LMFDB - Embedded newform 280.2.bo.a.33.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(17,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(12))

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

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

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

chi := DirichletCharacter("280.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.bo (of order $12$, degree $4$, 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:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			33.1
Character	$\chi$	$=$	280.33
Dual form			280.2.bo.a.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.75887 - 0.739238i) q^{3} +(-1.04631 - 1.97617i) q^{5} +(-1.91229 + 1.82843i) q^{7} +(4.46683 + 2.57893i) q^{9} +O(q^{10})$	\(q+(-2.75887 - 0.739238i) q^{3} +(-1.04631 - 1.97617i) q^{5} +(-1.91229 + 1.82843i) q^{7} +(4.46683 + 2.57893i) q^{9} +(2.37354 + 4.11109i) q^{11} +(1.92718 - 1.92718i) q^{13} +(1.42578 + 6.22547i) q^{15} +(-1.76751 + 6.59645i) q^{17} +(0.0439918 - 0.0761960i) q^{19} +(6.62741 - 3.63077i) q^{21} +(-0.242586 + 0.0650008i) q^{23} +(-2.81047 + 4.13537i) q^{25} +(-4.35808 - 4.35808i) q^{27} -0.284886i q^{29} +(-3.69058 + 2.13075i) q^{31} +(-3.50922 - 13.0966i) q^{33} +(5.61413 + 1.86589i) q^{35} +(1.05500 + 3.93731i) q^{37} +(-6.74148 + 3.89220i) q^{39} +9.16296i q^{41} +(-6.72406 - 6.72406i) q^{43} +(0.422691 - 11.5256i) q^{45} +(6.75301 - 1.80946i) q^{47} +(0.313692 - 6.99297i) q^{49} +(9.75269 - 16.8922i) q^{51} +(-2.27886 + 8.50482i) q^{53} +(5.64073 - 8.99198i) q^{55} +(-0.177695 + 0.177695i) q^{57} +(-1.56522 - 2.71104i) q^{59} +(-4.84125 - 2.79509i) q^{61} +(-13.2573 + 3.23564i) q^{63} +(-5.82485 - 1.79199i) q^{65} +(-2.19738 - 0.588786i) q^{67} +0.717316 q^{69} -3.53569 q^{71} +(8.72777 + 2.33860i) q^{73} +(10.8107 - 9.33136i) q^{75} +(-12.0557 - 3.52174i) q^{77} +(10.7043 + 6.18015i) q^{79} +(1.06496 + 1.84456i) q^{81} +(-10.1777 + 10.1777i) q^{83} +(14.8850 - 3.40904i) q^{85} +(-0.210599 + 0.785966i) q^{87} +(-7.02336 + 12.1648i) q^{89} +(-0.161611 + 7.20903i) q^{91} +(11.7570 - 3.15027i) q^{93} +(-0.196605 - 0.00721033i) q^{95} +(-5.72716 - 5.72716i) q^{97} +24.4847i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{7}+O(q^{10}) $ 48 * q - 4 * q^7	$ 48 q - 4 q^{7} + 4 q^{11} + 8 q^{15} - 4 q^{21} - 4 q^{23} - 8 q^{25} - 36 q^{33} + 24 q^{35} + 8 q^{37} - 16 q^{43} + 48 q^{45} + 24 q^{51} + 16 q^{53} - 96 q^{57} - 36 q^{61} - 68 q^{63} + 12 q^{65} - 16 q^{67} - 64 q^{71} - 48 q^{73} - 48 q^{75} + 4 q^{77} - 40 q^{85} - 12 q^{87} - 80 q^{91} + 24 q^{95}+O(q^{100}) $ 48 * q - 4 * q^7 + 4 * q^11 + 8 * q^15 - 4 * q^21 - 4 * q^23 - 8 * q^25 - 36 * q^33 + 24 * q^35 + 8 * q^37 - 16 * q^43 + 48 * q^45 + 24 * q^51 + 16 * q^53 - 96 * q^57 - 36 * q^61 - 68 * q^63 + 12 * q^65 - 16 * q^67 - 64 * q^71 - 48 * q^73 - 48 * q^75 + 4 * q^77 - 40 * q^85 - 12 * q^87 - 80 * q^91 + 24 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.75887	−	0.739238i	−1.59284	−	0.426799i	−0.649967	−	0.759962i	$-0.725217\pi$
$3$	−2.75887	−	0.739238i	−1.59284	−	0.426799i	−0.942869	+	0.333163i	$0.891884\pi$
$4$		0			0
$5$	−1.04631	−	1.97617i	−0.467925	−	0.883768i
$5$	−1.04631	−	1.97617i	−0.467925	−	0.883768i
$6$		0			0
$7$	−1.91229	+	1.82843i	−0.722777	+	0.691081i
$7$	−1.91229	+	1.82843i	−0.722777	+	0.691081i
$8$		0			0
$9$	4.46683	+	2.57893i	1.48894	+	0.859643i
$10$		0			0
$11$	2.37354	+	4.11109i	0.715648	+	1.23954i	0.962709	+	0.270539i	$0.0872020\pi$
$11$	2.37354	+	4.11109i	0.715648	+	1.23954i	−0.247061	+	0.969000i	$0.579465\pi$
$12$		0			0
$13$	1.92718	−	1.92718i	0.534503	−	0.534503i	−0.387406	−	0.921909i	$-0.626629\pi$
$13$	1.92718	−	1.92718i	0.534503	−	0.534503i	0.921909	+	0.387406i	$0.126629\pi$
$14$		0			0
$15$	1.42578	+	6.22547i	0.368136	+	1.60741i
$16$		0			0
$17$	−1.76751	+	6.59645i	−0.428685	+	1.59987i	0.327058	+	0.945004i	$0.393943\pi$
$17$	−1.76751	+	6.59645i	−0.428685	+	1.59987i	−0.755742	+	0.654869i	$0.772724\pi$
$18$		0			0
$19$	0.0439918	−	0.0761960i	0.0100924	−	0.0174806i	−0.860935	−	0.508715i	$-0.830121\pi$
$19$	0.0439918	−	0.0761960i	0.0100924	−	0.0174806i	0.871028	+	0.491234i	$0.163454\pi$
$20$		0			0
$21$	6.62741	−	3.63077i	1.44622	−	0.792299i
$22$		0			0
$23$	−0.242586	+	0.0650008i	−0.0505827	+	0.0135536i	−0.284022	−	0.958818i	$-0.591669\pi$
$23$	−0.242586	+	0.0650008i	−0.0505827	+	0.0135536i	0.233439	+	0.972371i	$0.425002\pi$
$24$		0			0
$25$	−2.81047	+	4.13537i	−0.562093	+	0.827074i
$26$		0			0
$27$	−4.35808	−	4.35808i	−0.838714	−	0.838714i
$28$		0			0
$29$		−	0.284886i		−	0.0529021i	−0.999650	−	0.0264510i	$-0.991579\pi$
$29$		−	0.284886i		−	0.0529021i	0.999650	−	0.0264510i	$-0.00842061\pi$
$30$		0			0
$31$	−3.69058	+	2.13075i	−0.662847	+	0.382695i	−0.793361	−	0.608752i	$-0.791671\pi$
$31$	−3.69058	+	2.13075i	−0.662847	+	0.382695i	0.130514	+	0.991446i	$0.458337\pi$
$32$		0			0
$33$	−3.50922	−	13.0966i	−0.610876	−	2.27982i
$34$		0			0
$35$	5.61413	+	1.86589i	0.948961	+	0.315393i
$36$		0			0
$37$	1.05500	+	3.93731i	0.173441	+	0.647290i	0.996812	+	0.0797867i	$0.0254239\pi$
$37$	1.05500	+	3.93731i	0.173441	+	0.647290i	−0.823371	+	0.567503i	$0.807909\pi$
$38$		0			0
$39$	−6.74148	+	3.89220i	−1.07950	+	0.623250i
$40$		0			0
$41$			9.16296i			1.43101i	0.698606	+	0.715507i	$0.253804\pi$
$41$			9.16296i			1.43101i	−0.698606	+	0.715507i	$0.746196\pi$
$42$		0			0
$43$	−6.72406	−	6.72406i	−1.02541	−	1.02541i	−0.999669	−	0.0257410i	$-0.991805\pi$
$43$	−6.72406	−	6.72406i	−1.02541	−	1.02541i	−0.0257410	−	0.999669i	$-0.508195\pi$
$44$		0			0
$45$	0.422691	−	11.5256i	0.0630110	−	1.71813i
$46$		0			0
$47$	6.75301	−	1.80946i	0.985028	−	0.263937i	0.269867	−	0.962898i	$-0.413020\pi$
$47$	6.75301	−	1.80946i	0.985028	−	0.263937i	0.715160	+	0.698960i	$0.246354\pi$
$48$		0			0
$49$	0.313692	−	6.99297i	0.0448131	−	0.998995i
$50$		0			0
$51$	9.75269	−	16.8922i	1.36565	−	2.36537i
$52$		0			0
$53$	−2.27886	+	8.50482i	−0.313025	+	1.16823i	0.612788	+	0.790247i	$0.290048\pi$
$53$	−2.27886	+	8.50482i	−0.313025	+	1.16823i	−0.925814	+	0.377980i	$0.876619\pi$
$54$		0			0
$55$	5.64073	−	8.99198i	0.760596	−	1.21248i
$56$		0			0
$57$	−0.177695	+	0.177695i	−0.0235363	+	0.0235363i
$58$		0			0
$59$	−1.56522	−	2.71104i	−0.203774	−	0.352947i	0.745967	−	0.665982i	$-0.231987\pi$
$59$	−1.56522	−	2.71104i	−0.203774	−	0.352947i	−0.949741	+	0.313036i	$0.898654\pi$
$60$		0			0
$61$	−4.84125	−	2.79509i	−0.619858	−	0.357875i	0.156956	−	0.987606i	$-0.449832\pi$
$61$	−4.84125	−	2.79509i	−0.619858	−	0.357875i	−0.776814	+	0.629730i	$0.783165\pi$
$62$		0			0
$63$	−13.2573	+	3.23564i	−1.67026	+	0.407652i
$64$		0			0
$65$	−5.82485	−	1.79199i	−0.722484	−	0.222270i
$66$		0			0
$67$	−2.19738	−	0.588786i	−0.268452	−	0.0719316i	0.122082	−	0.992520i	$-0.461043\pi$
$67$	−2.19738	−	0.588786i	−0.268452	−	0.0719316i	−0.390534	+	0.920588i	$0.627710\pi$
$68$		0			0
$69$	0.717316			0.0863547
$70$		0			0
$71$	−3.53569			−0.419610			−0.209805	−	0.977743i	$-0.567283\pi$
$71$	−3.53569			−0.419610			−0.209805	+	0.977743i	$0.567283\pi$
$72$		0			0
$73$	8.72777	+	2.33860i	1.02151	+	0.273712i	0.730430	−	0.682987i	$-0.239319\pi$
$73$	8.72777	+	2.33860i	1.02151	+	0.273712i	0.291078	+	0.956699i	$0.405986\pi$
$74$		0			0
$75$	10.8107	−	9.33136i	1.24832	−	1.07749i
$76$		0			0
$77$	−12.0557	−	3.52174i	−1.37388	−	0.401339i
$78$		0			0
$79$	10.7043	+	6.18015i	1.20433	+	0.695321i	0.961515	−	0.274751i	$-0.0885956\pi$
$79$	10.7043	+	6.18015i	1.20433	+	0.695321i	0.242816	+	0.970072i	$0.421929\pi$
$80$		0			0
$81$	1.06496	+	1.84456i	0.118329	+	0.204951i
$82$		0			0
$83$	−10.1777	+	10.1777i	−1.11715	+	1.11715i	−0.124989	+	0.992158i	$0.539889\pi$
$83$	−10.1777	+	10.1777i	−1.11715	+	1.11715i	−0.992158	+	0.124989i	$0.960111\pi$
$84$		0			0
$85$	14.8850	−	3.40904i	1.61451	−	0.369762i
$86$		0			0
$87$	−0.210599	+	0.785966i	−0.0225786	+	0.0842644i
$88$		0			0
$89$	−7.02336	+	12.1648i	−0.744474	+	1.28947i	0.205965	+	0.978559i	$0.433967\pi$
$89$	−7.02336	+	12.1648i	−0.744474	+	1.28947i	−0.950440	+	0.310908i	$0.899367\pi$
$90$		0			0
$91$	−0.161611	+	7.20903i	−0.0169414	+	0.755711i
$92$		0			0
$93$	11.7570	−	3.15027i	1.21914	−	0.326668i
$94$		0			0
$95$	−0.196605	−	0.00721033i	−0.0201713	−	0.000739764i
$96$		0			0
$97$	−5.72716	−	5.72716i	−0.581505	−	0.581505i	0.353812	−	0.935317i	$-0.384885\pi$
$97$	−5.72716	−	5.72716i	−0.581505	−	0.581505i	−0.935317	+	0.353812i	$0.884885\pi$
$98$		0			0
$99$			24.4847i			2.46081i
$100$		0			0
$101$	1.74942	−	1.01003i	0.174074	−	0.100501i	−0.410432	−	0.911891i	$-0.634622\pi$
$101$	1.74942	−	1.01003i	0.174074	−	0.100501i	0.584505	+	0.811390i	$0.301289\pi$
$102$		0			0
$103$	1.55642	+	5.80862i	0.153358	+	0.572341i	0.999240	+	0.0389708i	$0.0124079\pi$
$103$	1.55642	+	5.80862i	0.153358	+	0.572341i	−0.845882	+	0.533370i	$0.820925\pi$
$104$		0			0
$105$	−14.1093	−	9.29794i	−1.37693	−	0.907386i
$106$		0			0
$107$	4.59156	+	17.1359i	0.443883	+	1.65659i	0.718870	+	0.695145i	$0.244660\pi$
$107$	4.59156	+	17.1359i	0.443883	+	1.65659i	−0.274987	+	0.961448i	$0.588674\pi$
$108$		0			0
$109$	−1.79135	+	1.03423i	−0.171580	+	0.0990617i	−0.583331	−	0.812235i	$-0.698251\pi$
$109$	−1.79135	+	1.03423i	−0.171580	+	0.0990617i	0.411751	+	0.911297i	$0.364917\pi$
$110$		0			0
$111$		−	11.6424i		−	1.10505i
$112$		0			0
$113$	−3.54754	−	3.54754i	−0.333724	−	0.333724i	0.520275	−	0.853999i	$-0.325830\pi$
$113$	−3.54754	−	3.54754i	−0.333724	−	0.333724i	−0.853999	+	0.520275i	$0.825830\pi$
$114$		0			0
$115$	0.382273	+	0.411380i	0.0356471	+	0.0383613i
$116$		0			0
$117$	13.5784	−	3.63833i	1.25533	−	0.336364i
$118$		0			0
$119$	−8.68114	−	15.8461i	−0.795799	−	1.45261i
$120$		0			0
$121$	−5.76735	+	9.98935i	−0.524305	+	0.908123i
$122$		0			0
$123$	6.77360	−	25.2794i	0.610755	−	2.27937i
$124$		0			0
$125$	11.1128	+	1.22706i	0.993959	+	0.109752i
$126$		0			0
$127$	11.8913	−	11.8913i	1.05519	−	1.05519i	0.0568000	−	0.998386i	$-0.481910\pi$
$127$	11.8913	−	11.8913i	1.05519	−	1.05519i	0.998386	−	0.0568000i	$-0.0180897\pi$
$128$		0			0
$129$	13.5802	+	23.5215i	1.19567	+	2.07095i
$130$		0			0
$131$	−2.96850	−	1.71386i	−0.259359	−	0.149741i	0.364683	−	0.931132i	$-0.381177\pi$
$131$	−2.96850	−	1.71386i	−0.259359	−	0.149741i	−0.624042	+	0.781391i	$0.714511\pi$
$132$		0			0
$133$	0.0551941	+	0.226145i	0.00478593	+	0.0196092i
$134$		0			0
$135$	−4.05238	+	13.1722i	−0.348774	+	1.13368i
$136$		0			0
$137$	1.12687	+	0.301944i	0.0962751	+	0.0257968i	0.306635	−	0.951827i	$-0.400797\pi$
$137$	1.12687	+	0.301944i	0.0962751	+	0.0257968i	−0.210360	+	0.977624i	$0.567464\pi$
$138$		0			0
$139$	−2.74448			−0.232784			−0.116392	−	0.993203i	$-0.537133\pi$
$139$	−2.74448			−0.232784			−0.116392	+	0.993203i	$0.537133\pi$
$140$		0			0
$141$	−19.9683			−1.68164
$142$		0			0
$143$	12.4970	+	3.34857i	1.04505	+	0.280021i
$144$		0			0
$145$	−0.562983	+	0.298080i	−0.0467532	+	0.0247542i
$146$		0			0
$147$	−6.03490	+	19.0608i	−0.497750	+	1.57211i
$148$		0			0
$149$	−12.3425	−	7.12594i	−1.01114	−	0.583780i	−0.0996119	−	0.995026i	$-0.531760\pi$
$149$	−12.3425	−	7.12594i	−1.01114	−	0.583780i	−0.911524	+	0.411247i	$0.865093\pi$
$150$		0			0
$151$	−5.62795	−	9.74790i	−0.457996	−	0.793273i	0.540859	−	0.841114i	$-0.318099\pi$
$151$	−5.62795	−	9.74790i	−0.457996	−	0.793273i	−0.998855	+	0.0478406i	$0.984766\pi$
$152$		0			0
$153$	−24.9070	+	24.9070i	−2.01361	+	2.01361i
$154$		0			0
$155$	8.07222	+	5.06376i	0.648376	+	0.406731i
$156$		0			0
$157$	2.64552	−	9.87321i	0.211135	−	0.787968i	−0.776356	−	0.630295i	$-0.782934\pi$
$157$	2.64552	−	9.87321i	0.211135	−	0.787968i	0.987491	−	0.157673i	$-0.0503993\pi$
$158$		0			0
$159$	12.5742	−	21.7791i	0.997197	−	1.72720i
$160$		0			0
$161$	0.345045	−	0.567852i	0.0271934	−	0.0447530i
$162$		0			0
$163$	7.34761	−	1.96879i	0.575509	−	0.154207i	0.0406871	−	0.999172i	$-0.487045\pi$
$163$	7.34761	−	1.96879i	0.575509	−	0.154207i	0.534822	+	0.844965i	$0.320379\pi$
$164$		0			0
$165$	−22.2093	+	20.6379i	−1.72899	+	1.60666i
$166$		0			0
$167$	10.7090	+	10.7090i	0.828687	+	0.828687i	0.987335	−	0.158648i	$-0.0507135\pi$
$167$	10.7090	+	10.7090i	0.828687	+	0.828687i	−0.158648	+	0.987335i	$0.550714\pi$
$168$		0			0
$169$			5.57198i			0.428614i
$170$		0			0
$171$	0.393008	−	0.226903i	0.0300541	−	0.0173517i
$172$		0			0
$173$	−2.15020	−	8.02465i	−0.163477	−	0.610103i	−0.998230	−	0.0594785i	$-0.981056\pi$
$173$	−2.15020	−	8.02465i	−0.163477	−	0.610103i	0.834753	−	0.550625i	$-0.185610\pi$
$174$		0			0
$175$	−2.18681	−	13.0468i	−0.165308	−	0.986242i
$176$		0			0
$177$	2.31414	+	8.63647i	0.173941	+	0.649157i
$178$		0			0
$179$	−0.609128	+	0.351680i	−0.0455284	+	0.0262858i	−0.522591	−	0.852583i	$-0.675035\pi$
$179$	−0.609128	+	0.351680i	−0.0455284	+	0.0262858i	0.477063	+	0.878869i	$0.341701\pi$
$180$		0			0
$181$			14.2928i			1.06238i	0.847253	+	0.531189i	$0.178255\pi$
$181$			14.2928i			1.06238i	−0.847253	+	0.531189i	$0.821745\pi$
$182$		0			0
$183$	11.2901	+	11.2901i	0.834591	+	0.834591i
$184$		0			0
$185$	6.67692	−	6.20451i	0.490897	−	0.456164i
$186$		0			0
$187$	−31.3138	+	8.39051i	−2.28989	+	0.613575i
$188$		0			0
$189$	16.3024	+	0.365463i	1.18582	+	0.0265836i
$190$		0			0
$191$	8.49789	−	14.7188i	0.614886	−	1.06501i	−0.375519	−	0.926815i	$-0.622535\pi$
$191$	8.49789	−	14.7188i	0.614886	−	1.06501i	0.990405	−	0.138199i	$-0.0441313\pi$
$192$		0			0
$193$	3.89171	−	14.5240i	0.280131	−	1.04546i	−0.672193	−	0.740376i	$-0.734648\pi$
$193$	3.89171	−	14.5240i	0.280131	−	1.04546i	0.952324	−	0.305088i	$-0.0986858\pi$
$194$		0			0
$195$	14.7453	+	9.24984i	1.05593	+	0.662395i
$196$		0			0
$197$	−2.18377	+	2.18377i	−0.155587	+	0.155587i	−0.780608	−	0.625021i	$-0.785091\pi$
$197$	−2.18377	+	2.18377i	−0.155587	+	0.155587i	0.625021	+	0.780608i	$0.285091\pi$
$198$		0			0
$199$	−1.06910	−	1.85173i	−0.0757863	−	0.131266i	0.825642	−	0.564195i	$-0.190813\pi$
$199$	−1.06910	−	1.85173i	−0.0757863	−	0.131266i	−0.901428	+	0.432929i	$0.857480\pi$
$200$		0			0
$201$	5.62704	+	3.24877i	0.396900	+	0.229151i
$202$		0			0
$203$	0.520895	+	0.544785i	0.0365596	+	0.0382364i
$204$		0			0
$205$	18.1075	−	9.58730i	1.26468	−	0.669606i
$206$		0			0
$207$	−1.25122	−	0.335265i	−0.0869661	−	0.0233025i
$208$		0			0
$209$	0.417665			0.0288905
$210$		0			0
$211$	8.59667			0.591819			0.295910	−	0.955216i	$-0.404377\pi$
$211$	8.59667			0.591819			0.295910	+	0.955216i	$0.404377\pi$
$212$		0			0
$213$	9.75453	+	2.61372i	0.668370	+	0.179089i
$214$		0			0
$215$	−6.25240	+	20.3233i	−0.426410	+	1.38604i
$216$		0			0
$217$	3.16151	−	10.8226i	0.214617	−	0.734684i
$218$		0			0
$219$	−22.3500	−	12.9038i	−1.51028	−	0.871958i
$220$		0			0
$221$	9.30621	+	16.1188i	0.626004	+	1.08427i
$222$		0			0
$223$	−7.64095	+	7.64095i	−0.511676	+	0.511676i	−0.915040	−	0.403364i	$-0.867841\pi$
$223$	−7.64095	+	7.64095i	−0.511676	+	0.511676i	0.403364	+	0.915040i	$0.367841\pi$
$224$		0			0
$225$	−23.2187	+	11.2240i	−1.54791	+	0.748268i
$226$		0			0
$227$	−0.106829	+	0.398693i	−0.00709052	+	0.0264622i	−0.969380	−	0.245564i	$-0.921027\pi$
$227$	−0.106829	+	0.398693i	−0.00709052	+	0.0264622i	0.962290	+	0.272026i	$0.0876936\pi$
$228$		0			0
$229$	6.96704	−	12.0673i	0.460395	−	0.797427i	−0.538586	−	0.842571i	$-0.681041\pi$
$229$	6.96704	−	12.0673i	0.460395	−	0.797427i	0.998981	+	0.0451435i	$0.0143745\pi$
$230$		0			0
$231$	30.6568	+	18.6281i	2.01707	+	1.22564i
$232$		0			0
$233$	2.40099	−	0.643344i	0.157294	−	0.0421469i	−0.179313	−	0.983792i	$-0.557387\pi$
$233$	2.40099	−	0.643344i	0.157294	−	0.0421469i	0.336607	+	0.941645i	$0.390721\pi$
$234$		0			0
$235$	−10.6415	−	11.4518i	−0.694178	−	0.747033i
$236$		0			0
$237$	−24.9633	−	24.9633i	−1.62154	−	1.62154i
$238$		0			0
$239$		−	10.7870i		−	0.697753i	−0.937169	−	0.348877i	$-0.886563\pi$
$239$		−	10.7870i		−	0.697753i	0.937169	−	0.348877i	$-0.113437\pi$
$240$		0			0
$241$	−4.35718	+	2.51562i	−0.280671	+	0.162045i	−0.633727	−	0.773557i	$-0.718476\pi$
$241$	−4.35718	+	2.51562i	−0.280671	+	0.162045i	0.353056	+	0.935602i	$0.385142\pi$
$242$		0			0
$243$	3.21100	+	11.9836i	0.205985	+	0.768748i
$244$		0			0
$245$	−14.1475	+	6.69691i	−0.903850	+	0.427850i
$246$		0			0
$247$	−0.0620633	−	0.231623i	−0.00394899	−	0.0147378i
$248$		0			0
$249$	35.6027	−	20.5552i	2.25623	−	1.30263i
$250$		0			0
$251$		−	3.62098i		−	0.228554i	−0.993449	−	0.114277i	$-0.963545\pi$
$251$		−	3.62098i		−	0.228554i	0.993449	−	0.114277i	$-0.0364552\pi$
$252$		0			0
$253$	−0.843011	−	0.843011i	−0.0529997	−	0.0529997i
$254$		0			0
$255$	−43.5860	−	1.59848i	−2.72946	−	0.100101i
$256$		0			0
$257$	21.4562	−	5.74916i	1.33840	−	0.358623i	0.482559	−	0.875864i	$-0.339708\pi$
$257$	21.4562	−	5.74916i	1.33840	−	0.358623i	0.855840	+	0.517241i	$0.173041\pi$
$258$		0			0
$259$	−9.21656	−	5.60028i	−0.572689	−	0.347985i
$260$		0			0
$261$	0.734702	−	1.27254i	0.0454769	−	0.0787683i
$262$		0			0
$263$	0.415825	−	1.55188i	0.0256409	−	0.0956930i	−0.951920	−	0.306348i	$-0.900893\pi$
$263$	0.415825	−	1.55188i	0.0256409	−	0.0956930i	0.977561	+	0.210655i	$0.0675596\pi$
$264$		0			0
$265$	19.1913	−	4.39528i	1.17891	−	0.270000i
$266$		0			0
$267$	28.3692	−	28.3692i	1.73617	−	1.73617i
$268$		0			0
$269$	−11.9154	−	20.6380i	−0.726493	−	1.25832i	−0.958357	−	0.285574i	$-0.907816\pi$
$269$	−11.9154	−	20.6380i	−0.726493	−	1.25832i	0.231864	−	0.972748i	$-0.425518\pi$
$270$		0			0
$271$	−16.9698	−	9.79753i	−1.03084	−	0.595158i	−0.113617	−	0.993525i	$-0.536244\pi$
$271$	−16.9698	−	9.79753i	−1.03084	−	0.595158i	−0.917226	+	0.398367i	$0.869577\pi$
$272$		0			0
$273$	5.77505	−	19.7693i	0.349522	−	1.19649i
$274$		0			0
$275$	−23.6716	−	1.73861i	−1.42745	−	0.104842i
$276$		0			0
$277$	−12.9270	−	3.46378i	−0.776709	−	0.208119i	−0.151376	−	0.988476i	$-0.548370\pi$
$277$	−12.9270	−	3.46378i	−0.776709	−	0.208119i	−0.625333	+	0.780358i	$0.715037\pi$
$278$		0			0
$279$	−21.9803			−1.31592
$280$		0			0
$281$	−11.6570			−0.695398			−0.347699	−	0.937606i	$-0.613037\pi$
$281$	−11.6570			−0.695398			−0.347699	+	0.937606i	$0.613037\pi$
$282$		0			0
$283$	−21.9998	−	5.89484i	−1.30775	−	0.350412i	−0.463378	−	0.886161i	$-0.653363\pi$
$283$	−21.9998	−	5.89484i	−1.30775	−	0.350412i	−0.844377	+	0.535749i	$0.820029\pi$
$284$		0			0
$285$	0.537079	+	0.165230i	0.0318138	+	0.00978740i
$286$		0			0
$287$	−16.7538	−	17.5222i	−0.988947	−	1.03430i
$288$		0			0
$289$	−25.6666	−	14.8186i	−1.50980	−	0.871683i
$290$		0			0
$291$	11.5668	+	20.0342i	0.678056	+	1.17443i
$292$		0			0
$293$	21.4186	−	21.4186i	1.25129	−	1.25129i	0.296143	−	0.955144i	$-0.404300\pi$
$293$	21.4186	−	21.4186i	1.25129	−	1.25129i	0.955144	−	0.296143i	$-0.0957005\pi$
$294$		0			0
$295$	−3.71975	+	5.92972i	−0.216572	+	0.345241i
$296$		0			0
$297$	7.57239	−	28.2605i	0.439394	−	1.63984i
$298$		0			0
$299$	−0.342239	+	0.592775i	−0.0197922	+	0.0342810i
$300$		0			0
$301$	25.1528	+	0.563871i	1.44978	+	0.0325010i
$302$		0			0
$303$	−5.57307	+	1.49330i	−0.320165	+	0.0857878i
$304$		0			0
$305$	−0.458121	+	12.4916i	−0.0262319	+	0.715269i
$306$		0			0
$307$	3.23542	+	3.23542i	0.184655	+	0.184655i	0.793381	−	0.608726i	$-0.208319\pi$
$307$	3.23542	+	3.23542i	0.184655	+	0.184655i	−0.608726	+	0.793381i	$0.708319\pi$
$308$		0			0
$309$		−	17.1758i		−	0.977098i
$310$		0			0
$311$	−9.07682	+	5.24050i	−0.514699	+	0.297162i	−0.734763	−	0.678324i	$-0.762707\pi$
$311$	−9.07682	+	5.24050i	−0.514699	+	0.297162i	0.220064	+	0.975485i	$0.429373\pi$
$312$		0			0
$313$	5.51996	+	20.6008i	0.312007	+	1.16443i	0.926744	+	0.375693i	$0.122595\pi$
$313$	5.51996	+	20.6008i	0.312007	+	1.16443i	−0.614737	+	0.788732i	$0.710738\pi$
$314$		0			0
$315$	20.2654	+	22.8131i	1.14182	+	1.28537i
$316$		0			0
$317$	7.88745	+	29.4364i	0.443003	+	1.65331i	0.721155	+	0.692774i	$0.243611\pi$
$317$	7.88745	+	29.4364i	0.443003	+	1.65331i	−0.278152	+	0.960537i	$0.589722\pi$
$318$		0			0
$319$	1.17119	−	0.676188i	0.0655742	−	0.0378593i
$320$		0			0
$321$		−	50.6701i		−	2.82813i
$322$		0			0
$323$	0.424867	+	0.424867i	0.0236402	+	0.0236402i
$324$		0			0
$325$	2.55333	+	13.3859i	0.141633	+	0.742514i
$326$		0			0
$327$	5.70664	−	1.52909i	0.315578	−	0.0845589i
$328$		0			0
$329$	−9.60522	+	15.8076i	−0.529553	+	0.871502i
$330$		0			0
$331$	−2.65492	+	4.59846i	−0.145928	+	0.252754i	−0.929719	−	0.368271i	$-0.879950\pi$
$331$	−2.65492	+	4.59846i	−0.145928	+	0.252754i	0.783791	+	0.621025i	$0.213283\pi$
$332$		0			0
$333$	−5.44154	+	20.3081i	−0.298194	+	1.11288i
$334$		0			0
$335$	1.13560	+	4.95844i	0.0620446	+	0.270908i
$336$		0			0
$337$	6.43088	−	6.43088i	0.350312	−	0.350312i	−0.509913	−	0.860226i	$-0.670323\pi$
$337$	6.43088	−	6.43088i	0.350312	−	0.350312i	0.860226	+	0.509913i	$0.170323\pi$
$338$		0			0
$339$	7.16473	+	12.4097i	0.389135	+	0.674001i
$340$		0			0
$341$	−17.5194	−	10.1148i	−0.948730	−	0.547750i
$342$		0			0
$343$	12.1863	+	13.9461i	0.657997	+	0.753020i
$344$		0			0
$345$	−0.750536	−	1.41753i	−0.0404075	−	0.0763175i
$346$		0			0
$347$	21.5856	+	5.78384i	1.15877	+	0.310493i	0.786476	−	0.617621i	$-0.211903\pi$
$347$	21.5856	+	5.78384i	1.15877	+	0.310493i	0.372298	+	0.928113i	$0.378570\pi$
$348$		0			0
$349$	32.6644			1.74849			0.874244	−	0.485487i	$-0.161358\pi$
$349$	32.6644			1.74849			0.874244	+	0.485487i	$0.161358\pi$
$350$		0			0
$351$	−16.7976			−0.896589
$352$		0			0
$353$	23.3607	+	6.25948i	1.24336	+	0.333158i	0.819770	−	0.572694i	$-0.194101\pi$
$353$	23.3607	+	6.25948i	1.24336	+	0.333158i	0.423594	+	0.905852i	$0.360768\pi$
$354$		0			0
$355$	3.69944	+	6.98712i	0.196346	+	0.370838i
$356$		0			0
$357$	12.2362	+	50.1348i	0.647606	+	2.65341i
$358$		0			0
$359$	30.6942	+	17.7213i	1.61998	+	0.935293i	0.986924	+	0.161184i	$0.0515311\pi$
$359$	30.6942	+	17.7213i	1.61998	+	0.935293i	0.633051	+	0.774110i	$0.281802\pi$
$360$		0			0
$361$	9.49613	+	16.4478i	0.499796	+	0.865673i
$362$		0			0
$363$	23.2959	−	23.2959i	1.22272	−	1.22272i
$364$		0			0
$365$	−4.51051	−	19.6944i	−0.236091	−	1.03085i
$366$		0			0
$367$	−3.51883	+	13.1325i	−0.183682	+	0.685509i	0.811227	+	0.584731i	$0.198800\pi$
$367$	−3.51883	+	13.1325i	−0.183682	+	0.685509i	−0.994909	+	0.100778i	$0.967867\pi$
$368$		0			0
$369$	−23.6306	+	40.9294i	−1.23016	+	2.13070i
$370$		0			0
$371$	−11.1926	−	20.4304i	−0.581092	−	1.06069i
$372$		0			0
$373$	−16.6387	+	4.45833i	−0.861519	+	0.230843i	−0.662417	−	0.749135i	$-0.730469\pi$
$373$	−16.6387	+	4.45833i	−0.861519	+	0.230843i	−0.199102	+	0.979979i	$0.563803\pi$
$374$		0			0
$375$	−29.7517	−	11.6003i	−1.53637	−	0.599037i
$376$		0			0
$377$	−0.549027	−	0.549027i	−0.0282763	−	0.0282763i
$378$		0			0
$379$		−	3.68014i		−	0.189036i	−0.995523	−	0.0945181i	$-0.969869\pi$
$379$		−	3.68014i		−	0.189036i	0.995523	−	0.0945181i	$-0.0301310\pi$
$380$		0			0
$381$	−41.5972	+	24.0162i	−2.13109	+	1.23039i
$382$		0			0
$383$	5.85380	+	21.8467i	0.299115	+	1.11631i	0.937894	+	0.346923i	$0.112774\pi$
$383$	5.85380	+	21.8467i	0.299115	+	1.11631i	−0.638778	+	0.769391i	$0.720560\pi$
$384$		0			0
$385$	5.65450	+	27.5089i	0.288180	+	1.40199i
$386$		0			0
$387$	−12.6944	−	47.3761i	−0.645293	−	2.40826i
$388$		0			0
$389$	−1.31599	+	0.759787i	−0.0667234	+	0.0385227i	−0.532991	−	0.846121i	$-0.678932\pi$
$389$	−1.31599	+	0.759787i	−0.0667234	+	0.0385227i	0.466267	+	0.884644i	$0.345599\pi$
$390$		0			0
$391$		−	1.71510i		−	0.0867362i
$392$		0			0
$393$	6.92277	+	6.92277i	0.349207	+	0.349207i
$394$		0			0
$395$	1.01294	−	27.6199i	0.0509664	−	1.38971i
$396$		0			0
$397$	1.58354	−	0.424309i	0.0794757	−	0.0212954i	−0.218862	−	0.975756i	$-0.570234\pi$
$397$	1.58354	−	0.424309i	0.0794757	−	0.0212954i	0.298338	+	0.954460i	$0.403568\pi$
$398$		0			0
$399$	0.0149013	−	0.664706i	0.000745996	−	0.0332769i
$400$		0			0
$401$	1.21896	−	2.11129i	0.0608717	−	0.105433i	−0.833984	−	0.551789i	$-0.813945\pi$
$401$	1.21896	−	2.11129i	0.0608717	−	0.105433i	0.894855	+	0.446356i	$0.147279\pi$
$402$		0			0
$403$	−3.00605	+	11.2187i	−0.149742	+	0.558845i
$404$		0			0
$405$	2.53088	−	4.03451i	0.125760	−	0.200477i
$406$		0			0
$407$	−13.6825	+	13.6825i	−0.678219	+	0.678219i
$408$		0			0
$409$	8.03235	+	13.9124i	0.397174	+	0.687925i	0.993376	−	0.114909i	$-0.0366576\pi$
$409$	8.03235	+	13.9124i	0.397174	+	0.687925i	−0.596202	+	0.802834i	$0.703324\pi$
$410$		0			0
$411$	−2.88569	−	1.66605i	−0.142340	−	0.0821803i
$412$		0			0
$413$	7.95008	+	2.32239i	0.391198	+	0.114277i
$414$		0			0
$415$	30.7618	+	9.46378i	1.51004	+	0.464558i
$416$		0			0
$417$	7.57168	+	2.02883i	0.370787	+	0.0993521i
$418$		0			0
$419$	1.04323			0.0509652			0.0254826	−	0.999675i	$-0.491888\pi$
$419$	1.04323			0.0509652			0.0254826	+	0.999675i	$0.491888\pi$
$420$		0			0
$421$	−12.8512			−0.626331			−0.313165	−	0.949699i	$-0.601389\pi$
$421$	−12.8512			−0.626331			−0.313165	+	0.949699i	$0.601389\pi$
$422$		0			0
$423$	34.8310	+	9.33295i	1.69354	+	0.453784i
$424$		0			0
$425$	−22.3112	−	25.8484i	−1.08225	−	1.25383i
$426$		0			0
$427$	14.3685	−	3.50685i	0.695340	−	0.169708i
$428$		0			0
$429$	−32.0023	−	18.4765i	−1.54509	−	0.892056i
$430$		0			0
$431$	6.50366	+	11.2647i	0.313270	+	0.542600i	0.979068	−	0.203532i	$-0.0652421\pi$
$431$	6.50366	+	11.2647i	0.313270	+	0.542600i	−0.665798	+	0.746132i	$0.731909\pi$
$432$		0			0
$433$	−23.8441	+	23.8441i	−1.14587	+	1.14587i	−0.158518	+	0.987356i	$0.550672\pi$
$433$	−23.8441	+	23.8441i	−1.14587	+	1.14587i	−0.987356	+	0.158518i	$0.949328\pi$
$434$		0			0
$435$	1.77355	−	0.406186i	0.0850352	−	0.0194751i
$436$		0			0
$437$	−0.00571900	+	0.0213436i	−0.000273577	+	0.00102100i
$438$		0			0
$439$	−3.55919	+	6.16470i	−0.169871	+	0.294225i	−0.938374	−	0.345621i	$-0.887668\pi$
$439$	−3.55919	+	6.16470i	−0.169871	+	0.294225i	0.768503	+	0.639846i	$0.221002\pi$
$440$		0			0
$441$	19.4356	−	30.4274i	0.925503	−	1.44893i
$442$		0			0
$443$	−14.6235	+	3.91835i	−0.694783	+	0.186166i	−0.588892	−	0.808211i	$-0.700436\pi$
$443$	−14.6235	+	3.91835i	−0.694783	+	0.186166i	−0.105890	+	0.994378i	$0.533769\pi$
$444$		0			0
$445$	31.3883	+	1.15114i	1.48795	+	0.0545693i
$446$		0			0
$447$	28.7836	+	28.7836i	1.36142	+	1.36142i
$448$		0			0
$449$		−	23.7583i		−	1.12122i	−0.828079	−	0.560612i	$-0.810566\pi$
$449$		−	23.7583i		−	1.12122i	0.828079	−	0.560612i	$-0.189434\pi$
$450$		0			0
$451$	−37.6697	+	21.7486i	−1.77380	+	1.02410i
$452$		0			0
$453$	8.32079	+	31.0536i	0.390945	+	1.45903i
$454$		0			0
$455$	14.4153	−	7.22352i	0.675801	−	0.338644i
$456$		0			0
$457$	−7.12346	−	26.5851i	−0.333221	−	1.24360i	−0.905785	−	0.423738i	$-0.860718\pi$
$457$	−7.12346	−	26.5851i	−0.333221	−	1.24360i	0.572563	−	0.819861i	$-0.305949\pi$
$458$		0			0
$459$	36.4508	−	21.0449i	1.70138	−	0.982292i
$460$		0			0
$461$			12.0569i			0.561545i	0.959774	+	0.280773i	$0.0905907\pi$
$461$			12.0569i			0.561545i	−0.959774	+	0.280773i	$0.909409\pi$
$462$		0			0
$463$	−19.7680	−	19.7680i	−0.918695	−	0.918695i	0.0782395	−	0.996935i	$-0.475070\pi$
$463$	−19.7680	−	19.7680i	−0.918695	−	0.918695i	−0.996935	+	0.0782395i	$0.975070\pi$
$464$		0			0
$465$	−18.5269	−	19.9376i	−0.859165	−	0.924582i
$466$		0			0
$467$	−21.6402	+	5.79848i	−1.00139	+	0.268322i	−0.722028	−	0.691864i	$-0.756790\pi$
$467$	−21.6402	+	5.79848i	−1.00139	+	0.268322i	−0.279362	+	0.960186i	$0.590123\pi$
$468$		0			0
$469$	5.27857	−	2.89182i	0.243742	−	0.133532i
$470$		0			0
$471$	−14.5973	+	25.2833i	−0.672609	+	1.16499i
$472$		0			0
$473$	11.6834	−	43.6030i	0.537203	−	2.00487i
$474$		0			0
$475$	0.191461	+	0.396069i	0.00878485	+	0.0181729i
$476$		0			0
$477$	−32.1126	+	32.1126i	−1.47034	+	1.47034i
$478$		0			0
$479$	3.69565	+	6.40106i	0.168859	+	0.292472i	0.938019	−	0.346584i	$-0.112658\pi$
$479$	3.69565	+	6.40106i	0.168859	+	0.292472i	−0.769160	+	0.639056i	$0.779325\pi$
$480$		0			0
$481$	9.62107	+	5.55473i	0.438683	+	0.253274i
$482$		0			0
$483$	−1.37171	+	1.31156i	−0.0624152	+	0.0596781i
$484$		0			0
$485$	−5.32543	+	17.3102i	−0.241815	+	0.786016i
$486$		0			0
$487$	−31.5188	−	8.44544i	−1.42825	−	0.382699i	−0.539849	−	0.841762i	$-0.681519\pi$
$487$	−31.5188	−	8.44544i	−1.42825	−	0.382699i	−0.888404	+	0.459062i	$0.848186\pi$
$488$		0			0
$489$	−21.7265			−0.982507
$490$		0			0
$491$	−14.1324			−0.637785			−0.318893	−	0.947791i	$-0.603311\pi$
$491$	−14.1324			−0.637785			−0.318893	+	0.947791i	$0.603311\pi$
$492$		0			0
$493$	1.87924	+	0.503540i	0.0846366	+	0.0226783i
$494$		0			0
$495$	48.3859	−	25.6186i	2.17478	−	1.15147i
$496$		0			0
$497$	6.76127	−	6.46477i	0.303284	−	0.289984i
$498$		0			0
$499$	6.51132	+	3.75931i	0.291487	+	0.168290i	0.638612	−	0.769529i	$-0.279509\pi$
$499$	6.51132	+	3.75931i	0.291487	+	0.168290i	−0.347125	+	0.937819i	$0.612842\pi$
$500$		0			0
$501$	−21.6283	−	37.4613i	−0.966280	−	1.67365i
$502$		0			0
$503$	13.8563	−	13.8563i	0.617822	−	0.617822i	−0.327150	−	0.944972i	$-0.606088\pi$
$503$	13.8563	−	13.8563i	0.617822	−	0.617822i	0.944972	+	0.327150i	$0.106088\pi$
$504$		0			0
$505$	−3.82642	−	2.40034i	−0.170273	−	0.106814i
$506$		0			0
$507$	4.11902	−	15.3724i	0.182932	−	0.682711i
$508$		0			0
$509$	−14.3898	+	24.9239i	−0.637818	+	1.10473i	0.348092	+	0.937460i	$0.386830\pi$
$509$	−14.3898	+	24.9239i	−0.637818	+	1.10473i	−0.985911	+	0.167274i	$0.946504\pi$
$510$		0			0
$511$	−20.9660	+	11.4860i	−0.927480	+	0.508112i
$512$		0			0
$513$	−0.523789	+	0.140349i	−0.0231258	+	0.00619655i
$514$		0			0
$515$	9.85031	−	9.15336i	0.434056	−	0.403345i
$516$		0			0
$517$	23.4674	+	23.4674i	1.03209	+	1.03209i
$518$		0			0
$519$			23.7285i			1.04157i
$520$		0			0
$521$	16.1832	−	9.34339i	0.709000	−	0.409342i	−0.101690	−	0.994816i	$-0.532425\pi$
$521$	16.1832	−	9.34339i	0.709000	−	0.409342i	0.810691	+	0.585475i	$0.199092\pi$
$522$		0			0
$523$	7.01477	+	26.1795i	0.306735	+	1.14475i	0.931442	+	0.363890i	$0.118552\pi$
$523$	7.01477	+	26.1795i	0.306735	+	1.14475i	−0.624707	+	0.780859i	$0.714782\pi$
$524$		0			0
$525$	−3.61152	+	37.6109i	−0.157619	+	1.64148i
$526$		0			0
$527$	−7.53227	−	28.1108i	−0.328111	−	1.22453i
$528$		0			0
$529$	−19.8640	+	11.4685i	−0.863650	+	0.498629i
$530$		0			0
$531$		−	16.1463i		−	0.700691i
$532$		0			0
$533$	17.6586	+	17.6586i	0.764881	+	0.764881i
$534$		0			0
$535$	29.0592	−	27.0032i	1.25634	−	1.16745i
$536$		0			0
$537$	1.94048	−	0.519951i	0.0837380	−	0.0224375i
$538$		0			0
$539$	29.4933	−	15.3085i	1.27036	−	0.659382i
$540$		0			0
$541$	0.346702	−	0.600506i	0.0149059	−	0.0258178i	−0.858476	−	0.512853i	$-0.828588\pi$
$541$	0.346702	−	0.600506i	0.0149059	−	0.0258178i	0.873382	+	0.487036i	$0.161922\pi$
$542$		0			0
$543$	10.5658	−	39.4321i	0.453422	−	1.69219i
$544$		0			0
$545$	3.91813	+	2.45787i	0.167834	+	0.105283i
$546$		0			0
$547$	15.8425	−	15.8425i	0.677377	−	0.677377i	−0.282029	−	0.959406i	$-0.591007\pi$
$547$	15.8425	−	15.8425i	0.677377	−	0.677377i	0.959406	+	0.282029i	$0.0910074\pi$
$548$		0			0
$549$	−14.4167	−	24.9704i	−0.615290	−	1.06571i
$550$		0			0
$551$	−0.0217072	−	0.0125327i	−0.000924758	−	0.000533910i
$552$		0			0
$553$	−31.7697	+	7.75389i	−1.35099	+	0.329729i
$554$		0			0
$555$	−23.0074	+	12.1816i	−0.976610	+	0.517081i
$556$		0			0
$557$	−6.88206	−	1.84404i	−0.291602	−	0.0781346i	0.110052	−	0.993926i	$-0.464898\pi$
$557$	−6.88206	−	1.84404i	−0.291602	−	0.0781346i	−0.401655	+	0.915791i	$0.631565\pi$
$558$		0			0
$559$	−25.9169			−1.09617
$560$		0			0
$561$	92.5935			3.90930
$562$		0			0
$563$	9.00304	+	2.41236i	0.379433	+	0.101669i	0.443494	−	0.896277i	$-0.353739\pi$
$563$	9.00304	+	2.41236i	0.379433	+	0.101669i	−0.0640613	+	0.997946i	$0.520405\pi$
$564$		0			0
$565$	−3.29869	+	10.7223i	−0.138777	+	0.451092i
$566$		0			0
$567$	−5.40915	−	1.58013i	−0.227163	−	0.0663592i
$568$		0			0
$569$	30.8192	+	17.7935i	1.29201	+	0.745941i	0.979010	−	0.203812i	$-0.0653333\pi$
$569$	30.8192	+	17.7935i	1.29201	+	0.745941i	0.312998	+	0.949754i	$0.398667\pi$
$570$		0			0
$571$	10.9925	+	19.0395i	0.460020	+	0.796778i	0.998961	−	0.0455656i	$-0.0145090\pi$
$571$	10.9925	+	19.0395i	0.460020	+	0.796778i	−0.538942	+	0.842343i	$0.681176\pi$
$572$		0			0
$573$	−34.3253	+	34.3253i	−1.43396	+	1.43396i
$574$		0			0
$575$	0.412978	−	1.18587i	0.0172224	−	0.0494540i
$576$		0			0
$577$	2.05870	−	7.68316i	0.0857047	−	0.319854i	−0.909742	−	0.415174i	$-0.863721\pi$
$577$	2.05870	−	7.68316i	0.0857047	−	0.319854i	0.995447	+	0.0953198i	$0.0303874\pi$
$578$		0			0
$579$	−21.4734	+	37.1931i	−0.892406	+	1.54569i
$580$		0			0
$581$	0.853489	−	38.0719i	0.0354087	−	1.57949i
$582$		0			0
$583$	−40.3730	+	10.8179i	−1.67208	+	0.448032i
$584$		0			0
$585$	−21.3972	−	23.0264i	−0.884666	−	0.952025i
$586$		0			0
$587$	9.97309	+	9.97309i	0.411633	+	0.411633i	0.882307	−	0.470674i	$-0.155989\pi$
$587$	9.97309	+	9.97309i	0.411633	+	0.411633i	−0.470674	+	0.882307i	$0.655989\pi$
$588$		0			0
$589$			0.374943i			0.0154493i
$590$		0			0
$591$	7.63908	−	4.41043i	0.314230	−	0.181421i
$592$		0			0
$593$	−9.91736	−	37.0121i	−0.407257	−	1.51990i	−0.799854	−	0.600194i	$-0.795090\pi$
$593$	−9.91736	−	37.0121i	−0.407257	−	1.51990i	0.392597	−	0.919711i	$-0.371577\pi$
$594$		0			0
$595$	−22.2313	+	33.7353i	−0.911395	+	1.38301i
$596$		0			0
$597$	1.58063	+	5.89901i	0.0646910	+	0.241430i
$598$		0			0
$599$	6.66956	−	3.85067i	0.272511	−	0.157334i	−0.357517	−	0.933907i	$-0.616377\pi$
$599$	6.66956	−	3.85067i	0.272511	−	0.157334i	0.630028	+	0.776572i	$0.283043\pi$
$600$		0			0
$601$		−	6.91584i		−	0.282103i	−0.990002	−	0.141051i	$-0.954952\pi$
$601$		−	6.91584i		−	0.282103i	0.990002	−	0.141051i	$-0.0450483\pi$
$602$		0			0
$603$	−8.29689	−	8.29689i	−0.337875	−	0.337875i
$604$		0			0
$605$	25.7751	+	0.945279i	1.04791	+	0.0384310i
$606$		0			0
$607$	41.6534	−	11.1610i	1.69066	−	0.453011i	0.720101	−	0.693870i	$-0.244096\pi$
$607$	41.6534	−	11.1610i	1.69066	−	0.453011i	0.970560	+	0.240858i	$0.0774290\pi$
$608$		0			0
$609$	−1.03436	−	1.88806i	−0.0419143	−	0.0765080i
$610$		0			0
$611$	9.52709	−	16.5014i	0.385425	−	0.667575i
$612$		0			0
$613$	9.35702	−	34.9209i	0.377927	−	1.41044i	−0.471095	−	0.882083i	$-0.656141\pi$
$613$	9.35702	−	34.9209i	0.377927	−	1.41044i	0.849021	−	0.528359i	$-0.177192\pi$
$614$		0			0
$615$	−57.0437	+	13.0644i	−2.30022	+	0.526807i
$616$		0			0
$617$	−21.4356	+	21.4356i	−0.862966	+	0.862966i	−0.991682	−	0.128715i	$-0.958915\pi$
$617$	−21.4356	+	21.4356i	−0.862966	+	0.862966i	0.128715	+	0.991682i	$0.458915\pi$
$618$		0			0
$619$	13.5728	+	23.5088i	0.545538	+	0.944900i	0.998573	+	0.0534071i	$0.0170081\pi$
$619$	13.5728	+	23.5088i	0.545538	+	0.944900i	−0.453035	+	0.891493i	$0.649659\pi$
$620$		0			0
$621$	1.34049	+	0.773932i	0.0537920	+	0.0310568i
$622$		0			0
$623$	−8.81182	−	36.1043i	−0.353038	−	1.44649i
$624$		0			0
$625$	−9.20257	−	23.2446i	−0.368103	−	0.929785i
$626$		0			0
$627$	−1.15228	−	0.308754i	−0.0460178	−	0.0123304i
$628$		0			0
$629$	−27.8370			−1.10993
$630$		0			0
$631$	32.0140			1.27446			0.637229	−	0.770675i	$-0.280081\pi$
$631$	32.0140			1.27446			0.637229	+	0.770675i	$0.280081\pi$
$632$		0			0
$633$	−23.7171	−	6.35499i	−0.942672	−	0.252588i
$634$		0			0
$635$	−35.9413	−	11.0572i	−1.42629	−	0.438792i
$636$		0			0
$637$	−12.8721	−	14.0812i	−0.510013	−	0.557919i
$638$		0			0
$639$	−15.7934	−	9.11830i	−0.624776	−	0.360714i
$640$		0			0
$641$	11.3718	+	19.6966i	0.449160	+	0.777968i	0.998332	−	0.0577415i	$-0.0183899\pi$
$641$	11.3718	+	19.6966i	0.449160	+	0.777968i	−0.549171	+	0.835710i	$0.685057\pi$
$642$		0			0
$643$	14.6427	−	14.6427i	0.577453	−	0.577453i	−0.356748	−	0.934201i	$-0.616114\pi$
$643$	14.6427	−	14.6427i	0.577453	−	0.577453i	0.934201	+	0.356748i	$0.116114\pi$
$644$		0			0
$645$	32.2734	−	51.4475i	1.27076	−	2.02574i
$646$		0			0
$647$	5.67864	−	21.1930i	0.223250	−	0.833181i	−0.759848	−	0.650101i	$-0.774727\pi$
$647$	5.67864	−	21.1930i	0.223250	−	0.833181i	0.983098	−	0.183080i	$-0.0586068\pi$
$648$		0			0
$649$	7.43020	−	12.8695i	0.291661	−	0.505172i
$650$		0			0
$651$	−16.7227	+	27.5210i	−0.655413	+	1.07863i
$652$		0			0
$653$	−39.3632	+	10.5473i	−1.54040	+	0.412750i	−0.926396	−	0.376551i	$-0.877110\pi$
$653$	−39.3632	+	10.5473i	−1.54040	+	0.412750i	−0.614007	+	0.789301i	$0.710443\pi$
$654$		0			0
$655$	−0.280905	+	7.65949i	−0.0109759	+	0.299281i
$656$		0			0
$657$	32.9544	+	32.9544i	1.28567	+	1.28567i
$658$		0			0
$659$		−	14.1384i		−	0.550755i	−0.961336	−	0.275378i	$-0.911197\pi$
$659$		−	14.1384i		−	0.550755i	0.961336	−	0.275378i	$-0.0888029\pi$
$660$		0			0
$661$	−14.9892	+	8.65401i	−0.583011	+	0.336602i	−0.762329	−	0.647189i	$-0.775944\pi$
$661$	−14.9892	+	8.65401i	−0.583011	+	0.336602i	0.179318	+	0.983791i	$0.442611\pi$
$662$		0			0
$663$	−13.7590	−	51.3493i	−0.534356	−	1.99424i
$664$		0			0
$665$	0.389149	−	0.345690i	0.0150906	−	0.0134053i
$666$		0			0
$667$	0.0185178	+	0.0691095i	0.000717014	+	0.00267593i
$668$		0			0
$669$	26.7289	−	15.4319i	1.03340	−	0.596633i
$670$		0			0
$671$		−	26.5370i		−	1.02445i
$672$		0			0
$673$	14.1900	+	14.1900i	0.546983	+	0.546983i	0.925567	−	0.378584i	$-0.123589\pi$
$673$	14.1900	+	14.1900i	0.546983	+	0.546983i	−0.378584	+	0.925567i	$0.623589\pi$
$674$		0			0
$675$	30.2705	−	5.77405i	1.16511	−	0.222243i
$676$		0			0
$677$	11.9446	−	3.20054i	0.459068	−	0.123007i	−0.0218715	−	0.999761i	$-0.506962\pi$
$677$	11.9446	−	3.20054i	0.459068	−	0.123007i	0.480939	+	0.876754i	$0.340296\pi$
$678$		0			0
$679$	21.4237	+	0.480272i	0.822166	+	0.0184312i
$680$		0			0
$681$	0.589458	−	1.02097i	0.0225881	−	0.0391237i
$682$		0			0
$683$	−3.36173	+	12.5461i	−0.128633	+	0.480065i	−0.999943	−	0.0106680i	$-0.996604\pi$
$683$	−3.36173	+	12.5461i	−0.128633	+	0.480065i	0.871310	+	0.490733i	$0.163271\pi$
$684$		0			0
$685$	−0.582366	−	2.54281i	−0.0222511	−	0.0971559i
$686$		0			0
$687$	−28.1418	+	28.1418i	−1.07368	+	1.07368i
$688$		0			0
$689$	11.9985	+	20.7821i	0.457108	+	0.791733i
$690$		0			0
$691$	36.3838	+	21.0062i	1.38411	+	0.799114i	0.992643	−	0.121080i	$-0.0386359\pi$
$691$	36.3838	+	21.0062i	1.38411	+	0.799114i	0.391463	+	0.920194i	$0.371969\pi$
$692$		0			0
$693$	−44.7686	−	46.8218i	−1.70062	−	1.77861i
$694$		0			0
$695$	2.87158	+	5.42356i	0.108925	+	0.205727i
$696$		0			0
$697$	−60.4430	−	16.1956i	−2.28944	−	0.613454i
$698$		0			0
$699$	−7.09962			−0.268532
$700$		0			0
$701$	13.5398			0.511390			0.255695	−	0.966757i	$-0.417696\pi$
$701$	13.5398			0.511390			0.255695	+	0.966757i	$0.417696\pi$
$702$		0			0
$703$	0.346419	+	0.0928226i	0.0130654	+	0.00350087i
$704$		0			0
$705$	20.8931	+	39.4607i	0.786879	+	1.48618i
$706$		0			0
$707$	−1.49863	+	5.13015i	−0.0563617	+	0.192939i
$708$		0			0
$709$	10.4976	+	6.06080i	0.394246	+	0.227618i	0.683998	−	0.729484i	$-0.260240\pi$
$709$	10.4976	+	6.06080i	0.394246	+	0.227618i	−0.289752	+	0.957102i	$0.593573\pi$
$710$		0			0
$711$	31.8763	+	55.2114i	1.19546	+	2.07059i
$712$		0			0
$713$	0.756782	−	0.756782i	0.0283417	−	0.0283417i
$714$		0			0
$715$	−6.45845	−	28.1998i	−0.241532	−	1.05461i
$716$		0			0
$717$	−7.97416	+	29.7600i	−0.297801	+	1.11141i
$718$		0			0
$719$	11.1933	−	19.3874i	0.417441	−	0.723030i	−0.578240	−	0.815867i	$-0.696260\pi$
$719$	11.1933	−	19.3874i	0.417441	−	0.723030i	0.995681	+	0.0928372i	$0.0295936\pi$
$720$		0			0
$721$	−13.5970	−	8.26196i	−0.506378	−	0.307692i
$722$		0			0
$723$	13.8806	−	3.71928i	0.516224	−	0.138322i
$724$		0			0
$725$	1.17811	+	0.800663i	0.0437539	+	0.0297359i
$726$		0			0
$727$	−27.0366	−	27.0366i	−1.00273	−	1.00273i	−0.999996	−	0.00273448i	$-0.999130\pi$
$727$	−27.0366	−	27.0366i	−1.00273	−	1.00273i	−0.00273448	−	0.999996i	$-0.500870\pi$
$728$		0			0
$729$		−	41.8247i		−	1.54906i
$730$		0			0
$731$	56.2398	−	32.4700i	2.08010	−	1.20095i
$732$		0			0
$733$	−2.92004	−	10.8977i	−0.107854	−	0.402517i	0.890799	−	0.454397i	$-0.150145\pi$
$733$	−2.92004	−	10.8977i	−0.107854	−	0.402517i	−0.998653	+	0.0518799i	$0.983479\pi$
$734$		0			0
$735$	43.9817	−	8.01758i	1.62229	−	0.295733i
$736$		0			0
$737$	−2.79501	−	10.4311i	−0.102955	−	0.384235i
$738$		0			0
$739$	24.8452	−	14.3444i	0.913944	−	0.527666i	0.0322460	−	0.999480i	$-0.489734\pi$
$739$	24.8452	−	14.3444i	0.913944	−	0.527666i	0.881698	+	0.471814i	$0.156401\pi$
$740$		0			0
$741$			0.684899i			0.0251604i
$742$		0			0
$743$	−11.3200	−	11.3200i	−0.415290	−	0.415290i	0.468287	−	0.883577i	$-0.344871\pi$
$743$	−11.3200	−	11.3200i	−0.415290	−	0.415290i	−0.883577	+	0.468287i	$0.844871\pi$
$744$		0			0
$745$	−1.16795	+	31.8468i	−0.0427905	+	1.16677i
$746$		0			0
$747$	−71.7096	+	19.2145i	−2.62372	+	0.703023i
$748$		0			0
$749$	−40.1122	−	24.3735i	−1.46567	−	0.890588i
$750$		0			0
$751$	−1.31034	+	2.26958i	−0.0478151	+	0.0828182i	−0.888942	−	0.458019i	$-0.848559\pi$
$751$	−1.31034	+	2.26958i	−0.0478151	+	0.0828182i	0.841127	+	0.540837i	$0.181893\pi$
$752$		0			0
$753$	−2.67677	+	9.98983i	−0.0975468	+	0.364050i
$754$		0			0
$755$	−13.3749	+	21.3211i	−0.486762	+	0.775955i
$756$		0			0
$757$	−11.9396	+	11.9396i	−0.433953	+	0.433953i	−0.889971	−	0.456017i	$-0.849275\pi$
$757$	−11.9396	+	11.9396i	−0.433953	+	0.433953i	0.456017	+	0.889971i	$0.349275\pi$
$758$		0			0
$759$	1.70258	+	2.94895i	0.0617996	+	0.107040i
$760$		0			0
$761$	17.1993	+	9.93004i	0.623475	+	0.359964i	0.778221	−	0.627991i	$-0.216122\pi$
$761$	17.1993	+	9.93004i	0.623475	+	0.359964i	−0.154745	+	0.987954i	$0.549456\pi$
$762$		0			0
$763$	1.53455	−	5.25311i	0.0555543	−	0.190175i
$764$		0			0
$765$	75.2807	+	23.1598i	2.72178	+	0.837346i
$766$		0			0
$767$	−8.24110	−	2.20820i	−0.297569	−	0.0797333i
$768$		0			0
$769$	−4.79436			−0.172889			−0.0864445	−	0.996257i	$-0.527551\pi$
$769$	−4.79436			−0.172889			−0.0864445	+	0.996257i	$0.527551\pi$
$770$		0			0
$771$	−63.4448			−2.28491
$772$		0			0
$773$	−25.0979	−	6.72495i	−0.902707	−	0.241880i	−0.222529	−	0.974926i	$-0.571431\pi$
$773$	−25.0979	−	6.72495i	−0.902707	−	0.241880i	−0.680179	+	0.733046i	$0.738098\pi$
$774$		0			0
$775$	1.56077	−	21.2503i	0.0560646	−	0.763334i
$776$		0			0
$777$	21.2874	+	22.2637i	0.763681	+	0.798706i
$778$		0			0
$779$	0.698181	+	0.403095i	0.0250149	+	0.0144424i
$780$		0			0
$781$	−8.39210	−	14.5355i	−0.300293	−	0.520123i
$782$		0			0
$783$	−1.24156	+	1.24156i	−0.0443697	+	0.0443697i
$784$		0			0
$785$	−22.2791	+	5.10247i	−0.795177	+	0.182115i
$786$		0			0
$787$	−1.22159	+	4.55904i	−0.0435450	+	0.162512i	−0.984275	−	0.176646i	$-0.943475\pi$
$787$	−1.22159	+	4.55904i	−0.0435450	+	0.162512i	0.940730	+	0.339158i	$0.110142\pi$
$788$		0			0
$789$	−2.29442	+	3.97405i	−0.0816834	+	0.141480i
$790$		0			0
$791$	13.2703	+	0.297492i	0.471839	+	0.0105776i
$792$		0			0
$793$	−14.7166	+	3.94330i	−0.522601	+	0.140031i
$794$		0			0
$795$	−56.1956	−	2.06093i	−1.99305	−	0.0730936i
$796$		0			0
$797$	6.20691	+	6.20691i	0.219860	+	0.219860i	0.808439	−	0.588579i	$-0.200313\pi$
$797$	6.20691	+	6.20691i	0.219860	+	0.219860i	−0.588579	+	0.808439i	$0.700313\pi$
$798$		0			0
$799$			47.7441i			1.68907i
$800$		0			0
$801$	−62.7444	+	36.2255i	−2.21696	+	1.27996i
$802$		0			0
$803$	11.1015	+	41.4314i	0.391763	+	1.46208i
$804$		0			0
$805$	−1.48319	−	0.0877170i	−0.0522757	−	0.00309162i
$806$		0			0
$807$	17.6166	+	65.7460i	0.620133	+	2.31437i
$808$		0			0
$809$	−3.88093	+	2.24066i	−0.136446	+	0.0787773i	−0.566669	−	0.823945i	$-0.691768\pi$
$809$	−3.88093	+	2.24066i	−0.136446	+	0.0787773i	0.430223	+	0.902723i	$0.358435\pi$
$810$		0			0
$811$			1.95507i			0.0686518i	0.999411	+	0.0343259i	$0.0109284\pi$
$811$			1.95507i			0.0686518i	−0.999411	+	0.0343259i	$0.989072\pi$
$812$		0			0
$813$	39.5749	+	39.5749i	1.38795	+	1.38795i
$814$		0			0
$815$	−11.5785	−	12.4601i	−0.405578	−	0.436459i
$816$		0			0
$817$	−0.808150	+	0.216543i	−0.0282736	+	0.00757589i
$818$		0			0
$819$	−19.3134	+	31.7847i	−0.674866	+	1.11065i
$820$		0			0
$821$	8.68651	−	15.0455i	0.303161	−	0.525091i	−0.673689	−	0.739015i	$-0.735291\pi$
$821$	8.68651	−	15.0455i	0.303161	−	0.525091i	0.976850	+	0.213924i	$0.0686245\pi$
$822$		0			0
$823$	−2.84084	+	10.6022i	−0.0990254	+	0.369568i	−0.997599	−	0.0692551i	$-0.977938\pi$
$823$	−2.84084	+	10.6022i	−0.0990254	+	0.369568i	0.898574	+	0.438823i	$0.144604\pi$
$824$		0			0
$825$	64.0217	+	22.2956i	2.22895	+	0.776232i
$826$		0			0
$827$	−39.5694	+	39.5694i	−1.37596	+	1.37596i	−0.524637	+	0.851326i	$0.675799\pi$
$827$	−39.5694	+	39.5694i	−1.37596	+	1.37596i	−0.851326	+	0.524637i	$0.824201\pi$
$828$		0			0
$829$	14.8450	+	25.7123i	0.515587	+	0.893024i	0.999836	+	0.0180933i	$0.00575958\pi$
$829$	14.8450	+	25.7123i	0.515587	+	0.893024i	−0.484249	+	0.874930i	$0.660907\pi$
$830$		0			0
$831$	33.1034	+	19.1123i	1.14835	+	0.662997i
$832$		0			0
$833$	45.5743	+	14.4294i	1.57906	+	0.499949i
$834$		0			0
$835$	9.95781	−	32.3677i	0.344604	−	1.12013i
$836$		0			0
$837$	25.3698	+	6.79783i	0.876910	+	0.234967i
$838$		0			0
$839$	11.6348			0.401678			0.200839	−	0.979624i	$-0.435633\pi$
$839$	11.6348			0.401678			0.200839	+	0.979624i	$0.435633\pi$
$840$		0			0
$841$	28.9188			0.997201
$842$		0			0
$843$	32.1602	+	8.61729i	1.10765	+	0.296795i
$844$		0			0
$845$	11.0112	−	5.83002i	0.378795	−	0.200559i
$846$		0			0
$847$	−7.23598	−	29.6477i	−0.248631	−	1.01871i
$848$		0			0
$849$	56.3371	+	32.5262i	1.93348	+	1.11630i
$850$		0			0
$851$	−0.511857	−	0.886562i	−0.0175462	−	0.0303909i
$852$		0			0
$853$	32.0398	−	32.0398i	1.09702	−	1.09702i	0.102267	−	0.994757i	$-0.467391\pi$
$853$	32.0398	−	32.0398i	1.09702	−	1.09702i	0.994757	−	0.102267i	$-0.0326095\pi$
$854$		0			0
$855$	−0.859608	−	0.539238i	−0.0293980	−	0.0184415i
$856$		0			0
$857$	8.63382	−	32.2218i	0.294926	−	1.10068i	−0.646351	−	0.763040i	$-0.723706\pi$
$857$	8.63382	−	32.2218i	0.294926	−	1.10068i	0.941276	−	0.337637i	$-0.109628\pi$
$858$		0			0
$859$	24.8311	−	43.0087i	0.847227	−	1.46744i	−0.0364468	−	0.999336i	$-0.511604\pi$
$859$	24.8311	−	43.0087i	0.847227	−	1.46744i	0.883673	−	0.468104i	$-0.155063\pi$
$860$		0			0
$861$	33.2686	+	60.7266i	1.13379	+	2.06956i
$862$		0			0
$863$	10.6051	−	2.84164i	0.361003	−	0.0967305i	−0.0737584	−	0.997276i	$-0.523499\pi$
$863$	10.6051	−	2.84164i	0.361003	−	0.0967305i	0.434761	+	0.900546i	$0.356833\pi$
$864$		0			0
$865$	−13.6083	+	12.6454i	−0.462695	+	0.429958i
$866$		0			0
$867$	59.8564	+	59.8564i	2.03283	+	2.03283i
$868$		0			0
$869$			58.6752i			1.99042i
$870$		0			0
$871$	−5.36943	+	3.10004i	−0.181936	+	0.105041i
$872$		0			0
$873$	−10.8123	−	40.3522i	−0.365942	−	1.36572i
$874$		0			0
$875$	−23.4945	+	17.9725i	−0.794258	+	0.607581i
$876$		0			0
$877$	−14.7604	−	55.0866i	−0.498424	−	1.86014i	−0.509942	−	0.860209i	$-0.670333\pi$
$877$	−14.7604	−	55.0866i	−0.498424	−	1.86014i	0.0115182	−	0.999934i	$-0.496334\pi$
$878$		0			0
$879$	−74.9246	+	43.2577i	−2.52714	+	1.45905i
$880$		0			0
$881$		−	53.3306i		−	1.79675i	−0.439226	−	0.898377i	$-0.644747\pi$
$881$		−	53.3306i		−	1.79675i	0.439226	−	0.898377i	$-0.355253\pi$
$882$		0			0
$883$	−1.43984	−	1.43984i	−0.0484545	−	0.0484545i	0.682464	−	0.730919i	$-0.260908\pi$
$883$	−1.43984	−	1.43984i	−0.0484545	−	0.0484545i	−0.730919	+	0.682464i	$0.760908\pi$
$884$		0			0
$885$	14.6458	−	13.6096i	0.492313	−	0.457480i
$886$		0			0
$887$	−21.9860	+	5.89113i	−0.738218	+	0.197805i	−0.608286	−	0.793718i	$-0.708143\pi$
$887$	−21.9860	+	5.89113i	−0.738218	+	0.197805i	−0.129932	+	0.991523i	$0.541476\pi$
$888$		0			0
$889$	−0.997193	+	44.4821i	−0.0334448	+	1.49188i
$890$		0			0
$891$	−5.05543	+	8.75626i	−0.169363	+	0.293346i
$892$		0			0
$893$	0.159203	−	0.594154i	0.00532753	−	0.0198826i
$894$		0			0
$895$	1.33232	+	0.835771i	0.0445344	+	0.0279367i
$896$		0			0
$897$	1.38239	−	1.38239i	0.0461568	−	0.0461568i
$898$		0			0
$899$	0.607023	+	1.05139i	0.0202454	+	0.0350660i
$900$		0			0
$901$	−52.0737	−	30.0648i	−1.73483	−	1.00160i
$902$		0			0
$903$	−68.9766	−	20.1496i	−2.29540	−	0.670535i
$904$		0			0
$905$	28.2450	−	14.9548i	0.938896	−	0.497113i
$906$		0			0
$907$	13.8503	+	3.71117i	0.459890	+	0.123227i	0.481324	−	0.876543i	$-0.340156\pi$
$907$	13.8503	+	3.71117i	0.459890	+	0.123227i	−0.0214331	+	0.999770i	$0.506823\pi$
$908$		0			0
$909$	10.4191			0.345581
$910$		0			0
$911$	−39.5063			−1.30890			−0.654451	−	0.756105i	$-0.727100\pi$
$911$	−39.5063			−1.30890			−0.654451	+	0.756105i	$0.727100\pi$
$912$		0			0
$913$	−65.9985	−	17.6842i	−2.18423	−	0.585263i
$914$		0			0
$915$	10.4982	−	34.1242i	0.347060	−	1.12811i
$916$		0			0
$917$	8.81031	−	2.15029i	0.290942	−	0.0710089i
$918$		0			0
$919$	28.2336	+	16.3007i	0.931340	+	0.537710i	0.887235	−	0.461317i	$-0.152623\pi$
$919$	28.2336	+	16.3007i	0.931340	+	0.537710i	0.0441051	+	0.999027i	$0.485956\pi$
$920$		0			0
$921$	−6.53436	−	11.3178i	−0.215315	−	0.372936i
$922$		0			0
$923$	−6.81391	+	6.81391i	−0.224283	+	0.224283i
$924$		0			0
$925$	−19.2473	−	6.70286i	−0.632847	−	0.220389i
$926$		0			0
$927$	−8.02777	+	29.9600i	−0.263667	+	0.984017i
$928$		0			0
$929$	6.79790	−	11.7743i	0.223032	−	0.386302i	−0.732695	−	0.680557i	$-0.761738\pi$
$929$	6.79790	−	11.7743i	0.223032	−	0.386302i	0.955727	+	0.294254i	$0.0950713\pi$
$930$		0			0
$931$	−0.519037	−	0.331535i	−0.0170107	−	0.0108656i
$932$		0			0
$933$	28.9158	−	7.74796i	0.946660	−	0.253657i
$934$		0			0
$935$	49.3451	+	53.1022i	1.61376	+	1.73663i
$936$		0			0
$937$	−14.6879	−	14.6879i	−0.479834	−	0.479834i	0.425245	−	0.905078i	$-0.360188\pi$
$937$	−14.6879	−	14.6879i	−0.479834	−	0.479834i	−0.905078	+	0.425245i	$0.860188\pi$
$938$		0			0
$939$		−	60.9155i		−	1.98790i
$940$		0			0
$941$	28.0116	−	16.1725i	0.913154	−	0.527209i	0.0317091	−	0.999497i	$-0.489905\pi$
$941$	28.0116	−	16.1725i	0.913154	−	0.527209i	0.881444	+	0.472288i	$0.156572\pi$
$942$		0			0
$943$	−0.595599	−	2.22281i	−0.0193954	−	0.0723845i
$944$		0			0
$945$	−16.3351	−	32.5986i	−0.531382	−	1.06043i
$946$		0			0
$947$	6.30918	+	23.5462i	0.205021	+	0.765148i	0.989443	+	0.144921i	$0.0462927\pi$
$947$	6.30918	+	23.5462i	0.205021	+	0.765148i	−0.784423	+	0.620227i	$0.787041\pi$
$948$		0			0
$949$	21.3269	−	12.3131i	0.692299	−	0.399699i
$950$		0			0
$951$		−	87.0419i		−	2.82253i
$952$		0			0
$953$	−36.4835	−	36.4835i	−1.18182	−	1.18182i	−0.979273	−	0.202544i	$-0.935079\pi$
$953$	−36.4835	−	36.4835i	−1.18182	−	1.18182i	−0.202544	−	0.979273i	$-0.564921\pi$
$954$		0			0
$955$	−37.9782	−	1.39282i	−1.22895	−	0.0450706i
$956$		0			0
$957$	−3.73104	+	0.999728i	−0.120607	+	0.0323166i
$958$		0			0
$959$	−2.70699	+	1.48300i	−0.0874132	+	0.0478886i
$960$		0			0
$961$	−6.41977	+	11.1194i	−0.207089	+	0.358689i
$962$		0			0
$963$	−23.6826	+	88.3846i	−0.763161	+	2.84816i
$964$		0			0
$965$	−32.7739	+	7.50601i	−1.05503	+	0.241627i
$966$		0			0
$967$	41.4629	−	41.4629i	1.33336	−	1.33336i	0.431012	−	0.902346i	$-0.358157\pi$
$967$	41.4629	−	41.4629i	1.33336	−	1.33336i	0.902346	−	0.431012i	$-0.141843\pi$
$968$		0			0
$969$	−0.858077	−	1.48623i	−0.0275654	−	0.0477447i
$970$		0			0
$971$	−41.8779	−	24.1782i	−1.34393	−	0.775917i	−0.356546	−	0.934278i	$-0.616046\pi$
$971$	−41.8779	−	24.1782i	−1.34393	−	0.775917i	−0.987381	+	0.158361i	$0.949379\pi$
$972$		0			0
$973$	5.24824	−	5.01809i	0.168251	−	0.160873i
$974$		0			0
$975$	2.85103	−	38.8174i	0.0913059	−	1.24315i
$976$		0			0
$977$	57.7392	+	15.4712i	1.84724	+	0.494966i	0.999378	−	0.0352523i	$-0.0112235\pi$
$977$	57.7392	+	15.4712i	1.84724	+	0.494966i	0.847861	+	0.530219i	$0.177890\pi$
$978$		0			0
$979$	−66.6808			−2.13113
$980$		0			0
$981$	−10.6689			−0.340631
$982$		0			0
$983$	−7.28707	−	1.95257i	−0.232422	−	0.0622772i	0.140728	−	0.990048i	$-0.455056\pi$
$983$	−7.28707	−	1.95257i	−0.232422	−	0.0622772i	−0.373150	+	0.927771i	$0.621722\pi$
$984$		0			0
$985$	6.60041	+	2.03059i	0.210306	+	0.0647001i
$986$		0			0
$987$	38.1852	−	36.5107i	1.21545	−	1.16215i
$988$		0			0
$989$	2.06823	+	1.19410i	0.0657660	+	0.0379700i
$990$		0			0
$991$	8.85426	+	15.3360i	0.281265	+	0.487165i	0.971697	−	0.236233i	$-0.0759127\pi$
$991$	8.85426	+	15.3360i	0.281265	+	0.487165i	−0.690432	+	0.723398i	$0.742579\pi$
$992$		0			0
$993$	10.7240	−	10.7240i	0.340314	−	0.340314i
$994$		0			0
$995$	−2.54072	+	4.05020i	−0.0805462	+	0.128400i
$996$		0			0
$997$	−1.57466	+	5.87671i	−0.0498700	+	0.186117i	−0.986368	−	0.164556i	$-0.947381\pi$
$997$	−1.57466	+	5.87671i	−0.0498700	+	0.186117i	0.936498	+	0.350674i	$0.114047\pi$
$998$		0			0
$999$	12.5614	−	21.7569i	0.397424	−	0.688358i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.bo.a.33.1	yes	48
4.3	odd	2		560.2.ci.e.33.12		48
5.2	odd	4	inner	280.2.bo.a.257.1	yes	48
7.3	odd	6	inner	280.2.bo.a.73.1	yes	48
20.7	even	4		560.2.ci.e.257.12		48
28.3	even	6		560.2.ci.e.353.12		48
35.17	even	12	inner	280.2.bo.a.17.1	✓	48
140.87	odd	12		560.2.ci.e.17.12		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bo.a.17.1	✓	48	35.17	even	12	inner
280.2.bo.a.33.1	yes	48	1.1	even	1	trivial
280.2.bo.a.73.1	yes	48	7.3	odd	6	inner
280.2.bo.a.257.1	yes	48	5.2	odd	4	inner
560.2.ci.e.17.12		48	140.87	odd	12
560.2.ci.e.33.12		48	4.3	odd	2
560.2.ci.e.257.12		48	20.7	even	4
560.2.ci.e.353.12		48	28.3	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.bo (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.75887 - 0.739238i) q^{3} +(-1.04631 - 1.97617i) q^{5} +(-1.91229 + 1.82843i) q^{7} +(4.46683 + 2.57893i) q^{9} +O(q^{10})\)	\(q+(-2.75887 - 0.739238i) q^{3} +(-1.04631 - 1.97617i) q^{5} +(-1.91229 + 1.82843i) q^{7} +(4.46683 + 2.57893i) q^{9} +(2.37354 + 4.11109i) q^{11} +(1.92718 - 1.92718i) q^{13} +(1.42578 + 6.22547i) q^{15} +(-1.76751 + 6.59645i) q^{17} +(0.0439918 - 0.0761960i) q^{19} +(6.62741 - 3.63077i) q^{21} +(-0.242586 + 0.0650008i) q^{23} +(-2.81047 + 4.13537i) q^{25} +(-4.35808 - 4.35808i) q^{27} -0.284886i q^{29} +(-3.69058 + 2.13075i) q^{31} +(-3.50922 - 13.0966i) q^{33} +(5.61413 + 1.86589i) q^{35} +(1.05500 + 3.93731i) q^{37} +(-6.74148 + 3.89220i) q^{39} +9.16296i q^{41} +(-6.72406 - 6.72406i) q^{43} +(0.422691 - 11.5256i) q^{45} +(6.75301 - 1.80946i) q^{47} +(0.313692 - 6.99297i) q^{49} +(9.75269 - 16.8922i) q^{51} +(-2.27886 + 8.50482i) q^{53} +(5.64073 - 8.99198i) q^{55} +(-0.177695 + 0.177695i) q^{57} +(-1.56522 - 2.71104i) q^{59} +(-4.84125 - 2.79509i) q^{61} +(-13.2573 + 3.23564i) q^{63} +(-5.82485 - 1.79199i) q^{65} +(-2.19738 - 0.588786i) q^{67} +0.717316 q^{69} -3.53569 q^{71} +(8.72777 + 2.33860i) q^{73} +(10.8107 - 9.33136i) q^{75} +(-12.0557 - 3.52174i) q^{77} +(10.7043 + 6.18015i) q^{79} +(1.06496 + 1.84456i) q^{81} +(-10.1777 + 10.1777i) q^{83} +(14.8850 - 3.40904i) q^{85} +(-0.210599 + 0.785966i) q^{87} +(-7.02336 + 12.1648i) q^{89} +(-0.161611 + 7.20903i) q^{91} +(11.7570 - 3.15027i) q^{93} +(-0.196605 - 0.00721033i) q^{95} +(-5.72716 - 5.72716i) q^{97} +24.4847i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{7}+O(q^{10}) \) 48 * q - 4 * q^7	\( 48 q - 4 q^{7} + 4 q^{11} + 8 q^{15} - 4 q^{21} - 4 q^{23} - 8 q^{25} - 36 q^{33} + 24 q^{35} + 8 q^{37} - 16 q^{43} + 48 q^{45} + 24 q^{51} + 16 q^{53} - 96 q^{57} - 36 q^{61} - 68 q^{63} + 12 q^{65} - 16 q^{67} - 64 q^{71} - 48 q^{73} - 48 q^{75} + 4 q^{77} - 40 q^{85} - 12 q^{87} - 80 q^{91} + 24 q^{95}+O(q^{100}) \) 48 * q - 4 * q^7 + 4 * q^11 + 8 * q^15 - 4 * q^21 - 4 * q^23 - 8 * q^25 - 36 * q^33 + 24 * q^35 + 8 * q^37 - 16 * q^43 + 48 * q^45 + 24 * q^51 + 16 * q^53 - 96 * q^57 - 36 * q^61 - 68 * q^63 + 12 * q^65 - 16 * q^67 - 64 * q^71 - 48 * q^73 - 48 * q^75 + 4 * q^77 - 40 * q^85 - 12 * q^87 - 80 * q^91 + 24 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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