LMFDB - Embedded newform 280.2.x.a.97.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(97,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 1, 2]))

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

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

chi := DirichletCharacter("280.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.x (of order $4$, degree $2$, 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:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			97.9
Character	$\chi$	$=$	280.97
Dual form			280.2.x.a.153.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.03893 + 1.03893i) q^{3} +(-1.21973 + 1.87411i) q^{5} +(1.58883 + 2.11557i) q^{7} -0.841261i q^{9} +O(q^{10})$	\(q+(1.03893 + 1.03893i) q^{3} +(-1.21973 + 1.87411i) q^{5} +(1.58883 + 2.11557i) q^{7} -0.841261i q^{9} -2.34687 q^{11} +(1.96436 + 1.96436i) q^{13} +(-3.21426 + 0.679854i) q^{15} +(-5.15858 + 5.15858i) q^{17} +3.74821 q^{19} +(-0.547244 + 3.84860i) q^{21} +(6.08007 - 6.08007i) q^{23} +(-2.02454 - 4.57179i) q^{25} +(3.99079 - 3.99079i) q^{27} +5.89034i q^{29} -1.56648i q^{31} +(-2.43823 - 2.43823i) q^{33} +(-5.90273 + 0.397220i) q^{35} +(1.53441 + 1.53441i) q^{37} +4.08166i q^{39} -9.51977i q^{41} +(1.86313 - 1.86313i) q^{43} +(1.57661 + 1.02611i) q^{45} +(4.59474 - 4.59474i) q^{47} +(-1.95125 + 6.72254i) q^{49} -10.7188 q^{51} +(3.88128 - 3.88128i) q^{53} +(2.86254 - 4.39829i) q^{55} +(3.89412 + 3.89412i) q^{57} -4.62061 q^{59} -2.00065i q^{61} +(1.77974 - 1.33662i) q^{63} +(-6.07740 + 1.28544i) q^{65} +(2.69156 + 2.69156i) q^{67} +12.6335 q^{69} -0.392229 q^{71} +(-7.08543 - 7.08543i) q^{73} +(2.64640 - 6.85310i) q^{75} +(-3.72878 - 4.96497i) q^{77} -4.98717i q^{79} +5.76850 q^{81} +(-9.36651 - 9.36651i) q^{83} +(-3.37567 - 15.9598i) q^{85} +(-6.11964 + 6.11964i) q^{87} -9.83200 q^{89} +(-1.03471 + 7.27677i) q^{91} +(1.62746 - 1.62746i) q^{93} +(-4.57179 + 7.02454i) q^{95} +(11.8576 - 11.8576i) q^{97} +1.97433i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{7}+O(q^{10}) $ 24 * q + 4 * q^7	$ 24 q + 4 q^{7} + 8 q^{11} - 8 q^{15} + 16 q^{21} - 32 q^{23} + 8 q^{25} + 12 q^{35} - 8 q^{37} + 16 q^{43} - 24 q^{51} - 16 q^{53} + 20 q^{63} - 48 q^{65} - 32 q^{67} - 32 q^{71} - 40 q^{77} - 72 q^{81} + 16 q^{85} - 64 q^{91} + 72 q^{93} - 24 q^{95}+O(q^{100}) $ 24 * q + 4 * q^7 + 8 * q^11 - 8 * q^15 + 16 * q^21 - 32 * q^23 + 8 * q^25 + 12 * q^35 - 8 * q^37 + 16 * q^43 - 24 * q^51 - 16 * q^53 + 20 * q^63 - 48 * q^65 - 32 * q^67 - 32 * q^71 - 40 * q^77 - 72 * q^81 + 16 * q^85 - 64 * q^91 + 72 * q^93 - 24 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.03893	+	1.03893i	0.599825	+	0.599825i	0.940266	−	0.340441i	$-0.110576\pi$
$3$	1.03893	+	1.03893i	0.599825	+	0.599825i	−0.340441	+	0.940266i	$0.610576\pi$
$4$		0			0
$5$	−1.21973	+	1.87411i	−0.545478	+	0.838125i
$5$	−1.21973	+	1.87411i	−0.545478	+	0.838125i
$6$		0			0
$7$	1.58883	+	2.11557i	0.600520	+	0.799609i
$7$	1.58883	+	2.11557i	0.600520	+	0.799609i
$8$		0			0
$9$		−	0.841261i		−	0.280420i
$10$		0			0
$11$	−2.34687			−0.707609			−0.353804	−	0.935319i	$-0.615112\pi$
$11$	−2.34687			−0.707609			−0.353804	+	0.935319i	$0.615112\pi$
$12$		0			0
$13$	1.96436	+	1.96436i	0.544816	+	0.544816i	0.924937	−	0.380121i	$-0.124118\pi$
$13$	1.96436	+	1.96436i	0.544816	+	0.544816i	−0.380121	+	0.924937i	$0.624118\pi$
$14$		0			0
$15$	−3.21426	+	0.679854i	−0.829919	+	0.175537i
$16$		0			0
$17$	−5.15858	+	5.15858i	−1.25114	+	1.25114i	−0.295929	+	0.955210i	$0.595629\pi$
$17$	−5.15858	+	5.15858i	−1.25114	+	1.25114i	−0.955210	+	0.295929i	$0.904371\pi$
$18$		0			0
$19$	3.74821			0.859899			0.429949	−	0.902853i	$-0.358531\pi$
$19$	3.74821			0.859899			0.429949	+	0.902853i	$0.358531\pi$
$20$		0			0
$21$	−0.547244	+	3.84860i	−0.119419	+	0.839833i
$22$		0			0
$23$	6.08007	−	6.08007i	1.26778	−	1.26778i	0.320550	−	0.947232i	$-0.396132\pi$
$23$	6.08007	−	6.08007i	1.26778	−	1.26778i	0.947232	−	0.320550i	$-0.103868\pi$
$24$		0			0
$25$	−2.02454	−	4.57179i	−0.404908	−	0.914357i
$26$		0			0
$27$	3.99079	−	3.99079i	0.768028	−	0.768028i
$28$		0			0
$29$			5.89034i			1.09381i	0.837195	+	0.546905i	$0.184194\pi$
$29$			5.89034i			1.09381i	−0.837195	+	0.546905i	$0.815806\pi$
$30$		0			0
$31$		−	1.56648i		−	0.281348i	−0.990056	−	0.140674i	$-0.955073\pi$
$31$		−	1.56648i		−	0.281348i	0.990056	−	0.140674i	$-0.0449270\pi$
$32$		0			0
$33$	−2.43823	−	2.43823i	−0.424441	−	0.424441i
$34$		0			0
$35$	−5.90273	+	0.397220i	−0.997743	+	0.0671424i
$36$		0			0
$37$	1.53441	+	1.53441i	0.252256	+	0.252256i	0.821895	−	0.569639i	$-0.192917\pi$
$37$	1.53441	+	1.53441i	0.252256	+	0.252256i	−0.569639	+	0.821895i	$0.692917\pi$
$38$		0			0
$39$			4.08166i			0.653588i
$40$		0			0
$41$		−	9.51977i		−	1.48674i	−0.668882	−	0.743369i	$-0.733227\pi$
$41$		−	9.51977i		−	1.48674i	0.668882	−	0.743369i	$-0.266773\pi$
$42$		0			0
$43$	1.86313	−	1.86313i	0.284125	−	0.284125i	−0.550626	−	0.834752i	$-0.685611\pi$
$43$	1.86313	−	1.86313i	0.284125	−	0.284125i	0.834752	+	0.550626i	$0.185611\pi$
$44$		0			0
$45$	1.57661	+	1.02611i	0.235027	+	0.152963i
$46$		0			0
$47$	4.59474	−	4.59474i	0.670212	−	0.670212i	−0.287553	−	0.957765i	$-0.592842\pi$
$47$	4.59474	−	4.59474i	0.670212	−	0.670212i	0.957765	+	0.287553i	$0.0928418\pi$
$48$		0			0
$49$	−1.95125	+	6.72254i	−0.278750	+	0.960364i
$50$		0			0
$51$	−10.7188			−1.50093
$52$		0			0
$53$	3.88128	−	3.88128i	0.533135	−	0.533135i	−0.388369	−	0.921504i	$-0.626961\pi$
$53$	3.88128	−	3.88128i	0.533135	−	0.533135i	0.921504	+	0.388369i	$0.126961\pi$
$54$		0			0
$55$	2.86254	−	4.39829i	0.385985	−	0.593065i
$56$		0			0
$57$	3.89412	+	3.89412i	0.515789	+	0.515789i
$58$		0			0
$59$	−4.62061			−0.601552			−0.300776	−	0.953695i	$-0.597246\pi$
$59$	−4.62061			−0.601552			−0.300776	+	0.953695i	$0.597246\pi$
$60$		0			0
$61$		−	2.00065i		−	0.256156i	−0.991764	−	0.128078i	$-0.959119\pi$
$61$		−	2.00065i		−	0.256156i	0.991764	−	0.128078i	$-0.0408808\pi$
$62$		0			0
$63$	1.77974	−	1.33662i	0.224227	−	0.168398i
$64$		0			0
$65$	−6.07740	+	1.28544i	−0.753809	+	0.159439i
$66$		0			0
$67$	2.69156	+	2.69156i	0.328827	+	0.328827i	0.852140	−	0.523314i	$-0.175304\pi$
$67$	2.69156	+	2.69156i	0.328827	+	0.328827i	−0.523314	+	0.852140i	$0.675304\pi$
$68$		0			0
$69$	12.6335			1.52089
$70$		0			0
$71$	−0.392229			−0.0465491			−0.0232745	−	0.999729i	$-0.507409\pi$
$71$	−0.392229			−0.0465491			−0.0232745	+	0.999729i	$0.507409\pi$
$72$		0			0
$73$	−7.08543	−	7.08543i	−0.829287	−	0.829287i	0.158131	−	0.987418i	$-0.449453\pi$
$73$	−7.08543	−	7.08543i	−0.829287	−	0.829287i	−0.987418	+	0.158131i	$0.949453\pi$
$74$		0			0
$75$	2.64640	−	6.85310i	0.305580	−	0.791328i
$76$		0			0
$77$	−3.72878	−	4.96497i	−0.424934	−	0.565811i
$78$		0			0
$79$		−	4.98717i		−	0.561100i	−0.959839	−	0.280550i	$-0.909483\pi$
$79$		−	4.98717i		−	0.561100i	0.959839	−	0.280550i	$-0.0905169\pi$
$80$		0			0
$81$	5.76850			0.640944
$82$		0			0
$83$	−9.36651	−	9.36651i	−1.02811	−	1.02811i	−0.999593	−	0.0285148i	$-0.990922\pi$
$83$	−9.36651	−	9.36651i	−1.02811	−	1.02811i	−0.0285148	−	0.999593i	$-0.509078\pi$
$84$		0			0
$85$	−3.37567	−	15.9598i	−0.366143	−	1.73108i
$86$		0			0
$87$	−6.11964	+	6.11964i	−0.656094	+	0.656094i
$88$		0			0
$89$	−9.83200			−1.04219			−0.521095	−	0.853499i	$-0.674476\pi$
$89$	−9.83200			−1.04219			−0.521095	+	0.853499i	$0.674476\pi$
$90$		0			0
$91$	−1.03471	+	7.27677i	−0.108467	+	0.762813i
$92$		0			0
$93$	1.62746	−	1.62746i	0.168760	−	0.168760i
$94$		0			0
$95$	−4.57179	+	7.02454i	−0.469055	+	0.720703i
$96$		0			0
$97$	11.8576	−	11.8576i	1.20396	−	1.20396i	0.231006	−	0.972952i	$-0.425798\pi$
$97$	11.8576	−	11.8576i	1.20396	−	1.20396i	0.972952	−	0.231006i	$-0.0742016\pi$
$98$		0			0
$99$			1.97433i			0.198428i
$100$		0			0
$101$			8.41529i			0.837353i	0.908135	+	0.418676i	$0.137506\pi$
$101$			8.41529i			0.837353i	−0.908135	+	0.418676i	$0.862494\pi$
$102$		0			0
$103$	8.77874	+	8.77874i	0.864995	+	0.864995i	0.991913	−	0.126918i	$-0.0405085\pi$
$103$	8.77874	+	8.77874i	0.864995	+	0.864995i	−0.126918	+	0.991913i	$0.540509\pi$
$104$		0			0
$105$	−6.54519	−	5.71982i	−0.638745	−	0.558198i
$106$		0			0
$107$	10.3741	+	10.3741i	1.00290	+	1.00290i	0.999996	+	0.00290471i	$0.000924598\pi$
$107$	10.3741	+	10.3741i	1.00290	+	1.00290i	0.00290471	+	0.999996i	$0.499075\pi$
$108$		0			0
$109$			4.92724i			0.471944i	0.971760	+	0.235972i	$0.0758273\pi$
$109$			4.92724i			0.471944i	−0.971760	+	0.235972i	$0.924173\pi$
$110$		0			0
$111$			3.18828i			0.302618i
$112$		0			0
$113$	−3.79963	+	3.79963i	−0.357439	+	0.357439i	−0.862868	−	0.505429i	$-0.831334\pi$
$113$	−3.79963	+	3.79963i	−0.357439	+	0.357439i	0.505429	+	0.862868i	$0.331334\pi$
$114$		0			0
$115$	3.97868	+	18.8107i	0.371013	+	1.75411i
$116$		0			0
$117$	1.65254	−	1.65254i	0.152777	−	0.152777i
$118$		0			0
$119$	−19.1094	−	2.71723i	−1.75176	−	0.249088i
$120$		0			0
$121$	−5.49219			−0.499290
$122$		0			0
$123$	9.89034	−	9.89034i	0.891782	−	0.891782i
$124$		0			0
$125$	11.0374	+	1.78212i	0.987214	+	0.159397i
$126$		0			0
$127$	−0.777755	−	0.777755i	−0.0690146	−	0.0690146i	0.671757	−	0.740772i	$-0.265540\pi$
$127$	−0.777755	−	0.777755i	−0.0690146	−	0.0690146i	−0.740772	+	0.671757i	$0.765540\pi$
$128$		0			0
$129$	3.87132			0.340851
$130$		0			0
$131$			11.0373i			0.964336i	0.876079	+	0.482168i	$0.160151\pi$
$131$			11.0373i			0.964336i	−0.876079	+	0.482168i	$0.839849\pi$
$132$		0			0
$133$	5.95526	+	7.92959i	0.516387	+	0.687583i
$134$		0			0
$135$	2.61149	+	12.3468i	0.224762	+	1.06265i
$136$		0			0
$137$	2.65313	+	2.65313i	0.226672	+	0.226672i	0.811301	−	0.584629i	$-0.198760\pi$
$137$	2.65313	+	2.65313i	0.226672	+	0.226672i	−0.584629	+	0.811301i	$0.698760\pi$
$138$		0			0
$139$	7.15451			0.606838			0.303419	−	0.952857i	$-0.401872\pi$
$139$	7.15451			0.606838			0.303419	+	0.952857i	$0.401872\pi$
$140$		0			0
$141$	9.54720			0.804019
$142$		0			0
$143$	−4.61011	−	4.61011i	−0.385516	−	0.385516i
$144$		0			0
$145$	−11.0391	−	7.18460i	−0.916750	−	0.596649i
$146$		0			0
$147$	−9.01144	+	4.95702i	−0.743251	+	0.408848i
$148$		0			0
$149$			12.2552i			1.00399i	0.864872	+	0.501993i	$0.167400\pi$
$149$			12.2552i			1.00399i	−0.864872	+	0.501993i	$0.832600\pi$
$150$		0			0
$151$	−13.2221			−1.07600			−0.537998	−	0.842946i	$-0.680819\pi$
$151$	−13.2221			−1.07600			−0.537998	+	0.842946i	$0.680819\pi$
$152$		0			0
$153$	4.33971	+	4.33971i	0.350845	+	0.350845i
$154$		0			0
$155$	2.93575	+	1.91068i	0.235805	+	0.153469i
$156$		0			0
$157$	−8.35401	+	8.35401i	−0.666723	+	0.666723i	−0.956956	−	0.290233i	$-0.906267\pi$
$157$	−8.35401	+	8.35401i	−0.666723	+	0.666723i	0.290233	+	0.956956i	$0.406267\pi$
$158$		0			0
$159$	8.06474			0.639576
$160$		0			0
$161$	22.5230	+	3.20261i	1.77506	+	0.252401i
$162$		0			0
$163$	2.21768	−	2.21768i	0.173702	−	0.173702i	−0.614902	−	0.788604i	$-0.710804\pi$
$163$	2.21768	−	2.21768i	0.173702	−	0.173702i	0.788604	+	0.614902i	$0.210804\pi$
$164$		0			0
$165$	7.54347	−	1.59553i	0.587258	−	0.124212i
$166$		0			0
$167$	−15.1934	+	15.1934i	−1.17570	+	1.17570i	−0.194871	+	0.980829i	$0.562429\pi$
$167$	−15.1934	+	15.1934i	−1.17570	+	1.17570i	−0.980829	+	0.194871i	$0.937571\pi$
$168$		0			0
$169$		−	5.28257i		−	0.406352i
$170$		0			0
$171$		−	3.15322i		−	0.241133i
$172$		0			0
$173$	4.60458	+	4.60458i	0.350080	+	0.350080i	0.860139	−	0.510059i	$-0.170377\pi$
$173$	4.60458	+	4.60458i	0.350080	+	0.350080i	−0.510059	+	0.860139i	$0.670377\pi$
$174$		0			0
$175$	6.45528	−	11.5468i	0.487973	−	0.872859i
$176$		0			0
$177$	−4.80047	−	4.80047i	−0.360826	−	0.360826i
$178$		0			0
$179$		−	11.5721i		−	0.864939i	−0.901648	−	0.432470i	$-0.857642\pi$
$179$		−	11.5721i		−	0.864939i	0.901648	−	0.432470i	$-0.142358\pi$
$180$		0			0
$181$		−	5.28640i		−	0.392935i	−0.980510	−	0.196467i	$-0.937053\pi$
$181$		−	5.28640i		−	0.392935i	0.980510	−	0.196467i	$-0.0629470\pi$
$182$		0			0
$183$	2.07852	−	2.07852i	0.153649	−	0.153649i
$184$		0			0
$185$	−4.74721	+	1.00409i	−0.349022	+	0.0738220i
$186$		0			0
$187$	12.1065	−	12.1065i	0.885317	−	0.885317i
$188$		0			0
$189$	14.7835	+	2.10211i	1.07534	+	0.152906i
$190$		0			0
$191$	−11.6115			−0.840179			−0.420089	−	0.907483i	$-0.638001\pi$
$191$	−11.6115			−0.840179			−0.420089	+	0.907483i	$0.638001\pi$
$192$		0			0
$193$	−17.6369	+	17.6369i	−1.26954	+	1.26954i	−0.323207	+	0.946328i	$0.604761\pi$
$193$	−17.6369	+	17.6369i	−1.26954	+	1.26954i	−0.946328	+	0.323207i	$0.895239\pi$
$194$		0			0
$195$	−7.64945	−	4.97850i	−0.547789	−	0.356518i
$196$		0			0
$197$	−17.2130	−	17.2130i	−1.22637	−	1.22637i	−0.965325	−	0.261049i	$-0.915931\pi$
$197$	−17.2130	−	17.2130i	−1.22637	−	1.22637i	−0.261049	−	0.965325i	$-0.584069\pi$
$198$		0			0
$199$	6.95883			0.493299			0.246649	−	0.969105i	$-0.420670\pi$
$199$	6.95883			0.493299			0.246649	+	0.969105i	$0.420670\pi$
$200$		0			0
$201$			5.59267i			0.394477i
$202$		0			0
$203$	−12.4614	+	9.35874i	−0.874620	+	0.656855i
$204$		0			0
$205$	17.8410	+	11.6115i	1.24607	+	0.810982i
$206$		0			0
$207$	−5.11492	−	5.11492i	−0.355512	−	0.355512i
$208$		0			0
$209$	−8.79658			−0.608472
$210$		0			0
$211$	9.28431			0.639159			0.319579	−	0.947560i	$-0.396458\pi$
$211$	9.28431			0.639159			0.319579	+	0.947560i	$0.396458\pi$
$212$		0			0
$213$	−0.407498	−	0.407498i	−0.0279213	−	0.0279213i
$214$		0			0
$215$	1.21920	+	5.76422i	0.0831487	+	0.393117i
$216$		0			0
$217$	3.31400	−	2.48887i	0.224969	−	0.168955i
$218$		0			0
$219$		−	14.7225i		−	0.994854i
$220$		0			0
$221$	−20.2666			−1.36328
$222$		0			0
$223$	4.77582	+	4.77582i	0.319813	+	0.319813i	0.848695	−	0.528882i	$-0.177389\pi$
$223$	4.77582	+	4.77582i	0.319813	+	0.319813i	−0.528882	+	0.848695i	$0.677389\pi$
$224$		0			0
$225$	−3.84606	+	1.70317i	−0.256404	+	0.113545i
$226$		0			0
$227$	2.49990	−	2.49990i	0.165925	−	0.165925i	−0.619261	−	0.785185i	$-0.712568\pi$
$227$	2.49990	−	2.49990i	0.165925	−	0.165925i	0.785185	+	0.619261i	$0.212568\pi$
$228$		0			0
$229$	−18.0694			−1.19406			−0.597031	−	0.802218i	$-0.703653\pi$
$229$	−18.0694			−1.19406			−0.597031	+	0.802218i	$0.703653\pi$
$230$		0			0
$231$	1.28431	−	9.03217i	0.0845016	−	0.594273i
$232$		0			0
$233$	9.14278	−	9.14278i	0.598963	−	0.598963i	−0.341073	−	0.940037i	$-0.610790\pi$
$233$	9.14278	−	9.14278i	0.598963	−	0.598963i	0.940037	+	0.341073i	$0.110790\pi$
$234$		0			0
$235$	3.00671	+	14.2153i	0.196136	+	0.927307i
$236$		0			0
$237$	5.18130	−	5.18130i	0.336562	−	0.336562i
$238$		0			0
$239$			11.3719i			0.735590i	0.929907	+	0.367795i	$0.119887\pi$
$239$			11.3719i			0.735590i	−0.929907	+	0.367795i	$0.880113\pi$
$240$		0			0
$241$		−	19.6361i		−	1.26488i	−0.774611	−	0.632438i	$-0.782054\pi$
$241$		−	19.6361i		−	1.26488i	0.774611	−	0.632438i	$-0.217946\pi$
$242$		0			0
$243$	−5.97932	−	5.97932i	−0.383574	−	0.383574i
$244$		0			0
$245$	−10.2188	−	11.8565i	−0.652853	−	0.757485i
$246$		0			0
$247$	7.36284	+	7.36284i	0.468486	+	0.468486i
$248$		0			0
$249$		−	19.4622i		−	1.23337i
$250$		0			0
$251$		−	26.2420i		−	1.65638i	−0.560447	−	0.828190i	$-0.689371\pi$
$251$		−	26.2420i		−	1.65638i	0.560447	−	0.828190i	$-0.310629\pi$
$252$		0			0
$253$	−14.2691	+	14.2691i	−0.897094	+	0.897094i
$254$		0			0
$255$	13.0740	−	20.0881i	0.818723	−	1.25797i
$256$		0			0
$257$	−1.93157	+	1.93157i	−0.120488	+	0.120488i	−0.764780	−	0.644292i	$-0.777152\pi$
$257$	−1.93157	+	1.93157i	−0.120488	+	0.120488i	0.644292	+	0.764780i	$0.277152\pi$
$258$		0			0
$259$	−0.808236	+	5.68406i	−0.0502213	+	0.353191i
$260$		0			0
$261$	4.95532			0.306726
$262$		0			0
$263$	2.64248	−	2.64248i	0.162942	−	0.162942i	−0.620927	−	0.783869i	$-0.713243\pi$
$263$	2.64248	−	2.64248i	0.162942	−	0.162942i	0.783869	+	0.620927i	$0.213243\pi$
$264$		0			0
$265$	2.53984	+	12.0080i	0.156021	+	0.737648i
$266$		0			0
$267$	−10.2147	−	10.2147i	−0.625131	−	0.625131i
$268$		0			0
$269$	1.17948			0.0719143			0.0359572	−	0.999353i	$-0.488552\pi$
$269$	1.17948			0.0719143			0.0359572	+	0.999353i	$0.488552\pi$
$270$		0			0
$271$		−	14.7880i		−	0.898306i	−0.893455	−	0.449153i	$-0.851726\pi$
$271$		−	14.7880i		−	0.898306i	0.893455	−	0.449153i	$-0.148274\pi$
$272$		0			0
$273$	−8.63502	+	6.48505i	−0.522615	+	0.392493i
$274$		0			0
$275$	4.75134	+	10.7294i	0.286517	+	0.647007i
$276$		0			0
$277$	11.6478	+	11.6478i	0.699848	+	0.699848i	0.964378	−	0.264529i	$-0.0852166\pi$
$277$	11.6478	+	11.6478i	0.699848	+	0.699848i	−0.264529	+	0.964378i	$0.585217\pi$
$278$		0			0
$279$	−1.31782			−0.0788957
$280$		0			0
$281$	20.2153			1.20594			0.602971	−	0.797763i	$-0.293983\pi$
$281$	20.2153			1.20594			0.602971	+	0.797763i	$0.293983\pi$
$282$		0			0
$283$	5.53654	+	5.53654i	0.329113	+	0.329113i	0.852249	−	0.523136i	$-0.175238\pi$
$283$	5.53654	+	5.53654i	0.329113	+	0.329113i	−0.523136	+	0.852249i	$0.675238\pi$
$284$		0			0
$285$	−12.0477	+	2.54823i	−0.713647	+	0.150944i
$286$		0			0
$287$	20.1397	−	15.1253i	1.18881	−	0.892816i
$288$		0			0
$289$		−	36.2218i		−	2.13070i
$290$		0			0
$291$	24.6384			1.44433
$292$		0			0
$293$	−1.12050	−	1.12050i	−0.0654601	−	0.0654601i	0.673619	−	0.739079i	$-0.264739\pi$
$293$	−1.12050	−	1.12050i	−0.0654601	−	0.0654601i	−0.739079	+	0.673619i	$0.764739\pi$
$294$		0			0
$295$	5.63587	−	8.65950i	0.328133	−	0.504176i
$296$		0			0
$297$	−9.36588	+	9.36588i	−0.543463	+	0.543463i
$298$		0			0
$299$	23.8869			1.38141
$300$		0			0
$301$	6.90179	+	0.981388i	0.397812	+	0.0565662i
$302$		0			0
$303$	−8.74288	+	8.74288i	−0.502265	+	0.502265i
$304$		0			0
$305$	3.74942	+	2.44024i	0.214691	+	0.139728i
$306$		0			0
$307$	−9.43044	+	9.43044i	−0.538224	+	0.538224i	−0.923007	−	0.384783i	$-0.874276\pi$
$307$	−9.43044	+	9.43044i	−0.538224	+	0.538224i	0.384783	+	0.923007i	$0.374276\pi$
$308$		0			0
$309$			18.2409i			1.03769i
$310$		0			0
$311$		−	14.6035i		−	0.828090i	−0.910256	−	0.414045i	$-0.864116\pi$
$311$		−	14.6035i		−	0.828090i	0.910256	−	0.414045i	$-0.135884\pi$
$312$		0			0
$313$	−7.05535	−	7.05535i	−0.398792	−	0.398792i	0.479015	−	0.877807i	$-0.340994\pi$
$313$	−7.05535	−	7.05535i	−0.398792	−	0.398792i	−0.877807	+	0.479015i	$0.840994\pi$
$314$		0			0
$315$	0.334165	+	4.96574i	0.0188281	+	0.279787i
$316$		0			0
$317$	−11.2538	−	11.2538i	−0.632075	−	0.632075i	0.316513	−	0.948588i	$-0.397488\pi$
$317$	−11.2538	−	11.2538i	−0.632075	−	0.632075i	−0.948588	+	0.316513i	$0.897488\pi$
$318$		0			0
$319$		−	13.8239i		−	0.773989i
$320$		0			0
$321$			21.5558i			1.20313i
$322$		0			0
$323$	−19.3354	+	19.3354i	−1.07585	+	1.07585i
$324$		0			0
$325$	5.00371	−	12.9576i	0.277556	−	0.718757i
$326$		0			0
$327$	−5.11904	+	5.11904i	−0.283084	+	0.283084i
$328$		0			0
$329$	17.0207	+	2.42023i	0.938383	+	0.133432i
$330$		0			0
$331$	−33.6643			−1.85036			−0.925179	−	0.379531i	$-0.876085\pi$
$331$	−33.6643			−1.85036			−0.925179	+	0.379531i	$0.876085\pi$
$332$		0			0
$333$	1.29084	−	1.29084i	0.0707376	−	0.0707376i
$334$		0			0
$335$	−8.32724	+	1.76131i	−0.454965	+	0.0962304i
$336$		0			0
$337$	12.8298	+	12.8298i	0.698885	+	0.698885i	0.964170	−	0.265285i	$-0.0854661\pi$
$337$	12.8298	+	12.8298i	0.698885	+	0.698885i	−0.265285	+	0.964170i	$0.585466\pi$
$338$		0			0
$339$	−7.89507			−0.428802
$340$		0			0
$341$			3.67633i			0.199085i
$342$		0			0
$343$	−17.3222	+	6.55296i	−0.935311	+	0.353826i
$344$		0			0
$345$	−15.4094	+	23.6765i	−0.829614	+	1.27470i
$346$		0			0
$347$	−20.6439	−	20.6439i	−1.10822	−	1.10822i	−0.993384	−	0.114837i	$-0.963365\pi$
$347$	−20.6439	−	20.6439i	−1.10822	−	1.10822i	−0.114837	−	0.993384i	$-0.536635\pi$
$348$		0			0
$349$	−29.3356			−1.57030			−0.785150	−	0.619306i	$-0.787414\pi$
$349$	−29.3356			−1.57030			−0.785150	+	0.619306i	$0.787414\pi$
$350$		0			0
$351$	15.6787			0.836867
$352$		0			0
$353$	16.5837	+	16.5837i	0.882662	+	0.882662i	0.993805	−	0.111142i	$-0.0354509\pi$
$353$	16.5837	+	16.5837i	0.882662	+	0.882662i	−0.111142	+	0.993805i	$0.535451\pi$
$354$		0			0
$355$	0.478412	−	0.735079i	0.0253915	−	0.0390140i
$356$		0			0
$357$	−17.0303	−	22.6763i	−0.901338	−	1.20016i
$358$		0			0
$359$		−	30.4050i		−	1.60472i	−0.596843	−	0.802358i	$-0.703579\pi$
$359$		−	30.4050i		−	1.60472i	0.596843	−	0.802358i	$-0.296421\pi$
$360$		0			0
$361$	−4.95092			−0.260575
$362$		0			0
$363$	−5.70598	−	5.70598i	−0.299486	−	0.299486i
$364$		0			0
$365$	21.9211	−	4.63657i	1.14740	−	0.242689i
$366$		0			0
$367$	13.6007	−	13.6007i	0.709950	−	0.709950i	−0.256574	−	0.966525i	$-0.582594\pi$
$367$	13.6007	−	13.6007i	0.709950	−	0.709950i	0.966525	+	0.256574i	$0.0825938\pi$
$368$		0			0
$369$	−8.00861			−0.416911
$370$		0			0
$371$	14.3778	+	2.04443i	0.746459	+	0.106141i
$372$		0			0
$373$	13.8626	−	13.8626i	0.717776	−	0.717776i	−0.250373	−	0.968149i	$-0.580553\pi$
$373$	13.8626	−	13.8626i	0.717776	−	0.717776i	0.968149	+	0.250373i	$0.0805533\pi$
$374$		0			0
$375$	9.61556	+	13.3185i	0.496545	+	0.687766i
$376$		0			0
$377$	−11.5708	+	11.5708i	−0.595925	+	0.595925i
$378$		0			0
$379$		−	11.8896i		−	0.610727i	−0.952236	−	0.305363i	$-0.901222\pi$
$379$		−	11.8896i		−	0.610727i	0.952236	−	0.305363i	$-0.0987779\pi$
$380$		0			0
$381$		−	1.61606i		−	0.0827934i
$382$		0			0
$383$	16.5186	+	16.5186i	0.844059	+	0.844059i	0.989384	−	0.145325i	$-0.0464229\pi$
$383$	16.5186	+	16.5186i	0.844059	+	0.844059i	−0.145325	+	0.989384i	$0.546423\pi$
$384$		0			0
$385$	13.8530	−	0.932224i	0.706012	−	0.0475105i
$386$		0			0
$387$	−1.56738	−	1.56738i	−0.0796745	−	0.0796745i
$388$		0			0
$389$			9.62098i			0.487803i	0.969800	+	0.243902i	$0.0784274\pi$
$389$			9.62098i			0.487803i	−0.969800	+	0.243902i	$0.921573\pi$
$390$		0			0
$391$			62.7290i			3.17234i
$392$		0			0
$393$	−11.4670	+	11.4670i	−0.578433	+	0.578433i
$394$		0			0
$395$	9.34648	+	6.08297i	0.470272	+	0.306068i
$396$		0			0
$397$	−17.5393	+	17.5393i	−0.880270	+	0.880270i	−0.993562	−	0.113292i	$-0.963861\pi$
$397$	−17.5393	+	17.5393i	−0.880270	+	0.880270i	0.113292	+	0.993562i	$0.463861\pi$
$398$		0			0
$399$	−2.05119	+	14.4254i	−0.102688	+	0.722171i
$400$		0			0
$401$	−14.2238			−0.710302			−0.355151	−	0.934809i	$-0.615571\pi$
$401$	−14.2238			−0.710302			−0.355151	+	0.934809i	$0.615571\pi$
$402$		0			0
$403$	3.07713	−	3.07713i	0.153283	−	0.153283i
$404$		0			0
$405$	−7.03598	+	10.8108i	−0.349621	+	0.537192i
$406$		0			0
$407$	−3.60107	−	3.60107i	−0.178498	−	0.178498i
$408$		0			0
$409$	14.2602			0.705123			0.352562	−	0.935789i	$-0.385311\pi$
$409$	14.2602			0.705123			0.352562	+	0.935789i	$0.385311\pi$
$410$		0			0
$411$			5.51281i			0.271927i
$412$		0			0
$413$	−7.34135	−	9.77520i	−0.361244	−	0.481006i
$414$		0			0
$415$	28.9784	−	6.12926i	1.42249	−	0.300874i
$416$		0			0
$417$	7.43302	+	7.43302i	0.363996	+	0.363996i
$418$		0			0
$419$	−13.5802			−0.663434			−0.331717	−	0.943379i	$-0.607628\pi$
$419$	−13.5802			−0.663434			−0.331717	+	0.943379i	$0.607628\pi$
$420$		0			0
$421$	−12.7805			−0.622884			−0.311442	−	0.950265i	$-0.600812\pi$
$421$	−12.7805			−0.622884			−0.311442	+	0.950265i	$0.600812\pi$
$422$		0			0
$423$	−3.86537	−	3.86537i	−0.187941	−	0.187941i
$424$		0			0
$425$	34.0277	+	13.1402i	1.65058	+	0.637391i
$426$		0			0
$427$	4.23250	−	3.17868i	0.204825	−	0.153827i
$428$		0			0
$429$		−	9.57913i		−	0.462485i
$430$		0			0
$431$	37.7947			1.82051			0.910254	−	0.414049i	$-0.135886\pi$
$431$	37.7947			1.82051			0.910254	+	0.414049i	$0.135886\pi$
$432$		0			0
$433$	14.2122	+	14.2122i	0.682996	+	0.682996i	0.960674	−	0.277678i	$-0.0895649\pi$
$433$	14.2122	+	14.2122i	0.682996	+	0.682996i	−0.277678	+	0.960674i	$0.589565\pi$
$434$		0			0
$435$	−4.00457	−	18.9331i	−0.192005	−	0.907774i
$436$		0			0
$437$	22.7894	−	22.7894i	1.09016	−	1.09016i
$438$		0			0
$439$	−27.7697			−1.32538			−0.662688	−	0.748896i	$-0.730584\pi$
$439$	−27.7697			−1.32538			−0.662688	+	0.748896i	$0.730584\pi$
$440$		0			0
$441$	5.65541	+	1.64151i	0.269305	+	0.0781673i
$442$		0			0
$443$	11.8951	−	11.8951i	0.565152	−	0.565152i	−0.365615	−	0.930766i	$-0.619141\pi$
$443$	11.8951	−	11.8951i	0.565152	−	0.565152i	0.930766	+	0.365615i	$0.119141\pi$
$444$		0			0
$445$	11.9923	−	18.4262i	0.568491	−	0.873485i
$446$		0			0
$447$	−12.7323	+	12.7323i	−0.602216	+	0.602216i
$448$		0			0
$449$			3.92227i			0.185104i	0.995708	+	0.0925518i	$0.0295024\pi$
$449$			3.92227i			0.185104i	−0.995708	+	0.0925518i	$0.970498\pi$
$450$		0			0
$451$			22.3417i			1.05203i
$452$		0			0
$453$	−13.7367	−	13.7367i	−0.645409	−	0.645409i
$454$		0			0
$455$	−12.3754	−	10.8148i	−0.580166	−	0.507006i
$456$		0			0
$457$	17.6596	+	17.6596i	0.826083	+	0.826083i	0.986972	−	0.160889i	$-0.0514362\pi$
$457$	17.6596	+	17.6596i	0.826083	+	0.826083i	−0.160889	+	0.986972i	$0.551436\pi$
$458$		0			0
$459$			41.1736i			1.92182i
$460$		0			0
$461$		−	0.616064i		−	0.0286930i	−0.999897	−	0.0143465i	$-0.995433\pi$
$461$		−	0.616064i		−	0.0286930i	0.999897	−	0.0143465i	$-0.00456678\pi$
$462$		0			0
$463$	−11.9726	+	11.9726i	−0.556413	+	0.556413i	−0.928284	−	0.371871i	$-0.878716\pi$
$463$	−11.9726	+	11.9726i	−0.556413	+	0.556413i	0.371871	+	0.928284i	$0.378716\pi$
$464$		0			0
$465$	1.06498	+	5.03508i	0.0493871	+	0.233496i
$466$		0			0
$467$	−12.8767	+	12.8767i	−0.595861	+	0.595861i	−0.939208	−	0.343348i	$-0.888439\pi$
$467$	−12.8767	+	12.8767i	−0.595861	+	0.595861i	0.343348	+	0.939208i	$0.388439\pi$
$468$		0			0
$469$	−1.41775	+	9.97061i	−0.0654658	+	0.460400i
$470$		0			0
$471$	−17.3584			−0.799834
$472$		0			0
$473$	−4.37254	+	4.37254i	−0.201050	+	0.201050i
$474$		0			0
$475$	−7.58841	−	17.1360i	−0.348180	−	0.786254i
$476$		0			0
$477$	−3.26517	−	3.26517i	−0.149502	−	0.149502i
$478$		0			0
$479$	8.34016			0.381072			0.190536	−	0.981680i	$-0.438977\pi$
$479$	8.34016			0.381072			0.190536	+	0.981680i	$0.438977\pi$
$480$		0			0
$481$			6.02827i			0.274866i
$482$		0			0
$483$	20.0724	+	26.7270i	0.913328	+	1.21612i
$484$		0			0
$485$	7.75939	+	36.6854i	0.352336	+	1.66580i
$486$		0			0
$487$	−6.90541	−	6.90541i	−0.312914	−	0.312914i	0.533123	−	0.846037i	$-0.321018\pi$
$487$	−6.90541	−	6.90541i	−0.312914	−	0.312914i	−0.846037	+	0.533123i	$0.821018\pi$
$488$		0			0
$489$	4.60801			0.208381
$490$		0			0
$491$	25.1783			1.13628			0.568140	−	0.822932i	$-0.307663\pi$
$491$	25.1783			1.13628			0.568140	+	0.822932i	$0.307663\pi$
$492$		0			0
$493$	−30.3858	−	30.3858i	−1.36851	−	1.36851i
$494$		0			0
$495$	−3.70011	−	2.40814i	−0.166307	−	0.108238i
$496$		0			0
$497$	−0.623185	−	0.829788i	−0.0279537	−	0.0372211i
$498$		0			0
$499$			20.8907i			0.935197i	0.883941	+	0.467599i	$0.154881\pi$
$499$			20.8907i			0.935197i	−0.883941	+	0.467599i	$0.845119\pi$
$500$		0			0
$501$	−31.5696			−1.41043
$502$		0			0
$503$	−0.585795	−	0.585795i	−0.0261193	−	0.0261193i	0.693927	−	0.720046i	$-0.255879\pi$
$503$	−0.585795	−	0.585795i	−0.0261193	−	0.0261193i	−0.720046	+	0.693927i	$0.755879\pi$
$504$		0			0
$505$	−15.7711	−	10.2643i	−0.701807	−	0.456757i
$506$		0			0
$507$	5.48821	−	5.48821i	0.243740	−	0.243740i
$508$		0			0
$509$	38.2153			1.69386			0.846932	−	0.531701i	$-0.178447\pi$
$509$	38.2153			1.69386			0.846932	+	0.531701i	$0.178447\pi$
$510$		0			0
$511$	3.73218	−	26.2472i	0.165102	−	1.16111i
$512$		0			0
$513$	14.9583	−	14.9583i	0.660426	−	0.660426i
$514$		0			0
$515$	−27.1599	+	5.74464i	−1.19681	+	0.253139i
$516$		0			0
$517$	−10.7833	+	10.7833i	−0.474248	+	0.474248i
$518$		0			0
$519$			9.56765i			0.419973i
$520$		0			0
$521$			8.40522i			0.368239i	0.982904	+	0.184120i	$0.0589434\pi$
$521$			8.40522i			0.368239i	−0.982904	+	0.184120i	$0.941057\pi$
$522$		0			0
$523$	−14.1989	−	14.1989i	−0.620876	−	0.620876i	0.324879	−	0.945755i	$-0.394676\pi$
$523$	−14.1989	−	14.1989i	−0.620876	−	0.620876i	−0.945755	+	0.324879i	$0.894676\pi$
$524$		0			0
$525$	18.7029	−	5.28976i	0.816261	−	0.230864i
$526$		0			0
$527$	8.08081	+	8.08081i	0.352006	+	0.352006i
$528$		0			0
$529$		−	50.9344i		−	2.21454i
$530$		0			0
$531$			3.88713i			0.168687i
$532$		0			0
$533$	18.7003	−	18.7003i	0.809998	−	0.809998i
$534$		0			0
$535$	−32.0957	+	6.78860i	−1.38762	+	0.293497i
$536$		0			0
$537$	12.0226	−	12.0226i	0.518812	−	0.518812i
$538$		0			0
$539$	4.57934	−	15.7770i	0.197246	−	0.679562i
$540$		0			0
$541$	−38.9363			−1.67400			−0.837001	−	0.547202i	$-0.815693\pi$
$541$	−38.9363			−1.67400			−0.837001	+	0.547202i	$0.815693\pi$
$542$		0			0
$543$	5.49218	−	5.49218i	0.235692	−	0.235692i
$544$		0			0
$545$	−9.23416	−	6.00987i	−0.395548	−	0.257435i
$546$		0			0
$547$	2.30390	+	2.30390i	0.0985078	+	0.0985078i	0.754643	−	0.656135i	$-0.227810\pi$
$547$	2.30390	+	2.30390i	0.0985078	+	0.0985078i	−0.656135	+	0.754643i	$0.727810\pi$
$548$		0			0
$549$	−1.68306			−0.0718314
$550$		0			0
$551$			22.0783i			0.940565i
$552$		0			0
$553$	10.5507	−	7.92375i	0.448661	−	0.336952i
$554$		0			0
$555$	−5.97518	−	3.88883i	−0.253632	−	0.165072i
$556$		0			0
$557$	7.69913	+	7.69913i	0.326223	+	0.326223i	0.851148	−	0.524926i	$-0.175907\pi$
$557$	7.69913	+	7.69913i	0.326223	+	0.326223i	−0.524926	+	0.851148i	$0.675907\pi$
$558$		0			0
$559$	7.31974			0.309592
$560$		0			0
$561$	25.1556			1.06207
$562$		0			0
$563$	11.8855	+	11.8855i	0.500914	+	0.500914i	0.911722	−	0.410808i	$-0.134753\pi$
$563$	11.8855	+	11.8855i	0.500914	+	0.500914i	−0.410808	+	0.911722i	$0.634753\pi$
$564$		0			0
$565$	−2.48640	−	11.7554i	−0.104604	−	0.494554i
$566$		0			0
$567$	9.16515	+	12.2036i	0.384900	+	0.512505i
$568$		0			0
$569$			3.16924i			0.132861i	0.997791	+	0.0664307i	$0.0211611\pi$
$569$			3.16924i			0.132861i	−0.997791	+	0.0664307i	$0.978839\pi$
$570$		0			0
$571$	−24.8492			−1.03991			−0.519953	−	0.854195i	$-0.674050\pi$
$571$	−24.8492			−1.03991			−0.519953	+	0.854195i	$0.674050\pi$
$572$		0			0
$573$	−12.0635	−	12.0635i	−0.503960	−	0.503960i
$574$		0			0
$575$	−40.1061	−	15.4874i	−1.67254	−	0.645870i
$576$		0			0
$577$	29.2688	−	29.2688i	1.21848	−	1.21848i	0.250309	−	0.968166i	$-0.419468\pi$
$577$	29.2688	−	29.2688i	1.21848	−	1.21848i	0.968166	−	0.250309i	$-0.0805324\pi$
$578$		0			0
$579$	−36.6470			−1.52300
$580$		0			0
$581$	4.93372	−	34.6973i	0.204685	−	1.43948i
$582$		0			0
$583$	−9.10888	+	9.10888i	−0.377251	+	0.377251i
$584$		0			0
$585$	1.08139	+	5.11268i	0.0447100	+	0.211383i
$586$		0			0
$587$	16.3313	−	16.3313i	0.674065	−	0.674065i	−0.284586	−	0.958651i	$-0.591856\pi$
$587$	16.3313	−	16.3313i	0.674065	−	0.674065i	0.958651	+	0.284586i	$0.0918561\pi$
$588$		0			0
$589$		−	5.87150i		−	0.241931i
$590$		0			0
$591$		−	35.7661i		−	1.47122i
$592$		0			0
$593$	17.5540	+	17.5540i	0.720858	+	0.720858i	0.968780	−	0.247922i	$-0.0797477\pi$
$593$	17.5540	+	17.5540i	0.720858	+	0.720858i	−0.247922	+	0.968780i	$0.579748\pi$
$594$		0			0
$595$	28.4006	−	32.4988i	1.16431	−	1.33232i
$596$		0			0
$597$	7.22972	+	7.22972i	0.295893	+	0.295893i
$598$		0			0
$599$			21.4754i			0.877461i	0.898619	+	0.438731i	$0.144572\pi$
$599$			21.4754i			0.877461i	−0.898619	+	0.438731i	$0.855428\pi$
$600$		0			0
$601$		−	32.4373i		−	1.32314i	−0.749882	−	0.661572i	$-0.769890\pi$
$601$		−	32.4373i		−	1.32314i	0.749882	−	0.661572i	$-0.230110\pi$
$602$		0			0
$603$	2.26431	−	2.26431i	0.0922096	−	0.0922096i
$604$		0			0
$605$	6.69896	−	10.2929i	0.272351	−	0.418467i
$606$		0			0
$607$	−13.4507	+	13.4507i	−0.545947	+	0.545947i	−0.925266	−	0.379319i	$-0.876158\pi$
$607$	−13.4507	+	13.4507i	−0.545947	+	0.545947i	0.379319	+	0.925266i	$0.376158\pi$
$608$		0			0
$609$	−22.6696	−	3.22346i	−0.918617	−	0.130621i
$610$		0			0
$611$	18.0515			0.730284
$612$		0			0
$613$	−1.66986	+	1.66986i	−0.0674449	+	0.0674449i	−0.740025	−	0.672580i	$-0.765186\pi$
$613$	−1.66986	+	1.66986i	−0.0674449	+	0.0674449i	0.672580	+	0.740025i	$0.265186\pi$
$614$		0			0
$615$	6.47205	+	30.5990i	0.260978	+	1.23387i
$616$		0			0
$617$	−16.0944	−	16.0944i	−0.647938	−	0.647938i	0.304556	−	0.952494i	$-0.401492\pi$
$617$	−16.0944	−	16.0944i	−0.647938	−	0.647938i	−0.952494	+	0.304556i	$0.901492\pi$
$618$		0			0
$619$	−0.973019			−0.0391089			−0.0195545	−	0.999809i	$-0.506225\pi$
$619$	−0.973019			−0.0391089			−0.0195545	+	0.999809i	$0.506225\pi$
$620$		0			0
$621$		−	48.5285i		−	1.94738i
$622$		0			0
$623$	−15.6213	−	20.8003i	−0.625856	−	0.833345i
$624$		0			0
$625$	−16.8025	+	18.5115i	−0.672098	+	0.740462i
$626$		0			0
$627$	−9.13900	−	9.13900i	−0.364977	−	0.364977i
$628$		0			0
$629$	−15.8308			−0.631213
$630$		0			0
$631$	17.4830			0.695987			0.347994	−	0.937497i	$-0.386863\pi$
$631$	17.4830			0.695987			0.347994	+	0.937497i	$0.386863\pi$
$632$		0			0
$633$	9.64573	+	9.64573i	0.383383	+	0.383383i
$634$		0			0
$635$	2.40624	−	0.508948i	0.0954888	−	0.0201970i
$636$		0			0
$637$	−17.0385	+	9.37254i	−0.675089	+	0.371353i
$638$		0			0
$639$			0.329967i			0.0130533i
$640$		0			0
$641$	−25.0710			−0.990244			−0.495122	−	0.868823i	$-0.664877\pi$
$641$	−25.0710			−0.990244			−0.495122	+	0.868823i	$0.664877\pi$
$642$		0			0
$643$	−3.86619	−	3.86619i	−0.152468	−	0.152468i	0.626752	−	0.779219i	$-0.284384\pi$
$643$	−3.86619	−	3.86619i	−0.152468	−	0.152468i	−0.779219	+	0.626752i	$0.784384\pi$
$644$		0			0
$645$	−4.72195	+	7.25527i	−0.185927	+	0.285676i
$646$		0			0
$647$	24.4727	−	24.4727i	0.962119	−	0.962119i	−0.0371889	−	0.999308i	$-0.511840\pi$
$647$	24.4727	−	24.4727i	0.962119	−	0.962119i	0.999308	+	0.0371889i	$0.0118403\pi$
$648$		0			0
$649$	10.8440			0.425663
$650$		0			0
$651$	6.02875	+	0.857248i	0.236285	+	0.0335982i
$652$		0			0
$653$	23.1478	−	23.1478i	0.905845	−	0.905845i	−0.0900885	−	0.995934i	$-0.528715\pi$
$653$	23.1478	−	23.1478i	0.905845	−	0.905845i	0.995934	+	0.0900885i	$0.0287150\pi$
$654$		0			0
$655$	−20.6851	−	13.4625i	−0.808235	−	0.526024i
$656$		0			0
$657$	−5.96070	+	5.96070i	−0.232549	+	0.232549i
$658$		0			0
$659$			36.1548i			1.40839i	0.710006	+	0.704195i	$0.248692\pi$
$659$			36.1548i			1.40839i	−0.710006	+	0.704195i	$0.751308\pi$
$660$		0			0
$661$			33.4541i			1.30121i	0.759415	+	0.650606i	$0.225485\pi$
$661$			33.4541i			1.30121i	−0.759415	+	0.650606i	$0.774515\pi$
$662$		0			0
$663$	−21.0555	−	21.0555i	−0.817729	−	0.817729i
$664$		0			0
$665$	−22.1247	+	1.48886i	−0.857958	+	0.0577356i
$666$		0			0
$667$	35.8137	+	35.8137i	1.38671	+	1.38671i
$668$		0			0
$669$			9.92347i			0.383663i
$670$		0			0
$671$			4.69526i			0.181259i
$672$		0			0
$673$	−6.30998	+	6.30998i	−0.243232	+	0.243232i	−0.818186	−	0.574954i	$-0.805020\pi$
$673$	−6.30998	+	6.30998i	−0.243232	+	0.243232i	0.574954	+	0.818186i	$0.305020\pi$
$674$		0			0
$675$	−26.3246	−	10.1655i	−1.01323	−	0.391271i
$676$		0			0
$677$	6.88730	−	6.88730i	0.264700	−	0.264700i	−0.562260	−	0.826960i	$-0.690068\pi$
$677$	6.88730	−	6.88730i	0.264700	−	0.264700i	0.826960	+	0.562260i	$0.190068\pi$
$678$		0			0
$679$	43.9253	+	6.24588i	1.68570	+	0.239695i
$680$		0			0
$681$	5.19444			0.199051
$682$		0			0
$683$	1.06740	−	1.06740i	0.0408430	−	0.0408430i	−0.686390	−	0.727233i	$-0.740806\pi$
$683$	1.06740	−	1.06740i	0.0408430	−	0.0408430i	0.727233	+	0.686390i	$0.240806\pi$
$684$		0			0
$685$	−8.20832	+	1.73615i	−0.313624	+	0.0663350i
$686$		0			0
$687$	−18.7728	−	18.7728i	−0.716228	−	0.716228i
$688$		0			0
$689$	15.2485			0.580921
$690$		0			0
$691$		−	43.8638i		−	1.66866i	−0.551267	−	0.834329i	$-0.685855\pi$
$691$		−	43.8638i		−	1.66866i	0.551267	−	0.834329i	$-0.314145\pi$
$692$		0			0
$693$	−4.17683	+	3.13687i	−0.158665	+	0.119160i
$694$		0			0
$695$	−8.72654	+	13.4083i	−0.331016	+	0.508606i
$696$		0			0
$697$	49.1085	+	49.1085i	1.86012	+	1.86012i
$698$		0			0
$699$	18.9974			0.718546
$700$		0			0
$701$	−36.6200			−1.38312			−0.691559	−	0.722320i	$-0.743076\pi$
$701$	−36.6200			−1.38312			−0.691559	+	0.722320i	$0.743076\pi$
$702$		0			0
$703$	5.75130	+	5.75130i	0.216914	+	0.216914i
$704$		0			0
$705$	−11.6450	+	17.8925i	−0.438574	+	0.673869i
$706$		0			0
$707$	−17.8031	+	13.3705i	−0.669555	+	0.502848i
$708$		0			0
$709$			30.7975i			1.15662i	0.815816	+	0.578311i	$0.196288\pi$
$709$			30.7975i			1.15662i	−0.815816	+	0.578311i	$0.803712\pi$
$710$		0			0
$711$	−4.19551			−0.157344
$712$		0			0
$713$	−9.52431	−	9.52431i	−0.356688	−	0.356688i
$714$		0			0
$715$	14.2629	−	3.01676i	0.533402	−	0.112821i
$716$		0			0
$717$	−11.8146	+	11.8146i	−0.441225	+	0.441225i
$718$		0			0
$719$	36.9703			1.37876			0.689379	−	0.724401i	$-0.257883\pi$
$719$	36.9703			1.37876			0.689379	+	0.724401i	$0.257883\pi$
$720$		0			0
$721$	−4.62411	+	32.5199i	−0.172211	+	1.21111i
$722$		0			0
$723$	20.4005	−	20.4005i	0.758704	−	0.758704i
$724$		0			0
$725$	26.9294	−	11.9252i	1.00013	−	0.442893i
$726$		0			0
$727$	4.99011	−	4.99011i	0.185073	−	0.185073i	−0.608489	−	0.793562i	$-0.708224\pi$
$727$	4.99011	−	4.99011i	0.185073	−	0.185073i	0.793562	+	0.608489i	$0.208224\pi$
$728$		0			0
$729$		−	29.7297i		−	1.10110i
$730$		0			0
$731$			19.2222i			0.710960i
$732$		0			0
$733$	18.9857	+	18.9857i	0.701252	+	0.701252i	0.964679	−	0.263427i	$-0.0848528\pi$
$733$	18.9857	+	18.9857i	0.701252	+	0.701252i	−0.263427	+	0.964679i	$0.584853\pi$
$734$		0			0
$735$	1.70150	−	22.9346i	0.0627607	−	0.845956i
$736$		0			0
$737$	−6.31675	−	6.31675i	−0.232681	−	0.232681i
$738$		0			0
$739$			4.09135i			0.150503i	0.997165	+	0.0752515i	$0.0239759\pi$
$739$			4.09135i			0.150503i	−0.997165	+	0.0752515i	$0.976024\pi$
$740$		0			0
$741$			15.2989i			0.562019i
$742$		0			0
$743$	37.7330	−	37.7330i	1.38429	−	1.38429i	0.547451	−	0.836838i	$-0.315598\pi$
$743$	37.7330	−	37.7330i	1.38429	−	1.38429i	0.836838	−	0.547451i	$-0.184402\pi$
$744$		0			0
$745$	−22.9676	−	14.9480i	−0.841467	−	0.547652i
$746$		0			0
$747$	−7.87968	+	7.87968i	−0.288302	+	0.288302i
$748$		0			0
$749$	−5.46444	+	38.4297i	−0.199666	+	1.40419i
$750$		0			0
$751$	−21.3975			−0.780805			−0.390403	−	0.920644i	$-0.627664\pi$
$751$	−21.3975			−0.780805			−0.390403	+	0.920644i	$0.627664\pi$
$752$		0			0
$753$	27.2635	−	27.2635i	0.993538	−	0.993538i
$754$		0			0
$755$	16.1273	−	24.7795i	0.586931	−	0.901819i
$756$		0			0
$757$	24.8160	+	24.8160i	0.901952	+	0.901952i	0.995605	−	0.0936529i	$-0.0298544\pi$
$757$	24.8160	+	24.8160i	0.901952	+	0.901952i	−0.0936529	+	0.995605i	$0.529854\pi$
$758$		0			0
$759$	−29.6492			−1.07620
$760$		0			0
$761$			20.4451i			0.741135i	0.928806	+	0.370567i	$0.120837\pi$
$761$			20.4451i			0.741135i	−0.928806	+	0.370567i	$0.879163\pi$
$762$		0			0
$763$	−10.4239	+	7.82853i	−0.377371	+	0.283412i
$764$		0			0
$765$	−13.4263	+	2.83982i	−0.485430	+	0.102674i
$766$		0			0
$767$	−9.07654	−	9.07654i	−0.327735	−	0.327735i
$768$		0			0
$769$	6.20785			0.223861			0.111930	−	0.993716i	$-0.464297\pi$
$769$	6.20785			0.223861			0.111930	+	0.993716i	$0.464297\pi$
$770$		0			0
$771$	−4.01351			−0.144543
$772$		0			0
$773$	12.7179	+	12.7179i	0.457430	+	0.457430i	0.897811	−	0.440381i	$-0.145157\pi$
$773$	12.7179	+	12.7179i	0.457430	+	0.457430i	−0.440381	+	0.897811i	$0.645157\pi$
$774$		0			0
$775$	−7.16161	+	3.17141i	−0.257253	+	0.113920i
$776$		0			0
$777$	−6.74503	+	5.06563i	−0.241976	+	0.181728i
$778$		0			0
$779$		−	35.6821i		−	1.27844i
$780$		0			0
$781$	0.920513			0.0329385
$782$		0			0
$783$	23.5071	+	23.5071i	0.840076	+	0.840076i
$784$		0			0
$785$	−5.46670	−	25.8459i	−0.195115	−	0.922480i
$786$		0			0
$787$	−32.6842	+	32.6842i	−1.16506	+	1.16506i	−0.181713	+	0.983352i	$0.558164\pi$
$787$	−32.6842	+	32.6842i	−1.16506	+	1.16506i	−0.983352	+	0.181713i	$0.941836\pi$
$788$		0			0
$789$	5.49068			0.195474
$790$		0			0
$791$	−14.0753	−	2.00142i	−0.500461	−	0.0711622i
$792$		0			0
$793$	3.92999	−	3.92999i	0.139558	−	0.139558i
$794$		0			0
$795$	−9.83677	+	15.1142i	−0.348874	+	0.536045i
$796$		0			0
$797$	8.76878	−	8.76878i	0.310606	−	0.310606i	−0.534538	−	0.845144i	$-0.679514\pi$
$797$	8.76878	−	8.76878i	0.310606	−	0.310606i	0.845144	+	0.534538i	$0.179514\pi$
$798$		0			0
$799$			47.4046i			1.67706i
$800$		0			0
$801$			8.27127i			0.292251i
$802$		0			0
$803$	16.6286	+	16.6286i	0.586811	+	0.586811i
$804$		0			0
$805$	−33.4739	+	38.3041i	−1.17980	+	1.35004i
$806$		0			0
$807$	1.22540	+	1.22540i	0.0431360	+	0.0431360i
$808$		0			0
$809$			15.9362i			0.560287i	0.959958	+	0.280144i	$0.0903821\pi$
$809$			15.9362i			0.560287i	−0.959958	+	0.280144i	$0.909618\pi$
$810$		0			0
$811$		−	49.6560i		−	1.74366i	−0.489812	−	0.871828i	$-0.662935\pi$
$811$		−	49.6560i		−	1.74366i	0.489812	−	0.871828i	$-0.337065\pi$
$812$		0			0
$813$	15.3636	−	15.3636i	0.538826	−	0.538826i
$814$		0			0
$815$	1.45120	+	6.86112i	0.0508335	+	0.240334i
$816$		0			0
$817$	6.98342	−	6.98342i	0.244319	−	0.244319i
$818$		0			0
$819$	6.12166	+	0.870459i	0.213908	+	0.0304163i
$820$		0			0
$821$	−30.1755			−1.05313			−0.526566	−	0.850135i	$-0.676521\pi$
$821$	−30.1755			−1.05313			−0.526566	+	0.850135i	$0.676521\pi$
$822$		0			0
$823$	17.2900	−	17.2900i	0.602693	−	0.602693i	−0.338333	−	0.941026i	$-0.609863\pi$
$823$	17.2900	−	17.2900i	0.602693	−	0.602693i	0.941026	+	0.338333i	$0.109863\pi$
$824$		0			0
$825$	−6.21077	+	16.0834i	−0.216231	+	0.559951i
$826$		0			0
$827$	1.93183	+	1.93183i	0.0671761	+	0.0671761i	0.739897	−	0.672721i	$-0.234874\pi$
$827$	1.93183	+	1.93183i	0.0671761	+	0.0671761i	−0.672721	+	0.739897i	$0.734874\pi$
$828$		0			0
$829$	−31.2032			−1.08373			−0.541865	−	0.840465i	$-0.682282\pi$
$829$	−31.2032			−1.08373			−0.541865	+	0.840465i	$0.682282\pi$
$830$		0			0
$831$			24.2024i			0.839573i
$832$		0			0
$833$	−24.6131	−	44.7445i	−0.852793	−	1.55030i
$834$		0			0
$835$	−9.94226	−	47.0058i	−0.344066	−	1.62670i
$836$		0			0
$837$	−6.25150	−	6.25150i	−0.216083	−	0.216083i
$838$		0			0
$839$	7.79348			0.269061			0.134530	−	0.990909i	$-0.457047\pi$
$839$	7.79348			0.269061			0.134530	+	0.990909i	$0.457047\pi$
$840$		0			0
$841$	−5.69616			−0.196419
$842$		0			0
$843$	21.0022	+	21.0022i	0.723354	+	0.723354i
$844$		0			0
$845$	9.90010	+	6.44329i	0.340574	+	0.221656i
$846$		0			0
$847$	−8.72614	−	11.6191i	−0.299834	−	0.399237i
$848$		0			0
$849$			11.5041i			0.394821i
$850$		0			0
$851$	18.6586			0.639610
$852$		0			0
$853$	16.5954	+	16.5954i	0.568215	+	0.568215i	0.931628	−	0.363413i	$-0.118389\pi$
$853$	16.5954	+	16.5954i	0.568215	+	0.568215i	−0.363413	+	0.931628i	$0.618389\pi$
$854$		0			0
$855$	5.90947	+	3.84606i	0.202100	+	0.131533i
$856$		0			0
$857$	−29.2133	+	29.2133i	−0.997909	+	0.997909i	−0.999998	−	0.00208912i	$-0.999335\pi$
$857$	−29.2133	+	29.2133i	−0.997909	+	0.997909i	0.00208912	+	0.999998i	$0.499335\pi$
$858$		0			0
$859$	−18.3754			−0.626962			−0.313481	−	0.949594i	$-0.601495\pi$
$859$	−18.3754			−0.626962			−0.313481	+	0.949594i	$0.601495\pi$
$860$		0			0
$861$	36.6377	+	5.20964i	1.24861	+	0.177544i
$862$		0			0
$863$	−31.7261	+	31.7261i	−1.07997	+	1.07997i	−0.0834585	+	0.996511i	$0.526597\pi$
$863$	−31.7261	+	31.7261i	−1.07997	+	1.07997i	−0.996511	+	0.0834585i	$0.973403\pi$
$864$		0			0
$865$	−14.2458	+	3.01315i	−0.484372	+	0.102450i
$866$		0			0
$867$	37.6318	−	37.6318i	1.27804	−	1.27804i
$868$		0			0
$869$			11.7042i			0.397039i
$870$		0			0
$871$			10.5744i			0.358300i
$872$		0			0
$873$	−9.97534	−	9.97534i	−0.337614	−	0.337614i
$874$		0			0
$875$	13.7663	+	26.1818i	0.465387	+	0.885107i
$876$		0			0
$877$	−32.2606	−	32.2606i	−1.08936	−	1.08936i	−0.995594	−	0.0937674i	$-0.970109\pi$
$877$	−32.2606	−	32.2606i	−1.08936	−	1.08936i	−0.0937674	−	0.995594i	$-0.529891\pi$
$878$		0			0
$879$		−	2.32823i		−	0.0785292i
$880$		0			0
$881$			9.96766i			0.335819i	0.985802	+	0.167909i	$0.0537016\pi$
$881$			9.96766i			0.335819i	−0.985802	+	0.167909i	$0.946298\pi$
$882$		0			0
$883$	−36.7464	+	36.7464i	−1.23662	+	1.23662i	−0.275239	+	0.961376i	$0.588757\pi$
$883$	−36.7464	+	36.7464i	−1.23662	+	1.23662i	−0.961376	+	0.275239i	$0.911243\pi$
$884$		0			0
$885$	14.8518	−	3.14134i	0.499239	−	0.105595i
$886$		0			0
$887$	−9.82975	+	9.82975i	−0.330051	+	0.330051i	−0.852606	−	0.522555i	$-0.824979\pi$
$887$	−9.82975	+	9.82975i	−0.330051	+	0.330051i	0.522555	+	0.852606i	$0.324979\pi$
$888$		0			0
$889$	0.409675	−	2.88111i	0.0137401	−	0.0966294i
$890$		0			0
$891$	−13.5379			−0.453538
$892$		0			0
$893$	17.2221	−	17.2221i	0.576314	−	0.576314i
$894$		0			0
$895$	21.6873	+	14.1148i	0.724928	+	0.471805i
$896$		0			0
$897$	24.8167	+	24.8167i	0.828607	+	0.828607i
$898$		0			0
$899$	9.22711			0.307741
$900$		0			0
$901$			40.0438i			1.33405i
$902$		0			0
$903$	6.15086	+	8.19004i	0.204688	+	0.272548i
$904$		0			0
$905$	9.90727	+	6.44795i	0.329329	+	0.214337i
$906$		0			0
$907$	10.4096	+	10.4096i	0.345646	+	0.345646i	0.858485	−	0.512839i	$-0.171406\pi$
$907$	10.4096	+	10.4096i	0.345646	+	0.345646i	−0.512839	+	0.858485i	$0.671406\pi$
$908$		0			0
$909$	7.07946			0.234811
$910$		0			0
$911$	16.5150			0.547167			0.273583	−	0.961848i	$-0.411791\pi$
$911$	16.5150			0.547167			0.273583	+	0.961848i	$0.411791\pi$
$912$		0			0
$913$	21.9820	+	21.9820i	0.727498	+	0.727498i
$914$		0			0
$915$	1.36015	+	6.43060i	0.0449650	+	0.212589i
$916$		0			0
$917$	−23.3502	+	17.5364i	−0.771092	+	0.579104i
$918$		0			0
$919$		−	14.9494i		−	0.493134i	−0.969126	−	0.246567i	$-0.920697\pi$
$919$		−	14.9494i		−	0.493134i	0.969126	−	0.246567i	$-0.0793026\pi$
$920$		0			0
$921$	−19.5951			−0.645680
$922$		0			0
$923$	−0.770480	−	0.770480i	−0.0253607	−	0.0253607i
$924$		0			0
$925$	3.90852	−	10.1215i	0.128511	−	0.332792i
$926$		0			0
$927$	7.38521	−	7.38521i	0.242562	−	0.242562i
$928$		0			0
$929$	−2.36098			−0.0774611			−0.0387306	−	0.999250i	$-0.512331\pi$
$929$	−2.36098			−0.0774611			−0.0387306	+	0.999250i	$0.512331\pi$
$930$		0			0
$931$	−7.31371	+	25.1975i	−0.239697	+	0.825815i
$932$		0			0
$933$	15.1720	−	15.1720i	0.496709	−	0.496709i
$934$		0			0
$935$	7.92227	+	37.4555i	0.259086	+	1.22493i
$936$		0			0
$937$	2.28379	−	2.28379i	0.0746081	−	0.0746081i	−0.668818	−	0.743426i	$-0.733199\pi$
$937$	2.28379	−	2.28379i	0.0746081	−	0.0746081i	0.743426	+	0.668818i	$0.233199\pi$
$938$		0			0
$939$		−	14.6600i		−	0.478410i
$940$		0			0
$941$			30.1034i			0.981344i	0.871344	+	0.490672i	$0.163249\pi$
$941$			30.1034i			0.981344i	−0.871344	+	0.490672i	$0.836751\pi$
$942$		0			0
$943$	−57.8808	−	57.8808i	−1.88486	−	1.88486i
$944$		0			0
$945$	−21.9713	+	25.1418i	−0.714728	+	0.817862i
$946$		0			0
$947$	9.50072	+	9.50072i	0.308732	+	0.308732i	0.844417	−	0.535686i	$-0.179947\pi$
$947$	9.50072	+	9.50072i	0.308732	+	0.308732i	−0.535686	+	0.844417i	$0.679947\pi$
$948$		0			0
$949$		−	27.8367i		−	0.903617i
$950$		0			0
$951$		−	23.3837i		−	0.758269i
$952$		0			0
$953$	−21.9629	+	21.9629i	−0.711448	+	0.711448i	−0.966838	−	0.255390i	$-0.917796\pi$
$953$	−21.9629	+	21.9629i	−0.711448	+	0.711448i	0.255390	+	0.966838i	$0.417796\pi$
$954$		0			0
$955$	14.1628	−	21.7612i	0.458299	−	0.704175i
$956$		0			0
$957$	14.3620	−	14.3620i	0.464258	−	0.464258i
$958$		0			0
$959$	−1.39751	+	9.82823i	−0.0451279	+	0.317370i
$960$		0			0
$961$	28.5461			0.920843
$962$		0			0
$963$	8.72731	−	8.72731i	0.281234	−	0.281234i
$964$		0			0
$965$	−11.5413	−	54.5657i	−0.371527	−	1.75653i
$966$		0			0
$967$	14.6279	+	14.6279i	0.470400	+	0.470400i	0.902044	−	0.431644i	$-0.142066\pi$
$967$	14.6279	+	14.6279i	0.470400	+	0.470400i	−0.431644	+	0.902044i	$0.642066\pi$
$968$		0			0
$969$	−40.1762			−1.29065
$970$		0			0
$971$		−	14.5120i		−	0.465712i	−0.972511	−	0.232856i	$-0.925193\pi$
$971$		−	14.5120i		−	0.465712i	0.972511	−	0.232856i	$-0.0748071\pi$
$972$		0			0
$973$	11.3673	+	15.1359i	0.364419	+	0.485233i
$974$		0			0
$975$	18.6605	−	8.26348i	0.597613	−	0.264643i
$976$		0			0
$977$	3.07281	+	3.07281i	0.0983080	+	0.0983080i	0.754550	−	0.656242i	$-0.227855\pi$
$977$	3.07281	+	3.07281i	0.0983080	+	0.0983080i	−0.656242	+	0.754550i	$0.727855\pi$
$978$		0			0
$979$	23.0744			0.737463
$980$		0			0
$981$	4.14509			0.132343
$982$		0			0
$983$	−38.2010	−	38.2010i	−1.21842	−	1.21842i	−0.968184	−	0.250238i	$-0.919491\pi$
$983$	−38.2010	−	38.2010i	−1.21842	−	1.21842i	−0.250238	−	0.968184i	$-0.580509\pi$
$984$		0			0
$985$	53.2541	−	11.2638i	1.69682	−	0.358896i
$986$		0			0
$987$	15.1689	+	20.1977i	0.482830	+	0.642901i
$988$		0			0
$989$		−	22.6560i		−	0.720418i
$990$		0			0
$991$	42.3300			1.34466			0.672328	−	0.740253i	$-0.265294\pi$
$991$	42.3300			1.34466			0.672328	+	0.740253i	$0.265294\pi$
$992$		0			0
$993$	−34.9748	−	34.9748i	−1.10989	−	1.10989i
$994$		0			0
$995$	−8.48786	+	13.0416i	−0.269083	+	0.413446i
$996$		0			0
$997$	24.3987	−	24.3987i	0.772713	−	0.772713i	−0.205867	−	0.978580i	$-0.566001\pi$
$997$	24.3987	−	24.3987i	0.772713	−	0.772713i	0.978580	+	0.205867i	$0.0660013\pi$
$998$		0			0
$999$	12.2470			0.387479

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.x.a.97.9	yes	24
4.3	odd	2		560.2.bj.d.97.4		24
5.2	odd	4		1400.2.x.b.993.9		24
5.3	odd	4	inner	280.2.x.a.153.4	yes	24
5.4	even	2		1400.2.x.b.657.4		24
7.6	odd	2	inner	280.2.x.a.97.4	✓	24
20.3	even	4		560.2.bj.d.433.9		24
28.27	even	2		560.2.bj.d.97.9		24
35.13	even	4	inner	280.2.x.a.153.9	yes	24
35.27	even	4		1400.2.x.b.993.4		24
35.34	odd	2		1400.2.x.b.657.9		24
140.83	odd	4		560.2.bj.d.433.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.x.a.97.4	✓	24	7.6	odd	2	inner
280.2.x.a.97.9	yes	24	1.1	even	1	trivial
280.2.x.a.153.4	yes	24	5.3	odd	4	inner
280.2.x.a.153.9	yes	24	35.13	even	4	inner
560.2.bj.d.97.4		24	4.3	odd	2
560.2.bj.d.97.9		24	28.27	even	2
560.2.bj.d.433.4		24	140.83	odd	4
560.2.bj.d.433.9		24	20.3	even	4
1400.2.x.b.657.4		24	5.4	even	2
1400.2.x.b.657.9		24	35.34	odd	2
1400.2.x.b.993.4		24	35.27	even	4
1400.2.x.b.993.9		24	5.2	odd	4

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.x (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.03893 + 1.03893i) q^{3} +(-1.21973 + 1.87411i) q^{5} +(1.58883 + 2.11557i) q^{7} -0.841261i q^{9} +O(q^{10})\)	\(q+(1.03893 + 1.03893i) q^{3} +(-1.21973 + 1.87411i) q^{5} +(1.58883 + 2.11557i) q^{7} -0.841261i q^{9} -2.34687 q^{11} +(1.96436 + 1.96436i) q^{13} +(-3.21426 + 0.679854i) q^{15} +(-5.15858 + 5.15858i) q^{17} +3.74821 q^{19} +(-0.547244 + 3.84860i) q^{21} +(6.08007 - 6.08007i) q^{23} +(-2.02454 - 4.57179i) q^{25} +(3.99079 - 3.99079i) q^{27} +5.89034i q^{29} -1.56648i q^{31} +(-2.43823 - 2.43823i) q^{33} +(-5.90273 + 0.397220i) q^{35} +(1.53441 + 1.53441i) q^{37} +4.08166i q^{39} -9.51977i q^{41} +(1.86313 - 1.86313i) q^{43} +(1.57661 + 1.02611i) q^{45} +(4.59474 - 4.59474i) q^{47} +(-1.95125 + 6.72254i) q^{49} -10.7188 q^{51} +(3.88128 - 3.88128i) q^{53} +(2.86254 - 4.39829i) q^{55} +(3.89412 + 3.89412i) q^{57} -4.62061 q^{59} -2.00065i q^{61} +(1.77974 - 1.33662i) q^{63} +(-6.07740 + 1.28544i) q^{65} +(2.69156 + 2.69156i) q^{67} +12.6335 q^{69} -0.392229 q^{71} +(-7.08543 - 7.08543i) q^{73} +(2.64640 - 6.85310i) q^{75} +(-3.72878 - 4.96497i) q^{77} -4.98717i q^{79} +5.76850 q^{81} +(-9.36651 - 9.36651i) q^{83} +(-3.37567 - 15.9598i) q^{85} +(-6.11964 + 6.11964i) q^{87} -9.83200 q^{89} +(-1.03471 + 7.27677i) q^{91} +(1.62746 - 1.62746i) q^{93} +(-4.57179 + 7.02454i) q^{95} +(11.8576 - 11.8576i) q^{97} +1.97433i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{7}+O(q^{10}) \) 24 * q + 4 * q^7	\( 24 q + 4 q^{7} + 8 q^{11} - 8 q^{15} + 16 q^{21} - 32 q^{23} + 8 q^{25} + 12 q^{35} - 8 q^{37} + 16 q^{43} - 24 q^{51} - 16 q^{53} + 20 q^{63} - 48 q^{65} - 32 q^{67} - 32 q^{71} - 40 q^{77} - 72 q^{81} + 16 q^{85} - 64 q^{91} + 72 q^{93} - 24 q^{95}+O(q^{100}) \) 24 * q + 4 * q^7 + 8 * q^11 - 8 * q^15 + 16 * q^21 - 32 * q^23 + 8 * q^25 + 12 * q^35 - 8 * q^37 + 16 * q^43 - 24 * q^51 - 16 * q^53 + 20 * q^63 - 48 * q^65 - 32 * q^67 - 32 * q^71 - 40 * q^77 - 72 * q^81 + 16 * q^85 - 64 * q^91 + 72 * q^93 - 24 * q^95

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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