−0.678648	−	2.08867i	−0.0744913	−	0.229261i	0.906877	−	0.421395i	$-0.138459\pi$
$83$	−0.678648	−	2.08867i	−0.0744913	−	0.229261i	−0.981369	+	0.192134i	$0.938459\pi$
$84$		0			0
$85$	−6.84760	+	4.97507i	−0.742727	+	0.539623i
$86$		0			0
$87$	12.1962			1.30756
$88$		0			0
$89$	−16.4641			−1.74519			−0.872596	−	0.488443i	$-0.837565\pi$
$89$	−16.4641			−1.74519			−0.872596	+	0.488443i	$0.837565\pi$
$90$		0			0
$91$	−9.86689	+	7.16872i	−1.03433	+	0.751486i
$92$		0			0
$93$	−3.99503	−	12.2955i	−0.414266	−	1.27498i
$94$		0			0
$95$	−9.86689	−	7.16872i	−1.01232	−	0.735495i
$96$		0			0
$97$	−3.68602	+	11.3444i	−0.374258	+	1.15185i	0.569719	+	0.821839i	$0.307052\pi$
$97$	−3.68602	+	11.3444i	−0.374258	+	1.15185i	−0.943978	+	0.330009i	$0.892948\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	5.39670	−	16.6093i	0.536992	−	1.65269i	−0.202313	−	0.979321i	$-0.564846\pi$
$101$	5.39670	−	16.6093i	0.536992	−	1.65269i	0.739305	−	0.673371i	$-0.235154\pi$
$102$		0			0
$103$	5.28765	+	3.84170i	0.521008	+	0.378534i	0.816983	−	0.576661i	$-0.195645\pi$
$103$	5.28765	+	3.84170i	0.521008	+	0.378534i	−0.295976	+	0.955196i	$0.595645\pi$
$104$		0			0
$105$	8.60810	+	26.4930i	0.840065	+	2.58545i
$106$		0			0
$107$	−13.8539	+	10.0654i	−1.33931	+	0.973063i	−0.339837	+	0.940484i	$0.610372\pi$
$107$	−13.8539	+	10.0654i	−1.33931	+	0.973063i	−0.999469	+	0.0325790i	$0.989628\pi$
$108$		0			0
$109$	−12.4641			−1.19384			−0.596922	−	0.802299i	$-0.703610\pi$
$109$	−12.4641			−1.19384			−0.596922	+	0.802299i	$0.703610\pi$
$110$		0			0
$111$	15.6603			1.48641
$112$		0			0
$113$	−4.04508	+	2.93893i	−0.380530	+	0.276471i	−0.761564	−	0.648090i	$-0.775568\pi$
$113$	−4.04508	+	2.93893i	−0.380530	+	0.276471i	0.381034	+	0.924561i	$0.375568\pi$
$114$		0			0
$115$	2.53275	+	7.79500i	0.236180	+	0.726888i
$116$		0			0
$117$	16.1223	+	11.7135i	1.49050	+	1.08291i
$118$		0			0
$119$	1.91472	−	5.89289i	0.175522	−	0.540200i
$120$		0			0
$121$		0			0
$122$		0			0
$123$	−6.52778	+	20.0905i	−0.588591	+	1.81150i
$124$		0			0
$125$	11.8604	+	8.61708i	1.06083	+	0.770735i
$126$		0			0
$127$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$127$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$128$		0			0
$129$	17.6822	−	12.8469i	1.55683	−	1.13110i
$130$		0			0
$131$	8.00000			0.698963			0.349482	−	0.936943i	$-0.386358\pi$
$131$	8.00000			0.698963			0.349482	+	0.936943i	$0.386358\pi$
$132$		0			0
$133$	8.92820			0.774173
$134$		0			0
$135$	12.0772	−	8.77458i	1.03944	−	0.755195i
$136$		0			0
$137$	−0.783636	−	2.41178i	−0.0669505	−	0.206053i	0.911984	−	0.410225i	$-0.134550\pi$
$137$	−0.783636	−	2.41178i	−0.0669505	−	0.206053i	−0.978935	+	0.204172i	$0.934550\pi$
$138$		0			0
$139$	5.01279	+	3.64201i	0.425180	+	0.308911i	0.779718	−	0.626130i	$-0.215362\pi$
$139$	5.01279	+	3.64201i	0.425180	+	0.308911i	−0.354539	+	0.935041i	$0.615362\pi$
$140$		0			0
$141$	−2.75897	+	8.49123i	−0.232347	+	0.715090i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	−5.14830	+	15.8448i	−0.427543	+	1.31584i
$146$		0			0
$147$	−1.02579	−	0.745282i	−0.0846059	−	0.0614698i
$148$		0			0
$149$	1.71069	+	5.26495i	0.140145	+	0.431322i	0.996355	−	0.0853065i	$-0.0271869\pi$
$149$	1.71069	+	5.26495i	0.140145	+	0.431322i	−0.856210	+	0.516628i	$0.827187\pi$
$150$		0			0
$151$	−8.52372	+	6.19285i	−0.693651	+	0.503967i	−0.877858	−	0.478921i	$-0.841028\pi$
$151$	−8.52372	+	6.19285i	−0.693651	+	0.503967i	0.184208	+	0.982887i	$0.441028\pi$
$152$		0			0
$153$	−10.1244			−0.818506
$154$		0			0
$155$	17.6603			1.41851
$156$		0			0
$157$	16.8151	−	12.2169i	1.34199	−	0.975014i	0.342623	−	0.939473i	$-0.388685\pi$
$157$	16.8151	−	12.2169i	1.34199	−	0.975014i	0.999368	−	0.0355408i	$-0.0113154\pi$
$158$		0			0
$159$	1.00985	+	3.10800i	0.0800865	+	0.246481i
$160$		0			0
$161$	−4.85410	−	3.52671i	−0.382557	−	0.277944i
$162$		0			0
$163$	−7.26705	+	22.3657i	−0.569199	+	1.75181i	0.0859336	+	0.996301i	$0.472613\pi$
$163$	−7.26705	+	22.3657i	−0.569199	+	1.75181i	−0.655133	+	0.755514i	$0.727387\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.01970	+	6.21601i	−0.156289	+	0.481009i	−0.998289	−	0.0584685i	$-0.981378\pi$
$167$	−2.01970	+	6.21601i	−0.156289	+	0.481009i	0.842000	+	0.539478i	$0.181378\pi$
$168$		0			0
$169$	−5.60503	−	4.07230i	−0.431156	−	0.313254i
$170$		0			0
$171$	−4.50808	−	13.8744i	−0.344742	−	1.06101i
$172$		0			0
$173$	−2.05158	+	1.49056i	−0.155979	+	0.113325i	−0.663037	−	0.748586i	$-0.730733\pi$
$173$	−2.05158	+	1.49056i	−0.155979	+	0.113325i	0.507058	+	0.861912i	$0.330733\pi$
$174$		0			0
$175$	−24.3923			−1.84388
$176$		0			0
$177$	36.7846			2.76490
$178$		0			0
$179$	−12.9443	+	9.40456i	−0.967500	+	0.702930i	−0.954881	−	0.296990i	$-0.904017\pi$
$179$	−12.9443	+	9.40456i	−0.967500	+	0.702930i	−0.0126198	+	0.999920i	$0.504017\pi$
$180$		0			0
$181$	−0.866437	−	2.66662i	−0.0644017	−	0.198208i	0.913678	−	0.406439i	$-0.133230\pi$
$181$	−0.866437	−	2.66662i	−0.0644017	−	0.198208i	−0.978080	+	0.208231i	$0.933230\pi$
$182$		0			0
$183$	14.4461	+	10.4957i	1.06789	+	0.775867i
$184$		0			0
$185$	−6.61059	+	20.3453i	−0.486020	+	1.49582i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−3.37700	+	10.3933i	−0.245641	+	0.756004i
$190$		0			0
$191$	−3.55345	−	2.58173i	−0.257119	−	0.186808i	0.451757	−	0.892141i	$-0.350797\pi$
$191$	−3.55345	−	2.58173i	−0.257119	−	0.186808i	−0.708876	+	0.705333i	$0.750797\pi$
$192$		0			0
$193$	−5.14830	−	15.8448i	−0.370583	−	1.14054i	−0.946411	−	0.322966i	$-0.895320\pi$
$193$	−5.14830	−	15.8448i	−0.370583	−	1.14054i	0.575828	−	0.817571i	$-0.304680\pi$
$194$		0			0
$195$	−36.8238	+	26.7540i	−2.63700	+	1.91590i
$196$		0			0
$197$	−5.92820			−0.422367			−0.211183	−	0.977446i	$-0.567732\pi$
$197$	−5.92820			−0.422367			−0.211183	+	0.977446i	$0.567732\pi$
$198$		0			0
$199$	−6.53590			−0.463318			−0.231659	−	0.972797i	$-0.574415\pi$
$199$	−6.53590			−0.463318			−0.231659	+	0.972797i	$0.574415\pi$
$200$		0			0
$201$	0.433551	−	0.314993i	0.0305803	−	0.0222179i
$202$		0			0
$203$	−3.76882	−	11.5992i	−0.264519	−	0.814106i
$204$		0			0
$205$	−23.3453	−	16.9614i	−1.63051	−	1.18463i
$206$		0			0
$207$	−3.02956	+	9.32401i	−0.210569	+	0.648064i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−5.51793	+	16.9825i	−0.379870	+	1.16912i	0.560264	+	0.828314i	$0.310700\pi$
$211$	−5.51793	+	16.9825i	−0.379870	+	1.16912i	−0.940134	+	0.340806i	$0.889300\pi$
$212$		0			0
$213$	−5.60503	−	4.07230i	−0.384051	−	0.279029i
$214$		0			0
$215$	9.22614	+	28.3951i	0.629217	+	1.93653i
$216$		0			0
$217$	−10.4591	+	7.59901i	−0.710012	+	0.515854i
$218$		0			0
$219$	24.3923			1.64828
$220$		0			0
$221$	10.1244			0.681038
$222$		0			0
$223$	6.78952	−	4.93287i	0.454660	−	0.330330i	−0.336773	−	0.941586i	$-0.609336\pi$
$223$	6.78952	−	4.93287i	0.454660	−	0.330330i	0.791433	+	0.611256i	$0.209336\pi$
$224$		0			0
$225$	12.3163	+	37.9057i	0.821087	+	2.52705i
$226$		0			0
$227$	2.91869	+	2.12055i	0.193720	+	0.140746i	0.680417	−	0.732825i	$-0.261799\pi$
$227$	2.91869	+	2.12055i	0.193720	+	0.140746i	−0.486697	+	0.873571i	$0.661799\pi$
$228$		0			0
$229$	3.95661	−	12.1772i	0.261460	−	0.804691i	−0.731028	−	0.682348i	$-0.760959\pi$
$229$	3.95661	−	12.1772i	0.261460	−	0.804691i	0.992488	−	0.122343i	$-0.0390409\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.369631	−	1.13761i	0.0242154	−	0.0745272i	−0.938219	−	0.346043i	$-0.887525\pi$
$233$	0.369631	−	1.13761i	0.0242154	−	0.0745272i	0.962434	+	0.271516i	$0.0875250\pi$
$234$		0			0
$235$	−9.86689	−	7.16872i	−0.643645	−	0.467636i
$236$		0			0
$237$	14.0048	+	43.1024i	0.909710	+	2.79980i
$238$		0			0
$239$	15.7893	−	11.4716i	1.02133	−	0.742036i	0.0547714	−	0.998499i	$-0.482557\pi$
$239$	15.7893	−	11.4716i	1.02133	−	0.742036i	0.966554	+	0.256462i	$0.0825570\pi$
$240$		0			0
$241$	8.92820			0.575116			0.287558	−	0.957763i	$-0.407157\pi$
$241$	8.92820			0.575116			0.287558	+	0.957763i	$0.407157\pi$
$242$		0			0
$243$	−18.7321			−1.20166
$244$		0			0
$245$	1.40126	−	1.01807i	0.0895231	−	0.0650424i
$246$		0			0
$247$	4.50808	+	13.8744i	0.286842	+	0.882810i
$248$		0			0
$249$	4.85410	+	3.52671i	0.307616	+	0.223496i
$250$		0			0
$251$	5.33609	−	16.4228i	0.336811	−	1.03660i	−0.629012	−	0.777396i	$-0.716540\pi$
$251$	5.33609	−	16.4228i	0.336811	−	1.03660i	0.965823	−	0.259202i	$-0.0834596\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	7.14582	−	21.9926i	0.447489	−	1.37723i
$256$		0			0
$257$	3.61153	+	2.62393i	0.225281	+	0.163676i	0.694701	−	0.719299i	$-0.255537\pi$
$257$	3.61153	+	2.62393i	0.225281	+	0.163676i	−0.469419	+	0.882975i	$0.655537\pi$
$258$		0			0
$259$	−4.83928	−	14.8938i	−0.300699	−	0.925455i
$260$		0			0
$261$	−16.1223	+	11.7135i	−0.997943	+	0.725048i
$262$		0			0
$263$	2.33975			0.144275			0.0721375	−	0.997395i	$-0.477018\pi$
$263$	2.33975			0.144275			0.0721375	+	0.997395i	$0.477018\pi$
$264$		0			0
$265$	−4.46410			−0.274228
$266$		0			0
$267$	36.3902	−	26.4390i	2.22704	−	1.61804i
$268$		0			0
$269$	−5.88756	−	18.1201i	−0.358971	−	1.10480i	−0.953671	−	0.300852i	$-0.902729\pi$
$269$	−5.88756	−	18.1201i	−0.358971	−	1.10480i	0.594700	−	0.803948i	$-0.297271\pi$
$270$		0			0
$271$	−5.28765	−	3.84170i	−0.321202	−	0.233367i	0.415486	−	0.909599i	$-0.363611\pi$
$271$	−5.28765	−	3.84170i	−0.321202	−	0.233367i	−0.736688	+	0.676233i	$0.763611\pi$
$272$		0			0
$273$	10.2966	−	31.6897i	0.623179	−	1.91795i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	4.25968	−	13.1099i	0.255939	−	0.787700i	−0.737704	−	0.675124i	$-0.764090\pi$
$277$	4.25968	−	13.1099i	0.255939	−	0.787700i	0.993643	−	0.112576i	$-0.0359101\pi$
$278$		0			0
$279$	17.0900	+	12.4166i	1.02315	+	0.743361i
$280$		0			0
$281$	−2.42776	−	7.47189i	−0.144828	−	0.445735i	0.852161	−	0.523280i	$-0.175292\pi$
$281$	−2.42776	−	7.47189i	−0.144828	−	0.445735i	−0.996989	+	0.0775449i	$0.975292\pi$
$282$		0			0
$283$	25.0214	−	18.1791i	1.48737	−	1.08064i	0.512283	−	0.858817i	$-0.328800\pi$
$283$	25.0214	−	18.1791i	1.48737	−	1.08064i	0.975087	−	0.221821i	$-0.0712001\pi$
$284$		0			0
$285$	33.3205			1.97374
$286$		0			0
$287$	21.1244			1.24693
$288$		0			0
$289$	9.59203	−	6.96902i	0.564237	−	0.409942i
$290$		0			0
$291$	−10.0704	−	30.9935i	−0.590337	−	1.81687i
$292$		0			0
$293$	18.0577	+	13.1197i	1.05494	+	0.766459i	0.973146	−	0.230190i	$-0.0739348\pi$
$293$	18.0577	+	13.1197i	1.05494	+	0.766459i	0.0817947	+	0.996649i	$0.473935\pi$
$294$		0			0
$295$	−15.5277	+	47.7894i	−0.904058	+	2.78240i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	3.02956	−	9.32401i	0.175204	−	0.539222i
$300$		0			0
$301$	−17.6822	−	12.8469i	−1.01919	−	0.740481i
$302$		0			0
$303$	14.7441	+	45.3776i	0.847025	+	2.60687i
$304$		0			0
$305$	−19.7338	+	14.3374i	−1.12995	+	0.820959i
$306$		0			0
$307$	32.4449			1.85173			0.925863	−	0.377859i	$-0.123340\pi$
$307$	32.4449			1.85173			0.925863	+	0.377859i	$0.123340\pi$
$308$		0			0
$309$	−17.8564			−1.01582
$310$		0			0
$311$	−13.5790	+	9.86575i	−0.769996	+	0.559435i	−0.901960	−	0.431819i	$-0.857872\pi$
$311$	−13.5790	+	9.86575i	−0.769996	+	0.559435i	0.131964	+	0.991255i	$0.457872\pi$
$312$		0			0
$313$	−2.16312	−	6.65740i	−0.122267	−	0.376298i	0.871126	−	0.491059i	$-0.163390\pi$
$313$	−2.16312	−	6.65740i	−0.122267	−	0.376298i	−0.993393	+	0.114760i	$0.963390\pi$
$314$		0			0
$315$	−36.8238	−	26.7540i	−2.07478	−	1.50742i
$316$		0			0
$317$	1.19170	−	3.66766i	0.0669323	−	0.205996i	−0.911997	−	0.410198i	$-0.865460\pi$
$317$	1.19170	−	3.66766i	0.0669323	−	0.205996i	0.978929	+	0.204201i	$0.0654597\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	14.4572	−	44.4948i	0.806924	−	2.48346i
$322$		0			0
$323$	−5.99606	−	4.35640i	−0.333630	−	0.242396i
$324$		0			0
$325$	−12.3163	−	37.9057i	−0.683186	−	2.10263i
$326$		0			0
$327$	27.5491	−	20.0156i	1.52347	−	1.10686i
$328$		0			0
$329$	8.92820			0.492228
$330$		0			0
$331$	−1.07180			−0.0589113			−0.0294556	−	0.999566i	$-0.509377\pi$
$331$	−1.07180			−0.0589113			−0.0294556	+	0.999566i	$0.509377\pi$
$332$		0			0
$333$	−20.7015	+	15.0405i	−1.13444	+	0.824215i
$334$		0			0
$335$	0.226216	+	0.696222i	0.0123595	+	0.0380387i
$336$		0			0
$337$	5.82181	+	4.22979i	0.317134	+	0.230411i	0.734952	−	0.678120i	$-0.237205\pi$
$337$	5.82181	+	4.22979i	0.317134	+	0.230411i	−0.417817	+	0.908531i	$0.637205\pi$
$338$		0			0
$339$	4.22125	−	12.9917i	0.229267	−	0.705611i
$340$		0			0
$341$		0			0
$342$		0			0
$343$	5.51793	−	16.9825i	0.297940	−	0.916966i
$344$		0			0
$345$	−18.1158	−	13.1619i	−0.975319	−	0.708611i
$346$		0			0
$347$	7.53764	+	23.1985i	0.404642	+	1.24536i	0.921194	+	0.389103i	$0.127215\pi$
$347$	7.53764	+	23.1985i	0.404642	+	1.24536i	−0.516553	+	0.856255i	$0.672785\pi$
$348$		0			0
$349$	14.0707	−	10.2229i	0.753186	−	0.547221i	−0.143627	−	0.989632i	$-0.545877\pi$
$349$	14.0707	−	10.2229i	0.753186	−	0.547221i	0.896813	+	0.442410i	$0.145877\pi$
$350$		0			0
$351$	−17.8564			−0.953104
$352$		0			0
$353$	−7.92820			−0.421976			−0.210988	−	0.977489i	$-0.567668\pi$
$353$	−7.92820			−0.421976			−0.210988	+	0.977489i	$0.567668\pi$
$354$		0			0
$355$	7.65662	−	5.56286i	0.406371	−	0.295246i
$356$		0			0
$357$	5.23110	+	16.0997i	0.276859	+	0.852085i
$358$		0			0
$359$	20.4422	+	14.8521i	1.07890	+	0.783865i	0.977490	−	0.210980i	$-0.0676654\pi$
$359$	20.4422	+	14.8521i	1.07890	+	0.783865i	0.101408	+	0.994845i	$0.467665\pi$
$360$		0			0
$361$	−2.57118	+	7.91327i	−0.135325	+	0.416488i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−10.2966	+	31.6897i	−0.538949	+	1.65871i
$366$		0			0
$367$	−17.4073	−	12.6472i	−0.908656	−	0.660177i	0.0320186	−	0.999487i	$-0.489806\pi$
$367$	−17.4073	−	12.6472i	−0.908656	−	0.660177i	−0.940675	+	0.339310i	$0.889806\pi$
$368$		0			0
$369$	−10.6662	−	32.8273i	−0.555262	−	1.70892i
$370$		0			0
$371$	2.64383	−	1.92085i	0.137261	−	0.0997257i
$372$		0			0
$373$	1.46410			0.0758083			0.0379042	−	0.999281i	$-0.487932\pi$
$373$	1.46410			0.0758083			0.0379042	+	0.999281i	$0.487932\pi$
$374$		0			0
$375$	−40.0526			−2.06831
$376$		0			0
$377$	16.1223	−	11.7135i	0.830338	−	0.603276i
$378$		0			0
$379$	10.2522	+	31.5531i	0.526622	+	1.62077i	0.761087	+	0.648650i	$0.224666\pi$
$379$	10.2522	+	31.5531i	0.526622	+	1.62077i	−0.234465	+	0.972125i	$0.575334\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	5.97037	−	18.3749i	0.305071	−	0.938913i	−0.674579	−	0.738203i	$-0.735675\pi$
$383$	5.97037	−	18.3749i	0.305071	−	0.938913i	0.979651	−	0.200711i	$-0.0643251\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−11.0359	+	33.9649i	−0.560985	+	1.72653i
$388$		0			0
$389$	24.3711	+	17.7067i	1.23566	+	0.897763i	0.997302	−	0.0734132i	$-0.0233892\pi$
$389$	24.3711	+	17.7067i	1.23566	+	0.897763i	0.238363	+	0.971176i	$0.423389\pi$
$390$		0			0
$391$	1.53914	+	4.73699i	0.0778377	+	0.239560i
$392$		0			0
$393$	−17.6822	+	12.8469i	−0.891949	+	0.648039i
$394$		0			0
$395$	−61.9090			−3.11498
$396$		0			0
$397$	11.8756			0.596022			0.298011	−	0.954563i	$-0.403677\pi$
$397$	11.8756			0.596022			0.298011	+	0.954563i	$0.403677\pi$
$398$		0			0
$399$	−19.7338	+	14.3374i	−0.987925	+	0.717770i
$400$		0			0
$401$	−2.85801	−	8.79605i	−0.142722	−	0.439254i	0.853989	−	0.520291i	$-0.174177\pi$
$401$	−2.85801	−	8.79605i	−0.142722	−	0.439254i	−0.996711	+	0.0810376i	$0.974177\pi$
$402$		0			0
$403$	−17.0900	−	12.4166i	−0.851312	−	0.618514i
$404$		0			0
$405$	2.84177	−	8.74606i	0.141209	−	0.434595i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−8.56967	+	26.3747i	−0.423743	+	1.30415i	0.480449	+	0.877022i	$0.340474\pi$
$409$	−8.56967	+	26.3747i	−0.423743	+	1.30415i	−0.904193	+	0.427125i	$0.859526\pi$
$410$		0			0
$411$	5.60503	+	4.07230i	0.276476	+	0.200872i
$412$		0			0
$413$	−11.3671	−	34.9842i	−0.559337	−	1.72146i
$414$		0			0
$415$	−6.63083	+	4.81758i	−0.325494	+	0.236486i
$416$		0			0
$417$	−16.9282			−0.828978
$418$		0			0
$419$	−5.66025			−0.276522			−0.138261	−	0.990396i	$-0.544151\pi$
$419$	−5.66025			−0.276522			−0.138261	+	0.990396i	$0.544151\pi$
$420$		0			0
$421$	−10.1262	+	7.35711i	−0.493520	+	0.358564i	−0.806537	−	0.591184i	$-0.798661\pi$
$421$	−10.1262	+	7.35711i	−0.493520	+	0.358564i	0.313016	+	0.949748i	$0.398661\pi$
$422$		0			0
$423$	−4.50808	−	13.8744i	−0.219190	−	0.674599i
$424$		0			0
$425$	16.3816	+	11.9019i	0.794622	+	0.577327i
$426$		0			0
$427$	5.51793	−	16.9825i	0.267031	−	0.821838i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−1.35730	+	4.17733i	−0.0653787	+	0.201215i	−0.978410	−	0.206676i	$-0.933736\pi$
$431$	−1.35730	+	4.17733i	−0.0653787	+	0.201215i	0.913031	+	0.407891i	$0.133736\pi$
$432$		0			0
$433$	7.28115	+	5.29007i	0.349910	+	0.254224i	0.748831	−	0.662761i	$-0.230615\pi$
$433$	7.28115	+	5.29007i	0.349910	+	0.254224i	−0.398921	+	0.916985i	$0.630615\pi$
$434$		0			0
$435$	−14.0654	−	43.2889i	−0.674385	−	2.07554i
$436$		0			0
$437$	−5.80625	+	4.21848i	−0.277750	+	0.201797i
$438$		0			0
$439$	−36.5885			−1.74627			−0.873136	−	0.487477i	$-0.837917\pi$
$439$	−36.5885			−1.74627			−0.873136	+	0.487477i	$0.837917\pi$
$440$		0			0
$441$	2.07180			0.0986570
$442$		0			0
$443$	−12.0772	+	8.77458i	−0.573804	+	0.416893i	−0.836485	−	0.547990i	$-0.815393\pi$
$443$	−12.0772	+	8.77458i	−0.573804	+	0.416893i	0.262681	+	0.964883i	$0.415393\pi$
$444$		0			0
$445$	18.9875	+	58.4375i	0.900094	+	2.77020i
$446$		0			0
$447$	−12.2359	−	8.88987i	−0.578736	−	0.420477i
$448$		0			0
$449$	−0.353390	+	1.08762i	−0.0166775	+	0.0513281i	−0.959049	−	0.283240i	$-0.908591\pi$
$449$	−0.353390	+	1.08762i	−0.0166775	+	0.0513281i	0.942371	+	0.334568i	$0.108591\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	8.89493	−	27.3758i	0.417920	−	1.28623i
$454$		0			0
$455$	36.8238	+	26.7540i	1.72632	+	1.25425i
$456$		0			0
$457$	1.10889	+	3.41283i	0.0518719	+	0.159645i	0.973637	−	0.228104i	$-0.0732526\pi$
$457$	1.10889	+	3.41283i	0.0518719	+	0.159645i	−0.921765	+	0.387749i	$0.873253\pi$
$458$		0			0
$459$	7.33924	−	5.33227i	0.342566	−	0.248889i
$460$		0			0
$461$	22.3205			1.03957			0.519785	−	0.854297i	$-0.326012\pi$
$461$	22.3205			1.03957			0.519785	+	0.854297i	$0.326012\pi$
$462$		0			0
$463$	−36.7846			−1.70953			−0.854763	−	0.519019i	$-0.826298\pi$
$463$	−36.7846			−1.70953			−0.854763	+	0.519019i	$0.826298\pi$
$464$		0			0
$465$	−39.0340	+	28.3599i	−1.81016	+	1.31516i
$466$		0			0
$467$	−8.77370	−	27.0027i	−0.405999	−	1.24954i	−0.920059	−	0.391781i	$-0.871859\pi$
$467$	−8.77370	−	27.0027i	−0.405999	−	1.24954i	0.514060	−	0.857754i	$-0.328141\pi$
$468$		0			0
$469$	−0.433551	−	0.314993i	−0.0200195	−	0.0145450i
$470$		0			0
$471$	−17.5474	+	54.0054i	−0.808542	+	2.48844i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−9.01616	+	27.7489i	−0.413690	+	1.27321i
$476$		0			0
$477$	−4.31995	−	3.13862i	−0.197797	−	0.143708i
$478$		0			0
$479$	−4.03941	−	12.4320i	−0.184565	−	0.568033i	0.815375	−	0.578933i	$-0.196531\pi$
$479$	−4.03941	−	12.4320i	−0.184565	−	0.568033i	−0.999941	+	0.0108993i	$0.996531\pi$
$480$		0			0
$481$	20.7015	−	15.0405i	0.943907	−	0.685789i
$482$		0			0
$483$	16.3923			0.745876
$484$		0			0
$485$	44.5167			2.02140
$486$		0			0
$487$	14.7210	−	10.6954i	0.667072	−	0.484656i	−0.201972	−	0.979391i	$-0.564735\pi$
$487$	14.7210	−	10.6954i	0.667072	−	0.484656i	0.869044	+	0.494735i	$0.164735\pi$
$488$		0			0
$489$	−19.8539	−	61.1042i	−0.897826	−	2.76323i
$490$		0			0
$491$	−22.3776	−	16.2583i	−1.00989	−	0.733726i	−0.0457021	−	0.998955i	$-0.514553\pi$
$491$	−22.3776	−	16.2583i	−1.00989	−	0.733726i	−0.964186	+	0.265229i	$0.914553\pi$
$492$		0			0
$493$	−3.12860	+	9.62883i	−0.140905	+	0.433661i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−2.14093	+	6.58911i	−0.0960339	+	0.295562i
$498$		0			0
$499$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$499$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$500$		0			0
$501$	−5.51793	−	16.9825i	−0.246523	−	0.758720i
$502$		0			0
$503$	15.7893	−	11.4716i	0.704011	−	0.511494i	−0.177225	−	0.984170i	$-0.556712\pi$
$503$	15.7893	−	11.4716i	0.704011	−	0.511494i	0.881236	+	0.472677i	$0.156712\pi$
$504$		0			0
$505$	−65.1769			−2.90033
$506$		0			0
$507$	18.9282			0.840631
$508$		0			0
$509$	−34.6135	+	25.1482i	−1.53422	+	1.11467i	−0.580379	+	0.814347i	$0.697095\pi$
$509$	−34.6135	+	25.1482i	−1.53422	+	1.11467i	−0.953837	+	0.300326i	$0.902905\pi$
$510$		0			0
$511$	−7.53764	−	23.1985i	−0.333445	−	1.02624i
$512$		0			0
$513$	10.5753	+	7.68341i	0.466911	+	0.339231i
$514$		0			0
$515$	7.53764	−	23.1985i	0.332148	−	1.02225i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	2.14093	−	6.58911i	0.0939765	−	0.289230i
$520$		0			0
$521$	28.5749	+	20.7609i	1.25189	+	0.909550i	0.998330	−	0.0577696i	$-0.0183989\pi$
$521$	28.5749	+	20.7609i	1.25189	+	0.909550i	0.253559	+	0.967320i	$0.418399\pi$
$522$		0			0
$523$	−2.01970	−	6.21601i	−0.0883155	−	0.271807i	0.897139	−	0.441749i	$-0.145642\pi$
$523$	−2.01970	−	6.21601i	−0.0883155	−	0.271807i	−0.985454	+	0.169942i	$0.945642\pi$
$524$		0			0
$525$	53.9137	−	39.1706i	2.35299	−	1.70955i
$526$		0			0
$527$	10.7321			0.467495
$528$		0			0
$529$	−18.1769			−0.790301
$530$		0			0
$531$	−48.6261	+	35.3289i	−2.11019	+	1.53314i
$532$		0			0
$533$	10.6662	+	32.8273i	0.462006	+	1.42191i
$534$		0			0
$535$	51.7034	+	37.5647i	2.23533	+	1.62407i
$536$		0			0
$537$	13.5080	−	41.5734i	0.582913	−	1.79402i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	6.79837	−	20.9232i	0.292285	−	0.899560i	−0.691835	−	0.722056i	$-0.743197\pi$
$541$	6.79837	−	20.9232i	0.292285	−	0.899560i	0.984120	−	0.177505i	$-0.0568025\pi$
$542$		0			0
$543$	6.19728	+	4.50258i	0.265951	+	0.193224i
$544$		0			0
$545$	14.3744	+	44.2400i	0.615733	+	1.89503i
$546$		0			0
$547$	−28.8923	+	20.9915i	−1.23534	+	0.897530i	−0.997279	−	0.0737189i	$-0.976513\pi$
$547$	−28.8923	+	20.9915i	−1.23534	+	0.897530i	−0.238065	+	0.971249i	$0.576513\pi$
$548$		0			0
$549$	−29.1769			−1.24524
$550$		0			0
$551$	−14.5885			−0.621489
$552$		0			0
$553$	36.6651	−	26.6387i	1.55916	−	1.13279i
$554$		0			0
$555$	−18.0605	−	55.5844i	−0.766624	−	2.35943i
$556$		0			0
$557$	22.1028	+	16.0586i	0.936524	+	0.680424i	0.947581	−	0.319514i	$-0.103520\pi$
$557$	22.1028	+	16.0586i	0.936524	+	0.680424i	−0.0110576	+	0.999939i	$0.503520\pi$
$558$		0			0
$559$	11.0359	−	33.9649i	0.466767	−	1.43656i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−6.52778	+	20.0905i	−0.275113	+	0.846712i	0.714076	+	0.700068i	$0.246847\pi$
$563$	−6.52778	+	20.0905i	−0.275113	+	0.846712i	−0.989189	+	0.146644i	$0.953153\pi$
$564$		0			0
$565$	15.0965	+	10.9682i	0.635113	+	0.461437i
$566$		0			0
$567$	2.08032	+	6.40256i	0.0873651	+	0.268882i
$568$		0			0
$569$	3.35224	−	2.43554i	0.140533	−	0.102103i	−0.515297	−	0.857011i	$-0.672319\pi$
$569$	3.35224	−	2.43554i	0.140533	−	0.102103i	0.655831	+	0.754908i	$0.272319\pi$
$570$		0			0
$571$	8.05256			0.336989			0.168495	−	0.985703i	$-0.446109\pi$
$571$	8.05256			0.336989			0.168495	+	0.985703i	$0.446109\pi$
$572$		0			0
$573$	12.0000			0.501307
$574$		0			0
$575$	15.8630	−	11.5251i	0.661531	−	0.480630i
$576$		0			0
$577$	4.18282	+	12.8734i	0.174133	+	0.535927i	0.999593	−	0.0285343i	$-0.00908399\pi$
$577$	4.18282	+	12.8734i	0.174133	+	0.535927i	−0.825460	+	0.564461i	$0.809084\pi$
$578$		0			0
$579$	36.8238	+	26.7540i	1.53034	+	1.11186i
$580$		0			0
$581$	1.85410	−	5.70634i	0.0769211	−	0.236739i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	22.9825	−	70.7330i	0.950211	−	2.92445i
$586$		0			0
$587$	−15.1545	−	11.0104i	−0.625495	−	0.454449i	0.229342	−	0.973346i	$-0.426343\pi$
$587$	−15.1545	−	11.0104i	−0.625495	−	0.454449i	−0.854837	+	0.518897i	$0.826343\pi$
$588$		0			0
$589$	4.77867	+	14.7072i	0.196902	+	0.606001i
$590$		0			0
$591$	13.1030	−	9.51986i	0.538984	−	0.391595i
$592$		0			0
$593$	30.3731			1.24727			0.623636	−	0.781715i	$-0.285655\pi$
$593$	30.3731			1.24727			0.623636	+	0.781715i	$0.285655\pi$
$594$		0			0
$595$	−23.1244			−0.948006
$596$		0			0
$597$	14.4461	−	10.4957i	0.591241	−	0.429562i
$598$		0			0
$599$	6.52778	+	20.0905i	0.266718	+	0.820874i	0.991293	+	0.131677i	$0.0420363\pi$
$599$	6.52778	+	20.0905i	0.266718	+	0.820874i	−0.724575	+	0.689196i	$0.757964\pi$
$600$		0			0
$601$	−23.6202	−	17.1611i	−0.963487	−	0.700015i	−0.00952932	−	0.999955i	$-0.503033\pi$
$601$	−23.6202	−	17.1611i	−0.963487	−	0.700015i	−0.953958	+	0.299940i	$0.903033\pi$
$602$		0			0
$603$	−0.270589	+	0.832787i	−0.0110192	+	0.0339137i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−11.1852	+	34.4246i	−0.453994	+	1.39725i	0.418317	+	0.908301i	$0.362620\pi$
$607$	−11.1852	+	34.4246i	−0.453994	+	1.39725i	−0.872312	+	0.488950i	$0.837380\pi$
$608$		0			0
$609$	26.9569	+	19.5853i	1.09235	+	0.793637i
$610$		0			0
$611$	4.50808	+	13.8744i	0.182377	+	0.561300i
$612$		0			0
$613$	16.1223	−	11.7135i	0.651172	−	0.473104i	−0.212498	−	0.977161i	$-0.568160\pi$
$613$	16.1223	−	11.7135i	0.651172	−	0.473104i	0.863670	+	0.504057i	$0.168160\pi$
$614$		0			0
$615$	78.8372			3.17902
$616$		0			0
$617$	−44.3205			−1.78428			−0.892138	−	0.451763i	$-0.850795\pi$
$617$	−44.3205			−1.78428			−0.892138	+	0.451763i	$0.850795\pi$
$618$		0			0
$619$	−27.2317	+	19.7850i	−1.09454	+	0.795226i	−0.980159	−	0.198211i	$-0.936487\pi$
$619$	−27.2317	+	19.7850i	−1.09454	+	0.795226i	−0.114376	+	0.993438i	$0.536487\pi$
$620$		0			0
$621$	−2.71459	−	8.35466i	−0.108933	−	0.335261i
$622$		0			0
$623$	−36.3902	−	26.4390i	−1.45794	−	1.05926i
$624$		0			0
$625$	3.11236	−	9.57885i	0.124494	−	0.383154i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−4.01722	+	12.3637i	−0.160177	+	0.492974i
$630$		0			0
$631$	−25.9311	−	18.8400i	−1.03230	−	0.750009i	−0.0635318	−	0.997980i	$-0.520236\pi$
$631$	−25.9311	−	18.8400i	−1.03230	−	0.750009i	−0.968768	+	0.247970i	$0.920236\pi$
$632$		0			0
$633$	−15.0753	−	46.3969i	−0.599188	−	1.84411i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−2.07180			−0.0820876
$638$		0			0
$639$	11.3205			0.447832
$640$		0			0
$641$	8.46564	−	6.15064i	0.334373	−	0.242936i	−0.407911	−	0.913022i	$-0.633743\pi$
$641$	8.46564	−	6.15064i	0.334373	−	0.242936i	0.742284	+	0.670086i	$0.233743\pi$
$642$		0			0
$643$	10.5228	+	32.3859i	0.414979	+	1.27718i	0.912269	+	0.409591i	$0.134329\pi$
$643$	10.5228	+	32.3859i	0.414979	+	1.27718i	−0.497290	+	0.867585i	$0.665671\pi$
$644$		0			0
$645$	−65.9909	−	47.9452i	−2.59839	−	1.88784i
$646$		0			0
$647$	5.06550	−	15.5900i	0.199145	−	0.612906i	−0.800758	−	0.598988i	$-0.795570\pi$
$647$	5.06550	−	15.5900i	0.199145	−	0.612906i	0.999903	−	0.0139181i	$-0.00443042\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	10.9146	−	33.5918i	0.427778	−	1.31657i
$652$		0			0
$653$	−5.60503	−	4.07230i	−0.219342	−	0.159361i	0.472688	−	0.881230i	$-0.343284\pi$
$653$	−5.60503	−	4.07230i	−0.219342	−	0.159361i	−0.692030	+	0.721868i	$0.743284\pi$
$654$		0			0
$655$	−9.22614	−	28.3951i	−0.360495	−	1.10949i
$656$		0			0
$657$	−32.2445	+	23.4270i	−1.25798	+	0.913975i
$658$		0			0
$659$	−2.98076			−0.116114			−0.0580570	−	0.998313i	$-0.518491\pi$
$659$	−2.98076			−0.116114			−0.0580570	+	0.998313i	$0.518491\pi$
$660$		0			0
$661$	−17.3397			−0.674438			−0.337219	−	0.941426i	$-0.609486\pi$
$661$	−17.3397			−0.674438			−0.337219	+	0.941426i	$0.609486\pi$
$662$		0			0
$663$	−22.3776	+	16.2583i	−0.869075	+	0.631420i
$664$		0			0
$665$	−10.2966	−	31.6897i	−0.399285	−	1.22887i
$666$		0			0
$667$	7.93148	+	5.76256i	0.307108	+	0.223127i
$668$		0			0
$669$	−7.08520	+	21.8060i	−0.273930	+	0.843069i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	8.93931	−	27.5124i	0.344585	−	1.06052i	−0.617221	−	0.786790i	$-0.711741\pi$
$673$	8.93931	−	27.5124i	0.344585	−	1.06052i	0.961806	−	0.273733i	$-0.0882586\pi$
$674$		0			0
$675$	−28.8923	−	20.9915i	−1.11206	−	0.807962i
$676$		0			0
$677$	5.20892	+	16.0314i	0.200195	+	0.616137i	0.999877	+	0.0157123i	$0.00500160\pi$
$677$	5.20892	+	16.0314i	0.200195	+	0.616137i	−0.799682	+	0.600424i	$0.794998\pi$
$678$		0			0
$679$	−26.3646	+	19.1550i	−1.01178	+	0.735102i
$680$		0			0
$681$	−9.85641			−0.377698
$682$		0			0
$683$	−23.1244			−0.884829			−0.442414	−	0.896811i	$-0.645878\pi$
$683$	−23.1244			−0.884829			−0.442414	+	0.896811i	$0.645878\pi$
$684$		0			0
$685$	−7.65662	+	5.56286i	−0.292544	+	0.212546i
$686$		0			0
$687$	10.8096	+	33.2687i	0.412414	+	1.26928i
$688$		0			0
$689$	4.31995	+	3.13862i	0.164577	+	0.119572i
$690$		0			0
$691$	−6.54403	+	20.1404i	−0.248946	+	0.766179i	0.746016	+	0.665928i	$0.231964\pi$
$691$	−6.54403	+	20.1404i	−0.248946	+	0.766179i	−0.994962	+	0.100250i	$0.968036\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	7.14582	−	21.9926i	0.271056	−	0.834226i
$696$		0			0
$697$	−14.1868	−	10.3073i	−0.537365	−	0.390418i
$698$		0			0
$699$	1.00985	+	3.10800i	0.0381961	+	0.117556i
$700$		0			0
$701$	−10.1998	+	7.41062i	−0.385243	+	0.279895i	−0.763503	−	0.645804i	$-0.776522\pi$
$701$	−10.1998	+	7.41062i	−0.385243	+	0.279895i	0.378261	+	0.925699i	$0.376522\pi$
$702$		0			0
$703$	−18.7321			−0.706493
$704$		0			0
$705$	33.3205			1.25492
$706$		0			0
$707$	38.6005	−	28.0449i	1.45172	−	1.05474i
$708$		0			0
$709$	−0.0443728	−	0.136566i	−0.00166646	−	0.00512883i	0.950220	−	0.311580i	$-0.100858\pi$
$709$	−0.0443728	−	0.136566i	−0.00166646	−	0.00512883i	−0.951886	+	0.306451i	$0.900858\pi$
$710$		0			0
$711$	−59.9098	−	43.5270i	−2.24679	−	1.63239i
$712$		0			0
$713$	3.21140	−	9.88367i	0.120268	−	0.370146i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−16.4769	+	50.7108i	−0.615343	+	1.89383i
$718$		0			0
$719$	−8.24886	−	5.99315i	−0.307631	−	0.223507i	0.423249	−	0.906014i	$-0.360890\pi$
$719$	−8.24886	−	5.99315i	−0.307631	−	0.223507i	−0.730879	+	0.682507i	$0.760890\pi$
$720$		0			0
$721$	5.51793	+	16.9825i	0.205499	+	0.632460i
$722$		0			0
$723$	−19.7338	+	14.3374i	−0.733908	+	0.533215i
$724$		0			0
$725$	39.8564			1.48023
$726$		0			0
$727$	−2.19615			−0.0814508			−0.0407254	−	0.999170i	$-0.512967\pi$
$727$	−2.19615			−0.0814508			−0.0407254	+	0.999170i	$0.512967\pi$
$728$		0			0
$729$	35.4225	−	25.7359i	1.31194	−	0.953183i
$730$		0			0
$731$	5.60668	+	17.2556i	0.207371	+	0.638221i
$732$		0			0
$733$	26.6976	+	19.3969i	0.986097	+	0.716441i	0.959063	−	0.283193i	$-0.0913938\pi$
$733$	26.6976	+	19.3969i	0.986097	+	0.716441i	0.0270340	+	0.999635i	$0.491394\pi$
$734$		0			0
$735$	−1.46228	+	4.50045i	−0.0539372	+	0.166002i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−5.17049	+	15.9131i	−0.190199	+	0.585374i	−0.999999	−	0.00133273i	$-0.999576\pi$
$739$	−5.17049	+	15.9131i	−0.190199	+	0.585374i	0.809800	+	0.586707i	$0.199576\pi$
$740$		0			0
$741$	−32.2445	−	23.4270i	−1.18453	−	0.860613i
$742$		0			0
$743$	−12.7850	−	39.3481i	−0.469035	−	1.44354i	−0.853836	−	0.520543i	$-0.825730\pi$
$743$	−12.7850	−	39.3481i	−0.469035	−	1.44354i	0.384800	−	0.923000i	$-0.374270\pi$
$744$		0			0
$745$	16.7145	−	12.1438i	0.612372	−	0.444914i
$746$		0			0
$747$	−9.80385			−0.358704
$748$		0			0
$749$	−46.7846			−1.70947
$750$		0			0
$751$	27.3904	−	19.9003i	0.999490	−	0.726172i	0.0375114	−	0.999296i	$-0.488057\pi$
$751$	27.3904	−	19.9003i	0.999490	−	0.726172i	0.961979	+	0.273124i	$0.0880570\pi$
$752$		0			0
$753$	14.5785	+	44.8679i	0.531269	+	1.63508i
$754$		0			0
$755$	31.8110	+	23.1120i	1.15772	+	0.841132i
$756$		0			0
$757$	−11.7811	+	36.2584i	−0.428190	+	1.31783i	0.471716	+	0.881751i	$0.343635\pi$
$757$	−11.7811	+	36.2584i	−0.428190	+	1.31783i	−0.899906	+	0.436084i	$0.856365\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	7.16801	−	22.0609i	0.259840	−	0.799705i	−0.732997	−	0.680231i	$-0.761879\pi$
$761$	7.16801	−	22.0609i	0.259840	−	0.799705i	0.992837	−	0.119474i	$-0.0381207\pi$
$762$		0			0
$763$	−27.5491	−	20.0156i	−0.997344	−	0.724613i
$764$		0			0
$765$	11.6761	+	35.9353i	0.422150	+	1.29924i
$766$		0			0
$767$	48.6261	−	35.3289i	1.75579	−	1.27565i
$768$		0			0
$769$	−14.2679			−0.514515			−0.257258	−	0.966343i	$-0.582819\pi$
$769$	−14.2679			−0.514515			−0.257258	+	0.966343i	$0.582819\pi$
$770$		0			0
$771$	−12.1962			−0.439234
$772$		0			0
$773$	32.2445	−	23.4270i	1.15975	−	0.842611i	0.170007	−	0.985443i	$-0.445621\pi$
$773$	32.2445	−	23.4270i	1.15975	−	0.842611i	0.989747	+	0.142832i	$0.0456208\pi$
$774$		0			0
$775$	−13.0556	−	40.1809i	−0.468970	−	1.44334i
$776$		0			0
$777$	34.6135	+	25.1482i	1.24175	+	0.902185i
$778$		0			0
$779$	7.80823	−	24.0312i	0.279759	−	0.861009i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	5.51793	−	16.9825i	0.197195	−	0.606903i
$784$		0			0
$785$	−62.7548	−	45.5940i	−2.23982	−	1.62732i
$786$		0			0
$787$	−1.47853	−	4.55043i	−0.0527037	−	0.162205i	0.921240	−	0.388994i	$-0.127177\pi$
$787$	−1.47853	−	4.55043i	−0.0527037	−	0.162205i	−0.973944	+	0.226789i	$0.927177\pi$
$788$		0			0
$789$	−5.17148	+	3.75730i	−0.184110	+	0.133764i
$790$		0			0
$791$	−13.6603			−0.485703
$792$		0			0
$793$	29.1769			1.03610
$794$		0			0
$795$	9.86689	−	7.16872i	0.349943	−	0.254248i
$796$		0			0
$797$	12.5588	+	38.6519i	0.444854	+	1.36912i	0.882644	+	0.470043i	$0.155762\pi$
$797$	12.5588	+	38.6519i	0.444854	+	1.36912i	−0.437789	+	0.899078i	$0.644238\pi$
$798$		0			0
$799$	−5.99606	−	4.35640i	−0.212125	−	0.154118i
$800$		0			0
$801$	−22.7120	+	69.9002i	−0.802487	+	2.46980i
$802$		0			0
$803$		0			0
$804$		0			0
$805$	−6.91960	+	21.2963i	−0.243884	+	0.750598i
$806$		0			0
$807$	42.1114	+	30.5957i	1.48239	+	1.07702i
$808$		0			0
$809$	−4.23749	−	13.0417i	−0.148982	−	0.458520i	0.848519	−	0.529164i	$-0.177495\pi$
$809$	−4.23749	−	13.0417i	−0.148982	−	0.458520i	−0.997502	+	0.0706441i	$0.977495\pi$
$810$		0			0
$811$	−13.8114	+	10.0346i	−0.484983	+	0.352361i	−0.803252	−	0.595640i	$-0.796899\pi$
$811$	−13.8114	+	10.0346i	−0.484983	+	0.352361i	0.318269	+	0.948001i	$0.396899\pi$
$812$		0			0
$813$	17.8564			0.626252
$814$		0			0
$815$	87.7654			3.07429
$816$		0			0
$817$	−21.1506	+	15.3668i	−0.739966	+	0.537617i
$818$		0			0
$819$	16.8244	+	51.7801i	0.587892	+	1.80934i
$820$		0			0
$821$	10.6603	+	7.74520i	0.372049	+	0.270309i	0.758060	−	0.652185i	$-0.226147\pi$
$821$	10.6603	+	7.74520i	0.372049	+	0.270309i	−0.386011	+	0.922494i	$0.626147\pi$
$822$		0			0
$823$	2.47214	−	7.60845i	0.0861732	−	0.265214i	−0.898680	−	0.438605i	$-0.855473\pi$
$823$	2.47214	−	7.60845i	0.0861732	−	0.265214i	0.984853	+	0.173391i	$0.0554726\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	8.00631	−	24.6409i	0.278407	−	0.856848i	−0.709891	−	0.704311i	$-0.751256\pi$
$827$	8.00631	−	24.6409i	0.278407	−	0.856848i	0.988298	−	0.152536i	$-0.0487441\pi$
$828$		0			0
$829$	−1.28509	−	0.933672i	−0.0446330	−	0.0324278i	0.565245	−	0.824923i	$-0.308782\pi$
$829$	−1.28509	−	0.933672i	−0.0446330	−	0.0324278i	−0.609878	+	0.792495i	$0.708782\pi$
$830$		0			0
$831$	11.6377	+	35.8170i	0.403706	+	1.24248i
$832$		0			0
$833$	0.851538	−	0.618679i	0.0295040	−	0.0214359i
$834$		0			0
$835$	24.3923			0.844131
$836$		0			0
$837$	−18.9282			−0.654254
$838$		0			0
$839$	43.0635	−	31.2875i	1.48672	−	1.08016i	0.511405	−	0.859340i	$-0.329125\pi$
$839$	43.0635	−	31.2875i	1.48672	−	1.08016i	0.975313	−	0.220825i	$-0.0708749\pi$
$840$		0			0
$841$	−2.80334	−	8.62779i	−0.0966669	−	0.297510i
$842$		0			0
$843$	17.3648	+	12.6163i	0.598076	+	0.434528i
$844$		0			0
$845$	−7.99007	+	24.5909i	−0.274867	+	0.845953i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−26.1111	+	80.3618i	−0.896132	+	2.75801i
$850$		0			0
$851$	10.1843	+	7.39931i	0.349112	+	0.253645i
$852$		0			0
$853$	4.46965	+	13.7562i	0.153038	+	0.471003i	0.997957	−	0.0638920i	$-0.0203513\pi$
$853$	4.46965	+	13.7562i	0.153038	+	0.471003i	−0.844919	+	0.534895i	$0.820351\pi$
$854$		0			0
$855$	−44.0468	+	32.0019i	−1.50637	+	1.09444i
$856$		0			0
$857$	26.1436			0.893048			0.446524	−	0.894772i	$-0.352662\pi$
$857$	26.1436			0.893048			0.446524	+	0.894772i	$0.352662\pi$
$858$		0			0
$859$	54.6410			1.86433			0.932164	−	0.362037i	$-0.117919\pi$
$859$	54.6410			1.86433			0.932164	+	0.362037i	$0.117919\pi$
$860$		0			0
$861$	−46.6906	+	33.9227i	−1.59121	+	1.15608i
$862$		0			0
$863$	−4.50808	−	13.8744i	−0.153457	−	0.472292i	0.844544	−	0.535486i	$-0.179871\pi$
$863$	−4.50808	−	13.8744i	−0.153457	−	0.472292i	−0.998001	+	0.0631939i	$0.979871\pi$
$864$		0			0
$865$	7.65662	+	5.56286i	0.260333	+	0.189143i
$866$		0			0
$867$	−10.0098	+	30.8069i	−0.339950	+	1.04626i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	0.270589	−	0.832787i	0.00916856	−	0.0282179i
$872$		0			0
$873$	43.0791	+	31.2988i	1.45801	+	1.05930i
$874$		0			0
$875$	12.3769	+	38.0922i	0.418416	+	1.28775i
$876$		0			0
$877$	12.7700	−	9.27796i	0.431213	−	0.313294i	−0.350921	−	0.936405i	$-0.614131\pi$
$877$	12.7700	−	9.27796i	0.431213	−	0.313294i	0.782134	+	0.623111i	$0.214131\pi$
$878$		0			0
$879$	−60.9808			−2.05683
$880$		0			0
$881$	−9.67949			−0.326110			−0.163055	−	0.986617i	$-0.552135\pi$
$881$	−9.67949			−0.326110			−0.163055	+	0.986617i	$0.552135\pi$
$882$		0			0
$883$	−5.28765	+	3.84170i	−0.177944	+	0.129284i	−0.673192	−	0.739468i	$-0.735077\pi$
$883$	−5.28765	+	3.84170i	−0.177944	+	0.129284i	0.495248	+	0.868752i	$0.335077\pi$
$884$		0			0
$885$	−42.4225	−	130.563i	−1.42602	−	4.38883i
$886$		0			0
$887$	−34.9734	−	25.4096i	−1.17429	−	0.853172i	−0.182775	−	0.983155i	$-0.558508\pi$
$887$	−34.9734	−	25.4096i	−1.17429	−	0.853172i	−0.991516	+	0.129982i	$0.958508\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	3.30014	−	10.1568i	0.110435	−	0.339884i
$894$		0			0
$895$	48.3087	+	35.0983i	1.61478	+	1.17321i
$896$		0			0
$897$	8.27690	+	25.4737i	0.276358	+	0.850541i
$898$		0			0
$899$	17.0900	−	12.4166i	0.569982	−	0.414116i
$900$		0			0
$901$	−2.71281			−0.0903769
$902$		0			0
$903$	59.7128			1.98712
$904$		0			0
$905$	−8.46564	+	6.15064i	−0.281407	+	0.204454i
$906$		0			0
$907$	5.51793	+	16.9825i	0.183220	+	0.563893i	0.999913	−	0.0131791i	$-0.00419515\pi$
$907$	5.51793	+	16.9825i	0.183220	+	0.563893i	−0.816693	+	0.577072i	$0.804195\pi$
$908$		0			0
$909$	−63.0722	−	45.8246i	−2.09197	−	1.51991i
$910$		0			0
$911$	−4.07189	+	12.5320i	−0.134908	+	0.415203i	−0.995576	−	0.0939634i	$-0.970046\pi$
$911$	−4.07189	+	12.5320i	−0.134908	+	0.415203i	0.860668	+	0.509167i	$0.170046\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	20.5932	−	63.3794i	0.680790	−	2.09526i
$916$		0			0
$917$	17.6822	+	12.8469i	0.583918	+	0.424241i
$918$		0			0
$919$	3.70820	+	11.4127i	0.122322	+	0.376470i	0.993404	−	0.114669i	$-0.0365808\pi$
$919$	3.70820	+	11.4127i	0.122322	+	0.376470i	−0.871081	+	0.491139i	$0.836581\pi$
$920$		0			0
$921$	−71.7121	+	52.1019i	−2.36299	+	1.71682i
$922$		0			0
$923$	−11.3205			−0.372619
$924$		0			0
$925$	51.1769			1.68269
$926$		0			0
$927$	23.6046	−	17.1498i	0.775277	−	0.563272i
$928$		0			0
$929$	−6.15815	−	18.9528i	−0.202042	−	0.621823i	−0.999822	−	0.0188733i	$-0.993992\pi$
$929$	−6.15815	−	18.9528i	−0.202042	−	0.621823i	0.797779	−	0.602949i	$-0.206008\pi$
$930$		0			0
$931$	1.22700	+	0.891471i	0.0402134	+	0.0292168i
$932$		0			0
$933$	14.1704	−	43.6120i	0.463918	−	1.42779i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−11.2074	+	34.4929i	−0.366130	+	1.12683i	0.583140	+	0.812372i	$0.301824\pi$
$937$	−11.2074	+	34.4929i	−0.366130	+	1.12683i	−0.949270	+	0.314461i	$0.898176\pi$
$938$		0			0
$939$	15.4719	+	11.2410i	0.504907	+	0.366837i
$940$		0			0
$941$	−6.48936	−	19.9722i	−0.211547	−	0.651075i	−0.999381	−	0.0351867i	$-0.988797\pi$
$941$	−6.48936	−	19.9722i	−0.211547	−	0.651075i	0.787834	−	0.615888i	$-0.211203\pi$
$942$		0			0
$943$	−13.7377	+	9.98104i	−0.447362	+	0.325027i
$944$		0			0
$945$	40.7846			1.32672
$946$		0			0
$947$	−11.5167			−0.374241			−0.187121	−	0.982337i	$-0.559916\pi$
$947$	−11.5167			−0.374241			−0.187121	+	0.982337i	$0.559916\pi$
$948$		0			0
$949$	32.2445	−	23.4270i	1.04670	−	0.760473i
$950$		0			0
$951$	3.25577	+	10.0202i	0.105576	+	0.324928i
$952$		0			0
$953$	−13.9120	−	10.1076i	−0.450653	−	0.327419i	0.339200	−	0.940714i	$-0.389844\pi$
$953$	−13.9120	−	10.1076i	−0.450653	−	0.327419i	−0.789854	+	0.613295i	$0.789844\pi$
$954$		0			0
$955$	−5.06550	+	15.5900i	−0.163916	+	0.504481i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	2.14093	−	6.58911i	0.0691343	−	0.212774i
$960$		0			0
$961$	6.96377	+	5.05948i	0.224638	+	0.163209i
$962$		0			0
$963$	23.6228	+	72.7034i	0.761233	+	2.34283i
$964$		0			0
$965$	−50.3022	+	36.5467i	−1.61928	+	1.17648i
$966$		0			0
$967$	18.7321			0.602382			0.301191	−	0.953564i	$-0.402616\pi$
$967$	18.7321			0.602382			0.301191	+	0.953564i	$0.402616\pi$
$968$		0			0
$969$	20.2487			0.650482
$970$		0			0
$971$	−31.9696	+	23.2273i	−1.02595	+	0.745400i	−0.967495	−	0.252890i	$-0.918619\pi$
$971$	−31.9696	+	23.2273i	−1.02595	+	0.745400i	−0.0584598	+	0.998290i	$0.518619\pi$
$972$		0			0
$973$	5.23110	+	16.0997i	0.167701	+	0.516132i
$974$		0			0
$975$	88.0936	+	64.0038i	2.82125	+	2.04976i
$976$		0			0
$977$	8.08911	−	24.8957i	0.258794	−	0.796485i	−0.734265	−	0.678863i	$-0.762473\pi$
$977$	8.08911	−	24.8957i	0.258794	−	0.796485i	0.993058	−	0.117622i	$-0.0375270\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−17.1940	+	52.9178i	−0.548963	+	1.68953i
$982$		0			0
$983$	−29.2097	−	21.2221i	−0.931643	−	0.676878i	0.0147513	−	0.999891i	$-0.495304\pi$
$983$	−29.2097	−	21.2221i	−0.931643	−	0.676878i	−0.946395	+	0.323013i	$0.895304\pi$
$984$		0			0
$985$	6.83680	+	21.0415i	0.217839	+	0.670438i
$986$		0			0
$987$	−19.7338	+	14.3374i	−0.628133	+	0.456366i
$988$		0			0
$989$	17.5692			0.558669
$990$		0			0
$991$	17.8564			0.567227			0.283614	−	0.958939i	$-0.408467\pi$
$991$	17.8564			0.567227			0.283614	+	0.958939i	$0.408467\pi$
$992$		0			0
$993$	2.36897	−	1.72115i	0.0751769	−	0.0546192i
$994$		0			0
$995$	7.53764	+	23.1985i	0.238959	+	0.735441i
$996$		0			0
$997$	46.8649	+	34.0493i	1.48423	+	1.07835i	0.976164	+	0.217033i	$0.0696379\pi$
$997$	46.8649	+	34.0493i	1.48423	+	1.07835i	0.508062	+	0.861320i	$0.330362\pi$
$998$		0			0
$999$	7.08520	−	21.8060i	0.224166	−	0.689912i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.2.i.o.9.1		8
11.2	odd	10		968.2.i.n.729.2		8
11.3	even	5	inner	968.2.i.o.81.2		8
11.4	even	5		968.2.a.k.1.2	✓	2
11.5	even	5	inner	968.2.i.o.753.1		8
11.6	odd	10		968.2.i.n.753.1		8
11.7	odd	10		968.2.a.l.1.2	yes	2
11.8	odd	10		968.2.i.n.81.2		8
11.9	even	5	inner	968.2.i.o.729.2		8
11.10	odd	2		968.2.i.n.9.1		8
33.26	odd	10		8712.2.a.br.1.2		2
33.29	even	10		8712.2.a.bs.1.2		2
44.7	even	10		1936.2.a.p.1.1		2
44.15	odd	10		1936.2.a.q.1.1		2
88.29	odd	10		7744.2.a.bv.1.1		2
88.37	even	10		7744.2.a.bu.1.1		2
88.51	even	10		7744.2.a.cw.1.2		2
88.59	odd	10		7744.2.a.cx.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
968.2.a.k.1.2	✓	2	11.4	even	5
968.2.a.l.1.2	yes	2	11.7	odd	10
968.2.i.n.9.1		8	11.10	odd	2
968.2.i.n.81.2		8	11.8	odd	10
968.2.i.n.729.2		8	11.2	odd	10
968.2.i.n.753.1		8	11.6	odd	10
968.2.i.o.9.1		8	1.1	even	1	trivial
968.2.i.o.81.2		8	11.3	even	5	inner
968.2.i.o.729.2		8	11.9	even	5	inner
968.2.i.o.753.1		8	11.5	even	5	inner
1936.2.a.p.1.1		2	44.7	even	10
1936.2.a.q.1.1		2	44.15	odd	10
7744.2.a.bu.1.1		2	88.37	even	10
7744.2.a.bv.1.1		2	88.29	odd	10
7744.2.a.cw.1.2		2	88.51	even	10
7744.2.a.cx.1.2		2	88.59	odd	10
8712.2.a.br.1.2		2	33.26	odd	10
8712.2.a.bs.1.2		2	33.29	even	10

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:	\( N \)	\(=\)	\( 968 = 2^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	968.i (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.21028 + 1.60586i) q^{3} +(-1.15327 - 3.54939i) q^{5} +(2.21028 + 1.60586i) q^{7} +(1.37948 - 4.24561i) q^{9} +O(q^{10})\)	\(q+(-2.21028 + 1.60586i) q^{3} +(-1.15327 - 3.54939i) q^{5} +(2.21028 + 1.60586i) q^{7} +(1.37948 - 4.24561i) q^{9} +(-1.37948 + 4.24561i) q^{13} +(8.24886 + 5.99315i) q^{15} +(-0.700835 - 2.15695i) q^{17} +(2.64383 - 1.92085i) q^{19} -7.46410 q^{21} -2.19615 q^{23} +(-7.22307 + 5.24787i) q^{25} +(1.23607 + 3.80423i) q^{27} +(-3.61153 - 2.62393i) q^{29} +(-1.46228 + 4.50045i) q^{31} +(3.15078 - 9.69712i) q^{35} +(-4.63733 - 3.36921i) q^{37} +(-3.76882 - 11.5992i) q^{39} +(6.25536 - 4.54479i) q^{41} -8.00000 q^{43} -16.6603 q^{45} +(2.64383 - 1.92085i) q^{47} +(0.143415 + 0.441387i) q^{49} +(5.01279 + 3.64201i) q^{51} +(0.369631 - 1.13761i) q^{53} +(-2.75897 + 8.49123i) q^{57} +(-10.8927 - 7.91400i) q^{59} +(-2.01970 - 6.21601i) q^{61} +(9.86689 - 7.16872i) q^{63} +16.6603 q^{65} -0.196152 q^{67} +(4.85410 - 3.52671i) q^{69} +(0.783636 + 2.41178i) q^{71} +(-7.22307 - 5.24787i) q^{73} +(7.53764 - 23.1985i) q^{75} +(5.12612 - 15.7766i) q^{79} +(1.99350 + 1.44836i) q^{81} +(-0.678648 - 2.08867i) q^{83} +(-6.84760 + 4.97507i) q^{85} +12.1962 q^{87} -16.4641 q^{89} +(-9.86689 + 7.16872i) q^{91} +(-3.99503 - 12.2955i) q^{93} +(-9.86689 - 7.16872i) q^{95} +(-3.68602 + 11.3444i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} + 4 q^{5} + 2 q^{7} - 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^3 + 4 * q^5 + 2 * q^7 - 2 * q^9	\( 8 q - 2 q^{3} + 4 q^{5} + 2 q^{7} - 2 q^{9} + 2 q^{13} + 10 q^{15} + 8 q^{17} + 10 q^{19} - 32 q^{21} + 24 q^{23} - 4 q^{25} - 8 q^{27} - 2 q^{29} + 6 q^{31} - 10 q^{35} - 8 q^{37} + 14 q^{39} + 12 q^{41} - 64 q^{43} - 64 q^{45} + 10 q^{47} + 6 q^{49} + 2 q^{51} + 8 q^{53} + 4 q^{57} - 20 q^{59} + 20 q^{61} + 14 q^{63} + 64 q^{65} + 40 q^{67} + 12 q^{69} - 12 q^{71} - 4 q^{73} - 28 q^{75} - 2 q^{79} - 2 q^{81} - 6 q^{83} - 10 q^{85} + 56 q^{87} - 104 q^{89} - 14 q^{91} + 12 q^{93} - 14 q^{95} + 10 q^{97}+O(q^{100}) \) 8 * q - 2 * q^3 + 4 * q^5 + 2 * q^7 - 2 * q^9 + 2 * q^13 + 10 * q^15 + 8 * q^17 + 10 * q^19 - 32 * q^21 + 24 * q^23 - 4 * q^25 - 8 * q^27 - 2 * q^29 + 6 * q^31 - 10 * q^35 - 8 * q^37 + 14 * q^39 + 12 * q^41 - 64 * q^43 - 64 * q^45 + 10 * q^47 + 6 * q^49 + 2 * q^51 + 8 * q^53 + 4 * q^57 - 20 * q^59 + 20 * q^61 + 14 * q^63 + 64 * q^65 + 40 * q^67 + 12 * q^69 - 12 * q^71 - 4 * q^73 - 28 * q^75 - 2 * q^79 - 2 * q^81 - 6 * q^83 - 10 * q^85 + 56 * q^87 - 104 * q^89 - 14 * q^91 + 12 * q^93 - 14 * q^95 + 10 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more