LMFDB - Embedded newform 560.2.ci.e.17.2

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			17.2
Character	$\chi$	$=$	560.17
Dual form			560.2.ci.e.33.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.20364 + 0.590462i) q^{3} +(-0.352053 - 2.20818i) q^{5} +(1.22435 + 2.34541i) q^{7} +(1.90929 - 1.10233i) q^{9} +O(q^{10})$	\(q+(-2.20364 + 0.590462i) q^{3} +(-0.352053 - 2.20818i) q^{5} +(1.22435 + 2.34541i) q^{7} +(1.90929 - 1.10233i) q^{9} +(0.0644824 - 0.111687i) q^{11} +(-0.748741 - 0.748741i) q^{13} +(2.07964 + 4.65815i) q^{15} +(0.613222 + 2.28858i) q^{17} +(-3.81023 - 6.59951i) q^{19} +(-4.08291 - 4.44550i) q^{21} +(-4.11147 - 1.10166i) q^{23} +(-4.75212 + 1.55479i) q^{25} +(1.28303 - 1.28303i) q^{27} -0.163226i q^{29} +(-8.43321 - 4.86892i) q^{31} +(-0.0761489 + 0.284192i) q^{33} +(4.74806 - 3.52930i) q^{35} +(0.0241304 - 0.0900559i) q^{37} +(2.09206 + 1.20785i) q^{39} -11.9864i q^{41} +(-2.76959 + 2.76959i) q^{43} +(-3.10631 - 3.82798i) q^{45} +(-2.23164 - 0.597966i) q^{47} +(-4.00192 + 5.74323i) q^{49} +(-2.70264 - 4.68110i) q^{51} +(-1.96147 - 7.32032i) q^{53} +(-0.269326 - 0.103069i) q^{55} +(12.2931 + 12.2931i) q^{57} +(4.13495 - 7.16194i) q^{59} +(-11.5114 + 6.64609i) q^{61} +(4.92306 + 3.12843i) q^{63} +(-1.38976 + 1.91695i) q^{65} +(-6.84682 + 1.83460i) q^{67} +9.71067 q^{69} +9.50288 q^{71} +(1.80412 - 0.483412i) q^{73} +(9.55389 - 6.23214i) q^{75} +(0.340901 + 0.0144937i) q^{77} +(8.48250 - 4.89737i) q^{79} +(-5.37673 + 9.31277i) q^{81} +(8.43870 + 8.43870i) q^{83} +(4.83770 - 2.15980i) q^{85} +(0.0963790 + 0.359691i) q^{87} +(3.37880 + 5.85226i) q^{89} +(0.839383 - 2.67283i) q^{91} +(21.4586 + 5.74983i) q^{93} +(-13.2315 + 10.7371i) q^{95} +(-9.61378 + 9.61378i) q^{97} -0.284323i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.20364	+	0.590462i	−1.27227	+	0.340904i	−0.830900	−	0.556422i	$-0.812174\pi$
$3$	−2.20364	+	0.590462i	−1.27227	+	0.340904i	−0.441370	+	0.897325i	$0.645507\pi$
$4$		0			0
$5$	−0.352053	−	2.20818i	−0.157443	−	0.987528i
$5$	−0.352053	−	2.20818i	−0.157443	−	0.987528i
$6$		0			0
$7$	1.22435	+	2.34541i	0.462762	+	0.886483i
$7$	1.22435	+	2.34541i	0.462762	+	0.886483i
$8$		0			0
$9$	1.90929	−	1.10233i	0.636430	−	0.367443i
$10$		0			0
$11$	0.0644824	−	0.111687i	0.0194422	−	0.0336749i	−0.856141	−	0.516743i	$-0.827144\pi$
$11$	0.0644824	−	0.111687i	0.0194422	−	0.0336749i	0.875583	+	0.483068i	$0.160478\pi$
$12$		0			0
$13$	−0.748741	−	0.748741i	−0.207663	−	0.207663i	0.595610	−	0.803274i	$-0.296910\pi$
$13$	−0.748741	−	0.748741i	−0.207663	−	0.207663i	−0.803274	+	0.595610i	$0.796910\pi$
$14$		0			0
$15$	2.07964	+	4.65815i	0.536962	+	1.20273i
$16$		0			0
$17$	0.613222	+	2.28858i	0.148728	+	0.555061i	0.999561	+	0.0296247i	$0.00943123\pi$
$17$	0.613222	+	2.28858i	0.148728	+	0.555061i	−0.850833	+	0.525436i	$0.823902\pi$
$18$		0			0
$19$	−3.81023	−	6.59951i	−0.874127	−	1.51403i	−0.857690	−	0.514167i	$-0.828101\pi$
$19$	−3.81023	−	6.59951i	−0.874127	−	1.51403i	−0.0164365	−	0.999865i	$-0.505232\pi$
$20$		0			0
$21$	−4.08291	−	4.44550i	−0.890963	−	0.970088i
$22$		0			0
$23$	−4.11147	−	1.10166i	−0.857301	−	0.229713i	−0.196712	−	0.980461i	$-0.563026\pi$
$23$	−4.11147	−	1.10166i	−0.857301	−	0.229713i	−0.660588	+	0.750748i	$0.729693\pi$
$24$		0			0
$25$	−4.75212	+	1.55479i	−0.950423	+	0.310959i
$26$		0			0
$27$	1.28303	−	1.28303i	0.246918	−	0.246918i
$28$		0			0
$29$		−	0.163226i		−	0.0303104i	−0.999885	−	0.0151552i	$-0.995176\pi$
$29$		−	0.163226i		−	0.0303104i	0.999885	−	0.0151552i	$-0.00482423\pi$
$30$		0			0
$31$	−8.43321	−	4.86892i	−1.51465	−	0.874484i	−0.999853	−	0.0171718i	$-0.994534\pi$
$31$	−8.43321	−	4.86892i	−1.51465	−	0.874484i	−0.514797	−	0.857312i	$-0.672133\pi$
$32$		0			0
$33$	−0.0761489	+	0.284192i	−0.0132558	+	0.0494714i
$34$		0			0
$35$	4.74806	−	3.52930i	0.802568	−	0.596561i
$36$		0			0
$37$	0.0241304	−	0.0900559i	0.00396701	−	0.0148051i	−0.963914	−	0.266214i	$-0.914227\pi$
$37$	0.0241304	−	0.0900559i	0.00396701	−	0.0148051i	0.967881	+	0.251409i	$0.0808939\pi$
$38$		0			0
$39$	2.09206	+	1.20785i	0.334997	+	0.193411i
$40$		0			0
$41$		−	11.9864i		−	1.87195i	−0.352060	−	0.935977i	$-0.614519\pi$
$41$		−	11.9864i		−	1.87195i	0.352060	−	0.935977i	$-0.385481\pi$
$42$		0			0
$43$	−2.76959	+	2.76959i	−0.422358	+	0.422358i	−0.886015	−	0.463657i	$-0.846537\pi$
$43$	−2.76959	+	2.76959i	−0.422358	+	0.422358i	0.463657	+	0.886015i	$0.346537\pi$
$44$		0			0
$45$	−3.10631	−	3.82798i	−0.463062	−	0.570641i
$46$		0			0
$47$	−2.23164	−	0.597966i	−0.325518	−	0.0872223i	0.0923593	−	0.995726i	$-0.470559\pi$
$47$	−2.23164	−	0.597966i	−0.325518	−	0.0872223i	−0.417877	+	0.908503i	$0.637226\pi$
$48$		0			0
$49$	−4.00192	+	5.74323i	−0.571703	+	0.820461i
$50$		0			0
$51$	−2.70264	−	4.68110i	−0.378445	−	0.655485i
$52$		0			0
$53$	−1.96147	−	7.32032i	−0.269429	−	1.00552i	−0.959483	−	0.281766i	$-0.909080\pi$
$53$	−1.96147	−	7.32032i	−0.269429	−	1.00552i	0.690054	−	0.723758i	$-0.257587\pi$
$54$		0			0
$55$	−0.269326	−	0.103069i	−0.0363159	−	0.0138978i
$56$		0			0
$57$	12.2931	+	12.2931i	1.62826	+	1.62826i
$58$		0			0
$59$	4.13495	−	7.16194i	0.538324	−	0.932405i	−0.460670	−	0.887571i	$-0.652391\pi$
$59$	4.13495	−	7.16194i	0.538324	−	0.932405i	0.998994	−	0.0448333i	$-0.0142757\pi$
$60$		0			0
$61$	−11.5114	+	6.64609i	−1.47388	+	0.850945i	−0.999567	−	0.0294113i	$-0.990637\pi$
$61$	−11.5114	+	6.64609i	−1.47388	+	0.850945i	−0.474313	+	0.880356i	$0.657303\pi$
$62$		0			0
$63$	4.92306	+	3.12843i	0.620247	+	0.394145i
$64$		0			0
$65$	−1.38976	+	1.91695i	−0.172378	+	0.237768i
$66$		0			0
$67$	−6.84682	+	1.83460i	−0.836472	+	0.224132i	−0.651535	−	0.758618i	$-0.725875\pi$
$67$	−6.84682	+	1.83460i	−0.836472	+	0.224132i	−0.184937	+	0.982750i	$0.559208\pi$
$68$		0			0
$69$	9.71067			1.16903
$70$		0			0
$71$	9.50288			1.12778			0.563892	−	0.825848i	$-0.309303\pi$
$71$	9.50288			1.12778			0.563892	+	0.825848i	$0.309303\pi$
$72$		0			0
$73$	1.80412	−	0.483412i	0.211156	−	0.0565791i	−0.151690	−	0.988428i	$-0.548472\pi$
$73$	1.80412	−	0.483412i	0.211156	−	0.0565791i	0.362846	+	0.931849i	$0.381805\pi$
$74$		0			0
$75$	9.55389	−	6.23214i	1.10319	−	0.719626i
$76$		0			0
$77$	0.340901	+	0.0144937i	0.0388493	+	0.00165172i
$78$		0			0
$79$	8.48250	−	4.89737i	0.954355	−	0.550997i	0.0599241	−	0.998203i	$-0.480914\pi$
$79$	8.48250	−	4.89737i	0.954355	−	0.550997i	0.894431	+	0.447206i	$0.147581\pi$
$80$		0			0
$81$	−5.37673	+	9.31277i	−0.597414	+	1.03475i
$82$		0			0
$83$	8.43870	+	8.43870i	0.926267	+	0.926267i	0.997462	−	0.0711952i	$-0.0226813\pi$
$83$	8.43870	+	8.43870i	0.926267	+	0.926267i	−0.0711952	+	0.997462i	$0.522681\pi$
$84$		0			0
$85$	4.83770	−	2.15980i	0.524722	−	0.234264i
$86$		0			0
$87$	0.0963790	+	0.359691i	0.0103329	+	0.0385629i
$88$		0			0
$89$	3.37880	+	5.85226i	0.358153	+	0.620338i	0.987652	−	0.156662i	$-0.0500734\pi$
$89$	3.37880	+	5.85226i	0.358153	+	0.620338i	−0.629500	+	0.777001i	$0.716740\pi$
$90$		0			0
$91$	0.839383	−	2.67283i	0.0879912	−	0.280189i
$92$		0			0
$93$	21.4586	+	5.74983i	2.22516	+	0.596229i
$94$		0			0
$95$	−13.2315	+	10.7371i	−1.35752	+	1.10160i
$96$		0			0
$97$	−9.61378	+	9.61378i	−0.976132	+	0.976132i	−0.999722	−	0.0235902i	$-0.992490\pi$
$97$	−9.61378	+	9.61378i	−0.976132	+	0.976132i	0.0235902	+	0.999722i	$0.492490\pi$
$98$		0			0
$99$		−	0.284323i		−	0.0285756i
$100$		0			0
$101$	−9.52057	−	5.49670i	−0.947332	−	0.546942i	−0.0550809	−	0.998482i	$-0.517542\pi$
$101$	−9.52057	−	5.49670i	−0.947332	−	0.546942i	−0.892251	+	0.451540i	$0.850875\pi$
$102$		0			0
$103$	2.07137	−	7.73044i	0.204098	−	0.761703i	−0.785625	−	0.618703i	$-0.787658\pi$
$103$	2.07137	−	7.73044i	0.204098	−	0.761703i	0.989723	−	0.143000i	$-0.0456750\pi$
$104$		0			0
$105$	−8.37907	+	10.5808i	−0.817713	+	1.03258i
$106$		0			0
$107$	−4.51297	+	16.8426i	−0.436285	+	1.62824i	0.301687	+	0.953407i	$0.402450\pi$
$107$	−4.51297	+	16.8426i	−0.436285	+	1.62824i	−0.737972	+	0.674831i	$0.764216\pi$
$108$		0			0
$109$	−8.75633	−	5.05547i	−0.838704	−	0.484226i	0.0181193	−	0.999836i	$-0.494232\pi$
$109$	−8.75633	−	5.05547i	−0.838704	−	0.484226i	−0.856824	+	0.515610i	$0.827565\pi$
$110$		0			0
$111$			0.212699i			0.0201884i
$112$		0			0
$113$	5.02836	−	5.02836i	0.473028	−	0.473028i	−0.429865	−	0.902893i	$-0.641439\pi$
$113$	5.02836	−	5.02836i	0.473028	−	0.473028i	0.902893	+	0.429865i	$0.141439\pi$
$114$		0			0
$115$	−0.985219	+	9.46671i	−0.0918721	+	0.882775i
$116$		0			0
$117$	−2.25492	−	0.604204i	−0.208468	−	0.0558587i
$118$		0			0
$119$	−4.61685	+	4.24028i	−0.423226	+	0.388706i
$120$		0			0
$121$	5.49168	+	9.51188i	0.499244	+	0.864716i
$122$		0			0
$123$	7.07750	+	26.4136i	0.638156	+	2.38163i
$124$		0			0
$125$	5.10626	+	9.94616i	0.456718	+	0.889612i
$126$		0			0
$127$	−0.570478	−	0.570478i	−0.0506218	−	0.0506218i	0.681343	−	0.731965i	$-0.261396\pi$
$127$	−0.570478	−	0.570478i	−0.0506218	−	0.0506218i	−0.731965	+	0.681343i	$0.761396\pi$
$128$		0			0
$129$	4.46782	−	7.73850i	0.393370	−	0.681337i
$130$		0			0
$131$	2.88606	−	1.66627i	0.252156	−	0.145582i	−0.368595	−	0.929590i	$-0.620161\pi$
$131$	2.88606	−	1.66627i	0.252156	−	0.145582i	0.620751	+	0.784008i	$0.286828\pi$
$132$		0			0
$133$	10.8135	−	17.0167i	0.937650	−	1.47553i
$134$		0			0
$135$	−3.28484	−	2.38146i	−0.282714	−	0.204963i
$136$		0			0
$137$	15.1491	−	4.05920i	1.29428	−	0.346801i	0.454994	−	0.890495i	$-0.349641\pi$
$137$	15.1491	−	4.05920i	1.29428	−	0.346801i	0.839283	+	0.543694i	$0.182975\pi$
$138$		0			0
$139$	−1.31052			−0.111157			−0.0555783	−	0.998454i	$-0.517700\pi$
$139$	−1.31052			−0.111157			−0.0555783	+	0.998454i	$0.517700\pi$
$140$		0			0
$141$	5.27080			0.443881
$142$		0			0
$143$	−0.131905	+	0.0353439i	−0.0110305	+	0.00295560i
$144$		0			0
$145$	−0.360433	+	0.0574643i	−0.0299323	+	0.00477215i
$146$		0			0
$147$	5.42761	−	15.0190i	0.447662	−	1.23874i
$148$		0			0
$149$	9.31791	−	5.37970i	0.763353	−	0.440722i	−0.0671452	−	0.997743i	$-0.521389\pi$
$149$	9.31791	−	5.37970i	0.763353	−	0.440722i	0.830498	+	0.557021i	$0.188056\pi$
$150$		0			0
$151$	−1.38384	+	2.39688i	−0.112615	+	0.195055i	−0.916824	−	0.399292i	$-0.869256\pi$
$151$	−1.38384	+	2.39688i	−0.112615	+	0.195055i	0.804209	+	0.594347i	$0.202589\pi$
$152$		0			0
$153$	3.69358	+	3.69358i	0.298608	+	0.298608i
$154$		0			0
$155$	−7.78251	+	20.3362i	−0.625106	+	1.63344i
$156$		0			0
$157$	−6.18183	−	23.0709i	−0.493364	−	1.84126i	−0.539009	−	0.842300i	$-0.681201\pi$
$157$	−6.18183	−	23.0709i	−0.493364	−	1.84126i	0.0456452	−	0.998958i	$-0.485466\pi$
$158$		0			0
$159$	8.64475	+	14.9732i	0.685573	+	1.18745i
$160$		0			0
$161$	−2.45003	−	10.9919i	−0.193090	−	0.866284i
$162$		0			0
$163$	−10.4564	−	2.80178i	−0.819008	−	0.219452i	−0.175095	−	0.984552i	$-0.556023\pi$
$163$	−10.4564	−	2.80178i	−0.819008	−	0.219452i	−0.643913	+	0.765099i	$0.722690\pi$
$164$		0			0
$165$	0.654355	+	0.0681000i	0.0509414	+	0.00530158i
$166$		0			0
$167$	5.85335	−	5.85335i	0.452946	−	0.452946i	−0.443385	−	0.896331i	$-0.646223\pi$
$167$	5.85335	−	5.85335i	0.452946	−	0.452946i	0.896331	+	0.443385i	$0.146223\pi$
$168$		0			0
$169$		−	11.8788i		−	0.913752i
$170$		0			0
$171$	−14.5497	−	8.40025i	−1.11264	−	0.642383i
$172$		0			0
$173$	−2.66665	+	9.95209i	−0.202742	+	0.756643i	0.787384	+	0.616463i	$0.211435\pi$
$173$	−2.66665	+	9.95209i	−0.202742	+	0.756643i	−0.990126	+	0.140180i	$0.955232\pi$
$174$		0			0
$175$	−9.46490	−	9.24206i	−0.715479	−	0.698634i
$176$		0			0
$177$	−4.88306	+	18.2238i	−0.367033	+	1.36979i
$178$		0			0
$179$	−1.91773	−	1.10720i	−0.143338	−	0.0827560i	0.426616	−	0.904433i	$-0.359706\pi$
$179$	−1.91773	−	1.10720i	−0.143338	−	0.0827560i	−0.569954	+	0.821677i	$0.693039\pi$
$180$		0			0
$181$		−	7.59127i		−	0.564254i	−0.959377	−	0.282127i	$-0.908960\pi$
$181$		−	7.59127i		−	0.564254i	0.959377	−	0.282127i	$-0.0910400\pi$
$182$		0			0
$183$	21.4426	−	21.4426i	1.58508	−	1.58508i
$184$		0			0
$185$	−0.207355	−	0.0215798i	−0.0152450	−	0.00158658i
$186$		0			0
$187$	0.295146	+	0.0790841i	0.0215832	+	0.00578320i
$188$		0			0
$189$	4.58010	+	1.43835i	0.333153	+	0.104624i
$190$		0			0
$191$	0.417950	+	0.723911i	0.0302418	+	0.0523803i	0.880750	−	0.473581i	$-0.157039\pi$
$191$	0.417950	+	0.723911i	0.0302418	+	0.0523803i	−0.850508	+	0.525961i	$0.823706\pi$
$192$		0			0
$193$	5.11827	+	19.1017i	0.368421	+	1.37497i	0.862723	+	0.505677i	$0.168757\pi$
$193$	5.11827	+	19.1017i	0.368421	+	1.37497i	−0.494302	+	0.869290i	$0.664576\pi$
$194$		0			0
$195$	1.93063	−	5.04486i	0.138255	−	0.361270i
$196$		0			0
$197$	−9.57769	−	9.57769i	−0.682382	−	0.682382i	0.278154	−	0.960536i	$-0.410277\pi$
$197$	−9.57769	−	9.57769i	−0.682382	−	0.682382i	−0.960536	+	0.278154i	$0.910277\pi$
$198$		0			0
$199$	10.1367	−	17.5573i	0.718571	−	1.24460i	−0.242995	−	0.970028i	$-0.578130\pi$
$199$	10.1367	−	17.5573i	0.718571	−	1.24460i	0.961566	−	0.274574i	$-0.0885370\pi$
$200$		0			0
$201$	14.0046	−	8.08558i	0.987810	−	0.570313i
$202$		0			0
$203$	0.382833	−	0.199847i	0.0268696	−	0.0140265i
$204$		0			0
$205$	−26.4680	+	4.21983i	−1.84861	+	0.294726i
$206$		0			0
$207$	−9.06438	+	2.42879i	−0.630018	+	0.168813i
$208$		0			0
$209$	−0.982772			−0.0679797
$210$		0			0
$211$	8.14495			0.560721			0.280361	−	0.959895i	$-0.409546\pi$
$211$	8.14495			0.560721			0.280361	+	0.959895i	$0.409546\pi$
$212$		0			0
$213$	−20.9409	+	5.61110i	−1.43485	+	0.384466i
$214$		0			0
$215$	7.09079	+	5.14070i	0.483588	+	0.350593i
$216$		0			0
$217$	1.09439	−	25.7406i	0.0742920	−	1.74739i
$218$		0			0
$219$	−3.69018	+	2.13053i	−0.249359	+	0.143968i
$220$		0			0
$221$	1.25441	−	2.17269i	0.0843804	−	0.146151i
$222$		0			0
$223$	−8.23887	−	8.23887i	−0.551715	−	0.551715i	0.375220	−	0.926936i	$-0.377567\pi$
$223$	−8.23887	−	8.23887i	−0.551715	−	0.551715i	−0.926936	+	0.375220i	$0.877567\pi$
$224$		0			0
$225$	−7.35928	+	8.20695i	−0.490618	+	0.547130i
$226$		0			0
$227$	−0.167262	−	0.624229i	−0.0111015	−	0.0414315i	0.960153	−	0.279475i	$-0.0901605\pi$
$227$	−0.167262	−	0.624229i	−0.0111015	−	0.0414315i	−0.971254	+	0.238044i	$0.923494\pi$
$228$		0			0
$229$	10.5335	+	18.2445i	0.696071	+	1.20563i	0.969818	+	0.243829i	$0.0784036\pi$
$229$	10.5335	+	18.2445i	0.696071	+	1.20563i	−0.273747	+	0.961802i	$0.588263\pi$
$230$		0			0
$231$	−0.759780	+	0.169350i	−0.0499898	+	0.0111424i
$232$		0			0
$233$	−16.6188	−	4.45300i	−1.08874	−	0.291726i	−0.330566	−	0.943783i	$-0.607240\pi$
$233$	−16.6188	−	4.45300i	−1.08874	−	0.291726i	−0.758170	+	0.652057i	$0.773906\pi$
$234$		0			0
$235$	−0.534761	+	5.13838i	−0.0348840	+	0.335191i
$236$		0			0
$237$	−15.8006	+	15.8006i	−1.02636	+	1.02636i
$238$		0			0
$239$			5.00574i			0.323794i	0.986808	+	0.161897i	$0.0517613\pi$
$239$			5.00574i			0.323794i	−0.986808	+	0.161897i	$0.948239\pi$
$240$		0			0
$241$	17.5439	+	10.1290i	1.13010	+	0.652465i	0.943961	−	0.330058i	$-0.107068\pi$
$241$	17.5439	+	10.1290i	1.13010	+	0.652465i	0.186141	+	0.982523i	$0.440402\pi$
$242$		0			0
$243$	4.94065	−	18.4388i	0.316943	−	1.18285i
$244$		0			0
$245$	14.0910	+	6.81504i	0.900239	+	0.435397i
$246$		0			0
$247$	−2.08845	+	7.79420i	−0.132885	+	0.495933i
$248$		0			0
$249$	−23.5785	−	13.6131i	−1.49423	−	0.862694i
$250$		0			0
$251$			21.8184i			1.37716i	0.725159	+	0.688581i	$0.241766\pi$
$251$			21.8184i			1.37716i	−0.725159	+	0.688581i	$0.758234\pi$
$252$		0			0
$253$	−0.388159	+	0.388159i	−0.0244033	+	0.0244033i
$254$		0			0
$255$	−9.38525	+	7.61590i	−0.587727	+	0.476926i
$256$		0			0
$257$	3.79997	+	1.01820i	0.237036	+	0.0635136i	0.375381	−	0.926870i	$-0.377512\pi$
$257$	3.79997	+	1.01820i	0.237036	+	0.0635136i	−0.138345	+	0.990384i	$0.544178\pi$
$258$		0			0
$259$	0.240762	−	0.0536645i	0.0149602	−	0.00333455i
$260$		0			0
$261$	−0.179929	−	0.311646i	−0.0111373	−	0.0192904i
$262$		0			0
$263$	−3.71862	−	13.8781i	−0.229300	−	0.855759i	−0.980636	−	0.195839i	$-0.937257\pi$
$263$	−3.71862	−	13.8781i	−0.229300	−	0.855759i	0.751336	−	0.659920i	$-0.229410\pi$
$264$		0			0
$265$	−15.4740	+	6.90843i	−0.950563	+	0.424382i
$266$		0			0
$267$	−10.9012	−	10.9012i	−0.667142	−	0.667142i
$268$		0			0
$269$	−9.12700	+	15.8084i	−0.556483	+	0.963857i	0.441303	+	0.897358i	$0.354516\pi$
$269$	−9.12700	+	15.8084i	−0.556483	+	0.963857i	−0.997786	+	0.0664991i	$0.978817\pi$
$270$		0			0
$271$	−21.4793	+	12.4011i	−1.30478	+	0.753313i	−0.981219	−	0.192895i	$-0.938212\pi$
$271$	−21.4793	+	12.4011i	−1.30478	+	0.753313i	−0.323558	+	0.946208i	$0.604879\pi$
$272$		0			0
$273$	−0.271489	+	6.38557i	−0.0164312	+	0.386472i
$274$		0			0
$275$	−0.132778	+	0.631006i	−0.00800682	+	0.0380511i
$276$		0			0
$277$	−9.26511	+	2.48258i	−0.556687	+	0.149164i	−0.526184	−	0.850371i	$-0.676378\pi$
$277$	−9.26511	+	2.48258i	−0.556687	+	0.149164i	−0.0305030	+	0.999535i	$0.509711\pi$
$278$		0			0
$279$	−21.4686			−1.28529
$280$		0			0
$281$	8.86881			0.529069			0.264534	−	0.964376i	$-0.414782\pi$
$281$	8.86881			0.529069			0.264534	+	0.964376i	$0.414782\pi$
$282$		0			0
$283$	8.61070	−	2.30723i	0.511853	−	0.137151i	0.00635749	−	0.999980i	$-0.497976\pi$
$283$	8.61070	−	2.30723i	0.511853	−	0.137151i	0.505496	+	0.862829i	$0.331310\pi$
$284$		0			0
$285$	22.8176	−	31.4733i	1.35160	−	1.86432i
$286$		0			0
$287$	28.1130	−	14.6755i	1.65946	−	0.866270i
$288$		0			0
$289$	9.86090	−	5.69319i	0.580053	−	0.334894i
$290$		0			0
$291$	15.5087	−	26.8619i	0.909136	−	1.57467i
$292$		0			0
$293$	2.13912	+	2.13912i	0.124969	+	0.124969i	0.766825	−	0.641856i	$-0.221835\pi$
$293$	2.13912	+	2.13912i	0.124969	+	0.124969i	−0.641856	+	0.766825i	$0.721835\pi$
$294$		0			0
$295$	−17.2706	−	6.60932i	−1.00553	−	0.384810i
$296$		0			0
$297$	−0.0605644	−	0.226030i	−0.00351431	−	0.0131156i
$298$		0			0
$299$	2.25356	+	3.90329i	0.130327	+	0.225733i
$300$		0			0
$301$	−9.88677	−	3.10487i	−0.569864	−	0.178962i
$302$		0			0
$303$	24.2255	+	6.49119i	1.39172	+	0.372909i
$304$		0			0
$305$	18.7284	+	23.0794i	1.07238	+	1.32152i
$306$		0			0
$307$	−9.58335	+	9.58335i	−0.546950	+	0.546950i	−0.925558	−	0.378607i	$-0.876403\pi$
$307$	−9.58335	+	9.58335i	−0.546950	+	0.546950i	0.378607	+	0.925558i	$0.376403\pi$
$308$		0			0
$309$			18.2582i			1.03867i
$310$		0			0
$311$	−21.2979	−	12.2964i	−1.20769	−	0.697262i	−0.245439	−	0.969412i	$-0.578932\pi$
$311$	−21.2979	−	12.2964i	−1.20769	−	0.697262i	−0.962255	+	0.272150i	$0.912265\pi$
$312$		0			0
$313$	1.25975	−	4.70147i	0.0712055	−	0.265743i	−0.921141	−	0.389230i	$-0.872741\pi$
$313$	1.25975	−	4.70147i	0.0712055	−	0.265743i	0.992346	+	0.123487i	$0.0394078\pi$
$314$		0			0
$315$	5.17496	−	11.9724i	0.291576	−	0.674567i
$316$		0			0
$317$	0.439298	−	1.63948i	0.0246734	−	0.0920824i	−0.952491	−	0.304566i	$-0.901489\pi$
$317$	0.439298	−	1.63948i	0.0246734	−	0.0920824i	0.977165	+	0.212484i	$0.0681552\pi$
$318$		0			0
$319$	−0.0182302	−	0.0105252i	−0.00102070	−	0.000589300i
$320$		0			0
$321$		−	39.7798i		−	2.22029i
$322$		0			0
$323$	12.7670	−	12.7670i	0.710373	−	0.710373i
$324$		0			0
$325$	4.72224	+	2.39397i	0.261943	+	0.132793i
$326$		0			0
$327$	22.2808	+	5.97013i	1.23213	+	0.330149i
$328$		0			0
$329$	−1.32984	−	5.96624i	−0.0733163	−	0.328929i
$330$		0			0
$331$	5.56877	+	9.64540i	0.306087	+	0.530159i	0.977503	−	0.210922i	$-0.0676467\pi$
$331$	5.56877	+	9.64540i	0.306087	+	0.530159i	−0.671415	+	0.741081i	$0.734313\pi$
$332$		0			0
$333$	−0.0531993	−	0.198542i	−0.00291530	−	0.0108801i
$334$		0			0
$335$	6.46157	+	14.4731i	0.353033	+	0.790751i
$336$		0			0
$337$	−4.23464	−	4.23464i	−0.230675	−	0.230675i	0.582299	−	0.812975i	$-0.302153\pi$
$337$	−4.23464	−	4.23464i	−0.230675	−	0.230675i	−0.812975	+	0.582299i	$0.802153\pi$
$338$		0			0
$339$	−8.11162	+	14.0497i	−0.440562	+	0.763077i
$340$		0			0
$341$	−1.08759	+	0.627919i	−0.0588962	+	0.0340037i
$342$		0			0
$343$	−18.3700	−	2.35441i	−0.991887	−	0.127126i
$344$		0			0
$345$	−3.41867	−	21.4429i	−0.184055	−	1.15445i
$346$		0			0
$347$	13.1621	−	3.52677i	0.706578	−	0.189327i	0.112403	−	0.993663i	$-0.464145\pi$
$347$	13.1621	−	3.52677i	0.706578	−	0.189327i	0.594175	+	0.804336i	$0.297479\pi$
$348$		0			0
$349$	−5.43385			−0.290868			−0.145434	−	0.989368i	$-0.546458\pi$
$349$	−5.43385			−0.290868			−0.145434	+	0.989368i	$0.546458\pi$
$350$		0			0
$351$	−1.92131			−0.102552
$352$		0			0
$353$	−18.5104	+	4.95984i	−0.985208	+	0.263986i	−0.715236	−	0.698883i	$-0.753681\pi$
$353$	−18.5104	+	4.95984i	−0.985208	+	0.263986i	−0.269971	+	0.962868i	$0.587014\pi$
$354$		0			0
$355$	−3.34552	−	20.9841i	−0.177562	−	1.11372i
$356$		0			0
$357$	7.67014	−	12.0701i	0.405947	−	0.638818i
$358$		0			0
$359$	11.0456	−	6.37716i	0.582963	−	0.336574i	−0.179347	−	0.983786i	$-0.557399\pi$
$359$	11.0456	−	6.37716i	0.582963	−	0.336574i	0.762310	+	0.647212i	$0.224065\pi$
$360$		0			0
$361$	−19.5357	+	33.8368i	−1.02819	+	1.78089i
$362$		0			0
$363$	−17.7181	−	17.7181i	−0.929958	−	0.929958i
$364$		0			0
$365$	−1.70260	−	3.81363i	−0.0891184	−	0.199614i
$366$		0			0
$367$	6.73979	+	25.1532i	0.351814	+	1.31299i	0.884446	+	0.466642i	$0.154536\pi$
$367$	6.73979	+	25.1532i	0.351814	+	1.31299i	−0.532632	+	0.846347i	$0.678797\pi$
$368$		0			0
$369$	−13.2129	−	22.8854i	−0.687837	−	1.19137i
$370$		0			0
$371$	14.7676	−	13.5631i	0.766698	−	0.704162i
$372$		0			0
$373$	−11.3666	−	3.04568i	−0.588542	−	0.157699i	−0.0477550	−	0.998859i	$-0.515207\pi$
$373$	−11.3666	−	3.04568i	−0.588542	−	0.157699i	−0.540787	+	0.841160i	$0.681873\pi$
$374$		0			0
$375$	−17.1252	−	18.9027i	−0.884340	−	0.976129i
$376$		0			0
$377$	−0.122214	+	0.122214i	−0.00629435	+	0.00629435i
$378$		0			0
$379$		−	1.54915i		−	0.0795746i	−0.999208	−	0.0397873i	$-0.987332\pi$
$379$		−	1.54915i		−	0.0795746i	0.999208	−	0.0397873i	$-0.0126680\pi$
$380$		0			0
$381$	1.59397	+	0.920281i	0.0816617	+	0.0471474i
$382$		0			0
$383$	−7.38345	+	27.5554i	−0.377276	+	1.40802i	0.472713	+	0.881216i	$0.343275\pi$
$383$	−7.38345	+	27.5554i	−0.377276	+	1.40802i	−0.849990	+	0.526799i	$0.823392\pi$
$384$		0			0
$385$	−0.0880104	−	0.757873i	−0.00448543	−	0.0386248i
$386$		0			0
$387$	−2.23495	+	8.34094i	−0.113609	+	0.423994i
$388$		0			0
$389$	−2.08747	−	1.20520i	−0.105839	−	0.0611061i	0.446146	−	0.894960i	$-0.352796\pi$
$389$	−2.08747	−	1.20520i	−0.105839	−	0.0611061i	−0.551985	+	0.833854i	$0.686129\pi$
$390$		0			0
$391$		−	10.0850i		−	0.510019i
$392$		0			0
$393$	−5.37595	+	5.37595i	−0.271181	+	0.271181i
$394$		0			0
$395$	−13.8006	−	17.0067i	−0.694382	−	0.855702i
$396$		0			0
$397$	5.08642	+	1.36290i	0.255280	+	0.0684021i	0.384189	−	0.923254i	$-0.374481\pi$
$397$	5.08642	+	1.36290i	0.255280	+	0.0684021i	−0.128909	+	0.991656i	$0.541148\pi$
$398$		0			0
$399$	−13.7813	+	43.8836i	−0.689929	+	2.19693i
$400$		0			0
$401$	−4.96411	−	8.59809i	−0.247896	−	0.429368i	0.715046	−	0.699077i	$-0.246406\pi$
$401$	−4.96411	−	8.59809i	−0.247896	−	0.429368i	−0.962942	+	0.269709i	$0.913072\pi$
$402$		0			0
$403$	2.66873	+	9.95985i	0.132939	+	0.496135i
$404$		0			0
$405$	22.4572	+	8.59420i	1.11591	+	0.427049i
$406$		0			0
$407$	−0.00850207	−	0.00850207i	−0.000421432	−	0.000421432i
$408$		0			0
$409$	5.32115	−	9.21650i	0.263114	−	0.455727i	−0.703954	−	0.710246i	$-0.748584\pi$
$409$	5.32115	−	9.21650i	0.263114	−	0.455727i	0.967068	+	0.254519i	$0.0819172\pi$
$410$		0			0
$411$	−30.9864	+	17.8900i	−1.52844	+	0.882448i
$412$		0			0
$413$	21.8603	+	0.929414i	1.07568	+	0.0457335i
$414$		0			0
$415$	15.6633	−	21.6050i	0.768881	−	1.06055i
$416$		0			0
$417$	2.88790	−	0.773812i	0.141421	−	0.0378937i
$418$		0			0
$419$	−0.608681			−0.0297360			−0.0148680	−	0.999889i	$-0.504733\pi$
$419$	−0.608681			−0.0297360			−0.0148680	+	0.999889i	$0.504733\pi$
$420$		0			0
$421$	16.0504			0.782249			0.391125	−	0.920338i	$-0.372086\pi$
$421$	16.0504			0.782249			0.391125	+	0.920338i	$0.372086\pi$
$422$		0			0
$423$	−4.92000	+	1.31831i	−0.239219	+	0.0640984i
$424$		0			0
$425$	−6.47236	−	9.92215i	−0.313956	−	0.481295i
$426$		0			0
$427$	−29.6818	−	18.8617i	−1.43640	−	0.912784i
$428$		0			0
$429$	0.269802	−	0.155770i	0.0130261	−	0.00752065i
$430$		0			0
$431$	8.71860	−	15.1011i	0.419960	−	0.727393i	−0.575975	−	0.817468i	$-0.695377\pi$
$431$	8.71860	−	15.1011i	0.419960	−	0.727393i	0.995935	+	0.0900749i	$0.0287106\pi$
$432$		0			0
$433$	−6.77089	−	6.77089i	−0.325388	−	0.325388i	0.525442	−	0.850830i	$-0.323900\pi$
$433$	−6.77089	−	6.77089i	−0.325388	−	0.325388i	−0.850830	+	0.525442i	$0.823900\pi$
$434$		0			0
$435$	0.760332	−	0.339453i	0.0364552	−	0.0162755i
$436$		0			0
$437$	8.39519	+	31.3313i	0.401596	+	1.49878i
$438$		0			0
$439$	13.4260	+	23.2545i	0.640788	+	1.10988i	0.985257	+	0.171080i	$0.0547257\pi$
$439$	13.4260	+	23.2545i	0.640788	+	1.10988i	−0.344469	+	0.938798i	$0.611941\pi$
$440$		0			0
$441$	−1.30990	+	15.3769i	−0.0623761	+	0.732234i
$442$		0			0
$443$	−22.3427	−	5.98671i	−1.06153	−	0.284437i	−0.314523	−	0.949250i	$-0.601845\pi$
$443$	−22.3427	−	5.98671i	−1.06153	−	0.284437i	−0.747010	+	0.664813i	$0.768511\pi$
$444$		0			0
$445$	11.7333	−	9.52131i	0.556213	−	0.451354i
$446$		0			0
$447$	−17.3568	+	17.3568i	−0.820947	+	0.820947i
$448$		0			0
$449$		−	36.7511i		−	1.73439i	−0.497966	−	0.867197i	$-0.665920\pi$
$449$		−	36.7511i		−	1.73439i	0.497966	−	0.867197i	$-0.334080\pi$
$450$		0			0
$451$	−1.33872	−	0.772910i	−0.0630378	−	0.0363949i
$452$		0			0
$453$	1.63421	−	6.09894i	0.0767818	−	0.286553i
$454$		0			0
$455$	−6.19759	−	0.912530i	−0.290548	−	0.0427801i
$456$		0			0
$457$	4.08547	−	15.2472i	0.191110	−	0.713233i	−0.802129	−	0.597150i	$-0.796300\pi$
$457$	4.08547	−	15.2472i	0.191110	−	0.713233i	0.993240	−	0.116083i	$-0.0370337\pi$
$458$		0			0
$459$	3.72308	+	2.14952i	0.173778	+	0.100331i
$460$		0			0
$461$			27.9309i			1.30087i	0.759561	+	0.650436i	$0.225414\pi$
$461$			27.9309i			1.30087i	−0.759561	+	0.650436i	$0.774586\pi$
$462$		0			0
$463$	−15.2033	+	15.2033i	−0.706558	+	0.706558i	−0.965810	−	0.259252i	$-0.916524\pi$
$463$	−15.2033	+	15.2033i	−0.706558	+	0.706558i	0.259252	+	0.965810i	$0.416524\pi$
$464$		0			0
$465$	5.14207	−	49.4088i	0.238458	−	2.29128i
$466$		0			0
$467$	−3.29912	−	0.883995i	−0.152665	−	0.0409064i	0.181677	−	0.983358i	$-0.441847\pi$
$467$	−3.29912	−	0.883995i	−0.152665	−	0.0409064i	−0.334342	+	0.942452i	$0.608514\pi$
$468$		0			0
$469$	−12.6858	−	13.8124i	−0.585776	−	0.637798i
$470$		0			0
$471$	27.2450	+	47.1897i	1.25538	+	2.17439i
$472$		0			0
$473$	0.130737	+	0.487916i	0.00601128	+	0.0224344i
$474$		0			0
$475$	28.3675	+	25.4375i	1.30159	+	1.16715i
$476$		0			0
$477$	−11.8144	−	11.8144i	−0.540945	−	0.540945i
$478$		0			0
$479$	8.86000	−	15.3460i	0.404824	−	0.701176i	−0.589477	−	0.807785i	$-0.700666\pi$
$479$	8.86000	−	15.3460i	0.404824	−	0.701176i	0.994301	+	0.106610i	$0.0339995\pi$
$480$		0			0
$481$	−0.0854959	+	0.0493611i	−0.00389828	+	0.00225067i
$482$		0			0
$483$	11.8893	+	22.7755i	0.540982	+	1.03632i
$484$		0			0
$485$	24.6135	+	17.8444i	1.11764	+	0.810272i
$486$		0			0
$487$	13.5674	−	3.63537i	0.614797	−	0.164734i	0.0620356	−	0.998074i	$-0.480241\pi$
$487$	13.5674	−	3.63537i	0.614797	−	0.164734i	0.552761	+	0.833340i	$0.313574\pi$
$488$		0			0
$489$	24.6964			1.11681
$490$		0			0
$491$	16.9628			0.765519			0.382759	−	0.923848i	$-0.374974\pi$
$491$	16.9628			0.765519			0.382759	+	0.923848i	$0.374974\pi$
$492$		0			0
$493$	0.373556	−	0.100094i	0.0168241	−	0.00450800i
$494$		0			0
$495$	−0.627837	+	0.100097i	−0.0282192	+	0.00449902i
$496$		0			0
$497$	11.6349	+	22.2882i	0.521896	+	0.999761i
$498$		0			0
$499$	15.8081	−	9.12684i	0.707670	−	0.408573i	−0.102528	−	0.994730i	$-0.532693\pi$
$499$	15.8081	−	9.12684i	0.707670	−	0.408573i	0.810198	+	0.586157i	$0.199360\pi$
$500$		0			0
$501$	−9.44247	+	16.3548i	−0.421858	+	0.730680i
$502$		0			0
$503$	−9.44510	−	9.44510i	−0.421136	−	0.421136i	0.464459	−	0.885595i	$-0.346249\pi$
$503$	−9.44510	−	9.44510i	−0.421136	−	0.421136i	−0.885595	+	0.464459i	$0.846249\pi$
$504$		0			0
$505$	−8.78596	+	22.9583i	−0.390970	+	1.02163i
$506$		0			0
$507$	7.01397	+	26.1765i	0.311501	+	1.16254i
$508$		0			0
$509$	5.59042	+	9.68290i	0.247791	+	0.429187i	0.962913	−	0.269813i	$-0.0869620\pi$
$509$	5.59042	+	9.68290i	0.247791	+	0.429187i	−0.715121	+	0.699000i	$0.753629\pi$
$510$		0			0
$511$	3.34268	+	3.63953i	0.147871	+	0.161003i
$512$		0			0
$513$	−13.3560	−	3.57872i	−0.589680	−	0.158004i
$514$		0			0
$515$	−17.7994	−	1.85242i	−0.784337	−	0.0816275i
$516$		0			0
$517$	−0.210686	+	0.210686i	−0.00926598	+	0.00926598i
$518$		0			0
$519$		−	23.5053i		−	1.03177i
$520$		0			0
$521$	18.3874	+	10.6160i	0.805568	+	0.465095i	0.845414	−	0.534111i	$-0.179354\pi$
$521$	18.3874	+	10.6160i	0.805568	+	0.465095i	−0.0398466	+	0.999206i	$0.512687\pi$
$522$		0			0
$523$	−1.69368	+	6.32091i	−0.0740595	+	0.276394i	−0.993018	−	0.117959i	$-0.962365\pi$
$523$	−1.69368	+	6.32091i	−0.0740595	+	0.276394i	0.918959	+	0.394353i	$0.129031\pi$
$524$		0			0
$525$	26.3143	+	14.7775i	1.14845	+	0.644941i
$526$		0			0
$527$	5.97146	−	22.2858i	0.260121	−	0.970784i
$528$		0			0
$529$	−4.22807	−	2.44108i	−0.183829	−	0.106134i
$530$		0			0
$531$		−	18.2323i		−	0.791213i
$532$		0			0
$533$	−8.97467	+	8.97467i	−0.388736	+	0.388736i
$534$		0			0
$535$	38.7804	+	4.03595i	1.67662	+	0.174489i
$536$		0			0
$537$	4.87973	+	1.30752i	0.210576	+	0.0564236i
$538$		0			0
$539$	0.383389	+	0.817299i	0.0165138	+	0.0352036i
$540$		0			0
$541$	−5.87899	−	10.1827i	−0.252757	−	0.437789i	0.711527	−	0.702659i	$-0.248004\pi$
$541$	−5.87899	−	10.1827i	−0.252757	−	0.437789i	−0.964284	+	0.264870i	$0.914671\pi$
$542$		0			0
$543$	4.48236	+	16.7284i	0.192356	+	0.717884i
$544$		0			0
$545$	−8.08069	+	21.1153i	−0.346139	+	0.904482i
$546$		0			0
$547$	24.0098	+	24.0098i	1.02658	+	1.02658i	0.999637	+	0.0269473i	$0.00857865\pi$
$547$	24.0098	+	24.0098i	1.02658	+	1.02658i	0.0269473	+	0.999637i	$0.491421\pi$
$548$		0			0
$549$	−14.6524	+	25.3786i	−0.625348	+	1.08313i
$550$		0			0
$551$	−1.07721	+	0.621930i	−0.0458908	+	0.0264951i
$552$		0			0
$553$	21.8719	+	13.8988i	0.930089	+	0.591039i
$554$		0			0
$555$	0.469677	−	0.0748812i	0.0199367	−	0.00317853i
$556$		0			0
$557$	31.0663	−	8.32418i	1.31632	−	0.352707i	0.468722	−	0.883346i	$-0.344715\pi$
$557$	31.0663	−	8.32418i	1.31632	−	0.352707i	0.847598	+	0.530639i	$0.178048\pi$
$558$		0			0
$559$	4.14740			0.175416
$560$		0			0
$561$	−0.697090			−0.0294312
$562$		0			0
$563$	31.4838	−	8.43607i	1.32689	−	0.355538i	0.475333	−	0.879806i	$-0.342328\pi$
$563$	31.4838	−	8.43607i	1.32689	−	0.355538i	0.851553	+	0.524268i	$0.175661\pi$
$564$		0			0
$565$	−12.8738	−	9.33327i	−0.541604	−	0.392654i
$566$		0			0
$567$	−28.4253	−	1.20853i	−1.19375	−	0.0507535i
$568$		0			0
$569$	−2.61511	+	1.50983i	−0.109631	+	0.0632955i	−0.553813	−	0.832641i	$-0.686828\pi$
$569$	−2.61511	+	1.50983i	−0.109631	+	0.0632955i	0.444182	+	0.895937i	$0.353494\pi$
$570$		0			0
$571$	−8.68176	+	15.0372i	−0.363320	+	0.629289i	−0.988505	−	0.151188i	$-0.951690\pi$
$571$	−8.68176	+	15.0372i	−0.363320	+	0.629289i	0.625185	+	0.780477i	$0.285024\pi$
$572$		0			0
$573$	−1.34845	−	1.34845i	−0.0563324	−	0.0563324i
$574$		0			0
$575$	21.2510	−	1.15724i	0.886230	−	0.0482604i
$576$		0			0
$577$	0.546530	+	2.03968i	0.0227523	+	0.0849129i	0.976368	−	0.216112i	$-0.0693378\pi$
$577$	0.546530	+	2.03968i	0.0227523	+	0.0849129i	−0.953616	+	0.301025i	$0.902671\pi$
$578$		0			0
$579$	−22.5576	−	39.0709i	−0.937463	−	1.62373i
$580$		0			0
$581$	−9.46028	+	30.1242i	−0.392478	+	1.24976i
$582$		0			0
$583$	−0.944064	−	0.252961i	−0.0390992	−	0.0104766i
$584$		0			0
$585$	−0.540340	+	5.19198i	−0.0223403	+	0.214662i
$586$		0			0
$587$	30.8860	−	30.8860i	1.27480	−	1.27480i	0.331265	−	0.943538i	$-0.392525\pi$
$587$	30.8860	−	30.8860i	1.27480	−	1.27480i	0.943538	−	0.331265i	$-0.107475\pi$
$588$		0			0
$589$			74.2068i			3.05764i
$590$		0			0
$591$	26.7610	+	15.4505i	1.10080	+	0.635547i
$592$		0			0
$593$	−1.98009	+	7.38980i	−0.0813126	+	0.303463i	−0.994590	−	0.103875i	$-0.966876\pi$
$593$	−1.98009	+	7.38980i	−0.0813126	+	0.303463i	0.913278	+	0.407337i	$0.133543\pi$
$594$		0			0
$595$	10.9887	+	8.70204i	0.450492	+	0.356749i
$596$		0			0
$597$	−11.9707	+	44.6752i	−0.489927	+	1.82843i
$598$		0			0
$599$	−37.2778	−	21.5223i	−1.52313	−	0.879379i	−0.999626	−	0.0273556i	$-0.991291\pi$
$599$	−37.2778	−	21.5223i	−1.52313	−	0.879379i	−0.523504	−	0.852024i	$-0.675375\pi$
$600$		0			0
$601$			8.27437i			0.337518i	0.985657	+	0.168759i	$0.0539760\pi$
$601$			8.27437i			0.337518i	−0.985657	+	0.168759i	$0.946024\pi$
$602$		0			0
$603$	−11.0502	+	11.0502i	−0.450000	+	0.450000i
$604$		0			0
$605$	19.0706	−	15.4753i	0.775329	−	0.629161i
$606$		0			0
$607$	−15.3300	−	4.10766i	−0.622225	−	0.166725i	−0.0660860	−	0.997814i	$-0.521051\pi$
$607$	−15.3300	−	4.10766i	−0.622225	−	0.166725i	−0.556139	+	0.831089i	$0.687718\pi$
$608$		0			0
$609$	−0.725622	+	0.666438i	−0.0294037	+	0.0270054i
$610$		0			0
$611$	1.22320	+	2.11864i	0.0494853	+	0.0857110i
$612$		0			0
$613$	−4.85413	−	18.1158i	−0.196056	−	0.731692i	−0.991991	−	0.126309i	$-0.959687\pi$
$613$	−4.85413	−	18.1158i	−0.196056	−	0.731692i	0.795935	−	0.605383i	$-0.206980\pi$
$614$		0			0
$615$	55.8343	−	24.9274i	2.25145	−	1.00517i
$616$		0			0
$617$	−18.1371	−	18.1371i	−0.730172	−	0.730172i	0.240482	−	0.970654i	$-0.422695\pi$
$617$	−18.1371	−	18.1371i	−0.730172	−	0.730172i	−0.970654	+	0.240482i	$0.922695\pi$
$618$		0			0
$619$	−1.78199	+	3.08650i	−0.0716243	+	0.124057i	−0.899613	−	0.436687i	$-0.856152\pi$
$619$	−1.78199	+	3.08650i	−0.0716243	+	0.124057i	0.827989	+	0.560744i	$0.189485\pi$
$620$		0			0
$621$	−6.68858	+	3.86165i	−0.268404	+	0.154963i
$622$		0			0
$623$	−9.58911	+	15.0899i	−0.384180	+	0.604565i
$624$		0			0
$625$	20.1652	−	14.7771i	0.806610	−	0.591085i
$626$		0			0
$627$	2.16567	−	0.580290i	0.0864886	−	0.0231745i
$628$		0			0
$629$	0.220897			0.00880774
$630$		0			0
$631$	3.53048			0.140546			0.0702731	−	0.997528i	$-0.477613\pi$
$631$	3.53048			0.140546			0.0702731	+	0.997528i	$0.477613\pi$
$632$		0			0
$633$	−17.9485	+	4.80929i	−0.713389	+	0.191152i
$634$		0			0
$635$	−1.05888	+	1.46056i	−0.0420204	+	0.0579605i
$636$		0			0
$637$	7.29659	−	1.30379i	0.289101	−	0.0516580i
$638$		0			0
$639$	18.1438	−	10.4753i	0.717756	−	0.414397i
$640$		0			0
$641$	15.7198	−	27.2275i	0.620894	−	1.07542i	−0.368425	−	0.929657i	$-0.620103\pi$
$641$	15.7198	−	27.2275i	0.620894	−	1.07542i	0.989320	−	0.145763i	$-0.0465637\pi$
$642$		0			0
$643$	−32.1065	−	32.1065i	−1.26616	−	1.26616i	−0.948058	−	0.318098i	$-0.896956\pi$
$643$	−32.1065	−	32.1065i	−1.26616	−	1.26616i	−0.318098	−	0.948058i	$-0.603044\pi$
$644$		0			0
$645$	−18.6609	−	7.14140i	−0.734772	−	0.281192i
$646$		0			0
$647$	−6.19921	−	23.1358i	−0.243716	−	0.909561i	−0.974024	−	0.226443i	$-0.927290\pi$
$647$	−6.19921	−	23.1358i	−0.243716	−	0.909561i	0.730308	−	0.683118i	$-0.239376\pi$
$648$		0			0
$649$	−0.533263	−	0.923638i	−0.0209324	−	0.0362560i
$650$		0			0
$651$	12.7872	+	57.3692i	0.501172	+	2.24848i
$652$		0			0
$653$	−39.3513	−	10.5442i	−1.53994	−	0.412625i	−0.613691	−	0.789546i	$-0.710316\pi$
$653$	−39.3513	−	10.5442i	−1.53994	−	0.412625i	−0.926245	+	0.376921i	$0.876983\pi$
$654$		0			0
$655$	−4.69546	−	5.78632i	−0.183467	−	0.226090i
$656$		0			0
$657$	2.91170	−	2.91170i	0.113596	−	0.113596i
$658$		0			0
$659$			32.0510i			1.24853i	0.781212	+	0.624266i	$0.214602\pi$
$659$			32.0510i			1.24853i	−0.781212	+	0.624266i	$0.785398\pi$
$660$		0			0
$661$	−2.69967	−	1.55865i	−0.105005	−	0.0606246i	0.446578	−	0.894745i	$-0.352643\pi$
$661$	−2.69967	−	1.55865i	−0.105005	−	0.0606246i	−0.551583	+	0.834120i	$0.685976\pi$
$662$		0			0
$663$	−1.48136	+	5.52851i	−0.0575312	+	0.214709i
$664$		0			0
$665$	−41.3829	−	17.8874i	−1.60476	−	0.693643i
$666$		0			0
$667$	−0.179821	+	0.671100i	−0.00696268	+	0.0259851i
$668$		0			0
$669$	23.0202	+	13.2907i	0.890013	+	0.513849i
$670$		0			0
$671$			1.71423i			0.0661769i
$672$		0			0
$673$	3.60859	−	3.60859i	0.139101	−	0.139101i	−0.634127	−	0.773229i	$-0.718641\pi$
$673$	3.60859	−	3.60859i	0.139101	−	0.139101i	0.773229	+	0.634127i	$0.218641\pi$
$674$		0			0
$675$	−4.10225	+	8.09192i	−0.157896	+	0.311458i
$676$		0			0
$677$	−30.5704	−	8.19130i	−1.17491	−	0.314817i	−0.382007	−	0.924160i	$-0.624767\pi$
$677$	−30.5704	−	8.19130i	−1.17491	−	0.314817i	−0.792907	+	0.609342i	$0.791434\pi$
$678$		0			0
$679$	−34.3189	−	10.7776i	−1.31704	−	0.413607i
$680$		0			0
$681$	0.737167	+	1.27681i	0.0282483	+	0.0489275i
$682$		0			0
$683$	5.19321	+	19.3813i	0.198713	+	0.741605i	0.991274	+	0.131814i	$0.0420801\pi$
$683$	5.19321	+	19.3813i	0.198713	+	0.741605i	−0.792562	+	0.609791i	$0.791253\pi$
$684$		0			0
$685$	−14.2967	−	32.0229i	−0.546250	−	1.22353i
$686$		0			0
$687$	−33.9846	−	33.9846i	−1.29659	−	1.29659i
$688$		0			0
$689$	−4.01239	+	6.94966i	−0.152860	+	0.264761i
$690$		0			0
$691$	−18.6151	+	10.7475i	−0.708153	+	0.408853i	−0.810377	−	0.585909i	$-0.800738\pi$
$691$	−18.6151	+	10.7475i	−0.708153	+	0.408853i	0.102224	+	0.994761i	$0.467404\pi$
$692$		0			0
$693$	0.666856	−	0.348112i	0.0253318	−	0.0132237i
$694$		0			0
$695$	0.461372	+	2.89386i	0.0175008	+	0.109770i
$696$		0			0
$697$	27.4317	−	7.35030i	1.03905	−	0.278412i
$698$		0			0
$699$	39.2512			1.48462
$700$		0			0
$701$	42.9302			1.62145			0.810725	−	0.585427i	$-0.199073\pi$
$701$	42.9302			1.62145			0.810725	+	0.585427i	$0.199073\pi$
$702$		0			0
$703$	−0.686267	+	0.183885i	−0.0258831	+	0.00693535i
$704$		0			0
$705$	−1.85560	−	11.6389i	−0.0698860	−	0.438345i
$706$		0			0
$707$	1.23550	−	29.0596i	0.0464656	−	1.09290i
$708$		0			0
$709$	5.69705	−	3.28920i	0.213957	−	0.123528i	−0.389192	−	0.921157i	$-0.627246\pi$
$709$	5.69705	−	3.28920i	0.213957	−	0.123528i	0.603149	+	0.797628i	$0.293912\pi$
$710$		0			0
$711$	10.7970	−	18.7010i	0.404920	−	0.701342i
$712$		0			0
$713$	29.3090	+	29.3090i	1.09763	+	1.09763i
$714$		0			0
$715$	0.124483	+	0.278827i	0.00465541	+	0.0104276i
$716$		0			0
$717$	−2.95570	−	11.0308i	−0.110383	−	0.411953i
$718$		0			0
$719$	−17.4761	−	30.2695i	−0.651748	−	1.12886i	−0.982699	−	0.185212i	$-0.940703\pi$
$719$	−17.4761	−	30.2695i	−0.651748	−	1.12886i	0.330951	−	0.943648i	$-0.392631\pi$
$720$		0			0
$721$	20.6672	−	4.60659i	0.769685	−	0.171558i
$722$		0			0
$723$	−44.6411	−	11.9616i	−1.66022	−	0.444855i
$724$		0			0
$725$	0.253783	+	0.775670i	0.00942526	+	0.0288077i
$726$		0			0
$727$	−24.4451	+	24.4451i	−0.906619	+	0.906619i	−0.995998	−	0.0893785i	$-0.971512\pi$
$727$	−24.4451	+	24.4451i	−0.906619	+	0.906619i	0.0893785	+	0.995998i	$0.471512\pi$
$728$		0			0
$729$			11.2892i			0.418120i
$730$		0			0
$731$	−8.03678	−	4.64004i	−0.297251	−	0.171618i
$732$		0			0
$733$	1.88621	−	7.03942i	0.0696686	−	0.260007i	−0.922303	−	0.386468i	$-0.873695\pi$
$733$	1.88621	−	7.03942i	0.0696686	−	0.260007i	0.991972	+	0.126461i	$0.0403618\pi$
$734$		0			0
$735$	−35.0754	−	6.69767i	−1.29377	−	0.247047i
$736$		0			0
$737$	−0.236599	+	0.882999i	−0.00871523	+	0.0325257i
$738$		0			0
$739$	44.2240	+	25.5327i	1.62680	+	0.939236i	0.985038	+	0.172336i	$0.0551316\pi$
$739$	44.2240	+	25.5327i	1.62680	+	0.939236i	0.641767	+	0.766900i	$0.278202\pi$
$740$		0			0
$741$		−	18.4087i		−	0.676261i
$742$		0			0
$743$	−12.2443	+	12.2443i	−0.449200	+	0.449200i	−0.895089	−	0.445888i	$-0.852888\pi$
$743$	−12.2443	+	12.2443i	−0.449200	+	0.449200i	0.445888	+	0.895089i	$0.352888\pi$
$744$		0			0
$745$	−15.1597	−	18.6817i	−0.555410	−	0.684444i
$746$		0			0
$747$	25.4141	+	6.80970i	0.929854	+	0.249154i
$748$		0			0
$749$	−45.0284	+	10.0366i	−1.64530	+	0.366728i
$750$		0			0
$751$	−16.1555	−	27.9821i	−0.589521	−	1.02108i	−0.994295	−	0.106664i	$-0.965983\pi$
$751$	−16.1555	−	27.9821i	−0.589521	−	1.02108i	0.404774	−	0.914417i	$-0.367350\pi$
$752$		0			0
$753$	−12.8829	−	48.0797i	−0.469480	−	1.75212i
$754$		0			0
$755$	5.77992	+	2.21193i	0.210353	+	0.0805005i
$756$		0			0
$757$	−25.7314	−	25.7314i	−0.935223	−	0.935223i	0.0628033	−	0.998026i	$-0.479996\pi$
$757$	−25.7314	−	25.7314i	−0.935223	−	0.935223i	−0.998026	+	0.0628033i	$0.979996\pi$
$758$		0			0
$759$	0.626168	−	1.08455i	0.0227285	−	0.0393668i
$760$		0			0
$761$	−31.3036	+	18.0731i	−1.13475	+	0.655151i	−0.945126	−	0.326705i	$-0.894062\pi$
$761$	−31.3036	+	18.0731i	−1.13475	+	0.655151i	−0.189629	+	0.981856i	$0.560728\pi$
$762$		0			0
$763$	1.13632	−	26.7269i	0.0411376	−	0.967578i
$764$		0			0
$765$	6.85576	−	9.45643i	0.247870	−	0.341898i
$766$		0			0
$767$	−8.45843	+	2.26643i	−0.305416	+	0.0818361i
$768$		0			0
$769$	30.4018			1.09632			0.548159	−	0.836374i	$-0.315329\pi$
$769$	30.4018			1.09632			0.548159	+	0.836374i	$0.315329\pi$
$770$		0			0
$771$	−8.97497			−0.323226
$772$		0			0
$773$	21.5840	−	5.78340i	0.776321	−	0.208015i	0.151159	−	0.988509i	$-0.451700\pi$
$773$	21.5840	−	5.78340i	0.776321	−	0.208015i	0.625162	+	0.780495i	$0.285033\pi$
$774$		0			0
$775$	47.6458	+	10.0258i	1.71149	+	0.360136i
$776$		0			0
$777$	−0.498866	+	0.260418i	−0.0178967	+	0.00934245i
$778$		0			0
$779$	−79.1041	+	45.6708i	−2.83420	+	1.63633i
$780$		0			0
$781$	0.612769	−	1.06135i	0.0219266	−	0.0379780i
$782$		0			0
$783$	−0.209423	−	0.209423i	−0.00748418	−	0.00748418i
$784$		0			0
$785$	−48.7684	+	21.7728i	−1.74062	+	0.777103i
$786$		0			0
$787$	2.31825	+	8.65181i	0.0826366	+	0.308404i	0.994856	−	0.101298i	$-0.0322995\pi$
$787$	2.31825	+	8.65181i	0.0826366	+	0.308404i	−0.912220	+	0.409702i	$0.865633\pi$
$788$		0			0
$789$	16.3890	+	28.3865i	0.583463	+	1.01059i
$790$		0			0
$791$	17.9501	+	5.63709i	0.638231	+	0.200432i
$792$		0			0
$793$	13.5952	+	3.64283i	0.482781	+	0.129361i
$794$		0			0
$795$	30.0200	−	24.3605i	1.06470	−	0.863978i
$796$		0			0
$797$	32.4551	−	32.4551i	1.14962	−	1.14962i	0.162990	−	0.986628i	$-0.447886\pi$
$797$	32.4551	−	32.4551i	1.14962	−	1.14962i	0.986628	−	0.162990i	$-0.0521138\pi$
$798$		0			0
$799$		−	5.47396i		−	0.193655i
$800$		0			0
$801$	12.9022	+	7.44911i	0.455878	+	0.263201i
$802$		0			0
$803$	0.0623431	−	0.232668i	0.00220004	−	0.00821066i
$804$		0			0
$805$	−23.4096	+	9.27985i	−0.825080	+	0.327072i
$806$		0			0
$807$	10.7783	−	40.2252i	0.379414	−	1.41599i
$808$		0			0
$809$	−37.3411	−	21.5589i	−1.31284	−	0.757970i	−0.330276	−	0.943884i	$-0.607142\pi$
$809$	−37.3411	−	21.5589i	−1.31284	−	0.757970i	−0.982566	+	0.185915i	$0.940475\pi$
$810$		0			0
$811$		−	15.8129i		−	0.555267i	−0.960687	−	0.277634i	$-0.910450\pi$
$811$		−	15.8129i		−	0.555267i	0.960687	−	0.277634i	$-0.0895501\pi$
$812$		0			0
$813$	40.0103	−	40.0103i	1.40322	−	1.40322i
$814$		0			0
$815$	−2.50563	+	24.0760i	−0.0877685	+	0.843344i
$816$		0			0
$817$	28.8307	+	7.72516i	1.00866	+	0.270269i
$818$		0			0
$819$	−1.34371	−	6.02848i	−0.0469531	−	0.210652i
$820$		0			0
$821$	−18.0732	−	31.3037i	−0.630759	−	1.09251i	−0.987397	−	0.158264i	$-0.949410\pi$
$821$	−18.0732	−	31.3037i	−0.630759	−	1.09251i	0.356637	−	0.934243i	$-0.383923\pi$
$822$		0			0
$823$	−8.61252	−	32.1424i	−0.300214	−	1.12041i	−0.936988	−	0.349362i	$-0.886398\pi$
$823$	−8.61252	−	32.1424i	−0.300214	−	1.12041i	0.636774	−	0.771050i	$-0.280268\pi$
$824$		0			0
$825$	−0.0799906	−	1.46891i	−0.00278491	−	0.0511408i
$826$		0			0
$827$	−15.5915	−	15.5915i	−0.542171	−	0.542171i	0.381994	−	0.924165i	$-0.375237\pi$
$827$	−15.5915	−	15.5915i	−0.542171	−	0.542171i	−0.924165	+	0.381994i	$0.875237\pi$
$828$		0			0
$829$	14.1523	−	24.5126i	0.491531	−	0.851357i	−0.508421	−	0.861109i	$-0.669771\pi$
$829$	14.1523	−	24.5126i	0.491531	−	0.851357i	0.999952	+	0.00975135i	$0.00310400\pi$
$830$		0			0
$831$	18.9511	−	10.9414i	0.657405	−	0.379553i
$832$		0			0
$833$	−15.5979	−	5.63682i	−0.540434	−	0.195304i
$834$		0			0
$835$	−14.9859	−	10.8646i	−0.518610	−	0.375984i
$836$		0			0
$837$	−17.0670	+	4.57308i	−0.589921	+	0.158069i
$838$		0			0
$839$	−11.2714			−0.389133			−0.194566	−	0.980889i	$-0.562330\pi$
$839$	−11.2714			−0.389133			−0.194566	+	0.980889i	$0.562330\pi$
$840$		0			0
$841$	28.9734			0.999081
$842$		0			0
$843$	−19.5436	+	5.23670i	−0.673118	+	0.180361i
$844$		0			0
$845$	−26.2305	+	4.18196i	−0.902356	+	0.143864i
$846$		0			0
$847$	−15.5855	+	24.5262i	−0.535524	+	0.842729i
$848$		0			0
$849$	−17.6125	+	10.1686i	−0.604460	+	0.348985i
$850$		0			0
$851$	−0.198423	+	0.343678i	−0.00680185	+	0.0117811i
$852$		0			0
$853$	−36.3857	−	36.3857i	−1.24582	−	1.24582i	−0.957548	−	0.288274i	$-0.906919\pi$
$853$	−36.3857	−	36.3857i	−1.24582	−	1.24582i	−0.288274	−	0.957548i	$-0.593081\pi$
$854$		0			0
$855$	−13.4270	+	35.0856i	−0.459194	+	1.19990i
$856$		0			0
$857$	6.09802	+	22.7581i	0.208304	+	0.777402i	0.988417	+	0.151763i	$0.0484951\pi$
$857$	6.09802	+	22.7581i	0.208304	+	0.777402i	−0.780113	+	0.625639i	$0.784838\pi$
$858$		0			0
$859$	1.48878	+	2.57864i	0.0507964	+	0.0879820i	0.890306	−	0.455364i	$-0.150491\pi$
$859$	1.48878	+	2.57864i	0.0507964	+	0.0879820i	−0.839509	+	0.543345i	$0.817157\pi$
$860$		0			0
$861$	−53.2854	+	48.9392i	−1.81596	+	1.66784i
$862$		0			0
$863$	24.0804	+	6.45233i	0.819707	+	0.219640i	0.644218	−	0.764842i	$-0.277183\pi$
$863$	24.0804	+	6.45233i	0.819707	+	0.219640i	0.175489	+	0.984481i	$0.443849\pi$
$864$		0			0
$865$	22.9148	+	2.38479i	0.779127	+	0.0810853i
$866$		0			0
$867$	−18.3682	+	18.3682i	−0.623817	+	0.623817i
$868$		0			0
$869$		−	1.26318i		−	0.0428504i
$870$		0			0
$871$	6.50013	+	3.75285i	0.220248	+	0.127161i
$872$		0			0
$873$	−7.75794	+	28.9530i	−0.262567	+	0.979912i
$874$		0			0
$875$	−17.0760	+	24.1539i	−0.577274	+	0.816551i
$876$		0			0
$877$	6.58973	−	24.5932i	0.222520	−	0.830454i	−0.760864	−	0.648912i	$-0.775224\pi$
$877$	6.58973	−	24.5932i	0.222520	−	0.830454i	0.983383	−	0.181542i	$-0.0581089\pi$
$878$		0			0
$879$	−5.97692	−	3.45078i	−0.201596	−	0.116392i
$880$		0			0
$881$		−	47.6407i		−	1.60506i	−0.596614	−	0.802529i	$-0.703487\pi$
$881$		−	47.6407i		−	1.60506i	0.596614	−	0.802529i	$-0.296513\pi$
$882$		0			0
$883$	−0.852334	+	0.852334i	−0.0286833	+	0.0286833i	−0.721303	−	0.692620i	$-0.756456\pi$
$883$	−0.852334	+	0.852334i	−0.0286833	+	0.0286833i	0.692620	+	0.721303i	$0.256456\pi$
$884$		0			0
$885$	41.9606	+	4.36692i	1.41049	+	0.146792i
$886$		0			0
$887$	23.0295	+	6.17074i	0.773256	+	0.207193i	0.623809	−	0.781577i	$-0.285584\pi$
$887$	23.0295	+	6.17074i	0.773256	+	0.207193i	0.149446	+	0.988770i	$0.452251\pi$
$888$		0			0
$889$	0.639540	−	2.03647i	0.0214495	−	0.0683011i
$890$		0			0
$891$	0.693409	+	1.20102i	0.0232301	+	0.0402357i
$892$		0			0
$893$	4.55678	+	17.0061i	0.152487	+	0.569088i
$894$		0			0
$895$	−1.76975	+	4.62448i	−0.0591564	+	0.154579i
$896$		0			0
$897$	−7.27078	−	7.27078i	−0.242764	−	0.242764i
$898$		0			0
$899$	−0.794735	+	1.37652i	−0.0265059	+	0.0459096i
$900$		0			0
$901$	15.5503	−	8.97797i	0.518055	−	0.299099i
$902$		0			0
$903$	23.6202	+	1.00423i	0.786030	+	0.0334188i
$904$		0			0
$905$	−16.7629	+	2.67253i	−0.557217	+	0.0888379i
$906$		0			0
$907$	30.7853	−	8.24891i	1.02221	−	0.273900i	0.291488	−	0.956575i	$-0.405850\pi$
$907$	30.7853	−	8.24891i	1.02221	−	0.273900i	0.730723	+	0.682674i	$0.239183\pi$
$908$		0			0
$909$	−24.2367			−0.803881
$910$		0			0
$911$	7.74616			0.256642			0.128321	−	0.991733i	$-0.459041\pi$
$911$	7.74616			0.256642			0.128321	+	0.991733i	$0.459041\pi$
$912$		0			0
$913$	1.48664	−	0.398344i	0.0492006	−	0.0131833i
$914$		0			0
$915$	−54.8981	−	39.8002i	−1.81487	−	1.31575i
$916$		0			0
$917$	7.44163	+	4.72889i	0.245744	+	0.156162i
$918$		0			0
$919$	−25.6348	+	14.8002i	−0.845613	+	0.488215i	−0.859168	−	0.511693i	$-0.829018\pi$
$919$	−25.6348	+	14.8002i	−0.845613	+	0.488215i	0.0135550	+	0.999908i	$0.495685\pi$
$920$		0			0
$921$	15.4596	−	26.7768i	0.509411	−	0.882326i
$922$		0			0
$923$	−7.11519	−	7.11519i	−0.234199	−	0.234199i
$924$		0			0
$925$	0.0253478	+	0.465474i	0.000833429	+	0.0153047i
$926$		0			0
$927$	−4.56665	−	17.0430i	−0.149989	−	0.559765i
$928$		0			0
$929$	−12.6229	−	21.8634i	−0.414143	−	0.717316i	0.581195	−	0.813764i	$-0.302585\pi$
$929$	−12.6229	−	21.8634i	−0.414143	−	0.717316i	−0.995338	+	0.0964479i	$0.969252\pi$
$930$		0			0
$931$	53.1507	+	4.52770i	1.74194	+	0.148389i
$932$		0			0
$933$	54.1934	+	14.5211i	1.77421	+	0.475399i
$934$		0			0
$935$	0.0707249	−	0.679577i	0.00231295	−	0.0222245i
$936$		0			0
$937$	−26.1816	+	26.1816i	−0.855315	+	0.855315i	−0.990782	−	0.135467i	$-0.956746\pi$
$937$	−26.1816	+	26.1816i	−0.855315	+	0.855315i	0.135467	+	0.990782i	$0.456746\pi$
$938$		0			0
$939$			11.1042i			0.362371i
$940$		0			0
$941$	23.0609	+	13.3142i	0.751763	+	0.434031i	0.826331	−	0.563185i	$-0.190424\pi$
$941$	23.0609	+	13.3142i	0.751763	+	0.434031i	−0.0745676	+	0.997216i	$0.523758\pi$
$942$		0			0
$943$	−13.2049	+	49.2815i	−0.430012	+	1.60483i
$944$		0			0
$945$	1.56369	−	10.6201i	0.0508669	−	0.345470i
$946$		0			0
$947$	6.56000	−	24.4823i	0.213171	−	0.795566i	−0.773631	−	0.633636i	$-0.781562\pi$
$947$	6.56000	−	24.4823i	0.213171	−	0.795566i	0.986802	−	0.161930i	$-0.0517718\pi$
$948$		0			0
$949$	−1.71277	−	0.988866i	−0.0555987	−	0.0320999i
$950$		0			0
$951$			3.87221i			0.125565i
$952$		0			0
$953$	34.5345	−	34.5345i	1.11868	−	1.11868i	0.126747	−	0.991935i	$-0.459546\pi$
$953$	34.5345	−	34.5345i	1.11868	−	1.11868i	0.991935	−	0.126747i	$-0.0404537\pi$
$954$		0			0
$955$	1.45138	−	1.17776i	0.0469657	−	0.0381115i
$956$		0			0
$957$	0.0463875	+	0.0124295i	0.00149950	+	0.000401789i
$958$		0			0
$959$	28.0684	+	30.5611i	0.906375	+	0.986868i
$960$		0			0
$961$	31.9127	+	55.2745i	1.02944	+	1.78305i
$962$		0			0
$963$	9.94955	+	37.1322i	0.320620	+	1.19657i
$964$		0			0
$965$	40.3780	−	18.0269i	1.29981	−	0.580305i
$966$		0			0
$967$	−9.31362	−	9.31362i	−0.299506	−	0.299506i	0.541314	−	0.840820i	$-0.317927\pi$
$967$	−9.31362	−	9.31362i	−0.299506	−	0.299506i	−0.840820	+	0.541314i	$0.817927\pi$
$968$		0			0
$969$	−20.5953	+	35.6722i	−0.661617	+	1.14595i
$970$		0			0
$971$	9.73473	−	5.62035i	0.312402	−	0.180366i	−0.335599	−	0.942005i	$-0.608939\pi$
$971$	9.73473	−	5.62035i	0.312402	−	0.180366i	0.648001	+	0.761639i	$0.275605\pi$
$972$		0			0
$973$	−1.60454	−	3.07371i	−0.0514391	−	0.0985385i
$974$		0			0
$975$	−11.8196	−	2.48713i	−0.378532	−	0.0796518i
$976$		0			0
$977$	−2.96941	+	0.795651i	−0.0949999	+	0.0254551i	−0.306006	−	0.952030i	$-0.598993\pi$
$977$	−2.96941	+	0.795651i	−0.0949999	+	0.0254551i	0.211006	+	0.977485i	$0.432326\pi$
$978$		0			0
$979$	0.871494			0.0278531
$980$		0			0
$981$	−22.2912			−0.711702
$982$		0			0
$983$	−6.34688	+	1.70064i	−0.202434	+	0.0542421i	−0.358611	−	0.933487i	$-0.616750\pi$
$983$	−6.34688	+	1.70064i	−0.202434	+	0.0542421i	0.156177	+	0.987729i	$0.450083\pi$
$984$		0			0
$985$	−17.7774	+	24.5211i	−0.566435	+	0.781308i
$986$		0			0
$987$	6.45332	+	12.3622i	0.205411	+	0.393493i
$988$		0			0
$989$	14.4382	−	8.33591i	0.459109	−	0.265067i
$990$		0			0
$991$	13.2859	−	23.0119i	0.422041	−	0.730997i	−0.574098	−	0.818787i	$-0.694647\pi$
$991$	13.2859	−	23.0119i	0.422041	−	0.730997i	0.996139	+	0.0877900i	$0.0279804\pi$
$992$		0			0
$993$	−17.9668	−	17.9668i	−0.570159	−	0.570159i
$994$		0			0
$995$	−42.3383	−	16.2026i	−1.34221	−	0.513656i
$996$		0			0
$997$	1.75671	+	6.55613i	0.0556355	+	0.207635i	0.988148	−	0.153502i	$-0.0490553\pi$
$997$	1.75671	+	6.55613i	0.0556355	+	0.207635i	−0.932513	+	0.361137i	$0.882389\pi$
$998$		0			0
$999$	−0.0845841	−	0.146504i	−0.00267612	−	0.00463518i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.ci.e.17.2		48
4.3	odd	2		280.2.bo.a.17.11	✓	48
5.3	odd	4	inner	560.2.ci.e.353.2		48
7.5	odd	6	inner	560.2.ci.e.257.2		48
20.3	even	4		280.2.bo.a.73.11	yes	48
28.19	even	6		280.2.bo.a.257.11	yes	48
35.33	even	12	inner	560.2.ci.e.33.2		48
140.103	odd	12		280.2.bo.a.33.11	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bo.a.17.11	✓	48	4.3	odd	2
280.2.bo.a.33.11	yes	48	140.103	odd	12
280.2.bo.a.73.11	yes	48	20.3	even	4
280.2.bo.a.257.11	yes	48	28.19	even	6
560.2.ci.e.17.2		48	1.1	even	1	trivial
560.2.ci.e.33.2		48	35.33	even	12	inner
560.2.ci.e.257.2		48	7.5	odd	6	inner
560.2.ci.e.353.2		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)

\(f(q)\)	\(=\)	\(q+(-2.20364 + 0.590462i) q^{3} +(-0.352053 - 2.20818i) q^{5} +(1.22435 + 2.34541i) q^{7} +(1.90929 - 1.10233i) q^{9} +O(q^{10})\)	\(q+(-2.20364 + 0.590462i) q^{3} +(-0.352053 - 2.20818i) q^{5} +(1.22435 + 2.34541i) q^{7} +(1.90929 - 1.10233i) q^{9} +(0.0644824 - 0.111687i) q^{11} +(-0.748741 - 0.748741i) q^{13} +(2.07964 + 4.65815i) q^{15} +(0.613222 + 2.28858i) q^{17} +(-3.81023 - 6.59951i) q^{19} +(-4.08291 - 4.44550i) q^{21} +(-4.11147 - 1.10166i) q^{23} +(-4.75212 + 1.55479i) q^{25} +(1.28303 - 1.28303i) q^{27} -0.163226i q^{29} +(-8.43321 - 4.86892i) q^{31} +(-0.0761489 + 0.284192i) q^{33} +(4.74806 - 3.52930i) q^{35} +(0.0241304 - 0.0900559i) q^{37} +(2.09206 + 1.20785i) q^{39} -11.9864i q^{41} +(-2.76959 + 2.76959i) q^{43} +(-3.10631 - 3.82798i) q^{45} +(-2.23164 - 0.597966i) q^{47} +(-4.00192 + 5.74323i) q^{49} +(-2.70264 - 4.68110i) q^{51} +(-1.96147 - 7.32032i) q^{53} +(-0.269326 - 0.103069i) q^{55} +(12.2931 + 12.2931i) q^{57} +(4.13495 - 7.16194i) q^{59} +(-11.5114 + 6.64609i) q^{61} +(4.92306 + 3.12843i) q^{63} +(-1.38976 + 1.91695i) q^{65} +(-6.84682 + 1.83460i) q^{67} +9.71067 q^{69} +9.50288 q^{71} +(1.80412 - 0.483412i) q^{73} +(9.55389 - 6.23214i) q^{75} +(0.340901 + 0.0144937i) q^{77} +(8.48250 - 4.89737i) q^{79} +(-5.37673 + 9.31277i) q^{81} +(8.43870 + 8.43870i) q^{83} +(4.83770 - 2.15980i) q^{85} +(0.0963790 + 0.359691i) q^{87} +(3.37880 + 5.85226i) q^{89} +(0.839383 - 2.67283i) q^{91} +(21.4586 + 5.74983i) q^{93} +(-13.2315 + 10.7371i) q^{95} +(-9.61378 + 9.61378i) q^{97} -0.284323i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{7}+O(q^{10}) \) 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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