LMFDB - Embedded newform 560.2.ci.e.17.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(17,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, 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("560.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.ci (of order $12$, degree $4$, not 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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			17.7
Character	$\chi$	$=$	560.17
Dual form			560.2.ci.e.33.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0749389 - 0.0200798i) q^{3} +(-0.965007 + 2.01712i) q^{5} +(-1.45892 - 2.20716i) q^{7} +(-2.59286 + 1.49699i) q^{9} +O(q^{10})$	\(q+(0.0749389 - 0.0200798i) q^{3} +(-0.965007 + 2.01712i) q^{5} +(-1.45892 - 2.20716i) q^{7} +(-2.59286 + 1.49699i) q^{9} +(0.390978 - 0.677193i) q^{11} +(-3.28478 - 3.28478i) q^{13} +(-0.0318132 + 0.170538i) q^{15} +(1.40637 + 5.24865i) q^{17} +(-2.91828 - 5.05461i) q^{19} +(-0.153649 - 0.136108i) q^{21} +(-8.39046 - 2.24822i) q^{23} +(-3.13752 - 3.89306i) q^{25} +(-0.328824 + 0.328824i) q^{27} -0.303774i q^{29} +(5.04234 + 2.91120i) q^{31} +(0.0157015 - 0.0585989i) q^{33} +(5.85997 - 0.812878i) q^{35} +(1.90872 - 7.12345i) q^{37} +(-0.312116 - 0.180200i) q^{39} +4.39716i q^{41} +(-7.33155 + 7.33155i) q^{43} +(-0.517475 - 6.67472i) q^{45} +(-2.28130 - 0.611272i) q^{47} +(-2.74313 + 6.44013i) q^{49} +(0.210784 + 0.365088i) q^{51} +(-1.61262 - 6.01838i) q^{53} +(0.988682 + 1.44214i) q^{55} +(-0.320188 - 0.320188i) q^{57} +(-2.56228 + 4.43800i) q^{59} +(-8.91983 + 5.14987i) q^{61} +(7.08687 + 3.53889i) q^{63} +(9.79563 - 3.45595i) q^{65} +(1.47788 - 0.395996i) q^{67} -0.673916 q^{69} +5.83740 q^{71} +(12.9542 - 3.47108i) q^{73} +(-0.313295 - 0.228741i) q^{75} +(-2.06508 + 0.125017i) q^{77} +(-8.66781 + 5.00437i) q^{79} +(4.47293 - 7.74735i) q^{81} +(-2.94473 - 2.94473i) q^{83} +(-11.9443 - 2.22817i) q^{85} +(-0.00609973 - 0.0227645i) q^{87} +(6.43727 + 11.1497i) q^{89} +(-2.45783 + 12.0423i) q^{91} +(0.436324 + 0.116913i) q^{93} +(13.0119 - 1.00878i) q^{95} +(-0.0900545 + 0.0900545i) q^{97} +2.34116i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.0749389	−	0.0200798i	0.0432660	−	0.0115931i	−0.237121	−	0.971480i	$-0.576204\pi$
$3$	0.0749389	−	0.0200798i	0.0432660	−	0.0115931i	0.280387	+	0.959887i	$0.409537\pi$
$4$		0			0
$5$	−0.965007	+	2.01712i	−0.431564	+	0.902082i
$5$	−0.965007	+	2.01712i	−0.431564	+	0.902082i
$6$		0			0
$7$	−1.45892	−	2.20716i	−0.551418	−	0.834229i
$7$	−1.45892	−	2.20716i	−0.551418	−	0.834229i
$8$		0			0
$9$	−2.59286	+	1.49699i	−0.864288	+	0.498997i
$10$		0			0
$11$	0.390978	−	0.677193i	0.117884	−	0.204181i	−0.801045	−	0.598604i	$-0.795722\pi$
$11$	0.390978	−	0.677193i	0.117884	−	0.204181i	0.918929	+	0.394423i	$0.129055\pi$
$12$		0			0
$13$	−3.28478	−	3.28478i	−0.911035	−	0.911035i	0.0853189	−	0.996354i	$-0.472809\pi$
$13$	−3.28478	−	3.28478i	−0.911035	−	0.911035i	−0.996354	+	0.0853189i	$0.972809\pi$
$14$		0			0
$15$	−0.0318132	+	0.170538i	−0.00821413	+	0.0440327i
$16$		0			0
$17$	1.40637	+	5.24865i	0.341095	+	1.27298i	0.897108	+	0.441811i	$0.145664\pi$
$17$	1.40637	+	5.24865i	0.341095	+	1.27298i	−0.556013	+	0.831174i	$0.687670\pi$
$18$		0			0
$19$	−2.91828	−	5.05461i	−0.669499	−	1.15961i	−0.978044	−	0.208397i	$-0.933176\pi$
$19$	−2.91828	−	5.05461i	−0.669499	−	1.15961i	0.308545	−	0.951210i	$-0.400158\pi$
$20$		0			0
$21$	−0.153649	−	0.136108i	−0.0335290	−	0.0297011i
$22$		0			0
$23$	−8.39046	−	2.24822i	−1.74953	−	0.468786i	−0.765006	−	0.644024i	$-0.777264\pi$
$23$	−8.39046	−	2.24822i	−1.74953	−	0.468786i	−0.984526	+	0.175238i	$0.943931\pi$
$24$		0			0
$25$	−3.13752	−	3.89306i	−0.627505	−	0.778613i
$26$		0			0
$27$	−0.328824	+	0.328824i	−0.0632823	+	0.0632823i
$28$		0			0
$29$		−	0.303774i		−	0.0564094i	−0.999602	−	0.0282047i	$-0.991021\pi$
$29$		−	0.303774i		−	0.0564094i	0.999602	−	0.0282047i	$-0.00897903\pi$
$30$		0			0
$31$	5.04234	+	2.91120i	0.905632	+	0.522867i	0.879023	−	0.476779i	$-0.158196\pi$
$31$	5.04234	+	2.91120i	0.905632	+	0.522867i	0.0266086	+	0.999646i	$0.491529\pi$
$32$		0			0
$33$	0.0157015	−	0.0585989i	0.00273328	−	0.0102008i
$34$		0			0
$35$	5.85997	−	0.812878i	0.990515	−	0.137401i
$36$		0			0
$37$	1.90872	−	7.12345i	0.313792	−	1.17109i	−0.611317	−	0.791386i	$-0.709360\pi$
$37$	1.90872	−	7.12345i	0.313792	−	1.17109i	0.925109	−	0.379702i	$-0.123973\pi$
$38$		0			0
$39$	−0.312116	−	0.180200i	−0.0499785	−	0.0288551i
$40$		0			0
$41$			4.39716i			0.686722i	0.939204	+	0.343361i	$0.111565\pi$
$41$			4.39716i			0.686722i	−0.939204	+	0.343361i	$0.888435\pi$
$42$		0			0
$43$	−7.33155	+	7.33155i	−1.11805	+	1.11805i	−0.126023	+	0.992027i	$0.540221\pi$
$43$	−7.33155	+	7.33155i	−1.11805	+	1.11805i	−0.992027	+	0.126023i	$0.959779\pi$
$44$		0			0
$45$	−0.517475	−	6.67472i	−0.0771406	−	0.995008i
$46$		0			0
$47$	−2.28130	−	0.611272i	−0.332761	−	0.0891631i	0.0885698	−	0.996070i	$-0.471770\pi$
$47$	−2.28130	−	0.611272i	−0.332761	−	0.0891631i	−0.421331	+	0.906907i	$0.638437\pi$
$48$		0			0
$49$	−2.74313	+	6.44013i	−0.391876	+	0.920018i
$50$		0			0
$51$	0.210784	+	0.365088i	0.0295157	+	0.0511226i
$52$		0			0
$53$	−1.61262	−	6.01838i	−0.221510	−	0.826688i	−0.983773	−	0.179420i	$-0.942578\pi$
$53$	−1.61262	−	6.01838i	−0.221510	−	0.826688i	0.762262	−	0.647268i	$-0.224089\pi$
$54$		0			0
$55$	0.988682	+	1.44214i	0.133314	+	0.194459i
$56$		0			0
$57$	−0.320188	−	0.320188i	−0.0424100	−	0.0424100i
$58$		0			0
$59$	−2.56228	+	4.43800i	−0.333581	+	0.577779i	−0.983211	−	0.182471i	$-0.941590\pi$
$59$	−2.56228	+	4.43800i	−0.333581	+	0.577779i	0.649630	+	0.760250i	$0.274924\pi$
$60$		0			0
$61$	−8.91983	+	5.14987i	−1.14207	+	0.659373i	−0.946942	−	0.321405i	$-0.895845\pi$
$61$	−8.91983	+	5.14987i	−1.14207	+	0.659373i	−0.195126	+	0.980778i	$0.562511\pi$
$62$		0			0
$63$	7.08687	+	3.53889i	0.892862	+	0.445858i
$64$		0			0
$65$	9.79563	−	3.45595i	1.21500	−	0.428658i
$66$		0			0
$67$	1.47788	−	0.395996i	0.180551	−	0.0483786i	−0.167410	−	0.985887i	$-0.553541\pi$
$67$	1.47788	−	0.395996i	0.180551	−	0.0483786i	0.347962	+	0.937509i	$0.386874\pi$
$68$		0			0
$69$	−0.673916			−0.0811299
$70$		0			0
$71$	5.83740			0.692772			0.346386	−	0.938092i	$-0.387409\pi$
$71$	5.83740			0.692772			0.346386	+	0.938092i	$0.387409\pi$
$72$		0			0
$73$	12.9542	−	3.47108i	1.51618	−	0.406259i	0.597697	−	0.801722i	$-0.296082\pi$
$73$	12.9542	−	3.47108i	1.51618	−	0.406259i	0.918482	+	0.395463i	$0.129416\pi$
$74$		0			0
$75$	−0.313295	−	0.228741i	−0.0361762	−	0.0264127i
$76$		0			0
$77$	−2.06508	+	0.125017i	−0.235338	+	0.0142470i
$78$		0			0
$79$	−8.66781	+	5.00437i	−0.975205	+	0.563035i	−0.900819	−	0.434194i	$-0.857033\pi$
$79$	−8.66781	+	5.00437i	−0.975205	+	0.563035i	−0.0743862	+	0.997230i	$0.523700\pi$
$80$		0			0
$81$	4.47293	−	7.74735i	0.496992	−	0.860816i
$82$		0			0
$83$	−2.94473	−	2.94473i	−0.323226	−	0.323226i	0.526777	−	0.850003i	$-0.323400\pi$
$83$	−2.94473	−	2.94473i	−0.323226	−	0.323226i	−0.850003	+	0.526777i	$0.823400\pi$
$84$		0			0
$85$	−11.9443	−	2.22817i	−1.29554	−	0.241678i
$86$		0			0
$87$	−0.00609973	−	0.0227645i	−0.000653959	−	0.00244061i
$88$		0			0
$89$	6.43727	+	11.1497i	0.682350	+	1.18186i	0.974262	+	0.225419i	$0.0723751\pi$
$89$	6.43727	+	11.1497i	0.682350	+	1.18186i	−0.291912	+	0.956445i	$0.594292\pi$
$90$		0			0
$91$	−2.45783	+	12.0423i	−0.257650	+	1.26237i
$92$		0			0
$93$	0.436324	+	0.116913i	0.0452447	+	0.0121233i
$94$		0			0
$95$	13.0119	−	1.00878i	1.33499	−	0.103499i
$96$		0			0
$97$	−0.0900545	+	0.0900545i	−0.00914365	+	0.00914365i	−0.711664	−	0.702520i	$-0.752058\pi$
$97$	−0.0900545	+	0.0900545i	−0.00914365	+	0.00914365i	0.702520	+	0.711664i	$0.252058\pi$
$98$		0			0
$99$			2.34116i			0.235295i
$100$		0			0
$101$	5.24945	+	3.03077i	0.522340	+	0.301573i	0.737892	−	0.674919i	$-0.235822\pi$
$101$	5.24945	+	3.03077i	0.522340	+	0.301573i	−0.215551	+	0.976492i	$0.569155\pi$
$102$		0			0
$103$	−0.666178	+	2.48621i	−0.0656405	+	0.244973i	−0.990948	−	0.134243i	$-0.957140\pi$
$103$	−0.666178	+	2.48621i	−0.0656405	+	0.244973i	0.925308	+	0.379216i	$0.123806\pi$
$104$		0			0
$105$	0.422817	−	0.178583i	0.0412627	−	0.0174279i
$106$		0			0
$107$	2.20467	−	8.22792i	0.213133	−	0.795423i	−0.773682	−	0.633574i	$-0.781587\pi$
$107$	2.20467	−	8.22792i	0.213133	−	0.795423i	0.986815	−	0.161850i	$-0.0517460\pi$
$108$		0			0
$109$	−7.24069	−	4.18042i	−0.693533	−	0.400411i	0.111401	−	0.993775i	$-0.464466\pi$
$109$	−7.24069	−	4.18042i	−0.693533	−	0.400411i	−0.804934	+	0.593364i	$0.797799\pi$
$110$		0			0
$111$		−	0.572150i		−	0.0543061i
$112$		0			0
$113$	0.624674	−	0.624674i	0.0587644	−	0.0587644i	−0.677114	−	0.735878i	$-0.736770\pi$
$113$	0.624674	−	0.624674i	0.0587644	−	0.0587644i	0.735878	+	0.677114i	$0.236770\pi$
$114$		0			0
$115$	12.6318	−	14.7550i	1.17792	−	1.37591i
$116$		0			0
$117$	13.4343	+	3.59970i	1.24200	+	0.332793i
$118$		0			0
$119$	9.53284	−	10.7614i	0.873874	−	0.986498i
$120$		0			0
$121$	5.19427	+	8.99674i	0.472207	+	0.817886i
$122$		0			0
$123$	0.0882943	+	0.329519i	0.00796123	+	0.0297117i
$124$		0			0
$125$	10.8805	−	2.57192i	0.973181	−	0.230040i
$126$		0			0
$127$	−9.47330	−	9.47330i	−0.840620	−	0.840620i	0.148320	−	0.988939i	$-0.452613\pi$
$127$	−9.47330	−	9.47330i	−0.840620	−	0.840620i	−0.988939	+	0.148320i	$0.952613\pi$
$128$		0			0
$129$	−0.402202	+	0.696634i	−0.0354119	+	0.0613352i
$130$		0			0
$131$	5.71583	−	3.30004i	0.499394	−	0.288326i	−0.229069	−	0.973410i	$-0.573568\pi$
$131$	5.71583	−	3.30004i	0.499394	−	0.288326i	0.728463	+	0.685085i	$0.240235\pi$
$132$		0			0
$133$	−6.89881	+	13.8154i	−0.598203	+	1.19794i
$134$		0			0
$135$	−0.345960	−	0.980595i	−0.0297755	−	0.0843962i
$136$		0			0
$137$	−0.399466	+	0.107037i	−0.0341287	+	0.00914475i	−0.275843	−	0.961203i	$-0.588957\pi$
$137$	−0.399466	+	0.107037i	−0.0341287	+	0.00914475i	0.241714	+	0.970347i	$0.422290\pi$
$138$		0			0
$139$	16.1574			1.37045			0.685225	−	0.728332i	$-0.259704\pi$
$139$	16.1574			1.37045			0.685225	+	0.728332i	$0.259704\pi$
$140$		0			0
$141$	−0.183232			−0.0154309
$142$		0			0
$143$	−3.50871	+	0.940156i	−0.293413	+	0.0786198i
$144$		0			0
$145$	0.612748	+	0.293144i	0.0508859	+	0.0243443i
$146$		0			0
$147$	−0.0762506	+	0.537698i	−0.00628904	+	0.0443486i
$148$		0			0
$149$	4.87017	−	2.81179i	0.398979	−	0.230351i	−0.287064	−	0.957911i	$-0.592679\pi$
$149$	4.87017	−	2.81179i	0.398979	−	0.230351i	0.686044	+	0.727560i	$0.259346\pi$
$150$		0			0
$151$	−3.59720	+	6.23053i	−0.292736	+	0.507033i	−0.974456	−	0.224580i	$-0.927899\pi$
$151$	−3.59720	+	6.23053i	−0.292736	+	0.507033i	0.681720	+	0.731613i	$0.261232\pi$
$152$		0			0
$153$	−11.5037	−	11.5037i	−0.930020	−	0.930020i
$154$		0			0
$155$	−10.7381	+	7.36167i	−0.862507	+	0.591304i
$156$		0			0
$157$	−0.547542	−	2.04345i	−0.0436986	−	0.163085i	0.940628	−	0.339438i	$-0.110237\pi$
$157$	−0.547542	−	2.04345i	−0.0436986	−	0.163085i	−0.984327	+	0.176352i	$0.943570\pi$
$158$		0			0
$159$	−0.241696	−	0.418630i	−0.0191677	−	0.0331995i
$160$		0			0
$161$	7.27879	+	21.7991i	0.573649	+	1.71801i
$162$		0			0
$163$	−0.504944	−	0.135299i	−0.0395503	−	0.0105975i	0.238990	−	0.971022i	$-0.423184\pi$
$163$	−0.504944	−	0.135299i	−0.0395503	−	0.0105975i	−0.278540	+	0.960425i	$0.589850\pi$
$164$		0			0
$165$	0.103049	+	0.0882201i	0.00802234	+	0.00686793i
$166$		0			0
$167$	−0.418275	+	0.418275i	−0.0323671	+	0.0323671i	−0.723105	−	0.690738i	$-0.757286\pi$
$167$	−0.418275	+	0.418275i	−0.0323671	+	0.0323671i	0.690738	+	0.723105i	$0.257286\pi$
$168$		0			0
$169$			8.57959i			0.659969i
$170$		0			0
$171$	15.1334	+	8.73727i	1.15728	+	0.668156i
$172$		0			0
$173$	−2.64144	+	9.85798i	−0.200825	+	0.749488i	0.789857	+	0.613291i	$0.210155\pi$
$173$	−2.64144	+	9.85798i	−0.200825	+	0.749488i	−0.990682	+	0.136197i	$0.956512\pi$
$174$		0			0
$175$	−4.01524	+	12.6047i	−0.303523	+	0.952824i
$176$		0			0
$177$	−0.102900	+	0.384029i	−0.00773446	+	0.0288654i
$178$		0			0
$179$	−18.6482	−	10.7666i	−1.39384	−	0.804731i	−0.400098	−	0.916472i	$-0.631024\pi$
$179$	−18.6482	−	10.7666i	−1.39384	−	0.804731i	−0.993737	+	0.111741i	$0.964357\pi$
$180$		0			0
$181$			3.63457i			0.270155i	0.990835	+	0.135078i	$0.0431284\pi$
$181$			3.63457i			0.270155i	−0.990835	+	0.135078i	$0.956872\pi$
$182$		0			0
$183$	−0.565034	+	0.565034i	−0.0417685	+	0.0417685i
$184$		0			0
$185$	12.5269	+	10.7243i	0.920996	+	0.788466i
$186$		0			0
$187$	4.10421	+	1.09972i	0.300130	+	0.0804195i
$188$		0			0
$189$	1.20550	+	0.246042i	0.0876869	+	0.0178969i
$190$		0			0
$191$	−0.00324409	−	0.00561893i	−0.000234734	−	0.000406571i	0.865908	−	0.500203i	$-0.166741\pi$
$191$	−0.00324409	−	0.00561893i	−0.000234734	−	0.000406571i	−0.866143	+	0.499797i	$0.833408\pi$
$192$		0			0
$193$	0.678515	+	2.53225i	0.0488406	+	0.182275i	0.986037	−	0.166527i	$-0.0532552\pi$
$193$	0.678515	+	2.53225i	0.0488406	+	0.182275i	−0.937196	+	0.348802i	$0.886589\pi$
$194$		0			0
$195$	0.664679	−	0.455680i	0.0475986	−	0.0326319i
$196$		0			0
$197$	−6.64991	−	6.64991i	−0.473786	−	0.473786i	0.429351	−	0.903138i	$-0.358742\pi$
$197$	−6.64991	−	6.64991i	−0.473786	−	0.473786i	−0.903138	+	0.429351i	$0.858742\pi$
$198$		0			0
$199$	−0.846048	+	1.46540i	−0.0599747	+	0.103879i	−0.894454	−	0.447160i	$-0.852435\pi$
$199$	−0.846048	+	1.46540i	−0.0599747	+	0.103879i	0.834479	+	0.551040i	$0.185769\pi$
$200$		0			0
$201$	0.102799	−	0.0593510i	0.00725088	−	0.00418630i
$202$		0			0
$203$	−0.670478	+	0.443180i	−0.0470584	+	0.0311052i
$204$		0			0
$205$	−8.86960	−	4.24329i	−0.619479	−	0.296364i
$206$		0			0
$207$	25.1209	−	6.73112i	1.74602	−	0.467845i
$208$		0			0
$209$	−4.56393			−0.315693
$210$		0			0
$211$	−9.03597			−0.622062			−0.311031	−	0.950400i	$-0.600674\pi$
$211$	−9.03597			−0.622062			−0.311031	+	0.950400i	$0.600674\pi$
$212$		0			0
$213$	0.437448	−	0.117214i	0.0299735	−	0.00803137i
$214$		0			0
$215$	−7.71360	−	21.8636i	−0.526063	−	1.49108i
$216$		0			0
$217$	−0.930867	−	15.3765i	−0.0631914	−	1.04382i
$218$		0			0
$219$	0.901078	−	0.520238i	0.0608892	−	0.0351544i
$220$		0			0
$221$	12.6210	−	21.8603i	0.848984	−	1.47048i
$222$		0			0
$223$	−2.08617	−	2.08617i	−0.139700	−	0.139700i	0.633798	−	0.773499i	$-0.281495\pi$
$223$	−2.08617	−	2.08617i	−0.139700	−	0.139700i	−0.773499	+	0.633798i	$0.781495\pi$
$224$		0			0
$225$	13.9631	+	5.39734i	0.930870	+	0.359822i
$226$		0			0
$227$	−0.121724	−	0.454280i	−0.00807910	−	0.0301516i	0.961769	−	0.273863i	$-0.0883016\pi$
$227$	−0.121724	−	0.454280i	−0.00807910	−	0.0301516i	−0.969848	+	0.243712i	$0.921635\pi$
$228$		0			0
$229$	−12.6003	−	21.8244i	−0.832651	−	1.44219i	−0.895929	−	0.444198i	$-0.853489\pi$
$229$	−12.6003	−	21.8244i	−0.832651	−	1.44219i	0.0632774	−	0.997996i	$-0.479845\pi$
$230$		0			0
$231$	−0.152244	+	0.0508350i	−0.0100170	+	0.00334470i
$232$		0			0
$233$	−15.0074	−	4.02122i	−0.983168	−	0.263439i	−0.268790	−	0.963199i	$-0.586624\pi$
$233$	−15.0074	−	4.02122i	−0.983168	−	0.263439i	−0.714378	+	0.699760i	$0.753290\pi$
$234$		0			0
$235$	3.43447	−	4.01176i	0.224040	−	0.261699i
$236$		0			0
$237$	−0.549070	+	0.549070i	−0.0356659	+	0.0356659i
$238$		0			0
$239$			28.2271i			1.82586i	0.408117	+	0.912930i	$0.366186\pi$
$239$			28.2271i			1.82586i	−0.408117	+	0.912930i	$0.633814\pi$
$240$		0			0
$241$	−11.8212	−	6.82500i	−0.761473	−	0.439637i	0.0683514	−	0.997661i	$-0.478226\pi$
$241$	−11.8212	−	6.82500i	−0.761473	−	0.439637i	−0.829824	+	0.558025i	$0.811559\pi$
$242$		0			0
$243$	0.540706	−	2.01794i	0.0346863	−	0.129451i
$244$		0			0
$245$	−10.3434	−	11.7480i	−0.660813	−	0.750551i
$246$		0			0
$247$	−7.01737	+	26.1892i	−0.446505	+	1.66638i
$248$		0			0
$249$	−0.279804	−	0.161545i	−0.0177319	−	0.0102375i
$250$		0			0
$251$		−	8.14470i		−	0.514089i	−0.966400	−	0.257045i	$-0.917251\pi$
$251$		−	8.14470i		−	0.514089i	0.966400	−	0.257045i	$-0.0827487\pi$
$252$		0			0
$253$	−4.80296	+	4.80296i	−0.301960	+	0.301960i
$254$		0			0
$255$	−0.939834	+	0.0728631i	−0.0588547	+	0.00456287i
$256$		0			0
$257$	−10.0007	−	2.67967i	−0.623823	−	0.167153i	−0.0669581	−	0.997756i	$-0.521329\pi$
$257$	−10.0007	−	2.67967i	−0.623823	−	0.167153i	−0.556865	+	0.830603i	$0.687996\pi$
$258$		0			0
$259$	−18.5073	+	6.17965i	−1.14999	+	0.383985i
$260$		0			0
$261$	0.454747	+	0.787644i	0.0281481	+	0.0487540i
$262$		0			0
$263$	−7.62698	−	28.4643i	−0.470300	−	1.75518i	−0.638691	−	0.769463i	$-0.720524\pi$
$263$	−7.62698	−	28.4643i	−0.470300	−	1.75518i	0.168391	−	0.985720i	$-0.446143\pi$
$264$		0			0
$265$	13.6960	+	2.55493i	0.841337	+	0.156948i
$266$		0			0
$267$	0.706286	+	0.706286i	0.0432240	+	0.0432240i
$268$		0			0
$269$	10.2431	−	17.7415i	0.624531	−	1.08172i	−0.364100	−	0.931360i	$-0.618623\pi$
$269$	10.2431	−	17.7415i	0.624531	−	1.08172i	0.988631	−	0.150360i	$-0.0480433\pi$
$270$		0			0
$271$	−13.4287	+	7.75309i	−0.815738	+	0.470967i	−0.848945	−	0.528482i	$-0.822761\pi$
$271$	−13.4287	+	7.75309i	−0.815738	+	0.470967i	0.0332065	+	0.999449i	$0.489428\pi$
$272$		0			0
$273$	0.0576197	+	0.951787i	0.00348730	+	0.0576048i
$274$		0			0
$275$	−3.86306	+	0.602610i	−0.232951	+	0.0363387i
$276$		0			0
$277$	−2.32259	+	0.622335i	−0.139551	+	0.0373925i	−0.327918	−	0.944706i	$-0.606347\pi$
$277$	−2.32259	+	0.622335i	−0.139551	+	0.0373925i	0.188368	+	0.982099i	$0.439680\pi$
$278$		0			0
$279$	−17.4321			−1.04364
$280$		0			0
$281$	−16.9059			−1.00852			−0.504261	−	0.863552i	$-0.668235\pi$
$281$	−16.9059			−1.00852			−0.504261	+	0.863552i	$0.668235\pi$
$282$		0			0
$283$	−5.27738	+	1.41407i	−0.313708	+	0.0840578i	−0.412238	−	0.911076i	$-0.635253\pi$
$283$	−5.27738	+	1.41407i	−0.313708	+	0.0840578i	0.0985299	+	0.995134i	$0.468586\pi$
$284$		0			0
$285$	0.954841	−	0.336873i	0.0565599	−	0.0199547i
$286$		0			0
$287$	9.70525	−	6.41509i	0.572883	−	0.378671i
$288$		0			0
$289$	−10.8480	+	6.26310i	−0.638118	+	0.368418i
$290$		0			0
$291$	−0.00494031	+	0.00855687i	−0.000289606	+	0.000501612i
$292$		0			0
$293$	−9.62258	−	9.62258i	−0.562157	−	0.562157i	0.367762	−	0.929920i	$-0.380124\pi$
$293$	−9.62258	−	9.62258i	−0.562157	−	0.562157i	−0.929920	+	0.367762i	$0.880124\pi$
$294$		0			0
$295$	−6.47935	−	9.45113i	−0.377243	−	0.550266i
$296$		0			0
$297$	0.0941146	+	0.351241i	0.00546109	+	0.0203810i
$298$		0			0
$299$	20.1759	+	34.9457i	1.16680	+	2.02096i
$300$		0			0
$301$	26.8780	+	5.48581i	1.54922	+	0.316197i
$302$		0			0
$303$	0.454246	+	0.121715i	0.0260957	+	0.00699233i
$304$		0			0
$305$	−1.78019	−	22.9620i	−0.101933	−	1.31480i
$306$		0			0
$307$	−17.8381	+	17.8381i	−1.01807	+	1.01807i	−0.0182409	+	0.999834i	$0.505807\pi$
$307$	−17.8381	+	17.8381i	−1.01807	+	1.01807i	−0.999834	+	0.0182409i	$0.994193\pi$
$308$		0			0
$309$			0.199691i			0.0113600i
$310$		0			0
$311$	10.7681	+	6.21694i	0.610601	+	0.352530i	0.773200	−	0.634162i	$-0.218655\pi$
$311$	10.7681	+	6.21694i	0.610601	+	0.352530i	−0.162600	+	0.986692i	$0.551988\pi$
$312$		0			0
$313$	0.654518	−	2.44269i	0.0369955	−	0.138069i	−0.944958	−	0.327192i	$-0.893898\pi$
$313$	0.654518	−	2.44269i	0.0369955	−	0.138069i	0.981953	+	0.189123i	$0.0605643\pi$
$314$		0			0
$315$	−13.9772	+	10.8800i	−0.787528	+	0.613018i
$316$		0			0
$317$	−4.12570	+	15.3973i	−0.231722	+	0.864799i	0.747877	+	0.663837i	$0.231073\pi$
$317$	−4.12570	+	15.3973i	−0.231722	+	0.864799i	−0.979599	+	0.200962i	$0.935593\pi$
$318$		0			0
$319$	−0.205714	−	0.118769i	−0.0115178	−	0.00664978i
$320$		0			0
$321$		−	0.660861i		−	0.0368857i
$322$		0			0
$323$	22.4257	−	22.4257i	1.24780	−	1.24780i
$324$		0			0
$325$	−2.48178	+	23.0940i	−0.137664	+	1.28102i
$326$		0			0
$327$	−0.626552	−	0.167884i	−0.0346484	−	0.00928401i
$328$		0			0
$329$	1.97904	+	5.92699i	0.109108	+	0.326765i
$330$		0			0
$331$	−12.4183	−	21.5091i	−0.682572	−	1.18225i	−0.974193	−	0.225716i	$-0.927528\pi$
$331$	−12.4183	−	21.5091i	−0.682572	−	1.18225i	0.291621	−	0.956534i	$-0.405805\pi$
$332$		0			0
$333$	5.71468	+	21.3275i	0.313162	+	1.16874i
$334$		0			0
$335$	−0.627391	+	3.36319i	−0.0342780	+	0.183751i
$336$		0			0
$337$	−20.6822	−	20.6822i	−1.12663	−	1.12663i	−0.990721	−	0.135912i	$-0.956604\pi$
$337$	−20.6822	−	20.6822i	−1.12663	−	1.12663i	−0.135912	−	0.990721i	$-0.543396\pi$
$338$		0			0
$339$	0.0342690	−	0.0593557i	0.00186124	−	0.00322376i
$340$		0			0
$341$	3.94289	−	2.27643i	0.213519	−	0.123275i
$342$		0			0
$343$	18.2164	−	3.34107i	0.983593	−	0.180401i
$344$		0			0
$345$	0.650333	−	1.35937i	0.0350128	−	0.0731859i
$346$		0			0
$347$	−20.6497	+	5.53308i	−1.10854	+	0.297031i	−0.766236	−	0.642560i	$-0.777872\pi$
$347$	−20.6497	+	5.53308i	−1.10854	+	0.297031i	−0.342300	+	0.939591i	$0.611206\pi$
$348$		0			0
$349$	−14.6661			−0.785056			−0.392528	−	0.919740i	$-0.628399\pi$
$349$	−14.6661			−0.785056			−0.392528	+	0.919740i	$0.628399\pi$
$350$		0			0
$351$	2.16023			0.115305
$352$		0			0
$353$	−1.18700	+	0.318055i	−0.0631775	+	0.0169284i	−0.290269	−	0.956945i	$-0.593745\pi$
$353$	−1.18700	+	0.318055i	−0.0631775	+	0.0169284i	0.227092	+	0.973873i	$0.427078\pi$
$354$		0			0
$355$	−5.63313	+	11.7747i	−0.298975	+	0.624937i
$356$		0			0
$357$	0.498293	−	0.997868i	0.0263725	−	0.0528127i
$358$		0			0
$359$	15.3588	−	8.86741i	0.810607	−	0.468004i	−0.0365599	−	0.999331i	$-0.511640\pi$
$359$	15.3588	−	8.86741i	0.810607	−	0.468004i	0.847166	+	0.531328i	$0.178307\pi$
$360$		0			0
$361$	−7.53269	+	13.0470i	−0.396458	+	0.686685i
$362$		0			0
$363$	0.569906	+	0.569906i	0.0299123	+	0.0299123i
$364$		0			0
$365$	−5.49936	+	29.4798i	−0.287849	+	1.54305i
$366$		0			0
$367$	2.40926	+	8.99149i	0.125762	+	0.469352i	0.999866	−	0.0163883i	$-0.00521678\pi$
$367$	2.40926	+	8.99149i	0.125762	+	0.469352i	−0.874103	+	0.485740i	$0.838550\pi$
$368$		0			0
$369$	−6.58251	−	11.4012i	−0.342672	−	0.593525i
$370$		0			0
$371$	−10.9309	+	12.3396i	−0.567502	+	0.640641i
$372$		0			0
$373$	−14.5351	−	3.89467i	−0.752600	−	0.201659i	−0.137929	−	0.990442i	$-0.544045\pi$
$373$	−14.5351	−	3.89467i	−0.752600	−	0.201659i	−0.614671	+	0.788784i	$0.710711\pi$
$374$		0			0
$375$	0.763729	−	0.411216i	0.0394388	−	0.0212351i
$376$		0			0
$377$	−0.997831	+	0.997831i	−0.0513909	+	0.0513909i
$378$		0			0
$379$		−	16.5827i		−	0.851794i	−0.904772	−	0.425897i	$-0.859959\pi$
$379$		−	16.5827i		−	0.851794i	0.904772	−	0.425897i	$-0.140041\pi$
$380$		0			0
$381$	−0.900141	−	0.519697i	−0.0461156	−	0.0266249i
$382$		0			0
$383$	−7.35797	+	27.4603i	−0.375975	+	1.40316i	0.475941	+	0.879477i	$0.342108\pi$
$383$	−7.35797	+	27.4603i	−0.375975	+	1.40316i	−0.851916	+	0.523679i	$0.824559\pi$
$384$		0			0
$385$	1.74064	−	4.28615i	0.0887113	−	0.218442i
$386$		0			0
$387$	8.03445	−	29.9850i	0.408414	−	1.52422i
$388$		0			0
$389$	17.2501	+	9.95935i	0.874614	+	0.504959i	0.868879	−	0.495025i	$-0.164841\pi$
$389$	17.2501	+	9.95935i	0.874614	+	0.504959i	0.00573552	+	0.999984i	$0.498174\pi$
$390$		0			0
$391$		−	47.2004i		−	2.38703i
$392$		0			0
$393$	0.362074	−	0.362074i	0.0182642	−	0.0182642i
$394$		0			0
$395$	−1.72989	−	22.3132i	−0.0870404	−	1.12270i
$396$		0			0
$397$	10.4715	+	2.80583i	0.525549	+	0.140821i	0.511832	−	0.859085i	$-0.328967\pi$
$397$	10.4715	+	2.80583i	0.525549	+	0.140821i	0.0137171	+	0.999906i	$0.495634\pi$
$398$		0			0
$399$	−0.239580	+	1.17383i	−0.0119940	+	0.0587652i
$400$		0			0
$401$	−16.8238	−	29.1397i	−0.840142	−	1.45517i	−0.889774	−	0.456401i	$-0.849138\pi$
$401$	−16.8238	−	29.1397i	−0.840142	−	1.45517i	0.0496323	−	0.998768i	$-0.484195\pi$
$402$		0			0
$403$	−7.00035	−	26.1257i	−0.348712	−	1.30141i
$404$		0			0
$405$	11.3109	+	16.4987i	0.562043	+	0.819825i
$406$		0			0
$407$	−4.07768	−	4.07768i	−0.202123	−	0.202123i
$408$		0			0
$409$	5.99488	−	10.3834i	0.296428	−	0.513428i	−0.678888	−	0.734242i	$-0.737538\pi$
$409$	5.99488	−	10.3834i	0.296428	−	0.513428i	0.975316	+	0.220814i	$0.0708712\pi$
$410$		0			0
$411$	−0.0277863	+	0.0160424i	−0.00137059	+	0.000791313i
$412$		0			0
$413$	13.5335	−	0.819300i	0.665942	−	0.0403151i
$414$		0			0
$415$	8.78155	−	3.09818i	0.431069	−	0.152084i
$416$		0			0
$417$	1.21081	−	0.324437i	0.0592939	−	0.0158877i
$418$		0			0
$419$	1.15873			0.0566075			0.0283037	−	0.999599i	$-0.490989\pi$
$419$	1.15873			0.0566075			0.0283037	+	0.999599i	$0.490989\pi$
$420$		0			0
$421$	30.6438			1.49349			0.746744	−	0.665111i	$-0.231616\pi$
$421$	30.6438			1.49349			0.746744	+	0.665111i	$0.231616\pi$
$422$		0			0
$423$	6.83016	−	1.83014i	0.332094	−	0.0889843i
$424$		0			0
$425$	16.0208	−	21.9429i	0.777123	−	1.06439i
$426$		0			0
$427$	24.3799	+	12.1743i	1.17982	+	0.589155i
$428$		0			0
$429$	−0.244061	+	0.140909i	−0.0117834	+	0.00680313i
$430$		0			0
$431$	−20.2975	+	35.1563i	−0.977697	+	1.69342i	−0.306967	+	0.951720i	$0.599314\pi$
$431$	−20.2975	+	35.1563i	−0.977697	+	1.69342i	−0.670731	+	0.741701i	$0.734019\pi$
$432$		0			0
$433$	19.1716	+	19.1716i	0.921327	+	0.921327i	0.997123	−	0.0757959i	$-0.0241498\pi$
$433$	19.1716	+	19.1716i	0.921327	+	0.921327i	−0.0757959	+	0.997123i	$0.524150\pi$
$434$		0			0
$435$	0.0518049	+	0.00966402i	0.00248386	+	0.000463354i
$436$		0			0
$437$	13.1218	+	48.9714i	0.627703	+	2.34262i
$438$		0			0
$439$	−15.1874	−	26.3053i	−0.724854	−	1.25548i	−0.959034	−	0.283291i	$-0.908574\pi$
$439$	−15.1874	−	26.3053i	−0.724854	−	1.25548i	0.234179	−	0.972193i	$-0.424760\pi$
$440$		0			0
$441$	−2.52825	−	20.8048i	−0.120393	−	0.990705i
$442$		0			0
$443$	35.8429	+	9.60409i	1.70295	+	0.456304i	0.973679	−	0.227922i	$-0.0731930\pi$
$443$	35.8429	+	9.60409i	1.70295	+	0.456304i	0.729270	+	0.684226i	$0.239860\pi$
$444$		0			0
$445$	−28.7022	+	2.22522i	−1.36062	+	0.105485i
$446$		0			0
$447$	0.308505	−	0.308505i	0.0145918	−	0.0145918i
$448$		0			0
$449$			16.8567i			0.795516i	0.917490	+	0.397758i	$0.130212\pi$
$449$			16.8567i			0.795516i	−0.917490	+	0.397758i	$0.869788\pi$
$450$		0			0
$451$	2.97773	+	1.71919i	0.140216	+	0.0809536i
$452$		0			0
$453$	−0.144462	+	0.539140i	−0.00678742	+	0.0253310i
$454$		0			0
$455$	−21.9188	−	16.5786i	−1.02757	−	0.777217i
$456$		0			0
$457$	1.78496	−	6.66157i	0.0834971	−	0.311615i	−0.911528	−	0.411237i	$-0.865097\pi$
$457$	1.78496	−	6.66157i	0.0834971	−	0.311615i	0.995025	+	0.0996221i	$0.0317634\pi$
$458$		0			0
$459$	−2.18833	−	1.26343i	−0.102143	−	0.0589721i
$460$		0			0
$461$			0.948800i			0.0441900i	0.999756	+	0.0220950i	$0.00703363\pi$
$461$			0.948800i			0.0441900i	−0.999756	+	0.0220950i	$0.992966\pi$
$462$		0			0
$463$	−4.74202	+	4.74202i	−0.220380	+	0.220380i	−0.808659	−	0.588278i	$-0.799806\pi$
$463$	−4.74202	+	4.74202i	−0.220380	+	0.220380i	0.588278	+	0.808659i	$0.299806\pi$
$464$		0			0
$465$	−0.656882	+	0.767295i	−0.0304622	+	0.0355825i
$466$		0			0
$467$	26.6857	+	7.15041i	1.23487	+	0.330882i	0.816473	−	0.577384i	$-0.195926\pi$
$467$	26.6857	+	7.15041i	1.23487	+	0.330882i	0.418394	+	0.908266i	$0.362593\pi$
$468$		0			0
$469$	−3.03013	−	2.68419i	−0.139918	−	0.123944i
$470$		0			0
$471$	−0.0820644	−	0.142140i	−0.00378133	−	0.00654945i
$472$		0			0
$473$	2.09840	+	7.83135i	0.0964847	+	0.360086i
$474$		0			0
$475$	−10.5217	+	27.2200i	−0.482770	+	1.24894i
$476$		0			0
$477$	13.1908	+	13.1908i	0.603964	+	0.603964i
$478$		0			0
$479$	2.54289	−	4.40442i	0.116188	−	0.201243i	−0.802066	−	0.597235i	$-0.796266\pi$
$479$	2.54289	−	4.40442i	0.116188	−	0.201243i	0.918254	+	0.395992i	$0.129599\pi$
$480$		0			0
$481$	−29.6687	+	17.1292i	−1.35278	+	0.781026i
$482$		0			0
$483$	0.983186	+	1.48744i	0.0447365	+	0.0676809i
$484$		0			0
$485$	−0.0947473	−	0.268554i	−0.00430225	−	0.0121944i
$486$		0			0
$487$	18.4260	−	4.93722i	0.834961	−	0.223727i	0.184084	−	0.982911i	$-0.441068\pi$
$487$	18.4260	−	4.93722i	0.834961	−	0.223727i	0.650877	+	0.759184i	$0.274402\pi$
$488$		0			0
$489$	−0.0405567			−0.00183404
$490$		0			0
$491$	21.7497			0.981548			0.490774	−	0.871287i	$-0.336714\pi$
$491$	21.7497			0.981548			0.490774	+	0.871287i	$0.336714\pi$
$492$		0			0
$493$	1.59440	−	0.427219i	0.0718083	−	0.0192410i
$494$		0			0
$495$	−4.72239	−	2.25923i	−0.212256	−	0.101545i
$496$		0			0
$497$	−8.51627	−	12.8841i	−0.382007	−	0.577930i
$498$		0			0
$499$	28.7858	−	16.6195i	1.28863	−	0.743992i	0.310221	−	0.950664i	$-0.399597\pi$
$499$	28.7858	−	16.6195i	1.28863	−	0.743992i	0.978410	+	0.206673i	$0.0662636\pi$
$500$		0			0
$501$	−0.0229462	+	0.0397440i	−0.00102516	+	0.00177563i
$502$		0			0
$503$	25.2173	+	25.2173i	1.12438	+	1.12438i	0.991075	+	0.133307i	$0.0425598\pi$
$503$	25.2173	+	25.2173i	1.12438	+	1.12438i	0.133307	+	0.991075i	$0.457440\pi$
$504$		0			0
$505$	−11.1792	+	7.66405i	−0.497467	+	0.341046i
$506$		0			0
$507$	0.172277	+	0.642945i	0.00765108	+	0.0285542i
$508$		0			0
$509$	−7.44191	−	12.8898i	−0.329857	−	0.571329i	0.652626	−	0.757680i	$-0.273667\pi$
$509$	−7.44191	−	12.8898i	−0.329857	−	0.571329i	−0.982483	+	0.186351i	$0.940334\pi$
$510$		0			0
$511$	−26.5604	−	23.5281i	−1.17496	−	1.04082i
$512$		0			0
$513$	2.62168	+	0.702477i	0.115750	+	0.0310151i
$514$		0			0
$515$	−4.37211	−	3.74297i	−0.192658	−	0.164935i
$516$		0			0
$517$	−1.30589	+	1.30589i	−0.0574328	+	0.0574328i
$518$		0			0
$519$			0.791786i			0.0347555i
$520$		0			0
$521$	−23.3131	−	13.4598i	−1.02137	−	0.589686i	−0.106867	−	0.994273i	$-0.534082\pi$
$521$	−23.3131	−	13.4598i	−1.02137	−	0.589686i	−0.914500	+	0.404587i	$0.867415\pi$
$522$		0			0
$523$	−7.74842	+	28.9175i	−0.338815	+	1.26447i	0.560859	+	0.827911i	$0.310471\pi$
$523$	−7.74842	+	28.9175i	−0.338815	+	1.26447i	−0.899674	+	0.436563i	$0.856196\pi$
$524$		0			0
$525$	−0.0477979	+	1.02521i	−0.00208607	+	0.0447437i
$526$		0			0
$527$	−8.18845	+	30.5597i	−0.356695	+	1.33120i
$528$		0			0
$529$	45.4268	+	26.2271i	1.97508	+	1.14031i
$530$		0			0
$531$		−	15.3429i		−	0.665823i
$532$		0			0
$533$	14.4437	−	14.4437i	0.625627	−	0.625627i
$534$		0			0
$535$	14.4692	+	12.3871i	0.625557	+	0.535540i
$536$		0			0
$537$	−1.61367	−	0.432382i	−0.0696350	−	0.0186586i
$538$		0			0
$539$	3.28871	+	4.37558i	0.141655	+	0.188469i
$540$		0			0
$541$	12.1822	+	21.1003i	0.523755	+	0.907171i	0.999618	+	0.0276510i	$0.00880272\pi$
$541$	12.1822	+	21.1003i	0.523755	+	0.907171i	−0.475862	+	0.879520i	$0.657864\pi$
$542$		0			0
$543$	0.0729815	+	0.272371i	0.00313194	+	0.0116885i
$544$		0			0
$545$	15.4197	−	10.5712i	0.660508	−	0.452820i
$546$		0			0
$547$	−27.6642	−	27.6642i	−1.18283	−	1.18283i	−0.979007	−	0.203827i	$-0.934662\pi$
$547$	−27.6642	−	27.6642i	−1.18283	−	1.18283i	−0.203827	−	0.979007i	$-0.565338\pi$
$548$		0			0
$549$	15.4186	−	26.7058i	0.658050	−	1.13978i
$550$		0			0
$551$	−1.53546	+	0.886497i	−0.0654127	+	0.0377660i
$552$		0			0
$553$	23.6911	+	11.8303i	1.00745	+	0.503077i
$554$		0			0
$555$	1.15409	+	0.552129i	0.0489886	+	0.0234366i
$556$		0			0
$557$	13.3251	−	3.57044i	0.564601	−	0.151284i	0.0347817	−	0.999395i	$-0.488926\pi$
$557$	13.3251	−	3.57044i	0.564601	−	0.151284i	0.529819	+	0.848111i	$0.322260\pi$
$558$		0			0
$559$	48.1651			2.03717
$560$		0			0
$561$	0.329647			0.0139177
$562$		0			0
$563$	−19.1580	+	5.13338i	−0.807415	+	0.216346i	−0.638837	−	0.769342i	$-0.720584\pi$
$563$	−19.1580	+	5.13338i	−0.807415	+	0.216346i	−0.168578	+	0.985688i	$0.553917\pi$
$564$		0			0
$565$	0.657226	+	1.86285i	0.0276497	+	0.0783709i
$566$		0			0
$567$	−23.6253	+	1.43024i	−0.992169	+	0.0600643i
$568$		0			0
$569$	10.4442	−	6.02994i	0.437842	−	0.252788i	−0.264840	−	0.964292i	$-0.585319\pi$
$569$	10.4442	−	6.02994i	0.437842	−	0.252788i	0.702682	+	0.711504i	$0.251986\pi$
$570$		0			0
$571$	−1.69675	+	2.93885i	−0.0710067	+	0.122987i	−0.899343	−	0.437244i	$-0.855954\pi$
$571$	−1.69675	+	2.93885i	−0.0710067	+	0.122987i	0.828336	+	0.560232i	$0.189288\pi$
$572$		0			0
$573$	−0.000355935	0	0.000355935i	−1.48694e−5	0	1.48694e-5i
$574$		0			0
$575$	17.5728	+	39.7184i	0.732837	+	1.65637i
$576$		0			0
$577$	−6.53624	−	24.3936i	−0.272107	−	1.01552i	−0.957755	−	0.287585i	$-0.907148\pi$
$577$	−6.53624	−	24.3936i	−0.272107	−	1.01552i	0.685648	−	0.727933i	$-0.259519\pi$
$578$		0			0
$579$	0.101694	+	0.176140i	0.00422627	+	0.00732012i
$580$		0			0
$581$	−2.20338	+	10.7956i	−0.0914117	+	0.447877i
$582$		0			0
$583$	−4.70611	−	1.26100i	−0.194907	−	0.0522252i
$584$		0			0
$585$	−20.2252	+	23.6248i	−0.836209	+	0.976765i
$586$		0			0
$587$	−19.6875	+	19.6875i	−0.812589	+	0.812589i	−0.985021	−	0.172433i	$-0.944837\pi$
$587$	−19.6875	+	19.6875i	−0.812589	+	0.812589i	0.172433	+	0.985021i	$0.444837\pi$
$588$		0			0
$589$		−	33.9828i		−	1.40023i
$590$		0			0
$591$	−0.631866	−	0.364808i	−0.0259915	−	0.0150062i
$592$		0			0
$593$	4.42647	−	16.5198i	0.181773	−	0.678387i	−0.813525	−	0.581530i	$-0.802454\pi$
$593$	4.42647	−	16.5198i	0.181773	−	0.678387i	0.995298	−	0.0968573i	$-0.0308790\pi$
$594$		0			0
$595$	12.5078	+	29.6137i	0.512770	+	1.21404i
$596$		0			0
$597$	−0.0339770	+	0.126804i	−0.00139058	+	0.00518973i
$598$		0			0
$599$	16.8012	+	9.70017i	0.686478	+	0.396338i	0.802291	−	0.596933i	$-0.203614\pi$
$599$	16.8012	+	9.70017i	0.686478	+	0.396338i	−0.115813	+	0.993271i	$0.536947\pi$
$600$		0			0
$601$		−	26.7561i		−	1.09141i	−0.837979	−	0.545703i	$-0.816263\pi$
$601$		−	26.7561i		−	1.09141i	0.837979	−	0.545703i	$-0.183737\pi$
$602$		0			0
$603$	−3.23913	+	3.23913i	−0.131908	+	0.131908i
$604$		0			0
$605$	−23.1600	+	1.79554i	−0.941588	+	0.0729991i
$606$		0			0
$607$	8.62113	+	2.31003i	0.349921	+	0.0937611i	0.429498	−	0.903068i	$-0.358690\pi$
$607$	8.62113	+	2.31003i	0.349921	+	0.0937611i	−0.0795773	+	0.996829i	$0.525357\pi$
$608$		0			0
$609$	−0.0413459	+	0.0466745i	−0.00167542	+	0.00189135i
$610$		0			0
$611$	5.48567	+	9.50146i	0.221926	+	0.384388i
$612$		0			0
$613$	5.02936	+	18.7698i	0.203134	+	0.758107i	0.990010	+	0.140996i	$0.0450304\pi$
$613$	5.02936	+	18.7698i	0.203134	+	0.758107i	−0.786876	+	0.617111i	$0.788303\pi$
$614$		0			0
$615$	−0.749882	−	0.139888i	−0.0302382	−	0.00564082i
$616$		0			0
$617$	−12.8763	−	12.8763i	−0.518381	−	0.518381i	0.398700	−	0.917081i	$-0.369461\pi$
$617$	−12.8763	−	12.8763i	−0.518381	−	0.518381i	−0.917081	+	0.398700i	$0.869461\pi$
$618$		0			0
$619$	−5.08338	+	8.80468i	−0.204318	+	0.353890i	−0.949915	−	0.312507i	$-0.898831\pi$
$619$	−5.08338	+	8.80468i	−0.204318	+	0.353890i	0.745597	+	0.666397i	$0.232164\pi$
$620$		0			0
$621$	3.49826	−	2.01972i	0.140380	−	0.0810485i
$622$		0			0
$623$	15.2177	−	30.4746i	0.609685	−	1.22094i
$624$		0			0
$625$	−5.31188	+	24.4292i	−0.212475	+	0.977166i
$626$		0			0
$627$	−0.342016	+	0.0916428i	−0.0136588	+	0.00365986i
$628$		0			0
$629$	40.0729			1.59781
$630$		0			0
$631$	30.9143			1.23068			0.615339	−	0.788262i	$-0.289019\pi$
$631$	30.9143			1.23068			0.615339	+	0.788262i	$0.289019\pi$
$632$		0			0
$633$	−0.677146	+	0.181441i	−0.0269141	+	0.00721162i
$634$		0			0
$635$	28.2506	−	9.96696i	1.12109	−	0.395527i
$636$		0			0
$637$	30.1650	−	12.1438i	1.19518	−	0.481156i
$638$		0			0
$639$	−15.1356	+	8.73853i	−0.598754	+	0.345691i
$640$		0			0
$641$	9.22748	−	15.9825i	0.364463	−	0.631269i	−0.624226	−	0.781243i	$-0.714586\pi$
$641$	9.22748	−	15.9825i	0.364463	−	0.631269i	0.988690	+	0.149974i	$0.0479191\pi$
$642$		0			0
$643$	−15.3634	−	15.3634i	−0.605874	−	0.605874i	0.335991	−	0.941865i	$-0.390929\pi$
$643$	−15.3634	−	15.3634i	−0.605874	−	0.605874i	−0.941865	+	0.335991i	$0.890929\pi$
$644$		0			0
$645$	−1.01707	−	1.48355i	−0.0400469	−	0.0584145i
$646$		0			0
$647$	−10.5915	−	39.5282i	−0.416396	−	1.55401i	−0.782022	−	0.623250i	$-0.785812\pi$
$647$	−10.5915	−	39.5282i	−0.416396	−	1.55401i	0.365626	−	0.930762i	$-0.380855\pi$
$648$		0			0
$649$	2.00359	+	3.47032i	0.0786478	+	0.136222i
$650$		0			0
$651$	−0.378515	−	1.13360i	−0.0148352	−	0.0444294i
$652$		0			0
$653$	7.32658	+	1.96315i	0.286711	+	0.0768240i	0.399308	−	0.916817i	$-0.369250\pi$
$653$	7.32658	+	1.96315i	0.286711	+	0.0768240i	−0.112597	+	0.993641i	$0.535917\pi$
$654$		0			0
$655$	1.14075	+	14.7141i	0.0445726	+	0.574926i
$656$		0			0
$657$	−28.3924	+	28.3924i	−1.10769	+	1.10769i
$658$		0			0
$659$		−	4.25711i		−	0.165834i	−0.996556	−	0.0829168i	$-0.973576\pi$
$659$		−	4.25711i		−	0.165834i	0.996556	−	0.0829168i	$-0.0264236\pi$
$660$		0			0
$661$	−36.1264	−	20.8576i	−1.40515	−	0.811266i	−0.410238	−	0.911979i	$-0.634554\pi$
$661$	−36.1264	−	20.8576i	−1.40515	−	0.811266i	−0.994916	+	0.100713i	$0.967888\pi$
$662$		0			0
$663$	0.506857	−	1.89162i	0.0196847	−	0.0734643i
$664$		0			0
$665$	−21.2098	−	27.2476i	−0.822481	−	1.05662i
$666$		0			0
$667$	−0.682950	+	2.54880i	−0.0264439	+	0.0986900i
$668$		0			0
$669$	−0.198225	−	0.114445i	−0.00766384	−	0.00442472i
$670$		0			0
$671$			8.05393i			0.310919i
$672$		0			0
$673$	28.2067	−	28.2067i	1.08729	−	1.08729i	0.0914807	−	0.995807i	$-0.470840\pi$
$673$	28.2067	−	28.2067i	1.08729	−	1.08729i	0.995807	−	0.0914807i	$-0.0291600\pi$
$674$		0			0
$675$	2.31183	+	0.248439i	0.0889823	+	0.00956244i
$676$		0			0
$677$	19.7132	+	5.28215i	0.757641	+	0.203009i	0.616905	−	0.787038i	$-0.288386\pi$
$677$	19.7132	+	5.28215i	0.757641	+	0.203009i	0.140736	+	0.990047i	$0.455053\pi$
$678$		0			0
$679$	0.330147	+	0.0673830i	0.0126699	+	0.00258592i
$680$		0			0
$681$	−0.0182437	−	0.0315990i	−0.000699100	−	0.00121088i
$682$		0			0
$683$	11.6682	+	43.5462i	0.446470	+	1.66625i	0.712025	+	0.702154i	$0.247778\pi$
$683$	11.6682	+	43.5462i	0.446470	+	1.66625i	−0.265555	+	0.964096i	$0.585555\pi$
$684$		0			0
$685$	0.169582	−	0.909060i	0.00647939	−	0.0347334i
$686$		0			0
$687$	−1.38248	−	1.38248i	−0.0527450	−	0.0527450i
$688$		0			0
$689$	−14.4720	+	25.0662i	−0.551338	+	0.954945i
$690$		0			0
$691$	6.73905	−	3.89079i	0.256366	−	0.148013i	−0.366310	−	0.930493i	$-0.619379\pi$
$691$	6.73905	−	3.89079i	0.256366	−	0.148013i	0.622676	+	0.782480i	$0.286046\pi$
$692$		0			0
$693$	5.16732	−	3.41555i	0.196290	−	0.129746i
$694$		0			0
$695$	−15.5920	+	32.5913i	−0.591437	+	1.23626i
$696$		0			0
$697$	−23.0792	+	6.18405i	−0.874186	+	0.234237i
$698$		0			0
$699$	−1.20538			−0.0455918
$700$		0			0
$701$	−11.0999			−0.419237			−0.209618	−	0.977783i	$-0.567222\pi$
$701$	−11.0999			−0.419237			−0.209618	+	0.977783i	$0.567222\pi$
$702$		0			0
$703$	−41.5764	+	11.1404i	−1.56808	+	0.420167i
$704$		0			0
$705$	0.176820	−	0.369601i	0.00665944	−	0.0139200i
$706$		0			0
$707$	−0.969101	−	16.0080i	−0.0364468	−	0.602044i
$708$		0			0
$709$	−34.2204	+	19.7572i	−1.28517	+	0.741996i	−0.977790	−	0.209589i	$-0.932787\pi$
$709$	−34.2204	+	19.7572i	−1.28517	+	0.741996i	−0.307385	+	0.951585i	$0.599454\pi$
$710$		0			0
$711$	14.9830	−	25.9513i	0.561905	−	0.973249i
$712$		0			0
$713$	−35.7626	−	35.7626i	−1.33932	−	1.33932i
$714$		0			0
$715$	1.48952	−	7.98474i	0.0557050	−	0.298612i
$716$		0			0
$717$	0.566795	+	2.11531i	0.0211674	+	0.0789976i
$718$		0			0
$719$	−19.8400	−	34.3639i	−0.739908	−	1.28156i	−0.952536	−	0.304425i	$-0.901536\pi$
$719$	−19.8400	−	34.3639i	−0.739908	−	1.28156i	0.212628	−	0.977133i	$-0.431798\pi$
$720$		0			0
$721$	6.45936	−	2.15681i	0.240559	−	0.0803237i
$722$		0			0
$723$	−1.02292	−	0.274089i	−0.0380426	−	0.0101935i
$724$		0			0
$725$	−1.18261	+	0.953098i	−0.0439211	+	0.0353972i
$726$		0			0
$727$	−23.2801	+	23.2801i	−0.863410	+	0.863410i	−0.991733	−	0.128322i	$-0.959041\pi$
$727$	−23.2801	+	23.2801i	−0.863410	+	0.863410i	0.128322	+	0.991733i	$0.459041\pi$
$728$		0			0
$729$			26.6755i			0.987982i
$730$		0			0
$731$	−48.7916	−	28.1698i	−1.80462	−	1.04190i
$732$		0			0
$733$	4.27364	−	15.9494i	0.157850	−	0.589106i	−0.840994	−	0.541044i	$-0.818029\pi$
$733$	4.27364	−	15.9494i	0.157850	−	0.589106i	0.998844	−	0.0480612i	$-0.0153043\pi$
$734$		0			0
$735$	−1.01102	−	0.672688i	−0.0372919	−	0.0248125i
$736$		0			0
$737$	0.309651	−	1.15563i	0.0114062	−	0.0425683i
$738$		0			0
$739$	−37.3385	−	21.5574i	−1.37352	−	0.793001i	−0.382149	−	0.924101i	$-0.624816\pi$
$739$	−37.3385	−	21.5574i	−1.37352	−	0.793001i	−0.991369	+	0.131099i	$0.958149\pi$
$740$		0			0
$741$			2.10350i			0.0772739i
$742$		0			0
$743$	8.79757	−	8.79757i	0.322751	−	0.322751i	−0.527070	−	0.849822i	$-0.676710\pi$
$743$	8.79757	−	8.79757i	0.322751	−	0.322751i	0.849822	+	0.527070i	$0.176710\pi$
$744$		0			0
$745$	0.971971	+	12.5371i	0.0356103	+	0.459324i
$746$		0			0
$747$	12.0435	+	3.22705i	0.440649	+	0.118072i
$748$		0			0
$749$	−21.3768	+	7.13779i	−0.781091	+	0.260809i
$750$		0			0
$751$	1.89233	+	3.27761i	0.0690521	+	0.119602i	0.898484	−	0.439006i	$-0.144669\pi$
$751$	1.89233	+	3.27761i	0.0690521	+	0.119602i	−0.829432	+	0.558607i	$0.811336\pi$
$752$		0			0
$753$	−0.163544	−	0.610355i	−0.00595988	−	0.0222426i
$754$		0			0
$755$	−9.09639	−	13.2685i	−0.331051	−	0.482889i
$756$		0			0
$757$	14.6751	+	14.6751i	0.533375	+	0.533375i	0.921575	−	0.388200i	$-0.126903\pi$
$757$	14.6751	+	14.6751i	0.533375	+	0.533375i	−0.388200	+	0.921575i	$0.626903\pi$
$758$		0			0
$759$	−0.263486	+	0.456371i	−0.00956394	+	0.0165652i
$760$		0			0
$761$	−30.3893	+	17.5453i	−1.10161	+	0.636016i	−0.936644	−	0.350283i	$-0.886085\pi$
$761$	−30.3893	+	17.5453i	−1.10161	+	0.636016i	−0.164968	+	0.986299i	$0.552752\pi$
$762$		0			0
$763$	1.33670	+	22.0803i	0.0483919	+	0.799359i
$764$		0			0
$765$	34.3055	−	12.1032i	1.24032	−	0.437591i
$766$		0			0
$767$	22.9944	−	6.16134i	0.830280	−	0.222473i
$768$		0			0
$769$	17.2197			0.620959			0.310479	−	0.950580i	$-0.399510\pi$
$769$	17.2197			0.620959			0.310479	+	0.950580i	$0.399510\pi$
$770$		0			0
$771$	−0.803245			−0.0289282
$772$		0			0
$773$	19.0628	−	5.10786i	0.685641	−	0.183717i	0.100851	−	0.994902i	$-0.467844\pi$
$773$	19.0628	−	5.10786i	0.685641	−	0.183717i	0.584790	+	0.811185i	$0.301177\pi$
$774$		0			0
$775$	−4.48700	−	28.7641i	−0.161178	−	1.03324i
$776$		0			0
$777$	−1.26283	+	0.834719i	−0.0453037	+	0.0299454i
$778$		0			0
$779$	22.2259	−	12.8321i	0.796327	−	0.459759i
$780$		0			0
$781$	2.28229	−	3.95305i	0.0816669	−	0.141451i
$782$		0			0
$783$	0.0998883	+	0.0998883i	0.00356972	+	0.00356972i
$784$		0			0
$785$	4.65027	+	0.867490i	0.165975	+	0.0309621i
$786$		0			0
$787$	8.85989	+	33.0656i	0.315821	+	1.17866i	0.923223	+	0.384265i	$0.125545\pi$
$787$	8.85989	+	33.0656i	0.315821	+	1.17866i	−0.607402	+	0.794395i	$0.707788\pi$
$788$		0			0
$789$	−1.14312	−	1.97993i	−0.0406960	−	0.0704875i
$790$		0			0
$791$	−2.29010	−	0.467410i	−0.0814267	−	0.0166192i
$792$		0			0
$793$	46.2159	+	12.3835i	1.64117	+	0.439751i
$794$		0			0
$795$	1.07766	−	0.0835487i	0.0382208	−	0.00296317i
$796$		0			0
$797$	−26.5966	+	26.5966i	−0.942100	+	0.942100i	−0.998413	−	0.0563133i	$-0.982065\pi$
$797$	−26.5966	+	26.5966i	−0.942100	+	0.942100i	0.0563133	+	0.998413i	$0.482065\pi$
$798$		0			0
$799$		−	12.8334i		−	0.454013i
$800$		0			0
$801$	−33.3819	−	19.2731i	−1.17949	−	0.680981i
$802$		0			0
$803$	2.71423	−	10.1296i	0.0957830	−	0.357467i
$804$		0			0
$805$	−50.9954	−	6.35406i	−1.79735	−	0.223951i
$806$		0			0
$807$	0.411358	−	1.53521i	0.0144805	−	0.0540419i
$808$		0			0
$809$	−9.43671	−	5.44829i	−0.331777	−	0.191552i	0.324853	−	0.945765i	$-0.394685\pi$
$809$	−9.43671	−	5.44829i	−0.331777	−	0.191552i	−0.656630	+	0.754213i	$0.728019\pi$
$810$		0			0
$811$		−	39.7220i		−	1.39483i	−0.716668	−	0.697414i	$-0.754334\pi$
$811$		−	39.7220i		−	1.39483i	0.716668	−	0.697414i	$-0.245666\pi$
$812$		0			0
$813$	−0.850655	+	0.850655i	−0.0298338	+	0.0298338i
$814$		0			0
$815$	0.760189	−	0.887966i	0.0266283	−	0.0311041i
$816$		0			0
$817$	58.4536	+	15.6626i	2.04503	+	0.547965i
$818$		0			0
$819$	−11.6544	−	34.9033i	−0.407236	−	1.21962i
$820$		0			0
$821$	−7.63160	−	13.2183i	−0.266345	−	0.461323i	0.701570	−	0.712600i	$-0.252483\pi$
$821$	−7.63160	−	13.2183i	−0.266345	−	0.461323i	−0.967915	+	0.251278i	$0.919149\pi$
$822$		0			0
$823$	7.97924	+	29.7789i	0.278139	+	1.03803i	0.953709	+	0.300732i	$0.0972311\pi$
$823$	7.97924	+	29.7789i	0.278139	+	1.03803i	−0.675570	+	0.737296i	$0.736102\pi$
$824$		0			0
$825$	−0.277393	+	0.122728i	−0.00965759	+	0.00427286i
$826$		0			0
$827$	−2.11815	−	2.11815i	−0.0736553	−	0.0736553i	0.669319	−	0.742975i	$-0.266586\pi$
$827$	−2.11815	−	2.11815i	−0.0736553	−	0.0736553i	−0.742975	+	0.669319i	$0.766586\pi$
$828$		0			0
$829$	−10.6454	+	18.4384i	−0.369730	+	0.640392i	−0.989523	−	0.144374i	$-0.953883\pi$
$829$	−10.6454	+	18.4384i	−0.369730	+	0.640392i	0.619793	+	0.784765i	$0.287217\pi$
$830$		0			0
$831$	−0.161556	+	0.0932742i	−0.00560431	+	0.00323565i
$832$		0			0
$833$	−37.6598	−	5.34052i	−1.30484	−	0.185038i
$834$		0			0
$835$	−0.440072	−	1.24735i	−0.0152293	−	0.0431663i
$836$		0			0
$837$	−2.61532	+	0.700773i	−0.0903986	+	0.0242222i
$838$		0			0
$839$	17.0861			0.589879			0.294939	−	0.955516i	$-0.404701\pi$
$839$	17.0861			0.589879			0.294939	+	0.955516i	$0.404701\pi$
$840$		0			0
$841$	28.9077			0.996818
$842$		0			0
$843$	−1.26691	+	0.339467i	−0.0436347	+	0.0116919i
$844$		0			0
$845$	−17.3060	−	8.27936i	−0.595346	−	0.284819i
$846$		0			0
$847$	12.2793	−	24.5901i	0.421921	−	0.844926i
$848$		0			0
$849$	−0.367087	+	0.211938i	−0.0125984	+	0.00727369i
$850$		0			0
$851$	−32.0301	+	55.4778i	−1.09798	+	1.90175i
$852$		0			0
$853$	−4.45830	−	4.45830i	−0.152649	−	0.152649i	0.626651	−	0.779300i	$-0.284425\pi$
$853$	−4.45830	−	4.45830i	−0.152649	−	0.152649i	−0.779300	+	0.626651i	$0.784425\pi$
$854$		0			0
$855$	−32.2279	+	22.0943i	−1.10217	+	0.755609i
$856$		0			0
$857$	6.97152	+	26.0181i	0.238143	+	0.888761i	0.976707	+	0.214578i	$0.0688375\pi$
$857$	6.97152	+	26.0181i	0.238143	+	0.888761i	−0.738564	+	0.674183i	$0.764496\pi$
$858$		0			0
$859$	9.12384	+	15.8029i	0.311301	+	0.539190i	0.978644	−	0.205561i	$-0.0659018\pi$
$859$	9.12384	+	15.8029i	0.311301	+	0.539190i	−0.667343	+	0.744750i	$0.732569\pi$
$860$		0			0
$861$	0.598487	−	0.675620i	0.0203964	−	0.0230251i
$862$		0			0
$863$	−3.57400	−	0.957651i	−0.121660	−	0.0325988i	0.197475	−	0.980308i	$-0.436726\pi$
$863$	−3.57400	−	0.957651i	−0.121660	−	0.0325988i	−0.319136	+	0.947709i	$0.603393\pi$
$864$		0			0
$865$	−17.3357	−	14.8411i	−0.589431	−	0.504613i
$866$		0			0
$867$	−0.687176	+	0.687176i	−0.0233377	+	0.0233377i
$868$		0			0
$869$			7.82638i			0.265492i
$870$		0			0
$871$	−6.15527	−	3.55375i	−0.208563	−	0.120414i
$872$		0			0
$873$	0.0986883	−	0.368310i	0.00334009	−	0.0124654i
$874$		0			0
$875$	−21.5504	−	20.2628i	−0.728536	−	0.685008i
$876$		0			0
$877$	−10.5233	+	39.2734i	−0.355345	+	1.32617i	0.524704	+	0.851285i	$0.324176\pi$
$877$	−10.5233	+	39.2734i	−0.355345	+	1.32617i	−0.880049	+	0.474882i	$0.842491\pi$
$878$		0			0
$879$	−0.914326	−	0.527886i	−0.0308394	−	0.0178052i
$880$		0			0
$881$			39.2100i			1.32102i	0.750818	+	0.660509i	$0.229659\pi$
$881$			39.2100i			1.32102i	−0.750818	+	0.660509i	$0.770341\pi$
$882$		0			0
$883$	25.5883	−	25.5883i	0.861114	−	0.861114i	−0.130353	−	0.991468i	$-0.541611\pi$
$883$	25.5883	−	25.5883i	0.861114	−	0.861114i	0.991468	+	0.130353i	$0.0416111\pi$
$884$		0			0
$885$	−0.675333	−	0.578153i	−0.0227011	−	0.0194344i
$886$		0			0
$887$	−55.9980	−	15.0046i	−1.88023	−	0.503806i	−0.999547	−	0.0300998i	$-0.990418\pi$
$887$	−55.9980	−	15.0046i	−1.88023	−	0.503806i	−0.880683	−	0.473706i	$-0.842916\pi$
$888$		0			0
$889$	−7.08837	+	34.7299i	−0.237736	+	1.16480i
$890$		0			0
$891$	−3.49763	−	6.05808i	−0.117175	−	0.202953i
$892$		0			0
$893$	3.56772	+	13.3149i	0.119389	+	0.445567i
$894$		0			0
$895$	39.7131	−	27.2259i	1.32746	−	0.910061i
$896$		0			0
$897$	2.21367	+	2.21367i	0.0739122	+	0.0739122i
$898$		0			0
$899$	0.884346	−	1.53173i	0.0294946	−	0.0510861i
$900$		0			0
$901$	29.3204	−	16.9282i	0.976805	−	0.563959i
$902$		0			0
$903$	2.12436	−	0.128606i	0.0706944	−	0.00427973i
$904$		0			0
$905$	−7.33135	−	3.50738i	−0.243702	−	0.116589i
$906$		0			0
$907$	−16.3196	+	4.37283i	−0.541884	+	0.145197i	−0.519371	−	0.854549i	$-0.673834\pi$
$907$	−16.3196	+	4.37283i	−0.541884	+	0.145197i	−0.0225135	+	0.999747i	$0.507167\pi$
$908$		0			0
$909$	−18.1482			−0.601936
$910$		0			0
$911$	29.5708			0.979724			0.489862	−	0.871800i	$-0.337047\pi$
$911$	29.5708			0.979724			0.489862	+	0.871800i	$0.337047\pi$
$912$		0			0
$913$	−3.14547	+	0.842827i	−0.104100	+	0.0278935i
$914$		0			0
$915$	−0.594478	−	1.68500i	−0.0196528	−	0.0557044i
$916$		0			0
$917$	−15.6226	−	7.80129i	−0.515905	−	0.257621i
$918$		0			0
$919$	−49.6782	+	28.6817i	−1.63873	+	0.946123i	−0.657463	+	0.753486i	$0.728371\pi$
$919$	−49.6782	+	28.6817i	−1.63873	+	0.946123i	−0.981270	+	0.192637i	$0.938296\pi$
$920$		0			0
$921$	−0.978582	+	1.69495i	−0.0322454	+	0.0558506i
$922$		0			0
$923$	−19.1746	−	19.1746i	−0.631139	−	0.631139i
$924$		0			0
$925$	−33.7207	+	14.9192i	−1.10873	+	0.490541i
$926$		0			0
$927$	−1.99452	−	7.44366i	−0.0655088	−	0.244482i
$928$		0			0
$929$	2.59381	+	4.49261i	0.0851001	+	0.147398i	0.905434	−	0.424487i	$-0.139546\pi$
$929$	2.59381	+	4.49261i	0.0851001	+	0.147398i	−0.820334	+	0.571885i	$0.806212\pi$
$930$		0			0
$931$	40.5575	−	4.92864i	1.32922	−	0.161530i
$932$		0			0
$933$	0.931782	+	0.249670i	0.0305052	+	0.00817383i
$934$		0			0
$935$	−6.17885	+	7.21744i	−0.202070	+	0.236035i
$936$		0			0
$937$	27.5418	−	27.5418i	0.899750	−	0.899750i	−0.0956634	−	0.995414i	$-0.530497\pi$
$937$	27.5418	−	27.5418i	0.899750	−	0.899750i	0.995414	+	0.0956634i	$0.0304972\pi$
$938$		0			0
$939$		−	0.196195i		−	0.00640260i
$940$		0			0
$941$	−11.8890	−	6.86411i	−0.387570	−	0.223763i	0.293537	−	0.955948i	$-0.405168\pi$
$941$	−11.8890	−	6.86411i	−0.387570	−	0.223763i	−0.681107	+	0.732184i	$0.738501\pi$
$942$		0			0
$943$	9.88578	−	36.8942i	0.321925	−	1.20144i
$944$		0			0
$945$	−1.65961	+	2.19419i	−0.0539870	+	0.0713771i
$946$		0			0
$947$	0.258625	−	0.965201i	0.00840418	−	0.0313648i	−0.961596	−	0.274467i	$-0.911498\pi$
$947$	0.258625	−	0.965201i	0.00840418	−	0.0313648i	0.970001	+	0.243103i	$0.0781651\pi$
$948$		0			0
$949$	−53.9536	−	31.1501i	−1.75141	−	1.01118i
$950$		0			0
$951$			1.23670i			0.0401028i
$952$		0			0
$953$	19.8419	−	19.8419i	0.642742	−	0.642742i	−0.308487	−	0.951229i	$-0.599823\pi$
$953$	19.8419	−	19.8419i	0.642742	−	0.642742i	0.951229	+	0.308487i	$0.0998225\pi$
$954$		0			0
$955$	0.0144646	−	0.00112141i	0.000468063	−	3.62878e-5i
$956$		0			0
$957$	−0.0178008	−	0.00476971i	−0.000575419	−	0.000154183i
$958$		0			0
$959$	0.819034	+	0.725528i	0.0264480	+	0.0234285i
$960$		0			0
$961$	1.45016	+	2.51174i	0.0467792	+	0.0810240i
$962$		0			0
$963$	6.60073	+	24.6342i	0.212705	+	0.793827i
$964$		0			0
$965$	−5.76262	−	1.07500i	−0.185505	−	0.0346053i
$966$		0			0
$967$	17.7327	+	17.7327i	0.570244	+	0.570244i	0.932197	−	0.361952i	$-0.117890\pi$
$967$	17.7327	+	17.7327i	0.570244	+	0.570244i	−0.361952	+	0.932197i	$0.617890\pi$
$968$		0			0
$969$	1.23025	−	2.13086i	0.0395214	−	0.0684531i
$970$		0			0
$971$	15.3128	−	8.84086i	0.491412	−	0.283717i	−0.233748	−	0.972297i	$-0.575099\pi$
$971$	15.3128	−	8.84086i	0.491412	−	0.283717i	0.725160	+	0.688581i	$0.241766\pi$
$972$		0			0
$973$	−23.5722	−	35.6619i	−0.755691	−	1.14327i
$974$		0			0
$975$	0.277741	+	1.78047i	0.00889482	+	0.0570207i
$976$		0			0
$977$	−5.30768	+	1.42219i	−0.169808	+	0.0454998i	−0.342721	−	0.939437i	$-0.611349\pi$
$977$	−5.30768	+	1.42219i	−0.169808	+	0.0454998i	0.172913	+	0.984937i	$0.444682\pi$
$978$		0			0
$979$	10.0673			0.321753
$980$		0			0
$981$	25.0322			0.799216
$982$		0			0
$983$	−45.3892	+	12.1620i	−1.44769	+	0.387908i	−0.895220	−	0.445625i	$-0.852982\pi$
$983$	−45.3892	+	12.1620i	−1.44769	+	0.387908i	−0.552471	+	0.833532i	$0.686315\pi$
$984$		0			0
$985$	19.8309	−	6.99644i	0.631864	−	0.222925i
$986$		0			0
$987$	0.267320	+	0.404423i	0.00850890	+	0.0128729i
$988$		0			0
$989$	77.9980	−	45.0321i	2.48019	−	1.43194i
$990$		0			0
$991$	1.02005	−	1.76677i	0.0324029	−	0.0561234i	−0.849369	−	0.527799i	$-0.823017\pi$
$991$	1.02005	−	1.76677i	0.0324029	−	0.0561234i	0.881772	+	0.471676i	$0.156351\pi$
$992$		0			0
$993$	−1.36251	−	1.36251i	−0.0432381	−	0.0432381i
$994$		0			0
$995$	−2.13944	−	3.12070i	−0.0678247	−	0.0989327i
$996$		0			0
$997$	−7.12955	−	26.6078i	−0.225795	−	0.842678i	−0.982084	−	0.188441i	$-0.939656\pi$
$997$	−7.12955	−	26.6078i	−0.225795	−	0.842678i	0.756289	−	0.654237i	$-0.227010\pi$
$998$		0			0
$999$	1.71473	+	2.97000i	0.0542516	+	0.0939666i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.ci.e.17.7		48
4.3	odd	2		280.2.bo.a.17.6	✓	48
5.3	odd	4	inner	560.2.ci.e.353.7		48
7.5	odd	6	inner	560.2.ci.e.257.7		48
20.3	even	4		280.2.bo.a.73.6	yes	48
28.19	even	6		280.2.bo.a.257.6	yes	48
35.33	even	12	inner	560.2.ci.e.33.7		48
140.103	odd	12		280.2.bo.a.33.6	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bo.a.17.6	✓	48	4.3	odd	2
280.2.bo.a.33.6	yes	48	140.103	odd	12
280.2.bo.a.73.6	yes	48	20.3	even	4
280.2.bo.a.257.6	yes	48	28.19	even	6
560.2.ci.e.17.7		48	1.1	even	1	trivial
560.2.ci.e.33.7		48	35.33	even	12	inner
560.2.ci.e.257.7		48	7.5	odd	6	inner
560.2.ci.e.353.7		48	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.ci (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0749389 - 0.0200798i) q^{3} +(-0.965007 + 2.01712i) q^{5} +(-1.45892 - 2.20716i) q^{7} +(-2.59286 + 1.49699i) q^{9} +O(q^{10})\)	\(q+(0.0749389 - 0.0200798i) q^{3} +(-0.965007 + 2.01712i) q^{5} +(-1.45892 - 2.20716i) q^{7} +(-2.59286 + 1.49699i) q^{9} +(0.390978 - 0.677193i) q^{11} +(-3.28478 - 3.28478i) q^{13} +(-0.0318132 + 0.170538i) q^{15} +(1.40637 + 5.24865i) q^{17} +(-2.91828 - 5.05461i) q^{19} +(-0.153649 - 0.136108i) q^{21} +(-8.39046 - 2.24822i) q^{23} +(-3.13752 - 3.89306i) q^{25} +(-0.328824 + 0.328824i) q^{27} -0.303774i q^{29} +(5.04234 + 2.91120i) q^{31} +(0.0157015 - 0.0585989i) q^{33} +(5.85997 - 0.812878i) q^{35} +(1.90872 - 7.12345i) q^{37} +(-0.312116 - 0.180200i) q^{39} +4.39716i q^{41} +(-7.33155 + 7.33155i) q^{43} +(-0.517475 - 6.67472i) q^{45} +(-2.28130 - 0.611272i) q^{47} +(-2.74313 + 6.44013i) q^{49} +(0.210784 + 0.365088i) q^{51} +(-1.61262 - 6.01838i) q^{53} +(0.988682 + 1.44214i) q^{55} +(-0.320188 - 0.320188i) q^{57} +(-2.56228 + 4.43800i) q^{59} +(-8.91983 + 5.14987i) q^{61} +(7.08687 + 3.53889i) q^{63} +(9.79563 - 3.45595i) q^{65} +(1.47788 - 0.395996i) q^{67} -0.673916 q^{69} +5.83740 q^{71} +(12.9542 - 3.47108i) q^{73} +(-0.313295 - 0.228741i) q^{75} +(-2.06508 + 0.125017i) q^{77} +(-8.66781 + 5.00437i) q^{79} +(4.47293 - 7.74735i) q^{81} +(-2.94473 - 2.94473i) q^{83} +(-11.9443 - 2.22817i) q^{85} +(-0.00609973 - 0.0227645i) q^{87} +(6.43727 + 11.1497i) q^{89} +(-2.45783 + 12.0423i) q^{91} +(0.436324 + 0.116913i) q^{93} +(13.0119 - 1.00878i) q^{95} +(-0.0900545 + 0.0900545i) q^{97} +2.34116i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{7}+O(q^{10}) \) 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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