LMFDB - Embedded newform 2070.2.j.j.737.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2070,2,Mod(323,2070)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2070, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("2070.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2070.j (of order $4$, 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:	$16.5290332184$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 20 x^{18} + 187 x^{16} - 1012 x^{14} + 3533 x^{12} - 7896 x^{10} + 10837 x^{8} - 5668 x^{6} + \cdots + 3721 $ x^20 - 20x^18 + 187x^16 - 1012x^14 + 3533x^12 - 7896x^10 + 10837x^8 - 5668x^6 - 4125x^4 + 8700*x^2 + 3721
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			737.10
Root			$-0.0229150 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	2070.737
Dual form			2070.2.j.j.323.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(1.88578 - 1.20159i) q^{5} +(-1.61288 - 1.61288i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(1.88578 - 1.20159i) q^{5} +(-1.61288 - 1.61288i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.483797 - 2.18310i) q^{10} -3.53479i q^{11} +(-0.800168 + 0.800168i) q^{13} -2.28096 q^{14} -1.00000 q^{16} +(3.53479 - 3.53479i) q^{17} +2.63274i q^{19} +(-1.20159 - 1.88578i) q^{20} +(-2.49947 - 2.49947i) q^{22} +(0.707107 + 0.707107i) q^{23} +(2.11236 - 4.53188i) q^{25} +1.13161i q^{26} +(-1.61288 + 1.61288i) q^{28} -6.66723 q^{29} +4.22471 q^{31} +(-0.707107 + 0.707107i) q^{32} -4.99895i q^{34} +(-4.97957 - 1.10352i) q^{35} +(-4.02161 - 4.02161i) q^{37} +(1.86163 + 1.86163i) q^{38} +(-2.18310 - 0.483797i) q^{40} -0.501638i q^{41} +(-4.11236 + 4.11236i) q^{43} -3.53479 q^{44} +1.00000 q^{46} +(-3.72574 + 3.72574i) q^{47} -1.79723i q^{49} +(-1.71086 - 4.69819i) q^{50} +(0.800168 + 0.800168i) q^{52} +(-2.30313 - 2.30313i) q^{53} +(-4.24737 - 6.66585i) q^{55} +2.28096i q^{56} +(-4.71444 + 4.71444i) q^{58} +12.5135 q^{59} -13.2334 q^{61} +(2.98732 - 2.98732i) q^{62} +1.00000i q^{64} +(-0.547468 + 2.47042i) q^{65} +(-5.47961 - 5.47961i) q^{67} +(-3.53479 - 3.53479i) q^{68} +(-4.30139 + 2.74078i) q^{70} +10.0890i q^{71} +(9.57837 - 9.57837i) q^{73} -5.68742 q^{74} +2.63274 q^{76} +(-5.70120 + 5.70120i) q^{77} -0.108038i q^{79} +(-1.88578 + 1.20159i) q^{80} +(-0.354712 - 0.354712i) q^{82} +(5.67903 + 5.67903i) q^{83} +(2.41848 - 10.9132i) q^{85} +5.81575i q^{86} +(-2.49947 + 2.49947i) q^{88} -3.06520 q^{89} +2.58115 q^{91} +(0.707107 - 0.707107i) q^{92} +5.26899i q^{94} +(3.16348 + 4.96478i) q^{95} +(-7.17892 - 7.17892i) q^{97} +(-1.27083 - 1.27083i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 16 q^{7}+O(q^{10}) $ 20 * q - 16 * q^7	$ 20 q - 16 q^{7} + 12 q^{10} - 12 q^{13} - 20 q^{16} - 24 q^{25} - 16 q^{28} - 48 q^{31} - 60 q^{37} - 16 q^{43} + 20 q^{46} + 12 q^{52} - 32 q^{55} + 4 q^{58} + 104 q^{61} - 56 q^{67} - 8 q^{70} - 20 q^{73} + 40 q^{76} - 28 q^{82} - 40 q^{85} - 32 q^{91} - 44 q^{97}+O(q^{100}) $ 20 * q - 16 * q^7 + 12 * q^10 - 12 * q^13 - 20 * q^16 - 24 * q^25 - 16 * q^28 - 48 * q^31 - 60 * q^37 - 16 * q^43 + 20 * q^46 + 12 * q^52 - 32 * q^55 + 4 * q^58 + 104 * q^61 - 56 * q^67 - 8 * q^70 - 20 * q^73 + 40 * q^76 - 28 * q^82 - 40 * q^85 - 32 * q^91 - 44 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2070\mathbb{Z}\right)^\times$.

$n$	$461$	$1657$	$1891$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	1.88578	−	1.20159i	0.843348	−	0.537368i
$5$	1.88578	−	1.20159i	0.843348	−	0.537368i
$6$		0			0
$7$	−1.61288	−	1.61288i	−0.609612	−	0.609612i	0.333233	−	0.942845i	$-0.391861\pi$
$7$	−1.61288	−	1.61288i	−0.609612	−	0.609612i	−0.942845	+	0.333233i	$0.891861\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	0.483797	−	2.18310i	0.152990	−	0.690358i
$11$		−	3.53479i		−	1.06578i	−0.846185	−	0.532890i	$-0.821106\pi$
$11$		−	3.53479i		−	1.06578i	0.846185	−	0.532890i	$-0.178894\pi$
$12$		0			0
$13$	−0.800168	+	0.800168i	−0.221927	+	0.221927i	−0.809309	−	0.587383i	$-0.800158\pi$
$13$	−0.800168	+	0.800168i	−0.221927	+	0.221927i	0.587383	+	0.809309i	$0.300158\pi$
$14$	−2.28096			−0.609612
$15$		0			0
$16$	−1.00000			−0.250000
$17$	3.53479	−	3.53479i	0.857313	−	0.857313i	−0.133708	−	0.991021i	$-0.542688\pi$
$17$	3.53479	−	3.53479i	0.857313	−	0.857313i	0.991021	+	0.133708i	$0.0426884\pi$
$18$		0			0
$19$			2.63274i			0.603993i	0.953309	+	0.301996i	$0.0976530\pi$
$19$			2.63274i			0.603993i	−0.953309	+	0.301996i	$0.902347\pi$
$20$	−1.20159	−	1.88578i	−0.268684	−	0.421674i
$21$		0			0
$22$	−2.49947	−	2.49947i	−0.532890	−	0.532890i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$24$		0			0
$25$	2.11236	−	4.53188i	0.422471	−	0.906376i
$26$			1.13161i			0.221927i
$27$		0			0
$28$	−1.61288	+	1.61288i	−0.304806	+	0.304806i
$29$	−6.66723			−1.23807			−0.619037	−	0.785362i	$-0.712477\pi$
$29$	−6.66723			−1.23807			−0.619037	+	0.785362i	$0.712477\pi$
$30$		0			0
$31$	4.22471			0.758781			0.379390	−	0.925237i	$-0.376134\pi$
$31$	4.22471			0.758781			0.379390	+	0.925237i	$0.376134\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$		−	4.99895i		−	0.857313i
$35$	−4.97957	−	1.10352i	−0.841701	−	0.186529i
$36$		0			0
$37$	−4.02161	−	4.02161i	−0.661149	−	0.661149i	0.294502	−	0.955651i	$-0.404846\pi$
$37$	−4.02161	−	4.02161i	−0.661149	−	0.661149i	−0.955651	+	0.294502i	$0.904846\pi$
$38$	1.86163	+	1.86163i	0.301996	+	0.301996i
$39$		0			0
$40$	−2.18310	−	0.483797i	−0.345179	−	0.0764950i
$41$		−	0.501638i		−	0.0783428i	−0.999233	−	0.0391714i	$-0.987528\pi$
$41$		−	0.501638i		−	0.0783428i	0.999233	−	0.0391714i	$-0.0124718\pi$
$42$		0			0
$43$	−4.11236	+	4.11236i	−0.627128	+	0.627128i	−0.947345	−	0.320216i	$-0.896244\pi$
$43$	−4.11236	+	4.11236i	−0.627128	+	0.627128i	0.320216	+	0.947345i	$0.396244\pi$
$44$	−3.53479			−0.532890
$45$		0			0
$46$	1.00000			0.147442
$47$	−3.72574	+	3.72574i	−0.543454	+	0.543454i	−0.924540	−	0.381085i	$-0.875550\pi$
$47$	−3.72574	+	3.72574i	−0.543454	+	0.543454i	0.381085	+	0.924540i	$0.375550\pi$
$48$		0			0
$49$		−	1.79723i		−	0.256747i
$50$	−1.71086	−	4.69819i	−0.241953	−	0.664424i
$51$		0			0
$52$	0.800168	+	0.800168i	0.110963	+	0.110963i
$53$	−2.30313	−	2.30313i	−0.316359	−	0.316359i	0.531008	−	0.847367i	$-0.321814\pi$
$53$	−2.30313	−	2.30313i	−0.316359	−	0.316359i	−0.847367	+	0.531008i	$0.821814\pi$
$54$		0			0
$55$	−4.24737	−	6.66585i	−0.572716	−	0.898823i
$56$			2.28096i			0.304806i
$57$		0			0
$58$	−4.71444	+	4.71444i	−0.619037	+	0.619037i
$59$	12.5135			1.62912			0.814562	−	0.580076i	$-0.196977\pi$
$59$	12.5135			1.62912			0.814562	+	0.580076i	$0.196977\pi$
$60$		0			0
$61$	−13.2334			−1.69437			−0.847184	−	0.531300i	$-0.821704\pi$
$61$	−13.2334			−1.69437			−0.847184	+	0.531300i	$0.821704\pi$
$62$	2.98732	−	2.98732i	0.379390	−	0.379390i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−0.547468	+	2.47042i	−0.0679051	+	0.306418i
$66$		0			0
$67$	−5.47961	−	5.47961i	−0.669441	−	0.669441i	0.288145	−	0.957587i	$-0.406961\pi$
$67$	−5.47961	−	5.47961i	−0.669441	−	0.669441i	−0.957587	+	0.288145i	$0.906961\pi$
$68$	−3.53479	−	3.53479i	−0.428656	−	0.428656i
$69$		0			0
$70$	−4.30139	+	2.74078i	−0.514115	+	0.327586i
$71$			10.0890i			1.19734i	0.800996	+	0.598669i	$0.204304\pi$
$71$			10.0890i			1.19734i	−0.800996	+	0.598669i	$0.795696\pi$
$72$		0			0
$73$	9.57837	−	9.57837i	1.12106	−	1.12106i	0.129482	−	0.991582i	$-0.458669\pi$
$73$	9.57837	−	9.57837i	1.12106	−	1.12106i	0.991582	−	0.129482i	$-0.0413315\pi$
$74$	−5.68742			−0.661149
$75$		0			0
$76$	2.63274			0.301996
$77$	−5.70120	+	5.70120i	−0.649712	+	0.649712i
$78$		0			0
$79$		−	0.108038i		−	0.0121552i	−0.999982	−	0.00607758i	$-0.998065\pi$
$79$		−	0.108038i		−	0.0121552i	0.999982	−	0.00607758i	$-0.00193457\pi$
$80$	−1.88578	+	1.20159i	−0.210837	+	0.134342i
$81$		0			0
$82$	−0.354712	−	0.354712i	−0.0391714	−	0.0391714i
$83$	5.67903	+	5.67903i	0.623354	+	0.623354i	0.946388	−	0.323033i	$-0.104703\pi$
$83$	5.67903	+	5.67903i	0.623354	+	0.623354i	−0.323033	+	0.946388i	$0.604703\pi$
$84$		0			0
$85$	2.41848	−	10.9132i	0.262320	−	1.18371i
$86$			5.81575i			0.627128i
$87$		0			0
$88$	−2.49947	+	2.49947i	−0.266445	+	0.266445i
$89$	−3.06520			−0.324911			−0.162455	−	0.986716i	$-0.551941\pi$
$89$	−3.06520			−0.324911			−0.162455	+	0.986716i	$0.551941\pi$
$90$		0			0
$91$	2.58115			0.270578
$92$	0.707107	−	0.707107i	0.0737210	−	0.0737210i
$93$		0			0
$94$			5.26899i			0.543454i
$95$	3.16348	+	4.96478i	0.324566	+	0.509376i
$96$		0			0
$97$	−7.17892	−	7.17892i	−0.728909	−	0.728909i	0.241494	−	0.970402i	$-0.422363\pi$
$97$	−7.17892	−	7.17892i	−0.728909	−	0.728909i	−0.970402	+	0.241494i	$0.922363\pi$
$98$	−1.27083	−	1.27083i	−0.128373	−	0.128373i
$99$		0			0
$100$	−4.53188	−	2.11236i	−0.453188	−	0.211236i
$101$		−	12.0950i		−	1.20350i	−0.798686	−	0.601748i	$-0.794471\pi$
$101$		−	12.0950i		−	1.20350i	0.798686	−	0.601748i	$-0.205529\pi$
$102$		0			0
$103$	11.1195	−	11.1195i	1.09564	−	1.09564i	0.100726	−	0.994914i	$-0.467883\pi$
$103$	11.1195	−	11.1195i	1.09564	−	1.09564i	0.994914	−	0.100726i	$-0.0321165\pi$
$104$	1.13161			0.110963
$105$		0			0
$106$	−3.25712			−0.316359
$107$	0.592532	−	0.592532i	0.0572822	−	0.0572822i	−0.677885	−	0.735168i	$-0.737103\pi$
$107$	0.592532	−	0.592532i	0.0572822	−	0.0572822i	0.735168	+	0.677885i	$0.237103\pi$
$108$		0			0
$109$			4.85956i			0.465461i	0.972541	+	0.232731i	$0.0747660\pi$
$109$			4.85956i			0.465461i	−0.972541	+	0.232731i	$0.925234\pi$
$110$	−7.71682	−	1.71012i	−0.735769	−	0.163054i
$111$		0			0
$112$	1.61288	+	1.61288i	0.152403	+	0.152403i
$113$	10.0202	+	10.0202i	0.942624	+	0.942624i	0.998441	−	0.0558167i	$-0.0177763\pi$
$113$	10.0202	+	10.0202i	0.942624	+	0.942624i	−0.0558167	+	0.998441i	$0.517776\pi$
$114$		0			0
$115$	2.18310	+	0.483797i	0.203575	+	0.0451143i
$116$			6.66723i			0.619037i
$117$		0			0
$118$	8.84841	−	8.84841i	0.814562	−	0.814562i
$119$	−11.4024			−1.04526
$120$		0			0
$121$	−1.49475			−0.135886
$122$	−9.35745	+	9.35745i	−0.847184	+	0.847184i
$123$		0			0
$124$		−	4.22471i		−	0.379390i
$125$	−1.46202	−	11.0843i	−0.130767	−	0.991413i
$126$		0			0
$127$	−2.26465	−	2.26465i	−0.200955	−	0.200955i	0.599454	−	0.800409i	$-0.295384\pi$
$127$	−2.26465	−	2.26465i	−0.200955	−	0.200955i	−0.800409	+	0.599454i	$0.795384\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		0			0
$130$	1.35973	+	2.13397i	0.119256	+	0.187161i
$131$			19.4487i			1.69924i	0.527398	+	0.849618i	$0.323168\pi$
$131$			19.4487i			1.69924i	−0.527398	+	0.849618i	$0.676832\pi$
$132$		0			0
$133$	4.24630	−	4.24630i	0.368201	−	0.368201i
$134$	−7.74934			−0.669441
$135$		0			0
$136$	−4.99895			−0.428656
$137$	6.27923	−	6.27923i	0.536471	−	0.536471i	−0.386020	−	0.922491i	$-0.626150\pi$
$137$	6.27923	−	6.27923i	0.536471	−	0.536471i	0.922491	+	0.386020i	$0.126150\pi$
$138$		0			0
$139$		−	13.8264i		−	1.17274i	−0.810042	−	0.586372i	$-0.800556\pi$
$139$		−	13.8264i		−	1.17274i	0.810042	−	0.586372i	$-0.199444\pi$
$140$	−1.10352	+	4.97957i	−0.0932645	+	0.420850i
$141$		0			0
$142$	7.13397	+	7.13397i	0.598669	+	0.598669i
$143$	2.82843	+	2.82843i	0.236525	+	0.236525i
$144$		0			0
$145$	−12.5729	+	8.01129i	−1.04413	+	0.665301i
$146$		−	13.5459i		−	1.12106i
$147$		0			0
$148$	−4.02161	+	4.02161i	−0.330574	+	0.330574i
$149$	−8.28617			−0.678829			−0.339415	−	0.940637i	$-0.610229\pi$
$149$	−8.28617			−0.678829			−0.339415	+	0.940637i	$0.610229\pi$
$150$		0			0
$151$	23.8697			1.94249			0.971243	−	0.238089i	$-0.0765211\pi$
$151$	23.8697			1.94249			0.971243	+	0.238089i	$0.0765211\pi$
$152$	1.86163	−	1.86163i	0.150998	−	0.150998i
$153$		0			0
$154$			8.06271i			0.649712i
$155$	7.96689	−	5.07638i	0.639916	−	0.407745i
$156$		0			0
$157$	−11.4073	−	11.4073i	−0.910400	−	0.910400i	0.0859039	−	0.996303i	$-0.472622\pi$
$157$	−11.4073	−	11.4073i	−0.910400	−	0.910400i	−0.996303	+	0.0859039i	$0.972622\pi$
$158$	−0.0763940	−	0.0763940i	−0.00607758	−	0.00607758i
$159$		0			0
$160$	−0.483797	+	2.18310i	−0.0382475	+	0.172589i
$161$		−	2.28096i		−	0.179765i
$162$		0			0
$163$	−11.1588	+	11.1588i	−0.874029	+	0.874029i	−0.992909	−	0.118880i	$-0.962070\pi$
$163$	−11.1588	+	11.1588i	−0.874029	+	0.874029i	0.118880	+	0.992909i	$0.462070\pi$
$164$	−0.501638			−0.0391714
$165$		0			0
$166$	8.03136			0.623354
$167$	10.3599	−	10.3599i	0.801675	−	0.801675i	−0.181682	−	0.983357i	$-0.558154\pi$
$167$	10.3599	−	10.3599i	0.801675	−	0.801675i	0.983357	+	0.181682i	$0.0581542\pi$
$168$		0			0
$169$			11.7195i			0.901497i
$170$	−6.00670	−	9.42694i	−0.460692	−	0.723013i
$171$		0			0
$172$	4.11236	+	4.11236i	0.313564	+	0.313564i
$173$	0.0754036	+	0.0754036i	0.00573283	+	0.00573283i	0.709967	−	0.704235i	$-0.248710\pi$
$173$	0.0754036	+	0.0754036i	0.00573283	+	0.00573283i	−0.704235	+	0.709967i	$0.748710\pi$
$174$		0			0
$175$	−10.7164	+	3.90241i	−0.810081	+	0.294994i
$176$			3.53479i			0.266445i
$177$		0			0
$178$	−2.16743	+	2.16743i	−0.162455	+	0.162455i
$179$	0.500153			0.0373832			0.0186916	−	0.999825i	$-0.494050\pi$
$179$	0.500153			0.0373832			0.0186916	+	0.999825i	$0.494050\pi$
$180$		0			0
$181$	1.72888			0.128507			0.0642533	−	0.997934i	$-0.479533\pi$
$181$	1.72888			0.128507			0.0642533	+	0.997934i	$0.479533\pi$
$182$	1.82515	−	1.82515i	0.135289	−	0.135289i
$183$		0			0
$184$		−	1.00000i		−	0.0737210i
$185$	−12.4162	−	2.75155i	−0.912859	−	0.202298i
$186$		0			0
$187$	−12.4947	−	12.4947i	−0.913707	−	0.913707i
$188$	3.72574	+	3.72574i	0.271727	+	0.271727i
$189$		0			0
$190$	5.74755	+	1.27371i	0.416971	+	0.0924048i
$191$			17.9117i			1.29605i	0.761620	+	0.648023i	$0.224404\pi$
$191$			17.9117i			1.29605i	−0.761620	+	0.648023i	$0.775596\pi$
$192$		0			0
$193$	13.9989	−	13.9989i	1.00767	−	1.00767i	0.00769607	−	0.999970i	$-0.497550\pi$
$193$	13.9989	−	13.9989i	1.00767	−	1.00767i	0.999970	−	0.00769607i	$-0.00244976\pi$
$194$	−10.1525			−0.728909
$195$		0			0
$196$	−1.79723			−0.128373
$197$	−7.00601	+	7.00601i	−0.499158	+	0.499158i	−0.911176	−	0.412018i	$-0.864824\pi$
$197$	−7.00601	+	7.00601i	−0.499158	+	0.499158i	0.412018	+	0.911176i	$0.364824\pi$
$198$		0			0
$199$			6.94709i			0.492466i	0.969211	+	0.246233i	$0.0791928\pi$
$199$			6.94709i			0.492466i	−0.969211	+	0.246233i	$0.920807\pi$
$200$	−4.69819	+	1.71086i	−0.332212	+	0.120976i
$201$		0			0
$202$	−8.55244	−	8.55244i	−0.601748	−	0.601748i
$203$	10.7534	+	10.7534i	0.754744	+	0.754744i
$204$		0			0
$205$	−0.602764	−	0.945981i	−0.0420989	−	0.0660702i
$206$		−	15.7254i		−	1.09564i
$207$		0			0
$208$	0.800168	−	0.800168i	0.0554817	−	0.0554817i
$209$	9.30620			0.643723
$210$		0			0
$211$	10.1513			0.698842			0.349421	−	0.936966i	$-0.386378\pi$
$211$	10.1513			0.698842			0.349421	+	0.936966i	$0.386378\pi$
$212$	−2.30313	+	2.30313i	−0.158180	+	0.158180i
$213$		0			0
$214$		−	0.837966i		−	0.0572822i
$215$	−2.81364	+	12.6964i	−0.191889	+	0.865886i
$216$		0			0
$217$	−6.81396	−	6.81396i	−0.462562	−	0.462562i
$218$	3.43622	+	3.43622i	0.232731	+	0.232731i
$219$		0			0
$220$	−6.66585	+	4.24737i	−0.449412	+	0.286358i
$221$			5.65685i			0.380521i
$222$		0			0
$223$	−0.175419	+	0.175419i	−0.0117469	+	0.0117469i	−0.712956	−	0.701209i	$-0.752644\pi$
$223$	−0.175419	+	0.175419i	−0.0117469	+	0.0117469i	0.701209	+	0.712956i	$0.252644\pi$
$224$	2.28096			0.152403
$225$		0			0
$226$	14.1708			0.942624
$227$	−7.47975	+	7.47975i	−0.496449	+	0.496449i	−0.910331	−	0.413882i	$-0.864173\pi$
$227$	−7.47975	+	7.47975i	−0.496449	+	0.496449i	0.413882	+	0.910331i	$0.364173\pi$
$228$		0			0
$229$		−	0.990583i		−	0.0654596i	−0.999464	−	0.0327298i	$-0.989580\pi$
$229$		−	0.990583i		−	0.0654596i	0.999464	−	0.0327298i	$-0.0104201\pi$
$230$	1.88578	−	1.20159i	0.124345	−	0.0792306i
$231$		0			0
$232$	4.71444	+	4.71444i	0.309518	+	0.309518i
$233$	−0.544993	−	0.544993i	−0.0357037	−	0.0357037i	0.689030	−	0.724733i	$-0.258037\pi$
$233$	−0.544993	−	0.544993i	−0.0357037	−	0.0357037i	−0.724733	+	0.689030i	$0.758037\pi$
$234$		0			0
$235$	−2.54912	+	11.5027i	−0.166286	+	0.750356i
$236$		−	12.5135i		−	0.814562i
$237$		0			0
$238$	−8.06271	+	8.06271i	−0.522628	+	0.522628i
$239$	3.55006			0.229634			0.114817	−	0.993387i	$-0.463372\pi$
$239$	3.55006			0.229634			0.114817	+	0.993387i	$0.463372\pi$
$240$		0			0
$241$	11.6363			0.749559			0.374779	−	0.927114i	$-0.377718\pi$
$241$	11.6363			0.749559			0.374779	+	0.927114i	$0.377718\pi$
$242$	−1.05695	+	1.05695i	−0.0679432	+	0.0679432i
$243$		0			0
$244$			13.2334i			0.847184i
$245$	−2.15953	−	3.38918i	−0.137967	−	0.216527i
$246$		0			0
$247$	−2.10664	−	2.10664i	−0.134042	−	0.134042i
$248$	−2.98732	−	2.98732i	−0.189695	−	0.189695i
$249$		0			0
$250$	−8.87162	−	6.80400i	−0.561090	−	0.430323i
$251$			4.06452i			0.256550i	0.991739	+	0.128275i	$0.0409440\pi$
$251$			4.06452i			0.256550i	−0.991739	+	0.128275i	$0.959056\pi$
$252$		0			0
$253$	2.49947	−	2.49947i	0.157141	−	0.157141i
$254$	−3.20269			−0.200955
$255$		0			0
$256$	1.00000			0.0625000
$257$	2.36495	−	2.36495i	0.147521	−	0.147521i	−0.629489	−	0.777010i	$-0.716736\pi$
$257$	2.36495	−	2.36495i	0.147521	−	0.147521i	0.777010	+	0.629489i	$0.216736\pi$
$258$		0			0
$259$			12.9728i			0.806088i
$260$	2.47042	+	0.547468i	0.153209	+	0.0339525i
$261$		0			0
$262$	13.7523	+	13.7523i	0.849618	+	0.849618i
$263$	−15.1129	−	15.1129i	−0.931899	−	0.931899i	0.0659252	−	0.997825i	$-0.479000\pi$
$263$	−15.1129	−	15.1129i	−0.931899	−	0.931899i	−0.997825	+	0.0659252i	$0.979000\pi$
$264$		0			0
$265$	−7.11063	−	1.57578i	−0.436802	−	0.0967996i
$266$		−	6.00518i		−	0.368201i
$267$		0			0
$268$	−5.47961	+	5.47961i	−0.334721	+	0.334721i
$269$	29.4567			1.79601			0.898003	−	0.439990i	$-0.145018\pi$
$269$	29.4567			1.79601			0.898003	+	0.439990i	$0.145018\pi$
$270$		0			0
$271$	2.13173			0.129493			0.0647466	−	0.997902i	$-0.479376\pi$
$271$	2.13173			0.129493			0.0647466	+	0.997902i	$0.479376\pi$
$272$	−3.53479	+	3.53479i	−0.214328	+	0.214328i
$273$		0			0
$274$		−	8.88017i		−	0.536471i
$275$	−16.0193	−	7.46674i	−0.965997	−	0.450261i
$276$		0			0
$277$	2.93330	+	2.93330i	0.176245	+	0.176245i	0.789717	−	0.613472i	$-0.210228\pi$
$277$	2.93330	+	2.93330i	0.176245	+	0.176245i	−0.613472	+	0.789717i	$0.710228\pi$
$278$	−9.77678	−	9.77678i	−0.586372	−	0.586372i
$279$		0			0
$280$	2.74078	+	4.30139i	0.163793	+	0.257057i
$281$		−	24.1823i		−	1.44259i	−0.692626	−	0.721297i	$-0.743546\pi$
$281$		−	24.1823i		−	1.44259i	0.692626	−	0.721297i	$-0.256454\pi$
$282$		0			0
$283$	18.6817	−	18.6817i	1.11051	−	1.11051i	0.117430	−	0.993081i	$-0.462534\pi$
$283$	18.6817	−	18.6817i	1.11051	−	1.11051i	0.993081	−	0.117430i	$-0.0374655\pi$
$284$	10.0890			0.598669
$285$		0			0
$286$	4.00000			0.236525
$287$	−0.809083	+	0.809083i	−0.0477587	+	0.0477587i
$288$		0			0
$289$		−	7.98950i		−	0.469971i
$290$	−3.22558	+	14.5553i	−0.189413	+	0.854714i
$291$		0			0
$292$	−9.57837	−	9.57837i	−0.560532	−	0.560532i
$293$	17.9980	+	17.9980i	1.05145	+	1.05145i	0.998602	+	0.0528496i	$0.0168304\pi$
$293$	17.9980	+	17.9980i	1.05145	+	1.05145i	0.0528496	+	0.998602i	$0.483170\pi$
$294$		0			0
$295$	23.5978	−	15.0362i	1.37392	−	0.875439i
$296$			5.68742i			0.330574i
$297$		0			0
$298$	−5.85921	+	5.85921i	−0.339415	+	0.339415i
$299$	−1.13161			−0.0654426
$300$		0			0
$301$	13.2655			0.764610
$302$	16.8784	−	16.8784i	0.971243	−	0.971243i
$303$		0			0
$304$		−	2.63274i		−	0.150998i
$305$	−24.9554	+	15.9012i	−1.42894	+	0.910499i
$306$		0			0
$307$	−4.33275	−	4.33275i	−0.247283	−	0.247283i	0.572572	−	0.819855i	$-0.305946\pi$
$307$	−4.33275	−	4.33275i	−0.247283	−	0.247283i	−0.819855	+	0.572572i	$0.805946\pi$
$308$	5.70120	+	5.70120i	0.324856	+	0.324856i
$309$		0			0
$310$	2.04390	−	9.22298i	0.116086	−	0.523830i
$311$			7.04031i			0.399219i	0.979876	+	0.199610i	$0.0639674\pi$
$311$			7.04031i			0.399219i	−0.979876	+	0.199610i	$0.936033\pi$
$312$		0			0
$313$	−2.61936	+	2.61936i	−0.148055	+	0.148055i	−0.777249	−	0.629194i	$-0.783385\pi$
$313$	−2.61936	+	2.61936i	−0.148055	+	0.148055i	0.629194	+	0.777249i	$0.283385\pi$
$314$	−16.1323			−0.910400
$315$		0			0
$316$	−0.108038			−0.00607758
$317$	15.3511	−	15.3511i	0.862205	−	0.862205i	−0.129389	−	0.991594i	$-0.541301\pi$
$317$	15.3511	−	15.3511i	0.862205	−	0.862205i	0.991594	+	0.129389i	$0.0413015\pi$
$318$		0			0
$319$			23.5673i			1.31951i
$320$	1.20159	+	1.88578i	0.0671710	+	0.105418i
$321$		0			0
$322$	−1.61288	−	1.61288i	−0.0898824	−	0.0898824i
$323$	9.30620	+	9.30620i	0.517811	+	0.517811i
$324$		0			0
$325$	1.93603	+	5.31651i	0.107391	+	0.294907i
$326$			15.7810i			0.874029i
$327$		0			0
$328$	−0.354712	+	0.354712i	−0.0195857	+	0.0195857i
$329$	12.0183			0.662593
$330$		0			0
$331$	−5.76374			−0.316804			−0.158402	−	0.987375i	$-0.550634\pi$
$331$	−5.76374			−0.316804			−0.158402	+	0.987375i	$0.550634\pi$
$332$	5.67903	−	5.67903i	0.311677	−	0.311677i
$333$		0			0
$334$		−	14.6511i		−	0.801675i
$335$	−16.9176	−	3.74911i	−0.924308	−	0.204836i
$336$		0			0
$337$	−5.22074	−	5.22074i	−0.284392	−	0.284392i	0.550466	−	0.834858i	$-0.314450\pi$
$337$	−5.22074	−	5.22074i	−0.284392	−	0.284392i	−0.834858	+	0.550466i	$0.814450\pi$
$338$	8.28691	+	8.28691i	0.450749	+	0.450749i
$339$		0			0
$340$	−10.9132	−	2.41848i	−0.591853	−	0.131160i
$341$		−	14.9335i		−	0.808693i
$342$		0			0
$343$	−14.1889	+	14.1889i	−0.766128	+	0.766128i
$344$	5.81575			0.313564
$345$		0			0
$346$	0.106637			0.00573283
$347$	9.78861	−	9.78861i	0.525480	−	0.525480i	−0.393741	−	0.919221i	$-0.628819\pi$
$347$	9.78861	−	9.78861i	0.525480	−	0.525480i	0.919221	+	0.393741i	$0.128819\pi$
$348$		0			0
$349$			31.1049i			1.66501i	0.554020	+	0.832503i	$0.313093\pi$
$349$			31.1049i			1.66501i	−0.554020	+	0.832503i	$0.686907\pi$
$350$	−4.81820	+	10.3370i	−0.257543	+	0.552538i
$351$		0			0
$352$	2.49947	+	2.49947i	0.133222	+	0.133222i
$353$	18.1179	+	18.1179i	0.964320	+	0.964320i	0.999385	−	0.0350648i	$-0.0111638\pi$
$353$	18.1179	+	18.1179i	0.964320	+	0.964320i	−0.0350648	+	0.999385i	$0.511164\pi$
$354$		0			0
$355$	12.1228	+	19.0256i	0.643411	+	1.00977i
$356$			3.06520i			0.162455i
$357$		0			0
$358$	0.353662	−	0.353662i	0.0186916	−	0.0186916i
$359$	−16.8454			−0.889066			−0.444533	−	0.895762i	$-0.646630\pi$
$359$	−16.8454			−0.889066			−0.444533	+	0.895762i	$0.646630\pi$
$360$		0			0
$361$	12.0687			0.635193
$362$	1.22250	−	1.22250i	0.0642533	−	0.0642533i
$363$		0			0
$364$		−	2.58115i		−	0.135289i
$365$	6.55344	−	29.5720i	0.343023	−	1.54787i
$366$		0			0
$367$	4.94668	+	4.94668i	0.258215	+	0.258215i	0.824328	−	0.566113i	$-0.191553\pi$
$367$	4.94668	+	4.94668i	0.258215	+	0.258215i	−0.566113	+	0.824328i	$0.691553\pi$
$368$	−0.707107	−	0.707107i	−0.0368605	−	0.0368605i
$369$		0			0
$370$	−10.7252	+	6.83395i	−0.557579	+	0.355280i
$371$			7.42935i			0.385713i
$372$		0			0
$373$	5.80694	−	5.80694i	0.300672	−	0.300672i	−0.540605	−	0.841277i	$-0.681805\pi$
$373$	5.80694	−	5.80694i	0.300672	−	0.300672i	0.841277	+	0.540605i	$0.181805\pi$
$374$	−17.6702			−0.913707
$375$		0			0
$376$	5.26899			0.271727
$377$	5.33490	−	5.33490i	0.274762	−	0.274762i
$378$		0			0
$379$		−	21.6706i		−	1.11314i	−0.830799	−	0.556572i	$-0.812116\pi$
$379$		−	21.6706i		−	1.11314i	0.830799	−	0.556572i	$-0.187884\pi$
$380$	4.96478	−	3.16348i	0.254688	−	0.162283i
$381$		0			0
$382$	12.6655	+	12.6655i	0.648023	+	0.648023i
$383$	18.7484	+	18.7484i	0.957998	+	0.957998i	0.999153	−	0.0411544i	$-0.0131036\pi$
$383$	18.7484	+	18.7484i	0.957998	+	0.957998i	−0.0411544	+	0.999153i	$0.513104\pi$
$384$		0			0
$385$	−3.90071	+	17.6017i	−0.198799	+	0.897068i
$386$		−	19.7975i		−	1.00767i
$387$		0			0
$388$	−7.17892	+	7.17892i	−0.364454	+	0.364454i
$389$	19.8325			1.00555			0.502774	−	0.864418i	$-0.332313\pi$
$389$	19.8325			1.00555			0.502774	+	0.864418i	$0.332313\pi$
$390$		0			0
$391$	4.99895			0.252808
$392$	−1.27083	+	1.27083i	−0.0641867	+	0.0641867i
$393$		0			0
$394$			9.90800i			0.499158i
$395$	−0.129817	−	0.203735i	−0.00653180	−	0.0102510i
$396$		0			0
$397$	5.69108	+	5.69108i	0.285627	+	0.285627i	0.835348	−	0.549721i	$-0.185266\pi$
$397$	5.69108	+	5.69108i	0.285627	+	0.285627i	−0.549721	+	0.835348i	$0.685266\pi$
$398$	4.91233	+	4.91233i	0.246233	+	0.246233i
$399$		0			0
$400$	−2.11236	+	4.53188i	−0.105618	+	0.226594i
$401$			16.6697i			0.832445i	0.909263	+	0.416222i	$0.136646\pi$
$401$			16.6697i			0.832445i	−0.909263	+	0.416222i	$0.863354\pi$
$402$		0			0
$403$	−3.38048	+	3.38048i	−0.168394	+	0.168394i
$404$	−12.0950			−0.601748
$405$		0			0
$406$	15.2077			0.754744
$407$	−14.2156	+	14.2156i	−0.704639	+	0.704639i
$408$		0			0
$409$			12.1836i			0.602440i	0.953555	+	0.301220i	$0.0973938\pi$
$409$			12.1836i			0.602440i	−0.953555	+	0.301220i	$0.902606\pi$
$410$	−1.09513	−	0.242691i	−0.0540845	−	0.0119857i
$411$		0			0
$412$	−11.1195	−	11.1195i	−0.547820	−	0.547820i
$413$	−20.1829	−	20.1829i	−0.993134	−	0.993134i
$414$		0			0
$415$	17.5333	+	3.88554i	0.860675	+	0.190734i
$416$		−	1.13161i		−	0.0554817i
$417$		0			0
$418$	6.58047	−	6.58047i	0.321862	−	0.321862i
$419$	21.9674			1.07318			0.536588	−	0.843844i	$-0.319713\pi$
$419$	21.9674			1.07318			0.536588	+	0.843844i	$0.319713\pi$
$420$		0			0
$421$	22.6091			1.10190			0.550949	−	0.834539i	$-0.314266\pi$
$421$	22.6091			1.10190			0.550949	+	0.834539i	$0.314266\pi$
$422$	7.17803	−	7.17803i	0.349421	−	0.349421i
$423$		0			0
$424$			3.25712i			0.158180i
$425$	−8.55252	−	23.4860i	−0.414858	−	1.13924i
$426$		0			0
$427$	21.3440	+	21.3440i	1.03291	+	1.03291i
$428$	−0.592532	−	0.592532i	−0.0286411	−	0.0286411i
$429$		0			0
$430$	6.98816	+	10.9672i	0.336999	+	0.528887i
$431$		−	1.54720i		−	0.0745260i	−0.999305	−	0.0372630i	$-0.988136\pi$
$431$		−	1.54720i		−	0.0745260i	0.999305	−	0.0372630i	$-0.0118639\pi$
$432$		0			0
$433$	5.99288	−	5.99288i	0.287999	−	0.287999i	−0.548289	−	0.836289i	$-0.684721\pi$
$433$	5.99288	−	5.99288i	0.287999	−	0.287999i	0.836289	+	0.548289i	$0.184721\pi$
$434$	−9.63639			−0.462562
$435$		0			0
$436$	4.85956			0.232731
$437$	−1.86163	+	1.86163i	−0.0890539	+	0.0890539i
$438$		0			0
$439$		−	9.83159i		−	0.469236i	−0.972088	−	0.234618i	$-0.924616\pi$
$439$		−	9.83159i		−	0.469236i	0.972088	−	0.234618i	$-0.0753839\pi$
$440$	−1.71012	+	7.71682i	−0.0815268	+	0.367885i
$441$		0			0
$442$	4.00000	+	4.00000i	0.190261	+	0.190261i
$443$	12.9526	+	12.9526i	0.615395	+	0.615395i	0.944347	−	0.328952i	$-0.106695\pi$
$443$	12.9526	+	12.9526i	0.615395	+	0.615395i	−0.328952	+	0.944347i	$0.606695\pi$
$444$		0			0
$445$	−5.78031	+	3.68312i	−0.274013	+	0.174597i
$446$			0.248080i			0.0117469i
$447$		0			0
$448$	1.61288	−	1.61288i	0.0762015	−	0.0762015i
$449$	23.7495			1.12081			0.560403	−	0.828220i	$-0.310646\pi$
$449$	23.7495			1.12081			0.560403	+	0.828220i	$0.310646\pi$
$450$		0			0
$451$	−1.77319			−0.0834961
$452$	10.0202	−	10.0202i	0.471312	−	0.471312i
$453$		0			0
$454$			10.5780i			0.496449i
$455$	4.86749	−	3.10149i	0.228192	−	0.145400i
$456$		0			0
$457$	−9.26532	−	9.26532i	−0.433414	−	0.433414i	0.456374	−	0.889788i	$-0.349148\pi$
$457$	−9.26532	−	9.26532i	−0.433414	−	0.433414i	−0.889788	+	0.456374i	$0.849148\pi$
$458$	−0.700448	−	0.700448i	−0.0327298	−	0.0327298i
$459$		0			0
$460$	0.483797	−	2.18310i	0.0225571	−	0.101788i
$461$		−	7.63694i		−	0.355688i	−0.984059	−	0.177844i	$-0.943088\pi$
$461$		−	7.63694i		−	0.355688i	0.984059	−	0.177844i	$-0.0569122\pi$
$462$		0			0
$463$	−13.7886	+	13.7886i	−0.640811	+	0.640811i	−0.950755	−	0.309944i	$-0.899690\pi$
$463$	−13.7886	+	13.7886i	−0.640811	+	0.640811i	0.309944	+	0.950755i	$0.399690\pi$
$464$	6.66723			0.309518
$465$		0			0
$466$	−0.770736			−0.0357037
$467$	23.4675	−	23.4675i	1.08595	−	1.08595i	0.0900068	−	0.995941i	$-0.471311\pi$
$467$	23.4675	−	23.4675i	1.08595	−	1.08595i	0.995941	−	0.0900068i	$-0.0286889\pi$
$468$		0			0
$469$			17.6759i			0.816199i
$470$	6.33117	+	9.93617i	0.292035	+	0.458321i
$471$		0			0
$472$	−8.84841	−	8.84841i	−0.407281	−	0.407281i
$473$	14.5363	+	14.5363i	0.668381	+	0.668381i
$474$		0			0
$475$	11.9313	+	5.56129i	0.547445	+	0.255170i
$476$			11.4024i			0.522628i
$477$		0			0
$478$	2.51027	−	2.51027i	0.114817	−	0.114817i
$479$	−30.3143			−1.38509			−0.692547	−	0.721373i	$-0.743512\pi$
$479$	−30.3143			−1.38509			−0.692547	+	0.721373i	$0.743512\pi$
$480$		0			0
$481$	6.43593			0.293453
$482$	8.22809	−	8.22809i	0.374779	−	0.374779i
$483$		0			0
$484$			1.49475i			0.0679432i
$485$	−22.1640	−	4.91176i	−1.00642	−	0.223031i
$486$		0			0
$487$	12.6493	+	12.6493i	0.573193	+	0.573193i	0.933019	−	0.359827i	$-0.117164\pi$
$487$	12.6493	+	12.6493i	0.573193	+	0.573193i	−0.359827	+	0.933019i	$0.617164\pi$
$488$	9.35745	+	9.35745i	0.423592	+	0.423592i
$489$		0			0
$490$	−3.92353	−	0.869493i	−0.177247	−	0.0392797i
$491$			37.8083i			1.70626i	0.521695	+	0.853132i	$0.325300\pi$
$491$			37.8083i			1.70626i	−0.521695	+	0.853132i	$0.674700\pi$
$492$		0			0
$493$	−23.5673	+	23.5673i	−1.06142	+	1.06142i
$494$	−2.97923			−0.134042
$495$		0			0
$496$	−4.22471			−0.189695
$497$	16.2723	−	16.2723i	0.729912	−	0.729912i
$498$		0			0
$499$			27.8424i			1.24640i	0.782063	+	0.623199i	$0.214167\pi$
$499$			27.8424i			1.24640i	−0.782063	+	0.623199i	$0.785833\pi$
$500$	−11.0843	+	1.46202i	−0.495707	+	0.0653837i
$501$		0			0
$502$	2.87405	+	2.87405i	0.128275	+	0.128275i
$503$	−2.38940	−	2.38940i	−0.106538	−	0.106538i	0.651828	−	0.758367i	$-0.274002\pi$
$503$	−2.38940	−	2.38940i	−0.106538	−	0.106538i	−0.758367	+	0.651828i	$0.774002\pi$
$504$		0			0
$505$	−14.5332	−	22.8085i	−0.646720	−	1.01497i
$506$		−	3.53479i		−	0.157141i
$507$		0			0
$508$	−2.26465	+	2.26465i	−0.100477	+	0.100477i
$509$	18.3476			0.813242			0.406621	−	0.913597i	$-0.366707\pi$
$509$	18.3476			0.813242			0.406621	+	0.913597i	$0.366707\pi$
$510$		0			0
$511$	−30.8976			−1.36683
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$		−	3.34454i		−	0.147521i
$515$	7.60789	−	34.3302i	0.335244	−	1.51277i
$516$		0			0
$517$	13.1697	+	13.1697i	0.579203	+	0.579203i
$518$	9.17313	+	9.17313i	0.403044	+	0.403044i
$519$		0			0
$520$	2.13397	−	1.35973i	0.0935807	−	0.0596282i
$521$			5.35895i			0.234780i	0.993086	+	0.117390i	$0.0374527\pi$
$521$			5.35895i			0.234780i	−0.993086	+	0.117390i	$0.962547\pi$
$522$		0			0
$523$	−6.40538	+	6.40538i	−0.280088	+	0.280088i	−0.833144	−	0.553056i	$-0.813461\pi$
$523$	−6.40538	+	6.40538i	−0.280088	+	0.280088i	0.553056	+	0.833144i	$0.313461\pi$
$524$	19.4487			0.849618
$525$		0			0
$526$	−21.3728			−0.931899
$527$	14.9335	−	14.9335i	0.650512	−	0.650512i
$528$		0			0
$529$			1.00000i			0.0434783i
$530$	−6.14222	+	3.91373i	−0.266801	+	0.170001i
$531$		0			0
$532$	−4.24630	−	4.24630i	−0.184101	−	0.184101i
$533$	0.401395	+	0.401395i	0.0173863	+	0.0173863i
$534$		0			0
$535$	0.405405	−	1.82937i	0.0175272	−	0.0790905i
$536$			7.74934i			0.334721i
$537$		0			0
$538$	20.8290	−	20.8290i	0.898003	−	0.898003i
$539$	−6.35282			−0.273635
$540$		0			0
$541$	−22.8297			−0.981526			−0.490763	−	0.871293i	$-0.663282\pi$
$541$	−22.8297			−0.981526			−0.490763	+	0.871293i	$0.663282\pi$
$542$	1.50736	−	1.50736i	0.0647466	−	0.0647466i
$543$		0			0
$544$			4.99895i			0.214328i
$545$	5.83920	+	9.16407i	0.250124	+	0.392546i
$546$		0			0
$547$	−6.55956	−	6.55956i	−0.280467	−	0.280467i	0.552828	−	0.833295i	$-0.313548\pi$
$547$	−6.55956	−	6.55956i	−0.280467	−	0.280467i	−0.833295	+	0.552828i	$0.813548\pi$
$548$	−6.27923	−	6.27923i	−0.268235	−	0.268235i
$549$		0			0
$550$	−16.6071	+	6.04754i	−0.708129	+	0.257868i
$551$		−	17.5531i		−	0.747787i
$552$		0			0
$553$	−0.174252	+	0.174252i	−0.00740993	+	0.00740993i
$554$	4.14831			0.176245
$555$		0			0
$556$	−13.8264			−0.586372
$557$	27.2379	−	27.2379i	1.15411	−	1.15411i	0.168386	−	0.985721i	$-0.446144\pi$
$557$	27.2379	−	27.2379i	1.15411	−	1.15411i	0.985721	−	0.168386i	$-0.0538556\pi$
$558$		0			0
$559$		−	6.58115i		−	0.278353i
$560$	4.97957	+	1.10352i	0.210425	+	0.0466322i
$561$		0			0
$562$	−17.0995	−	17.0995i	−0.721297	−	0.721297i
$563$	−3.21571	−	3.21571i	−0.135526	−	0.135526i	0.636089	−	0.771615i	$-0.280551\pi$
$563$	−3.21571	−	3.21571i	−0.135526	−	0.135526i	−0.771615	+	0.636089i	$0.780551\pi$
$564$		0			0
$565$	30.9362	+	6.85576i	1.30150	+	0.288424i
$566$		−	26.4199i		−	1.11051i
$567$		0			0
$568$	7.13397	−	7.13397i	0.299335	−	0.299335i
$569$	21.6013			0.905573			0.452786	−	0.891619i	$-0.350430\pi$
$569$	21.6013			0.905573			0.452786	+	0.891619i	$0.350430\pi$
$570$		0			0
$571$	7.72370			0.323227			0.161613	−	0.986854i	$-0.448330\pi$
$571$	7.72370			0.323227			0.161613	+	0.986854i	$0.448330\pi$
$572$	2.82843	−	2.82843i	0.118262	−	0.118262i
$573$		0			0
$574$			1.14422i			0.0477587i
$575$	4.69819	−	1.71086i	0.195928	−	0.0713479i
$576$		0			0
$577$	−21.9276	−	21.9276i	−0.912857	−	0.912857i	0.0836391	−	0.996496i	$-0.473346\pi$
$577$	−21.9276	−	21.9276i	−0.912857	−	0.912857i	−0.996496	+	0.0836391i	$0.973346\pi$
$578$	−5.64943	−	5.64943i	−0.234985	−	0.234985i
$579$		0			0
$580$	8.01129	+	12.5729i	0.332651	+	0.522063i
$581$		−	18.3192i		−	0.760008i
$582$		0			0
$583$	−8.14109	+	8.14109i	−0.337169	+	0.337169i
$584$	−13.5459			−0.560532
$585$		0			0
$586$	25.4530			1.05145
$587$	0.700257	−	0.700257i	0.0289027	−	0.0289027i	−0.692508	−	0.721410i	$-0.743494\pi$
$587$	0.700257	−	0.700257i	0.0289027	−	0.0289027i	0.721410	+	0.692508i	$0.243494\pi$
$588$		0			0
$589$			11.1226i			0.458298i
$590$	6.05401	−	27.3184i	0.249240	−	1.12468i
$591$		0			0
$592$	4.02161	+	4.02161i	0.165287	+	0.165287i
$593$	−20.1495	−	20.1495i	−0.827442	−	0.827442i	0.159720	−	0.987162i	$-0.448941\pi$
$593$	−20.1495	−	20.1495i	−0.827442	−	0.827442i	−0.987162	+	0.159720i	$0.948941\pi$
$594$		0			0
$595$	−21.5025	+	13.7010i	−0.881515	+	0.561687i
$596$			8.28617i			0.339415i
$597$		0			0
$598$	−0.800168	+	0.800168i	−0.0327213	+	0.0327213i
$599$	−23.1574			−0.946186			−0.473093	−	0.881012i	$-0.656863\pi$
$599$	−23.1574			−0.946186			−0.473093	+	0.881012i	$0.656863\pi$
$600$		0			0
$601$	−38.6669			−1.57726			−0.788628	−	0.614871i	$-0.789208\pi$
$601$	−38.6669			−1.57726			−0.788628	+	0.614871i	$0.789208\pi$
$602$	9.38011	−	9.38011i	0.382305	−	0.382305i
$603$		0			0
$604$		−	23.8697i		−	0.971243i
$605$	−2.81877	+	1.79608i	−0.114599	+	0.0730210i
$606$		0			0
$607$	−30.0848	−	30.0848i	−1.22110	−	1.22110i	−0.967240	−	0.253865i	$-0.918298\pi$
$607$	−30.0848	−	30.0848i	−1.22110	−	1.22110i	−0.253865	−	0.967240i	$-0.581702\pi$
$608$	−1.86163	−	1.86163i	−0.0754991	−	0.0754991i
$609$		0			0
$610$	−6.40229	+	28.8899i	−0.259221	+	1.16972i
$611$		−	5.96243i		−	0.241214i
$612$		0			0
$613$	10.7603	−	10.7603i	0.434604	−	0.434604i	−0.455587	−	0.890191i	$-0.650571\pi$
$613$	10.7603	−	10.7603i	0.434604	−	0.434604i	0.890191	+	0.455587i	$0.150571\pi$
$614$	−6.12743			−0.247283
$615$		0			0
$616$	8.06271			0.324856
$617$	7.03135	−	7.03135i	0.283071	−	0.283071i	−0.551261	−	0.834333i	$-0.685853\pi$
$617$	7.03135	−	7.03135i	0.283071	−	0.283071i	0.834333	+	0.551261i	$0.185853\pi$
$618$		0			0
$619$			27.1742i			1.09222i	0.837713	+	0.546111i	$0.183892\pi$
$619$			27.1742i			1.09222i	−0.837713	+	0.546111i	$0.816108\pi$
$620$	−5.07638	−	7.96689i	−0.203872	−	0.319958i
$621$		0			0
$622$	4.97825	+	4.97825i	0.199610	+	0.199610i
$623$	4.94381	+	4.94381i	0.198069	+	0.198069i
$624$		0			0
$625$	−16.0759	−	19.1459i	−0.643036	−	0.765836i
$626$			3.70433i			0.148055i
$627$		0			0
$628$	−11.4073	+	11.4073i	−0.455200	+	0.455200i
$629$	−28.4311			−1.13362
$630$		0			0
$631$	−1.07800			−0.0429146			−0.0214573	−	0.999770i	$-0.506831\pi$
$631$	−1.07800			−0.0429146			−0.0214573	+	0.999770i	$0.506831\pi$
$632$	−0.0763940	+	0.0763940i	−0.00303879	+	0.00303879i
$633$		0			0
$634$		−	21.7098i		−	0.862205i
$635$	−6.99181	−	1.54945i	−0.277461	−	0.0614881i
$636$		0			0
$637$	1.43808	+	1.43808i	0.0569790	+	0.0569790i
$638$	16.6646	+	16.6646i	0.659757	+	0.659757i
$639$		0			0
$640$	2.18310	+	0.483797i	0.0862947	+	0.0191237i
$641$		−	9.94612i		−	0.392848i	−0.980519	−	0.196424i	$-0.937067\pi$
$641$		−	9.94612i		−	0.392848i	0.980519	−	0.196424i	$-0.0629329\pi$
$642$		0			0
$643$	22.5664	−	22.5664i	0.889931	−	0.889931i	−0.104585	−	0.994516i	$-0.533352\pi$
$643$	22.5664	−	22.5664i	0.889931	−	0.889931i	0.994516	+	0.104585i	$0.0333515\pi$
$644$	−2.28096			−0.0898824
$645$		0			0
$646$	13.1609			0.517811
$647$	11.7501	−	11.7501i	0.461943	−	0.461943i	−0.437349	−	0.899292i	$-0.644083\pi$
$647$	11.7501	−	11.7501i	0.461943	−	0.461943i	0.899292	+	0.437349i	$0.144083\pi$
$648$		0			0
$649$		−	44.2328i		−	1.73629i
$650$	5.12832	+	2.39036i	0.201149	+	0.0937576i
$651$		0			0
$652$	11.1588	+	11.1588i	0.437014	+	0.437014i
$653$	−33.7171	−	33.7171i	−1.31945	−	1.31945i	−0.914210	−	0.405240i	$-0.867188\pi$
$653$	−33.7171	−	33.7171i	−1.31945	−	1.31945i	−0.405240	−	0.914210i	$-0.632812\pi$
$654$		0			0
$655$	23.3693	+	36.6759i	0.913116	+	1.43305i
$656$			0.501638i			0.0195857i
$657$		0			0
$658$	8.49825	−	8.49825i	0.331296	−	0.331296i
$659$	3.68407			0.143511			0.0717554	−	0.997422i	$-0.477140\pi$
$659$	3.68407			0.143511			0.0717554	+	0.997422i	$0.477140\pi$
$660$		0			0
$661$	−35.4206			−1.37770			−0.688851	−	0.724903i	$-0.741884\pi$
$661$	−35.4206			−1.37770			−0.688851	+	0.724903i	$0.741884\pi$
$662$	−4.07558	+	4.07558i	−0.158402	+	0.158402i
$663$		0			0
$664$		−	8.03136i		−	0.311677i
$665$	2.90528	−	13.1099i	0.112662	−	0.508381i
$666$		0			0
$667$	−4.71444	−	4.71444i	−0.182544	−	0.182544i
$668$	−10.3599	−	10.3599i	−0.400838	−	0.400838i
$669$		0			0
$670$	−14.6136	+	9.31154i	−0.564572	+	0.359736i
$671$			46.7774i			1.80582i
$672$		0			0
$673$	−5.92268	+	5.92268i	−0.228302	+	0.228302i	−0.811983	−	0.583681i	$-0.801612\pi$
$673$	−5.92268	+	5.92268i	−0.228302	+	0.228302i	0.583681	+	0.811983i	$0.301612\pi$
$674$	−7.38325			−0.284392
$675$		0			0
$676$	11.7195			0.450749
$677$	35.5674	−	35.5674i	1.36697	−	1.36697i	0.502238	−	0.864729i	$-0.332510\pi$
$677$	35.5674	−	35.5674i	1.36697	−	1.36697i	0.864729	−	0.502238i	$-0.167490\pi$
$678$		0			0
$679$			23.1575i			0.888703i
$680$	−9.42694	+	6.00670i	−0.361506	+	0.230346i
$681$		0			0
$682$	−10.5596	−	10.5596i	−0.404347	−	0.404347i
$683$	−35.4420	−	35.4420i	−1.35615	−	1.35615i	−0.878611	−	0.477538i	$-0.841529\pi$
$683$	−35.4420	−	35.4420i	−1.35615	−	1.35615i	−0.477538	−	0.878611i	$-0.658471\pi$
$684$		0			0
$685$	4.29620	−	19.3863i	0.164149	−	0.740714i
$686$			20.0661i			0.766128i
$687$		0			0
$688$	4.11236	−	4.11236i	0.156782	−	0.156782i
$689$	3.68578			0.140417
$690$		0			0
$691$	37.8836			1.44116			0.720580	−	0.693372i	$-0.243876\pi$
$691$	37.8836			1.44116			0.720580	+	0.693372i	$0.243876\pi$
$692$	0.0754036	−	0.0754036i	0.00286641	−	0.00286641i
$693$		0			0
$694$		−	13.8432i		−	0.525480i
$695$	−16.6137	−	26.0737i	−0.630195	−	0.989031i
$696$		0			0
$697$	−1.77319	−	1.77319i	−0.0671642	−	0.0671642i
$698$	21.9945	+	21.9945i	0.832503	+	0.832503i
$699$		0			0
$700$	3.90241	+	10.7164i	0.147497	+	0.405041i
$701$			43.6828i			1.64988i	0.565222	+	0.824939i	$0.308791\pi$
$701$			43.6828i			1.64988i	−0.565222	+	0.824939i	$0.691209\pi$
$702$		0			0
$703$	10.5879	−	10.5879i	0.399329	−	0.399329i
$704$	3.53479			0.133222
$705$		0			0
$706$	25.6226			0.964320
$707$	−19.5078	+	19.5078i	−0.733665	+	0.733665i
$708$		0			0
$709$			24.9488i			0.936970i	0.883471	+	0.468485i	$0.155200\pi$
$709$			24.9488i			0.936970i	−0.883471	+	0.468485i	$0.844800\pi$
$710$	22.0252	+	4.88100i	0.826592	+	0.183181i
$711$		0			0
$712$	2.16743	+	2.16743i	0.0812277	+	0.0812277i
$713$	2.98732	+	2.98732i	0.111876	+	0.111876i
$714$		0			0
$715$	8.73241	+	1.93519i	0.326574	+	0.0723719i
$716$		−	0.500153i		−	0.0186916i
$717$		0			0
$718$	−11.9115	+	11.9115i	−0.444533	+	0.444533i
$719$	3.27211			0.122029			0.0610145	−	0.998137i	$-0.480566\pi$
$719$	3.27211			0.122029			0.0610145	+	0.998137i	$0.480566\pi$
$720$		0			0
$721$	−35.8690			−1.33583
$722$	8.53383	−	8.53383i	0.317596	−	0.317596i
$723$		0			0
$724$		−	1.72888i		−	0.0642533i
$725$	−14.0836	+	30.2151i	−0.523050	+	1.12216i
$726$		0			0
$727$	0.698234	+	0.698234i	0.0258961	+	0.0258961i	0.719936	−	0.694040i	$-0.244171\pi$
$727$	0.698234	+	0.698234i	0.0258961	+	0.0258961i	−0.694040	+	0.719936i	$0.744171\pi$
$728$	−1.82515	−	1.82515i	−0.0676446	−	0.0676446i
$729$		0			0
$730$	−16.2766	−	25.5446i	−0.602424	−	0.945447i
$731$			29.0726i			1.07529i
$732$		0			0
$733$	−26.1581	+	26.1581i	−0.966171	+	0.966171i	−0.999446	−	0.0332750i	$-0.989406\pi$
$733$	−26.1581	+	26.1581i	−0.966171	+	0.966171i	0.0332750	+	0.999446i	$0.489406\pi$
$734$	6.99566			0.258215
$735$		0			0
$736$	−1.00000			−0.0368605
$737$	−19.3693	+	19.3693i	−0.713477	+	0.713477i
$738$		0			0
$739$		−	21.9979i		−	0.809206i	−0.914492	−	0.404603i	$-0.867410\pi$
$739$		−	21.9979i		−	0.809206i	0.914492	−	0.404603i	$-0.132590\pi$
$740$	−2.75155	+	12.4162i	−0.101149	+	0.456429i
$741$		0			0
$742$	5.25335	+	5.25335i	0.192856	+	0.192856i
$743$	11.4363	+	11.4363i	0.419559	+	0.419559i	0.885052	−	0.465493i	$-0.154123\pi$
$743$	11.4363	+	11.4363i	0.419559	+	0.419559i	−0.465493	+	0.885052i	$0.654123\pi$
$744$		0			0
$745$	−15.6259	+	9.95659i	−0.572489	+	0.364781i
$746$		−	8.21225i		−	0.300672i
$747$		0			0
$748$	−12.4947	+	12.4947i	−0.456853	+	0.456853i
$749$	−1.91137			−0.0698398
$750$		0			0
$751$	30.2815			1.10499			0.552495	−	0.833516i	$-0.313676\pi$
$751$	30.2815			1.10499			0.552495	+	0.833516i	$0.313676\pi$
$752$	3.72574	−	3.72574i	0.135864	−	0.135864i
$753$		0			0
$754$		−	7.54469i		−	0.274762i
$755$	45.0130	−	28.6816i	1.63819	−	1.04383i
$756$		0			0
$757$	9.28391	+	9.28391i	0.337430	+	0.337430i	0.855399	−	0.517970i	$-0.173312\pi$
$757$	9.28391	+	9.28391i	0.337430	+	0.337430i	−0.517970	+	0.855399i	$0.673312\pi$
$758$	−15.3234	−	15.3234i	−0.556572	−	0.556572i
$759$		0			0
$760$	1.27371	−	5.74755i	0.0462024	−	0.208486i
$761$			48.1847i			1.74669i	0.487100	+	0.873346i	$0.338055\pi$
$761$			48.1847i			1.74669i	−0.487100	+	0.873346i	$0.661945\pi$
$762$		0			0
$763$	7.83789	−	7.83789i	0.283751	−	0.283751i
$764$	17.9117			0.648023
$765$		0			0
$766$	26.5142			0.957998
$767$	−10.0129	+	10.0129i	−0.361546	+	0.361546i
$768$		0			0
$769$			18.5877i			0.670291i	0.942166	+	0.335145i	$0.108785\pi$
$769$			18.5877i			0.670291i	−0.942166	+	0.335145i	$0.891215\pi$
$770$	9.68809	+	15.2045i	0.349134	+	0.547933i
$771$		0			0
$772$	−13.9989	−	13.9989i	−0.503833	−	0.503833i
$773$	−0.879146	−	0.879146i	−0.0316207	−	0.0316207i	0.691120	−	0.722740i	$-0.257118\pi$
$773$	−0.879146	−	0.879146i	−0.0316207	−	0.0316207i	−0.722740	+	0.691120i	$0.757118\pi$
$774$		0			0
$775$	8.92410	−	19.1459i	0.320563	−	0.687741i
$776$			10.1525i			0.364454i
$777$		0			0
$778$	14.0237	−	14.0237i	0.502774	−	0.502774i
$779$	1.32068			0.0473184
$780$		0			0
$781$	35.6623			1.27610
$782$	3.53479	−	3.53479i	0.126404	−	0.126404i
$783$		0			0
$784$			1.79723i			0.0641867i
$785$	−35.2185	−	7.80476i	−1.25700	−	0.278564i
$786$		0			0
$787$	2.33598	+	2.33598i	0.0832689	+	0.0832689i	0.747514	−	0.664246i	$-0.231247\pi$
$787$	2.33598	+	2.33598i	0.0832689	+	0.0832689i	−0.664246	+	0.747514i	$0.731247\pi$
$788$	7.00601	+	7.00601i	0.249579	+	0.249579i
$789$		0			0
$790$	−0.235857	−	0.0522682i	−0.00839142	−	0.00185962i
$791$		−	32.3229i		−	1.14927i
$792$		0			0
$793$	10.5890	−	10.5890i	0.376025	−	0.376025i
$794$	8.04840			0.285627
$795$		0			0
$796$	6.94709			0.246233
$797$	−35.3851	+	35.3851i	−1.25340	+	1.25340i	−0.299221	+	0.954184i	$0.596727\pi$
$797$	−35.3851	+	35.3851i	−1.25340	+	1.25340i	−0.954184	+	0.299221i	$0.903273\pi$
$798$		0			0
$799$			26.3394i			0.931821i
$800$	1.71086	+	4.69819i	0.0604881	+	0.166106i
$801$		0			0
$802$	11.7873	+	11.7873i	0.416222	+	0.416222i
$803$	−33.8576	−	33.8576i	−1.19481	−	1.19481i
$804$		0			0
$805$	−2.74078	−	4.30139i	−0.0965998	−	0.151604i
$806$			4.78072i			0.168394i
$807$		0			0
$808$	−8.55244	+	8.55244i	−0.300874	+	0.300874i
$809$	−20.5766			−0.723436			−0.361718	−	0.932288i	$-0.617810\pi$
$809$	−20.5766			−0.723436			−0.361718	+	0.932288i	$0.617810\pi$
$810$		0			0
$811$	−14.4264			−0.506581			−0.253290	−	0.967390i	$-0.581513\pi$
$811$	−14.4264			−0.506581			−0.253290	+	0.967390i	$0.581513\pi$
$812$	10.7534	−	10.7534i	0.377372	−	0.377372i
$813$		0			0
$814$			20.1038i			0.704639i
$815$	−7.63479	+	34.4515i	−0.267435	+	1.20679i
$816$		0			0
$817$	−10.8268	−	10.8268i	−0.378781	−	0.378781i
$818$	8.61510	+	8.61510i	0.301220	+	0.301220i
$819$		0			0
$820$	−0.945981	+	0.602764i	−0.0330351	+	0.0210494i
$821$			46.4913i			1.62256i	0.584659	+	0.811279i	$0.301228\pi$
$821$			46.4913i			1.62256i	−0.584659	+	0.811279i	$0.698772\pi$
$822$		0			0
$823$	32.9684	−	32.9684i	1.14921	−	1.14921i	0.162496	−	0.986709i	$-0.448045\pi$
$823$	32.9684	−	32.9684i	1.14921	−	1.14921i	0.986709	−	0.162496i	$-0.0519545\pi$
$824$	−15.7254			−0.547820
$825$		0			0
$826$	−28.5429			−0.993134
$827$	−5.53139	+	5.53139i	−0.192345	+	0.192345i	−0.796709	−	0.604364i	$-0.793427\pi$
$827$	−5.53139	+	5.53139i	−0.192345	+	0.192345i	0.604364	+	0.796709i	$0.293427\pi$
$828$		0			0
$829$			53.6875i			1.86464i	0.361630	+	0.932322i	$0.382220\pi$
$829$			53.6875i			1.86464i	−0.361630	+	0.932322i	$0.617780\pi$
$830$	15.1454	−	9.65041i	0.525704	−	0.334971i
$831$		0			0
$832$	−0.800168	−	0.800168i	−0.0277408	−	0.0277408i
$833$	−6.35282	−	6.35282i	−0.220112	−	0.220112i
$834$		0			0
$835$	7.08818	−	31.9850i	0.245296	−	1.10689i
$836$		−	9.30620i		−	0.321862i
$837$		0			0
$838$	15.5333	−	15.5333i	0.536588	−	0.536588i
$839$	−7.53085			−0.259994			−0.129997	−	0.991514i	$-0.541497\pi$
$839$	−7.53085			−0.259994			−0.129997	+	0.991514i	$0.541497\pi$
$840$		0			0
$841$	15.4519			0.532826
$842$	15.9870	−	15.9870i	0.550949	−	0.550949i
$843$		0			0
$844$		−	10.1513i		−	0.349421i
$845$	14.0820	+	22.1004i	0.484436	+	0.760276i
$846$		0			0
$847$	2.41085	+	2.41085i	0.0828379	+	0.0828379i
$848$	2.30313	+	2.30313i	0.0790898	+	0.0790898i
$849$		0			0
$850$	−22.6546	−	10.5596i	−0.777048	−	0.362190i
$851$		−	5.68742i		−	0.194962i
$852$		0			0
$853$	−18.1305	+	18.1305i	−0.620775	+	0.620775i	−0.945730	−	0.324954i	$-0.894651\pi$
$853$	−18.1305	+	18.1305i	−0.620775	+	0.620775i	0.324954	+	0.945730i	$0.394651\pi$
$854$	30.1849			1.03291
$855$		0			0
$856$	−0.837966			−0.0286411
$857$	−7.42858	+	7.42858i	−0.253756	+	0.253756i	−0.822508	−	0.568753i	$-0.807426\pi$
$857$	−7.42858	+	7.42858i	−0.253756	+	0.253756i	0.568753	+	0.822508i	$0.307426\pi$
$858$		0			0
$859$		−	32.7031i		−	1.11582i	−0.829903	−	0.557908i	$-0.811604\pi$
$859$		−	32.7031i		−	1.11582i	0.829903	−	0.557908i	$-0.188396\pi$
$860$	12.6964	+	2.81364i	0.432943	+	0.0959443i
$861$		0			0
$862$	−1.09404	−	1.09404i	−0.0372630	−	0.0372630i
$863$	−1.87770	−	1.87770i	−0.0639175	−	0.0639175i	0.674425	−	0.738343i	$-0.264391\pi$
$863$	−1.87770	−	1.87770i	−0.0639175	−	0.0639175i	−0.738343	+	0.674425i	$0.764391\pi$
$864$		0			0
$865$	0.232799	+	0.0515905i	0.00791541	+	0.00175413i
$866$		−	8.47521i		−	0.287999i
$867$		0			0
$868$	−6.81396	+	6.81396i	−0.231281	+	0.231281i
$869$	−0.381890			−0.0129547
$870$		0			0
$871$	8.76922			0.297134
$872$	3.43622	−	3.43622i	0.116365	−	0.116365i
$873$		0			0
$874$			2.63274i			0.0890539i
$875$	−15.5196	+	20.2358i	−0.524660	+	0.684095i
$876$		0			0
$877$	−15.6766	−	15.6766i	−0.529360	−	0.529360i	0.391022	−	0.920381i	$-0.372122\pi$
$877$	−15.6766	−	15.6766i	−0.529360	−	0.529360i	−0.920381	+	0.391022i	$0.872122\pi$
$878$	−6.95198	−	6.95198i	−0.234618	−	0.234618i
$879$		0			0
$880$	4.24737	+	6.66585i	0.143179	+	0.224706i
$881$		−	17.2472i		−	0.581072i	−0.956864	−	0.290536i	$-0.906166\pi$
$881$		−	17.2472i		−	0.581072i	0.956864	−	0.290536i	$-0.0938336\pi$
$882$		0			0
$883$	18.3941	−	18.3941i	0.619009	−	0.619009i	−0.326268	−	0.945277i	$-0.605791\pi$
$883$	18.3941	−	18.3941i	0.619009	−	0.619009i	0.945277	+	0.326268i	$0.105791\pi$
$884$	5.65685			0.190261
$885$		0			0
$886$	18.3177			0.615395
$887$	−17.9950	+	17.9950i	−0.604213	+	0.604213i	−0.941428	−	0.337214i	$-0.890515\pi$
$887$	−17.9950	+	17.9950i	−0.604213	+	0.604213i	0.337214	+	0.941428i	$0.390515\pi$
$888$		0			0
$889$			7.30521i			0.245009i
$890$	−1.48293	+	6.69165i	−0.0497081	+	0.224305i
$891$		0			0
$892$	0.175419	+	0.175419i	0.00587347	+	0.00587347i
$893$	−9.80891	−	9.80891i	−0.328243	−	0.328243i
$894$		0			0
$895$	0.943180	−	0.600980i	0.0315270	−	0.0200885i
$896$		−	2.28096i		−	0.0762015i
$897$		0			0
$898$	16.7934	−	16.7934i	0.560403	−	0.560403i
$899$	−28.1671			−0.939426
$900$		0			0
$901$	−16.2822			−0.542438
$902$	−1.25383	+	1.25383i	−0.0417481	+	0.0417481i
$903$		0			0
$904$		−	14.1708i		−	0.471312i
$905$	3.26029	−	2.07741i	0.108376	−	0.0690553i
$906$		0			0
$907$	−15.6868	−	15.6868i	−0.520871	−	0.520871i	0.396963	−	0.917835i	$-0.370064\pi$
$907$	−15.6868	−	15.6868i	−0.520871	−	0.520871i	−0.917835	+	0.396963i	$0.870064\pi$
$908$	7.47975	+	7.47975i	0.248224	+	0.248224i
$909$		0			0
$910$	1.24875	−	5.63492i	0.0413958	−	0.186796i
$911$			5.22176i			0.173005i	0.996252	+	0.0865023i	$0.0275690\pi$
$911$			5.22176i			0.173005i	−0.996252	+	0.0865023i	$0.972431\pi$
$912$		0			0
$913$	20.0742	−	20.0742i	0.664358	−	0.664358i
$914$	−13.1031			−0.433414
$915$		0			0
$916$	−0.990583			−0.0327298
$917$	31.3684	−	31.3684i	1.03587	−	1.03587i
$918$		0			0
$919$		−	31.7484i		−	1.04728i	−0.851939	−	0.523642i	$-0.824573\pi$
$919$		−	31.7484i		−	1.04728i	0.851939	−	0.523642i	$-0.175427\pi$
$920$	−1.20159	−	1.88578i	−0.0396153	−	0.0621724i
$921$		0			0
$922$	−5.40013	−	5.40013i	−0.177844	−	0.177844i
$923$	−8.07286	−	8.07286i	−0.265721	−	0.265721i
$924$		0			0
$925$	−26.7205	+	9.73039i	−0.878566	+	0.319933i
$926$			19.5000i			0.640811i
$927$		0			0
$928$	4.71444	−	4.71444i	0.154759	−	0.154759i
$929$	−33.8766			−1.11145			−0.555727	−	0.831365i	$-0.687560\pi$
$929$	−33.8766			−1.11145			−0.555727	+	0.831365i	$0.687560\pi$
$930$		0			0
$931$	4.73164			0.155073
$932$	−0.544993	+	0.544993i	−0.0178518	+	0.0178518i
$933$		0			0
$934$		−	33.1881i		−	1.08595i
$935$	−38.5760	−	8.54880i	−1.26157	−	0.279576i
$936$		0			0
$937$	−26.3824	−	26.3824i	−0.861875	−	0.861875i	0.129681	−	0.991556i	$-0.458605\pi$
$937$	−26.3824	−	26.3824i	−0.861875	−	0.861875i	−0.991556	+	0.129681i	$0.958605\pi$
$938$	12.4988	+	12.4988i	0.408099	+	0.408099i
$939$		0			0
$940$	11.5027	+	2.54912i	0.375178	+	0.0831431i
$941$		−	54.2994i		−	1.77011i	−0.465487	−	0.885055i	$-0.654121\pi$
$941$		−	54.2994i		−	1.77011i	0.465487	−	0.885055i	$-0.345879\pi$
$942$		0			0
$943$	0.354712	−	0.354712i	0.0115510	−	0.0115510i
$944$	−12.5135			−0.407281
$945$		0			0
$946$	20.5575			0.668381
$947$	−40.0242	+	40.0242i	−1.30061	+	1.30061i	−0.372632	+	0.927979i	$0.621545\pi$
$947$	−40.0242	+	40.0242i	−1.30061	+	1.30061i	−0.927979	+	0.372632i	$0.878455\pi$
$948$		0			0
$949$			15.3286i			0.497588i
$950$	12.3691	−	4.50426i	0.401307	−	0.146138i
$951$		0			0
$952$	8.06271	+	8.06271i	0.261314	+	0.261314i
$953$	1.64340	+	1.64340i	0.0532348	+	0.0532348i	0.733223	−	0.679988i	$-0.238015\pi$
$953$	1.64340	+	1.64340i	0.0532348	+	0.0532348i	−0.679988	+	0.733223i	$0.738015\pi$
$954$		0			0
$955$	21.5226	+	33.7776i	0.696454	+	1.09302i
$956$		−	3.55006i		−	0.114817i
$957$		0			0
$958$	−21.4354	+	21.4354i	−0.692547	+	0.692547i
$959$	−20.2553			−0.654078
$960$		0			0
$961$	−13.1518			−0.424252
$962$	4.55089	−	4.55089i	0.146727	−	0.146727i
$963$		0			0
$964$		−	11.6363i		−	0.374779i
$965$	9.57797	−	43.2200i	0.308326	−	1.39130i
$966$		0			0
$967$	14.2437	+	14.2437i	0.458048	+	0.458048i	0.898014	−	0.439967i	$-0.145010\pi$
$967$	14.2437	+	14.2437i	0.458048	+	0.458048i	−0.439967	+	0.898014i	$0.645010\pi$
$968$	1.05695	+	1.05695i	0.0339716	+	0.0339716i
$969$		0			0
$970$	−19.1455	+	12.1992i	−0.614724	+	0.391692i
$971$			25.4989i			0.818297i	0.912468	+	0.409149i	$0.134174\pi$
$971$			25.4989i			0.818297i	−0.912468	+	0.409149i	$0.865826\pi$
$972$		0			0
$973$	−22.3004	+	22.3004i	−0.714919	+	0.714919i
$974$	17.8888			0.573193
$975$		0			0
$976$	13.2334			0.423592
$977$	0.0445427	−	0.0445427i	0.00142505	−	0.00142505i	−0.706394	−	0.707819i	$-0.749679\pi$
$977$	0.0445427	−	0.0445427i	0.00142505	−	0.00142505i	0.707819	+	0.706394i	$0.249679\pi$
$978$		0			0
$979$			10.8348i			0.346283i
$980$	−3.38918	+	2.15953i	−0.108263	+	0.0689837i
$981$		0			0
$982$	26.7345	+	26.7345i	0.853132	+	0.853132i
$983$	−0.899337	−	0.899337i	−0.0286844	−	0.0286844i	0.692619	−	0.721304i	$-0.256457\pi$
$983$	−0.899337	−	0.899337i	−0.0286844	−	0.0286844i	−0.721304	+	0.692619i	$0.756457\pi$
$984$		0			0
$985$	−4.79346	+	21.6302i	−0.152732	+	0.689195i
$986$			33.3291i			1.06142i
$987$		0			0
$988$	−2.10664	+	2.10664i	−0.0670210	+	0.0670210i
$989$	−5.81575			−0.184930
$990$		0			0
$991$	4.84937			0.154045			0.0770226	−	0.997029i	$-0.475459\pi$
$991$	4.84937			0.154045			0.0770226	+	0.997029i	$0.475459\pi$
$992$	−2.98732	+	2.98732i	−0.0948476	+	0.0948476i
$993$		0			0
$994$		−	23.0125i		−	0.729912i
$995$	8.34756	+	13.1007i	0.264635	+	0.415320i
$996$		0			0
$997$	5.08969	+	5.08969i	0.161192	+	0.161192i	0.783095	−	0.621902i	$-0.213640\pi$
$997$	5.08969	+	5.08969i	0.161192	+	0.161192i	−0.621902	+	0.783095i	$0.713640\pi$
$998$	19.6876	+	19.6876i	0.623199	+	0.623199i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2070.2.j.j.737.10	yes	20
3.2	odd	2	inner	2070.2.j.j.737.1	yes	20
5.3	odd	4	inner	2070.2.j.j.323.1	✓	20
15.8	even	4	inner	2070.2.j.j.323.10	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2070.2.j.j.323.1	✓	20	5.3	odd	4	inner
2070.2.j.j.323.10	yes	20	15.8	even	4	inner
2070.2.j.j.737.1	yes	20	3.2	odd	2	inner
2070.2.j.j.737.10	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2070.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(1.88578 - 1.20159i) q^{5} +(-1.61288 - 1.61288i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(1.88578 - 1.20159i) q^{5} +(-1.61288 - 1.61288i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.483797 - 2.18310i) q^{10} -3.53479i q^{11} +(-0.800168 + 0.800168i) q^{13} -2.28096 q^{14} -1.00000 q^{16} +(3.53479 - 3.53479i) q^{17} +2.63274i q^{19} +(-1.20159 - 1.88578i) q^{20} +(-2.49947 - 2.49947i) q^{22} +(0.707107 + 0.707107i) q^{23} +(2.11236 - 4.53188i) q^{25} +1.13161i q^{26} +(-1.61288 + 1.61288i) q^{28} -6.66723 q^{29} +4.22471 q^{31} +(-0.707107 + 0.707107i) q^{32} -4.99895i q^{34} +(-4.97957 - 1.10352i) q^{35} +(-4.02161 - 4.02161i) q^{37} +(1.86163 + 1.86163i) q^{38} +(-2.18310 - 0.483797i) q^{40} -0.501638i q^{41} +(-4.11236 + 4.11236i) q^{43} -3.53479 q^{44} +1.00000 q^{46} +(-3.72574 + 3.72574i) q^{47} -1.79723i q^{49} +(-1.71086 - 4.69819i) q^{50} +(0.800168 + 0.800168i) q^{52} +(-2.30313 - 2.30313i) q^{53} +(-4.24737 - 6.66585i) q^{55} +2.28096i q^{56} +(-4.71444 + 4.71444i) q^{58} +12.5135 q^{59} -13.2334 q^{61} +(2.98732 - 2.98732i) q^{62} +1.00000i q^{64} +(-0.547468 + 2.47042i) q^{65} +(-5.47961 - 5.47961i) q^{67} +(-3.53479 - 3.53479i) q^{68} +(-4.30139 + 2.74078i) q^{70} +10.0890i q^{71} +(9.57837 - 9.57837i) q^{73} -5.68742 q^{74} +2.63274 q^{76} +(-5.70120 + 5.70120i) q^{77} -0.108038i q^{79} +(-1.88578 + 1.20159i) q^{80} +(-0.354712 - 0.354712i) q^{82} +(5.67903 + 5.67903i) q^{83} +(2.41848 - 10.9132i) q^{85} +5.81575i q^{86} +(-2.49947 + 2.49947i) q^{88} -3.06520 q^{89} +2.58115 q^{91} +(0.707107 - 0.707107i) q^{92} +5.26899i q^{94} +(3.16348 + 4.96478i) q^{95} +(-7.17892 - 7.17892i) q^{97} +(-1.27083 - 1.27083i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 16 q^{7}+O(q^{10}) \) 20 * q - 16 * q^7	\( 20 q - 16 q^{7} + 12 q^{10} - 12 q^{13} - 20 q^{16} - 24 q^{25} - 16 q^{28} - 48 q^{31} - 60 q^{37} - 16 q^{43} + 20 q^{46} + 12 q^{52} - 32 q^{55} + 4 q^{58} + 104 q^{61} - 56 q^{67} - 8 q^{70} - 20 q^{73} + 40 q^{76} - 28 q^{82} - 40 q^{85} - 32 q^{91} - 44 q^{97}+O(q^{100}) \) 20 * q - 16 * q^7 + 12 * q^10 - 12 * q^13 - 20 * q^16 - 24 * q^25 - 16 * q^28 - 48 * q^31 - 60 * q^37 - 16 * q^43 + 20 * q^46 + 12 * q^52 - 32 * q^55 + 4 * q^58 + 104 * q^61 - 56 * q^67 - 8 * q^70 - 20 * q^73 + 40 * q^76 - 28 * q^82 - 40 * q^85 - 32 * q^91 - 44 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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