LMFDB - Embedded newform 1040.2.bp.b.287.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1040,2,Mod(287,1040)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1040, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1040.287");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1040 = 2^{4} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1040.bp (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:	$8.30444181021$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			287.9
Character	$\chi$	$=$	1040.287
Dual form			1040.2.bp.b.703.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.611027 - 0.611027i) q^{3} +(0.509549 - 2.17724i) q^{5} +(-1.48685 + 1.48685i) q^{7} -2.25329i q^{9} +O(q^{10})$	\(q+(-0.611027 - 0.611027i) q^{3} +(0.509549 - 2.17724i) q^{5} +(-1.48685 + 1.48685i) q^{7} -2.25329i q^{9} -2.63864i q^{11} +(-0.707107 + 0.707107i) q^{13} +(-1.64170 + 1.01900i) q^{15} +(0.501721 + 0.501721i) q^{17} -5.25764 q^{19} +1.81701 q^{21} +(2.39508 + 2.39508i) q^{23} +(-4.48072 - 2.21882i) q^{25} +(-3.20990 + 3.20990i) q^{27} -6.31845i q^{29} +3.70802i q^{31} +(-1.61228 + 1.61228i) q^{33} +(2.47960 + 3.99484i) q^{35} +(-0.738916 - 0.738916i) q^{37} +0.864123 q^{39} -6.68438 q^{41} +(-2.31168 - 2.31168i) q^{43} +(-4.90595 - 1.14816i) q^{45} +(-2.31671 + 2.31671i) q^{47} +2.57857i q^{49} -0.613131i q^{51} +(5.12271 - 5.12271i) q^{53} +(-5.74494 - 1.34451i) q^{55} +(3.21256 + 3.21256i) q^{57} -8.79066 q^{59} -5.44054 q^{61} +(3.35030 + 3.35030i) q^{63} +(1.17923 + 1.89984i) q^{65} +(-0.136001 + 0.136001i) q^{67} -2.92692i q^{69} -7.29428i q^{71} +(1.75025 - 1.75025i) q^{73} +(1.38208 + 4.09360i) q^{75} +(3.92325 + 3.92325i) q^{77} -15.6028 q^{79} -2.83720 q^{81} +(5.29752 + 5.29752i) q^{83} +(1.34802 - 0.836714i) q^{85} +(-3.86075 + 3.86075i) q^{87} +7.06196i q^{89} -2.10272i q^{91} +(2.26570 - 2.26570i) q^{93} +(-2.67903 + 11.4471i) q^{95} +(-1.06266 - 1.06266i) q^{97} -5.94562 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 8 q^{5}+O(q^{10}) $ 48 * q + 8 * q^5	$ 48 q + 8 q^{5} - 16 q^{17} + 32 q^{21} + 16 q^{25} - 24 q^{33} + 24 q^{37} - 16 q^{41} - 48 q^{45} + 40 q^{53} - 8 q^{57} - 16 q^{61} + 40 q^{73} - 72 q^{77} - 160 q^{81} - 64 q^{85} - 8 q^{93} + 16 q^{97}+O(q^{100}) $ 48 * q + 8 * q^5 - 16 * q^17 + 32 * q^21 + 16 * q^25 - 24 * q^33 + 24 * q^37 - 16 * q^41 - 48 * q^45 + 40 * q^53 - 8 * q^57 - 16 * q^61 + 40 * q^73 - 72 * q^77 - 160 * q^81 - 64 * q^85 - 8 * q^93 + 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times$.

$n$	$261$	$417$	$561$	$911$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.611027	−	0.611027i	−0.352777	−	0.352777i	0.508365	−	0.861142i	$-0.330250\pi$
$3$	−0.611027	−	0.611027i	−0.352777	−	0.352777i	−0.861142	+	0.508365i	$0.830250\pi$
$4$		0			0
$5$	0.509549	−	2.17724i	0.227877	−	0.973690i
$5$	0.509549	−	2.17724i	0.227877	−	0.973690i
$6$		0			0
$7$	−1.48685	+	1.48685i	−0.561975	+	0.561975i	−0.929868	−	0.367893i	$-0.880079\pi$
$7$	−1.48685	+	1.48685i	−0.561975	+	0.561975i	0.367893	+	0.929868i	$0.380079\pi$
$8$		0			0
$9$		−	2.25329i		−	0.751097i
$10$		0			0
$11$		−	2.63864i		−	0.795579i	−0.917477	−	0.397790i	$-0.869777\pi$
$11$		−	2.63864i		−	0.795579i	0.917477	−	0.397790i	$-0.130223\pi$
$12$		0			0
$13$	−0.707107	+	0.707107i	−0.196116	+	0.196116i
$13$	−0.707107	+	0.707107i	−0.196116	+	0.196116i
$14$		0			0
$15$	−1.64170	+	1.01900i	−0.423885	+	0.263105i
$16$		0			0
$17$	0.501721	+	0.501721i	0.121685	+	0.121685i	0.765327	−	0.643642i	$-0.222577\pi$
$17$	0.501721	+	0.501721i	0.121685	+	0.121685i	−0.643642	+	0.765327i	$0.722577\pi$
$18$		0			0
$19$	−5.25764			−1.20619			−0.603093	−	0.797671i	$-0.706065\pi$
$19$	−5.25764			−1.20619			−0.603093	+	0.797671i	$0.706065\pi$
$20$		0			0
$21$	1.81701			0.396504
$22$		0			0
$23$	2.39508	+	2.39508i	0.499409	+	0.499409i	0.911254	−	0.411845i	$-0.135116\pi$
$23$	2.39508	+	2.39508i	0.499409	+	0.499409i	−0.411845	+	0.911254i	$0.635116\pi$
$24$		0			0
$25$	−4.48072	−	2.21882i	−0.896144	−	0.443763i
$26$		0			0
$27$	−3.20990	+	3.20990i	−0.617746	+	0.617746i
$28$		0			0
$29$		−	6.31845i		−	1.17331i	−0.809838	−	0.586654i	$-0.800445\pi$
$29$		−	6.31845i		−	1.17331i	0.809838	−	0.586654i	$-0.199555\pi$
$30$		0			0
$31$			3.70802i			0.665980i	0.942930	+	0.332990i	$0.108058\pi$
$31$			3.70802i			0.665980i	−0.942930	+	0.332990i	$0.891942\pi$
$32$		0			0
$33$	−1.61228	+	1.61228i	−0.280662	+	0.280662i
$34$		0			0
$35$	2.47960	+	3.99484i	0.419128	+	0.675251i
$36$		0			0
$37$	−0.738916	−	0.738916i	−0.121477	−	0.121477i	0.643755	−	0.765232i	$-0.277376\pi$
$37$	−0.738916	−	0.738916i	−0.121477	−	0.121477i	−0.765232	+	0.643755i	$0.777376\pi$
$38$		0			0
$39$	0.864123			0.138370
$40$		0			0
$41$	−6.68438			−1.04392			−0.521962	−	0.852969i	$-0.674800\pi$
$41$	−6.68438			−1.04392			−0.521962	+	0.852969i	$0.674800\pi$
$42$		0			0
$43$	−2.31168	−	2.31168i	−0.352528	−	0.352528i	0.508521	−	0.861049i	$-0.330192\pi$
$43$	−2.31168	−	2.31168i	−0.352528	−	0.352528i	−0.861049	+	0.508521i	$0.830192\pi$
$44$		0			0
$45$	−4.90595	−	1.14816i	−0.731336	−	0.171158i
$46$		0			0
$47$	−2.31671	+	2.31671i	−0.337927	+	0.337927i	−0.855587	−	0.517659i	$-0.826803\pi$
$47$	−2.31671	+	2.31671i	−0.337927	+	0.337927i	0.517659	+	0.855587i	$0.326803\pi$
$48$		0			0
$49$			2.57857i			0.368367i
$50$		0			0
$51$		−	0.613131i		−	0.0858555i
$52$		0			0
$53$	5.12271	−	5.12271i	0.703659	−	0.703659i	−0.261535	−	0.965194i	$-0.584229\pi$
$53$	5.12271	−	5.12271i	0.703659	−	0.703659i	0.965194	+	0.261535i	$0.0842287\pi$
$54$		0			0
$55$	−5.74494	−	1.34451i	−0.774647	−	0.181294i
$56$		0			0
$57$	3.21256	+	3.21256i	0.425514	+	0.425514i
$58$		0			0
$59$	−8.79066			−1.14445			−0.572223	−	0.820098i	$-0.693919\pi$
$59$	−8.79066			−1.14445			−0.572223	+	0.820098i	$0.693919\pi$
$60$		0			0
$61$	−5.44054			−0.696590			−0.348295	−	0.937385i	$-0.613239\pi$
$61$	−5.44054			−0.696590			−0.348295	+	0.937385i	$0.613239\pi$
$62$		0			0
$63$	3.35030	+	3.35030i	0.422098	+	0.422098i
$64$		0			0
$65$	1.17923	+	1.89984i	0.146266	+	0.235647i
$66$		0			0
$67$	−0.136001	+	0.136001i	−0.0166151	+	0.0166151i	−0.715366	−	0.698750i	$-0.753740\pi$
$67$	−0.136001	+	0.136001i	−0.0166151	+	0.0166151i	0.698750	+	0.715366i	$0.253740\pi$
$68$		0			0
$69$		−	2.92692i		−	0.352360i
$70$		0			0
$71$		−	7.29428i		−	0.865672i	−0.901473	−	0.432836i	$-0.857513\pi$
$71$		−	7.29428i		−	0.865672i	0.901473	−	0.432836i	$-0.142487\pi$
$72$		0			0
$73$	1.75025	−	1.75025i	0.204852	−	0.204852i	−0.597223	−	0.802075i	$-0.703729\pi$
$73$	1.75025	−	1.75025i	0.204852	−	0.204852i	0.802075	+	0.597223i	$0.203729\pi$
$74$		0			0
$75$	1.38208	+	4.09360i	0.159589	+	0.472688i
$76$		0			0
$77$	3.92325	+	3.92325i	0.447096	+	0.447096i
$78$		0			0
$79$	−15.6028			−1.75545			−0.877724	−	0.479167i	$-0.840939\pi$
$79$	−15.6028			−1.75545			−0.877724	+	0.479167i	$0.840939\pi$
$80$		0			0
$81$	−2.83720			−0.315244
$82$		0			0
$83$	5.29752	+	5.29752i	0.581478	+	0.581478i	0.935309	−	0.353831i	$-0.115121\pi$
$83$	5.29752	+	5.29752i	0.581478	+	0.581478i	−0.353831	+	0.935309i	$0.615121\pi$
$84$		0			0
$85$	1.34802	−	0.836714i	0.146213	−	0.0907544i
$86$		0			0
$87$	−3.86075	+	3.86075i	−0.413916	+	0.413916i
$88$		0			0
$89$			7.06196i			0.748567i	0.927314	+	0.374283i	$0.122111\pi$
$89$			7.06196i			0.748567i	−0.927314	+	0.374283i	$0.877889\pi$
$90$		0			0
$91$		−	2.10272i		−	0.220425i
$92$		0			0
$93$	2.26570	−	2.26570i	0.234942	−	0.234942i
$94$		0			0
$95$	−2.67903	+	11.4471i	−0.274862	+	1.17445i
$96$		0			0
$97$	−1.06266	−	1.06266i	−0.107897	−	0.107897i	0.651097	−	0.758994i	$-0.274309\pi$
$97$	−1.06266	−	1.06266i	−0.107897	−	0.107897i	−0.758994	+	0.651097i	$0.774309\pi$
$98$		0			0
$99$	−5.94562			−0.597557
$100$		0			0
$101$	11.4637			1.14069			0.570343	−	0.821407i	$-0.306810\pi$
$101$	11.4637			1.14069			0.570343	+	0.821407i	$0.306810\pi$
$102$		0			0
$103$	−8.64260	−	8.64260i	−0.851581	−	0.851581i	0.138747	−	0.990328i	$-0.455692\pi$
$103$	−8.64260	−	8.64260i	−0.851581	−	0.851581i	−0.990328	+	0.138747i	$0.955692\pi$
$104$		0			0
$105$	0.925855	−	3.95606i	0.0903542	−	0.386072i
$106$		0			0
$107$	8.98059	−	8.98059i	0.868186	−	0.868186i	−0.124085	−	0.992272i	$-0.539600\pi$
$107$	8.98059	−	8.98059i	0.868186	−	0.868186i	0.992272	+	0.124085i	$0.0395996\pi$
$108$		0			0
$109$		−	8.29462i		−	0.794480i	−0.917715	−	0.397240i	$-0.869968\pi$
$109$		−	8.29462i		−	0.794480i	0.917715	−	0.397240i	$-0.130032\pi$
$110$		0			0
$111$			0.902995i			0.0857085i
$112$		0			0
$113$	−11.8986	+	11.8986i	−1.11933	+	1.11933i	−0.127491	+	0.991840i	$0.540692\pi$
$113$	−11.8986	+	11.8986i	−1.11933	+	1.11933i	−0.991840	+	0.127491i	$0.959308\pi$
$114$		0			0
$115$	6.43507	−	3.99425i	0.600073	−	0.372465i
$116$		0			0
$117$	1.59332	+	1.59332i	0.147302	+	0.147302i
$118$		0			0
$119$	−1.49197			−0.136768
$120$		0			0
$121$	4.03759			0.367054
$122$		0			0
$123$	4.08434	+	4.08434i	0.368272	+	0.368272i
$124$		0			0
$125$	−7.11404	+	8.62499i	−0.636299	+	0.771443i
$126$		0			0
$127$	14.5683	−	14.5683i	1.29272	−	1.29272i	0.359629	−	0.933095i	$-0.382903\pi$
$127$	14.5683	−	14.5683i	1.29272	−	1.29272i	0.933095	−	0.359629i	$-0.117097\pi$
$128$		0			0
$129$			2.82500i			0.248727i
$130$		0			0
$131$		−	10.4525i		−	0.913238i	−0.889662	−	0.456619i	$-0.849060\pi$
$131$		−	10.4525i		−	0.913238i	0.889662	−	0.456619i	$-0.150940\pi$
$132$		0			0
$133$	7.81731	−	7.81731i	0.677846	−	0.677846i
$134$		0			0
$135$	5.35312	+	8.62432i	0.460723	+	0.742264i
$136$		0			0
$137$	−12.1986	−	12.1986i	−1.04220	−	1.04220i	−0.999070	−	0.0431275i	$-0.986268\pi$
$137$	−12.1986	−	12.1986i	−1.04220	−	1.04220i	−0.0431275	−	0.999070i	$-0.513732\pi$
$138$		0			0
$139$	−9.11261			−0.772922			−0.386461	−	0.922306i	$-0.626303\pi$
$139$	−9.11261			−0.772922			−0.386461	+	0.922306i	$0.626303\pi$
$140$		0			0
$141$	2.83115			0.238426
$142$		0			0
$143$	1.86580	+	1.86580i	0.156026	+	0.156026i
$144$		0			0
$145$	−13.7568	−	3.21956i	−1.14244	−	0.267370i
$146$		0			0
$147$	1.57558	−	1.57558i	0.129951	−	0.129951i
$148$		0			0
$149$		−	4.36830i		−	0.357865i	−0.983861	−	0.178933i	$-0.942736\pi$
$149$		−	4.36830i		−	0.357865i	0.983861	−	0.178933i	$-0.0572644\pi$
$150$		0			0
$151$		−	1.33290i		−	0.108470i	−0.998528	−	0.0542349i	$-0.982728\pi$
$151$		−	1.33290i		−	0.108470i	0.998528	−	0.0542349i	$-0.0172720\pi$
$152$		0			0
$153$	1.13052	−	1.13052i	0.0913974	−	0.0913974i
$154$		0			0
$155$	8.07324	+	1.88942i	0.648458	+	0.151762i
$156$		0			0
$157$	7.53961	+	7.53961i	0.601726	+	0.601726i	0.940770	−	0.339044i	$-0.110104\pi$
$157$	7.53961	+	7.53961i	0.601726	+	0.601726i	−0.339044	+	0.940770i	$0.610104\pi$
$158$		0			0
$159$	−6.26024			−0.496469
$160$		0			0
$161$	−7.12224			−0.561311
$162$		0			0
$163$	0.624096	+	0.624096i	0.0488830	+	0.0488830i	0.731126	−	0.682243i	$-0.238995\pi$
$163$	0.624096	+	0.624096i	0.0488830	+	0.0488830i	−0.682243	+	0.731126i	$0.738995\pi$
$164$		0			0
$165$	2.68878	+	4.33185i	0.209321	+	0.337234i
$166$		0			0
$167$	16.2476	−	16.2476i	1.25728	−	1.25728i	0.304890	−	0.952388i	$-0.401380\pi$
$167$	16.2476	−	16.2476i	1.25728	−	1.25728i	0.952388	−	0.304890i	$-0.0986197\pi$
$168$		0			0
$169$		−	1.00000i		−	0.0769231i
$170$		0			0
$171$			11.8470i			0.905962i
$172$		0			0
$173$	6.72258	−	6.72258i	0.511108	−	0.511108i	−0.403758	−	0.914866i	$-0.632296\pi$
$173$	6.72258	−	6.72258i	0.511108	−	0.511108i	0.914866	+	0.403758i	$0.132296\pi$
$174$		0			0
$175$	9.96119	−	3.36310i	0.752995	−	0.254227i
$176$		0			0
$177$	5.37133	+	5.37133i	0.403734	+	0.403734i
$178$		0			0
$179$	8.58638			0.641776			0.320888	−	0.947117i	$-0.396019\pi$
$179$	8.58638			0.641776			0.320888	+	0.947117i	$0.396019\pi$
$180$		0			0
$181$	24.0366			1.78663			0.893314	−	0.449432i	$-0.148374\pi$
$181$	24.0366			1.78663			0.893314	+	0.449432i	$0.148374\pi$
$182$		0			0
$183$	3.32432	+	3.32432i	0.245741	+	0.245741i
$184$		0			0
$185$	−1.98531	+	1.23228i	−0.145963	+	0.0905991i
$186$		0			0
$187$	1.32386	−	1.32386i	0.0968102	−	0.0968102i
$188$		0			0
$189$		−	9.54527i		−	0.694316i
$190$		0			0
$191$			5.66217i			0.409700i	0.978793	+	0.204850i	$0.0656706\pi$
$191$			5.66217i			0.409700i	−0.978793	+	0.204850i	$0.934329\pi$
$192$		0			0
$193$	−3.31296	+	3.31296i	−0.238472	+	0.238472i	−0.816217	−	0.577745i	$-0.803933\pi$
$193$	−3.31296	+	3.31296i	−0.238472	+	0.238472i	0.577745	+	0.816217i	$0.303933\pi$
$194$		0			0
$195$	0.440313	−	1.88140i	0.0315315	−	0.134730i
$196$		0			0
$197$	11.1688	+	11.1688i	0.795742	+	0.795742i	0.982421	−	0.186679i	$-0.0597724\pi$
$197$	11.1688	+	11.1688i	0.795742	+	0.795742i	−0.186679	+	0.982421i	$0.559772\pi$
$198$		0			0
$199$	5.83825			0.413863			0.206931	−	0.978355i	$-0.433652\pi$
$199$	5.83825			0.413863			0.206931	+	0.978355i	$0.433652\pi$
$200$		0			0
$201$	0.166200			0.0117228
$202$		0			0
$203$	9.39457	+	9.39457i	0.659370	+	0.659370i
$204$		0			0
$205$	−3.40602	+	14.5535i	−0.237887	+	1.01646i
$206$		0			0
$207$	5.39681	−	5.39681i	0.375105	−	0.375105i
$208$		0			0
$209$			13.8730i			0.959616i
$210$		0			0
$211$		−	21.3181i		−	1.46760i	−0.679367	−	0.733799i	$-0.737745\pi$
$211$		−	21.3181i		−	1.46760i	0.679367	−	0.733799i	$-0.262255\pi$
$212$		0			0
$213$	−4.45701	+	4.45701i	−0.305389	+	0.305389i
$214$		0			0
$215$	−6.21099	+	3.85516i	−0.423586	+	0.262920i
$216$		0			0
$217$	−5.51326	−	5.51326i	−0.374265	−	0.374265i
$218$		0			0
$219$	−2.13891			−0.144534
$220$		0			0
$221$	−0.709541			−0.0477289
$222$		0			0
$223$	17.9853	+	17.9853i	1.20439	+	1.20439i	0.972819	+	0.231567i	$0.0743854\pi$
$223$	17.9853	+	17.9853i	1.20439	+	1.20439i	0.231567	+	0.972819i	$0.425615\pi$
$224$		0			0
$225$	−4.99964	+	10.0964i	−0.333309	+	0.673091i
$226$		0			0
$227$	−3.37290	+	3.37290i	−0.223867	+	0.223867i	−0.810125	−	0.586257i	$-0.800601\pi$
$227$	−3.37290	+	3.37290i	−0.223867	+	0.223867i	0.586257	+	0.810125i	$0.300601\pi$
$228$		0			0
$229$			4.76164i			0.314658i	0.987546	+	0.157329i	$0.0502883\pi$
$229$			4.76164i			0.314658i	−0.987546	+	0.157329i	$0.949712\pi$
$230$		0			0
$231$		−	4.79443i		−	0.315450i
$232$		0			0
$233$	−12.7330	+	12.7330i	−0.834167	+	0.834167i	−0.988084	−	0.153917i	$-0.950811\pi$
$233$	−12.7330	+	12.7330i	−0.834167	+	0.834167i	0.153917	+	0.988084i	$0.450811\pi$
$234$		0			0
$235$	3.86355	+	6.22451i	0.252030	+	0.406042i
$236$		0			0
$237$	9.53371	+	9.53371i	0.619281	+	0.619281i
$238$		0			0
$239$	6.65908			0.430740			0.215370	−	0.976533i	$-0.430904\pi$
$239$	6.65908			0.430740			0.215370	+	0.976533i	$0.430904\pi$
$240$		0			0
$241$	22.0500			1.42036			0.710182	−	0.704018i	$-0.248613\pi$
$241$	22.0500			1.42036			0.710182	+	0.704018i	$0.248613\pi$
$242$		0			0
$243$	11.3633	+	11.3633i	0.728957	+	0.728957i
$244$		0			0
$245$	5.61416	+	1.31391i	0.358676	+	0.0839425i
$246$		0			0
$247$	3.71771	−	3.71771i	0.236552	−	0.236552i
$248$		0			0
$249$		−	6.47385i		−	0.410264i
$250$		0			0
$251$		−	8.31174i		−	0.524632i	−0.964982	−	0.262316i	$-0.915514\pi$
$251$		−	8.31174i		−	0.524632i	0.964982	−	0.262316i	$-0.0844863\pi$
$252$		0			0
$253$	6.31975	−	6.31975i	0.397319	−	0.397319i
$254$		0			0
$255$	−1.33493	−	0.312420i	−0.0835966	−	0.0195645i
$256$		0			0
$257$	−5.97816	−	5.97816i	−0.372907	−	0.372907i	0.495628	−	0.868535i	$-0.334938\pi$
$257$	−5.97816	−	5.97816i	−0.372907	−	0.372907i	−0.868535	+	0.495628i	$0.834938\pi$
$258$		0			0
$259$	2.19731			0.136534
$260$		0			0
$261$	−14.2373			−0.881268
$262$		0			0
$263$	−0.251024	−	0.251024i	−0.0154788	−	0.0154788i	0.699325	−	0.714804i	$-0.253484\pi$
$263$	−0.251024	−	0.251024i	−0.0154788	−	0.0154788i	−0.714804	+	0.699325i	$0.753484\pi$
$264$		0			0
$265$	−8.54309	−	13.7636i	−0.524798	−	0.845493i
$266$		0			0
$267$	4.31505	−	4.31505i	0.264077	−	0.264077i
$268$		0			0
$269$		−	17.7014i		−	1.07927i	−0.841898	−	0.539636i	$-0.818562\pi$
$269$		−	17.7014i		−	1.07927i	0.841898	−	0.539636i	$-0.181438\pi$
$270$		0			0
$271$		−	25.9270i		−	1.57495i	−0.616344	−	0.787477i	$-0.711387\pi$
$271$		−	25.9270i		−	1.57495i	0.616344	−	0.787477i	$-0.288613\pi$
$272$		0			0
$273$	−1.28482	+	1.28482i	−0.0777608	+	0.0777608i
$274$		0			0
$275$	−5.85465	+	11.8230i	−0.353049	+	0.712953i
$276$		0			0
$277$	16.8140	+	16.8140i	1.01025	+	1.01025i	0.999947	+	0.0103069i	$0.00328083\pi$
$277$	16.8140	+	16.8140i	1.01025	+	1.01025i	0.0103069	+	0.999947i	$0.496719\pi$
$278$		0			0
$279$	8.35525			0.500216
$280$		0			0
$281$	3.69552			0.220456			0.110228	−	0.993906i	$-0.464842\pi$
$281$	3.69552			0.220456			0.110228	+	0.993906i	$0.464842\pi$
$282$		0			0
$283$	−14.1317	−	14.1317i	−0.840041	−	0.840041i	0.148823	−	0.988864i	$-0.452452\pi$
$283$	−14.1317	−	14.1317i	−0.840041	−	0.840041i	−0.988864	+	0.148823i	$0.952452\pi$
$284$		0			0
$285$	8.63146	−	5.35755i	0.511284	−	0.317354i
$286$		0			0
$287$	9.93864	−	9.93864i	0.586660	−	0.586660i
$288$		0			0
$289$		−	16.4966i		−	0.970385i
$290$		0			0
$291$			1.29863i			0.0761272i
$292$		0			0
$293$	−15.6026	+	15.6026i	−0.911515	+	0.911515i	−0.996392	−	0.0848760i	$-0.972951\pi$
$293$	−15.6026	+	15.6026i	−0.911515	+	0.911515i	0.0848760	+	0.996392i	$0.472951\pi$
$294$		0			0
$295$	−4.47927	+	19.1394i	−0.260793	+	1.11434i
$296$		0			0
$297$	8.46977	+	8.46977i	0.491466	+	0.491466i
$298$		0			0
$299$	−3.38716			−0.195884
$300$		0			0
$301$	6.87423			0.396224
$302$		0			0
$303$	−7.00466	−	7.00466i	−0.402407	−	0.402407i
$304$		0			0
$305$	−2.77222	+	11.8454i	−0.158737	+	0.678263i
$306$		0			0
$307$	16.4758	−	16.4758i	0.940324	−	0.940324i	−0.0579929	−	0.998317i	$-0.518470\pi$
$307$	16.4758	−	16.4758i	0.940324	−	0.940324i	0.998317	+	0.0579929i	$0.0184701\pi$
$308$		0			0
$309$			10.5617i			0.600836i
$310$		0			0
$311$		−	11.1639i		−	0.633045i	−0.948585	−	0.316522i	$-0.897485\pi$
$311$		−	11.1639i		−	0.633045i	0.948585	−	0.316522i	$-0.102515\pi$
$312$		0			0
$313$	−6.07211	+	6.07211i	−0.343216	+	0.343216i	−0.857575	−	0.514359i	$-0.828030\pi$
$313$	−6.07211	+	6.07211i	−0.343216	+	0.343216i	0.514359	+	0.857575i	$0.328030\pi$
$314$		0			0
$315$	9.00154	−	5.58725i	0.507179	−	0.314806i
$316$		0			0
$317$	−17.1201	−	17.1201i	−0.961563	−	0.961563i	0.0377250	−	0.999288i	$-0.487989\pi$
$317$	−17.1201	−	17.1201i	−0.961563	−	0.961563i	−0.999288	+	0.0377250i	$0.987989\pi$
$318$		0			0
$319$	−16.6721			−0.933459
$320$		0			0
$321$	−10.9748			−0.612552
$322$		0			0
$323$	−2.63787	−	2.63787i	−0.146775	−	0.146775i
$324$		0			0
$325$	4.73729	−	1.59941i	0.262777	−	0.0887191i
$326$		0			0
$327$	−5.06824	+	5.06824i	−0.280274	+	0.280274i
$328$		0			0
$329$		−	6.88919i		−	0.379814i
$330$		0			0
$331$		−	22.5893i		−	1.24162i	−0.783960	−	0.620811i	$-0.786803\pi$
$331$		−	22.5893i		−	1.24162i	0.783960	−	0.620811i	$-0.213197\pi$
$332$		0			0
$333$	−1.66499	+	1.66499i	−0.0912410	+	0.0912410i
$334$		0			0
$335$	0.226806	+	0.365404i	0.0123918	+	0.0199642i
$336$		0			0
$337$	13.1743	+	13.1743i	0.717647	+	0.717647i	0.968123	−	0.250476i	$-0.0805870\pi$
$337$	13.1743	+	13.1743i	0.717647	+	0.717647i	−0.250476	+	0.968123i	$0.580587\pi$
$338$		0			0
$339$	14.5408			0.789748
$340$		0			0
$341$	9.78413			0.529840
$342$		0			0
$343$	−14.2419	−	14.2419i	−0.768989	−	0.768989i
$344$		0			0
$345$	−6.37260	−	1.49141i	−0.343089	−	0.0802947i
$346$		0			0
$347$	−24.3136	+	24.3136i	−1.30522	+	1.30522i	−0.380397	+	0.924823i	$0.624213\pi$
$347$	−24.3136	+	24.3136i	−1.30522	+	1.30522i	−0.924823	+	0.380397i	$0.875787\pi$
$348$		0			0
$349$		−	11.7713i		−	0.630106i	−0.949074	−	0.315053i	$-0.897978\pi$
$349$		−	11.7713i		−	0.630106i	0.949074	−	0.315053i	$-0.102022\pi$
$350$		0			0
$351$		−	4.53949i		−	0.242300i
$352$		0			0
$353$	−19.1201	+	19.1201i	−1.01766	+	1.01766i	−0.0178203	+	0.999841i	$0.505673\pi$
$353$	−19.1201	+	19.1201i	−1.01766	+	1.01766i	−0.999841	+	0.0178203i	$0.994327\pi$
$354$		0			0
$355$	−15.8814	−	3.71679i	−0.842896	−	0.197267i
$356$		0			0
$357$	0.911631	+	0.911631i	0.0482486	+	0.0482486i
$358$		0			0
$359$	−18.0235			−0.951242			−0.475621	−	0.879650i	$-0.657777\pi$
$359$	−18.0235			−0.951242			−0.475621	+	0.879650i	$0.657777\pi$
$360$		0			0
$361$	8.64278			0.454883
$362$		0			0
$363$	−2.46708	−	2.46708i	−0.129488	−	0.129488i
$364$		0			0
$365$	−2.91888	−	4.70256i	−0.152781	−	0.246143i
$366$		0			0
$367$	21.6995	−	21.6995i	1.13270	−	1.13270i	0.142978	−	0.989726i	$-0.454332\pi$
$367$	21.6995	−	21.6995i	1.13270	−	1.13270i	0.989726	−	0.142978i	$-0.0456677\pi$
$368$		0			0
$369$			15.0618i			0.784088i
$370$		0			0
$371$			15.2334i			0.790878i
$372$		0			0
$373$	12.3687	−	12.3687i	0.640425	−	0.640425i	−0.310235	−	0.950660i	$-0.600408\pi$
$373$	12.3687	−	12.3687i	0.640425	−	0.640425i	0.950660	+	0.310235i	$0.100408\pi$
$374$		0			0
$375$	9.61698	−	0.923235i	0.496618	−	0.0476756i
$376$		0			0
$377$	4.46782	+	4.46782i	0.230104	+	0.230104i
$378$		0			0
$379$	−24.8494			−1.27643			−0.638213	−	0.769860i	$-0.720326\pi$
$379$	−24.8494			−1.27643			−0.638213	+	0.769860i	$0.720326\pi$
$380$		0			0
$381$	−17.8032			−0.912086
$382$		0			0
$383$	14.6281	+	14.6281i	0.747458	+	0.747458i	0.974001	−	0.226543i	$-0.0727423\pi$
$383$	14.6281	+	14.6281i	0.747458	+	0.747458i	−0.226543	+	0.974001i	$0.572742\pi$
$384$		0			0
$385$	10.5409	−	6.54276i	0.537216	−	0.333450i
$386$		0			0
$387$	−5.20889	+	5.20889i	−0.264783	+	0.264783i
$388$		0			0
$389$		−	12.2269i		−	0.619931i	−0.950748	−	0.309965i	$-0.899683\pi$
$389$		−	12.2269i		−	0.619931i	0.950748	−	0.309965i	$-0.100317\pi$
$390$		0			0
$391$			2.40332i			0.121541i
$392$		0			0
$393$	−6.38676	+	6.38676i	−0.322169	+	0.322169i
$394$		0			0
$395$	−7.95037	+	33.9709i	−0.400026	+	1.70926i
$396$		0			0
$397$	−3.98379	−	3.98379i	−0.199941	−	0.199941i	0.600034	−	0.799975i	$-0.295154\pi$
$397$	−3.98379	−	3.98379i	−0.199941	−	0.199941i	−0.799975	+	0.600034i	$0.795154\pi$
$398$		0			0
$399$	−9.55318			−0.478257
$400$		0			0
$401$	34.0809			1.70192			0.850958	−	0.525233i	$-0.176022\pi$
$401$	34.0809			1.70192			0.850958	+	0.525233i	$0.176022\pi$
$402$		0			0
$403$	−2.62197	−	2.62197i	−0.130610	−	0.130610i
$404$		0			0
$405$	−1.44569	+	6.17725i	−0.0718369	+	0.306950i
$406$		0			0
$407$	−1.94973	+	1.94973i	−0.0966446	+	0.0966446i
$408$		0			0
$409$		−	3.77425i		−	0.186625i	−0.995637	−	0.0933123i	$-0.970255\pi$
$409$		−	3.77425i		−	0.186625i	0.995637	−	0.0933123i	$-0.0297455\pi$
$410$		0			0
$411$			14.9074i			0.735326i
$412$		0			0
$413$	13.0704	−	13.0704i	0.643151	−	0.643151i
$414$		0			0
$415$	14.2333	−	8.83460i	0.698685	−	0.433674i
$416$		0			0
$417$	5.56806	+	5.56806i	0.272669	+	0.272669i
$418$		0			0
$419$	23.4895			1.14754			0.573768	−	0.819018i	$-0.305481\pi$
$419$	23.4895			1.14754			0.573768	+	0.819018i	$0.305481\pi$
$420$		0			0
$421$	−27.7990			−1.35484			−0.677420	−	0.735596i	$-0.736902\pi$
$421$	−27.7990			−1.35484			−0.677420	+	0.735596i	$0.736902\pi$
$422$		0			0
$423$	5.22023	+	5.22023i	0.253816	+	0.253816i
$424$		0			0
$425$	−1.13484	−	3.36130i	−0.0550480	−	0.163047i
$426$		0			0
$427$	8.08926	−	8.08926i	0.391467	−	0.391467i
$428$		0			0
$429$		−	2.28011i		−	0.110085i
$430$		0			0
$431$			38.0220i			1.83146i	0.401800	+	0.915728i	$0.368385\pi$
$431$			38.0220i			1.83146i	−0.401800	+	0.915728i	$0.631615\pi$
$432$		0			0
$433$	−14.2787	+	14.2787i	−0.686190	+	0.686190i	−0.961388	−	0.275197i	$-0.911257\pi$
$433$	−14.2787	+	14.2787i	−0.686190	+	0.686190i	0.275197	+	0.961388i	$0.411257\pi$
$434$		0			0
$435$	6.43852	+	10.3730i	0.308703	+	0.497347i
$436$		0			0
$437$	−12.5925	−	12.5925i	−0.602380	−	0.602380i
$438$		0			0
$439$	−8.80608			−0.420291			−0.210146	−	0.977670i	$-0.567394\pi$
$439$	−8.80608			−0.420291			−0.210146	+	0.977670i	$0.567394\pi$
$440$		0			0
$441$	5.81027			0.276680
$442$		0			0
$443$	−10.9660	−	10.9660i	−0.521012	−	0.521012i	0.396865	−	0.917877i	$-0.370098\pi$
$443$	−10.9660	−	10.9660i	−0.521012	−	0.521012i	−0.917877	+	0.396865i	$0.870098\pi$
$444$		0			0
$445$	15.3756	+	3.59842i	0.728872	+	0.170581i
$446$		0			0
$447$	−2.66915	+	2.66915i	−0.126247	+	0.126247i
$448$		0			0
$449$			16.5999i			0.783397i	0.920094	+	0.391699i	$0.128112\pi$
$449$			16.5999i			0.783397i	−0.920094	+	0.391699i	$0.871888\pi$
$450$		0			0
$451$			17.6376i			0.830524i
$452$		0			0
$453$	−0.814438	+	0.814438i	−0.0382656	+	0.0382656i
$454$		0			0
$455$	−4.57812	−	1.07144i	−0.214625	−	0.0502298i
$456$		0			0
$457$	−28.7131	−	28.7131i	−1.34314	−	1.34314i	−0.892914	−	0.450227i	$-0.851343\pi$
$457$	−28.7131	−	28.7131i	−1.34314	−	1.34314i	−0.450227	−	0.892914i	$-0.648657\pi$
$458$		0			0
$459$	−3.22095			−0.150341
$460$		0			0
$461$	−9.24538			−0.430600			−0.215300	−	0.976548i	$-0.569073\pi$
$461$	−9.24538			−0.430600			−0.215300	+	0.976548i	$0.569073\pi$
$462$		0			0
$463$	2.81066	+	2.81066i	0.130622	+	0.130622i	0.769395	−	0.638773i	$-0.220558\pi$
$463$	2.81066	+	2.81066i	0.130622	+	0.130622i	−0.638773	+	0.769395i	$0.720558\pi$
$464$		0			0
$465$	−3.77848	−	6.08746i	−0.175223	−	0.282299i
$466$		0			0
$467$	−6.41595	+	6.41595i	−0.296895	+	0.296895i	−0.839796	−	0.542902i	$-0.817326\pi$
$467$	−6.41595	+	6.41595i	−0.296895	+	0.296895i	0.542902	+	0.839796i	$0.317326\pi$
$468$		0			0
$469$		−	0.404424i		−	0.0186746i
$470$		0			0
$471$		−	9.21381i		−	0.424550i
$472$		0			0
$473$	−6.09968	+	6.09968i	−0.280464	+	0.280464i
$474$		0			0
$475$	23.5580	+	11.6657i	1.08092	+	0.535261i
$476$		0			0
$477$	−11.5430	−	11.5430i	−0.528516	−	0.528516i
$478$		0			0
$479$	−12.6990			−0.580232			−0.290116	−	0.956992i	$-0.593694\pi$
$479$	−12.6990			−0.580232			−0.290116	+	0.956992i	$0.593694\pi$
$480$		0			0
$481$	1.04498			0.0476472
$482$		0			0
$483$	4.35188	+	4.35188i	0.198017	+	0.198017i
$484$		0			0
$485$	−2.85515	+	1.77219i	−0.129646	+	0.0804711i
$486$		0			0
$487$	−25.1702	+	25.1702i	−1.14057	+	1.14057i	−0.152224	+	0.988346i	$0.548643\pi$
$487$	−25.1702	+	25.1702i	−1.14057	+	1.14057i	−0.988346	+	0.152224i	$0.951357\pi$
$488$		0			0
$489$		−	0.762680i		−	0.0344896i
$490$		0			0
$491$		−	40.7973i		−	1.84116i	−0.390558	−	0.920578i	$-0.627718\pi$
$491$		−	40.7973i		−	1.84116i	0.390558	−	0.920578i	$-0.372282\pi$
$492$		0			0
$493$	3.17010	−	3.17010i	0.142774	−	0.142774i
$494$		0			0
$495$	−3.02958	+	12.9450i	−0.136170	+	0.581835i
$496$		0			0
$497$	10.8455	+	10.8455i	0.486486	+	0.486486i
$498$		0			0
$499$	−33.4505			−1.49745			−0.748726	−	0.662880i	$-0.769334\pi$
$499$	−33.4505			−1.49745			−0.748726	+	0.662880i	$0.769334\pi$
$500$		0			0
$501$	−19.8555			−0.887077
$502$		0			0
$503$	11.2853	+	11.2853i	0.503187	+	0.503187i	0.912427	−	0.409240i	$-0.134206\pi$
$503$	11.2853	+	11.2853i	0.503187	+	0.503187i	−0.409240	+	0.912427i	$0.634206\pi$
$504$		0			0
$505$	5.84134	−	24.9593i	0.259936	−	1.11067i
$506$		0			0
$507$	−0.611027	+	0.611027i	−0.0271367	+	0.0271367i
$508$		0			0
$509$		−	28.3653i		−	1.25727i	−0.777700	−	0.628636i	$-0.783614\pi$
$509$		−	28.3653i		−	1.25727i	0.777700	−	0.628636i	$-0.216386\pi$
$510$		0			0
$511$			5.20472i			0.230243i
$512$		0			0
$513$	16.8765	−	16.8765i	0.745117	−	0.745117i
$514$		0			0
$515$	−23.2208	+	14.4132i	−1.02323	+	0.635120i
$516$		0			0
$517$	6.11296	+	6.11296i	0.268848	+	0.268848i
$518$		0			0
$519$	−8.21536			−0.360614
$520$		0			0
$521$	18.8559			0.826094			0.413047	−	0.910710i	$-0.364465\pi$
$521$	18.8559			0.826094			0.413047	+	0.910710i	$0.364465\pi$
$522$		0			0
$523$	−5.66369	−	5.66369i	−0.247656	−	0.247656i	0.572352	−	0.820008i	$-0.306031\pi$
$523$	−5.66369	−	5.66369i	−0.247656	−	0.247656i	−0.820008	+	0.572352i	$0.806031\pi$
$524$		0			0
$525$	−8.14150	−	4.03161i	−0.355324	−	0.175954i
$526$		0			0
$527$	−1.86039	+	1.86039i	−0.0810400	+	0.0810400i
$528$		0			0
$529$		−	11.5272i		−	0.501182i
$530$		0			0
$531$			19.8079i			0.859591i
$532$		0			0
$533$	4.72657	−	4.72657i	0.204730	−	0.204730i
$534$		0			0
$535$	−14.9768	−	24.1289i	−0.647504	−	1.04318i
$536$		0			0
$537$	−5.24651	−	5.24651i	−0.226404	−	0.226404i
$538$		0			0
$539$	6.80392			0.293065
$540$		0			0
$541$	−21.2853			−0.915126			−0.457563	−	0.889177i	$-0.651278\pi$
$541$	−21.2853			−0.915126			−0.457563	+	0.889177i	$0.651278\pi$
$542$		0			0
$543$	−14.6870	−	14.6870i	−0.630281	−	0.630281i
$544$		0			0
$545$	−18.0593	−	4.22651i	−0.773577	−	0.181044i
$546$		0			0
$547$	11.0773	−	11.0773i	0.473631	−	0.473631i	−0.429456	−	0.903088i	$-0.641295\pi$
$547$	11.0773	−	11.0773i	0.473631	−	0.473631i	0.903088	+	0.429456i	$0.141295\pi$
$548$		0			0
$549$			12.2591i			0.523207i
$550$		0			0
$551$			33.2202i			1.41523i
$552$		0			0
$553$	23.1989	−	23.1989i	0.986518	−	0.986518i
$554$		0			0
$555$	1.96603	+	0.460120i	0.0834535	+	0.0195310i
$556$		0			0
$557$	6.98027	+	6.98027i	0.295763	+	0.295763i	0.839352	−	0.543588i	$-0.182935\pi$
$557$	6.98027	+	6.98027i	0.295763	+	0.295763i	−0.543588	+	0.839352i	$0.682935\pi$
$558$		0			0
$559$	3.26921			0.138273
$560$		0			0
$561$	−1.61783			−0.0683048
$562$		0			0
$563$	11.2309	+	11.2309i	0.473325	+	0.473325i	0.902989	−	0.429664i	$-0.141368\pi$
$563$	11.2309	+	11.2309i	0.473325	+	0.473325i	−0.429664	+	0.902989i	$0.641368\pi$
$564$		0			0
$565$	19.8432	+	31.9691i	0.834811	+	1.34495i
$566$		0			0
$567$	4.21848	−	4.21848i	0.177159	−	0.177159i
$568$		0			0
$569$		−	19.8120i		−	0.830563i	−0.909693	−	0.415282i	$-0.863683\pi$
$569$		−	19.8120i		−	0.830563i	0.909693	−	0.415282i	$-0.136317\pi$
$570$		0			0
$571$		−	33.6189i		−	1.40691i	−0.710740	−	0.703455i	$-0.751640\pi$
$571$		−	33.6189i		−	1.40691i	0.710740	−	0.703455i	$-0.248360\pi$
$572$		0			0
$573$	3.45974	−	3.45974i	0.144533	−	0.144533i
$574$		0			0
$575$	−5.41744	−	16.0459i	−0.225923	−	0.669162i
$576$		0			0
$577$	5.19662	+	5.19662i	0.216338	+	0.216338i	0.806953	−	0.590615i	$-0.201115\pi$
$577$	5.19662	+	5.19662i	0.216338	+	0.216338i	−0.590615	+	0.806953i	$0.701115\pi$
$578$		0			0
$579$	4.04862			0.168255
$580$		0			0
$581$	−15.7532			−0.653552
$582$		0			0
$583$	−13.5170	−	13.5170i	−0.559816	−	0.559816i
$584$		0			0
$585$	4.28090	−	2.65716i	0.176994	−	0.109860i
$586$		0			0
$587$	−20.6229	+	20.6229i	−0.851200	+	0.851200i	−0.990281	−	0.139081i	$-0.955585\pi$
$587$	−20.6229	+	20.6229i	−0.851200	+	0.851200i	0.139081	+	0.990281i	$0.455585\pi$
$588$		0			0
$589$		−	19.4954i		−	0.803296i
$590$		0			0
$591$		−	13.6488i		−	0.561439i
$592$		0			0
$593$	4.50113	−	4.50113i	0.184839	−	0.184839i	−0.608622	−	0.793461i	$-0.708277\pi$
$593$	4.50113	−	4.50113i	0.184839	−	0.184839i	0.793461	+	0.608622i	$0.208277\pi$
$594$		0			0
$595$	−0.760229	+	3.24836i	−0.0311664	+	0.133170i
$596$		0			0
$597$	−3.56733	−	3.56733i	−0.146001	−	0.146001i
$598$		0			0
$599$	7.07739			0.289174			0.144587	−	0.989492i	$-0.453815\pi$
$599$	7.07739			0.289174			0.144587	+	0.989492i	$0.453815\pi$
$600$		0			0
$601$	3.27920			0.133761			0.0668807	−	0.997761i	$-0.478695\pi$
$601$	3.27920			0.133761			0.0668807	+	0.997761i	$0.478695\pi$
$602$		0			0
$603$	0.306449	+	0.306449i	0.0124796	+	0.0124796i
$604$		0			0
$605$	2.05735	−	8.79079i	0.0836432	−	0.357397i
$606$		0			0
$607$	−33.8574	+	33.8574i	−1.37423	+	1.37423i	−0.520165	+	0.854066i	$0.674130\pi$
$607$	−33.8574	+	33.8574i	−1.37423	+	1.37423i	−0.854066	+	0.520165i	$0.825870\pi$
$608$		0			0
$609$		−	11.4807i		−	0.465221i
$610$		0			0
$611$		−	3.27633i		−	0.132546i
$612$		0			0
$613$	−9.26883	+	9.26883i	−0.374364	+	0.374364i	−0.869064	−	0.494700i	$-0.835278\pi$
$613$	−9.26883	+	9.26883i	−0.374364	+	0.374364i	0.494700	+	0.869064i	$0.335278\pi$
$614$		0			0
$615$	10.9737	−	6.81140i	0.442504	−	0.274662i
$616$		0			0
$617$	−18.8082	−	18.8082i	−0.757190	−	0.757190i	0.218620	−	0.975810i	$-0.429844\pi$
$617$	−18.8082	−	18.8082i	−0.757190	−	0.757190i	−0.975810	+	0.218620i	$0.929844\pi$
$618$		0			0
$619$	−3.24279			−0.130339			−0.0651694	−	0.997874i	$-0.520759\pi$
$619$	−3.24279			−0.130339			−0.0651694	+	0.997874i	$0.520759\pi$
$620$		0			0
$621$	−15.3760			−0.617016
$622$		0			0
$623$	−10.5001	−	10.5001i	−0.420676	−	0.420676i
$624$		0			0
$625$	15.1537	+	19.8838i	0.606148	+	0.795352i
$626$		0			0
$627$	8.47679	−	8.47679i	0.338530	−	0.338530i
$628$		0			0
$629$		−	0.741459i		−	0.0295639i
$630$		0			0
$631$			15.0312i			0.598383i	0.954193	+	0.299192i	$0.0967169\pi$
$631$			15.0312i			0.598383i	−0.954193	+	0.299192i	$0.903283\pi$
$632$		0			0
$633$	−13.0259	+	13.0259i	−0.517734	+	0.517734i
$634$		0			0
$635$	−24.2953	−	39.1418i	−0.964130	−	1.55330i
$636$		0			0
$637$	−1.82333	−	1.82333i	−0.0722428	−	0.0722428i
$638$		0			0
$639$	−16.4361			−0.650204
$640$		0			0
$641$	−5.07951			−0.200628			−0.100314	−	0.994956i	$-0.531985\pi$
$641$	−5.07951			−0.200628			−0.100314	+	0.994956i	$0.531985\pi$
$642$		0			0
$643$	−34.1374	−	34.1374i	−1.34625	−	1.34625i	−0.889700	−	0.456547i	$-0.849086\pi$
$643$	−34.1374	−	34.1374i	−1.34625	−	1.34625i	−0.456547	−	0.889700i	$-0.650914\pi$
$644$		0			0
$645$	6.15069	+	1.43948i	0.242183	+	0.0566793i
$646$		0			0
$647$	−3.74021	+	3.74021i	−0.147043	+	0.147043i	−0.776796	−	0.629753i	$-0.783156\pi$
$647$	−3.74021	+	3.74021i	−0.147043	+	0.147043i	0.629753	+	0.776796i	$0.283156\pi$
$648$		0			0
$649$			23.1954i			0.910498i
$650$		0			0
$651$			6.73751i			0.264064i
$652$		0			0
$653$	−9.89152	+	9.89152i	−0.387085	+	0.387085i	−0.873646	−	0.486561i	$-0.838251\pi$
$653$	−9.89152	+	9.89152i	−0.387085	+	0.387085i	0.486561	+	0.873646i	$0.338251\pi$
$654$		0			0
$655$	−22.7575	−	5.32605i	−0.889211	−	0.208106i
$656$		0			0
$657$	−3.94383	−	3.94383i	−0.153864	−	0.153864i
$658$		0			0
$659$	−11.3306			−0.441378			−0.220689	−	0.975344i	$-0.570831\pi$
$659$	−11.3306			−0.441378			−0.220689	+	0.975344i	$0.570831\pi$
$660$		0			0
$661$	10.8951			0.423771			0.211886	−	0.977294i	$-0.432040\pi$
$661$	10.8951			0.423771			0.211886	+	0.977294i	$0.432040\pi$
$662$		0			0
$663$	0.433549	+	0.433549i	0.0168376	+	0.0168376i
$664$		0			0
$665$	−13.0368	−	21.0034i	−0.505546	−	0.814478i
$666$		0			0
$667$	15.1332	−	15.1332i	0.585960	−	0.585960i
$668$		0			0
$669$		−	21.9790i		−	0.849759i
$670$		0			0
$671$			14.3556i			0.554193i
$672$		0			0
$673$	22.6598	−	22.6598i	0.873471	−	0.873471i	−0.119378	−	0.992849i	$-0.538090\pi$
$673$	22.6598	−	22.6598i	0.873471	−	0.873471i	0.992849	+	0.119378i	$0.0380901\pi$
$674$		0			0
$675$	21.5049	−	7.26049i	0.827723	−	0.279456i
$676$		0			0
$677$	−9.14717	−	9.14717i	−0.351554	−	0.351554i	0.509133	−	0.860688i	$-0.329966\pi$
$677$	−9.14717	−	9.14717i	−0.351554	−	0.351554i	−0.860688	+	0.509133i	$0.829966\pi$
$678$		0			0
$679$	3.16004			0.121271
$680$		0			0
$681$	4.12187			0.157950
$682$		0			0
$683$	29.0547	+	29.0547i	1.11175	+	1.11175i	0.992914	+	0.118835i	$0.0379159\pi$
$683$	29.0547	+	29.0547i	1.11175	+	1.11175i	0.118835	+	0.992914i	$0.462084\pi$
$684$		0			0
$685$	−32.7750	+	20.3435i	−1.25227	+	0.777284i
$686$		0			0
$687$	2.90949	−	2.90949i	0.111004	−	0.111004i
$688$		0			0
$689$			7.24461i			0.275998i
$690$		0			0
$691$			35.2518i			1.34104i	0.741891	+	0.670520i	$0.233929\pi$
$691$			35.2518i			1.34104i	−0.741891	+	0.670520i	$0.766071\pi$
$692$		0			0
$693$	8.84023	−	8.84023i	0.335812	−	0.335812i
$694$		0			0
$695$	−4.64332	+	19.8403i	−0.176131	+	0.752586i
$696$		0			0
$697$	−3.35369	−	3.35369i	−0.127030	−	0.127030i
$698$		0			0
$699$	15.5604			0.588549
$700$		0			0
$701$	27.9422			1.05536			0.527681	−	0.849443i	$-0.323062\pi$
$701$	27.9422			1.05536			0.527681	+	0.849443i	$0.323062\pi$
$702$		0			0
$703$	3.88495	+	3.88495i	0.146524	+	0.146524i
$704$		0			0
$705$	1.44261	−	6.16408i	0.0543318	−	0.232153i
$706$		0			0
$707$	−17.0448	+	17.0448i	−0.641037	+	0.641037i
$708$		0			0
$709$			45.8932i			1.72355i	0.507287	+	0.861777i	$0.330649\pi$
$709$			45.8932i			1.72355i	−0.507287	+	0.861777i	$0.669351\pi$
$710$		0			0
$711$			35.1576i			1.31851i
$712$		0			0
$713$	−8.88101	+	8.88101i	−0.332596	+	0.332596i
$714$		0			0
$715$	5.01300	−	3.11157i	0.187476	−	0.116366i
$716$		0			0
$717$	−4.06888	−	4.06888i	−0.151955	−	0.151955i
$718$		0			0
$719$	24.4463			0.911692			0.455846	−	0.890059i	$-0.349337\pi$
$719$	24.4463			0.911692			0.455846	+	0.890059i	$0.349337\pi$
$720$		0			0
$721$	25.7004			0.957135
$722$		0			0
$723$	−13.4731	−	13.4731i	−0.501071	−	0.501071i
$724$		0			0
$725$	−14.0195	+	28.3112i	−0.520671	+	1.05145i
$726$		0			0
$727$	1.78497	−	1.78497i	0.0662009	−	0.0662009i	−0.673231	−	0.739432i	$-0.735094\pi$
$727$	1.78497	−	1.78497i	0.0662009	−	0.0662009i	0.739432	+	0.673231i	$0.235094\pi$
$728$		0			0
$729$		−	5.37500i		−	0.199074i
$730$		0			0
$731$		−	2.31964i		−	0.0857949i
$732$		0			0
$733$	25.2099	−	25.2099i	0.931149	−	0.931149i	−0.0666290	−	0.997778i	$-0.521224\pi$
$733$	25.2099	−	25.2099i	0.931149	−	0.931149i	0.997778	+	0.0666290i	$0.0212244\pi$
$734$		0			0
$735$	−2.62757	−	4.23324i	−0.0969195	−	0.156145i
$736$		0			0
$737$	0.358856	+	0.358856i	0.0132186	+	0.0132186i
$738$		0			0
$739$	−4.43416			−0.163113			−0.0815566	−	0.996669i	$-0.525989\pi$
$739$	−4.43416			−0.163113			−0.0815566	+	0.996669i	$0.525989\pi$
$740$		0			0
$741$	−4.54325			−0.166900
$742$		0			0
$743$	−1.44367	−	1.44367i	−0.0529631	−	0.0529631i	0.680129	−	0.733092i	$-0.261924\pi$
$743$	−1.44367	−	1.44367i	−0.0529631	−	0.0529631i	−0.733092	+	0.680129i	$0.761924\pi$
$744$		0			0
$745$	−9.51083	−	2.22586i	−0.348450	−	0.0815493i
$746$		0			0
$747$	11.9368	−	11.9368i	0.436746	−	0.436746i
$748$		0			0
$749$			26.7055i			0.975799i
$750$		0			0
$751$		−	14.6970i		−	0.536302i	−0.963377	−	0.268151i	$-0.913587\pi$
$751$		−	14.6970i		−	0.536302i	0.963377	−	0.268151i	$-0.0864127\pi$
$752$		0			0
$753$	−5.07870	+	5.07870i	−0.185078	+	0.185078i
$754$		0			0
$755$	−2.90204	−	0.679177i	−0.105616	−	0.0247178i
$756$		0			0
$757$	28.1421	+	28.1421i	1.02284	+	1.02284i	0.999733	+	0.0231088i	$0.00735640\pi$
$757$	28.1421	+	28.1421i	1.02284	+	1.02284i	0.0231088	+	0.999733i	$0.492644\pi$
$758$		0			0
$759$	−7.72308			−0.280330
$760$		0			0
$761$	12.2583			0.444362			0.222181	−	0.975005i	$-0.428682\pi$
$761$	12.2583			0.444362			0.222181	+	0.975005i	$0.428682\pi$
$762$		0			0
$763$	12.3328	+	12.3328i	0.446478	+	0.446478i
$764$		0			0
$765$	−1.88536	−	3.03748i	−0.0681654	−	0.109820i
$766$		0			0
$767$	6.21594	−	6.21594i	0.224444	−	0.224444i
$768$		0			0
$769$		−	29.6250i		−	1.06830i	−0.845389	−	0.534152i	$-0.820631\pi$
$769$		−	29.6250i		−	1.06830i	0.845389	−	0.534152i	$-0.179369\pi$
$770$		0			0
$771$			7.30563i			0.263106i
$772$		0			0
$773$	−15.2575	+	15.2575i	−0.548775	+	0.548775i	−0.926086	−	0.377311i	$-0.876849\pi$
$773$	−15.2575	+	15.2575i	−0.548775	+	0.548775i	0.377311	+	0.926086i	$0.376849\pi$
$774$		0			0
$775$	8.22742	−	16.6146i	0.295538	−	0.596814i
$776$		0			0
$777$	−1.34262	−	1.34262i	−0.0481661	−	0.0481661i
$778$		0			0
$779$	35.1440			1.25917
$780$		0			0
$781$	−19.2470			−0.688711
$782$		0			0
$783$	20.2816	+	20.2816i	0.724806	+	0.724806i
$784$		0			0
$785$	20.2573	−	12.5737i	0.723015	−	0.448775i
$786$		0			0
$787$	0.233349	−	0.233349i	0.00831801	−	0.00831801i	−0.702936	−	0.711254i	$-0.748128\pi$
$787$	0.233349	−	0.233349i	0.00831801	−	0.00831801i	0.711254	+	0.702936i	$0.248128\pi$
$788$		0			0
$789$			0.306765i			0.0109211i
$790$		0			0
$791$		−	35.3829i		−	1.25807i
$792$		0			0
$793$	3.84705	−	3.84705i	0.136613	−	0.136613i
$794$		0			0
$795$	−3.18990	+	13.6300i	−0.113134	+	0.483407i
$796$		0			0
$797$	8.99819	+	8.99819i	0.318732	+	0.318732i	0.848280	−	0.529548i	$-0.177638\pi$
$797$	8.99819	+	8.99819i	0.318732	+	0.318732i	−0.529548	+	0.848280i	$0.677638\pi$
$798$		0			0
$799$	−2.32469			−0.0822415
$800$		0			0
$801$	15.9127			0.562246
$802$		0			0
$803$	−4.61829	−	4.61829i	−0.162976	−	0.162976i
$804$		0			0
$805$	−3.62913	+	15.5068i	−0.127910	+	0.546543i
$806$		0			0
$807$	−10.8160	+	10.8160i	−0.380742	+	0.380742i
$808$		0			0
$809$			38.6815i			1.35997i	0.733227	+	0.679984i	$0.238013\pi$
$809$			38.6815i			1.35997i	−0.733227	+	0.679984i	$0.761987\pi$
$810$		0			0
$811$			32.8989i			1.15524i	0.816307	+	0.577619i	$0.196018\pi$
$811$			32.8989i			1.15524i	−0.816307	+	0.577619i	$0.803982\pi$
$812$		0			0
$813$	−15.8421	+	15.8421i	−0.555607	+	0.555607i
$814$		0			0
$815$	1.67681	−	1.04080i	0.0587362	−	0.0364575i
$816$		0			0
$817$	12.1540	+	12.1540i	0.425214	+	0.425214i
$818$		0			0
$819$	−4.73804			−0.165560
$820$		0			0
$821$	−31.9555			−1.11525			−0.557627	−	0.830092i	$-0.688288\pi$
$821$	−31.9555			−1.11525			−0.557627	+	0.830092i	$0.688288\pi$
$822$		0			0
$823$	7.14798	+	7.14798i	0.249163	+	0.249163i	0.820627	−	0.571464i	$-0.193624\pi$
$823$	7.14798	+	7.14798i	0.249163	+	0.249163i	−0.571464	+	0.820627i	$0.693624\pi$
$824$		0			0
$825$	10.8015	−	3.64682i	0.376061	−	0.126966i
$826$		0			0
$827$	−1.33722	+	1.33722i	−0.0464996	+	0.0464996i	−0.729974	−	0.683475i	$-0.760468\pi$
$827$	−1.33722	+	1.33722i	−0.0464996	+	0.0464996i	0.683475	+	0.729974i	$0.260468\pi$
$828$		0			0
$829$			39.1937i			1.36125i	0.732631	+	0.680626i	$0.238292\pi$
$829$			39.1937i			1.36125i	−0.732631	+	0.680626i	$0.761708\pi$
$830$		0			0
$831$		−	20.5476i		−	0.712788i
$832$		0			0
$833$	−1.29372	+	1.29372i	−0.0448249	+	0.0448249i
$834$		0			0
$835$	−27.0959	−	43.6538i	−0.937694	−	1.51070i
$836$		0			0
$837$	−11.9024	−	11.9024i	−0.411407	−	0.411407i
$838$		0			0
$839$	19.1042			0.659551			0.329776	−	0.944059i	$-0.393027\pi$
$839$	19.1042			0.659551			0.329776	+	0.944059i	$0.393027\pi$
$840$		0			0
$841$	−10.9229			−0.376650
$842$		0			0
$843$	−2.25806	−	2.25806i	−0.0777718	−	0.0777718i
$844$		0			0
$845$	−2.17724	−	0.509549i	−0.0748992	−	0.0175290i
$846$		0			0
$847$	−6.00328	+	6.00328i	−0.206275	+	0.206275i
$848$		0			0
$849$			17.2697i			0.592694i
$850$		0			0
$851$		−	3.53953i		−	0.121333i
$852$		0			0
$853$	−10.2018	+	10.2018i	−0.349304	+	0.349304i	−0.859850	−	0.510546i	$-0.829443\pi$
$853$	−10.2018	+	10.2018i	−0.349304	+	0.349304i	0.510546	+	0.859850i	$0.329443\pi$
$854$		0			0
$855$	25.7937	+	6.03662i	0.882126	+	0.206448i
$856$		0			0
$857$	−26.0775	−	26.0775i	−0.890792	−	0.890792i	0.103806	−	0.994598i	$-0.466898\pi$
$857$	−26.0775	−	26.0775i	−0.890792	−	0.890792i	−0.994598	+	0.103806i	$0.966898\pi$
$858$		0			0
$859$	26.4998			0.904162			0.452081	−	0.891977i	$-0.350682\pi$
$859$	26.4998			0.904162			0.452081	+	0.891977i	$0.350682\pi$
$860$		0			0
$861$	−12.1456			−0.413920
$862$		0			0
$863$	20.3050	+	20.3050i	0.691190	+	0.691190i	0.962494	−	0.271304i	$-0.0874548\pi$
$863$	20.3050	+	20.3050i	0.691190	+	0.691190i	−0.271304	+	0.962494i	$0.587455\pi$
$864$		0			0
$865$	−11.2112	−	18.0621i	−0.381191	−	0.614131i
$866$		0			0
$867$	−10.0798	+	10.0798i	−0.342329	+	0.342329i
$868$		0			0
$869$			41.1700i			1.39660i
$870$		0			0
$871$		−	0.192334i		−	0.00651698i
$872$		0			0
$873$	−2.39449	+	2.39449i	−0.0810412	+	0.0810412i
$874$		0			0
$875$	−2.24656	−	23.4015i	−0.0759476	−	0.791116i
$876$		0			0
$877$	−6.52229	−	6.52229i	−0.220242	−	0.220242i	0.588358	−	0.808600i	$-0.299774\pi$
$877$	−6.52229	−	6.52229i	−0.220242	−	0.220242i	−0.808600	+	0.588358i	$0.799774\pi$
$878$		0			0
$879$	19.0673			0.643123
$880$		0			0
$881$	40.4179			1.36171			0.680856	−	0.732417i	$-0.261608\pi$
$881$	40.4179			1.36171			0.680856	+	0.732417i	$0.261608\pi$
$882$		0			0
$883$	−9.90318	−	9.90318i	−0.333268	−	0.333268i	0.520558	−	0.853826i	$-0.325724\pi$
$883$	−9.90318	−	9.90318i	−0.333268	−	0.333268i	−0.853826	+	0.520558i	$0.825724\pi$
$884$		0			0
$885$	14.4316	−	8.95771i	0.485114	−	0.301110i
$886$		0			0
$887$	29.7509	−	29.7509i	0.998939	−	0.998939i	−0.00106048	−	0.999999i	$-0.500338\pi$
$887$	29.7509	−	29.7509i	0.998939	−	0.998939i	0.999999	+	0.00106048i	$0.000337560\pi$
$888$		0			0
$889$			43.3216i			1.45296i
$890$		0			0
$891$			7.48633i			0.250802i
$892$		0			0
$893$	12.1804	−	12.1804i	0.407603	−	0.407603i
$894$		0			0
$895$	4.37518	−	18.6946i	0.146246	−	0.624891i
$896$		0			0
$897$	2.06964	+	2.06964i	0.0691034	+	0.0691034i
$898$		0			0
$899$	23.4290			0.781400
$900$		0			0
$901$	5.14035			0.171250
$902$		0			0
$903$	−4.20034	−	4.20034i	−0.139779	−	0.139779i
$904$		0			0
$905$	12.2478	−	52.3334i	0.407132	−	1.73962i
$906$		0			0
$907$	−32.7082	+	32.7082i	−1.08606	+	1.08606i	−0.0901288	+	0.995930i	$0.528728\pi$
$907$	−32.7082	+	32.7082i	−1.08606	+	1.08606i	−0.995930	+	0.0901288i	$0.971272\pi$
$908$		0			0
$909$		−	25.8312i		−	0.856766i
$910$		0			0
$911$		−	41.0735i		−	1.36083i	−0.732828	−	0.680414i	$-0.761800\pi$
$911$		−	41.0735i		−	1.36083i	0.732828	−	0.680414i	$-0.238200\pi$
$912$		0			0
$913$	13.9782	−	13.9782i	0.462612	−	0.462612i
$914$		0			0
$915$	8.93174	−	5.54393i	0.295274	−	0.183277i
$916$		0			0
$917$	15.5413	+	15.5413i	0.513217	+	0.513217i
$918$		0			0
$919$	42.3842			1.39813			0.699063	−	0.715060i	$-0.253601\pi$
$919$	42.3842			1.39813			0.699063	+	0.715060i	$0.253601\pi$
$920$		0			0
$921$	−20.1343			−0.663449
$922$		0			0
$923$	5.15784	+	5.15784i	0.169772	+	0.169772i
$924$		0			0
$925$	1.67136	+	4.95039i	0.0549538	+	0.162768i
$926$		0			0
$927$	−19.4743	+	19.4743i	−0.639620	+	0.639620i
$928$		0			0
$929$			43.5064i			1.42740i	0.700453	+	0.713699i	$0.252981\pi$
$929$			43.5064i			1.42740i	−0.700453	+	0.713699i	$0.747019\pi$
$930$		0			0
$931$		−	13.5572i		−	0.444319i
$932$		0			0
$933$	−6.82142	+	6.82142i	−0.223323	+	0.223323i
$934$		0			0
$935$	−2.20779	−	3.55693i	−0.0722023	−	0.116324i
$936$		0			0
$937$	−33.1473	−	33.1473i	−1.08288	−	1.08288i	−0.996240	−	0.0866351i	$-0.972389\pi$
$937$	−33.1473	−	33.1473i	−1.08288	−	1.08288i	−0.0866351	−	0.996240i	$-0.527611\pi$
$938$		0			0
$939$	7.42045			0.242157
$940$		0			0
$941$	−9.94504			−0.324199			−0.162099	−	0.986774i	$-0.551827\pi$
$941$	−9.94504			−0.324199			−0.162099	+	0.986774i	$0.551827\pi$
$942$		0			0
$943$	−16.0096	−	16.0096i	−0.521345	−	0.521345i
$944$		0			0
$945$	−20.7823	−	4.86378i	−0.676049	−	0.158219i
$946$		0			0
$947$	41.5122	−	41.5122i	1.34897	−	1.34897i	0.462179	−	0.886787i	$-0.347068\pi$
$947$	41.5122	−	41.5122i	1.34897	−	1.34897i	0.886787	−	0.462179i	$-0.152932\pi$
$948$		0			0
$949$			2.47523i			0.0803495i
$950$		0			0
$951$			20.9217i			0.678434i
$952$		0			0
$953$	28.3113	−	28.3113i	0.917092	−	0.917092i	−0.0797252	−	0.996817i	$-0.525404\pi$
$953$	28.3113	−	28.3113i	0.917092	−	0.917092i	0.996817	+	0.0797252i	$0.0254043\pi$
$954$		0			0
$955$	12.3279	+	2.88515i	0.398921	+	0.0933613i
$956$		0			0
$957$	10.1871	+	10.1871i	0.329303	+	0.329303i
$958$		0			0
$959$	36.2749			1.17138
$960$		0			0
$961$	17.2506			0.556470
$962$		0			0
$963$	−20.2359	−	20.2359i	−0.652092	−	0.652092i
$964$		0			0
$965$	5.52499	+	8.90122i	0.177856	+	0.286540i
$966$		0			0
$967$	2.40005	−	2.40005i	0.0771803	−	0.0771803i	−0.667463	−	0.744643i	$-0.732620\pi$
$967$	2.40005	−	2.40005i	0.0771803	−	0.0771803i	0.744643	+	0.667463i	$0.232620\pi$
$968$		0			0
$969$			3.22362i			0.103558i
$970$		0			0
$971$		−	34.6338i		−	1.11145i	−0.831366	−	0.555726i	$-0.812440\pi$
$971$		−	34.6338i		−	1.11145i	0.831366	−	0.555726i	$-0.187560\pi$
$972$		0			0
$973$	13.5491	−	13.5491i	0.434363	−	0.434363i
$974$		0			0
$975$	−3.87189	−	1.91733i	−0.124000	−	0.0614037i
$976$		0			0
$977$	39.3531	+	39.3531i	1.25902	+	1.25902i	0.951563	+	0.307453i	$0.0994765\pi$
$977$	39.3531	+	39.3531i	1.25902	+	1.25902i	0.307453	+	0.951563i	$0.400523\pi$
$978$		0			0
$979$	18.6340			0.595544
$980$		0			0
$981$	−18.6902			−0.596732
$982$		0			0
$983$	22.0871	+	22.0871i	0.704471	+	0.704471i	0.965367	−	0.260896i	$-0.0840181\pi$
$983$	22.0871	+	22.0871i	0.704471	+	0.704471i	−0.260896	+	0.965367i	$0.584018\pi$
$984$		0			0
$985$	30.0081	−	18.6260i	0.956137	−	0.593474i
$986$		0			0
$987$	−4.20949	+	4.20949i	−0.133989	+	0.133989i
$988$		0			0
$989$		−	11.0733i		−	0.352111i
$990$		0			0
$991$			13.4417i			0.426990i	0.976944	+	0.213495i	$0.0684847\pi$
$991$			13.4417i			0.426990i	−0.976944	+	0.213495i	$0.931515\pi$
$992$		0			0
$993$	−13.8027	+	13.8027i	−0.438015	+	0.438015i
$994$		0			0
$995$	2.97487	−	12.7113i	0.0943098	−	0.402974i
$996$		0			0
$997$	−15.5057	−	15.5057i	−0.491071	−	0.491071i	0.417573	−	0.908643i	$-0.362881\pi$
$997$	−15.5057	−	15.5057i	−0.491071	−	0.491071i	−0.908643	+	0.417573i	$0.862881\pi$
$998$		0			0
$999$	4.74370			0.150084

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1040.2.bp.b.287.9	✓	48
4.3	odd	2	inner	1040.2.bp.b.287.16	yes	48
5.3	odd	4	inner	1040.2.bp.b.703.16	yes	48
20.3	even	4	inner	1040.2.bp.b.703.9	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1040.2.bp.b.287.9	✓	48	1.1	even	1	trivial
1040.2.bp.b.287.16	yes	48	4.3	odd	2	inner
1040.2.bp.b.703.9	yes	48	20.3	even	4	inner
1040.2.bp.b.703.16	yes	48	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1040.bp (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.611027 - 0.611027i) q^{3} +(0.509549 - 2.17724i) q^{5} +(-1.48685 + 1.48685i) q^{7} -2.25329i q^{9} +O(q^{10})\)	\(q+(-0.611027 - 0.611027i) q^{3} +(0.509549 - 2.17724i) q^{5} +(-1.48685 + 1.48685i) q^{7} -2.25329i q^{9} -2.63864i q^{11} +(-0.707107 + 0.707107i) q^{13} +(-1.64170 + 1.01900i) q^{15} +(0.501721 + 0.501721i) q^{17} -5.25764 q^{19} +1.81701 q^{21} +(2.39508 + 2.39508i) q^{23} +(-4.48072 - 2.21882i) q^{25} +(-3.20990 + 3.20990i) q^{27} -6.31845i q^{29} +3.70802i q^{31} +(-1.61228 + 1.61228i) q^{33} +(2.47960 + 3.99484i) q^{35} +(-0.738916 - 0.738916i) q^{37} +0.864123 q^{39} -6.68438 q^{41} +(-2.31168 - 2.31168i) q^{43} +(-4.90595 - 1.14816i) q^{45} +(-2.31671 + 2.31671i) q^{47} +2.57857i q^{49} -0.613131i q^{51} +(5.12271 - 5.12271i) q^{53} +(-5.74494 - 1.34451i) q^{55} +(3.21256 + 3.21256i) q^{57} -8.79066 q^{59} -5.44054 q^{61} +(3.35030 + 3.35030i) q^{63} +(1.17923 + 1.89984i) q^{65} +(-0.136001 + 0.136001i) q^{67} -2.92692i q^{69} -7.29428i q^{71} +(1.75025 - 1.75025i) q^{73} +(1.38208 + 4.09360i) q^{75} +(3.92325 + 3.92325i) q^{77} -15.6028 q^{79} -2.83720 q^{81} +(5.29752 + 5.29752i) q^{83} +(1.34802 - 0.836714i) q^{85} +(-3.86075 + 3.86075i) q^{87} +7.06196i q^{89} -2.10272i q^{91} +(2.26570 - 2.26570i) q^{93} +(-2.67903 + 11.4471i) q^{95} +(-1.06266 - 1.06266i) q^{97} -5.94562 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 8 q^{5}+O(q^{10}) \) 48 * q + 8 * q^5	\( 48 q + 8 q^{5} - 16 q^{17} + 32 q^{21} + 16 q^{25} - 24 q^{33} + 24 q^{37} - 16 q^{41} - 48 q^{45} + 40 q^{53} - 8 q^{57} - 16 q^{61} + 40 q^{73} - 72 q^{77} - 160 q^{81} - 64 q^{85} - 8 q^{93} + 16 q^{97}+O(q^{100}) \) 48 * q + 8 * q^5 - 16 * q^17 + 32 * q^21 + 16 * q^25 - 24 * q^33 + 24 * q^37 - 16 * q^41 - 48 * q^45 + 40 * q^53 - 8 * q^57 - 16 * q^61 + 40 * q^73 - 72 * q^77 - 160 * q^81 - 64 * q^85 - 8 * q^93 + 16 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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