LMFDB - Embedded newform 280.2.bo.a.73.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("280.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			73.11
Character	$\chi$	$=$	280.73
Dual form			280.2.bo.a.257.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.590462 + 2.20364i) q^{3} +(1.73631 + 1.40898i) q^{5} +(-2.34541 + 1.22435i) q^{7} +(-1.90929 + 1.10233i) q^{9} +O(q^{10})$	\(q+(0.590462 + 2.20364i) q^{3} +(1.73631 + 1.40898i) q^{5} +(-2.34541 + 1.22435i) q^{7} +(-1.90929 + 1.10233i) q^{9} +(-0.0644824 + 0.111687i) q^{11} +(0.748741 - 0.748741i) q^{13} +(-2.07964 + 4.65815i) q^{15} +(2.28858 - 0.613222i) q^{17} +(-3.81023 - 6.59951i) q^{19} +(-4.08291 - 4.44550i) q^{21} +(-1.10166 + 4.11147i) q^{23} +(1.02957 + 4.89285i) q^{25} +(1.28303 + 1.28303i) q^{27} +0.163226i q^{29} +(8.43321 + 4.86892i) q^{31} +(-0.284192 - 0.0761489i) q^{33} +(-5.79746 - 1.17877i) q^{35} +(-0.0900559 - 0.0241304i) q^{37} +(2.09206 + 1.20785i) q^{39} -11.9864i q^{41} +(2.76959 + 2.76959i) q^{43} +(-4.86828 - 0.776156i) q^{45} +(0.597966 - 2.23164i) q^{47} +(4.00192 - 5.74323i) q^{49} +(2.70264 + 4.68110i) q^{51} +(7.32032 - 1.96147i) q^{53} +(-0.269326 + 0.103069i) q^{55} +(12.2931 - 12.2931i) q^{57} +(4.13495 - 7.16194i) q^{59} +(-11.5114 + 6.64609i) q^{61} +(3.12843 - 4.92306i) q^{63} +(2.35501 - 0.245090i) q^{65} +(-1.83460 - 6.84682i) q^{67} -9.71067 q^{69} -9.50288 q^{71} +(0.483412 + 1.80412i) q^{73} +(-10.1741 + 5.15784i) q^{75} +(0.0144937 - 0.340901i) q^{77} +(8.48250 - 4.89737i) q^{79} +(-5.37673 + 9.31277i) q^{81} +(8.43870 - 8.43870i) q^{83} +(4.83770 + 2.15980i) q^{85} +(-0.359691 + 0.0963790i) q^{87} +(-3.37880 - 5.85226i) q^{89} +(-0.839383 + 2.67283i) q^{91} +(-5.74983 + 21.4586i) q^{93} +(2.68281 - 16.8273i) q^{95} +(9.61378 + 9.61378i) q^{97} -0.284323i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.590462	+	2.20364i	0.340904	+	1.27227i	0.897325	+	0.441370i	$0.145507\pi$
$3$	0.590462	+	2.20364i	0.340904	+	1.27227i	−0.556422	+	0.830900i	$0.687826\pi$
$4$		0			0
$5$	1.73631	+	1.40898i	0.776503	+	0.630114i
$5$	1.73631	+	1.40898i	0.776503	+	0.630114i
$6$		0			0
$7$	−2.34541	+	1.22435i	−0.886483	+	0.462762i
$7$	−2.34541	+	1.22435i	−0.886483	+	0.462762i
$8$		0			0
$9$	−1.90929	+	1.10233i	−0.636430	+	0.367443i
$10$		0			0
$11$	−0.0644824	+	0.111687i	−0.0194422	+	0.0336749i	−0.875583	−	0.483068i	$-0.839522\pi$
$11$	−0.0644824	+	0.111687i	−0.0194422	+	0.0336749i	0.856141	+	0.516743i	$0.172856\pi$
$12$		0			0
$13$	0.748741	−	0.748741i	0.207663	−	0.207663i	−0.595610	−	0.803274i	$-0.703090\pi$
$13$	0.748741	−	0.748741i	0.207663	−	0.207663i	0.803274	+	0.595610i	$0.203090\pi$
$14$		0			0
$15$	−2.07964	+	4.65815i	−0.536962	+	1.20273i
$16$		0			0
$17$	2.28858	−	0.613222i	0.555061	−	0.148728i	0.0296247	−	0.999561i	$-0.490569\pi$
$17$	2.28858	−	0.613222i	0.555061	−	0.148728i	0.525436	+	0.850833i	$0.323902\pi$
$18$		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
$23$	−1.10166	+	4.11147i	−0.229713	+	0.857301i	0.750748	+	0.660588i	$0.229693\pi$
$23$	−1.10166	+	4.11147i	−0.229713	+	0.857301i	−0.980461	+	0.196712i	$0.936974\pi$
$24$		0			0
$25$	1.02957	+	4.89285i	0.205914	+	0.978570i
$26$		0			0
$27$	1.28303	+	1.28303i	0.246918	+	0.246918i
$28$		0			0
$29$			0.163226i			0.0303104i	0.999885	+	0.0151552i	$0.00482423\pi$
$29$			0.163226i			0.0303104i	−0.999885	+	0.0151552i	$0.995176\pi$
$30$		0			0
$31$	8.43321	+	4.86892i	1.51465	+	0.874484i	0.999853	+	0.0171718i	$0.00546622\pi$
$31$	8.43321	+	4.86892i	1.51465	+	0.874484i	0.514797	+	0.857312i	$0.327867\pi$
$32$		0			0
$33$	−0.284192	−	0.0761489i	−0.0494714	−	0.0132558i
$34$		0			0
$35$	−5.79746	−	1.17877i	−0.979949	−	0.199249i
$36$		0			0
$37$	−0.0900559	−	0.0241304i	−0.0148051	−	0.00396701i	0.251409	−	0.967881i	$-0.419106\pi$
$37$	−0.0900559	−	0.0241304i	−0.0148051	−	0.00396701i	−0.266214	+	0.963914i	$0.585773\pi$
$38$		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	$-0.153463\pi$
$43$	2.76959	+	2.76959i	0.422358	+	0.422358i	−0.463657	+	0.886015i	$0.653463\pi$
$44$		0			0
$45$	−4.86828	−	0.776156i	−0.725720	−	0.115703i
$46$		0			0
$47$	0.597966	−	2.23164i	0.0872223	−	0.325518i	−0.908503	−	0.417877i	$-0.862774\pi$
$47$	0.597966	−	2.23164i	0.0872223	−	0.325518i	0.995726	+	0.0923593i	$0.0294408\pi$
$48$		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
$53$	7.32032	−	1.96147i	1.00552	−	0.269429i	0.281766	−	0.959483i	$-0.409080\pi$
$53$	7.32032	−	1.96147i	1.00552	−	0.269429i	0.723758	+	0.690054i	$0.242413\pi$
$54$		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
$63$	3.12843	−	4.92306i	0.394145	−	0.620247i
$64$		0			0
$65$	2.35501	−	0.245090i	0.292103	−	0.0303997i
$66$		0			0
$67$	−1.83460	−	6.84682i	−0.224132	−	0.836472i	−0.982750	−	0.184937i	$-0.940792\pi$
$67$	−1.83460	−	6.84682i	−0.224132	−	0.836472i	0.758618	−	0.651535i	$-0.225875\pi$
$68$		0			0
$69$	−9.71067			−1.16903
$70$		0			0
$71$	−9.50288			−1.12778			−0.563892	−	0.825848i	$-0.690697\pi$
$71$	−9.50288			−1.12778			−0.563892	+	0.825848i	$0.690697\pi$
$72$		0			0
$73$	0.483412	+	1.80412i	0.0565791	+	0.211156i	0.988428	−	0.151690i	$-0.0484717\pi$
$73$	0.483412	+	1.80412i	0.0565791	+	0.211156i	−0.931849	+	0.362846i	$0.881805\pi$
$74$		0			0
$75$	−10.1741	+	5.15784i	−1.17481	+	0.595576i
$76$		0			0
$77$	0.0144937	−	0.340901i	0.00165172	−	0.0388493i
$78$		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	−0.0711952	−	0.997462i	$-0.522681\pi$
$83$	8.43870	−	8.43870i	0.926267	−	0.926267i	0.997462	+	0.0711952i	$0.0226813\pi$
$84$		0			0
$85$	4.83770	+	2.15980i	0.524722	+	0.234264i
$86$		0			0
$87$	−0.359691	+	0.0963790i	−0.0385629	+	0.0103329i
$88$		0			0
$89$	−3.37880	−	5.85226i	−0.358153	−	0.620338i	0.629500	−	0.777001i	$-0.283260\pi$
$89$	−3.37880	−	5.85226i	−0.358153	−	0.620338i	−0.987652	+	0.156662i	$0.949927\pi$
$90$		0			0
$91$	−0.839383	+	2.67283i	−0.0879912	+	0.280189i
$92$		0			0
$93$	−5.74983	+	21.4586i	−0.596229	+	2.22516i
$94$		0			0
$95$	2.68281	−	16.8273i	0.275250	−	1.72645i
$96$		0			0
$97$	9.61378	+	9.61378i	0.976132	+	0.976132i	0.999722	−	0.0235902i	$-0.00750969\pi$
$97$	9.61378	+	9.61378i	0.976132	+	0.976132i	−0.0235902	+	0.999722i	$0.507510\pi$
$98$		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
$103$	−7.73044	−	2.07137i	−0.761703	−	0.204098i	−0.143000	−	0.989723i	$-0.545675\pi$
$103$	−7.73044	−	2.07137i	−0.761703	−	0.204098i	−0.618703	+	0.785625i	$0.712342\pi$
$104$		0			0
$105$	−0.825598	−	13.4715i	−0.0805702	−	1.31468i
$106$		0			0
$107$	−16.8426	−	4.51297i	−1.62824	−	0.436285i	−0.674831	−	0.737972i	$-0.735784\pi$
$107$	−16.8426	−	4.51297i	−1.62824	−	0.436285i	−0.953407	+	0.301687i	$0.902450\pi$
$108$		0			0
$109$	8.75633	+	5.05547i	0.838704	+	0.484226i	0.856824	−	0.515610i	$-0.172435\pi$
$109$	8.75633	+	5.05547i	0.838704	+	0.484226i	−0.0181193	+	0.999836i	$0.505768\pi$
$110$		0			0
$111$		−	0.212699i		−	0.0201884i
$112$		0			0
$113$	5.02836	+	5.02836i	0.473028	+	0.473028i	0.902893	−	0.429865i	$-0.141439\pi$
$113$	5.02836	+	5.02836i	0.473028	+	0.473028i	−0.429865	+	0.902893i	$0.641439\pi$
$114$		0			0
$115$	−7.70580	+	5.58658i	−0.718570	+	0.520951i
$116$		0			0
$117$	−0.604204	+	2.25492i	−0.0558587	+	0.208468i
$118$		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
$123$	26.4136	−	7.07750i	2.38163	−	0.638156i
$124$		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	$-0.738604\pi$
$127$	0.570478	−	0.570478i	0.0506218	−	0.0506218i	0.731965	+	0.681343i	$0.238604\pi$
$128$		0			0
$129$	−4.46782	+	7.73850i	−0.393370	+	0.681337i
$130$		0			0
$131$	−2.88606	+	1.66627i	−0.252156	+	0.145582i	−0.620751	−	0.784008i	$-0.713172\pi$
$131$	−2.88606	+	1.66627i	−0.252156	+	0.145582i	0.368595	+	0.929590i	$0.379839\pi$
$132$		0			0
$133$	17.0167	+	10.8135i	1.47553	+	0.937650i
$134$		0			0
$135$	0.419981	+	4.03549i	0.0361462	+	0.347319i
$136$		0			0
$137$	−4.05920	−	15.1491i	−0.346801	−	1.29428i	−0.890495	−	0.454994i	$-0.849641\pi$
$137$	−4.05920	−	15.1491i	−0.346801	−	1.29428i	0.543694	−	0.839283i	$-0.317025\pi$
$138$		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
$143$	0.0353439	+	0.131905i	0.00295560	+	0.0110305i
$144$		0			0
$145$	−0.229982	+	0.283412i	−0.0190990	+	0.0235361i
$146$		0			0
$147$	15.0190	+	5.42761i	1.23874	+	0.447662i
$148$		0			0
$149$	−9.31791	+	5.37970i	−0.763353	+	0.440722i	−0.830498	−	0.557021i	$-0.811944\pi$
$149$	−9.31791	+	5.37970i	−0.763353	+	0.440722i	0.0671452	+	0.997743i	$0.478611\pi$
$150$		0			0
$151$	1.38384	−	2.39688i	0.112615	−	0.195055i	−0.804209	−	0.594347i	$-0.797411\pi$
$151$	1.38384	−	2.39688i	0.112615	−	0.195055i	0.916824	+	0.399292i	$0.130744\pi$
$152$		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
$157$	−23.0709	+	6.18183i	−1.84126	+	0.493364i	−0.998958	−	0.0456452i	$-0.985466\pi$
$157$	−23.0709	+	6.18183i	−1.84126	+	0.493364i	−0.842300	+	0.539009i	$0.818799\pi$
$158$		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
$163$	−2.80178	+	10.4564i	−0.219452	+	0.819008i	0.765099	+	0.643913i	$0.222690\pi$
$163$	−2.80178	+	10.4564i	−0.219452	+	0.819008i	−0.984552	+	0.175095i	$0.943977\pi$
$164$		0			0
$165$	−0.386154	−	0.532638i	−0.0300620	−	0.0414658i
$166$		0			0
$167$	5.85335	+	5.85335i	0.452946	+	0.452946i	0.896331	−	0.443385i	$-0.146223\pi$
$167$	5.85335	+	5.85335i	0.452946	+	0.452946i	−0.443385	+	0.896331i	$0.646223\pi$
$168$		0			0
$169$			11.8788i			0.913752i
$170$		0			0
$171$	14.5497	+	8.40025i	1.11264	+	0.642383i
$172$		0			0
$173$	−9.95209	−	2.66665i	−0.756643	−	0.202742i	−0.140180	−	0.990126i	$-0.544768\pi$
$173$	−9.95209	−	2.66665i	−0.756643	−	0.202742i	−0.616463	+	0.787384i	$0.711435\pi$
$174$		0			0
$175$	−8.40534	−	10.2152i	−0.635384	−	0.772196i
$176$		0			0
$177$	18.2238	+	4.88306i	1.36979	+	0.367033i
$178$		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
$185$	−0.122366	−	0.168785i	−0.00899653	−	0.0124093i
$186$		0			0
$187$	−0.0790841	+	0.295146i	−0.00578320	+	0.0215832i
$188$		0			0
$189$	−4.58010	−	1.43835i	−0.333153	−	0.104624i
$190$		0			0
$191$	−0.417950	−	0.723911i	−0.0302418	−	0.0523803i	0.850508	−	0.525961i	$-0.176294\pi$
$191$	−0.417950	−	0.723911i	−0.0302418	−	0.0523803i	−0.880750	+	0.473581i	$0.842961\pi$
$192$		0			0
$193$	−19.1017	+	5.11827i	−1.37497	+	0.368421i	−0.869290	−	0.494302i	$-0.835424\pi$
$193$	−19.1017	+	5.11827i	−1.37497	+	0.368421i	−0.505677	+	0.862723i	$0.668757\pi$
$194$		0			0
$195$	1.93063	+	5.04486i	0.138255	+	0.361270i
$196$		0			0
$197$	−9.57769	+	9.57769i	−0.682382	+	0.682382i	−0.960536	−	0.278154i	$-0.910277\pi$
$197$	−9.57769	+	9.57769i	−0.682382	+	0.682382i	0.278154	+	0.960536i	$0.410277\pi$
$198$		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
$203$	−0.199847	−	0.382833i	−0.0140265	−	0.0268696i
$204$		0			0
$205$	16.8885	−	20.8121i	1.17954	−	1.45358i
$206$		0			0
$207$	−2.42879	−	9.06438i	−0.168813	−	0.630018i
$208$		0			0
$209$	0.982772			0.0679797
$210$		0			0
$211$	−8.14495			−0.560721			−0.280361	−	0.959895i	$-0.590454\pi$
$211$	−8.14495			−0.560721			−0.280361	+	0.959895i	$0.590454\pi$
$212$		0			0
$213$	−5.61110	−	20.9409i	−0.384466	−	1.43485i
$214$		0			0
$215$	0.906587	+	8.71115i	0.0618287	+	0.594096i
$216$		0			0
$217$	−25.7406	−	1.09439i	−1.74739	−	0.0742920i
$218$		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	−0.926936	−	0.375220i	$-0.877567\pi$
$223$	−8.23887	+	8.23887i	−0.551715	+	0.551715i	0.375220	+	0.926936i	$0.377567\pi$
$224$		0			0
$225$	−7.35928	−	8.20695i	−0.490618	−	0.547130i
$226$		0			0
$227$	0.624229	−	0.167262i	0.0414315	−	0.0111015i	−0.238044	−	0.971254i	$-0.576506\pi$
$227$	0.624229	−	0.167262i	0.0414315	−	0.0111015i	0.279475	+	0.960153i	$0.409839\pi$
$228$		0			0
$229$	−10.5335	−	18.2445i	−0.696071	−	1.20563i	−0.969818	−	0.243829i	$-0.921596\pi$
$229$	−10.5335	−	18.2445i	−0.696071	−	1.20563i	0.273747	−	0.961802i	$-0.411737\pi$
$230$		0			0
$231$	0.759780	−	0.169350i	0.0499898	−	0.0111424i
$232$		0			0
$233$	4.45300	−	16.6188i	0.291726	−	1.08874i	−0.652057	−	0.758170i	$-0.726094\pi$
$233$	4.45300	−	16.6188i	0.291726	−	1.08874i	0.943783	−	0.330566i	$-0.107240\pi$
$234$		0			0
$235$	4.18258	−	3.03231i	0.272842	−	0.197806i
$236$		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
$243$	−18.4388	−	4.94065i	−1.18285	−	0.316943i
$244$		0			0
$245$	15.0407	−	4.33343i	0.960912	−	0.276853i
$246$		0			0
$247$	−7.79420	−	2.08845i	−0.495933	−	0.132885i
$248$		0			0
$249$	23.5785	+	13.6131i	1.49423	+	0.862694i
$250$		0			0
$251$		−	21.8184i		−	1.37716i	−0.725159	−	0.688581i	$-0.758234\pi$
$251$		−	21.8184i		−	1.37716i	0.725159	−	0.688581i	$-0.241766\pi$
$252$		0			0
$253$	−0.388159	−	0.388159i	−0.0244033	−	0.0244033i
$254$		0			0
$255$	−1.90294	+	11.9358i	−0.119167	+	0.747450i
$256$		0			0
$257$	1.01820	−	3.79997i	0.0635136	−	0.237036i	−0.926870	−	0.375381i	$-0.877512\pi$
$257$	1.01820	−	3.79997i	0.0635136	−	0.237036i	0.990384	+	0.138345i	$0.0441784\pi$
$258$		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
$263$	−13.8781	+	3.71862i	−0.855759	+	0.229300i	−0.659920	−	0.751336i	$-0.729410\pi$
$263$	−13.8781	+	3.71862i	−0.855759	+	0.229300i	−0.195839	+	0.980636i	$0.562743\pi$
$264$		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	$-0.645484\pi$
$269$	9.12700	−	15.8084i	0.556483	−	0.963857i	0.997786	−	0.0664991i	$-0.0211829\pi$
$270$		0			0
$271$	21.4793	−	12.4011i	1.30478	−	0.753313i	0.323558	−	0.946208i	$-0.395121\pi$
$271$	21.4793	−	12.4011i	1.30478	−	0.753313i	0.981219	+	0.192895i	$0.0617877\pi$
$272$		0			0
$273$	−6.38557	−	0.271489i	−0.386472	−	0.0164312i
$274$		0			0
$275$	−0.612856	−	0.200514i	−0.0369566	−	0.0120914i
$276$		0			0
$277$	2.48258	+	9.26511i	0.149164	+	0.556687i	0.999535	+	0.0305030i	$0.00971091\pi$
$277$	2.48258	+	9.26511i	0.149164	+	0.556687i	−0.850371	+	0.526184i	$0.823622\pi$
$278$		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
$283$	−2.30723	−	8.61070i	−0.137151	−	0.511853i	−0.999980	−	0.00635749i	$-0.997976\pi$
$283$	−2.30723	−	8.61070i	−0.137151	−	0.511853i	0.862829	−	0.505496i	$-0.168690\pi$
$284$		0			0
$285$	38.6654	−	4.02399i	2.29034	−	0.238361i
$286$		0			0
$287$	14.6755	+	28.1130i	0.866270	+	1.65946i
$288$		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	$-0.778165\pi$
$293$	−2.13912	+	2.13912i	−0.124969	+	0.124969i	0.641856	+	0.766825i	$0.278165\pi$
$294$		0			0
$295$	17.2706	−	6.60932i	1.00553	−	0.384810i
$296$		0			0
$297$	−0.226030	+	0.0605644i	−0.0131156	+	0.00351431i
$298$		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
$303$	6.49119	−	24.2255i	0.372909	−	1.39172i
$304$		0			0
$305$	−29.3515	−	4.67956i	−1.68066	−	0.267951i
$306$		0			0
$307$	−9.58335	−	9.58335i	−0.546950	−	0.546950i	0.378607	−	0.925558i	$-0.376403\pi$
$307$	−9.58335	−	9.58335i	−0.546950	−	0.546950i	−0.925558	+	0.378607i	$0.876403\pi$
$308$		0			0
$309$		−	18.2582i		−	1.03867i
$310$		0			0
$311$	21.2979	+	12.2964i	1.20769	+	0.697262i	0.962255	−	0.272150i	$-0.0877346\pi$
$311$	21.2979	+	12.2964i	1.20769	+	0.697262i	0.245439	+	0.969412i	$0.421068\pi$
$312$		0			0
$313$	4.70147	+	1.25975i	0.265743	+	0.0712055i	0.389230	−	0.921141i	$-0.372741\pi$
$313$	4.70147	+	1.25975i	0.265743	+	0.0712055i	−0.123487	+	0.992346i	$0.539408\pi$
$314$		0			0
$315$	12.3684	−	4.14009i	0.696881	−	0.233268i
$316$		0			0
$317$	−1.63948	−	0.439298i	−0.0920824	−	0.0246734i	0.212484	−	0.977165i	$-0.431845\pi$
$317$	−1.63948	−	0.439298i	−0.0920824	−	0.0246734i	−0.304566	+	0.952491i	$0.598511\pi$
$318$		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
$325$	4.43436	+	2.89260i	0.245974	+	0.160452i
$326$		0			0
$327$	−5.97013	+	22.2808i	−0.330149	+	1.23213i
$328$		0			0
$329$	1.32984	+	5.96624i	0.0733163	+	0.328929i
$330$		0			0
$331$	−5.56877	−	9.64540i	−0.306087	−	0.530159i	0.671415	−	0.741081i	$-0.265687\pi$
$331$	−5.56877	−	9.64540i	−0.306087	−	0.530159i	−0.977503	+	0.210922i	$0.932353\pi$
$332$		0			0
$333$	0.198542	−	0.0531993i	0.0108801	−	0.00291530i
$334$		0			0
$335$	6.46157	−	14.4731i	0.353033	−	0.790751i
$336$		0			0
$337$	−4.23464	+	4.23464i	−0.230675	+	0.230675i	−0.812975	−	0.582299i	$-0.802153\pi$
$337$	−4.23464	+	4.23464i	−0.230675	+	0.230675i	0.582299	+	0.812975i	$0.302153\pi$
$338$		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
$343$	−2.35441	+	18.3700i	−0.127126	+	0.991887i
$344$		0			0
$345$	−16.8608	−	13.6821i	−0.907753	−	0.736620i
$346$		0			0
$347$	3.52677	+	13.1621i	0.189327	+	0.706578i	0.993663	+	0.112403i	$0.0358548\pi$
$347$	3.52677	+	13.1621i	0.189327	+	0.706578i	−0.804336	+	0.594175i	$0.797479\pi$
$348$		0			0
$349$	5.43385			0.290868			0.145434	−	0.989368i	$-0.453542\pi$
$349$	5.43385			0.290868			0.145434	+	0.989368i	$0.453542\pi$
$350$		0			0
$351$	1.92131			0.102552
$352$		0			0
$353$	−4.95984	−	18.5104i	−0.263986	−	0.985208i	−0.962868	−	0.269971i	$-0.912986\pi$
$353$	−4.95984	−	18.5104i	−0.263986	−	0.985208i	0.698883	−	0.715236i	$-0.253681\pi$
$354$		0			0
$355$	−16.5000	−	13.3893i	−0.875728	−	0.710632i
$356$		0			0
$357$	−12.0701	−	7.67014i	−0.638818	−	0.405947i
$358$		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
$367$	−25.1532	+	6.73979i	−1.31299	+	0.351814i	−0.846347	−	0.532632i	$-0.821203\pi$
$367$	−25.1532	+	6.73979i	−1.31299	+	0.351814i	−0.466642	+	0.884446i	$0.654536\pi$
$368$		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
$373$	3.04568	−	11.3666i	0.157699	−	0.588542i	−0.841160	−	0.540787i	$-0.818127\pi$
$373$	3.04568	−	11.3666i	0.157699	−	0.588542i	0.998859	−	0.0477550i	$-0.0152067\pi$
$374$		0			0
$375$	−24.9328	−	5.37950i	−1.28752	−	0.277796i
$376$		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
$383$	27.5554	+	7.38345i	1.40802	+	0.377276i	0.881216	−	0.472713i	$-0.156725\pi$
$383$	27.5554	+	7.38345i	1.40802	+	0.377276i	0.526799	+	0.849990i	$0.323392\pi$
$384$		0			0
$385$	0.505487	−	0.571490i	0.0257620	−	0.0291258i
$386$		0			0
$387$	−8.34094	−	2.23495i	−0.423994	−	0.113609i
$388$		0			0
$389$	2.08747	+	1.20520i	0.105839	+	0.0611061i	0.551985	−	0.833854i	$-0.313871\pi$
$389$	2.08747	+	1.20520i	0.105839	+	0.0611061i	−0.446146	+	0.894960i	$0.647204\pi$
$390$		0			0
$391$			10.0850i			0.510019i
$392$		0			0
$393$	−5.37595	−	5.37595i	−0.271181	−	0.271181i
$394$		0			0
$395$	21.6286	+	3.44827i	1.08825	+	0.173501i
$396$		0			0
$397$	1.36290	−	5.08642i	0.0684021	−	0.255280i	−0.923254	−	0.384189i	$-0.874481\pi$
$397$	1.36290	−	5.08642i	0.0684021	−	0.255280i	0.991656	+	0.128909i	$0.0411476\pi$
$398$		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
$403$	9.95985	−	2.66873i	0.496135	−	0.132939i
$404$		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	−0.967068	−	0.254519i	$-0.918083\pi$
$409$	−5.32115	+	9.21650i	−0.263114	+	0.455727i	0.703954	+	0.710246i	$0.251416\pi$
$410$		0			0
$411$	30.9864	−	17.8900i	1.52844	−	0.882448i
$412$		0			0
$413$	−0.929414	+	21.8603i	−0.0457335	+	1.07568i
$414$		0			0
$415$	26.5421	−	2.76229i	1.30290	−	0.135596i
$416$		0			0
$417$	−0.773812	−	2.88790i	−0.0378937	−	0.141421i
$418$		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
$423$	1.31831	+	4.92000i	0.0640984	+	0.239219i
$424$		0			0
$425$	5.35665	+	10.5663i	0.259836	+	0.512541i
$426$		0			0
$427$	18.8617	−	29.6818i	0.912784	−	1.43640i
$428$		0			0
$429$	−0.269802	+	0.155770i	−0.0130261	+	0.00752065i
$430$		0			0
$431$	−8.71860	+	15.1011i	−0.419960	+	0.727393i	−0.995935	−	0.0900749i	$-0.971289\pi$
$431$	−8.71860	+	15.1011i	−0.419960	+	0.727393i	0.575975	+	0.817468i	$0.304623\pi$
$432$		0			0
$433$	6.77089	−	6.77089i	0.325388	−	0.325388i	−0.525442	−	0.850830i	$-0.676100\pi$
$433$	6.77089	−	6.77089i	0.325388	−	0.325388i	0.850830	+	0.525442i	$0.176100\pi$
$434$		0			0
$435$	−0.760332	−	0.339453i	−0.0364552	−	0.0162755i
$436$		0			0
$437$	31.3313	−	8.39519i	1.49878	−	0.401596i
$438$		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
$443$	−5.98671	+	22.3427i	−0.284437	+	1.06153i	0.664813	+	0.747010i	$0.268511\pi$
$443$	−5.98671	+	22.3427i	−0.284437	+	1.06153i	−0.949250	+	0.314523i	$0.898155\pi$
$444$		0			0
$445$	2.37904	−	14.9220i	0.112777	−	0.707371i
$446$		0			0
$447$	−17.3568	−	17.3568i	−0.820947	−	0.820947i
$448$		0			0
$449$			36.7511i			1.73439i	0.497966	+	0.867197i	$0.334080\pi$
$449$			36.7511i			1.73439i	−0.497966	+	0.867197i	$0.665920\pi$
$450$		0			0
$451$	1.33872	+	0.772910i	0.0630378	+	0.0363949i
$452$		0			0
$453$	6.09894	+	1.63421i	0.286553	+	0.0767818i
$454$		0			0
$455$	−5.22339	+	3.45820i	−0.244876	+	0.162123i
$456$		0			0
$457$	−15.2472	−	4.08547i	−0.713233	−	0.191110i	−0.116083	−	0.993240i	$-0.537034\pi$
$457$	−15.2472	−	4.08547i	−0.713233	−	0.191110i	−0.597150	+	0.802129i	$0.703700\pi$
$458$		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	$-0.0834760\pi$
$463$	15.2033	+	15.2033i	0.706558	+	0.706558i	−0.259252	+	0.965810i	$0.583476\pi$
$464$		0			0
$465$	−40.2182	+	29.1576i	−1.86508	+	1.35215i
$466$		0			0
$467$	0.883995	−	3.29912i	0.0409064	−	0.152665i	−0.942452	−	0.334342i	$-0.891486\pi$
$467$	0.883995	−	3.29912i	0.0409064	−	0.152665i	0.983358	+	0.181677i	$0.0581526\pi$
$468$		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
$473$	−0.487916	+	0.130737i	−0.0224344	+	0.00601128i
$474$		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
$483$	22.7755	−	11.8893i	1.03632	−	0.540982i
$484$		0			0
$485$	3.14694	+	30.2381i	0.142895	+	1.37304i
$486$		0			0
$487$	3.63537	+	13.5674i	0.164734	+	0.614797i	0.998074	+	0.0620356i	$0.0197592\pi$
$487$	3.63537	+	13.5674i	0.164734	+	0.614797i	−0.833340	+	0.552761i	$0.813574\pi$
$488$		0			0
$489$	−24.6964			−1.11681
$490$		0			0
$491$	−16.9628			−0.765519			−0.382759	−	0.923848i	$-0.625026\pi$
$491$	−16.9628			−0.765519			−0.382759	+	0.923848i	$0.625026\pi$
$492$		0			0
$493$	0.100094	+	0.373556i	0.00450800	+	0.0168241i
$494$		0			0
$495$	0.400605	−	0.493675i	0.0180059	−	0.0221890i
$496$		0			0
$497$	22.2882	−	11.6349i	0.999761	−	0.521896i
$498$		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	−0.885595	−	0.464459i	$-0.846249\pi$
$503$	−9.44510	+	9.44510i	−0.421136	+	0.421136i	0.464459	+	0.885595i	$0.346249\pi$
$504$		0			0
$505$	−8.78596	−	22.9583i	−0.390970	−	1.02163i
$506$		0			0
$507$	−26.1765	+	7.01397i	−1.16254	+	0.311501i
$508$		0			0
$509$	−5.59042	−	9.68290i	−0.247791	−	0.429187i	0.715121	−	0.699000i	$-0.246371\pi$
$509$	−5.59042	−	9.68290i	−0.247791	−	0.429187i	−0.962913	+	0.269813i	$0.913038\pi$
$510$		0			0
$511$	−3.34268	−	3.63953i	−0.147871	−	0.161003i
$512$		0			0
$513$	3.57872	−	13.3560i	0.158004	−	0.589680i
$514$		0			0
$515$	−10.5040	−	14.4886i	−0.462860	−	0.638442i
$516$		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
$523$	6.32091	+	1.69368i	0.276394	+	0.0740595i	0.394353	−	0.918959i	$-0.370969\pi$
$523$	6.32091	+	1.69368i	0.276394	+	0.0740595i	−0.117959	+	0.993018i	$0.537635\pi$
$524$		0			0
$525$	17.5475	−	24.5540i	0.765837	−	1.07162i
$526$		0			0
$527$	22.2858	+	5.97146i	0.970784	+	0.260121i
$528$		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
$535$	−22.8854	−	31.5668i	−0.989423	−	1.36475i
$536$		0			0
$537$	1.30752	−	4.87973i	0.0564236	−	0.210576i
$538$		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
$543$	16.7284	−	4.48236i	0.717884	−	0.192356i
$544$		0			0
$545$	8.08069	+	21.1153i	0.346139	+	0.904482i
$546$		0			0
$547$	−24.0098	+	24.0098i	−1.02658	+	1.02658i	−0.0269473	+	0.999637i	$0.508579\pi$
$547$	−24.0098	+	24.0098i	−1.02658	+	1.02658i	−0.999637	+	0.0269473i	$0.991421\pi$
$548$		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
$553$	−13.8988	+	21.8719i	−0.591039	+	0.930089i
$554$		0			0
$555$	0.299687	−	0.369311i	0.0127210	−	0.0156764i
$556$		0			0
$557$	−8.32418	−	31.0663i	−0.352707	−	1.31632i	−0.883346	−	0.468722i	$-0.844715\pi$
$557$	−8.32418	−	31.0663i	−0.352707	−	1.31632i	0.530639	−	0.847598i	$-0.321952\pi$
$558$		0			0
$559$	4.14740			0.175416
$560$		0			0
$561$	−0.697090			−0.0294312
$562$		0			0
$563$	−8.43607	−	31.4838i	−0.355538	−	1.32689i	−0.879806	−	0.475333i	$-0.842328\pi$
$563$	−8.43607	−	31.4838i	−0.355538	−	1.32689i	0.524268	−	0.851553i	$-0.324339\pi$
$564$		0			0
$565$	1.64597	+	15.8156i	0.0692463	+	0.665369i
$566$		0			0
$567$	1.20853	−	28.4253i	0.0507535	−	1.19375i
$568$		0			0
$569$	2.61511	−	1.50983i	0.109631	−	0.0632955i	−0.444182	−	0.895937i	$-0.646506\pi$
$569$	2.61511	−	1.50983i	0.109631	−	0.0632955i	0.553813	+	0.832641i	$0.313172\pi$
$570$		0			0
$571$	8.68176	−	15.0372i	0.363320	−	0.629289i	−0.625185	−	0.780477i	$-0.714976\pi$
$571$	8.68176	−	15.0372i	0.363320	−	0.629289i	0.988505	+	0.151188i	$0.0483097\pi$
$572$		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
$577$	2.03968	−	0.546530i	0.0849129	−	0.0227523i	−0.216112	−	0.976368i	$-0.569338\pi$
$577$	2.03968	−	0.546530i	0.0849129	−	0.0227523i	0.301025	+	0.953616i	$0.402671\pi$
$578$		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
$583$	−0.252961	+	0.944064i	−0.0104766	+	0.0390992i
$584$		0			0
$585$	−4.22622	+	3.06394i	−0.174733	+	0.126678i
$586$		0			0
$587$	30.8860	+	30.8860i	1.27480	+	1.27480i	0.943538	+	0.331265i	$0.107475\pi$
$587$	30.8860	+	30.8860i	1.27480	+	1.27480i	0.331265	+	0.943538i	$0.392525\pi$
$588$		0			0
$589$		−	74.2068i		−	3.05764i
$590$		0			0
$591$	−26.7610	−	15.4505i	−1.10080	−	0.635547i
$592$		0			0
$593$	−7.38980	−	1.98009i	−0.303463	−	0.0813126i	0.103875	−	0.994590i	$-0.466876\pi$
$593$	−7.38980	−	1.98009i	−0.303463	−	0.0813126i	−0.407337	+	0.913278i	$0.633543\pi$
$594$		0			0
$595$	−13.9908	+	0.857421i	−0.573565	+	0.0351508i
$596$		0			0
$597$	44.6752	+	11.9707i	1.82843	+	0.489927i
$598$		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
$605$	−3.86673	+	24.2533i	−0.157205	+	0.986035i
$606$		0			0
$607$	4.10766	−	15.3300i	0.166725	−	0.622225i	−0.831089	−	0.556139i	$-0.812282\pi$
$607$	4.10766	−	15.3300i	0.166725	−	0.622225i	0.997814	−	0.0660860i	$-0.0210512\pi$
$608$		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
$613$	18.1158	−	4.85413i	0.731692	−	0.196056i	0.126309	−	0.991991i	$-0.459687\pi$
$613$	18.1158	−	4.85413i	0.731692	−	0.196056i	0.605383	+	0.795935i	$0.293020\pi$
$614$		0			0
$615$	55.8343	+	24.9274i	2.25145	+	1.00517i
$616$		0			0
$617$	−18.1371	+	18.1371i	−0.730172	+	0.730172i	−0.970654	−	0.240482i	$-0.922695\pi$
$617$	−18.1371	+	18.1371i	−0.730172	+	0.730172i	0.240482	+	0.970654i	$0.422695\pi$
$618$		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
$623$	15.0899	+	9.58911i	0.604565	+	0.384180i
$624$		0			0
$625$	−22.8800	+	10.0750i	−0.915199	+	0.403002i
$626$		0			0
$627$	0.580290	+	2.16567i	0.0231745	+	0.0864886i
$628$		0			0
$629$	−0.220897			−0.00880774
$630$		0			0
$631$	−3.53048			−0.140546			−0.0702731	−	0.997528i	$-0.522387\pi$
$631$	−3.53048			−0.140546			−0.0702731	+	0.997528i	$0.522387\pi$
$632$		0			0
$633$	−4.80929	−	17.9485i	−0.191152	−	0.713389i
$634$		0			0
$635$	1.79432	−	0.186738i	0.0712054	−	0.00741049i
$636$		0			0
$637$	−1.30379	−	7.29659i	−0.0516580	−	0.289101i
$638$		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	−0.318098	+	0.948058i	$0.603044\pi$
$643$	−32.1065	+	32.1065i	−1.26616	+	1.26616i	−0.948058	+	0.318098i	$0.896956\pi$
$644$		0			0
$645$	−18.6609	+	7.14140i	−0.734772	+	0.281192i
$646$		0			0
$647$	23.1358	−	6.19921i	0.909561	−	0.243716i	0.226443	−	0.974024i	$-0.427290\pi$
$647$	23.1358	−	6.19921i	0.909561	−	0.243716i	0.683118	+	0.730308i	$0.260624\pi$
$648$		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
$653$	10.5442	−	39.3513i	0.412625	−	1.53994i	−0.376921	−	0.926245i	$-0.623017\pi$
$653$	10.5442	−	39.3513i	0.412625	−	1.53994i	0.789546	−	0.613691i	$-0.210316\pi$
$654$		0			0
$655$	−7.35883	−	1.17323i	−0.287533	−	0.0458418i
$656$		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
$663$	5.52851	+	1.48136i	0.214709	+	0.0575312i
$664$		0			0
$665$	14.3103	+	42.7518i	0.554931	+	1.65784i
$666$		0			0
$667$	−0.671100	−	0.179821i	−0.0259851	−	0.00696268i
$668$		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	0.773229	−	0.634127i	$-0.218641\pi$
$673$	3.60859	+	3.60859i	0.139101	+	0.139101i	−0.634127	+	0.773229i	$0.718641\pi$
$674$		0			0
$675$	−4.95669	+	7.59861i	−0.190783	+	0.292471i
$676$		0			0
$677$	−8.19130	+	30.5704i	−0.314817	+	1.17491i	0.609342	+	0.792907i	$0.291434\pi$
$677$	−8.19130	+	30.5704i	−0.314817	+	1.17491i	−0.924160	+	0.382007i	$0.875233\pi$
$678$		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
$683$	19.3813	−	5.19321i	0.741605	−	0.198713i	0.131814	−	0.991274i	$-0.457920\pi$
$683$	19.3813	−	5.19321i	0.741605	−	0.198713i	0.609791	+	0.792562i	$0.291253\pi$
$684$		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	−0.102224	−	0.994761i	$-0.532596\pi$
$691$	18.6151	−	10.7475i	0.708153	−	0.408853i	0.810377	+	0.585909i	$0.199262\pi$
$692$		0			0
$693$	0.348112	+	0.666856i	0.0132237	+	0.0253318i
$694$		0			0
$695$	−2.27547	−	1.84649i	−0.0863135	−	0.0700413i
$696$		0			0
$697$	−7.35030	−	27.4317i	−0.278412	−	1.03905i
$698$		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
$703$	0.183885	+	0.686267i	0.00693535	+	0.0258831i
$704$		0			0
$705$	9.15176	+	7.42643i	0.344675	+	0.279696i
$706$		0			0
$707$	29.0596	+	1.23550i	1.09290	+	0.0464656i
$708$		0			0
$709$	−5.69705	+	3.28920i	−0.213957	+	0.123528i	−0.603149	−	0.797628i	$-0.706088\pi$
$709$	−5.69705	+	3.28920i	−0.213957	+	0.123528i	0.389192	+	0.921157i	$0.372754\pi$
$710$		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
$717$	−11.0308	+	2.95570i	−0.411953	+	0.110383i
$718$		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
$723$	−11.9616	+	44.6411i	−0.444855	+	1.66022i
$724$		0			0
$725$	−0.798642	+	0.168053i	−0.0296608	+	0.00624132i
$726$		0			0
$727$	−24.4451	−	24.4451i	−0.906619	−	0.906619i	0.0893785	−	0.995998i	$-0.471512\pi$
$727$	−24.4451	−	24.4451i	−0.906619	−	0.906619i	−0.995998	+	0.0893785i	$0.971512\pi$
$728$		0			0
$729$		−	11.2892i		−	0.418120i
$730$		0			0
$731$	8.03678	+	4.64004i	0.297251	+	0.171618i
$732$		0			0
$733$	7.03942	+	1.88621i	0.260007	+	0.0696686i	0.386468	−	0.922303i	$-0.373695\pi$
$733$	7.03942	+	1.88621i	0.260007	+	0.0696686i	−0.126461	+	0.991972i	$0.540362\pi$
$734$		0			0
$735$	18.4302	+	30.5854i	0.679810	+	1.12816i
$736$		0			0
$737$	0.882999	+	0.236599i	0.0325257	+	0.00871523i
$738$		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	$-0.147112\pi$
$743$	12.2443	+	12.2443i	0.449200	+	0.449200i	−0.445888	+	0.895089i	$0.647112\pi$
$744$		0			0
$745$	−23.7587	−	3.78788i	−0.870451	−	0.138777i
$746$		0			0
$747$	−6.80970	+	25.4141i	−0.249154	+	0.929854i
$748$		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	$0.0340170\pi$
$751$	16.1555	+	27.9821i	0.589521	+	1.02108i	−0.404774	+	0.914417i	$0.632650\pi$
$752$		0			0
$753$	48.0797	−	12.8829i	1.75212	−	0.469480i
$754$		0			0
$755$	5.77992	−	2.21193i	0.210353	−	0.0805005i
$756$		0			0
$757$	−25.7314	+	25.7314i	−0.935223	+	0.935223i	−0.998026	−	0.0628033i	$-0.979996\pi$
$757$	−25.7314	+	25.7314i	−0.935223	+	0.935223i	0.0628033	+	0.998026i	$0.479996\pi$
$758$		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
$763$	−26.7269	−	1.13632i	−0.967578	−	0.0411376i
$764$		0			0
$765$	−11.6174	+	1.20904i	−0.420027	+	0.0437131i
$766$		0			0
$767$	−2.26643	−	8.45843i	−0.0818361	−	0.305416i
$768$		0			0
$769$	−30.4018			−1.09632			−0.548159	−	0.836374i	$-0.684671\pi$
$769$	−30.4018			−1.09632			−0.548159	+	0.836374i	$0.684671\pi$
$770$		0			0
$771$	8.97497			0.323226
$772$		0			0
$773$	5.78340	+	21.5840i	0.208015	+	0.776321i	0.988509	+	0.151159i	$0.0483005\pi$
$773$	5.78340	+	21.5840i	0.208015	+	0.776321i	−0.780495	+	0.625162i	$0.785033\pi$
$774$		0			0
$775$	−15.1403	+	46.2753i	−0.543856	+	1.66226i
$776$		0			0
$777$	0.260418	+	0.498866i	0.00934245	+	0.0178967i
$778$		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
$787$	−8.65181	+	2.31825i	−0.308404	+	0.0826366i	−0.409702	−	0.912220i	$-0.634367\pi$
$787$	−8.65181	+	2.31825i	−0.308404	+	0.0826366i	0.101298	+	0.994856i	$0.467701\pi$
$788$		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
$793$	−3.64283	+	13.5952i	−0.129361	+	0.482781i
$794$		0			0
$795$	−6.08682	+	38.1783i	−0.215877	+	1.35405i
$796$		0			0
$797$	−32.4551	−	32.4551i	−1.14962	−	1.14962i	−0.986628	−	0.162990i	$-0.947886\pi$
$797$	−32.4551	−	32.4551i	−1.14962	−	1.14962i	−0.162990	−	0.986628i	$-0.552114\pi$
$798$		0			0
$799$		−	5.47396i		−	0.193655i
$800$		0			0
$801$	12.9022	+	7.44911i	0.455878	+	0.263201i
$802$		0			0
$803$	−0.232668	−	0.0623431i	−0.00821066	−	0.00220004i
$804$		0			0
$805$	11.2333	−	22.5375i	0.395923	−	0.794341i
$806$		0			0
$807$	40.2252	+	10.7783i	1.41599	+	0.379414i
$808$		0			0
$809$	37.3411	+	21.5589i	1.31284	+	0.757970i	0.982566	−	0.185915i	$-0.0595248\pi$
$809$	37.3411	+	21.5589i	1.31284	+	0.757970i	0.330276	+	0.943884i	$0.392858\pi$
$810$		0			0
$811$			15.8129i			0.555267i	0.960687	+	0.277634i	$0.0895501\pi$
$811$			15.8129i			0.555267i	−0.960687	+	0.277634i	$0.910450\pi$
$812$		0			0
$813$	40.0103	+	40.0103i	1.40322	+	1.40322i
$814$		0			0
$815$	−19.5976	+	14.2079i	−0.686473	+	0.497682i
$816$		0			0
$817$	7.72516	−	28.8307i	0.270269	−	1.00866i
$818$		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
$823$	−32.1424	+	8.61252i	−1.12041	+	0.300214i	−0.771050	−	0.636774i	$-0.780268\pi$
$823$	−32.1424	+	8.61252i	−1.12041	+	0.300214i	−0.349362	+	0.936988i	$0.613602\pi$
$824$		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	$-0.624763\pi$
$827$	15.5915	−	15.5915i	0.542171	−	0.542171i	0.924165	+	0.381994i	$0.124763\pi$
$828$		0			0
$829$	−14.1523	+	24.5126i	−0.491531	+	0.851357i	−0.999952	−	0.00975135i	$-0.996896\pi$
$829$	−14.1523	+	24.5126i	−0.491531	+	0.851357i	0.508421	+	0.861109i	$0.330229\pi$
$830$		0			0
$831$	−18.9511	+	10.9414i	−0.657405	+	0.379553i
$832$		0			0
$833$	5.63682	−	15.5979i	0.195304	−	0.540434i
$834$		0			0
$835$	1.91602	+	18.4105i	0.0663064	+	0.637121i
$836$		0			0
$837$	4.57308	+	17.0670i	0.158069	+	0.589921i
$838$		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
$843$	5.23670	+	19.5436i	0.180361	+	0.673118i
$844$		0			0
$845$	−16.7369	+	20.6253i	−0.575768	+	0.709531i
$846$		0			0
$847$	−24.5262	−	15.5855i	−0.842729	−	0.535524i
$848$		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	0.288274	−	0.957548i	$-0.406919\pi$
$853$	36.3857	−	36.3857i	1.24582	−	1.24582i	0.957548	−	0.288274i	$-0.0930814\pi$
$854$		0			0
$855$	13.4270	+	35.0856i	0.459194	+	1.19990i
$856$		0			0
$857$	22.7581	−	6.09802i	0.777402	−	0.208304i	0.151763	−	0.988417i	$-0.451505\pi$
$857$	22.7581	−	6.09802i	0.777402	−	0.208304i	0.625639	+	0.780113i	$0.284838\pi$
$858$		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
$863$	6.45233	−	24.0804i	0.219640	−	0.819707i	−0.764842	−	0.644218i	$-0.777183\pi$
$863$	6.45233	−	24.0804i	0.219640	−	0.819707i	0.984481	−	0.175489i	$-0.0561505\pi$
$864$		0			0
$865$	−13.5227	−	18.6524i	−0.459785	−	0.634201i
$866$		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
$873$	−28.9530	−	7.75794i	−0.979912	−	0.262567i
$874$		0			0
$875$	−0.201328	−	29.5797i	−0.00680612	−	0.999977i
$876$		0			0
$877$	−24.5932	−	6.58973i	−0.830454	−	0.222520i	−0.181542	−	0.983383i	$-0.558109\pi$
$877$	−24.5932	−	6.58973i	−0.830454	−	0.222520i	−0.648912	+	0.760864i	$0.724776\pi$
$878$		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	$-0.243544\pi$
$883$	0.852334	+	0.852334i	0.0286833	+	0.0286833i	−0.692620	+	0.721303i	$0.743544\pi$
$884$		0			0
$885$	24.7622	+	34.1555i	0.832371	+	1.14812i
$886$		0			0
$887$	−6.17074	+	23.0295i	−0.207193	+	0.773256i	0.781577	+	0.623809i	$0.214416\pi$
$887$	−6.17074	+	23.0295i	−0.207193	+	0.773256i	−0.988770	+	0.149446i	$0.952251\pi$
$888$		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
$893$	−17.0061	+	4.55678i	−0.569088	+	0.152487i
$894$		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
$903$	1.00423	−	23.6202i	0.0334188	−	0.786030i
$904$		0			0
$905$	10.6959	−	13.1808i	0.355544	−	0.438145i
$906$		0			0
$907$	8.24891	+	30.7853i	0.273900	+	1.02221i	0.956575	+	0.291488i	$0.0941502\pi$
$907$	8.24891	+	30.7853i	0.273900	+	1.02221i	−0.682674	+	0.730723i	$0.739183\pi$
$908$		0			0
$909$	24.2367			0.803881
$910$		0			0
$911$	−7.74616			−0.256642			−0.128321	−	0.991733i	$-0.540959\pi$
$911$	−7.74616			−0.256642			−0.128321	+	0.991733i	$0.540959\pi$
$912$		0			0
$913$	0.398344	+	1.48664i	0.0131833	+	0.0492006i
$914$		0			0
$915$	−7.01895	−	67.4432i	−0.232039	−	2.22960i
$916$		0			0
$917$	4.72889	−	7.44163i	0.156162	−	0.245744i
$918$		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
$927$	17.0430	−	4.56665i	0.559765	−	0.149989i
$928$		0			0
$929$	12.6229	+	21.8634i	0.414143	+	0.717316i	0.995338	−	0.0964479i	$-0.0307481\pi$
$929$	12.6229	+	21.8634i	0.414143	+	0.717316i	−0.581195	+	0.813764i	$0.697415\pi$
$930$		0			0
$931$	−53.1507	−	4.52770i	−1.74194	−	0.148389i
$932$		0			0
$933$	−14.5211	+	54.1934i	−0.475399	+	1.77421i
$934$		0			0
$935$	−0.553168	+	0.401038i	−0.0180905	+	0.0131153i
$936$		0			0
$937$	26.1816	+	26.1816i	0.855315	+	0.855315i	0.990782	−	0.135467i	$-0.0432535\pi$
$937$	26.1816	+	26.1816i	0.855315	+	0.855315i	−0.135467	+	0.990782i	$0.543254\pi$
$938$		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
$943$	49.2815	+	13.2049i	1.60483	+	0.430012i
$944$		0			0
$945$	−5.92589	−	8.95067i	−0.192769	−	0.291165i
$946$		0			0
$947$	24.4823	+	6.56000i	0.795566	+	0.213171i	0.633636	−	0.773631i	$-0.281562\pi$
$947$	24.4823	+	6.56000i	0.795566	+	0.213171i	0.161930	+	0.986802i	$0.448228\pi$
$948$		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	0.991935	+	0.126747i	$0.0404537\pi$
$953$	34.5345	+	34.5345i	1.11868	+	1.11868i	0.126747	+	0.991935i	$0.459546\pi$
$954$		0			0
$955$	0.294281	−	1.84582i	0.00952271	−	0.0597293i
$956$		0			0
$957$	0.0124295	−	0.0463875i	0.000401789	−	0.00149950i
$958$		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
$963$	37.1322	−	9.94955i	1.19657	−	0.320620i
$964$		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	$-0.682073\pi$
$967$	9.31362	−	9.31362i	0.299506	−	0.299506i	0.840820	+	0.541314i	$0.182073\pi$
$968$		0			0
$969$	20.5953	−	35.6722i	0.661617	−	1.14595i
$970$		0			0
$971$	−9.73473	+	5.62035i	−0.312402	+	0.180366i	−0.648001	−	0.761639i	$-0.724395\pi$
$971$	−9.73473	+	5.62035i	−0.312402	+	0.180366i	0.335599	+	0.942005i	$0.391061\pi$
$972$		0			0
$973$	3.07371	−	1.60454i	0.0985385	−	0.0514391i
$974$		0			0
$975$	−3.75591	+	11.4797i	−0.120285	+	0.367644i
$976$		0			0
$977$	0.795651	+	2.96941i	0.0254551	+	0.0949999i	0.977485	−	0.211006i	$-0.0676740\pi$
$977$	0.795651	+	2.96941i	0.0254551	+	0.0949999i	−0.952030	+	0.306006i	$0.901007\pi$
$978$		0			0
$979$	0.871494			0.0278531
$980$		0			0
$981$	−22.2912			−0.711702
$982$		0			0
$983$	1.70064	+	6.34688i	0.0542421	+	0.202434i	0.987729	−	0.156177i	$-0.0499170\pi$
$983$	1.70064	+	6.34688i	0.0542421	+	0.202434i	−0.933487	+	0.358611i	$0.883250\pi$
$984$		0			0
$985$	−30.1246	+	3.13513i	−0.959850	+	0.0998935i
$986$		0			0
$987$	−12.3622	+	6.45332i	−0.393493	+	0.205411i
$988$		0			0
$989$	−14.4382	+	8.33591i	−0.459109	+	0.265067i
$990$		0			0
$991$	−13.2859	+	23.0119i	−0.422041	+	0.730997i	−0.996139	−	0.0877900i	$-0.972020\pi$
$991$	−13.2859	+	23.0119i	−0.422041	+	0.730997i	0.574098	+	0.818787i	$0.305353\pi$
$992$		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
$997$	6.55613	−	1.75671i	0.207635	−	0.0556355i	−0.153502	−	0.988148i	$-0.549055\pi$
$997$	6.55613	−	1.75671i	0.207635	−	0.0556355i	0.361137	+	0.932513i	$0.382389\pi$
$998$		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	280.2.bo.a.73.11	yes	48
4.3	odd	2		560.2.ci.e.353.2		48
5.2	odd	4	inner	280.2.bo.a.17.11	✓	48
7.5	odd	6	inner	280.2.bo.a.33.11	yes	48
20.7	even	4		560.2.ci.e.17.2		48
28.19	even	6		560.2.ci.e.33.2		48
35.12	even	12	inner	280.2.bo.a.257.11	yes	48
140.47	odd	12		560.2.ci.e.257.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bo.a.17.11	✓	48	5.2	odd	4	inner
280.2.bo.a.33.11	yes	48	7.5	odd	6	inner
280.2.bo.a.73.11	yes	48	1.1	even	1	trivial
280.2.bo.a.257.11	yes	48	35.12	even	12	inner
560.2.ci.e.17.2		48	20.7	even	4
560.2.ci.e.33.2		48	28.19	even	6
560.2.ci.e.257.2		48	140.47	odd	12
560.2.ci.e.353.2		48	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.590462 + 2.20364i) q^{3} +(1.73631 + 1.40898i) q^{5} +(-2.34541 + 1.22435i) q^{7} +(-1.90929 + 1.10233i) q^{9} +O(q^{10})\)	\(q+(0.590462 + 2.20364i) q^{3} +(1.73631 + 1.40898i) q^{5} +(-2.34541 + 1.22435i) q^{7} +(-1.90929 + 1.10233i) q^{9} +(-0.0644824 + 0.111687i) q^{11} +(0.748741 - 0.748741i) q^{13} +(-2.07964 + 4.65815i) q^{15} +(2.28858 - 0.613222i) q^{17} +(-3.81023 - 6.59951i) q^{19} +(-4.08291 - 4.44550i) q^{21} +(-1.10166 + 4.11147i) q^{23} +(1.02957 + 4.89285i) q^{25} +(1.28303 + 1.28303i) q^{27} +0.163226i q^{29} +(8.43321 + 4.86892i) q^{31} +(-0.284192 - 0.0761489i) q^{33} +(-5.79746 - 1.17877i) q^{35} +(-0.0900559 - 0.0241304i) q^{37} +(2.09206 + 1.20785i) q^{39} -11.9864i q^{41} +(2.76959 + 2.76959i) q^{43} +(-4.86828 - 0.776156i) q^{45} +(0.597966 - 2.23164i) q^{47} +(4.00192 - 5.74323i) q^{49} +(2.70264 + 4.68110i) q^{51} +(7.32032 - 1.96147i) q^{53} +(-0.269326 + 0.103069i) q^{55} +(12.2931 - 12.2931i) q^{57} +(4.13495 - 7.16194i) q^{59} +(-11.5114 + 6.64609i) q^{61} +(3.12843 - 4.92306i) q^{63} +(2.35501 - 0.245090i) q^{65} +(-1.83460 - 6.84682i) q^{67} -9.71067 q^{69} -9.50288 q^{71} +(0.483412 + 1.80412i) q^{73} +(-10.1741 + 5.15784i) q^{75} +(0.0144937 - 0.340901i) q^{77} +(8.48250 - 4.89737i) q^{79} +(-5.37673 + 9.31277i) q^{81} +(8.43870 - 8.43870i) q^{83} +(4.83770 + 2.15980i) q^{85} +(-0.359691 + 0.0963790i) q^{87} +(-3.37880 - 5.85226i) q^{89} +(-0.839383 + 2.67283i) q^{91} +(-5.74983 + 21.4586i) q^{93} +(2.68281 - 16.8273i) q^{95} +(9.61378 + 9.61378i) q^{97} -0.284323i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{7}+O(q^{10}) \) 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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