LMFDB - Embedded newform 560.2.bw.a.529.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(289,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(6))

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("560.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.bw (of order $6$, degree $2$, 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:	$1$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-19})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} - 5x + 25 $ x^4 - x^3 - 4x^2 - 5x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			529.1
Root			$-1.63746 - 1.52274i$ of defining polynomial
Character	$\chi$	$=$	560.529
Dual form			560.2.bw.a.289.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 - 0.866025i) q^{3} +(-0.500000 - 2.17945i) q^{5} +(-2.63746 - 0.209313i) q^{7} +O(q^{10})$	\(q+(-1.50000 - 0.866025i) q^{3} +(-0.500000 - 2.17945i) q^{5} +(-2.63746 - 0.209313i) q^{7} +(1.13746 - 1.97014i) q^{11} +6.09095i q^{13} +(-1.13746 + 3.70219i) q^{15} +(-4.13746 - 2.38876i) q^{17} +(2.13746 + 3.70219i) q^{19} +(3.77492 + 2.59808i) q^{21} +(0.774917 - 0.447399i) q^{23} +(-4.50000 + 2.17945i) q^{25} +5.19615i q^{27} +3.27492 q^{29} +(-2.13746 + 3.70219i) q^{31} +(-3.41238 + 1.97014i) q^{33} +(0.862541 + 5.85286i) q^{35} +(-4.86254 + 2.80739i) q^{37} +(5.27492 - 9.13642i) q^{39} -11.2749 q^{41} -6.50958i q^{43} +(-1.86254 + 1.07534i) q^{47} +(6.91238 + 1.10411i) q^{49} +(4.13746 + 7.16629i) q^{51} +(6.41238 + 3.70219i) q^{53} +(-4.86254 - 1.49397i) q^{55} -7.40437i q^{57} +(-2.13746 + 3.70219i) q^{59} +(-0.774917 - 1.34220i) q^{61} +(13.2749 - 3.04547i) q^{65} +(-12.0498 - 6.95698i) q^{67} -1.54983 q^{69} -10.5498 q^{71} +(1.86254 + 1.07534i) q^{73} +(8.63746 + 0.627940i) q^{75} +(-3.41238 + 4.95807i) q^{77} +(0.137459 + 0.238085i) q^{79} +(4.50000 - 7.79423i) q^{81} +5.67232i q^{83} +(-3.13746 + 10.2118i) q^{85} +(-4.91238 - 2.83616i) q^{87} +(-3.50000 - 6.06218i) q^{89} +(1.27492 - 16.0646i) q^{91} +(6.41238 - 3.70219i) q^{93} +(7.00000 - 6.50958i) q^{95} -6.92820i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{3} - 2 q^{5} - 3 q^{7}+O(q^{10}) $ 4 * q - 6 * q^3 - 2 * q^5 - 3 * q^7	$ 4 q - 6 q^{3} - 2 q^{5} - 3 q^{7} - 3 q^{11} + 3 q^{15} - 9 q^{17} + q^{19} - 12 q^{23} - 18 q^{25} - 2 q^{29} - q^{31} + 9 q^{33} + 11 q^{35} - 27 q^{37} + 6 q^{39} - 30 q^{41} - 15 q^{47} + 5 q^{49} + 9 q^{51} + 3 q^{53} - 27 q^{55} - q^{59} + 12 q^{61} + 38 q^{65} - 18 q^{67} + 24 q^{69} - 12 q^{71} + 15 q^{73} + 27 q^{75} + 9 q^{77} - 7 q^{79} + 18 q^{81} - 5 q^{85} + 3 q^{87} - 14 q^{89} - 10 q^{91} + 3 q^{93} + 28 q^{95}+O(q^{100}) $ 4 * q - 6 * q^3 - 2 * q^5 - 3 * q^7 - 3 * q^11 + 3 * q^15 - 9 * q^17 + q^19 - 12 * q^23 - 18 * q^25 - 2 * q^29 - q^31 + 9 * q^33 + 11 * q^35 - 27 * q^37 + 6 * q^39 - 30 * q^41 - 15 * q^47 + 5 * q^49 + 9 * q^51 + 3 * q^53 - 27 * q^55 - q^59 + 12 * q^61 + 38 * q^65 - 18 * q^67 + 24 * q^69 - 12 * q^71 + 15 * q^73 + 27 * q^75 + 9 * q^77 - 7 * q^79 + 18 * q^81 - 5 * q^85 + 3 * q^87 - 14 * q^89 - 10 * q^91 + 3 * q^93 + 28 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$	$1$

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
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$4$		0			0
$5$	−0.500000	−	2.17945i	−0.223607	−	0.974679i
$5$	−0.500000	−	2.17945i	−0.223607	−	0.974679i
$6$		0			0
$7$	−2.63746	−	0.209313i	−0.996866	−	0.0791130i
$7$	−2.63746	−	0.209313i	−0.996866	−	0.0791130i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.13746	−	1.97014i	0.342957	−	0.594018i	−0.642024	−	0.766685i	$-0.721905\pi$
$11$	1.13746	−	1.97014i	0.342957	−	0.594018i	0.984980	+	0.172666i	$0.0552383\pi$
$12$		0			0
$13$			6.09095i			1.68933i	0.535299	+	0.844663i	$0.320199\pi$
$13$			6.09095i			1.68933i	−0.535299	+	0.844663i	$0.679801\pi$
$14$		0			0
$15$	−1.13746	+	3.70219i	−0.293691	+	0.955901i
$16$		0			0
$17$	−4.13746	−	2.38876i	−1.00348	−	0.579360i	−0.0942047	−	0.995553i	$-0.530031\pi$
$17$	−4.13746	−	2.38876i	−1.00348	−	0.579360i	−0.909276	+	0.416193i	$0.863364\pi$
$18$		0			0
$19$	2.13746	+	3.70219i	0.490367	+	0.849340i	0.999939	−	0.0110882i	$-0.00352954\pi$
$19$	2.13746	+	3.70219i	0.490367	+	0.849340i	−0.509572	+	0.860428i	$0.670196\pi$
$20$		0			0
$21$	3.77492	+	2.59808i	0.823754	+	0.566947i
$22$		0			0
$23$	0.774917	−	0.447399i	0.161581	−	0.0932891i	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	0.774917	−	0.447399i	0.161581	−	0.0932891i	0.578610	+	0.815604i	$0.303595\pi$
$24$		0			0
$25$	−4.50000	+	2.17945i	−0.900000	+	0.435890i
$26$		0			0
$27$			5.19615i			1.00000i
$28$		0			0
$29$	3.27492			0.608137			0.304068	−	0.952650i	$-0.401655\pi$
$29$	3.27492			0.608137			0.304068	+	0.952650i	$0.401655\pi$
$30$		0			0
$31$	−2.13746	+	3.70219i	−0.383899	+	0.664932i	−0.991616	−	0.129221i	$-0.958752\pi$
$31$	−2.13746	+	3.70219i	−0.383899	+	0.664932i	0.607717	+	0.794154i	$0.292086\pi$
$32$		0			0
$33$	−3.41238	+	1.97014i	−0.594018	+	0.342957i
$34$		0			0
$35$	0.862541	+	5.85286i	0.145796	+	0.989315i
$36$		0			0
$37$	−4.86254	+	2.80739i	−0.799397	+	0.461532i	−0.843260	−	0.537506i	$-0.819367\pi$
$37$	−4.86254	+	2.80739i	−0.799397	+	0.461532i	0.0438633	+	0.999038i	$0.486033\pi$
$38$		0			0
$39$	5.27492	−	9.13642i	0.844663	−	1.46300i
$40$		0			0
$41$	−11.2749			−1.76085			−0.880423	−	0.474189i	$-0.842741\pi$
$41$	−11.2749			−1.76085			−0.880423	+	0.474189i	$0.842741\pi$
$42$		0			0
$43$		−	6.50958i		−	0.992701i	−0.868122	−	0.496351i	$-0.834673\pi$
$43$		−	6.50958i		−	0.992701i	0.868122	−	0.496351i	$-0.165327\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.86254	+	1.07534i	−0.271680	+	0.156854i	−0.629651	−	0.776878i	$-0.716802\pi$
$47$	−1.86254	+	1.07534i	−0.271680	+	0.156854i	0.357971	+	0.933733i	$0.383469\pi$
$48$		0			0
$49$	6.91238	+	1.10411i	0.987482	+	0.157730i
$50$		0			0
$51$	4.13746	+	7.16629i	0.579360	+	1.00348i
$52$		0			0
$53$	6.41238	+	3.70219i	0.880808	+	0.508534i	0.870925	−	0.491417i	$-0.163521\pi$
$53$	6.41238	+	3.70219i	0.880808	+	0.508534i	0.00988297	+	0.999951i	$0.496854\pi$
$54$		0			0
$55$	−4.86254	−	1.49397i	−0.655665	−	0.201446i
$56$		0			0
$57$		−	7.40437i		−	0.980733i
$58$		0			0
$59$	−2.13746	+	3.70219i	−0.278273	+	0.481984i	−0.970956	−	0.239259i	$-0.923095\pi$
$59$	−2.13746	+	3.70219i	−0.278273	+	0.481984i	0.692682	+	0.721243i	$0.256429\pi$
$60$		0			0
$61$	−0.774917	−	1.34220i	−0.0992180	−	0.171851i	0.812143	−	0.583458i	$-0.198301\pi$
$61$	−0.774917	−	1.34220i	−0.0992180	−	0.171851i	−0.911361	+	0.411608i	$0.864967\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	13.2749	−	3.04547i	1.64655	−	0.377745i
$66$		0			0
$67$	−12.0498	−	6.95698i	−1.47212	−	0.849930i	−0.472613	−	0.881270i	$-0.656689\pi$
$67$	−12.0498	−	6.95698i	−1.47212	−	0.849930i	−0.999509	+	0.0313404i	$0.990022\pi$
$68$		0			0
$69$	−1.54983			−0.186578
$70$		0			0
$71$	−10.5498			−1.25204			−0.626018	−	0.779809i	$-0.715316\pi$
$71$	−10.5498			−1.25204			−0.626018	+	0.779809i	$0.715316\pi$
$72$		0			0
$73$	1.86254	+	1.07534i	0.217994	+	0.125859i	0.605021	−	0.796209i	$-0.293165\pi$
$73$	1.86254	+	1.07534i	0.217994	+	0.125859i	−0.387027	+	0.922068i	$0.626498\pi$
$74$		0			0
$75$	8.63746	+	0.627940i	0.997368	+	0.0725083i
$76$		0			0
$77$	−3.41238	+	4.95807i	−0.388876	+	0.565024i
$78$		0			0
$79$	0.137459	+	0.238085i	0.0154653	+	0.0267867i	0.873654	−	0.486547i	$-0.161744\pi$
$79$	0.137459	+	0.238085i	0.0154653	+	0.0267867i	−0.858189	+	0.513334i	$0.828410\pi$
$80$		0			0
$81$	4.50000	−	7.79423i	0.500000	−	0.866025i
$82$		0			0
$83$			5.67232i			0.622618i	0.950309	+	0.311309i	$0.100767\pi$
$83$			5.67232i			0.622618i	−0.950309	+	0.311309i	$0.899233\pi$
$84$		0			0
$85$	−3.13746	+	10.2118i	−0.340305	+	1.10762i
$86$		0			0
$87$	−4.91238	−	2.83616i	−0.526662	−	0.304068i
$88$		0			0
$89$	−3.50000	−	6.06218i	−0.370999	−	0.642590i	0.618720	−	0.785611i	$-0.287651\pi$
$89$	−3.50000	−	6.06218i	−0.370999	−	0.642590i	−0.989720	+	0.143022i	$0.954318\pi$
$90$		0			0
$91$	1.27492	−	16.0646i	0.133648	−	1.68403i
$92$		0			0
$93$	6.41238	−	3.70219i	0.664932	−	0.383899i
$94$		0			0
$95$	7.00000	−	6.50958i	0.718185	−	0.667868i
$96$		0			0
$97$		−	6.92820i		−	0.703452i	−0.936103	−	0.351726i	$-0.885595\pi$
$97$		−	6.92820i		−	0.703452i	0.936103	−	0.351726i	$-0.114405\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−0.774917	+	1.34220i	−0.0771071	+	0.133553i	−0.902001	−	0.431735i	$-0.857902\pi$
$101$	−0.774917	+	1.34220i	−0.0771071	+	0.133553i	0.824894	+	0.565288i	$0.191235\pi$
$102$		0			0
$103$	2.22508	−	1.28465i	0.219244	−	0.126581i	−0.386356	−	0.922350i	$-0.626266\pi$
$103$	2.22508	−	1.28465i	0.219244	−	0.126581i	0.605600	+	0.795769i	$0.292933\pi$
$104$		0			0
$105$	3.77492	−	9.52628i	0.368394	−	0.929670i
$106$		0			0
$107$	12.0498	−	6.95698i	1.16490	−	0.672556i	0.212428	−	0.977177i	$-0.431863\pi$
$107$	12.0498	−	6.95698i	1.16490	−	0.672556i	0.952474	+	0.304621i	$0.0985297\pi$
$108$		0			0
$109$	1.77492	−	3.07425i	0.170006	−	0.294459i	−0.768416	−	0.639951i	$-0.778955\pi$
$109$	1.77492	−	3.07425i	0.170006	−	0.294459i	0.938422	+	0.345492i	$0.112288\pi$
$110$		0			0
$111$	9.72508			0.923064
$112$		0			0
$113$		−	13.0192i		−	1.22474i	−0.790572	−	0.612369i	$-0.790217\pi$
$113$		−	13.0192i		−	1.22474i	0.790572	−	0.612369i	$-0.209783\pi$
$114$		0			0
$115$	−1.36254	−	1.46519i	−0.127058	−	0.136630i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	10.4124	+	7.16629i	0.954501	+	0.656933i
$120$		0			0
$121$	2.91238	+	5.04438i	0.264761	+	0.458580i
$122$		0			0
$123$	16.9124	+	9.76436i	1.52494	+	0.880423i
$124$		0			0
$125$	7.00000	+	8.71780i	0.626099	+	0.779744i
$126$		0			0
$127$		−	1.78959i		−	0.158801i	−0.996843	−	0.0794004i	$-0.974699\pi$
$127$		−	1.78959i		−	0.158801i	0.996843	−	0.0794004i	$-0.0253006\pi$
$128$		0			0
$129$	−5.63746	+	9.76436i	−0.496351	+	0.859704i
$130$		0			0
$131$	−9.13746	−	15.8265i	−0.798343	−	1.38277i	−0.920694	−	0.390285i	$-0.872377\pi$
$131$	−9.13746	−	15.8265i	−0.798343	−	1.38277i	0.122351	−	0.992487i	$-0.460957\pi$
$132$		0			0
$133$	−4.86254	−	10.2118i	−0.421636	−	0.885472i
$134$		0			0
$135$	11.3248	−	2.59808i	0.974679	−	0.223607i
$136$		0			0
$137$	−7.96221	−	4.59698i	−0.680258	−	0.392747i	0.119695	−	0.992811i	$-0.461808\pi$
$137$	−7.96221	−	4.59698i	−0.680258	−	0.392747i	−0.799952	+	0.600064i	$0.795142\pi$
$138$		0			0
$139$	−17.0997			−1.45037			−0.725187	−	0.688551i	$-0.758247\pi$
$139$	−17.0997			−1.45037			−0.725187	+	0.688551i	$0.758247\pi$
$140$		0			0
$141$	3.72508			0.313709
$142$		0			0
$143$	12.0000	+	6.92820i	1.00349	+	0.579365i
$144$		0			0
$145$	−1.63746	−	7.13752i	−0.135984	−	0.592738i
$146$		0			0
$147$	−9.41238	−	7.64246i	−0.776320	−	0.630339i
$148$		0			0
$149$	3.77492	+	6.53835i	0.309253	+	0.535642i	0.978199	−	0.207669i	$-0.0665876\pi$
$149$	3.77492	+	6.53835i	0.309253	+	0.535642i	−0.668946	+	0.743311i	$0.733254\pi$
$150$		0			0
$151$	−10.1375	+	17.5586i	−0.824975	+	1.42890i	0.0769640	+	0.997034i	$0.475477\pi$
$151$	−10.1375	+	17.5586i	−0.824975	+	1.42890i	−0.901939	+	0.431864i	$0.857856\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	9.13746	+	2.80739i	0.733938	+	0.225495i
$156$		0			0
$157$	−9.41238	−	5.43424i	−0.751189	−	0.433699i	0.0749341	−	0.997188i	$-0.476125\pi$
$157$	−9.41238	−	5.43424i	−0.751189	−	0.433699i	−0.826123	+	0.563489i	$0.809459\pi$
$158$		0			0
$159$	−6.41238	−	11.1066i	−0.508534	−	0.880808i
$160$		0			0
$161$	−2.13746	+	1.01779i	−0.168455	+	0.0802135i
$162$		0			0
$163$	−6.41238	+	3.70219i	−0.502256	+	0.289978i	−0.729645	−	0.683826i	$-0.760315\pi$
$163$	−6.41238	+	3.70219i	−0.502256	+	0.289978i	0.227389	+	0.973804i	$0.426981\pi$
$164$		0			0
$165$	6.00000	+	6.45203i	0.467099	+	0.502290i
$166$		0			0
$167$		−	12.6005i		−	0.975058i	−0.873107	−	0.487529i	$-0.837898\pi$
$167$		−	12.6005i		−	0.975058i	0.873107	−	0.487529i	$-0.162102\pi$
$168$		0			0
$169$	−24.0997			−1.85382
$170$		0			0
$171$		0			0
$172$		0			0
$173$	16.2371	−	9.37451i	1.23449	−	0.712731i	0.266524	−	0.963828i	$-0.414125\pi$
$173$	16.2371	−	9.37451i	1.23449	−	0.712731i	0.967962	+	0.251097i	$0.0807915\pi$
$174$		0			0
$175$	12.3248	−	4.80630i	0.931664	−	0.363322i
$176$		0			0
$177$	6.41238	−	3.70219i	0.481984	−	0.278273i
$178$		0			0
$179$	−0.137459	+	0.238085i	−0.0102741	+	0.0177953i	−0.871117	−	0.491076i	$-0.836604\pi$
$179$	−0.137459	+	0.238085i	−0.0102741	+	0.0177953i	0.860843	+	0.508871i	$0.169937\pi$
$180$		0			0
$181$	−16.7251			−1.24317			−0.621583	−	0.783348i	$-0.713510\pi$
$181$	−16.7251			−1.24317			−0.621583	+	0.783348i	$0.713510\pi$
$182$		0			0
$183$			2.68439i			0.198436i
$184$		0			0
$185$	8.54983	+	9.19397i	0.628596	+	0.675954i
$186$		0			0
$187$	−9.41238	+	5.43424i	−0.688301	+	0.397391i
$188$		0			0
$189$	1.08762	−	13.7046i	0.0791130	−	0.996866i
$190$		0			0
$191$	11.4124	+	19.7668i	0.825771	+	1.43028i	0.901329	+	0.433135i	$0.142593\pi$
$191$	11.4124	+	19.7668i	0.825771	+	1.43028i	−0.0755585	+	0.997141i	$0.524074\pi$
$192$		0			0
$193$	−7.96221	−	4.59698i	−0.573132	−	0.330898i	0.185267	−	0.982688i	$-0.440685\pi$
$193$	−7.96221	−	4.59698i	−0.573132	−	0.330898i	−0.758399	+	0.651790i	$0.774018\pi$
$194$		0			0
$195$	−22.5498	−	6.92820i	−1.61483	−	0.496139i
$196$		0			0
$197$			26.0383i			1.85515i	0.373634	+	0.927576i	$0.378112\pi$
$197$			26.0383i			1.85515i	−0.373634	+	0.927576i	$0.621888\pi$
$198$		0			0
$199$	−4.86254	+	8.42217i	−0.344696	+	0.597032i	−0.985299	−	0.170841i	$-0.945351\pi$
$199$	−4.86254	+	8.42217i	−0.344696	+	0.597032i	0.640602	+	0.767873i	$0.278685\pi$
$200$		0			0
$201$	12.0498	+	20.8709i	0.849930	+	1.47212i
$202$		0			0
$203$	−8.63746	−	0.685484i	−0.606231	−	0.0481115i
$204$		0			0
$205$	5.63746	+	24.5731i	0.393737	+	1.71626i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	9.72508			0.672698
$210$		0			0
$211$	19.6495			1.35273			0.676364	−	0.736568i	$-0.263555\pi$
$211$	19.6495			1.35273			0.676364	+	0.736568i	$0.263555\pi$
$212$		0			0
$213$	15.8248	+	9.13642i	1.08429	+	0.626018i
$214$		0			0
$215$	−14.1873	+	3.25479i	−0.967565	+	0.221975i
$216$		0			0
$217$	6.41238	−	9.31697i	0.435300	−	0.632477i
$218$		0			0
$219$	−1.86254	−	3.22602i	−0.125859	−	0.217994i
$220$		0			0
$221$	14.5498	−	25.2011i	0.978728	−	1.69521i
$222$		0			0
$223$			8.71780i			0.583787i	0.956451	+	0.291893i	$0.0942853\pi$
$223$			8.71780i			0.583787i	−0.956451	+	0.291893i	$0.905715\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−5.58762	−	3.22602i	−0.370864	−	0.214118i	0.302972	−	0.952999i	$-0.402021\pi$
$227$	−5.58762	−	3.22602i	−0.370864	−	0.214118i	−0.673836	+	0.738881i	$0.735354\pi$
$228$		0			0
$229$	−2.13746	−	3.70219i	−0.141247	−	0.244647i	0.786719	−	0.617311i	$-0.211778\pi$
$229$	−2.13746	−	3.70219i	−0.141247	−	0.244647i	−0.927967	+	0.372663i	$0.878445\pi$
$230$		0			0
$231$	9.41238	−	4.48190i	0.619289	−	0.294887i
$232$		0			0
$233$	−16.1375	+	9.31697i	−1.05720	+	0.610375i	−0.924656	−	0.380802i	$-0.875648\pi$
$233$	−16.1375	+	9.31697i	−1.05720	+	0.610375i	−0.132544	+	0.991177i	$0.542314\pi$
$234$		0			0
$235$	3.27492	+	3.52165i	0.213632	+	0.229727i
$236$		0			0
$237$		−	0.476171i		−	0.0309306i
$238$		0			0
$239$	−14.5498			−0.941151			−0.470575	−	0.882360i	$-0.655954\pi$
$239$	−14.5498			−0.941151			−0.470575	+	0.882360i	$0.655954\pi$
$240$		0			0
$241$	6.41238	−	11.1066i	0.413057	−	0.715436i	−0.582165	−	0.813071i	$-0.697794\pi$
$241$	6.41238	−	11.1066i	0.413057	−	0.715436i	0.995222	+	0.0976343i	$0.0311275\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−1.04983	−	15.6172i	−0.0670715	−	0.997748i
$246$		0			0
$247$	−22.5498	+	13.0192i	−1.43481	+	0.828389i
$248$		0			0
$249$	4.91238	−	8.50848i	0.311309	−	0.539203i
$250$		0			0
$251$	5.45017			0.344011			0.172006	−	0.985096i	$-0.444975\pi$
$251$	5.45017			0.344011			0.172006	+	0.985096i	$0.444975\pi$
$252$		0			0
$253$		−	2.03559i		−	0.127976i
$254$		0			0
$255$	13.5498	−	12.6005i	0.848524	−	0.789076i
$256$		0			0
$257$	−21.4124	+	12.3624i	−1.33567	+	0.771148i	−0.986162	−	0.165786i	$-0.946984\pi$
$257$	−21.4124	+	12.3624i	−1.33567	+	0.771148i	−0.349506	+	0.936934i	$0.613650\pi$
$258$		0			0
$259$	13.4124	−	6.38658i	0.833404	−	0.396843i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−23.3248	−	13.4666i	−1.43827	−	0.830383i	−0.440536	−	0.897735i	$-0.645212\pi$
$263$	−23.3248	−	13.4666i	−1.43827	−	0.830383i	−0.997729	+	0.0673516i	$0.978545\pi$
$264$		0			0
$265$	4.86254	−	15.8265i	0.298704	−	0.972217i
$266$		0			0
$267$			12.1244i			0.741999i
$268$		0			0
$269$	−14.7749	+	25.5909i	−0.900843	+	1.56031i	−0.0744400	+	0.997225i	$0.523717\pi$
$269$	−14.7749	+	25.5909i	−0.900843	+	1.56031i	−0.826403	+	0.563080i	$0.809616\pi$
$270$		0			0
$271$	−6.41238	−	11.1066i	−0.389524	−	0.674676i	0.602861	−	0.797846i	$-0.294027\pi$
$271$	−6.41238	−	11.1066i	−0.389524	−	0.674676i	−0.992386	+	0.123170i	$0.960694\pi$
$272$		0			0
$273$	−15.8248	+	22.9928i	−0.957758	+	1.39159i
$274$		0			0
$275$	−0.824752	+	11.3446i	−0.0497344	+	0.684108i
$276$		0			0
$277$	−16.1375	−	9.31697i	−0.969606	−	0.559802i	−0.0704898	−	0.997512i	$-0.522456\pi$
$277$	−16.1375	−	9.31697i	−0.969606	−	0.559802i	−0.899116	+	0.437710i	$0.855790\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	6.00000			0.357930			0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000			0.357930			0.178965	+	0.983855i	$0.442725\pi$
$282$		0			0
$283$	16.9622	+	9.79314i	1.00830	+	0.582142i	0.910693	−	0.413084i	$-0.135548\pi$
$283$	16.9622	+	9.79314i	1.00830	+	0.582142i	0.0976056	+	0.995225i	$0.468882\pi$
$284$		0			0
$285$	−16.1375	+	3.70219i	−0.955901	+	0.219299i
$286$		0			0
$287$	29.7371	+	2.35999i	1.75533	+	0.139306i
$288$		0			0
$289$	2.91238	+	5.04438i	0.171316	+	0.296728i
$290$		0			0
$291$	−6.00000	+	10.3923i	−0.351726	+	0.609208i
$292$		0			0
$293$		−	6.92820i		−	0.404750i	−0.979308	−	0.202375i	$-0.935134\pi$
$293$		−	6.92820i		−	0.404750i	0.979308	−	0.202375i	$-0.0648660\pi$
$294$		0			0
$295$	9.13746	+	2.80739i	0.532003	+	0.163453i
$296$		0			0
$297$	10.2371	+	5.91041i	0.594018	+	0.342957i
$298$		0			0
$299$	2.72508	+	4.71998i	0.157596	+	0.272964i
$300$		0			0
$301$	−1.36254	+	17.1687i	−0.0785356	+	0.989590i
$302$		0			0
$303$	2.32475	−	1.34220i	0.133553	−	0.0771071i
$304$		0			0
$305$	−2.53779	+	2.35999i	−0.145313	+	0.135133i
$306$		0			0
$307$			3.99782i			0.228167i	0.993471	+	0.114084i	$0.0363932\pi$
$307$			3.99782i			0.228167i	−0.993471	+	0.114084i	$0.963607\pi$
$308$		0			0
$309$	−4.45017			−0.253161
$310$		0			0
$311$	6.41238	−	11.1066i	0.363612	−	0.629795i	−0.624940	−	0.780673i	$-0.714877\pi$
$311$	6.41238	−	11.1066i	0.363612	−	0.629795i	0.988552	+	0.150878i	$0.0482099\pi$
$312$		0			0
$313$	−12.5120	+	7.22383i	−0.707223	+	0.408315i	−0.810032	−	0.586386i	$-0.800550\pi$
$313$	−12.5120	+	7.22383i	−0.707223	+	0.408315i	0.102809	+	0.994701i	$0.467217\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3.31271	−	1.91259i	0.186060	−	0.107422i	−0.404077	−	0.914725i	$-0.632407\pi$
$317$	3.31271	−	1.91259i	0.186060	−	0.107422i	0.590137	+	0.807303i	$0.299074\pi$
$318$		0			0
$319$	3.72508	−	6.45203i	0.208565	−	0.361244i
$320$		0			0
$321$	−24.0997			−1.34511
$322$		0			0
$323$		−	20.4235i		−	1.13640i
$324$		0			0
$325$	−13.2749	−	27.4093i	−0.736360	−	1.52039i
$326$		0			0
$327$	−5.32475	+	3.07425i	−0.294459	+	0.170006i
$328$		0			0
$329$	5.13746	−	2.44631i	0.283237	−	0.134869i
$330$		0			0
$331$	−2.41238	−	4.17836i	−0.132596	−	0.229663i	0.792080	−	0.610417i	$-0.208998\pi$
$331$	−2.41238	−	4.17836i	−0.132596	−	0.229663i	−0.924677	+	0.380753i	$0.875665\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−9.13746	+	29.7405i	−0.499233	+	1.62490i
$336$		0			0
$337$		−	13.0192i		−	0.709198i	−0.935018	−	0.354599i	$-0.884617\pi$
$337$		−	13.0192i		−	0.709198i	0.935018	−	0.354599i	$-0.115383\pi$
$338$		0			0
$339$	−11.2749	+	19.5287i	−0.612369	+	1.06065i
$340$		0			0
$341$	4.86254	+	8.42217i	0.263321	+	0.456086i
$342$		0			0
$343$	−18.0000	−	4.35890i	−0.971909	−	0.235358i
$344$		0			0
$345$	0.774917	+	3.37779i	0.0417201	+	0.181854i
$346$		0			0
$347$	10.5000	+	6.06218i	0.563670	+	0.325435i	0.754617	−	0.656165i	$-0.227823\pi$
$347$	10.5000	+	6.06218i	0.563670	+	0.325435i	−0.190947	+	0.981600i	$0.561156\pi$
$348$		0			0
$349$	11.2749			0.603532			0.301766	−	0.953382i	$-0.402424\pi$
$349$	11.2749			0.603532			0.301766	+	0.953382i	$0.402424\pi$
$350$		0			0
$351$	−31.6495			−1.68933
$352$		0			0
$353$	18.4124	+	10.6304i	0.979992	+	0.565799i	0.902268	−	0.431176i	$-0.141901\pi$
$353$	18.4124	+	10.6304i	0.979992	+	0.565799i	0.0777242	+	0.996975i	$0.475235\pi$
$354$		0			0
$355$	5.27492	+	22.9928i	0.279964	+	1.22033i
$356$		0			0
$357$	−9.41238	−	19.7668i	−0.498156	−	1.04617i
$358$		0			0
$359$	0.687293	+	1.19043i	0.0362739	+	0.0628283i	0.883592	−	0.468257i	$-0.155118\pi$
$359$	0.687293	+	1.19043i	0.0362739	+	0.0628283i	−0.847318	+	0.531085i	$0.821784\pi$
$360$		0			0
$361$	0.362541	−	0.627940i	0.0190811	−	0.0330495i
$362$		0			0
$363$		−	10.0888i		−	0.529523i
$364$		0			0
$365$	1.41238	−	4.59698i	0.0739271	−	0.240617i
$366$		0			0
$367$	−12.7749	−	7.37560i	−0.666845	−	0.385003i	0.128035	−	0.991770i	$-0.459133\pi$
$367$	−12.7749	−	7.37560i	−0.666845	−	0.385003i	−0.794880	+	0.606766i	$0.792466\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−16.1375	−	11.1066i	−0.837815	−	0.576624i
$372$		0			0
$373$	−4.86254	+	2.80739i	−0.251773	+	0.145361i	−0.620576	−	0.784146i	$-0.713101\pi$
$373$	−4.86254	+	2.80739i	−0.251773	+	0.145361i	0.368803	+	0.929508i	$0.379768\pi$
$374$		0			0
$375$	−2.95017	−	19.1389i	−0.152346	−	0.988327i
$376$		0			0
$377$			19.9474i			1.02734i
$378$		0			0
$379$	23.6495			1.21479			0.607397	−	0.794399i	$-0.292214\pi$
$379$	23.6495			1.21479			0.607397	+	0.794399i	$0.292214\pi$
$380$		0			0
$381$	−1.54983	+	2.68439i	−0.0794004	+	0.137526i
$382$		0			0
$383$	17.3248	−	10.0025i	0.885253	−	0.511101i	0.0128665	−	0.999917i	$-0.495904\pi$
$383$	17.3248	−	10.0025i	0.885253	−	0.511101i	0.872387	+	0.488816i	$0.162571\pi$
$384$		0			0
$385$	12.5120	+	4.95807i	0.637673	+	0.252686i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−2.68729	+	4.65453i	−0.136251	+	0.235994i	−0.926075	−	0.377340i	$-0.876839\pi$
$389$	−2.68729	+	4.65453i	−0.136251	+	0.235994i	0.789824	+	0.613334i	$0.210172\pi$
$390$		0			0
$391$	−4.27492			−0.216192
$392$		0			0
$393$			31.6531i			1.59669i
$394$		0			0
$395$	0.450166	−	0.418627i	0.0226503	−	0.0210634i
$396$		0			0
$397$	13.1375	−	7.58492i	0.659350	−	0.380676i	−0.132679	−	0.991159i	$-0.542358\pi$
$397$	13.1375	−	7.58492i	0.659350	−	0.380676i	0.792029	+	0.610483i	$0.209025\pi$
$398$		0			0
$399$	−1.54983	+	19.5287i	−0.0775888	+	0.977659i
$400$		0			0
$401$	−1.50000	−	2.59808i	−0.0749064	−	0.129742i	0.826139	−	0.563466i	$-0.190532\pi$
$401$	−1.50000	−	2.59808i	−0.0749064	−	0.129742i	−0.901046	+	0.433724i	$0.857199\pi$
$402$		0			0
$403$	−22.5498	−	13.0192i	−1.12329	−	0.648530i
$404$		0			0
$405$	−19.2371	−	5.91041i	−0.955901	−	0.293691i
$406$		0			0
$407$			12.7732i			0.633142i
$408$		0			0
$409$	5.04983	−	8.74657i	0.249698	−	0.432490i	−0.713744	−	0.700407i	$-0.753002\pi$
$409$	5.04983	−	8.74657i	0.249698	−	0.432490i	0.963442	+	0.267917i	$0.0863352\pi$
$410$		0			0
$411$	7.96221	+	13.7910i	0.392747	+	0.680258i
$412$		0			0
$413$	6.41238	−	9.31697i	0.315532	−	0.458458i
$414$		0			0
$415$	12.3625	−	2.83616i	0.606853	−	0.139222i
$416$		0			0
$417$	25.6495	+	14.8087i	1.25606	+	0.725187i
$418$		0			0
$419$	17.0997			0.835373			0.417687	−	0.908591i	$-0.362841\pi$
$419$	17.0997			0.835373			0.417687	+	0.908591i	$0.362841\pi$
$420$		0			0
$421$	3.27492			0.159610			0.0798048	−	0.996811i	$-0.474570\pi$
$421$	3.27492			0.159610			0.0798048	+	0.996811i	$0.474570\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	23.8248	+	1.73205i	1.15567	+	0.0840168i
$426$		0			0
$427$	1.76287	+	3.70219i	0.0853114	+	0.179161i
$428$		0			0
$429$	−12.0000	−	20.7846i	−0.579365	−	1.00349i
$430$		0			0
$431$	9.68729	−	16.7789i	0.466620	−	0.808210i	−0.532653	−	0.846334i	$-0.678805\pi$
$431$	9.68729	−	16.7789i	0.466620	−	0.808210i	0.999273	+	0.0381236i	$0.0121381\pi$
$432$		0			0
$433$			26.8756i			1.29156i	0.763525	+	0.645778i	$0.223467\pi$
$433$			26.8756i			1.29156i	−0.763525	+	0.645778i	$0.776533\pi$
$434$		0			0
$435$	−3.72508	+	12.1244i	−0.178604	+	0.581318i
$436$		0			0
$437$	3.31271	+	1.91259i	0.158468	+	0.0914917i
$438$		0			0
$439$	−0.587624	−	1.01779i	−0.0280458	−	0.0485767i	0.851662	−	0.524092i	$-0.175595\pi$
$439$	−0.587624	−	1.01779i	−0.0280458	−	0.0485767i	−0.879708	+	0.475515i	$0.842262\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−10.5000	+	6.06218i	−0.498870	+	0.288023i	−0.728247	−	0.685315i	$-0.759665\pi$
$443$	−10.5000	+	6.06218i	−0.498870	+	0.288023i	0.229377	+	0.973338i	$0.426331\pi$
$444$		0			0
$445$	−11.4622	+	10.6592i	−0.543361	+	0.505293i
$446$		0			0
$447$		−	13.0767i		−	0.618507i
$448$		0			0
$449$	25.8248			1.21875			0.609373	−	0.792884i	$-0.291421\pi$
$449$	25.8248			1.21875			0.609373	+	0.792884i	$0.291421\pi$
$450$		0			0
$451$	−12.8248	+	22.2131i	−0.603894	+	1.04598i
$452$		0			0
$453$	30.4124	−	17.5586i	1.42890	−	0.824975i
$454$		0			0
$455$	−35.6495	+	5.25370i	−1.67127	+	0.246297i
$456$		0			0
$457$	17.6873	−	10.2118i	0.827377	−	0.477686i	−0.0255769	−	0.999673i	$-0.508142\pi$
$457$	17.6873	−	10.2118i	0.827377	−	0.477686i	0.852954	+	0.521987i	$0.174809\pi$
$458$		0			0
$459$	12.4124	−	21.4989i	0.579360	−	1.00348i
$460$		0			0
$461$	−14.0000			−0.652045			−0.326023	−	0.945362i	$-0.605709\pi$
$461$	−14.0000			−0.652045			−0.326023	+	0.945362i	$0.605709\pi$
$462$		0			0
$463$			6.50958i			0.302526i	0.988494	+	0.151263i	$0.0483340\pi$
$463$			6.50958i			0.302526i	−0.988494	+	0.151263i	$0.951666\pi$
$464$		0			0
$465$	−11.2749	−	12.1244i	−0.522862	−	0.562254i
$466$		0			0
$467$	16.5997	−	9.58382i	0.768141	−	0.443486i	−0.0640700	−	0.997945i	$-0.520408\pi$
$467$	16.5997	−	9.58382i	0.768141	−	0.443486i	0.832211	+	0.554459i	$0.187075\pi$
$468$		0			0
$469$	30.3248	+	20.8709i	1.40027	+	0.963730i
$470$		0			0
$471$	9.41238	+	16.3027i	0.433699	+	0.751189i
$472$		0			0
$473$	−12.8248	−	7.40437i	−0.589683	−	0.340453i
$474$		0			0
$475$	−17.6873	−	12.0014i	−0.811549	−	0.550660i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	6.41238	−	11.1066i	0.292989	−	0.507472i	−0.681526	−	0.731794i	$-0.738683\pi$
$479$	6.41238	−	11.1066i	0.292989	−	0.507472i	0.974515	+	0.224322i	$0.0720168\pi$
$480$		0			0
$481$	−17.0997	−	29.6175i	−0.779678	−	1.35044i
$482$		0			0
$483$	4.08762	+	0.324401i	0.185993	+	0.0147608i
$484$		0			0
$485$	−15.0997	+	3.46410i	−0.685641	+	0.157297i
$486$		0			0
$487$	28.9622	+	16.7213i	1.31240	+	0.757716i	0.982494	−	0.186296i	$-0.0596485\pi$
$487$	28.9622	+	16.7213i	1.31240	+	0.757716i	0.329909	+	0.944013i	$0.392982\pi$
$488$		0			0
$489$	12.8248			0.579955
$490$		0			0
$491$	13.4502			0.606997			0.303499	−	0.952832i	$-0.401845\pi$
$491$	13.4502			0.606997			0.303499	+	0.952832i	$0.401845\pi$
$492$		0			0
$493$	−13.5498	−	7.82300i	−0.610254	−	0.352330i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	27.8248	+	2.20822i	1.24811	+	0.0990523i
$498$		0			0
$499$	−19.6873	−	34.0994i	−0.881324	−	1.52650i	−0.849869	−	0.526993i	$-0.823319\pi$
$499$	−19.6873	−	34.0994i	−0.881324	−	1.52650i	−0.0314548	−	0.999505i	$-0.510014\pi$
$500$		0			0
$501$	−10.9124	+	18.9008i	−0.487529	+	0.844425i
$502$		0			0
$503$		−	16.1797i		−	0.721418i	−0.932678	−	0.360709i	$-0.882535\pi$
$503$		−	16.1797i		−	0.721418i	0.932678	−	0.360709i	$-0.117465\pi$
$504$		0			0
$505$	3.31271	+	1.01779i	0.147414	+	0.0452913i
$506$		0			0
$507$	36.1495	+	20.8709i	1.60546	+	0.926910i
$508$		0			0
$509$	−14.7749	−	25.5909i	−0.654887	−	1.13430i	−0.981922	−	0.189285i	$-0.939383\pi$
$509$	−14.7749	−	25.5909i	−0.654887	−	1.13430i	0.327036	−	0.945012i	$-0.393950\pi$
$510$		0			0
$511$	−4.68729	−	3.22602i	−0.207354	−	0.142711i
$512$		0			0
$513$	−19.2371	+	11.1066i	−0.849340	+	0.490367i
$514$		0			0
$515$	−3.91238	−	4.20713i	−0.172400	−	0.185388i
$516$		0			0
$517$			4.89261i			0.215177i
$518$		0			0
$519$	−32.4743			−1.42546
$520$		0			0
$521$	6.41238	−	11.1066i	0.280931	−	0.486587i	−0.690683	−	0.723158i	$-0.742690\pi$
$521$	6.41238	−	11.1066i	0.280931	−	0.486587i	0.971614	+	0.236570i	$0.0760234\pi$
$522$		0			0
$523$	10.1375	−	5.85286i	0.443280	−	0.255928i	−0.261708	−	0.965147i	$-0.584286\pi$
$523$	10.1375	−	5.85286i	0.443280	−	0.255928i	0.704988	+	0.709219i	$0.250952\pi$
$524$		0			0
$525$	−22.6495	−	3.46410i	−0.988505	−	0.151186i
$526$		0			0
$527$	17.6873	−	10.2118i	0.770471	−	0.444831i
$528$		0			0
$529$	−11.0997	+	19.2252i	−0.482594	+	0.835878i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		−	68.6750i		−	2.97464i
$534$		0			0
$535$	−21.1873	−	22.7835i	−0.916007	−	0.985017i
$536$		0			0
$537$	0.412376	−	0.238085i	0.0177953	−	0.0102741i
$538$		0			0
$539$	10.0378	−	12.3624i	0.432358	−	0.532488i
$540$		0			0
$541$	1.22508	+	2.12191i	0.0526704	+	0.0912278i	0.891159	−	0.453692i	$-0.149893\pi$
$541$	1.22508	+	2.12191i	0.0526704	+	0.0912278i	−0.838488	+	0.544920i	$0.816560\pi$
$542$		0			0
$543$	25.0876	+	14.4843i	1.07661	+	0.621583i
$544$		0			0
$545$	−7.58762	−	2.33122i	−0.325018	−	0.0998585i
$546$		0			0
$547$		−	36.1271i		−	1.54468i	−0.635208	−	0.772341i	$-0.719086\pi$
$547$		−	36.1271i		−	1.54468i	0.635208	−	0.772341i	$-0.280914\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	7.00000	+	12.1244i	0.298210	+	0.516515i
$552$		0			0
$553$	−0.312707	−	0.656712i	−0.0132977	−	0.0279262i
$554$		0			0
$555$	−4.86254	−	21.1953i	−0.206403	−	0.899692i
$556$		0			0
$557$	−4.86254	−	2.80739i	−0.206032	−	0.118953i	0.393434	−	0.919353i	$-0.371287\pi$
$557$	−4.86254	−	2.80739i	−0.206032	−	0.118953i	−0.599466	+	0.800400i	$0.704620\pi$
$558$		0			0
$559$	39.6495			1.67700
$560$		0			0
$561$	18.8248			0.794782
$562$		0			0
$563$	−10.5997	−	6.11972i	−0.446723	−	0.257916i	0.259722	−	0.965683i	$-0.416369\pi$
$563$	−10.5997	−	6.11972i	−0.446723	−	0.257916i	−0.706445	+	0.707768i	$0.749702\pi$
$564$		0			0
$565$	−28.3746	+	6.50958i	−1.19373	+	0.273860i
$566$		0			0
$567$	−13.5000	+	19.6150i	−0.566947	+	0.823754i
$568$		0			0
$569$	−14.6873	−	25.4391i	−0.615723	−	1.06646i	−0.990257	−	0.139251i	$-0.955531\pi$
$569$	−14.6873	−	25.4391i	−0.615723	−	1.06646i	0.374534	−	0.927213i	$-0.377803\pi$
$570$		0			0
$571$	−0.137459	+	0.238085i	−0.00575246	+	0.00996356i	−0.868887	−	0.495010i	$-0.835164\pi$
$571$	−0.137459	+	0.238085i	−0.00575246	+	0.00996356i	0.863135	+	0.504974i	$0.168498\pi$
$572$		0			0
$573$		−	39.5336i		−	1.65154i
$574$		0			0
$575$	−2.51204	+	3.70219i	−0.104760	+	0.154392i
$576$		0			0
$577$	7.13746	+	4.12081i	0.297136	+	0.171552i	0.641156	−	0.767411i	$-0.278455\pi$
$577$	7.13746	+	4.12081i	0.297136	+	0.171552i	−0.344019	+	0.938963i	$0.611789\pi$
$578$		0			0
$579$	7.96221	+	13.7910i	0.330898	+	0.573132i
$580$		0			0
$581$	1.18729	−	14.9605i	0.0492572	−	0.620667i
$582$		0			0
$583$	14.5876	−	8.42217i	0.604158	−	0.348811i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			13.9715i			0.576665i	0.957530	+	0.288333i	$0.0931009\pi$
$587$			13.9715i			0.576665i	−0.957530	+	0.288333i	$0.906899\pi$
$588$		0			0
$589$	−18.2749			−0.753005
$590$		0			0
$591$	22.5498	−	39.0575i	0.927576	−	1.60661i
$592$		0			0
$593$	−17.5876	+	10.1542i	−0.722237	+	0.416984i	−0.815576	−	0.578651i	$-0.803579\pi$
$593$	−17.5876	+	10.1542i	−0.722237	+	0.416984i	0.0933384	+	0.995634i	$0.470246\pi$
$594$		0			0
$595$	10.4124	−	26.2764i	0.426866	−	1.07723i
$596$		0			0
$597$	14.5876	−	8.42217i	0.597032	−	0.344696i
$598$		0			0
$599$	1.13746	−	1.97014i	0.0464753	−	0.0804976i	−0.841852	−	0.539709i	$-0.818534\pi$
$599$	1.13746	−	1.97014i	0.0464753	−	0.0804976i	0.888327	+	0.459211i	$0.151868\pi$
$600$		0			0
$601$	14.0000			0.571072			0.285536	−	0.958368i	$-0.407828\pi$
$601$	14.0000			0.571072			0.285536	+	0.958368i	$0.407828\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	9.53779	−	8.86957i	0.387766	−	0.360599i
$606$		0			0
$607$	27.8746	−	16.0934i	1.13139	−	0.653211i	0.187109	−	0.982339i	$-0.440088\pi$
$607$	27.8746	−	16.0934i	1.13139	−	0.653211i	0.944285	+	0.329128i	$0.106755\pi$
$608$		0			0
$609$	12.3625	+	8.50848i	0.500955	+	0.344781i
$610$		0			0
$611$	−6.54983	−	11.3446i	−0.264978	−	0.458955i
$612$		0			0
$613$	32.0619	+	18.5109i	1.29497	+	0.747650i	0.979530	−	0.201297i	$-0.0645156\pi$
$613$	32.0619	+	18.5109i	1.29497	+	0.747650i	0.315437	+	0.948947i	$0.397849\pi$
$614$		0			0
$615$	12.8248	−	41.7419i	0.517144	−	1.68319i
$616$		0			0
$617$			3.57919i			0.144093i	0.997401	+	0.0720464i	$0.0229530\pi$
$617$			3.57919i			0.144093i	−0.997401	+	0.0720464i	$0.977047\pi$
$618$		0			0
$619$	−21.9622	+	38.0397i	−0.882736	+	1.52894i	−0.0344487	+	0.999406i	$0.510968\pi$
$619$	−21.9622	+	38.0397i	−0.882736	+	1.52894i	−0.848287	+	0.529537i	$0.822366\pi$
$620$		0			0
$621$	2.32475	+	4.02659i	0.0932891	+	0.161581i
$622$		0			0
$623$	7.96221	+	16.7213i	0.318999	+	0.669926i
$624$		0			0
$625$	15.5000	−	19.6150i	0.620000	−	0.784602i
$626$		0			0
$627$	−14.5876	−	8.42217i	−0.582574	−	0.336349i
$628$		0			0
$629$	26.8248			1.06957
$630$		0			0
$631$	−2.90033			−0.115460			−0.0577302	−	0.998332i	$-0.518386\pi$
$631$	−2.90033			−0.115460			−0.0577302	+	0.998332i	$0.518386\pi$
$632$		0			0
$633$	−29.4743	−	17.0170i	−1.17150	−	0.676364i
$634$		0			0
$635$	−3.90033	+	0.894797i	−0.154780	+	0.0355089i
$636$		0			0
$637$	−6.72508	+	42.1029i	−0.266457	+	1.66818i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−14.0498	+	24.3350i	−0.554935	+	0.961176i	0.442973	+	0.896535i	$0.353924\pi$
$641$	−14.0498	+	24.3350i	−0.554935	+	0.961176i	−0.997909	+	0.0646411i	$0.979410\pi$
$642$		0			0
$643$			38.3353i			1.51180i	0.654689	+	0.755898i	$0.272800\pi$
$643$			38.3353i			1.51180i	−0.654689	+	0.755898i	$0.727200\pi$
$644$		0			0
$645$	24.0997	+	7.40437i	0.948924	+	0.291547i
$646$		0			0
$647$	0.675248	+	0.389855i	0.0265468	+	0.0153268i	0.513215	−	0.858260i	$-0.328454\pi$
$647$	0.675248	+	0.389855i	0.0265468	+	0.0153268i	−0.486668	+	0.873587i	$0.661788\pi$
$648$		0			0
$649$	4.86254	+	8.42217i	0.190871	+	0.330599i
$650$		0			0
$651$	−17.6873	+	8.42217i	−0.693220	+	0.330091i
$652$		0			0
$653$	32.0619	−	18.5109i	1.25468	−	0.724389i	0.282643	−	0.959225i	$-0.408789\pi$
$653$	32.0619	−	18.5109i	1.25468	−	0.724389i	0.972035	+	0.234836i	$0.0754554\pi$
$654$		0			0
$655$	−29.9244	+	27.8279i	−1.16924	+	1.08733i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−25.4502			−0.991398			−0.495699	−	0.868494i	$-0.665088\pi$
$659$	−25.4502			−0.991398			−0.495699	+	0.868494i	$0.665088\pi$
$660$		0			0
$661$	7.77492	−	13.4666i	0.302409	−	0.523788i	−0.674272	−	0.738483i	$-0.735542\pi$
$661$	7.77492	−	13.4666i	0.302409	−	0.523788i	0.976681	+	0.214695i	$0.0688758\pi$
$662$		0			0
$663$	−43.6495	+	25.2011i	−1.69521	+	0.978728i
$664$		0			0
$665$	−19.8248	+	15.7035i	−0.768771	+	0.608957i
$666$		0			0
$667$	2.53779	−	1.46519i	0.0982636	−	0.0567325i
$668$		0			0
$669$	7.54983	−	13.0767i	0.291893	−	0.505574i
$670$		0			0
$671$	−3.52575			−0.136110
$672$		0			0
$673$		−	3.57919i		−	0.137968i	−0.997618	−	0.0689838i	$-0.978024\pi$
$673$		−	3.57919i		−	0.137968i	0.997618	−	0.0689838i	$-0.0219757\pi$
$674$		0			0
$675$	−11.3248	−	23.3827i	−0.435890	−	0.900000i
$676$		0			0
$677$	21.3127	−	12.3049i	0.819114	−	0.472916i	−0.0309969	−	0.999519i	$-0.509868\pi$
$677$	21.3127	−	12.3049i	0.819114	−	0.472916i	0.850111	+	0.526604i	$0.176535\pi$
$678$		0			0
$679$	−1.45017	+	18.2728i	−0.0556522	+	0.701248i
$680$		0			0
$681$	5.58762	+	9.67805i	0.214118	+	0.370864i
$682$		0			0
$683$	13.5997	+	7.85177i	0.520377	+	0.300440i	0.737089	−	0.675796i	$-0.236200\pi$
$683$	13.5997	+	7.85177i	0.520377	+	0.300440i	−0.216712	+	0.976236i	$0.569533\pi$
$684$		0			0
$685$	−6.03779	+	19.6517i	−0.230692	+	0.750854i
$686$		0			0
$687$			7.40437i			0.282494i
$688$		0			0
$689$	−22.5498	+	39.0575i	−0.859080	+	1.48797i
$690$		0			0
$691$	−3.68729	−	6.38658i	−0.140271	−	0.242957i	0.787327	−	0.616535i	$-0.211464\pi$
$691$	−3.68729	−	6.38658i	−0.140271	−	0.242957i	−0.927599	+	0.373578i	$0.878131\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	8.54983	+	37.2679i	0.324314	+	1.41365i
$696$		0			0
$697$	46.6495	+	26.9331i	1.76698	+	1.02016i
$698$		0			0
$699$	32.2749			1.22075
$700$		0			0
$701$	−13.8248			−0.522154			−0.261077	−	0.965318i	$-0.584078\pi$
$701$	−13.8248			−0.522154			−0.261077	+	0.965318i	$0.584078\pi$
$702$		0			0
$703$	−20.7870	−	12.0014i	−0.783995	−	0.452640i
$704$		0			0
$705$	−1.86254	−	8.11863i	−0.0701474	−	0.305765i
$706$		0			0
$707$	2.32475	−	3.37779i	0.0874313	−	0.127035i
$708$		0			0
$709$	−12.7749	−	22.1268i	−0.479772	−	0.830990i	0.519959	−	0.854191i	$-0.325947\pi$
$709$	−12.7749	−	22.1268i	−0.479772	−	0.830990i	−0.999731	+	0.0232018i	$0.992614\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$			3.82518i			0.143254i
$714$		0			0
$715$	9.09967	−	29.6175i	0.340308	−	1.10763i
$716$		0			0
$717$	21.8248	+	12.6005i	0.815060	+	0.470575i
$718$		0			0
$719$	−3.68729	−	6.38658i	−0.137513	−	0.238179i	0.789042	−	0.614340i	$-0.210577\pi$
$719$	−3.68729	−	6.38658i	−0.137513	−	0.238179i	−0.926555	+	0.376160i	$0.877244\pi$
$720$		0			0
$721$	−6.13746	+	2.92248i	−0.228571	+	0.108839i
$722$		0			0
$723$	−19.2371	+	11.1066i	−0.715436	+	0.413057i
$724$		0			0
$725$	−14.7371	+	7.13752i	−0.547323	+	0.265081i
$726$		0			0
$727$			18.6915i			0.693228i	0.938008	+	0.346614i	$0.112669\pi$
$727$			18.6915i			0.693228i	−0.938008	+	0.346614i	$0.887331\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−15.5498	+	26.9331i	−0.575131	+	0.996157i
$732$		0			0
$733$	−28.8625	+	16.6638i	−1.06606	+	0.615491i	−0.927103	−	0.374807i	$-0.877709\pi$
$733$	−28.8625	+	16.6638i	−1.06606	+	0.615491i	−0.138959	+	0.990298i	$0.544376\pi$
$734$		0			0
$735$	−11.9502	+	24.3350i	−0.440788	+	0.897611i
$736$		0			0
$737$	−27.4124	+	15.8265i	−1.00975	+	0.582978i
$738$		0			0
$739$	−15.9622	+	27.6474i	−0.587179	+	1.01702i	0.407420	+	0.913241i	$0.366428\pi$
$739$	−15.9622	+	27.6474i	−0.587179	+	1.01702i	−0.994600	+	0.103784i	$0.966905\pi$
$740$		0			0
$741$	45.0997			1.65678
$742$		0			0
$743$		−	19.5287i		−	0.716440i	−0.933637	−	0.358220i	$-0.883384\pi$
$743$		−	19.5287i		−	0.716440i	0.933637	−	0.358220i	$-0.116616\pi$
$744$		0			0
$745$	12.3625	−	11.4964i	0.452928	−	0.421196i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−33.2371	+	15.8265i	−1.21446	+	0.578289i
$750$		0			0
$751$	−11.1375	−	19.2906i	−0.406412	−	0.703926i	0.588073	−	0.808808i	$-0.299887\pi$
$751$	−11.1375	−	19.2906i	−0.406412	−	0.703926i	−0.994485	+	0.104882i	$0.966553\pi$
$752$		0			0
$753$	−8.17525	−	4.71998i	−0.297923	−	0.172006i
$754$		0			0
$755$	43.3368	+	13.3148i	1.57719	+	0.484575i
$756$		0			0
$757$			9.43996i			0.343101i	0.985175	+	0.171551i	$0.0548777\pi$
$757$			9.43996i			0.343101i	−0.985175	+	0.171551i	$0.945122\pi$
$758$		0			0
$759$	−1.76287	+	3.05338i	−0.0639882	+	0.110831i
$760$		0			0
$761$	14.9622	+	25.9153i	0.542380	+	0.939429i	0.998767	+	0.0496479i	$0.0158099\pi$
$761$	14.9622	+	25.9153i	0.542380	+	0.939429i	−0.456387	+	0.889781i	$0.650857\pi$
$762$		0			0
$763$	−5.32475	+	7.73668i	−0.192769	+	0.280087i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−22.5498	−	13.0192i	−0.814227	−	0.470094i
$768$		0			0
$769$	14.0000			0.504853			0.252426	−	0.967616i	$-0.418771\pi$
$769$	14.0000			0.504853			0.252426	+	0.967616i	$0.418771\pi$
$770$		0			0
$771$	42.8248			1.54230
$772$		0			0
$773$	−23.5876	−	13.6183i	−0.848388	−	0.489817i	0.0117187	−	0.999931i	$-0.496270\pi$
$773$	−23.5876	−	13.6183i	−0.848388	−	0.489817i	−0.860107	+	0.510114i	$0.829603\pi$
$774$		0			0
$775$	1.54983	−	21.3183i	0.0556717	−	0.765777i
$776$		0			0
$777$	−25.6495	−	2.03559i	−0.920171	−	0.0730264i
$778$		0			0
$779$	−24.0997	−	41.7419i	−0.863460	−	1.49556i
$780$		0			0
$781$	−12.0000	+	20.7846i	−0.429394	+	0.743732i
$782$		0			0
$783$			17.0170i			0.608137i
$784$		0			0
$785$	−7.13746	+	23.2309i	−0.254747	+	0.829147i
$786$		0			0
$787$	−1.50000	−	0.866025i	−0.0534692	−	0.0308705i	0.473027	−	0.881048i	$-0.343161\pi$
$787$	−1.50000	−	0.866025i	−0.0534692	−	0.0308705i	−0.526496	+	0.850177i	$0.676495\pi$
$788$		0			0
$789$	23.3248	+	40.3997i	0.830383	+	1.43827i
$790$		0			0
$791$	−2.72508	+	34.3375i	−0.0968928	+	1.22090i
$792$		0			0
$793$	8.17525	−	4.71998i	0.290312	−	0.167611i
$794$		0			0
$795$	−21.0000	+	19.5287i	−0.744793	+	0.692613i
$796$		0			0
$797$		−	29.3873i		−	1.04095i	−0.853876	−	0.520476i	$-0.825754\pi$
$797$		−	29.3873i		−	1.04095i	0.853876	−	0.520476i	$-0.174246\pi$
$798$		0			0
$799$	10.2749			0.363500
$800$		0			0
$801$		0			0
$802$		0			0
$803$	4.23713	−	2.44631i	0.149525	−	0.0863283i
$804$		0			0
$805$	3.28696	+	4.14959i	0.115850	+	0.146254i
$806$		0			0
$807$	44.3248	−	25.5909i	1.56031	−	0.900843i
$808$		0			0
$809$	21.5997	−	37.4117i	0.759404	−	1.31533i	−0.183751	−	0.982973i	$-0.558824\pi$
$809$	21.5997	−	37.4117i	0.759404	−	1.31533i	0.943155	−	0.332353i	$-0.107843\pi$
$810$		0			0
$811$	−22.5498			−0.791832			−0.395916	−	0.918287i	$-0.629573\pi$
$811$	−22.5498			−0.791832			−0.395916	+	0.918287i	$0.629573\pi$
$812$		0			0
$813$			22.2131i			0.779048i
$814$		0			0
$815$	11.2749	+	12.1244i	0.394943	+	0.424698i
$816$		0			0
$817$	24.0997	−	13.9140i	0.843141	−	0.486788i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−8.68729	−	15.0468i	−0.303189	−	0.525138i	0.673668	−	0.739034i	$-0.264718\pi$
$821$	−8.68729	−	15.0468i	−0.303189	−	0.525138i	−0.976856	+	0.213896i	$0.931385\pi$
$822$		0			0
$823$	27.9743	+	16.1509i	0.975121	+	0.562987i	0.900794	−	0.434247i	$-0.142986\pi$
$823$	27.9743	+	16.1509i	0.975121	+	0.562987i	0.0743276	+	0.997234i	$0.476319\pi$
$824$		0			0
$825$	11.0619	−	16.3027i	0.385125	−	0.567588i
$826$		0			0
$827$			45.5670i			1.58452i	0.610183	+	0.792261i	$0.291096\pi$
$827$			45.5670i			1.58452i	−0.610183	+	0.792261i	$0.708904\pi$
$828$		0			0
$829$	0.962210	−	1.66660i	0.0334189	−	0.0578833i	−0.848832	−	0.528662i	$-0.822694\pi$
$829$	0.962210	−	1.66660i	0.0334189	−	0.0578833i	0.882251	+	0.470779i	$0.156027\pi$
$830$		0			0
$831$	16.1375	+	27.9509i	0.559802	+	0.969606i
$832$		0			0
$833$	−25.9622	−	21.0802i	−0.899537	−	0.730387i
$834$		0			0
$835$	−27.4622	+	6.30026i	−0.950369	+	0.218030i
$836$		0			0
$837$	−19.2371	−	11.1066i	−0.664932	−	0.383899i
$838$		0			0
$839$	10.9003			0.376321			0.188161	−	0.982138i	$-0.439747\pi$
$839$	10.9003			0.376321			0.188161	+	0.982138i	$0.439747\pi$
$840$		0			0
$841$	−18.2749			−0.630170
$842$		0			0
$843$	−9.00000	−	5.19615i	−0.309976	−	0.178965i
$844$		0			0
$845$	12.0498	+	52.5240i	0.414527	+	1.80688i
$846$		0			0
$847$	−6.62541	−	13.9140i	−0.227652	−	0.478089i
$848$		0			0
$849$	−16.9622	−	29.3794i	−0.582142	−	1.00830i
$850$		0			0
$851$	−2.51204	+	4.35099i	−0.0861118	+	0.149150i
$852$		0			0
$853$			30.4547i			1.04275i	0.853327	+	0.521375i	$0.174581\pi$
$853$			30.4547i			1.04275i	−0.853327	+	0.521375i	$0.825419\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−28.8625	−	16.6638i	−0.985926	−	0.569224i	−0.0818717	−	0.996643i	$-0.526090\pi$
$857$	−28.8625	−	16.6638i	−0.985926	−	0.569224i	−0.904054	+	0.427418i	$0.859423\pi$
$858$		0			0
$859$	−17.6873	−	30.6353i	−0.603483	−	1.04526i	−0.992289	−	0.123943i	$-0.960446\pi$
$859$	−17.6873	−	30.6353i	−0.603483	−	1.04526i	0.388807	−	0.921319i	$-0.372887\pi$
$860$		0			0
$861$	−42.5619	−	29.2931i	−1.45050	−	0.998306i
$862$		0			0
$863$	−21.7749	+	12.5718i	−0.741227	+	0.427947i	−0.822515	−	0.568743i	$-0.807430\pi$
$863$	−21.7749	+	12.5718i	−0.741227	+	0.427947i	0.0812884	+	0.996691i	$0.474097\pi$
$864$		0			0
$865$	−28.5498	−	30.7007i	−0.970723	−	1.04386i
$866$		0			0
$867$		−	10.0888i		−	0.342632i
$868$		0			0
$869$	0.625414			0.0212157
$870$		0			0
$871$	42.3746	−	73.3949i	1.43581	−	2.48689i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−16.6375	−	24.4580i	−0.562449	−	0.826832i
$876$		0			0
$877$	−38.6873	+	22.3361i	−1.30638	+	0.754237i	−0.981490	−	0.191516i	$-0.938660\pi$
$877$	−38.6873	+	22.3361i	−1.30638	+	0.754237i	−0.324887	+	0.945753i	$0.605326\pi$
$878$		0			0
$879$	−6.00000	+	10.3923i	−0.202375	+	0.350524i
$880$		0			0
$881$	40.0241			1.34845			0.674223	−	0.738528i	$-0.264479\pi$
$881$	40.0241			1.34845			0.674223	+	0.738528i	$0.264479\pi$
$882$		0			0
$883$			20.6695i			0.695585i	0.937572	+	0.347792i	$0.113069\pi$
$883$			20.6695i			0.695585i	−0.937572	+	0.347792i	$0.886931\pi$
$884$		0			0
$885$	−11.2749	−	12.1244i	−0.379002	−	0.407556i
$886$		0			0
$887$	−33.9743	+	19.6150i	−1.14074	+	0.658609i	−0.946615	−	0.322367i	$-0.895521\pi$
$887$	−33.9743	+	19.6150i	−1.14074	+	0.658609i	−0.194129	+	0.980976i	$0.562188\pi$
$888$		0			0
$889$	−0.374586	+	4.71998i	−0.0125632	+	0.158303i
$890$		0			0
$891$	−10.2371	−	17.7312i	−0.342957	−	0.594018i
$892$		0			0
$893$	−7.96221	−	4.59698i	−0.266445	−	0.153832i
$894$		0			0
$895$	0.587624	+	0.180541i	0.0196421	+	0.00603483i
$896$		0			0
$897$		−	9.43996i		−	0.315191i
$898$		0			0
$899$	−7.00000	+	12.1244i	−0.233463	+	0.404370i
$900$		0			0
$901$	−17.6873	−	30.6353i	−0.589249	−	1.02061i
$902$		0			0
$903$	16.9124	−	24.5731i	0.562809	−	0.817742i
$904$		0			0
$905$	8.36254	+	36.4515i	0.277980	+	1.21169i
$906$		0			0
$907$	39.2492	+	22.6605i	1.30325	+	0.752430i	0.980960	−	0.194212i	$-0.0622148\pi$
$907$	39.2492	+	22.6605i	1.30325	+	0.752430i	0.322288	+	0.946642i	$0.395548\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−5.09967			−0.168960			−0.0844798	−	0.996425i	$-0.526923\pi$
$911$	−5.09967			−0.168960			−0.0844798	+	0.996425i	$0.526923\pi$
$912$		0			0
$913$	11.1752	+	6.45203i	0.369847	+	0.213531i
$914$		0			0
$915$	5.85050	−	1.34220i	0.193411	−	0.0443716i
$916$		0			0
$917$	20.7870	+	43.6544i	0.686446	+	1.44160i
$918$		0			0
$919$	−2.96221	−	5.13070i	−0.0977143	−	0.169246i	0.813024	−	0.582230i	$-0.197820\pi$
$919$	−2.96221	−	5.13070i	−0.0977143	−	0.169246i	−0.910738	+	0.412984i	$0.864486\pi$
$920$		0			0
$921$	3.46221	−	5.99672i	0.114084	−	0.197599i
$922$		0			0
$923$		−	64.2585i		−	2.11509i
$924$		0			0
$925$	15.7629	−	23.2309i	0.518280	−	0.763828i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−8.95017	−	15.5021i	−0.293645	−	0.508609i	0.681023	−	0.732262i	$-0.261535\pi$
$929$	−8.95017	−	15.5021i	−0.293645	−	0.508609i	−0.974669	+	0.223653i	$0.928202\pi$
$930$		0			0
$931$	10.6873	+	27.9509i	0.350262	+	0.916054i
$932$		0			0
$933$	−19.2371	+	11.1066i	−0.629795	+	0.363612i
$934$		0			0
$935$	16.5498	+	17.7967i	0.541237	+	0.582014i
$936$		0			0
$937$		−	10.5074i		−	0.343262i	−0.985161	−	0.171631i	$-0.945096\pi$
$937$		−	10.5074i		−	0.343262i	0.985161	−	0.171631i	$-0.0549036\pi$
$938$		0			0
$939$	25.0241			0.816630
$940$		0			0
$941$	−2.13746	+	3.70219i	−0.0696792	+	0.120688i	−0.898760	−	0.438441i	$-0.855531\pi$
$941$	−2.13746	+	3.70219i	−0.0696792	+	0.120688i	0.829081	+	0.559129i	$0.188864\pi$
$942$		0			0
$943$	−8.73713	+	5.04438i	−0.284520	+	0.164268i
$944$		0			0
$945$	−30.4124	+	4.48190i	−0.989315	+	0.145796i
$946$		0			0
$947$	−36.1495	+	20.8709i	−1.17470	+	0.678214i	−0.954783	−	0.297304i	$-0.903912\pi$
$947$	−36.1495	+	20.8709i	−1.17470	+	0.678214i	−0.219918	+	0.975518i	$0.570579\pi$
$948$		0			0
$949$	−6.54983	+	11.3446i	−0.212617	+	0.368263i
$950$		0			0
$951$	−6.62541			−0.214844
$952$		0			0
$953$			29.6175i			0.959405i	0.877431	+	0.479702i	$0.159255\pi$
$953$			29.6175i			0.959405i	−0.877431	+	0.479702i	$0.840745\pi$
$954$		0			0
$955$	37.3746	−	34.7561i	1.20941	−	1.12468i
$956$		0			0
$957$	−11.1752	+	6.45203i	−0.361244	+	0.208565i
$958$		0			0
$959$	20.0378	+	13.7910i	0.647054	+	0.445333i
$960$		0			0
$961$	6.36254	+	11.0202i	0.205243	+	0.355492i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−6.03779	+	19.6517i	−0.194363	+	0.632611i
$966$		0			0
$967$			6.50958i			0.209334i	0.994507	+	0.104667i	$0.0333777\pi$
$967$			6.50958i			0.209334i	−0.994507	+	0.104667i	$0.966622\pi$
$968$		0			0
$969$	−17.6873	+	30.6353i	−0.568198	+	0.984147i
$970$		0			0
$971$	7.96221	+	13.7910i	0.255519	+	0.442573i	0.965036	−	0.262116i	$-0.0844202\pi$
$971$	7.96221	+	13.7910i	0.255519	+	0.442573i	−0.709517	+	0.704688i	$0.751087\pi$
$972$		0			0
$973$	45.0997	+	3.57919i	1.44583	+	0.114744i
$974$		0			0
$975$	−3.82475	+	52.6103i	−0.122490	+	1.68488i
$976$		0			0
$977$	14.5876	+	8.42217i	0.466699	+	0.269449i	0.714857	−	0.699271i	$-0.246492\pi$
$977$	14.5876	+	8.42217i	0.466699	+	0.269449i	−0.248158	+	0.968720i	$0.579825\pi$
$978$		0			0
$979$	−15.9244			−0.508947
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−32.2251	−	18.6052i	−1.02782	−	0.593412i	−0.111461	−	0.993769i	$-0.535553\pi$
$983$	−32.2251	−	18.6052i	−1.02782	−	0.593412i	−0.916360	+	0.400356i	$0.868886\pi$
$984$		0			0
$985$	56.7492	−	13.0192i	1.80818	−	0.414825i
$986$		0			0
$987$	−9.82475	−	0.779710i	−0.312725	−	0.0248184i
$988$		0			0
$989$	−2.91238	−	5.04438i	−0.0926082	−	0.160402i
$990$		0			0
$991$	−17.2371	+	29.8556i	−0.547555	+	0.948394i	0.450886	+	0.892582i	$0.351108\pi$
$991$	−17.2371	+	29.8556i	−0.547555	+	0.948394i	−0.998441	+	0.0558122i	$0.982225\pi$
$992$		0			0
$993$			8.35671i			0.265192i
$994$		0			0
$995$	20.7870	+	6.38658i	0.658991	+	0.202468i
$996$		0			0
$997$	−4.13746	−	2.38876i	−0.131035	−	0.0756529i	0.433050	−	0.901370i	$-0.357437\pi$
$997$	−4.13746	−	2.38876i	−0.131035	−	0.0756529i	−0.564084	+	0.825717i	$0.690771\pi$
$998$		0			0
$999$	−14.5876	−	25.2665i	−0.461532	−	0.799397i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bw.a.529.1		4
4.3	odd	2		140.2.q.b.109.1	yes	4
5.4	even	2		560.2.bw.e.529.1		4
7.2	even	3		560.2.bw.e.289.1		4
12.11	even	2		1260.2.bm.b.109.2		4
20.3	even	4		700.2.i.f.501.1		8
20.7	even	4		700.2.i.f.501.4		8
20.19	odd	2		140.2.q.a.109.1	yes	4
28.3	even	6		980.2.e.c.589.3		4
28.11	odd	6		980.2.e.f.589.2		4
28.19	even	6		980.2.q.g.569.2		4
28.23	odd	6		140.2.q.a.9.1	✓	4
28.27	even	2		980.2.q.b.949.2		4
35.9	even	6	inner	560.2.bw.a.289.2		4
60.59	even	2		1260.2.bm.a.109.2		4
84.23	even	6		1260.2.bm.a.289.2		4
140.3	odd	12		4900.2.a.bf.1.2		4
140.19	even	6		980.2.q.b.569.1		4
140.23	even	12		700.2.i.f.401.1		8
140.39	odd	6		980.2.e.f.589.4		4
140.59	even	6		980.2.e.c.589.1		4
140.67	even	12		4900.2.a.be.1.2		4
140.79	odd	6		140.2.q.b.9.2	yes	4
140.87	odd	12		4900.2.a.bf.1.4		4
140.107	even	12		700.2.i.f.401.4		8
140.123	even	12		4900.2.a.be.1.4		4
140.139	even	2		980.2.q.g.949.2		4
420.359	even	6		1260.2.bm.b.289.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.q.a.9.1	✓	4	28.23	odd	6
140.2.q.a.109.1	yes	4	20.19	odd	2
140.2.q.b.9.2	yes	4	140.79	odd	6
140.2.q.b.109.1	yes	4	4.3	odd	2
560.2.bw.a.289.2		4	35.9	even	6	inner
560.2.bw.a.529.1		4	1.1	even	1	trivial
560.2.bw.e.289.1		4	7.2	even	3
560.2.bw.e.529.1		4	5.4	even	2
700.2.i.f.401.1		8	140.23	even	12
700.2.i.f.401.4		8	140.107	even	12
700.2.i.f.501.1		8	20.3	even	4
700.2.i.f.501.4		8	20.7	even	4
980.2.e.c.589.1		4	140.59	even	6
980.2.e.c.589.3		4	28.3	even	6
980.2.e.f.589.2		4	28.11	odd	6
980.2.e.f.589.4		4	140.39	odd	6
980.2.q.b.569.1		4	140.19	even	6
980.2.q.b.949.2		4	28.27	even	2
980.2.q.g.569.2		4	28.19	even	6
980.2.q.g.949.2		4	140.139	even	2
1260.2.bm.a.109.2		4	60.59	even	2
1260.2.bm.a.289.2		4	84.23	even	6
1260.2.bm.b.109.2		4	12.11	even	2
1260.2.bm.b.289.1		4	420.359	even	6
4900.2.a.be.1.2		4	140.67	even	12
4900.2.a.be.1.4		4	140.123	even	12
4900.2.a.bf.1.2		4	140.3	odd	12
4900.2.a.bf.1.4		4	140.87	odd	12

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.bw (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 - 0.866025i) q^{3} +(-0.500000 - 2.17945i) q^{5} +(-2.63746 - 0.209313i) q^{7} +O(q^{10})\)	\(q+(-1.50000 - 0.866025i) q^{3} +(-0.500000 - 2.17945i) q^{5} +(-2.63746 - 0.209313i) q^{7} +(1.13746 - 1.97014i) q^{11} +6.09095i q^{13} +(-1.13746 + 3.70219i) q^{15} +(-4.13746 - 2.38876i) q^{17} +(2.13746 + 3.70219i) q^{19} +(3.77492 + 2.59808i) q^{21} +(0.774917 - 0.447399i) q^{23} +(-4.50000 + 2.17945i) q^{25} +5.19615i q^{27} +3.27492 q^{29} +(-2.13746 + 3.70219i) q^{31} +(-3.41238 + 1.97014i) q^{33} +(0.862541 + 5.85286i) q^{35} +(-4.86254 + 2.80739i) q^{37} +(5.27492 - 9.13642i) q^{39} -11.2749 q^{41} -6.50958i q^{43} +(-1.86254 + 1.07534i) q^{47} +(6.91238 + 1.10411i) q^{49} +(4.13746 + 7.16629i) q^{51} +(6.41238 + 3.70219i) q^{53} +(-4.86254 - 1.49397i) q^{55} -7.40437i q^{57} +(-2.13746 + 3.70219i) q^{59} +(-0.774917 - 1.34220i) q^{61} +(13.2749 - 3.04547i) q^{65} +(-12.0498 - 6.95698i) q^{67} -1.54983 q^{69} -10.5498 q^{71} +(1.86254 + 1.07534i) q^{73} +(8.63746 + 0.627940i) q^{75} +(-3.41238 + 4.95807i) q^{77} +(0.137459 + 0.238085i) q^{79} +(4.50000 - 7.79423i) q^{81} +5.67232i q^{83} +(-3.13746 + 10.2118i) q^{85} +(-4.91238 - 2.83616i) q^{87} +(-3.50000 - 6.06218i) q^{89} +(1.27492 - 16.0646i) q^{91} +(6.41238 - 3.70219i) q^{93} +(7.00000 - 6.50958i) q^{95} -6.92820i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{3} - 2 q^{5} - 3 q^{7}+O(q^{10}) \) 4 * q - 6 * q^3 - 2 * q^5 - 3 * q^7	\( 4 q - 6 q^{3} - 2 q^{5} - 3 q^{7} - 3 q^{11} + 3 q^{15} - 9 q^{17} + q^{19} - 12 q^{23} - 18 q^{25} - 2 q^{29} - q^{31} + 9 q^{33} + 11 q^{35} - 27 q^{37} + 6 q^{39} - 30 q^{41} - 15 q^{47} + 5 q^{49} + 9 q^{51} + 3 q^{53} - 27 q^{55} - q^{59} + 12 q^{61} + 38 q^{65} - 18 q^{67} + 24 q^{69} - 12 q^{71} + 15 q^{73} + 27 q^{75} + 9 q^{77} - 7 q^{79} + 18 q^{81} - 5 q^{85} + 3 q^{87} - 14 q^{89} - 10 q^{91} + 3 q^{93} + 28 q^{95}+O(q^{100}) \) 4 * q - 6 * q^3 - 2 * q^5 - 3 * q^7 - 3 * q^11 + 3 * q^15 - 9 * q^17 + q^19 - 12 * q^23 - 18 * q^25 - 2 * q^29 - q^31 + 9 * q^33 + 11 * q^35 - 27 * q^37 + 6 * q^39 - 30 * q^41 - 15 * q^47 + 5 * q^49 + 9 * q^51 + 3 * q^53 - 27 * q^55 - q^59 + 12 * q^61 + 38 * q^65 - 18 * q^67 + 24 * q^69 - 12 * q^71 + 15 * q^73 + 27 * q^75 + 9 * q^77 - 7 * q^79 + 18 * q^81 - 5 * q^85 + 3 * q^87 - 14 * q^89 - 10 * q^91 + 3 * q^93 + 28 * q^95

Introduction

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