LMFDB - Embedded newform 280.2.bo.a.73.1

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			73.1
Character	$\chi$	$=$	280.73
Dual form			280.2.bo.a.257.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.739238 - 2.75887i) q^{3} +(-2.23457 - 0.0819508i) q^{5} +(-1.82843 + 1.91229i) q^{7} +(-4.46683 + 2.57893i) q^{9} +O(q^{10})$	\(q+(-0.739238 - 2.75887i) q^{3} +(-2.23457 - 0.0819508i) q^{5} +(-1.82843 + 1.91229i) q^{7} +(-4.46683 + 2.57893i) q^{9} +(2.37354 - 4.11109i) q^{11} +(-1.92718 + 1.92718i) q^{13} +(1.42578 + 6.22547i) q^{15} +(-6.59645 + 1.76751i) q^{17} +(-0.0439918 - 0.0761960i) q^{19} +(6.62741 + 3.63077i) q^{21} +(0.0650008 - 0.242586i) q^{23} +(4.98657 + 0.366249i) q^{25} +(4.35808 + 4.35808i) q^{27} -0.284886i q^{29} +(-3.69058 - 2.13075i) q^{31} +(-13.0966 - 3.50922i) q^{33} +(4.24246 - 4.12329i) q^{35} +(-3.93731 - 1.05500i) q^{37} +(6.74148 + 3.89220i) q^{39} -9.16296i q^{41} +(-6.72406 - 6.72406i) q^{43} +(10.1928 - 5.39672i) q^{45} +(1.80946 - 6.75301i) q^{47} +(-0.313692 - 6.99297i) q^{49} +(9.75269 + 16.8922i) q^{51} +(8.50482 - 2.27886i) q^{53} +(-5.64073 + 8.99198i) q^{55} +(-0.177695 + 0.177695i) q^{57} +(1.56522 - 2.71104i) q^{59} +(-4.84125 + 2.79509i) q^{61} +(3.23564 - 13.2573i) q^{63} +(4.46434 - 4.14847i) q^{65} +(0.588786 + 2.19738i) q^{67} -0.717316 q^{69} -3.53569 q^{71} +(2.33860 + 8.72777i) q^{73} +(-2.67583 - 14.0281i) q^{75} +(3.52174 + 12.0557i) q^{77} +(-10.7043 + 6.18015i) q^{79} +(1.06496 - 1.84456i) q^{81} +(10.1777 - 10.1777i) q^{83} +(14.8850 - 3.40904i) q^{85} +(-0.785966 + 0.210599i) q^{87} +(7.02336 + 12.1648i) q^{89} +(-0.161611 - 7.20903i) q^{91} +(-3.15027 + 11.7570i) q^{93} +(0.0920582 + 0.173870i) q^{95} +(5.72716 + 5.72716i) q^{97} +24.4847i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

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

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
$3$	−0.739238	−	2.75887i	−0.426799	−	1.59284i	−0.759962	−	0.649967i	$-0.774783\pi$
$3$	−0.739238	−	2.75887i	−0.426799	−	1.59284i	0.333163	−	0.942869i	$-0.391884\pi$
$4$		0			0
$5$	−2.23457	−	0.0819508i	−0.999328	−	0.0366495i
$5$	−2.23457	−	0.0819508i	−0.999328	−	0.0366495i
$6$		0			0
$7$	−1.82843	+	1.91229i	−0.691081	+	0.722777i
$7$	−1.82843	+	1.91229i	−0.691081	+	0.722777i
$8$		0			0
$9$	−4.46683	+	2.57893i	−1.48894	+	0.859643i
$10$		0			0
$11$	2.37354	−	4.11109i	0.715648	−	1.23954i	−0.247061	−	0.969000i	$-0.579465\pi$
$11$	2.37354	−	4.11109i	0.715648	−	1.23954i	0.962709	−	0.270539i	$-0.0872020\pi$
$12$		0			0
$13$	−1.92718	+	1.92718i	−0.534503	+	0.534503i	−0.921909	−	0.387406i	$-0.873371\pi$
$13$	−1.92718	+	1.92718i	−0.534503	+	0.534503i	0.387406	+	0.921909i	$0.373371\pi$
$14$		0			0
$15$	1.42578	+	6.22547i	0.368136	+	1.60741i
$16$		0			0
$17$	−6.59645	+	1.76751i	−1.59987	+	0.428685i	−0.945004	−	0.327058i	$-0.893943\pi$
$17$	−6.59645	+	1.76751i	−1.59987	+	0.428685i	−0.654869	+	0.755742i	$0.727276\pi$
$18$		0			0
$19$	−0.0439918	−	0.0761960i	−0.0100924	−	0.0174806i	0.860935	−	0.508715i	$-0.169879\pi$
$19$	−0.0439918	−	0.0761960i	−0.0100924	−	0.0174806i	−0.871028	+	0.491234i	$0.836546\pi$
$20$		0			0
$21$	6.62741	+	3.63077i	1.44622	+	0.792299i
$22$		0			0
$23$	0.0650008	−	0.242586i	0.0135536	−	0.0505827i	−0.958818	−	0.284022i	$-0.908331\pi$
$23$	0.0650008	−	0.242586i	0.0135536	−	0.0505827i	0.972371	+	0.233439i	$0.0749979\pi$
$24$		0			0
$25$	4.98657	+	0.366249i	0.997314	+	0.0732498i
$26$		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	0.130514	−	0.991446i	$-0.458337\pi$
$31$	−3.69058	−	2.13075i	−0.662847	−	0.382695i	−0.793361	+	0.608752i	$0.791671\pi$
$32$		0			0
$33$	−13.0966	−	3.50922i	−2.27982	−	0.610876i
$34$		0			0
$35$	4.24246	−	4.12329i	0.717107	−	0.696964i
$36$		0			0
$37$	−3.93731	−	1.05500i	−0.647290	−	0.173441i	−0.0797867	−	0.996812i	$-0.525424\pi$
$37$	−3.93731	−	1.05500i	−0.647290	−	0.173441i	−0.567503	+	0.823371i	$0.692091\pi$
$38$		0			0
$39$	6.74148	+	3.89220i	1.07950	+	0.623250i
$40$		0			0
$41$		−	9.16296i		−	1.43101i	−0.698606	−	0.715507i	$-0.746196\pi$
$41$		−	9.16296i		−	1.43101i	0.698606	−	0.715507i	$-0.253804\pi$
$42$		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
$45$	10.1928	−	5.39672i	1.51945	−	0.804496i
$46$		0			0
$47$	1.80946	−	6.75301i	0.263937	−	0.985028i	−0.698960	−	0.715160i	$-0.746354\pi$
$47$	1.80946	−	6.75301i	0.263937	−	0.985028i	0.962898	−	0.269867i	$-0.0869797\pi$
$48$		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
$53$	8.50482	−	2.27886i	1.16823	−	0.313025i	0.377980	−	0.925814i	$-0.376619\pi$
$53$	8.50482	−	2.27886i	1.16823	−	0.313025i	0.790247	+	0.612788i	$0.209952\pi$
$54$		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	$-0.768013\pi$
$59$	1.56522	−	2.71104i	0.203774	−	0.352947i	0.949741	+	0.313036i	$0.101346\pi$
$60$		0			0
$61$	−4.84125	+	2.79509i	−0.619858	+	0.357875i	−0.776814	−	0.629730i	$-0.783165\pi$
$61$	−4.84125	+	2.79509i	−0.619858	+	0.357875i	0.156956	+	0.987606i	$0.449832\pi$
$62$		0			0
$63$	3.23564	−	13.2573i	0.407652	−	1.67026i
$64$		0			0
$65$	4.46434	−	4.14847i	0.553733	−	0.514554i
$66$		0			0
$67$	0.588786	+	2.19738i	0.0719316	+	0.268452i	0.992520	−	0.122082i	$-0.0389570\pi$
$67$	0.588786	+	2.19738i	0.0719316	+	0.268452i	−0.920588	+	0.390534i	$0.872290\pi$
$68$		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
$73$	2.33860	+	8.72777i	0.273712	+	1.02151i	0.956699	+	0.291078i	$0.0940139\pi$
$73$	2.33860	+	8.72777i	0.273712	+	1.02151i	−0.682987	+	0.730430i	$0.739319\pi$
$74$		0			0
$75$	−2.67583	−	14.0281i	−0.308978	−	1.61982i
$76$		0			0
$77$	3.52174	+	12.0557i	0.401339	+	1.37388i
$78$		0			0
$79$	−10.7043	+	6.18015i	−1.20433	+	0.695321i	−0.961515	−	0.274751i	$-0.911404\pi$
$79$	−10.7043	+	6.18015i	−1.20433	+	0.695321i	−0.242816	+	0.970072i	$0.578071\pi$
$80$		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	$-0.460111\pi$
$83$	10.1777	−	10.1777i	1.11715	−	1.11715i	0.992158	−	0.124989i	$-0.0398895\pi$
$84$		0			0
$85$	14.8850	−	3.40904i	1.61451	−	0.369762i
$86$		0			0
$87$	−0.785966	+	0.210599i	−0.0842644	+	0.0225786i
$88$		0			0
$89$	7.02336	+	12.1648i	0.744474	+	1.28947i	0.950440	+	0.310908i	$0.100633\pi$
$89$	7.02336	+	12.1648i	0.744474	+	1.28947i	−0.205965	+	0.978559i	$0.566033\pi$
$90$		0			0
$91$	−0.161611	−	7.20903i	−0.0169414	−	0.755711i
$92$		0			0
$93$	−3.15027	+	11.7570i	−0.326668	+	1.21914i
$94$		0			0
$95$	0.0920582	+	0.173870i	0.00944498	+	0.0178387i
$96$		0			0
$97$	5.72716	+	5.72716i	0.581505	+	0.581505i	0.935317	−	0.353812i	$-0.115115\pi$
$97$	5.72716	+	5.72716i	0.581505	+	0.581505i	−0.353812	+	0.935317i	$0.615115\pi$
$98$		0			0
$99$			24.4847i			2.46081i
$100$		0			0
$101$	1.74942	+	1.01003i	0.174074	+	0.100501i	0.584505	−	0.811390i	$-0.301289\pi$
$101$	1.74942	+	1.01003i	0.174074	+	0.100501i	−0.410432	+	0.911891i	$0.634622\pi$
$102$		0			0
$103$	5.80862	+	1.55642i	0.572341	+	0.153358i	0.533370	−	0.845882i	$-0.320925\pi$
$103$	5.80862	+	1.55642i	0.572341	+	0.153358i	0.0389708	+	0.999240i	$0.487592\pi$
$104$		0			0
$105$	−14.5118	−	8.65631i	−1.41621	−	0.844770i
$106$		0			0
$107$	−17.1359	−	4.59156i	−1.65659	−	0.443883i	−0.695145	−	0.718870i	$-0.744660\pi$
$107$	−17.1359	−	4.59156i	−1.65659	−	0.443883i	−0.961448	+	0.274987i	$0.911326\pi$
$108$		0			0
$109$	1.79135	+	1.03423i	0.171580	+	0.0990617i	0.583331	−	0.812235i	$-0.301749\pi$
$109$	1.79135	+	1.03423i	0.171580	+	0.0990617i	−0.411751	+	0.911297i	$0.635083\pi$
$110$		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
$115$	−0.165129	+	0.536748i	−0.0153983	+	0.0500520i
$116$		0			0
$117$	3.63833	−	13.5784i	0.336364	−	1.25533i
$118$		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
$123$	−25.2794	+	6.77360i	−2.27937	+	0.610755i
$124$		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	−0.624042	−	0.781391i	$-0.714511\pi$
$131$	−2.96850	+	1.71386i	−0.259359	+	0.149741i	0.364683	+	0.931132i	$0.381177\pi$
$132$		0			0
$133$	0.226145	+	0.0551941i	0.0196092	+	0.00478593i
$134$		0			0
$135$	−9.38128	−	10.0956i	−0.807412	−	0.868889i
$136$		0			0
$137$	−0.301944	−	1.12687i	−0.0257968	−	0.0962751i	0.951827	−	0.306635i	$-0.0992031\pi$
$137$	−0.301944	−	1.12687i	−0.0257968	−	0.0962751i	−0.977624	+	0.210360i	$0.932536\pi$
$138$		0			0
$139$	2.74448			0.232784			0.116392	−	0.993203i	$-0.462867\pi$
$139$	2.74448			0.232784			0.116392	+	0.993203i	$0.462867\pi$
$140$		0			0
$141$	−19.9683			−1.68164
$142$		0			0
$143$	3.34857	+	12.4970i	0.280021	+	1.04505i
$144$		0			0
$145$	−0.0233467	+	0.636597i	−0.00193884	+	0.0528665i
$146$		0			0
$147$	−19.0608	+	6.03490i	−1.57211	+	0.497750i
$148$		0			0
$149$	12.3425	−	7.12594i	1.01114	−	0.583780i	0.0996119	−	0.995026i	$-0.468240\pi$
$149$	12.3425	−	7.12594i	1.01114	−	0.583780i	0.911524	+	0.411247i	$0.134907\pi$
$150$		0			0
$151$	−5.62795	+	9.74790i	−0.457996	+	0.793273i	−0.998855	−	0.0478406i	$-0.984766\pi$
$151$	−5.62795	+	9.74790i	−0.457996	+	0.793273i	0.540859	+	0.841114i	$0.318099\pi$
$152$		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
$157$	9.87321	−	2.64552i	0.787968	−	0.211135i	0.157673	−	0.987491i	$-0.449601\pi$
$157$	9.87321	−	2.64552i	0.787968	−	0.211135i	0.630295	+	0.776356i	$0.282934\pi$
$158$		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
$163$	−1.96879	+	7.34761i	−0.154207	+	0.575509i	0.844965	+	0.534822i	$0.179621\pi$
$163$	−1.96879	+	7.34761i	−0.154207	+	0.575509i	−0.999172	+	0.0406871i	$0.987045\pi$
$164$		0			0
$165$	28.9776	+	8.91485i	2.25590	+	0.694020i
$166$		0			0
$167$	−10.7090	−	10.7090i	−0.828687	−	0.828687i	0.158648	−	0.987335i	$-0.449286\pi$
$167$	−10.7090	−	10.7090i	−0.828687	−	0.828687i	−0.987335	+	0.158648i	$0.949286\pi$
$168$		0			0
$169$			5.57198i			0.428614i
$170$		0			0
$171$	0.393008	+	0.226903i	0.0300541	+	0.0173517i
$172$		0			0
$173$	−8.02465	−	2.15020i	−0.610103	−	0.163477i	−0.0594785	−	0.998230i	$-0.518944\pi$
$173$	−8.02465	−	2.15020i	−0.610103	−	0.163477i	−0.550625	+	0.834753i	$0.685610\pi$
$174$		0			0
$175$	−9.81796	+	8.86609i	−0.742168	+	0.670214i
$176$		0			0
$177$	−8.63647	−	2.31414i	−0.649157	−	0.173941i
$178$		0			0
$179$	0.609128	+	0.351680i	0.0455284	+	0.0262858i	0.522591	−	0.852583i	$-0.324965\pi$
$179$	0.609128	+	0.351680i	0.0455284	+	0.0262858i	−0.477063	+	0.878869i	$0.658299\pi$
$180$		0			0
$181$		−	14.2928i		−	1.06238i	−0.847253	−	0.531189i	$-0.821745\pi$
$181$		−	14.2928i		−	1.06238i	0.847253	−	0.531189i	$-0.178255\pi$
$182$		0			0
$183$	11.2901	+	11.2901i	0.834591	+	0.834591i
$184$		0			0
$185$	8.71172	+	2.68013i	0.640499	+	0.197047i
$186$		0			0
$187$	−8.39051	+	31.3138i	−0.613575	+	2.28989i
$188$		0			0
$189$	−16.3024	+	0.365463i	−1.18582	+	0.0265836i
$190$		0			0
$191$	8.49789	+	14.7188i	0.614886	+	1.06501i	0.990405	+	0.138199i	$0.0441313\pi$
$191$	8.49789	+	14.7188i	0.614886	+	1.06501i	−0.375519	+	0.926815i	$0.622535\pi$
$192$		0			0
$193$	−14.5240	+	3.89171i	−1.04546	+	0.280131i	−0.740376	−	0.672193i	$-0.765352\pi$
$193$	−14.5240	+	3.89171i	−1.04546	+	0.280131i	−0.305088	+	0.952324i	$0.598686\pi$
$194$		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	$-0.809187\pi$
$199$	1.06910	−	1.85173i	0.0757863	−	0.131266i	0.901428	+	0.432929i	$0.142520\pi$
$200$		0			0
$201$	5.62704	−	3.24877i	0.396900	−	0.229151i
$202$		0			0
$203$	0.544785	+	0.520895i	0.0382364	+	0.0365596i
$204$		0			0
$205$	−0.750912	+	20.4752i	−0.0524460	+	1.43005i
$206$		0			0
$207$	0.335265	+	1.25122i	0.0233025	+	0.0869661i
$208$		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
$213$	2.61372	+	9.75453i	0.179089	+	0.668370i
$214$		0			0
$215$	14.4743	+	15.5764i	0.987140	+	1.06230i
$216$		0			0
$217$	10.8226	−	3.16151i	0.734684	−	0.214617i
$218$		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	−0.403364	−	0.915040i	$-0.632159\pi$
$223$	7.64095	−	7.64095i	0.511676	−	0.511676i	0.915040	+	0.403364i	$0.132159\pi$
$224$		0			0
$225$	−23.2187	+	11.2240i	−1.54791	+	0.748268i
$226$		0			0
$227$	−0.398693	+	0.106829i	−0.0264622	+	0.00709052i	−0.272026	−	0.962290i	$-0.587694\pi$
$227$	−0.398693	+	0.106829i	−0.0264622	+	0.00709052i	0.245564	+	0.969380i	$0.421027\pi$
$228$		0			0
$229$	−6.96704	−	12.0673i	−0.460395	−	0.797427i	0.538586	−	0.842571i	$-0.318959\pi$
$229$	−6.96704	−	12.0673i	−0.460395	−	0.797427i	−0.998981	+	0.0451435i	$0.985625\pi$
$230$		0			0
$231$	30.6568	−	18.6281i	2.01707	−	1.22564i
$232$		0			0
$233$	−0.643344	+	2.40099i	−0.0421469	+	0.157294i	−0.983792	−	0.179313i	$-0.942613\pi$
$233$	−0.643344	+	2.40099i	−0.0421469	+	0.157294i	0.941645	+	0.336607i	$0.109279\pi$
$234$		0			0
$235$	−4.59678	+	14.9418i	−0.299861	+	0.974693i
$236$		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	0.353056	−	0.935602i	$-0.385142\pi$
$241$	−4.35718	−	2.51562i	−0.280671	−	0.162045i	−0.633727	+	0.773557i	$0.718476\pi$
$242$		0			0
$243$	11.9836	+	3.21100i	0.768748	+	0.205985i
$244$		0			0
$245$	0.127886	+	15.6520i	0.00817031	+	0.999967i
$246$		0			0
$247$	0.231623	+	0.0620633i	0.0147378	+	0.00394899i
$248$		0			0
$249$	−35.6027	−	20.5552i	−2.25623	−	1.30263i
$250$		0			0
$251$			3.62098i			0.228554i	0.993449	+	0.114277i	$0.0364552\pi$
$251$			3.62098i			0.228554i	−0.993449	+	0.114277i	$0.963545\pi$
$252$		0			0
$253$	−0.843011	−	0.843011i	−0.0529997	−	0.0529997i
$254$		0			0
$255$	−20.4087	−	38.5459i	−1.27804	−	2.41384i
$256$		0			0
$257$	5.74916	−	21.4562i	0.358623	−	1.33840i	−0.517241	−	0.855840i	$-0.673041\pi$
$257$	5.74916	−	21.4562i	0.358623	−	1.33840i	0.875864	−	0.482559i	$-0.160292\pi$
$258$		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
$263$	−1.55188	+	0.415825i	−0.0956930	+	0.0256409i	−0.306348	−	0.951920i	$-0.599107\pi$
$263$	−1.55188	+	0.415825i	−0.0956930	+	0.0256409i	0.210655	+	0.977561i	$0.432440\pi$
$264$		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	−0.231864	−	0.972748i	$-0.574482\pi$
$269$	11.9154	−	20.6380i	0.726493	−	1.25832i	0.958357	−	0.285574i	$-0.0921844\pi$
$270$		0			0
$271$	−16.9698	+	9.79753i	−1.03084	+	0.595158i	−0.917226	−	0.398367i	$-0.869577\pi$
$271$	−16.9698	+	9.79753i	−1.03084	+	0.595158i	−0.113617	+	0.993525i	$0.536244\pi$
$272$		0			0
$273$	−19.7693	+	5.77505i	−1.19649	+	0.349522i
$274$		0			0
$275$	13.3415	−	19.6309i	0.804522	−	1.18379i
$276$		0			0
$277$	3.46378	+	12.9270i	0.208119	+	0.776709i	0.988476	+	0.151376i	$0.0483703\pi$
$277$	3.46378	+	12.9270i	0.208119	+	0.776709i	−0.780358	+	0.625333i	$0.784963\pi$
$278$		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
$283$	−5.89484	−	21.9998i	−0.350412	−	1.30775i	−0.886161	−	0.463378i	$-0.846637\pi$
$283$	−5.89484	−	21.9998i	−0.350412	−	1.30775i	0.535749	−	0.844377i	$-0.320029\pi$
$284$		0			0
$285$	0.411633	−	0.382509i	0.0243830	−	0.0226578i
$286$		0			0
$287$	17.5222	+	16.7538i	1.03430	+	0.988947i
$288$		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	$0.595700\pi$
$293$	−21.4186	+	21.4186i	−1.25129	+	1.25129i	−0.955144	+	0.296143i	$0.904300\pi$
$294$		0			0
$295$	−3.71975	+	5.92972i	−0.216572	+	0.345241i
$296$		0			0
$297$	28.2605	−	7.57239i	1.63984	−	0.439394i
$298$		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
$303$	1.49330	−	5.57307i	0.0857878	−	0.320165i
$304$		0			0
$305$	11.0471	−	5.84908i	0.632557	−	0.334917i
$306$		0			0
$307$	−3.23542	−	3.23542i	−0.184655	−	0.184655i	0.608726	−	0.793381i	$-0.291681\pi$
$307$	−3.23542	−	3.23542i	−0.184655	−	0.184655i	−0.793381	+	0.608726i	$0.791681\pi$
$308$		0			0
$309$		−	17.1758i		−	0.977098i
$310$		0			0
$311$	−9.07682	−	5.24050i	−0.514699	−	0.297162i	0.220064	−	0.975485i	$-0.429373\pi$
$311$	−9.07682	−	5.24050i	−0.514699	−	0.297162i	−0.734763	+	0.678324i	$0.762707\pi$
$312$		0			0
$313$	20.6008	+	5.51996i	1.16443	+	0.312007i	0.788732	−	0.614737i	$-0.210738\pi$
$313$	20.6008	+	5.51996i	1.16443	+	0.312007i	0.375693	+	0.926744i	$0.377405\pi$
$314$		0			0
$315$	−8.31669	+	29.3591i	−0.468592	+	1.65420i
$316$		0			0
$317$	−29.4364	−	7.88745i	−1.65331	−	0.443003i	−0.692774	−	0.721155i	$-0.743611\pi$
$317$	−29.4364	−	7.88745i	−1.65331	−	0.443003i	−0.960537	+	0.278152i	$0.910278\pi$
$318$		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
$325$	−10.3158	+	8.90417i	−0.572219	+	0.493915i
$326$		0			0
$327$	1.52909	−	5.70664i	0.0845589	−	0.315578i
$328$		0			0
$329$	9.60522	+	15.8076i	0.529553	+	0.871502i
$330$		0			0
$331$	−2.65492	−	4.59846i	−0.145928	−	0.252754i	0.783791	−	0.621025i	$-0.213283\pi$
$331$	−2.65492	−	4.59846i	−0.145928	−	0.252754i	−0.929719	+	0.368271i	$0.879950\pi$
$332$		0			0
$333$	20.3081	−	5.44154i	1.11288	−	0.298194i
$334$		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
$343$	13.9461	+	12.1863i	0.753020	+	0.657997i
$344$		0			0
$345$	1.60289	+	0.0587846i	0.0862966	+	0.00316486i
$346$		0			0
$347$	−5.78384	−	21.5856i	−0.310493	−	1.15877i	−0.928113	−	0.372298i	$-0.878570\pi$
$347$	−5.78384	−	21.5856i	−0.310493	−	1.15877i	0.617621	−	0.786476i	$-0.288097\pi$
$348$		0			0
$349$	−32.6644			−1.74849			−0.874244	−	0.485487i	$-0.838642\pi$
$349$	−32.6644			−1.74849			−0.874244	+	0.485487i	$0.838642\pi$
$350$		0			0
$351$	−16.7976			−0.896589
$352$		0			0
$353$	6.25948	+	23.3607i	0.333158	+	1.24336i	0.905852	+	0.423594i	$0.139232\pi$
$353$	6.25948	+	23.3607i	0.333158	+	1.24336i	−0.572694	+	0.819770i	$0.694101\pi$
$354$		0			0
$355$	7.90074	+	0.289753i	0.419328	+	0.0153785i
$356$		0			0
$357$	−50.1348	−	12.2362i	−2.65341	−	0.647606i
$358$		0			0
$359$	−30.6942	+	17.7213i	−1.61998	+	0.935293i	−0.633051	+	0.774110i	$0.718198\pi$
$359$	−30.6942	+	17.7213i	−1.61998	+	0.935293i	−0.986924	+	0.161184i	$0.948469\pi$
$360$		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
$367$	−13.1325	+	3.51883i	−0.685509	+	0.183682i	−0.584731	−	0.811227i	$-0.698800\pi$
$367$	−13.1325	+	3.51883i	−0.685509	+	0.183682i	−0.100778	+	0.994909i	$0.532133\pi$
$368$		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
$373$	4.45833	−	16.6387i	0.230843	−	0.861519i	−0.749135	−	0.662417i	$-0.769531\pi$
$373$	4.45833	−	16.6387i	0.230843	−	0.861519i	0.979979	−	0.199102i	$-0.0638026\pi$
$374$		0			0
$375$	4.82970	+	31.5659i	0.249404	+	1.63006i
$376$		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
$383$	21.8467	+	5.85380i	1.11631	+	0.299115i	0.769391	−	0.638778i	$-0.220560\pi$
$383$	21.8467	+	5.85380i	1.11631	+	0.299115i	0.346923	+	0.937894i	$0.387226\pi$
$384$		0			0
$385$	−6.88158	−	27.2279i	−0.350718	−	1.38766i
$386$		0			0
$387$	47.3761	+	12.6944i	2.40826	+	0.645293i
$388$		0			0
$389$	1.31599	+	0.759787i	0.0667234	+	0.0385227i	0.532991	−	0.846121i	$-0.321068\pi$
$389$	1.31599	+	0.759787i	0.0667234	+	0.0385227i	−0.466267	+	0.884644i	$0.654401\pi$
$390$		0			0
$391$			1.71510i			0.0867362i
$392$		0			0
$393$	6.92277	+	6.92277i	0.349207	+	0.349207i
$394$		0			0
$395$	24.4260	−	12.9327i	1.22901	−	0.650716i
$396$		0			0
$397$	0.424309	−	1.58354i	0.0212954	−	0.0794757i	−0.954460	−	0.298338i	$-0.903568\pi$
$397$	0.424309	−	1.58354i	0.0212954	−	0.0794757i	0.975756	+	0.218862i	$0.0702345\pi$
$398$		0			0
$399$	−0.0149013	−	0.664706i	−0.000745996	−	0.0332769i
$400$		0			0
$401$	1.21896	+	2.11129i	0.0608717	+	0.105433i	0.894855	−	0.446356i	$-0.147279\pi$
$401$	1.21896	+	2.11129i	0.0608717	+	0.105433i	−0.833984	+	0.551789i	$0.813945\pi$
$402$		0			0
$403$	11.2187	−	3.00605i	0.558845	−	0.149742i
$404$		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	$-0.963342\pi$
$409$	−8.03235	+	13.9124i	−0.397174	+	0.687925i	0.596202	+	0.802834i	$0.296676\pi$
$410$		0			0
$411$	−2.88569	+	1.66605i	−0.142340	+	0.0821803i
$412$		0			0
$413$	2.32239	+	7.95008i	0.114277	+	0.391198i
$414$		0			0
$415$	−23.5768	+	21.9087i	−1.15734	+	1.07545i
$416$		0			0
$417$	−2.02883	−	7.57168i	−0.0993521	−	0.370787i
$418$		0			0
$419$	−1.04323			−0.0509652			−0.0254826	−	0.999675i	$-0.508112\pi$
$419$	−1.04323			−0.0509652			−0.0254826	+	0.999675i	$0.508112\pi$
$420$		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
$423$	9.33295	+	34.8310i	0.453784	+	1.69354i
$424$		0			0
$425$	−33.5410	+	6.39788i	−1.62698	+	0.310343i
$426$		0			0
$427$	3.50685	−	14.3685i	0.169708	−	0.695340i
$428$		0			0
$429$	32.0023	−	18.4765i	1.54509	−	0.892056i
$430$		0			0
$431$	6.50366	−	11.2647i	0.313270	−	0.542600i	−0.665798	−	0.746132i	$-0.731909\pi$
$431$	6.50366	−	11.2647i	0.313270	−	0.542600i	0.979068	+	0.203532i	$0.0652421\pi$
$432$		0			0
$433$	23.8441	−	23.8441i	1.14587	−	1.14587i	0.158518	−	0.987356i	$-0.449328\pi$
$433$	23.8441	−	23.8441i	1.14587	−	1.14587i	0.987356	−	0.158518i	$-0.0506717\pi$
$434$		0			0
$435$	1.77355	−	0.406186i	0.0850352	−	0.0194751i
$436$		0			0
$437$	−0.0213436	+	0.00571900i	−0.00102100	+	0.000273577i
$438$		0			0
$439$	3.55919	+	6.16470i	0.169871	+	0.294225i	0.938374	−	0.345621i	$-0.112332\pi$
$439$	3.55919	+	6.16470i	0.169871	+	0.294225i	−0.768503	+	0.639846i	$0.778998\pi$
$440$		0			0
$441$	19.4356	+	30.4274i	0.925503	+	1.44893i
$442$		0			0
$443$	3.91835	−	14.6235i	0.186166	−	0.694783i	−0.808211	−	0.588892i	$-0.799564\pi$
$443$	3.91835	−	14.6235i	0.186166	−	0.694783i	0.994378	−	0.105890i	$-0.0337692\pi$
$444$		0			0
$445$	−14.6972	−	27.7586i	−0.696716	−	1.31589i
$446$		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
$453$	31.0536	+	8.32079i	1.45903	+	0.390945i
$454$		0			0
$455$	−0.229656	+	16.1223i	−0.0107664	+	0.755824i
$456$		0			0
$457$	26.5851	+	7.12346i	1.24360	+	0.333221i	0.819861	−	0.572563i	$-0.194051\pi$
$457$	26.5851	+	7.12346i	1.24360	+	0.333221i	0.423738	+	0.905785i	$0.360718\pi$
$458$		0			0
$459$	−36.4508	−	21.0449i	−1.70138	−	0.982292i
$460$		0			0
$461$		−	12.0569i		−	0.561545i	−0.959774	−	0.280773i	$-0.909409\pi$
$461$		−	12.0569i		−	0.561545i	0.959774	−	0.280773i	$-0.0905907\pi$
$462$		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
$465$	8.00298	−	26.0135i	0.371129	−	1.20635i
$466$		0			0
$467$	−5.79848	+	21.6402i	−0.268322	+	1.00139i	0.691864	+	0.722028i	$0.256790\pi$
$467$	−5.79848	+	21.6402i	−0.268322	+	1.00139i	−0.960186	+	0.279362i	$0.909877\pi$
$468$		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
$473$	−43.6030	+	11.6834i	−2.00487	+	0.537203i
$474$		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	$-0.887342\pi$
$479$	−3.69565	+	6.40106i	−0.168859	+	0.292472i	0.769160	+	0.639056i	$0.220675\pi$
$480$		0			0
$481$	9.62107	−	5.55473i	0.438683	−	0.253274i
$482$		0			0
$483$	1.31156	−	1.37171i	0.0596781	−	0.0624152i
$484$		0			0
$485$	−12.3284	−	13.2671i	−0.559802	−	0.602426i
$486$		0			0
$487$	8.44544	+	31.5188i	0.382699	+	1.42825i	0.841762	+	0.539849i	$0.181519\pi$
$487$	8.44544	+	31.5188i	0.382699	+	1.42825i	−0.459062	+	0.888404i	$0.651814\pi$
$488$		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
$493$	0.503540	+	1.87924i	0.0226783	+	0.0846366i
$494$		0			0
$495$	2.00654	−	54.7127i	0.0901874	−	2.45915i
$496$		0			0
$497$	6.46477	−	6.76127i	0.289984	−	0.303284i
$498$		0			0
$499$	−6.51132	+	3.75931i	−0.291487	+	0.168290i	−0.638612	−	0.769529i	$-0.720491\pi$
$499$	−6.51132	+	3.75931i	−0.291487	+	0.168290i	0.347125	+	0.937819i	$0.387158\pi$
$500$		0			0
$501$	−21.6283	+	37.4613i	−0.966280	+	1.67365i
$502$		0			0
$503$	−13.8563	+	13.8563i	−0.617822	+	0.617822i	−0.944972	−	0.327150i	$-0.893912\pi$
$503$	−13.8563	+	13.8563i	−0.617822	+	0.617822i	0.327150	+	0.944972i	$0.393912\pi$
$504$		0			0
$505$	−3.82642	−	2.40034i	−0.170273	−	0.106814i
$506$		0			0
$507$	15.3724	−	4.11902i	0.682711	−	0.182932i
$508$		0			0
$509$	14.3898	+	24.9239i	0.637818	+	1.10473i	0.985911	+	0.167274i	$0.0534963\pi$
$509$	14.3898	+	24.9239i	0.637818	+	1.10473i	−0.348092	+	0.937460i	$0.613170\pi$
$510$		0			0
$511$	−20.9660	−	11.4860i	−0.927480	−	0.508112i
$512$		0			0
$513$	0.140349	−	0.523789i	0.00619655	−	0.0231258i
$514$		0			0
$515$	−12.8522	−	3.95393i	−0.566336	−	0.174231i
$516$		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	0.810691	−	0.585475i	$-0.199092\pi$
$521$	16.1832	+	9.34339i	0.709000	+	0.409342i	−0.101690	+	0.994816i	$0.532425\pi$
$522$		0			0
$523$	26.1795	+	7.01477i	1.14475	+	0.306735i	0.780859	−	0.624707i	$-0.214782\pi$
$523$	26.1795	+	7.01477i	1.14475	+	0.306735i	0.363890	+	0.931442i	$0.381448\pi$
$524$		0			0
$525$	31.7182	+	20.5324i	1.38430	+	0.896106i
$526$		0			0
$527$	28.1108	+	7.53227i	1.22453	+	0.328111i
$528$		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
$535$	37.9151	+	11.6644i	1.63921	+	0.504298i
$536$		0			0
$537$	0.519951	−	1.94048i	0.0224375	−	0.0837380i
$538$		0			0
$539$	−29.4933	−	15.3085i	−1.27036	−	0.659382i
$540$		0			0
$541$	0.346702	+	0.600506i	0.0149059	+	0.0258178i	0.873382	−	0.487036i	$-0.161922\pi$
$541$	0.346702	+	0.600506i	0.0149059	+	0.0258178i	−0.858476	+	0.512853i	$0.828588\pi$
$542$		0			0
$543$	−39.4321	+	10.5658i	−1.69219	+	0.453422i
$544$		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
$553$	7.75389	−	31.7697i	0.329729	−	1.35099i
$554$		0			0
$555$	0.954108	−	26.0158i	0.0404996	−	1.10431i
$556$		0			0
$557$	1.84404	+	6.88206i	0.0781346	+	0.291602i	0.993926	−	0.110052i	$-0.0351019\pi$
$557$	1.84404	+	6.88206i	0.0781346	+	0.291602i	−0.915791	+	0.401655i	$0.868435\pi$
$558$		0			0
$559$	25.9169			1.09617
$560$		0			0
$561$	92.5935			3.90930
$562$		0			0
$563$	2.41236	+	9.00304i	0.101669	+	0.379433i	0.997946	−	0.0640613i	$-0.0204053\pi$
$563$	2.41236	+	9.00304i	0.101669	+	0.379433i	−0.896277	+	0.443494i	$0.853739\pi$
$564$		0			0
$565$	7.63648	+	8.21792i	0.321269	+	0.345731i
$566$		0			0
$567$	1.58013	+	5.40915i	0.0663592	+	0.227163i
$568$		0			0
$569$	−30.8192	+	17.7935i	−1.29201	+	0.745941i	−0.979010	−	0.203812i	$-0.934667\pi$
$569$	−30.8192	+	17.7935i	−1.29201	+	0.745941i	−0.312998	+	0.949754i	$0.601333\pi$
$570$		0			0
$571$	10.9925	−	19.0395i	0.460020	−	0.796778i	−0.538942	−	0.842343i	$-0.681176\pi$
$571$	10.9925	−	19.0395i	0.460020	−	0.796778i	0.998961	+	0.0455656i	$0.0145090\pi$
$572$		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
$577$	7.68316	−	2.05870i	0.319854	−	0.0857047i	−0.0953198	−	0.995447i	$-0.530387\pi$
$577$	7.68316	−	2.05870i	0.319854	−	0.0857047i	0.415174	+	0.909742i	$0.363721\pi$
$578$		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
$583$	10.8179	−	40.3730i	0.448032	−	1.67208i
$584$		0			0
$585$	−9.24285	+	30.0437i	−0.382145	+	1.24216i
$586$		0			0
$587$	−9.97309	−	9.97309i	−0.411633	−	0.411633i	0.470674	−	0.882307i	$-0.344011\pi$
$587$	−9.97309	−	9.97309i	−0.411633	−	0.411633i	−0.882307	+	0.470674i	$0.844011\pi$
$588$		0			0
$589$			0.374943i			0.0154493i
$590$		0			0
$591$	7.63908	+	4.41043i	0.314230	+	0.181421i
$592$		0			0
$593$	−37.0121	−	9.91736i	−1.51990	−	0.407257i	−0.600194	−	0.799854i	$-0.704910\pi$
$593$	−37.0121	−	9.91736i	−1.51990	−	0.407257i	−0.919711	+	0.392597i	$0.871577\pi$
$594$		0			0
$595$	−20.6972	+	34.6977i	−0.848502	+	1.42247i
$596$		0			0
$597$	−5.89901	−	1.58063i	−0.241430	−	0.0646910i
$598$		0			0
$599$	−6.66956	−	3.85067i	−0.272511	−	0.157334i	0.357517	−	0.933907i	$-0.383623\pi$
$599$	−6.66956	−	3.85067i	−0.272511	−	0.157334i	−0.630028	+	0.776572i	$0.716957\pi$
$600$		0			0
$601$			6.91584i			0.282103i	0.990002	+	0.141051i	$0.0450483\pi$
$601$			6.91584i			0.282103i	−0.990002	+	0.141051i	$0.954952\pi$
$602$		0			0
$603$	−8.29689	−	8.29689i	−0.337875	−	0.337875i
$604$		0			0
$605$	12.0689	+	22.7945i	0.490670	+	0.926728i
$606$		0			0
$607$	11.1610	−	41.6534i	0.453011	−	1.69066i	−0.240858	−	0.970560i	$-0.577429\pi$
$607$	11.1610	−	41.6534i	0.453011	−	1.69066i	0.693870	−	0.720101i	$-0.255904\pi$
$608$		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
$613$	−34.9209	+	9.35702i	−1.41044	+	0.377927i	−0.882083	−	0.471095i	$-0.843859\pi$
$613$	−34.9209	+	9.35702i	−1.41044	+	0.377927i	−0.528359	+	0.849021i	$0.677192\pi$
$614$		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	0.453035	+	0.891493i	$0.350341\pi$
$619$	−13.5728	+	23.5088i	−0.545538	+	0.944900i	−0.998573	+	0.0534071i	$0.982992\pi$
$620$		0			0
$621$	1.34049	−	0.773932i	0.0537920	−	0.0310568i
$622$		0			0
$623$	−36.1043	−	8.81182i	−1.44649	−	0.353038i
$624$		0			0
$625$	24.7317	+	3.65265i	0.989269	+	0.146106i
$626$		0			0
$627$	0.308754	+	1.15228i	0.0123304	+	0.0460178i
$628$		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
$633$	−6.35499	−	23.7171i	−0.252588	−	0.942672i
$634$		0			0
$635$	−27.5465	+	25.5975i	−1.09315	+	1.01580i
$636$		0			0
$637$	14.0812	+	12.8721i	0.557919	+	0.510013i
$638$		0			0
$639$	15.7934	−	9.11830i	0.624776	−	0.360714i
$640$		0			0
$641$	11.3718	−	19.6966i	0.449160	−	0.777968i	−0.549171	−	0.835710i	$-0.685057\pi$
$641$	11.3718	−	19.6966i	0.449160	−	0.777968i	0.998332	+	0.0577415i	$0.0183899\pi$
$642$		0			0
$643$	−14.6427	+	14.6427i	−0.577453	+	0.577453i	−0.934201	−	0.356748i	$-0.883886\pi$
$643$	−14.6427	+	14.6427i	−0.577453	+	0.577453i	0.356748	+	0.934201i	$0.383886\pi$
$644$		0			0
$645$	32.2734	−	51.4475i	1.27076	−	2.02574i
$646$		0			0
$647$	21.1930	−	5.67864i	0.833181	−	0.223250i	0.183080	−	0.983098i	$-0.441393\pi$
$647$	21.1930	−	5.67864i	0.833181	−	0.223250i	0.650101	+	0.759848i	$0.274727\pi$
$648$		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
$653$	10.5473	−	39.3632i	0.412750	−	1.54040i	−0.376551	−	0.926396i	$-0.622890\pi$
$653$	10.5473	−	39.3632i	0.412750	−	1.54040i	0.789301	−	0.614007i	$-0.210443\pi$
$654$		0			0
$655$	6.77376	−	3.58647i	0.264673	−	0.140135i
$656$		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	0.179318	−	0.983791i	$-0.442611\pi$
$661$	−14.9892	−	8.65401i	−0.583011	−	0.336602i	−0.762329	+	0.647189i	$0.775944\pi$
$662$		0			0
$663$	−51.3493	−	13.7590i	−1.99424	−	0.534356i
$664$		0			0
$665$	−0.500812	−	0.141868i	−0.0194207	−	0.00550139i
$666$		0			0
$667$	−0.0691095	−	0.0185178i	−0.00267593	−	0.000717014i
$668$		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
$675$	20.1357	+	23.3280i	0.775025	+	0.897896i
$676$		0			0
$677$	3.20054	−	11.9446i	0.123007	−	0.459068i	−0.876754	−	0.480939i	$-0.840296\pi$
$677$	3.20054	−	11.9446i	0.123007	−	0.459068i	0.999761	+	0.0218715i	$0.00696247\pi$
$678$		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
$683$	12.5461	−	3.36173i	0.480065	−	0.128633i	−0.0106680	−	0.999943i	$-0.503396\pi$
$683$	12.5461	−	3.36173i	0.480065	−	0.128633i	0.490733	+	0.871310i	$0.336729\pi$
$684$		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	0.391463	−	0.920194i	$-0.371969\pi$
$691$	36.3838	−	21.0062i	1.38411	−	0.799114i	0.992643	+	0.121080i	$0.0386359\pi$
$692$		0			0
$693$	−46.8218	−	44.7686i	−1.77861	−	1.70062i
$694$		0			0
$695$	−6.13273	−	0.224913i	−0.232628	−	0.00853143i
$696$		0			0
$697$	16.1956	+	60.4430i	0.613454	+	2.28944i
$698$		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
$703$	0.0928226	+	0.346419i	0.00350087	+	0.0130654i
$704$		0			0
$705$	44.6205	+	1.63642i	1.68051	+	0.0616312i
$706$		0			0
$707$	−5.13015	+	1.49863i	−0.192939	+	0.0563617i
$708$		0			0
$709$	−10.4976	+	6.06080i	−0.394246	+	0.227618i	−0.683998	−	0.729484i	$-0.739760\pi$
$709$	−10.4976	+	6.06080i	−0.394246	+	0.227618i	0.289752	+	0.957102i	$0.406427\pi$
$710$		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
$717$	−29.7600	+	7.97416i	−1.11141	+	0.297801i
$718$		0			0
$719$	−11.1933	−	19.3874i	−0.417441	−	0.723030i	0.578240	−	0.815867i	$-0.303740\pi$
$719$	−11.1933	−	19.3874i	−0.417441	−	0.723030i	−0.995681	+	0.0928372i	$0.970406\pi$
$720$		0			0
$721$	−13.5970	+	8.26196i	−0.506378	+	0.307692i
$722$		0			0
$723$	−3.71928	+	13.8806i	−0.138322	+	0.516224i
$724$		0			0
$725$	0.104339	−	1.42061i	0.00387507	−	0.0527600i
$726$		0			0
$727$	27.0366	+	27.0366i	1.00273	+	1.00273i	0.999996	+	0.00273448i	$0.000870412\pi$
$727$	27.0366	+	27.0366i	1.00273	+	1.00273i	0.00273448	+	0.999996i	$0.499130\pi$
$728$		0			0
$729$		−	41.8247i		−	1.54906i
$730$		0			0
$731$	56.2398	+	32.4700i	2.08010	+	1.20095i
$732$		0			0
$733$	−10.8977	−	2.92004i	−0.402517	−	0.107854i	0.0518799	−	0.998653i	$-0.483479\pi$
$733$	−10.8977	−	2.92004i	−0.402517	−	0.107854i	−0.454397	+	0.890799i	$0.650145\pi$
$734$		0			0
$735$	43.0872	−	11.9233i	1.58930	−	0.439799i
$736$		0			0
$737$	10.4311	+	2.79501i	0.384235	+	0.102955i
$738$		0			0
$739$	−24.8452	−	14.3444i	−0.913944	−	0.527666i	−0.0322460	−	0.999480i	$-0.510266\pi$
$739$	−24.8452	−	14.3444i	−0.913944	−	0.527666i	−0.881698	+	0.471814i	$0.843599\pi$
$740$		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
$745$	−28.1641	+	14.9119i	−1.03185	+	0.546330i
$746$		0			0
$747$	−19.2145	+	71.7096i	−0.703023	+	2.62372i
$748$		0			0
$749$	40.1122	−	24.3735i	1.46567	−	0.890588i
$750$		0			0
$751$	−1.31034	−	2.26958i	−0.0478151	−	0.0828182i	0.841127	−	0.540837i	$-0.181893\pi$
$751$	−1.31034	−	2.26958i	−0.0478151	−	0.0828182i	−0.888942	+	0.458019i	$0.848559\pi$
$752$		0			0
$753$	9.98983	−	2.67677i	0.364050	−	0.0975468i
$754$		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	−0.154745	−	0.987954i	$-0.549456\pi$
$761$	17.1993	−	9.93004i	0.623475	−	0.359964i	0.778221	+	0.627991i	$0.216122\pi$
$762$		0			0
$763$	−5.25311	+	1.53455i	−0.190175	+	0.0555543i
$764$		0			0
$765$	−57.6974	+	53.6151i	−2.08605	+	1.93846i
$766$		0			0
$767$	2.20820	+	8.24110i	0.0797333	+	0.297569i
$768$		0			0
$769$	4.79436			0.172889			0.0864445	−	0.996257i	$-0.472449\pi$
$769$	4.79436			0.172889			0.0864445	+	0.996257i	$0.472449\pi$
$770$		0			0
$771$	−63.4448			−2.28491
$772$		0			0
$773$	−6.72495	−	25.0979i	−0.241880	−	0.902707i	−0.974926	−	0.222529i	$-0.928569\pi$
$773$	−6.72495	−	25.0979i	−0.241880	−	0.902707i	0.733046	−	0.680179i	$-0.238098\pi$
$774$		0			0
$775$	−17.6229	−	11.9768i	−0.633034	−	0.430220i
$776$		0			0
$777$	−22.2637	−	21.2874i	−0.798706	−	0.763681i
$778$		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
$787$	−4.55904	+	1.22159i	−0.162512	+	0.0435450i	−0.339158	−	0.940730i	$-0.610142\pi$
$787$	−4.55904	+	1.22159i	−0.162512	+	0.0435450i	0.176646	+	0.984275i	$0.443475\pi$
$788$		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
$793$	3.94330	−	14.7166i	0.140031	−	0.522601i
$794$		0			0
$795$	26.3130	+	49.6973i	0.933226	+	1.76258i
$796$		0			0
$797$	−6.20691	−	6.20691i	−0.219860	−	0.219860i	0.588579	−	0.808439i	$-0.299687\pi$
$797$	−6.20691	−	6.20691i	−0.219860	−	0.219860i	−0.808439	+	0.588579i	$0.799687\pi$
$798$		0			0
$799$			47.7441i			1.68907i
$800$		0			0
$801$	−62.7444	−	36.2255i	−2.21696	−	1.27996i
$802$		0			0
$803$	41.4314	+	11.1015i	1.46208	+	0.391763i
$804$		0			0
$805$	−0.724491	−	1.29718i	−0.0255349	−	0.0457196i
$806$		0			0
$807$	−65.7460	−	17.6166i	−2.31437	−	0.620133i
$808$		0			0
$809$	3.88093	+	2.24066i	0.136446	+	0.0787773i	0.566669	−	0.823945i	$-0.308232\pi$
$809$	3.88093	+	2.24066i	0.136446	+	0.0787773i	−0.430223	+	0.902723i	$0.641565\pi$
$810$		0			0
$811$		−	1.95507i		−	0.0686518i	−0.999411	−	0.0343259i	$-0.989072\pi$
$811$		−	1.95507i		−	0.0686518i	0.999411	−	0.0343259i	$-0.0109284\pi$
$812$		0			0
$813$	39.5749	+	39.5749i	1.38795	+	1.38795i
$814$		0			0
$815$	5.00152	−	16.2574i	0.175196	−	0.569471i
$816$		0			0
$817$	−0.216543	+	0.808150i	−0.00757589	+	0.0282736i
$818$		0			0
$819$	19.3134	+	31.7847i	0.674866	+	1.11065i
$820$		0			0
$821$	8.68651	+	15.0455i	0.303161	+	0.525091i	0.976850	−	0.213924i	$-0.0686245\pi$
$821$	8.68651	+	15.0455i	0.303161	+	0.525091i	−0.673689	+	0.739015i	$0.735291\pi$
$822$		0			0
$823$	10.6022	−	2.84084i	0.369568	−	0.0990254i	−0.0692551	−	0.997599i	$-0.522062\pi$
$823$	10.6022	−	2.84084i	0.369568	−	0.0990254i	0.438823	+	0.898574i	$0.355396\pi$
$824$		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	0.484249	+	0.874930i	$0.339093\pi$
$829$	−14.8450	+	25.7123i	−0.515587	+	0.893024i	−0.999836	+	0.0180933i	$0.994240\pi$
$830$		0			0
$831$	33.1034	−	19.1123i	1.14835	−	0.662997i
$832$		0			0
$833$	14.4294	+	45.5743i	0.499949	+	1.57906i
$834$		0			0
$835$	23.0523	+	24.8076i	0.797759	+	0.858501i
$836$		0			0
$837$	−6.79783	−	25.3698i	−0.234967	−	0.876910i
$838$		0			0
$839$	−11.6348			−0.401678			−0.200839	−	0.979624i	$-0.564367\pi$
$839$	−11.6348			−0.401678			−0.200839	+	0.979624i	$0.564367\pi$
$840$		0			0
$841$	28.9188			0.997201
$842$		0			0
$843$	8.61729	+	32.1602i	0.296795	+	1.10765i
$844$		0			0
$845$	0.456628	−	12.4509i	0.0157085	−	0.428326i
$846$		0			0
$847$	29.6477	+	7.23598i	1.01871	+	0.248631i
$848$		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	$0.532609\pi$
$853$	−32.0398	+	32.0398i	−1.09702	+	1.09702i	−0.994757	+	0.102267i	$0.967391\pi$
$854$		0			0
$855$	−0.859608	−	0.539238i	−0.0293980	−	0.0184415i
$856$		0			0
$857$	32.2218	−	8.63382i	1.10068	−	0.294926i	0.337637	−	0.941276i	$-0.390372\pi$
$857$	32.2218	−	8.63382i	1.10068	−	0.294926i	0.763040	+	0.646351i	$0.223706\pi$
$858$		0			0
$859$	−24.8311	−	43.0087i	−0.847227	−	1.46744i	−0.883673	−	0.468104i	$-0.844937\pi$
$859$	−24.8311	−	43.0087i	−0.847227	−	1.46744i	0.0364468	−	0.999336i	$-0.488396\pi$
$860$		0			0
$861$	33.2686	−	60.7266i	1.13379	−	2.06956i
$862$		0			0
$863$	−2.84164	+	10.6051i	−0.0967305	+	0.361003i	−0.997276	−	0.0737584i	$-0.976501\pi$
$863$	−2.84164	+	10.6051i	−0.0967305	+	0.361003i	0.900546	+	0.434761i	$0.143167\pi$
$864$		0			0
$865$	17.7554	+	5.46239i	0.603702	+	0.185727i
$866$		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
$873$	−40.3522	−	10.8123i	−1.36572	−	0.365942i
$874$		0			0
$875$	22.6655	−	19.0073i	0.766233	−	0.642563i
$876$		0			0
$877$	55.0866	+	14.7604i	1.86014	+	0.498424i	0.999934	−	0.0115182i	$-0.00366644\pi$
$877$	55.0866	+	14.7604i	1.86014	+	0.498424i	0.860209	+	0.509942i	$0.170333\pi$
$878$		0			0
$879$	74.9246	+	43.2577i	2.52714	+	1.45905i
$880$		0			0
$881$			53.3306i			1.79675i	0.439226	+	0.898377i	$0.355253\pi$
$881$			53.3306i			1.79675i	−0.439226	+	0.898377i	$0.644747\pi$
$882$		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
$885$	19.1091	+	5.87886i	0.642346	+	0.197616i
$886$		0			0
$887$	−5.89113	+	21.9860i	−0.197805	+	0.738218i	0.793718	+	0.608286i	$0.208143\pi$
$887$	−5.89113	+	21.9860i	−0.197805	+	0.738218i	−0.991523	+	0.129932i	$0.958524\pi$
$888$		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
$893$	−0.594154	+	0.159203i	−0.0198826	+	0.00532753i
$894$		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
$903$	−20.1496	−	68.9766i	−0.670535	−	2.29540i
$904$		0			0
$905$	−1.17131	+	31.9383i	−0.0389357	+	1.06166i
$906$		0			0
$907$	−3.71117	−	13.8503i	−0.123227	−	0.459890i	0.876543	−	0.481324i	$-0.159844\pi$
$907$	−3.71117	−	13.8503i	−0.123227	−	0.459890i	−0.999770	+	0.0214331i	$0.993177\pi$
$908$		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
$913$	−17.6842	−	65.9985i	−0.585263	−	2.18423i
$914$		0			0
$915$	−24.3033	−	26.1538i	−0.803443	−	0.864618i
$916$		0			0
$917$	2.15029	−	8.81031i	0.0710089	−	0.290942i
$918$		0			0
$919$	−28.2336	+	16.3007i	−0.931340	+	0.537710i	−0.887235	−	0.461317i	$-0.847377\pi$
$919$	−28.2336	+	16.3007i	−0.931340	+	0.537710i	−0.0441051	+	0.999027i	$0.514044\pi$
$920$		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
$927$	−29.9600	+	8.02777i	−0.984017	+	0.263667i
$928$		0			0
$929$	−6.79790	−	11.7743i	−0.223032	−	0.386302i	0.732695	−	0.680557i	$-0.238262\pi$
$929$	−6.79790	−	11.7743i	−0.223032	−	0.386302i	−0.955727	+	0.294254i	$0.904929\pi$
$930$		0			0
$931$	−0.519037	+	0.331535i	−0.0170107	+	0.0108656i
$932$		0			0
$933$	−7.74796	+	28.9158i	−0.253657	+	0.946660i
$934$		0			0
$935$	21.3153	−	69.2852i	0.697086	−	2.26587i
$936$		0			0
$937$	14.6879	+	14.6879i	0.479834	+	0.479834i	0.905078	−	0.425245i	$-0.139812\pi$
$937$	14.6879	+	14.6879i	0.479834	+	0.479834i	−0.425245	+	0.905078i	$0.639812\pi$
$938$		0			0
$939$		−	60.9155i		−	1.98790i
$940$		0			0
$941$	28.0116	+	16.1725i	0.913154	+	0.527209i	0.881444	−	0.472288i	$-0.156572\pi$
$941$	28.0116	+	16.1725i	0.913154	+	0.527209i	0.0317091	+	0.999497i	$0.489905\pi$
$942$		0			0
$943$	−2.22281	−	0.595599i	−0.0723845	−	0.0193954i
$944$		0			0
$945$	36.4586	+	0.519340i	1.18600	+	0.0168941i
$946$		0			0
$947$	−23.5462	−	6.30918i	−0.765148	−	0.205021i	−0.144921	−	0.989443i	$-0.546293\pi$
$947$	−23.5462	−	6.30918i	−0.765148	−	0.205021i	−0.620227	+	0.784423i	$0.712959\pi$
$948$		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
$955$	−17.7829	−	33.5865i	−0.575441	−	1.08683i
$956$		0			0
$957$	−0.999728	+	3.73104i	−0.0323166	+	0.120607i
$958$		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
$963$	88.3846	−	23.6826i	2.84816	−	0.763161i
$964$		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	−0.987381	−	0.158361i	$-0.949379\pi$
$971$	−41.8779	+	24.1782i	−1.34393	+	0.775917i	−0.356546	+	0.934278i	$0.616046\pi$
$972$		0			0
$973$	−5.01809	+	5.24824i	−0.160873	+	0.168251i
$974$		0			0
$975$	32.1913	+	21.8778i	1.03095	+	0.700649i
$976$		0			0
$977$	−15.4712	−	57.7392i	−0.494966	−	1.84724i	−0.530219	−	0.847861i	$-0.677890\pi$
$977$	−15.4712	−	57.7392i	−0.494966	−	1.84724i	0.0352523	−	0.999378i	$-0.488777\pi$
$978$		0			0
$979$	66.6808			2.13113
$980$		0			0
$981$	−10.6689			−0.340631
$982$		0			0
$983$	−1.95257	−	7.28707i	−0.0622772	−	0.232422i	0.927771	−	0.373150i	$-0.121722\pi$
$983$	−1.95257	−	7.28707i	−0.0622772	−	0.232422i	−0.990048	+	0.140728i	$0.955056\pi$
$984$		0			0
$985$	5.05875	−	4.70082i	0.161185	−	0.149781i
$986$		0			0
$987$	36.5107	−	38.1852i	1.16215	−	1.21545i
$988$		0			0
$989$	−2.06823	+	1.19410i	−0.0657660	+	0.0379700i
$990$		0			0
$991$	8.85426	−	15.3360i	0.281265	−	0.487165i	−0.690432	−	0.723398i	$-0.742579\pi$
$991$	8.85426	−	15.3360i	0.281265	−	0.487165i	0.971697	+	0.236233i	$0.0759127\pi$
$992$		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
$997$	−5.87671	+	1.57466i	−0.186117	+	0.0498700i	−0.350674	−	0.936498i	$-0.614047\pi$
$997$	−5.87671	+	1.57466i	−0.186117	+	0.0498700i	0.164556	+	0.986368i	$0.447381\pi$
$998$		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.73.1	yes	48
4.3	odd	2		560.2.ci.e.353.12		48
5.2	odd	4	inner	280.2.bo.a.17.1	✓	48
7.5	odd	6	inner	280.2.bo.a.33.1	yes	48
20.7	even	4		560.2.ci.e.17.12		48
28.19	even	6		560.2.ci.e.33.12		48
35.12	even	12	inner	280.2.bo.a.257.1	yes	48
140.47	odd	12		560.2.ci.e.257.12		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bo.a.17.1	✓	48	5.2	odd	4	inner
280.2.bo.a.33.1	yes	48	7.5	odd	6	inner
280.2.bo.a.73.1	yes	48	1.1	even	1	trivial
280.2.bo.a.257.1	yes	48	35.12	even	12	inner
560.2.ci.e.17.12		48	20.7	even	4
560.2.ci.e.33.12		48	28.19	even	6
560.2.ci.e.257.12		48	140.47	odd	12
560.2.ci.e.353.12		48	4.3	odd	2

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)

\(f(q)\)	\(=\)	\(q+(-0.739238 - 2.75887i) q^{3} +(-2.23457 - 0.0819508i) q^{5} +(-1.82843 + 1.91229i) q^{7} +(-4.46683 + 2.57893i) q^{9} +O(q^{10})\)	\(q+(-0.739238 - 2.75887i) q^{3} +(-2.23457 - 0.0819508i) q^{5} +(-1.82843 + 1.91229i) q^{7} +(-4.46683 + 2.57893i) q^{9} +(2.37354 - 4.11109i) q^{11} +(-1.92718 + 1.92718i) q^{13} +(1.42578 + 6.22547i) q^{15} +(-6.59645 + 1.76751i) q^{17} +(-0.0439918 - 0.0761960i) q^{19} +(6.62741 + 3.63077i) q^{21} +(0.0650008 - 0.242586i) q^{23} +(4.98657 + 0.366249i) q^{25} +(4.35808 + 4.35808i) q^{27} -0.284886i q^{29} +(-3.69058 - 2.13075i) q^{31} +(-13.0966 - 3.50922i) q^{33} +(4.24246 - 4.12329i) q^{35} +(-3.93731 - 1.05500i) q^{37} +(6.74148 + 3.89220i) q^{39} -9.16296i q^{41} +(-6.72406 - 6.72406i) q^{43} +(10.1928 - 5.39672i) q^{45} +(1.80946 - 6.75301i) q^{47} +(-0.313692 - 6.99297i) q^{49} +(9.75269 + 16.8922i) q^{51} +(8.50482 - 2.27886i) q^{53} +(-5.64073 + 8.99198i) q^{55} +(-0.177695 + 0.177695i) q^{57} +(1.56522 - 2.71104i) q^{59} +(-4.84125 + 2.79509i) q^{61} +(3.23564 - 13.2573i) q^{63} +(4.46434 - 4.14847i) q^{65} +(0.588786 + 2.19738i) q^{67} -0.717316 q^{69} -3.53569 q^{71} +(2.33860 + 8.72777i) q^{73} +(-2.67583 - 14.0281i) q^{75} +(3.52174 + 12.0557i) q^{77} +(-10.7043 + 6.18015i) q^{79} +(1.06496 - 1.84456i) q^{81} +(10.1777 - 10.1777i) q^{83} +(14.8850 - 3.40904i) q^{85} +(-0.785966 + 0.210599i) q^{87} +(7.02336 + 12.1648i) q^{89} +(-0.161611 - 7.20903i) q^{91} +(-3.15027 + 11.7570i) q^{93} +(0.0920582 + 0.173870i) q^{95} +(5.72716 + 5.72716i) q^{97} +24.4847i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{7}+O(q^{10}) \) 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

Related objects

Downloads

Learn more