LMFDB - Embedded newform 1380.2.t.a.1057.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1380,2,Mod(1057,1380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1380, 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("1380.1057");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1380.t (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:	$11.0193554789$
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			1057.15
Character	$\chi$	$=$	1380.1057
Dual form			1380.2.t.a.1333.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{3} +(-2.23126 + 0.146576i) q^{5} +(2.93317 - 2.93317i) q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{3} +(-2.23126 + 0.146576i) q^{5} +(2.93317 - 2.93317i) q^{7} -1.00000i q^{9} +6.31685i q^{11} +(0.106466 - 0.106466i) q^{13} +(-1.47409 + 1.68138i) q^{15} +(-2.74862 + 2.74862i) q^{17} +7.24616 q^{19} -4.14813i q^{21} +(4.53063 + 1.57269i) q^{23} +(4.95703 - 0.654098i) q^{25} +(-0.707107 - 0.707107i) q^{27} -9.94170i q^{29} +6.76853 q^{31} +(4.46668 + 4.46668i) q^{33} +(-6.11473 + 6.97460i) q^{35} +(-1.65576 + 1.65576i) q^{37} -0.150565i q^{39} +8.29087 q^{41} +(-5.22159 - 5.22159i) q^{43} +(0.146576 + 2.23126i) q^{45} +(-3.00474 - 3.00474i) q^{47} -10.2070i q^{49} +3.88714i q^{51} +(-8.34794 - 8.34794i) q^{53} +(-0.925898 - 14.0945i) q^{55} +(5.12381 - 5.12381i) q^{57} +1.05589i q^{59} -1.36075i q^{61} +(-2.93317 - 2.93317i) q^{63} +(-0.221947 + 0.253158i) q^{65} +(-4.30746 + 4.30746i) q^{67} +(4.31570 - 2.09158i) q^{69} +10.7517 q^{71} +(-5.69127 + 5.69127i) q^{73} +(3.04263 - 3.96767i) q^{75} +(18.5284 + 18.5284i) q^{77} +5.92020 q^{79} -1.00000 q^{81} +(4.73628 + 4.73628i) q^{83} +(5.73000 - 6.53577i) q^{85} +(-7.02985 - 7.02985i) q^{87} +15.3203 q^{89} -0.624564i q^{91} +(4.78607 - 4.78607i) q^{93} +(-16.1681 + 1.06211i) q^{95} +(3.23025 - 3.23025i) q^{97} +6.31685 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 8 q^{13} - 16 q^{23} - 8 q^{25} + 8 q^{31} + 8 q^{35} - 24 q^{41} + 8 q^{47} - 32 q^{55} - 24 q^{71} + 8 q^{73} + 32 q^{75} + 40 q^{77} - 48 q^{81} + 24 q^{85} - 40 q^{87}+O(q^{100}) $ 48 * q - 8 * q^13 - 16 * q^23 - 8 * q^25 + 8 * q^31 + 8 * q^35 - 24 * q^41 + 8 * q^47 - 32 * q^55 - 24 * q^71 + 8 * q^73 + 32 * q^75 + 40 * q^77 - 48 * q^81 + 24 * q^85 - 40 * q^87

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$691$	$1201$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$	$-1$

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
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$		0			0
$5$	−2.23126	+	0.146576i	−0.997849	+	0.0655508i
$5$	−2.23126	+	0.146576i	−0.997849	+	0.0655508i
$6$		0			0
$7$	2.93317	−	2.93317i	1.10863	−	1.10863i	0.115304	−	0.993330i	$-0.463216\pi$
$7$	2.93317	−	2.93317i	1.10863	−	1.10863i	0.993330	−	0.115304i	$-0.0367843\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$			6.31685i			1.90460i	0.305162	+	0.952300i	$0.401289\pi$
$11$			6.31685i			1.90460i	−0.305162	+	0.952300i	$0.598711\pi$
$12$		0			0
$13$	0.106466	−	0.106466i	0.0295283	−	0.0295283i	−0.692189	−	0.721717i	$-0.743353\pi$
$13$	0.106466	−	0.106466i	0.0295283	−	0.0295283i	0.721717	+	0.692189i	$0.243353\pi$
$14$		0			0
$15$	−1.47409	+	1.68138i	−0.380609	+	0.434131i
$16$		0			0
$17$	−2.74862	+	2.74862i	−0.666639	+	0.666639i	−0.956936	−	0.290298i	$-0.906246\pi$
$17$	−2.74862	+	2.74862i	−0.666639	+	0.666639i	0.290298	+	0.956936i	$0.406246\pi$
$18$		0			0
$19$	7.24616			1.66238			0.831191	−	0.555986i	$-0.187659\pi$
$19$	7.24616			1.66238			0.831191	+	0.555986i	$0.187659\pi$
$20$		0			0
$21$		−	4.14813i		−	0.905196i
$22$		0			0
$23$	4.53063	+	1.57269i	0.944702	+	0.327929i
$23$	4.53063	+	1.57269i	0.944702	+	0.327929i
$24$		0			0
$25$	4.95703	−	0.654098i	0.991406	−	0.130820i
$26$		0			0
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$		−	9.94170i		−	1.84613i	−0.384647	−	0.923064i	$-0.625677\pi$
$29$		−	9.94170i		−	1.84613i	0.384647	−	0.923064i	$-0.374323\pi$
$30$		0			0
$31$	6.76853			1.21566			0.607832	−	0.794066i	$-0.292040\pi$
$31$	6.76853			1.21566			0.607832	+	0.794066i	$0.292040\pi$
$32$		0			0
$33$	4.46668	+	4.46668i	0.777550	+	0.777550i
$34$		0			0
$35$	−6.11473	+	6.97460i	−1.03358	+	1.17892i
$36$		0			0
$37$	−1.65576	+	1.65576i	−0.272205	+	0.272205i	−0.829987	−	0.557782i	$-0.811652\pi$
$37$	−1.65576	+	1.65576i	−0.272205	+	0.272205i	0.557782	+	0.829987i	$0.311652\pi$
$38$		0			0
$39$		−	0.150565i		−	0.0241097i
$40$		0			0
$41$	8.29087			1.29482			0.647409	−	0.762143i	$-0.275853\pi$
$41$	8.29087			1.29482			0.647409	+	0.762143i	$0.275853\pi$
$42$		0			0
$43$	−5.22159	−	5.22159i	−0.796285	−	0.796285i	0.186223	−	0.982508i	$-0.440375\pi$
$43$	−5.22159	−	5.22159i	−0.796285	−	0.796285i	−0.982508	+	0.186223i	$0.940375\pi$
$44$		0			0
$45$	0.146576	+	2.23126i	0.0218503	+	0.332616i
$46$		0			0
$47$	−3.00474	−	3.00474i	−0.438286	−	0.438286i	0.453149	−	0.891435i	$-0.350301\pi$
$47$	−3.00474	−	3.00474i	−0.438286	−	0.438286i	−0.891435	+	0.453149i	$0.850301\pi$
$48$		0			0
$49$		−	10.2070i		−	1.45814i
$50$		0			0
$51$			3.88714i			0.544308i
$52$		0			0
$53$	−8.34794	−	8.34794i	−1.14668	−	1.14668i	−0.987202	−	0.159475i	$-0.949020\pi$
$53$	−8.34794	−	8.34794i	−1.14668	−	1.14668i	−0.159475	−	0.987202i	$-0.550980\pi$
$54$		0			0
$55$	−0.925898	−	14.0945i	−0.124848	−	1.90050i
$56$		0			0
$57$	5.12381	−	5.12381i	0.678665	−	0.678665i
$58$		0			0
$59$			1.05589i			0.137465i	0.997635	+	0.0687324i	$0.0218955\pi$
$59$			1.05589i			0.137465i	−0.997635	+	0.0687324i	$0.978105\pi$
$60$		0			0
$61$		−	1.36075i		−	0.174226i	−0.996198	−	0.0871128i	$-0.972236\pi$
$61$		−	1.36075i		−	0.174226i	0.996198	−	0.0871128i	$-0.0277640\pi$
$62$		0			0
$63$	−2.93317	−	2.93317i	−0.369545	−	0.369545i
$64$		0			0
$65$	−0.221947	+	0.253158i	−0.0275291	+	0.0314003i
$66$		0			0
$67$	−4.30746	+	4.30746i	−0.526240	+	0.526240i	−0.919449	−	0.393209i	$-0.871365\pi$
$67$	−4.30746	+	4.30746i	−0.526240	+	0.526240i	0.393209	+	0.919449i	$0.371365\pi$
$68$		0			0
$69$	4.31570	−	2.09158i	0.519550	−	0.251796i
$70$		0			0
$71$	10.7517			1.27599			0.637994	−	0.770041i	$-0.279764\pi$
$71$	10.7517			1.27599			0.637994	+	0.770041i	$0.279764\pi$
$72$		0			0
$73$	−5.69127	+	5.69127i	−0.666112	+	0.666112i	−0.956814	−	0.290701i	$-0.906111\pi$
$73$	−5.69127	+	5.69127i	−0.666112	+	0.666112i	0.290701	+	0.956814i	$0.406111\pi$
$74$		0			0
$75$	3.04263	−	3.96767i	0.351333	−	0.458147i
$76$		0			0
$77$	18.5284	+	18.5284i	2.11151	+	2.11151i
$78$		0			0
$79$	5.92020			0.666075			0.333038	−	0.942914i	$-0.391926\pi$
$79$	5.92020			0.666075			0.333038	+	0.942914i	$0.391926\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	4.73628	+	4.73628i	0.519874	+	0.519874i	0.917533	−	0.397659i	$-0.130177\pi$
$83$	4.73628	+	4.73628i	0.519874	+	0.519874i	−0.397659	+	0.917533i	$0.630177\pi$
$84$		0			0
$85$	5.73000	−	6.53577i	0.621506	−	0.708903i
$86$		0			0
$87$	−7.02985	−	7.02985i	−0.753679	−	0.753679i
$88$		0			0
$89$	15.3203			1.62395			0.811973	−	0.583695i	$-0.198394\pi$
$89$	15.3203			1.62395			0.811973	+	0.583695i	$0.198394\pi$
$90$		0			0
$91$		−	0.624564i		−	0.0654721i
$92$		0			0
$93$	4.78607	−	4.78607i	0.496292	−	0.496292i
$94$		0			0
$95$	−16.1681	+	1.06211i	−1.65881	+	0.108970i
$96$		0			0
$97$	3.23025	−	3.23025i	0.327982	−	0.327982i	−0.523836	−	0.851819i	$-0.675500\pi$
$97$	3.23025	−	3.23025i	0.327982	−	0.327982i	0.851819	+	0.523836i	$0.175500\pi$
$98$		0			0
$99$	6.31685			0.634867
$100$		0			0
$101$	−4.13229			−0.411178			−0.205589	−	0.978638i	$-0.565911\pi$
$101$	−4.13229			−0.411178			−0.205589	+	0.978638i	$0.565911\pi$
$102$		0			0
$103$	−0.0148961	−	0.0148961i	−0.00146776	−	0.00146776i	0.706373	−	0.707840i	$-0.250330\pi$
$103$	−0.0148961	−	0.0148961i	−0.00146776	−	0.00146776i	−0.707840	+	0.706373i	$0.750330\pi$
$104$		0			0
$105$	0.608016	+	9.25555i	0.0593363	+	0.903249i
$106$		0			0
$107$	8.78001	−	8.78001i	0.848795	−	0.848795i	−0.141187	−	0.989983i	$-0.545092\pi$
$107$	8.78001	−	8.78001i	0.848795	−	0.848795i	0.989983	+	0.141187i	$0.0450920\pi$
$108$		0			0
$109$	8.07610			0.773550			0.386775	−	0.922174i	$-0.373589\pi$
$109$	8.07610			0.773550			0.386775	+	0.922174i	$0.373589\pi$
$110$		0			0
$111$			2.34160i			0.222254i
$112$		0			0
$113$	3.67779	+	3.67779i	0.345978	+	0.345978i	0.858609	−	0.512631i	$-0.171329\pi$
$113$	3.67779	+	3.67779i	0.345978	+	0.345978i	−0.512631	+	0.858609i	$0.671329\pi$
$114$		0			0
$115$	−10.3395	−	2.84501i	−0.964166	−	0.265298i
$116$		0			0
$117$	−0.106466	−	0.106466i	−0.00984275	−	0.00984275i
$118$		0			0
$119$			16.1244i			1.47812i
$120$		0			0
$121$	−28.9025			−2.62750
$122$		0			0
$123$	5.86253	−	5.86253i	0.528607	−	0.528607i
$124$		0			0
$125$	−10.9645	+	2.18604i	−0.980699	+	0.195526i
$126$		0			0
$127$	10.8751	+	10.8751i	0.965008	+	0.965008i	0.999408	−	0.0343998i	$-0.0109520\pi$
$127$	10.8751	+	10.8751i	0.965008	+	0.965008i	−0.0343998	+	0.999408i	$0.510952\pi$
$128$		0			0
$129$	−7.38444			−0.650164
$130$		0			0
$131$	−6.40858			−0.559920			−0.279960	−	0.960012i	$-0.590321\pi$
$131$	−6.40858			−0.559920			−0.279960	+	0.960012i	$0.590321\pi$
$132$		0			0
$133$	21.2542	−	21.2542i	1.84298	−	1.84298i
$134$		0			0
$135$	1.68138	+	1.47409i	0.144710	+	0.126870i
$136$		0			0
$137$	0.578043	−	0.578043i	0.0493855	−	0.0493855i	−0.681983	−	0.731368i	$-0.738882\pi$
$137$	0.578043	−	0.578043i	0.0493855	−	0.0493855i	0.731368	+	0.681983i	$0.238882\pi$
$138$		0			0
$139$			5.06060i			0.429235i	0.976698	+	0.214617i	$0.0688504\pi$
$139$			5.06060i			0.429235i	−0.976698	+	0.214617i	$0.931150\pi$
$140$		0			0
$141$	−4.24934			−0.357859
$142$		0			0
$143$	0.672527	+	0.672527i	0.0562395	+	0.0562395i
$144$		0			0
$145$	1.45721	+	22.1825i	0.121015	+	1.84216i
$146$		0			0
$147$	−7.21743	−	7.21743i	−0.595284	−	0.595284i
$148$		0			0
$149$	−12.7441			−1.04403			−0.522017	−	0.852935i	$-0.674820\pi$
$149$	−12.7441			−1.04403			−0.522017	+	0.852935i	$0.674820\pi$
$150$		0			0
$151$	−3.76352			−0.306271			−0.153135	−	0.988205i	$-0.548937\pi$
$151$	−3.76352			−0.306271			−0.153135	+	0.988205i	$0.548937\pi$
$152$		0			0
$153$	2.74862	+	2.74862i	0.222213	+	0.222213i
$154$		0			0
$155$	−15.1023	+	0.992103i	−1.21305	+	0.0796877i
$156$		0			0
$157$	−15.2000	+	15.2000i	−1.21310	+	1.21310i	−0.243092	+	0.970003i	$0.578162\pi$
$157$	−15.2000	+	15.2000i	−1.21310	+	1.21310i	−0.970003	+	0.243092i	$0.921838\pi$
$158$		0			0
$159$	−11.8058			−0.936258
$160$		0			0
$161$	17.9021	−	8.67614i	1.41088	−	0.683776i
$162$		0			0
$163$	1.10629	−	1.10629i	0.0866513	−	0.0866513i	−0.662453	−	0.749104i	$-0.730484\pi$
$163$	1.10629	−	1.10629i	0.0866513	−	0.0866513i	0.749104	+	0.662453i	$0.230484\pi$
$164$		0			0
$165$	−10.6210	−	9.31162i	−0.826847	−	0.724909i
$166$		0			0
$167$	−6.17558	−	6.17558i	−0.477881	−	0.477881i	0.426573	−	0.904453i	$-0.359721\pi$
$167$	−6.17558	−	6.17558i	−0.477881	−	0.477881i	−0.904453	+	0.426573i	$0.859721\pi$
$168$		0			0
$169$			12.9773i			0.998256i
$170$		0			0
$171$		−	7.24616i		−	0.554128i
$172$		0			0
$173$	1.66960	−	1.66960i	0.126937	−	0.126937i	−0.640784	−	0.767721i	$-0.721391\pi$
$173$	1.66960	−	1.66960i	0.126937	−	0.126937i	0.767721	+	0.640784i	$0.221391\pi$
$174$		0			0
$175$	12.6212	−	16.4584i	0.954076	−	1.24414i
$176$		0			0
$177$	0.746625	+	0.746625i	0.0561197	+	0.0561197i
$178$		0			0
$179$		−	0.183978i		−	0.0137512i	−0.999976	−	0.00687558i	$-0.997811\pi$
$179$		−	0.183978i		−	0.0137512i	0.999976	−	0.00687558i	$-0.00218858\pi$
$180$		0			0
$181$			6.17646i			0.459092i	0.973298	+	0.229546i	$0.0737242\pi$
$181$			6.17646i			0.459092i	−0.973298	+	0.229546i	$0.926276\pi$
$182$		0			0
$183$	−0.962192	−	0.962192i	−0.0711273	−	0.0711273i
$184$		0			0
$185$	3.45173	−	3.93712i	0.253776	−	0.289463i
$186$		0			0
$187$	−17.3626	−	17.3626i	−1.26968	−	1.26968i
$188$		0			0
$189$	−4.14813			−0.301732
$190$		0			0
$191$		−	3.64744i		−	0.263919i	−0.991255	−	0.131960i	$-0.957873\pi$
$191$		−	3.64744i		−	0.263919i	0.991255	−	0.131960i	$-0.0421269\pi$
$192$		0			0
$193$	−0.0597192	+	0.0597192i	−0.00429868	+	0.00429868i	−0.709253	−	0.704954i	$-0.750968\pi$
$193$	−0.0597192	+	0.0597192i	−0.00429868	+	0.00429868i	0.704954	+	0.709253i	$0.250968\pi$
$194$		0			0
$195$	0.0220692	+	0.335950i	0.00158041	+	0.0240579i
$196$		0			0
$197$	7.46537	+	7.46537i	0.531886	+	0.531886i	0.921133	−	0.389248i	$-0.127265\pi$
$197$	7.46537	+	7.46537i	0.531886	+	0.531886i	−0.389248	+	0.921133i	$0.627265\pi$
$198$		0			0
$199$	3.48802			0.247259			0.123630	−	0.992328i	$-0.460547\pi$
$199$	3.48802			0.247259			0.123630	+	0.992328i	$0.460547\pi$
$200$		0			0
$201$			6.09167i			0.429673i
$202$		0			0
$203$	−29.1607	−	29.1607i	−2.04668	−	2.04668i
$204$		0			0
$205$	−18.4991	+	1.21524i	−1.29203	+	0.0848763i
$206$		0			0
$207$	1.57269	−	4.53063i	0.109310	−	0.314901i
$208$		0			0
$209$			45.7729i			3.16618i
$210$		0			0
$211$	−14.5777			−1.00357			−0.501787	−	0.864991i	$-0.667324\pi$
$211$	−14.5777			−1.00357			−0.501787	+	0.864991i	$0.667324\pi$
$212$		0			0
$213$	7.60258	−	7.60258i	0.520920	−	0.520920i
$214$		0			0
$215$	12.4161	+	10.8854i	0.846769	+	0.742375i
$216$		0			0
$217$	19.8532	−	19.8532i	1.34773	−	1.34773i
$218$		0			0
$219$			8.04867i			0.543879i
$220$		0			0
$221$			0.585267i			0.0393693i
$222$		0			0
$223$	9.74761	−	9.74761i	0.652748	−	0.652748i	−0.300906	−	0.953654i	$-0.597289\pi$
$223$	9.74761	−	9.74761i	0.652748	−	0.652748i	0.953654	+	0.300906i	$0.0972889\pi$
$224$		0			0
$225$	−0.654098	−	4.95703i	−0.0436065	−	0.330469i
$226$		0			0
$227$	−12.6157	+	12.6157i	−0.837330	+	0.837330i	−0.988507	−	0.151176i	$-0.951694\pi$
$227$	−12.6157	+	12.6157i	−0.837330	+	0.837330i	0.151176	+	0.988507i	$0.451694\pi$
$228$		0			0
$229$	6.80818			0.449897			0.224949	−	0.974371i	$-0.427779\pi$
$229$	6.80818			0.449897			0.224949	+	0.974371i	$0.427779\pi$
$230$		0			0
$231$	26.2031			1.72404
$232$		0			0
$233$	−7.92399	+	7.92399i	−0.519118	+	0.519118i	−0.917304	−	0.398187i	$-0.869640\pi$
$233$	−7.92399	+	7.92399i	−0.519118	+	0.519118i	0.398187	+	0.917304i	$0.369640\pi$
$234$		0			0
$235$	7.14477	+	6.26392i	0.466073	+	0.408613i
$236$		0			0
$237$	4.18622	−	4.18622i	0.271924	−	0.271924i
$238$		0			0
$239$			2.60910i			0.168768i	0.996433	+	0.0843842i	$0.0268923\pi$
$239$			2.60910i			0.168768i	−0.996433	+	0.0843842i	$0.973108\pi$
$240$		0			0
$241$			10.5739i			0.681123i	0.940222	+	0.340562i	$0.110617\pi$
$241$			10.5739i			0.681123i	−0.940222	+	0.340562i	$0.889383\pi$
$242$		0			0
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$		0			0
$245$	1.49610	+	22.7744i	0.0955823	+	1.45501i
$246$		0			0
$247$	0.771467	−	0.771467i	0.0490873	−	0.0490873i
$248$		0			0
$249$	6.69811			0.424475
$250$		0			0
$251$		−	19.1440i		−	1.20836i	−0.796849	−	0.604178i	$-0.793502\pi$
$251$		−	19.1440i		−	1.20836i	0.796849	−	0.604178i	$-0.206498\pi$
$252$		0			0
$253$	−9.93447	+	28.6193i	−0.624575	+	1.79928i
$254$		0			0
$255$	−0.569761	−	8.67321i	−0.0356798	−	0.543137i
$256$		0			0
$257$	−14.1968	−	14.1968i	−0.885570	−	0.885570i	0.108524	−	0.994094i	$-0.465387\pi$
$257$	−14.1968	−	14.1968i	−0.885570	−	0.885570i	−0.994094	+	0.108524i	$0.965387\pi$
$258$		0			0
$259$			9.71324i			0.603552i
$260$		0			0
$261$	−9.94170			−0.615376
$262$		0			0
$263$	−6.96207	−	6.96207i	−0.429299	−	0.429299i	0.459090	−	0.888390i	$-0.348175\pi$
$263$	−6.96207	−	6.96207i	−0.429299	−	0.429299i	−0.888390	+	0.459090i	$0.848175\pi$
$264$		0			0
$265$	19.8500	+	17.4028i	1.21938	+	1.06905i
$266$		0			0
$267$	10.8331	−	10.8331i	0.662973	−	0.662973i
$268$		0			0
$269$			7.98055i			0.486583i	0.969953	+	0.243291i	$0.0782271\pi$
$269$			7.98055i			0.486583i	−0.969953	+	0.243291i	$0.921773\pi$
$270$		0			0
$271$	−8.22574			−0.499678			−0.249839	−	0.968287i	$-0.580378\pi$
$271$	−8.22574			−0.499678			−0.249839	+	0.968287i	$0.580378\pi$
$272$		0			0
$273$	−0.441633	−	0.441633i	−0.0267289	−	0.0267289i
$274$		0			0
$275$	4.13184	+	31.3128i	0.249159	+	1.88823i
$276$		0			0
$277$	21.4074	+	21.4074i	1.28625	+	1.28625i	0.937048	+	0.349200i	$0.113547\pi$
$277$	21.4074	+	21.4074i	1.28625	+	1.28625i	0.349200	+	0.937048i	$0.386453\pi$
$278$		0			0
$279$		−	6.76853i		−	0.405221i
$280$		0			0
$281$			16.1447i			0.963114i	0.876415	+	0.481557i	$0.159929\pi$
$281$			16.1447i			0.963114i	−0.876415	+	0.481557i	$0.840071\pi$
$282$		0			0
$283$	−18.4428	−	18.4428i	−1.09631	−	1.09631i	−0.994839	−	0.101470i	$-0.967645\pi$
$283$	−18.4428	−	18.4428i	−1.09631	−	1.09631i	−0.101470	−	0.994839i	$-0.532355\pi$
$284$		0			0
$285$	−10.6815	+	12.1836i	−0.632718	+	0.721692i
$286$		0			0
$287$	24.3186	−	24.3186i	1.43548	−	1.43548i
$288$		0			0
$289$			1.89017i			0.111186i
$290$		0			0
$291$		−	4.56827i		−	0.267797i
$292$		0			0
$293$	−0.405108	−	0.405108i	−0.0236667	−	0.0236667i	0.695174	−	0.718841i	$-0.255327\pi$
$293$	−0.405108	−	0.405108i	−0.0236667	−	0.0236667i	−0.718841	+	0.695174i	$0.755327\pi$
$294$		0			0
$295$	−0.154768	−	2.35596i	−0.00901092	−	0.137169i
$296$		0			0
$297$	4.46668	−	4.46668i	0.259183	−	0.259183i
$298$		0			0
$299$	0.649795	−	0.314919i	0.0375786	−	0.0182122i
$300$		0			0
$301$	−30.6316			−1.76558
$302$		0			0
$303$	−2.92197	+	2.92197i	−0.167863	+	0.167863i
$304$		0			0
$305$	0.199453	+	3.03617i	0.0114206	+	0.173851i
$306$		0			0
$307$	−10.0982	−	10.0982i	−0.576335	−	0.576335i	0.357557	−	0.933891i	$-0.383610\pi$
$307$	−10.0982	−	10.0982i	−0.576335	−	0.576335i	−0.933891	+	0.357557i	$0.883610\pi$
$308$		0			0
$309$	−0.0210663			−0.00119842
$310$		0			0
$311$	−26.6681			−1.51221			−0.756105	−	0.654451i	$-0.772900\pi$
$311$	−26.6681			−1.51221			−0.756105	+	0.654451i	$0.772900\pi$
$312$		0			0
$313$	−20.3355	−	20.3355i	−1.14943	−	1.14943i	−0.986665	−	0.162764i	$-0.947959\pi$
$313$	−20.3355	−	20.3355i	−1.14943	−	1.14943i	−0.162764	−	0.986665i	$-0.552041\pi$
$314$		0			0
$315$	6.97460	+	6.11473i	0.392974	+	0.344526i
$316$		0			0
$317$	17.6180	+	17.6180i	0.989527	+	0.989527i	0.999946	−	0.0104187i	$-0.00331643\pi$
$317$	17.6180	+	17.6180i	0.989527	+	0.989527i	−0.0104187	+	0.999946i	$0.503316\pi$
$318$		0			0
$319$	62.8002			3.51614
$320$		0			0
$321$		−	12.4168i		−	0.693039i
$322$		0			0
$323$	−19.9169	+	19.9169i	−1.10821	+	1.10821i
$324$		0			0
$325$	0.458114	−	0.597392i	0.0254116	−	0.0331374i
$326$		0			0
$327$	5.71067	−	5.71067i	0.315801	−	0.315801i
$328$		0			0
$329$	−17.6268			−0.971798
$330$		0			0
$331$	28.3715			1.55944			0.779719	−	0.626130i	$-0.215362\pi$
$331$	28.3715			1.55944			0.779719	+	0.626130i	$0.215362\pi$
$332$		0			0
$333$	1.65576	+	1.65576i	0.0907350	+	0.0907350i
$334$		0			0
$335$	8.97969	−	10.2424i	0.490613	−	0.559604i
$336$		0			0
$337$	10.2664	−	10.2664i	0.559247	−	0.559247i	−0.369846	−	0.929093i	$-0.620589\pi$
$337$	10.2664	−	10.2664i	0.559247	−	0.559247i	0.929093	+	0.369846i	$0.120589\pi$
$338$		0			0
$339$	5.20119			0.282490
$340$		0			0
$341$			42.7557i			2.31535i
$342$		0			0
$343$	−9.40665	−	9.40665i	−0.507911	−	0.507911i
$344$		0			0
$345$	−9.32288	+	5.29943i	−0.501927	+	0.285312i
$346$		0			0
$347$	10.0938	+	10.0938i	0.541864	+	0.541864i	0.924075	−	0.382211i	$-0.124837\pi$
$347$	10.0938	+	10.0938i	0.541864	+	0.541864i	−0.382211	+	0.924075i	$0.624837\pi$
$348$		0			0
$349$		−	19.8622i		−	1.06320i	−0.846996	−	0.531600i	$-0.821591\pi$
$349$		−	19.8622i		−	1.06320i	0.846996	−	0.531600i	$-0.178409\pi$
$350$		0			0
$351$	−0.150565			−0.00803657
$352$		0			0
$353$	−6.91280	+	6.91280i	−0.367931	+	0.367931i	−0.866722	−	0.498791i	$-0.833777\pi$
$353$	−6.91280	+	6.91280i	−0.367931	+	0.367931i	0.498791	+	0.866722i	$0.333777\pi$
$354$		0			0
$355$	−23.9898	+	1.57594i	−1.27324	+	0.0836420i
$356$		0			0
$357$	11.4016	+	11.4016i	0.603439	+	0.603439i
$358$		0			0
$359$	1.15659			0.0610427			0.0305213	−	0.999534i	$-0.490283\pi$
$359$	1.15659			0.0610427			0.0305213	+	0.999534i	$0.490283\pi$
$360$		0			0
$361$	33.5068			1.76352
$362$		0			0
$363$	−20.4372	+	20.4372i	−1.07267	+	1.07267i
$364$		0			0
$365$	11.8645	−	13.5329i	0.621016	−	0.708344i
$366$		0			0
$367$	−22.0789	+	22.0789i	−1.15251	+	1.15251i	−0.166460	+	0.986048i	$0.553234\pi$
$367$	−22.0789	+	22.0789i	−1.15251	+	1.15251i	−0.986048	+	0.166460i	$0.946766\pi$
$368$		0			0
$369$		−	8.29087i		−	0.431606i
$370$		0			0
$371$	−48.9719			−2.54249
$372$		0			0
$373$	−19.1301	−	19.1301i	−0.990520	−	0.990520i	0.00943553	−	0.999955i	$-0.496997\pi$
$373$	−19.1301	−	19.1301i	−0.990520	−	0.990520i	−0.999955	+	0.00943553i	$0.996997\pi$
$374$		0			0
$375$	−6.20734	+	9.29887i	−0.320545	+	0.480192i
$376$		0			0
$377$	−1.05845	−	1.05845i	−0.0545129	−	0.0545129i
$378$		0			0
$379$	−3.43150			−0.176264			−0.0881321	−	0.996109i	$-0.528090\pi$
$379$	−3.43150			−0.176264			−0.0881321	+	0.996109i	$0.528090\pi$
$380$		0			0
$381$	15.3797			0.787926
$382$		0			0
$383$	−7.46410	−	7.46410i	−0.381398	−	0.381398i	0.490208	−	0.871606i	$-0.336921\pi$
$383$	−7.46410	−	7.46410i	−0.381398	−	0.381398i	−0.871606	+	0.490208i	$0.836921\pi$
$384$		0			0
$385$	−44.0575	−	38.6258i	−2.24538	−	1.96855i
$386$		0			0
$387$	−5.22159	+	5.22159i	−0.265428	+	0.265428i
$388$		0			0
$389$	−23.7776			−1.20557			−0.602786	−	0.797903i	$-0.705943\pi$
$389$	−23.7776			−1.20557			−0.602786	+	0.797903i	$0.705943\pi$
$390$		0			0
$391$	−16.7757	+	8.13025i	−0.848385	+	0.411165i
$392$		0			0
$393$	−4.53155	+	4.53155i	−0.228587	+	0.228587i
$394$		0			0
$395$	−13.2095	+	0.867760i	−0.664643	+	0.0436617i
$396$		0			0
$397$	−11.5571	−	11.5571i	−0.580033	−	0.580033i	0.354880	−	0.934912i	$-0.384522\pi$
$397$	−11.5571	−	11.5571i	−0.580033	−	0.580033i	−0.934912	+	0.354880i	$0.884522\pi$
$398$		0			0
$399$		−	30.0580i		−	1.50478i
$400$		0			0
$401$			9.76249i			0.487516i	0.969836	+	0.243758i	$0.0783802\pi$
$401$			9.76249i			0.487516i	−0.969836	+	0.243758i	$0.921620\pi$
$402$		0			0
$403$	0.720615	−	0.720615i	0.0358964	−	0.0358964i
$404$		0			0
$405$	2.23126	−	0.146576i	0.110872	−	0.00728342i
$406$		0			0
$407$	−10.4592	−	10.4592i	−0.518442	−	0.518442i
$408$		0			0
$409$		−	2.98559i		−	0.147628i	−0.997272	−	0.0738139i	$-0.976483\pi$
$409$		−	2.98559i		−	0.147628i	0.997272	−	0.0738139i	$-0.0235171\pi$
$410$		0			0
$411$		−	0.817476i		−	0.0403231i
$412$		0			0
$413$	3.09710	+	3.09710i	0.152398	+	0.152398i
$414$		0			0
$415$	−11.2621	−	9.87364i	−0.552834	−	0.484678i
$416$		0			0
$417$	3.57839	+	3.57839i	0.175234	+	0.175234i
$418$		0			0
$419$	−36.6516			−1.79055			−0.895275	−	0.445515i	$-0.853021\pi$
$419$	−36.6516			−1.79055			−0.895275	+	0.445515i	$0.853021\pi$
$420$		0			0
$421$		−	26.4164i		−	1.28745i	−0.765255	−	0.643727i	$-0.777387\pi$
$421$		−	26.4164i		−	1.28745i	0.765255	−	0.643727i	$-0.222613\pi$
$422$		0			0
$423$	−3.00474	+	3.00474i	−0.146095	+	0.146095i
$424$		0			0
$425$	−11.8271	+	15.4229i	−0.573700	+	0.748119i
$426$		0			0
$427$	−3.99130	−	3.99130i	−0.193152	−	0.193152i
$428$		0			0
$429$	0.951097			0.0459194
$430$		0			0
$431$		−	2.35855i		−	0.113607i	−0.998385	−	0.0568037i	$-0.981909\pi$
$431$		−	2.35855i		−	0.113607i	0.998385	−	0.0568037i	$-0.0180909\pi$
$432$		0			0
$433$	−18.8910	−	18.8910i	−0.907845	−	0.907845i	0.0882534	−	0.996098i	$-0.471871\pi$
$433$	−18.8910	−	18.8910i	−0.907845	−	0.907845i	−0.996098	+	0.0882534i	$0.971871\pi$
$434$		0			0
$435$	16.7158	+	14.6550i	0.801462	+	0.702653i
$436$		0			0
$437$	32.8297	+	11.3960i	1.57046	+	0.545144i
$438$		0			0
$439$		−	14.9535i		−	0.713692i	−0.934163	−	0.356846i	$-0.883852\pi$
$439$		−	14.9535i		−	0.713692i	0.934163	−	0.356846i	$-0.116148\pi$
$440$		0			0
$441$	−10.2070			−0.486047
$442$		0			0
$443$	6.13367	−	6.13367i	0.291419	−	0.291419i	−0.546221	−	0.837641i	$-0.683934\pi$
$443$	6.13367	−	6.13367i	0.291419	−	0.291419i	0.837641	+	0.546221i	$0.183934\pi$
$444$		0			0
$445$	−34.1835	+	2.24558i	−1.62045	+	0.106451i
$446$		0			0
$447$	−9.01141	+	9.01141i	−0.426225	+	0.426225i
$448$		0			0
$449$		−	22.6266i		−	1.06782i	−0.845543	−	0.533908i	$-0.820723\pi$
$449$		−	22.6266i		−	1.06782i	0.845543	−	0.533908i	$-0.179277\pi$
$450$		0			0
$451$			52.3722i			2.46611i
$452$		0			0
$453$	−2.66121	+	2.66121i	−0.125034	+	0.125034i
$454$		0			0
$455$	0.0915461	+	1.39356i	0.00429175	+	0.0653313i
$456$		0			0
$457$	−13.7282	+	13.7282i	−0.642178	+	0.642178i	−0.951091	−	0.308912i	$-0.900035\pi$
$457$	−13.7282	+	13.7282i	−0.642178	+	0.642178i	0.308912	+	0.951091i	$0.400035\pi$
$458$		0			0
$459$	3.88714			0.181436
$460$		0			0
$461$	22.9835			1.07045			0.535224	−	0.844710i	$-0.320227\pi$
$461$	22.9835			1.07045			0.535224	+	0.844710i	$0.320227\pi$
$462$		0			0
$463$	−6.97713	+	6.97713i	−0.324255	+	0.324255i	−0.850397	−	0.526142i	$-0.823638\pi$
$463$	−6.97713	+	6.97713i	−0.324255	+	0.324255i	0.526142	+	0.850397i	$0.323638\pi$
$464$		0			0
$465$	−9.97744	+	11.3805i	−0.462693	+	0.527757i
$466$		0			0
$467$	−3.22506	+	3.22506i	−0.149238	+	0.149238i	−0.777778	−	0.628540i	$-0.783653\pi$
$467$	−3.22506	+	3.22506i	−0.149238	+	0.149238i	0.628540	+	0.777778i	$0.283653\pi$
$468$		0			0
$469$			25.2690i			1.16682i
$470$		0			0
$471$			21.4961i			0.990488i
$472$		0			0
$473$	32.9840	−	32.9840i	1.51660	−	1.51660i
$474$		0			0
$475$	35.9194	−	4.73970i	1.64810	−	0.217472i
$476$		0			0
$477$	−8.34794	+	8.34794i	−0.382226	+	0.382226i
$478$		0			0
$479$	18.7869			0.858394			0.429197	−	0.903211i	$-0.358797\pi$
$479$	18.7869			0.858394			0.429197	+	0.903211i	$0.358797\pi$
$480$		0			0
$481$			0.352563i			0.0160755i
$482$		0			0
$483$	6.52374	−	18.7937i	0.296840	−	0.855141i
$484$		0			0
$485$	−6.73405	+	7.68101i	−0.305778	+	0.348777i
$486$		0			0
$487$	0.126953	+	0.126953i	0.00575279	+	0.00575279i	0.709977	−	0.704225i	$-0.248705\pi$
$487$	0.126953	+	0.126953i	0.00575279	+	0.00575279i	−0.704225	+	0.709977i	$0.748705\pi$
$488$		0			0
$489$		−	1.56453i		−	0.0707505i
$490$		0			0
$491$	−14.3584			−0.647987			−0.323993	−	0.946059i	$-0.605026\pi$
$491$	−14.3584			−0.647987			−0.323993	+	0.946059i	$0.605026\pi$
$492$		0			0
$493$	27.3260	+	27.3260i	1.23070	+	1.23070i
$494$		0			0
$495$	−14.0945	+	0.925898i	−0.633501	+	0.0416160i
$496$		0			0
$497$	31.5365	−	31.5365i	1.41460	−	1.41460i
$498$		0			0
$499$			32.7714i			1.46705i	0.679663	+	0.733525i	$0.262126\pi$
$499$			32.7714i			1.46705i	−0.679663	+	0.733525i	$0.737874\pi$
$500$		0			0
$501$	−8.73359			−0.390188
$502$		0			0
$503$	−1.77769	−	1.77769i	−0.0792632	−	0.0792632i	0.666364	−	0.745627i	$-0.267850\pi$
$503$	−1.77769	−	1.77769i	−0.0792632	−	0.0792632i	−0.745627	+	0.666364i	$0.767850\pi$
$504$		0			0
$505$	9.22021	−	0.605695i	0.410294	−	0.0269531i
$506$		0			0
$507$	9.17636	+	9.17636i	0.407536	+	0.407536i
$508$		0			0
$509$			17.6802i			0.783660i	0.920038	+	0.391830i	$0.128158\pi$
$509$			17.6802i			0.783660i	−0.920038	+	0.391830i	$0.871842\pi$
$510$		0			0
$511$			33.3869i			1.47695i
$512$		0			0
$513$	−5.12381	−	5.12381i	−0.226222	−	0.226222i
$514$		0			0
$515$	0.0354206	+	0.0310537i	0.00156082	+	0.00136839i
$516$		0			0
$517$	18.9805	−	18.9805i	0.834760	−	0.834760i
$518$		0			0
$519$		−	2.36117i		−	0.103644i
$520$		0			0
$521$		−	20.3631i		−	0.892125i	−0.895002	−	0.446063i	$-0.852826\pi$
$521$		−	20.3631i		−	0.892125i	0.895002	−	0.446063i	$-0.147174\pi$
$522$		0			0
$523$	−7.12123	−	7.12123i	−0.311390	−	0.311390i	0.534058	−	0.845448i	$-0.320666\pi$
$523$	−7.12123	−	7.12123i	−0.311390	−	0.311390i	−0.845448	+	0.534058i	$0.820666\pi$
$524$		0			0
$525$	−2.71328	−	20.5624i	−0.118417	−	0.897417i
$526$		0			0
$527$	−18.6041	+	18.6041i	−0.810408	+	0.810408i
$528$		0			0
$529$	18.0533	+	14.2506i	0.784925	+	0.619591i
$530$		0			0
$531$	1.05589			0.0458216
$532$		0			0
$533$	0.882693	−	0.882693i	0.0382337	−	0.0382337i
$534$		0			0
$535$	−18.3035	+	20.8774i	−0.791331	+	0.902609i
$536$		0			0
$537$	−0.130092	−	0.130092i	−0.00561389	−	0.00561389i
$538$		0			0
$539$	64.4760			2.77718
$540$		0			0
$541$	35.5846			1.52990			0.764950	−	0.644090i	$-0.222764\pi$
$541$	35.5846			1.52990			0.764950	+	0.644090i	$0.222764\pi$
$542$		0			0
$543$	4.36742	+	4.36742i	0.187424	+	0.187424i
$544$		0			0
$545$	−18.0199	+	1.18376i	−0.771887	+	0.0507068i
$546$		0			0
$547$	24.8186	+	24.8186i	1.06117	+	1.06117i	0.998003	+	0.0631656i	$0.0201196\pi$
$547$	24.8186	+	24.8186i	1.06117	+	1.06117i	0.0631656	+	0.998003i	$0.479880\pi$
$548$		0			0
$549$	−1.36075			−0.0580752
$550$		0			0
$551$		−	72.0392i		−	3.06897i
$552$		0			0
$553$	17.3650	−	17.3650i	0.738434	−	0.738434i
$554$		0			0
$555$	−0.343222	−	5.22471i	−0.0145690	−	0.221776i
$556$		0			0
$557$	4.04871	−	4.04871i	0.171549	−	0.171549i	−0.616110	−	0.787660i	$-0.711292\pi$
$557$	4.04871	−	4.04871i	0.171549	−	0.171549i	0.787660	+	0.616110i	$0.211292\pi$
$558$		0			0
$559$	−1.11184			−0.0470258
$560$		0			0
$561$	−24.5544			−1.03669
$562$		0			0
$563$	13.2808	+	13.2808i	0.559718	+	0.559718i	0.929227	−	0.369509i	$-0.120474\pi$
$563$	13.2808	+	13.2808i	0.559718	+	0.559718i	−0.369509	+	0.929227i	$0.620474\pi$
$564$		0			0
$565$	−8.74519	−	7.66703i	−0.367913	−	0.322554i
$566$		0			0
$567$	−2.93317	+	2.93317i	−0.123182	+	0.123182i
$568$		0			0
$569$	−25.5541			−1.07129			−0.535643	−	0.844445i	$-0.679931\pi$
$569$	−25.5541			−1.07129			−0.535643	+	0.844445i	$0.679931\pi$
$570$		0			0
$571$		−	2.55410i		−	0.106886i	−0.998571	−	0.0534428i	$-0.982981\pi$
$571$		−	2.55410i		−	0.106886i	0.998571	−	0.0534428i	$-0.0170195\pi$
$572$		0			0
$573$	−2.57913	−	2.57913i	−0.107745	−	0.107745i
$574$		0			0
$575$	23.4872	+	4.83242i	0.979483	+	0.201526i
$576$		0			0
$577$	−23.6735	−	23.6735i	−0.985542	−	0.985542i	0.0143549	−	0.999897i	$-0.495431\pi$
$577$	−23.6735	−	23.6735i	−0.985542	−	0.985542i	−0.999897	+	0.0143549i	$0.995431\pi$
$578$		0			0
$579$			0.0844557i			0.00350986i
$580$		0			0
$581$	27.7846			1.15270
$582$		0			0
$583$	52.7326	−	52.7326i	2.18396	−	2.18396i
$584$		0			0
$585$	0.253158	+	0.221947i	0.0104668	+	0.00917638i
$586$		0			0
$587$	−30.3244	−	30.3244i	−1.25162	−	1.25162i	−0.954992	−	0.296632i	$-0.904137\pi$
$587$	−30.3244	−	30.3244i	−1.25162	−	1.25162i	−0.296632	−	0.954992i	$-0.595863\pi$
$588$		0			0
$589$	49.0458			2.02090
$590$		0			0
$591$	10.5576			0.434283
$592$		0			0
$593$	−2.87145	+	2.87145i	−0.117916	+	0.117916i	−0.763603	−	0.645686i	$-0.776571\pi$
$593$	−2.87145	+	2.87145i	−0.117916	+	0.117916i	0.645686	+	0.763603i	$0.276571\pi$
$594$		0			0
$595$	−2.36344	−	35.9776i	−0.0968917	−	1.47494i
$596$		0			0
$597$	2.46640	−	2.46640i	0.100943	−	0.100943i
$598$		0			0
$599$		−	32.4702i		−	1.32670i	−0.748311	−	0.663348i	$-0.769135\pi$
$599$		−	32.4702i		−	1.32670i	0.748311	−	0.663348i	$-0.230865\pi$
$600$		0			0
$601$	17.4240			0.710738			0.355369	−	0.934726i	$-0.384355\pi$
$601$	17.4240			0.710738			0.355369	+	0.934726i	$0.384355\pi$
$602$		0			0
$603$	4.30746	+	4.30746i	0.175413	+	0.175413i
$604$		0			0
$605$	64.4891	−	4.23642i	2.62185	−	0.172235i
$606$		0			0
$607$	11.5614	+	11.5614i	0.469264	+	0.469264i	0.901676	−	0.432412i	$-0.142337\pi$
$607$	11.5614	+	11.5614i	0.469264	+	0.469264i	−0.432412	+	0.901676i	$0.642337\pi$
$608$		0			0
$609$	−41.2395			−1.67111
$610$		0			0
$611$	−0.639802			−0.0258836
$612$		0			0
$613$	1.08084	+	1.08084i	0.0436548	+	0.0436548i	0.728597	−	0.684942i	$-0.240173\pi$
$613$	1.08084	+	1.08084i	0.0436548	+	0.0436548i	−0.684942	+	0.728597i	$0.740173\pi$
$614$		0			0
$615$	−12.2215	+	13.9401i	−0.492819	+	0.562121i
$616$		0			0
$617$	−1.85476	+	1.85476i	−0.0746698	+	0.0746698i	−0.743455	−	0.668786i	$-0.766814\pi$
$617$	−1.85476	+	1.85476i	−0.0746698	+	0.0746698i	0.668786	+	0.743455i	$0.266814\pi$
$618$		0			0
$619$	−31.3231			−1.25898			−0.629492	−	0.777007i	$-0.716737\pi$
$619$	−31.3231			−1.25898			−0.629492	+	0.777007i	$0.716737\pi$
$620$		0			0
$621$	−2.09158	−	4.31570i	−0.0839322	−	0.173183i
$622$		0			0
$623$	44.9370	−	44.9370i	1.80036	−	1.80036i
$624$		0			0
$625$	24.1443	−	6.48477i	0.965772	−	0.259391i
$626$		0			0
$627$	32.3663	+	32.3663i	1.29259	+	1.29259i
$628$		0			0
$629$		−	9.10210i		−	0.362925i
$630$		0			0
$631$			30.5906i			1.21779i	0.793250	+	0.608896i	$0.208387\pi$
$631$			30.5906i			1.21779i	−0.793250	+	0.608896i	$0.791613\pi$
$632$		0			0
$633$	−10.3080	+	10.3080i	−0.409707	+	0.409707i
$634$		0			0
$635$	−25.8592	−	22.6711i	−1.02619	−	0.899676i
$636$		0			0
$637$	−1.08669	−	1.08669i	−0.0430564	−	0.0430564i
$638$		0			0
$639$		−	10.7517i		−	0.425329i
$640$		0			0
$641$			16.7055i			0.659828i	0.944011	+	0.329914i	$0.107020\pi$
$641$			16.7055i			0.659828i	−0.944011	+	0.329914i	$0.892980\pi$
$642$		0			0
$643$	−13.0718	−	13.0718i	−0.515501	−	0.515501i	0.400706	−	0.916207i	$-0.368765\pi$
$643$	−13.0718	−	13.0718i	−0.515501	−	0.515501i	−0.916207	+	0.400706i	$0.868765\pi$
$644$		0			0
$645$	16.4766	−	1.08238i	0.648765	−	0.0426187i
$646$		0			0
$647$	31.7003	+	31.7003i	1.24627	+	1.24627i	0.957356	+	0.288912i	$0.0932936\pi$
$647$	31.7003	+	31.7003i	1.24627	+	1.24627i	0.288912	+	0.957356i	$0.406706\pi$
$648$		0			0
$649$	−6.66987			−0.261815
$650$		0			0
$651$		−	28.0767i		−	1.10041i
$652$		0			0
$653$	15.2125	−	15.2125i	0.595311	−	0.595311i	−0.343750	−	0.939061i	$-0.611697\pi$
$653$	15.2125	−	15.2125i	0.595311	−	0.595311i	0.939061	+	0.343750i	$0.111697\pi$
$654$		0			0
$655$	14.2992	−	0.939344i	0.558716	−	0.0367032i
$656$		0			0
$657$	5.69127	+	5.69127i	0.222037	+	0.222037i
$658$		0			0
$659$	9.36828			0.364936			0.182468	−	0.983212i	$-0.441591\pi$
$659$	9.36828			0.364936			0.182468	+	0.983212i	$0.441591\pi$
$660$		0			0
$661$			41.9718i			1.63251i	0.577689	+	0.816257i	$0.303955\pi$
$661$			41.9718i			1.63251i	−0.577689	+	0.816257i	$0.696045\pi$
$662$		0			0
$663$	0.413846	+	0.413846i	0.0160725	+	0.0160725i
$664$		0			0
$665$	−44.3083	+	50.5390i	−1.71820	+	1.95982i
$666$		0			0
$667$	15.6353	−	45.0422i	0.605400	−	1.74404i
$668$		0			0
$669$		−	13.7852i		−	0.532967i
$670$		0			0
$671$	8.59562			0.331830
$672$		0			0
$673$	−26.5699	+	26.5699i	−1.02419	+	1.02419i	−0.0244944	+	0.999700i	$0.507798\pi$
$673$	−26.5699	+	26.5699i	−1.02419	+	1.02419i	−0.999700	+	0.0244944i	$0.992202\pi$
$674$		0			0
$675$	−3.96767	−	3.04263i	−0.152716	−	0.117111i
$676$		0			0
$677$	28.5890	−	28.5890i	1.09877	−	1.09877i	0.104210	−	0.994555i	$-0.466769\pi$
$677$	28.5890	−	28.5890i	1.09877	−	1.09877i	0.994555	−	0.104210i	$-0.0332314\pi$
$678$		0			0
$679$		−	18.9498i		−	0.727225i
$680$		0			0
$681$			17.8412i			0.683677i
$682$		0			0
$683$	−27.7372	+	27.7372i	−1.06134	+	1.06134i	−0.0633437	+	0.997992i	$0.520176\pi$
$683$	−27.7372	+	27.7372i	−1.06134	+	1.06134i	−0.997992	+	0.0633437i	$0.979824\pi$
$684$		0			0
$685$	−1.20504	+	1.37449i	−0.0460421	+	0.0525166i
$686$		0			0
$687$	4.81411	−	4.81411i	0.183670	−	0.183670i
$688$		0			0
$689$	−1.77754			−0.0677188
$690$		0			0
$691$	−23.0366			−0.876355			−0.438178	−	0.898888i	$-0.644376\pi$
$691$	−23.0366			−0.876355			−0.438178	+	0.898888i	$0.644376\pi$
$692$		0			0
$693$	18.5284	−	18.5284i	0.703835	−	0.703835i
$694$		0			0
$695$	−0.741763	−	11.2915i	−0.0281367	−	0.428311i
$696$		0			0
$697$	−22.7885	+	22.7885i	−0.863175	+	0.863175i
$698$		0			0
$699$			11.2062i			0.423858i
$700$		0			0
$701$			33.7206i			1.27361i	0.771024	+	0.636806i	$0.219745\pi$
$701$			33.7206i			1.27361i	−0.771024	+	0.636806i	$0.780255\pi$
$702$		0			0
$703$	−11.9979	+	11.9979i	−0.452509	+	0.452509i
$704$		0			0
$705$	9.48137	−	0.622851i	0.357089	−	0.0234579i
$706$		0			0
$707$	−12.1207	+	12.1207i	−0.455847	+	0.455847i
$708$		0			0
$709$	−0.943683			−0.0354408			−0.0177204	−	0.999843i	$-0.505641\pi$
$709$	−0.943683			−0.0354408			−0.0177204	+	0.999843i	$0.505641\pi$
$710$		0			0
$711$		−	5.92020i		−	0.222025i
$712$		0			0
$713$	30.6657	+	10.6448i	1.14844	+	0.398652i
$714$		0			0
$715$	−1.59916	−	1.40201i	−0.0598051	−	0.0524320i
$716$		0			0
$717$	1.84491	+	1.84491i	0.0688994	+	0.0688994i
$718$		0			0
$719$		−	14.9715i		−	0.558343i	−0.960241	−	0.279171i	$-0.909940\pi$
$719$		−	14.9715i		−	0.558343i	0.960241	−	0.279171i	$-0.0900597\pi$
$720$		0			0
$721$	−0.0873859			−0.00325442
$722$		0			0
$723$	7.47686	+	7.47686i	0.278067	+	0.278067i
$724$		0			0
$725$	−6.50285	−	49.2813i	−0.241510	−	1.83026i
$726$		0			0
$727$	−8.05219	+	8.05219i	−0.298639	+	0.298639i	−0.840481	−	0.541841i	$-0.817727\pi$
$727$	−8.05219	+	8.05219i	−0.298639	+	0.298639i	0.541841	+	0.840481i	$0.317727\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	28.7043			1.06167
$732$		0			0
$733$	7.80288	+	7.80288i	0.288206	+	0.288206i	0.836370	−	0.548165i	$-0.184673\pi$
$733$	7.80288	+	7.80288i	0.288206	+	0.288206i	−0.548165	+	0.836370i	$0.684673\pi$
$734$		0			0
$735$	17.1619	+	15.0461i	0.633025	+	0.554982i
$736$		0			0
$737$	−27.2096	−	27.2096i	−1.00228	−	1.00228i
$738$		0			0
$739$			33.5645i			1.23469i	0.786693	+	0.617344i	$0.211792\pi$
$739$			33.5645i			1.23469i	−0.786693	+	0.617344i	$0.788208\pi$
$740$		0			0
$741$		−	1.09102i		−	0.0400796i
$742$		0			0
$743$	14.5754	+	14.5754i	0.534721	+	0.534721i	0.921974	−	0.387252i	$-0.126576\pi$
$743$	14.5754	+	14.5754i	0.534721	+	0.534721i	−0.387252	+	0.921974i	$0.626576\pi$
$744$		0			0
$745$	28.4353	−	1.86797i	1.04179	−	0.0684372i
$746$		0			0
$747$	4.73628	−	4.73628i	0.173291	−	0.173291i
$748$		0			0
$749$		−	51.5065i		−	1.88201i
$750$		0			0
$751$		−	42.4139i		−	1.54770i	−0.633366	−	0.773852i	$-0.718327\pi$
$751$		−	42.4139i		−	1.54770i	0.633366	−	0.773852i	$-0.281673\pi$
$752$		0			0
$753$	−13.5368	−	13.5368i	−0.493309	−	0.493309i
$754$		0			0
$755$	8.39738	−	0.551641i	0.305612	−	0.0200763i
$756$		0			0
$757$	2.60003	−	2.60003i	0.0944998	−	0.0944998i	−0.658276	−	0.752776i	$-0.728714\pi$
$757$	2.60003	−	2.60003i	0.0944998	−	0.0944998i	0.752776	+	0.658276i	$0.228714\pi$
$758$		0			0
$759$	13.2122	+	27.2616i	0.479572	+	0.989535i
$760$		0			0
$761$	−9.88477			−0.358323			−0.179161	−	0.983820i	$-0.557338\pi$
$761$	−9.88477			−0.358323			−0.179161	+	0.983820i	$0.557338\pi$
$762$		0			0
$763$	23.6886	−	23.6886i	0.857585	−	0.857585i
$764$		0			0
$765$	−6.53577	−	5.73000i	−0.236301	−	0.207169i
$766$		0			0
$767$	0.112416	+	0.112416i	0.00405909	+	0.00405909i
$768$		0			0
$769$	−35.4565			−1.27859			−0.639297	−	0.768960i	$-0.720775\pi$
$769$	−35.4565			−1.27859			−0.639297	+	0.768960i	$0.720775\pi$
$770$		0			0
$771$	−20.0773			−0.723065
$772$		0			0
$773$	6.54553	+	6.54553i	0.235426	+	0.235426i	0.814953	−	0.579527i	$-0.196763\pi$
$773$	6.54553	+	6.54553i	0.235426	+	0.235426i	−0.579527	+	0.814953i	$0.696763\pi$
$774$		0			0
$775$	33.5518	−	4.42728i	1.20522	−	0.159033i
$776$		0			0
$777$	6.86830	+	6.86830i	0.246399	+	0.246399i
$778$		0			0
$779$	60.0770			2.15248
$780$		0			0
$781$			67.9166i			2.43025i
$782$		0			0
$783$	−7.02985	+	7.02985i	−0.251226	+	0.251226i
$784$		0			0
$785$	31.6873	−	36.1432i	1.13097	−	1.29001i
$786$		0			0
$787$	−11.9311	+	11.9311i	−0.425296	+	0.425296i	−0.887022	−	0.461726i	$-0.847230\pi$
$787$	−11.9311	+	11.9311i	−0.425296	+	0.425296i	0.461726	+	0.887022i	$0.347230\pi$
$788$		0			0
$789$	−9.84585			−0.350522
$790$		0			0
$791$	21.5752			0.767126
$792$		0			0
$793$	−0.144873	−	0.144873i	−0.00514458	−	0.00514458i
$794$		0			0
$795$	26.3417	−	1.73044i	0.934244	−	0.0613724i
$796$		0			0
$797$	3.02206	−	3.02206i	0.107047	−	0.107047i	−0.651555	−	0.758602i	$-0.725883\pi$
$797$	3.02206	−	3.02206i	0.107047	−	0.107047i	0.758602	+	0.651555i	$0.225883\pi$
$798$		0			0
$799$	16.5178			0.584356
$800$		0			0
$801$		−	15.3203i		−	0.541315i
$802$		0			0
$803$	−35.9509	−	35.9509i	−1.26868	−	1.26868i
$804$		0			0
$805$	−38.6725	+	21.9827i	−1.36303	+	0.774790i
$806$		0			0
$807$	5.64310	+	5.64310i	0.198646	+	0.198646i
$808$		0			0
$809$		−	31.6163i		−	1.11157i	−0.831326	−	0.555785i	$-0.812418\pi$
$809$		−	31.6163i		−	1.11157i	0.831326	−	0.555785i	$-0.187582\pi$
$810$		0			0
$811$	52.8020			1.85413			0.927064	−	0.374902i	$-0.122324\pi$
$811$	52.8020			1.85413			0.927064	+	0.374902i	$0.122324\pi$
$812$		0			0
$813$	−5.81647	+	5.81647i	−0.203993	+	0.203993i
$814$		0			0
$815$	−2.30626	+	2.63057i	−0.0807849	+	0.0921450i
$816$		0			0
$817$	−37.8364	−	37.8364i	−1.32373	−	1.32373i
$818$		0			0
$819$	−0.624564			−0.0218240
$820$		0			0
$821$	−30.0997			−1.05049			−0.525244	−	0.850952i	$-0.676026\pi$
$821$	−30.0997			−1.05049			−0.525244	+	0.850952i	$0.676026\pi$
$822$		0			0
$823$	20.1196	−	20.1196i	0.701326	−	0.701326i	−0.263369	−	0.964695i	$-0.584834\pi$
$823$	20.1196	−	20.1196i	0.701326	−	0.701326i	0.964695	+	0.263369i	$0.0848337\pi$
$824$		0			0
$825$	25.0631	+	19.2198i	0.872587	+	0.669149i
$826$		0			0
$827$	−19.4610	+	19.4610i	−0.676725	+	0.676725i	−0.959258	−	0.282532i	$-0.908826\pi$
$827$	−19.4610	+	19.4610i	−0.676725	+	0.676725i	0.282532	+	0.959258i	$0.408826\pi$
$828$		0			0
$829$			6.60357i			0.229352i	0.993403	+	0.114676i	$0.0365829\pi$
$829$			6.60357i			0.229352i	−0.993403	+	0.114676i	$0.963417\pi$
$830$		0			0
$831$	30.2747			1.05022
$832$		0			0
$833$	28.0551	+	28.0551i	0.972053	+	0.972053i
$834$		0			0
$835$	14.6845	+	12.8741i	0.508178	+	0.445527i
$836$		0			0
$837$	−4.78607	−	4.78607i	−0.165431	−	0.165431i
$838$		0			0
$839$	−43.7680			−1.51104			−0.755520	−	0.655125i	$-0.772616\pi$
$839$	−43.7680			−1.51104			−0.755520	+	0.655125i	$0.772616\pi$
$840$		0			0
$841$	−69.8374			−2.40819
$842$		0			0
$843$	11.4160	+	11.4160i	0.393190	+	0.393190i
$844$		0			0
$845$	−1.90217	−	28.9558i	−0.0654365	−	0.996109i
$846$		0			0
$847$	−84.7761	+	84.7761i	−2.91294	+	2.91294i
$848$		0			0
$849$	−26.0820			−0.895133
$850$		0			0
$851$	−10.1056	+	4.89763i	−0.346417	+	0.167889i
$852$		0			0
$853$	−25.3300	+	25.3300i	−0.867282	+	0.867282i	−0.992171	−	0.124889i	$-0.960143\pi$
$853$	−25.3300	+	25.3300i	−0.867282	+	0.867282i	0.124889	+	0.992171i	$0.460143\pi$
$854$		0			0
$855$	1.06211	+	16.1681i	0.0363235	+	0.552936i
$856$		0			0
$857$	13.7542	+	13.7542i	0.469834	+	0.469834i	0.901861	−	0.432027i	$-0.142201\pi$
$857$	13.7542	+	13.7542i	0.469834	+	0.469834i	−0.432027	+	0.901861i	$0.642201\pi$
$858$		0			0
$859$		−	13.5835i		−	0.463464i	−0.972780	−	0.231732i	$-0.925561\pi$
$859$		−	13.5835i		−	0.463464i	0.972780	−	0.231732i	$-0.0744393\pi$
$860$		0			0
$861$		−	34.3916i		−	1.17206i
$862$		0			0
$863$	−16.9035	+	16.9035i	−0.575404	+	0.575404i	−0.933633	−	0.358230i	$-0.883380\pi$
$863$	−16.9035	+	16.9035i	−0.575404	+	0.575404i	0.358230	+	0.933633i	$0.383380\pi$
$864$		0			0
$865$	−3.48059	+	3.97003i	−0.118343	+	0.134985i
$866$		0			0
$867$	1.33655	+	1.33655i	0.0453916	+	0.0453916i
$868$		0			0
$869$			37.3970i			1.26861i
$870$		0			0
$871$			0.917193i			0.0310779i
$872$		0			0
$873$	−3.23025	−	3.23025i	−0.109327	−	0.109327i
$874$		0			0
$875$	−25.7488	+	38.5729i	−0.870470	+	1.30400i
$876$		0			0
$877$	−24.1266	−	24.1266i	−0.814697	−	0.814697i	0.170637	−	0.985334i	$-0.445418\pi$
$877$	−24.1266	−	24.1266i	−0.814697	−	0.814697i	−0.985334	+	0.170637i	$0.945418\pi$
$878$		0			0
$879$	−0.572910			−0.0193238
$880$		0			0
$881$		−	8.45862i		−	0.284978i	−0.989796	−	0.142489i	$-0.954489\pi$
$881$		−	8.45862i		−	0.284978i	0.989796	−	0.142489i	$-0.0455106\pi$
$882$		0			0
$883$	28.9736	−	28.9736i	0.975038	−	0.975038i	−0.0246583	−	0.999696i	$-0.507850\pi$
$883$	28.9736	−	28.9736i	0.975038	−	0.975038i	0.999696	+	0.0246583i	$0.00784979\pi$
$884$		0			0
$885$	−1.77535	−	1.55648i	−0.0596777	−	0.0523204i
$886$		0			0
$887$	−34.8411	−	34.8411i	−1.16985	−	1.16985i	−0.982244	−	0.187606i	$-0.939927\pi$
$887$	−34.8411	−	34.8411i	−1.16985	−	1.16985i	−0.187606	−	0.982244i	$-0.560073\pi$
$888$		0			0
$889$	63.7970			2.13968
$890$		0			0
$891$		−	6.31685i		−	0.211622i
$892$		0			0
$893$	−21.7728	−	21.7728i	−0.728599	−	0.728599i
$894$		0			0
$895$	0.0269668	+	0.410503i	0.000901400	+	0.0137216i
$896$		0			0
$897$	0.236793	−	0.682155i	0.00790628	−	0.0227765i
$898$		0			0
$899$		−	67.2907i		−	2.24427i
$900$		0			0
$901$	45.8906			1.52884
$902$		0			0
$903$	−21.6598	+	21.6598i	−0.720794	+	0.720794i
$904$		0			0
$905$	−0.905320	−	13.7813i	−0.0300939	−	0.458105i
$906$		0			0
$907$	12.3992	−	12.3992i	0.411708	−	0.411708i	−0.470625	−	0.882333i	$-0.655972\pi$
$907$	12.3992	−	12.3992i	0.411708	−	0.411708i	0.882333	+	0.470625i	$0.155972\pi$
$908$		0			0
$909$			4.13229i			0.137059i
$910$		0			0
$911$		−	11.2952i		−	0.374228i	−0.982338	−	0.187114i	$-0.940087\pi$
$911$		−	11.2952i		−	0.374228i	0.982338	−	0.187114i	$-0.0599134\pi$
$912$		0			0
$913$	−29.9183	+	29.9183i	−0.990153	+	0.990153i
$914$		0			0
$915$	2.28793	+	2.00587i	0.0756368	+	0.0663119i
$916$		0			0
$917$	−18.7975	+	18.7975i	−0.620747	+	0.620747i
$918$		0			0
$919$	−32.9795			−1.08789			−0.543946	−	0.839120i	$-0.683070\pi$
$919$	−32.9795			−1.08789			−0.543946	+	0.839120i	$0.683070\pi$
$920$		0			0
$921$	−14.2810			−0.470575
$922$		0			0
$923$	1.14468	−	1.14468i	0.0376777	−	0.0376777i
$924$		0			0
$925$	−7.12462	+	9.29067i	−0.234256	+	0.305475i
$926$		0			0
$927$	−0.0148961	+	0.0148961i	−0.000489254	+	0.000489254i
$928$		0			0
$929$		−	44.3308i		−	1.45445i	−0.686401	−	0.727224i	$-0.740810\pi$
$929$		−	44.3308i		−	1.45445i	0.686401	−	0.727224i	$-0.259190\pi$
$930$		0			0
$931$		−	73.9615i		−	2.42399i
$932$		0			0
$933$	−18.8572	+	18.8572i	−0.617357	+	0.617357i
$934$		0			0
$935$	41.2854	+	36.1955i	1.35018	+	1.18372i
$936$		0			0
$937$	31.5012	−	31.5012i	1.02910	−	1.02910i	0.0295365	−	0.999564i	$-0.490597\pi$
$937$	31.5012	−	31.5012i	1.02910	−	1.02910i	0.999564	−	0.0295365i	$-0.00940311\pi$
$938$		0			0
$939$	−28.7587			−0.938505
$940$		0			0
$941$		−	46.2358i		−	1.50724i	−0.657308	−	0.753622i	$-0.728305\pi$
$941$		−	46.2358i		−	1.50724i	0.657308	−	0.753622i	$-0.271695\pi$
$942$		0			0
$943$	37.5629	+	13.0390i	1.22322	+	0.424609i
$944$		0			0
$945$	9.25555	−	0.608016i	0.301083	−	0.0197788i
$946$		0			0
$947$	37.5069	+	37.5069i	1.21881	+	1.21881i	0.968049	+	0.250761i	$0.0806808\pi$
$947$	37.5069	+	37.5069i	1.21881	+	1.21881i	0.250761	+	0.968049i	$0.419319\pi$
$948$		0			0
$949$			1.21185i			0.0393383i
$950$		0			0
$951$	24.9157			0.807945
$952$		0			0
$953$	7.45623	+	7.45623i	0.241531	+	0.241531i	0.817483	−	0.575952i	$-0.195369\pi$
$953$	7.45623	+	7.45623i	0.241531	+	0.241531i	−0.575952	+	0.817483i	$0.695369\pi$
$954$		0			0
$955$	0.534627	+	8.13838i	0.0173001	+	0.263352i
$956$		0			0
$957$	44.4065	−	44.4065i	1.43546	−	1.43546i
$958$		0			0
$959$		−	3.39100i		−	0.109501i
$960$		0			0
$961$	14.8129			0.477837
$962$		0			0
$963$	−8.78001	−	8.78001i	−0.282932	−	0.282932i
$964$		0			0
$965$	0.124496	−	0.142002i	0.00400766	−	0.00457122i
$966$		0			0
$967$	−23.7966	−	23.7966i	−0.765245	−	0.765245i	0.212020	−	0.977265i	$-0.431996\pi$
$967$	−23.7966	−	23.7966i	−0.765245	−	0.765245i	−0.977265	+	0.212020i	$0.931996\pi$
$968$		0			0
$969$			28.1668i			0.904848i
$970$		0			0
$971$			20.0517i			0.643489i	0.946827	+	0.321744i	$0.104269\pi$
$971$			20.0517i			0.643489i	−0.946827	+	0.321744i	$0.895731\pi$
$972$		0			0
$973$	14.8436	+	14.8436i	0.475864	+	0.475864i
$974$		0			0
$975$	−0.0984843	−	0.746356i	−0.00315402	−	0.0239025i
$976$		0			0
$977$	38.1637	−	38.1637i	1.22096	−	1.22096i	0.253673	−	0.967290i	$-0.418361\pi$
$977$	38.1637	−	38.1637i	1.22096	−	1.22096i	0.967290	−	0.253673i	$-0.0816389\pi$
$978$		0			0
$979$			96.7758i			3.09297i
$980$		0			0
$981$		−	8.07610i		−	0.257850i
$982$		0			0
$983$	8.33397	+	8.33397i	0.265812	+	0.265812i	0.827410	−	0.561598i	$-0.189813\pi$
$983$	8.33397	+	8.33397i	0.265812	+	0.265812i	−0.561598	+	0.827410i	$0.689813\pi$
$984$		0			0
$985$	−17.7514	−	15.5629i	−0.565607	−	0.495876i
$986$		0			0
$987$	−12.4640	+	12.4640i	−0.396735	+	0.396735i
$988$		0			0
$989$	−15.4451	−	31.8691i	−0.491127	−	1.01338i
$990$		0			0
$991$	−26.7694			−0.850359			−0.425179	−	0.905109i	$-0.639789\pi$
$991$	−26.7694			−0.850359			−0.425179	+	0.905109i	$0.639789\pi$
$992$		0			0
$993$	20.0617	−	20.0617i	0.636638	−	0.636638i
$994$		0			0
$995$	−7.78268	+	0.511260i	−0.246727	+	0.0162080i
$996$		0			0
$997$	14.5895	+	14.5895i	0.462054	+	0.462054i	0.899328	−	0.437274i	$-0.144056\pi$
$997$	14.5895	+	14.5895i	0.462054	+	0.462054i	−0.437274	+	0.899328i	$0.644056\pi$
$998$		0			0
$999$	2.34160			0.0740848

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1380.2.t.a.1057.15	✓	48
5.3	odd	4	inner	1380.2.t.a.1333.16	yes	48
23.22	odd	2	inner	1380.2.t.a.1057.16	yes	48
115.68	even	4	inner	1380.2.t.a.1333.15	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1380.2.t.a.1057.15	✓	48	1.1	even	1	trivial
1380.2.t.a.1057.16	yes	48	23.22	odd	2	inner
1380.2.t.a.1333.15	yes	48	115.68	even	4	inner
1380.2.t.a.1333.16	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:	\( N \)	\(=\)	\( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1380.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{3} +(-2.23126 + 0.146576i) q^{5} +(2.93317 - 2.93317i) q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{3} +(-2.23126 + 0.146576i) q^{5} +(2.93317 - 2.93317i) q^{7} -1.00000i q^{9} +6.31685i q^{11} +(0.106466 - 0.106466i) q^{13} +(-1.47409 + 1.68138i) q^{15} +(-2.74862 + 2.74862i) q^{17} +7.24616 q^{19} -4.14813i q^{21} +(4.53063 + 1.57269i) q^{23} +(4.95703 - 0.654098i) q^{25} +(-0.707107 - 0.707107i) q^{27} -9.94170i q^{29} +6.76853 q^{31} +(4.46668 + 4.46668i) q^{33} +(-6.11473 + 6.97460i) q^{35} +(-1.65576 + 1.65576i) q^{37} -0.150565i q^{39} +8.29087 q^{41} +(-5.22159 - 5.22159i) q^{43} +(0.146576 + 2.23126i) q^{45} +(-3.00474 - 3.00474i) q^{47} -10.2070i q^{49} +3.88714i q^{51} +(-8.34794 - 8.34794i) q^{53} +(-0.925898 - 14.0945i) q^{55} +(5.12381 - 5.12381i) q^{57} +1.05589i q^{59} -1.36075i q^{61} +(-2.93317 - 2.93317i) q^{63} +(-0.221947 + 0.253158i) q^{65} +(-4.30746 + 4.30746i) q^{67} +(4.31570 - 2.09158i) q^{69} +10.7517 q^{71} +(-5.69127 + 5.69127i) q^{73} +(3.04263 - 3.96767i) q^{75} +(18.5284 + 18.5284i) q^{77} +5.92020 q^{79} -1.00000 q^{81} +(4.73628 + 4.73628i) q^{83} +(5.73000 - 6.53577i) q^{85} +(-7.02985 - 7.02985i) q^{87} +15.3203 q^{89} -0.624564i q^{91} +(4.78607 - 4.78607i) q^{93} +(-16.1681 + 1.06211i) q^{95} +(3.23025 - 3.23025i) q^{97} +6.31685 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 8 q^{13} - 16 q^{23} - 8 q^{25} + 8 q^{31} + 8 q^{35} - 24 q^{41} + 8 q^{47} - 32 q^{55} - 24 q^{71} + 8 q^{73} + 32 q^{75} + 40 q^{77} - 48 q^{81} + 24 q^{85} - 40 q^{87}+O(q^{100}) \) 48 * q - 8 * q^13 - 16 * q^23 - 8 * q^25 + 8 * q^31 + 8 * q^35 - 24 * q^41 + 8 * q^47 - 32 * q^55 - 24 * q^71 + 8 * q^73 + 32 * q^75 + 40 * q^77 - 48 * q^81 + 24 * q^85 - 40 * q^87

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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