LMFDB - Embedded newform 882.2.f.s.295.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(295,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("882.295");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.f (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			295.1
Root			$0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	882.295
Dual form			882.2.f.s.589.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-1.22474 - 1.22474i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.965926 - 1.67303i) q^{5} +(-1.67303 + 0.448288i) q^{6} -1.00000 q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-1.22474 - 1.22474i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.965926 - 1.67303i) q^{5} +(-1.67303 + 0.448288i) q^{6} -1.00000 q^{8} +3.00000i q^{9} -1.93185 q^{10} +(-2.73205 + 4.73205i) q^{11} +(-0.448288 + 1.67303i) q^{12} +(1.22474 + 2.12132i) q^{13} +(-0.866025 + 3.23205i) q^{15} +(-0.500000 + 0.866025i) q^{16} -6.31319 q^{17} +(2.59808 + 1.50000i) q^{18} +1.93185 q^{19} +(-0.965926 + 1.67303i) q^{20} +(2.73205 + 4.73205i) q^{22} +(2.96410 + 5.13397i) q^{23} +(1.22474 + 1.22474i) q^{24} +(0.633975 - 1.09808i) q^{25} +2.44949 q^{26} +(3.67423 - 3.67423i) q^{27} +(0.366025 - 0.633975i) q^{29} +(2.36603 + 2.36603i) q^{30} +(-3.67423 - 6.36396i) q^{31} +(0.500000 + 0.866025i) q^{32} +(9.14162 - 2.44949i) q^{33} +(-3.15660 + 5.46739i) q^{34} +(2.59808 - 1.50000i) q^{36} -8.00000 q^{37} +(0.965926 - 1.67303i) q^{38} +(1.09808 - 4.09808i) q^{39} +(0.965926 + 1.67303i) q^{40} +(2.82843 + 4.89898i) q^{41} +(0.901924 - 1.56218i) q^{43} +5.46410 q^{44} +(5.01910 - 2.89778i) q^{45} +5.92820 q^{46} +(-4.76028 + 8.24504i) q^{47} +(1.67303 - 0.448288i) q^{48} +(-0.633975 - 1.09808i) q^{50} +(7.73205 + 7.73205i) q^{51} +(1.22474 - 2.12132i) q^{52} +3.26795 q^{53} +(-1.34486 - 5.01910i) q^{54} +10.5558 q^{55} +(-2.36603 - 2.36603i) q^{57} +(-0.366025 - 0.633975i) q^{58} +(2.50026 + 4.33057i) q^{59} +(3.23205 - 0.866025i) q^{60} +(-1.48356 + 2.56961i) q^{61} -7.34847 q^{62} +1.00000 q^{64} +(2.36603 - 4.09808i) q^{65} +(2.44949 - 9.14162i) q^{66} +(7.09808 + 12.2942i) q^{67} +(3.15660 + 5.46739i) q^{68} +(2.65754 - 9.91808i) q^{69} -11.1962 q^{71} -3.00000i q^{72} -9.52056 q^{73} +(-4.00000 + 6.92820i) q^{74} +(-2.12132 + 0.568406i) q^{75} +(-0.965926 - 1.67303i) q^{76} +(-3.00000 - 3.00000i) q^{78} +(5.06218 - 8.76795i) q^{79} +1.93185 q^{80} -9.00000 q^{81} +5.65685 q^{82} +(-4.94975 + 8.57321i) q^{83} +(6.09808 + 10.5622i) q^{85} +(-0.901924 - 1.56218i) q^{86} +(-1.22474 + 0.328169i) q^{87} +(2.73205 - 4.73205i) q^{88} -13.2827 q^{89} -5.79555i q^{90} +(2.96410 - 5.13397i) q^{92} +(-3.29423 + 12.2942i) q^{93} +(4.76028 + 8.24504i) q^{94} +(-1.86603 - 3.23205i) q^{95} +(0.448288 - 1.67303i) q^{96} +(1.93185 - 3.34607i) q^{97} +(-14.1962 - 8.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8}+O(q^{10}) $ 8 * q + 4 * q^2 - 4 * q^4 - 8 * q^8	$ 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8} - 8 q^{11} - 4 q^{16} + 8 q^{22} - 4 q^{23} + 12 q^{25} - 4 q^{29} + 12 q^{30} + 4 q^{32} - 64 q^{37} - 12 q^{39} + 28 q^{43} + 16 q^{44} - 8 q^{46} - 12 q^{50} + 48 q^{51} + 40 q^{53} - 12 q^{57} + 4 q^{58} + 12 q^{60} + 8 q^{64} + 12 q^{65} + 36 q^{67} - 48 q^{71} - 32 q^{74} - 24 q^{78} - 8 q^{79} - 72 q^{81} + 28 q^{85} - 28 q^{86} + 8 q^{88} - 4 q^{92} + 36 q^{93} - 8 q^{95} - 72 q^{99}+O(q^{100}) $ 8 * q + 4 * q^2 - 4 * q^4 - 8 * q^8 - 8 * q^11 - 4 * q^16 + 8 * q^22 - 4 * q^23 + 12 * q^25 - 4 * q^29 + 12 * q^30 + 4 * q^32 - 64 * q^37 - 12 * q^39 + 28 * q^43 + 16 * q^44 - 8 * q^46 - 12 * q^50 + 48 * q^51 + 40 * q^53 - 12 * q^57 + 4 * q^58 + 12 * q^60 + 8 * q^64 + 12 * q^65 + 36 * q^67 - 48 * q^71 - 32 * q^74 - 24 * q^78 - 8 * q^79 - 72 * q^81 + 28 * q^85 - 28 * q^86 + 8 * q^88 - 4 * q^92 + 36 * q^93 - 8 * q^95 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−1.22474	−	1.22474i	−0.707107	−	0.707107i
$3$	−1.22474	−	1.22474i	−0.707107	−	0.707107i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.965926	−	1.67303i	−0.431975	−	0.748203i	0.565068	−	0.825044i	$-0.308850\pi$
$5$	−0.965926	−	1.67303i	−0.431975	−	0.748203i	−0.997043	+	0.0768413i	$0.975517\pi$
$6$	−1.67303	+	0.448288i	−0.683013	+	0.183013i
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$			3.00000i			1.00000i
$10$	−1.93185			−0.610905
$11$	−2.73205	+	4.73205i	−0.823744	+	1.42677i	0.0791309	+	0.996864i	$0.474785\pi$
$11$	−2.73205	+	4.73205i	−0.823744	+	1.42677i	−0.902875	+	0.429903i	$0.858548\pi$
$12$	−0.448288	+	1.67303i	−0.129410	+	0.482963i
$13$	1.22474	+	2.12132i	0.339683	+	0.588348i	0.984373	−	0.176096i	$-0.0563468\pi$
$13$	1.22474	+	2.12132i	0.339683	+	0.588348i	−0.644690	+	0.764444i	$0.723014\pi$
$14$		0			0
$15$	−0.866025	+	3.23205i	−0.223607	+	0.834512i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−6.31319			−1.53117			−0.765587	−	0.643332i	$-0.777551\pi$
$17$	−6.31319			−1.53117			−0.765587	+	0.643332i	$0.777551\pi$
$18$	2.59808	+	1.50000i	0.612372	+	0.353553i
$19$	1.93185			0.443197			0.221599	−	0.975138i	$-0.428873\pi$
$19$	1.93185			0.443197			0.221599	+	0.975138i	$0.428873\pi$
$20$	−0.965926	+	1.67303i	−0.215988	+	0.374101i
$21$		0			0
$22$	2.73205	+	4.73205i	0.582475	+	1.00888i
$23$	2.96410	+	5.13397i	0.618058	+	1.07051i	0.989840	+	0.142188i	$0.0454136\pi$
$23$	2.96410	+	5.13397i	0.618058	+	1.07051i	−0.371782	+	0.928320i	$0.621253\pi$
$24$	1.22474	+	1.22474i	0.250000	+	0.250000i
$25$	0.633975	−	1.09808i	0.126795	−	0.219615i
$26$	2.44949			0.480384
$27$	3.67423	−	3.67423i	0.707107	−	0.707107i
$28$		0			0
$29$	0.366025	−	0.633975i	0.0679692	−	0.117726i	−0.830038	−	0.557707i	$-0.811681\pi$
$29$	0.366025	−	0.633975i	0.0679692	−	0.117726i	0.898007	+	0.439981i	$0.145015\pi$
$30$	2.36603	+	2.36603i	0.431975	+	0.431975i
$31$	−3.67423	−	6.36396i	−0.659912	−	1.14300i	−0.980638	−	0.195829i	$-0.937260\pi$
$31$	−3.67423	−	6.36396i	−0.659912	−	1.14300i	0.320726	−	0.947172i	$-0.396073\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	9.14162	−	2.44949i	1.59135	−	0.426401i
$34$	−3.15660	+	5.46739i	−0.541352	+	0.937649i
$35$		0			0
$36$	2.59808	−	1.50000i	0.433013	−	0.250000i
$37$	−8.00000			−1.31519			−0.657596	−	0.753371i	$-0.728427\pi$
$37$	−8.00000			−1.31519			−0.657596	+	0.753371i	$0.728427\pi$
$38$	0.965926	−	1.67303i	0.156694	−	0.271402i
$39$	1.09808	−	4.09808i	0.175833	−	0.656217i
$40$	0.965926	+	1.67303i	0.152726	+	0.264530i
$41$	2.82843	+	4.89898i	0.441726	+	0.765092i	0.997818	−	0.0660290i	$-0.0210330\pi$
$41$	2.82843	+	4.89898i	0.441726	+	0.765092i	−0.556092	+	0.831121i	$0.687700\pi$
$42$		0			0
$43$	0.901924	−	1.56218i	0.137542	−	0.238230i	−0.789024	−	0.614363i	$-0.789413\pi$
$43$	0.901924	−	1.56218i	0.137542	−	0.238230i	0.926566	+	0.376133i	$0.122746\pi$
$44$	5.46410			0.823744
$45$	5.01910	−	2.89778i	0.748203	−	0.431975i
$46$	5.92820			0.874066
$47$	−4.76028	+	8.24504i	−0.694358	+	1.20266i	0.276039	+	0.961147i	$0.410978\pi$
$47$	−4.76028	+	8.24504i	−0.694358	+	1.20266i	−0.970397	+	0.241517i	$0.922355\pi$
$48$	1.67303	−	0.448288i	0.241481	−	0.0647048i
$49$		0			0
$50$	−0.633975	−	1.09808i	−0.0896575	−	0.155291i
$51$	7.73205	+	7.73205i	1.08270	+	1.08270i
$52$	1.22474	−	2.12132i	0.169842	−	0.294174i
$53$	3.26795			0.448887			0.224444	−	0.974487i	$-0.427944\pi$
$53$	3.26795			0.448887			0.224444	+	0.974487i	$0.427944\pi$
$54$	−1.34486	−	5.01910i	−0.183013	−	0.683013i
$55$	10.5558			1.42335
$56$		0			0
$57$	−2.36603	−	2.36603i	−0.313388	−	0.313388i
$58$	−0.366025	−	0.633975i	−0.0480615	−	0.0832449i
$59$	2.50026	+	4.33057i	0.325506	+	0.563793i	0.981615	−	0.190874i	$-0.0611321\pi$
$59$	2.50026	+	4.33057i	0.325506	+	0.563793i	−0.656109	+	0.754666i	$0.727799\pi$
$60$	3.23205	−	0.866025i	0.417256	−	0.111803i
$61$	−1.48356	+	2.56961i	−0.189951	+	0.329005i	−0.945234	−	0.326394i	$-0.894166\pi$
$61$	−1.48356	+	2.56961i	−0.189951	+	0.329005i	0.755283	+	0.655399i	$0.227500\pi$
$62$	−7.34847			−0.933257
$63$		0			0
$64$	1.00000			0.125000
$65$	2.36603	−	4.09808i	0.293469	−	0.508304i
$66$	2.44949	−	9.14162i	0.301511	−	1.12526i
$67$	7.09808	+	12.2942i	0.867168	+	1.50198i	0.864878	+	0.501982i	$0.167396\pi$
$67$	7.09808	+	12.2942i	0.867168	+	1.50198i	0.00228979	+	0.999997i	$0.499271\pi$
$68$	3.15660	+	5.46739i	0.382794	+	0.663018i
$69$	2.65754	−	9.91808i	0.319930	−	1.19400i
$70$		0			0
$71$	−11.1962			−1.32874			−0.664369	−	0.747404i	$-0.731300\pi$
$71$	−11.1962			−1.32874			−0.664369	+	0.747404i	$0.731300\pi$
$72$		−	3.00000i		−	0.353553i
$73$	−9.52056			−1.11430			−0.557148	−	0.830413i	$-0.688105\pi$
$73$	−9.52056			−1.11430			−0.557148	+	0.830413i	$0.688105\pi$
$74$	−4.00000	+	6.92820i	−0.464991	+	0.805387i
$75$	−2.12132	+	0.568406i	−0.244949	+	0.0656339i
$76$	−0.965926	−	1.67303i	−0.110799	−	0.191910i
$77$		0			0
$78$	−3.00000	−	3.00000i	−0.339683	−	0.339683i
$79$	5.06218	−	8.76795i	0.569540	−	0.986471i	−0.427072	−	0.904218i	$-0.640455\pi$
$79$	5.06218	−	8.76795i	0.569540	−	0.986471i	0.996611	−	0.0822537i	$-0.0262118\pi$
$80$	1.93185			0.215988
$81$	−9.00000			−1.00000
$82$	5.65685			0.624695
$83$	−4.94975	+	8.57321i	−0.543305	+	0.941033i	0.455406	+	0.890284i	$0.349494\pi$
$83$	−4.94975	+	8.57321i	−0.543305	+	0.941033i	−0.998711	+	0.0507487i	$0.983839\pi$
$84$		0			0
$85$	6.09808	+	10.5622i	0.661429	+	1.14563i
$86$	−0.901924	−	1.56218i	−0.0972569	−	0.168454i
$87$	−1.22474	+	0.328169i	−0.131306	+	0.0351835i
$88$	2.73205	−	4.73205i	0.291238	−	0.504438i
$89$	−13.2827			−1.40797			−0.703983	−	0.710217i	$-0.748597\pi$
$89$	−13.2827			−1.40797			−0.703983	+	0.710217i	$0.748597\pi$
$90$		−	5.79555i		−	0.610905i
$91$		0			0
$92$	2.96410	−	5.13397i	0.309029	−	0.535254i
$93$	−3.29423	+	12.2942i	−0.341596	+	1.27485i
$94$	4.76028	+	8.24504i	0.490985	+	0.850411i
$95$	−1.86603	−	3.23205i	−0.191450	−	0.331601i
$96$	0.448288	−	1.67303i	0.0457532	−	0.170753i
$97$	1.93185	−	3.34607i	0.196150	−	0.339741i	−0.751127	−	0.660158i	$-0.770489\pi$
$97$	1.93185	−	3.34607i	0.196150	−	0.339741i	0.947277	+	0.320416i	$0.103823\pi$
$98$		0			0
$99$	−14.1962	−	8.19615i	−1.42677	−	0.823744i
$100$	−1.26795			−0.126795
$101$	−0.776457	+	1.34486i	−0.0772604	+	0.133819i	−0.902067	−	0.431596i	$-0.857951\pi$
$101$	−0.776457	+	1.34486i	−0.0772604	+	0.133819i	0.824807	+	0.565415i	$0.191284\pi$
$102$	10.5622	−	2.83013i	1.04581	−	0.280224i
$103$	4.19187	+	7.26054i	0.413037	+	0.715402i	0.995220	−	0.0976561i	$-0.0311345\pi$
$103$	4.19187	+	7.26054i	0.413037	+	0.715402i	−0.582183	+	0.813058i	$0.697801\pi$
$104$	−1.22474	−	2.12132i	−0.120096	−	0.208013i
$105$		0			0
$106$	1.63397	−	2.83013i	0.158706	−	0.274886i
$107$	16.9282			1.63651			0.818256	−	0.574855i	$-0.194941\pi$
$107$	16.9282			1.63651			0.818256	+	0.574855i	$0.194941\pi$
$108$	−5.01910	−	1.34486i	−0.482963	−	0.129410i
$109$	−20.5885			−1.97202			−0.986008	−	0.166696i	$-0.946690\pi$
$109$	−20.5885			−1.97202			−0.986008	+	0.166696i	$0.946690\pi$
$110$	5.27792	−	9.14162i	0.503230	−	0.871619i
$111$	9.79796	+	9.79796i	0.929981	+	0.929981i
$112$		0			0
$113$	−1.33013	−	2.30385i	−0.125128	−	0.216728i	0.796655	−	0.604434i	$-0.206601\pi$
$113$	−1.33013	−	2.30385i	−0.125128	−	0.216728i	−0.921783	+	0.387706i	$0.873267\pi$
$114$	−3.23205	+	0.866025i	−0.302709	+	0.0811107i
$115$	5.72620	−	9.91808i	0.533971	−	0.924865i
$116$	−0.732051			−0.0679692
$117$	−6.36396	+	3.67423i	−0.588348	+	0.339683i
$118$	5.00052			0.460335
$119$		0			0
$120$	0.866025	−	3.23205i	0.0790569	−	0.295045i
$121$	−9.42820	−	16.3301i	−0.857109	−	1.48456i
$122$	1.48356	+	2.56961i	0.134316	+	0.232641i
$123$	2.53590	−	9.46410i	0.228654	−	0.853349i
$124$	−3.67423	+	6.36396i	−0.329956	+	0.571501i
$125$	−12.1087			−1.08304
$126$		0			0
$127$	7.92820			0.703514			0.351757	−	0.936091i	$-0.385584\pi$
$127$	7.92820			0.703514			0.351757	+	0.936091i	$0.385584\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−3.01790	+	0.808643i	−0.265711	+	0.0711970i
$130$	−2.36603	−	4.09808i	−0.207514	−	0.359425i
$131$	0.120118	+	0.208051i	0.0104948	+	0.0181775i	0.871225	−	0.490884i	$-0.163326\pi$
$131$	0.120118	+	0.208051i	0.0104948	+	0.0181775i	−0.860730	+	0.509061i	$0.829993\pi$
$132$	−6.69213	−	6.69213i	−0.582475	−	0.582475i
$133$		0			0
$134$	14.1962			1.22636
$135$	−9.69615	−	2.59808i	−0.834512	−	0.223607i
$136$	6.31319			0.541352
$137$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$137$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$138$	−7.26054	−	7.26054i	−0.618058	−	0.618058i
$139$	0.915158	+	1.58510i	0.0776227	+	0.134446i	0.902224	−	0.431268i	$-0.141934\pi$
$139$	0.915158	+	1.58510i	0.0776227	+	0.134446i	−0.824601	+	0.565715i	$0.808600\pi$
$140$		0			0
$141$	15.9282	−	4.26795i	1.34140	−	0.359426i
$142$	−5.59808	+	9.69615i	−0.469780	+	0.813683i
$143$	−13.3843			−1.11925
$144$	−2.59808	−	1.50000i	−0.216506	−	0.125000i
$145$	−1.41421			−0.117444
$146$	−4.76028	+	8.24504i	−0.393963	+	0.682365i
$147$		0			0
$148$	4.00000	+	6.92820i	0.328798	+	0.569495i
$149$	−9.19615	−	15.9282i	−0.753378	−	1.30489i	−0.946177	−	0.323651i	$-0.895090\pi$
$149$	−9.19615	−	15.9282i	−0.753378	−	1.30489i	0.192798	−	0.981238i	$-0.438244\pi$
$150$	−0.568406	+	2.12132i	−0.0464102	+	0.173205i
$151$	−1.69615	+	2.93782i	−0.138031	+	0.239077i	−0.926751	−	0.375676i	$-0.877411\pi$
$151$	−1.69615	+	2.93782i	−0.138031	+	0.239077i	0.788720	+	0.614752i	$0.210744\pi$
$152$	−1.93185			−0.156694
$153$		−	18.9396i		−	1.53117i
$154$		0			0
$155$	−7.09808	+	12.2942i	−0.570131	+	0.987496i
$156$	−4.09808	+	1.09808i	−0.328109	+	0.0879165i
$157$	12.1781	+	21.0931i	0.971918	+	1.68341i	0.689752	+	0.724046i	$0.257720\pi$
$157$	12.1781	+	21.0931i	0.971918	+	1.68341i	0.282166	+	0.959366i	$0.408947\pi$
$158$	−5.06218	−	8.76795i	−0.402725	−	0.697541i
$159$	−4.00240	−	4.00240i	−0.317411	−	0.317411i
$160$	0.965926	−	1.67303i	0.0763631	−	0.132265i
$161$		0			0
$162$	−4.50000	+	7.79423i	−0.353553	+	0.612372i
$163$	−20.9282			−1.63922			−0.819612	−	0.572919i	$-0.805811\pi$
$163$	−20.9282			−1.63922			−0.819612	+	0.572919i	$0.805811\pi$
$164$	2.82843	−	4.89898i	0.220863	−	0.382546i
$165$	−12.9282	−	12.9282i	−1.00646	−	1.00646i
$166$	4.94975	+	8.57321i	0.384175	+	0.665410i
$167$	−8.05558	−	13.9527i	−0.623359	−	1.07969i	−0.988856	−	0.148877i	$-0.952434\pi$
$167$	−8.05558	−	13.9527i	−0.623359	−	1.07969i	0.365497	−	0.930813i	$-0.380899\pi$
$168$		0			0
$169$	3.50000	−	6.06218i	0.269231	−	0.466321i
$170$	12.1962			0.935402
$171$			5.79555i			0.443197i
$172$	−1.80385			−0.137542
$173$	−7.26054	+	12.5756i	−0.552008	+	0.956107i	0.446121	+	0.894973i	$0.352805\pi$
$173$	−7.26054	+	12.5756i	−0.552008	+	0.956107i	−0.998130	+	0.0611340i	$0.980528\pi$
$174$	−0.328169	+	1.22474i	−0.0248785	+	0.0928477i
$175$		0			0
$176$	−2.73205	−	4.73205i	−0.205936	−	0.356692i
$177$	2.24167	−	8.36603i	0.168494	−	0.628829i
$178$	−6.64136	+	11.5032i	−0.497791	+	0.862200i
$179$	2.19615			0.164148			0.0820741	−	0.996626i	$-0.473846\pi$
$179$	2.19615			0.164148			0.0820741	+	0.996626i	$0.473846\pi$
$180$	−5.01910	−	2.89778i	−0.374101	−	0.215988i
$181$	8.72552			0.648563			0.324281	−	0.945961i	$-0.394878\pi$
$181$	8.72552			0.648563			0.324281	+	0.945961i	$0.394878\pi$
$182$		0			0
$183$	4.96410	−	1.33013i	0.366957	−	0.0983258i
$184$	−2.96410	−	5.13397i	−0.218516	−	0.378482i
$185$	7.72741	+	13.3843i	0.568130	+	0.984030i
$186$	9.00000	+	9.00000i	0.659912	+	0.659912i
$187$	17.2480	−	29.8744i	1.26130	−	2.18463i
$188$	9.52056			0.694358
$189$		0			0
$190$	−3.73205			−0.270751
$191$	−1.59808	+	2.76795i	−0.115633	+	0.200282i	−0.918033	−	0.396505i	$-0.870223\pi$
$191$	−1.59808	+	2.76795i	−0.115633	+	0.200282i	0.802400	+	0.596787i	$0.203556\pi$
$192$	−1.22474	−	1.22474i	−0.0883883	−	0.0883883i
$193$	10.1340	+	17.5526i	0.729459	+	1.26346i	0.957112	+	0.289718i	$0.0935617\pi$
$193$	10.1340	+	17.5526i	0.729459	+	1.26346i	−0.227652	+	0.973742i	$0.573105\pi$
$194$	−1.93185	−	3.34607i	−0.138699	−	0.240233i
$195$	−7.91688	+	2.12132i	−0.566939	+	0.151911i
$196$		0			0
$197$	−7.66025			−0.545771			−0.272885	−	0.962047i	$-0.587978\pi$
$197$	−7.66025			−0.545771			−0.272885	+	0.962047i	$0.587978\pi$
$198$	−14.1962	+	8.19615i	−1.00888	+	0.582475i
$199$	3.10583			0.220166			0.110083	−	0.993922i	$-0.464888\pi$
$199$	3.10583			0.220166			0.110083	+	0.993922i	$0.464888\pi$
$200$	−0.633975	+	1.09808i	−0.0448288	+	0.0776457i
$201$	6.36396	−	23.7506i	0.448879	−	1.67524i
$202$	0.776457	+	1.34486i	0.0546313	+	0.0946242i
$203$		0			0
$204$	2.83013	−	10.5622i	0.198149	−	0.739500i
$205$	5.46410	−	9.46410i	0.381629	−	0.661002i
$206$	8.38375			0.584123
$207$	−15.4019	+	8.89230i	−1.07051	+	0.618058i
$208$	−2.44949			−0.169842
$209$	−5.27792	+	9.14162i	−0.365081	+	0.632339i
$210$		0			0
$211$	−2.36603	−	4.09808i	−0.162884	−	0.282123i	0.773018	−	0.634384i	$-0.218746\pi$
$211$	−2.36603	−	4.09808i	−0.162884	−	0.282123i	−0.935902	+	0.352261i	$0.885413\pi$
$212$	−1.63397	−	2.83013i	−0.112222	−	0.194374i
$213$	13.7124	+	13.7124i	0.939560	+	0.939560i
$214$	8.46410	−	14.6603i	0.578594	−	1.00215i
$215$	−3.48477			−0.237659
$216$	−3.67423	+	3.67423i	−0.250000	+	0.250000i
$217$		0			0
$218$	−10.2942	+	17.8301i	−0.697213	+	1.20761i
$219$	11.6603	+	11.6603i	0.787927	+	0.787927i
$220$	−5.27792	−	9.14162i	−0.355837	−	0.616328i
$221$	−7.73205	−	13.3923i	−0.520114	−	0.900864i
$222$	13.3843	−	3.58630i	0.898293	−	0.240697i
$223$	−10.3664	+	17.9551i	−0.694183	+	1.20236i	0.276272	+	0.961079i	$0.410901\pi$
$223$	−10.3664	+	17.9551i	−0.694183	+	1.20236i	−0.970455	+	0.241281i	$0.922432\pi$
$224$		0			0
$225$	3.29423	+	1.90192i	0.219615	+	0.126795i
$226$	−2.66025			−0.176957
$227$	0.448288	−	0.776457i	0.0297539	−	0.0515353i	−0.850765	−	0.525546i	$-0.823861\pi$
$227$	0.448288	−	0.776457i	0.0297539	−	0.0515353i	0.880519	+	0.474011i	$0.157194\pi$
$228$	−0.866025	+	3.23205i	−0.0573539	+	0.214048i
$229$	−9.02150	−	15.6257i	−0.596158	−	1.03258i	−0.993382	−	0.114854i	$-0.963360\pi$
$229$	−9.02150	−	15.6257i	−0.596158	−	1.03258i	0.397225	−	0.917721i	$-0.369973\pi$
$230$	−5.72620	−	9.91808i	−0.377575	−	0.653979i
$231$		0			0
$232$	−0.366025	+	0.633975i	−0.0240307	+	0.0416225i
$233$	−19.3923			−1.27043			−0.635216	−	0.772334i	$-0.719089\pi$
$233$	−19.3923			−1.27043			−0.635216	+	0.772334i	$0.719089\pi$
$234$			7.34847i			0.480384i
$235$	18.3923			1.19978
$236$	2.50026	−	4.33057i	0.162753	−	0.281896i
$237$	−16.9384	+	4.53862i	−1.10027	+	0.294815i
$238$		0			0
$239$	2.76795	+	4.79423i	0.179044	+	0.310113i	0.941553	−	0.336864i	$-0.109366\pi$
$239$	2.76795	+	4.79423i	0.179044	+	0.310113i	−0.762510	+	0.646977i	$0.776033\pi$
$240$	−2.36603	−	2.36603i	−0.152726	−	0.152726i
$241$	6.36396	−	11.0227i	0.409939	−	0.710035i	−0.584944	−	0.811074i	$-0.698883\pi$
$241$	6.36396	−	11.0227i	0.409939	−	0.710035i	0.994882	+	0.101039i	$0.0322167\pi$
$242$	−18.8564			−1.21214
$243$	11.0227	+	11.0227i	0.707107	+	0.707107i
$244$	2.96713			0.189951
$245$		0			0
$246$	−6.92820	−	6.92820i	−0.441726	−	0.441726i
$247$	2.36603	+	4.09808i	0.150547	+	0.260754i
$248$	3.67423	+	6.36396i	0.233314	+	0.404112i
$249$	16.5622	−	4.43782i	1.04959	−	0.281236i
$250$	−6.05437	+	10.4865i	−0.382912	+	0.663223i
$251$	−1.93185			−0.121937			−0.0609687	−	0.998140i	$-0.519419\pi$
$251$	−1.93185			−0.121937			−0.0609687	+	0.998140i	$0.519419\pi$
$252$		0			0
$253$	−32.3923			−2.03649
$254$	3.96410	−	6.86603i	0.248730	−	0.430813i
$255$	5.46739	−	20.4046i	0.342381	−	1.27778i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−10.3664	−	17.9551i	−0.646636	−	1.12001i	−0.983921	−	0.178604i	$-0.942842\pi$
$257$	−10.3664	−	17.9551i	−0.646636	−	1.12001i	0.337285	−	0.941403i	$-0.390491\pi$
$258$	−0.808643	+	3.01790i	−0.0503439	+	0.187886i
$259$		0			0
$260$	−4.73205			−0.293469
$261$	1.90192	+	1.09808i	0.117726	+	0.0679692i
$262$	0.240237			0.0148419
$263$	7.33013	−	12.6962i	0.451995	−	0.782878i	−0.546515	−	0.837449i	$-0.684046\pi$
$263$	7.33013	−	12.6962i	0.451995	−	0.782878i	0.998510	+	0.0545711i	$0.0173792\pi$
$264$	−9.14162	+	2.44949i	−0.562628	+	0.150756i
$265$	−3.15660	−	5.46739i	−0.193908	−	0.335859i
$266$		0			0
$267$	16.2679	+	16.2679i	0.995582	+	0.995582i
$268$	7.09808	−	12.2942i	0.433584	−	0.750990i
$269$	0.0371647			0.00226597			0.00113299	−	0.999999i	$-0.499639\pi$
$269$	0.0371647			0.00226597			0.00113299	+	0.999999i	$0.499639\pi$
$270$	−7.09808	+	7.09808i	−0.431975	+	0.431975i
$271$	−5.00052			−0.303760			−0.151880	−	0.988399i	$-0.548533\pi$
$271$	−5.00052			−0.303760			−0.151880	+	0.988399i	$0.548533\pi$
$272$	3.15660	−	5.46739i	0.191397	−	0.331509i
$273$		0			0
$274$		0			0
$275$	3.46410	+	6.00000i	0.208893	+	0.361814i
$276$	−9.91808	+	2.65754i	−0.596998	+	0.159965i
$277$	2.90192	−	5.02628i	0.174360	−	0.302000i	−0.765580	−	0.643341i	$-0.777548\pi$
$277$	2.90192	−	5.02628i	0.174360	−	0.302000i	0.939940	+	0.341341i	$0.110881\pi$
$278$	1.83032			0.109775
$279$	19.0919	−	11.0227i	1.14300	−	0.659912i
$280$		0			0
$281$	−1.69615	+	2.93782i	−0.101184	+	0.175256i	−0.912173	−	0.409806i	$-0.865596\pi$
$281$	−1.69615	+	2.93782i	−0.101184	+	0.175256i	0.810989	+	0.585062i	$0.198930\pi$
$282$	4.26795	−	15.9282i	0.254153	−	0.948511i
$283$	8.55463	+	14.8171i	0.508520	+	0.880783i	0.999951	+	0.00986623i	$0.00314057\pi$
$283$	8.55463	+	14.8171i	0.508520	+	0.880783i	−0.491431	+	0.870916i	$0.663526\pi$
$284$	5.59808	+	9.69615i	0.332185	+	0.575361i
$285$	−1.67303	+	6.24384i	−0.0991019	+	0.369853i
$286$	−6.69213	+	11.5911i	−0.395714	+	0.685397i
$287$		0			0
$288$	−2.59808	+	1.50000i	−0.153093	+	0.0883883i
$289$	22.8564			1.34449
$290$	−0.707107	+	1.22474i	−0.0415227	+	0.0719195i
$291$	−6.46410	+	1.73205i	−0.378932	+	0.101535i
$292$	4.76028	+	8.24504i	0.278574	+	0.482505i
$293$	2.19067	+	3.79435i	0.127980	+	0.221668i	0.922894	−	0.385054i	$-0.125817\pi$
$293$	2.19067	+	3.79435i	0.127980	+	0.221668i	−0.794914	+	0.606723i	$0.792484\pi$
$294$		0			0
$295$	4.83013	−	8.36603i	0.281221	−	0.487089i
$296$	8.00000			0.464991
$297$	7.34847	+	27.4249i	0.426401	+	1.59135i
$298$	−18.3923			−1.06544
$299$	−7.26054	+	12.5756i	−0.419888	+	0.727267i
$300$	1.55291	+	1.55291i	0.0896575	+	0.0896575i
$301$		0			0
$302$	1.69615	+	2.93782i	0.0976026	+	0.169053i
$303$	2.59808	−	0.696152i	0.149256	−	0.0399929i
$304$	−0.965926	+	1.67303i	−0.0553996	+	0.0959550i
$305$	5.73205			0.328216
$306$	−16.4022	−	9.46979i	−0.937649	−	0.541352i
$307$	29.0793			1.65964			0.829822	−	0.558028i	$-0.188442\pi$
$307$	29.0793			1.65964			0.829822	+	0.558028i	$0.188442\pi$
$308$		0			0
$309$	3.75833	−	14.0263i	0.213804	−	0.797927i
$310$	7.09808	+	12.2942i	0.403144	+	0.698265i
$311$	−10.5051	−	18.1953i	−0.595688	−	1.03176i	−0.993449	−	0.114273i	$-0.963546\pi$
$311$	−10.5051	−	18.1953i	−0.595688	−	1.03176i	0.397762	−	0.917489i	$-0.369787\pi$
$312$	−1.09808	+	4.09808i	−0.0621663	+	0.232008i
$313$	−0.896575	+	1.55291i	−0.0506774	+	0.0877759i	−0.890251	−	0.455470i	$-0.849471\pi$
$313$	−0.896575	+	1.55291i	−0.0506774	+	0.0877759i	0.839574	+	0.543245i	$0.182805\pi$
$314$	24.3562			1.37450
$315$		0			0
$316$	−10.1244			−0.569540
$317$	−0.705771	+	1.22243i	−0.0396401	+	0.0686586i	−0.885165	−	0.465278i	$-0.845954\pi$
$317$	−0.705771	+	1.22243i	−0.0396401	+	0.0686586i	0.845525	+	0.533936i	$0.179288\pi$
$318$	−5.46739	+	1.46498i	−0.306596	+	0.0821521i
$319$	2.00000	+	3.46410i	0.111979	+	0.193952i
$320$	−0.965926	−	1.67303i	−0.0539969	−	0.0935254i
$321$	−20.7327	−	20.7327i	−1.15719	−	1.15719i
$322$		0			0
$323$	−12.1962			−0.678612
$324$	4.50000	+	7.79423i	0.250000	+	0.433013i
$325$	3.10583			0.172280
$326$	−10.4641	+	18.1244i	−0.579553	+	1.00382i
$327$	25.2156	+	25.2156i	1.39443	+	1.39443i
$328$	−2.82843	−	4.89898i	−0.156174	−	0.270501i
$329$		0			0
$330$	−17.6603	+	4.73205i	−0.972165	+	0.260491i
$331$	−13.0263	+	22.5622i	−0.715989	+	1.24013i	0.246588	+	0.969120i	$0.420691\pi$
$331$	−13.0263	+	22.5622i	−0.715989	+	1.24013i	−0.962577	+	0.271009i	$0.912643\pi$
$332$	9.89949			0.543305
$333$		−	24.0000i		−	1.31519i
$334$	−16.1112			−0.881563
$335$	13.7124	−	23.7506i	0.749190	−	1.29764i
$336$		0			0
$337$	−6.66025	−	11.5359i	−0.362807	−	0.628400i	0.625615	−	0.780132i	$-0.284848\pi$
$337$	−6.66025	−	11.5359i	−0.362807	−	0.628400i	−0.988422	+	0.151732i	$0.951515\pi$
$338$	−3.50000	−	6.06218i	−0.190375	−	0.329739i
$339$	−1.19256	+	4.45069i	−0.0647709	+	0.241728i
$340$	6.09808	−	10.5622i	0.330715	−	0.572815i
$341$	40.1528			2.17440
$342$	5.01910	+	2.89778i	0.271402	+	0.156694i
$343$		0			0
$344$	−0.901924	+	1.56218i	−0.0486285	+	0.0842270i
$345$	−19.1603	+	5.13397i	−1.03155	+	0.276404i
$346$	7.26054	+	12.5756i	0.390329	+	0.676069i
$347$	16.8564	+	29.1962i	0.904899	+	1.56733i	0.821052	+	0.570853i	$0.193387\pi$
$347$	16.8564	+	29.1962i	0.904899	+	1.56733i	0.0838470	+	0.996479i	$0.473279\pi$
$348$	0.896575	+	0.896575i	0.0480615	+	0.0480615i
$349$	−12.3998	+	21.4770i	−0.663744	+	1.14964i	0.315881	+	0.948799i	$0.397700\pi$
$349$	−12.3998	+	21.4770i	−0.663744	+	1.14964i	−0.979624	+	0.200839i	$0.935633\pi$
$350$		0			0
$351$	12.2942	+	3.29423i	0.656217	+	0.175833i
$352$	−5.46410			−0.291238
$353$	9.84873	−	17.0585i	0.524195	−	0.907932i	−0.475408	−	0.879765i	$-0.657700\pi$
$353$	9.84873	−	17.0585i	0.524195	−	0.907932i	0.999603	−	0.0281669i	$-0.00896698\pi$
$354$	−6.12436	−	6.12436i	−0.325506	−	0.325506i
$355$	10.8147	+	18.7315i	0.573982	+	0.994166i
$356$	6.64136	+	11.5032i	0.351992	+	0.609667i
$357$		0			0
$358$	1.09808	−	1.90192i	0.0580351	−	0.100520i
$359$	−0.0717968			−0.00378929			−0.00189464	−	0.999998i	$-0.500603\pi$
$359$	−0.0717968			−0.00378929			−0.00189464	+	0.999998i	$0.500603\pi$
$360$	−5.01910	+	2.89778i	−0.264530	+	0.152726i
$361$	−15.2679			−0.803576
$362$	4.36276	−	7.55652i	0.229302	−	0.397162i
$363$	−8.45310	+	31.5474i	−0.443672	+	1.65581i
$364$		0			0
$365$	9.19615	+	15.9282i	0.481349	+	0.833720i
$366$	1.33013	−	4.96410i	0.0695269	−	0.259478i
$367$	7.20977	−	12.4877i	0.376347	−	0.651852i	−0.614181	−	0.789165i	$-0.710513\pi$
$367$	7.20977	−	12.4877i	0.376347	−	0.651852i	0.990528	+	0.137313i	$0.0438468\pi$
$368$	−5.92820			−0.309029
$369$	−14.6969	+	8.48528i	−0.765092	+	0.441726i
$370$	15.4548			0.803457
$371$		0			0
$372$	12.2942	−	3.29423i	0.637426	−	0.170798i
$373$	2.56218	+	4.43782i	0.132665	+	0.229782i	0.924703	−	0.380690i	$-0.124313\pi$
$373$	2.56218	+	4.43782i	0.132665	+	0.229782i	−0.792038	+	0.610471i	$0.790980\pi$
$374$	−17.2480	−	29.8744i	−0.891871	−	1.54477i
$375$	14.8301	+	14.8301i	0.765824	+	0.765824i
$376$	4.76028	−	8.24504i	0.245493	−	0.425206i
$377$	1.79315			0.0923520
$378$		0			0
$379$	17.5167			0.899770			0.449885	−	0.893086i	$-0.351465\pi$
$379$	17.5167			0.899770			0.449885	+	0.893086i	$0.351465\pi$
$380$	−1.86603	+	3.23205i	−0.0957251	+	0.165801i
$381$	−9.71003	−	9.71003i	−0.497460	−	0.497460i
$382$	1.59808	+	2.76795i	0.0817647	+	0.141621i
$383$	−9.76079	−	16.9062i	−0.498753	−	0.863866i	0.501246	−	0.865305i	$-0.332875\pi$
$383$	−9.76079	−	16.9062i	−0.498753	−	0.863866i	−0.999999	+	0.00143898i	$0.999542\pi$
$384$	−1.67303	+	0.448288i	−0.0853766	+	0.0228766i
$385$		0			0
$386$	20.2679			1.03161
$387$	4.68653	+	2.70577i	0.238230	+	0.137542i
$388$	−3.86370			−0.196150
$389$	14.5622	−	25.2224i	0.738332	−	1.27883i	−0.214914	−	0.976633i	$-0.568947\pi$
$389$	14.5622	−	25.2224i	0.738332	−	1.27883i	0.953246	−	0.302195i	$-0.0977194\pi$
$390$	−2.12132	+	7.91688i	−0.107417	+	0.400887i
$391$	−18.7129	−	32.4118i	−0.946354	−	1.63913i
$392$		0			0
$393$	0.107695	−	0.401924i	0.00543250	−	0.0202744i
$394$	−3.83013	+	6.63397i	−0.192959	+	0.334215i
$395$	−19.5588			−0.984108
$396$			16.3923i			0.823744i
$397$	−1.89469			−0.0950916			−0.0475458	−	0.998869i	$-0.515140\pi$
$397$	−1.89469			−0.0950916			−0.0475458	+	0.998869i	$0.515140\pi$
$398$	1.55291	−	2.68973i	0.0778406	−	0.134824i
$399$		0			0
$400$	0.633975	+	1.09808i	0.0316987	+	0.0549038i
$401$	−6.52628	−	11.3038i	−0.325907	−	0.564487i	0.655789	−	0.754945i	$-0.272336\pi$
$401$	−6.52628	−	11.3038i	−0.325907	−	0.564487i	−0.981695	+	0.190457i	$0.939003\pi$
$402$	−17.3867	−	17.3867i	−0.867168	−	0.867168i
$403$	9.00000	−	15.5885i	0.448322	−	0.776516i
$404$	1.55291			0.0772604
$405$	8.69333	+	15.0573i	0.431975	+	0.748203i
$406$		0			0
$407$	21.8564	−	37.8564i	1.08338	−	1.87647i
$408$	−7.73205	−	7.73205i	−0.382794	−	0.382794i
$409$	−13.1440	−	22.7661i	−0.649930	−	1.12571i	−0.983139	−	0.182859i	$-0.941465\pi$
$409$	−13.1440	−	22.7661i	−0.649930	−	1.12571i	0.333209	−	0.942853i	$-0.391869\pi$
$410$	−5.46410	−	9.46410i	−0.269853	−	0.467399i
$411$		0			0
$412$	4.19187	−	7.26054i	0.206519	−	0.357701i
$413$		0			0
$414$			17.7846i			0.874066i
$415$	19.1244			0.938778
$416$	−1.22474	+	2.12132i	−0.0600481	+	0.104006i
$417$	0.820508	−	3.06218i	0.0401805	−	0.149955i
$418$	5.27792	+	9.14162i	0.258151	+	0.447131i
$419$	2.13990	+	3.70642i	0.104541	+	0.181070i	0.913551	−	0.406725i	$-0.133329\pi$
$419$	2.13990	+	3.70642i	0.104541	+	0.181070i	−0.809010	+	0.587796i	$0.799996\pi$
$420$		0			0
$421$	5.02628	−	8.70577i	0.244966	−	0.424293i	−0.717156	−	0.696913i	$-0.754557\pi$
$421$	5.02628	−	8.70577i	0.244966	−	0.424293i	0.962122	+	0.272619i	$0.0878899\pi$
$422$	−4.73205			−0.230353
$423$	−24.7351	−	14.2808i	−1.20266	−	0.694358i
$424$	−3.26795			−0.158706
$425$	−4.00240	+	6.93237i	−0.194145	+	0.336269i
$426$	18.7315	−	5.01910i	0.907546	−	0.243176i
$427$		0			0
$428$	−8.46410	−	14.6603i	−0.409128	−	0.708630i
$429$	16.3923	+	16.3923i	0.791428	+	0.791428i
$430$	−1.74238	+	3.01790i	−0.0840252	+	0.145536i
$431$	14.7846			0.712150			0.356075	−	0.934457i	$-0.384115\pi$
$431$	14.7846			0.712150			0.356075	+	0.934457i	$0.384115\pi$
$432$	1.34486	+	5.01910i	0.0647048	+	0.241481i
$433$	−28.7375			−1.38104			−0.690519	−	0.723314i	$-0.742618\pi$
$433$	−28.7375			−1.38104			−0.690519	+	0.723314i	$0.742618\pi$
$434$		0			0
$435$	1.73205	+	1.73205i	0.0830455	+	0.0830455i
$436$	10.2942	+	17.8301i	0.493004	+	0.853908i
$437$	5.72620	+	9.91808i	0.273922	+	0.474446i
$438$	15.9282	−	4.26795i	0.761079	−	0.203931i
$439$	−0.656339	+	1.13681i	−0.0313253	+	0.0542571i	−0.881263	−	0.472626i	$-0.843306\pi$
$439$	−0.656339	+	1.13681i	−0.0313253	+	0.0542571i	0.849938	+	0.526883i	$0.176639\pi$
$440$	−10.5558			−0.503230
$441$		0			0
$442$	−15.4641			−0.735552
$443$	−7.49038	+	12.9737i	−0.355879	+	0.616400i	−0.987268	−	0.159066i	$-0.949152\pi$
$443$	−7.49038	+	12.9737i	−0.355879	+	0.616400i	0.631389	+	0.775466i	$0.282485\pi$
$444$	3.58630	−	13.3843i	0.170198	−	0.635189i
$445$	12.8301	+	22.2224i	0.608206	+	1.05344i
$446$	10.3664	+	17.9551i	0.490862	+	0.850197i
$447$	−8.24504	+	30.7709i	−0.389977	+	1.45541i
$448$		0			0
$449$	17.7846			0.839308			0.419654	−	0.907684i	$-0.362151\pi$
$449$	17.7846			0.839308			0.419654	+	0.907684i	$0.362151\pi$
$450$	3.29423	−	1.90192i	0.155291	−	0.0896575i
$451$	−30.9096			−1.45548
$452$	−1.33013	+	2.30385i	−0.0625639	+	0.108364i
$453$	5.67544	−	1.52073i	0.266655	−	0.0714501i
$454$	−0.448288	−	0.776457i	−0.0210392	−	0.0364409i
$455$		0			0
$456$	2.36603	+	2.36603i	0.110799	+	0.110799i
$457$	12.8660	−	22.2846i	0.601847	−	1.04243i	−0.390694	−	0.920521i	$-0.627765\pi$
$457$	12.8660	−	22.2846i	0.601847	−	1.04243i	0.992541	−	0.121909i	$-0.0389017\pi$
$458$	−18.0430			−0.843094
$459$	−23.1962	+	23.1962i	−1.08270	+	1.08270i
$460$	−11.4524			−0.533971
$461$	10.9162	−	18.9074i	0.508418	−	0.880605i	−0.491535	−	0.870858i	$-0.663564\pi$
$461$	10.9162	−	18.9074i	0.508418	−	0.880605i	0.999952	−	0.00974723i	$-0.00310269\pi$
$462$		0			0
$463$	5.33013	+	9.23205i	0.247712	+	0.429050i	0.962891	−	0.269892i	$-0.0869880\pi$
$463$	5.33013	+	9.23205i	0.247712	+	0.429050i	−0.715179	+	0.698942i	$0.753655\pi$
$464$	0.366025	+	0.633975i	0.0169923	+	0.0294315i
$465$	23.7506	−	6.36396i	1.10141	−	0.295122i
$466$	−9.69615	+	16.7942i	−0.449166	+	0.777978i
$467$	4.79744			0.221999			0.111000	−	0.993820i	$-0.464595\pi$
$467$	4.79744			0.221999			0.111000	+	0.993820i	$0.464595\pi$
$468$	6.36396	+	3.67423i	0.294174	+	0.169842i
$469$		0			0
$470$	9.19615	−	15.9282i	0.424187	−	0.734713i
$471$	10.9186	−	40.7487i	0.503102	−	1.87760i
$472$	−2.50026	−	4.33057i	−0.115084	−	0.199331i
$473$	4.92820	+	8.53590i	0.226599	+	0.392481i
$474$	−4.53862	+	16.9384i	−0.208466	+	0.778005i
$475$	1.22474	−	2.12132i	0.0561951	−	0.0973329i
$476$		0			0
$477$			9.80385i			0.448887i
$478$	5.53590			0.253206
$479$	8.05558	−	13.9527i	0.368069	−	0.637514i	−0.621195	−	0.783656i	$-0.713352\pi$
$479$	8.05558	−	13.9527i	0.368069	−	0.637514i	0.989264	+	0.146142i	$0.0466858\pi$
$480$	−3.23205	+	0.866025i	−0.147522	+	0.0395285i
$481$	−9.79796	−	16.9706i	−0.446748	−	0.773791i
$482$	−6.36396	−	11.0227i	−0.289870	−	0.502070i
$483$		0			0
$484$	−9.42820	+	16.3301i	−0.428555	+	0.742279i
$485$	−7.46410			−0.338927
$486$	15.0573	−	4.03459i	0.683013	−	0.183013i
$487$	2.32051			0.105152			0.0525761	−	0.998617i	$-0.483257\pi$
$487$	2.32051			0.105152			0.0525761	+	0.998617i	$0.483257\pi$
$488$	1.48356	−	2.56961i	0.0671578	−	0.116321i
$489$	25.6317	+	25.6317i	1.15911	+	1.15911i
$490$		0			0
$491$	9.46410	+	16.3923i	0.427109	+	0.739774i	0.996615	−	0.0822129i	$-0.0261988\pi$
$491$	9.46410	+	16.3923i	0.427109	+	0.739774i	−0.569506	+	0.821987i	$0.692865\pi$
$492$	−9.46410	+	2.53590i	−0.426675	+	0.114327i
$493$	−2.31079	+	4.00240i	−0.104073	+	0.180259i
$494$	4.73205			0.212905
$495$			31.6675i			1.42335i
$496$	7.34847			0.329956
$497$		0			0
$498$	4.43782	−	16.5622i	0.198864	−	0.742169i
$499$	13.6603	+	23.6603i	0.611517	+	1.05918i	0.990985	+	0.133974i	$0.0427737\pi$
$499$	13.6603	+	23.6603i	0.611517	+	1.05918i	−0.379468	+	0.925205i	$0.623893\pi$
$500$	6.05437	+	10.4865i	0.270760	+	0.468970i
$501$	−7.22243	+	26.9545i	−0.322674	+	1.20424i
$502$	−0.965926	+	1.67303i	−0.0431114	+	0.0746711i
$503$	−19.1427			−0.853529			−0.426764	−	0.904363i	$-0.640347\pi$
$503$	−19.1427			−0.853529			−0.426764	+	0.904363i	$0.640347\pi$
$504$		0			0
$505$	3.00000			0.133498
$506$	−16.1962	+	28.0526i	−0.720007	+	1.24709i
$507$	−11.7112	+	3.13801i	−0.520114	+	0.139364i
$508$	−3.96410	−	6.86603i	−0.175879	−	0.304631i
$509$	10.8840	+	18.8516i	0.482425	+	0.835585i	0.999796	−	0.0201764i	$-0.00642278\pi$
$509$	10.8840	+	18.8516i	0.482425	+	0.835585i	−0.517371	+	0.855761i	$0.673089\pi$
$510$	−14.9372	−	14.9372i	−0.661429	−	0.661429i
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	7.09808	−	7.09808i	0.313388	−	0.313388i
$514$	−20.7327			−0.914482
$515$	8.09808	−	14.0263i	0.356844	−	0.618072i
$516$	2.20925	+	2.20925i	0.0972569	+	0.0972569i
$517$	−26.0106	−	45.0518i	−1.14395	−	1.98137i
$518$		0			0
$519$	24.2942	−	6.50962i	1.06640	−	0.285741i
$520$	−2.36603	+	4.09808i	−0.103757	+	0.179713i
$521$	32.5269			1.42503			0.712515	−	0.701657i	$-0.247556\pi$
$521$	32.5269			1.42503			0.712515	+	0.701657i	$0.247556\pi$
$522$	1.90192	−	1.09808i	0.0832449	−	0.0480615i
$523$	−7.41284			−0.324141			−0.162070	−	0.986779i	$-0.551817\pi$
$523$	−7.41284			−0.324141			−0.162070	+	0.986779i	$0.551817\pi$
$524$	0.120118	−	0.208051i	0.00524739	−	0.00908875i
$525$		0			0
$526$	−7.33013	−	12.6962i	−0.319609	−	0.553579i
$527$	23.1962	+	40.1769i	1.01044	+	1.75013i
$528$	−2.44949	+	9.14162i	−0.106600	+	0.397838i
$529$	−6.07180	+	10.5167i	−0.263991	+	0.457246i
$530$	−6.31319			−0.274228
$531$	−12.9917	+	7.50077i	−0.563793	+	0.325506i
$532$		0			0
$533$	−6.92820	+	12.0000i	−0.300094	+	0.519778i
$534$	22.2224	−	5.95448i	0.961659	−	0.257676i
$535$	−16.3514	−	28.3214i	−0.706932	−	1.22444i
$536$	−7.09808	−	12.2942i	−0.306590	−	0.531030i
$537$	−2.68973	−	2.68973i	−0.116070	−	0.116070i
$538$	0.0185824	−	0.0321856i	0.000801143	−	0.00138762i
$539$		0			0
$540$	2.59808	+	9.69615i	0.111803	+	0.417256i
$541$	17.2679			0.742407			0.371204	−	0.928552i	$-0.378945\pi$
$541$	17.2679			0.742407			0.371204	+	0.928552i	$0.378945\pi$
$542$	−2.50026	+	4.33057i	−0.107395	+	0.186014i
$543$	−10.6865	−	10.6865i	−0.458603	−	0.458603i
$544$	−3.15660	−	5.46739i	−0.135338	−	0.234412i
$545$	19.8869	+	34.4452i	0.851862	+	1.47547i
$546$		0			0
$547$	2.26795	−	3.92820i	0.0969705	−	0.167958i	−0.813459	−	0.581623i	$-0.802418\pi$
$547$	2.26795	−	3.92820i	0.0969705	−	0.167958i	0.910429	+	0.413665i	$0.135751\pi$
$548$		0			0
$549$	−7.70882	−	4.45069i	−0.329005	−	0.189951i
$550$	6.92820			0.295420
$551$	0.707107	−	1.22474i	0.0301238	−	0.0521759i
$552$	−2.65754	+	9.91808i	−0.113112	+	0.422141i
$553$		0			0
$554$	−2.90192	−	5.02628i	−0.123291	−	0.213546i
$555$	6.92820	−	25.8564i	0.294086	−	1.09754i
$556$	0.915158	−	1.58510i	0.0388113	−	0.0672232i
$557$	27.1244			1.14930			0.574648	−	0.818401i	$-0.305139\pi$
$557$	27.1244			1.14930			0.574648	+	0.818401i	$0.305139\pi$
$558$		−	22.0454i		−	0.933257i
$559$	4.41851			0.186883
$560$		0			0
$561$	−57.7128	+	15.4641i	−2.43664	+	0.652895i
$562$	1.69615	+	2.93782i	0.0715479	+	0.123925i
$563$	−4.31199	−	7.46859i	−0.181729	−	0.314763i	0.760741	−	0.649056i	$-0.224836\pi$
$563$	−4.31199	−	7.46859i	−0.181729	−	0.314763i	−0.942469	+	0.334293i	$0.891503\pi$
$564$	−11.6603	−	11.6603i	−0.490985	−	0.490985i
$565$	−2.56961	+	4.45069i	−0.108104	+	0.187242i
$566$	17.1093			0.719156
$567$		0			0
$568$	11.1962			0.469780
$569$	−6.53590	+	11.3205i	−0.273999	+	0.474580i	−0.969882	−	0.243575i	$-0.921680\pi$
$569$	−6.53590	+	11.3205i	−0.273999	+	0.474580i	0.695883	+	0.718155i	$0.255013\pi$
$570$	4.57081	+	4.57081i	0.191450	+	0.191450i
$571$	−2.00000	−	3.46410i	−0.0836974	−	0.144968i	0.821138	−	0.570730i	$-0.193340\pi$
$571$	−2.00000	−	3.46410i	−0.0836974	−	0.144968i	−0.904835	+	0.425762i	$0.860006\pi$
$572$	6.69213	+	11.5911i	0.279812	+	0.484649i
$573$	5.34727	−	1.43280i	0.223385	−	0.0598559i
$574$		0			0
$575$	7.51666			0.313466
$576$			3.00000i			0.125000i
$577$	17.8028			0.741139			0.370569	−	0.928805i	$-0.379163\pi$
$577$	17.8028			0.741139			0.370569	+	0.928805i	$0.379163\pi$
$578$	11.4282	−	19.7942i	0.475351	−	0.823331i
$579$	9.08587	−	33.9089i	0.377596	−	1.40921i
$580$	0.707107	+	1.22474i	0.0293610	+	0.0508548i
$581$		0			0
$582$	−1.73205	+	6.46410i	−0.0717958	+	0.267946i
$583$	−8.92820	+	15.4641i	−0.369768	+	0.640458i
$584$	9.52056			0.393963
$585$	12.2942	+	7.09808i	0.508304	+	0.293469i
$586$	4.38134			0.180992
$587$	−16.6102	+	28.7697i	−0.685577	+	1.18745i	0.287679	+	0.957727i	$0.407117\pi$
$587$	−16.6102	+	28.7697i	−0.685577	+	1.18745i	−0.973255	+	0.229727i	$0.926217\pi$
$588$		0			0
$589$	−7.09808	−	12.2942i	−0.292471	−	0.506575i
$590$	−4.83013	−	8.36603i	−0.198853	−	0.344424i
$591$	9.38186	+	9.38186i	0.385918	+	0.385918i
$592$	4.00000	−	6.92820i	0.164399	−	0.284747i
$593$	21.4906			0.882513			0.441257	−	0.897381i	$-0.354533\pi$
$593$	21.4906			0.882513			0.441257	+	0.897381i	$0.354533\pi$
$594$	27.4249	+	7.34847i	1.12526	+	0.301511i
$595$		0			0
$596$	−9.19615	+	15.9282i	−0.376689	+	0.652445i
$597$	−3.80385	−	3.80385i	−0.155681	−	0.155681i
$598$	7.26054	+	12.5756i	0.296905	+	0.514255i
$599$	−4.19615	−	7.26795i	−0.171450	−	0.296960i	0.767477	−	0.641077i	$-0.221512\pi$
$599$	−4.19615	−	7.26795i	−0.171450	−	0.296960i	−0.938927	+	0.344116i	$0.888179\pi$
$600$	2.12132	−	0.568406i	0.0866025	−	0.0232051i
$601$	−8.72552	+	15.1130i	−0.355921	+	0.616474i	−0.987275	−	0.159021i	$-0.949166\pi$
$601$	−8.72552	+	15.1130i	−0.355921	+	0.616474i	0.631354	+	0.775495i	$0.282500\pi$
$602$		0			0
$603$	−36.8827	+	21.2942i	−1.50198	+	0.867168i
$604$	3.39230			0.138031
$605$	−18.2139	+	31.5474i	−0.740500	+	1.28258i
$606$	0.696152	−	2.59808i	0.0282793	−	0.105540i
$607$	6.45189	+	11.1750i	0.261874	+	0.453580i	0.966740	−	0.255761i	$-0.0823261\pi$
$607$	6.45189	+	11.1750i	0.261874	+	0.453580i	−0.704866	+	0.709341i	$0.748993\pi$
$608$	0.965926	+	1.67303i	0.0391735	+	0.0678504i
$609$		0			0
$610$	2.86603	−	4.96410i	0.116042	−	0.200991i
$611$	−23.3205			−0.943447
$612$	−16.4022	+	9.46979i	−0.663018	+	0.382794i
$613$	−38.4449			−1.55277			−0.776387	−	0.630257i	$-0.782950\pi$
$613$	−38.4449			−1.55277			−0.776387	+	0.630257i	$0.782950\pi$
$614$	14.5397	−	25.1834i	0.586773	−	1.01632i
$615$	−18.2832	+	4.89898i	−0.737251	+	0.197546i
$616$		0			0
$617$	−10.8038	−	18.7128i	−0.434947	−	0.753349i	0.562345	−	0.826903i	$-0.309899\pi$
$617$	−10.8038	−	18.7128i	−0.434947	−	0.753349i	−0.997291	+	0.0735534i	$0.976566\pi$
$618$	−10.2679	−	10.2679i	−0.413037	−	0.413037i
$619$	7.27912	−	12.6078i	0.292572	−	0.506750i	−0.681845	−	0.731497i	$-0.738822\pi$
$619$	7.27912	−	12.6078i	0.292572	−	0.506750i	0.974417	+	0.224746i	$0.0721554\pi$
$620$	14.1962			0.570131
$621$	29.7542	+	7.97262i	1.19400	+	0.319930i
$622$	−21.0101			−0.842430
$623$		0			0
$624$	3.00000	+	3.00000i	0.120096	+	0.120096i
$625$	8.52628	+	14.7679i	0.341051	+	0.590718i
$626$	0.896575	+	1.55291i	0.0358344	+	0.0620669i
$627$	17.6603	−	4.73205i	0.705283	−	0.188980i
$628$	12.1781	−	21.0931i	0.485959	−	0.841706i
$629$	50.5055			2.01379
$630$		0			0
$631$	−28.1244			−1.11961			−0.559806	−	0.828623i	$-0.689125\pi$
$631$	−28.1244			−1.11961			−0.559806	+	0.828623i	$0.689125\pi$
$632$	−5.06218	+	8.76795i	−0.201363	+	0.348770i
$633$	−2.12132	+	7.91688i	−0.0843149	+	0.314668i
$634$	0.705771	+	1.22243i	0.0280298	+	0.0485490i
$635$	−7.65806	−	13.2641i	−0.303901	−	0.526371i
$636$	−1.46498	+	5.46739i	−0.0580903	+	0.216796i
$637$		0			0
$638$	4.00000			0.158362
$639$		−	33.5885i		−	1.32874i
$640$	−1.93185			−0.0763631
$641$	−17.5263	+	30.3564i	−0.692246	+	1.19901i	0.278854	+	0.960334i	$0.410046\pi$
$641$	−17.5263	+	30.3564i	−0.692246	+	1.19901i	−0.971100	+	0.238672i	$0.923288\pi$
$642$	−28.3214	+	7.58871i	−1.11776	+	0.299502i
$643$	6.50266	+	11.2629i	0.256440	+	0.444167i	0.965286	−	0.261197i	$-0.0841171\pi$
$643$	6.50266	+	11.2629i	0.256440	+	0.444167i	−0.708846	+	0.705364i	$0.750784\pi$
$644$		0			0
$645$	4.26795	+	4.26795i	0.168050	+	0.168050i
$646$	−6.09808	+	10.5622i	−0.239926	+	0.415563i
$647$	1.13681			0.0446927			0.0223463	−	0.999750i	$-0.492886\pi$
$647$	1.13681			0.0446927			0.0223463	+	0.999750i	$0.492886\pi$
$648$	9.00000			0.353553
$649$	−27.3233			−1.07253
$650$	1.55291	−	2.68973i	0.0609103	−	0.105500i
$651$		0			0
$652$	10.4641	+	18.1244i	0.409806	+	0.709805i
$653$	3.33975	+	5.78461i	0.130694	+	0.226369i	0.923944	−	0.382527i	$-0.124946\pi$
$653$	3.33975	+	5.78461i	0.130694	+	0.226369i	−0.793250	+	0.608896i	$0.791613\pi$
$654$	34.4452	−	9.22955i	1.34691	−	0.360904i
$655$	0.232051	−	0.401924i	0.00906698	−	0.0157045i
$656$	−5.65685			−0.220863
$657$		−	28.5617i		−	1.11430i
$658$		0			0
$659$	7.43782	−	12.8827i	0.289736	−	0.501838i	−0.684010	−	0.729472i	$-0.739766\pi$
$659$	7.43782	−	12.8827i	0.289736	−	0.501838i	0.973747	+	0.227634i	$0.0730990\pi$
$660$	−4.73205	+	17.6603i	−0.184195	+	0.687424i
$661$	16.8504	+	29.1858i	0.655406	+	1.13520i	0.981792	+	0.189960i	$0.0608359\pi$
$661$	16.8504	+	29.1858i	0.655406	+	1.13520i	−0.326385	+	0.945237i	$0.605831\pi$
$662$	13.0263	+	22.5622i	0.506281	+	0.876904i
$663$	−6.93237	+	25.8719i	−0.269231	+	1.00478i
$664$	4.94975	−	8.57321i	0.192087	−	0.332705i
$665$		0			0
$666$	−20.7846	−	12.0000i	−0.805387	−	0.464991i
$667$	4.33975			0.168036
$668$	−8.05558	+	13.9527i	−0.311680	+	0.539845i
$669$	34.6865	−	9.29423i	1.34106	−	0.359336i
$670$	−13.7124	−	23.7506i	−0.529757	−	0.917567i
$671$	−8.10634	−	14.0406i	−0.312942	−	0.542031i
$672$		0			0
$673$	−11.0885	+	19.2058i	−0.427429	+	0.740328i	−0.996644	−	0.0818605i	$-0.973914\pi$
$673$	−11.0885	+	19.2058i	−0.427429	+	0.740328i	0.569215	+	0.822189i	$0.307247\pi$
$674$	−13.3205			−0.513087
$675$	−1.70522	−	6.36396i	−0.0656339	−	0.244949i
$676$	−7.00000			−0.269231
$677$	7.91688	−	13.7124i	0.304270	−	0.527012i	−0.672828	−	0.739799i	$-0.734921\pi$
$677$	7.91688	−	13.7124i	0.304270	−	0.527012i	0.977099	+	0.212787i	$0.0682541\pi$
$678$	3.25813	+	3.25813i	0.125128	+	0.125128i
$679$		0			0
$680$	−6.09808	−	10.5622i	−0.233851	−	0.405041i
$681$	−1.50000	+	0.401924i	−0.0574801	+	0.0154018i
$682$	20.0764	−	34.7733i	0.768765	−	1.33154i
$683$	−34.3923			−1.31598			−0.657992	−	0.753024i	$-0.728594\pi$
$683$	−34.3923			−1.31598			−0.657992	+	0.753024i	$0.728594\pi$
$684$	5.01910	−	2.89778i	0.191910	−	0.110799i
$685$		0			0
$686$		0			0
$687$	−8.08846	+	30.1865i	−0.308594	+	1.15169i
$688$	0.901924	+	1.56218i	0.0343855	+	0.0595575i
$689$	4.00240	+	6.93237i	0.152479	+	0.264102i
$690$	−5.13397	+	19.1603i	−0.195447	+	0.729418i
$691$	12.1273	−	21.0052i	0.461345	−	0.799074i	−0.537683	−	0.843147i	$-0.680700\pi$
$691$	12.1273	−	21.0052i	0.461345	−	0.799074i	0.999028	+	0.0440735i	$0.0140336\pi$
$692$	14.5211			0.552008
$693$		0			0
$694$	33.7128			1.27972
$695$	1.76795	−	3.06218i	0.0670621	−	0.116155i
$696$	1.22474	−	0.328169i	0.0464238	−	0.0124392i
$697$	−17.8564	−	30.9282i	−0.676360	−	1.17149i
$698$	12.3998	+	21.4770i	0.469338	+	0.812916i
$699$	23.7506	+	23.7506i	0.898331	+	0.898331i
$700$		0			0
$701$	27.4641			1.03730			0.518652	−	0.854985i	$-0.326434\pi$
$701$	27.4641			1.03730			0.518652	+	0.854985i	$0.326434\pi$
$702$	9.00000	−	9.00000i	0.339683	−	0.339683i
$703$	−15.4548			−0.582889
$704$	−2.73205	+	4.73205i	−0.102968	+	0.178346i
$705$	−22.5259	−	22.5259i	−0.848374	−	0.848374i
$706$	−9.84873	−	17.0585i	−0.370662	−	0.642005i
$707$		0			0
$708$	−8.36603	+	2.24167i	−0.314414	+	0.0842471i
$709$	14.7321	−	25.5167i	0.553274	−	0.958298i	−0.444762	−	0.895649i	$-0.646712\pi$
$709$	14.7321	−	25.5167i	0.553274	−	0.958298i	0.998036	−	0.0626494i	$-0.0199550\pi$
$710$	21.6293			0.811733
$711$	26.3038	+	15.1865i	0.986471	+	0.569540i
$712$	13.2827			0.497791
$713$	21.7816	−	37.7269i	0.815728	−	1.41288i
$714$		0			0
$715$	12.9282	+	22.3923i	0.483487	+	0.837425i
$716$	−1.09808	−	1.90192i	−0.0410370	−	0.0710782i
$717$	2.48168	−	9.26174i	0.0926799	−	0.345886i
$718$	−0.0358984	+	0.0621778i	−0.00133972	+	0.00232046i
$719$	−19.8733			−0.741150			−0.370575	−	0.928803i	$-0.620839\pi$
$719$	−19.8733			−0.741150			−0.370575	+	0.928803i	$0.620839\pi$
$720$			5.79555i			0.215988i
$721$		0			0
$722$	−7.63397	+	13.2224i	−0.284107	+	0.492088i
$723$	−21.2942	+	5.70577i	−0.791941	+	0.212200i
$724$	−4.36276	−	7.55652i	−0.162141	−	0.280836i
$725$	−0.464102	−	0.803848i	−0.0172363	−	0.0298541i
$726$	23.0943	+	23.0943i	0.857109	+	0.857109i
$727$	12.0580	−	20.8850i	0.447206	−	0.774583i	−0.550997	−	0.834507i	$-0.685753\pi$
$727$	12.0580	−	20.8850i	0.447206	−	0.774583i	0.998203	+	0.0599240i	$0.0190858\pi$
$728$		0			0
$729$		−	27.0000i		−	1.00000i
$730$	18.3923			0.680730
$731$	−5.69402	+	9.86233i	−0.210601	+	0.364771i
$732$	−3.63397	−	3.63397i	−0.134316	−	0.134316i
$733$	4.03459	+	6.98811i	0.149021	+	0.258112i	0.930866	−	0.365361i	$-0.119054\pi$
$733$	4.03459	+	6.98811i	0.149021	+	0.258112i	−0.781845	+	0.623473i	$0.785721\pi$
$734$	−7.20977	−	12.4877i	−0.266117	−	0.460929i
$735$		0			0
$736$	−2.96410	+	5.13397i	−0.109258	+	0.189241i
$737$	−77.5692			−2.85730
$738$			16.9706i			0.624695i
$739$	−43.8564			−1.61328			−0.806642	−	0.591040i	$-0.798717\pi$
$739$	−43.8564			−1.61328			−0.806642	+	0.591040i	$0.798717\pi$
$740$	7.72741	−	13.3843i	0.284065	−	0.492015i
$741$	2.12132	−	7.91688i	0.0779287	−	0.290834i
$742$		0			0
$743$	−10.1244	−	17.5359i	−0.371427	−	0.643330i	0.618359	−	0.785896i	$-0.287798\pi$
$743$	−10.1244	−	17.5359i	−0.371427	−	0.643330i	−0.989785	+	0.142566i	$0.954465\pi$
$744$	3.29423	−	12.2942i	0.120772	−	0.450728i
$745$	−17.7656	+	30.7709i	−0.650881	+	1.12736i
$746$	5.12436			0.187616
$747$	−25.7196	−	14.8492i	−0.941033	−	0.543305i
$748$	−34.4959			−1.26130
$749$		0			0
$750$	20.2583	−	5.42820i	0.739730	−	0.198210i
$751$	−6.08846	−	10.5455i	−0.222171	−	0.384811i	0.733296	−	0.679910i	$-0.237981\pi$
$751$	−6.08846	−	10.5455i	−0.222171	−	0.384811i	−0.955467	+	0.295098i	$0.904648\pi$
$752$	−4.76028	−	8.24504i	−0.173590	−	0.300666i
$753$	2.36603	+	2.36603i	0.0862228	+	0.0862228i
$754$	0.896575	−	1.55291i	0.0326514	−	0.0565538i
$755$	6.55343			0.238504
$756$		0			0
$757$	−28.2487			−1.02672			−0.513358	−	0.858174i	$-0.671599\pi$
$757$	−28.2487			−1.02672			−0.513358	+	0.858174i	$0.671599\pi$
$758$	8.75833	−	15.1699i	0.318117	−	0.550995i
$759$	39.6723	+	39.6723i	1.44001	+	1.44001i
$760$	1.86603	+	3.23205i	0.0676879	+	0.117239i
$761$	−2.74049	−	4.74668i	−0.0993428	−	0.172067i	0.812070	−	0.583560i	$-0.198341\pi$
$761$	−2.74049	−	4.74668i	−0.0993428	−	0.172067i	−0.911413	+	0.411493i	$0.865007\pi$
$762$	−13.2641	+	3.55412i	−0.480509	+	0.128752i
$763$		0			0
$764$	3.19615			0.115633
$765$	−31.6865	+	18.2942i	−1.14563	+	0.661429i
$766$	−19.5216			−0.705344
$767$	−6.12436	+	10.6077i	−0.221138	+	0.383022i
$768$	−0.448288	+	1.67303i	−0.0161762	+	0.0603704i
$769$	−2.20925	−	3.82654i	−0.0796677	−	0.137989i	0.823439	−	0.567405i	$-0.192053\pi$
$769$	−2.20925	−	3.82654i	−0.0796677	−	0.137989i	−0.903107	+	0.429416i	$0.858719\pi$
$770$		0			0
$771$	−9.29423	+	34.6865i	−0.334723	+	1.24920i
$772$	10.1340	−	17.5526i	0.364730	−	0.631730i
$773$	3.62347			0.130327			0.0651635	−	0.997875i	$-0.479243\pi$
$773$	3.62347			0.130327			0.0651635	+	0.997875i	$0.479243\pi$
$774$	4.68653	−	2.70577i	0.168454	−	0.0972569i
$775$	−9.31749			−0.334694
$776$	−1.93185	+	3.34607i	−0.0693494	+	0.120117i
$777$		0			0
$778$	−14.5622	−	25.2224i	−0.522079	−	0.904268i
$779$	5.46410	+	9.46410i	0.195772	+	0.339087i
$780$	5.79555	+	5.79555i	0.207514	+	0.207514i
$781$	30.5885	−	52.9808i	1.09454	−	1.89580i
$782$	−37.4259			−1.33835
$783$	−0.984508	−	3.67423i	−0.0351835	−	0.131306i
$784$		0			0
$785$	23.5263	−	40.7487i	0.839689	−	1.45438i
$786$	−0.294229	−	0.294229i	−0.0104948	−	0.0104948i
$787$	3.95164	+	6.84443i	0.140861	+	0.243978i	0.927821	−	0.373026i	$-0.121680\pi$
$787$	3.95164	+	6.84443i	0.140861	+	0.243978i	−0.786960	+	0.617004i	$0.788346\pi$
$788$	3.83013	+	6.63397i	0.136443	+	0.236326i
$789$	−24.5271	+	6.57201i	−0.873187	+	0.233970i
$790$	−9.77938	+	16.9384i	−0.347935	+	0.602640i
$791$		0			0
$792$	14.1962	+	8.19615i	0.504438	+	0.291238i
$793$	−7.26795			−0.258092
$794$	−0.947343	+	1.64085i	−0.0336200	+	0.0582315i
$795$	−2.83013	+	10.5622i	−0.100374	+	0.374602i
$796$	−1.55291	−	2.68973i	−0.0550416	−	0.0953348i
$797$	11.0549	+	19.1476i	0.391584	+	0.678244i	0.992659	−	0.120949i	$-0.0385938\pi$
$797$	11.0549	+	19.1476i	0.391584	+	0.678244i	−0.601074	+	0.799193i	$0.705260\pi$
$798$		0			0
$799$	30.0526	−	52.0526i	1.06318	−	1.84149i
$800$	1.26795			0.0448288
$801$		−	39.8482i		−	1.40797i
$802$	−13.0526			−0.460902
$803$	26.0106	−	45.0518i	0.917896	−	1.58984i
$804$	−23.7506	+	6.36396i	−0.837620	+	0.224440i
$805$		0			0
$806$	−9.00000	−	15.5885i	−0.317011	−	0.549080i
$807$	−0.0455173	−	0.0455173i	−0.00160229	−	0.00160229i
$808$	0.776457	−	1.34486i	0.0273157	−	0.0473121i
$809$	−1.32051			−0.0464266			−0.0232133	−	0.999731i	$-0.507390\pi$
$809$	−1.32051			−0.0464266			−0.0232133	+	0.999731i	$0.507390\pi$
$810$	17.3867			0.610905
$811$	−17.6269			−0.618964			−0.309482	−	0.950905i	$-0.600156\pi$
$811$	−17.6269			−0.618964			−0.309482	+	0.950905i	$0.600156\pi$
$812$		0			0
$813$	6.12436	+	6.12436i	0.214791	+	0.214791i
$814$	−21.8564	−	37.8564i	−0.766067	−	1.32687i
$815$	20.2151	+	35.0136i	0.708104	+	1.22647i
$816$	−10.5622	+	2.83013i	−0.369750	+	0.0990743i
$817$	1.74238	−	3.01790i	0.0609583	−	0.105583i
$818$	−26.2880			−0.919140
$819$		0			0
$820$	−10.9282			−0.381629
$821$	20.6603	−	35.7846i	0.721048	−	1.24889i	−0.239532	−	0.970888i	$-0.576994\pi$
$821$	20.6603	−	35.7846i	0.721048	−	1.24889i	0.960580	−	0.278003i	$-0.0896726\pi$
$822$		0			0
$823$	−13.6603	−	23.6603i	−0.476167	−	0.824745i	0.523461	−	0.852050i	$-0.324641\pi$
$823$	−13.6603	−	23.6603i	−0.476167	−	0.824745i	−0.999627	+	0.0273053i	$0.991307\pi$
$824$	−4.19187	−	7.26054i	−0.146031	−	0.252933i
$825$	3.10583	−	11.5911i	0.108131	−	0.403551i
$826$		0			0
$827$	−49.2679			−1.71321			−0.856607	−	0.515969i	$-0.827432\pi$
$827$	−49.2679			−1.71321			−0.856607	+	0.515969i	$0.827432\pi$
$828$	15.4019	+	8.89230i	0.535254	+	0.309029i
$829$	26.3896			0.916548			0.458274	−	0.888811i	$-0.348468\pi$
$829$	26.3896			0.916548			0.458274	+	0.888811i	$0.348468\pi$
$830$	9.56218	−	16.5622i	0.331908	−	0.574882i
$831$	−9.71003	+	2.60179i	−0.336837	+	0.0902552i
$832$	1.22474	+	2.12132i	0.0424604	+	0.0735436i
$833$		0			0
$834$	−2.24167	−	2.24167i	−0.0776227	−	0.0776227i
$835$	−15.5622	+	26.9545i	−0.538551	+	0.932798i
$836$	10.5558			0.365081
$837$	−36.8827	−	9.88269i	−1.27485	−	0.341596i
$838$	4.27981			0.147843
$839$	6.91876	−	11.9837i	0.238862	−	0.413722i	−0.721526	−	0.692388i	$-0.756559\pi$
$839$	6.91876	−	11.9837i	0.238862	−	0.413722i	0.960388	+	0.278666i	$0.0898922\pi$
$840$		0			0
$841$	14.2321	+	24.6506i	0.490760	+	0.850022i
$842$	−5.02628	−	8.70577i	−0.173217	−	0.300021i
$843$	5.67544	−	1.52073i	0.195472	−	0.0523767i
$844$	−2.36603	+	4.09808i	−0.0814420	+	0.141062i
$845$	−13.5230			−0.465204
$846$	−24.7351	+	14.2808i	−0.850411	+	0.490985i
$847$		0			0
$848$	−1.63397	+	2.83013i	−0.0561109	+	0.0971870i
$849$	7.66987	−	28.6244i	0.263229	−	0.982385i
$850$	4.00240	+	6.93237i	0.137281	+	0.237778i
$851$	−23.7128	−	41.0718i	−0.812865	−	1.40792i
$852$	5.01910	−	18.7315i	0.171951	−	0.641732i
$853$	−13.9205	+	24.1110i	−0.476628	+	0.825544i	−0.999641	−	0.0267804i	$-0.991475\pi$
$853$	−13.9205	+	24.1110i	−0.476628	+	0.825544i	0.523013	+	0.852325i	$0.324808\pi$
$854$		0			0
$855$	9.69615	−	5.59808i	0.331601	−	0.191450i
$856$	−16.9282			−0.578594
$857$	−16.8690	+	29.2180i	−0.576235	+	0.998068i	0.419671	+	0.907676i	$0.362145\pi$
$857$	−16.8690	+	29.2180i	−0.576235	+	0.998068i	−0.995906	+	0.0903921i	$0.971188\pi$
$858$	22.3923	−	6.00000i	0.764461	−	0.204837i
$859$	−14.7477	−	25.5438i	−0.503185	−	0.871542i	−0.999993	−	0.00368192i	$-0.998828\pi$
$859$	−14.7477	−	25.5438i	−0.503185	−	0.871542i	0.496808	−	0.867860i	$-0.334505\pi$
$860$	1.74238	+	3.01790i	0.0594148	+	0.102909i
$861$		0			0
$862$	7.39230	−	12.8038i	0.251783	−	0.436101i
$863$	10.8038			0.367767			0.183884	−	0.982948i	$-0.441133\pi$
$863$	10.8038			0.367767			0.183884	+	0.982948i	$0.441133\pi$
$864$	5.01910	+	1.34486i	0.170753	+	0.0457532i
$865$	28.0526			0.953816
$866$	−14.3688	+	24.8874i	−0.488271	+	0.845710i
$867$	−27.9933	−	27.9933i	−0.950701	−	0.950701i
$868$		0			0
$869$	27.6603	+	47.9090i	0.938310	+	1.62520i
$870$	2.36603	−	0.633975i	0.0802158	−	0.0214938i
$871$	−17.3867	+	30.1146i	−0.589125	+	1.02039i
$872$	20.5885			0.697213
$873$	10.0382	+	5.79555i	0.339741	+	0.196150i
$874$	11.4524			0.387384
$875$		0			0
$876$	4.26795	−	15.9282i	0.144201	−	0.538164i
$877$	7.02628	+	12.1699i	0.237261	+	0.410947i	0.959927	−	0.280249i	$-0.0904171\pi$
$877$	7.02628	+	12.1699i	0.237261	+	0.410947i	−0.722667	+	0.691197i	$0.757084\pi$
$878$	0.656339	+	1.13681i	0.0221504	+	0.0383656i
$879$	1.96410	−	7.33013i	0.0662475	−	0.247239i
$880$	−5.27792	+	9.14162i	−0.177919	+	0.308164i
$881$	−24.9754			−0.841442			−0.420721	−	0.907190i	$-0.638223\pi$
$881$	−24.9754			−0.841442			−0.420721	+	0.907190i	$0.638223\pi$
$882$		0			0
$883$	−10.2487			−0.344897			−0.172448	−	0.985019i	$-0.555168\pi$
$883$	−10.2487			−0.344897			−0.172448	+	0.985019i	$0.555168\pi$
$884$	−7.73205	+	13.3923i	−0.260057	+	0.450432i
$885$	−16.1619	+	4.33057i	−0.543277	+	0.145571i
$886$	7.49038	+	12.9737i	0.251644	+	0.435861i
$887$	23.2838	+	40.3286i	0.781792	+	1.35410i	0.930897	+	0.365282i	$0.119027\pi$
$887$	23.2838	+	40.3286i	0.781792	+	1.35410i	−0.149105	+	0.988821i	$0.547639\pi$
$888$	−9.79796	−	9.79796i	−0.328798	−	0.328798i
$889$		0			0
$890$	25.6603			0.860134
$891$	24.5885	−	42.5885i	0.823744	−	1.42677i
$892$	20.7327			0.694183
$893$	−9.19615	+	15.9282i	−0.307738	+	0.533017i
$894$	22.5259	+	22.5259i	0.753378	+	0.753378i
$895$	−2.12132	−	3.67423i	−0.0709079	−	0.122816i
$896$		0			0
$897$	24.2942	−	6.50962i	0.811161	−	0.217350i
$898$	8.89230	−	15.4019i	0.296740	−	0.513969i
$899$	−5.37945			−0.179415
$900$		−	3.80385i		−	0.126795i
$901$	−20.6312			−0.687325
$902$	−15.4548	+	26.7685i	−0.514589	+	0.891294i
$903$		0			0
$904$	1.33013	+	2.30385i	0.0442394	+	0.0766248i
$905$	−8.42820	−	14.5981i	−0.280163	−	0.485256i
$906$	1.52073	−	5.67544i	0.0505228	−	0.188554i
$907$	−9.56218	+	16.5622i	−0.317507	+	0.549938i	−0.979967	−	0.199159i	$-0.936179\pi$
$907$	−9.56218	+	16.5622i	−0.317507	+	0.549938i	0.662460	+	0.749097i	$0.269512\pi$
$908$	−0.896575			−0.0297539
$909$	−4.03459	−	2.32937i	−0.133819	−	0.0772604i
$910$		0			0
$911$	6.89230	−	11.9378i	0.228352	−	0.395518i	−0.728968	−	0.684548i	$-0.760000\pi$
$911$	6.89230	−	11.9378i	0.228352	−	0.395518i	0.957320	+	0.289030i	$0.0933329\pi$
$912$	3.23205	−	0.866025i	0.107024	−	0.0286770i
$913$	−27.0459	−	46.8449i	−0.895089	−	1.55034i
$914$	−12.8660	−	22.2846i	−0.425570	−	0.737109i
$915$	−7.02030	−	7.02030i	−0.232084	−	0.232084i
$916$	−9.02150	+	15.6257i	−0.298079	+	0.516288i
$917$		0			0
$918$	8.49038	+	31.6865i	0.280224	+	1.04581i
$919$	−56.3731			−1.85958			−0.929788	−	0.368096i	$-0.880010\pi$
$919$	−56.3731			−1.85958			−0.929788	+	0.368096i	$0.880010\pi$
$920$	−5.72620	+	9.91808i	−0.188787	+	0.326989i
$921$	−35.6147	−	35.6147i	−1.17355	−	1.17355i
$922$	−10.9162	−	18.9074i	−0.359506	−	0.622682i
$923$	−13.7124	−	23.7506i	−0.451350	−	0.781761i
$924$		0			0
$925$	−5.07180	+	8.78461i	−0.166760	+	0.288836i
$926$	10.6603			0.350318
$927$	−21.7816	+	12.5756i	−0.715402	+	0.413037i
$928$	0.732051			0.0240307
$929$	−17.5761	+	30.4428i	−0.576654	+	0.998794i	0.419206	+	0.907891i	$0.362309\pi$
$929$	−17.5761	+	30.4428i	−0.576654	+	0.998794i	−0.995860	+	0.0909031i	$0.971025\pi$
$930$	6.36396	−	23.7506i	0.208683	−	0.778814i
$931$		0			0
$932$	9.69615	+	16.7942i	0.317608	+	0.550113i
$933$	−9.41858	+	35.1506i	−0.308351	+	1.15078i
$934$	2.39872	−	4.15471i	0.0784886	−	0.135946i
$935$	−66.6410			−2.17939
$936$	6.36396	−	3.67423i	0.208013	−	0.120096i
$937$	−21.9711			−0.717764			−0.358882	−	0.933383i	$-0.616842\pi$
$937$	−21.9711			−0.717764			−0.358882	+	0.933383i	$0.616842\pi$
$938$		0			0
$939$	3.00000	−	0.803848i	0.0979013	−	0.0262326i
$940$	−9.19615	−	15.9282i	−0.299945	−	0.519521i
$941$	−18.1767	−	31.4830i	−0.592544	−	1.02632i	−0.993888	−	0.110389i	$-0.964790\pi$
$941$	−18.1767	−	31.4830i	−0.592544	−	1.02632i	0.401344	−	0.915927i	$-0.368543\pi$
$942$	−29.8301	−	29.8301i	−0.971918	−	0.971918i
$943$	−16.7675	+	29.0421i	−0.546025	+	0.945742i
$944$	−5.00052			−0.162753
$945$		0			0
$946$	9.85641			0.320459
$947$	9.16987	−	15.8827i	0.297981	−	0.516118i	−0.677693	−	0.735345i	$-0.737020\pi$
$947$	9.16987	−	15.8827i	0.297981	−	0.516118i	0.975674	+	0.219227i	$0.0703535\pi$
$948$	12.3998	+	12.3998i	0.402725	+	0.402725i
$949$	−11.6603	−	20.1962i	−0.378508	−	0.655595i
$950$	−1.22474	−	2.12132i	−0.0397360	−	0.0688247i
$951$	2.36156	−	0.632777i	0.0765787	−	0.0205192i
$952$		0			0
$953$	−31.7128			−1.02728			−0.513639	−	0.858006i	$-0.671703\pi$
$953$	−31.7128			−1.02728			−0.513639	+	0.858006i	$0.671703\pi$
$954$	8.49038	+	4.90192i	0.274886	+	0.158706i
$955$	6.17449			0.199802
$956$	2.76795	−	4.79423i	0.0895219	−	0.155056i
$957$	1.79315	−	6.69213i	0.0579643	−	0.216326i
$958$	−8.05558	−	13.9527i	−0.260264	−	0.450790i
$959$		0			0
$960$	−0.866025	+	3.23205i	−0.0279508	+	0.104314i
$961$	−11.5000	+	19.9186i	−0.370968	+	0.642535i
$962$	−19.5959			−0.631798
$963$			50.7846i			1.63651i
$964$	−12.7279			−0.409939
$965$	19.5773	−	33.9089i	0.630217	−	1.09157i
$966$		0			0
$967$	−3.23205	−	5.59808i	−0.103936	−	0.180022i	0.809367	−	0.587303i	$-0.199810\pi$
$967$	−3.23205	−	5.59808i	−0.103936	−	0.180022i	−0.913303	+	0.407281i	$0.866477\pi$
$968$	9.42820	+	16.3301i	0.303034	+	0.524870i
$969$	14.9372	+	14.9372i	0.479851	+	0.479851i
$970$	−3.73205	+	6.46410i	−0.119829	+	0.207550i
$971$	13.0425			0.418553			0.209277	−	0.977856i	$-0.432889\pi$
$971$	13.0425			0.418553			0.209277	+	0.977856i	$0.432889\pi$
$972$	4.03459	−	15.0573i	0.129410	−	0.482963i
$973$		0			0
$974$	1.16025	−	2.00962i	0.0371769	−	0.0643923i
$975$	−3.80385	−	3.80385i	−0.121821	−	0.121821i
$976$	−1.48356	−	2.56961i	−0.0474877	−	0.0822512i
$977$	21.9282	+	37.9808i	0.701545	+	1.21511i	0.967924	+	0.251244i	$0.0808396\pi$
$977$	21.9282	+	37.9808i	0.701545	+	1.21511i	−0.266378	+	0.963869i	$0.585827\pi$
$978$	35.0136	−	9.38186i	1.11961	−	0.299999i
$979$	36.2891	−	62.8545i	1.15980	−	2.00884i
$980$		0			0
$981$		−	61.7654i		−	1.97202i
$982$	18.9282			0.604023
$983$	27.3741	−	47.4133i	0.873098	−	1.51225i	0.0143228	−	0.999897i	$-0.495441\pi$
$983$	27.3741	−	47.4133i	0.873098	−	1.51225i	0.858775	−	0.512353i	$-0.171226\pi$
$984$	−2.53590	+	9.46410i	−0.0808415	+	0.301705i
$985$	7.39924	+	12.8159i	0.235759	+	0.408347i
$986$	2.31079	+	4.00240i	0.0735905	+	0.127463i
$987$		0			0
$988$	2.36603	−	4.09808i	0.0752733	−	0.130377i
$989$	10.6936			0.340036
$990$	27.4249	+	15.8338i	0.871619	+	0.503230i
$991$	49.3205			1.56672			0.783359	−	0.621570i	$-0.213505\pi$
$991$	49.3205			1.56672			0.783359	+	0.621570i	$0.213505\pi$
$992$	3.67423	−	6.36396i	0.116657	−	0.202056i
$993$	43.5868	−	11.6790i	1.38318	−	0.370623i
$994$		0			0
$995$	−3.00000	−	5.19615i	−0.0951064	−	0.164729i
$996$	−12.1244	−	12.1244i	−0.384175	−	0.384175i
$997$	8.46670	−	14.6648i	0.268143	−	0.464437i	−0.700239	−	0.713908i	$-0.746923\pi$
$997$	8.46670	−	14.6648i	0.268143	−	0.464437i	0.968382	+	0.249471i	$0.0802567\pi$
$998$	27.3205			0.864816
$999$	−29.3939	+	29.3939i	−0.929981	+	0.929981i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.f.s.295.1	✓	8
3.2	odd	2		2646.2.f.q.883.4		8
7.2	even	3		882.2.e.q.655.4		8
7.3	odd	6		882.2.h.t.79.3		8
7.4	even	3		882.2.h.t.79.2		8
7.5	odd	6		882.2.e.q.655.1		8
7.6	odd	2	inner	882.2.f.s.295.4	yes	8
9.2	odd	6		7938.2.a.co.1.1		4
9.4	even	3	inner	882.2.f.s.589.2	yes	8
9.5	odd	6		2646.2.f.q.1765.4		8
9.7	even	3		7938.2.a.cj.1.4		4
21.2	odd	6		2646.2.e.t.2125.4		8
21.5	even	6		2646.2.e.t.2125.1		8
21.11	odd	6		2646.2.h.q.667.1		8
21.17	even	6		2646.2.h.q.667.4		8
21.20	even	2		2646.2.f.q.883.1		8
63.4	even	3		882.2.e.q.373.4		8
63.5	even	6		2646.2.h.q.361.4		8
63.13	odd	6	inner	882.2.f.s.589.3	yes	8
63.20	even	6		7938.2.a.co.1.4		4
63.23	odd	6		2646.2.h.q.361.1		8
63.31	odd	6		882.2.e.q.373.1		8
63.32	odd	6		2646.2.e.t.1549.4		8
63.34	odd	6		7938.2.a.cj.1.1		4
63.40	odd	6		882.2.h.t.67.3		8
63.41	even	6		2646.2.f.q.1765.1		8
63.58	even	3		882.2.h.t.67.2		8
63.59	even	6		2646.2.e.t.1549.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.e.q.373.1		8	63.31	odd	6
882.2.e.q.373.4		8	63.4	even	3
882.2.e.q.655.1		8	7.5	odd	6
882.2.e.q.655.4		8	7.2	even	3
882.2.f.s.295.1	✓	8	1.1	even	1	trivial
882.2.f.s.295.4	yes	8	7.6	odd	2	inner
882.2.f.s.589.2	yes	8	9.4	even	3	inner
882.2.f.s.589.3	yes	8	63.13	odd	6	inner
882.2.h.t.67.2		8	63.58	even	3
882.2.h.t.67.3		8	63.40	odd	6
882.2.h.t.79.2		8	7.4	even	3
882.2.h.t.79.3		8	7.3	odd	6
2646.2.e.t.1549.1		8	63.59	even	6
2646.2.e.t.1549.4		8	63.32	odd	6
2646.2.e.t.2125.1		8	21.5	even	6
2646.2.e.t.2125.4		8	21.2	odd	6
2646.2.f.q.883.1		8	21.20	even	2
2646.2.f.q.883.4		8	3.2	odd	2
2646.2.f.q.1765.1		8	63.41	even	6
2646.2.f.q.1765.4		8	9.5	odd	6
2646.2.h.q.361.1		8	63.23	odd	6
2646.2.h.q.361.4		8	63.5	even	6
2646.2.h.q.667.1		8	21.11	odd	6
2646.2.h.q.667.4		8	21.17	even	6
7938.2.a.cj.1.1		4	63.34	odd	6
7938.2.a.cj.1.4		4	9.7	even	3
7938.2.a.co.1.1		4	9.2	odd	6
7938.2.a.co.1.4		4	63.20	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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.22474 - 1.22474i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.965926 - 1.67303i) q^{5} +(-1.67303 + 0.448288i) q^{6} -1.00000 q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.22474 - 1.22474i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.965926 - 1.67303i) q^{5} +(-1.67303 + 0.448288i) q^{6} -1.00000 q^{8} +3.00000i q^{9} -1.93185 q^{10} +(-2.73205 + 4.73205i) q^{11} +(-0.448288 + 1.67303i) q^{12} +(1.22474 + 2.12132i) q^{13} +(-0.866025 + 3.23205i) q^{15} +(-0.500000 + 0.866025i) q^{16} -6.31319 q^{17} +(2.59808 + 1.50000i) q^{18} +1.93185 q^{19} +(-0.965926 + 1.67303i) q^{20} +(2.73205 + 4.73205i) q^{22} +(2.96410 + 5.13397i) q^{23} +(1.22474 + 1.22474i) q^{24} +(0.633975 - 1.09808i) q^{25} +2.44949 q^{26} +(3.67423 - 3.67423i) q^{27} +(0.366025 - 0.633975i) q^{29} +(2.36603 + 2.36603i) q^{30} +(-3.67423 - 6.36396i) q^{31} +(0.500000 + 0.866025i) q^{32} +(9.14162 - 2.44949i) q^{33} +(-3.15660 + 5.46739i) q^{34} +(2.59808 - 1.50000i) q^{36} -8.00000 q^{37} +(0.965926 - 1.67303i) q^{38} +(1.09808 - 4.09808i) q^{39} +(0.965926 + 1.67303i) q^{40} +(2.82843 + 4.89898i) q^{41} +(0.901924 - 1.56218i) q^{43} +5.46410 q^{44} +(5.01910 - 2.89778i) q^{45} +5.92820 q^{46} +(-4.76028 + 8.24504i) q^{47} +(1.67303 - 0.448288i) q^{48} +(-0.633975 - 1.09808i) q^{50} +(7.73205 + 7.73205i) q^{51} +(1.22474 - 2.12132i) q^{52} +3.26795 q^{53} +(-1.34486 - 5.01910i) q^{54} +10.5558 q^{55} +(-2.36603 - 2.36603i) q^{57} +(-0.366025 - 0.633975i) q^{58} +(2.50026 + 4.33057i) q^{59} +(3.23205 - 0.866025i) q^{60} +(-1.48356 + 2.56961i) q^{61} -7.34847 q^{62} +1.00000 q^{64} +(2.36603 - 4.09808i) q^{65} +(2.44949 - 9.14162i) q^{66} +(7.09808 + 12.2942i) q^{67} +(3.15660 + 5.46739i) q^{68} +(2.65754 - 9.91808i) q^{69} -11.1962 q^{71} -3.00000i q^{72} -9.52056 q^{73} +(-4.00000 + 6.92820i) q^{74} +(-2.12132 + 0.568406i) q^{75} +(-0.965926 - 1.67303i) q^{76} +(-3.00000 - 3.00000i) q^{78} +(5.06218 - 8.76795i) q^{79} +1.93185 q^{80} -9.00000 q^{81} +5.65685 q^{82} +(-4.94975 + 8.57321i) q^{83} +(6.09808 + 10.5622i) q^{85} +(-0.901924 - 1.56218i) q^{86} +(-1.22474 + 0.328169i) q^{87} +(2.73205 - 4.73205i) q^{88} -13.2827 q^{89} -5.79555i q^{90} +(2.96410 - 5.13397i) q^{92} +(-3.29423 + 12.2942i) q^{93} +(4.76028 + 8.24504i) q^{94} +(-1.86603 - 3.23205i) q^{95} +(0.448288 - 1.67303i) q^{96} +(1.93185 - 3.34607i) q^{97} +(-14.1962 - 8.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8}+O(q^{10}) \) 8 * q + 4 * q^2 - 4 * q^4 - 8 * q^8	\( 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8} - 8 q^{11} - 4 q^{16} + 8 q^{22} - 4 q^{23} + 12 q^{25} - 4 q^{29} + 12 q^{30} + 4 q^{32} - 64 q^{37} - 12 q^{39} + 28 q^{43} + 16 q^{44} - 8 q^{46} - 12 q^{50} + 48 q^{51} + 40 q^{53} - 12 q^{57} + 4 q^{58} + 12 q^{60} + 8 q^{64} + 12 q^{65} + 36 q^{67} - 48 q^{71} - 32 q^{74} - 24 q^{78} - 8 q^{79} - 72 q^{81} + 28 q^{85} - 28 q^{86} + 8 q^{88} - 4 q^{92} + 36 q^{93} - 8 q^{95} - 72 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 - 4 * q^4 - 8 * q^8 - 8 * q^11 - 4 * q^16 + 8 * q^22 - 4 * q^23 + 12 * q^25 - 4 * q^29 + 12 * q^30 + 4 * q^32 - 64 * q^37 - 12 * q^39 + 28 * q^43 + 16 * q^44 - 8 * q^46 - 12 * q^50 + 48 * q^51 + 40 * q^53 - 12 * q^57 + 4 * q^58 + 12 * q^60 + 8 * q^64 + 12 * q^65 + 36 * q^67 - 48 * q^71 - 32 * q^74 - 24 * q^78 - 8 * q^79 - 72 * q^81 + 28 * q^85 - 28 * q^86 + 8 * q^88 - 4 * q^92 + 36 * q^93 - 8 * q^95 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more