LMFDB - Embedded newform 2070.2.j.h.323.2

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:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 24 x^{14} - 48 x^{13} + 160 x^{12} - 292 x^{11} + 436 x^{10} - 176 x^{9} - 914 x^{8} + \cdots + 81 $ x^16 - 4x^15 + 24x^14 - 48x^13 + 160x^12 - 292x^11 + 436x^10 - 176x^9 - 914x^8 + 820x^7 + 1624x^6 - 768x^5 - 568x^4 - 636x^3 + 540x^2 + 432*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			323.2
Root			$-0.283623 - 0.684727i$ of defining polynomial
Character	$\chi$	$=$	2070.323
Dual form			2070.2.j.h.737.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-0.401104 - 2.19980i) q^{5} +(0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-0.401104 - 2.19980i) q^{5} +(0.707107 - 0.707107i) q^{8} +(-1.27187 + 1.83912i) q^{10} +6.12629i q^{11} +(-2.54374 - 2.54374i) q^{13} -1.00000 q^{16} +(2.98538 + 2.98538i) q^{17} -6.81272i q^{19} +(2.19980 - 0.401104i) q^{20} +(4.33194 - 4.33194i) q^{22} +(0.707107 - 0.707107i) q^{23} +(-4.67823 + 1.76469i) q^{25} +3.59739i q^{26} +9.75692 q^{29} -6.00000 q^{31} +(0.707107 + 0.707107i) q^{32} -4.22197i q^{34} +(6.24548 - 6.24548i) q^{37} +(-4.81732 + 4.81732i) q^{38} +(-1.83912 - 1.27187i) q^{40} -6.28325i q^{41} +(-8.55391 - 8.55391i) q^{43} -6.12629 q^{44} -1.00000 q^{46} +(-6.92850 - 6.92850i) q^{47} +7.00000i q^{49} +(4.55584 + 2.06018i) q^{50} +(2.54374 - 2.54374i) q^{52} +(0.227524 - 0.227524i) q^{53} +(13.4766 - 2.45728i) q^{55} +(-6.89919 - 6.89919i) q^{58} -1.10174 q^{59} -6.07313 q^{61} +(4.24264 + 4.24264i) q^{62} -1.00000i q^{64} +(-4.57541 + 6.61602i) q^{65} +(9.14466 - 9.14466i) q^{67} +(-2.98538 + 2.98538i) q^{68} -6.30210i q^{71} +(1.35545 + 1.35545i) q^{73} -8.83244 q^{74} +6.81272 q^{76} +5.13449i q^{79} +(0.401104 + 2.19980i) q^{80} +(-4.44293 + 4.44293i) q^{82} +(2.28842 - 2.28842i) q^{83} +(5.36980 - 7.76469i) q^{85} +12.0971i q^{86} +(4.33194 + 4.33194i) q^{88} -9.75692 q^{89} +(0.707107 + 0.707107i) q^{92} +9.79837i q^{94} +(-14.9866 + 2.73261i) q^{95} +(-5.12116 + 5.12116i) q^{97} +(4.94975 - 4.94975i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 8 q^{10} - 16 q^{13} - 16 q^{16} + 8 q^{22} - 16 q^{25} - 96 q^{31} + 24 q^{37} + 8 q^{43} - 16 q^{46} + 16 q^{52} - 32 q^{58} + 16 q^{61} - 8 q^{67} - 32 q^{73} + 16 q^{76} + 32 q^{82} + 96 q^{85} + 8 q^{88} + 80 q^{97}+O(q^{100}) $ 16 * q - 8 * q^10 - 16 * q^13 - 16 * q^16 + 8 * q^22 - 16 * q^25 - 96 * q^31 + 24 * q^37 + 8 * q^43 - 16 * q^46 + 16 * q^52 - 32 * q^58 + 16 * q^61 - 8 * q^67 - 32 * q^73 + 16 * q^76 + 32 * q^82 + 96 * q^85 + 8 * q^88 + 80 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$461$	$1657$	$1891$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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
$5$	−0.401104	−	2.19980i	−0.179379	−	0.983780i
$5$	−0.401104	−	2.19980i	−0.179379	−	0.983780i
$6$		0			0
$7$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$7$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$	−1.27187	+	1.83912i	−0.402201	+	0.581580i
$11$			6.12629i			1.84715i	0.383423	+	0.923573i	$0.374745\pi$
$11$			6.12629i			1.84715i	−0.383423	+	0.923573i	$0.625255\pi$
$12$		0			0
$13$	−2.54374	−	2.54374i	−0.705506	−	0.705506i	0.260081	−	0.965587i	$-0.416251\pi$
$13$	−2.54374	−	2.54374i	−0.705506	−	0.705506i	−0.965587	+	0.260081i	$0.916251\pi$
$14$		0			0
$15$		0			0
$16$	−1.00000			−0.250000
$17$	2.98538	+	2.98538i	0.724062	+	0.724062i	0.969430	−	0.245368i	$-0.0789088\pi$
$17$	2.98538	+	2.98538i	0.724062	+	0.724062i	−0.245368	+	0.969430i	$0.578909\pi$
$18$		0			0
$19$		−	6.81272i		−	1.56295i	−0.623939	−	0.781473i	$-0.714469\pi$
$19$		−	6.81272i		−	1.56295i	0.623939	−	0.781473i	$-0.285531\pi$
$20$	2.19980	−	0.401104i	0.491890	−	0.0896895i
$21$		0			0
$22$	4.33194	−	4.33194i	0.923573	−	0.923573i
$23$	0.707107	−	0.707107i	0.147442	−	0.147442i
$23$	0.707107	−	0.707107i	0.147442	−	0.147442i
$24$		0			0
$25$	−4.67823	+	1.76469i	−0.935646	+	0.352939i
$26$			3.59739i			0.705506i
$27$		0			0
$28$		0			0
$29$	9.75692			1.81182			0.905908	−	0.423475i	$-0.139190\pi$
$29$	9.75692			1.81182			0.905908	+	0.423475i	$0.139190\pi$
$30$		0			0
$31$	−6.00000			−1.07763			−0.538816	−	0.842424i	$-0.681128\pi$
$31$	−6.00000			−1.07763			−0.538816	+	0.842424i	$0.681128\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$		0			0
$34$		−	4.22197i		−	0.724062i
$35$		0			0
$36$		0			0
$37$	6.24548	−	6.24548i	1.02675	−	1.02675i	0.0271180	−	0.999632i	$-0.491367\pi$
$37$	6.24548	−	6.24548i	1.02675	−	1.02675i	0.999632	−	0.0271180i	$-0.00863299\pi$
$38$	−4.81732	+	4.81732i	−0.781473	+	0.781473i
$39$		0			0
$40$	−1.83912	−	1.27187i	−0.290790	−	0.201100i
$41$		−	6.28325i		−	0.981278i	−0.871363	−	0.490639i	$-0.836763\pi$
$41$		−	6.28325i		−	0.981278i	0.871363	−	0.490639i	$-0.163237\pi$
$42$		0			0
$43$	−8.55391	−	8.55391i	−1.30446	−	1.30446i	−0.925353	−	0.379106i	$-0.876232\pi$
$43$	−8.55391	−	8.55391i	−1.30446	−	1.30446i	−0.379106	−	0.925353i	$-0.623768\pi$
$44$	−6.12629			−0.923573
$45$		0			0
$46$	−1.00000			−0.147442
$47$	−6.92850	−	6.92850i	−1.01063	−	1.01063i	−0.999943	−	0.0106822i	$-0.996600\pi$
$47$	−6.92850	−	6.92850i	−1.01063	−	1.01063i	−0.0106822	−	0.999943i	$-0.503400\pi$
$48$		0			0
$49$			7.00000i			1.00000i
$50$	4.55584	+	2.06018i	0.644293	+	0.291354i
$51$		0			0
$52$	2.54374	−	2.54374i	0.352753	−	0.352753i
$53$	0.227524	−	0.227524i	0.0312529	−	0.0312529i	−0.691308	−	0.722561i	$-0.742965\pi$
$53$	0.227524	−	0.227524i	0.0312529	−	0.0312529i	0.722561	+	0.691308i	$0.242965\pi$
$54$		0			0
$55$	13.4766	−	2.45728i	1.81719	−	0.331339i
$56$		0			0
$57$		0			0
$58$	−6.89919	−	6.89919i	−0.905908	−	0.905908i
$59$	−1.10174			−0.143434			−0.0717169	−	0.997425i	$-0.522848\pi$
$59$	−1.10174			−0.143434			−0.0717169	+	0.997425i	$0.522848\pi$
$60$		0			0
$61$	−6.07313			−0.777584			−0.388792	−	0.921325i	$-0.627108\pi$
$61$	−6.07313			−0.777584			−0.388792	+	0.921325i	$0.627108\pi$
$62$	4.24264	+	4.24264i	0.538816	+	0.538816i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−4.57541	+	6.61602i	−0.567510	+	0.820616i
$66$		0			0
$67$	9.14466	−	9.14466i	1.11720	−	1.11720i	0.125048	−	0.992151i	$-0.460092\pi$
$67$	9.14466	−	9.14466i	1.11720	−	1.11720i	0.992151	−	0.125048i	$-0.0399085\pi$
$68$	−2.98538	+	2.98538i	−0.362031	+	0.362031i
$69$		0			0
$70$		0			0
$71$		−	6.30210i		−	0.747922i	−0.927444	−	0.373961i	$-0.877999\pi$
$71$		−	6.30210i		−	0.747922i	0.927444	−	0.373961i	$-0.122001\pi$
$72$		0			0
$73$	1.35545	+	1.35545i	0.158643	+	0.158643i	0.781965	−	0.623322i	$-0.214217\pi$
$73$	1.35545	+	1.35545i	0.158643	+	0.158643i	−0.623322	+	0.781965i	$0.714217\pi$
$74$	−8.83244			−1.02675
$75$		0			0
$76$	6.81272			0.781473
$77$		0			0
$78$		0			0
$79$			5.13449i			0.577676i	0.957378	+	0.288838i	$0.0932688\pi$
$79$			5.13449i			0.577676i	−0.957378	+	0.288838i	$0.906731\pi$
$80$	0.401104	+	2.19980i	0.0448447	+	0.245945i
$81$		0			0
$82$	−4.44293	+	4.44293i	−0.490639	+	0.490639i
$83$	2.28842	−	2.28842i	0.251187	−	0.251187i	−0.570270	−	0.821457i	$-0.693161\pi$
$83$	2.28842	−	2.28842i	0.251187	−	0.251187i	0.821457	+	0.570270i	$0.193161\pi$
$84$		0			0
$85$	5.36980	−	7.76469i	0.582436	−	0.842199i
$86$			12.0971i			1.30446i
$87$		0			0
$88$	4.33194	+	4.33194i	0.461786	+	0.461786i
$89$	−9.75692			−1.03423			−0.517116	−	0.855915i	$-0.672994\pi$
$89$	−9.75692			−1.03423			−0.517116	+	0.855915i	$0.672994\pi$
$90$		0			0
$91$		0			0
$92$	0.707107	+	0.707107i	0.0737210	+	0.0737210i
$93$		0			0
$94$			9.79837i			1.01063i
$95$	−14.9866	+	2.73261i	−1.53760	+	0.280360i
$96$		0			0
$97$	−5.12116	+	5.12116i	−0.519975	+	0.519975i	−0.917564	−	0.397589i	$-0.869847\pi$
$97$	−5.12116	+	5.12116i	−0.519975	+	0.519975i	0.397589	+	0.917564i	$0.369847\pi$
$98$	4.94975	−	4.94975i	0.500000	−	0.500000i
$99$		0			0
$100$	−1.76469	−	4.67823i	−0.176469	−	0.467823i
$101$			0.332772i			0.0331121i	0.999863	+	0.0165560i	$0.00527019\pi$
$101$			0.332772i			0.0331121i	−0.999863	+	0.0165560i	$0.994730\pi$
$102$		0			0
$103$	−6.00000	−	6.00000i	−0.591198	−	0.591198i	0.346757	−	0.937955i	$-0.387283\pi$
$103$	−6.00000	−	6.00000i	−0.591198	−	0.591198i	−0.937955	+	0.346757i	$0.887283\pi$
$104$	−3.59739			−0.352753
$105$		0			0
$106$	−0.321768			−0.0312529
$107$	−2.75786	−	2.75786i	−0.266612	−	0.266612i	0.561121	−	0.827734i	$-0.310370\pi$
$107$	−2.75786	−	2.75786i	−0.266612	−	0.266612i	−0.827734	+	0.561121i	$0.810370\pi$
$108$		0			0
$109$			14.1201i			1.35246i	0.736689	+	0.676232i	$0.236388\pi$
$109$			14.1201i			1.35246i	−0.736689	+	0.676232i	$0.763612\pi$
$110$	−11.2670	−	7.79184i	−1.07426	−	0.742923i
$111$		0			0
$112$		0			0
$113$	−0.279234	+	0.279234i	−0.0262682	+	0.0262682i	−0.720119	−	0.693851i	$-0.755913\pi$
$113$	−0.279234	+	0.279234i	−0.0262682	+	0.0262682i	0.693851	+	0.720119i	$0.255913\pi$
$114$		0			0
$115$	−1.83912	−	1.27187i	−0.171498	−	0.118602i
$116$			9.75692i			0.905908i
$117$		0			0
$118$	0.779045	+	0.779045i	0.0717169	+	0.0717169i
$119$		0			0
$120$		0			0
$121$	−26.5314			−2.41195
$122$	4.29435	+	4.29435i	0.388792	+	0.388792i
$123$		0			0
$124$		−	6.00000i		−	0.538816i
$125$	5.75843	+	9.58334i	0.515050	+	0.857160i
$126$		0			0
$127$	−0.409247	+	0.409247i	−0.0363148	+	0.0363148i	−0.725031	−	0.688716i	$-0.758175\pi$
$127$	−0.409247	+	0.409247i	−0.0363148	+	0.0363148i	0.688716	+	0.725031i	$0.258175\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$		0			0
$130$	7.91354	−	1.44293i	0.694063	−	0.126553i
$131$		−	3.26462i		−	0.285231i	−0.989778	−	0.142616i	$-0.954449\pi$
$131$		−	3.26462i		−	0.285231i	0.989778	−	0.142616i	$-0.0455512\pi$
$132$		0			0
$133$		0			0
$134$	−12.9325			−1.11720
$135$		0			0
$136$	4.22197			0.362031
$137$	1.11468	+	1.11468i	0.0952340	+	0.0952340i	0.753119	−	0.657885i	$-0.228549\pi$
$137$	1.11468	+	1.11468i	0.0952340	+	0.0952340i	−0.657885	+	0.753119i	$0.728549\pi$
$138$		0			0
$139$		−	20.5113i		−	1.73975i	−0.493276	−	0.869873i	$-0.664201\pi$
$139$		−	20.5113i		−	1.73975i	0.493276	−	0.869873i	$-0.335799\pi$
$140$		0			0
$141$		0			0
$142$	−4.45626	+	4.45626i	−0.373961	+	0.373961i
$143$	15.5837	−	15.5837i	1.30317	−	1.30317i
$144$		0			0
$145$	−3.91354	−	21.4633i	−0.325002	−	1.78243i
$146$		−	1.91689i		−	0.158643i
$147$		0			0
$148$	6.24548	+	6.24548i	0.513375	+	0.513375i
$149$	−2.19613			−0.179914			−0.0899568	−	0.995946i	$-0.528673\pi$
$149$	−2.19613			−0.179914			−0.0899568	+	0.995946i	$0.528673\pi$
$150$		0			0
$151$	7.52939			0.612733			0.306367	−	0.951914i	$-0.400887\pi$
$151$	7.52939			0.612733			0.306367	+	0.951914i	$0.400887\pi$
$152$	−4.81732	−	4.81732i	−0.390737	−	0.390737i
$153$		0			0
$154$		0			0
$155$	2.40662	+	13.1988i	0.193304	+	1.06015i
$156$		0			0
$157$	16.4674	−	16.4674i	1.31425	−	1.31425i	0.395991	−	0.918254i	$-0.370401\pi$
$157$	16.4674	−	16.4674i	1.31425	−	1.31425i	0.918254	−	0.395991i	$-0.129599\pi$
$158$	3.63063	−	3.63063i	0.288838	−	0.288838i
$159$		0			0
$160$	1.27187	−	1.83912i	0.100550	−	0.145395i
$161$		0			0
$162$		0			0
$163$	−5.82707	−	5.82707i	−0.456412	−	0.456412i	0.441064	−	0.897476i	$-0.354601\pi$
$163$	−5.82707	−	5.82707i	−0.456412	−	0.456412i	−0.897476	+	0.441064i	$0.854601\pi$
$164$	6.28325			0.490639
$165$		0			0
$166$	−3.23632			−0.251187
$167$	−11.9401	−	11.9401i	−0.923953	−	0.923953i	0.0733533	−	0.997306i	$-0.476630\pi$
$167$	−11.9401	−	11.9401i	−0.923953	−	0.923953i	−0.997306	+	0.0733533i	$0.976630\pi$
$168$		0			0
$169$		−	0.0587785i		−	0.00452142i
$170$	−9.28749	+	1.69345i	−0.712318	+	0.129882i
$171$		0			0
$172$	8.55391	−	8.55391i	0.652230	−	0.652230i
$173$	−0.626393	+	0.626393i	−0.0476237	+	0.0476237i	−0.730518	−	0.682894i	$-0.760721\pi$
$173$	−0.626393	+	0.626393i	−0.0476237	+	0.0476237i	0.682894	+	0.730518i	$0.260721\pi$
$174$		0			0
$175$		0			0
$176$		−	6.12629i		−	0.461786i
$177$		0			0
$178$	6.89919	+	6.89919i	0.517116	+	0.517116i
$179$	−15.9382			−1.19128			−0.595638	−	0.803253i	$-0.703101\pi$
$179$	−15.9382			−1.19128			−0.595638	+	0.803253i	$0.703101\pi$
$180$		0			0
$181$	−18.0731			−1.34337			−0.671683	−	0.740839i	$-0.734428\pi$
$181$	−18.0731			−1.34337			−0.671683	+	0.740839i	$0.734428\pi$
$182$		0			0
$183$		0			0
$184$		−	1.00000i		−	0.0737210i
$185$	−16.2439	−	11.2337i	−1.19427	−	0.825919i
$186$		0			0
$187$	−18.2893	+	18.2893i	−1.33745	+	1.33745i
$188$	6.92850	−	6.92850i	0.505313	−	0.505313i
$189$		0			0
$190$	12.5294	+	8.66490i	0.908977	+	0.628618i
$191$		−	23.8802i		−	1.72791i	−0.503568	−	0.863955i	$-0.667980\pi$
$191$		−	23.8802i		−	1.72791i	0.503568	−	0.863955i	$-0.332020\pi$
$192$		0			0
$193$	−10.6254	−	10.6254i	−0.764836	−	0.764836i	0.212356	−	0.977192i	$-0.431886\pi$
$193$	−10.6254	−	10.6254i	−0.764836	−	0.764836i	−0.977192	+	0.212356i	$0.931886\pi$
$194$	7.24241			0.519975
$195$		0			0
$196$	−7.00000			−0.500000
$197$	16.3729	+	16.3729i	1.16652	+	1.16652i	0.983019	+	0.183505i	$0.0587444\pi$
$197$	16.3729	+	16.3729i	1.16652	+	1.16652i	0.183505	+	0.983019i	$0.441256\pi$
$198$		0			0
$199$		−	25.2019i		−	1.78651i	−0.449549	−	0.893256i	$-0.648415\pi$
$199$		−	25.2019i		−	1.78651i	0.449549	−	0.893256i	$-0.351585\pi$
$200$	−2.06018	+	4.55584i	−0.145677	+	0.322146i
$201$		0			0
$202$	0.235305	−	0.235305i	0.0165560	−	0.0165560i
$203$		0			0
$204$		0			0
$205$	−13.8219	+	2.52023i	−0.965362	+	0.176021i
$206$			8.48528i			0.591198i
$207$		0			0
$208$	2.54374	+	2.54374i	0.176377	+	0.176377i
$209$	41.7367			2.88699
$210$		0			0
$211$	−15.8004			−1.08774			−0.543872	−	0.839168i	$-0.683042\pi$
$211$	−15.8004			−1.08774			−0.543872	+	0.839168i	$0.683042\pi$
$212$	0.227524	+	0.227524i	0.0156264	+	0.0156264i
$213$		0			0
$214$			3.90020i			0.266612i
$215$	−15.3859	+	22.2479i	−1.04931	+	1.51729i
$216$		0			0
$217$		0			0
$218$	9.98445	−	9.98445i	0.676232	−	0.676232i
$219$		0			0
$220$	2.45728	+	13.4766i	0.165670	+	0.908593i
$221$		−	15.1881i		−	1.02166i
$222$		0			0
$223$	15.7263	+	15.7263i	1.05311	+	1.05311i	0.998508	+	0.0546000i	$0.0173884\pi$
$223$	15.7263	+	15.7263i	1.05311	+	1.05311i	0.0546000	+	0.998508i	$0.482612\pi$
$224$		0			0
$225$		0			0
$226$	0.394897			0.0262682
$227$	−8.72863	−	8.72863i	−0.579339	−	0.579339i	0.355382	−	0.934721i	$-0.384351\pi$
$227$	−8.72863	−	8.72863i	−0.579339	−	0.579339i	−0.934721	+	0.355382i	$0.884351\pi$
$228$		0			0
$229$			20.3421i			1.34424i	0.740440	+	0.672122i	$0.234617\pi$
$229$			20.3421i			1.34424i	−0.740440	+	0.672122i	$0.765383\pi$
$230$	0.401104	+	2.19980i	0.0264480	+	0.145050i
$231$		0			0
$232$	6.89919	−	6.89919i	0.452954	−	0.452954i
$233$	−5.20181	+	5.20181i	−0.340782	+	0.340782i	−0.856661	−	0.515880i	$-0.827465\pi$
$233$	−5.20181	+	5.20181i	−0.340782	+	0.340782i	0.515880	+	0.856661i	$0.327465\pi$
$234$		0			0
$235$	−12.4623	+	18.0203i	−0.812948	+	1.17552i
$236$		−	1.10174i		−	0.0717169i
$237$		0			0
$238$		0			0
$239$	−15.2265			−0.984917			−0.492459	−	0.870336i	$-0.663902\pi$
$239$	−15.2265			−0.984917			−0.492459	+	0.870336i	$0.663902\pi$
$240$		0			0
$241$	29.3972			1.89364			0.946819	−	0.321768i	$-0.104277\pi$
$241$	29.3972			1.89364			0.946819	+	0.321768i	$0.104277\pi$
$242$	18.7605	+	18.7605i	1.20597	+	1.20597i
$243$		0			0
$244$		−	6.07313i		−	0.388792i
$245$	15.3986	−	2.80773i	0.983780	−	0.179379i
$246$		0			0
$247$	−17.3298	+	17.3298i	−1.10267	+	1.10267i
$248$	−4.24264	+	4.24264i	−0.269408	+	0.269408i
$249$		0			0
$250$	2.70462	−	10.8483i	0.171055	−	0.686105i
$251$			9.51319i			0.600467i	0.953866	+	0.300233i	$0.0970646\pi$
$251$			9.51319i			0.600467i	−0.953866	+	0.300233i	$0.902935\pi$
$252$		0			0
$253$	4.33194	+	4.33194i	0.272347	+	0.272347i
$254$	0.578763			0.0363148
$255$		0			0
$256$	1.00000			0.0625000
$257$	6.15953	+	6.15953i	0.384221	+	0.384221i	0.872620	−	0.488399i	$-0.162419\pi$
$257$	6.15953	+	6.15953i	0.384221	+	0.384221i	−0.488399	+	0.872620i	$0.662419\pi$
$258$		0			0
$259$		0			0
$260$	−6.61602	−	4.57541i	−0.410308	−	0.283755i
$261$		0			0
$262$	−2.30843	+	2.30843i	−0.142616	+	0.142616i
$263$	3.16120	−	3.16120i	0.194928	−	0.194928i	−0.602894	−	0.797822i	$-0.705986\pi$
$263$	3.16120	−	3.16120i	0.194928	−	0.194928i	0.797822	+	0.602894i	$0.205986\pi$
$264$		0			0
$265$	−0.591769	−	0.409247i	−0.0363521	−	0.0251399i
$266$		0			0
$267$		0			0
$268$	9.14466	+	9.14466i	0.558599	+	0.558599i
$269$	−16.0387			−0.977899			−0.488949	−	0.872312i	$-0.662620\pi$
$269$	−16.0387			−0.977899			−0.488949	+	0.872312i	$0.662620\pi$
$270$		0			0
$271$	4.78979			0.290959			0.145480	−	0.989361i	$-0.453527\pi$
$271$	4.78979			0.290959			0.145480	+	0.989361i	$0.453527\pi$
$272$	−2.98538	−	2.98538i	−0.181016	−	0.181016i
$273$		0			0
$274$		−	1.57640i		−	0.0952340i
$275$	−10.8110	−	28.6602i	−0.651930	−	1.72828i
$276$		0			0
$277$	19.4766	−	19.4766i	1.17024	−	1.17024i	0.188083	−	0.982153i	$-0.439773\pi$
$277$	19.4766	−	19.4766i	1.17024	−	1.17024i	0.982153	−	0.188083i	$-0.0602273\pi$
$278$	−14.5037	+	14.5037i	−0.869873	+	0.869873i
$279$		0			0
$280$		0			0
$281$			16.3526i			0.975517i	0.872979	+	0.487759i	$0.162185\pi$
$281$			16.3526i			0.975517i	−0.872979	+	0.487759i	$0.837815\pi$
$282$		0			0
$283$	−3.39330	−	3.39330i	−0.201711	−	0.201711i	0.599022	−	0.800733i	$-0.295556\pi$
$283$	−3.39330	−	3.39330i	−0.201711	−	0.201711i	−0.800733	+	0.599022i	$0.795556\pi$
$284$	6.30210			0.373961
$285$		0			0
$286$	−22.0387			−1.30317
$287$		0			0
$288$		0			0
$289$			0.825042i			0.0485319i
$290$	−12.4095	+	17.9441i	−0.728713	+	1.05371i
$291$		0			0
$292$	−1.35545	+	1.35545i	−0.0793216	+	0.0793216i
$293$	8.22451	−	8.22451i	0.480481	−	0.480481i	−0.424804	−	0.905285i	$-0.639657\pi$
$293$	8.22451	−	8.22451i	0.480481	−	0.480481i	0.905285	+	0.424804i	$0.139657\pi$
$294$		0			0
$295$	0.441910	+	2.42360i	0.0257290	+	0.141107i
$296$		−	8.83244i		−	0.513375i
$297$		0			0
$298$	1.55290	+	1.55290i	0.0899568	+	0.0899568i
$299$	−3.59739			−0.208042
$300$		0			0
$301$		0			0
$302$	−5.32408	−	5.32408i	−0.306367	−	0.306367i
$303$		0			0
$304$			6.81272i			0.390737i
$305$	2.43595	+	13.3597i	0.139482	+	0.764972i
$306$		0			0
$307$	−4.44394	+	4.44394i	−0.253629	+	0.253629i	−0.822457	−	0.568828i	$-0.807397\pi$
$307$	−4.44394	+	4.44394i	−0.253629	+	0.253629i	0.568828	+	0.822457i	$0.307397\pi$
$308$		0			0
$309$		0			0
$310$	7.63122	−	11.0347i	0.433424	−	0.626729i
$311$		−	4.82284i		−	0.273478i	−0.990607	−	0.136739i	$-0.956338\pi$
$311$		−	4.82284i		−	0.273478i	0.990607	−	0.136739i	$-0.0436622\pi$
$312$		0			0
$313$	−19.9580	−	19.9580i	−1.12809	−	1.12809i	−0.990487	−	0.137604i	$-0.956060\pi$
$313$	−19.9580	−	19.9580i	−1.12809	−	1.12809i	−0.137604	−	0.990487i	$-0.543940\pi$
$314$	−23.2885			−1.31425
$315$		0			0
$316$	−5.13449			−0.288838
$317$	18.3659	+	18.3659i	1.03153	+	1.03153i	0.999486	+	0.0320464i	$0.0102024\pi$
$317$	18.3659	+	18.3659i	1.03153	+	1.03153i	0.0320464	+	0.999486i	$0.489798\pi$
$318$		0			0
$319$			59.7737i			3.34669i
$320$	−2.19980	+	0.401104i	−0.122973	+	0.0224224i
$321$		0			0
$322$		0			0
$323$	20.3386	−	20.3386i	1.13167	−	1.13167i
$324$		0			0
$325$	16.3891	+	7.41128i	0.909105	+	0.411104i
$326$			8.24073i			0.456412i
$327$		0			0
$328$	−4.44293	−	4.44293i	−0.245320	−	0.245320i
$329$		0			0
$330$		0			0
$331$	5.70435			0.313539			0.156770	−	0.987635i	$-0.449892\pi$
$331$	5.70435			0.313539			0.156770	+	0.987635i	$0.449892\pi$
$332$	2.28842	+	2.28842i	0.125594	+	0.125594i
$333$		0			0
$334$			16.8859i			0.923953i
$335$	−23.7844	−	16.4485i	−1.29948	−	0.898676i
$336$		0			0
$337$	3.02510	−	3.02510i	0.164788	−	0.164788i	−0.619896	−	0.784684i	$-0.712825\pi$
$337$	3.02510	−	3.02510i	0.164788	−	0.164788i	0.784684	+	0.619896i	$0.212825\pi$
$338$	−0.0415627	+	0.0415627i	−0.00226071	+	0.00226071i
$339$		0			0
$340$	7.76469	+	5.36980i	0.421100	+	0.291218i
$341$		−	36.7577i		−	1.99054i
$342$		0			0
$343$		0			0
$344$	−12.0971			−0.652230
$345$		0			0
$346$	0.885853			0.0476237
$347$	22.9890	+	22.9890i	1.23411	+	1.23411i	0.962370	+	0.271742i	$0.0875997\pi$
$347$	22.9890	+	22.9890i	1.23411	+	1.23411i	0.271742	+	0.962370i	$0.412400\pi$
$348$		0			0
$349$			19.9446i			1.06761i	0.845607	+	0.533806i	$0.179239\pi$
$349$			19.9446i			1.06761i	−0.845607	+	0.533806i	$0.820761\pi$
$350$		0			0
$351$		0			0
$352$	−4.33194	+	4.33194i	−0.230893	+	0.230893i
$353$	9.06404	−	9.06404i	0.482430	−	0.482430i	−0.423477	−	0.905907i	$-0.639190\pi$
$353$	9.06404	−	9.06404i	0.482430	−	0.482430i	0.905907	+	0.423477i	$0.139190\pi$
$354$		0			0
$355$	−13.8634	+	2.52780i	−0.735791	+	0.134162i
$356$		−	9.75692i		−	0.517116i
$357$		0			0
$358$	11.2700	+	11.2700i	0.595638	+	0.595638i
$359$	27.1555			1.43321			0.716607	−	0.697477i	$-0.245694\pi$
$359$	27.1555			1.43321			0.716607	+	0.697477i	$0.245694\pi$
$360$		0			0
$361$	−27.4132			−1.44280
$362$	12.7796	+	12.7796i	0.671683	+	0.671683i
$363$		0			0
$364$		0			0
$365$	2.43804	−	3.52539i	0.127613	−	0.184527i
$366$		0			0
$367$	11.9530	−	11.9530i	0.623941	−	0.623941i	−0.322596	−	0.946537i	$-0.604555\pi$
$367$	11.9530	−	11.9530i	0.623941	−	0.623941i	0.946537	+	0.322596i	$0.104555\pi$
$368$	−0.707107	+	0.707107i	−0.0368605	+	0.0368605i
$369$		0			0
$370$	3.54272	+	19.4296i	0.184177	+	1.01010i
$371$		0			0
$372$		0			0
$373$	18.6894	+	18.6894i	0.967702	+	0.967702i	0.999494	−	0.0317930i	$-0.0101217\pi$
$373$	18.6894	+	18.6894i	0.967702	+	0.967702i	−0.0317930	+	0.999494i	$0.510122\pi$
$374$	25.8650			1.33745
$375$		0			0
$376$	−9.79837			−0.505313
$377$	−24.8191	−	24.8191i	−1.27825	−	1.27825i
$378$		0			0
$379$			16.6581i			0.855670i	0.903857	+	0.427835i	$0.140724\pi$
$379$			16.6581i			0.855670i	−0.903857	+	0.427835i	$0.859276\pi$
$380$	−2.73261	−	14.9866i	−0.140180	−	0.768798i
$381$		0			0
$382$	−16.8859	+	16.8859i	−0.863955	+	0.863955i
$383$	−0.577326	+	0.577326i	−0.0295000	+	0.0295000i	−0.721703	−	0.692203i	$-0.756640\pi$
$383$	−0.577326	+	0.577326i	−0.0295000	+	0.0295000i	0.692203	+	0.721703i	$0.256640\pi$
$384$		0			0
$385$		0			0
$386$			15.0267i			0.764836i
$387$		0			0
$388$	−5.12116	−	5.12116i	−0.259987	−	0.259987i
$389$	−13.0548			−0.661904			−0.330952	−	0.943648i	$-0.607370\pi$
$389$	−13.0548			−0.661904			−0.330952	+	0.943648i	$0.607370\pi$
$390$		0			0
$391$	4.22197			0.213514
$392$	4.94975	+	4.94975i	0.250000	+	0.250000i
$393$		0			0
$394$		−	23.1548i		−	1.16652i
$395$	11.2949	−	2.05946i	0.568306	−	0.103623i
$396$		0			0
$397$	11.4583	−	11.4583i	0.575075	−	0.575075i	−0.358467	−	0.933542i	$-0.616700\pi$
$397$	11.4583	−	11.4583i	0.575075	−	0.575075i	0.933542	+	0.358467i	$0.116700\pi$
$398$	−17.8204	+	17.8204i	−0.893256	+	0.893256i
$399$		0			0
$400$	4.67823	−	1.76469i	0.233912	−	0.0882347i
$401$		−	30.7422i		−	1.53519i	−0.640934	−	0.767596i	$-0.721453\pi$
$401$		−	30.7422i		−	1.53519i	0.640934	−	0.767596i	$-0.278547\pi$
$402$		0			0
$403$	15.2624	+	15.2624i	0.760276	+	0.760276i
$404$	−0.332772			−0.0165560
$405$		0			0
$406$		0			0
$407$	38.2616	+	38.2616i	1.89656	+	1.89656i
$408$		0			0
$409$		−	25.2509i		−	1.24858i	−0.781194	−	0.624288i	$-0.785389\pi$
$409$		−	25.2509i		−	1.24858i	0.781194	−	0.624288i	$-0.214611\pi$
$410$	11.5556	+	7.99147i	0.570691	+	0.394671i
$411$		0			0
$412$	6.00000	−	6.00000i	0.295599	−	0.295599i
$413$		0			0
$414$		0			0
$415$	−5.95197	−	4.11618i	−0.292171	−	0.202055i
$416$		−	3.59739i		−	0.176377i
$417$		0			0
$418$	−29.5123	−	29.5123i	−1.44349	−	1.44349i
$419$	−19.7469			−0.964699			−0.482349	−	0.875979i	$-0.660216\pi$
$419$	−19.7469			−0.964699			−0.482349	+	0.875979i	$0.660216\pi$
$420$		0			0
$421$	9.68026			0.471787			0.235894	−	0.971779i	$-0.424198\pi$
$421$	9.68026			0.471787			0.235894	+	0.971779i	$0.424198\pi$
$422$	11.1726	+	11.1726i	0.543872	+	0.543872i
$423$		0			0
$424$		−	0.321768i		−	0.0156264i
$425$	−19.2346	−	8.69803i	−0.933016	−	0.421916i
$426$		0			0
$427$		0			0
$428$	2.75786	−	2.75786i	0.133306	−	0.133306i
$429$		0			0
$430$	26.6111	−	4.85217i	1.28330	−	0.233993i
$431$			36.4873i			1.75753i	0.477254	+	0.878765i	$0.341632\pi$
$431$			36.4873i			1.75753i	−0.477254	+	0.878765i	$0.658368\pi$
$432$		0			0
$433$	−3.32278	−	3.32278i	−0.159683	−	0.159683i	0.622743	−	0.782426i	$-0.286018\pi$
$433$	−3.32278	−	3.32278i	−0.159683	−	0.159683i	−0.782426	+	0.622743i	$0.786018\pi$
$434$		0			0
$435$		0			0
$436$	−14.1201			−0.676232
$437$	−4.81732	−	4.81732i	−0.230444	−	0.230444i
$438$		0			0
$439$			10.7416i			0.512670i	0.966588	+	0.256335i	$0.0825150\pi$
$439$			10.7416i			0.512670i	−0.966588	+	0.256335i	$0.917485\pi$
$440$	7.79184	−	11.2670i	0.371462	−	0.537131i
$441$		0			0
$442$	−10.7396	+	10.7396i	−0.510830	+	0.510830i
$443$	0.835451	−	0.835451i	0.0396935	−	0.0396935i	−0.686981	−	0.726675i	$-0.741065\pi$
$443$	0.835451	−	0.835451i	0.0396935	−	0.0396935i	0.726675	+	0.686981i	$0.241065\pi$
$444$		0			0
$445$	3.91354	+	21.4633i	0.185519	+	1.01746i
$446$		−	22.2403i		−	1.05311i
$447$		0			0
$448$		0			0
$449$	10.4050			0.491045			0.245522	−	0.969391i	$-0.421041\pi$
$449$	10.4050			0.491045			0.245522	+	0.969391i	$0.421041\pi$
$450$		0			0
$451$	38.4930			1.81256
$452$	−0.279234	−	0.279234i	−0.0131341	−	0.0131341i
$453$		0			0
$454$			12.3441i			0.579339i
$455$		0			0
$456$		0			0
$457$	25.3411	−	25.3411i	1.18541	−	1.18541i	0.207083	−	0.978323i	$-0.433603\pi$
$457$	25.3411	−	25.3411i	1.18541	−	1.18541i	0.978323	−	0.207083i	$-0.0663971\pi$
$458$	14.3840	−	14.3840i	0.672122	−	0.672122i
$459$		0			0
$460$	1.27187	−	1.83912i	0.0593012	−	0.0857492i
$461$			25.9126i			1.20687i	0.797411	+	0.603436i	$0.206202\pi$
$461$			25.9126i			1.20687i	−0.797411	+	0.603436i	$0.793798\pi$
$462$		0			0
$463$	9.12217	+	9.12217i	0.423943	+	0.423943i	0.886559	−	0.462616i	$-0.153089\pi$
$463$	9.12217	+	9.12217i	0.423943	+	0.423943i	−0.462616	+	0.886559i	$0.653089\pi$
$464$	−9.75692			−0.452954
$465$		0			0
$466$	7.35646			0.340782
$467$	−0.465355	−	0.465355i	−0.0215341	−	0.0215341i	0.696258	−	0.717792i	$-0.254847\pi$
$467$	−0.465355	−	0.465355i	−0.0215341	−	0.0215341i	−0.717792	+	0.696258i	$0.754847\pi$
$468$		0			0
$469$		0			0
$470$	21.5545	−	3.93016i	0.994233	−	0.181285i
$471$		0			0
$472$	−0.779045	+	0.779045i	−0.0358584	+	0.0358584i
$473$	52.4037	−	52.4037i	2.40953	−	2.40953i
$474$		0			0
$475$	12.0224	+	31.8715i	0.551625	+	1.46236i
$476$		0			0
$477$		0			0
$478$	10.7667	+	10.7667i	0.492459	+	0.492459i
$479$	21.6508			0.989252			0.494626	−	0.869106i	$-0.335305\pi$
$479$	21.6508			0.989252			0.494626	+	0.869106i	$0.335305\pi$
$480$		0			0
$481$	−31.7737			−1.44876
$482$	−20.7869	−	20.7869i	−0.946819	−	0.946819i
$483$		0			0
$484$		−	26.5314i		−	1.20597i
$485$	13.3196	+	9.21140i	0.604813	+	0.418268i
$486$		0			0
$487$	21.1201	−	21.1201i	0.957045	−	0.957045i	−0.0420697	−	0.999115i	$-0.513395\pi$
$487$	21.1201	−	21.1201i	0.957045	−	0.957045i	0.999115	+	0.0420697i	$0.0133952\pi$
$488$	−4.29435	+	4.29435i	−0.194396	+	0.194396i
$489$		0			0
$490$	−12.8738	−	8.90309i	−0.581580	−	0.402201i
$491$		−	0.162866i		−	0.00735002i	−0.999993	−	0.00367501i	$-0.998830\pi$
$491$		−	0.162866i		−	0.00735002i	0.999993	−	0.00367501i	$-0.00116979\pi$
$492$		0			0
$493$	29.1282	+	29.1282i	1.31187	+	1.31187i
$494$	24.5080			1.10267
$495$		0			0
$496$	6.00000			0.269408
$497$		0			0
$498$		0			0
$499$			21.3278i			0.954762i	0.878696	+	0.477381i	$0.158414\pi$
$499$			21.3278i			0.954762i	−0.878696	+	0.477381i	$0.841586\pi$
$500$	−9.58334	+	5.75843i	−0.428580	+	0.257525i
$501$		0			0
$502$	6.72684	−	6.72684i	0.300233	−	0.300233i
$503$	9.00969	−	9.00969i	0.401722	−	0.401722i	−0.477117	−	0.878840i	$-0.658318\pi$
$503$	9.00969	−	9.00969i	0.401722	−	0.401722i	0.878840	+	0.477117i	$0.158318\pi$
$504$		0			0
$505$	0.732032	−	0.133476i	0.0325750	−	0.00593961i
$506$		−	6.12629i		−	0.272347i
$507$		0			0
$508$	−0.409247	−	0.409247i	−0.0181574	−	0.0181574i
$509$	15.6583			0.694043			0.347022	−	0.937857i	$-0.387193\pi$
$509$	15.6583			0.694043			0.347022	+	0.937857i	$0.387193\pi$
$510$		0			0
$511$		0			0
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$		−	8.71089i		−	0.384221i
$515$	−10.7922	+	15.6054i	−0.475560	+	0.687657i
$516$		0			0
$517$	42.4460	−	42.4460i	1.86677	−	1.86677i
$518$		0			0
$519$		0			0
$520$	1.44293	+	7.91354i	0.0632765	+	0.347032i
$521$			23.0177i			1.00843i	0.863580	+	0.504213i	$0.168217\pi$
$521$			23.0177i			1.00843i	−0.863580	+	0.504213i	$0.831783\pi$
$522$		0			0
$523$	−23.6127	−	23.6127i	−1.03251	−	1.03251i	−0.999453	−	0.0330574i	$-0.989476\pi$
$523$	−23.6127	−	23.6127i	−1.03251	−	1.03251i	−0.0330574	−	0.999453i	$-0.510524\pi$
$524$	3.26462			0.142616
$525$		0			0
$526$	−4.47061			−0.194928
$527$	−17.9123	−	17.9123i	−0.780272	−	0.780272i
$528$		0			0
$529$		−	1.00000i		−	0.0434783i
$530$	0.129062	+	0.707825i	0.00560611	+	0.0307460i
$531$		0			0
$532$		0			0
$533$	−15.9829	+	15.9829i	−0.692298	+	0.692298i
$534$		0			0
$535$	−4.96055	+	7.17293i	−0.214463	+	0.310113i
$536$		−	12.9325i		−	0.558599i
$537$		0			0
$538$	11.3411	+	11.3411i	0.488949	+	0.488949i
$539$	−42.8840			−1.84715
$540$		0			0
$541$	0.170893			0.00734727			0.00367364	−	0.999993i	$-0.498831\pi$
$541$	0.170893			0.00734727			0.00367364	+	0.999993i	$0.498831\pi$
$542$	−3.38690	−	3.38690i	−0.145480	−	0.145480i
$543$		0			0
$544$			4.22197i			0.181016i
$545$	31.0615	−	5.66364i	1.33053	−	0.242604i
$546$		0			0
$547$	4.39490	−	4.39490i	0.187912	−	0.187912i	−0.606881	−	0.794793i	$-0.707579\pi$
$547$	4.39490	−	4.39490i	0.187912	−	0.187912i	0.794793	+	0.606881i	$0.207579\pi$
$548$	−1.11468	+	1.11468i	−0.0476170	+	0.0476170i
$549$		0			0
$550$	−12.6213	+	27.9104i	−0.538173	+	1.19010i
$551$		−	66.4712i		−	2.83177i
$552$		0			0
$553$		0			0
$554$	−27.5441			−1.17024
$555$		0			0
$556$	20.5113			0.869873
$557$	3.54712	+	3.54712i	0.150296	+	0.150296i	0.778250	−	0.627954i	$-0.216107\pi$
$557$	3.54712	+	3.54712i	0.150296	+	0.150296i	−0.627954	+	0.778250i	$0.716107\pi$
$558$		0			0
$559$			43.5178i			1.84061i
$560$		0			0
$561$		0			0
$562$	11.5631	−	11.5631i	0.487759	−	0.487759i
$563$	−19.1843	+	19.1843i	−0.808524	+	0.808524i	−0.984410	−	0.175887i	$-0.943721\pi$
$563$	−19.1843	+	19.1843i	−0.808524	+	0.808524i	0.175887	+	0.984410i	$0.443721\pi$
$564$		0			0
$565$	0.726261	+	0.502258i	0.0305540	+	0.0211301i
$566$			4.79886i			0.201711i
$567$		0			0
$568$	−4.45626	−	4.45626i	−0.186981	−	0.186981i
$569$	14.6530			0.614285			0.307142	−	0.951664i	$-0.400627\pi$
$569$	14.6530			0.614285			0.307142	+	0.951664i	$0.400627\pi$
$570$		0			0
$571$	−44.8044			−1.87500			−0.937502	−	0.347979i	$-0.886868\pi$
$571$	−44.8044			−1.87500			−0.937502	+	0.347979i	$0.886868\pi$
$572$	15.5837	+	15.5837i	0.651587	+	0.651587i
$573$		0			0
$574$		0			0
$575$	−2.06018	+	4.55584i	−0.0859155	+	0.189992i
$576$		0			0
$577$	−1.99898	+	1.99898i	−0.0832188	+	0.0832188i	−0.747491	−	0.664272i	$-0.768742\pi$
$577$	−1.99898	+	1.99898i	−0.0832188	+	0.0832188i	0.664272	+	0.747491i	$0.268742\pi$
$578$	0.583393	−	0.583393i	0.0242659	−	0.0242659i
$579$		0			0
$580$	21.4633	−	3.91354i	0.891214	−	0.162501i
$581$		0			0
$582$		0			0
$583$	1.39388	+	1.39388i	0.0577286	+	0.0577286i
$584$	1.91689			0.0793216
$585$		0			0
$586$	−11.6312			−0.480481
$587$	12.0638	+	12.0638i	0.497927	+	0.497927i	0.910792	−	0.412865i	$-0.135472\pi$
$587$	12.0638	+	12.0638i	0.497927	+	0.497927i	−0.412865	+	0.910792i	$0.635472\pi$
$588$		0			0
$589$			40.8763i			1.68428i
$590$	1.40126	−	2.02622i	0.0576891	−	0.0834182i
$591$		0			0
$592$	−6.24548	+	6.24548i	−0.256688	+	0.256688i
$593$	−30.9527	+	30.9527i	−1.27108	+	1.27108i	−0.325551	+	0.945525i	$0.605550\pi$
$593$	−30.9527	+	30.9527i	−1.27108	+	1.27108i	−0.945525	+	0.325551i	$0.894450\pi$
$594$		0			0
$595$		0			0
$596$		−	2.19613i		−	0.0899568i
$597$		0			0
$598$	2.54374	+	2.54374i	0.104021	+	0.104021i
$599$	29.7084			1.21385			0.606926	−	0.794758i	$-0.292402\pi$
$599$	29.7084			1.21385			0.606926	+	0.794758i	$0.292402\pi$
$600$		0			0
$601$	−19.7215			−0.804457			−0.402229	−	0.915539i	$-0.631764\pi$
$601$	−19.7215			−0.804457			−0.402229	+	0.915539i	$0.631764\pi$
$602$		0			0
$603$		0			0
$604$			7.52939i			0.306367i
$605$	10.6418	+	58.3638i	0.432653	+	2.37283i
$606$		0			0
$607$	−5.01537	+	5.01537i	−0.203567	+	0.203567i	−0.801527	−	0.597959i	$-0.795978\pi$
$607$	−5.01537	+	5.01537i	−0.203567	+	0.203567i	0.597959	+	0.801527i	$0.295978\pi$
$608$	4.81732	−	4.81732i	0.195368	−	0.195368i
$609$		0			0
$610$	7.72423	−	11.1692i	0.312745	−	0.452227i
$611$			35.2486i			1.42600i
$612$		0			0
$613$	−25.1861	−	25.1861i	−1.01726	−	1.01726i	−0.999848	−	0.0174105i	$-0.994458\pi$
$613$	−25.1861	−	25.1861i	−1.01726	−	1.01726i	−0.0174105	−	0.999848i	$-0.505542\pi$
$614$	6.28468			0.253629
$615$		0			0
$616$		0			0
$617$	6.33535	+	6.33535i	0.255051	+	0.255051i	0.823038	−	0.567986i	$-0.192277\pi$
$617$	6.33535	+	6.33535i	0.255051	+	0.255051i	−0.567986	+	0.823038i	$0.692277\pi$
$618$		0			0
$619$			27.7006i			1.11338i	0.830720	+	0.556691i	$0.187929\pi$
$619$			27.7006i			1.11338i	−0.830720	+	0.556691i	$0.812071\pi$
$620$	−13.1988	+	2.40662i	−0.530076	+	0.0966522i
$621$		0			0
$622$	−3.41026	+	3.41026i	−0.136739	+	0.136739i
$623$		0			0
$624$		0			0
$625$	18.7717	−	16.5113i	0.750868	−	0.660452i
$626$			28.2248i			1.12809i
$627$		0			0
$628$	16.4674	+	16.4674i	0.657123	+	0.657123i
$629$	37.2903			1.48686
$630$		0			0
$631$	4.89421			0.194835			0.0974177	−	0.995244i	$-0.468942\pi$
$631$	4.89421			0.194835			0.0974177	+	0.995244i	$0.468942\pi$
$632$	3.63063	+	3.63063i	0.144419	+	0.144419i
$633$		0			0
$634$		−	25.9733i		−	1.03153i
$635$	1.06441	+	0.736111i	0.0422399	+	0.0292117i
$636$		0			0
$637$	17.8062	−	17.8062i	0.705506	−	0.705506i
$638$	42.2664	−	42.2664i	1.67334	−	1.67334i
$639$		0			0
$640$	1.83912	+	1.27187i	0.0726974	+	0.0502751i
$641$			17.0211i			0.672292i	0.941810	+	0.336146i	$0.109124\pi$
$641$			17.0211i			0.672292i	−0.941810	+	0.336146i	$0.890876\pi$
$642$		0			0
$643$	−6.00814	−	6.00814i	−0.236938	−	0.236938i	0.578643	−	0.815581i	$-0.303582\pi$
$643$	−6.00814	−	6.00814i	−0.236938	−	0.236938i	−0.815581	+	0.578643i	$0.803582\pi$
$644$		0			0
$645$		0			0
$646$	−28.7631			−1.13167
$647$	−6.49374	−	6.49374i	−0.255295	−	0.255295i	0.567842	−	0.823137i	$-0.307778\pi$
$647$	−6.49374	−	6.49374i	−0.255295	−	0.255295i	−0.823137	+	0.567842i	$0.807778\pi$
$648$		0			0
$649$		−	6.74955i		−	0.264943i
$650$	−6.34830	−	16.8294i	−0.249001	−	0.660105i
$651$		0			0
$652$	5.82707	−	5.82707i	0.228206	−	0.228206i
$653$	21.8698	−	21.8698i	0.855832	−	0.855832i	−0.135012	−	0.990844i	$-0.543107\pi$
$653$	21.8698	−	21.8698i	0.855832	−	0.855832i	0.990844	+	0.135012i	$0.0431074\pi$
$654$		0			0
$655$	−7.18151	+	1.30945i	−0.280605	+	0.0511645i
$656$			6.28325i			0.245320i
$657$		0			0
$658$		0			0
$659$	28.6126			1.11459			0.557294	−	0.830315i	$-0.311840\pi$
$659$	28.6126			1.11459			0.557294	+	0.830315i	$0.311840\pi$
$660$		0			0
$661$	4.59279			0.178639			0.0893193	−	0.996003i	$-0.471531\pi$
$661$	4.59279			0.178639			0.0893193	+	0.996003i	$0.471531\pi$
$662$	−4.03358	−	4.03358i	−0.156770	−	0.156770i
$663$		0			0
$664$		−	3.23632i		−	0.125594i
$665$		0			0
$666$		0			0
$667$	6.89919	−	6.89919i	0.267138	−	0.267138i
$668$	11.9401	−	11.9401i	0.461976	−	0.461976i
$669$		0			0
$670$	5.18728	+	28.4489i	0.200402	+	1.09908i
$671$		−	37.2057i		−	1.43631i
$672$		0			0
$673$	−2.17394	−	2.17394i	−0.0837993	−	0.0837993i	0.663965	−	0.747764i	$-0.268873\pi$
$673$	−2.17394	−	2.17394i	−0.0837993	−	0.0837993i	−0.747764	+	0.663965i	$0.768873\pi$
$674$	−4.27814			−0.164788
$675$		0			0
$676$	0.0587785			0.00226071
$677$	14.1547	+	14.1547i	0.544009	+	0.544009i	0.924702	−	0.380693i	$-0.124314\pi$
$677$	14.1547	+	14.1547i	0.544009	+	0.544009i	−0.380693	+	0.924702i	$0.624314\pi$
$678$		0			0
$679$		0			0
$680$	−1.69345	−	9.28749i	−0.0649408	−	0.356159i
$681$		0			0
$682$	−25.9916	+	25.9916i	−0.995272	+	0.995272i
$683$	1.45337	−	1.45337i	0.0556115	−	0.0556115i	−0.678754	−	0.734366i	$-0.737480\pi$
$683$	1.45337	−	1.45337i	0.0556115	−	0.0556115i	0.734366	+	0.678754i	$0.237480\pi$
$684$		0			0
$685$	2.00498	−	2.89919i	0.0766063	−	0.110772i
$686$		0			0
$687$		0			0
$688$	8.55391	+	8.55391i	0.326115	+	0.326115i
$689$	−1.15753			−0.0440982
$690$		0			0
$691$	24.3865			0.927708			0.463854	−	0.885912i	$-0.346466\pi$
$691$	24.3865			0.927708			0.463854	+	0.885912i	$0.346466\pi$
$692$	−0.626393	−	0.626393i	−0.0238119	−	0.0238119i
$693$		0			0
$694$		−	32.5113i		−	1.23411i
$695$	−45.1207	+	8.22716i	−1.71153	+	0.312074i
$696$		0			0
$697$	18.7579	−	18.7579i	0.710506	−	0.710506i
$698$	14.1030	−	14.1030i	0.533806	−	0.533806i
$699$		0			0
$700$		0			0
$701$			13.8643i			0.523649i	0.965116	+	0.261824i	$0.0843241\pi$
$701$			13.8643i			0.523649i	−0.965116	+	0.261824i	$0.915676\pi$
$702$		0			0
$703$	−42.5487	−	42.5487i	−1.60476	−	1.60476i
$704$	6.12629			0.230893
$705$		0			0
$706$	−12.8185			−0.482430
$707$		0			0
$708$		0			0
$709$		−	7.75598i		−	0.291282i	−0.989338	−	0.145641i	$-0.953476\pi$
$709$		−	7.75598i		−	0.291282i	0.989338	−	0.145641i	$-0.0465244\pi$
$710$	11.5903	+	8.01546i	0.434976	+	0.300815i
$711$		0			0
$712$	−6.89919	+	6.89919i	−0.258558	+	0.258558i
$713$	−4.24264	+	4.24264i	−0.158888	+	0.158888i
$714$		0			0
$715$	−40.5316	−	28.0303i	−1.51580	−	1.04827i
$716$		−	15.9382i		−	0.595638i
$717$		0			0
$718$	−19.2019	−	19.2019i	−0.716607	−	0.716607i
$719$	5.44780			0.203169			0.101584	−	0.994827i	$-0.467609\pi$
$719$	5.44780			0.203169			0.101584	+	0.994827i	$0.467609\pi$
$720$		0			0
$721$		0			0
$722$	19.3841	+	19.3841i	0.721400	+	0.721400i
$723$		0			0
$724$		−	18.0731i		−	0.671683i
$725$	−45.6452	+	17.2180i	−1.69522	+	0.639460i
$726$		0			0
$727$	−13.0588	+	13.0588i	−0.484323	+	0.484323i	−0.906509	−	0.422186i	$-0.861263\pi$
$727$	−13.0588	+	13.0588i	−0.484323	+	0.484323i	0.422186	+	0.906509i	$0.361263\pi$
$728$		0			0
$729$		0			0
$730$	−4.21678	+	0.768872i	−0.156070	+	0.0284572i
$731$		−	51.0734i		−	1.88902i
$732$		0			0
$733$	0.962143	+	0.962143i	0.0355376	+	0.0355376i	0.724652	−	0.689115i	$-0.242000\pi$
$733$	0.962143	+	0.962143i	0.0355376	+	0.0355376i	−0.689115	+	0.724652i	$0.742000\pi$
$734$	−16.9041			−0.623941
$735$		0			0
$736$	1.00000			0.0368605
$737$	56.0229	+	56.0229i	2.06363	+	2.06363i
$738$		0			0
$739$			8.99345i			0.330829i	0.986224	+	0.165415i	$0.0528963\pi$
$739$			8.99345i			0.330829i	−0.986224	+	0.165415i	$0.947104\pi$
$740$	11.2337	−	16.2439i	0.412959	−	0.597137i
$741$		0			0
$742$		0			0
$743$	−12.5189	+	12.5189i	−0.459273	+	0.459273i	−0.898417	−	0.439144i	$-0.855282\pi$
$743$	−12.5189	+	12.5189i	−0.459273	+	0.459273i	0.439144	+	0.898417i	$0.355282\pi$
$744$		0			0
$745$	0.880874	+	4.83104i	0.0322727	+	0.176995i
$746$		−	26.4308i		−	0.967702i
$747$		0			0
$748$	−18.2893	−	18.2893i	−0.668724	−	0.668724i
$749$		0			0
$750$		0			0
$751$	−5.40551			−0.197250			−0.0986249	−	0.995125i	$-0.531444\pi$
$751$	−5.40551			−0.197250			−0.0986249	+	0.995125i	$0.531444\pi$
$752$	6.92850	+	6.92850i	0.252656	+	0.252656i
$753$		0			0
$754$			35.0995i			1.27825i
$755$	−3.02007	−	16.5631i	−0.109911	−	0.602795i
$756$		0			0
$757$	−18.4147	+	18.4147i	−0.669292	+	0.669292i	−0.957552	−	0.288260i	$-0.906923\pi$
$757$	−18.4147	+	18.4147i	−0.669292	+	0.669292i	0.288260	+	0.957552i	$0.406923\pi$
$758$	11.7791	−	11.7791i	0.427835	−	0.427835i
$759$		0			0
$760$	−8.66490	+	12.5294i	−0.314309	+	0.454489i
$761$		−	40.4042i		−	1.46465i	−0.680955	−	0.732325i	$-0.738435\pi$
$761$		−	40.4042i		−	1.46465i	0.680955	−	0.732325i	$-0.261565\pi$
$762$		0			0
$763$		0			0
$764$	23.8802			0.863955
$765$		0			0
$766$	0.816462			0.0295000
$767$	2.80253	+	2.80253i	0.101193	+	0.101193i
$768$		0			0
$769$		−	33.7737i		−	1.21791i	−0.793204	−	0.608956i	$-0.791589\pi$
$769$		−	33.7737i		−	1.21791i	0.793204	−	0.608956i	$-0.208411\pi$
$770$		0			0
$771$		0			0
$772$	10.6254	−	10.6254i	0.382418	−	0.382418i
$773$	−5.04077	+	5.04077i	−0.181304	+	0.181304i	−0.791924	−	0.610620i	$-0.790920\pi$
$773$	−5.04077	+	5.04077i	−0.181304	+	0.181304i	0.610620	+	0.791924i	$0.290920\pi$
$774$		0			0
$775$	28.0694	−	10.5882i	1.00828	−	0.380338i
$776$			7.24241i			0.259987i
$777$		0			0
$778$	9.23113	+	9.23113i	0.330952	+	0.330952i
$779$	−42.8060			−1.53369
$780$		0			0
$781$	38.6085			1.38152
$782$	−2.98538	−	2.98538i	−0.106757	−	0.106757i
$783$		0			0
$784$		−	7.00000i		−	0.250000i
$785$	−42.8302	−	29.6199i	−1.52868	−	1.05718i
$786$		0			0
$787$	20.4338	−	20.4338i	0.728385	−	0.728385i	−0.241913	−	0.970298i	$-0.577775\pi$
$787$	20.4338	−	20.4338i	0.728385	−	0.728385i	0.970298	+	0.241913i	$0.0777748\pi$
$788$	−16.3729	+	16.3729i	−0.583262	+	0.583262i
$789$		0			0
$790$	−9.44293	−	6.53041i	−0.335964	−	0.232341i
$791$		0			0
$792$		0			0
$793$	15.4485	+	15.4485i	0.548591	+	0.548591i
$794$	−16.2045			−0.575075
$795$		0			0
$796$	25.2019			0.893256
$797$	3.29522	+	3.29522i	0.116723	+	0.116723i	0.763056	−	0.646333i	$-0.223698\pi$
$797$	3.29522	+	3.29522i	0.116723	+	0.116723i	−0.646333	+	0.763056i	$0.723698\pi$
$798$		0			0
$799$		−	41.3685i		−	1.46351i
$800$	−4.55584	−	2.06018i	−0.161073	−	0.0728384i
$801$		0			0
$802$	−21.7380	+	21.7380i	−0.767596	+	0.767596i
$803$	−8.30386	+	8.30386i	−0.293037	+	0.293037i
$804$		0			0
$805$		0			0
$806$		−	21.5843i		−	0.760276i
$807$		0			0
$808$	0.235305	+	0.235305i	0.00827801	+	0.00827801i
$809$	25.8270			0.908028			0.454014	−	0.890994i	$-0.349992\pi$
$809$	25.8270			0.908028			0.454014	+	0.890994i	$0.349992\pi$
$810$		0			0
$811$	36.8456			1.29382			0.646912	−	0.762564i	$-0.276060\pi$
$811$	36.8456			1.29382			0.646912	+	0.762564i	$0.276060\pi$
$812$		0			0
$813$		0			0
$814$		−	54.1101i		−	1.89656i
$815$	−10.4811	+	15.1557i	−0.367138	+	0.530879i
$816$		0			0
$817$	−58.2754	+	58.2754i	−2.03880	+	2.03880i
$818$	−17.8551	+	17.8551i	−0.624288	+	0.624288i
$819$		0			0
$820$	−2.52023	−	13.8219i	−0.0880104	−	0.482681i
$821$		−	31.6523i		−	1.10467i	−0.833621	−	0.552337i	$-0.813736\pi$
$821$		−	31.6523i		−	1.10467i	0.833621	−	0.552337i	$-0.186264\pi$
$822$		0			0
$823$	−13.2844	−	13.2844i	−0.463063	−	0.463063i	0.436595	−	0.899658i	$-0.356184\pi$
$823$	−13.2844	−	13.2844i	−0.463063	−	0.463063i	−0.899658	+	0.436595i	$0.856184\pi$
$824$	−8.48528			−0.295599
$825$		0			0
$826$		0			0
$827$	−1.61137	−	1.61137i	−0.0560328	−	0.0560328i	0.678535	−	0.734568i	$-0.262615\pi$
$827$	−1.61137	−	1.61137i	−0.0560328	−	0.0560328i	−0.734568	+	0.678535i	$0.762615\pi$
$828$		0			0
$829$		−	16.6189i		−	0.577198i	−0.957450	−	0.288599i	$-0.906811\pi$
$829$		−	16.6189i		−	0.577198i	0.957450	−	0.288599i	$-0.0931895\pi$
$830$	1.29810	+	7.11926i	0.0450577	+	0.247113i
$831$		0			0
$832$	−2.54374	+	2.54374i	−0.0881883	+	0.0881883i
$833$	−20.8977	+	20.8977i	−0.724062	+	0.724062i
$834$		0			0
$835$	−21.4766	+	31.0550i	−0.743229	+	1.07470i
$836$			41.7367i			1.44349i
$837$		0			0
$838$	13.9632	+	13.9632i	0.482349	+	0.482349i
$839$	10.5788			0.365221			0.182610	−	0.983185i	$-0.441545\pi$
$839$	10.5788			0.365221			0.182610	+	0.983185i	$0.441545\pi$
$840$		0			0
$841$	66.1976			2.28267
$842$	−6.84498	−	6.84498i	−0.235894	−	0.235894i
$843$		0			0
$844$		−	15.8004i		−	0.543872i
$845$	−0.129301	+	0.0235763i	−0.00444809	+	0.000811048i
$846$		0			0
$847$		0			0
$848$	−0.227524	+	0.227524i	−0.00781322	+	0.00781322i
$849$		0			0
$850$	7.45049	+	19.7514i	0.255550	+	0.677466i
$851$		−	8.83244i		−	0.302772i
$852$		0			0
$853$	0.718698	+	0.718698i	0.0246077	+	0.0246077i	0.719304	−	0.694696i	$-0.244461\pi$
$853$	0.718698	+	0.718698i	0.0246077	+	0.0246077i	−0.694696	+	0.719304i	$0.744461\pi$
$854$		0			0
$855$		0			0
$856$	−3.90020			−0.133306
$857$	−6.92993	−	6.92993i	−0.236722	−	0.236722i	0.578769	−	0.815491i	$-0.303533\pi$
$857$	−6.92993	−	6.92993i	−0.236722	−	0.236722i	−0.815491	+	0.578769i	$0.803533\pi$
$858$		0			0
$859$			23.0321i			0.785845i	0.919571	+	0.392923i	$0.128536\pi$
$859$			23.0321i			0.785845i	−0.919571	+	0.392923i	$0.871464\pi$
$860$	−22.2479	−	15.3859i	−0.758647	−	0.524654i
$861$		0			0
$862$	25.8004	−	25.8004i	0.878765	−	0.878765i
$863$	−15.9585	+	15.9585i	−0.543233	+	0.543233i	−0.924475	−	0.381242i	$-0.875496\pi$
$863$	−15.9585	+	15.9585i	−0.543233	+	0.543233i	0.381242	+	0.924475i	$0.375496\pi$
$864$		0			0
$865$	1.62919	+	1.12669i	0.0553940	+	0.0383086i
$866$			4.69913i			0.159683i
$867$		0			0
$868$		0			0
$869$	−31.4554			−1.06705
$870$		0			0
$871$	−46.5233			−1.57638
$872$	9.98445	+	9.98445i	0.338116	+	0.338116i
$873$		0			0
$874$			6.81272i			0.230444i
$875$		0			0
$876$		0			0
$877$	−23.9205	+	23.9205i	−0.807740	+	0.807740i	−0.984291	−	0.176552i	$-0.943506\pi$
$877$	−23.9205	+	23.9205i	−0.807740	+	0.807740i	0.176552	+	0.984291i	$0.443506\pi$
$878$	7.59548	−	7.59548i	0.256335	−	0.256335i
$879$		0			0
$880$	−13.4766	+	2.45728i	−0.454296	+	0.0828348i
$881$			8.66876i			0.292058i	0.989280	+	0.146029i	$0.0466493\pi$
$881$			8.66876i			0.292058i	−0.989280	+	0.146029i	$0.953351\pi$
$882$		0			0
$883$	30.0224	+	30.0224i	1.01033	+	1.01033i	0.999946	+	0.0103874i	$0.00330647\pi$
$883$	30.0224	+	30.0224i	1.01033	+	1.01033i	0.0103874	+	0.999946i	$0.496694\pi$
$884$	15.1881			0.510830
$885$		0			0
$886$	−1.18151			−0.0396935
$887$	−27.8022	−	27.8022i	−0.933507	−	0.933507i	0.0644164	−	0.997923i	$-0.479481\pi$
$887$	−27.8022	−	27.8022i	−0.933507	−	0.933507i	−0.997923	+	0.0644164i	$0.979481\pi$
$888$		0			0
$889$		0			0
$890$	12.4095	−	17.9441i	0.415969	−	0.601488i
$891$		0			0
$892$	−15.7263	+	15.7263i	−0.526554	+	0.526554i
$893$	−47.2019	+	47.2019i	−1.57955	+	1.57955i
$894$		0			0
$895$	6.39286	+	35.0608i	0.213690	+	1.17195i
$896$		0			0
$897$		0			0
$898$	−7.35748	−	7.35748i	−0.245522	−	0.245522i
$899$	−58.5415			−1.95247
$900$		0			0
$901$	1.35850			0.0452581
$902$	−27.2187	−	27.2187i	−0.906282	−	0.906282i
$903$		0			0
$904$			0.394897i			0.0131341i
$905$	7.24920	+	39.7573i	0.240971	+	1.32158i
$906$		0			0
$907$	−8.01594	+	8.01594i	−0.266165	+	0.266165i	−0.827553	−	0.561388i	$-0.810268\pi$
$907$	−8.01594	+	8.01594i	−0.266165	+	0.266165i	0.561388	+	0.827553i	$0.310268\pi$
$908$	8.72863	−	8.72863i	0.289670	−	0.289670i
$909$		0			0
$910$		0			0
$911$			19.4186i			0.643367i	0.946847	+	0.321683i	$0.104249\pi$
$911$			19.4186i			0.643367i	−0.946847	+	0.321683i	$0.895751\pi$
$912$		0			0
$913$	14.0196	+	14.0196i	0.463980	+	0.463980i
$914$	−35.8377			−1.18541
$915$		0			0
$916$	−20.3421			−0.672122
$917$		0			0
$918$		0			0
$919$		−	12.1259i		−	0.399997i	−0.979796	−	0.199998i	$-0.935906\pi$
$919$		−	12.1259i		−	0.399997i	0.979796	−	0.199998i	$-0.0640937\pi$
$920$	−2.19980	+	0.401104i	−0.0725252	+	0.0132240i
$921$		0			0
$922$	18.3230	−	18.3230i	0.603436	−	0.603436i
$923$	−16.0309	+	16.0309i	−0.527664	+	0.527664i
$924$		0			0
$925$	−18.1964	+	40.2392i	−0.598295	+	1.32306i
$926$		−	12.9007i		−	0.423943i
$927$		0			0
$928$	6.89919	+	6.89919i	0.226477	+	0.226477i
$929$	−37.4941			−1.23014			−0.615070	−	0.788472i	$-0.710872\pi$
$929$	−37.4941			−1.23014			−0.615070	+	0.788472i	$0.710872\pi$
$930$		0			0
$931$	47.6891			1.56295
$932$	−5.20181	−	5.20181i	−0.170391	−	0.170391i
$933$		0			0
$934$			0.658111i			0.0215341i
$935$	47.5688	+	32.8969i	1.55567	+	1.07584i
$936$		0			0
$937$	−19.0538	+	19.0538i	−0.622461	+	0.622461i	−0.946160	−	0.323699i	$-0.895073\pi$
$937$	−19.0538	+	19.0538i	−0.622461	+	0.622461i	0.323699	+	0.946160i	$0.395073\pi$
$938$		0			0
$939$		0			0
$940$	−18.0203	−	12.4623i	−0.587759	−	0.406474i
$941$		−	13.8821i		−	0.452543i	−0.974064	−	0.226271i	$-0.927346\pi$
$941$		−	13.8821i		−	0.452543i	0.974064	−	0.226271i	$-0.0726536\pi$
$942$		0			0
$943$	−4.44293	−	4.44293i	−0.144682	−	0.144682i
$944$	1.10174			0.0358584
$945$		0			0
$946$	−74.1101			−2.40953
$947$	6.51404	+	6.51404i	0.211678	+	0.211678i	0.804980	−	0.593302i	$-0.202176\pi$
$947$	6.51404	+	6.51404i	0.211678	+	0.211678i	−0.593302	+	0.804980i	$0.702176\pi$
$948$		0			0
$949$		−	6.89581i		−	0.223847i
$950$	14.0355	−	31.0377i	0.455370	−	1.00699i
$951$		0			0
$952$		0			0
$953$	−18.7131	+	18.7131i	−0.606176	+	0.606176i	−0.941945	−	0.335769i	$-0.891004\pi$
$953$	−18.7131	+	18.7131i	−0.606176	+	0.606176i	0.335769	+	0.941945i	$0.391004\pi$
$954$		0			0
$955$	−52.5316	+	9.57843i	−1.69988	+	0.309951i
$956$		−	15.2265i		−	0.492459i
$957$		0			0
$958$	−15.3095	−	15.3095i	−0.494626	−	0.494626i
$959$		0			0
$960$		0			0
$961$	5.00000			0.161290
$962$	22.4674	+	22.4674i	0.724379	+	0.724379i
$963$		0			0
$964$			29.3972i			0.946819i
$965$	−19.1119	+	27.6358i	−0.615235	+	0.889626i
$966$		0			0
$967$	−36.7563	+	36.7563i	−1.18200	+	1.18200i	−0.202780	+	0.979224i	$0.564998\pi$
$967$	−36.7563	+	36.7563i	−1.18200	+	1.18200i	−0.979224	+	0.202780i	$0.935002\pi$
$968$	−18.7605	+	18.7605i	−0.602987	+	0.602987i
$969$		0			0
$970$	−2.90496	−	15.9318i	−0.0932726	−	0.511541i
$971$		−	19.6641i		−	0.631050i	−0.948917	−	0.315525i	$-0.897819\pi$
$971$		−	19.6641i		−	0.631050i	0.948917	−	0.315525i	$-0.102181\pi$
$972$		0			0
$973$		0			0
$974$	−29.8684			−0.957045
$975$		0			0
$976$	6.07313			0.194396
$977$	−1.93944	−	1.93944i	−0.0620481	−	0.0620481i	0.675402	−	0.737450i	$-0.263970\pi$
$977$	−1.93944	−	1.93944i	−0.0620481	−	0.0620481i	−0.737450	+	0.675402i	$0.763970\pi$
$978$		0			0
$979$		−	59.7737i		−	1.91038i
$980$	2.80773	+	15.3986i	0.0896895	+	0.491890i
$981$		0			0
$982$	−0.115163	+	0.115163i	−0.00367501	+	0.00367501i
$983$	−33.5625	+	33.5625i	−1.07048	+	1.07048i	−0.0731563	+	0.997320i	$0.523307\pi$
$983$	−33.5625	+	33.5625i	−1.07048	+	1.07048i	−0.997320	+	0.0731563i	$0.976693\pi$
$984$		0			0
$985$	29.4499	−	42.5844i	0.938353	−	1.35685i
$986$		−	41.1935i		−	1.31187i
$987$		0			0
$988$	−17.3298	−	17.3298i	−0.551334	−	0.551334i
$989$	−12.0971			−0.384664
$990$		0			0
$991$	20.0267			0.636168			0.318084	−	0.948063i	$-0.396961\pi$
$991$	20.0267			0.636168			0.318084	+	0.948063i	$0.396961\pi$
$992$	−4.24264	−	4.24264i	−0.134704	−	0.134704i
$993$		0			0
$994$		0			0
$995$	−55.4390	+	10.1086i	−1.75753	+	0.320463i
$996$		0			0
$997$	24.7370	−	24.7370i	0.783429	−	0.783429i	−0.196979	−	0.980408i	$-0.563113\pi$
$997$	24.7370	−	24.7370i	0.783429	−	0.783429i	0.980408	+	0.196979i	$0.0631130\pi$
$998$	15.0810	−	15.0810i	0.477381	−	0.477381i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2070.2.j.h.323.2	✓	16
3.2	odd	2	inner	2070.2.j.h.323.7	yes	16
5.2	odd	4	inner	2070.2.j.h.737.7	yes	16
15.2	even	4	inner	2070.2.j.h.737.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2070.2.j.h.323.2	✓	16	1.1	even	1	trivial
2070.2.j.h.323.7	yes	16	3.2	odd	2	inner
2070.2.j.h.737.2	yes	16	15.2	even	4	inner
2070.2.j.h.737.7	yes	16	5.2	odd	4	inner

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)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-0.401104 - 2.19980i) q^{5} +(0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-0.401104 - 2.19980i) q^{5} +(0.707107 - 0.707107i) q^{8} +(-1.27187 + 1.83912i) q^{10} +6.12629i q^{11} +(-2.54374 - 2.54374i) q^{13} -1.00000 q^{16} +(2.98538 + 2.98538i) q^{17} -6.81272i q^{19} +(2.19980 - 0.401104i) q^{20} +(4.33194 - 4.33194i) q^{22} +(0.707107 - 0.707107i) q^{23} +(-4.67823 + 1.76469i) q^{25} +3.59739i q^{26} +9.75692 q^{29} -6.00000 q^{31} +(0.707107 + 0.707107i) q^{32} -4.22197i q^{34} +(6.24548 - 6.24548i) q^{37} +(-4.81732 + 4.81732i) q^{38} +(-1.83912 - 1.27187i) q^{40} -6.28325i q^{41} +(-8.55391 - 8.55391i) q^{43} -6.12629 q^{44} -1.00000 q^{46} +(-6.92850 - 6.92850i) q^{47} +7.00000i q^{49} +(4.55584 + 2.06018i) q^{50} +(2.54374 - 2.54374i) q^{52} +(0.227524 - 0.227524i) q^{53} +(13.4766 - 2.45728i) q^{55} +(-6.89919 - 6.89919i) q^{58} -1.10174 q^{59} -6.07313 q^{61} +(4.24264 + 4.24264i) q^{62} -1.00000i q^{64} +(-4.57541 + 6.61602i) q^{65} +(9.14466 - 9.14466i) q^{67} +(-2.98538 + 2.98538i) q^{68} -6.30210i q^{71} +(1.35545 + 1.35545i) q^{73} -8.83244 q^{74} +6.81272 q^{76} +5.13449i q^{79} +(0.401104 + 2.19980i) q^{80} +(-4.44293 + 4.44293i) q^{82} +(2.28842 - 2.28842i) q^{83} +(5.36980 - 7.76469i) q^{85} +12.0971i q^{86} +(4.33194 + 4.33194i) q^{88} -9.75692 q^{89} +(0.707107 + 0.707107i) q^{92} +9.79837i q^{94} +(-14.9866 + 2.73261i) q^{95} +(-5.12116 + 5.12116i) q^{97} +(4.94975 - 4.94975i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 8 q^{10} - 16 q^{13} - 16 q^{16} + 8 q^{22} - 16 q^{25} - 96 q^{31} + 24 q^{37} + 8 q^{43} - 16 q^{46} + 16 q^{52} - 32 q^{58} + 16 q^{61} - 8 q^{67} - 32 q^{73} + 16 q^{76} + 32 q^{82} + 96 q^{85} + 8 q^{88} + 80 q^{97}+O(q^{100}) \) 16 * q - 8 * q^10 - 16 * q^13 - 16 * q^16 + 8 * q^22 - 16 * q^25 - 96 * q^31 + 24 * q^37 + 8 * q^43 - 16 * q^46 + 16 * q^52 - 32 * q^58 + 16 * q^61 - 8 * q^67 - 32 * q^73 + 16 * q^76 + 32 * q^82 + 96 * q^85 + 8 * q^88 + 80 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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